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<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes>      <info>        <author>Caverni, Raffaello</author>        <title>Storia del Metodo Sperimentale in Italia</title>        <date>1891</date>        


<place>Florence</place>		<translator></translator>	<lang>it</lang>	      <cvs_file>caver_metod_020_it_1891.xml</cvs_file><cvs_version>1.11</cvs_version>	<locator>020.xml</locator>      </info>      <text>          <front>          </front>          <body>            <chap>	
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<pb xlink:href="020/01/001.jpg"/><s><foreign lang="en">350478 Storia Del Metodo Sperimentale Italia </foreign></s></p><p type="main">

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s><emph type="center"/>DEPUTATA ALL'ESAME<emph.end type="center"/></s></p><p type="main">

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

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

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

<s>Per la seconda volta &egrave; chiamato il R. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Ed anzitutto ammetteremo che l'esemplare, il quale ne abbiamo sot&shy;<lb/>t'occhio, sia l'opera di un amanuense, e che all'autore sia mancato anche <lb/>il tempo di rileggerlo, perch&egrave;, quando cos&igrave; non fosse, alcuni grossolani er&shy;<lb/>rori ci avrebbero consigliato a chiudere senz'altro il volume, per non spre&shy;<lb/>care il tempo, che pure abbiamo dovuto spendervi intorno per diligente&shy;<lb/>mente esaminarlo. </s>

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

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

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

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

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

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

<s><emph type="center"/>&ldquo; Da questa instanzia pu&ograve; deliberarti <lb/>Esperienza, se giammai la provi <lb/>Ch'esser suol fonte a'rivi di vostr'arti &rdquo;.<emph.end type="center"/></s></p><p type="main">

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

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

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

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

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

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

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

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

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

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

<s>Cosi, dal quadro, del quale andiamo riproducendo le linee massime, <lb/>appariscono disposte le cose per modo che la instituzione dell'arte speri&shy;<lb/>mentale dovesse occorrere alla Toscana; cosi avvenne di fat<emph type="italics"/>t<emph.end type="italics"/>o, per il magi&shy;<lb/>stero di Galileo Galilei, a cui i posteri, plaudendo e gratulando, attribuirono, <lb/>del pari che al maestro, dal quale prese la ispirazione, il nome di divino. </s>

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

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

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

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

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

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

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

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

<s>Tale fu l'Accademia del Cimento, nella quale, sebbene gli scien&shy;<lb/>tifici consessi incominciassero inf&igrave;no dal 1657, non ostante, al pubblico, non <lb/>se ne comunicarono le scoperte, se non che nel 1666 in quel volume, a <lb/>cui si volle dar giustamente il titolo di <emph type="italics"/>Saggi,<emph.end type="italics"/> perch&egrave; nient'altro son vera&shy;<lb/>mente se non che saggi di quella ricca e feconda miniera d'oro, che si ri&shy;<lb/>man tuttavia nascosta e involta nella scoria dei manoscritti. </s></p><p type="main">

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

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

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

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

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

<s>&ldquo; Co'tre ponderosi volumi per&ograve;, co'quali usciamo in campo noi, che <lb/>ci sentiamo di cos&igrave; lieve armatura, non vuol farsi credere che si pretenda <lb/>essere stato trattato in tutta la sua estensione, e nella sua intensione il <lb/>s&igrave; difficile tema. </s>

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

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

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

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

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

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

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

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

<s>E poich&egrave; quesa imputazione non pu&ograve; mantenersi campata in <lb/>aria; ma &egrave; pur mestieri fornirne una qualche giustificazione, &egrave; d'uopo che <lb/>noi entriamo in alcuni particolari. </s></p><p type="main">

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

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

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

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

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

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

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

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

<s>E ci&ograve; che avvertiamo rispetto alle fonti, ripeteremmo volontieri per <lb/>certi apprezzamenti. </s>

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

<s>Queste poche, fra molte altre osservazioni di simil genere, le quali <lb/>pure potrebbero farsi, abbiamo voluto notare, poich&egrave; a quelle della prima <lb/>categoria egli potr&agrave; facilmente ovviare con una pi&ugrave; frequente e regolare ci&shy;<lb/>tazione delle fonti, e fors'anche con una pi&ugrave; accurata critica di esse, ed a <pb xlink:href="020/01/033.jpg" pagenum="14"/>quelle della seconda baster&agrave; certamente l'avervi richiamata sopra la d&igrave; lui <lb/>attenzione. </s>

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

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

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

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

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

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

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

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

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

<s>L'Autore, in certo punto del suo lavoro <lb/>si dice &ldquo; nato per fortuna sulle rive dell'Arno &rdquo;: dichiarazione superflua, <lb/>poich&egrave;, pur non sapendolo, avremmo potuto dirgli: </s></p><p type="main">

<s><emph type="center"/>&ldquo; La tua loquela ti fa manifesto <lb/>Di quella nobil patria nat&igrave;o &rdquo;.<emph.end type="center"/></s></p><p type="main">

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Ci narra come fossero incerti que'primi passi e <lb/>fallaci, e pi&ugrave; tontani dal vero di quel che ne fossero gli stessi suo&igrave; prede&shy;<lb/>cessori. </s>

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

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

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

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

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

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

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

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

<s><lb/>Del ritrovamento e delle vicende sub&igrave;te dal manoscritto di questo ultimo dia&shy;<lb/>logo o Congresso, come chiamavalo Galileo, &egrave; fatto soggetto particolare di <lb/>storia, concludendo che egli lo ripudi&ograve;, e che, quando non lo avesse cos&igrave; <lb/>ripudiato, quel dialogo doveva andare in ordine il quinto e non il sesto. </s></p><p type="main">

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Dott. </s>

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

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

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

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

<s>Citiamo, coll'abbreviatura <emph type="italics"/>Alb.,<emph.end type="italics"/> l'opere complete di Galileo stampate in Firenze, dal <lb/>1842 al 1856, dalla societ&agrave; editrice fiorentina, in quindici tomi, con pi&ugrave; un tomo di <emph type="italics"/>Sup&shy;<lb/>plemento,<emph.end type="italics"/> sotto la direzione di Eugenio Alb&egrave;ri. </s>

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

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

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

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

<s>Coll'abbreviatura <emph type="italics"/>MSS. Gal. </s>

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

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

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

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

<s><emph type="center"/>DELL'ORIGINE E DE'PROGRESSI<emph.end type="center"/></s></p><p type="main">

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

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

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

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

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

<s>I. </s>

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

<s>&mdash; II. </s>

<s>Platone e Aristotile. </s>

<s>&mdash; III. </s>

<s>Della Filosofia naturale de&shy;<lb/>rivata dall'Accademia e dal Peripato &mdash; IV. </s>

<s>Come le due Filosofie, la platonica e l'aristotelica, <lb/>venissero a introdursi nella Societ&agrave; cristiana. </s>

<s>&mdash; V. De'medici peripatetici: Girolamo Fracastoro, <lb/>Andrea Cisalpino. </s>

<s>&mdash; VI Girolamo Cardano, Giuseppe Scaligero, Niccol&ograve; Tartaglia. </s>

<s>&mdash; VII. </s>

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

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

<s>&mdash; <lb/>X. </s>

<s>Leonardo da Vinci &mdash; XI. </s>

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

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

<s>&mdash; XIII. De'pi&ugrave; immediati precursori e cooperatori alla grande Instaurazione galileiana: <lb/>Giovan Battista Benedetti e Santorre Santorio. </s>

<s>&mdash; XIV. </s>

<s>Paolo Sarpi. </s>

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

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

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

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

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

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

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

<s>Una delle principali e delle pi&ugrave; importanti conclusioni, che de&shy;<lb/>rivarono immediatamente da cos&igrave; fatte esperienze, fu che le prime <lb/>notizie delle cose hanno origine nell'intelletto da tutt'altra fonte <lb/>che dai sensi. </s>

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

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

<s>Da queste nuove dottrine, e da quelle, altres&igrave;, pi&ugrave; antiche, <lb/>scende un'altra importantissima conclusione, ed &egrave; la necessit&agrave; delle <lb/>tradizioni. </s>

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

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

<s>&Egrave; perci&ograve; la necessit&agrave; delle tradizioni una legge, alla quale <lb/>inesorabilmente soggiace ogni svolgimento dell'umano pensiero, <pb xlink:href="020/01/046.jpg" pagenum="27"/>cosicch&egrave; l'ammettere l'esistenza d'ingegni veramente <emph type="italics"/>creatori<emph.end type="italics"/> &egrave; un <lb/>errore in filosofia, com'&egrave; un errore in fisica l'ammettere la gene&shy;<lb/>razione spontanea. </s></p><p type="main">

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

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

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

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

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

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

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

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

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

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

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

<s>Quel bambinello intanto, il quale aveva poco pi&ugrave; <lb/>che quaranta giorni, ha passato gi&agrave; dell'et&agrave; sua il primo anno. </s>

<s>Tor&shy;<lb/>niamo ad osservarne gli atti, e a veder quali novit&agrave; presentano i <lb/>suoi costumi. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Che la civilt&agrave; e la cultura, nella nostra Italia approdasse dalla <lb/>contigua Grecia &egrave; cosa tanto nota, e cos&igrave; naturale, che la Geografia <lb/>stessa quasi serve di prova. </s>

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

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

<s>Socrate gli educ&ograve;, nella patria Atene, il cuore e la mente. </s>

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

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

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

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

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

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

<s><lb/>Della necessit&agrave; delle tradizioni poi &egrave; cos&igrave; ben persuaso il filosofo <lb/>greco, da doversi anzi dire che tutto il suo sistema &egrave; informato di <lb/>quel principio. </s>

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

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

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

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

<s>Ed ecco infatti il Filo&shy;<lb/>sofo greco proclamare l'utilit&agrave; grandissima e l'importanza, che per <lb/>l'acquisto delle verit&agrave; naturali ha la geometria e la scienza dei nu&shy;<lb/>meri in generale. </s>

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

<s>Il numero non entra per nulla in ogni specie <lb/>di metro, dove non regna n&egrave; regime, n&egrave; ordine, n&egrave; figura, n&egrave; mi&shy;<lb/>sura, n&egrave; armonia: in una parola, in tutto ci&ograve; che partecipa a qualche <lb/>male. </s>

<s>&rdquo; Cos&igrave; par si voglia insinuar dall'Autore, che la Matematica <lb/>&egrave; tutto insieme principio di moralit&agrave;, e fondamento di scienza. </s></p><p type="main">

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

<s>Questo &egrave; il famosissimo Aristotile, il quale, nato <lb/>in Stagira, bench&egrave; di sangue greco, piccola e ignobile citt&agrave; della <lb/>Tracia, risente alquanto della ruvidezza natia e della operosit&agrave; del <lb/>montanaro. </s>

<s>Ma quella sua ruvidezza e quella operosit&agrave;, che f&agrave; cos&igrave; <lb/>risentito contrasto colla placida contemplazione platonica, &egrave; la rap&shy;<lb/>presentazione pi&ugrave; viva di quella irrequietezza che vedemmo succe&shy;<lb/>dere alle estatiche e serene centemplazioni del bambinello. </s>

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

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

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

<s>Perch&egrave; cos&igrave; il bambino come Aristotile vor&shy;<lb/>rebbero che la Natura si governasse a loro proprio modo, e preten&shy;<lb/>derebbero d'imporre piuttosto che assoggettarsi alle leggi di lei. </s>

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

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

<s>Ecco <lb/>quello che si pu&ograve; chiamare un indiarsi della ragione, la quale, come <lb/>fecondamente produce i concetti universali, per opera dialettica del&shy;<lb/>l'astrazione; cos&igrave; d&agrave; leggi ai particolari via via che occorra di rico&shy;<lb/>noscerli per la percezione de'sensi. </s>

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

<s>Che cos'&egrave; alle mani di Ari&shy;<lb/>stotile il sillogismo? </s>

<s>&Egrave; un artificio lusinghiero, per cui si d&agrave; a cre&shy;<lb/>dere con gran facilit&agrave; che la conclusione derivi dalle premesse, non <lb/>per necessit&agrave; logica, ma per sola opera dialettica della mente ragio&shy;<lb/>natrice. </s>

<s>Perci&ograve; egli, nell'investigare le cause de'fatti naturali aborre <lb/>dalla troppa semplicit&agrave;: quelle cause non son vere, per lui, se non <lb/>quando sieno state ritrovate da'pi&ugrave; sottili e artificiosi ragionamenti. </s>

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

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

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

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

<s>Nel Pro&shy;<lb/>tagora poi aveva gi&agrave; con pari arte eloquente, confutato il sensismo, <lb/>conchiudendo che, se regola del nostro conoscere sono i sensi, nulla <lb/>&egrave; pi&ugrave; nel mondo d'immutabile e di vero. </s>

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

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

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

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

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

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

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

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

<s>La qualit&agrave; principale e il carattere distintivo di quella platonica <lb/>scuola, gi&agrave; dicemmo essere la contemplazione. </s>

<s>&ldquo; La verit&agrave;, va tut&shy;<lb/>tavia ripetendo il gran maestro, non si pu&ograve; conoscere da noi quaggi&ugrave; <lb/>in terra, se non isforzandoci a rompere i vincoli che ci tengono <lb/>strinti e avviluppati nel corpo. </s>

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

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

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

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

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

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

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

<s>Egli &egrave; infatti, il filosofo atienese, gran maestro di Geometria. </s>

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

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

<s>Tratteniamoci a cons&iuml;derare un poco il sublime aspetto e la <lb/>maest&agrave; veneranda del nostro Siracusano. </s>

<s>Egli &egrave; la prima splendida <lb/>apparizione, e la rappresentazione pi&ugrave; viva di ci&ograve; che fosse l'arte <lb/>sperimentale in Italia nel III secolo prima di Ges&ugrave; Cristo. </s>

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

<s>Considerando per&ograve; pi&ugrave; sottilmente, si trover&agrave; che l'abito del <lb/>Siracusano non differisce in nulla dal pallio del filosofo atienese. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Gi&agrave; <lb/>noi lo mostrammo apertamente pi&ugrave; sopra, e dicemmo consistere <lb/>quel principio nel far dipendere dalla nostra ragione le leggi che <lb/>governano la Natura. </s>

<s>In conseguenza di ci&ograve;, l'esperienza &egrave; inutile, <lb/>e la ragione legislatrice e signora non ha bisogno di travagliarsi <lb/>servilmente a osservare e a cimentare i fatti naturali. </s>

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

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

<s>Quali potevano essere insomma i frutti di cos&igrave; fatte dottrine? </s>

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

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

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

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

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

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

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

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

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

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

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

<s>Fra'due <lb/>filosofi &egrave; cos&igrave; aperto il dissidio, che &egrave; impossibile trovar ordine e <lb/>modo da ricongiungerli insieme. </s>

<s>Pur nonostante &egrave; vero che in al&shy;<lb/>cuni punti si riscontrano, ma per&ograve; si riscontrano a quel modo che <lb/>avvien delle vie tortuose che s'intersecano e procedono per qualche <lb/>tratto con le diritte rendendo pi&ugrave; che mai per&ograve; intralciato il viaggio. </s>

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

<s>All'impossibilit&agrave; riducesi <lb/>evidentemente da Platone, insegnando che i sensi non rappresentano <lb/>all'anima altro che larve fuggitive ed inganni, e si riduce ad una <lb/>inutilit&agrave; per Aristotile, il quale professa che al difetto dei sensi pu&ograve; <lb/>supplire, per s&egrave; medesima, la ragione. </s>

<s>Cos&igrave; &egrave; che se, per gli Acca&shy;<lb/>demici, la Filosofia naturale &egrave; un ludibrio spettacoloso, per i Peri&shy;<lb/>patetici non &egrave; altro pi&ugrave; che una sottile esercitazion<gap/> d'ingegno. </s>

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

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

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

<s>Che se, avuto ri&shy;<lb/>guardo all'utilit&agrave; e alla eccellenza delle due discipline, si vorr&agrave; <lb/>decidere che i meriti sono uguali, avuto riguardo all'applicabilit&agrave; <lb/>delle stesse due discipline all'interpetrazion de'fatti naturali, si vedr&agrave; <lb/>che, mentre la Geometria &egrave; ala da sollevar la mente sublime alla <lb/>contemplazione del mondo, l'Algebra non &egrave; che strumento da fa&shy;<lb/>cilitare alcune delle pi&ugrave; faticose esercitazioni del nostro ingegno. </s>

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

<s>Perci&ograve;, mentre la Geometria <lb/>&egrave; rimasta sempre nella sua incorruttibile dignit&agrave;, l'Algebra s'&egrave; ve&shy;<lb/>duta degenerar talvolta negli abusi e ne'vizii della Dialettica. </s></p><p type="main">

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

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

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

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

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

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

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

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

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

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

<s>&Egrave; per&ograve; vero <lb/>che una tal messe di fisiche verit&agrave; non fu e non poteva esser rac&shy;<lb/>colta dagli orti dell'Accademia: essa fu, come si vedr&agrave; meglio tra <lb/>poco in altri esempi, frutto di una sapienza che non sarebbe po&shy;<lb/>tuta derivar da nessuna scuola. </s></p><p type="main">

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

<s>Roma &egrave; ancora, <lb/>passato lo splendore dei Cesari, e forse con pi&ugrave; vivo senso di prima, <lb/>capo e cuore del mondo. </s>

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

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

<s><lb/>La nuova arte oratoria per&ograve; &egrave; varia, perch&egrave; varii ne sono i fini, ma <lb/>non per questo manco nobili e generose ne sono le intenzioni. </s>

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

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

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

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

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

<s>Ma la <lb/>Filosofia di Aristotile vi s'introdusse molto pi&ugrave; tardi, e per un ma&shy;<lb/>gistero tanto diverso, quanto esser pu&ograve; diversa, dalla toga magnifica <lb/>di un romano, la cappa voluttuosa di un arabo. </s>

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

<s>Quel maestro, <lb/>che insegnava a ridur tutto a regola di compasso, e dagli ammaestra&shy;<lb/>menti del quale si concludeva cos&igrave; facilmente la libert&agrave; del poter <lb/>governare s&egrave; stesso e la natura a proprio talento, non poteva non <lb/>piacere a quegli uomini, tutti dediti a riconoscere freddamente e a <lb/>noverar gli oggetti, che pi&ugrave; fanno impressione e pi&ugrave; dilettano i <lb/>sensi. </s></p><p type="main">

<s>Sotto le larghe pieghe della bianca cappa dell'arabo, veniva <lb/>cos&igrave; dunque Aristotile a introdursi in mezzo alla societ&agrave; cristiana. </s>

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

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

<s>Era gi&agrave; incominciato il tempo delle eresie, per cui, piuttosto <lb/>che badare a insinuare la verit&agrave;, si sentiva il bisogno di confutare <lb/>l'errore. </s>

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

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

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

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

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

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

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

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

<s>Non &egrave; del presente nostro proposito il dar giudizio di S. </s>

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

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

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

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

<s>La grande autorit&agrave; di S. </s>

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

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

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

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

<s>Ch&igrave; ripensi ora che i chiostri erano i soli asili <lb/>in cui si rifugiava e da cui si diffondeva la scienza, comprender&agrave; <lb/>quali dovessero essere le condizioni delle scienze naturali per tutto <lb/>il tempo che domin&ograve; quella scuola. </s>

<s>Condizioni generali per&ograve;, per&shy;<lb/>ch&egrave; non manc&ograve; fin d'allora chi si volse a filosofar, piuttosto che <lb/>sui libri, sull'osservazione e sull'esperienza de'fatti, come si vedr&agrave; <lb/>seguitando il nostro Discorso. </s></p><p type="main">

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

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

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

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

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

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

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

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

<s>E perch&egrave; pi&ugrave; efficace riesca una tale testimonianza, <lb/>leggansi i soggetti che si trattano ne'tre libri, ne'quali la Raccolta <lb/>stessa dal compilatore venne divisa. </s>

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

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

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

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

<s>Niente altro, si capir&agrave; bene, che voci di cerretani. </s>

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

<s>La sottilit&agrave; dialettica, o per dir meglio, la pi&ugrave; sfrenata fantasia <lb/>del medico &egrave; quella che dee operar nel malato ogni efficacia. </s></p><p type="main">

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

<s><lb/>Il primo di questi, veronese di patria e vissuto dal 1483 al 1553, <lb/>se si vuol pareggiar nell'ingegno agli altri due, non &egrave; dubbio per&ograve; <lb/>ch'egli &egrave; d'assai superiore a loro nella dignit&agrave; della vita. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>In qualunque modo per&ograve;, il Fracastoro &egrave; un ingegno serio e <lb/>se cade in errore non se ne compiace e non lo scansa, perch&egrave; non <lb/>lo conosce. </s>

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

<s>Qualunque <lb/>siasi per&ograve; la moralit&agrave; de'suoi costumi, a noi non s'appartiene di <lb/>parlare che della scienza, la quale, perch&egrave; forse insozzata di fango <lb/>e rimescolata ai pi&ugrave; strani errori e alle fantasie pi&ugrave; stravaganti, &egrave; <lb/>stata, secondo noi, fin qui mal giudicata. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Nel cap. </s>

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

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

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

<s>&rdquo; <lb/>(Alb. </s>

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

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

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

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

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

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

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

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

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

<s>pag. </s>

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

<s>Ma il cap. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Ma un'altro discepolo di Galileo, Evangelista Torricelli, in fatto <lb/>della pi&ugrave; rumorosa e pi&ugrave; importante scoperta che sia stata fatta, <lb/>va a riscontrarsi colle stesse sottilit&agrave; della fisica antica. </s>

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

<s>L&agrave; dove si prova a render la ragione del moto ne'sifoni <lb/>da travasare i liquidi, accenna all'aria sopraincombente che ne aiuta <lb/>quel moto, bench&egrave; sarebbe senza dubbio temerit&agrave; l'asserire che <lb/>avesse riconosciuto in quel fatto idrostatico l'intervento della pres&shy;<lb/>sione atmosferica. </s>

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

<s>&rdquo; (De subtil. </s>

<s>Francof. </s>

<s>1592, pag. </s>

<s>58). Il Car&shy;<lb/>dano insomma non si appose al vero, ma non &egrave; piccola gloria per <lb/>lui l'aver, bench&egrave; cos&igrave; dalla lontana, aperti i chiusi e intricati sen&shy;<lb/>tieri al Torricelli, sostituendo a un nome vano un fatto. </s>

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

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

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

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

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

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

<s>Una delle sottigliezze cardaniche da farne pi&ugrave; conto, vedemmo <lb/>esser quella, che l'Autore esercit&ograve; a definir la natura del moto vio&shy;<lb/>lento e a stabilire il principio d'inerzia. </s>

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

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

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

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

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

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

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

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

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

<s>E pi&ugrave; di un secolo prima aveva lo stesso Scaligero preannun&shy;<lb/>ziata quella verit&agrave; tanto contraria agli oracoli aristotelici che cio&egrave; la <lb/>luce, come il suono, si muove in tempo e n&ograve; in istante, verit&agrave; a <lb/>dimostrar la quale, si faticarono inutilmente Galileo e i pi&ugrave; insigni <lb/>sperimentatori della sua scuola. &ldquo; Non enim ab immaterialitate <lb/>ductum argumentum, egli dice, satis validum est. </s>

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

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

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

<s>Un altro nome, oltre allo Scaligero, che si collega, bench&egrave; con <lb/>altro vincolo e per altro richiamo al Cardano, &egrave; quello di Niccol&ograve; <lb/>Tartaglia, nato in Brescia intorno al 1500 e morto 57 anni dopo. </s>

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

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

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

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

<s>Ma il Bresciano, che rimane inferiore a quel da Vinci nella <lb/>variet&agrave; e nella estensione de'soggetti naturali trattati, lo supera <lb/>nella intensit&agrave; e nel lucido ordine con che &egrave; riuscito a trattare le <lb/>parti. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>&ldquo; Ma regnate, egli dice in la&shy;<lb/>tino eloquio, regnate, infintanto che a voi &egrave; lecito o piace. </s>

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

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

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

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

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

<s>Non ci siate tiranni n&egrave; vogliate implicarci nelle reti <lb/>delle vostre contenzioni o avvolgerci fra le tenebre de'vostri dom&shy;<lb/>mi &rdquo; (Ferrariae, 1584, pag. </s>

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

<s>Da cos&igrave; fatte parole del Patrizio, come da altre simili che si <lb/>potrebbero citar dal Telesio, si sentono spirar con impeto le aure <lb/>della libert&agrave;, ma quell'impeto &egrave; temperato, e se fa piegar gagliar&shy;<lb/>damente le fronde, pur non le schianta. </s>

<s>Non &egrave; cos&igrave; de'due altri <lb/>insorti a detronizzare Aristotile poco dopo i tempi del filosofo con&shy;<lb/>sentino e del dalmata. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Non &egrave; per&ograve;, secondo pretendono i suoi adoratori, cos&igrave; di Gior&shy;<lb/>dano Bruno: egli &egrave; per essi il riformatore della nuova Astronomia. </s>

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

<s>Noi, a tanto fulgore di scienza, ci sentiamo inchinare maravi&shy;<lb/>gliati le ciglia, e levandole poi in alto, domandiamo, con quella <lb/>libert&agrave; che ci &egrave; permessa da'nuovi evangelizzatori del libero esame: <lb/>in che modo scoperse il Bruno e annunzi&ograve; tante astronomiche ve&shy;<lb/>rit&agrave;? </s>

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

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

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

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

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

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

<s>Divis. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Non si sa perci&ograve; com&shy;<lb/>prender da noi, com'essendo cos&igrave;, intendano gli uni di contrapporre <lb/>i loro metodi e le loro dottrine ai metodi e alle dottrine professate <lb/>dagli altri. </s>

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

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

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

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

<s>Un indizio per&ograve; pi&ugrave; sicuro che quelle due scuole apparten&shy;<lb/>gono alla medesima stirpe &egrave; il vederle ambedue affette dal medesimo <lb/>peccato originale, peccato, che secondo s'accenn&ograve; altrove, consiste <lb/>nella vanit&agrave; e nell'orgoglio. </s>

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

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

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

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

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

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

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

<s>Questi secondi furono de'pi&ugrave; arditi e intesero a scuotere <lb/>il giogo di ogni autorit&agrave;, per cui da molti sono stati encomiati e <lb/>benedetti. </s>

<s>Non si accorgon per&ograve; costoro, che scotendosi cos&igrave; anche <lb/>il giogo della Natura, e invece di assoggettarsi essi a lei, preten&shy;<lb/>dendo che ella debba assoggettarsi a loro, tornano perci&ograve; alla scienza, <lb/>lasciamo star la Religione e la Morale, pi&ugrave; nocivi degli stessi pe&shy;<lb/>ripatetici. </s></p><p type="main">

<s>Che sia anzi cos&igrave; di fatto, che cio&egrave; il razionalismo sia riuscito <lb/>pi&ugrave; nocivo alle scienze sperimentali dello stesso peripaticismo, si <lb/>pu&ograve; vedere dai frutti. </s>

<s>Imperocch&egrave; essendosi quello ribellato a ogni <lb/>autorit&agrave; magistrale, rimase come un ramo reciso dall'albero di cia&shy;<lb/>scuna delle due scuole, della platonica e della aristotelica, e si rese <lb/>perci&ograve; incapace di menar frutti proprii dell'una e dell'altra. </s>

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

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

<s>Ora &egrave; un fatto che dalla scuola <lb/>del razionalismo del Patrizio e del Bruno non usc&igrave; fuori n&egrave; un <lb/>geometra mai n&egrave; un algebrista. </s></p><p type="main">

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

<s>Se Luca Paciolo, aveva gi&agrave; nel secolo precedente <lb/>ritrovato il metodo da risolvere l'equazioni de'due primi gradi, <lb/>Girolamo Cardano e Niccol&ograve; Tartaglia rivaleggiano insieme a fare <lb/>a chi produce la pi&ugrave; semplice formula da risolvere l'equazioni del <lb/>terzo e del quarto grado. </s>

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

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

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

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

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

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

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

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

<s>Ella concepisce <lb/>intanto per opera del sole e s'impregna dell'annuale suo parto. </s>

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

<s>&rdquo; </s></p><p type="main">

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

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

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

<s>&rdquo; </s></p><p type="main">

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

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

<s>Dell'Ottica per&ograve; scrisse anche Tolomeo, le dottrine del <lb/>quale furono accolte e diffuse dall'arabo Alhazen, cosicch&egrave; pu&ograve; dirsi <lb/>che fosse questa scienza coltivata con egual profitto dalle due scuole. </s>

<s><lb/>N&egrave; ci&ograve; fa maraviglia, perch&egrave; se la platonica s'aiutava della Geome&shy;<lb/>tria, l'aristotelica si giovava del principio dell'intromissione delle <lb/>specie nell'occhio, mentre il principio platonico dell'estramissione <lb/>impediva grandemente alla scienza di progredire. </s>

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

<s>&rdquo; Le prove di ci&ograve; addotte dall'Autore sono inoppugnabili. </s>

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

<s>Se corporei, com'&egrave; possibile che lo spirito visivo si <lb/>diffonda cos&igrave; corporalmente infino alle pi&ugrave; lontane stelle? </s>

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

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

<s>Francesco Maurolico non riusc&igrave; a risolvere la difficile questione, <lb/>ma egli &egrave; nulladimeno il primo che preluda ai progressi dell'ottica <lb/>neutoniana. </s>

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

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

<s>Fu il nostro messinese altres&igrave; il primo a <lb/>dimostrar le aberrazioni di sfericit&agrave;, e a divisare il modo del di&shy;<lb/>pingersi le immagini reali e rovesciate attraverso alle sfere cristal&shy;<lb/>line e alle lenti convesse. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Ben per&ograve; pi&ugrave; risentitamente erano gi&agrave; que'dissidii insorti nel&shy;<lb/>l'animo di un'altra gente che, o dalle condizioni della nascita o dagli <lb/>esercizi della vita erano tenuti lontani dal partecipare ai puhblici <lb/>insegnamenti. </s>

<s>Amerigo Vespucci abbandona in giovent&ugrave; la scuola <lb/>di umanit&agrave;, per darsi alla mercanzia, e poi pi&ugrave; tardi ai viaggi. </s>

<s>Egli <lb/>non ha perci&ograve; a che far nulla con la scuola de'filosofi, e anzi si fa <lb/>ardito di rinfacciare i loro errori &ldquo; Parmi, Magnifico Lorenzo, che <lb/>la maggior parte dei filosofi in questo mio viaggio sia reprobata, <lb/>che dicono che dentro della torrida zona non si pu&ograve; abitare a causa <lb/>del gran calore, e io ho trovato in questo mio viaggio essere il <lb/>contrario &rdquo; (Bandini, Vita e lettere di A. Vespucci, Firenze 1745, <lb/>pag. </s>

<s>73). Egli sa di scrivere <emph type="italics"/>in barbaro stile e fuori di ogni ordine <lb/>di umanit&agrave;,<emph.end type="italics"/> e d&agrave; nonostante opera a scrivere un libro, che egli in&shy;<lb/>titola le <emph type="italics"/>Quattro Giornate<emph.end type="italics"/> &ldquo; nel quale ho relato, egli dice, la maggior <lb/>parte delle cose, che io vidi assai distintamente .... Quivi dunque io <lb/>viddi molte altre stelle i varii movimenti delle quali diligentemente <lb/>osservando, ne composi assegnatamente un libro &rdquo; (ivi, pag. </s>

<s>18 e <lb/>115). Ei si compiace delle tante nuove cose scoperte, e ripensando <lb/>alle sterilit&agrave;, e anzi agli errori in che versavano i filosofi <emph type="italics"/>in libris,<emph.end type="italics"/><lb/>conclude essere certo che <emph type="italics"/>pi&ugrave; vale la pratica che la teorica.<emph.end type="italics"/></s></p><pb xlink:href="020/01/086.jpg" pagenum="67"/><p type="main">

<s>Ben pi&ugrave; sdegnoso, perch&egrave; pi&ugrave; irritato, &egrave; l'animo di Leonardo <lb/>da Vinci, che scrive cos&igrave; contro i filosofi <emph type="italics"/>schonfiati<emph.end type="italics"/> e <emph type="italics"/>pomposi,<emph.end type="italics"/> non <lb/>ritrovatori di cose nuove, ma <emph type="italics"/>recitatori e trombetti delle opere al&shy;<lb/>trui.<emph.end type="italics"/> &ldquo; Se, bene, come loro, non sapessi allegare gli autori, molto <lb/>maggiore e pi&ugrave; degna cosa allegher&ograve; allegando l'esperienza maestra <lb/>ai loro maestri &rdquo;. (Libri Histoire et cet. </s>

<s>T. III, Paris 1840, pag. </s>

<s>238). </s></p><figure id="id.020.01.086.1.jpg" xlink:href="020/01/086/1.jpg"/><p type="main">

<s>Amerigo e Leonardo, che basterebbero per se stessi a provare <lb/>come la scienza della Natura si ricover&ograve; ne'suoi primi principii <lb/>altrove che per gli alloggiamenti de'Filosofi, non sono soli: essi <lb/>rappresentano un ordine di persone, che attende all'esercizio o delle <lb/>arti utili, o delle arti belle; ordine a cui principalmente apparten&shy;<lb/>gono Dante Alighieri, Cristoforo Colombo, Leon Battista Alberti. <pb xlink:href="020/01/087.jpg" pagenum="68"/>Illustre stuolo egli &egrave; questo, innanzi al quale il mondo de'Filosofi <lb/>sperimentali inchina per gran riverenza spontaneamente le ciglia. </s>

<s><lb/>Ebbene: di chi son discepoli tutti costoro, di Platone o di Aristo&shy;<lb/>tele? </s>

<s>Non hanno maestro nessun filosofo o accademico o peripate&shy;<lb/>tico, n&egrave; pretendono di farla da filosofi essi stessi come i razionalisti: <lb/>libro e maestro a loro &egrave; la Natura. </s>

<s>Dai faticosi esercizii dell'arte <lb/>si persuasero facilmente che la materia, sotto alle forme della <lb/>quale s'agita la vita dell'Universo, tutt'altro che essere arrendevole <lb/>al nostro ingegno, &egrave; sorda alle intenzioni dell'artista, ond'&egrave; che ap&shy;<lb/>presero di qui la soggezione agli ordini naturali e impararono ad <lb/>osservarli con diligente riverenza amorosa, ministri e sacerdoti nel <lb/>sacro Tempio, e non Iddei. </s>

<s>Essi dunque rappresentano quel terzo <lb/>stato, in cui vedemmo passar finalmente il bambino, dopo le prime <lb/>platoniche illusioni e i primi aristotelici delirii; lo stato in cui l'uomo <lb/>incomincia, per il sincero uso de'sensi, a pigliare stabile possesso <lb/>del mondo. </s>

<s>Su questi che sono i naturali e legittimi iniziatori <lb/>del metodo di osservazione, giova intrattenere alquanto il nostro <lb/>discorso. </s></p><p type="main">

<s>Nei primi palpiti del nostro risorgimento nazionale, quando <lb/>l'Italia si sentiva potentemente convenire in un animo solo, e in <lb/>un solo intendimento, si rivolse, con pi&ugrave; desideroso amore che mai, <lb/>a quell'uomo di carattere fiero e generoso, che pi&ugrave; al vivo la rap&shy;<lb/>presentava di ogni altro Fu allora che s'incominci&ograve; a magnificare <lb/>e a superesaltare i meriti di lui, cosicch&egrave; non si lasci&ograve; indietro arte <lb/>n&egrave; scienza, di cui non si predicasse Dante per gran precursore. </s>

<s><lb/>Lo zelo degli animi e la leggerezza degl'ingegni hanno spinto ora&shy;<lb/>mai l'esagerazione a tal punto, che il severo tribunale della critica <lb/>ha da sentenziar molte cose contro a loro, ed &egrave; rimasto a quel tri&shy;<lb/>bunale il debito di ridur dentro i termini del vero ogni eccesso <lb/>inconsiderato. </s></p><p type="main">

<s>Gli antichi furono, nell'ammirazione dell'Alighieri, assai pi&ugrave; <lb/>temperati, e perch&egrave; nella temperanza consiste la verit&agrave;, lo amarono <lb/>perci&ograve; e lo intesero molto meglio di noi. </s>

<s>Una delle prime e pi&ugrave; <lb/>rilevanti qualit&agrave; che distinguono l'ingegno dantesco &egrave; l'armonia: <lb/>armonia di numeri, che risuona nel verso, simmetria di linee, a <lb/>regola delle quali &egrave; architettato il divino Poema. </s>

<s>Il Landino e il <lb/>Vellutello, i due pi&ugrave; antichi e rinomati commentatori, non trascu&shy;<lb/>rano di avvertire come il teatro, in cui si rappresenta l'infernale <lb/>tragedia, sia stato prima cos&igrave; ben compassato dalla mente geome&shy;<lb/>trica del Poeta, che tutto procede e corrisponde a una preordinata <pb xlink:href="020/01/088.jpg" pagenum="69"/>misura. </s>

<s>Quale per&ograve; si fosse questa misura cadde in controversia <lb/>fra il Landino, che sosteneva l'opinione di Antonio Manetti, e il Vel&shy;<lb/>lutello, che seguiva un'opinione alquanto diversa. </s>

<s>Baccio Valori, <lb/>consolo dell'Accademia fiorentina, dette poi a decidere la contro&shy;<lb/>versia a Galileo, ci&ograve; che egli fece in due lezioni accademiche, pub&shy;<lb/>blicate nel 1855 da Ottavio Gigli, sentenziando in favor del Manetti. </s></p><p type="main">

<s>Se la Conca infernale e il Monte purgatorio dimostrano in Dante <lb/>una gran perizia di arte, diremo cos&igrave;, topografica, il gran Pano&shy;<lb/>rama del Paradiso attesta che egli doveva essere esercitatissimo <lb/>ne'calcoli dell'astronomia. </s>

<s>La distanza de'pianeti dalla Terra, le <lb/>loro grandezze relative, le paralassi del Sole e della Luna, tutto ci&ograve; <lb/>insomma che poteva servire a que'calcoli di fondamento, &egrave; de&shy;<lb/>sunto, com'appar dal <emph type="italics"/>Convito,<emph.end type="italics"/> da Tolomeo, da Alfagrano e da si&shy;<lb/>mili altri autori di opere astronomiche, delle quali d&agrave; prova il <lb/>Nostro di essere massimamente erudito. </s>

<s>Su tali dati poi, qualunque <lb/>ne sia la certezza, i calcoli astronomici danteschi son condotti con <lb/>tal matematico rigore, che noi pi&ugrave; volte, per nostro giovanile eser&shy;<lb/>cizio, ci siam provati a ritesserli e gli abbiamo trovati riscontrar <lb/>sempre, con maraviglioso diletto. </s></p><p type="main">

<s>Che l'Alighieri si fosse accorto del sonno delle piante, e avesse <lb/>riconosciuto la causa dell'ascensione della linfa su per i vasi; che <lb/>il velocitarsi delle acque correnti l'attribuisse alla pressione degli <lb/>strati superiori; che ne'condensamenti e nelle dilatazioni dell'aria <lb/>prodotta dal calor del sole riconoscesse l'origine dei venti; che i <lb/>vapori acquosi disseminati nell'aria, condensati dal freddo, tornino <lb/>in pioggia: queste e simili altre cose che vanno a ripescare a gara <lb/>qua e l&agrave; pel Poema sacro i dantisti, son senza dubbio esagerazioni, <lb/>specialmente se si vogliono intendere quelle parole nel preciso si&shy;<lb/>gnificato scientifico de'moderni; son conati di farfallette, che in&shy;<lb/>tendono a sollevare pi&ugrave; in alto che mai un gigante col leggiero <lb/>tremolare delle ali. </s></p><p type="main">

<s>Il vero si &egrave; che il Poeta riassume tutta la scienza de'suoi <lb/>tempi, e la commenta e la condensa ne'suoi splendidi versi, na&shy;<lb/>scondendola talvolta cos&igrave; fra le loro pieghe, che occhio poco esperto <lb/>non se ne accorge. </s>

<s>Un esempio di quei commenti si pu&ograve; citare, <lb/>nel XV canto del Purgatorio, dalle terzine 6 e 7, nelle quali si <lb/>rendono compiute le leggi della Calottrica, soggiungendo che il rag&shy;<lb/>gio d'incidenza e quello di riflessione si ritrovano in un medesimo <lb/>piano perpendicolare alla superficie riflettente. </s></p><p type="main">

<s>Dell'ardito modo come il grande artefice del verso toscano sa-<pb xlink:href="020/01/089.jpg" pagenum="70"/>pesse condensare, e quasi trafugare una proposizione di scienza di&shy;<lb/>mostrata, in un semplice inciso, molti si potrebbero recare esempi, <lb/>de'quali nonostante pu&ograve; bastare uno solo, che si toglie dalla t. </s>

<s>17 <lb/>del XII canto del Paradiso. </s>

<s>Per la <emph type="italics"/>lunga foga<emph.end type="italics"/> i commentatori <lb/>tutti intendono la distanza del sole nel parallelo di longitudine, <lb/>ma &egrave; chiaro che dee intendersi della lunga foga del mare, per cui, <lb/>a cagione della convessit&agrave; della superficie delle acque, si nasconde <lb/>la vista delle cose lontane. </s>

<s>Ecco in due parole risoluta una que&shy;<lb/>stione, che dette occasione fra'dotti di que'tempi a tante contro&shy;<lb/>versie; Questione che Dante stesso tratt&ograve; in Verona, il d&igrave; 20 di <lb/>Gennaio 1320, in una eruditissima dissertazione latina. </s></p><p type="main">

<s>Del resto, se il gran Vate pieno di tutta scienza, non precorse <lb/>i tempi di Galileo, con nessuna importante scoperta, prepar&ograve; senza <lb/>dubbio dalla lontana quel sicuro metodo di osservare la Natura, <lb/>che fu poi fecondo di ogni pi&ugrave; bella e pi&ugrave; nuova scoperta. </s>

<s>Se nulla <lb/>scopri di nuovo nella fisiologia delle piante, pure attentamente ne <lb/>osserv&ograve; i fiori e le foglie, e ne descrisse i moti prodotti dalla luce <lb/>e dal calore. </s>

<s>Se non pose i fondamenti all'Idraulica, present&igrave; pure <lb/>in qualche modo, che le acque stesse sottostavano a una legge, in <lb/>quel loro correre apparentemente scomposto, e se va ripetendo le <lb/>viete dottrine aristoteliche intorno a molti fatti di Meteorologia, <lb/>pur gli osserva e gli descrive, non accomodandoli alla sua propria <lb/>ragione, ma ricevendoli tali e quali glieli porge sotto gli occhi la <lb/>Natura. </s></p><p type="main">

<s>Da leggere questo gran Libro della Natura, forse troppo fu <lb/>distratto l'Alighieri dalla lettura de'libri dei filosofi. </s>

<s>Ma ecco suc&shy;<lb/>cedere a lui un altro grande spirito italiano, a cui la Natura stessa <lb/>ampiamente si rivel&ograve; squadernandogli innanzi agli occhi il volume <lb/>del Mondo Universo. </s>

<s>Egli &egrave; &igrave;l gran Cristoforo Colombo, e nessuno <lb/>meglio dell'ardito navigator genovese potrebbe stare a lato al su&shy;<lb/>blime Poeta fiorentino. </s>

<s>Ma prima di parlar di lui, che ebbe la Na&shy;<lb/>tura per solo e immediato Maestro, dobbiamo trattenerci sopra un'al&shy;<lb/>tra grande figura d'uomo, a cui fu maestra la Natura stessa per <lb/>mezzo dell'arte. </s></p><p type="main">

<s>Leon Battista Alberti &egrave; costui, nato, come l'Alighieri, d'illustre <lb/>e antica famiglia fiorentina e vissuto nel secolo posteriore a quello <lb/>del Poeta, dal 1404 al 1485. Informato alle scienze dagli insegna&shy;<lb/>menti delle scuole, pi&ugrave; forse dal proprio genio che dalle consue&shy;<lb/>tudini dei tempi, fu portato da giovane a secondare i placiti della <lb/>Filosofia platonica, la quale sodisfaceva, meglio della peripatetica, <pb xlink:href="020/01/090.jpg" pagenum="71"/>agl'ingegni meditativi. </s>

<s>Egli perci&ograve; si dette allo studio delle mate&shy;<lb/>matiche, applicando queste discipline alle arti, che posson meglio <lb/>servire agli usi della vita e a sodisfarne ai bisogni. </s>

<s>Ma l'Alberti, <lb/>indulgendo al genio proprio dei giovani, tien pi&ugrave; spesso dietro e <lb/>vagheggia le curiosit&agrave; e gli spettacoli, informato da quello spirito <lb/>del platonismo, che, se scende talvolta a implicarsi ne'fatti parti&shy;<lb/>colari della Natura, non gli riguarda altrimenti che come scherzi. </s>

<s><lb/>Il titolo di <emph type="italics"/>Ludi matematici<emph.end type="italics"/> dato dall'Autore a un'operetta, nella <lb/>quale &egrave; la Geometria applicata all'altimetria, alla topografia, alla <lb/>gnomonica, alla meccanica e a simili altre discipline, per s&egrave; dice <lb/>assai, ma pi&ugrave; efficacemente a noi sembra che di ci&ograve; facciano prova <lb/>quelle cos&igrave; dette <emph type="italics"/>Dimostrazioni,<emph.end type="italics"/> le quali niente altro eran poi, se <lb/>non che spettacoli ottici, o come Leon Battista stesso gli chiamava <lb/><emph type="italics"/>Miracoli della Pittura.<emph.end type="italics"/> Con queste Dimostrazioni spettacolose e con <lb/>questi Miracoli racconta l'Autore stesso d'essersi ricreato pi&ugrave; volte <lb/>in Roma insieme coi suoi compagni. </s>

<s>Di cos&igrave; fatte Dimostrazioni <lb/>nessuno sa dirci nulla di particolare, da quell'Anonimo biografo in <lb/>fuori contemporaneo dell'Alberti, la scrittura del quale fu raccolta <lb/>e pubblicata dal Muratori. </s>

<s>Da essa chiaramente si rileva in che <lb/>propriamente consistessero quelle Albertiane Dimostrazioni. </s>

<s>Ma per&shy;<lb/>ch&egrave; oramai i ciechi ammiratori del grande artista si sono fitti in <lb/>testa non essere quelle cos&igrave; fatte Dimostrazioni altro che le stesse <lb/>ottiche rappresentanze degli oggetti sul fondo di una camera oscura, <lb/>con manifesta intenzione di dare al loro Autore la precedenza su <lb/>Leonardo e sul Porta; si son ridotti a dire che le parole del Bio&shy;<lb/>grafo anonimo non son troppo chiare. </s>

<s>Ma chiarissime sembrano a <lb/>noi, e siamo certi che tali pur sembreranno agli intelligenti e im&shy;<lb/>parziali, che, dopo un'attenta lettura, concluderanno come i giochi <lb/>ottici dell'Alberti consistevano nel contraffare e trasformare le im&shy;<lb/>magini per via di colori artificiali e di artificiali riflessioni di spec&shy;<lb/>chi, mostrandole agli spettatori curiosi proiettate sulla parete di una <lb/>camera oscura. </s>

<s>L'apparecchio ottico dunque dell'Alberti era cosa <lb/>pi&ugrave; artificiosa e applicata ad uso un po'diverso dallo strumento <lb/>del Porta. </s></p><p type="main">

<s>Nel libro insomma dei Ludi, e in quello che si pu&ograve; chiamar <lb/>Magia delle Dimostrazioni, come in altre operette, a cui piace a <lb/>noi di dare il titolo di giovanili o minori, troppo il nostro Autore <lb/>si compiace di quella curiosit&agrave;, che &egrave; sodisfatta, non dall'esser veri <lb/>i fatti della Natura, ma dall'apparir nuovi e maravigliosi. </s>

<s>Il libro <lb/>della Prospettiva, pubblicato nel IV Tomo delle opere volgari da <pb xlink:href="020/01/091.jpg" pagenum="72"/>Anicio Bonucci, non &egrave; pi&ugrave; che un commentario assai magro del&shy;<lb/>l'Ottica di Euclide, e tra que'Ludi stessi, che si leggono in fine di <lb/>questo Tomo, molti son quelli che si risentono de'difetti notati dal <lb/>Sagredo ne'Ludi del Porta. </s>

<s>Anco l'VIII, che &egrave; del misurare la <lb/>profondit&agrave; di qualunque mare, subodorato da Silvio Belli e pub&shy;<lb/>blicato nel 1565 dai manoscritti albertiani, ha il difetto di riposar <lb/>sul principio dell'equabilit&agrave; del moto de'gravi cadenti in mezzo al&shy;<lb/>l'acqua, senza che l'Autore cerchi di assicurarsene in qualche modo, <lb/>per via dell'esperienza. </s>

<s>&Egrave; vero che l'esperienze dell'Oliva fatta di&shy;<lb/>poi nell'Accademia del Cimento parvero essere favorevoli al prin&shy;<lb/>cipio, dall'Alberti ammesso per vero, ma il Borelli poco dopo, nella <lb/>propos. </s>

<s>246. <emph type="italics"/>De motion. </s>

<s>natur.,<emph.end type="italics"/> dimostr&ograve; che la discesa da gravi e <lb/>l'ascesa de'galleggianti erano velocitate, confermando le teorie con <lb/>isperimenti ingegnosi. </s></p><p type="main">

<s>Venne tempo per&ograve; che, lasciata la curiosit&agrave; delle cose nuove, <lb/>e la leggerezza degli spettacoli, si rivolse l'Alberti tutto alla Natura, <lb/>ed essa invoc&ograve; ed elesse per sua principale Maestra. </s>

<s>La nuova vo&shy;<lb/>cazione incominci&ograve; dallo studio d'imitare coll'arte quella simmetria <lb/>ed eleganza di forma, che ella &egrave; solita dare alla fabbrica di tutte <lb/>le cose mondane. </s>

<s>Leon Battista vien cos&igrave; a farsi autore di Archi&shy;<lb/>tettura, non imitando servilmente, ma rinnovellando fibre e dando <lb/>altra forma di membra agli spiriti dell'antico Vitruvio. </s>

<s>Ecco l'opera <lb/>dove propriamente il Nostro investiga le occulte cause, scioglie <lb/>questioni di fatti naturali e inventa strumenti facendo uso di quel&shy;<lb/>l'arte, e proseguendo quello stesso metodo sperimentale, di cui il <lb/>regolare istituto dovea stabilirsi un secolo e mezzo dopo. </s>

<s>Lo studio <lb/>intorno all'origine delle fonti e alle scaturigini delle acque, attri&shy;<lb/>buite dal Nostro Autore all'umidit&agrave; delle pioggie e delle nevi pe&shy;<lb/>netrate nei crepacci e imbevute dai pori della terra, lo conduce <lb/>impensatamente a fare una nuova esperienza, e ad applicarla alla <lb/>costruzione di uno strumento, che egli offre qual primizia alla Me&shy;<lb/>teorologia &ldquo; Noi abbiamo provato, egli scrive, che una spugna di&shy;<lb/>venta umida per la umidit&agrave; dell'aria e di qui caviamo una regola <lb/>da pesare, colla quale noi pesiamo quanto siano gravi e quanto <lb/>secchi i venti e l'aria &rdquo;. </s></p><p type="main">

<s>Lo studio scientifico e sperimentale dei fatti meteorologici, che <lb/>l'Alberti inizi&ograve; colla invenzione dell'Igrometro, rimase cos&igrave; profon&shy;<lb/>damente impresso d'un tal qual carattere di nazionalit&agrave;, che la Me&shy;<lb/>teorologia dur&ograve; ad essere una scienza di special cultura italiana, <lb/>anco quando ne incominciarono a riconoscere l'importanza e a darvi <pb xlink:href="020/01/092.jpg" pagenum="73"/>opera efficacemente gli scienziati di Europa. </s>

<s>Ma a confermarle quel <lb/>carattere, con pi&ugrave; profonda impressione che mai, confer&igrave; quel Cri&shy;<lb/>stoforo Colombo, intorno a cui dianzi interrompemmo il discorso. </s></p><p type="main">

<s>Il genio di osservare con quasi religiosa venerazione i fatti <lb/>della Natura, che egli ora sperimentava in s&egrave; dolcemente benefici, <lb/>ora potentemente tremendi, si rivela da quel Giornale, di cui parla <lb/>Ferdinando, nel cap. </s>

<s>XVI, della Vita che scrisse di suo padre. </s>

<s>In <lb/>quel giornale il Discopritore del Nuovo mondo andava via via no&shy;<lb/>tando tutto quel che gli occorreva ad osservare e a considerare di <lb/>pi&ugrave; memorabile. </s>

<s>&ldquo; Fu diligentissimo l'Ammiraglio, dice ivi il bio&shy;<lb/>grafo, a scrivere di giorno in giorno minutamente tutto quello che <lb/>succedeva nel viaggio, specificando i venti che soffiavano, quanto <lb/>viaggio egli facea con ciascuno, e con quali vele e correnti, e quali <lb/>cose per la via egli vedeva, uccelli o pesci, od altri cos&igrave; fatti segni &rdquo;. </s></p><p type="main">

<s>L'Humboldt, che amorosamente e da quel grande scienziato <lb/>che egli era, prese ad esaminare un tal giornale, rest&ograve; maravigliato <lb/>della copia delle osservazioni, e dell'acume, con cui moltissimi e <lb/>varii fatti naturali vi sono investigati. </s>

<s>La direzione dei venti tropi&shy;<lb/>cali da occidente in oriente, per cui nello stesso verso &egrave; sospinta <lb/>la gran corrente marina, vi si trova per la prima volta diligente&shy;<lb/>mente descritta; vi &egrave; notata l'efficacia, che ha il verde fogliame delle <lb/>foreste di condensare i vapori acquosi dell'aria, facendoli tornare <lb/>in pioggia. </s>

<s>Vi &egrave; assegnata l'altezza dell'aria, a cui sono limitati i vari <lb/>e pi&ugrave; consueti fatti meteorologici che avvengono in essa, e vi son <lb/>riconosciuti i pi&ugrave; notabili effetti, che il calore del sole produce sul&shy;<lb/>l'Oceano e sull'ammosfera. </s></p><p type="main">

<s>Il medesimo Humboldt non cessa di far le meraviglie e di <lb/>magnificare una osservazione importantissima allo studio della nuova <lb/>Geologia; osservazione che il Colombo stesso lasci&ograve; fra le molte al&shy;<lb/>tre registrata nel suo Giornale. </s>

<s>L'osservazione fatta dal nostro in&shy;<lb/>signe Navigatore, nel suo primo viaggio, &egrave; quella del vedere vege&shy;<lb/>tare insieme e pacificamente convivere nell'isola di Cuba, conifore <lb/>e palme. </s>

<s>E perch&egrave; l'osservazione che pare ovvia si giudichi come <lb/>ella dovesse essere fatta con sottile intendimento scientifico, giova <lb/>notare che il nostro Botanico del secolo XV aveva tanto tempo <lb/>prima dell'Heritier riconosciuto che i <emph type="italics"/>podocarpi<emph.end type="italics"/> hanno altri carat&shy;<lb/>teri, per cui si distinguono dagli <emph type="italics"/>abietini.<emph.end type="italics"/></s></p><p type="main">

<s>Quanto poi l'Alunno della Natura, sapesse, nello studiare le <lb/>ammirande opere di lei, congiungere alle osservazioni passive la <lb/>sagace attivit&agrave; delle esperienze, si dimostra per quel che egli os-<pb xlink:href="020/01/093.jpg" pagenum="74"/>serv&ograve;, speriment&ograve; e specul&ograve; intorno alle propriet&agrave; naturali e agli <lb/>effetti della calamita. </s>

<s>La variazione della declinazione, al variare <lb/>delle latitudini, fu diligentemente osservata da lui, e a lui si deve <lb/>il primo concetto, bench&egrave; poi in pratica riuscisse inefficace, di ser&shy;<lb/>virsi dell'ago magnetico a risolvere l'importantissimo problema delle <lb/>longitudini. </s></p><p type="main">

<s>Lo spirito di Cristoforo Colombo si trasfuse poi negli altri na&shy;<lb/>vigatori, che gli successero, specialmente italiani, i quali con rive&shy;<lb/>rente amore, leggendo nel cielo, nel mare e nella terra le opere <lb/>ammirande della Natura, seppero investigarne il segreto magistero, <lb/>meglio di tanti filosofi non dediti a leggere altro che i libri. </s>

<s>Ame&shy;<lb/>rigo Vespucci fu il primo a proporre i metodi astronomici per tro&shy;<lb/>vare le longitudini; metodi che rimasero unicamente efficaci negli <lb/>usi dei navigatori, specialmente da poi che Giovanni da Empoli e <lb/>Filippo Sassetti ebbero sperimentato che i gradi della declinazione <lb/>magnetica non serbano alcuna regola di proporzione coi gradi dei <lb/>meridiani. </s></p><p type="main">

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

<s>Fra coloro che a osservare diligentemente e a investigare le <lb/>cause degli effetti naturali vi furono rivolti dall'esercizio dell'arte, <lb/>vuol essere commemorato principale fra tutti Leonardo da Vinci. </s>

<s><lb/>L'ingegno perci&ograve; del figliuolo di Ser Piero, e la speranza dei frutti <lb/>che si vedranno raccolti da lui nel campo delle scienze naturali, <lb/>non in altro si potranno meglio conoscere, n&egrave; da altro pi&ugrave; sicura&shy;<lb/>mente indovinare, che da quelle opere d'arte condotte da lui, e <lb/>nelle quali ritrova la Natura, con maravigliosa rassomiglianza, effi&shy;<lb/>giato il suo volto. </s>

<s>Chi contempla, nel cartone di Adamo e di Eva, <lb/>lumeggiato di biacca quel praticello verdeggiante di un infinita <lb/>sorta di erbe, fra le quali vanno pascendo varie specie di animali, <lb/>o vi stanno a loro diletto; chi osserva in quel fico lo scortar delle <lb/>foglie e la veduta dei rami, e in que'palmizi le nervature che <lb/>s'aprono a formare la rotondit&agrave; delle ruote, e le sottoposte vena&shy;<lb/>ture e la minuta peluria dell'epidermide, dice: colui che ha fatto <lb/>un tal lavoro &egrave; senza dubbio o ha grande attitudine a diventare <lb/>un zoologo, un botanico. </s></p><pb xlink:href="020/01/094.jpg" pagenum="75"/><p type="main">

<s>Chi pon mente a que'nudi, che nelle varie attitudini occorrono <lb/>a vedere per questi dipinti e per questi disegni; a quel gruppo di <lb/>cavalli e di cavalieri, che nella storia di Niccol&ograve; Piccinino si con&shy;<lb/>tendono rabbiosamente una bandiera, e vede con qual verit&agrave; sono <lb/>disegnate le masse muscolari, di cui si seguono con l'occhio nei <lb/>solchi le testure delle fibre e i complicati andamenti; dice: costui <lb/>&egrave; certamente maestro d'Anatomia descrittiva e d'Anatomia compa&shy;<lb/>rata. </s>

<s>Ma chi guarda nel ritratto di Mona Lisa que'lustri e quegli <lb/>acquitrini degli occhi, quei pori della pelle nelle guance e nel <lb/>volto, e la peluria leggerissima e delicata che n'esce, soggiunge, <lb/>non dover essere costui contento all'anatomia superficiale, ma dover <lb/>esser di pi&ugrave; penetrato addentro a indagarne l'istologia. </s></p><p type="main">

<s>Chi poi non guarda solamente con gli occhi, ma considera con <lb/>l'intelletto, avvedendosi bene che in que'volti son cos&igrave; vivamente <lb/>espressi gli interiori pensieri e le passioni e gli affetti, conclude <lb/>che l'Artefice deve essere entrato addentro a speculare le segrete <lb/>cause e gli organi, per cui l'interiore spirito si rivela al di fuori. </s>

<s><lb/>Il pittore da Vinci insomma si riconosce nelle opere sue per uno <lb/>che ha sperimentato e ha speculato, o che almeno ha grandissima <lb/>attitudine a sperimentare e a speculare intorno a ogni sorta di fatti <lb/>naturali. </s>

<s>E cos&igrave; &egrave; veramente come lo attestano i documenti-che ci <lb/>son rimasti di lui. </s></p><p type="main">

<s>Cos&igrave; fatti documenti, che non potrebbero essere per verit&agrave; pi&ugrave; <lb/>autentici, consistono nelle stesse carte di Leonardo scritte, per uno <lb/>de'soliti capricci degli artisti, alla rovescia. </s>

<s>I biografi ce lo dipingono <lb/>con un lapis e un libretto pendenti dalla cintola, ad uso dei cos&igrave; <lb/>detti taccuini moderni, dov'egli andava notando tutto ci&ograve; che gli <lb/>occorreva di osservare, di sperimentare o di speculare via via. </s>

<s><lb/>Cos&igrave; fatti libretti, che si empivano rapidamente, vennero, in parte <lb/>dall'Autore stesso, e in parte dagli eredi di lui, in qualche modo <lb/>ordinati e rilegati in volumi, le prime vicende sub&igrave;te dai quali son <lb/>narrate in quel documento, che da pag. </s>

<s>130-33 si legge nelle <emph type="italics"/>Me&shy;<lb/>morie storiche<emph.end type="italics"/> dell'Amoretti, (Milano, 1804). Per quel che riguarda <lb/>poi le ultime vicende, si sa come dalla Biblioteca Ambrosiana, fos&shy;<lb/>sero quelle preziose carte rapite e trasportate a Parigi, dove a nostro <lb/>dispetto rimangono tuttavia. </s></p><p type="main">

<s>Giorgio Vasari, del contenuto in quei volumi accenn&ograve; a qual&shy;<lb/>che cosa, non concernente per&ograve; se non l'arte. </s>

<s>Per quel che s'ap&shy;<lb/>partiene alla scienza, si content&ograve; di dire che Leonardo &ldquo; fra gli <lb/>altri tanti suoi capricci ebbe anco quello che, filosofando delle cose <pb xlink:href="020/01/095.jpg" pagenum="76"/>naturali, attese a intendere le propriet&agrave; dell'erbe, continuando ed <lb/>osservando il moto del cielo, il corso della luna e gli andamenti <lb/>del sole &rdquo;. </s>

<s>Anche l'Oltrocchi, bibliotecario dell'Ambrosiana, che <lb/>perci&ograve; ebbe agio di consultare i manoscritti vinciani, mentre che <lb/>ancora erano ivi esistenti, non si cur&ograve; di trascriverne e di com&shy;<lb/>mentarne, se non solo quelle parti che riguardano le arti del <lb/>disegno. </s></p><p type="main">

<s>Il primo che rivolgesse l'attenzione alle preziose note, per leg&shy;<lb/>gervi ci&ograve; che ne concerne la scienza, fu Giovan Battista Venturi, <lb/>in quel tempo che soggiornava a Parigi, dove scrisse e nel 1797 <lb/>pubblic&ograve; quel suo celebre <emph type="italics"/>Essai,<emph.end type="italics"/> verso cui si rivolsero e da cui <lb/>presero l'inspirazione tutti quegli italiani, che incominciarono allora <lb/>e seguitano tuttavia a magnificare l'ingegno scientifico di Leonardo. </s>

<s><lb/>Il Venturi fece senza dubbio opera pia verso la patria, per cui con&shy;<lb/>viene che gliene professiamo la gratitudine dovuta. </s>

<s>Ma pi&ugrave; grati ci <lb/>sentiremmo all'illustre fisico modanese, se le parole almeno ce le <lb/>avesse trascritte nella favella che risuona dolcemente ancora sul <lb/>labbro de'villici da Vinci, e pi&ugrave; che mai grata gli sarebbe la sto&shy;<lb/>ria, se interpretando i concetti scientifici del suo Autore, non ci <lb/>avesse inteso spesso una cosa per un'altra, o non avesse intraveduto <lb/>talvolta nelle parole espresso ci&ograve; che veramente non ci era. </s></p><p type="main">

<s>Nel 1840, Guglielmo Libri apre il secondo libro della sua <emph type="italics"/>Hi&shy;<lb/>stoire des sciences mathematiques en Italie,<emph.end type="italics"/> col trattar di Leonardo <lb/>da Vinci, i manoscritti del quale dice che non erano stati ancora <lb/>seriamente studiati. </s>

<s>Egli poi gli descrive minutamente, e prolissa&shy;<lb/>mente ivi si studia di annoverarne i soggetti varii toccati, e di <lb/>porre in rilievo la novit&agrave; de'concetti e la importanza delle in&shy;<lb/>venzioni. </s>

<s>Dei quali concetti pi&ugrave; notabili e delle quali invenzioni, <lb/>accioch&egrave; possano i lettori averne qualche saggio, trascrive alcuni <lb/>passi dai vari manoscritti e gli pon sott'occhio in quelle <emph type="italics"/>XXI Notes<emph.end type="italics"/><lb/>apposte in calce al III Tomo della citata <emph type="italics"/>Histoire.<emph.end type="italics"/> Eppure si pos&shy;<lb/>sono ancora, dop'aver letto le prime 58 pagine del <emph type="italics"/>livre second,<emph.end type="italics"/> e <lb/>le <emph type="italics"/>XXI Notes,<emph.end type="italics"/> ripetere al Libri le sue stesse parole, che egli pro&shy;<lb/>nunziava dop'aver dato il suo giudizio sull'<emph type="italics"/>Essai<emph.end type="italics"/> del Venturi: &ldquo; Or <lb/>ces manuscrits n'ont jamais &eacute;t&eacute; serieusement &eacute;tudi&eacute;s &rdquo; (Paris 1840, <lb/>Tome III, pag. </s>

<s>39). A studiarli seriamente poi pi&ugrave; tardi incomin&shy;<lb/>ciarono due stranieri, Carlo Ravaisson-Mollien a Parigi, e Giovan <lb/>Paulo Richter a Londra. </s>

<s>Gli italiani che van buccinando il nome <lb/>di Leonardo con tuba s&igrave; sonora, non hanno dato, fin qui, opera <lb/>che a'illustrare alcuni disegni scelti dal Codice Atlantico, pub-<pb xlink:href="020/01/096.jpg" pagenum="77"/>blicati in XXIV tavole litografate, per modo di saggio, in Milano <lb/>nel 1872: lavoro non scientifico, ma accademico, e benissimo atto <lb/>a secondare il genio de'convenuti a una festa. </s></p><p type="main">

<s>Toccheremo qualche cosa pi&ugrave; qua delle pubblicazioni fatte dai <lb/>due benemeriti stranieri: quel che ora per&ograve; pi&ugrave; preme, &egrave; di offerir <lb/>qualche esempio delle osservazioni naturali e delle speculazioni di <lb/><figure id="id.020.01.096.1.jpg" xlink:href="020/01/096/1.jpg"/><lb/>Leonardo, che quasi promesseci nei dipinti, si trovano poi fedel&shy;<lb/>mente osservate nei manoscritti. </s></p><p type="main">

<s>Dicemmo che il cartone, il quale doveva servire al dipinto di <lb/>quelle portiere, da eseguirsi pel re di Portogallo, rivelava nell'ar&shy;<lb/>tefice un botanico squisito, e soggiungemmo potersi argomentare <lb/>da tutto insieme che l'artefice stesso non dovess'essere un semplice <pb xlink:href="020/01/097.jpg" pagenum="78"/>osservatore, ma un filosofante delle propriet&agrave; naturali dell'erbe. </s>

<s><lb/>Ecco infatti una nota dai Manoscritti, nella quale apparisce che ve&shy;<lb/>ramente Leonardo attese a quell'ordine simmetrico e vario, nelle <lb/>varie specie di piante, che le foglie tengono nel disporsi intorno <lb/>all'asse del ramo, e che i moderni appellano col nome di <emph type="italics"/>fillotassi.<emph.end type="italics"/><lb/>&ldquo; Tale &egrave; il nascimento, egli dice, delle ramificazioni delle piante <lb/>sopra i lor rami principali, qual &egrave; quello del nascimento delle fo&shy;<lb/>glie sopra i ramicoli del medesimo anno di esse foglie, le quali <lb/>foglie hanno quattro modi di procedere l'una pi&ugrave; alta che l'altra. </s>

<s><lb/>Il primo pi&ugrave; universale &egrave; che sempre la sesta di sopra nasce sopra <lb/>la sesta di sotto: e il secondo &egrave; che le due terze di sopra son <lb/>sempre le due terze di sotto; e il terzo modo &egrave; che la terza di <lb/>sopra &egrave; sopra la terza di sotto. </s>

<s>&rdquo; (Richter, Londra, 1883, T.I, pag. </s>

<s>211). </s></p><p type="main">

<s>Che se di qui non trasparisce altro pi&ugrave; che il semplice osser&shy;<lb/>vatore, la seguente nota ci rivela il filosofo: &ldquo; Sempre la foglia <lb/>volge il suo diritto inverso il cielo acci&ograve; possa meglio ricevere con <lb/>tutta la sua superficie la rugiada che con lento moto discende dal&shy;<lb/>l'aria, e tali foglie sono in modo compartite sopra le loro piante, <lb/>che l'una occupa l'altra il men che sia possibile, coll'interzarsi <lb/>l'una sopra dell'altra, come si vede fare all'edera che copre li <lb/>muri; e tale intrecciamento serve a due cose: cio&egrave; al lasciare l'in&shy;<lb/>tervallo che l'aria e il sole possa penetrare in fra loro e che le <lb/>goccie che caggiono dalla prima foglia possan cadere sopra la quarta <lb/>e la sesta degli altri alberi. </s>

<s>&rdquo; (ivi, pag. </s>

<s>214). </s></p><p type="main">

<s>L'osservazione, che port&ograve; Leonardo sulla realt&agrave; dei modelli, <lb/>per ritrarre al vivo la carne degli uomini, gli serv&igrave; d'occasione a <lb/>coltivar lo studio di quell'altra fra le scienze naturali, che &egrave; l'Ana&shy;<lb/>tomia. </s>

<s>Quali aiuti gli venissero intorno a ci&ograve; da Marcantonio Della <lb/>Torre non &egrave; facile definire, ma forse la perizia del sezionare di <lb/>questo, era compiuta dalla sagacia delle osservazioni e delle inda&shy;<lb/>gini dell'altro. </s>

<s>Nel dipingere un occhio s'accorge Leonardo di un <lb/>fatto assai curioso; di un fatto, che Galileo scommette non esser&shy;<lb/>vene due fra mille che l'abbiano osservato (Alb. </s>

<s>I, 394) e par che <lb/>voglia insinuar collo stesso silenzio che l'osservazione &egrave; sua, ben&shy;<lb/>ch&egrave; il Porta l'avesse descritta nella Diottrica e l'Acquapendente <lb/>avesse pubblicato com'occorresse al Sarpi di farla negli occhi dei <lb/>gatti e poi degli uomini. </s>

<s>Ma pi&ugrave; di un secolo prima del Porta e <lb/>del Sarpi avea il nostro pittore da Vinci osservato il fenomeno, e <lb/>v'avea filosofato attorno con assai retto giudizio. </s>

<s>Hanno inteso i <lb/>lettori che il fenomeno di cui si tratta &egrave; il dilatarsi e il restrin-<pb xlink:href="020/01/098.jpg" pagenum="79"/>gersi della pupilla, sotto le impressioni della varia intensit&agrave; della <lb/>luce; fenomeno che non solo fu da Leonardo materialmente osser&shy;<lb/>vato, ma altres&igrave; filosoficamente illustrato, in ordine a ci&ograve; che con&shy;<lb/>cerne la teoria della visione. </s>

<s>&ldquo; Questa nostra pupilla, ci lasci&ograve; scritto, <lb/>cresce e diminuisce secondo la chiarit&agrave; o scurit&agrave; del suo obietto, <lb/>e perch&egrave; con qualche tempo fa esso crescere o descrescere, esso <lb/>non vede cos&igrave; presto uscendo dal lume e andando all'oscuro, e <lb/>similmente dall'oscuro al luminoso, e questa cosa gi&agrave; m'ingann&ograve; <lb/>nel dipingere un occhio e di l&igrave; l'imparai. </s>

<s>&rdquo; (Ivi, pag. </s>

<s>23). </s></p><p type="main">

<s>Il curioso fatto imparato nel dipingere la pupilla, invogli&ograve; forse <lb/>Leonardo a penetrare pi&ugrave; addentro all'anatomia dell'occchio, e ad <lb/>estrarlo dal cadavere per sezionarlo. </s>

<s>In altro modo riuscirebbe assai <lb/>difficile intendere com'egli vi avesse potuto scoprir l'inversioni delle <lb/>immagini, a cui accenna nella nota seguente: &ldquo; Nessuno spazio di s&igrave; <lb/>minimo corpo penetra nell'occhio che non si volti sottosopra. </s>

<s>&rdquo; No&shy;<lb/>tabili son poi le parole, colle quali prosegue e in che si studia di <lb/>risolvere quel famoso problema, che ha tenuto gli ottici in cos&igrave; lungo <lb/>travaglio, problema che &egrave; quello del vedersi da noi le immagini <lb/>dirette, mentre sul fondo del nostro occhio son dipinte a rovescio. </s>

<s><lb/>Leonardo n'esce da par suo ammettendo un'ipotesi assai strana. </s>

<s><lb/>Professando le dottrine galeniche, secondo le quali la lente cristal&shy;<lb/>lina &egrave; la sede della visione, e ingannato forse da alcuni effetti ve&shy;<lb/>duti fare ai processi ciliari, credette che fosse a questi stessi com&shy;<lb/>messo l'ufficio di capovolgere la medesima lente cristallina, per cui <lb/>venissero cos&igrave; a raddrizzarsi le immagini degli oggetti &ldquo; e nel pe&shy;<lb/>netrare, (tali son le parole soggiunte alle precedenti citate), la spera <lb/>cristallina ancora si rivolta sottosopra e cos&igrave; ritorna diritto lo spa&shy;<lb/>zio dentro all'occhio, com'era l'obietto di fuori dell'occhio. </s>

<s>&rdquo; (ivi, <lb/>pag. </s>

<s>48). Da ci&ograve; dovette seguitar senza dubbio l'invenzione della <lb/>camera ottica e l'applicazione ch'ei ne fa alla teoria della visione, <lb/>conforme a ci&ograve; che leggesi in quell'altra nota trascritta e pubbli&shy;<lb/>cata gi&agrave; dal Venturi. </s>

<s>L'invenzione della camera oscura par dunque <lb/>certo esser cosa appartenente a Leonardo, almeno per ci&ograve; che con&shy;<lb/>cerne l'applicazione di lei alla teorica del vedere: applicazione alla <lb/>quale non poteva pensare l'Alberti, professando egli apertamente <lb/>le dottrine platoniche de'raggi visivi che escon dagli occhi, e vanno <lb/>a ricongiungersi col fuoco celeste, essendo parole espresse di lui <lb/>che la visione si porge e distende verso la cosa visibile. (Op. </s>

<s>volg. </s>

<s><lb/>Firenze, 1847, T. IV, pag. </s>

<s>100) e che il raggio della veduta esce <lb/>dall'occhio di chi riguarda. (Archit. </s>

<s>Milano, 1833, pag. </s>

<s>362). </s></p><pb xlink:href="020/01/099.jpg" pagenum="80"/><p type="main">

<s>Delle molte altre scoperte o speculazioni di Fisica, e osserva&shy;<lb/>zioni di Storia naturale, occorrer&agrave; via via di far parola per entro <lb/>ai volumi che si parano innanzi agli occhi dei nostri lettori; sco&shy;<lb/>perte che Leonardo faceva non consultando libri, ma direttamente <lb/>interrogando la stessa Natura per via dell'esperienza. </s>

<s>Che tale fosse <lb/>l'indole e il metodo seguito dall'Autore, noi lo abbiamo fin qui <lb/>argomentato dai fatti, e sono i nostri argomenti confermati dalle <lb/>stesse parole di lui, che egli scrive contro l'arroganza dei filosofi <lb/><emph type="italics"/>in libris.<emph.end type="italics"/> &ldquo; Molti mi crederanno ragionevolmente, egli nota, poter <lb/>riprendere allegando le mie prove esser contro all'antorit&agrave; di al&shy;<lb/>quanti uomini di gran riverenza appresso de'loro inesperti giudizii, <lb/>non considerando le mie cose essere nate sotto la semplice espe&shy;<lb/>rienza, la quale &egrave; maestra vera. </s>

<s>&rdquo; (Richter, ivi, pag. </s>

<s>15). </s></p><p type="main">

<s>E che veramente potesse l'esperienza, assai meglio de'libri, <lb/>condurre Leonardo alla scoperta della camera ottica, e l'osserva&shy;<lb/>zione rivelargli la fillotassi, come altres&igrave; que'molti e varii fatti na&shy;<lb/>turali, che si leggon notati qua e l&agrave; ne'suoi Manoscritti, &egrave; cosa <lb/>facilissima a comprendersi da tutti. </s>

<s>N&egrave; difficile &egrave; pure intendere <lb/>come l'osservazione stessa e la propria esperienza potessero con&shy;<lb/>durlo a scoprir quella legge fondamentale, che governa il moto <lb/>dell'acque, a cui, per la stessa via, eran giunti Frontino, i Pretori <lb/>romani, e pi&ugrave; recentemente l'Alberti; legge, dalla quale, filosofando <lb/>e sperimentando, non difficilmente si sarebbero svolti nell'ingegno <lb/>di Leonardo que'teoremi, che raccolti insieme e ordinati, compon&shy;<lb/>gono quel Trattato idraulico, il quale va sotto il nome di lui. </s></p><p type="main">

<s>Ma non sempre le note che ricorrono per i manoscritti vin&shy;<lb/>ciani versano circa a soggetti di Fisica sperimentale, o di Storia na&shy;<lb/>turale, o di Meccanica pratica. </s>

<s>La miglior parte e pi&ugrave; importante <lb/>di quelle note contiene dimostrazioni di Meccanica razionale, alle <lb/>quali non sarebbe potuto Leonardo riuscire in qualche modo, sen&shy;<lb/>z'esservisi prima preparato con discipline e con istudii, che non <lb/>si apprendono se non dalla lettura dei libri o dalla voce dei mae&shy;<lb/>stri. </s>

<s>Luca Paciolo, amico suo, gli dovett'essere, senza dubbio, nelle <lb/>Matematiche di grande aiuto, e l'Amoretti a pag. </s>

<s>86 delle citate <lb/><emph type="italics"/>Memorie<emph.end type="italics"/> fa menzione di una scrittura del Nostro, nella quale ri&shy;<lb/>chiede l'Archimede del vescovo di Padova. </s>

<s>Per ci&ograve; a noi sembra <lb/>ragionevolissimo il credere che il Matematico di Siracusa colla let&shy;<lb/>tera morta, e il Matematico del Borgo colla parola viva, iniziassero <lb/>l'ingegno di Leonardo a intendere le proposizioni della Geometria <lb/>e al farne l'applicazione ai teoremi della Meccanica. </s></p><pb xlink:href="020/01/100.jpg" pagenum="81"/><p type="main">

<s>Bench&egrave; si ritenga da noi una tal credenza, per cosa certissima, <lb/>il veder nonostante il discepolo far cos&igrave; gran progressi nella scuola <lb/>de'due pi&ugrave; insigni Maestri di scienza matematica, di che si glorii <lb/>l'Italia, ha tanto del maraviglioso, e tanto esce fuori de'consueti <lb/>ordini della storia, che ne rimane stupefatto il nostro povero in&shy;<lb/>telletto. </s>

<s>Ci&ograve; che quell'artista seppe speculare della Scienza del moto <lb/>e per quanto largo spazio riuscisse a conquistare le incognite pro&shy;<lb/>vincie, nelle quali Galileo stabil&igrave; il suo Nuovo Regno, i lettori, a <lb/>cui baster&agrave; la pazienza di seguirci in questo lungo viaggio, lo ve&shy;<lb/>dranno bene a suo tempo. </s>

<s>S'abbatteranno, leggendo, in un Tratta&shy;<lb/>tello di <emph type="italics"/>Meccanica razionale,<emph.end type="italics"/> da noi con diligente amore compilato <lb/>da quei manoscritti vinciani, che abbiamo potuto vedere alla pub&shy;<lb/>blica luce, e che si son potuti da noi, con qualche comodit&agrave;, con&shy;<lb/>sultare. </s>

<s>Con pari amor diligente &egrave; stato pure compilato da noi quel&shy;<lb/>l'altro Trattatello d'Idraulica, che vedranno i nostri lettori inserito <lb/>a suo luogo, compendiato da quello, che per la prima volta fu <lb/>nel 1828 pubblicato in Bologna. </s>

<s>La brevit&agrave; stessa, se non il nuovo <lb/>ordine che noi ci siamo studiati di dare alle parti di quel Tratta&shy;<lb/>tello, gioveranno a porre in pi&ugrave; vivo rilievo la scienza di Leonardo, <lb/>perciocch&egrave; il compilator primo e pi&ugrave; antico di quel Trattato in&shy;<lb/>tiero, oltre ad esser trascorso in errori gravissimi materiali e for&shy;<lb/>mali, non ha usato discrezione alcuna cos&igrave; nella scelta come nel&shy;<lb/>l'ordine dei teoremi. </s></p><p type="main">

<s>Un'altra compilazione fatta allo stesso modo &egrave; pure il Trattato <lb/>della Pittura, n&egrave; sappiamo intendere come gli artisti e i letterati <lb/>lo abbiano potuto cos&igrave; confidentemente ritener per legittimo parto <lb/>del Vinci, tanto nella materia che nella forma. </s>

<s>Il sospetto ragio&shy;<lb/>vole del Venturi sarebbe confermato dal ripensare a quel carattere <lb/>incontentabile, come &egrave; il grande Artista dipinto dal Vasari, il quale <lb/>dice di lui che il cercar nell'opere eccellenza sopra eccellenza, <lb/>com'ei sempre faceva, <emph type="italics"/>era cagione che nessuna ne lasciasse asso&shy;<lb/>luta.<emph.end type="italics"/> Da un'altra parte Leonardo si confessa da s&egrave; medesimo per <lb/>uomo senza lettere, e inetto a ben dire quello che voleva trattare. <lb/></s>

<s>&ldquo; Diranno che per non avere io lettere non poterei ben dire quello <lb/>che voglio trattare. </s>

<s>Or non sanno questi che le mie cose son pi&ugrave; <lb/>da esser trattate dalla sperienza che d'altra parola, la quale fu <lb/>maestra di chi bene scrisse e cos&igrave; per maestra la, in tutti i casi, <lb/>allegher&ograve;. </s>

<s>&rdquo; (ivi, pag. </s>

<s>14). </s></p><p type="main">

<s>Sopra questi certissimi argomenti noi crediamo di potere af&shy;<lb/>fermare che Leonardo non ebbe quella pazienza o quella costanza, <pb xlink:href="020/01/101.jpg" pagenum="82"/>e diciam pure quell'arte letteraria, che si richiedeva a dar forma <lb/>di Trattato alle varie materie e a ordinarle in libri, in capitoli, in <lb/>proposizioni, come asseriscono molti. </s>

<s>Ond'&egrave; che da noi si potrebbe <lb/>facilmente mostrar l'inganno che fu preso dall'Amoretti nel &sect; XXXII <lb/>delle <emph type="italics"/>Memorie,<emph.end type="italics"/> dove annovera un lungo catalogo di Trattati, gi&agrave; <lb/>bell'e messi all'ordine da Leonardo, alcuni de'quali anco scritti <lb/>in latino; si potrebbe far ci&ograve; diciamo assai facilmente, se l'Autore <lb/>stesso non avesse dato a vedere d'essersi gi&agrave; per s&egrave; medesimo ac&shy;<lb/>corto di quell'inganno. </s>

<s>N&egrave; pi&ugrave; difficile pure sarebbe il mostrar <lb/>qual conto si debba fare e in qual significato debbono interpetrarsi <lb/>le autorevoli testimonianze di Luca Pacioli. </s></p><p type="main">

<s>Concludiamo insomma come tutto quello che &egrave; propriet&agrave; let&shy;<lb/>teraria del Nostro, si contiene in quelle note, in quegli appunti, <lb/>in quei ricordi, che ci son rimasti tuttavia manoscritti autografi <lb/>nella carte di lui. </s>

<s>La non breve vita decorsagli dal 1452 al 1519 <lb/>e la costante abitudine di nulla tralasciar d'inosservato, fa ragio&shy;<lb/>nevolmente presupporre che molti pi&ugrave; de'pervenuti infino a noi <lb/>dovessero essere i libretti vinciani, e dall'altra parte non &egrave; possi&shy;<lb/>bile che, in tanto tramestar di mani e traslocar di paesi, non an&shy;<lb/>dassero in qualche parte smarriti. </s>

<s>Pure &egrave; tanta l'eredit&agrave; scientifica <lb/>a noi trasmessa, che ce ne dovremmo contentare e pensar piuttosto <lb/>al miglior modo di usufruirla. </s></p><p type="main">

<s>Si diceva dianzi che ad usufruirla pens&ograve;, de'primi, in Francia, <lb/>il Ravaisson-Mollien, che ci dette fotografata una buona parte delle <lb/>carte vinciane sottovi trascritte le note conforme all'ortografia mo&shy;<lb/>derna, e di rincontro al testo la traduzione francese. </s>

<s>&Egrave; naturalis&shy;<lb/>simo ch'ei dovesse incontrarsi in grandissime difficolt&agrave;, s&igrave; rispetto <lb/>alla materia, s&igrave; rispetto al modo d'interpetrarla, ci&ograve; che troppo <lb/>bene apparisce dalle stesse versioni e da quegl'indici posti in fine <lb/>ai volumi, dove l'egregio uomo and&ograve; a rifugiare i commenti scien&shy;<lb/>tifici, talvolta importantissimi, ch'ei fa al testo vinciano. </s>

<s>Ma un'oc&shy;<lb/>casione insuperabile di errori &egrave; in lui, e ne'pari suoi, il non aver <lb/>senso di quel vernacolo toscano, di che fa uso nelle solitarie sue <lb/>scritture Leonardo. </s>

<s>Ci&ograve; conduce il benemerito editor parigino in <lb/>errori gravissimi, e di ci&ograve; in fine della presente parte del nostro <lb/>Discorso sottoporremo al giudizio de'nostri lettori, in nota, un <lb/>esempio. </s></p><p type="main">

<s>&Egrave; ben vero per&ograve; che ad apparecchiar l'ordinamento de'con&shy;<lb/>cetti di Leonardo, e a pubblicarli in modo che se ne possano gio&shy;<lb/>vare gli studiosi, non si richiedeva di meglio della laboriosissima <pb xlink:href="020/01/102.jpg" pagenum="83"/>opera del Parigino, che noi facciamo voto di veder presto condotta <lb/>alla sua m&egrave;ta. </s>

<s>Con tutti quei materiali alla mano si potr&agrave; allora <lb/>incominciare a costruire, e il giudizioso Architetto, fra quegli stessi <lb/>materiali di ugual sostanza e di non differente forma, sceglier&agrave; <lb/>opportunamente i migliori e lascer&agrave; indietro i disutili, per qualsi&shy;<lb/>voglia ragion di difetto che ritrovisi in essi. </s></p><p type="main">

<s>Chi attende con qualche studio ai Manoscritti vinciani, facil&shy;<lb/>mente ritrova che ora una nota, perch&egrave; l'Autore v'ha ripensato <lb/>un po'meglio, contradice a un'altra; ora il concetto che qui viene <lb/>espresso in confuso, altrove &egrave; meglio spiegato; ora &egrave; una specula&shy;<lb/>zione interrotta che poi viene ripresa e continuata, aggiungendo <lb/>qualche cosa al gi&agrave; detto, che &egrave; ripetuto sotto altra forma. </s>

<s>Qui &egrave; <lb/>trascorso un errore, e pi&ugrave; qua lo troviamo o confermato o corretto. </s>

<s><lb/>Molte volte quel che sente d'averlo espresso male, si prova a ri&shy;<lb/>dirlo un po'meglio. </s>

<s>Il non voler far uso in questi casi di una giu&shy;<lb/>diziosa scelta, &egrave; un volere stampar volumi sopra volumi per de&shy;<lb/>corarne le biblioteche, non perch&egrave; se ne giovino gli studiosi. </s></p><p type="main">

<s>Siam venuti cos&igrave; preparando le file a intessere il nostro giu&shy;<lb/>dizio intorno all'opera fatta dal Richter, il quale ha gi&agrave; dato <lb/>mano, non come il Mollien a preparare o mettere all'ordine i ma&shy;<lb/>teriali, ma a costruire. </s>

<s>Forse egli ha avuto in ci&ograve; far troppa fretta <lb/>e non avendo potuto giustamente estimare ogni pi&ugrave; minuta par&shy;<lb/>ticolarit&agrave;; non &egrave; riuscito a farne convenientemente la scelta. </s>

<s>Ma <lb/>pure ha di una scelta riconosciuto giudiziosamente il bisogno, e <lb/>poniamo che la difficile impresa non sia andata, com'asseriscono i <lb/>censori di lui, esente da gravissimi difetti; a noi par nonostante <lb/>che l'editor londinese abbia tenuta la via conveniente a chi si <lb/>dava cura di pubblicar le opere di Leonardo, per benefizio degli <lb/>studiosi. </s></p><p type="main">

<s>Alcuno ha apposto per difetto al Richter l'aver trascurati i <lb/>commenti, n&egrave; si sa di qual sorte commenti abbia inteso costui. </s>

<s><lb/>Commenti filologici, senza dubbio sarebbero stati opportuni, ma <lb/>non era in grado di farli un inglese, che anzi cade anch'egli assai <lb/>spesso negli errori, notati di sopra nel Mollien, per non aver senso <lb/>e pratica del vernacolo toscano. </s>

<s>Commenti scientifici, pi&ugrave; che op&shy;<lb/>portuni, sembrerebbero necessari, ma per farli occorrerebbe di co&shy;<lb/>noscer lo stato della scienza a'tempi di Leonardo, scienza affidata <lb/>alla viva voce dei maestri e alle carte neglette e perci&ograve; disperse <lb/>n&egrave;, per umana industria forse recuperabili. </s>

<s>Se si potessero aver <lb/>sott'occhio quei documenti, Leonardo da Vinci apparirebbe sempre <pb xlink:href="020/01/103.jpg" pagenum="84"/>un'ingegno straordinario, ma cesserebbe di rappresentarsi al nostro <lb/>giudizio sotto l'aspetto d'ingegno miracoloso, ritrovandosi che an&shy;<lb/>ch'egli ha, per legge ordinaria, dovuto soggiacere alle necessit&agrave; <lb/>delle tradizioni, a ministrar le quali gli dovevano esser soccorsi i <lb/>libri antichi e gl'insegnamenti de'suoi tempi. </s>

<s>Quella po'di luce che <lb/>poteva venirgli da cos&igrave; fatti insegnamenti era sufficiente a indirizzar <lb/>Leonardo per i sentieri del vero, a proseguir lungo i quali lo con&shy;<lb/>duceva per mano la stessa Natura, negli amati esercizi dell'arte. </s></p><p type="main">

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

<s>Trattenendo il pensiero meditativo, cos&igrave; sopra questa maravi&shy;<lb/>gliosa figura d&igrave; Leonardo, come su quella degli altri cultori del&shy;<lb/>l'arte, sia essa l'arte del verso nell'Alighieri, sia l'arte navigatoria <lb/>nel Colombo, sia l'arte edilizia nell'Alberti, ci persuadiam facilmente <lb/>che quegli uomini singolari attesero non ad assottigliar l'ingegno <lb/>nella dialettica dei sofismi, ma a inacutire i sensi per pigliar pi&ugrave; <lb/>sicuro possesso delle cose reali. </s>

<s>L'arte navigatoria e quella della <lb/>stampa felicemente ritrovate nel medesimo tempo, eran come i due <lb/>remi maestri che a quel possesso conducevano la navicella, dentro <lb/>alla quale fa, la mente dell'uomo, da nocchiero. </s>

<s>Di qui &egrave; che in <lb/>affidarsi al mar periglioso, vollesi a quella stessa navicella rivedere <lb/>ogni testura, e far esperienza di ci&ograve; che potesse incontro all'in&shy;<lb/>sorger tempestoso dei flutti e del vento. </s>

<s>Se ci si conceda ora che <lb/>si possa, per una tal navicella, rappresentare il corpo dell'uomo, <lb/>si comprender&agrave; come la condizione dei tempi e il progredir nelle <lb/>cognizioni, dovessero portare allo studio dell'Anatomia, e di quegli <lb/>organi dei sensi in particolare, per cui l'uomo entra nel pieno e <lb/>reale possesso del mondo. </s></p><p type="main">

<s>Fino al terminar di quel secolo, in cui fu spento Leonardo, <lb/>tutto ci&ograve; che si sapeva della fabbrica del corpo umano s'appren&shy;<lb/>deva dai libri dell'antico Galeno, il quale era ai medici, come Ari&shy;<lb/>stotile ai filosofi, l'oracolo venerato degl'infallibili responsi. </s>

<s>Ma <lb/>scese dal Belgio in Italia un uomo che, colle sacrileghe mani, os&ograve; <lb/>di atterrar dagli altari quell'idolo, con audace pretensione di di&shy;<lb/>mostrare che la maggior parte di que'suoi responsi erano bugiardi. </s>

<s><lb/>Un tale uomo nativo di Bruxelles si chiamava Andrea Vesalio, il <pb xlink:href="020/01/104.jpg" pagenum="85"/>quale, eletto a professar Anatomia nello studio di Padova, sezionando <lb/>cadaveri umani e mettendo sott'occhio le parti nelle loro vere forme <lb/>naturali, le veniva sagacemente comparando alle forme stesse de&shy;<lb/>scritte da Galeno, e ad ogni passo ne scopriva un errore. </s>

<s>Additava <lb/>anco il Vesalio la fonte originaria di tali errori, ch'ei loquacemente <lb/>riconosceva nell'aver l'anatomico greco descritta non la fabbrica <lb/>del corpo dell'uomo, ma quella del bruto. </s></p><p type="main">

<s>Le religiose superstizioni pagane, per le quali si reputava atto <lb/>sacrilego lo scompaginar violentemente le membra anco ad un uomo <lb/>morto, e l'opinione che fossero similmente configurate le membra <lb/>al di dentro, com'appariscono al di fuori, negli uomini e nei bruti, <lb/>furono senza dubbio le due principali sorgenti di quegli antichi <lb/>errori, che il Vesalio era venuto a scoprire al troppo credulo mondo. </s>

<s><lb/>La scienza perci&ograve; professer&agrave; eterna gratitudine a quell'uomo, e lo <lb/>riconoscer&agrave; per primo Istitutore dell'Anatomia. </s>

<s>Ma, o fosse giova&shy;<lb/>nile baldanza o nat&igrave;o orgoglio, non serb&ograve;, nel geloso esercizio del <lb/>suo ministero, il debito modo, per cui gli si concitarono incontro <lb/>dai Galenisti inimicizie e persecuzioni s&igrave; fiere, che quelle esercitate <lb/>poi da'peripatetici contro Galileo, al paragone, sembran carezze. </s></p><p type="main">

<s>Successe al Vesalio, nello studio padovano, Realdo Colombo <lb/>di Cremona, il quale era stato gi&agrave; spettatore delle sezioni e udi&shy;<lb/>tore delle acerbe diatribe declamate dall'ardente brussellese. </s>

<s>Nel <lb/>temperato animo del nostro italiano parvero, infin da giovane, quelle <lb/>diatribe contro l'antico maestro un po'troppo esagerate, e succe&shy;<lb/>duto nella cattedra di lui non manc&ograve; di confessarle e di dare esempii <lb/>d'una critica pi&ugrave; mite e pi&ugrave; giudiziosa. </s>

<s>Il Vesalio aveva atterrate <lb/>le mura del tempio galenico, il primo, con ardimento inaudito, per <lb/>cui, mentre da una parte perseguitavasi a morte, s'esaltava, dal&shy;<lb/>l'altra, col titolo di <emph type="italics"/>divino.<emph.end type="italics"/> Il Colombo, entrato il primo per quella <lb/>breccia aperta, v'instaur&ograve; il nuovo regno dell'Anatomia descrittiva <lb/>e sperimentale, e oper&ograve; con tant'arte giudiziosa, che la violenta <lb/>conquista vesaliana prese aspetto di una successione legittima. </s></p><p type="main">

<s>Chi vuol giustamente apprezzare i meriti dell'Anatomico cre&shy;<lb/>monese, e ravvisar quella fina arte ch'egli us&ograve; per diffondere la <lb/>nuova scienza, non distruggendo con rabbioso orgoglio l'antico edi&shy;<lb/>fizio, ma correggendolo con giudiziosa industria e ampliandone la <lb/>struttura; non dee far altro che svolgere quelle splendide pagine, <lb/>che egli scrisse e intitol&ograve; <emph type="italics"/>De re anatomica,<emph.end type="italics"/> stampate nel 1559 in <lb/>Venezia dalla tipografia di Niccol&ograve; Bevilacqua. </s>

<s>A noi sembra questo <lb/>il pi&ugrave; bel libro, che in materia scientifica sia uscito fuori in quel <pb xlink:href="020/01/105.jpg" pagenum="86"/>tempo, ed &egrave; tanta la sobriet&agrave; dell'erudizione, tanta l'arte colla quale <lb/>sa nuotar fuori del gazzabuglio delle opinioni e sollevarsi alto sulla <lb/>nebbia uggiosa de'placiti delle scuole, tanta la lucidezza delle ar&shy;<lb/>gomentazioni e la oppurtunit&agrave; delle esperienze, che sembra essere <lb/>stata scritta quell'opera dopo i tempi di Galileo. </s>

<s>Se si ripensa anzi <lb/>a quella generosa e temperata franchezza, colla quale egli emenda <lb/>gli errori, in che incorsero Aristotile e Galeno e lo stesso Vesalio, <lb/>si creder&agrave; che l'Autore non iscrivesse, come Galileo stesso, in tempi <lb/>di controversie, ma nella pacifica dominazione del Metodo speri&shy;<lb/>mentale, tanto &egrave; serena la mente di Realdo Colombo nello stesso <lb/>fervoroso zelo dell'eloquente parola. </s></p><p type="main">

<s>Il primo libro anatomico del Cremonese tratta delle ossa. </s>

<s>Egli <lb/>ivi diligentemente attende a descrivere le <emph type="italics"/>epifisi,<emph.end type="italics"/> dell'utilit&agrave; delle <lb/>quali, egli dice, Galeno, d'altra parte solertissimo investigatore <lb/>della Natura, non scrisse, e ci&ograve; che pi&ugrave; fa meraviglia, non scrisse <lb/>nemmeno il Vesalio, <emph type="italics"/>quippe qui ardiret cupiditate increbili in <lb/>Galenum invehendi et eius errores adnotandi.<emph.end type="italics"/> (Da re anat. </s>

<s>edit. </s>

<s><lb/>cit. </s>

<s>pag. </s>

<s>4). Nel divisare, delle ossa una classificazione veramente <lb/>scientifica, dice di non aver seguito gli esempii n&egrave; di Galeno an&shy;<lb/>tico n&egrave; del Vesalio moderno, intorno a che tanto vivo sente il <lb/>dovere di non dilungarsi capricciosamente dall'insegnamento dei <lb/>primi maestri, che vuol, del fatto, mostrar di averne la sua buona <lb/>ragione. &ldquo; Nam licet Galenum, tamquam numen veneremur, Vesa&shy;<lb/>lioque in dissectionis arte plurimum tribuamus, ubi cum rei na&shy;<lb/>tura consentiunt: tamen cum aliquando videamus rem aliter multo <lb/>se habere ac ipsi descripserint, veritas eadem, cui magis addicti <lb/>sumus, nos coegit ab illis interdum recedere &rdquo; (ibi, pag. </s>

<s>10). </s></p><p type="main">

<s>Memoranda sentenza sulla bocca di uno scienziato, che scrive <lb/>nella prima met&agrave; del secolo XVI: io seguo, nell'investigare i fatti <lb/>della Natura, la verit&agrave;, non il maestro, e sia pure un Galeno, un <lb/>Vesalio. </s>

<s>E conforme a una tal professione di fede, il Colombo os&shy;<lb/>serva i fatti, e come gli si rappresentano agli occhi, fedelmente <lb/>cos&igrave; gli descrive, facendo tratto tratto le maraviglie che quello stesso <lb/>gran Vesalio, il quale non la finisce mai contro Galeno, per aver <lb/>descritta l'anatomia non dell'uomo, ma delle scimmie, egli, il cen&shy;<lb/>sore ardente, l'obiurgatore ingiurioso sia bene spesso caduto negli <lb/>errori stessi rinfacciati a Galeno. </s>

<s>Questa specie di recriminazione <lb/>occorre al Nostro di farla a ogni pi&egrave; sospinto, ma specialmente a <lb/>proposito de'muscoli della laringa e dell'occhio. </s></p><p type="main">

<s><emph type="italics"/>De oculis<emph.end type="italics"/> &egrave; il soggetto proprio del X libro, intorno a che &egrave; <pb xlink:href="020/01/106.jpg" pagenum="87"/>per prima cosa sollecito di avvertire il lettore che, innanzi a lui, <lb/>nessun altro anatomico non aveva descritto veramente, se non l'oc&shy;<lb/>chio del bruto. </s>

<s>Ond'&egrave; che egli esce con ardente zelo a rimprove&shy;<lb/>rare e a muovere accuse contro gli uomini della scienza, e special&shy;<lb/>mente contro Galeno e il Vesalio, <emph type="italics"/>qui tantam rem, tam illustrem, <lb/>tam optatam, tam negligenter scribendam putarent, belluinum <lb/>oculum pro humano dissecantes<emph.end type="italics"/> (ibi, pag. </s>

<s>216). </s></p><p type="main">

<s>Quando per&ograve; il Colombo, invitato dalla nobilt&agrave; e dalla impor&shy;<lb/>tanza del soggetto, entra a far l'anatomia dei mezzi refringenti e <lb/>a speculare intorno a'loro ottici effetti, par che non sappia ripeter <lb/>altro di meglio delle dottrine ricevute per tradizione da'suoi mag&shy;<lb/>giori. </s>

<s>Il principale strumento del vedere, &egrave;, secondo lui, come per <lb/>Galeno e per il Vesalio, l'umor cristallino, il qual cristallino perci&ograve; <lb/><emph type="italics"/>idolum simulacrumque visionis non iniure appellatur<emph.end type="italics"/> (ibi, pag. </s>

<s>219). <lb/>Nonostante si dee al Nostro una curiosa esperienza in proposito, <lb/>che egli ivi accenna, ed &egrave; quella dell'avere estratto il cristallino <lb/>dall'occhio, e dell'aver trovato che i caratteri di uno scritto appa&shy;<lb/>riscono ingranditi a chi traguarda con esso, e questa dice esser <lb/>forse l'occasione che port&ograve; a far la prima scoperta degli occhiali. <lb/>&ldquo; Huius substantia durinscula est, quam sia sua sede dimoveris, et <lb/>ad scriptos caracteres accedat, maiores esse videntur et facilius <lb/>conspiciuntur, suspicorque hinc specillorum inventionem origi&shy;<lb/>nem duxisse &rdquo; (ibi). </s></p><p type="main">

<s>Fin qui il grande anatomico cremonese non ha fatto altro che <lb/>insistere sulle orme del Vesalio, il quale, nel descriver la fabbrica <lb/>del corpo umano si trattenne principalmente intorno alle parti este&shy;<lb/>riori composte delle ossa, dei muscoli e dei ligamenti. </s>

<s>La Splacno&shy;<lb/>logia, la parte pi&ugrave; importante e pi&ugrave; nuova, dal Brussellese fu ap&shy;<lb/>pena sfiorata. </s>

<s>Ma Realdo ha nell'Opera sua due libri insigni, il <lb/>VII che &egrave; <emph type="italics"/>De corde et arteriis,<emph.end type="italics"/> e l'XI che &egrave; <emph type="italics"/>De visceribus,<emph.end type="italics"/> e se&shy;<lb/>gnatamente <emph type="italics"/>De pulmone.<emph.end type="italics"/></s></p><p type="main">

<s>In generale dagli storici dell'anatomia non si d&agrave; altro merito <lb/>al Nostro, che di aver detto il mediastino del cuore non essere <lb/>perforato. &ldquo; Inter hos ventriculos septum adest, per quod fere omnes <lb/>existimant sanguini a dextro ventriculo ad sinistrum aditum pa&shy;<lb/>tefieri.... sed longa errant via, nam sanguis per arteriosam venam <lb/>ad pulmonem fertur, ibique attenuatur, deinde cum aere una per <lb/>arteriam venalem ad sinistrum cordis ventriculum defertur. </s>

<s>Quod <lb/>nemo hactenus aut animadvertit aut scriptum reliquit, licet maxime <lb/>sit ab omnibus animadvertendum &rdquo; (ibi, pag. </s>

<s>177). La piccola cir-<pb xlink:href="020/01/107.jpg" pagenum="88"/>colazione pulmonare si persuadono gli storici che fosse stata de&shy;<lb/>scritta gi&agrave; da Galeno, e che fosse il Cesalpino precursore non solo, <lb/>ma competitor coll'Harvey. </s>

<s>In quel capitolo dove da noi, dietro un <lb/>diligente esame dei documenti, si narra la storia della scoperta del <lb/>circolo sanguigno, troveranno dimostrato i lettori come le teorie <lb/>galeniche non consistessero in altro che in un giochetto di parole, <lb/>e vedranno come il Cesalpino sciogliesse quel giochetto, riducendo <lb/>al loro vero valore anatomico l'espressioni che ricorrono nell'autor <lb/>greco di <emph type="italics"/>vena arteriosa<emph.end type="italics"/> e di <emph type="italics"/>arteria venosa.<emph.end type="italics"/></s></p><p type="main">

<s>Ma quel giochetto era stato sciolto prima da Realdo Colombo, <lb/>il quale, dimostrando che tra il cuore e il polmone intercede un <lb/>circolo continuo di sangue, disse che i dutti erano una vera arteria <lb/>e una vera vena, nonostante che quella movesse dal ventricolo de&shy;<lb/>stro e questa dal ventricolo sinistro del cuore. </s></p><p type="main">

<s>Scrivono gli Anatomici, cos&igrave; con memorande parole si esprime <lb/>il Colombo, che ufficio proprio dell'arteria venosa sia quello di por&shy;<lb/>tar l'aria alterata nel cuore, ai polmoni, i quali, a guisa di flabelli <lb/>stanno l&igrave; ordinati a fargli vento e a rinfrescarlo dai soverchi ardori. </s>

<s><lb/>Quegli stessi poco prudenti, prosegue a dire, si persuadono che nel <lb/>cuore si generino fumi, quasi fosse un focolare sopra a cui siano <lb/>state gittate ad ardere legna verdi. &ldquo; Ego vero oppositum prorsus <lb/>sentio hanc scilicet arteriam venalem factam esse ut sanguinem <lb/>cum aere e pulmonibus mixtum adferant ad sinistrum cordis <lb/>ventriculum &rdquo; (ibi, pag. </s>

<s>178). </s></p><p type="main">

<s>Ecco la grande rivelazione fatta alla scienza, ecco una grande <lb/>scoperta: l'arteria venosa non ha nulla delle propriet&agrave; naturali delle <lb/>vene, ma &egrave; una vera arteria, perch&egrave;, anch'essa, come la grande <lb/>arteria riversa il sangue nel ventricolo sinistro del cuore. </s>

<s>E che ci&ograve; <lb/>sia vero, verissimo, che cio&egrave; per quel dutto arterioso, che dal pol&shy;<lb/>mone viene al cuore scorra sangue e non aria fuligginosa, com'era <lb/>fin allora generalmente creduto, il nostro Autore lo prova invocando <lb/>l'esperienza, non solo sui cadaveri, ma sopra gli stessi animali vivi, <lb/>nei quali <emph type="italics"/>hanc arteriam in omnibus sanguine refertam invenies, <lb/>quod nullo pacto eveniret si ob aerem dumtaxat, et vapores con&shy;<lb/>structa foret. </s>

<s>Quocirca ego illos anatomicos non possum satis mi&shy;<lb/>rari qui rem tam praeclaram, tantique momenti non animadverte&shy;<lb/>rint<emph.end type="italics"/> (ibi). </s></p><p type="main">

<s>E questo, si pu&ograve; dire, il primo elettissimo frutto dell'esperienza <lb/>applicata alla Fisiologia, la quale esperienza com'ha condotto Realdo <lb/>a scoprire il fatto della circolazion polmonare, cos&igrave; lo conduce alla <pb xlink:href="020/01/108.jpg" pagenum="89"/>scoperta di quell'altro importantissimo fatto a lui relativo, a quello <lb/>della respirazione. </s>

<s>I polmoni non son flabelli, come scioccamente <lb/>credevano gli antichi, ma loro ufficio proprio &egrave; quello di rimescolar <lb/>l'aria col sangue rendendolo pi&ugrave; tenue e pi&ugrave; spiritoso. </s>

<s>Questo san&shy;<lb/>gue &egrave; per l'arteria venosa ricondotto al cuore e di l&igrave;, per la grande <lb/>arteria, a tutto quanto il corpo (ivi, pag. </s>

<s>223). A questo punto per&ograve; <lb/>il nostro Autore sente come la novit&agrave; del fatto, che nessuno ancora <lb/>ha sognato, sar&agrave; per commuovere gli animi degl'increduli e pi&ugrave; <lb/>vivamente quello degli aristotelici, i quali s'aspetta che lo repute&shy;<lb/>ranno un paradosso. </s>

<s>Ma egli vuol che gli sia fatta ragione, non <lb/>dall'autorit&agrave; dei maestri, ma da quella della esperienza, per cui <lb/>cos&igrave; caldamente conclude rivolgendo tali eloquenti parole al suo <lb/>lettore: &ldquo; Tu vero, candide lector, doctorum hominum studiose, ve&shy;<lb/>ritatis autem studiosissime, experire, obsecro, in brutis animanti&shy;<lb/>bus, quae viva ut seces moneo atque hortor: experire inquam an <lb/>id quod dixi cum re ipsa consentiat, nam in illis arteriam venalem <lb/>illiusmodi sanguinis plenam invenies non aere plenam aut fumis, <lb/>ut vocant, capinosis &rdquo; (ibi, pag. </s>

<s>224). </s></p><p type="main">

<s>Che se mirabile &egrave; un tal sicuro uso dell'esperienza, in un <lb/>autore della prima met&agrave; del secolo XVI, non men mirabile &egrave; l'uso <lb/>ch'egli sa fare dell'induzione. </s>

<s>La verit&agrave; del circolo sanguigno egli <lb/>sagacemente la induce dall'artifizio e dai manifesti ufficii, a cui <lb/>sono ordinate le valvole del cuore, le quali son, per maggior sicu&shy;<lb/>rezza, fermate e mantenute in posto da certi filamenti, che, presi <lb/>da Aristotile per nervi, lo fecero andare in quella perniciosa sen&shy;<lb/>tenza che i nervi stessi avessero origine dal cuore e non dal cer&shy;<lb/>vello e dalla midolla spinale (ivi, pag. </s>

<s>179). Altro bell'esempio di <lb/>un argomento d'induzione ci si porge da quel ragionamento ch'ei <lb/>fa, per dimostrar che il sangue vitale, il sangue arterioso, non pu&ograve; <lb/>in altro organo generarsi che nel polmone. </s>

<s>Quel ragionamento, a <lb/>cui chiede poi cos&igrave; caldamente il conforto dell'esperienza, &egrave; rivolto <lb/>a persuadere gl'increduli aristotelici <emph type="italics"/>quos oro rogoque ut pulmo&shy;<lb/>nis magnitudinem contemplentur, quae absque vitali sanyuine per&shy;<lb/>manere non poterat, cum nulla sit tam minima corporis particula, <lb/>quae illo destituatur. </s>

<s>Quod si vitalis hic sanguis in pulmonibus <lb/>non gignitur, a qua parte trasmitti poterat, praeter quam ab ahorti <lb/>arteria? </s>

<s>et ab ahorti arteria ramus nullus neque magnus neque <lb/>parvulus ad pulmones mittitur<emph.end type="italics"/> &rdquo; (ibi, pag. </s>

<s>223). </s></p><p type="main">

<s>Tali erano gl'inizii, che Realdo Colombo, non finito mai d'am&shy;<lb/>mirare dai giusti estimatori, dava in Italia alla scienza sperimentale <pb xlink:href="020/01/109.jpg" pagenum="90"/>applicata alla fabbrica anatomica del corpo umano e alle funzioni <lb/>fisiologiche di lui. </s>

<s>Egli ebbe una illustre sequela ne'nomi di Bar&shy;<lb/>tolommeo Eustachio, di Gabriele Falloppio, di Girolamo Fabrizi <lb/>d'Acquapendente, a'quali ripensando la scienza italiana si sopra&shy;<lb/>esalta. </s>

<s>Or chi non crederebbe mai che succedendo cos&igrave; fatti uomini <lb/>al Cremonese, per non interrotta catena infino alla fine del se&shy;<lb/>colo XVI, non dovessero portare infino a'suoi pi&ugrave; alti fastigi l'ana&shy;<lb/>tomia sperimentale? </s>

<s>Chi non s'aspetterebbe che la luminosa dimo&shy;<lb/>strazione data da Realdo della piccola circolazione polmonare non <lb/>dovesse alle mani di tre tali insigni anatomici suoi successori com&shy;<lb/>piersi nella scoperta del circolo universale del sangue ne'suoi vasi? </s></p><p type="main">

<s>Eppure &egrave; un fatto, che desta gran maraviglia in chi vi ripensa, <lb/>&egrave; un fatto, dico, che cos&igrave; l'Eustachio come il Falloppio e l'Acqua&shy;<lb/>pendente non fecero altro pi&ugrave; che ripetere le viete dottrine di <lb/>Galeno e del Vesalio intorno alle funzioni fisiologiche del cuore e <lb/>del polmone. </s>

<s>Il libro <emph type="italics"/>De re anatomica<emph.end type="italics"/> fu per loro come se fosse <lb/>stato scritto al vento. </s>

<s>Solamente il Vidio e l'Aranzio, un po'pi&ugrave; <lb/>tardi dell'Eustachio e del Falloppio, si rivolsero a confermare a il&shy;<lb/>lustrare e a difendere il sistema cardiaco del grande Maestro cre&shy;<lb/>monese, ma non osando negare al fegato le funzioni di secernere <lb/>il sangue venoso alimentatore, n&egrave; sapendo a quale altro pi&ugrave; cospi&shy;<lb/>cuo ufficio potesse essere ordinato quel viscere dalla Natura, s'ar&shy;<lb/>restarono a quel punto dov'era, speculando e sperimentando, per&shy;<lb/>venuto il Colombo. </s>

<s>Il Cesalpino pose con nuovi argomenti in piena <lb/>evidenza la circolazion polmonare, e non badando troppo al fegato, <lb/>rivolse principalmente la sua attenzione sulle funzioni del cuore. </s>

<s><lb/>Ma il troppo servile ossequio di lui ai placiti aristotelici gl'imped&igrave; <lb/>di precorrere con libero piede alla gloriosa scoperta arveiana. </s></p><p type="main">

<s>Cos&igrave;, maestro in cattedra rimase unico Andrea Vesalio, da cui <lb/>s'impar&ograve; a coltivare l'Anatomia descrittiva, infaustamente lasciando <lb/>negletta quell'anatomia sperimentale instituita dal successore di lui, <lb/>a cui pi&ugrave; meritamente forse s'apparterrebbe il titolo di divino. </s>

<s><lb/>Seguendo per&ograve; i discepoli gli ammaestramenti dell'odiato e perse&shy;<lb/>guitato Brussellese, non ne imitarono gli esempi, quanto al modo <lb/>di porgerli o con la viva voce o con gli scritti. </s>

<s>Che se non ci s'in&shy;<lb/>travedesse sotto sotto uno splendor vivo di luce, apertamente poi <lb/>sfolgorata nelle dottrine darviniane de'nostri giorni, si chiamerebbe <lb/>un sottile artifizio di furberia quello, col quale il Falloppio intende <lb/>a conciliar, nelle anatomiche dissezioni fetali, Galeno e il Vesalio. </s>

<s><lb/>Ma n&egrave; furberia n&egrave; arte scaltrita si direbbe quella, colla quale <pb xlink:href="020/01/110.jpg" pagenum="91"/>l'Acquapendente &egrave; geloso di non offendere la reputazion di Galeno, <lb/>e di non mostrarsi apertamente mai ribelle alle dottrine aristote&shy;<lb/>liche. </s>

<s>Quella &egrave; religiosa fede non finta, sebbene il medico milio&shy;<lb/>nario, il latinista eloquente senta alitarsi in petto le aure della <lb/>nascente libert&agrave;, invocando talvolta, contro Aristotile stesso e contro <lb/>Galeno, la sua propria esperienza. </s></p><p type="main">

<s>Forse le splendide illustrazioni splacnologiche del Colombo si <lb/>neglessero dai successori di lui, e si neglessero insieme gl'iniziati <lb/>metodi sperimentali, per secondar ci&ograve; che altamente si reclamava <lb/>dai tempi; tempi in cui risvegliato l'uomo dai sonni contemplativi <lb/>di Platone e sollevatosi dai fanciulleschi trastulli aristotelici, si sen&shy;<lb/>tiva trasportato a impossessarsi del mondo, mettendo in esercizio <lb/>e invocando aiuti agli organi de'sensi, tra'quali &egrave; tenuto il primo <lb/>luogo dalla vista e dall'udito. </s>

<s>S'intende perci&ograve; come dovessero esser <lb/>questi i primi ad essere anatomicamente investigati. </s>

<s>E infatti l'Eu&shy;<lb/>stachio scopre e descrive quella tuba aerea, alla quale &egrave; rimasto <lb/>tuttavia il nome del discopritore, e che mette in comunicazione le <lb/>cavit&agrave; interne dell'orecchio con quelle della bocca. </s>

<s>Il Falloppio ci d&agrave; <lb/>quella mirabile descrizione di tutte le pi&ugrave; minute parti della rocca <lb/>petrosa, e l'Acquapendente scrive un Trattato intero sugli organi e <lb/>sulle funzioni della voce, della vista e dell'udito, che diletta col bello <lb/>stile ed erudisce colla dottrina. </s></p><p type="main">

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

<s>Cos&igrave; con Bartolommeo Eustachio, morto nel 1574, con Gabriele <lb/>Falloppio morto in giovane et&agrave; di 40 anni nel 1563, e con Giro&shy;<lb/>lamo Fabrizi che dal 1537 protrasse la lunga e onorata vecchiezza <lb/>infino al 1619, si varcava di alquanti passi la soglia che s'interpone <lb/>fra l'uscir del secolo XVI e l'entrar del seguente secolo alle scienze <lb/>sperimentali tanto altamente glorioso. </s>

<s>Pervenuti a questo punto giova <lb/>ritornare indietro e raccogliere in un pensiero le cose fin qui lun&shy;<lb/>gamente discorse. </s>

<s>La filosofia accademica, per s&egrave; contemplativa e <lb/>sterile di scoperte sperimentali, veniva fecondata dai cultori del&shy;<lb/>l'arte, i quali mostraron di fatto non esser vero che sempre i sensi <lb/>sono a noi occasione inevitabile d'inganni. </s>

<s>La filosofia peripatetica <lb/>anch'essa veniva emendata dal Razionalismo, uscito a dimostrar che <pb xlink:href="020/01/111.jpg" pagenum="92"/>il diritto riserbato al solo Aristotile era proprio del libero ingegno <lb/>di ogni uomo. </s>

<s>Dall'altra parte Realdo Colombo aveva dato i pi&ugrave; <lb/>savii esempii di quella filosofica libert&agrave;, e ne avea raccolti squisi&shy;<lb/>tissimi frutti. </s>

<s>Infin dalla seconda met&agrave; del secolo XVI, s'eran dun&shy;<lb/>que fatti nella via del metodo sperimentale notabili progressi, a <lb/>rendere i quali pi&ugrave; spediti mancavano ancora due cose: che dai <lb/>cultori dell'arte passassero gli esercizii sperimentali ne'libri dei <lb/>filosofi, e che il soggetto anatomico in che erasi ristretto il Colombo <lb/>si estendesse a ogni sorta di fatti naturali. </s>

<s>Ad adempire a un tale <lb/>ufficio furono deputati, nell'ordine della Storia, due napoletani, <lb/>Giovan Battista Porta e Ferrante Imperato, o come altri vuole Co&shy;<lb/>lantonio Stalliola, su'due quali conviene a noi ora intrattenere al&shy;<lb/>quanto il nostro Discorso. </s></p><p type="main">

<s>Il Porta, che mor&igrave; nel 1615, si trov&ograve; spettatore e parte alla <lb/>inaugurazione de'trionfi di Galileo, e vide sboccare i rivi della sua <lb/>scienza a rimescolarsi con le larghe onde sonanti di questo fiume <lb/>reale. </s>

<s>A molti que'rivi parvero scarsi, alcuni altri di pi&ugrave; gli repu&shy;<lb/>tarono impuri e limacciosi. </s>

<s>Martino Hasdale si sforza di convincere <lb/>con infinite tare il nostro Napoletano, dicendo ch'ei <emph type="italics"/>non intendeva <lb/>molti capitoli della Mag&igrave;a, n&egrave; manco la sapeva spiegare in vol&shy;<lb/>gare, iscusandosi che erano tutte cose avute da altri cos&igrave; scritte <lb/>in latino, come stavano stampate nel suo libro<emph.end type="italics"/> (Alb. </s>

<s>VIII, 84). Il <lb/>Sagredo giudica il libro della Mag&igrave;a Naturale <emph type="italics"/>goffissimo al possibile,<emph.end type="italics"/><lb/>e stima che l'Autore fra'dotti <emph type="italics"/>tenga il luogo che tengono le cam&shy;<lb/>pane tra gli strumenti di musica<emph.end type="italics"/> (Alb. </s>

<s>Suppl., pag. </s>

<s>67, 68). Que&shy;<lb/>sti giudizi erano pronunziati al cospetto di Galileo, che tacendo, <lb/>compiacente acconsentiva. </s>

<s>Il Kepler per&ograve; ne giudicava pi&ugrave; retta&shy;<lb/>mente, e con animo imparziale. </s>

<s>Ringraziava da un lato il Porta che <lb/>gli avesse insegnato il modo come si fa la vista, e dall'altro non <lb/>taceva che certe conclusioni ottiche di lui erano <emph type="italics"/>ex insufficienti et <lb/>non universali demonstratione profectae<emph.end type="italics"/> (Paralip. </s>

<s>ad Vitell., Fran&shy;<lb/>cof. </s>

<s>1604, pag. </s>

<s>180). </s></p><p type="main">

<s>Con questo giudizio del Kepler per&ograve; si concilia il giudizio dello <lb/>stesso Sagredo, uomo da non perdere il senno per compiacere al <lb/>suo Galileo. </s>

<s>Egli infatti veniva a dire che nel libro della Mag&igrave;a vi <lb/>erano delle gofferie, ma ci aveva pur trovata anco quella gran ve&shy;<lb/>rit&agrave; della teorica della visione. </s>

<s>Dall'altra parte l'esempio delle cam&shy;<lb/>pane, alle quali si fa dir quel che uno vuole, era benissimo applicato <lb/>a qualificar quegli enimmi, di cui il Porta tanto si compiace. </s>

<s>Il <lb/>sentenziar poi che il Napoletano seguiva lo stile dei filosofi piut-<pb xlink:href="020/01/112.jpg" pagenum="93"/>tosto che quello dei matematici (Alb. </s>

<s>Suppl., pag. </s>

<s>60) includeva un <lb/>giudizio acutissimo e vero. </s>

<s>Per filosofi infatti intendeva il Sagredo <lb/>i settatori di Aristotile, e per matematici, i seguaci del retto me&shy;<lb/>todo sperimentale. </s>

<s>Ora &egrave; verissimo che, per la massima parte, nel <lb/>libro del Porta la Natura scaturisce al modo aristotelico, per quasi <lb/>magica incantazione dalla fantasia dell'Autore. </s>

<s>Verissime altres&igrave; pos&shy;<lb/>sono essere le tare appostegli dall'Hasdale, e anche molte se si <lb/>vuole, non per&ograve;, com'egli dice, infinite. </s>

<s>Si ripensi poi che cos&igrave; fatte <lb/>tare erano inevitabili a chi si era proposto di allettare col maravi&shy;<lb/>glioso, e si era dato a raccoglier per ogni parte la scienza naturale <lb/>dispersa, in un libro solo. </s>

<s>Nella prefazione alla Mag&igrave;a Naturale in <lb/>XX libri, l'Autore dice chiaramente di avere a compor l'opera sua <lb/>sfiorate le carte di tutti, che ne avevano scritto prima di lui. &ldquo; Dein, <lb/>quum Italiani, Galliam et Hispaniam peragrassem, bibliothecas et <lb/>doctissimos quosque adii, artifices etiam conveni, ut si quid novi <lb/>curiosique nacti essent ediscerem. </s>

<s>&rdquo; Poco di poi soggiunge che <lb/>prima di consegnare al suo libro le raccolte notizie, <emph type="italics"/>intensissimo <lb/>studio pertinacique experientia<emph.end type="italics"/> erasi dato a sceverar le vere dalle <lb/>false, ma pur troppo sar&agrave; talora mancato al suo proposito come <lb/>disse l'Hasdale, e tal altra non vi sar&agrave; riuscito. </s></p><p type="main">

<s>L'Opera della Mag&igrave;a Naturale per&ograve;, che &egrave; quella sola su cui <lb/>par che l'Hasdale e il Sagredo e il Kepler giudicassero dei meriti <lb/>scientifici del Porta, non vuole esser passata da noi senza qualche <lb/>breve, ma pur diligente esame. </s>

<s>Comparve prima in quattro libri <lb/>pubblicata dall'Autore, quando aveva quindici anni, poi in libri XX <lb/>quando, come dice l'Autore stesso nella Prefazione, ne aveva cin&shy;<lb/>quanta. </s>

<s>Essendo egli nato nel 4535, come s'ha dal Catalogo de'Lin&shy;<lb/>cei, sotto la prima forma il libro dee esser dunque stato pubblicato <lb/>nel 1550; sotto la seconda, nel 1585. Nonostante, della Mag&igrave;a in <lb/>IV libri, dicono i Bibliografi, la prima edizione che si conosca esser <lb/>quella fatta da Mattia Cancer in Napoli, nel 1558, otto anni dunque <lb/>posteriore a quella, che veramente, secondo attesta lo stesso Autore, <lb/>&egrave; la prima. </s>

<s>Qui, di ci&ograve; che pi&ugrave; importa alla storia della Scienza, <lb/>non s'ha che l'ultimo libro, nel secondo capitolo del quale si legge <lb/>la descrizione della camera oscura, con l'applicazione di lei alla <lb/>teoria della vista. </s>

<s>Nel cap. </s>

<s>XVIII, dove insegna in che modo s'im&shy;<lb/>piombino i vetri per uso di specchi, &egrave; notabile quel che dice del <lb/>fondo dell'occhio rassomigliato nella forma e nell'ufficio a uno spec&shy;<lb/>chio concavo, in cui fa da amalgama il pimmento coroideo. </s></p><p type="main">

<s>La prima edizione della Mag&igrave;a Naturale in XX libri, se quel-<pb xlink:href="020/01/113.jpg" pagenum="94"/>l'anno della nascita &egrave; vero, e se &egrave; vero ci&ograve; che dice l'Autore, do&shy;<lb/>vendo esser del 1585, forse &egrave; quella in 16.&deg;, che nelle recensioni <lb/>bibliografiche ha la data &ldquo; Antuerpiae ex officina Christofori Plan&shy;<lb/>tini M.D.LXXXV. &rdquo; Procediamo cos&igrave; dubitativi, vedendo notate altre <lb/>tre edizioni anteriori all'LXXXV, una del LXIX, e le altre due <lb/>del LXXVI e dell'LXXXI: ch&egrave;, se, non &egrave; abbaglio preso da'biblio&shy;<lb/>grafi non sapremmo per verit&agrave; conciliare il fatto coi detti dell'Autore. </s></p><p type="main">

<s>In qualunque modo, abbiamo in questa nuova Mag&igrave;a moltipli&shy;<lb/>cate le curiosit&agrave;, e diciamolo francamente col Sagredo, le gofferie, <lb/>ma abbiamo anco insieme moltiplicati i contributi alla scienza. </s>

<s>Ch&egrave; <lb/>l&agrave; dove questi contributi si riducevano a un libro solo, qui si di&shy;<lb/>stendono in quattro: nel VII <emph type="italics"/>De miraculis magnetis<emph.end type="italics"/> nel XVII <emph type="italics"/>De <lb/>catoptricis imaginibus,<emph.end type="italics"/> nel XVIII <emph type="italics"/>De staticis experimentis,<emph.end type="italics"/> nel XIX <lb/><emph type="italics"/>De pneumaticis.<emph.end type="italics"/></s></p><p type="main">

<s>Nel VII son raccolte l'esperienze sul magnete fatte da Paolo <lb/>Sarpi, che l'Autore nella prefazioncella al libro, chiama splendor di <lb/>Venezia, anzi d'Italia. </s>

<s>Il magnetizzamento delle verghe di ferro per <lb/>confricazione e per influenza, con molti altri fatti nuovamente os&shy;<lb/>servati e diligentemente descritti, attestano che la scienza magne&shy;<lb/>tica ebbe in Italia gl'inizii quindici anni per lo meno prima che in <lb/>Inghilterra. </s>

<s>Nel XVII libro la camera oscura nella sua descrizione <lb/>vien perfezionata coll'aggiunta della lente cristallina biconvessa, che <lb/>si applica al foro per cui s'intromettono i raggi, e ci&ograve; conduce <lb/>l'Autore, a modificar la prima teorica della visione, sostituendo le <lb/>refringenze del cristallino alle riflessioni speculari della coroide <lb/>(Cap. </s>

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

<s>Il Capitolo VIII del XVIII libro &egrave; notabile per la descrizione <lb/>della bilancetta idrostatica a risolvere praticamente il <emph type="italics"/>Problema della <lb/>Corona,<emph.end type="italics"/> e a ritrovare il peso specifico de'varii corpi duri. </s>

<s>Anco <lb/>quando fosse vero quel che dice il Viviani, che cio&egrave; Galileo avesse in&shy;<lb/>ventato quello strumento nel 1586, tempo in cui incominci&ograve; ad atten&shy;<lb/>dere agli studii intorno alle opere di Archimede, il Porta lo avrebbe <lb/>preceduto di un anno per lo meno, e di 18 anni avrebbe preceduto <lb/>il Ghetaldo. </s>

<s>Comunque siasi, il Porta nel Cap. </s>

<s>VI di questo stesso <lb/>libro dette in que'galleggianti volgari, meglio che nella bilancetta, <lb/>i veri e legittimi progenitori di quegli idrostammi o densimetri o <lb/>pesa liquori inventati gi&agrave; e messi in uso in que'Medicei consessi, <lb/>che precedettero all'Accademia del Cimento. </s>

<s>La Pneumatica per&ograve; <lb/>del libro XIX non ha nulla, a voler dire il vero, che la renda no&shy;<lb/>tabile sopra quella dell'antico Herone. </s></p><pb xlink:href="020/01/114.jpg" pagenum="95"/><p type="main">

<s>N&egrave; si creda poi che negli altri libri della Mag&igrave;a tutto sia goffag&shy;<lb/>gine e stravaganze. </s>

<s>Quando, nella citata prefazioncella al VII libro, <lb/>l'Autore indovinava che due uomini si potessero parlar di lontano <lb/><emph type="italics"/>duobus nauticis pyxidibus alphabeto circumscriptis,<emph.end type="italics"/> parve certa&shy;<lb/>mente a Galileo che avesse detto una stravaganza, e nel I Dialogo <lb/>dei Massimi Sistemi (Alb. </s>

<s>I, 107) se ne ride e inventa su quel fatto <lb/>argutamente una burla. </s>

<s>Qual sarebbe rimasto se si fosse trovato a <lb/>veder nel telegrafo a galvanometro perfettamente avverata la tanto <lb/>stravagante profezia! </s></p><p type="main">

<s>Tutte le goffaggini poi e le stravaganze son dall'Autore assom&shy;<lb/>mate nell'ultimo libro, che meritamente &egrave; intitolato <emph type="italics"/>Chaos.<emph.end type="italics"/> Eppure <lb/>anche qui, come pietre preziose rotolate fra'ciottoli di un fiume, <lb/>s'ha nel Cap. </s>

<s>V la descrizione del corno acustico, strumento che <lb/>serve a inacutir l'udito, come a inacutir la vista servono, egli dice, <lb/>acconciamente disposte, due lenti. </s>

<s>Notabile quel ch'egli scrive es&shy;<lb/>sergli stata una tale invenzione suggerita dalle orecchie degli ani&shy;<lb/>mali, e particolarmente delle lepri, e pi&ugrave; notabile il principio ge&shy;<lb/>nerale che ivi professa del doversi perscrutar la natura, e imitar <lb/>con l'arte i macchinamenti di lei. </s></p><p type="main">

<s>Ci&ograve; che s'&egrave; fin qui discorso, pu&ograve; servire a giustificare il Porta <lb/>dalle imputazioni dell'Hasdale e del Sagredo, ma non si vuol tacere <lb/>come que'severi giudizi non furon dati che sul libro della Mag&igrave;a, <lb/>quasi non avesse l'Autore pubblicati altri documenti della sua scienza. </s>

<s><lb/>Eppure, quando l'Hasdale e il Sagredo scrissero i due sopra citati <lb/>giudizii in due lettere scritte a Galileo, aveva il Porta pubblicati, <lb/>fra gli altri, due libri, de'quali sarebbe colpa tacere nella storia <lb/>de'progressi fatti, in sul finir del secolo XVI dalla scienza speri&shy;<lb/>mentale italiana. </s>

<s>Di que'due libri il primo &egrave; <emph type="italics"/>De refractione optices<emph.end type="italics"/><lb/>pubblicato in Napoli nel 1593, il secondo &egrave; <emph type="italics"/>Pneumaticorum libri <lb/>tres<emph.end type="italics"/> che vide pure in Napoli la luce nel 1601. Il Sagredo non dee <lb/>aver veduto quel libro di Ottica, forse perch&egrave; difficile a trovarsi <lb/>venale. </s>

<s>Anche il Kepler infatti, che ardeva di gran desiderio di ve&shy;<lb/>der quel che vi avesse scritto l'Autore intorno alle rifrazioni della <lb/>luce attraverso le lenti, dice nei Paralipomeni a Vitellione &ldquo; a li&shy;<lb/>brariis frustra hactenus requisivi &rdquo; (edit. </s>

<s>cit. </s>

<s>pag. </s>

<s>202). Non dee il <lb/>Sagredo, lo ripetiamo, aver veduto quel libro, perch&egrave;, sagace e giu&shy;<lb/>dizioso qual'era, non par possibile ch'ei non si sentisse come noi <lb/>sorpreso di maraviglia e non restasse alla prima in dubbio se quello <lb/>l&igrave; era proprio l'Autore goffissimo della Mag&igrave;a. </s>

<s>Il Kepler senza dub&shy;<lb/>bio si sarebbe dalla lettura confermato in quel suo giudizio, che il <pb xlink:href="020/01/115.jpg" pagenum="96"/>fisico napoletano avesse mente davvero e cognizioni diottriche tali, <lb/>da specular l'invenzione del canocchiale. </s>

<s>Di ci&ograve; pure si persuade&shy;<lb/>ranno con facilit&agrave; i nostri lettori, dop'avere scorso anche brevemente <lb/>i IX libri delle Diottriche rifrazioni, ma prima di far ci&ograve; vediamo <lb/>in qual modo si studiasse di raccogliere le disperse membra della <lb/>scienza naturale Ferrante Imperato. </s></p><p type="main">

<s>Il libro di lui s'intitola giusto <emph type="italics"/>Historia naturale<emph.end type="italics"/> e si pubblic&ograve; <lb/>in Napoli la prima volta nel 1599. Antonio Nardi, discepolo di Ga&shy;<lb/>lileo, in quelle sue <emph type="italics"/>Scene Accademiche,<emph.end type="italics"/> delle quali, essendo rimaste <lb/>inedite, daremo in quest'altra parte del nostro Discorso, qualche <lb/>breve notizia ai nostri lettori, giudic&ograve; il Naturalista napoletano per <lb/>uno de'pi&ugrave; avveduti e giudiziosi scrittori di cose naturali che avesse <lb/>veduto mai (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XX, p. </s>

<s>592). I libri e le sentenze <lb/>dei tanti autori antichi e moderni da cui raccoglie, non le cita mai <lb/>senza darne, come dice lo stesso Nardi, <emph type="italics"/>una candida e valida cen&shy;<lb/>sura.<emph.end type="italics"/> Candida sempre, valida a seconda delle cognizioni che si po&shy;<lb/>tevano avere a que'tempi. </s>

<s>Non fa perci&ograve; maraviglia se l'Imperato <lb/>annoverando le bufoniti, gli entrochi, le pietre giudaiche, le frumen&shy;<lb/>tarie fra le sostanze minerali, ammettesse la vegetazion delle pietre; <lb/>errore largamente ricompensato da quel che poi nel rimanente del <lb/>XXV libro si specula delle pietre stesse, aprendo cos&igrave; tanto dalla <lb/>lontana le vie ai progressi della moderna cristallografia. </s></p><p type="main">

<s>Soggiunge il Nardi, nel passo sopra citato, d'aver sentito vivis&shy;<lb/>simo il desiderio che l'Autore v'avesse trattato non di sola una <lb/>parte, ma di tutta la <emph type="italics"/>fisica,<emph.end type="italics"/> alla qual parola egli d&agrave; senza dubbio <lb/>il significato di Scienza della Natura. </s>

<s>Ma accettando pure quella <lb/>parola <emph type="italics"/>fisica<emph.end type="italics"/> nel significato che suole avere oggid&igrave;, sentiamo anche <lb/>noi il desiderio che egli avesse pi&ugrave; largamente trattato di quei sog&shy;<lb/>getti di Meteorologia, di Ottica, di Magnetismo, intorno ai quali <lb/>scopre e annunzia alcune di quelle recondite verit&agrave; della fisica mo&shy;<lb/>derna, cacciando gli ostinati errori peripatetici col raziocinio e con <lb/>l'esperienza. </s>

<s>Di queste verit&agrave; scoperte e insegnate non si vuol la&shy;<lb/>sciar di dare ai lettori qualche notizia, e cos&igrave;, dopo avere accennato <lb/>alle due diverse maniere tenute in compilare la scienza ereditata <lb/>dai due scrittori napoletani, trapassare a veder ci&ograve; che seppero am&shy;<lb/>bedue speculare coi loro proprii intelletti. </s></p><p type="main">

<s>Tornando perci&ograve; al Porta, poniamoci innanzi agli occhi i due <lb/>libri sopra citati e incominciamo dallo scorrer per primo quello che <lb/>&egrave; forse di minore importanza, e che, per la rarit&agrave; dell'originale, <lb/>leggiamo nella versione italiana fatta da Ivan Escrivano e pubblicata <pb xlink:href="020/01/116.jpg" pagenum="97"/>col titolo di <emph type="italics"/>Tre libri di Spiritali<emph.end type="italics"/> in Napoli nel 1606. Le materie <lb/>ivi trattate, molto meglio che il titolo, dicono che il primo impulso <lb/>&egrave; venuto da Herone, ma l&agrave; dove il Fisico alessandrino trascura i <lb/>fondamenti della scienza e descrive le sue macchine, senza avvedersi <lb/>che a provar di metterle a gioco, non rispondono bene spesso alle <lb/>intenzioni; il Porta incomincia nel libro I dallo sperimentare sulla <lb/>elasticit&agrave; dell'aria, e dal confermare i principii dell'Idrostatica. </s>

<s>Gli <lb/>effetti dell'elaterio dell'aria compressa da uno stantuffo dentro a <lb/>una canna da archibuso, son descritti nel cap. </s>

<s>VI, ma nel X nota&shy;<lb/>bilissima &egrave; quella teoria delle pressioni de'liquidi, che per comune <lb/>sentimento degli eruditi s'attribuisce allo Stevino. </s>

<s>Vedremo che <lb/>parecchi anni prima aveva il Benedetti, nelle sue <emph type="italics"/>Speculazioni,<emph.end type="italics"/> di&shy;<lb/>mostrato gi&agrave; quel principio idrostatico, ma il Porta vi procede con <lb/>passo pi&ugrave; largo e pi&ugrave; sicuro, e che &egrave; pi&ugrave;, conferma le teorie col&shy;<lb/>l'esperienze. </s>

<s>Fra queste esperienze, a provar che le pressioni ope&shy;<lb/>rano secondo l'altezza del perpendicolo, &egrave; notabile quella del liquido <lb/>contenuto dentro una gran botte, che vien sollevato dal premer <lb/>d'altro liquido infuso in un sottil cannello comunicante, come pure <lb/>&egrave; notabile quell'altra esperienza degli zampilli, che si sollevano a <lb/>uguale altezza e raggiungon precisamente il livello del liquido nella <lb/>conserva: notabili diciamo queste esperienze del disprezzato fisico <lb/>napoletano, perch&egrave; ci fanno ripensare alla fama in che vennero poi, <lb/>per quelle stesse esperienze, il Mariotte e il Torricelli. </s></p><p type="main">

<s>Il secondo libro &egrave; applicato alla descrizione delle macchine da <lb/>sollevar l'acqua, gareggiandosi con Herone a chi sa immaginarne <lb/>delle pi&ugrave; nuovamente ingegnose. </s>

<s>Ma &egrave; qui per&ograve; debito confessare <lb/>che il Nostro cade, e forse pi&ugrave; spesso che mai, ne'difetti stessi <lb/>notati da lui nel fisico antico, proponendo macchinalmenti, che o <lb/>per l'elasticit&agrave; dell'aria o per la pressione dell'acqua, non in altro <lb/>giocano che nella esaltata fantasia dell'inventore. </s>

<s>Ne sia esempio <lb/>fra gli altri quel che nel cap. </s>

<s>I del terzo libro dice del potersi tra&shy;<lb/>vasare un lago in un altro lago o nel mare, per via di un sifone <lb/>che cavalchi l'altura di un monte: strana impresa che riuscita pa&shy;<lb/>recchi anni dopo, vuota di effetto alle mani del Baliani, gli dette <lb/>occasione a specular sulla pressione ammosferica e a indovinar la <lb/>prima teoria del barometro ad acqua. </s></p><p type="main">

<s>Questo terzo libro, che incomincia con una stranezza, termina <lb/>coll'invenzione di un utilissimo strumento, di cui da quasi tutti <lb/>s'ignora l'autore, ed &egrave; la livella ad acqna, nemmeno oggid&igrave; uscita <lb/>affatto fuor d'uso, e che il Porta fu il primo a sostituire all'antico <pb xlink:href="020/01/117.jpg" pagenum="98"/>corobate vitruviano. </s>

<s>De'capitoli di mezzo, notabile &egrave; il IV, dove si <lb/>descrive l'esperienza della diffusione del vino di un bicchiere at&shy;<lb/>traverso al piccolo foro di una palla di vetro ripiena d'acqua: espe&shy;<lb/>rienza, che nel I Dialogo delle Due Nuove scienze fu amorevolmente <lb/>raccolta da Galileo e tenuta per sua (Alb. </s>

<s>XIII, 74), come pure per <lb/>sua volle rivendicar quell'altra descritta qui dal Nostro, nel cap. </s>

<s>VII, <lb/>del materazzo o caraffella, dentro al collo della quale il calore am&shy;<lb/>biente fa scender l'acqua e il freddo la fa risalire, la quale espe&shy;<lb/>rienza il Porta stesso aveva gi&agrave; 47 anni prima descritta nel cap. </s>

<s>XXII <lb/>del secondo fra i quattro libri della Mag&igrave;a. </s></p><p type="main">

<s>Pi&ugrave; commemorabili di questi tre degli Spiritali, son per l'im&shy;<lb/>portanza e la difficolt&agrave; del soggetto, i nove libri delle <emph type="italics"/>Ottiche rifra&shy;<lb/>zioni.<emph.end type="italics"/> La scienza, infino a qui, non aveva fatto grandi progressi: <lb/>si ripetevano le dottrine antiche di Tolomeo e di Euclide, non molto <lb/>per verit&agrave; promosse da Alhazen e da Vitellione. </s>

<s>Gli scritti dell'Al&shy;<lb/>berti, del Vinci, del Maurolico a'tempi del Porta, erano sconosciuti, <lb/>cosicch&egrave;, questo Trattato del Fisico napoletano &egrave; il primo da cui la <lb/>Diottrica incomincia i suoi progressi. </s></p><p type="main">

<s>A cos&igrave; fatti progressi il primo valido impulso vien dalla pro&shy;<lb/>posizione VIII del libro I, dove l'Autore dimostra esser falso quel <lb/>che insegn&ograve; Vitellione, che cio&egrave; gli angoli dell'incidenza e della <lb/>rifrazione serbino costante proporzione geometrica, variandosi l'obli&shy;<lb/>quit&agrave; con cui cade il raggio luminoso. </s>

<s>A confermar la sua dimo&shy;<lb/>strazione, contro l'autorevole e inveterato magistero dell'Ottico po&shy;<lb/>lacco, invoca lo sperimento da farsi con un vaso ripieno d'acqua. </s></p><p type="main">

<s>Contro un altro magistero non meno autorevole per que'tempi, <lb/>ed &egrave; quello del Fracastoro settatore di pi&ugrave; antiche dottrine, &egrave; pure <lb/>la proposizione XI di questo stesso libro I, nella quale si dimostra <lb/>che la refringenza alle superficie piane non ingrandisce le immagini, <lb/>ma s&igrave; le ingrandisce alle superficie curve, conforme a ci&ograve; che pure <lb/>accennava il giovane Galileo (Ediz. </s>

<s>naz., Firenze, 1890, Vol. </s>

<s>I, <lb/>pag. </s>

<s>314). E mentre che lo stesso Galileo meditava arguzie, da tor <lb/>fede a Ticone, che fu il primo, osservando gli astri, a tener conto <lb/>degli effetti prodotti sulla vista dalle rifrazioni, &egrave; notabile quel che <lb/>nelle proposizioni XVII e XIX avverte il Porta delle fallacie che, <lb/>per via de'raggi refratti nell'aria, si commettono osservando oggetti <lb/>che radono l'orizzonte o livellando collo strumento, per lunghi tratti. </s></p><p type="main">

<s>Il secondo libro, che &egrave; delle immagini e dell'andamento dei <lb/>raggi rifratti nelle sfere cristalline, ha strettissima relazione col li&shy;<lb/>bro VIII, dove si espongono le teorie diottriche delle lenti. </s>

<s>&Egrave; questa <pb xlink:href="020/01/118.jpg" pagenum="99"/>parte del Trattato che principalmente eccitava, di vederlo, i desiderii <lb/>al Keplero, e non sappiamo se ne fosse stato poi sodisfatto, quando <lb/>nel 1611 pubblic&ograve; il Trattato suo della Diottrica. </s>

<s>Facendo per&ograve; il <lb/>confronto fra'due autori, non temiam di asserire che il secondo nel <lb/>tempo riman secondo altres&igrave; nel merito, perch&egrave; il Porta introduce, <lb/>nel divisar le immagini reali e virtuali rappresentate dalle lenti, i <lb/><emph type="italics"/>cateti,<emph.end type="italics"/> ossia gli <emph type="italics"/>assi principali e secondari,<emph.end type="italics"/> senza che, nel Kepler <lb/>e negli altri autori di que'tempi, le immagini stesse rimangono in&shy;<lb/>determinate di grandezza e di luogo. </s>

<s>Di pi&ugrave;, l'Ottico alemanno nella <lb/>proposizione sua XCVI fa convergere i raggi che escon refratti dalle <lb/>lenti concave verso l'occhio, quasi che il loro foco fosse reale e non <lb/>virtuale: errore gravissimo cansato assai destramente dal nostro Na&shy;<lb/>poletano. </s></p><p type="main">

<s>L'anatomia dell'occhio professata nel III libro &egrave; conforme alla <lb/>descrizione che ne dette il Vesalio, n&egrave; fa maraviglia che sia ripe&shy;<lb/>tuto qui l'errore, sull'autorit&agrave; di Galeno oramai divenuto comune, <lb/>del far organo della rappresentazion visiva il cristallino: senza ma&shy;<lb/>raviglia per&ograve; non si pu&ograve; passar da chi legge la proposizione VI, al <lb/>vedervisi pubblicata quella osservazione del dilatamento e del re&shy;<lb/>stringimento della pupilla annunziata sette anni dopo dall'Acqua&shy;<lb/>pendente come una osservazione nuova del Sarpi o sua. </s>

<s>Galileo <lb/>ripete quasi a parole nel III Dialogo de'Massimi Sistemi (Alb. </s>

<s>I, <lb/>394) ci&ograve; che qui avea scritto il disprezzato fisico napoletano, e nelle <lb/><emph type="italics"/>Operazioni astronomiche<emph.end type="italics"/> procede Galileo stesso in un modo simile <lb/>al Porta, per determinar l'ampiezza del foro pupillare, con una tal <lb/>sola differenza, che mentre questi attribuisce il metodo ad Archi&shy;<lb/>mede, quello, e nelle citate <emph type="italics"/>Operazioni<emph.end type="italics"/> e nelle lettere al Renieri <lb/>lo d&agrave; per invenzione sua propria. </s></p><p type="main">

<s>Se il fortunato discopritore de'satelliti di Giove si fosse mai <lb/>degnato di rivolger lo sguardo sul sesto libro di questa Diottrica, <lb/>non &egrave; qui luogo a ricercare. </s>

<s>Non si vuol tacere per&ograve;, per la novit&agrave; <lb/>e l'importanza del tema, che, secondo il Borelli, i metodi usati da <lb/>Galileo per ritrovar collo strumento la media distanza de'Gioviali <lb/>dal centro del pianeta, avrebbero avuto il loro principio dai curiosi <lb/>fenomeni, che, per l'artificiosa e forzata direzione degli assi ottici <lb/>de'due occhi, si producono nel guardare gli oggetti; fenomeni mi&shy;<lb/>rabilmente osservati e descritti dal Nostro nelle varie proposizioni <lb/>di quello stesso sesto libro. </s></p><p type="main">

<s>Nel trattare all'ultimo dell'iride e de'colori il Porta non pro&shy;<lb/>muove nemmen di un passo la scienza e si rimane anzi indietro al <pb xlink:href="020/01/119.jpg" pagenum="100"/>Maurolico per lungo tratto di via. </s>

<s>Ma Ferrante Imperato, all'<emph type="italics"/>Historia <lb/>naturale<emph.end type="italics"/> del quale ora si torna, largamente ristora il difetto del <lb/>suo concittadino, divisando dell'iride interna e della esterna la vera <lb/>teoria ottica 38 anni prima che a menarne vanto uscisse fuori il <lb/>Cartesio. </s></p><p type="main">

<s>Ma perch&egrave; il rispondere ai vanti con altrettanti vanti esaltati <lb/>&egrave; triste vezzo, che ha tolto fede oramai alle osservazioni de'pi&ugrave; <lb/>giudiziosi, vadasi all'XI libro di questa Storia, e si leggano atten&shy;<lb/>tamente i capitoli VIII e IX, osservando che l'Autore, quanto alla <lb/>vista, professa l'opinion platonica della emissione. </s>

<s>Conforme a queste <lb/>professate dottrine egli dice perci&ograve;: <emph type="italics"/>li raggi visivi infratti dagli <lb/>corpuscoli delle gocce andar dalla vista al lummare<emph.end type="italics"/> (Venetia 1672, <lb/>pag. </s>

<s>288). Come poi nelle gocciole si facciano queste infrazioni e <lb/>dalle infrazioni congiunte a riflessioni si produca l'iride colorata, <lb/>a quel modo che si vede <emph type="italics"/>negli globi et ampolle chiarissime di vetro <lb/>e nelle colonne (prismi) triangolari<emph.end type="italics"/> (ivi, pag. </s>

<s>294); lo aveva detto <lb/>con mirabile esattezza pi&ugrave; sopra, ove scrisse: &ldquo; Occorrendo la vista <lb/>alla sua superficie convessa, fa semplice riflessione e penetrando, <lb/>il che si fa con infrazione, alla cava, ivi riflessa, ritorna ad uscir <lb/>con la seconda infrazione. </s>

<s>Sono dunque due infrazioni, l'una men&shy;<lb/>tre dal pi&ugrave; raro entra nel denso, l'altra, nella quale dal pi&ugrave; denso <lb/>ritorna nel pi&ugrave; raro, quali ambe infrazioni sono nella superficie <lb/>prima che occorra, et vi &egrave; la riflessione tramezzo fatta nella super&shy;<lb/>ficie pi&ugrave; lontana &rdquo; (ivi, pag. </s>

<s>288). </s></p><p type="main">

<s>Quanto all'iride esterna che egli rimprovera ad Aristotile, <lb/>l'aver promesso, ma non mantenuto di trattarne, o trattandone di <lb/>aver ridotto il fenomeno a cause vane; ecco quel che egli dice nel <lb/>cap. </s>

<s>IX: &ldquo; Essendo della goccia due semisferi, l'uno dalla parte <lb/>dell'asse (del cono che ha l'iride per base) l'altro dalla parte op&shy;<lb/>posta, e potendo il raggio visivo nell'uno e nell'altro incorrere a <lb/>riflettersi al luminare: nel primo penetrando nell'interno ed uscendo <lb/>per l'esterno, e nel secondo penetrando per l'esterno ed uscendo <lb/>per l'interno, nel qual secondo modo il raggio che esce e va al <lb/>sole per la molta infrazione si taglia col raggio della vista che entra; <lb/>&egrave; necessario per questo che due siano gli archi celesti e che ab&shy;<lb/>biano li colori a contrario &rdquo; (ivi, pag. </s>

<s>290). Conclude notando il <lb/>licenzioso accoppiamento che Aristotile, a spiegare il fenomeno, fa <lb/>di due cause contrarie, e accennando ad altre dottrine del Filosofo <lb/>meritevoli di maggior riprensione. </s></p><p type="main">

<s>Se qui l'Imperato emenda gli errori ripetuti dal Porta nell'ul-<pb xlink:href="020/01/120.jpg" pagenum="101"/>timo libro della Diottrica, altrove intorno all'argomento del Magnete <lb/>ne compie le teorie divisate nel VII libro della <emph type="italics"/>Magia.<emph.end type="italics"/> Anche il <lb/>nostro autor dell'<emph type="italics"/>Historia naturale<emph.end type="italics"/> parlando nel libro XXVI della <lb/>pietra calamita ne avverte il magnetismo per influenza e lo illustra <lb/>con luminoso concetto, rassomigliando le linee radiose, in che si <lb/>dispongono le particelle della limatura del ferro intorno ai poli ma&shy;<lb/>gnetici, alla dirittura delle linee, in che intorno al centro della <lb/>Terra, insistendo l'uno sull'altro, si dispongono i corpi gravi (ivi, <lb/>pag. </s>

<s>614). Or che altro mancava se non che formular questo stesso <lb/>concetto a modo del Gilberto perch&egrave; riuscisse a dire che la Terra <lb/>&egrave; un magnete, e che il Magnete stesso &egrave; una terrella? </s></p><p type="main">

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

<s>La filosofica libert&agrave;, con la quale esamina e scopre gli errori <lb/>di Aristotile Ferrante Imperato, in quasi tutte le parti dell'opera <lb/>sua voluminosa, e specialmente dove tocca soggetti di Meteorologia, <lb/>fra'quali &egrave; notabilissimo quel che nel cap. </s>

<s>III del X libro dice del <lb/>tuono e del baleno contro il Filosofo; basterebbe a meritargli uno <lb/>dei primi seggi fra coloro che pi&ugrave; efficacemente cooperarono a re&shy;<lb/>staurare le scienze sperimentali. </s>

<s>I due libri pure del Porta da noi <lb/>sopra brevemente discorsi, son dettati col medesimo intento di sco&shy;<lb/>prir gli errori de'peripatetici non solo, ma di ogni sorta di autori <lb/>le dottrine de'quali non si conformino alla rettitudine de'raziocinii <lb/>e alla prova degli sperimenti. </s>

<s>Ma il primo de'due fisici napoletani <lb/>rimase dimenticato per ragioni che troppo lungo sarebbe l'inve&shy;<lb/>stigare, e il secondo, competitore di Galileo, rimase oscurato dai <lb/>trionfi di lui. </s>

<s>Non ebbero perci&ograve; le molte e importanti verit&agrave; sco&shy;<lb/>perte e dimostrate da'due autori quell'incontro che si sarebbero <lb/>meritato, n&egrave; recarono quegli aiuti a'progressi della scienza, che <lb/>avrebbero veramente potuto. </s></p><p type="main">

<s>Pi&ugrave; diffusa e pi&ugrave; intensa, e perci&ograve; pi&ugrave; giovevole riusc&igrave; l'opera <lb/>di tre grandi uomini nati sulle rive di quel mare, su cui regn&ograve; <lb/>libera Venezia. </s>

<s>Giovan Batista Benedetti, Santorre Santorio e Paolo <lb/>Sarpi, hanno, dopo tanto lungo tempo e tante prove tentate dai loro <lb/>predecessori, aperta alla scienza la retta via, e v'hanno impresse <lb/>oramai orme cos&igrave; profonde, che non &egrave; possibile pi&ugrave; lo smarrirle. <pb xlink:href="020/01/121.jpg" pagenum="102"/>Rimasti tutti e tre nascosti nelle fondamenta dell'edifizio galileiano, <lb/>non pu&ograve; farsi la giusta stima della loro grandezza, se non da chi <lb/>penetri addentro colla vista attenta ed acuta. </s>

<s>E a chi riguardi il <lb/>Benedetti in questo modo, se lo vede presentare innanzi in sereno <lb/>e dignitoso abito di libero filosofo, che vuol contemperare l'osse&shy;<lb/>quio all'autorit&agrave; delle tradizioni, con l'ossequio alle verit&agrave; scoperte <lb/>dalla ragione. &ldquo; Liberum enim est cuique scribere quod libet, nec <lb/>Aristotilem afficit iniuria, quicumque illi fidem suam non acco&shy;<lb/>modat, etsi valde iniquus sit quisquis maiorum opiniones veras <lb/>et ab omnibus merito comprobatas non admittit &rdquo; (Speculationum <lb/>lib. </s>

<s>Venetiis 1599, pag. </s>

<s>228). </s></p><p type="main">

<s>Nella Prefazioncella alle Disputazioni <emph type="italics"/>De quibusdam placitis <lb/>Aristotelis,<emph.end type="italics"/> dove d&agrave; il Benedetti il pi&ugrave; bell'esempio di quella filo&shy;<lb/>sofica libert&agrave; vendicatrice dei diritti della ragione, dop'avere accen&shy;<lb/>nato ai pericoli corsi da colui, che scrive cose contrarie all'am&shy;<lb/>mirabile sapienza dell'antico Maestro &ldquo; Verumtamen, egli tosto <lb/>francamente soggiunge, studio veritatis impulsus, cuius ipse amore <lb/>in seipsum si viveret excitaretur, in medium quaedam proferre <lb/>non dubitavi, in quibus me inconcussa mathematicae philosophiae <lb/>basis, cui semper insisto, ab eo dissentire coegit &rdquo; (ibi, pag. </s>

<s>168). </s></p><p type="main">

<s>Da Parma, dove insegnava, fu chiamato a Torino, dal Duca, il <lb/>quale, secondo il costume de'principi di allora, si compiaceva, spe&shy;<lb/>cialmente in tempo di villeggiatura, d'interrogare il suo Filosofo <lb/>e Matematico e di proporgli a risolvere questioni d'Aritmetica, di <lb/>Geometria, di Ottica, di Musica e anco di Astrologia. </s>

<s>Gli amici pure <lb/>lo interrogavano, e ad essi mandava i suoi <emph type="italics"/>Responsi,<emph.end type="italics"/> i quali, come <lb/>prima, egli dice &ldquo; per ocium licuit, collegi, relegi, ac tandem de <lb/>manu mittere decrevi. </s>

<s>Tum, ut scientia ipsa quo magis diffun&shy;<lb/>deretur, crescat, et quidquid valeo sine invidia, in communem <lb/>utilitatem conferam &rdquo; (ibi, pag. </s>

<s>204). </s></p><p type="main">

<s>Cos&igrave; fatti Responsi, sotto forma epistolare, son gran parte del <lb/>libro <emph type="italics"/>Speculationum<emph.end type="italics"/> stampato prima nel 1580 in Torino, e poi nuo&shy;<lb/>vamente nel 1599 in Venezia: speculazioni, che l'Autore presenta <lb/>al suo lettore per nuove, se non sempre nella sostanza, certo nel <lb/>modo di dimostrarle. </s>

<s>Ed &egrave; verissimo: &egrave; anzi per entro a quelle <lb/>pagine tanta novit&agrave;, che, scomparso affatto il vecchio mondo ari&shy;<lb/>stotelico, ti senti trasportar nell'ampie e libere regioni di un Mondo <lb/>nuovo. </s></p><p type="main">

<s>Nelle sopra citate Disputazioni contro Aristotile, quelle parole, <lb/>nelle quali chiama il nuovo Sistema del Mondo &ldquo; pulcherrimam <pb xlink:href="020/01/122.jpg" pagenum="103"/>Aristarchi Samii opinionem, divinitus a Nicolao Copernico ex&shy;<lb/>pressam, contra quam nil plane valent rationes ab Aristotile, <lb/>neque etiam a Ptolomeo propositae &rdquo; (ibi, pag. </s>

<s>195) dicono ab&shy;<lb/>bastanza chiaro quanto fosse il Benedetti inclinato a cooperare ai <lb/>progressi dell'Astronomia, ma perch&egrave; ei non fu in tempo a veder <lb/>l'invenzione del canocchiale, fu nella Meccanica e nella Fisica, dove <lb/>principalmente esercit&ograve; le sue nuove speculazioni. </s></p><p type="main">

<s>La scienza del moto, resa impossibile dagli errori di Aristotile, <lb/>era si pu&ograve; dir rimasta stazionaria ne'libri dell'antico Archimede. </s>

<s><lb/>Il nostro Benedetti fu de'pi&ugrave; validi in promuoverla, confutando con <lb/>argomenti di ragione quegli aristotelici errori, in parecchi de'quali <lb/>era incorso lo stesso Niccol&ograve; Tartaglia s&igrave; rispetto ai moti naturali <lb/>che ai violenti. </s>

<s>Cos&igrave; l'antico Filosofo di Stagira come il nuovo di <lb/>Brescia avevano insegnato che ne'gravi cadenti le velocit&agrave; son pro&shy;<lb/>porzionali alle moli, ma il nostro Veneziano gli avverte in proposito <lb/>com'e'non avevan posto mente &ldquo; quam magna resistentiarum sit <lb/>differentia, quae tam diversitate figurarum quam ex magnetudi&shy;<lb/>num varietate exoriri potest &rdquo; (ibi, pag. </s>

<s>168) e svolgendo queste <lb/>sottili speculazioni relative alle varie resistenze opposte ai mobili, <lb/>dalle varie densit&agrave; dei mezzi, conclude: &ldquo; quod in vacuo corpora <lb/>eiusdem materiae aequali velocitate moverentur &rdquo; (pag. </s>

<s>174). </s></p><p type="main">

<s>Il medesimo Aristotile aveva detto, nel cap. </s>

<s>VIII del I libro <emph type="italics"/>De <lb/>coelo,<emph.end type="italics"/> che il mobile tanto pi&ugrave; si accelera quanto pi&ugrave; si avvicina al <lb/>termine <emph type="italics"/>ad quem,<emph.end type="italics"/> ma il Benedetti avverte che avrebbe dovuto il <lb/>Filosofo dire invece che anzi il mobile si accelera tanto pi&ugrave;, quanto <lb/>pi&ugrave; si dilunga dal termine <emph type="italics"/>a quo,<emph.end type="italics"/> &ldquo; quia tanto maior fit semper <lb/>impressio quanto magis movetur naturaliter corpus, et continuo <lb/>novum impetum recipit, cum in se motus causam contineat, quae <lb/>est inclinatio ad locum suum eundi &rdquo; (ibi, pag. </s>

<s>184). </s></p><p type="main">

<s>Il Nostro insomma, un quarto di secolo prima che a queste <lb/>stesse speculazioni rivolgesse la mente Galileo, aveva pubblicamente <lb/>insegnato che ne'moti accelerati le velocit&agrave; son proporziali ai tempi, <lb/>concludendo come Galileo questo teorema fondamentale da quel <lb/>principio d'inerzia, stabilito gi&agrave; dal Cardano, e confermato colle <lb/>bellissime esperienze dello Scaligero. </s></p><p type="main">

<s>Tanto &egrave; vero che il Benedetti accoglie quel principio come cosa <lb/>gi&agrave; certa nella scienza, e dimostrata, da non vedere il bisogno di <lb/>assumersi altro ufficio, che di rimuoverne le difficolt&agrave;, come giusto <lb/>si vede far da lui nel Trattato <emph type="italics"/>De Mechanicis<emph.end type="italics"/> e nell'Epistola a Paolo <lb/>Capra <emph type="italics"/>De motu molae et trochi.<emph.end type="italics"/> Si propone ivi il quesito come mai <pb xlink:href="020/01/123.jpg" pagenum="104"/>una mola mossa non perpetua il suo moto, come dovrebbe per il <lb/>principio d'inerzia, e risponde che ci&ograve; avviene per pi&ugrave; ragioni: per <lb/>l'attrito de'perni, per la resistenza, dell'aria e per gli effetti della <lb/>forza centrifuga (ivi, pag. </s>

<s>159). E qui l'Autore, che fu primo di <lb/>tutti i meccanici a specular su questo genere di forza, stabilisce <lb/>quella legge verissima delle forze centrifughe, bench&egrave; poi stimata <lb/>falsissima da Galileo (Alb. </s>

<s>I, 233) che cio&egrave; <emph type="italics"/>quanto maior est aliqua <lb/>rota tanto maiorem quoque impetum et impressionem motus eius <lb/>circumferentiae partes necipiant<emph.end type="italics"/> (Speculat. </s>

<s>lib. </s>

<s>pag. </s>

<s>159). Ma nella <lb/>sopra citata Lettera al Capra, le speculazioni in tal proposito son <lb/>anco pi&ugrave; sottili, e, dal risolversi in orizzontale, per la vertigine, <lb/>l'impeto naturalmente diretto per la verticale, scioglie alcuni curiosi <lb/>problemi relativi allo star ritte sul punzone le trottole giranti, e al <lb/>leggerissimo gravitar sul sostegno un corpo, che vi si muova sopra <lb/>veloce (ivi, pag. </s>

<s>286). </s></p><p type="main">

<s>Rispetto ai moti violenti, il Benedetti conferma le verit&agrave; di&shy;<lb/>mostrate gi&agrave; dal Cardano contro Aristotile, ma perch&egrave; il Tartaglia <lb/>aveva al Cardano stesso negato poter muoversi un grave nel mede&shy;<lb/>simo tempo con moto naturale e con moto violento, il Nostro sottil&shy;<lb/>mente dimostra come veramente ogni punto della traiettoria risulti <lb/>dalla composizione di quei due moti (ivi, pag. </s>

<s>365) per cui ebbe <lb/>a concludere altrove, contro ambedue, il Cardano cio&egrave; e il Tarta&shy;<lb/>glia, come per nessun suo tratto quella stessa traiettoria &egrave; retta, e <lb/>com'ella, appena uscito il proietto dal proiciente, <emph type="italics"/>cito fiat curva<emph.end type="italics"/><lb/>(ivi, pag. </s>

<s>161). </s></p><p type="main">

<s>E pur contro lo stesso Tartaglia &egrave; quella Epistola del Benedetti <lb/>che s'intitola <emph type="italics"/>De ictu bombardae,<emph.end type="italics"/> nella quale si propone a scio&shy;<lb/>gliere il quesito come mai la palla faccia pi&ugrave; gran percossa, quando <lb/>il cannone &egrave; elevato, che quando &egrave; livellato coll'orizzonte. </s>

<s>Giudica <lb/>le ragioni del Matematico bresciano <emph type="italics"/>nullius momenti<emph.end type="italics"/> (pag. </s>

<s>258) e <lb/>veramente son tali, ma n&egrave; quelle del Nostro colgono pure, questa <lb/>volta nel segno, come non colgon nel segno quelle che Galileo (Ediz. </s>

<s><lb/>naz. </s>

<s>cit. </s>

<s>Vol. </s>

<s>I, pag. </s>

<s>337-40) fedelmente ripete dal matematico ve&shy;<lb/>neziano. </s></p><p type="main">

<s>Se a queste che concernono i moti naturali e i violenti s'ag&shy;<lb/>giungano le speculazioni del Benedetti intorno alla leva angolare e <lb/>intorno al cuneo, s'argomenter&agrave; quanto gran maestro egli fosse <lb/>nella scienza del moto. </s>

<s>E perch&egrave; Galileo nelle Meccaniche s'apre <lb/>la via a trattar del piano inclinato e della vite, rimovendo l'antico <lb/>errore di Pappo, &egrave; giusto si aggiunge qui da noi come il Benedetti <pb xlink:href="020/01/124.jpg" pagenum="105"/>stesso aveva, nel Trattatello suo <emph type="italics"/>De mechanicis,<emph.end type="italics"/> rimosso gi&agrave; quel&shy;<lb/>l'errore del Matematico alessandrino, dimostrando che una sfera <lb/>grave posata su un piano orizzontale pu&ograve; rimuoversi dalla sua <lb/>quiete <emph type="italics"/>absque ulla difficultate<emph.end type="italics"/> (ivi, pag. </s>

<s>155). </s></p><p type="main">

<s>Si dice che dopo Archimede uno de'primi e principali pro&shy;<lb/>motori dell'Idrostatica fosse, in sull'entrar del secolo XVII, Simeone <lb/>Stevino, e s'attribuisce a lui il paradosso che, indipendentemente <lb/>dalla sua mole, il liquido preme secondo l'altezza sua verticale, il <lb/>fondo del vaso. </s>

<s>Ma il nostro Benedetti aveva gi&agrave; da vent'anni di&shy;<lb/>mostrato questo stesso paradosso idrostatico, applicandolo, come i <lb/>fisici moderni fanno, a spiegar l'equilibrio de'liquidi in due vasi <lb/>di varia capacit&agrave;, comunicanti. </s>

<s>Chi vuol persuadersene legga l'Epi&shy;<lb/>stola o Responso a Giovan Paolo Capra <emph type="italics"/>De machina quae aquam <lb/>impellit et sublevat<emph.end type="italics"/> a pag. </s>

<s>287-88 della citata edizione. </s></p><p type="main">

<s>Fosse stato cos&igrave; felice il Matematico del Duca di Savoia in in&shy;<lb/>vestigar le leggi delle acque correnti! Tutt'all'opposto egli incorre <lb/>in tali errori, che non si crederebbero da chi ammira la sagacia di <lb/>quell'ingegno, se al citato Responso non si vedesse, nel Libro Delle <lb/>Speculazioni, seguitar l'altro col titolo <emph type="italics"/>Nova solutio problematis de <lb/>vase pleno liquoris<emph.end type="italics"/> (pag. </s>

<s>289) a risolvere il quale ammette, come <lb/>principio notissimo e vero, che le quantit&agrave; di liquido, fluito da un <lb/>vaso di qualunque figura, sieno sempre proporzionali ai tempi. </s>

<s>In <lb/>ci&ograve; egli &egrave; tanto inferiore al Cardano, quanto in Fisica &egrave; superiore <lb/>a tutti. </s></p><p type="main">

<s>E per incominciar di l&agrave;, dove primo s'introdusse a speculare <lb/>il Cardano, si not&ograve; com'egli volesse banditi dalla scienza que'nomi <lb/>vani di fuga e di orrore del vacuo, e come, a spiegare il fatto del <lb/>vaso, dentro cui, succhiata l'aria, entra l'acqua, dicesse che questa <lb/>era attratta da quella. </s>

<s>Lo Scaligero non seppe veder dove mai rise&shy;<lb/>desse questa forza di attrazione, ma, facile a negare, null'altro in <lb/>sostanza, a supplire al difetto e a mostrare il vero, asserisce. </s>

<s>Il Tar&shy;<lb/>taglia, attendendo a quell'altro modo del rarefarsi l'aria per opera <lb/>del calore, e al fatto che pur cos&igrave; il vaso attrae l'acqua, avea pro&shy;<lb/>clamato il principio che sia propriet&agrave; del calore l'attrarre. </s>

<s>Ma il <lb/>Benedetti se ne ride, e dice esser propriet&agrave; del calore non l'attrarre <lb/>ma il dilatare. </s>

<s>Cosa poi notabile &egrave; che, estendendo questo poter di&shy;<lb/>latante a tutti i corpi, soggiunge come per via del dilatarsi e del <lb/>restringersi, al crescere e al diminuir del calore, i vasi si rompono <lb/>nelle loro parti pi&ugrave; deboli (pag. </s>

<s>27). Nelle Disputazioni sui Placiti <lb/>di Aristotile (pag. </s>

<s>194) torna su questo stesso argomento, rendendo <pb xlink:href="020/01/125.jpg" pagenum="106"/>la ragione dell'aderire cos&igrave; tenacemente che fanno alla carne le <lb/>cucurbite mediche e del salir dell'acqua o del vino ne'cannellini, <lb/>che poi servirono ad uso di termometro; ragioni che son quelle <lb/>stesse che rendeva Galileo tanti anni dopo, e delle quali si trovava <lb/>cos&igrave; soddisfatto e ammirato il Sagredo. </s></p><p type="main">

<s>N&egrave; si vuol tacer qui, a proposito degli effetti calorifici, un er&shy;<lb/>rore aristotelico emendato dal Benedetti, bench&egrave; ripetuto poi da <lb/>tutti gli addetti alla Scuola galileiana infino al Borelli. </s>

<s>Aveva detto <lb/>il Filosofo, nel II Libro Delle Meteore, che il calor del sole &egrave; che <lb/>attrae e solleva i vapori. </s>

<s>E il nostro Fisico veneziano dice, pi&ugrave; di <lb/>ottant'anni prima del Fisico messinese, che ci&ograve; &egrave; apertamente falso, <lb/><emph type="italics"/>quia sol nil aliud facit quam calefacere cuius caloris ratione ea <lb/>materia rarefit et ob rarefactionem levior facta ascendit, non quia <lb/>sursum a sole feratur,<emph.end type="italics"/> (ibi, pag. </s>

<s>194). </s></p><p type="main">

<s>Ma intorno agli effetti del raro e del denso seguita sottilmente <lb/>a disputar contro Aristotile il Nostro, e dice la ragione perch&egrave; si <lb/>condensi nell'inverno e si renda visibile il vapor acqueo esalato <lb/>dalla bocca e dalle narici degli animali (pag. </s>

<s>191) e perch&egrave; sudino <lb/>nell'estate ripieni d'acqua fresca i vasi, ridendosi dei filosofi che <lb/>dicevano quel sudore esalare attraverso ai sottilissimi pori. </s>

<s>Soggiunge <lb/>poi le notabilissime parole seguenti: &ldquo; Neque silentio involvendum <lb/>est nec Aristotilem, neque alium ex suis fautoribus animadvertisse <lb/>densum et rarum esse causam ventorum &rdquo; (pag. </s>

<s>192). Non solo <lb/>non aveva avvertito questo nessun seguace di Aristotile, ma nessun <lb/>seguace di Galileo, e dur&ograve; l'errore infin tanto che non vennero <lb/>alla luce le sepolte <emph type="italics"/>Lezioni accademiche<emph.end type="italics"/> del Torricelli, nelle quali <lb/>insegn&ograve; l'Autore, a quel modo stesso che aveva tanti anni prima <lb/>fatto il Benedetti, come dal dilatarsi dell'aria al calor del sole ave&shy;<lb/>vano origine tutti i venti. </s>

<s>Gentile &egrave; poi quell'osservazione fatta della <lb/>nuvola che produce vento al di sotto, velando e rivelando al sole <lb/>il suo raggio, secondo che si legge a pag. </s>

<s>192 del citato Libro delle <lb/>Speculazioni. </s></p><p type="main">

<s>Un'altra cosa ben assai pi&ugrave; notabile delle dette fin qui &egrave; che <lb/>il Benedetti, in tempi cos&igrave; remoti abbia tanto chiaramente veduta, <lb/>in quegli stessi effetti di rarefazione e di condensazione la causa <lb/>vera de'suoni. </s>

<s>La storia dell'Acustica rimane in certo modo umi&shy;<lb/>liata a dover narrare che un Fisico della qualit&agrave; del Montanari, <lb/>presso al fine del secolo XVII, dicesse come il suono si produce <lb/>dalla collisione dell'aria coi corpi duri. </s>

<s>Eppure il fisico veneziano <lb/>aveva un secolo avanti insegnato che l'aria corre velocemente a <pb xlink:href="020/01/126.jpg" pagenum="107"/>riempire i luoghi rimasti vacui <emph type="italics"/>unde generatur sonus quod hucusque <lb/>a nemine animadversum fuisse comperio<emph.end type="italics"/> (pag. </s>

<s>289). E pi&ugrave; sottil&shy;<lb/>mente altrove esponendo le sue speculazioni soggiunge esser neces&shy;<lb/>sario che il corpo tremi. &ldquo; Neque etiam absque aere sonus effici <lb/>potest, quia aer sonat ingrediendo velociter ad implendum locum <lb/>ut non remaneat vacuus &rdquo; (pag. </s>

<s>190). </s></p><p type="main">

<s>Se non fosse cosa certa che Giovan Batista Porta, infin dal 1558, <lb/>descrisse la camera oscura e applic&ograve; quello strumento alla teorica <lb/>della visione, diremmo che il Benedetti era ben meritevole che fosse <lb/>riserbata a lui questa primizia delle sue speculazioni. </s>

<s>Forse egli fu <lb/>il primo ad applicar la lente biconvessa al foro, per cui s'introdu&shy;<lb/>cono i raggi solari (pag. </s>

<s>270) e senza dubbio l'applicazion ch'ei ne <lb/>fa al modo del vedere per l'organo fisiologico dell'occhio (pag. </s>

<s>297), <lb/>&egrave; di ben altro scienzato dall'Autor della <emph type="italics"/>Magia Naturale.<emph.end type="italics"/></s></p><p type="main">

<s>Bench&egrave; nell'Ottica non abbia fatto il Benedetti que'gran pro&shy;<lb/>gressi che fece nell'Acustica, nella Meteorologia e in altre parti della <lb/>Fisica o pi&ugrave; difficili o pi&ugrave; importanti, non &egrave; da tacer nondimeno <lb/>la ragion ch'ei rende del color rosso negli ecclissi di Luna, desunta <lb/>dalle rifrazioni che subiscono i raggi solari che perci&ograve; entrano nel <lb/>cono ombroso (pag. </s>

<s>257) e quell'altra ragion ben pi&ugrave; nuova dello <lb/>scintillar che fanno le stelle fisse; ragione desunta dal vario indice <lb/>di refrazione degli strati aerei e vaporosi che s'interpongono fra <lb/>que'lontanissimi corpi lucidi e il proprio occhio nostro (pag. </s>

<s>186). </s></p><p type="main">

<s>Il titolo di <emph type="italics"/>Speculazioni<emph.end type="italics"/> dato al libro, d'onde tante nuove verit&agrave; <lb/>della scienza si diffondevano a illuminar le tenebre di quei tempi, <lb/>&egrave; benissimo appropriato, perch&egrave; infatti l'Autore non si contenta che <lb/>di speculare. </s>

<s>Santorre Santorio invece, nato 31 anno dopo il Bene&shy;<lb/>detti in Capo d'Istria nel 1561, &egrave; l'uomo d'azione e l'arte medica <lb/>professata da lui &egrave; che potentemente l'inclina a mettere in esercizio <lb/>le solitarie speculazioni della scienza. </s>

<s>Cos&igrave;, mentre lo stesso Bene&shy;<lb/>detti s'era contentato di specular le ragioni per cui, in un cannel&shy;<lb/>lino di vetro, condensata l'aria, vi sottentra l'acqua, e variando la <lb/>temperatura l'acqua stessa ora s'alza nel cannellino ora s'abbassa; <lb/>il Santorio pensa di sottoporre a misura quegli alzamenti e quegli <lb/>abbassamenti, per servirsene come di sicuro argomento a misurare <lb/>il giusto grado degli accessi e dei recessi ne'calori febbrili. </s>

<s>E mentre <lb/>dall'altra parte Galileo, sperimentando coi pendoli le prime leggi <lb/>della caduta dei gravi, s'accorge dell'isocronismo delle loro vibra&shy;<lb/>zioni, e accenna all'uso che se ne potrebbe far nella misura dei <lb/>minimi tempi, il Santorio pensa d'applicar quello strumento a ri-<pb xlink:href="020/01/127.jpg" pagenum="108"/>conoscer da un giorno a un altro negli infermi la frequenza dei <lb/>polsi. </s></p><p type="main">

<s>Ma di simili altri strumenti, applicabili tutti all'arte sua pre&shy;<lb/>diletta, il Santorio &egrave; inventore fecondo, e aveva gi&agrave; divisato di con&shy;<lb/>sacrare a descriverli tutti insieme un libro intero. </s>

<s>Se fosse un tal <lb/>d&igrave;visamento poi mandato ad effetto, non si sa, perch&egrave; il libro degli <lb/><emph type="italics"/>Istrumenti medici<emph.end type="italics"/> a noi non &egrave; noto. </s>

<s>&Egrave; certo per&ograve; che l'inventore <lb/>non teneva il segreto, e secondo che egli stesso scrive, la sua casa <lb/>in Padova era aperta a tutti coloro, che o per curiosit&agrave; o per amore <lb/>di scienza accorrevano a veder tutte insieme raccolte, e come in <lb/>un piccolo museo ordinate e messe in mostra, quelle sue nuove <lb/>invenzioni. </s></p><p type="main">

<s>Quali che si fossero le dottrine professate dal nostro medico <lb/>giustinopolitano, &egrave; un fatto che questa cos&igrave; feconda vena d'inven&shy;<lb/>tare e di costruire e di utilmente applicare strumenti, era una pro&shy;<lb/>testa viva e parlante contro i principii aristotelici, i quali, procla&shy;<lb/>mando la mente sovrana e legislatrice della Natura, venivano a <lb/>concluder che la mente stessa sovrasta ai sensi anco infermi e non <lb/>bisognosi perci&ograve; di aiuti. </s></p><p type="main">

<s>Che se il Santorio non sa talvolta tener monde le vesti della <lb/>mota peripatetica, non &egrave; per&ograve; che egli strascichi, come tanti suoi <lb/>pari fanno, in quel lurido fango la toga. </s>

<s>Egli non sempre forse pro&shy;<lb/>ceder&agrave; a diritto col raziocinio, ma sentendosi vacillare s'aiuta delle <lb/>esperienze delle quali &egrave; senza dubbio un insigne monumento quella <lb/><emph type="italics"/>Medicina Statica,<emph.end type="italics"/> ordinata a riformar l'arte ippocratica Chi ripensi <lb/>che quel Trattatello dettato in forma aforistica e divisato con me&shy;<lb/>todo quasi geometrico, fu scritto in tempi, in cui si soleva affogar <lb/>da tutti le idee in un mar di parole, non finir&agrave; mai di ammirare <lb/>il Santorio, il quale fu primo a concluder le regole dell'arte me&shy;<lb/>dica dal fatto fisiologico dell'insensibile traspirazione dimostrata con <lb/>tutto il pi&ugrave; rigoroso procedere del metodo sperimentale. </s></p><p type="main">

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

<s>E ora che abbiamo veduto come la speculativa del Benedetti <lb/>e la pratica del Santorio compiendosi preparassero le fondamenta <lb/>alla grande Instaurazione galileana, convien passare a parlare di <pb xlink:href="020/01/128.jpg" pagenum="109"/>quel terzo che aggiungemmo a que'due primi compagno, e che <lb/>dette valida mano alla stessa grande Instaurazione insieme con <lb/>Galileo. </s></p><p type="main">

<s>Non si pu&ograve; pronunziare il nome di Paolo Sarpi, senza che <lb/>l'animo di chi ascolta non esca in ammirazioni declamatorie o in <lb/>disprezzi triviali. </s>

<s>Le trivialit&agrave; e le declamazioni son l'eccesso di <lb/>que'giudizii, che sempre si fanno da coloro, i quali non ben cono&shy;<lb/>scono l'uomo giudicato. </s>

<s>E in fatti, lasciando da parte la Religione <lb/>e la Politica, per non curarsi d'altro che della scienza, a convin&shy;<lb/>cersi che il Sarpi dee essere stato mal giudicato perch&egrave; non inteso, <lb/>basta il modo come sono state pubblicate le Lettere di lui. </s>

<s>Quella, <lb/>per esemp&inodot;o, del 2 Settembre 1602 diretta a Galileo, fu per questo <lb/>lasciata addietro dall'Alb&egrave;rti perch&egrave; <emph type="italics"/>oscura e mal dettata.<emph.end type="italics"/> Il Poli&shy;<lb/>dori, nonostante, cred&egrave; bene di pubblicarla insiem con l'altre dili&shy;<lb/>gentemente raccolte in due volumi stampati nel 1863 in Firenze. </s>

<s><lb/>Ma l'oscurit&agrave;, a voler dire il vero, non dipende gi&agrave; da chi scrive: <lb/>dipende piuttosto da chi legge e non sa di qual soggetto pro&shy;<lb/>priamente si parla. </s>

<s>A chi sapesse che l'Autore citato ivi &egrave; il Gil&shy;<lb/>bert; che la questione &egrave; trattata nella Fisiologia nuova del Magnete, <lb/>che ivi trovasi disegnata la figura, alla quale il Sarpi si richiama; <lb/>le difficolt&agrave; spariscono e la scienza si vede a un tratto scaturir, <lb/>come da un arido masso, acqua viva. </s>

<s>Allo stesso modo son nella <lb/>Raccolta del Polidori aombrate le altre lettere del Sarpi, unico do&shy;<lb/>cumento pubblico, da cui si possa giudicare della scienza naturale <lb/>di lui. </s>

<s>Ma bench&egrave; sieno, in materia scientifica quelle lettere poche, <lb/>pure apparecchiano innanzi a chi ha buono stomaco da digerirlo, <lb/>cibo che nutrisce assai meglio delle pi&ugrave; squisite vivande imbandite <lb/>al pi&ugrave; liberale convito. </s>

<s>Anzi quella concisione di linguaggio scien&shy;<lb/>tifico, quasi ridotto a formule matematiche, per cui a chi non ha <lb/>acume da entrarci bene addentro pare enimmaticamente oscuro, &egrave;, <lb/>secondo noi, uno dei pregi pi&ugrave; singolari del Sarpi, di che in lui e <lb/>nel Santorio s'ha esempio unico in quei tempi </s></p><p type="main">

<s>Del resto, anco quando non s'avesse nessuna scrittura scien&shy;<lb/>tifica dell'Autore, basterebbero a testimoniar della scienza di lui le <lb/>sincere ammirazioni e le lodi dei contemporanei, fra'quali Galileo <lb/>e il Gilbert soli varrebbero per tutti gli altri. </s>

<s>Ma giacch&egrave; quelle <lb/>scritture ci sono e son vive e parlanti, studiamoci di leggerle, con <lb/>la serenit&agrave; stessa di chi nulla altro ama e null'altro vuole annun&shy;<lb/>ziar che il vero. </s></p><p type="main">

<s>Nel 1608, immerso tutto nelle faccende politiche, scriveva il <pb xlink:href="020/01/129.jpg" pagenum="110"/>di 22 Luglio al Groslot, come innanzi che le occorrenze del mondo <lb/>lo invitassero a pensar come cose serie e non come passatempi a <lb/>quelle faccende, aveva tutti i suoi gusti nelle scienze naturali e <lb/>nelle matematiche (Polidori, ivi, vol. </s>

<s>I, pag. </s>

<s>76). Qual fosse poi il <lb/>metodo ch'ei proseguiva, s'argomenta da ci&ograve; che altrove, allo stesso <lb/>Groslot scrive del non doversi filosofar, conforme al precetto di So&shy;<lb/>crate, sopra esperienze non vedute da s&egrave; proprio (ivi, pag. </s>

<s>181). In <lb/>questo modo protestava apertamente contro Aristotile, e soggiun&shy;<lb/>gendo poco appresso ch'ei sentiva qualche opposizione in trattar <lb/>cose astratte, perch&egrave; non si metteva in conto la repugnanza della <lb/>materia, mostrava di voler seguire altra via da coloro, che, fedeli <lb/>troppo a Platone, discorrevano, colle astrazioni matematiche, de'fatti <lb/>particolari della Natura. </s></p><p type="main">

<s>Fra'soggetti naturali, che pi&ugrave; vivamente richiamassero a s&egrave; <lb/>l'attenzione de'Filosofi e la voglia de'curiosi, eran que'moti irre&shy;<lb/>golari veduti fare alla calamita, i quali scoperti prima dal Colombo <lb/>furono poi confermati dalle osservazioni degli altri navigatori. </s>

<s>Cos&igrave; <lb/>il Colombo per&ograve; come Giovanni da Empoli si stettero contenti a <lb/>osservare e a descrivere i semplici fatti: il Sassetti che si volle <lb/>provare a filosofarvi sopra, assai presto se ne tolse gi&ugrave;, atterrito <lb/>dalla difficolt&agrave; del soggetto. </s></p><p type="main">

<s>Il primo che ardisse d'affrontare quelle difficolt&agrave;, predisponendo <lb/>l'ingegno alle filosofiche speculazioni colle osservazioni sensate e <lb/>colle pi&ugrave; sottili esperienze, fu il nostro Sarpi, di cui il Porta, nel <lb/>settimo libro della Mag&igrave;a raccolse per avventura gli studi e le sco&shy;<lb/>perte magnetiche, le quali sarebbero andate altrimenti con grave <lb/>danno perdute. </s></p><p type="main">

<s>N&egrave; a quella vigorosa giovent&ugrave; di mente questo fra'soggetti na&shy;<lb/>turali poteva esaurire le forze. </s>

<s>Si vuole anzi che nulla fosse dal <lb/>Sarpi lasciato addietro di ci&ograve; che allora, o in cose di fisica o in <lb/>cose di storia naturale potesse attrarre a s&egrave; l'attenzione degli in&shy;<lb/>gegni speculativi. </s>

<s>Il Grisellini, fra le altre, vorrebbe attribuirgli la <lb/>scoperta delle valvole delle vene e fargli di l&igrave; indurre l'altra pi&ugrave; <lb/>grande scoperta della circolazione del sangue. </s>

<s>E perch&egrave; l'argomento <lb/>&egrave; di troppo alta importanza, non si vuol lasciar qui da noi senza <lb/>esame. </s></p><p type="main">

<s>&ldquo; Mediante dunque le sue esercitazioni anatom&inodot;che (cos&igrave; scrive <lb/>lo stesso Grisellini di fra Paolo quando aveva 26 anni) avendo sco&shy;<lb/>perte le valvole delle vene onde la successione del sangue da que&shy;<lb/>ste nelle arterie si rende manifesta, ne veniva quinci dimostrata <pb xlink:href="020/01/130.jpg" pagenum="111"/>e stabilita la circolazione del sangue, che per alcune anteriori os&shy;<lb/>servazioni di Realdo Colombo, del Serveto e del Cesalpino era stata <lb/>accennata, egli, io dico avendo scoperte esse valvole non tacque la <lb/>sua scoperta al celebre Fabrizio d'Acquapendente, il quale, coll'oc&shy;<lb/>casione di trasferirsi in Venezia.... aveva contratto seco amicizia. </s>

<s>&rdquo; <lb/>(Mem. </s>

<s>aned. </s>

<s>Losanna 1760, pag. </s>

<s>20). </s></p><p type="main">

<s>Che il Sarpi facesse veramente soggetto di speculazioni e di <lb/>esperienze anco l'Anatomia &egrave; cosa probabilissima, ed &egrave; certo che <lb/>l'Acquapendente apprese dallo stesso Sarpi quel curioso fatto del <lb/>ristringersi e del dilatarsi delle pupille osservato gi&agrave; molto tempo <lb/>prima, senza che si sapesse, da Leonardo. </s>

<s>Ma che l'Acquapendente <lb/>apprendesse dal Sarpi, come il Grisellini asserisce, la scoperta delle <lb/>valvole delle vene, non solo non s'ha certa dimostrazione da nes&shy;<lb/>sun documento, ma i documenti che abbiamo stanno a provar tutto <lb/>il contrario. </s></p><p type="main">

<s>Il Falloppio ha un passo notabilissimo, che si vedr&agrave; trascritto <lb/>a suo luogo, dal quale apparisce che in alcune vene l'esistenza <lb/>delle valvole fu ritrovata gi&agrave; da Giovan Batista Canani. </s>

<s>La scoperta <lb/>fu divulgata da G. </s>

<s>Rodriguez conosciuto sotto il nome di Amato <lb/>Lusitano, ed &egrave; contro a lui che fieramente se la prende il Fallop&shy;<lb/>pio, asserendo che l'illustre Canano non poteva essere incorso in <lb/>un errore cos&igrave; madornale. </s>

<s>La scoperta, che in tal modo il grande <lb/>anatomico modenese lasci&ograve; scapparsi di mano, venne tutta alle mani <lb/>dell'Acquapendente, il quale con gran diligenza racconta da s&egrave; me&shy;<lb/>desimo qual fosse l'anno e a quale occasione gli occorresse di far <lb/>quella scoperta invidiata. </s></p><p type="main">

<s>Leggesi un tal racconto scritto nel Trattatello stampato in Pa&shy;<lb/>dova nel 1603 dalla tipografia di Lorenzo Pasquati. </s>

<s>Ci &egrave; nato il <lb/>sospetto che, o per la rarit&agrave; o per altra ragione quel Trattatello <lb/>dell'Acquapendente non fosse veduto mai da nessun di coloro che <lb/>lo citano, incominciando dall'alterare il titolo stesso da quello che <lb/>dall'Autore gli &egrave; imposto. <emph type="italics"/>De valvulis<emph.end type="italics"/> lo intitola il Magiotti, <emph type="italics"/>De <lb/>ostiolis sanguinis<emph.end type="italics"/> il Grisellini, <emph type="italics"/>De ostiolis venarum<emph.end type="italics"/> il Puccinotti; <lb/>ma &egrave; un fatto che il titolo vero &egrave; <emph type="italics"/>De venarum ostiolis.<emph.end type="italics"/> Non fa <lb/>perci&ograve; maraviglia se quegli autori, i quali o non poterono o non <lb/>si curarono di consultar ci&ograve; che lo scopritore delle valvole delle <lb/>vene ne scrisse, raccontano a uria e giudicano delle cose. </s></p><p type="main">

<s>Consultando per&ograve; senz'animo preoccupato quella scrittura, ci si <lb/>trova un tal carattere di verit&agrave;, nella narrazione e nella descrizione, <lb/>che il voler negar fede alle parole dell'Autore sarebbe un profes-<pb xlink:href="020/01/131.jpg" pagenum="112"/>sare addirittura il pi&ugrave; assoluto pirronismo storico. </s>

<s>Incomincia da <lb/>far le meraviglie come mai l'esistenza delle valvole delle vene po&shy;<lb/>tesse esser rimasta agli anatomici per cos&igrave; lungo tempo occulta, e <lb/>soggiunge che nel sezionare i cadaveri s'abbatt&egrave; a vederle per la <lb/>prima volta nel 1574. (De ven. </s>

<s>ost. </s>

<s>pag. </s>

<s>1). La via della scoperta <lb/>gli era stata preparata gi&agrave; da ci&ograve; che eragli occorso d'osservare <lb/>nelle vene allacciate o compresse (ivi, pag. </s>

<s>2) le quali inturgidendo <lb/>di sangue mostrano nel loro decorso certi nodi, come quei delle <lb/>canne, ond'&egrave; che mettendosi a dissecare per veder ci&ograve; che fossero <lb/>veramente quei nodi, ritrov&ograve; che egli eran dovuti a un ristagno di <lb/>sangue, operatovi dalle valvole, a quel modo che si vede fare alle <lb/>cateratte attraverso al corso di un fiume. </s></p><p type="main">

<s>Ora, &egrave; egli credibile che Girolamo Fabrizi d'Acquapendente, <lb/>nella vita sua civile e scientifica cos&igrave; dignitoso, avesse osato d'as&shy;<lb/>serire tali falsit&agrave; e di scriverle sotto gli occhi di Fra Paolo? </s>

<s>E <lb/>dall'altra parte egli invoca, a far testimonianza del vero, l'inclita <lb/>nazione Germanica, alla quale dedica il Trattatello, e nella stessa <lb/>Lettera dedicatoria ringrazia Salomone Alberto, per aver nella sua <lb/>nazione divulgata quella scoperta. </s></p><p type="main">

<s>Ritornando ora alle osservazioni del Grisellini, diciamo che, <lb/>sebbene debba credersi vero autore della scoperta delle valvole delle <lb/>vene n&ograve; il Sarpi, ma l'Acquapendente, &egrave; falso nulladimeno che i <lb/>due grandi uomini o di li o d'altronde pigliassero argomento a di&shy;<lb/>mostrar il circolo del sangue. </s>

<s>Vari passi potrebbero citarsi dalle <lb/>opere dell'Acquapendente, e specie dal cap. </s>

<s>VIII, Parte II. <emph type="italics"/>De for&shy;<lb/>mato foetu,<emph.end type="italics"/> da'quali si proverebbe com'egli, trattando degli usi <lb/>del polmone, ripete le antiche dottrine galeniche approvate gi&agrave; dal <lb/>Vesalio e dal Falloppio, nulla accettando nemmeno di ci&ograve; che, ri&shy;<lb/>spetto alla piccola circolazione, avevano dimostrato il Colombo e il <lb/>Cesalpino. </s>

<s>Dall'altra parte, per lo stesso Trattato <emph type="italics"/>De venarum ostiolis<emph.end type="italics"/><lb/>si par chiaro che l'Autore attribuiva alle valvole un ufficio ben di&shy;<lb/>verso da quello che veramente hanno in natura, il qual'&egrave; di faci&shy;<lb/>litare il corso del sangue verso il lago del cuore. </s>

<s>L'Acquapendente <lb/>infatti ammettendo che il sangue venoso abbia virt&ugrave; di alimentare, <lb/>dice che le valvole sono ordinate a distribuir quell'alimonia per <lb/>tutto equamente. </s>

<s>Che se nelle vene pi&ugrave; lontane dal centro del cuore, <lb/>come in quelle delle braccia e delle gambe, osserva le valvole ri&shy;<lb/>correre ivi pi&ugrave; spesse, non sospetta per niente che ci&ograve; sia perch&egrave; <lb/>il sangue abbisogna, in quelle condizioni, d'aiuti maggiori, avendo <lb/>a fare un viaggio pi&ugrave; lungo per tornarsene al suo principio; ma <pb xlink:href="020/01/132.jpg" pagenum="113"/>dice che, essendo le gambe e le braccia soggette a fare sforzi, per <lb/>cui il sangue correrebbevi troppo veloce, a temperarne la forza vi <lb/>bisogna un pi&ugrave; frequente uso di valvole. </s>

<s>Che poi ne anco il Sarpi <lb/>non avesse nemmen la pi&ugrave; lontana idea del circolo del sangue, <lb/>s'argomenta da alcune espressioni che ricorrono negli scritti di lui <lb/>e segnatamente ne'principii delle Lettere CXXIV e CCXX, fra le <lb/>pubblicate dal Polidori. </s></p><p type="main">

<s>Gli ammiratori ferventi del frate servita intesero a glorificarlo <lb/>altres&igrave; coll'attribuirgli l'invenzione di alcuni de'principali strumenti <lb/>del metodo sperimentale, fra'quali &egrave; il Telescopio. </s>

<s>Ma del Tele&shy;<lb/>scopio tratta il Sarpi nelle sue Lettere a varie occasioni, e ne tratta <lb/>in modo da potere informare sulle sue stesse parole il pi&ugrave; retto <lb/>giudizio. </s>

<s>In una Lettera al Groslot, che &egrave; la LII della Raccolta del <lb/>Polidori, dop'essersi fatto intendere che verso la fine del Novem&shy;<lb/>bre 1608 ebbe avviso <emph type="italics"/>delli nuovi occhiali<emph.end type="italics"/> sei mesi prima che quello <lb/>stesso avviso pervenisse alle orecchie di Galileo, soggiunge che, <lb/>quando egli era giovane, pens&ograve; ad una tal cosa e gli pass&ograve; per la <lb/>mente che un occhial fatto di figura di parabola potesse far tale <lb/>effetto. </s></p><p type="main">

<s>Le lenti paraboliche poi dettero soggetto di specular lunga&shy;<lb/>mente agli ottici infino ai tempi del Newton, nonostante che il Ca&shy;<lb/>valieri avesse geometricamente dimostrato, nel suo <emph type="italics"/>Specchio Ustorio,<emph.end type="italics"/><lb/>esser quella una inutile squisitezza, stante che, tra un menisco sfe&shy;<lb/>rico e un iperbolico, &egrave; trascurabile la differenza. </s>

<s>Ma &egrave;, in tal pro&shy;<lb/>posito assai importante una lettera del 4 Ottobre 1614, nella quale <lb/>Bartolommeo Imperiali propone a Galileo la soluzione di quell'enim&shy;<lb/>ma, che il Porta scrisse nel cap. </s>

<s>XI del XVII libro della Mag&igrave;a. </s>

<s><lb/>Quell'enimma concerne uno strumento da veder le cose lontane, <lb/>e l'Imperiali indovinerebbe che consistesse nella lente parabolica. </s>

<s><lb/>Dice ivi che il Porta, <emph type="italics"/>per quanta istanza li sia stata fatta da prin&shy;<lb/>cipi b letterati s'&egrave; potuto mai inchinare a dichiarar l'animo suo: <lb/>solo disse che maestro Paolo da Venezia servita l'aveva capito.<emph.end type="italics"/><lb/>(Mss. </s>

<s>Gal. </s>

<s>Div. </s>

<s>II, P. VI, T. IX, c. </s>

<s>206). Di qui facilmente si rac&shy;<lb/>coglie d'onde attingesse il Porta l'idea dello strumento da veder <lb/>le cose lontane, e poniamo pure che rimanesse un'idea, nonostante <lb/>non &egrave; piccola gloria di lui e del Sarpi l'aver creduto possibile il <lb/>Telescopio, a cui il gran Kepler non ebbe fede, in fin tanto che <lb/>non se lo vide fra le mani, e non ne fece esperienza con gli occhi. </s></p><p type="main">

<s>Divenuta la possibilit&agrave; in atto, per la fortunatissima opera di <lb/>Galileo, il Sarpi non rimase indietro nelle osservazioni celesti. </s>

<s>In <pb xlink:href="020/01/133.jpg" pagenum="114"/>una lettera del 16 marzo 1610, dopo aver fra Paolo annunziato al <lb/>Leschassier che pi&ugrave; di due anni fa gli Olandesi avevano scoperto <lb/>uno strumento pel quale si vedevano le cose lontane. </s>

<s>&ldquo; Di questo <lb/>trovato, soggiunge, un nostro Matematico di Padova e altri italiani <lb/>intendenti della materia principiarono a valersi per l'Astronomia, <lb/>e dalla esperienza avvalorati lo ridussero pi&ugrave; atto e perfezionato. </s>

<s>&rdquo; <lb/>(Polidori, vol. </s>

<s>II, pag. </s>

<s>41). Che quel matematico di Padova sia Ga&shy;<lb/>lileo, &egrave; fuor di dubbio, ma giacch&egrave; lo scrittore di quelle parole ci <lb/>rive&igrave;a l'importantissima notizia che cio&egrave;, contemporaneamente a <lb/>Galileo, il quale si crede da tutti il primo e il solo, ci fossero <emph type="italics"/>altri <lb/>italiani,<emph.end type="italics"/> i quali attendevano a perfezionare il canocchiale, e a far <lb/>con esso osservazioni celesti; chi sono, si domanda, questi italiani? </s>

<s><lb/>E alla domanda si risponde da noi dicendo che quegli italiani erano <lb/>appunto il Sarpi e gli altri che in Venezia conferivan con lui. </s></p><p type="main">

<s>Giunger&agrave; forse come cosa nuova ai lettori e per la novit&agrave; parr&agrave; <lb/>non credibile, che il <emph type="italics"/>Nuncio Sidereo,<emph.end type="italics"/> e quanto alle osservazioni <lb/>degli occhi, e quanto alle speculazioni della mente, sia opera tutto <lb/>insieme, e forse per egual merito, di Galileo e del Sarpi. </s>

<s>Eppure <lb/>i documenti, che ai giudiziosi e agli spassionati appariranno chia&shy;<lb/>rissimi, tolgon via intorno a ci&ograve; tutti i dubbi. </s></p><p type="main">

<s>In quella lettera al Leschassier, ora ultimamente citata, pro&shy;<lb/>segue a dire il Sarpi, a proposito delle osservazioni celesti fatte col <lb/>canocchiale, come in Toscana erano state osservate nuove cose nella <lb/>stella di Giove, che ei legger&agrave; nell'<emph type="italics"/>opuscolo<emph.end type="italics"/> offertogli a nome suo <lb/>dal Legato. </s>

<s>Quell'opuscolo era senza dubbio il Nunzio Sidereo, al&shy;<lb/>quante copie del quale Galileo, appresso allo stampatore avea rila&shy;<lb/>sciate a disposizione di Fra Paolo, che le dispensava agli amici. </s>

<s><lb/>Mentre che per&ograve; era sollecito di diffondere quel libro negli altri, <lb/>egli ancora non lo aveva letto, e nonostante torna poco dopo a <lb/>scrivere una nuova lettera allo stesso Leschassier, nella quale si <lb/>contengono annunziate le principali fra le scoperte celesti, che ve&shy;<lb/>nivano annunziate al mondo dall'opuscolo di Galileo. </s>

<s>Questo &egrave; poi <lb/>un argomento certo della verit&agrave; di quel che vedremo pi&ugrave; sotto es&shy;<lb/>sere asserito dallo stesso Sarpi, che cio&egrave; egli aveva conferito quelle <lb/>osservazioni celesti coll'Autor dell'opuscolo, per cui s'intende come <lb/>potesse render conto di quel che trattava, senza averlo letto. </s></p><p type="main">

<s>Anco quando il Nunzio Sidereo fosse andato smarrito, questa <lb/>lettera CXXXVI della citata Roccolta varrebbe a ristorar la scienza <lb/>di quella iattura, per ci&ograve; almeno che concerne le macchie della <lb/>Luna. </s>

<s>L'antico Plutarco ebbe la felicissima idea che la Luna fosse <pb xlink:href="020/01/134.jpg" pagenum="115"/>fisicamente costituita come la Terra, e aveva ad occhio distinte due <lb/>diverse qualit&agrave; di macchie, alcune variabili che egli attribuiva al&shy;<lb/>l'ombra de'monti insolati, e altre permanenti, che egli attribuiva <lb/>alla superficie dei mari. </s>

<s>Una tal novit&agrave;, fu, com'&egrave; naturale, rifiu&shy;<lb/>tata dai Peripatetici, ma i pi&ugrave; sagaci che vi sentiron dentro alitare <lb/>un soave spirito di verit&agrave;, l'accolsero con amore. </s>

<s>Dubitavano per&ograve; <lb/>se pi&ugrave; di luce si dovesse rifletter dai mari o dai continenti. </s>

<s>Il pro&shy;<lb/>blema veramente era illusorio e vi rimase preso anco il Keplero, <lb/>che lietamente accogliendo i placiti del Cheronese <emph type="italics"/>hac in parte,<emph.end type="italics"/><lb/>soggiunge, <emph type="italics"/>non assentior. </s>

<s>Magis est consentaneum quae sunt in <lb/>Luna partes lucidae maria credi, quae maculosae terras, conti&shy;<lb/>nentes et insulas.<emph.end type="italics"/> (Paralip. </s>

<s>edit. </s>

<s>cit. </s>

<s>pag. </s>

<s>201). Galileo nel <emph type="italics"/>Nuncio<emph.end type="italics"/><lb/>esce destramente dalla controversia saettando simili parole: &ldquo; La <lb/>terra dee apparir pi&ugrave; chiara del mare, e intorno a ci&ograve; <emph type="italics"/>mihi dubuim <lb/>fiut unquam.<emph.end type="italics"/> &rdquo; (Alb. </s>

<s>III, pag. </s>

<s>65). </s></p><p type="main">

<s>Che il Keplero alla contraria sentenza, cos&igrave; laconicamente pro&shy;<lb/>nunziata da Galileo, ne rimanesse persuaso, e tornasse anco per <lb/>questa parte al suo Plutarco, non fa maraviglia. </s>

<s>Fa per&ograve; maraviglia <lb/>il sentirlo dire che fu condotto in quella persuasione di creder cio&egrave; <lb/>mari le macchie della luna, da ci&ograve; che ne disse Galileo stesso <emph type="italics"/>di&shy;<lb/>sputatione exactissima<emph.end type="italics"/> e di pi&ugrave; <emph type="italics"/>illatione argutissima et invicta.<emph.end type="italics"/><lb/>(Alb. </s>

<s>V, 418, 19) mentre Galileo nel <emph type="italics"/>Nuncio<emph.end type="italics"/> tutt'altro che dispu&shy;<lb/>tare e argomentare, si sta contento ad asserir semplicemente il fatto <lb/>che egli tiene anzi cos&igrave; certo, da non aver bisogno alcuno di prove. </s></p><p type="main">

<s>Chi veramente disputa su tale importante soggetto e argomenta <lb/>&egrave; il Sarpi, nella citata lettera al suo Leschassier e le disputazioni <lb/>e gli argomenti son suggellati dalla esperienza. </s>

<s>&ldquo; Se Ella porr&agrave; di <lb/>contro al sole ma lungi da s&egrave; una pietra rotonda e uno specchio <lb/>sferico della stessa grandezza, vedr&agrave; l'emisfero della pietra rischia&shy;<lb/>rato e tutto lo specchio oscuro, all'infuori di quella minima parti&shy;<lb/>cella, in cui le si offrir&agrave; alla vista un certo piccol sole. </s>

<s>Che se <lb/>tanto l'allontaner&agrave; da essere insensibile l'angolo, cio&egrave; quel piccol <lb/>sole, appena Ella vedr&agrave; lo specchio; il sole poi apparir&agrave; splendi&shy;<lb/>dissimo. </s>

<s>L'acqua e la terra sono sferiche e la Luna ha una parte <lb/>lucida ed una macchiata: applichi ad essa questi riflessi e toccher&agrave; <lb/>con mano la cosa. </s>

<s>&rdquo; (Polidori, vol. </s>

<s>II, pag. </s>

<s>63). </s></p><p type="main">

<s>Galileo non argomenta n&egrave; disputa intorno alla ragion fisica <lb/>delle macchie permanenti della Luna, se non parecchi anni dopo <lb/>nel primo Dialogo dei Due Massimi Sistemi (Alb. </s>

<s>I, 15, 88) ricor&shy;<lb/>rendo all'esperienza dello specchio sferico e della pietra scabrosa <pb xlink:href="020/01/135.jpg" pagenum="116"/>o del muro, a quel modo che aveva fatto gi&agrave; il Sarpi nelle lettere <lb/>e nelle parole sopra trascritte ond'&egrave; che non a torto si pu&ograve; quella <lb/>stessa lettera al Leschassier riguardar come un trattatello d'Astro&shy;<lb/>nomia fisica lunare, pi&ugrave; compiuto del Nuncio Sidereo. </s></p><p type="main">

<s>A chi rifletta con giudiziosa mente a queste cose non sembrer&agrave; <lb/>perci&ograve; alieno dal vero quel che s'asseriva di sopra, che cio&egrave; in <lb/>gran parte si debbano al Sarpi le novit&agrave; scoperte e annunziate da <lb/>Galileo. </s>

<s>La nostra asserzione poi fondata sui fatti d&agrave; suggello di <lb/>verit&agrave; alle parole con le quali fra Paolo, accennando al matematico <lb/>dello studio di Padova esordisce il suo compendioso Nunzio Astro&shy;<lb/>nomico: &ldquo; Spesso abbiamo conferito insieme su quell'argomento e <lb/>molte osservazioni ci scambiammo. </s>

<s>&rdquo; (Polid. </s>

<s>vol. </s>

<s>II, pag. </s>

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

<s>Ed ecco insieme i fatti stessi confermare altri detti citati pi&ugrave; <lb/>sopra a proposito di quegli italiani che attendevano in Venezia a <lb/>perfezionare il canocchiale e a far con esso osservazioni celesti. </s>

<s>A <lb/>quel numero appartenevano gli eruditi di cui il Sarpi scrive nella <lb/>lettera CXLI, i quali comprendendo che mal si sarebbe riusciti a <lb/>perfezionare il canocchiale senza prima conoscerne le teorie, dise&shy;<lb/>gnavano di fare un piccolo commentorio sulla visione <emph type="italics"/>ove esporranno <lb/>la maniera e la cagione del trovato olandese<emph.end type="italics"/> (ivi, pag. </s>

<s>81). Nel&shy;<lb/>l'agosto 1610 quel Commentario, che senza dubbio &egrave; il Trattato <lb/>del De Dominis <emph type="italics"/>De radiis visus et lucis,<emph.end type="italics"/> non era ancora finito di <lb/>stampare e si attendeva a mettere all'ordine le incisioni (ivi, <lb/>pag. </s>

<s>108). </s></p><p type="main">

<s>A chi poi si maravigliasse come mai l'Autore del Nunzio Si&shy;<lb/>dereo non facesse il pi&ugrave; piccolo accenno al suo collaboratore nelle <lb/>osservazioni celesti, si risponder&agrave; pi&ugrave; avanti, quando altri simili <lb/>fatti ci faranno meglio conoscere un'indole propria di Galileo. </s>

<s>Ba&shy;<lb/>sti r&igrave;sponder per ora che, nella prima lettera familiare la quale <lb/>gli occorresse di scrivere al Sarpi dopo la pubblicazione del Mes&shy;<lb/>saggero, Galileo ne esalta le virt&ugrave; e i meriti e professa di tenergli <lb/>obblighi infiniti (Alb. </s>

<s>VI, 141). </s></p><p type="main">

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

<s>Chi si rivolge indietro a comprendere in una occhiata sola la <lb/>lunga schiora passata da noi fin qui in rassegna, da Dante Alighieri <lb/>a Paolo Sarpi, non pu&ograve; non restar sorpreso da maraviglia, e non <pb xlink:href="020/01/136.jpg" pagenum="117"/>confessare a s&egrave; medesimo ch'ei non l'avrebbe creduta mai n&egrave; s&igrave; <lb/>eletta, n&egrave; s&igrave; numerosa. </s>

<s>Essa rimane ancora immobile sotto lo sguardo <lb/>dei nostri lettori e par che voglia star l&igrave; a fronte alta per chieder <lb/>ragione e vendicar l'accusa che fu data a loro da tanti d'esser e <lb/>vissuti cio&egrave; in secoli di barbarie, e di non aver saputo cacciar di&shy;<lb/>nanzi a s&egrave; le tenebre dell'ignoranza. </s>

<s>A chi li rimprover&ograve; e gli <lb/>compianse, perch&egrave; avessero tenute aggiogate le loro cervici sotto <lb/>l'autorit&agrave; di Aristotile, e non avessero saputo far altro che ridire <lb/>in prosa gli errori declamati da lui, rispondono squadernando in&shy;<lb/>nanzi agli occhi i loro volumi, e accennando colla punta del dito <lb/>alle nuove speculazioni e alle nuove scoperte, frutto di libera filo&shy;<lb/>sofia e d'ingegnosa arte sperimentale. </s></p><p type="main">

<s>Si sentiva nonostante in sul primo entrar del secolo XVII che <lb/>i frutti menati dall'albero della scienza non rispondevano, n&egrave; in <lb/>qualit&agrave;, n&egrave; in numero, all'abbondanza dei rami, per cui fu creduto <lb/>si potesse utilmente provvedere alla loro ubert&agrave; col moitiplicare i <lb/>cultori a ci&ograve; chiamati ed eletti. </s>

<s>Un tal pensiero accolto in un animo <lb/>generoso e che per opera di un Principe romano d'animo non <lb/>men generoso si pot&egrave; mettere in atto, di&egrave; luogo all'istituzione del&shy;<lb/>l'Accademia de'Lincei, la seconda forse, che dopo la Platonica fio&shy;<lb/>rentina, si vedesse in Italia. </s></p><p type="main">

<s>Il principio informativo della nuova Accademia &egrave; notabile che <lb/>si desumesse dall'istituzione dei Cherici regolari, e che, come questi <lb/>si proponevano di diffonder la fede cristiana e i buoni costumi, cos&igrave; <lb/>gli Accademici lincei si proponessero di diffonder la scienza natu&shy;<lb/>rale e i retti metodi sperimentali. </s>

<s>Il <emph type="italics"/>Linceografo<emph.end type="italics"/> infatti s'assomi&shy;<lb/>glia molto alle regole dei frati, i Collegi lincei ai conventi, e l'isti&shy;<lb/>tuzione delle colonie lincee alle Missioni. </s>

<s>Di qui &egrave; che avendo le <lb/>leggi stesse e le costituzioni risentendo molto dell'aristotelico e ci&ograve; <lb/>vuol dire del gretto e del compassato, male erano atte a predisporre <lb/>quel nobile e generoso consesso al libero filosofare, e a coglier quei <lb/>buoni frutti, che si ripromettevano le speranze del Principe insti&shy;<lb/>tutore. </s></p><p type="main">

<s>Ben assai pi&ugrave; efficaci erano stati e duravano tuttavia ad esser <lb/>gli influssi dell'Accademia platonica, bench&egrave; non facesse professione <lb/>di scienze naturali, ma di sola Filosofia speculativa. </s>

<s>Tommaso Cam&shy;<lb/>panella, in una sua lettera del d&igrave; 6 Luglio 1628 al Granduca Fer&shy;<lb/>dinando, dice che noi italiani &ldquo; portiamo grande obbligo ai Principi <lb/>medicei, che facendo comparire i libri platonici in Italia, non visti <lb/>da'nostri antichi, fur cagione di levarci dalle spalle il giogo d'Ari-<pb xlink:href="020/01/137.jpg" pagenum="118"/>stotile, e per conseguenza poi tutti i sofisti, e cominci&ograve; l'Italia ad <lb/>esaminare la Filosofia delle Nazioni con ragione ed esperienza nella <lb/>Natura, e no nelle parole degli uomini &rdquo; (MSS. Cim. </s>

<s>T. XXVI, c. </s>

<s>13). <lb/>La cosa &egrave; tanto vera che ha il suo pieno riscontro nei fatti da noi <lb/>discorsi e pi&ugrave; in quelli che si discorreranno fra poco. </s></p><p type="main">

<s>Ma per tornare all'Accademia de'Lincei, le intenzioni, per quanto <lb/>generose fossero, dello Stelluti e del Cesi, tornarono vane, perch&egrave; <lb/>principalmente non era quella l'opportunit&agrave; n&egrave; il bisogno richie&shy;<lb/>deva di convocare un Accademia. </s>

<s>Il difetto che si ritrovava allora <lb/>nell'albero della scienza era quello stesso, che si vede negli alberi <lb/>naturali, quando per lunga et&agrave; son trascorsi, a rimediare ai quali, <lb/>invece di moltiplicare i rami alla chioma e i polloni al piede, con&shy;<lb/>vien reciderli, e in un tronco solo avviar l'alimento e fomentarvi <lb/>gli spiriti vitali. </s>

<s>Non una Repubblica in altre parole conveniva isti&shy;<lb/>tuire, ma un Regno assoluto, in cui risedesse la tirannica potest&agrave; <lb/>nelle mani di un solo. </s>

<s>Ci&ograve; non poteva ottenersi che per via di una <lb/>conquista, la quale veramente fu tentata in Inghilterra da Francesco <lb/>Bacone, ma con poco felice riuscita, si consegu&igrave; in parte da Renato <lb/>Cartesio in Francia, e Galileo Galilei in Italia riport&ograve; la completa <lb/>vittoria. </s></p><p type="main">

<s>Francesco Bacone dette al suo nuovo Regno scientifico il nome <lb/>d'<emph type="italics"/>Instauratio Magna,<emph.end type="italics"/> e si cred&egrave; di dover esserne investito Monarca, <lb/>per avere architettata l'Enciclopedia d'ogni scienza e arte nel libro <lb/><emph type="italics"/>De augmentis scientiarum,<emph.end type="italics"/> e per aver nel <emph type="italics"/>Novum Organum<emph.end type="italics"/> minu&shy;<lb/>tamente divisate le regole da seguirsi nel metodo sperimentale. </s>

<s>&Egrave; <lb/>facile per&ograve; persuadersi che quella sua Monarchia non era altro che <lb/>di un nome vuoto, o se si vuole, di un regno gi&agrave; trapassato. </s>

<s>Se, <lb/>infatti, scienza veramente non ci &egrave;, e non ci &egrave; stata mai, come <lb/>vuole Bacone, egli divisa dunque nella sua Enciclopedia i loculi <lb/>senza avere di che riempirli. </s>

<s>E dall'altro lato le regole di un arte <lb/>suppongono gi&agrave; l'istituzione dell'arte stessa. </s>

<s>Cos&igrave;, dopo gli scrittori, <lb/>venne la Grammatica, dopo i pittori le regole per l'arte della pit&shy;<lb/>tura e dopo i gran capitani le regole dell'arte della guerra. </s>

<s>N&egrave; <lb/>l'arte di sperimentare pu&ograve; perci&ograve; trascendere da questa legge uni&shy;<lb/>versale: ella pure suppone sperimentatori dei fatti naturali. </s>

<s>Ma nes&shy;<lb/>suno, dice il Barone di Verulamio, ha saputo fin qui sperimentare <lb/>e osservare, e se qualcuno vi s'&egrave; provato mai, avendo sbagliato <lb/>via, non pu&ograve; assicurarsi di riuscire a trovar qualche cosa di nuovo. </s></p><p type="main">

<s>Niccol&ograve; Copernico ha contemplato da filosofo il cielo, ma a noi <lb/>giova meglio di contemplarlo alla maniera del volgo, senza punto <pb xlink:href="020/01/138.jpg" pagenum="119"/>badare a quel che se ne dicano gli astronomi, o a quel che s'in&shy;<lb/>segni nelle scuole, che senza ragione, bene spesso, godono di con&shy;<lb/>tradire al senso con sofisticherie (Nov. </s>

<s>Org. </s>

<s>Lib. </s>

<s>II, &sect; 36). Altrove, <lb/>nel IV libro <emph type="italics"/>De augmentis scientiarum,<emph.end type="italics"/> dice che la sentenza coper&shy;<lb/>nicana, come non repugnante alle apparenze, non si pu&ograve; confutar <lb/>co'principii astronomici, ma si pu&ograve; bene coi principii della Filosofia <lb/>naturale <emph type="italics"/>recte positis<emph.end type="italics"/> (Lugani 1763, pag. </s>

<s>235). Si capisce bene che <lb/>i principii della Filosofia naturale invocati qui erano quegli stessi <lb/>de'peripatetici contradittori del Copernico e del Galilei. </s></p><p type="main">

<s>Il qual Galilei, prosegue a dire il Cancellier d'Inghilterra, ha <lb/>inventato un nuovo maraviglioso strumento, con cui &egrave; ruscito a <lb/>scoprir ne'cieli cose non pi&ugrave; vedute, ma chi potrebbe con sicurezza <lb/>prestargli fede? </s>

<s>Il mio sospetto nasce principalmente dal veder <lb/>poche osservazioni, mentre se ne sarebbero potute far moltissime <lb/>in una innumerevole variet&agrave; di oggetti (Nov. </s>

<s>Org. </s>

<s>Lib. </s>

<s>II, &sect; 39). <lb/>In questo stesso errore dice di essere incorso il connazionale suo <lb/>Guglielmo Gilbert, il quale, da ripetute esperienze sopra un soggetto <lb/>solo, volle dedurne una filosofia generale, sull'esempio di Aristotile, <lb/>e perci&ograve; una filosofia fantastica e povera, qual &egrave; quella che deriva&shy;<lb/>rono i chimici dai loro alambicchi (ivi, Lib. </s>

<s>I, &sect; 44). Egli, il Gilbert, <lb/>dur&ograve; tanta fatica e us&ograve; tanta diligenza per venire a capo di uno <lb/>sperimento particolare intorno alla calamita, come gli alchimisti <lb/>intorno all'oro (ivi, &sect; 70). </s></p><p type="main">

<s>Ne &egrave; solo il male che nessuno fin qui abbia seguito il retto <lb/>filosofare, il peggio si &egrave; che Bacone prevede e presagisce che, anco <lb/>quando gli uomini eccitati da'suoi impulsi, si daranno seriamente <lb/>all'esperienza, rinunziando alle sofistiche dottrine, nonostante, per <lb/>la fretta e ansiet&agrave; del loro intelletto voglioso di volare alle gene&shy;<lb/>ralit&agrave;, le loro filosofie soggiaceranno inevitabilmente a grave pe&shy;<lb/>ricolo (ivi, &sect; 74). Per Bacone insomma, non solo non ci &egrave; stato mai <lb/>scienza e non ci &egrave;, ma prevede e presagisce che nemmen ci sar&agrave;. </s>

<s><lb/>Ci&ograve; che vuol dire per noi che il suo Regno non &egrave; e non &egrave; per <lb/>venire. </s></p><p type="main">

<s>Potrebbe esser per&ograve; che egli pretendesse di costituire il regno <lb/>della scienza col suo proprio intelletto, e perci&ograve; giova investigarne <lb/>le dovizie e mostrar quali e quante elle sono. </s></p><p type="main">

<s>Nel secondo libro del Nuovo Organo al &sect; 45 descrive per ve&shy;<lb/>rit&agrave; alcune poche esperienze, delle quali per&ograve; nessuna ha l'impronta <lb/>di originale, da quella infuori, forse, della incompressibilit&agrave; del&shy;<lb/>l'acqua rinchiusa dentro una sfera di metallo, che fortemente com-<pb xlink:href="020/01/139.jpg" pagenum="120"/>pressa da un torchio, deformata trasuda. </s>

<s>Delle altre esperienze, come <lb/>di quella dell'aria che estratta per succhiamento dall'uovo filosofico, <lb/>d&agrave; luogo a sottentrarvi spontaneamente l'acqua, gli esempii sono anti&shy;<lb/>chi, e risalgono al Cardano, anzi pi&ugrave; su, fino ad Herone di Alessandria. </s></p><p type="main">

<s>Rispetto alle varie forze sollecitanti la materia, non si puo la&shy;<lb/>sciar di notare quelle sottili osservazioni, che ricorrono in questo <lb/>stesso II libro al &sect; 25, relative alle propriet&agrave; che hanno l'acqua e <lb/>l'aria, ridotte in minime particelle, di attrarsi a vicenda; e l&agrave; dove <lb/>al &sect; 36 entra a parlar de'proietti, non &egrave; priva certo di sottilit&agrave; <lb/>l'esperienza citata delle lamine elastiche, per provar che la forza <lb/>d'impulso non vien dall'aria. </s>

<s>Ma quelle tante distinzioni di moti <lb/>ridotte in numero di diciannove, qui nel &sect; 48, sono il parto e il <lb/>portato di una filosofia, che non &egrave; punto varia dalla aristotelica. </s></p><p type="main">

<s>Del resto, per quanto &egrave; a noi noto, non ha il Verulamio, in <lb/>soggetto di scienze fisiche e sperimentali, pubblicato altro libro da <lb/>quello in fuori che s'intitola <emph type="italics"/>Historia naturalis et experimentalis <lb/>de ventis.<emph.end type="italics"/> Giacch&egrave; dunque egli ha raccolto dentro a queste pagine <lb/>tutto il frutto de'suoi metodi elaborati, il sapore attester&agrave; della <lb/>bont&agrave; dell'albero che gli ha prodotti. </s>

<s>N&egrave; la prima vista, per verit&agrave; <lb/>ci d&agrave; liete speranze. </s>

<s>Quelle distinzioni di distinzioni prolisse e <lb/>ignude, come di ramo che si divide, e suddivide poi in rami aridi <lb/>e brulli, con qualche ciuffo di foglie in sulle cime, ci assicurano <lb/>non per altro esser venuto l'Autore a sconfiggere Aristotile, che per <lb/>indossare le stesse sue divise. </s>

<s>Che poi egli ne abbia di pi&ugrave; imbe&shy;<lb/>vuti gli spiriti si parr&agrave; dall'esame delle dottrine. </s></p><p type="main">

<s>La causa generale dei venti, egli dice, &egrave; il moto del cielo, <lb/>che rapisce e mena seco in volta la sfera dell'aria. </s>

<s>Sotto i tropici, <lb/>per essere i circoli maggiori, il vento generale &egrave; pi&ugrave; manifesto, ma <lb/>non &egrave; per&ograve; che non dia luogo ai venti particolari. &ldquo; Si quis sit talis <lb/>ventus generalis ex ordine motus coeli, non adeo firmus est quin <lb/>ventis particularibus cedat. </s>

<s>Manifestior est autem intra tropicos <lb/>propter circulos quos conficit maiores &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1648, pa&shy;<lb/>gina 15). In fin qui per&ograve; non si sente nulla di nuovo, vi si ripete <lb/>la Fisica antica divinamente cantata dall'Alighieri, nella terzina 35 <lb/>e 36 del XXVIII del Purgatorio. </s></p><p type="main">

<s>Pi&ugrave; avanti per&ograve;, trattando dei venti particolari o delle <emph type="italics"/>brezze,<emph.end type="italics"/><lb/>aveva sentita la possibilit&agrave; che v'abbia anche parte a produrle il <lb/>calor del sole, <emph type="italics"/>quia calor omnem aerem dilatat.<emph.end type="italics"/> Proseguendo poi a <lb/>ragionare, questa tal possibilit&agrave; gli si converte in certezza, affer&shy;<lb/>mando che senza dubbio &egrave; il sole causa efficiente e primaria della <pb xlink:href="020/01/140.jpg" pagenum="121"/>massima parte dei venti, operando per via del calore sopra duplice <lb/>materia, <emph type="italics"/>corpus scilicet aeris et vapores sive exhalationes<emph.end type="italics"/> (ivi, pa&shy;<lb/>gina 53). Che sia veramente il calore efficace a produrre il vento <lb/>dice di averlo sperimentato in una torricella chiusa, dentro alla <lb/>quale ardeva un buon fuoco, osservando che girava un molinello <lb/>fatto di piume sospeso a un filo, e che usciva fuori con forza il <lb/>fiato da uno spiraglio. </s></p><p type="main">

<s>Che poi sia varia la materia de'venti, aria cio&egrave; e vapori, e che <lb/>da ci&ograve; si produca variet&agrave; di effetti, intende a provarlo pure col&shy;<lb/>l'esperienza, rinchiudendo nella medesima torricella, un vaso pieno <lb/>d'acqua bollente, che esala vapori in copia. </s>

<s>Dice di avere osservato <lb/>che il molinello girava ancora mosso dal fumo, per&ograve; pi&ugrave; languida&shy;<lb/>mente assai di quando ardeva il fuoco vivo, e l'esalazione spiritosa <lb/>era secca. </s>

<s>Ond'egli cos&igrave; conclude: &ldquo; Itaque excitationes motus in <lb/>ventis causa est praecipua superesoneratio aeris ex nova acces&shy;<lb/>sione aeris facti ex vaporibus &rdquo; (ivi, pag. </s>

<s>65). </s></p><p type="main">

<s>Che si pu&ograve; ora egli giudicare di questa teoria, se non che ad <lb/>essa manca un principio generale che l'informa, rimanendo, al <lb/>modo aristotelico, sminuzzata ne'fatti particolari? </s>

<s>Bacone insomma <lb/>non seppe sollevarsi a veder quel che chiarissimamente poi vide il <lb/>Torricelli, che cio&egrave; dai condensamenti e dalle dilatazioni dell'aria <lb/>prodotte dal variar dell'intensit&agrave; calorifica del sole, hanno, come <lb/>da causa generale semplice e unica, origine ogni sorta di venti. </s></p><p type="main">

<s>Il tesoro dunque del gran Cancelliere non par che sia troppo <lb/>dovizioso, almeno quanto a scienza sperimentale. </s>

<s>Che se si fosse <lb/>dovuta una tale scienza promuovere da lui solo, potremmo star si&shy;<lb/>curi che la non avrebbe fatto nemmeno un passo per uscir fuori <lb/>de'libri del Filosofo antico. </s>

<s>Molti che convengono in questo giudizio, <lb/>danno per&ograve; il merito all'Autor <emph type="italics"/>De augmentis<emph.end type="italics"/> d'aver profondamente <lb/>filosofato intorno alle ragioni de'progressi sperimentali. </s>

<s>N&egrave; ci&ograve; si <lb/>nega da noi, si vuol dir solo che spesso, in queste stesse filosofiche <lb/>speculazioni, manca quel giudizioso acume e quell'ampiezza di ve&shy;<lb/>dute, che qualificano i veri innovatori della scienza. </s>

<s>Si veda, per <lb/>esempio quel che nel cap. </s>

<s>IV del III libro dice delle cause finali. </s>

<s><lb/>Che queste, sostituendosi alle cause fisiche e reali, abbiano vera&shy;<lb/>mente indugiati i progressi della scienza, si comprende assai facil&shy;<lb/>mente e si consente da tutti. </s>

<s>Non si consente per&ograve; al Verulamio <lb/>il dir che, nella filosofia di Aristotile e di Platone, s'inculcano quelle <lb/>cause finali allo stesso modo, contentandosi di ammetter come sola <lb/>differenza una reit&agrave; maggiore nel discepolo che nel maestro. </s></p><pb xlink:href="020/01/141.jpg" pagenum="122"/><p type="main">

<s>Ma il vero si &egrave;, che le cause finali son parto legittimo ed esclu&shy;<lb/>sivo della filosofia aristotelica, di quella filosofia cio&egrave; che accomoda <lb/>la Natura ai cervelli. </s>

<s>Perch&egrave;, secondo il Cremonino, non possono <lb/>esistere i satelliti di Giove? </s>

<s>Perch&egrave; non s'intenderebbe altrimenti <lb/>quali potessero essere i loro influssi. </s>

<s>Perch&egrave; il canal toracico si <lb/>nega dal Riolano? </s>

<s>Perch&egrave; non s'intende come mai il chilo crudo <lb/>e non concotto nel fegato debba, per una via lunga, risalir su fino <lb/>alla vena cava ascendente, mentre pel fegato e per la cava discen&shy;<lb/>dente la via &egrave; tanto pi&ugrave; facile e pi&ugrave; spedita. </s></p><p type="main">

<s>La Filosofia di Platone, che ammetteva Dio legislatore della <lb/>Natura, non era punto favorevole, n&egrave; come vuol Bacone, inculcava <lb/>le cause finali, ma l&agrave; dove le cause fisiche riuscivano ignote, s'at&shy;<lb/>tribuivano gli effetti immediatamente a Dio stesso Prima Causa <lb/>universale. </s>

<s>Ora, se ben si osserva, &egrave; conforme ai placiti di questa <lb/>Filosofia il processo storico <emph type="italics"/>De augmentis scientiarum.<emph.end type="italics"/> Cos&igrave; per <lb/>esempio in fatto di Cosmoteoria, la scienza antica attribuiva il moto <lb/>circolare de'pianeti immediatamente alla mano di Dio, che gli so&shy;<lb/>stenta e gli mantiene ne'loro orbi. </s>

<s>Il Boulliaud dopo Galileo intro&shy;<lb/>dusse il moto naturale de'corpi cadenti, e il Borelli il principio <lb/>delle forze centrali, ma &egrave; sempre il dito di Dio che volge i moti <lb/>diretti in circolari, e determina a suo placito l'eccentricit&agrave; delle <lb/>orbite ellittiche. </s>

<s>Il Newt&ograve;n poi dimostra che quella eccentricit&agrave; &egrave; <lb/>determinata dal grado dell'intension delle forze attrattive e repul&shy;<lb/>sive. </s>

<s>Cos&igrave;, progredendo la scienza col sostituire via via la cause fisiche <lb/>e particolari, non si sent&igrave;, ai tempi del Filosofo inglese, bisogno di <lb/>ricorrere alla Causa prima per altro, che per ispiegiar l'origine <lb/>dell'attrazione universale. </s>

<s>Par che con simile processo la scienza <lb/>insegua e cacci dalla Natura Iddio, ma non fa in sostanza che ri&shy;<lb/>durlo sempre pi&ugrave; su nella Maest&agrave; della sua sede. </s></p><p type="main">

<s>Grande &egrave; dunque la differenza tra le due filosofie, che il Ve&shy;<lb/>rulamio accusa della medesima colpa, e il non avere avvertito questa <lb/>tal differenza, &egrave; uno di que'difetti notabili in un filosofo, il quale <lb/>vuole insegnare al mondo ignorante il modo d'investigar le vie, <lb/>che conducon la mente dell'uomo o a scoprir la verit&agrave; o a cader <lb/>nell'errore. </s></p><p type="main">

<s>Dalle cose fin qui discorse perci&ograve; si conclude che il vantato <lb/>Instauratore inglese non promosse veramente le scienze sperimen&shy;<lb/>tali, n&egrave; coll'esempio n&egrave; colle dottrine. </s>

<s>Ma non per questo si po&shy;<lb/>trebbe con giustizia asserire che i libri scritti da lui non avesser <lb/>nessuna efficacia, specie sulla mente de'suoi connazionali. </s>

<s>Il Boyle, <pb xlink:href="020/01/142.jpg" pagenum="123"/>l'Hook il Wren si sentirono venir l'impulso a filosofare dalla let&shy;<lb/>tura di que'libri, ma niente altro &egrave; che la loro facondia, la quale <lb/>gli commuove: &egrave; quella voce potente di un che grida nella solitu&shy;<lb/>dine: lasciate i sofismi e studiate la Natura. </s>

<s>Di questa efficacia in <lb/>fuori, che egli ebbe sui contemporanei e sui discendenti, Bacone &egrave; <lb/>un filosofo de'tempi passati imbevuto di quegli spiriti aristotelici, <lb/>che egli, sotto le forme di un razionalismo medio fra quello del <lb/>Campanella e del Patrizio, largamente diffonde in tutti i suoi libri. </s>

<s><lb/>All'albero perci&ograve; della scienza, per troppo lunga et&agrave; trascorso e <lb/>infiacchito, non solo egli non ha saputo trovare efficace rimedio da <lb/>ringiovanirlo, ma ne ha di pi&ugrave; esaurite le forze col moltiplicare le <lb/>sterili fronde sul ramo vecchio. </s>

<s>Sicch&egrave; non riman che l'opera sola <lb/>fatta da Galileo e dal Cartesio, l'azion de'quali che ora si vuol <lb/>mettere in vista de'nostri lettori, fa mutare scena alla rappresen&shy;<lb/>tazione di questo Dramma. </s></p><pb xlink:href="020/01/143.jpg" pagenum="124"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Nota I relativa a pag. </s>

<s>69 lin. </s>

<s>19.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Di questi problemi, ci piace qui di recarne uno per saggio ai nostri lettori, e ab&shy;<lb/>biamo scelto il seguente, a mostrar come si possa rendere pi&ugrave; compiuta la illustrazione <lb/>data nella prima delle <emph type="italics"/>Lettere astronomiche<emph.end type="italics"/> credute di Galileo, e pubblicate, da pa&shy;<lb/>gina 135-44, negli <emph type="italics"/>Studii sulla Divina Commedia<emph.end type="italics"/> da Ottavio Gigli (Firenze, Le Mon&shy;<lb/>nier, 1885). </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Problema di Astronomia dantesca:<emph.end type="italics"/><emph.end type="center"/><lb/>Si come quando i primi raggi vibra, <lb/>La dove il suo Fattore il sangue sparse <lb/>(Cadendo Ibero sotto l'alta libra). <lb/>E l'onde in Gange, da nona riarse; <lb/>Si stava il Sole; onde il giorno sen gia, <lb/>Quando l'Angel di Dio lieto ci apparse. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>(Purg.,<emph.end type="italics"/> C. XXVIII, t. </s>

<s>1, 2).<emph.end type="center"/></s></p><p type="main">

<s>Posto che, a muovere dall'Isole Fortunate, ora Canarie, la longitudine della fonte <lb/>dell'Ibero sia 12&deg; 30&prime;, e 16&deg; la longitudine della sua foce; posto che sia 66&deg; la longi&shy;<lb/>tudine di Gerusalemme, e 148&deg; 30&prime; quella della foce pi&ugrave; orientale del Gange; si domanda <lb/><emph type="italics"/>come stava,<emph.end type="italics"/> secondo la descrizione fattane dal Poeta, il sole rispetto all'orizzonte del <lb/>Purgatorio o di Gerusalemme? </s></p><p type="main">

<s>Rappresenti il gran cerchio AEDF (fig. </s>

<s>I) l'Equatore celeste, e il piccolo cerchio <lb/><figure id="id.020.01.143.1.jpg" xlink:href="020/01/143/1.jpg"/></s></p><p type="caption">

<s>Fig. </s>

<s>I<lb/>HSGT concentrico a lui, un cerchio massimo della Terra. </s>

<s><lb/>Sia P il polo, PL il meridiano principale delle Isole Fortu&shy;<lb/>nate, PM il meridiano, che passa sull'Ibero e per la Libbra, <lb/>PN quello che passa sulla foce del Gange, PO il meridiano del <lb/>sole, nel tempo a cui si riferisce l'osservazione, e AHD il <lb/>meridiano comune al Purgatorio e a Gerusalemme. </s>

<s>Si cerca <lb/>l'angolo FPO=FDE&mdash;EDO=180&deg;&mdash;EDO. </s>

<s>Ma EDO= <lb/>EL+LM+MO perci&ograve;, a risolvere il problema, conviene <lb/>cercare i tre angoli che compongono il secondo membro di <lb/>questa equazione: EL=90&deg;&mdash;LD=90&mdash;66=24. LM <lb/>potrebbe tanto farsi uguale a 12&deg; 30&prime;, quanto a 16&deg; non di&shy;<lb/>cendo nulla il Poeta che accenni, dell'Ibero, o alla sorgente o alla foce. </s>

<s>Ma osservando <lb/>anche noi con Galileo (ivi, pag. </s>

<s>135) che <emph type="italics"/>caggiono propriamente i fiumi dalle loro <lb/>fonti,<emph.end type="italics"/> crediamo di poter fare LM=12&deg;, 30&prime;, MO, dall'altra parte, &egrave; uguale a 360&deg;&mdash;OAM, <lb/>e quest'angolo OAM sarebbe l'ascensione retta di un punto M, o di una delle stelle, in <lb/>cui si configura la Libbra. </s>

<s>Qui sembra anche a noi con Galileo d'avere un indizio pi&ugrave; <lb/>certo, imperocch&egrave;, dando il Poeta l'epiteto di <emph type="italics"/>alta<emph.end type="italics"/> alla Libbra, par chiaro volere accen&shy;<lb/>nare alla lance di lei pi&ugrave; settentrionale, e di questa lance pi&ugrave; settentrionale, alla stella <lb/>pi&ugrave; cospicua. </s>

<s>Nelle <emph type="italics"/>Tavole alfonsine,<emph.end type="italics"/> delle quali si dovette anche Dante servire, si re&shy;<lb/>gistra, del bacino settentrionale della Libbra, una stella di seconda grandezza, la quale <pb xlink:href="020/01/144.jpg" pagenum="125"/>aveva allora 221&deg; di longitudine e di latitudine 8&deg; 30&prime;. </s>

<s>A questa stella par doversi riferire <lb/>il meridiano, al quale accenna il Poeta. </s>

<s>Ond'&egrave; che posto <foreign lang="greek">i</foreign>=221, <foreign lang="greek">l</foreign>=8&deg;, 30&prime;, <foreign lang="greek">e</foreign>=23&deg;, 30&prime;, <lb/>si potr&agrave; colle ordinarie formule date dai <emph type="italics"/>Formularii<emph.end type="italics"/> di Trigonometria cos.P=cos.<foreign lang="greek">*i</foreign>.cos.<foreign lang="greek">l</foreign>, <lb/>tang <foreign lang="greek">f</foreign>=(tang.<foreign lang="greek">l</foreign>)/(sen <foreign lang="greek">i</foreign>), tang.<foreign lang="greek">a</foreign>=tang.<foreign lang="greek">f</foreign> cos (<foreign lang="greek">e</foreign>+<foreign lang="greek">f</foreign>), calcolare OAM=<foreign lang="greek">a</foreign>, che, eseguiti con&shy;<lb/>venientemente i calcoli, si trover&agrave; uguale a 221&deg;, 13&prime;. </s>

<s>Perci&ograve; avremo MO=138&deg; 47&prime;, <lb/>EDO=175&deg; 17&prime;, FO=4&deg; 43&prime;. </s>

<s>Onde il sole, quando l'Angel di Dio apparse ai Poeti, <lb/><emph type="italics"/>stava<emph.end type="italics"/> cos&igrave;: era alto cio&egrave; 4&deg; 43&prime; sull'orizzonte di Gerusalemme. </s></p><p type="main">

<s>Sarebbe cos&igrave; tutto bene aggiustato, per modo che l'interpretazione astronomica, la <lb/>quale abbiamo data sulle orme di Galileo, risponderebbe a tutte le parti della descrizione <lb/>fatta nelle due sopra citate terzine dal Poeta, imperocch&egrave; PN, meridiano che passa per <lb/>la foce del Gange non sarebbe lontano da PO, meridiano del Sole, che di soli 2&deg; 47&prime;; <lb/>onde s'accomoda, anco per questa parte, l'interpretazione astronomica a quel che sog&shy;<lb/>giunge alla sua descrizione il Poeta: <emph type="italics"/>E l'onde in Gange da nona riarse.<emph.end type="italics"/></s></p><p type="main">

<s>Se non che ci si fanno qui incontro alcune difficolt&agrave;. </s>

<s>Come mai poteva dire il Poeta <lb/>che il sole vibrava i primi raggi sui colli di Gerusalemme, essendo gi&agrave; alto pi&ugrave; di quattro <lb/>gradi e mezzo sull'orizzonte? </s>

<s>Di pi&ugrave;, noi abbiamo supposto con Galileo che fosse il sole <lb/>nel punto preciso dell'Equinozio di Primavera. </s>

<s>Ma &egrave; ci&ograve; contrario all'opinione di tutti <lb/>quanti i commentatori, i quali dicono che a tempo dell'Equinozio incomincia la rappre&shy;<lb/>sentazione del Dramma, e che la scena, la quale qui si dipinge, dovette seguire almeno <lb/>tre o quattro giorni dopo, nel qual tempo si doveva il sole esser dilungato da quel punto <lb/>equinoziale, in longitudine, tre o quattro gradi. </s></p><p type="main">

<s>Le difficolt&agrave; a noi sembrano giuste, ond'&egrave; che proporremmo di riformare l'inter&shy;<lb/>pretazione galileiana al modo seguente. </s>

<s>Osservando che anche Gerusalemme &egrave; situata in <lb/>altura, e che &egrave; contrapposta, nella fantasia del Poeta, alla montagna altissima del Purga&shy;<lb/>torio, ci sembra assai ragionevole che, com'egli mise in conto una notevole depressione <lb/>dell'orizzonte per l'una, cos&igrave; qualche depressione dovesse pure mettere in conto per <lb/>l'altra. </s>

<s>Immaginiamo perci&ograve; che sulla vetta delle pi&ugrave; alte torri di Gerusalemme inco&shy;<lb/>minciasse il sole a vibrare i suoi raggi, quand'era ancora di 1&deg; 17&prime; sotto all'orizzonte <lb/>razionale. </s>

<s>In questa ipotesi, ritenute tutte le altre parti della dimostrazione, si potrebbe <lb/>dare al sole sei gradi di ascensione retta, i quali, calcolando la formula tang. </s>

<s>c=. . . <lb/>tang. </s>

<s>a cos. </s>

<s>B, si trovano corrispondere a 4&deg; 9&prime; di longitudine. </s>

<s>Cos&igrave; rimarrebbero, come <lb/>sopra, tutte le partt aggiustate, n&egrave; sarebbe a dubitar che non si potesse, con quella posizione <lb/>del sole, accordar l'effetto del riardere l'onde del Gange, perch&egrave; l'ora di nona, com&shy;<lb/>prendendo le prime sei ore avanti mezzogiorno, comprende certamente anco quella, nella <lb/>quale si trova il sole sei gradi di distanza dal meridiano, e potea perci&ograve; ben dire il Poeta <lb/>che in quella posizione del sole le onde del Gange eran riarse dall'ore di nona. </s></p><p type="main">

<s>Se l'aver concordate cos&igrave; tutte quante le parti astronomiche e geografiche della de&shy;<lb/>scrizione dantesca, ci potesse assicurare della verit&agrave; della nostra interpetrazione, avremmo <lb/>di qui un dato certo a poter inferire il mese e il giorno preciso, nel quale immagina il <lb/>Poeta essersi rappresentata la scena. </s>

<s>Poniamo, infatti, secondo la pi&ugrave; probabile e pi&ugrave; co&shy;<lb/>mune opinione, che fosse il 1300 l'anno della visione dantesca. </s>

<s>Quando l'Angel di Dio <lb/>apparse ai Poeti, abbiam veduto che il sole dovea avere 4&deg; 9&prime; in longitudine, e dovevan <lb/>perci&ograve; esser trascorsi pi&ugrave; di quattro giorni, da quello in cui entra il sole nel punto di <lb/>Primavera. </s>

<s>Se, come a noi, cos&igrave; ai tempi di Dante, fosse entrata la Primavera il d&igrave; 21 di <lb/>Marzo, &egrave; certo che la scena descritta nel XXVII del Purgatorio, si sarebbe rappresentata <lb/>la sera del d&igrave; 25 di quello stesso mese. </s>

<s>Ma per que'disordini cronologici, che hanno la <lb/>loro origine in quella parte frammentaria de'giorni, ne'quali compiesi la tropica rivolu-<pb xlink:href="020/01/145.jpg" pagenum="126"/>zione del sole, disordini non potuti evitare dagli emendamenti giuliani; nel 1300 doveva <lb/>l'Equinozio di Primavera precedere il d&igrave; 21 di Marzo di alquanti giorni. </s>

<s>Il numero poi <lb/>preciso di questi giorni si trova assai facilmente osservando che, dall'anno 325 in cui <lb/>l'Equinozio di Primavera cadde il d&igrave; 21 Marzo, al 1300, decorsero 975 giorni, ne'quali <lb/>s'aggiunsero, secondo il calendario giuliano, 243 bisestili. </s>

<s>Ma secondo la riforma nuova <lb/>gregoriana i bisestili da aggiungere dovevano essere non 975/4, ma (975X125)/516, ossia 236; <lb/>ond'&egrave; che nel 1300 l'Equinozio di Primavera precedeva il d&igrave; 21 di 7 giorni, e che &egrave; <lb/>lo stesso, avveniva quell'Equinozio il d&igrave; 14 di Marzo, e perci&ograve; la scena, che Dante l&igrave; <lb/>rappresenta, si dovrebbe precisamente riferire alla sera del d&igrave; 18 di Marzo. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nota II relativa a pag. </s>

<s>82 lin. </s>

<s>37.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Perch&egrave; abbiano i lettori qualche saggio degli errori, in che incorse il Mollien per <lb/>ragion della lingua, citeremo il seguente passo, prima nell'ortografia originale, poi ridetto <lb/>da noi all'ortografia moderna, poi dallo stessio Mollien tradotto in francese. </s></p><p type="main">

<s>&ldquo; eglie . un pozo . il quale . a nel suo fondo unotro . di tal . grandezza e intal <lb/>modo . situato . che disotto . e dalato . non sitrova pi&ugrave; . duno dito . di grossezza dacqua . <lb/>imodo chellacqua che si posa sul fondo pesa . libbre 100 . e quella chessiposa . sopra . <lb/>della baga . pesa libbre 10000 . se cosie la baga scopiera avendo soprasse . tanto peso . <lb/>esequel peso . nolla prieme . chello sostiene . esseppure esso fussi sostenuto . perche <lb/>arebbe appassare . l'otro sopra . l'acqua . esseppure lacqua charicha . sopra . il suo . <lb/>fondo . perche non patisce passione unomo (<emph type="italics"/>menomo<emph.end type="italics"/> intende il Mollien!) passione . di <lb/>peso . stando . sopra il suo fondo . adunque sella ba sostiene lacqua la baga . toglie il <lb/>peso . dessa acqua . alfondo . del pozzo &rdquo;. </s></p><p type="main">

<s>&ldquo; Egli &egrave; un pozzo, il quale ha nel suo fondo un otro di tal grandezza e in tal <lb/>modo situato, che di sotto e da lato non si trova pi&ugrave; di un dito di grossezza d'acqua, <lb/>in modo che l'acqua che riposa sul fondo pesa libbre 100, e quella che si posa sopra <lb/>della baga pesa libbre 10,000. Se cos&igrave; &egrave; la baga scoppier&agrave; avendo sopra s&egrave; tanto peso. </s>

<s><lb/>E se quel peso non la preme, che lo sostiene? </s>

<s>E se pure esso fussi sostenuto, perch&egrave; <lb/>avrebbe a passare l'otro sopra l'acqua? </s>

<s>E se pure l'acqua carica sopra il suo fondo, per&shy;<lb/>ch&egrave; non patisce passione un uomo, passione di peso, stando sopra il suo fondo? </s>

<s>Adunque <lb/>se la baga sostiene l'acqua, la baga toglie il peso di essa acqua al fondo del pozzo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il y &egrave; un puits, le qual a dans sons fonds une outre, de telle grandeur et situee <lb/>di telle fac<gap/>n, que dessous et sur les cotes, ne se trouve pas plus d'un doigt d'<gap/>paisseur <lb/>d'eau. </s>

<s>l'<emph type="italics"/>eau<emph.end type="italics"/> en sorte que l'eau qui se pose sur le fond p&egrave;se 100 livres et celle qui pose <lb/>au-dessus de l'outre p&egrave;se 10,000 livres; s'il en est ainsi, l'outre celetera. </s>

<s>en ayant sur <lb/>elle <emph type="italics"/>cette<emph.end type="italics"/> un tel poids, et si ce poids ne la presse pas qu'elle soutient, et si aussi il etait <lb/>soutenou, parce que l'outre avrait a passer au-dessus de l'eau, et aussi si l'eau charge <lb/>(p&egrave;se) sur son fond, parce qu'elle ne supportarien, ne supporte qu'un moindre poids, <lb/>&egrave;tant sur son fond. </s>

<s>Donc, si l'outre soutient l'eau, l'outre &ocirc;te le poids de cette eau au <lb/>fond du puits. </s>

<s>&rdquo; (Manos. </s>

<s>A fol. </s>

<s>25 verso). </s></p><pb xlink:href="020/01/146.jpg"/><p type="main">

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

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

<s>I. </s>

<s>Di Galileo Galilei e dell'indole propria della sua nuova Instaurazione scientifica. </s>

<s>&mdash; II. </s>

<s>Si giustifi&shy;<lb/>cano le cose asserite nel paragrafo precedente. </s>

<s>&mdash; III. </s>

<s>Dei benefizi che derivarono alle scienze <lb/>sperimentali dalla nuova Instaurazione galileiana. </s>

<s>&mdash; IV. </s>

<s>Renato Cartesio. </s>

<s>&mdash; V. De'primi e <lb/>principali discepoli di Galileo. </s>

<s>&mdash; VI. </s>

<s>Della grande esperienza torricelliana dell'argento vivo, e <lb/>come per lei si diffondessero, d'Italia in tutta Europa, l'amore e gli esercizi dell'arte speri&shy;<lb/>mentale. </s>

<s>&mdash; VII. </s>

<s>Di Evangelista Torricelli e di Vincenzio Viviani, e di ci&ograve; che operassero nelle <lb/>Instituzioni della sperimentale Accademia Medicea. </s>

<s>&mdash; VIII. </s>

<s>Del primo periodo della Fiorentina <lb/>Accademia del Cimento. </s>

<s>&mdash; IX. </s>

<s>Del secondo periodo della Fiorentina Accademia del Cimento. </s>

<s>&mdash; <lb/>X. </s>

<s>Delle principali Accademie private istituite in Italia a imitazione di quella del Cimento; del <lb/>felice esito dell'Istituzione Medicea, nonostante le rivalit&agrave; con gli stranieri, i dissensi fra i Socii, <lb/>le opposizioni dei Peripatetici. </s></p><p type="main">

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

<s>Egli &egrave; verissimo che tutte le cose del mondo son soggette a <lb/>invecchiare, e invecchiando andare irreparabilmente alla morte. </s>

<s>Non <lb/>vi &egrave; perci&ograve; altro rimedio per loro, che quello di tentare di ringio&shy;<lb/>vanirle e, il miglior modo a far ci&ograve;, trattandosi d'istituzioni umane, <lb/>disse argutamente il Machiavelli che consisteva nel ritirarle verso <lb/>i loro principii. </s>

<s>L'esempio che s'adduceva dianzi degli alberi tra&shy;<lb/>scorsi, i quali si ringiovaniscono recidendo i rami e talvolta lo stesso <lb/>tronco infino al piede, commenta le dottrine del Segretario fioren&shy;<lb/>tino, secondo le quali un principato, che va a dissolversi, ringio&shy;<lb/>vanisce spesso per via di una tirannide. </s></p><p type="main">

<s>Per una tirannide o per una conquista, in quella che &egrave; delle <lb/>nobilissime fra le istituzioni umane, si qualific&ograve; da noi sopra l'opera <pb xlink:href="020/01/147.jpg" pagenum="128"/>di Galileo, il quale volle scrivere in una cocca del suo vessillo queste <lb/>parole: <emph type="italics"/>Molti si pregiano di aver molte autorit&agrave; d'uomini per con&shy;<lb/>fermazione delle loro opinioni, ed io vorrei essere stato il PRIMO <lb/>e il SOLO a trovarle.<emph.end type="italics"/> Abbiamo detto in una cocca, perch&egrave; spie&shy;<lb/>gatamente in campo non sarebbero state lette tali parole dagli occhi <lb/>abbagliati de'riguardanti, se gli editori non le avessero accolte in <lb/>una nota apposta a pi&egrave; di pagina (Alb. </s>

<s>I, 440). Ma che giova l'espres&shy;<lb/>sione delle parole, se d'ogni parte si sente alitar quello spirito di <lb/>conquista proprio di un che ha fermo oramai di voler essere in <lb/>tutto il <emph type="italics"/>primo<emph.end type="italics"/> e il <emph type="italics"/>solo?<emph.end type="italics"/></s></p><p type="main">

<s>I fatti che saranno candidamente narrati, nelle varie parti di <lb/>questa Storia, mostrano que'propositi fermi coraggiosamente man&shy;<lb/>dati ad effetto, ma perch&egrave; troppo importa a noi di rappresentar fin <lb/>d'ora al giudizio dei nostri lettori l'opera galileiana sotto l'aspetto <lb/>di una conquista, e troppo ci preme di persuader fin d'ora i ritrosi <lb/>esser quello il vero aspetto, sotto cui s'appresenta la nuova instau&shy;<lb/>razione scientifica, crederemmo di dover esser notati d'imprudenza, <lb/>asserendo cose tanto lontane dalla comune opinione, senza preva&shy;<lb/>lerci di qualche discorso da servirsene come di prova. </s></p><p type="main">

<s>Bacone scrive in un luogo del suo libro <emph type="italics"/>De augmentis scien&shy;<lb/>tiarum<emph.end type="italics"/> che non parve ad Aristotile potersi bene assicurare del <lb/>Regno, <emph type="italics"/>nisi, more Ottomannorum, fratres suos omnes contruci&shy;<lb/>dasset<emph.end type="italics"/> (Lugani 1763, Part. </s>

<s>I, pag. </s>

<s>211), e son, secondo il Verulamio, <lb/>de'pi&ugrave; illustri fra que'trucidati fratelli, Pitagora, Filolao, Xenofane, <lb/>Anassagora, Parmenide, Leucippo, Democrito. </s>

<s>Aveva cos&igrave; Galileo, <lb/>della Tirannide che meditava d'&igrave;nstaurare, nello stesso Aristotile, <lb/>un esempio di tanto felice riuscita, che in ogni modo conveniva <lb/>imitare. </s></p><p type="main">

<s>Platone e Archimede son tanto lontani e tanto innocui, che <lb/>non gli turbano i sonni. </s>

<s>Ma glieli turba bene Ticone, glieli turba <lb/>il Keplero, i quali ambedue, a voler regnar solo, bisogna contru&shy;<lb/>cidare. </s>

<s>E bench&egrave; non si convenga, n&egrave; sia espediente tenere il modo <lb/>degli Ottomanni, son dirette pure a trapassare il cuore, colle loro <lb/>acute punte, e a trafigger Ticone quelle parole di Galileo, nelle <lb/>quali scrive del grande Astronomo danese, che calcol&ograve; le Tavole <lb/>Rodolfine, senza punto intender n&egrave; l'Almagesto di Tolomeo n&egrave; le <lb/>Rivoluzioni del Copernico, e che non sapeva neanco i primi ele&shy;<lb/>menti di Geometria (Alb. </s>

<s>VI, 329). Che se egli, e il suo seguace e <lb/>ammiratore Keplero, credessero di toglierli di mano lo scettro, non <lb/>gli fanno spavento que'due <emph type="italics"/>Primati:<emph.end type="italics"/> egli gli assicura d'aver tanto <pb xlink:href="020/01/148.jpg" pagenum="129"/>valore da sentirsi crescere il coraggio a seguitar contro a loro la <lb/>intrapresa conquista (ivi, pag. </s>

<s>310). </s></p><p type="main">

<s>Ma il Keplero, per verit&agrave;, era uno di quei giganti da non ce&shy;<lb/>dere al primo colpo, per cui, meglio che il ferro tagliente e nudo, <lb/>conobbe Galileo che avrebbe servito bene il veleno confettato con <lb/>arte per toglierli l'amaro. </s>

<s>Una fra le tante di cos&igrave; fatte confezioni <lb/><figure id="id.020.01.148.1.jpg" xlink:href="020/01/148/1.jpg"/><lb/>&egrave; quella che ha nell'ultimo Dialogo dei Due Massimi Sistemi, dove <lb/>l'influenze della Luna sulla marea, sagacemente indovinate dal&shy;<lb/>l'Alemanno, <emph type="italics"/>ingegno libero e acuto,<emph.end type="italics"/> sono annoverate fra le altre <lb/><emph type="italics"/>fanciullezze<emph.end type="italics"/> (Alb. </s>

<s>I, 499). E perch&egrave;, anco le confezioni pi&ugrave; avvele&shy;<lb/>nate, quello era tale stomaco da digerirle, Galileo si risolv&egrave; di esi&shy;<lb/>liar quell'ombra paurosa da'suoi confini, dichiarando di non aver <pb xlink:href="020/01/149.jpg" pagenum="130"/>nulla a che rivedere con lui. </s>

<s>Che se talvolta s'incontra in qualche <lb/>concetto simile, afferma esser ci&ograve; tanto avvenuto di rado, da non <lb/>si verificare di uno in cento de'suoi pensieri (Alb. </s>

<s>VII, 56). </s></p><p type="main">

<s>Quell'esilio, dall'altra parte, &egrave; decretato con editto irrevoca&shy;<lb/>bile. </s>

<s>L'Autore del Commentario sulla stella di Marte, dimostra co&shy;<lb/>me cosa di fatto, che le orbite dei pianeti sono ellittiche. </s>

<s>Ma Ga&shy;<lb/>lileo non si rimuove dalla platonica perfezione delle orbite circolari. </s>

<s><lb/>L'Autore dei Paralipomeni a Vitellione, dimostra ad evidenza, per, <lb/>ci&ograve; che si sperimenta nella camera oscura, che le immagini si di&shy;<lb/>pingono rovesciate sulla retina, ma Galileo persiste nelle viete gale&shy;<lb/>niche dottrine, a seconda delle quali il luogo, dove si rappresentan <lb/>diritte le immagini, &egrave; il centro della pupilla, ossia il cristallino. </s>

<s><lb/>L'Autore della <emph type="italics"/>Diottrica<emph.end type="italics"/> aveva divisate le leggi del rifrangersi i <lb/>raggi luminosi nelle lenti concave e nelle convesse, e s'era, per <lb/>teoria, incontrato nella scoperta del canocchiale astronomico, ma <lb/>Galileo dice al Tarde che quel Trattatello &egrave; cos&igrave; oscuro, da non <lb/>restarne sodisfatto nemmeno l'Autore stesso. </s></p><p type="main">

<s>Che il Kepler non tutto abbia dimostrato e concluso con chia&shy;<lb/>rezza, potrebbe anco esser vero. </s>

<s>Ma vero certamente non &egrave; quel che <lb/>Galileo stesso soggiungeva non aver nel 1614, quand'ebbe quel col&shy;<lb/>loquio col Tarde, nessuno ancora scritto della teoria del canocchiale. </s>

<s><lb/>Ne aveva gi&agrave; scritto il De Dominis, il Trattato del quale gli fu spe&shy;<lb/>dito a Firenze dal Sagredo (Alb. </s>

<s>Supplem. </s>

<s>pag. </s>

<s>58), e ne aveva in <lb/>certo modo scritto anco il Maurolico, bench&egrave; non trattasse propria&shy;<lb/>mente delle lenti composte nel canocchiale, ma della diottrica delle <lb/>lenti separate, in quel libretto postumo che vide, nel 1611, la luce <lb/>insiem con quello del De Dominis e del Keplero. </s></p><p type="main">

<s>L'esilio dunque, a quel che pare, &egrave; bandito contro di tutti <lb/>senza eccezione, e basta legger le Opere di Galileo per vederne <lb/>eseguito il decreto. </s>

<s>Egli non ha, e non riconosce maestro: nessuno <lb/>dee venirgli innanzi a dir che egli abbia scoperto qualche cosa di <lb/>nuovo: tutte le nuove scoperte vuole averle fatte da s&egrave;, il primo <lb/>e il solo. </s>

<s>Gli si cita dal Sarsi il Cardano e il Telesio: quel che <lb/>abbiano scritto, risponde, il Cardano e il Telesio, io non l'ho veduto <lb/>(Alb. </s>

<s>IV, 178). Non ha veduto o fa vista di non aver veduto il Tar&shy;<lb/>taglia, che fu de'primi a notare gli errori meccanici di Aristotile, <lb/>e a porre i fondamenti alla teoria e alla pratica de'proietti, non <lb/>ha veduto il Fracastoro, che al corso obliquo del sole applicava il <lb/>teorema della composizione dei moti. </s></p><p type="main">

<s>Lorenzo Crasso fra gli Elogi degli uomini letterati raccolse an-<pb xlink:href="020/01/150.jpg" pagenum="131"/>che quello di Galileo, e ce lo rappresenta timido in dar fuori i suoi <lb/>sentimenti circa la Filosofia Naturale, i quali vuol che egli cavasse <lb/>da Celio Calcagnini e dal Patrizio. </s>

<s>Michelangiolo Ricci, l'amico e <lb/>il Discepolo prediletto del Torricelli, e il consultore dell'Accademia <lb/>del Cimento, in una lettera al principe Leopoldo dei Medici, rim&shy;<lb/>provera l'Autore di quegli Elogi per aver taciuto di annoverare <lb/>fra'maestri di Galileo il Benedetti, <emph type="italics"/>che gli apr&igrave; la strada pi&ugrave; che <lb/>ogni altro e forse fu solo a lui scorta nel suo filosofare, come avr&agrave; <lb/>ben notato V. A. paragonando i concetti dell'uno e dell'altro che <lb/>sono tanto conformi.<emph.end type="italics"/> (MSS. Gal. </s>

<s>Cim. </s>

<s>XVIII, 359). </s></p><p type="main">

<s>I nostri lettori, i quali hanno passato in esame con noi, di so&shy;<lb/>pra, il libro delle Speculazioni del Fisico veneziano, sentono la ve&shy;<lb/>rit&agrave; del giudizio del Ricci, e dall'altra parte chi collaziona le parole <lb/>scritte da Galileo, in sul principio della sua Lettera al Mazzoni <lb/>(Alb. </s>

<s>II, 1), con quel che il Mazzoni stesso dice nel Cap. </s>

<s>XVIII, <lb/>de'<emph type="italics"/>Preludi alla Filosofia di Platone e di Aristotile,<emph.end type="italics"/> da pag. </s>

<s>187-95 <lb/>dell'edizion di Venezia 1597; rileva chiaramente che in Pisa i due <lb/>professori conferivano insieme sulle Questioni Meccaniche del Be&shy;<lb/>nedetti, intorno alle quali il giovane Galileo s'esercit&ograve; tanto studio&shy;<lb/>samente, che ne compose quel Trattato informe <emph type="italics"/>De motu<emph.end type="italics"/> dato ora <lb/>che &egrave; poco alla luce da pag. </s>

<s>251-419 del volume primo dell'edizion <lb/>Nazionale (Firenze 1890). Eppure, bench&egrave; Michelangiolo Ricci, e, <lb/>che pi&ugrave; conta, i fatti attestino che Galileo bevve cos&igrave; largamente al <lb/>libro delle Speculazioni, non &egrave; possibile il trovare in nessuna delle <lb/>Scritture galileiane, o edite o inedite o pubbliche o familiari, ricor&shy;<lb/>dato mai o almeno accennato al nome di Giovan Battista Benedetti. </s></p><p type="main">

<s>Solenne maestro in Idrostatica, poco prima che Galileo dasse <lb/>opera alle <emph type="italics"/>Galleggianti,<emph.end type="italics"/> era dalla lontana Bruges apparito Simeone <lb/>Stevino, un'altra di quelle ombre paurose che, a voler regnar solo, <lb/>o bisognava contrucidare, o in qualche modo esiliare dai proprii <lb/>confini. </s>

<s>Or avvenne che codesto bandito straniero, allacciato quasi <lb/>alla coda di un Discorso accademico letto in Roma da Giovanni <lb/>Bardi, comparisse al cospetto di Galileo. </s>

<s>Quel Discorso &egrave; inti&shy;<lb/>tolato <emph type="italics"/>Eorum quae vehuntur in aquis Experimenta<emph.end type="italics"/> (Targioni, Ag&shy;<lb/>grandim. </s>

<s>T. II, P. I, pag. </s>

<s>2) e si termina dall'Autore coll'aggiungervi <lb/>quel curioso paradosso, dimostrato dallo Stevino ne'suoi Elementi <lb/>d'Idrostatica, di un vaso cilindrico pieno d'acqua che, sollevato in <lb/>alto sotto un cilindro solido fisso nel muro, in modo che entri dentro <lb/>a quello di sotto, scacciandone via l'acqua, da rimanerne quasi vuoto; <lb/>pesa nonostante sulla stadera, allo stesso modo che quando era pieno. <pb xlink:href="020/01/151.jpg" pagenum="132"/>&mdash; Quale sciocchezza sarebbe a lasciar questa perla cos&igrave; preziosa ad&shy;<lb/>addosso a questo straniero? </s>

<s>Facciamola nostra, pens&ograve; Galileo, e poi <lb/>rimandiamolo addietro. </s>

<s>&mdash; Chi legge la Lettera a Tolomeo Nozzolini <lb/>(Alb. </s>

<s>XII, 112) ritrova questo appropriamento fatto con s&igrave; maravi&shy;<lb/>gliosa destrezza, che la poca facondia di qualunque oratore baste&shy;<lb/>rebbe a rimandare il colpevole assoluto. </s>

<s>N&egrave; minor destrezza, per <lb/>non moltiplicare in esempi, us&ograve; nel III Dialogo de'Due Massimi Si&shy;<lb/>stemi, in appropriarsi l'osservazione dei varii dilatamenti della pu&shy;<lb/>pilla, al variar dell'intensit&agrave; luminosa. (Alb. </s>

<s>I, 394). </s></p><p type="main">

<s>In un altro Autore cos&igrave; fatte destrezze di mano passerebbero <lb/>inosservate, ma in Galileo rivelano l'esecuzione di un tenace pro&shy;<lb/>posito, qual era di voler essere in qualunque modo o di apparire <lb/>in tutto il primo e il solo. </s>

<s>Da questo stesso genio veniva frugato <lb/>a moltissime occasioni, quando si trattava di rivendicare scoperte, <lb/>che sarebbero state per giustizia appartenute agli odiati molesti <lb/>competitori. </s>

<s>Gli d&agrave; nuova il Sagredo di aver veduto in Padova, ap&shy;<lb/>presso il Santorio, uno strumento da misurar col compasso i gradi <lb/>del calore e del freddo. </s>

<s>Galileo risponde che quello strumento era <lb/>di sua propria invenzione. </s>

<s>Ma in effetto, col pretesto di rivendicare <lb/>a s&egrave; l'esperienza, intendeva usurparsi l'applicazione della esperienza <lb/>stessa, nella quale sola consisteva il merito dell'invenzione del ter&shy;<lb/>mometro. </s>

<s>Che anzi, sebbene egli dice di aver fatto quella tale espe&shy;<lb/>rienza in Padova nel 1606 (Alb. </s>

<s>VI), 313) gli si pu&ograve; rispondere che, <lb/>fin dal 1550, l'aveva pubblicata il Porta nel II Libro fra'quattro <lb/>della <emph type="italics"/>Magia,<emph.end type="italics"/> e nel 1601, nel III Libro degli Spiritali l'aveva ar&shy;<lb/>gutamente illustrata, applicandola alla soluzione di un importantis&shy;<lb/>simo problema, qual'&egrave; quello di trovare il volume, a cui pu&ograve;, per <lb/>la massima dilatazione, ridursi l'aria. </s>

<s>La teoria poi dello strumento <lb/>fondata sul principio materiale degli egnicoli, di che tanto rimase <lb/>sodisfatto il Sagredo, a una lettera di Galileo, l'avea data gi&agrave; il Be&shy;<lb/>nedetti con pi&ugrave; squisito giudizio. </s></p><p type="main">

<s>E intorno alla scoperta delle macchie solari, che fiera guerra <lb/>non muove questo ardito conquistatore! E perch&egrave;? </s>

<s>Se si riguarda <lb/>la materiale e occasionale osservazione del fatto, non ci &egrave; dubbio <lb/>che il Fabricio, e tutti coloro che, eccitati dall'<emph type="italics"/>Avviso sidereo,<emph.end type="italics"/> eb&shy;<lb/>bero il coraggio di farsi bruciare gli occhi, osservando direttamente <lb/>il sole, o si prevalsero dell'ingegno di riguardarlo per proiezione; <lb/>precedettero lo Scheiner e Galileo. </s>

<s>Se si ha riguardo a chi primo <lb/>si rivolse all'osservazione del fatto, con vero intendimento scienti&shy;<lb/>fico, i documenti attestano che lo Scheiner preced&egrave; Galileo Se si <pb xlink:href="020/01/152.jpg" pagenum="133"/>attende poi a chi primo filosof&ograve; sulla natura del fatto, e investig&ograve; <lb/>la fisica costituzione del sole nelle sue macchie, nessuno pu&ograve; venire <lb/>alle prove con Galileo. </s>

<s>Ora &egrave; chiaro che tutto il merito scientifico <lb/>consisteva qui, e di ci&ograve; solo poteva meritamente gloriarsi e con&shy;<lb/>tentarsi l'Autore delle Lettere velseriane. </s>

<s>Eppure egli sputa fuoco <lb/>e veleno contro il Gesuita tedesco, perch&egrave;, anche nell'osservazione <lb/>materiale del fatto, anche in averne conosciuta e apprezzata l'im&shy;<lb/>portanza scientifica, non vuol competitori, vuole in tutto e per tutto <lb/>essere il primo ed il solo. </s>

<s>E da quale altro genio era mosso, se <lb/>non da questo, quando s'indusse a tacer della cooperazione, che <lb/>ebbe il Sarpi in quelle osservazioni celesti, di cui volle apparire <lb/>al mondo primo e unico Messaggero? </s></p><p type="main">

<s>Il canocchiale, che andava oramai per le mani di molti signori, <lb/>e si sapeva per fatto certo da tutti esser venuto d'Olanda, non era, <lb/>com'altri ritrovati, di cos&igrave; facile conquista. </s>

<s>Perci&ograve; qui procede Ga&shy;<lb/>lileo con pi&ugrave; liberalit&agrave;, che nell'affar delle macchie solari. </s>

<s>Renunzia <lb/>alla fortuita materialit&agrave; dell'invenzione, e si contenta di appropriarsi <lb/>la soluzione di un problema diottrico, gi&agrave; formulato; soluzione a <lb/>che egli dice esser riuscito per opera di solo discorso, e in che egli <lb/>afferma consistere tutto il vero merito di quella stessa invenzione. <lb/>(Alb. </s>

<s>IV, 207, 8). Altri prima di noi ha notato l'incongruenza, che <lb/>&egrave; fra questa storia del ritrovamento del canocchiale data nel Sag&shy;<lb/>giatore, e in altre varie Scritture di Galileo, e ci&ograve; sarebbe segno <lb/>che quelle narrazioni non avevano i fondamenti sinceri e confer&shy;<lb/>mati nel vero. </s>

<s>Ma quanto vana pretensione fosse quella sua d'aver <lb/>ritrovata la composizione dell'ammirabile strumento per via di di&shy;<lb/>scorso, si parr&agrave; dai fatti che a suo luogo si narreranno. </s>

<s>Giova in&shy;<lb/>tanto osservare, a proposito di questi diottrici discorsi fatti nel <lb/>Nunzio Sidereo e nel Saggiatore, le variet&agrave; e anzi le contradizioni <lb/>che si rilevano apertamente collazionando l'uno coll'altro. </s>

<s>L&agrave;, nel <lb/>Nunzio, aveva riconosciuto il modo e la ragion dell'operare del ca&shy;<lb/>nocchiale, nel condensamento de'raggi attraverso al diafano delle <lb/>lenti (Alb. </s>

<s>III, 62); qui, nel Saggiatore, confuta quelle medesime <lb/>dottrine, contradicendo a se stesso, nell'atto che vuol contradire al <lb/>Sarsi. </s>

<s>Notabile di pi&ugrave; che in questa strana argomentazione di Ga&shy;<lb/>lileo contro il suo avversario, si trova aggirato in un altra contra&shy;<lb/>dizione, la quale consiste in ammetter che i raggi <emph type="italics"/>entrino<emph.end type="italics"/> nelle <lb/>pupille, mentre sempre, e in questa stessa scrittura del Saggiatore, <lb/>dice che <emph type="italics"/>escono,<emph.end type="italics"/> professando le platoniche teorie dell'estramissione. <lb/>(Alb. </s>

<s>IV, 203). </s></p><pb xlink:href="020/01/153.jpg" pagenum="134"/><p type="main">

<s>Cos&igrave; fatte contradizioni hanno in tutti gli Autori origine dal <lb/>progredir della mente, e piuttosto che contradizioni si dovrebbero <lb/>dire e sono ritrattazioni. </s>

<s>Ma Galileo, se si corregge, lo fa con tale <lb/>studioso accorgimento, da non fare apparir che egli abbia errato, <lb/>specialmente se da qualcuno gli &egrave; stato suggerito di corregger l'er&shy;<lb/>rore. </s>

<s>Di ci&ograve; pure &egrave; bene sodisfare ai nostri lettori di qualche esempio. </s></p><p type="main">

<s>Nel Nunzio Sidereo dice che il piccolo corpo globoso delle stelle, <lb/>per via dell'irradiazione, s'accresce di grandezza nell'occhio, co&shy;<lb/>sicch&egrave; il canocchiale radendo all'astro il capellizio, &egrave; cagione di <lb/>rappresentarlo pi&ugrave; terminato s&igrave; nel suo contorno, ma pur alquanto <lb/>rimpiccolito. </s>

<s>Dall'esser soggetto per&ograve; a tale accrescimento e decre&shy;<lb/>mento di grandezza apparente esclude la Luna (Alb. </s>

<s>III, 74). Un <lb/>anno dopo, scrivendo al Grienberger, dice che <emph type="italics"/>la Luna s'incorona <lb/>ella ancora come ogni altro corpo luminoso de'suoi raggi<emph.end type="italics"/> (ivi, pa&shy;<lb/>gina 65), ma, soggiungendo che il Telescopio <emph type="italics"/>toglie in gran parte <lb/>la detta irradiazione col portarci la specie della luna molto vicina<emph.end type="italics"/><lb/>(ivi, pag. </s>

<s>168), d&agrave; a diveder che egli persiste tuttavia in credere la <lb/>irradiazione risieder nell'astro e no nell'occhio. </s>

<s>Nel Saggiatore, che <lb/>vuol dire nel 1623, dodici anni dopo avere scritta la citata lettera <lb/>al Grienbergero, l'Autore ha mutato opinione anco rispetto a questa <lb/>seconda parte della sua dottrina. </s>

<s>Afferma ivi, senz'altro, che <emph type="italics"/>quel <lb/>fulgore ascitizio delle stelle non &egrave; realmente intorno alle stelle ma <lb/>&egrave; nel nostro occhio<emph.end type="italics"/> (Alb. </s>

<s>IV, 194) e ci&ograve; torna solennemente a con&shy;<lb/>fermare nel III Dialogo dei Massimi Sistemi, dove descrivendo la <lb/>corda tesa ad uso di micrometro, dice che essa, <emph type="italics"/>nel coprire il nudo <lb/>corpicello della stella, leva via i capelli che non son suoi ma del <lb/>nostro occhio<emph.end type="italics"/> (Alb. </s>

<s>I, 393). Ora tutti questi che paion frutti germo&shy;<lb/>gliati spontaneamente, sono invece il portato di un ramo nuovo ri&shy;<lb/>messo in luogo del vecchio, reciso dalla forbice del Keplero, il quale <lb/>aveva, nella Dissertazione sul Nunzio Sidereo, richiamato sopra la <lb/>sua <emph type="italics"/>Ottica<emph.end type="italics"/> l'attenzione di Galileo, e aveva concluso contro di lui <lb/>&ldquo; Neque perspicillum in terra adimit aliquid stellis in coelo, sed <lb/>adimit aliquid lucis retiformi, quantum eius redundat &rdquo; (Alb. </s>

<s>V, 425). </s></p><p type="main">

<s>Uno de'pi&ugrave; curiosi problemi, proposti all'Ottica astronomica, <lb/>era quello del Sole ellittico sull'orizzonte. </s>

<s>Ticone, il Keplero, e pi&ugrave; <lb/>particolarmente lo Scheiner, che ne scrisse un libro apposito e ne <lb/>offer&igrave; una copia a Galileo (Campori, Carteg. </s>

<s>galil. </s>

<s>Modena 1881, <lb/>pag. </s>

<s>86), avevano tentato in qualche modo di risolvere il problema. </s>

<s><lb/>Ma l'Autore del Saggiatore, che non aveva potuto ancora perdonare <lb/>al gesuita tedesco l'avere osato d'ingerirsi del suo Regno, in ri-<pb xlink:href="020/01/154.jpg" pagenum="135"/>compensa del dono ricevuto, deride amaramente l'Autore, per avere <lb/>scritto del sole ellittico, come di problema astruso, un intiero trat&shy;<lb/>tato, <emph type="italics"/>ancorch&egrave; tutto il mistero non ricerchi maggior profondit&agrave; di <lb/>dottrina che l'intender per qual ragione un cerchio veduto in <lb/>maest&agrave; ci paia rotondo, ma guardato in iscorcio ci apparisce ovato<emph.end type="italics"/><lb/>(Alb. </s>

<s>IV, 344). Ma come c'entra il cerchio se si tratta del sole che <lb/>&egrave; una sfera? </s>

<s>La cosa dovette sembrare allo stesso Autore assai <lb/>strana, e tornandoci sopra a speculare, s'avvide che il problema <lb/>non era di cos&igrave; facile soluzione, come l'aveva prima creduto, e <lb/>perci&ograve; nelle <emph type="italics"/>Operazioni astronomiche,<emph.end type="italics"/> correggendo colle rifrazioni <lb/>di Ticone e del Keplero le riflessioni speculari dello Scheiner, riusc&igrave; <lb/>finalmente a incontrarsi nel vero, bench&egrave; seguitasse a esprimersi <lb/>ancora sotto forma di dubbio. </s>

<s>Se il sole si mostra bislungo, credo <lb/>io veramente accadere, egli scrive, <emph type="italics"/>perch&egrave;, merc&egrave; dei vapori bassi, <lb/>l'inferior parte del disco solare viene pi&ugrave; inalzata che la superiore, <lb/>restando l'altra dimensione, cio&egrave; la lunghezza, inalterata<emph.end type="italics"/> (Alb. </s>

<s>V, <lb/>383, 84). Anco questo per&ograve; appar sotto tutt'altro aspetto che di una <lb/>ritrattazione, e anzi &egrave; notabile lo studio posto dall'Autore in cansar <lb/>ogni pi&ugrave; piccolo accenno, per cui potessero risovvenirsi i lettori e <lb/>accorgersi di un errore trascorso. </s></p><p type="main">

<s>La libidine del regnare non conosce ritegni: si trucidano gli <lb/>stranieri e i fratelli, si spogliano delle sostanze i nemici paurosi, e <lb/>gli amici pi&ugrave; confidenti. </s>

<s>Fra questi pi&ugrave; confidenti amici di Galileo <lb/>era Bonaventura Cavalieri, il quale aveva appresi i principii dimo&shy;<lb/>strativi delle leggi del moto dalla meditazione dei Dialoghi de'Due <lb/>Massimi Sistemi. </s>

<s>Or avendo, in un suo libro, a trattar delle sezioni <lb/>del cono, applicando quei meccanici principii, si trov&ograve;, quasi senz'av&shy;<lb/>vedersene, condotta in mano la dimostrazione che i proietti, non <lb/>avuto riguardo alle resistenze, descrivevano nel libero spazio vuoto <lb/>una parabola. </s>

<s>Nel mentre che il libro faceva i primi passi per <lb/>uscire alla luce, il modesto Autore dello <emph type="italics"/>Specchio Ustorio<emph.end type="italics"/> d&agrave; avviso <lb/>all'amato Maestro della bella e nuova proposizione dimostrata, spe&shy;<lb/>rando se ne dovesse assai compiacere. </s>

<s>Ma qual divenne l'umile <lb/>fraticello, quando Cesare Marsili ebbe a leggergli quella lettera di <lb/>Galileo, piena di rimproveri sdegnosi saettati in mezzo all'imper&shy;<lb/>versare pi&ugrave; tempestoso dell'ira? </s>

<s>E perch&egrave; mai tanto sdegno? </s>

<s>Perch&egrave; <lb/>colui che in tutto voleva essere il primo e il solo, pretendeva che <lb/>il teorema delle traiettorie paraboliche fosse suo. </s>

<s>Il fatto e il modo <lb/>di una tale usurpazione, forniranno un soggetto de'pi&ugrave; nuovi e <lb/>importanti alla nostra storia, ma intanto, perch&egrave; in brevi tratti <pb xlink:href="020/01/155.jpg" pagenum="136"/>di penna si concluda, ecco l'esempio di un'altra usurpazione pi&ugrave; <lb/>manifesta di quella e pi&ugrave; violenta. </s></p><p type="main">

<s>Il d&igrave; 19 Dicembre 1634 il Cavalieri scriveva una lettera a Ga&shy;<lb/>lileo, nella quale gli domandava il suo giudizio intorno alla <emph type="italics"/>Geo&shy;<lb/>metria degli indivisibili,<emph.end type="italics"/> non ancora finita di stampare, poi soggiunge <lb/>le seguenti parole: &ldquo; Scrivo in fretta, perci&ograve; mi scusi della negli&shy;<lb/>genza dello scrivere, e ci&ograve; per avere io voluto trascrivere un pen&shy;<lb/>siero intorno alla definizione V. del Quinto d'Euclide, quale le <lb/>mando per sentirne il suo parere.... Se le paresse cosa buona, <lb/>averei pensiero di metterla nel fine della mia Geometria &rdquo; (Campori, <lb/>ivi, pag. </s>

<s>423). Al sagace lettore quel Pensiero del Cavalieri parve <lb/>anzi tanto buono, che disegn&ograve; di farlo suo, e perci&ograve; distolse, con <lb/>lusinghiera persuasione, l'Autore dal pubblicarlo. </s>

<s>Ci&ograve; si rileva da <lb/>un altra lettera dello stesso Cavalieri, il quale troppo facilmente <lb/>lasciatosi vincere alle lusinghe, proponeva d'aspettare a pubblicar <lb/>ci&ograve; che intendeva di metter per appendice alla sua Geometria, <emph type="italics"/>pi&ugrave; <lb/>opportuna occasione<emph.end type="italics"/> (ivi, pag. </s>

<s>429). Ma il fatto si &egrave; che, invece di <lb/>andar quell'appendice a incoronar la Geometria degli indivisibili, <lb/>and&ograve; ad aggiungersi ai quattro Dialoghi delle Due Nuove Scienze. </s>

<s><lb/>Ii Pensiero trascritto e mandato da Bologna a Galileo, il giorno, il <lb/>mese e l'anno suddetto, non &egrave; smarrito. </s>

<s>Quando noi lo sottopor&shy;<lb/>remo all'esame de'nostri lettori, vedranno che, non la materia sola, <lb/>ma la mossa stessa e gli stessi andamenti del dialogo galileiano son <lb/>ritratti da quel <emph type="italics"/>Pensiero<emph.end type="italics"/> scritto dal Cavalieri. </s></p><p type="main">

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

<s>Bench&egrave; non la fantasia o il passionato giudizio ma i fatti ci <lb/>abbiano rappresentato Galileo, come Aristotile si rappresent&ograve; al Ve&shy;<lb/>rulamio, sotto l'aspetto di un conquistatore, che stabilisca il suo <lb/>regno a somiglianza de'pi&ugrave; scaltri e coraggiosi tiranni; prevediamo, <lb/>nonostante, che molti resteranno scandalizzati alla verit&agrave;, che ha <lb/>sapore di amaro. </s>

<s>Anzi siam di ci&ograve; pi&ugrave; che certi, tanto vanno a ri&shy;<lb/>troso della corrente opinione quelle nostre storiche conclusioni. </s>

<s>E <lb/>come infatti si possono conciliare insieme i titoli di tiranno e di <lb/>divino? </s>

<s>Se nei conquistatori politici gli concili&ograve; spesso l'adulazione <lb/>o il timore, non hanno simili passioni alcun effetto nel caso nostro, <pb xlink:href="020/01/156.jpg" pagenum="137"/>in cui nulla s'ha da perdere o da sperare. </s>

<s>Non si pu&ograve; altro dir <lb/>dunque se non che questa invalsa e corrente opinione, che contra&shy;<lb/>dice ai fatti storici, abbia tolta la libera serenit&agrave; dei giudiz&icirc;. </s></p><p type="main">

<s>Che sia veramente cos&igrave;, ne possiamo vedere gli esempi in due <lb/>dei pi&ugrave; grandi uomini, che, tra il finire del secolo passato e il co&shy;<lb/>minciare del nostro, fiorirono fra i cultori degli studi galileiani. </s>

<s>Da <lb/>che il Lagrangia afferm&ograve; e il Venturi diffuse la sentenza, s'&egrave; ripe&shy;<lb/>tuto e si ripete da tutti che Galileo fu primo a introdurre nella <lb/>Meccanica il principio della composizione delle forze e delle velocit&agrave; <lb/>virtuali. </s>

<s>Ora &egrave; un fatto che, fra tutte le sentenze, nessun altra &egrave; <lb/>pi&ugrave; aliena dal vero di questa. </s></p><p type="main">

<s>Qual documento che attesti aver Galileo veramente professato <lb/>il principio, che la resultante di due forze &egrave; determinata in inten&shy;<lb/>sit&agrave; e in direzione dalla diagonale, si cita il teorema II della quarta <lb/>Giornata delle Due Nuove. </s>

<s>Scienze. </s>

<s>Ma il Cartesio, nel tempo stesso, <lb/>aveva applicato quel teorema alla luce, come si pu&ograve; veder dal &sect; 2&deg; <lb/>del secondo capitolo della <emph type="italics"/>Diottrica<emph.end type="italics"/> pubblicata in francese nel 1637. <lb/>Ed &egrave; a notar che l'Autore, il quale, come altrove, anco qui insiste <lb/>sulle orme del Keplero, ripete i processi dimostrativi della propo&shy;<lb/>sizione XIX dei <emph type="italics"/>Paralipomeni a Vitellione,<emph.end type="italics"/> dove il moto obliquo del <lb/>raggio luminoso e incidente sopra lo specchio si decompone in due, <lb/>uno perpendicolare e l'altro parallelo alla superficie del medesimo <lb/>specchio (Francof. </s>

<s>1604, pag. </s>

<s>15). Anzi quell'ingenuo e schietto ca&shy;<lb/>rattere del grande Alemanno non tace che l'applicazione del teo&shy;<lb/>rema meccanico ai moti della luce risale su fino ad Alhazen e a <lb/>Vitellione, de'quali autori scrive queste parole: &ldquo; Et addunt subtile <lb/>nescio quid motum lucis oblique incidentis componi ex motu per&shy;<lb/>pendiculari et motu parallelo ad densi superficiem &rdquo; (ibi, pag. </s>

<s>84). </s></p><p type="main">

<s>Galileo propriamente non fece altro che tentar del teorema una <lb/>dimostrazione, la quale &egrave; fondata sopra l'equivoco tra <emph type="italics"/>potenza di&shy;<lb/>namica<emph.end type="italics"/> e <emph type="italics"/>potenza numerica.<emph.end type="italics"/> Preso a quell'equivoco rimase a prin&shy;<lb/>cipio anche il Mersenno, come si par dalla proposizione XXII della <lb/>sua <emph type="italics"/>Meccanica<emph.end type="italics"/> (Parisiis 1644, pag. </s>

<s>81) e se ne accorse o ne fu fatto <lb/>accorto appena stampato il libro. </s>

<s>Perci&ograve;, nella Prefazione innume&shy;<lb/>rata, fra le altre cose di che si ricrede, ci &egrave; anche quella proposi&shy;<lb/>zione, della quale, dopo aver detto che <emph type="italics"/>est ex mente Galilaei pag. </s>

<s>250 <lb/>Dialogorum,<emph.end type="italics"/> immediatamente soggiunge: &ldquo; quod tamen minime <lb/>verum esse videtur. </s>

<s>&rdquo; Non falso il teorema, falso il principio dimo&shy;<lb/>strativo, che cio&egrave; la potenza della resultante sia uguale alla somma <lb/>delle potenze o de'quadrati delle due componenti: anzi il teorema <pb xlink:href="020/01/157.jpg" pagenum="138"/>stesso, secondo i principii galileiani, non sarebbe vero, se non nel <lb/>caso delle forze ortogonali. </s>

<s>Le perniciose conseguenze di cos&igrave; fatte <lb/>dottrine daranno alla nostra storia della Meccanica soggetto di lungo <lb/>e importante discorso, ma intanto passiamo a veder quel che si dice <lb/>di Galileo, rispetto alle velocit&agrave; virtuali. </s></p><p type="main">

<s>Ch'ei veramente professasse questo principio &egrave; chiaro da quel <lb/>che nella <emph type="italics"/>Scienza Meccanica<emph.end type="italics"/> si legge (Alb. </s>

<s>XI, 93), e da quel che <lb/>dice altrove (Alb. </s>

<s>XIII, 176) raccogliesi che, nel trattar delle Mec&shy;<lb/>caniche, quello stesso principio non era nuovo agli autori. </s>

<s>Guidu&shy;<lb/>baldo Del Monte infatti, bench&egrave; non sapesse formularlo e renderlo <lb/>generale, pur ne fece in qualche modo l'applicazione nella proposi&shy;<lb/>zione XIII <emph type="italics"/>De trochlea,<emph.end type="italics"/> e nel corollario I della prima proposizione <emph type="italics"/>De <lb/>axe in peritochio,<emph.end type="italics"/> come in altre parti del suo <emph type="italics"/>Machenicorum liber.<emph.end type="italics"/></s></p><p type="main">

<s>Galileo poi &egrave; verissimo che, di quel princip&igrave;o delle velocit&agrave; <lb/>virtuali, ne fece due insigni applicazioni, distanti cos&igrave; di tempo fra <lb/>loro, da segnare i due termini estremi della gloriosa scientifica sua <lb/>carriera: l'una all'equilibrio dei liquidi nei vasi comunicanti, l'altra <lb/>alla teoria dei piani inclinati. </s>

<s>Non sapremmo dir propriamente se <lb/>l'Autore del Discorso intorno ai galleggianti presentisse le difficolt&agrave; <lb/>promosse contro la sua dimostrazione, la quale in verit&agrave; non con&shy;<lb/>clude, se non nel caso che i due vasi comunicanti sien cilindrici <lb/>e verticali, e ambedue di ugual calibro. </s>

<s>Quel che possiamo per&ograve; <lb/>asserire per cosa certa &egrave; che, non appena ebbe trattata, in quell'Ag&shy;<lb/>giunta da farsi alla stampa leydese del III Dialogo, la nuova teoria <lb/>del piano inclinato col principio delle velocit&agrave; virtuali, che cominci&ograve; <lb/>a scrupoleggiare intorno alla verit&agrave; di quello stesso principio. </s></p><p type="main">

<s>Si fonda questa nostra certezza sull'esame di quelle carte in&shy;<lb/>formi e disordinate, su cui la mano dell'Autore e del Torricelli <lb/>divisarono la riforma, in gran parte radicale, da farsi al Trattato <lb/>delle Due Nuove Scienze. </s>

<s>Si rileva da queste carte che uno dei <lb/>principii da riformare era quello appunto delle velocit&agrave; virtuali, <lb/>avendo qualche durezza nell'apprendersi come mai <emph type="italics"/>quella mag&shy;<lb/>gioranza che non &egrave;, ma ancora ha da essere, possa produrre un <lb/>effetto presente<emph.end type="italics"/> (MSS. Gal. </s>

<s>Div. </s>

<s>II. P. V. T. IV. c. </s>

<s>29). S'accenna evi&shy;<lb/>dentemente, con s&igrave; fatte parole, alla teoria della libbra di braccia <lb/>disuguali; teoria applicata da Galileo alle braccia di disugual ca&shy;<lb/>pacit&agrave; di un sifone pieno di liquido: ma che il dubbio si estendesse <lb/>altres&igrave; alla nuova teoria del piano inclinato, si par da quell'altra <lb/>nota che dice: <emph type="italics"/>pensare se &egrave; vero che, per ritenere un peso, serva <lb/>tanta forza quanta ne fa quello per scendere<emph.end type="italics"/> (ivi). </s></p><pb xlink:href="020/01/158.jpg" pagenum="139"/><p type="main">

<s>Che il principio delle velocit&agrave; virtuali si ritenesse poi per dubbio <lb/>e inconcludente, s'argomenta dai modi che il Torricelli, il Borelli <lb/>e il Viviani, con tutta l'altra scuola galileiana, tennero nei loro <lb/>meccanici teoremi, nei quali quello stesso principio, non solamente <lb/>non si vede promosso, ma vi &egrave; cansato con ogni pi&ugrave; sollecito studio. </s></p><p type="main">

<s>Antonio Nardi, anzi, nelle <emph type="italics"/>Scene Accademiche,<emph.end type="italics"/> adduce quella <lb/>stessa di Galileo per ragione del suo repudio, dichiarandosi aper&shy;<lb/>tamente &ldquo; che male si persuadono i Meccanici comunemente com&shy;<lb/>pensarsi in una bilancia di disuguali braccia la velocit&agrave; del moto <lb/>con la grandezza del momento, onde cercano di render ragione, <lb/>perch&egrave; questi pesi disuguali, da distanze reciprocamente disuguali, <lb/>pesino ugualmente, ma ci&ograve; non &egrave; in vero cagione dell'equilibrio, <lb/>perch&egrave; cos&igrave; discorrendo s'adduce di un effetto in atto una ragione <lb/>in potenza &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XX, pag. </s>

<s>862). </s></p><p type="main">

<s>N&egrave; era, in quegli ingegni sagaci, senza un giusto motivo il re&shy;<lb/>pudio di una dottrina, dall'altra parte, verissima, perciocch&egrave;, man&shy;<lb/>cando essi del calcolo infinitesimale, sentivano che, senza gli aiuti <lb/>di quello, il principio delle velocit&agrave; virtuali mancava di fondamento <lb/>dimostrativo. </s>

<s>E infatti all'aiuto degli infinitesimi ebbe in ultimo a <lb/>ricorrere il Grandi, per tentar di salvare il teorema galileiano del&shy;<lb/>l'equilibrio dei liquidi nei vasi comunicanti, bench&egrave; non riuscisse, <lb/>a parer nostro, a metterlo al sicuro di quelle argute censure pro&shy;<lb/>mossegli incontro dallo stesso Nardi, nel seguito del discorso ora <lb/>citato. </s>

<s>Si vede dunque, per ridursi alla conclusione, con quanta <lb/>storica verit&agrave; ed esattezza, nella comune opinione, si tenga che i <lb/>principii delle velocit&agrave; virtuali e della composizione de'moti s'in&shy;<lb/>cominciassero ad introdurre e ad applicarsi al trattato delle Mec&shy;<lb/>caniche da Galileo e dalla scuola di lui. </s></p><p type="main">

<s>Si comprende, dopo ci&ograve;, assai facilmente in qual conto si possan <lb/>tener da noi le sentenze di uomini reputati autorevolissimi, quali <lb/>sono il Lagrangia e il Venturi, per tacere di altri. </s>

<s>Che se noi ve&shy;<lb/>niamo a concludere altrimenti da loro, non vorranno i lettori far&shy;<lb/>sene maraviglia, e anzi speriamo che si arrenderanno docili a ci&ograve; <lb/>che ne rappresenta la Storia, le conseguenze della quale, solo, ci <lb/>rendon la ragione di alcuni fatti, e ci scoprono nel tempo stesso o <lb/>la falsit&agrave; o l'insufficienza delle ragioni invocate fin qui, per ispiegarli. </s></p><p type="main">

<s>L'aspetto, sotto cui si &egrave; presentato Galileo agli occhi affascinati <lb/>di tutti, &egrave; proprio quello ch'ei divisava nelle sue intenzioni: a nessun <lb/>altro meglio che a lui &egrave; riuscito mai di farsi credere al mondo <lb/>qual'ei voleva apparire, l'unico sole che sorge, senz'esser prece-<pb xlink:href="020/01/159.jpg" pagenum="140"/>duto da aurora, a illuminare le tenebre del mondo; il creatore in&shy;<lb/>somma dal nulla di ogni scienza sperimentale. </s>

<s>Ma chiunque, dai <lb/>pregiudizi, non s'&egrave; lasciato in tutto privare del senno, comprende <lb/>assai facilmente che una tal pretensione &egrave; contraria ai fatti, ed &egrave; <lb/>contraria ai consueti ordini della natura, com'&egrave; giusto contrario a <lb/>questi stessi ordini che il sole nasca sull'orizzonte, senz'esser pre&shy;<lb/>ceduto da aurora. </s></p><p type="main">

<s>Che sia veramente quella tal pretensione contraria ai fatti, lo <lb/>mostra ad evidenza, ci sembra, la prima parte del nostro Discorso. </s>

<s><lb/>Quale eletto e numeroso stuolo di combattenti per la verit&agrave;, contro <lb/>gli aristotelici errori, non ci pass&ograve; allora ordinata sotto i nostri occhi <lb/>maravigliati? </s>

<s>Or tutti costoro precedettero Galileo, nello speculare <lb/>e nello sperimentare intorno ai fatti della Natura, e gli furono o <lb/>gli potevano esser maestri. </s></p><p type="main">

<s>Che quella pretensione poi di non voler Galileo riconoscere, <lb/>fuor che qualche antico, nessun altro a maestro, sia contraria ai <lb/>consueti ordini della Natura, si dimostr&ograve; da noi infin dai primi prin&shy;<lb/>cipii del nostro Discorso, quando, a investigar l'origine del nostro <lb/>conoscere, ci incontrammo nella necessit&agrave; delle tradizioni. </s>

<s>I fatti <lb/>naturali hanno ultimamente dimostrato che son rimasti lungamente <lb/>immobil&igrave; nella cos&igrave; detta et&agrave; della pietra o in istato anco pi&ugrave; sel&shy;<lb/>vaggio i popoli, infintantoch&egrave; non siano approdati a loro altri popoli <lb/>pi&ugrave; inciviliti. </s>

<s>Da Platone e da Archimede voler d'un salto giungere <lb/>a Galileo sarebbe lo stesso che, da'gioghi della Falterona, voler <lb/>saltare alle foci dell'Arno. </s>

<s>Troppi altri rivi, troppi altri fiumi sono <lb/>scesi per ogni parte e si sono aggiunti a far la piena a quell'acqua. </s></p><p type="main">

<s>&Egrave; forza dunque di confessare che son rimasti ingannati tutti <lb/>coloro, i quali, non ripensando a que'rivi, a que'fiumi e anzi ne&shy;<lb/>gando la loro confluenza, hanno creduto che d'un unico fonte, prin&shy;<lb/>cipio di s&egrave; medesimo, sia scaturita l'ubert&agrave; di quel fiume reale. </s>

<s><lb/>Le nostre conclusioni storiche perci&ograve; cos&igrave; repugnanti all'opinione <lb/>comune svelano quell'inganno, e nelle sue ragioni spiegano il fatto. </s>

<s><lb/>Perciocch&egrave; noi non neghiamo, contrariamente alla verit&agrave; delle cose, <lb/>quella confluenza, ma la mettiamo anzi all'aperto degli artifizii di <lb/>colui, che s'era studiato d'occultare i segreti canali, d'onde gli de&shy;<lb/>riv&ograve; tale abbondanza d'acqua fluente. </s></p><p type="main">

<s>L'albero della scienza, per tornare a quell'altra nostra prima <lb/>immagine, era stato troncato dal ferro infino alla sua ceppaia. </s>

<s>Sorse <lb/>dal taglio un solitario pollone, che attrasse tutti a s&egrave; i succhi nu&shy;<lb/>tritizi ricircolanti nelle barbe sottoterra. </s>

<s>Quella profonda ceppaia, <pb xlink:href="020/01/160.jpg" pagenum="141"/>lungo lavor&igrave;o di secoli, rimasta un po'per natura un po'per arte <lb/>nascosta, second&ograve; le intenzioni di Galileo, in dare a credere che <lb/>non fosse quello veramente un pollone rigoglioso, ma un albero, <lb/>il quale non riconoscesse altra origine che dal suo proprio seme. </s>

<s><lb/>Il nostro scandolezzante discorso ha messo quella sotterranea cep&shy;<lb/>paia allo scoperto, e al miracolo (giacch&egrave; l'albero in che si vuole <lb/>impersonar Galileo, se fosse nato di seme e giunto a s&igrave; grande altezza <lb/>sarebbe miracoloso) ha sostituito un fatto naturale e perci&ograve; vero. </s></p><p type="main">

<s>In altro modo, per ripigliar quell'altra similitudine forse meglio <lb/>appropriata, Galileo institu&igrave; una Tirannide in un Principato decre&shy;<lb/>pito, usando l'arte di tutti i conquistatori, che &egrave; quella di arric&shy;<lb/>chirsi delle spoglie degli uccisi. </s>

<s>Queste spoglie volle far credere che <lb/>non fossero appartenute a nessuno, e il nostro Discorso ha scoperto <lb/>che ci&ograve; non &egrave; vero, come lo attestano i fatti e lo conferma la na&shy;<lb/>tura di ogni conquista. </s>

<s>Ma un'altra pi&ugrave; efficace conferma, che ve&shy;<lb/>ramente l'istaurazione galileiana avesse la natura di una conquista, <lb/>s'ha dal vederne conseguitare al conquistatore i consueti danno&shy;<lb/>sissimi effetti. </s></p><p type="main">

<s>Le usurpazioni, l'esilio, le stragi, che &egrave; costretto a commettere <lb/>colui, il quale vuol solo partecipare del Regno, sono per necessit&agrave; <lb/>occasioni di odii e di vendette, che si suscitano pi&ugrave; che mai feroci, <lb/>dal sangue e dalle ceneri stesse dei vinti. </s>

<s>Di questi odii e di queste <lb/>vendette il Regno di Galileo v&agrave; famoso, n&egrave; par che sieno state fin <lb/>qui ritrovate, di tanto effetto, le giuste e proporzionate cagioni. </s>

<s>Son <lb/>ricorsi, per consueto refugio, all'ignoranza dei tempi e alle reli&shy;<lb/>giose superstizioni, quasi che le innovatrici dottrine dei nostri giorni, <lb/>che son giorni di libert&agrave; e di progressi, non abbiano avuto e non <lb/>sieno per avere sempre, fra gli uomini che adombrano ad ogni <lb/>novit&agrave;, i medesimi sfavorevoli incontri. </s></p><p type="main">

<s>Come si concilii la condanna dei Dialoghi dei Due Massimi <lb/>Sistemi, e la dedica al Papa, del libro <emph type="italics"/>De revolutionibus,<emph.end type="italics"/> &egrave; proble&shy;<lb/>ma lasciato irresoluto ancora da tanti declamatori, ai quali riman <lb/>pure a spiegare come mai fosse tolta libert&agrave; a Galileo di toccar delle <lb/>dottrine del Copernico, e fosse largamente concessa al Bullialdo, <lb/>mutato nome in quello di Filolao. </s>

<s>Come mai cos&igrave; franco il Roberval, <lb/>per fare una burla agli scienziati, facesse pubblicare al Mersanne <lb/>l'<emph type="italics"/>Aristarco,<emph.end type="italics"/> e il Borelli nella Lettera sulla Cometa uscisse fuori in <lb/>abito pitagorico, tanto pauroso, adombrando dell'Inquisitore, pa&shy;<lb/>rendogli di vederselo innanzi sulla punta dei piedi (MSS. Gal. </s>

<s>Cim. </s>

<s><lb/>T. XVIII, c. </s>

<s>125). E chi volesse per curiosit&agrave; seguitare a interrogare <pb xlink:href="020/01/161.jpg" pagenum="142"/>i muti, domanderebbe ancora come si concil&icirc;no i rigorosi divieti <lb/>di Roma colla pubblicazione delle <emph type="italics"/>Theoricae Mediceorum.<emph.end type="italics"/> Il prin&shy;<lb/>cipe Leopoldo st&agrave; in gran trepidazione, perch&egrave; ha saputo che l'In&shy;<lb/>quisitor di Firenze fa difficolt&agrave; d'approvar la stampa del libro. </s>

<s>Manda <lb/>il Redi, il quale torna dicendo che all'Inquisitore era giunta cosa <lb/>totalmente nuova, asserendo che egli <emph type="italics"/>non aveva mai fatta minima <lb/>difficolt&agrave;<emph.end type="italics"/> (ivi, c. </s>

<s>132). </s></p><p type="main">

<s>Ma perch&egrave; da troppe parti tornerebbe provato che nell'igno&shy;<lb/>ranza dei tempi e nelle religiose superstizioni non si trova la causa <lb/>sufficiente degli odii suscitati contro Galileo, noi crediamo per&ograve; di <lb/>non andare errati, attribuendo quella causa alle offese fatte ai tanti, <lb/>che rimasero segno alla sua conquista. </s>

<s>Michelangiolo Ricci, che <lb/>poteva intender quell'animo grande meglio di nessun altro, attri&shy;<lb/>buiva le contradizioni patite da Galileo all'<emph type="italics"/>essersela voluta prendere <lb/>con questo e con quello<emph.end type="italics"/> (ivi, T. XIX, c. </s>

<s>205). N&egrave; senza profonda <lb/>considerazione si pu&ograve; passar questo fatto: che, mentre tanti decla&shy;<lb/>matori son sorti, specialmente oggidi, a rimpiangere sopra le sue <lb/>sventure; egli, Galileo, non ne abbia fatto mai motto, nemmeno nelle <lb/>lettere pi&ugrave; segrete e pi&ugrave; confidenti. </s>

<s>Nella schiettezza della sua co&shy;<lb/>scienza, e nell'altezza del suo proprio senno, troppo ben conosceva <lb/>il vizio di noi uomini di dar la colpa ora a una cosa ora a un altra, <lb/>mentre siam quasi sempre noi stessi occasione e causa della nostra <lb/>sventura. </s>

<s>In conformit&agrave; di questi sentimenti, che non gli abbiamo <lb/>attribuiti a caso, nella solitudine di Arcetri, vicino a lasciar quel <lb/>Regno che avea con tanta contrariet&agrave; conquistato, dava al suo di&shy;<lb/>letto Viviani questo documento: <emph type="italics"/>procurare ad ogni potere di sfug&shy;<lb/>g&igrave;re ogni lite e controversie letterarie con chi si sia<emph.end type="italics"/> (ivi, T. XVII, <lb/>c. </s>

<s>69). Egli riport&ograve; &egrave; vero le pene delle liti e delle controversie <lb/>da s&egrave; in tanti modi contro s&egrave; provocate, ma gli riman la gloria <lb/>d'avere egli solo recato inestimabili benefizi alla scienza. </s></p><p type="main">

<s>Come mai il male sia quasi una necessit&agrave;, d'onde tante volte <lb/>vedesi derivare un gran bene, &egrave; un mistero che a noi non tocca <lb/>d'investigare. </s>

<s>Ma &egrave; forza in ogni modo riconoscere che i vizii, no&shy;<lb/>tati da noi cos&igrave; liberamente e irreverentemente se si vuole, nella <lb/>vita scientifica di Galileo, furono una necessit&agrave; a condur la difficile <lb/>impresa. </s>

<s>Perch&egrave;, o la si rappresenta la scienza sotto l'immagine <lb/>di un albero, e ci bisognava la violenza del ferro per recidere i <lb/>rami vecchi e farvi sopra ripullulare un ramo nuovo: o la si rap&shy;<lb/>presenta sotto l'immagine di un Regno, e bisognava contrucidare <lb/>i fratelli, perch&egrave; il potere vacillante e disperso, si riducesse alle <pb xlink:href="020/01/162.jpg" pagenum="143"/>mani di un solo. </s>

<s>Contristati fin qui dai mali licenziosi e dalle pene <lb/>della Tirannide, passiamo a rasserenare il pensiero ne'grandissimi <lb/>benefizi che ne son conseguiti. </s></p><p type="main">

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

<s>Il primo e principale dei benefizi che possa un conquistatore <lb/>arrecare al suo principato, e che sarebbe sufficiente per s&egrave; solo a <lb/>dover perdonargli le offese, &egrave; quello d'istituirvi ordini savi, per i <lb/>quali possa la Repubblica prosperamente vivere e progredire. </s>

<s>Galileo <lb/>veramente incominci&ograve; a instituire questa saviezza di ordini, nella <lb/>Repubblica delle scienze, le quali ebbero perci&ograve; di qui il pi&ugrave; valido <lb/>impulso ai loro progressi. </s>

<s>Fra'due pi&ugrave; grandi antichi Maestri e Le&shy;<lb/>gislatori dell'umana sapienza, prefer&igrave; i plaeiti di Platone, in con&shy;<lb/>formit&agrave; dei quali sentenziava che &ldquo; il voler trattar le questioni na&shy;<lb/>turali, senza Geometria, &egrave; tentar di far quello che &egrave; impossibile ad <lb/>esser fatto &rdquo; (Alb. </s>

<s>I, 224). La vera Filosofia, egli dice &ldquo; &egrave; scritta in <lb/>questo grandissimo libro che continuamente ci sta aperto innanzi <lb/>agli occhi (io dico l'Universo) ma non si pu&ograve; intendere, se prima <lb/>non s'impara a intender la lingua e conoscere i caratteri ne'quali <lb/>&egrave; scritto. </s>

<s>Egli &egrave; scritto in lingua matematica, e i caratteri son trian&shy;<lb/>goli, cerchi ed altre figure geometriche, senza i quali mezzi &egrave; im&shy;<lb/>possibile intenderne umanamente parola: senza questi &egrave; un aggirarsi <lb/>vanamente per un oscuro laberinto &rdquo; (Alb. </s>

<s>IV, 171). </s></p><p type="main">

<s>Quell'altra Filosofia pi&ugrave; comunemente segu&igrave;ta gli parve un'or&shy;<lb/>gogliosa vanit&agrave;, una temerit&agrave; estrema. </s>

<s>&ldquo; Estrema temerit&agrave; mi &egrave; <lb/>parsa sempre quella di coloro che voglion fare la capacit&agrave; umana <lb/>misura di quanto possa e sappia operar la Natura &rdquo; (Alb. </s>

<s>I, 114). <lb/>Che se Aristotile fa scaturir le cause degli effetti naturali dalla <lb/>dialettica de'suoi sillogismi, Galileo gli si oppone cos&igrave; con animosa <lb/>franchezza: &ldquo; A me pare che la Logica insegni a conoscere se i <lb/>discorsi e le dimostrazioni.... procedono concludentemente, ma che <lb/>ella insegni a trovare i discorsi.... non credo io &rdquo; (Alb. </s>

<s>XIII, 135). <lb/>E se il Principe dei peripatetici va cos&igrave; studiosamente in cerca delle <lb/>argute speculazioni, e quanto son pi&ugrave; recondite, tanto pi&ugrave; volentieri <lb/>le d&agrave; per vere; Galileo, tutto al contrario sentenzia che &ldquo; la pi&ugrave; <lb/>ammirabile e pi&ugrave; da stimarsi condizione delle scienze dimostrative <lb/>&egrave; lo scaturire e pullulare da principii notissimi (ivi, pag. </s>

<s>90). </s></p><pb xlink:href="020/01/163.jpg" pagenum="144"/><p type="main">

<s>Ma a poco gioverebbe istituire ordini savi un principe, che non <lb/>volesse o non sapesse seguirli con gli esempi. </s>

<s>Ci&ograve;, come si vide, <lb/>tanto poco giov&ograve; al Verulamio, che per questo solo and&ograve; a vuoto <lb/>la sua cos&igrave; ben divisata Instaurazione. </s>

<s>Galileo invece non si con&shy;<lb/>tent&ograve; di segnar la via o di ordinare il campo della battaglia, usc&igrave; <lb/>fuori con le armi in mano, contro l'errore, e tanta gloria riport&ograve; <lb/>dalle sue vittorie e tanta autorit&agrave; ne consegu&igrave;, che, non Tirannide <lb/>apparve o si disse la sua, ma legittimo principato. </s>

<s>Or questo &egrave; un <lb/>altro benefizio grandissimo recato alla scienza da quell'uomo. </s></p><p type="main">

<s>L'intrattenersi qui a noverar quelle vittorie parrebbe opera <lb/>vana, perch&egrave; troppo anzi bene son conosciute da tutti e da tutti <lb/>cos&igrave; magnificate, che Colui, il quale le riport&ograve;, non &egrave; solamente <lb/>tenuto come principe valoroso, ma &egrave; adorato come un Nume. </s>

<s>Or <lb/>perch&egrave; questa &egrave; una esagerazione, e ogni vizio conduce nell'errore, <lb/>non far&agrave; maraviglia se da noi si asserisce che Galileo, da'suoi stessi <lb/>adoratori, &egrave; cos&igrave; poco inteso e cos&igrave; poco studiato. </s>

<s>Chi fa oggid&igrave; pi&ugrave; <lb/>speciale professione di studii galileiani, non entra mica addentro <lb/>alle speculazioni della gran mente: crede aver fatto assai a venire <lb/>a contarci del suo processo, delle amicizie, del numero de'suoi libri <lb/>stampati, o dei manoscritti. </s>

<s>E ha ragione costui, perch&egrave;, se quella <lb/>mente divina &agrave; un sacro tempio, non debbono entrarvi dentro a <lb/>celebrarne i misteri piedi profani. </s></p><p type="main">

<s>Ma a noi per verit&agrave; &egrave; sembrato altrimenti. </s>

<s>Persuasi che Galileo <lb/>&egrave; un grand'uomo, ma pur un uomo come noi, soggetto a vizii e <lb/>ad errori, gli ci siamo avvicinati per vederlo e intenderlo meglio, <lb/>e abbiamo imparato da lui a non credere e sostener per vera una <lb/>cosa, perch&egrave; l'ha detta un uomo. </s>

<s>Que'fanatici, che inorridiscono <lb/>a sentir dire che Galileo ha sbagliato, non imitano certo i pi&ugrave; affe&shy;<lb/>zionati e valorosi discepoli, come il Sagredo l'Aggiunti il Nardi, il <lb/>Viviani stesso, i quali notarono con libert&agrave; gli errori detti dal loro <lb/>venerato Maestro, e ne lasciarono scritte argute censure. </s>

<s>Non si <lb/>avvedono quegli stessi fanatici che, se fossero nati tre secoli addietro, <lb/>si sarebbero sottoscritti nella lista dei Cremonini, e non ripensano <lb/>che Aristotile, verso cui si commisero tante irreverenze, era vene&shy;<lb/>rando a quei tempi, ben assai pi&ugrave; di quel che non sia ora lo stesso <lb/>Galileo, lodato a cielo, perch&egrave; fu il pi&ugrave; irriverente di tutti. </s></p><p type="main">

<s>Ripigliando il costrutto del discorso interrotto si voleva dunque <lb/>dire che giusto appunto, per essere le opere scientifiche di Galileo <lb/>esageratamente note, e perci&ograve;, ci si perdoni il bisticcio, ignote, ave&shy;<lb/>vano bisogno di essere con pi&ugrave; discrezione esaminate. </s>

<s>Ma perch&egrave; <pb xlink:href="020/01/164.jpg" pagenum="145"/>dall'altra parte si pu&ograve; dir che questo &egrave; l'intento principale di tutta <lb/>la nostra Storia, crediamo perci&ograve; di dovercene passare, contentan&shy;<lb/>doci solo di notare una cosa: che mentre gli adoratori attribuiscono <lb/>a Galileo, perch&egrave; qualche uomo autorevole e male informato glie <lb/>l'ha suggerito, meriti che non gli appartengono, non si curano poi <lb/>di riconoscerne e di esaltarne i meriti veri. </s></p><p type="main">

<s>Nella scienza del moto i meriti veri di Galileo incominciano <lb/>dalla dimostrazione delle leggi dei gravi, che cadono naturalmente <lb/>o scendono per gli archi di un cerchio. </s>

<s>Tutte le altre scoperte, che <lb/>precedono a questa, son retaggio di una scienza pi&ugrave; antica. </s>

<s>Di qui <lb/>&egrave; che, se i suoi ammiratori male a ragione lo dicono creatore della <lb/>Dinamica, troppo debolmente, dall'altra parte mettono in opera le <lb/>loro armi, per chiarir l'efficacia, che ebbero le galileiane scoperte <lb/>in aprire alla Meccanica la via de'suoi gloriosi progressi. </s></p><p type="main">

<s>In Idrostatica, Galileo riman forse inferiore a Simeone Stevino. </s>

<s><lb/>Il Discorso intorno alle Galleggianti &egrave; uno splendido commento alle <lb/>teorie di Archimede, ma se pure la scienza vi si illustra, non per&ograve; <lb/>si promuove. </s>

<s>Le tavolette d'ebano, o d'altra materia pi&ugrave; grave in <lb/>specie dell'acqua, non galleggiano per la spinta idrostatica di sotto <lb/>in su, come si poteva concludere dai teoremi steviniani, ma si so&shy;<lb/>stengono a galla, perch&egrave;, secondo Galileo, aderiscono all'aria, la quale <lb/>per attrazione le tien sospese come il ferro la calamita. </s>

<s>Nonostante, <lb/>l'aver dichiarate cos&igrave; eloquentamente quelle dottrine, rimaste nei <lb/>libri di Archimede, o ignorate o male intese, fu merito grande, e <lb/>occasione che altri, come poi presto si vide nel Castelli e nel Tor&shy;<lb/>ricelli, vi facessero grandi progressi. </s></p><p type="main">

<s>Nell'Idraulica, qualunque sieno le pretensioni degli idolatri, <lb/>Galileo &egrave; seguace del Castelli, ma il Trattato in forma di lettera <lb/>sul fiume Bisenzio, bench&egrave; la matematica astrattezza delle dottrine <lb/>non le faccia applicabili alla pratica delle acque correnti, apri no&shy;<lb/>nostante largamente la via a nuove speculazioni. </s></p><p type="main">

<s>Nell'Astronomia, l'ingegno in Galileo concorse colla fortuna. </s>

<s><lb/>Il felice accorgimento che egli ebbe di badare, non alla chiarezza <lb/>dei vetri ma alla figura, lo fece uno de'pi&ugrave; abili fabbricatori del <lb/>canocchiale, che, rivoltolo alle plaghe del cielo, gli svel&ograve; quelle sue <lb/>gran maraviglie. </s>

<s>Ma in tutto ci&ograve;, per cui vien esaltato lo scopritore, <lb/>ha pi&ugrave; merito la fortuna che non l'ingegno, o per dir pi&ugrave; giusto, <lb/>quello &egrave; merito di un esperto meccanico, no di uno scienziato. </s>

<s>Cos&igrave;, <lb/>n&egrave; il Fontana, n&egrave; il Campani, n&egrave; il Divini, squisitissimi artefici di <lb/>canocchiali, hanno giusto merito perci&ograve; di esser chiamati astronomi. </s></p><pb xlink:href="020/01/165.jpg" pagenum="146"/><p type="main">

<s>Astronomo &egrave; Galileo quando, posato lo strumento e chiusi gli <lb/>occhi della vista materiale, apre quelli dell'intelletto a specular sui <lb/>fenomeni osservati intorno a Giove, o nella faccia della Luna e del <lb/>Sole. </s>

<s>Astronomo &egrave; quando inventa nuovi strumenti e divisa nuovi <lb/>metodi a prefinir, nei moti planetarii, gli spazii giustissimi e i tempi. </s>

<s><lb/>S'ammira e s'esalta, per avere egli il primo scoperto il mondo <lb/>gioviale, e se alcuno mai muove voce d'averlo preceduto nella sco&shy;<lb/>perta, &egrave; afferrato dal furore degli zelanti, che gli soffocano le parole <lb/>nella strozza. </s>

<s>Ma quando pur fosse che o Simon Mario o altri aves&shy;<lb/>sero veduto le quattro lune intorno a Giove prima di Galileo, che <lb/>vorrebb'egli dir ci&ograve;, se non che que'tali avevano strumenti pi&ugrave; <lb/>squisiti, e occhi pi&ugrave; acuti di lui? </s>

<s>Or chi oserebbe dire che ci&ograve; non <lb/>fosse possibile? </s></p><p type="main">

<s>Il merito dunque non consiste qui, e chi ce lo fa consistere <lb/>mal provvede alla gloria di Galileo. </s>

<s>Il merito vero, e per cui ver&shy;<lb/>rebbe giustamente esaltato quell'uomo, consiste nell'aver dimostrato <lb/>esser le stelle circungioviali veramente lune, e nell'averne esatta&shy;<lb/>mente misurati i tempi periodici e le medie distanze dal centro di <lb/>Giove. </s>

<s>Ma chi &egrave;, tra i fanatici ammiratori, che si sia curato d'in&shy;<lb/>vestigare per quali ingegnosissimi metodi e strumenti riuscisse con <lb/>tanta felicit&agrave; Galileo, in quest'operazione affatto nuova nell'Astro&shy;<lb/>nomia? </s>

<s>Parve aver fatto una grande scoperta a colui che trov&ograve; e <lb/>dette alla luce l'Effemeridi de'Satelliti di Giove, ma codeste son le <lb/>scompaginate e rimescolate ossa di un cadavere; per cui vera sco&shy;<lb/>perta sarebbe stata piuttosto l'infondere in quelle membra il primo <lb/>loro, e antico spirito della vita. </s></p><p type="main">

<s>In ogni modo, tanta varia novit&agrave; di scoperte e di dottrine, <lb/>uscite fuori con quella splendida veste che ritraeva cos&igrave; bene in s&egrave; <lb/>la magnificenza del pallio filosofico di Platone, conferiva, per una&shy;<lb/>nime consenso a Galileo l'autorevole dignit&agrave; del Principato. </s>

<s>Ecco <lb/>felicemente conseguito il fine della nobile e altissima impresa. </s>

<s>Tutti <lb/>i dotti di que'tempi, non eccettuato il Keplero che primeggia fra <lb/>tutti, s'inchinano a quella Autorit&agrave; o con le voci congratulanti o <lb/>col silenzio. </s>

<s>Quei che possono ascoltar la viva voce del Maestro di <lb/>tante verit&agrave; o aver con lui familiari colloqui, e corrispondenza epi&shy;<lb/>stolare, se ne tengon beati. </s></p><p type="main">

<s>Son de'principali fra costoro Daniele Antonini, che il vuoto <lb/>lasciatogli dentro dalla vita diplomatica riempiva di speculazioni e <lb/>di fisici sperimenti, Cesare Marsili, studioso di Astronomia e delle <lb/>propriet&agrave; del magnete, Paolo Aproino inventore del corno acustico, <pb xlink:href="020/01/166.jpg" pagenum="147"/>e Giovan Francesco Sagredo, la pi&ugrave; amabile figura, fra le tante <lb/>comparse sopra questa magnifica scena. </s>

<s>Gentiluomo e patrizio ve&shy;<lb/>neziano, fra le delizie della vita signorile e le gravi cure della poli&shy;<lb/>tica, attende alla fabbrica dei vetri per i canocchiali e de'cannellini <lb/>per uso dei termometri, co'quali, da s&egrave; perfezionati, sperimenta <lb/>ne'varii ambienti le varie temperature dell'aria. </s>

<s>Tanti anni avanti <lb/>all'invenzione dello strumento torricelliano e della macchina pneu&shy;<lb/>matica, egli &egrave; il primo a far l'esperienza del suono nel vuoto, e <lb/>indovina la vera teorica della visione, senza pensare al Porta o aver <lb/>letto ancora il Keplero. </s>

<s>Ei, con libera franchezza, sostiene in tal <lb/>proposito, la sua propria opinione, contro il diverso parere di Ga&shy;<lb/>lileo, che a lui sembra e apertamente lo dichiara per un errore. </s></p><p type="main">

<s>Anche l'arte si rivolse a riconoscere l'autorit&agrave; di questo prin&shy;<lb/>cipato, presaga forse de'nuovi benefizi e iniziatrice de'nuovi connubi, <lb/>che sarebbe per contrar colla scienza. </s>

<s>Bell'esempio di questi nuovi <lb/>connubi l'abbiamo in due eccellenti pittori, Domenico Passignani <lb/>e Lodovico Cardi Cigoli, che appuntano la matita dei pittori a di&shy;<lb/>segnare le macchie solari. </s>

<s>Anzi il Passignani ne fu osservatore cos&igrave; <lb/>diligente e appassionato, da venire in contesa con Galileo. </s>

<s>A lui in <lb/>ogni modo si dee la prima osservazione di quelle profondit&agrave; vora&shy;<lb/>ginose, che ammannirono al Wilson, tanti anni dopo, le sue teorie <lb/>(Alb. </s>

<s>VIII, 170). a lui le prime osservazioni delle montuosit&agrave; nella <lb/>circonferenza lunare (MSS. Galil. </s>

<s>Div. </s>

<s>II. P. I. T. VII, c. </s>

<s>12). </s></p><p type="main">

<s>Il Cigoli lasci&ograve; manoscritto un libro di Prospettiva, a cui, per <lb/>essere stampato, non manc&ograve; nemmeno l'approvazione ecclesiastica <lb/>sottoscritta nel d&igrave; 6 di Febbraio 1628 (MSS. Gal. </s>

<s>Div. </s>

<s>III. T. VIII, <lb/>c. </s>

<s>107). L'Alberti e il Vinci avevano immaginato qualche ingegno, <lb/>per eseguire con pi&ugrave; facilit&agrave; e prestezza, che non per le solite regole <lb/>delle linee, i disegni di Prospettiva, ma il Cigoli riconoscendoli <lb/>all'arte di piccolo aiuto, invent&ograve; due nuovi strumenti, nella loro <lb/>semplicit&agrave; ingegnosissimi, che egli nel II libro del suo Trattato <lb/>minutamente descrive nelle parti e nell'uso. </s>

<s>Bench&egrave; le regole, che <lb/>ivi egli espone dell'arte sua, sieno puramente pratiche, senz'altra <lb/>dimostrazione; non si pu&ograve; tuttavia lasciar di notare che v'&egrave; trattata <lb/>un importante questione scientifica, ed &egrave; quella del modo e del <lb/>luogo dove si rappresenta la vista. </s>

<s>Che la vista non si faccia nella <lb/>parte anteriore dell'occhio, e nemmeno del centro del cristallino, <lb/>come diceva Galileo, il Pittore lo dimostra con argomenti e con <lb/>esperienze si nuove, che se ne potrebbe onorar degnamente qua&shy;<lb/>lunque filosofo. </s>

<s>&ldquo; Quando si fa qualche concorso di materia fra il <pb xlink:href="020/01/167.jpg" pagenum="148"/>cristallino e la cornea, egli dice, ci par veder per l'aria alquanto <lb/>lontano qualche cosa di simile alla tela del ragno, e cos&igrave; di colore <lb/>oscuro...... il che ci fa manifesto che la sensazione &egrave; pi&ugrave; interna <lb/>dell'umore acqueo e non pare che possa essere il centro del cri&shy;<lb/>stallino perch&egrave; come centro non &egrave; capace della diversa quantit&agrave; &rdquo; <lb/>(ivi, c. </s>

<s>25). </s></p><p type="main">

<s>Il Cigoli per&ograve;, cos&igrave; come il Sagredo, erano alieni dal far pro&shy;<lb/>fessione di scienza: l'Antonini, il Marsili, l'Aproino non ne ave&shy;<lb/>vano nemmeno essi la pretensione, il Passignani che pretendeva <lb/>qualche cosa di pi&ugrave;, come impotente di studii e di esercizi letterari, <lb/>era sotto sotto da'suoi amici deriso. </s>

<s>Ma bisognava pure che l'au&shy;<lb/>torit&agrave; del nuovo principato galileiano fosse primieramente ricono&shy;<lb/>sciuta da coloro che esercitavano il ministero della scienza o nel <lb/>pubblico insegnamento delle scuole o ne'libri. </s>

<s>Nelle scuole per&ograve; i <lb/>professori facevano assai, se approvavano col silenzio. </s>

<s>Fra coloro poi <lb/>che diffondevano la scienza sperimentale ne'libri val per tutti l'esem&shy;<lb/>pio del genovese Giovan Batista Baliani. </s></p><p type="main">

<s>Chi dipinse il Baliani invidioso delle glorie di Galileo e suo <lb/>competitore, non lesse bene addentro nell'animo, e ne'libri di lui. </s>

<s><lb/>Il Trattato <emph type="italics"/>De motu naturali<emph.end type="italics"/> &egrave;, nell'aperta intenzione dello stesso <lb/>autore, una conferma dei teoremi dimostrati ne'Dialoghi delle <lb/>Scienze Nuove, conclusi per una via diversa e in un altro modo, <lb/>che, per il lucido ordine e per la brevit&agrave;, riesce maraviglioso. </s>

<s>Chi <lb/>vuol vedere qual fosse l'animo del filosofo genovese verso il Prin&shy;<lb/>cipe della Nuova Filosofia, ne legga il commercio epistolare, spe&shy;<lb/>cialmente l&agrave; dove la libert&agrave; del giudizio concilia fede alla sincerit&agrave; <lb/>dell'ossequio. </s>

<s>Cos&igrave; l&agrave; dove critica la teoria delle comete data nel <lb/>Saggiatore (Alb. </s>

<s>Supplem. </s>

<s>pag. </s>

<s>136); cos&igrave; l&agrave; dove dice che non &egrave; <lb/>tolta una delle maggiori difficolt&agrave;, nel risolvere, nell'ultimo Dialogo <lb/>dei Due Massimi Sistemi, il maraviglioso problema del flusso del <lb/>mare (Alb. </s>

<s>IX, 266). </s></p><p type="main">

<s>Con fiducia di discepolo ricorre il Baliani a Galileo, quando <lb/>vuol saper quanto vada lungo il pendolo che batte i secondi, per <lb/>servirsene, fra i tanti usi, a quello di trovare le longitudini; quando <lb/>vuol imparare il modo di ritrovare il peso specifico dell'aria, quando <lb/>conferisce con lui i suoi pensieri intorno alla pressione atmosferica, <lb/>per cui si sostien l'acqua dentro i sifoni, non pi&ugrave; su che a una <lb/>determinata altezza. </s></p><p type="main">

<s>Ma che ci tratteniamo noi con gli ammiratori seguaci o dietro <lb/>a coloro che ne professarono le dottrine, con ossequio di discepoli? <pb xlink:href="020/01/168.jpg" pagenum="149"/>A confermar Galileo nel principato della scienza conferirono massi&shy;<lb/>mamente gli stessi suoi contradittori. </s>

<s>Si venne a verificare cos&igrave; anche <lb/>da questa parte quella approvata sentenza, che i nostri pi&ugrave; grandi <lb/>benefattori sono i nostri propri nemici. </s>

<s>Quanti gran benefizi infatti <lb/>non vennero alla scienza dalle contradizioni dei peripatetici? </s>

<s>Si dee <lb/>senza dubbio a costoro l'aver dato occasione a Galileo di scrivere <lb/>pi&ugrave; che la met&agrave; de'suoi libri, e dei pi&ugrave; belli: essi, nel fare ogni <lb/>sforzo di toglierla, gli confermarono in fronte la corona del Principato. </s></p><p type="main">

<s>E ora che, co'savii ordini instaurati e coll'esempio del suo <lb/>valore, &egrave; riuscito a conquistarsi quella corona, concludiamo i gran&shy;<lb/>dissimi benefizi che alla Repubblica della scienza seguitarono da <lb/>tale conquista. </s>

<s>A far ci&ograve; non bisogna oramai a noi troppo lunghe <lb/>parole, ritornando indietro colla memoria ai principii del nostro <lb/>Discorso. </s>

<s>Dicemmo infatti che la miglior maniera da ringiovanire <lb/>l'albero della scienza, per troppo lunga et&agrave; trascorso, era quello di <lb/>ravviare i succhi nutritivi dispersi, e condensar gli spiriti dissipati <lb/>in un tronco solo. </s>

<s>Questo &egrave; ci&ograve; appunto che riusc&igrave; di fare a Galileo, <lb/>e per cui egli &egrave; cos&igrave; meritamente glorioso. </s></p><p type="main">

<s>Noi rassomigliammo col Verulamio la grande impresa a una <lb/>conquista politica, nella quale la forza sola non basta, se non v&agrave; <lb/>spesso congiunta coll'astuzia. </s>

<s>Di queste astuzie, da noi di sopra <lb/>notate nella vita scientifica di Galileo, molti saranno rimasti scan&shy;<lb/>dalizzati, ma costoro se non s'acquietano ai fatti si acquietino al&shy;<lb/>meno in quel principio che, nella infermit&agrave; delle operazioni umane, <lb/>suol prevalere alla retta morale, del fine che giustifica i mezzi. </s>

<s>Tru&shy;<lb/>cidare i fratelli e arricchirsi delle loro spoglie, &egrave; un mezzo illecito, <lb/>ma pure era necessario a instituire una Monarchia nella scienza, <lb/>com'&egrave; necessario al fine del villico il trucidare in un albero i rami. </s>

<s><lb/>Fossero rimaste le varie speculazioni e le varie scoperte disperse <lb/>nello Stevino, nel Santorio, nel Cavalieri e in tanti altri, non sareb&shy;<lb/>bero riuscite ai progressi delle scienze sperimentali tanto efficaci, <lb/>come digeste in uno stomaco solo, d'onde si dispenseranno a tante <lb/>membra la vita e gli alimenti. </s></p><p type="main">

<s>Ripensando quello a che fu dalla Provvidenza riserbato Galileo, <lb/>chi meglio lo riconosce nell'esser suo, e pi&ugrave; l'ammira. </s>

<s>Egli non <lb/>fu, ne poteva essere il creatore della scienza sperimentale, ma ne <lb/>fu il rigeneratore, e tra poco vedremo la fecondit&agrave; della sua prole. </s>

<s><lb/>Prima per&ograve; convien che ci tratteniamo intorno agli ordini e agli <lb/>effetti di quell'altra Instaurazione, a cui s'accennava gi&agrave; in quel <lb/>primo nostro introdursi a discorrer di questa. </s></p><pb xlink:href="020/01/169.jpg" pagenum="150"/><p type="main">

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

<s>Non aveva ancora Galileo dato l'ultima mano alla costituzione <lb/>del suo nuovo Regno, che si leva dalla montagnosa Bretagna un <lb/>vento impetuoso a ferire, abbattere e disperdere tutto ci&ograve; che egli <lb/>incontra per via. </s>

<s>Quel vento &egrave; l'orgoglio filosofico di Renato Car&shy;<lb/>tesio, il quale proclamando ad alta voce che tutto il mondo era fino <lb/>a quel tempo vissuto nelle tenebre e nell'errore, viene ad abbat&shy;<lb/>tere il tristo e buio tugurio dell'ignoranza per sostituire ad esso, <lb/>di sua propria mano ricostruito, il nuovo edifizio della scienza. </s></p><p type="main">

<s>&Egrave; questo dunque un conquistatore ben assai pi&ugrave; ardito: Galileo <lb/>rispett&ograve; i placiti dell'antica filosofia, e fecesi discepolo di Platone, <lb/>seguace di Archimede; il suo Regno &egrave; circoscritto, e non esce fuori <lb/>della cerchia dei fatti naturali. </s>

<s>Il Cartesio invece protesta di non <lb/>riconoscere tradizioni di nessuna maniera; la sua impresa &egrave; quella <lb/>di voler da s&egrave; solo restaurar la scienza universale. </s>

<s>Se egli avesse <lb/>confidato in segreto a qualche suo savio amico questa ardita inten&shy;<lb/>zione, ei ne lo avrebbe senza dubbio distolto, dicendogli non poter <lb/>esser quella altro che una follia. </s>

<s>Ma pure &egrave; mirabile che uscito il <lb/>Cartesio in pubblico, a divisare gli ordini e i modi di quella sua <lb/>titanica impresa, tutt'altro ch'esser tenuto folle, ebbe plauso dalla <lb/>turba maravigliata e titolo di sapiente. </s></p><p type="main">

<s>Il libro, in cui si divisano quegli ordini e quei modi, usc&igrave; in <lb/>pubblico nel 1637 con un titolo, che si tradusse in quello di <emph type="italics"/>Spe&shy;<lb/>cimina Fhilosophiae<emph.end type="italics"/> o altrimenti <emph type="italics"/>Dissertatio de methodo recte re&shy;<lb/>gendae rationis.<emph.end type="italics"/> La bellezza del patrio l&igrave;nguaggio, in cui prima usc&igrave; <lb/>fuori alla luce il libro, fu una delle principali cagioni per cui ri&shy;<lb/>masero cos&igrave; dolcemente allettati, e quasi si direbbe sedotti i lettori. </s>

<s><lb/>Altra poi di quelle cagioni fu senza dubbio un aura conciliatrice <lb/>di pace nella prima, e un approvato sentimento di verit&agrave; nell'altre <lb/>due regole provvisorie da seguirsi, intanto che, distrutta la vecchia, <lb/>non si sia rifatta dall'Autore e ricostruita la nuova scienza morale. </s></p><p type="main">

<s>L'efficacia poi di queste regole sull'animo del lettore, e quel&shy;<lb/>l'aura conciliatrice di pace che si diceva, si rendono manifeste dal <lb/>considerar che la bellezza e la verit&agrave; di quelle stesse regole son che <lb/>tolgono ai divisamenti dell'Autore il carattere della follia. </s>

<s>Perci&ograve; <pb xlink:href="020/01/170.jpg" pagenum="151"/>questi son passati e quasi non sentiti in grazia di quelle, e la con&shy;<lb/>tradizione, che fra loro &egrave; manifesta, finisce poi di operare la seduzion <lb/>dell'effetto. </s></p><p type="main">

<s>Che fra le regole del metodo e i divisamenti del Cartesio passi <lb/>un'aperta contradizione si prova con facilit&agrave; in poche parole. </s>

<s>&Egrave; la <lb/>prima di quelle regole infatti che si debbono seguir le usanze del <lb/>proprio paese. </s>

<s>Questa regola &egrave; senza dubbio conciliatrice di pace, <lb/>ma &egrave; in aperta contradizione coi principii professati dall'Autore, <lb/>secondo i quali son quelle usanze false, perch&egrave; suggerite dalla igno&shy;<lb/>ranza universale. </s></p><p type="main">

<s>La terza regola bellissima &egrave; che non si dee voler mutar l'or&shy;<lb/>dine al mondo, ma alle nostre cupidigie. </s>

<s>Ora se si trasporta questa <lb/>regola dalla Filosofia morale, alla naturale, contradice apertamente <lb/>ai metodi filosofici del Cartesio, conforme ai quali il mondo si muta <lb/>veramente a seconda delle cupidigie del nostro intelletto. </s>

<s>E di ci&ograve; <lb/>basti la famosa teoria dei vortici per esempio. </s></p><p type="main">

<s>Senz'altro, s'intravede gi&agrave; che se Galileo &egrave; il Platone di questo <lb/>nuovo periodo del risorgimento della scienza, il Cartesio &egrave; l'Aristo&shy;<lb/>tile. </s>

<s>E tanto &egrave; vivo e incarnato lo spirito del filosofo di Stagira nelle <lb/>membra del Filosofo bretone, che d'ogni parte ne traspira la so&shy;<lb/>miglianza. </s>

<s>Aristotile accomoda la Natura alla capacit&agrave; del proprio <lb/>intelletto, e la ragion dei fatti la fa scaturire dall'artificiosa dialet&shy;<lb/>tica dei sillogismi. </s>

<s>Perci&ograve; quanto una di queste ragioni &egrave; pi&ugrave; sottile <lb/>e arguta, tanto ha secondo lui pi&ugrave; sapore di vero. </s>

<s>La facilit&agrave; di <lb/>spiegare i fatti naturali si aborrisce da lui e dalla sua scuola, come <lb/>segno della impotenza della ragione a dominarli. </s></p><p type="main">

<s>Che da un simile principio sien pure informate le fisiche spe&shy;<lb/>culazioni del Cartesio, due soli fra i molti esempii piace a noi di <lb/>sciegliere per provarlo, e son questi due esempi l'uno tolto dalla <lb/>ragion ch'ei rende dell'origine dei venti, l'altro dell'origine delle <lb/>fonti. </s>

<s>La vecchia fisica ammetteva che le esalazioni di sotto terra <lb/>commovessero i vapori dell'aria, e cos&igrave; avessero origine i venti. </s>

<s>Al <lb/>Cartesio troppo facile parve questa spiegazione, n&egrave; men semplice <lb/>e quasi puerile gli sembr&ograve; quell'altra delle dilatazioni e dei con&shy;<lb/>densamenti, che l'avvicendarsi del calore e del freddo producono <lb/>sulla mole dell'aria. </s>

<s>Perci&ograve; soccorse cos&igrave; a quel difetto colle arguzie <lb/>della sua nuova filosofia. </s>

<s>Immagin&ograve; che le dilatazioni, da cui vien <lb/>commossa l'aria, si producessero nelle minime particelle del vapore, <lb/>le quali, agitate e mosse in giro dal secondo elemento, occupano <lb/>maggiore spazio, a somiglianza di una bandiera menata in volta <pb xlink:href="020/01/171.jpg" pagenum="152"/>dalle agili mani dell'alfiere. </s>

<s>&ldquo; Quum vaporis formam habent, agi&shy;<lb/>tatio illarum adeo est concitata ut celerrime rotentur in omnes <lb/>partes, quemadmodum baculo per quem funiculus traiectus est, ce&shy;<lb/>lerrime rotato, videmus funiculum rectum atque extensum porrigi &rdquo; <lb/>(Meter. </s>

<s>Francof. </s>

<s>1692, pag. </s>

<s>131). </s></p><p type="main">

<s>La scmplicit&agrave; della fisica antica ammetteva che dagli stillicidi <lb/>delle nevi e dalla infiltrazione delle acque piovane avessero la loro <lb/>origine le fonti. </s>

<s>Ma il Cartesio, come di sopra era ricorso all'arguzia <lb/>delle banderuole, cos&igrave; qui ricorre all'arguzia degli alambicchi. </s>

<s>Im&shy;<lb/>magin&ograve; che le acque del mare s'insinuassero di sottoterra e si sol&shy;<lb/>levassero allo stato di vapori, i quali condensati poi dal freddo sotto <lb/>le cupole dei monti, giusto come nel cappello dell'alambicco, tor&shy;<lb/>nassero ad apparire qua e l&agrave; in acque sorgenti. </s></p><p type="main">

<s>Questa nuova sorta di Filosofia naturale, che tanto al vivo si <lb/>rassomiglia alla vecchia filosofia di Aristotile, viziata nelle radici, <lb/>non poteva non riuscir, al pari di quella, sterile di buoni frutti. </s>

<s><lb/>Quali frutti in verit&agrave; dette la Filosofia cartesiana alle scienze speri&shy;<lb/>mentali? </s>

<s>&Egrave; vero che il celebre Autore della Dissertazione del Me&shy;<lb/>todo formul&ograve; nella Diottrica la legge delle rifrazioni, e divis&ograve; nella <lb/>Meteorologia il modo vero del dipingersi e del rappresentarsi ai <lb/>nostri occhi l'iride in cielo, ma sta a vedere se questi sieno ve&shy;<lb/>ramente frutti della Filosofia cartesiana. </s>

<s>Il Newton, a principio gli <lb/>credette tali, ma poi si ridisse, e attribu&igrave; la legge delle rifrazioni <lb/>allo Snellio, e al De Dominis la teoria dell'arco baleno. </s></p><p type="main">

<s>Meglio che al manoscritto dello Snellio, come fu primo a in&shy;<lb/>sinuare l'Huyghens, il quale per&ograve;, a riscontrare il fatto sulle pagine <lb/>dello stesso manoscritto fu secondo dopo Isacco Vossio; noi credia&shy;<lb/>mo che il Cartesio attingesse piuttosto a un libro stampato, qual'&egrave; <lb/>il Corso matematico di Pietro Herigonio. </s>

<s>Perci&ograve;, non &egrave; merito del&shy;<lb/>l'Autore della Diottrica nemmeno l'aver formulata, come l'Huyghens <lb/>e il Newton par che gli concedano, quella legge della proporzione <lb/>costante fra i seni degli angoli incidenti e dei rifratti: n&egrave; suoi pure, <lb/>ma del Keplero, ne sono i principii dimostrativi. </s></p><p type="main">

<s>Quanto all'iride, il Newton che nelle Lezioni di Ottica s'era <lb/>contentato di dire essere stata dal Cartesio, a spiegare il fenomeno, <lb/>apparecchiata la via, nel Trattato di Ottica poi dice che fu il De <lb/>Dominis <emph type="italics"/>vir celeberrimus,<emph.end type="italics"/> il quale prima insegn&ograve; che l'iride inte&shy;<lb/>riore si fa per due rifrazioni e una riflessione e l'esteriore per due <lb/>rifrazioni e due riflessioni. </s>

<s>Or, per amore alla verit&agrave;, convien dire <lb/>che questo &egrave; falso, e siam costretti a concludere che il Newton o <pb xlink:href="020/01/172.jpg" pagenum="153"/>non vedesse o non esaminasse bene il Trattato <emph type="italics"/>De radiis visus et <lb/>lucis<emph.end type="italics"/> del celebre spalatrese. </s>

<s>&Egrave; chiaro infatti che le doppie rifrazioni <lb/>e le doppie riflessioni del De Dominis hanno tutt'altro significato <lb/>che nel Cartesio, e se queste son conformi alla verit&agrave;, quelle son <lb/>delle solite peripatetiche immaginazioni. </s>

<s>N&egrave; affatto giusta sembra <lb/>a noi quell'altra sentenza del Newton che cio&egrave; il Cartesio non in&shy;<lb/>tendesse la natura dei colori, avendo egli rassomigliati i colori del&shy;<lb/>l'iride a quelli in che si disperdono i raggi del sole refratti attra&shy;<lb/>verso ai prismi triangolari. </s></p><p type="main">

<s>Se qualcuno perci&ograve; preced&egrave; il Cartesio nella scientifica spie&shy;<lb/>gazione del fenomeno meteorologico, questi fu, n&ograve; il De Dominis <lb/>ma Ferrante Imperato. </s>

<s>E perch&egrave; non &egrave; facile che il lontano e su&shy;<lb/>perbo Bretone si piegasse a leggere l'Historia Naturale del nostro <lb/>Napoletano, non resta ad ammettere se non che egli attingesse, <lb/>come da prima fonte, al Maurolico citato dallo stesso Cartesio con <lb/>orgoglioso disprezzo. </s></p><p type="main">

<s>Or il Maurolico, che fra tutti i precursori del Newton fu primo <lb/>a intraveder la teoria dei colori e a trattar dell'iride come d'un <lb/>fenomeno d'ottica matematica, bastava solo ad aprir la via al Car&shy;<lb/>tesio, a cui, prevenuto gi&agrave; nell'esperienza delle palle piene d'acqua <lb/>che appariscono iridescenti collocate, rispetto all'occhio, in deter&shy;<lb/>minata posizione e distanza; non bisogn&ograve;, a risolvere il problema, <lb/>altro pi&ugrave; che l'uso del calcolo e della geometria. </s></p><p type="main">

<s>Qui poi, cio&egrave; nel calcolo geometrico consistono i meriti singo&shy;<lb/>lari del Cartesio, il quale ci rivela anco da questa parte lo spirito <lb/>aristotelico informatore della sua nuova Filosofia. </s>

<s>Si vide infatti che <lb/>unico frutto della scuola peripatetica non fu che l'algebra, come <lb/>l'algebra applicata fu pure l'unico frutto della scuola cartesiana. </s>

<s><lb/>Questa stessa applicazione dell'Algebra alla Geometria rende la ra&shy;<lb/>gione di qualcuno di quei progressi, che lo stesso Cartesio fece nella <lb/>Meccanica, bench&egrave; anco di qui trasudi la pece aristotelica in quelle <lb/>sofistiche sottigliezze, tese qua e l&agrave;, per le sue Lettere, come lacci <lb/>insidiosi, a cogliere in fallo i teoremi di Galileo. </s></p><p type="main">

<s>Ma della sterilit&agrave; d'ogni buon frutto di scienza sperimentale il <lb/>Cartesio da s&egrave; stesso s'accusa e si confessa. </s>

<s>S'accusa, quando, nella <lb/>Prefazione alla traduzione latina dei Principii della Filosofia, dice <lb/>che gli resterebbe a trattar della Medicina e delle arti meccaniche, <lb/>per le quali si richiedono sperimenti e spese <emph type="italics"/>quibus privatus qualis <lb/>ego sum nisi a publico adiuvaretur par esse non posset.<emph.end type="italics"/> Galileo, <lb/>che fu tanto pi&ugrave; povero di lui, non fece mai di queste scuse, e si <pb xlink:href="020/01/173.jpg" pagenum="154"/>liber&ograve; dalle spese, che occorrono a sperimentare, fabbricando gli <lb/>strumenti colle sue proprie mani. </s></p><p type="main">

<s>Il Cartesio altres&igrave; da se stesso si confessa, quando in sulla fine <lb/>della sua celebre Dissertazione del Metodo, dop'avere accennato <lb/>alle dottrine fisiche professate ed esposte nella Diottrica e nella <lb/>Meteorologia, soggiunge queste parole: &ldquo; Nec me etiam primum <lb/>ullarum inventorem esse iacto, sed tantum me nunquam illas pro <lb/>meis adoptasse, vel quod ab aliis prius receptae fuissent, vel quod <lb/>non fuissent, verum unicam hanc ob causam quod mihi eas ratio <lb/>persuasisset &rdquo; (Francof. </s>

<s>1692, pag. </s>

<s>40). E cos&igrave; intende forse di sde&shy;<lb/>bitarsi col Maurolico e col Keplero, col De Dominis e con lo Snellio. </s></p><p type="main">

<s>Ma come si conciliano cos&igrave; fatte confessioni colle orgogliose <lb/>pretese del Cartesio? </s>

<s>Una tal domanda non pu&ograve; mover che da co&shy;<lb/>loro, i quali si persuadono che l'Autore della Dissertazione del Me&shy;<lb/>todo dasse qualche importanza alla spiegazione di un particolar fatto <lb/>di Ottica o di Meleorologia. </s>

<s>Queste non son per lui altro che miche <lb/>cadute gi&ugrave; da pi&ugrave; lauta mensa. </s>

<s>Miche son tutte quelle raccattale <lb/>ne'suoi libri da Galileo, e fra quelle stesse miche, dalla teoria della <lb/>musica in fuori, non ci &egrave; nulla di buono. </s>

<s>Che se tu vuoi sedere <lb/>al convito della scienza, par che egli dica al lettore, cerca il mio <lb/>libro che s'intitola <emph type="italics"/>Principii della Filosofia.<emph.end type="italics"/> Vedrai come dalle co&shy;<lb/>gitazioni del lilosofo, nella prima parte dello stesso libro, esca fuori <lb/>l'esistenza di Dio e del mondo. </s>

<s>Vedrai, nella terza parte, come, per <lb/>mezzo di moti vertiginosi, si stabiliscan le leggi che governano <lb/>l'Universo, e nell'ultima di quelle parti assisterai da te stesso al <lb/>nascere e al trasformarsi il seno della tua madre Terra. </s></p><p type="main">

<s>Quando si pubblic&ograve; il Cosmoleoro dell'Huyghens e il Newton <lb/>dimostr&ograve; della Filosofia naturale pi&ugrave; veri Principii, disparvero quei <lb/>seducenti fantasmi cartesiani dagli occhi di tutti. </s>

<s>E che ci rimase <lb/>di realt&agrave;? </s>

<s>Ci rimase l'Algebra geometrica e i due Trattati <emph type="italics"/>Passiones <lb/>animae<emph.end type="italics"/> e <emph type="italics"/>De homine,<emph.end type="italics"/> dove s'instituisce l'interiore esame della <lb/>coscienza, e i fatti psicologici s'illustrano colle matematiche e colla <lb/>fisiologia. </s>

<s>Ecco quel che di scienza vera rimane al Cartesio e alla <lb/>Francia. </s>

<s>Tutto il resto vi approd&ograve; d'Italia, come frutto di quell'al&shy;<lb/>bero che unico seppe metter le radici nel buon terreno, e che ri&shy;<lb/>mase perci&ograve; unico a regnare in mezzo alla foresta. </s></p><p type="main">

<s>Mentre la patria insomma, lusingata dal seducente linguaggio <lb/>e dalle belle promesse, s'aspettava di riposare all'ombra, e sten&shy;<lb/>dendo la mano ai rami dell'amata indigena pianta, largamente <lb/>saziar la fame della scienza, si trov&ograve; a mendicare altri frutti ma-<pb xlink:href="020/01/174.jpg" pagenum="155"/>turati sotto altro sole in terra straniera. </s>

<s>Per men vergogna, e quasi <lb/>che alla mendicit&agrave; si volesse attribuire qualche parte del merito, <lb/>il pietoso ufficio fu commesso a due uomini, i quali partecipavano <lb/>delle due patrie: Niccol&ograve; Fabrizi di Peiresc ed Elia Diodati. </s>

<s>Nati <lb/>ambedue di stirpe Toscana, dalla Toscana trapiantarono in Francia <lb/>la scienza, come i loro avi vi avevano gi&agrave; trapiantata la famiglia, <lb/>e per loro mezzo principalmente risuon&ograve; in fin l&agrave; il nome di Ga&shy;<lb/>lileo, e vi si diffusero le dottrine. </s>

<s>Ismaele Bullialdo ne illustrava <lb/>le dottrine astronomiche e Pier Gassendo le meccaniche. </s>

<s>La fisica <lb/>sperimentale, anch'essa dal Cartesio antivacuista resa impotente, <lb/>fu introdotta in Francia da Marino Mersenno, l'insetto volante, che <lb/>port&ograve; d'Italia sull'ali il polline fecondatore. </s></p><p type="main">

<s>Qual pi&ugrave; piena conquista, qual pi&ugrave; larga vittoria si poteva ri&shy;<lb/>promettere il nostro grande Italiano? </s>

<s>Quell'orgoglioso Bretone, che, <lb/>per libidine di regnar solo, intendeva non tanto di trucidare i fra&shy;<lb/>telli, ma disperdere per fino ogni memoria degli avi, rimase tru&shy;<lb/>cidato anch'esso, non dalla punta, ma dall'ombra della spada di <lb/>Galileo, il cui Regno unico dura, e i discendenti del quale son come <lb/>terribile oste ordinata in battaglia contro l'errore. </s></p><p type="main">

<s>Sarebbe ora il tempo per noi di passare in rivista quei com&shy;<lb/>battenti sotto un unica insegna, se non ci attraessero a s&egrave; gli sguardi <lb/>due ombre solitarie, che avvolte nel pallio filosofale procedono con <lb/>regal maest&agrave; indipendenti. </s>

<s>Come mai, in mezzo alla strage otto&shy;<lb/>manna de'due fieri conquistatori, essi soli son rimasti superstiti, <lb/>quasi fossero giudicati i soli meritevoli di compartecipare alle glorie <lb/>del Regno? </s>

<s>Sono essi Guglielmo Gilbert, e Guglielmo Harvey, sui <lb/>quali due, per conoscerli meglio, convien tener alquanto fisso lo <lb/>sguardo. </s></p><p type="main">

<s>Fruga senza dubbio la nostra curiosit&agrave; il veder che Galileo, <lb/>unico fra i contemporanei, accoglie il Gilbert e l'esalta quasi alla <lb/>dignit&agrave; dei Filosofi antichi. </s>

<s>N&egrave; con minore curiosit&agrave; pure si osserva <lb/>che il Cartesio, nel Gilbert e nell'Harvey, come nelle due sole im&shy;<lb/>mobili torri, abbia fiaccato il vento desolatore della sua superbia. </s>

<s><lb/>Ci&ograve; vuol dire esser grandi davvero, se come tali furon sentiti e <lb/>temuti da quei due che volevano sovraneggiare su tutti; ond'ei non <lb/>&egrave; fuor di proposito l'investigar qui brevemente, di quella grandezza <lb/>che esce cos&igrave; fuori dell'ordinario, la ragione e i meriti. </s></p><p type="main">

<s>N&egrave; in ordine a ci&ograve; &egrave; da lasciar di notare per prima cosa che <lb/>i due grandi Inglesi si distinguono per due qualit&agrave; diverse; l'uno <lb/>dedito principalmente all'esperienza, l'altro alla speculazione. </s>

<s>Il <pb xlink:href="020/01/175.jpg" pagenum="156"/>libro <emph type="italics"/>De magnete<emph.end type="italics"/> &egrave; una sequela di fisici sperimenti, senza dubbio <lb/>avvedutissimi e nuovi, ma che tutti si aggirano intorno al medesimo <lb/>soggetto, con una certa prol&igrave;ssit&agrave;, non forse ingiustamente notata <lb/>dal Verulamio. </s>

<s>Di speculazioni veramente non ha il Gilbert altro <lb/>che quel concetto lodato da Galileo, e qualificato per istupendo, di <lb/>riguardar cio&egrave; la Terra come un magnete e il magnete stesso come <lb/>una terrella. </s>

<s>Del resto egli rifugge dall'approvar que'fluidi magne&shy;<lb/>tici introdotti dal Sarpi e dal Porta, e gli piace meglio di dar, con <lb/>l'antico Talete e con lo Scaligero, alla calamita spirito di vita e <lb/>senso animale. </s></p><p type="main">

<s>L'esercitazione anatomica <emph type="italics"/>De motu cordis<emph.end type="italics"/> dell'Harvey &egrave; al <lb/>contrario tutta una speculazione. </s>

<s>Non &egrave; egli mica che dimostri spe&shy;<lb/>rimentalmente il moto del sangue nel circolo universale dei vasi. </s>

<s><lb/>Egli lo induce principalmente dall'anatomia delle arterie e dalle <lb/>valvole delle vene. </s>

<s>Del resto, egli non sa se veramente il sangue <lb/>arterioso ritorni nelle vene per anastomosi, o perch&egrave; le vene stesse <lb/>lo risorbono disperso e ristagnante in mezzo alle fibre muscolari. </s>

<s><lb/>L'esperienza stessa proposta da Galeno a lui pare impossibile d'ese&shy;<lb/>guirla negli animali vivi. </s>

<s>Non gli par che possa riuscire a nessuno <lb/>d'introdurre un cannellino di materia trasparente nelle due imboc&shy;<lb/>cature dell'arteria recisa, e ci&ograve; per la gran violenza del sangue <lb/>che irrompe. </s>

<s>Eppure il nostro Tommaso Cornelio dimostr&ograve;, contro <lb/>l'Harveio, che l'esperienza di Galeno si poteva benissimo praticare, <lb/>e, negli animali vivi, por, sotto gli occhi de'riguardanti stupiti, il <lb/>sangue che fugge espulso dalla sistole del cuore. </s></p><p type="main">

<s>L'altro libro non men celebre dell'Harvey &egrave; quello <emph type="italics"/>De gene&shy;<lb/>ratione animalium.<emph.end type="italics"/> Si disse che per lui f&ugrave; finalmente cacciato quel <lb/>pernicioso errore della generazione spontanea. </s>

<s>Chi vi torna sopra <lb/>per&ograve; con pi&ugrave; maturo giudizio, &egrave; costretto a concludere che il gran <lb/>Filosofo inglese niente altro fa che sostituire a un errore, un errore <lb/>pi&ugrave; vieto. </s>

<s>Egli ammette infatti nella materia certi principii animali, <lb/>predisposti dall'Artefice eterno, nella primitiva creazion delle cose: <lb/>principii che l'Elmont chiam&ograve; col nome di <emph type="italics"/>archei,<emph.end type="italics"/> e l'Harveio, con <lb/>fedel traduzione, primordii. </s>

<s>Da cos&igrave; fatti principii disseminati qua <lb/>e l&agrave; per l'aria e caduti per caso in parte dove trovassero favore&shy;<lb/>voli condizioni al loro incubamento, avrebbero, secondo l'Autore, <lb/>origine tutti quegl'insetti, che non riconoscono un padre. </s>

<s>Ma a di&shy;<lb/>mostrar che veramente ogni animale, sia pure di qualunque infimo <lb/>ordine, riconosce un padre e una madre della medesima specie, vi <lb/>bisognavano quelle attente e pazientemente ripetute esperienze, alle <pb xlink:href="020/01/176.jpg" pagenum="157"/>quali si credeva l'Harvey di poter supplir con le ipotesi e con le <lb/>induzioni: esperienze che poi riuscirono cos&igrave; bene alle mani del <lb/>Redi e del Malpighi. </s></p><p type="main">

<s>In ogni modo, il Gilbert e l'Harvey sono due ingegni singo&shy;<lb/>lari: il primo &egrave; mirabile per l'arte squisitissima di sperimentare e <lb/>l'altro per una potentissima virt&ugrave; d'indurre la verit&agrave; dai fatti sem&shy;<lb/>plicemente osservati. </s>

<s>Se avessero avuta comune la potenza dell'in&shy;<lb/>gegno, com'ebbero comune la patria, d'ambedue loro insieme sa&shy;<lb/>rebbe uscita al mondo una cosa perfetta. </s></p><p type="main">

<s>Or su quale albero mai &egrave; maturata quella tal perfezione? </s>

<s>Sul&shy;<lb/>l'albero vecchio, rispondasi, della scienza italiana. </s>

<s>Chi legge la Fi&shy;<lb/>siologia Nuova del Magnete non ha bisogno di tanti argomenti a <lb/>persuadersi che il Gilbert non attinge d'altronde le prime tradi&shy;<lb/>zioni della scienza magnetica che dall'Italia; dal Fracastoro, dal <lb/>Sarpi, dal Porta. </s>

<s>Chi legge l'Esercitazione anatomica <emph type="italics"/>De motu cordis<emph.end type="italics"/><lb/>non ha bisogno di far tante domande: risponde da s&egrave; medesimo <lb/>l'Autore, pi&ugrave; coi fatti che con le parole, esser quello il frutto elet&shy;<lb/>tissimo degli insegnamenti padovani. </s></p><p type="main">

<s>Consolati dall'ammirar tali due frutti che insaporarono sotto i <lb/>soli d'Italia, sopra i pi&ugrave; sporgenti rami del vecchio albero della <lb/>scienza, ora &egrave; tempo di venire una volta a veder quai rigogliosi <lb/>rampolli, e quale ubert&agrave; di frutti si producessero nell'albero nuovo. </s></p><p type="main">

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

<s>Il primo e pi&ugrave; eletto di quei rampolli, &egrave; il bresciano don Be&shy;<lb/>nedetto Castelli. </s>

<s>Come nella generazione animale il primogenito <lb/>suol, meglio degli altri parti, rassomigliar le virt&ugrave; e le fattezze stesse <lb/>del padre; cos&igrave; nelle opere dell'ingegno il Castelli ha pi&ugrave; strette <lb/>le somiglianze con Galileo. </s>

<s>L'Autore dei Dialoghi del moto, pot&egrave; <lb/>con diritto intitolar quell'opera <emph type="italics"/>Scienza Nuova,<emph.end type="italics"/> e Scienza Nuova, <lb/>con pari diritto, poteva intitolare i suoi libri l'Autore della Misura <lb/>delle acque correnti. </s>

<s>N&egrave; l'esser preceduto dall'Alberti e dal Cardano <lb/>o dal pi&ugrave; antico Frontino gli toglie nulla a quella novit&agrave;, o gli detrae <lb/>del suo principato, se per poco si ripensi che non consiste la scienza <lb/>in alcune pratiche cognizioni, ma nell'ordinata sequela di teoremi <lb/>dimostrati e conclusi da veri e approvati principii. </s>

<s>Non gli detrae <pb xlink:href="020/01/177.jpg" pagenum="158"/>nulla Leonardo da Vinci, le speculazioni e l'esperienze del quale <lb/>rimanevano tuttavia informi e sepolte nei manoscritti. </s>

<s>In ogni modo, <lb/>gli errori che si commettevano nelle dispense delle acque in Lom&shy;<lb/>bardia, con s&igrave; grave danno ora dei compratori, ora dei venditori, <lb/>attestano che a quei tempi nessuno ancora gli aveva notati, e se <lb/>tanto zelo bisogn&ograve; al Castelli per persuader quelle verit&agrave; negli usi <lb/>inveterati, &egrave; ci&ograve; manifestissimo segno dell'apparir nuove fra gli <lb/>uomini le verit&agrave; stesse predicate da lui. </s>

<s>Nuove, non che ad altri, <lb/>apparvero al medesimo Galileo, come, per citare un fatto solo, po&shy;<lb/>trebbesi argomentar facilmente comparando il Discorso contro il <lb/>Bertazzolo, con la Lettera sul fiume Bisenzio. </s></p><p type="main">

<s>Altro punto di rassomiglianza, che il Castelli ha con Lui che <lb/>lo aveva generato alla scienza, &egrave; l'ardor di diffondere quelle astro&shy;<lb/>nomiche verit&agrave;, che un profondo sentimento sincero di Religione <lb/>gli persuadeva esser tanto meglio adattate degli antichi sistemi a <lb/>rivelar le glorie del Creatore. </s>

<s>Nelle fasi di Venere, prima che Ga&shy;<lb/>lileo gli avesse palesati i suoi pensieri, nei moti di alcune stelle, che <lb/>ei dubita esser effetti della parallasse annuale, sagacemente intra&shy;<lb/>vede argomenti concludenti<gap/>simi a confermare la verit&agrave; del sistema <lb/>copernicano. </s>

<s>Nel piccolo mondo gioviale riconosce perfettamente <lb/>ritratta l'immagine del pi&ugrave; gran mondo solare, e nelle quattro lune <lb/>che si rivolgono intorno al centro di Giove, gli par avere il pi&ugrave; <lb/>bello argomento a provar che i pianeti si rivolgono in simil modo <lb/>intorno al centro del sole. </s>

<s>Egli, pi&ugrave; infaticabile forse di quel che <lb/>non apparisce dai pochi documenti rimasti, a calcolar l'Effemeridi <lb/>dei quattro satelliti cooperava con Galileo, che di quando in quando <lb/>nota ne'suoi Registri, che l'osservazione fatta, per quel tal giorno <lb/>e per quell'ora, &egrave; <emph type="italics"/>Patris Benedicti.<emph.end type="italics"/> E quando il Cassini attendeva <lb/>all'Effemeridi bolognesi, il Viviani, perch&egrave; se ne potesse giovare, <lb/>e perch&egrave; le riscontrasse con le sue nuove osservazioni, gli mandava <lb/>una tavola dei moti de'Medicei, incerto se essa apparteneva a Ga&shy;<lb/>lileo o al Castelli. </s></p><p type="main">

<s>N&egrave; da passare inconsiderata, a proposito delle esercitazioni <lb/>astronomiche del p. </s>

<s>Benedetto, &egrave; la prima osservazione di quella <lb/>fascia, che precinge il corpo di Giove, con quell'altra, che concerne <lb/>la luce secondaria, di che va suffusa la Luna vicina al primo quarto. </s>

<s><lb/>Dice che, facendo egli riflessione a quel che Galileo ne'Dialoghi del <lb/>Sistema accenna della medesima luce secondaria, pi&ugrave; cospicua la <lb/>mattina che la sera, adducendone per ragione l'essere in quel tempo <lb/>la Luna illuminata dal riflesso di vastissimi continenti della Terra; <pb xlink:href="020/01/178.jpg" pagenum="159"/>giudic&ograve; che ritrovandosi, in quel tempo che faceva le sue osserva&shy;<lb/>zioni, la Luna meridionale, dovesse essere illustrata dalla Terra, e <lb/>perci&ograve; gli venne in mente che le terre meridionali, allora incognite, <lb/>dovessero essere vastissime provincie (Alb. </s>

<s>X, 244). Galileo approv&ograve; <lb/>la congettura (ivi, pag. </s>

<s>248), e le scoperte geografiche avverarono <lb/>il vaticinio. </s></p><p type="main">

<s>Educatosi alla lettura del Saggiatore, che, spiegava come testo <lb/>di Fisica nuova nella sua scuola, il Castelli scrisse, in soggetto di <lb/>fisica sperimentale, alcuni Trattatelli o Discorsi, amorosamente rac&shy;<lb/>colti o fatti pubblicare nel 1669 dal principe Leopoldo dei Medici, <lb/>venticinque anni dopo la morte dell'Autore. </s>

<s>Quello <emph type="italics"/>Sulla vista<emph.end type="italics"/> non <lb/>&egrave; per verit&agrave; che un commentario delle dottrine ottiche del Keplero. </s>

<s><lb/>In quello che egli intitola <emph type="italics"/>Mattonata<emph.end type="italics"/> si descrivono le prime espe&shy;<lb/>rienze e si tentano le prime teorie del calorico raggiante, e in <lb/>quell'altro <emph type="italics"/>Del modo di conservare i grani<emph.end type="italics"/> si notano per la prima <lb/>volta i varii gradi di conducibilit&agrave; del calore nelle varie costituzioni <lb/>dei corpi. </s>

<s>Il <emph type="italics"/>Discorso sulla Calamila,<emph.end type="italics"/> pubblicato in questi ultimi <lb/>anni, non ha, a voler esser giusti, di che la scienza del Magnete <lb/>s'avvantaggi. </s></p><p type="main">

<s>Immediatamente dopo il Castelli, si dovrebbe collocare, in questo <lb/>splendido Senato della scienza italiana, Bonaventura Cavalieri, se, <lb/>piuttosto che alle scienze sperimentali, non avesse atteso alla Ma&shy;<lb/>tematica pura e alla Geometria, nelle quali discipline fece cos&igrave; <lb/>grandi progressi, da meritarsi che Galileo lo onorasse pubblicamente <lb/>asserendo di lui ch'ei sarebbe per riuscire uno de'principali ma&shy;<lb/>tematici di quei tempi (Alb. </s>

<s>XIII, 45). Dallo sperimentare il Cava&shy;<lb/>lieri non &egrave; alieno, ma non ha, o non sa trovare il modo d'eserci&shy;<lb/>tarvisi. </s>

<s>Si prova a disegnar qualche macchina, ma nell'effetto non <lb/>riesce. </s>

<s>Proposto dal Torricelli al Granduca per uno degli arbitri a <lb/>decidere le famose controversie del regolamento delle Chiane, se <lb/>ne scusa, rispondendo che a lui <emph type="italics"/>mancava quella esperienza che <lb/>bisogneria ancora aver fatto per poter parlar francamente in simil <lb/>materia<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XLI, c. </s>

<s>223). Nonostante a lui si deb&shy;<lb/>bono alcuni utili avvertimenti intorno alle figure geometriche da <lb/>darsi ai vetri, per uso dei canocchiali, e fu il primo che pubbli&shy;<lb/>casse, nel suo <emph type="italics"/>Specchio Ustorio,<emph.end type="italics"/> il pensiero sovvenutogli di com&shy;<lb/>porre insieme, negli strumenti astronomici, le lenti cristalline e gli <lb/>specchi. </s>

<s>Richiestone dal Castelli, egli fu che distese la famosa Di&shy;<lb/>mostrazione della proposizione II, inserita dal suo stesso Autore. </s>

<s><lb/>senza mutar parola, nel II Libro della Misura delle Acque correnti. <pb xlink:href="020/01/179.jpg" pagenum="160"/>Egli fu che di splendidi e nuovi concetti illustr&ograve; la dimostrazione <lb/>galileiana delle leggi dei moti naturali e dei proietti. </s></p><p type="main">

<s>Alla fama, che &egrave; certa di non essere smentita, alla fede che <lb/>s'alimenta d'affetto, alla morte che fa l'uomo credulo e piamente <lb/>indulgente, piuttosto che alle opere scritte e stampate, va debitore <lb/>d'essere annoverato qui in terzo luogo, Vincenzio Renieri. </s>

<s>Nel tempo <lb/>che il negoziato delle Longitudini con gli Stati Uniti di Olanda sol&shy;<lb/>lecitava Galileo di dar compiuto ordine alle Effemeridi gioviali, il <lb/>Renieri pensava a stampar le sue <emph type="italics"/>Tabulae Secundorum mobilium,<emph.end type="italics"/><lb/>che il Cavalieri giudic&ograve; degne di essere dagli studiosi dell'Astro&shy;<lb/>nomia annoverate fra.i libri di maggiore utilit&agrave; (Alb. </s>

<s>X, 398). Della <lb/>stampa ne trattava l'Autore, nel marzo del 1637, con Galileo, pre&shy;<lb/>gandolo volesse scrivere a Roma due righe al Castelli, perch&egrave; si <lb/>prendesse cura di muovere parola allo stampatore Guglielmo Fa&shy;<lb/>ciotti (ivi, pag. </s>

<s>200). Le trattative andarono per&ograve; a vuoto, e le Tavole <lb/>dei Secondi Mobili, intitolate Medicee, perch&egrave; dedicale al Granduca <lb/>Ferdinando II, si stamparono in Firenze nel 1639. Largamente poi <lb/>ampliate e corrette, quelle stesse Tavole, furono nuovamente im&shy;<lb/>presse dal medesimo stampatore nel 1647. Pregato il Torricelli di <lb/>riveder le bozze di stampa, in sul punto che doveva incoglierlo la <lb/>morte, suppl&igrave; al tedioso ufficio il Viviani (MSS. Gal.Dis. </s>

<s>T. CXLIV, c.4). </s></p><p type="main">

<s>Tornando ora indietro al 1637, Galileo, che sollecitato dal ne&shy;<lb/>gozio delle Longitudini si sentiva, per la vecchiezza e per la cecit&agrave;, <lb/>a cos&igrave; faticosa opera impotente, pens&ograve; di chieder l'aiuto del Renieri, <lb/>riconosciuto per i calcoli delle Tavole Medicee, il pi&ugrave; esperto fra i <lb/>suoi Discepoli. </s>

<s>Il Renieri, dall'altra parte, con lettera del d&igrave; 11 Di&shy;<lb/>cembre 1637, rispose che non avrebbe tralasciato cura o diligenza <lb/>alcuna possibile per servirlo (Alb. </s>

<s>X, 247). </s></p><p type="main">

<s>Preordinate cos&igrave; le cose, Galileo incominci&ograve; col padre Vincenzio <lb/>una specie d'istituzione intorno alle operazioni astronomiche ne&shy;<lb/>cessarie a perfezionare i calcoli delle Medicee, e per prima gli in&shy;<lb/>segna la sua invenzione del misurare il foro della pupilla. </s>

<s>Poi torna <lb/>a descrivergli l'uso dello strumento per misurarne pi&ugrave; esattamente <lb/>le distanze dei pianeti dal centro di Giove, e gli consegna, perch&egrave; <lb/>gli possano servire di norma, le Effemeridi calcolate gi&agrave; da s&egrave; e <lb/>dal Castelli. </s>

<s>Nell'Aprile del 1639 l'Osservatore di Genova scrive a <lb/>Galileo poco mancargli per avere emendato in tutto il moto delle <lb/>Medicee, e per rendere assolute l'Effemeridi di sei mesi futuri <lb/>(Alb. </s>

<s>X, 336). Nel maggio ammalato, tornato nel giugno al faticoso <lb/>lavoro, s'accorse che, ad emendar que'moti, all'equazion tolemaica <pb xlink:href="020/01/180.jpg" pagenum="161"/>dei giorni naturali conveniva aggiungervene in ogni modo un'altra, <lb/><emph type="italics"/>cagionata dal mancar la velocit&agrave; del moto diurno nell'allontanarsi <lb/>la Terra dal sole apogeo<emph.end type="italics"/> (ivi, pag. </s>

<s>339). </s></p><p type="main">

<s>Proseguiva il valente osservatore, con grande alacrit&agrave; nell'im&shy;<lb/>presa, tanto pi&ugrave; ch'ei ci vedeva infervorati il Granduca e il Prin&shy;<lb/>cipe Leopoldo, che lo fornivano de'pi&ugrave; eccellenti canocchiali, che <lb/>si sapesse essere stati fabbricati in Europa. </s>

<s>Perci&ograve;, alla corte di <lb/>Firenze, il Renieri mandava l'Effemeridi calcolate via via, prima <lb/>che ad Arcetri. </s>

<s>Il principe Leopoldo per&ograve; ne faceva riscontrar l'esat&shy;<lb/>tezza, e avute quelle per l'aprile e pel maggio 1640, nelle notti del <lb/>due e degli otto di quel medesimo mese di Maggio, furono osservati <lb/>tre satelliti sempre occidentali e uno orientale. </s>

<s>&ldquo; Ora avendosi dal&shy;<lb/>l'Effemeridi (scrive lo stesso Principe al Renieri) che in tal notte <lb/>si dovevano vedere due di quelle stelle orientali e due occidentali, <lb/>mi fa venir dubbio che una tanta differenza, quale non pu&ograve; nascere, <lb/>n&egrave; per lo svariar degli orioli n&egrave; per negligenza dell'osservatore, <lb/>possa venire dall'errore della stampa &rdquo; (MSS. Gal. </s>

<s>Dis. </s>

<s>T. V. c. </s>

<s>248). </s></p><p type="main">

<s>Par che dunque fossero quelle Effemeridi stampate, e cos&igrave; forse <lb/>l'Autore intendeva di mettere insieme a poco per volta il suo libro. </s>

<s><lb/>Ma in sette anni, quanti ne decorsero dalla data di questa lettera, <lb/>che &egrave; del 13 maggio 1640, alla morte dell'Autore, la pubblicazione <lb/>di quelle Tavole di tanti desiderii, non solo non ebbe effetto, ma <lb/>nessuno sa dir se nemmeno ella avesse avuto principio. </s>

<s>Ragione di <lb/>una tale incertezza &egrave; il celebre fatto della dispersione delle carte <lb/>e degli strumenti astronomici del Renieri, immediatamente avve&shy;<lb/>nuta dopo la morte di lui. </s>

<s>Celebre fatto diciamo, per le tante cose <lb/>che da tanti ne sono scritte. </s>

<s>A noi basta richiamar l'attenzione <lb/>sopra una lettera, che, pochi giorni dopo la morte del fratello, scri&shy;<lb/>veva a uno sconosciuto cortigiano de'Medici Giovan Battista Renieri. <lb/></s>

<s>&ldquo; Vivo in speranza, egli dice, circa la ricuperazione delli scritti <lb/>della felice memoria di mio fratello: ne attendo pertanto l'avviso <lb/>dell'effetto, avendo intenzione di pubblicare alle stampe l'opera che <lb/>egli ha composto del moto de'pianeti medicei di Giove. </s>

<s>E perch&egrave; <lb/>forse l'immatura sua morte gli ha tronco que'concetti, che sperava <lb/>col tempo di produrre alla luce, desidererei pertanto, avendomeli <lb/>in sua vita partecipati, farli pubblicare sotto il suo nome &rdquo; (MSS. Gal. </s>

<s><lb/>Disc. </s>

<s>T. V. c. </s>

<s>232). Da chi Giovan Battista sperasse di recuperare <lb/>quei manoscritti, non si sa, perch&egrave; non lo dice. </s>

<s>Forse potrebb'esser <lb/>quel Giuseppe Agostini, su cui fecero cadere un sospetto di furto <lb/>Cosimo Galilei e il Viviani. </s>

<s>In ogni modo per&ograve;, n&egrave; Giovan Batista <pb xlink:href="020/01/181.jpg" pagenum="162"/>Renieri, n&egrave; Cosimo Galilei riuscirono a recuperare le carte del fra&shy;<lb/>tello e dell'avo. </s>

<s>Che le venissero poi da Pisa alla Biblioteca pala&shy;<lb/>tina di Firenze, non si sa per&ograve; come n&egrave; quando, lo afferma l'Alberi; <lb/>e se delle Effemeridi e degli altri studii intorno al sistema di Giove <lb/>non si trovarono veramente, fra le carte del Monaco olivetano, altro <lb/>che le cose pubblicate dal medesimo Alb&egrave;ri, si pu&ograve; ripetere quel <lb/>che si diceva dianzi, che cio&egrave; la gloria scientifica di Vincenzio Re&shy;<lb/>nieri &egrave; affidata alla fama, alla fede, a quella riverenza che inspira <lb/>la morte. </s></p><p type="main">

<s>Men famoso nei posteri e men fortunato, perch&egrave; nell'opere <lb/>pubblicamente note pot&egrave; la censura esercitare il suo dente, fu don <lb/>Famiano Michelini, una strana figura di uomo, che sognando di <lb/>chiappar milioni con le sue scoperte, mor&igrave; nel 1666, vecchio di 73 <lb/>anni, nell'indigenza. </s>

<s>Propugnatore della Medicina statica del Santo&shy;<lb/>rio, perch&egrave; pi&ugrave; volte il giorno, quand'era ancora scolopio sotto il nome <lb/>di fra Francesco da S. Giuseppe, si pesava sulla stadera, per fare <lb/>esperienza in se dell'insensibile traspirazione; i ragazzi lo additavano <lb/>per le vie di Firenze chiamandolo il <emph type="italics"/>Padre Staderone.<emph.end type="italics"/> Spacciando <lb/>nelle bibite limonate il migliore specifico per cacciar la febbre, i <lb/>fiorentini lo proverbiarono con motti arguti, e con epigrammi. </s>

<s>Il <lb/>Cavalieri, confondendo insieme l'abilit&agrave; d'idraulico con quella di <lb/>medico, illuso prima e poi deluso dell'efficacia della ricetta, scriveva <lb/>al Torricelli, a proposito delle Chiane, &ldquo; che la proposta del padre <lb/>Francesco ander&agrave; al pari con l'altra di risanarmi dalla podagra &rdquo; <lb/>(MSS. Gal. </s>

<s>Dis. </s>

<s>T. XL. c. </s>

<s>223) e il Granduca, in ogni modo, non gli <lb/>poteva perdonare l'apostasia dall'ordine calasanziano. </s>

<s>Ci&ograve; nonostante, <lb/>fu eletto ad ammaestrare nelle matematiche il giovanetto principe <lb/>Leopoldo, in cui infuse un grande amore alle scienze sperimentali, <lb/>e gli raffin&ograve; il gusto a sentir quanto fosse di vero nelle nuove dot&shy;<lb/>trine promulgate da Galileo. </s>

<s>Se non avesse altro merito, basterebbe <lb/>questo per dovere annoverare il Michelini tra i pi&ugrave; validi coope&shy;<lb/>ratori ai progressi della scienza italiana. </s>

<s>Ma egli vi cooper&ograve;, e pi&ugrave; <lb/>efficacemente di quel che non si stimi, con le proprie speculazioni <lb/>e con le proprie esperienze, esposte in iscritti, in cui la bellezza <lb/>del dettato aggiunge splendore all'importanza della materia. </s></p><p type="main">

<s>Il Trattato della <emph type="italics"/>Direzione dei fiumi,<emph.end type="italics"/> co'suoi errori non lievi, <lb/>&egrave; pure il primo che dirige l'opera da praticarsi sui fiumi, con la <lb/>scorta di una scienza, che quasi sempre &egrave; sicura. </s>

<s>Il Viviani, dietro <lb/>quegli insegnamenti, regolava l'Arno con altri fiumi della Toscana, <lb/>e per mezzo di Ottavio Falconieri insegnava a regolar similmente <pb xlink:href="020/01/182.jpg" pagenum="163"/>il Tevere agli ingegneri romani. </s>

<s>Nei Discorsi medici don Famiano <lb/>ha senza dubbio delle stranezze, ma egli &egrave; il primo, co'suoi metodi <lb/>matematici, a cacciar l'empirismo e ad esaltar l'arte medica al <lb/>grado e alla dignit&agrave; di scienza. </s>

<s>Fu dagli insegnamenti di lui che <lb/>ebbe principio la tanto benemerita scuola medica sperimentale isti&shy;<lb/>tuita dal Redi. </s></p><p type="main">

<s>Men noti dei quattro annoverati fin qui, sono altri illustri allievi <lb/>di quella prima scuola galileiana, i quali, dallo scrivere e dal pub&shy;<lb/>blicar gli scritti delle loro speculazioni, o furon divietati da una <lb/>morte immatura, o ne furon distratti dall'attendere a varii altri <lb/>ufficii. </s>

<s>Primo fra questi occorre a commemorare Niccol&ograve; Aggiunti <lb/>che, nato nel 1600, in 35 anni comp&igrave; tutto insieme il corso delle <lb/>scienze e della vita. </s>

<s>Quel che egli speriment&ograve; di fisica o dimostr&ograve; <lb/>di meccanica &egrave; rimasto negli informi manoscritti di lui, chi svolge <lb/>i quali, si sente stringere il cuore da piet&agrave;, che gli impedisse la <lb/>morte di maturare quella cos&igrave; feconda novit&agrave; di pensieri. </s>

<s>Si direbbe, <lb/>a leggere quelle note e quegli appunti rimasti di lui, che Galileo <lb/>infuse nel giovane alunno quegli spiriti latenti, che si manifestarono <lb/>poi nei Dialoghi delle Due Nuove Scienze. </s>

<s>Chi non direbbe infatti <lb/>che quelle proposizioni dimostrate dall'Aggiunti intorno alla ten&shy;<lb/>sione delle corde sonore, non fossero cadute dalla penna di Galileo, <lb/>quando pensava di dar fondamenti matematici all'Acustica? </s>

<s>Le so&shy;<lb/>luzioni di parecchi problemi, che si leggono in questi manoscritti, <lb/>come quello delle condizioni dell'equilibrio di un pezzo di legno, <lb/>in parte campato in aria e in parte sostenuto da un piano, somi&shy;<lb/>gliante a quell'altro, qui pur risoluto, della catena in parte distesa <lb/>su un asse e in parte pendula, rivelano che l'Autore, nella scienza <lb/>del moto, precorreva al Maestro. </s></p><p type="main">

<s>Ma che egli lo precorresse veramente finiscono di persuaderlo <lb/>quei meccanici teoremi, la matematica dimostrazione dei quali non <lb/>par che avesse altro intento, che di supplire al difetto dei Dialoghi <lb/>de'Due Massimi Sistemi. </s>

<s>Galileo infatti, contento ad enunciarli, lascia <lb/>ivi i principali teoremi del moto indimostrati, riserbandosi a farlo <lb/>negli altri Dialoghi, che meditava di scrivere intorno a quel proprio <lb/>soggetto. </s>

<s>Ma intanto l'Aggiunti cerca e ritrova da s&egrave; cos&igrave; fatte di&shy;<lb/>mostrazioni. </s>

<s>Tale &egrave; quella del pendolo, pubblicata nei Saggi di storia <lb/>letteraria dal Nelli (Lucca 1759, pag. </s>

<s>89, 90), tal'&egrave; quella del teore&shy;<lb/>ma, cos&igrave; formulato: &ldquo; La medesima velocit&agrave; nelle maggiori o minori <lb/>quantit&agrave; di materia, opera pi&ugrave; o meno potentemente secondo la <lb/>proporzione di essa materia &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XVIII, c. </s>

<s>95), tale, <pb xlink:href="020/01/183.jpg" pagenum="164"/>per tacere di altre, la dimostrazione della palla perfettamente sfe&shy;<lb/>rica, posata su un piano perfettamente orizzontale, che non tende <lb/>a muoversi pi&ugrave; verso l'una parte che l'altra (ivi, c. </s>

<s>100). </s></p><p type="main">

<s>Che poi l'Aggiunti procedesse, nella dimostrazione di questi <lb/>teoremi galileiani del moto, indipendentemente dalla guida del Mae&shy;<lb/>stro, lo prova quella stessa libert&agrave;, colla quale ne censura alcune <lb/>dottrine. </s>

<s>Esempio ne sia quello delle forze centrifughe, delle quali <lb/>tratta Galileo nel II Dialogo dei Massimi Sistemi (Alb. </s>

<s>I. 213,38). <lb/>Ammesso dall'Aggiunti il principio che &ldquo; acciocch&egrave; un mobile <lb/>acquisti, da virt&ugrave; intrinseca, impeto di muoversi per una tal dire&shy;<lb/>zione, bisogna che il motore l'abbia movendo accompagnato per <lb/>qualche spazio in essa dirittura &rdquo; perciocch&egrave; in un cerchio non ci <lb/>&egrave; dirittura alcuna, conclude: &ldquo; laonde sar&agrave; falso che dalla vertigine <lb/>di una ruota si conferisca alle sue parti impeto di muoversi per la <lb/>tangente, com'asserisce l'eccellentissimo signor Galileo &rdquo; (ivi, c. </s>

<s>59). </s></p><p type="main">

<s>La censura se non &egrave; vera, &egrave; senza dubbio assai arguta, come <lb/>argute sono altre censure, che promuove contro lo stesso Galileo <lb/>rispetto alla teoria de'galleggianti. </s>

<s>Accomodato un parallelepipedo <lb/>nelle condizioni di galleggiamento richieste da Galileo, l'Aggiunti <lb/>cos&igrave; soggiunge: &ldquo; Tutto questo passa bene, secondo la dottrina del <lb/>signor Galileo, se porremo che l'acqua sia solamente da una banda. </s>

<s><lb/>Ma qui mi nascono molte difficolt&agrave;, che fanno contro al Galileo <lb/>ancora, perch&egrave; non pare che basti, acci&ograve; un solido men grave in <lb/>specie dell'acqua, sia alzato, che l'acqua lo bagni da una parte sola, <lb/>e secondo quell'altezza che vuole il Galileo, ma tal sollevamento <lb/>bisogna che sia a mio giudizio d'ogni intorno &rdquo; (ivi, c. </s>

<s>107). Qui <lb/>l'Autore del manoscritto, che nota come la cosa vuol esser pensata <lb/>meglio, ha pi&ugrave; ragione di censurare che dianzi: quelle galileiane <lb/>dottrine son difettose, perch&egrave;, nello spiegar l'effetto de'galleggia&shy;<lb/>menti, s'esclude l'intervento delle pressioni idrostatiche, per cui <lb/>con ragione, l'Aggiunti che non seppe pensar da s&egrave; all'efficacia di <lb/>quelle pressioni, si sentiva aggirar la mente da quei dubbi penosi. </s></p><p type="main">

<s>Ben pi&ugrave; sicuro per&ograve; del fatto suo &egrave; l&agrave; dove, per supplire ai <lb/>difetti di Erone, divisa la nuova teoria del moto delle acque nei <lb/>sifoni ritorti. </s>

<s>Si lagnava il Castelli con Galileo, perch&egrave; l'Aggiunti, <lb/>senza fargliene parola, andava spacciando che nel Discorso Della <lb/>Misura delle Acque correnti ci erano alcuni errori gravi (Campori <lb/>Cartag. </s>

<s>gal. </s>

<s>cit. </s>

<s>pag. </s>

<s>417). Quali fossero gli errori gravi notati dal&shy;<lb/>l'Aggiunti, bench&egrave; il Castelli non si spieghi davvantaggio, si pu&ograve; <lb/>arguir facilmente da queste teorie del sifone eroniano, nel dimostrar <pb xlink:href="020/01/184.jpg" pagenum="165"/>le quali si ammette dall'Autore che le velocit&agrave; nel flusso dell'acqua, <lb/>come nella caduta di tutti gli altri corpi gravi sieno proporzionali <lb/>alle radici delle altezze. </s>

<s>Ora perch&egrave; il Castelli in quel suo Trattato, <lb/>professava il principio che le stesse velocit&agrave; fossero proporzionali <lb/>alle semplici altezze, pu&ograve; esser benissimo che l'Aggiunti spacciasse <lb/>questo per un errore. </s>

<s>Un errore poi lo credette il Torricelli, e i <lb/>seguaci delle teorie di lui, ond'&egrave; che nel proporre quelle nuove <lb/>teorie, l'Aggiunti prevenne di parecchi anni lo stesso Torricelli. </s></p><p type="main">

<s>Fra le molte esperienze di fisica, che si trovano descritte o <lb/>accennate per questi manoscritti, la pi&ugrave; importante, a nostro giu&shy;<lb/>dizio, e la pi&ugrave; nuova &egrave; quella del dilatarsi de'solidi al calore, ci&ograve; <lb/>che egli dimostra in un filo metallico o in un ago, e per cui spiega <lb/>la variet&agrave; de'suoni dati dalle corde degli strumenti, al variare delle <lb/>stagioni. </s>

<s>Notabile &egrave; che gli effetti di quel dilatamento lineare dei <lb/>solidi l'attribuisca all'aria che s'interpone fra i pori di tutti i corpi, <lb/>e pi&ugrave; notabili che mai quei pensieri intorno al vacuo, e alla forza <lb/>necessaria a superarlo, che gli occorrono in tal proposito: pensieri <lb/>che fanno cos&igrave; perfetto riscontro con quelli che, nel primo Dialogo <lb/>delle Due Nuove Scienze, alquanti anni dopo la morte del Nostro, <lb/>rivel&ograve; Galileo. </s>

<s>Che poi l'Aggiunti, dalle speculate esperienze e dalle <lb/>minute osservazioni, sapesse con ardito volo risalire ai principii ge&shy;<lb/>nerali, lo dimostra quella sottile ipotesi del moto occulto dell'acqua, <lb/>con cui spiega e applica gli effetti di capillarit&agrave; a innumerabili e <lb/>inesplicati fatti della Natura. </s>

<s>N&egrave; si pu&ograve; senza gran maraviglia pen&shy;<lb/>sare, che egli spieghi per questo modo il moto del chilo negli ani&shy;<lb/>mali, mentre parecchi anni dopo il gran Pecquet aveva bisogno di <lb/>ricorrere miseramente al moto vermicolare dei vasi, e alla com&shy;<lb/>pressione toracica degli atti respiratorii. </s></p><p type="main">

<s>Dei danni recati all'incremento della scienza dagli inesorabili <lb/>casi della vita, in questa cos&igrave; ristretta cerchia dei primi Discepoli <lb/>di Galileo, due altri esempi abbiamo a deplorare in Cosimo Noferi, <lb/>e in Antonio Nardi. </s>

<s>Per cominciare a parlar del primo, ei lasci&ograve; <lb/>quattro bei volumi manoscritti, di carettere nitido, e ornati, nei <lb/>frontespizi e altrove, di tocchi in penna cos&igrave; ben condotti, da esser <lb/>tenuti in qualche pregio artistico dagl'intendenti. </s>

<s>Son que'volumi <lb/>altrettanti libri divisi ciascuno in Discorsi, che par l'Autore gli leg&shy;<lb/>gesse via via in qualche Accademia fiorentina. </s>

<s>Si discorre princi&shy;<lb/>cipalmente nel I libro dell'ordine di fabbricare le fondamenta, in <lb/>qualsivoglia luogo, dell'ordine delle armature e fabbriche delle volte, <lb/>dell'ordine di diversi cavalletti per le coperte. </s>

<s>Si passa nel II libro <pb xlink:href="020/01/185.jpg" pagenum="166"/>a discorrere dell'ordine e della fabbrica dei ponti murati, dei ponti <lb/>di un solo arco, dei ponti sui fiumi reali. </s></p><p type="main">

<s>Nel III libro, che &egrave; il pi&ugrave; importante per noi, si discorre del <lb/>modo di regolare i fiumi; libro che, se fosse stato pubblicato a suo <lb/>tempo, o avrebbe risparmiato in parte o avrebbe diminuiti i meriti <lb/>al Trattato del Michelini. </s>

<s>Incomincia a dire che fino allora, nei la&shy;<lb/>vori fatti sui fiumi, s'erano commessi di grandi errori, e s'era speso, <lb/>dal pubblico e dai privati, in false operazioni. </s>

<s>Nota poi come quegli <lb/>errori dipendessero principalmente da non essere conosciuti bene <lb/>i moti, a cui va soggetta l'acqua, e distingue quei moti in tre: <lb/><emph type="italics"/>spulsivo, naturale<emph.end type="italics"/> e <emph type="italics"/>laterale.<emph.end type="italics"/> Ammettendo nell'acqua il moto late&shy;<lb/>rale, o obliquo, come l'Autore stesso lo chiama, scansa il gravissimo <lb/>errore, in che incorse il Michelini, ma poi ci incappa al pari di lui, <lb/>quando distingue il moto <emph type="italics"/>spulsivo,<emph.end type="italics"/> ossia quello fatto nella pendenza <lb/>dell'alveo, dal naturale fatto nella perpendicolare, essendo che lo <lb/>spulsivo, non &egrave; un moto diverso, ma &egrave; una delle parti dello stesso <lb/>moto naturale, decomposto in due. </s></p><p type="main">

<s>Il moto spulsivo poi il Noferi lo riguarda come efficiente nel <lb/>venir premuta l'acqua dall'altr'acqua che lo precede, e cos&igrave; rende <lb/>la ragione dello scorrere i liquidi, anche in canali perfettamente <lb/>livellati. </s>

<s>Questa cos&igrave; importante dottrina era stata professata gi&agrave;, <lb/>contro la comune opinione degli idraulici, da Galileo, che il Noferi <lb/>ormeggia spesso con studio, che si direbbe servile. </s>

<s>Cos&igrave; occorren&shy;<lb/>dogli di trattar del problema della corda tesa, ricopia a parola ci&ograve; <lb/>che sta scritto nel IV Dialogo delle Due Nuove Scienze, e dettando <lb/>i suoi Discorsi in tempi, in cui certamente doveva essere stata fatta <lb/>e divulgata la celebre esperienza torricelliana, discorre della teoria <lb/>delle trombe idrauliche allo stesso modo, che se ne discorre nel I <lb/>dei citati Dialoghi, da Galileo. </s>

<s>Rimasto preso di grande ammira&shy;<lb/>zione alla lettura delle opere di lui, ne sceglie i pi&ugrave; curiosi e im&shy;<lb/>portanti problemi, e sotto il titolo di <emph type="italics"/>Ricreazioni matematiche<emph.end type="italics"/> gli <lb/>ordina in due libretti &ldquo; quali due libretti spero in breve farvi ve&shy;<lb/>dere. </s>

<s>Ma quell'opera poi che pi&ugrave; mi ha ritardato, &egrave; l'avere con&shy;<lb/>dotto a fine il mio Apollonio Pergeo, per benefizio ed utile degli <lb/>studiosi &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XIV, c. </s>

<s>2). </s></p><p type="main">

<s>Quanto per&ograve; il Noferi &egrave; ossequioso verso Galileo, tanto par ir&shy;<lb/>riverente verso il Castelli. </s>

<s>La censura che egli fa della proposizione <lb/>fondamentale dimostrata nel Trattato delle Acque Correnti, che cio&egrave; <lb/>le velocit&agrave; sono in ragione inversa delle sezioni, non &egrave; per verit&agrave; di <lb/>matematico, n&egrave; si saprebbe altrimenti spiegare che in una smania <pb xlink:href="020/01/186.jpg" pagenum="167"/>del censore, d'introdur nella scienza quella sua novit&agrave; del <emph type="italics"/>moto <lb/>spulsivo.<emph.end type="italics"/></s></p><p type="main">

<s>Antonio Nardi, aretino, componeva col Magiotti e col Torricelli, <lb/>in Roma, quel triumvirato, che Galileo manda cos&igrave; spesso a salu&shy;<lb/>tare nelle sue lettere familiari. </s>

<s>Pi&ugrave; tardi, quando quel triumvirato <lb/>si sciolse, Michelangiolo Ricci, dando al Torricelli stesso venuto in <lb/>Firenze, le nuove degli amici lontani, in una sua lettera cos&igrave; gli <lb/>scriveva: &ldquo; Il signor Antonio Nardi fatica intorno l'Opera sua. </s>

<s>Ha <lb/>dato perfezione alla parte metafisica, ora &egrave; d'intorno la fisica, e <lb/>poi vedr&agrave; le matematiche, il che non potr&agrave; seguire prima di dieci <lb/>mesi ovvero in un anno. </s>

<s>E mi duole che tardi tanto ad uscire in <lb/>luce Opera, che si spera che debba essere doviziosa di tutte le <lb/>speculazioni, cio&egrave; pasto per ogni sorta di professori di scienza &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc. </s>

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

<s>121). Nel Giugno 1645 torna a scrivergli: <lb/>&ldquo; Il signor Antonio Nardi riverisce V. S. con ogni affetto, e nella <lb/>stampa del libro suo va un poco lento, perch&egrave; ci restano da rive&shy;<lb/>dere le materie matematiche, e non ha potuto attendere per molti <lb/>giorni, impedito da un poco d'indisposizione &rdquo; (ivi, c. </s>

<s>136). Non <lb/>sapremmo precisamente dire quanto quella indisposizione durasse, <lb/>ma sembra che l'Autore fosse impedito per qualche anno, dopo il <lb/>qual tempo scriveva il medesimo Ricci al Torricelli: &ldquo; Il sig. </s>

<s>Nardi <lb/>si trattiene in Arezzo e li giorni passati mi mand&ograve; l'Opera sua ori&shy;<lb/>ginale, perch&egrave; la facessi rivedere al S. </s>

<s>Uffizio &rdquo; (ivi, c. </s>

<s>183). </s></p><p type="main">

<s>Il libro e l'Opera originale del Nardi, di che qui si parla, porta <lb/>il titolo di <emph type="italics"/>Scene,<emph.end type="italics"/> senz'altro aggiunto nella fronte, ma, nell'Indice <lb/>finale, il titolo compiuto &egrave; di <emph type="italics"/>Scene Accademiche.<emph.end type="italics"/> &Egrave; un volumone <lb/>di pagine 1392, che riman tuttavia manoscritto, copiato da pi&ugrave; <lb/>mani, e non ha di autografo che alcune correzioni e postille, i <lb/>passi greci, e i disegni abbozzati delle figure geometriche. </s>

<s>Una certa <lb/>somiglianza di carattere calligrafico fece credere a qualcuno che <lb/>v'avesse dato mano, a copiar quelle carte, anche il Torricelli, ma <lb/>le sopra citate lettere del Ricci par che rendano poco probabile <lb/>quel supposto. </s></p><p type="main">

<s>Impedita per la morte dell'Autore la stampa, per la quale <lb/>tutto era preparato, il manoscritto, dagli eredi del Nardi pass&ograve; nel <lb/>concittadino di lui Francesco Redi, che par avesse intenzione di <lb/>mandarlo alla luce (Targioni, Aggrandim. </s>

<s>T. I. P. I. pag. </s>

<s>173). Ma <lb/>qualunque fosse il motivo, rimasto il volume tuttavia inedito, dal <lb/>Granduca Cosimo III che l'ebbe dal Redi, pass&ograve; alla biblioteca del <lb/>Museo fiorentino di Fisica e di Storia Naturale, d'onde finalmente <pb xlink:href="020/01/187.jpg" pagenum="168"/>and&ograve; a prender posto al numero XX, fra i tomi che compongono <lb/>la seconda Divisione dei manoscritti galileiani. </s></p><p type="main">

<s>Le scene in tutto son nove, e ciascuna &egrave; divisa in articoli, col <lb/>titolo di <emph type="italics"/>Vedute.<emph.end type="italics"/> Vi si tratta, senz'ordine, d'ogni soggetto scientifico, <lb/>cosicch&egrave; l'Opera somiglia a tanti numeri messi insieme di un gior&shy;<lb/>nale enciclopedico. </s>

<s>A que'tempi forse era questo il miglior modo <lb/>a diffondere la scienza, e tale dee essere stata senza dubbio l'in&shy;<lb/>tenzion dell'Autore. </s>

<s>Ora per&ograve;, un'opera scritta in quelle forme, non <lb/>sarebbe comportabile, per cui par che sia condannata in perpetuo <lb/>a rimanersene manoscritta. </s>

<s>Chi facesse, nonostante, una scelta degli <lb/>articoli di matematica o di fisica sperimentale, potrebbe arrecar <lb/>qualche giovamento alla storia della scienza, bench&egrave; il non aver <lb/>risentito il Nardi gli impulsi, che alle stesse scienze sperimentali <lb/>provennero dalla grande esperienza torricelliana, a que'medesimi <lb/>articoli, si diminuisca notabilmente l'importanza. </s></p><p type="main">

<s>La veduta 41 della Scena VII &egrave; intitolata: <emph type="italics"/>Censure sopra varii <lb/>pensieri di Galileo<emph.end type="italics"/> (pag. </s>

<s>967-74) pensieri tutti per&ograve; che concernono <lb/>le teorie galileiane del moto. </s>

<s>Ma qua e l&adot;, per le altre Scene, oc&shy;<lb/>corre pure all'Autore di intrattener l'esame critico sopra altre dot&shy;<lb/>trine del suo Maestro, le quali ora, con temperato zelo difende dalle <lb/>ingiuste censure altrui, e ora con filosofica libert&agrave; condanna ed <lb/>emenda. </s></p><p type="main">

<s>L'argutissima censura, che in quella Veduta, la quale porta il <lb/>titolo: <emph type="italics"/>Sopra la definizione dell'umido e sua Natura posta da Ar&shy;<lb/>chimede nei principii delle cose che galleggiano<emph.end type="italics"/> (pag. </s>

<s>873), fa il <lb/>Nardi del principio delle velocit&agrave; virtuali applicato da Galileo a di&shy;<lb/>mostrar l'equilibrio dei liquidi ne'vasi comunicanti, ci fa sovvenire <lb/>di un altro Discepolo, che, pure in materie idrauliche, oppose libere <lb/>censure alle dottrine dello stesso Galileo, e che, per aver affidata la <lb/>sua scienza a lettere, per la maggior parte inedite, &egrave; rimasto nella <lb/>Repubblica scientifica oscuro, o quanto pur si meriterebbe non ap&shy;<lb/>prezzato. </s>

<s>Costui &egrave; il fiorentino Senatore Andrea Arrighetti, di cui <lb/>cos&igrave;, in un poscritto di lettera a Galileo, scriveva il Castelli: &ldquo; Tengo <lb/>una lettera lunga del sig. </s>

<s>Andrea Arrighetti, sottilissima e bella, in <lb/>proposito di fiumi, nella quale ho avuto che imparare assai &rdquo; (Alb. </s>

<s><lb/>Supplem. </s>

<s>pag. </s>

<s>239). Questa, che forse &egrave; ancora inedita, dee essere <lb/>una di quelle fra le prime lettere, che Andrea scriveva a Niccol&ograve; <lb/>Arrighetti suo cugino intorno al fiume Bisenzio, professandovi dot&shy;<lb/>trine vere contro a quelle, riconosciute erronee, di Galileo. </s>

<s>E l'avere <lb/>il discepolo con sicurt&agrave; e dirittura colto nel segno meglio del suo <pb xlink:href="020/01/188.jpg" pagenum="169"/>Maestro, e il confessar che il Castelli fa dell'aver trovato da imparare <lb/>assai dalla scrittura di lui, compongono il pi&ugrave; bell'elogio, che si possa <lb/>fare di Andrea Arrighetti. </s>

<s>Nella grande raccolta fiorentina degli <lb/>Autori, che trattano del moto dell'acque, s'inserirono, nel IV Tomo, <lb/>sei lettere dell'Arrighetti al Castelli, nelle quali s'apre il fiore di <lb/>alcuni pensieri, che allegarono poi in squisitissimi frutti. </s>

<s>Tale &egrave;, <lb/>nella II Lettera, la legge della velocit&agrave; dei flussi, fior di pensiero <lb/>allegato nel Torricelli, e nel Newton fatto poi pi&ugrave; maturo; tale la <lb/>speculazione del librarsi i liquidi che scendono e risalgono per <lb/>lunghi canali, qual sarebbe quello che dalle fontane di Boboli faceva <lb/>zampillar le acque condottevi da Pratolino: sottile speculazione e <lb/>fecondo fiore di novit&agrave;, che se pure &egrave; allegato in frutto, non par <lb/>che la scienza ancora l'abbia colto maturo. </s></p><p type="main">

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

<s>Chi si trattiene a meditare alquanto su questo primo e cos&igrave; <lb/>largo svolgimento delle nuove dottrine, in s&igrave; breve spazio di tempo, <lb/>che non oltrepassa, se non di pochissimi anni quello della morte di <lb/>Galileo, non pu&ograve; non rimanere ammirato di quella forza potente, <lb/>che valse a dare e a diffondere nella scienza tant'onda di vita. </s>

<s>Ma <lb/>pure, quella scienza ancora ha poco dello sperimentale. </s>

<s>La forma <lb/>dura tuttavia a signoreggiare sulla materia, la matematica prevale <lb/>alla fisica, e la speculazione, troppo sicura di s&egrave;, non degna di <lb/>scendere dalle sue alture per cimentarsi colla esperienza. </s>

<s>Che sia <lb/>veramente cos&igrave;, insigni esempii ci son porti in fin da coloro, che si <lb/>dissero precursori, ma che son da dir forse meglio attori di questa, <lb/>che per la nostra scienza si appella et&agrave; del Rinnovamento. </s>

<s>Tali <lb/>sarebbero, principali fra gli altri, il Maurolico e il Benedetti. </s>

<s>Il <lb/>primo di questi, nel trattar dell'iride, assegna all'angolo formato <lb/>dai raggi, che vengon da una gocciola della nube rorida all'occhio, <lb/>45 gradi, per l'iride interna, e 56 e un quarto per l'iride esterna. </s>

<s><lb/>Le dignit&agrave; matematiche son quelle, che lo conducono alla certezza <lb/>di cos&igrave; fatte conclusioni. </s>

<s>Ma pure, &egrave; vero che quegli angoli sono <lb/>alquanto minori, e il Maurolico lo sa, e a chi gli domanda come <lb/>la cosa vada <emph type="italics"/>nescio quid hic respondeam,<emph.end type="italics"/> ma la matematica non <lb/>pu&ograve; fallire, e potrebb'esser, soggiunge, che il non rispondere il fatto <pb xlink:href="020/01/189.jpg" pagenum="170"/>incerto ai calcoli certissimi, dipendesse dal non esser le gocciole <lb/>perfettamente sferiche, ma notabilmente allungate in ovale. </s></p><p type="main">

<s>In Galileo poi gli esempi, che si potrebbero citare, del prevaler <lb/>nelle sue dottrine le speculazioni alle esperienze, son tanti, che, <lb/>anche ai pi&ugrave; ritrosi a consentir con noi, parrebbero da vantaggio. </s>

<s><lb/>Egli par gi&agrave; che da s&egrave; stesso lo senta, e che si voglia far quasi <lb/>percotere il petto di rimbalzo dalla punta delle parole, che pone <lb/>in bocca a Simplicio: &ldquo; queste sottigliezze matematiche son vere <lb/>in astratto, ma applicate poi alla materia sensibile e fisica non ri&shy;<lb/>spondono &rdquo; (Alb. </s>

<s>I, 224). </s></p><p type="main">

<s>Sia primo a citare fra questi notabilissimi esempi il pendolo, <lb/>intorno al quale il giudizio di Galileo procede in modo simile a <lb/>quello del Maurolico, ora citato. </s>

<s>La matematica gli ha fatto con&shy;<lb/>cludere, per certissima dimostrazione, che le vibrazioni o ampie <lb/>per tutto il quadrante, o ristrette in piccolissimi archi sono in ogni <lb/>modo isocrone. </s>

<s>Nel fatto per&ograve; non son tali, e Galileo lo s&agrave;: sa che <lb/>le pi&ugrave; ampie sono alquanto pi&ugrave; diuturne. </s>

<s>A chi gli domanda come <lb/>quel fatto vada, <emph type="italics"/>Nescio quid hic respondeam,<emph.end type="italics"/> ma potrebb'esser, <lb/>soggiunge, che ci&ograve; dipenda dall'esser le vibrazioni, che vanno pi&ugrave; <lb/>al largo, alquanto di pi&ugrave; indugiate dalla resistenza maggior che <lb/>incontran nell'aria. </s>

<s>Eppure si sarebbe potuto anche da ci&ograve; facil&shy;<lb/>mente deliberare, con una tale esperienza, che pu&ograve; sovvenire alla <lb/>mente di tutti, bench&egrave; l'Huyghens sia stato quello che primo l'ha <lb/>suggerita. </s>

<s>Consiste quella facilissima e concludentissima esperienza <lb/>in prender due pendoli di lunghezza uguale, e in dar le mosse a <lb/>ciascuno dalla medesima parte, in modo per&ograve; che l'uno scenda <lb/>molto da alto e l'altro da basso. </s>

<s>&Egrave; facile veder che presto i due <lb/>pendoli non passano pi&ugrave; il perpendicolo insieme, ma quel che va <lb/>pi&ugrave; ristretto &egrave; giusto quello che precede. </s></p><p type="main">

<s>E la celebre dimostrazione della legge della caduta dei gravi, <lb/>egli &egrave; pure un fatto che Galileo non la raccolse altrimenti, che per <lb/>una matematica conclusione dal principio che le velocit&agrave; sono pro&shy;<lb/>porzionali ai tempi. </s>

<s>Il riscontro dell'esperienza, cos&igrave; minutamente <lb/>descritta nel III Dialogo delle Due Nuove Scienze (Alb. </s>

<s>XIII, 172, 73), <lb/>&egrave; affatto superfluo, perch&egrave; nessun crede all'Autore che, dal pesar <lb/>dell'acqua sgocciolante dalla clessidra, potesse aver la misura giusta <lb/>di que'minimi tempi, difficilissimi a trovar con gli stessi pi&ugrave; squisiti <lb/>cronometri moderni. </s></p><p type="main">

<s>Altro insigne esempio del prevaler nella mente di Galileo la <lb/>precisione matematica e l'ordine geometrico alla osservazione dei <pb xlink:href="020/01/190.jpg" pagenum="171"/>fatti, &egrave; quello che concerne le orbite dei pianeti. </s>

<s>Il Keplero aveva <lb/>dimostrato, come cosa di fatto, che quelle orbite sono ellittiche. </s>

<s>Ma <lb/>ci&ograve;, secondo Galileo, repugna alla platonica perfezione degli ordi&shy;<lb/>namenti celesti, per cui tenacemente si attiene alla geometria dei <lb/>circoli, e rifugge dalla fisica delle ellissi. </s>

<s>Quando poi pi&ugrave; tardi ri&shy;<lb/>trov&ograve; la legge dei moti ne'pendoli di varie lunghezze, ritrov&ograve; anco <lb/>insieme un nuovo argomento per non dover consentire a un'altra <lb/>delle leggi planetarie, scoperte pur dal Keplero. </s>

<s>Rassomigliando nei <lb/><emph type="italics"/>Massimi Sistemi<emph.end type="italics"/> i pianeti a tanti pendoli, che abbiano il loro centro <lb/>di sospensione nel sole, la sua matematica gli concludeva che i <lb/>tempi periodici debbono essere proporzionali alle radici degli assi. </s>

<s><lb/>Or questa sua matematica volle Galileo che prevalesse al fatto con&shy;<lb/>cluso dal Keplero, secondo il quale, i quadrati dei tempi periodici <lb/>sarebbero come i cubi delle medie lunghezze degli assi. </s>

<s>Cos&igrave; venne <lb/>a persuadersi di pi&ugrave;, che le tre leggi Kepleriane, in cui parevagli <lb/>di non ravvisar la solita Natura geometrizzante, non fossero pi&ugrave; che <lb/>altrettante chimere. </s></p><p type="main">

<s>Ma che molte dottrine di Galileo sien vere in astratto e poi <lb/>non corrispondano ai fatti, come diceva Simplicio, abbiamo, a per&shy;<lb/>suadere i pi&ugrave; ritrosi, un argomento concludentissimo, in quei teo&shy;<lb/>remi del moto applicato all'acque correnti nella celebre Lettera sul <lb/>fiume Bisenzio. </s>

<s>Ivi si professa dall'Autore il principio che l'acqua, <lb/>fra tutti i corpi gravi, &egrave; quella, in cui si verificano pi&ugrave; esattamente <lb/>le leggi della caduta dei gravi, specialmente lungo i piani inclinati, <lb/>e ci&ograve; perch'ella non &egrave; soggetta, per sua propria natura, agli urti <lb/>e agli attriti, che sogliono essere le pi&ugrave; valide cause, per cui si <lb/>alterano quelle stesse leggi. </s>

<s>Cos&igrave;, immaginandosi un piano liquido <lb/>tangente ne'punti di sporgenza delle asperit&agrave; delle rive o dell'alveo, <lb/>l'acqua, che riceve impedimento da s&igrave; fatte asperit&agrave;, non &egrave; che <lb/>quella sola, la quale si trova rinchiusa fra quel piano immaginario <lb/>e le sinuosit&agrave; e le sporgenze delle rive e dell'alveo. </s>

<s>Il rimanente <lb/>scorre, per mezzo a quello stesso piano liquido, senza violenza di <lb/>attrito, come un corpo duro sopra un tersissimo specchio. </s>

<s>Da ci&ograve; <lb/>derivava per legittima conseguenza che la corrente dovesse giungere <lb/>al suo termine con tutta la velocit&agrave;, che conviene alla caduta. </s>

<s>Or <lb/>non par credibile che Galileo approvasse tali teorie, tanto eviden&shy;<lb/>temente contrarie all'esperienza. </s>

<s>&Egrave; chiaro infatti, secondo quelle <lb/>teorie, che, dovendo essere le fila superficiali della corrente tutte <lb/>ugualmente veloci, non vi si dovrebbe mai vedere nel mezzo il <lb/>filone. </s>

<s>Che se davvero ogni fiume, specialmente in tempo di piena, <pb xlink:href="020/01/191.jpg" pagenum="172"/>giunge allo sbocco con tutta la velocit&agrave; conveniente alla caduta, <lb/>chi non vede che, arrivate a un punto, le sezioni non si potrebbero <lb/>ritenere pi&ugrave; insieme, come giusto si osserva nel cader delle trosce <lb/>d'acqua da qualche grande altezza? </s>

<s>Fu per questo che il Barattieri, <lb/>con giudizio diverso da quello di Galileo, stimando i fatti pi&ugrave; con&shy;<lb/>cludenti delle matematiche dimostrazioni, si rivolse a professar, per <lb/>l'acqua e per tutti i gravi cadenti in generale, la legge dimostrata <lb/>dal Tartaglia delle velocit&agrave; proporzionali ai semplici spazi, a pre&shy;<lb/>ferenza della vera, dimostrata gi&agrave; dallo stesso Galileo. </s>

<s>Anzi, paren&shy;<lb/>dogli dover esser la corrente, anco velocitata cos&igrave;, troppo pi&ugrave; pre&shy;<lb/>cipitosa di quel che non dimostrano i fatti, considera che ella vien <lb/>giustamente rattemperata, nel suo corso, da tanti impedimenti. </s></p><p type="main">

<s>Qual pi&ugrave; valido argomento di questo si potrebb'egli recare a <lb/>prova del nostro assunto, che cio&egrave; Galileo faceva prevalere le astratte <lb/>speculazioni ai fatti? </s>

<s>E i fatti, dall'altra parte, oltre ad essere per <lb/>s&egrave; medesimi cos&igrave; manifesti, gli eran messi in considerazione da <lb/>quelle lunghe e dotte lettere che, a dimostrar la fallacia di que'suoi <lb/>idraulici insegnamenti, con tanta filosofica libert&agrave;, gli scriveva Andrea <lb/>Arrighetti. </s></p><p type="main">

<s>Questo Arrighetti, coll'Aggiunti, col Castelli e con pochi altri, <lb/>son senza dubbio de'primi che, progredendo negli studi sperimen&shy;<lb/>tali, passano dalle astratte forme geometriche a considerare le par&shy;<lb/>ticolari affezioni della materia. </s>

<s>Ma gli esempi ancora, come si disse, <lb/>son pochi: le vie sono incerte, e da tutto apparisce che l'arte di <lb/>sperimentare &egrave; tuttavia ne'suo&igrave; principii. </s>

<s>Per vederla nel suo pieno <lb/>esercizio conviene ancora aspettare che la celebre Accademia del <lb/>Cimento sia convocata, e che ella abbia almeno pubblicati i suoi <lb/><emph type="italics"/>Saggi.<emph.end type="italics"/> Ma, in questo non breve spazio di tempo, la Francia &egrave; com&shy;<lb/>mossa di maraviglia alle esperienze del Pascal, dell'Auzout, del <lb/>Roberval, del Pacquet; l'Inghilterra a quelle del Boyle; la Ger&shy;<lb/>mania a quelle del Guericke, e, a restare ammirata alle nuove <lb/>esperienze di Valeriano Magno, non ultima di tutte &egrave; la solitaria <lb/>Polonia. </s>

<s>Il vantarsi perci&ograve; che la nostra Accademia del Cimento <lb/>sia stata la prima, fra tutte le altre instituite in Europa, si riduce <lb/>a una vanit&agrave;, considerando che i nomi ora citati valgono, ciascuno <lb/>per s&egrave;, quanto un'intiera Accademia, e che i <emph type="italics"/>Saggi di Naturali <lb/>Esperienze<emph.end type="italics"/> paragonati agli <emph type="italics"/>Esperimenti fisico meccanici,<emph.end type="italics"/> appariscon <lb/>non pi&ugrave; che come una spigolatura dopo la messe. </s></p><p type="main">

<s>In ogni modo per&ograve; &egrave; verissimo, a nostro conforto, che quelle <lb/>onde di scienza sperimentale che si diffondono cos&igrave; al largo per <pb xlink:href="020/01/192.jpg" pagenum="173"/>tutta l'Europa, ebbero il loro centro d'impulsione in Italia. </s>

<s>Che fa, <lb/>in vero, il Pascal a Roano, in mezzo a quella folla di popolo, per <lb/>gran curiosit&agrave; concorsavi d'ogni parte? </s>

<s>Verifica un'esperienza ve&shy;<lb/>nuta d'Italia, la conferma con altre nuove stupende esperienze, e <lb/>si studia in ogni modo di persuadere i contradicenti. </s>

<s>Che fanno <lb/>l'Auzout, e il Roberval a Parigi, se non che diffonder la notizia di <lb/>quella esperienza italiana nelle pubbliche scuole, alla presenza dei <lb/>giovani studiosi; e che fa il Pacquet, se non che applicare quella <lb/>stessa esperienza a risolvere compiutamente il problema arveiano <lb/>della circolazione del sangue? </s>

<s>E che altro mai fa il Guericke, in <lb/>mezzo ai principi, ai magnati e al popolo concorsi sulle pubbliche <lb/>piazze di Magdeburgo, se non che sottoporre a nuove e maravi&shy;<lb/>gliose esperienze i concetti stessi di Galileo? </s>

<s>Valeriano Magno fa <lb/>stupire la corte del Re di Polonia con una esperienza, che tutti <lb/>dicono esser venuta di Firenze, ma che egli spaccia per invenzione <lb/>sua propria. </s>

<s>Nessuno per&ograve; di questi stranieri s'esercit&ograve; mai con <lb/>tant'arte e con tanto studio intorno a quella italiana esperienza, <lb/>quanto Roberte Boyle, emulo al connazionale suo Guglielmo Gilbert, <lb/>in dare al pubblico i primi e pi&ugrave; splendidi esempi dell'arte spe&shy;<lb/>rimentale. </s></p><p type="main">

<s>S'indovina assai facilmente che l'esperienza italiana, di cui si <lb/>parla, &egrave; quella celeberrima dell'argento vivo, fatta dal Torricelli, <lb/>e da cui veramente l'arte sperimentale ha principio. </s>

<s>Scriveva il <lb/>Pecquet, negli Esperimenti nuovi anatomici, e dava gran lode al <lb/>Pascal &ldquo; qui primus in Gallia nostra vix natum apud exteros, et in <lb/>cunabulis pene suffocatum de vacuo experimentum hydrargirio non <lb/>solum, sed et liquoribus suscitavit, imo tam felici provexit mirabilis <lb/>industriae successu, ut per totam Europam tentandi vacui studium <lb/>verae sapientiae cultoribus indiderit &rdquo; (Parisiis, 1654, pag. </s>

<s>55). Ora <lb/>si domanda: aveva egli ragione il Pecquet d'affermare che l'espe&shy;<lb/>rienza torricelliana fosse rimasta soffocata nella cuna? </s>

<s>Si comprende <lb/>che la ragione del vantato nostro primato, sopra le altre nazioni <lb/>europee, dipende da questa risposta. </s>

<s>E noi, dandola con la solita <lb/>nostra imparzialit&agrave;, diciamo che, a giudicar dai pubblici documenti, <lb/>il Pecquet aveva ragione. </s>

<s>Nel 1648 infatti si pubblicarono le prime <lb/>esperienze del Pascal fatte a Roano; nel 1654, il Pecquet stesso <lb/>pubblicava i suoi Nuovi Esperimenti anatomici; nel 1657 lo Schott <lb/>dava notizia al pubblico, a nome del Guericke, dei primi Esperi&shy;<lb/>menti Nuovi di Magdeburgo, e il Boyle, nel 1659, pubblicava i suoi <lb/>Esperimenti fisico meccanici. </s>

<s>In Italia, dall'epistola di Timeo Lo-<pb xlink:href="020/01/193.jpg" pagenum="174"/>crese in fuori, che &egrave; del 1648, nessuna esercitazione sull'esperienza <lb/>torricelliana comparve in pubblico prima del 1666, anno in cui si <lb/>misero in luce i <emph type="italics"/>Saggi<emph.end type="italics"/> della fiorentina Accademia. </s>

<s>Se poi si va a <lb/>ricercare quel che rimase rinchiuso fra le splendide pareti del pa&shy;<lb/>lazzo Pitti, o venne affidato a carte mutilate e neglette, il Pecquet <lb/>non afferm&ograve; cosa che fosse mai tanto lontana dal vero. </s></p><p type="main">

<s>Non si pu&ograve;, in questo proposito, non meditar profondamente <lb/>sopra certi fatti particolari, che altri forse direbbe dipendere da un <lb/>Destino, ma che meglio si attribuirebbero a un indole propria della <lb/>gente italiana. </s>

<s>A legger la Narrazione, che il Roberval fa nella sua <lb/>Lettera al Noyers, o quel che scrive il Magno nella <emph type="italics"/>Dimostrazione <lb/>oculare,<emph.end type="italics"/> e lo Schott e il Guericke negli Esperimenti di Magdeburgo, <lb/>si resta maravigliati a sentir che francesi, alemanni, polacchi, no&shy;<lb/>bili e plebe, principi e magnati concorressero a veder lo spettacolo <lb/>dell'esperienza del vuoto in tanta folla, da non esserne capaci le <lb/>pubbliche piazze; mentre in Roma, Gaspero Berti, alquanti anni <lb/>prima che ne sapessero nulla que'francesi, quegli alemanni, quei <lb/>pollacchi, al suo pubblico spettacolo non aveva assistenti che il Ma&shy;<lb/>giotti, il Kircher, lo Zucchi, e pochi altri dotti. </s>

<s>Anche in Firenze <lb/>il Granduca, per compiacer talvolta qualche straniero erudito, chia&shy;<lb/>mava il Torricelli a ripetere l'esperienza sotto le solitarie amene <lb/>ombre del giardino di Boboli; compiacenza offerta raramente per&ograve;, <lb/>e toccata a pochi altri, oltre al Moncony e al Mersenno, che primo <lb/>ne di&egrave; avviso al Pascal, da cui, come scintilla, divamp&ograve; l'incendio <lb/>per tutta l'Europa. </s></p><p type="main">

<s>Che si dir&agrave;, a spiegar questi fatti, dell'indole degli italiani? </s>

<s><lb/>Si dir&agrave; che non avevano amore alla scienza? </s>

<s>Ma il non trarre il <lb/>popolo nostro, come gli stranieri, a spettacolo s&igrave; fatto, forse niente <lb/>altro dice, se non ch'egli era pi&ugrave; colto, essendo sempre la curio&shy;<lb/>sit&agrave; figliola dell'ignoranza. </s>

<s>Una tal curiosit&agrave; &egrave; poi naturale che non <lb/>frugasse troppo a vivo una gente avvezza oramai a sentir delle tante <lb/>maraviglie operate da Galileo. </s></p><p type="main">

<s>Si dir&agrave; che non presentivano i Nostri le conseguenze di quei <lb/>fatti spettacolosi, dai quali sarebbe incominciato, e avrebbe ricevuto <lb/>la fisica sperimentale cos&igrave; valido impulso? </s>

<s>Che non avessero cos&igrave; <lb/>vivo quel presentimento forse &egrave; vero, perch&egrave; non si saprebbe spie&shy;<lb/>gare altrimenti il silenzio, che si tenne da tutti intorno alla storia <lb/>della grande scoperta. </s>

<s>Non &egrave; cosa che tanto rechi meraviglia, quanto <lb/>il veder il Viviani, che v'ebbe tanta parte, e molti altri che, anche <lb/>morto il Torricelli, potevano attinger notizia da lui; come ci lascino <pb xlink:href="020/01/194.jpg" pagenum="175"/>cos&igrave; al buio intorno a ci&ograve; che dette occasione alla esperienza del&shy;<lb/>l'argento vivo, contentandosi di accennare ai concetti di Galileo, <lb/>che saranno stati un occasione s&igrave;, ma un occasione troppo remota. </s>

<s><lb/>Il Mersenno, e tutti noi si vorrebbe saper qual fu l'immediata <lb/>scintilla, da cui si accese la gran fiamma, e nessun lo sa dire, n&egrave; <lb/>si legge in nessuna di quelle tante carte dei manoscritti galileiani, <lb/>d'onde pur s'attinge la segreta storia di tante cose. </s>

<s>Altra gran ma&shy;<lb/>raviglia &egrave; che il Torricelli non pubblicasse e nemmeno scrivesse <lb/>di proposito nulla intorno alla sua grande invenzione. </s>

<s>Le lettere <lb/>stesse a Michelangiolo Ricci, che sarebbero forse andate smarrite <lb/>se il Borelli, recatele da Roma, non l'avesse consegnate al principe <lb/>Leopoldo de'Medici, non si pubblicarono prima del 1663, nella Let&shy;<lb/>tera di Timauro ai Filaleti. </s>

<s>Il Torricelli e il Viviani &egrave; verosimile <lb/>che non avrebbero operato cos&igrave;, se avessero presentito i benefizi <lb/>immensi, che sarebbero derivati alla scienza universale da quel loro <lb/>cannello di vetro, mezzo pieno di mercurio e mezzo vuoto. </s></p><p type="main">

<s>Il non aver per&ograve; questo presentimento e il non aver dato a <lb/>quel loro sperimentale apparato tutta quella importanza, che gli <lb/>dettero gli stranieri, non vuol dir, com'affermava il Pecquet, che <lb/>l'avessero lasciato morire appena nato. </s>

<s>A rivendicar l'onta, che si <lb/>fa all'Italia con quelle parole dall'anatomico francese, sovverranno <lb/>i fatti, pochi ma concludenti, da cui si prova come, dopo le prime <lb/>esperienze, proseguisse, nello studio delle propriet&agrave; del vacuo e <lb/>degli effetti naturali della pressione ammosferica, il Torricelli aiu&shy;<lb/>tato e sollecitato all'opera dall'amico suo Raffaello Magiotti. </s></p><p type="main">

<s>La lettera del di 11 di Giugno 1644, dove l'Autore descrive a <lb/>Michelangiolo Ricci l'esperienza dell'argomento vivo, perch&egrave; la pri&shy;<lb/>ma fra le rimaste, si d&agrave; come primo documento degli studi speri&shy;<lb/>mentali su quel soggetto. </s>

<s>Ma chi attende bene, rileva con facilit&agrave;, <lb/>dalle sue proprie parole, che lo scrivente era gi&agrave; fatto certo, non <lb/>solo che l'aria pesa, ma che il peso di lei varia da un giorno al&shy;<lb/>l'altro, per cui l'assunto di quella Lettera al Ricci non &egrave; che di <lb/>dargli notizia de'tentativi fatti per costruire un nuovo strumento, <lb/>da servir di misura a quelle ammosferiche variazioni. </s>

<s>Or perch&egrave; la <lb/>notizia di una cosa tanto nuova, qual'&egrave; quella dell'aria, che preme <lb/>con varia forza di torchio da un giorno all'altro, non poteva esser <lb/>se non che frutto di ripetute diligentissime esperienze, si veda <lb/>quanto mal s'appongono coloro, che riguardano l'esperienza del <lb/>mercurio nel cannello di vetro, alle mani del Torricelli, come un <lb/>fatto solitario e indipendente, senza principio e senza sequele. </s>

<s>Delle <pb xlink:href="020/01/195.jpg" pagenum="176"/>notizie delle esperienze precedenti a quella del mercurio sodisfa&shy;<lb/>remo ai lettori in luogo pi&ugrave; opportuno: quanto alle conseguenti, <lb/>basti il citar la testimonianza dei nostri Accademici del Cimento, <lb/>i quali riconoscono il Torricelli per primo Autore, che sperimen&shy;<lb/>tasse la vita degli animali nel vuoto. </s>

<s>E quando pur ci mancassero <lb/>altre testimonianze, chi potrebbe creder che colui, il quale apr&igrave; la <lb/>via a cos&igrave; nuove e importanti esperienze, si rimanesse dal vagar <lb/>per altre parti della spaziosa ubert&agrave; di quel campo? </s>

<s>Vero egli &egrave; <lb/>bene che mancava uno strumento adattato, perch&egrave;, diffidando forse <lb/>delle legature, non pens&ograve; n&egrave; ard&igrave; di aprire i fondi dei vasi, per <lb/>introdurvi dentro gli oggetti. </s>

<s>Ma chi oserebbe prescrivere cos&igrave; fatti <lb/>limiti a quel grandissimo ingegno? </s>

<s>Chi potrebbe decider se sia <lb/>vero che non avesse tempo di mettersi attorno a raffinare quelle <lb/>esperienze nel vuoto, o non sia avvenuto piuttosto che ne sia per&shy;<lb/>duta la memoria, come di tante altre cose di lui e del Magiotti? </s></p><p type="main">

<s>Raffaello Magiotti, nato in Toscana nel paesello di Montevarchi, <lb/>&egrave; un elettissimo ingegno, ma sventuratamente rimasto soffocato dalla <lb/>polvere della Biblioteca Vaticana. </s>

<s>Quella corrispondenza di amiche&shy;<lb/>voli ufficii e di studii, che pass&ograve; fra lui e il Torricelli, quando gio&shy;<lb/>vani in Roma s'educavano l'ingegno alle nuove dottrine galileiane <lb/>sotto la disciplina del P. Castelli; si mantenne integra e viva anco <lb/>dappoi, che il Torricelli stesso era venuto a Firenze, e vi s'era <lb/>stabilito in qualit&agrave; di Matematico del Granduca. </s>

<s>Le lettere fra i due <lb/>amici intercedevano assai frequenti, e non occorreva speculazione <lb/>o scoperta all'ingegno e all'esercizio dell'uno, che non fosse co&shy;<lb/>municata o conferita con l'altro. </s>

<s>Pensa il Torricelli che le velocit&agrave; <lb/>del flusso dei liquidi non siano proporzionali alle semplici altezze <lb/>ma alle loro radici, e il Magiotti conferma il fatto con ripetute e <lb/>diligenti esperienze. </s>

<s>Si &egrave; il Torricelli stesso abbattuto a nuovi fatti <lb/>curiosi circa il galleggiare e il sommergersi alcune palline di vetro <lb/>vuote e aperte in un sottilissimo foro, per dove pu&ograve; passare o acqua <lb/>o nuov'aria, e avvisa di questa curiosit&agrave; proponendogliela sotto forma <lb/>di Problemi il Magiotti, che gli risolve mirabilmente nell'unica <lb/>scrittura, che di lui s'abbia alle stampe, sotto il titolo di <emph type="italics"/>Renitenza <lb/>certissima dell'acqua alla compressione.<emph.end type="italics"/></s></p><p type="main">

<s>Che le prime scoperte del variar della pressione ammosferica <lb/>fossero comunicate dall'Autore al suo amico in Roma, pi&ugrave; che pro&shy;<lb/>babile, sembra a noi cosa certa, e se ci fossero rimaste le lettere, <lb/>nelle quali il Torricelli conferiva col Magiotti quelle sue stesse sco&shy;<lb/>perte, non sarebbe lasciato forse altro pi&ugrave; da desiderare alla cu-<pb xlink:href="020/01/196.jpg" pagenum="177"/>riosit&agrave; della storia. </s>

<s>In ogni modo, anco dai pochi documenti che <lb/>ci son pervenuti, o da qualche accenno, che si trova fatto qua e l&agrave; <lb/>dagli scrittori, s'argomenta che il Magiotti s'esercit&ograve; intorno all'espe&shy;<lb/>rienza del vuoto in pi&ugrave; varii modi, e con pi&ugrave; solerzia, di quel che <lb/>non facessero qualche anno dopo tanti stranieri. </s>

<s>Lo Schott l'anno&shy;<lb/>vera fra coloro che assisterono al pubblico esperimento del vuoto, <lb/>fatto con l'acqua dentro un lungo tubo applicato alla parete esterna <lb/>della propria casa d'abitazione da Gaspero Berti. </s>

<s>Il Mersenno per&ograve;, <lb/>non come semplice spettatore ce lo rappresenta, ma come princi&shy;<lb/>pale attore della nuova e importante esperienza. </s>

<s>Nel capitolo VI <lb/>delle sue <emph type="italics"/>Nuove Osservazioni,<emph.end type="italics"/> dopo avere accennato alla possibilit&agrave; <lb/>del vacuo, e all'esperienze pi&ugrave; opportune per dimostrarlo, soggiunge: <lb/>&ldquo; Bombus volantis crabronis aptissimus videtur, sed et aquae, vel <lb/>alterius liquoris guttulas possis in illo tubo vacuo experiri, num <lb/>tubo concusso guttulae illae, lapidum instar parietes internos cy&shy;<lb/>lindri percussurae sint ut clariss. </s>

<s>Magiottus in tubo factum esse <lb/>dicebat, ex quo fuerat haustus aer diabete &rdquo; (T. III. Parisiis, 1647, <lb/>pag. </s>

<s>104, 5). Da s&igrave; importante documento si raccoglie dunque, che <lb/>infin dal 1644, o in quel torno che il Mersenno trovavasi a Roma, <lb/>il Magiotti usava di fare il vuoto colla siringa, e per tal modo spe&shy;<lb/>riment&ograve; il colpo secco, che danno i liquidi, non impediti ne fra&shy;<lb/>stagliati dall'aria. </s>

<s>Questo solo fatto attesta che il nostro sperimen&shy;<lb/>tatore era proceduto cos&igrave; avanti, da raggiungere quasi il Boyle, e <lb/>da emulare gli stessi Accademici fiorentini, che sarebbero venuti <lb/>parecchi anni dipoi. </s></p><p type="main">

<s>Anzi di questa ultima nostra asserzione abbiam certezza di <lb/>prove da alcune lettere del Borelli. </s>

<s>Essendo egli nell'estate del 1658 <lb/>in Roma, ebbe ordine dal principe Leopoldo d'informarsi di ci&ograve; <lb/>che fosse avvenuto dei manoscritti lasciati dopo la morte dal Ma&shy;<lb/>giotti. </s>

<s>E raccolse dalle sue informazioni, il Borelli, come il cardinal <lb/>Sacchetti, alle mani del quale erano venuti que'fogli, avessegli con&shy;<lb/>segnati a Michelangiolo Ricci, perch&egrave; gli ordinasse in quel modo <lb/>che sapesse migliore. </s>

<s>&ldquo; Mi dice per&ograve; il detto Signore (cio&egrave; il Ricci, <lb/>e son parole dello stesso Borelli) che pochissime cose buone ha <lb/>ritrovato fra i detti scartafacci, particolarmente di quelle belle cose <lb/>geometriche e filosofiche che aveva ritrovato quel grande ingegno, <lb/>e queste per esser notate in cartucce furono disprezzate e poi bru&shy;<lb/>ciate da quella canaglia che aveva cura di spurgare le case dopo <lb/>la peste &rdquo; (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XVI. c. </s>

<s>100). </s></p><p type="main">

<s>Non sodisfatto, il Principe insiste per aver pi&ugrave; particolari in-<pb xlink:href="020/01/197.jpg" pagenum="178"/>formazioni, e dopo pochi giorni, il d&igrave; 3 d'Agosto, il Borelli risponde: <lb/>&ldquo; Mi sono poi meglio informato di quelle poche scritture rimaste <lb/>del signor Magiotti.... Di pi&ugrave; vi sono alcune poche sperienze sopra <lb/>il vaso d'argento vivo.... e per quanto mi dice il signor Michelan&shy;<lb/>giolo non vi &egrave; niente di pi&ugrave; di quello, che si &egrave; sperimentato nel&shy;<lb/>l'Accademia di Vostra Altezza &rdquo; (ivi, c.103). Ora, se si ripensi che <lb/>tra le prime e principali cure dell'Accademia del Cimento fu quella <lb/>di sperimentare nel vaso dell'argento vivo, e che moltissime e delle <lb/>principali fra queste stesse esperienze ne erano state fatte gi&agrave; nel&shy;<lb/>l'estate del 58, quando appunto scriveva il Borelli; si concluder&agrave; <lb/>dunque dalle parole di lui che il Magiotti, se non aveva fatto di <lb/>pi&ugrave;, aveva fatto almeno, intorno all'esperienza torricelliana, tutto <lb/>quel che nel Libro dei Saggi di Naturali Esperienze, dopo pi&ugrave; che <lb/>22 anni, vi fu particolarmente narrato e descritto. </s>

<s>Che se veramente <lb/>&egrave; cos&igrave;, vedasi quanto a torto asserisse il Pecquet essere l'esperi&shy;<lb/>mento dell'idrargiro <emph type="italics"/>vix natum<emph.end type="italics"/> appresso noi italiani, <emph type="italics"/>et in cuna&shy;<lb/>bulis suffocatum.<emph.end type="italics"/></s></p><p type="main">

<s>Ma insomma, la ragione e i diritti del primato d'Italia ne'pro&shy;<lb/>gressi delle scienze sperimentali resultano da documenti sconosciuti <lb/>non solo al Pecquet, e agli altri stranieri, ma non saputi nemmeno <lb/>da molti di noi italiani, che pure abbiamo cos&igrave; gran pretensioni, e <lb/>meniamo cos&igrave; gran vanto. </s>

<s>I nostri competitori perci&ograve; hanno avuto <lb/>fin qui ragione o di andare in collera con noi, o di deriderci, com&shy;<lb/>patendo alla nostra vanit&agrave;, e avranno ragione ancora di farlo, in&shy;<lb/>fintanto che non si confermi quel nostro primato sopra pi&ugrave; stabile <lb/>fondamento. </s>

<s>Alla patria nostra non mancher&agrave;, speriamo, chi voglia <lb/>e sappia degnamente farlo, ma intanto ne tratteremo qualche cosa <lb/>noi, quanto lo comporti la sufficienza nostra e la brevit&agrave; richiesta <lb/>al presente Discorso. </s></p><p type="main">

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

<s>Perch&egrave; noi teniamo per cosa certa aver l'arte sperimentale <lb/>avuto i suoi primi principii e i suoi primi istituti dal Torricelli, e <lb/>perch&egrave; i cenni gi&agrave; fatti, essendo troppo scarsi all'importanza del <lb/>soggetto, richiedono d'esser suppliti e confortati d'altri argomenti; <lb/>giova, prima, intrattenere alquanto la nostra considerazione sulla <pb xlink:href="020/01/198.jpg" pagenum="179"/>persona di lui, che, dopo Galileo, &egrave; al parer nostro il principale <lb/>attore di questa Parte della nostra Storia. </s></p><p type="main">

<s>Evangelista Torricelli, a cui si d&agrave; da molti per patria Faenza, <lb/>si sent&igrave; consapevole della potenza del proprio ingegno alla lettura <lb/>dei Dialoghi delle Due Nuove Scienze, ai teoremi dimostrati ne'quali <lb/>fece alcune aggiunte o <emph type="italics"/>progressi,<emph.end type="italics"/> com'ei stesso si esprime (MSS. <lb/>Gal. </s>

<s>Disc. </s>

<s>T. XL, c. </s>

<s>78), che ordinati e trascritti, verso il Febbraio <lb/><figure id="id.020.01.198.1.jpg" xlink:href="020/01/198/1.jpg"/><lb/>del 1641, mand&ograve; al suo Maestro e Protettore Benedetto Castelli. </s>

<s>Il <lb/>Castelli fece di ci&ograve; consapevole Galileo, che se ne rallegr&ograve; molto, <lb/>e nel seguente aprile invitava l'Autore di quei <emph type="italics"/>progressi<emph.end type="italics"/> a tratte&shy;<lb/>nersi per qualche giorno seco in Arcetri. </s>

<s>Il principe Leopoldo poi <lb/>fece s&igrave;, che la semplice visita si riducesse a stabile soggiorno. </s>

<s>Tal <lb/>notizia raccogliesi dalla minuta autografa di una lettera, che lo <lb/>stesso principe indirizzava a Michelangiolo Ricci, nella quale, a <pb xlink:href="020/01/199.jpg" pagenum="180"/>proposito del nuovo libro che meditava il Borelli sulla forza della <lb/>percossa, scrive che la buona memoria di Galileo gli aveva detto <lb/>pi&ugrave; volte d'aver ritrovata la misura di quella forza &ldquo; ma non pot&egrave; <lb/>per l'et&agrave; o per qualsivoglia altro accidente, che ne fosse cagione, <lb/>darla fuori, com'io le feci ben cento volte istanza, ed al qual fine <lb/>condussi qui il Torricelli di suo consenso, perch&egrave; potesse servire <lb/>in mettere in carta i suoi pensieri, ma tutto fu invano &rdquo; (MSS. Gal. </s>

<s><lb/>Cim. </s>

<s>T. XXIII. c. </s>

<s>113). Galileo che, secondo narreremo a suo luogo, <lb/>aveva gi&agrave; nell'animo repudiata quella speculazione della percossa, <lb/>si proponeva di conferire col Torricelli altri suoi pensieri matema&shy;<lb/>tici e fisici, per poter con l'aiuto di lui ripulirli e mandarli alla <lb/>luce (Alb. </s>

<s>VII. pag. </s>

<s>367). In effetto per&ograve; non fece aiutarsi che nelle <lb/>aggiunte, nelle correzioni dei Dialoghi del Moto, e nel nuovo ordine <lb/>che meditava di dare ai teoremi dimostrati nel Dialogo terzo. </s>

<s>N&egrave;, <lb/>a quel che apparisce dai manoscritti galileiani, furono scarsi intorno <lb/>a ci&ograve; gli aiuti prestati dal Torricelli, tanto pi&ugrave; se si ripensi ch'ei <lb/>non istette ospite in Arcetri che dall'Ottobre al Gennaio. </s></p><p type="main">

<s>Morto Galileo, il Torricelli fu trattenuto in Firenze e onorato, <lb/>ad insinuazione di Andrea Arrighetti, di un duplice ufficio; di quello <lb/>di Filosofo e matematico del Granduca Ferdinando II, e dell'altro <lb/>di Lettore di Matematiche nel pubblico Studio fiorentino. </s>

<s>Ai due <lb/>speciali ufficii corrispose con opere, diverse di natura e di successo. </s>

<s><lb/>Come professore di Matematiche raccolse in un volume, sotto il <lb/>titolo di <emph type="italics"/>Opere geometriche,<emph.end type="italics"/> ci&ograve; che aveva speculato cos&igrave; intorno <lb/>alle propriet&agrave; della sfera e dei solidi sferali, come intorno al moto <lb/>de'gravi solidi e liquidi naturalmente discendenti e proietti, e con&shy;<lb/>tiene quel volume, pubblicato in Firenze nel 1644, tutto ci&ograve; che <lb/>vide la pubblica luce vivente l'Autore. </s></p><p type="main">

<s>Tutte le altre scritture rimaste inedite pervennero, alla morte <lb/>del Torricelli avvenuta nel 1647, dopo soli 39 anni di vita, nelle <lb/>mani di Lodovico Serenai, che, copiate in gran parte le consegn&ograve; <lb/>al Viviani, affinch&egrave; le ordinasse per dare alle stampe. </s>

<s>L'accusa <lb/>mossagli poi dal Nelli e ripetuta da altri, di non aver adempiuto <lb/>per invidia al pietoso amichevole ufficio, parr&agrave; ingiustissima a tutti <lb/>coloro, i quali sanno come il Viviani, e per la mal ferma salute e <lb/>per i pubblici impieghi, fosse impedito di pubblicare le molte opere <lb/>sue proprie. </s></p><p type="main">

<s>Le Lezioni Accademiche del Torricelli, alcune delle quali trattan <lb/>soggetti di Meccanica e di Fisica, importantissimi, ignote a quel che <lb/>che sembra al Borelli, ma vedute gi&agrave; dal Viviani, furono pubbli-<pb xlink:href="020/01/200.jpg" pagenum="181"/>cate, per la prima volta nel 1715, da Tommaso Bonaventuri, e le <lb/>varie Scritture sopra le Chiane capitate, dopo varie vicende, alle <lb/>mani del p. </s>

<s>Guido Grandi, s'inserirono, nel 1768, nella Raccolta <lb/>fiorentina degli Autori, che trattano del moto delle acque. </s></p><p type="main">

<s>Come Filosofo e Matematico del Granduca Ferdinando II, il <lb/>Torricelli, infino dal 1642, dette opera a istituire la sperimentale <lb/>Accademia Medicea, nella quale, quasi con mano ostetricante, si <lb/>estraevano dalle Opere di Galileo esperienze e invenzioni di strumenti <lb/>nuovi, da scoprir le pi&ugrave; recondite cause di tanti effetti della Natura. </s>

<s><lb/>Dicemmo che cos&igrave; fatti studi ed esercizi sperimentali, com'erano <lb/>in soggetto diverso, cos&igrave; ebbero diverso successo da quegli altri <lb/>studi, che fece lo stesso Torricelli come pubblico professore, per&shy;<lb/>ciocch&egrave; questi furono principalmente di argomento geometrico, e <lb/>andarono sotto il nome del loro proprio Autore, mentre l'espe&shy;<lb/>rienze fatte e gli strumenti inventati e costruiti nel palazzo dei Pitti, <lb/>s'attribuirono, per cortigiano ossequio, al granduca Ferdinando. </s></p><p type="main">

<s>Che sia andata veramente la cosa a questo modo, non par che <lb/>ci sia bisogno di troppo lunghe parole a provarlo, e perci&ograve;, ammesso <lb/>che le belle esperienze e gli utili strumenti attribuiti al Granduca, <lb/>fossero veramente opera e studio del Torricelli, vediamo quali fos&shy;<lb/>sero quelle particolari esperienze e quelle invenzioni, primaticci <lb/>frutti della nascente Accademia sperimentale di Firenze. </s></p><p type="main">

<s>Si disse che il Torricelli ostetric&ograve; i suoi parti sperimentali dalle <lb/>Opere di Galileo, a conferma di che, occorre prima di tutto a notar <lb/>l'origine di quei vari strumenti inventati. </s>

<s>Son questi principalmente <lb/>il Termometro a liquido, l'Igrometro a condensazione, e varie sorta <lb/>d'Idrostammi o pesa liquori, che furono poi tutti diligentemente <lb/>descritti nel libro dei Saggi di Naturali esperienze. </s>

<s>Ma che essi <lb/>appartengano veramente a questi primordii dell'Accademia Medicea, <lb/>si argomenta da quel <emph type="italics"/>Registro di varie Esperienze fatte e osservate <lb/>dal Serenissimo Granduca Ferdinando II<emph.end type="italics"/> che redatto da Paolo Mi&shy;<lb/>nucci, e copiato poi dal Viviani, fu inserito nella prima carta del <lb/>primo Tomo dei Manoscritti del Cimento, e pubblicato dal Targioni. </s>

<s><lb/>Il primo concetto di quella importantissima trasformazione del Ter&shy;<lb/>mometro ad aria, nello strumento perpetuo che, secondo si legge <lb/>nel citato Registro, <emph type="italics"/>dimostra la differenza di caldo e freddo dell'aria <lb/>e de'liquidi,<emph.end type="italics"/> sovvenne senza dubbio al Torricelli da quella espe&shy;<lb/>rienza della caraffa col collo assai lungo, empiuta d'acqua insino <lb/>al collo, e messa al fuoco, che si legge nella <emph type="italics"/>Risposta a Lodovico <lb/>delle Colombe.<emph.end type="italics"/> L'Igrometro a condensazione, di cui dava notizia lo <pb xlink:href="020/01/201.jpg" pagenum="182"/>stesso Torricelli a Michelangiolo Ricci, (tanto &egrave; vero che l'inven&shy;<lb/>zione &egrave; sua e non del Granduca) occorse facilmente all'inventore, <lb/>a fin di decidere la questione che s'agita, fra le tante, nella citata <lb/>Risposta al Colombo, se cio&egrave; quella rugiada, che si depone sulla <lb/>superficie dei corpi divenuti pi&ugrave; freddi dell'ambiente, sia aria tra&shy;<lb/>sformata nell'elemento dell'acqua. </s>

<s>I densimetri poi torricelliani, di <lb/>che il Serenissimo si serviva per riconoscer le qualit&agrave; delle varie <lb/>acque sorgenti, e per distinguer le varie bont&agrave; dei vini, scaturirono <lb/>senza dubbio dal primo Dialogo delle Due Nuove Scienze, dove <lb/>Galileo propone d'immergere una palla di cera, per conoscer negli <lb/>usi medici i vari gradi della gravit&agrave; o leggerezza dell'acqua. </s></p><p type="main">

<s>Anzi ebbero di qui origine quelle belle e feconde esperienze <lb/>delle palline di vetro vuote e galleggianti dentro un bocciol pieno <lb/>d'acqu&agrave;, che il Torricelli mostrava al Moncony, primo tra'francesi <lb/>a testimoniare nelle scienze sperimentali il primato dell'Italia. </s>

<s>Co&shy;<lb/>teste palline dettero occasione a scoprire altri fatti idrostatici curiosi <lb/>e nuovi, che si mandarono a risolvere ai varii dotti, sotto le velate <lb/>forme di problemi, per cui non fa maraviglia che, venuti a notizia <lb/>del Cartesio, o egli si appropriasse o altri spontaneamente gli attri&shy;<lb/>buissero quegli idrostatici giochetti. </s>

<s>Giochetti non furon per&ograve; alle <lb/>mani del Torricelli, che, dal veder variare il modo del galleggia&shy;<lb/>mento di quelle palline, al vario premer col dito l'aria alla bocca <lb/>del vaso, ebbe i primi indizii del variar della pressione atmosferica: <lb/>giochetti non furono alle mani del Magiotti, che di li prese occa&shy;<lb/>sione a dimostrar la verit&agrave; di quell'importantissimo fatto idrostatico <lb/>delle pressioni dei liquidi per tutti i versi, e della instantanea dif&shy;<lb/>fusione dei loro moti. </s></p><p type="main">

<s>Quel Moncony, di cui si diceva, rec&ograve; d'Italia in Francia, e anzi <lb/>trasport&ograve; seco ne'suoi viaggi in Egitto, uno de'pi&ugrave; squisiti canoc&shy;<lb/>chiali che fossero usciti dalle mani del Torricelli, giacch&egrave;, a questi <lb/>primordii o primo periodo della sperimentale Accademia fiorentina, <lb/>appartiene altres&igrave; il perfezionamento del Canocchiale galileiano e <lb/>del Microscopio. </s>

<s>Anzi, il Microscopio, cos&igrave; detto <emph type="italics"/>della perlina,<emph.end type="italics"/> che <lb/>trov&ograve; poi tanto facile accoglienza in Olanda, &egrave; invenzione tutta pro&shy;<lb/>pria del Torricelli e noi diremo a suo luogo il modo, ch'ei teneva <lb/>facilissimo di fabbricar questo, che par, fra gli strumenti di ottica, <lb/>un balocco, ma che &egrave; pure di grandissimo effetto. </s></p><p type="main">

<s>Notabile &egrave; per&ograve; che il costruttore e l'inventore di questi cos&igrave; <lb/>squisiti ottici strumenti non pensasse d'applicarli o alle osservazioni <lb/>naturali o alle celesti. </s>

<s>Vero &egrave; bene che, in questi stessi tempi della <pb xlink:href="020/01/202.jpg" pagenum="183"/>sperimentale Accademia fiorentina, si riscontrarono i moti dei sa&shy;<lb/>telliti di Giove sulle Effemeridi, che mandava il Renieri, ma forse <lb/>que'riscontri eran fatti, per ordine del principe Leopoldo, dal Vi&shy;<lb/>viani. </s>

<s>Il Torricelli pare che non fosse molto inclinato a cos&igrave; fatti <lb/>esercizi, e in ogni modo, bench&egrave; gareggiasse col Fontana e si van&shy;<lb/>tasse di aver superato in perfezione i canocchiali di lui, non fece, <lb/>in Astronomia, nessuna scoperta. </s>

<s>Nella Primavera del 1647 racconta <lb/>al Renieri come gli occorresse di veder Mercurio in congiunzione <lb/>con Venere &ldquo; e cos&igrave; all'improvviso, sul campanile del Duomo, di&shy;<lb/>scorrendo con alcuni giovani, che erano meco, feci un certo calco&shy;<lb/>laccio, per la prima volta che avevo veduto Mercurio, e conietturai <lb/>che egli di diametro reale fosse meno di otto miglia delle nostre &rdquo; <lb/>(MSS. Gal. </s>

<s>Dis. </s>

<s>T. XL, c. </s>

<s>13). </s></p><p type="main">

<s>Alla morte del Torricelli, sopravvenuta inaspettatamente nel&shy;<lb/>l'anno stesso in cui scriveva queste parole, non cess&ograve; nel Granduca <lb/>Ferdinando il prnrito, e nel principe Leopoldo quella nobile e gen&shy;<lb/>tile predilezione, che egli ebbe sempre per le scienze sperimentali. </s>

<s><lb/>A tale servizio in corte fu sostituito quel Vincenzio Viviani, che si <lb/>soleva chiamar l'ultimo, ma il pi&ugrave; affezionato dei discepoli di Ga&shy;<lb/>lileo. </s>

<s>Che egli fosse anzi svisceratamente affezionato, lo dimostr&ograve; <lb/>nello zelo dell'illustrarne e diffonderne le dottrine, come, e anco <lb/>pi&ugrave;, in sostener l'onore e rivendicarne i diritti delle scoperte. </s>

<s>Fanno <lb/>al proposito le seguenti relazioni, che dava a un amico: &ldquo; Le dir&ograve; <lb/>ancora come tra quelle povere fatiche di matematica abbozzate da <lb/>me, dal 1639 fin al 1644, quando per servizio attuale del Serenis&shy;<lb/>simo G. D. mio Signore convennemi abbandonare s&igrave; fatti studi, io <lb/>pensavo di fare scelta di quella, che ne'continui impieghi e con la <lb/>poca salute che io mi trovavo, mi fosse stata di pi&ugrave; facile esecu&shy;<lb/>zione. </s>

<s>Questa era l'illustrazione e promozione delle opere di Galileo <lb/>mio Maestro, da accoppiarsi con la descrizione della sua vita, la quale <lb/>da ogni altro assai meglio s&igrave;, ma non gi&agrave; s&igrave; veridica n&egrave; di notizie <lb/>cos&igrave; copiosa potesse scriversi &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLII, c. </s>

<s>130). </s></p><p type="main">

<s>Nonostante per&ograve; la mal ferma salute e gli impieghi, fu il Vi&shy;<lb/>viani fecondissimo nello speculare e infaticabile nell'operare. </s>

<s>A <lb/>raccogliere tutti insieme, e ad ordinare i varii teoremi, che dimostr&ograve; <lb/>e i varii problemi, che risolse intorno alle dottrine del moto, si <lb/>comporrebbe un Trattato di <emph type="italics"/>aggiunte e progressi<emph.end type="italics"/> ai Dialoghi delle <lb/>Nuove Scienze, che se cede al Torricelli nell'elegante facilit&agrave; di <lb/>dimostrare, lo supera senza dubbio nella variet&agrave; e nell'abbondanza. </s>

<s><lb/>In Idrometr&igrave;a, il Viviani fu instancabile, e d'ogni parte traspira <pb xlink:href="020/01/203.jpg" pagenum="184"/>un ardentissimo zelo di diffondere le dottrine torricelliane. </s>

<s>A lui <lb/>il principio delle velocit&agrave; proporzionali alle altezze professato dal <lb/>Castelli sembrava men vero di quel che non si concludeva dalle <lb/>teorie o si verificava nei fatti; e intorno alle controversie se l'acque <lb/>giungono allo sbocco con tutta la velocit&agrave; conveniente alla caduta, <lb/>oppur ricevano impedimento e patiscano indugio dagli attriti, la&shy;<lb/>sciato per amor della verit&agrave; da parte il suo Galileo, consentiva <lb/>pienamente coll'Arrighetti. </s>

<s>Moltissime e importantissime son l'espe&shy;<lb/>rienze fatte dal Viviani, per misurar le varie quantit&agrave; d'acqua, che <lb/>in egual tempo si raccolgono dalle varie figure delle bocche di ero&shy;<lb/>gazione, ora radenti, ora sporgenti in tubi addizionali, o brevi o <lb/>lunghi, o diritti o flessuosi. </s></p><p type="main">

<s>Il Trattato del votamento dei vasi o delle <emph type="italics"/>Clessidre,<emph.end type="italics"/> diviso in <lb/>quattro libri, col titolo un po'romantico di <emph type="italics"/>Sogno idrometrico,<emph.end type="italics"/> sa&shy;<lb/>rebbe riuscito opera insigne e da risparmiare il Trattato del Moto <lb/>delle Acque del Grandi, e di altri Autori, se avesse avuto il Nostro <lb/>il tempo e la comodit&agrave; di pubblicarlo. </s>

<s>Quest'opera, nella quale, <lb/>come si diceva dianzi, il principio torricelliano delle velocit&agrave; pro&shy;<lb/>porzionali alle radici delle altezze ha il suo ampio svolgimento e <lb/>la sua pi&ugrave; compiuta dimostrazione, con altri teoremi speculati a <lb/>solo fine di promuovere il trattato <emph type="italics"/>De motu aquarum,<emph.end type="italics"/> finiscono di <lb/>persuader coloro, che dissero temerariamente aver il Viviani tenute <lb/>per invidia e per gelosia nascoste le scritture inedite del Torricelli. </s></p><p type="main">

<s>Col segreto dello stesso Torricelli, avuto dal Granduca che lo <lb/>teneva gelosamente custodito, e con altre regole proprie apprese <lb/>dalla teoria e dalla pratica, il Viviani dava opera alla costruzione <lb/>dei canocchiali, e attendeva, ora per proprio genio, ora per parti&shy;<lb/>ticolare ordine del principe Leopoldo, alle osservazioni celesti. </s>

<s>Ma <lb/>la mal ferma salute non permettendogli le lunghe e faticose vigilie, <lb/>non fece, come il Torricelli, in Astronomia molti progressi. </s>

<s>Dei mol&shy;<lb/>tissimi per&ograve; fatti nella Fisica sperimentale diremo pi&ugrave; qua, quando <lb/>c'incontreremo un'altra volta nel Viviani come accademico del Ci&shy;<lb/>mento, ma intanto, a svolgere que'cento tanti e pi&ugrave; volumi delle <lb/>sue carte, non par possibile che un uomo, e sia pur che la vita gli <lb/>decorresse lunghissima dal 1622 al 1703 potesse attendere a tante <lb/>e s&igrave; difficili cose. </s>

<s>Stanco delle proprie speculazioni, si ricreava in <lb/>tradurre dal latino o dal francese ci&ograve; che di nuovo e di bello aves&shy;<lb/>sero speculato gli altri nei loro proprii libri; ora compendiava trat&shy;<lb/>tati intieri, forse per uso dei principi padroni, ora ne disegnava e <lb/>in parte coloriva de'nuovi, in soggetto di matematiche, di cosmo-<pb xlink:href="020/01/204.jpg" pagenum="185"/>grafia o di qualsivoglia altro. </s>

<s>&ldquo; Se io avessi, scriveva a un amico, a <lb/>cucire tutte le mie speculazioni imbastite e finire di riempir tutti i <lb/>miei orditi con obbligo ancora di non dover pensare a niun altra cosa <lb/>di nuovo, non mi sarebbe tanto il vivere fino a cent'anni, con sanit&agrave; <lb/>perfetta e disoccupazione da ogni altro impiego &rdquo; (ivi, T. CXLII, c.270). </s></p><p type="main">

<s>Quando scriveva cos&igrave;, il Viviani contava 56 anni, e non aveva <lb/>altro pubblicato che <emph type="italics"/>De maximis et minimis,<emph.end type="italics"/> la <emph type="italics"/>Scienza Universale <lb/>delle proporzioni,<emph.end type="italics"/> il <emph type="italics"/>Diporto geometrico,<emph.end type="italics"/> l'<emph type="italics"/>Enodatio problematum<emph.end type="italics"/><lb/>che son piccola parte, e non la pi&ugrave; importante delle opere di lui. </s>

<s><lb/>Il rimanente, da poche altre cose in fuori, &egrave; tuttavia inedito, e ci&ograve; <lb/>vuol dire che un dovizioso tesoro della scienza italiana &egrave; rimasto da <lb/>tanto tempo, disutile e infruttuoso. </s>

<s>A lui vecchio di settantott'anni <lb/>il p. </s>

<s>ab. </s>

<s>Grandi, scrivendogli di Roma, faceva questa domanda: <lb/>&ldquo; &Egrave; fuori voce in Roma che le opere di V. S. si ristampino in <lb/>Londra, e che que'signori della Societ&agrave; Regia abbiano impetrato <lb/>dal Serenissimo Granduca li di lei scritti, per imprimerli con altre <lb/>sue opere .... &Egrave; egli vero tuttoci&ograve;, oppure posso io seguitare ad as&shy;<lb/>sicurare l'Italia che le di lei fatiche saranno impresse per opera <lb/>del sig. </s>

<s>Panzanini? </s>

<s>&rdquo; (ivi, T. CXLVII. c. </s>

<s>189). A che il buon vecchio <lb/>cos&igrave; rispondeva: &ldquo; &Egrave; ben falsa quella voce che &egrave; fuori, perch&egrave; l'opere <lb/>di quello scimunito dolcissimo, n&egrave; per mano di lui n&egrave; di altri non <lb/>v'&egrave; apparenza che si sieno per vedere, se Dio non fa miracoli &rdquo; <lb/>(ivi, T. CXLVIII. c. </s>

<s>36). E i miracoli ancora non sono stati fatti. </s></p><p type="main">

<s>Ma passiamo a veder quel che operasse il Viviani in questo, <lb/>che da noi si distingue col nome di secondo periodo della speri&shy;<lb/>mentale Accademia medicea. </s>

<s>Soggetto principale di queste espe&shy;<lb/>rienze, che si direbbero, alla maniera dei nostri giorni, esperienze <lb/>di gabinetto, furon quelle degli agghiacciamenti dell'acque, per <lb/>veder che variet&agrave; facessero esposti i vasi in varie situazioni all'aria <lb/>aperta. </s>

<s>Cominciarono queste esperienze nel Dicembre 1648, e si <lb/>proseguirono per pi&ugrave; altre invernate successive (MSS. Cim. </s>

<s>T. I, c. </s>

<s>5, <lb/>13 ecc.). Appartengono pure a questo periodo dell'Accademia quelle <lb/>osservazioni, di non lieve importanza per la teoria della conduci&shy;<lb/>bilit&agrave; del calore, che concernono il vario tempo del consumarsi il <lb/>ghiaccio nelle varie materie, di che son formati i recipienti. </s>

<s>Di tali <lb/>osservazioni poi si fece qualche cenno anco nel Libro dei <emph type="italics"/>Saggi,<emph.end type="italics"/><lb/>ma vi si tace di un'altra esperienza, fatta pure in questo medesimo <lb/>tempo, ed &egrave; quella del traforare in vario tempo, pallottole di varia <lb/>materia e di ugual grossezza, posate sopra una larga lastra di <lb/>ghiaccio. (Targioni, Aggrandim. </s>

<s>T. II. P. II. pag. </s>

<s>164). </s></p><pb xlink:href="020/01/205.jpg" pagenum="186"/><p type="main">

<s>Oltre a queste, si fecero pure altre esperienze, che non si sa&shy;<lb/>rebbero potute praticare fra le chiuse pareti di una stanza, n&egrave; <lb/>eseguire da un osservatore solo. </s>

<s>Ed ecco di qui l'occasione e il <lb/>bisogno d'organar la sua vita in varie membra, e pigliar la Medicea <lb/>sperimentale istituzione pi&ugrave; conveniente ordine di Accademia. </s>

<s>Queste <lb/>esperienze furon quelle che si fecero, tra il 1656 e 57, intorno alle <lb/>velocit&agrave; del suono e della luce, e nelle quali, ad aiutare il Viviani, <lb/>venivan chiamati il Borelli e il Rinaldini. </s>

<s>Dall'altra parte, il bisogno <lb/>di avere, a sperimentar simili effetti naturali, strumenti e spazii che <lb/>non erano n&egrave; potevano essere di propriet&agrave; e di diritto di uomini <lb/>privati, fece sentir vivo il bisogno che la scienza aveva della pro&shy;<lb/>tezione dei principi, e ai principi stessi fece pregustar la gloria di <lb/>partecipare ai meriti scientifici dei privati. </s>

<s>D'ond'&egrave; che i consessi <lb/>scientifici, nel palazzo granducale dei Medici, passarono a pigliar <lb/>ordinamento e instituto pi&ugrave; proprio di Accademia, in un-terzo pe&shy;<lb/>riodo, che si distinse dagli altri col titolo di <emph type="italics"/>Cimento.<emph.end type="italics"/></s></p><p type="main">

<s>I principi Medicei, dai quali invocava la scienza i validi aiuti, <lb/>erano il granduca Ferdinando II e Leopoldo fratello di lui. </s>

<s>Che <lb/>fosse Ferdinando inclinato a favorire gli studi sperimentali, lo pro&shy;<lb/>verebbe, senz'altro, l'essersi egli ingerito nell'invenzione di quegli <lb/>strumenti, che certamente &egrave; dovuta al Torricelli. </s>

<s>Ma pur di qui <lb/>s'argomenta che predominasse in lui all'ingegno la curiosit&agrave; e <lb/>l'ambizione. </s>

<s>Dall'altra parte chi aveva largamente speso per far <lb/>quelle esperienze, e per eseguire quegli strumenti, pareva in certo <lb/>modo che avesse il diritto di usarli per se, di dirli o di farli dir <lb/>suoi. </s>

<s>In seguito, se ced&egrave; alquanto nell'animo suo l'ambizione, non <lb/>cess&ograve; per questo la curiosit&agrave;, o una certa sua particolar prurigine <lb/>di sapere. </s>

<s>Noi, non potremmo in altro miglior modo rappresentare <lb/>ai lettori o qualificare quella curiosit&agrave; granducale, che per la se&shy;<lb/>guente scenetta, colorita da noi su una nota, che si legge a carte 120 <lb/>del X Tomo dei Manoscritti del Cimento. </s></p><p type="main">

<s>La sera del di 5 Dicembre 1665, a qualche ora di notte, una <lb/>carrozza di corte si ferma dinanzi alla porta di casa del Viviani. </s>

<s><lb/>Scende uno staffiere, entra: &mdash; Sor Vincenzio, il Padron Serenissimo <lb/>l'attende a palazzo &mdash; E il signor Vincenzio vestirsi, entrare in car&shy;<lb/>rozza, scendere nel cortile, e su per lo scalone dei Pitti. </s>

<s>Francesco <lb/>Redi l'introduce in camera: il Granduca era a letto. </s>

<s>&mdash; V'ho man&shy;<lb/>dato a chiamare, dice il Serenissimo, sollevandosi sulle coltri e <lb/>accennando alla fiamma del camminetto, per saper da voi in che <lb/>maniera, dagli spiragli della porta di camera e della finestra, bench&egrave; <pb xlink:href="020/01/206.jpg" pagenum="187"/>il tutto serrato, entri in camera vento, come si manifesta dal veder <lb/>muoversi indentro la fiammella di una candela: e perch&egrave; sia la <lb/>stessa fiammella con gran velocit&agrave; rapita, accostatala agli spiragli <lb/>dell'asse del cammino. </s>

<s>&mdash; </s></p><p type="main">

<s>Il principe Leopoldo aveva della scienza pi&ugrave; nobili e dignitosi <lb/>sentimenti, e se la sua condizione non rendesse difficile il farne la <lb/>giusta stima, diremmo che aveva altra cultura scientifica e altra <lb/>forza d'ingegno. </s>

<s>Difficile &egrave; il farne la giusta stima, perch&egrave; alcune <lb/>speculazioni e scoperte si dubita che sieno attribuite a lui dall'os&shy;<lb/>sequio e dalla adulazione. </s>

<s>Cos&igrave;, per citare un esempio, la causa del <lb/>cos&igrave; detto <emph type="italics"/>salto dell'immersione<emph.end type="italics"/> osservato nelle caraffe a lungo collo <lb/>ripiene d'acqua e sommerse nella neve, il Borelli, con tutti gli altri, <lb/>dice essere stata investigata e scoperta dal Principe, quando per&ograve; <lb/>discorre con lui e gli scrive in lettere familiari. </s>

<s>Ma liberato poi da <lb/>ogni servit&ugrave; cortigianesca, dice francamente, nel libro <emph type="italics"/>De motioni&shy;<lb/>bus natural.<emph.end type="italics"/> del salto dell'immersione: &ldquo; Ego animadverti et docui <lb/>hoc contingere a restrictione eiusdem vasis &rdquo; (Regio Julio 1670, <lb/>pag. </s>

<s>547). </s></p><p type="main">

<s>Ma pure, la giudiziosa critica fatta dal Principe ad alcune spe&shy;<lb/>culazioni, come sarebbe giusto quella dello stesso Borelli concer&shy;<lb/>nente le cause del variar la pressione ammosferica, quando il tempo <lb/>si dispone o si scioglie in pioggia, e come sarebbe l'altra con la <lb/>quale il Renieri, per similitudine della varia disposizione delle lenti <lb/>nel canocchiale, spiegava il ricrescer l'apparente figura degli astri, <lb/>giunti vicino a toccar l'orizzonte; mentre rivelano una non ordi&shy;<lb/>naria acutezza d'ingegno, rendon nel medesimo tempo bella testi&shy;<lb/>monianza di quel modesto riserbo, con cui il Principe stesso entrava <lb/>nel pericolo di quelle scientifiche discussioni. </s></p><p type="main">

<s>Quel che per&ograve; abbiam per certissimo, &egrave; che in mezzo ai pia&shy;<lb/>ceri e agli svaghi di una splendida corte, attese con grande amore <lb/>agli studii matematici, infino da giovanetto. </s>

<s>Di ventun'anno faceva <lb/>richiedere a Galileo la dimostrazione allora allora trovata dal famoso <lb/>supposto meccanico, per mezzo del suo precettore don Famiano Mi&shy;<lb/>chelini, il quale cos&igrave; scriveva al medesimo Galileo: &ldquo; Il Serenissimo <lb/>ha di gi&agrave; visti i sei libri di Euclide e di presente vede l'undecimo, <lb/>e il detto libro del Moto (i Dial. </s>

<s>delle Due N. S.) con pensiero di <lb/>veder prima le Opere di V. S. </s>

<s>Molto Illustre ed Eccellentissima e <lb/>poi il resto dei matematici &rdquo; (MSS. Gal. </s>

<s>Div. </s>

<s>II. P. VI. T. XIII. c. </s>

<s>112). </s></p><p type="main">

<s>L'anno dopo, avendo Fortunio Liceti gi&agrave; pubblicato il suo libro <lb/><emph type="italics"/>De Lapide bononiensi,<emph.end type="italics"/> nel capitolo L, del quale, contro le dottrine <pb xlink:href="020/01/207.jpg" pagenum="188"/>di Galileo, attribuiva il color cinereo della Luna a un fenomeno di <lb/>fosforescenza, il principe Leopoldo, nel dar relazione del nuovo libro <lb/>peripatetico, sollecita Galileo stesso a difender le sue dottrine, ci&ograve; <lb/>che egli poi fece in quella Lettera sul Candore lunare, che &egrave; una <lb/>delle pi&ugrave; belle scritture astronomiche del nostro Autore. </s>

<s>Di questa <lb/>lettera, scrivendo il giovane principe Leopoldo da Siena, il d&igrave; 14 <lb/>maggio 1640, diceva a Galileo: &ldquo; Io, tra le altre cose che in essa <lb/>sono, ho ammirato quella di dimostrare, bench&egrave; tanto lontani dalla <lb/>Luna, che il lume in essa riflesso dalla Terra sia maggiore del <lb/>nostro lume crepuscolino, e in conseguenza di quello che la me&shy;<lb/>desima Luna sopra di noi riflette. </s>

<s>E perch&egrave; io non posso godere e <lb/>cavar quel frutto che desidererei dalla conversazione sua, cerco di <lb/>trattenermi e di ammaestrarmi in qualche parte, nel leggere le sue <lb/>Opere. </s>

<s>E per&ograve;, avendo finito di scorrere l'undecimo e duodecimo <lb/>di Euclide, sto vedendo adesso il suo Libretto delle Galleggianti, <lb/>parto non meno degli altri degno del suo intelletto, soggiungendole <lb/>che far&ograve; ancora un poco di sessione con Mons. </s>

<s>Arcivescovo Picco&shy;<lb/>lomini, tanto affezionato a V.S. e alle cose sue, dove si legger&agrave; la <lb/>scrittura sopra il lume secondario della Luna. </s>

<s>Spero io d'esser poi <lb/>da lei in questa state dove discorrer&ograve; seco di alcune cose, che mi <lb/>sono sovvenute in diverse materie, non lo potendo tanto bene fare <lb/>con la penna, quanto con la voce &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLVIII. <lb/>c. </s>

<s>37). E venuta l'estate non manc&ograve; il giovane Principe di scender <lb/>dalle splendide sale dei Pitti, per salir su al tugurio di Arcetri, a <lb/>trattenervisi col venerando vecchio che l'abitava in scientifici col&shy;<lb/>loqui. </s>

<s>Frutto di quei colloqui fu la chiamata del Torricelli a Firenze, <lb/>da cui ebbe principio, come si vide, la sperimentale Accademia <lb/>Medicea, e d'onde s'avviarono a istituirsi quegli altri celebri con&shy;<lb/>sessi accademici detti del Cimento, ai quali convien che si rivolga <lb/>il nostro Discorso. </s></p><p type="main">

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

<s>Incominciarono quei consessi nel mese di Giugno del 1657, e <lb/>i primi e principali collaboratori all'esperienze naturali che vi si <lb/>fecero, furon quei tre, che vedemmo esercitarsi in Firenze e in <lb/>Pisa intorno al misurare la velocit&agrave; della luce e del suono. </s>

<s>Pare <lb/>che, anche in questo nuovo ordinamento, il Viviani serbi una certa <pb xlink:href="020/01/208.jpg" pagenum="189"/>preminenza, che giustamente gli &egrave; attribuita, s&igrave; per essere stato col&shy;<lb/>lega e successore al Torricelli in quell'ufficio, e s&igrave; per lo zelo, per la <lb/>dottrina, e per l'operosit&agrave; con cui, da parecchi anni, l'aveva esercitato. </s></p><p type="main">

<s>Gian Alfonso Borelli, chiamato di Messina a professare le Ma&shy;<lb/>tematiche nello studio pisano, aveva fin d'allora dato saggio del&shy;<lb/>l'acume e della novit&agrave; delle sue speculazioni, non che di un'arte <lb/>squisitissima di sottoporle al cimento. </s>

<s>Tutti gli studii sperimentali <lb/>di lui, anche in apparenza pi&ugrave; disparati, convenivano in un unica <lb/>intenzione, che era quella di applicar la Meccanica e la Fisica al <lb/>moto degli animali. </s>

<s>Si preparava perci&ograve; il nostro Autore a scrivere <lb/>il celeberrimo Trattato con due libri, uno di Meccanica, intitolato <lb/><emph type="italics"/>De vi percussionis,<emph.end type="italics"/> pubblicato nel 1667, e l'altro col titolo <emph type="italics"/>De mo&shy;<lb/>tionibus naturalibus,<emph.end type="italics"/> pubblicato nel 1670, quasi lemmi premessi <lb/>alla grande Opera <emph type="italics"/>De motu animalium.<emph.end type="italics"/> Alle osservazioni naturali, <lb/>che bisognavano a condurla, attendeva gi&agrave; da lungo tempo, e il d&igrave; <lb/>16 Marzo 1663 pregava per mezzo del Michelini, che il principe <lb/>Leopoldo si compiacesse di farlo venire a Livorno, per <emph type="italics"/>far espe&shy;<lb/>rienze sui pesci vivi, per capire perfettamente come si muovono e <lb/>nuotano i pesci<emph.end type="italics"/> (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XVII. c. </s>

<s>188). Sotto il di 6 d'Aprile <lb/>1665, scriveva direttamente al Principe che era entrato a specular <lb/>la natura e la propriet&agrave; della percossa, intorno alla quale il gran <lb/>Galileo nulla aveva lasciato in iscritto (ivi, T. XVIII. c. </s>

<s>152), prepa&shy;<lb/>randosi cos&igrave; a distendere il primo libro da premettersi al Trattato <lb/>dei Moti animali. </s>

<s>Quattro anni dopo, nel Luglio, scriveva allo stesso, <lb/>rendendogli conto cos&igrave; de'suoi studi: &ldquo; Ho gi&agrave; all'ordine questo <lb/>secondo Tomo pur preparatorio della materia principale. </s>

<s>Tratto in <lb/>questo dei moti naturali dipendenti dalla gravit&agrave; &rdquo; (ivi, T. XIX, <lb/>c. </s>

<s>263) e verso la met&agrave; d'Aprile del 71: &ldquo; Spero poi questa state <lb/>perfezionare il terzo libro della immensa forza de'muscoli con le <lb/>sue cause meccaniche dimostrate, cosa affatto nuova. </s>

<s>Appresso rac&shy;<lb/>corr&ograve; in un altro libro tutto il resto di questa ammirabile Filosofia &rdquo; <lb/>(ivi, T. XX, c. </s>

<s>49). E infatti, mantenuto il proposito, torna a scri&shy;<lb/>vere sotto il d&igrave; 22 Luglio &ldquo; porr&ograve; mano subito allo stampa del mio <lb/>libro della forza dei muscoli, il quale &egrave; ridotto quasi a perfezione &rdquo; <lb/>(ivi, c. </s>

<s>65). Le pubbliche e private sventure per&ograve; non permisero al <lb/>Borelli di mandare ad effetto cos&igrave; questo proposito, com'avea man&shy;<lb/>dato quello, e la prima parte della grande Opera, dove si tratta <lb/>della forza immensa dei muscoli, fu pubblicata postuma in Roma <lb/>nel 1680: l'altra parte, dove si tratta il resto di quella ammirabile <lb/>Filosofia, vide ivi pure la luce nell'anno dopo. </s></p><pb xlink:href="020/01/209.jpg" pagenum="190"/><p type="main">

<s>Dicemmo che, a specular questa Filosofia, la quale fu poi ve&shy;<lb/>ramente riconosciuta da tutti per ammirabile e nuova, concorrevano <lb/>nell'intenzion dell'Autore gli studi pi&ugrave; varii della sua vita. </s>

<s>E in&shy;<lb/>fatti, quando, venutagli occasione d'appuntare in Giove uno squi&shy;<lb/>sitissimo canocchial del Campani, si trov&ograve; senza volere implicato <lb/>negli studii astronomici, frutto de'quali fu l'Opera insigne <emph type="italics"/>Theo&shy;<lb/>ricae Mediceorum,<emph.end type="italics"/> cos&igrave; nel pubblicare il libro scriveva il Borelli <lb/>al Lettore: &ldquo; Erit igitur huiusmodi opusculum non interruptio mei <lb/>prioris instituti, sed veluti parenthesis quaedam meorum studiorum, <lb/>nam denuo ad intermissum opus De motu anim. </s>

<s>redii &rdquo; (Floren&shy;<lb/>tiae, 1665, pag. </s>

<s>VII). Figuriamoci quel che dee essere il periodo, se <lb/>la Teorica de'pianeti medicei, che &egrave; il preludio alla nuova Astrono&shy;<lb/>mia neutoniana, non &egrave; che una parentesi! Parentesi, nella quale, <lb/>come inciso, concludesi la teoria planetaria delle comete. </s>

<s>La for&shy;<lb/>tezza di S. </s>

<s>Miniato al Monte era la specula, dove il Borelli faceva <lb/>le sue osservazioni, e dov'egli aveva erette quelle macchine, a di&shy;<lb/>mostrare il viaggio parabolico descritto da que'corpi celesti creduti <lb/>vagabondi per lo spazio e senza leggi. </s>

<s>Gli strumenti, che adorna&shy;<lb/>vano le stanze di S. </s>

<s>Miniato sopra Firenze, primo osservatorio astro&shy;<lb/>nomico d'Italia, eran lavorati con semplicit&agrave;, ed eran pure tanto <lb/>precisi. </s>

<s>&ldquo; Ho fatto, con grandissimo frutto, scriveva al principe Leo&shy;<lb/>poldo, fabbricare un istrumento da servir di sestante, il cui semi&shy;<lb/>diametro sar&agrave; 5 braccia. </s>

<s>&Egrave; composto di semplici regoli, facilissimo <lb/>a fabbricarsi ed adoperarsi, col quale spero di fare osservazioni cos&igrave; <lb/>squisite, come coloro che spendono centinaia di scudi in simiglianti <lb/>strumenti &rdquo; (ivi, T. XVIII. c. </s>

<s>154). </s></p><p type="main">

<s>Gli strumenti e l'esperienze del Torricelli, nel primo periodo <lb/>dell'Accademia Medicea, vedemmo essere un frutto allegato nel fiore <lb/>delle opere di Galileo: anco l'esperienze intorno alle quali, nel se&shy;<lb/>condo periodo, si travagli&ograve; il Viviani, per decidere se la luce si <lb/>muove in tempo, non avevano altra intenzione, che di mandare ad <lb/>effetto un pensiero proposto nel I Dialogo delle Due Nuove Scienze. </s>

<s><lb/>N&egrave; il Borelli, a ricercar le tradizioni della scienza galileiana, fu <lb/>punto inferiore agli stessi suoi colleghi. </s>

<s>Molte delle Scritture del <lb/>gran Maestro, come sarebbero le Tavole de'moti medii dei satelliti <lb/>di Giove, l'Istruzione intorno al modo d'usar lo strumento nelle <lb/>osservazioni gioviali, il Discorso dell'ufficio meccanico del timone <lb/>nel diriger le navi, e altre scritture galileiane, delle quali s'&egrave; perduta <lb/>la copia e l'originale, rivivono nelle opere o manoscritte o stam&shy;<lb/>pate dello stesso Borelli. </s></p><pb xlink:href="020/01/210.jpg" pagenum="191"/><p type="main">

<s>Quel che egli poi, per far progredire le dottrine sperimentali, <lb/>conforme ai metodi di Galileo, operasse in questo terzo periodo <lb/>dell'Accademia Medicea, o del Cimento, l'abbiamo diligentemente <lb/>annoverato da lui medesimo, nel libro <emph type="italics"/>De motionibus naturalibus,<emph.end type="italics"/><lb/>nello scrivere il quale, anzi, secondo che egli stesso dichiara, ebbe <lb/>questa particolare intenzione. </s>

<s>Accennando ivi al fatto della bilancia <lb/>equilibrata, che riscaldando l'aria ambiente a un de'piattelli tra&shy;<lb/>bocca dall'altra parte, soggiunge: &ldquo; Rationem huius admirabilis <lb/>effectus excogitavi et amico petenti reddidi, eamque communicavi <lb/>Societati doctissimorum virorum a Sereniss. </s>

<s>et Eminentiss. </s>

<s>Cardi&shy;<lb/>nali Leopoldo Mediceo erectam, quam deinceps more italico Aca&shy;<lb/>demiam experimentalem mediceam vocabo &rdquo; (Regio Julio 1670, <lb/>pag. </s>

<s>126). Di quel gentile esperimento del fumo, che discende nel <lb/>vuoto torricelliano, dice &ldquo; quod Florentiae Serenissimo Leopoldo <lb/>cardinali mediceo communicavi &rdquo; (ivi, pag. </s>

<s>128) e il medesimo dice <lb/>pure di quel barometro a sifone, di cui &ldquo; ichon habetur fig. </s>

<s>34 libri <lb/>Experimentorum eiusdem Academiae &rdquo; (ivi, pag. </s>

<s>209). </s></p><p type="main">

<s>De'varii modi per trovare il peso specifico dell'aria proposti <lb/>nell'Accademia, ne commemora &ldquo; aliquos ex multis a me ibidem <lb/>propositi &rdquo; (ivi, pag. </s>

<s>247) e son quegli ingegnosi strumenti chiamati <lb/>da lui <emph type="italics"/>Termostatici,<emph.end type="italics"/> all'invenzion dei quali aveva pensato infino <lb/>dal 1656 (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XVII. c. </s>

<s>1). &ldquo; Sed praecipuus ac pul&shy;<lb/>cherrimus modus experiendi aeris gravitatem hic est, quem Aca&shy;<lb/>demiae medicaee experimentali anno 1660 comunicavi una cum <lb/>eius demonstratione &rdquo; (De mot. </s>

<s>nat. </s>

<s>pag. </s>

<s>251). Nella stessa Acca&shy;<lb/>demia dice pure d'aver dimostrato con innumerevoli esperimenti <lb/>che il ghiaccio occupa maggiore spazio dell'acqua liquida; &ldquo; experi&shy;<lb/>menta quae omnia legi possunt in praedicto libro Experimentorum <lb/>a folio 127 usque ad fol. </s>

<s>165 &rdquo; (ivi, pag. </s>

<s>546). </s></p><p type="main">

<s>Anche il Viviani non si volle defraudare della sodisfazione di <lb/>dire quel che egli oper&ograve; nell'Accademia, e ci&ograve; fece palese, non al <lb/>pubblico, ma in una nota autografa, che si legge a c. </s>

<s>259 del Tomo X <lb/>dei MSS. del Cimento, e che poi il Nelli pubblic&ograve; nel suo Saggio <lb/>di Storia Letteraria (Lucca 1759, pag. </s>

<s>110, 11). &ldquo; Miei sono, lasci&ograve; <lb/>ivi iscritto il Viviani, I. </s>

<s>Li tre strumenti, per provar la pressione <lb/>dell'aria e che mancando quella il mercurio e l'acqua discendono <lb/>in qualunque cannello. </s>

<s>II. </s>

<s>Miei sono li cinque strumenti per pro&shy;<lb/>vare la costituzione dell'aria bassa ed alta. </s>

<s>III. </s>

<s>Mio lo strumento <lb/>cilindrico con la canna dentro, per esaminar la gravezza in specie <lb/>dei fluidi. </s>

<s>IV. </s>

<s>Mia la scatola per le rifrazioni de'fluidi. </s>

<s>V. </s>

<s>Miei li <pb xlink:href="020/01/211.jpg" pagenum="192"/>due strumenti per conoscere la gravit&agrave; in specie dei fluidi e dei <lb/>metalli. </s>

<s>VI. </s>

<s>Mie l'osservazioni circa l'ondata de'fluidi nei sifoni. </s>

<s><lb/>VII. </s>

<s>Mia l'osservazione de'balzi delle galleggianti. </s>

<s>VIII. </s>

<s>Mio il con&shy;<lb/>cetto dell'equabilit&agrave; de'suoni e dei loro usi. </s>

<s>IX. </s>

<s>Mio il nuovo modo <lb/>di misurar le distanze senza la vampa. </s>

<s>X. </s>

<s>Mie l'osservazioni in&shy;<lb/>torno l'ambra. </s>

<s>XI. </s>

<s>Miei li due strumenti per conoscer se l'alzar <lb/>dell'acqua nei cannellini proceda dalla pressione dell'aria ambiente <lb/>con succhiar collo schizzatoio. </s>

<s>XII. </s>

<s>Mie l'esperienze due proposte <lb/>per invalidar la detta pressione attorno li cannellini. </s>

<s>XIII. </s>

<s>Miei li <lb/>due strumenti intorno la pressione dell'acqua. </s>

<s>XIV. </s>

<s>Mia l'osser&shy;<lb/>vazione che tutti i legni vanno al fondo nell'acqua (provar se nel&shy;<lb/>l'olio). XV. </s>

<s>Mio lo strumento per aver la lunghezza de'pendoli di <lb/>desiderata durazione. </s>

<s>XVI. </s>

<s>Mio lo strumento a palla, per la gravit&agrave; <lb/>in specie de'fluidi col mettere i pesi dentro la palla. </s>

<s>&rdquo; Quest'ultimo <lb/>strumento, da cui si son trasformati gli Areometri moderni, come <lb/>quello pure annoverato qui in III luogo, sono illustrati con abbozzi <lb/>di figure, che suppliscono a una lunga e minuta descrizione, nel <lb/>seguente T. XI dei Manoscritti sopra citati a carte 101 e 105. </s></p><p type="main">

<s>Dopo essersi presa cos&igrave; la sua porzione ciascuno di que'due <lb/>validi commensali, si vede bene che la tavola riman quasi sparec&shy;<lb/>chiata, e che non resta, se non che poco o nulla a quegli altri, ivi <lb/>attorno seduti. </s>

<s>Fra questi occorre primo a riguardare Carlo Rinal&shy;<lb/>dini, che, messogli innanzi, non saprebbe in coscienza a che stender <lb/>la mano per prenderlo e tenerlo per suo. </s>

<s>Vero &egrave; che egli afferma <lb/>l'esperienza dell'anello riscaldato, a verificar se i solidi si dilatano al <lb/>calore, essere stata proposta da s&egrave; nell'Accademia (ivi, T. XXIV. c. </s>

<s>24) <lb/>ma tessendo e ritessendo le speculazioni del proprio cervello colla <lb/>pretensione di farle valere, eziandio contro la verit&agrave; dei fatti, non <lb/>riusc&igrave; ad altro che a far perdere la pazienza al Borelli e al Viviani. </s></p><p type="main">

<s>Un'altra volta s'era messo in testa che il tuonar di un can&shy;<lb/>none tanto pu&ograve; corresse veloce, quanto in maggior numero vi fos&shy;<lb/>sero accesi dentro i granelli della polvere. </s>

<s>Il Borelli dimostr&ograve; di <lb/>fatto, alla presenza del Granduca sulla Piazza dei Pitti, che i tuoni <lb/>si propagavano colla stessa velocit&agrave; da una piccola spingarda e da <lb/>un grosso cannone. </s>

<s>Il Rinaldini disse allora che ci&ograve; seguiva perch&egrave; <lb/>le bocche erano rivolte verso il Palazzo, e il Granduca subito mand&ograve; <lb/>due lacch&egrave;, che volgessero i pezzi da lato, e nonostante anco questa <lb/>volta i tuoni arrivarono alle solite distanze, in tempi misurati dalle <lb/>vibrazioni del pendolo sempre esattamente uguali. </s></p><p type="main">

<s>Il Magalotti che, colla sua solita vivacit&agrave;, racconta in una sua <pb xlink:href="020/01/212.jpg" pagenum="193"/>Lettera questa storia, prosegue: &ldquo; Pure il Rinaldini, che &egrave; capo <lb/>sodo, ma sodo bene, volle che si rifacesse ieri sera con la culatta <lb/>volta al Palazzo e la bocca all'ins&ugrave;, e senza alterazione nessuna <lb/>tutti i suoni arrivarono in tempi uguali. </s>

<s>Sicch&egrave; V. S. si puole im&shy;<lb/>maginare che il poveraccio cos&igrave; cammina per Firenze che pare un <lb/>gatto bagnato dall'acqua fredda &rdquo; (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XXV, c. </s>

<s>181). <lb/>Capo sodo si mostr&ograve; pure, quando, a profondare il vasetto del mer&shy;<lb/>curio sott'acqua, disse d'aver trovato che il mercurio stesso dentro <lb/>la canna non saliva pi&ugrave; su che un braccio e un quarto; capo sodo, <lb/>quando nel livello dell'argento vivo, a pi&egrave; e in cima del campanile <lb/>di Pisa, non gli riusc&igrave; di trovarci differenza. (Ivi, T. VIII, c. </s>

<s>69). </s></p><p type="main">

<s>Bench&egrave; il Viviani scrivesse che l'impressione delle Opere di <lb/>Galileo, fatta in Bologna, era stata promossa ed ultimata per mezzo <lb/>del Rinaldini (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLII, c. </s>

<s>3), sembra nonostante <lb/>che questi poco le avesse lette, o poco le ritenesse a memoria. </s>

<s>Co&shy;<lb/>me prova di ci&ograve; si potrebbe citare il fatto, che, avendo il Rinaldini <lb/>stesso eseguita a Livorno l'esperienza che nel medesimo tempo <lb/>giungono al piano dell'orizzonte e la palla cadente dalla bocca del <lb/>cannone e quella spinta per forza di polvere; domanda poi al Vi&shy;<lb/>viani dove Galileo tratti di questo (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XXIV. c. </s>

<s>43), <lb/>quasi che il secondo Dialogo de'due Massimi Sistemi non fosse <lb/>luogo abbastanza cospicuo. (Alb. </s>

<s>I, 172). Incerto in ogni cosa, per <lb/>la smania d'andare in cerca, non di verit&agrave; ma di novit&agrave;, pi&ugrave; che <lb/>galileiano, &egrave; aristotelico, e in ogni modo non ha saputo scoter dal <lb/>pallio filosofico la polvere appiccaticcia del Peripato. </s>

<s>A persuaderci <lb/>di ci&ograve;, basta leggere la Prefazione a quel ponderoso volume della <lb/><emph type="italics"/>Filosofia Razionale<emph.end type="italics"/> dove, dopo aver sottilmente discorso del me&shy;<lb/>todo sperimentale, e aver confessato che delle cose trattate ivi pa&shy;<lb/>recchie saranno quelle da lui attinte <emph type="italics"/>ex peripateticorum fonte,<emph.end type="italics"/> cos&igrave; <lb/>soggiunge: &ldquo; Dum interim intelligis aliquando me paululum ab <lb/>Aristotelico calle declinasse, et abiecta, quam superioribus annis <lb/>tuebar opinione, longe diversam suscepisse, non est cur de hoc tibi <lb/>admiratio incessat, neminem enim praeterit scite admodum ab an&shy;<lb/>tiquis veritatem Saturni, hoc est temporis, filiam habitam fuisse &rdquo; <lb/>(Patavii 1681, pag. </s>

<s>XII). Che fosse veramente a principio addetto <lb/>alla setta peripatetica, e che poi l'avesse talvolta abbandonata per <lb/>seguir piuttosto la retta ragione, lo dice da s&egrave; il Rinaldini, colle <lb/>seguenti parole, le quali per&ograve; non corrispondono ai fatti della sua <lb/>vita scientifica: &ldquo; Quamvis a teneris annis salebrosam philosophandi <lb/>viam calcaverim, ac animum Peripateticae doctrinae studiis mirum <pb xlink:href="020/01/213.jpg" pagenum="194"/>in modum imbuerim, me tamen nunquam veritatis amor deseruit, <lb/>quin potius illo factus ardentior, me coegit omnem auctoritatem <lb/>negligere solidasque rationes inquirere ut iis denique suffultus quod <lb/>magis rationi consentaneum est amplecti possem &rdquo; (ibi, pag. </s>

<s>314). </s></p><p type="main">

<s>Fra gli altri chiamati a partecipare ai consessi sperimentali me&shy;<lb/>dicei, s'ha memoria dei tre fratelli Del Buono: Paolo che fece le <lb/>prime esperienze sulle soluzioni dell'aria nell'acqua, e Candido e <lb/>Anton Maria, i quali immaginarono e costruirono una macchina da <lb/>maneggiar facilmente i canocchiali, di lunga distanza focale; mac&shy;<lb/>china che si distinse col nome proprio di <emph type="italics"/>Arcicanna.<emph.end type="italics"/> Carlo Roberto <lb/>Dati pure vi fu chiamato e ivi lesse un Discorso astronomico sul <lb/>sistema Saturnio in favor dell'Huyghens. </s>

<s>Un'altra strana e torbida <lb/>figura di uomo venuto di Reggio di Calabria, col nome di Antonio <lb/>Oliva, si vede pure trasparir di mezzo a questi gentiluomini eruditi <lb/>fiorentini. </s>

<s>Il Borelli, nel riferir di lui un'esperienza fatta, per de&shy;<lb/>terminare il peso specifico dell'aria, lo chiama <emph type="italics"/>ingeniossimus,<emph.end type="italics"/> e al&shy;<lb/>trove, uomo <emph type="italics"/>perspicacissimi et ignei ingenii<emph.end type="italics"/> (De mot. </s>

<s>nat. </s>

<s>pag. </s>

<s>470). <lb/>Se per&ograve; si debba giudicare dai frutti, queste lodi e altre pi&ugrave; ma&shy;<lb/>gnifiche, con le quali si messe a esaltarlo il Redi, si riconoscono <lb/>per non meritate. </s></p><p type="main">

<s>A valer per tutti insieme i cinque sopra commemorati, il <lb/>principe Leopoldo aveva rivolte le sue mire anche su Gian Do&shy;<lb/>menico Cassini, il quale intanto pensava ad alcune esperienze da <lb/>farsi nell'Accademia sopra la calamita. (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XXI, c. </s>

<s>64). <lb/>Ma poco dopo avvenne caso, che la Corte medicea dovesse adom&shy;<lb/>brare di esso, e fu quando, trovandosi col Viviani a trattar del <lb/>negozio delle Chiane, faceva del s&igrave; no, di che il Viviani stesso dole&shy;<lb/>vasi col principe Leopoldo, qualificando l'ingegnere di Papa Ales&shy;<lb/>sandro VII per uomo doppio. (Ivi, T. XVII, c. </s>

<s>236). Millantatore, a <lb/>proposito delle sue scoperte celesti, nelle quali troppo esagerata&shy;<lb/>mente vantava l'eccellenza dei canocchiali di Giuseppe Campani, <lb/>parve al Borelli (ivi, T. XVIII, c. </s>

<s>90), e una certa sua ruvidezza <lb/>nizzarda lo faceva accusar di malcreato alla cortigiana galanteria del <lb/>Magalotti. (Targioni, Aggrandim. </s>

<s>T. I. P. I. pag. </s>

<s>249). Per tutte queste <lb/>ragioni, il Principe dell'Accademia fiorentina par che se lo tenesse <lb/>un po'alla lontana, bench&egrave; dispensasse anco a lui favori, e si cu&shy;<lb/>rasse di far verificare in Astronomia tutte le grandi scoperte, che <lb/>di Roma veniva annunziando e di Parigi. </s>

<s>Duole nulladimeno a pen&shy;<lb/>sare che molte di quelle insigni scoperte cassiniane, come l'ombre <lb/>dei satelliti proiettate sul disco di Giove, e le quattro nuove lune <pb xlink:href="020/01/214.jpg" pagenum="195"/>saturnie, fossero messe in dubbio dai Nostri, e con poca dignit&agrave; di <lb/>conte e con minore acume di scienziato, lo deridesse il Magalotti <lb/>e gli negasse fede, perch&egrave; non gli pareva possibile che avesse ve&shy;<lb/>duto lui tanti mondi lontani, che non valeva a leggere un carattere <lb/>chiaro e ben formato, senza gli occhiali. (Targioni, ivi, pag. </s>

<s>395). </s></p><p type="main">

<s>Il Borelli e il Viviani avevano nulladimeno supplito nell'Acca&shy;<lb/>demia alla mancanza del Cassini, ma le belle invenzioni e le belle <lb/>scoperte fatte da ingegni tanto eccellenti rimanevano tuttavia rin&shy;<lb/>chiuse fra le dorate pareti del Palazzo Pitti. </s>

<s>Intanto, incominciava <lb/>a destarsi nell'animo dei Nostri qualche sentimento di gelosia e di <lb/>rivalit&agrave; coll'Accademia sperimentale instituita in Francia, e ci&ograve; ri&shy;<lb/>dest&ograve; qualche proposito di far noto ai nuovi Filosofi parigini quel <lb/>che prima di loro era stato sperimentato gi&agrave; in Firenze. </s>

<s>Intorno a <lb/>che, da Pisa il di primo Dicembre 1658 scriveva cos&igrave; il Borelli al <lb/>principe Leopoldo: &ldquo; Il sig. </s>

<s>M. A. </s>

<s>Ricci mi replica questa settimana <lb/>e con molte ragioni vive ed efficaci procura mostrare quanto pre&shy;<lb/>giudizio si faccia alla nostra Accademia ed all'Italia tutta con il <lb/>nostro tacere, e non scrivere a quei signori di Francia. </s>

<s>Vorrebbe <lb/>egli insomma che si palesassero le conclusioni da noi ritrovate e <lb/>dimostrate, tacendo per&ograve; ed occultando le ragioni e le dimostra&shy;<lb/>zioni. </s>

<s>In questa maniera, dice egli, potremo esser sicuri che non <lb/>ci possa esser tolto il primo luogo dell'invenzione preoccupata e <lb/>palesata da noi &rdquo; (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XVI, c. </s>

<s>130). </s></p><p type="main">

<s>Nel di primo di Febbraio del 1663, Carlo Dati avvisa il Principe <lb/>dell'Accademia che eran gi&agrave; pronte &ldquo; quattro casse di carta bonis&shy;<lb/>sima per la stampa del Libro delle Esperienze &rdquo; (ivi, T. XVII, c. </s>

<s>184) <lb/>la quale stampa, qualunque ne fosse la ragione, non ebbe effetto <lb/>che nel 1666. Il titolo di <emph type="italics"/>Saggi di Naturali esperienze<emph.end type="italics"/> dato al libro, <lb/>corrisponde benissimo alla realt&agrave; dei fatti, non essendovisi dato, dei <lb/>varii ordini di esperienze naturali, che la descrizione di qualcune <lb/>fra le molte, come per saggio. </s>

<s>Solo &egrave; da notare che nulla vi fu <lb/>saggiato di cose astronomiche, e ce ne avevan pure i nostri Acca&shy;<lb/>demici delle importanti. </s>

<s>L'intenzione del Principe era veramente <lb/>di non lasciarle addietro, e il Magalotti aveva gi&agrave;, fra le descrizioni <lb/>degli altri strumenti, distesa anche quella dei canocchiali e delle <lb/>macchine da maneggiarli servite nelle ossvrvazioni di Saturno (ivi, <lb/>T. VII, c. </s>

<s>23) con manifesto proposito di dar, anche di queste os&shy;<lb/>servazioni, un qualche saggio, fra gli altri del libro. </s>

<s>Ma la causa, <lb/>per cui un tal proposito del Principe e del Segretario non si man&shy;<lb/>dasse ad effetto, si viene a conoscere da una Lettera del Borelli, <pb xlink:href="020/01/215.jpg" pagenum="196"/>in cui scriveva da Pisa il di 20 Aprile 1665, le parole seguenti: <lb/>&ldquo; &Egrave; venuta la scrittura inviata dal sig. </s>

<s>Magalotti, nella quale veggo <lb/>registrato parte di quelle cose che io speculai e diedi in iscritto al&shy;<lb/>l'A. V. S. cinque anni sono intorno al sistema di Saturno del signor <lb/>Hugenio. </s>

<s>E bench&egrave; il pensiero del sig. </s>

<s>Magalotti sia di toglier <lb/>l'occasione, con la stampa, che altri non si vada usurpando le cose <lb/>da noi ritrovate, tuttavia, avendoci io in questo negozio il maggior <lb/>interesse, perch&egrave; io proposi, predissi e dimostrai l'effetto della <lb/>macchinetta, e poi recai molte scritture, in tutte le quali i signori <lb/>Accademici non ci ebbero altra parte che l'onore che mi fecero <lb/>di vederle ed approvarle per lor gentilezza; mi par di trovarmi in <lb/>obbligo di supplicar umilmente V. A. che si compiaccia di darmi <lb/>tempo per far la scelta, ed impinguare e stabilir bene le cose per <lb/>esser di maggiore importanza lo stampare che scrivere una lettera <lb/>privata &rdquo; (ivi, T. XVIII, c. </s>

<s>164). Il Borelli per&ograve; non prese mai il <lb/>tempo, e quelle astronomiche Scritture rimasero allora e rimangono <lb/>tuttavia in gran parte manoscritte. </s>

<s>Manoscritto pure, nonostante la <lb/>benemerita opera fattavi attorno dal Targioni, dal Gazzeri, e da <lb/>qualcun altro, rimase gran parte di quel ricco tesoro di esperienze, <lb/>da cui si tolsero i <emph type="italics"/>Saggi.<emph.end type="italics"/></s></p><p type="main">

<s>Bench&egrave; poi s'aggiunga al titolo di Naturali Esperienze, che <lb/>furon fatte <emph type="italics"/>nell'Accademia del Cimento sotto l&agrave; protezione del prin&shy;<lb/>cipe Leopoldo di Toscana,<emph.end type="italics"/> nonostante vi si accolgono anche descri&shy;<lb/>zioni di esperienze e di strumenti, che appartengono al primo e al <lb/>secondo periodo dell'Accademia Medicea. </s>

<s>Cos&igrave;, l'esperienza dell'in&shy;<lb/>compressibilit&agrave; dell'acqua dimostrata per mezzo della sfera ammac&shy;<lb/>cata, il Borelli ci dice essere stata fatta <emph type="italics"/>in Aula Serenissimi M. D. He&shy;<lb/>truriae. </s>

<s>Is iussit (ut mihi relatum fuit) cavam pilam argenteam <lb/>aqua repleri, ecc.<emph.end type="italics"/> (De moti. </s>

<s>natur. </s>

<s>ed. </s>

<s>cit. </s>

<s>pag. </s>

<s>333). Il Termo&shy;<lb/>metro a liquido e l'Igrometro a condensazione appartengono, come <lb/>si vide, al primo periodo, e al secondo appartengono l'esperienze <lb/>per la misura della velocit&agrave; della luce e dei suoni. </s></p><p type="main">

<s>Da ci&ograve; si conclude che il Libro, pubblicato nel 1666, contiene <lb/>i <emph type="italics"/>Saggi<emph.end type="italics"/> di tutta la sperimentale Accademia Medicea, che ebbe nel <lb/>Torricelli, infino dal 1642, i suoi primi principii. </s>

<s>Essendo cos&igrave;, pu&ograve; <lb/>a ragione vantar l'Italia il primato nella Scienza sperimentale sopra <lb/>tutte le altre Nazioni, avendo ella gi&agrave; maturati da qualche tempo i <lb/>suoi frutti, quando gl'ingegni del Pascal e del Roberval, dell'Auzout, <lb/>del Pacquet, del Boyle e di simili altri celebri stranieri non erano <lb/>ancora appena aperti nel fiore. </s></p><pb xlink:href="020/01/216.jpg" pagenum="197"/><p type="main">

<s>Il disteso di quel Libro, che &egrave; pure il pi&ugrave; insigne monumento <lb/>che sia stato eretto alla Scienza sperimentale italiana, fu fatto da <lb/>Lorenzo Magalotti succeduto ad Alessandro Segni nell'ufficio di Se&shy;<lb/>gretario dell'Accademia. </s>

<s>I meriti del Magalotti, come scienziato, non <lb/>sono per verit&agrave; di gran rilievo. </s>

<s>Pi&ugrave; inclinato forse allo speculare che <lb/>allo sperimentare, non sappiam di lui se non ch'ei lesse, ne'con&shy;<lb/>sessi accademici, un Discorso, in cui si proponeva di rassomigliar <lb/>l'anello di Saturno agli aloni e alle corone. </s>

<s>Come letterato per&ograve; <lb/>&egrave; tenuto in pregio da tutti, e s'ammira l'eleganza, la propriet&agrave; <lb/>del dire, e l'efficace evidenza delle sue descrizioni. </s></p><p type="main">

<s>I distesi del Magalotti, via via che erano all'ordine per la stampa, <lb/>si mandavano a rivedere al Borelli, che vi faceva sopra assai av&shy;<lb/>vertimenti, di molti de'quali si tenne conto; al Viviani, pi&ugrave; arren&shy;<lb/>devole in lasciar andar le cose a modo altrui, al Rinaldini, che, <lb/>seguitando a fare il capo sodo, aggiungeva a i cimenti dei fatti <lb/>naturali, il cimento della pazienza del Principe e del Segretario. </s>

<s><lb/>Poi si mandava tutto a Roma, e si sottostava, come a tribunale <lb/>inappellabile, a ci&ograve; che ne decidesse il giudizio di M. A. Ricci, <lb/>eletto, infin da principio, da Leopoldo dei Medici a consultore della <lb/>sua sperimentale Accademia. </s></p><p type="main">

<s>Il Ricci era geometra di gran valore e uomo di gran senno e <lb/>prudenza. </s>

<s>A lui il Torricelli indirizzava quelle lettere, che valgono <lb/>per un intiero Trattato, in cui si descrive la celebre esperienza <lb/>dell'argento vivo, e si risponde alle difficolt&agrave; promosse contro alla <lb/>natura del vacuo, e agli effetti della pressione ammosferica. </s>

<s>A ri&shy;<lb/>chiesta di lui chiamato <emph type="italics"/>ingeniosissimus iuvenis,<emph.end type="italics"/> il Torricelli stesso <lb/>risolse il problema della Clessidra, o del vaso che versa uguali quan&shy;<lb/>tit&agrave; d'acqua in tempi uguali, dimostrando che la forma propria di <lb/>un tal vaso, &egrave; il conoide generato dalla rotazione di una semipa&shy;<lb/>rabola biquadratica; problema che il Mariotte, il Grandi e lo stesso <lb/>Viviani credettero che l'Autor del Trattato <emph type="italics"/>De motu aquarum<emph.end type="italics"/> si <lb/>contentasse di proporlo agl'Idrometri, ma che poi l'avesse, per la <lb/>difficolt&agrave;, lasciato irresoluto. </s></p><p type="main">

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

<s>La pubblicazione del Libro dei Saggi di Naturali Esperienze, <lb/>parve quasi un raccoglier le vele, e un ridursi in porto a riposo, <lb/>dopo una lunga navigazione. </s>

<s>Eppure il viaggio dura ancora e non <pb xlink:href="020/01/217.jpg" pagenum="198"/>breve, bench&egrave; avesse cambiato abito il piloto, fossero ai primi sot&shy;<lb/>tentrati altri nuovi e men validi remigatori, a nuova foggia si fosse <lb/>ricomposta la nave, e si dirigesse ad altro segno di stella. </s></p><p type="main">

<s>Il di 4 di Aprile 1667 il Borelli scriveva da Pisa una lettera <lb/>al principe Leopoldo, in cui gli diceva che andava <emph type="italics"/>disponendo le <lb/>cose per la partenza che non potr&agrave; esser prima di mezzo maggio,<emph.end type="italics"/><lb/>e intanto gli offeriva in dono e gli lasciava come ricordo di un <lb/>amico, che si allontana dall'amico, le <emph type="italics"/>macchine astronomiche<emph.end type="italics"/> da s&egrave; <lb/>erette e costruite nella specula di S. Miniato. (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XIX, <lb/>c. </s>

<s>180). Il Borelli abbandonava cos&igrave; l'ospitale Toscana per tornar&shy;<lb/>sene &igrave;n Sicilia. </s>

<s>Il d&igrave; 10 Febbraio 1668 Leopoldo de'Medici, nella <lb/>persona del quale s'era gi&agrave; al civile sopraggiunto il principato eccle&shy;<lb/>siastico, annunziava con accorata mestizia all'Huyghens che s'erano <lb/>partiti dal suo servizio tre dei migliori soggetti, che fossero nel&shy;<lb/>l'Accademia (Targioni, Aggrandim. </s>

<s>T. I, pag. </s>

<s>462) ed eran questi, <lb/>oltre al Borelli, il Rinaldini, e l'Oliva. </s>

<s>Tutto in sollecitudine per&shy;<lb/>ch&egrave;, da cos&igrave; fatta dispersione, non ne dovesse alla sua prediletta <lb/>Accademia conseguitare la morte, si rallegrava il Principe e Car&shy;<lb/>dinale col Magalotti, per avere intanto, a sostituire a uno dei tre <lb/>mancati, chiamato Niccol&ograve; Stenone, danese di patria, ma divenuto <lb/>italiano per elezione. </s>

<s>Il Magalotti rispondeva cos&igrave; alla lieta novella: <lb/>&ldquo; Veramente nella dispersione presente della nostra Accademia, per <lb/>la partenza del Borelli, dell'Oliva e del Rinaldini, non poteva a mio <lb/>credere, succedere cosa pi&ugrave; desiderabile, e se gli altri due luoghi si <lb/>riempissero a questa proporzione, mi parrebbe che avessimo qual&shy;<lb/>che motivo da consolarci della perdita fatta, la quale tutta insieme <lb/>bisogna confessare che &egrave; considerabile, perch&egrave; solamente dando al <lb/>Rinaldini e all'Oliva quel che v&agrave; loro per giustizia di approvazione <lb/>e di stima, il Borelli era un uomo fastidioso, e presso che io non <lb/>dissi affatto intollerabile, ma in sostanza era un letterato da far ri&shy;<lb/>splendere una corte, perch&egrave; aveva sodezza e giudizio. (Ivi, pag. </s>

<s>463). </s></p><p type="main">

<s>Un altro di que'posti lasciato vuoto nell'Accademia, fu sosti&shy;<lb/>tuito e, forse meglio che dallo Stenone, da Francesco Redi, il quale, <lb/>sebben fosse nel periodo precedente fra gli Accademici come ini&shy;<lb/>ziato, e avesse parte nelle esperienze sulla digestione degli animali, <lb/>su cui poi ritorn&ograve; nella Lettera al Kircher (Opera, T. II. </s>

<s>Napoli 1731, <lb/>pag. </s>

<s>49, 50), si vede nonostante esercitare con larga autorit&agrave; il suo <lb/>ministero in questo, che &egrave; il quarto periodo della sperimentale Ac&shy;<lb/>cademia Medicea, e, che va a terminare colla morte del Cardinale <lb/>Leopoldo. </s></p><pb xlink:href="020/01/218.jpg" pagenum="199"/><p type="main">

<s>Il Viviani distratto, per le continue richieste del Principe e dei <lb/>privati, a sopraintendere ai tanti e spinosi negozii d'ingegneria <lb/>idraulica, il Magalotti che aveva oramai preso diletto de'lontani <lb/>viaggi, lasciavano a collaborar nell'Accademia lo Stenone e il Redi, <lb/>i quali proseguendo l'indirizzo dei loro studii, le fecero in parte <lb/>cangiare istituto, trapassando, dalle scienze fisiche, a coltivar con <lb/>pi&ugrave; genio la Storia naturale. </s></p><p type="main">

<s>Lo Stenone fu anatomico espertissimo, e fece fare notabili pro&shy;<lb/>gressi alla Miologia. </s>

<s>La Dissertazione <emph type="italics"/>De solido intra solidum na&shy;<lb/>turaliter contento,<emph.end type="italics"/> nella stampa della quale tanta amorosa cura si <lb/>prese il Viviani, &egrave; forse dalla fama esaltata sopra i meriti proprii, <lb/>bench&egrave; non si possa negar che non sia un precorrere alla scienza <lb/>dei nostri giorni l'insegnar, che ivi si fa dall'Autore, a riconoscer <lb/>l'et&agrave; della formazione di uno strato terrestre, congetturandola dalla <lb/>natura delle sostanze fossili trascinate e deposte dalle acque. (Flo&shy;<lb/>rentiae 1669, pag. </s>

<s>28). N&egrave; si pu&ograve; passar senza lode d'ingegno l'at&shy;<lb/>tribuir gli effetti del trasformarsi l'arida in mare e il mare in arida, <lb/>al non coincidere il centro di gravit&agrave; della terra col centro di figura. <lb/>(Ivi, pag. </s>

<s>172). Nel Tomo XXXII del Cimento son raccolti i mano&shy;<lb/>scritti dello Stenone in folio, di carattere minutissimo, informi, di&shy;<lb/>sordinati. </s>

<s>A ricercarvi, in tanta variet&agrave;, quel che &egrave; pi&ugrave; confacente al <lb/>proposito nostro, nel breve esame che ne abbiam fatto, si nota par&shy;<lb/>ticolarmente l'anatomia dei muscoli locomotori dell'occhio, e alcune <lb/>osservazioni intorno alla funzione fisiologica dell'organo della vista. </s></p><p type="main">

<s>Il Redi era tutt'altro ingegno, e se non sodo come quel dello <lb/>Stenone, pi&ugrave; elegante e pi&ugrave; vario. </s>

<s>Il Cardinale Leopoldo annunziava <lb/>con gran compiacenza al Borelli un nuovo libro scritto dallo stesso <lb/>Redi sopra gl'insetti, e il Borelli rispondeva di Messina, nell'Agosto <lb/>1668, che vedr&agrave; quel nuovo libro assai volentieri. (MSS. Gal. </s>

<s>Cim. </s>

<s><lb/>T. XIX, c. </s>

<s>202). N&egrave; il Serenissimo Cardinale di tale annunzio si <lb/>compiaceva senza ragione, perch&egrave; sentiva l'efficacia che avrebbero <lb/>avuto quelle pagine, in isgombrar largamente i sentieri ai progressi <lb/>della Zoologia, e anzi di tutta la Storia Naturale. </s>

<s>Il nuovo Autore <lb/>infatti dell'Esperienze intorno alla generazione degl'insetti, dimo&shy;<lb/>strava con sensati argomenti, ci&ograve; che non era riuscito al grandissimo <lb/>Harvey, esser la generazione spontanea un gravissimo e dannosis&shy;<lb/>simo errore, e che anco gli animali de'pi&ugrave; infimi ordini non hanno <lb/>origine dalla putredine, ma vi son deposti allo stato di uovo dalle <lb/>sollecite madri pregnanti. </s></p><p type="main">

<s>In un grave ostacolo per&ograve; offese il libero piede del nostro Redi, <pb xlink:href="020/01/219.jpg" pagenum="200"/>e fu quando s'incontr&ograve; a decider dell'origine dei vermi, nella carne <lb/>de'frutti maturi, e dentro alle galle cresciute sui rami o sulle foglie <lb/>di alcuni alberi. </s>

<s>Parve a lui non &ldquo; esser gran peccato in Filosofia <lb/>il credere che i vermi de'frutti sieno generati da quella stessa <lb/>anima, e da quella stessa natural virtude, che fa nascere i frutti <lb/>stessi nelle piante &rdquo; (Opera, ivi. </s>

<s>T. I, pag. </s>

<s>103). Ma pure, bench&egrave; <lb/>cos&igrave; si andasse lusingando il celebre Autore, era quello di dar ani&shy;<lb/>ma e senso alle piante, tal peccato in Filosofia, da viziare il merito <lb/>delle altre sue insigni scoperte. </s></p><p type="main">

<s>Due anni dopo, lo stesso Eminentissimo Principe dell'Accade&shy;<lb/>mia fiorentina, dava, pure a proposito del Redi, un'altra nuova al <lb/>Borelli, ed era intorno all'esperienze fatte sulle gocciole bataviche <lb/>o sopra quelle perline di vetro, a rompere le codette alle quali, si <lb/>sgretolano tutte riducendosi in polvere. </s>

<s>Il Borelli, rispondendo da <lb/>Francavilla, ricorda come quindici anni prima il Card. </s>

<s>Giovan Carlo <lb/>avea mandato al Granduca una cassettina di quelle stesse perle, <lb/>sugli effetti curiosi delle quali speculando allora, si compiace che <lb/>si fosse riscontrato nei pensieri medesimi del Redi. (Fabbroni, Let&shy;<lb/>tere, T. I. pag. </s>

<s>139). </s></p><p type="main">

<s>Quel peccato filosofico, in che offese il Nostro, e di cui si par&shy;<lb/>lava dianzi a proposito della generazione di alcuni insetti, fu emen&shy;<lb/>dato da Marcello Malpighi, il quale dimostr&ograve; che anche i vermi <lb/>delle galle e dei frutti nascevano da un uovo deposto dalle madri. </s>

<s><lb/>Se gli onori si dispensassero sempre nel mondo a seconda dei me&shy;<lb/>riti, il Malpighi non dovrebb'esser, nei fasti della scienza, men <lb/>glorioso del celeberrimo Harvey. </s>

<s>Imperciocch&egrave;, se l'Inglese restaur&ograve; <lb/>la Fisiologia animale con la scoperta della circolazione del sangue, <lb/>il nostro Bolognese, con la scoperta del circolo della linfa, restaur&ograve; <lb/>la Fisiologia vegetabile. </s>

<s>L'anatomia microscopica degli organi e <lb/>della pi&ugrave; intima testura delle parti componenti le varie membra <lb/>delle piante e degli animali, &egrave; dovuta principalmente a lui. </s>

<s>Nella <lb/>mente di lui balen&ograve; il primo vero intorno alla teoria chimica della <lb/>respirazione, e fu egli il primo a dar la dimostrazione oculare del <lb/>moto del sangue nel circolo universale dei vasi. </s></p><p type="main">

<s>Al nome del Malpighi, non pu&ograve; andar disgiunto quello di Lo&shy;<lb/>renzo Bellini, con l'altro di Carlo Fracassati, i quali ambedue, con&shy;<lb/>corsero, ciascuno per la sua parte, a dar l'anatomia e la fisiologia <lb/>dell'organo del gusto. </s>

<s>Nessuno di questi tre insigni anatomici ap&shy;<lb/>partenne, &egrave; vero, all'Accademia Medicea; anzi il Malpighi, cosa <lb/>notabilissima in uomo di tanto merito, non solo fu tenuto lontano <pb xlink:href="020/01/220.jpg" pagenum="201"/>dal partecipar la sua scienza con Firenze, ma si direbbe che fu <lb/>tenuto lontano dall'Italia, dalla quale, n&ograve; nella persona ma nelle <lb/>opere dell'ingegno, par che esulasse in Inghilterra, dove, nella <lb/>R. </s>

<s>Societ&agrave; di Londra, le tante e mirabili scoperte di lui ebbero <lb/>liete accoglienze, e gli scritti, cos&igrave; vivente l'Autore che postumi, vi <lb/>trovarono le sollecite e amorevoli cure della pubblica stampa. </s>

<s>Non <lb/>appartengono propriamente, ripigliando qui il costrutto interrotto, <lb/>i tre grandi anatomici all'Accademia fiorentina, ma son tutt'e tre <lb/>discepoli del Borelli, e incominciarono i loro esercizi anatomici col <lb/>collaborare alla grande Opera dei Moti animali, che il loro Maestro <lb/>preparava gi&agrave; in Pisa e in Livorno, dove a spese e sotto la prote&shy;<lb/>zione dei principi Medicei si facevano le dissezioni. </s></p><p type="main">

<s>In ogni modo, quello stesso Borelli che, instituendo, in mezzo <lb/>alle scienze sperimentali, la nuova scuola iatromatematica, v'aveva <lb/>allevati il Malpighi, il Bellini e il Fracassati, i quali applicavan sa&shy;<lb/>pientemente le nuove scoperte d'Anatomia e di Fisiologia all'eser&shy;<lb/>cizio dell'arte medica; dalla lontana Sicilia tornava spesso col pen&shy;<lb/>siero in Toscana. </s>

<s>E ci&ograve; segu&igrave;, con pi&ugrave; vivo desiderio che mai, quando <lb/>il Cardinal Leopoldo gli annunziava di aver riscontrato nella sua <lb/>Accademia un'esperienza bellissima venuta d'Inghilterra. </s>

<s>&ldquo; Ralle&shy;<lb/>gromi sommamente, cos&igrave; incominciava lo stesso Borelli una sua <lb/>lettera del 2 Luglio 1669, scritta da Messina, dell'esperienza del <lb/>Boyle, che V. A. ha fatto confrontare la qual veramente &egrave; mirabile <lb/>e di gran conseguenza, ed ha risvegliato in me il desiderio di To&shy;<lb/>scana &rdquo; (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XIX, c. </s>

<s>263). E sotto il d&igrave; 14 Agosto <lb/>tornava a scrivere cos&igrave; sul medesimo argomento: &ldquo; Avevo io letto <lb/>nella Gazzetta letteraria di Roma l'esperienza del Boyle, e mi pa&shy;<lb/>reva veramente mirabile e per&ograve; desideravo sommamente di con&shy;<lb/>frontarla, sicch&egrave; pu&ograve; giudicare quanta consolazione io abbia avuto <lb/>sentendo che l'A. V. l'abbi sperimentata nella sua eruditissima Ac&shy;<lb/>cademia; e poi con tante belle circostanze di pi&ugrave; di quelle che <lb/>aveva osservate il Boyle &rdquo; (ivi, c. </s>

<s>267). </s></p><p type="main">

<s>La Lettera missiva del Serenissimo Cardinale, in data del 25 <lb/>Luglio 1669, e alla quale si riferisce la sopra citata responsiva del <lb/>Borelli, diceva cos&igrave; a proposito dell'esperienza del Boyle, riscon&shy;<lb/>trata, variata e ampliata nell'Accedemia del Cimento: &ldquo; In oltre le <lb/>diedi conto di un'esperienza fatta in Inghilterra, e rifatta qui da <lb/>me, la qual &egrave; che, mettendosi un pezzetto di pesce o interiora di <lb/>quelle che son vicine a infradiciarsi, fanno lume da s&egrave; stesse, dato <lb/>il solito strumento del vacuo, e facendosi la consueta operazione <pb xlink:href="020/01/221.jpg" pagenum="202"/>di quello, che comunemente si dice il vacuo, il lume del pesce si <lb/>perde, e facendo appresso un piccolo foro per introdurvi l'aria, <lb/>all'ingresso di quella di nuovo ritorna a risplendere il pezzetto di <lb/>pesce. </s>

<s>Ed io ho gi&agrave; fatto l'esperienza con un pezzetto di polpa e <lb/>grasso di pesce spada. </s>

<s>Mi venne poi in mente di fare l'esperienza <lb/>stessa con le lucciole, le quali ancora nel vuoto persero il lume. <lb/></s>

<s>&Egrave; ben vero che nell'istante dell'introduzione dell'aria s'illumin&ograve; <lb/>per brevissimo tempo tutto il vaso, ed io dubitando che questo <lb/>splendore potessi procedere che nel ricever le lucciole la consola&shy;<lb/>zione del ritorno dell'aria facessero moto, nel quale scoprissero la <lb/>parte lummosa, rifeci l'esperienza, mettendo dentro nel vaso tutte <lb/>le lucciole morte, e nondimeno successe l'istessa istantanea illu&shy;<lb/>minazione del vaso, nell'atto dell'introdurvi l'aria per il solito pic&shy;<lb/>colo foro formato da uno spillo. </s>

<s>Or &egrave; da sapersi di pi&ugrave; che, dopo <lb/>questa illuminazione, il lume che hanno le lucciole &egrave; rimasto, <lb/>(sempre che si &egrave; fatta l'esperienza) meno vivace, ma con tale dif&shy;<lb/>ferenza che non si &egrave; potuto mettere in dubbio che non sia cos&igrave;. </s>

<s><lb/>Questa &egrave; un'esperienza facile e galante, ma tale che io credo che <lb/>meriti che vi si faccia riflessione &rdquo; (ivi, T. XXIII, c. </s>

<s>171, e Fabbroni, <lb/>Lett. </s>

<s>I, pag. </s>

<s>144). </s></p><p type="main">

<s>Nel principio di questa lettera, passata fra Leopoldo de'Medici <lb/>e Gian Alfonso Borelli, s'accennava altresi a un altro soggetto di <lb/>scienza alquanto diversa. </s>

<s>Il Cardinale scriveva di sentir <emph type="italics"/>desiderio <lb/>d'aver qualche particolare informazione delli accidenti del fuoco <lb/>di Catania,<emph.end type="italics"/> e il Borelli rispondeva d'aver gi&agrave; scritto prolissamente <lb/>intorno a quegli accidenti e d'avervi di pi&ugrave; accompagnata una <lb/>pianta e disegno grande della Montagna e citt&agrave; di Catania, disegno <lb/>e scrittura che andarono forse smarriti e a cui suppl&igrave; l'anno dopo <lb/>l'Autore pubblicando l'<emph type="italics"/>Historia et Meteorologia Incendii Actnaei.<emph.end type="italics"/><lb/>Nella Prefazione al libro si leggono le notabilissime parole seguenti: <lb/>&ldquo; At non potui petitionibus plurimorum insignium virorum non <lb/>obtemperare, et praecipue Serenissimi ac Reverendissimi Cardinalis <lb/>Medicei, qui, cum proximum Incendium Aetnae undique fama cir&shy;<lb/>cumferret, primis suis humanissimis literis iussit ut scientiam Na&shy;<lb/>turalem promovere pro viribus satagerem, edendo Historiam et <lb/>Meteorologiam huius conflagrationis, iuxta praescriptum Societatis <lb/>seu Academiae Experimentalis Medicaee, cuius inter socios me re&shy;<lb/>censere olim dignatus fuerat. </s>

<s>&rdquo; </s></p><p type="main">

<s>Di qui si raccoglie che il Borelli, bench&egrave; assente dalla Toscana, <lb/>seguitava ad appartenere e a collaborare ancora, sotto gli ordini <pb xlink:href="020/01/222.jpg" pagenum="203"/>del Principe, nell'Accademia del Cimento. </s>

<s>Vi collaborava altresi, <lb/>quando riferiva allo stesso Principe le sue osservazioni ed esperienze <lb/>chimiche fatte nella grotta del lago di Agnano, qualificando l'ani&shy;<lb/>dride carbonica per un <emph type="italics"/>fluore simile in sembianza all'aria ma assai <lb/>pi&ugrave; denso.... che smorza i lumi e soffoca le persone<emph.end type="italics"/> (ivi, T. XIX, <lb/>c. </s>

<s>35); vi collaborava, quando, speculando sull'origine delle reliquie <lb/>fossili trovate da'suoi Colleghi Accademici in Toscana, e da s&egrave; stesso <lb/>in Sicilia, poneva, insieme con lo Stenone, i fondamenti scientifici <lb/>alla moderna Paleontologia. </s></p><p type="main">

<s>Anche il Viviani, tornando a quando a quando in Firenze con <lb/>gli stivaloni inzaccherati dal diguazzar lungo l'argine e per i greti <lb/>de'fiumi, o intorno alle gore de'mulini, attendeva a collaborar <lb/>qualche poco nell'Accademia. </s>

<s>Ne'suoi Manoscritti si legge, fra le <lb/>altre, autografa questa nota: &ldquo; D'ordine del Serenissimo Principe <lb/>Cardinale Leopoldo de'Medici, nel giardino del Serenissimo Gran&shy;<lb/>duca, la sera delli 17 Luglio 1674 in Firenze, con occhiale di braccia <lb/>tre e mezzo, con due lenti, l'obiettiva cio&egrave; e l'oculare, e con oriolo <lb/>col pendolo aggiustato a mezzogiorno, a ore otto e un quarto po&shy;<lb/>meridiane, fu principiata da me l'osservazione dell'ecclisse lunare &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc. </s>

<s>T. XXXIX, c. </s>

<s>46). </s></p><p type="main">

<s>In questo quarto periodo della Sperimentale Accadem&igrave;a toscana, <lb/>non si vede pi&ugrave; quella regolarit&agrave; di sessioni, e quegli ordini, con <lb/>che si regolava nel periodo precedente, ma ci&ograve;, come si notava negli <lb/>esempii ora citati del Borelli, da null'altro dipende che dall'esser <lb/>la maggior parte dei collaboratori dispersi, per cui, invece di trattar <lb/>de'soggetti sperimentali colla parola viva, al cospetto del Principe, <lb/>ne trattavano in iscritture, le quali avevano forma di Dissertazioni <lb/>o di lettere che via via s'indirizzavano a Firenze. </s>

<s>Due de'pi&ugrave; in&shy;<lb/>faticabili e valorosi, fra'cos&igrave; fatti collaboratori, furono Geminiano <lb/>Montanari e Donato Rossetti, diversi d'indole e d'ingegno, e perci&ograve; <lb/>contenziosi. </s>

<s>Le controversie fra questi due, o incominciarono o in&shy;<lb/>fierirono vie pi&ugrave;, a proposito delle esperienze sui capillari, intorno <lb/>a che il Borelli ebbe a risentirsi e a muover lagnanza per lettera <lb/>al Cardinal Leopoldo, contro lo stesso Montanari, tacciandolo di <lb/>discepolo ingrato e accusandolo di plagio, perch&egrave;, mentre costui <lb/>dimorava in Firenze, e conversava coi fratelli Del Buono, infor&shy;<lb/>mandolo di tuttoci&ograve; che si faceva ne'consessi dell'Accademia spe&shy;<lb/>rimentale, ebbe dagli stessi Del Buono la notizia dell'attrarsi, per <lb/>effetto di capillarit&agrave;, i galleggianti sull'acqua, e poi divulg&ograve; la cosa <lb/>come per sua. </s>

<s>Di ci&ograve; il Borelli infuriava e rivendicava a s&egrave; la sco-<pb xlink:href="020/01/223.jpg" pagenum="204"/>perta chiamando in testimonio lo stesso Granduca, e altri signori <lb/>della sua corte, alla presenza de'quali, infino dal 1655, aveva mo&shy;<lb/>strata la curiosit&agrave; di quella nuova esperienza. (MSS. Gal. </s>

<s>Cim. </s>

<s><lb/>T. XIX, c. </s>

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

<s>Comunque sia, il Montanari era ingegno pi&ugrave; maturo e pi&ugrave; as&shy;<lb/>sennato del Rossetti, e a giudicar dall'opere si direbbe che il primo <lb/>ritrae pi&ugrave; al vivo quella profondit&agrave; e quell'ampiezza di studi spe&shy;<lb/>rimentali, propria del Borelli, che egli, con lo stesso Rossetti, ebbe <lb/>a comune maestro. </s>

<s>Il micrometro e il canocchiale livellatore fanno <lb/>annoverare il Montanari fra gli inventori di strumenti pi&ugrave; utili e <lb/>pi&ugrave; necessarii ai progressi della scienza. </s>

<s>Le sue esperienze e i suoi <lb/>Discorsi intorno alle propriet&agrave; de'liquidi, e i suoi esami sopra la <lb/>direzione, le sue speculazioni sopra le cause e gli effetti delle cor&shy;<lb/>renti marine, lo sollevano al grado di primo e principale maestro <lb/>nella scienza del moto dell'acque. </s></p><p type="main">

<s>Per ci&ograve; che direttamente riguarda l'Accademia del Cimento <lb/>poi, riferisce al Principe e Cardinale l'esperienza della trasfusione <lb/>del sangue, pi&ugrave; particolarmente descritta in una Relazione, che <lb/>pass&ograve; per le mani del Cassini, prima di arrivare a Firenze; discute <lb/>la controversia ch'egli ha col Rossetti intorno alle dottrine di Ar&shy;<lb/>chimede e di Galileo sui galleggianti, e intorno agli effetti mec&shy;<lb/>canici della bilancia di braccia uguali; racconta la storia degli <lb/>effetti, e specula sulla natura delle folgori, dissipando vecchi pre&shy;<lb/>giudizi e presentendo le teorie elettriche dei moderni; riferisce <lb/>osservazioni di ecclissi di sole e di luna, di apparizioni di comete <lb/>e di molti altri fenomeni celesti. </s></p><p type="main">

<s>Il Rossetti, dall'altra parte, mandava all'Accademia fiorentina <lb/>una scrittura contenente XIX osservazioni fatte sulla brinata in <lb/>Torino nel mese di Gennaio 1675 (ivi, T. XX, c. </s>

<s>192-95), dava parte <lb/>di un nuovo pesce apparito nei nostri mari (ivi, c. </s>

<s>230) e riferiva <lb/>altre simili curiosit&agrave; scoperte in fatto di storia Naturale. </s>

<s>Rendendo <lb/>conto degli altri suoi studi, diceva di esser per metter mano alla <lb/>sua Architettura militare, trattata in Dialogo &ldquo; nella quale (son sue <lb/>parole) dove si discorrer&agrave; di fortificarsi vicino ai fiumi, piglier&ograve; <lb/>l'occasione di pubblicare il mio nuovo modo di frenare i fiumi, <lb/>acci&ograve; non si avanzino dove noi non vogliamo, e quivi, mentre non <lb/>abbia sentore che possa esser discaro cost&agrave; in Toscana, dimostrer&ograve; <lb/>le falsit&agrave; di alcuni principii del Michelini. </s>

<s>E dove si discorrer&agrave; di <lb/>fortificare accanto al mare, insegner&ograve; il modo di murare sott'acqua &rdquo; <lb/>(ivi, T. XX, c. </s>

<s>166). </s></p><pb xlink:href="020/01/224.jpg" pagenum="205"/><p type="main">

<s>Da tutte queste cose ora discorse &egrave; facile persuadersi che l'Ac&shy;<lb/>cademia del Cimento, in questo secondo periodo, s'allarg&ograve; ad ab&shy;<lb/>bracciare ogni sorta di scienza sperimentale, mentre nel periodo <lb/>precedente parve quasi ristringersi nel campo della Fisica. </s>

<s>Si di&shy;<lb/>rebbe che Leopoldo dei Medici volle onorar la Religione, nella <lb/>porpora cardinalizia, col coltivar pi&ugrave; largamente e col promuover <lb/>con pi&ugrave; ardore che mai la scienza, e non la sola scienza specula&shy;<lb/>tiva, ma le utili applicazioni altres&igrave; che si posson fare di lei al de&shy;<lb/>coro e alle comodit&agrave; della vita. </s>

<s>Basterebbe, oltre alle cose dette, <lb/>per conferma di ci&ograve;, commemorare, non direm l'accoglienza, ma gli <lb/>eccitamenti che dal Cardinale Leopoldo ebbero i due fratelli Cam&shy;<lb/>pani, quando, per utilit&agrave; della navigazione, proponevano una nuova <lb/>e, secondo loro, inalterabile costruzion di orologi. </s></p><p type="main">

<s>La sera del d&igrave; 10 di November dell'anno 1675, colla morte del <lb/>Cardinale Leopoldo de'Medici, le porte dell'Accademia del Cimento <lb/>furon chiuse per sempre. </s></p><p type="main">

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

<s>Le virt&ugrave; che risplendono dall'alto raro &egrave; che non accendan <lb/>gli animi di chi da pi&ugrave; basso luogo le guarda, a imitarne gli esempi. </s>

<s><lb/>Molti furono i signori privati in Italia che, ad imitazione di ci&ograve; che <lb/>facevasi in Firenze nella corte de'Medici, incominciarono a intrat&shy;<lb/>tener nei loro palazzi una scelta conversazione d'uomini dotti, a <lb/>speculare e a sperimentare di cose naturali. </s>

<s>Di queste private Ac&shy;<lb/>cademie si pu&ograve; commemorar fra le prime quella convocata nel 1674 <lb/>in Roma dal Cardinal Flavio Chigi, dove secondo il Porzio (Opera <lb/>omnia, T. II. Neap. </s>

<s>1736, pag. </s>

<s>280) si ripeterono tutte l'esperienze <lb/>fatte nel vuoto dall'Accademia fiorentina. </s>

<s>In secondo luogo poi non <lb/>si pu&ograve; tacer di quell'altra istituita in Bologna nella casa dell'abate <lb/>Sampieri, dove il Montanari fece quelle sue cos&igrave; importanti espe&shy;<lb/>rienze sulla viscosit&agrave; dei liquidi, e dove pure ei lesser que'suoi Di&shy;<lb/>scorsi sull'Idrostatica, da'quali poi largamente attinse il Guglielmini. </s></p><p type="main">

<s>Ma sopra queste due, come sopra parecchie altre, primeggia <lb/>l'Accademia napoletana convocata da don Andrea Conclubet, mar&shy;<lb/>chese d'Arena. </s>

<s>Il Borelli, nel dedicare a lui il suo libro <emph type="italics"/>De motio&shy;<lb/>nibus naturalibus.<emph.end type="italics"/> &ldquo; Tu ipse es, gli scriveva, qui in praeclara Urbe <pb xlink:href="020/01/225.jpg" pagenum="206"/>Partenopaea, mea parente, societatem seu Academiam in tuo Museo <lb/>erexisti, in qua certis et indubitatis experimentis, non vero inanibus <lb/>ac rixosis disputatiunculis, philosophicas veritates ad Reipublicae <lb/>litterariae bonum indagarentur, idque summa cura, ac munificentia <lb/>praestitisti, in unum collectis clarissimis doctissimisque viris, Cara&shy;<lb/>muele, Thoma Cornelio, Francisco De Andrea, Leonardo Capua, <lb/>Luca Antonio Portio, innumerisque aliis. </s>

<s>&rdquo; Fra questi soggiunge <lb/>tosto il Borelli d'essere stato annoverato anch'egli, ond'&egrave; che, per <lb/>non presentarsi in casa il Marchese a mani vuote, gli offerisce quel <lb/>suo nuovo Libro &ldquo; in quo rationes Philosophiae quam plurimum <lb/>experimentorum naturalium afferentur, quae Florentiae in Academia <lb/>experimentali Medicaea vidi, pariterque accuratissime sunt observata <lb/>in tua Neapolitana. </s>

<s>&rdquo; </s></p><p type="main">

<s>L'avere il Borelli dedicato all'Istitutore un Libro, che contiene <lb/>la Filosofia de'fatti semplicemente narrati o storicamente descritti <lb/>ne'<emph type="italics"/>Saggi,<emph.end type="italics"/> &egrave; grande onore e attestato de'meriti dell'Accademia napo&shy;<lb/>letana, assai pi&ugrave; valido di quel che non sia il citare i nomi dei primi <lb/>fra coloro che vi appartennero. </s>

<s>Leonardo da Capua ebbe princi&shy;<lb/>palmente fama da alcune <emph type="italics"/>Lezioni<emph.end type="italics"/> che, in affettata lingua del trecento <lb/>e in stil boccaccevole, pubblic&ograve; nel 1683 intorno alla natura delle <lb/>mofete. </s>

<s>Quel che egli ivi discorre delle esalazioni gazose del lago <lb/>di Agnano, della Grotta del Cane, e di simili, &egrave; una vera mofeta <lb/>di parole, e tutt'altro che apporsi al vero intorno all'essenza del&shy;<lb/>l'anidride carbonica, riman di molto inferiore al Borelli in quali&shy;<lb/>ficarne la chimica natura. </s>

<s>Quel che egli poi, nella II Lezione, vi <lb/>discorre del circolo sanguigno nell'animal che respira o nel feto, <lb/>non ha nulla che non sia stato prima insegnato dall'Harvey, dal <lb/>Boyle, nei Proginnasmi, dal Carnelio, e, nell'epistole sparse, dal <lb/>Malpighi. </s></p><p type="main">

<s>Luc'Antonio Porzio, che non sembra abbia da vantare altra <lb/>invenzione da quella in fuori delle fontane intermittenti applicate <lb/>a svelare il celebre mistero dei fonti plimani, e rivendicate da lui <lb/>sullo Chales, con tanto ardore; fu il pi&ugrave; zelante e ardito banditore <lb/>della filosofia cartesiana in Italia. </s>

<s>Nel Trattatello <emph type="italics"/>De motu corporum<emph.end type="italics"/><lb/>raffina la sofistica del Cartesio contro i principii meccanici comu&shy;<lb/>nemente approvati, e si compiace d'aver colto in fallo Galileo e i <lb/>seguaci di lui, i quali riguardaron le sfere gravi discendenti lungo <lb/>un piano inclinato, come non aventi alcuna sensibile proporzione <lb/>con la grandezza della sfera terrestre. </s>

<s>Cos&igrave; pure, ne'Discorsi IV e V, <lb/>in argomento d'acque correnti e della loro misura, applica la me-<pb xlink:href="020/01/226.jpg" pagenum="207"/>desima sofistica cartesiana a cogliere in fallo il Castelli, assottigliando <lb/>l'ingegno a dimostrare a quali false conseguenze condurrebbe in <lb/>qualche caso l'ammettere che le velocit&agrave; sieno in ragion reciproca <lb/>delle sezioni. </s>

<s>Lo stesso sofistico genio port&ograve; il Porzio in trattar <lb/>l'interminabile questione del vacuo; sofistico genio diciamo, perch&egrave; <lb/>il Cartesio inopportunamente introdusse la teoria antivacuista degli <lb/>spiriti eterei penetranti il vetro, insensibili, come gli stessi effluvii <lb/>magnetici. </s>

<s>Una tale inopportunit&agrave; poi si riconosce dal veder che <lb/>n&egrave; il Torricelli, n&egrave; nessun altro de'seguaci di lui, pretesero mai <lb/>altro, come sufficiente allo scopo loro, se non che lo spazio lascia&shy;<lb/>tosi dietro dall'argento vivo fosse vuoto di aria, non curandosi, del <lb/>resto, se in luogo di lei vi sottentrasse o vi rimanesse persistente, <lb/>e non avvertito da alcuno de'nostri sensi, quell'etere, che, col <lb/>Cartesio, il Porzio chiama <emph type="italics"/>primo elemento.<emph.end type="italics"/> Il principio della cir&shy;<lb/>cumpulsione invocato da Galileo contro la leggerezza positiva, e <lb/>confermato con varii e cos&igrave; concludenti esperienze nell'Accademia <lb/>fiorentina, vuole il Porzio che sia merce cartesiana. </s>

<s>&ldquo; Sempre, egli <lb/>dice, ne'moti dei corpi viene ad essere necessaria la circumpulsione, <lb/>che Tommaso Cornelio chiam&ograve; platonica, ed &egrave; la stessa che Renato <lb/>Des Cartes, prima di Tommaso Cornelio, riconobbe darsi in tutti <lb/>i moti de'corpi &rdquo; (Op. </s>

<s>cit. </s>

<s>pag. </s>

<s>200). </s></p><p type="main">

<s>Ma Tommaso Cornelio di Cosenza &egrave; pure il miglior soggetto <lb/>fra gli Accademici napoletani annoverati di sopra dal Borelli, bench&egrave; <lb/>il sentirlo, nel Proemio ai Proginnasmi, esaltare il Telesio e il Bruno, <lb/>il Campanella e lo Stelliola, il Digby e l'Hobbes al grado di gran <lb/>filosofi a pari del Gilberto e di Galileo, possa farlo odorar di poco <lb/>fino giudizio. </s>

<s>Nonostante l'avere avuto in Roma a Maestro, e di&shy;<lb/>rettor de'suoi studii Michelangiolo Ricci, confer&igrave; a infondergli quel <lb/>sano gusto nelle scienze sperimentali, di che dette poi splendidi <lb/>saggi il Cornelio, specialmente nella Fisiologia e nell'Anatomia. </s>

<s>A <lb/>lui, come altrove si disse, &egrave; dovuta, a dimostrar la direzion del <lb/>moto del sangue nelle arterie, l'esecuzione della esperienza gale&shy;<lb/>nica, che l'Harvey reputava impossibile; a lui l'anatomia delle <lb/>tuniche, che compaginano gli intestini; a lui la prima caccia contro <lb/>l'error del calore nativo, con attribuirne l'origine al moto del sangue. </s>

<s><lb/>Della circumpulsione platonica, di che facevasi cenno dal Porzio <lb/>nelle parole citate di sopra, ne tratta il Cornelio in una sua Lettera <lb/>pubblicata fin dal 1648, sotto il pseudonimo di Timeo Locrese, e <lb/>inserita poi in calce ai Proginnasmi. </s>

<s>In cotesta Lettera, che merit&ograve; <lb/>la traduzione italiana del Viviani, rimasta incompiuta fra'Mano-<pb xlink:href="020/01/227.jpg" pagenum="208"/>scritti di lui, si confermano le teorie torricelliane con argomenti <lb/>nuovi, e con nuove esperienze. </s>

<s>&Egrave; notabile questa scrittura del Fi&shy;<lb/>losofo e Medico Consentino, perch&egrave; la prima che, sopra cos&igrave; famoso <lb/>e importante soggetto, si vedesse in Italia, ci&ograve; che segu&igrave; in quel&shy;<lb/>l'anno stesso, in cui il N&ouml;el pubblicava le otto celebri esperienze <lb/>fatte gi&agrave; dal Pascal a Roano e a Parigi. </s></p><p type="main">

<s>La Filosofia cartesiana infaustamente fu introdotta dal Porzio <lb/>in Italia, e ci&ograve;, non perch&egrave; non fosse desiderabile tor di mezzo le <lb/>rivalit&agrave; e le inimicizie fra nostrali e stranieri, ma perch&egrave; quel cer&shy;<lb/>vello un po'leggiero del Fisico napoletano non parve vagheggiar <lb/>del Cartesio altro che i capogiroli e i sofismi. </s>

<s>Dall'altra parte <lb/>quelle rivalit&agrave; erano antiche, incominciate gi&agrave; fra il Cartesio stesso <lb/>e Galileo, due conquistatori venuti insieme a contesa del medesimo <lb/>principato. </s>

<s>Nell'Italiano per&ograve; era altera noncuranza, ma l'animo <lb/>del Bretone covava odio e recalcitrava con invidioso dispetto. </s>

<s>Dai <lb/>maestri quelle stesse rivalit&agrave; si tradussero poi ne'discepoli e se, <lb/>per non avere occasione a partecipare dei vizii, da una parte riu&shy;<lb/>scirono salutari, precludendo dall'altra gli aditi a partecipare delle <lb/>virt&ugrave;, tornarono, senza dubbio, nocive ai progressi scientifici delle <lb/>due Nazioni. </s></p><p type="main">

<s>Segnalato esempio di tali effetti nocivi lo abbiam noi Itallani <lb/>nella Diottrica diffusa nella <emph type="italics"/>Dissertazione del Metodo<emph.end type="italics"/> e, nonostante <lb/>alcune valide difficolt&agrave;, resa infin dal 1637 familiare in Francia. </s>

<s>Il <lb/>Mersenno consigliava nelle sue Lettere il Torricelli che leggesse <lb/>quella <emph type="italics"/>Dissertazione,<emph.end type="italics"/> ma questi se ne scusava, a principio, dicendo <lb/>che non intendeva la lingua francese. </s>

<s>Poi, quando fu fatta la tra&shy;<lb/>duzione latina, torna lo stesso Mersenno a sollecitar l'amico perch&egrave; si <lb/>risolva a comprare il libro, che trover&agrave; venale per tutto: non ostante <lb/>noi, dietro quel che abbiam potuto raccogliere dalla lettura del <lb/>carteggio manoscritto fra'due celebri uomini, non siamo in grado <lb/>di assicurare i nostri lettori della risoluzion del Torricelli. </s>

<s>Come <lb/>pur siamo incerti se questi entrasse veramente in quella corrispon&shy;<lb/>denza epistolare col Cartesio, dentro alla quale lo voleva ficcare il <lb/>Mersenno. (MSS. Gal. </s>

<s>Dis. </s>

<s>T. XLI, c. </s>

<s>42). </s></p><p type="main">

<s>Eppure il Torricelli lavorava allora attorno a cercar la miglior <lb/>figura da dare alle lenti dei canocchiali, e perch&egrave; si sentiva man<gap/><lb/>la scienza delle rifrazioni, non gl'importa nulla d'impararla alla <lb/>Diottrica del Cartesio, ma ne interroga in proposito il Cavalieri. </s>

<s>Il <lb/>Cavalieri poi rispondeva non saperne altro, da quello in fuori che <lb/>aveva trovato scritto nel <emph type="italics"/>Corso matematico<emph.end type="italics"/> dell'Herigonio; prote-<pb xlink:href="020/01/228.jpg" pagenum="209"/>stando per&ograve; di non credergli, per non gli parer possibile d'applicare <lb/>alla luce le leggi stesse del moto dei gravi. </s>

<s>Or perch&egrave; la Diottrica <lb/>del Cartesio era trattata allo stesso modo che dall'Herigonio, si <lb/>capisce d'onde mai movesse, anco indipendentemente dalle rivalit&agrave; <lb/>della scuola, la ritrosia del Torricelli e del Cavalieri, in accettar <lb/>la legge delle rifrazioni direttamente conclusa dai teoremi della <lb/>Meccanica. </s></p><p type="main">

<s>Tal ritrosia per&ograve; non fu sentita dal Viviani, in mano al quale, <lb/>capitata per caso, nel 1660, la Dissertazione del Metodo, ne rimase <lb/>maravigliato e rapito come a una nuova e inaspettata rivelazione. </s>

<s><lb/>Fu egli che primo introdusse nell'Accademia del Cimento e per <lb/>essa in Italia, derivandola dal Cartesio, la scienza della luce rifratta. </s>

<s><lb/>La ritrosia per&ograve; de'Colleghi f&ugrave; quella forse che gl'imped&igrave; di dif&shy;<lb/>fondere le nuove diottriche dottrine, ci&ograve; che f&ugrave; riserbato al Gri&shy;<lb/>maldi, il quale, riguardando la luce come un fluido qualunque, e <lb/>perci&ograve; anch'essa soggetta alle leggi di tutti gli altri fludi in moto, <lb/>s'apr&igrave; la via e riusc&igrave; alle sue insigni scoperte. </s></p><p type="main">

<s>Abbiamo accennato alla ritrosia de'colleghi del Viviani, fra'quali <lb/>il pi&ugrave; esagerato di tutti fu il Borelli, solito di chiamar le specula&shy;<lb/>zioni filosofiche del Cartesio col nome di <emph type="italics"/>arcolai.<emph.end type="italics"/> E non il Cartesio <lb/>solo aveva in dispetto il Borelli, ma adombrava, bench&egrave; senza mo&shy;<lb/>tivo, di tutti gli stranieri. </s>

<s>Quando, nel 1658, essendo a Roma, fa&shy;<lb/>ceva, per ordine del principe Leopoldo, ricerca de'manoscritti del <lb/>Magiotti e del Torricelli, e si trov&ograve; in mano la Lettera di questo <lb/>al Ricci sopra la celebre esperienza dell'argento vivo, ne dava parte <lb/>allo stesso Principe, cos&igrave; scrivendo: &ldquo; Alla mia venuta recher&ograve; la <lb/>copia di tutte queste lettere scientifiche del Torricelli, per farle <lb/>stampare, acciocch&egrave; non venga l'umore a qualche francese di pre&shy;<lb/>tendere anteriorit&agrave; (come gi&agrave; mi par che ve ne sia alcuno) sopra <lb/>questo gran concetto della compressione dell'aria cagione potissima <lb/>ed indubitabile del sollevamento dell'argento vivo nel cannello &rdquo; <lb/>(MSS. Gal. </s>

<s>Cim. </s>

<s>T. XVI. c. </s>

<s>103). Ora, questo del Borelli parr&agrave; un <lb/>temerario sospetto per chiunque ripensi che nessuno in Europa <lb/>ard&igrave; attribuirsi la grande scoperta torricelliana, da Valeriano Magno <lb/>in fuori, di cui un francese palesava pubblicamente il furto, resti&shy;<lb/>tuendo per giustizia la propriet&agrave; al Matematico del Granduca di <lb/>Toscana. </s>

<s>La data della Lettera del Roberval al Noyers, dove con <lb/>tanto zelo si fa una tale rivendicazione, ha la data di Parigi, otto&shy;<lb/>bre 1647, e fu ristampata in calce alla <emph type="italics"/>Demonstratio ocularis<emph.end type="italics"/> dello <lb/>stesso Magno, data in luce a Venezia due anni dopo la Lettera del <pb xlink:href="020/01/229.jpg" pagenum="210"/>Francese, e nove anni prima che nell'animo del Borelli entrasse <lb/>quel sospetto. </s></p><p type="main">

<s>E poich&egrave; non si poteva ragionevolmente sospettar da nessuno <lb/>de'francesi un attentato di furto, colla Lettera robervelliana sott'oc&shy;<lb/>chio, si direbbe che quasi i Nostri non fossero troppo bene infor&shy;<lb/>mati di quel che si scriveva in Francia delle cose loro. </s>

<s>Ci&ograve; che poi <lb/>si pu&ograve; ritenere per certo, &egrave; che i nostri Accademici non rivolsero <lb/>la debita attenzione al libro degli Esperimenti del Pecquet, ne'quali <lb/>tant'oltre si promuove dall'Autore la scienza torricelliana. </s>

<s>Prova <lb/>di questo sarebbe per noi il vedere in un Diario manoscritto essere <lb/>il Segretario incerto se sia del Roberval l'esperienza della vescica <lb/>nel vuoto, e nel Libro de'<emph type="italics"/>Saggi<emph.end type="italics"/> (Firenze 1841, pag. </s>

<s>27) s'attri&shy;<lb/>buisce al Roberval stesso l'esperienza del vuoto nel vuoto, mentre <lb/>il Pacquet chiaramente dice che fu prima felicemente tentata <emph type="italics"/>acu&shy;<lb/>tissimi Auzotii sagacitate.<emph.end type="italics"/> Bench&egrave;, a voler dir giusto, quel bellis&shy;<lb/>simo esperimento non fu primo a farlo n&egrave; il Roberval n&egrave; l'Auzout, <lb/>ma il Pascal, in pi&ugrave; elegante e facile modo. </s></p><p type="main">

<s>Che si vedesse poi da'Nostri questo ingerirsi degli stranieri <lb/>nella loro scienza di mal occhio, si prova per l'esempio del Boyle, <lb/>i Nuovi Esperimenti fisico meccanici del quale furono pubblicati <lb/>in inglese ne&igrave; 1659, e poco dopo a benefizio di tutti tradotti in la&shy;<lb/>tino. </s>

<s>Quei celebri esperimenti furono tutti fatti nel vuoto operato <lb/>per mezzo della macchina pneumatica, che perci&ograve; si disse <emph type="italics"/>vuoto <lb/>boileiano.<emph.end type="italics"/> Eppure i nostri Accademici tanto di mal animo s'indus&shy;<lb/>sero a far uso di quella macchina! Forse che essi credevano il <lb/>vuoto torricelliano dover riuscir pi&ugrave; perfetto? </s>

<s>Ma pure il Boyle <lb/>stesso ne'suoi Nuovi esperimenti <emph type="italics"/>circa relationem inter flammam <lb/>et acrem<emph.end type="italics"/> aveva discusso la questione, e aveva mostrato in quali <lb/>casi giovi sperimentar nel voto boileiano, e in quali nel torricel&shy;<lb/>liano; cosa dall'altra parte che i Nostri potevano saper benissimo <lb/>per loro propria esperienza. </s>

<s>Ma la ragion potissima perch'essi ri&shy;<lb/>fuggissero cos&igrave; dal vuoto boileiano, ce la dice chiara il Borelli, <lb/>quando, trovatasi dagli Accademici del Cimento gran difficolt&agrave; nel&shy;<lb/>l'agitare il bastoncino per confricar nel vuoto la pallottolina del&shy;<lb/>l'ambra, disperati pensarono di ricorrere alla Macchina boileiana. </s>

<s><lb/>Allora il Borelli immagin&ograve; un nuovo apparecchio, colla pratica del <lb/>quale sperava di agevolar l'esperienza <emph type="italics"/>senza chiedere aiuto a stra&shy;<lb/>nieri.<emph.end type="italics"/> (Targioni, Aggrandim. </s>

<s>T. II. P. II. pag. </s>

<s>606). Mossi pure da <lb/>questa intenzione il Borelli stesso e il Viviani gareggiarono insieme <lb/>a inventare il pi&ugrave; sicuro e pi&ugrave; comodo <emph type="italics"/>vaso del gran vacuo,<emph.end type="italics"/> dentro <pb xlink:href="020/01/230.jpg" pagenum="211"/>il quale per&ograve; non riuscirono a far l'esperienza del suono collo <lb/>strumento a fiato; e bench&egrave; l'unica, questa volta per&ograve; i nostri Ita&shy;<lb/>liani s'ebbero a umiliare e a chiedere aiuto allo straniero. </s></p><p type="main">

<s>Questo starsene a s&egrave; i Nostri e non voler partecipare con gli <lb/>stranieri, specialmente francesi, si potrebbe da qualche giudice se&shy;<lb/>vero sentenziare per un proceder d'animi appassionati, piuttosto <lb/>che d'uomini prudenti. </s>

<s>&Egrave; da osservar nonostante che non erano <lb/>cos&igrave; fatti sentimenti, nell'animo dei nostri Accademici, senza giusti <lb/>motivi, essendo consapevoli, e in parte testimoni, di ci&ograve; che il Mer&shy;<lb/>senno aveva fatto con Galileo e col Torricelli. </s>

<s>Il Magiotti poneva <lb/>in tumulto l'animo del buon Vecchio di Arcetri scrivendogli che <lb/>a quel frate era capitato in Francia il Libro <emph type="italics"/>De Motu,<emph.end type="italics"/> sopra il quale <lb/>egli, il frate stesso francese, <emph type="italics"/>voleva scompuzzare ogni cosa<emph.end type="italics"/> (Alb. </s>

<s>X, <lb/>205). Ma peggio che mai volle scompuzzare le cose al Torricelli, <lb/>quando, pi&ugrave; tardi venuto in Italia, e soggiornando in Roma, si <lb/>messe dietro al Magiotti e al Ricci, per saper le particolarit&agrave; delle <lb/>speculazioni torricelliane, specie intorno al moto dell'acque e dei <lb/>proietti; speculazioni che, tornato a Parigi, divulg&ograve; ne'suoi librac&shy;<lb/>cioni in gran fretta, prevenendo la pubblicazione delle <emph type="italics"/>Opere Geo&shy;<lb/>metriche<emph.end type="italics"/> dell'Autore, che lentamente in quel medesimo tempo si <lb/>stampavano in Firenze. </s></p><p type="main">

<s>Non credendo il Mersenno capace di commettere un atto di <lb/>tanta vilt&agrave;, quegli scienziati Romani conversavano volentieri con <lb/>lui, e bench&egrave; ridessero sotto sotto del sentirlo parlar familiarmente <lb/>un latino, <emph type="italics"/>che l'impatta talvolta con Merlin Coccaio, io per&ograve;,<emph.end type="italics"/> scrive <lb/>il Ricci al Torricelli, <emph type="italics"/>devo sempre dirne bene, se mi fa tutto quello <lb/>che mi ha promesso, cio&egrave; di procurarmi manoscritti e libri a noi <lb/>sconosciuti.<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc. </s>

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

<s>71). Sembra che le promesse <lb/>non fossero mantenute, per cui, sciolto ogni ritegno, il Ricci qua&shy;<lb/>lifica il Mersenno per quel che egli era, colafizzandolo col titolo di <lb/><emph type="italics"/>Gesuito,<emph.end type="italics"/> bench&egrave; sentisse quanto quel di <emph type="italics"/>Minimo<emph.end type="italics"/> fosse, per altra <lb/>parte, tanto meglio appropriato. </s>

<s>E per ci&ograve; di lui stesso, accennando <lb/>in un'altra Lettera al Torricelli le difficolt&agrave; immaginate contro i <lb/>principii meccanici di Galileo, soggiunge: &ldquo; Con questo fondamento <lb/>presume il Gesuito d'alzar rocca inespugnabile a'danni di Galileo <lb/>e della sua scuola, e con mille vanti di s&egrave; medesimo e scherno del <lb/>Galileo, si dimostra non men leggiero ne'costumi che sia nelle dot&shy;<lb/>trine &rdquo; (ivi, c. </s>

<s>116). Cos&igrave; il Mersenno rimeritava l'ospitalit&agrave; degli <lb/>scienziati italiani colla sfacciataggine degli insulti, e con l'abbiet&shy;<lb/>tezza de'furti. </s></p><pb xlink:href="020/01/231.jpg" pagenum="212"/><p type="main">

<s>Quel Ricci nonostante era uomo di cos&igrave; perfetto giudizio da cono&shy;<lb/>scer quanto decoro sarebbe sopraggiunto all'Italia, e quanto se ne <lb/>sarebbe avvantaggiata la scienza dal partecipare insieme gli studi con <lb/>gli stranieri. </s>

<s>Volle perci&ograve; che la nostra del Cimento corrispondesse <lb/>coll'Accademia di Francia, e vi riusc&igrave; col mandare al Thevenot la <lb/>relazione dell'esperienza del fumo nel vuoto. </s>

<s>Il Thevenot stette <lb/>alquanto, ma poi rispose che era stata straordinariamente adunata <lb/>l'Accademia parigina, a fine di partecipare a que'signori <emph type="italics"/>l'esperienza <lb/>graziosissima venuta di Firenze.<emph.end type="italics"/> (Ivi, Cim. </s>

<s>T. XVII, c. </s>

<s>81). </s></p><p type="main">

<s>I consigli e le risoluzioni prese dal Ricci non potevano non <lb/>esser conformi alle intenzioni del principe Leopoldo, il quale era <lb/>intanto egli stesso entrato in relazione scientifica con uno de'pi&ugrave; <lb/>celebri e dotti uomini, che dimorassero allora in Parigi, Ismaele <lb/>Bullialdo. </s>

<s>Il Bullialdo poi introdusse in queste relazioni un altro <lb/>non men celebre e dotto uomo, che dall'Aja frequentava Parigi, <lb/>Cristiano Hugenio, e ci&ograve; fu a proposito della celebre controversia <lb/>sulla priorit&agrave; dell'applicazione del pendolo all'orologio. </s>

<s>Bench&egrave; dallo <lb/>zelo un po'troppo ardente, con che intendeva il Viv&igrave;ani d'esaltar <lb/>Galileo, l'altero Barone di Zulichemme sentisse qualche disgusto, <lb/>nonostante ei dovette dar pace e sentirsi anzi grato dell'accoglienze <lb/>che, fra i nostri Accademici, ebbero le sue dottrine e le sue sco&shy;<lb/>perte. </s>

<s>Il Viviani stesso, non sappiamo se per suo diporto o se per <lb/>servizio de'Principi, dava mano a tradurre l'Astroscopia, o la Nuova <lb/>arte di osservare le stelle (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXXXVIII, c. </s>

<s>124-47), <lb/>e per ordine espresso del Serenissimo Cardinale Leopoldo, faceva <lb/>un sunto, da leggersi nell'Accademia, di una Relazione intorno ad <lb/>alcune osservazioni fatte dall'Hugenio a Parigi, il d&igrave; 12 Maggio 1667, <lb/>di un alone o corona apparsa in quel giorno intorno al sole. (ivi, <lb/>T. CXXXIII, c. </s>

<s>135-44). Il Viviani altres&igrave; riferiva agli Accademici <lb/>suoi colleghi la nuova costruzione del canocchiale ugeniano, e i <lb/>primi tentativi e le speranze concepute dall'Olandese d'aver trovato <lb/>il modo di acromatizzare le lenti. </s>

<s>E il sistema Saturnio chi sa quante <lb/>contradizioni ancora avrebbe patito, se le ingegnose macchine im&shy;<lb/>maginate e descritte dal Borelli, non avessero fatto quasi scender <lb/>dal cielo il lontano pianeta, e rappresentarsi agli Accademici e agli <lb/>stessi pi&ugrave; volgari spettatori, sott'occhio. </s></p><p type="main">

<s>Non si pu&ograve; far motto del sistema Saturnio e dell'Accademia <lb/>fiorentina, senza fare a quel dell'Hugenio seguitar dietro il nome <lb/>di un altro straniero, a cui non sapremmo nemmen noi dar altro <lb/>nome che di <emph type="italics"/>cervellaccio.<emph.end type="italics"/> &ldquo; A quel cervellaccio, scriveva il Borelli <pb xlink:href="020/01/232.jpg" pagenum="213"/>di Onorato Fabry, gli son sovvenuti concetti assai simili a'miei, <lb/>con i quali spieg&ograve; le cagioni fisiche del moto de'pianeti &rdquo; (MSS. <lb/>Gal. </s>

<s>Cim. </s>

<s>T. XVIII, c. </s>

<s>110). Quel cervellaccio, per sostenere il gioco <lb/>di que'suoi globi bianchi e neri, danzanti intorno a Saturno, onde <lb/>cos&igrave; spiegare i fenomeni dell'anello, avrebbe seguitato ad agitare <lb/>interminabilmente la questione contro l'Hugenio, se il Ricci non <lb/>avesse consigliato e operato a troncarla. </s>

<s>Tanto era poi incaponito <lb/>di compor Saturno a suo modo, e tanto era persuaso non avercene <lb/>altro miglior di quello immaginato, che avendo ricevuto invito pi&ugrave; <lb/>volte da Giuseppe e da Matteo Campani di far esperienza della <lb/>verit&agrave; delle cose, guardando con uno de'pi&ugrave; eccellenti canocchiali <lb/>fabbricati da loro, non ci volle comparir mai. (MSS. Gal. </s>

<s>Disc. </s>

<s><lb/>T. CXLIV, c. </s>

<s>269). Dopo tanto combattere, fin&igrave; per rassegnarsi sotto <lb/>le bandiere del suo nemico, e nella fine del II de'suoi Dialoghi <lb/>fisici annovera, tra le nuove maraviglie scoperte nel cielo, l'anello <lb/>di Saturno <emph type="italics"/>a Christiano Hugenio viro clarissimo et omnigena lite&shy;<lb/>ratura probe instructo<emph.end type="italics"/> (Lugduni 1665, pag. </s>

<s>65). Cos&igrave; in pari modo, <lb/>dop'essersi fatto spacciare per primo autore dell'esperienza dell'ar&shy;<lb/>gento vivo, con facilit&agrave; e docilit&agrave; veramente filosofica, secondo <lb/>l'espression del Borelli, cant&ograve; la sua palinodia scrivendo nel IV <lb/>de'Dialoghi sopra citati: &ldquo; Primus illius inventor fuit doctissimus <lb/>Torricell&igrave;us, vir certe, quem inter principes huius temporis geo&shy;<lb/>metras iure innumero &rdquo; (ibi, pag. </s>

<s>182). </s></p><p type="main">

<s>Il Fabry, oltre ad essere straniero, era gesuita, che vuol dire <lb/>peripatetico o filosofante alla maniera di Aristotele intorno ai fatti <lb/>della Natura. </s>

<s>Assecondando perci&ograve; docilmente le cose al suo proprio <lb/>cervello, non risolve problema, non conclude questione ch'ei non <lb/>la coroni compiacente con dire: <emph type="italics"/>quid facilius, quid clarius?<emph.end type="italics"/> Ora <lb/>una tal Filosofia era tutta contraria a quella professata dai nostri <lb/>Accademici, i quali, trepitando in dover render la ragion fisica delle <lb/>cose, si contentarono quasi sempre, dopo lunghi e ripetuti esperi&shy;<lb/>menti, di descrivere i fatti come s'eran rappresentati ai loro sensi. </s>

<s><lb/>Non &egrave; maraviglia perci&ograve; se nessuno de'gesuiti fu chiamato mai a <lb/>partecipare de'Medicei sperimentali consessi. </s>

<s>E nonostante n'erano <lb/>in quel numero due, l'uno e l'altro italiani, che se fossero rimasti <lb/>nel loro filosofare liberi dal giogo peripatetico, avrebbero fatto ri&shy;<lb/>splendere, non una corte, come il Magalotti diceva del Borelli, ma <lb/>un'intera nazione. </s></p><p type="main">

<s>Giovan Batista Riccioli voleva tutto <emph type="italics"/>riformare,<emph.end type="italics"/> ossia ridur le <lb/>cose agli ordini antichi, o a que'nuovi da s&egrave; immaginati. </s>

<s>E perci&ograve;, <pb xlink:href="020/01/233.jpg" pagenum="214"/>tutt'altro che cimentare, metteva i fatti naturali a tortura, e voleva <lb/>che corrispondessero in ogni modo a'suoi preconcetti. </s>

<s>Nessuno che <lb/>si mette a svolgere i suoi ponderosi volumi non pu&ograve; non deplorare <lb/>che tanta infaticabile assiduit&agrave;, e tanta pazienza di sperimentare, <lb/>siano state rivolte piuttosto a compiacere una setta, che a benefizio <lb/>della scienza universale. </s></p><p type="main">

<s>Francesco Maria Grimaldi, concittadino e collega di lui negli <lb/>studii, presenta il caso pi&ugrave; strano, che si sia incontrato mai nella <lb/>storia letteraria. </s>

<s>Il celebre Trattato <emph type="italics"/>De Lumine<emph.end type="italics"/> lo divide in due <lb/>parti, nella seconda delle quali disdice tutto ci&ograve; che avea detto nella <lb/>prima. </s>

<s>Ma la stranezza maggiore consiste nel veder che l'Autore <lb/>s'adagia nel falso, dop'aver cos&igrave; strenuamente combattuto pel vero. </s>

<s><lb/>Qualunque sieno le ragioni pensate a spiegare un fatto tanto sin&shy;<lb/>golare, le due parti contradittorie del Trattato grimaldiano ebbero <lb/>una grande efficacia in promuover l'ottica, perch&egrave; par che la prima <lb/>di quelle parti abbia il precipuo scopo di dimostrare, che supposto <lb/>esser la luce soggetta alle passioni degli altri fluidi, si spiegano <lb/>facilmente gli antichi, e si scuoprono fenomeni nuovi; mentre sup&shy;<lb/>posto esser la luce una qualit&agrave;, conforme ai placiti peripatetici, come <lb/>si fa dall'Autore nella parte seconda, non s'incontrano che mani&shy;<lb/>feste contradizioni ed errori. </s></p><p type="main">

<s>Il Riccioli ebbe qualche raro commercio con alcuni de'nostri <lb/>Accademici privati: del Grimaldi non ne abbiamo trovato vestigio. </s>

<s><lb/>Si potrebbe sospettare che il principe Leopoldo non avesse cos&igrave; <lb/>fatta gente in buona grazia, e darebbe al sospetto qualche fon&shy;<lb/>damento una lettera, che il Rinaldini scriveva da Pisa al Viviani, <lb/>nel d&igrave; 9 Marzo 1658. &ldquo; Mi vien detto, scriveva, per cosa certissima <lb/>che i padri Gesuiti fanno strepito avanti il tempo, conciossiach&egrave; <lb/>dicono che, se nel Libro delle Osservazioni naturali fatte cost&igrave;, ci <lb/>sar&agrave; cosa che possi toccar qualcheduno di loro, che averanno uo&shy;<lb/>mini, a'quali d&agrave; l'animo di rispondere, e che frattanto, tutto che <lb/>possono sapere delle cose fatte procurano di sperimentare e di farne <lb/>un libro &rdquo; (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XXIV, c. </s>

<s>45) e seguita a rivelare in <lb/>gran segretezza alcune trame, e a dire un gran male de'gesuiti, <lb/>concludendo al Viviani, se lo credesse ben fatto, di confidare il tutto <lb/>al principe Leopoldo. </s></p><p type="main">

<s>Che quella setta peripatotica possa aver congiurato ai danni <lb/>dell'Accademia del Cimento, non fa maraviglia: per&ograve;, da questa <lb/>lettera del Rinaldini in fuori, non son noti a noi, per provare il <lb/>fatto, altri documenti, n&egrave; ci siamo curati di ricercarli. </s>

<s>Forse il prin-<pb xlink:href="020/01/234.jpg" pagenum="215"/>cipe Leopoldo, che sapeva non esser nella sua Accademia stato <lb/>offeso nessuno, se ne viveva tranquillo, e uomo di senno, piuttosto <lb/>che irritarsi, come da tanti si fa, avr&agrave; pensato ai benefizi grandis&shy;<lb/>simi, che conseguitano sempre dalle contradizioni, e come, se il <lb/>verno non li mortifica, poco giova a fecondare il seme de'campi <lb/>il tiepore di primavera. </s>

<s>Pi&ugrave; assai delle contrariet&agrave; de'peripatetici <lb/>dovevano mettere in sollecitudine il Principe le dissensioni fra'suoi <lb/>stessi Accademici, e specialmente quelle insorte fra il Borelli e il <lb/>Viviani. </s>

<s>Nate all'occasione della teoria dell'anello riscaldato e di&shy;<lb/>latato al calore, infierirono, le inimicizie fra'due grandi Geometri, <lb/>nella concorrenza che ebbero in tradurre i rimasti, e in divinare i <lb/>libri smarriti di Apollonio di Perga. </s>

<s>Chi conosce il carattere del <lb/>Borelli ammira la potenza che ebbe il principe Leopoldo in mante&shy;<lb/>nerlo collega e collaboratore, per dieci anni, all'odiato Viviani, e <lb/>in trattenerlo fino alla morte, o vicino o lontano, a suoi servigi; <lb/>potenza, nella quale, pi&ugrave; che l'altezza del grado, concorse l'affa&shy;<lb/>bilit&agrave; e la dolcezza dei modi. </s></p><p type="main">

<s>Pi&ugrave; tardi, quello stesso fastidioso Borelli, da cui tanti dispetti <lb/>ebbe a patire il docile Malpighi, entr&ograve; in fiera battaglia, direttamente <lb/>con Stefano Angeli, discepolo del Cavalieri e uno dei deputati a <lb/>rivedere il Trattato del Michelini, e indirettamente col Riccioli, a <lb/>proposito di un argomento sperimentale che questi adduce contro <lb/>il moto della Terra. </s>

<s>Era quella battaglia, piuttosto che condotta dal <lb/>valore, menata dalla rabbia, e perci&ograve; cos&igrave; accoratamente il principe <lb/>Leopoldo ne scriveva in proposito al Ricci: &ldquo; Mi dispiace, quando, <lb/>in queste occasioni di differenze letterarie, s'esce dai termini delle <lb/>dispute &rdquo; (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XXIII, c. </s>

<s>149). </s></p><p type="main">

<s>Ammirabile uomo da qualunque lato si guardi! sia qual si voglia <lb/>la cultura o la forza dell'ingegno di Leopoldo de'Medici, egli &egrave; pi&ugrave; <lb/>benemerito della scienza italiana di quegli stessi che sudarono sui <lb/>libri, o si affaticarono intorno agli esperimenti. </s>

<s>Cessata l'Accademia <lb/>colla morte di lui, le dottrine di Galileo parvero essere esaurite, per <lb/>essersi svolte in soverchiante abbondanza. </s>

<s>Or essendo legge natu&shy;<lb/>rale che in ogni tralcio trascorso, a voler mantenergli la virt&ugrave; di <lb/>fruttificare, conviene o di ritirarlo col ferro verso il suo principio, <lb/>o infondergli in qualche altro modo vigore novello; &egrave; perci&ograve; che <lb/>dopo l'Accademia del Cimento, incomincia per la Storia della nostra <lb/>Scienza un'altra et&agrave;, e cos&igrave; apresi innanzi ai nostri proprii occhi <lb/>una nuova scena, a rappresentare il terzo atto di questo Dramma. <pb xlink:href="020/01/235.jpg"/></s></p><pb xlink:href="020/01/236.jpg"/><p type="main">

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

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

<s>I. </s>

<s>Isacco Newton. </s>

<s>&mdash; II. De'principii e de'progressi delle speculazioni neutoniane, e quale efficace <lb/>concorso v'abbiano avuto le tradizioni scientifiche de'nostri italiani. </s>

<s>&mdash; III. </s>

<s>Delle Istituzioni <lb/>idrauliche di Domenico Guglielmini, e in che modo, i principii della Filosofia neutoniana, nel <lb/>secolo XVIII, concorressero a farle progredire. </s>

<s>&mdash; IV. Dell'elettricismo, della Chimica, dell'elettro <lb/>chimica, e come si svolgessero, queste nuove parti della scienza, dai principii della Filosofia <lb/>neutoniana. </s>

<s>&mdash; V. De'progressi della Storia Naturale, nel secolo XVIII. &mdash; Delle condizioni pre&shy;<lb/>senti delle scienze sperimentali: qualche parola intorno alla nostra Storia. </s></p><p type="main">

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

<s>Chi ripensa ai progressi straordinari fatti dalle scienze speri&shy;<lb/>mentali nel secolo XVIII, s'avvede assai facilmente che non pu&ograve;, <lb/>di tale effetto, esser unica tra le cause quella consueta d'operarsi <lb/>negli ordini trascorsi, e che &egrave; di ritirarli verso i loro principii. </s>

<s><lb/>Quell'effetto straordinario non poteva non esser prodotto da una <lb/>causa straordinaria, la quale consista in infondere in quegli stessi <lb/>ordini trascorsi, e ritirati gi&agrave; verso i loro principii, un vigor nuovo <lb/>di vita, come spesso avviene degli alberi fruttiferi della campagna. </s>

<s><lb/>In questo esempio si prova che sempre s'accresce o si perfeziona <lb/>la virt&ugrave; fruttificante de'rami, dall'infonder nel tronco la virt&ugrave; di <lb/>un altr'albero, che sia affine di genere, ma di specie alquanto di&shy;<lb/>versa. </s>

<s>Or la causa per cui, nel secolo XVIII, s'avvantaggiarono le <lb/>scienze sperimentali, in modo tanto straordinario, a noi sembra do&shy;<lb/>versi riconoscere in qualche cosa di simile a quel che si vede per <lb/>gli esempii degli alberi stessi; doversi cio&egrave; riconoscere in una specie <pb xlink:href="020/01/237.jpg" pagenum="218"/>d'innesto, il quale non &egrave; altro poi che un far concorrere insieme <lb/>due virt&ugrave; coniugate a produrre un unico effetto. </s></p><p type="main">

<s>L'innesto, di che si tratta, fu quello appunto che si fece in <lb/>quel tempo con tanto felice riuscita fra la Fisica e la Matematica. </s>

<s><lb/>Non si vuol gi&agrave; dir per questo che fosse, nel secolo precedente, <lb/>sconosciuto un tale efficacissimo connubio: aveva anzi Galileo mi&shy;<lb/>rabilmente promossa la scienza, insegnando a interpretar, per mezzo <lb/>delle Matematiche, i Misteri della Natura, e il Castell&igrave; aveva dimo&shy;<lb/>strato gi&agrave; come si dovesse trattar del moto delle acque, con rigo&shy;<lb/>roso ordine di Geometria. </s>

<s>Ci&ograve; per&ograve; non vuol dir altro, se non che, <lb/>da'due grandi Maestri della Scienza del moto de'gravi e delle Acque <lb/>correnti, s'eran felicemente coniugate insieme, nel secolo XVII, la <lb/>Fisica e la Geometria. </s>

<s>Non per&ograve; s'erano coniugate la Fisica con <lb/>la Matematica, per la quale non s'intende solo la Geometria, ma <lb/>la Geometria coniugata essa stessa coll'Algebra, ossia quell'<emph type="italics"/>Analisi,<emph.end type="italics"/><lb/>che la Scuola galileiana non conobbe, n&egrave; volle poi riconoscere, abor&shy;<lb/>rendo dal parteciparne come da contagiosa merce straniera. </s></p><p type="main">

<s>Vincenzio Viviani, in una di quelle sue prefazioni, o meglio, <lb/>in uno di quegli abbozzi di scritture, che dovevan poi ridursi a <lb/>servir di prefazione a quello e quell'altro libro del suo <emph type="italics"/>Sogno Idro&shy;<lb/>metrico,<emph.end type="italics"/> scritto in tempo che l'analisi, appresso gli stranieri e <lb/>specialmente i Francesi, era largamente e utilmente applicata; si <lb/>scusa del non essersene egli servito, nel trattar le sue quistioni <lb/>d'Idrometria, e dell'aver seguitato piuttosto l'antico metodo in&shy;<lb/>valso nella scuola galileiana, adducendo per sua ragione che se <lb/>l'Analisi, conferisce alla brevit&agrave;, recide per&ograve; i nervi, e rende anzi <lb/>impossibile, in trattar di soggetti fisici matematici, l'uso dell'elo&shy;<lb/>quenza. </s>

<s>Senza dubbio, una pagina irta di segni algebrici, tutt'altro <lb/>che incantar con quella dilettevole armonia, che risuona ne'Dialoghi <lb/>delle Due Nuove Scienze, farebbe gittar via il libro a chi ama veder <lb/>il vero uscir fragrante di mezzo ai fiori del bello, e in ci&ograve; il Viviani <lb/>aveva ragione. </s>

<s>Ma, come a tutti i vecchi avviene, era tenace troppo <lb/>degli usi antichi, e male secondava la gente nuova, anco per essere <lb/>straniera, la quale, al bello dell'eloquenza, preferiva la facilit&agrave;, con <lb/>la quale la nuova Analisi dimostrava la stessa cosa. </s>

<s>Ch&egrave;, dove le <lb/>proposizioni di Galileo e del Torricelli e degli altri simili, prima <lb/>di concludere, divagavano la mente per lungo e faticoso discorso, <lb/>i nuovi Analisti, con pochi simboli, conducevan diritti, e veloci, <lb/>come saette, a coglier nel segno. </s></p><p type="main">

<s>L'istituzione dell'Analisi matematica non si pu&ograve; negar che non <pb xlink:href="020/01/238.jpg" pagenum="219"/>fosse un gran benefizio, sebben l'unico, recato alle scienze speri&shy;<lb/>mentali dalla Filosofia cartesiana. </s>

<s>E dall'essersi quell'Analisi inco&shy;<lb/>minciata a coniugar con la Fisica, noi riconosciamo la prima di <lb/>quelle valide cagioni del progredir cos&igrave; straordinariamente le scienze, <lb/>nell'et&agrave;, che &egrave; soggetto della presente Parte del nostro Discorso. </s>

<s><lb/>A infonder nel vecchio albero, naturalmente esausto per la stra&shy;<lb/>boccante raccolta, rigoglio nuovo di vita, concorsero, in questa nuova <lb/>stagione felicemente congiunte le virt&ugrave; di Galileo e del Cartesio. </s>

<s><lb/>Cos&igrave; vennesi, nella cultura intellettuale, a conseguir quello stesso <lb/>intento e ad operar quel medesimo miracolo, che si vede operar <lb/>cos&igrave; spesso nella cultura fisica delle piante, quando a un tronco, <lb/>rimasto o infecondo, o di frutto insipido, s'inocula la vermena di <lb/>un albero, che dia frutto abbondante e squisito. </s>

<s>La Filosofia car&shy;<lb/>tesiana, che nell'et&agrave; precedente era rimasta di frutti sperimentali <lb/>cos&igrave; infeconda, inoculatasi, per mezzo dell'Analisi, alla Fisica gali&shy;<lb/>leiana, fecond&ograve; di nuovi e miracolosi parti la scienza. </s>

<s>S'aggiunse <lb/>poi di pi&ugrave; all'Analisi il Calcolo differenziale, che fu come un im&shy;<lb/>pennar d'ali il dorso a tentar voli pi&ugrave; arditi e pi&ugrave; sublimi: s'ag&shy;<lb/>giunse di pi&ugrave; l'uso di comporre e decomporre le forze, con la regola <lb/>del parallelogrammo, che fu, al dir del Frisi, come il filo d'Arianna, <lb/>da ritrovarsi in mezzo ai pi&ugrave; intricati laberinti della Meccanica. </s></p><p type="main">

<s>Gi&agrave;, fin dal primo rappresentarsi al pensiero e dalla lontana <lb/>questa nuova disposizione di cose, un mesto presentimento si sa&shy;<lb/>rebbe affacciato all'animo di un italiano, e gli avrebbe detto che, <lb/>al cambiarsi scena a questo terzo Atto del Dramma, si sarebbe anco <lb/>trasferito il luogo della rappresentazione fuori d'Italia. </s>

<s>L'Analisi, di <lb/>origine affatto straniera, il Calcolo differenziale di origine schietta&shy;<lb/>mente italiano, ma andato ad elaborarsi in Germania e in Inghil&shy;<lb/>terra, il principio della composizione delle forze, lasciato in dimen&shy;<lb/>ticanza da'Nostri com'inutile e anzi fallace strumento; bastavano a <lb/>confermar nell'animo que'mesti presentimenti di ci&ograve; che sarebbe <lb/>avvenuto, e che avvenne di fatto. </s>

<s>Il luogo della rappresentazione si <lb/>trasferisce d'Italia in Inghilterra, e alla persona di Galileo Galilei <lb/>succede quella d'Isacco Newton, a far le parti di Protagonista. </s></p><p type="main">

<s>La nuova successione per&ograve; non avvenne al solito modo, che <lb/>nell'Istituzione de'Principati aristotelico, galileiano, cartesiano: fu <lb/>insomma una pacifica e legittima successione, e non una battagliera <lb/>conquista. </s>

<s>Il Newton non ripudi&ograve; com'Aristotile, Galileo, il Cartesio, <lb/>le tradizioni scientifiche de'maggiori, e non pretese di farsi primo <lb/>e solo Maestro e Duce di coloro che sanno. </s>

<s>Riconobbe anzi il ma-<pb xlink:href="020/01/239.jpg" pagenum="220"/>gistero del grande nostro Italiano, ne segui fedelmente i metodi, e <lb/>ne accolse con amore e ne promosse gl'insegnamenti. </s></p><p type="main">

<s>Il Newton, come Galileo, non se ne st&agrave; che ai fatti. </s>

<s>Anch'egli <lb/>il tentar l'essenza l'ha per impresa non manco impossibile, e per <lb/>fatica non men vana nelle prossime sostanze elementari, che nelle <lb/>remotissime e celesti (Alb. </s>

<s>III, 462). Di quel che non ha potuto far <lb/>soggetto di sperimento ne parla come di cosa da questioni. <emph type="italics"/>Que&shy;<lb/>stioni<emph.end type="italics"/> infatti egli chiama quell'alto e sottil modo di speculare in&shy;<lb/>torno alle prime e pi&ugrave; recondite cause degli effetti naturali. </s>

<s>Cos&igrave; <lb/>fatte Questioni, trattando delle propriet&agrave; della luce, volle egli ac&shy;<lb/>cogliere tutte insieme, e perch&egrave; rappresentavano piuttosto le sue <lb/>proprie opinioni che la dimostrata certezza del vero, volle egli te&shy;<lb/>nerle separate e metterle come Appendice al suo Libro. </s></p><p type="main">

<s>Se qualcuno, per esempio, si fa a domandargli: che cos'&egrave; quel&shy;<lb/>l'attrazione, che tu poni per fondamento alla scienza del Cosmo? </s>

<s><lb/>Ed ei risponde: Un fatto osservato e confermato da leggi matema&shy;<lb/>tiche, il qual consiste in quel conato che fanno i corpi d'avvicinarsi <lb/>e di congiungersi insieme, dipenda egli un tal conato o da aliti <lb/>emessi, che commovano e sospingano i corpi, o dall'azion dell'etere, <lb/>che diffondendosi, prema, o dagli elaterii dell'aria o di altro mezzo <lb/>qualunque. (Principia Philos. </s>

<s>Coloniae 1760, T. I, pag. </s>

<s>464). </s></p><p type="main">

<s>Ma pure, soggiunge altrove, per dir qualche cosa della gravit&agrave; <lb/>e di questa misteriosa attrazione &ldquo; quaestionem unam de eius causa <lb/>investiganda subieci, quaestionem inquam, quippe qui experimentis <lb/>rem istam nondum habeam exploratam &rdquo; (Optices, Avvertim. alla <lb/>2. a ediz. del 1717).</s><s> La questione accennata &egrave; la XXI, nella quale <lb/>si ammette l'esistenza dell'etere cosmico, com'efficiente dell'attra&shy;<lb/>zione universale. </s></p><p type="main">

<s>E pur rispetto alla luce, com'entra il Newton in mezzo ai di&shy;<lb/>sputanti sull'essenza di lei? </s>

<s>Dop'aver, nella Sezione XIV del I Libro <lb/>dei <emph type="italics"/>Princippi,<emph.end type="italics"/> dimostrato che un minimo corpo vibrato e attratto <lb/>da un mezzo pi&ugrave; denso, vi descrive, penetrandolo addentro, una pa&shy;<lb/>rabola, per modo che il seno dell'angolo dell'incidenza serbi ragion <lb/>costante col seno dell'angolo dell'emergenza; soggiunge che s&igrave; fatte <lb/>attrazioni non sono molto dissimili da quelle, percui si riflette e si <lb/>rifrange la luce. </s>

<s>&mdash; Dunque anche la luce &egrave; un corpo? </s>

<s>&mdash; Sembre&shy;<lb/>rebbe di s&igrave;, risponde il Newton, giacch&egrave; ella si vede pure moversi <lb/>in tempo, com'&egrave; dimostrato dagli ecclissi dei satelliti di Giove, e <lb/>viene altres&igrave; attratta dai corpi, com'io stesso osservai nel fenomeno <lb/>grimaldiano. </s>

<s>Ma per&ograve; di questo io non voglio disputare, solo io <pb xlink:href="020/01/240.jpg" pagenum="221"/>dimostro matematimente correre una grande analogia fra le traiet&shy;<lb/>torie de'minimi corpi gettati e attratti dai mezzi diafani. </s>

<s>&ldquo; Nihil <lb/>omnium disputans, sed traiectorias corporum traiectoriis radiorum <lb/>persimiles solummodo determinans &rdquo; (Principia etc. </s>

<s>ibi, pag. </s>

<s>541). </s></p><p type="main">

<s>E quanto al modo cos&igrave; controverso del diffondersi la luce nello <lb/>spazio? </s>

<s>&mdash; Riguardando il Newton la luce come un fluido qualunque, <lb/>col principio della repulsione molecolare ne spiegava l'elasticit&agrave;, <lb/>della quale il grado s'argomentava per lui dal vederla correre tanto <lb/><figure id="id.020.01.240.1.jpg" xlink:href="020/01/240/1.jpg"/><lb/>veloce (Optices, quaest. </s>

<s>XXI). Cos&igrave; fatta elasticit&agrave;, come l'attrazione <lb/>verso i corpi taglienti e acuminati nel fenomeno grimaldiano, e le <lb/>traiettorie paraboliche descritte nel mezzo refringente dal raggio, <lb/>includevano senza dubbio l'ipotesi della <emph type="italics"/>emissione.<emph.end type="italics"/> L'Hook intanto <lb/>e l'Huyghens professavano un'ipotesi diversa, qual'era quella delle <lb/>ondulazioni eteree. </s>

<s>Ebbene: come si govern&ograve; il Newton in questo <lb/>negozio che era tanta parte del suo nuovo sistema ottico? </s>

<s>Trat&shy;<lb/>tandosi di cosa, da non si poter decidere con gli esperimenti, la <lb/>lascia a trattar nelle <emph type="italics"/>Questioni.<emph.end type="italics"/> Confessava ivi che il fosfeno nel-<pb xlink:href="020/01/241.jpg" pagenum="222"/>l'occhio compresso era molto favorevole all'ipotesi delle onde eteree <lb/>(quaest. </s>

<s>XVI), ma poi nella Questione XXVIII promuove contro <lb/>quella stessa ipotesi alcune difficolt&agrave;, la principale delle quali &egrave; <lb/>questa: Se la luce si diffondesse in onde, come il suono, dovrebbe, <lb/>a somiglianza di questo, insinuarsi anco dietro gli ostacoli, come si <lb/>pruova del suono delle campane, che si sente anco al di l&agrave; di un <lb/>monte &ldquo; At lumen nunquam compertum est vias incurvas ingredi, <lb/>nec sese in umbram inflectere (quest. </s>

<s>XXVIII). Volle forse perci&ograve; <lb/>il Newton asserir la verit&agrave; di quel moto vibrante della luce, a cui <lb/>applic&ograve; i teoremi dimostrati in fine del suo I Libro dei <emph type="italics"/>Principii?<emph.end type="italics"/><lb/>Ecco quel che egli si contenta di dire, nella XXIX Questione: &ldquo; An <lb/>non radii luminis exigua sunt corpuscula a corporibus lucentibus <lb/>emissa? </s>

<s>&rdquo; </s></p><p type="main">

<s>Parimenti intorno all'origine e a'fenomeni presentati dalla coda <lb/>delle comete, non ha appena il Newton accennato alla sua ipotesi, <lb/>che cio&egrave; sia quella coda una esalazione fumosa del corpo della stessa <lb/>cometa, respinta per circumpulsione dal centro del Sole, come i <lb/>nostri fumi si vedono esser respinti dal centro della Terra; che <lb/>egli tosto soggiunge: &ldquo; Ceterum rerum naturalium causas reddere <lb/>non est huius instituti &rdquo; (Opusc. </s>

<s>Lausannae 1744. T. II, pag. </s>

<s>58). </s></p><p type="main">

<s>Che poi il Newton prosegua veramente i metodi stessi di Ga&shy;<lb/>lileo non vorremmo dedurlo dal citar ch'ei fa il nome di lui cos&igrave; <lb/>spesso e con amore. </s>

<s>Quelle citazioni anzi rivelano che il Filosofo <lb/>inglese non attinse le dottrine del Nostro, alla loro sorgente. </s>

<s>Cos&igrave; <lb/>per esempio, dop'avere stabilito, per prima legge del moto, l'inerzia <lb/>della materia e gli effetti proporzionali alle forze motrici, col pa&shy;<lb/>rallelogrammo delle forze posto per corollario di quelle stesse leggi, <lb/>soggiunge: &ldquo; per leges duas primas et corollaria duo primo, Galileus <lb/>invenit descensum gravium esse in duplicata ratione temporum. <lb/>(Principia, ibi, pag. </s>

<s>45). Ma Galileo tenne, in dimostrare quel teo&shy;<lb/>rema, altri metodi. </s>

<s>Quello accennato ivi dal Newton &egrave; il metodo <lb/>dell'Huyghens, da cui il Newton stesso par che attingesse le dot&shy;<lb/>trine galileiane. </s>

<s>Vorremmo dire piuttosto che nel Professore di <lb/>Cambridge si trasfuse lo spirito del Professore di Padova, il quale <lb/>vi trov&ograve; gli organi pi&ugrave; acconci al suo perfezionamento, e pi&ugrave; adulte <lb/>ed esercitaie le membra. </s></p><p type="main">

<s>D'onde avesse i primi aliti quello spirito, i nostri Lettori lo <lb/>sanno, e la Filosofia neutoniana segnal&ograve; la pi&ugrave; compiuta vittoria, <lb/>che, sopra Aristotile, abbia conseguita Platone, sul campo della <lb/>scienza. </s>

<s>La Filosofia peripatetica, nuovamente apparita a sedurre <pb xlink:href="020/01/242.jpg" pagenum="223"/>gl'ingegni con la lusinghiera eloquenza cartesiana, ebbe nel Newton <lb/>la sua piena sconfitta, quando nel suo Libro immortale dimostr&ograve; che <lb/>la Natura geometrizza veramente a modo platonico, e non fantastica <lb/>a modo aristotelico. </s>

<s>Che, nel dare a quel Libro il titolo di <emph type="italics"/>Prin&shy;<lb/>cipia mathematica Philosophiae<emph.end type="italics"/> non pensasse il Filosofo inglese di <lb/>contrapporre, infino dal frontespizio, l'opera sua dimostrata, e quel&shy;<lb/>l'altra immaginata dal Filosofo Bretone, con simil titolo di <emph type="italics"/>Prin&shy;<lb/>cipia Philosophiae;<emph.end type="italics"/> non par credibile, bench&egrave;, senza rivolgersi n&egrave; a <lb/>destra n&egrave; a sinistra, l'Autore della Nuova filosofia matematica pro&shy;<lb/>ceda a diritto per la sua via. </s>

<s>Rogero Cotes per&ograve;, in quel suo bel <lb/>Discorso premesso alla seconda edizione dei Principii neutoniani, <lb/>non tace del mal animo, con cui questi stessi Principii furon veduti <lb/>da'seguaci del Cartesio, i quali sentivan pur troppo com'esalasse da <lb/>quelle pagine uno spirito di verit&agrave;, potente a cacciar via i nuvolosi <lb/>errori del loro Maestro. </s></p><p type="main">

<s>Dal Cartesio il Newton apprese l'analisi, e va anzi debitore a <lb/>lui se riusc&igrave; a instituire il calcolo differenziale, e ad applicarlo cos&igrave; <lb/>utilmente alla Fisica sperimentale galileiana. </s>

<s>Giova infatti osservare <lb/>che il Calcolo differenziale ebbe origine dall'applicar l'Analisi car&shy;<lb/>tesiana alla Geometria degli indiv&icirc;sibili del Cavalieri, e perci&ograve; non <lb/>sarebbe il Newton, o il Leibniz che ne sia l'Autore, potuto riuscir <lb/>felicemente a quella nuova istituzione, se il Cartesio non mostrava <lb/>come si potesse l'Algebra comporre colla Geometria. </s></p><p type="main">

<s>L'inspirazione poi del proprio genio, meglio che i pochi esempii <lb/>dell'Huyghens, fu che fece presentire al Newton la fecondit&agrave; del <lb/>metodo di comporre e decomporre le forze colla regola del parel&shy;<lb/>logrammo insegnata dall'Herigonio. </s>

<s>I discepoli di Galileo, fra'quali <lb/>il Borelli, riputarono sventuratamente quella regola fallace, e l&agrave; dove <lb/>avrebbero potuto procedere per via diretta e spedita a risolvere <lb/>astrusi problemi di Meccanica, s'avvolsero spesso, come si mostrer&agrave; <lb/>per gli esempii a suo luogo, in incredibili paralogismi. </s>

<s>Ma il Newton, <lb/>con libero ingegno non preoccupato da pregiudizii di scuola, n&egrave; <lb/>soggiogato dall'autorit&agrave; di Galileo, riconobbe invece che quella re&shy;<lb/>gola erigoniana era verissima, e sentenzi&ograve; e dimostr&ograve; di fatto nel <lb/>corollario II alle leggi del moto premesse ai <emph type="italics"/>Principii matematici,<emph.end type="italics"/><lb/>che la regola prescritta dall'Herigonio per comporre e decomporre <lb/>le forze <emph type="italics"/>abunde confirmatur ex Mechanica.<emph.end type="italics"/></s></p><p type="main">

<s>Cos&igrave; alle virt&ugrave; ereditate da Galileo s'aggiunsero, nel Filosofo <lb/>britanno, le tre nuove potenze enumerate, per cui s'inizi&ograve; e si co&shy;<lb/>stitu&igrave; questo nuovo e cos&igrave; splendido Principato della scienza. </s>

<s>Prin-<pb xlink:href="020/01/243.jpg" pagenum="224"/>cipato glorioso, che il Newton consegu&igrave; felicemente senza troppo <lb/>dissipar le valide forze a difendersi contro i nemici, e senza tanto <lb/>arrovellarsi a riconquistar le proprie scoperte dagli arditi usurpa&shy;<lb/>tori. </s>

<s>Qualche sua semplice lettera basta a far tacere il Cassegrain, <lb/>che pretendeva un diritto di anteriorit&agrave; nell'invenzione del canoc&shy;<lb/>chiale catadiottrico, e un inciso, con cui cominci&ograve; lo scolio della <lb/>quarta proposizione del libro primo de'<emph type="italics"/>Principii,<emph.end type="italics"/> parve assai a <lb/>sodisfare il Wrenn, l'Hook e l'Halley de'pretesi meriti loro con&shy;<lb/>cernenti la teoria delle forze centrali. </s></p><p type="main">

<s>Chi, dalle onorificenze tributate anche in vita al Newton, passa <lb/>a considerare le persecuzioni che ebbe anche dopo morte a patir <lb/>Galileo, o maledice arrabbiatamente alla malignit&agrave; e all'ingiustizia <lb/>degli uomini, o pi&ugrave; rassegnato invoca un destino cieco distributore <lb/>a chi di sventure a chi di favori. </s>

<s>Noi crediamo invece che sia l'uo&shy;<lb/>mo stesso, il quale operando in un modo piuttosto che in un altro, <lb/>ora induce gli altri uomini a favorirlo, e ora al contrario gli pro&shy;<lb/>voca a perseguitarlo. </s>

<s>Se anco il Newton, come Galileo, se la fosse <lb/>voluta prendere con quello e con questo, non gli sarebbero, senza <lb/>dubbio, in Inghilterra e nel secolo XVIII, mancate persecuzioni e <lb/>sventure. </s>

<s>Tutto altrimenti, egli aborriva dall'attaccar brighe con <lb/>chicchessia, e per non aver che dire con l'Hook, uomo litigioso, <lb/>tenne per tredici anni il celebre suo Trattato dell'Ottica rinchiuso <lb/>e avvolto nel manoscritto. </s></p><p type="main">

<s>Pur troppo &egrave; vero che non &egrave; da fare il confronto fra Galileo, <lb/>che ebbe a fondare il suo Regno a mano armata, contro i Peripa&shy;<lb/>tetici, e il Newton, che ricev&egrave; quel Regno di gi&agrave; stabilito, e che <lb/>non aveva bisogno d'altro che d'essere ampliato. </s>

<s>Pur troppo si <lb/>potrebbero dir tante altre cose, a intrigar piuttosto che a risolvere <lb/>la questione, e perci&ograve;, lasciando d'investigar questi, che anche noi <lb/>chiameremo destini della vita o civile o morale, passeremo a veder <lb/>del Newton i principii e i progressi della vita intellettuale, e <lb/>qual'efficace concorso v'abbiano avuto le tradizioni scientifiche dei <lb/>nostri italiani. </s></p><p type="main">

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

<s>All'entrar dell'anno 1666 era in Cambridge tutto intento a <lb/>lavorare i vetri da canocchiali, studiandosi con ogni artificio di <lb/>configurarli in quella nuova foggia di superficie o paraboliche o <pb xlink:href="020/01/244.jpg" pagenum="225"/>iperboliche, le quali un'antica tradizione veniva predicando per le <lb/>pi&ugrave; accomodate a produr l'effetto di avvalorare la virt&ugrave; visiva, <lb/>nonostante che il laborioso esercizio fosse stato dimostrato inutile <lb/>dal Cavalieri. </s>

<s>Cos&igrave;, trattando i cristalli, venne voglia al Newton di <lb/>preparare uno di quei prismi triangolari, per dilettarsi nella pia&shy;<lb/>cevole contemplazione degli svariati e splendidi colori. </s>

<s>Chiuse perci&ograve; <lb/>la finestra di camera e aperto un foro nell'imposta, riceveva per <lb/>esso un raggio di sole, che, rifranto nel prisma, andava a dipingere <lb/>lo spettro colorato sopra una carta bianca. </s>

<s>Si sarebbe aspettato di <lb/>veder quello spettro dipinto in figura circolare com'era il foro, e <lb/>trova con sua gran maraviglia che si distende invece allungato in <lb/>figura di una striscia, la quale, misurata diligentemente, riesce lunga <lb/>cinque tanti, presso a poco, quant'ella &egrave; larga. </s>

<s>Ne osserva le due <lb/>estremit&agrave;, e gli sembran terminare in un arco di cerchio. </s>

<s>Il raggio, <lb/>dunque, conclude, ha subito, attraversando il prisma, una disper&shy;<lb/>sione, e ci&ograve; senza dubbio per essere alcune parti di quello stesso <lb/>raggio pi&ugrave; refrangibili di alcune altre &ldquo; Unde patet veram imaginis <lb/>sic exporrectae causam hanc unam esse quod scilicet lux constat <lb/>ex radiis, quorum alii aliis magis refrangibiles sunt &rdquo; (Op. </s>

<s>omn. </s>

<s>opt. </s>

<s><lb/>Patavii 1773, App. </s>

<s>pag. </s>

<s>5). </s></p><p type="main">

<s>Il primo frutto che raccolse da questa scoperta, fu quello di <lb/>abbandonare ogni speranza di dover giungere alla desiderata per&shy;<lb/>fezione del canocchiale diottrico, avendo ben conosciuto che, anco <lb/>quando fosse riuscito a trovar la figura del perfetto concorso, quel <lb/>concorso, nonostante, non avrebbe mai avuto il suo effetto, &ldquo; quia <lb/>lux ipsa est mixtura quaedam heterogenea composita ex radiis di&shy;<lb/>versae refrangibilitatis. </s>

<s>&rdquo; Il secondo frutto che si credette di poter <lb/>raccoglier l'Autore dalla sua scoperta, fu quello di aver finalmente <lb/>riconosciuta l'origine e le propriet&agrave; de'colori. </s>

<s>Non son dunque i <lb/>colori, concludeva il Newton, qualificazioni della luce nate dalle <lb/>riflessioni o dalle rifrazioni de'corpi naturali, come volgarmente si <lb/>crede, &ldquo; sed primigeniae et congenitae proprietates in diversis ra&shy;<lb/>diis diversae. </s>

<s>Aliqui radii tantum ad rubrum, alii solum ad flavum, <lb/>alii ad viridem effingendum apti sunt &rdquo; (ibi, pag. </s>

<s>6). E nella seconda <lb/>Parte delle Lezioni Ottiche, riserbata a trattar di proposito <emph type="italics"/>De co&shy;<lb/>lorum origine,<emph.end type="italics"/> accenna alle due principali ipotesi peripatetica e <lb/>cartesiana seguitate da tutti prima di lui, e mostra quanto fosser <lb/>lontane dalla verit&agrave; delle cose. </s></p><p type="main">

<s>Che prima del Newton si seguisse in generale dagli Ottici <lb/>l'ipotesi di Aristotile, secondo la quale i colori si generano da una <pb xlink:href="020/01/245.jpg" pagenum="226"/>proporzionata mistura d'ombra e di luce, &egrave; vero, e fu quell'ipotesi <lb/>accolta anche dagli Accademici del Cimento. </s>

<s>Il Viviani ha lasciato <lb/>fra'suoi Manoscritti una schedula autografa, nella quale, assegnati <lb/>i due estremi del bianco e del nero, fa nascere il rosso dalla mi&shy;<lb/>stura di sei gradi di bianco con uno di nero, il ranciato da cinque <lb/>gradi di bianco mescolato con due di nero, e cos&igrave; gradatamente <lb/>per tutti e sette i colori dello spettro. </s>

<s>Nonostante, anche prima del <lb/>Newton, si trovano in alcuni Autori italiani ipotesi nuove e pi&ugrave; giu&shy;<lb/>diziose e conformi ai fatti, delle antiche peripatetiche. </s>

<s>Il Maurolico, <lb/>per esempio, aveva, nel Teorema XVIII del primo libro <emph type="italics"/>Diapha&shy;<lb/>norum,<emph.end type="italics"/> dimostrato l'aberrazione di sfericit&agrave; delle lenti, al qual teo&shy;<lb/>rema, se avesse atteso il Newton, avrebbe lasciato assai prima di <lb/>travagliarsi intorno a'canocchiali diottrici, e pi&ugrave; per tempo si sa&shy;<lb/>rebbe rivolto ai canoccbiali per riflessione. </s>

<s>Il Maurolico stesso, ri&shy;<lb/>fiutando i placiti aristotelici, fu primo a dir che i colori avevano <lb/>origine dalla luce, la quale rifrangendosi, si trova in varie parti dello <lb/>spettro pi&ugrave; o men costipata; dottrina insegnata pure dall'Imperato <lb/>o dallo Stelliola, dodici anni prima che fosse nota al pubblico la <lb/>Diottrica del celebre Abate di Santa Maria in Porto. </s>

<s>E f&ugrave; l'Impe&shy;<lb/>rato, che pi&ugrave; di un mezzo secolo prima del Newton, quando il <lb/>prisma triangolare non serviva ad altro che alle piacevoli ricrea&shy;<lb/>zioni, ei lo predic&ograve; <emph type="italics"/>strumento di refrazione all'osservazione della <lb/>generazion dei colori tra gli altri tutti ottimo<emph.end type="italics"/> (Hist. </s>

<s>nat. </s>

<s>Venezia <lb/>1672, pag. </s>

<s>294). Le dottrine ottiche dei due nostri italiani furono <lb/>poi dal Bullialdo divulgate nella XXIX proposizione del suo celebre <lb/>Trattato <emph type="italics"/>De natura lucis,<emph.end type="italics"/> e pi&ugrave; solennemente poi sanzionate dal <lb/>Grimaldi; dottrine ottiche, le quali, convenendo colle neutoniane <lb/>in professar che i colori non riseggan nei corpi e in dir che non <lb/>sian luce in potenza, come teneva il Keplero, ma che sian la luce <lb/>stessa in atto; ne differivan solo in ammettere una <emph type="italics"/>costipazione<emph.end type="italics"/><lb/>de'raggi rifratti, invece di una <emph type="italics"/>dispersione.<emph.end type="italics"/></s></p><p type="main">

<s>La scoperta della dispersion della luce ne'prismi triangolari, <lb/>e la
nuova teoria de'colori che indi ne segue, furono pubblicate <lb/>dall'Autore in una Epistola stampata prima in Cambridge e inse&shy;<lb/>rita pochi anni dopo nel n. o 80 delle <emph type="italics"/>Transazioni filosofiche<emph.end type="italics"/> di <lb/>Londra, sotto il d&igrave; 19 Febbraio 1672. </s><s>Appena furon divulgate le <lb/>nuove dottrine, il gesuita Ignazio Pardies si mosse incontro ad <lb/>oppugnarle, dicendo che l'allungamento dello spettro colorato non <lb/>dipendeva da una dispersione per via del vario grado di refrangi&shy;<lb/>bilit&agrave; del raggio composto, come voleva il Newton, ma avveniva per <pb xlink:href="020/01/246.jpg" pagenum="227"/>un fenomeno somigliantissimo a quello osservato gi&agrave; e descritto nel <lb/>Trattato <emph type="italics"/>De Lumine<emph.end type="italics"/> dal Grimaldi. </s>

<s>Ecco annunziarsi il titolo di un <lb/>libro, ecco pronunziarsi il nome di un Italiano, a cui il Filosofo <lb/>inglese va debitore della sua gloria. </s>

<s>Cos&igrave; i voli sublimi distesi pel <lb/>grandissimo mondo, come le sottili penetrazioni addentro alle chiuse <lb/>e buie regioni del piccolissimo, ebbero occasione dal rimeditar che <lb/>fece il Newton le pagine di quel libro. </s></p><p type="main">

<s>Veniva insomma il Pardies, operando i soliti benefici effetti di <lb/>tutti gli oppositori, a far provvidamente capitare a Cambridge il <lb/>Trattato <emph type="italics"/>De Lumine<emph.end type="italics"/> stampato in Bologna, e colui che sentiva con&shy;<lb/>trapporre alle sue nuove, altre nuove scoperte annunziate in quel <lb/>Trattato, non poteva non ricercarvele dentro avidamente. </s>

<s>Legge alla <lb/>prima apertura del Volume che l'Autore, oltre alle riflessioni e alle <lb/>rifrazioni, ammette nella luce una terza passione, che egli appella <lb/>col nome nuovo di <emph type="italics"/>diffrazione.<emph.end type="italics"/> Tutto attento ha il pensiero sopra <lb/>i due esperimenti ivi descritti a dimostrare in che modo un raggio <lb/>luminoso, che rasenta gli orli di un corpo opaco, vi si diffrange. </s>

<s><lb/>Ripete in altra maniera l'esperimento, e trova che di fatto l'ombre <lb/>riescon sempre alquanto maggiori di quel che se il raggio proce&shy;<lb/>desse a diritto. </s>

<s>Non ci &egrave; dubbio dunque: ei si diffrange. </s>

<s>Ma qual'&egrave; <lb/>la causa di quella diffrazione? </s>

<s>Il Grimaldi, contento a descrivere <lb/>il fatto, non lo dice: la risposta data da altri interrogati in propo&shy;<lb/>sito, che cio&egrave; risegga la causa del fenomeno nelle solite rifrazioni <lb/>dell'aria, non sodisfa il sagace investigatore. </s>

<s>Gli balena alla mente <lb/>un pensiero ardito: che il raggio si diffranga perch&egrave; &egrave; attratto dagli <lb/>orli taglienti del corpo opaco interposto? </s>

<s>&ldquo; Annon corpora agunt <lb/>in lumen interiecto aliquo intervallo, suaque illa actione radios eius <lb/>inflectunt? </s>

<s>&rdquo; (Optices, Lib. </s>

<s>III, quaest. </s>

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

<s>L'ardita ipotesi per&ograve; supponeva risoluta gi&agrave; la gran questione <lb/>della natura della luce, se cio&egrave; essa sia corporea e soggetta alle <lb/>passioni stesse degli altri corpi ponderosi. </s>

<s>La legge delle rifrazioni <lb/>conclusa dalla meccanica, specialmente in Italia, dai pi&ugrave; si ripu&shy;<lb/>diava, e, per tante prove fatte, non s'era ancora riusciti ad assi&shy;<lb/>curarsi se un raggio luminoso si muove in tempo o si diffonde in <lb/>istante. </s>

<s>Il Grimaldi per&ograve; tenne per risoluta la gran questione, e <lb/>posto per cosa certa che fosse anche la luce un corpo come tutti <lb/>gli altri, ammise, anteriormente a qualunque dimostrazione speri&shy;<lb/>mentale, che ella si movesse in tempo. </s>

<s>Applicando poi al moto di <lb/>lei la legge della velocit&agrave; in ragion reciproca delle sezioni, come <lb/>segue nel moto di tutti i fluidi, riusc&igrave; a concludere, in modo sicuro, <pb xlink:href="020/01/247.jpg" pagenum="228"/>che i seni degli angoli d'incidenza hanno ragion costante co'seni <lb/>degli angoli di refrazione. </s></p><p type="main">

<s>L'esempio del Grimaldi e la felice scoperta del Roemer per&shy;<lb/>suasero il Newton della natura corporea della luce, il quale anzi <lb/>tanto oltre and&ograve;, che, ammettendo un nucleo duro in tutte le par&shy;<lb/>ticelle componenti ogni sorta di corpi, non dubit&ograve; di soggiungere: <lb/>&ldquo; quin et ipsi etiam radii luminis corpora dura esse videntur &rdquo; (ibi, <lb/>quaest. </s>

<s>XXXI). E mentre i discepoli di Galileo avevano adombrato <lb/>e recalcitrato contro la Meccanica ottica del Cartesio e dell'Heri&shy;<lb/>gonio, egli incomincia i suoi studii sopra la luce, applicando alla <lb/>stessa, nella Sez. </s>

<s>XIV del I Libro de'<emph type="italics"/>Principii,<emph.end type="italics"/> le propriet&agrave; delle <lb/>traiettorie paraboliche, che Galileo avea dimostrato venir descritte <lb/>da tutti i corpi gravi proietti. </s></p><p type="main">

<s>Ma sia pure la luce un corpo duro, s'ammetta pur possibile <lb/>che la diffrazione avvenga perch&egrave; le molecole dure della luce ven&shy;<lb/>gono attratte dalle molecole dure che circondan gli orli del foro <lb/>nel fenomeno grimaldiano: con quali argomenti si possono dimo&shy;<lb/>strare o si possono almeno render credibili queste cose tanto lon&shy;<lb/>tane dalla comune opinione? </s></p><p type="main">

<s>Ecco aprirsi di qui la via a nuove e peregrine speculazioni, <lb/>dalle quali sarebbe per esser promossa tant'oltre la scienza nel <lb/>secolo XVIII. Galileo, nel Discorso intorno alle galleggianti, non <lb/>pensando alle pressioni idrostatiche, dalle quali si sostengono alla <lb/>superficie le tavolette di gravit&agrave; specifica maggiore dell'acqua, si <lb/>ridusse ad ammettere una specie di attrazione fra l'aria e la su&shy;<lb/>perficie solida del galleggiante. </s>

<s>E di li pass&ograve; a specular la ragione <lb/>di quella copula, che tiene unite insieme le minime particelle dei <lb/>corpi, attribuendola a una indefinita virt&ugrave; calamitica del contatto, <lb/><emph type="italics"/>senza interposizione alcuna di fluidi cedenti<emph.end type="italics"/> (Alb. </s>

<s>XII, 54). Per&shy;<lb/>suaso poi, dalle opposizioni giustissime che gli furon fatte, dell'in&shy;<lb/>sufficienza e anzi della falsit&agrave; del suo principio, neg&ograve; nel Saggiatore <lb/>(Alb. </s>

<s>IV. 299) quella virt&ugrave; dell'attrazione calamitica dell'aria che <lb/>aveva prima ammessa come causa del sostenersi le tavolette d'ebano, <lb/>non bagnate, sulla superficie dell'acqua, e finalmente, nel I Dialogo <lb/>dello Due Nuove Scienze, tornato a specular sul fatto dell'adesione <lb/>di due marmi venuti fra loro a squisito contatto, e sulla virt&ugrave; co&shy;<lb/>pulatrice della materia, non dubit&ograve; di riconoscer nella forza del <lb/>vacuo la causa generalissima di questo effetto (Alb. </s>

<s>XIII. pag. </s>

<s>22, 23). </s></p><p type="main">

<s>Quando poi al vacuo si sostitu&igrave; la pressione ammosferica, oc&shy;<lb/>corse in tal proposito un fatto singolare nella storia delle scienze. <pb xlink:href="020/01/248.jpg" pagenum="229"/>Il Boyle aveva sottoposto alla campana della sua macchina pneu&shy;<lb/>matica uno strumento simile al termometro ad aria, se non che <lb/>tutto, cannello e bulbo, era pieno di acqua sostenuta, come si sa, <lb/>dalla pressione dell'aria sulla superficie del liquido, dentro a cui <lb/>il cannello stesso, con la sua bocca, era immerso. </s>

<s>Fatto perci&ograve; il <lb/>vuoto, se questo fosse riuscito assoluto, la caraffella piena d'acqua <lb/>si sarebbe dovuta votare affatto. </s>

<s>Ma perch&egrave; qualche poco di liquido <lb/>seguitava ancora a sostenersi a mezzo il cannello, il Boyle diceva <lb/>avvenir ci&ograve; perch&egrave; &egrave; impossibile colla macchina estrar tutta l'aria, <lb/>e farvi sotto la campana il vuoto perfetto. </s></p><p type="main">

<s>Venne voglia all'Huyghens di ripetere l'esperienza boileiana, <lb/>e trov&ograve; che il caso descritto dall'Autore non si avverava se non che <lb/>quando l'acqua tien dentro a s&egrave; sciolta qualche particella d'aria. </s>

<s><lb/>Sperimentando coll'acqua bollita, anco fatto il vuoto, vide con sua <lb/>gran maraviglia che la caraffella seguitava tuttavia a rimaner piena. </s>

<s><lb/>Divulgato il fatto, non gli si voleva credere, per cui l'Huyghens <lb/>stesso nel 1663, indusse la Societ&agrave; Reale di Londra a ripetere so&shy;<lb/>lennemente l'esperienza. </s>

<s>V'era fra gli altri presente lo stesso Boyle, <lb/>sorpreso da tanto stupore, a veder davvero la caraffella rimaner <lb/>piena, che quasi non credeva a'suoi proprii occhi. </s>

<s>Volle che ivi, <lb/>prima di sciogliere l'Adunanza, fosse fatta l'esperienza col mercurio <lb/>nel consueto strumento torricelliano di cannello assai stretto, e si <lb/>vide il liquido, solido ridursi ai 27 e 28 pollici, rimaner sostenuto <lb/>a 52 e talvolta anco infino a 75. </s></p><p type="main">

<s>A spiegar questo e altri simili fatti straordinari, fra'quali quello <lb/>di due lastre di vetro che seguitano ad aderire nel vuoto, l'Huy&shy;<lb/>ghens, ne'suoi <emph type="italics"/>Esperimenti fisici,<emph.end type="italics"/> si ridusse ad ammetter che sotto <lb/>la campana della macchina pneumatica, estratta l'aria, rimanesse <lb/>un corpo pi&ugrave; ponderoso di lei, l'etere, causa straordinaria di quegli <lb/>effetti (Opera Varia, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>769-76). </s></p><p type="main">

<s>Era dunque il Newton sopra pensiero di trovare argomenti, <lb/>onde render probabile, se non dimostrata la reciproca attrazione <lb/>fra le minime particelle de'corpi, e applicarla a spiegare i fatti <lb/>della diffrazion della luce, da lui stesso confermati con nuovi espe&shy;<lb/>rimenti; quando gli occorse di tornar sopra con maggiore atten&shy;<lb/>zione all'esperienza ugeniana ora narrata, e sopra l'ipotesi imma&shy;<lb/>ginata per ispiegarla. </s>

<s>Quell'ipotesi dell'etere ponderoso, che riman <lb/>dopo estratta l'aria, era merce introdotta dal Cartesio antivacuista, <lb/>e l'Huyghens la gabell&ograve; perch&egrave; favoriva le teorie, che insiem con <lb/>l'Hook professava intorno alla luce. </s>

<s>Al Newton per&ograve; a cui l'ipotesi <pb xlink:href="020/01/249.jpg" pagenum="230"/>dell'etere ponderante sapeva dell'immaginario, venne in pensiero <lb/>che il sostenersi i liquidi ne'cannelli stretti sopra il naturale livello <lb/>dipendesse piuttosto da quella attrazion molecolare, di cui andava <lb/>sagacemente investigando argomenti, che servissero di prova spe&shy;<lb/>rimentale. </s></p><p type="main">

<s>E non questi fatti soli, ma tutta la serie percorse dei cos&igrave; detti <lb/>fenomeni capillari, che ritrovaron tutti la loro adeguata ragione <lb/>nell'attrarsi vicendevolmente le molecole fra solidi e liquidi. </s>

<s>Lo <lb/>stesso agglomerarsi delle minime gocciole dell'acqua, o campate <lb/>libere in aria o posate sopra superficie a cui il liquido non aderisce, <lb/>serv&igrave; al Newton di valido argomento a dimostrar l'effetto dell'at&shy;<lb/>trazione molecolare prevalente intorno al centro di figura. </s>

<s>Niccol&ograve; <lb/>Aggiunti aveva introdotto un <emph type="italics"/>moto occulto<emph.end type="italics"/> dell'acqua, senza per&ograve; <lb/>determinare la natura di questo moto. </s>

<s>Donato Rossetti era gi&agrave; ri&shy;<lb/>corso a un <emph type="italics"/>istinto di appetenza,<emph.end type="italics"/> col quale felicemente spiegava <lb/>alcuni fatti de'pi&ugrave; singolari, ma il Filosofo inglese generalizz&ograve; la <lb/>teoria delle forze attrattive molecolari e la rend&egrave; compiuta colla <lb/>dualit&agrave; contrapposta delle repulsioni &ldquo; Et sicut in algebra ubi quan&shy;<lb/>titates affermativae evanescunt et desinunt, ibi negativae incipiunt; <lb/>ita in mechanicis ubi attractio desinit, ibi vis repellens succedere <lb/>debet &rdquo; (Optices, Lib. </s>

<s>III, quaest. </s>

<s>XXXI). D'onde, soggiunge il <lb/>Newton, ne conseguitano gli effetti della emission della luce e la <lb/>risoluzione de'corpi solidi in sostanze aerose e in vapori, impe&shy;<lb/>rocch&egrave; le particelle de'corpi, distratte o dalla forza del calore o <lb/>dalla agitazione intestina delle fermentazioni, tosto che sono uscite <lb/>dalla sfera dell'attrazione del loro centro, se ne dilungano con <lb/>grand'impeto, e rifuggono di tornarci di nuovo. </s>

<s>Cos&igrave; produconsi <lb/>quelle violente espansioni, che si vedono in tante volgari esperienze, <lb/>parendo impossibile che sia contratta in un granello di polvere <lb/>quell'aria, che s'espande in un volume centinaia e migliaia di volte <lb/>maggiore. </s>

<s>&ldquo; Quae tam ingens contractio et expansio animo sane <lb/>concipi vix potest, si particolae aeris fingantur elasticae et ramosae, <lb/>vel viminum lentorum intra se in circulos intortorum instar esse, <lb/>vel ulla alia ratione, nisi ita si vim repellentem habent, qua a se <lb/>mutuo fugiant &rdquo; (ibi). </s></p><p type="main">

<s>Da queste immortali pagine neutoniane si sente alitare uno <lb/>spirito nuovo che vivifica; si vede aprirsi un chiarore di luce che <lb/>rallegra l'intelletto offuscato dalla nebbia cartesiana. </s>

<s>Anche nella <lb/>scienza del mondo dei piccolissimi, sopra Aristotile, trionfa Platone: <lb/>alle finzioni peripatetiche sottentra la legge matematica. </s>

<s>E perch&egrave; <pb xlink:href="020/01/250.jpg" pagenum="231"/>il mondo dei piccolissimi riconosce il medesimo Autore, e soggiace <lb/>alle medesime leggi del Mondo dei grandissimi, ecco uscire le spe&shy;<lb/>culazioni del Newton dalle angustie che intercedono fra un atomo <lb/>e l'altro, e risalir con ardito volo per gli spazii smisurati del cielo. <lb/></s>

<s>&ldquo; Atque haec quidem omnia si ita sint, iam Natura universa valde <lb/>erit simplex et consimilis sui: perficiens nimirum magnos omnes <lb/>corporum coelestium motus attractione gravitatis, quae est multa <lb/>inter corpora illa omnia, et minores fere omnes particularum sua&shy;<lb/>rum motus alia aliqua vi attrahente et repellente, quae est inter <lb/>particulas illas mutuas &rdquo; (ibi). </s></p><p type="main">

<s>Ecco il discepolo di Platone e di Galileo, che nella semplicit&agrave; <lb/>degli ordini matematici ritrova le leggi universali della natura, fa&shy;<lb/>ticosamente cercate da Aristotile e dal Cartesio nell'arguzie de'loro <lb/>cervelli. </s>

<s>Gian Alfonso Borelli aveva impresse larghe e profonde <lb/>orme per quella via platonica, la quale fu anzi prima aperta da <lb/>lui, introducendo la matematica semplicit&agrave; delle forze centrali. </s>

<s>Ma <lb/>poi, sedotto dall'autorit&agrave; del Keplero, si dette a fantasticare pue&shy;<lb/>rilmente intorno ai pianeti galleggianti nell'etere, e non seppe sco&shy;<lb/>prire il gran paralogismo che commetteva l'Astronomo alemanno, <lb/>quando concludeva che l'intensit&agrave; della luce, al diffondersi della <lb/>quale si rassomigliava il diffondersi delle forze impulsive del sole; <lb/>scemasse a proporzione che crescono le semplici distanze. </s>

<s>E tanto <lb/>fu sottile l'inganno, che vi rimase colto anche il Newton, quando <lb/>la prima volta istitui il calcolo della velocit&agrave;, con cui sarebbe ca&shy;<lb/>duta la Luna, se fosse veramente attratta, com'ei supponeva, al <lb/>centro della Terra. </s></p><p type="main">

<s>Il Bullialdo, procedendo conforme alle vere regole della Foto&shy;<lb/>metria, s'era maravigliato grandemente dell'errore, in che vedeva <lb/>essere incorso il Keplero, e aveva concluso che la luce decresce in <lb/>intensit&agrave;, non a proporzione che crescono le semplici distanze, ma <lb/>i quadrati delle distanze. </s>

<s>E ci&ograve; dette occasione all'Hook e all'Halley <lb/>d'applicar la medesima legge al decrescer l'intensit&agrave; delle forze <lb/>attrattive. </s>

<s>Pervenuta quella notizia alle orecchie del Newton, gli <lb/>parve la nuova legge assai ragionevole, e tornato ad applicarla al <lb/>calcolo della velocit&agrave;, con cui sarebbe verso noi caduta la Luna, <lb/>trov&ograve; che quello stesso calcolo rispondeva esattamente all'ipotesi <lb/>dell'attrazione. </s>

<s>Applicato poi ed esteso, dalla Luna a tutti gli altri <lb/>sistemi, quel principio dell'attrazione divenne universale. </s>

<s>Per ultimo <lb/>suggello, che la semplicit&agrave; e uniformit&agrave; della legge scoperta era <lb/>conforme alla verit&agrave; delle cose, il Newton applic&ograve; quel principio <pb xlink:href="020/01/251.jpg" pagenum="232"/>alla teoria delle comete, alla precessione degli equinozii, alla nu&shy;<lb/>tazione de'poli, al flusso e riflusso del mare, a spiegare insomma <lb/>i pi&ugrave; astrusi e reconditi misteri. </s></p><p type="main">

<s>Porre il flusso marino nel numero de'pi&ugrave; astrusi misteri, non <lb/>parr&agrave; alieno dal vero a chi ripensi quanto sottilmente vi stillassero <lb/>attorno il cervello i filosofi, da Aristotile a Galileo, e come tutti <lb/>rimanessero lontani dal coglier nel segno. </s>

<s>Non sentenzierebbe per&ograve; <lb/>in conformit&agrave; del vero storico colui, che volesse ancora seguitare <lb/>a dire essere stato il Newton il primo a risolvere l'astruso pro&shy;<lb/>blema col principio universale dell'attrazione. </s>

<s>Era infino dal 1624 <lb/>apparita in Roma alla luce una Dissertazione di poche pagine, che <lb/>portava in fronte il titolo di <emph type="italics"/>Euripus,<emph.end type="italics"/> e sottoscritto il nome di un <lb/>Autore, appellato dal Newton stesso ad altro proposito <emph type="italics"/>Vir celeber&shy;<lb/>rimus.<emph.end type="italics"/> Quell'Autore &egrave; Marcantonio De Dominis, Arcivescovo di Spa&shy;<lb/>latro, &egrave; quel <emph type="italics"/>certo prelato,<emph.end type="italics"/> di cui parla Galileo nella IV Giornata <lb/>de'Due Massimi Sistemi. </s>

<s>L'aver ivi taciuto il nome dell'uomo <lb/>celeberrimo, e l'aver commesso di parlarne e di darne giudizio a <lb/>Simplicio, sarebbe segno di disprezzo, se non &egrave; piuttosto una scusa <lb/>dell'esser temerariamente entrato a sentenziare di una dottrina, <lb/>senza aver letto colla debita attenzione il libro. </s>

<s>Che quel Simplicio <lb/>galileiano infatti non abbia veramente letto l'<emph type="italics"/>Euripus<emph.end type="italics"/> dello Spala&shy;<lb/>trese, par chiaro dall'apporgli un errore, che non si trova a parer <lb/>nostro in nessuna parte di quel Trattato, ed &egrave; che, la Luna abbia <lb/>potere d'attrar l'acqua marina agli antipodi, <emph type="italics"/>per aver ella possanza <lb/>di conferire una tal facolt&agrave; a quel grado del zodiaco che gli &egrave; <lb/>opposto<emph.end type="italics"/> (Alb. </s>

<s>I, 458). </s></p><p type="main">

<s>Il Newton che pure, a proposito dell'Iride celeste, citava il <lb/>Trattato <emph type="italics"/>De radiis visus et lucis<emph.end type="italics"/> senz'averlo letto, &egrave; probabilissimo <lb/>che non vedesse del nostro Autore nemmen questa <emph type="italics"/>Sentenza<emph.end type="italics"/> sul <lb/>flusso marino, ma &egrave; mirabile in ogni modo, il riscontro che &egrave; fra <lb/>le dottrine del Filosofo inglese e quelle stesse che il nostro Dalmata <lb/>professava un mezzo secolo avanti. </s>

<s>L'intumescenza e delumescenza <lb/>dell'acqua marina non &egrave; per lui, come da molti si diceva, un ef&shy;<lb/>fetto di condensazione o di rarefazione &ldquo; Sed vere fieri motu locali <lb/>aquae, eiusque a loco ad locum vera confluentia et refluentia &rdquo; <lb/>(Euripus, Romae, 1624, pag. </s>

<s>10). Il quale effetto non &egrave; dal calore <lb/>del sole, ma dalle due virt&ugrave; insieme congiunte del Sole e della <lb/>Luna, i quali due corpi celesti attraggon con varia intensit&agrave; l'acqua <lb/>marina, a quel modo che il magnete attrae a s&egrave; il ferro, e, se non <lb/>gli si congiunge con immediato contatto, par che pure lo renda <pb xlink:href="020/01/252.jpg" pagenum="233"/>pi&ugrave; leggero. </s>

<s>&ldquo; Si enim Magnes, hoc est terra quaedam crassa et <lb/>rudis, mirabili illa sua vi naturali et qualitate non occulta, sed <lb/>quoad effectum omnibus manifestissima, trahit ad se ferrum ex una <lb/>parte, ex alia vero opposita id a se propellit et amovet; cur ali&shy;<lb/>quid simile esse in coelestibus illis corporibus multo nobilioribus, <lb/>et efficacioribus negabimus? </s>

<s>&rdquo; (ibi, pag. </s>

<s>4). Da ci&ograve; ne segue che <lb/>concorrendo insieme il Sole e la Luna a produr l'effetto, bench&egrave; <lb/>questa sia assai pi&ugrave; efficace e potente di quello, l'effetto stesso <lb/>varier&agrave; al variar gli aspetti de'due astri, secondoche, cio&egrave;, la Luna <lb/>sar&agrave; in congiunzione col Sole o nell'opposizione o nelle quadrature. <lb/></s>

<s>&ldquo; Cum enim non sola Luna sed etiam Sol, pro suo modulo, suum <lb/>culmen, licet minorem efficiat, ex diversis aspectibus, qui sunt inter <lb/>solem et lunam, maior et minor fieri debet fluxus et refluxus &rdquo; <lb/>(ibi, pag. </s>

<s>59). </s></p><p type="main">

<s>Dir che il De Dominis risolva il problema, con quella sicurt&agrave; <lb/>e con quella pienezza che lo risolve il Newton, sarebbe troppo pre&shy;<lb/>tendere. </s>

<s>Lo Spalatrese attribuisce l'intumescenza marina a una <lb/>forza attrattiva, simile a quella che si vede operar nel Magnete, <lb/>ma di una tal forza non conosce la legge, e perci&ograve;, fatto certo <lb/>dall'esperienze che nel produr l'effetto la Luna &egrave; pi&ugrave; potente, non <lb/>sa veder di ci&ograve; la ragione in altro, che in una simpatia per gli <lb/>umidi maggior in lei che nel Sole. </s>

<s>&ldquo; Luna enim habet longe ma&shy;<lb/>iorem sympathiam cum humidis quam Sol &rdquo; (ibi, pag. </s>

<s>10). Questo <lb/>&egrave; senza dubbio un ridursi ai peripatetici alloggiamenti, ma &egrave; del <lb/>resto, dal nostro Autore, il flusso e riflusso marino esaminato con <lb/>tanta diligenza, e i molteplici casi dispersi ridotti con tanta potenza <lb/>di raziocinio a trovar la loro spiegazione in una causa generale e <lb/>suprema; che se si fossero degnati di leggere queste cose Galileo <lb/>e il Newton ne dovrebbero esser rimasti ammirati, e avrebbero <lb/>cos&igrave; tramandato ai posteri la memoria di un Libro, che meritava <lb/>di superar la fama di suo fratello, essendo il De Dominis proceduto <lb/>per la pi&ugrave; diritta via in investigar la causa del flusso del mare, <lb/>che non quella della vista e dell'arco baleno. </s></p><p type="main">

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

<s>L'Huyghens disegn&ograve; maestrevolmente, in brevi tratti, nel II Li&shy;<lb/>bro del suo <emph type="italics"/>Cosmoteoro<emph.end type="italics"/> i progressi storici della Meccanica celeste. </s>

<s><lb/>Plutarco, nel suo Libro <emph type="italics"/>De facie in orbe Lunae,<emph.end type="italics"/> aveva detto che <pb xlink:href="020/01/253.jpg" pagenum="234"/>la Luna riman sospesa nello spazio, per l'equilibrio della sua forza <lb/>di circolazione con quello di gravit&agrave;; dottrina che fu seguita poi <lb/>dal Borelli, e applicata al moto di tutti i satelliti, e di tutti i pia&shy;<lb/>neti. </s>

<s>Il Newton dimostr&ograve; matematicamente le leggi di que'moti, e <lb/>fece veder che i fatti osservati dal Keplero erano una conseguenza <lb/>immediata di quelle leggi. </s>

<s>Io poi, soggiunge l'Huyghens, immaginai <lb/>un ipotesi, da investigar la prima causa e i primi impulsi de'moti <lb/>planetari, per via de'vortici eterei, che son tutt'altra cosa da quelli <lb/>cartesiani. </s>

<s>Anzi, io mi maraviglio, come mai il Filosofo bretone <lb/>possa avere sciupato il suo tempo in dare assetto a quelle sue <lb/>strane finzioni &ldquo; De planetarum et mundi origine commentatio <lb/>apud Cartesium tam levibus rationibus contexta est, ut saepe mirer <lb/>tantum operae in talibus concinnandis figmentis eum impendere <lb/>potuisse &rdquo; (Op. </s>

<s>varia, Lugd. </s>

<s>1724, pag. </s>

<s>721). La grande Opera dei <lb/>Principii matematici della Filosofia Naturale dissip&ograve; quel fantastico <lb/>edifizio cartesiano, e pos&ograve; la Nuova Astronomia sopra i suoi pi&ugrave; <lb/>solidi fondamenti. </s>

<s>Tutto il mistero dei Grandissimi fu allora svelato <lb/>dal Filosofo inglese, e i posteri non hanno fatto altro che confer&shy;<lb/>mare quelle scoperte, e ampliarle nell'Astronomia fisica o nella <lb/>Uranografia, di cui il merito &egrave; dovuto principalmente a quella per&shy;<lb/>fezione, a che l'arte, meglio che la scienza, ha saputo condurre i <lb/>canocchiali. </s></p><p type="main">

<s>Ma il Newton, come da noi s'accennava di sopra, aveva prima <lb/>scoperto il mondo dei Piccolissimi, intorno a che il Cartesio e il <lb/>Gassendo eran venuti a gara delle pi&ugrave; sottili e stravaganti finzioni. </s>

<s><lb/>Cos&igrave; fatte finzioni son quelle stesse, che illudevano il grande in&shy;<lb/>gegno del Borelli, quando, per esempio, a spiegar gli effetti di <lb/>capillarit&agrave;, da lui stesso scoperti ne'corpiccioli galleggianti, im&shy;<lb/>maginava quella lanugine e que'cigli flessibili, con cui, s&ugrave; per le <lb/>asperit&agrave; de'corpi solidi attaccandosi, potessero risalir sul naturale <lb/>livello le minime particelle dell'acqua. </s>

<s>Il Newton, come fece pel <lb/>Mondo dei Grandissimi, disperse anco quest'altre filosofiche finzioni, <lb/>introducendo il principio delle forze molecolari. </s>

<s>A ci&ograve; fare egli <lb/>attese in quelle celebri Questioni, che, ridotte al numero di XXXI, <lb/>nella seconda edizione dell'Ottica, appose in fine del suo Trattato. </s>

<s><lb/>Tali Questioni, bench&egrave; possano essere facilmente sfuggite, per il <lb/>modesto luogo che fu loro assegnato e per l'umile veste, alla debita <lb/>estimazione dei dotti, hanno nulladimeno tutta l'importanza, ch'ebbe <lb/>la grande Opera de'<emph type="italics"/>Principii.<emph.end type="italics"/></s></p><p type="main">

<s>A noi piace di rassomigliare i due libri del Filosofo inglese <pb xlink:href="020/01/254.jpg" pagenum="235"/>a'due strati estremi di una profonda acqua corrente. </s>

<s>Quello dei <lb/>Principii della Filosofia, in cui le leggi del Grandissimo Mondo si <lb/>risolvono nell'unico principio delle forze centrali, rappresenta lo <lb/>strato pi&ugrave; alto, e pi&ugrave; largamente visibile della corrente; quell'altro, <lb/>che &egrave; il libro delle <emph type="italics"/>Questioni,<emph.end type="italics"/> e in cui le leggi del Piccolissimo <lb/>Mondo si risolvono nell'unico principio delle forze molecolari, rap&shy;<lb/>presenta lo strato pi&ugrave; basso, e men visibile della medesima corrente. </s>

<s><lb/>Questo strato, quasi soffrisse la compressione de'soprastanti, con&shy;<lb/>tiene in s&egrave; strettamente condensate e contratte le nuove parti di <lb/>scienza sperimentale, che si videro svolgere e fluire nel secolo XVIII. <lb/>Anzi, come gli strati intermedii delle acque correnti son rapiti e <lb/>accelerati per la comunicazione del moto de'due strati estremi; <lb/>cos&igrave; da que'due strati estremi de'Principii neutoniani e delle Que&shy;<lb/>stioni, in mezzo a cui corre, vien rapita e accelerata, in questo <lb/>nuovo tratto de'suoi progressi, la larga e alto sonante fiumana della <lb/>Scienza. </s></p><p type="main">

<s>Gran parte della scienza sperimentale, che si volge e corre giu <lb/>per questa fiumana, &egrave;, per la nobilt&agrave; sua propria e per l'impor&shy;<lb/>tanza e l'utilit&agrave; delle applicazioni, l'Idraulica. </s>

<s>Il potente impulso, <lb/>che ella ricevette nella scuola galileiana per opera del Guglielmini, <lb/>era per se sufficiente a promuoverla ne'suoi progressi, senz'altri <lb/>estrinseci aiuti; nonostante risent&igrave; anch'essa i benefici influssi delle <lb/>dottrine neutoniane, influssi, che si posson rassomigliare a quel&shy;<lb/>l'aura di vento, che, secondando il moto della corrente, giova a <lb/>velocitare la piena di un fiume. </s></p><p type="main">

<s>Giovan Domenico Guglielmini, gi&agrave; l'abbiamo accennato, ap&shy;<lb/>partiene alla scuola galileiana, nella quale fu allevato dal Montanari, <lb/>discepolo del Borelli. </s>

<s>Egli aveva gi&agrave;, il Guglielmini, in sul finir del <lb/>secolo XVII, diffuso in Bologna il suo magistero ne'varii ordini <lb/>delle scienze sperimentali, quand'ancora il sole della nuova Filo&shy;<lb/>sofia inglese non era apparito sul nostro orizzonte. </s>

<s>Il Guglielmini <lb/>perci&ograve; appartiene al periodo storico precedente, e in quella parte <lb/>del Dramma si svolge la sua azione, ond'&egrave; che tutt'altro che ricever <lb/>beneficio all'ingegno dalle nuove dottrine neutoniane, &egrave; ragionevole <lb/>pensar che il Newton stesso s'ispirasse in parte alle speculazioni di <lb/>lui, e se ne giovasse nelle aggiunte alle succissive impressioni dei <lb/>suoi libri. </s>

<s>Senz'ammetter ci&ograve;, non si potrebbero attribuire ad altro <lb/>che al caso que'mirabili riscontri, che si notano fra certe idee <lb/>espresse negli opuscoli minori del nostro Filosofo di Bologna, e <lb/>certe altre idee simili, che balenano qua e l&agrave; per le Questioni del <pb xlink:href="020/01/255.jpg" pagenum="236"/>Filosofo di Cambridge. </s>

<s>Alcuni di que'riscontri ci occorreranno a <lb/>notare in questo stesso Discorso, ma giova intanto intrattenerci <lb/>brevemente sopra quegli argomenti, da cui si conclude che, in <lb/>Idrometria, le speculazioni del Newton prendevano probabilmente <lb/>l'indirizzo da quelle del Guglielmini. </s></p><p type="main">

<s>Fra i Principii matematici della Filosofia Naturale non pote&shy;<lb/>vano non trovar luogo quelli concernenti le leggi del moto, con cui <lb/>l'acque fluiscono dai fori aperti ne'vasi. </s>

<s>La proposizione XXXVII <lb/>infatti del secondo Libro di que'Principii, conforme alla prima <lb/>edizione che fu fatta nel 1686, ha per soggetto il problema degli <lb/>efflussi, che dall'Autor si risolve pi&ugrave; coi calcoli arguti, che coll'ap&shy;<lb/>plicarvi le leggi del moto dei gravi. </s>

<s>Nella successiva edizione, che <lb/>&egrave; del 1713, l'Autore introduce, in questa parte del suo Libro, una <lb/>notabilissima riforma. </s>

<s>La proposizione de'flussi, ricorre in ordine <lb/>al numero XXXVI, e vi si professa espressamente il principio, che <lb/>le velocit&agrave; de'liquidi nel fluire da'fori de'vasi, son proporzionali <lb/>alle radici delle altezze. </s>

<s>Cos&igrave; fatto principio &egrave; concluso da'teoremi <lb/>galileiani della caduta de'gravi, riscontrati di fatto ne'pi&ugrave; squisiti <lb/>esperimenti. </s>

<s>Da'teoremi sui proietti conclude il Newton che gli <lb/>zampilli obliqui descrivono tutti una parabola, il parametro della <lb/>quale varia secondo la varia distanza che passa, tra la superficie <lb/>del liquido, e il centro dell'apertura del vaso. </s>

<s>Misurati diligente&shy;<lb/>mente questi parametri e attendendo agli effetti della resistenza <lb/>dell'aria e della contrazion della vena, trovava che gli zampilli <lb/>parabolici rispondevan prossimamente alle traiettorie che sarebbero <lb/>state descritte da un grave gettato con quell'impeto, che avrebbe <lb/>conceputo nel cadere da tanta altezza, quanta &egrave; quella del liquido <lb/>sul centro del foro, da cui fluisce. </s>

<s>Questo, che fu tentato anche dai <lb/>nostri Accademici del Cimento, &egrave; senza dubbio il pi&ugrave; diretto, ma <lb/>il pi&ugrave; difficile modo d'eseguir l'esperienza: difficolt&agrave;, che dalla sola <lb/>raffinatissima arte del Newton sarebbesi potuta superare. </s></p><p type="main">

<s>Insistendo sempre sull'applicazione de'teoremi galileiani, il <lb/>nostro Autore conclude teoricamente, a modo del Torricelli, e spe&shy;<lb/>rimentalmente conferma che gli zampilli verticali risalgono s&ugrave; con <lb/>l'impeto stesso dovuto alla caduta, e soggiunge appresso che la <lb/>quantit&agrave; del moto si dee misurar dal prodotto della sezione del <lb/>foro, per il doppio della colonna e non per la semplice colonna del <lb/>liquido sopraincombente. </s>

<s>Le controversie insorte in tal proposito <lb/>fra il Jurin e il Michelotti, son notabili nella storia, ma pure il <lb/>Newton, professando quel principio, non faceva altro pi&ugrave; che appli-<pb xlink:href="020/01/256.jpg" pagenum="237"/>care al moto de'fluidi il primo de'Teoremi dimostrati, nel III Dia&shy;<lb/>logo, da Galileo, dovendo l'acqua, in conformit&agrave; di questo teorema, <lb/>passar con moto equabile un doppio spazio di quello che ha pas&shy;<lb/>sato in cader dalla superficie e scender fino a fluire dall'apertura <lb/>del vaso. </s>

<s>E bench&egrave; i nostri Accademici fiorentini, come si par dai <lb/>loro Manoscritti, avessero gi&agrave; fatte osservazioni e sperimenti in pro&shy;<lb/>posito, nonostante &egrave; il primo il Newton a descrivere, in quella stessa <lb/>Proposizione citata, il contrarsi della vena all'esito, e il formarsi <lb/>della <emph type="italics"/>cateratta<emph.end type="italics"/> alla superficie del liquido. </s>

<s>In occasione di questa <lb/>cateratta, osserva Eustachio Manfredi, nella Annotazione alla pro&shy;<lb/>posizione VI del I Libro della <emph type="italics"/>Natura dei fiumi,<emph.end type="italics"/> che il Guglielmini <lb/>l'aveva gi&agrave; descritta e matematicamente considerata, nel IV e V Li&shy;<lb/>bro della sua <emph type="italics"/>Misura delle acque correnti.<emph.end type="italics"/> Esamineremo a suo luogo <lb/>cos&igrave; fatta osservazione del Manfredi, ma intanto, ripensando a ci&ograve; <lb/>che potesse aver dato occasione al Newton di ritornare ai prin&shy;<lb/>cipii idrometrici professati dagl'Italiani, ci occorre alla memoria il <lb/>Trattato della Misura delle Acque correnti, citato ora dallo stesso <lb/>Manfredi. </s></p><p type="main">

<s>Il d&igrave; 19 Novembre 1690, Antonio Magliabechi, celebre biblio&shy;<lb/>tecario in Firenze, annunziava al Granduca d'aver da qualche giorno <lb/>ricevuto, dal signor Guglielmini, un libro intitolato <emph type="italics"/>Aquarum fluen&shy;<lb/>tium mensura nova methodo inquisita<emph.end type="italics"/> stampato a Bologna (MSS. <lb/>Gal. </s>

<s>Cim. </s>

<s>T. XXI, c. </s>

<s>16), e il 27 Ottobre 1691, lo stesso Magliabechi <lb/>annunziava d'aver ricevuto l'altra parte del libro (ivi, c. </s>

<s>18). Ci&shy;<lb/>tiamo questi documenti bibliografici, per dir che la prima parte, <lb/>ossia i primi tre libri della Misura delle Acque correnti furono <lb/>pubblicati nel 1690, e gli altri tre l'anno dopo. </s>

<s>L'Autore di quel&shy;<lb/>l'Opera si assumeva un difficile incarico, qual'era quello di decider <lb/>se la velocit&agrave; delle acque correnti seguiva la legge ammessa dal <lb/>Castelli e confermata dalla grande autorit&agrave; del Cassini, o seguiva <lb/>l'altra dimostrata dal Torricelli, e confermata in tanti modi poi dal <lb/>Viviani. </s>

<s>Il Guglielmini s'affid&ograve; a quella maniera di sperimenti, che <lb/>sembrano men soggetti ad errori di tutti gli altri, e de'quali il <lb/>Magiotti per il primo aveva dato gli esempii. </s>

<s>Perci&ograve;, dalla quantit&agrave; <lb/>dell'acqua raccolta, in determinati tempi, dal flusso di un vaso, <lb/>concludeva le sue esperienze riscontrar colla legge professata dal <lb/>Torricelli. </s>

<s>Il Guglielmini veniva altres&igrave;, con questo libro, a intro&shy;<lb/>durre nell'ldrometria le <emph type="italics"/>velocit&agrave; medie,<emph.end type="italics"/> senza l'uso delle quali ri&shy;<lb/>manevano incerte tutte le proposizioni dimostrate prima di lui dal <lb/>Castelli. </s></p><pb xlink:href="020/01/257.jpg" pagenum="238"/><p type="main">

<s>Dietro ci&ograve;, par probabile anche a noi ci&ograve; che accennavasi dal <lb/>Manfredi, ed &egrave; che il Newton, dal 1686 al 1713, nel quale spazio <lb/>di tempo si divulg&ograve; l'Opera del Guglielmini, potesse aver riformate <lb/>le sue idee, intorno alla legge della velocit&agrave; delle acque correnti, <lb/>e potesse anche aver preso occasione di rivolgersi a considerare la <lb/>cateratta, da ci&ograve; che ne trov&ograve; scritto dall'Autore, nell'Opera stessa <lb/><emph type="italics"/>Aquarum fluentium Mensura.<emph.end type="italics"/></s></p><p type="main">

<s>Con questa, e con le <emph type="italics"/>Lettere idrostatiche<emph.end type="italics"/> contro il Papin, nelle <lb/>quali si dimostra ad evidenza in che modo, per la pressione am&shy;<lb/>mosferica, s'alterino le leggi del moto dell'Acque, ne'tubi chiusi, il <lb/>Guglielmini si preparava a dar mano all'altra insigne opera <emph type="italics"/>Della <lb/>Natura de'fiumi,<emph.end type="italics"/> in cui, riducendo a un unico principio lo stabi&shy;<lb/>lirsi degli alvei, parve non meritar lode minore del Newton, che <lb/>a un principio unico aveva pure ridotto lo stabilirsi, nella regolare <lb/>perpetuit&agrave; degli orbi, i moti di tutti i pianeti. </s></p><p type="main">

<s>Cos&igrave;, l'Idraulica, indipendentemente da qualunque insegna&shy;<lb/>mento straniero, si serb&ograve; schiettamente italiana, ma, promossa dai <lb/>discepoli e dai seguaci del Guglielmini, sent&igrave; pure, nel secolo XVIII, <lb/>qualche benefico influsso dai nuovi metodi e dalle nuove dottrine <lb/>neutoniane. </s>

<s>Uno dei principali fra questi benefizii fu quello del per&shy;<lb/>suadersi che fecero gli Idraulici italiani essere una reale tegnenza <lb/>fra le minime particelle dell'acqua; tegnenza che, con pi&ugrave; grave <lb/>danno di quel che non si crederebbe, Galileo le avea negata. </s>

<s>Il <lb/>Guglielmini rimedi&ograve; felicemente al danno, proseguendo gli inse&shy;<lb/>gnamenti del maestro suo Geminiano Montanari, che avrebbe potuto <lb/>arricchire la scienza di un nuovo e impertantissimo Trattato sulla <lb/><emph type="italics"/>Natura dei fluidi,<emph.end type="italics"/> se non l'avesse il Senato distratto in costruir <lb/>nuovi mulini, da arricchire il pubblico erario e i mercanti di seta <lb/>bolognesi (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLV, c. </s>

<s>230). Nonostante, nella pri&shy;<lb/>vata Accademia dell'Ab. </s>

<s>Sampieri, ei fu il primo a richiamar l'at&shy;<lb/>tenzione de'fisici, non sulla sola viscosit&agrave; dell'acqua, ma sulle pro&shy;<lb/>porzioni che questa ha colla viscosit&agrave; degli altri liquidi. </s>

<s>Le nuove <lb/>ricerche sperimentali ebbero occasione dall'avere osservato <emph type="italics"/>che li <lb/>corpi gravi discendono pi&ugrave; velocemente per l'acqua comune, che <lb/>per l'acquavite e per l'olio<emph.end type="italics"/> (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XIX, c. </s>

<s>69) ci&ograve; che <lb/>fu sospettato dipendere dalla viscosit&agrave; maggiore in questi due li&shy;<lb/>quidi e in altri simili, che no nell'acqua. </s></p><p type="main">

<s>A queste esperienze, fatte nel 1667, non sar&agrave; stato presente il <lb/>Guglielmini, che aveva allora dodici anni, ma le avr&agrave; apprese in <lb/>seguito dal Maestro, per applicarle, come poi fece, a spiegar la <pb xlink:href="020/01/258.jpg" pagenum="239"/>natura e gli effetti del filone nella corrente, non che a mostrar <lb/>l'efficacia, che gli strati superiori di essa hanno in promuovere le <lb/>velocit&agrave; degli strati inferiori. </s>

<s>Nonostante, il principio della viscosit&agrave; <lb/>dell'acqua ammesso dal Guglielmini, e applicato alla Natura dei <lb/>fiumi, non aveva altro valor che di un ipotesi, appoggiata ai fatti <lb/>osservati nella sperimentale Accademia bolognese; fatti, e il Mon&shy;<lb/>tanari stesso non lo nega, che potevano anche dipendere da tutt'altra <lb/>cagione. </s></p><p type="main">

<s>Come ipotesi, perci&ograve;, quella della viscosit&agrave; dell'acqua fu nuo&shy;<lb/>vamente cacciata via dalla scienza, per la grande autorit&agrave; di uno <lb/>scrittore, che succede in tempo e in dignit&agrave; al Guglielmini, il p. </s>

<s>abate <lb/>Guido Grandi, il quale, troppo matematico e troppo ossequioso a <lb/>Galileo, ne illustra, nel suo Trattato del <emph type="italics"/>Movimento dell'acque,<emph.end type="italics"/> le <lb/>dottrine, e ne commenta insieme gli errori. </s>

<s>Cacciare un errore in&shy;<lb/>trodotto nella scienza da una tanta autorit&agrave;, qual'era quella di Ga&shy;<lb/>lileo, non sembrava possibile che a un'altra autorit&agrave; di pari grado, <lb/>e tale era appunto quella del Newton, dalla nuova filosofia del quale <lb/>si concludeva la viscosit&agrave; dell'acqua e di tutti gli altri liquidi, <lb/>com'un effetto naturalissimo dell'attrazione molecolare. </s>

<s>Cosi l'ipo&shy;<lb/>tesi del Montanari, seguita dal Guglielmini, torn&ograve; in quasi certezza <lb/>di matematica conclusione e Paolo Frisi, uno de'pi&ugrave; illustri seguaci <lb/>dello stesso Guglielmini, fu primo a risentire questi benefici effetti <lb/>della Filosofia neutoniana, applicando il principio della viscosit&agrave; <lb/>dell'acqua a spiegar quel particolar fatto dell'accelerarsi della cor&shy;<lb/>rente, che si design&ograve; col nome di <emph type="italics"/>chiamata allo sbocco,<emph.end type="italics"/> e intro&shy;<lb/>ducendo quello stesso principio nel general modo di regolare i <lb/>Fiumi e i torrenti, di che arricch&igrave; la scienza di un Trattato diviso <lb/>in tre libri. </s></p><p type="main">

<s>Questo, d'aver per sempre sconfitto un errore, che cacciato la <lb/>prima volta minacciava, coll'autorit&agrave; di Galileo, di tornare a in&shy;<lb/>vadere dannosamente la scienza, fu uno de'principali, ma non il <lb/>solo de'benefizii, che venisse all'Idraulica dalla Filosofia neutoniana. </s>

<s><lb/>Altro rilevantissimo benefizio provenne dagli impulsi efficaci e dai <lb/>luminosi esempi, che dava il Newton a trattar de'moti delle acque <lb/>correnti co'metodi analitici, e col buon uso di comporre e di risolver <lb/>le forze. </s>

<s>Il Guglielmini, n&egrave; nel Trattato Della Misura delle acque <lb/>correnti, n&egrave; in quell'altro Della Natura de'fiumi, non s'era dilun&shy;<lb/>gato un passo dagli antichi metodi galileiani, e occorrendogli di <lb/>dover assegnar la direzione e misurar la quantit&agrave; di forza risultante <lb/>dal comporsi insieme due correnti, una delle quali confluisce con <pb xlink:href="020/01/259.jpg" pagenum="240"/>l'altra, incespica e s'avvolge ne'paralogismi stessi del Maestro suo <lb/>Montanari, a cui, in determinar la natura e il moto della Corrente <lb/>adriatica e delle correnti marine in generale, tanto nocquero quei <lb/>meccanici paralogismi. </s></p><p type="main">

<s>Primo a lasciar le vie vecchie, per seguitare le nuove, in trattar <lb/>del moto dell'acque, fu Bernardino Zendrini, che in comporre il <lb/>suo Trattato, a cui di&egrave; il titolo di <emph type="italics"/>Leggi e fenomeni, regolazioni ed <lb/>usi delle acque correnti,<emph.end type="italics"/> dava opera nel 1739 (Firenze 1770, pag. </s>

<s>49). <lb/>Chi legge la Prefazione al libro, s'accorge tosto che l'Autore intro&shy;<lb/>duceva, col metodo analitico, una novit&agrave; nella scienza italiana, e <lb/>perci&ograve; intrattien, fin da principio, i lettori, studiandosi di persua&shy;<lb/>derli ad accogliere una tal novit&agrave;, e a voler fare la giusta stima <lb/>de'vantaggi di lei. </s>

<s>Fu pure il Zendrini stesso de'primi, che, fattosi <lb/>oramai seguace de'nuovi metodi neutoniani, mostrasse il retto uso <lb/>che doveva farsi della composizione e risoluzion delle forze, colla <lb/>regola del parallelogrammo. </s>

<s>Vero &egrave; che di ci&ograve; i primi esempi erano <lb/>stati dati dal Grandi, ma fu il nostro Matematico della Serenissima <lb/>Repubblica di Venezia che, richiamandosi giusto a una proposizione <lb/>dimostrata dallo stesso Grandi, not&ograve;, il primo, un gravissimo errore, <lb/>sfuggito a tutti i censori, in che era incorso il Michelini; errore, <lb/>che consisteva nello scambiar con una delle componenti la resul&shy;<lb/>tante di quella forza, con che le acque scavano il fondo dei fiumi. </s></p><p type="main">

<s>Noi riconosciamo anche questo per uno di quei gran benefizi <lb/>derivati alla scienza italiana, nel secolo XVIII, dagli esempi dei <lb/>metodi neutoniani, non solamente, perch&egrave; la prima edizione dei <lb/>Principii matematici di Natural Filosofia preced&egrave; di un anno il <lb/>progetto della <emph type="italics"/>Nouvelle mechanique<emph.end type="italics"/> del Varignon, pubblicata po&shy;<lb/>stuma nel 1725, ma, perch&egrave;, com'ad altro proposito si diceva pi&ugrave; <lb/>sopra, a sradicar dalle menti degli Italiani l'opinion che fosse falso <lb/>il teorema dell'Herigonio, opinione invalsa e confermata da due <lb/>grandi autorit&agrave; quali eran quelle di Galileo e del Borelli; ci voleva <lb/>un'altra autorit&agrave;, che non fosse punto minore, l'autorit&agrave; insomma <lb/>d'Isacco Newton. </s></p><p type="main">

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

<s>Che i metodi della nuova Filosofia neutoniana si riscontrino <lb/>con quegli stessi di Galileo, e che da un tale felicissimo incontro <lb/>ne sien conseguiti i progressi, che fecero le scienze sperimentali <pb xlink:href="020/01/260.jpg" pagenum="241"/>nel secolo XVIII, i lettori ne saranno meglio persuasi dalla verit&agrave; <lb/>delle cose, che dai nostri discorsi. </s>

<s>Giova nonostante osservare che, <lb/>mentre Galileo col suo Platone instituisce la sua Filosofia naturale <lb/>nella regolarit&agrave; geometrica delle forme, ch'ei serenamente contem&shy;<lb/>pla, senza troppo pensare al concorso delle cause, che le hanno <lb/>prodotte; il Newton soggiunge, nella sua Nuova Filosofia, l'opera <lb/>concorrente di quelle cause, che egli riconosce nella gran dualit&agrave; <lb/>delle forze di attrazione e di repulsione. </s>

<s>Di qui &egrave; che il metodo <lb/>neutoniano, bench&egrave; non differisca sostanzialmente da quello di Ga&shy;<lb/>lileo, &egrave; cos&igrave; concluso in una formula nuova: &ldquo; In mathesi investi&shy;<lb/>gandae sunt virium quantitates, et rationes illae, quae ex conditio&shy;<lb/>nibus quibuscumque positis consequentur: deinde, ubi in physicam <lb/>descenditur, conferendae sunt hae rationes cum phaenomenis, ut <lb/>innotescat quaenam virium conditiones singulis corporum attracti&shy;<lb/>vorum generibus competant &rdquo; (Princip. </s>

<s>Lib. </s>

<s>I. </s>

<s>Coloniae 1760, pa&shy;<lb/>gina 464). </s></p><p type="main">

<s>La scienza fisica dunque si riduce, pel Newton, a conoscer la <lb/>natura e l'intensit&agrave; delle forze, non che le condizioni del loro vario <lb/>operare. </s>

<s>E perch&egrave; da queste forze &egrave; commossa ogni minima par&shy;<lb/>ticella componente de'corpi, si vede di qui aprirsi altri campi a <lb/>una fisica nuova, la quale fu detta molecolare, ma che si potrebbe <lb/>pi&ugrave; volgarmente chiamar col nome di fisica sottile. </s>

<s>La legge da <lb/>noi, nella prima Parte di questo Discorso formulata, che l'intelli&shy;<lb/>gibilit&agrave; della forma precede l'intelligibilit&agrave; della materia, e l'in&shy;<lb/>telligibilit&agrave; della materia crassa precede l'intelligibilit&agrave; della ma&shy;<lb/>teria via via pi&ugrave; sottile; qui si vede avverarsi esattamente, essendo <lb/>quelle due nuove parti della Fisica sottile, che si conoscono sotto il <lb/>nome di Elettricismo, e sotto l'altro pi&ugrave; esteso di Chimica, non <lb/>prima venute alla luce, che nel secolo XVIII, come parto e portato <lb/>della nuova Filosofia neutoniana. </s></p><p type="main">

<s>Dappoi che Ottone di Guericke dimostr&ograve;, nel Cap. </s>

<s>XV del <lb/>quarto Libro de'suoi Esperimenti magdeburgici, come tutte le virt&ugrave; <lb/>della materia universale sien rappresentate da una sfera di zolfo, <lb/>confricata colle mani, mentre che celerissimamente &egrave; girata attorno; <lb/>e come quella stessa sfera dia evidenti segni della virt&ugrave; calorifica <lb/>e della lucente; invalse l'opinione che sieno le sostanze sulfuree <lb/>primo e principale elemento del calore e della luce. </s>

<s>Il Guglielmini <lb/>se ne giov&ograve; per cacciar dalla Fisiologia l'errore della <emph type="italics"/>fiamma vi&shy;<lb/>tale,<emph.end type="italics"/> asserendo esser causa del calore negli animali l'agitazione <lb/>delle sostanze sulfuree contenute nel sangue. </s>

<s>Tutti i fenomeni elet-<pb xlink:href="020/01/261.jpg" pagenum="242"/>trici e fosforici, non eccettuati i baleni e le folgori, eran ridotti a <lb/>esalazioni sulfuree, disperse per l'aria e per le sostanze dei corpi. </s>

<s><lb/>N&egrave; da queste stesse idee si dilunga il Newton nell'VIII delle sue <lb/>Questioni. </s></p><p type="main">

<s>S'era intanto osservato che la virt&ugrave; di attrarre i minimi cor&shy;<lb/>piccioli e d'investirli di luce, non era propria a soli i globi di zolfo, <lb/>ma conveniva altres&igrave;, e forse meglio, ai globi o ai cilindri di vetro, <lb/>celermente girati e confricati allo stesso modo. </s>

<s>Cos&igrave;, il globo me&shy;<lb/>tafisico del Guericke dette occasione a costruir le prime macchine, <lb/>per via delle quali, dice il Newton stesso, nella citata Questione: <lb/>&ldquo; vapor electricus, frictione manus e vitro excitatus, et ad cartam <lb/>albam, linteum vel digitum allisus, ita agitabitur, ut lucem continuo <lb/>emittat. </s>

<s>&rdquo; Questo vapore elettrico fu largo e glorioso soggetto al <lb/>Franklin, al Symmer al Nollet d'esperienze e di teorie, ma di cos&igrave; <lb/>fatte teorie quelle che pi&ugrave; giovassero alla scienza, e che furon pi&ugrave; <lb/>tenute in onore, si debbono ai due grandi elettricisti italiani, a <lb/>Giovan Batista Beccaria di Mondov&igrave;, e al comasco Alessandro Volta, <lb/>l'ingegno de'quali il Newton fecond&ograve; con gli spiriti della sua Nuova <lb/>Filosofia. </s></p><p type="main">

<s>Che siano le speculazioni del Fisico monregalese veramente <lb/>avvivate da quelli spiriti, se ne avvede presto ogni lettore che svolge <lb/>i due Libri <emph type="italics"/>Dell'elettricismo artificiale e naturale,<emph.end type="italics"/> avendo quelle <lb/>stesse speculazioni ivi esposte, trovato nell'Autore conforto e scusa <lb/>da una sentenza ch'ei cita dalla XXXI Questione neutoniana (Del&shy;<lb/>l'elettric. </s>

<s>Torino 1753, pag. </s>

<s>40). N&egrave; solo il metodo attinge il Nostro <lb/>a quelle filosofiche fonti, ma il principio altres&igrave;, che informa le sue <lb/>nuove dottrine: principio ch'ei sagacemente ritrova nella parola <lb/>stessa di <emph type="italics"/>vapore,<emph.end type="italics"/> con cui il Newton qualifica la natura propria della <lb/>sostanza elettrica &ldquo; Chiamo, egli dice, vapore elettrico, il fluido che <lb/>ne'corpi elettrizzati seintilla, fa sentire il venticello elettrico, forma <lb/>il fiocco elettrico, e la stelletta elettrica, ritenendo il nome datoli <lb/>da Newton lib. </s>

<s>III Ottica, questione VIII &rdquo; (ivi, pag. </s>

<s>10). Dall'avere <lb/>infatti l'elettricit&agrave; natura di vapore conclude il Beccaria l'esistenza <lb/>e il modo di quell'elettricismo <emph type="italics"/>effluente<emph.end type="italics"/> e di quell'altro elettricismo <lb/><emph type="italics"/>affluente,<emph.end type="italics"/> ambedue costituiti di materie somigliantissime, che egli <lb/>sostituisce all'elettricit&agrave; vitrea e resinosa del Symmer, e all'elet&shy;<lb/>tricit&agrave; positiva e negativa del Franklin. </s></p><p type="main">

<s>Dal riguardar la materia elettrica sotto l'aspetto neutoniano, <lb/>conclude il Nostro una legge unica e universalissima, ci&ograve; che nes&shy;<lb/>suno aveva tentato prima di lui, dalla quale dipende e si regola <pb xlink:href="020/01/262.jpg" pagenum="243"/>una variet&agrave; complicatissima di effetti. </s>

<s>L'applicazione di quella legge <lb/>non fu sempre trovata sufficiente, e talvolta fu scoperta anco fal&shy;<lb/>lace, ma pur conduce spesso l'Autore a incontrarsi in concetti, <lb/>che un secolo e pi&ugrave; dopo, ad alcuni scrittori di elettricit&agrave;, parvero <lb/>nuovi. </s>

<s>Di tali concetti si potrebbe, per esempio, citar quello del <lb/>riconoscer la causa del pi&ugrave; violento irrompere della scarica in quel <lb/>punto, in cui pi&ugrave; si ristringe un cilindro conduttore, nella legge <lb/>di tutti i fluidi in moto applicata alla elettricit&agrave;, che cio&egrave; le velocit&agrave; <lb/>stanno in ragion reciproca delle sezioni, e perci&ograve;, dove la sezione <lb/>&egrave; minima, come nelle punte, ivi il vapore elettrico acquista impeto <lb/>da vincer la resistenza che gli fa l'aria attraversata (ivi, pag. </s>

<s>57). </s></p><p type="main">

<s>Ma il Volta sente penetrarsi anco pi&ugrave; addentro gli spiriti della <lb/>Filosofia neutoniana. </s>

<s>I nuovi scritti sull'<emph type="italics"/>Elettricit&agrave; vindice<emph.end type="italics"/> e sopra <lb/>le <emph type="italics"/>Ammosfere elettriche,<emph.end type="italics"/> pubblicati in seguito alla citata Opera del <lb/>Beccaria, fanno pensare al giovane Fisico di Como che tutto si pu&ograve; <lb/>ridurre a una legge semplicissima, qual'&egrave; quella dell'attrazione, <lb/>intorno a che scriveva un Epistola diretta allo stesso Beccaria col <lb/>titolo: <emph type="italics"/>De vi attractiva ignis electrici.<emph.end type="italics"/> Lo splendido pensiero lo <lb/>aveva, infin dal 1763, comunicato al Nollet, il qual gli rispose pa&shy;<lb/>rergli difficilissimo il poter ridurre i fenomeni elettrici a consentir <lb/>colle leggi dell'attrazion neutoniana. </s>

<s>Ma il Volta soggiunge ch'ei <lb/>non intendeva insistere su quella attrazione universale &ldquo; quae est <lb/>massae proportionalis, et decrescit in ratione duplicata distantiarum, <lb/>qua nimirum et corpora adducuntur in centrum et Planetae in <lb/>eorum orbitis continentur &rdquo; (Opere, Firenze 1816, T. I. p. </s>

<s>6). Oltre <lb/>di questa, soggiunge, vi &egrave; un altro genere di attrazione, che inter&shy;<lb/>cede fra le minime particelle de'corpi, e da cui hanno origine <lb/>effetti particolari. </s>

<s>Sono indizio manifesto e argomento certo di cos&igrave; <lb/>fatto genere di attrazione, le riflessioni e le rifrazioni della luce, <lb/>con tutte le varie specie di fenomeni capillari &ldquo; quod quidem vel <lb/>in sola postrema Quaestione Opticae Newtoni abunde patet &rdquo; (ibi, <lb/>pag. </s>

<s>7). Cosi, viene a concluder che, non ammettendo queste forze <lb/>attrattive, &egrave; impossibile trovare in altro principio la ragion de'pi&ugrave; <lb/>ovvii e principali effetti dell'elettricit&agrave; sulla varia natura dei corpi. </s></p><p type="main">

<s>Il Volta stesso, nel passo ora citato, a provar l'esistenza e il <lb/>fatto dell'attrazione molecolare, adduceva fra gli altri argomenti <lb/>anche quello delle chimiche operazioni &ldquo; cuius nulla est pars, egli <lb/>dice, in qua praeter inertiam massae et specificam gravitatem, alia <lb/>virium mutuarum genera, non ubique se prodant et, vel invitis, <lb/>incurrant in oculos. </s>

<s>&rdquo; Chi pu&ograve; negare infatti che la Chimica, quella <pb xlink:href="020/01/263.jpg" pagenum="244"/>che con tal proprio nome si vide nel secolo passato acquistare essere <lb/>e dignit&agrave; di scienza, non sia venuta a un tal essere e a una tal <lb/>dignit&agrave;, dappoich&egrave; il Newton scoperse e dimostr&ograve; le attrazioni e le <lb/>repulsioni molecolari? </s>

<s>Le chimiche affinit&agrave;, che presiedono alla <lb/>composizione de'corpi sono effetti di quelle attrazioni: l'elasticit&agrave; <lb/>delle materie aerose, in che si decompongono i corpi sono effetto <lb/>di quelle repulsioni: d'onde &egrave; che, nelle scoperte neutoniane, trovan <lb/>loro principio e ragione, sien per sintesi o per analisi, tutte quante <lb/>le chimiche operazioni. </s></p><p type="main">

<s>La pi&ugrave; gloriosa et&agrave; per la Chimica, incomincia, senza dubbio, <lb/>dalla scoperta dell'ossigeno, nella quale si dice, ed &egrave; vero, che <lb/>non ebbero parte i nostri Italiani, bench&egrave; se la sentisse presente <lb/>Gianfrancesco Cigna, quando volle prima sperimentar sul fatto del&shy;<lb/>l'estinguersi le fiamme e del morir gli animali nell'aria chiusa. </s>

<s><lb/>Era nulladimeno italiano di Savoia quel Claudio Luigi Berthollet, <lb/>che tanta parte ebbe in istituir la nuova nomenclatura, e che di&shy;<lb/>mostr&ograve; al Lavoisier e agli altri Accademici francesi come troppo <lb/>affrettatamente era stato imposto il nome di <emph type="italics"/>ossigeno<emph.end type="italics"/> all'antico <lb/><emph type="italics"/>flogisto,<emph.end type="italics"/> essendo che anco l'idrogeno pu&ograve; acidificare una base, co&shy;<lb/>me fece veder per l'esempio del gas acido solfidrico. </s>

<s>Fu pure il <lb/>Berthollet che scoperse i varii modi tenuti dall'ossigeno in com&shy;<lb/>binarsi a una medesima base, a compor con essa acidi di diversa <lb/>natura, facendo veder che l'acido solforoso non &egrave; altro che lo stesso <lb/>acido solforico con un equivalente di ossigeno di meno. </s>

<s>Ma perch&egrave; <lb/>i grandi meriti del Berthollet son troppo pi&ugrave; noti ai francesi che <lb/>a noi, domandiamo quali furono i principii filosofici seguiti dal <lb/>nostro Autore? </s>

<s>e si risponde che furon quelli dell'attrazion mole&shy;<lb/>colare, i quali ei contrappose alle sterili teorie del Bergmann, ond'&egrave; <lb/>che fu, il Berthollet stesso, appellato col nome di Newton della <lb/>Chimica. </s></p><p type="main">

<s>Pi&ugrave; gloriosa et&agrave; di quella della scoperta dell'ossigeno, ricorse <lb/>per&ograve; alla Chimica, quand'ella strinse coll'Elettricit&agrave; quel nuovo <lb/>connubio, della fecondit&agrave; del quale v&agrave; la scienza in tutto debitrice <lb/>all'Italia. </s>

<s>Come poi il fatto avesse le sue prime e pi&ugrave; remote inspi&shy;<lb/>razioni dalla Filosofia neutoniana, si raccoglie dal ripensare a ci&ograve;, <lb/>che prima inspir&ograve; e dette occasione alla grande scoperta dell'Elet&shy;<lb/>tricit&agrave; dinamica. </s></p><p type="main">

<s>Il Beccaria, nella sua Opera sopra citata <emph type="italics"/>Dell'Elettricismo,<emph.end type="italics"/> ri&shy;<lb/>serba il Cap. </s>

<s>VII del primo Libro a trattar dell'elettricismo stesso, <lb/>per rispetto ai vegetabili, agli animali e ai metalli. </s>

<s>E studiandosi <pb xlink:href="020/01/264.jpg" pagenum="245"/>d'avvalorare le sue proprie speculazioni coll'autorit&agrave; dei placiti <lb/>neutoniani, cita varii passi qua e l&agrave; dalle varie <emph type="italics"/>Questioni,<emph.end type="italics"/> tradu&shy;<lb/>cendo, dalla XXIV, fra gli altri, il passo seguente: &ldquo; Il moto ani&shy;<lb/>male non farebbesi esso dalle vibrazioni del suddetto mezzo (etereo) <lb/>che si eccitino pella potest&agrave; del volere, e indi si propaghino affine <lb/>di accorciarsi e dilatarsi ne'muscoli, per li solidi, pellucidi, ed uni&shy;<lb/>formi capilllamenti de'nervi? </s>

<s>&rdquo; Dopo il qual passo il Beccaria im&shy;<lb/>mediatamente soggiunge: &ldquo; Le ulteriori esperienze e scoperte fatte <lb/>nell'elettricismo, di che Newton non ha visto che il principio, pare <lb/>che aggiungano forza a'dubbi del gran filosofo. </s>

<s>La velocit&agrave; con che <lb/>si muove, cambia direzione, s'arresta e di nuovo si slancia l'elet&shy;<lb/>trico vapore, pare che possano sodisfare alla velocit&agrave; e cambiamento <lb/>delle sensazioni e movimenti animali &rdquo; (ediz. </s>

<s>cit. </s>

<s>pag. </s>

<s>126). Queste <lb/>parole, scritte da chi era reputato solenne maestro nelle elettriche <lb/>dottrine, ebbero grande efficacia sull'ingegno, specialmente de'Fi&shy;<lb/>siologi italiani, i quali dalle ipotesi passando ai fatti, trovarono che <lb/>davvero, sotto l'azione dell'elettricit&agrave;, s'eccitavano le membra agli <lb/>animali, &egrave; pi&ugrave; vivamente che mai ai pi&ugrave; sensibili, come alle rane. </s></p><p type="main">

<s>Uno de'pi&ugrave; indefessamente studiosi, tra questi Fisiologi, era il <lb/>bolognese Luigi Galvani, il quale fu fatto accorto, da coloro che lo <lb/>assistevano nelle esperienze, come le rane morte o scorticate si <lb/>commovevano, anche trovandosi fuori della sfera di azione della <lb/>macchina elettrica, a pur toccarne, con uno scalpello di ferro, i <lb/>nervi crurali. </s>

<s>Avendo trovato con sua gran sorpresa che il fatto <lb/>era vero, volle farne esperienza coll'elettricit&agrave; naturale, esponendo <lb/>all'aria le rane attaccate per un uncino alla ringhiera di ferro del <lb/>terrazzo, su cui davan le finestre di casa. </s>

<s>Sotto il ciel tempestoso, <lb/>osservava le solite commozioni che sotto l'azione della macchina <lb/>elettrica, non per&ograve; cos&igrave; a ciel sereno, bench&egrave; fosse fatto certo, dalle <lb/>osservazioni dell'elettometro, che l'aria, anche in quello stato me&shy;<lb/>teorologico, era imbevuta di elettricit&agrave; come sotto il ciel nuvoloso. </s>

<s><lb/>Ritornato a tentar per molti giorni, e non vedendoci risoluzione, <lb/>port&ograve; una di quelle rane, attaccate per l'uncino alla ringhiera, in <lb/>una stanza al coperto, e posatala sopra una lamiera di ferro, che <lb/>egli teneva per una mano, cominci&ograve; coll'altra a stuzzicare i nervi <lb/>del giacente animale, servendosi di quello stesso uncino, a cui era <lb/>affissa. </s>

<s>Si ridest&ograve; l'animo dell'intento osservatore a nuovi sensi <lb/>di maraviglia, quando vide seguitar da quell'atto le solite contra&shy;<lb/>zioni nelle gambe della rana, e i soliti guizzi. </s>

<s>Ripetuta l'esperienza <lb/>in varii altri modi, esult&ograve;, parendogli che venissero i fatti a sin-<pb xlink:href="020/01/265.jpg" pagenum="246"/>cerarlo dei dubbii del Newton, e delle congetture del Beccaria. </s>

<s>Il <lb/>fluido etereo, concluse, risiede ne'musculi dell'animale, i quali ve <lb/>lo tengono dentro condensato come l'elettricit&agrave; fra le due armature <lb/>di una bottiglia di Leyda: i nervi sono i conduttori di quel fluido <lb/>latente, che salta a commuover le membra all'animale, scaricandosi <lb/>attraverso a un arco di metallico, che fa l'ufficio di eccitatore. </s></p><p type="main">

<s>La storia della maravigliosa scoperta e delle esperienze, che <lb/>lo condussero ad essa, il Galvani ce la narr&ograve; ne'suoi pi&ugrave; minuti <lb/>particolari, nelle tre prime parti di un suo Commentario in latino <lb/>pubblicato in Bologna nel 1791. L'ultima parte di quel Commen&shy;<lb/>tario la riserb&ograve; l'Autore a dichiarare alcune sue congetture e con&shy;<lb/>seguenze di quel suo nuovo elettricismo animale. </s></p><p type="main">

<s>La lettura di quel Commentario eccit&ograve;, nell'animo de'Fisiologi, <lb/>commozioni non meno vive e inaspettate di quelle, che l'elettricit&agrave; <lb/>producesse ne'muscoli delle rane. </s>

<s>Chi pi&ugrave; di tutti poi si commosse <lb/>fu il Volta, il quale, trovate vere l'esperienze descritte dal Galvani, <lb/>a principio ne approv&ograve; anco insieme le congetture. </s>

<s>Altre esperienze <lb/>per&ograve; lo indussero poi in seguito a dubitarne, e fin&igrave; per convincersi <lb/>che non eran le rane da rassomigliarsi a bottiglie di Leyda, ma s&igrave; <lb/>meglio a sensibilissimi elettroscopi, svolgendosi ed eccitandosi il <lb/>fluido elettrico, non da'muscoli, ma dal contatto de'due metalli di <lb/>che si componevano gli archi eccitatori. </s>

<s>A confermare i contradi&shy;<lb/>centi in questa sua persuasione, dimostr&ograve; che sempre, al contatto <lb/>di due metalli di natura diversa, come sarebbe un disco di zinco <lb/>accoppiato a un altro di rame, si svolge un'elettricit&agrave; in tutto si&shy;<lb/>mile a quella, che si produce dai cilindri o dai dischi di vetro <lb/>confricati nelle macchine ordinarie. </s>

<s>E perch&egrave; l'elettricit&agrave; svolta da <lb/>sola una coppia metallica &egrave; debole, mostr&ograve; come si potevano far <lb/>concorrere insieme le virt&ugrave; di pi&ugrave; coppie, ponendo l'una in co&shy;<lb/>municazione coll'altra, o per mezzo dell'acqua pura, o per l'inter&shy;<lb/>posizione di dischi porosi imbevuti di acqua. </s>

<s>Di qui ebbe origine <lb/>quel portentoso elettromotore a tazze, e a pila, che il Volta stesso <lb/>descrive in sue varie scritture, ma specialmente nelle tre Lettere <lb/>al Gren, e in quell'altra al De-la-Metherie; lettere che si possono <lb/>veder raccolte nella II Parte del Tomo II delle Opere, stampate <lb/>nel 1816, in Firenze. </s></p><p type="main">

<s>Le applicazioni della Pila voltaia son note oramai ai dotti e <lb/>al volgo, com'&egrave; nota la stessa sfera del sole, ma non era nostra <lb/>intenzione d'accennar se non a sole quelle applicazioni, che pi&ugrave; <lb/>specialmente concernon la chimica. </s>

<s>L'elettricit&agrave; dinamica, scriveva <pb xlink:href="020/01/266.jpg" pagenum="247"/>lo stesso Volta, apre un campo fecondo di nuove speculazioni e <lb/>ricerche intorno all'influenza del fluido elettrico ne'fenomeni chi&shy;<lb/>mici, alle mutue relazioni di questi con quelle &rdquo; (Opera cit. </s>

<s>T. II, <lb/>P. II. pag. </s>

<s>142), e cos&igrave; appunto scriveva, il celebre inventor della <lb/>Pila, rispondendo al Landriani, il quale gli annunziava come il <lb/>Nicholson a Londra era felicemente riuscito a decompor l'acqua <lb/>fredda. </s>

<s>Presto s'avverarono que'presentimenti del Volta, quando, <lb/>oltre all'acqua, si decomposero i sali; di che si trov&ograve; la Pila aver <lb/><figure id="id.020.01.266.1.jpg" xlink:href="020/01/266/1.jpg"/><lb/>la pi&ugrave; squisita virt&ugrave; analitica. </s>

<s>Il veder gli acidi concorrere costan&shy;<lb/>temente al polo positivo, e le basi al negativo, parve ai chimici <lb/>una sperimentale dimostrazione di ci&ograve; che avea sospettato il Newton, <lb/>quando scrisse, ne'principii della Questione XXXI: &ldquo; et fortasse <lb/>attractio electrica ad huiusmodi exigua intervalla extendi potest, <lb/>etiamsi non excitetur frictione. </s>

<s>&rdquo; Ammisero infatti i Chimici che <lb/>fossero le molecole circondate da ammosfere elettriche, le quali <lb/>perturbate, fosser cagione del portarsi ciascuna di quelle molecole, <lb/>per attrazione, al polo di nome contrario. </s></p><pb xlink:href="020/01/267.jpg" pagenum="248"/><p type="main">

<s>Cos&igrave; ebbe origine l'elettrochimica, di che il Volta stesso, nella <lb/>citata risposta al Landriani, accenna ai principii e a'primi fonda&shy;<lb/>menti posti da lui. </s>

<s>Ma molto prima aveva concorso, il celebre pro&shy;<lb/>fessor di Pavia, a promuover le chimiche scoperte con gli studii <lb/>sulle esalazioni delle varie arie infiammabili, da cui ebbero origine, <lb/>non diremo i moschetti e le prime lampade a gasse, che pure tanto <lb/>piacquero al Furstenberger, da farle sue; ma quel nuovo <emph type="italics"/>Eudio&shy;<lb/>metro,<emph.end type="italics"/> che fu trovato il pi&ugrave; squisito strumento, da servire all'analisi <lb/>volumetrica de'corpi aerosi. </s></p><p type="main">

<s>La Meteorologia elettrica ebbe pure efficacissimi impulsi, per <lb/>opera del Volta e del Beccaria, a cui si dee la pratica applicazione <lb/>de'parafulmini in Italia, e gli studii sopra l'elettricit&agrave; a ciel sereno. </s>

<s><lb/>Ma bench&egrave;, s&igrave; il Franklin che lo stesso Beccaria, avessero dimo&shy;<lb/>strato in tante varie maniere l'esistenza dell'elettricit&agrave; nelle nubi, <lb/>non avevano conosciuto per&ograve; n&egrave; il modo n&egrave; l'origine di quelli <lb/>effluvi. </s>

<s>La scoperta di ci&ograve; occorse al Volta nel fare in Parigi, in <lb/>compagnia del Lavoisier e del La-Place, esperienze sull'elettricit&agrave; <lb/>che si svolge, quando l'acqua si trasforma in vapore. </s>

<s>&ldquo; L'esperienze <lb/>fatte fin qui, egli scrive nell'Appendice alla II Parte della Memoria <lb/>sul Condensatore, bench&egrave; non sien molte, tutte per&ograve; concorrono a <lb/>mostrarci che i vapori dell'acqua, e generalmente le parti d'ogni <lb/>corpo, che si staccan volatizzandosi, portano via seco una quantit&agrave; <lb/>di fluido elettrico, a spese dei corpi fissi che rimangono, lasciandoli <lb/>perci&ograve; elettrizzati negativamente &rdquo; (Op. </s>

<s>cit. </s>

<s>T. II. P. I. pag. </s>

<s>275). <lb/>Cos&igrave; per analogia veniva a dimostrarsi l'origine dell'elettricit&agrave; po&shy;<lb/>sitiva delle nubi. </s></p><p type="main">

<s>Ma perch&egrave; il Volta, sempre nelle esperienze cercava lume alle <lb/>teorie, ricorreva col pensiero alle somiglianze, che passano tra questi <lb/>nuovi fatti elettrici e altri fatti calorifici nuovamente scoperti. </s>

<s>Il <lb/>Guglielmini, tre anni prima che fossero pubblicate le celebri Que&shy;<lb/>stioni neutoniane, aveva gi&agrave;, nel suo Trattato <emph type="italics"/>De sanguinis natura,<emph.end type="italics"/><lb/>fatto distinzione fra calore e luce, attribuendone la variet&agrave; dell'ef&shy;<lb/>fetto al vario modo di ondulare dell'etere. </s>

<s>&ldquo; Quid enim impedit <lb/>quominus undulationes iis similes, quae ab ignis agitatione profi&shy;<lb/>ciscuntur, etiam ab aliis motibus aetheri imprimantur? </s>

<s>An excita&shy;<lb/>bitur in retina igniculus, cum, presso oculo, lucis scintillae videntur <lb/>observari? </s>

<s>&rdquo; (Venetiis, 1701, pag. </s>

<s>93). Il Newton poi pi&ugrave; solenne&shy;<lb/>mente aveva esposto, sotto la solita forma di dubbio, il pensiero <lb/>che l'elettricit&agrave;, il calore e la luce si potessero ridurre al vario <lb/>moto del mezzo etereo, ci&ograve; che oggid&igrave; si ritien dai fisici per la <pb xlink:href="020/01/268.jpg" pagenum="249"/>pi&ugrave; probabile ipotesi, a ridurre in unit&agrave; di principio la molteplice <lb/>variet&agrave; dei nuovi fatti osservati. </s>

<s>Cos&igrave;, prima che s'accogliessero <lb/>d'unanime consenso queste dottrine, aveva il Volta trovata un'altra <lb/>analogia fra l'elettricit&agrave; e il calore. </s>

<s>L'acquistare infatti maggior <lb/>capacit&agrave;, rispetto al fluido elettrico, i corpi che si risolvono in va&shy;<lb/>pori, l'assomiglia a ci&ograve; che si osserva del calorico latente. </s>

<s>&ldquo; Chi <lb/>non sar&agrave; colpito, egli scrive, da cos&igrave; bella analogia, per cui l'elet&shy;<lb/>tricit&agrave; porta del lume alla novella dottrina del calore e ne riceve <lb/>a vicenda? </s>

<s>Parlo della dottrina del calor latente o specifico, come <lb/>si vuol chiamare, di cui Black e Wilke colle stupende loro scoperte <lb/>han gittato i semi &rdquo; (ivi, pag. </s>

<s>275). </s></p><p type="main">

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

<s>Quell'Antonio Conti, che va debitore della sua fama alla va&shy;<lb/>riet&agrave; dell'erudizione, e alla sua faccendiera eloquenza, scriveva in <lb/>una lettera del d&igrave; 16 Settembre 1747 a Francesco Maria Zanotti: <lb/>&ldquo; Pare adesso cangiarsi tutta la Filosofia e ridursi alle forze elet&shy;<lb/>triche, di cui tante sono l'esperienze in tutti i paesi &rdquo; (Lett. </s>

<s>d'il&shy;<lb/>lustri ital. </s>

<s>Milano 1830, pag. </s>

<s>127). Eppure non erano ancora, quando <lb/>il Conti cos&igrave; scriveva, uscite alla luce le nuove Filosofie del Bec&shy;<lb/>caria, del Galvani e del Volta. </s>

<s>Che non si fossero, dietro alla nuova <lb/>preda, i Naturalisti cacciati in troppo numero e con troppa furia, <lb/>non si potrebbe per verit&agrave; negare n&egrave; al Conti n&egrave; a qualche altro <lb/>che l'afferm&ograve;, pi&ugrave; giudizioso di lui. </s>

<s>Nonostante, quel creder che <lb/>tutti i misteri della Natura fossero rimasti fin allora occulti agli <lb/>occhi de'Filosofi, sotto un medesimo velo intessuto di materia elet&shy;<lb/>trica, giov&ograve;, non foss'altro, con gli stessi arditi tentativi, a far pro&shy;<lb/>gredire la scienza. </s></p><p type="main">

<s>De'tanti misteri, quel che pi&ugrave; vivamente frugasse la curiosit&agrave; <lb/>de'Fisiologi, era quello concernente il principio della vita, la quale <lb/>si rivela a noi principalmente, per la spontaneit&agrave; de'moti muscu&shy;<lb/>lari. </s>

<s>Il Cartesio, giocando sempre al suo solito di fantasia, aveva <lb/>ammesso che gli spiriti animali, stillati dal cerebro, scendessero <lb/>in uno o pi&ugrave; musculi, dalle fibre canoliculate de'quali passassero <lb/>nelle fibre di altri muscoli opposti, in modo da riversarvi dentro <lb/>tutti i loro succhi spiritosi e cos&igrave; impinguarli, mentre essi stessi <lb/>perci&ograve; ne rimanevano esausti. </s>

<s>&ldquo; Qua ratione omnes spiritus antea, <pb xlink:href="020/01/269.jpg" pagenum="250"/>contenti in his duobus musculis confluunt celerrime in unum eo&shy;<lb/>rum, et sic inflant et contrahunt eum, dum alter extenditur et re&shy;<lb/>mittitur &rdquo; (Passion. </s>

<s>animae, Francof. </s>

<s>1692, pag. </s>

<s>5). Da questo passo, <lb/>e da tutto ci&ograve; che nel resto del Trattato ne dice, si vede ben che <lb/>l'Autore non aveva nemmen la pi&ugrave; lontana idea dell'Anatomia mu&shy;<lb/>scolare, la quale fu per&ograve; posta dal Borelli per fondamento alle sue <lb/>nuove dottrine de'moti animali. </s>

<s>Nel Cap. </s>

<s>III della Parte II di quel&shy;<lb/>l'Opera insigne, rifiutati gli spiriti cartesiani, ammette l'esistenza <lb/>del succo nerveo, che, stillando in mezzo alle fibre muscolari e <lb/>mescendosi ivi alla linfa e al sangue, vi produce una sub&igrave;ta effer&shy;<lb/>vescenza, com'a versare olio di tartaro sullo spirito di vetriolo. <lb/></s>

<s>&ldquo; Igitur pariter in musculis non dissimilis mistura fieri potest, ex <lb/>quo fermentatio et ebullitio subitanea subsequatur, a cuius mole <lb/>porositates musculorum repleantur, et amplientur et consequantur <lb/>turgentia et inflatio &rdquo; (Romae 1681, pag. </s>

<s>57). </s></p><p type="main">

<s>Al principio vitale e troppo grossolano del Borelli il Newton <lb/>sostitu&igrave; il mezzo etereo, il quale s'incarn&ograve; nell'elettricismo animale <lb/>del Galvani, che, nonostant&egrave; le valide opposizioni del Volta, rimase <lb/>il pi&ugrave; sicuro rifugio, che avesse in s&egrave; la Fisiologia, intantoch&egrave; Vin&shy;<lb/>cenzio Malacarne giunse a rassomigliare il cervello a una vera pila <lb/>voltaia. </s>

<s>Pretender d'aver con ci&ograve; svelati i misteri della vita, sarebbe <lb/>senza dubbio una follia, ma pure, non si pu&ograve; negar che non sieno <lb/>pi&ugrave; sodisfacenti le ipotesi del Galvani, di quelle del Borelli, e sa&shy;<lb/>rebbe una ingratitudine il non riconoscer le benemerenze del Gal&shy;<lb/>vanismo nella Terapeutica. </s></p><p type="main">

<s>Molto prima che a svelare i misteri della vita animale, s'era <lb/>applicata l'elettricit&agrave; a spiegar le funzioni della vita vegetativa. </s>

<s>Da <lb/>che il Nollet, nel Discorso IV delle sue <emph type="italics"/>Ricerche sulle ragioni par&shy;<lb/>ticolari dell'elettricit&agrave;,<emph.end type="italics"/> dimostr&ograve; che il fluido elettrico aveva virt&ugrave; <lb/>d'accelerar l'evaporazione dell'umidit&agrave; delle piante e delle frutte, <lb/>si pens&ograve; da'Botanici che lo stesso fluido elettrico potesse efficace&shy;<lb/>mente concorrere nelle funzioni della vegetazione. </s>

<s>Perci&ograve; molti fu&shy;<lb/>rono coloro, che si misero dietro a questo nuovo genere di espe&shy;<lb/>rienze, fra'quali si distinse il Jallebert di Ginevra, a cui parve che <lb/>i bulbi de'narcisi, delle giunchiglie e dei giacinti pi&ugrave; rigogliosa&shy;<lb/>mente vegetassero nell'acqua delle caraffe elettrizzate, che no nelle <lb/>naturali. </s></p><p type="main">

<s>Il Beccaria, nel Cap. </s>

<s>VII del I Libro dell'<emph type="italics"/>Elettricismo,<emph.end type="italics"/> dietro <lb/>la considerazione di questi fatti, esprime cosi un suo pensiero: <lb/>&ldquo; Ora questo vapore elettrico, che spinto dall'arte entro i vegeta-<pb xlink:href="020/01/270.jpg" pagenum="251"/>bili, sensibilmente agevola ed accresce la loro nutritura e vegeta&shy;<lb/>zione, non sarebbe esso (giacch&egrave; la Natura l'ha in ogni corpo in <lb/>certa quantit&agrave; e misura universalmente distribuito) una delle prin&shy;<lb/>cipali cause efficienti delle suddette naturali funzioni ne'vegetabili <lb/>e negli animali? </s>

<s>&rdquo; (ediz. </s>

<s>cit. </s>

<s>pag. </s>

<s>125, 26). E prosegue ivi a con&shy;<lb/>fortare questo suo pensiero con altri pensieri scelti dalle <emph type="italics"/>Questioni<emph.end type="italics"/><lb/>del Newton, in cui si sospetta che, per mezzo del fluido etereo, <lb/>s'esercitino le funzioni del senso e della vita negli animali. </s>

<s>Cos&igrave;, la <lb/>Botanica sperava d'usufruir bene dell'elettricit&agrave;, non punto meno <lb/>di quel che ne avesse usufruito la Fisiologia, e poniamo che da <lb/>ambedue queste scienze si fosse raccolto qualche buon frutto, l'ab&shy;<lb/>bondanza per&ograve; non corrispose agli ardori delle prime concepute <lb/>speranze. </s></p><p type="main">

<s>Da tutt'altra parte che dalla Fisica elettrica, vennero nel se&shy;<lb/>colo XVIII, alla Botanica le speranze e l'efficacia de'suoi progressi. </s>

<s><lb/>Carlo Linneo aveva scoperto il mistero della fecondazione de'fiori <lb/>e avendo riconosciuto in essi organi e funzioni somigliantissime a <lb/>quelle degli animali, le design&ograve; co'medesimi nomi. </s>

<s>Cos&igrave; si distin&shy;<lb/>sero anco le piante in maschi e in femmine, e s'attribu&igrave; pure ad <lb/>esse un'intelligenza di amore, e si prescrissero nuovi riti alle loro <lb/>nozze. </s>

<s>Alla strana novit&agrave; annunziata dallo Svedese, recalcitrarono, <lb/>secondo il solito, molti, fra'quali uno de'pi&ugrave; illustri botanici d'Italia, <lb/>Giulio Pontedera. </s>

<s>L'autorit&agrave; di lui sarebbe stata di grande ostacolo <lb/>a introdur le nuove dottrine fra noi, se non gli fosse sorto incontro <lb/>uno scrittore, oggid&igrave; pochissimo conosciuto, il siciliano Filippo Arena, <lb/>che nel suo Trattato <emph type="italics"/>Della Natura e cultura de'fiori,<emph.end type="italics"/> messo in luce <lb/>nel 1768 in Palermo, conferm&ograve; con nuove osservazioni il sistema, <lb/>e dimostr&ograve; che le verit&agrave; scoperte dal Linneo s'estendevano ad ogni <lb/>maniera d'inflorescenza. </s></p><p type="main">

<s>A leggere il Trattato del Beccaria, che noi abbiamo oramai <lb/>citato pi&ugrave; volte, si vede che i Fisici avevano nell'Elettricit&agrave; sperato <lb/>di trovar non solo le recondite cause efficienti della vita delle piante <lb/>e degli animali, ma avevano altres&igrave; distese quelle loro ardite spe&shy;<lb/>ranze a scrutar altri di que'misteri, che la Natura celebra ne'pi&ugrave; <lb/>riposti suoi nascondigli. </s>

<s>Si trattava di riconoscer nell'elettricit&agrave; <lb/>l'origine di quel fuoco sotterraneo, l'esistenza del quale veniva <lb/>resa manifesta dalle fusioni de'metalli scavati, e dalle visibili eru&shy;<lb/>zioni de'Vulcani. </s>

<s>Da questo fatto del fuoco centrale bene consi&shy;<lb/>derato, e dagli effetti che naturalmente ne conseguitano, ebbe il <lb/>principio quella nuova scienza, la quale nel suo studio comprende <pb xlink:href="020/01/271.jpg" pagenum="252"/>tutta intera la Storia Naturale, e che ha avuto il nome proprio di <lb/>Geologia. </s></p><p type="main">

<s>La Geologia, che penetra addentro alle viscere della Terra, e <lb/>per riconoscerle nelle loro cause e ne'loro effetti ne notomizza la <lb/>materia, appartiene alla Fisica sottile, ed &egrave; perci&ograve; nata in questi <lb/>ultimi tempi, e risente, quanto pure &egrave; disposta a riceverli, gl'in&shy;<lb/>flussi neutoniani. </s>

<s>Notabile che questi influssi stranieri fossero pi&ugrave; <lb/>efficacemente sentiti da un Italiano, che non dal Burnet o dal <lb/>Woodward, i quali seguitaron piuttosto i metodi del rinnovato <lb/>aristotelismo cartesiano. </s></p><p type="main">

<s>Uno de'pi&ugrave; curiosi problemi, che si proponesse a risolvere ai <lb/>Naturalisti, era quello dell'esistenza delle reliquie fossili di alcuni <lb/>animali marini, che si trovano, anche scavando a fior di terra, di&shy;<lb/>spersi per le alture de'monti. </s>

<s>Leonardo da Vinci si rideva di co&shy;<lb/>loro, che volevan dire &ldquo; li nicchi esser prodotti dalla Natura in essi <lb/>monti, mediante le costellazioni &rdquo; affermando sapientemente che <lb/>essi eran reliquie di molluschi vissuti un tempo fa e, dopo morte, <lb/>ivi deposti dalle acque dei diluvii. </s></p><p type="main">

<s>Pi&ugrave; di due secoli dopo, uno de'pi&ugrave; grandi nostri Naturalisti, <lb/>Antonio Vallisnieri, a risolvere il difficile problema, non sapeva in <lb/>sostanza dir punto nulla di pi&ugrave; o di meglio di quel che ne avesse <lb/>detto gi&agrave; Leonardo. </s>

<s>Il Vallisnieri per&ograve;, in quel suo Trattato, in cui <lb/>descrive i varii crostacei e le produzioni di mare, che si trovan sui <lb/>monti di Verona, e pi&ugrave; particolarmente i pesci e le erbe marine, <lb/>che quasi imbalsamate si trovan fra una pagina schistosa e l'altra <lb/>comprese nelle pietre del monte Bolca; faceva inconsapevolmente <lb/>un gran passo, trattenendosi a esaminar que'fatti, che ne assicura&shy;<lb/>vano del ritiramento del mare, e delle trasformazioni sub&igrave;te dalla <lb/>faccia della Terra. </s>

<s>Altro gran passo poi fece lo stesso Vallisnieri, <lb/>quando, nell'altro Trattatello pi&ugrave; importante di quello che ora ab&shy;<lb/>biamo citato, sull'origine delle fontane, descriveva cos&igrave; avveduta&shy;<lb/>mente le direzioni e le disposizioni degli strati petrosi, quasi nuova <lb/>Anatomia sottile dell'ossatura de'monti. </s>

<s>Fu questa nuova anatomia <lb/>descrittiva, che serv&igrave; d'uno de'pi&ugrave; validi argomenti, da risolvere il <lb/>problema dell'origine delle produzioni marine fra terra; problema <lb/>che fu felicemente risoluto da Anton Lazzaro Moro, friulano, di&shy;<lb/>mostrando la seguente proposizione: &ldquo; Gli animali e vegetabili ma&shy;<lb/>rini, le cui spoglie in oggi o sopra o sotto certi monti si trovano, <lb/>nati, nutriti e cresciuti nelle marine acque, innanzi che que'monti <lb/>sopra la superficie del mare si alzassero, allora l&agrave; furono spinti <pb xlink:href="020/01/272.jpg" pagenum="253"/>dove ora esistono per lo pi&ugrave; impietriti, quando que'monti, uscendo <lb/>dal seno della terra coperta, si alzarono a quelle altezze in cui ora <lb/>si vedono &rdquo; (De crostacei, ecc. </s>

<s>Venezia 1740, pag. </s>

<s>231). La mecca&shy;<lb/>nica di questi sollevamenti, di che s'aveva a que'tempi sotto gli <lb/>occhi l'esempio nella nuova isola di Santorino, l'attribuiva il Moro <lb/>al fuoco sotterraneo. </s>

<s>Di questo fuoco per&ograve;, manifesto ne'fatti, non <lb/>si conosceva ancora la causa, e bench&egrave; il Lemery si avvisasse di <lb/>ritrovarla nelle chimiche combinazioni, e ne'loro effetti di effer&shy;<lb/>vescenza, parve nulladimeno assai meglio di ricorrere a quel panurgo <lb/>dell'elettricit&agrave;, per cui cos&igrave;, nel sopra citato Libro Dell'Elettricismo, <lb/>scriveva il Beccaria: &ldquo; Congetturo che circoli esso vapore (elettrico) <lb/>in particolare maniera per alcuni particolari sotterranei corpi; im&shy;<lb/>perocch&egrave; la sua grande attivit&agrave; non ne farebbe essa pensare che <lb/>sia egli principio motore del fuoco centrale, che i Filosofi hanno <lb/>riconosciuto dentro la Terra? </s>

<s>&rdquo; (pag. </s>

<s>225). </s></p><p type="main">

<s>Cos&igrave;, da pi&ugrave; parti, in Italia concorrevasi a confermare quei <lb/>fondamenti, che aveva posti Lazzaro Moro alla nuova scienza della <lb/>Geologia. </s>

<s>Come poi della stessa cultura di questa scienza si sien <lb/>fatta esclusiva gloria gli studiosi stranieri, troppo lungo sarebbe <lb/>a dire, ma le usurpazioni incominciarono infino da Odoardo King, <lb/>che, nel 1767, espose innanzi alla R. </s>

<s>Societ&agrave; di Londra, come spe&shy;<lb/>culazione sua propria, il sistema geologico pubblicato, trentasei anni <lb/>prima, dal nostro Friulano. </s>

<s>Forse intesero quegli inglesi di trar <lb/>larga usura delle inspirazioni, che ebbe il Moro a ricevere dall'in&shy;<lb/>glese Filosofia neutoniana, da lui invocata a varie occasioni, e verso <lb/>la quale si rivolge come a faro di sicurezza, quando teme di smar&shy;<lb/>rirsi in quell'alto mare, da nessun altro corso prima di lui. </s></p><p type="main">

<s>Meglio per&ograve; che le ipotesi degli elettricisti, venivano prepa&shy;<lb/>rando i progressi alla Geologia le nuove osservazioni e le nuove <lb/>esperienze di Lazzero Spallanzani. </s>

<s>Cimentando egli le produzioni <lb/>vulcaniche e le rocce primitive nel fuoco delle fornaci, concluse <lb/>che i filosofi troppo avevano esagerato nell'apprezzare il grado di <lb/>attivit&agrave; e di intensit&agrave; del fuoco centrale. </s>

<s>Ritrovava altres&igrave;, per queste <lb/>sue esperienze, che le lave al calore si risolvevano in un gasse, <lb/>d'origine misterioso al par di quello, in che si risolve e per cui <lb/>rendesi bollicosa l'acqua ghiacciata. </s>

<s>Alla elasticit&agrave; di questi gassi <lb/>credette lo Spallanzani di dover attribuire la forza di deizione delle <lb/>lave, in fin su alla bocca de'vulcani. </s>

<s>Ma perch&egrave; poi l'esperienze <lb/>parvero dimostrargli che quelle sole forze non erano sufficienti; <lb/>riconobbe in ci&ograve; l'opera, ch'ei dimostr&ograve; con varii argomenti effi-<pb xlink:href="020/01/273.jpg" pagenum="254"/>cacissima, delle acque circolanti sottoterra, trasformate in vapori. </s>

<s><lb/>Ora i Geologi moderni, cos&igrave; italiani come stranieri, professano le <lb/>medesime dottrine, senza punto risovvenirsi di ci&ograve; che fu scritto, <lb/>molti anni prima, nel Cap. </s>

<s>XXI <emph type="italics"/>De'Viaggi alle due Sicilie,<emph.end type="italics"/> dove <lb/>l'Autore osserva di pi&ugrave; come cosa notabile, bench&egrave; qualche mo&shy;<lb/>derno siasi creduto d'essere stato il primo a notarla &ldquo; che i vul&shy;<lb/>cani sparsi nel globo, e che attualmente gettan fuoco, sono o cir&shy;<lb/>condati dal mare, o poco da esso discosti, e che quelli che da lungo <lb/>hanno lasciato di bruciare, esistono ora la pi&ugrave; parte lungi da lui &rdquo; <lb/>(Opere, M&igrave;lano 1825, T. II, pag. </s>

<s>305); osservazione che soccorreva <lb/>opportunissima a confermare il sistema di Lazzaro Moro. </s>

<s>Le De&shy;<lb/>scrizioni de'Viaggi alle Due Sicilie e in alcune parti dell'Appennino, <lb/>son del resto uno de'pi&ugrave; varii, e de'pi&ugrave; ricchi monumenti, che <lb/>sia stato eretto in Italia, nel secolo XVIII, alla Storia Naturale, <lb/>che vi si trova discorsa per quasi ogni sua parte. </s>

<s>Ora il lettore <lb/>&egrave; istruito dallo scienziato che scopre cose nuove, ora &egrave; dilettato <lb/>dall'Alpinista, che descrive viaggi non pi&ugrave; tentati, qual sarebbe <lb/>l'ascesa e la discesa del cono dell'Etna, con che incomincia il <lb/>Capitolo IX. </s></p><p type="main">

<s>Le insigni scoperte anatomiche fatte in questo secolo, princi&shy;<lb/>palmente dal Valsalva e dal Morgagni, dal Cotugno e dallo Scarpa, <lb/>sembrava che dovessero ammannire ad altre scoperte nuove in <lb/>Fisiologia. </s>

<s>Ma que'grandi uomini, a differenza degli anatomici an&shy;<lb/>tichi, sapevano tutto insieme l'arte di descrivere e d'indurre, d'os&shy;<lb/>servare e di sperimentare. </s>

<s>Cos&igrave;, dop'avere il Cotugno scoperta la <lb/>linfa nel labirinto, e dop'aver lo Scarpa descritta la finestra rotonda <lb/>e il timpano secondario, risalgono alle pi&ugrave; alte e sottili speculazioni <lb/>fisiologiche e filosofiche intorno al senso dell'udito. </s>

<s>Lo Spallanzani, <lb/>non essendo anatomico, non poteva sperare di far scoperte fisiolo&shy;<lb/>giche in soggetto nuovo: egli torna perci&ograve; su soggetti tentati gi&agrave; <lb/>prima di lui, e che in lui ritrovano la loro soluzione finale. </s>

<s>Egli <lb/>&egrave; in vero, il primo a dimostrare il fatto della circolazione del san&shy;<lb/>gue, nel giro universale de'vasi, divinata dall'Harvey, e in soli gli <lb/>animali a sangue freddo mostrata dal Malpighi; egli &egrave; il primo a <lb/>illustrare, se non a scoprir la chimica della respirazione, e a di&shy;<lb/>mostrar che la pelle, in alcuni animali degl'infimi ordini, supplisce <lb/>largamente al difetto, e fa l'ufficio stesso de'polmoni. </s></p><p type="main">

<s>Occorre, in questo periodo della scienza sperimentale italiana, <lb/>un fatto, che a noi sembra degno di esser notato, ed &egrave; la relazione <lb/>intima e la corrispondenza che passa, fra gli studi de'Nostri e <pb xlink:href="020/01/274.jpg" pagenum="255"/>quegli degli stranieri. </s>

<s>Quanta differenza tra ci&ograve; che si osserva in <lb/>questo, e nel secolo precedente, quando, a indurre i nostri Acca&shy;<lb/>demici fiorentini a corrispondere con gli Accademici di Parigi, ci <lb/>bisognarono le insinuazioni di Michelangiolo Ricci, e l'Autorit&agrave; di <lb/>Leopoldo de'Medici! In questo secolo il Volta sperimenta a Parigi <lb/>col Lavoisier e col La-Place, come co'suoi pi&ugrave; familiari amici e <lb/>colleghi, e lo Spallanzani dedica al Nollet le sue esperienze sugli <lb/>animali, e all'Haller le sue fisiologiche speculazioni. </s>

<s>Sembra a noi <lb/>che l'anello di congiunzione, meglio che il Cartesio, sia stato il <lb/>Newton, il quale, avendo ricevuto lume dall'Italia, sull'Italia stessa <lb/>lo rimand&ograve; potentemente riflesso. </s>

<s>Altro soggetto degno di conside&shy;<lb/>razione ci si porge dal comparar, co'due precedenti, il secolo XIX. </s>

<s><lb/>Ora son nuovamente rotte le relazioni e i commerci di studi fra <lb/>italiani e stranieri, con questa differenza, che, mentre i Discepoli <lb/>di Galileo si tenevan da parte, per non si degnare degli stranieri, <lb/>ora invece gli stranieri si tengon da parte, perch&egrave; non si degnan <lb/>di noi. </s></p><p type="main">

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

<s>Non infruttuoso riuscirebbe l'andare investigando le cause di <lb/>quell'altero contegno e di quello sprezzante riserbo, usato oggidi <lb/>dagli scienziati stranieri verso i nostri italiani. </s>

<s>Ma perch&egrave; ci&ograve; non <lb/>potrebbesi fare, senz'entrare in confronti, i quali sempre riescono <lb/>odiosi, e perch&egrave; sempre si vede seguitar male a colui, che si vuol <lb/>mettere a dar giudizio de'contemporanei, meglio &egrave; lasciar gli uo&shy;<lb/>mini, e rivolgere uno sguardo fuggitivo alle cose, considerando le <lb/>condizioni, in cui le scienze sperimentali si trovano al presente. </s></p><p type="main">

<s>Quella legge da noi pi&ugrave; volte ricordata, in conformit&agrave; della <lb/>quale il soggetto propostoci a investigar dalla mente procede dal&shy;<lb/>l'intelligibilit&agrave; della forma all'intelligibilit&agrave; della materia, e dalla <lb/>materia crassa prosegue via via alla pi&ugrave; sottile; si vede verificarsi <lb/>anche in questo nostro secolo, in cui par che l'intento de'fisici, <lb/>sia tutto rivolto a trovar, ne'moti e nelle altre affezioni dell'etere, <lb/>quell'unit&agrave; di principio, a cui, come a causa unica, ridurre quella <lb/>complicata moltiplicit&agrave; di effetti, che producon sui nostri sensi, <lb/>l'elettricit&agrave;, il calore e la luce. </s>

<s>Sotto questo lato perci&ograve; riguardata, <pb xlink:href="020/01/275.jpg" pagenum="256"/>non par che la scienza abbia nulla cambiato il suo andamento: <lb/>ella non ha fatto altro che accelerare, a proporzione della distanza, <lb/>que'primi impulsi che, infin dal primo entrar del secolo scorso, <lb/>ricev&egrave; dalla Filosofia neutoniana. </s>

<s>Quel compiacersi, che fanno i con&shy;<lb/>temporanei dello stato attuale, &egrave; forse una di quelle solite lusinghe, <lb/>in cui si trattien l'animo di un padre, che, qualunque ella sia, si <lb/>compiace della sua prole. </s>

<s>Ma non si pu&ograve; negar che la scienza fisica <lb/>sperimentale, oggid&igrave;, per lo troppo lungo decorrere, non sia defa&shy;<lb/>tigata, e perci&ograve; ella, o invoca il soccorso che si suole apprestare <lb/>agli ordini trascorsi, d'esser ritirata verso i suoi principii, o ella <lb/>aspetta che le sia trasfuso per le vene uno spirito di giovent&ugrave; no&shy;<lb/>vello. </s>

<s>Ella aspetta insomma o un altro Newton o un altro Galileo. </s></p><p type="main">

<s>A molti sembra che l'aspettato sia gi&agrave; venuto e salutano in <lb/>Carlo Darwin un nuovo Restauratore della scienza sperimentale. </s>

<s><lb/>Egli come Galileo, e come il Newton, pone a fondamento della sua <lb/>nuova Filosofia un principio semplicissimo, e che non pu&ograve; non es&shy;<lb/>sere ammesso e comprovato dall'esperienza di ognuno: il principio <lb/>che tutto quaggi&ugrave; si trasforma col tempo. </s></p><p type="main">

<s>Ecco una parola, con cui si esprime il concetto pi&ugrave; misterioso, <lb/>che sia nella vita e nella scienza dell'uomo. </s>

<s>Noi viviamo nel tempo, <lb/>e perci&ograve; non &egrave; possibile il definire a noi stessi che cosa sia il tempo, <lb/>giusto a quel modo che non &egrave; possibile il definir la figura e la gran&shy;<lb/>dezza del sole, all'occhio che &egrave; tutto immerso nella sfera del sole. </s>

<s><lb/>Ma pure, il tempo &egrave; uno degli elementi, che entrano a compor quel&shy;<lb/>l'altro non meno misterioso concetto di forza. </s>

<s>Galileo e il Newton <lb/>avevano piuttosto rappresentato le forze, con quell'altro elemento <lb/>loro componente, e che pare a prima vista men misterioso, lo spazio, <lb/>e perci&ograve; fecero uso della Geometria. </s>

<s>Il Darwin insiste sull'elemento <lb/>del tempo, e come quell'antico Archimede chiedeva che gli fosse <lb/>dato spazio sufficiente, e prometteva di trovar la forza necessaria <lb/>a commuovere l'Universo; cos&igrave; il Darwin non chiede che tempo, <lb/>e promette di svelar con esso molti de misteri della Natura. </s>

<s>Il <lb/>tempo &egrave; una dinamia, &egrave; una forza che opera instancabile sempre, <lb/>ma degli effetti della quale non ci avvediamo, se non quando i <lb/>momenti sieno in molto numero accumulati. </s>

<s>La nuova dinamica <lb/>darviniana non &egrave; trattata coi processi matematici, ma &egrave; pure una <lb/>matematica anch'essa, e l'Autore non si dilunga in sostanza dai <lb/>metodi e dai precetti neutoniani, secondo i quali convien prima, <lb/>nelle matematiche, investigare le quantit&agrave; delle forze e le ragioni. <lb/></s>

<s>&ldquo; Deinde, ubi in physicam descenditur, conferendae sunt hae ra-<pb xlink:href="020/01/276.jpg" pagenum="257"/>tiones cum phaenomenis ut innotescat quaenam virium conditiones <lb/>singulis corporum attractivorum generibus competant. </s>

<s>&rdquo; Se non che <lb/>il Darwin, non discende a trattar la Fisica, propriamente detta, ma <lb/>la Storia Naturale, e perci&ograve; le forze attrattive essendo differenti, <lb/>vengono anche designate con un nome speciale, qual'&egrave; quello di <lb/><emph type="italics"/>selezione.<emph.end type="italics"/> Nel conferir poi la ragione di quelle forze, coi fenomeni <lb/>particolari, il nuovo Filosofo si studia d'osservare i precetti del pi&ugrave; <lb/>antico Filosofo inglese, ed &egrave; per l'osservanza di quegli stessi pre&shy;<lb/>cetti, quando altro non gli si frapponga a rimuoverlo dalla retta via, <lb/>che vien condotto alle sue nuove scoperte. </s></p><p type="main">

<s>I germi di queste novit&agrave; per&ograve; scoppiano da radice pi&ugrave; antica <lb/>e di origine schiettamente italiana, intanto che, se la moderna Fi&shy;<lb/>losofia naturale f&ugrave; istituita nella patria del Newton, si pu&ograve; dir che <lb/>ella niente altro fa propriamente che ripigliare un costrutto rimasto <lb/>per lungo tempo interrotto sulla punta della penna, e per le carte <lb/>de'predecessori e de'contemporanei di Galileo. </s>

<s>Le sottili osserva&shy;<lb/>zioni che fa il Darwin intorno al feto degli animali d'ordini supe&shy;<lb/>riori, al qual feto ritrova le membra organizzate a quel modo, che <lb/>si convien meglio all'organismo di animali di specie inferiori; erano <lb/>state fatte prima in gran parte dal Falloppio, quando, a conciliar <lb/>la nuova Anatomia del Vesalio con quella di Galeno, dimostrava <lb/>che l'antico Maestro si poteva in certo modo scusar d'errore, per <lb/>avere attribuito all'uomo l'anatomia de'cani e delle scimmie, ri&shy;<lb/>scontrandosi veramente una tal somiglianza anatomica con gli ani&shy;<lb/>mali degli ordini inferiori, nel feto umano, n&egrave; essendone in tutto <lb/>cancellate le vestigie nel neonato. </s>

<s>Alcuni anzi de'pi&ugrave; curiosi pro&shy;<lb/>blemi naturali, che si proponga a risolvere la Filosofia darviniana, <lb/>trovano ne'principii professati dal Falloppio una soluzione pi&ugrave; di&shy;<lb/>retta, pi&ugrave; facile e pi&ugrave; dimostrativa. </s>

<s>Che se dalle osservazioni ana&shy;<lb/>tomiche si passa a quelle, che concernono gl'istinti animali, noi <lb/>non vediamo che nessuno de'pi&ugrave; celebri Naturalisti moderni possa <lb/>venire al confronto dell'Acquapendente, in quel suo Libro, che egli <lb/>intitol&ograve; <emph type="italics"/>De Brutorum loquela.<emph.end type="italics"/> Egli osserva il tuono vario e il vario <lb/>modular de'suoni negli animali, per esprimere le loro varie pas&shy;<lb/>sioni. </s>

<s>La descrizione che egli fa di una gallina, co'suoi pulcini in&shy;<lb/>torno, insidiata da un cane; il vario modo del chiocciar di lei, <lb/>quando impone a'suoi piccoli che si allontanino dal pericolo, quando <lb/>v&agrave; incontro al cane per invitarlo disperatamente alla battaglia, <lb/>quando finalmente, rimasta vincitrice, richiama a s&egrave; i suoi pulcini, <lb/>perch&egrave; tornin sicuri a ricoverarsi sotto la protezione delle ali ma-<pb xlink:href="020/01/277.jpg" pagenum="258"/>terne (Patavii, 1603, pag. </s>

<s>23, 24); son, fra le molte, una di quelle <lb/>pagine, che sarebbe difficile trovar l'eguale nella moderna lette&shy;<lb/>ratura darviniana. </s></p><p type="main">

<s>Ma il Falloppio e l'Acquapendente, professando cos&igrave; fatte dot&shy;<lb/>trine, seppero sinceramente mantenersi credenti in Dio e nella di&shy;<lb/>gnit&agrave; dell'anima umana, n&egrave; si vede in che i settatori della novella <lb/>Filosofia sappiano ritrovar giuste ragioni di non doverne imitare <lb/>gli esempi. </s>

<s>Perci&ograve;, se non possiam non approvare i nuovi metodi <lb/>e non plaudire alle scoperte fatte dai Filosofi novelli, non sappiamo <lb/>approvar quel loro ingerirsi a definir cose, che si spettano alla <lb/>Metafisica e alla Teologia. </s>

<s>E dall'altra parte se mal provvedono al <lb/>lieto e pacifico progredir della Scienza que'Naturalisti, che la vo&shy;<lb/>glion fare da Metafisici e da Teologi, mal provvedono a mantenere <lb/>in dignit&agrave; e in rispetto le loro contemplazioni que'Teologi, che <lb/>voglion farla da Naturalisti. </s></p><p type="main">

<s>Non &egrave; uscito mai fuori nessun sistema di Filosofia Naturale a <lb/>insegnar cose contrarie alla corrente opinione, che non si sia ten&shy;<lb/>tato di oppugnarlo con l'armi teologiche. </s>

<s>Per tacere del Coperni&shy;<lb/>cismo, le vicende del quale sono oramai troppo note, la vera scienza <lb/>sperimentale in Italia, e di li in tutta Europa, ebbe i primi prin&shy;<lb/>cipii e i pi&ugrave; validi impulsi, com'altre volte si &egrave; detto, dalla cele&shy;<lb/>berrima dimostrazione torricelliana del vacuo. </s>

<s>Insorsero, chi se lo <lb/>sarebbe aspettato mai? </s>

<s>i Teologi ad oppugnare anco questo fatto, <lb/>tassandolo di quell'eresia, derivata dagli errori epicurei, e secondo <lb/>la quale si veniva, a parer de'nuovi censori, a negar l'unione e la <lb/>conservazione nell'Universo. </s>

<s>Ma qual giudizio si facesse, infino dal <lb/>loro primo insorgere, di que'teologici argomenti, vogliamo ce lo <lb/>dica un uomo, il quale, essendo uno de'pi&ugrave; benemeriti de'pro&shy;<lb/>gressi delle scienze sperimentali in Italia, ed essendo dall'altra <lb/>parte monsignore in Roma e poi cardinale, &egrave; atto a inspirar, me&shy;<lb/>glio di qualunque altro, riverenza e tacito ossequio negli animi <lb/>de'professanti contrarie opinioni. </s>

<s>Michelangiolo Ricci, dop'avere in <lb/>una sua lettera riferito al Torricelli la nuova maniera d'argomentar <lb/>di que'Teologi, da'quali veniva l'Autor dell'esperienza dell'argento <lb/>vivo ad essere annoverato fra il gregge di Epicuro, cos&igrave; tosto pro&shy;<lb/>segue: &ldquo; Ci&ograve; sia detto con riverenza di V. S., la quale non vo'tediare <lb/>con altro che le potrei soggiungere appresso, in questa materia, <lb/>perch&egrave; stimo che sar&agrave; pur troppo nauseata dalla temeraria opinione <lb/>de'suddetti Teologi, e dal costume suo costante di mescolar subito <lb/>le cose di Dio ne'ragionamenti naturali, dovecch&egrave; quelle dovrebbero <pb xlink:href="020/01/278.jpg" pagenum="259"/>con maggior rispetto e riverenza esser trattate &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

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

<s>32). </s></p><p type="main">

<s>Ma perch&egrave; i dissidenti, a cui manca il senno e la scienza di <lb/>Michelangiolo Ricci, non &egrave; da sperare che sieno per convertirsi al <lb/>vero, persuasi dalle parole di lui, ci sentiam lieti in pensare e in <lb/>dovere avvertire i nostri lettori, che la Filosofia Naturale da cui <lb/>son venute alla scienza le vitali riforme e i bene augurati incre&shy;<lb/>menti, non entra affatto nella nostra Storia, soggetto della quale <lb/>non &egrave; propriamente che la Filosofia di Galileo e de'seguaci di lui <lb/>nella fiorentina Accademia del Cimento. </s>

<s>I secoli che precedettero <lb/>a questo, e quello che immediatamente lo segue, in tanto son per <lb/>noi soggetto storico, in quanto, in quegli stessi secoli anteriori si <lb/>prepararono, e nel posteriore si svolsero o s'infusero nuovi spiriti <lb/>di vita nelle dottrine insegnate e promulgate dalla scuola galileiana. </s></p><p type="main">

<s>La nostra Storia sar&agrave; ripartita in sette Tomi. </s>

<s>In questo primo, <lb/>al presente Discorso preliminare, seguiter&agrave; la storia dell'invenzione <lb/>de'principali strumenti, che servono al Metodo sperimentale. </s>

<s>Nel <lb/>secondo, si dar&agrave; la storia del Metodo sperimentale applicato alle <lb/>scienze fisiche, e nel terzo narreremo i progressi fatti, per l'appli&shy;<lb/>cazione dello stesso metodo, da quella, a cui diamo nel pi&ugrave; largo <lb/>significato il nome di Storia Naturale. </s></p><p type="main">

<s>Con questi primi tre Tomi sembrerebbe che si fosse sodisfatto, <lb/>in qualche modo, al debito che ci siamo imposti. </s>

<s>Ma se pu&ograve; dirsi <lb/>che siasi cos&igrave; storicamente dimostrato ai nostri lettori come la <lb/>scuola galileiana, applicando i metodi sperimentali abbia scoperto <lb/>verit&agrave; nuove, in ogni parte della Natura; non saremmo per&ograve; an&shy;<lb/>cora penetrati addentro a scoprir da quali occulte radici attingessero, <lb/>quegli stessi metodi, i succhi nutritizii. </s>

<s>Que'succhi dell'altra parte <lb/>derivano sottilmente stillati, e vitalmente trasfusi nella nuova arte <lb/>sperimentale, dalla scienza del moto, ignorandosi la quale, vien <lb/>necessariamente a ignorarsi ogni altra scienza della Natura. </s>

<s>E per&shy;<lb/>ci&ograve;, mentre in quei tre primi Tomi la nostra Storia pareva essere <lb/>di ogni parto assoluta, ora si comprende come, terminandosi qui, <lb/>a quell'edifizio che studiosamente attendiamo a costruire manche&shy;<lb/>rebbero le fondamenta, fondamenta che noi poniamo ne'due Tomi <lb/>appresso, dove si narra la storia de'processi dimostrativi matema&shy;<lb/>tici e sperimentali della Meccanica. </s>

<s>Nel Tomo IV perci&ograve;, si d&agrave; <lb/>la storia delle dottrine meccaniche di Galileo, e nel V vedremo <lb/>come fossero quelle stesse dottrine svolte e confermate da'seguaci <lb/>di lui. </s></p><pb xlink:href="020/01/279.jpg" pagenum="260"/><p type="main">

<s>Ma perch&egrave; apparisca anche meglio evidente la verit&agrave; di quel&shy;<lb/>l'antica sentenza, pronunziata dal Filosofo, che cio&egrave;, <emph type="italics"/>ignorato motu <lb/>ignoratur Natura,<emph.end type="italics"/> abbiamo sentito vivo il bisogno di mostrar come <lb/>fosse la Meccanica immediatamente feconda di un'altra scienza, al <lb/>pari di lei Nuova, e al pari di lei Italiana di origine e di cultura; <lb/>scienza che &egrave; una delle pi&ugrave; splendide e pi&ugrave; benefiche applicaz&igrave;oni <lb/>delle matematiche astratte alle naturali esperienze. </s>

<s>Gli altri due <lb/>Tomi perci&ograve; s'intratterranno intorno alla Storia dell'Idraulica, nar&shy;<lb/>randosi di lei nel VI Tomo l'origine e i progressi fatti per opera <lb/>di Galileo e del Castelli, e riserbando il VII a mostrare in qual <lb/>grado di perfezione fosse ridotta la scienza del Moto delle acque <lb/>da'discepoli e da'seguaci de'due grandi Maestri. </s>

<s>E perch&egrave;, nell'ap&shy;<lb/>plicazione del metodo sperimentale, oltre alle scienze fisiche, hanno <lb/>sperato di trovar aiuti e validi impulsi a progredire, anche le scienze <lb/>morali, se ci basteranno le forze dell'ingegno, daremo anche di ci&ograve; <lb/>qualche saggio: e perch&egrave; tutto il nostro lavoro storico &egrave; condotto <lb/>sui documenti, per la massima parte non molto noti, se l'acco&shy;<lb/>glienza de'lettori ci dar&agrave; qualche speranza che non sieno per riuscire <lb/>inutili affatto le nostre fatiche, ai sette gi&agrave; designati faremo suc&shy;<lb/>cedere via via, come Appendice alla nostra Storia, altri volumi. </s></p><p type="main">

<s>Al pararsi innanzi la macchina di questo ponderoso edifizio, <lb/>sentiamo gemerci sotto affaticate le nostre povere spalle, che ora <lb/>procedono vacillanti, ora temono il pi&ugrave; grave pericolo di rimanere <lb/>oppresse. </s>

<s>Ma comunque ci avvenga di poter condurre al desiderato <lb/>termine l'Opera nostra, non &egrave; credibile che ella non debba riuscir <lb/>per moltissime parti difettosa. </s>

<s>E perch&egrave; sappiano i lettori che non <lb/>si dice ci&ograve; per iscusa o per modestia, ma perch&egrave; siamo fermamente <lb/>persuasi in quella credenza, accenneremo ad una delle principali <lb/>occasioni, d'onde inevitabilmente avranno origine i pi&ugrave; temuti fra <lb/>que'difetti. </s></p><p type="main">

<s>La storia della scienza ha avuto sempre una certa predilezione <lb/>nella cultura, qualunque ella siasi, de'nostri studi. </s>

<s>Gi&agrave;, infin dal&shy;<lb/>l'anno 1878, si mandava a Roma, all'egregio Principe D. </s>

<s>Baldassarre <lb/>Boncompagni, alcune <emph type="italics"/>Notizie Storiche intorno all'invenzione del <lb/>Termometro,<emph.end type="italics"/> pubblicate, in quello stesso anno, nel <emph type="italics"/>Bullettino di <lb/>bibliografia e di storia delle scienze matematiche e fisiche,<emph.end type="italics"/> nel fa&shy;<lb/>scicolo del Settembre. </s>

<s>Dal 1878 al 1885 le <emph type="italics"/>Letture di Famiglia<emph.end type="italics"/><lb/>dispensavano a sorsi, in Firenze, alcune nostre scritture in forma <lb/>di Lezioni, contenenti <emph type="italics"/>Saggi di storia della Fisica sperimentale <lb/>italiana,<emph.end type="italics"/> dai tempi di Dante a quelli di Galileo: scritture che si <pb xlink:href="020/01/280.jpg" pagenum="261"/>interpolavano, nello stesso Periodico, con altre sotto il titolo di <emph type="italics"/>Ri&shy;<lb/>creazioni scientifiche,<emph.end type="italics"/> raccolte e pubblicate dal Direttore, pure in <lb/>Firenze, nel 1883, in un volumetto elegante. </s>

<s>Anche nel dare quelle <lb/>Nozioni di Fisica e di Botanica, sotto le dilettevoli forme di Rac&shy;<lb/>conto o di domestiche scene, in que'due libretti, che portano il titolo <lb/>di <emph type="italics"/>Estate in Montagna<emph.end type="italics"/> e <emph type="italics"/>Fra il Verde e i fiori,<emph.end type="italics"/> pubblicati nel 1884, <lb/>e nel 1886, con s&igrave; amorevoli cure, dai Successori Le Monnier di <lb/>Firenze, in quella loro elegantissima Biblioteca delle Giovanette; <lb/>com'anche in quell'altro libretto di Mineralogia, che il signor Paggi <lb/>pubblic&ograve;, pure in Firenze, nel 1888, e che s'intitola <emph type="italics"/>Con gli occhi <lb/>per terra;<emph.end type="italics"/> abbiamo colto volentieri qua e l&agrave; l'occasione di trattar <lb/>qualche punto di storia della scienza italiana, sembrandoci che a <lb/>concepire stima e a ricevere impulsi d'imitar ci&ograve; che hanno sco&shy;<lb/>perto e speculato gli avi nostri, fossero benissimo accomodati e <lb/>disposti gli animi delle fanciulle italiane, e de'giovanetti. </s></p><p type="main">

<s>Parecchie delle notizie storiche per&ograve;, che ne'citati volumetti, <lb/>pubblicati nel corso di dieci anni, si davano come cosa certa, si <lb/>sono ora dovute da noi riformare, narrando molto altrimenti i fatti, <lb/>e secondo che alla verit&agrave; storica gli abbiano trovati meglio con&shy;<lb/>formi. </s>

<s>Il pi&ugrave; notevole esempio di ci&ograve;, vien posto dal paragonar la <lb/>storia dell'invenzion del Termometro, com'&egrave; narrata qui appresso, <lb/>e nel citato fascicolo del Bullettino romano di Bibliografia fisica e <lb/>matematica. </s>

<s>Similmente, per tacere di altro, l'Igrometro descritto <lb/>nella Lettera del Magalotti, &egrave; tutt'altro da quello, che fu disegnato <lb/>a pag. </s>

<s>129 dell'<emph type="italics"/>Estate in Montagna.<emph.end type="italics"/></s></p><p type="main">

<s>L'esperienza insomma ci ha pur troppo, a pi&ugrave; incontri, dimo&shy;<lb/>strato come cosa di fatto, che, assumendo noi gli uffici di storici, <lb/>abbiam creduto, e che &egrave; peggio, si &egrave; dato qualche volta a credere <lb/>cose, che non son vere. </s>

<s>L'occasione poi di cadere, e di far cadere <lb/>altrui in errore, si &egrave; riconosciuta provenir da due parti: prima dal <lb/>non aver potuto ancora vedere, e dal non aver bene esaminati i <lb/>documenti: seconda, dall'avere anche noi creduta una cosa vera, <lb/>perch&egrave; tutti gli altri l'hanno creduta, sull'autorit&agrave; di uomini re&shy;<lb/>putati sapienti. </s></p><p type="main">

<s>Ora son queste per l'appunto le occasioni, donde si diceva <lb/>dianzi che avrebbero avuto origine i pi&ugrave; temuti difetti della nostra <lb/>Storia. </s>

<s>Inevitabili si credon da noi questi difetti, perch&egrave;, come si <lb/>pu&ograve; presumere d'aver veduti sempre e d'essersi felicemente in&shy;<lb/>contrati in que'documenti dimostrativi de'fatti storici, o come ci <lb/>possiam lusingare d'aver noi soli spogliato un abito, che &egrave; nelle <pb xlink:href="020/01/281.jpg" pagenum="262"/>consuetudini di tutti? </s>

<s>Perci&ograve;, come noi trovando nuovi documenti, <lb/>abbiam colto in fallo noi stessi, cos&igrave; in fallo ci possono cogliere <lb/>gli altri. </s>

<s>In qualunque modo, &egrave; stato nostro sollecito studio di scan&shy;<lb/>sare il mal vezzo del creder vere e del raccontar per vere le cose, <lb/>perch&egrave; altri prima di noi l'hanno dette. </s>

<s>Con questo studio, che pur <lb/>ci pu&ograve; tante volte esser fallito, abbiam condotta l'opera nostra, che, <lb/>qualunque ella sia, si vuol da noi dedicare alle glorie scientifiche <lb/>dell'Italia. </s></p><pb xlink:href="020/01/282.jpg"/><p type="main">

<s><emph type="center"/>DE'PRINCIPALI STRUMENTI<emph.end type="center"/></s></p><p type="main">

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

<s><emph type="center"/>METODO SPERIMENTALE<emph.end type="center"/><pb xlink:href="020/01/283.jpg"/></s></p><pb xlink:href="020/01/284.jpg"/><p type="main">

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

<s><emph type="center"/><emph type="bold"/>Del Termometro<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

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

<s>I. Dell'invenzione e degli usi del Termometro santoriano. </s>

<s>&mdash; II. </s>

<s>Delle applicazioni dell'antichissima <lb/>esperienza eroniana, e segnatamente di quella fatta da Daniele Antonini, e da Cornelio Dreb&shy;<lb/>bellio. </s>

<s>&mdash; III. </s>

<s>Della medesima esperienza fatta da Galileo. </s>

<s>&mdash; IV. </s>

<s>Se si debba giustamente at&shy;<lb/>tribuire a Galileo l'invenzion del Termometro ad aria; de'perfezionamenti che tent&ograve; Giovan <lb/>Francesco Sagredo d'introdurre nello strumento. </s>

<s>&mdash; V. </s>

<s>Della prima invenzione del Termometro <lb/>a liquido. </s>

<s>&mdash; VI. </s>

<s>Della prima scoperta, e delle prime ragioni rese del fatto del dilatarsi i liquidi <lb/>al calore. </s>

<s>&mdash; VII. </s>

<s>Della scoperta della dilatazion cubica de'solidi al calore, e delle applicazioni <lb/>di lei alla Termometria. </s></p><p type="main">

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

<s>La storia dell'invenzion del Termometro &egrave; stata fin qui una delle pi&ugrave; <lb/>controverse, forse perch&egrave; non si sono esaminati, colla debita diligenza, i <lb/>documenti, e i giudizi non sono stati imparziali. </s></p><p type="main">

<s>Il primo e certo documento storico da potersi citar da noi in cos&igrave; fatto <lb/>proposito, &egrave; senza dubbio quello che si legge ne'Commentari del Santorio <lb/>sull'Arte medicinale di Galeno. </s>

<s>La prima pubblicazione di quest'opera si sa <lb/>che fu fatta in Venezia, nel 1612, e in essa, alla fine della particola X del <lb/>Capitolo LXXXV della Parte III, si legge: &ldquo; Volo vos admonere mirabilem <lb/>modum quo ego, quodam instrumento vitreo, soleo demetiri temperaturam <lb/>frigidam et calidam aeris omnium regionum, omnium locorum et omnium <lb/>partium corporis, et adeo exacte, ut qualibet hora diei possimus gradus et <lb/>ultimas mansiones caliditatis et frigiditalis circino dimetiri: illudque est in <lb/>aede nostra patavina, illudque omnibus libentissime ostendimus. </s>

<s>Nos polli&shy;<lb/>cemur vel brevius in lucem daturos librum <emph type="italics"/>De instrumentis medicis,<emph.end type="italics"/> in <pb xlink:href="020/01/285.jpg" pagenum="266"/>quo iconem, constructionem, et usus huius instrumenti antiquissimi propo&shy;<lb/>nemus &rdquo; (Santorii Op. </s>

<s>Omnia Venetiis 1660, T. I, pag. </s>

<s>538). </s></p><p type="main">

<s>E altrove, nella particula III del Cap. </s>

<s>86 della Parte citata, &ldquo; Nos enim, <lb/>egli dice, habemus instrumentum, quo metimur, non solum aeris caliditatem <lb/>et frigiditatem, sed omnes gradus caliditatis et frigiditatis corporis partium, <lb/>quod Patavii ostendimus auditoribus nostris, eiusque usus docuimus &rdquo; (ibi, <lb/>pag. </s>

<s>568). </s></p><p type="main">

<s>Il Libro <emph type="italics"/>De instrumentis medicis<emph.end type="italics"/> del Santorio, come abbiamo udito, <lb/>promesso al pubblico, o non fu scritto altrimenti dall'Autore, o non fu pub&shy;<lb/>blicato, ma la descrizione dello strumento vitreo misuratore, per via di una <lb/>scala graduata, (circino) del calore e del freddo, non manc&ograve; di darcela l'Au&shy;<lb/>tore stesso in un altro suo libro intitolato Commentari sopra la prima Fen <lb/>del primo libro del Canone di Avicenna, che vide la prima volta la luce, <lb/><figure id="id.020.01.285.1.jpg" xlink:href="020/01/285/1.jpg"/></s></p><p type="caption">

<s>Figura 2.<lb/>nel 1625, in Venezia. </s>

<s>Nella VI Questione infatti, dop'aver <lb/>descritto il Pulsilogio, illustrato dalla prima figura, passa <lb/>immediatamente a descrivere il Termometro illustrato dalla <lb/>figura seconda, scrivendo nella seguente forma. </s>

<s>&ldquo; Secunda <lb/>figura est vas vitreus, quo facillime possumus singulis horis <lb/>dimetiri temperaturam frigidam vel calidam, et perfecte scire <lb/>horis quantum temperatura recedat a naturali statu prius <lb/>mensurati. </s>

<s>Quod vas ab Herone in alium usum proponitur. </s>

<s><lb/>Nos vero illud accomodavimus et pro dignoscenda temperatura <lb/>calida et frigida aeris, et omnium partium corporis et pro di&shy;<lb/>gnoscendo gradu caloris febricitantium, quod fit duobus modis: <lb/>alter est dum aegri manu apprehendunt partem supernam <lb/>vitri, quae est D (fig. </s>

<s>2); alter dum aegri ori applicant eam&shy;<lb/>dem vitri partem exufflando, sicut ostenditur fol. </s>

<s>219 instru&shy;<lb/>mento primo, idque fit per aliquod breve spatium, veluti per <lb/>decem pulsilogii pulsationes, ut possimus diei sequenti expe&shy;<lb/>riri, an eodem spatio aqua idem faciendo aeque descendat; <lb/>ob frigus nam ascendit, sicuti ubi est in O: ob calorem vero <lb/>rarefacientem aerem descendit, inde enim colligemus an aeger in melius vel <lb/>in peius labatur, quae differentiae si exiguae sint, a medicis, sine instrumento, <lb/>minime percipi possunt &rdquo; (ivi, T. III, pag. </s>

<s>30, 31). </s></p><p type="main">

<s>Per adattar poi lo strumento medico al primo uso accennato, qual'&egrave; <lb/>quello di riconoscere la temperatura del corpo dell'infermo, per la imposi&shy;<lb/>zione e comprensione della palla vitrea fatta colla mano, non che per esplo&shy;<lb/>rare i varii gradi di temperatura, in cui rimane o per cui passa via via un <lb/>ambiente; il Santorio immagin&ograve; un tripode, dentro il quale, infilato il lungo <lb/>collo dell'ampolla vitrea, potesse questa trasportarsi con facilit&agrave; e mante&shy;<lb/>nersi sempre in posizione verticale ed eretta. </s>

<s>&ldquo; In prima figura, quae tripodi <lb/>ad aedium ornatum superimponi potest, singulis horae momentis, observari <lb/>possunt gradus caloris, frigoris et gradus temperati ipsius aeris. </s>

<s>Aquae <lb/>descensus in tubulo incluso existentis indicat caloris gradus; ascensus fri-<pb xlink:href="020/01/286.jpg" pagenum="267"/>giditatis. </s>

<s>Si aer fiat calidior, aqua descendit, quia caliditas rarefacit aerem <lb/>in globulo inclusum, qui rarefactus occupat maiorem locum. </s>

<s>Inde aqua <lb/>descendat oportet. </s>

<s>Ut aqua vero nobis clarior appareat, viridis efficitur. </s>

<s>Si&shy;<lb/>militer, manum temperatam et intemperatam, ex eodem instrumento, digno&shy;<lb/>scemus, ut superius docuimus (ibi, p. </s>

<s>426). </s></p><p type="main">

<s>Ma nella questione XXXIV, insieme con questo della imposizion della <lb/>mano sopra la palla dello strumento sostenuto dal tripode, descrive parti&shy;<lb/>colarmente gli altri modi di ritrovare il grado della temperatura negli am&shy;<lb/>malati. </s>

<s>Il primo consiste nel far tener loro in bocca, per uno spazio deter&shy;<lb/>minato di tempo, la palla vitrea dello strumento, il cannello del quale non <lb/>&egrave; diritto, ma tortuoso, o avvolto in spira, senza dubbio per renderlo pi&ugrave; <lb/>sensibile alle variazioni di temperatura, o come esprimevansi gli Accademici <lb/>del Cimento, pi&ugrave; geloso. </s>

<s>Il secondo modo consiste nell'applicar la palla vitrea <lb/>a contatto della parte del corpo, di cui vuolsi esplorare la temperatura, <lb/>riducendola alla figura di un emisfero, terminato da una superficie piana, <lb/>per aver maggiore estensione degli stessi punti del contatto. </s>

<s>Il terzo modo <lb/>consiste nel terminare o chiudere l'emisfero con una superficie concava, <lb/>dentro alla quale, alitando l'infermo, fa risentire gli effetti o il grado del <lb/>suo proprio calore all'aria inchiusa dentro alla cavit&agrave; della palla. </s></p><p type="main">

<s>Da cos&igrave; fatti documenti sembra a noi che risulti chiaramente avere il <lb/>Santorio fatto uso medico del Termometro ad aria, il qual Termometro era <lb/>graduato, comunque poi fosse fatta una tale graduazione, ed aveva il liquido <lb/>colorito in verde, per poter meglio distinguere i gradi indicati sopra la scala <lb/>adiacente. </s></p><p type="main">

<s>Abbiamo udito in oltre come chiami l'Autore stesso questo strumento <lb/><emph type="italics"/>antichissimo,<emph.end type="italics"/> la quale espressione vien poi chiaramente commentata da quel <lb/>che soggiunge altrove, aver egli accomodato, all'uso proprio di riconoscere le <lb/>varie temperature dell'aria, una esperienza dell'antichissimo Erone. </s>

<s>L'espe&shy;<lb/>rienza del Fisico alessandrino, a cui accenna, nelle sopra citate parole, il <lb/>Santorio, &egrave; senza dubbio quella che, nel libro degli <emph type="italics"/>Spiritali,<emph.end type="italics"/> si legge sotto <lb/>il numero XLVII e che porta il titolo &ldquo; Della goccia che stilla percossa dal <lb/>sole &rdquo; Il giochetto pneumatico &egrave; fondato sopra le dilatazioni e le conden&shy;<lb/>sazioni dell'aria prodotte dal calore o dal freddo, la quale aria, ora dilatan&shy;<lb/>dosi ora contraendosi, fa s&igrave; che il liquido sottoposto ora si veda essere spinto <lb/>innanzi, e ora ritirato indietro, dentro un cannello di vetro trasparente, e <lb/>perci&ograve; visibile all'occhio dello spettatore curioso. </s></p><p type="main">

<s>Comprendesi bene esser questo il principio, su cui &egrave; fondato il Termo&shy;<lb/>metro ad aria, e il Santorio perci&ograve; cita quel fatto fisico, attribuendolo al suo <lb/>primo osservatore antichissimo. </s>

<s>Il Santorio stesso, insomma, confessa di non <lb/>avere altro merito, nell'invenzione di quel suo strumento medico, da quello <lb/>in fuori di avere applicato a un caso particolare un fatto fisico gi&agrave; molto <lb/>prima scoperto, e a quel suo tempo a tutti notissimo. </s></p><p type="main">

<s>Ma perch&egrave; intanto si sappia dai lettori della nostra Storia e si dia quella <lb/>giusta parte del merito che s'appartiene al nostro Giustinopolitano, giova <pb xlink:href="020/01/287.jpg" pagenum="268"/>qui di non passar sotto silenzio com'egli, oltre all'uso medico, tent&ograve; di ap&shy;<lb/>plicare il Termometro alla soluzion di un problema, che frug&ograve; vivamente <lb/>la curiosit&agrave; de'Fisici, la quale non parve essere pienamente sodisfatta, se <lb/>non dai moderni inventori di strumenti ben assai pi&ugrave; sensibili dei santoriani. </s>

<s><lb/>Il problema, e la ricercata soluzione di lui, concernono il sensibile effetto <lb/>dei raggi calorifici della Luna. </s>

<s>Geminiano Montanari, nella sua <emph type="italics"/>Astrologia <lb/>convinta di falso,<emph.end type="italics"/> pi&ugrave; di un secolo e mezzo prima, che il Melloni venisse <lb/>a confermare il fatto, per mezzo del suo <emph type="italics"/>Termo moltiplicatore,<emph.end type="italics"/> aveva tro&shy;<lb/>vato che il raggio lunare, riflesso da uno specchio ustorio grande su un <lb/><figure id="id.020.01.287.1.jpg" xlink:href="020/01/287/1.jpg"/></s></p><p type="caption">

<s>Figura 3.<lb/><emph type="italics"/>Termometro delicato di moto,<emph.end type="italics"/> (Ve&shy;<lb/>nezia 1685, pag. </s>

<s>8) si rendeva sen&shy;<lb/>sibile, e bench&egrave; non faccia alcun <lb/>cenno dell'Autore pi&ugrave; antico, no&shy;<lb/>nostante l'esperienza e il fatto son <lb/>quegli stessi descritti nelle se&shy;<lb/>guenti parole dal nostro Santorio: <lb/>&ldquo; Figura A (fig. </s>

<s>3) est luna plena: <lb/>figura B est speculum concavum <lb/>quod lumen Lunae recipit: figu&shy;<lb/>ra C est vas ex vitro, quo dimeti&shy;<lb/>mur gradus caloris et frigoris. </s>

<s>A <lb/>speculo concavo lumen facit cu&shy;<lb/>spidatam figuram C. </s>

<s>Permittimus ut luminis Lunae cuspis <lb/>feriat figuram C per spatium decem, vel plurium pulsationum <lb/>instrumenti (un orologio a pendolo di cui parleremo a suo <lb/>luogo) ut inde possit observari per quot gradus rarefiat aer <lb/>inclusus in figura C .... Praeterea, si velimus dignoscere <lb/>differentiam inter calorem solis et Lunae, curamus ut specu&shy;<lb/>lum radios solis recipiat hoc fine, ut turbinate cuspis radio&shy;<lb/>rum solis feriat vas vitreum signatum litera C: tunc statim <lb/>apparet quantum calefaciet sol, et quaenam sit proportio ca&shy;<lb/>loris Lunae ad Solem. </s>

<s>Observavimus per spacium decem <lb/>pulsationum luminis Lunae cuspidem decem caloris gradus <lb/>efficere. </s>

<s>Solis vero lumen in eodem instrumento cuspidatim <lb/>tangendo, idem vas vitreum, in unica pulsatione, 120 gradus caloris efficere. </s>

<s><lb/>Varii tamen gradus fiunt prout varia sunt instrumenta, et variae sunt pul&shy;<lb/>sationes &rdquo; (Sanctorii, Comment. </s>

<s>in prim. </s>

<s>Fen. </s>

<s>Op. </s>

<s>Omn. </s>

<s>Venetiis 1660, T. III, <lb/>pag. </s>

<s>108), per cui non pu&ograve; rilevarsi, da questa santoriana notabilissima <lb/>esperienza, il grado assoluto del calor della Luna, bench&egrave; si raccolga chia&shy;<lb/>ramente essersi al Santorio mostrato, quello stesso calore, assai sensibile. </s>

<s><lb/>Soggiunge ivi poi d'avere altre volte sostituito allo specchio una palla di <lb/>vetro piena di acqua, o un globo di cristallo, ci&ograve; che particolarmente descrive <lb/>pi&ugrave; sotto a pag. </s>

<s>486 della citata edizione di questo stesso Commentario. </s></p><p type="main">

<s>Sembrerebbe da cos&igrave; fatti documenti indubitabilmente potersi conclu-<pb xlink:href="020/01/288.jpg" pagenum="269"/>dere che al Santorio si dovesse il merito della prima invenzione del Ter&shy;<lb/>mometro e a una tal conclusione di fatti vennero molti scrittori, non sola&shy;<lb/>mente di quegli che si possono credere male informati o pregiudicati contro <lb/>Galileo, come sarebbe, per esempio il Biancani o Giovanni Nardi, ma di <lb/>quegli stessi, che appartennero alla scuola del gran Filosofo, o che furono <lb/>ammaestrati da coloro, i quali, conversando familiarmente con lui, potevano <lb/>far testimonianza degli oracoli raccolti dalla bocca dei loro proprii Maestri. </s>

<s><lb/>Tali sarebbero fra gli altri, il Borelli e il Malpighi. </s></p><p type="main">

<s>Il primo di questi, discepolo del Castelli, e uno de'pi&ugrave; diligenti racco&shy;<lb/>glitori delle tradizioni scientifiche di Galileo, sempre che gli occorre, nelle <lb/>lettere familiari o nelle Opere minori, di commemorare il Termometro, <lb/>ne fa autore il Santorio: sentenza che egli poi solennemente pronunzi&ograve; <lb/>nella CLXXV proposizione della II Parte <emph type="italics"/>De motu animalium,<emph.end type="italics"/> cos&igrave; scri&shy;<lb/>vendo: &ldquo; Omnium primus Sanctorius excogitavit organum, quo mensurantur <lb/>aeris gradus caliditatis, quod postea Thermometrum appellarunt, cuius <lb/>structura talis est... &rdquo; (Romae, 1681, pag. </s>

<s>358) e seguita a descrivere lo <lb/>strumento, conforme alla descrizione fattane, come vedemmo di sopra, dalla <lb/>penna medesima del Santorio. </s></p><p type="main">

<s>L'altra autorevole testimonianza del Malpighi non &egrave; certamente diretta, <lb/>ma pure, bench&egrave; indiretta, ha gran peso, perch&egrave; il Papadopoli, medico mes&shy;<lb/>sinese, scriveva a nome di lui, che era suo Maestro, e che perci&ograve; tacitamente <lb/>approvava, e facevasi quasi mallevadore di tutto ci&ograve; che asseriva il discepolo, <lb/>per prova di che occorre osservare che la <emph type="italics"/>Risposta alle opposizioni de'Ga&shy;<lb/>lenisti<emph.end type="italics"/> fatta dal Messinese, venne accolta fra le Opere postume dello stesso <lb/>Malpighi. </s>

<s>Il Papadopoli dunque ha nella citata <emph type="italics"/>Risposta<emph.end type="italics"/> le parole seguenti: <lb/>&ldquo; Il Santorio, fra gli altri inventi suoi gloriosi, lasci&ograve; uno strumento chia&shy;<lb/>mato il Termometro, quale se dall'Oppositore o da altro curioso sar&agrave; posto <lb/>ne'ventricoli del cuore d'un bue, cervo, o altro animale vivente, e far&agrave; il <lb/>simile nelle carni ed intestini, trover&agrave; che il grado del calore &egrave; uguale, e <lb/>che il pi&ugrave; intenso non passa la temperie dell'aria riscaldata dal sole nel <lb/>Leone &rdquo; (Malpighi, Op. </s>

<s>posth. </s>

<s>Londini 1697, P. II, pag. </s>

<s>30). </s></p><p type="main">

<s>I sopraccitati Autori per&ograve; non dovettero venire a quella tal conclusione <lb/>per altra via, che per la lettura delle Opere del Santorio, in che trovarono <lb/>il documento pi&ugrave; giusto, e raccolsero l'argomento pi&ugrave; certo, a dover con&shy;<lb/>cluderne il vero storico. </s>

<s>Ma Giovan Francesco Sagredo ebbe la notizia <lb/>dell'invenzion santoriana da uno di quegli stessi, a cui liberalmente l'Autore <lb/>l'aveva mostrata nelle sue proprie case in Padova, e fu costui appunto <lb/>Agostino Mula. </s>

<s>Il Sagredo infatti, scrivendo il d&igrave; 30 Giugno 1612 a Galileo, <lb/>cos&igrave; gli diceva: &ldquo; Il signor Mula fu al Santo, e mi riferi aver veduto uno <lb/>strumento dal signor Santorio, col quale si misurava il freddo ed il caldo <lb/>col compasso, e finalmente mi comunic&ograve; questo essere una gran bolla di <lb/>vetro con un collo lungo, onde subito mi son dato a fabbricarne de'molto <lb/>squisiti e belli &rdquo; (Alb. </s>

<s>XIII, 218). Il Sagredo in vero erasi dato in questo <lb/>tempo studiosamente a perfezionare il Termometro santoriano, e vi fece tali <pb xlink:href="020/01/289.jpg" pagenum="270"/>progressi, che non pu&ograve; tacer di loro la nostra Storia. </s>

<s>Ma prima, convien tratte&shy;<lb/>nerci alquanto sulle applicazioni di quella esperienza eroniana, che per es&shy;<lb/>sere stata genitrice dello strumento da misurare il calore, e per essere stata <lb/>soggetto di novit&agrave; spettacolose, si &egrave; acquistata perci&ograve;, per noi, una parti&shy;<lb/>colare importanza. </s></p><p type="main">

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

<s>Nel libro degli <emph type="italics"/>Spiritali<emph.end type="italics"/> tradotto, come i nostri lettori sanno, nel 1606, <lb/>ma scritto originalmente in latino nel 1601, il Porta descriveva cos&igrave; l'espe&shy;<lb/>rienza eroniana, con intenzione d'applicarla ad uso diverso s&igrave;, ma non punto <lb/>meno importante di quello, a cui seppe ingegnosamente applicarla il Santorio: </s></p><p type="main">

<s>&ldquo; Sia il vaso A (fig. </s>

<s>4); questo abbi la bocca dentro <lb/><figure id="id.020.01.289.1.jpg" xlink:href="020/01/289/1.jpg"/></s></p><p type="caption">

<s>Figura 4.<lb/>un vaso B, piano, pieno d'acqua, il quale vaso sar&agrave; pieno <lb/>di aria, grosso nella sua consistenza, pi&ugrave; o meno, secondo <lb/>il luogo e la stagione. </s>

<s>Poi accosterete un vaso pieno di <lb/>fuoco al corpo del vaso in A, e l'aria, subito riscaldan&shy;<lb/>dosi, si ander&agrave; assottigliando, e fatta pi&ugrave; sottile, vuole pi&ugrave; <lb/>gran luogo, e cercando uscir fuori, verr&agrave; fuori dell'acqua, <lb/>e si vedr&agrave; l'acqua bollire, che &egrave; segno che l'aria fugge, <lb/>e quanto si andr&agrave; pi&ugrave; riscaldando, l'acqua pi&ugrave; boglier&agrave;, <lb/>ma, essendo ridotta tenuissima, l'acqua non boglier&agrave; pi&ugrave;. </s>

<s><lb/>All'hora rimovete il vaso del fuoco dal ventre A, e l'aria <lb/>rinfrescandosi, s'andr&agrave; ingrossando, e vuol minor luogo, e <lb/>non havendo come riempir il vano del vaso, perch&egrave; ha la <lb/>bocca sotto l'acqua, tirer&agrave; a s&egrave; l'acqua del vaso, e si vedr&agrave; <lb/>salir l'acqua su con gran furia a riempir tutto il vaso, lasciando vacua quella <lb/>parte, dove l'aria st&agrave; ridotta gi&agrave; nella sua natura di prima. </s>

<s>E se di nuovo <lb/>accostarete il fuoco a quella poca aria, attenuandosi di nuovo, caler&agrave; gi&ugrave; <lb/>tutta l'acqua, e rimovendo il fuoco torner&agrave; a salir l'acqua &rdquo; (Napoli 1606, <lb/>pag. </s>

<s>77). L'esperienza stessa per&ograve;, come semplice curiosit&agrave; spettacolosa, era <lb/>stata descritta gi&agrave; dall'Autore nel cap. </s>

<s>XXII del secondo fra i Quattro libri <lb/>della Magia, e nel cap. </s>

<s>I dell'ottavo della Magia stessa in XX libri. </s></p><p type="main">

<s>La gran diffusione, che ebbero queste varie opere del Porta, rese l'espe&shy;<lb/>rienza eroniana quasi diremmo popolare, e alcuni destramente pensarono di <lb/>servirsene a dimostrarla al pubblico, qual'effetto spettacoloso, e per metterla <lb/>a prezzo, con Re e con principi, come un segreto de'pi&ugrave; preziosamente ge&shy;<lb/>losi. </s>

<s>Giuliano de'Medici scriveva cos&igrave; da Praga a Galileo, nell'Ottobre del <lb/>1610: &ldquo; Non voglio restar di dirle che qui ci &egrave; un Fiammingo, che viene <lb/>d'Inghilterra, che pretende avere trovato il moto perpetuo, ed avendone <lb/>solo prima dato uno strumento al Re d'Inghilterra, ne ha dato un altro a <pb xlink:href="020/01/290.jpg" pagenum="271"/>S. M. Cesarea, che dimostra di pregiarsene molto, ed ha caro che non lo <lb/>comunichi con altri, e consiste questo moto d'acqua che in un cannello, <lb/>fatto quasi in forma di Luna, v&agrave; ora in su ed ora in giu da una banda al&shy;<lb/>l'altra. </s>

<s>Il signor Gleppero (Kepler) non ci ha una fede al mondo, se non <lb/>vede come gli sta &rdquo; (Campori, Carteggio ecc. </s>

<s>Modena 1881, pag. </s>

<s>38). </s></p><p type="main">

<s>Due anni dopo, la notizia del curioso spettacolo era pervenuta a Bru&shy;<lb/>xelles, alle orecchie di Daniele Antonini, il quale, sotto il di 4 di Febbraio 1612, <lb/>scriveva cos&igrave; al medesimo Galileo: &ldquo; Molti giorni sono io intesi che il R&egrave; <lb/>d'Inghilterra aveva un moto perpetuo, nel quale, entro un canale di vetro, <lb/>si muove certa acqua or abbassandosi a guisa (dicevasi) del flusso e riflusso <lb/>del mare (MSS Gal. </s>

<s>Div. </s>

<s>II. P. VI. T. VIII, c. </s>

<s>82). </s></p><p type="main">

<s>Parecchi anni ancora dopo, o fosse quello stesso che era andato in In&shy;<lb/>ghilterra o in Germania, o fosse qualcun'altro che avesse imparato da lui, <lb/>della viva rappresentazione del flusso marino dentro l'ampolla vitrea, si <lb/>venne a farne pubblico spettacolo in Italia, e Cesare Marsili, con lettera del <lb/>d&igrave; 3 Aprile 1624, ne dava, al solito, avviso a Galileo, il quale rispondeva in <lb/>proposito: &ldquo; Quanto al flusso e riflusso di che mi accenna, ne sentirei vo&shy;<lb/>lentieri l'effetto, il quale, per mio parere non credo che possa dipendere da <lb/>altra cagione celeste, che dallo scaldarsi l'aria il giorno, e rinfrescarsi la <lb/>notte, e l'elezione dell'acqua salsa credo che sia una coperta all'artificio, <lb/>e che l'istesso farebbe la dolce, e un tale scherzo feci io venti anni sono <lb/>in Padova &rdquo; (Alb. </s>

<s>VI, 313). Di questo stesso parere era stato gi&agrave; l'Antonini, <lb/>il quale, nella lettera sopra citata, dop'avere accennato allo spettacolo del <lb/>flusso marino, dentro l'ampolla, cos&igrave; soggiunge: &ldquo; Sopra il che, conside&shy;<lb/>rando io, caddi in pensiero che questo non fusse altrimenti flusso e reflusso, <lb/>ma cos&igrave; si dicesse per coprir la vera causa e la verit&agrave; fusse che questo moto <lb/>fusse dalla mutazione dell'aria, cio&egrave; di caldo e freddo fusse causato, cavando <lb/>questo dalla speculativa di quella esperienza del bellicone, che V. S. sa, e <lb/>perci&ograve; m'ingegnai di fare anch'io uno di questi moti, e fecilo, non come <lb/>m'era stato disegnato quel d'Inghilterra, che ha il canale rotondo a guisa <lb/>d'un anello, ma con il canal retto, come V. S. potr&agrave;, dal profilo, che io le <lb/>mando, vedere &rdquo; e seguita a descrivere uno strumento, dove l'acqua entra <lb/>ed esce o si alza, e si abbassa, al dilatarsi e al condensarsi dell'aria, dentro <lb/>un tubo assai pi&ugrave; capace di quello, in cui si fa visibile il moto della stes&shy;<lb/>s'acqua. </s>

<s>Pochi giorni dopo torna a descrivere un nuovo strumento pi&ugrave; in&shy;<lb/>gegnosamente costruito, e in cui si mostra il medesimo spettacoloso effetto. </s></p><p type="main">

<s>Da questi due strumenti dell'Antonini non diversifica in sostanza quello, <lb/>che descrisse Cornelio Drebbel, a pag. </s>

<s>25 e 26 del suo libro <emph type="italics"/>De natura <lb/>elementorum,<emph.end type="italics"/> stampato a Ginevra nel 1628, colle seguenti parole, che noi <lb/>traduciamo, perch&egrave; sieno meno offese le orecchie de'nostri lettori dalla bar&shy;<lb/>barie originale del linguaggio latino: &ldquo; Se tu prendi un vaso di vetro, il <lb/>collo del quale, essendo assai lungo, si ripieghi incurvandosi a guisa di <lb/>corno, e la bocca vada a immergersi in acqua fredda, mentre tu avrai ac&shy;<lb/>ceso il fuoco sotto il ventre del vaso, vedrai poco dopo gorgogliar l'acqua, <pb xlink:href="020/01/291.jpg" pagenum="272"/>per l'aria che va via; che se poi tu ritirerai il fuoco, l'aria, che prima <lb/>riscaldata erasi espansa, si contrarr&agrave; nuovamente in s&egrave; stessa, e si far&agrave; pi&ugrave; <lb/>che mai densa, e su per il vetro incomincer&agrave; a risalir l'acqua che verr&agrave; a <lb/>occupare quello stesso spazio, dove prima il fuoco avea fatto distendere l'aria. </s>

<s><lb/>Se, senza pericolo di romperlo, puoi fortemente riscaldare il vetro, lo ve&shy;<lb/>drai, nel raffreddarsi, tanto succiar dell'acqua, che quasi se n'empier&agrave; tutto. </s>

<s><lb/>Un simil vaso di terra reggerebbe al fuoco assai meglio, ma impedirebbe <lb/>all'occhio il poterne veder l'effetto. </s>

<s>Ch&egrave;, se, invece di aria tu mettessi nel <lb/>vaso al fuoco, acqua, la vedresti dilatarsi con tanto pi&ugrave; di forza, quanto <lb/>l'acqua stessa e pi&ugrave; densa dell'aria, e diecimila tanti di pi&ugrave; ricrescer&agrave; sopra <lb/>quel che l'aria stessa non faccia. </s>

<s>&rdquo; </s></p><p type="main">

<s>Ora &egrave; notabile che sia stata attribuita al Drebbel l'invenzion del Ter&shy;<lb/>mometro non sopr'altro argomento che sopra la descrizione di questa espe&shy;<lb/>rienza, la quale, quand'avesse veramente il diritto di conferire il titolo <lb/>d'inventore a chi prima l'ha fatta o l'ha pubblicamente descritta, non do&shy;<lb/>vrebbe, per giustizia, parteciparne il merito al Drebbel, ma al Cerretano <lb/>fiammingo, ma all'Antonini, ma al Porta, e anzi ad Herone stesso prima che <lb/>ad ogni altro. </s>

<s>Questa considerazione &egrave; quella appunto che ci apre la via a <lb/>discorrer di Galileo, a cui pure, come al Drebbellio, fu attribuito il merito <lb/>dell'invenzion del Termometro, per avere anch'egli, fra'tanti altri, atteso <lb/>all'esperienza eroniana. </s></p><p type="main">

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

<s>Un anno dopo avere il Sagredo dato avviso per lettera a Galileo dello <lb/>strumento veduto in Padova dal Mula, appresso il Santorio, torna in altra <lb/>sua a scrivere allo stesso in questa maniera: &ldquo; L'istrumento per misurare <lb/>il caldo <emph type="italics"/>inventato da V. S. E.<emph.end type="italics"/> &egrave; stato da me ridotto in diverse forme assai <lb/>comode ed esquisite, intanto che la differenza di temperie da una stanza <lb/>all'altra si vede fin cento gradi &rdquo; (Alb. </s>

<s>VIII, 218). </s></p><p type="main">

<s>Riscontrando i due passi delle due lettere citate, apparisce evidente&shy;<lb/>mente una variet&agrave; di giudizi, imperocch&egrave;, nel primo, pare apertamente at&shy;<lb/>tribuirsi l'invenzion del Termometro al Santorio, e nel secondo pi&ugrave; aper&shy;<lb/>tamente che mai attribuiscesi a Galileo. </s>

<s>L'Alb&egrave;ri, a render qualche ragione <lb/>di queste parole scritte in tempi diversi e in cos&igrave; diverse sentenze, disse <lb/>che, dopo la prima lettera, Galileo dee aver fatto sapere al Sagredo che <lb/>l'invenzione non era altrimenti del Santorio ma sua, per cui il Gentiluomo <lb/>veneziano, credette, senza voler discuterla, alla franca affermazione di lui. </s></p><p type="main">

<s>Nella medesima opinion del Sagredo, dalle informazioni avute a voce <lb/>dallo stesso Galileo, fu condotto il Castelli, come si par da una lettera pub&shy;<lb/>blicata nella sua integrit&agrave;, pochi anni addietro, nel <emph type="italics"/>Bullettino<emph.end type="italics"/> del principe <pb xlink:href="020/01/292.jpg" pagenum="273"/>Boncompagni. </s>

<s>Quella lettera &egrave; indirizzata a mons. </s>

<s>Ferdinando Cesarini, ed <lb/>ha per soggetto la cura di un ferito, a cui le intestina erano uscite fuori <lb/>del ventre. </s>

<s>Il Castelli, applicando un fatto fisico a un caso patologico, in&shy;<lb/>tende a dimostrar, per la dilatazione e la contrazione dell'aria chiusa dentro <lb/>il tubo intestinale, quel rigonfiamento straordinario, che si vide fare al me&shy;<lb/>desimo intestino, subito che fu uscito fuori del ventre al povero ferito, e <lb/>l'esperienza del fatto fisico, che l'Autore intende di applicare al caso pato&shy;<lb/>logico, l'attribuisce, per sua propria testimonianza, a Galileo. </s></p><p type="main">

<s>Dopo avere infatti narrato il caso, e aver detto del felicissimo esito che <lb/>ebbe la cura di quell'infermo affidata al celebre Trullo, soggiunge il Ca&shy;<lb/>stelli stesso le parole seguenti: &ldquo; Il caso fu bello, ed il rimedio facilissimo <lb/>ed intelligibile. </s>

<s>Ma io rimasi da una difficolt&agrave; sopraggiunto, la quale mi ha <lb/>dato che pensare assai a questo fatto: poich&egrave; alcuni giorni sono, discorrendo <lb/>col medesimo signor Trullo di questa cura, egli mi disse che sempre, in <lb/>simili ferite, coll'uscita dell'intestino, seguiva l'istesso accidente del rigon&shy;<lb/>fiarsi, e di pi&ugrave;, che sempre il ferito veniva da crudelissimi dolori tormentato. </s>

<s><lb/>In questo, mi sovvenne un'esperienza fattami vedere, gi&agrave; pi&ugrave; di trentacinque <lb/>anni sono, dal nostro signor Galileo, la quale fu che, presa una caraffella di <lb/>vetro di grandezza di un piccolo uovo di gallina, col collo lungo due palmi <lb/>in circa, e sottile quanto un gambo di pianta di grano, e riscaldata bene <lb/>colle palme delle mani la detta caraffella, e poi rivoltando la bocca di essa <lb/>in un vaso sottoposto, nel quale era un poco di acqua, lasciando libera dal <lb/>calor delle mani la caraffella, subito l'acqua cominci&ograve; a salire nel collo, e <lb/>sormont&ograve; sopra il livello dell'acqua del vaso, pi&ugrave; di un palmo, del quale <lb/>effetto poi, il medesimo signor Galileo si era servito per fabbricare un <lb/>istrumento da esaminare i gradi del caldo e del freddo, intorno al quale <lb/>strumento sarebbe che dire assai, ma, per quanto fa al proposito nostro <lb/>basta che, in sostanza, si osserva che l'acqua, quanto pi&ugrave; l'aria circonfusa <lb/>intorno alla caraffella si trova pi&ugrave; e pi&ugrave; fredda, tanto pi&ugrave; sale l'acqua sopra <lb/>il livello della sotto posta, e quanto lo strum&egrave;nto vien portato in aria meno <lb/>fredda, tanto pi&ugrave; l'acqua si va abbassando nel collo della caraffella &rdquo; (Bul&shy;<lb/>lettino ecc, T. XI, pag. </s>

<s>645, 46). </s></p><p type="main">

<s>In queste parole &egrave; evidentemente descritto dal Castelli il Termometro <lb/>ad aria, nella precisa forma del Santoriano, ma nonostante assai pi&ugrave; imper&shy;<lb/>fetto di questo, non facendosi menzione n&egrave; della scala di graduazione, n&egrave; <lb/>delle molte altre raffinatezze introdottevi dal Medico di Capo d'Istria. </s>

<s>Pur <lb/>si volle, dietro cos&igrave; fatto documento, inferir da'critici, che Galileo aveva <lb/>inventato lo strumento gi&agrave; fin dal 1603, mentre i Commentarii santoriani <lb/>sull'arte medica di Galeno non videro la pubblica luce che nel 1612, come <lb/>vedemmo. </s>

<s>L'et&agrave; della invenzione galileiana la desumono dalla data della <lb/>lettera al Cesarini, che &egrave; del 1638, per cui, dicendo ivi il Castelli essergli <lb/>stata mostrata da Galileo quella fisica esperienza <emph type="italics"/>trentacinque anni sono,<emph.end type="italics"/><lb/>confidentemente concludono che infino dal 1603 aveva Galileo stesso mo&shy;<lb/>strato al Castelli il suo Termometro. </s></p><pb xlink:href="020/01/293.jpg" pagenum="274"/><p type="main">

<s>Vincenzio Viviani, nella Vita che scrisse dell'amatissimo suo Maestro, <lb/>fa risalir la scoperta dello strumento da misurare il calore anche a pi&ugrave;u anni <lb/>avanti, cio&egrave; tra il 1593 e il 1597 (Alb. </s>

<s>XV, 337). Su quali fondamenti poi <lb/>posi il Viviani quella sua asserzione, a noi n&egrave; a nessuno &egrave; possibile saperlo, <lb/>perch&egrave; l'Autore della Vita di Galileo non ne fa motto, cosicch&egrave; pochissima <lb/>&egrave; la fede che possiamo avere nella verit&agrave; di questa, come di altre asser&shy;<lb/>zioni storiche di lui. </s></p><p type="main">

<s>N&egrave; maggior certezza di fede crediamo che si possa dar da noi alle pa&shy;<lb/>role, che ne scrisse il Castelli, imperocch&egrave;, a trattenersi, per prima cosa sui <lb/>numeri che sono i pi&ugrave; precisi testimoni di tutti, quell'affermarsi che l'espe&shy;<lb/>rienza della caraffella fu fatta da Galileo nel 1603 &egrave; uno sbaglio manifesto, <lb/>asserendo Galileo stesso che fu fatta invece nel 1606. Ci&ograve; rilevasi dalla so&shy;<lb/>pracitata lettera del Marsili, la quale fu scritta il di 25 Aprile 1626. E perci&ograve; <lb/>dicendo ivi che l'esperienza stessa era stata fatta venti anni prima, conclu&shy;<lb/>desi che dunque nel 1606 e n&ograve; nel 1603, come asseriva il Castelli, Galileo <lb/>dee essersi ricreato a far lo scherzo della esperienza eroniana. </s></p><p type="main">

<s>Dall'altra parte poi n&egrave; il Castelli fa n&egrave; da luogo a fare una distinzione <lb/>importante, ed &egrave; tra la esperienza pneumatica e l'applicazione di lei allo <lb/>strumento misuratore de'gradi del calore. </s>

<s>Da una tal confusione dipende <lb/>appunto l'incertezza, che ha la lettera al Cesarini, invocata come documento <lb/>storico, da cui non pu&ograve; concludersi come e quando occorresse a Galileo di <lb/>far l'esperienza, e come e quando pensasse d'applicarla a costruire il nuovo <lb/>strumento, di che la critica imparziale pu&ograve; negargli il merito ambito. </s></p><p type="main">

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

<s>Ma perch&egrave; defraudare all'ambizion di un tant'uomo, favorita dal cre&shy;<lb/>dulo ossequio di altri grandi uomini, come il Sagredo, il Castelli, il Viviani, <lb/>non si pu&ograve; far da noi senza pericolo di essere accusati di temerarii, doman&shy;<lb/>diamo alla coscienza de'nostri lettori se credono che, dai documenti sopra <lb/>citati, si possa avere una prova certa dell'appartenere allo stesso Galileo un <lb/>qualche diritto di preferenza sopra il Santorio. </s>

<s>Noi siam sicuri che rispon&shy;<lb/>deranno di no, perch&egrave; in tutti i modi ha diritto alla prima invenzione colui, <lb/>che prima di tutti l'ha pubblicata. </s>

<s>Ora il Santorio pubblic&ograve; la invenzione <lb/>sua del Termometro ad aria in un'opera diffusissima a que'tempi, e che <lb/>vide la luce nel 1612. Quali sono, domandiamo, le opere di Galileo anteriori <lb/>al 1612, nelle quali faccia pure un cenno di questo suo nuovo strumento <lb/>inventato? </s>

<s>Anzi, non solo nelle opere anteriori a quell'anno non fa Galileo <lb/>menzione alcuna dello strumento, ma nemmen nelle altre, pubblicate dopo, <lb/>e che son delle maggiori, come i Dialoghi dei Massimi Sistemi e delle Due <lb/>Nuove Scienze. </s>

<s>Nel Tomo IV della Parte V de'manoscritti di Galileo, a <lb/>carte 33, si leggono alcune postille e note da apporsi ai Dialoghi del Moto <pb xlink:href="020/01/294.jpg" pagenum="275"/>della prima edizione di Leyda, di cui lo scrittore cita via via la pagina, a <lb/>cui si riferiscono quelle stesse postille e lo scrittore &egrave; Vincenzio Viviani, di <lb/>propria mano. </s>

<s>Tali postille, poche di numero, non sono per verit&agrave; molto <lb/>importanti, e in una, che si riferisce a pag. </s>

<s>70 della citata edizione leidese, <lb/>il Viviani stesso scrive queste parole: &ldquo; Nel discorso del Salviati potrebbesi <lb/>aggiungere la fabbrica delle due palline, e con questa occasione accennare <lb/>come l'istrumento per conoscere le mutazioni del caldo e del freddo nel&shy;<lb/>l'aria &egrave; invenzione del Galileo &rdquo;. </s>

<s>Ma perch&egrave; Galileo, domandiamo noi, tra&shy;<lb/>scur&ograve; di far questo cenno, o come mai si mostr&ograve; cos&igrave; smemorato da aver <lb/>bisogno de'suggerimenti del suo discepolo? </s>

<s>Perch&egrave; non colse una cos&igrave; fa&shy;<lb/>vorevole occasione di rivendicar la scoperta, egli che tante altre volte, di <lb/>tali rivendicazioni anche meno importanti, si mostra cos&igrave; geloso? </s></p><p type="main">

<s>Tutti sanno che Galileo non fa menzion del Termometro, dalle Lettere <lb/>familiari in fuori, altro che in que'frammenti, i quali, raccolti poi dal Vi&shy;<lb/>viani, si pubblicarono sotto il titolo di <emph type="italics"/>Pensieri varii.<emph.end type="italics"/> E qui pure suppone <lb/>lo strumento gi&agrave; come noto, e piuttosto che attendere con diligente amor <lb/>d'inventore a farne la descrizione delle parti componenti, e del modo di <lb/>operare e dell'uso, nient'altro fa che ripeter de'fisici le teorie, per render <lb/>la ragione del moto dell'acqua dentro il cannello dello strumento. </s>

<s>Il San&shy;<lb/>torio invece vedemmo che applic&ograve; la sua nuova invenzione, non a soli gli <lb/>usi medici ma a ricerche scientifiche di non lieve importanza. </s>

<s>Galileo del <lb/>Termometro non si sa ch'ei ne facesse alcun uso. </s>

<s>Anzi, rispondendo a un <lb/>problema termico propostogli dal conte Piero de'Bardi (Alb. </s>

<s>XIV, pag. </s>

<s>297-99) <lb/>giudica della temperie dell'aria e dell'acqua dalle impressioni fatte sui sensi, <lb/>per cui Giuseppe del Papa, e tutti i savii con lui, conclusero che, quando <lb/>Galileo fece quella risposta non dovette aver nessuna idea, n&egrave; conosciuto nem&shy;<lb/>meno dalla lontana, il possibile uso del Termometro. </s>

<s>&Egrave; questa una tal conclu&shy;<lb/>sione, che mette i galileiani in grande imbarazzo, perch&egrave;, dicendo ivi l'Autore <lb/>che il problema gli fu proposto nella sua villa di Arcetri, cio&egrave; dopo il 1633, <lb/>come v&agrave;, si domanda che Galileo mostra d'ignorar quello strumento, che si <lb/>vorrebbe dare ad intendere essere stato 37 anni prima da lui stesso inventato? </s></p><p type="main">

<s>Molte cose ci si potrebbero qui rispondere &egrave; vero. </s>

<s>Si potrebbe dir che <lb/>nel problema proposto dal Bardi era implicata la teoria del calorico latente <lb/>sconosciuta a que'tempi: si potrebbe dir che il Termometro ad aria, a quel <lb/>modo che solevasi costruire allora, non era atto ad immergersi ne'liquidi, <lb/>per esplorarne la temperatura. </s>

<s>Ma tutte queste risposte non bastano a sodisfar <lb/>punto a coloro, i quali seguitano a credere ancora che Galileo non comprese <lb/>come quella proposta del Bardi era in sostanza un problema di Termome&shy;<lb/>tria. </s>

<s>Ond'&egrave; che agli stessi pi&ugrave; gelosi di Galileo convien confessare come, a <lb/>voler attribuire a lui l'invenzione del Termometro, mancano i documenti, <lb/>e come i documenti che in fino a questo presente giorno, son noti, stanno <lb/>a provar che la prima invenzion dello strumento e le prime applicazioni di <lb/>lui agli usi della scienza, son giustamente dovute al Santorio. </s></p><p type="main">

<s>In conferma di che e delle altre cose fin qui discorse, senza entrare <pb xlink:href="020/01/295.jpg" pagenum="276"/>in pi&ugrave; minuti particolari, ci basti sottoporre alla considerazione dei nostri <lb/>lettori le parole seguenti, che il Sagredo scriveva a Galileo, in una lettera <lb/>del d&igrave; 15 marzo 1615: &ldquo; All'istrumento, dice egli, per misurare li tempe&shy;<lb/>ramenti, io sono andato giornalmente aggiungendo e mutando, in modo che, <lb/>quando avessi a bocca e di presenza a trattare con lei, potrei principiando <lb/>ab ovo facilmente raccontarle tutta l'istoria delle mie invenzioni, o per dire, <lb/>miglioramenti. </s>

<s>Ma perch&egrave;, com'ella mi scrisse, e io certamente credo, V. S. E. <lb/>n'&egrave; stata il primo autore e inventore, perci&ograve; credo che gli strumenti fatti <lb/>da lei e dal suo esquisitissimo artefice avanzino di gran lunga i miei; onde <lb/>la prego con la prima occasione, scrivermi qual sorta di opere finora ella <lb/>abbia fatto fare, ch&egrave; io le scriver&ograve; quel di pi&ugrave; o di meno che finora s'&egrave; <lb/>operato di qu&agrave;, e toccando in ogni nostra lettera alcune cose in questo pro&shy;<lb/>posito, io le scriver&ograve; alcune mie imperfette speculazioni, le quali dal per&shy;<lb/>fettissimo suo giudizio ed intelligenza saranno senza studio e ancora con <lb/>gusto perfezionate. </s>

<s>Quello che si fa autore di questi strumenti &egrave; poco atto, <lb/>per non dire in tutto inetto ad istruirmi conforme al bisogno e desiderio <lb/>mio, siccome io veramente mi sono affaticato a dargli ad intendere la ca&shy;<lb/>gione degli effetti che si vedono in alcuni de'miei strumenti, dir&ograve; cos&igrave;, com&shy;<lb/>positi e multiplicati &rdquo; (Alb. </s>

<s>VIII, 363, 64). </s></p><p type="main">

<s>Da tali parole si rilevano in proposito importanti notizie, e prima di <lb/>tutto siamo certificati essersi fatto Galileo, come l'Alb&egrave;ri sospett&ograve;, e dichia&shy;<lb/>rato al Sagredo, primo autore e inventor del Termometro. </s>

<s>Sappiamo, in <lb/>secondo luogo, che Galileo stesso aveva scritto di esercitare e di fare eser&shy;<lb/>citare la mano agli artefici intorno alla costruzion de'Termometri e in <lb/>intorno ad alcune esperienze fatte con essi. </s>

<s>Ma quale fosse la squisita com&shy;<lb/>posizione de'Termometri galileiani, quai le osservazioni o l'esperienze ter&shy;<lb/>miche fatte con essi, non &egrave; facile a saperlo, essendo sventuratamente smar&shy;<lb/>rite le corrispondenze epistolari col gentiluomo veneziano. </s>

<s>In ogni modo per&ograve; <lb/>sembra che poco potrebbero quelle lettere giovare a coloro, che intendono <lb/>di attribuire a Galileo l'invenzion dello strumento, essendo documenti po&shy;<lb/>steriori alla pubblicazione fatta gi&agrave; dal Santorio. </s></p><p type="main">

<s>Ma la notizia pi&ugrave; importante, che si possa attinger dalle parole del Sa&shy;<lb/>gredo sopra trascritte, &egrave; che egli speculava intensamente intorno al migliorar <lb/>le forme del Termometro, e intorno alle teorie fisiche degli effetti, che sopra <lb/>l'aria inclusa vi produce il calore. </s>

<s>Circa a ci&ograve; s'intrattien lungamente il <lb/>Gentiluomo veneto in un'altra sua lettera, scritta il d&igrave; 11 aprile di quel <lb/>medesimo anno 1615, dalla quale apparisce che, non avendo potuto per s&egrave; <lb/>medesimo ritrovar la ragione dell'ascendere e del discendere il liquido nel <lb/>cannello, al variar della temperatura, ebbe ricorso all'oracolo di Galileo e <lb/>de'responsi di lui rimase sodisfatto. </s>

<s>&ldquo; Ho intesa l'opinione sua, cos&igrave; scrive, <lb/>circa la ragione dell'operare di essi strumenti, la quale mi &egrave; riuscita ca&shy;<lb/>rissima e molto ingegnosa ed ardirei di dire ancor vera, se non fosse che <lb/>questa non &egrave; per s&egrave; stessa palese al senso, n&egrave; credo che per le cose palesi <lb/>al medesimo senso si possa perfettamente procurare &rdquo; (Alb. </s>

<s>VIII, 371). </s></p><pb xlink:href="020/01/296.jpg" pagenum="277"/><p type="main">

<s>La ragione dell'operare dello strumento, insegnata da Galileo al Sagredo, <lb/>doveva esser quella degli egnicoli, che presenti ingrossan l'aria di mole, <lb/>e assenti la diminuiscono, per cui il calore dilata e il freddo restringe. </s>

<s>E <lb/>bench&egrave; il discepolo dica che quella ragione non si rende manifesta al senso, <lb/>il Maestro nonstante credeva di vederla con gli occhi in quelle bollicelle <lb/>di aria, che si sciolgono dal liquido riscaldato, e che egli teneva essere mi&shy;<lb/>nime particelle di fuoco. </s>

<s>In ogni modo per&ograve;, il Sagredo non sapeva rendersi <lb/>la ragione di un altro fatto notabilissimo, osservato nel suo strumento, e il <lb/>fatto era che il liquido nel cannello vedevasi risalir con pi&ugrave; lunghi passi <lb/>ne'gradi inferiori, che nei superiori. </s>

<s>Ci&ograve; &egrave; cosa ora nota che dipende dalla <lb/>varia elasticit&agrave; dell'aria; elasticit&agrave; della quale a que'tempi, come si vedr&agrave; <lb/>meglio a suo luogo, non si aveva chiarissima idea. </s></p><p type="main">

<s>I miglioramenti poi che dal Fisico veneziano si tent&ograve; d'introdurre nello <lb/>strumento, consistono principalmente nel diminuire il calibro del tubo e nel <lb/><figure id="id.020.01.296.1.jpg" xlink:href="020/01/296/1.jpg"/></s></p><p type="caption">

<s>Figura 5.<lb/>piegarlo orizzontalmente, affin&shy;<lb/>ch&egrave; nell'ascesa non dovesse tro&shy;<lb/>var qualche impedimento nel <lb/>suo proprio peso. </s></p><p type="main">

<s>Il passo, che nella sopra <lb/>citata lettera, appella a questi <lb/>perfezionamenti, &egrave; dall'Alb&egrave;ri, <lb/>non si sa perch&egrave;, mutilato, ond'&egrave; <lb/>che noi crediamo opportuno di <lb/>ridurlo qui alla sua integrit&agrave;, <lb/>servendosi dell'autografo, che <lb/>si trova inserito nel Tomo IX <lb/>della Parte VI dei Manoscritti <lb/>di Galileo: &ldquo; Quanto alla dif&shy;<lb/>ferenza e disugualit&agrave; dell'ascesa <lb/>dell'acqua e del vino (tali sono <lb/>le autentiche parole che si leggono in quella scrittura) sebben da principio io <lb/>feci una esperienza in tutto simile alla sua, dell'applicazione della cannella pi&ugrave; <lb/>grossa, ma per&ograve; senza vino, regolata da un'altra misura equivalente; tuttavia <lb/>usai altra maniera, che fu col lasciare attraer nella cannella una determi&shy;<lb/>nata quantit&agrave; di liquore, e levato il vasetto di sotto lasciavo ascendere e <lb/>discendere quel liquore; maniera per&ograve;, che fu da me lasciata in poco tempo, <lb/>siccome un'altra che fu il torcere ad angoli retti il capo della cannella verso <lb/>la palla, e parimenti dalla parte contraria l'altro capo, sicch&egrave; posto a questo <lb/>vasetto la cannella restasse a livello in questo modo . . . . . &rdquo; (c. </s>

<s>252) che <lb/>pi&ugrave; scolpitamente si rappresenta da noi nella Fig. </s>

<s>5. </s></p><p type="main">

<s>Di qui si pare che le molte squisitezze, studiatesi d'introdur nella fab&shy;<lb/>brica del Termometro, furono presto riconosciute inutili dallo stesso Sagredo, <lb/>e ci&ograve; &egrave; manifesto indizio della sua sagacia, specialmente per aver ricono&shy;<lb/>sciuto, almeno in pratica, se non in teoria, che verso la forza che ha il <pb xlink:href="020/01/297.jpg" pagenum="278"/>calore di dilatare un corpo, quella del suo proprio peso, riesce a nulla. </s>

<s>In <lb/>ogni modo egli giustamente si compiace di aver costruito Termometri <emph type="italics"/>mol&shy;<lb/>tiplicatori,<emph.end type="italics"/> co'quali sperimentando pot&egrave; avvedersi che l'aria nell'inverno &egrave; <lb/>assai pi&ugrave; fredda del ghiaccio, e che alcuni ambienti hanno molto diverso <lb/>grado di temperatura, da quel che se ne suol talvolta stimare dai sensi. </s></p><p type="main">

<s>Il Sagredo per&ograve; non si compiace d'altro che della pratica dell'artefice, <lb/>professandosi ignorante delle teoriche dello scienziato per imparar le quali <lb/>si rivolge, come s'&egrave; visto, a Galileo, asserendo che <emph type="italics"/>quello che si fa inven&shy;<lb/>tore di questi strumenti non era atto a istruirlo conforme al bisogno.<emph.end type="italics"/> Se <lb/>non intende qui il Sagredo del Porta, morto in quel medesimo anno 1615, <lb/>non si pu&ograve; creder che la censura cada sopr'altri che sul Santorio. </s>

<s>Eppur <lb/>potrebb'essere che Galileo abbia operato ad avvilir cos&igrave; il suo rivale nella <lb/>stima del troppo credulo e ossequioso amico. </s>

<s>I giudici imparziali per&ograve; non <lb/>crederanno mai che l'Autor de'Commentari sopr'Avicenna non intendesse gli <lb/>effetti del Termometro, ch'ei descrive, almeno a quel modo che pretendeva <lb/>Galileo d'essere stato, a intenderli e a farli intendere, il primo. </s>

<s>Perch&egrave;, in <lb/>ogni modo, la teoria del Termometro e la ragion fisica dell'antichissima <lb/>esperienza eroniana era gi&agrave; divulgata in un libro, da cui potevano facilmente <lb/>apprenderla il Santorio, il Sagredo e Galileo. </s>

<s>Infatti, nelle celebri Disputa&shy;<lb/>zioni <emph type="italics"/>De quibusdam placitis Aristotelis,<emph.end type="italics"/> raccolte poi fra le altre <emph type="italics"/>Specula&shy;<lb/>zioni<emph.end type="italics"/> del Benedetti, dop'aver l'Autore insegnata la ragione dell'attrar che <lb/>fanno la cucurbite la carne dell'infermo, soggiunge: &ldquo; Idem cum amphora, <lb/>in qua nullum aliud quam aereum sit corpus experiri possumus, si eam <lb/>ad ignem primo calefactam, deinde eam ore in amplo aliquo cyatho, aut <lb/>alio vase, vino aut aqua pleno, ubi videbimus huiusmodi liquorem statim <lb/>sursum ferri, quia, dum calefit amphora, rarefit quoque aer, qui in ea con&shy;<lb/>tinetur. </s>

<s>Et, quia rarescit, dilatatur, et quia dilatatur eget maiore loco, et <lb/>ideo magna pars eius foras exit. </s>

<s>Cum vero ea aeris portio quae intus re&shy;<lb/>manserit, iterum condensatur ob defectum caloris restringitur, minorique <lb/>indiget loco. </s>

<s>Quod cum ita se habeat, necessarium est, ne aliquis locus va&shy;<lb/>cuus remaneat, ut aliud quoddam corpus ingrediatur, cum ad ingrediendum <lb/>aeri non patuerit aditus &rdquo; (Venetiis 1599, pag. </s>

<s>193). Ai quali insegnamenti <lb/>del Fisico veneziano ripensando, e a tutto l'altro che s'&egrave; fin qui discorso, <lb/>ci sembrerebbe un voler rimanere ostinati ne'soliti pregiudizii a riguardarsi <lb/>del concluder che a Galileo non si compete alcuna anteriorit&agrave;, n&egrave; quanto <lb/>all'invenzione, n&egrave; quanto agli usi, n&egrave; quanto alla stessa teoria del Termo&shy;<lb/>metro, che egli pure pretende d'attribuirsi, non per alcun diritto, ma per <lb/>secondar quel suo genio di voler essere in tutto il primo ed il solo. </s></p><pb xlink:href="020/01/298.jpg" pagenum="279"/><p type="main">

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

<s>Il Termometro ad aria, di cui faceva uso il Santorio, nonostante le <lb/>modificazioni e i miglioramenti ingegnosamente introdottivi dal Sagredo, se&shy;<lb/>guit&ograve; per lungo tempo a serbar le medesime forme immaginate dal suo <lb/>primo autore, e sotto le quali oramai erasi divulgato. </s>

<s>Bacone infatti, nel <lb/>paragrafo 28 del secondo libro del suo <emph type="italics"/>Nuovo Organo,<emph.end type="italics"/> pubblicato otto anni <lb/>dopo i Commentarii del Santorio, descrive lo strumento, e ne insegna gli <lb/>usi, a quel modo per l'appunto che aveva fatto il nostro Medico giustino&shy;<lb/>politano, tanto &egrave; certo di qui che non compete al Filosofo inglese per nulla <lb/>il merito dell'invenzione, che alcuni pure gli hanno attribuito. </s>

<s>N&egrave; in altro <lb/>modo descrive il barone di Verulamio il Termometro stesso negli altri suoi <lb/>libri, succeduti al Nuovo Organo, come sarebbe l'<emph type="italics"/>Historia naturalis ven&shy;<lb/>torum,<emph.end type="italics"/> nella quale, da pag. </s>

<s>135-75 della edizione, nell'originale latino <lb/>(Lugduni Batav. </s>

<s>1648), si traducono a parole, e s'inseriscono gli aforismi <lb/>del citato libro secondo dello stesso Nuovo Organo, dove si descrive, ne'pre&shy;<lb/>cisi termini come s'&egrave; detto, il Termometro santoriano. </s></p><p type="main">

<s>&ldquo; Infra tutti i corpi, che ci son noti, scrisse ivi Bacone, l'aria &egrave; quella <lb/>che pi&ugrave; presto acquista e perde il calore. </s>

<s>&rdquo; Fu per questa propriet&agrave;, molto <lb/>ben conosciuta infin dai tempi dell'antichissimo Herone, che primi occorsero <lb/>a inventarsi, a tenersi in seguito in pregio, e ad usarsi nelle ricerche scien&shy;<lb/>tifiche i Termometri ad aria. </s>

<s>Il Borelli, in alcune sue Annotazioni al ma&shy;<lb/>noscritto de'<emph type="italics"/>Saggi di Naturali Esperienze,<emph.end type="italics"/> in tal proposito scriveva: &ldquo; Di <lb/>pi&ugrave; ricordo che i nostri Strumenti, ne'quali s'adopra aria rinchiusa in <lb/>qualche vaso, sono tanto gelosi, che non vi &egrave; Termometro di acqua arzente <lb/>(alcool) per grande che egli si sia, che si alteri dal caldo e dal freddo con <lb/>tanta facilit&agrave;: e veramente non v'&egrave; fluido, nel quale il caldo e il freddo operi <lb/>pi&ugrave; dilatandolo e restringendolo, e senza metodo regolato atto a misurarsi <lb/>di quel che sia l'aria &rdquo; (Targioni, Aggrandim. </s>

<s>T. II. P. II. pag. </s>

<s>604). E il <lb/>Montanari, nel sopra citato passo dell'<emph type="italics"/>Astrologia,<emph.end type="italics"/> diceva che sarebbe difficile <lb/>il render sensibile il calor de'raggi lunari, usando Termometri <emph type="italics"/>pieni d'altro <lb/>che d'aria.<emph.end type="italics"/></s></p><p type="main">

<s>Nonostante, avevano que'cos&igrave; fatti Strumenti un d&inodot;fetto notabilissimo, <lb/>ed era quello di risentirsi, non tanto delle variazioni della temperatura, quanto <lb/>di quelle della pressione ammosferica. </s>

<s>La ragione per&ograve; da cui dipende un <lb/>tal difetto non poteva esser riconosciuta, se non che dopo la grande Espe&shy;<lb/>rienza torricelliana. </s>

<s>Fu infatti quello stesso difetto notato colle seguenti <lb/>parole, che si leggono nel Tomo IV de'Manoscritti del Cimento, dove si <lb/>descrivono <emph type="italics"/>alcune varie esperienze attenenti alla questione dell'aria:<emph.end type="italics"/> &ldquo; Da <pb xlink:href="020/01/299.jpg" pagenum="280"/>questa variet&agrave; di pressioni e costipazioni dell'aria gi&agrave; molto bene scoperta <lb/>dal variar d'altezza, che fa l'argento vivo ne'soliti strumenti, la quale &egrave; <lb/>tale che da che io osservo, trovo la sua massima altezza superare la minima <lb/>intorno alla quattordicesima parte di s&egrave; stessa; parmi che si possa dedurre <lb/>un'altra notizia da non sprezzarsi, ed &egrave; che i Termometri a aria non son <lb/>cos&igrave; veridichi, n&egrave; cos&igrave; atti a mostrare il caldo e il freddo dell'ambiente, <lb/>come quelli a acqua serrati dell'ultima invenzione del Galileo, e ci&ograve; perch&egrave; <lb/>in quelli l'acqua nel cannello va mutando altezza, non per l'ingresso ed <lb/>uscita del caldo solamente, come bisognerebbe (oltre al non essere eterni <lb/>perch&egrave; l'acqua per l'apertura si pu&ograve; asciugare) ma perch&egrave; la pressione del&shy;<lb/>l'istessa aria esterna si va mutando dalla pressione dell'interno del vaso, e <lb/>nel voler queste forze equilibrarsi fra loro, l'acqua del cannello ne va di <lb/>mezzo con alzarsi ed abbassarsi, il che non segue nei Termometri a acqua <lb/>serrati, dove non &egrave; contrasto di pressioni, e solo v'opera il caldo che entra <lb/>ed esce. </s>

<s>Se per&ograve;, acci&ograve; si conosca che negli umani artifizi non si pu&ograve; dar <lb/>perfezione, non si voglia dire, che pur questi ancora non son del tutto fe&shy;<lb/>deli, per l'alterazione ultimamente scoperta nella capacit&agrave; delli stessi vasi di <lb/>vetro contenenti l'acqua, per cagione del caldo e del freddo, bench&egrave; questa <lb/>eccezione saria forse tenuta scrupolosa di soverchio e di niuno sensibile <lb/>pregiudizio &rdquo; (c. </s>

<s>9). </s></p><p type="main">

<s>In ogni modo poi, tanto &egrave; vero esser soggetto il Termometro santoriano, <lb/>a risentirsi delle variazioni della pressione ammosferica, che il Boyle pens&ograve; <lb/>di potersene servire, e se ne serv&igrave; di fatto utilmente ad uso di Barometro <lb/>quando volle verificar la celebre esperienza del Pascal sui monti inglesi. <lb/></s>

<s>&ldquo; Sed communis tubi loco (scrive egli nel Cap. </s>

<s>IV della Difesa contro Fran&shy;<lb/>cesco Lini) Thermometro quodam utebamur, ut inclusus aer ad eventum <lb/>reddendum notabilem conferret, ob rationem paulo infra commemorandam, <lb/>mercuriique vice communem aquam in tubo ad Thermometrum pertinente <lb/>adhibebamus, ut leves mutationes in pondere seu resistentia atmosphaerae, <lb/>aeri incluso oppositae dignosci magis possent &rdquo; (Op. </s>

<s>Omn. </s>

<s>Venetiis 1697, <lb/>T. I, pag. </s>

<s>162). </s></p><p type="main">

<s>Un altro inconveniente del Termometro ad aria, a quel modo almeno <lb/>che solevasi costruire dietro i primi modelli offerti dal Santorio, era quello <lb/>di non si poter trasportare comodamente, n&egrave; di poter immergerlo ne'liquidi, <lb/>per esplorarne la temperatura. </s>

<s>&Egrave; vero che s'era cercato di correggere questi <lb/>difetti con lo adottare una costruzione diversa dalla santoriana, facendo cio&egrave; <lb/>servire il vasetto tutto insieme da recipiente dell'aria e dell'acqua, e sal&shy;<lb/>dando il cannello, che mezzo entra dentro e mezzo esce fuori, alla bocca <lb/>dello stesso vasetto, a quel modo per l'appunto, che vedesi disegnato a pa&shy;<lb/>gina 89 de'Circoli Pisani del Beriguardi, stampati in Udine nel 1643 dallo <lb/>Schiratti. </s>

<s>A solo guardar questo nuovo disegno di Termometro ad aria, che <lb/>noi poniam sotto gli occhi de'lettori nella Fig. </s>

<s>6, si vede che lo strumento <lb/>&egrave; facilmente maneggevole, potendosi prendere per la sommit&agrave; del cannello <lb/>a quest'uopo piegato a manico, e potendosi altres&igrave; immergere dentro un <pb xlink:href="020/01/300.jpg" pagenum="281"/>liquido per esser chiuso da ogni parte, e per avere il cannello stesso saldato <lb/>alla bocca del vaso. </s></p><p type="main">

<s>Ma, nonostante questa nuova e pi&ugrave; comoda costruzione, bench&egrave; ivi lo <lb/>chiami il Beriguardi <emph type="italics"/>instrumentum vitreum satis vulgare ad caloris et <lb/><figure id="id.020.01.300.1.jpg" xlink:href="020/01/300/1.jpg"/></s></p><p type="caption">

<s>Figura 6.<lb/>frigoris gradus dignoscendos,<emph.end type="italics"/> non era pure cos&igrave; divulgato, <lb/>quanto poi furono divulgati quegli altri Strumenti, i quali, <lb/>avendo per loro corpo termometrico non l'aria ma un liquido, <lb/>si prestavan comodamente ad esser con tutta facilit&agrave; traspor&shy;<lb/>tati, e ad essere immersi negli altri liquidi, per esplorarli. </s>

<s><lb/>Quando e come avvenisse d'introdur nella costruzione dei <lb/>Termometri un cos&igrave; notabile perfezionamento, &egrave; soggetto <lb/>meritevole delle nostre storiche investigazioni. </s></p><p type="main">

<s>In Italia fu senza dubbio divulgato il nuovo Misuratore <lb/>del caldo tra il 1643 e il 1660, e ci&ograve; pu&ograve; argomentarsi dal <lb/>collazionare le due edizioni che fece, in quelle due date di&shy;<lb/>verse, de'suoi Circoli Pisani, il Beriguardi. </s>

<s>Nella prima di <lb/>quelle edizioni infatti, nel Circolo IV dedicato al principe <lb/>Leopoldo de'Medici, descrive il Termometro ad aria, come si <lb/>disse di sopra. </s>

<s>Ma venendo l'autore a far dell'Opera sua <lb/>una nuova edizione, che ebbe luogo in Padova nel 1660, per opera del <lb/>tipografo Frambolti, e volendola condurre, come oggid&igrave; si direbbe alla al&shy;<lb/>tezza de'tempi, sostituisce alla descrizione e al disegno del Termometro <lb/>ad aria la descrizione e il disegno del Termometro a liquido, che pur se&shy;<lb/>guita anche qui a chiamare <emph type="italics"/>instrumentum vitreum satis vulgare<emph.end type="italics"/> (ivi, <lb/>pag. </s>

<s>447). </s></p><p type="main">

<s>Nel 1644 in Francia non si conosceva altro Termometro che quel pneu&shy;<lb/>matico, e a far fede di ci&ograve;, pu&ograve; bastar, fra tutti gli altri documenti, la <emph type="italics"/>Hy&shy;<lb/>draulica pneumatica<emph.end type="italics"/> del Mersenno, il quale venuto a fiutar per tutto in <lb/>Italia, dove sentiva venir l'odore di qualche invenzione, non sarebbe man&shy;<lb/>cato di far preda, per trasportarla a Parigi, anco di questo Termometro a <lb/>liquido, se davvero ce lo avesse trovato. </s>

<s>Anzi nemmen dieci anni dopo, <lb/>sembra che fosse diffuso in Francia il nuovo strumento, imperocch&egrave;, negli <lb/><emph type="italics"/>Esperimenti nuovi anatomici,<emph.end type="italics"/> il Pecquet seguit&ograve; ancora a descrivere, come <lb/>avea fatto il Mersenno, la prima e pi&ugrave; antica forma del Termometro san&shy;<lb/>toriano. </s>

<s>E bench&egrave; nel 1666 i nuovi Strumenti a liquido si divulgassero <lb/>solennemente nelle descrizioni e negli iconismi de'<emph type="italics"/>Saggi di Naturali Espe&shy;<lb/>rienze,<emph.end type="italics"/> nonostante al lontano Giorgio Sinclaro non pervenne una tale im&shy;<lb/>portante notizia che verso il 1669, come s'ha dalle seguenti sue parole, che <lb/>si trascrivon qui dal I Dialogo del lib. </s>

<s>III della sua <emph type="italics"/>Ars nova et magna <lb/>gravitatis et levitatis:<emph.end type="italics"/> &ldquo; Aquam imbutam asse virtute rarefactiva, multum <lb/>mihi persuadetur ex nobili quodam experimento, quod <emph type="italics"/>nudiustertius<emph.end type="italics"/> solum <lb/>vidi. </s>

<s>Fuit enim Thermoscopium utrinque hermetice occlusum. </s>

<s>Nam inferne <lb/>rotundam habuit ampullam superne etiam aliam, sed altera multo minorem. </s>

<s><lb/>Inter has tenuem admodum fistulam. </s>

<s>Eius dimidium inferius aqua, vel po-<pb xlink:href="020/01/301.jpg" pagenum="282"/>tius praestantissimo vini spiritu, superius vero aere repletum &rdquo; (Roteroda&shy;<lb/>mi, 1669, pag. </s>

<s>273, 74). </s></p><p type="main">

<s>Il Termoscopio descritto qui dal Sinclaro &egrave; quello stesso, che i nostri <lb/>Accademici del Cimento descrissero in primo luogo, fra i loro strumenti, <lb/>per conoscer le mutazioni del caldo e del freddo dell'aria. </s>

<s>&ldquo; Egli &egrave; tutto <lb/>di cristallo finissimo (fig. </s>

<s>7) lavorato per opra di quegli artefici, i quali, ser&shy;<lb/>vendosi delle proprie gote per mantice, tramandano il fiato per un organo <lb/>di cristallo alla fiamma d'una lucerna; e quella o intera o in varie linguette <lb/>divisa, di mano in mano dove richiede il bisogno di lor lavoro spirando, <lb/>vengono a formar opere di cristallo delicatissime e maravigliose. </s>

<s>Noi un <lb/>tal artefice chiamiamo il Gonfia. </s>

<s>A lui dunque s'apparterr&agrave; di formar la <lb/><figure id="id.020.01.301.1.jpg" xlink:href="020/01/301/1.jpg"/></s></p><p type="caption">

<s>Figura 7.<lb/>palla dello strumento d'una tal capacit&agrave; e grandezza, e di attac&shy;<lb/>carvi un cannello di tal misura di vano, che riempiendolo fin a <lb/>certo segno del suo collo con acquarzente, il semplice freddo <lb/>della neve e del ghiaccio non basti a condensarlo sotto i 20 <lb/>gradi del cannellino; come per lo contrario, la massima attivit&agrave; <lb/>de'raggi solari eziandio nel cuor della state non abbia forza di <lb/>rarefarlo sopra gli 80 gradi. </s>

<s>Il modo d'empierlo sar&agrave; con arro&shy;<lb/>ventar la palla, e poi subito tuffar la bocca del cannellino aperta <lb/>nell'acquarzente, sicch&egrave; vada a poco a poco succiandola. </s>

<s>Ma <lb/>poich&egrave; &egrave; difficile, se non affatto impossibile, di cavar tutta l'aria <lb/>per via di rarefazione, e per ogni poca che ve ne resti la palla <lb/>rimane scema, si potr&agrave; finir d'empiere con un imbuto di cri&shy;<lb/>stallo, ch'abbia il collo ridotto ad un'estrema sottigliezza. </s>

<s>Ci&ograve; <lb/>s'otterr&agrave;, quando la pasta del cristallo &egrave; rovente, poich&egrave; allora <lb/>si tira in fila sottilissime dentro accanalate e vote, com'&egrave; ma&shy;<lb/>nifesto a chi di lavorare il cristallo ha notizia. </s>

<s>Con un simile <lb/>imbuto adunque si potr&agrave; finir d'empiere il Termometro, intro&shy;<lb/>ducendo nel cannellino il suo sottilissimo collo, e spingendovi <lb/>dentro, colla forza del fiato il liquore, o risucciandone se fosse <lb/>troppo. </s>

<s>&Egrave; ancora da avvertire che i gradi sopra il cannello ven&shy;<lb/>gano segnati giusti; e per&ograve; bisogna scompartirlo tutto colle se&shy;<lb/>ste diligentemente in dieci parti uguali, segnando le divisioni con un bot&shy;<lb/>toncino di smalto bianco. </s>

<s>Poi si segneranno gli altri gradi di mezzo con <lb/>bottoncini di vetro o di smalto nero; e questo scompartimento si potr&agrave; fare <lb/>a occhio essendoch&egrave; l'esercizio, studio e industria dell'arte insegna da per <lb/>s&egrave; stessa a ragguagliare gli spazi, e a ben aggiustare la divisione; e chi <lb/>v'ha fatto la pratica suole sbagliar di poco. </s>

<s>Come queste cose son fatte, e <lb/>col cimento del sole e del ghiaccio s'&egrave; aggiustata la dose dell'acquarzente, <lb/>allora si serra la bocca del cannello col sigillo detto volgarmente d'Ermete, <lb/>cio&egrave;, colla fiamma, ed &egrave; fatto il Termometro &rdquo; (Firenze 1841, pag. </s>

<s>12, 13). </s></p><p type="main">

<s>Da questa bellissima descrizione, lasciando indietro le altre, nelle quali <lb/>si dice il modo di render pi&ugrave; sensibile lo strumento, allungando il cannello <lb/>e rigirandolo a spira, o compartendo in altro numero di divisioni la scala; <pb xlink:href="020/01/302.jpg" pagenum="283"/>abbiamo la pi&ugrave; compiuta notizia di ci&ograve; che fosse il nuovo Termometro, pi&ugrave; <lb/>comodamente trasformato e costruito sopra un altro fatto fisico diverso da <lb/>quello che dette origine all'invenzione del Termometro santoriano. </s>

<s>Ma qui <lb/>occorrono a fare alcune domande, che troppo importano alla nostra storia, <lb/>e delle quali non d&agrave; alcuna sodisfazione l'Autor de'<emph type="italics"/>Saggi,<emph.end type="italics"/> che primo di&shy;<lb/>vulg&ograve; la notizia de'nuovi strumenti. </s></p><p type="main">

<s>Si pu&ograve; per prima cosa domandare: Fu veramente il Termometro ad al&shy;<lb/>cool, descritto nel Libro De'Saggi di Naturali esperienze, un'invenzione degli <lb/>Accademici del Cimento? </s>

<s>E a ci&ograve; &egrave; stato risposto gi&agrave; altrove ai nostri let&shy;<lb/>tori, i quali sanno che fu quella invenzione attribuita al Granduca Ferdi&shy;<lb/>nando II, nel primo periodo della Sperimentale Accademia medicea. </s>

<s>L'Au&shy;<lb/>tore per&ograve; della descrizione sopra riferita, ossia il segretario Lorenzo Magalotti, <lb/>non fa nemmen di ci&ograve; il minimo accenno, cosicch&egrave; &egrave; impossibile saper da <lb/>quelli stessi, che furon primi a farne uso, chi fu l'inventore del nuovo Ter&shy;<lb/>mometro a liquido. </s>

<s>N&egrave; pur cercando per i Manoscritti, sien essi i Diarii o <lb/>sieno altre carte appartenenti all'Accademia Fiorentina, abbiam trovato modo <lb/>di sodisfare a questa nostra curiosit&agrave;: solamente l'Autore della Nota ora <lb/>ultimamente trascritta l'abbiam sentito chiamare il nuovo Strumento <emph type="italics"/>Ter&shy;<lb/>mometro dell'ultima invenzione di Galileo.<emph.end type="italics"/> Una tal sentenza riduce in <lb/>certezza il sospetto che Autore di quella Nota fosse il Viviani, di cui &egrave; ora&shy;<lb/>mai noto lo zelo esagerato di volere ogni nuovo genere d'invenzioni attri&shy;<lb/>buire al suo adorato Maestro. </s>

<s>Fa nulladimeno assai maraviglia che si risol&shy;<lb/>vesse d'attribuire a Galileo il nuovo Strumento colui, che trascrisse di <lb/>propria mano il <emph type="italics"/>Registro di varie esperienze fatte e osservate dal Serenis&shy;<lb/>simo G. D. </s>

<s>Ferdinando II e raccolte da Paolo Minucci per propria cu&shy;<lb/>riosit&agrave;.<emph.end type="italics"/></s></p><p type="main">

<s>In un tal Registro, di cui la copia fattane dal Viviani, &egrave; inserita a c. </s>

<s>10 <lb/>del T. </s>

<s>I de'Manoscritti del Cimento, si vedono in margine disegnati o di&shy;<lb/>ciam meglio abbozzati, due strumenti, il primo de'quali, distinto colla let&shy;<lb/>tera A, rappresentante l'antico Termometro santoriano, e l'altro, distinto <lb/>colla lettera B, rappresenta precisamente il Termometro a liquido, qual fu <lb/>poi descritto nel libro dei <emph type="italics"/>Saggi,<emph.end type="italics"/> e qual noi di sopra abbiam riprodotto nella <lb/>Figura settima sotto gli occhi dei nostri lettori. </s>

<s>Allato ai due disegni, nel <lb/>citato <gap/>anoscritto, si legge: &ldquo; Lo strumento A &egrave; continuo e dimostra il caldo <lb/>e il freddo dell'aria, per mezzo dell'acqua..... Lo strumento B dimostra <lb/>la differenza di caldo e di freddo dell'aria e de'liquidi, ed &egrave; perpetuo &rdquo;. </s>

<s>Alla <lb/>carta 3 in un'altra bozza di questo stesso Registro, &egrave; alla Figura A no&shy;<lb/>tato: &ldquo; strumento contrario, che al freddo sale e al caldo scende &rdquo;. </s>

<s>In que&shy;<lb/>ste noterelle si pu&ograve; dir che si contenga la storia autentica del Termometro <lb/>a liquido, la quale storia sar&agrave; per tornar tanto meglio conforme al vero, se <lb/>al nome di Ferdinando II Granduca, si sostituisce nel titolo del Registro il <lb/>nome del Torricelli, fisico e matematico. </s></p><p type="main">

<s>Gioverebbe ora proseguire a cercare a quale occasione venisse fatto al <lb/>Torricelli d'inventare e di costruire il nuovo Termometro a liquido. </s>

<s>Ma viene <pb xlink:href="020/01/303.jpg" pagenum="284"/>ad arrestarci il passo un documento, che fa
cos&igrave; scrivere a Guglielmo Libri, <lb/>nel porgerlo fedelmente trascritto ai suoi lettori: &ldquo; Le premier qui, &agrave; ma <lb/>connaissance, ait ferm&egrave; le thermom&egrave;tre et l'ait soustrait ainsi &agrave; l'influence <lb/>de la variation de la pression atmosph&egrave;rique, a &egrave;t&egrave; un ing&egrave;nieur romain <lb/>appel&egrave; Telioux, auteur d'une <emph type="italics"/>Matematica maravigliosa,<emph.end type="italics"/> r&egrave;dig&egrave;e &agrave; Rome <lb/>en 1611, et qui se trouve maintenant &agrave; la Biblioth&egrave;que de l'Arsenal (<emph type="italics"/>MSS <lb/>italiens<emph.end type="italics"/> n. o20, pag. 44). </s><s>Voici la description que Telioux donne du <lb/> thermo&shy;<lb/>m&egrave;tre: <emph type="italics"/>Instrumento composto da due fiale, col quale si conosce il cam&shy;<lb/>biamento del tempo in caldo e in freddo, secondo gradi e minuti &rdquo;.<emph.end type="italics"/> (His&shy;<lb/>toire des Sciences math&egrave;m. T. IV, Paris 1841, pag. 471) e prosegue recando <lb/>la descrizione dell'Ingegnere romano, illustrata da un'apposita figura. </s>

<s>Lo <lb/>strumento del Telioux ha senza dubbio qualche cosa di singolare, parteci&shy;<lb/>pando del Termometro ad aria, descritto dal Beriguardi nella prima edizione <lb/>dei Circoli Pisani, e del Termometro a liquido del Torricelli. </s>

<s>Attendendo <lb/>bene infatti si vede che l'acqua al caldo sale e per impulso dell'aria dila&shy;<lb/>tata nell'ampolla inferiore, e per la dilatazione sua propria. </s>

<s>Non si pu&ograve; <lb/>per&ograve; in ogni modo negare all'inventore di questo strumento che egli non <lb/>abbia, molto prima del Torricelli, conosciuta la propriet&agrave; che hanno i liquidi <lb/>di dilatarsi al calore, e ch'ei non abbia saputo farne suo pr&ograve;, nel costruire <lb/>un Termometro nuovo. </s>

<s>Ma perch&egrave; &egrave; difficile il far la giusta ragion del me&shy;<lb/>rito a un Autore ignoto, e a un manoscritto rimasto per due secoli e mezzo <lb/>sepolto in paese straniero, riprendiamo l'ordine della nostra storia, per ve&shy;<lb/>nire a vedere a quale occasione il Torricelli pensasse di usar per misura <lb/>pi&ugrave; comoda del calore le dilatazioni de'liquidi, piuttosto che quelle dell'aria. </s></p><p type="main">

<s>Ei, fedel seguace degli ammaestramenti di Galileo, non poteva non pren&shy;<lb/>der parte alle controversie, e con tanto pi&ugrave; ardore &egrave; da credere che vi si <lb/>mettesse, quando, a combattere gli avversari, vedeva scendere in campo a <lb/>viso scoperto il suo diletto Maestro Benedetto Castelli. </s>

<s>Perci&ograve;, nel leggere <lb/>la <emph type="italics"/>Risposta a Lodovico delle Colombe,<emph.end type="italics"/> il pensiero meditativo dell'illustre <lb/>Discepolo dov&egrave; trattenersi intorno a quella esperienza, che si legge ivi de&shy;<lb/>scritta colle seguenti parole: &ldquo; Presa poi per nostro maggiore avvertimento <lb/>una caraffa col collo assai lungo, e empiutala d'acqua sino a mezzo il collo, <lb/>e messala al fuoco, ci mostr&ograve; come, nello scaldarsi, ella andava ricrescendo, <lb/>sicch&egrave;, avanti che levasse il bollore, era accresciuta pi&ugrave; di tre dita: rimos&shy;<lb/>sala poi dal fuoco, nell'intepidirsi, andava decrescendo e riducendosi al pri&shy;<lb/>miero stato &rdquo; (Alb. </s>

<s>XII, 419, 20). </s></p><p type="main">

<s>Di qui era facile il passaggio al Termometro a liquido, e il Torricelli <lb/>pens&ograve; ingegnosamente di costruire sul fondamento di questa esperienza de&shy;<lb/>scritta dal Castelli e da Galileo, il suo nuovo strumento. </s>

<s>Se poi l'invenzione <lb/>di questo fu applicata al Granduca Ferdinando II non si pu&ograve; attribuir ci&ograve;, <lb/>ripetiamo, ad altro che a un cortigianesco ossequio, e a quell'ingerirsi che <lb/>faceva il <emph type="italics"/>Padrone<emph.end type="italics"/> nelle esperienze fisiche del suo Matematico pensionato. </s>

<s><lb/>In ogni modo, circa all'anno 1644, questo nuovo Misuratore de'gradi del <lb/>calore che, chiuso d'ogni sua parte, si poteva, senza pericolo di versare il <pb xlink:href="020/01/304.jpg" pagenum="285"/>liquido rinchiuso, e senza il tedio di dovervene infonder del nuovo, quando, <lb/>come avveniva ne'primi Termometri ad aria, fosse esalato dal vasetto, tra&shy;<lb/>sportar comodamente e immerger ne'liquidi e sommergersi nella neve, per <lb/>conoscerne la temperatura; questo nuovo strumento era usato nell'Accade&shy;<lb/>mia medica in fin da quel tempo, quando ancora gli scienziati stranieri se&shy;<lb/>guitavano a travagliarsi con l'incomodo e imperfetto Termometro santoriano. </s>

<s><lb/>Dalle mani del Torricelli o del Granduca Ferdinando ebbero questo Termo&shy;<lb/>metro nuovo, come per legittima e necessaria eredit&agrave;, gli Accademici del <lb/>Cimento, i quali ne diffusero nel loro Libro la notizia e l'uso per ogni parte <lb/>d'Europa. </s></p><p type="main">

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

<s>Il nuovo Strumento, misuratore de'gradi del calore, il quale, inventato <lb/>in Firenze e usato agli sperimenti, che si facevano nella Corte medicea, fu <lb/>perci&ograve; meritamente appellato col nome di <emph type="italics"/>Termometro fiorentino;<emph.end type="italics"/> se nella <lb/>pratica si rassomigliava ai Termometri santoriani, era per&ograve; nella teorica al&shy;<lb/>quanto diverso, fondandosi sulla propriet&agrave; che ha il calore di dilatare i li&shy;<lb/>quidi. </s>

<s>Ora &egrave; notabile come questa propriet&agrave; s'appresenti nella storia della <lb/>scienza sotto l'aspetto di nuova, e contenga perci&ograve; in s&egrave; il pregio di una <lb/>vera scoperta. </s>

<s>Per primo indizio e avvedimento di ci&ograve;, giova sottoporre alla <lb/>considerazione dei nostri lettori il seguente passo, che il Torricelli leggeva <lb/>e che noi pure possiamo rileggere nella citata <emph type="italics"/>Risposta a Lodovico delle <lb/>Colombe:<emph.end type="italics"/> &ldquo; Ma poich&egrave; la sottigliezza del fuoco avanza quella del discorso <lb/>di molti, quindi hanno avuto origine quelle qualit&agrave; calde, delle quali in que&shy;<lb/>sto luogo scrivete, dicendo che si comunicano per lo contatto al vetro e poi <lb/>dal vetro all'acqua, onde poi l'acqua alterata si commuove per quella qua&shy;<lb/>lit&agrave; sua contraria, si raref&agrave;, gonfia, circola in s&egrave; medesima per refrigerarsi <lb/>e conservarsi contro il suo distruttivo, n&egrave; potendo resistere interamente si <lb/>risolve in vapore aereo e calido, e finalmente, dopo tanti suoi decorsi e ma&shy;<lb/>nifatture, facendo forza d'evaporare all'aria, solleva le dette falde (galleg&shy;<lb/>gianti sull'acqua)..... Io voglio anco in questo particolare, come in tanti <lb/>altri, vedere di arrecarvi qualche giovamento e cavarvi d'errore .... Pigliate <lb/>una palla di vetro col collo lungo e assai sottile, simile a quelle che i no&shy;<lb/>stri fanciulli chiamano gozzi: empietela d'acqua sino a mezzo il collo, e se&shy;<lb/>gnate diligentemente il termine sin dove arriva l'acqua; tenete poi tal vaso <lb/>sopra alcuni carboni accesi, ed osservate che, come prima il fuoco percuo&shy;<lb/>ter&agrave; nel vetro, l'acqua comincia a ricrescere (n&egrave; ci &egrave; bisogno aspettare che <lb/>ella bolla per vedere tal effetto, come forse vi eri immaginato).... Volendo <lb/>poi vedere sensatamente da che derivi questo ricrescimento, andate con di&shy;<lb/>ligenza osservando e vedrete che, secondo che gli atomi di fuoco si vanno <pb xlink:href="020/01/305.jpg" pagenum="286"/>moltiplicando per l'acqua, ed aggregandosene molti insieme, formano alcuni <lb/>piccoli globettini, li quali in gran numero vanno ascendendo per l'acqua, e <lb/>scappando fuori della sua superficie; e secondo che per entro l'acqua ne <lb/>sar&agrave; maggior numero, ella pi&ugrave; si alzer&agrave; nel collo del vaso, e continuando <lb/>di tenergli sotto i carboni lungo tempo, vedrete molte migliaia di tali glo&shy;<lb/>betti ascendere e scappar via. </s>

<s>Questi, signor Colombo, non sono come vi <lb/>credete, vapori generati da alcune parti d'acqua, che, mediante la qualit&agrave; <lb/>celida del fuoco si vada in quelli risolvendo e tramutando: il che &egrave; mani&shy;<lb/>festo, perch&egrave; se, dopo che ne saranno andate moltissime migliaia, voi rimuo&shy;<lb/>verete i carboni ed aspetterete che anco gli altri, che pi&ugrave; sparsamente e <lb/>perci&ograve; invisibili, per l'acqua erano disseminati, si partano loro ancora, ve&shy;<lb/>drete l'acqua andare pian piano abbassandosi, e finalmente ridursi al segno <lb/>medesimo che notaste nel collo del gozzo, senza essere scemata pure una <lb/>gocciola; e se voi mille volte tornerete a far tale operazione, vedrete pas&shy;<lb/>sare per l'acqua milioni di tale sferette di fuoco, senza che l'acqua scemi <lb/>mai un capello &rdquo; (Alb. </s>

<s>XII, 466, 67). </s></p><p type="main">

<s>Da ci&ograve; si raccolgono due notizie importanti: l'osservazione del ricre&shy;<lb/>scer l'acqua, anco prima di bollire, al calore, proposta dal Castelli e da Ga&shy;<lb/>lileo alla considerazione dei Peripatetici come nuova, e le ragioni del fatto <lb/>riconosciute nell'introdursi, fra le particelle del liquido, gli atomi ignei, resi <lb/>sensibili in quelle bollicelle, che noi siamo ora certi non essere altrimenti <lb/>piene di fuoco, ma d'aria. </s>

<s>Quella osservazione diciamo che conteneva in s&egrave; <lb/>una nuova scoperta, n&egrave; fa nulla in contrario il sentire i Peripatetici andar <lb/>con gran solennit&agrave; professando quel loro principio: <emph type="italics"/>caloris est rarefacere et <lb/>frigoris condensare.<emph.end type="italics"/> Bench&egrave; derivi un tal principio dall'antica scuola, e for&shy;<lb/>mulato in modo cos&igrave; generale sembri dover essere stato applicato ad ogni <lb/>qualit&agrave; di corpi, nulladimeno &egrave; un fatto che i Fisici, coll'attenzione tutta <lb/>rivolta alle esperienze pneumatiche di Herone, e alle applicazioni che se ne <lb/>fecero in tante varie e curiose maniere, non seppero applicarlo ad altro <lb/>corpo che all'aria. </s>

<s>Gli atomi ignei infatti di Galileo, forse perch&egrave; troppo <lb/>manifestamente si tradivano sotto l'aspetto visibile e riconoscibile dell'aria, <lb/>furono abbandonati, specialmente dagli stranieri, per ritornar poi rimessi in <lb/>onore dal Borelli, e ritenuto il fatto prima notato nella citata <emph type="italics"/>Risposta al <lb/>Colombo,<emph.end type="italics"/> i Fisici vollero piuttosto attribuir l'effetto del dilatarsi i liquidi <lb/>all'aria insinuata dentro alle loro particelle; aria che si dilata ivi dentro al <lb/>calore, a quel modo che nel termometro santoriano. </s></p><p type="main">

<s>Una tal dottrina &egrave; quella che fu apertamente professata da Stefano <lb/>No&euml;l o Natale, in quel libretto che intitol&ograve; <emph type="italics"/>Plenum experimentis novis con&shy;<lb/>firmatum,<emph.end type="italics"/> e in cui, coll'intenzione di dimostrar la falsit&agrave; del vacuo, si dif&shy;<lb/>fusero in Francia le otto celebri esperienze istituite dal Pascal in Roano e <lb/>a Parigi, per confermar la verit&agrave; della grande Esperienza torricelliana. </s>

<s>Il <lb/>Capitolo VIII dunque, della prima parte, Sezione V, di quel libro, &egrave; dal&shy;<lb/>l'Autore intitolato: &ldquo; Unde motus aquae in Thermometro &rdquo; e cos&igrave; dice del <lb/>soggetto, che s'era proposto di trattare in quel capitolo: &ldquo; Sensibiles mo-<pb xlink:href="020/01/306.jpg" pagenum="287"/>tus aquae in Thermometro nulla alia ratione explicari posse mihi videntur <lb/>quam per ingressionem motumque spirituum igneorum, qui ab aere calido <lb/>vel manu calefacta erumpunt. </s>

<s>Spiritus calidi qui continuo absistunt ex manu <lb/>calida, vel pruna accensa, quae vel contigua est vel vicina phialae Ther&shy;<lb/>mometro, dilatant aerem, qui est in tubo, insinuando se in eius poros. </s>

<s>Hic <lb/>autem aer, cum iam ampliorem in Thermometro locum occupat, propellit <lb/>aquam eamque dum subit in eius poros se insinuat, extendit. </s>

<s>Hunc aquae <lb/>recessum ac tumorem ipsis etiam oculis intuemur &rdquo; (Parisiis 1648, pag. </s>

<s>24). </s></p><p type="main">

<s>Si vede bene che gli spiriti ignei, cos&igrave; ben distinti dall'aria, secondo <lb/>il No&euml;l, son tutt'altra cosa dagli atomi ignei di Galieo, ne &egrave; da passar sotto <lb/>silenzio che il Gesuita francese par che fosse de'primi a conoscere il Ter&shy;<lb/>mometro a liquido, la notizia del quale attratta da Firenze per i soliti invi&shy;<lb/>sibili aliti aspirati dal Collegio Romano, poteva di li, nel 1648, essere stata <lb/><figure id="id.020.01.306.1.jpg" xlink:href="020/01/306/1.jpg"/></s></p><p type="caption">

<s>Figura 8.<lb/>trasmessa ai colleghi di Parigi. </s>

<s>Ma che non fosse allora in <lb/>Francia quello strumento molto diffuso, si prova dal seguente <lb/>passo che noi trascriviamo dal celebre libro <emph type="italics"/>Experimenta <lb/>nova anatomica,<emph.end type="italics"/> dove il Pecquet, attentamente osservando <lb/>gli effetti prodotti dal calore nel Termometro santoriano, nota <lb/>di avere scoperto che non solo si dilata l'aria, ma l'acqua <lb/>altres&igrave;, ci&ograve; che egli attribuisce al dilatarsi e all'insinuarsi <lb/>delle particelle aeree calde, o contenute nell'ampolla, o pree&shy;<lb/>sistenti gi&agrave; nell'acqua stessa: &ldquo; Ita impacta superiori Ther&shy;<lb/>mometro ampullae manus aut admotae prunae vicinia conten&shy;<lb/>tam deprimit aquam: insigni sane argumento, dilatatum intus <lb/>aerem, exterioris, quem aqueo cedere descensui cogit robori <lb/>praecellere. </s>

<s>Nec suos duntaxat fines caloris incentivo producit <lb/>aer: etiam aquae moles extenditur. </s>

<s>Id expertu facile, si pen&shy;<lb/>dulum medio Thermometri caule placeat aquae particulam C <lb/>(fig. </s>

<s>8), in infimam sustinentis aeris sedem reprimere; nam <lb/>admotus ignis superiori lagunculae A, non inclusam C, solum&shy;<lb/>modo deorsnm adigit aquam, sed et eamdem (sive quem dilatat aerem A, in <lb/>descendentem C, aquam immergat, sive descendentis aquae partes aereas <lb/>ad rarefactionem excitet) ad certum usque, puta gradum, quae vix geminus <lb/>occupabat, cogit excrescere &rdquo; (Parisiis 1654, pag. </s>

<s>67, 68). </s></p><p type="main">

<s>Non dissimili dottrine da queste son quelle professate dal Sinclaro, nel <lb/>Dialogo fra Alessandro e Francesco sopra citato. </s>

<s>Dop'avere Alessandro par&shy;<lb/>ticolarmente descritti gli effetti degli accessi e de'recessi del calore, nel cre&shy;<lb/>scere o diminuir la lunghezza della colonnetta liquida nel cannello del Ter&shy;<lb/>moscopio, Francesco dice: &ldquo; Opinor hoc phoenomenon evenire non ab ipsa <lb/>aqua, sed potins a nonnullis in ea latitantibus particulis aereis, quarum ma&shy;<lb/>gna copia scatet &rdquo; a che Alessandro acconsente dicendo esser l'espression <lb/>dell'amico <emph type="italics"/>verisimile.<emph.end type="italics"/> (Ars Magna edit. </s>

<s>cit., pag. </s>

<s>274). </s></p><p type="main">

<s>Tutti insomma gli Autori sopra citati concordano in ammetter che il <lb/>calore non operi direttamente sul liquido in dilatarlo, ma indirettamente <pb xlink:href="020/01/307.jpg" pagenum="288"/>sull'aria, intorno alla quale il Pecquet rimane incerto se ella introducasi <lb/>per accidentalit&agrave; dal di fuori, o se vi si trovi in mezzo di gi&agrave; sciolta. </s>

<s>Il Sin&shy;<lb/>claro, quindici anni dopo, parla con pi&ugrave; sicurt&agrave;, asseverando che, d'aria, <lb/>l'acqua <emph type="italics"/>magna copia scatet.<emph.end type="italics"/> E infatti la dimostrazione sperimentale della <lb/>soluzione dell'aria ne'liquidi, fu data dai nostri Accademici del Cimento, <lb/>dopo che avea pubblicati i Nuovi esperimenti anatomici il Pecquet, e prima <lb/>che apparisse alla luce l'Arte Magna del Sinclaro. </s></p><p type="main">

<s>In qualunque modo per&ograve;, &egrave; notabile che, in aguzzar l'ingegno per tro&shy;<lb/>var la ragion degli effetti del calore ne'liquidi termometrici, i Filosofi na&shy;<lb/>turali di que'tempi intravedessero, per ipotesi, l'esistenza dell'aria annida&shy;<lb/>tasi dentro i pori de'corpi anche pi&ugrave; continui. </s>

<s>De'Filosofi per&ograve; pubblicamente <lb/>conosciuti nessuno a parer nostro &egrave; pi&ugrave; acuto di un autore italiano, i con&shy;<lb/>cetti del quale son rimasti sepolti e dimenticati ne'suoi Manoscritti. </s>

<s>Niccol&ograve; <lb/>Aggiunti che, morto nel 1635, non fu in tempo a veder pubblicati i Dialo&shy;<lb/>ghi delle Due Nuove Scienze del suo Maestro, ha, per render la ragione di <lb/>alcuni effetti molecolari prodotti dall'azion del calore e, per ispiegar le mec&shy;<lb/>caniche trazioni sui corpi, teorie singolarissime e, giacch&egrave; non son punto <lb/>fuori del proposito nostro, degnissime di esser sapute. </s></p><p type="main">

<s>Egli dunque, non solo aveva scoperto che il calore dilata un filo liquido, <lb/>ma che dilata altresi un filo solido di metallo: &ldquo; Cordas e metallo per se <lb/>contrahi et diduci, experimento adverteris si cordae pendenti e lacunari, <lb/>plumbeum alligaveris acuminatum: etenim subiecto signo, videbis acumen <lb/>modo proprius modo longius dimitti vel attolli, prout calor aut frigus impe&shy;<lb/>ritaveris &rdquo; (MSS Gal. </s>

<s>Dis. </s>

<s>T. XVIII, c. </s>

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

<s>L'esperimento semplicissimo &egrave; per la sua stessa novit&agrave; <lb/><figure id="id.020.01.307.1.jpg" xlink:href="020/01/307/1.jpg"/></s></p><p type="caption">

<s>Figura 9.<lb/>stupendo, ma &egrave; bene assai pi&ugrave; stupenda la teoria dal suo Au&shy;<lb/>tore escogitata, per ispiegarlo. </s>

<s>Una tal teoria non &egrave; di quelle, <lb/>com'usava a que'tempi, ripescate con gli uncini aristotati&shy;<lb/>lici nel cervello di un Penpaletico, ma essa pure &egrave; fondata <lb/>sopra un altro nuovo e singolarissimo esperimento: &ldquo; Hoc <lb/>proponimus animadvertendum. </s>

<s>Si fuerit poculus vel syphun&shy;<lb/>culus AB (fig. </s>

<s>9) eiusque manubrium EC cui annexum sit <lb/>optimum obturamentum E, quod paullulum distet a fundo <lb/>CA ori fistulae probe occluso, cum voluerimus manubrium <lb/>attrahere, multo maiorem vim nobis obsistentem sentiemus, <lb/>quam si recluso fistulae osculo traheretur. </s>

<s>Hanc tamen vim <lb/>superabimus, neque enim infinita est. </s>

<s>Pertracto igitur vi ma&shy;<lb/>nubrio EC, perveniet tandem ad partes MG. </s>

<s>Aer igitur, qui <lb/>antea concludebatur in spatio CB, iam ampliabitur, ac deducetur in maius <lb/>spatium CM. </s>

<s>Quia vero haec diductio violenta fuit, violenter, et sic didu&shy;<lb/>ctus, manebit. </s>

<s>Quanta autem vis est, qua manubrium retinemus pertractum <lb/>ad loca MG, tanta est naturalis propensio atque impetus, quo rediret ad <lb/>pristina loca BE. </s>

<s>Quapropter statim atque vim removeris manubrium, illico <lb/>celeriter redibit ad partes BE, ut oculatim testatur experimentum &rdquo; (ibi). </s></p><pb xlink:href="020/01/308.jpg" pagenum="289"/><p type="main">

<s>Chi, da queste informi carte manoscritte, passa a legger quelle nitide <lb/>pagine 18 e 19 del primo Dialogo delle Due Nuove Scienze, nel Tomo XIII <lb/>dell'edizione curata dall'Alb&egrave;ri, non pu&ograve; non ripensar con sorpresa come i <lb/>fecondi concetti sulla natura del vacuo, ivi espressi alcuni anni dopo da Ga&shy;<lb/>lileo, si riscontrino mirabilmente con quelli dell'Aggiunti; e come l'espe&shy;<lb/>rimento l&agrave; descritto dal Discepolo aprisse la via all'altro importantissimo <lb/>esperimento, con cui qu&agrave; il Maestro tent&ograve; di misurar la forza del vacuo <lb/>stesso. </s>

<s>Si pu&ograve; con facilit&agrave; credere che que'concetti gli avesse Galileo inspi&shy;<lb/>rati nell'Aggiunti, nel privato insegnamento, prima di pubblicarli solenne&shy;<lb/>mente ne'Dialoghi, ma se i concetti dello stesso Aggiunti non si vuole am&shy;<lb/>mettere che fossero originali per rispetto al principio scenziale, non si potr&agrave; <lb/>per&ograve; negare che non fossero originali per rispetto alle applicazioni, ch'ei ne <lb/>fece ad alcuni fatti fisici; applicazioni, che avrebbero forse potuto aggiun&shy;<lb/>gere splendore agli stessi Dialoghi galileiani. </s></p><p type="main">

<s>La prima e principale di quelle applicazioni &egrave; diretta dal nostro Autore <lb/>a spiegar gli effetti di elasticit&agrave; e di trazione de'corpi: &ldquo; Hinc igitur facile <lb/>intelligemus cur nonnulla corpora vi quadam extendamus, quae postmodum <lb/>extensa, si vim extendentem adimas, remittuntur. </s>

<s>Si enim animo concipia&shy;<lb/>mus cellulas quasdam corpori quod extenditur esse aere aut alio dissipabili <lb/>corpore oppletas, atque has in ipsa protractione dilatari atque ampliari, et <lb/>interstitia, dum dilatantur, nullo alio subeunte corpore repleri; necessario <lb/>idem fiet atque eveniet quod in tractione manubrii syphonis: vis enim erit <lb/>adhibenda ut corpus illud extendatur, et cum de contractione remiseris, corda <lb/>vel corpus extensum contrahetur, et ad pristinum statum redigetur &rdquo; (ibi). </s></p><p type="main">

<s>L'altra applicazione, che fa l'Aggiunti dello sperimento dello stantuffo <lb/>dentro un corpo di tromba col fondo chiuso, &egrave; quella del calore, che dila&shy;<lb/>tando l'aria o altro corpo dissipabile, come quello che i moderni chiaman o <lb/>etere annidato dentro i pori de'fili metallici, fa s&igrave; che questi si vadano allun&shy;<lb/>gando, per cui le corde degli strumenti si sentono mutar suono, al variar <lb/>temperatura, nelle varie stagioni: &ldquo; Consimiliter, quia aer calori et frigori <lb/>rarior et densior, inde fit ut cordae nunc laxiores, nunc contractiores sint, <lb/>et musica organa .... possint amittere concentum &rdquo; (ibi). </s></p><p type="main">

<s>Ecco l'Aggiunti, che prima del No&euml;l, del Pecquet, del Sinclaro, e di <lb/>tutti i fisici di que'tempi, professa l'azion diretta esercitata dal calore sul&shy;<lb/>l'aria, piuttostoch&egrave; sulla stessa sostanza de'corpi liquidi e solidi. </s>

<s>Ma come <lb/>poteva la forza espansiva dell'aria operar cos&igrave; validi effetti? </s>

<s>Il dubbio non <lb/>turbava allora il sereno di quelli ingegni, perch&egrave; forse non avvevano atteso <lb/>con la debita diligenza a quegli effetti, e l'Aggiunti stesso, che fu de'primi <lb/>a sperimentare gli effetti della dilatabilit&agrave; lineare de'corpi solidi, non par <lb/>che avesse presentito quella prepotente incommensurabile forza, con cui i <lb/>solidi si dilatano al calore per tutti i versi, Quel primo padre e Maestro della <lb/>Fisica Nuova, che fu Giovan Batista Benedetti, aveva sagacemente specu&shy;<lb/>lato intorno alla forza del calore in frangere le cucurbite mediche o altri <lb/>simili vasi: &ldquo; Dum aliquod corpus calefit dilatatur et per consequens cir-<pb xlink:href="020/01/309.jpg" pagenum="290"/>cumcirca undique trudit, et partes vasis debiliores cedunt: dum vero dictum <lb/>corpus refrigeratur, restringitur &rdquo; (Speculat. </s>

<s>Lib. </s>

<s>Venetiis 1599, pag. </s>

<s>27), <lb/>ma ci &egrave; ancora nel Fisico veneziano troppa speculativa che riflette, com'eco, <lb/>il principio aristotelico <emph type="italics"/>caloris est rarefacere et frigoris condensare<emph.end type="italics"/> senza <lb/>saper vederlo o distinguerlo applicato ne'fatti particolari. </s></p><p type="main">

<s>La dilatazione cubica insomma, operata dal calore sui corpi solidi, e un <lb/>pi&ugrave; probabile principio operante di quel che non sia l'aria annidata ne'loro <lb/>pori, causa insufficiente per s&egrave; di tanto effetto; era tuttavia, dopo la prima <lb/>met&agrave; del secolo XVII, una scoperta e una speculazione da farsi. </s>

<s>E perch&egrave; <lb/>la scoperta e la speculazione fu fatta veramente dai nostri Italiani, e perch&egrave;, <lb/>per essa, oltre all'aria e a'liquidi, si poterono eleggere, come corpi termo&shy;<lb/>metrici, i solidi, e si pot&egrave; cos&igrave; dar maggior variet&agrave;, e talvolta anco maggior <lb/>precisione agli Strumenti; noi crediamo di dover trattenere alquanto i let&shy;<lb/>tori sopra quest'altro punto di storia scientifica italiana. </s></p><p type="main">

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

<s>Che la dilatazione cubica dei solidi, per l'azion del calore, fosse vera&shy;<lb/>mente ignota ai Fisici, nonostante l'esperienza dei Termometri a liquido, <lb/>e quella dell'Aggiunti sulla dilatazion lineare de'fili metallici; s'argomenta <lb/>da un fatto occorso al Torricelli, nell'esercitarsi a lavorare con la maggior <lb/>diligenza possibile i vetri dei canocchiali. </s>

<s>Il fatto, che form&ograve; il soggetto di <lb/>un suo segreto famoso, perch&egrave; diceva non essere ad altri noto che a lui <lb/>solo e a Dio, consisteva nell'avere osservato che il calor della mestura, con <lb/>la quale si solevano, per levigarli, attaccare i vetri ai macinelli, gli faceva <lb/>ritirar pi&ugrave; da una parte che dall'altra, per cui cos&igrave; venivano a deformarsi <lb/>le lenti. </s>

<s>Il segreto fatto osservato lo confida il geloso Discopritore cos&igrave; scri&shy;<lb/>vendo in una sua lettera al prediletto amico Raffaello Magiotti: &ldquo; Il segreto, <lb/>che pi&ugrave; m'importa e che non si sa da altri che da Dio e da me, &egrave; questo: <lb/>Non attaccare i vetri da lavorarsi con pece n&egrave; con altro per via di fuoco. </s>

<s><lb/>Perch&egrave; quelle materie nel freddarsi si ritirano pi&ugrave; da una parte che dall'al&shy;<lb/>tra, ed inarcano il vetro, il quale, finch&egrave; sta attaccato sul macinello, ha la <lb/>figura colma, ma quando lo stacchiamo per metter nell'occhiale, egli si <lb/>spiana come prima, e la figura si guasta. </s>

<s>Questo segreto che dico adesso a <lb/>V. S. &egrave; stato da me osservato evidentemente tanto che l'ho toccato con <lb/>mano, e direi anco a V. S. il come, ma lo lascio per brevit&agrave; &rdquo; (MSS Gal. </s>

<s><lb/>Disc. </s>

<s>T. XL, c. </s>

<s>35). </s></p><p type="main">

<s>La meraviglia, fuor che al. </s>

<s>Torricelli non nota ad altri che a Dio, con&shy;<lb/>sisteva evidentemente negli effetti della dilatazion cubica prodotta sulla ma&shy;<lb/>teria de'vetri, dal calore. </s>

<s>Per&ograve;, sebbene sia cosa certa che lo stesso Torri&shy;<lb/>celli osserv&ograve; il fatto, si riman, per la sopra citata lettera, tuttavia in dubbio <pb xlink:href="020/01/310.jpg" pagenum="291"/>se egli veramente conoscesse o si fosse dato a speculare la ragione del fatto. </s>

<s><lb/>Comunque sia, tanto lo stesso fatto quanto la ragion fisica di lui, non s'ha <lb/>certezza che fossero osservati e speculati se non alquanti anni dopo, in <lb/>que'primi esercizii sperimentali, a cui dette opera l'Accademia del Cimento. </s>

<s><lb/>Si sa che di que'primi esercizii furono prediletto tema per gli Accademici <lb/>le osservazioni e l'esperienze intorno agli artificiali agghiacciamenti. </s>

<s>Frugati <lb/>da un vivissimo desiderio di scoprir dove mai si ritirasse a nascondersi la <lb/>Natura, in quell'atto che agli occhi dell'osservatore pareva di vedersela in&shy;<lb/>nanzi pi&ugrave; ovvia e pi&ugrave; manifesta; prepararono alcuni vasi, per empirli d'acqua <lb/>o d'altri liquori, e per vedere ivi dentro la Natura stessa, con qual rito vi <lb/>celebrasse i suoi occulti misteri. </s>

<s>Il primo vaso, di cui si servirono da prin&shy;<lb/>cipio fu una palla di cristallo o ampolla con lungo collo piena d'acqua na&shy;<lb/>turale, e sommersa nel ghiaccio. </s>

<s>Fatto ci&ograve;, prosegue a dire il Segretario: <lb/>&ldquo; cominciammo ad osservare con puntualissima attenzione tutti i movimenti <lb/>dell'acqua, ponendo mente al suo livello. </s>

<s>Gi&agrave; sapevamo per innanzi, e lo sa <lb/>ognuno, che il freddo da principio opera in tutti i liquori restringimento e <lb/>diminuzione di mole, e di ci&ograve;, non solamente n'avevamo la riprova ordi&shy;<lb/>naria dell'acquarzente de'Termometri, ma n'avevamo fatta esperienza nel&shy;<lb/>l'acqua, nell'olio, nell'argento vivo, ed in molti altri fluidi. </s>

<s>Dall'altro canto <lb/>sapevamo ancora che nel passaggio che fa l'acqua dall'esser sem plicemente <lb/>fredda al rimoversi dalla sua fluidit&agrave; e ricever consistenza e durezza con <lb/>l'agghiacciamento, non solo ritorna alla mole che ell'aveva prima di raf&shy;<lb/>freddarsi, ma trapassa ad una maggiore, mentre se le veggon rompere vasi <lb/>di vetro e di metallo con tanta forza. </s>

<s>Ma qual poi si fosse il periodo di que&shy;<lb/>ste varie alterazioni che in esse opera il freddo, questo non sapevamo an&shy;<lb/>cora, n&egrave; era possibile d'arrivarvi con agghiacciarla dentro a vasi opachi, <lb/>come quei d'argento, d'ottone e d'oro, ne'quali s'era fin allora agghiac&shy;<lb/>ciata: onde, per non mancare di quella notizia, che parea esser l'anima di <lb/>tutte quest'esperienze, ricorremmo al cristallo ed al vetro, sperando per la <lb/>trasparenza delle materie d'aver presto ad assicurarci come la cosa andasse, <lb/>mentre si poteva a ciascun movimento che fosse apparso nell'acqua del collo, <lb/>cavar subito la palla dal ghiaccio, e riconoscer in essa quali alterazioni gli <lb/>corrispondessero. </s>

<s>Ma la verit&agrave; si &egrave; che noi stentammo assai pi&ugrave; che non ci <lb/>saremmo mai dati ad intendere, prima di poter rinvenire alcuna cosa di certo <lb/>intorno a'periodi di questi accidenti. </s>

<s>E per dirne pi&ugrave; distintamente il suc&shy;<lb/>cesso, &egrave; da sapere che nella prima immersione che facevamo della palla, <lb/>subito che ella toccava l'acqua del ghiaccio, s'osservava nell'acqua del collo <lb/>un piccolo sollevamento, ma assai veloce, dopo il quale con moto assai or&shy;<lb/>dinato e di mezzana velocit&agrave; s'andava ritirando verso la palla, finch&egrave; arri&shy;<lb/>vata a un certo grado non proseguiva pi&ugrave; oltre a discendere ma si fermava <lb/>quivi per qualche tempo, a giudizio degli occhi affatto priva di movimento. </s>

<s><lb/>Poi a poco a poco si vedea ricominciare a salire &rdquo; (Saggi Natur. </s>

<s>Esp. </s>

<s>Fi&shy;<lb/>renze 1841, pag. </s>

<s>89, 90). </s></p><p type="main">

<s>Quel fatto del sollevamento dell'acqua nel collo della palla di cristallo, <pb xlink:href="020/01/311.jpg" pagenum="292"/>appena immersa nell'acqua ghiacciata, richiam&ograve; a s&egrave; l'attenzione degli Ac&shy;<lb/>cademici, i quali designarono il fatto stesso col nome di <emph type="italics"/>salto dell'immer&shy;<lb/>sione,<emph.end type="italics"/> e notarono che non dipendeva da alcuna alterazione intrinseca del&shy;<lb/>l'acqua, ma da cagioni estrinseche del vaso (ivi, pag. </s>

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

<s>Intraveduta sagacemente la causa produttrice di quell'inaspettato salto, <lb/>vollero veder che altro effetto facesse a sommerger le palle stesse, tuttavia <lb/>piene di varii liquori, nell'acqua calda, piuttosto che nella ghiacciata, e tro&shy;<lb/>varono che avveniva tutto il contrario &ldquo; perch&egrave; i livelli de'suddetti liquori <lb/>s'abbassano sensibilmente e quasi pigliano un tempo per sollevarsi, come <lb/>chi vuole spiccare un salto &rdquo; (ivi, pag. </s>

<s>117). </s></p><p type="main">

<s>L'una e l'altra di queste due nuove e curiose osservazioni occorsero <lb/>ad esser fatte dall'Accademia, nell'autunno del 1657, e bench&egrave; la notizia <lb/>potesse esser trapelata al di fuori e andata attorno molto tempo innanzi, <lb/>non fu nulladimeno divulgata che dal libro dei <emph type="italics"/>Saggi.<emph.end type="italics"/> Comunque sia per&ograve;, <lb/>Isacco Vossio, nel 1663, in un suo libro intitolato <emph type="italics"/>De motu maris et ven&shy;<lb/>torum,<emph.end type="italics"/> divulg&ograve; le osservazioni fatte gi&agrave; sei anni prima dai Nostri, colle pa&shy;<lb/>role seguenti: &ldquo; Porro aquam etiam modico calore aut frigore dilatari et <lb/>constringi manifeste patebit si quis vitrum amplioris uteri et angusti orifi&shy;<lb/>cii aqua frigida plenum calidae aut tepenti tantum aquae immerserit. </s>

<s>Post <lb/>primam coarctationem, quae momentanea est et aquam frigidam ad subitum <lb/>contactum paululum facit subsidere, eadem mox adscendet, idque ad legem, <lb/>et proportionem calidae foras ambientis. </s>

<s>Quod si aquam vitro contentam mo&shy;<lb/>dice calefeceris, ac frigidae immerseris, contrarium videre est. </s>

<s>Primo quippe <lb/>aliquantisper ascendit aqua propter repentinum frigidae contactum <figure id="id.020.01.311.1.jpg" xlink:href="020/01/311/1.jpg"/> qui, <lb/>dum calorem inclusum per orificium expellere conatur, una quoque inclu&shy;<lb/>sam propellit aquam. </s>

<s>Peracto hoc momentaneo motu, sensim contrahitur <lb/>moles aquae, et ad inferiores orificii partes descendit &rdquo; (Hagae Com. </s>

<s>pag. </s>

<s>49). </s></p><p type="main">

<s>La copia del libro, da cui s'&egrave; trascritto questo passo, conservasi nella <lb/>Biblioteca del R. </s>

<s>Arcispedale di S. M. N. di Firenze, ed appartenne a Vin&shy;<lb/>cenzio Viviani, che vi fece di mano propria e v'appose in calce e in mar&shy;<lb/>gine osservazioni e note scritte con lapis piombino. </s>

<s>In una di queste osser&shy;<lb/>vazioni, che si riferisce al passo, nel punto da noi sopra contrassegnato con <lb/>asterisco, il Viviani dice: &ldquo; Goffa ragione! Oh quanto vi torner&agrave; nuovo, si&shy;<lb/>gnor Vossi, l'allargamento e stringimento del vaso per cagione del caldo <lb/>e del freddo! &rdquo; </s></p><p type="main">

<s>Bench&egrave; dunque fosse gi&agrave; divulgato il fatto del salto dell'immersione, <lb/>par che ancora nel 1663, dai fisici stranieri non se ne sia indovinata la causa, <lb/>la quale fu subito speculata e sperimentalmente dimostrata in varii modi <lb/>nella stessa nostra Accademia. </s>

<s>E in verit&agrave; il Segretario, dop'aver descritto <lb/>le due osservazioni del repentino sollevarsi nel collo i liquori, quando la <lb/>palla di cristallo sia immersa nell'acqua ghiacciata, e del repentino abbas&shy;<lb/>sarsi quando invece sia immersa nell'acqua calda; soggiunge essere un tal <lb/>pensiero venuto in mente agli Accademici per render la ragione dei nuovi <lb/>fatti osservati: &ldquo; Il pensiero fu che l'apparenza di que'subiti movimenti, <pb xlink:href="020/01/312.jpg" pagenum="293"/>nell'acqua e negli altri fluidi, non derivi da alcuna intrinseca alterazione di <lb/>raro e di denso .... ma bens&igrave; vogliono piuttosto che ci&ograve; avvenga per lo fic&shy;<lb/>camento de'volanti corpicelli del fuoco che dall'acqua svapora nell'esterne <lb/>porosit&agrave; del vetro; i quali, a guisa di tante biette sforzandolo, ne vien ne&shy;<lb/>cessariamente sforzata l'interna capacit&agrave; del vaso, anche prima che per l'oc&shy;<lb/>culte vie dello stesso vetro si trasmettano nel liquor contenutovi: che il <lb/>freddo poi ristringendo gli stessi pori faccia divenir misero il vaso alla mole <lb/>dell'acqua che v'&egrave; dentro &rdquo; (Saggi ecc. </s>

<s>Ediz. </s>

<s>cit., pag. </s>

<s>118). </s></p><p type="main">

<s>Bench&egrave; sempre per&ograve;, secondo l'istituto, si attribuisca dal Segretario in <lb/>generale ogni scoperta a tutta intiera l'Accademia, il Borelli &egrave; sollecito di <lb/>far sapere al mondo scientifico come la scoperta, e la ragione speculata del <lb/>salto dell'immersione &egrave; particolarmente cosa tutta sua, per cui, nel Libro <lb/><emph type="italics"/>De motion. </s>

<s>natur.,<emph.end type="italics"/> lasci&ograve; cos&igrave; scritto: &ldquo; Verum est quod in principio im&shy;<lb/>mersionis, vasi vitrei intra nivem sale aspersam primo aqua a gradu 142 <lb/>brevi saltu trium fere graduum elevatur, et hic licet videatur augeri et ra&shy;<lb/>refieri moles aquae ipsius vasis, nihilominus <emph type="italics"/>ego animadverti et docui hoc <lb/>contingere a restrictione eiusdem vasis<emph.end type="italics"/> (Regio Julio, 1670, pag. </s>

<s>547). </s></p><p type="main">

<s>Che la nuova teoria del dilatamento de'vasi, per l'intrusion del calore <lb/>dentro i loro pori, fosse oppugnata dai Peripatetici, i quali si appagano, <lb/>dice lo stesso Borelli &ldquo; di quei sottili, sufficienti e virtuosissimi vocaboli, <lb/>cio&egrave; di qualit&agrave; calda e fredda, perch&egrave; <emph type="italics"/>caloris est rarefacere et frigoris con&shy;<lb/>densare &rdquo;<emph.end type="italics"/> (Fabbr. </s>

<s>Lett. </s>

<s>I, 93); non fa maraviglia: maggior maraviglia per&ograve; <lb/>farebbe il veder muovere le opposizioni da uno degli stessi Accademici, se <lb/>non si sapesse oramai lo spirito che lo frugava di contradire e di mettere <lb/>scrupolo in tutto ci&ograve; che di nuovo s'annunziava dall'Accademia. </s>

<s>Carlo Ri&shy;<lb/>naldini negava che si potessero quelle borelliane teorie applicare al fatto del <lb/>salto dell'immersione, perch&egrave;, dilatandosi al calore tutta insieme la mole <lb/>del vetro, l'interna superficie del cannello, come respinta in dentro, non si <lb/>dilata ma si ristringe. </s>

<s>Proponeva, a persuadere sperimentalmente questo suo <lb/>assunto, di prendere un maschio, che scorresse a freddo esattamente in un <lb/>anello di ferro, e presagiva che, riscaldandosi questo anello, per via del ri&shy;<lb/>crescimento operatovi dal calore, il maschio non vi si sarebbe potuto infi&shy;<lb/>lare altrimenti. </s>

<s>Su tale proposta, nell'Accademia, il principe Leopoldo fece <lb/>far l'esperienza, e fu trovato che, tutto al contrario di quel che avea pre&shy;<lb/>sagito il Rinaldini, il maschio nell'anello cos&igrave; riscaldato, v'entrava e usciva <lb/>con molta pi&ugrave; facilit&agrave; di prima. </s>

<s>Poi l'esperienza, a dimostrar lo stesso ef&shy;<lb/>fetto, fu, diciamo cos&igrave;, ringentilita, facendo gli Accademici tornire un'ar&shy;<lb/>milla di bronzo che incastrasse per l'appunto in un mastietto dello stesso <lb/>metallo (Saggi ecc., pag. </s>

<s>120). Il Principe, per mezzo del medesimo Bo&shy;<lb/>relli, fece partecipare il resultato di questa esperienza al Rinaldini, il quale <lb/>cos&igrave; rispondeva da Pisa in una lettera del d&igrave; 11 Novembre 1657 diretta al <lb/>Viviani: &ldquo; Il signor Borelli mi ha partecipato una scrittagli dal serenissimo <lb/>principe Leopoldo, circa l'esperienza che io gli proposi da farsi quanto al&shy;<lb/>l'anello riscaldato ecc. </s>

<s>e sento, come posto freddo nel mascolo, sicch&egrave; ci an-<pb xlink:href="020/01/313.jpg" pagenum="294"/>dasse calzante, poi il medesimo postovi riscaldato vi giocasse.... Dubito che <lb/>l'effetto possa venir da altra cagione. </s>

<s>Pare che sia cosa certa che un chia&shy;<lb/>vistello di ferro giochi meno ne'suoi occhi pure di ferro, secondo che l'aria <lb/>si ritruova di tale e tale costituzione &rdquo; (MSS Cim. </s>

<s>T. XXIV, c. </s>

<s>12). </s></p><p type="main">

<s>Ma il Viviani, ben persuaso della peripatetica caponaggine del Rinal&shy;<lb/>dini, e aspettandosi che, come aveva gi&agrave; fatto perdere la pazienza a quello <lb/>stizzoso del Borelli volesse seguitar a mettere a pi&ugrave; duro cimento la sua, <lb/>si studiava di persuader colle seguenti parole l'amico e il collega della ve&shy;<lb/>rit&agrave; delle ragioni e dei fatti osservati intorno alla virt&ugrave; che ha il calore di <lb/>dilatare i corpi: &ldquo; Il dubbio di V. S. E. fondato sull'effetto del chiavistello, <lb/>veramente mi giunge nuovo, perch&egrave; mi credevo che, per dimostrare l'al&shy;<lb/>largamento e stringimento del vaso, mediante il caldo e il freddo, non si po&shy;<lb/>tesse far pi&ugrave; che trovar modo di toccarlo con mano, come ultimamente ci <lb/>ha fatto osservare S. A. S. per mezzo di quell'anima di metallo applicata <lb/>dentro l'anello pur di metallo ora caldo ed ora freddo. </s>

<s>Se dunque il senso <lb/>del tatto non gli par giusto giudice, giacch&egrave; ella attribuisce l'effetto del me&shy;<lb/>glio giocar del maschio nell'anello riscaldato, all'attenuazione dell'aria in&shy;<lb/>clusa tra l'uno e l'altro cagionata dal calor dell'anello; consideri di grazia <lb/>V. S. se gli par di prestar pi&ugrave; fede ad alcuno degli altri sensi.... Io ho <lb/>tese all'unisono due corde di rame di ugual lunghezza e giustezza .... ed <lb/>assai distanti fra loro, sotto una delle quali ho rappresentato un caldanuzzo <lb/>con poco fuoco per riscaldarla, e toccata l'una e l'altra nel medesimo tempo, <lb/>ho sempre osservato, insieme con molti altri ai quali ho conferita questa <lb/>esperienza, che la corda riscaldata ingravisce notabilmente di suono.... <lb/>Quanto poi al senso della vista, ho preso un filo o corda di rame delle pi&ugrave; <lb/>grosse da clavicembalo ben ricotta .... e ad una delle sue estremit&agrave; ho at&shy;<lb/>taccata una palla di piombo .... e, formato cos&igrave; un pendolo, sotto alla palla <lb/>ho accomodato una lastra di vetro distante la grossezza di un testone. </s>

<s>Ho <lb/>di poi, mentre tal pendolo stava fermo, o quando aveva poco moto, acco&shy;<lb/>stata la fiamma d'un moccolino al fil di rame, scorrendo in gi&ugrave; e in su <lb/>colla mano, e ho mille volte osservato e veduto patentemente che appena <lb/>riscaldato il filo la palla arrivava a toccare il vetro, e rimossa la fiammella <lb/>tornava immediatamente a discostarsene all'altezza di prima.... Per la qual <lb/>dimostrazione (dell'effetto dell'introduzione de'calidi) mi sarei persuaso che <lb/>il solo e semplice effetto di veder, nell'atto dell'immersione della boccia <lb/>nell'acqua calda, abbassar gi&ugrave; per il collo l'acqua inclusa, e per il contra&shy;<lb/>rio alzar per l'immersione della medesima boccia nell'acqua fredda;.... <lb/>fosse stata prova bastante.... Ma gi&agrave; parmi che omai si possa concludere <lb/>il signor Borelli avere intorno a questo effetto ottimamente discorso &rdquo; (MSS. <lb/>Gal. </s>

<s>Dis. </s>

<s>T. CXLII, c. </s>

<s>31, 32). </s></p><p type="main">

<s>Le due esperienze descritte qui dal Viviani si trasformarono in quel&shy;<lb/>l'altre due, che si leggon nel libro de'<emph type="italics"/>Saggi<emph.end type="italics"/> a pag. </s>

<s>122, 23 della citata <lb/>edizione. </s>

<s>Ma l'esperienza della palla pendula, che in sostanza &egrave; quella fatta <lb/>parecchi anni prima dall'Aggiunti, fu dal Viviani stesso resa pi&ugrave; evidente, <pb xlink:href="020/01/314.jpg" pagenum="295"/>col farla oscillare, mostrando cos&igrave; che, allungandosi il filo al calore, la palla <lb/>fregando sulla lastra di vetro vi si arresta il suo moto (ivi, T. CXXXV, c. </s>

<s>14). </s></p><p type="main">

<s>Il Rinaldini per&ograve; non cos&igrave; facile ad arrendersi rispondeva contro quelle <lb/>esperienze e contro quegli argomenti: &ldquo; Io non dico n&egrave; parlo del vaso con <lb/>l'acqua posto nell'acqua calda o fredda .... dico bene che l'anello ingrossa <lb/>parimenti facendosi l'accrescimento delle dimensioni per tutti i versi, che &egrave; <lb/>quello che io ho preteso &rdquo; (MSS. Cim. </s>

<s>T. XXIV, c. </s>

<s>16). </s></p><p type="main">

<s>Contro una tal pretensione del Rinaldini e de'suoi seguaci il Borelli <lb/>scriveva che ancorch&egrave; gli desse l'animo di poter con evidenza geometrica <lb/>persuadere ai dissidenti la sua teoria, nonostante <emph type="italics"/>non sar&agrave; se non bene ocu&shy;<lb/>latamente far loro vedere, se &egrave; possibile, che per l'inzuppamento di <lb/>qualche corpo venga l'interna superficie di un vaso accresciuta.<emph.end type="italics"/> (Fabbr. </s>

<s><lb/>Lett. </s>

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

<s>L'esperienza del ricrescer gli anelli per inzuppamento di qualche li&shy;<lb/>quido, e che fu poi veramente eseguita nell'Accademia e descritta ne'<emph type="italics"/>Saggi<emph.end type="italics"/><lb/><figure id="id.020.01.314.1.jpg" xlink:href="020/01/314/1.jpg"/></s></p><p type="caption">

<s>Figura 10.<lb/>a pag. </s>

<s>21 della citata edizione, era senza dub&shy;<lb/>bio, meglio che per via geometrica, atta a per&shy;<lb/>suadere l'ingegno grosso dei Peripatetici, ma <lb/>bench&egrave; il Borelli si vantasse d'aver animo da <lb/>persuaderli della verit&agrave;, anche per via di geo&shy;<lb/>metriche dimostrazioni, non si sa per&ograve; che vi <lb/>si provasse. </s>

<s>Vi si prov&ograve; bene, e vi riusci da pari <lb/>suo il Viviani, il quale dimostr&ograve;, con tutto il <lb/>rigore geometrico, il seguente Teorema: &ldquo; Sia <lb/>base d'un anello di metallo o di vetro l'ar&shy;<lb/>milla, il di cui centro sia C (fig. </s>

<s>10) la circon&shy;<lb/>ferenza esteriore AO, l'interiore BM, e la cir&shy;<lb/>conferenza di mezzo DI, la quale &egrave; sempre la <lb/>misura della lunghezza o giro delle armille. </s>

<s>Dico che, quantunque si am&shy;<lb/>metta com'&egrave; probabile che, per l'introduzione de'corpuscoli calidi nella <lb/>solidit&agrave; dell'anello, si facci la dilatazione della larghezza AB per tutti i versi, <lb/>cio&egrave; tanto per indentro che in fuori, dovendo nello stesso tempo crescere <lb/>ancora la lunghezza DI o giro dell'anello, &egrave; necessario che la interna cir&shy;<lb/>conferenza BM si dilati ed acquisti maggior capacit&agrave; &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s><lb/>T. CXLII, c. </s>

<s>38). </s></p><p type="main">

<s>Lo dimostr&ograve; in due varii modi e del primo modo mand&ograve; copia al Bo&shy;<lb/>relli e del secondo al Rinaldini, come ivi not&ograve; l'Autore stesso di propria <lb/>mano: &ldquo; Mandatone copia al signor Borelli con lettera del 17 Novembre 1657 <lb/>del primo modo, ed al signor Rinaldini, con lettera del 26 detto, del secondo <lb/>modo &rdquo;. </s>

<s>Il Rinaldini, a quel che pare da una sua risposta del d&igrave; 3 Dicem&shy;<lb/>bre (MSS. Cim. </s>

<s>T. XXIV, c. </s>

<s>24) rest&ograve; persuaso dalla forza di quella geo&shy;<lb/>metrica dimostrazione, e il Borelli pure rispondeva all'Autore che <emph type="italics"/>la gli era <lb/>sembrata bella e squisita quanto mai si pu&ograve; desiderare<emph.end type="italics"/> (ivi, c. </s>

<s>19) ma poi <lb/>soggiunge queste parole, che il Viviani stesso qualific&ograve; per <emph type="italics"/>artificiosissime:<emph.end type="italics"/><pb xlink:href="020/01/315.jpg" pagenum="296"/>&ldquo; Averei per&ograve; avuto caro che ella avesse veduto a Firenze quelle molte pro&shy;<lb/>posizioni, che io allora abbozzai su questo proposito, ma &egrave; bene che ella an&shy;<lb/>cora abbia avuto la parte del gusto nell'incontrare una delle ragioni di <lb/>quella conclusione che &egrave; verissima &rdquo;. </s></p><p type="main">

<s>Tali parole son testualmente trascritte dal Viviani in una lettera al Ri&shy;<lb/>naldini, nella quale spassionandosi coll'amico, prosegue cos&igrave; a dire contro <lb/>il Borelli: &ldquo; Risposta in vero che ha stomacato me non solo, ma ciascun <lb/>altro a cui l'ho partecipata, riconoscendovisi manifestissimo il dolore di non <lb/>aver mai incontrata tal dimostrazione, e la grandissima volont&agrave; di appro&shy;<lb/>priarsi questa, che per altro io averei stimato bagattella, ma che ora stimo <lb/>qualcosa, in vedendo che quelli, che in ricchezza si reputano superiori al <lb/>Re di Spagna, procurano con artifizii spogliarne altri di quella poca di sup&shy;<lb/>pellettile, che &egrave; toccata per sorte a chi si riconosce o si credeva poveris&shy;<lb/>simo.... Che se tal conclusione egli l'aveva dimostrata, perch&egrave; non dirla <lb/>almeno al signor Principe, al quale egli aveva fatto il discorso prima che <lb/>ad altri? </s>

<s>discorso di que'tanti cunei di fuoco penetranti et cet. </s>

<s>et cet.? Ba&shy;<lb/>sta, non &egrave; poco arrivare a conoscere la natura degli uomini. </s>

<s>V. S. tenga <lb/>per&ograve; in s&egrave;, perch&egrave; non intendo venire a rottura aperta, sebbene a san&shy;<lb/>gue caldo non so quello che io me gli abbia risposto &rdquo; (MSS. Gal. </s>

<s>Dis. </s>

<s><lb/>T. CXLII, c. </s>

<s>40). </s></p><p type="main">

<s>Vennero pur troppo i due grandi nostri Fisici a rottura, e anzi a fiera <lb/>rottura aperta, quando si fecero insieme la concorrenza in tradurre e divi&shy;<lb/>nare i Conici di Apollonio di Perga. </s>

<s>E bench&egrave; la storia sopra narrata sveli <lb/>i principii occulti di quella rottura, che segu&igrave; non senza recar gravi danni <lb/>ai progressi delle scienze sperimentali in Italia, non vuol nulladimeno diva&shy;<lb/>gar l'attenzione dal nostro tema, a cui ritorniam per concludere essere stati <lb/>i nostri Italiani che primi costruirono e usarono i Termometri ad aria e a <lb/>liquido, e che, scoprendo la propriet&agrave; de'solidi di dilatarsi al calore, apri&shy;<lb/>ron la via e dettero il modo alla costruzion de'Pirometri e di simili altri <lb/>strumenti termici. </s></p><p type="main">

<s>Bench&egrave; sia tutto ci&ograve; chiaramente dimostrato dai fatti storici, che noi <lb/>abbiamo sopra narrati, non si dee per&ograve; per amor del vero tacere che se i <lb/>Termometri, specialmente a liquido, ebbero in Italia il loro principio, ritro&shy;<lb/>varono appresso gli stranieri i loro ultimi perfezionamenti. </s>

<s>Uno di questi <lb/>perfezionamenti, e de'pi&ugrave; importanti, fu senza dubbio quello di contrasse&shy;<lb/>gnare il cannello dello strumento e distinguerlo in gradi. </s>

<s>Una graduazione, <lb/>come vedemmo, l'aveva pure anche il primo Termometro santoriano, ma <lb/>non sappiamo per&ograve; quali fossero i due punti fissi, intra i quali si determi&shy;<lb/>navano dall'inventore i limiti degli accessi e dei recessi. </s>

<s>Dai testi sopra al&shy;<lb/>legati nient'altro si pu&ograve; comprendere se non che que'due punti fissi, nel <lb/>Termomatro del Santorio, erano affatto arbitrarii, come pure arbitrarii erano <lb/>quelli fissati dal Sagredo, che, per uniformarsi al circolo, ne divideva lo spa&shy;<lb/>zio compreso sul cannello in 360 gradi. </s></p><p type="main">

<s>Gli Accademici del Cimento fecero nel determinare i punti estremi della <pb xlink:href="020/01/316.jpg" pagenum="297"/>scala termometrica, un passo importante, fissando il pi&ugrave; basso o del minimo <lb/>recesso nel punto della fusione del ghiaccio. </s>

<s>Ma quello del massimo ac&shy;<lb/>cesso rimase tuttavia arbitrario, fissandolo nel punto de'massimi ardori del <lb/>sole in una delle pi&ugrave; affannose giornate. </s></p><p type="main">

<s>Il grado termico dell'acqua bollente, sotto una pressione atmosferica <lb/>invariabile, non fu assegnato come termine dei massimi accessi altro che <lb/>dai fisici moderni stranieri, che al trasformato strumento apposero i loro <lb/>nomi. </s>

<s>Cosicch&egrave; non si pu&ograve; pi&ugrave; oramai parlar di Termometro senz'aggiun&shy;<lb/>gervi il nome o del Farenheit o del R&egrave;aumur, i quali, per coloro che non <lb/>si curano di saperne la storia, son creduti e passano per i primi inventori <lb/>de'Termometri ad alcool o a mercurio, usciti un secolo e mezzo avanti <lb/>dalle mani del Torr&inodot;celli. </s></p><p type="main">

<s>Se per&ograve; fra i perfezionamenti di questo Misuratore termico si vogliano <lb/>annoverare que'macchinamenti, nella loro semplicit&agrave; pi&ugrave; o meno ingegnosi, <lb/>per i quali si ridussero a nuova forma, o a mera curiosit&agrave; spettacolosa, o a <lb/>renderne pi&ugrave; comode le osservazioni, riducendoli per esempio a segnare i <lb/>gradi del calore sopra una mostra come gl&igrave; orologi; i nostri Italiani del se&shy;<lb/>colo XVII non si lasciaron togliere, nemmeno rispetto a ci&ograve;, i primi posti. </s>

<s><lb/>Ma perch&egrave; lungo, e forse alieno dal nostro istituto, sarebbe il trattenersi a <lb/>descriver que'macchinamente quali furono immaginati dai loro inventori, ci <lb/>contenteremo di por termine al presente capitolo col recar la descrizione, <lb/>che del suo nuovo Termometro a mostra fa Urbano Daviso. </s></p><p type="main">

<s>&ldquo; Mi venne in pensiero, dice egli nel <lb/><figure id="id.020.01.316.1.jpg" xlink:href="020/01/316/1.jpg"/></s></p><p type="caption">

<s>Figura 11.<lb/><emph type="italics"/>Trattato della Sfera,<emph.end type="italics"/> di trovare il modo <lb/>che questo crescimento e diminuzione di <lb/>caldo fosse dimostrato da un indice con&shy;<lb/>forme si fa negli orologi per mostrare le <lb/>ore, e mi riusc&igrave; nella maniera seguente: <lb/>Feci fare un cannone di piombo, come nella <lb/>figura (11) ABCD, quale empii di acqua, <lb/>e nella parte DC vi posi un vasetto di <lb/>vetro con dentrovi migliarole di tal gravit&agrave; <lb/>che, unite con detto vasetto, restasse a <lb/>galla in detta acqua, ed attaccata detta <lb/>ampolla con detto piombo G ad un filo <lb/>facevo passare questo sopra la girella E, <lb/>e lo rivoltavo attorno a quella, ed al capo <lb/>di detto filo, che pendeva dall'altro lato, <lb/>appesi un'altro pezzetto di piombo F di <lb/>poco minor peso di quello pesasse il piombo <lb/>e il vasetto del cannone. </s>

<s>Nella parte poi <lb/>del cannone AB ci mettei una boccia di vetro col collo lungo tre palmi, <lb/>ed essa era grossa tre quarti di palmo nel diametro del vuoto. </s>

<s>Questa, <lb/>avanti d'immergere il collo nell'acqua, riscaldai bene al fuoco e dopo im-<pb xlink:href="020/01/317.jpg" pagenum="298"/>mersi il detto collo nell'acqua del cannone AB, e ci&ograve; feci per esser certo <lb/>che il caldo dell'aria non potesse essere maggiore in detta boccia in alcun <lb/>tempo dell'anno, e subito che l'aria si raffredd&ograve; sal&igrave; l'acqua per il collo <lb/>della boccia, e l'acqua che era nell'altro braccio del cannone di piombo DC <lb/>cal&ograve;, e cos&igrave; ancora il detto vasetto cal&ograve;, e perch&egrave; era pi&ugrave; grave del piombo F, <lb/>alz&ograve; questo e fece tornare la girella E, il pernio della quale, avendo in un <lb/>capo annesso l'indice HI, questo mostrava, nella circonferenza d'un gran <lb/>cerchio che era avanti a detta girella, li gradi maggiori o minori del caldo, <lb/>e questi con esattezza, mentre, ad ogni poco di moto della girella, il detto <lb/>indice, che era in maggior proporzione con la sua lunghezza di quello fosse <lb/>il diametro della girella, passava maggiore spazio e veniva a mostrare in <lb/>parti minime le alterazioni dell'aria, la quale con il riscaldarsi e raffred&shy;<lb/>darsi della palla della boccia occupava in essa maggiore o minor luogo, e <lb/>cos&igrave; veniva a fare scendere e salire l'acqua per il suo collo, e conseguen&shy;<lb/>temente ancora il vasetto del cannone opposto. </s>

<s>Bisogna per&ograve; avvertire di <lb/>fare la detta girella di latta, che sar&agrave; leggerissima, e l'indice similmente, e <lb/>farli stare in bilico, acci&ograve; il detto cilindro si possa voltare ad ogni picciol <lb/>moto, che far&agrave; l'acqua del cannone, e questo l'ho fatto alto un piede antico <lb/>romano e grosso quasi tre once, e la girella ha di diametro quattro once &rdquo; <lb/>(Roma 1682, pag. </s>

<s>240-43). </s></p><pb xlink:href="020/01/318.jpg"/><p type="main">

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

<s><emph type="center"/><emph type="bold"/>Dell'Orologio a pendolo<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

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

<s>I. De'primi Orologi a pendolo del Santorio. </s>

<s>&mdash; II. De'varii modi, proposti da Galileo, d'applicare il <lb/>pendolo agli Orologi. </s>

<s>&mdash; III. </s>

<s>Del primo Orologio descritto da Cristiano Huyghens; della sim&shy;<lb/>patia de'pendoli. </s>

<s>&mdash; IV. </s>

<s>Del Cronoscopio di Giorgio Sinclaro, e dell'Orologio circloidale del&shy;<lb/>l'Huyghens. </s>

<s>&mdash; V. </s>

<s>Del Cronometro degli Accademici del Cimento. </s>

<s>&mdash; VI. </s>

<s>Come probabilmente <lb/>il Cronometro degli Accademici fiorentini sia invenzion del Viviani; della ricerca de'centri di <lb/>oscillazione, ne'pendoli degli Orologi. </s>

<s>&mdash; VII. </s>

<s>Degli effetti prodotti dal calore sugli Orologi; <lb/>dell'invenzione degli Orologi a bilanciere, o da tasca; della compensazione de'pendoli. </s></p><p type="main">

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

<s>La storia autentica dell'applicazione del pendolo alla misura del tempo, <lb/>per chi vuol proseguire l'istituto da noi intrapreso, che &egrave; quello di non ri&shy;<lb/>ferire le opinioni o le sentenze altrui, ma di narrare i fatti quali risultano <lb/>dai documenti pi&ugrave; certi; presenta difficolt&agrave; non punto minori di quelle, che <lb/>ci si paravano innanzi nel primo entrare alla storia del Termometro. </s></p><p type="main">

<s>Noi dunque attendendo ai documenti dimostrativi dei fatti, che abbiamo <lb/>preso a narrare, c'incontriamo anche questa volta nel Santorio, il quale, <lb/>nel suo Libro <emph type="italics"/>Methodi vitandorum errorum,<emph.end type="italics"/> ci dice di avere, fra gli altri, <lb/>inventato un nuovo strumento da lui chiamato il <emph type="italics"/>Pulsilogio<emph.end type="italics"/> &ldquo; in quo mo&shy;<lb/>tus et quietis arteriae quisque poterit exactissime dimetiri, observare, et <lb/>firma memoria tenere, et inde collationem facere cum pulsibus praeterita&shy;<lb/>rum dierum &rdquo; (Sanctorii Sanctorii Op. </s>

<s>Omn. </s>

<s>Venetiis, 1660, T. II, pag. </s>

<s>223). <lb/>E poco appresso soggiunge che non vuol trattenersi a far qui la descrizione <lb/>minuta dello strumento, essendo sua intenzione di parlarne di proposito in <lb/>un suo libro da pubblicarsi, dove descriver&agrave; tutti gli strumenti da s&egrave;, via <lb/>via inventati, per servire agli usi medici. </s></p><pb xlink:href="020/01/319.jpg" pagenum="300"/><p type="main">

<s>Il libro, come altrove avvertimmo, non fu scritto, o per dir meglio non <lb/>fu pubblicato, n&egrave; &egrave; pervenuto alla nostra notizia, ma non lasci&ograve; per questo <lb/>l'Autore, come fece del Termometro, di darci la promessa descrizione nella <lb/>Questione V dei Commentarii sopra i canoni di Avicenna. </s>

<s>Noi sottoporremo <lb/>qui all'esame dei nostri lettori le parole testuali, da cui, meglio che da quel <lb/>che riferiscono gli scrittori, i quali van ripetendo ci&ograve; che ne dicono altri <lb/>storici, potranno giudicare quali fossero in proposito le speculate invenzioni <lb/>del nostro Fisico giustinopolitano. </s></p><p type="main">

<s>&ldquo; Primum (egli dunque scrive nella Questione citata) <lb/><figure id="id.020.01.319.1.jpg" xlink:href="020/01/319/1.jpg"/></s></p><p type="caption">

<s>Figura 12.<lb/>est nostrum pulsilogium, in quo per certitudinem mathe&shy;<lb/>maticam et non per coniecturam, dimetiri possumus ulti&shy;<lb/>mos gradus recessus pulsusque ad frequentiam et raritata&shy;<lb/>tem, de quo instrumento aliquid diximus in libro V <emph type="italics"/>Methodi <lb/>nostrae.<emph.end type="italics"/> A dicto Pulsilogio desumpsimus hoc paratu facile, <lb/>quod explicatur per primam figuram, ut infra, quae conti&shy;<lb/>net funiculum ex lino vel serico contextum, cui, ut vides, <lb/>appensa est pila plumbea (fig. </s>

<s>12), qua impulsa, si funi&shy;<lb/>culus est longior, motus pilae fit tardior et rarior: si bre&shy;<lb/>vior, fit frequentior et velocior. </s>

<s>Dum igitur volumus fre&shy;<lb/>quentiam vel raritatem pulsus dimetiri digitis impellimus <lb/>pilam laxando, vel contrahendo funiculum usque eo, quo <lb/>motus pilae omnino conveniat cum frequentia vel raritate <lb/>pulsus ipsius arteriae: quo adinvento, illico e regione ob&shy;<lb/>servamus gradus 70 ostensum a linea alba ipsius pilae ubi <lb/>est C. </s>

<s>Quo gradu memoriae consignato, iterum eadem vel <lb/>sequenti die, eodem instrumento, experimur an pulsus ar&shy;<lb/>teriae factus sit aliquantulum frequentior vel tardior. </s>

<s>Di&shy;<lb/>cimus aliquantulum quia usu istius instrumenti non quae&shy;<lb/>rimus pulsus notabiles raritatis vel tarditatis differentias, <lb/>quas medici memoria tenere possunt, sed illas minimas, <lb/>quarum differentiae inter unum et alterum diem non sunt <lb/>scibiles. </s>

<s>In eumdem usum est aliud simile instrumentum <lb/>cuius ieonem videbis fol. </s>

<s>78. fig. </s>

<s>E. </s>

<s>At notandum quod <lb/>pila plumbea, per maiorem vel minorem vim impulsa, non <lb/>mutat raritatem seu frequentiam, quia in impellendo, quan&shy;<lb/>tum amittitur de spacio tantum remittitur de violentia. </s>

<s>Per <lb/>tale instrumentum tempore sanitatis pulsus dimetimur, deinde tempore aegri&shy;<lb/>tudinis animadvertimus recessum a naturali statu, qui in effectibus digno&shy;<lb/>scendis, praedicendis, et curandis est maxime necessarius &rdquo; (ibi, T. III, <lb/>pag. </s>

<s>29). </s></p><p type="main">

<s>La nuova disposizione, certamente pi&ugrave; comoda, data dal Santorio al filo <lb/>pendulo misuratore del polso, vedesi disegnata a pagina 110 del citato <lb/>Tomo III, e consiste nell'accorciare o scorciare il filo, ritirandolo innanzi <lb/>e in dietro, per mezzo di un manubrio scorrente dentro la scanalatura di <pb xlink:href="020/01/320.jpg" pagenum="301"/>un regolo orizzontale graduato, come vedesi nella nostra figura 13, imita&shy;<lb/>tiva di quella stessa, che disegna ivi l'Autore. </s></p><p type="main">

<s>Intanto, dal sopra allegato testo si rilevano le seguenti importantissime <lb/><figure id="id.020.01.320.1.jpg" xlink:href="020/01/320/1.jpg"/></s></p><p type="caption">

<s>Figura 13.<lb/>notizie: Prima, che il Santorio ha ricono&shy;<lb/>sciuto l'isocronismo del pendolo, cos&igrave; per <lb/>le ampie che per le pi&ugrave; ristrette sue vi&shy;<lb/>brazioni, assegnando per causa di quel fatto <lb/>straordinario il principio meccanico delle <lb/>velocit&agrave; proporzionali agli spazii. </s>

<s>Seconda, <lb/>che i tempi delle vibrazioni fatte da pendoli <lb/>pi&ugrave; o meno lunghi sieno reciprocamente <lb/>proporzionali alle semplici lunghezze dei fili. </s></p><p type="main">

<s>Notabile &egrave; per&ograve; che il nostro Santorio, <lb/>non parla solo del pendolo come misuratore <lb/>della relativa frequenza e remissione del <lb/>polso, ma ne parla altres&igrave; come di stru&shy;<lb/>mento assolutamente misuratore del tempo. </s>

<s>Nella citata pagina 110, insieme <lb/>con quella nuova disposizione data al Pulsilogio, per allungare o scorciare <lb/>misuratamente il filo pendulo, vedesi disegnata un'altra figura, a contorno <lb/>ellittico, nel mezzo della quale son rappresentati due indici, che van no im&shy;<lb/>perniati nel centro di due archi di cerchio, l'uno maggiore dell'altro, ma <lb/>graduati ambedue in sette parti, che perci&ograve; riescono disuguali. </s>

<s>La figura <lb/><figure id="id.020.01.320.2.jpg" xlink:href="020/01/320/2.jpg"/></s></p><p type="caption">

<s>Figura 14.<lb/>che abbiamo qui ricopiata (fig. </s>

<s>14) il nostro Autore <lb/>la illustra colle parole seguenti: &ldquo; Figura D est pul&shy;<lb/>silogium, quod nos adinvenimus, quo non solum <lb/>tempus sed etiam frequentiam et raritatem pulsus <lb/>dimetimur. </s>

<s>In hoc instrumento sunt septem diffe&shy;<lb/>rentiae frequentioris vel rarioris motus quae per ra&shy;<lb/>dium observantur: deinde quilibet gradus dividitur <lb/>in septem minuta quae, per radiolum distinguntur, <lb/>cuius instrumenti constructionem in libro <emph type="italics"/>De medicis instrumentis<emph.end type="italics"/> doce&shy;<lb/>bimus &rdquo; (ibi, pag. </s>

<s>108). </s></p><p type="main">

<s>Lo strumento cos&igrave; disegnato e descritto dal Santorio non &egrave; solo appli&shy;<lb/>cato all'uso particolare del polso ma a quello generale della misura del <lb/>tempo, e infatti alla pagina, o diciam meglio alla colonna 486 di questa <lb/>stessa opera citata, dove descrive l'apparecchio per misurare il calor sensi&shy;<lb/>bile dei raggi della luna, col Termometro, sopra il bulbo del quale vanno <lb/>a ferire gli stessi raggi condensati nel fuoco di uno specchio ustorio; si <lb/>serve, per misurare il tempo dell'azione de'raggi lunari sul bulbo termo&shy;<lb/>metrico, dello strumento sopra disegnato. </s>

<s>&ldquo; Per instrumentum vero secun&shy;<lb/>dae figurae temporis spatium dimetimur quod declaravimus folio citato &rdquo; (ibi). </s></p><p type="main">

<s>Non potendosi consultare il Libro degli Strumenti medici, nel quale ci <lb/>promette l'Autore di descriverci gli organi di questo Misuratore del tempo, <lb/>n&egrave; altrove dicendo nulla di pi&ugrave; chiaro, noi non sappiam dire in che modo <pb xlink:href="020/01/321.jpg" pagenum="302"/>si movessero i due indici nel sopra disegnato orologio, ma non rappresen&shy;<lb/>tando altro le due mostre che due archi di cerchio, si pu&ograve; asserir con cer&shy;<lb/>tezza che non dovesse essere il moto n&egrave; continuo, n&egrave; regolato a una mi&shy;<lb/><figure id="id.020.01.321.1.jpg" xlink:href="020/01/321/1.jpg"/></s></p><p type="caption">

<s>Figura 15.<lb/>sura prefinita, da non si poter variare all'arbitrio e al fine <lb/>dell'osservatore. </s>

<s>Ma pure, insiem con quello, il Santorio <lb/>descrive un altro strumento, che ha l'esteriore figura e <lb/>forma di un vero orologio a pendolo. </s>

<s>La figura che si vede <lb/>nella colonna 307 &egrave; una mostra circolare digradata in 12 <lb/>parti, di sotto alla quale vedesi uscire il pendolo. </s>

<s>E per&shy;<lb/>ch&egrave;, fra le altre figure, disegnate insieme nel campo della <lb/>pagina citata, questa di cui particolarmente intendiamo &egrave; <lb/>in ordine la terza, &ldquo; tertium est (ivi dice l'Autore per illu&shy;<lb/>strarla) ad instar cotylae depressae, ex qua egreditur filum <lb/>cui appensa est pila plumbea &rdquo;. </s>

<s>Noi rappresentiamo sotto <lb/>gli occhi de'nostri lettori l'immagine di questa <emph type="italics"/>Cotyla<emph.end type="italics"/><lb/>fedelmente disegnata nella figura 15. </s></p><p type="main">

<s>Alla colonna 510 ricorre la medesima figura, della <emph type="italics"/>Cotyla<emph.end type="italics"/> sopra ac&shy;<lb/>cennata, con questa sola differenza: che la mostra non &egrave; in 12, ma &egrave; di&shy;<lb/>visa in 24 parti uguali, com'usava agli orologi pubblici di que'tempi. </s>

<s>Que&shy;<lb/>sto orologio a pendolo, di cui si vede con fedelt&agrave; nella nostra figura 16 <lb/><figure id="id.020.01.321.2.jpg" xlink:href="020/01/321/2.jpg"/></s></p><p type="caption">

<s>Figura 16.<lb/>riprodotto il disegno, &egrave; ordinato dall'Inventore a mi&shy;<lb/>surare i moti della inspirazione e della espirazione <lb/>dell'infermo, e intorno ad esso il nostro Medico au&shy;<lb/>tore ivi scrive le seguenti parole: &ldquo; Modus vero di&shy;<lb/>metiendi inspirationem et espirationem habetur per <lb/>instrumentum propositum. </s>

<s>Dimetimur enim facillime <lb/>expirationem prius manu ad cor admota, deinde cum <lb/>filo, cui alligatus sit globulus plumbeus satis longo, <lb/>motum et quietem respirationis observamus. </s>

<s>Dicimus <lb/>satis longo, quia, quo longuis est, motus tardior fit &rdquo;. </s></p><p type="main">

<s>Non sembra a noi poter esservi nessun dubbio <lb/>che questa cos&igrave; detta <emph type="italics"/>Cotyla,<emph.end type="italics"/> descrittaci o mostrataci <lb/>sotto velo dal Santorio, non sia un vero e proprio <lb/>orologio a pendolo. </s>

<s>La chiama <emph type="italics"/>Cotyla<emph.end type="italics"/> perch&egrave;, come <lb/>udimmo dire a lui stesso, la mostra era alquanto <lb/>incavata da presentar l'immagine di una scodella, <lb/>ma dietro alla scodella doveva esservi qualche con&shy;<lb/>gegno, il quale comunicasse all'indice i moti vibra&shy;<lb/>torii del pendolo. </s>

<s>In che propriamente consistesse un tal congegno, e come <lb/>fosse connesso con gli stessi moti vibratorii, non possiamo noi dirlo con cer&shy;<lb/>tezza, ma &egrave; facile indovinare che consistesse tutto in ruote dentate, a somi&shy;<lb/>glianza di quell'altro orologio a pendolo, che per uso di trovar le longitudini <lb/>fu proposto da Galileo. </s></p><p type="main">

<s>Abbiamo detto di sopra esser questo il primo documento storico pub-<pb xlink:href="020/01/322.jpg" pagenum="303"/>blicamente conosciuto, e in che si abbatte colui, che vuol narrar le cose <lb/>non sull'autorit&agrave; degli scrittori, ma sopra la verit&agrave; dimostrata dai fatti, co&shy;<lb/>sicch&egrave; in conclusione parrebbe fosse stato il Santorio il primo a riconoscer <lb/>la propriet&agrave; dell'isocronismo de'pendoli, e ad applicarla sagacemente alla <lb/>misura dei tempi. </s>

<s>Contro una siffatta conclusione per&ograve; insorgono molti, e <lb/>affermano, senza il minimo dubbio, che l'isocronismo del pendolo e la prima <lb/>applicazione di lui all'orologio, sono scoperte e invenzioni di Galileo. </s>

<s>Il fon&shy;<lb/>damento principale di una tale affermazione non &egrave; in altro per costoro, che <lb/>nella autorit&agrave; di Vincenzio Viviani, della quale sar&agrave; da noi lungamente di&shy;<lb/>scorso a suo luogo. </s>

<s>Ma intanto vogliamo far conoscere ai nostri lettori altri <lb/>documenti, diversi dai gi&agrave; noti, per i quali ci potremo chiarire anche me&shy;<lb/>glio come e quanto il soverchio zelo, nel fervente Ammiratore del suo Mae&shy;<lb/>stro, facesse ombra a veder chiaro e a scrivere il vero. </s></p><p type="main">

<s>Nel Tomo CXVII dunque dei <emph type="italics"/>Discepoli,<emph.end type="italics"/> nella preziosa collezione dei <lb/>Manoscritti galileiani, dalla carta 60-63 si leggono alcuni studii dello stesso <lb/>Viviani sulle propriet&agrave; meccaniche de'pendoli, e sulle matematiche loro di&shy;<lb/>mostrazioni. </s>

<s>&Egrave; una scrittura informe, ma dentro alla quale si leggono di <lb/>propria mano le parole stesse, che noi qui trascriviamo. </s></p><p type="main">

<s>&ldquo; Questa del pendolo (cos&igrave; par che il Viviani voglia dare il principio a <lb/>una sua Trattazione) si &egrave; una delle pi&ugrave; antiche invenzioni e scoperte in na&shy;<lb/>tura del Galileo, e fu circa l'anno 1580, quando egli era studente a Pisa, <lb/>nel trovarsi egli un giorno in quel Duomo, dove si abbatt&egrave; di vedere, la&shy;<lb/>sciata in moto, una lampada pendente da una lunghissima corda. </s>

<s>E, come <lb/>quello che da giovanetto s'era anche esercitato nella Musica, sotto la disci&shy;<lb/>plina di quel gran Vincenzio suo Padre, che s&igrave; dottamente scrisse poi in Dia&shy;<lb/>logo della Musica antica e moderna; perciocch&egrave; aveva impressa nell'anima <lb/>l'egualit&agrave; de'tempi, co'quali essa si regola, riflettendo a quel moto, gli fu <lb/>facile il giudicarlo in mente sua equitemporaneo, s&igrave; nelle andate lunghe e <lb/>larghe al principio del moto, come nelle strette sul fine verso la quiete. </s>

<s>In <lb/>casa poi se ne chiar&igrave; in pi&ugrave; modi con replicate esperienze esattissime, tro&shy;<lb/>vando, coll'aiuto de'suoi compagni, che in un determinato numero di vibra&shy;<lb/>zioni d'un certo pendolo, lasciato andar sempre da una distanza medesima <lb/>del perpendicolo, quante ne faceva un altro pendolo delle larghe, altrettante <lb/>in ciascuno ne faceva delle strette e delle strettissime. </s>

<s>Che se il numero di <lb/>queste eccedeva di qualcosa il numero di quelle, il che per&ograve; si fa visibile <lb/>solamente dopo un numero grandissimo delle une e delle altre, attribuiva <lb/>questa piccola maggioranza al minore ostacolo, che arreca l'aria al mobile <lb/>pi&ugrave; tardo, qual'&egrave; quello del grave pendolo nel passar gli archi pi&ugrave; piccoli, <lb/>che al mobile pi&ugrave; veloce, qual'&egrave; il medesimo nel passar gli archi grandi &rdquo;. </s></p><p type="main">

<s>La storia narrata in quest'abbozzo di scrittura inedita &egrave; simile a quella <lb/>che pubblic&ograve; il Viviani nella Vita di Galileo, e che noi vedremo esaminata <lb/>diligentemente a suo luogo, dove dimostreremo la inverisimiglianza che la <lb/>prima occasione di scoprir l'isocronismo del pendolo si porgesse a Galileo <lb/>stesso nell'attendere a misurar la durata delle oscillazioni o pi&ugrave; ampie o <pb xlink:href="020/01/323.jpg" pagenum="304"/>pi&ugrave; ristrette della lampada nel Duomo di Pisa. </s>

<s>Ma non si pu&ograve; negare, in <lb/>ogni modo, che verso quel tempo indicato dal Viviani, o poco dopo, il gran <lb/>Maestro della nuova Scienza del moto non fosse veramente il primo a no&shy;<lb/>tare quella insigne propriet&agrave; dei corpi oscillanti. </s></p><p type="main">

<s>Comunque sia, abbiamo documento certissimo che nel 1602 Galileo si <lb/>faticava intorno alla dimostrazione di quella propriet&agrave; naturale de'corpi gravi <lb/>sospesi, gi&agrave; prima sperimentalmente scoperta, e il documento &egrave; una lettera <lb/>diretta a Guidubaldo del Monte, da Padova, dove da poco insegnava, collega <lb/>e amico di Santorre Santorio. </s>

<s>&Egrave; probabilissimo perci&ograve; che il giovane Mate&shy;<lb/>matico conferisse questa sua nuova speculazione col Medico gi&agrave; provetto, e <lb/>la probabilit&agrave; vien maggiormente confermata dal veder che i principii mec&shy;<lb/>canici dell'uno erano quegli stessi professati dall'altro. </s>

<s>Imperocch&egrave; il San&shy;<lb/>torio ammette l'isocronismo assoluto, come Galileo, per ogni ampiezza di <lb/>arco, e ritien che i tempi delle vibrazioni fatte da due pendoli di differente <lb/>lunghezza fossero ad esse lunghezze in semplice ragion reciproca propor&shy;<lb/>zionali. </s>

<s>Bench&egrave; insomma il primo a pubblicar questa propriet&agrave; del pendolo <lb/>fosse il Santorio, &egrave; certo nulladimeno che dieci anni prima aveva privata&shy;<lb/>mente fatta nota quella scoperta Galileo, come principale fondamento al <lb/>grande edifizio meccanico, a cui egli gi&agrave; incominciava a por mano. </s></p><p type="main">

<s>Ma seguitiamo a leggere quel che nella sopra allegata scrittura sog&shy;<lb/>giunge appresso il Viviani: &ldquo; Assicuratosi allora di cos&igrave; bella notizia, come <lb/>che Egli era d'ingegno che de'primi acquisti di qualche vero non si con&shy;<lb/>tenta, pens&ograve; subito di applicarlo ad uso giovevole della Medicina, nella quale, <lb/>per secondare il gusto del proprio Padre, faceva allora i suoi studii, ond'ei <lb/>propose ai medici di quel tempo di valersi di un picciol pendolo, per esa&shy;<lb/>minare, con un tal giudice, inalterabile e spassionato, senza dover, come <lb/>solevano, confidar nella propria fallace reminiscenza, la variet&agrave; della fre&shy;<lb/>quenza de'polsi de'febbricitanti, e chiarirsi de'tempi dell'accesso, dell'au&shy;<lb/>gumento, dello stato e della declinazione delle febbri. </s>

<s>Di tal semplicissimo <lb/>strumento, bench&egrave; dai pi&ugrave; fosse poco apprezzato, non mancarono per&ograve; de'pi&ugrave; <lb/>docili che ne fecer conto, e di qui &egrave; che spargendosene l'uso per l'Italia <lb/>ed oltr&egrave; i monti, vi fu chi se ne appropri&ograve; l'invenzione, senza neppur far <lb/>parola del suo primo e vero Autore, se non con pregiudizio di quell'onore, <lb/>che s&igrave; giustamente gli era dovuto. </s>

<s>Il medesimo strumento fu di poi dal no&shy;<lb/>stro Accademico, subito che si fu introdotto nelle Matematiche, il che segui <lb/>sui 22 anni della sua et&agrave;, cio&egrave; intorno al 1885, adattato alla cognizione delle <lb/>minuzie dei tempi, per conseguir la precisione tanto necessaria nelle osser&shy;<lb/>vazioni astronomiche, e per lo cui mezzo, che &egrave; in apparenza debolissimo, <lb/>comecch&egrave; ad un debolissimo filo stia appeso il grave pendulo misuratore, <lb/>ed egli e tutti gli osservatori che ne son proceduti, hanno avuto campo di <lb/>restaurare l'Astronomia, la Nautica e la Geogralia. </s>

<s>Che perci&ograve; &egrave; verissimo <lb/>doversi in Natura far capitale non meno delle cose piccole che delle grandi, <lb/>essendo ella massima nelle minime, non che nelle grandissime. </s>

<s>Di qui &egrave; <lb/>che il nostro Accademico, bene sciente di ci&ograve;, seppe sempre delle cose <pb xlink:href="020/01/324.jpg" pagenum="305"/>naturali notabilmente approfittarsi d'ogni minuzia, anco in apparenza vi&shy;<lb/>lissima. </s>

<s>&rdquo; </s></p><p type="main">

<s>Apparisce da queste parole essere una ferma persuasione del Viviani che <lb/>si debba attribuire a Galileo, non la sola scoperta del fatto concernente l'iso&shy;<lb/>cronismo del pendolo, ma l'applicazione del fatto stesso altresi alla misura <lb/>delle minuzie del tempo in generale, e delle pulsazioni delle arterie in par&shy;<lb/>ticolare. </s>

<s>Secondo lui, il Santorio sarebbe stato uno di quelli, che si attri&shy;<lb/>buirono l'invenzione di Galileo, a cui venne il primo pensiero d'applicare <lb/>il pendolo all'orologio per le mediche ascoltazioni del polso. </s>

<s>&Egrave; notabile per&ograve; <lb/>che l'egregio Autore, cos&igrave; scrivendo, non fece altro che secondare le inspi&shy;<lb/>razioni del suo cuore fervente di sviscerato ossequio verso il suo venerato <lb/>Maestro, avendo noi documenti che nel 1669 non aveva veduta ancora nes&shy;<lb/>suna delle opere del Santorio. </s>

<s>Cos&igrave; fatti documenti consistono in due lettere <lb/>di Geminiano Montanari, nella prima delle quali, che &egrave; del d&igrave; 29 di Otto&shy;<lb/>bre, avendo avuta commissione dal Viviani di guardar se appresso i librai <lb/>di Bologna si trovassero le Opere del Santorio venali, il Montanari stesso <lb/>cos&igrave; gli risponde: &ldquo; Del Santorio non ho mai trovato cosa alcuna, e questi <lb/>Medici qui gli asciugano tutti. </s>

<s>Solo ho trovato un'Opera di questo Autore <lb/><emph type="italics"/>De vitandis erroribus<emph.end type="italics"/> ecc. <emph type="italics"/>in re medica,<emph.end type="italics"/> in folio, e mi fanno l'ultimo prezzo <lb/>di lire 4. Se ella comanda ne sar&agrave; servita &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLV, <lb/>c. </s>

<s>120). E in altra del d&igrave; 3 Dicembre torna cos&igrave; a scrivere intorno al me&shy;<lb/>desimo soggetto: &ldquo; Non mi ricordo se dissi a V. S. che quel Santorio <emph type="italics"/>De <lb/>vitandis erroribus<emph.end type="italics"/> non sapeva se gli uscirebbe cos&igrave; grato, poich&egrave; non vi si <lb/>contiene cosa alcuna n&egrave; circa la statica, n&egrave; circa l'esperienza pi&ugrave; curiosa <lb/>del Metrosfigmo ed altre osservazioni sue, lo che credo esser lo scopo pri&shy;<lb/>mario della curiosit&agrave; di V. S. circa di questo Autore, ma &egrave; ella tutta l'opera <lb/>dottrinale medica intorno gli errori pi&ugrave; comuni, n&egrave; forse diversa, quanto al <lb/>soggetto e materia principale, dall'opuscolo del Cardano <emph type="italics"/>Consideratio me&shy;<lb/>dica<emph.end type="italics"/> ecc. </s>

<s>&rdquo; (ivi, c. </s>

<s>122). </s></p><p type="main">

<s>Si par chiaro di qui che alle orecchie del Viviani era pervenuto il ru&shy;<lb/>more che fosse dal Santorio stato pubblicamente descritto il pulsilogio, e <lb/>senz'aver letto e bene esaminato il Libro, si dette a creder con ferma per&shy;<lb/>suasione che il Medico di Capo d'Istria ne avesse destramente involata l'in&shy;<lb/>venzione a Galileo. </s>

<s>Ma non &egrave; ci&ograve; un proceder conforme al criterio storico, <lb/>come pure non &egrave; in conformit&agrave; di questo criterio l'asserir che fa il Viviani <lb/>avere il suo Galileo applicato il pendolo alla misura del tempo nelle osser&shy;<lb/>vazioni astronomiche, infino dal 1585, essendo che resulti chiarissimamente <lb/>dai documenti che il pendolo non s'incominci&ograve; ad usar per misuratore del <lb/>tempo in Astronomia, se non che verso il 1638, come da noi verr&agrave; dimo&shy;<lb/>strato a suo luogo. </s></p><p type="main">

<s>Prima di quel tempo il pendolo, per Galileo, non era altro che uno <lb/>strumento meccanico, per cui crediamo di poter giustamente asserire che <lb/>il primo, il quale si servisse del pendolo come di strumento cronologico fu <lb/>il Santorio. </s>

<s>N&egrave; la critica sa suggerirci nessun buon motivo di credere che <pb xlink:href="020/01/325.jpg" pagenum="306"/>la prima idea del Pulsilogio l'avesse il celebre Medico attinta dai colloqui <lb/>con Galileo, ripensando che questi non attendeva in Padova all'arte medica, <lb/>mentre l'altro la professava ivi con gran celebrit&agrave;, e per l'invenzione di <lb/>altri strumenti era divenuto in gran fama. </s>

<s>Dall'altra parte sappiamo per <lb/>cosa certa che Galileo non si serv&igrave; del pendolo per misuratore del tempo, <lb/>nemmeno nelle sue sperimentali meccaniche esercitazioni, preferendo l'an&shy;<lb/>tica clessidra, col pesar l'acqua in un dato tempo stillata. </s>

<s>Se non ne fece <lb/>dunque l'applicazione in materia propria e in soggetto cos&igrave; geloso, qual'era <lb/>quello di misurare i tempi della caduta de'gravi rispetto agli spazii succes&shy;<lb/>sivamente passati; com'&egrave; credibile che facesse uso del pendolo, o pensasse <lb/>a suggerirlo a un'arte aliena dalla sua professione? </s>

<s>E come si pu&ograve; con giu&shy;<lb/>stizia asserire che il Santorio tanto solo avesse d'ingegno, quanto gliene bi&shy;<lb/>sognava a furar destramente una scoperta a Galileo? </s></p><p type="main">

<s>In conclusione, i documenti a favor del Santorio son certi, ma quali <lb/>altri documenti a favore di Galileo reca il Viviani? </s>

<s>Dov'&egrave; fra le galileiane <lb/>una pagina o manoscritta o stampata, in cui si faccia il minimo accenno a <lb/>queste cose? </s>

<s>N&egrave; l'occasione solenne di far ci&ograve; sarebbe pure mancata al&shy;<lb/>l'Autore, l&agrave; dove parla del pendolo ne'<emph type="italics"/>Massimi Sistemi<emph.end type="italics"/> o pi&ugrave; opportuna&shy;<lb/>mente nel primo Dialogo delle <emph type="italics"/>Due Nuove Scienze.<emph.end type="italics"/> Perch&egrave; qui se ne passa <lb/>con tanta fretta, lasciando la legge importantissima, che governa il moto <lb/>de'pendoli di lunghezza varia, senza il conforto di una matematica dimo&shy;<lb/>strazione? </s></p><p type="main">

<s>A supplire al difetto di Galileo, soccorse, l'anno dopo la pubblicazione <lb/>fatta dagli Elzevirii, uno straniero tedesco Giovan Marco De'Marchi, il quale <lb/>in un suo Trattato <emph type="italics"/>De proportione motus<emph.end type="italics"/> dimostr&ograve; con rigoroso processo <lb/>matematico la proposizione seguente: &ldquo; Motus circulorum sunt in ratione <lb/>temporum quam habent diametri ad se duplicatam &rdquo; (Pragae, 1639, pag. </s>

<s>I, <lb/>4 vers). </s></p><p type="main">

<s>Il De Marchi si riserb&ograve; nell'ultima parte del suo Trattato di parlar <lb/>del pendolo per uso di Pulsilogio, la descrizione del quale &egrave; similissima a <lb/>quella della seconda maniera del Santorio, ma la teoria &egrave; diversa, imperoc&shy;<lb/>ch&egrave;, mentre il Nostro ignora la legge del ritirarsi e del rilassarsi il filo per&shy;<lb/>ch&egrave; faccia il pendolo le sue vibrazioni in tempi determinati; il Tedesco ne <lb/>d&agrave; regola certa, applicando la legge sperimentalmente scoperta da Galileo, <lb/>e da s&egrave; matematicamente dimostrata che cio&egrave; i tempi delle vibrazioni stanno <lb/>in ragione delle radici delle lunghezze de'fili. </s></p><p type="main">

<s>Lo stesso Autore termina il suo Trattato col proporsi di risolvere que&shy;<lb/>sto problema: &ldquo; Horologium construere, quod suo motu tempus numeret <lb/>divisum in partes minores quam tertias unius secundi &rdquo; e la soluzione di&shy;<lb/>pende dall'applicare ai pendoli la dimostrata legge del variar de'tempi al <lb/>variar delle lunghezze stesse a cui son sospesi. </s></p><pb xlink:href="020/01/326.jpg" pagenum="307"/><p type="main">

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

<s>Bench&egrave; sia un fatto che Galileo non si rivolse a principio, con fiducioso <lb/>amore e con sollecito studio, al pendolo, per far di lui il pi&ugrave; squisito mi&shy;<lb/>suratore del tempo, venne nulladimeno assai presto l'occasione che gli fece <lb/>sentir come l'importante problema era riserbato a risolversi da quel suo ne&shy;<lb/>gletto strumento. </s>

<s>Venne appunto quell'occasione, quando, per mezzo delle <lb/>osservazioni de'Satelliti di Giove, gli cadde in pensiero che si potesse, me&shy;<lb/>glio che in qualunque altro modo, ritrovar le longitudini dai naviganti. </s>

<s>Al&shy;<lb/>lora torn&ograve; il suo pendolo oscillatorio a incorargli una fiducia che i tempi <lb/>necessarii per valersi di quelle gioviali osservazioni, non si sarebbero potuti <lb/>misurar n&egrave; pi&ugrave; comodamente n&egrave; pi&ugrave; esattamente, che dai moti invariabili <lb/>di lui. </s>

<s>&ldquo; Io ho tale misuratore del tempo (scriveva nell'Agosto del 1636 <lb/>agli Stati Generali di Olanda) che se si fabbricassero quattro o sei di tali <lb/>strumenti, e si lasciassero scorrere, troveremmo, in confermazione della loro <lb/>giustezza, che i tempi di quelli misurati e mostrati, non solamente d'ora in <lb/>ora, ma di giorno in giorno, e di mese in mese, non differirebbero tra di <lb/>loro, n&egrave; anco di un minuto secondo, tanto uniformemente camminano &rdquo; <lb/>(Alb. </s>

<s>VII, 86). </s></p><p type="main">

<s>In queste parole &egrave; evidentemente inteso il semplice pendolo, le vibra&shy;<lb/>zioni del quale direttamente numerate esibiscono, senz'altro meccanismo ag&shy;<lb/>giuntovi, la misura esatta del tempo. </s>

<s>Ma quelle misurazioni, oltre ad esser <lb/>bene spesso fallaci, per mancanza di attenzione o per accidental divagamento <lb/>degli osservatori, riuscivan sommamente tediose, per cui parve al Renieri di <lb/>aver fatto in tal proposito qualche progresso, quando, avendo osservata una <lb/>nuova propriet&agrave; nel moto de'pendoli, credette di poter per essa dedurre il <lb/>numero delle vibrazioni, senz'aver bisogno di star l&igrave; pazientemente a con&shy;<lb/>tarle a una a una. </s></p><p type="main">

<s>&ldquo; Voglio dar parte (cos&igrave; egli scrive in una lettera a Galileo del 27 Mar&shy;<lb/>zo 1637) a V. S. di una osservazione fatta da me nelle vibrazioni de'corpi <lb/>pendoli, che forse, se da lei non &egrave; stata avvertita, non le dispiacer&agrave;; ed &egrave; <lb/>che lasciandosi andar dall'uno de'lati dell'arco da loro descritto e restrin&shy;<lb/>gendosi sempre pi&ugrave;, tante vibrazioni pongono la prima volta nel restringersi <lb/>un palmo, quanto &igrave;a seconda e la terza ecc. </s>

<s>Coll'esempio mi lascer&ograve; forse <lb/>meglio intendere. </s>

<s>Sia sospeso il pendolo A (fig. </s>

<s>17) dal punto E fino all'al&shy;<lb/>tezza dell'arco LF. </s>

<s>Lasciandosi poi andar libero fino ad H, nel ritorno far&agrave; <lb/>la vibrazione d'arco minore in B, la terza in C, ecc. </s>

<s>Ora, se, per esempio, <lb/>la decima vibrazione avr&agrave; slontanato il pendolo dalla perpendicolare all'oriz&shy;<lb/>zonte EI, per la quantit&agrave; dell'arco GL, ogni volta che il pendolo si torner&agrave; <lb/>a lasciar cader libero dal punto F, e che avr&agrave; ristrette le sue vibrazioni al-<pb xlink:href="020/01/327.jpg" pagenum="308"/>l'arco GD, saranno sempre dieci vibrazioni e non pi&ugrave; il che potr&agrave; ser&shy;<lb/>vire per numerare le vibrazioni senz'averle a contare a una a una &rdquo; (ivi, <lb/>T. X, 201). <lb/><figure id="id.020.01.327.1.jpg" xlink:href="020/01/327/1.jpg"/></s></p><p type="caption">

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

<s>Sia che Galileo avesse notata o <lb/>no questa singolarit&agrave; de'pendoli pro&shy;<lb/>postagli a considerar dal Renieri, ebbe <lb/>forse di qui occasione a speculare un <lb/>modo e a immaginare un congegno <lb/>per levare il tedio di contar le vibra&shy;<lb/>zioni, d'onde poi dedurne con facilit&agrave; <lb/>la misura dei tempi trascorsi. </s>

<s>&Egrave; perci&ograve; <lb/>che tornando nel Giugno del 1637, <lb/>tre mesi dopo la lettera scrittagli dal <lb/>Renieri, a trattar con Lorenzo Realio <lb/>del negozio delle Longitudini, gli pro&shy;<lb/>pone, per la pi&ugrave; facile ed esatta riso&shy;<lb/>luzion del problema, uno strumento <lb/>misuratore del tempo da lui perfe&shy;<lb/>zionato e reso di pi&ugrave; comodo uso. </s>

<s><lb/>Dop'avere infatti discorso delle pro&shy;<lb/>priet&agrave; meccaniche de'pendoli, cos&igrave; di <lb/>lunghezza invariabile come di differenti lunghezze di fili, &ldquo; Da questo verissimo <lb/>e stabile principio (egli tosto soggiunge) traggo io la struttura del mio Misura&shy;<lb/>tore del tempo, servendomi non d'un peso pendente da un filo, ma d'un pen&shy;<lb/>dolo di materia solida e grave, qual sarebbe ottone o rame; il qual pendulo <lb/>fo in forma di settore di cerchio di dodici o quindici gradi, il cui semidia&shy;<lb/>metro sia due o tre palmi, e quanto maggiore sar&agrave;, con tanto minor tedio <lb/>se gli potr&agrave; assistere. </s>

<s>Questo tal settore fo pi&ugrave; grosso nel semidiametro di <lb/>mezzo avendolo assottigliato verso i lati estremi, dove fo che termini in una <lb/>linea assai tagliente, per evitare quanto si possa l'impedimento dell'aria, <lb/>che sola lo va ritardando. </s>

<s>Questo &egrave; perforato nel centro, pel quale passa un <lb/>ferretto in forma di quelli sopra i quali si voltano le stadere; il qual fer&shy;<lb/>retto, terminando nella parte di sotto in un angolo, e posando sopra due so&shy;<lb/>stegni di bronzo, acci&ograve; meno consumino, pel lungo muovergli, il settore; <lb/>rimosso esso settore per molti gradi dallo stato perpendicolare quando sia <lb/>bene bilicato, prima che fermi, ander&agrave; reciprocando di qua e di l&agrave; numero <lb/>grandissimo di vibrazioni, le quali, per potere andare continuando secondo <lb/>il bisogno, converr&agrave; che chi gli assiste, gli dia a tempo un impulso ga&shy;<lb/>gliardo, riducendolo alle vibrazioni ample. </s>

<s>E fatta, per una volta tanto, con <lb/>pazienza, la numerazione delle vibrazioni che si fanno in un giorno naturale, <lb/>misurato colla rivoluzione di una stella fissa, s'aver&agrave; il numero delle vibra&shy;<lb/>zioni d'un'ora, d'un minuto, o d'altra minima parte &rdquo; (ivi, T. VII, 169, 70). </s></p><p type="main">

<s>Squisiti son senza dubbio questi perfezionamenti introdotti da Galileo <lb/>nella costruzione dello strumento, e con tanta accortezza soccorre a rimuo-<pb xlink:href="020/01/328.jpg" pagenum="309"/>verne gl'impedimenti, cos&igrave; per mezzo del coltello sopra cui si appoggia il <lb/>settore pendulo, come per mezzo degli orli taglienti dati allo stesso settore <lb/>oscillatorio; che son rimaste tuttavia nella fabbrica degli orologi moderni, <lb/>quelle ingegnose disposizioni, nella struttura delle lenti, e nella forma degli <lb/>appoggi, per diminuire pi&ugrave; che sia possibile, gli attriti. </s>

<s>Ma rimaneva ancora, <lb/>come non evitato inconveniente, il tedio di numerare e la facilit&agrave; di com&shy;<lb/>mettere, cos&igrave; numerando, sbagli. </s>

<s>A ci&ograve; attese Galileo a provvedere, forse <lb/>come dicemmo per impulso e per suggerimento del p. </s>

<s>Renieri, ond'&egrave; che <lb/>cos&igrave;, nel sopraccitato luogo, prosegue a dire al Realio: </s></p><p type="main">

<s>&ldquo; Per evitar poi il tedio di chi dovesse perpetuamente assistere a nu&shy;<lb/>merare le vibrazioni, ci &egrave; un assai comodo provvedimento in questo modo: <lb/>cio&egrave; facendo che dal mezzo della circonferenza del settore sporga infuori un <lb/>piccolissimo e sottilissimo stiletto, il quale, nel passare, percuota in una se&shy;<lb/>tola fissa in una delle sue estremit&agrave;, la qual setola posi sopra i denti d'una <lb/>ruota leggeriss&igrave;ma quanto una carta, la quale sia posta in piano orizzontale <lb/>vicina al pendolo, ed avendo intorno intorno denti a guisa di quelli d'una <lb/>sega, cio&egrave; con uno de'lati posti a squadra sopra il piano della ruota e l'al&shy;<lb/>tro inclinato obliquamente, presti questo ufficio: che nell'urtare la setoletta <lb/>nel lato perpendicolare del dente lo muova, ma nel ritorno poi la medesima <lb/>setola nel lato obliquo del dente non lo muova altrimenti, ma lo vada stri&shy;<lb/>sciando a pi&egrave; del dente susseguente. </s>

<s>E cos&igrave;, nel passaggio del pendolo, si <lb/>muover&agrave; la ruota per lo spazio d'uno de'suoi denti, ma nel ritorno del pen&shy;<lb/>dolo, essa ruota non si muover&agrave; punto; onde il suo moto ne riuscir&agrave; cir&shy;<lb/>colare, sempre per l'istesso verso. </s>

<s>Ed avendo contrassegnati con numeri i <lb/>denti si vedr&agrave; ad arbitramento la moltitudine dei denti passati, ed in con&shy;<lb/>seguenza il numero delle vibrazioni e delle particelle del tempo decorso &rdquo; <lb/>(ivi, pag. </s>

<s>170, 71). </s></p><p type="main">

<s>Si dovrebbe dir senza dubbio, questo immaginato da Galileo, il primo <lb/>macchinamento adattabile all'orologio, quando non ci si rappresentasse scol&shy;<lb/>pito nella memoria il disegno di quella <emph type="italics"/>Cotyla<emph.end type="italics"/> santoriana; disegno impresso <lb/>nelle pagine di un libro che vide la pubblica luce dodici anni prima che <lb/>Galileo scrivesse quella pr&igrave;vata lettera a Lorenzo Realio. </s>

<s>L'indice, la mo&shy;<lb/>stra divisa in 12 parti, la maglietta e il chiodo che lo rappresentano appeso <lb/>a una parete, fanno immaginar che l'Orologio santoriano non differisse, al&shy;<lb/>meno esteriormente, da uno di questi dell'uso moderno. </s>

<s>&Egrave; vero che non vi <lb/>&egrave; rappresentato n&egrave; accennato in disegno il macchinamento interiore, n&egrave; con <lb/>parole ci vien dall'Autore in alcun modo descritto; ma &egrave; pure una ragio&shy;<lb/>nevole congettura quella di creder che il pendolo comunicasse il moto cir&shy;<lb/>colare all'indice per mezzo di ruote dentate, e cos&igrave; venisse a rassomigliarsi <lb/>a un vero Orologio a pendolo meglio di quello che Galileo progett&ograve; all'Am&shy;<lb/>miraglio olandese. </s></p><p type="main">

<s>Comunque sia di ci&ograve;, e in qualunque modo fosse interiormente con&shy;<lb/>gegnato l'Oriolo a pendolo conforme al disegno esteriore, che si vede im&shy;<lb/>presso nelle pagine del Commentario santoriano sopr'Avicenne, &egrave; un fatto <pb xlink:href="020/01/329.jpg" pagenum="310"/>che il primo a descriverci quel congegno fu nel 1637 il Galileo. </s>

<s>Quel con&shy;<lb/>gegno, sebbene in s&egrave; semplicissimo, pur conteneva e quasi diremmo com&shy;<lb/>pendiava gli organi essenziali a ogni macchinamento d'orologeria. </s></p><p type="main">

<s>Il Viviani ci narra e fa testimonianza che il medesimo Galileo, anche raf&shy;<lb/>freddato il negozio delle Longitudini, non si rimase per questo di speculare, <lb/>negli ultimi anni della sua vita, e gi&agrave; divenuto cieco, intorno ai perfeziona&shy;<lb/>menti dell'Orologio. </s>

<s>I germi di questi ideati perfezionamenti s'intravedono <lb/>nella stessa Lettera al Realio, in quelle speculazioni ch'ei soggiunge dopo <lb/>aver descritto il pendolo e dopo aver detto del modo come il pendolo stesso <lb/>partecipava il moto alla ruota a denti di sega, per mezzo dello sfregamento <lb/>e dell'urto di una setola. </s>

<s>&ldquo; Si pu&ograve; ancora, egli scrive, intorno al centro di <lb/>questa prima ruota adattarne un'altra di piccol numero di denti, la quale <lb/>tocchi un'altra maggior ruota dentata, dal moto della quale potremo appren&shy;<lb/>dere il numero delle interne rivoluzioni della prima ruota, compartendo la <lb/>moltitudiee de'denti in modo che per esempio, quando la seconda ruota <lb/>avr&agrave; dato una conversione, la prima ne abbia date 20, 30 o 40, o quante <lb/>pi&ugrave; ne piacesse. </s>

<s>Ma il significar questo alle SS. Loro, che hanno uomini <lb/>esquisitissimi ed ingegnosissimi in fabbricare Orologi ed altre macchine am&shy;<lb/>mirande, &egrave; cosa superflua, perch&egrave; essi medesimi sopra questo fondamento <lb/>nuovo di sapere che il pendolo, muovasi per grandi o per brevi spazii, fa <lb/>le sue reciprocazioni ugualissime, troveranno conseguenze pi&ugrave; sottili di quelle, <lb/>che io possa immaginarmi. </s>

<s>E siccome la fallacia degli Orologi consiste prin&shy;<lb/>cipalmente nel non s'essere fin qui potuto fabbricare quello che noi chia&shy;<lb/>miamo il <emph type="italics"/>tempo dell'orologio,<emph.end type="italics"/> tanto aggiustatamente che faccia le sue vi&shy;<lb/>brazioni uguali; cos&igrave; in questo mio pendolo semplicissimo e non soggetto <lb/>ad alterazione alcuna si contiene il modo di mantener sempre egualissima <lb/>la misura del tempo &rdquo; (ivi, pag. </s>

<s>171). </s></p><p type="main">

<s>Si vede chiaramente di qui che, infino dal 1637, Galileo pensava di <lb/>adattare il pendolo a quegli Orologi, i quali si componevano di un macchi&shy;<lb/>namento di ruote dentate, la prima delle quali mossa o dalla gravit&agrave; di un <lb/>peso o dall'elasticit&agrave; di una molla, partecipava il suo moto a tutte le altre <lb/>via via, infino a quella, nel centro della quale era appuntato l'indice muo&shy;<lb/>ventesi sopra la mostra. </s>

<s>L'azione del peso o della molla non era equabile, <lb/>perch&egrave; il peso scendendo si accelerava e la molla svolgendosi si ritardava e <lb/>l'indice perci&ograve; che movevasi a quel tenore non mostrava l'ora giusta. </s>

<s>A <lb/>ci&ograve; attendevasi a rimediare per mezzo dei volanti, ma il rimedio per&ograve; era <lb/>precario essendoch&egrave; se il peso s'attemperava a un'ora, non s'attemperava <lb/>ad un'altra, se non che stando l&igrave; frequente a ritirare il peso stesso sopra <lb/>il volante ora innanzi ora indietro dal centro del moto. </s>

<s>Ma anche ci&ograve; non <lb/>poteva esser fatto altro che a caso, non essendo facile il misurar precisa&shy;<lb/>mente quanto si dovesse ritirare il peso sopra il volante, affinch&egrave; contem&shy;<lb/>perasse giusto il velocitarsi del contrappeso o il rilassarsi della molla, che <lb/>l'una colla sua libera gravit&agrave; e l'altra col suo elaterio, davano impulso alle <lb/>ruote. </s>

<s>Questo giusto bilanciamento del peso sopra il volante era appunto <pb xlink:href="020/01/330.jpg" pagenum="311"/>quello che chiamavasi il <emph type="italics"/>tempo dell'orologio,<emph.end type="italics"/> dall'ignorar la regola del <lb/>quale, dice Galileo, che dipendeva ogni fallacia, a cui eran soggetti i mac&shy;<lb/>chinamenti fabbricati allora per la misura del tempo. </s></p><p type="main">

<s>Egli sperava di poter trovar quella regola con l'applicare, invece del <lb/>bilanciere gravato dal contrappeso, il pendolo alle ruote degli antichi oro&shy;<lb/>logi da Torre. </s>

<s>Ma la difficolt&agrave; d'adattare il nuovo organo oscillatorio gli si <lb/>present&ograve; grave per modo, che pens&ograve; di trovare altrove che nei pesi e nelle <lb/>molle quella equabilit&agrave; di forza necessaria al regolare e costante andamento <lb/>dell'Orologio. </s>

<s>Questa forza cred&egrave; Galileo che potesse esser somministrata <lb/>dall'acqua. </s>

<s>E in fatti un liquido che esca fuori dall'orifizio di un vaso man&shy;<lb/>tenuto sempre allo stesso livello, conserva, in un punto determinato del suo <lb/>getto parabolico, una velocit&agrave; e una quantit&agrave; di moto sempre costante, ond'&egrave; <lb/>che venendo a urtare contro l'aletta di una ruota, questa si volger&agrave; attorno <lb/>equabilmente. </s>

<s>Pongasi ora questa ruota idraulica in luogo del tempo del&shy;<lb/>l'orologio, e servir&agrave; per misura inalterabile dell'ore. </s>

<s>Di questo pensiero, che <lb/>rivela non tanto la sagacia della mente, quanto l'attivit&agrave; dell'investigazione, <lb/>ne lasci&ograve; Galileo le tracce in una di quelle Aggiunte, che fece di propria <lb/>mano ai Dialoghi dei Due Massimi Sistemi, su un esemplare posseduto dalla <lb/>Biblioteca del Seminario di Padova. </s>

<s>Quell'Aggiunta cos&igrave; dice: &ldquo; Il tempo <lb/>dell'Oriolo mosso per l'acqua pu&ograve; forse servire per misurar l'ore &rdquo;. </s></p><p type="main">

<s>Ma questo in ogni modo non poteva riuscir quel Misuratore del tempo, <lb/>che richiedevasi per i regolati esercizii della vita domestica e civile, e tanto <lb/>meno era atto a corrispondere alle scrupolose esigenze della scienza. </s>

<s>Non <lb/>si pu&ograve;, pensava Galileo, uscir dal pendolo, e ci dee esser pur la maniera di <lb/>adattarlo alle ruote degli Orologi, che segnano l'ore sulle pubbliche piazze. </s>

<s><lb/>Quella maniera vedeva egli consistere nell'adattare opportunamente un con&shy;<lb/>gegno, il quale facesse s&igrave; che il pendolo, invece di dare impulso, lo rice&shy;<lb/>vesse dalle stesse ruote, e fosse ufficio di lui quello di regolare e di perpe&shy;<lb/>tuare nelle macchine il moto cos&igrave; regolato. </s></p><p type="main">

<s>Il Viviani ci assicura che Galileo riusc&igrave; veramente a trovar quel con&shy;<lb/>gegno che rispondeva all'intento, e racconta come negli ultimi anni della <lb/>vita l'avesse ideato, e a lui stesso, che ne racconta la storia, fatto noto. </s>

<s>In <lb/>quella storia, lasciando addietro tante altre particolarit&agrave; che non fanno per <lb/>ora al caso nostro, cos&igrave; appunto si legge: &ldquo; Mentre dunque il Padre Re&shy;<lb/>nieri attendeva alla composizione delle Tavole, si pose il Galileo a speculare <lb/>intorno al suo Misuratore del tempo, ed un giorno del 1641, quando io di&shy;<lb/>morava appresso di lui nella Villa d'Arcetri, sovviemmi che gli cadde in <lb/>concetto che si saria potuto adattare il pendolo agli oriuoli da contrappesi <lb/>e da molle, con valersene invece del solito tempo, sperando che il moto <lb/>egualissimo e naturale di esso pendolo avesse a correggere tutti i difetti <lb/>dell'arte in essi oriuoli. </s>

<s>Ma perch&egrave; l'esser privo di vista gli toglieva di poter <lb/>far disegni e modelli, a fine d'incontrare quell'artifizio, che pi&ugrave; proporzio&shy;<lb/>nato fosse all'effetto concepito, venendo un giorno di Firenze in Arcetri il <lb/>detto signor Vincenzio suo figliuolo, gli conferi il Galileo il suo pensiero, e <pb xlink:href="020/01/331.jpg" pagenum="312"/>di poi pi&ugrave; volte vi fecero sopra varii discorsi, e finalmente stabilirono il <lb/>modo che dimostra il qui aggiunto disegno, e di metterlo intanto in opera <lb/>per venire in cognizione del fatto di quelle difficolt&agrave;, che il pi&ugrave; delle volte <lb/>nelle macchine con la semplice speculativa non si possono prevedere. </s>

<s>Ma <lb/>perch&egrave; il signor Vincenzio intendeva di fabbricar lo strumento di propria <lb/>mano, acci&ograve; questo, per mezzo degli Artefici non si divulgasse prima che <lb/>fosse presentato al Serenissimo Granduca suo Signore, ed appresso alli Si&shy;<lb/>gnori Stati per uso della longitudine; and&ograve; differendo tanto l'esecuzione che <lb/>indi a pochi mesi il Galileo, autore di tutte queste ammirabili invenzioni, cadde <lb/>ammalato, ed agli 8 di Gennaio 1642, stile Romano, manc&ograve; di vita, per lo <lb/>che si raffreddarono tanto i fervori nel signor Vincenzio, che non prima di <lb/>Aprile del 1649 intraprese la fabbrica del presente oriuolo, sul concetto som&shy;<lb/>ministratogli gi&agrave;, me, presente, dal Galileo suo padre &rdquo; (Alb. </s>

<s>XIV, 352, 53). </s></p><p type="main">

<s>Prosegue a narrare ivi il Viviani che Vincenzio di Galileo si serv&igrave;, per <lb/>la fabbrica di quel nuovo strumento dell'opera di un tal Domenico Ba&shy;<lb/>lestrieri, magnano, che aveva a quel tempo bottega al Ponte Vecchio. </s>

<s>Il con&shy;<lb/>gegno fabbricato in parte dal Balestrieri conforme al disegno di Galileo e <lb/>agli ordini avuti da Vincenzio, il Viviani stesso seguita a descriverlo nel se&shy;<lb/>guente modo: &ldquo; Da esso fecesi fabbricare il telaio di ferro, le ruote con i <lb/>loro fusti e rocchetti, senza intagliarle, ed il restante lavor&ograve; di propria mano, <lb/>facendo nella ruota pi&ugrave; alta, detta delle tacche, numero 12 denti, con al&shy;<lb/>trettanti pironi scompartiti in mezzo fra dente e dente, e col rocchetto nel <lb/>fusto di num. </s>

<s>6, ed altra ruota che muove la sopraddetta di num. </s>

<s>90. Ferm&ograve; <lb/>poi da una parte del bracciuolo, che fa la croce al telaio, la chiave a scatto, <lb/>che posa sulla detta ruota superiore, e dall'altra impern&ograve; il pendolo, che era <lb/>formato di un filo di ferro, nel quale stava infilata una palla di piombo, che <lb/>vi poteva scorrere a vite, a fine di allungarlo o scorciarlo secondo il biso&shy;<lb/>gno di aggiustarlo col contrappeso. </s>

<s>Ci&ograve; fatto, volle il signor Vincenzio che <lb/>io (come quegli che era consapevole di questa invenzione e che l'avevo sti&shy;<lb/>molato ad effettuarla) vedessi cos&igrave; per prova e pi&ugrave; d'una volta la congiunta <lb/>operazione del contrappeso e del pendolo; il quale, stando fermo tratteneva <lb/>il discender di quello, ma sollevato in fuori e lasciato poi in libert&agrave;, nel <lb/>passare oltre al perpendicolo, con la pi&ugrave; lunga delle due code annesse al&shy;<lb/>l'imperniatura del dondolo, alzava la chiave che posa ed incastra nella ruota <lb/>delle tacche, la quale tirata dal contrappeso, voltandosi con le parti supe&shy;<lb/>riori verso il dondolo, con uno de'suoi pironi calcava per di sopra l'altra <lb/>codetta pi&ugrave; corta, e le dava nel principio del suo ritorno un impulso tale, <lb/>che serviva d'una certa accompagnatura al pendolo che lo faceva sollevare <lb/>fino all'altezza d'onde s'era partito; il qual ricadendo naturalmente, e tra&shy;<lb/>passando il perpendicolo, tornava a sollevare la chiave, e subito la ruota <lb/>delle tacche, in vigore del contrappeso, ripigliava il suo moto seguendo a <lb/>volgersi e spignere col pirone susseguente il detto pendolo; e cos&igrave; in un <lb/>certo modo si andava perpetuando l'andata e tornata del pendolo, sino a che <lb/>il peso poteva calare a basso &rdquo; (ivi, pag. </s>

<s>253). </s></p><pb xlink:href="020/01/332.jpg" pagenum="313"/><p type="main">

<s>Il Viviani nel far la storia e la descrizione di questo Orologio accenna <lb/>di mandarlo accompagnato da un disegno illustrativo. </s>

<s>Di que'disegni anzi <lb/>ne furono fatti due, il primo de'quali in lapis piombino e che noi riprodu&shy;<lb/>ciamo nella figura 18 dall'originale, inserito a carte 54 del Tomo IV, Parte VI <lb/>de'Manoscritti di Galileo; rappresenta l'Orologio in maest&agrave; dalla parte della <lb/><figure id="id.020.01.332.1.jpg" xlink:href="020/01/332/1.jpg"/></s></p><p type="caption">

<s>Figura 18.<lb/>crociera, sul fusto della quale sono <lb/>imperniate le ruote, e la traversa <lb/>vedesi terminare i bracci in due <lb/>volute, infissavi in una la chiave a <lb/>scatto, e nell'altra le due codette <lb/>ordinate a percuotere ora sull'orlo <lb/>della ruota a tacche, ora sui pironi <lb/>menati in giro da lei. </s>

<s>Ma perch&egrave; di <lb/>questi, che sono gli organi essenziali <lb/>della macchina, cio&egrave; della ruota delle <lb/>tacche, della chiave a scatto e delle <lb/>due codette, non si poteva con quel <lb/>disegno mostrare il gioco, rimanendo <lb/>essi organi riparati dietro le volute <lb/>della traversa, si pens&ograve; di rappresen&shy;<lb/>tar la macchina stessa con isguardo <lb/>un po'obliquo, e in modo che, ta&shy;<lb/>gliata la colonnetta o sostegno op&shy;<lb/>posto e parallelo al fusto della cro&shy;<lb/>ciera, la ruota pi&ugrave; alta e il gioco <lb/>delle codette su lei e sullo scatto, <lb/>rimanesse allo scoperto. </s>

<s>Il disegno <lb/>che accompagnava la descrizione del <lb/>Viviani, mandata come vedremo tra <lb/>poco in Olanda, era una copia di <lb/>questo secondo, che vedesi con assai <lb/>diligenza delineato in una Tavola ripiegata, perch&egrave; eccedente in lunghezza <lb/>e larghezza il foglio 50 del Tomo manoscritto sopra citato. </s>

<s>L'Alb&egrave;ri lo fece <lb/>incidere e imprimere nella II delle Tavole apposte al Tomo XIV della sua <lb/><emph type="italics"/>Edizione completa,<emph.end type="italics"/> e noi lo rappresentiamo ai nostri lettori nella figura 19. </s></p><p type="main">

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

<s>Chi attentamente fissa lo sguardo sopra questo disegno, e si mette a <lb/>considerar quelle ruote e que'pironi, quelle codette e quegli scatti, ci vede <lb/>la laboriosit&agrave; dell'ingegno, ma non ci sente l'ispirazione del genio. </s>

<s>Il Vi&shy;<lb/>viani ci fa saper, nel seguito delle parole da noi lasciate sopra interrotte, <lb/>che Vincenzio di Galileo conosceva troppo bene l'imperfezione di quel mac-<pb xlink:href="020/01/333.jpg" pagenum="314"/>chinamento e le difficolt&agrave; che si presentavano nel sollecito studio di miglio&shy;<lb/>rarlo. </s>

<s>Ma pure eran tutte quelle difficolt&agrave;, ch'ei si riprometteva di supe&shy;<lb/>rare, e ch'egli avrebbe forse superato di fatto, se non gli fosse sopraggiunta <lb/>in questo mezzo tempo la morte. </s></p><p type="main">

<s>In qualunque modo gli Orologi di Galileo rimanevano sterili progetti e <lb/><figure id="id.020.01.333.1.jpg" xlink:href="020/01/333/1.jpg"/></s></p><p type="caption">

<s>Figura 19.<lb/>infecondi di ogni utilit&agrave; per la vita <lb/>civile o domestica, e per la scienza. </s>

<s><lb/>Era preordinato che que'progetti <lb/>non dovessero aver la loro esecu&shy;<lb/>zione in Italia e Galileo stesso parve <lb/>che fosse di ci&ograve; presago quando, <lb/>nella sopra allegata Lettera al Rea&shy;<lb/>lio, scriveva che, sul fondamento <lb/>del suo pendolo, qualcuno di quegli <lb/>Olandesi, fra'quali erano uomini <lb/>squisitissimi e ingegnosissimi in fab&shy;<lb/>bricare Oriuoli e altre macchine am&shy;<lb/>mirande, avrebbe trovato conse&shy;<lb/>guenze pi&ugrave; sottili di quelle ch'ei <lb/>non si sarebbe potuto immaginare. </s></p><p type="main">

<s>Nell'anno 1658 infatti usciva al&shy;<lb/>l'Aja, dall'officina di Adriano Ulacq, <lb/>un libretto di poche pagine intitolato <lb/><emph type="italics"/>Horologium,<emph.end type="italics"/> in cui l'autore che era <lb/>Cristiano Huyghens descriveva il <lb/>modo di ridur con leggerissime tra&shy;<lb/>sformazioni i vecchi orologi a ruote, <lb/>ne'nuovi orologi regolati col pen&shy;<lb/>dolo. </s>

<s>Ismaele Boulliaud dava di Pa&shy;<lb/>rigi, il di 28 Febbraio 1659, nuova <lb/>della pubblicazione al principe Leo&shy;<lb/>poldo de'Medici, cos&igrave; scrivendo: <lb/>&ldquo; Sunt aliquot menses cum scripto <lb/>edito, additaque figura Horologium <lb/>a se inventum explicuit Christia&shy;<lb/>nus Hugenius et Hagae Comitis in <lb/>Batavia edidit &rdquo; (MSS. Cim. </s>

<s>T. XVI, <lb/>c. </s>

<s>134). A un tal annunzio entrato il Principe in gran curiosit&agrave; di sapere <lb/>qual relazione avesse questa nuova macchina con quella proposta gi&agrave; da Ga&shy;<lb/>lileo, mand&ograve; a richieder di quel libretto lo stesso Boulliaud, e avutolo e let&shy;<lb/>tolo, forse perch&egrave; era difficile averne un altro esemplare stampato, lo fece <lb/>trascrivere a ma<gap/> per Vincenzio Viviani, in un quinternetto che si trova <lb/>mserito da <gap/>arte 115-23 nel Tomo CXXXVIII de'Manoscritti appartenenti, <lb/>fra'Discepoli di Galileo, allo stesso Viviani. </s>

<s>Non &egrave; possibile che egli, testi-<pb xlink:href="020/01/334.jpg" pagenum="315"/>mone e compartecipe alle fatiche durate da Galileo e dal figlio di lui Vin&shy;<lb/>cenzio, per adattare il pendolo agli antichi orologi a ruote, non sia rimasto <lb/>di quella mirabile facilit&agrave; con cui l'Huyghens era giunto all'intento. </s>

<s>Lo <lb/>scappamento a serpe, che scivola ora da una parte ora dall'altra, d'infra <lb/>gli incastri della ruota a denti di sega, invece che dal vecchio bilanciere o <lb/>volante, veniva regolarmente governato dalle oscillazioni del pendolo. </s>

<s>Ecco <lb/>qui la somma di tutta l'invenzione, la quale pur si conosce che sarebbesi <lb/>potuta avere anco con pi&ugrave; semplicit&agrave;, applicando direttamente il pendolo al&shy;<lb/>l'asse dello scappamento a serpe, come poi fece il Sinclaro, senza l'aggiunta <lb/>del rocchetto portato in capo dallo stesso scappamento, e della ruota coro&shy;<lb/>nata, all'asse della quale si raccomanda la clavicola governatrice del metro <lb/>oscillatorio. </s></p><p type="main">

<s>Nonostante che l'Autore non avesse dimenticato di dire esser dovuto <lb/>a Galileo <emph type="italics"/>viro sagacissimo<emph.end type="italics"/> questo primo uso del pendolo, il Viviani suggeri <lb/>le seguenti parole, che il principe Leopoldo scrisse al Boulliaud, dopo aver <lb/>letto e veduto l'<emph type="italics"/>Horologium:<emph.end type="italics"/> &ldquo; Circa l'oriolo regolato dal pendolo certo &egrave; <lb/>che l'invenzione &egrave; quella, ma non si deve defraudar della gloria dovutagli <lb/>il nostro .... Galileo, che fin nel mille secento trentasei, se non erro, pro&shy;<lb/>pose questa s&igrave; utile invenzione alli Signori Stati di Olanda, e io ne ho ri&shy;<lb/>trovato, bench&egrave; un poco diverso circa la costituzione delle ruote, un modello <lb/>fatto gi&agrave; dal medesimo signor Galileo, e tre anni sono che qua si studia so&shy;<lb/>pra l'istesso soggetto. </s>

<s>Ne fu fatto uno da un virtuoso che spero riuscir&agrave; la <lb/>sua fabbrica ridotta al pulito di non minor facilit&agrave; e resistenza del ritrovato <lb/>dal signor Cristiano Hugenio &rdquo; (ivi, T. XXIII, c. </s>

<s>201). </s></p><p type="main">

<s>Ricevuta questa lettera, dalla quale traspariva l'accusa data all'Huy&shy;<lb/>ghens d'aver defraudato ne'suoi meriti Galileo, il Boulliaud, dopo pochi <lb/>giorni, il d&igrave; 2 di Maggio 1659, risponde: &ldquo; De pendulo ad regendam Horo&shy;<lb/>logii rotarum conversionem a summo viro Galileo olim reperto, V. Cel. </s>

<s>Christ. </s>

<s><lb/>Hugenius mihi monendus est &rdquo; (ivi, T. VI, c. </s>

<s>152). Ma lo zelo venne cos&igrave; <lb/>nell'ardente animo rattemperato da un'altra lettera, che venti giorni dopo <lb/>scrisse a Parigi lo stesso Principe Leopoldo: &ldquo; Quand'io le accennai che <lb/>l'invenzione di adattare il pendolo era stata trovata molto tempo fa ancora <lb/>dal nostro signor Galileo, non intesi dire che il signor Cristiano Hugenio <lb/>non la potessi avere anch'egli inventata da s&egrave; medesimo .... Si pu&ograve; ricor&shy;<lb/>dare V. S. che io le accennai che altro Virtuoso tre anni sono ne invent&ograve; <lb/>uno simile, ma per sua disgrazia non fu applicato l'animo al valersi della <lb/>sua invenzione &rdquo; (ivi, T. XXIII, c. </s>

<s>14). </s></p><p type="main">

<s>Nonostante il Boulliaud non manc&ograve; di dar parte di tutto quel che gli <lb/>era venuto scritto di Toscana all'Hugenio, il quale rispose all'amico a Pa&shy;<lb/>rigi parole di accoramento, per avere il Principe conceputa cos&igrave; falsa opi&shy;<lb/>nione di lui, nella quale parevagli di vedersi rassomigliato a un'altro Simon <lb/>Mario. </s>

<s>&ldquo; Mais enfin que faut-il faire pour oter &agrave; ce Prince l'opinion, qu'il <lb/>semble avoir con&ccedil;ue de moi, comme si je m'attribuois l'invention d'autrui, <lb/>et que je ressemblasse &agrave; ce Simon Marius? </s>

<s>&rdquo; (Fabbroni, Lett. </s>

<s>I, 226). N&egrave; <pb xlink:href="020/01/335.jpg" pagenum="316"/>questo accoramento dopo parecchi mesi gli era ancora passato, e anzi lo <lb/>coceva di pi&ugrave; per non veder risposta dal principe Leopoldo, a cui aveva gi&agrave; <lb/>dedicato il suo Sistema Saturnio. </s>

<s>Di ci&ograve; faceva amichevole sfogo in Parigi <lb/>con Cosimo Brunetti, il quale cos&igrave; rappresentava per lettera al Principe <lb/>stesso la turbazion dell'animo, i timori, bench&egrave; incoscienti di aver mancato, <lb/>e i propositi dell'emenda fatti dal gentiluomo olandese: &ldquo; Ma l'Hugens io <lb/>lo trovai in somma perplessit&agrave;, non sapendo egli per qual ragione non re&shy;<lb/>stava onorato di risposta alla Lettera del suo Sistema dedicato e mandato a <lb/>V. A. S. la quale ei temeva che potesse stimarsi offesa per due principali <lb/>cagioni, nella persona di Galileo. </s>

<s>La prima &egrave; ch'ei potesse aver veduto una <lb/>Lettera che il Galileo scrisse del 1636 agli Stati d'Olanda circa l'invenzione <lb/>del pendolo, con che ei sperava di poter trovar le longitudini, sopra di che <lb/>egli esagger&ograve; grandemente asserendomi di non aver mai veduto tal lettera. </s>

<s><lb/>L'altra &egrave; che, per quel che riguarda i Telescopii, ei non abbia forse parlato <lb/>del Galileo con gli encomii dovutili, e in questo ei vorrebbe che il suo Sistema <lb/>non fosse ancora stampato, per poter parlar con termini che testificassero <lb/>davvantaggio quanto egli sia parziale di s&igrave; grand'uomo &rdquo; (ivi, T. XVII, c. </s>

<s>30). </s></p><p type="main">

<s>Dietro questa lettera del Brunetti il Principe si mosse a scriver parole <lb/>che acquietarono l'animo dell'Hugenio, il quale era intanto rimasto sodi&shy;<lb/>sfatto di un altro suo desiderio. </s>

<s>Quel desiderio veniva cos&igrave; espresso nel&shy;<lb/>l'<emph type="italics"/>Estratto<emph.end type="italics"/> di lettera francese pubblicato dal Fabbroni nel luogo sopra citato: <lb/>&ldquo; Si j'avois l'honneur d'&ecirc;tre plus connu de Son Altesse, et essez de har&shy;<lb/>diesse, je la r&eacute;qu&eacute;rerois pour en avoir une figure, pour voir en quoi elle <lb/>diff&eacute;re de la mienne &rdquo;. </s>

<s>E perch&egrave; questo Estratto di lettera dell'Huyghens <lb/>si fece dal Boulliaud a quest'unico fine d'inviarlo al Principe Leopoldo, il <lb/>Principe, lieto di poter sodisfare al desiderio dell'Hugenio, fece preparare <lb/>il disegno, e il d&igrave; 21 Agosto 1659 lo faceva spedire al Bullialdo, accompa&shy;<lb/>gnandolo con una sua lettera, nella quale cos&igrave; scriveva: &ldquo; Sar&agrave; dunque an&shy;<lb/>nesso a questa il disegno del principio dell'oriuolo regolato dal pendolo, che <lb/>invent&ograve; il Nostro per sempre ammirabile signor Galileo. </s>

<s>Lo invio delineato <lb/>con quella rozzezza, con la quale &egrave; fabbricato il modello del medesimo, che <lb/>nella mia camera ora mi ritrovo. </s>

<s>Potr&agrave; pertanto V. S. mandarlo al Virtuo&shy;<lb/>sissimo signor Cristiano Hugenio che desiderava di vederlo, e forse di que&shy;<lb/>st'altra settimana invier&ograve; a lei la Storia, dir&ograve; cos&igrave; del ritrovamento del pen&shy;<lb/>dolo, che spero dovr&agrave; riuscir curiosa a V. S.... Far&ograve; fare ancora un disegno <lb/>di come si &egrave; accomodato da noi il pendolo a'nostri Orioli, ed in particolare <lb/>ad uno assai grande che mostra le ore, e suona nella piazza del nostro Pa&shy;<lb/>lazzo dove abitiamo e glielo invier&ograve; &rdquo; (ivi T. XXIII, c. </s>

<s>16). </s></p><p type="main">

<s>Il disegno accompagnato da questa Lettera diretta al Bullialdo, &egrave; quello <lb/>stesso che &egrave; stato da noi fedelissimamente nella figura XIX ritratto, e la <lb/>Storia del ritrovamento del pendolo, di che qui pure si fa parola, &egrave; senza <lb/>dubbio quella scritta dal Viviani in forma di Lettera indirizzata allo stesso <lb/>Principe Leopoldo, sottoscritta nel d&igrave; 20 Agosto 1659 e da cui estraemmo, <lb/>nel paragrafo precedente, i documenti alla nostra narrazione. </s></p><pb xlink:href="020/01/336.jpg" pagenum="317"/><p type="main">

<s>Come queste cose son certe per&ograve;, altrettanto incerto a definirsi &egrave; qual <lb/>fosse e come fosse rappresentato l'adattamento del pendolo all'Orologio, che <lb/>mostrava l'ore o suonava sulla piazza de'Pitti. </s>

<s>In tale incertezza noi pre&shy;<lb/>ghiamo i nostri Lettori a voler rivolger la loro attenzione sopra il disegno <lb/><figure id="id.020.01.336.1.jpg" xlink:href="020/01/336/1.jpg"/></s></p><p type="caption">

<s>Figura 20.<lb/>abbozzato e informe che noi sotto i <lb/>loro occhi fedelmente rappresentia&shy;<lb/>mo nella figura 20. Un tal disegno <lb/>a penna, con altri informi pi&ugrave; che <lb/>mai da'quali &egrave; preceduto, vedesi ab&shy;<lb/>bozzato a carte 57 di quel Tomo IV <lb/>de'citati Manoscritti, in cui son di&shy;<lb/>segnati gli altri adattamenti secondo <lb/>il concetto di Galileo. </s>

<s>Se all'estre&shy;<lb/>mit&agrave; dell'asse orizzontale, a cui &egrave; <lb/>raccomandato il pendolo, son da <lb/>mano sinistra veramente alette quel&shy;<lb/>le, che noi vediamo in immaginazio&shy;<lb/>ne, e se queste alette giocano, come <lb/>lo scappamento a serpe su quell'ab&shy;<lb/>bozzo di ruota, che pur la nostra <lb/>immaginazione ci fa credere aver le <lb/>tacche disposte a denti di sega; si <lb/>dovrebbe dire che fra tutti i modi di <lb/>adattare il pendolo agli orologi a <lb/>ruote &egrave; questo quello de'nostri Fio&shy;<lb/>rentini, che pi&ugrave; si rassomigli a ci&ograve; <lb/>che fu ideato e mandato ad effetto <lb/>in Olanda. </s></p><p type="main">

<s>Se fosse vero insomma quel <lb/>che noi ci immaginiam di vedere in <lb/>questo schizzo a penna, sarebbe ci&ograve; <lb/>di gran conseguenza per la nostra <lb/>Storia. </s>

<s>Ma perch&egrave; noi non ne ab&shy;<lb/>biam nessuna certezza contentiamoci di assicurare i Lettori di un altro <lb/>fatto, di non forse minore importanza, il qual si &egrave; che la Storia del ritrova&shy;<lb/>mento del pendolo e il disegno dell'Orologio del Palazzo Pitti, promessi di <lb/>mandar la settimana seguente per mezzo del Bullialdo all'Hugenio, furono <lb/>veramente mandati, e d'averli ricevuti e fatti recapitare dava lo stesso Bul&shy;<lb/>lialdo sicurt&agrave; al Principe cos&igrave; scrivendo: &ldquo; Ad Christianum Hugenium Zu&shy;<lb/>lichemium utriusque Horologii pendulo directi, quas a Celsitudine Tua ac&shy;<lb/>cepi, picturas misi; et si mihi vacasset historiam inventi a Galilaeo penduli <lb/>ed adnotatas primum ab ipso acqualitatis motus. </s>

<s>transcriptam adiunxissem &rdquo; <lb/>(Fabbroni, ivi, pag. </s>

<s>199). </s></p><p type="main">

<s>Non si pu&ograve; dubitar che il Boulliaud non mantenesse le sue promesse <pb xlink:href="020/01/337.jpg" pagenum="318"/>e che venutogli tempo e ozio opportuno non si fosse messo veramente a <lb/>trascriver la storia del pendolo per inviarla, secondo il geloso ufficio affida&shy;<lb/>togli, in Olanda all'Hugenio. </s>

<s>Qual fosse poi il giudizio che dette di quella <lb/>storia e di quei disegni lo stesso Hugenio, lo vedremo quando nel 1673 tor&shy;<lb/>ner&agrave; pubblicamente a trattar di questo argomento dell'Orologio. </s></p><p type="main">

<s>Intanto giacch&egrave; abbiam sentito dire, ne'documenti sopra citati, dal prin&shy;<lb/>cipe Leopoldo che tre anni prima del 1659 in Toscana si pensava gi&agrave; ad ap&shy;<lb/>plicare il pendolo alle misure dell'ore, da un Virtuoso, che non seppe per sua <lb/>disgrazia valersi di un'invenzione, la quale ridotta a pulito avrebbe dato la <lb/>fabbrica di un Orologio pi&ugrave; facile e pi&ugrave; consistente di quella stessa del signor <lb/>Cristiano Hugenio; crediamo esser di grande importanza per la nostra Sto&shy;<lb/>ria l'investigar chi fosse quel Virtuoso, e come fosse costruito quell'Orolo&shy;<lb/>gio Toscano, inventato in quello stesso anno 1656, in cui s'invent&ograve; l'olan&shy;<lb/>dese, conforme alle parole con cui l'Hugenio incominci&ograve; la sua Descrizione: <lb/>&ldquo; Temporis dimetiendi rationem novam quam exeunte anno 1656 escogita&shy;<lb/>vimus.... &rdquo; (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>5). Ma pure a far ci&ograve; vogliamo <lb/>differire alquanto per dire altre cose, dalle quali forse verr&agrave; a diffondersi <lb/>un po'di luce su quella via, che ci si para innanzi chiusa di nebbia. </s></p><p type="main">

<s>Diciamo dunque che sebben l'Huyghens dal 1658 al 1673 non avesse <lb/>nulla d'importanza pubblicato in proposito di perfezionare gli Orologi a pen&shy;<lb/>dolo, pure egli aveva altissime e recondite cose speculato in questi quindici <lb/>anni. </s>

<s>A noi qui conviene far di quelle speculazioni soggetto alla nostra Sto&shy;<lb/>ria, e vi ci vogliamo apparecchiare accennando a una curiosit&agrave;, a cui pre&shy;<lb/>sero parte gli Accademici nostri di Firenze. </s></p><p type="main">

<s>Occorrendo all'Huyghens, sui principii dell'anno 1665, di fare osser&shy;<lb/>vazioni comparative fra due Orologi a pendolo, gli teneva a tal intento appesi <lb/>a un medesimo bastone nella sua stanza, quando scopr&igrave; in essi un effetto <lb/><emph type="italics"/>mirum et a nemine umquam vel cogitandum.<emph.end type="italics"/> L'effetto consisteva in una <lb/>certa segreta simpatia, nata fra'due pendoli per modo, che il vibrar dell'uno <lb/>non differiva dal vibrar dell'altro: che se anzi si turbava ad arte il loro <lb/>metro, tornavano dopo una mezz'ora a corrispondersi esattamente, come <lb/>prima. </s>

<s>La storia diligente e minuta di cos&igrave; fatte nuove e curiose osserva&shy;<lb/>zioni, fu divulgata dall'Autore stesso con una Lettera data dall'Aja il d&igrave; <lb/>25 di Febbraio 1665 (ivi, pag. </s>

<s>213, 14), che pervenuta a notizia del prin&shy;<lb/>cipe Leopoldo, egli stesso faceva motto del contenuto ai due principali sog&shy;<lb/>getti della sua Accademia, al Borelli e al Viviani. </s>

<s>Il Borelli di Pisa, il d&igrave; <lb/>13 Aprile 1665, rispondeva al Principe di non aver bene inteso &ldquo; perch&egrave; <lb/>non so, egli dice, se in quelle vibrazioni vi concorra suono unisono, oppure <lb/>sono muti. </s>

<s>Circa il suono gi&agrave; &egrave; stato avvertito dal Galileo, e resone la vera <lb/>ragione ne'suoi ultimi Dialoghi delle cose che si spezzano. </s>

<s>Ma quando non <lb/>vi sia suono, non ho ancora potuto vedere che due pendoli egualmente lun&shy;<lb/>ghi, discostando l'uno dall'altro un braccio, le vibrazioni dell'uno si comu&shy;<lb/>nichino all'altro a segno tale, che gli facciano fare balzi uguali; tuttavia ci <lb/>penser&ograve; meglio &rdquo; (MSS. Cim. </s>

<s>T. XVIII, c. </s>

<s>158). Poi, dal Principe fu avvi-<pb xlink:href="020/01/338.jpg" pagenum="319"/>sato di una condizione particolare, in cui si trovavano i due pendoli sim&shy;<lb/>patici, ed era quella di essere appesi ambedue gli orologi a un medesimo <lb/>bastone. </s>

<s>Allora il Borelli, due giorni dopo la precedente, tornando a scri&shy;<lb/>vere, soggiunge: &ldquo; Circa i pendoli mi par molto vario il caso dell'essere <lb/>attaccati al medesimo bastone all'esser rinchiusi in due oriuoli, e faccia <lb/>Dio che finalmente il detto bastone non divenga una bacchetta assai fles&shy;<lb/>sibile e mobile, se pur &egrave; vero che questo basta a produr quel tale effetto &rdquo; <lb/>(ivi, c. </s>

<s>162). </s></p><p type="main">

<s>In conclusione il Borelli non seppe n&egrave; osservare il fatto n&egrave;, suppostolo <lb/>vero, intravedere alcuna fisica ragione di quella strana simpatia. </s>

<s>L'Huy&shy;<lb/>ghens, nella Lettera sopra citata, aveva accennato alle agitazioni prodotte <lb/>nell'aria dai moti de'pendoli, ma poi, sulla fine della Prima Parte dell'Oro&shy;<lb/>logio Oscillatorio, <emph type="italics"/>instituto diligenti examine<emph.end type="italics"/> credette d'affermare il vero <lb/>dicendo: &ldquo; a motu tigni ipsius, licet haudquaquam sensibili causam pe&shy;<lb/>tendam esse &rdquo; (Op. </s>

<s>Var., pag. </s>

<s>49). </s></p><p type="main">

<s>Il Viviani per verit&agrave; non sappiamo che decidesse nulla in proposito <lb/>standosene contento a descrivere cos&igrave; i fatti osservati, i quali par che ten&shy;<lb/>dano a confermar che il simpatico mistero consiste tutto nelle agitazioni <lb/>dell'aria comunicantisi da un pendolo all'altro: &ldquo; Di due pendoli uguali di <lb/>filo dal centro delle palle, appesi ad un medesimo sostegno e posti in quiete <lb/>nel perpendicolo, se si rimuover&agrave; uno di loro e si lascer&agrave; vibrare, si vedr&agrave; <lb/>che l'altro subito comincer&agrave; a muoversi ed a poco a poco va continuando, <lb/>fino ad un particolar segno, a crescer li archi delle sue vibrazioni e poi <lb/>decrescerli, ed esser sempre concorde con l'altro nell'andare e tornare. </s>

<s>E <lb/>se quello, a cui si d&agrave; l'andata, sar&agrave; il pi&ugrave; grave, muover&agrave; pi&ugrave; facilmente e <lb/>per maggiori archi il minore, che non farebbe il minore il maggiore &rdquo; (MSS. <lb/>Cim. </s>

<s>T. X, c. </s>

<s>47). </s></p><p type="main">

<s>Ma &egrave; tempo che ritorniamo alla Storia dell'Orologio. </s></p><p type="main">

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

<s>Bench&egrave; l'Huyghens, infino dal d&igrave; 16 Giugno 1657, avesse ottenuto dagli <lb/>Stati Uniti di Olanda il privilegio, o come oggid&igrave; si direbbe il brevetto d'in&shy;<lb/>venzione; bench&egrave; il libretto stampato da Adriano Ulacq nel 1658 fosse di&shy;<lb/>vulgato per tutta l'Europa, e per tutta l'Europa si fossero veduti, bench&egrave; <lb/>rari in numero, orologi fabbricati su quel disegno; nonostante Giorgio Si&shy;<lb/>nelaro, professore nell'Universit&agrave; di Glascow, pubblicando nel 1699 in Rot&shy;<lb/>terdam la sua <emph type="italics"/>Ars nova et Magna,<emph.end type="italics"/> vi poneva in Appendice, con altri, un <lb/>Dialogo intitolato <emph type="italics"/>De Cronoscopio;<emph.end type="italics"/> strumento, che egli d&agrave; come cosa di re&shy;<lb/>cente invenzione, e da lui stesso <emph type="italics"/>nova methodo excogitata.<emph.end type="italics"/> Gli interlocu&shy;<lb/>tori son Francesco e Alessandro, sotto la persona del quale si nasconde <lb/>l'Autore. </s>

<s>Incomincia Alessandro a magnificare l'eccellenza di questo <emph type="italics"/>quod<emph.end type="italics"/><pb xlink:href="020/01/339.jpg" pagenum="320"/><emph type="italics"/>infinitis parasangis, omnibus praecellit Chronoscopiis in hunc usque diem <lb/>excogitatis,<emph.end type="italics"/> per modo che fa venir voglia a Francesco di veder questa nuova <lb/>maraviglia, di che &egrave; appagato da Alessandro stesso, il quale avendo intro&shy;<lb/>dotto l'amico nel suo Museo, &ldquo; vides iam, mi Francisce, gli dice, duo illa <lb/>eadem forma Automata, quod libet tres palmos habere, quarum prima <emph type="italics"/>hora&shy;<lb/>ria<emph.end type="italics"/> horis duodecim circumlata, tempus diurnum et nocturnum examussim <lb/>definit. </s>

<s>Secunda minutorum, quae horis singulis integrum circulum descri&shy;<lb/>bens, minuita prima quam exactissime determinat. </s>

<s>Tertia <emph type="italics"/>secundum,<emph.end type="italics"/> quae <lb/>singulis horis sexagies, singulisque <emph type="italics"/>minutis<emph.end type="italics"/> semel circumlata, <emph type="italics"/>secunda hora&shy;<lb/>ria<emph.end type="italics"/> ad amussim demonstrat. </s>

<s>Quoad pendulum attinet, scito id globulum <lb/>plumbeum esse acto unciarum, tenuissimo filo aeneo, triginta octo digitis <lb/>longo, cum parte decima, suspensum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> Mirum! pilo equino vix est crassius. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> Ob id facilius et liberius transcurrit globulus. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> Sed demiror valde quomodo huc illuc agitatur. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> Videsne <emph type="italics"/>claviculam centralem<emph.end type="italics"/> extremo inquieti (<emph type="italics"/>scappamento<emph.end type="italics"/>) <lb/>paulo altiorem? </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> Imo. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> Eius ope solummodo suspenditur globulus, ac super eo tam&shy;<lb/>quam centro transcurrit. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> Nullatenus ergo penduli gravitate <emph type="italics"/>inquietum<emph.end type="italics"/> gravatur? </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> Nullatenus, sed eius extremo <emph type="italics"/>tibiam aeneam<emph.end type="italics"/> cum <emph type="italics"/>pede<emph.end type="italics"/> de&shy;<lb/>scendentem vides. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; France.<emph.end type="italics"/> Clare. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> Ac pedem parvulo feraminulo perforatum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> Imo. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> Per id transit funiculus, cuius vibrationes eius agitatione perse&shy;<lb/>verant. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> At pars superior videtur testudinis chorda. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> Sic est. </s>

<s>Ad haec, praeter rotulas, quibus indices circummoven&shy;<lb/>tur, tres alias vides, quarum prima et secunda verticales sunt: tertia hori&shy;<lb/>zontalis inaequalibus numero denticulis, quibus huc illuc <emph type="italics"/>inquietum<emph.end type="italics"/> agita&shy;<lb/>tur. </s>

<s>Potissima iam huius Horologii perfectio est quod vibratio quaelibet sit <lb/><emph type="italics"/>secundum horarium,<emph.end type="italics"/> nam singulis horis ter millies et sexcenties transcur&shy;<lb/>rit examussim Pendulum &rdquo; (Roterodami, 1669, pag. </s>

<s>600, 1). </s></p><p type="main">

<s>Si raccoglie di qui come la sostituzione dell'<emph type="italics"/>antico tempo<emph.end type="italics"/> al nuovo pen&shy;<lb/>dolo, che tanto dette a pensare a Galileo e al figliuolo di lui Vincenzio, <lb/>occorse con grandissima facilit&agrave; al Sinclaro, a cui, per avere il vecchio Oro&shy;<lb/>logio trasformato nel nuovo, bast&ograve; mantenere lo scappamento a serpe, disporlo <lb/>orizzontale, e appendere all'estremit&agrave; di lui un corpo oscillante. </s>

<s>Si direbbe <lb/>che l'Orologio Scozzese, &egrave; pi&ugrave; semplice di quello Olandese, ma non &egrave; che <lb/>anco all'Huyghens non fosse sovvenuta in mente quella facilit&agrave; di costru&shy;<lb/>zione; &egrave; che voleva non facesse il pendolo troppo ampie le sue vibrazioni, <lb/>per cui non l'applic&ograve; immediatamente allo scappamento, che era la pi&ugrave; fa-<pb xlink:href="020/01/340.jpg" pagenum="321"/>cile via seguita dal Sinclaro, ma l'applic&ograve; piuttosto all'asse della ruota co&shy;<lb/>ronata, mossa dal rocchetto portato in capo dallo stesso scappamento. </s></p><p type="main">

<s>Comunque sia, fin qui il solitario professor di Glascovia non ci ha an&shy;<lb/>nunziato nulla di nuovo. </s>

<s>Per&ograve;, aggiunta a quella sua descrizione del Cro&shy;<lb/>nosccpio, ha una cosa, della quale forse &egrave; vero quel che egli dice <emph type="italics"/>nemini <lb/>adhuc in mentem venisse,<emph.end type="italics"/> ed &egrave; l'applicazione del pendolo orizzontale o del <lb/>pendolo conico agli Orologi. </s>

<s>Abbiamo detto che forse &egrave; vero, ritrovando che <lb/>l'Huyghens esordisce cos&igrave; la V Parte del suo <emph type="italics"/>Oscillatorio:<emph.end type="italics"/> &ldquo; Est et aliud <lb/>oscillatorii motus genus, praeter id quod hactenus pertractavimus. </s>

<s>Eiusmodi <lb/>nempe quo per circuli ambitum, pendulum pondus circumfertur. </s>

<s>Unde aliud <lb/>quoque Horologii commentum deduximus, eodem fere tempore, quo illud <lb/>prius &rdquo; (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>185). </s></p><p type="main">

<s>Non sarebbe dunque vero quel che credeva il Sinclaro che cio&egrave; cos&igrave; <lb/>fatta maniera di pendoli non fosse ancora nel 1669 venuta in mente a nes&shy;<lb/>suno. </s>

<s>L'Huyghens asserisce che eragli venuta anzi in mente tredici anni <lb/>prima. </s>

<s>Ma perch&egrave; non si trova che abbia pubblicameute palesato questo suo <lb/>pensiero prima del 1673, resta, per giustizia il diritto di quattro anni di <lb/>precedenza al Sinclaro, che per verit&agrave; non speriment&ograve; n&egrave; specul&ograve; su quel <lb/>pendolo conico molto pi&ugrave; oltre di quel che v'avessero esperimentato i no&shy;<lb/>stri Accademici del Cimento. </s></p><p type="main">

<s>In qualunque modo, fu quel pendolo, alle mani del grande Olandese, <lb/>il fecondo seme che fruttific&ograve; alla Meccanica la teoria delle forze centrifu&shy;<lb/>ghe, e alla Geometria quella delle Evolute. </s>

<s>A noi di tante alte e peregrine <lb/>speculazioni non occorre entrare in discorso, se non di quelle sole che tro&shy;<lb/>varono un'applicazione immediata alla fabbrica del nuovo Orologio. </s></p><p type="main">

<s>Vedemmo, infino da'suoi primi principii, l'Huyghens esser sollecito di <lb/>restringere pi&ugrave; che fosse possibile al pendolo l'arco delle vibrazioni. </s>

<s>Si ca&shy;<lb/>pisce bene come una tale sollecitudine dovesse avere origine dalla ferma <lb/>persuasione che non fosse altrimenti vero quel perfetto isocronismo preteso <lb/>dal Galileo. </s>

<s>Certo non avr&agrave; avuto il remoto Olandese notizia di quelle nu&shy;<lb/>merosissime esperienze fatte gi&agrave; nel secondo periodo della sperimentale <lb/>Accademia Medicea, nelle sale del Palazzo Pitti (Targ. </s>

<s>Aggrandim. </s>

<s>T. II, <lb/>pag. </s>

<s>142-62), ma, a persuadersi che le vibrazioni, quanto sono pi&ugrave; ampie, <lb/>tanto pi&ugrave; sono diuturne, gli bast&ograve; la seguente facile esperienza: &ldquo; Si enim <lb/>fila accipiantur eiusdem longitudinis duo, paribusque in parte ima ponderi&shy;<lb/>bus religatis, utrumque scorsum suspendatur, tumque alterum eorum pro&shy;<lb/>cul a linea perpendiculari, alterum parumper duntaxat extrahatur, simulque <lb/>e manu dimittantur, non diu utrumque simul in partes easdem ferri vide&shy;<lb/>bitur, sed praevertet illud, cuius exiliores erunt recursus &rdquo; (Op. </s>

<s>Var. </s>

<s>ibi, <lb/>pag. </s>

<s>38). La differenza &egrave; cos&igrave; notabile, soggiunge l'Autore, che non si pu&ograve; <lb/>attribuire alla resistenza dell'aria. </s>

<s>Galileo insomma, era, cos&igrave; dalla geome&shy;<lb/>tria come dall'esperienza, ingannato in credere che la curva tautocrona fosse <lb/>il cerchio. </s>

<s>Qual'&egrave; dunque questa curva? </s>

<s>si domand&ograve; l'Huyghens, e la Geo&shy;<lb/>metria gli rispose essere la cicloide. </s>

<s>Se si potesse dunque far vibrare il pen-<pb xlink:href="020/01/341.jpg" pagenum="322"/>dolo in archi di cicloide, e allora sarebbe tolta ai costruttori degli Orologi <lb/>ogni sollecitudine di far s&igrave; che quelle stesse vibrazioni vadano pi&ugrave; ristrette <lb/>che sia possibile, e non sarebbe negli usi nautici alterata la regolarit&agrave; del <lb/>moto da'sussulti della nave, perch&egrave;, divarichi pure il pendolo quanto si <lb/>vuole, si manterranno in ogni modo isocrone le sue corse e ricorse. </s></p><p type="main">

<s>Come segno ultimo perci&ograve; a cui tendere, nel perfezionamento degli Oro&shy;<lb/>logi, specialmente nautici, all'insigne inventore paravasi innanzi la Cicloide. </s>

<s><lb/>Ma in che modo farne l'applicazione? </s>

<s>La difficolt&agrave; era tale che a superarla <lb/>si ricercava l'esplorazione e la scoperta di un nuovo campo geometrico. </s>

<s>E <lb/>l'Huyghens attese veramente a questa esplorazione e fece questa scoperta, <lb/><figure id="id.020.01.341.1.jpg" xlink:href="020/01/341/1.jpg"/></s></p><p type="caption">

<s>Figura 21.<lb/>venendogli giusto l'occasione di farla da quel pen&shy;<lb/>dolo conico, di che si parlava pi&ugrave; sopra. </s></p><p type="main">

<s>Udimmo come infino dal 1656 avesse pensato <lb/>d'applicare all'Orologio questa nuova maniera di <lb/>pendolo, e soggiunge anzi nel luogo citato che ne <lb/>furon veramente costruiti alquanti di cos&igrave; fatti Oro&shy;<lb/>logi con felice successo. </s>

<s>Pure l'applicazione del <lb/>pendolo conico presentava qualche difficolt&agrave; mag&shy;<lb/>giore di quella del pendolo piano. </s>

<s>Il filo non si <lb/>poteva applicare al prolungamento dell'asse della <lb/>ruota regolatrice, ma conveniva sospenderlo a un <lb/>braccio infisso in quel medesimo asse. </s>

<s>Conveniva <lb/>inoltre di dare allo stesso filo un'appoggiatura, che <lb/>gli facesse insieme da falsaredine. </s>

<s>Cos&igrave; veramente <lb/>ide&ograve; ed esegu&igrave; il sagace Inventore: &ldquo; Axis DH <lb/>(fig. </s>

<s>21) ad horizontem erectus intelligendus est, <lb/>ac super polis duobus mobilis. </s>

<s>Huic ad A affixa <lb/>est lamina, latitudine aliqua praedita, curvamque <lb/>secundum lineam AB .... Pondus illi affixum F. </s>

<s><lb/>Dum axis DH in sese vertitur, filum BGF in rectam <lb/>lineam extensum, sphaerulam F una circumducit, ita ut circulos horizonti <lb/>parallelos percurrat qui maiores minoresve erunt, prout maiori aut minori <lb/>vi axis DH ab rotis Horologii in tympanidium K agentibus, incitabitur &rdquo; <lb/>(ibi, pag. </s>

<s>186). </s></p><p type="main">

<s>Lo studio della forza che fa descrivere alla palla tanto pi&ugrave; ampii cer&shy;<lb/>chi, quanto la vertigine dell'asse &egrave; pi&ugrave; concitata, fece s&igrave; che l'Huyghens <lb/>riuscisse a formulare i XIII Teoremi <emph type="italics"/>De vi centrifuga,<emph.end type="italics"/> e dalla lamina AB, <lb/>sulla quale s'appoggia il filo, scatur&igrave; la teoria delle Evolute. </s>

<s>&Egrave; facile infatti <lb/>vedere che la figura del conoide, sulla superficie del quale s'aggira sem&shy;<lb/>pre nell'alzarsi e nell'abbassarsi la palla, dipende dalla curvatura di quella <lb/>lamina. </s>

<s>Or ecco il primo problema, che occorse di risolvere in questo pro&shy;<lb/>posito al gran Geometra olandese: Perch&egrave; sempre i tempi de'circuiti si <lb/>mantengano uguali, di che figura dee essere il conoide, sulla superficie del <lb/>quale, ne'suoi giri or pi&ugrave; alti or pi&ugrave; bassi si mantiene la palla? </s>

<s>O altrimenti: <pb xlink:href="020/01/342.jpg" pagenum="323"/>in qual genere di curva dee inflettersi la lamina AB perch&egrave; la palla, disten&shy;<lb/>dendosi il filo, descriva l'apotema del conoide isocrono? </s>

<s>E trov&ograve; che quella <lb/>lamina dovea esser piegata in figura di parabola, che &egrave; l'evoluta da cui si <lb/>descrive per evoluzione la curva genitrice di quello stesso conoide. </s></p><p type="main">

<s>Avviate per questa nuova luminosa via le idee, tutta la difficolt&agrave; del&shy;<lb/>l'applicare il pendolo cicloidale consisteva in trovare qual dovesse essere <lb/>l'evoluta, dall'evoluzione della quale si descrivesse una Cicloide. </s>

<s>Suppon&shy;<lb/>gasi infatti che sia AB (fig. </s>

<s>22) questa evoluta configurata in lamina me&shy;<lb/>tallica e che sia alla sommit&agrave; di lei appeso il filo pendulo AC. </s>

<s>Nel salire <lb/>da C verso D avvolgendosi alla lamina, e nello scendere da D verso C svol&shy;<lb/>gendosi dalla medesima, si descriver&agrave; dall'estremit&agrave; di quel filo una mezza <lb/><figure id="id.020.01.342.1.jpg" xlink:href="020/01/342/1.jpg"/></s></p><p type="caption">

<s>Figura 22.<lb/>Cicloide o un mezzo arco di Cicloide. </s>

<s>Che se si <lb/>assetti un'altra lamina uguale, dall'altra parte AE, <lb/>il filo stesso col peso, ricaduto da D, nel risalire <lb/>in F descriver&agrave; un altro arco di Cicloide, cosicch&egrave; <lb/>tutta la curva DCF descritta dal pendolo sar&agrave; ci&shy;<lb/>cloidale, e perci&ograve; isocrona da qualunque punto ri&shy;<lb/>salga il peso C e da qualunque altro punto di&shy;<lb/>scenda. </s>

<s>Or la Geometria rivel&ograve; all'Huyghens che le <lb/>due lamine AB, AE, perch&egrave; riuscissero a dare il <lb/>desiderato isocronismo, dovevano essere configu&shy;<lb/>rate in semicicloide, conforme al Teorema da lui <lb/>dimostrato, nella proposiz. </s>

<s>VI della Parte III del&shy;<lb/>l'Orologio Oscillatorio, che cio&egrave; la curva descritta per evoluzione da un'emi&shy;<lb/>cicloide &egrave; un'altra emicicloide uguale e simile all'evoluta. </s></p><p type="main">

<s>Tale &egrave; il macchinamento che l'Huyghens venne applicando, colla ferma <lb/>speranza di aver dato cos&igrave; la massima perfezione all'Orologio. </s>

<s>Una verga <lb/>metallica raccomandata alla solida armatura della macchina sostiene le due <lb/>laminette piegate in figura di semicicloide, in mezzo alle quali pende il filo <lb/>flessibile, a cui &egrave; raccomandata la verghetta metallica del pendolo. </s>

<s>Questa <lb/>stessa verghetta passa attraverso al foro della clavicola fissata all'estremit&agrave; <lb/>dello scappamento a serpe, che gioca con le sue alette in posizione oriz&shy;<lb/>zontale, fra le tacche della ruota a denti di sega, precisamente come nel <lb/>Cronoscopio descrittoci dal Sinclaro. </s></p><p type="main">

<s>La descrizione di questo nuovo Misuratore del tempo, insiem coi Teo&shy;<lb/>remi concernenti la caduta de'gravi per gli archi di Cicloide, e le Evolute, <lb/>e i Centri di oscillazione, e le Forze centrifughe furono pubblicati nel 1673 <lb/>in Parigi, in quell'Opera immortale che s'intitola <emph type="italics"/>Orologium oscillatorium.<emph.end type="italics"/><lb/>E ora &egrave; questa stessa pubblicazione, che ravvia la nostra Storia in Italia. </s></p><pb xlink:href="020/01/343.jpg" pagenum="324"/><p type="main">

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

<s>Quando prima pubblicatosi all'Aja l'<emph type="italics"/>Horologium<emph.end type="italics"/> il principe Leopoldo <lb/>e il Viviani, coll'intenzione di rivendicare a favor di Galileo la priorit&agrave; della <lb/>scoperta, inviarono i due disegni e la Storia del ritrovamento del pendolo, <lb/>perch&egrave;, per mezzo del Boulliaud, capitassero in Olanda; l'Huyghens e nel <lb/>commercio epistolare co'Nostri e in pubblico si tacque, aspettando ad aprir <lb/>l'animo suo a pi&ugrave; propizia occasione. </s>

<s>E l'occasione venne giusto in sul&shy;<lb/>l'atto di pubblicar solennemente l'Orologio Oscillatorio, dedicato il d&igrave; 25 di <lb/>Marzo 1673 a Luigi XIV. </s></p><p type="main">

<s>Nella Prefazione infatti all'Opera, dopo aver rimproverati coloro che, <lb/>parecchi anni decorsi dal 1658, attribuirono a s&egrave; o a'loro connazionali l'in&shy;<lb/>venzione del pendolo automatico, avventa aguzzando pi&ugrave; che mai la penna <lb/>cos&igrave; fatte parole: &ldquo; Qui vero Galileo primas hic deferre conantur, si ten&shy;<lb/>tasse eum non vero perfecisse inventum dicant, illius magis quam meae <lb/>laudi detrahere videntur, quippe qui rem eamdem, meliori quam ille eventu <lb/>investigaverim. </s>

<s>Cum autem vel ab ipso Galileo vel a filio eius, quod nuper <lb/>voluit vir quidam eruditus, ad exitum perductum fuisse contendent, horo&shy;<lb/>logiaque eiusmodi re ipsa exhibita, nescio quomodo sibi creditum iri spe&shy;<lb/>rent, cum vix verisimile sit adeo utile inventum ignoratum manere potuisse <lb/>annis totis octo, donec a me in lucem ederetur &rdquo; (Op. </s>

<s>Var. </s>

<s>ibi, pag. </s>

<s>32). </s></p><p type="main">

<s>Chi sia quel <emph type="italics"/>vir quidam eruditus<emph.end type="italics"/> lo dice espressamente in una lettera <lb/>al principe Leopoldo: dice che egli era lo scrittore degli Esperimenti del&shy;<lb/>l'Accademia fiorentina (Fabbroni, Lett. </s>

<s>I, 223). Nel Libro de'<emph type="italics"/>Saggi di Na&shy;<lb/>turali esperienze,<emph.end type="italics"/> infatti, l&agrave; dove si descrivono alcuni strumenti adoperati <lb/>per misuratori del tempo, si legge: &ldquo; Pertanto in quelle esperienze che ri&shy;<lb/>chiedono squisitezza maggiore, e che sono di s&igrave; lunga osservazione, che le <lb/>minime disuguaglianze di tali vibrazioni dopo un gran numero arrivano a <lb/>farsi sensibili, fu stimato bene applicare il pendolo all'orivolo, sull'andar di <lb/>quello che prima di ogni altro immagin&ograve; il Galileo, e che dell'anno 1649 <lb/>messe in pratica Vincenzio Galilei suo figliolo &rdquo; (Firenze, 1841, pag. </s>

<s>21, 22). </s></p><p type="main">

<s>Ma queste cose erano state pubblicamente scritte infino dal 1666, e <lb/>nonostante quello sdegno par che sia suscitato nell'animo dell'Hugenio da <lb/>causa recente, venendo a rinfocolar la fiamma accesavi gi&agrave; dall'Autor della <lb/>Storia del ritrovamento del pendolo, e da 14 anni rimasta sopita. </s>

<s>Che sia <lb/>stato quel risentimento suscitato di fresco, lo dice abbastanza chiaro qnel <lb/><emph type="italics"/>nuper,<emph.end type="italics"/> per cui parrebbe che da poco tempo avesse l'Huyghens letto nel <lb/>libro de'<emph type="italics"/>Saggi<emph.end type="italics"/> della nostra Accademia. </s>

<s>E anzi questo dubbio si riduce a <lb/>certezza, rileggendo la sopra citata lettera fra le pubblicate dal Fabbroni, in <lb/>cui, il d&igrave; 22 Maggio 1673, l'Huyghens stesso manda a ringraziare il Prin&shy;<lb/>cipe del Libro degli Esperimenti donatogli insieme con gli opuscoli di Fran&shy;<lb/>cesco Redi. </s></p><pb xlink:href="020/01/344.jpg" pagenum="325"/><p type="main">

<s>Qui resterebbe di due cose sodisfare ai curiosi: la prima, come mai il <lb/>Principe Leopoldo, che fu tanto sollecito e largo dispensatore del Libro a <lb/>tutti i dotti nostrali e stranieri, facesse cos&igrave; lungo indugio coll'Huyghens <lb/>corrispondente dell'Accademia infin quasi da'primi anni, e fra quegli stessi <lb/>dotti il pi&ugrave; insigne di tutti. </s>

<s>L'altra, come mai l'Huyghens cos&igrave; poca atten&shy;<lb/>zione facesse nello svolgere il Libro, da non accorgersi che era stato pub&shy;<lb/>blicato gi&agrave; da sette anni, bench&egrave; lo avesse ricevuto di fresco. </s>

<s>Ma perch&egrave; <lb/>cos&igrave; fatte questioni appartengono piuttosto all'erudizione che alla Scienza, <lb/>lasceremo ad altre mani a risolvere il nodo. </s></p><p type="main">

<s>Quel rinfocolamento poi aveva il suo giusto motivo, perch&egrave; mentre l'Au&shy;<lb/>tore della Storia del ritrovamento del pendolo si contentava d'attribuire a <lb/>Galileo il primo progetto e al figliuolo di lui il primo tentativo, lo Scrittore <lb/>del Libro degli Esperimenti sentenziava addirittura che Vincenzio di Galileo <lb/>aveva messo in pratica il pendolo all'Orologio. </s>

<s>Per ci&ograve; privatamente l'Huy&shy;<lb/>ghens, nella lettera sopra citata al principe Leopoldo, si rammaricava di es&shy;<lb/>sere stato tacitamente accusato di plagio, e al cospetto del pubblico poi, <lb/>nella Prefazione all'<emph type="italics"/>Oscillatorio,<emph.end type="italics"/> faceva le sue ragioni, domandando come <lb/>mai fu tenuta per otto anni a tutti occulta l'invenzione de'Galilei. </s>

<s>Che se <lb/>ci&ograve; fu ad arte, sia mia gloria conclude l'altero Olandese, <emph type="italics"/>id quod omnes <lb/>latebat mihi soli innotuisse.<emph.end type="italics"/> E perch&egrave; sapeva bene che a'Galilei, padre e <lb/>figlio, di pubblicare quelle loro invenzioni ne avevano avuto il divieto ine&shy;<lb/>sorabile dalla morte, le parole del Toparca di Zulichemme vanno diretta&shy;<lb/>mente a ferire il Principe di Toscana, il quale forse non aveva ancora letta <lb/>quella Prefazione, perch&egrave; M. </s>

<s>De Gondy, a cui era stato commesso, non gli <lb/>aveva fatto recapitare il libro. </s>

<s>Ma insomma, in una sua lettera, il Principe <lb/>non fa altro che rispondere, in quegli stessi termini che nel 1659 scriveva <lb/>al Bullialdo, a quell'altra lettera, nella quale l'Hugenio, parendogli di es&shy;<lb/>sere stato imputato di plagio, ripete le scuse antiche d'aver pubblicato il suo <lb/>primo Orologio, senza nulla aver saputo di Galileo. </s></p><p type="main">

<s>Ma se il Principe Leopoldo de'Medici e Vincenzio Viviani avranno poi <lb/>letta quella Prefazione all'Orologio Oscillatorio, come la lessero certemente, <lb/>non potevano non sentirsi configgere nel cuore la punta acuta di quelle <lb/>alate parole. </s>

<s>Se era vero infatti che Vincenzio di Galileo infin dal 1649 aveva <lb/>messo in pratica l'orologio a pendolo, com'asseriva il Segretario Magalotti <lb/>a insinuazione senza dubbio del Viviani, e se era vero che infin da 1656 in <lb/>Toscana un Virtuoso aveva costruito un orologio pi&ugrave; perfetto di quello del <lb/>signor Cristiano Hugenio; non pare anche a noi che sieno veramente degni <lb/>di riprensione il Principe dell'Accademia fiorentina e il discepolo idolatra e <lb/>l'amico intimo de'Galilei per aver cos&igrave; lunghi anni tenuta occulta un'in&shy;<lb/>venzione di tanta importanza? </s>

<s>E avessero almeno alla tarda occasione che <lb/>presero di pubblicarla, provveduto degnamente! Quell'Orologio, che fu pie&shy;<lb/>tra di scandalo allo sdegnoso Olandese, &egrave; l&agrave; nelle Tavole del Libro dell'Ac&shy;<lb/>cademia diligentemente disegnato s&igrave;, ma chiuso in s&egrave; stesso e d'ogni loquela <lb/>muto. </s>

<s>Eppure, se egli parlasse, potrebbe rivendicare all'Italia qualche me-<pb xlink:href="020/01/345.jpg" pagenum="326"/>rito sopra l'Olanda, non solo quanto alla priorit&agrave; del concetto, ma quanto <lb/>altres&igrave; alla precedenza dell'esecuzione. </s>

<s>Studiamoci dunque, se ci riesce, di <lb/>farlo parlare. </s></p><p type="main">

<s>La chiavetta (fig. </s>

<s>23) che pende legata a un nastro allacciato al colon&shy;<lb/>nino tornito, in capo al quale riposa la cassa chiusa dell'orologio, ci dice <lb/>intanto che era impresso il moto alle ruote dall'elaterio di una molla e non <lb/><figure id="id.020.01.345.1.jpg" xlink:href="020/01/345/1.jpg"/></s></p><p type="caption">

<s>Figura 23.<lb/>dal peso. </s>

<s>La figura stessa e le poche parole soggiunte a <lb/>illustrarla ci dicono di pi&ugrave; che la mostra indicava il nu&shy;<lb/>mero delle oscillazioni del pendolo da una infino a 15, e <lb/>il tempo di quelle stesse oscillazioni si variava a piacere <lb/>avvitandovi pendoli ora pi&ugrave; lunghi, ora pi&ugrave; corti. </s>

<s>D'onde <lb/>s'argomenta che la ruota alla quale &egrave; imperniato l'indice <lb/>doveva avere 15 denti come quell'altra mossa dal pen&shy;<lb/>dolo. </s>

<s>In che modo poi questo giocasse par che possa con <lb/>non minor certezza argomentarsi da quelle parole che <lb/>dicono essere stato applicato il pendolo all'oriuolo <emph type="italics"/>sul&shy;<lb/>l'andare di quello che prima di ogni altro immagin&ograve; <lb/>il Galileo.<emph.end type="italics"/> Dunque il pendolo giocava sulla ruota a denti <lb/>di sega, menando in qua e in l&agrave; le due sue code, che, <lb/>ora dischiavandosi da'denti, ora urtando ne'pironi, fanno <lb/>a ogni vibrazione passare un dente alla ruota stessa. </s>

<s>Al&shy;<lb/>l'ultimo la ruota mossa dalla molla poteva avere qualun&shy;<lb/>que numero di denti, non avendo altro ufficio che di <lb/>dare impulso a quella a denti di sega, la quale dovendo <lb/>essere collocata verticalmente, per via di una ruota coro&shy;<lb/>nata faceva volgere una lanterna e con essa l'indice <lb/>sulla mostra orizzontale. </s></p><p type="main">

<s>Se quelle acetose parole <emph type="italics"/>messe in pratica Vincenzio <lb/>Galilei<emph.end type="italics"/> non avessero cos&igrave; a un tratto irritate le narici del Barone olandese, <lb/>e piuttosto che gittar via il Libro, senza pi&ugrave; degnarsi nemmeno di guardare <lb/>il frontespizio, per assicurarsi dell'anno dell'impressione; avesse letto con <lb/>calma, si sarebbe assai facilmente persuaso che, descrivendosi ivi un orolo&shy;<lb/>gio diverso affatto dal suo, non ci era luogo a citare il suo nome e la sua <lb/>invenzione, e che citandosi invece il nome e l'invenzione di Galileo non ve&shy;<lb/>niva egli per niente a esser colto dall'accusa di plagio. </s></p><p type="main">

<s>L'Orologio ugeniano infatti era una macchina in s&egrave; per ogni parte <lb/>compiuta e applicabile a tutti gli usi: l'orologio invece degli Accademici del <lb/>Cimento era una macchinetta costruita a solo uso di misurare le minime <lb/>frazioni del tempo ne'fisici esperimenti. </s>

<s>Il modo stesso dell'applicazione del <lb/>pendolo era nell'una e nell'altra costruzione molto diverso. </s>

<s>Si ricompone <lb/>dunque la lite dicendo competersi all'Huyghens due meriti che nessuno per <lb/>verit&agrave; gli potrebbe contendere: quello di avere inventato l'orologio perfetto, <lb/>e l'altro di essere stato il primo a pubblicarlo. </s>

<s>Resta dall'altra parte a Ga&shy;<lb/>lileo il merito di aver avuto di quella invenzione il primo concetto e a un <pb xlink:href="020/01/346.jpg" pagenum="327"/>nostro Toscano quello altres&igrave; d'averlo in qualche modo eseguito o poco prima <lb/>o contemporaneamente all'Hugenio, bench&egrave; non se ne fosse saputo preva&shy;<lb/>lere per sua sventura. </s>

<s>Ma perch&egrave; tuttoci&ograve; non si asserisca che sulle parole <lb/>di Vincenzio Viviani e di Leopoldo de'Medici, negando fede alle quali si ver&shy;<lb/>rebbe necessariamente a negar fede alla nostra Storia, che si potrebb'egli <lb/>dire della veracit&agrave; di que'due uomini? </s></p><p type="main">

<s>E quanto al Viviani non pu&ograve; negarsi che quando narra i fatti della <lb/>prima vita scientifica di Galileo, non si mostri spesso male informato e che <lb/>non si lasci talvolta trasportar da uno zelo soverchio d'esaltar la gloria del <lb/>venerato maestro. </s>

<s>Questa stessa storia del pendolo ne porger&agrave; in seguito di <lb/>ci&ograve; molti esempii, ma intanto basti richiamar l'attenzione de'nostri lettori <lb/>su quel che egli dice della scoperta galileiana della lunghezza de'pendoli in <lb/>proporzion duplicata dei tempi. </s>

<s>Dice che Galileo giunse a una tale scoperta <lb/>guidato dalla Geometria e dalla sua Nuova Scienza del moto (Alb. </s>

<s>XIV, 443). <lb/>Eppure &egrave; un fatto che Galileo scoperse quella legge senza geometria e senza <lb/>scienza del moto, per semplice esperienza. </s>

<s>Tanto poi era al Viviani questo <lb/>fatto ben noto, che nelle postille autografe all'edizione di Leyda, crede d'es&shy;<lb/>sere egli stato il primo a dar alla legge sperimentale di Galileo fondamenti <lb/>stabili di Geometria e di Scienza del moto. </s>

<s>Ma quando il Viviani narra con <lb/>tutte le particolarit&agrave; fatti de'quali fu spettatore e attore nella sua convivenza <lb/>d'Arcetri, parrebbe un negar fede all'umana natura, e perci&ograve; a ogni parte <lb/>di Storia, il negar fede alla parola di lui. </s></p><p type="main">

<s>La dignit&agrave; poi e l'integrit&agrave; di Leopoldo de'Medici lascia anche meno <lb/>a dubitare de'suoi asserti. </s>

<s>Poich&egrave; noi dunque, sulla fede del Principe, ac&shy;<lb/>cettiamo per vero che un Toscano avesse costruito un'orologio a pendolo <lb/>in quello stesso tempo e forse un po'prima che in Olanda pensasse a co&shy;<lb/>struirlo l'Hugenio, rimane d'investigar qual fosse il nome di lui e la ma&shy;<lb/>niera di quella costruzione. </s></p><p type="main">

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

<s>Collazionando le lettere del Principe Leopoldo scritte il d&igrave; 20 Aprile e <lb/>22 Maggio 1659 al Bullialdo e da noi riferite pi&ugrave; sopra, con la Storia del <lb/>ritrovamento del pendolo scritta dal Viviani pochi mesi dopo, s'ha in que&shy;<lb/>sta una dichiarazione importante degli studii fatti intorno alla applicazione <lb/>del pendolo e delle persone che v'esercitarono l'ingegno, di che in quelle <lb/>non si fa che un semplice accenno. </s>

<s>Si ha infatti che Filippo Treffler chia&shy;<lb/>mato da Augusta a Firenze per servire in qualit&agrave; di <emph type="italics"/>torniaio<emph.end type="italics"/> il Granduca, <lb/>fabbric&ograve; in quel tempo quella galante macchinetta nella quale s'incarnava <lb/>il concetto rivelato nella Lettera di Galileo a Lorenzo Realio; s'ha che Fran&shy;<lb/>cesco Generini present&ograve; allo stesso Granduca un modello in ferro, nel quale <lb/>era unito al pendolo il contrappeso, in modo simile a quello che 14 anni <pb xlink:href="020/01/347.jpg" pagenum="328"/>avanti immagin&ograve; Galileo, bench&egrave; con diversa e molto ingegnosa applicazione; <lb/>s'ha che lo stesso Filippo adatt&ograve; l'invenzione a un oriuolo da camera per <lb/>S. A. e che ridusse a questa foggia di oriuoli a pendolo quello pubblico <lb/>sulla piazza de'Pitti. </s></p><p type="main">

<s>Che sia dunque Francesco Generini quel Virtuoso di cui parla nelle due <lb/>lettere sopra citate il Principe Leopoldo? </s>

<s>A chi volesse dire cos&igrave;, non <lb/>avremmo per verit&agrave; argomenti da mostrar la falsit&agrave; del suo detto, ma par <lb/>nonostante assai pi&ugrave; probabile che il Principe stesso intendesse di un altro, <lb/>che il Viviani ivi per modestia si tace o per altra pi&ugrave; complicata ragione. </s>

<s><lb/>Potrebb'essere insomma che l'Automato inventato in Toscana e da Leo&shy;<lb/>poldo de'Medici messo a concorso con quello costruito in Olanda, fosse quello <lb/>che vedesi nelle Tavole de'<emph type="italics"/>Saggi di Naturali Esperienze<emph.end type="italics"/> costruito da Fi&shy;<lb/>lippo Treffler sul disegno avutone dal Viviani. </s></p><p type="main">

<s>A render questa nostra congettura in qualche modo probabile soccorre <lb/>prima di tutto il fatto che fra il 1656 e il 57 lo stesso Viviani, aiutato ta&shy;<lb/>lora dal Borelli e dal Rinaldini, attendeva a far esperienze sopra la velocit&agrave; <lb/>del suono e della luce (MSS. Cim. </s>

<s>T. X, c. </s>

<s>181), per le quali si richiede&shy;<lb/>vano misuratori squisiti de'minimi tempi. </s>

<s>Or chi non direbbe che un tal <lb/>Cronometro descritto o diciam meglio disegnato nel Libro de'<emph type="italics"/>Saggi<emph.end type="italics"/> non <lb/>fosse proprio inventato a quest'uso? </s>

<s>E chi potrebbe negare che a Vincen&shy;<lb/>zio Viviani, il quale ebbe mano alla costruzione dell'Orologio di Galileo in&shy;<lb/>siem col figliuolo di lui, non cadesse in mente di rendere automatiche le <lb/>vibrazioni del pendolo, aos&igrave; difficilmente osservabili coll'occhio, per via della <lb/>macchinetta di cui s'&egrave; di sopra indagato il disegno, a costruir la quale aveva <lb/>l'opera del Treffler artefice in orologeria cos&igrave; famoso? </s></p><p type="main">

<s>Tutto questo sembra a noi e sembrer&agrave; altres&igrave; probabile ai nostri let&shy;<lb/>tori, ma ora annunziamo non pi&ugrave; come probabilit&agrave;, ma come cosa certa <lb/>l'essersi applicato lo stesso Viviani a descrivere il modo per trovar grafi&shy;<lb/>camente le lunghezze varie che occorre di dare ai pendoli, secondo si vuol <lb/>che l'indice sulla mostra segni ora una, ora un'altra minima misura dei <lb/>tempi trascorsi. </s>

<s>In una nota autografa infatti, dop'aver matematicamente <lb/>dimostrato che le lunghezze dei pendoli hanno ragion duplicata dei tempi, <lb/>cos&igrave; per modo di corollario soggiunge il Viviani: </s></p><p type="main">

<s>&ldquo; Questa s&igrave; bella propriet&agrave; mi somministr&ograve; la fabbrica di uno stru&shy;<lb/>mento assai facile, per aggiustar con esso speditamente la lunghezza di un <lb/>pendolo con quella di un altro (i tempi delle lor vibrazioni abbiano qua&shy;<lb/>lunque proporzione) sfuggendo per tal via il tedio di far prove e riprove <lb/>con diverse lunghezze di fili, e di replicar le numerazioni delle loro dondo&shy;<lb/>late, finch&egrave; si avr&agrave; a tentoni, a trovar quella che dia la divisione del tempo <lb/>cercata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pongasi aversi nota la lunghezza del filo AB (fig. </s>

<s>24) di quel pendolo, <lb/>che in ciascuna sua vibrazione scempia di sola andata o ritorno, consumi il <lb/>tempo di un minuto secondo. </s>

<s>Dipoi, dentro l'angolo retto CDL di un telaio <lb/>rettangolo CDLF di legno o di metallo, sostenuto dal piede E, si adatti e <pb xlink:href="020/01/348.jpg" pagenum="329"/>fermi una sottil lamina di rame o di ottone tagliata in figura di mezza pa&shy;<lb/>rabola, colla cima in G, il di cui asse GD sia precisamente uguale a detto <lb/>filo AB, e la base DL si divida nel telaio in minute parti uguali, come in 60, <lb/>cominciando la numerazione di 5, in 5 o di 10, in 10 da D e terminando <lb/><figure id="id.020.01.348.1.jpg" xlink:href="020/01/348/1.jpg"/></s></p><p type="caption">

<s>Figura 24.<lb/>in L, che cos&igrave; lo strumento sar&agrave; fatto, av&shy;<lb/>vertendo che, quanto questo telaio sar&agrave; pi&ugrave; <lb/>lungo da C verso F, mantenuta la lun&shy;<lb/>ghezza GD dell'asse della parabola; tanto <lb/>la curva GHIL sar&agrave; pi&ugrave; distesa, e pi&ugrave; atta <lb/>all'uso il quale &egrave; tale. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cerchisi per esempio la lunghezza <lb/>del filo di quel pendolo, che in ogni sua <lb/>vibrazione scempia metta la met&agrave; di un <lb/>minuto secondo, nel qual si fa la semplice <lb/>vibrazione col filo AB. </s>

<s>Si accomodi prima <lb/>lo strumento verticalmente. </s>

<s>Di poi, perch&egrave; <lb/>il n. o 30 notato qui colla lettera P, &egrave; la <lb/>met&agrave; di tutta la numerazione delle parti&shy;<lb/>celle segnate sul regolo DL, si presenti <lb/>davanti e rasente al detto n.o 30 il pendolo quieto AB in PN, e fuor del <lb/>lembo GNL della parabola avanzer&agrave; la parte IN del filo, la quale sar&agrave; ap&shy;<lb/>punto la cercata, perch&egrave;, con essa ogni scempia vibrazione del pendolo si <lb/>far&agrave; nella met&agrave; del tempo di quella del pendolo AB, cio&egrave; si far&agrave; in 30 terzi, <lb/>cio&egrave; in un mezzo secondo, sicch&egrave; ogni sua doppia vibrazione di andare e di <lb/>tornare sar&agrave; un secondo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Similmente cercando la lunghezza del pendolo, che si faccia ogni sua <lb/>mossa scendente nella terza parte di un minuto secondo, cio&egrave; in 20 terzi, <lb/>si applichi come sopra il termine del filo AB in Q, dove sta segnato il <lb/>n.o 20, terza parte di 60, sicch&egrave; AB penda in H, ch&egrave; l'avanzo HO del filo <lb/>sodisfar&agrave; al quesito. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Talmente che se si trover&agrave; modo di fermare in L, H, sul lembo della <lb/>lamina parabolica i fili pendoli LM, IN, HO e questi si allontanino unita&shy;<lb/>mente dal perpendicolo, si vedr&agrave; che ad ogni sola gita del primo, il secondo <lb/>ne fa due, il terzo tre, ecc. </s>

<s>ecc. </s>

<s>E la ragione di ci&ograve; si &egrave; perch&egrave;, avendo <lb/>la lunghezza LM alla IN suddupla proporzione del tempo di una vibrazione <lb/>di quelle al tempo di una di queste, come qui a principio s'&egrave; dimostrato, ed <lb/>avendo anche per propriet&agrave; della parabola la LM alla IN suddupla ragione <lb/>della MG alla GN, ovver del n.o DL al n.o DP; essendo 60 doppio del 30, <lb/>anco il tempo d'una vibrazione di LM sar&agrave; doppio del tempo di una vibra&shy;<lb/>zione di IN, e per le stesse ragioni il tempo di una del pendolo LM sar&agrave; <lb/>triplo del tempo di una del pendolo HO. &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXVII, c. </s>

<s>64). </s></p><p type="main">

<s>Della descrizione, per&ograve; un po'meno perfetta, e della costruzione di que&shy;<lb/>sto strumento lasci&ograve; nota altrove lo stesso Viviani (MSS. Cim. </s>

<s>T. X, c. </s>

<s>49) <lb/>e pare se ne compiacesse alquanto, annoverando anco questa fra le altre sue <pb xlink:href="020/01/349.jpg" pagenum="330"/>invenzioni: (Nelli, Saggio ecc., Lucca 1759, pag. </s>

<s>111). Si sarebbe forse al&shy;<lb/>tres&igrave; compiaciuto in questo medesimo luogo dell'invenzion del Cronometro, <lb/>per servigio del quale invent&ograve; lo strumento sopra descritto, so non avesse <lb/>voluto farne intiera oblazione al suo Galileo. </s></p><p type="main">

<s>Ma che egli attendesse per s&egrave; medesimo a cos&igrave; fatte speculazioni e ci <lb/>avesse acquistato meriti proprii da venire in qualche parte a contesa di <lb/>quella gloria che, per la pubblicit&agrave; dell'opera, s'and&ograve; a cumular tutta in <lb/>fronte all'Hugenio; si concluder&agrave; da ci&ograve; che siamo per dire della ricerca <lb/>de'centri di oscillazione a proposito della fabbrica degli orologi. </s></p><p type="main">

<s>Nel 1635 Giovanni Pieroni attendeva con massima diligenza ad osser&shy;<lb/>vare i moti di alcune stelle fisse per accertarsi se ell'erano veramente sog&shy;<lb/>gette, come da alcuni copernicani si sospettava, a parallasse annuale. </s>

<s>A tali <lb/>delicatissime ricerche gli bisognavano misuratori squisiti de'minimi tempi. </s>

<s><lb/>Ma a supplire al bisogno riconosceva l'inutilit&agrave; de'pendoli, cos&igrave; magnificati <lb/>da Galileo, se prima non si sapeva la loro lunghezza precisa e il pi&ugrave; esatto <lb/>modo di computarla. </s>

<s>Perci&ograve; scriveva, in una sua lettera diretta allo stesso <lb/>Galileo, che gli sarebbe stato grandissimo vantaggio saper da lui <emph type="italics"/>quanto <lb/>vadia lungo un pendolo per misurare uno o alquanti secondi di tempo, <lb/>e se la lunghezza si prende insino a tutto il corpo grave pendente o in&shy;<lb/>sino al centro di esso.<emph.end type="italics"/> (Alb. </s>

<s>X, 68). </s></p><p type="main">

<s>La responsiva a questa del Pieroni non si trova nell'Epistolario gali&shy;<lb/>leiano, ma in ogni modo siam certi che egli non era in grado di rispon&shy;<lb/>dere alla prima domanda, perch&egrave; non aveva ancora scoperta la legge del <lb/>tempo relativamente alle varie lunghezze de'pendoli: n&egrave; men certi siam pure <lb/>in dire che egli non era in grado di rispondere scientificamente nemmeno <lb/>alla seconda, la quale includeva in s&egrave; la soluzione del celebre problema dei <lb/>centri oscillatorii. </s>

<s>Un tal problema era senza dubbio occorso a Galileo nella <lb/>corda o nella catena che s'incurva, oscillando il pendolo (Alb. </s>

<s>I, 254) ma <lb/>perch&egrave; di questo, nella misura del tempo, dica pure quel che si vuole il <lb/>Viviani, Galileo non ne fece mai uso, non sent&igrave; perci&ograve; nemmeno il bisogno <lb/>di decider se alla lunghezza del filo dovesse aggiungersi il diametro o il <lb/>raggio o altra parte della dimensione del peso pendolo, come voleva il Pie&shy;<lb/>roni sapere dal suo Maestro. </s></p><p type="main">

<s>Quando nel primo periodo dell'Accademia medicea si ripresero questi <lb/>studii, e si volle cominciare a mettere una volta in pratica quel che Gali&shy;<lb/>leo si era contentato di progettare, si sent&igrave; allora seriamente il bisogno di <lb/>rispondere alla seconda domanda di Giovanni Pieroni e si rispose in modo <lb/>che in pratica almeno fu trovato conforme al vero. </s>

<s>Si rispose che essendo <lb/>il filo sottilissimo e il peso di materia omogenea e di figura sferica, la lun&shy;<lb/>ghezza del pendolo si dovea computar dal punto di sospensione del filo al <lb/>centro di gravit&agrave; dello stesso peso. </s>

<s>Una s&igrave; fatta risposta, se non si trova <lb/>espressa a parole, si trova per&ograve; eloquentemente espressa ne'fatti, sapendosi <lb/>che per le squisite osservazioni e sperienze i nostri Accademici si valevano <lb/>di palle di oro sospese a sottilissimi fili di seta. </s>

<s>Ma pi&ugrave; eloquentemente che <pb xlink:href="020/01/350.jpg" pagenum="331"/>mai parla il disegno di quella macchinetta, che nella Tavola de'<emph type="italics"/>Saggi<emph.end type="italics"/> si <lb/>vede impressa allato del sopra descritto Cronometro. </s>

<s>Quella macchinetta fu <lb/>pensata e fu pensato di appender la palla a due fili che le facessero di fal&shy;<lb/>saredine, <emph type="italics"/>perch&egrave; l'ordinario pendolo a un sol filo, in quella sua libert&agrave; <lb/>di vagare (qualunque ne sia la cagione) insensibilmente va traviando dalla <lb/>prima sua gita, e verso il fine, secondo ch'ei s'avvicina alla quiete, il <lb/>suo movimento non &egrave; pi&ugrave; per un arco verticale, ma par fatto per una <lb/>spirale ovata, in cui pi&ugrave; non posson distinguersi n&egrave; noverarsi le vibra&shy;<lb/>zioni.<emph.end type="italics"/> (Firenze 1841, pag. </s>

<s>20). </s></p><p type="main">

<s>Ma che ci sarebb'egli stato bisogno di quel macchinamento? </s>

<s>vien, leg&shy;<lb/>gendo, in mente a ciascuno: quell'effetto si poteva ottener con naturale fa&shy;<lb/>cilit&agrave;, sospendendo le palle non a fili flessibili, ma a rigide verghe di metallo. </s>

<s><lb/>Ora, quel che viene in mente a ciascuno non &egrave; credibile che non venisse <lb/>in mente ai nostri Accademici, e perci&ograve;, se non usarono di appendere il <lb/>peso a una verga metallica, dovevano averne qualche buona ragione. </s>

<s>La ra&shy;<lb/>gione poi era questa: che, avendo la verga rigida qualche peso sensibile <lb/>rispetto al peso della palla, la regola di computar la lunghezza giusta del <lb/>pendolo non era pi&ugrave; quella assegnata di sopra, per cui conveniva cercarne <lb/>altra con certezza di ragion matematica. </s>

<s>N&egrave; di trovarla per verit&agrave; era fa&shy;<lb/>cile presentandosi alquanto complicato il problema de'centri di oscillazione. </s></p><p type="main">

<s>Pure, quando il Viviani invent&ograve; e il Treffler costru&igrave; il Cronometro, biso&shy;<lb/>gnava sospendere il filo a una verga metallica e non s&igrave; gracile, avendo ella a <lb/>resistere agli urti de'pironi e ai contraccolpi delle ruote. </s>

<s>E da un'altra parte, <lb/>se precisa bisognava mai computar la lunghezza de'pendoli, qui proprio era <lb/>il caso, dipendendo da quella stessa precisione tutta l'utilit&agrave; e il peculiare <lb/>uso del nuovo misuratore delle pi&ugrave; sminuzzate minuzie del tempo. </s>

<s>Condi&shy;<lb/>zione inevitabile alla fabbrica di questo strumento era la ricerca del centro <lb/>oscillatorio, e il Viviani fece questa ricerca e riusc&igrave; e trovar la regola pra&shy;<lb/>tica &ldquo; per conoscer qual punto del pendolo sia quello dal quale si regola <lb/>il moto &rdquo; (MSS. Cim. </s>

<s>T. X, c. </s>

<s>48). </s></p><p type="main">

<s>Nella ricerca del centro di oscillazione de'pendoli l'elegante ingegno del <lb/>Viviani, che si compiaceva di sparger di qualche fiore le aride vie della Ma&shy;<lb/>tematica, s'abbatt&egrave; a inventare il gioco di quelle figurine che si soglion <lb/>rappresentare in molti Trattati di Fisica come grazioso esempio dell'equili&shy;<lb/>brio stabile dei pesi. </s>

<s>Correvano quelle figurine a fare spettacolo di s&egrave; per <lb/>tutta l'Italia, e il padre Giuseppe Ferroni cos&igrave; da Bologna scriveva in pro&shy;<lb/>posito allo stesso Viviani: &ldquo; Ho visto in casa del marchese Cospi una sta&shy;<lb/>tuetta di legno di un maestro, la quale tenendo in mano un'asta rigida con <lb/>due contrappesi, ed avendo nel piede una punta ferrata di trottola, posata <lb/>su un candeliere di legno, su quello si gira facendo molti ondeggiamenti, <lb/>come se volesse cadere, ma pur sempre si mantiene in piedi. </s>

<s>Io pensai a que&shy;<lb/>sto equilibrio.... So questa invenzione esser venuta di Firenze, onde la stimo <lb/>parto dell'ingegno di V. S. </s>

<s>Illustrissima &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLVI, c. </s>

<s>281). </s></p><p type="main">

<s>Il Ferroni s'era bene apposto dell'inventore, ma non aveva rettamente <pb xlink:href="020/01/351.jpg" pagenum="332"/>pensato intorno alle ragioni dell'equilibrio, per cui il Viviani glie ne espone <lb/>la teoria in relazione ai centri oscillatorii concludendogli che &ldquo; il pendolo <lb/>composto di asta rigida, farebbe quegli ondeggiamenti che la macchina am&shy;<lb/>mirata &rdquo; (ivi, c. </s>

<s>282). La teoria poi dell'equilibrio stabile, nelle figure on&shy;<lb/>deggianti, il Viviani stesso la lasci&ograve; scritta cos&igrave; in una sua nota: &ldquo; Tutto <lb/>il segreto dentro la figuretta ondeggiante col bilico senza mai cadere, ben&shy;<lb/>ch&egrave; ella non sia collegata col sostegno, ma solamente ci posi colla punta, <lb/>sta che il centro di gravit&agrave; del composto si trova sempre sotto il punto del <lb/>sostegno &rdquo; (ivi, T. CXLIII, c. </s>

<s>64). </s></p><p type="main">

<s>L'Huyghens non s'incontr&ograve; nelle sue ricerche in cos&igrave; fatte eleganze, <lb/>ma molto pi&ugrave; largamente e altamente del Viviani sollev&ograve; l'ala del poten&shy;<lb/>tissimo ingegno a quelle nuove e difficili speculazioni. </s>

<s>Il problema del <lb/>centro di oscillazione fu proposto dal Mersenno all'Huyghens, quand'era <lb/>giovanetto. </s>

<s>Il Cartesio e il Fabry lo risolsero ne'pi&ugrave; facili casi, e senza di&shy;<lb/>mostrazione, ma quello stesso giovanetto divenuto gi&agrave; adulto, ne propose <lb/>teorie condotte su principii matematici, e le trov&ograve; riscontrare con gli spe&shy;<lb/>rimenti. </s>

<s>L'occasione di ci&ograve;, cos&igrave; a lui come al Viviani, gli fu porta dal&shy;<lb/>l'Orologio. </s>

<s>In quelli della prima fabbrica, a computar la lunghezza de'pen&shy;<lb/>doli e a variarla secondo i bisogni, segu&igrave; la regola de'nostri Accademici, <lb/>facendo pi&ugrave; sottile che fosse possibile la verga, e pi&ugrave; pesante la palla, la <lb/>quale si poteva alzare o abbassare per mezzo di una vite. </s>

<s>Ma negli orologi <lb/>della seconda fabbrica, ossia ne'cicloidali, cercando sempre nuove squisi&shy;<lb/>tezze, alla palla sostitu&igrave; la lente, la quale cred&egrave; bene di mantener fissa in <lb/>quella posizione che la rendesse pi&ugrave; atta a fender l'aria, e a incontrar perci&ograve; <lb/>in lei minore la resistenza. </s>

<s>Mobile a vite e infilato nell'asta lasci&ograve; un pic&shy;<lb/>colo peso, che doveva servire, ora alzandolo ora abbassandolo, a regolare il <lb/>tempo dell'Orologio. </s>

<s>Ma a saper con certezza di scienza quanto questo moto <lb/>di ascesa e discesa importasse nell'abbreviare o allungare la misura prefi&shy;<lb/>nita al moto del pendolo, occorreva la ricerca del centro d'oscillazione, per <lb/>cui il pendolo composto si poteva ridurre alla vera lunghezza del pendolo <lb/>semplice, o pendolo matematico. </s>

<s>Cos&igrave; fatte ricerche furono dall'Huyghens <lb/>instituite ed esposte nella IV Parte del suo <emph type="italics"/>Orologio Oscillatorio,<emph.end type="italics"/> dove alla <lb/>proposizione XXIII, insegna il modo di risolvere praticamente l'importante <lb/>problema. </s></p><p type="main">

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

<s>A questo punto si conclude la somma della Storia cos&igrave; controversa, che <lb/>concerne l'applicazione del pendolo agli Orologi, nella quale tanta parte <lb/>ebbe, com'abbiamo veduto, il nostro Viviani. </s>

<s>Egli, piuttosto che Galileo, e <lb/>l'Huyghens si pu&ograve; dire che sieno i due competitori. </s>

<s>Ma pure &egrave; cosa nota&shy;<lb/>bilissima che il Discepolo di Galileo dopo varie vicende passate non si fosse <pb xlink:href="020/01/352.jpg" pagenum="333"/>punto rimosso da quelle sue prime persuasioni, in cui la verit&agrave; storica ri&shy;<lb/>man cos&igrave; spesso sopraffatta dai pregiudizii. </s>

<s>E chi, fra'tanti esempii che se <lb/>ne potrebbero addurre, non riconosce la passione che ha tolto oramai l'equi&shy;<lb/>librio e fatto prevaler dalla sua parte il giudizio, in quelle parole che gli <lb/>scrive Matteo Campani, a proposito della pubblicazione di un certo capitolo <lb/>in cui trattavasi dell'Orologio a pendolo? </s>

<s>&ldquo; Mi permisi bens&igrave; che Ella, per <lb/>gloria di Galileo, avesse avuto a caro la pubblicazione di esso, mentre non si <lb/>fa menzione nessuna del signor Huyghens &rdquo; MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLV, c. </s>

<s>150). </s></p><p type="main">

<s>Che nel 1682 poi, dopo tante private e pubbliche controversie, il Vi&shy;<lb/>viani fosse rimasto in quelle stesse persuasioni in cui egli era prima che <lb/>desse mano a scriver la Storia del ritrovamento del pendolo, si par da ci&ograve; <lb/>che scrisse, e che aveva in animo di pubblicare come Prefazione alla <emph type="italics"/>Tavola <lb/>espansa perpetua, ad uso della Toscana per l'osservanza delle ore ne'pre&shy;<lb/>cetti ecclesiastici,<emph.end type="italics"/> e che si trova inserita, da carte 67-86, nel Tomo CXXXVIII <lb/>manoscritto dei Discepoli di Galileo; Tavola che doveva servir di comple&shy;<lb/>mento a quell'altra <emph type="italics"/>Tavola dell'ore, del levar del sole, mezzo giorno, mezza <lb/>notte<emph.end type="italics"/> ecc., stampata per cura dello stesso Viviani in Firenze, nella stampe&shy;<lb/>ria granducale, nel 1660 e di cui, inserita nel Tomo manoscritto ora citato, <lb/>si trova una copia. </s>

<s>In quell'abbozzo di Prefazione dunque gettato gi&ugrave; dalla <lb/>penna nel 1682 il Calcolator della <emph type="italics"/>Tavola espansa<emph.end type="italics"/> cos&igrave; scriveva: </s></p><p type="main">

<s>&ldquo; E qui in tale occasione sia permesso far noto ci&ograve; che, non essendo <lb/>forse cos&igrave; comune, sar&agrave; gradito il sapere, ed &egrave; che questo Oriuolo pubblico, <lb/>trovandosi venti anni sono, per la sua antichit&agrave; avere scapitato molto della <lb/>sua perfezione, e facendo perci&ograve; col suo sregolato batter dell'ore anticipare <lb/>o posticipare quelle operazioni, che gli abitanti si presumevano di far tutte <lb/>ben regolate; il medesimo Serenissimo Gran Duca Ferdinando, conoscendo <lb/>l'importanza di rimediarvi in servizio e comodo, non tanto de'secolari che <lb/>degli ecclesiastici, non solamente lo fece fabbricar di nuovo, senza riguardo <lb/>a spesa alcuna, ma perch&egrave; e'fosse pi&ugrave; esatto vi fece anche adattare, in luogo <lb/>dell'usato <emph type="italics"/>tempo,<emph.end type="italics"/> quell'altro nominato il pendolo, d'invenzione ammiranda <lb/>del suo incomparabil Filosofo e Matematico Galileo Galilei, intorno al quale, <lb/>son gi&agrave; passati cento anni, perch&egrave; fu nel 1582, esso Galileo, nel trovarsi <lb/>studente a Pisa, con la sua veramente lincea accortezza in riflettere a tutti <lb/>gli effetti, bench&egrave; minimi della Natura, osserv&ograve; un giorno, in una lampada <lb/>di quel Duomo stata poco prima lasciata in moto, un'assai precisa ugualit&agrave; <lb/>de'passaggi delle sue andate e tornate tanto larghe per archi grandi, quanto <lb/>strette per piccolissimi, del qual Misuratore di tempo, da allora in poi, egli <lb/>si valse prima per conoscere la variazione delle frequenze del polso, e di <lb/>poi in servizio delle osservazioni astronomiche, bisognose della divisione <lb/>de'brevi tempi in parti uguali minutissime, quali le somministra il pendolo <lb/>che sia d'assai corto filo; e nel 1610, avendo il medesimo Galileo col suo <lb/>nuovo Occhiale, oltre agli innumerabili soli non pi&ugrave; veduti da esso scoperti <lb/>in cielo, prima di ogni altro, ritrovato ancora le quattro Lune vaganti in&shy;<lb/>torno al corpo di Giove, le quali, ad onore dell'Augusta prosapia del G. D. Co-<pb xlink:href="020/01/353.jpg" pagenum="334"/>simo II suo signore volle si nominassero Stelle medicee, e giudicatele mezzi <lb/>proporzionati a dimostrar la via gi&agrave; per tanti secoli cercata, di navigar con <lb/>sicurezza per longitudine; pens&ograve; esso d'accomodare esso pendolo agli oriuoli <lb/>a molla ed a contrappesi, per valersene in sussidio delle predette Medicee <lb/>ne'tempi, che queste non fossero osservabili, e a tale effetto nel 1615 pro&shy;<lb/>poselo, insieme con le Tavole calcolate da lui, per le future osservazioni di <lb/>quelle a Filippo III Re di Spagna, e di poi nel 1637 agli Stati di Olanda, <lb/>con farne loro libero dono, e descrivere un suo pensiero, per accomodare <lb/>esso pendolo agli usati orivoli a ruote, lo che per ultimo fece nel 1649 il <lb/>Dottor Vincenzio suo figliuolo, che fu il primo ad adattarlo ad un nuovo <lb/>Orivolo a contrappesi, intorno al quale lavor&ograve; anch'egli ancora di propria <lb/>mano sul concetto che glie ne aveva somministrato gi&agrave; il proprio Padre, ed <lb/>in oggi sull'esempio di questo, con tanto semplice ed ingegnoso trovato del <lb/>nostro ammirabile Galileo, si perfezionano tutti gli altri orivoli, poich&egrave; la <lb/>naturale ugualit&agrave; delle vibrazioni del pendolo, necessita l'artifizio a portar <lb/>le ore ugualissime &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXXXVIII, c. </s>

<s>101). </s></p><p type="main">

<s>Cos&igrave; il Viviani conclude a quel modo stesso che egli esordisce, e perci&ograve; <lb/>riescono inutili le pagine della nostra Storia, oggetto della quale non dee <lb/>esser per lui quello d'investigare e di dire la verit&agrave;, ma di esaltare il suo <lb/>Galileo. </s>

<s>Comunque sia, dicevasi dianzi che a quel punto a cui l'abbiamo <lb/>condotta restavasi conclusa la somma della storia del pendolo applicato al&shy;<lb/>l'Orologio. </s>

<s>Ma qual'&egrave; quello strumento, che esca dalle mani del suo primo <lb/>artefice perfetto? </s>

<s>L'Huyghens credette, come si vide, di aver fatto un gran <lb/>passo nella via di questo perfezionamento, applicando il pendolo cicloidale, <lb/>che poi subito si vide andare in disuso. </s>

<s>Ci&ograve; fu per due ragioni: prima, <lb/>perch&egrave; col pendolo circolare s'otteneva il medesimo intento, e poi, perch&egrave; <lb/>non era quello il vero modo d'ovviare all'inconveniente per cui si escogit&ograve; <lb/>quella nuova arguta invenzione. </s></p><p type="main">

<s>L'inconveniente consisteva in certe ineguaglianze, che alcuni riduce&shy;<lb/>vano a due: l'una dipendente dal non esser quelle stesse vibrazioni iso&shy;<lb/>crone, e l'altra dipendente dal variar delle stagioni. </s>

<s>L'Huyghens, ammet&shy;<lb/>tendo la causa produttrice della prima ineguaglianza, rinnegava assolutamente <lb/>l'altra: &ldquo; Penduli vero ipsius, quas adnotant, binas inaequalitates, alii au&shy;<lb/>tem contra pernegant, earum alteram admittimus .... alteram plane nullam <lb/>esse adseverare non dubitamus &rdquo; (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>1724, pag. </s>

<s>12). Perci&ograve; <lb/>tutto il suo studio di recare all'ultima perfezione l'Orologio era rivolto al&shy;<lb/>l'isocronismo, e tanto era ben persuaso che a questa sola si riducesse la <lb/>causa di quelle inegualit&agrave;, senza che le stagioni vi concorressere per nulla, <lb/>che, inventato il pendolo cicloidale, si vantava d'aver cos&igrave; provveduto alla <lb/>massima perfezione dell'Orologio. </s>

<s>Potr&agrave; bene, egli dice, il mio Automato <lb/>guastarsi o per vizio di fabbrica o per difficolt&agrave;, che al volgersi delle ruote <lb/>gli sia fatta dall'aria, ma non &egrave; da temer mai che in lui s'alteri la misura <lb/>del tempo, cosicch&egrave; sempre <emph type="italics"/>aut recte tempus metietur, aut omnino non <lb/>metietur<emph.end type="italics"/> (ibi, pag. </s>

<s>35). Ecco a che riduceva l'Huyghens l'influenza delle <pb xlink:href="020/01/354.jpg" pagenum="335"/>stagioni in alterare il moto degli orologi: al far pi&ugrave; difficilmente volubili le <lb/>ruote attorno ai loro assi, per la maggior crassizie sopravvenuta nell'aria. </s>

<s><lb/>Nessuno si crederebbe che tanto si fosse dovuto pensare prima d'esser giunti <lb/>a riconoscere gli effetti del calore in alterare la giusta misura de'pendoli, <lb/>e prima d'avervi saputo trovar rimedio, per via delle compensazioni. </s>

<s>Perci&ograve; <lb/>non inutile n&egrave; discara crediamo dover riuscire ai Lettori la pagina, che si <lb/>aggiunge per ultima parte di questa storia. </s></p><p type="main">

<s>Golifredo Wendelin, diligentissimamente numerando le vibrazioni di un <lb/>medesimo pendolo in tutto il corso di un anno, s'era accorto che nell'estate <lb/>andava pi&ugrave; pigro che nell'inverno. </s>

<s>Maravigliato di questa strana novit&agrave;, ri&shy;<lb/>pet&egrave; piu diligentemente che mai le sue osservazioni, e gli parve non esserci <lb/>dubbio: il pendolo estivo faceva in un giorno circa a 20 vibrazioni meno <lb/>dell'iemale. </s>

<s>Reso pubblicamente noto il resultato di queste esperienze, nes&shy;<lb/>suno gli volle credere. </s>

<s>Il Mersenno, nel Cap. </s>

<s>XIII delle sue Riflessioni fisico <lb/>matematiche, sottoponeva alle sue critiche, per verit&agrave; non troppo acute, que&shy;<lb/>sto fatto, e concludeva che il Wendelin in ogni modo si doveva essere in&shy;<lb/>gannato. </s>

<s>Perch&egrave; ora, egli argomenta, misurava il tempo delle vibrazioni <lb/>de'pendoli colle clessidre a sabbia, e queste danno veramente una differenza <lb/>notabile nel loro flusso, essendo che le sabbie nell'estate son pi&ugrave; sciolte <lb/>che nell'inverno. </s>

<s>Ora misurava quel tempo colle classidre ad acqua, e sono <lb/>anche queste soggette a patir le medesime differenze, perch&egrave; l'acqua, quanto <lb/>&egrave; pi&ugrave; calda, e pi&ugrave; facilmente scorre, e velocemente fluisce. </s>

<s>&ldquo; Quibus adde <lb/>calidam aquam frigida velocius fluere, si forte clariss. </s>

<s>Wendelinus aquae <lb/>fluxu, instar Galilaei, in Horologio suo usus est &rdquo; (Parisiis, 1647, T. III, <lb/>pag. </s>

<s>124). </s></p><p type="main">

<s>L'Huyghens, descrivendo il suo primo Orologio, soggiunge di pi&ugrave; che, <lb/>misurando talora il Wendelin il tempo delle vibrazioni per via degli orologi <lb/>scioterici, questi non dovevano essere stati con tutta la necessaria precisione <lb/>descritti, per cui, come ne dubitavano tutti gli altri, crede ragionevolmente <lb/>di doverne dubitare anch'egli. </s>

<s>Ma comunque sia, conclude: &ldquo; Mihi certe <lb/>nihil eiusmodi licuit animadvertere &rdquo; (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>1724, pag. </s>

<s>13). N&egrave; <lb/>di questo pare se ne fosse accorto nemmeno quindici anni dopo, quando <lb/>pubblic&ograve; l'Orologio oscillatorio. </s></p><p type="main">

<s>Che al Wendelin, assicuratosi con tante lunghe e pazienti esperienze <lb/>venir dal calor dell'estate ritardato il pendolo, dovesse il fatto riuscirgli un <lb/>mistero; che l'Huyghens, il quale a tutt'altro ne assegnava la causa per lui <lb/>certissima e dimostrata, confessasse che quello stesso fatto non gli era oc&shy;<lb/>corso mai di avvertirlo, &egrave; cosa che non fa poi gran maraviglia. </s>

<s>Fa mara&shy;<lb/>viglia per&ograve; che in quelle medesime condizioni si trovasse la scienza de'no&shy;<lb/>stri Italiani, i quali s'erano gi&agrave; allora, per tante esperienze, assicurati della <lb/>dilatazione cos&igrave; lineare come cubica sub&igrave;ta per effetto del calore da tutti <lb/>i corpi. </s></p><p type="main">

<s>Giuseppe Campani, per esempio, erasi veramente persuaso (n&egrave; pareva <lb/>possibile il non persuadersene, com'ebbe a confessare l'Hugenio) che il va-<pb xlink:href="020/01/355.jpg" pagenum="336"/>riar delle stagioni influisce in far variare il moto agli Orologi. </s>

<s>&ldquo; Ho tardato <lb/>(incomincia cos&igrave; una sua lettera scritta il d&igrave; 22 Novembre 1667 al principe <lb/>Leopoldo) perch&egrave; io volevo prima chiarirmi di un effetto del quale dubi&shy;<lb/>tai &rdquo;. </s>

<s>Or sentiamo qual'&egrave; questo effetto, e quale egli creda esserne la causa <lb/>di lui. </s>

<s>L'effetto &egrave; che &ldquo; l'orologio fosse per ricever qualche alterazione <lb/>dalle strane mutazioni de'tempi, come sarebbe da tramontana a scirocco, a <lb/>cagione della maggiore o minore resistenza che gli vien fatta dall'aria am&shy;<lb/>biente, nella quale si muove, e la quale ora ingrossa e ora s'assottiglia, ora <lb/>s'aggrava pi&ugrave; o meno &rdquo; (MSS. Cim. </s>

<s>T. XXIX, c. </s>

<s>92). </s></p><p type="main">

<s>Matteo Campani era pure della medesima opinione di suo fratello Giu&shy;<lb/>seppe, per cui, studiando alla perfezione degli Orologi e attribuendo anche <lb/>egli la causa delle loro variazioni al vario condensamento dell'aria ambiente, <lb/>non ci vide altro miglior rimedio, a preservarli dagli insulti ammosferici, da <lb/>quello in fuori di custodirli per ogni parte ben chiusi. </s>

<s>Tanto era poi per&shy;<lb/>suaso dovere esser questo il pi&ugrave; efficace rimedio, che se ne gloriava come <lb/>di una peregrina invenzione da dover tenersi gelosamente suggellata sotto <lb/>segreto. </s>

<s>&ldquo; Quanto a questi difetti (scriveva al princ. </s>

<s>Leopoldo) esteriormente <lb/>sopravvegnenti all'oriuolo per l'aria ambiente, V. A. sa che abbiamo pro&shy;<lb/>curato di rimediarvi con la nostra invenzione di fabbricare in varia guisa <lb/>gli oriuoli chiusi, com'andai accennando e descrivendo nel libretto, da me <lb/>due anni fa pubblicato sotto il nome anagrammatico d'Antimo Tempera, ed <lb/>a V. A. dedicato.... Potendosi dare il caso che qualche altro ancora si fosse <lb/>riscontrato ne'medesimi miei pensieri e maniera da me sin'ora immagi&shy;<lb/>nata,.... vengono da me contrassegnate le seguenti lettere,.... le quali, <lb/>combinate in lingua latina nel loro vero senso, spiegano individualmente la <lb/>mia invenzione &rdquo; (MSS. Cim. </s>

<s>T. XX, c. </s>

<s>14). </s></p><p type="main">

<s>Ora &egrave; da saper che Matteo, su questo soggetto degli orologi chiusi, che <lb/>egli principalmente proponeva per gli usi nautici; ebbe lunga corrispendenza <lb/>epistolare con Vincenzio Viviani, il quale secondava e approvava l'opera del&shy;<lb/>l'artefice, persuaso anch'egli della regolarit&agrave; e quasi infallibilit&agrave; dell'Auto&shy;<lb/>mato sottratto alle variazioni e all'esteriori influenze dell'aria. </s>

<s>Eppure era <lb/>quel Viviani, il quale, primo dopo l'Aggiunti, aveva sperimentato che la <lb/>fiamma di un moccolino passata in su e in gi&ugrave; rasente al filo metallico, <lb/>faceva immediatamente allungare il pendolo: era quel Viviani che, primo in <lb/>Italia, aveva matematicamente dimostrato ehe i tempi delle oscillazioni stanno <lb/>come le radici delle lunghezze de'pendoli. </s>

<s>Si diceva perci&ograve; d&igrave;anzi far gran&shy;<lb/>dissima maraviglia che lo stesso Viviani non avesse riconosciuti applicabili <lb/>questi medesimi effetti ai pendoli adattati agli orologi, per i quali effetti s'in&shy;<lb/>tendeva chiarissimamente la recondita causa di quelle variazioni avvertite <lb/>gi&agrave; dal Wendelin tanti anni avanti. </s>

<s>S'intendeva cio&egrave; esser veramente il ca&shy;<lb/>lor dell'estate che facendolo allungare ritardava il pendolo, mentre al con&shy;<lb/>trario il freddo nell'inverno lo faceva velocitare. </s>

<s>Dietro ci&ograve;, lo Scienziato <lb/>avrebbe dovuto consigliar l'Artefice e persuaderlo che, a rinchiudere gli <lb/>orologi, non si otteneva l'intento, perch&egrave; non l&igrave; consisteva la causa delle <pb xlink:href="020/01/356.jpg" pagenum="337"/>variazioni, ma negli effetti del calore, il quale passa attraverso alle pareti <lb/>pi&ugrave; ben chiuse, e ben custodite. </s>

<s>Ond'&egrave; che sarebbesi dovuto rivolgere ogni <lb/>studio a trovarci quel rimedio, rendendo ai pendoli le lunghezze inalterate, <lb/>nelle vicende inevitabili ora de'caldi ora de'freddi. </s>

<s>Prima per&ograve; di giungere <lb/>a tanto, dovette l'Orologeria fare altri progressi. </s></p><p type="main">

<s>Il pendolo rendeva l'Orologio male atto a trasportarsi, e sempre lo te&shy;<lb/>neva in pericolo sui navigli ondeggianti. </s>

<s>Il bilanciere, antico regolatore del <lb/>tempo negli Orologi, soccorse, bench&egrave; tardi, utilissimo a risolvere con fa&shy;<lb/>cilit&agrave; il nuovo e importante problema. </s>

<s>E perch&egrave; l'andare e il ritornare di <lb/>una molla elastica si fa presso a poco in tempi uguali, come l'andare e il <lb/>ritornar di una sfera pendula, bast&ograve; applicare al bilanciere antico una sot&shy;<lb/>tile e delicata molla avvolta a spira, per ottener gli orologi portatili, o come <lb/>si dice, da tasca. </s></p><p type="main">

<s>L'Huyghens cos&igrave; svela il segreto dell'artificiosa macchinetta, della quale <lb/>s'attribuisce altres&igrave; l'invenzione: &ldquo; Arcanum inventionis consistit in pinna <lb/>quadam spirali, quae altera sui extremitate interiore affixa est hastae ani&shy;<lb/>mulae seu rastri aequilibris (<emph type="italics"/>bilanciere<emph.end type="italics"/>) sed maioris ac ponderosioris quam <lb/>pro solito, ac supra suos cardines ultro citroque mobilis: altera vero extre&shy;<lb/>mitate cohaeret particulae cuidam supra Horologii superius tegmen eminenti: <lb/>quaeque vibrato semel Horologii libramento spiras suas alternis comprimit <lb/>ac relaxat, ac accedente sibi parvulo adiumento ab Horologii rotis veniente, <lb/>rastri seu aequilibri motum conservat, ita quidem, ut licet maiores aut mi&shy;<lb/>nores faciat excursus, eius reciprocationes tamen una alteri sint tempore <lb/>prorsus aequales &rdquo; (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>1724, pag. </s>

<s>254). </s></p><p type="main">

<s>Gl'Inglesi per&ograve; contendono all'Olandese una s&igrave; bella e utile invenzione, <lb/>ma perch&egrave; non appartiene a noi il decider la controversia, basti il ricor&shy;<lb/>dare come Lorenzo Magalotti, il d&igrave; primo di Marzo del 1668 si trov&ograve; pre&shy;<lb/>sente all'adunanza della Societ&agrave; Reale di Londra, invitatovi dall'Oldembourg <lb/>segretario di essa. </s>

<s>Ivi, fra le altre cose, dice di aver veduto &ldquo; una mostra <lb/>da portare in tasca con una nuova invenzione di pendolo, ch'io chiamerei <lb/>piuttosto una mostra con la falsaredine, essendo regolato il tempo da una <lb/>piccola minugia temperata a uso di molla, la quale da una delle sue estre&shy;<lb/>mit&agrave; &egrave; attaccata al tempo, e dall'altra &egrave; raccomandata al tamburo dell'oriolo. </s>

<s><lb/>Quell&agrave; dunque opera s&igrave;, che le corse e le ricorse del tempo son sempre <lb/>uguali, e se qualche irregolarit&agrave; della ruota dentata lo trasportasse di van&shy;<lb/>taggio, la minugia lo tiene in briglia, obbligandolo a far sempre la stessa <lb/>gita &rdquo; (Fabbroni, Lett. </s>

<s>I, 300). </s></p><p type="main">

<s>In questi Orologi fu notata anche un'altra curiosit&agrave;, ed era che, men&shy;<lb/>tre a tenerli attaccati si movevano regolarmente, portandoli in tasca il loro <lb/>moto si alterava, e si dovettero accorger di pi&ugrave; niente altro esser cagione <lb/>di ci&ograve;, se non che il calore proprio della persona. </s>

<s>Non essendosi per&ograve; an&shy;<lb/>cora indovinati i veri effetti che produceva il calore, andavasi dicendo che <lb/>egli alterava la tempera della molla, la quale, divenuta pi&ugrave; dolce, lasciava <lb/>correre il tempo con pi&ugrave; libert&agrave;. </s>

<s>Ecco le parole proprie del Magalotti: &ldquo; Di-<pb xlink:href="020/01/357.jpg" pagenum="338"/>cono che a tenerlo attaccato l'invenzione operi bene il suo effetto, e che <lb/>corregga gli errori delle ruote, non meno del pendolo, ma che a portarlo <lb/>in tasca, a misura del calore ch'ei sente, s'alteri la tempera della molla, e <lb/>divenendo pi&ugrave; dolce lasci correre il tempo con maggior libert&agrave; &rdquo; (ivi). </s></p><p type="main">

<s>Verso la fine di quel secolo, all'ultimo, s'intese che il calore operava <lb/>in alterare il moto degli Orologi, cos&igrave; da tasca com'a pendolo, co'suoi na&shy;<lb/>turali e consueti effetti di dilatazione, e l'Harrison e altri, applicando varii <lb/>e ingegnosi <emph type="italics"/>compensatori<emph.end type="italics"/> riuscirono a costruir finalmente que'perfetti oro&shy;<lb/>logi astronomici e nautici, intorno a'quali s'erano affaticati invano fra noi <lb/>Giuseppe e Matteo Campani. </s></p>
<pb xlink:href="020/01/358.jpg"/><p type="main">

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

<s><emph type="center"/><emph type="bold"/>Dell'invenzione e della teoria del Canocchiale<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

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

<s>I. </s>

<s>Del primo inventore del Canocchiale. </s>

<s>&mdash; II. </s>

<s>Di ci&ograve; che, intorno all'invenzione dello strumento, Ga&shy;<lb/>lileo dicesse di s&egrave;, e di quel che di lui si diceva dagli altri. </s>

<s>&mdash; III. </s>

<s>Del primo concetto, e di ci&ograve; che <lb/>possa aver dato occasione al ritrovamento del Canocchiale. </s>

<s>&mdash; IV. </s>

<s>Delle prime speculazioni diot&shy;<lb/>triche intorno alla teoria del Canocchiale. </s>

<s>&mdash; V. </s>

<s>Di altre vie tentate per risolvere il problema <lb/>diottrico del Canocchiale, e come fosse finalmente risoluto dall'Huyghens; breve conclusione <lb/>delle cose fin qui discorse. </s></p><p type="main">

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

<s>Notabile &egrave; quel che Galileo racconta, nella Giornata seconda dei Due <lb/>Massimi Sistemi, di quel dottore leggente in uno studio famoso, il quale <lb/>avendo sentito descrivere il Telescopio, da lui ancora non veduto, disse che <lb/>l'invenzione era tolta da Aristotile. </s>

<s>Perci&ograve; &ldquo; fattosi portare un testo, trov&ograve; <lb/>certo luogo, dove si rende la ragione, onde avvenga che dal fondo d'un <lb/>pozzo molto cupo si possano di giorno veder le stelle in cielo, e disse ai <lb/>circostanti: Eccovi il pozzo che dinota il cannone, eccovi i vapori grossi, <lb/>dai quali &egrave; tolta l'invenzione dei cristalli, ed eccovi finalmente fortificata <lb/>la vista col passare i raggi per il diafano pi&ugrave; denso ed oscuro &rdquo; (Alb. </s>

<s>I, <lb/>pag. </s>

<s>122, 23). </s></p><p type="main">

<s>La similitudine, per chi non giudica con quella leggerezza che sogliono <lb/>alcuni, non &egrave; poi tanto strana quanto parrebbe, potendosi dir che il pozzo <lb/>fa l'ufficio del tubo, il quale senza dubbio rischiara, e perci&ograve; rischiarandoli <lb/>mostra in certo modo ingranditi gli oggetti. </s>

<s>Il fatto pu&ograve; esser con facile <lb/>esperienza osservato da tutti, imperocch&egrave; non occorre far altro che prendere <lb/>una strisciola di carta, avvolgerla intorno, in modo che se ne venga a com-<pb xlink:href="020/01/359.jpg" pagenum="340"/>porre un cannello di piccola luce, e con un occhio guardarci dentro e at&shy;<lb/>traverso un oggetto. </s>

<s>Non fa perci&ograve; maraviglia se, conosciutosi dagli antichi <lb/>un tal fatto, si servissero o di un cannellino per osservare i piccoli oggetti, <lb/>come noi ci serviamo del Microscopio, o facessero uso di un tubo pi&ugrave; lungo <lb/>per le osservazioni celesti, come noi ci serviam de'Canocchiali. </s>

<s>Di questo <lb/>tubo e de'macchinamenti annessi, per osservare e per misurare esatto il <lb/>diametro apparente del sole sull'orizzonte, si trova fatta una descrizione mi&shy;<lb/>nuta da Archimede nell'Arenario (Opera, Parisiis 1615, pag. </s>

<s>452, 53) e di <lb/>uno di questi stessi tubi, per le osservazioni celesti, sembra che si servisse, <lb/>o fu creduto almeno che si scrvisse lo stesso tolomeo, se dee darsi fede al <lb/>Mabillon, il quale dice di aver veduto nella biblioteca dell'abbadia di Scheir, <lb/>diocesi di Frisinga, una copia della Storia ecclesiastica di Pietro Comestore, <lb/>nel frontespizio della quale, essendovisi voluto personificare le arti liberali, <lb/>vi si vedeva, per l'Astronomia, rappresentato Tolomeo che osservava gli astri <lb/>coll'occhio appuntato all'estremit&agrave; di un lungo tubo, presso a poco a quel <lb/>modo, che si rappresenterebbe Galileo da un pittore moderno, in atto di ri&shy;<lb/>guardare attraverso all'oculare del suo Telescopio. </s></p><p type="main">

<s>Di qui ha avuto, senza dubbio, occasione l'errore di alcuni, un po'si&shy;<lb/>mile a quel del Dottore argutamente deriso dal Salviati, i quali, trattando <lb/>della storia delle invenzioni hanno creduto, e voluto far credere che questi <lb/>tubi o quelle <emph type="italics"/>diottre,<emph.end type="italics"/> come le chiamavan Plutarco e Strabone, non fossero <lb/>propriamente altro che Canocchiali, non molto dissimili dai moderni. </s>

<s>Una <lb/>tale erronea opinione, &egrave; notabile che fosse accolta anche da Francesco Fon&shy;<lb/>tana, celebre fabbricatore di Canocchiali, il quale scrisse: &ldquo; Antiquissimum <lb/>fuisse tubi optici usum in comperto est &rdquo; imperocch&egrave;, soggiunge, rimonta <lb/>infino a'tempi di Tolomeo che visse 130 anni prima di G. Cristo. (Novae <lb/>Observat. </s>

<s>Neap. </s>

<s>1646, pag. </s>

<s>11). Ma che quelli di Archimede, di Tolomeo o <lb/>di altri antichi non fossero veramente canocchiali, ossia tubi muniti di lenti <lb/>cristalline o di specchi metallici, se ne persuader&agrave; facilmente ciascuno che <lb/>pensi come quegli antichi cannoni aperti non prestavano altro ufficio, a quei <lb/>primi osservatori del cielo, da quello in fuori di riparar l'occhio dalle ri&shy;<lb/>flessioni irregolari, e di diriger la linea di mira, come nell'Alidada, che <lb/>s'incominci&ograve; ad usare agli strumenti geodetici, da'Geometri arabi e dagli <lb/>egiziani. </s></p><p type="main">

<s>Non &egrave; in tal proposito da passar sotto silenzio un modo proposto da <lb/>Leonardo da Vinci, per veder le cose pi&ugrave; da lontano; modo che consiste <lb/>giusto in far uso di uno di que'tubi nudi o di quelle Diottre, di cui si ser&shy;<lb/>virono gli antichi. </s>

<s>Il Venturi respigol&ograve; l'invenzione da uno de'celebri Ma&shy;<lb/>noscritti, e fu cos&igrave; la nota vinciana da lui stesso tradotta e pubblicata in <lb/>francese: &ldquo; Il est possible de faire en sorte que l'oeil voie les obiets eloi&shy;<lb/>gnes sans qu'ls souffrent toute la diminution de grandeur qui leur est cau&shy;<lb/>s&eacute;e par les loix de la vision. </s>

<s>Cette diminution provient des pyramides de <lb/>l'image des obiets qui sont coup&eacute;es a angle droit par le sphericit&eacute; de l'oeil. </s>

<s><lb/>Dans le fig. (25) on voit qui en pout couper ces pyramides d'une autre ma-<pb xlink:href="020/01/360.jpg" pagenum="341"/>niere au-devante le prunelle. </s>

<s>Il est bien vrai que le prunelle nous d&eacute;cou&shy;<lb/>vr&eacute; tout l'hemisph&egrave;re &agrave; la fois: l'artefice que j indique ne decouvrir&agrave; qu'un <lb/>astre. </s>

<s>Mais cet astre ser&agrave; grand: la Lune aussi deviendr&agrave; plus grande, et <lb/><figure id="id.020.01.360.1.jpg" xlink:href="020/01/360/1.jpg"/></s></p><p type="caption">

<s>Figura 25.<lb/>nous conno&icirc;trons mieux la figure de sas <lb/>taches &rdquo; (Essai, etc., Paris 1797, pag. </s>

<s>23). </s></p><p type="main">

<s>Il Venturi vorrebbe far credere che qui <lb/>Leonardo avesse descritto un canocchiale, <lb/>ma pure &egrave; chiaro che il modo d'avvalorar <lb/>la vista in tale vinciana invenzione &egrave; fondato <lb/>sopra un effetto ottico molto differente da <lb/>quelli soliti d'operarsi o dalle lenti cristalline o dagli specchi. </s>

<s>L'effetto ottico <lb/>ivi speculato, e l'applicazione di lui a veder, secondo Leonardo, gli oggetti pi&ugrave; <lb/>di lontano, son cose meritevolissime della nostra attenzione, riconoscendo&shy;<lb/>visi l'Autore studioso di adattare un tubo a portar lontano la luce, o, se&shy;<lb/>condo lui, le specie visibili, a quel modo che si adatta cos&igrave; efficacemente a <lb/>portar pi&ugrave; lontano i suoni. </s>

<s>Mirabile &egrave; questo inaspettato riscontro intrave&shy;<lb/>duto tra il <emph type="italics"/>Portaluce<emph.end type="italics"/> e il <emph type="italics"/>Portavoce,<emph.end type="italics"/> ma &egrave; ben pi&ugrave; mirabile che a quello <lb/>stesso riscontro vi fosse condotto Leonardo, non a caso, ma per via di re&shy;<lb/>condita scienza della natura della luce e de'suoni, e delle propriet&agrave; de'raggi <lb/>sonori; scienza ignorata in gran parte, come si dimostrer&agrave; nel progresso <lb/>della nostra Storia, dagli stessi Fisici del secolo XVII. </s>

<s>Per Leonardo tanto <lb/>la luce che i suoni si diffondono in sfere o in raggi divergenti, ed &egrave; que&shy;<lb/>sta la ragione per cui va languendo, per via delle distanze, la vivacit&agrave; <lb/>delle immagini e la intensit&agrave; delle voci. </s>

<s>Dentro i tubi i raggi lucidi e i so&shy;<lb/>nori, impediti di divergere, si mantengono paralleli e portan perci&ograve; pi&ugrave; lon&shy;<lb/>tano le specie visibili e i tremori armonici. </s>

<s>Si comprende bene che la spe&shy;<lb/>culazione del nuovo strumento ottico proposto nel Manoscritto vinciano &egrave; <lb/>fondato sopra la falsa ipotesi platonica de'raggi luminosi che si muovon dal&shy;<lb/>l'occhio di chi guarda, come i raggi sonori si muovon dalle labbra di chi <lb/>parla, ma se &egrave; vero che la luce si propaghi in onde come il suono, non vi <lb/>&egrave; dubbio che, per lo strumento e per la teoria di Leonardo, i tubi chiusi <lb/>debbono operar sulla vista qualche altro pi&ugrave; sottile e pi&ugrave; recondito effetto, <lb/>oltre i consueti assegnati dagli Ottici, che son quelli di riparar l'occhio dalla <lb/>soverchia luce diffusa, e dalle riflessioni irregolari. </s></p><p type="main">

<s>In ogni modo riman pur ancora lontana dal vero la sentenza del Ven&shy;<lb/>turi, che nel <emph type="italics"/>Portaluce<emph.end type="italics"/> di Leonardo da Vinci vorrebbe veder descritto uno <lb/>de'canocchiali moderni, essendo tutti gli scrittori concordi in affermare che <lb/>l'invenzione di cos&igrave; utile strumento non occorse prima che al cominciar del <lb/>secolo XVII Cercar chi ne fosse primo Autore e come vi riuscisse, &egrave; im&shy;<lb/>presa vana, perch&egrave; segue delle invenzioni quel che segue dell'erbe, le quali <lb/>avendo i germi piccoli e sotto terra, non se ne conoscon le virt&ugrave; n&egrave; se ne <lb/>sanno i nomi, se non dappoich&egrave; sono uscite fuori e hanno aperte le foglie <lb/>all'aria. </s>

<s>Pure, non son mancati alcuni, i quali hanno preteso di saper la <lb/>prima origine e il nome dell'inventore del Canocchiale e ne hanno compo-<pb xlink:href="020/01/361.jpg" pagenum="342"/>ste storie, che vanno attorno, ne'loro libri, stampate, il contenuto delle quali <lb/>non &egrave; permesso al nostro ufficio di lasciar senza rammemorarlo ai nostri <lb/>Lettori. </s></p><p type="main">

<s>Ci si appresenta per primo Girolamo Sirturo, il quale scrivendo, in sog&shy;<lb/>getto proprio del Telescopio, un Trattato, incomincia dal far la storia del&shy;<lb/>l'invenzione, che noi porgiamo cos&igrave; tradotta dal latino. </s></p><p type="main">

<s>&ldquo; Comparve nel 1609 un genio o che altro si fosse, di nazione olandese, <lb/>il quale capit&ograve; in Middelburgo, citt&agrave; della Zelanda, alla bottega di Giovanni <lb/>Lipperseim, unico artefice di occhiali che si ritrovasse allora in quella citt&agrave;. </s>

<s><lb/>Quell'olandese ordin&ograve; all'occhialaio alcuni vetri, cos&igrave; concavi come convessi, <lb/>e il d&igrave; stabilito torn&ograve; per veder se il lavoro era fatto. </s>

<s>L'occhialaio allora <lb/>present&ograve; i vetri bell'e fatti a quell'uomo, che si mise a specularli attraverso <lb/>alla mira dell'occhio, ora avvicinandoli ora dilungandoli, o ci&ograve; egli facesse <lb/>per far prova della bont&agrave; del lavoro, o per trovare il giusto punto del con&shy;<lb/>corso. </s>

<s>Cos&igrave; fatto, pag&ograve; l'artefice e se ne and&ograve;. </s>

<s>Ma quell'artefice stesso, che <lb/>era d'ingegno acuto e molto curioso di novit&agrave;, incominci&ograve; a imitare il giuoco <lb/>veduto fare a quell'uomo, e cos&igrave; gli occorse, nello speculare attraverso a <lb/>que'vetri concavi e convessi, di vedere gli oggetti ingranditi, per cui pens&ograve; <lb/>di sostenerli congiunti insieme per mezzo di un tubo. </s>

<s>Cos&igrave; vennegli fatto il <lb/>primo Telescopio che vol&ograve; subito a mostrarlo al principe Maurizio. </s>

<s>Il Prin&shy;<lb/>cipe, o l'avesse veduto prima o no, pens&ograve; subito di servirsene agli usi della <lb/>milizia, per cui voleva tenere la cosa occulta, ma divulgatasi comunque si <lb/>fosse, si presero a fare di simili altri strumenti, bench&egrave;, come questo pre&shy;<lb/>sentato al principe Maurizio, non fossero riusciti cos&igrave; perfetti. </s>

<s>Dicevasi che <lb/>in antico non fosse questa invenzione conosciuta da nessuno, e che comin&shy;<lb/>ciasse allora, ma pure il Porta ne aveva fatto un cenno nel suo libro della <lb/><emph type="italics"/>Magia,<emph.end type="italics"/> ed era opinione di molti, che ne discorrevano alla mia presenza, non <lb/>esser molto difficile a chi avesse qualche po'd'ingegno, udito il fatto, imi&shy;<lb/>tarlo. </s>

<s>Concorsero molti attratti dalla cupidit&agrave; del guadagno, cos&igrave; Belgi che <lb/>Francesi e Italiani, e tutti se ne spacciavano inventori. </s>

<s>Nel mese di Maggio <lb/>capit&ograve; in Milano un Francese che present&ograve; uno di cos&igrave; fatti Telescopi al <lb/>conte De Fuentes, dicendo esser socio d'industria di un Olandese, che della <lb/>costruzione dello strumento era stato primo autore. </s>

<s>Avendolo il Conte dato <lb/>a un orefice perch&egrave; legasse quelle lenti in un tubo di argento, venne cos&igrave; <lb/>per caso a capitare alle mie mani: lo smontai, lo esaminai e mi detti a <lb/>fabbricarne di simili &rdquo; (Telescop. </s>

<s>P. I, Cap. </s>

<s>I, Francof. </s>

<s>1618, pag. </s>

<s>23, 24). </s></p><p type="main">

<s>Si vede che al Tarde non era ancora capitato in mano questo libro del <lb/>nostro Milanese quando nella <emph type="italics"/>Borbonia Sidera,<emph.end type="italics"/> libro stampato in Parigi <lb/>nel 1620, scriveva: &ldquo; Miror ego neminem adhuc quem viderim, huius tubi <lb/>Dioptrici inventoris nomen in publicum edidisse, nec modum quo in inve&shy;<lb/>niendo usus est docuisse. </s>

<s>Meretur enim nobilitate decorari et laudibus or&shy;<lb/>nari, qui sensum omnium nobilissimum docuit ita iuvari &rdquo; (ibi, pag. </s>

<s>85). </s></p><p type="main">

<s>A sodisfar poi meglio ai generosi desiderii del Tarde soccorse il Rheita, <lb/>il quale narra come Giovanni Lippens, occhialaio di Zelanda, s'abbattesse <pb xlink:href="020/01/362.jpg" pagenum="343"/>per caso a trovar che due lenti, una concava e una convessa, congiunte in&shy;<lb/>sieme ingrandivano gli oggetti traguardati. </s>

<s>Di qui fu condotto all'invenzione <lb/>del primo Telescopio, il quale, essendo stato comprato dal marchese Spi&shy;<lb/>nola, che allora soggiornava all'Aja, fu da lui stesso poi regalato all'arci&shy;<lb/>duca Alberto di Brabante. (Oculus. </s>

<s>Enoch et Eliae, lib. </s>

<s>IV, Antuerpiae 1645). </s></p><p type="main">

<s>Ma a ricercare il nome di s&igrave; benemerito inventore si dette pi&ugrave; di pro&shy;<lb/>posito Pietro Borel, il quale ne scrisse un libro stampato all'Aja nel 1655. <lb/>Egli dunque, nel capitolo XII di quello stesso libro che s'intitola <emph type="italics"/>De vero <lb/>Telescopii inventore,<emph.end type="italics"/> dopo varii esami, per verit&agrave; non di grande importanza, <lb/>conclude che il primo inventore del Telescopio fu Zaccaria Jansen di Middel&shy;<lb/>burgo, il quale fece nel 1590 l'esperienza de'vetri concavi e de'convessi, <lb/>non a caso, come dicono molti, ma ad arte, e applic&ograve; quella stessa espe&shy;<lb/>rienza alle osservazioni del cielo, scoprendo altre nuove stelle nell'Orsa mag&shy;<lb/>giore. </s>

<s>Lo strumento cos&igrave; felicemente inventato fu dall'inventore medesimo <lb/>offerto in dono al principe Maurizio, e un altro simile fu donato pure al&shy;<lb/>l'arciduca Alberto. </s>

<s>Il secondo inventore, pur esso middelburgese, soggiunge <lb/>ivi il Borel, essere stato Hans, ossia Giovanni Lipperehy, a cui, capitata a <lb/>caso quella prima invenzione di Zaccaria, si dee l'averla condotta a mag&shy;<lb/>gior perfezione. </s></p><p type="main">

<s>Abbiamo udito il Borel francamente affermare che la maravigliosa in&shy;<lb/>venzione non fu fatta a caso, ma ad arte, ci&ograve; che verrebbe a confermare <lb/>storicamente l'opinione del Tarde, il quale, dopo aver riprovata la sentenza <lb/>di coloro che fanno intervenir la fortuna come se da lei sola avesse rice&shy;<lb/>vuto il mondo il benefizio del Canocchiale; cos&igrave; tosto soggiunge: &ldquo; Ego vero <lb/>qui nobiliori quodam modo hoc accidisse existimo, cum accuratius rem con&shy;<lb/>sidero et diligentiori studio meditor, a viro optices peritissimo, non casu <lb/>sed arte, et exacta quadam ac diligenti investigatione inventum iudico. </s>

<s>Hic <lb/>enim cum novisset lentem convexam nimis augere visibilia, si remota sint, <lb/>et cavam nimis imminuere, ob contrarias radiorum fractiones, in mentem <lb/>revocavit Fhilosophiae decretum quo asseritur contrar&igrave;a contrariis pelli vel <lb/>saltem emendari; excogitavit periculum facere num quaedam lentium com&shy;<lb/>positio, aut radiorum utraque lente refractorum proportio invenire posset, <lb/>qua diversae hae refractiones, variaeque radiorum flectiones sese invicem <lb/>emendarent &rdquo; (Loc. </s>

<s>cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Ma pure, anco di quest'altro desiderio il Tarde era stato di gi&agrave; sodi&shy;<lb/>sfatto, da chi facendo intervenir nel fatto di questa invenzione la scienza <lb/>piuttosto che il caso, aveva di quella stessa scienza additati i principii diot&shy;<lb/>trici, e gli Autori che furon primi a insegnarli. </s>

<s>Giulio Cesare La Galla, pe&shy;<lb/>ripatetico, ma pi&ugrave; dotto degli altri suoi Colleghi, nella sua prima Disserta&shy;<lb/>zione <emph type="italics"/>De phaenomenis in orbe Lunae,<emph.end type="italics"/> al cap. </s>

<s>V ha le seguenti parole che <lb/>noi liberamente cos&igrave; traduciamo dal latino: </s></p><p type="main">

<s>&ldquo; Fu di questa invenzione, per consenso di tutti, e per particolar te&shy;<lb/>stimonianza di Giovanni Keplero, matematico chiarissimo, autore il napole&shy;<lb/>tano Giovan Batista della Porta, gentiluomo dottissimo e solerte indagatore <pb xlink:href="020/01/363.jpg" pagenum="344"/>degli arcani della Natura, il quale nel XVII Libro della sua <emph type="italics"/>Magia Natu&shy;<lb/>rale,<emph.end type="italics"/> capitolo X e XI, dette fuori da scienziato l'invenzione di questo am&shy;<lb/>mirabile strumento. </s>

<s>Dissi da scienziato, perch&egrave; settant'anni prima Girolamo <lb/>Fracastoro ne aveva fatto qualche cenno confuso nel cap. </s>

<s>VIII de'suoi Omo&shy;<lb/>centrici, con queste parole: <emph type="italics"/>Qua de causa in eadem aqua, quae in summo <lb/>cernuntur minora apparent, quae in fundo maiora, et per duo specilla <lb/>ocularia, si quis perspiciat, altero alteri superposito, maiora multo et pro&shy;<lb/>prinquiora vibebit omnia.<emph.end type="italics"/> Ma qui il Fracastoro non accenna distintamente <lb/>alla fabbrica dello strumento che ingrandisce e avvicina gli oggetti, n&egrave; pur <lb/>ne dice qual ne sia la ragione, ci&ograve; che fu fatto in bel modo dal Porta nel <lb/>descriver l'uso delle lenti cristalline, le quali composte giudiziosamente in&shy;<lb/>sieme e moltiplicate, possono trasportar, ci&ograve; che sembra impossibile, la virt&ugrave; <lb/>visiva per spazio immenso e grandissimamente accrescer le specie delle cose. </s>

<s><lb/>Ma perch&egrave; egli non messe in pratica questa sua teoria, o se la messe, non <lb/>si cur&ograve; di renderla pubblicamente nota, pochi auni or sono se ne vide fatta <lb/>l'applicazione nel Belgio a uno strumento, per dir la verit&agrave; assai rozzo e <lb/>imperfetto, a cui poi da Galileo, celebre matematico dello Studio di Padova, <lb/>fu data l'ultima mano, e con esso, accomodato agli usi astronomici, fece <lb/>maravigliose scoperte nel cielo &rdquo; (Gal. </s>

<s>Op. </s>

<s>Alb. </s>

<s>T. III, pag. </s>

<s>253, 54). </s></p><p type="main">

<s>L'Autorit&agrave; del Kepler, invocata di sopra dal La Galla, a proposito di <lb/>ci&ograve; che tocca al Porta del merito dell'invenzione, &egrave; di tal rilievo, che non <lb/>si pu&ograve; da noi trascurare, e perci&ograve;, dalla <emph type="italics"/>Dissertazione sul Nunzio Sidereo,<emph.end type="italics"/><lb/>trascriveremo tradotte dal latino le sue proprie parole. </s>

<s>Dop'aver dunque <lb/>ivi il Kepler accennato alle grandi meraviglie mostrate dal canocchiale, cos&igrave; <lb/>prosegue: </s></p><p type="main">

<s>&ldquo; Sembra incredibile a molti l'uso e l'effetto di questo occhiale, ma <lb/>impossibile e nuovo non &egrave;, n&egrave; ci venne poco fa dal Belgio, ma fu tanti anni <lb/>prima messo fuori da Giovan Batista della Porta, nel XVII libro, cap. </s>

<s>X <lb/>della <emph type="italics"/>Magia Naturale,<emph.end type="italics"/> dove tratta degli effetti delle lenti cristalline. </s>

<s>E per&shy;<lb/>ch&egrave; apparisca chiaro non esser nuova nemmeno la composizione delle due <lb/>lenti, una delle quali concava e l'altra convessa, permettimi, o Galileo, che <lb/>io ti rechi innanzi le parole stesse del Porta, le quali suonano a questo modo: <lb/><emph type="italics"/>Posto l'occhio nel centro dietro la lente, vedrai gli oggetti lontani fartisi <lb/>cos&igrave; vicini, che ti sembrer&agrave; di toccarli, e cos&igrave; potrai riconoscere gli amici <lb/>lontani, e potrai correntemente leggere una lettera collocata a conveniente <lb/>distanza. </s>

<s>Se tu inclinerai la lente in modo che ti si debba il foglio rap&shy;<lb/>presentare obliquo, vedrai farsi le lettere tanto maggiori, che tu potrai <lb/>leggerle anco alla distanza d'una ventina di passi, e se tu avrai cura ed <lb/>arte di moltiplicar quelle lenti, non temo d'affermar che tu potrai di&shy;<lb/>stinguere le piccole lettere scritte anche a un cento di passi, &iuml;mperocch&egrave; <lb/>i caratteri s'ingrandiscono via via sempre pi&ugrave;, passando attraverso dalla <lb/>prima alla seconda lente. </s>

<s>Chi ha difetto di occhi scelga secondo la qua&shy;<lb/>lit&agrave; della vista, e faccia variamente uso di questi occhiali: avr&agrave; scoperto <lb/>non piccolo segreto se giudiziosamente <gap/><emph.end type="italics"/><pb xlink:href="020/01/364.jpg" pagenum="345"/><emph type="italics"/>cave mostrano chiarissime le cose lontane, e le convesse chiarissime fanno <lb/>veder piuttosto le cose vicine, cosicch&egrave; ognuno potr&agrave;, secondo il bisogno <lb/>o la comodit&agrave; della sua vista, servirsi ora delle une ora delle altre. </s>

<s>Con <lb/>una lente concava vedrai gli oggetti impiccoliti e lontani, ma distinti; <lb/>con una convessa invece pi&ugrave; vicini e maggiori, ma un poco annebbiati. </s>

<s><lb/>Che se saprai, con discrezione, comporre insieme l'una lente concava col&shy;<lb/>l'altra convessa, vedrai chiari e distinti tutti gli oggetti, cos&igrave; vicini come <lb/>lontani. </s>

<s>Io con tale arte ho potuto recar non poco giovamento agli amici, <lb/>che vedevano abbacinati gli oggetti lontani, e velati di nebbia i pi&ugrave; vi&shy;<lb/>cini, facendo in modo che discernessero poi sempre bene cos&igrave; questi come <lb/>quelli. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nel Cap. </s>

<s>XI tratta il Porta di quegli occhiali, con cui si posson ve&shy;<lb/>dere le cose tanto lontane da vincere la stessa immaginativa, ma la dimo&shy;<lb/>strazione, ad arte, come l'Autore da s&egrave; stesso confessa, &egrave; s&igrave; involuta, che <lb/>non ti sai raccapezzar se egli intenda solo delle lenti di rifrangenza o delle <lb/>lenti combinate agli specchi. </s>

<s>Avendo io letto in questa parte del libro che <lb/>la ragione del vario operar delle lenti concave e delle convesse non era data <lb/>ancora da nessuno, mi ci volli provare, e sei anni or sono, nella parte Ot&shy;<lb/>tica della mia Astronomia, divisai quel che accade nelle semplici lenti. </s>

<s>Tu <lb/>potresti vederlo ivi al capitolo V dove dimostro quelle cose che apparten&shy;<lb/>gono al modo del vedere, e dove al foglio 202 &egrave; disegnata la figura di un <lb/>concavo e di un convesso, a quel modo che si soglion ne'tubi congiungere <lb/>insieme quelle due lenti. </s>

<s>Che se non dette occasione all'invenzione di que&shy;<lb/>sto strumento la lettura del libro del Porta, e l'istruzione che forse il Porta <lb/>stesso dette familiarmente conversando con qualche Belga, il quale, giovan&shy;<lb/>dosi de'silenzii del sepolcro, riusc&igrave; a spacciarlo per cosa sua; poteva senza <lb/>dubbio la figura impressa nel mio libro fare avvertito il lettore della strut&shy;<lb/>tura e composizione dello strumento &rdquo; (Gal. </s>

<s>Op. </s>

<s>Alb. </s>

<s>V, 410-12). </s></p><p type="main">

<s>Ma come in sintesi raccolte e con fino criterio sceverate le varie sen&shy;<lb/>tenze storiche da'varii scrittori sopra esposte, si possono veder nell'Huy&shy;<lb/>ghens, l&agrave; dove, nella <emph type="italics"/>Diottrica,<emph.end type="italics"/> si dispone a trattar de'Telescopii. </s>

<s>&ldquo; Sunt <lb/>qui inventionis, egli scrive, sed ut dixi, fortuitae, primae laudem Jacobo <lb/>Metio Batavo Alcmariae civi tribuant. </s>

<s>Mihi vero certo compertum est ante <lb/>ipsum Telescopia fabricasse Artificem quendam Medioburgensem, apud Se&shy;<lb/>landos, circa annum huius saeculi nonum, sive is fuerit cuius Sirturus <lb/>meminit Joh. </s>

<s>Lippersheim nomine, sive cui Borellus in libello <emph type="italics"/>De vero Te&shy;<lb/>lescopii inventore,<emph.end type="italics"/> primas defert, Zacharias. </s>

<s>Hi tunc non maiores sesquipe&shy;<lb/>dalibus tubos factitabant. </s>

<s>Utroque vero multo prior rudimenta artis tradi&shy;<lb/>derat Joh. </s>

<s>Bapt. </s>

<s>Porta Neapolitanus, cuius extant de rebus Dioptricis et <lb/>Magia Naturali libri, totis 15 annis ante editi quam in Belgio nostro exo&shy;<lb/>rirentur. </s>

<s>In quibus libris de Specillis, ut vocat, suis, memorat res procul <lb/>positas quasi proprinquae essent ostendentibus, deque coniunctione cavarum <lb/>et convexarum lentium. </s>

<s>Nihil tamen magnopere eum profecisse, hoc ipsum <lb/>probat quod tanto tempore ars iam coepta non ultra inclaruit, neque ipse <pb xlink:href="020/01/365.jpg" pagenum="346"/>Porta quidquam in coelo observavit eorum quae postea apparuerunt. </s>

<s>Hoc <lb/>inde est quod casui fortuitisque experimentis originem inventi debere constat. </s>

<s><lb/>Neque enim hic vir licet Mathematicarum aliquatenus gnarus reconditas ra&shy;<lb/>tiones, quibus ars ea pro fundamentis utitur, comprehenderat ut medita&shy;<lb/>tione eam eruere posset, multoque minus illi, quos ante memoravi, homi&shy;<lb/>nes opifices ac scientiarum rudes. </s>

<s>Fortuna vero et casu eodem perventum <lb/>nihil mirum est, cum frequens usus esset, iam a trecentis atque amplius <lb/>annis utriusque generis lentium, quibus seorsim adhibitis vitia oculorum <lb/>emendantur. </s>

<s>Ut potius mirandum sit tamdiu rem obviam latuisse. </s>

<s>Ceterum <lb/>ut primum Teloscopiorum Belgicorum fama sparsa erat continuo Galileus <lb/>similia illis, ac brevi multo praestantiora effecit, quibus celeberrima illa coeli <lb/>phaenomena omnium primus intuitus est &rdquo; (Lugduni Batav. </s>

<s>1703, pag. </s>

<s>163, 64). </s></p><p type="main">

<s>Le autorit&agrave; del Keplero e dell'Huyghens concordi in ammetter probabi&shy;<lb/>lissimo che l'invenzione del Telescopio fosse stata inspirata a qualche ottico <lb/>dalla lettura della <emph type="italics"/>Magia Naturale,<emph.end type="italics"/> son di gran momento in dover aggiu&shy;<lb/>dicare al Porta i primi meriti contesigli con pi&ugrave; ardore da'seguaci di Gali&shy;<lb/>leo che dagli stessi stranieri. </s>

<s>&Egrave; perci&ograve; che su que'due soggetti particolar&shy;<lb/>mente, su Galileo cio&egrave; e sul Porta, viene ora a indirizzarsi il filo del nostro <lb/>discorso. </s></p><p type="main">

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

<s>A chi conosce oramai l'indole e quel passionato ardore che trasportava <lb/>Galileo a voler essere ed apparire il solo e il primo in tutte quante le cose, <lb/>non far&agrave; maraviglia che egli si studiasse, con le arguzie dell'ingegno e col <lb/>fascino dell'eloquenza, d'ingerir nella comune opinione giudizi tutto affatto <lb/>diversi da quelli del Kepler, dell'Huyghens e degli altri sopra citati, che le <lb/>prime parti nell'invenzione del canocchiale attribuiscono al Porta. </s>

<s>Di quelle <lb/>arguzie incominci&ograve; a fare studio il Conquistatore ambizioso infino dal primo <lb/>apparire del Nunzio Sidereo, in cui, confessando di avere avuto una vaga <lb/>notizia dell'invenzione, afferma che dietro quella ritrov&ograve;, nella sua propria <lb/>scienza delle rifrazioni, <emph type="italics"/>doctrinae de refractionibus innixus,<emph.end type="italics"/> la fabbrica dello <lb/>strumento. </s>

<s>Il Keplero per&ograve; gli opponeva che quella dottrina delle rifrazioni, <lb/>la quale sarebbe sola potuta bastar cos&igrave; a lui come all'occhialaio belga, per <lb/>riuscire alla composizione delle due lenti da veder le cose lontane; era stata <lb/>scritta prima e poteva averla ognuno pubblicamente letta nella Magia Na&shy;<lb/>turale e nei Paralipomeni a Vitellione. </s></p><p type="main">

<s>Galileo non si sarebbe aspettato che le franche parole del Matematico <lb/>alemanno fossero venute cos&igrave; presto a rintuzzare le sue pretese, ma non si <lb/>scor&ograve; per questo, n&egrave; lasciava occasione di confermar nella stima degli amici <lb/>a cui scriveva, o de'signori con cui trattava, che il Canocchiale inventato <lb/>era parto della scienza diottrica della sua mente. </s>

<s>Alla Signoria di Venezia <pb xlink:href="020/01/366.jpg" pagenum="347"/>scriveva dello stesso Canocchiale di averlo <emph type="italics"/>cavato dalle pi&ugrave; recondite spe&shy;<lb/>culazioni di Prospettiva<emph.end type="italics"/> (Venturi, Memor., Modena 1818, P. I, pag. </s>

<s>81) e <lb/>si difendeva appresso mons. </s>

<s>Piero Dini, contro l'imputazion di coloro che <lb/>dicevano il Canocchiale non mostrar altro che ingannevoli apparenze, affer&shy;<lb/>mando che della verit&agrave; mostrata dallo strumento nessun altro poteva esser <lb/>miglior giudice di lui, che era intendente dell'arte, da cui il modo di ope&shy;<lb/>rar dello strumento stesso dipende, <emph type="italics"/>sapendosi che la fabbrica e la teorica <lb/>di questo occhiale dipende dalla cognizione delle rifrazioni, che &egrave; parte <lb/>delle scienze matematiche mia particolar professione<emph.end type="italics"/> (Alb. </s>

<s>VI, 164). N&egrave; <lb/>in altri termini diversi da quelli con cui s'era espresso nel Nunzio Sidereo, <lb/>prima che venisse il Kepler ad amareggiargli le compiacenze dell'animo, con <lb/>lo squadernargli sotto gli occhi il XVII libro della Magia, e il cap. </s>

<s>V della <lb/>sua Ottica astronomica; scriveva Galileo il d&igrave; 29 Agosto 1609 a Benedetto <lb/>Landucci: &ldquo; Dovete dunque sapere che sono circa a due mesi che qua fu <lb/>sparsa fama, che in Fiandra era stato presentato al conte Maurizio un <lb/>Occhiale fabbricato con tale artifizio che le cose molto lontane le faceva ve&shy;<lb/>der come vicinissime, sicch&egrave; un uomo per la distanza di due miglia si po&shy;<lb/>teva distintamente vedere. </s>

<s>Questo mi parve effetto tanto maraviglioso che <lb/>mi dette occasione di pensarvi sopra, e parendomi che dovesse avere fon&shy;<lb/>damento nella Scienza di Prospettiva, mi messi a pensare sopra la sua fab&shy;<lb/>brica, la quale finalmente ritrovai cos&igrave; perfettamente, che uno che ne ho <lb/>fabbricato supera di assai la fama di quello di Fiandra &rdquo; (Alb. </s>

<s>VI, 75, 76). </s></p><p type="main">

<s>Cos&igrave;, mentre da una parte provvedeva Galileo, con sollecita accortezza, <lb/>a ingerir nell'animo degli amici la stima di s&egrave;, studiavasi dall'altra di av&shy;<lb/>vilire il suo rivale. </s>

<s>Gli trasparisce viva sul volto la compiacenza in leggere <lb/>queste parole che Martino Hasdale scrivevagli da quella stessa citt&agrave; di Praga, <lb/>d'onde, a ferirlo, il Kepler gli avea scoccato le saette acute: &ldquo; Per&ograve; l'altra <lb/>sera cenando io seco (col Wacker amico del Keplero) insiem con altri, avemmo <lb/>contesa sopra chi fosse stato il primo inventore di questo strumento, vo&shy;<lb/>lendo egli sostenere che Giovanni della Porta avesse detto strumento, con <lb/>il quale Porta dice di avere egli parlato quattro volte e che l'aveva trovato <lb/>uomo singolarissimo, nonostante che io dicessi tutto il contrario, sforzandomi <lb/>di convincerlo con infinite tare che so contro il Porta, il quale non inten&shy;<lb/>deva molti capitoli della sua Magia, n&egrave; manco la sapeva spiegare in volgare, <lb/>scusandosi che erano tutte cose avute da altri, cos&igrave; scritte in latino come <lb/>stavano stampate nel suo libro &rdquo; (Alb. </s>

<s>VIII, 83, 84). </s></p><p type="main">

<s>Queste contese fra il Wacker e l'Hasdale erano fra amici e muovevano <lb/>in questo, dall'ammirazione che sentiva per Galileo, in quello, da pi&ugrave; retto <lb/>e imparziale giudizio informato alla lettura del libro del Porta. </s>

<s>In ogni modo <lb/>per&ograve; n&egrave; il Wacker n&egrave; il Kepler erano, in assegnar la giusta parte del me&shy;<lb/>rito al Fisico napoletano, trasportati o da odio o da invidiosa rivalit&agrave; o da <lb/>altra inimicizia, che avessero contro Galileo, il quale perci&ograve; sentiva l'ama&shy;<lb/>rezza de'giudizi in qualche modo addolcita dalla sincerit&agrave; de'giudici e da <lb/>una certa benevolenza. </s></p><pb xlink:href="020/01/367.jpg" pagenum="348"/><p type="main">

<s>Ma non tutti erano a questo modo benevoli: le glorie e i trionfi della <lb/>scoperta che apparivano a tutti maravigliose, avevan suscitato gi&agrave; contro Ga&shy;<lb/>lileo inimici invidiosi, i quali raccogliendo gli strali caduti di mano al Ke&shy;<lb/>plero gli venivano avventando, con pi&ugrave; insano furore, contro chi sapevano <lb/>di poter coglier nel vivo. </s>

<s>Uno de'pi&ugrave; ardenti fra questi saettatori fu quel <lb/>padre Orazio Grassi, che, mascherato sotto il nome di Lotario Sarsi, ebbe <lb/>questione intorno alla natura delle Comete, e ad altre cose accessorie, con <lb/>l'Autor del <emph type="italics"/>Saggiatore.<emph.end type="italics"/> Il Sarsi dunque, a proposito del Canocchiale, diceva <lb/>che il nuovo strumento era <emph type="italics"/>allievo<emph.end type="italics"/> di Galileo e non <emph type="italics"/>figliolo.<emph.end type="italics"/> Galileo, dal&shy;<lb/>l'altra parte, che sentiva quelle parole uscir dalle labbra del gesuita asperse <lb/>di veleno, dette mano a pi&ugrave; sottili arguzie e pi&ugrave; gagliardo fiato alla sua elo&shy;<lb/>quenza, per convincer di falso l'asserto altrui, e per ammannir nuovi colori <lb/>da far pigliare aspetto di vero alle sue stesse finzioni. </s></p><p type="main">

<s>&ldquo; Qual parte io abbia, scriveva, nel ritrovamento di questo strumento, <lb/>e s'io lo possa ragionevolmente nominar mio parto, l'ho gran tempo fa ma&shy;<lb/>nifestato nel mio Avviso Sidereo, scrivendo come in Venezia, dove allora mi <lb/>ritrovava, giunsero nuove come al sig. </s>

<s>conte Maurizio era stato presentato <lb/>da un Olandese un occhiale, col quale le cose lontane si vedevano cos&igrave; per&shy;<lb/>fettamente come se fossero state molto vicine, n&egrave; pi&ugrave; fu aggiunto. </s>

<s>Su que&shy;<lb/>sta relazione io tornai a Padova, dove allora stanziava, e mi posi a pensar <lb/>sopra tal problema, e la prima notte dopo il mio ritorno lo ritrovai, ed il <lb/>giorno seguente fabbricai lo strumento &rdquo; (Alb. </s>

<s>IV, 26, 7). </s></p><p type="main">

<s>Una tal prontezza e facilit&agrave; di esecuzione poteva ingerir qualche so&shy;<lb/>spetto che la cosa fosse in s&egrave; ovvia, e che la facilit&agrave; di risolvere il problema <lb/>consistesse nell'avere avuto gi&agrave; prima notizia dell'enunciato dello stesso pro&shy;<lb/>blema, per cui Galileo, a superesaltare il merito della sua invenzione, &egrave; sol&shy;<lb/>lecito di rimuover dagli animi quel sospetto, dimostrando che quella stessa <lb/>creduta facilit&agrave; induce anzi, in eseguir l'opera, una certa difficolt&agrave; maggiore. </s>

<s><lb/>Ripigliando perci&ograve; il costrutto lasciato pi&ugrave; sopra interrotto, cos&igrave; soggiunge: </s></p><p type="main">

<s>&ldquo; Ma forse alcuno mi potrebbe dire che di non piccolo aiuto &egrave; al ri&shy;<lb/>trovamento e risoluzion di alcun problema l'esser prima in qualche modo <lb/>renduto consapevole della verit&agrave; della conclusione, e sicuro di non cercar <lb/>l'impossibile, e che perci&ograve; l'avviso e la certezza che l'Occhiale era di gi&agrave; <lb/>stato fatto, mi fosse d'aiuto tale che per avventura senza quello non l'avrei <lb/>ritrovato. </s>

<s>A questo io rispondo distinguendo e dico che l'aiuto recatomi dal&shy;<lb/>l'avviso svegli&ograve; la volont&agrave; ad applicarvi il pensiero, che senza quello pu&ograve; <lb/>esser che io mai non v'avessi pensato, ma che oltre a questo tale avviso <lb/>possa agevolar l'invenzione io non lo credo, e dico di pi&ugrave; che il ritrovar <lb/>la risoluzione d'un problema pensato e nominato &egrave; opera di maggiore in&shy;<lb/>gegno assai che il ritrovarne uno non pensato n&egrave; nominato, perch&egrave; in que&shy;<lb/>sto pu&ograve; aver grandissima parte il caso, ma quello &egrave; tutto opera del di&shy;<lb/>scorso &rdquo; (ivi, pag. </s>

<s>107, 8). </s></p><p type="main">

<s>E prosegue l'Autore affermando che egli appunto, avutone il detto <lb/>avviso, ritrov&ograve; lo strumento per via di discorso. </s>

<s>Se non che l&agrave; dove avea <pb xlink:href="020/01/368.jpg" pagenum="349"/>detto ai Signori di Venezia che quel discorso si fondava sopra le <emph type="italics"/>pi&ugrave; recon&shy;<lb/>dite speculazioni di Prospettiva<emph.end type="italics"/> qui confessa che quello stesso discorso in&shy;<lb/>vece fu <emph type="italics"/>assai facile,<emph.end type="italics"/> e perch&egrave; facile torna a ripeterlo al Sarsi con le se&shy;<lb/>guenti parole: </s></p><p type="main">

<s>&ldquo; Questo artifizio o consta d'un vetro solo o di pi&ugrave; di uno: d'un <lb/>solo non pu&ograve; essere, perch&egrave; la sua figura o &egrave; convessa, cio&egrave; pi&ugrave; grossa nel <lb/>mezzo che verso gli estremi, o &egrave; concava, cio&egrave; pi&ugrave; sottile nel mezzo, o &egrave; <lb/>compresa tra superficie parallele. </s>

<s>Ma questa non altera punto gli oggetti vi&shy;<lb/>sibili col crescergli e diminuirli: la concava gli diminuisce; la convessa gli <lb/>accresce bene, ma gli mostra assai indistinti ed abbagliati; adunque un ve&shy;<lb/>tro solo non basta per produr l'effetto. </s>

<s>Passando poi a due, e sapendo che <lb/>il vetro di superficie parallele non altera niente, come si &egrave; detto, conchiusi <lb/>che l'effetto non poteva n&egrave; anco seguir dall'accoppiamento di questo con <lb/>alcuno degli altri due, onde mi ristrinsi a volere esperimentare quello che <lb/>facesse la composizione degli altri due, cio&egrave; del convesso e del concavo, e <lb/>vidi come questa mi dava l'intento, e tale fu il progresso del mio ritrova&shy;<lb/>mento &rdquo; (ivi, pag. </s>

<s>208). </s></p><p type="main">

<s>Singolar cosa &egrave; davvero questo discorso, ma &egrave; pi&ugrave; singolare che mai <lb/>il Filosofo da cui fu congegnato, il quale volendolo spacciar come specula&shy;<lb/>zione sua propria coll'intenzione di escludere ogni intervento del Porta, ri&shy;<lb/>pete a parole il discorso fatto gi&agrave; 38 anni prima e letto da tutti nel cap. </s>

<s>X <lb/>del XVII libro della Magia. </s>

<s>Chi crederebbe mai che l'ambizione avesse tanto <lb/>offuscato a Galileo l'intelletto da non renderlo accorto che quel suo discorso <lb/>era una ripetizione esatta e una traduzion fedele delle parole stesse del suo <lb/>disprezzato rivale? <emph type="italics"/>Concavo longe parva vides, sed perspicua: convexo pro&shy;<lb/>prinqua maiora, sed turbida; si utrunque recte componere noveris et lon&shy;<lb/>ginqua et proxima maiora et clara videbis<emph.end type="italics"/> (Lugd. </s>

<s>Batav. </s>

<s>1651, pag. </s>

<s>596). </s></p><p type="main">

<s>Non vi &egrave; perci&ograve; nessun lettore il quale non cominci intanto seriamente <lb/>a dubitare della sincerit&agrave; d&igrave; quelle galileiane conclusioni. </s>

<s>Il dubbio si ve&shy;<lb/>dr&agrave; poi tornare in certezza, quando dimostreremo quale imperfetta scienza <lb/>avesse Galileo delle rifrazioni, per cui lo ebbe a dir meritamente il Carte&shy;<lb/>sio <emph type="italics"/>parum in Opticis versatum.<emph.end type="italics"/> E anzi quella stessa certezza apparir&agrave; ne'giu&shy;<lb/>dizi pi&ugrave; presto, quando in questo medesimo capitolo di storia tratteremo <lb/>della teoria del Telescopio. </s>

<s>Ma di poca sincerit&agrave; e di poca fede &egrave; pure un <lb/>argomento certo l'incoerenza che si nota ne'particolari della narrazione fatta <lb/>da Galileo a varie occasioni. </s>

<s>Se il mendacio &egrave; sempre traditor di s&egrave; stesso, <lb/>si pu&ograve; dir che si tradisca anco l'Autor del Saggiatore, rimandando a ci&ograve; <lb/>che, della prima invenzione del Canocchiale, n'era stato scritto da lui stesso <lb/>nell'Annunzio Sidereo. </s></p><p type="main">

<s>Qui aveva prima narrata la cosa a questo modo: &ldquo; Mensibus adhuc <lb/>decem fere, rumor ad aures nostras increpuit fuisse a quodam Belga Perspi&shy;<lb/>cillum elaboratum cuius beneficio obiecta visibilia, licet ab oculo inspicien&shy;<lb/>tis longe dissita, veluti proprinqua cernebantur.... Idem paucos post dies <lb/>mihi per literas a nobili Gallo Jacobo Badovere ex Lutetia confirmatum est, <pb xlink:href="020/01/369.jpg" pagenum="350"/>quod tandem in causa fuit ut ad rationes inquirendas, nec non media exco&shy;<lb/>gitanda, per quae ad consimilis Organi inventionem devenirem, me totum <lb/>converterem, quam paulo post doctrinae de refractionibus innixus assequtus <lb/>sum &rdquo; (Alb. </s>

<s>III, 60). </s></p><p type="main">

<s>Quegli avverbi <emph type="italics"/>tandem<emph.end type="italics"/> e <emph type="italics"/>paulo post,<emph.end type="italics"/> che si leggon qui e quel <emph type="italics"/>final&shy;<lb/>mente<emph.end type="italics"/> uscito dalla penna di chi scrisse la sopra citata Lettera a Benedetto <lb/>Landucci, attestano espressamente essere interceduta una certa oscitanza ed <lb/>esservi infra pposta qualche penosa difficolt&agrave; fra l'annunzio avutone e l'ese&shy;<lb/>cuzione dell'opera, mentre invece vuol far credere al Sarsi che venutogliene <lb/>il giorno in Venezia l'avviso, la sera tornato a Padova, nella notte specul&ograve; <lb/>e il giorno dopo ebbe eseguito fra le mani lo strumento. </s></p><p type="main">

<s>A chi crede che Gal&igrave;leo fosse un uomo come tutti gli altri e non un <lb/>taumaturgo, sembrer&agrave; impossibile una cos&igrave; facile e pronta esecuzione, ond'&egrave; <lb/>che altrove, piuttosto che alla lettura del Saggiatore e del Nunzio Sidereo, <lb/>penser&agrave; di doversi rivolgere ognuno, il quale voglia di un punto cos&igrave; im&shy;<lb/>portante di storia conoscere il vero. </s>

<s>Intorno a ci&ograve; appunto abbiamo docu&shy;<lb/>menti in alcune lettere che scriveva Giovanni Bartoli, Residente toscano in <lb/>Venezia, al Segretario di stato Belisario Vinta. </s></p><p type="main">

<s>&ldquo; &Egrave; capitato qu&agrave; (son parole dello stesso Bartoli) un tale che vuol dare <lb/>in Signoria un segreto d'un occhiale o cannone o altro istrumento, col quale <lb/>si vede lontano sino a 25 o 30 miglia tanto chiaro, che dicono che pare <lb/>presente, e molti l'hanno visto e provato dal campanile di San Marco, <lb/>ma dicesi che in Francia ed altrove sia oramai volgare e che per pochi <lb/>soldi si compra, e molti dicono averne avuti e visti &rdquo; (MSS. Gal., P. III, <lb/>T. III, c. </s>

<s>6). </s></p><p type="main">

<s>E in altra sua cos&igrave; lo stesso Bartoli scr&igrave;ve pi&ugrave; al proposito nostro: &ldquo; Pi&ugrave; <lb/>di tutti quasi ha dato da discorrere questa settimana il sig. </s>

<s>Galileo Galilei <lb/>matematico di Padova, con l'invenzione dell'occhiale o cannone da veder <lb/>da lontano. </s>

<s>E si racconta che quel tale forestiere che venne qua col segreto, <lb/>avendo inteso da non so chi (dicesi da fra Paolo Teologo servita) che non <lb/>farebbe qui frutto alcuno, pretendendo mille zecchini, se ne part&igrave; senza ten&shy;<lb/>tare altro, sicch&egrave; essendo amici insieme fra Paolo et il Galilei, e datogli <lb/>conto del secreto veduto, dicono che esso Galilei con la mente e con l'aiuto <lb/>di un altro simile strumento, ma non di tanto buona qualit&agrave; venuto di <lb/>Francia, abbia investigato e trovato il segreto. </s>

<s>E, messolo in atto, con l'aura <lb/>e favore di alcuni Senatori, si sia acquistato da questi Signori augumento <lb/>alle sue provvisioni sino a 10,000 fiorini l'anno, con l'obbligo per&ograve; parmi <lb/>di servire nelle sue Letture perpetuamente &rdquo; (ivi). </s></p><p type="main">

<s>Ecco raccontarsi cos&igrave; storie che hanno faccia di vero. </s>

<s>Galileo, il quale, <lb/>mancando della scienza delle rifrazioni, non poteva aver tanto discorso da <lb/>esser da lui solo condotto all'invenzione del Telescopio, vi giunse col ve&shy;<lb/>derne ed esaminarne uno venuto di Francia e capitato in Venezia. </s>

<s>Cosicch&egrave;, <lb/>se avesse egli avuto la sincerit&agrave; del Sirturo, avrebbe potuto ripeter le parole <lb/>stesse pronunziate da lui, dop'aver, nella bottega dell'orefice milanese, ve-<pb xlink:href="020/01/370.jpg" pagenum="351"/>duto il Telescopio del conte De Fuentes: <emph type="italics"/>incidit in manus meas, tractavi, <lb/>examinavi et similia confeci.<emph.end type="italics"/></s></p><p type="main">

<s>E giacch&egrave; il Bartoli ha introdotto in questa storia Paolo Sarpi, non dob&shy;<lb/>biam perderlo di vista, essendo che muove da lui il principio della maravi&shy;<lb/>gliosa invenzione, come zampillo d'acqua scaturito d'arido masso in monte <lb/>solitario, che, dopo esser corso per varii anfratti, s'allarga in fiume e irriga <lb/>i campi ubertosi, e fa sonare le valli. </s></p><p type="main">

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

<s>Nonostante che, dai sopra citati estratti di lettere di Giovanni Bartoli, <lb/>si rilevi che il Sarpi dette avviso dell'invenzione del Canocchiale a Galileo <lb/>nel Giugno del 1609, all'occasione che quel forestiero francese era venuto <lb/>a tentar la sorte in Venezia, esso fra Paolo, ne aveva avuto gi&agrave; avviso in <lb/>fin dal Novembre del 1608. &ldquo; L'avviso delli nuovi occhiali, scriveva il d&igrave; <lb/>6 di Gennaio 1609 al Groslot, l'ho avuto gi&agrave; pi&ugrave; di un mese &rdquo; (Polidori, <lb/>Lett. </s>

<s>1863, T. I, pag. </s>

<s>181) e soggiunge di aver fede nella possibile riuscita <lb/>dello strumento, tanto pi&ugrave; ch'egli stesso da giovane, quando tutto era in&shy;<lb/>tento allo studio delle Matematiche, aveva pensato al modo di ottener quel <lb/>tanto desiderato effetto, di veder le cose lontane, che ora dicevasi essere <lb/>stato raggiunto. </s>

<s>Ecco dunque, se non si vuol dare importanza al Portaluce <lb/>di Leonardo, d'onde balena la prima idea dell'invenzione del Canocchiale. <lb/></s>

<s>&ldquo; Quando io era giovane pensai ad una tal cosa e mi pass&ograve; per la mente <lb/>che un occhial fatto di figura di parabola potesse far tal effetto e avevo ra&shy;<lb/>gione da farne la dimostrazione &rdquo; (ivi). </s></p><p type="main">

<s>Al Sarpi era noto per diottrica dimostrazione ci&ograve; che pochi anni prima <lb/>aveva, ne'solitari suoi manoscritti, diottricamente dimostrato il Maurolico, <lb/>che cio&egrave; le lenti convesse fanno convergere i raggi e le lenti concave gli <lb/>fanno divergere. </s>

<s>Ripensando perci&ograve; il giovane Ottico che per veder le cose <lb/>lontane ci bisognavano lenti che non facessero n&egrave; convergere n&egrave; divergere <lb/>i raggi luminosi, ma che gli mandassero paralleli, cred&egrave; che si potesse un <lb/>tale effetto ottenere per mezzo degli occhiali parabolici. </s>

<s>La nuova specula&shy;<lb/>zione era fondata sopra due ipotesi: sulla prima, alla quale era pure infor&shy;<lb/>mato il Portaluce di Leonardo, che cio&egrave; le specie o i raggi visibili moves&shy;<lb/>sero dall'occhio; e sulla seconda che cio&egrave; i raggi passassero per rifrazione <lb/>attraverso al diafano parabolico, a quello stesso modo che si riflettono da <lb/>uno specchio. </s></p><p type="main">

<s>Intorno alla verit&agrave; della prima ipotesi il Sarpi non dubitava, avendosi <lb/>per cosa certa che egli riprovava l'opinion del Sagredo, da cui sostenevasi <lb/>che l'occhio, nell'atto del vedere, riceve dentro s&egrave; i raggi della luce e non <lb/>gli manda fuori, come Platone insegna, agli oggetti (Alb. </s>

<s>VIII, 204). Dubi&shy;<lb/>tava bene della seconda ipotesi, ed esprimeva il dubbio con queste parole <pb xlink:href="020/01/371.jpg" pagenum="352"/>immediatamente soggiunte alle sopra citate; parole che fanno la pi&ugrave; bella <lb/>testimonianza del senno pratico, e di quello squisito senso che, delle vere <lb/>regole dell'arte sperimentale, aveva il nostro Servita: &ldquo; Ma poich&egrave; queste <lb/>sono cose astratte e non mettono in conto la repugnanza della materia, sen&shy;<lb/>tivo qualche opposizione. </s>

<s>Per questo non son molto inchinato all'opera, e <lb/>questa sarebbe stata faticosa; onde n&egrave; confermai n&egrave; riprovai il concetto mio <lb/>con l'esperienza &rdquo; (Polid. </s>

<s>Lett., ivi). </s></p><p type="main">

<s>Le giovanili speculazioni, a che fra Paolo accenna in questa lettera fa&shy;<lb/>miliare al Groslot, sarebbero senza dubbio andate in dimenticanza e il germe <lb/>da cui doveva svolgersi l'invenzione del Canocchiale sarebbe rimasto ancora <lb/>per lungo tempo sepolto, se, conferite quelle speculazioni dallo stesso fra Paolo <lb/>al Porta, questi non le avesse solennemente divulgate nel XVII libro della <lb/>Magia. </s>

<s>Proponendosi di darne la dimostrazione matematica nel libro <emph type="italics"/>De re&shy;<lb/>fractione,<emph.end type="italics"/> non d&agrave; l'Autore, nel cap. </s>

<s>X del citato libro, intorno alle propriet&agrave; <lb/>diottriche delle lenti concave e delle convesse, altro che le conclusioni, e <lb/>non son pure altro che conclusioni quelle che d&agrave;, nel capitolo appresso, degli <lb/>occhiali parabolici <emph type="italics"/>quibus supra omne cogitatum quis inspicere longis&shy;<lb/>sime queat.<emph.end type="italics"/></s></p><p type="main">

<s>Se il cap. </s>

<s>X richiam&ograve; a s&egrave; l'attenzione de'fabbricanti di occhiali, que&shy;<lb/>sto XI che a lui segue pose, colle sue enimmatiche espressioni, a tortura <lb/>gli ingegni speculativi e fra questi quel del Keplero, il quale nelle parole <lb/>ivi scritte dal Porta notava pi&ugrave; cose. </s>

<s>Prima di tutto che <emph type="italics"/>etsi de speculis <lb/>loquitur videtur tamen de perspicillis intelligi debere quia de industria <lb/>occultavit sententiam<emph.end type="italics"/> (Dioptric. </s>

<s>Aug. </s>

<s>Vindel. </s>

<s>1611, pag. </s>

<s>55). Notava altres&igrave; <lb/>che ivi mescolavansi <emph type="italics"/>incredibilia probabilibus,<emph.end type="italics"/> e che di pi&ugrave; le espressioni <lb/>del titolo di quel cap. </s>

<s>XI non erano in coerenza con le dottrine professate <lb/>e dimostrate dall'Autore intorno alla vista: &ldquo; Et titulus capitis XI verbis <lb/><emph type="italics"/>supra omnem cogitatum quam longissime prospicere<emph.end type="italics"/> videbatur absurdita&shy;<lb/>tem opticam involvere, quasi visio fiat emittendo, et perspicilla acuant oculi <lb/>iaculos, ut ad remotiora penetrent, quam si nullo perspicillo adhiberentur: <lb/>aut si ut agnovit Porta, visio fit recipiendo, quasi tunc specilla rebus vi&shy;<lb/>dendis lucem concilient vel augeant &rdquo; (Alb. </s>

<s>V, 412). </s></p><p type="main">

<s>Il Keplero notava queste cose giustamente, ma non sapeva che l'Autor <lb/>della Magia Naturale riferiva ivi speculazioni, che non erano sue proprie, <lb/>ma del Sarpi, il quale, rispetto alla vista, riteneva l'ipotesi platonica del&shy;<lb/>l'emissione, n&egrave; seppe il Matematico alemanno indovinar che il Porta stesso <lb/>dando per cosa riuscibile ci&ograve; di che il Sarpi dubitava, per non averne fatta <lb/>esperienza, confondeva insieme gli specchi e le lenti, per potere attribuire <lb/>a queste le propriet&agrave; dimostrate per quelli. </s></p><p type="main">

<s>Pi&ugrave; ingenui per&ograve; del Keplero sorsero a travagliarsi intorno a voler de&shy;<lb/>cifrare gli enimmi del Porta, persuasi che tutto fosse nelle parole di lui <lb/>probabile e nulla d'incredibile, due eletti ingegni italiani, seguaci delle dot&shy;<lb/>trine di Galileo, a cui, il primo di que'due Bartolommeo Imperiali, cos&igrave; scri&shy;<lb/>veva il di 4 Ottobre 1614: &ldquo; &Egrave; il mio desiderio che V. S. applichi il pen-<pb xlink:href="020/01/372.jpg" pagenum="353"/>siero al cap. </s>

<s>XI del libro XVII della Magia di Giov. </s>

<s>Battista della Porta. <lb/></s>

<s>&Egrave; passo di cui confessa a V. S. il Keplero che non l'intende, n&egrave; ho io sa&shy;<lb/>puto giammai che matematico alcuno l'abbia saputo dichiarare, come so che <lb/>l'istesso Magini ha confessato, n&egrave; il Porta, per quante istanze li sia state <lb/>fatte da principi e letterati, si &egrave; potuto mai inchinare a dichiarare l'animo <lb/>suo. </s>

<s>Solo che disse che maestro Paolo da Venezia servita, l'aveva capito, e <lb/>quanto a me pare assai difficile il credere che questo sia un sibilo di vento <lb/>bugiardo, poich&egrave; si vede che, nel capitolo precedente, aveva cos&igrave; bene in&shy;<lb/>segnato il modo di accoppiar le due lenti, il che per&ograve; parve tanto strano <lb/>per tanto tempo. </s>

<s>Aggiungo che egli stesso protesta di volere nascondere <lb/>l'artificio al volgo, ma che ai Prospettivi era cosa manifesta, sicch&egrave; uno di&shy;<lb/>visando che in quelle parole sia qualche scambio o svario, siccome egli con&shy;<lb/>fessa nella prefazione del libro, e di pi&ugrave; che tal cosa non sia tanto difficol&shy;<lb/>tosa ad un dotto; per tanto prego V. S. a considerare se preso quel testo <lb/>e trasportando le parole sicch&egrave; cominci <emph type="italics"/>Costituatur ....<emph.end type="italics"/> oppure <emph type="italics"/>Construi&shy;<lb/>tur hoc modo speculum ....<emph.end type="italics"/> e poi tornar da capo alle parole <emph type="italics"/>Virtus costi&shy;<lb/>tuatur ....<emph.end type="italics"/> si potesse per la prima aver la lettera ordinata. </s>

<s>Tanto pi&ugrave; che <lb/>in questa parte, che &egrave; scritta innanzi, dice <emph type="italics"/>praedicti speculi<emph.end type="italics"/> non avendolo <lb/>ancora nominato. </s>

<s>Inoltre quelle parole <emph type="italics"/>sectionibus illis accomodetur<emph.end type="italics"/> sve&shy;<lb/>gliano la memoria delle sezioni coniche, tanto celebri, sicch&egrave; par che egli <lb/>voglia intendere di una di quelle, perch&egrave; dalle opere sue par che si possa <lb/>cavare che questa sia la sezione parab olica, e questa &egrave; la ragione che egli <lb/>nel cap. </s>

<s>XIX, trattando della refrazione, insegna che con la lente parabolica <lb/>gagliardissimamente si accenda il fuoco, perch&egrave; tutti i raggi che passano si <lb/>uniscono in un punto. </s>

<s>E nel canocchiale, secondo la dottrina del Keplero <lb/>e l'esperienza, non si richiede altro che quell'unione, tanto pi&ugrave; bella nella <lb/>parabola, quanto che toglie tutte le altre coincidenze pi&ugrave; lunghe e pi&ugrave; corte, <lb/>che caggiono da diverse parti della linea sferica. </s>

<s>Onde potrebbe il convesso <lb/>parabolico esser pi&ugrave; grande di quantit&agrave; della sferica, abbracciando pi&ugrave; parti <lb/>in un tempo dell'oggetto, e riuscirebbe chiarissimo. </s>

<s>E per quanto spetta <lb/>all'incavato, di cui par che intenda il Porta in quelle parole <emph type="italics"/>ubi valentis&shy;<lb/>sime universales solares radii disperguntur et coeunt minime,<emph.end type="italics"/> vorrebbe la <lb/>ragione che fosse anch'egli incavato parabolico, il quale per forza disgre&shy;<lb/>gherebbe i raggi, poich&egrave; fossero passati, per la contraria ragione del con&shy;<lb/>cavo e del convesso, secondo la regola del Porta nel fine della 2a proposi&shy;<lb/>zione del 2&deg; libro <emph type="italics"/>De refractione.<emph.end type="italics"/> E dalla formazione, che egli insegna della <lb/>sezione parabolica, nel cap. </s>

<s>XV della Magia XVII, per via del triangolo ret&shy;<lb/>tangolo, similmente si ha qualche luce da intendere quelle parole, nelle quali <lb/>fa menzione del triangolo e delle linee trasversali. </s>

<s>Or sar&agrave; fatica di V. S. giu&shy;<lb/>dicar queste congetture, e quando pure stimasse che fosse molto lontano il <lb/>pensiero dal Porta, tornerei a pregarla che applicasse l'animo a questo ne&shy;<lb/>gozio, speculando se potesse riuscir migliore un Canocchiale fatto di cri&shy;<lb/>stalli parabolici, per le ragioni che si son ricordate dal Porta, poich&egrave;, seb&shy;<lb/>bene il Keplero ha pi&ugrave; fede nell'iperbola che nella parabola, nondimeno i <pb xlink:href="020/01/373.jpg" pagenum="354"/>concorsi e le unioni paiono pi&ugrave; manifeste nelle sezioni paraboliche. </s>

<s>Poich&egrave; <lb/>se i raggi cos&igrave; passano come si riflettono, riflettendosi ad un punto negli <lb/>specchi da abbruciare, anderanno anche ad unirsi passando in un punto, vi&shy;<lb/>cino al quale, posto un incavato parabolico, par che debba con maggior <lb/>forza distinguere quella confusione maggiore. </s>

<s>Il tutto per&ograve; &egrave; rimesso al giu&shy;<lb/>dizio di V. S. &rdquo; (MSS. Gal., P. VI, T. IX, c. </s>

<s>206). </s></p><p type="main">

<s>Ma perch&egrave; il giudizio di Galileo fu che il comporre il Canocchiale di <lb/>due lenti paraboliche, secondo il pensiero del Porta, non poteva riuscire a <lb/>buon effetto, l'Imperiali in altra sua lettera conclude: &ldquo; Sono restato afflit&shy;<lb/>tissimo, perch&egrave; avendo qualche opinione che potesse farsi quanto accenna <lb/>il Porta, l'avermi ella accennato che stima non potersi arrivare, per essere <lb/>impossibile il farsi, mi ha posto in disperazione che tal cosa possa riuscire. </s>

<s><lb/>E l'argomento ha gran forza: se il signor Galileo non l'arriva, daddovero che <lb/>non &egrave; arrivabile &rdquo; (ivi, c. </s>

<s>218). </s></p><p type="main">

<s>Altro ardito pensiero del Porta fu quello di applicare ai raggi calori&shy;<lb/>fici, negli specchi ustorii, ci&ograve; che, pe'raggi luminosi, avea creduto possibile <lb/>nei Canocchiali; ond'&egrave; che appresso ai citati pone, in quello stesso libro <lb/>della Magia, i due capitoli XVI e XVII, il primo de'quali intitola: <emph type="italics"/>Quomodo <lb/>parabolica sectio describi possit quae oblique comburat et in longissimam <lb/>distantiam,<emph.end type="italics"/> e l'altro: <emph type="italics"/>Parabolica sectio quae in infinitum comburat.<emph.end type="italics"/> Il <lb/>Keplero stim&ograve; queste due proposizioni impossibili, sia che s'intendesse di <lb/>potere ottener l'effetto di abbruciare in lunghissima e in infinita distanza, <lb/>per via di lenti cristalline, o per via di specchi: &ldquo; J. </s>

<s>Baptista Porta polli&shy;<lb/>cetur problema in infinitum comburere per lineam ustoriam, quod ille de <lb/>speculo tradit: alii vero de lente convexa, verum esse opinantur. </s>

<s>Utrum <lb/>sequaris, impossibilia aggrederis &rdquo; (Dioptr., pag. </s>

<s>20). </s></p><p type="main">

<s>Nonostante, come l'Imperiali aveva creduto pi&ugrave; volentieri al Porta che <lb/>al Keplero, rispetto al Canocchiale parabolico, cos&igrave; il Cavalieri ebbe pi&ugrave; fede <lb/>al Porta che al Keplero, per ci&ograve; che riguarda la possibilit&agrave; di costruire e di <lb/>ottenere gli effetti dello specchio Ustorio. </s>

<s>Ammesso che la linea comburente <lb/>del Porta non si debba intendere per una vera linea geometrica, ma per un <lb/><emph type="italics"/>cilindro o cannoncino di lume, di che sottigliezza vogliamo indiffinita&shy;<lb/>mente prolungato<emph.end type="italics"/> (Lo Specchio Ust. </s>

<s>Bologna 1650, pag. </s>

<s>61) stima il Cava&shy;<lb/>lieri, secondo egli dimostra nel cap. </s>

<s>XXXII del libro citato, potersi ottener <lb/>l'effetto di abbruciare in qualunque direzione e per lunghissima distanza, <lb/>applicando uno specchietto parabolico, girevole sopra un pernio a discre&shy;<lb/>zione di chi vuol verso una parte o verso l'altra dirigere l'incendio, nel <lb/>fuoco di un altro specchio parabolico e pi&ugrave; grande, in cui diano i liberi e <lb/>ardenti raggi del sole. </s></p><p type="main">

<s>Gli esempi dell'Imperiali e del Cavalieri attestano che non tutti quegli <lb/>appartenenti alla scuola di Galileo concorrevano in far del Porta giudizi si&shy;<lb/>mili a quelli dell'Hasdale e del Sagredo. </s>

<s>Che se il libro della <emph type="italics"/>Magia Na&shy;<lb/>turale<emph.end type="italics"/> valse a risvegliar tanto ardore di scientifiche investigazioni nel Fisico <lb/>genovese di sopra commemorato, e nell'Autore della Geometria degl'indivi-<pb xlink:href="020/01/374.jpg" pagenum="355"/>sibili, si pensi con quanto maggior desiderio dovesse esser cercato quel li&shy;<lb/>bro, in tempi di minor cultura e da gente che teneva dietro curiosa a tutto <lb/>ci&ograve; che sapesse del nuovo e dello spettacoloso. </s>

<s>Le numerosissime edizioni, <lb/>che forse non se ne contano tante di nessun altro libro di quel genere, di&shy;<lb/>cono che la <emph type="italics"/>Magia Naturale<emph.end type="italics"/> doveva esser diffusa e letta per ogni parte <lb/>d'Europa, non senza frugar vivamente la curiosit&agrave; ne'lettori di veder sotto <lb/>i loro occhi incarnati i seducenti fantasmi ivi dipinti. </s>

<s>Narra il Keplero che <lb/>da queste curiosit&agrave; fu pi&ugrave; volte preso il suo Imperatore (Alb. </s>

<s>V, 412) e chi <lb/>poteva non sentirsi commuovere alla speranza ingeritagli di poter mandare <lb/>a infinita distanza da s&egrave; il lume da'suoi occhi e il fuoco dalle sue mani? </s></p><p type="main">

<s>Queste considerazioni concorrono a render probabilissimo il fatto che <lb/>a qualche fabbricante di occhiali, di qualunque nazione si fosse, e comun&shy;<lb/>que avesse nome, per suggerimento del Porta, venisse in pensiero di com&shy;<lb/>porre insieme due paia di occhiali, uno da miopi e l'altro da presbipi, e <lb/>che ritrovasse in effetto quell'ingrandimento degli oggetti traguardati, dal <lb/>Porta stesso promesso. </s>

<s>In principio dovea aver quell'artefice le due paia di <lb/>occhiali tenute congiunte insieme per via di verghette metalliche saldate, e <lb/>poi facilmente, per la propriet&agrave; benissimo allora sperimentata, che hanno i <lb/>tubi di diriger la linea di mira, e di togliere le riflessioni irregolari, dee <lb/>avere alle verghette sostituito il cannoncino. </s>

<s>Cos&igrave; il primo canocchiale sa&shy;<lb/>rebbe stato un binoculo, e par che la congettura prenda qualche colore di <lb/>verit&agrave; da ci&ograve; che Filippo Salviati aveva sentito dire, che cio&egrave; quell'occhia&shy;<lb/>laio, che aveva fatto l'occhiale al conte Maurizio, aveva trovato anche inven&shy;<lb/>zione di moltiplicare il vedere con due occhiali ordinari, da portare al naso <lb/>(MSS. Gal. </s>

<s>P. I, T. VII, c. </s>

<s>119). </s></p><p type="main">

<s>In qualunque modo, quel fatto che si diceva dianzi esser probabilissimo, <lb/>fu dal Porta, senza troppo esitare, tenuto e dato per cosa certa. </s>

<s>Appena <lb/>infatti ebbe dal principe Cesi nuova dell'invenzione del Canocchiale, cos&igrave; gli <lb/>rispose da Napoli il d&igrave; 28 Agosto 1609: &ldquo; Del secreto dell'occhiale l'ho <lb/>visto, ed &egrave; una minchioneria, ed &egrave; preso dal mio libro IX <emph type="italics"/>De refractione &rdquo;<emph.end type="italics"/><lb/>(Venturi, Memorie ecc., Modena 1818, P. I, pag. </s>

<s>82). </s></p><p type="main">

<s>Qui &egrave; notabile che, invece della <emph type="italics"/>Magia Naturale,<emph.end type="italics"/> citi il trattato <emph type="italics"/>De re&shy;<lb/>fractione<emph.end type="italics"/> e di questo il libro IX, forse per isbaglio, invece dell'VIII, dove <lb/>appunto si tratta <emph type="italics"/>De specillis.<emph.end type="italics"/> Ma il citar quel libro, che fu primo nella <lb/>storia della Diottrica a dar la teoria delle lenti, invece di quell'altro, dove <lb/>non si fa che accennarne le conclusioni, non era senza una particolare in&shy;<lb/>tenzion dell'Autore, nell'atto di revocare a s&egrave; il diritto d'aver, colle teorie <lb/>stesse che prefulgono alla mente, preparata la pratica esecuzione del Canoc&shy;<lb/>chiale. </s>

<s>Galileo e i partigiani di lui contesero al Porta quel diritto, e le cose <lb/>narrate fin qui ci dispongono a credere che glielo contendessero ingiusta&shy;<lb/>mente. </s>

<s>Ma ora che l'ordine della nostra Storia ci conduce a discorrer della <lb/>teoria diottrica dello Strumento, dai fatti che esamineremo, forse anche me&shy;<lb/>glio verr&agrave; decisa la questione. </s></p><pb xlink:href="020/01/375.jpg" pagenum="356"/><p type="main">

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

<s>Da quali principii diottrici fosse condotto Galileo in trattar della ra&shy;<lb/>gione e del modo come si vengono a ingrandire gli oggetti, per opera del <lb/>Telescopio, si par manifesto da ci&ograve; che, in presentar per la prima volta al <lb/>pubblico il suo nuovo strumento, ne scrisse nel Nunzio Sidereo. </s>

<s>Preghiamo <lb/>i nostri lettori ad attender bene alla scienza ottica dalla quale sono infor&shy;<lb/>mate le parole seguenti: &ldquo; Sit enim facilioris intelligentiae gratia, tubus ABCD <lb/><figure id="id.020.01.375.1.jpg" xlink:href="020/01/375/1.jpg"/></s></p><p type="caption">

<s>Figura 26.<lb/>(fig. </s>

<s>26) oculus inspicientis esto <lb/>E. Radii, dum nulla in tubo ades&shy;<lb/>sent Perspicilla, ab obiecto FG ad <lb/>oculum E, secundum lineas rectas <lb/>FCE, GDE ferrentur: sed, apposi&shy;<lb/>tis Perspicillis, ferentur secundum <lb/>lineas refractas HCE, IDE: coar&shy;<lb/>ctantur enim, et qui prius liberi <lb/>ad FG obiectum dirigebantur, par&shy;<lb/>tem tantummodo HI comprehendent &rdquo; (Alb. </s>

<s>III, 62). </s></p><p type="main">

<s>Che strana teoria del modo di operar del Canocchiale &egrave; mai questa? </s>

<s><lb/>Chi cos&igrave; ne discorse, tutt'altro che aver cavato il suo discorso <emph type="italics"/>dalle pi&ugrave; re&shy;<lb/>condite speculazioni di Prospettiva,<emph.end type="italics"/> si direbbe che di Prospettiva, ossia di <lb/>scienza diottrica, non ne aveva nemmeno la prima idea. </s>

<s>Come mai s'ingran&shy;<lb/>discono gli oggetti per refrazione coartando i raggi, <emph type="italics"/>coarctantur enim?<emph.end type="italics"/> e <lb/>come posson le lenti mostrare ingranditi gli oggetti, se per l'esempio del&shy;<lb/>l'Autore non si rappresenta dell'oggetto FG all'occhio altro che una por&shy;<lb/>zione HI di lui? </s></p><p type="main">

<s>A svelare il mistero giova intanto sapere esser qui da Galileo profes&shy;<lb/>sata l'opinione che le lenti mostrino per refrangenza ingrandite le cose, <lb/>perch&egrave;, condensandone i raggi, le rappresentano all'occhio pi&ugrave; intensamente <lb/>illuminate. </s>

<s>Che poi, per opera delle rifrazioni, facendosi gli stessi raggi di&shy;<lb/>vergere, si accresca l'angolo visuale, non passa per la mente dell'Autore. </s>

<s><lb/>L'obiettivo per lui opera a quello stesso modo che opera l'oculare, e am&shy;<lb/>messo, a modo platonico, che le linee radiose muovan dall'occhio per an&shy;<lb/>dare a incontrar l'oggetto <emph type="italics"/>(ad obiectum FG dirigebantur),<emph.end type="italics"/> non sospetta <lb/>nemmen dalla lontana che i raggi s'incrocino mai in tutto quel tragitto che <lb/>fanno per venir dall'oggetto lontano ad appuntarsi nell'occhio. </s></p><p type="main">

<s>Poco dopo aver professate Galileo cos&igrave; fatte dottrine, seppure si meri&shy;<lb/>tano il nome di dottrine, soggiunge ivi la promessa di dare alla prima oc&shy;<lb/>casione al pubblico <emph type="italics"/>absolutam huius Organi theoriam,<emph.end type="italics"/> e par che questa <lb/>occasione aspettasse a venir tredici anni dopo, quando dette mano a scri&shy;<lb/>vere il <emph type="italics"/>Saggiatore.<emph.end type="italics"/> Qui si torna a trattar della teoria del <gap/><pb xlink:href="020/01/376.jpg" pagenum="357"/>dell'Autore, in mezzo a molte tenebre, son pure alquanto lumeggiate di <lb/>quella scienza diottrica, la quale nel Nunzio Sidereo assolutamente manca. </s></p><p type="main">

<s>Ivi infatti incominci&ograve; dal confutare il Sarsi, le dottrine del quale, in&shy;<lb/>torno al modo d'operare del Telescopio, le riduce ai due casi seguenti: &ldquo; Il <lb/>Telescopio rappresenta gli oggetti maggiori, perch&egrave; gli porta sotto maggior <lb/>angolo, che quando son veduti senza lo strumento: Il medesimo, restrin&shy;<lb/>gendo quasi a un punto le specie de'corpi luminosi ed i raggi sparsi, rende <lb/>il cono visivo, o vogliam dire la piramide luminosa, per la quale si vedono <lb/>gli oggetti, di gran lunga pi&ugrave; lucida, e per&ograve; gli oggetti splendidi di pari ci <lb/>si rappresentano ingranditi, e di maggior luce illustrati &rdquo; (Alb. </s>

<s>IV, 201). </s></p><p type="main">

<s>Conceduto dunque ed ammesso esser vero che il Telescopio ingrandi&shy;<lb/>sce gli oggetti col portargli sotto maggior angolo, conclude Galileo, contro <lb/>l'altra proposizione del Sarsi, dicendo esser <emph type="italics"/>falsissimo che gli oggetti lu&shy;<lb/>minosi ci si rappresentino col Telescopio pi&ugrave; lucidi che senza, anzi &egrave; vero <lb/>che li veggiamo assai pi&ugrave; oscuri<emph.end type="italics"/> (ivi, pag. </s>

<s>202). </s></p><p type="main">

<s>Distingue inoltre l'Autor del <emph type="italics"/>Saggiatore<emph.end type="italics"/> il vario modo d'operar delle <lb/>lenti concave e delle convesse, dicendo che queste accrescon bene gli og&shy;<lb/>getti, ma gli mostrano <emph type="italics"/>assai indistinti ed abbagliati,<emph.end type="italics"/> mentre quelle gli rap&shy;<lb/>presentano chiari ma impiccoliti (ivi, pag. </s>

<s>208) e nonostante attribuisce a <lb/>questa stessa concava nel Telescopio la parte pi&ugrave; importante perch&egrave; &egrave; quella, <lb/>appresso alla quale si tien l'occhio, e per la quale passano gli ultimi raggi <lb/>(ivi, pag. </s>

<s>202) che, dilatandosi nell'uscir dalla lente stessa, formano il cono <lb/>inverso, come si sperimenta nel modo di disegnar le macchie solari per <lb/>proiezione (ivi, pag. </s>

<s>203). La dottrina platonica dell'emissione che cio&egrave; <emph type="italics"/>la <lb/>luce ingagliardita mediante l'unione de'raggi rende l'oggetto veduto pi&ugrave; <lb/>luminoso<emph.end type="italics"/> &egrave; qui pure da Galileo riputata falsa, asserendo che <emph type="italics"/>sarebbe vero <lb/>questo, quando tal luce andasse a trovar l'oggetto, ma ella vien verso <lb/>l'occhio, il che produce poi contrario effetto<emph.end type="italics"/> (ivi). </s></p><p type="main">

<s>Or non pu&ograve; chi legge e medita queste cose non sentirsi preso da una <lb/>gran maraviglia, in ritrovar che Galileo confuta nel Saggiatore dottrine, che <lb/>egli aveva prima professate nel Nunzio Sidereo, per cui, mentre confuta il <lb/>Sarsi, vien nello stesso tempo a confutare e a contradire a s&egrave; stesso. </s>

<s>Avesse <lb/>fatto cenno a qualche ritrattazione, e la maraviglia cesserebbe, perch&egrave; in <lb/>tutti la verit&agrave; &egrave; figliola del tempo, ma pur si vuol fare apparire da tutte le <lb/>parti che la mente dell'Autor nostro sia sempre stata ugualmente amica alla <lb/>verit&agrave;, e non abbia fornicato mai coll'errore. </s>

<s>Anzi, sebben egli citi le dot&shy;<lb/>trine dei Prospettivi, quelle antiche calottriche dottrine non hanno a che far <lb/>nulla colle sue nuove diottriche, le quali egli &egrave; venuto il primo a insegnare <lb/>al mondo, e senza le quali il mondo stesso ignorerebbe ancora col Sarsi il <lb/>modo vero com'opera sulla nostra vista il Telescopio. </s>

<s>Che una tal pretesa <lb/>fosse veramente radicata nell'animo di Galileo, lo dimostrano i fatti, intorno <lb/>ai quali dobbiamo ora divagare il discorso, dai quali fatti pur si conferma <lb/>quello spirito di conquista che, per esaltar s&egrave;, portava il Filosofo ad oppri&shy;<lb/>mere gl&igrave; altri <gap/></s></p><pb xlink:href="020/01/377.jpg" pagenum="358"/><p type="main">

<s>Infin dal 1521 Francesco Maurolico aveva dato mano ai suoi Trattati <lb/>di Ottica, e nel 1554 erano gi&agrave; compiuti. </s>

<s>La teoria diottrica delle lenti con&shy;<lb/>cave e delle convesse &egrave; ivi per la prima volta matematicamente dimostrata, <lb/>e tanto lume si conobbe, da chi vide il Manoscritto, potersi diffondere, da <lb/>questa teoria delle lenti separate, sulla teoria delle lenti stesse composte nel <lb/>Canocchiale; che fu pensato di dar quelle sepolte carte alla luce, in quel <lb/>tempo che, de'mirabili effetti dello strumento, sentivasi vivo desiderio da <lb/>tutti d'intenderne la ragione. </s>

<s>Tarquinio Longhi infatti cos&igrave; diceva a Giovan <lb/>Battista Airolo, nel dedicargli la stampa del libro, eseguita in Napoli nel 1611: <lb/>&ldquo; Nam sapientiae studiosis non nisi gratissimi accident hi libri, qui veluti <lb/>fontes et capita sunt Perspectivae; hoc potissimum tempore, quo ingens <lb/>eius desiderium in omnium pectoribus excitavit novum illud et admirabile <lb/>Opticae fistulae inventum &rdquo;. </s></p><p type="main">

<s>La pubblicazione, intesa cos&igrave; dal Longhi a fine di preparare i fonda&shy;<lb/>menti scienziali alla teoria del Canocchiale, era forse pi&ugrave; opportuna di quel <lb/>che non si potesse presentire allora, imperocch&egrave; ha il Maurolico due Teo&shy;<lb/>remi insigni, i quali parvero appositamente preparati per coloro, che avreb&shy;<lb/>bero dato opera a costruire e a perfezionare i futuri Telescopi. </s>

<s>&Egrave; il primo <lb/>di que'Teoremi il XVIII del I Libro <emph type="italics"/>Diaphanorum,<emph.end type="italics"/> dove si dimostrano le <lb/>aberrazioni di sfericit&agrave; prodotte per rifrazione nelle sfere cristalline: &ldquo; Pa&shy;<lb/>rallelorum radiorum, intra perspicuum orbem, a centro inaequaliter distan&shy;<lb/>tium, remotior, cum axe sibi parallelo propius sphaerae, concurret, quam <lb/>reliquus (ibi, pag. </s>

<s>41). Fu questo Teorema, che fece poi disperare il Newton <lb/>di poter aver ne'canocchiali diottrici la desiderata perfezione. </s></p><p type="main">

<s>L'altro maurolicano Teorema &egrave; il XXIII dove si dimostra il modo del <lb/>rappresentarsi per rifrazione le immagini nelle sfere cristalline e nelle lenti <lb/>convesse: &ldquo; Patet ergo ratio quare lux vel aliquod illuminatum, per conspi&shy;<lb/>cilliorum vitrum trasparens, ad terminum quendam conversam porrigit ef&shy;<lb/>figiem: quando quidem conspicilla superficiem habent utrinque convexam. </s>

<s><lb/>Immo in huiusmodi vitro talis conversa effigies expressior trasparet, quam <lb/>si vitrum ipsum sphaericum esset &rdquo; (ibi, pag. </s>

<s>48). </s></p><p type="main">

<s>Diciannove anni prima che questo Trattato del Maurolico fosse noto al <lb/>pubblico, il Porta aveva gi&agrave; dimostrate le propriet&agrave; diottriche delle lenti, e <lb/>molti altri effetti delle rifrazioni, con norme pi&ugrave; sicure, e con pi&ugrave; largo stu&shy;<lb/>dio di quel che non avesse fatto l'Ottico siciliano. </s>

<s>Questo infatti, nel Teo&shy;<lb/>rema X del libro sopra citato, professa il principio di Vitellione, che cio&egrave; <lb/>gli angoli incidenti e i refratti stieno in proporzione uniformemente difforme, <lb/>o geometrica: <emph type="italics"/>Anguli inclinationum sunt fractionum angulis proportio&shy;<lb/>nales<emph.end type="italics"/> (ibi, pag. </s>

<s>36). Quanto poi alle immagini il Mauralico dimostr&ograve; bene <lb/>il rappresentarsi delle immagini reali nelle lenti biconvesse, ma delle im&shy;<lb/>magini virtuali, nelle biconvesse stesse e nelle concave, non fa parola, con&shy;<lb/>tentandosi di concludere per le prime: <emph type="italics"/>Hinc ergo satis constat quod con&shy;<lb/>vexa congregat,<emph.end type="italics"/> e per le seconde: <emph type="italics"/>Hinc ergo satis constat quod concava <lb/>disgregat<emph.end type="italics"/> (Diaph. </s>

<s>Lib. </s>

<s>III, pag. </s>

<s>73). </s></p><pb xlink:href="020/01/378.jpg" pagenum="359"/><p type="main">

<s>Il Porta, nella proposizione VIII del Libro I <emph type="italics"/>De refractione,<emph.end type="italics"/> dimostra <lb/>che il principio assunto da Vitellione, e seguito poi dal Maurolico, &egrave; falso, <lb/>e che i raggi incidenti e i refratti formano angoli, i quali stanno in pro&shy;<lb/>porzioni non uniformemente, ma difformemente difformi: &ldquo; Sed Vitellio in <lb/>hoc falsus est, quod etsi aequaliter inter se distant in fundo iacentia colo&shy;<lb/>rata, non ob id aequaliter distant in aquae summo puncta refractionum &rdquo; <lb/>(Neapoli 1593, pag. </s>

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

<s>Per quel che poi riguarda la rappresentazione delle immagini, il Porta <lb/>&egrave; il pi&ugrave; compiuto di tutti gli Ottici che lo seguirono appresso fino allo stesso <lb/>Cartesio. </s>

<s>Notabile che egli primo introducesse, in questa nuova grafia diot&shy;<lb/>trica, l'uso degli <emph type="italics"/>assi,<emph.end type="italics"/> che egli appella col nome di <emph type="italics"/>cateti,<emph.end type="italics"/> da cui &egrave; con ve&shy;<lb/>rit&agrave; guidato a dimostrar il rappresentarsi delle immagini cos&igrave; reali come <lb/>virtuali nelle due forme di lenti. </s>

<s>Essendo la Diottrica una scienza nuova a <lb/>que'tempi mirabile &egrave; in questo Trattato <emph type="italics"/>De refractione<emph.end type="italics"/> il libro VIII <emph type="italics"/>De <lb/>spicillis,<emph.end type="italics"/> del qual soggetto ha l'Autore gran ragione di dire che egli era <lb/><emph type="italics"/>res ardua, mirabilis utilis iucunda nec ab aliquibus adhuc tentata<emph.end type="italics"/> (ibi, <lb/>pag. </s>

<s>173). La dimostrazione delle immagini, che in vario modo si rappre&shy;<lb/>sentano dalle varie forme di lenti, &egrave; ivi data principalmente nelle tre pro&shy;<lb/>posizioni: nella VII &ldquo; In convexis specillis oculo specillo proprinquo, magni&shy;<lb/>tudine prope, ut procul posita, semper recta videbitur &rdquo; (pag. </s>

<s>179); nella VIII <lb/>&ldquo; In convexis specillis, magnitudine et oculo longe positis, inversa videbitur <lb/>magnitudo et proprinquior &rdquo; (pag. </s>

<s>180), e nella XV &ldquo; In concavis specillis <lb/>res semper minor videbitur &rdquo; pag. </s>

<s>185). </s></p><p type="main">

<s>In quel tempo stesso che il Porta dava opera a pubblicare il Trattato <lb/><emph type="italics"/>De Refractione,<emph.end type="italics"/> un altro Italiano aveva rivolte le sue speculazioni intorno <lb/>alle propriet&agrave; diottriche delle lenti, e ne avea dimostrati teoremi, che an&shy;<lb/>davano attorno manoscritti. </s>

<s>Inventato il canocchiale, fu da alcuni, e segna&shy;<lb/>tamente da quel Giovanni Bartoli che dell'invenzione del canocchiale dava <lb/>particolari notizie al Vinta, pregato l'Autore di quel Manoscritto, che era <lb/>Marc'Antonio De Dominis, a voler applicare i teoremi dimostrati alla teo&shy;<lb/>ria dello stesso Canocchiale, tanto desiderata. </s>

<s>Il <emph type="italics"/>De Dominis,<emph.end type="italics"/> nonostante la <lb/>dignit&agrave; di Arcivescovo di Spalatro, della quale era stato insignito, condiscese, <lb/>preparando quel Trattato, che ebbe poi il titolo <emph type="italics"/>De radiis visus et lucis.<emph.end type="italics"/> Di <lb/>ci&ograve; appunto dava cos&igrave; notizia il Sarpi al Leschassier, con lettera del d&igrave; 8 Giu&shy;<lb/>gno 1610: &ldquo; Quanto alle lenti oculari, per dirne alcun che, ci ha qui (in <lb/>Venezia) alcuni eruditi, che disegnano di fare un piccolo Commentario sulla <lb/>visione, ove esporranno la maniera e la cagione del ritrovato olandese, e <lb/>tutte le teorie a un tempo del Canocchiale &rdquo; (Polidori, Lettere ediz. </s>

<s>cit. </s>

<s><lb/>T. II, pag. </s>

<s>81). Due mesi dopo, torna lo stesso Sarpi a scrivere all'amico, <lb/>dicendogli che il libricciuolo intorno agli occhiali non era ancora stampato, <lb/>ma che l'Autore attendeva alle incisioni, delle quali aveva bisogno per <lb/>ispiegare i suoi sentimenti (ivi, pag. </s>

<s>108). Fu stampato poi quel libric&shy;<lb/>ciuolo, a cui dev'aver preso non piccola parte lo stesso Sarpi, in Venezia <lb/>nel 1611, col titolo<gap/> <emph type="italics"/>De radiis visus et lucis in vitris perspectivis et iride,<emph.end type="italics"/><pb xlink:href="020/01/379.jpg" pagenum="360"/><emph type="italics"/>Tractatus Marci Antonii De Dominis, per Joannem Bartolum in lucem <lb/>editus.<emph.end type="italics"/></s></p><p type="main">

<s>L'Autore mostra di avere avuto e di aver tuttavia una gran fiducia di <lb/>esser coll'opera sua riuscito a sodisfar pienamente e con gran facilit&agrave; al de&shy;<lb/>siderio di coloro, che volevan saper la maniera e la ragione del ritrovato <lb/>olandese. </s>

<s>Una tal fiducia vien da lui stesso espressa per le seguenti parole: <lb/>&ldquo; Ex hactenus a nobis dictis et explicatis de vitreis perspicillis, facillimum <lb/>negotium redditur in conficiendo instrumento illo quod nuper videtur in&shy;<lb/>ventum aut saltem, praesertim in Italia, publicatum. </s>

<s>Id enim, quemadmo&shy;<lb/>dum maxima admiratione affecit et afficit plurimos, ita mihi certe qui in <lb/>perspectivis ante multos, sed per multos etiam annos delectationis causa men&shy;<lb/>tem exercui, nulli prorsus fuit admirationi, sed cum primum illud vidi, erat <lb/>autem valde imperfectum, effectum duorum vitrorum aperte cognovi &rdquo; (ivi, <lb/>pag. </s>

<s>37, 38). </s></p><p type="main">

<s>Questa vantata facilit&agrave; d'intendere ci&ograve; che a tutti era sembrato tanto <lb/>difficile, il <emph type="italics"/>De Dominis<emph.end type="italics"/> la riconosce dunque dall'essersi per tanti anni eser&shy;<lb/>citato negli studi di Prospettiva, e dall'aver saputo spiegare le propriet&agrave; delle <lb/>lenti. </s>

<s>E infatti egli aveva sufficientemente bene dimostrato l'ingrandimento <lb/>virtuale delle immagini nelle lenti convesse, concludendo cos&igrave; la sua dimo&shy;<lb/>strazione: &ldquo; Itaque oculus non videt quantitatem sub angulo directo et na&shy;<lb/>turali, sed sub angulo, qui est angulus maior &rdquo; (pag. </s>

<s>19). Aveva pure in <lb/>sufficiente maniera descritto il rappresentarsi delle immagini virtuali nelle <lb/>lenti concave, concludendo cos&igrave; intorno ad esse: &ldquo; Oculus videt quantitatem <lb/>sub angulo qui est minor et strictior angulo naturali, et minorem vitri par&shy;<lb/>tem occupat et consequenter res quidem minor apparebit, sed clarior et <lb/>distinctior &rdquo; (ibi). </s></p><p type="main">

<s>Tali diottriche conclusioni per&ograve;, bench&egrave; vere e sufficientemente dimo&shy;<lb/>strate, non eran quelle che pi&ugrave; facevano all'uopo. </s>

<s>Imperocch&egrave;, consistendo <lb/>la ragione del Canocchiale nell'immagine reale e rovesciata dell'obiettivo, <lb/>che viene ingrandita e raddirizzata dall'oculare, il De Dominis intorno a ci&ograve; <lb/>mostra di non saperne niente, e perci&ograve;, riguardandosi da lui l'obiettivo stesso <lb/>come una lente d'ingrandimento virtuale, ecco come frantende l'ufficio del&shy;<lb/>l'oculare, e come allo stesso tempo lasci gli studiosi in quella fame, a cui <lb/>con tanta facilit&agrave; aveva fiducia di sodisfare. </s>

<s>&ldquo; Caeterum iam vidimus quae <lb/>valde remota sunt, per vitrum lenticulare cerni quidem cum ipsorum in&shy;<lb/>cremento, remoto usque ad certum spacium ab oculo vitro praedicto, sed <lb/>turbate et indistincte, et confuse, propter mixtionem radiorum visualium di&shy;<lb/>rectorum cum fractis. </s>

<s>Si igitur aliqua ratione tolli posset haec confusio, ita <lb/>ut sublatis radiis directis per solos refractos fiat visio, ex duplici capite illa <lb/>clara esset et distincta, tum ex sublata confusione praedicta, tum ex rerum <lb/>visibilium dilatatione. </s>

<s>Tollitur igitur confusio illa et extinguntur radii di&shy;<lb/>recti, per appositionem vitri excavati inter oculum et vitrum lenticulare &rdquo; <lb/>(ibi, pag. </s>

<s>34). </s></p><p type="main">

<s>Tale e tanto in <gap/> era il fervor de'nuovi studi dioffrici in Ita-<pb xlink:href="020/01/380.jpg" pagenum="361"/>lia, che si risvegli&ograve; all'esempio, in Germania, quel gran Keplero, il quale <lb/>avendo, ne'suoi Paralipomeni a Vitellione, sfiorato appena questi stessi nuovi <lb/>studii, volle tornarci sopra di proposito, a coltivarli col principale intento di <lb/>derivar luce di l&igrave; a intendere la ragione del Canocchiale. </s>

<s>Il Trattatello, che <lb/>vide pure nel 1611 in Augusta la luce, s'intitol&ograve; <emph type="italics"/>Dioptrice, seu demonstra&shy;<lb/>tio eorum quae visui et visibilibus, propter conspicilla non ita pridem in&shy;<lb/>venta, accidunt,<emph.end type="italics"/> e nella teoria delle lenti semplici si va anche qui prepa&shy;<lb/>rando la teoria per le lenti composte. </s></p><p type="main">

<s>Il rappresentarsi delle immagini reali nelle lenti convesse &egrave; dimostrato <lb/>nella proposizione XXC con tanta esattezza, che non potrebbe di meglio de&shy;<lb/>siderare la scienza. </s>

<s>Ivi &egrave; invocato per la prima volta il principio che l'oc&shy;<lb/>chio riferisce la vista nella direzione del raggio rifratto, e con ci&ograve; venivasi <lb/><figure id="id.020.01.380.1.jpg" xlink:href="020/01/380/1.jpg"/></s></p><p type="caption">

<s>Figura 27.<lb/>a intendere in che modo il teorema di Tolomeo, che <lb/>cio&egrave; gli oggetti si vedon dall'occhio nostro ingranditi <lb/>a proporzione dell'angolo visuale, si potesse, dai di&shy;<lb/>retti e naturali, applicare ai raggi rifratti. </s>

<s>Quella <lb/>citata proposizione XXC, in cui si dimostra cos&igrave; bene <lb/>la teoria del microscopio semplice, &egrave; conclusa dal&shy;<lb/>l'Autore nella forma seguente: &ldquo; Ut igitur totum DE <lb/>(fig. </s>

<s>27) apprehendatur, oportet venire ab oculo exte&shy;<lb/>riores quam CI, CK, puta CA, CB. </s>

<s>Hae igitur si iusto <lb/>spacio distiterint a CI, CK, refractione in A, B facta, <lb/>apprehendent D, E ut sint visivae CAD, CBE. </s>

<s>Cum <lb/>autem ACB angulus sit maior quam ICK, quo spe&shy;<lb/>ctatur visibile, remota lente, maius igitur putabitur visibile DE quam est. </s>

<s><lb/>Nam nescit oculus quid radiis CA, CB accidat in transitu A et B, putatque <lb/>illos continuari in rectum ac si essent CAF, CBG, ubi FG imaginata quantitas <lb/>est maior quam DE &rdquo; (ibi, pag. </s>

<s>36). </s></p><p type="main">

<s>Quanto per&ograve; il Keplero &egrave; esatto in questa, altrettanto si mostra impro&shy;<lb/>prio nell'altra proposizione XCVI, dove tratta delle immagini rappresentate <lb/>dalle lenti concave. </s>

<s>L'enunciato <emph type="italics"/>visibilia per cavas lentes rapraesentantur <lb/>minora<emph.end type="italics"/> (pag. </s>

<s>49) &egrave; vero, ma nel processo della dimostrazione si tien che i <lb/>raggi convergano verso l'occhio quasi abbiano le lenti concave, come le con&shy;<lb/>vesse, un foco reale. </s>

<s>Da questo errore principalmente dipende l'insufficienza <lb/>del Keplero a spiegar la ragione del Canocchiale, imperocch&egrave;, sebbene egli, <lb/>nelle due proposizioni XLIV e LXXV, dimostri assai bene il rappresentarsi <lb/>delle immagini reali o rovesciate nelle lenti convesse, non seppe poi vedere <lb/>come, contrapposta una tale immagine reale per oggetto alla lente concava, <lb/>questa, collocata presso l'occhio, per la divergenza e l'incrociamento de'raggi <lb/>in lei rifratti, venisse a ripresentar l'oggetto stesso assai pi&ugrave; grande e di&shy;<lb/>ritto. </s>

<s>&Egrave; perci&ograve; che il nostro Autore nella proposizione CVII, smarrita la sua <lb/>scienza diottrica, si abbandona alla fantasia, la quale gli fa tesser cos&igrave; fatto <lb/>discorso: La lente convessa fa troppo convergere i raggi; la concava gli fa <lb/>roppo divergere, ma composte insieme nel Canocchiale si emendano i due <pb xlink:href="020/01/381.jpg" pagenum="362"/>eccessi, e da ci&ograve; ne segue la visione distinta. </s>

<s>&ldquo; Cavae lentes de circulo ni&shy;<lb/>mis angusto, si proxime oculum applicentur, confusa reddunt, propter ni&shy;<lb/>miam radiorum divergentiam. </s>

<s>Sed radiationes unius puncti, per convexam <lb/>lentem solitariam oculo posito intra centrum concursus, praestant confusam <lb/>visionem propter convergentiam, et illa nimietas divergentiae et haec con&shy;<lb/>vergentia, lentibus in tubum compositis, se mutuo tollunt; sublata ergo <lb/>convergentia et emendata nimia divergentia, sequitur distincta visio &rdquo; (ibi, <lb/>pag. </s>

<s>56). </s></p><p type="main">

<s>Che veramente l'error fatto dal Keplero intorno al divisar le immagini <lb/>nelle lenti concave sia stato precipua causa, per cui egli riusc&igrave; tanto infe&shy;<lb/>riore a s&egrave; stesso nello spiegar la ragione del canocchiale olandese, lo dimo&shy;<lb/>stra l'invenzion del <emph type="italics"/>Canocchiale astronomico,<emph.end type="italics"/> alla quale riusc&igrave; il Diottrico <lb/>alemanno, per avere escluse le lenti concave e per essersi attenuto alle sole <lb/>convesse, delle quali cos&igrave; bene aveva intesa e dimostrata la teoria. </s>

<s>Questo <lb/>&egrave; davvero il primo Canocchiale che non sia stato offerto dal caso, e di cui <lb/>pu&ograve; dir con coscienza il suo Autore che lo ritrov&ograve; <emph type="italics"/>doctrinae de refractio&shy;<lb/>nibus innixus.<emph.end type="italics"/> Intorno alla ragione di questo nuovo strumento, annunziato <lb/>cos&igrave; per la prima volta al pubblico sotto forma di problema: <emph type="italics"/>duobus con&shy;<lb/>vexis maiora et distincta praestare visibilia sed everso situ,<emph.end type="italics"/> il Keplero di&shy;<lb/>scorre al modo seguente: &ldquo; Et quia imago rei visibilis est eversa per unam <lb/>lentem, lens vero propior non evertit denuo quod accipit a remotiori, sed <lb/>sic ut accipit ad oculum transmittit ex supposito: accipit autem respectu <lb/>rei visibilis imaginem eversam; eversam igitur respectu rei visibilis ad ocu&shy;<lb/>lum mittit. </s>

<s>Et quia imago ipsa eversa, prope punctum concursus maior ap&shy;<lb/>paret re ipsa, remotius aequalis et adhuc remotius minor; imago igitur haec <lb/>sic eversa, ubi fuerit ampliata per lentem propiorem, duobus primis casi&shy;<lb/>bus maior omnino evadet re ipsa, ultimo casu vel maior vel aequalis vel <lb/>minor, prout fuerit lentium inter se proportio, quae est in arbitrio artifi&shy;<lb/>cis &rdquo; (ibi, pag. </s>

<s>43). La teoria insomma di questo nuovo Telescopio, &egrave; se&shy;<lb/>condo il Keplero semplicissima: L'immagine reale e rovesciata dell'obiettivo, <lb/>si rappresenta come oggetto alla vista dell'oculare, ed &egrave; da lui virtualmente <lb/>ingrandito, come nel Microscopio. </s></p><p type="main">

<s>Bench&egrave; primo inventore di questo Canocchiale astronomico sia general&shy;<lb/>mente riconosciuto l'Autore della LXXVI proposizione della Diottrica, stam&shy;<lb/>pata nel 1611 in Augusta, nonostante Francesco Fontana, pubblicando in <lb/>Napoli nel 1646 le sue <emph type="italics"/>Novae coelestium terrestriumque verum obser&shy;<lb/>vationes,<emph.end type="italics"/> incomincia cos&igrave; la sua Prefazione: &ldquo; Tubi quadam Optici a me <lb/>anno 1608 duobus lentibus convexis compositi inventione reperta.... &rdquo; </s></p><p type="main">

<s>Ma del Canocchiale astronomico che egli afferma essere stato da s&egrave; in&shy;<lb/>ventato, <emph type="italics"/>de optico tubo astronomico ab Auctore invento<emph.end type="italics"/> ne tratta il Fon&shy;<lb/>tana di proposito nel cap. </s>

<s>VII del libro, dove fra le altre si leggono le se&shy;<lb/>guenti parole: &ldquo; Insuper anno 1608 alium tubum opticum armatum scilicet <lb/>duplici lente convexa construxi &rdquo;. </s>

<s>Non &egrave; per questo che l'Artefice napole&shy;<lb/>tano voglia venire in contesa con l'astronomo tedesco<gap/> dopo aver chiamato <pb xlink:href="020/01/382.jpg" pagenum="363"/>testimoni del fatto che cio&egrave; egli non vide la Diottrica del Keplero prima <lb/>del 1614, cos&igrave; conclude: &ldquo; Mirum autem non est recensitum Keplerum Ger&shy;<lb/>maniae, meque Neapoli talis inventionis authores existere: enimvero omnes <lb/>duobus talentis, intellectu videlicet et operatione ditati sumus &rdquo; (pag. </s>

<s>20). </s></p><p type="main">

<s>Se si potesse provar con documenti pi&ugrave; certi che il Fontana costru&igrave; per <lb/>pratica il canocchiale nel 1608, converrebbe dire che l'occhialaio napoletano <lb/>s'incontr&ograve; nell'invenzione dello strumento nel tempo stesso con l'occhialaio <lb/>olandese, ma perch&egrave;, ripetiamo, non abbiamo di ci&ograve; i documenti certi, e il <lb/>Fontana non fa autorit&agrave; in causa propria, concludiamo il discorso, che ci ha <lb/>divagato dal primo soggetto, dicendo che nel 1611 erano stati fatti intorno <lb/>alla Diottrica specialmente in Italia notabili progressi. </s>

<s>Il Porta e il Mauro&shy;<lb/>lico avevano applicato la Geometria ai raggi rifratti nelle lenti concave e nelle <lb/>convesse; il De Dominis aveva tentato di concluder la teoria del Canocchiale <lb/>da quegli stessi teoremi diottrici dimostrati, e il Keplero aveva di pi&ugrave; ritro&shy;<lb/>vato il nuovo Canocchiale astronomico scortovi dalla scienza delle rifrazioni. </s></p><p type="main">

<s>Tre anni dopo, nel 1614, Giovanni Tarde, passando per Firenze, fu a <lb/>far visita a Galileo, e dopo varii discorsi &ldquo; je l'interpellay, dice lo stesso <lb/>Tarde, sur les r&eacute;fractions et moyen de former le cristal du Telescope en <lb/>telle sorte que les obiets s'agrandissent et s'approchent &agrave; telle proportion <lb/>qu'on vout. </s>

<s>A cela il me respondit que ceste science n'estoit pas encore <lb/>bien cogneue; qu'il ne s&ccedil;avoit pas que personne l'&ecirc;ut traict&eacute; autres que <lb/>ceux qui traitent la Perspective, si ce n'est Joannes Keplerus, math&eacute;mati&shy;<lb/>cien de l'Empereur, qui en a faict un livre expr&egrave;s, mais si obscur, qu'il <lb/>semble que l'autheur mesme ne s'est pas entendu &rdquo; (Boncompagni, Bullet&shy;<lb/>tino ecc, T. XX, Luglio 1887). </s></p><p type="main">

<s>Se nel numero di coloro <emph type="italics"/>qui traitent la Perspective,<emph.end type="italics"/> intendesse Ga&shy;<lb/>lileo di comprendere i soli Alhazen e Vitellione con quel poco e inconclu&shy;<lb/>dente che toccarono delle rifrazioni, o se intendesse aggiungervi il Porta e <lb/>il Maurolico, per quel tanto di pi&ugrave;, di che avevano fatto progredire la scienza; <lb/>&egrave; per noi cosa dubbia, ma pur possiamo con certezza affermare che ingiu&shy;<lb/>stamente escluse Galileo il De Dominis dal numero di coloro che avevano <lb/>trattato delle rifrazioni applicate al Canocchiale. </s>

<s>N&egrave; si pu&ograve; scusare coll'igno&shy;<lb/>ranza del fatto, giacch&egrave; sappiamo che il Sagredo nel Giugno del 1612, aven&shy;<lb/>dogli prima domandato se aveva <emph type="italics"/>veduto un trattato dell'Arcivescovo di Spa&shy;<lb/>latro circa l'occhiale<emph.end type="italics"/> (Alb. </s>

<s>VIII, 213) e avendogli Galileo risposto di no, <lb/>il Sagredo stesso, accompagnatolo con lettera del d&igrave; 7 Luglio, gli mand&ograve; <lb/>poi quel Trattato (Alb. </s>

<s>Suppl., pag. </s>

<s>58). </s></p><p type="main">

<s>Quanto al Keplero non si pu&ograve; negar che, cos&igrave; nella Diottrica come in <lb/>tutte l'altre sue opere, non sia ad esprimersi difficile e duro, n&egrave; si potrebbe <lb/>pure affermare che tutti con chiarezza fossero condotti e conclusi i suoi teo&shy;<lb/>remi diottrici, ma in ogni modo sembrer&agrave; ingiusto a ciascuno imparziale <lb/>Galileo, il quale, non potendo negare il fatto, che cio&egrave; il Matematico del&shy;<lb/>l'Imperatore aveva scritto intorno al Canocchiale <emph type="italics"/>un livre expr&egrave;s,<emph.end type="italics"/> soggiunge <lb/><emph type="italics"/>mais si obscur qu'il semble que l'autheur mesme ne s'est pas entendu.<emph.end type="italics"/></s></p><pb xlink:href="020/01/383.jpg" pagenum="364"/><p type="main">

<s>Questi discorsi insomma fatti al Tarde a noi sembrano tante premesse <lb/>preparate da Galileo all'unico fine di poter concludere, che nessun altro <lb/>prima di lui aveva chiaramente trattato delle rifrazioni nel canocchiale, e <lb/>che questa nuova scienza si doveva aspettar da quel Trattato promesso nel <lb/>Nunzio Sidereo: Trattato che and&ograve; a stemperarsi in poche pagine, scritte <lb/>per incidenza nel Saggiatore. </s>

<s>E ora &egrave; necessario che riprendiamo in mano <lb/>questo libro per decider se tanto vi sia veramente promossa dall'Autore la <lb/>scienza del Canocchiale, da doversi tenere a vile ci&ograve; che vi specularono at&shy;<lb/>torno il Porta, il De Dominis e il Keplero. </s>

<s>Ma prima conviene ai tre com&shy;<lb/>memorati aggiungerne un quarto, nella persona stessa del Tarde, a cui pa&shy;<lb/>rendo queste cose da'suoi predecessori <emph type="italics"/>a quibusdam quidem leviter delibata <lb/>fuisse et ab aliis nimia quodam obscuritate,<emph.end type="italics"/> venne in pensiero di dover <lb/>egli entrare a trattarne pi&ugrave; di proposito e con chiarezza maggiore. </s></p><p type="main">

<s>In appendice infatti alla <emph type="italics"/>Borbonia Sidera,<emph.end type="italics"/> libro stampato in Parigi <lb/>nel 1620, pose un trattatello intitolato <emph type="italics"/>Telescopium.<emph.end type="italics"/> Si prepara, come gli <lb/>altri che lo avevano preceduto, a concluder la ragione dello strumento dal <lb/>modo di operar delle lenti, e nella proposizione XLI dimostra la teoria del <lb/>Microscopio semplice in termini non punto differenti da quelli del Keplero. </s>

<s>Se <lb/>non che egli mesce alla verit&agrave; quell'errore, in cui cadde a principio Gali&shy;<lb/>leo, del creder cio&egrave; che le lenti condensando la luce faccian s&igrave; che gli og&shy;<lb/>getti appariscan pi&ugrave; grandi: &ldquo; Dico, beneficio influentiae, plures radios oculi <lb/>pupillam ingredi et ob illam confluentiam obiectum videri mole auctum &rdquo; <lb/>(ibi, pag. </s>

<s>80). </s></p><p type="main">

<s>Nel divisar poi il modo del rappresentarsi le immagini virtuali nelle <lb/>lenti concave, il Tarde &egrave; il pi&ugrave; preciso di tutti gli Autori che l'hanno pre&shy;<lb/>ceduto. </s>

<s>Leggasi nella proposizione XLVIII cos&igrave; formulata: <emph type="italics"/>Cava lente obiectum <lb/>videtur mole auctum.<emph.end type="italics"/> Ecco com'ei la conduce e la conclude: &ldquo; Cava lens <lb/>extrorsum frangit radios, qui ad oculum accedunt diffluentes, et ad concur&shy;<lb/>sum versus obiectum tendentes. </s>

<s>At res existimantur asse in loco ex quo <lb/>radii deferuntur, cum pupillam intrant; venientes ergo quasi ex concursu, <lb/>visibile repraesentatur minus quam sit &rdquo; (pag. </s>

<s>80). </s></p><p type="main">

<s>Nonostante, nel venire ad applicare la lente concava per oculare del <lb/>Telescopio, anch'egli, come il De Dominis e il Keplero, non ne conosce l'uf&shy;<lb/>ficio, per cui, abbandonata la scienza diottrica, ricorre a una certa Filoso&shy;<lb/>fia, che si potrebbe chiamare <emph type="italics"/>allopatica,<emph.end type="italics"/> assioma della quale &egrave;: <emph type="italics"/>contraria <lb/>contrariis pelli vel saltem emendari<emph.end type="italics"/> (ibi, pag. </s>

<s>86). Ecco infatti come, an&shy;<lb/>ch'egli ammettendo che la divergenza della concava emendi il soverchio con&shy;<lb/>verger della convessa, concluda il modo d'operar delle lenti nel Canocchiale: <lb/>&ldquo; Oculus in concursu omnia videt confusa et obliterata. </s>

<s>Post concursum <lb/>imminuta et eversa positione. </s>

<s>Lens cava radios dispergit, quae dispersio vi&shy;<lb/>sui obest, et eadem prope oculum confusionem parit. </s>

<s>Horum ergo vitrorum <lb/>opus est certa et debita compositione &rdquo; (pag. </s>

<s>84). </s></p><p type="main">

<s>Il Tarde, che ce ne aveva dianzi sviato, &egrave; quello che ora ci riconduce <lb/>al <emph type="italics"/>Saggiatore,<emph.end type="italics"/> imperocch&egrave; chi non riconosce in queste ultime parole citate <pb xlink:href="020/01/384.jpg" pagenum="365"/>quello stesso famoso discorso riferito nel paragrafo XIII dello stesso libro <lb/>del Saggiatore a pag. </s>

<s>208 del IV Tomo delle Opere; discorso da cui dice <lb/>Galileo di essere stato condotto a incontrarsi nell'invenzione del Telesco&shy;<lb/>pio? </s>

<s>E per di pi&ugrave; non ricorre anch'egli, Galileo, in certo modo alla Filo&shy;<lb/>sofia allopatica del Tarde, quando dice che la lente concava &egrave; come la <emph type="italics"/>con&shy;<lb/>traffaccia<emph.end type="italics"/> della convessa, e <emph type="italics"/>l'ultimo bilancio e saldo delle partite?<emph.end type="italics"/> &rdquo; (ivi, <lb/>pag. </s>

<s>202). </s></p><p type="main">

<s>Potrebb'esser che il Francese ripetesse i detti stessi di Galileo, pub&shy;<lb/>blicandoli tre anni prima di lui, ma in ogni modo que'detti erano stati <lb/>pronunziati prima dal De Dominis e dal Keplero, i quali ambedue insomma <lb/>consuonano con quell'altro celebre pronunziato, scritto tanti anni prima nel <lb/>cap. </s>

<s>X del XVII libro della <emph type="italics"/>Magia Naturale: &ldquo; Concavo longe parva vides <lb/>sed perspicua; convexo proprinqua maiora sed turbida: si utrumque recte <lb/>componere noveris, et longinqua et proxima maiora et clara videbis &rdquo;.<emph.end type="italics"/></s></p><p type="main">

<s>Ripensando ora a ci&ograve; che fu ostacolo a tutti i predetti speculatori, in <lb/>riuscir felicemente a intendere la ragione del Telescopio, si vede come si <lb/>riduca tutto quell'ostacolo nella lente concava, il modo d'operar della quale <lb/>sull'immagine rappresentata dalla convessa era rimasto a tutti un mistero. </s>

<s><lb/>N&egrave; il De Dominis n&egrave; il Keplero, n&egrave; il Tarde n&egrave; Galileo s'erano ancora ac&shy;<lb/>corti che l'oggettivo dipinge un'immagine reale e rovesciata innanzi all'ocu&shy;<lb/>lare, il quale l'ingrandisce virtualmente e tutt'insieme la renda diretta. </s>

<s>Vero <lb/>&egrave; bene che Galileo parla del vetro concavo che dilata i raggi <emph type="italics"/>e forma il <lb/>cono inverso<emph.end type="italics"/> (ivi, pag. </s>

<s>202), ma, lasciamo stare che il cono inverso &egrave; for&shy;<lb/>mato pure dal vetro convesso, quando si riceva l'immagine al di l&agrave; del foco, <lb/>questo anzi veniva a complicare pi&ugrave; che mai il mistero, perch&egrave; restava an&shy;<lb/>cora a intendere come mai l'immagine ricevuta per proiezione si rappre&shy;<lb/>sentasse al rovescio, e l'occhio nonostante direttamente applicato la rendesse <lb/>nella posizione sua naturale. </s></p><p type="main">

<s>Eppure, prima che da'quattro insigni Autori sopra citati si venisse in <lb/>pubblico a profferire una scienza del Canocchiale, riuscita nel suo princi&shy;<lb/>pale intento fallace, eravi stato gi&agrave; chi molto meglio di loro aveva colto nel <lb/>segno. </s>

<s>Il solo Porta, infino dall'Agosto del 1609 avea dato a vedere di es&shy;<lb/>sersi inteso che l'ufficio dell'oculare era quello di render le immagini rap&shy;<lb/>presentate dall'obiettivo <emph type="italics"/>chiare e diritte. </s>

<s>&ldquo;<emph.end type="italics"/> Mirando con quel solo primo (col <lb/>vetro convesso) si vedranno le cose lontane vicine, ma perch&egrave; la vista non <lb/>si fa nel cateto, paiono oscure ed indistinte. </s>

<s>Ponendovi l'altro come con&shy;<lb/>cavo, che fa il contrario effetto, si vedranno le cose <emph type="italics"/>chiare e diritte &rdquo;<emph.end type="italics"/> (Ven&shy;<lb/>turi, Memor. </s>

<s>ecc. </s>

<s>ediz. </s>

<s>cit., P. I, pag. </s>

<s>83). Aveva perci&ograve; ragione di dire al <lb/>principe Cesi che tutti i libri che gli aveva mandato del Telescopio, primi <lb/>fra'quali saranno stati quelli del De Dominis e del Keplero, <emph type="italics"/>non sanno se <lb/>sieno vivi e parlano allo sproposito, perch&egrave; non sanno di Prospettiva<emph.end type="italics"/> (ivi, <lb/>pag. </s>

<s>85). Soggiunge poi di aver dato mano egli stesso a scrivere sull'im&shy;<lb/>portante soggetto un libro, che se fosse stato visto prima dal mondo, <emph type="italics"/>non<emph.end type="italics"/><lb/><gap/></s></p><pb xlink:href="020/01/385.jpg" pagenum="366"/><p type="main">

<s>Ci &egrave; senza dubbio in queste parole molto di presunzione, ma pure &egrave; <lb/>un fatto che il Porta aveva penetrato pi&ugrave; addentro al mistero diottrico di <lb/>tutti gli altri, che vi si stillarono il cervello dopo di lui; ond'&egrave; che dietro <lb/>que'teorici insegnamenti pot&egrave; in Roma il principe Cesi aver canocchiali <lb/>avanti che l&agrave; capitasse nessun esempio de'galileiani. </s>

<s>In ogni modo per&ograve; <lb/>prima di riuscire alla difficile soluzion del problema bisognava fare alla Diot&shy;<lb/>trica altri e pi&ugrave; segnalati progressi de'quali dobbiamo ora passare a fare <lb/>brevemente la storia. </s></p><p type="main">

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

<s>Disperando oramai, per gli esempi de'predecessori, di aver a ritrovar <lb/>nella nuova scienza Diottrica una guida sicura da non andare smarriti per <lb/>quegli intricati laberinti, dentro a cui si aggirano i raggi luminosi tra'due <lb/>vetri de'Canocchiali; Cristoforo Scheiner pens&ograve; meglio di ridursi ne'termini <lb/>pi&ugrave; positivi dell'esperienza. </s>

<s>Egli dunque cos&igrave; and&ograve; investigando le propriet&agrave; <lb/>diottriche delle lenti e giunse per questa via a conclusioni non nuove, ma <lb/>in vario modo dimostrate e, per quel ehe riguarda le immagini rappresen&shy;<lb/>tate nelle lenti concave, dall'osservazione de'fatti rese pi&ugrave; chiare: &ldquo; Deinde <lb/>omnibus (concavis) hoc est commune ut baseos communis stationem et pictu&shy;<lb/>ram in charta amplificent, et porro a vitro convexo protrudant, ita ut di&shy;<lb/>stantia eiusdem ab eodem maior evadat, quam si ipsum concavum ad con&shy;<lb/>vexum non esset adhibitum &rdquo; (Oculus, Oeniponti, 1619, pag. </s>

<s>160). </s></p><p type="main">

<s>L'esperienza confermatrice di questa proposizione vien cos&igrave; dall'Autore <lb/>stesso descritta: &ldquo; Statue convexum sphaerae parvae segmentum ad fora&shy;<lb/>men obscurae camerae, obtende chartam ut excipias certam aliquam rei <lb/>extra positae imaginem, picturam praecisam et accuratam. </s>

<s>Intersere omni&shy;<lb/>bus immotis vitrum concavum ea vitrorum intercapedine, quam ipsa in tu&shy;<lb/>bum compacta requirunt: videbis obiectum multo maius esse, quam fuerat <lb/>ante per solum convexum, et si speciem illam distinctam exoptas, oportet <lb/>ut chartam aliquanto amplius a priore statione elonges &rdquo; (ibi, pag. </s>

<s>161). </s></p><p type="main">

<s>Questa esperienza per&ograve; &egrave; viziata da un'ipotesi falsa, la quale consiste <lb/>nell'ammetter che la lente concava, la quale protrude e ingrandisce l'im&shy;<lb/>magine, sia collocata, rispetto alla convessa, in quella positura conveniente <lb/>a dover produrre gli effetti del Canocchiale, imperocch&egrave; allora l'immagine <lb/>stessa, ricevuta per proiezione, &egrave; protrusa e ingrandita si, ma pure anco &egrave; <lb/>rovesciata. </s>

<s>Notabile &egrave; che ci&ograve; non fosse avvertito dallo Scheiner, il quale <lb/>altrove si propone a risolvere il problema <emph type="italics"/>Cur vitrum interius, ante con&shy;<lb/>cursum anterioris collocatum, species non erigit?<emph.end type="italics"/> (ibi, pag. </s>

<s>180) e lo ri&shy;<lb/>solve assai bene, e in modo che applicata quella soluzione al Canocchiale, <lb/>gli avrebbe fatto forse, meglio che a tutti gli altri, intender l'ufficio proprto <lb/>dell'oculare, che &egrave; quello d'ingrandire <emph type="italics"/>et post binam decussationem<emph.end type="italics"/> d'ad&shy;<lb/><gap/></s></p><pb xlink:href="020/01/386.jpg" pagenum="367"/><p type="main">

<s>Non ritrovando perci&ograve;, nemmen cos&igrave;, quella felice riuscita she s'aspet&shy;<lb/>tava, si rivolse lo Scheiner agli argomenti di analogia, e gli parve di ritro&shy;<lb/>varli nella somiglianza che passa tra il modo come opera la natura nell'oc&shy;<lb/>chio, e l'arte nel Telescopio. </s>

<s>Come la camera oscura aveva rivelati i misteri <lb/>dell'occhio, cos&igrave; sperava il nostro Autore che l'occhio stesso rivelerebbe i <lb/>misteri del nuovo strumento. </s>

<s>Nella <emph type="italics"/>Rosa Ursina<emph.end type="italics"/> infatti, stampata in Brac&shy;<lb/>ciano tra il 1626 e il 1630, lo Scheiner intitola il cap. </s>

<s>XXIII del II libro: <lb/><emph type="italics"/>Oculi et Telescopii lentiumque telescopicarum comparatio: naturae et artis <lb/>admirabilis conspiratio<emph.end type="italics"/> (pag. </s>

<s>106) e nel capitolo appresso si propone di <lb/>dimostrare: <emph type="italics"/>Ut tubus oculum, sic oculus in multis arte sequitur tubum<emph.end type="italics"/><lb/>(ibi, pag. </s>

<s>112). Se veramente l'Autore con quella Tavola, che rappresenta <lb/><emph type="italics"/>expressas septem diversas Tubi cum oculo et huius cum Tubo, in specie&shy;<lb/>bus visibilibus recipiendis et praesentandis, rationes et comparationes<emph.end type="italics"/> (ibi, <lb/>pag. </s>

<s>106), riuscisse nell'intento, lasceremo giudicarlo a fra Fulgenzio Mi&shy;<lb/>canzio, in una sua lettera, dove si trovano le seguenti parole dirette a Ga&shy;<lb/>lileo: &ldquo; Il signor Aproino &egrave; qui in Venezia ed &egrave; dietro alla Rosa Ursina <lb/>colle male parole. </s>

<s>L'ho pregato a veder particolarmente quelle tante figure, <lb/>ove il Gesuita vuole dichiarar la natura del Canocchiale col confronto del&shy;<lb/>l'occhio, perch&egrave;, a dirla, in tal cosa dove avevo gran curiosit&agrave; d'intendere <lb/>la dimostrazione, o che io non ne sono stato capace, come credo, o li detti <lb/>dello Scheiner sono pure affermazioni senza prova &rdquo; (Alb. </s>

<s>X, 140). </s></p><p type="main">

<s>Pur troppo &egrave; vero che quelle dell'Autor della Rosa Ursina sono affer&shy;<lb/>mazioni senza prova, n&egrave; poteva essere altrimenti, perch&egrave; lo Scheiner s'era <lb/>grandemente ingannato, credendo che tra l'occhio e il Canocchiale passasse <lb/>quella stretta rassomiglianza che tra l'occhio e la camera oscura, della quale <lb/>qui cade opportuno accennar brevemente alla storia. </s></p><p type="main">

<s>Leonardo da Vinci, nello studiar l'anatomia dell'occhio per poi poterlo <lb/>dipingere con pi&ugrave; verit&agrave; e con maggiore espressione, osservando le pitture <lb/>che si rappresentavano arrovesciate sul fondo di lui, per via de'raggi colorati <lb/>passati attraverso al foro della pupilla, invent&ograve; la camera oscura, che de&shy;<lb/>scrisse ne'suoi Manoscritti, colle seguenti parole, tradotte dal Venturi in <lb/>francese: &ldquo; Lorsque les images des obiets &eacute;clair&eacute;s penetrent par un petit <lb/>trou rond dans un appartement tres-obscur, recevez ces images dans l'in&shy;<lb/>terieur de l'appartement sur un papier blanc situ&eacute; a quelque distance du <lb/>trou, vous verrez sur le papier tous les obiets avec leurs propres formes et <lb/>couleurs, il seront diminu&eacute;s de grandeur, il se presenteront dans une situa&shy;<lb/>tion renvers&eacute;e &rdquo; (Essai ecc., Parigi 1797, pag. </s>

<s>23). </s></p><p type="main">

<s>Il nuovo strumento non doveva servire a semplice curiosit&agrave;, ma fu ap&shy;<lb/>plicato agli usi del disegno, per cui ne fu trasmessa la memoria, non dai <lb/>Manoscritti, da nessuno veduti, ma dalla parola viva e dalle pratiche ope&shy;<lb/>razioni de'Discepoli di Leonardo. </s>

<s>Da qualcuno di essi ne ebbe notizia il gio&shy;<lb/>vanetto Giovan Batista Porta, cbe andava pellegrinando a raccogliere di que&shy;<lb/>ste novit&agrave;, dovunque ne trovasse, ma specialmente appresso ai cultori dell'arte. </s>

<s><lb/>Ei pubblic&ograve; l'invenzione nel cap. </s>

<s>II dell'ultimo de'quattro libri della <emph type="italics"/>Magia<emph.end type="italics"/><pb xlink:href="020/01/387.jpg" pagenum="368"/><emph type="italics"/>Naturale,<emph.end type="italics"/> di cui la prima edizione fu fatta, come altrove dicemmo, nel 1550. <lb/>La descrizione del Porta consuona pienamente con quella di Leonardo, e per <lb/>indizio che una tal primizia fu presentata all'Autore da qualcuno de'pro&shy;<lb/>fessori dell'arte del disegno, si legga ci&ograve; che ivi ne scrive delle applicazioni <lb/>da farsi dello strumento agli usi della pittura: &ldquo; Hinc evenit ut quisque <lb/>picturae ignarus rei alicuius stylo describere possit, dummodo solum colo&shy;<lb/>res assimilare discat hoc in subiectam tabulam vel soli diusculum papyrum <lb/>imagine repercussa. </s>

<s>Erit enim perito facillimum. </s>

<s>Si sol defecerit id alio imi&shy;<lb/>taberis lumine, pleraque alia eveniunt et cognosces, quam et enarrare possi&shy;<lb/>mus, praecipue si diligens inspector pertractaverit &rdquo; (Neapoli, 1558, pag. </s>

<s>144). </s></p><p type="main">

<s>Il Benedetti poi perfezion&ograve; l'invenzione di Leonardo, applicando al foro <lb/>una lente convessa, secondo la descrizione ch'ei ne fa in una delle sue Epi&shy;<lb/>stole, raccolte nel libro delle Speculazioni, la prima edizione del quale si sa <lb/>essere stata fatta nel 1580, e nel 1599 fu fatta in Venezia la seconda, dalla <lb/>quale trascriviamo qui le parole dell'Autore: &ldquo; Ad hoc tamen propositum <lb/>nolo tibi silentio involvi mirabilem quendam effectum eiusmodi rei. </s>

<s>Hoc est <lb/>ut fiat foramen illud rotundum, magnitudinis tamen unius specilli, quod <lb/>foramen obturatur mediante uno illorum specillorum, quae pro senibus (non <lb/>brevis visionis) conficiuntur, hoc est quorum ambae superficies convexae <lb/>sunt, non autem concavae. </s>

<s>Deinde apponatur folium album papiri, adeo <lb/>distans a foramine ut extrinseca obiecta in eo appareant. </s>

<s>Quae quidem obiecta <lb/>si a sole illustrata fuerint, tam clara et distincta videbuntur ut nihil pul&shy;<lb/>chrius delectabiliusque videri poterit, inversa tamen. </s>

<s>Sed si ea directa vi&shy;<lb/>dere voluerimus, hoc optime faciemus mediante reflexione alicuius speculi <lb/>plani &rdquo; (pag. </s>

<s>270). Il Porta, cinque anni dopo, tornando a pubblicar la sua <lb/>Magia in XX libri, nel cap. </s>

<s>VI del XVII torn&ograve; a descrivere la Camera <lb/>oscura, con quegli stessi perfezionamenti che v'avea gi&agrave; introdotto il Fisico <lb/>veneziano. </s></p><p type="main">

<s>Dietro ci&ograve; si comprende bene come la lente cristallina, applicata dal <lb/>Benedetti al foro della camera oscura, presentava una somiglianza con l'oc&shy;<lb/>chio pi&ugrave; parvente e pi&ugrave; provata di quel che non facesse lo strumento di <lb/>Leonardo, specialmente da poi che il Maurolico era venuto a render cos&igrave; <lb/>evidenti gli uffici, che fa nell'occhio l'umor cristallino. </s>

<s>Ma passar dall'oc&shy;<lb/>chio al Canocchiale, come pretendeva l&ograve; Scheiner, era cosa pi&ugrave; ardua, per&shy;<lb/>ch&egrave; la fisiologia della vista naturale implicava maggiori difficolt&agrave; di quelle, <lb/>che si potevano incontrar nella diottrica della vista artificiale. </s>

<s>Piuttosto che <lb/>servirsi dell'occhio a intendere il Canocchiale sarebbe stato pi&ugrave; conveniente <lb/>servirsi di questo a intender quello, come per esempio si vede nella cele&shy;<lb/>bre questione delle immagini rovesciate sopra la retina, le quali si vedon <lb/>diritte a quel modo e per quella stessa ragione, che si vedon diritte nel <lb/>Canocchiale, bench&egrave; si rappresentino a rovescio ricevute sopra una carta per <lb/>proiezione. </s></p><p type="main">

<s>In ogni modo, la principale delle ragioni per cui cos&igrave; lo Scheiner come <lb/>tutti gli altri s'incontrarono in quelle insuperabili difficolt&agrave;, dee senza dub-<pb xlink:href="020/01/388.jpg" pagenum="369"/>bio ripetersi dall'aver tutti a un modo ignorata la legge dei raggi refratti. </s>

<s>Or <lb/>perch&egrave; una tal legge fu dal Cartesio cos&igrave; ben dimostrata, chi non s'aspet&shy;<lb/>terebbe mai che la teoria del Canocchiale non si dovesse aver finalmente <lb/>chiara e spiegata dal celebre Autore, in quel cap. </s>

<s>VII della <emph type="italics"/>Diottrica,<emph.end type="italics"/> or&shy;<lb/>dinato giusto a trattar <emph type="italics"/>De modis visionem perficiendi?<emph.end type="italics"/> Eppure &egrave; un fatto <lb/>che la teoria cartesiana &egrave; la pi&ugrave; goffa di quante altre mai ne avessero spe&shy;<lb/>culate i suoi predecessori. </s></p><p type="main">

<s>Parte l'Autore da questo principio: che tanto cio&egrave; pi&ugrave; grandi si rap&shy;<lb/>presentino all'occhio gli oggetti, quanto pi&ugrave; di lontano v'entrano per la <lb/>pupilla i raggi luminosi incrociati. </s>

<s>&ldquo; Unicus tamen adhuc modus has ima&shy;<lb/>gines augendi restat, quo nempe efficimus ut radii, ex diversis punctis missi, <lb/>quam longissime fieri potest ab oculi fundo decussentur &rdquo; (Francof. </s>

<s>1692, <lb/>pag. </s>

<s>80). Ora, pensava il Cartesio, che il Canocchiale &egrave; un tal artifizio, per <lb/>cui i raggi, che s'incrocerebbero sulla superficie dell'occhio, s'incrociano <lb/>invece sulla superficie dell'obiettivo, di guisa che il massimo e principale <lb/>efficiente della visione telescopica non sarebbe mica costituito dalle lenti, le <lb/>quali poco importa che abbiano una figura piuttosto che un'altra, ma s&igrave; <lb/>dalla lunghezza del tubo: la qual lunghezza potendosi ridurre a qualunque <lb/>misura illimitata, fa s&igrave; che la potenza, che si pu&ograve; dar dall'artefice a un Ca&shy;<lb/>nocchiale, &egrave; indefinita. </s>

<s>&ldquo; Unicus utpote qui ad obiecta tam accessa quam <lb/>inaccessa, usum sui praebere possit, et cuius effectus nullis terminis cir&shy;<lb/>cumscribitur; ita ut huius ope, imagines semper in maius augendo usque ad <lb/>indefinitam quantitatem expandere possimus &rdquo; (ibi). </s></p><p type="main">

<s>L'Huyghens, dop'aver notate queste cartesiane goffaggini, soggiunge: <lb/><emph type="italics"/>Quod vix credibile de tanto viro, tamque in his rebus versato.<emph.end type="italics"/> Noi per&ograve;, <lb/>che conosciamo oramai il Cartesio, sappiamo che cos&igrave; fatte goffaggini sono <lb/>il frutto legittimo della sua Filosofia naturale, e siam persuasi che, se fosse <lb/>tornato a filosofare Aristotile nel 1637, non avrebbe discorso altrimenti dal&shy;<lb/>l'Autor della Diottrica intorno alle ragioni del Canocchiale. </s></p><p type="main">

<s>Le parole sopra citate le scriveva l'Huyghens a pag. </s>

<s>166 di un suo <lb/>libro, che pur s'intitola la <emph type="italics"/>Dioptrica,<emph.end type="italics"/> ma che tanto differisce dalla Dioptrica <lb/>cartesiana, quanto dalle fucate immagini differisce la realt&agrave; degli oggetti. </s>

<s><lb/>Bench&egrave; fosse quell'opera insigne, dalla quale il Newton e la scienza della <lb/>luce rifratta ebbero cos&igrave; validi impulsi, pubblicata postuma in Leyda nel 1703, <lb/>nonostante erano stati gi&agrave; infino dal 1659 dimostrati e posti in ordine di <lb/>trattato i principali teoremi. </s>

<s>Nel <emph type="italics"/>Systema Saturnium<emph.end type="italics"/> infatti citava l'Huy&shy;<lb/>ghens la sua Diottrica ne'termini seguenti: &ldquo; Illud enim in <emph type="italics"/>Dioptricis no&shy;<lb/>stris<emph.end type="italics"/> demonstratum invenietur, speciei per tubum visae ad eam quae nudo <lb/>oculo percipitur, hanc secundum diametrum esse rationem, quae distantiae <lb/>foci in exteriori vitro, ad illam quae in interiori sive oculari vitro est, foci <lb/>distantiam &rdquo; (Oper. </s>

<s>var. </s>

<s>Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>538). </s></p><p type="main">

<s>Questo stesso teorema fu posto poi nella Diottrica per fondamento alla <lb/>teoria del Canocchiale, e intorno a ci&ograve; cos&igrave; l'Huyghens stesso scrive: &ldquo; Quod <lb/>enim hic prae caeteris requirebatur, ut data lentium forma ac positu, ex <pb xlink:href="020/01/389.jpg" pagenum="370"/>his modus mensuraque amplificandae rei visivac definiretur, id hactenus <lb/>praestitum non est. </s>

<s>Nam neque Keplerus hoc docuit, etsi multa laude di&shy;<lb/>gnus ob ea quae in Dioptricis primus explicuit. </s>

<s>Neque illo felicior fuit Car&shy;<lb/>tesius, imo ut vere dicam a via potius aberravit in his quae de ratione <lb/>et effectu Telescopii demonstranda susceperat &rdquo; (Dioptr. </s>

<s>Lugd. </s>

<s>Bat. </s>

<s>1703, <lb/>pag. </s>

<s>166). </s></p><p type="main">

<s>Rispetto a Galileo per&ograve; &egrave; certissimo ch'ei non seppe dimostrare il teo&shy;<lb/>rema diottrico ugeniano, e infatti nel Nunzio Sidereo (Alb. </s>

<s>III, 61, 62) in&shy;<lb/>segna il modo di trovar la potenza amplificativa del Canocchiale, non desu&shy;<lb/>mendola dall'intrinseca costituzione diottrica di lui, ma dalla comparazione <lb/>degli effetti estrinsecamente osservati. </s>

<s>Sembra per&ograve; che avesse ritrovato di <lb/>quello stesso diottrico teorema la conclusione pratica, e ci&ograve; s'argomenta da <lb/>quel che ne riferisce il Tarde del citato colloquio avuto con Galileo, dal qual <lb/>colloquio il Francese trov&ograve; da raccoglier e far capitale di due notizie im&shy;<lb/>portanti, <emph type="italics"/>le premier<emph.end type="italics"/> delle quali &egrave; <emph type="italics"/>que tant plus le cristal convexe prend <lb/>une portion d'un plus grand cercle et le concave d'un plus petit, tant <lb/>plus on voit loin.<emph.end type="italics"/></s></p><p type="main">

<s>Ma l'Huyghens &egrave; veramente il primo che dimostri, nella proposi&shy;<lb/>zione XLVIII, con tutto il rigor matematico, e sui fondamenti della scienza <lb/>diottrica il teorema che il Telescopio amplifica <emph type="italics"/>secundum rationem foci <lb/>distantiae lentis convexae ad distantiam puncti dispersus lentis cavae<emph.end type="italics"/> (ibi, <lb/>pag. </s>

<s>167). Come pure &egrave; il primo che, in quella stessa proposizione, intorno <lb/>alla teoria del Canocchiale, conduce a felice porto i Diottrici, dop'esservisi <lb/>tante volte imbarcati, e aver fatti altrettanti naufragi. </s>

<s>Nelle altre proposi&shy;<lb/>zioni poi seguita a dimostrare il modo e la ragion dell'ingrandimento degli <lb/>astri nel canocchial Kepleriano con due lenti convesse, e ne'canocchiali a tre <lb/>e a quattro lenti, procedendo in tutto con quell'ordine e con quell'acume <lb/>e profondit&agrave; d'investigazioni, che &egrave; proprio dell'Autore. </s></p><p type="main">

<s>Dovrebbesi a questo punto terminare il presente capitolo della nostra <lb/>Storia, ma per tante vie tortuose ci siam dovuti aggirare, e tante volte ab&shy;<lb/>biamo dovuto interrompere e riappiccar poi il filo al nostro discorso, che <lb/>per maggior chiarezza sentiamo il bisogno e il dovere di ristringerlo in una <lb/>breve conclusione. </s></p><p type="main">

<s>A chi ebbe il primo concetto e ne fece intraveder la possibilit&agrave;, si deb&shy;<lb/>bono i primi meriti di un'invenzione, e se cos&igrave; l'avesse intesa il Grisellini <lb/>non irragionevolmente avrebbe chiamato, a pigliar una delle prime parti <lb/>nell'invenzione del Canocchiale, il suo Paolo Sarpi. </s>

<s>Che poi il giovane Ser&shy;<lb/>vita con proporre quella sua lente parabolica avesse ingerito nelle menti il <lb/>fermento delle speculazioni, oltre agli esempi sopra citati, giova addur quello <lb/>di un uomo, che ebbe amichevoli consuetudini e ricev&egrave; ammaestramenti da <lb/>fra Paolo, Daniele Antonini, il quale scriveva cos&igrave; in una sua lettera a Ga&shy;<lb/>lileo: &ldquo; Pensavo questi giorni circa l'effetto di questi occhiali e dietro alle <lb/>mie speculazioni parevami che il solo vetro convesso dovesse fare questi ef&shy;<lb/>fetti e in maggior perfezione di quello che dal convesso e concavo insieme <pb xlink:href="020/01/390.jpg" pagenum="371"/>far veggiamo. </s>

<s>E questo seguivami supponendo che il vetro convesso, nel <lb/>rifrangere i raggi, li unisse tutti in un punto, e preso un tal vetro in mano <lb/>vedevo che, nell'allontanarlo dall'occhio, mi cresceva l'oggetto mirato, ma <lb/>sempre pi&ugrave; me lo confondeva, sicch&egrave; ho creduto poi e credo ancora che <lb/>quel confondersi dell'oggetto non sia per altro, che perch&egrave; i raggi fratti non <lb/>concorrono nell'istesso punto, ma in diversi, alle quali diversit&agrave; di concorsi <lb/>rimedii, poi in parte il concavo, talch&egrave; potendo noi fare un convesso di tal <lb/>natura che mandi i raggi fratti ad unirsi in un sol punto, a me pare che, <lb/>senz'altro concavo, mettendo l'occhio nel punto dell'unione, vedremmo una <lb/>cosa infinitamente lontana, non maggior per s&egrave; stessa che il vetro, nello <lb/>stesso angolo che veggiamo il vetro. </s>

<s>Ora di tal natura parmi che debba es&shy;<lb/>sere un vetro, che abbia la superficie parabolica, e siccome la forma para&shy;<lb/>bolica concava riflette i raggi tutti in un punto, il che non fa la sferica; <lb/>cos&igrave; debba anco, l'istesso che nella riflessione, serbare nella rifrazione &rdquo; <lb/>(Alb. </s>

<s>VIII, 139). </s></p><p type="main">

<s>Galileo rispondeva che sarebbe quell'effetto stato meglio prodotto da un <lb/>vetro che <emph type="italics"/>piuttosto si accosti all'iperbola che alla parabola<emph.end type="italics"/> (ivi, pag. </s>

<s>152) <lb/>ma non aveva altra ragione d'asserir ci&ograve; dall'autorit&agrave; in fuori di quel Ke&shy;<lb/>plero, che in mezzo a'trucidati fratelli, volutisi ingerire del Canocchiale, &egrave; il <lb/>solo rimasto semivivo. </s>

<s>Il Kepler in fatti, nella proposizione LIX della Diottrica <lb/>aveva, contro il Porta e perci&ograve; contro lo stesso Sarpi, cos&igrave; concluso: &ldquo; Su&shy;<lb/>perficies densi quae parallelos per corpus venientes, post corpus refractione <lb/>facta, perfecte concurrere facit, est hyperbolicae adfinis.... Parabola vero, <lb/>etsi idem facit, non est tamen similis quaesitae superficiei, ob hanc causam: <lb/>nullum enim ad certum angulum sese accomodat &rdquo; (Aug. </s>

<s>Vind. </s>

<s>1611, pag. </s>

<s>21). </s></p><p type="main">

<s>Abbiamo detto che Galileo non poteva aver del suo asserto nessuna <lb/>buona ragione, perch&egrave; tanto egli quanto il Kepler e il Sarpi, erano tutti <lb/>ugualmente in un inganno, scoperto poi cos&igrave; dal Cavalieri: &ldquo; Gli specchi <lb/>sferici e le lenti, le quali sieno poco colme, saranno quasi insieme e para&shy;<lb/>boliche e iperboliche, e per&ograve; accostandosegli tanto faranno ancora gli effetti <lb/>a quelli proprinquissimi, il che insieme potr&agrave; credo, servire per isgannare <lb/>alcuni, che stimano che un paro d'occhiali parabolici o iperbolici fossero per <lb/>far l'effetto del Canocchiale, perch&egrave;, se cos&igrave; fosse, accostandosi tanto vicino <lb/>le lenti sferiche e pochissimo colme alla detta curvit&agrave;, ce ne dariano pur <lb/>qualche segno, il che non si vede, mentre non si accompagnino co&igrave; tra&shy;<lb/>guardo (oculare) &rdquo; (Specchio Ust., Bologna 1650, pag. </s>

<s>130). </s></p><p type="main">

<s>Il modo dunque di mettere in pratica il primo concetto del Sarpi fu <lb/>cos&igrave; finalmente dimostrato fallace dalla Geometria del Cavalieri, ma non &egrave; <lb/>perci&ograve; che fra Paolo si debba, nell'invenzione dello strumento da veder le <lb/>cose lontane, defraudare dei primi onori. </s>

<s>I secondi onori si debbono al Porta, <lb/>che divulg&ograve; i concetti del Sarpi nella <emph type="italics"/>Magia<emph.end type="italics"/> e che addirizz&ograve;, col Trattato <lb/>delle Rifrazioni, le prime vie a sciogliere il difficile problema della vision <lb/>telescopica: si debbono i terzi onori a quell'artefice, che primo esegu&igrave; ci&ograve; <lb/>che il Porta aveva proposto, e i quarti onori convengono a Galileo. </s></p><pb xlink:href="020/01/391.jpg" pagenum="372"/><p type="main">

<s>Or resta a sodisfar chi legge di una curiosit&agrave;: come mai Galileo, che <lb/>viene in quarto luogo, riusc&igrave; a legare cos&igrave; strettamente il suo nome al nuovo <lb/>strumento, da non si poter definire altrimenti che chiamandolo <emph type="italics"/>Canocchiale <lb/>galileiano?<emph.end type="italics"/> Le ragioni di ci&ograve; son varie e la prima si riduce a quell'auto&shy;<lb/>rit&agrave;, che s'era oramai conquistata il Principe della nuova Filosofia, il quale, <lb/>bench&egrave; non fosse nella invenzione soccorso dalla scienza delle rifrazioni, n&egrave; <lb/>da altro vi fosse scorto, come dalla somiglianza che in qualche modo passa <lb/>tra il Canocchiale e l'occhio, intorno al modo del veder del quale egli cos&igrave;, <lb/>contro all'opinion comune aberrava; pot&egrave; nulladimeno con quella sua au&shy;<lb/>torit&agrave; far velo al difetto delle proprie speculazioni, e far creder sue quelle <lb/>mendicate dagli altri. </s>

<s>Si aggiunga lo zelo de'partigiani, i quali si studiavano <lb/>d'avvilire i concorrenti nell'invenzione, e di negar loro i diritti, come il Sa&shy;<lb/>gredo fece rispetto al Porta, e come, rispetto al Sarpi, poi fece il Dati, rim&shy;<lb/>proverandolo di aver fatto un gran torto a Galileo, da lui ben conosciuto e <lb/>praticato, <emph type="italics"/>non lo nominando punto n&egrave; poco dove fa menzione del Canoc&shy;<lb/>chiale e delli scoprimenti celesti<emph.end type="italics"/> (Lettere, Firenze 1825, pag. </s>

<s>160). Eppure <lb/>&egrave; il vero che il Sarpi invece avrebbe potuto rimproverar giustamente Ga&shy;<lb/>lileo, rispetto agli scoprimenti celesti, e rispetto al Canocchiale i documenti <lb/>dimostrano che il Dati asser&igrave; il falso, forse per non aver ben lette le let&shy;<lb/>tere di fra Paolo, o per non avere atteso a quel <emph type="italics"/>Matematico di Padova,<emph.end type="italics"/> di <lb/>cui ivi si parla, e che si commemora primo fra tutti coloro, che del Ca&shy;<lb/>nocchiale <emph type="italics"/>principiarono a valersi per l'Astronomia &rdquo;<emph.end type="italics"/> (Polid., Lett. </s>

<s>cit., <lb/>T. II, pag. </s>

<s>41). </s></p><p type="main">

<s>Un'altra delle ragioni, per cui si congiunse con quello del Canocchiale <lb/>il nome di Galileo, fu perch'egli riusc&igrave; artefice pi&ugrave; esperto di tutti gli altri. </s>

<s><lb/>Si sa che egli aveva certi suoi <emph type="italics"/>artificii da lavorare gli occhiali, delli quali <lb/>artificii parte vanno murati<emph.end type="italics"/> (Alb. </s>

<s>VI, 124) ma s'ignorano i modi partico&shy;<lb/>lari di quegli artificii, che l'inventore si studiava di tener, quanto fosse pos&shy;<lb/>sibile, segreti. </s></p><p type="main">

<s>Il pi&ugrave; efficace segreto per&ograve; che condusse Galileo a perfezionar di tanto <lb/>il Canocchiale, sopra l'opera di tutti gli altri artefici ordinarii, consisteva <lb/>nell'aver conosciuto che il buon effetto delle lenti dipende principalmente <lb/>dalla loro figura. </s>

<s>Fu per lui una fortuna l'aver da giovane atteso a un'an&shy;<lb/>tico insegnamento di Seneca, rinfrescato nel I libro <emph type="italics"/>De refractione<emph.end type="italics"/> dal Porta, <lb/>dove, nella proposizione XI, l'Autore cos&igrave; scriveva: &ldquo; Sed cur sub vitro et <lb/>aquis maiora videantur aliam quoque (Seneca) habet rationem ex rotunda <lb/>vasis forma, quam reddemus quum de vitrea pila loquemur &rdquo; (Neapoli 1593, <lb/>pag. </s>

<s>20). Conforme a questi insegnamenti, occorrendo al giovane Galileo di <lb/>toccar la ragione perch&egrave; le frutta nel rinfrescatoio appariscano pi&ugrave; grandi, <lb/>la riconosce anch'egli, come il Filosofo antico, non nell'acqua, ma nella <lb/>forma conica del vaso di vetro: &ldquo; Verum, non aqua, sed calicis figura, ta&shy;<lb/>lis effectus causa &rdquo; (Opere, Ediz. </s>

<s>nazion., Firenze 1890, Vol. </s>

<s>I, pag. </s>

<s>314). </s></p><p type="main">

<s>Ma in ogni modo, la principal ragione per cui il Canocchiale a due <lb/>lenti, una concava e l'altra convessa, si disse, e non immeritatamente si <pb xlink:href="020/01/392.jpg" pagenum="373"/>dura tuttavia a chiamare <emph type="italics"/>galileiano,<emph.end type="italics"/> consiste nell'aver Galileo il primo ap&shy;<lb/>plicato lo strumento e scoprir tante nuove maraviglie nel cielo, e nell'averlo <lb/>saputo adattare a varii usi astronomici, come per esempio a misurar le <lb/>piccole distanze fra le stelle, e fra i satelliti gioviali. </s>

<s>Questa &egrave; vera gloria <lb/>di lui, e la massima gloria, alla quale egli avrebbe senza dubbio maggior&shy;<lb/>mente conferito, se avesse renunziato alle pretensioni di apparir Autore del <lb/>Canocchiale, e se, con pi&ugrave; sincerit&agrave;, avesse al pubblico confessato niente <lb/>altro pi&ugrave; spettargli che le ultime parti nella tanto ambita invenzione. </s></p><pb xlink:href="020/01/393.jpg"/><p type="main">

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

<s><emph type="center"/><emph type="bold"/>De'Canocchiali del Fontana, del Torricelli e di altri; <lb/>del Telescopio a riflessione<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

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

<s>I. De'Canocchiali di Girolamo Sirturo e di Francesco Fontana. </s>

<s>&mdash; II. De'Canocchiali di Evangelista <lb/>Torricelli. </s>

<s>&mdash; III. </s>

<s>Del segreto usato dal Torricelli, per lavorare i vetri da Canocchiali. </s>

<s>&mdash; IV. </s>

<s>Con&shy;<lb/>siderazioni e giudizi intorno al Torricelli come costruttore di Canocchiali, specialmente da ser&shy;<lb/>vire per gli usi astronomici. </s>

<s>&mdash; V. De'Canocchiali di Cristiano Huyghens. </s>

<s>&mdash; VI. De'Canocchiali. </s>

<s><lb/>di Giuseppe Campani e di Eustachio Divini. </s>

<s>&mdash; VII. De'Telescopi a riflessione. </s></p><p type="main">

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

<s>L'ammirazione e la gloria, che Galileo erasi acquistata per s&egrave;, e l'uti&shy;<lb/>lit&agrave; che era venuta ai progressi dell'Astronomia, per la invenzione, o di&shy;<lb/>ciam pi&ugrave; propriamente per la nuova arte squisita, che egli ebbe di fabbri&shy;<lb/>care i Canocchiali, non potevano non eccitare gl'ingegni ad emularne gli <lb/>esempii, e a studiarsi d'introdurre un qualche perfezionamento in quell'arte <lb/>stessa, che dalle mani di un uomo solo, non poteva essere uscita perfetta. </s></p><p type="main">

<s>Fra costoro, che si misero all'opera &egrave; da annoverar per primo quel <lb/>Girolamo Sirturo, che sul campanile di S. </s>

<s>Marco in Venezia, a cui tocc&ograve; <lb/>la sorte di essere il primo teatro, su cui si rappresent&ograve; la nuova scena me&shy;<lb/>ravigliosa, faceva spettacolosa mostra de'suoi Canocchiali, rivaleggiando con <lb/>Galileo. </s>

<s>Egli ci si mostra quasi cavalier di ventura, che va in cerca di chi <lb/>gli insegni la nuova arte stupenda, e trov&ograve;, girando cos&igrave; il mondo, in Spa&shy;<lb/>gna quell'uomo che andava cercando, e che lo fece penetrare addentro alla <lb/>sua segreta officina. </s>

<s>Uscito di l&igrave; e tornato a Milano, si dette tutto agli eser&shy;<lb/>cizii della Diottrica, ma non gi&agrave; di quella scientifica, s&igrave; bene di quella pra&shy;<lb/>tica, che egli aveva appresa dal suo buono Spagnuolo in Gironda. </s>

<s>Il Kenlero, <pb xlink:href="020/01/394.jpg" pagenum="375"/>egli dice, ha scritto del Canocchiale per scienza, e ha insegnate nel suo libro <lb/>tante altre belle cose, le quali <emph type="italics"/>quid tamen nobis contulerint, aut quid fa&shy;<lb/>cient ad rem nostram, peritorum iudicio relinquam. </s>

<s>Hoc scio neminem <lb/>hueusque praestitisse ex arte. </s>

<s>Ego non ex demonstrationibus opticis, non <lb/>ex scientia, sed ex innumeris experimentis hausisse fateor, sumptu, la&shy;<lb/>bore, et sanitatis detrimento<emph.end type="italics"/> (pag. </s>

<s>75). </s></p><p type="main">

<s>E perch&egrave; della sua arte, cos&igrave; con tanti sacrifizii imparata, ne possa usu&shy;<lb/>fruire il mondo, e tu, studioso lettore, possa saper <emph type="italics"/>me non mihi ipsi, sed <lb/>aliis natum, celebri omni aevo futurum adinventum non adhuc editum, <lb/>nec cuiquam praeter uni amico datum, tibi reseratum eo, quisquis es, vir&shy;<lb/>tuti addictus libenter suscepturus, ut studii et laboris mei monumentum <lb/>aliquod perpetuo apud te et alios studiosos extet<emph.end type="italics"/> (ibi). </s></p><p type="main">

<s>Il memoriale, di cui qui intende il Sirturo, &egrave; il suo <emph type="italics"/>Telescopium, sive <lb/>Ars perficiendi novum illud Galilaei visorium instrumentum ad Sydera,<emph.end type="italics"/><lb/>libretto di 81 pagine, stampato a Francfort nel 1618, a cui si riferiscono i <lb/>passi e i luoghi sopra citati, e dove l'Autore generosamente rivela i pi&ugrave; ge&shy;<lb/>losi segreti dell'arte sua. </s></p><p type="main">

<s>E bench&egrave; questi segreti si risolvano in molti minuti particolari, &egrave; da <lb/>notar nonostante ci&ograve; che egli dice del torno, e del modo di attaccare al ma&shy;<lb/>cinello le lenti. </s>

<s>Il Sagredo, che pur ebbe esperta la mano nel fabbricar ca&shy;<lb/>nocchiali, confessa di aver <emph type="italics"/>fatto inutilmente prova di lavorare al torno i <lb/>vetri e pulirli<emph.end type="italics"/> (Campori, Cart. </s>

<s>gal., Modena 1881, pag. </s>

<s>139), ma il Sirturo <lb/>riconosce quello strumento, non solamente utile, ma necessario, ad arroton&shy;<lb/>dare le lenti uscite fuori dalla fornace, purch&egrave; per&ograve; sia costruito di ferro <lb/>adamantino, come son costruiti i torni, i quali <emph type="italics"/>Augustae venundantur.<emph.end type="italics"/></s></p><p type="main">

<s>Quanto al modo poi di attaccare le lenti, perch&egrave; stieno, nel lavorarle, <lb/>ben salde in sul tornio, ha il Sirturo un segreto importante, il quale con&shy;<lb/>siste nel suggerir, per materia cementizia, non l'uso della pece o di altro <lb/>caldo bitume, ma del gesso: &ldquo; Utere igitur gypso, ubi lens sive plano, sive <lb/>convexo adlaboretur &rdquo; (ibi, pag. </s>

<s>48). </s></p><p type="main">

<s>Con tutti i suoi segreti ingegnosi artifizii per&ograve;, non giunse il Sirturo <lb/>a lavorar Canocchiali punto migliori di que'primi, che erano usciti dalle <lb/>mani di Galileo, e bench&egrave; racconti che asceso in cima alla Torre di S. Marco, <lb/>per fare esperienza del suo strumento, <emph type="italics"/>inde nobilis iuventutis turba tanta <lb/>curiositate sursum ferebatur, ut parum abfuerit quin me obrueret<emph.end type="italics"/> (ibi, <lb/>pag. </s>

<s>25) fu nonostante l'Ottico milanese all'ultimo lasciato solo, e al Ma&shy;<lb/>tematico di Padova furono dalla Signoria regalati que'tanti zecchini, quanti <lb/>Giovanni Bartoli ne contava nella sua lettera al Vinta. </s></p><p type="main">

<s>Mentre intanto Galileo si compiaceva della sua vittoria, la quale veni&shy;<lb/>vagli tutti i giorni sempre pi&ugrave; confermata da que'tanti, che d'ogni parte <lb/>eran costretti di ricorrere a lui, se volevano aver Canocchiali di qualche ef&shy;<lb/>fetto; sorse un altro pi&ugrave; valido concorrente a tentargli l'animo di gelosia, <lb/>e ad amareggiargli il gusto di quella compiacenza. </s>

<s>Fu costui quel France&shy;<lb/>sco Fontana che, nell'altro capitolo, udimmo vantarsi d'aver per pratica co-<pb xlink:href="020/01/395.jpg" pagenum="376"/>struito il Canocchiale astronomico, tre anni prima che il Keplero lo proget&shy;<lb/>tasse per teoria. </s>

<s>Com'ei riuscisse a far ci&ograve;, quando ancora alle orecchie di <lb/>nessuno in Italia non era approdata la notizia del ritrovato olandese, sarebbe <lb/>cosa a sapersi molto importante, ma pur l'Inventore si tace, contentandosi <lb/>di addur le testimonianze del padre Cysat, che fa il Canocchiale antico quanto <lb/>Tolomeo, e trascrivendo ci&ograve; che ne disse il Porta, nel cap. </s>

<s>X del XVII li&shy;<lb/>bro della Magia. </s>

<s>&ldquo; Adscribitur etiam, egli poi soggiunge, inventio Galilaeo, <lb/>sed meo iudicio, vel quia theoricam Portae in praxim deduxit, vel quia per&shy;<lb/>fecit &rdquo; (Novae Observ., Neap. </s>

<s>1646, pag. </s>

<s>12). Ma perch&egrave; la teorica del Porta <lb/>appella al Canocchiale coll'oculare concavo, &egrave; difficile indovinar se di l&igrave; o <lb/>d'altrove, deducesse il Fontana la pratica del suo primo canocchiale coll'ocu&shy;<lb/>lare convesso, n&egrave; men facile pure &egrave; rilevar dalle parole di lui come e quando <lb/>gli occorresse di dar mano a fabbricar canocchiali sull'andare di quello di <lb/>Galileo. </s></p><p type="main">

<s>Comunque sia, di questi nuovi canocchiali venuti da Napoli le prime <lb/>notizie e le prime prove testimoniali della loro eccellenza sembra che giun&shy;<lb/>gessero alle orecchie, e pervenissero nelle mani di Benedetto Castelli. </s>

<s>Col <lb/>nuovo strumento s'eran fatte gi&agrave; nella Luna osservazioni importanti, nelle <lb/>sere de'31 Ottobre 1629 e 20 e 24 Giugno 1630. Di ci&ograve; dava notizia fra <lb/>Fulgenzio Micanzio a Galileo, cos&igrave; scrivendo: &ldquo; &Egrave; stato mandato qui un'os&shy;<lb/>servazione della Luna fatta nel 1629 e 1630 da un Francesco Fontana in <lb/>Napoli. </s>

<s>Questo, per le relazioni che ho, non &egrave; uomo di lettere, ma col con&shy;<lb/>tinuo operare e fabbricar canocchiali, si dice esser caduto in una tal sin&shy;<lb/>golarit&agrave; che per le cose del cielo &egrave; un miracolo &rdquo; (MSS. Gal., P. VI, <lb/>T. XIII, c. </s>

<s>110). </s></p><p type="main">

<s>La Selenografia, di cui parla il Micanzio in questa lettera, che &egrave; del <lb/>31 Luglio 1638; Selenografia che fu pubblicata dall'Autore nelle tre Ta&shy;<lb/>vole, che si vedono a pag. </s>

<s>81, 83, 85 della <emph type="italics"/>Novae Observationes,<emph.end type="italics"/> era stata <lb/>gi&agrave;, parecchi mesi prima che al frate Veneziano, mandata al Castelli, e da <lb/>lui spedita in Genova al Renieri, il quale ne scrive in questi termini a Ga&shy;<lb/>lileo: &ldquo; &Egrave; giunto a Genova un ritratto della Luna inviato qu&agrave; dal P. D. </s>

<s>Be&shy;<lb/>nedetto Castelli, con voce d'un Telescopio nuovo inventato da un tal Fon&shy;<lb/>tana a Napoli, che mostra pi&ugrave; squisitamente le cose che non fanno i consueti. </s>

<s><lb/>Non so se ella ne abbia notizia; tuttavia, per quel che dalla detta Seleno&shy;<lb/>grafia posso comprendere, non so se sia per corrispondere al grido. </s>

<s>Se ne <lb/>ha intesa cosa alcuna, di grazia, me ne dia parte &rdquo; (Alb. </s>

<s>X, 285). </s></p><p type="main">

<s>Il Castelli, che della nuova invenzione aveva diffusa la notizia a Ge&shy;<lb/>nova, non &egrave; credibile che non l'avesse comunicata prima al suo venerato <lb/>maestro d'Arcetri. </s>

<s>Comunque sia, &egrave; certissimo, che, nel Marzo del 1638, <lb/>quando il Renieri scrisse quella lettera, Galileo aveva avuto gi&agrave; da un anno, <lb/>la notizia del canocchiale napoletano, e l'aveva avuta da Roma da Raffaello <lb/>Magiotti, il quale, il d&igrave; 21 Marzo 1637, cos&igrave; gli scriveva: &ldquo; Frattanto gli d&ograve; <lb/>nuova come da Napoli &egrave; venuto un cristallo che porta 15 palmi di cannone: <lb/><gap/> alle stelle <pb xlink:href="020/01/396.jpg" pagenum="377"/>Medicee, ma per&ograve; non termina bene il disco di Giove, mostrandolo imban&shy;<lb/>bagiato. </s>

<s>Cos&igrave; ne sono venuti dal medesimo maestro al padre Benedetto di <lb/>pi&ugrave; corti, ma per&ograve;, per mio giudizio, molto migliori, talch&egrave; tengo per si&shy;<lb/>curo che questo strumento sia per avanzare pi&ugrave; che mai, nonostante che <lb/>molti peripatetici di Roma affermino ostinatamente esser tutte illusioni degli <lb/>occhi &rdquo; (MSS. Gal., P. VI, T. XIII, c. </s>

<s>14). </s></p><p type="main">

<s>Quando dunque il Renieri faceva quella domanda suggestiva, Galileo <lb/>era bene informato dell'eccellenza a cui era giunto, e di quella a cui pro&shy;<lb/>metteva di giungere l'Artefice napoletano, ma chi negherebbe che la gelo&shy;<lb/>sia non gli venisse a far ombra al giudizio? </s>

<s>Galileo insomma rispondeva al <lb/>Renieri che i nuovi Canocchiali del Fontana non erano poi cos&igrave; miracolosi <lb/>come si diceva, d'onde ne traeva il buon padre una consolazione curiosa: <lb/>&ldquo; Ho caro d'intendere che i cristalli di Napoli non siano cos&igrave; miracolosi <lb/>com'altri scriveva, perch&egrave; al gran prezzo, che di l&agrave; ne veniva chiesto, mi <lb/>disperavo di poterne mai avere &rdquo; (Alb. </s>

<s>X, 296). </s></p><p type="main">

<s>Ma pur le acclamazioni, il vento delle quali spiratogli tutto intorno fa&shy;<lb/>ceva gelar l'animo a Galileo, si facevano ogni giorno maggiori. </s>

<s>Il Castelli <lb/>quasi volesse rintuzzar quel giudizio, di che s'era consolato il Renieri, an&shy;<lb/>dava predicando allo stesso Galileo quello del Fontana essere un'<emph type="italics"/>occhiale <lb/>veramente maraviglioso<emph.end type="italics"/> (ivi, pag. </s>

<s>307) e il Cavalieri, nel fargli motto di un <lb/>Canocchiale napoletano posseduto dal Gassendo, gli soggiungeva: &ldquo; onde po&shy;<lb/>tr&agrave; dire al Serenissimo Granduca che li suoi canocchiali son per niente, <lb/>come anco saranno quelli di V. S. Ecc.ma rispetto a questo &rdquo; (MSS. Gal., <lb/>P. VI, T. XIII, c. </s>

<s>100). </s></p><p type="main">

<s>Sembran queste parole dette dal Cavalieri per ironia, ma pure egli si <lb/>ebbe poco di poi a persuadere che il Granduca aveva avuto da Napoli un <lb/>canocchiale da doversi, quello di Galileo davvero, tener per niente. </s>

<s>&ldquo; S'in&shy;<lb/>tende, cos&igrave; scrive al Castelli, che un tale signor Francesco Fontana in Na&shy;<lb/>poli abbia talmente migliorato il Telescopio, che scopre in cielo, cose nuove <lb/>e massime nei pianeti, e perch&egrave; mi scrivono che V. P. R. ha corrispon&shy;<lb/>denza con questo tale, e che egli le abbia mandato uno di questi suoi oc&shy;<lb/>chiali, per il Serenissimo Granduca, perci&ograve; la prego a farmi tanto favore di <lb/>dirmi se &egrave; vero o no che quello trapassi di eccellenza quello che ha il si&shy;<lb/>gnor Galileo &rdquo; (Alb. </s>

<s>X, 319). Il Castelli non poteva non rispondere al Ca&shy;<lb/>valieri se non affermando, cosicch&egrave; oramai Galileo e i suoi fautori si davan <lb/>per vinti. </s></p><p type="main">

<s>Quell'astutissimo fra Fulgenzio per&ograve; seppe trovare il verso di sollevar <lb/>l'animo dell'amico nell'atto stesso di metterlo a confronto coll'emulo vit&shy;<lb/>torioso, cos&igrave; scrivendo: &ldquo; Sento bene, nei discorsi di tutti li virtuosi e cu&shy;<lb/>riosi, quanto sia grave il danno pubblico che V. S. non goda la sanit&agrave; e <lb/>particolarmente quella degli occhi, perch&egrave; con li nuovi scoprimenti di que&shy;<lb/>sto Occhiale napoletano, avressimo certo qualche considerazione e discorso <lb/>degno del signor Galileo. </s>

<s>Mi pare per&ograve; cosa strana che dal padre Castelli, <lb/>che ha veduto e usato l'occhiale, dal padre Cavalieri e dal Glorioso, non si <pb xlink:href="020/01/397.jpg" pagenum="378"/>abbia pur un verso sopra tale materia, e nemmeno dallo Scheiner, che vuol <lb/>saper tutto ed essere il ritrovatore di tutte le novit&agrave; &rdquo; (ivi, pag. </s>

<s>318). </s></p><p type="main">

<s>Fra Fulgenzio o non era bene informato o non eransi troppo ancora <lb/>divulgate le scoperte celesti, che facevansi col nuovo Canocchiale, ma il Ba&shy;<lb/>liani un anno dopo scriveva in altri termini allo stesso Galileo: &ldquo; Sento gran <lb/>cose di ci&ograve; che si ritrova in cielo con l'aiuto de'Telescopii lunghissimi di <lb/>Napoli, e che Marte sia corniculare, e che sian molte cose nella Luna e <lb/>altro. </s>

<s>Che se ci&ograve; &egrave; vero V. S. ne avr&agrave; avuto ragguaglio, e mi duole che <lb/>non possa osservarlo &rdquo; (ivi, pag. </s>

<s>367). Cos&igrave;, a turbar maggiormente l'animo <lb/>di Galileo, veniva il rumore delle nuove scoperte astronomiche, alle quali, <lb/>la cecit&agrave; e la vecchiezza gli toglievano miserabilmente di prender parte. </s></p><p type="main">

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

<s>Quell'Artefice napoletano, che aveva mosso le gelosie nell'animo di <lb/>Galileo, era venuto, poco di poi, a ridestar nell'animo del Torricelli una <lb/>grande emulazione, e anzi una ferma fiducia di superarlo. </s>

<s>Era quell'emu&shy;<lb/>lazione fomentata dallo stesso Galileo, a cui pareva di veder sorgere nel <lb/>giovane allievo chi venisse a rivendicare l'onore del suo nome, e perci&ograve; gli <lb/>apriva i suoi segreti, e gli dava que'consigli, e quegli ammaestramenti ap&shy;<lb/>presi dall'esperienza e dal lungo e paziente esercizio di tanti anni: era <lb/>quella fiducia avvivata dall'eloquente parola e dal valido aiuto del Granduca <lb/>Ferdinando, il quale mal sopportava che un illetterato occhialaio di Napoli <lb/>avesse cos&igrave; a prevalere sul suo Matematico di Firenze. </s></p><p type="main">

<s>Appena morto Galileo, e succeduto ai servigi del Granduca in suo luogo <lb/>il Torricelli, spinto da quella emulazione e incorato da quella fiducia, ei si <lb/>dette alacremente all'opera di fabbricare e di dar conveniente figura ai vetri <lb/>da Canocchiali, cercando nelle rivelazioni della scienza qualche lume, che <lb/>gli fosse scorta nella pratica del suo lavoro. </s>

<s>A questo effetto cos&igrave; scriveva <lb/>da Firenze, il d&igrave; 25 Ottobre 1642, al Cavalieri: &ldquo; Intesi poi che V. P. aveva <lb/>qualche speculazione intorno alla figura de'vetri per l'occhiale. </s>

<s>La supplico <lb/>a conferirmi qualche cosa, per&ograve; senza dimostrazione, ma la conclusione sola, <lb/>non per filosofarvi, ma per operare. </s>

<s>Vo lavorando conforme ad alcune con&shy;<lb/>siderazioni del Galileo e mie, e fino ad ora non ho passato la mediocrit&agrave;; <lb/>non ho per&ograve; arrivato alli vetri del Fontana &rdquo; (MSS. Gal. </s>

<s>Disc., T. 40, c. </s>

<s>119). </s></p><p type="main">

<s>Le ricercate speculazioni diottriche del Cavalieri erano per verit&agrave; troppo <lb/>scarse al bisogno, e non poteva di l&igrave; il Torricelli avere speranza di niun <lb/>progresso. </s>

<s>Perci&ograve;, dandosi pi&ugrave; assiduamente che mai a speculare da s&egrave;, e a <lb/>fare esperienze, poco pi&ugrave; che tre mesi dopo scriveva cos&igrave; tutto esultando al <lb/>carissimo amico suo Raffaello Magiotti: &ldquo; Finalmente, dopo mille vani di&shy;<lb/>scorsi e mille castelli in aria, laudato sia Dio, l'invenzione de'vetri mi &egrave; <lb/>data nelle mani. </s>

<s>Ho gusto che quel Napoletano s'accorga che il Granduca <pb xlink:href="020/01/398.jpg" pagenum="379"/>ha in casa sua chi fa quanto lui ed anco pi&ugrave; di lui. </s>

<s>Da pochi giorni in qua <lb/>ne ho lavorati solo sei, tra i quali quattro ne sono riusciti con difetto ap&shy;<lb/>parente; gli altri due sono stati a prova con quel perfettissimo del Gran&shy;<lb/>duca fatto dal Fontana, e non si trova una minima differenza, se non che <lb/>quello &egrave; il meglio che sia stato fatto tra mille vetri, nello spazio di 20 anni, <lb/>dal Fontana, ed i miei sono scelti fra sei fatti nello spazio di otto giorni. </s>

<s><lb/>Io spero di passar anco pi&ugrave; avanti, sebbene il Granduca mi dica di esser <lb/>soddisfatto cos&igrave;, ed ieri appunto mi don&ograve; di sua mano una collana di 300 <lb/>scudi, con medaglia e motto <emph type="italics"/>Virtutis praemia.<emph.end type="italics"/> Spero che V. S. n'aver&agrave; <lb/>gusto e gli sar&agrave; sprone di seguitare pi&ugrave; avanti. </s>

<s>Mi dispiace bene di non <lb/>poter darle qualche luce, poich&egrave; il Granduca m'ha imposto silenzio e se&shy;<lb/>gretezza. </s>

<s>Che l'invenzione sia la medesima che quella del Fontana, mi par <lb/>quasi impossibile: io pagherei bene qualche cosa che la sua non fosse come <lb/>la mia &rdquo; (ivi, c. </s>

<s>36). </s></p><p type="main">

<s>In questo stesso giorno 6 Febbraio 1643 dava sfogo il Torricelli alla <lb/>sua esultanza, scrivendo all'altro suo carissimo amico M. A. Ricci, per dargli <lb/>nuova del dono della collana e dell'invenzione de'vetri, che non gli era oc&shy;<lb/>corsa per caso, ma l'avea <emph type="italics"/>trovata per via di speculazione geometrica, e <lb/>con la dottrina e cognizione di queste figurine coniche, e con la scienza <lb/>delle rifrazioni<emph.end type="italics"/> (ivi, c. </s>

<s>83). In che consistesse quella scienza delle rifrazioni <lb/>e in che quel segreto scoperto, che gli dette in mano l'invenzione di lavo&shy;<lb/>rar vetri pi&ugrave; perfetti di quelli stessi di Napoli, lo vedremo tra poco. </s>

<s>Ma in&shy;<lb/>tanto seguitiamo i progressi di questo ardente emulo di Francesco Fontana. </s></p><p type="main">

<s>Nel 1646 credeva di esser giunto a tal perfezione, che ai limiti dell'arte <lb/>umana non fosse conceduto di passare pi&ugrave; avanti. </s>

<s>Scorto dal principio pra&shy;<lb/>tico galileiano, secondo il quale i Canocchiali tanto pi&ugrave; ingrandiscono, quanto <lb/>la distanza focale dell'obiettivo &egrave; maggior, rispetto alla distanza focale del&shy;<lb/>l'oculare, si dette a fabbricar convessi di segmenti di grandissima sfera, per <lb/>i quali convessi riuscivano scarsi, traforati nell'anima per servir di tubi, i <lb/>pi&ugrave; lunghi abeti delle foreste toscane. </s></p><p type="main">

<s>&ldquo; Il Serenissimo Granduca, cos&igrave; scriveva al Ricci, mi comand&ograve; che io <lb/>facessi un Occhiale di 20 braccia: lo feci, cio&egrave; lavorai un vetro d'un palmo <lb/>di diametro, che andava lungo 24 passi andanti. </s>

<s>S. A. lo faceva tenere in <lb/>mano di un uomo, e poi si allontanava perch&egrave; facesse il suo ufficio, e con <lb/>quel vetro solo, senz'altro vetro all'occhio, vedeva gli oggetti e chiari giu&shy;<lb/>sto come averebbe fatto l'occhialone, ancorch&egrave; ci&ograve; si facesse in campagna, <lb/>nell'aria aperta e luminosa, e che il vetro si tenesse da un uomo a caso e <lb/>non fermo bene. </s>

<s>Questa sperienza l'ha replicata tante volte, che &egrave; stata ve&shy;<lb/>duta da chi non l'ha voluta vedere. </s>

<s>Ultimamente comand&ograve; che si facesse <lb/>il cannone, e si prese un abete di 20 braccia fiorentine, e fu incavato male <lb/>e commesso peggio per la fretta, poich&egrave; guardando io, dopo commesso, veddi <lb/>che la cavit&agrave;, in cambio di esser conica circolare, faceva questa apparenza O. </s>

<s><lb/>La mattina, che S. A. era per partire alla volta di Pisa, lo feci tirar su per <lb/><gap/> sue camere e vi mettemmo il vetro: fu guardata una villa <pb xlink:href="020/01/399.jpg" pagenum="380"/>con infinita scomodit&agrave;: non avevamo concavo proporzionato e trovammo che <lb/>il vetro voleva sette braccia pi&ugrave; che l'abete di lunghezza. </s>

<s>Cos&igrave; non si pot&egrave; <lb/>aver gusto. </s>

<s>Mi lasci&ograve; ordine S. A. che io facessi un altro vetro un po'mi&shy;<lb/>nore, e facessi accomodar meglio il cannone. </s>

<s>Ho gi&agrave; fatto il vetro, ma &egrave; <lb/>riuscito pienissimo di tortiglioni. </s>

<s>Voglio nondimeno che, come torna, lo trovi <lb/>in ordine. </s>

<s>Quella mattina nondimeno, sebben con infinita scomodit&agrave;, vede&shy;<lb/>vamo certi coppi, con le macchie che vi erano s&ugrave;, di grandezza stermi&shy;<lb/>nata.... Quel signore Eustachio orologiaro (il Divini) &egrave; mio amico e per&shy;<lb/>sona di molto buon gusto, discorso e giudizio, e non dubito che non sia per <lb/>far bene, ma per&ograve; che sia per arrivare al segno, che ho arrivato io, non lo <lb/>credo &rdquo; (ivi, c. </s>

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

<s>Sien pure confidate in una lettera familiare a un intimo amico, queste <lb/>ultime espressioni suonano alquanto immodeste. </s>

<s>Si direbbe che i regali e <lb/>le compiacenze del Granduca, colle lodi e le adulazioni di tanti, avessero <lb/>fatto salire il fumo agli occhi del povero Torricelli. </s>

<s>Il Fontana dall'altra <lb/>parte, bench&egrave; povero artefice, senza protezione di principi e senza scienza, <lb/>non poteva patire i fastidiosi orgogli di quel suo fortunato rivale. </s>

<s>&ldquo; Mi vien <lb/>riferito, scrivevagli il Ricci, il Fontana essersi piccato per l'emulazione di <lb/>V. S. nel lavoro dei vetri, e ha mandato qua in Roma un suo vetro squi&shy;<lb/>sitissimo, che lo teneva presso di s&egrave;, come singolare, acci&ograve; sia paragonato <lb/>con alcuni di quelli di V. S. e mi dicono che superi di gran lunga uno che <lb/>hanno di V. S. </s>

<s>Non so chi sian questi che hanno i vetri di V. S. </s>

<s>Lo dissi <lb/>al signor Raffaello (Magiotti) e mi consigli&ograve; ad accennarle questo, perch&egrave; <lb/>avverta di non mandar vetri se non in mano di persone discrete, le quali <lb/>abbiano discrezione in paragonare i vetri, che siano stimati pari dai loro <lb/>maestri &rdquo; (ivi, T. XLII, c. </s>

<s>153). </s></p><p type="main">

<s>&Egrave; facile indovinar che i giudici del paragone, i quali erano tutti amici <lb/>e ammiratori del Torricelli, non eccettuato il Thevenot, il quale, ritrovan&shy;<lb/>dosi allora a Roma, si volle <emph type="italics"/>far trombetta del valor<emph.end type="italics"/> del Matematico di Fi&shy;<lb/>renze <emph type="italics"/>s&igrave; per le ragioni della Geometria s&igrave; nei paragoni fatti tra i vetri <lb/>di lui e del Fontana<emph.end type="italics"/> (ivi, c. </s>

<s>154) dovessero esaltare il Torricelli stesso Ma&shy;<lb/>tematico del Granduca, a scapito del povero e disprezzato occhialaio na&shy;<lb/>poletano. </s></p><p type="main">

<s>Solo, in mezzo alla turba plaudente, si faceva sentir la voce del Mer&shy;<lb/>senno, che co'suoi rotti modi frateschi rintuzzava i vanti torricelliani, e <lb/>prendeva le difese per il pi&ugrave; debole fra i contendenti. </s>

<s>&ldquo; Optimus Magiot&shy;<lb/>tus, egli scrive, mihi ostendit vitrum perspicilli, quod ad eum misisti, quod <lb/>cum Fontanae vitro, quod etiam habet collatum, minus bonum apparet. </s>

<s><lb/>Cumque legissem in tuo libro vitra a te parata superare quae hucusque ap&shy;<lb/>paruere, nempe et vitra galileiana et Fontanae, miratus sum quod in illo <lb/>tuo vitro non deprehenderetur &rdquo; (ibi, T. XLI, c. </s>

<s>57). E in un'altra lettera, <lb/>scritta da Parigi, gli dice liberamente che in Francia si fabbricavano ca&shy;<lb/>nocchiali migliori de'suoi, de'quali uno eccellentissimo ne aveva il Gassendo, <lb/>e gli soggiunge che migliori di tutti sono i Telescopi binoculi del Rehita. <pb xlink:href="020/01/400.jpg" pagenum="381"/>&ldquo; Porro te monitum velim iam Augustae Vindelicorum fieri Telescopia longe <lb/>meliora quam tua vel cuiuspiam alterius communia, quae serviunt duobus <lb/>oculis, quaeque propterea capuccinus Rehita, qui nuper edidit Tractatum de <lb/>hoc Tubo, quem rocat <emph type="italics"/>Oculum Enoch et Eliae,<emph.end type="italics"/> vocat <emph type="italics"/>Binocula.<emph.end type="italics"/> Habent <lb/>itaque quatuor convexa, nullum concavum, duo pro quovis oculo quae, quia <lb/>obiectum invertunt, quod parum refert in astris, si tertium concavum abde&shy;<lb/>tur, rectum est obiectum &rdquo; (ibi, T. XLI, c. </s>

<s>19). </s></p><p type="main">

<s>Ma il coro tutt'intorno plaudente assordiva la voce rauca di Marino <lb/>Mersenno, cosicch&egrave;, in mezzo a quella nuvola profumata d'incenso, non ve&shy;<lb/>dendo altri che s&egrave; con quella sua collana di trecento scudi pendente dal <lb/>collo, salivano, pi&ugrave; che mai vertiginosi dal petto, i fumi in quell'ardente <lb/>spirito romagnolo. </s>

<s>Il Fontana, per far qualche ragione di s&egrave; col pubblico, e <lb/>non soccombere oppresso e invendicato, ebbe ricorso ai gesuiti del Collegio <lb/>napoletano, Giovan Batista Zuppi e Girolamo Sirsale, coll'aiuto de'quali riu&shy;<lb/>sc&igrave; a mettere insieme e a pubblicare in Napoli, nel 1646, le sue <emph type="italics"/>Novae <lb/>Coelestium terrestriumque rerum Observationes.<emph.end type="italics"/> Pel Torricelli questo &egrave; <emph type="italics"/>il <lb/>libro delle bestialit&agrave; osservate o piuttosto sognate dal Fontana nel cielo<emph.end type="italics"/><lb/>(ivi, T. XL, c. </s>

<s>13). E prosegue a dire al Renieri: &ldquo; Se ella vuol vedere <lb/>pazze cose, cio&egrave; spropositi, finzioni, sfacciataggini, e mille vituperi simili, io <lb/>gli mander&ograve; il libro: potr&agrave; forse cavar roba da ridere per l'opera sua &rdquo; (ivi). </s></p><p type="main">

<s>Mentre cos&igrave; fieramente menava il Torricelli i denti a lacerare quella <lb/>misera vittima napoletana, venne a dargli sotto l'ugne un altro poveretto, <lb/>che s'era fitto in testa di lavorare i vetri de'Canocchiali, facendo a gara <lb/>con lui. </s>

<s>Chi, tra le Vite de'Professori del Disegno scritte da Filippo Bal&shy;<lb/>dinucci, s'abbattesse a leggere quella di Antonio Novelli, si formerebbe, del <lb/>carattere del Matematico del Granduca, un'idea tutt'affatto diversa da quella <lb/>che ci siamo dovuti formar noi. </s>

<s>Il buon Baldinucci scrisse ivi, intorno al <lb/>Torricelli, una pagina, che vorrebbe essere scelta e collocata in primo luogo <lb/>fra gli esempi di generosit&agrave; offerti all'imitazione degli uomini. </s>

<s>Dop'aver <lb/>detto che Antonio Novelli s'esercitava, fra le altre cose, a lavorare i vetri <lb/>da Telescopi, lo stesso Baldinucci cos&igrave; soggiunge: </s></p><p type="main">

<s>&ldquo; Il Granduca Ferdinando, che molto di tale strumento si dilettava, fa&shy;<lb/>cevane far molti al Torricelli, e poi con lodi e premii da suo pari il ricom&shy;<lb/>pensava; ond'egli, vedendosi cos&igrave; regalato da quel grande, e riflettendo al&shy;<lb/>l'incontro al sollievo che egli avrebbe potuto arrecare alla povert&agrave; del nostro <lb/>Artefice, con far conoscere suo gran talento in simile materia a Sua Al&shy;<lb/>tezza, un giorno gli venne a dire essere in Firenze persona, che operava <lb/>meglio di lui, e che questi era Antonio Novelli, e ne riport&ograve; per risposta <lb/>di dovergli far vedere qualche cosa di suo. </s>

<s>Il Torricelli in questo, in vero <lb/>poco avveduto, per troppo desio di favorire l'amico, prese un occhiale fatto <lb/>da s&egrave; stesso, che si estendeva per dodici braccia in circa, e mostrollo un <lb/>giorno al Granduca, il quale, credendolo del Novelli, disse: egli &egrave; un bonis&shy;<lb/>simo Occhiale, ma e'non ha che fare punto co'vostri. </s>

<s>Dopo pochi giorni, il <lb/>Torricelli presone uno del Novelli de'migliori e portatolo allo stesso Sere-<pb xlink:href="020/01/401.jpg" pagenum="382"/>nissimo, gli disse aver fatto questo vetro, nel quale, avendo molto sodisfatto <lb/>a s&egrave; stesso, desiderava che S. A. sel conservasse per s&egrave; in sua memoria. </s>

<s><lb/>Presolo il Granduca e fatto venire altri vetri di mano del Torricelli, e con <lb/>quello paragonatigli, disse: veramente questo &egrave; meglio di tutti gli altri vo&shy;<lb/>stri. </s>

<s>Sicch&egrave;, replic&ograve; il Torricelli, il Novelli &egrave; miglior maestro di me, perch&egrave; <lb/>questo vetro &egrave; fatto dalle sue mani, non dalle mie. </s>

<s>Quell'accortissimo Prin&shy;<lb/>cipe, in primo moto, diede alcun segno, e con ragione, che poco le fosse <lb/>piaciuto quel modo di portar negozi di un suddito al suo Sovrano, ma vin&shy;<lb/>cendo in lui il grande amore ch'ei portava al Matematico, e il zelo che egli <lb/>conobbe in esso d'aiutar l'amico, rivolt&ograve; galantemente il fatto, ed al Tor&shy;<lb/>ricelli ordin&ograve; che mettesse il prezzo all'Occhiale. </s>

<s>Il Torricelli esegu&igrave;, e il <lb/>Novelli ne fu nobilmente ricompensato &rdquo; (Firenze 1773, T. XVI, pag. </s>

<s>220, 21). </s></p><p type="main">

<s>Ma questo del Baldinucci &egrave; un bel romanzetto trasportato al morale: la <lb/>storia vera la caveranno da s&egrave; i lettori dal seguente passo di lettera, che il <lb/>Torricelli stesso scriveva al Renieri: &ldquo; &Egrave; verissimo che il Novelli ha volont&agrave; <lb/>di fare gli Occhiali come me. </s>

<s>&Egrave; anco vero che ne ha fatto finalmente qual&shy;<lb/>cuno, che ha avuto ardire di farlo comparire in palazzo. </s>

<s>Basta, &egrave; stato pro&shy;<lb/>vato con i miei e pu&ograve; essere che qualcuno suo parziale l'abbia lodato. </s>

<s>Ma <lb/>per&ograve; il Serenissimo Padrone non veggo che si degni di parlarne. </s>

<s>Ma parl&ograve; <lb/>bene di quello romanesco, ancorch&egrave; poi non adegui altri Occhiali che i miei. </s>

<s><lb/>Un'altra volta, gi&agrave; sono un anno e mezzo, questo medesimo Novelli ne mand&ograve; <lb/>due al Poggio a Caiano, mentre S. A. S. era in villa. </s>

<s>Si provarono e furono <lb/>ributtati coll'<emph type="italics"/>oib&ograve;!<emph.end type="italics"/> Mi ci trovavo ancor io, e v'era anco Tordo. </s>

<s>Quello che <lb/>propose gli occhiali fu un cav. </s>

<s>Rucellai. </s>

<s>&Egrave; ben vero che mai volle nomi&shy;<lb/>narne l'Autore a noialtri, e solo per coniettura sapemmo che erano del No&shy;<lb/>velli. </s>

<s>Quelli poi che scrivono ch&egrave; fanno miracoli, bisogna che siano genti <lb/>che non hanno pratica de'miei. </s>

<s>Ed io ho sempre detto che, non solo il No&shy;<lb/>velli ed il Divini e Tordo e Fontana, ma mille altri faranno occhiali che <lb/>daranno grandissimo gusto, e parr&agrave; che non si possa far pi&ugrave;. </s>

<s>Bisogna avere <lb/>il paragone presente de'miei e degli altri e poi bisogna anco di pi&ugrave; che il <lb/>giudice non sia novizio nel guardare, perch&egrave; molte volte non vedr&agrave; la dif&shy;<lb/>ferenza, la quale vi &egrave;, sebben piccola; in ogni modo si stima assaissimo &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>13). </s></p><p type="main">

<s>L'orgoglio, nell'animo di tutti gli uomini o piccoli o grandi, &egrave; come <lb/>elaterio di molla che, quanto risale in su, altrettanto ricade in basso, infin&shy;<lb/>tanto che la quiete non la riduca nel suo giusto mezzo. </s>

<s>Quel Torricelli, che <lb/>cosi viene magnificando al Renieri la sua merce, al di sopra di tutti gli altri <lb/>concorrenti, s'era poco prima raccomandato allo stesso Renieri che s'accor&shy;<lb/>dasse con lui a secondarlo, e a procacciare a quella sua merce, con le lodi, <lb/>in pubblica piazza, un pi&ugrave; facile smercio. </s>

<s>&ldquo; La prego a voler nella sua Opera <lb/>(Le Tavole dei Secondi Mobili) o a proposito di queste osservazioni, ovvero <lb/>nel trattar di Giove e suoi Pianetini, voler, dico, far qualche servigio alli <lb/>miei Occhiali, per interesse mio. </s>

<s>Spero che ella conosca di poter dire la ve&shy;<lb/>rit&agrave;. </s>

<s>Certo &egrave; che ella ha avuto occasione, per mezzo del Serenissimo Pa-<pb xlink:href="020/01/402.jpg" pagenum="383"/>drone in ci&ograve; curiosissimo, di vedere ed esperimentare i pi&ugrave; famosi Occhiali, <lb/>che si facciano in Europa. </s>

<s>Che poi i miei non si possano superare la rendo <lb/>certa io &rdquo; (ivi, c. </s>

<s>15). </s></p><p type="main">

<s>Ma insomma quel che rendeva i Canocchiali del Torricelli insuperabili <lb/>era, secondo lui, tutt'opera di quel famoso segreto, di che parlava dianzi al <lb/>Ricci e al Magiotti, e intorno al quale debbono i nostri lettori essere en&shy;<lb/>trati in curiosit&agrave;, e venuti in desiderio di vederlo svelato. </s></p><p type="main">

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

<s>La sera del d&igrave; 8 Dicembre 1647, a ore quattro di notte, il Granduca <lb/>Ferdinando fa chiamare a s&egrave;, nelle sue stanze pi&ugrave; riposte, il Viviani, come <lb/>avesse a confidargli qualche affare geloso e di grande importanza. </s>

<s>Sedeva <lb/>il Sovrano a una tavola, colle mani posate sopra una cassetta gelosamente <lb/>serrata a chiave, e dalle espressioni degli occhi e dai gesti faceva trasparir <lb/>che l&igrave; dentro ci dovess'esser custodito qualche cosa di veramente prezioso. </s>

<s><lb/>Prende la chiave, apre la cassetta, ne trae fuori alcuni fogli manoscritti, e <lb/>nel mostrargli al Viviani cos&igrave; gli dice: Qui si contiene svelato il famoso <lb/>segreto, che la buona memoria del nostro Torricelli aveva per lavorare le <lb/>lenti dei Canocchiali, con altri documenti e avvertimenti utilissimi. </s>

<s>Poi ri&shy;<lb/>pose quelle carte dentro <emph type="italics"/>e serrando,<emph.end type="italics"/> cos&igrave; racconta lo stesso Viviani, <emph type="italics"/>di pro&shy;<lb/>pria mano il recipiente di detto strumento, siccome da s&egrave; stesso l'aveva <lb/>aperto, mi consegn&ograve; la chiave che lo teneva serrato.<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., <lb/>T. CXXXIII, c. </s>

<s>3). </s></p><p type="main">

<s>Prima per&ograve; che al Viviani, era stato il segreto dall'Autore stesso con&shy;<lb/>fidato al Magiotti. </s>

<s>Udimmo da un passo di lettera trascritto di sopra come <lb/>al Torricelli fosse imposto silenzio dallo stesso Granduca, ma il Magiotti, <lb/>messo in gran curiosit&agrave;, tanto fece appresso all'amico, che questi ebbe final&shy;<lb/>mentente a condiscendere, svelandogli il segreto in una lettera sotto il d&igrave; <lb/>4 Dicembre 1643 a lui diretta, che senza l'invocativo e le solite cerimonie, <lb/>corrisponde quasi a parola collo strumento stesso consegnato al Viviani dal <lb/>Granduca. </s></p><p type="main">

<s>&ldquo; Sappia dunque che la centina &egrave; facilissima da farsi, e la natura me&shy;<lb/>desima la fa perfetta, dove l'arte non potrebbe mai arrivare. </s>

<s>Si piglia un <lb/>pezzo di vetro piano, ovvero rozzo, tondo e grande per l'appunto, quanto <lb/>il vetro da lavorarsi, o pochissima cosa di pi&ugrave;. </s>

<s>Si attacca sopra qualche cosa <lb/>grave, acci&ograve; la mano non porti la centina in giro. </s>

<s>Io adopro una rotella di <lb/>piombo, ovvero un mattone o altro. </s>

<s>Dopo questo comincio ad affondarla con <lb/>un vetro piccolo, pur piano, a smeriglio tagliente. </s>

<s>Nell'affondarla, non os&shy;<lb/>servo altro se non che il vetro, con che lo affondo, pratichi pi&ugrave; spesso in&shy;<lb/>torno al mezzo, che dalle bande della futura centina. </s>

<s>Insomma non passa <lb/><gap/><pb xlink:href="020/01/403.jpg" pagenum="384"/>per un occhiale di tre braccia e mezzo, lavorata da ambe le parti, inten&shy;<lb/>dendo per&ograve; che la centina non sia di diametro pi&ugrave; che una piastra e due <lb/>terzi fiorentina. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Non vorrei che ella avesse scrupolo nella centina, perch&egrave; basta che <lb/>ella sia incavata alla peggio, e poi, nel lavorare il vetro, la si fa perfetta <lb/>dalla natura medesima. </s>

<s>Fatto questo, si mette da parte quel vetro piccolo, <lb/>che ha incavata la centina, e si piglia il vetro, che si vuol lavorare, ben <lb/>tondato ed anco abbozzato in una centinuccia di rame o d'altro, purch&egrave; sia <lb/>affatto piano, e neanco tanto colmo, che sia sproporzionato affatto con la <lb/>centina di gi&agrave; preparata. </s>

<s>Questo poi si incomincia a lavorare con spoltiglia <lb/>fine, sintanto che ella giudica che si sia adattato con la centina, il che si <lb/>conosce anco a vista, perch&egrave; il vetro, che era abbozza<emph type="italics"/>t<emph.end type="italics"/>o con lo smeriglio, <lb/>aveva la grana grossa, ma dopo, dove avesse trovata la spoltiglia, l'aver&agrave; <lb/>pi&ugrave; minuta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quando dunque il vetro sar&agrave; arrivato da per tutto, non vi si d&agrave; pi&ugrave; <lb/>spoltiglia, ma si continua a lavorare con quel residuo, che sar&agrave; tra l'un <lb/>vetro e l'altro, ed anco negli orli. </s>

<s>Quest'operazione si continua, fintanto <lb/>che quella materia sia consumata e ridotta bianca, palpabile e untuosa, come <lb/>burro, bagnando la centina, quando s'asciugasse, con una mezza gocciolina <lb/>di acqua, ovvero con l'alito della bocca messa l&igrave; vicino. </s>

<s>Se tali operazioni <lb/>saranno ben fatte, il vetro verr&agrave; senza graffi, e senza segni, ed aver&agrave; una <lb/>pelle tale, che, obliquandolo all'asse della visione, circa un mezzo angolo <lb/>retto, far&agrave; specchio delle cose luminose. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto al pulire, mai si pulisce sulla centina, che l'ha lavorato, per&shy;<lb/>ch&egrave; pulisce dalle bande prima, e poi tardissimo nel mezzo, e non sempre <lb/>bene. </s>

<s>Bisogna dunque darvi centina pi&ugrave; dolce. </s>

<s>Io adopro una rotella di la&shy;<lb/>vagna, larga circa otto dita, e quasi direi piana. </s>

<s>Solo vi d&ograve; quattro b&ograve;tte di <lb/>pomice, fintantoch&egrave; l'occhio cominci a conoscere che la non &egrave; pi&ugrave; piana. </s>

<s><lb/>Questa la metto in una tavola, con una rotella di panno sotto, acci&ograve; non si <lb/>rompa, e poi vi conficco sopra, con bullettine da impannata, un pezzo di <lb/>panno fine senza nodi, tarme, ecc., e tirato da tutte le bande quanto mai <lb/>&egrave; possibile. </s>

<s>Quest'invenzione &egrave; meglio che legare il panno intorno alla cen&shy;<lb/>tina, perch&egrave; si tira meglio, e poi, perch&egrave; essendo panno conficcato nella ta&shy;<lb/>vola sottoposta, la centina viene a restare immobile sotto i giri della mano. </s>

<s><lb/>Il tripolo poi vi si d&agrave; in forma d'unguento tanto scarso, che non faccia <lb/>massa intorno agli orli del panno e della centina aggiungendo ora una goc&shy;<lb/>ciola d'acqua, ed ora un poco di tripolo, conforme il panno ne aver&agrave; biso&shy;<lb/>gno. </s>

<s>Solo conviene avere un poco di pazienza nel pulire, perch&egrave; vada via <lb/>ogni minima bruttura od inegualit&agrave;, che sia nella superficie del vetro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto alla piccolezza della centina di vetro sopraddetta, cio&egrave; che sia <lb/>uguale al vetro da lavorarsi, V. S. lo stima un gran segreto. </s>

<s>Credo che ella <lb/>intendesse brevemente che se la centina non &egrave; sferica, n&egrave; anco il vetro pu&ograve; <lb/>essere di buona sferit&agrave;. </s>

<s>E chi mi assicura che la centina si mantenga sfe&shy;<lb/><gap/><pb xlink:href="020/01/404.jpg" pagenum="385"/>stra? </s>

<s>Ma quando siano uguali, e che la mano del lavorante far&agrave; moti irre&shy;<lb/>golari e stravaganti, cio&egrave; spire, ghirigori, circoli, e sopratutto diametri molti <lb/>e per tutti i versi; allora s&igrave; che neanche un angelo potr&agrave; dare al vetro figura <lb/>pi&ugrave; perfettamente sferica. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il segreto che pi&ugrave; m'importa, e che non si s&agrave; da altri che da Dio e <lb/>da me, &egrave; questo: Non attaccare i vetri da lavorarsi con pece, n&egrave; con altro, <lb/>per via di fuoco. </s>

<s>Perch&egrave; quelle materie, nel freddarsi, si ritirano pi&ugrave; da <lb/>una parte che dall'altra, ed inarcano il vetro, il quale, finch&egrave; sta attaccato <lb/>al macinello, ha la figura colma, ma quando lo stacchiamo, per metter nel&shy;<lb/>l'occhiale, egli si spiana come prima e la figura si guasta. </s>

<s>Questo segreto, <lb/>che dico adesso a V. S., &egrave; stato da me osservato evidentemente, tanto che <lb/>l'ho toccato con mano, e direi anco a V. S. il come, ma lo lascio per <lb/>brevit&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, io attacco i vetri cos&igrave;: piglio un macinello di piombo di que&shy;<lb/>sta proporzione: (fig. </s>

<s>28). Alla faccia A spianata metto una rotella di ra&shy;<lb/><figure id="id.020.01.404.1.jpg" xlink:href="020/01/404/1.jpg"/></s></p><p type="caption">

<s>Figura 28.<lb/>scia o altro panno fino, cedente, acci&ograve; il vetro toc&shy;<lb/>chi sul morbido, e dopo cingo sopra detto panno <lb/>il macinetto con una pelle di guanto tiratissima, <lb/>e la lego con lo spago CD stretta assai. </s>

<s>Dopo, <lb/>impiastro la faccia di detta pelle A con cera rossa, <lb/>calda e distesa sottilmente. </s>

<s>Cos&igrave; il vetro, purch&egrave; <lb/>non sia bagnato, si attaccher&agrave; sempre, sebben <lb/>freddo, e quando occorresse, si d&agrave; una strofina&shy;<lb/>tina a detta pelle, con una palla della medesima cera rossa, che attaccher&agrave; <lb/>assai forte. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cos&igrave; ne seguita che il vetro non sar&agrave; sforzato, ma quella figura che <lb/>ricever&agrave; dalla centina, l'istessa riterr&agrave;, quando sia staccato dal macinello. </s>

<s><lb/>Oltre di ci&ograve;, V. S. aver&agrave; comodit&agrave; di cominciare a provare il vetro, se fa <lb/>bene o male, subito che si comincia a pulire, e potr&agrave; staccarlo e attaccare <lb/>cento volte, senza danno alcuno, e piuttosto con giovamento. </s>

<s>Ch&egrave;, quando si <lb/>adopra la pece, la regola &egrave; non lo staccar mai, se non quando egli &egrave; finito. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto all'invenz&igrave;one del macinello di piombo, non &egrave; mia, ma &egrave; bo&shy;<lb/>nissima, perch&egrave; nel dare la pelle, non occorre aggravare quasi niente la <lb/>mano, ma il piombo medesimo fa quasi da per lui. </s>

<s>Anco nel pulire aiuta <lb/>assai, ed acci&ograve; faccia meglio il servigio, abbiamo i macinelli, che son quasi <lb/>due dita pi&ugrave; di diametro, che il vetro stesso, acci&ograve; gravitino quel di pi&ugrave;, <lb/>ed osservi che il fare il macinello alto assai &egrave; male, perch&egrave; fa lieva e fa <lb/>traballare il vetro. </s>

<s>Quando V. S. prover&agrave; queste invenzioni, che non son se <lb/>non due: centina piccola e non adoprar fuoco, l'assicuro che far&agrave; i vetri <lb/>buoni, anco quando la materia fosse cattiva, e non glie ne riuscir&agrave; mai nes&shy;<lb/>suno cattivo affatto, ma sempre pi&ugrave; che mediocri, e bisogna accordar molte <lb/>cose, la figura, la materia, e il pulimento. </s>

<s>L'osservazione m'ha insegnato <lb/>che nei vetri, la figura importa assaissimo, e il pulimento pochissimo. </s>

<s>La <lb/>ragione &egrave; questa: io ho provato molti de'miei vetri che appena comincia-<pb xlink:href="020/01/405.jpg" pagenum="386"/>vano a trasparire, ed ho veduto che, nonostante la grana grossissima che <lb/>avevano, in ogni modo facevano bene, per essere la figura buona. </s>

<s>Altri poi <lb/>puliti, come diamanti, per un tantin di mancanza inimmaginabile che sia <lb/>nella figura, non fanno nulla. </s>

<s>La prego a tener segreto quanto le scrivo, in <lb/>particolare quello dell'attaccare, perch&egrave; &egrave; cosa che nessuno ne sospetta, e <lb/>non vi &egrave; cosa che rovini pi&ugrave; i vetri, quando per&ograve; non si adoprino grossis&shy;<lb/>simi &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>34, 35). </s></p><p type="main">

<s>Nella cassetta, la chiave della quale fu dal Granduca consegnata al Vi&shy;<lb/>viani, s'accennava di sopra che ci erano dentro custoditi, oltre al segreto, <lb/>documenti e avvertimenti utilissimi per la perfetta fabbrica delle lenti da <lb/>Canocchiali. </s>

<s>Quegli avvertimenti erano scritti in latino col titolo <emph type="italics"/>Monita circa <lb/>usum Telescopii<emph.end type="italics"/> e il Viviani, nel ricopiarli fedelmente, nota in capo alla <lb/>pagina, per chi non lo sapesse, di averli avuti <emph type="italics"/>Ex munificentia Serenissimi <lb/>Ferdinandi M. D.<emph.end type="italics"/> Ecco in che consistono que'Moniti: </s></p><p type="main">

<s>&ldquo; Illud praecipue non est negligendum tubi fabrica ne in ipso usu in&shy;<lb/>flectatur, sitque maioris crassitiei, quam radios convergentes intercipere pos&shy;<lb/>sit. </s>

<s>Detur etiam tribus aut quatuor internodiis, sive diaphragmatibus, qua&shy;<lb/>lia sunt in grandioribus, sed perforatis, esse interseptos, ne lumen quoddam <lb/>intra os tubi oblique receptum incidens in cavam tubi superficiem, ad ocu&shy;<lb/>lum ullo modo repercuti possit. </s>

<s>Curandum insuper est quam partem vitri <lb/>dissectam, sive apertam relinquamus, quod experientia manifestum est. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ad res vero minutas aspiciendas minori circulo utendum est. </s>

<s>Ete&shy;<lb/>nim, quanquam vitra perfectissima sint, perraro bonitatem suam ostendere <lb/>possunt, ob aeris temperiem, vel enim nebula quaedam, sive caligo, sive <lb/>fumus tenuissimus in aere est, quarum rerum athomos, non secus ae reli&shy;<lb/>qua obiecta auget, et visibilia reddit Telescopium. </s>

<s>Praeterea aer saepissime <lb/>tremit, et quodammodo scintillat, credo quidem ob vapores ascendentes, non <lb/>tantum aestate, et sub ardente sole, sed et hyeme etiam, et saepe flante <lb/>Borea, immo et de nocte, quando Lunam contemplanti patebit, tunc enim <lb/>ambitus eius tremit, maculaeque minutiores maligne cernuntur. </s>

<s>Malignius <lb/>autem tunc temporis figura Saturni conspicitur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Perfectissima visio fit, ut plurimum, matutino et vespertino tempore <lb/>averso semper sole nubilo etiam coelo, quod inverisimile est, et post plu&shy;<lb/>viam clarissimus conspectus est, per tubum, dummodo species obiectorum <lb/>non ferantur supra frequentissima urbium loca. </s>

<s>Urbs enim ingenti copia <lb/>vaporum, quae de fumariis emittitur, species omnes visibiles perturbat. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Plura monere poteram: pauca haec sufficiant, quae nonnisi longo usu <lb/>observari solent. </s>

<s>Multi enim perfectionem accusant vitrorum, cum iis contra&shy;<lb/>rio tempore utantur, ipsique potius accusandi sunt &rdquo; (ivi, T. CXXXIII, c. </s>

<s>9). </s></p><p type="main">

<s>I documenti torricelliani, scritti in lingua volgare, si custodivano pure, <lb/>dentro la famosa cassetta, dal Granduca, e il Viviani ce ne tramand&ograve; copia <lb/>di sua propria mano col titolo: <emph type="italics"/>Condizioni richieste ne'vetri.<emph.end type="italics"/> Quelle condi&shy;<lb/>zioni si riducono alle seguenti: </s></p><p type="main">

<s>&ldquo; Che le <gap/><pb xlink:href="020/01/406.jpg" pagenum="387"/>poche e piccolissime: che i <emph type="italics"/>tortiglioni,<emph.end type="italics"/> cio&egrave; quell'onde interne che talvolta <lb/>hanno i vetri, non vi siano di nessuna sorta, ma ne'vetri piani &egrave; difficilis&shy;<lb/>simo il vedergli ed &egrave; anzi impossibile, per&ograve; questo documento sar&agrave; quasi <lb/>superfluo. </s>

<s>Il colore sia poco; qualunque sia o avvinato o bianco o capellino, <lb/>o verde giallo, si conosce facilmente col mettere il vetro sopra nn foglio di <lb/>carta o sulla pezzuola. </s>

<s>La condizione poi pi&ugrave; necessaria di tutte &egrave; la limpi&shy;<lb/>dezza, perch&egrave;, sendovi questa, ancorch&egrave; manchino le altre tutte, i vetri ver&shy;<lb/>ranno buoni: quando manchi questa, ancorch&egrave; per le altre sieno perfetti, <lb/>mai faranno bene. </s>

<s>Il modo di conoscerli &egrave; il guardare i vetri per taglio, ma <lb/>che non sieno larghi pi&ugrave; di quattro ovvero di sei dita. </s>

<s>Se il taglio sar&agrave; di&shy;<lb/>ritto &ecedil; seguito, come fa il fuoco, si vedr&agrave; guardando verso il lume, per la <lb/>crassizie del vetro fino alla parte opposta, come se fosse ambra, o meglio <lb/>come acqua, e si vedr&agrave; la materia omogenea tutta di un colore e senza <lb/>strisce o righe, ovvero onde. </s>

<s>Quando sar&agrave; altrimenti, la pasta sar&agrave; cattiva. </s>

<s><lb/>Se poi il taglio sia smollettato colle tanaglie, sar&agrave; pi&ugrave; difficile a conoscere <lb/>la sua bont&agrave;, ma nondimeno se si vedr&agrave; qualche poco di spanaturina, da <lb/>poter guardar dentro e da per tutto, si vede un'allegria che brilla come dia&shy;<lb/>mante. </s>

<s>Se poi si vede torbido e offuscato la pasta &egrave; cattiva &rdquo; (ivi, c. </s>

<s>10). </s></p><p type="main">

<s>Che il Granduca Ferdinando facesse benissimo a custodir quegli scritti, <lb/>che noi abbiamo tirati fuori dalla sua gelosa cassetta, per metterli sotto gli <lb/>occhi di tutti, non si potrebbe negare: tutti per&ograve; siamo un po'rimasti come <lb/>quel buon uomo, che, stando a veder partorire un monte, n'ebbe a veder <lb/>finalmente uscire quel che canta, nella sua favola, Esopo. </s>

<s>&Egrave; perci&ograve; che, trat&shy;<lb/>tandosi di uno scienziato tanto insigne qual'&egrave; il Torricelli, non ci dobbiam <lb/>passar senza trattenerci alquanto a considerare come davvero in lui, rispetto <lb/>all'opera del Telescopio, le fronde e i fiori non corrispondano ai frutti. </s></p><p type="main">

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

<s>Chi ripensa che il famoso segreto fu detto dal suo Autore essere stato <lb/>trovato per via di speculazioni geometriche e con la dottrina e cognizione <lb/>delle figure coniche e con la scienza delle rifrazioni; e chi ripensa, di pi&ugrave;, <lb/>che colui, il quale annunziava queste cose, era un Torricelli, non pu&ograve; non <lb/>restar maravigliato al veder che poi in effetto quel gran segreto consisteva <lb/>in tutt'altro che o nella Geometria o nella scienza delle rifrazioni. </s>

<s>Si ridu&shy;<lb/>ceva in fatti quel segreto dal suo stesso discopritore a due capi, il pi&ugrave; im&shy;<lb/>portante de'quali era che non si dovessero attaccar le lenti con pece o altro <lb/>caldo bitume, e ci&ograve; asseriva il Torricelli esser cosa non saputa da nessun <lb/>altro che da lui solo e da Dio. </s>

<s>Eppure a noi par provato che da 25 anni <lb/>avesse saputa quella stessa cosa o l'avesse almeno potuta saper tutto il <lb/>mondo, avendola il Sirturo gi&agrave; pubblicata nel cap. </s>

<s>IX della II Parte del suo <lb/><emph type="italics"/>Telescopio.<emph.end type="italics"/> &ldquo; Idipsum autem nec pice nec bitumine unquam poteris, quia <pb xlink:href="020/01/407.jpg" pagenum="388"/>igne primo est semper opus emolliendae pici: calor autem liquatae picis, sive <lb/>bituminis maxime obest christallo, ac aliquam transmittit pinguedinem &rdquo; <lb/>(Francofurti 1618, pag. </s>

<s>48). Forse il Sirturo non vide chiaro, com'avea sa&shy;<lb/>gacemente riconosciuto il Torricelli, esser causa del guasto prodotto dal bi&shy;<lb/>tume caldo sopra le lenti la dilatazione cubica operata dal calore, ma il se&shy;<lb/>greto non consisteva qui, consisteva nella semplice osservazione del fatto <lb/>rispetto alla quale, ripetiamo, il Sirturo avea preceduto di 25 anni il Tor&shy;<lb/>ricelli e avea rivelato il suo segreto a tutti coloro che volevano saperlo. </s></p><p type="main">

<s>Ma che il Torricelli, nell'avere osservato gli effetti di dilatazion del ca&shy;<lb/>lore per cui s'altera la figura de'vetri, e nell'aver saputo mettere insieme <lb/>que'pratici avvertimenti, potesse far consistere tutta la sua diottrica geome&shy;<lb/>trica e la sua scienza delle rifrazioni, parr&agrave; cosa dura ad ammetter da tutti <lb/>coloro, che in Geometria e in Fisica conoscono il valor sommo di lui. </s>

<s>Si <lb/>direbbe che l'amico intimo del Ricci, per dar pi&ugrave; importanza alla cosa, si <lb/>credesse permesso in una lettera familiare di spacciar per scienza ci&ograve; che <lb/>scienza veramente non era, se uscito poi in pubblico colla sua operetta <emph type="italics"/>De <lb/>solido acuto Hyperbolico,<emph.end type="italics"/> non vi avesse cos&igrave; lasciato scritto: &ldquo; Decidit in&shy;<lb/>termedio hoc tempore, ut plurium mensium studio, atque labore, inciderim <lb/>in solutionem optimi illius Problematis, tandiu perquisiti, cuius videlicet figu&shy;<lb/>rae esse debeant, superficies vitrorum, quae ad usum Telescopii elaboran&shy;<lb/>tur &rdquo; (Op. </s>

<s>Geom., Flor. </s>

<s>1644, pag. </s>

<s>149). </s></p><p type="main">

<s>Sembrerebbe (con tanta solennit&agrave; &egrave; qui espresso) che il Problema della <lb/>figura de'vetri dovesse esser tutt'altro da quello risoluto nella lettera al <lb/>Magiotti, d'onde si vede uscir fuori chi la scrisse, non in pallio filosofale, <lb/>ma vestito in farsetto colle maniche rimboccate. </s>

<s>Ma che insomma, nella ri&shy;<lb/>soluzione di questo rumoroso Problema torricelliano non ci entrasse per <lb/>nulla n&egrave; la Geometria n&egrave; la scienza delle rifrazioni, baster&agrave;, a persuader&shy;<lb/>sene facilmente, dimostrare che il TorriceHi reput&ograve; falsa e inconcludente la <lb/>legge, formulata in Francia infino dal 1637, che cio&egrave; i seni degli angoli <lb/>d'incidenza e di refrazione serbino per qualunque obliquit&agrave; una proporzione <lb/>costante. </s></p><p type="main">

<s>Pubblicando, nel 1632, il Cavalieri il suo <emph type="italics"/>Specchio Ustorio,<emph.end type="italics"/> deplorava <lb/>nelle rifrazioni il <emph type="italics"/>m&agrave;ncamento di regola universale qual'&egrave; nelle riflessioni <lb/>che l'angolo della incidenza sia uguale a quello della riflessione,<emph.end type="italics"/> e con&shy;<lb/>cludeva non essersi potuto fin allora con modo sicuro e dimostrativamente <lb/>provare <emph type="italics"/>con che regola si vadano diminuendo gli angoli della rifrazione <lb/>in un diafano, ovvero accrescendo in relazione degli angoli dell'incidenza.<emph.end type="italics"/><lb/>(Bologna 1650, pag. </s>

<s>47). </s></p><p type="main">

<s>La regola dal Cavalieri tanto desiderata, il Cartesio la divulg&ograve; nel 1637, <lb/>con gran solennit&agrave; nella <emph type="italics"/>Diottrica.<emph.end type="italics"/> Il Torricelli nonostante, persuaso che il <lb/>Cavalieri fosse uomo da specular pi&ugrave; sottilmente del Filosofo Francese, a lui <lb/>si rivolge, per aver qualche lume di scienza diottrica, che, in cos&igrave; fatti ter&shy;<lb/>mini, rispondeva in proposito da Bologna. </s>

<s>&ldquo; Quanto poi ai vetri, non gli <lb/>posso dir altro se non di avere speculato alquanto sopra di essi, per ritro-<pb xlink:href="020/01/408.jpg" pagenum="389"/>vare ove sia il concorso di varie lenti fatto da raggi paralleli, qualunque <lb/>siano le loro due superficie, quali per&ograve; suppongo sempre sferiche, e mi pare <lb/>d'averlo trovato, almeno prossimamente, cio&egrave; non facendo caso d'errore dal <lb/>vero, quanto &egrave; la grossezza della lente. </s>

<s>Ora perch&egrave; non ho mai applicato al <lb/>fabbricar lenti, perci&ograve; non posso distintamente sapere che servizio mi potr&agrave; <lb/>fare simile trovato, ma stimo, cos&igrave; in universale, che forse se ne potr&agrave; ca&shy;<lb/>vare qualche benefizio &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>32). </s></p><p type="main">

<s>Tornando poi lo stesso Cavalieri su questo tema delle rifrazioni trattava <lb/>col Torricelli dello speculare sopra la linea che possa per refrazione unire <lb/>in un punto, dicendo esser questa <emph type="italics"/>cosa da tanti ricercata, ma tentata in <lb/>vano.<emph.end type="italics"/> &ldquo; Sebbene, poi tosto soggiunge, mi pare che l'Erigonio nel suo Corso <lb/>Matematico .... supponga d'averla trovata, fondandosi sopra questo principio <lb/>che i seni delle inclinazioni sieno proporzionali con i seni delle rifrazioni, <lb/>ma perch&egrave; questo principio lo prova solo facendo un trapasso dalla Mecca&shy;<lb/>nica alla Diottrica ... per questo sono stato sempre dubbioso &rdquo; (Lez. </s>

<s>Accad. </s>

<s><lb/>Torricelli, Milano 1823, pag. </s>

<s>25). </s></p><p type="main">

<s>Nel dubbio stesso rest&ograve; pure involto pi&ugrave; che mai il Torricelli, il quale, <lb/>come non volle saper dell'Herigonio, cos&igrave; non volle veder nemmeno la Diot&shy;<lb/>trica del Cartesio. </s>

<s>Il Mersenno gli faceva di ci&ograve; premura, ma il Nostro si <lb/>scusava dicendo che non intendeva la lingua francese. </s>

<s>Il Mersenno stesso, <lb/>pi&ugrave; tardi, ha una buona notizia da dargli ed &egrave; che la diottrica cartesiana &egrave; <lb/>tradotta in latino <emph type="italics"/>quae si desiderat V. D. confestim a Lutetia missurus <lb/>sum<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>16) e perch&egrave; il Torricelli non rispondeva, <lb/>dopo dieci mesi, il frate francese torna a scrivergli da Parigi: &ldquo; Moneo prae&shy;<lb/>terea Dioptricam cartesianam hic latine venalem esse, quam tibi facile possis <lb/>comparare, qui gallicam intelligere non potuisti &rdquo; (ibi, c. </s>

<s>19). Finalmente <lb/>il Mersenno intese che quello era un cantar la favola ai sordi. </s></p><p type="main">

<s>Se dunque &egrave; vero che il Torricelli non riconobbe la verit&agrave; della legge <lb/>annunziata e meccanicamente dimostrata delle rifrazioni; se &egrave; vero che per <lb/>nulla ci entrano le sezioni coniche, come nello specchio Ustorio aveva gi&agrave; <lb/>dimostrato il Cavalieri, non si pu&ograve; altro concludere se non che il Problema <lb/>della figura dei vetri fu praticamente risoluto dallo stesso Torricelli a quel <lb/>modo che, da occhialaio e non gi&agrave; da geometra, rivel&ograve; nella lettera famosa <lb/>al Magiotti. </s></p><p type="main">

<s>Il Matematico insomma di Firenze, bench&egrave; volesse far credere di es&shy;<lb/>sersi sublimato nelle alte speculazioni della Geometria, procedeva per quelle <lb/>basse e trite vie della pratica esperienza, da rimaner di molti passi indietro <lb/>allo stesso Occhialaio napoletano, che in sostanza non fu mai potuto arri&shy;<lb/>vare. </s>

<s>E in fatti, se i Canocchiali del Torricelli bastavano a dar gusto al <lb/>Granduca nel riguardar le ville e i paesetti circostanti, o nell'esaminar l'aria <lb/>ora pi&ugrave; trasparente e ora pi&ugrave; caliginosa, a seconda che i fumaioli della citt&agrave; <lb/>o il suolo facevano esalar fumi e vapor&iacute; in pi&ugrave; e in meno copia; non riu&shy;<lb/>scivan per&ograve; che di pochissimo profitto all'Astronomia, la quale non fece con <lb/>essi in cielo mai nessuna importante scoperta. </s>

<s>Il Torricelli stesso confessa <pb xlink:href="020/01/409.jpg" pagenum="390"/>in una sua lettera del d&igrave; primo di Febbraio 1647 al Mersenno, che co'suoi <lb/>lunghissimi tubi non s'era fatta ancora altra osservazione che delle fascie di <lb/>Giove: &ldquo; Tubis nostris longissimis n&igrave;hil adhuc novi deteximus in coelo prae&shy;<lb/>ter fascias ioviales quae ipsum Jovis globum tamquam terrestres nostrae <lb/>zonae ambiunt &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>55). </s></p><p type="main">

<s>Ma perch&egrave; il Granduca intendeva d'aver buoni Canocchiali per servir&shy;<lb/>sene a suo diletto, il Torricelli che, inebriato dalle lodi e dai premi, non <lb/>aveva ad altro rivolti i suoi pensieri, che a compiacerlo, dell'Astronomia se <lb/>ne curava assai poco. </s>

<s>Egli abitava allora in Firenze dietro il Duomo, nelle <lb/>case dell'<emph type="italics"/>Opera,<emph.end type="italics"/> e i grandi palazzi signorili che le fiancheggiano, e l'am&shy;<lb/>pia e alta mole del Tempio che a lor si para di faccia, circoscrivevano al&shy;<lb/>l'Osservatore troppo angusto spazio di cielo, in che egli principalmente tro&shy;<lb/>vava, a que'suoi ozii astronomici, una scusa. </s>

<s>Nel passo di lettera al Mersenno <lb/>sopra citato soggiunge infatti, a proposito delle fascie di Giove: &ldquo; Ipse enim <lb/>fere nunquam in coelum aspicio, ob inopportunitatem aedium quas inha&shy;<lb/>bito &rdquo; (ivi). </s></p><p type="main">

<s>A quella osservazione anzi di Giove, che fu l'unica, pare si risolvesse <lb/>il Torricelli, non per amor della scienza, ma per alcune importune richie&shy;<lb/>ste fattegli poco prima dal Ricci, a cui rispondeva: &ldquo; Quanto al veder le <lb/>fascie in Giove io non l'ho mai vedute perch&egrave; non si vedono sempre, e <lb/>quando io ho avuto l'occasione di guardarlo, il che &egrave; stato da quattro o sei <lb/>volte, dopo che son tornato in Firenze, non si vedevano.... Quanto al gi&shy;<lb/>rarsi in s&egrave; io lo tengo per certo, senza vedervi altro contrassegno. </s>

<s>Ogni <lb/>corpo lass&ugrave;, intorno al quale si girino altri corpi, V. S. dica pure che gira <lb/>anch'esso, ma in tempo pi&ugrave; breve che qualunque altro corpo che gli si <lb/>muova intorno, per&ograve; io credo che s'inganneranno coloro, che pensano che <lb/>Giove mette pi&ugrave; giorni in fare una rivoluzione sola &rdquo; (ivi, c. </s>

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

<s>Il tener per certa il Torricelli la rivoluzione di Giove, prima che il <lb/>Cassini l'avesse dimostrata, e l'indovinar la brevit&agrave; del periodo di quella <lb/>stessa rotazione, potrebbero esser forse argomento di molto acume che fosse <lb/>in lui, e di molta veggenza in cose di Astronomia, se non si sapesse ch'ei <lb/>non faceva poi altro che ripetere quel che avea scritto il Keplero nella sua <lb/>Prefazione alla Diottrica. </s></p><p type="main">

<s>Pure, una volta il Torricelli trov&ograve; sul campanile del Duomo, uscito fuori <lb/>dalle sue umili case, la pi&ugrave; aperta specula, che potesse mai desiderare, e <lb/>cost&igrave; fece un'osservazione e un calcolo intorno a Mercurio, di che cos&igrave; dava <lb/>parte al Renieri: &ldquo; Osservai questa settimana passata Mercurio quando era <lb/>in congiunzione di Venere, e cos&igrave; all'improvviso, sul campanile del Duomo, <lb/>discorrendo con alcuni giovani che erano meco, feci un certo calcolaccio, per <lb/>la prima volta che avevo veduto Mercurio, e conietturai che egli, di diametro <lb/>reale, fosse meno di otto miglia delle nostre. </s>

<s>Lo paragonai a Venere, giudi&shy;<lb/>cando quanto egli apparisse minore, poi colla memoria paragonai Venere a <lb/>qalche macchia di quelle tonde della Luna, e feci conto anco della lontananza: <lb/><gap/></s></p><pb xlink:href="020/01/410.jpg" pagenum="391"/><p type="main">

<s>Ora, con buona riverenza del Torricelli, tutti converranno che nel <emph type="italics"/>Li&shy;<lb/>bro delle bestialit&agrave;<emph.end type="italics"/> di Francesco Fontana, ce ne sien pure quante il suo <lb/>censore ce ne volle vedere, non ci pu&ograve; esser bestialit&agrave; che sia simile a questa. </s></p><p type="main">

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

<s>L'intenzione del Granduca Ferdinando, nel consegnar che fece al Vi&shy;<lb/>viani la chiave della cassetta, dentro alla quale si custodiva il segreto tor&shy;<lb/>ricelliano, fu quella di veder proseguita nel successore del Torricelli l'opera <lb/>dei Canocchiali. </s>

<s>Ma perch&egrave; il Viviani non avea tanto bene esercitata la mano <lb/>nel lavoro de'cristalli, ebbe ordine dallo stesso Granduca di servirsi dell'arte <lb/>di Filippo Treffler, a cui dovesse suggerir quelle regole che aveva apprese <lb/>per scienza e per esperienza sua propria, oltre agli insegnamenti ricavati dai <lb/>manoscritti del Torricelli. </s>

<s>&ldquo; Essendoch&egrave; il Serenissimo Granduca (cos&igrave; lo <lb/>stesso Viviani lasci&ograve; scritto di sua propria mano) una sera di Dicembre <lb/>prossimo passato (1664), prima di andare a Pisa, tra le altre cose coman&shy;<lb/>dasse a me Vincenzio Viviani scrittore della presente, che nel tempo di que&shy;<lb/>sta sua campagna assistessi a M. </s>

<s>Filippo Treffler, suo torniaio che S. A. la&shy;<lb/>sciava apposta in Firenze, con introdurlo e instruirlo in quelle proposizioni <lb/>che, per l'arte del lavorare i vetri da occhialoni, si cavano dalla teorica e <lb/>dai fondamenti diottrici, ed avendo io come devotissimo suddito promesso di <lb/>ubbidire, conferii al suddetto Filippo le infrascritte cose, nel modo che ap&shy;<lb/>presso, ma pure tutte in somma confidenza &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXIII, <lb/>c. </s>

<s>20). E seguita a scrivere, sotto varii capi numerati, gl'insegnamenti che <lb/>dette al Treffler, i quali per&ograve; tutt'altro che esser cavati dalla <emph type="italics"/>teorica e dai <lb/>fondamenti diottrici,<emph.end type="italics"/> consistono in regole pratiche, non molto diverse da <lb/>quelle insegnate dal Torricelli. </s>

<s>O sien sue o d'altri, il Viviani stesso lasci&ograve; <lb/>scritte alcune <emph type="italics"/>Ricette per far lo stucco a freddo<emph.end type="italics"/> (ivi, c. </s>

<s>4) onde attaccar <lb/>con esso e non colla pece i vetri; per&ograve; si conosce assai bene che egli at&shy;<lb/>tendeva a queste cose, non per suo proprio genio, ma per compiacere al <lb/>Granduca. </s></p><p type="main">

<s>Tenue &egrave; pure lo studio che fece intorno all'uso dei Canocchiali, ben&shy;<lb/>ch&egrave; vi si riveli il solito acume e la fecondit&agrave; dell'ingegno. </s>

<s>Descrisse un <lb/><emph type="italics"/>Modo di ritrovar con l'Occhiale o senza, da un dato luogo, la distanza <lb/>di un oggetto di nota altezza o larghezza<emph.end type="italics"/> (ivi, T. CXXXIV, c. </s>

<s>2) e inse&shy;<lb/>gn&ograve; una regola <emph type="italics"/>per conoscere l'aggrandimento di un Occhiale<emph.end type="italics"/> (ivi, c. </s>

<s>3) <lb/>pi&ugrave; precisa di quella insegnata gi&agrave; da Galileo, nel suo Nunzio Sidereo. </s></p><p type="main">

<s>Altre regole lasci&ograve; qua e l&agrave; sparse per i suoi Manoscritti, alcune delle <lb/>quali, oltre ad essere utili a chi allora, senza troppa scienza diottrica, ma&shy;<lb/>neggiava Canocchiali, si direbbero, nella loro stessa facilit&agrave;, quasi eleganti. </s>

<s><lb/>Tal sarebbe, per esempio, la regola ch'egli insegna <emph type="italics"/>per conoscere se l'ocu&shy;<lb/>lare di un Telescopio &egrave; distante dall'obiettivo per la dovuta lunghezza.<emph.end type="italics"/><pb xlink:href="020/01/411.jpg" pagenum="392"/>&ldquo; Osserva, egli dice, se l'oggetto luminoso apparisce rosso, che allora sar&agrave; <lb/>corto, e se si vede turchino, che allora sar&agrave; troppo lungo; onde da tai con&shy;<lb/>trassegni averai modo d'aggiustarlo a dovere &rdquo; (ivi, T. CXXXV, c. </s>

<s>8). </s></p><p type="main">

<s>Mentre che dal Treffler e dal Viviani s'attendeva in Toscana a costruir <lb/>Canocchiali, per mantener vive le tradizioni di Galileo e del Torricelli, e <lb/>per compiacere al Granduca, Cristiano Huyghens, nella mente del quale ri&shy;<lb/>fulgeva pi&ugrave; che in altra mai la scienza diottrica, speculava intorno a per&shy;<lb/>fezionar lo strumento, che gli dovea rivelare altre nuove meraviglie nel cielo. </s>

<s><lb/>Egli &egrave; veramente il primo che possa dire di aver cavati dai fondamenti diot&shy;<lb/>trici i principii dell'arte, a esercitar la quale veniva aiutato dal fratello suo <lb/>Costantino, che, morto, ei nel Cosmoteoro commemora con parole tuttavia <lb/>vive e fragranti di affetto. </s>

<s>&ldquo; Fortasse autem, ubi ad signa Borea Saturnus <lb/>revertetur, alteque supra horizontem attolletur, nam quo tempore haec scri&shy;<lb/>bimus maxime deprimitur, aliquid circa haec novi observari continget, si <lb/>quis tuas tunc lentes, Frater optime, ad Telescopia pedum 170 et 210 para&shy;<lb/>tas, sideribus applicet &rdquo; (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>698). E dopo aver <lb/>commemorati gli sperimenti, <emph type="italics"/>in ambulacris suburbanis sub noctem,<emph.end type="italics"/> col dol&shy;<lb/>cissimo fratello suo istituiti; cos&igrave;, con mestizia ineffabile, conclude: &ldquo; Quo&shy;<lb/>rum equidem lubens reminiscor, simulque iucundi laboris nostri, quem in <lb/>elaborandis expoliendisque vitreis huiusmodi discis, impendere una soleba&shy;<lb/>mus, excogitatis novis artificiis machinisque, semperque ulteriora agitan&shy;<lb/>tes &rdquo; (ibi). </s></p><p type="main">

<s>Tanto era giunto nel 1655 l'Huyghens, a perfezionare il suo nuovo <lb/>Canocchiale, che gli rivel&ograve; una luna, non pi&ugrave; veduta ricircolare intorno a <lb/>Saturno. </s>

<s>Ma la sua attenzione era tutta rivolta al Pianeta, e fu quello stesso <lb/>Canocchiale che fecegli nascere un sospetto di ci&ograve; che fosse veramente ca&shy;<lb/>gione di tanto strane apparenze. </s>

<s>Non si assicurava per&ograve; ancora, infintantoch&egrave; <lb/>non si fosse preparato uno strumento pi&ugrave; che mai perfetto, e studiava in <lb/>che modo vi potesse riuscire. </s>

<s>Sagace com'egli era, conobbe che doveva quel <lb/>modo principalmente consistere in toglier l'iridescenza alle lenti, ardua im&shy;<lb/>presa e da tutti allora reputata impossibile. </s>

<s>Ma l'Huyghens aveva con sua <lb/>gran meraviglia osservato che, nei Canocchiali a tre o a quattro lenti, gli <lb/>effetti d'iridescenza, che pareva dovessero moltiplicarsi, riuscivano invece <lb/>alquanto minori. </s>

<s>Incominci&ograve; a pensare intorno a ci&ograve; attentamente, cosicch&egrave; <lb/>all'ultimo vide quella sua prima maraviglia risolversi tutta in una ragione, <lb/>la quale, secondo lui, consisteva in far s&igrave; che l'una lente correggesse o to&shy;<lb/>gliesse via i colori, che le si venivano a rappresentare dall'altra. </s>

<s>Fu questa <lb/>speculazione che condusse l'Huyghens a compor di due convessi, invece che <lb/>d'un solo, l'oculare del suo Canocchiale astronomico. </s></p><p type="main">

<s>La voce di una tale e tanta novit&agrave;, introdotta nella fabbrica dei Tele&shy;<lb/>scopi, corse tosto di Olanda alle orecchie di tutti gli Astronomi, e special&shy;<lb/>mente d'Italia, i quali entrarono in gran curiosit&agrave; di sapere il vero di que&shy;<lb/>sta cosa. </s>

<s>Il Cassini sollecitava un amico suo, perch&egrave; s'informasse, per mezzo <lb/><gap/><pb xlink:href="020/01/412.jpg" pagenum="393"/><emph type="italics"/>altra combinazione di lenti per Telescopi, che tolga ogni colore agli og&shy;<lb/>getti, e gli conservi inalterabili di figura<emph.end type="italics"/> (MSS. Gal. </s>

<s>Cim., T. XIV, c. </s>

<s>51). <lb/>Ma il Viviani annunzia nell'Accademia del Cimento la cosa come certa, con&shy;<lb/>forme alla seguente nota che di sua propria mano lasci&ograve; cos&igrave; scritta: &ldquo; Uge&shy;<lb/>nio ha fatto occhiali anco pi&ugrave; rari di nuova invenzione, dove i cristalli sono <lb/>composti di due convessi da una parte e piani dall'altra, che cos&igrave; tolgono <lb/>i colori e mantengono tutti gli oggetti diritti &rdquo; (ivi, T. IV, c. </s>

<s>252). </s></p><p type="main">

<s>La curiosit&agrave; fu poi sodisfatta in tutti e tutti pur s'acquietarono nella <lb/>certezza del fatto, quando nel 1659 l'Huyghens stesso usc&igrave; fuori col suo <lb/><emph type="italics"/>Systema Saturnium.<emph.end type="italics"/> &ldquo; Sed antequam, egli cos&igrave; avverte in principio, obser&shy;<lb/>vationes exhibeamus, de Telescopiis nostris .... pauca referre expediat &rdquo; <lb/>(Op. </s>

<s>Var. </s>

<s>cit. </s>

<s>1724, pag. </s>

<s>537). E proseguendo a far la descriziono del suo <lb/>astronomico strumento, cos&igrave; particolarmente scrive dell'oculare: &ldquo; Ab altera <lb/>parte, quae nimirum oculo admovetur, bina sunt vitra minora, 1 1/2 polli&shy;<lb/>cum diametro aequantia iuncta invicem, quaeque hoc pacto aequipollent con&shy;<lb/>vexo colligenti radios parallelos ad intervallum unciarum 3 aut paulo etiam <lb/>angustius &rdquo; (ibi). Che poi da una tale composizione di lenti glie ne fossero <lb/>risultati mirabili effetti, oltre al venir da s&egrave; naturalmente insinuato per la <lb/>scoperta che poi passa a descrivere dell'anello Saturnio, lo prefinisce meglio <lb/>l'Autore, asserendo di essere riuscito per quel modo ad ottenere un in&shy;<lb/>grandimento centuplicato. </s>

<s>&ldquo; Centuplam itaque fere rationem hanc in perspi&shy;<lb/>cillis nostris esse constat, cum Galileiana non ultra trigecuplam processe&shy;<lb/>rint &rdquo; (ibi, pag. </s>

<s>538). </s></p><p type="main">

<s>Ma bench&egrave; tutti fossero oramai resi certi delle invenzioni delle due lenti <lb/>accoppiate, nessun sapeva per&ograve; intendere, di quell'efficace accoppiamento, <lb/>le vere ragioni. </s>

<s>Di qui ebbero origine que'giudizi vaghi, che si fecero in&shy;<lb/>torno ai nuovi Canocchiali ugeniani, l'&egrave;ccellenza de'quali, non essendo stata <lb/>ancora diottricamente dimostrata, s'ammetteva come possibile a spiegare i <lb/>maravigliosi fatti osservati. </s>

<s>Cos&igrave;, per esempio, il Borelli dovendo fare un <lb/>confronto tra i Canocchiali dell'Huyghens e quelli del Divini, si esprime <lb/>nella forma seguente: &ldquo; Ma un giudice disappassionato direbbe che, senza <lb/>pregiudizio della non mai abbastanza lodata perfezione degli Occhiali di Eu&shy;<lb/>stachio, potrebbero essere le lenti di quelli dell'Ugenio formate d'altra figura <lb/>che della sferica, conforme hanno creduto poter lavorarsi molti uomini in&shy;<lb/>signi: di pi&ugrave; quel raddoppiare le lenti vicino all'occhio <emph type="italics"/>forse potrebbe<emph.end type="italics"/> far <lb/>buon effetto &rdquo; (MSS. Gal. </s>

<s>Cim., T. XII, c. </s>

<s>99). </s></p><p type="main">

<s>Non manc&ograve; nonostante chi apertamente uscisse fuori a mettere in dub&shy;<lb/>bio, e anzi a negare in particolar modo che le due lenti accoppiate avessero <lb/>virt&ugrave; di toglier via l'iridescenza ne'Canocchiali ugeniani. </s>

<s>Il marchese Cor&shy;<lb/>nelio Malvasia, avendone interrogato in proposito M. Petit, n'ebbe da lui <lb/>cos&igrave; fatta risposta: &ldquo; Cum autem de ipsius invento duorum ocularium simul <lb/>iunctorum, ad evitandos iridis colores spatiumque amplificandum, sermonem <lb/>facis, id seponam iamdudum nobis in mentem venisse, eoque usos fuisse <lb/><gap/> convenientis ad confectionem ocularium, <pb xlink:href="020/01/413.jpg" pagenum="394"/>ex utraque parte convexorum. </s>

<s>Is enim ad alios usus inutilis satis videtur, <lb/>nec interest convexitates istorum duorum ocularium contiguas esse ut <lb/>sic D&Drev;, vel oppositas &Drev;D ut sic, aut hoc modo, quod aliis praefertur, dispo&shy;<lb/>sitas &Drev;&Drev;: nullis enim tollitur obsolute iris. </s>

<s>Si aliunde emanet hoc, est ab <lb/>incidentia nimis obliqua radiorum in superficiem refringen&shy;<lb/>tem &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXVI, c. </s>

<s>19). </s></p><p type="main">

<s>Ma non era ancora dell'Huyghens pubblicata la Diottrica, <lb/><figure id="id.020.01.413.1.jpg" xlink:href="020/01/413/1.jpg"/></s></p><p type="caption">

<s>Figura 29.<lb/>nella quale si riserbava a dar quella teoria dell'acromatismo, <lb/>di che aveva fatto gi&agrave; l'applicazione alle lenti del suo Tele&shy;<lb/>scopio. </s>

<s>Nella proposiz&igrave;one LIV di quel celebre Trattato, uscito <lb/>postumo nel 1703 come sappiamo, dop'aver l'Autore descritto <lb/>l'andamento dei raggi refratti ne'Telescopi di quattro lenti, <lb/>cos&igrave; soggiunge, per sodisfare co'principii diottrici a coloro, <lb/>i quali non intendevano il segreto effetto del suo oculare <lb/>composto: &ldquo; Mirum videtur in hoc Telescopio colores iridis <lb/>oriri plurium ocularium refractione, non magis quam cum una <lb/>ocularis adhibetur. </s>

<s>Sed ratio haec est quod lens QR (fig. </s>

<s>29) <lb/>corrigit et aufert colores quas lens KL produxit. </s>

<s>Idem enim <lb/>accidit radio OKRN, per superficies inclinatas ad K ac deinde <lb/>ad R transeunti, ac si per cuneos binos contrarie positos SS, TT (fig. </s>

<s>30) <lb/>transiret parallelis lateribus qui colore non inficitur non magis quam si per <lb/>laminam vitream incederet &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1703, pag. </s>

<s>195, 96). <lb/><figure id="id.020.01.413.2.jpg" xlink:href="020/01/413/2.jpg"/></s></p><p type="caption">

<s>Figura 30.</s></p><p type="main">

<s>Aveva senza dubbio ragione il Petit a dire che a que&shy;<lb/>sto modo <emph type="italics"/>nullis tollitur absolute iris,<emph.end type="italics"/> ma, a riuscire al <lb/>tanto desiderato effetto, aveva pure l'Huyghens aperta cos&igrave; <lb/>e raddirizzata la via agli ottici futuri. </s>

<s>Il Newton poi dimo&shy;<lb/>str&ograve; che non bastava comporre insieme due mezzi rifran&shy;<lb/>genti della stessa natura, ma che bisognava fossero di na&shy;<lb/>tura alquanto diversa e propose di accoppiare insieme lenti <lb/>cristalline con lenti ripiene d'acqua. </s>

<s>&ldquo; Si perspicillorum <lb/>vitra obiectiva ex vitris duobus sphaerice figuratis et aquam <lb/>inter se claudentibus constentur, fieri potest ut a refractionibus aquae er&shy;<lb/>rores refractionum quae fiunt in vitrorum superficiebus extremis satis ac&shy;<lb/>curate corrigantur &rdquo; (Principia Philos. </s>

<s>T. I, Genevae 1739, pag. </s>

<s>547). L'Eu&shy;<lb/>lero ridusse a calcolo, di quelle lenti di varia rifrangibilit&agrave;, lo spessore e la <lb/>forma, e il Dollond, componendo insieme i due cunei ugeniani sopra de&shy;<lb/>scritti, di due cristalli di vario poter dispersivo, riusc&igrave; finalmente a risol&shy;<lb/>vere il problema. </s></p><p type="main">

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

<s>Non senza una giusta ragione, ripensando l'Huyghens alla numerosa se&shy;<lb/>quela, che ebbero gli esempi galileiani, si compiaceva seco stesso di essere <lb/>stato il primo, nel numero de'costruttori del Telescopio, a farsi, dopo Ga-<pb xlink:href="020/01/414.jpg" pagenum="395"/>lileo, messaggero agli uomini d'altre nuove maravigliose novit&agrave; celesti. </s>

<s>Quasi <lb/>tutti coloro che lo avevano preceduto, e specialmente il Torricelli, bench&egrave; aves&shy;<lb/>sero di molto accresciute le lunghezze dei tubi, e con gli obiettivi di grande <lb/>sfera avessero ottenuti notabili ingrandimenti, fecero nonostante poco pro&shy;<lb/>fitto nell'osservazione degli astri, essendoch&egrave; l'iridescenza e l'aberrazione <lb/>di sfericit&agrave; non ne lasciassero con esattezza intravedere i contorni. </s>

<s>&ldquo; Nos <lb/>autem, soggiunge l'Huyghens, magis auspicato rem eamdem aggressi, cum, <lb/>quae ad refractiones radiorum attinent perspecta haberemus, ipsique nobis <lb/>lentes effecissemus, ac telescopia pedes vigin ti et amplius longe, his Saturni <lb/>formas non ante visas deprehendimus, causamque earum annulum globo cir&shy;<lb/>cumdatum nullo in caeteris planetis exemplo &rdquo; (Dioptr. </s>

<s>ibi, pag. </s>

<s>165). E prose&shy;<lb/>guendo a dir di Saturno, poco appresso conclude: &ldquo; Nostris autem observatio&shy;<lb/>nibus excitati Astronomi atque artifices maiora subinde Telescopia paraverunt <lb/>in quibus optima, quae a Josepho Campano Romae fabricata &rdquo; (ibi). </s></p><p type="main">

<s>Giuseppe Campani scrive di s&egrave; stesso dicendo di essere stato, per lungo <lb/>tempo, esortato ad applicar la mente e la mano agli studi diottrici, dal ce&shy;<lb/>lebre padre Daniello Bartoli della compagnia di Ges&ugrave; (Ragguaglio ecc., <lb/>Roma 1664, pag. </s>

<s>9). Con la scorta di lui, ei soggiunge, rivoltomi agli studii <lb/>della Diottrica &ldquo; applicai tutto l'animo e tutto il mio studio all'invenzione <lb/>d'un Torno esattissimo da lavorare i vetri, senza altro mezzo di forma. </s>

<s>E <lb/>riuscitomi finalmente di conseguirlo, non senza lunghissime fatiche, ed in&shy;<lb/>numerabili esperienze, riconosco, non dalla debolezza del mio ingegno, ma <lb/>da Dio questo dono; parendomi in vero, se non l'intero compimento del&shy;<lb/>l'arte, l'unico mezzo almeno da giungerne alla perfezione. </s>

<s>Perch&egrave;, con <lb/>l'aiuto di questo Torno mi riescono gli Occhialoni, non dico d'ultima squi&shy;<lb/>sitezza, che non presumo d'aver fissate le mete agli ingegni degli uomini, <lb/>ma tali certo, che da altri sono stati stimati migliori de'veduti fin ora &rdquo; <lb/>(ivi, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>In che consistesse per&ograve; l'artifizio di questo Torno, non si pot&egrave; mai <lb/>saper da nessuno, per cui, in Italia e fuori, si sospett&ograve; e s'and&ograve; spargendo <lb/>voce che fosse una mera finzione dell'artefice, per tener pi&ugrave; sicuramente <lb/>occulto alle altrui perquisizioni qualche suo nuovo segreto. </s>

<s>In una bella e <lb/>importante lettera al principe Leopoldo de'Medici tradotta dal latino, forse <lb/>dal Dati, l'Huyghens, dop'aver parlato d'altre cose e tutte in soggetto astro&shy;<lb/>nomico, soggiunge: &ldquo; M'era prima capitata una Narrazione delle nuove os&shy;<lb/>servazioni intorno a Saturno di Giuseppe Campani, nella quale, oltre alla <lb/>confermazione della mia ipotesi dell'anello saturnino, trovai un bellissimo <lb/>ritrovamento d'un Torno per far le lenti, proposto allora per la prima volta. </s>

<s><lb/>Ma siccome ci&ograve;, a prima vista, parve a me appena possibile, cos&igrave; mi accorsi <lb/>poi che anche altri ne dubitavano, siccome ancora di quello che importa <lb/>pi&ugrave;, cio&egrave; se fossero migliori le lenti che si diceva che fossero state lavorate <lb/>a quel Torno, che quell'altre che sono lavorate col metodo solito, senza <lb/>macchina alcuna, n&egrave; ancor per quel che io sappia &egrave; finita quella contro&shy;<lb/><gap/> &rdquo; (MSS. Gal. </s>

<s>Cim., T. XVIII, c. </s>

<s>316). </s></p><pb xlink:href="020/01/415.jpg" pagenum="396"/><p type="main">

<s>Ma la controversia fu poi insomma definita dai fatti, avendo il Campani <lb/>apparecchiato al Cassini Canocchiali tanto pi&ugrave; eccellenti di quelli stessi del&shy;<lb/>l'Huyghens, che pot&egrave; il nostro celebre Astronomo italiano veder presto Sa&shy;<lb/>turno circondato da due altri satelliti, oltre a quello ugeniano, e scoprir le <lb/>macchie in Giove e in Marte, da prefinire il periodo della loro rotazione. </s>

<s>Di <lb/>ci&ograve;, e della eccellenza de'canocchiali del suo rivale romano, fu fatta gene&shy;<lb/>rosa testimonianza dallo stesso Huyghens, il quale, dop'essersi compiaciuto <lb/>che il Campani avesse ricevuto da'suoi stessi esempi eccitamento a perfe&shy;<lb/>zionare i suoi ottici strumenti, soggiunge: &ldquo; Quorum opera feliciter, decen&shy;<lb/>nio post, duos alios praeter nostrum illum Comites apud Saturnum reperit <lb/>Dominus Cassinus. </s>

<s>Idemque in Jovis ac Martis sideribus maculas quosdam <lb/>observavit, ex quarum motu etiam globorum, quibus inerant, conversiones, <lb/>certis periodis definiret &rdquo; (Dioptr. </s>

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

<s>Comunque sia, se pu&ograve; mettersi in dubbio che il Campani avesse vera&shy;<lb/>mente ritrovato un artifizio nuovo da formare e da pulire le lenti, &egrave; per&ograve; <lb/>cosa certa ch'ei pens&ograve; de'primi a dare alle lenti stesse una nuova compo&shy;<lb/>sizione nei Telescopi, e tale da diminuirne notabilmente la lunghezza del <lb/>tubo, e da ricavarne altri migliori effetti. </s>

<s>Richiesto da un signore, che era <lb/>entrato in gran curiosit&agrave; di sapere il modo di quella nuova composizione, <lb/>cos&igrave; il Campani stesso, in una sua lettera del d&igrave; 6 di Settembre 1664, gliela <lb/>descrive: </s></p><p type="main">

<s>&ldquo; Il mio Canocchiale, che V. S. Ill.ma mi ha comandato che le descriva, <lb/>&egrave; fatto nella seguente maniera: ED &egrave; il canocchiale (fig. </s>

<s>31). In D sta il <lb/><figure id="id.020.01.415.1.jpg" xlink:href="020/01/415/1.jpg"/></s></p><p type="caption">

<s>Figura 31.<lb/>vetro oggettivo. </s>

<s>In C sta una lente <lb/>piana convessa, inclinata, secondo la <lb/>linea BC, nel piano verso D. </s>

<s>Nel can&shy;<lb/>noncino AB vi &egrave; una lente oculare <lb/>convessa proporzionata all'oggettivo D, <lb/>qual lente &egrave; collocata per piano oriz&shy;<lb/>zontale in B, in distanza proporzionata alla lente C. </s>

<s>In A si mette l'occhio, <lb/>che pure deve star tanto distante dalla lente B, quanto se ne terrebbe lon&shy;<lb/>tano, se con essa si guardasse, e per il canocchiale, secondo il modo ordi&shy;<lb/>nario. </s>

<s>In E vi &egrave; un coperchietto amovibile, e questo serve per poter diriz&shy;<lb/>zare comodamente il canocchiale all'oggetto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Questo mio Canocchiale mostra l'oggetto con tutta quella terminazione, <lb/>ovvero distinzione e nettezza, che pu&ograve; desiderarsi, ed in qualunque parte <lb/>della lente inclinata, dove s'imbattano a cadere le specie dell'oggetto, e con <lb/>maggior campo ed ingrandimento di quello, che a mio parere possa aversi <lb/>dal Canocchiale, del quale V. S. mi ha parlato questa mattina, quand'io <lb/>sono venuto ad invitarla a vedere il mio, e con occasione com'ho raccon&shy;<lb/>tato, che iersera il sig. </s>

<s>ab. </s>

<s>Falconieri mi accenn&ograve; un non so che di cosa <lb/>simile avvisatagli da Firenze, a cui io subito mi esibii di farnele vedere l'ar&shy;<lb/>tificio, da me gi&agrave; molto prima praticato, ma poco stimato, per esserne riu&shy;<lb/>scito vano il fine, che io ne pretendeva. </s>

<s>In questo l'oggetto apparisce pi&ugrave; <pb xlink:href="020/01/416.jpg" pagenum="397"/>che negli altri, ma assai men chiaro, e quindi nasce questa s&igrave; fatta net&shy;<lb/>tezza, tanto che tolta da'miei Canocchiali di quattro lenti la gran quantit&agrave; <lb/>e grossezza delle puliche, le quali spesse volte s'incontrano nel vetro, e <lb/>tolta la luce superflua, cio&egrave; ridotti ad ugual chiarezza degli altri del nuovo <lb/>modo, mostrano l'oggetto ugualmente netto e terminato, e scoprono assai <lb/>pi&ugrave; campo, e riescono molto pi&ugrave; comodi. </s>

<s>Inoltre l'occhiale del nuovo modo, <lb/>sebbene pu&ograve; avere il vetro oggettivo tutto aperto, ad ogni modo, per l'uso <lb/>delle stelle, poco o niente serve, tanto che gli altri miei Canocchiali di quat&shy;<lb/>tro lenti sono migliori, e possono con molto gusto e sodisfazione adoperarsi <lb/>anche per gli oggetti celesti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io ne trovai l'invenzione nel primo Canocchiale, che feci di quattro <lb/>lenti, mentre io ne andava cercando un'altra, che poi non mi riusc&igrave;. </s>

<s>In luogo <lb/>del cannoncino e lente AB applicai un Microscopio, ed in luogo della lente C <lb/>una carta finissima e bianchissima, perch&egrave; speravo che forse forse quelle <lb/>specie dell'oggetto, che dal vetro D venivano portate in C, venissero ricre&shy;<lb/>sciute e vedute cos&igrave; bene e da vicino, come, col medesimo Microscopio av&shy;<lb/>verrebbe di una piccola pittura fatta col pennello nell'istessa carta, dove <lb/>questa doveva dipingersi, e meglio formarsi dalla natura, mediante il vetro D, <lb/>ed il cannone oscuro DE. </s>

<s>Ma essendomi tutto riuscito vano, il resto del&shy;<lb/>l'invenzione non mi par degna di molto applauso, non ritraendosene altro <lb/>che una certa soddisfazione di propria curiosit&agrave;, senza utile considerabile, e <lb/>con qualche incomodo &rdquo; (MSS. Gal. </s>

<s>Cim., T. XXIV, c. </s>

<s>162). </s></p><p type="main">

<s>Bench&egrave; il Campani non sapesse tenere in debito pregio la sua nuova <lb/>invenzione, vedremo nonostante fra poco l'utile partito che trassero di l&igrave; il <lb/>Newton e l'Hudley nella costruzione de'Telescopi catadiottrici, sostituendo <lb/>alla carta, sopra la quale si doveva dipinger dall'obiettivo l'immagine mi&shy;<lb/>croscopica, uno specchio metallico o un prisma isoscele cristallino. </s>

<s>Ma in&shy;<lb/>tanto non &egrave; possibile parlar di Giuseppe Campani, senza accoppiar necessa&shy;<lb/>riamente al suo nome, il nome di un altro ottico, che teneva pure bottega <lb/>aperta in Roma, Eustachio Divini. </s>

<s>Egli &egrave; quell'Eustachio orologiaro, di cui <lb/>parlava di sopra, in una sua lettera il Torricelli, onorandolo col titolo di <lb/>amico suo, perch&egrave;, sebben quello stesso orologiaro si fosse dato, infin da <lb/>quel tempo, a fabbricar Canocchiali, confessava nulladimeno di non esser <lb/>venuto ancora a quella eccellenza, a cui pretendeva di esser gi&agrave; arrivato il <lb/>Matematico del Granduca. </s>

<s>Ma se i primi e incerti passi fatti nell'arte, e la <lb/>gran fama del Torricelli poterono per allora tener basso il Divini, s'esalt&ograve; <lb/>fieramente, quando si trov&ograve; poi a dover competere con un suo pari. </s>

<s>&ldquo; E a <lb/>dirlo a V. A. S. (scriveva M. A. </s>

<s>Ricci al principe Leopoldo de'Medici) que&shy;<lb/>sti due artefici e virtuosi (il Campani e il Divini) sono in una s&igrave; forte emu&shy;<lb/>lazione, che altri non pu&ograve; aprir la bocca a favor dell'uno, senza che l'al&shy;<lb/>tro se ne offenda, quindi &egrave; che ognun si astiene dal dire il parer suo. </s>

<s>Il <lb/>signor Cassini ha gran sodisfazione di quello del Campani, e con esso va <lb/>tuttavia scoprendo cose nuove nel cielo &rdquo; (Targioni, Notizie Aggrandim., <lb/>T. II, P. II, pag. </s>

<s>748). </s></p><pb xlink:href="020/01/417.jpg" pagenum="398"/><p type="main">

<s>Ma come il Cassini restava sodisfatto dell'opera del Campani, cos&igrave; il <lb/>Borelli sembrava fosse sodisfatto ugualmente dell'opera del Divini, e delle <lb/>rivalit&agrave; fra gli artefici venivano a farsi cos&igrave; strumento attizzatore le rivalit&agrave; <lb/>fra'due grandi Astronomi. </s>

<s>A decider per&ograve; da qual parte fosse veramente il <lb/>vantaggio furono invocate le nuove apparenze di Saturno, per cui preten&shy;<lb/>deva il Campani che, mostrando i suoi Canocchiali la vera figura dell'anello, <lb/>dovessero esser pi&ugrave; eccellenti di quelli del Divini, che avean dato occasione <lb/>al Fabry di frantendere il sistema del lontano Pianeta, introducendovi il <lb/>gioco di que'globi bianchi e neri. </s>

<s>Il Campani stesso, traduceva, cos&igrave; pero&shy;<lb/>rando in causa propria, a decider la gran questione innanzi all'autorevole <lb/>tribunale del principe Leopoldo: </s></p><p type="main">

<s>&ldquo; Resta dunque da vedere chi de'suoi cultori (della Diottrica) sia pi&ugrave; <lb/>degli altri avanzato nella perfezione del lavoro. </s>

<s>Gli anni passati, a cagione <lb/>che Saturno apparve con volto diverso a diversi spettatori, che adoprarono <lb/>diversi Occhiali, suscitaronsi in tutta Europa, ma particolarmente in Roma <lb/>e in Firenze, due gagliarde controversie. </s>

<s>La prima fu circa il sistema di <lb/>esso Pianeta, e la seconda, dove poi venne a terminarsi dai disputanti la <lb/>prima, fu circa il valore dei Canocchiali, e V. A. S. fu dalle parti litiganti <lb/>deputato giudice della causa. </s>

<s>L'ombra segante il disco di Saturno, che il <lb/>signor Cristiano Hugenio asseriva di aver veduta co'suoi occhiali, siccome <lb/>rendeva verisimile il suo ingegnoso sistema, cos&igrave; poteva dare gran sospetto <lb/>dell'imperfezione degli Occhialoni dell'altra parte, che costantemente negava <lb/>l'ombra suddetta, ed asseriva un altro pure assai diverso sistema, tutto <lb/>composto di globi bianchi e neri, perch&egrave; cos&igrave; glie ne davano indizio manife&shy;<lb/>sto, diceva egli, le apparenze vedute in Saturno co'suoi squisitissimi vetri. </s>

<s><lb/>Queste dispute, siccome distrassero molti a varii sentimenti, cos&igrave; trassero la <lb/>mia mente e la mano a procurar di far vetri tali, con i quali si fosse po&shy;<lb/>tuto ocularmente mostrare la verit&agrave; di uno dei due sistemi, parendomi di <lb/>fare non poco acquisto, quando ci&ograve; mi fosse riuscito, mentre, oltre al do&shy;<lb/>vermisi in tal caso il nome di primo scopritore di quella verit&agrave;, che era <lb/>dubbia ed incerta a tutti, averei liberati i seguaci di una delle parti liti&shy;<lb/>ganti dagli errori cos&igrave; del falso sistema, come della supposta e non sussi&shy;<lb/>stente bont&agrave; degli Occhiali da loro erroneamente tenuti per i migliori, ed <lb/>ultimamente averei fatto a me stesso questo servigio di rendere sopra quelli <lb/>avvantaggio li miei vetri, tuttavolta che con essi avessi io potuto far vedere <lb/>al mondo o quel cerchio o quell'ombra o altra particolarit&agrave;, che sotto a <lb/>quest'istesso cielo romano non si erano ancora vedute con gli altri vetri, <lb/>nemmeno quando gli anni addietro erano molto pi&ugrave; visibili, che non sono <lb/>al presente. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sebbene V. A. S. ha udite tutte queste cose, e ne ha vedute le mie <lb/>osservazioni, imprese ad ogni modo, perch&egrave; assai pi&ugrave; efficacemente muo&shy;<lb/>vansi gli animi dalla potenza visiva che dall'udito; io sono a supplicare <lb/>che, immediatamente e subito che l'A. V. aver&agrave; fatte le osservazioni di Sa&shy;<lb/>turno e di Giove, con gli altri canocchiali romani, voglia farmi questo onore <pb xlink:href="020/01/418.jpg" pagenum="399"/>di nuovamente osservare questi Pianeti col mio Canocchiale, levatene per&ograve; <lb/>le due lenti oculari pi&ugrave; lontane dall'occhio, e dopo che si sar&agrave; servita della <lb/>propria lente oculare di questo Canocchiale, potr&agrave; anche, in luogo di que&shy;<lb/>sta, servirsi di un'altra lente pi&ugrave; acuta, che ho mandata a questo fine, con <lb/>la quale venerd&igrave; sera, nel giardino del Papa a Monte Cavallo, si videro a <lb/>maraviglia distinti il cerchio ed il globo di Saturno, senza ombra veruna, <lb/>apparendovi solamente i meri contorni che seco porta la ragione di Pro&shy;<lb/>spettiva. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Supplico intanto l'A. V. a degnarsi di fare adoperare ogni esatta di&shy;<lb/>ligenza ed aggiustatezza de'vetri, cos&igrave; del mio come degli altri Canocchiali, <lb/>in tutte le prove ed in tutti i paragoni che si faranno .... e se, dopo i pa&shy;<lb/>ragoni, V. A. si compiacer&agrave; di farmene dare pieno ragguaglio per lettera, .... <lb/>lo ricever&ograve; per grazia speciale di V. A. &rdquo; (MSS. Gal. </s>

<s>Cim., T. XVIII, c. </s>

<s>198). </s></p><p type="main">

<s>Forse astennesi il principe Leopoldo di dar sentenza finale, per le ra&shy;<lb/>gioni sopra dette dal Ricci, ma la storia ha pronunziato oramai il suo giu&shy;<lb/>dizio a favore del Campani, concludendo che i Canocchiali di lui, giovarono <lb/>meglio di quelli del Divini ai progressi dell'Astronomia, facendone di ci&ograve; <lb/>chiara testimonianza le insigni scoperte del Cassini. </s>

<s>Ma perch&egrave;, cos&igrave; il Cam&shy;<lb/>pani come tutti gli altri artefici di vetri rifrattori, s'incontrarono in una di <lb/>quelle difficolt&agrave;, credute allora insuperabili, nel tentar nuovi progressi, ebbe <lb/>a rivolgersi l'arte ai Telescopi catottrici, il profittevole uso de'quali, bench&egrave; <lb/>incominci dal Newton, ne fu speculato lungo tempo prima l'artifizio dai no&shy;<lb/>stri italiani. </s></p><p type="main">

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

<s>Il d&igrave; 7 Luglio 1626 Cesare Marsili, incominciava cos&igrave; una sua lettera, <lb/>scritta da Bologna e indirizzata a Firenze a Galileo: &ldquo; Un certo messer Gio&shy;<lb/>vanni, il quale pretende, dopo la morte di messer Cesare Carafaggi bolo&shy;<lb/>gnese (che negli scoprimenti e segreti della natura, come nell'ingegno pi&ugrave; <lb/>che nello studio era eccellentissimo) di essere unico suo erede nel modo di <lb/>fabbricare specchi tanto di cristallo, che operano per rifrazione, quanto di <lb/>altre materie, che operano per riflessione, mi port&ograve; alcuni giorni sono l'in&shy;<lb/>cluso disegno, acci&ograve; l'inviassi a V. S. E,, ov'ella vede che egli pretende po&shy;<lb/>ter fare uno specchio concavo, che non solo nella quarta, come dicono i <lb/>moderni, ma nel centro, come dicevano gli antichi, e oltre ancora, come anco <lb/>dentro della quarta in dati luoghi, possa accendere il fuoco, e in tutti i luo&shy;<lb/>ghi in un medesimo tempo o in un solo, come a lui pi&ugrave; piace. </s>

<s>Questi due <lb/>erano quelli che si vantavano, com'egli anco professa di presente, sebbene <lb/>con gran tempo e con gran dispendio, di poter fare uno specchio, il quale <lb/>per riflessione possa fare, anzi faccia, l'effetto del perspicillo &rdquo; (Alb. </s>

<s>IX, 156, 7). <lb/><gap/> accomodato ad uso di ca-<pb xlink:href="020/01/419.jpg" pagenum="400"/>nocchiale per rifrazione, veduto da alcuni cavalieri, bench&egrave; poco o nulla in&shy;<lb/>tendenti delle ragioni di Prospettiva, gli avesse uditi asserire della verit&agrave; del <lb/>fatto, che cio&egrave;, con quello specchio concavo, s'ingrandivano ai riguardanti <lb/>gli oggetti, al modo stesso che nel Canocchiale ordinario. </s></p><p type="main">

<s>Dopo dieci giorni, rispondeva Galileo: &ldquo; Quanto all'altro specchio, che <lb/>per riflessione faccia l'effetto del Telescopio, lo stimerei per cosa maravi&shy;<lb/>gliosa, e molto volentieri lo vedrei &rdquo; (ivi, VI, 316). Ma il Marsili, che non <lb/>poteva sodisfar la curiosit&agrave; dell'amico, si contenta d'assicurarlo esser vera <lb/>la cosa stimata da lui maravigliosa: &ldquo; Ho poi inteso in confidenza da M. </s>

<s>Gio&shy;<lb/>vanni il modo come il specchio concavo accenda in tanti luoghi. </s>

<s>Non ho ve&shy;<lb/>duto l'effetto ma lo vedr&ograve;, e, senza vederlo, lo credo. </s>

<s>Non riferisco il modo, <lb/>per avermelo detto in confidenza. </s>

<s>Intorno allo specchio, nel quale si vede <lb/>per riflessione, che io non ho mai potuto vedere, per pi&ugrave; che mai sicuri <lb/>indizi, non &egrave; il specchio d'acciaio solo che facci l'effetto, ma al sicuro vi <lb/>si aggiungono lenti o traguardi di cristallo o ambedue &rdquo; (Campori, Carteg&shy;<lb/>gio ecc., Modena 1881, pag. </s>

<s>247). Galileo, dall'altra parte, conveniva dovere <lb/>esser vera quest'ultima congettura del Marsili: &ldquo; Dell'altro effetto concorro <lb/>con lei che il semplice specchio concavo non basti, ma vi bisogni l'aggiunta <lb/>di lente o di traguardo; ma perch&egrave; non ho specchio concavo, non posso <lb/>tentare esperienza alcuna &rdquo; (Alb. </s>

<s>VI, 318). </s></p><p type="main">

<s>La morte di Cesare Carafaggi, e la poca stima che, forse meritamente, <lb/>facevasi del successore di lui, messer Giovanni, dovettero essere la potissima <lb/>ragione, per cui l'invenzione non fu divulgata, ma in ogni modo, sulle con&shy;<lb/>getture e sugli indizii, che equivalgono a una certezza morale, di Galileo e <lb/>del Marsili, possiamo asserire essere lo strumento carafaggiano il primo Te&shy;<lb/>lescopio a riflessione. </s></p><p type="main">

<s>L'artefice bolognese, ingegnosissimo al dir del Marsili, ma di poco stu&shy;<lb/>dio, fu condotto alla sua nuova maravigliosa invenzione dalla pratica: il Ca&shy;<lb/>valieri, amicissimo del Marsili e professore di Matematiche nella patria del <lb/>Carafaggi, pubblicando nel 1632 il suo <emph type="italics"/>Specchio Ustorio,<emph.end type="italics"/> discorreva cos&igrave; della <lb/>stessa invenzione per teoria: &ldquo; Potrei anco dire come l'effetto del Canoc&shy;<lb/>chiale si averebbe forse anco dalla combinazione di questi specchi o degli <lb/>specchi con le lenti, sebben la facilit&agrave; del produrre la figura sferica far&agrave; <lb/>che ci prevagliamo piuttosto di questa che dell'altra. </s>

<s>Conciossia cosa adun&shy;<lb/>que che lo specchio concavo faccia l'operazione della lente convessa, e lo <lb/>specchio convesso della lente cava, &egrave; manifesto che, se combineremo lo spec&shy;<lb/>chio concavo con il convesso, ovvero con la lente cava, dovremo aver l'ef&shy;<lb/>fetto del Canocchiale, e tale forse fu lo specchio di Tolomeo. </s>

<s>Laonde, con <lb/>tale occasione, non mancher&ograve; di dire com'avendo pi&ugrave; volte sentito cercar da <lb/>alcuni il modo di fare un paro d'occhiali, che facessero l'effetto del Canoc&shy;<lb/>chiale, io pensai che ci&ograve; in tal modo si potesse fare: cio&egrave; che si collocasse <lb/>un traguardo da una banda e dall'altra un specchietto cavo, poich&egrave;, met&shy;<lb/>tendoci noi questo paro di occhiali, con il contrapporvi uno specchio piano <lb/><gap/><pb xlink:href="020/01/420.jpg" pagenum="401"/>dentro lo specchietto cavo; (scorgendosi per&ograve; l'uno e l'altro nello specchio <lb/>piano anteposto alla nostra faccia) si otterr&agrave; l'effetto del Canocchiale. </s>

<s>Egli <lb/>&egrave; per&ograve; vero che, dovendo stare questi allo scoperto, faranno il medesimo <lb/>che il vetro cavo o convesso, adoperato fuor della canna: anzi per farsi una <lb/>riflessione di pi&ugrave;, cio&egrave; dallo specchio piano, verremo anco perci&ograve; a scapitar <lb/>pi&ugrave; nell'operazione. </s>

<s>Ci&ograve; per&ograve; con questa occasione ho voluto accennare, come <lb/>per una bizzarria, per dar qualche sodisfazione a'curiosi, che vogliono cer&shy;<lb/>car miglior pane che di farina, poich&egrave; all'eccellenza del Canocchiale non <lb/>arriveranno mai, per mio credere, n&egrave; gli specchi combinati insieme, n&egrave; ac&shy;<lb/>compagnati con le lenti, come chi ne vorr&agrave; far prova, credo si potr&agrave; assi&shy;<lb/>sicurare &ldquo; (Bologna 1650, pag. </s>

<s>76, 77). </s></p><p type="main">

<s>La prova, andata in dimenticanza quella fatta gi&agrave; dal Caravaggi, stette <lb/>ancora parecchi anni a farsi, ma poi all'ultimo sment&igrave;, almeno in parte, le <lb/>previsioni del Cavalieri. </s>

<s>Il Gregory, pubblicando, nel 1663, la sua <emph type="italics"/>Optica <lb/>promota<emph.end type="italics"/> proponeva quel nuovo Telescopio a tutti notissimo, perch&egrave; descritto <lb/>in tutti i Trattati di Fisica, ma in quello stesso tempo si faceva uso in Fran&shy;<lb/>cia di un altro Telescopio calottrico, dal Petit magnificato come utile Pole&shy;<lb/>moscopio, e come Selenoscopio e Selenografo squisitissimo. </s>

<s>Non consisteva <lb/>il nuovo strumento in altro, che in uno de'soliti Canocchiali Kepleriani a <lb/>due convessi, in cui l'immagine rovesciata si faceva tornare all'occhio di&shy;<lb/>ritta, per via di uno specchio piano. </s>

<s>Il Petit stesso, in una sua lettera del <lb/>d&igrave; 25 Aprile 1664, cos&igrave; da Parigi lo descriveva al marchese Cornelio Malvasia: </s></p><p type="main">

<s>&ldquo; Quod autem spectat ad Telescopia, quae constant lente obiectiva, ocu&shy;<lb/>lari convexo et speculo plano, quod corrigat visibilia secus inversa; haec est <lb/>constructio: Sumo lentem trium aut quatuor pedum, cui adhibeatur ocu&shy;<lb/>lare A (fig. </s>

<s>32) cuius focus sit digitorum 1 1/2 aut duorum ad summum, <lb/><figure id="id.020.01.420.1.jpg" xlink:href="020/01/420/1.jpg"/></s></p><p type="caption">

<s>Figura 32.<lb/>inter quod et oculum adapta <lb/>exiguum illud speculum me&shy;<lb/>tallicum B, inclinatum ad ho&shy;<lb/>rizontem, seu tubos D, 30 <lb/>aut 35 grad, capsula simili <lb/>infundibulo contentum, et <lb/>undique obturatum, excepto foramine C, medii circiter digiti, per quod e <lb/>speculo reflectantur ad oculum (in distantia seu foco ipsius vitri ocularis col&shy;<lb/>locatum) obiecta erecto situ, quae alioquin cernerentur inversa. </s>

<s>Et haec est <lb/>fabrica Telescopii catoptrici, non parum bello et integris aciebus conspicien&shy;<lb/>dis utilis, sicut ad Lunam sectam, totam, et sine capitis ad coelum erectione <lb/>repraesentandam, ut in charta delineentur exacte ipsius maculae, montes, <lb/>faculae et caetera, quae Ricciolus, Hevelius, Eustachius, tu ipse et alii Sele&shy;<lb/>nographi praetermiserunt, aut praepostere exhibuerunt, ad quod nos etiam <lb/>cum sociis accingimus &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXVI, c. </s>

<s>22). </s></p><p type="main">

<s>Ma non consiste nell'uso e nell'applicazione degli specchi piani, i quali <lb/>non concorrono a ingrandire le immagini, il vero Canocchiale catottrico, la <lb/><gap/><pb xlink:href="020/01/421.jpg" pagenum="402"/>la invi&ograve; alla Societ&agrave; Reale di Londra, e fu inserita nelle Transazioni filo&shy;<lb/>sofiche, colle seguenti parole scritte dallo stesso inventore: </s></p><p type="main">

<s>&ldquo; Novum hoc instrumentum constat ex duobus e metallo speculis, al&shy;<lb/>tero concavo, quod vitri obiectivi munere fungitur, altero plano: habet prae&shy;<lb/>terea exiguam lentem ocularem plano convexam. </s>

<s>Huius constructio facile .... <lb/>potest concipi, nempe quod Telescopii huius tubus apertus est ad eam extre&shy;<lb/>mitatem quae ad obiecta convertitur, quod altera extremitate clausa est, ubi <lb/>locatum est speculum concavum, de quo supra meminimus; quod prope <lb/>extremitatem apertam est speculum planum ovale, quam potest exiguum, <lb/>quo minus impediat ingredientis lucis radios, et quod idem speculum incli&shy;<lb/>natum ad superiorem Tubi partem versus, quae parvo terebrata est fora&shy;<lb/>mine munito lente oculari, ita ut radii a re perspicienda prodeuntes prius <lb/>incidant in speculum concavum in imo Tubo positum, unde reflectuntur al&shy;<lb/>teram Tubi extremitatem versus, ubi intercipiantur a plano speculo obli&shy;<lb/>que collocato, a quo reflexi diriguntur ad exiguam lentem oculare plano <lb/>convexam atque adeo ad spectatoris oculum, qui, deorsum versus intuens, <lb/>ea videt ad quae Telescopium conversum est. </s>

<s>Ut haec plenius et melius in&shy;<lb/>telligantur, Lector inspiciat, si libet, figuram 33 in qua AB est concavum <lb/><figure id="id.020.01.421.1.jpg" xlink:href="020/01/421/1.jpg"/></s></p><p type="caption">

<s>Figura 33.<lb/>speculum, cuius radius aut semidia&shy;<lb/>meter est pollicum duodecim cum <lb/>besse vel tredecim, CD aliud specu&shy;<lb/>lum metallicum, cuius superficies <lb/>plana est, peripheria vero ovalis, GD <lb/>est filum ferreum, quod solide retinet <lb/>amulum cupreum, et cui affixum est <lb/>speculum CD, F parva lens ocularis <lb/>plana superius et convexa inferius, cuius radius est uncialis, vel etiam minor. </s>

<s>&rdquo; <lb/>E cos&igrave; prosegue a descriver gli altri organi inservienti alla montatura e al <lb/>maneggio dello strumento (Op. </s>

<s>omn. </s>

<s>opt., Patavii 1773, Apendix, pag. </s>

<s>11, 12). </s></p><p type="main">

<s>Ma in un'Epistola precedente, data del 6 Febbraio 1672, e inserita nel <lb/>numero 80 delle Transazioni filosofiche, aveva il Newton fatto partecipare <lb/>alla Societ&agrave; Reale di Londra la sua scoperta <emph type="italics"/>De luce et coloribus,<emph.end type="italics"/> la quale <lb/>gli fu occasione, ed efficace consiglio di rivolgersi a ritrovare il nuovo stru&shy;<lb/>mento. </s>

<s>&ldquo; Ineunte anno 1666, quo tempore operam dabam conficiendis opti&shy;<lb/>cis vitris figurarum a sphaerica diversarum, mihi vitreum prisma tr&igrave;angu&shy;<lb/>lare paravi, eo notissima phaenomena colorum experturus &rdquo; (ibi, pag. </s>

<s>3). E <lb/>prosegue a dire come, per mezzo di quel prisma, gli occorresse a far la <lb/>scoperta de'varii gradi di refrangibilit&agrave; de'raggi della luce, d'onde egli venne <lb/>a persuadersi esser vana e inutile fatica il pretendere di ridurre i vetri da <lb/>canocchiali alla loro desiderata perfezione. </s>

<s>&rdquo; Postquam haec intellexi, circa <lb/>vitra laborare destiti. </s>

<s>Noveram enim Telescopia perfectiora hucusque haberi <lb/>non potuisse, non solum quia deerant vitra reipsa praedita figuris quas optici <lb/>Auctores praescripserant .... sed etiam quia lux ipsa est mistura quaedam <lb/><gap/></s></p><pb xlink:href="020/01/422.jpg" pagenum="403"/><p type="main">

<s>Da queste considerazioni fu consigliato a lasciare addietro i vetri, per <lb/>rivolgersi tutto agli specchi. </s>

<s>&ldquo; Haec me duxerunt ad reflexiones conside&shy;<lb/>randas, quas cum sibi constare reperissem, ita ut in omnibus radiorum ge&shy;<lb/>neribus esset angulus reflexionis par angulo incidentiae, intellexi, quod ea&shy;<lb/>rum ope instrumenta optica poterant ad quemlibet perfectionem extolli, <lb/>dummodo reperire liceret substantiam reflectentem, quae accuratam pulitu&shy;<lb/>ram, aeque ac vitrum, reciperet, ut tantum lucis reflecteret, quantum trans&shy;<lb/>mittit vitrum &rdquo; (ibi, pag. </s>

<s>6, 7). </s></p><p type="main">

<s>In questo, sopraggiunse la peste che lo costrinse a fuggir di Cambridge, <lb/>e a interrompere gli amati studii, non ripresi che solo nel 1668, dopo due <lb/>anni. </s>

<s>Allora riusc&igrave; a dar tal pulitura ai metalli, che pot&egrave; con essi costruire <lb/>uno strumento a riflessione, <emph type="italics"/>quo videre poteram,<emph.end type="italics"/> egli dice, <emph type="italics"/>quatuor Iovis <lb/>Satellites illosque ostendi pluries duobus amicis<emph.end type="italics"/> (ibi). </s></p><p type="main">

<s>Nell'Autunno del 1771 si dette a costruire un altro simile Telescopio, <lb/>il quale, sebben conoscesse e confessasse l'Autore stesso, che non gli era <lb/>riuscito molto pi&ugrave; perfetto del primo, nonostante, non dubito, egli soggiunge, <lb/><emph type="italics"/>quin instrumentum hoc multo perfectius reddi possit conatibus eorum, <lb/>qui, ut ex re audivi, operam illi Londini navant<emph.end type="italics"/> (ibi). </s></p><p type="main">

<s>Divulgatasi cos&igrave;, per l'organo delle Transazioni filosofiche la descrizione <lb/>del nuovo Telescopio, un tal Cassegrain francese ebbe ricorso alla R. </s>

<s>So&shy;<lb/>ciet&agrave; di Londra, reclamando un'anteriorit&agrave; di tre mesi sopra la stessa in&shy;<lb/>venzione neutoniana. </s>

<s>Il segretario partecip&ograve; ad esso Newton il reclamo, <lb/>trasmettendogli cos&igrave; insieme la breve descrizione e il disegno che l'inventor <lb/><figure id="id.020.01.422.1.jpg" xlink:href="020/01/422/1.jpg"/></s></p><p type="caption">

<s>Figura 34.<lb/>francese faceva del suo nuovo stru&shy;<lb/>mento: &ldquo; Est ABCD (fig. </s>

<s>34) fortis <lb/>tubus, in cuius infima parte est spe&shy;<lb/>culum concavum CD, perforatum circa <lb/>medeluttium E. </s>

<s>Sed F est speculum <lb/>convexum, cuius convexitas ita est <lb/>disposita, ut reflectat imagines, quas <lb/>recipit a magno speculo, foramen E <lb/>versus, ubi locata est lens ocularis per quam dispiciuntur obiecta &rdquo; (ibi, <lb/>pag. </s>

<s>18). </s></p><p type="main">

<s>Il Newton allora scrisse una lettera di risposta al reclamo, confessando <lb/>essergli venuta l'idea del suo Telescopio da quello, che il Gregory descrisse <lb/>e fece, a pag. </s>

<s>94 della sua <emph type="italics"/>Optica promota,<emph.end type="italics"/> rappresentare in disegno, che <lb/>secondo lui &egrave; simile al cassegreniano; ma per&ograve; asseriva che fra que'due <lb/>Telescopi e il suo ci correva quella differenza, che passa fra un concetto e <lb/>la sua pratica esecuzione, o fra una cosa possibile e una reale. </s>

<s>Citava, per <lb/>prova contro il Gregory, il Riveo, il quale, bench&egrave; fosse artefice tanto pe&shy;<lb/>rito, messosi nonostante a costruire un Telescopio su quel modello, <emph type="italics"/>successu <lb/>caruit.<emph.end type="italics"/> Concludeva poi contro lo stesso Cassegrain, che avrebbe avuto molto <lb/>caro <emph type="italics"/>huius constructionis periculum fecisse antequam eam vulgaret: quod <lb/>si facere volet, in posterum sibimet satisfacturus arbitror futurum ut<emph.end type="italics"/><pb xlink:href="020/01/423.jpg" pagenum="404"/><emph type="italics"/>eventus eum doceat quam parvi momenti sint cogitationes huiusmodi, <lb/>donec actu quis illas exsequatur &rdquo;<emph.end type="italics"/> (ibi, pag. </s>

<s>19). </s></p><p type="main">

<s>N&egrave; queste del Newton sono rapaci usurpazioni, o vane pretese, essendo <lb/>un fatto che l'uso de'Telescopi riflettori, nelle osservazioni celesti, ebbe i <lb/>primi principii da lui. </s>

<s>Che se poi ai meriti dell'invenzione concorse il Gre&shy;<lb/>gory co'suoi progetti, forse pi&ugrave; efficacemente v'avrebbe potuto concorrere <lb/>il nostro Campani, il quale, due anni prima della peste di Cambridge, pens&ograve; <lb/>di far uso delle lenti microscopiche per oculari, e di applicar pi&ugrave; comoda&shy;<lb/>mente la vista in direzione perpendicolare all'asse dello strumento. </s>

<s>Fu pure <lb/>il Campani che, nelle solitarie sue speculazioni, prefulse all'Hudley, il quale, <lb/>al candor della carta e al nitor degli specchi, sostituendo un prisma isoscele <lb/>di cristallo, ottenne vivamente riflesse, e senza perdita sensibile di luce, le <lb/>immagini trasmesse dall'obiettivo, e cos&igrave; ebbe effetto il Telescopio catot&shy;<lb/>trico, che non fece buona prova alle mani del nostro Artefice romano, e <lb/>quello del Filosofo inglese consegu&igrave; perci&ograve; un notabile perfezionamento. </s></p><pb xlink:href="020/01/424.jpg"/><p type="main">

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

<s><emph type="center"/><emph type="bold"/>Degli organi aggiunti <lb/>e de'nuovi usi strumentali del Canocchiale<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

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

<s>I. </s>

<s>Del primo Micrometro e delle prime operazioni micrometriche di Galileo. </s>

<s>&mdash; II. </s>

<s>Del Micrometro <lb/>ugeniano e del Micrometro a reticolo. </s>

<s>&mdash; III. </s>

<s>Della Livella diottrica. </s>

<s>&mdash; IV. </s>

<s>Del Canocchiale bi&shy;<lb/>noculo. </s>

<s>&mdash; V. Dell'Elioscopio, dell'Eliostata, de'Diaframmi de'Canocchiali. </s></p><p type="main">

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

<s>Il padre Francesco Lana, proponendosi di trattare, nel capitolo VIII e <lb/>ultimo del suo <emph type="italics"/>Prodromo all'Arte maestra,<emph.end type="italics"/> dell'uso de'Canocchiali, scrive, <lb/>fra le altre, le parole seguenti: &ldquo; Egli &egrave; dunque (il Canocchiale) utile s&igrave; <lb/>nella guerra, come nella pace; e primieramente nella guerra serve per os&shy;<lb/>servare tutti gli andamenti del nimico e spiare le azioni e le persone. </s>

<s>Cos&igrave;, <lb/>per mezzo del Canocchiale, essendo stato riconosciuto il Duca Francesco di <lb/>Modena, che si era inoltrato sotto la citt&agrave; di Cremona, gli fu tirato un colpo <lb/>con il cannone, da cui rest&ograve; ucciso il marchese Villa, che gli stava a lato. </s>

<s><lb/>Pu&ograve; anche servire per leggere di notte lettere di segreto nella piazza asse&shy;<lb/>diata e fuori. </s>

<s>Di pi&ugrave;, non solo si potr&agrave; numerare quanti siano i pezzi di <lb/>alcuna batteria scoperta, quanti i soldati, ma anche si potranno vedere quelli <lb/>che di nascosto si avvicinano per riconoscere i posti, e questi, all'incontro, <lb/>senza mettersi a pericolo, con troppo avvicinarsi, li potranno riconoscere da <lb/>lontano, con il Canocchiale. </s>

<s>Inoltre dico che, con il Canocchiale noi potremo <lb/>misurare l'altezza delle mura, le distanze de'baluardi, la lunghezza delle <lb/>loro facce, delle cortine, con tutto ci&ograve; che pratica la Trigonometria, il che <lb/>potr&agrave; servire anche in altre occasioni, quando vorremo sapere le altezze e <lb/>distanze di alcune case o siti, a'quali non ci potiamo accostare. </s>

<s>Questa cosa, <pb xlink:href="020/01/425.jpg" pagenum="406"/><emph type="italics"/>che da altri ch'io sappia non &egrave; stata osservata,<emph.end type="italics"/> si potr&agrave; facilmente prati&shy;<lb/>care in questo modo: &rdquo; (Brescia 1670, pag. </s>

<s>240). </s></p><p type="main">

<s>Il Lana adunque promette d'insegnar nuovi usi del Canocchiale, che <lb/>egli crede non sieno stati, prima di lui, praticati da nessuno. </s>

<s>E perch&egrave; que&shy;<lb/>sti usi si distinguono in due classi, l'una delle quali appartiene a ci&ograve; che <lb/>concerne l'arte della guerra, e l'altra all'Altimetria, vediamo se veramente, <lb/>nel 1670, come il Lana pretende, fosse tutta questa, alla scienza, una rive&shy;<lb/>lazione nuova. </s></p><p type="main">

<s>Gi&agrave; il Porta, nella sua <emph type="italics"/>Magia Naturale,<emph.end type="italics"/> aveva in varii modi insegnato <lb/>il segreto di leggere lettere dalla lontana, e Galileo nel 1617, scrivendo al <lb/>conte d'Elci, in proposito dell'uso che pu&ograve; farsi del Canocchiale, per rico&shy;<lb/>noscere dalla lontana e scoprir le insidie delle navi nemiche, cos&igrave; gli dice: <lb/>&ldquo; Finalmente ho scoperto una maniera d'Occhiale differente dall'altra, col <lb/>quale si trovano gli oggetti coll'istessa prestezza che coll'occhio libero.... <lb/>Questa invenzione &egrave; stata tanto stimata da queste AA. SS. che per tenerla <lb/>segreta, sicch&egrave; non possa venire in notizia dell'inimico, hanno deputato due <lb/>cavalieri nobilissimi all'uso di questo strumento sul calcese &rdquo; (Alb. </s>

<s>VI, 270). </s></p><p type="main">

<s>E gi&agrave; l'Hevelio, infino dal 1637, aveva inventato e messo in pratica un <lb/>suo Canocchiale, accomodato di lenti e di specchi, per mezzo del quale gli <lb/>atti e le mosse del nemico venivano ritratte in vicinanza e rappresentate <lb/>sotto il chiuso di qualche tenda; strumento che, giusto dagli usi speciali a <lb/>cui venne applicato, ebbe, dal suo proprio inventore, il nome di <emph type="italics"/>Polemo&shy;<lb/>scopio<emph.end type="italics"/> (Selenographia, Gedani 1647, pag. </s>

<s>24-31). </s></p><p type="main">

<s>Essendo dunque cosa certissima che, per quello riguarda la prima parte <lb/>dell'invenzione, fu il Lana lungamente prevenuto e dal Porta e dal Galileo <lb/>e dall'Hevelio, e da tanti altri che si potrebbero citare, insieme con quel <lb/>Petit, di cui fu lo strumento polemoscopico da noi descritto nel capitolo pre&shy;<lb/>cedente; vediamo se la novit&agrave; dell'invenzione possa attribuirsi al Gesuita <lb/>bresciano, per quello che particolarmente concerne l'Altimetria. </s>

<s>La propo&shy;<lb/>sizione &egrave; per la scienza ben assai pi&ugrave; importante di quel che non sia sco&shy;<lb/>prire un segreto altrui, o riconoscere un capitano in guerra, per appuntar&shy;<lb/>gli un cannone e ammazzarlo. </s>

<s>Molta gloria perci&ograve; meriterebbesi il Lana, se <lb/>l'applicazione del Canocchiale, a misurar le distanze e i diametri degli astri, <lb/>e gli angoli sottesi dagli oggetti apparentemente piccoli, si potesse dire un <lb/>suo ritrovato. </s>

<s>Ma molti concorrono insieme a contendergli quella gloria, e <lb/>cos&igrave; valorosi da soggiogar qualunque altro, che si faccia a loro incontro, <lb/>con la sola potenza del nome. </s></p><p type="main">

<s>Si tratta insomma, come bene intendono i nostri Lettori, del <emph type="italics"/>Microme&shy;<lb/>tro,<emph.end type="italics"/> dell'invenzione del quale, se questa non pu&ograve;, com'abbiamo accennato, <lb/>credersi opera di Francesco Lana, dobbiamo ora narrar la storia. </s>

<s>E intanto, <lb/>per non dilungarci di troppo dalla lettera galileiana, dianzi citata, seguitando <lb/>a leggere ivi, troviamo che Galileo proponeva il sopra descritto Canocchiale, <lb/>oltre a quello di scoprire le navi nimiche, a un'altr'uso, qual'era di misu&shy;<lb/>rar la distanza delle medesime navi. </s>

<s>&ldquo; Apportaci l'istesso strumento un'al-<pb xlink:href="020/01/426.jpg" pagenum="407"/>tra utilit&agrave;, stimata grande da'medesimi signori periti del mare, ed &egrave; che, <lb/>nello scoprire vascelli, si pu&ograve;, senza nessuna fatica o dispendio di tempo, <lb/>sapere immediatamente la lontananza tra loro e noi &rdquo; (Alb. </s>

<s>VI, 270). </s></p><p type="main">

<s>Nel 1638 poi Galileo stesso dava di ci&ograve; regola al padre Renieri, il quale, <lb/>di Genova, il d&igrave; 5 di Marzo di quello stesso anno, gli risponde in proposito <lb/>cos&igrave; scrivendo: &ldquo; Dalla prima vista della sua lettera non ho ben compreso <lb/>il modo di misurar le distanze coll'occhiale, ma forse, col porre in opera <lb/>lo strumento, l'intender&ograve; meglio &rdquo; (ivi, X, 285). </s></p><p type="main">

<s>Ma di questa applicazione del Canocchiale alla misura delle distanze, <lb/>Galileo ne aveva trattato gi&agrave; molti anni prima, infin da quando egli veniva <lb/>annunziando al mondo le sue scoperte celesti. </s>

<s>Nell'introduzione infatti al&shy;<lb/>l'<emph type="italics"/>Astronomicus Nuncius,<emph.end type="italics"/> dop'avere insegnato il modo di misurare i gradi <lb/>dell'ingrandimento del Canocchiale, cos&igrave; soggiunge: &ldquo; Consimili parato instru&shy;<lb/>mento, de ratione distantiarum dimetiendarum inquirendum erit. </s>

<s>Quod tali <lb/>artificio assequemur: Sit enim, facilioris intelligentiae gratia, tubus ABCD <lb/>(fig. </s>

<s>35), oculus inspicientis esto E. Radii, dum nulla in tubo adessent perspi&shy;<lb/><figure id="id.020.01.426.1.jpg" xlink:href="020/01/426/1.jpg"/></s></p><p type="caption">

<s>Figura 35.<lb/>cilla, ab obiecto FG ad oculum E, <lb/>secundum lineas rectas FCE, GDE <lb/>ferrentur, sed appositis perspicillis <lb/>ferentur secundum lineas refractas <lb/>HCE, IDE; coarctantur enim, et qui <lb/>prius liberi ad FG obiectum diri&shy;<lb/>gebantur, partem tantummodo III <lb/>comprehendent. </s>

<s>Accepta deinde ra&shy;<lb/>tione distantiae EH ad lineam HI, <lb/>per Tabulam sinum reperietur quantitas anguli in oculo ex obiecto III con&shy;<lb/>stituto, quem minuta quaedam tantum continere comperiemus. </s>

<s>Quod si spe&shy;<lb/>cillo CD bracteas alias maioribus alias vero minoribus perforatas foramini&shy;<lb/>bus aptaverimus, modo hanc, modo illam, prout opus fuerit superimponentes, <lb/>angulos alios atque alios pluribus pancioribusque minutis subtendentes, pro <lb/>libito constituimus: quorum ope stellarum intercapedines, per aliquot mi&shy;<lb/>nuta, ad invicem dissitarum, citra unius aut alterius minuti peccatum, com&shy;<lb/>mode dimetiri poterimus &rdquo; (Alb. </s>

<s>III, 62) </s></p><p type="main">

<s>Chi non riconosce in quelle lamine perforate con fori ora pi&ugrave; ora meno <lb/>aperti e variamente adattabili all'obiettivo del Canocchiale, secondo i varii <lb/>bisogni, chi non riconosce la prima idea e anzi il primo e vero uso di quello <lb/>strumento, che poi, ridotto a maggior perfezione, ebbe, dagli Astronomi e <lb/>dai Geodeti, il nome proprio di <emph type="italics"/>Micrometro?<emph.end type="italics"/> E fuor di dubbio dunque che i <lb/>primi meriti dell'invenzione si debbono a Galileo. </s>

<s>Ma quanto, nelle sopraccitate <lb/>parole, &egrave; chiaramente espressa l'idea e designata la natura dello strumento, <lb/>altrettanto &egrave; oscuro il modo come ivi se ne insegna a far uso. </s>

<s>Non par che <lb/>l'Autore applichi la sua nuova invenzione ad altro, che a ritrovar l'angolo sot&shy;<lb/>teso dal diametro apparente, ma come poi di l&igrave; se ne deduca la misura giusta <lb/>delle distanze lo lasci&ograve; a investigare all'ingegno matematico del suo Lettore. </s></p><pb xlink:href="020/01/427.jpg" pagenum="408"/><p type="main">

<s>Nella III Giornata per&ograve; dei <emph type="italics"/>Massimi Sistemi<emph.end type="italics"/> si esprime con molto mag&shy;<lb/>gior chiarezza, all'occasion di proporre un modo per misurare il diametro <lb/>apparente di una stella, servendosi di un micrometro semplicissimo e da po&shy;<lb/>tersi usar facilmente anche a occhio nudo. </s>

<s>&ldquo; Ho fatto pendere una cordi&shy;<lb/>cella verso qualche stella, e io mi son servito della Lira che nasc&egrave; tra set&shy;<lb/>tentrione e greco, e poi con l'appressarmi e slontanarmi da essa corda <lb/>traposta tra me e la stella, ho trovato il posto, dal quale la grossezza della <lb/>corda puntualmente mi nasconde la stella: fatto questo, ho preso la lonta&shy;<lb/>nanza dall'occhio alla corda, che viene ad essere un de'lati che compren&shy;<lb/>dono l'angolo, che si forma nell'occhio, e che insiste sopra la grossezza <lb/>della corda, e che &egrave; simile, anzi l'istesso che l'angolo, che nella sfera stel&shy;<lb/>lata insiste sopra il diametro della stella, e dalla proporzione della gros&shy;<lb/>sezza della corda alla distanza dall'occhio alla corda, ho immediatamente <lb/>trovata le quantit&agrave; dell'angolo, usando per&ograve; la solita cautela, che si os&shy;<lb/>serva nel prendere angoli cos&igrave; acuti, di non formare il concorso de'raggi <lb/>visuali nel centro dell'occhio, dove non vanno se non refratti, ma oltre al&shy;<lb/>l'occhio, dove realmente la grandezza della pupilla gli manda a concorrere &rdquo; <lb/>(ivi, I, 393). </s></p><p type="main">

<s>La pratica &egrave; insegnata qui con pi&ugrave; matematica precisione che nel Nun&shy;<lb/>zio Sidereo, dove si propone a risolvere un triangolo, senza far conoscere <lb/>come son noti di lui i necessari elementi. </s>

<s>Nel presente caso ci son noti il <lb/><figure id="id.020.01.427.1.jpg" xlink:href="020/01/427/1.jpg"/></s></p><p type="caption">

<s>Figura 36.<lb/>diametro della corda e la distanza di lei <lb/>dall'occhio, ci&ograve; che basta per risolvere un <lb/>triangolo rettangolo, e son note col diame&shy;<lb/>tro le due visuali tangenti alla stessa corda, <lb/>ci&ograve; che pur basta a risolvere un triangolo <lb/>isoscele, di cui si conoscono i lati. </s>

<s>Sia CH <lb/>(fig. </s>

<s>36) infatti la grossezza della corda, che <lb/>copre all'occhio posto in O il diametro EG <lb/>della stella. </s>

<s>Misurata OC o la sua uguale OH, <lb/>il triangolo OCH, nel quale si conoscono i tre lati, far&agrave;, risoluto che sia, <lb/>conoscere l'angolo COH. </s>

<s>Se poi si volesse prendere OD per la pi&ugrave; vera e <lb/>pi&ugrave; precisa distanza, il triangolo rettangolo COD far&agrave; immediatamente cono&shy;<lb/>scere COD semiangolo cercato. </s></p><p type="main">

<s>Qui Galileo non accenna a misura di distanze, ma il metodo proposto <lb/>gi&agrave; nel Nunzio Sidereo non poteva non ridursi se non a questo, quando per&ograve; <lb/>fosse stata misurata prima la lunghezza del tubo, e fossero anche insieme <lb/>note la virt&ugrave; dell'ingrandimento del Telescopio, e la grandezza reale del&shy;<lb/>l'oggetto. </s>

<s>Suppongasi infatti che AB sia il semidiametro noto del foro della <lb/>lamina micrometrica apposta all'oggettivo, e che EG sia la statura di un <lb/>uomo di cui si conosce la misura media: i triangoli simili ABO, EFO, in <lb/>cui son noti i lati OB, AB, EF danno immediatamente la cercata distanza, <lb/>senz'altro bisogno di Trigonometria. </s></p><p type="main">

<s><gap/><pb xlink:href="020/01/428.jpg" pagenum="409"/>&egrave; perfezionato, sopra quello accennato nel <emph type="italics"/>Nunzio,<emph.end type="italics"/> di una squisitezza e raf&shy;<lb/>finatezza nuova, qual'&egrave; quella di tener conto e pigliar misura esatta del foro <lb/>della pupilla. </s>

<s>Qui per verit&agrave; Galileo perde il tempo inutilmente, e anzi, peg&shy;<lb/>gio che nella inutilit&agrave;, versa nell'errore, essendo che lo scrupolo di misu&shy;<lb/>rar l'ampiezza del foro pupillare, non da altro gli sia suggerito che dall'er&shy;<lb/>ronea dottrina professata da lui intorno al modo della visione. </s>

<s>Eppure Galileo <lb/>di quella raffinatezza di metodo se ne compiace e insegna a praticarla, dan&shy;<lb/>dola com'un'invenzione sua propria. </s>

<s>Nel citato luogo de'Due Massimi Si&shy;<lb/>stemi si content&ograve; di descrivere il metodo per ritrovar l'ampiezza della pu&shy;<lb/>pilla e con essa il concorso de'raggi, quando l'angolo visuale sia molto <lb/>piccolo, senz'accennare a nessuna pretensione di novit&agrave;, ma poi, quando <lb/>torn&ograve;, nel 1637, a mettere insieme e a riordinare le sue <emph type="italics"/>Operazioni astro&shy;<lb/>miche,<emph.end type="italics"/> non manc&ograve; di far notare a coloro a'quali comunicava quello stesso <lb/>metodo, com'era una tal cosa non praticata ancora da altri prima di lui. </s></p><p type="main">

<s>Fra coloro infatti, a'quali in quel tempo comunic&ograve; Galileo quel suo me&shy;<lb/>todo di misurare il diametro apparente di un astro, tenendo conto dell'am&shy;<lb/>piezza del foro della pupilla, fu Vincenzio Renieri, che, con lettera del di <lb/>29 Gennaio 1638, cos&igrave; rispondeva: &ldquo; Ho poi sommamente gustato l'inven&shy;<lb/>zione sua della misura pupillare, ed io fo conto di servirmene in questo <lb/>modo: Produrre una linea lunga dieci e pi&ugrave; braccia, tanto che sia capace <lb/>della divisione del seno totale di 100,000, e poi accomodarvi in cima una <lb/>tavoletta bianca divisa in parti proporzionali a quelle della linea, in modo <lb/>che, stando ad angoli retti, rappresenti la tangente dell'arco che si sottende <lb/>dall'altro punto della linea, e dalla larghezza di detta tavola. </s>

<s>Indi, nel mezzo <lb/>di detta linea, dispor la seconda tavoletta nera, com'ella mi accenna. </s>

<s>Ma <lb/>perch&egrave; lo allontanare e avvicinare della pupilla alla estremit&agrave; di detta linea, <lb/>stimo cosa assai lubrica, ho pensato di supplire a questo difetto col muover <lb/>non l'occhio ma la tavoletta di mezzo, poich&egrave; dalla prima stazione nel mezzo <lb/>della linea, e dalla seconda pi&ugrave; verso l'occhio, non v'ha difficolt&agrave; nel tro&shy;<lb/>vare il diametro cercato della pupilla &rdquo; (Alb. </s>

<s>X, 261, 62). </s></p><p type="main">

<s>Il metodo che veniva cos&igrave; proponendo Galileo al Renieri &egrave; alquanto mo&shy;<lb/>dificato da quello che s'insegna nel III Dialogo dei Due Massimi Sistemi, <lb/>e nella prima delle <emph type="italics"/>Astronomiche operazioni<emph.end type="italics"/> (Alb. </s>

<s>V, 376-78), ma &egrave; in so&shy;<lb/>stanza lo stesso, non essendovi altra differenza che l&agrave; si muove l'occhio e <lb/>qui si muovono invece le tavolette guardate dall'occhio. </s></p><p type="main">

<s>Se il Renieri accogliesse con sincerit&agrave; questa galileiana invenzione, la&shy;<lb/>sciano le sue stesse parole qualche luogo a dubitarne, imperocch&egrave;, per non <lb/>dire espressamente ch'ei credeva fuor di proposito quella operazione, ei ne <lb/>vien suggerendo un'altra, che senza dubbio sar&agrave; stimata da tutti gl'impar&shy;<lb/>ziali pi&ugrave; giudiziosa: &ldquo; Solo mi occorre di soggiungere (egli cos&igrave; ripiglia il <lb/>costrutto da noi sopra lasciato interrotto) che vorrei sapere se si potesse <lb/>fare l'istessa operazione del misurare i diametri delle stelle col fare un buco <lb/>piccolo in una carta o lamina, del cui diametro saressimo pi&ugrave; certi che di <lb/><gap/><pb xlink:href="020/01/429.jpg" pagenum="410"/>pilla, parmi che dovrebbe seguirne l'istessa operazione. </s>

<s>Star&ograve; aspettando la <lb/>sua risposta, per far poi quello che ella stimer&agrave; meglio &rdquo; (Alb. </s>

<s>X, 262). </s></p><p type="main">

<s>Non sembra che Galileo rispondesse in proposito, giacch&egrave;, nel Marzo <lb/>successivo, torna il Renieri a scrivere cos&igrave;: &ldquo; Circa il misurare la gran&shy;<lb/>dezza delle stelle, con un foro fatto in una lamina, stimo che si potrebbe <lb/>fare, servendosi del diametro di detto foro, nello stesso modo che ci ser&shy;<lb/>viamo di quello della pupilla, mentre per&ograve; detto foro si faccia pi&ugrave; piccolo <lb/>di quello. </s>

<s>Mi avvisi per grazia se ci ha difficolt&agrave; &rdquo; (ivi, pag. </s>

<s>285). </s></p><p type="main">

<s>Nemmeno un mese e undici giorni dopo, le insistenti preghiere del Re&shy;<lb/>nieri furono esaudite, giacch&egrave; torna cos&igrave; a ripetere: &ldquo; Il modo col quale io <lb/>stimava di misurare i diametri delle stelle, &egrave; quello stesso con cui dagl&igrave; an&shy;<lb/>tichi si misuravano i diametri del sole, che era di fare un piccol foro in una <lb/>lamina, alla quale ponendo l'occhio, e poi fermandolo nel fine di una riga <lb/>di legno divisa in parti proporzionali al sino, con un altro pezzetto di ta&shy;<lb/>vola, che ad angoli retti ora in su ora in gi&ugrave; potesse muoversi su tal riga, <lb/>notando il punto nel quale la tavoletta ricopre la stella, si poteva da detta <lb/>tavoletta, come tangente, venire in cognizione del diametro. </s>

<s>Star&ograve; attendendo <lb/>in ci&ograve; il suo parere &rdquo; (ivi, pag. </s>

<s>296). </s></p><p type="main">

<s>&Egrave; intanto la terza volta che il Renieri invoca da Galileo e attende que&shy;<lb/>sto parere, e il parere, com'&egrave; certo che fu atteso per quasi tre mesi inu&shy;<lb/>tilmente, cos&igrave; &egrave; probabile che non fosse pronunziato mai. </s>

<s>Saremmo da ci&ograve; <lb/>condotti a sospettare che lo stesso Galileo non volesse entrare a discuter <lb/>nell'argomento, e che cercasse ogni scusa di scansarne il caso, per paura <lb/>di non trovarsi scop&egrave;rto in faccia al Renieri e costretto a confessar quasi <lb/>un attentato di furto. </s></p><p type="main">

<s>Il Matematico genovese infatti, accenna nelle sopra allegate parole che <lb/>il metodo inteso praticare da lui era il metodo stesso che praticavano gli <lb/>Astronomi antichi. </s>

<s>E in verit&agrave; una simile pratica si vede descritta nell'opera <lb/>pi&ugrave; insigne, che dell'antichit&agrave; ci sia rimasta, nell'<emph type="italics"/>Arenario<emph.end type="italics"/> vogliam dir di <lb/>Archimede. </s>

<s>L'Astronomo siracusano, dop'avere ivi accennato che Eudossio <lb/>e Aristarco avevano assegnato al diametro apparente del sole una misura <lb/>non molto conforme alla vera, propone un nuovo metodo pi&ugrave; esatto, che, <lb/>da alcune leggiere variazioni in fuori, &egrave; quello stesso insegnato da Galileo: <lb/>&ldquo; Caeterum satis mihi est ut propositum demonstrem angulum sumere qui <lb/>maior sit angulo, cui sol accomodatur, habeatque verticem in visu. </s>

<s>Et rur&shy;<lb/>sum alium angulum sumere, qui non minor sit angulo, cui sol accomoda&shy;<lb/>tur, ut apicem in visu habeat. </s>

<s>Constituta ergo ad normam longa regula <lb/>super plano recto in loco iacente, unde sol oriens inspici queat, tum parvo <lb/>cylindro tornatili supra regula posito, confestim ab aurora et ortu solis, <lb/>postquam inceperit eiaculari radios in horizontem, potueritque ex opposito <lb/>videri, convertetur regula ad solem. </s>

<s>Deinde visus statuatur in extremo ipsius <lb/>regulae. </s>

<s>Cylindrus vero in medio admoveatur inter visum et solem, ita ut <lb/>adumbretur soli, tum separetur paulatim cylindrus ab oculo: et ubi ince&shy;<lb/><gap/><pb xlink:href="020/01/430.jpg" pagenum="411"/>drus. </s>

<s>Sic enim accidit ut oculus ab uno puncto intueatur sub rectis ductis <lb/>ab extremo regulae in loco ubi consistit visus, tangentibus cylindrum, et <lb/>quidem angulo comprehenso sub istis ductis, minori eo angulo cui sol ac&shy;<lb/>comodatur, habenti verticem in oculo, propterea, quod apparet aliquid solis <lb/>undequaque cylindri &rdquo; (Archimedis Opera, Parisiis 1615, pag. </s>

<s>452, 53). </s></p><p type="main">

<s>N&egrave; qui lo stesso Archimede lascia indietro l'attenzione di prendere esat&shy;<lb/>tamente la misura del foro pupillare, considerando, come fa Galileo, che i <lb/>raggi non escono dall'occhio movendo da un punto solo, ma da pi&ugrave;. </s>

<s>&ldquo; Porro <lb/>quoniam visus non respicit ab uno puncto, sed ab aliqua quantitate, suma&shy;<lb/>tur aliqua magnitudo teres non minor visu, et hoc rotundo corpore collo&shy;<lb/>cato in extremitate regulae ubi oculus sistitur, recta agatur tangens et hoc <lb/>teres corpus et item cylindrum. </s>

<s>Etenim qui comprehenditur angulus sub <lb/>lineis ductis, minor est angulo in quo sol accomodatur, habente apicem in <lb/>visu. </s>

<s>Magnitudo autem non minor visu hoc pacto reperietur: &rdquo; (ibi, pag. </s>

<s>453). <lb/>E prosegue a descrivere il metodo di trovare il concorso de'raggi visuali, in <lb/>ragion dell'apertura della pupilla, al modo stesso di Galileo, colla differenza <lb/>che, invece di strisce di carta o di tavolette, come questi propone, Archi&shy;<lb/>mede suggerisce cilindri o corpi arrotondati di diverso colore. </s></p><p type="main">

<s>L'operazione insomma, che Galileo insegnava fare, dandola per una <lb/>speculazione sua nuova, il Renieri poteva averla appresa molto tempo prima <lb/>dall'antico Matematico di Siracusa, e anco quando, ci&ograve; che non par credi&shy;<lb/>bile, non gli fosse mai venuto a mano il volume delle Opere di Archimede, <lb/>illustrate gi&agrave; dal Rivalt e tradotte in latino, il Keplero, infino dal 1604, aveva <lb/>solennemente divulgate le dottrine dell'antico Maestro, che erano divenute <lb/>oramai, ai tempi di Galileo e del Renieri, comun retaggio della scienza ot&shy;<lb/><figure id="id.020.01.430.1.jpg" xlink:href="020/01/430/1.jpg"/></s></p><p type="caption">

<s>Figura 37.<lb/>tica moderna. </s>

<s>L'Autore de'Paralipomeni a Vitellione in&shy;<lb/>fatti intitola il &sect; V del V capitolo: <emph type="italics"/>Quac ex visionis modo <lb/>in Astronomiam redundant, seu de vitiata visione,<emph.end type="italics"/> e in <lb/>trattar di ci&ograve;, cos&igrave; scrive: &ldquo; Cum itaque stellarum distan&shy;<lb/>tiae instrumentis astronomicis sunt capiendae, diligentiores <lb/>Astronomi, ut dictum, non fidunt oculo. </s>

<s>Sciunt enim, etsi <lb/>oculus ipsum instrumenti centrum attingat (quod tamen <lb/>difficulter obtinetur), non attingere tamen nisi superficie <lb/>tenus, in qua quidem linaee, ex utraque stella per supe&shy;<lb/>riora pinnicidia ductae, non concurrant. </s>

<s>Sint F, G (fig. </s>

<s>37) <lb/>stellae. </s>

<s>BAC instrumentum, centro A, DA superficies oculi, <lb/>E centrum oculi. </s>

<s>Cum igitur non ex A sed ex E centro <lb/>oculi fingendae sint egredi rectae in F, G incidentes: Ap&shy;<lb/>plicatis ergo pinnicidiis B, C, ut EBF, ECG sint in rectae, <lb/>angulus BAC vitiose metietur distantiam, critque iusto <lb/>maior, quia interior quam BEC super eadem basi. </s>

<s>Arcus itaque BC maior <lb/>iusto, quia oculi profunditas EA non patitur centra A, E instrumenti et oculi <lb/>coniungi .... Archimedes igitur in libello De Arenae numero cautionem.... &rdquo; <lb/>(Francof. </s>

<s>1604, pag. </s>

<s>212). E seguita a descrivere e a commentare i metodi <pb xlink:href="020/01/431.jpg" pagenum="412"/>archimedei, conforme a ci&ograve; che leggesi nell'Arenario espresso con le parole <lb/>da noi citate di sopra. </s></p><p type="main">

<s>Per chi vede Galileo con altr'occhio da quello che &egrave; veduto da noi re&shy;<lb/>sterebbe misterioso a intendere come mai dottrine cos&igrave; divulgate e dalla <lb/>scienza antica e dalla moderna, si potessero proporre da lui come sue nuove <lb/>peregrine speculazioni. </s>

<s>Eppure, se non fosse stato trasportato da quel suo <lb/>genio di voler essere e apparire in tutto il primo ed il solo, e si fosse aste&shy;<lb/>nuto dall'insidiare le ricchezze altrui, avrebbe forse potuto pensare a tute&shy;<lb/>lar meglio e a mettere in mostra le proprie. </s></p><p type="main">

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

<s>Di quest'ultimo asserto la prova ricorre opportuna a proposito del Mi&shy;<lb/>crometro. </s>

<s>In quella intromessa, fuor del soggetto principale, che Galileo pone <lb/>in principio del suo <emph type="italics"/>Discorso intorno i Galleggianti,<emph.end type="italics"/> dopo aver riferito le <lb/>misure fin allora trovate delle rivoluzioni periodiche de'satelliti intorno al <lb/>centro di Giove, non sodisfatto della loro precisione, per mancanza di osser&shy;<lb/>vazioni pi&ugrave; esatte delle passate, soggiunge: &ldquo; Per simili precisioni non mi <lb/>bastano le prime osservazioni, non solo per li brevi intervalli di tempo, ma <lb/>perch&egrave; non avendo io allora ritrovato modo di misurar con istrumento al&shy;<lb/>cuno le distanze di luogo tra essi pianeti, notai tali interstizi con le sem&shy;<lb/>plici relazioni al diametro del corpo di Giove, prese, come diciamo a oc&shy;<lb/>chio &rdquo; (Alb. </s>

<s>X, 10). </s></p><p type="main">

<s>Lo strumento, a cui accenna in queste parole Galileo, non fu da lui <lb/>ritrovato prima della fine del 1611, ne l'ebbe preparato prima del seguente <lb/>Gennaio 1612, e la notte del 31 di questo mese, nella seconda osservazione <lb/>che istitui intorno ai Gioviali, incominci&ograve; a fare di quello stesso strumento <lb/>il primo uso. </s>

<s>&ldquo; In hac secunda observatione primum usus sum instrumento <lb/>ad intercapedines exacte accipiendas, ac distantiam orientalioris proxime ac&shy;<lb/>cepi: non enim fuit instrumentum adhuc exactissime paratum &rdquo; (ibi, V, 84). </s></p><p type="main">

<s>Ora, vien la curiosit&agrave; di domandare: in che consiste questo nuovo stru&shy;<lb/>mento <emph type="italics"/>ad intercapedines exacte accipiendas,<emph.end type="italics"/> e che non &egrave; certamente quello <lb/>delle lamine perforate applicate al Canocchiale, secondo la descrizione fatta <lb/>in principio del Nunzio Sidereo? </s>

<s>Della nuova invenzione, men semplice della <lb/>prima, e cavata da pi&ugrave; reconditi principii, si sarebbe potuto compiacer Ga&shy;<lb/>lileo con pi&ugrave; ragione di quel che non facesse a proposito dell'avere inse&shy;<lb/>gnato il modo di trovar l'angolo del concorso de'raggi visuali nell'occhio, <lb/>eppure non si cur&ograve; l'Autore di lasciarne nessuna descrizione, e se ne sa&shy;<lb/>rebbe anzi perduta la notizia, se gli scolari e i seguaci di lui non l'aves&shy;<lb/>sero amorosamente raccolta e trasmessa alla nostra memoria. </s></p><p type="main">

<s>Di questo stesso ingegnoso strumento galileiano, che serve ad uso di Mi&shy;<lb/>crometro, sarebbe qui luogo a trattare, se non avessimo stimato esser forse <pb xlink:href="020/01/432.jpg" pagenum="413"/>per riuscir pi&ugrave; opportuno, quando avremo a entrare in discorso delle sco&shy;<lb/>perte fatte intorno al pianeta di Giove. </s>

<s>Intanto &egrave; certo che Galieo, il primo <lb/>di ogni altro che si sappia, propose l'uso di due Micrometri, senza l'altro ap&shy;<lb/>positamente preparato per le osservazioni gioviali: quello delle lamine per&shy;<lb/>forate da applicarsi al Canocchiale, e quello della cordicella tesa traguar&shy;<lb/>data dall'occhio nudo. </s></p><p type="main">

<s>Questa seconda maniera di misurar le piccole distanze, parve, nella sua <lb/>semplicit&agrave;, a Candido del Buono cos&igrave; bella, che pens&ograve; di accoppiarla essa <lb/>pure al Canocchiale e di renderla vie maggiormente squisita. </s>

<s>Invece di una <lb/>corda di certa grossezza, come richiedeva la pratica di Galileo, pens&ograve; di far <lb/>uso di un sottilissimo filo, attraversato al tubo, in luogo opportuno tra la <lb/>lente oculare e l'obiettivo del Telescopio. </s>

<s>Comunic&ograve; il Del Buono questo <lb/>suo pensiero al Borelli, il quale non ne riconobbe l'importanza, se non dap&shy;<lb/>poi che l'Huyghens ne pubblic&ograve; l'invenzione applicandola a trovar le rela&shy;<lb/>zioni di misura tra la grandezza dell'anello e il corpo di Saturno. </s>

<s>Nel cap. </s>

<s>IV <lb/>infatti delle <emph type="italics"/>Theoricae Mediceorum,<emph.end type="italics"/> dopo avere in primo luogo insegnato <lb/>il modo di misurar le massime digressioni de'satelliti dal centro di Giove, <lb/>il Borelli stesso cos&igrave; soggiunge: &ldquo; Idipsum praestari potest praeclaro arti&shy;<lb/>ficio nuper ab ingeniosissimo Christiano Hugenio editum (licet multo prius <lb/>idipsum mihi Dominus Candidus Buonus florentinus comunicaverit): Adapta&shy;<lb/>tur in tubo optico prope lentem ocularem, in eiusque foco, tenuissimum <lb/>filum aeneum.... &rdquo; (Florentiae 1665, pag. </s>

<s>145, 46). Ma giova, meglio che <lb/>alla descrizione che qui seguita a fare il Borelli, attendere a quella che ne <lb/>fa l'Huyghens stesso nel suo <emph type="italics"/>Systema Saturnium,<emph.end type="italics"/> colle parole seguenti: </s></p><p type="main">

<s>&ldquo; Locus quidam est intra tubos, qui solis convexis vitris instructi sunt, <lb/>circiter altero tanto amplius quam convexum oculare ab oculo distans, quo <lb/>in loco si quid intra tubi cavitatem visui obiieiatur, quantumvis subtile aut <lb/>exiguum, id distincte prorsus ambituque exquisite terminato conspicitur, <lb/>atque ita pro ratione latitudinis suae partem aliquam rei lucidae, velut Lu&shy;<lb/>nae per Telescopium spectatae, visui subducit. </s>

<s>Exacte loci determinatio, his <lb/>quibus nullo vitio visus laborat, in focum convexi ocularis cadit.... Hic igi&shy;<lb/>tur si primo annulus statuatur cum foramine paulo angustiore, quam sit <lb/>vitrum ipsum oculo proximum, eo tota tubi apertura, sive spatium circu&shy;<lb/>lare, quod uno obtutu in coelo detegitur, praecisa circumferentia descriptum <lb/>habetur. </s>

<s>Cuius spatii diameter, quot scrupula comprehendat, aliquo pacto <lb/>inquirendum est, atque optime quidem ex transitu sideris alicuius, cuius <lb/>tempus numeretur vibrationibus perpendiculi, vel ope Horologii nostri oscilla&shy;<lb/>torii nuper inventi, Telescopio interim immoto manente. </s>

<s>Scimus enim 4 scru&shy;<lb/>pulis horariis unum coeli gradum et exiguum quid amplius transire: ideoque, <lb/>si verbi gratia numerentur scrupula secunda 69, interea dum stella quaedam <lb/>fixa totam Telescopii capacitatem metitur, argumento id erit 17 1/2 scrupula <lb/>prima Telescopii huiusmodi apertura comprehendi, sicut nostro evenit. </s>

<s>Quo <lb/>invento, virgulam unam atque alteram, ex aere aliave materia, parare opor&shy;<lb/>tet, decrescenti paulatim latitudine, tubumque perforare utrinque circa lo-<pb xlink:href="020/01/433.jpg" pagenum="414"/>cum illum paulo ante memoratum, quo possint in ipso eius puncto virgu&shy;<lb/>lae transversae ante oculum obtendi. </s>

<s>Cum igitur Planetae alicuius diametrum <lb/>metiri cupimus, adhibita ex quo diximus loco virgula, notandum est quae&shy;<lb/>nam huius latitudo totum planetam contingere possit. </s>

<s>Ea enim latitudine <lb/>acuto deinde circino accepta, atque ad totius amplitudinem collata, Planetae <lb/>diameter apparens facili ratiocinio innotescet &rdquo; (Op. </s>

<s>Omn., Lugd. </s>

<s>Batav. </s>

<s>1724, <lb/>pag. </s>

<s>593, 94). E per recare un esempio, applica lo strumento a misurare <lb/>il diametro apparente di Venere, che egli trova essere 51&Prime; 45&tprime;. </s></p><p type="main">

<s>Questo ugeniano &egrave; il primo Micrometro di che faccia menzione la Sto&shy;<lb/>ria dell'Astronomia, ma Eustachio Divini viene a rivendicar per s&egrave; il di&shy;<lb/>ritto di dieci anni di anteriorit&agrave; sul ritrovato olandese. </s>

<s>Il reticolo, di che <lb/>servivansi i disegnatori per ritrarre gli oggetti in prospettiva, ei l'applic&ograve; a <lb/>descrivere le macchie della Luna, osservate con uno de'suoi Canocchiali <lb/>vantato per il pi&ugrave; eccellente che si fosse veduto. </s>

<s>Una tal Selenografia, con <lb/>altre apparenze osservate in Venere, in Giove e in Saturno, fece il Divini <lb/>inciderla in una Mappa, dedicata nel 1649 al granduca Ferdinando II, e le <lb/>poche copie tirate la resero rarissima. </s>

<s>Una di queste copie Giovanni Tar&shy;<lb/>gioni Tozzetti la compr&ograve; dagli eredi di Antonio Cocchi, e la inser&igrave; fra'suoi <lb/>farraginosi manoscritti. </s>

<s>Sotto la detta Mappa &egrave; impressa un'inscrizione, colla <lb/>quale l'Autore si fa innanzi a presentare i suoi disegni al Granduca, e vi <lb/>si leggon fra le altre le seguenti parole: &ldquo; Plenilunium Martii 1649 Tele&shy;<lb/>scopio palmorum 24 observatum, quo minimas et minutissimas Lunae ma&shy;<lb/>culas scrutatus est. </s>

<s>Et altero palmorum 16 instructo versus oculum non <lb/>vitro concavo, sed lente vitrea subtilissimis filis ad instar craticulae dispo&shy;<lb/>sitis operta, qua ipsas Lunae maculas delineavit et suo quemque loco pro&shy;<lb/>pria manu exactissime posuit &rdquo; (Targ. </s>

<s>Notiz. </s>

<s>aggrandim., Firenze 1780, T. I, <lb/>P. I, pag. </s>

<s>246). </s></p><p type="main">

<s>L'applicazione della reticola fatta dal Divini a ritrarre in prospettiva <lb/>gli astri col Canocchiale, segna senza dubbio un notabile progresso nelle <lb/>Operazioni dell'Astronomia, ma se non pu&ograve; negarsi al reticolo stesso, e al <lb/>modo come il suo Inventore l'usava, la natura e l'essere di vero Microme&shy;<lb/>tro, &egrave; pure di necessit&agrave; il confessare che un tal Micrometro non era appli&shy;<lb/>cabile a tutti quegli usi, a cui si porgeva il Micrometro ugeniano. </s>

<s>Questo <lb/>dall'altra parte era assai incomodo, e al tedio di tentar qual grossezza di <lb/>virgula fosse quella che s'adattava all'osservazione, s'aggiungevano, in chi <lb/>non fosse stato cos&igrave; paziente e destro, molte occasioni di errore. </s></p><p type="main">

<s>Allora venne in mente a Geminiano Montanari di tender, sul cerchietto <lb/>descritto dall'Huyghens, non un filo solo di variabile grossezza, ma pi&ugrave; fili <lb/>sottilissimi, come sarebbero capelli, tutti equidistanti e paralleli tra loro, im&shy;<lb/>immobili e invariabili, e con i quali si veniva a comporre un reticolo, di <lb/>cui l'Inventore intese di servirsi principalmente per gli usi dell'Altimetria. </s></p><p type="main">

<s>&ldquo; Pongasi, egli scrive, dentro la canna dell'oculare, nel concorso de'fo&shy;<lb/>chi, invece del cerchietto, ove dissi si ponesse il capello per livellare, un al&shy;<lb/>tro cerchietto guernito di molti capelli v. </s>

<s>g. </s>

<s>12 o 15, tutti equidistanti e <pb xlink:href="020/01/434.jpg" pagenum="415"/>paralleli fra di loro, e con essi in primo luogo si faccia la seguente pruova: <lb/>In luogo comodo a ci&ograve; si ponga una pertica o altra misura esatta, in di&shy;<lb/>stanza di 100 pertiche, pi&ugrave; o meno, come pu&ograve; portare il Canocchiale per <lb/>vedere l'oggetto esattamente distinto, e s'osservi quanti di quelli spazi fra <lb/>un capello e l'altro occupa tutta detta pertica, oppur mezza, come torna co&shy;<lb/>modo, e se non comprende spazi interi, s'accomodi o s'allontani all'oggetto <lb/>quanto basta, perch&egrave; gli comprenda per l'appunto, il che serve per comodo <lb/>maggiore, anzi &egrave; meglio fare in modo che ogni spazio comprenda tant'on&shy;<lb/>cie per appunto, e allora si misuri esattamente la distanza dell'occhio alla <lb/>pertica suddetta, e questa si divida in tante parti, quant'oncie abbiamo tro&shy;<lb/>vato comprendersi dentro ad uno spazio. </s>

<s>Dar&ograve; l'esempio: con la Livella diot&shy;<lb/>trica che ho fabbricata e donata a questo illustrissimo Senato, il di cui Ca&shy;<lb/>nocchiale &egrave; come dissi 9 piedi, in distanza di 100 pertiche, io comprendeva <lb/>tra l'un filo e l'altro per appunto cinque oncie, onde divise in cinque parti <lb/>le 100 pertiche, ne toccano 20 pertiche per oncia, il che deve servirmi di <lb/>regola in avvenire. </s>

<s>Volendo adunque sapere quanto &egrave; lontano qualunque <lb/>luogo ch'io possa vedere con detto Canocchiale, basta osservare l'altezza <lb/>d'una finestra, porta o colonna, torre o altra simil cosa, quanto spazio cio&egrave; <lb/>ella occuper&agrave; li fili suddetti posti nel Canocchiale, e far misurare sul luogo <lb/>la giusta altezza di detta finestra, o porta ecc. </s>

<s>per trovare quant'once di <lb/>piede restavano comprese tra un filo e l'altro, e dando 20 pertiche per oncia <lb/>o quel tanto che ho veduto per esperienza che porta quel Canocchiale, sapr&ograve; <lb/>benissimo quante pertiche lontano &egrave; quell'oggetto. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il passo fin qui trascritto si legge a pag. </s>

<s>17, 18 della <emph type="italics"/>Livella Diottrica,<emph.end type="italics"/><lb/>pubblicata dal Montanari in Bologna nel 1674, ma in una lettera indirizzata <lb/>da Padova al Magliabechi, in data del d&igrave; 11 Settembre 1682, l'Autore stesso <lb/>dice di avere applicata la reticola al Canocchiale infin dal 1664, e di aver <lb/>con essa ritrovata facilmente la parallasse della Cometa apparita allora nel <lb/>cielo: &ldquo; Se la cometa si fosse lasciata vedere in siti assai alti, ond'io avessi <lb/>potuto osservarla col mio Canocchiale a reticola, avrei trovata facilmente la <lb/>sua vera parallasse, col modo che adoprai in quella del 1664 allora da me <lb/>inventato e pubblicato.... &rdquo; (Padova 1682, pag. </s>

<s>6). </s></p><p type="main">

<s>La pubblicazione non fu fatta per&ograve; formalmente per le stampe, altro <lb/>che nel 1674, come di sopra abbiamo veduto, e il padre Lana avea pubbli&shy;<lb/>cato il Prodromo all'Arte maestra quattro anni prima, descrivendovi il re&shy;<lb/>ticolo applicato al Canocchiale e l'uso che se ne poteva fare all'Altimetria. </s>

<s><lb/>Il Montanari, che seco stesso si compiaceva di essere stato l'inventore del <lb/>nuovo strumento, e che sperava di essere stato in tempo a pubblicare la sua <lb/>invenzione, bench&egrave; indugiata infino al 1674, rest&ograve; colpito, quand&ograve; poco dopo <lb/>gli capit&ograve; alle mani e gli cadde sotto gli occhi il Cap. </s>

<s>VIII del citato <emph type="italics"/>Pro&shy;<lb/>dromo.<emph.end type="italics"/> Allora, conoscendo bene di aver perduto ogni diritto di difendere <lb/>la sua ragione in pubblico, si content&ograve; di farlo in privato colla seguente let&shy;<lb/>tera del d&igrave; 13 Agosto 1675 indirizzata a Vincenzio Viviani: </s></p><p type="main">

<s>&ldquo; Post varios casus ecco finalmente a V. S. Ecc.ma la sua Livella diot-<pb xlink:href="020/01/435.jpg" pagenum="416"/>trica, che dal signor Vincenzio Landi .... sar&agrave; mandata in una cassetta, ove <lb/>l'ho ben serrata e legata dentro per modo, che non patisca le scosse. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sar&agrave; nella stessa cassa, in una scatoletta, una Reticola da porre in <lb/>luogo dell'altra, che &egrave; nella Livella, quando V. S. Ecc.ma vorr&agrave; valersi del <lb/>Canocchiale per misurar le distanze con una sola stazione, e vi saranno si&shy;<lb/>milmente li vasettini di vetro da mettere nell'acqua, per mettere in oriz&shy;<lb/>zonte la Livella, ed una breve istruzione dell'uso di essi e della Reticola <lb/>per l'Altimetria, avendo ridotto tutte le misure a braccia e soldi fiorentini, <lb/>per maggior sua comodit&agrave;. </s>

<s>Vedr&agrave; il mio modo di far la Reticola, e potr&agrave; <lb/>favorirmi di mostrarlo all'Ecc.mo Sig. </s>

<s>Accademico Svetoni, per occasione di <lb/>valersene egli ancora per l'ecclissi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pochi giorni sono mi fu mostrato, nel <emph type="italics"/>Prodromo<emph.end type="italics"/> Della Lana, il pen&shy;<lb/>siero di misurar con la Reticola le distanze, il che non poco mi ha fatto <lb/>senso. </s>

<s>Rimettendomi a memoria che sul principio del 1665 mi trovai in <lb/>Mantova, mentre si vedeva la seconda Cometa e conferii questa ed altre mie <lb/>coserelle col p. </s>

<s>Ferroni, con cui feci allora stretta amicizia, siccome nel <lb/>viaggio di ritorno di l&agrave; la conferii col p. </s>

<s>Urbano Davisi allora Generale delli <lb/>PP. Gesuati, che tuttavia se ne ricorda, anzi spontaneamente ne scrisse al <lb/>p. </s>

<s>ab. </s>

<s>Pepoli, l'anno passato, dicendogli che erano dieci anni che io glie&shy;<lb/>l'aveva conferita, ond'egli ne aveva bramata la pubblicazione: Ora, che il <lb/>p. </s>

<s>Lana avesse da s&egrave; incontrata la medesima speculazione, non me ne ma&shy;<lb/>raviglierei, se io non vedessi che la sua barca da navigare per aria ed il <lb/>suo Orologio, da durare 15 anni una caricatura, lo dichiarano troppo <emph type="italics"/>levis <lb/>armaturae,<emph.end type="italics"/> e perci&ograve; non sono senza sospetto che l'abbia avuto dal p. </s>

<s>Fer&shy;<lb/>roni suo amicissimo, e che l'ha protetto per la pubblicazione del suo libro <lb/>altre volte rigettato da'suoi superiori, e maggiormente che io vedo ivi ad&shy;<lb/>dotti, bench&egrave; indigesti molti altri usi della Reticola nel Telescopio, di cui <lb/>aveva promesso io un Trattato nel mio opuscolo della Cometa, i capi del <lb/>quale, cos&igrave; per l'Astronomia come per le cose terrestri, aveva letto al me&shy;<lb/>desimo p. </s>

<s>Ferroni, uno de'quali era <emph type="italics"/>De usu Reticolae ad distantias inac&shy;<lb/>cessas una statione dimetiendas, cum Corollariis De navium distantia in <lb/>mari.<emph.end type="italics"/> Ma mio sia il danno perch&egrave;, sentito che Eustachio (il Divini) preten&shy;<lb/>deva di esser l'inventore della Reticola per descrivere la Luna, ancorch&egrave; <lb/>egli diversamente da me l'avesse adoprata, ed io non pretendessi d'essere <lb/>il primo a mettere i fili nel concorso de'fochi; tuttavia, per timore che <lb/>quell'uomo non la pigliasse con me, come fece coll'Hugenio, ho procrasti&shy;<lb/>nato tanto, che ho dato campo a costoro di farmela. </s>

<s>Non importa: ne tro&shy;<lb/>ver&ograve; dell'altre, se Dio vuole, e tacer&ograve; meglio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Del signor Auzout, che, in una sua lettera al P. Oldemburgo, pro&shy;<lb/>poneva, come suo segreto da farne baratto con Mons. </s>

<s>Hook, il modo di <lb/>misurare <emph type="italics"/>unica statione distantias inaccessas,<emph.end type="italics"/> non ho dubbio che non coin&shy;<lb/>cidesse ne'medesimi pensieri, ma egli &egrave; altro ingegno che il p. </s>

<s>Lana, e non <lb/>ha quella presunzione che ha questo e per l'uso della sua setta e per altre <lb/><gap/><pb xlink:href="020/01/436.jpg" pagenum="417"/>passato, con farsene appresso molti l'inventore in Venezia. </s>

<s>Gli turai la bocca <lb/>con poco suo gusto, ma pure, se nasceva da litigarne fra noi, ci era chi <lb/>portava via l'.osso per altra parte. </s>

<s>Ma <emph type="italics"/>nimium hucusque &rdquo;<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., <lb/>T. CXLVI, c. </s>

<s>58, 59). </s></p><p type="main">

<s>Ogni avvocato in causa propria &egrave; naturalmente, e quasi sempre ragio&shy;<lb/>nevolmente sospetto, ma pur volendo fare pel Montanari in questo caso un <lb/>eccezione, si pu&ograve; concedere che egli avesse, infino dal 1664, pensato al suo <lb/>Reticolo e lo avesse altres&igrave; applicato all'Altimetria e alla Astronomia. </s>

<s>No&shy;<lb/>nostante &egrave; un fatto che il p. </s>

<s>Lana in Italia pubblic&ograve; per le stampe quella <lb/>invenzione quattro anni prima, e l'Auzout in Francia si dice che, del Reticolo <lb/>per misurar le distanze <emph type="italics"/>unica statione,<emph.end type="italics"/> se ne fosse servito infino dal 1666. </s></p><p type="main">

<s>A precisar l'anno, in cui l'Astronomo francese s'incontr&ograve; nel suo nuovo <lb/>strumento, ci mancano i documenti certi, ma pure &egrave; debito confessare che <lb/>se il Reticolo dell'Auzout &egrave; posteriore in tempo a quello del Montanari, lo <lb/>supera nonostante in perfezione. </s>

<s>Nel Reticolo del nostro Italiano infatti i ca&shy;<lb/>pelli tesi sul telaio rimangono immobili, e se l'oggetto non &egrave; compreso <lb/>esattamente ne'loro interstizi, s'insegna a rimoverne o ad avvicinarne il Ca&shy;<lb/>nocchiale. </s>

<s>Il Francese invece pens&ograve;, per mezzo di un congegno a vite mi&shy;<lb/>crometrica, di rimovere e di avvicinare agli altri uno de'fili, mantenendo <lb/>immobile lo stesso Canocchiale, e ne risult&ograve; uno strumento assai pi&ugrave; comodo <lb/>e pi&ugrave; squisito. </s>

<s>Il De La Hire poi rese mobile non un filo, ma un telaio di <lb/>fili sopra un altro telaio, e dette cos&igrave; alla Geodesia e all'Astronomia il Mi&shy;<lb/>crometro, che in sostanza &egrave; quello ancora dell'uso moderno. </s></p><p type="main">

<s>Spettatore de'progress&igrave; fatti in questa invenzione, che dovea tanti e <lb/>cos&igrave; segnalati servigi prestare alla scienza degli astri, fu quell'Huyghens <lb/>che ne avea posti i principii. </s>

<s>Egli per&ograve; non solo non ebbe la generosit&agrave; di <lb/>confessar que'progressi, ma li neg&ograve; dicendo che la sua <emph type="italics"/>Virguia<emph.end type="italics"/> rimaneva <lb/>tuttavia micrometro pi&ugrave; perfetto di quello a rete di fili, ultimamente inven&shy;<lb/>tato. </s>

<s>&ldquo; Quomodo autem hae nostrae magnitudinum rationes inventae sint, <lb/>tum ex cognita proportione distantiarum a sole, tum ex mensura diame&shy;<lb/>trorum, Telescopiis capta, eo, quem dixi libro ostendi: neque adhuc video <lb/>cur multum ab iis quas tunc definivi, recedam, etsi nihil eis deesse non <lb/>contenderim. </s>

<s>Nam quod multi existimant, in metiendis apparentibus diame&shy;<lb/>tris praestare lamellis nostris usum <emph type="italics"/>Micrometrorum<emph.end type="italics"/> quae vocant, quibus fila <lb/>tenuissima in foco lentis maioris praetenduntur, nondum iis assentiri possum, <lb/>sed aptiores esse lamellas virgulasve tenues arbitror, quas eo loco obiicien&shy;<lb/>das docueram &rdquo; (Cosmoth. </s>

<s>Lib. </s>

<s>I, Op. </s>

<s>Var., Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>652). </s></p><p type="main">

<s>Ma il Newton, sentendo questo giudizio essere nell'Huyghens alterato <lb/>dall'affetto paterno, dimostr&ograve; che ci era veramente nella <emph type="italics"/>Virgula<emph.end type="italics"/> di lui <lb/>un'occasione di errore, evitata poi ne'Micrometri a reticolo. </s>

<s>Quell'occasione <lb/>fu acutamente ritrovata dal grande Ottico inglese nel fatto che la luce er&shy;<lb/>ratica o ascitizia, come Galileo la chiamava, s'espande pi&ugrave; al largo, coperto <lb/>che sia il Pianeta, ond'&egrave; che col metodo ugeniano le misure de'diametri <lb/>apparenti degli astri si debbono per necessit&agrave; e si trovan di fatto riuscire <pb xlink:href="020/01/437.jpg" pagenum="418"/>alquanto maggiori del giusto. </s>

<s>&ldquo; Hinc est quod Hugenius latitudine obsta&shy;<lb/>culi, quod lucem omnem interciperet, maiores exhibuit planetarum diame&shy;<lb/>tros quam ab aliis Micrometro definitum est, nam lux erratica, tecto Pla&shy;<lb/>neta, latius cernitur, radiis fortioribus non amplius obscurata. </s>

<s>Hinc denique <lb/>est, quod planetae in sole tam graciles appareant luce dilatata attenuati &rdquo; <lb/>(Opusc. </s>

<s>T. II, Lausannae 1744, pag. </s>

<s>16). </s></p><p type="main">

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

<s>La Livella diottrica, della quale faceva il Montanari menzione in prin&shy;<lb/>cipio della lettera al Viviani di sopra trascritta, &egrave; un nuovo ritrovato per <lb/>cui venne il Canocchiale ad applicarsi a un altr'uso geodetico importantis&shy;<lb/>simo. </s>

<s>Il pensiero di servirsi del Telescopio come strumento livellatore, so&shy;<lb/>spendendolo pel suo centro di gravit&agrave;, era sovvenuto in mente all'Huyghens, <lb/>che l'esplic&ograve; in una sua scrittura intitolata <emph type="italics"/>Nova Libella Telescopio instructa <lb/>propriam secus ferens probationem et quae in unica statione verificatur <lb/>et rectificatur<emph.end type="italics"/> (Op. </s>

<s>Var., Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>254-61). Ma troppo inco&shy;<lb/>modo a trasportarsi in campagna, e troppo complicato nell'uso era il nuovo <lb/>Canocchiale livellatore cos&igrave; proposto. </s></p><p type="main">

<s>Il pensiero del vero Livello diottrico s'incarn&ograve; con mirabile semplicit&agrave; <lb/>nella mente del Montanari, ma prima di narrar come per lui si facesse il <lb/>felice connubio, giova toccar brevemente la storia dell'invenzione del sem&shy;<lb/>plice strumento da livellare, il quale col suo stesso nome di <emph type="italics"/>Corobate<emph.end type="italics"/> ri&shy;<lb/>vela l'origine sua antica e l'uso, che ne fecero i Greci e gli Ingegneri <lb/>romani. </s></p><p type="main">

<s>Vitruvio, nel libro VIII della sua <emph type="italics"/>Architettura,<emph.end type="italics"/> trattando nel capi&shy;<lb/>tolo VI <emph type="italics"/>De perductionibus et librationibus aquarum et instrumentis ad hunc <lb/>usum,<emph.end type="italics"/> ne lasci&ograve; la seguente descrizione: &ldquo; Chorobates autem est regula <lb/>longa circiter pedum viginti: ea habet ancones in capitibus extremis acquali <lb/>modo perfectos inque regulae capitibus ad normam coagmentatos, et inter <lb/>regulam et ancones a cardinibus compacta transversaria, quae habent lineas <lb/>ad perpendiculum recte descriptas, pendentiaque ex regula perpendicula in <lb/>singulis partibus singula, quae, cum regula fuerit collocata, eaque tanget <lb/>aeque ac pariter lineas descriptionis, indicabunt libratam collocationem &rdquo; <lb/>(Venetiis 1511, pag. </s>

<s>80, v.). </s></p><p type="main">

<s>Lo strumento insomma &egrave; fondato sul principio della linea verticale de&shy;<lb/>scritta dal filo a piombo, ogni normale alla quale &egrave; la linea del cercato li&shy;<lb/>vello. </s>

<s>Ma succede spesso in campagna che il filo pendulo venga agitato dal <lb/>vento, per cui si rende difficile il segnarne esattamente la direzione. </s>

<s>Allora <lb/>Vitruvio insegna di ricorrere all'espediente dell'acqua, la quale, versata den&shy;<lb/>tro un canale lungo, si livella per tutto il tratto di lui dovunque alla me&shy;<lb/>desima altezza: &ldquo; Sin autem ventus interpellaverit et motionibus linaee non <pb xlink:href="020/01/438.jpg" pagenum="419"/>potuerint certam significationem facere, tunc habeat in superiore parte ca&shy;<lb/>nalem longum pedes quinque, latum digitum, altum sesquidigitum, eoque <lb/>aqua infundatur, et si aequaliter aqua canalis summa labra tanget, scietur <lb/>esse libratum &rdquo; (ibi, pag. </s>

<s>81, v.) </s></p><p type="main">

<s>Ma pur volle Giovan Battista Porta che la difficolt&agrave;, nemmeno intro&shy;<lb/>ducendo l'uso dell'acqua, al modo che prescrive Vitruvio, fosse tolta di <lb/>mezzo: soggiunse anzi di pi&ugrave; esser quella stessa difficolt&agrave;, che rende inu&shy;<lb/>tile lo strumento vitruviano: &ldquo; Questa difficolt&agrave; l'ha resa disutile, perch&egrave;, <lb/>avendosi sempre a por acqua in quella cava, bisognava che portassimo sem&shy;<lb/>pre l'acqua con noi &rdquo; (Spiritali, Napoli 1606, pag. </s>

<s>97). </s></p><p type="main">

<s>Fu perci&ograve; che il nostro Fisico napoletano si dette a speculare il modo <lb/>di toglier via le notate difficolt&agrave;, e di ridurre a pi&ugrave; comodo uso e pi&ugrave; per&shy;<lb/>fetto la livella ad acqua, a che poi felicemente riusc&igrave;, sostituendo al canale <lb/>aperto un tubo chiuso, che sorgesse alle sue due estremit&agrave; in due tubi di <lb/>vetro, attraverso ai quali traguardando, si veniva cos&igrave; la mira a disporre na&shy;<lb/>turalmente nella linea del perfetto livello. </s>

<s>&ldquo; Stimo, egli scrive, aver ritro&shy;<lb/>vato il vero modo che l'acqua non si gonfi sopra il canale, n&egrave; i piombi che <lb/>pendono saranno turbati dal vento, n&egrave; bisogna che poniamo appresso noi <lb/>le botti con i carri con l'acqua, quando avemo da livellar lunga distanza. </s>

<s><lb/>Sia la regola che abbiamo descritta di sopra AB (fig. </s>

<s>38) nel cui mezzo si <lb/><figure id="id.020.01.438.1.jpg" xlink:href="020/01/438/1.jpg"/></s></p><p type="caption">

<s>Figura 38.<lb/>cavi un canale di due diti di altezza e <lb/>di qua e di l&agrave; s'alzino duo cilindri di <lb/>vetro C, D di un piede di lunghezza <lb/>ben saldati nel basso del canale, e sia <lb/>il canal coverto di legno molto bene <lb/>impeciato intorno, che postovi l'acqua <lb/>una volta non se ne scorra da qualche parte. </s>

<s>Ovvero, nella regola, se cos&igrave; <lb/>piace, sia un canale di piombo che non si assorba l'acqua, che empiendosi <lb/>d'acqua si riempiano i canaletti. </s>

<s>Dopo bisogna aggiustar molto bene la re&shy;<lb/>gola che sia pianissima e che abbia i canaletti segnati nella superficie <lb/>egualmente intorno intorno o col smeriglio ovvero con alcun color fisso. </s>

<s>E <lb/>ripieno il canale d'acqua infino al detto segno, si coprano all'ultimo le boc&shy;<lb/>che con cera. </s>

<s>Quando poi ci vogliamo servir dell'istrumento, la regola si <lb/>deve drizzare fra duo scannetti, tanto alzando e calando i suoi estremi, fin&shy;<lb/>ch&egrave; l'acqua tocchi egualmente la linea descritta ne'canali, e allora lo stru&shy;<lb/>mento sar&agrave; aggiustato &rdquo; (ivi, pag. </s>

<s>98). </s></p><p type="main">

<s>La Livella ad acqua cos&igrave;, infin dal 1601, inventata dal Porta, e ne'suoi <lb/><emph type="italics"/>Libri tres Pneumaticorum<emph.end type="italics"/> resa pubblicamente nota, &egrave; quella stessa che, <lb/>per la sua semplicit&agrave; e facilit&agrave; di costruzione, non &egrave;, nemmeno oggid&igrave;, uscita <lb/>affatto fuor d'uso, ed &egrave; quella altres&igrave; che il Montanari, come s'accennava <lb/>di sopra, ebbe il felice pensiero di accoppiare allo strumento diottrico. </s>

<s>Gli <lb/>balen&ograve; quel pensiero un giorno che essendo a livellare in campagna, piut&shy;<lb/>tosto che traguardar la mira, segnata con due fili tesi e una pallina, ad oc&shy;<lb/>chio nudo, si mise a traguardarla con un canocchialetto Biconoscinti allora <pb xlink:href="020/01/439.jpg" pagenum="420"/>per esperienza i vantaggi che l'uno strumento recava all'altro, deliber&ograve; di <lb/>accoppiarli indivisibilmente insieme e di comporne uno strumento solo. </s>

<s>&ldquo; Io <lb/>perci&ograve;, cos&igrave; narra lo stesso Inventore, feci prova in certe occasioni di pub&shy;<lb/>blico servigio, dop'avere aggiustata una di queste livelle da acqua, ritirarmi <lb/>indietro da quella alquanti passi e riguardare con un canocchialetto in mano, <lb/>col quale, trovando ambi quei fili insieme con la pallina, distinguevo assai <lb/>meglio che con l'occhio nudo, quando que'fili mi venivano sotto un piano <lb/>e quando la pallina stava esattamente a suo luogo, oltre che poteva con <lb/>questo aiuto livellar molto pi&ugrave; da lungi, e dove, con l'occhio libero, in <lb/>25 stazioni che si fanno, il meno per miglio potevo errare 25 volte; co&igrave; ca&shy;<lb/>nocchialetto alla mano, facevo molte meno stazioni, e per conseguenza molti <lb/>meno errori &rdquo; (Livella Diottr., Bologna 1674, pag. </s>

<s>8). </s></p><p type="main">

<s>Questa <emph type="italics"/>Livella diottrica<emph.end type="italics"/> poi, che &egrave; il pi&ugrave; semplice e pi&ugrave; naturale ac&shy;<lb/>coppiamento della Livella ad acqua inventata dal Porta, col Canocchiale di <lb/><figure id="id.020.01.439.1.jpg" xlink:href="020/01/439/1.jpg"/></s></p><p type="caption">

<s>Figura 39.<lb/>Galileo; &egrave; dal Montanari stesso <lb/>cos&igrave; descritta in semplici e brevi <lb/>parole: &ldquo; AB (fig. </s>

<s>39) &egrave; il ca&shy;<lb/>nocchiale tutto d'un pezzo di lat&shy;<lb/>toni per&ograve; saldati insieme, con <lb/>solo il cannello B ove sta il tra&shy;<lb/>guardo che pu&ograve; allungarsi e ac&shy;<lb/>corciarsi conforme richiede la vi&shy;<lb/>sta. </s>

<s>DE altra canna di latta saldata <lb/>con il Canocchiale, grossa dentro <lb/>pi&ugrave; d'un dito grosso, che dai capi <lb/>si rivolta in su per saldarvi li can&shy;<lb/>nellini di vetro DC ed EF grossi anch'essi pi&ugrave; di un pollice. </s>

<s>&rdquo; (ivi, pag. </s>

<s>12). </s></p><p type="main">

<s>Il semplice e comodo strumento livellatore del Porta era per 69 anni <lb/>pacificamente convivuto con i geodeti e con gli agrimensori, quando, a tur&shy;<lb/>bar quella sua lunga pace e a metterlo in sospetto di chi in buona fede <lb/>l'apprezzava e lo ricercava, vennero le censure di Gian Alfonso Borelli. </s>

<s><lb/>Egli, presa occasione dall'inganno che, in segnare il giusto livello ne'tubi, <lb/>fanno all'occhio del riguardante i liquidi, per via de'cos&igrave; detti fenomeni ca&shy;<lb/>pillari; prosegue con una tal sequela di difetti scoperti a dir tanto male di <lb/>quella povera invenzione del Porta, da finir per consigliare coloro che ne <lb/>facevano uso ad abbandonarla e a tornare all'antico Corobate di Vitruvio. </s></p><p type="main">

<s>&ldquo; Ex dictis colligitur quod fistula vitrea libellatoria (quam hydrostati&shy;<lb/>cam libellam nonnulli vocant) nonnullis difficultatibus et fallaciis obnoxia <lb/>sit, primo, quia si fistulae vitraee erectae perpendiculariter ad planum hori&shy;<lb/>zontis non fuerint praecise aeque amplae, procul dubio argines aqueos inter&shy;<lb/>nos inaequales efficient, ideoque planum per summitates arginum aqueorum <lb/>extensum non erit horizonti aequidistans. </s>

<s>Idipsum continget si praedictae <lb/>duae fistulae erectae fuerint aequales inter se, at non sint omnino sordibus <lb/><gap/> illa prohibeat arginis aquei ele-<pb xlink:href="020/01/440.jpg" pagenum="421"/>vationem magis aut minus, pro copia aut defectu praedictae pinguedinis. </s>

<s><lb/>Praeterea, si una fistularum fuerit interne arida, reliqua vero madefacta, <lb/>argines quoque aquei in madida fistula elevantur, non vero in arida. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Alio insuper nomine fallax est praedictum instrumentum, cum enim <lb/>aqua nunquam pura et sincera haberi possit, fit ut nisi bullulae aeraee, <lb/>quibus nunquam aqua spoliatur, aeque distributae sint in utraque fistula, <lb/>erunt moleculae illae aquaee inaequaliter graves specie, et ideo earum sum&shy;<lb/>mitates habebunt inaequales elevationes, proindeque non ostendent exactam <lb/>libellam horizontalem. </s>

<s>Idipsum continget, quotiescumque fistulae praedictae <lb/>non fuerint ab eodem gradu caliditatis rarefactae, nempe si una a solaribus <lb/>radiis illustratur, reliqua vero in loco umbroso, aut magis frigido degat, non <lb/>secus si sordes terrae, aut sales inaequaliter distributi fuerint in utroque <lb/>canaliculo, nunquam praecise organum praedictum veram horizontalem li&shy;<lb/>bellam indicabit. </s>

<s>At si loco aquae mercurium in praedicta fistula incluseri&shy;<lb/>mus, non effugiemus omnes difficultates, nec in summa certi esse possumus <lb/>nunquam in operationibus errasse, quanta est fili alicuius tenuis crassities. </s>

<s><lb/>Proinde conducit laboriosam hanc machinam relinquere et more antiquo re&shy;<lb/>gulis normalibus cum fune pendulo libellam horizontalem exquirere &rdquo; (De <lb/>Motion. </s>

<s>natur. </s>

<s>Regio Julio 1670, pag. </s>

<s>417, 18). </s></p><p type="main">

<s>Nonostante che il Borelli avesse contro la <emph type="italics"/>laboriosa macchina<emph.end type="italics"/> mosse <lb/>tali fiere accuse, e l'avesse messa cos&igrave; in mala voce appresso agl'ingegneri, <lb/>il Montanari non disper&ograve; di ridurla ad emenda, n&egrave; si rimosse per questo <lb/>dal proposito di esaltarla anco a maggior grado, disposandola al Telescopio. </s>

<s><lb/>Le verit&agrave;, da che erano in gran parte avvalorate le accuse borelliane, e la <lb/>terribilit&agrave; dell'accusatore, consigliarono l'Inventor della Livella diottrica a <lb/>soccorrere ai principali difetti, che presentava lo strumento inventato e <lb/>descritto negli <emph type="italics"/>Spiritali<emph.end type="italics"/> del Fisico napoletano. </s>

<s>E perch&egrave; la prima e princi&shy;<lb/>pale fra quelle accuse fondavasi sull'inganno, che, per i fenomeni di capil&shy;<lb/>larit&agrave;, si fa nell'occhio; il Montanari pens&ograve; di ovviarvi facendo contrasse&shy;<lb/>gnare il giusto livello dagl'indici applicati a due galleggianti. </s>

<s>Provvide lo <lb/>stesso Montanari altres&igrave; a tor via alcuni altri inconvenienti, che presentava la <lb/>Livella ad acqua, e tutto ci&ograve; egli descrive colle seguenti parole, in una sua <lb/>lettera indirizzata da Bologna, il d&igrave; primo dell'anno 1675, a Vincenzio Viviani: </s></p><p type="main">

<s>&ldquo; Con questa occasione voglio avvertire V. S. Ecc.ma un <lb/><figure id="id.020.01.440.1.jpg" xlink:href="020/01/440/1.jpg"/></s></p><p type="caption">

<s>Figura 40.<lb/>modo, che mi &egrave; sovvenuto di mettere nella Livella Diottrica <lb/>l'acqua al suo segno, ed adattare l'Instrumento con esattezza <lb/>al suo piano, perch&egrave;, com'Ella sa, ed io anche nell'Istruzione <lb/>di essa notai alla pag. </s>

<s>7, l'acqua ne'cannelli non pieni fa la <lb/>superficie concava, che perci&ograve; resta alquanto incerta la deter&shy;<lb/>minazione del vero sito, sin dove ella deve collocarsi, il che <lb/>non resta di cagionare qualche svarietto, che solo poteva cor&shy;<lb/>reggersi in parte col fare assai lunga la Livella. </s>

<s>Ora ho pensato far due <lb/>corpi galleggianti come questo A (fig. </s>

<s>40), che pu&ograve; esser di rame, con la <lb/>pallina vuota e chiusa, che abbia appeso al peduccio un sottile circoletto di <pb xlink:href="020/01/441.jpg" pagenum="422"/>lastra, onde, posta in acqua detta lastra, stia prossimamente orizzontale, ed <lb/>abbia questa una punta sottile nell'estremit&agrave; B, che servir&agrave; d'indice. </s>

<s>Percioc&shy;<lb/>ch&egrave; posti a galla, ne'cannelli di vetro della Livella, due tali corpi, e segnato <lb/>il luogo, ove la punta B deve stare, quando la Livella sar&agrave; orizzontale, con&shy;<lb/>forme dissi in detta Istruzione, serviranno poscia per sempre a ritornarla nel <lb/>medesimo sito ed indicheranno, per la sottigliezza di dette punte, esattissima&shy;<lb/>mente il piano desiderato. </s>

<s>E perch&egrave; alle volte pare noioso l'aggiungere acqua <lb/>nella Livella, per ridurla precisamente a'luoghi segnati, anzi la state scorsa <lb/>osservai, operando, per prova, in campagna, che riscaldata la livella dal sole <lb/>l'acqua anch'essa rarefatta cresceva e mutava luogo; perci&ograve; ho segnato <lb/>molti segni uno sopra l'altro, co'suoi numeri, in alcune, ed in una aggiunsi <lb/>un terzo cannello senza segni, nel mezzo del quale, con uno strumentino <lb/>di vetro, cavavo acqua, quella poca quantit&agrave; per volta, che volevo &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXLVI, c. </s>

<s>28). </s></p><p type="main">

<s>La strana risoluzione presa dal Borelli di ritornare allo strumento li&shy;<lb/>vellatore antico, e le sollecitudini che si dava il Montanari in restaurare il <lb/>nuovo, farebbero argomentar da chi vi ripensa, che nel 1670, quando si <lb/>pubblic&ograve; il libro <emph type="italics"/>De motionibus naturalibus,<emph.end type="italics"/> e nel 74 e nel 75, quando l'In&shy;<lb/>ventore pubblic&ograve; e pens&ograve; ad emendare la Livella Diottrica, non dovess'es&shy;<lb/>sere stata ancora inventata la <emph type="italics"/>Livella a bolla d'aria.<emph.end type="italics"/> Non &egrave; credibile in&shy;<lb/>fatti che, venendosi con questa nuova invenzione a toglier via la massima <lb/>parte de'difetti notati nella ordinaria Livella ad acqua, il Borelli non volesse <lb/>preferirla al Corobate antico, n&egrave; &egrave; pur credibile che il Montanari, il quale <lb/>troppo ben per prova sapeva quanto fosse incomodo l'operare in campa&shy;<lb/>gna, volesse sopraccaricar s&egrave; e i suoi colleghi del fastidio di aggiustar quei <lb/>suoi galleggianti. </s></p><p type="main">

<s>In quale anno preciso la bolla d'aria, rinchiusa dentro un tubo di ve&shy;<lb/>tro, venisse a porgersi comodo ed esatto strumento libellatorio, non sapremmo <lb/>dirlo; ma si pu&ograve; congetturar facilmente che ci&ograve; fosse intorno al 1670. La <lb/>prima notizia di un s&igrave; bel ritrovato si sarebbe potuta diffondere in Italia da <lb/>una descrizioncella, che ne fece il Viviani, se non fosse rimasta fra le carte <lb/>di lui cos&igrave; manoscritta: </s></p><p type="main">

<s>&ldquo; Strumento per mettere un piano o un regolo ecc. </s>

<s>in livello orizzon&shy;<lb/>tale. </s>

<s>&mdash; Questo &egrave; un cilindretto di cristallo serrato da ambe le parti, lungo <lb/>circa un palmo, grosso quanto il dito anulare, e pieno d'acqua, lasciatovi <lb/>per&ograve; un solo sonaglio d'aria, la quale, avendo la natura di star sopra l'acqua, <lb/>allora dar&agrave; segno che il piano stia livellato, quando essa si ridurr&agrave;, posa&shy;<lb/>tovi sopra il cilindro, a stare in mezzo di detto cilindro, in dubbio di muo&shy;<lb/>versi o verso l'una o verso l'altra estremit&agrave; del bocciolo &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. CXXXV, c. </s>

<s>8). </s></p><p type="main">

<s>Il legger cos&igrave; fatte parole in un volume, che s'intitola <emph type="italics"/>Raccolta di espe&shy;<lb/>rienze, senz'ordine, e di pensieri diversi di me Vincenzio Viviani, in di&shy;<lb/>versi propositi sovvenutimi intorno a materie meccaniche, fisiche, astro&shy;<lb/>nomiche, filosofiche e altro,<emph.end type="italics"/> potrebbe far credere che fosse stato inventore <pb xlink:href="020/01/442.jpg" pagenum="423"/>dell'elegante strumento l'Autore stesso del Manoscritto. </s>

<s>Altri documenti <lb/>per&ograve; attestano che il Viviani non per altro scrisse quelle parole, che per <lb/>serbar memoria di una invenzione, la quale, cos&igrave; per lettera, in cui manca <lb/>l'anno della data, il Th&egrave;venot, con lusinghiera eloquenza, descrivevagli da <lb/>Parigi: </s></p><p type="main">

<s>&ldquo; Ma e che cosa potrei io fare per meritare che V. S. allargasse un <lb/>poco quella confidenza, colla quale ella mi onora, coll'accennarmi qualche <lb/>cosa delle scoperte, che ella ha fatto nei studi di Geometria? </s>

<s>Se con confi&shy;<lb/>dargli i miei vaneggiamenti credessi di poterlo meritare, lo farei volentieri. </s>

<s><lb/>E qui, per obbligare V. S. a farmene quella parte, che me ne giudicher&agrave; <lb/>degno, per cavarne dell'oro, le mando un poco di vetro. </s>

<s>Sia il cannoncino <lb/><figure id="id.020.01.442.1.jpg" xlink:href="020/01/442/1.jpg"/></s></p><p type="caption">

<s>Figura 41.<lb/>di vetro AB (fig. </s>

<s>41) con i suoi lati <lb/>ben paralleli, e turata una bocca di <lb/>esso, s'empia d'acqua per l'altra <lb/>parte, sin per esempio al segno C, e <lb/>poi si sigilli e turi l'apertura. </s>

<s>Sar&agrave; <lb/>fatto uno strumento di grand'uso nelle arti, cio&egrave; un livello d'aria esente di <lb/>molti difetti, che s'incontrano nel livello ordinario. </s>

<s>Affinch&egrave; il moto dell'aria <lb/>sia pi&ugrave; libero &egrave; bene che il diametro del cannoncino sia di una linea &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXLVII, c. </s>

<s>230). </s></p><p type="main">

<s>Se per&ograve; il Viviani non fu l'inventore della Livella a bolla d'aria, egli <lb/>fu il primo che tent&ograve; di diffonderne l'uso in Italia. </s>

<s>E perch&egrave; i gonfiatori <lb/>di vetro in Firenze trovavano gran difficolt&agrave; in condurre uguali i tubetti, <lb/>pens&ograve; di rivolgersi in Roma a Matteo Campani, artefice espertissimo, e che <lb/>nella sua officina poteva avere arnesi e operai da condurre a perfezione il <lb/>lavoro. </s>

<s>I vetrai romani per&ograve; s'incontrarono nelle difficolt&agrave; medesime de'fio&shy;<lb/>rentini, e perci&ograve;, essendo allora in Roma l'Auzout, lo stesso Campani si <lb/>rivolse a lui, per saper come facevano in Francia a tirare i tubetti di vetro <lb/>da livello, e appresono il modo lo riferisce al Viviani, consigliandolo ad af&shy;<lb/>fidarne l'esecuzione agli artefici di Firenze: &ldquo; Quanto al cilindretto di vetro <lb/>per livellare, mi dice il signor Auzout che, avendo qui provato pi&ugrave; volte a <lb/>farne fabbricare, non gli &egrave; mai riuscito di poterne avere un pezzo total&shy;<lb/>mente eguale. </s>

<s>Che per&ograve; V. S. cost&igrave; potr&agrave; farsi servir meglio, facendo dagli <lb/>artefici tirare le cannucce di vetro, non molto calde, sopra un'asse di legno <lb/>diritta e bene spianata, perch&egrave; cos&igrave; dice che gli fanno in Francia &rdquo; (ivi, <lb/>T. CXLV, c. </s>

<s>195). </s></p><p type="main">

<s>Il Viviani, cos&igrave; affaccendato com'era in operazioni livellatorie, e che <lb/>perci&ograve; meglio di ogni altro poteva conoscere e apprezzare la comodit&agrave; e la <lb/>perfezione del nuovo strumento, non se ne sar&agrave; stato, e avr&agrave; sollecitamente <lb/>fatto eseguire il lavoro in Firenze, al modo che Matteo Campani aveva in&shy;<lb/>teso operarsi a Parigi. </s>

<s>Ma convien pur dir che n&egrave; ancora fosse da fidarsi <lb/>della precisione di que'tubi, se il Viviani stesso, nel 1675, quattro anni dopo <lb/>gl'insegnamenti pratici ricevuti da Roma, approva e loda il Montanari, che <lb/>tuttavia attende a perfezionare l'antica livella ad acqua. </s></p><pb xlink:href="020/01/443.jpg" pagenum="424"/><p type="main">

<s>L'invenzione del Th&egrave;venot, per le sopra dette difficolt&agrave;, s'introdusse <lb/>poi pi&ugrave; tardi fra noi, e sostituita all'invenzione del Porta, in quel felice <lb/>connubio, che pens&ograve; il Montanari far di lei col Telescopio, prest&ograve; ai misu&shy;<lb/>ratori de'cieli non meno importanti servigi, che ai misuratori de'campi. </s></p><p type="main">

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

<s>Anche il <emph type="italics"/>Binoculo<emph.end type="italics"/> entra propriamente nell'ordine degli strumenti, la <lb/>storia de'quali forma il soggetto del presente Capitolo. </s>

<s>Il Nelli, il Frisi, il <lb/>Fabbroni crederono e fecer credere a molti che il pensiero di applicare ai <lb/>due occhi due tubi simili, come negli occhiali semplici s'erano applicate <lb/>due lenti, fosse sovvenuto e fatto eseguire da Galileo. </s>

<s>Il primo de'tre citati <lb/>Autori infatti cos&igrave; scrive: &ldquo; Il tempo, nel quale incominci&ograve; Galileo a porre <lb/>in uso il Binoculo, che denominava <emph type="italics"/>Testiera<emph.end type="italics"/> o <emph type="italics"/>Celatone,<emph.end type="italics"/> fu nel mese di <lb/>Marzo 1617, nel quale portatosi a Livorno, fece di esso esperienze con fe&shy;<lb/>lice successo, sul molo &rdquo; (Vita di Gal., Losanna 1793, pag. </s>

<s>281). </s></p><p type="main">

<s>Il Frisi pure, nell'Elogio che tanto dottamente distese del grande no&shy;<lb/>stro Filosofo, ha opinioni conformi, espresse nel modo seguente: &ldquo; Colle <lb/>suddette Tavole (de'satelliti di Giove) aveva anche esibito la Celata o Te&shy;<lb/>stiera o Binoculo, che in varie prove fatte a Livorno nel 1617 s'era speri&shy;<lb/>mentata assai comoda, per seguitar colla vista gli oggetti in mare &rdquo; (Li&shy;<lb/>vorno, 1775, pag. </s>

<s>91). </s></p><p type="main">

<s>N&egrave; diversa punto da questa dei due citati Autori &egrave; l'opinione del <lb/>Fabbroni, espressa cos&igrave; in nota a pag. </s>

<s>59 del I Tomo delle <emph type="italics"/>Lettere inedite <lb/>di Uomini illustri:<emph.end type="italics"/> &ldquo; L'invenzione del Galileo, per usare navigando del&shy;<lb/>l'Occhiale, e ritrovare coll'istessa prestezza gli oggetti, come con l'occhio <lb/>libero, e trovati seguitarli senza rischio di perderli; consisteva in uno stru&shy;<lb/>mento fatto a guisa di morione, che si adattava al capo dell'osservatore, e <lb/>che era munito di due occhiali. </s>

<s>Il Galileo ebbe in uso di nominarlo <emph type="italics"/>Testiera<emph.end type="italics"/><lb/>o <emph type="italics"/>Celatone &rdquo;<emph.end type="italics"/> (Firenze, 1773). </s></p><p type="main">

<s>Concordano dunque pienamente tutti e tre insieme i citati scrittori, <lb/>nell'asserire che un Canocchiale binoculo fosse da Galileo applicato a quel <lb/>Celatone, che egli immagin&ograve; e propose per uso de'marinari, affinch&egrave; potes&shy;<lb/>sero osservare con comodit&agrave; gli oggetti, e avessero nel tempo stesso espe&shy;<lb/>dite le mani. </s>

<s>Ma &egrave; veramente singolare l'abbaglio preso in tal proposito da <lb/>scrittori di tanta erudizione e di tanto senno, quali sono specialmente il <lb/>Frisi e il Fabbroni, essendo chiarissimo a chi legge, che Galileo, parlando <lb/>dell'occhiale commesso alla Celata, non fa parola che di un cannoncino solo <lb/>applicato da una parte, essendo dall'altra l'occhio libero. </s>

<s>De'molti passi, <lb/>che noi potremmo sottoporre alla considerazione de'nostri lettori, basti ci&shy;<lb/>tarne uno dalla celebre Lettera scritta nel 1637, da Arcetri, a Lorenzo Rea-<pb xlink:href="020/01/444.jpg" pagenum="425"/>vatore col Telescopio non ricevesse turbamento dalle agitazioni della nave, <lb/>collocandolo sopra una sedia accomodata a imperniatura cardanica, cos&igrave; sog&shy;<lb/>giunge: &ldquo; Io feci gi&agrave; sul principio, per l'uso delle nostre Galere, certa cuf&shy;<lb/>fia in forma di celata, che tenendola in capo l'osservatore, ed avendo a <lb/>quella affisso <emph type="italics"/>un Telescopio,<emph.end type="italics"/> aggiustato in modo che rimirava sempre l'istesso <lb/>punto, al quale l'altro occhio libero indirizzava la vista, senza farci altro, <lb/>l'oggetto, che egli riguardava con l'occhio libero, si trovava sempre incon&shy;<lb/>tro al Telescopio &rdquo; (Alb. </s>

<s>VII, 166). </s></p><p type="main">

<s>Ma nel 1617, il Binoculo vero era stato gi&agrave; ideato ed eseguito, alquanti <lb/>anni prima, da tutt'altri inventori, che da Galileo. </s>

<s>Dicemmo altrove che <lb/>probabilmente la forma binoculare fu quella della prima invenzione, occorsa <lb/>per l'accoppiamento di due paia di occhiali da naso. </s>

<s>Che per&ograve; in sulla fine <lb/>del 1611 il Keplero avesse dato mano a tentar cos&igrave; fatta foggia di Canoc&shy;<lb/>chiali, non &egrave; una probabilit&agrave; ma un fatto. </s>

<s>Il motivo poi per cui il grande <lb/>Ottico alemanno abbandon&ograve; la speculazione e l'opera intrapresa, &egrave; uno de'pi&ugrave; <lb/>curiosi che ne porga a legger la nostra Storia. </s></p><p type="main">

<s>Un giorno dunque chiama un legnaiolo di Linz, e gli ordina che assetti <lb/>un pezzo di legno, di figura parallelepipeda, con due occhiaie trapanate pro&shy;<lb/>fondamente da parte a parte, e i rigoletti da incastrarvi dentro le lenti. </s>

<s>Torna <lb/>poco dopo l'artefice col lavoro eseguito: il Keplero lo guarda, arriccia il <lb/>naso, poi fa: &mdash; Uhm! La mi pare una trappola da topi. </s>

<s>&mdash; Torna a guar&shy;<lb/>dar, con pi&ugrave; dispetto che mai, e rivolto al pover uomo, che stava l&igrave; tutto mor&shy;<lb/>tificato, per la poca approvazione del suo lavoro, soggiunge: &mdash; Oramai tu <lb/>l'hai fatto; ma per non mi far canzonare .... &mdash; e butta, in dir cos&igrave;, ogni <lb/>cosa fuor di finestra. </s></p><p type="main">

<s>Chi ha in visione una di queste macchinette da chiappar topi, che in <lb/>Toscana si chiama col nome di <emph type="italics"/>Boia,<emph.end type="italics"/> vede al tempo stesso il Binoculo, co&shy;<lb/>m'era lavorato dal legnaiolo di Linz, sul disegno avutone dal Keplero. </s>

<s>Le <lb/>due occhiaie profonde eran trapanate e larghe allo stesso modo: erano alla <lb/>stessa distanza l'una dall'altra, che i due fori del Boia, dove i topolini fic&shy;<lb/>cano il muso, per giungere ad addentare addentro l'esca insidiosa. </s>

<s>I rigo&shy;<lb/>letti, da incastrar le lenti, erano allo stesso punto e allo stesso modo inca&shy;<lb/>vati, che le scanalature delle due cateratte, fra le quali scatta e scorre l'anello <lb/>di fil di ferro, destinato a strozzar gl'incauti animaletti. </s></p><p type="main">

<s>La storiella curiosa la sentiremo fra poco raccontar dallo stesso Keplero <lb/>a Ottavio Pisani, matematico napoletano, il quale per benefizio di coloro, <lb/>che ricevevan nocumento all'un occhio, con cui continuamente riguardavan <lb/>nel Telescopio, volle, a costo di qualunque difficolt&agrave;, riuscire a geminar lo <lb/>strumento. </s>

<s>Delle speculazioni, che dovean guidarlo all'esecuzione dell'opera, <lb/>dava cos&igrave; conto, da Anversa, il d&igrave; 15 Settembre 1613, a Galileo, in una let&shy;<lb/>tera latina scritta coll'ortografia della pronunzia napoletana: &ldquo; De pespicillo <lb/>autem dicam meam opinionem: ego paro librum de tota Prospectiva, et habeo <lb/>multa circa construxionem huius pespicilli, et symmetriam vitrorum, quanta <lb/><gap/> modus formandi. </s>

<s>Verum ego non facio hunc pespi-<pb xlink:href="020/01/445.jpg" pagenum="426"/>cillum uno oculo apponendum sed duobus oculis, et ambos oculos volvo in <lb/>unum, si placet tibi scribam pluribus omnia &rdquo; (Campori, Cart. </s>

<s>gal., Mo&shy;<lb/>dena 1881, pag. </s>

<s>72). </s></p><p type="main">

<s>Ma perch&egrave; Galileo o non rispose, o rispose freddamente all'invito, l'im&shy;<lb/>paziente Pisani pens&ograve; di rivolgersi al Keplero, a cui, il d&igrave; 5 d'Ottobre di <lb/>quell'anno 1613, scriveva trepidante da Anversa, per la prima volta, inco&shy;<lb/>minciando dallo scusarsi della sua audacia. </s>

<s>&ldquo; Audax videbor tibi.... &rdquo; (Epi&shy;<lb/>stolae ad Kepl., Lipsiae 1717, Epist. </s>

<s>CCCXLIX, pag. </s>

<s>565). Due giorni dopo, <lb/>non essendosi voluto spiegar nella prima, torna a scrivere una seconda let&shy;<lb/>tera, aprendo cos&igrave; la sua intenzione al gran Maestro della scienza ottica in <lb/>Germania: &ldquo; Alio autem modo perspicillum construere molior, nempe duo&shy;<lb/>bus oculis aptatum. </s>

<s>Multos enim scio qui, cum diutium uno oculo inspicere <lb/>commorantur, fere fere, inquam altero oculo caligant. </s>

<s>Tu vero, qui optime <lb/>in tua Optica perspicilli rationem doces, quaeso responde quid sentis. </s>

<s>Sym&shy;<lb/>metriam enim seu praxin construendi non invenio a te traditam. </s>

<s>Quod si <lb/>respondes, plura tecum conferenda aperiam &rdquo; (ihi, epist. </s>

<s>CCCL, pag. </s>

<s>566). </s></p><p type="main">

<s>Il Keplero non manc&ograve; di rispondere, bench&egrave; un po'tardi, da Linz il d&igrave; <lb/>16 di Dicembre. </s>

<s>Avvisa il Pisani di aver ricevute insieme le sue due let&shy;<lb/>tere, e poi, a proposito del Binoculo, passa a raccontar la storiella della <lb/>Trappola, che gli fu precipuo motivo d'abbandonare il pensiero di un'in&shy;<lb/>venzione da lui stimata ridicola e inutile. </s>

<s>&ldquo; Perspicillum optas aptum duo&shy;<lb/>bus oculis, et a me fabricam. </s>

<s>Difficile puto. </s>

<s>Tentare coepi ante biennium. </s>

<s><lb/>Postquam enim capsulam exhibuit Arcularius, qualem praescripseram, visa <lb/>est muscipulae figuram nacta esse: &mdash; Fecisti igitur; ne essem deridi&shy;<lb/>culo.... &mdash; Ac etsi faciemus qualem optas, non erit apta promiscue omni&shy;<lb/>bus, nec semper eidem. </s>

<s>Crescunt homines in latitudinem, usque ad pro&shy;<lb/>vectam aetatem: tum autem difficultas maxima, ut duos tubos eiusdem <lb/>effectus in colore, copia luminis et quantitate speciei comparemus. </s>

<s>Si mi&shy;<lb/>nima discrepantia, quanta incommoditas in usu? </s>

<s>Credo autem, si diligentia <lb/>accedat, aliquo usque promoveri opus posse, usu unius convexi in arundine <lb/>admodum longa duorumque cavorum: nec multum nocituram obliquitatem <lb/>convexi tantulam ad cava &rdquo; (ibi, epist. </s>

<s>CCCLII, pag. </s>

<s>567). </s></p><p type="main">

<s>Il Pisani, sentendo che s'arretrava alle difficolt&agrave; dell'impresa un cos&igrave; <lb/>gran capitano, egli semplice milite ne rimase a principio scoraggiato, ma, <lb/>poi presto ripreso animo, volle provarsi a incarnare quel suo concetto, per&shy;<lb/>suaso di far cosa utilissima agli amici, i quali si lagnavano di esser quasi <lb/>rimasti ciechi dal guardar pur coll'uno, rimanendone offeso gravemente l'al&shy;<lb/>tro: &ldquo; Scripsisti, con tali parole il Pisani risponde al Keplero, quod diu <lb/>tentasti et tandem destitisti. </s>

<s>Si tu tantus Dux fugis, quid facient milites? </s>

<s><lb/>O quid audeam! Immo superaddis quod quamvis inveniretur, tamen opus <lb/>inutile esset. </s>

<s>Sane territus obstupui, sed non funditus eieci spem. </s>

<s>Nam mihi <lb/>videtur aliquanto bene succedere. </s>

<s>Ego adhuc laboro, et multa experior, et <lb/>si quid boni succedet, illico ad te mittam. </s>

<s>Ego vellem hadere tale perspi&shy;<lb/>cillum duobus oculis <gap/><pb xlink:href="020/01/446.jpg" pagenum="427"/>vastat alterum. </s>

<s>Ego vidi duos amicos sane excaecatos, ob diuturnam unius <lb/>oculi inspectionem, altero clauso. </s>

<s>Quare omnino mihi videtur necessaria ta&shy;<lb/>lis perspicilli inventio &rdquo; (ibi, epist. </s>

<s>CCCLIII, pag. </s>

<s>568, 69). </s></p><p type="main">

<s>Essendosi, per principal difficolt&agrave;, presentata al Pisani quella della sim&shy;<lb/>metrica visione co'due Telescopii gemelli, aveva, infin da quel primo tempo <lb/>che si confid&ograve; con Galileo, pensato ad ovviarvi, applicando due oculari di&shy;<lb/>retti a un obiettivo solo: <emph type="italics"/>ambos oculos volvo in unum.<emph.end type="italics"/> Sentendo ora che <lb/>anche il Keplero si riscontrava in quel medesimo pensiero, e che veniva di <lb/>pi&ugrave; ad assicurarlo <emph type="italics"/>nec multum nocituram obliquitatem convexi tantulam <lb/>ad cava,<emph.end type="italics"/> deliber&ograve; senz'altro di costruire il nuovo Binoculo, su quel dise&shy;<lb/>gno. </s>

<s>Alla capsula, che portava i due oculari, forse per evitar la ridicola im&shy;<lb/>magine della Trappola, dette, dalla parte anteriore, una figura ovale, e in&shy;<lb/>dietro prolungavasi, a guisa di coda, in un tubo, all'estremit&agrave; del quale era <lb/>applicato l'obiettivo. </s>

<s>Nel Luglio del 1614 il nuovo Binoculo era costruito, <lb/>e il Pisani aveva fatto pensiero di mandarlo a Firenze a Galileo, e di offe&shy;<lb/>rirlo, per mezzo di lui, al Granduca. </s>

<s>&ldquo; Io ho fatto uno di quelli occhiali <lb/>che V. S., quasi nuovo e celeste Amerigo, ave rivolto al cielo; ho fatto dico <lb/><emph type="italics"/>uno Teloscopio a due occhi,<emph.end type="italics"/> come gli altri sono ad uno. </s>

<s>Il corpo &egrave; poco e <lb/>di figura ovale. </s>

<s>Quando piacesse a S. A. </s>

<s>Serenissima farmi carit&agrave;, io man&shy;<lb/>daria queste cose, ed intitolaria al suo serenissimo nome &rdquo; (Campori, ivi, <lb/>pag. </s>

<s>82). </s></p><p type="main">

<s>Il Binoculo finalmente, da <emph type="italics"/>Telescopio a due occhi,<emph.end type="italics"/> si ridusse a due Te&shy;<lb/>lescopii congiunti, per opera di Anton Maria Rheita, il quale affront&ograve; ardi&shy;<lb/>tamente le difficolt&agrave; della visione simmetrica, che avevan fatto cos&igrave; adom&shy;<lb/>brare il Pisani e il Keplero. </s>

<s>L'invenzione &egrave; descritta in un libro, che porta <lb/>lo strano titolo di <emph type="italics"/>Oculus Enoch et Eliae,<emph.end type="italics"/> stampato nel 1645 in quella stessa <lb/>citt&agrave; di Anversa, in cui soggiornava il nostro Pisani. </s>

<s>Nel cap. </s>

<s>VI di quel <lb/>libro l'Autore scrive le seguenti parole, che noi traduciamo liberamente, <lb/>perch&egrave; l'importanza delle notizie non ricompensano il tedio di legger nella <lb/>lingua latina originale: </s></p><p type="main">

<s>&ldquo; Bench&egrave; Galileo avesse costruito gi&agrave; Canocchiali eccellenti, quanto a <lb/>inacutire la vista, avevano nonostante quegli strumenti un difetto, qual era <lb/>quello di circoscrivere in troppo angusto spazio il campo della visione. </s>

<s>Per&shy;<lb/>ci&ograve;, mettendomi io a ridurre alla pratica i principii diottrici del Keplero, <lb/>con due lenti convesse in debite proporzionali distanze fra loro insieme con&shy;<lb/>giunte, e con felice artifizio segate, mi venne costruito un Telescopio, per <lb/>mezzo del quale si comprendevano in una occhiata sola e si annoveravano <lb/>distintamente infino a 50 stelle. </s>

<s>Ecco un Telescopio, che pu&ograve; dirsi propria&shy;<lb/>mente astronomico, perch&egrave; apre un campo alla visione cento volte pi&ugrave; am&shy;<lb/>pio di quel che non facesse il primo e pi&ugrave; antico occhiale di Galileo. </s>

<s>Non <lb/>contenti a solo questo monoculo, ne aggiungemmo ad esso un altro simile, <lb/>con felicissimo ardimento. </s>

<s>Cos&igrave; ci si videro comparire innanzi gli oggetti il <lb/>doppio pi&ugrave; grandi e pi&ugrave; distinti di quel che non apparissero col Monoculo, <lb/>e insomma passava fra l'uno e l'altro strumento quella differenza, che &egrave; <pb xlink:href="020/01/447.jpg" pagenum="428"/>tra il veder con due occhi e un occhio solo. </s>

<s>Avendo poi noi, per gli am&shy;<lb/>maestramenti dell'eruditissimo Cartesio, il modo di segare i vetri, secondo <lb/>la vera ragione e potenza delle loro rifrazioni; abbiamo speranza di scoprir, <lb/>con un tal Canocchiale Binoculo, i pi&ugrave; occulti segreti del cielo. </s>

<s>&rdquo; </s></p><p type="main">

<s>De'nuovi strumenti binoculari del Rheita, dava cos&igrave; il Mersenno, co'suoi <lb/>soliti modi sgarbati, conto al Torricelli, consigliandolo ad andare a scuola <lb/>dal frate cappuccino tedesco, se voleva imparare a fabbricar Canocchiali: <lb/>&ldquo; Porro te monitum velim iam Augustae Vindelicorum fieri Telescopia longa <lb/>meliora quam tua, vel cuiuspiam alterius communia, quae serviunt duo&shy;<lb/>bus oculis, quaeque propterea capuccinus Rheita (qui nuper edidit tracta&shy;<lb/>tum de hoc tubo, quem vocat <emph type="italics"/>Oculum Enoch et Eliae<emph.end type="italics"/>) vocat <emph type="italics"/>Binocula.<emph.end type="italics"/><lb/>Habent itaque quatuor convexa, nullum concavum, duo per quovis oculo, <lb/>quae, quia obiecta invertunt, quod parum refert in astris, si tertium conca&shy;<lb/>vum adlabetur, rectum est obiectum. </s>

<s>Sed iam fortassis librum illum vide&shy;<lb/>ris, nec dubito quin eadem Telescopia possis imitari, quin et superare &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>19). </s></p><p type="main">

<s>In ogni modo, il Rheita che raddoppiando lo strumento credeva di po&shy;<lb/>ter raddoppiare anche insieme la potenza visiva, e che, dalla Diottrica del <lb/>Keplero e del Cartesio non aveva altro imparato che la pratica di quel Ca&shy;<lb/>nocchiale astronomico, costruito fra noi dal Fontana tanti anni prima; era <lb/>un illuso. </s>

<s>A dimostrarlo tale basterebbe rivolgere gli occhi su quella Ta&shy;<lb/>vola disegnata dalla sua stessa penna, e che fu inserita fra le carte astro&shy;<lb/>nomiche di Galileo. </s>

<s>Le due note illustrative, scritte in due quadretti incor&shy;<lb/>niciati, con cappuccinesca raffinatezza, appi&egrave; della stessa Tavola, servono di <lb/>conferma. </s>

<s>Dice l'una di quelle note: &ldquo; Observatio stupenda Novem Comi&shy;<lb/>tum Jovis a me habita die 29 Xbris 1642, qua et aliis vicibus, praeter qua&shy;<lb/>tuor interiores Galilaei, alios quinque exteriores et multo maiores inveni, <lb/>tali prorsus dispositione et ordine, ut hic notantur. </s>

<s>&rdquo; Dice l'altra nota: <lb/>&ldquo; Qui postea, die 4 Januarii 1643, notabilissime et taliter de loco suo moti <lb/>et mutati sunt, prout 0, 0, 0, 0 denotant. </s>

<s>F et G vero ea die disparuere ver&shy;<lb/>sus Apogaeos, aut in umbram Jovis forsan intrantes &rdquo; (MSS. Gal., P. III, <lb/>T. VII, c. </s>

<s>6). </s></p><p type="main">

<s>Tanto poi bene il fatto prov&ograve; l'illusione dell'Astronomo cappuccino, <lb/>che andarono in dimenticanza i Binoculi astronomici di lui, insieme col suo <lb/>nuovo sistema gioviale. </s>

<s>Ben per&ograve; rivissero lieta e splendida vita i Binoculi <lb/>terrestri, n&egrave; avrebbe senza dubbio il Keplero fatto un s&igrave; mal garbo a quella <lb/>sua ridicola Trappola da topi, se avesse potuto immaginar di vedersela tra&shy;<lb/>sformata in quegli elegantissimi diottrici gemelli, di che si servono le signore, <lb/>per t&ograve;rre a s&egrave; gli attori lontani, e le decorazioni sceniche de'teatri. </s></p><pb xlink:href="020/01/448.jpg" pagenum="429"/><p type="main">

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

<s>Uno degli usi pi&ugrave; speciali, a cui si fece servire il Telescopio, fu quello <lb/>di rivolgerlo a guardar direttamente nella sfera del Sole. </s>

<s>Vi furon pur troppo, <lb/>e fra'nostri e fra gli stranieri, alcuni audaci, che aprirono il loro occhio a <lb/>ricever quell'onda condensata di luce scaturiente dal diafano dell'oculare, <lb/>e bench&egrave; Galileo avesse notato gi&agrave; l'efficacia de'veli e de'vetri coloriti <lb/>(Alb. </s>

<s>III, 74) in radere il capellizio alle stelle, per cui venisse l'occhio a <lb/>riceverle con assai meno abbagliore, non par nulladimeno che gli cadesse in <lb/>mente d'applicar quegli stessi veli e que'vetri coloriti al Telescopio, per le <lb/>dirette osservazioni solari. </s>

<s>E da ci&ograve; fu il caso che venisse a perdere quel <lb/>primato nelle osservazioni delle macchie, che egli poi usc&igrave; a rivendicar sopra <lb/>lo Scheiner, senza giusta ragione. </s></p><p type="main">

<s>Fra gli osservatori per&ograve;, eccitati dall'esempio di Galileo, non manc&ograve; <lb/>chi pensasse a provvedere alla vista degli occhi, difendendoli, in osservare <lb/>il sole, con vetri e lenti tinte di verdi colori. </s>

<s>&ldquo; Le macchie del sole, scri&shy;<lb/>veva a Galileo, il di 23 Marzo 1612, Lodovico Cigoli, con il vetro bianco <lb/>piccolo, non potevo fissar l'occhio, che mi lacrimava, ma poi con un vetro <lb/>verde grosso, e perch&egrave; &egrave; incavato come il bianco ve ne pongo sopra un altro <lb/>piano similmente verde, di maniera che non mi d&agrave; fastidio niente a tutte <lb/>l'ore il guardarlo &rdquo; (MSS. Gal., P. III, T. X, c. </s>

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

<s>Se questa, di fabbricar gli oculari di vetro verde, piuttosto che bianco, <lb/>fosse veramente invenzione del Cigoli o glie ne fosse venuta la notizia di <lb/>Germania, &egrave; incerto n&egrave; cos&igrave; facile a decider sui documenti che ci son noti. </s>

<s><lb/>In ogni modo, lo Scheiner pretende di essersi, un anno e pi&ugrave; prima del <lb/>Cigoli, servito delle lenti colorite nelle osservazioni dirette del Sole, e pre&shy;<lb/>tende altres&igrave; di essere stato egli il primo a trasformar cos&igrave; il Canocchiale, <lb/>da meritar che gli venga anche imposto il nuovo nome di <emph type="italics"/>Elioscopio.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nomine porro illius (Helioscopii) intelligo Tubum opticum vitris co&shy;<lb/>loratis cum debito artificio ad istud elaboratis adornatum, ut colorum ipsis <lb/>inhaerentium beneficio vehementior solis radius fractus atque hebetatus, ad <lb/>visum moderatior minusque noxius penetret, atque, ob hanc prerogativam <lb/>merito huiusmodi instrumentum <emph type="italics"/>Helioscopii<emph.end type="italics"/> nomenclatura gaudet.... &rdquo; </s></p><p type="main">

<s>&ldquo; Helioscopium igitur vitris constat coloratis minimum duobus, convexo <lb/>et concavo, materia bene crassa, pura, solida, non bullis, non arenulis, mi&shy;<lb/>nime vero venis, tractibus, seu undis insessa, elaborata in segmentum seu <lb/>frustum perfecte sphaericum, quorum alterum sit vel una ex parte, vel <lb/>utrinque convexum; alterum concavum vel utrinque vel concavo planum, <lb/>prout in Tubis non coloratis fieri consuevit.... Color omnium, quantum <lb/>fieri potest, sit unius generis, v. </s>

<s>g. </s>

<s>coeruleus, viridis, flavus, aut quicum&shy;<lb/>que tandem aliis. </s>

<s>Quod si uniusmodi color haberi nequit, accipiantur mixtim <pb xlink:href="020/01/449.jpg" pagenum="430"/>qui possint. </s>

<s>Talem ego tubum ab initio composui e fragmentis caeruleis la&shy;<lb/>minarum vitreorum, quo et maculas in <emph type="italics"/>Apelle<emph.end type="italics"/> meo editas observavi &rdquo; (Rosa <lb/>Ursina, Bracciani, 1626-30, pag. </s>

<s>70). </s></p><p type="main">

<s>L'Elioscopio nonostante parve esser licenziato dai primi e importanti <lb/>servigi, che aveva prestati agli Osservatori del sole, quando la CV proposi&shy;<lb/>zione della Diottrica del Keplero venne a suggerire al Castelli quel pi&ugrave; co&shy;<lb/>modo e riposato modo di osservarne e di disegnarne le macchie, descritto <lb/>da Galileo in sulla fine della seconda lettera velseriana. </s>

<s>&ldquo; Ma conviene, av&shy;<lb/>verte ivi l'Autore, andare destramente secondando il movimento del sole, e <lb/>spesso movendo il Telescopio, bisogna procurare di mantenerlo ben diritto <lb/>verso il Sole &rdquo; (Alb. </s>

<s>III, 420). </s></p><p type="main">

<s>Lo Scheiner pure, parecchi anni dopo, ripetendo gl'insegnamenti dati <lb/>dal Castelli, per dipinger con un pennello sopra una carta l'immagine te&shy;<lb/>lescopica del sole, avverte: &ldquo; Et quia is continue movetur, evehit statim <lb/>imaginem sui e deputato atque occupato chartae loco, unde cadem propor&shy;<lb/>tione est movendum instrumentum, qua sol promovetur in coelo: alias uno <lb/>codemque loco non continebis circulum solis, non signabis maculas &rdquo; (Rosa <lb/>Urs., ibi, pag. </s>

<s>78). </s></p><p type="main">

<s>Il tedio del dover sempre tenere in esercizio e impacciata la mano, a <lb/>muovere il Telescopio a seconda del moto del sole, non veniva evitato nem&shy;<lb/>meno in quella cos&igrave; complicata macchina grienbergeriana, che lo stesso <lb/>Scheiner descrive, sotto lo specioso nome di <emph type="italics"/>Eliotropio,<emph.end type="italics"/> e che rappresenta <lb/>in ripetuti iconismi, da pag. </s>

<s>347-54 della citata sua <emph type="italics"/>Rosa Ursina.<emph.end type="italics"/></s></p><p type="main">

<s>Eppure, infin dal 1613, eravi stato fra noi chi aveva pensato gi&agrave; a le&shy;<lb/>vare il tedio e a disegnar pi&ugrave; perfettamente le macchie, facendo automati&shy;<lb/>camente muovere il Telescopio, e la carta al moto del sole. </s>

<s>Il pensiero fu <lb/>cos&igrave; da Fabio Colonna espresso in una sua lettera a Galileo: &ldquo; Per dimo&shy;<lb/>strare che abbi cominciato ad aver gusto delle osservazioni celesti, ancorch&egrave; <lb/>con cattivo strumento, massime di Agosto, ebbi osservato le macchie solari, <lb/>e con poca pratica a saperle segnare. </s>

<s>Pure, veda qualche vestigio di buona <lb/>intenzione, che possa con il tempo migliorare, e gi&agrave; ho pensato un modo <lb/>che, essendo solo, si possa muovere il Telescopio e carta al moto del sole <lb/>e tempo, acci&ograve; non abbi altro che far che segnar le macchie perfettamente, <lb/>ed ora abbisogna in pi&ugrave; volte rimettere a sesto l'istrumento e la carta, e <lb/>se ci &egrave; difetto, &egrave; causa la sopraddetta occasione e il tremar la mano nel&shy;<lb/>l'istesso segnare &rdquo; (MSS. Gal., P. VI, T. IX, c. </s>

<s>99). </s></p><p type="main">

<s>Ma questo stesso concetto dell'<emph type="italics"/>Eliostata<emph.end type="italics"/> si riaccese e apparve pi&ugrave; vi&shy;<lb/>vamente colorito nella mente del Borelli, quando volle provarsi a misurar <lb/>la velocit&agrave; della luce del sole, dal tempo che ella metterebbe a saltar da <lb/>uno a un altro, per una serie numerosa di specchi. </s>

<s>Gli si obiettava che l'ul&shy;<lb/>timo raggio riflesso non era pi&ugrave; quello stesso primo incidente, rinnovandosi <lb/>a ogni istante del moto del sole, e che perci&ograve; l'esperienza, seppure era riu&shy;<lb/>scibile, si sarebbe dovuta fare con qualche altra immobile sorgente di luce. <lb/></s>

<s>&ldquo; Ma a questo proposito (cos&igrave; Cosimo Galilei riferisce in una lettera al Vi-<pb xlink:href="020/01/450.jpg" pagenum="431"/>viani) ha scritto il signor Dottore (il Borelli) cinque o sei proposizioni bel&shy;<lb/>lissime, mostrando di potersi servire del sole, bench&egrave; continuamente si muova, <lb/>e con una macchina che si volta al piacer suo, e con un oriuolo a ruote <lb/>aggiustato, prova che sempre possa (movendo quella macchina dove dev'es&shy;<lb/>ser fermo lo specchio che ha da ricevere la prima riflessione o per dir meglio <lb/>il raggio solare) far andar sempre la riflessione per la medesima linea, che <lb/>vale a dire, sempre nel medesimo modo &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLIII, c. </s>

<s>101). </s></p><p type="main">

<s>Come, per le pi&ugrave; comode e pi&ugrave; perfette osservazioni del sole gli Astro&shy;<lb/>nomi inventarono l'Elioscopio e l'Eliostata; cos&igrave; per le pi&ugrave; perfette osser&shy;<lb/>vazioni degli astri, apparentemente minori, sentirono il bisogno di assettare <lb/>intorno al Canocchiale altri organi, per cui si venissero que'minutissimi punti <lb/>lucidi a rappresentare nel vero esser loro, senz'illusione d'ingrandimenti <lb/>ascitizii. </s>

<s>Due modi erano stati proposti gi&agrave; da Galileo: quello della cordi&shy;<lb/>cella tesa e l'altro de'veli e de'vetri colorati, ma non avendo avuto l'ac&shy;<lb/>corgimento di applicar questi organi al Canocchiale, si lasci&ograve; rapir di mano <lb/>all'Huyghens l'invenzione del Micrometro propriamente detto, e allo Schei&shy;<lb/>ner quella dell'Elioscopio. </s></p><p type="main">

<s>Bench&egrave; per&ograve; non venisse in mente a Galileo di tender la cordicella o il <lb/>filo micrometrico nel foco delle lenti, e di tinger le lenti stesse in qualche <lb/>variet&agrave; di colori, non par nulladimeno che trascurasse l'uso dei diaframmi, <lb/>come s'argomenta dal seguente poscritto di lettera del p. </s>

<s>Clavio: &ldquo; Si sono <lb/>visti qui in Roma alcuni occhiali mandati da V. S., i quali hanno li vetri <lb/>convessi assai pi&ugrave; grandi, ma coverti, con restarvi solamente un buco pic&shy;<lb/>colo libero. </s>

<s>Desidererei di sapere che serve tanta grandezza, se ha da co&shy;<lb/>prirsi in questo modo. </s>

<s>Pensano alcuni che sieno fatti grandi, acci&ograve;, sco&shy;<lb/>prendosi tutti la notte, si possano meglio vedere le stelle &rdquo; (Alb. </s>

<s>VIII, 122). </s></p><p type="main">

<s>Dall'altra parte i diaframmi venivano facilmente suggeriti dalla maestra <lb/>Natura, che fu prima a farne uso nella fabbrica dell'occhio. </s>

<s>&ldquo; Quod autem <lb/>facit ad visum adumbrandum (aveva gi&agrave; lasciato scritto il Maurolico nel <lb/>lib. </s>

<s>III <emph type="italics"/>Diaphanorum)<emph.end type="italics"/> ea fuit uvea tunica opaca villositate adumbrans prae&shy;<lb/>dictos humores.... Talis autem adumbratio facit rerum visibilium radios <lb/>expressius apparere, et efficacius ab humoribus praedictis sentire; siquidem <lb/>radii luminum inter opaca aedium recepti sunt evidentiores &rdquo; (Neap. </s>

<s>1611, <lb/>pag. </s>

<s>70). </s></p><p type="main">

<s>Ma nella CXXII proposizione della <emph type="italics"/>Diottrica,<emph.end type="italics"/> formulata: <emph type="italics"/>Angusta len&shy;<lb/>tis convexae portione, caeteris paribus, distinctiora repraesentantur visi&shy;<lb/>bilia, lata confusiora,<emph.end type="italics"/> il Keplero tratt&ograve; de'diaframmi per iscienza, e in modo <lb/>da sodisfar pienamente ai desiderii, e da risolvere i dubbii del p. </s>

<s>Clavio: <lb/>&ldquo; Nam (cos&igrave; passa l'Autore a dimostrar quella diottrica proposizione) quae <lb/>per magnam portionem convexitatis in oculum radiant, illa, per CXIX, for&shy;<lb/>tius radiant, qua fortitudine primum iridis colores, inde nebulae excitantur. </s>

<s><lb/>Oculorum cava et retiformis tunica est spiritu plena, et licet a puncto so&shy;<lb/>lum tangatur, tamen si id punctum ex concursu radiorum multorum sit im&shy;<lb/><gap/><pb xlink:href="020/01/451.jpg" pagenum="432"/>imbuitur contagione passionis penetrantis: vide LXI. Itaque, pro commo&shy;<lb/>ditate oculi, instrumenti, et lucis diurnae vel nocturnae, ampliatur et rete&shy;<lb/>gitur convexa lens, aut angustatur et tegitur, seu immediate, seu loco in&shy;<lb/>termedio inter lentes, adhibito diaphragmate pertuso, aut collo instrumenti <lb/>introrsum flexo et angustato, aut productione tubi ultra lentem convexam, <lb/>ut eius cylindracaei orificium remotus, per LXVII, minori angulo cernatur, <lb/>valeatque tantum quantum angustius aliquid. </s>

<s>Natura praeclusit ampliatione <lb/>foraminis uvaee ad lucem nocturnam, contractione ad diurnam. </s>

<s>Habet Dia&shy;<lb/>phragma et hunc usum, ut intus obscuritatem faciat, quorsum et color niger <lb/>intus obductus servit, et litui figura, progressu extrorsum flexa habent la&shy;<lb/>tera, in medio introrsum, ne radii prope convexam ingressi, rursum pror&shy;<lb/>sumque revibrentur et claritatem faciant. </s>

<s>Eodem servit et productio tubi <lb/>longe ultra lentem convexam, ne convexum irradietur a lateralibus hemi&shy;<lb/>sphaerii partibus &rdquo; (Augustae, 1611, pag. </s>

<s>65). </s></p><p type="main">

<s>Fu de'primi a mettere in pratica fra noi questi teorici Kepleriani in&shy;<lb/>segnamenti il Sagredo, il quale, nel d&igrave; 4 Agosto 1618, scriveva in cos&igrave; fatti <lb/>termini a Galileo: &ldquo; In questo tempo nondimeno ho avvertito quello che <lb/>per altre scrissi a V. S. E. cio&egrave; che aggiunto alcun cannone all'ultimo vetro <lb/>che lo copre dal lume, si vede molto pi&ugrave; chiaro e distinto; e per tempe&shy;<lb/>rare i lumi che vanno riflettendo dentro i cannoni, che generano vista nu&shy;<lb/>volosa, ho trovato buon rimedio nell'ultimo cannone, in conveniente distanza e <lb/>grandezza, porre un riparo di un arcoletto forato &rdquo; (Alb. </s>

<s>Supplem., pag. </s>

<s>123). </s></p><p type="main">

<s>Il gentiluomo veneziano per&ograve; applicava cos&igrave; fatti organi al Canocchiale, <lb/>per servirsene a suo diletto. (Campori, Cart. </s>

<s>gal. </s>

<s>ediz. </s>

<s>cit., pag. </s>

<s>134). Ma <lb/>uno de'primi e principali, che seppe prevalersi dell'efficacia dei diaframmi <lb/>nelle osservazioni celesti, fu Giovanni Hevelio, il quale pens&ograve; di trasformare <lb/>il Canocchiale ordinario in Elioscopio, applicando presso all'oculare due vetri <lb/>piani colorati, in mezzo a ciascun de'quali sia collocato <emph type="italics"/>papyrus eiusdem <lb/>quantitatis, uno foramine parvo pertusa, quae cum vitris firmiter, vel filo, <lb/>vel .... glutino .... connectatur.<emph.end type="italics"/> (Selenographia, Gedani 1647, pag. </s>

<s>23). </s></p><p type="main">

<s>Per poi osservar particolarmente le stelle, insegnava cos&igrave; lo stesso He&shy;<lb/>velio ad accomodare i diaframmi all'obiettivo del Telescopio: &ldquo; Accipe Tu&shy;<lb/>bum, qui observationibus Jovis ac Lunae accomodatus est, et angustius redde <lb/>foramen convexi lenti proximum, vel novam chartam impone, cuius forami&shy;<lb/>nis circumferentiae magno piso sit aequalis &rdquo; (ibi, pag. </s>

<s>37). Cos&igrave; dice di <lb/>aver potuto l'Autore veder perfettamente rotondo il corpo delle stelle fisse, <lb/>senza raggi avventizi, ci&ograve; che non era riuscito n&egrave; a Galileo n&egrave; al Keplero, <lb/>n&egrave; a nessun altro prima di lui. </s>

<s>L'Huyghens nonostante trov&ograve; che cos&igrave; fatti <lb/>diaframmi heveliani non erano i pi&ugrave; opportuni per le osservazioni delle stelle <lb/><emph type="italics"/>maxime splendidarum,<emph.end type="italics"/> e che meglio giovava, <emph type="italics"/>ad auferendos radios,<emph.end type="italics"/> servirsi <lb/>a vetri <emph type="italics"/>fuligine leviter infectis.<emph.end type="italics"/> (Syst. </s>

<s>Sat, Op. </s>

<s>Var., cit. </s>

<s>1724, pag. </s>

<s>540). </s></p><p type="main">

<s>Pi&ugrave; tardi, lo stesso Huyghens pens&ograve; a un altro modo di Diaframma <lb/>oculare, di cui si giov&ograve; utilmente a distinguere i due satelliti di Saturno, <lb/><gap/><pb xlink:href="020/01/452.jpg" pagenum="433"/>con quel suo stesso Telescopio, e col solo diaframma heveliano applicato <lb/>all'obiettivo: &ldquo; Cum Saturni comites illos cassinianos diligentius requirerem <lb/>eosque difficulter adsequerer, praesertim noctibus non admodum obscuris, <lb/>intellexi in causa esse lucem tenuem quendam ab aere ad oculum manan&shy;<lb/>tem, non eam quae per lentem maiorem advenit, sed quae extrinsecus cir&shy;<lb/>cum latam praeterlabitur. </s>

<s>Huic importunae luculae excludendae, nonnihil <lb/>quidem conducere sciebam, si circulum illum papyraceum, quo in Luna ob&shy;<lb/>servanda utebar, etiam hic lenti maiori circumponerem. </s>

<s>Sed aliud efficacius <lb/>remedium circa haec occupato incidit, priori illi iungendum, ut nempe per&shy;<lb/>foratae laminae oppositu, oculi pupilla arctaretur, quae alioqui per tenebras <lb/>late patere solet. </s>

<s>Cuius simul ac experimentum feci, iam clare tres Saturni <lb/>comites conspexi, cum amoto exiguo foramine media illa nostra tantum cer&shy;<lb/>neretur &rdquo; (Astroscopia, Op. </s>

<s>Var., cit., pag. </s>

<s>275). </s></p><p type="main">

<s>Non vogliamo all'ultimo passare in tal soggetto senza commemorare <lb/>que'macchinamenti, che, sotto il nome di <emph type="italics"/>Arcicanna,<emph.end type="italics"/> proponevano agli Ac&shy;<lb/>cademici del Cimento i due fratelli Candido e Anton Maria Del Buono, per <lb/>render maneggevoli in qualche modo i Telescopii, come solevano usarsi al&shy;<lb/>lora, a lungo foco. </s>

<s>Intorno a ci&ograve; cos&igrave; scriveva il Magalotti, con intenzione, <lb/>che poi non ebbe effetto per le ragioni altrove accennate, d'inserire anche <lb/>questa fra le descrizioni degli stumenti premesse al Libro de'<emph type="italics"/>Saggi:<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Avvegnach&egrave; di niun uso sieno in queste presenti <emph type="italics"/>Esperienze<emph.end type="italics"/> i dise&shy;<lb/>gni delle macchin&egrave; de'nostri Occhiali, de'quali principalmente ci servimmo <lb/>nell'anno 1660 all'osservazioni di Saturno, per esserci paruto che in essi <lb/>si ritrovi alcuna cosa di particolare e degna della curiosit&agrave; altrui, ci siamo <lb/>risoluti di aggiungere le tre precedenti figure, acci&ograve; ritrovandovi altri, per <lb/>accidente, alcuna cosa di buono, possa servirsene, volendo &rdquo; (MSS. Cim., <lb/>T. VII, c. </s>

<s>23). E prosegue a rilevar le utilit&agrave; e i comodi di cos&igrave; fatte mac&shy;<lb/>chine telescopiche, descrivendone particolarmente gli organi rappresentati in <lb/>disegno nelle tre figure citate, e impresse nelle Tavole IX, X e XI che s'al&shy;<lb/>legarono infine al Tomo II, P. II delle <emph type="italics"/>Notizie degli Aggrandimenti delle <lb/>Scienze Fisiche in Toscana,<emph.end type="italics"/> pubblicate, nel 1780, in Firenze dal Targioni <lb/>Tozzetti. </s></p><pb xlink:href="020/01/453.jpg"/><p type="main">

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

<s><emph type="center"/><emph type="bold"/>Del Barometro<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

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

<s>I. </s>

<s>Delle prime idee, che ebbero i Fisici intorno alla possibilit&agrave; e all esistenza dei vacuo, e delle loro <lb/>prime esperienze intorno al peso e alle pressioni dell'aria. </s>

<s>&mdash; II. </s>

<s>Della celebre esperienza del&shy;<lb/>l'argento vivo; delle esperienze del Pascal e di altri Francesi. </s>

<s>&mdash; III. </s>

<s>Come l'esperienza dell ar&shy;<lb/>gento vivo fosse, per unanime consenso degli stessi stranieri, attribuita al Torricelli. </s>

<s>&mdash; IV. </s>

<s>Delle <lb/>Lettere torricelliane sull'esperienza dell'argento vivo. </s>

<s>&mdash; V. </s>

<s>Come il Torricelli attendesse a co&shy;<lb/>struir lo strumento da misurar le variazioni del peso dell'aria, e come non gli riuscisse la sua <lb/>intenzione. </s>

<s>&mdash; VI. </s>

<s>Come e da chi lo strumento torricelliano dell'argento vivo fosse applicato <lb/>ad uso di Barometro. </s></p><p type="main">

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

<s>Cadere in pioggia dall'alto, penetrare il suolo e sott'esso scorrere in <lb/>sottilissime vene, ora inquinandosi di limo e ora chiarificandosi di nuovo; <lb/>risalire a un tratto in zampilli da un fesso, e di l&igrave; volgere in basso per tor&shy;<lb/>nare a nascondersi in canaletti coperti; poi uscire in rivi mormoreggianti <lb/>ed, aggiungendosi ad altri rivi, riversarsi insieme in un fiume, che sonante <lb/>e ondoso, fra il verde delle sue rive, s'affretta a scender nel mare; &egrave; la <lb/>continua vicenda con che si regola il corso dell'acque, e a loro simiglianza <lb/>altres&igrave; il corso delle idee. </s>

<s>Il tema che prendiamo ora a trattare, e che si <lb/>aggira intorno alla scienza del peso dell'aria e della natura del vuoto, offre, <lb/>di quel corso che naturalmente fanno le idee stesse, il pi&ugrave; notabile esempio. </s></p><p type="main">

<s>Che sia l'aria veramente un corpo; che ella occupi uno spazio deter&shy;<lb/>minato, rimossa dal quale, o per attrazione o per esservi fugata dagli av&shy;<lb/>versi ardori del fuoco, lo lasci di s&egrave; o d'altri visibili corpi affatto vuoto; lo <lb/>aveva gi&agrave; con sottili speculazioni insegnato e con numerose e variate espe&shy;<lb/>rienze dimostrato quel maestro antico della Fisica pneumatica, Herone Ales-<pb xlink:href="020/01/454.jpg" pagenum="435"/>sandrino. </s>

<s>Egli, addetto alla scuola di Platone, non dubit&ograve; di professar libe&shy;<lb/>ramente dottrine opposte a quelle di Aristotile, il qual negava la possibilit&agrave; <lb/>di ogni spazio vuoto. </s>

<s>Gli argomenti del Filosofo son celebri nella storia della <lb/>Meccanica, riducendosi a dire che, se il vacuo si d&agrave; veramente in natura, <lb/>non &egrave; possibile che nessun corpo si muova da luogo a luogo. </s>

<s>A un errore <lb/>cos&igrave; pernicioso erasi gi&agrave; contrapposto G. </s>

<s>Cesare Scaligero, il quale anzi prov&ograve; <lb/>che il vacuo &egrave; condizione essenziale e principio del moto. </s>

<s>&ldquo; In natura va&shy;<lb/>cuum dari necesse est. </s>

<s>Nempe, si non daretur, aut non esset motus, aut <lb/>subiret corpus in corpus. </s>

<s>Caeterum non sicut antiqui. </s>

<s>Illi enim ponebant <lb/>vacuum sine corpore. </s>

<s>At nos illud profitemur vacuum in quo corpus est. </s>

<s><lb/>Idemque esse vacuum et locum, neque differre nisi nomine. </s>

<s>Sane, si non <lb/>esset vacuum non esset locus. </s>

<s>Est enim vacuum spatium in quo est corpus, <lb/>cuius natura per se talis est ut, cedente corpore corpori, fiat vacuum ut <lb/>impleatur. </s>

<s>Est igitur vacuum principium motus &rdquo; (De Subtil., Francof. </s>

<s>1592, <lb/>pag. </s>

<s>15). </s></p><p type="main">

<s>Queste nuove dottrine per&ograve; dello Scaligero conferirono pi&ugrave; a sgombrare <lb/>i sentieri alla Meccanica, che non alla Fisica pneumatica. </s>

<s>Ma il Cardano fu <lb/>quegli che dette mano all'opera, e se Herone nel Proemio agli <emph type="italics"/>Spiritali<emph.end type="italics"/> in&shy;<lb/>segnava che, succhiando l'aria da un vaso, le labbra son tirate indietro dal <lb/>vacuo per riempirne il luogo, e se i Fisici dopo l'Alessandrino spiegarono <lb/>questo e altri simili fatti colla fuga o coll'orrore del vacuo; il Cardano nega <lb/>l'operar d'una forza inerente in un subietto che non esiste, e cerca di spie&shy;<lb/>gar quel medesimo fatto con un principio, che se non &egrave;, almeno ha l'ap&shy;<lb/>parenza di vero. </s>

<s>&ldquo; Ergo in universum tres erunt motus naturales. </s>

<s>Primus <lb/>quidem ac validissimus a vacui fuga, sed verius a forma elementi, cum ma&shy;<lb/>iorem raritatem non admittat, nec materiae partes separari numquam que&shy;<lb/>ant. </s>

<s>Cum igitur in follibus apertio maior est quam paucus ille aer ferre <lb/>possit, primum rarior redditur, cum materia prima separationem non admit&shy;<lb/>tat: aer ille non sustinens maiorem raritatem aut aliquid ad se trahit, aut <lb/>folles ommino disrumpit. </s>

<s>Non igitur a vacuo motus ullus, sed a formis ipsis, <lb/>maxime aeris, dum amplius divelli nequit nec separari, fieri consuevit &rdquo; (De <lb/>Subtilitate, Lugduni 1580, pag. </s>

<s>17, 18). </s></p><p type="main">

<s>Le idee dello Scaligero, che ammettevano l'esistenza del vuoto, e quelle <lb/>del Cardano che avevano dalla Pneumatica bandito il falso principio della <lb/>fuga del vacuo, s'andarono con rapido corso a congiungersi, come due soli&shy;<lb/>tarie vene in un rivo, nella mente di Bernardino Telesio. </s>

<s>I pensamenti di <lb/>lui furono dal suo concittadino Tommaso Cornelio, nella celebre Epistola <emph type="italics"/>De <lb/>circumpulsione platonica,<emph.end type="italics"/> commentati ed esposti al modo che segue: </s></p><p type="main">

<s>&ldquo; Bernardinus Telesius, singulari vir ingenio, ratus est posse in rarum <lb/>natura existere spatium omnis corporaee substantiae expers, atque adeo pror&shy;<lb/>sus inane: quamquam id non sine vi, conatuque aliquo fieri posse conten&shy;<lb/>dit. </s>

<s>Ait enim mundi corpora mutuo contactu gaudere, atque conniti ne in&shy;<lb/>vicem separentur seiunganturque, ac proinde quocumque corpus cesserit, <lb/>aliud illico subsequi ne scilicet contactu privetur. </s>

<s>Verum ubi vis nisusque <pb xlink:href="020/01/455.jpg" pagenum="436"/>validus contigua corpora separat, nec interea aliud corpus succederc datur, <lb/>cedere quidem, quamvis invita, spatiumque interiectum inane relinquere. </s>

<s>Ad&shy;<lb/>ducit autem assertionis suae testem experientiam siquidem e clepsydrarum <lb/>foraminibus, a quibus aqua non defluit, mel liquoresque alii graviores de&shy;<lb/>cidunt, pondere videlicet deorsum magno nisu premente &rdquo; (Neapoli, Rail&shy;<lb/>lard 1688, pag. </s>

<s>312). </s></p><p type="main">

<s>Chi prosegue a leggere quel che ivi soggiunge l'Autore s'accorge as&shy;<lb/>sai facilmente che egli vedeva nella Clessidra del Telesio una di quelle can&shy;<lb/>nncce di vetro chiuse di sopra e aperte in un piccolo foro di sotto da cui, <lb/>secondo l'esperienze fatte dagli Accademici del Cimento (Saggi di Nat. </s>

<s>esp., <lb/>Firenze 1841, pag. </s>

<s>37), <emph type="italics"/>tenute con la bocca volta allo ingi&ugrave;, e appese in <lb/>aria a piombo,<emph.end type="italics"/> se non fluisce l'acqua, fluisce per&ograve; il mercurio, infintantoch&egrave; <lb/>non sia sceso a far col suo premere equilibrio al premere esterno dell'aria. </s>

<s><lb/>Il Cornelio insomma vedeva nell'esperienza telesiana una immagine della <lb/>torricelliana, colla differenza del mele sostituito al mercurio. </s></p><p type="main">

<s>Comunque sia di ci&ograve;, corse ancora un mezzo secolo dai tempi del Te&shy;<lb/>lesio, e quella che pur si pu&ograve; anche da noi chiamare immagine disegnata <lb/>collo stile e dipinta coi colori del Filosofo Razionalista, prese aspetto di realt&agrave; <lb/>e colore di Fisica in alcune speculazioni del Keplero. </s>

<s>Finge egli starsenc <lb/>uno sopra i confini dell'aria nel puro etere o nel vuoto, e di l&igrave; versar den&shy;<lb/>tro un sifone da una parte aria e dall'altra acqua, e dice che un bicchiere <lb/>di questa farebbe equilibrio a 15 miriadi di miriadi di bicchieri di quella. <lb/></s>

<s>&ldquo; Nec dubium si quis in puro aethere consisteret, funderet hinc 1 cyathum <lb/>aquae inde quindecim myriadas myriadum cyathorum aeris, quin haec aequi&shy;<lb/>ponderatura sint.... Non ignoro, ne credas, me physicorum reprehensionem <lb/>incursurum, qui aerem et hic et antea gravem seu ponderosum esse sta&shy;<lb/>tuam. </s>

<s>At me sic docuit totius naturae contemplatio &rdquo; (Paralip. </s>

<s>ad Vitell., <lb/>Francof. </s>

<s>1604, pag. </s>

<s>128). </s></p><p type="main">

<s>Pochi anni dopo da che il Keplero scriveva cos&igrave; fatte parole, tenevasi <lb/>fra noi come cosa certa il peso dell'aria, senza tanta paura di riprensioni. </s>

<s><lb/>Galileo aveva gi&agrave;, con molto maggior precisione dell'Autore de'Paralipo&shy;<lb/>meni, ritrovato il peso specifico dell'aria, e a ci&ograve; fare usava tre varii modi. </s>

<s><lb/>Uno di questi, con lettera del d&igrave; 12 Marzo 1613 pubblicata in Pisa nel 1864 <lb/>dalla tipografia Nistri, ei lo insegnava a Giovan Batista Baliani, in cui, a <lb/>conferirgli il merito d'avere egli il primo accesa quella gran face di scienza, <lb/>che diffuse i suoi splendori per tutta l'Europa, concorsero insieme il caso <lb/>e l'ingegno come ora vedremo. </s></p><p type="main">

<s>Nell'ottavo libro dell'Architettura intitola Vitruvio il cap. </s>

<s>VII: <emph type="italics"/>Quot <lb/>modis ducantur aquae,<emph.end type="italics"/> e per via di condotti o metallici o murati insegna <lb/>come l'acque si posson fare scender da un monte e risalire al monte op&shy;<lb/>posto, attraversando la valle. </s>

<s>Or, non pensandosi che portasse differenza fra <lb/>il far salire l'acqua per impulsione o per attrazione, il Porta, nel Libro III <lb/>degli <emph type="italics"/>Spiritali,<emph.end type="italics"/> vuole al cap. </s>

<s>I insegnare <emph type="italics"/>Come si possano condurre i fiumi <lb/>dalle basse ralli per le altissime cime dei monti<emph.end type="italics"/> <gap/><pb xlink:href="020/01/456.jpg" pagenum="437"/>modo consiste nel far cavalcare il monte a un sifone, una delle bocche del <lb/>quale attinga dal fiume, quasi dovesse operare come i sifoni ordinarii, che <lb/>s'usan per travasare i liquidi o ne'servigi domestici, o nell'esercizio delle <lb/>arti. </s>

<s>Il Porta, non essendo stato sgannato dall'esperienza, si credeva sicuro <lb/>del fatto e lo dava come cosa certa. </s>

<s>Ma il Baliani, riconosciutane l'utilit&agrave;, <lb/>volle vederne l'esecuzione e trov&ograve; tutt'altrimenti, ed ebbe a osservar cose <lb/>che lo riempirono di stupore. </s>

<s>Non sapendo che si pensare, rivolsesi a Ga&shy;<lb/>lileo da Genova con lettera del d&igrave; 27 Luglio 1630, cos&igrave; esponendo il caso <lb/>e chiedendo consiglio: </s></p><p type="main">

<s>&ldquo; Ci conviene far che un'acqua di due once di diametro in circa tra&shy;<lb/>versi un monte, e per farlo conviene che l'acqua salisca a piombo 85 palmi <lb/>di Genova, che son circa 70 piedi geometrici: e per farlo abbiamo fatto un <lb/>sifone di rame conforme al disegno inchiuso, ove CA (fig. </s>

<s>42) &egrave; il livello: <lb/>A ove si piglia l'acqua, B ove ha da uscire, D l'imbottatoio per dove si <lb/>empie il sifone, DE <lb/><figure id="id.020.01.456.1.jpg" xlink:href="020/01/456/1.jpg"/></s></p><p type="caption">

<s>Figura 42.<lb/>l'altezza a piombo <lb/>che l'acqua ha da <lb/>salire. </s>

<s>Per&ograve; questo <lb/>sifone non fa l'ef&shy;<lb/>fetto desiderato, anzi <lb/>aperto, ancorch&egrave; <lb/>chiuso dal di sopra, <lb/>l'acqua esce da tutte <lb/>due le parti, e se si <lb/>tien chiuso da una parte, in aprendo dall'altra, ad ogni modo da questa esce <lb/>l'acqua. </s>

<s>Io non mi posso dar a credere che l'acqua abbia in questa occasione <lb/>voluto appartarsi dalle sue propriet&agrave; naturali, ond'&egrave; forza che uscendo l'acqua <lb/>vi sottentri aria dalla parte di sopra, per&ograve; non si vede di dove. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Avviene un'altra cosa che mi fa stupire, ed &egrave; che, aprendosi la <lb/>bocca A, esce l'acqua sin che dalla parte D sia scesa per la met&agrave; in circa <lb/>sino a F, e poi si ferma. </s>

<s>Io sono andato considerando se possa essere che <lb/>il canale o sifone abbia qualche pori, ma che l'acqua non possa passarvi, e <lb/>n&egrave; anche l'aria senza gran violenza, e perci&ograve; se il canale &egrave; pieno, l'acqua A <lb/>sia tanto premuta che faccia forza tale, che l'aria sottentri per li pori che <lb/>sono verso la parte di sopra, in modo che l'acqua possa scendere per esso <lb/>sino a F, senza che vi rimanga vacuo. </s>

<s>Scesa poi in F, non restando nel ca&shy;<lb/>nale altra acqua che la FA, questa non abbia forza di far violenza tale al&shy;<lb/>l'aria che possa sforzarla ad entrare per li pori suddetti.... Ho voluto nar&shy;<lb/>rare questa cosa, a fine che V. S. possa pi&ugrave; facilmente ritrovare in che <lb/>consista il mio errore, e favorire di avvertirmene &rdquo; (Alb. </s>

<s>IX, 195, 96). </s></p><p type="main">

<s>L'Alb&egrave;ri osserva a questo punto in nota che <emph type="italics"/>ci manca la responsiva <lb/>di Galileo,<emph.end type="italics"/> ma il Venturi, dop'aver nella Seconda Parte delle <emph type="italics"/>Memorie ine&shy;<lb/>dite<emph.end type="italics"/> riferito il sunto della missiva del Baliani da noi trascritto, asserisce <lb/>confidentemente, quasi avesse letto nel documento galileiano: &ldquo; Il Galileo <pb xlink:href="020/01/457.jpg" pagenum="438"/>avea risposto alla lettera precedente che l'altezza dell'acqua sospesa entro <lb/>il tubo era la misura dell'orrore che la natura ha contro il vacuo &rdquo; (Mo&shy;<lb/>dena 1821, pag. </s>

<s>103). </s></p><p type="main">

<s>L'asserto dell'Autore si capisce bene non esser che una ripetizione <lb/>della favolosa risposta data da Galileo ai fontanieri di Boboli, ma l'Alb&egrave;ri <lb/>pi&ugrave; saviamente avvertiva, che la verit&agrave; di quella risposta poteva argomen&shy;<lb/>tarsi dall'altra lettera, che sotto il d&igrave; 26 di Ottobre replicava il Baliani, la <lb/>quale, essendo stata veduta gi&agrave; e pubblicata in parte nel citato luogo dallo <lb/>stesso Venturi, porge un nuovo argomento fra i tanti della poco fina critica, <lb/>colla quale condusse il suo Lavoro. </s>

<s>Molto pi&ugrave; torto poi fa all'illustre Fisico <lb/>modanese quel suo temerario asserto, ripensando che poteva dal I Dialogo <lb/>delle Due Nuove Scienze ricavar con certezza a qual causa attribuisse Gali&shy;<lb/>leo il salir l'acqua attratta ne'tubi non pi&ugrave; su che a una determinata altezza. </s></p><p type="main">

<s>Comunque sia, la lettera di risposta al quesito del Baliani, ignota al Ven&shy;<lb/>turi e all'Alb&egrave;ri, venne poi alla luce in Pisa nel 1864 dalla Tipografia Ni&shy;<lb/>stri. </s>

<s>In quella lettera, che &egrave; del d&igrave; 6 Agosto 1630, Galileo rispondeva cos&igrave; <lb/>in proposito al postulante: &ldquo; Mi dispiace bene che ella mi abbia domandato <lb/>il mio parere circa l'esito del sifone, prima che la spesa fosse stata fatta, <lb/>perch&egrave; gliel'avrei potuta risparmiare col mostrare, s'io non m'inganno, l'im&shy;<lb/>possibilit&agrave; del quesito, la quale dipende da un mio problema pi&ugrave; tempo fa <lb/>esaminato e che veramente ha del maraviglioso assai &rdquo; (Lettere di Galileo <lb/>pubblicate per la prima volta pel suo Trecentes. </s>

<s>natalizio in Pisa, XVIII Feb&shy;<lb/>braio M.DCCC.LXIV, Tip. </s>

<s>Nistri, 1864, pag. </s>

<s>26). </s></p><p type="main">

<s>Il maraviglioso problema, da cui faceva Galileo dipendere la causa del <lb/>sostenersi l'acqua nel tubo non pi&ugrave; su che a quella altezza osservata dal <lb/>Baliani, era, secondo che seguita ivi a dire lo stesso Galileo, il problema mec&shy;<lb/>canico della resistenza de'solidi allo spezzarsi, paragonando un cilindro d'acqua <lb/>a una corda o a una verga, la quale tirata gi&ugrave; dal suo soverchio peso final&shy;<lb/>mente si strappa. </s></p><p type="main">

<s>Ricevuta una tal risposta, il Baliani ringrazia, riconosce di non aver <lb/>saputo far distinzione fra il salir dell'acqua per attrazione o per impulso, <lb/>approva il ricorrere ingegnosamente al problema meccanico della resistenza <lb/>de solidi allo spezzarsi, per ispiegare il fatto maraviglioso, ma pur libera&shy;<lb/>mente confessa che non valgon cos&igrave; fatte ragioni a toglierli via tutti i dubbi. </s>

<s><lb/>In quel tempo ch'egli attendeva la risposta di Galileo non si rimase dallo <lb/>specular da s&egrave;, e sagacemente ne indovin&ograve; il vero. </s>

<s>Se l'aria &egrave; pesa, ragio&shy;<lb/>nava l'arguto Genovese, l'acqua dee esser sostenuta a quell'altezza nel tubo <lb/>dal premere esteriormente dell'aria stessa, e tale &egrave; la misura della forza che <lb/>si richiede a causare il vacuo. </s>

<s>Il ragionamento &egrave; cos&igrave; sottile, cos&igrave; la splen&shy;<lb/>dida face del vero conduceva il Filosofo per quelle inesplorate sottigliezze, <lb/>che i principii della celebrata Scienza torricelliana, concludonsi nelle seguenti <lb/>parole, scritte il d&igrave; 26 Ottobre 1630 da Genova in una lettera a Galileo: </s></p><p type="main">

<s>&ldquo; Io non sono gi&agrave; della opinione volgare che non si dia vacuo; per&ograve; <lb/>nen mi <gap/>otei dar a credere che si desse il vacuo in tanta <gap/><pb xlink:href="020/01/458.jpg" pagenum="439"/>facilmente. </s>

<s>E per non mancar di dirle la mia opinione intorno a ci&ograve;, io ho <lb/>creduto che naturalmente il vacuo si dia, da quel tempo che io ritrovai <lb/>che l'aria ha peso sensibile, e che V. S. m'insegn&ograve; in una sua lettera il <lb/>modo di ritrovarne il peso esatto, ancorch&egrave; non mi sia riuscito fin ora il <lb/>farne esperienza. </s>

<s>Io dunque allora formai questo concetto, che non sia vero <lb/>che repugni alla natura delle cose che si dia vacuo, ma ben che sia diffi&shy;<lb/>cile ch'esso si dia, e che non si possa dar senza gran violenza, e che si <lb/>possa ritrovar quanta debba essere questa tal violenza, che si richiede per <lb/>darsi vacuo. </s>

<s>E per dichiararmi meglio, essendo che se l'aria pesa non sia <lb/>differenza fra l'aria e l'acqua che nel pi&ugrave; e nel meno, &egrave; meglio parlar del&shy;<lb/>l'acqua, il cui peso &egrave; pi&ugrave; sensibile, perch&egrave; poi lo stesso dovr&agrave; avvenire <lb/>dell'aria. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io mi figuro dunque di essere nel fondo del mare, ove sta l'acqua <lb/>profonda dieci mila piedi, e se non fosse il bisogno di rifiatare, io credo che <lb/>vi starei, sebbene mi sentirei pi&ugrave; compresso e premuto da ogni parte di quel <lb/>ch'io mi sia di presente: e perci&ograve; io credo che non potrei star nel fondo <lb/>di qualsivoglia profondit&agrave; d'acqua, la quale, crescendo in infinito, cresce&shy;<lb/>rebbe per mio avviso tal compressione in modo, che le mie membra non <lb/>vi potrebbon resistere. </s>

<s>Ma per ritornare, dalla detta compressione in fuori, <lb/>io non sentirei altro travaglio, n&egrave; sentirei maggiormente il peso dell'acqua <lb/>di quel ch'io mi faccia, quando, entrando sotto acqua la state bagnandomi <lb/>nel mare, io ho dieci piedi d'acqua sul capo, senza che io ne senta il peso. </s>

<s><lb/>Ma se io non fossi entro l'acqua, che mi preme da ogni parte, e fussi, non <lb/>dico in vacuo, ma nell'aria e che dalla mia testa in su vi fosse l'acqua, al&shy;<lb/>lora io sentirei un peso, ch'io non potrei sostenere che quando avessi forza <lb/>a lui proporzionata; in modo che, ancorch&egrave; separando io violentemente le <lb/>parti superiori dell'acqua dalle inferiori, non vi rimanesse vacuo, ma vi su&shy;<lb/>bentrasse aria, ad ogni modo vi vorrebbe forza a seperarle, per&ograve; non infi&shy;<lb/>nita ma determinata, e via via maggiore secondo che la profondit&agrave; dell'acqua, <lb/>sotto la quale io fossi, fosse maggiore; la quale non vi ha dubbio che chi <lb/>fusse nel fondo detto di sopra di dieci mila piedi d'acqua, stimerebbe impos&shy;<lb/>sibile far detta separazione con qualunque forza, come che egli mai non ne <lb/>farebbe la prova; eppur si vede che non sarebbe vero che fosse impossibile, <lb/>ma che l'impedimento gli verrebbe da non aver lui tanta forza da poter <lb/>far all'acqua una tal violenza, che fusse bastante a separarla. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Lo stesso mi &egrave; avviso che ci avvenga nell'aria, che siamo nel fondo <lb/>della sua immensit&agrave;, n&egrave; sentiamo n&egrave; il suo peso n&egrave; la compressione che ci <lb/>fa da ogni parte, perch&egrave; il nostro corpo &egrave; stato fatto da Dio di tal qualit&agrave;, <lb/>che possa resistere benissimo a questa compressione senza sentirne offesa, <lb/>anzi ci &egrave; per avventura necessaria n&egrave; senza di lei si potrebbe stare; onde <lb/>io credo che, ancorch&egrave; non avessimo a respirare, non potremmo stare nel <lb/>vacuo, ma se fossimo nel vacuo allora si sentirebbe il peso dell'aria che <lb/>avessimo sopra il capo, il quale io credo grandissimo, perch&egrave;, ancorch&egrave; io <lb/>stimi che quanto l'aria &egrave; pi&ugrave; alta sia sempre pi&ugrave; leggera, io credo che s&igrave;a <pb xlink:href="020/01/459.jpg" pagenum="440"/>tanta la sua immensit&agrave;, che, per poco che sia il suo peso, conviene che si <lb/>sentisse quel di tutta l'aria che ci sta sopra, peso molto grande ma non <lb/>infinito, e perci&ograve; determinato, e che con forza a lui proporzionata si possa <lb/>superare, e perci&ograve; causarsi il vacuo. </s>

<s>Chi volesse ritrovar questa proporzione, <lb/>converrebbe che si sapesse l'altezza dell'aria e il suo peso in qualunque al&shy;<lb/>tezza. </s>

<s>Ma comunque sia, io veramente lo giudicava tale che per causar va&shy;<lb/>cuo, io credeva che vi si richiedesse maggior violenza di quello che pu&ograve; far <lb/>l'acqua nel canale non pi&ugrave; lungo di 80 piedi &rdquo; (Alb. </s>

<s>IX, 211-13). </s></p><p type="main">

<s>Il Baliani che teme di aver noiato Galileo <emph type="italics"/>con s&igrave; lunga diceria<emph.end type="italics"/> e se ne <lb/>scusa, lascia di far l'applicazione di queste sue dottrine al fatto particolare <lb/>dell'acqua sostenuta dentro il tubo o sifone di rame; applicazione che dal&shy;<lb/>l'altra parte risulta chiarissima, e che pu&ograve; concludersi in brevi parole: <lb/>L'acqua che dalla parte F (figura precedente) termina col vuoto sente dal&shy;<lb/>l'opposta parte A il peso dell'altezza dell'aria come noi la sentiremmo sul <lb/>capo nostro se, dalle spalle in gi&ugrave; fossimo costituiti nel vuoto, e da quel <lb/>peso vien l'acqua stessa sostenuta e proibita di scendere al basso. </s>

<s>Aprendo <lb/>l'imbottatoio D, e di l&igrave; riempiutosi d'aria lo spazio DF, la colonna acquea <lb/>non sente pi&ugrave; quel peso, come noi non lo sentiamo quando l'aria ci cir&shy;<lb/>conda e ci preme per ogni parte, e perci&ograve; cade e fluisce liberamente dalla <lb/>bocca A, non per altro impulso che della sua propria gravezza. </s>

<s>Insomma, <lb/>la pressione fatta in A dalla colonna d'acqua FA uguale alla pressione fatta <lb/>in H dalla colonna perpendicolare FH, era per il Baliani forza proporzionata <lb/>a superare il peso dell'aria e perci&ograve; a causare il vuoto; forza che dice po&shy;<lb/>trebbesi calcolare esattamente, quando si sapesse <emph type="italics"/>l'altezza dell'aria e il suo <lb/>peso in qualunque altezza.<emph.end type="italics"/></s></p><p type="main">

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

<s><emph type="italics"/>Se questa dottrina &egrave; vera,<emph.end type="italics"/> soggiunge ivi il Baliani a Galileo, <emph type="italics"/>so che <lb/>l'avr&agrave; speculata prima:<emph.end type="italics"/> e pur troppo la dottrina del Baliani era vera, ma <lb/>Galileo sventuratamente non l'avea speculata. </s>

<s>Quand'egli osserv&ograve; nella ci&shy;<lb/>terna che le pompe non attraevan l'acqua pi&ugrave; su che alle diciotto braccia, <lb/>aveva nella dottrina del Fisico genovese la ragione vera del fatto, onde potea <lb/>concluderne che il peso di una corda d'acqua lunga diciotto braccia &egrave; forza <lb/>proporzionata a vincere il vacuo, ossia a far contrappeso al premere dell'al&shy;<lb/>tezza dell'aria. </s></p><p type="main">

<s>Ma Galileo tutt'altro che progredire cos&igrave; nelle sue speculazioni, misera&shy;<lb/>mente invece indietreggiava. </s>

<s>Il Cardano aveva tentato di bandir dalla scienza <lb/>quel paralogismo della forza del vacuo, e il Baliani aveva ritrovato di quella <lb/>stessa forza la causa vera, mentre Galileo torna indietro ad appiccar il filo <lb/>delle idee agli ami insidiosi di quel paralogismo. </s>

<s>Rifiutato il felice pensiero <lb/>che gli balen&ograve; alla mente nelle sue prime speculazioni intorno alle forze mo-<pb xlink:href="020/01/460.jpg" pagenum="441"/>lecolari, il pensiero cio&egrave; di attribuire la coesione a una specie d'attrazion <lb/>magnetica, si volse a professar il principio che la forza del vacuo sia l'unico <lb/>glutine, e per se solo sufficiente a tenere insieme compaginati i corpi. </s>

<s>Am&shy;<lb/>mette, com'ammetteva il Telesio e tanti altri, che una tal forza di vacuo <lb/>sia superabile; che ella possa di pi&ugrave; anco misurarsi, e che ne sian perci&ograve; <lb/>natural misura le corde di canapa e le verghe di metallo, quando finalmente <lb/>si strappano aggravate o tirate da soverchio peso. </s>

<s>Da questo effetto mecca&shy;<lb/>nico faceva Galileo, nel 1630, dipender la causa del sostenersi l'acqua nel <lb/>sifone di rame preparato dal Baliani, e da questo effetto meccanico, nono&shy;<lb/>stante le belle speculazioni suggeritegli dallo stesso Baliani, nel 1638, nel <lb/>primo Dialogo delle Due Nuove Scienze, faceva pure dipendere il non risa&shy;<lb/>lir l'acqua nelle trombe pi&ugrave; su che alle diciotto braccia. </s>

<s>&ldquo; Ed io sin ora <lb/>sono stato cos&igrave; poco accorto che intendendo che una corda, una mazza di <lb/>legno, o una verga di ferro si pu&ograve; tanto e tanto allungare che finalmente <lb/>il suo proprio peso la strappi tenendola attaccata in alto, non mi &egrave; sovve&shy;<lb/>nuto che l'istesso molto pi&ugrave; agevolmente accader&agrave; di una corda o verga di <lb/>acqua. </s>

<s>E che altro &egrave; quello che si attrae nella tromba che un cilindro di <lb/>acqua, il quale, avendo la sua attaccatura di sopra, allungato pi&ugrave; e pi&ugrave;, final&shy;<lb/>mente arriva a quel termine, oltre al quale, tirato dal suo gi&agrave; fatto sover&shy;<lb/>chio peso, non altrimenti che se fosse una corda si strappa? </s>

<s>&rdquo; (Alb. </s>

<s>XIII, 21). </s></p><p type="main">

<s>Essendo la forza del vacuo proporzionale alla superficie di contatto e, <lb/>ne'cilindri d'ugual materia e di uguale altezza, essendo i pesi proporzionali <lb/>alle basi, spiegava cos&igrave; Galileo come al salir dell'acqua nelle trombe fosse <lb/>in tutti casi prefinita la medesima misura, o sian le stesse trombe <emph type="italics"/>larghis&shy;<lb/>sime o strette o strettissime quanto un filo di paglia<emph.end type="italics"/> (ivi). </s></p><p type="main">

<s>Dir queste cose in uno de'Dialoghi galileiani Del Moto era un porre la <lb/>face sul candelabro; avventurata la scienza se fosse stata quella luce per <lb/>ogni parte sincera! Ma nonostante che fosse alquanto filigginosa giov&ograve; ri&shy;<lb/>splendendo cos&igrave; dall'alto, e giov&ograve; perch&egrave; insorsero i Peripatetici a reclamare <lb/>contro una dottrina, la quale, non solamente ammetteva il vacuo, ma ne in&shy;<lb/>segnava il modo di misurarne la forza. </s>

<s>Reclamavano i Filosofi peripatetici <lb/>perch&egrave; quella nuova dottrina contradiceva agl'insegnamenti di Aristotile; re&shy;<lb/>clamavano i Teologi peripatetici, perch&egrave; contradire all'autorit&agrave; di Aristotile, <lb/>era quasi come un contradire all'autorit&agrave; stessa di Dio, in mano a cui te&shy;<lb/>mevano che, dandosi il vacuo, si dovesse dissolvere l'Universo. </s></p><p type="main">

<s>Bisognava dunque a que'Filosofi e a que'Teologi dimostrare che lo spa&shy;<lb/>zio lasciatosi dietro dall'acqua nelle trombe pi&ugrave; lunghe delle diciotto brac&shy;<lb/>cia, non era, com'insegnava Galileo, uno spazio vuoto. </s>

<s>Si dettero mano <lb/>insieme a tentar l'opera in Roma un solenne Filosofo e un Teologo peri&shy;<lb/>patetico solenne, Gaspero Berti e Atanasio Kircher, e mostrarono in con&shy;<lb/>durla, maggior acume di quel che non ci saremmo potuti aspettare. </s>

<s>Il par&shy;<lb/>ticolar modo poi come l'ingegnosa opera fu condotta, ci vien narrato dal <lb/>padre Gaspero Schott, nella sua <emph type="italics"/>Mechanica hydraulico-pneumatica,<emph.end type="italics"/> e a lui <lb/>prestiamo volentieri fede, perch&egrave; dice di avere attinta la storia del fatto <pb xlink:href="020/01/461.jpg" pagenum="442"/>dalla bocca dello stesso Raffaello Magiotti, che &egrave; per noi il giudice e il te&shy;<lb/>stimone pi&ugrave; autorevole che possa desiderarsi, s&igrave; per le relazioni che egli <lb/>ebbe poi intorno a tal soggetto col Torricelli, e s&igrave; per essere stato spettatore <lb/>al pubblico sperimento del Berti. </s></p><p type="main">

<s>Dop'avere ivi accennato alla dottrina professata da coloro, che ammet&shy;<lb/><figure id="id.020.01.461.1.jpg" xlink:href="020/01/461/1.jpg"/></s></p><p type="caption">

<s>Figura 43.<lb/>tevano l'esistenza del vacuo, dottrina che &egrave; secondo lo <lb/>Schott <emph type="italics"/>non tantum in Philosophia absurda, sed et in <lb/>fide orthodoxa periculosa,<emph.end type="italics"/> soggiunge: &ldquo; Alii tamen me&shy;<lb/>lioris notae Philosophi negant in praedicto tubi spatio esse <lb/>vere vacuum, idque variis probant rationibus atque expe&shy;<lb/>rimentis. </s>

<s>Omnium pulcherrimum ingeniosissimumque vi&shy;<lb/>detur esse istud, quod, suadente p. </s>

<s>Athanasio Kirchero, <lb/>exhibuit Romae Gaspar Bertus romanus, vir nobilis, et in <lb/>physicis mathematicisque solide doctus, singularisque in <lb/>experimentis capiendis solertiae.... Is cum audisset non&shy;<lb/>nullos .... probare dari vacuum, saltem ad breve tempus, <lb/>inter corpora, quod aqua intra tubos ultra certam men&shy;<lb/>suram elevata sisti non posset.... tubum in maiori multo <lb/>quam illi exposcerent longitudine, plumbeum erexit in <lb/>aedibus suis. </s>

<s>Centum is pedum erat in longitudine, et <lb/>digiti crassitudine ad supremum domus solarium pertin&shy;<lb/>gens, ea forma, quam altera supra posita figura DKL <lb/>(fig. </s>

<s>43) monstrat. </s>

<s>In superiori huius tubi extremo .... <lb/>phialam primo aeream deinde vitream insignis crassitudinis <lb/>et studio in hunc finem conflatam imposuit, tali industria <lb/>a tubi collo coagmentatam, talique ingenio munitam, ut <lb/>omnis aeri esset ad eum interclusus aditus. </s>

<s>Intra vero <lb/>phialam, suggerente Kirchero, campanulam C, una cum <lb/>ferreo malleolo O lateribus phialae ea dexteritate inseruit, <lb/>ut malleolus ferreus magnete A ab extra attractus eleva&shy;<lb/>tusque et mox a magnete retracto, liber, proprio pondere <lb/>campanulae illideretur ac sonum ederet. </s>

<s>Inferiorem vero <lb/>tubi partem epistomio seu aenea clavi volubili munivit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Comparatis omnibus ad experimentum capiendum <lb/>requisitis, tubi extremum orificium espistomio G munitum, <lb/>dolio MIKL aqua semiplenum immersit, totumque tubum <lb/>una cum phiala replevit aquis, facto in phialae vertice <lb/>foramine, quod postmodum diligentissime clausum sin&shy;<lb/>gulari arte stamno solidavit. </s>

<s>Tum unco ferreo epistomium <lb/>G aperiut, viamque fecit aquae tubi ut libera posset ex <lb/>illo in subiectum vas defluere. </s>

<s>Et vero, ut assurgens in vase subiecto aqua <lb/>indicavit, defluxit quantum decem circiter pedes tubi ante replebat, reli&shy;<lb/>quum intra tubum perstitit, patente licet ad multum tempus eadem via, <lb/>quae postea revoluta clavi, iterum conclusa est. </s>

<s>Tum vero admoto magnete <pb xlink:href="020/01/462.jpg" pagenum="443"/>ad superiorem phialam vitream e regione malleoli ferrei, malleolus allectus, <lb/>et remoto, dimissus est, a quo percussa campanula limpidissimum edidit so&shy;<lb/>num, ab omnibus experimento spectatoribus auditum. </s>

<s>Sic tubo utrinque <lb/>probe clauso per noctem relicto, mane clavi aenea iterum convoluta, iterum <lb/>aperta est aquae via. </s>

<s>Verum non solum nihil amplius ex ea dimisit tubus, <lb/>sed ex pridie dimissa resorbuit. </s>

<s>Iteratum coram viris eruditis experimentum <lb/>fuit saepius, eodem semper successu, quos inter fuit Raphael Magiottus ma&shy;<lb/>thematicus doctissimus a quo totam rei seriem oretenus intellexi &rdquo; (Herbi&shy;<lb/>poli, 1657, pag. </s>

<s>307-9). </s></p><p type="main">

<s>Cos&igrave; l'esperimento del Berti veniva a rassicurare i Peripatetici che lo <lb/>spazio lasciatosi indietro dall'acqua ne'tubi non era altrimenti vuoto, ma <lb/>che doveva esser ripieno di qualche mezzo, attraverso al quale si potessero <lb/>diffondere i tremori del suono. </s></p><p type="main">

<s>Si riposavan quieti i militanti per l'onor di Aristotile e lieti della vit&shy;<lb/>toria riportata in Roma su Galileo, quando da Firenze, in sull'entrar del&shy;<lb/>l'anno 1644 si leva un rumore a commovere il mondo, come romba di ura&shy;<lb/>gano che muova ad assalir le tende sotto cui in pace alloggiavasi il Peripato. </s>

<s><lb/>Il Mersenno ha ricevuto in Parigi da Michelangiolo Ricci alcune lettere scit&shy;<lb/>tegli dal Torricelli, nelle quali descriveva allo stesso Ricci un'esperienza <lb/>nuovamente da s&egrave; fatta, esperienza che consisteva nel prendere un lungo <lb/>tubo di vetro empierlo di mercurio, turarlo col dito, capovolgerlo in una ca&shy;<lb/>tinella pur essa piena di mercurio e osservar lo spettacolo del pesante fluido <lb/>che, libero di uscir dal foro aperto, ritiratosi il dito, nonostante, per un <lb/>braccio e un quarto, ivi dentro restava sospeso. </s>

<s>Il Mersenno frugato da quella <lb/>sua natural curiosit&agrave; viene a Firenze in cerca del Torricelli, <emph type="italics"/>qui Tubum <lb/>observatorium,<emph.end type="italics"/> egli stesso scrive, nel III Tomo delle Nuove osservazioni, <lb/><emph type="italics"/>mihi anno 1644 ostendit in Magni ducis Etruriae pergulis admirandis.<emph.end type="italics"/><lb/>(Parisiis 1647, pag. </s>

<s>216). </s></p><p type="main">

<s>Sulla fine dell'anno dopo (1645) tornato in Francia divulg&ograve; ne'suoi <lb/>connazionali ci&ograve; che aveva sentito dire e veduto co'suoi proprii occhi in Ita&shy;<lb/>lia. </s>

<s>&ldquo; Neque tamen (soggiunge il Roberval nella celebre lettera <emph type="italics"/>De vacuo<emph.end type="italics"/><lb/>ad D. Des-Noyers, ristampata in fine alla <emph type="italics"/>Demonstratio<emph.end type="italics"/> di Valeriano Ma&shy;<lb/>gno) neque tamen eo anno aut sequenti tubos aptos Parisiis recuperare po&shy;<lb/>tuit, tum quia ibi tales non fabricantur, tum etiam quia ipsa toto ferme eo <lb/>tempore per meridionales Regni gallici partes peregrinatus est. </s>

<s>Tandem ergo <lb/>idem scripsit Rotomagium ad amicos suos. </s>

<s>Ibi enim celeberrima habetur <lb/>vitri et chrystalli officina. </s>

<s>Sed antequam is inde tubos haberet vulgatum fue&shy;<lb/>rat et ibidem experimentum et plurimis modis, tum privatim coram ami&shy;<lb/>cos, tum publice coram omnibus eruditis multoties exhibitum a nobiliss. </s>

<s>viro <lb/>Domino De Paschal mense Januario et Februario huius anni (1647). Neque <lb/>id solum beneficio hydrargirii, tubis minoribus, puta 3 aut 4, aut 5 pedum <lb/>regiorum mensurae nostrae, sed, quod mirandum multis videbatur, benefi&shy;<lb/>cio aquae et vini in tubis 40 pedum ex chrystallo mira arte fabricatis, atque <lb/><gap/> ad id paratis ita libratum erat, ut <pb xlink:href="020/01/463.jpg" pagenum="444"/>et attolli et deprimi ad usum requisitum facile posset &rdquo; (Venetiis Herz. </s>

<s>1649, <lb/>pag. </s>

<s>31, 32). </s></p><p type="main">

<s>Prosegue il Roberval in questa sua importantissima storia a dipinger <lb/>con vivi colori il Pascal tutto acceso in filosofico zelo di diffonder la verit&agrave;, <lb/>e infaticabile in persuadere i perfidi Peripatetici coll'eloquenza delle ragioni <lb/>e colle prove pi&ugrave; decisive dei fatti. </s>

<s>Gli opponevano che lo spazio da lui pre&shy;<lb/>dicato per vuoto era pieno d'invisibili esalazioni, e di spiriti. </s>

<s>E il Pascal: <lb/>&mdash; Che ne dite, esaler&agrave; pi&ugrave; di spirito dal vino o dall'acqua? </s>

<s>&mdash; e rispon&shy;<lb/>devano dal vino. </s>

<s>&mdash; Dunque il vino &mdash; proseguiva l'Apostolo di Roano &mdash; <lb/>dovrebbe lasciar dietro a s&egrave; maggior vuoto? </s>

<s>&mdash; S&igrave;. </s>

<s>&mdash; Ma eseguito l'espe&shy;<lb/>rimento, con tubi lunghi sospesi agli alberi delle navi, faceva veder col fatto <lb/>che avveniva tutto al contrario. </s></p><p type="main">

<s>Non contento alla viva voce, il Pascal si volle far banditore del vero <lb/>con gli scritti, pubblicando in Parigi un libretto col titolo <emph type="italics"/>Experiences <lb/>nouvelles touchant le vuide.<emph.end type="italics"/> La gran diffusione che ebbe in Francia, in <lb/>Svezia, in Olanda, in Polonia, in Alemagna e in Italia lo rese rarissimo, <lb/>per cui ne rimase pi&ugrave; ferma la notizia appresso i dotti in un altro li&shy;<lb/>bretto stampato l'anno dopo, pur esso in Parigi, da Stefano N&ouml;el col titolo <lb/><emph type="italics"/>Le plein du vuide<emph.end type="italics"/> e tradotto in quello stesso anno 1648 dall'Autore in <lb/>latino. </s></p><p type="main">

<s>Il N&ouml;el per&ograve; era gesuita e perci&ograve; peripatetico e non pubblicava le otto <lb/>esperienze del Pascal per altro fine, che per impugnarne la conclusione. </s>

<s><lb/>Chi nonostante legge sente che le parole del Gesuita son come soffio di <lb/>vento ne'carboni accesi, i quali levando pi&ugrave; che mai viva la fiamma fanno <lb/>a quello splendore riconoscer meglio e apprezzar l'ingegno del Pascal, che <lb/>variando i tubi di vetro in sifoni, in siringhe, in soffietti, riesce a dimo&shy;<lb/>strare il medesimo vero, com'abile musico che sa cavar da nobile o da rozzo <lb/>strumento la medesima dolce armonia. </s></p><p type="main">

<s>Tanta dovizia di scienza o diciam meglio di arte sperimentale era nel <lb/>Pascal inspirata da una voce che <emph type="italics"/>l'apprit<emph.end type="italics"/> (dice l'Autor della Prefazione al <lb/>Trattato postumo <emph type="italics"/>De l'equilibre des liqueurs<emph.end type="italics"/> dello stesso Pascal) <emph type="italics"/>de monsieur <lb/>Petit Intendant des Fortifications, et tres habile dans ces sortes de scien&shy;<lb/>ces, qui l'avoit apprise du P. Mersenne,<emph.end type="italics"/> e la voce sparsa dal Mersenne era <lb/>che il Torricelli aveva fatta l'esperienza dell'argento vivo per dimostrare il <lb/>vuoto. </s>

<s>Se il Torricelli stesso avesse scritto nulla in proposito o quel che <lb/>avesse scritto, il Pascal lo ignorava, per cui, seguitando a tener dietro alle <lb/>voci sparse, <emph type="italics"/>cette mesme ann&eacute;e 1647,<emph.end type="italics"/> dice l'Autor della citata Prefazione, <lb/><emph type="italics"/>fut avertis d'une pens&eacute;e qu'avoit eue Torricelli que l'air estoit pesant, et <lb/>que sa pesanteur pouvoit estre le cause de tous les effets qu'on avoit jus&shy;<lb/>qu'a lors attribuez &agrave; l'horreur du vuide. </s>

<s>Il trouva cette pens&eacute;e tout a fait <lb/>belle; mais comme ce n'estoit qu'une simple coniecture et dont on n'avoit <lb/>aucune preuve, pour en connoistre ou la verit&eacute; ou la fausset&eacute;, il fit plu&shy;<lb/>sieurs experiences. </s>

<s>L'une des plus considerables fut celle du vuide dans <lb/>le vuide.<emph.end type="italics"/> (Paris 1663). </s></p><pb xlink:href="020/01/464.jpg" pagenum="445"/><p type="main">

<s>L'esperienza bellissima del vuoto nel vuoto, fatta ne'primi di Novem&shy;<lb/>bre del 1647 alla presenza di Monsieur Perier, leggesi descritta dallo stesso <lb/>Pascal in calce al citato <emph type="italics"/>Traitez de l'equilibre des liqueurs.<emph.end type="italics"/> Essa dall'altra <lb/>parte &egrave; cos&igrave; semplice che basta rivolger l'attenzione alla qui apposta figura 44, <lb/>nella quale &egrave; trasformato il Tubo torricelliano ordinario. <lb/><figure id="id.020.01.464.1.jpg" xlink:href="020/01/464/1.jpg"/></s></p><p type="caption">

<s>Figura 44.<lb/>Riempito allo stesso modo e capovolto, parte del mer&shy;<lb/>curio rimane nel tubo MN alla solita altezza, e parte <lb/>rimane nella scodella B. Rotta, coll'unghie, la codetta M di <lb/>vetro che sigillava la parte superiore di quello stesso tubo, <lb/>a un tratto il mercurio MN precipita nella catinella N, e <lb/>quello della scodella B risale violentemente a riempire <lb/>il tubo AB. </s></p><p type="main">

<s>&ldquo; Mais cette experience, per ripigliar la storia in&shy;<lb/>terrotta del nostro Autore, ne le satisfaisant pas encore <lb/>enti&egrave;rement, il medita d&egrave;s la fin de cette mesme an&shy;<lb/>n&eacute;e 1647 l'experience celebre qui fut faite en 1648 au <lb/>haut, et au bas d'une montagne d'Auvergne appellee le <lb/>Puy de Domme. </s>

<s>&rdquo; </s></p><p type="main">

<s>Argomentava, con sottile e splendido concetto il Pa&shy;<lb/>scal, che se l'argento vivo sostentavasi nel cannello di <lb/>vetro per la pressione dell'aria, come il Torricelli diceva, l'altezza del livello <lb/>doveva riscontrarsi varia a pi&egrave; e in cima della montagna. </s>

<s>Confidato il pen&shy;<lb/>siero al Perier, ei fu che lo mand&ograve; con grande amore ad effetto, e delle <lb/>cose osservate ne distese una Relazione col titolo <emph type="italics"/>Recit de la grande Expe&shy;<lb/>rience du Puy de Domme.<emph.end type="italics"/> Fu fatto cos&igrave; noto al pubblico, per questa Rela&shy;<lb/>zione, come i fatti rispondessero puntualmente ai concetti del Pascal, e <lb/>confermassero le ragioni del Torricelli. </s></p><p type="main">

<s>&ldquo; Qu'en l'experience faite au plus bas lieu le vif argent r&egrave;stoit &agrave; la <lb/>hauteur de 26 poulces 3 lignes et demie. </s>

<s>En celle qui &agrave; est&eacute; faite en un <lb/>lieu &eacute;lev&eacute; au dessus du plus bas d'environ sept toises, le vif argent est rest&eacute; <lb/>a la hauteur de 26 poulces, 3 lignes.... &rdquo; (Traites de l'Equilib., Paris 1663, <lb/>pag. </s>

<s>185). E prosegue a riferir via via le misure sempre pi&ugrave; basse ritrovate <lb/>nel livello del mercurio nel tubo, secondo che pi&ugrave; e pi&ugrave; s'ascendeva in alto, <lb/>cosicch&egrave; alla massima altezza di 500 tese <emph type="italics"/>le vif argent s'est trouve &agrave; la <lb/>hauter de'23 poulces, deux lignes<emph.end type="italics"/> (ivi, pag. </s>

<s>186). </s></p><p type="main">

<s>Questa esperienza, che si appell&ograve; meritamente col nome di <emph type="italics"/>grande,<emph.end type="italics"/> fu <lb/>confermata dallo stesso Pascal con quell'altra del manticetto che si pu&ograve;, con <lb/>non minor ragione chiamare <emph type="italics"/>elegante;<emph.end type="italics"/> esperienza, la quale, tanto piacque al <lb/>Royle, che volle ripeterla, e descriverla con le seguenti parole: &ldquo; Alterum <lb/>quod in hypothesis nostrae confirmationem adducam, est experimentum il&shy;<lb/>lud,.... ab eodem Domino Paschalio factum, Harpastum scilicet languide <lb/>inflatum ab montis radice ad eius verticem portandi. </s>

<s>Id quippe magis, ma&shy;<lb/>gisque turgescebat, quo altius portabatur, adeo ut penitus quasi tensum in <lb/><gap/> gradatim vero rursum flaccesceret prout deorsum <pb xlink:href="020/01/465.jpg" pagenum="446"/>ferebatur, essetque ad imum montis aeque flaccidum ac prius &rdquo; (Op. </s>

<s>Omn., <lb/>Venetiis 1697, T. I, pag. </s>

<s>163). </s></p><p type="main">

<s>A confermare il gran concetto del Torricelli coll'esperienza, sorsero in <lb/>Francia, incitati dall'esempio del Pascal, il Roberval che fece l'esperienza <lb/>della vescica nel vuoto, e l'Auzout che modific&ograve; alquanto l'esperienza dello <lb/>stesso Pascal del vuoto nel vuoto. </s>

<s>Queste belle prove d'arte sperimentale <lb/>furon fatte note al mondo dal Pecquet, il quale, accingendosi nel suo cele&shy;<lb/>bre Trattato anatomico <emph type="italics"/>De circulatione sanguinis et chyli motu<emph.end type="italics"/> a farne la <lb/>descrizione, cos&igrave; avverte: &ldquo; Auctores adducam non librorum, quos hanc in <lb/>rem ne audivi quidem circumferri, sed eorum, saltem quae sequuntur Expe&shy;<lb/>rimentorum, et quorum grandis auctoritas et nomen venerabile &rdquo; (Pari&shy;<lb/>siis 1654, pag. </s>

<s>50). </s></p><p type="main">

<s>Alle due esperienze del Roberval e dell'Auzout il Pecquet stesso ne ag&shy;<lb/>giunge una sua, che &egrave; quella dell'acqua sornotante al mercurio. </s>

<s>Ma egli &egrave; <lb/>per altro benemerito della scienza torricelliana, la quale fu per lui splendi&shy;<lb/>damente applicata al moto del sangue nel cuore, come s'era applicata ai <lb/>moti dell'acqua nelle trombe. </s></p><p type="main">

<s>L'espressione di scienza Torricelliana che ci &egrave; uscita dalla penna, non <lb/>sembrer&agrave; impropria a coloro i quali considerano le tante altre applicazioni <lb/>che se ne fecero a ogni sorta di fatti naturali, per cui ne uscirono tante <lb/>nuove insigni scoperte. </s>

<s>Ma a ci&ograve; confer&igrave; l'uso della Macchina pneumatica <lb/>la quale, ritrovata verso il 1654 da Ottone di Guericke, fu col consenso del&shy;<lb/>l'inventore divulgata nel 1657 dal p. </s>

<s>Gaspero Schott sotto il titolo di <emph type="italics"/>Expe&shy;<lb/>rimentum novum magdeburgicum.<emph.end type="italics"/> (Mechanica hydraul. </s>

<s>pneum., Herbi&shy;<lb/>poli 1657, pag. </s>

<s>444-65). </s></p><p type="main">

<s>Questa macchina del Guericke era assai faticosa, dovendosi agitar la <lb/>pompa, per semplice moto di leva, e gli oggetti da sperimentare, ora era <lb/>difficile e ora affatto impossibile introdurgli nella campana. </s>

<s>Il Boyle, il quale, <lb/>dopo di aver fatto cenno degli Esperimenti di Magdeburgo, chiama in te&shy;<lb/>stimonio il conte di Corke a cui dice <emph type="italics"/>me rebus ex eodem principio expe&shy;<lb/>riendis sollicitum iam ante fuisse<emph.end type="italics"/> perfezion&ograve; la stessa Macchina facendo <lb/>muover la pompa pneumatica da un'asta dentata, che menavasi in su e in <lb/>gi&ugrave; dai moti alternativi di una manovella, e sostituendo al pallone chiuso <lb/>del Guericke un pallone di vetro coll'apertura da introdurvi il braccio di <lb/>un uomo, e poi sigillata, con turacciolo a vite. </s>

<s>Questa nuova macchina boi&shy;<lb/>leiana fu descritta dal suo inventore nel Proemio ai <emph type="italics"/>Nuovi esperimenti fisico&shy;<lb/>meccanici,<emph.end type="italics"/> pubblicati prima in inglese e dedicati dall'Autore al detto conte <lb/>di Corke suo nipote, colla data del d&igrave; 20 Dicembre 1659. Col mezzo di que&shy;<lb/>sta macchina principalmente si fecero dal Boyle que'XLIII Esperimenti, <lb/>da'quali si pu&ograve; dir che venisse a promuoversi e ad illustrarsi ogni parte <lb/>della scienza della Natura. </s></p><p type="main">

<s>Ma proseguendo i suoi fisici esercizii, che ogni giorno pi&ugrave; gli diveni&shy;<lb/>van tra mano fecondi, il Boyle stesso introdusse nella prima sua macchina <lb/>altre nuove perfezioni <emph type="italics"/>partim<emph.end type="italics"/> com'egli dice <emph type="italics"/>ab in<gap/>enioso Domino Hooke<emph.end type="italics"/><pb xlink:href="020/01/466.jpg" pagenum="447"/><emph type="italics"/>aliis suggestas, partim proprio marte excogitatas<emph.end type="italics"/> (Novor. </s>

<s>Experim. </s>

<s>cont. </s>

<s>I, <lb/>Praemonitiones, Op. </s>

<s>cit., T. I, pag. </s>

<s>207), e di questa nuova macchina cosi <lb/>perfezionata si serv&igrave; per condurre i Nuovi esperimenti descritti nella <emph type="italics"/>Con&shy;<lb/>tinuazione prima e seconda.<emph.end type="italics"/></s></p><p type="main">

<s>Questa nuova Macchina pneumatica boileiana, che fu costruita nell'of&shy;<lb/>ficina del celebre Dionigi Papin, si pu&ograve; dire che non s'avvantaggiasse sopra <lb/>la prima in altro, che nella migliore disposizione data al recipiente, il quale, <lb/>invece di essere un pallone avvitato al corpo di tromba, era una campana <lb/>di vetro posata con l'orlo intasato di cemento su un piano, in mezzo al <lb/>quale s'apriva il cannello aspiratore. </s>

<s>Il maneggio per&ograve; rimaneva quel me&shy;<lb/>desimo del rocchetto e dell'asta dentata, e poniamo che fosse alquanto pi&ugrave; <lb/>facile di quello della semplice leva guerricchiana, si rendeva nulladimeno, <lb/>via via che votavasi il recipiente, sempre pi&ugrave; faticoso. </s>

<s>Ad alleviar la fatica <lb/>riusc&igrave; ingegnosamente l'Hawksbee, che &egrave; il vero perfezionatore della mac&shy;<lb/>china pneumatica, introducendo, invece dell'unica boileiana, il gioco alter&shy;<lb/>nativo di due trombe. </s>

<s>Da ci&ograve; avviene che, quando il recipiente diventa quasi <lb/>esausto, la compressione dell'aria esteriore sopra la tromba attraente che di&shy;<lb/>scende, &egrave; quasi tanto grande quant'&egrave; la potenza che si richiede per solle&shy;<lb/>var l'altra tromba. </s>

<s>Cosicch&egrave;, mentre a muover le macchine del Guericke e <lb/>del Boyle, a misura che si avvicinano al vuoto, divengon pi&ugrave; dure; <emph type="italics"/>que&shy;<lb/>sta che io son per descrivere,<emph.end type="italics"/> dice lo stesso Inventore, <emph type="italics"/>nelle medesime circo&shy;<lb/>stanze &egrave; tutto all'opposto.<emph.end type="italics"/> (Esper. </s>

<s>fisico mecc., trad. </s>

<s>it., Firenze 1716, pag. </s>

<s>2). </s></p><p type="main">

<s>Miglior&ograve; altres&igrave; l'Hawksbee la disposizione del recipiente o della cam&shy;<lb/>pana facendole arrotare ben bene l'orlo, e posandola sopra un cuoio bagnato. </s>

<s><lb/>Cos&igrave; liberava s&egrave; e gli altri sperimentatori dal tedio di dovere smurare il <lb/>recipiente stesso, e staccarlo dal piano, ogni volta che volevasi rinnovare <lb/>l'esperienza. </s>

<s>Non senza grande commodit&agrave; introdusse poi quel filo scorsoio <lb/>da mandar gi&ugrave;, tirare in su, tener sospesa o muovere qualunque cosa, che <lb/>pi&ugrave; piacesse di sperimentare nel vuoto. </s>

<s>Mun&igrave; inoltre la macchina di uno <lb/>squisito <emph type="italics"/>provino,<emph.end type="italics"/> che consisteva in un lungo tubo di vetro aperto di sopra <lb/>nel vano del recipiente e di sotto immerso in un bicchiere pieno di mer&shy;<lb/>curio. </s>

<s>Un'assicella graduata e applicata al tubo stesso, dal risalirvi dentro <lb/>pi&ugrave; o meno alto il mercurio, segnava i gradi della rarefazione dell'aria. </s>

<s>Si <lb/>vede dunque come, da leggerissime modificazioni in fuori, la Macchina pnen&shy;<lb/>matica che s'apparecchi&ograve; l'Hawksbee per condurre i suoi <emph type="italics"/>Physico-mecha&shy;<lb/>nical Experiments<emph.end type="italics"/> pubblicati in Londra nel 1709, &egrave; quella stessa che si <lb/>maneggia dai fisici moderni. </s></p><p type="main">

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

<s>Dalle esperienze francesi di Roano a quelle inglesi del Boyle e del&shy;<lb/>l'Hawksbee, in un breve corso di anni, la scienza ha fatto tali e tanti pro&shy;<lb/>gressi, da recare stupore a chiunque vi ripensa. </s>

<s>E in tanta operosit&agrave; di <pb xlink:href="020/01/467.jpg" pagenum="448"/>studii, e in tanto straboccante abbondanza di frutti, francesi e inglesi e ale&shy;<lb/>manni riconoscono d'unanime consenso, per loro primo e principale Mae&shy;<lb/>stro in questa scienza, il Torricelli. </s>

<s>Il Boyle, che &egrave; senza dubbio il pi&ugrave; va&shy;<lb/>lente di tutti, stima che non si sarebbe potuto proporre altro miglior soggetto <lb/>a'suoi studii, <emph type="italics"/>quam si nobile illud experimentum torricellianum exco&shy;<lb/>lere et promovere studerem.<emph.end type="italics"/> (Nova, exper. </s>

<s>Proem. </s>

<s>Op. </s>

<s>Omn., Ven. </s>

<s>1697, <lb/>T. I, pag. </s>

<s>2). </s></p><p type="main">

<s>Ma pur, fra'tanti, non manc&ograve; chi ebbe ardire di appropriarsi la nobile <lb/>esperienza, e fu Valeriano Magno, se non il primo, senza dubbio, il pi&ugrave; avido <lb/>di tutti. </s>

<s>Egli pubblic&ograve; un libricciolo col titolo <emph type="italics"/>Demonstratio ocularis,<emph.end type="italics"/> in cui, <lb/>dopo d'avere accennato alla lettura del I Dialogo delle Nuove Scienze di Ga&shy;<lb/>lileo, dice come di l&igrave; gli venisse il pensiero di far l'esperienza del vuoto col <lb/>mercurio. </s>

<s>Finita la sua breve <emph type="italics"/>Dimostrazione<emph.end type="italics"/> l'Autore, come fanciullo che <lb/>tresca colle braccia in aria per cansare i colpi della ferza che il pedagogo <lb/>tien sotto la toga, aggiunge la seguente nota: &ldquo; Haec scribebam Varsaviae <lb/>die 12 Julii anni 1647, quae dum exhiberentur Serenissimis Principibus Regi <lb/>et Reginae spectaculo iucundissimo, inde erupit fama huiuscemodi miraculi <lb/>in natura, quae excitavit multorum ingenia ad contradicendum &rdquo; (Demon&shy;<lb/>stratio ecc., Venetiis 1649, pag. </s>

<s>15). </s></p><p type="main">

<s>I pi&ugrave; temuti per&ograve; fra questi contradittori eran quelli, che gli avreb&shy;<lb/>bero potuto rinfacciare i suoi furti, il pi&ugrave; animoso fra i quali insorse quel <lb/>Roberval che, insieme col Pascal e con l'Auzout, aveva tanto ferventemente <lb/>in Francia coltivato la scienza torricelliana. </s>

<s>Egli, sotto forma di Epistola al <lb/>Des-Noyers, data di Parigi nell'Ottobre del 1647, scrisse una <emph type="italics"/>Narratio de <lb/>vacuo,<emph.end type="italics"/> la quale, ristampandosi in Venezia dall'Herz, nel 1649, la <emph type="italics"/>Demon&shy;<lb/>stratio<emph.end type="italics"/> del Magno, fu aggiunta al volumetto. </s>

<s>In tal Narrazione, con quella <lb/>dignitosa e gentile franchezza di chi &egrave; mosso dall'amore del vero, il cele&shy;<lb/>bre Matematico francese cos&igrave; scriveva: &ldquo; Ignoscat mihi R. P. capuccinus <lb/>Valerianus Magnus si dixero illum parum candide egisse in eo libello quem <lb/>de hac re in lucem nuperrime emisit mense Julio huius anni 1647, dum <lb/>celeberrimi huiusce experimenti ille primus author haberi voluit. </s>

<s>Quod certo <lb/>constat iam ab a. </s>

<s>1643 in Italia vulgatum fuisse ac ibidem, praecipue vero <lb/>Romae atque Florentiae, celeberrimas inter eruditos de ea re viguisse con&shy;<lb/>troversias, quas non potuit ignorare Valerianus, qui circa eadem tempora <lb/>illis in regionibus degebat, et cum doctis illis conversabatur &rdquo; (ibi, pag. </s>

<s>31). </s></p><p type="main">

<s>Un altro non men celebre straniero insorse, dopo il Roberval a riven&shy;<lb/>dicare al Torricelli quella esperienza, che volevasi poco onestamente appro&shy;<lb/>priare il Magno, e fu Ottone di Guericke, il quale incomincia il cap. </s>

<s>XXXIV <lb/>del III Libro de'suoi <emph type="italics"/>Experimenti magdeburgici<emph.end type="italics"/> con le parole seguenti: <lb/>&ldquo; Cum Ratisbonae in Comitiis Imperialibus inter alia Electoribus ac Prin&shy;<lb/>cipibus quibusdam ut et Legatis, meorum quaedam Experimentorum exhi&shy;<lb/>berem, et per hanc occasionem mihi cum admodum Rev. </s>

<s>Patre Capuccino <lb/>Domino Valeriano Magno, familiaritas intercederet; ille mihi exhibuit quod&shy;<lb/>dam experimentum a se, uti dicebat, ad demonstrandum vacuum excogita-<pb xlink:href="020/01/468.jpg" pagenum="449"/>tum .... mihique communicabat Libellum suum cuius titulus <emph type="italics"/>Demonstratio <lb/>ocularis ecc.<emph.end type="italics"/> quamquam deinde tam ex ipso libello collegi, quam postea ex <lb/>aliis authoribus vidi, Experimentum hoc, primum a clarissimo viro Johanne <lb/>Torricello Magni Ducis Hetruriae Mathematico detectum fuisse &rdquo; (Amstelo&shy;<lb/>dami, 1672, pag. </s>

<s>117, 18). </s></p><p type="main">

<s>Quel cervellaccio del padre Onorato Fabry che, sciabordando infatica&shy;<lb/>bile nel fiume della scienza si credeva di aver chiappati tanti squisitissimi <lb/>pesci quanti tra le maglie della sua rete, rimanevan presi fuscelli infradi&shy;<lb/>ciati e sterpi motosi; volle anch'egli ingegnarsi di nobilitar la sua pesca <lb/>coll'appropriarsi la nobilissima preda del Torricelli. </s>

<s>E perch&egrave; meglio gli riu&shy;<lb/>scisse pens&ograve;, con sottile arte, di servirsi di un suo discepolo, Pietro Mou&shy;<lb/>sner, a cui, in un'Appendice <emph type="italics"/>De vacuo<emph.end type="italics"/> a un libro che stava per pubblicar <lb/>col titolo di <emph type="italics"/>Metaphisica Demonstrativa,<emph.end type="italics"/> fece scriver queste parole: &ldquo; Ante <lb/>aliquot annos luculento sane experimento, evinci omnino vacuum nonnulli <lb/>existimarunt. </s>

<s>De huius experimenti authore nihil dicam, cuius inventionem <lb/>non pauci quidem sibi vindicant Galli, Itali, Germani: unum scio iam sex <lb/>ab hinc annis a nostro Philosopho P. Hon. </s>

<s>Fabry propositum fuisse et expli&shy;<lb/>catum nec nisi proxime sequenti anno ex Italia in Galliam, sub Torricelli <lb/>nomine migrasse; hoc demum praesenti anno a R. P. </s>

<s>Valeriano Magno <lb/>capuccino in Polonia edito super ea re parvo libello publicatum &rdquo; (Lug&shy;<lb/>duni, 1648, pag. </s>

<s>570). </s></p><p type="main">

<s>A scoprire la sottil frode del padre Onorato e a rivendicar gli onori al <lb/>Torricelli e all'Italia, sorse, chi il crederebbe, un altro padre gesuita, il te&shy;<lb/>desco Gaspero Schott, il quale, dop'aver riferite le sopra trascritte parole <lb/>del Mousnero, cos&igrave; nella sua <emph type="italics"/>Tecnica curiosa<emph.end type="italics"/> immediatamente soggiunge: <lb/>&ldquo; Scripsit haec Mousnerius anno 1647: ante sex annos, hoc est 1641, fuit <lb/>explicatum experimentum in Gallia a p. </s>

<s>Honorato Fabry: sequenti anno, hoc <lb/>est 1642, ex Italia migravit in Galliam. </s>

<s>Conciliet haec qui potest. </s>

<s>Si anno 1648 <lb/>ea scripsit citatus Mousnerius, migravit experimentum ex Italia in Galliam <lb/>anno 1643, adeoque anno praecedenti potuit a Torricello fuisse deprehen&shy;<lb/>sum, quod consonat iis de quibus Dominus de Roberval scripsit &rdquo; (Norim&shy;<lb/>bergae, 1664, pag. </s>

<s>167). </s></p><p type="main">

<s>Ma il padre Onorato stesso, trovatosi cos&igrave; scoperto di furto e con rara <lb/>generosit&agrave; restituendo al padrone, vuol che restituiscano anche gli altri che <lb/>avevan rubato come lui. </s>

<s>Nel IV de'suoi Dialoghi fisici infatti dop'avere as&shy;<lb/>serito per bocca di <emph type="italics"/>Antimo<emph.end type="italics"/> che del bellissimo e celeberrimo sperimento <emph type="italics"/>pri&shy;<lb/>mus inventor fuit doctissimus Torricellius,<emph.end type="italics"/> fa insinuar dall'interlocutore <lb/><emph type="italics"/>Crisocomo<emph.end type="italics"/> la notizia: &ldquo; Huius experimenti primum inventorem et aucto&shy;<lb/>rem P. </s>

<s>Valerianum Magnum fuisse accepi &rdquo; a cui in nome dell'Autore e in <lb/>conferma di ci&ograve; che Antimo avea detto di sopra, <emph type="italics"/>Agostino<emph.end type="italics"/> risponde: &ldquo; Nihil <lb/>profecto magis a veritate alienum: Torricellius haud dubie et citra omnem <lb/>controversiam primus inventor fuit &rdquo; (Lugd., 1665, pag. </s>

<s>182, 83). </s></p><p type="main">

<s>E perch&egrave; la storia degli atti e dei pensamenti umani ha sempre col <lb/>serio, assai pi&ugrave; di quel che non pare o non si crede, mescolato il faceto, <pb xlink:href="020/01/469.jpg" pagenum="450"/>mentre francesi e gesuiti rassicurano la fama del Torricelli, ecco uno ze&shy;<lb/>lantissimo italiano tornar dopo pi&ugrave; di un secolo a trepidare al pericolo di <lb/>vederla spiumata da un Francese venuto di Moulinx a professare Filosofia <lb/>peripatetica nello Studio pisano. </s></p><p type="main">

<s>Giovanni Targioni, nel I Tomo delle sue <emph type="italics"/>Notizie,<emph.end type="italics"/> avendo riferito il do&shy;<lb/>cumento di un'osservazione barometrica fatta dal Borelli sul poggio di Ar&shy;<lb/>timino, prosegue: &ldquo; L'epoca di questa osservazione barometrica relativa a <lb/>quella del Pascal, parrebbe che, secondo il testo del Borelli, si dovesse fis&shy;<lb/>sare intorno alll'anno 1657: eppure ecco un indizio ch'ella sia molto an&shy;<lb/>teriore, e per lo meno del 1642, il che veramente mi rende perplesso, sa&shy;<lb/>pendosi che il vacuo torricelliano fu messo in uso nel 1643, e che Biagio <lb/>Pascal solo nel 1646, ne fece uso per misurare le altezze dei monti. </s>

<s>Clau&shy;<lb/>dio Berigardi (Beauregard) nella P. VI del suo Circolo Pisano pubblicato <lb/>colla data del 1&deg; Gennaio 1643, cio&egrave; avanti a queste epoche dice: <emph type="italics"/>&ldquo; Com&shy;<lb/>pertum est aquam vel aliud corpus liquidum, tanto magis premi, quanto <lb/>plus aeris ipsi incumbit. </s>

<s>Demonstratur in Tubo illo vitreo in cuius parte <lb/>superiori argentum vivum videtur relinquere spatium vacuum, ut iam <lb/>dictum est. </s>

<s>Nam in alta turri ubi minus est aeris incumbentis stagnanti <lb/>hydrargirio, in quo est tubus, plus relinquitur vaeui quam ad basim turris <lb/>vel montis, ubi altior aer magis premit hydrargirium eumque compellit <lb/>per tubum paulo altius efferri et sic relinquere minus vacui....<emph.end type="italics"/> Io non <lb/>pretendo qui di decidere dell'anteriorit&agrave; dell'esperienza in pregiudizio della <lb/>gloria di Biagio Paschal, e lascer&ograve; giudicare ad altri se il medesimo Torri&shy;<lb/>celli possa essere stato il primo a fare del Barometro l'uso soprannotato, <lb/>appunto nei primi giorni della sua invenzione, e che subito ne avesse la <lb/>notizia il Berigardi, che era allora professore di Filosofia in Padova &rdquo; (Fi&shy;<lb/>renze, 1780, pag. </s>

<s>207). </s></p><p type="main">

<s>Impacciato allo stesso modo si trov&ograve; l'Antinori, che nelle <emph type="italics"/>Notizie sto&shy;<lb/>riche<emph.end type="italics"/> premesse ai <emph type="italics"/>Saggi di Naturali esperienze<emph.end type="italics"/> (Firenze, 1841, pag. </s>

<s>29) <lb/>si assottiglia per veder pur di uscirne in qualche modo. </s>

<s>A ripensarvi per&ograve; <lb/>sembra impossibile che due cos&igrave; valentuomini sieno affogati, come suol dirsi, <lb/>proprio in un bicchier d'acqua. </s>

<s>Il Targioni stesso aveva gi&agrave; avvertito che <lb/>de'<emph type="italics"/>Circoli Pisani<emph.end type="italics"/> furono fatte due edizioni: la prima in Udine dallo Schi&shy;<lb/>ratti nel 1643 e la seconda in Padova dal Frambotti nel 1661. Ora, a risol&shy;<lb/>vere il dubbio, che tenevalo in tanta pena, sarebbe bastato a lui e all'An&shy;<lb/>tinori collazionar insieme le due edizioni, per ritrovar che nella prima non <lb/>si fa alcuna menzione n&egrave; dell'esperienza dell'argento vivo, n&egrave; del variar del <lb/>livello di lui secondo le altezze, ma che l'Autore aggiunse quelle notizie <lb/>nell'edizione del 1661, diciotto anni dopo l'esperienza del Torricelli, e tre&shy;<lb/>dici anni dopo quella del Pascal, eseguita dal Perier sul Puy De-Domme. </s></p><p type="main">

<s>Se dunque cos&igrave; poco basta ad assicurar la fama del Torricelli, ella pu&ograve; <lb/>seguitare ancora a batter libere le ali. </s>

<s>Spettatore di cos&igrave; nobili trionfi, fu, <lb/>infino al 1666, quel Giovan Batista Baliani, a cui si dovrebbero per giusti&shy;<lb/>zia i primi meriti, ma &egrave; credibile che egli voglia starsene e non uscir fuori <pb xlink:href="020/01/470.jpg" pagenum="451"/>a far col mondo le sue ragioni? </s>

<s>Il Mersenno &egrave; che gli d&agrave; la notizia della <lb/>celebre esperienza torricelliana, e il Baliani risponde a lui di Savona il d&igrave; <lb/>25 Novembre 1647 una lettera, nella quale cos&igrave; dice fra le molte altre cose <lb/>importanti: &ldquo; Ego iam abhinc pluribus annis, expertus aeris pondus, arbi&shy;<lb/>tratus sum non repugnare dari vacuum. </s>

<s>&rdquo; E perch&egrave; i gloriosi scientifici suc&shy;<lb/>cessi fecero poi conoscere a&igrave; Baliani la grande importanza di quelle sue spe&shy;<lb/>culazioni, fatte 36 anni avanti, volle nella Raccolta delle sue <emph type="italics"/>Opere diverse<emph.end type="italics"/><lb/>inserire anche la citata lettera al Mersenno, dopo la quale, in nota, cos&igrave; <lb/>soggiunge: &ldquo; Dictam epistolam ad Mersennum typis mandavi, cuius exem&shy;<lb/>pla, dum essem Savonae Gubernator, misi pluribus amicis. </s>

<s>Et quoniam ex <lb/>eorum responsionibus patet me fuisse veracem ubi dixi me multis abhinc <lb/>annis amicis communicasse causam quod vacuum palam non esset, lubet <lb/>hic unam aut alteram ex dictis responsionibus apponere &rdquo; (Genova, Calen&shy;<lb/>zani, 1666, pag. </s>

<s>281). E seguita a recar, come testimoniali, varie lettere di <lb/>amici, fra le quali una del gesuita Francesco Ghiringhello, e un'altra di <lb/>Giacomo Filippo Durazzo. </s>

<s>Fa per&ograve; gran maraviglia che egli, come testimo&shy;<lb/>niali pi&ugrave; autorevoli di tutte le altre, non rechi le lettere scritte e le rispo&shy;<lb/>ste di Galileo, le quali sarebbero state bastanti a mostrar che in gran parte <lb/>era dovuta a lui quella gloria che tutto il mondo dispensava cos&igrave; largamente <lb/>a solo il Torricelli. </s></p><p type="main">

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

<s>A questo punto non possiamo non soffermare il passo, per fare alcune <lb/>considerazioni sopra le cose fin qui narrate. </s>

<s>Ci ha mosso a maraviglia il <lb/>vedere il Baliani mostrarsi cos&igrave; debole in difender le sue ragioni, quasi te&shy;<lb/>messe di offender la gloria del Torricelli, ma che diremo a veder francesi <lb/>e gesuiti, i quali con invidiose rivalit&agrave; si son quasi sempre studiati o di av&shy;<lb/>vilire o di appropriarsi i meriti della scienza italiana, fosse pur ella affidata <lb/>ai pi&ugrave; certi e pubblici documenti; che diremo ora di que'francesi e di que'ge&shy;<lb/>suiti, a vederli con tanto zelo difender contro gli usurpatori la invenzione <lb/>di un italiano, la quale non s'appoggia sopr'altro documento, che sulla fama <lb/>volante, e sopra alcune inedite lettere familiari? </s></p><p type="main">

<s>Coloro che conoscon bene il Mersenno, in mano a cui pervennero quelle <lb/>lettere familiari, s'aspetterebbero come cosa certa ch'ei l'avesse dovute bru&shy;<lb/>ciare, e dar l'esperienza dell'argento vivo per cosa sua, com'aveva date per <lb/>sue tante altre speculazioni dello stesso Torricelli: e nonostante ei, con rara <lb/>sincerit&agrave;, confessa al pubblico che inventor della celebre esperienza &egrave; l'il&shy;<lb/>lustre Geometra italiano, <emph type="italics"/>qui Tubum observatorium mihi anno 1644 osten&shy;<lb/>dit in Magni Ducis Etruriae pergulis admirandis. </s>

<s>De cuius observatione <lb/>nos etiam prius monuerat illius singularis amicus Michael Angelus Ric&shy;<lb/>cius. </s>

<s>Romae .... cuius Epistola docebat ex tubo ....<emph.end type="italics"/> (Nov. </s>

<s>Observ., T. III, <pb xlink:href="020/01/471.jpg" pagenum="452"/>Parisiis 1647, pag. </s>

<s>216). E con generosit&agrave; ben pi&ugrave; rara divulg&ograve; l'epistole <lb/>torricelliane, facendone prender copia ai principali scienziati di Francia. </s>

<s>&ldquo; Ha&shy;<lb/>beo ego, scriveva il Roberval al Des Noyers, epistolam quam clariss. </s>

<s>Vir <lb/>Evang. </s>

<s>Torricellius Magni Ducis Hetruriae mathematicus misit Romam ad <lb/>amicum suum doctiss. </s>

<s>virum Angelum Ricci sub finem anni 1643 italice <lb/>scriptam, quae nihil aliud continet quam controversiam inter duos illos vi&shy;<lb/>ros egregios, qui, quod et fere omnibus accidit, de tali experimento diverse <lb/>sentiebant. </s>

<s>Ea autem epistola cum quibusdam aliis ab ipso Ricci missa est <lb/>Parisios ad R. P. Mersennum, Ord. </s>

<s>Minim. </s>

<s>sub initium anni 1644 &rdquo; (Loc. </s>

<s><lb/>cit., pag. </s>

<s>31). </s></p><p type="main">

<s>Tanta sincerit&agrave; e generosit&agrave; del Mersenno, da qual che si voglia fonte <lb/>ella scaturisse nell'animo di lui e nell'ingegno, possiamo accettarla come <lb/>una riparazione dei danni e delle ingiurie che fece alla scienza italiana; ri&shy;<lb/>parazione che cresce alquanto nella virt&ugrave; espiatrice, se si ripensi che pel <lb/>ministero del Frate parigino si diffuse per la Francia, infin dal 1644, la copia <lb/>delle lettere torricelliane da nessuno o da pochissimi sapute in Italia. </s>

<s>Chi <lb/>pu&ograve; intender come mai il Ricci, cos&igrave; sollecito in divulgare i pensieri del <lb/>Torricelli fra gli stranieri, non si curasse poi di farli conoscere a'suoi, i quali <lb/>forse ignorerebbero ancora quel che l'Autor dell'esperienza dell'argento vivo <lb/>ne scrisse in proposito, se il Borelli, ritrovandosi a Roma, non avesse fatto <lb/>richiesta dell'Epistola torricelliana <emph type="italics"/>ad Clarissimum Michaelem Angelum <lb/>Riccium missa, quam humanissime mihi communicavit anno 1658, eam&shy;<lb/>que Florentiae postea serenissimo principi Leopoldo tradidi et inter ami&shy;<lb/>cos evulgavi.<emph.end type="italics"/></s></p><p type="main">

<s>Queste parole il Borelli le scriveva a pag. </s>

<s>228 del Trattato <emph type="italics"/>De motion. </s>

<s><lb/>natur.<emph.end type="italics"/> stampato, come si sa, nel 1670, ma in una Lettera familiare, diretta <lb/>da Roma il d&igrave; 3 d'Agosto 1658 al principe Leopoldo, dop'aver fatto cenno <lb/>di quella e di altre lettere del Torricelli al Ricci, il Borelli stesso cos&igrave; sog&shy;<lb/>giungeva: &ldquo; Alla mia venuta recher&ograve; la copia di tutte queste lettere scien&shy;<lb/>tifiche del Torricelli per farle stampare, acciocch&egrave; non venga l'umore a qual&shy;<lb/>che francese di pretendere anteriorit&agrave;, come gi&agrave; mi par che ve ne sia alcuno, <lb/>sopra questo gran concetto della compressione dell'aria, cagione potissima <lb/>ed indubitabile del'sollevamento dell'arg. </s>

<s>v. </s>

<s>nel cannello &rdquo; (MSS. Cim., <lb/>T. XVI, c. </s>

<s>103). </s></p><p type="main">

<s>I fatti per&ograve; fin qui esposti dimostrano che le sollecitudini del Borelli <lb/>e i timori non eran giustificati, perch&egrave; anzi i francesi ci hanno data occa&shy;<lb/>sion di ammirare la loro sincerit&agrave; e generosit&agrave; in riconoscere e in attribuire <lb/>al Torricelli il gran concetto della compression dell'aria, cagione potissima <lb/>e indubitabile del sollevamento dell'argento vivo nel cannello. </s>

<s>Fosse per que&shy;<lb/>sto o per altri motivi &egrave; un fatto che tutt'altro che mostrarsi solleciti e pre&shy;<lb/>murosi i Fiorentini di fare stampar le Lettere torricelliane, indugiarono infino <lb/>al 1663, quando Carlo Dati le inser&igrave; nella pubblicazione della <emph type="italics"/>Lettera di <lb/>Timauro Anziate ai Filaleti.<emph.end type="italics"/></s></p><p type="main">

<s><gap/><pb xlink:href="020/01/472.jpg" pagenum="453"/>del d&igrave; 11, e l'altra del d&igrave; 28 Giugno 1664. Questa seconda fu provocata da <lb/>una del Ricci, nella quale promoveva alcune difficolt&agrave; contro il concetto della <lb/>compressione dell'aria; lettera che il Dati ivi pure pubblic&ograve; e di cui dee <lb/>aver preso copia il Borelli. </s>

<s>Non par per&ograve;, ci&ograve; che pi&ugrave; importa, che pren&shy;<lb/>desse copia o che gli fosse mostrata dal Ricci un'altra delle Lettere torri&shy;<lb/>celliane, che esso Ricci deve aver mandata colle due sopra citate a Parigi. </s>

<s><lb/>Di questa terza Lettera, in cui, per ispiegar la compressione dell'aria sulla <lb/>superficie del mercurio nella scodella chiusa, ricorre il Torricell&igrave; all'esem&shy;<lb/>pio de'flussi dell'acqua; il Mersenno fa menzione nel T. III delle sue <emph type="italics"/>Nuove <lb/>Osservazioni<emph.end type="italics"/> dove cos&igrave; dice: &ldquo; Si intelligatur cylindrus aqueus vel aereus <lb/>inferior pedalis a superiore ita separari atque dividi, ut sit eiusdem roboris <lb/>et resistentiae, quibus superiori coniunctus pollebat, peracque contranitatur <lb/>cylindro mercuriali, eodem modo quo cylindrus a reliquo cylindro aqueo <lb/>15 v. </s>

<s>g. </s>

<s>pedum, per lumen aliquod fluens, tantumdem aquae tribueret, quan&shy;<lb/>tum cylindrus integer 16 pedum, si fingatur ille cylindrus pedalis in ea sem&shy;<lb/>per manere pressione, quam a 15 pedibus prementibus acquisierat: quam <lb/>fuisse clarissimi Torricelli sententiam ex Litteris Excellentissimi Riccii anno, <lb/>si bene memini 1644, didici &rdquo; (Parisiis 1647, Praefatio innum). </s></p><p type="main">

<s>Noi argomentiamo che la lettera commemorata qui dal Mersenno, ap&shy;<lb/>pelli a una terza dopo le due pubblicate dal Dati, e come un seguito di <lb/>quella del d&igrave; 28 Giugno, nella quale, a spiegare il medesimo concetto, in&shy;<lb/>vece dell'esempio scientifico della pressione dell'acqua, il Torricelli adduce <lb/>quello volgare della lana compressa. </s></p><p type="main">

<s>Del resto, nemmeno aggiunta questa terza alle altre due prime Lettere <lb/>torricelliane, s'ha compiuta la rappresentanza del Dramma, a cui manca <lb/>l'introduzione. </s>

<s>Quella del d&igrave; 11 Giugno, nella quale entra il Torricelli in <lb/>argomento, scrivendo al Ricci: <emph type="italics"/>Le accennai gi&agrave; che si stava facendo non <lb/>so che esperienza filosofica intorno al vacuo,<emph.end type="italics"/> richiama altre lettere prece&shy;<lb/>denti, le quali non pervennero in mano n&egrave; al Mersenno n&egrave; al Borelli. </s>

<s>Il <lb/>soggiunger poi che l'esperienza filosofica intorno al vacuo non era <emph type="italics"/>per far <lb/>semplicemente il vacuo,<emph.end type="italics"/> fa argomentar che il soggetto preso a trattare dal <lb/>Torricelli, in quella sua prima citata lettera al Ricci, non era nuovo. </s>

<s>Cos&igrave; <lb/>infatti argomentava anche il Roberval, che al Des-Noyers, scriveva: &ldquo; Sed <lb/>in eadem epistola ex discursu apparet minime novum tunc fuisse illis expe&shy;<lb/>rimentum cum multoties repetitum &rdquo; (Loc. </s>

<s>cit., pag. </s>

<s>31). </s></p><p type="main">

<s>Come e quando fosse stato fatto, prima di quel discorso torricelliano, <lb/>l'esperimento, era ci&ograve; che vivamente frugava la curiosit&agrave; nel Mersenno: <lb/>&ldquo; In cuius vero mentem prius illa vacui cogitatio venerit, et quis prior <lb/>animadverterit collum tubi sive lagenam in extremo habentis, sive solitarium <lb/>et in cylindri modum conformati, scire fortassis incundum fuerit. </s>

<s>Chymici <lb/>cuiusdam fortuitum inventum nonnulli dicent: alii referent ad acutissimi <lb/>philosophi meditationem, qualis philosophorum princeps Galilaeus et amici <lb/>Magiottus et Nardius, quos si nos docuerit incomparabilis Torricellius, gra&shy;<lb/>tissimum erit &rdquo; (Nov. </s>

<s>ob. </s>

<s>servat., T. III, Parisiis 1647, pag. </s>

<s>217). </s></p><pb xlink:href="020/01/473.jpg" pagenum="454"/><p type="main">

<s>Gratissimo sarebbe stato, non a solo il Mersenno, ma alla Storia della <lb/>scienza italiana, che il Torricelli si fosse pi&ugrave; chiaramente aperto intorno a <lb/>ci&ograve; che dette occasione alla celebre esperienza: egli avrebbe altres&igrave; provve&shy;<lb/>duto meglio a glorificare il suo nome, se men sollecito della fabbrica de'Ca&shy;<lb/>nocchiali, avesse atteso con pi&ugrave; costanza alla costruzion del Barometro, e a <lb/>coltivar la fisica sperimentale, da lui stesso cos&igrave; efficacemente iniziata. </s>

<s>Ma <lb/>egli non previde la gran fiamma, che sarebbe secondata alla sua scintilla; <lb/>la troppo sollecita morte gli imped&igrave; perfino di vederne gli albori, e dall'al&shy;<lb/>tra parte l'ossequio cortigiano lo consigliava a contentarsi della Geometria, <lb/>per fare omaggio delle scoperte sue fisiche al Granduca. </s></p><p type="main">

<s>Avrebbero nonostante potuto supplire in dar sodisfazione alla storia gli <lb/>amici, che ragionevolmente si pu&ograve; credere dover essere informati de'fatti. </s>

<s><lb/>Ma il Nardi, a quel che par dalle sue <emph type="italics"/>Scene Accademiche,<emph.end type="italics"/> non sa nemmeno <lb/>che il Torricelli abbia fatto la grande esperienza; il Magiotti, morto nel 1656 <lb/>di peste, non ne lasci&ograve; che qualche ricordo in alcune cartucce sparse, e il <lb/>Ricci, com'abbiamo veduto, sollecito di diffonder le Lettere torricelliane in <lb/>Francia, le tenne chiuse, infino al 1658, agli scienziati d'Italia. </s>

<s>Nonostante <lb/>egli, indirettamente tramandava alla storia una notizia importante, per mezzo <lb/>di quel Tommaso Cornelio, che ebbe lo stesso Ricci a maestro, e a cui de&shy;<lb/>dicando un suo <emph type="italics"/>Proginnasma<emph.end type="italics"/> cos&igrave; scriveva: &ldquo; Tu enim unus omnium, iam <lb/>inde ab adolescentia, mihi amicissimus, studiorum meorum adiutor author&shy;<lb/>que fuisti &rdquo; (Neapoli, 1688, pag. </s>

<s>263). </s></p><p type="main">

<s>Il Cornelio, mentre con tuba sonora si diffondeva per tutta Europa la <lb/>notizia dell'Esperienza torricelliana, fu il primo e l'unico che ne scrivesse <lb/>in Italia in quella sua Epistola <emph type="italics"/>De Circumpulsione platonica,<emph.end type="italics"/> data i primi di <lb/>Giugno del 1648. La notizia importante che si diceva, e ch'egli ivi d&agrave;, &egrave; <lb/>che l'esperienza del Berti fu che dette occasione a quella del Torricelli: <lb/>&ldquo; Gaspar Bertius mathematicarum artium in-Academia romana professor <lb/>plumbeum tubum longitudine viginti ulnarum erexit, apicique inseruit vi&shy;<lb/>tream sphaeram, ut animadverteret aquam supra ulnas decem et octo as&shy;<lb/>surgentem in subiectum vas continenter defluere. </s>

<s>Tandem vero Evangelista <lb/>Torricellius, ut praegrandis machinae laboriosam structuram vitaret, coepit <lb/>periculum in argento vivo facere &rdquo; (ibi, pag. </s>

<s>297, 98) </s></p><p type="main">

<s>Una tal notizia, se gli fosse giunta alle orecchie un anno prima, avrebbe <lb/>forse potuto appagar la curiosit&agrave; nel Mersenno, ma pur le Lettere del Tor&shy;<lb/>ricelli mettevano in desiderio di saperne qualche altra cosa di pi&ugrave;; deside&shy;<lb/>rio a soddisfare al quale, meglio de'commemorati di sopra, pareva atto il <lb/>Viviani. </s>

<s>Eppure &egrave; cosa singolare che non se ne trovi fatto il minimo cenno <lb/>ne'suoi manoscritti, pieni di tante altre minute notizie meno importanti. </s>

<s>Egli <lb/>dee, senza dubbio, aver riveduta la <emph type="italics"/>Lettera a'Filaleti,<emph.end type="italics"/> e dee esser vero quel <lb/>che il Dati ivi scrive di lui, che cio&egrave; conferitogli il suo pensiero dal Tor&shy;<lb/>ricelli, egli <emph type="italics"/>ansioso di vedere questa operazione fece di presente fabbricar <lb/>lo strumento, e procurando l'argento vivo fu il primo a fare cos&igrave; nobile <lb/>csperienza:<emph.end type="italics"/> vero dee esser quel che il Dati appresso soggiunge, che cio&egrave; <pb xlink:href="020/01/474.jpg" pagenum="455"/>tosto il Viviani ragguagli&ograve; del segu&igrave;to il Torricelli, <emph type="italics"/>recandogli straordinario <lb/>contento, attesoch&egrave; si conferm&ograve; nell'opinione conceputa che la ponderosit&agrave; <lb/>dell'aria, equilibrandosi con l'acqua, e con l'argento vivo, per la diver&shy;<lb/>sit&agrave; del peso, sostenesse quelli ad altezze diverse.<emph.end type="italics"/> (Firenze, 1663, pag. </s>

<s>20). </s></p><p type="main">

<s>Da questa notizia per&ograve; in fuori il Dati non racconta nulla di nuovo, che <lb/>non fosse stato scritto alquanti anni prima dal Roberval, o contemporanea&shy;<lb/>mente dall'Autor della Prefazione al <emph type="italics"/>Traitez de l'equilibre des liqueurs,<emph.end type="italics"/> il <lb/>quale, con impropria e imperfetta notizia storica, riconosce come inspiratore <lb/>immediato dell'Esperienza torricelliana Galileo, che <emph type="italics"/>est celuy qui a remar&shy;<lb/>qu&eacute; le primier que les pompes aspirantes ne pouvioent &eacute;lever l'eau plus <lb/>haut que 32 ou 33 pi&egrave;ds:<emph.end type="italics"/> parole che sembrano esser una fedel traduzione <lb/>di quelle del Dati: &ldquo; Considerando il Torricelli quanto scrive il Galileo nel <lb/>primo Dialogo della Resistenza de'corpi solidi che l'acqua nelle trombe che <lb/>operano per attrazione non s'alza oltre a 18 braccia in circa.... &rdquo; (ivi). </s></p><p type="main">

<s>Pi&ugrave; copiose notizie storiche intorno all'importante soggetto ne dava, <lb/>l'anno dopo il 1663, lo Schott nella sua <emph type="italics"/>Tecnica curiosa,<emph.end type="italics"/> ma lo stesso ti&shy;<lb/>tolo posto in fronte al &sect; III del III Libro <emph type="italics"/>Experimenti in Italia exhibiti <lb/>historia ex P. </s>

<s>Athanasio Kirchero et p. </s>

<s>Nicolao Zucchio,<emph.end type="italics"/> pone in sospetto <lb/>della sincerit&agrave; della sorgente, a cui furono attinte quelle notizie. </s>

<s>Lo Sturm, <lb/>nella III Appendice al <emph type="italics"/>Collegium experimentale sive curiosum,<emph.end type="italics"/> Appendice <lb/>che s'intitola <emph type="italics"/>Baroscopii Auctor Torricellus et tota historia,<emph.end type="italics"/> &egrave; diligente rac&shy;<lb/>coglitor di notizie, e il pi&ugrave; compiuto storico della Esperienza torricelliana, <lb/>che, infino al 1676, ne abbia scritto, ma pur lascia ancora molto a deside&shy;<lb/>rare. </s>

<s>Se a sodisfare a questi desiderii siam per riuscir noi, non isperiamo, <lb/>ma pure ci proveremo, studiandoci di prender di mira alle nostre indagini <lb/>i documenti, e di li e per l&igrave; condurre la nostra storia, a imitazion del Geo&shy;<lb/>metra che, ricongiungendo alcuni punti dati, disegna a mano una curva, <lb/>quando non pu&ograve; andantemente descriverla o col girare del raggio o appog&shy;<lb/>giato alla riga. </s></p><p type="main">

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

<s>Bench&egrave; il fine principale, per cui il principe Leopoldo de'Medici chiam&ograve; <lb/>a Firenze il Torricelli, fosse quello di aiutar Galileo, vecchio e infermo, a <lb/>distendere le sue speculazioni intorno alla forza della percossa, nonostante <lb/>&egrave; certo che, nel breve soggiorno di Arcetri, lo stesso Torricelli non in altro <lb/>fu adoperato dall'illustre ospite suo, che in riordinare i Dialoghi delle Due <lb/>Nuove Scienze. </s>

<s>Discutevano insieme, in que'solitarii colloqui, le dottrine in&shy;<lb/>torno il vacuo esposte nel Dialogo I, e Galileo, perseverando nel credere che <lb/>la ragione per cui l'acqua nelle trombe non sale pi&ugrave; su che alle diciotto <lb/>braccia, fosse quella speculata da lui, rivelava al tempo stesso al giovane <lb/>alunno, mostrandogli le lettere scritte da Genova, le speculazioni che molto <lb/><gap/> faceva il Baliani. </s></p><pb xlink:href="020/01/475.jpg" pagenum="456"/><p type="main">

<s>Qualunque fosse il giudizio, che apertamente allora fece delle dottrine <lb/>del Fisico genovese al cospetto di Galileo, il Torricelli sent&igrave; da quelle lettere <lb/>venire un'aura di verit&agrave; a fecondargli mirabilmente l'ingegno. </s>

<s>Il Baliani, <lb/>soggiogato dall'autorit&agrave; di Galileo, che era uscito in pubblico a professare <lb/>dottrine diverse, e travolto dalla comune opinione, secondo la quale si di&shy;<lb/>ceva non potersi dare il vacuo se non con grandissima difficolt&agrave; e violenza, <lb/>aveva oramai abbandonate le sue speculazioni, lusingato che il peso di quel&shy;<lb/>l'acqua rimasta sospesa nel tubo di rame non potess'esser forza sufficiente <lb/>a contrastare col peso di tutta l'altezza dell'aria. </s>

<s>Ma il Torricelli non si la&shy;<lb/>scia trasportar dalla corrente delle opinioni: sente l'autorit&agrave; di Galileo, ma <lb/>pi&ugrave; potentemente quella del vero, e ritenuto collo stesso Galileo che il peso <lb/>dell'aria sia una quattrocentesima parte del peso dell'acqua, e che l'aria <lb/>vaporosa e visibile, come dimostrano gli Autori de'crepuscoli, si alzi sopra <lb/>di noi intorno a cinquanta o cinquantaquattro miglia, trova calcolando, che <lb/>la pressione di tanta altezza d'aria, se pu&ograve; parer alquanto soverchia, non &egrave; <lb/>per&ograve; di troppo sproporzionata al peso contrastante di una colonna d'acqua <lb/>alta diciotto braccia. </s>

<s>Quando perci&ograve; il Magiotti gli rifer&igrave; l'esperienza fatta <lb/>in Roma da Gaspero Berti, il Torricelli non dubit&ograve; di applicare, a spiegare <lb/>il fatto spettacoloso, le ragioni del Baliani, che ogni giorno pi&ugrave; veniva tanto <lb/>facendo sue, da non accorgersi che erano state prima di altri. </s>

<s>Cos&igrave;, per <lb/>esempio, quando nella Lettera del d&igrave; 11 Giugno scriveva al Ricci: <emph type="italics"/>Noi siamo <lb/>sommersi nel fondo d'un pelago d'aria elementare, la quale per espe&shy;<lb/>rienza indubitata si sa che pesa,<emph.end type="italics"/> non si sar&agrave; accorto ch'ei si serviva delle <lb/>medesimi immagini e delle medesime espressioni, di che s'era servito lo <lb/>scrittor delle Lettere dirette a Galileo da Genova, quattordici anni prima. </s></p><p type="main">

<s>Quelle per&ograve; che nel Baliani erano vacillanti speculazioni, nel Torricelli <lb/>si ridussero a dottrine certe, dimostrate dall'esperienza, le quali furono nel <lb/>sagace ingegno feconde di nuove scoperte. </s>

<s>Di tali scoperte notabilissima &egrave; <lb/>quella del variar l'aria la sua pressione sui corpi sottoposti da un giorno <lb/>a un altro, e talvolta altres&igrave; da un'ora a un'altra. </s>

<s>Come il Torricelli riu&shy;<lb/>scisse a fare un'osservazione tanto nuova e tanto importante, &egrave; nostro prin&shy;<lb/>cipal debito investigare, appuntandosi qui i desiderii di tutti coloro, che <lb/>amano di sapere i principii, rimasti fin qui occulti, dell'invenzion del Ba&shy;<lb/>rometro. </s></p><p type="main">

<s>Quel che Galileo scrive nel I Dialogo delle Nuove Scienze della palla <lb/>di cera, che ora galleggia, ora affonda nell'acqua, non solamente coll'ingra&shy;<lb/>vir l'acqua stessa colla mistione di qualche materia pi&ugrave; grave di lei, ma <lb/>col riscaldarla o col raffreddarla (Alb. </s>

<s>XIII, 72), dette occasione al Torri&shy;<lb/>celli d'inventar quel Termometro, che fu in quinto luogo descritto dagli Ac&shy;<lb/>cademici del Cimento fra gli strumenti, da conoscer le alterazioni dell'aria <lb/>derivanti dal caldo e dal freddo. (Saggi Nat. </s>

<s>esp., Firenze 1841, pag. </s>

<s>16). <lb/>E perch&egrave; di tali esperienze, fatte con palline di vetro o di rame sottile in <lb/>parte piene d'acqua e in parte di aria, che ora spontaneamente scendevano <lb/><gap/><pb xlink:href="020/01/476.jpg" pagenum="457"/>celli le modific&ograve; in varie guise, studiandosi di rendere agli occhi del So&shy;<lb/>vrano lo spettacolo pi&ugrave; giocondo coll'invenzione dello strumento, che ne'Re&shy;<lb/>gistri appartenenti al primo periodo della Sperimentale Accademia medicea <lb/>si trova cos&igrave; descritto: &ldquo; Fatto un vaso di vetro cilindrico con la bocca stretta <lb/>e pieno d'acqua fin vicino alla bocca, dentro si metta una palla di rame <lb/>sottile, che abbia un piccolo buco: con un dito andando turando pi&ugrave; o meno <lb/>la bocca del vaso, la palla ander&agrave; salendo e scendendo &rdquo; (Targioni, Notiz. </s>

<s><lb/>Aggrand. </s>

<s>ed. </s>

<s>cit., T. I, pag. </s>

<s>155). La notizia di questo strumento e la de&shy;<lb/>scrizione di que'giochetti termostatici l'apprese un de'primi il Moncony, il <lb/>quale viaggiando per la prima volta in Italia, e passando per Firenze, and&ograve; <lb/>la mattina del d&igrave; 6 di Novembre 1646 a far visita al Torricelli, <emph type="italics"/>qui me dit,<emph.end type="italics"/><lb/>scrive nella <emph type="italics"/>Premiere Partie<emph.end type="italics"/> de'suoi <emph type="italics"/>Voyages, que le Gran Due avoit di&shy;<lb/>vers Thermometres pour conno&icirc;tre le chaud et le froid.... Il m'en dit <lb/>une autre d'une boule pleine d'air &agrave; moiti&eacute;, et la moiti&eacute; d'eau, avec un <lb/>trou en bas, et emp&ecirc;ch&eacute;e de monter en haut par une cha&icirc;ne de verre: <lb/>quand l'air se condense il y entre plus d'eau, et ainsi la cha&icirc;ne s'accour&shy;<lb/>cit, et la bouteille d&eacute;cend; quand au contraire l'air se rarefie, l'eau sort, <lb/>la bouteille monte et la cha&icirc;ne est plus longue.<emph.end type="italics"/> (Paris, Delaulne 1695, <lb/>pag. </s>

<s>261). </s></p><p type="main">

<s>La ragione per&ograve; del muoversi cos&igrave; le palline di vetro accomodate den&shy;<lb/>tro i boccioli, il Torricelli o la confid&ograve; al Moncony in segretezza o si fid&ograve; <lb/>di lui che, essendo straniero e di passaggio, non l'avrebbe divulgata in Fi&shy;<lb/>renze, perch&egrave; il Granduca voleva non solamente far credere che fosse sua <lb/>l'invenzione, ma che egli solo ne sapesse il mistero. </s></p><p type="main">

<s>Mosso da questa sua ambizione, appena morto il Torricelli il Granduca <lb/>stesso incominci&ograve;, in quegli scientifici consessi, che distinguono il secondo <lb/>periodo della sperimentale Accademia medicea, a dar lo spettacolo de'suoi <lb/>giuochetti termostatici, proponendo ai convocati che ne indovinessero le ra&shy;<lb/>gioni. </s>

<s>Il Viviani che, fra gli stessi convocati teneva le prime parti, fa men&shy;<lb/>zione di ci&ograve; in una sua nota: &ldquo; Dopo scritto, mi &egrave; sovvenuto un modo di <lb/>risolvere un altro problema, che ne&igrave; medesimo Congresso d'ieri fu messo <lb/>in campo, ed &egrave; come si possa far due corpi, come due pescetti di vetro, <lb/>che stando nell'istesso tempo uno di loro a galla in un'acqua, e l'altro in <lb/>fondo nella medesima, ad un'istessa mutazione che si faccia nell'acqua di <lb/>pi&ugrave; calore, quello che &egrave; galleggiante se ne vadi in fondo, e nell'istesso mo&shy;<lb/>mento quello che &egrave; in fondo ne venga a galla; e tornando a raffreddar <lb/>l'acqua, quello di fondo torni a galla e l'altro ne vadi in fondo, onde la <lb/>medesima causa, nel medesimo tempo, partorisca contrarii modi &rdquo; (MSS. <lb/>Cim., T. X, c. </s>

<s>102). </s></p><p type="main">

<s>Non contento il Granduca di tentare i suoi di Firenze, volle proporre <lb/>il curioso problema ai principali Fisici d'Italia, fra'quali Bartolommeo Im&shy;<lb/>periali e Raffaello Magiotti. </s>

<s>L'Imperiali, con lettera di Genova del 1649 a <lb/>cui manca il mese e il giorno, rispondeva cos&igrave; all'invito: &ldquo; Sono in obbligo <lb/><gap/><pb xlink:href="020/01/477.jpg" pagenum="458"/>sua grandezza, e complire alla mia parola di accennare qualche cosa intorno <lb/>agli effetti che si veggono e si osservano, non senza maraviglia, degli stru&shy;<lb/>menti, de'quali V. A. si degn&ograve; di farmi grazia. </s>

<s>Per quanto abbia, per cos&igrave; <lb/>dire, chiamato a consiglio le deboli forze del mio intelletto, nel rintracciar <lb/>le cagioni de'buccioli di vetro, entro li quali sono le ballottine di cristallo; <lb/>non trovo che ci&ograve; possa dipendere che entro sono vacui gli stessi ballottini, <lb/>onde, col premersi l'aria e acqua di sopra, premesi pur anco tutta l'acqua &rdquo; <lb/>(ivi, T. XXI, c. </s>

<s>12). </s></p><p type="main">

<s>Il Magiotti aveva allo stesso modo, ma pi&ugrave; completamente dell'Impe&shy;<lb/>riali, risoluto il Problema termostatico <emph type="italics"/>inviato da Fiorenza,<emph.end type="italics"/> di che rendeva <lb/>conto, non direttamente al Granduca, ma al principe Don Lorenzo, in una <lb/>breve Scrittura data da Roma l&igrave; 26 di Luglio 1648, col titolo di <emph type="italics"/>Renitenza <lb/>certissima dell'acqua alla compressione.<emph.end type="italics"/> In essa, rispetto all'esperienza che <lb/>pi&ugrave; fa al proposito nostro, e alla quale pure appellavan le parole sopra tra&shy;<lb/>scritte dell'Imperiali, il Magiotti scriveva: &ldquo; Aggiungo che questi scherzi <lb/>son pi&ugrave; sicuri in un cilindro pien d'acqua, perch&egrave; quel serrarlo ed impri&shy;<lb/>mervi leggermente la mano o dito grosso, basta e n'avanza per forzar quel <lb/>poco d'aria che sta dentro alle caraffine &rdquo; (Targioni, Notizie ecc. </s>

<s>ediz. </s>

<s>cit., <lb/>T. II, pag. </s>

<s>188). </s></p><p type="main">

<s>Or essendo un fatto che questa esperienza del danzar le palline o le <lb/>caraffine dentro l'acqua de'boccioli, premutane colla mano o col dito grosso <lb/>l'aria sovrastante alla bocca, fu fatta gi&agrave; dal Torricelli, e fu proposta a spie&shy;<lb/>gar dal Granduca, fra gli altri all'Imperiali e al Magiotti; giova investigare <lb/>a quali occasioni e come il Torricelli stesso sapesse tanto trovar di serio <lb/>in ci&ograve; che, per il Sovrano e per chi lo secondava, non avea che l'apparenza <lb/>di uno scherzo. </s></p><p type="main">

<s>Tenendo preparati que'boccioli pieni d'acqua, dentro alla quale stavano <lb/>immerse le palline di vetro, congiunte con que'tubetti descritti al Moncony, <lb/>tubi che la fantasia del Magiotti seppe trasformar nel dorso traforato delle <lb/>sue figurine danzanti, e poi il Cartesio nelle code de'suoi <emph type="italics"/>Diavoli;<emph.end type="italics"/> il Tor&shy;<lb/>ricelli si accorse di un fatto singolare, che cio&egrave; quelle palline di vetro tal&shy;<lb/>volta spontaneamente salivano o si abbassavano per l'acqua, anco quando <lb/>il Termometro mostrava rimaner costante la temperatura. </s>

<s>&mdash; Che pu&ograve; esser <lb/>ragione di ci&ograve;? </s>

<s>&mdash; si domandava l'arguto osservatore. </s>

<s>E tutto allora dietro <lb/>a ripensare e a calcolar gli effetti della pressione dell'aria, gli venne il so&shy;<lb/>spetto che il moto delle palline immerse, il quale non poteva dipendere dal <lb/>costiparsi e dilatarsi dell'aria rinchiusa dentro alle stesse palline per variar <lb/>del freddo e del caldo, dipendesse invece dal variar la pressione dell'aria <lb/>soprincombente alla superficie dell'acqua. </s>

<s>Per assicurarsene, cominci&ograve; a pre&shy;<lb/>mere e a rilassar colla palma della mano l'aria alla bocca del bocciolo, e <lb/>trov&ograve; che premendo le palline affondavan di pi&ugrave;, e rilassando tornavano <lb/>a galla. </s></p><p type="main">

<s>Fatto omaggio al Granduca di ci&ograve; che di dilettevole e di giocoso con&shy;<lb/><gap/><pb xlink:href="020/01/478.jpg" pagenum="459"/>scoperta che ne avea ricavata, aggiungendo al fatto noto, e per altre vie <lb/>dimostrato, del premer che fa l'aria con tutto il peso della sua altezza i <lb/>corpi sottoposti, l'altro fatto nuovo della variabilit&agrave;, a cui la forza di quel <lb/>torchio soggiace da un giorno all'altro. </s></p><p type="main">

<s>Or erano rivolti tutti i pensieri del Torricelli a costruire uno strumento, <lb/>che desse indizio certo e segnasse allo stesso tempo la precisa misura di <lb/>quelle variazioni. </s>

<s>Poteva esser fondamento alla nuova invenzione quello stesso <lb/>bocciolo pien d'acqua dentrovi immersa una pallina, alla quale, applicato un <lb/>filo metallico digradato, come in quei <emph type="italics"/>Termostatici<emph.end type="italics"/> descritti nelle proposi&shy;<lb/>zioni CXVIII e CXIX <emph type="italics"/>De motionibus naturalibus<emph.end type="italics"/> dal Borelli, dal sollevarsi <lb/>e abbassarsi lo stesso filo sulla superficie dell'acqua ne facesse argomentare <lb/>il premere or pi&ugrave; grave, or pi&ugrave; leggiero dell'aria. </s>

<s>Ma il Torricelli rivolse <lb/>piuttosto il pensiero all'esperienza del Berti, in cui il variar di livello l'acqua <lb/>nel tubo indicherebbe il giusto variar della misura cercata. </s>

<s>Per&ograve; quel tubo, <lb/>dovend'essere pi&ugrave; lungo delle diciotto braccia, non poteva tirarsi facilmente <lb/>di vetro, che ne facesse all'occhio dell'osservatore trasparir le variazioni di <lb/>livello, e dall'altra parte quella era troppo gran macchina da non prestarsi <lb/>alle comodit&agrave; di uno strumento osservatorio. </s></p><p type="main">

<s>Allora, s'avvide il Torricelli che il grandioso e incomodo macchina&shy;<lb/>mento dipendeva dall'aver l'acqua troppo piccola gravit&agrave; specifica, da far <lb/>contrasto coll'aria: che se invece si fosse adoperato un liquido pi&ugrave; grave, <lb/>forse potevasi ridurre il tubo a tal lunghezza da maneggiarlo con facilit&agrave;, e <lb/>da farlo anco di vetro. </s>

<s>Gli venne in mente il mercurio, al quale, essendo <lb/>egli 13 volte e mezzo in circa pi&ugrave; grave dell'acqua, poteva esser d'avanzo <lb/>una canna di vetro lunga due braccia. </s>

<s>Una tal canna era facil cosa empirla <lb/>e capovolgerla nel mercurio, facendo il dito, a turarne e sturarne la bocca, <lb/>ci&ograve; che si faceva nel tubo del Berti col laborioso epistomio. </s>

<s>Conferito il pen&shy;<lb/>siero col Viviani, come il Dati racconta, il giorno dopo la piccola macchi&shy;<lb/>netta Torricelliana in Firenze mostrava l'esperienza del vacuo, come l'aveva <lb/>alquanti anni prima mostrata in Roma la grande e faticosa macchina Bertiana. </s></p><p type="main">

<s>Da questo punto dunque, dal punto cio&egrave; in cui il Torricelli pens&ograve; di co&shy;<lb/>struire uno strumento che misurasse le variazioni dell'aria, sostituendo nel <lb/>tubo e nell'apparecchio del Berti il mercurio all'acqua, taciuti i precedenti, <lb/>incomincia la storia del celebre fatto narrata dal Torricelli stesso al Ricci <lb/>nella sua prima Lettera del d&igrave; 11 Giugno 1644. &ldquo; Le accennai gi&agrave; che si <lb/>stava facendo non so che esperienza filosofica intorno al vacuo, non per far <lb/>semplicemente il vacuo, ma per fare uno strumento che mostrasse le mu&shy;<lb/>tazioni dell'aria ora pi&ugrave; grave e grossa, ora pi&ugrave; leggera e sottile. </s>

<s>Molti hanno <lb/>detto che non si dia, altri che si dia, ma con repugnanza della Natura e <lb/>con fatica: non so gi&agrave; che alcuno abbia detto che si dia senza fatica e senza <lb/>resistenza della Natura &rdquo; (Lett. </s>

<s>a'Filaleti, Firenze 1663, pag. </s>

<s>20). E che <lb/>appunto il vuoto si dia, senza fatica e senza resistenza della Natura, passa <lb/>a dimostrarlo coll'esperienza dell'argento vivo da lui descritta in un breve <lb/>tratto di penna, perch&egrave; in sostanza non era al Ricci una cosa nuova. </s></p><pb xlink:href="020/01/479.jpg" pagenum="460"/><p type="main">

<s>Quel che di nuovo insegnava il Torricelli consisteva nel confermare con&shy;<lb/>tro i Peripatetici le svanite dottrine del Baliani, secondo le quali lo spazio <lb/>lasciatosi indietro dall'argento vivo era vuoto, e la causa del sostenersi il <lb/>liquido nel tubo era esterna e non interna. </s>

<s>Alcune per&ograve; di quelle peripa&shy;<lb/>tetiche contradizioni erano vecchie, e Galileo le imperson&ograve; in quel Simpli&shy;<lb/>cio, che, per negare al Salviati il vuoto, che egli affermava esser rimasto <lb/>tra il fondo del corpo di tromba e l'embolo dello stantuffo, ritirato a gran <lb/>forza indietro; diceva che poteva esser <emph type="italics"/>penetrata aria o esalazioni o altre <lb/>materie pi&ugrave; sottili per le porosit&agrave; del legno, e anche dall'istesso vetro<emph.end type="italics"/><lb/>(Alb. </s>

<s>XIII, 20). Il Salviati rispondeva richiamando Simplicio all'esperienza, <lb/>e, fatto nel fondo del corpo di tromba <emph type="italics"/>un poco di umbilico prominente,<emph.end type="italics"/><lb/>diceva che li si sarebbero dovute raccoglier le esalazioni, di che per&ograve;, es&shy;<lb/>sendo quel corpo di tromba un cilindro di vetro, nulla se ne scorgeva. </s></p><p type="main">

<s>Ma come pretendesse il Salviati che si potessero dal suo e dall'occhio <lb/>di Simplicio scorgere quelle esalazioni spiritose, e invisibili anche attraverso <lb/>all'acqua, non si capisce. </s>

<s>Il Torricelli dimostr&ograve; bene l'esistenza del vacuo <lb/>in un altro modo, facendo salire, in luogo del mercurio, l'acqua, la quale <lb/>con orribile impeto and&ograve; a riempir tutto il tubo. </s></p><p type="main">

<s>Ad altre peripatetiche, eppur vecchie contradizioni, Galileo non solo non <lb/>rispose, ma egli fu che le aveva promosse e avvalorate. </s>

<s>Que'peripatetici <lb/>infatti, i quali sostenevano che la causa del rimanere cos&igrave; sospeso il mer&shy;<lb/>curio era per forza interna di vacuo, professavano le dottrine stesse pro&shy;<lb/>fessate contro il Baliani, nel I Dialogo delle Nuove Scienze, da Galileo; e <lb/>quegli altri, i quali dicevano che il mercurio dentro il tubo era attratto da <lb/><emph type="italics"/>quella roba sommamente rarefatta,<emph.end type="italics"/> ripetevano le dottrine galileiane del&shy;<lb/>l'aria che sostien, per attrazione calamitica, a galla le tavolette di ebano o <lb/>di metallo tanto pi&ugrave; gravi in specie dell'acqua. </s>

<s>A queste contradizioni, in&shy;<lb/>torno a che i peripatetici stessi si facevan forti dell'autorit&agrave; di Galileo, il <lb/>Torricelli rispondeva coll'esperienza, facendo il vuoto in un tubo terminato <lb/>alla sua sommit&agrave; in una palla, mostrando che qui, dove si raccoglieva pi&ugrave; <lb/>roba attraente, il mercurio era nulladimeno sostenuto alla medesima altezza. </s></p><p type="main">

<s>Alle vecchie contradizioni e difficolt&agrave; il Ricci ne aggiunse delle nuove, <lb/>e l'espose in una sua Lettera indirizzata da Roma, il d&igrave; 18 Giugno 1644, <lb/>allo stesso Torricelli. </s>

<s>Quelle difficolt&agrave; si riducono a tre, ma pi&ugrave; importanti <lb/>son la prima e la seconda. </s>

<s>Consisteva la prima nel dir che, chiusa la sco&shy;<lb/>della del mercurio, non doveva il peso dell'aria gravar che sul coperchio. </s>

<s><lb/>A che il Torricelli rispondeva coll'esempio della lana premuta da un peso, <lb/>la quale, tagliata da un ferro presso il fondo, riman pure allo stesso modo <lb/>compressa. </s>

<s>La seconda difficolt&agrave; del Ricei consisteva nel dire che l'aria non <lb/>esercita il suo peso che dall'alto in basso, a che il Torricelli risponde con <lb/>parole, in cui compendiasi un trattato nuovo d'Idrostatica, che cos&igrave; l'aria <lb/>come l'acqua, con ogni gas e con ogni liquido, esercitano la loro pr&egrave;ssione <lb/>ugualmente per tutti i versi. </s></p><p type="main">

<s>A illustrare cos&igrave; fatte idrostatiche dottrine, prima del 1658, cio&egrave; prima <pb xlink:href="020/01/480.jpg" pagenum="461"/>che fosse nota in Italia la prima Lettera torricelliana, aveva atteso pure il <lb/>Borelli, il quale anzi confessa al principe Leopoldo di aver sentito un gran <lb/>dispiacere in trovar che dal Torricelli stesso era stato prevenuto nelle sue <lb/>speculazioni. </s>

<s>&ldquo; In questo proposito dir&ograve; di un gusto dispiacevole che ho avuto, <lb/>vedendo una lettera della b. </s>

<s>m. </s>

<s>del Torrirelli diretta al signor M. A. Ricci, <lb/>nella quale accenna quella stessa ragione dimostrativa, che io trovai perch&egrave;, <lb/>otturando l'inferior bocca del vaso dell'argento vivo, ed impedendo la com&shy;<lb/>pressione di tutta la regione aerea, tuttavia si mantiene l'argento vivo nel <lb/>cannello alla altezza di un braccio e un quarto in circa, e per maggior mio <lb/>martello adopra il medesimo esempio della lana, conforme io esemplicavo la <lb/>cosa con molti materazzi &rdquo; (MSS. Cim., T. XVI, c. </s>

<s>103). Non manc&ograve; per&ograve; <lb/>modo al Borelli di distinguersi per altre novit&agrave; di speculazioni e di espe&shy;<lb/>rienze, tutte ordinate a illustrare i principii torricelliani, e ci&ograve; egli fece con <lb/>grande ardore nel suo Trattato <emph type="italics"/>De motionibus naturalibus,<emph.end type="italics"/> in varie parti del <lb/>libro, ma segnatamente in quella sequela di proposizioni, dalla C alla CIX. </s></p><p type="main">

<s>Scriveva il Cornelio, dedicando la sua celebre Epistola <emph type="italics"/>De Circumpul&shy;<lb/>sione<emph.end type="italics"/> a Marcello Crescenzio, del cos&igrave; decantato esperimento dell'argento vivo: <lb/>&ldquo; de quo tot tantaque brevi temporis spatio scripta sunt volumina, quae in&shy;<lb/>tegram bibliothecam possint explere. </s>

<s>&rdquo; Non fu senza dubbio questione che <lb/>tanto venisse agitata quanto questa, non eccettuata la non men celebre con&shy;<lb/>troversia copernicana, che tanto le si assomiglia e nelle avventure e nell'im&shy;<lb/>portanza. </s>

<s>Ma lasciando da parte quel turbolento e violento che veniva a <lb/>metter nella questione del vuoto la Teologia peripatetica, a intender come <lb/>un tal questionar di vuoto e non vuoto riuscisse tanto loquace, basta il pen&shy;<lb/>sar che i contradittori del vero avevano una parte di ragione. </s>

<s>Non parliam <lb/>di Francesco Lino, e di quel suo <emph type="italics"/>funicolo<emph.end type="italics"/> tanto poderosamente rotto dal <lb/>Boyle, ma il gran Grimaldi si contrappose ai fautori del vuoto, dicendo che <lb/>la sommit&agrave; della canna era invece piena delle invisibili esalazioni del mer&shy;<lb/>curio. </s>

<s>&ldquo; Est autem substantia illa ab hydrargirio extracta magis quam vitrum <lb/>ipsum perspicua, ideoque ab aliquibus creditum fuit eam non adesse sed <lb/>remanere in fistula vitrea spatium aliquod vacuum &rdquo; (De Lumine, Bono&shy;<lb/>niae 1665, pag. </s>

<s>52). E confortava il suo asserto coll'esperienza, imperocch&egrave; <lb/>soggiunge: &ldquo; si fistulae summitati applicetur aliquod calefactivum, hydrar&shy;<lb/>girium magis descendit in fistula; si vero applicetur aliquod frigefactivum <lb/>eidem summitati, hydrargirium in reliquo fistulae contentum ascendit &rdquo; (ibi). <lb/>Le premesse si appoggiavano sopra un vero sperimentale, ma la conclusione <lb/>era falsa, e in ogni modo giocava il grand'uomo di fantasia, quando diceva <lb/>che le vibrazioni fatte dal mercurio, prima di equilibrarsi dentro la canna, <lb/>erano ordinate dalla natura a far pi&ugrave; facilmente esalare que'sottilissimi pro&shy;<lb/>fluvii, onde provveder che lo spazio non rimanesse vuoto; fantasia che sva&shy;<lb/>niva all'esperienza e al discorso fatto da Donato Rossetti nella sua <emph type="italics"/>Dimo&shy;<lb/>strazione fisico-matematica<emph.end type="italics"/> delle <emph type="italics"/>sette proposizioni<emph.end type="italics"/> (Firenze, 1668, prop. </s>

<s>III, <lb/>pag. </s>

<s>23). E sacrificava pure il Grimaldi il grande ingegno all'idolo peripa&shy;<lb/><gap/> in <gap/>uelle esalazioni mercuriali, piuttosto che nella pressione <pb xlink:href="020/01/481.jpg" pagenum="462"/>esterna dell'aria, riconosceva la forza che teneva sospeso l'argento vivo nella <lb/>canna torricelliana. </s>

<s>Il padre Daniello Bartoli, senza nominarlo, per amor fra&shy;<lb/>terno e per riverenza, parve che volesse scrivere principalmente contro di <lb/>lui quel suo pregevole <emph type="italics"/>Discorso,<emph.end type="italics"/> che ha per titolo <emph type="italics"/>La tensione e la pressione <lb/>disputanti qual di loro sostenga l'argento vivo ne'cannelli dopo fattone il <lb/>vuoto:<emph.end type="italics"/> Discorso stampato in Bologna nel 1677, e dove, con sottili ragiona&shy;<lb/>menti confortati d'esperienze, che in tanta dovizia hanno pure del nuovo; si <lb/>conclude a favor della pressione torricelliana contro la tensione grimaldiana. </s></p><p type="main">

<s>Cos&igrave; il Bartoli, gesuita, parve che venisse a offerir la vittoria, anche a <lb/>nome de'peripatetici, al Torricelli, la Lettera del quale al Ricci rimase ve&shy;<lb/>nerando documento e sincero pascolo di scienza. </s>

<s>E ora, ritornando a leg&shy;<lb/>ger quella celebre lettera, la quale contiene in una carta sola la sapienza <lb/>dispersa per innumerevoli volumi, duole a sentir l'Autore cos&igrave; concludere <lb/>il suo discorso: <emph type="italics"/>La mia intenzion principale poi non &egrave; potuta riuscire, <lb/>cio&egrave; di conoscere quando l'aria fosse pi&ugrave; grossa e grave, e quando pi&ugrave; <lb/>sottile e leggera collo strumento<emph.end type="italics"/> (Lett. </s>

<s>a'Fil. </s>

<s>cit., pag. </s>

<s>21). Or se dunque <lb/>il Torricelli stesso confessa di non esser riuscito a far lo strumento da mi&shy;<lb/>surar le variazioni del peso dell'aria, s'avvedono i nostri Lettori che la sto&shy;<lb/>ria dell'invenzion del Barometro incomincia qui, dove noi stessi e tutti ci <lb/>saremmo aspettati che dovess'esser di gi&agrave; terminata. </s></p><p type="main">

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

<s>Se le nostre indagini storiche, con le quali ci siamo studiati di sodi&shy;<lb/>sfare alla viva curiosit&agrave; del Mersenno, abbiano conseguito l'intento, lo la&shy;<lb/>sceremo all'imparziale giudizio de'nostri lettori, ma in tanto non pu&ograve; non <lb/>muoverci a gran maraviglia il trovar come sia stata dal Mersenno stesso e <lb/>da tutti gli altri frantesa quella parte cos&igrave; chiara di storia, che si contiene <lb/>nella Lettera prima del Torricelli. </s>

<s>Il Torricelli incomincia ivi a dire che la <lb/>sua esperienza non <emph type="italics"/>era per far semplicemente il vacuo,<emph.end type="italics"/> e il Mersenno d&agrave; <lb/>fuori voce, o s'intende quella sua voce come un dir che il Torricelli abbia <lb/>fatta l'esperienza del vacuo. </s>

<s>In ogni modo il Pascal l'intese cos&igrave;, e fu da <lb/>ci&ograve; mosso a speculare con tanto ingegno e ad eseguir con tant'arte quelle <lb/>sue otto esperienze, con le quali, credendo di promuover l'esperienza tor&shy;<lb/>ricelliana, tornava invece in dietro a far, con que'suoi lunghi tubi pieni <lb/>d'acqua e di vino, carrucolati su per le antenne de'vascelli roanesi, quel <lb/>che parecchi anni prima aveva fatto in Roma Gaspero Berti. </s></p><p type="main">

<s>Pi&ugrave; tardi, quest'altra voce si sparse e giunse essa pure alle orecchie <lb/>del Pascal: che il Torricelli rendeva ragione dello star sospesi i liquidi nei <lb/>tubi del vuoto, attribuendo il fatto spettacoloso alla pressione dell'aria. </s>

<s>Que&shy;<lb/>sto s&igrave; era vero, e conforme a ci&ograve; che leggevasi nella prima Lettera al Ricci, <lb/>ma per&ograve; non era la principale intenzione che si proponesse, in trattar di <lb/><gap/><pb xlink:href="020/01/482.jpg" pagenum="463"/>chiaro in principio, e lo ripete in fine della Lettera stessa: l'intenzion di <lb/>adattar lo strumento dell'argento vivo a servir da Barometro. </s></p><p type="main">

<s>Ora &egrave; notabilissimo, e da non lasciarsi senza considerazione, che l'in&shy;<lb/>tenzion principale venisse ad essere sopraffatta dalla secondaria. </s>

<s>&ldquo; Questa, <lb/>scriveva il Dati, non &egrave;, come molte altre esperienze, che in s&egrave; stessa fini&shy;<lb/>sca, ma ell'&egrave; una perenne scaturigine d'innumerevoli e profondi misteri <lb/>della Natura &rdquo; (Lett. </s>

<s>a'Fil. </s>

<s>cit., pag. </s>

<s>24). L'avere il Pecquet, per esempio, <lb/>svelati que'misteri nella Fisiologia, il Guericke nella Meteorologia, il Boyle in <lb/>quasi tutti gli ordini della scienza sperimentale, senza dubbio, ricompensava <lb/>largamente l'iattura dell'aver trascurato l'esperienza in s&egrave; stessa. </s>

<s>Ma non <lb/>s'intende perch&egrave; mai coloro, che videro la Lettera torricelliana al Ricci, non <lb/>attendessero per prima cosa a ricercar la ragione per cui non riusc&igrave; al Tor&shy;<lb/>ricelli stesso d'applicar la sua esperienza a misurare la variabilit&agrave; del peso del&shy;<lb/>l'aria. </s>

<s>Quella ragione, dall'altra parte, egli da s&egrave;, il Torricelli, dice che ell'era <lb/><emph type="italics"/>perch&egrave; il livello AB si muta per un'altra causa, che io non credeva mai, <lb/>cio&egrave; pel caldo e freddo, e molto sensibilmente, appunto come se il vaso AE <lb/>fosse pieno d'aria<emph.end type="italics"/> (Lett. </s>

<s>Fil., pag. </s>

<s>21). Gli effetti termometrici insomma <lb/>dubitava il Torricelli che venissero a complicarsi cos&igrave; coi barometrici, da <lb/>non poter discernere gli uni dagli altri. </s>

<s>Ecco la gran difficolt&agrave;, innanzi a <lb/>cui, con troppo frettolosa impazienza, si arretr&ograve; e che lo fece disperar di <lb/>ridurre il suo strumento dell'argento vivo ad uso di Barometro. </s></p><p type="main">

<s>Fra'tanti cultori della scienza torricelliana nulladimeno, uno ve ne fu, <lb/>e de'pi&ugrave; illustri di tutti, il quale incor&ograve; anzi speranza da ci&ograve; che aveva fatto <lb/>prima disperare il Torricelli. </s>

<s>Roberto Boyle ebbe anch'egli a osservar che <lb/>il mercurio nel tubo torricelliano imitava, bench&egrave; con pi&ugrave; tardo passo, i <lb/>moti stessi del Termometro. </s>

<s>&ldquo; Dum per aliquas hebdomadas tubus in fe&shy;<lb/>nestra, quam raro aperuimus, consisteret, ansa mihi data est observandi <lb/>hydrargirium saepius motum liquoris in Thermometro contenti, passu de&shy;<lb/>biliori tamen, imitari: calidiori enim coelo paulum subsidere, frigidiore ali&shy;<lb/>quantulum ascendere solebat, quod nos maiori vel minori aeris in tubi summo <lb/>pressioni vertendum duximus, expansi nimirum aut condensati, per calorem <lb/>nempe vel per frigus, quibus successive ambiens aer afficiebatur &rdquo; (Experim. </s>

<s><lb/>Nova, Op. </s>

<s>Omn., T. I, Venetiis 1697, pag. </s>

<s>38). </s></p><p type="main">

<s>A questa osservazione il Torricelli adombr&ograve;, e abbandon&ograve; il suo nobile <lb/>intento, ma il Boyle prosegu&igrave; animoso e ritrov&ograve; che se talvolta il mercurio <lb/>nello strumento del vacuo e il liquido del Termometro s'imitavan nel moto, ben <lb/>pi&ugrave; spesso per&ograve; avveniva che si movesse questo mentre l'altro restava fermo, <lb/>e che l'uno facesse il passo in contraria parte dell'altro. </s>

<s>&ldquo; Res autem cuius <lb/>observationi intentius inhaerebam, haec erat: quod mercurius saepe nunc <lb/>subsideret, nunc in tubo prosurgeret notabiliter, secus atque in Thermometris <lb/>usuvenit, quibus in tubi summitate aer continetur: imo nonnunquam modo <lb/>plane contrario se movere visus est. </s>

<s>Vidimus enim aliquando sub frigidissimo <lb/>coelo .... mercurium molto inferius quam aliis temporibus decidisse &rdquo; (ibi). </s></p><p type="main">

<s>Da ci&ograve; il Boyle ne concludeva ci&ograve; che aveva concluso il Torricelli, <pb xlink:href="020/01/483.jpg" pagenum="464"/>17 anni prima, per l'osservazione delle palline immerse dentro l'acqua dei <lb/>boccioli. </s>

<s>&ldquo; Experimentum quippe, quod huic dissertationi ansam praebuit, <lb/>satis probat verisimile esse quod ipsi etiam atmosphaerae non desint quasi <lb/>fluxus et refluxus plane admirabiles, aut saltem quod varias patiatur per <lb/>magnas et repentinas, secundum altitudinem suam aut densitatem mutatio&shy;<lb/>nes, quarum tam causae quam et ipsi effectus incautos nos atque nihil <lb/>eiusmodi speculantes praetereunt &rdquo; (ibi, pag. </s>

<s>40). </s></p><p type="main">

<s>Sembrerebbe cos&igrave;, che da questo XVIII Esperimento boileiano incomin&shy;<lb/>ciasse l'applicazione dell'esperienza torricelliana ad uso di Barometro, ma <lb/>pure era un'applicazione barometrica l'esperienza fatta nel 1648 da M. </s>

<s>Pe&shy;<lb/>rier sul Puy De Domme, e anzi in quel tempo che lo stesso Perier speri&shy;<lb/>mentava il variar della pressione ammosferica secondo il variar delle altezze, <lb/>sperimentava altres&igrave; il variar di lei ne'varii giorni e nelle varie stagioni. </s>

<s><lb/>L'editor del <emph type="italics"/>Traitez de l'equilibre des liqueurs<emph.end type="italics"/> pubblic&ograve; un <emph type="italics"/>Recit des obser&shy;<lb/>vations faites par Monsieur Perier continuellement jour par jour, pendant <lb/>les annees 1649, 1650, 1651 en la ville de Clermont en Auvergne, sur <lb/>la diversit&eacute; des elevations ou abaissement du vif argent dans les tuyaux, <lb/>et de celles qui ont est&eacute; faites en mesme temps sur le mesme sujet a Paris <lb/>par un de ses amis, et a Stokolm, en Suede par Messieurs Chanut et <lb/>Descartes.<emph.end type="italics"/> E il Capitolo IV <emph type="italics"/>De la pesanteur de l'air<emph.end type="italics"/> del Pascal, pubblicato <lb/>postumo dallo stesso editore, s'intitola: &ldquo; Que comme la pesanteur de la <lb/>masse de l'air augmente, quand il est plus charg&eacute; de vapeurs, et diminu&eacute; <lb/>quand il l'est moins; aussi les effets qu'elle produit augmentent et dimi&shy;<lb/>nuent a proportion &rdquo; (Paris, 1663, pag. </s>

<s>96). </s></p><p type="main">

<s>Ma l'esser queste scritture del Pascal rimaste inedite infino al 1663, <lb/>dette luogo al Boyle di specular come cosa nuova intorno al suo XVIII Espe&shy;<lb/>rimento, e ad Isacco Vossio d'uscir fuori a descrivere <emph type="italics"/>constructionem Aero&shy;<lb/>scopii, a nemine quod sciam, hactenus observati, unde quam latissime, ni <lb/>fallor, colligi possit quinam sit aeris status .... quod enim aeri, ipsum <lb/>quoque hoc hydrargiro fistulis incluso contingit &rdquo;<emph.end type="italics"/> (De motu marium et <lb/>vent. </s>

<s>Hagae Com., 1663, pag. </s>

<s>120, 21). </s></p><p type="main">

<s>Pi&ugrave; tardi ancora, cio&egrave; nel 1669, il Sinclaro credeva di essere stato il <lb/>primo ad applicar lo strumento torricelliano alla misura delle variabilit&agrave; del <lb/>peso dell'aria secondo il variar delle altezze, e a imporre allo strumento <lb/>stesso il nome di <emph type="italics"/>Baroscopio.<emph.end type="italics"/> In un dialogo dell'<emph type="italics"/>Ars Magna<emph.end type="italics"/> tra Francesco <lb/>e Alessandro, dop'aver questi esposta la teoria del Baroscopio e dop'aver <lb/>detto com'ella venga confermata dall'osservare le variazioni del livello del <lb/>mercurio nel salire e nel discender da un monte, Francesco soggiunge: <lb/>&ldquo; Rem quidem clarissime demonstrat hoc novum experimentum, sed scias <lb/>velim me prius de eo audivisse. <emph type="italics"/>Alex.<emph.end type="italics"/> Quid tu narras? <emph type="italics"/>Franc.<emph.end type="italics"/> Imo ad eam&shy;<lb/>dem conclusionem illustrandam idemmet adductum vidi experimentum in <lb/>libello quodam nuper excuso cui epigraphe <emph type="italics"/>Philosophia experimentalis<emph.end type="italics"/> lin&shy;<lb/>gua vulgari. </s>

<s>Quam vercor ne nimis trita tua feceris experimenta prius non&shy;<lb/><gap/></s></p><pb xlink:href="020/01/484.jpg" pagenum="465"/><p type="main">

<s>Noi crediamo che queste cose il Sinclaro le dica in buona fede, e forse <lb/>nella remota Scozia non era veramente ancora approdata la notizia di quelle <lb/>scoperte, che il buon professor di Glascovia si lusingava di presentare egli <lb/>al mondo come primizia. </s>

<s>Ma l'esperienza sul Puy De Domme fu dalla fama <lb/>tanto largamente diffusa, che par impossibile non ne penetrasse il suono <lb/>anco attraverso alle montagne Scozzesi, e il Boyle, ne'suoi <emph type="italics"/>Nuovi experi&shy;<lb/>menti,<emph.end type="italics"/> cio&egrave; dieci anni prima che fosse pubblicata l'<emph type="italics"/>Ars Magna,<emph.end type="italics"/> aveva in&shy;<lb/>differentemente chiamato Baroscopio e Barometro lo strumento torricelliano. </s></p><p type="main">

<s>Non volendo per&ograve; disputar sui nomi, e lasciando liberamento al Vossio <lb/>chiamarlo Aeroscopio, al Sinelario Baroscopio, al Boyle Barometro, &egrave; un fatto <lb/>che il celebre strumento alle mani di tutti questi osservatori, non eccettuato <lb/>il Sinclaro, che lo trasport&ograve; non solamente sulle alture de'monti, ma nelle <lb/>profondit&agrave; delle miniere e de'mari; si trova esser composto ancora di quella <lb/>canna di vetro e di quella catinella d'immersione, che serv&igrave; alla prima espe&shy;<lb/>rienza del Torricelli. </s></p><p type="main">

<s>Ma questo apparecchio torricelliano non era con troppa facilit&agrave; traspor&shy;<lb/>tabile, e n&egrave; perci&ograve; riuscivano comparabili le osservazioni fatte in luoghi di&shy;<lb/>versi. </s>

<s>Quanto alla comodit&agrave; sarebbesi senza dubbio, assai meglio prestato <lb/>quel semplice tubo, senza catinella d'immersione, che ci descrive il Viviani <lb/>ne'suoi manoscritti (Gal. </s>

<s>Disc., T. CXXXII, c. </s>

<s>113) e che poi il Borelli pub&shy;<lb/>blic&ograve; nel Trattato <emph type="italics"/>De motion. </s>

<s>naturalibus.<emph.end type="italics"/> &ldquo; Idipsum nostrae fistulae di&shy;<lb/>rectae in aere constitutae adaptari potest, sitque illa AC (fig. </s>

<s>45) duorum <lb/><figure id="id.020.01.484.1.jpg" xlink:href="020/01/484/1.jpg"/></s></p><p type="caption">

<s>Figura 45.<lb/>cubitorum, habeatque orificium C insignis exiguitatis, re&shy;<lb/>pleaturque mercurio, deorsumque invertatur in aere libero <lb/>(non enim necesse est ut os C intra scutellam mercurii <lb/>plenam infundatur, quando valde stricta est os eius C) <lb/>tunc ab infimo orificio C mercurius in aere profluet, quou&shy;<lb/>sque altitudo CB fuerit unius cubiti, et quadrantis pro&shy;<lb/>xime &rdquo; (Regio Julio, 1670, pag. </s>

<s>214). Un tale strumento <lb/>per&ograve; non era applicabile che a sola la misura della discesa <lb/>del livello del mercurio, via via che l'aria esterna rimette <lb/>della sua pressione. </s></p><p type="main">

<s>Il Borelli stesso aveva immaginato un altro Baro&shy;<lb/>metro semplicissimo, comodo quanto quello ora descritto, <lb/>perch&egrave; composto anch'esso di un solo tubo di vetro, e atto ugualmente a <lb/>misurar le pressioni ammosferiche ne'loro accessi e ne'loro recessi. </s>

<s>A mezzo <lb/>il tubo era insinuata una gocciola di mercurio, che serviva per indice della <lb/><figure id="id.020.01.484.2.jpg" xlink:href="020/01/484/2.jpg"/></s></p><p type="caption">

<s>Figura 46.<lb/>scala, e il tubo stesso tenevasi non eretto <lb/>verticalmente ma in posizione orizzon&shy;<lb/>tale L'inventore stesso, ne descrive cos&igrave; <lb/>la forma e l'uso: &ldquo; Sia il cilindro sot&shy;<lb/>tilissimo di cristallo serrato estremamente in B (fig. </s>

<s>46) ed aperto in A: si <lb/>metta in esso una minuta gocciola di argento vivo, e si spinga verso il <lb/>fondo B, come in C. </s>

<s>Questo si faccia al fondo di una torre dalla cima della, <pb xlink:href="020/01/485.jpg" pagenum="466"/>quale pendano due fili, a'quali legando il cilindro, nel tirarlo poscia in su, <lb/>lo sollevino orizzontalmente. </s>

<s>Intanto diversi osservatori disposti a varie fine&shy;<lb/><figure id="id.020.01.485.1.jpg" xlink:href="020/01/485/1.jpg"/></s></p><p type="caption">

<s>Figura 47.<lb/>stre della torre, nel passaggio che fa <lb/>da loro il cilindro, segnino con pal&shy;<lb/>line di cera o con una pennata d'in&shy;<lb/>chiostro il luogo che occupa quivi la <lb/>gocciola dell'argento, che condotto <lb/>finalmente sulla cima pi&ugrave; alta, dal <lb/>luogo che ivi occuper&agrave; l'istessa goc&shy;<lb/>ciola e da'segni fatti sopra il cilindro <lb/>(se le finestre saranno state in egual <lb/>distanza) si raccorr&agrave; quanto sia stata <lb/>dilatata l'aria e con qual proporzione &rdquo; <lb/>(Targioni, Not. </s>

<s>aggrand., T. II, P. II, <lb/>pag. </s>

<s>690). </s></p><p type="main">

<s>Nonostante, la stessa sua sover&shy;<lb/>chia semplicit&agrave; non conferiva a un <lb/>tal Barometro borelliano quelle qua&shy;<lb/>lit&agrave;, che si ricercavano per render lo <lb/>strumento abile a rispondere a tutte <lb/>le intenzioni della scienza. </s>

<s>A ridurlo <lb/>tale rivolse verso il 1667 i suoi pen&shy;<lb/>sieri il Boyle, introducendo nello stru&shy;<lb/>mento stesso torricelliano il tubo a <lb/>sifone, solidamente applicato a una <lb/>tavoletta di legno. </s>

<s>&ldquo; Hisce stimulis <lb/>accito et ad Baroscopios portatiles <lb/>atque itinerarios (si sic loqui liceat) <lb/>factitandos memet accingenti, trina <lb/>haec moliri subiit. </s>

<s>Primo vas illud <lb/>qua sustentum, qua stagnantem mer&shy;<lb/>curium conclusurum e vitro continuo <lb/>ac diametri aequalis adfiat: dein ut <lb/>post vasis istius impletionem tali illud <lb/>loculamento collocarem, quod et facile <lb/>transfretari posset, et moderatam sal&shy;<lb/>tem vitro adversum illatam ab extra <lb/>vim defensionem praeberet, nulla eius <lb/>parte a machina prominente, quod in <lb/>aliis Baroscopiis fieri solet. </s>

<s>Tertio, ita <lb/>illius locationi incubui, ut fracturae <lb/>facill ob violentum inhospitantis mer&shy;<lb/>curii motum non sit obnoxium &rdquo; <lb/>(Novor. </s>

<s>experim. </s>

<s>contin. </s>

<s>I, Experim. </s>

<s>XXII, Venetiis 1697, T. I, pag. </s>

<s>248). <pb xlink:href="020/01/486.jpg" pagenum="467"/>Una tal costruzione, che il Boyle stesso esegu&igrave; e fece rappresentare in un <lb/>iconismo da noi riprodotto qui nella figura 47, si pu&ograve; dire il tipo di tutti <lb/>i Barometri a mercurio. </s></p><p type="main">

<s>Il celebre Fisico inglese, che nel suo Nuovo esperimento XXXIV, fu <lb/>primo a far l'esperienza del Baroscopio, cos&igrave; propriamente detto, nel vuoto, <lb/>pens&ograve; altres&igrave; di sostituire il Baroscopio stesso nell'aria, per servirsene a mi&shy;<lb/>surar la variabilit&agrave; della pressione. </s>

<s>A questo nuovo strumento, che si di&shy;<lb/>stinse col nome di <emph type="italics"/>Baroscopio statico,<emph.end type="italics"/> rivolse la sua attenzione il Viviani, e <lb/>studiandosi a perfezionarlo, proluse all'invenzione di simili altri strumenti <lb/>delicatissimi, di che s'onorarono poi alcuni stranieri. </s></p><p type="main">

<s>&ldquo; Il Boyle, cos&igrave; appunto di propria mano scrive il Viviani, propone di <lb/>fare un Baroscopio statico, pigliando un paio di bilance e ponendovi da una <lb/>parte una palla di vetro fatta alla lucerna, della grandezza di un'arancia, e <lb/>dall'altra un contrappeso di bronzo che stesse in equilibrio colla palla piena <lb/>d'aria, col quale strumento, allorch&egrave; preponderava o la palla di vetro o <lb/>quella di bronzo, veniva in cognizione delle variazioni dell'aria nella stessa <lb/>forma che col Barometro pieno di argento vivo. </s>

<s>Questo strumento del Boyle <lb/>patisce un'eccezione, alla quale non pens&ograve; e questo si &egrave; che pel caldo e <lb/><figure id="id.020.01.486.1.jpg" xlink:href="020/01/486/1.jpg"/></s></p><p type="caption">

<s>Figura 48.<lb/>pel freddo l'aria contenuta nella palla <lb/>si raref&agrave; e si condensa e cos&igrave; viene <lb/>a esercitare minore o maggior forza, <lb/>come che la molla o vogliam dire ela&shy;<lb/>sticit&agrave; dell'aria cresca con proporzion <lb/>reciproca della grandezza. </s>

<s>Per rime&shy;<lb/>diare a questa difficolt&agrave; si pu&ograve; fare <lb/>il Barometro statico in questa guisa: <lb/>Si pigli un pezzo di acciaio, sopra il <lb/>quale si segnino minutamente i gradi <lb/>e vi si metta un romano, e alle estremit&agrave; vi si attacchino due palle di vetro <lb/>aperte in cima, una delle quali si serri con una cartapecora ben sigillata e <lb/>l'altra si lasci aperta, e posta in equilibrio col romano: si aver&agrave; sempre la <lb/>differenza dell'aria. </s>

<s>Sia l'istrumento in questa guisa: (fig. </s>

<s>48). Oppure si <lb/><figure id="id.020.01.486.2.jpg" xlink:href="020/01/486/2.jpg"/></s></p><p type="caption">

<s>Figura 49.<lb/>potrebbe fare questo stesso strumento <lb/>in altra guisa, empiendolo d'argento <lb/>vivo, facendo un cannello di vetro pieno <lb/>di mercurio, nell'estremit&agrave; del quale <lb/>fossero attaccate allo stesso cannello due <lb/>palle di vetro, che una di serrassi come <lb/>si &egrave; detto, l'altra stesse aperta, e che si <lb/>notassero nel cannello i gradi, per vedere <lb/>l'ascesa e la discesa del mercurio, il <lb/>che potrebbe farsi in talforma: (fig. </s>

<s>49). <lb/>Cos&igrave;, potendosi aprire la parte che si dice che dee star chiusa, ed in <lb/><gap/><pb xlink:href="020/01/487.jpg" pagenum="468"/>e condensazione, che s'incontra nel Barometro statico proposto dal Boyle &rdquo; <lb/>(MSS. Gal., T. CXXXII, c. </s>

<s>16). </s></p><p type="main">

<s>Lasciamo ai nostri Lettori il ripensare alle somiglianze che passano fra <lb/>questo nuovo Barometro statico del Viviani e il <emph type="italics"/>Termometro differenziale<emph.end type="italics"/><lb/>del Leslie e il <emph type="italics"/>Termoscopio<emph.end type="italics"/> del Rumford, contentaudoci di richiamar la loro <lb/>attenzione sopra ci&ograve; che il Wolf, nel Cap. </s>

<s>IV del II Volume, Parte I, della <lb/>sua <emph type="italics"/>Fisica sperimentale,<emph.end type="italics"/> dice, per rivendicar l'invenzione dello strumento <lb/>del Boyle a Ottone di Guericke. </s>

<s>Ottone, secondo il Fisico prussiano, &egrave; ve&shy;<lb/>ramente l'Autore dello strumento da misurar le variazioni di densit&agrave;, che <lb/>subisce l'aria e ch'egli chiama col nome di <emph type="italics"/>Manometro.<emph.end type="italics"/> &ldquo; Primus Mano&shy;<lb/>metri inventor fuit Otho Guerickius, qui hoc instrumentum anno 1661 in <lb/>Epistola ad eruditum Jesuitam Gasparem Schottum describit &rdquo; (Trad. </s>

<s>A. Bina, <lb/>Venetiis 1756, pag. </s>

<s>93). Ma la questione si dirime assai facilmente dallo <lb/>stesso Wolf, il quale confessa che altro era l'uso del Barometro statico del <lb/>Boyle, altro l'uso del Manometro del Guericke. </s></p><p type="main">

<s>Men facile forse potrebbe parere a trovar ragioni da rispondere al me&shy;<lb/>desimo Autore della Fisica sperimentale prussiana, il quale, nel capitolo pre&shy;<lb/>cedente al citato, vorrebbe far lo stesso Ottone, prima del Boyle, autor del <lb/>Barometro; se a ognun che guarda il X iconismo, impresso a pag. </s>

<s>99 degli <lb/><emph type="italics"/>Esperimenti nuovi<emph.end type="italics"/> di Magdeburgo (Amstelodami 1672), non fosse ovvio il <lb/>giudicare che, sebben quella figurina, la quale mostra col dito, sulla parete <lb/>del tubo di vetro dentro cui &egrave; inclusa, i gradi dell'ascesa e della discesa, <lb/>pu&ograve; esser comoda e dilettevole a prognosticare il bel tempo e la pioggia, non <lb/>d&agrave; nulladimeno alcuna buona speranza di porgersi docile a prestar que'de&shy;<lb/>licati e scrupolosi servigi, a che il Barometro portatile del Boyle colle mo&shy;<lb/>dificazioni introdottevi dai Meteorologi e dai Geodeti, sarebbe stato poi in&shy;<lb/>vocato a prestare, nelle sue tanto gelose operazioni, alla scienza. </s></p><pb xlink:href="020/01/488.jpg"/><p type="main">

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

<s><emph type="center"/><emph type="bold"/>Della Macchina elettrica e della Pila voltaia<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

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

<s>I. </s>

<s>Del globo di zolfo del Guericke, e del globo di vetro dell'Hawksbee; della Macchina elettrica di <lb/>Lipsia, del Winkler, del Nollet, del Ramsden. </s>

<s>&mdash; II. </s>

<s>Della Bottiglia di Leyda; dell'Elettroforo <lb/>e del Condensatore del Volta. </s>

<s>&mdash; III. De'primi Elettroscopii: dell'Elettroscopio a boccetta, del&shy;<lb/>l'Elettrometro condensatore, e dell'Elettrometro a quadrante. </s>

<s>&mdash; IV. </s>

<s>Della grande scoperta gal&shy;<lb/>vanica dell'Elettricit&agrave; animale, e della nuova Elettricit&agrave; metallica scoperta dal Volta. </s>

<s>&mdash; V. Del&shy;<lb/>l'Elettromotore del Volta a Colonna, e a Corona di tazze. </s></p><p type="main">

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

<s>Passar dal Barometro, per chi, in questi nostri capitoli di storia, cer&shy;<lb/>casse un nesso o un ordine evidente di successione, a parlar della Macchina <lb/>elettrica, potrebbe a prima vista parer quasi un saltar d'Arno in Bacchi&shy;<lb/>glione, come per proverbio si dice. </s>

<s>Nonostante, se &egrave; vero quel che s'&egrave; da <lb/>noi asserito pi&ugrave; volte, che cio&egrave; dalla celebre esperienza torricelliana dell'ar&shy;<lb/>gento vivo fu promosso ogni ordine di scienza sperimentale, non possono <lb/>altro aspettarsi i nostri Lettori se non che si mostri a loro come mai da <lb/>quella stessa esperienza torricelliana fosse promossa la scienza elettrica, la <lb/>quale non fu prima vista fiorire che un secolo dopo. </s>

<s>I fatti che siamo qui <lb/>per narrare saranno quelli, da cui si concluder&agrave; la desiderata dimostrazione, <lb/>bench&egrave; non sia, ne'suoi primi principii, per apparire evidente, avendo anche <lb/>noi a pigliar le mosse da Ottone di Guericke. </s></p><p type="main">

<s>Ha il celebre Filosofo di Magdeburgo, ai fisici esperimenti, troppo spesso <lb/>e con troppo amore disposate le metafisiche speculazioni, con le quali ardi&shy;<lb/>tamente risale a considerare le virt&ugrave; mondane, ch'egli poi vede tutte insieme <lb/>rappresentate, come in immagine viva, in un globo di zolfo. </s>

<s>Il piccolo Mondo <lb/>metafisico, a render pi&ugrave; perfetta la rassomiglianza col grande Mondo fisico, <pb xlink:href="020/01/489.jpg" pagenum="470"/>&egrave; configurato in isfera velocemente girata attorno; e perch&egrave;, per la sua pic&shy;<lb/>colezza, e per non essere altro che immagine di cosa vera, l'attrito che ri&shy;<lb/>ceve dall'aria ambiente non basta, vi s'aggiunge lo sfregar della palma della <lb/>mano. </s>

<s>Cos&igrave; le virt&ugrave; mondane latenti nel piccolo globo sulfureo vengono vi&shy;<lb/>vamente eccitate, e una leggera piuma che vi si appressi, essendovi ora <lb/>attratta e ora respinta, d&agrave; sicuro indizio della mondana virt&ugrave; attrattiva e re&shy;<lb/>pulsiva, e le tenebre rivelano all'occhio di chi rimira il piccolo Mondo la <lb/>sua propria virt&ugrave; lucente. </s>

<s>&ldquo; Nam si eum (globum sulphureum) in conclave <lb/>obscurum tecum conferas et palma sicca praeprimis noctu atteras, eadem <lb/>ratione lucet, qua saccharum si tundatur &rdquo; (Experim. </s>

<s>nova magd., Amste&shy;<lb/>lodami 1672, pag. </s>

<s>149, 50). </s></p><p type="main">

<s>Da ci&ograve; si volle riconoscere Ottone come primo inventore della Macchina <lb/>elettrica, n&egrave; potendosi da noi negar ci&ograve;, e anzi soggiungendo che il Fisico <lb/>di Magdeburgo fece importantissime esperienze elettriche col macchinamento <lb/>di quel suo globo sulfureo; non possiamo non sentirci compresi di gran mara&shy;<lb/>viglia in considerare che le scoperte, per le quali iniziava un nuovo e splen&shy;<lb/>didissimo mondo della scienza, rimanessero per un mezzo secolo dimenticate. </s>

<s><lb/>Cos&igrave;, a un impulso che si riconosce per validissimo, non solo non fu visto <lb/>succedere, ne'progressi della scienza elettrica, un proporzionato effetto, ma <lb/>nessuno effetto veramente ne consegu&igrave;, come se giusto si fosse quell'im&shy;<lb/>pulso esercitato nella cedevole aria a produrvi una passeggera commozione <lb/>di vento. </s></p><p type="main">

<s>Pi&ugrave; sottilmente per&ograve; considerando, si trova che un cos&igrave; fatto impulso, <lb/>riusc&igrave; per questo inefficace, perch&egrave; non venne per la diritta via. </s>

<s>La Metafi&shy;<lb/>sica, pi&ugrave; presto che la Fisica, era che lo dirigeva, e le aeree speculazioni <lb/>distolsero gli occhi dello stesso Ottone dal proseguire pi&ugrave; attentamente i <lb/>fatti. </s>

<s>Ma quando questi fatti rientrarono nel loro ordine fisico, e allora la <lb/>scienza elettrica progred&igrave;, con lento, ma non interrotto passo, e d'un sottile <lb/>zampillo d'acqua si vide a poco a poco diventare un gran fiume, che poi <lb/>va a distendersi in un gran lago, da meritarsi, per l'ampiezza e per la pro&shy;<lb/>fondit&agrave;, meglio il nome di mare. </s>

<s>Quel sottile zampillo scaturisce, come d'arida <lb/>selce, dal vetro di uno di que'tubi dello Strumento torricelliano, e di l&igrave; ha <lb/>origine il fiume, che si dilaga nella scienza di tutto quel calore, di tutta <lb/>quella luce, e di tutta quella vita, che commove il secolo presente. </s></p><p type="main">

<s>Nell'anno 1675, una notte, occorse al celebre Picard di dover traspor&shy;<lb/>tare da un luogo all'altro un suo Barometro a mercurio, e qui fu sorpreso <lb/>da uno spettacolo nuovo: la cos&igrave; detta <emph type="italics"/>camera del vuoto<emph.end type="italics"/> gli appar&igrave; splen&shy;<lb/>dente di una luce in tutto simile a quella, che si vede esalar dal fosforo <lb/>posto in un luogo oscuro. </s>

<s>Ripensando poi che il fenomeno non appariva in <lb/>tutti i Barometri, e non sempre n&egrave; allo stesso modo si riproduceva nel Ba&shy;<lb/>rometro medesimo, riguard&ograve; quella fosforescenza come un'apparizione straor&shy;<lb/>dinaria, e da non farsene caso, piuttosto che come un fatto naturale meri&shy;<lb/>tevole di essere speculato. </s></p><p type="main">

<s>Ma presto poi si conobbe che i Barometri atti a fosforeggiare erano <pb xlink:href="020/01/490.jpg" pagenum="471"/>assai pi&ugrave; frequentati di quel che il Picard non pensasse, e il Cassini fece <lb/>cos&igrave; notare agli Accademici di Francia quella frequenza, da richiamarvi sopra <lb/>l'attenzione di Giovanni Bernoulli. </s>

<s>Egli diligentemente sperimentando ritrov&ograve; <lb/>che il fosforo mercuriale, nel vuoto barometrico, non &egrave; un'apparenza straor&shy;<lb/>dinaria, propria e particolare di uno strumento o di un altro, ma dimostr&ograve; <lb/>che era un fatto naturalissimo, e ch'egli avviene in tutti gli strumenti, pur&shy;<lb/>ch&egrave; per&ograve; sodisfacciano alle richieste condizioni. </s>

<s>Del resultato di queste sue <lb/>nuove esperienze rendeva conto il Bernoulli, nel 1700, in una Memoria in&shy;<lb/>serita negli Atti della R. </s>

<s>Accademia di Scienze. </s>

<s>Essendosi cos&igrave; divulgata <lb/>fra'dotti la scoperta del fosforo mercuriale, il Musschenbroeck la diffuse nel <lb/>popolo, fabbricando alcuni tubi di vetro ripieni in parte di mercurio e vo&shy;<lb/>tati d'aria, i quali, agitati colla mano, apparivano al buio miracolosamente <lb/>splendenti. </s></p><p type="main">

<s>Cos&igrave;, scienziati e volgo quietavano nella persuasione che il mercurio <lb/>agitato nel vuoto acquistasse la virt&ugrave; di esalare quella fosforica luce, quando <lb/>uno de'tubi spettacolosi del Musschenbroeck capit&ograve; in Londra alle mani <lb/>dell'Hawksbee. </s>

<s>Il giochetto, in che gli altri fanciullescamente si dilettavano, <lb/>a lui parve degno delle speculazioni del Filosofo, e avendo risaputo degli <lb/>studii, che vi aveva fatto attorno il Bernoulli, se ne volle informare con gran <lb/>diligenza. </s>

<s>Di quelle bernulliane osservazioni due principalmente rimasero <lb/>impresse nell'Hawksbee: la prima, che la luce fosforica &egrave; solamente visi&shy;<lb/>b&igrave;le quando il mercurio nel vuoto barometrico discende; e l'altra, che quella <lb/>fosforica luce &egrave; pi&ugrave; intensa, quando il tubo di vetro non &egrave; per tutto uguale <lb/>e andante, ma ora s'allarga in ventri e ora si ristringe in istrozzature. </s>

<s>La <lb/>prima di quelle osservazioni, che egli sperimentando ritrov&ograve; verissima, gli <lb/>fece nascere il sospetto che la luce fosforica non esalasse, come dicevasi, dal <lb/>mercurio, ma scaturisse dal vetro; e la seconda osservazione gli fece con&shy;<lb/>getturare che una tal luce, per questo appunto scaturisse dal vetro, perch&egrave; <lb/>eccitata dalla confricazion del mercurio. </s>

<s>Confermavasi in questa sua conget&shy;<lb/>tura l'arguto Fisico inglese, vedendo che, anche stando quieto il mercurio <lb/>al di dentro, potevasi eccitar la solita luce a pure stropicciar il vetro di fuori <lb/>colle dita: &ldquo; Si potrebbe, egli dice, con qualche probabilit&agrave; congetturare che la <lb/>luce prodotta, proceda da qualche qualit&agrave; nel vetro, per una tal confrica&shy;<lb/>zione o moto datogli, e non dal mercurio per altro conto, se non solamente <lb/>in quanto egli &egrave; un corpo proprio, quale battendo o strofinando sopra il <lb/>vetro produca la luce. </s>

<s>E quello che pare che confermi tal congettura si &egrave; <lb/>che avendo stropicciato colle dita la parte superiore e vota d'un Barometro <lb/>mercuriale, ne scatur&igrave; una luce, senza che l'argento vivo si movesse &rdquo; (Esper. </s>

<s><lb/>fisico meccan., Firenze 1716, pag. </s>

<s>32). </s></p><p type="main">

<s>Per rendere il fenomeno pi&ugrave; parvente l'Hawksbee, invece della piccola <lb/>camera barometrica, speriment&ograve; sopra un pallone di vetro votato d'aria colla <lb/>Macchina pneumatica, e, invece di fregar col dito, fregava con tutta la palma <lb/>della mano il pallone stesso fatto girare velocemente attorno, per mezzo di <lb/><gap/> un globo di vetro, di circa nove dita di dia-<pb xlink:href="020/01/491.jpg" pagenum="472"/>metro, e ne cavai l'aria.... Essendo in questa maniera assicurato il globo, <lb/>lo fermai ad una macchina che gli dava un moto veloce col suo asse per&shy;<lb/>pendicolare all'orizzonte, e dipoi, applicando la mia nuda mano distesa alla <lb/>superficie di quello, ne risult&ograve; che in brevissimo tempo si produsse una <lb/>considerabil luce &rdquo; (ivi, pag. </s>

<s>30). </s></p><p type="main">

<s>L'artificio di votare il pallone dell'aria contenutavi era per conformarsi <lb/>all'esperienza del fenomeno nel vuoto barometrico, ma venuta poi voglia al&shy;<lb/>l'industre sparimentatore di riammettere dentro il pallone stesso l'aria ca&shy;<lb/>vata, rest&ograve; sorpreso dal vederne uscir fuori, scoppiettando in scintille vive, <lb/>quella luce, che prima rimanevasi dentro ugualmente diffusa. </s>

<s>&ldquo; Procurai un <lb/>vetro, di figura pi&ugrave; sferica che fusse possibile, di diametro e di lunghezza <lb/>di circa sette dita. </s>

<s>L'asse di questo vetro, trovandosi parallelo all'orizzonte, <lb/>ed essendone cavata l'aria contenuta, gli fu dato moto da una macchina di <lb/>nuova invenzione. </s>

<s>E gli effetti di questa, rispetto alla luce, prodotta per l'at&shy;<lb/>trizione di essa, furono assai simili a quelli delle antecedenti sperienze. </s>

<s>Ma <lb/>quando fu lasciata rientrar l'aria e fu dato come da principio il moto e <lb/>l'attrizione, restai sorpreso dall'apparenza d'una vivace vigorosa luce, con&shy;<lb/>tinuata tralla punta del mio dito ed il vetro. </s>

<s>Non era solamente chiara e <lb/>visibile sopra il dito, ma di pi&ugrave; pareva, in una certa maniera, che perco&shy;<lb/>tesse con qualche forza sopra di quello, essendo ci&ograve; facile a distinguersi al <lb/>tatto, mediante una forza di gentil compressione, bench&egrave; il movente corpo <lb/>non ne fosse toccato per quasi la grossezza d'un mezzo dito. </s>

<s>Questa luce <lb/>pareva che uscisse dal vetro con rumore considerabile, non dissimile d'una <lb/>voce roca, quantunque alquanto pi&ugrave; forte &rdquo; (ivi, pag. </s>

<s>42, 43). </s></p><p type="main">

<s>La nuova scoperta del globo di vetro, che, confricato colla palma della <lb/>mano, anche nella luce del giorno, all'appressarvi un dito o altro corpo di&shy;<lb/>viene scintillante, fu descritta dall'Hawksbee nel patrio linguaggio e inse&shy;<lb/>rita fra'suoi <emph type="italics"/>Physico-mechanical Experiments<emph.end type="italics"/> pubblicati in Londra nel 1609 <lb/>e tradotti, sette anni dopo, nella nostra lingua, in Firenze. </s>

<s>Presto se ne dif&shy;<lb/>fuse in Inghilterra e per tutta l'Europa la notizia, specialmente pel magi&shy;<lb/>stero autorevole e universale del Newton, il quale, nella VIII Questione <lb/>commemor&ograve; il fatto elettrico nuovamente scoperto colle seguenti parole: &ldquo; Si&shy;<lb/>militer globus vitreus, diametro circiter 8 aut 10 unciarum, machinae ver&shy;<lb/>satili infixus, ut circa axem suum motu celerrimo circumagatur, qua sui <lb/>parte vola manus apposita inter volvendum confricetur, lucebit. </s>

<s>Quod si <lb/>eodem tempore charta alba, aut linteum album vel etiam digitus extremus ita <lb/>admoveatur, ut circiter quarta vel dimidia unciae parte distet a vitro, qua parte <lb/>motus eius est celerrimus, vapor elettricus frictione manus a vitro excitatus, <lb/>et ad chartam albam, linteum, vel digitum allisus, ita agitabitur, ut lucem <lb/>continuo emittat, efficiatque ut charta illa alba, linteum vel digitus, tanquam <lb/>cicindela lucescat, quin et a vitro erumpens, ea vi nonnunquam ad digitum <lb/>allidatur, ut etiam tactu percipi queat. </s>

<s>Quod idem quoque evenit, quando cy&shy;<lb/>lindrus e vitro electrove, longus et amplus, charta manu admota eousque con&shy;<lb/>fricetur donec vitrum <gap/></s></p><pb xlink:href="020/01/492.jpg" pagenum="473"/><p type="main">

<s>L'uso di confricar colla carta, piuttosto che colla palma della mano <lb/>ignuda, di qui si vede che cominci&ograve; presto a precorrere all'ufficio de'guan&shy;<lb/>cialetti, nella costruzione della Macchina elettrica, come pure assai presto si <lb/>pens&ograve; ai glob&igrave; di sostituire i cilindri, e si volle, invece del vetro, veder se <lb/>migliore effetto si faceva dall'ambra. </s>

<s>L'Hawksbee stesso volle tentar lo spe&shy;<lb/>rimento anche con cilindri di legno intonacati di ceralacca, di zolfo e di <lb/>pece mescolata con matton pesto, ma trov&ograve; che nulla agguagliava all'effi&shy;<lb/>cacia del vetro, specie avendosi cura di mantenerlo asciutto. </s></p><p type="main">

<s>Cos&igrave; aveva mostrato il celebre Inglese da che masso e con qual verga <lb/>miracolosa, potesse il Fisico fare scaturire la sorgente elettrica: mancava, <lb/>diciam cos&igrave;, la secchia da attingerla, mancavano i canali da condurla e da <lb/>dispensarla. </s>

<s>Aveva gi&agrave; Ottone di Guericke osservato e descritto, ne'suoi Espe&shy;<lb/>rimenti Nuovi di Magdeburgo, un fatto assai singolare, ed era che la virt&ugrave; <lb/>attrattiva di quel suo globo di zolfo, poteva comunicarsi a un filo di lino, e <lb/>diffondersi per tutta la lunghezza di lui, in modo da attrarre a s&egrave; e da ran&shy;<lb/>nodarsi al capo di un altro filo posatogli alquanto discosto. </s>

<s>&ldquo; Filum lineum <lb/>si acumini ligni acuminati, inque mensa vel scamno firmati inhaerescere fa&shy;<lb/>cias, atque filum ulna longius demittas, ita quidem ut infra ibi aliud quid, <lb/>spatio pollicari remotius attingere possit (quoties scilicet globus excitatus, <lb/>summitati huius ligni admoveatur); inferius fili cum iuxsta apposito coniungi: <lb/>quo ad oculos demonstrandum hanc virtutem in filo lineo usque ad partes <lb/>infimae se extendisse, dum hoc, aut attrahit, aut seipsum alligat &rdquo; (Ed. </s>

<s>cit., <lb/>pag. </s>

<s>149). Lo sperimento fu molti anni dopo ripetuto dal Gray, il quale <lb/>trasmise la virt&ugrave; elettrica di un cilindro di vetro confricato a una cordicella <lb/>di canapa assai lunga, e vide l'estremit&agrave; di lei attrarre assai vivamente i <lb/>fiocchetti del cotone. </s></p><p type="main">

<s>Sono i fili di lino e le cordicelle di canapa, senza dubbio, i primi con&shy;<lb/>duttori elettrici, che siano stati scoperti; ma era riserbato a quel medesimo <lb/>Gray di rivelar la natura di que'corpi, a'quali eminentemente si compete&shy;<lb/>rebbe la virt&ugrave; di essere <emph type="italics"/>conduttori.<emph.end type="italics"/> Egli osserv&ograve; che, confricando i globi <lb/>o i cilindri nella macchina dell'Hawksbee, l'elettricit&agrave; del vetro si comu&shy;<lb/>nicava alle viere di metallo, fossero pur lunghe quanto si volesse, che face&shy;<lb/>vano da poli al volgere del torno. </s>

<s>Di qui ebbe origine la importantissima <lb/>scoperta de'corpi <emph type="italics"/>anelettrici,<emph.end type="italics"/> che si elettrizzano per comunicazione, rice&shy;<lb/>vendone la virt&ugrave; dagli <emph type="italics"/>idioelettrici,<emph.end type="italics"/> e, senz'altro; diffondendola per tutta la <lb/>loro lunghezza. </s></p><p type="main">

<s>La nuova e rilevantissima distinzione fra corpi <emph type="italics"/>idioelettrici<emph.end type="italics"/> o <emph type="italics"/>coibenti,<emph.end type="italics"/><lb/>e <emph type="italics"/>anelettrici<emph.end type="italics"/> o <emph type="italics"/>conduttori,<emph.end type="italics"/> fu per opera dello stesso Gray, introdotta nella <lb/>scienza elettrica, nel 1729, e di l&igrave; s'incominci&ograve; a immaginare, e a far uso <lb/>di quegli organi riconosciuti per pi&ugrave; atti e meglio disposti a condurre l'elet&shy;<lb/>tricit&agrave; attinta ai globi di vetro confricati. </s>

<s>Cos&igrave;, nel 1741, i Fisici tedeschi <lb/>erano riusciti a comporre un assai buono e comodo strumento, che, sotto il <lb/>nome di <emph type="italics"/>Macchina elettrica di Lipsia,<emph.end type="italics"/> fu descritto da Giovan Maria Della <lb/><gap/><pb xlink:href="020/01/493.jpg" pagenum="474"/>A condurre il fluido elettrico s'adoperava una catenella metallica tenuta so&shy;<lb/>spesa da cordoncini di seta, ma ad attingere il fluido e a comunicarlo alla <lb/>stessa catenella, s'adoperava una lastra di ferro, sopra la quale, come su <lb/>mensa, posavansi tre cannoncini, accostati insieme, di latta. </s>

<s>Poi, fra quat&shy;<lb/>tro pioli di legno perpendicolarmente eretti all'estremit&agrave; di una crociera <lb/>portata da un piede pur di legno secco, s'intesseva, d'un cordoncino di seta, <lb/>una coltricella a rete, sopra la quale adagiavasi la lamiera di ferro, e dispo&shy;<lb/>nevasi in modo, che i tre cannoncini di latta aprissero le loro bocche molto <lb/>presso al globo di vetro, per beverne avidamente l'elettricit&agrave;, che ne sca&shy;<lb/>turiva. </s>

<s>Ma perch&egrave; talvolta, fra i labbri taglienti della rigida latta e il gire&shy;<lb/>vole globo, succedeva qualche urto pericoloso, si pens&ograve; di far tre fascetti di <lb/>trucioli d'orpello, i quali, uscendo fuori da'tre cannoncini, si confregavano <lb/>con maggior superficie e cedevano nello stesso tempo agli urti del torno. <lb/>(Torre, Scienza della Natura, P. II, Napoli 1749, pag. </s>

<s>308-10). </s></p><p type="main">

<s>Fra que'Tedeschi per&ograve; uno ne fu, Enrico Winkler, il quale stim&ograve; di <lb/>ottenere miglior effetto, sostituendo al torno continuo della ruota, quello di <lb/>va e vieni di un arcoletto, che si faceva ora andare, ora tornare co'moti <lb/>alternativi del piede. </s>

<s>Egli sostituiva altres&igrave;, allo sfregamento della palma della <lb/>mano, quello di un cuscinetto ricoperto di pelle aspersa di creta secca. </s></p><p type="main">

<s>La Macchina elettrica di Lipsia, colle modificazioni suggerite dal Win&shy;<lb/>kler, quasi nello stesso tempo che da noi, s'introdusse in Francia, dove il <lb/>Nollet esercitava il pi&ugrave; autorevole magistero nella scienza. </s>

<s>Egli rifiut&ograve; il Tor&shy;<lb/>nio del Winkler, parendogli <emph type="italics"/>che uno stropicciamento sostenuto o reiterato <lb/>nello stesso verso riesca meglio, che quando alternativamente si faceva in <lb/>un verso contrario.<emph.end type="italics"/> (Lezioni di Fisica, trad. </s>

<s>it., T. V, Venezia 1764, pag. </s>

<s>175). <lb/>Rifiut&ograve; altres&igrave;, preferendogli lo stropicciamento delle mani, l'uso de'guancia&shy;<lb/>letti, intorno ai quali cos&igrave; scriveva: </s></p><p type="main">

<s>&ldquo; I Fisici, che si sono applicati all'esperienze dell'Elettricit&agrave;, non sono <lb/>ben d'accordo tra di loro circa la materia, che debbono preferire nello stro&shy;<lb/>picciare il vetro, e gli altri corpi da elettrizzarsi. </s>

<s>Gli uni raccomandano di <lb/>strofinare colla man nuda, gli altri vogliono che tra la mano e il corpo che <lb/>si strofina, vi sia un foglio di carta grigia, o una pezza di lana o un tocco <lb/>di pelle di camoscio saleggiata di bianco di Spagna o di Tripoli. </s>

<s>Molti fanno <lb/>girare i loro globi di rincontro a guancialetti di pelle di bufalo, pieni di <lb/>crino, o di qualche altra materia animalesca, ed altri fanno i loro strofinac&shy;<lb/>cioli con molti fogli di carta dorata o inargentata, posti gli uni sopra degli <lb/>altri, oppure con drappi nel cui tessuto sia entrato oro, argento o qualche <lb/>altro metallo.... Dir&ograve; solamente .... che nulla m'&egrave; paruto cos&igrave; atto a que&shy;<lb/>st'uso, quanto la man nuda, purch&egrave; non sia umida per traspirazione o <lb/>altrimenti &rdquo; (ivi, pag. </s>

<s>176, 77). </s></p><p type="main">

<s>La Macchina elettrica insomma, che il Nollet prima introdusse in Fran&shy;<lb/>cia, consisteva nello stesso globo tornatile dell'Hawksbee, applicatovi con&shy;<lb/>duttori molto pi&ugrave; semplici e pi&ugrave; efficaci. </s>

<s>Una catenella pendente sopra l'equa&shy;<lb/><gap/><pb xlink:href="020/01/494.jpg" pagenum="475"/>elettricit&agrave; a una lunga asta metallica sospesa da cordoncini di seta, la quale <lb/>asta spesso mettevasi in comunicazione con altre aste similmente sospese, <lb/>di che tutto insieme componevasi il conduttore. </s></p><p type="main">

<s>Una tal nuova efficacissima disposizione di conduttori elettrici fu sug&shy;<lb/>gerita al Nollet dall'avere il Gordon e il Monnier osservato che un condut&shy;<lb/>tore tanto meglio riesce quant'egli &egrave; pi&ugrave; lungo. </s>

<s>Quando poi una tal con&shy;<lb/>clusione venne, colle teorie e colle esperienze cos&igrave; luminosamente dimostrata <lb/>dal Volta, mentre che il Beccaria aveva rese cos&igrave; evidenti le propriet&agrave; gi&agrave; <lb/>prima scoperte nelle punte; s'intende come la Macchina elettrica potesse <lb/>allora giungere a que'perfezionamenti, oramai notissimi a tutti, a ricevere <lb/>i quali l'aveva, infin dal 1766, preparata il Ramsden a Londra. </s></p><p type="main">

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

<s>I conduttori che s'adopravano alle Macchine elettriche, prima del 1778, <lb/>cio&egrave; prima che il Volta dimostrasse con qual ragione se ne poteva aumen&shy;<lb/>tare la capacit&agrave;, non erano, colla loro scarica, atti a produrre nessuna com&shy;<lb/>mozione sui muscoli degli animali, e ci&ograve; perch&egrave; il fluido non vi si accumulava <lb/>nella quantit&agrave; necessaria. </s>

<s>Se insomma erasi ritrovata, ad attinger l'elettricit&agrave;, <lb/>la secchia, e s'eran pure ritrovati i canali da condurla e da dispensarla, <lb/>non s'aveva per&ograve; ancora la cisterna da riporvela e da conservarla. </s>

<s>Il ritro&shy;<lb/>vamento di cos&igrave; fatta cisterna occorse per un fatto assai singolare, e in che <lb/>modo si narrer&agrave; qui da noi brevemente. </s></p><p type="main">

<s>Nel 1746 il Winkler pubblicava a Lipsia un libro intitolato <emph type="italics"/>Della virt&ugrave; <lb/>elettrica dell'acqua elettrizzata in vasi di vetro.<emph.end type="italics"/> Si vollero l'esperienze del <lb/>Fisico tedesco verificare in Leyda, dove s'elettrizzava l'acqua, facendo ripe&shy;<lb/>tutamente scoccare la scintilla fra il conduttore della Macchina elettrica e <lb/>una verga metallica immersa, colla sua estremit&agrave; inferiore, nell'acqua stessa. </s>

<s><lb/>Ora avvenne allo sperimentatore, il quale con una mano teneva il vaso di <lb/>vetro, di appressar l'altra mano alla verga di metallo, e nell'atto stesso sent&igrave; <lb/>un'improvvisa commozion dolorosa, nelle braccia, nel petto, e in altra parte <lb/>del corpo. </s></p><p type="main">

<s>La notizia del fatto giunse in Francia in quello stesso anno 1746, scri&shy;<lb/>veva il Nollet, <emph type="italics"/>per via di due lettere in data di Leyden, l'una del de&shy;<lb/>funto sig. </s>

<s>Musschenbroeck al defunto signor di Reaumur, e l'altra del <lb/>sig. </s>

<s>Alaman a me diretta, le quali ce l'annunziarono come una scoperta <lb/>nuova e con termini capaci di sgomentare. </s>

<s>Non avendoci i detti signori <lb/>espressamente assegnato da chi, per la prima volta, fosse stata fatta, mi <lb/>sono appigliato al partito di chiamarla l'esperienza di Leyden.<emph.end type="italics"/> (Lez. </s>

<s>di <lb/>Fis., ediz. </s>

<s>cit., T. V, pag. </s>

<s>301, 2). </s></p><p type="main">

<s>Prosegue ivi a dire l'Autore che, per ordine della R. Accademia, si <lb/>dette a studiare le ragioni del fatto, ed esaminandone le condizioni, trov&ograve; <pb xlink:href="020/01/495.jpg" pagenum="476"/>che, essendo indifferente la figura del vaso, potevasi comodamente comporre <lb/>a foggia di bottiglia, dentro alla quale era lo stesso, invece di acqua, intro&shy;<lb/>dur mercurio, migliarole, trucioli o limatura di qualunque metallo. </s>

<s>Cos&igrave; venne <lb/>ad aver la Fisica, dalle mani dello stesso Nollet, quella cisterna accumula&shy;<lb/>trice dell'elettricit&agrave; via via raccolta, a cui non si sa ancora dare altro nome <lb/>che di <emph type="italics"/>Bottiglia di Leyda.<emph.end type="italics"/></s></p><p type="main">

<s>Un'altra di cos&igrave; fatte cisterne trovaron poco dipoi il Wilke e l'Epino <lb/>potersi avere da due larghi piani deferenti, affacciantisi a poca distanza, e <lb/>il Franklin trov&ograve; che un vetro da finestra incorniciato del suo telaio di le&shy;<lb/>gno, e incollatavi sopra ambedue le facce una foglia metallica, era esso pure <lb/>una cisterna da elettricit&agrave;, o, come in linguaggio scientifico si dice, un <emph type="italics"/>con&shy;<lb/>densatore.<emph.end type="italics"/></s></p><p type="main">

<s>Gli organi dunque pi&ugrave; necessarii non solo ad eccitare, ma a trattare il <lb/>fluido elettrico, erano stati tutti cos&igrave; trovati dall'industria e dalla diligenza <lb/>de'Fisici, fra'quali, cosa nuova in questi Capitoli di Storia, non s'ha da <lb/>commemorar nessuno de'nostri Italiani. </s>

<s>Ma sorse all'ultimo chi valse a ri&shy;<lb/>vendicare, anche per questa parte, la gloria all'Italia, no col concorrere a <lb/>perfezionare la Macchina elettrica dell'Hawksbee, come fecero tedeschi e fran&shy;<lb/>cesi, ma inventando una macchina nuova, che per l'effetto e la comodit&agrave;, <lb/>per non risentirsi dello stato igrometrico dell'aria, e per mantenere quasi <lb/>indeficiente il fluido, una volta eccitatovi dallo stropicciamento; si rendeva <lb/>tanto eccellente sopra la Macchina antica. </s>

<s>S'intende gi&agrave; che le nostre parole <lb/>accennano all'<emph type="italics"/>Elettroforo<emph.end type="italics"/> del Volta, frutto non del caso ma dell'esperienza, <lb/>e di quelle speculazioni intorno alla natura dell'Elettricit&agrave;, che s'incomin&shy;<lb/>ciarono ad istituire in Italia. </s></p><p type="main">

<s>Si proponeva da'nostri Fisici a risolvere un cos&igrave; fatto problema: Quando <lb/>si stropiccia un nastro sopra un piano, e dopo lo stropicciamento gli resta <lb/>aderente, ritiene egli in tale stato l'elettricit&agrave; sua, ovvero la smarrisce in <lb/>esso, e non ritiene che la disposizione di ripigliarla, quando ne &egrave; disgiunto? </s>

<s><lb/>Giovan Batista Beccaria, che era giusto colui il quale proponeva un tal pro&shy;<lb/>blema, risolveva la questione dicendo che, in quel caso, il nastro veramente <lb/>smarriva la sua elettricit&agrave;, per <emph type="italics"/>rivendicarsela<emph.end type="italics"/> nell'atto stesso che n'&egrave; stac&shy;<lb/>cato, d'onde vennesi a qualificar col nome di <emph type="italics"/>vindice<emph.end type="italics"/> l'elettricit&agrave; produt&shy;<lb/>trice di un tale effetto. </s></p><p type="main">

<s>Al Volta per&ograve; parve una cos&igrave; fatta teoria del tutto immaginaria, perch&egrave;, <lb/>poniamo che potess'esser l'elettricit&agrave; dal corpo smarrita, non si vedeva per <lb/>qual virt&ugrave; poi si venisse a ricuperarla. </s>

<s>Perci&ograve; sostenne che l'elettricit&agrave; <emph type="italics"/>per&shy;<lb/>maneva<emph.end type="italics"/> tuttavia, e sugger&igrave; da savio che non <emph type="italics"/>elettricit&agrave; vindice<emph.end type="italics"/> si sarebbe <lb/>dovuta dir quella, ma s&igrave; invece <emph type="italics"/>elettricit&agrave; permanente.<emph.end type="italics"/> E perch&egrave; il Becca&shy;<lb/>ria studiavasi di confortar le sue teorie, discorrendo sopra i fenomeni pre&shy;<lb/>sentati da un'armatura metallica, della quale rivestivasi una lastra di vetro <lb/>elettrizzata; il Volta, per rispondere al suo contradittore, si trov&ograve; cos&igrave;, senza <lb/>volere, richiamato a studiar, sopra quelle lastre di vetro, l'elettricit&agrave; per&shy;<lb/>manente. </s></p><pb xlink:href="020/01/496.jpg" pagenum="477"/><p type="main">

<s>A questo fine, osservando, s'accorse che l'elettricit&agrave; non permaneva sul <lb/>vetro sempre per il medesimo spazio di tempo, ci&ograve; ch'egli attribuiva al va&shy;<lb/>riar dello stato igrometrico dell'aria. </s>

<s>Da ci&ograve; venne condotto a sperimentar <lb/>sopra corpi meno igrometrici del vetro stesso, e togliendo e riponendo al&shy;<lb/>ternativamente l'armatura a una lastra di legno o di resina, trov&ograve; che, dopo <lb/>la scarica, le vicende di elettricit&agrave; si protraevano per pi&ugrave; lungo tempo, e i <lb/>segnali elettrici si estinguevano molto pi&ugrave; lentamente, che sopra il vetro. </s>

<s><lb/>Ond'&egrave; che, datosi tutto a studiar l'elettricit&agrave;, che per istropicciamento ec&shy;<lb/>citavasi dalle resine stesse, ebbe a dirla non solo <emph type="italics"/>permanente,<emph.end type="italics"/> ma <emph type="italics"/>indeficiente,<emph.end type="italics"/><lb/>e sopr'essa fond&ograve; le sue speranze di costruire una Macchina, la quale fosse <lb/>di fluido elettrico perenne e perpetua sorgente. </s></p><p type="main">

<s>Cos&igrave; fatte speranze di costruire un Elettriforo perpetuo si ridestarono <lb/>nell'animo del Volta pi&ugrave; lusinghiere e pi&ugrave; vive, quando si diffuse la noti&shy;<lb/>zia di un'esperienza nuova fatta da Gian Francesco Cigna. </s>

<s>Consisteva que&shy;<lb/>sta esperienza nell'elettrizzare un nastro di seta applicato a una lamina di <lb/>piombo, e nel ritirarlo violentemente, nell'atto che si toccava la lamina stessa <lb/>colla punta del dito. </s>

<s>Ripetendo pi&ugrave; volte il gioco, era riuscito il Cigna, a <lb/>caricar, con questa nuova Macchina elettrica, una Bottiglia di Leyda. </s></p><p type="main">

<s>La bella esperienza veniva da Torino ad avvivar le speranze del Volta, <lb/>perch&egrave; vedeva in essa la forma propria che avrebbe preso il suo strumento; <lb/>veniva inoltre a lusingarle, perch&egrave; vedeva di poter fare con mirabile spedi&shy;<lb/>tezza quel che al Cigna stesso non era riuscito che a stento. </s>

<s>Il vantaggio <lb/>sarebbe provenuto dal sostituire al nastro di seta una focaccia di resina e <lb/>all'armatura immobile un mobile scudo di legno dorato. </s>

<s>Ed ecco di quali <lb/>semplicissimi organi componevasi la nuova e perpetua macchina elettrica, <lb/>dal suo proprio inventore descritta al Priestley colle seguenti parole: </s></p><p type="main">

<s>&ldquo; Ho dunque un piatto di stagno con l'orlo che rileva poco pi&ugrave; di una <lb/>mezza linea, d'un piede di diametro: entro ho versato un mastice fuso com&shy;<lb/>posto di trementina, ragia e cera, steso e rassodato in una superficie piana <lb/>e lucida. </s>

<s>Ne ho parecchi altri e pi&ugrave; grandi e pi&ugrave; piccoli di legno eziandio, <lb/>al cui fondo &egrave; incollata una laminetta di piombo, e in cui ho versato ove <lb/>zolfo, ove ceralacca ed ove altri mastici di varia composizione, ma l'indi&shy;<lb/>cato di sopra, ch'io fo di tre parti di trementina, due di ragia ed una di <lb/>cera bollite insieme per pi&ugrave; ore, mescendovi infine alquanto di minio, ad <lb/>oggetto di avvivarne il colore; l'ho trovato il pi&ugrave; comodo e il migliore. </s>

<s>Fa <lb/>l'ufficio di armatura al di sopra un legno dorato della figura a un di presso <lb/>d'uno scudo di dieci pollici di diametro, e alto due all'incirca, piano nella <lb/>base, che dee combaciare col mastice, alquanto convesso nei lati ossia nel <lb/>contorno. </s>

<s>Dal centro della concavit&agrave; sorge un manico di vetro, o meglio di <lb/>ceralacca ben levigato, che ha gli spigoli, e ci&ograve; rileva assai, smussati e ro&shy;<lb/>tondati. </s>

<s>Chiamer&ograve; dunque quest'armatura col nome di <emph type="italics"/>Scudo.<emph.end type="italics"/> Stimo super&shy;<lb/>fluo l'avvertire che mi attengo ordinariamente ad uno scudo di legno do&shy;<lb/>rato, perch&egrave; meno dispendioso, e pi&ugrave; leggero e manesco che uno di metallo <lb/><gap/> tutto cavo <pb xlink:href="020/01/497.jpg" pagenum="478"/>interiormente a foggia di una scatola, che serve per un altro apparato mi&shy;<lb/>nore portatile in tasca, trovo che m'offre in compenso non piccoli vantaggi, <lb/>uno rilevante, che &egrave; quello d'essere pi&ugrave; forbito, e perci&ograve; di dissipare meno <lb/>l'elettricit&agrave;; gli altri di sola appariscenza e comodo, per atto d'esempio di <lb/>render sonore le scintille, anche meno vive; e di poter racchiudere in esso <lb/>varii strumenti che vengono ad uso, come caraffe, manichi per isolare, palle, <lb/>fili, ecc. </s>

<s>Ed eccovi, signore, tutto l'apparato &rdquo; (Opere, Firenze 1816, T. I, <lb/>pag. </s>

<s>109, 10). </s></p><p type="main">

<s>La nuova e semplicissima Macchina italiana, cos&igrave; descritta, agli stra&shy;<lb/>nieri che si compiacevano de'perfezionamenti a cui il Ramsden aveva ri&shy;<lb/>dotti i globi versatili dell'Hawksbee, comparve inaspettata, e com'&egrave; con&shy;<lb/>sueto, alcuni l'accolsero con applauso, mentre altri con invidiosa gelosia si <lb/>studiavano di detrarre ai meriti dell'Inventore. </s>

<s>Non sapendo attaccarsi ad <lb/>altro, rassomigliavano l'invenzione del nostro Italiano a un'esperienza fatta <lb/>gi&agrave; dal Wilke insiem con l'Epino, la quale esperienza consisteva nell'em&shy;<lb/>pir di zolfo fuso una coppa di metallo, e nel mostrar che s'avevano i se&shy;<lb/>gnali elettrici, cos&igrave; dal recipiente come dal zolfo medesimo strofinato, ogni <lb/>volta che l'uno si disgiungeva dall'altro, e ci&ograve; anche dopo qualche settimana <lb/>e qualche mese. </s></p><p type="main">

<s>A que'suoi detrattori rispondeva il Volta con una Lettera scritta nel <lb/>Maggio del 1776, e diretta a Giuseppe Klinkosch (Op. </s>

<s>cit., T. I, pag. </s>

<s>144-63), <lb/>ma, meglio che con le parole, rispondeva co'fatti, mostrando che il suo Elet&shy;<lb/>troforo compendiava in s&egrave; tutte le virt&ugrave; dell'antica Macchina elettrica, e si <lb/>porgeva assai comodo a molti di que'servigi, per i quali la Macchina stessa <lb/>del Ramsden invocava l'aiuto di strumenti stranieri. </s>

<s>Cos&igrave; insegnava come, <lb/>dando alla focaccia resinosa poco spessore, avevasi nell'Elettroforo uno stru&shy;<lb/>mento atto a ricevere una gran carica, e a dar perci&ograve; un'esplosione, e una <lb/>commozione ai muscoli degli animali, pi&ugrave; violenta di quella eccitata col Qua&shy;<lb/>dro magico, o colla Bottiglia di Leyda. </s></p><p type="main">

<s>Ma se le scosse elettriche erano spettacolose, non promovevan per&ograve; la <lb/>scienza. </s>

<s>Il pi&ugrave; eloquente argomento, con cui il Volta rispose a'suoi detrat&shy;<lb/>tori, fu quando egli mostr&ograve; che il suo Elettroforo si trasformava in un im&shy;<lb/>portantissimo strumento per cui rendevasi cospicua quella virt&ugrave; elettrica nel&shy;<lb/>l'aria serena, che altrimenti per la sua debolezza, alla percezione de'semplici <lb/>sensi, sarebbe sfuggita. </s>

<s>Perci&ograve; all'Elettroforo cos&igrave; trasformato impose il nome <lb/>di <emph type="italics"/>Condensatore,<emph.end type="italics"/> e nel seguente modo con brevi parole insegnava a far nello <lb/>strumento la facile e preziosissima trasformazione: </s></p><p type="main">

<s>&ldquo; Convien prendere un piatto d'Elettroforo, che abbia l'incrostatura di <lb/>resina assai sottile, e a cui o non sia stata dianzi impressa alcuna elettri&shy;<lb/>cit&agrave;, e se mai vi &egrave; stata, vi sia spenta affatto. </s>

<s>A questa faccia resinosa im&shy;<lb/>mune da ogni elettricit&agrave; si soprapponga convenientemente il suo scudo .... <lb/>collocandolo nel bel mezzo, in modo che non tocchi in alcun punto l'orlo <lb/>metallico del piatto, ma rimanga isolato. </s>

<s>Cos&igrave; congiunti essendo, si adattino <lb/>al filo conduttore dell'elettricit<gap/><pb xlink:href="020/01/498.jpg" pagenum="479"/>toccato dove che sia dal detto filo, esso solo lo scudo e in niun modo il <lb/>piatto. </s>

<s>In questa situazione si lascino le cose per un certo tempo, fin che <lb/>lo scudo possa aver raccolta competente dose di quell'elettricit&agrave;, che dal filo <lb/>conduttore gli viene molto lentamente instillata. </s>

<s>Da ultimo sottraggasi al <lb/>contatto e influsso del filo conduttore lo scudo tuttavia unito al suo piatto, <lb/>e combaciante la faccia resinosa; indi si disgiunga anche da questa, levan&shy;<lb/>dolo in alto al consueto modo per il suo manico isolante: e allora sar&agrave; che <lb/>se ne otterranno gli aspettati segni cospicui di attrazione, di repulsione, e di <lb/>qualche scintilla eziandio, di pennoncelli, ecc., nel tempo che il conduttore <lb/>di per s&egrave; non giunge a mostrar nulla o appena un'ombra di elettricit&agrave; &rdquo; <lb/>(Opere, ivi, pag. </s>

<s>224, 25). </s></p><p type="main">

<s>A cos&igrave; fatto strumento era in dubbio il Volta se gli dava piuttosto il <lb/>nome di <emph type="italics"/>Elettroscopio,<emph.end type="italics"/> o anzi di <emph type="italics"/>Micro elettroscopio,<emph.end type="italics"/> imperocch&egrave; egli &egrave; ve&shy;<lb/>ramente tale da far l'ufficio designato da questo nome. </s>

<s>Ma i segnali inven&shy;<lb/>tati a riconoscer l'esistenza della virt&ugrave; elettrica e a misurarne i gradi, e in <lb/>che il Volta stesso, oltre a quello del semplice Condensatore, ha molti altri <lb/>meriti singolari, son tanta parte de'progressi fatti da questa scienza, da non <lb/>dover esser dimenticati nella nostra storia. </s></p><p type="main">

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

<s>Gli Elettroscopi riconoscono senza dubbio la loro prima e pi&ugrave; antica <lb/>origine in que'corpuscoli leggerissimi, che si vedevano ora essere vivamente <lb/>attratti e ora respinti da'cannelli di vetro, d'ambra, o di zolfo confricati. </s>

<s>Il <lb/>primo per&ograve; che attendesse a studiare il modo e le particolarit&agrave; di cos&igrave; fatte <lb/>attrazioni e repulsioni fu Ottone di Guericke, ed ei le studiava in un Elet&shy;<lb/>troscopio, offertogli spontaneamente dalla stessa Natura, nelle barbe di una <lb/>leggerissima piuma. </s>

<s>Notava, come segno della virt&ugrave; elettrica partecipata dal <lb/>globo di zolfo alla piuma stessa, lo stendersi delle barbe di lei, e il vibrare <lb/>come se per incantesimo fosse tornata viva. </s>

<s>&ldquo; Circa quod praeterea notanda <lb/>sunt: Primo, eiusmodi plumam molliorem, cum in globo, tum in aere sese <lb/>extendere et vividam quodammodo praestare, atque omne quod propius exi&shy;<lb/>stit, aut lubenter attrahere, aut si non valeat, ei scipsam applicare &rdquo; (Experim. </s>

<s><lb/>nova magdeb., edit. </s>

<s>cit., pag. </s>

<s>147). E prosegue a fare altre osservazioni elet&shy;<lb/>troscopiche importantissime, risalendo dalla piuma attratta che rivolge verso <lb/>il globo di zolfo sempre la medesima faccia, alla Luna attratta verso il globo <lb/>della Terra, a cui pure, forse per una somigliante cagione, tien sempre ri&shy;<lb/>volta la medesima faccia. </s></p><p type="main">

<s>&Egrave; singolare che un simile volo dalle umili attrazioni elettriche alle su&shy;<lb/>blimi attrazioni cosmiche, sollevasse la mente anche all'Hawksbee, e che <lb/>ricevesse anch'egli i primi impulsi da un Elettroscopio alquanto pi&ugrave; artifi&shy;<lb/>cioso di quello del Guericke, e meglio rappresentativo delle virt&ugrave; mondane. <pb xlink:href="020/01/499.jpg" pagenum="480"/>&ldquo; Ho scoperto, scrive egli, alcune propriet&agrave; di questa materia elettrica, che <lb/>possono parere maravigliose a quelli che minutamente le considereranno. </s>

<s><lb/>Conciossiach&egrave; ci somministrano una sorta di rappresentazione de'grandi fe&shy;<lb/>nomeni dell'Universo. </s>

<s>Poich&egrave; avendo osservato che i corpi leggeri, posti vi&shy;<lb/>cini a qualche parte dello strofinato cilindro, parevano egualmente attratti, <lb/>inventai un semicircolo di fil di ferro da potersi fermare a una costante di&shy;<lb/>stanza, facendolo circondare la semicilindrica superfice del vetro alla distanza <lb/>di quattro o cinque dita. </s>

<s>Questo fil di ferro aveva diversi fili di lana fer&shy;<lb/>mati sopra di esso, che stavano pendenti dal medesimo a distanze fra loro <lb/>quasi eguali. </s>

<s>La lunghezza di essi era tale che venendo a stendersi diretta&shy;<lb/>mente verso il centro di quello immaginario circolo sopra la superficie del <lb/>vetro, nel cui piano era posto il fil di ferro, arrivassero a meno della gros&shy;<lb/>sezza di un dito alla circonferenza di quel circolo, ma se erano lasciati in <lb/>libert&agrave; stavano pendenti in una parallela positura reciproca. </s>

<s>Il cilindro fu <lb/>messo col suo asse parallelo all'orizzonte e in questa positura fu girato ve&shy;<lb/>locemente intorno, e allora per lo rapido moto e agitamento della circon&shy;<lb/>dante aria i fili .... venivano alzati su e piegati all'in su dall'asse del ci&shy;<lb/>lindro &rdquo; (Esper. </s>

<s>fisico-meccaniche, trad. </s>

<s>ital. </s>

<s>cit., pag. </s>

<s>44). </s></p><p type="main">

<s>Nonostante, gli Elettroscopi erano ancora lontani dall'aver le loro pro&shy;<lb/>prie forme distinte, non essendosi bene ancora distinto l'essere e la natura <lb/>di quella elettricit&agrave;, ch'egli erano ordinati a rivelare. </s>

<s>Ma quando si distinse <lb/>poi l'elettricit&agrave; in vitrea e in resinosa e in positiva e negativa, e si formul&ograve; <lb/>il principio che due elettricit&agrave; dello stesso nome si respingono e tanto pi&ugrave; <lb/>vivamente si respingono, quanto la loro carica &egrave; pi&ugrave; forte; fu allora che si <lb/>trov&ograve; modo e ragione a costruire l'Elettroscopio, e se ne conobbe anche, <lb/>nello stesso tempo, il bisogno e la necessit&agrave; dell'usarlo. </s></p><p type="main">

<s>L'invenzione del primo di questi nuovi Elettroscopi, rispondenti ai pro&shy;<lb/>gressi e ai bisogni della scienza, &egrave; dovuta al napoletano Tiberio Cavallo. </s>

<s>Il <lb/>semplice e gelosissimo strumento, a cui tutti i Fisici fecero cos&igrave; lieta e li&shy;<lb/>berale accoglienza, consisteva in due sottilissimi fili di metallo accoppiati in&shy;<lb/>sieme e penduli, terminanti nelle loro estremit&agrave; in due leggerissime pallot&shy;<lb/>tole di midolla di sambuco. </s>

<s>S'introducevano poi i due fili, tenuti insieme <lb/>nella loro parte superiore, in una boccetta di vetro, affinch&egrave; i moti esterni <lb/>dell'aria non turbassero gl'intestini moti elettrici. </s>

<s>Quasi contemporaneamente <lb/>all'<emph type="italics"/>Elettroscopio a boccetta<emph.end type="italics"/> l'Henley inventava il suo <emph type="italics"/>Elettrometro a qua&shy;<lb/>drante,<emph.end type="italics"/> e tutt'e due erano riserbati questi nuovi strumenti a ricevere il loro <lb/>ultimo grado di perfezione dalle mani del Volta. </s></p><p type="main">

<s>Incominciando dall'Elettroscopio del Cavallo, uno de'perfezionamenti, <lb/>che sembra una cosa da nulla, ma che &egrave; pure della massima importanza, <lb/>consisteva nell'aver cambiato il Volta, ai pendolini, forma e materia, soppri&shy;<lb/>mendo le pallottole di midolla di sambuco, e sostituendo ai fili metallici due <lb/>nude paglie, lunghe circa due pollici, le quali, sospese per mezzo di due mo&shy;<lb/>bilissimi anelletti, pendessero contigue, o quasi contigue per tutta la loro <lb/>lunghezza. </s>

<s>Il vantaggio poi ottenuto dal sostituire ai fili le pagliette, e dal <pb xlink:href="020/01/500.jpg" pagenum="481"/>sopprimere i pendoli, secondo che si esprime lo stesso Volta, &egrave; &ldquo; che il mi&shy;<lb/>nimo loro scostamento, la minima divergenza si rende pi&ugrave; facilmente osser&shy;<lb/>vabile, mercecch&egrave; tutta la linea del loro contatto, o quasi contatto, cade sot&shy;<lb/>t'occhio, onde scorgesi tosto se da un tale contatto o dal parallelismo escono <lb/>i due fili di paglia un minimo che, se vengono a formare il pi&ugrave; piccolo an&shy;<lb/>golo: laddove coi fili metallici aventi in fondo le palline, restando quelli un <lb/>dall'altro discosti quanto porta la grossezza di coteste palline, ed essendo <lb/>altronde poco discernibili quei fili esilissimi, massime quando l'Elettroscopio <lb/>tiensi a qualche distanza, o quando si sperimenta all'aria alquanto oscura, <lb/>non si pu&ograve; cos&igrave; facilmente notare una piccola divergenza de'medesimi, o un <lb/>angolo di pochissimi gradi che facciano, e puossi soltanto giudicare all'in&shy;<lb/>grosso dello scostamento delle pallottole &rdquo; (Op. </s>

<s>cit., T. II, P. II, pag. </s>

<s>8, 9). </s></p><p type="main">

<s>Questi miglioramenti sono sostanziali e intrinseci allo strumento, ma <lb/>un'altro ve ne introdusse il Volta, che si pu&ograve; riguardare come accessorio, <lb/>e che consiste nell'accoppiamento fecondo ch'ei fece dell'Elettroscopio a <lb/>boccetta col Condensatore. </s>

<s>Intorno a un tal felicissimo accoppiamento, per <lb/>cui venne la Fisica a possedere l'esplorator pi&ugrave; sottile della elettricit&agrave; nei <lb/>corpi, cos&igrave; ne scriveva il suo stesso insigne Inventore. </s>

<s>&ldquo; Solamente un anno <lb/>dopo che io ebbi pubblicato nelle Transazioni anglicane cotesta mia inven&shy;<lb/>zione del Condensator dell'elettricit&agrave;, mi sugger&igrave; di unirlo immediatamente <lb/>e farne un corpo solo coll'Elettrometro a boccetta nel modo che or ora <lb/>dico.... Adatto a vite un piattello di due pollici circa di diametro, al bot&shy;<lb/>tone del mio Elettrometro, ed applico ad esso piattello, allorch&egrave; voglio con&shy;<lb/>densarvi l'elettricit&agrave;, il piano di marmo, l'incerato, il taffet&agrave; o quel qualun&shy;<lb/>que corpo semicoibente che trovo pi&ugrave; a proposito. </s>

<s>Per maggior mio comodo <lb/>mi servo ordinariamente d'una zona di taffet&agrave; cerato o verniciato che forma <lb/>come un mezzo guanto aperto d'ambi i lati, nel quale entrano quattro diti <lb/>riuniti della mano. </s>

<s>Con questi diti cos&igrave; fasciati io copro e premo alquanto <lb/>quel piattello posto in cima all'Elettrometro, intantoch&egrave; il medesimo riceve <lb/>da un lato o per di sotto l'elettricit&agrave;, sia da una boccia di Leyden, sia da <lb/>un'altra sorgente qualunque. </s>

<s>Infine ritirata la boccia, o qualsiasi il corpo <lb/>elettrizzante dal contatto del piattello, ne levo via anche la mano coperta <lb/>dal suo guanto con prestezza (giacch&egrave; la prestezza contribuisce molto al buon <lb/>successo) e allora veggio i pendolini balzare con vivacit&agrave;, e prendere quelle <lb/>divergenze, che l'elettricit&agrave; condensata nel piattello, di cui sono dipendenze, <lb/>pu&ograve; loro dare &rdquo; (ivi, pag. </s>

<s>49-51). </s></p><p type="main">

<s>Era l'Agosto del 1787, nel qual tempo il Volta scriveva la prima delle <lb/>sue Lettere meteorologiche al Lichtenberg, d'onde abbiamo trascritte que&shy;<lb/>ste parole, quando il Tralles di Amburgo, professore di Fisica a Berna, pas&shy;<lb/>sando per Como, and&ograve; a far visita a Colui, ch'era gi&agrave; la gloria della piccola <lb/>e illustre citt&agrave; lombarda. </s>

<s>Per intrattenere e onorare l'ospite suo, il grande <lb/>Fisico comasco gli mise innanzi il suo Elettrometro condensatore, a vedere <lb/>e a sentir dire del quale il Tralles soggiunse che pensava anch'egli, da <lb/><gap/> a costruire un simile delicatissimo strumento, sostituendo, <pb xlink:href="020/01/501.jpg" pagenum="482"/>ai fili metallici e alle stesse pagliette, due peli di qualche animale che gli <lb/>abbia finissimi o due capelli. </s>

<s>Tacque il Volta, per gentilezza a quella pro&shy;<lb/>posta, ma pensava fra s&egrave; che l'invenzione dell'Amburghese non sarebbe per <lb/>riuscire, perch&egrave;, oltre alla difficolt&agrave; di mantenere que'due capelli diritti, son <lb/>essi piuttosto coibenti che conduttori, ond'&egrave; che a stento riceverebbero e <lb/>perderebbero l'elettricit&agrave;, massimamente trattandosi di quella cos&igrave; tenue, a <lb/>rivelar la quale sono ordinati gli Elettroscopi. </s></p><p type="main">

<s>Pure, aveva il Tralles, con quella sua proposta, fatto ravvedere il Volta <lb/>della poca squisitezza di quelle sue pagliette, anch'esse non leggerissime, <lb/>n&egrave; cos&igrave; perfette conduttrici, per cui vide conveniente pensare a eleggere <lb/>qualche altro corpo elettroscopico, che rendesse anche pi&ugrave; geloso che mai, <lb/>il suo geloso strumento. </s></p><p type="main">

<s>Si trovava dunque l'Inventor dell'Elettroscopio a pagliette, sopra pen&shy;<lb/>siero di ci&ograve;, quando nel Settembre di quell'anno 1787 essendo andato a Gi&shy;<lb/>nevra, s'incontr&ograve; col Zimmermann, il quale fu il primo a dargli la notizia <lb/>che il Bennet inglese aveva eletto per corpi elettroscopici due listerelle di <lb/>foglia d'oro, e n'avea cos&igrave; felicemente composto un Elettroscopio di tanto <lb/>prodigiosa sensibilit&agrave;, da dar manifesti segnali elettrici, a pure alitar sul <lb/>cappelletto metallico di lui col fiato della bocca. </s>

<s>Finalmente nell'Aprile del&shy;<lb/>l'anno 1788 pervenne alle mani del Volta la terza edizione dell'<emph type="italics"/>Essay on <lb/>Electricity<emph.end type="italics"/> dell'Adams, pubblicato sulla fine dell'anno avanti, dove trov&ograve;, <lb/>in un supplemento al libro, la descrizione del nuovo Elettroscopio a fogliette <lb/>d'oro, e di molte curiose osservazioni che il Bennet aveva fatte con esso. </s>

<s><lb/>Cos&igrave; il Fisico inglese venne a togliere la preoccupazione al Volta, e por&shy;<lb/>gendogli in mano quel ch'egli cercava, concorse efficacemente a render, <lb/>quanto mai si potesse desiderar, sensibile l'Elettrometro condensatore. </s></p><p type="main">

<s>Tali furono i progressi fatti dal primo Elettroscopio a boccetta di Ti&shy;<lb/>berio Cavallo, ma lo stesso Volta, che andava predicando l'Elettrometro a <lb/>quadrante dell'Henley <emph type="italics"/>per il migliore di quanti elettrometri si fossero im&shy;<lb/>maginati<emph.end type="italics"/> (Op. </s>

<s>I, pag. </s>

<s>251), rivolse anche intorno a questo strumento i suoi <lb/>studi, lo miglior&ograve; assai, e, che pi&ugrave; importa, lo rese comparabile con gli altri. </s></p><p type="main">

<s>L'Elettrometro henleiano, &egrave; noto che consiste in un pendolo leggeris&shy;<lb/>simo imperniato al centro di un quadrante affisso a un'asticella metallica <lb/>elettrizzata per comunicazione. </s>

<s>La virt&ugrave; repulsiva, che intercede fra il pen&shy;<lb/>dolo e l'asta, &egrave; che fa sollevare il pendolo stesso, e i vari gradi segnati sul <lb/>quadrante misurano la varia intensit&agrave; di quella forza, e perci&ograve; della carica <lb/>elettrica. </s>

<s>Or qui sembrerebbe che dovesse lo strumento elettrico soggiacere <lb/>alle leggi meccaniche, conforme alle quali i pesi penduli, via via che si sol&shy;<lb/>levano, non crescono a proporzione degli angoli di elevazione, ma s&igrave; a pro&shy;<lb/>porzione de'seni degli angoli, cosicch&egrave;, per esempio, se per sollevare il pen&shy;<lb/>dolo all'altezza di un grado, ci vuole una data forza, per sollevarlo all'altezza <lb/>di due gradi non basta una forza precisamente doppia, ma se ne richiede <lb/>una alquanto maggiore. </s></p><p type="main">

<s>Applicando questa teoria al pendolo dell'Henley, i numeri del quadrante <pb xlink:href="020/01/502.jpg" pagenum="483"/>che vanno in progressione aritmetica, non potrebbero ridursi a misurare il <lb/>proporzionato crescere dell'intensit&agrave; elettrica essendo che una intensit&agrave; dop&shy;<lb/>pia non possa aver virt&ugrave; di sollevare il pendolo a un'altezza dopp&igrave;a, ma al&shy;<lb/>cun poco minore. </s></p><p type="main">

<s>Studiandosi il Volta di comparare l'Elettrometro a quadrante con l'Elet&shy;<lb/>trometro a pagliette, rest&ograve; sorpreso da maraviglia, ritrovando che, almeno <lb/>dentro i limiti compresi fra i 10 e i 40 gradi, il pendolo elettrico, sottraen&shy;<lb/>dosi alle leggi del pendolo meccanico, cresceva di peso a proporzion, non <lb/>de'seni, ma degli angoli di elevazione, cosicch&egrave; veramente l'intensit&agrave; elet&shy;<lb/>trica, la quale portava il pendolo a 30 gradi, era il doppio pi&ugrave; potente di <lb/>quella che lo portava a 15. Al di sotto dei 10 gradi e al di sopra dei qua&shy;<lb/>ranta, trov&ograve; che il pendolo elettrico si conformava pi&ugrave; d'appresso col pen&shy;<lb/>dolo meccanico, e cos&igrave;, a rendere utile questo strumento e comparabile con <lb/>gli altri, ebbe a costruire alcune Tavole di correzione, delle quali cos&igrave; scri&shy;<lb/>veva: &ldquo; Dir&ograve; .... per puro amore del vero che io mostrava gi&agrave; questo Qua&shy;<lb/>drante elettrometro perfezionato a un buon segno fin dall'anno 1781, e al <lb/>principio del 1784 anche la comparabilit&agrave; de'suoi gradi dentro i limiti as&shy;<lb/>segnati (Op., T. I, P. II, pag. </s>

<s>36). </s></p><p type="main">

<s>A ripensar quali sollecite cure si dava il Volta di ridurre l'Elettrosco&shy;<lb/>pio a boccetta alle sue ultime perfezioni, e a render utile colle Tavole di <lb/>correzione l'Elettrometro a quadrante, si sarebbe detto allora che quelle <lb/>cure forse eran superflue, e che non meritava il conto che un genio di tal <lb/>fatta s'occupasse di tali minuzie. </s>

<s>Ma presentiva bene quel genio come cos&igrave; <lb/>fatte spregevoli minuzie, spese nell'apparecchiarsi i pi&ugrave; squisiti Elettrome&shy;<lb/>tri, gli avrebbero raffinato il senso a discerner la generazione elettrica da <lb/>un tal concorso di cause tanto straordinario, che ne sarebbe stupito il mondo <lb/>intiero. </s>

<s>Stupito a veder due metalli, venuti a filosofico contatto, fremere <lb/>negli spiriti della vita e coruscare di luce. </s></p><p type="main">

<s>Come l'umile e paziente perfezionatore degli Elettrometri meritasse di <lb/>venire esaltato alla gloria d'essere egli il primo ad annunziare al mondo <lb/>un tale e tanto miracolo, &egrave; ci&ograve; che a noi resta a narrare. </s>

<s>Ma perch&egrave; ora&shy;<lb/>mai l'Italia, concorsa tardi a coltivare gli studi elettrici, dovea mostrare che <lb/>ci&ograve; non era un sonno inerte, ma un riposo ristoratore di forze; la scoperta <lb/>del moto elettrico generato dal contatto de'metalli dovea esser preceduta e <lb/>occasionata dall'altra grande scoperta della generazione del moto elettrico <lb/>dai muscoli degli animali. </s>

<s>Le garrule abitatrici delle paludi, che immolate <lb/>da Marcello Malpighi sull'altare di Minerva in Bologna, rivelarono agli oc&shy;<lb/>chi del Filosofo, per la prima volta, il circolo del sangue nel giro univer&shy;<lb/>sale de'vasi; le medesime, immolate pure in Bologna da Luigi Galvani, ri&shy;<lb/>velarono per la prima volta agli occhi del Filosofo come circolassero per le <lb/>loro membra gli occulti spiriti della vita. </s>

<s>Il nuovo sagrificio immolato nel <lb/>Tempio della scienza, merita di esser cos&igrave; fedelmente descritto nelle parti&shy;<lb/>colarit&agrave; de'suoi riti, che noi ci sentiamo accesi di sdegno contro alcuni scrit&shy;<lb/><gap/> Quegli scrittori, per buona ventura, <pb xlink:href="020/01/503.jpg" pagenum="484"/>non sono italiani, ma non &egrave; gi&agrave; che gli stessi italiani si sien mostrati sol&shy;<lb/>leciti e diligenti di saper la storia sincera di un fatto, che forma una delle <lb/>principali glorie scientifiche della loro nazione. </s>

<s>Per essi invano Luigi Gal&shy;<lb/>vani scriveva: &ldquo; Operae itaque pretium facturum me esse existimavi, si bre&shy;<lb/>vem et accuratam inventorum historiam afferrem eo ordine, et ratione, qua <lb/>mihi illam partim casus, et fortuna obtulit, partim industria et diligentia <lb/>detexit &rdquo; (De virib. </s>

<s>electr., Mutinae 1792, pag. </s>

<s>1), imperocch&egrave;, tutt'altro che <lb/>ascoltar ci&ograve; che delle sue scoperte riferisce l'Autore, alterano i fatti colle <lb/>loro arguzie, o li fingono coi loro cervelli. </s></p><p type="main">

<s>Noi perci&ograve;, volendo raccontar la storia genuina di que'fatti, crediamo <lb/>per sincerit&agrave; e per riverenza, di dover cedere la nostra parte al Galvani, il <lb/>quale non isdegner&agrave; di tornare a dire delle sue scoperte e l'ordine e la ra&shy;<lb/>gione colla sua propria bocca. </s>

<s>Narrer&agrave;, per esser breve, la nuda storia, ta&shy;<lb/>cendo le prolisse digressioni ch'ei fa nel suo Commentario <emph type="italics"/>De viribus electri&shy;<lb/>citatis,<emph.end type="italics"/> e, per minor tedio e fatica di chi ascolta, render&agrave; il suo latino in <lb/>schietta favella italiana. </s></p><p type="main">

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

<s>&ldquo; Dissecai una rana e la scorticai, ponendole a nudo i muscoli e gli <lb/>interni nervi erurali, e la tenevo, cos&igrave; preparata, non molto distante dal con&shy;<lb/>duttore della Macchina elettrica, mentre, a uno di coloro che mi aiutavano <lb/>nelle esperienze, vien per caso toccato leggermente un nervo colla punta di <lb/>uno scarpello: vede a un tratto contrarsi i muscoli della rana, come se fos&shy;<lb/>sero presi da toniche convulsioni. </s>

<s>A un altro di coloro, che mi stavano pi&ugrave; <lb/>d'appresso, mentr'io tentavo nuove elettriche esperienze, parve d'avere os&shy;<lb/>servato che le rane si contraevano nell'atto stesso, che dalla Macchina si <lb/>faceva scoccare una scintilla. </s>

<s>Maravigliato del fatto ne fece avvertito me, che <lb/>a tutt'altro pensavo, ond'io mi rivolsi con incredibile studio a ripetere quelle <lb/>stesse esperienze, per veder ci&ograve; che sarebbe di l&igrave; per uscirne di nuovo. </s>

<s>Ac&shy;<lb/>costai la punta dello scarpello ora all'uno ora all'altro de'nervi crurali, <lb/>nell'atto che un di coloro che v'erano presenti provocava una scintilla, ed <lb/>ecco rinnovarsi i medesimi spettacoli: i muscoli si mettevano in convulsione, <lb/>quasi gli dibattesse il tetano. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Mi nacque allora un sospetto: sarebb'egli mai che, no dalla scintilla <lb/>nascesse lo stimolo, ma dal confricare colla punta dello scarpello? </s>

<s>provo a <lb/>pungere i nervi, mentre la Macchina &egrave; in quiete, ma la rana non si muove. </s>

<s><lb/>Di qui ebbi a concludere che due cause concorrevano insieme in quel fatto: <lb/>il toccamento del ferro, e lo scocco della scintilla. </s>

<s>Ripetendo per&ograve; l'espe&shy;<lb/>rienza restai maravigliato dal veder come, concorrendo le due dette cause, <lb/>non perci&ograve; sempre infallibile ne seguiva l'effetto. </s>

<s>Tenta e ritenta, per isco&shy;<lb/>prir qual di questa novit&agrave; ne fosse la cagione, finalmente trovai che tutto <pb xlink:href="020/01/504.jpg" pagenum="485"/>dipendeva dalle parti componenti lo scarpello, il quale aveva il manico d'osso. </s>

<s><lb/>Se la mano lo impugnava, senza nulla toccar del ferro, lo spettacolo non si <lb/>vedeva, e scintillasse pure la Macchina, e se le avvicinasse meglio la rana. </s>

<s><lb/>Ripensando allora che l'osso &egrave; un coibente, conclusi che il toccamento del <lb/>nervo voleva esser fatto da un corpo conduttore, in che venne a confer&shy;<lb/>marmi il veder che i muscoli rimanevano immoti a toccarli con una bac&shy;<lb/>chetta di vetro. </s>

<s>A quel conduttore poi, che &egrave; condizione cos&igrave; essenziale al <lb/>buon successo, mi piacque di applicargli il nome di <emph type="italics"/>conduttore de'nervi &rdquo;<emph.end type="italics"/><lb/>(Comment. </s>

<s>cit., Pars I, pag. </s>

<s>2-4). </s></p><p type="main">

<s>&ldquo; Scoperte le cose, che vi ho narrate fin qui, intorno alla virt&ugrave; del&shy;<lb/>l'elettricit&agrave; artificiale sopra le contrazioni muscolari, mi rimaneva a investi&shy;<lb/>gare se i medesimi spettacoli fossero offerti dall'elettricit&agrave; naturale ammo&shy;<lb/>sferica; mi restava a veder cio&egrave; se seguiva colla folgore quel ch'io avevo <lb/>sperimentato colla scintilla. </s>

<s>Perci&ograve;, eretto sul comignolo della mia casa un <lb/>palo di ferro, bene isolato, all'appressarsi della tempesta ne appendevo al <lb/>conduttore, pe'nervi, le rane preparate, o le gambe di qualche animale a <lb/>sangue caldo. </s>

<s>Le cose avvennero secondo i miei desiderii: il coruscar delle <lb/>folgori metteva i muscoli nelle solite convulsioni. </s>

<s>E non gi&agrave; le folgori sole <lb/>eccitavano cos&igrave; fatti moti convulsi, ma, imperversando il cielo, gli eccitavano <lb/>gli stessi nuvoloni non molto al di sopra della punta del conduttore ondeg&shy;<lb/>gianti &rdquo; (Comment. </s>

<s>cit., Pars II, pag. </s>

<s>14, 15). </s></p><p type="main">

<s>&ldquo; Degli effetti dell'elettricit&agrave;, per cos&igrave; dir, procellosa, e de'consensi di <lb/>lei coll'artificiale, oramai m'ero cos&igrave; assicurato per ogni parte, ma perch&egrave; <lb/>la sete della scienza accende nuova sete, volli fare esperienza anche del&shy;<lb/>l'elettricit&agrave; placida a ciel sereno. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Son le finestre della mia casa circondate da un terrazzo, dov'io vi <lb/>tengo sopra posati vasi con pianticelle, che mi rallegrino col loro verde e <lb/>co'fiori. </s>

<s>Tenendo attaccate le rane con uncini di rame, infissi nella midolla <lb/>spinale, alla ringhiera di ferro di quel mio o giardino pensile o terrazzo che <lb/>vogliate chiamarlo, le avevo qualche volta vedute contrarsi, anco a ciel se&shy;<lb/>reno, e ci&ograve; fu che venne ad accendermi quella sete, che ho detto. </s>

<s>Sto per <lb/>parecchie ore a guardare, seguito per molti giorni, e aspetta, aspetta non <lb/>si vede nulla di nuovo. </s>

<s>Finalmente, per riposarmi della stanchezza del lungo <lb/>osservare, incomincio a pigiar que'fili di rame, da cui pendevano le rane <lb/>attaccate, e a stropicciarli contro il ferro della ringhiera, per veder se nulla <lb/>ne nasceva di nuovo, e non di rado qualche guizzo ne'muscoli lo vedevo, <lb/>ma per&ograve; indipendente affatto dallo stato elettrico dell'ammosfera. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Siccome io non avevo veduto mai que'moti convulsi, altro che all'aria <lb/>aperta, e altrove non avevo ancora sperimentato, poco ci corse ch'io non <lb/>dicessi esser l'elettricit&agrave; ammosferica, penetrata nell'animale, che, al toc&shy;<lb/>carsi dell'uncino di rame col ferro della ringhiera, esce fuori, e in uscire <lb/>commove i muscoli. </s>

<s>Tanto &egrave; facile ingannarsi nelle esperienze, e immagi&shy;<lb/>narsi di aver veduto e trovato ci&ograve; che s'immaginava di vedere e di tro&shy;<lb/>vare! Ma trasportata la rana in una camera chiusa, e collocata sopra una <pb xlink:href="020/01/505.jpg" pagenum="486"/>lamiera di ferro, vi pigio contro quell'uncino di rame .... oh! ecco le me&shy;<lb/>desime contrazioni, i medesimi moti. </s>

<s>Muto stanza, muto metalli, provo in <lb/>altre ore, provo in altri giorni, e vedo sempre le medesime cose, colla sola <lb/>differenza che alcuni metalli eccitavano le convulsioni pi&ugrave; languide, altri pi&ugrave; <lb/>veementi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Potete figurarvi che questi fatti ridestarono in me una grande am&shy;<lb/>mirazione, e fu allora che incominci&ograve; a entrarmi il sospetto di un'elettricit&agrave; <lb/>inerente allo stesso animale. </s>

<s>Mi pareva di veder quella elettricit&agrave; da'nervi <lb/>ritornare ai muscoli, come, fra le armature e il conduttore della Bottiglia <lb/>di Leyda, si avverte. </s>

<s>Venne a confermarmi in questa persuasione l'espe&shy;<lb/>rienza, ch'io vi dir&ograve;. </s>

<s>Tenevo una rana preparata al solito modo per l'un&shy;<lb/>cino, a cui l'avevo infilata, e le facevo toccar colle gambe il piano di un <lb/>piattello d'argento. </s>

<s>Poi, con una verga di metallo, tenuta nell'altra mano, <lb/>toccavo gli orli dello stesso piattello, e vedevo, oltre alla mia speranza, quelle <lb/>gambe contrarsi, e sempre far lo stesso ogni volta ch'io tornavo a ripetere <lb/>il gioco. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Avendo avvertito gi&agrave; queste cose, mi trovavo a villeggiare appresso <lb/>quel nobilissimo uomo, che &egrave; il signor Giacomo Zambeccari, insiem con <lb/>un dottissimo spagnolo, appartenuto un tempo alla compagnia di Ges&ugrave;, <lb/>di cognome Rialpo, il quale, poich&egrave; dilettavasi delle mie esperienze, pregai <lb/>che teness'egli la rana per l'uncino ed io avrei toccato l'orlo del piattello <lb/>di argento. </s>

<s>Ma le contrazioni muscolari sparirono. </s>

<s>Ripeto come prima l'espe&shy;<lb/>rienza da me solo, e subito ritornarono. </s>

<s>Da ci&ograve; fui indotto a tener io so&shy;<lb/>speso l'uncino, e coll'altra prendere per la destra il Rialpo, pregandolo a <lb/>toccar colla sinistra libera il piattello. </s>

<s>Che piacere per noi, in veder che, a <lb/>lasciarsi e a tenersi per la mano, si poteva ora far posar quelle gambe, e <lb/>ora nuovamente metterle in danza! &rdquo; </s></p><p type="main">

<s>&ldquo; Bench&egrave; mi paresse venir cos&igrave; dimostrato assai bene il circolo elet&shy;<lb/>trico del fluido nerveo attraverso alla catena delle nostre mani, &egrave; nulladi&shy;<lb/>meno la cosa tanto nuova e di tanta importanza, che non volli trascurare <lb/>di confermarla anche in altra maniera. </s>

<s>La catena si chiudeva, fra le mani <lb/>mie e quelle del Rialpo, ora interpostavi una bacchetta di vetro e ora una <lb/>verga di metallo, e s'accrebbe in noi il piacere in veder che col metallo <lb/>uscivano dalle membra della rana i soliti moti, e col vetro restavano rin&shy;<lb/>tuzzati &rdquo; (Comment. </s>

<s>cit., Pars III, pag. </s>

<s>16-18). </s></p><p type="main">

<s>&ldquo; Or da tutte queste esperienze mi pareva ne resultasse chiaro e di&shy;<lb/>mostrato ricircolare per le membra degli animali un fluido, che sia a me, <lb/>come fu ad altri, lecito appellar col nome di <emph type="italics"/>Elettricit&agrave; animale.<emph.end type="italics"/> Una tale <lb/>elettricit&agrave;, senza dubbio, diffusa per tutte quante le membra, par che abbia <lb/>la sua propria sede ne'muscoli e ne'nervi, da quelli trapassando a questi, <lb/>attraverso a un arco metallico o a una catena di uomini, o di qualunque <lb/>altra sorta di corpi deferenti &rdquo; (Comment. </s>

<s>cit., Pars IV, pag. </s>

<s>38, 39). </s></p><p type="main">

<s>Questa storia e le particolari esperienze, che concorrevano ad illustrarla, <lb/>il Galvani la fece nota al pubblico, in un libretto in 4&deg;, di 58 nagine stam-<pb xlink:href="020/01/506.jpg" pagenum="487"/>pato a Bologna nel 1791. Una copia fu dallo stesso Autore, mandata in dono <lb/>a Bassiano Carminati, professore nell'Universit&agrave; di Pavia, dove aveva amici <lb/>e colleghi il Barletti, il Rezia, il Malacarne, e sovraeminenti a tutti lo Spal&shy;<lb/>lanzani e il Volta. </s>

<s>A quest'ultimo celebre oramai per le sue scoperte elet&shy;<lb/>triche e per le sue invenzioni, dop'averlo letto, mostr&ograve; il Carminati il Com&shy;<lb/>mentario <emph type="italics"/>De viribus electricitatis<emph.end type="italics"/> inviatogli da Bologna. </s>

<s>Qual effetto producesse <lb/>nell'animo e nell'ingegno del Volta quella lettura, &egrave; bene ascoltarlo da lui <lb/>medesimo, il quale cos&igrave; ne scriveva: </s></p><p type="main">

<s>&ldquo; Una scoperta di questa fatta non poteva che eccitare grande entusia&shy;<lb/>smo da per tutto, ove ne pervenne la notizia, e massime tra noi, essendo <lb/>di un nostro Italiano. </s>

<s>Ed ecco che molti si fecero a gara a ripetere le espe&shy;<lb/>rienze. </s>

<s>Io fui il primo qui a Pavia eccitato da varii miei Colleghi, partico&shy;<lb/>larmente da Carminati, che cortesemente prestommi la Dissertazione di Gal&shy;<lb/>vani, e da Rezia, che mi favor&igrave; dell'opera ed aiuto suo nelle preparazioni; <lb/>e il primo fui anche a Milano non molti giorni dopo, cio&egrave; verso il fine di <lb/>Quaresima. </s>

<s>Debbo per&ograve; confessare che, incredulo e con non molta speranza <lb/>di buon successo, mi ridussi a fare le prime prove, tanto sorprendenti pa&shy;<lb/>revanmi i descritti fenomeni, e se non contrarii, superiori troppo a tutto <lb/>quello che dell'elettricit&agrave; ci era noto, talch&egrave; mi avevano del prodigioso. </s>

<s>Della <lb/>quale incredulit&agrave; mia e quasi ostinazione, non che mi vergogni, domando <lb/>perdono all'Autore della scoperta, cui mi fo altrettanto maggior premura e <lb/>gloria di esaltare, ora che ho veduto e toccato con mano, quanto fui diffi&shy;<lb/>cile a credere, prima di toccare e di vedere. </s>

<s>Infine eccomi convertito, dac&shy;<lb/>ch&egrave; cominciai ad essere testimonio oculare e operatore io stesso dei mira&shy;<lb/>coli, e passato forse dall'incredulit&agrave; al fanatismo &rdquo; (Op. </s>

<s>cit., T. II, P. I, <lb/>pag. </s>

<s>35, 36). </s></p><p type="main">

<s>Verificate ch'ebbe il Volta le principali esperienze galvaniche, come <lb/>quegli che si sentiva un grande ardore di promoverle, si dette tutto a ri&shy;<lb/>cercare la qualit&agrave;, la quantit&agrave; e il modo di quella nuova elettricit&agrave; propria <lb/>degli organi animali. </s>

<s>Da cos&igrave; fatte delicatissime ricerche, nelle quali ottima&shy;<lb/>mente lo serv&igrave; quel suo squisito Elettrometro condensatore, concludeva che <lb/>un elettricit&agrave; molto debole era sufficiente ad eccitar nelle rane, per le mem&shy;<lb/>bra, non solo piccoli moti, ma gagliardissime convulsioni; ond'&egrave; che quegli <lb/>animaletti, cos&igrave; preparati a modo del Galvani, si presentavano all'osserva&shy;<lb/>tore sotto l'aspetto di <emph type="italics"/>Elettrometri naturali,<emph.end type="italics"/> molto pi&ugrave; sensibili degli stessi <lb/>Elettrometri artificiali. </s></p><p type="main">

<s>In questa rassomiglianza s'includeva, tuttavia latente allo stesso Volta, <lb/>il principio che, di discorso in discorso, l'avrebbe presto condotto a dissen&shy;<lb/>tir dal Galvani. </s>

<s>Nonostante approvando per ora la scoperta dell'elettricit&agrave; <lb/>animale, e accettando la somiglianza tra la scarica muscolare e la scarica <lb/>della Bottiglia di Leyda, si contentava di notar che l'insigne scopritore aveva <lb/>errato intorno a qualificar l'elettricit&agrave; propria a ciascuna parte dell'organo <lb/>elettrico animale, e intorno al modo proprio della scarica. </s>

<s>Diceva infatti il <lb/>bolognese Autore del Commentario che, rappresentando due muscoli o due <pb xlink:href="020/01/507.jpg" pagenum="488"/>fibre muscolari a contatto le due armature della Bottiglia, e il nervo o le <lb/>fibrille nervee inserite nel loro mezzo, rappresentando il conduttore della <lb/>stessa Bottiglia; la scarica si faceva dal nervo al muscolo, cio&egrave; dal di den&shy;<lb/>tro al di fuori. </s>

<s>Cos&igrave; venendosi ad ammettere che l'influsso nerveo non mo&shy;<lb/>vesse dal cervello, ma fosse diretto verso il cervello, riusciva difficilissimo <lb/>al Galvani il render la ragione dei moti volontarii. </s>

<s>Egli si trov&ograve; costretto in <lb/>fatti ad ammettere che l'anima operi, non forse direttamente sopra il cer&shy;<lb/>vello, ma &ldquo; ut proclivius est credere aut extra idem .... aut a membranis, <lb/>aut a contiguis aliis deferentibus partibus, per easque, ceu per arcum, ad&shy;<lb/>musculum a quo discessit restituatur, ut nempe iuxta aequilibrii legem ad <lb/>negative muscularium fibrarum electricam partem ea copia tandem confluat, <lb/>qua a positive electrica earumdem parte per impulsum in nervo, ut opinari <lb/>placuit, antea effluxerit &rdquo; (Comment. </s>

<s>cit., pag. </s>

<s>53). </s></p><p type="main">

<s>Il Volta dunque trov&ograve; sperimentando che il fluido elettrico trascorre <lb/>nelle membra della rana, non gi&agrave; dal nervo al muscolo, come opinava il <lb/>Galvani, ma s&igrave; dal muscolo al nervo, ossia dal dl fuori al di dentro, o al&shy;<lb/>trimenti, non dal nervo al cerebro, ma dal cerebro al nervo. </s>

<s>&ldquo; Or se, col <lb/>ministero del fluido elettrico, operansi anche nell'animale vivo ed intiero le <lb/>contrazioni e moti volontarii de'muscoli, come tutto ne porta a credere, e <lb/>se, come dee pure presumersi, operansi questi nel modo pi&ugrave; facile, si far&agrave; <lb/>ci&ograve; collo spingere gi&ugrave; dal cerebro pe'nervi il detto fluido verso i muscoli, <lb/>bastando allora una minima forza, anzich&egrave; col tirarlo in s&ugrave; &rdquo; (Op. </s>

<s>cit., T. II, <lb/>P. I, pag. </s>

<s>42). E tanto sentivasi ancora alieno dal dissentire, che immediata&shy;<lb/>mente soggiunge: &ldquo; sebbene possano anche in questo modo effettuarsi i me&shy;<lb/>desimi moti, sol che s'impieghi maggior forza, cio&egrave; determinarsi una cor&shy;<lb/>rente pi&ugrave; rapida e pi&ugrave; copiosa di fluido elettrico &rdquo; (ivi, pag. </s>

<s>43). </s></p><p type="main">

<s>Di ci&ograve; che aveva con grande esaltazione di animo approvato, e con gran <lb/>remissione riprovato intorno alle grandi scoperte di Fisiologia elettrica, de&shy;<lb/>scritte nel Commentario suo dal Galvani; il Volta ne riferiva a Giuseppe <lb/>Baronio, con Lettera data da Milano il d&igrave; 3 Aprile 1792 (ivi, pag. </s>

<s>3-10). In <lb/>quel medesimo giorno, da Pavia, il Carminati, che fino allora aveva taciuto, <lb/>scriveva a Bologna ringraziando l'amico del dono fattogli della <emph type="italics"/>Dissertazione <lb/>contenente l'originale bellissima scoperta dell'Elettricit&agrave; naturale e spon&shy;<lb/>tanea degli animali,<emph.end type="italics"/> adducendo, per iscusa dell'indugio, il desiderio che <lb/>aveva vivissimo d'informarlo di quel tanto, che v'aveva il Volta gustato di <lb/>vero, e di quel pochissimo che vi aveva sospettato di falso. </s></p><p type="main">

<s>Pi&ugrave; di un mese appresso, il d&igrave; 8 Maggio, il Galvani rispondeva com&shy;<lb/>piacendosi, non solo in sentir che il Volta aveva confermate le sue scoperte, <lb/>ma in pensare altres&igrave; che l'avere egli trovata la vera direzione del flusso <lb/>nerveo rendeva applicabili quelle stesse scoperte alla teoria de'moti volon&shy;<lb/>tarii. </s>

<s>&ldquo; Infatti gli esperimenti di lui chiaro dimostrerebbono potersi avere i <lb/>moti muscolari diretto il fluido elettrico non solo dal muscolo al nervo, sic&shy;<lb/>come io supponeva, ma eziandio dal nervo al muscolo, ossia dal cervello al <lb/>muscolo, e potersi avere non solo per <gap/><pb xlink:href="020/01/508.jpg" pagenum="489"/>una sopraccarica forzata ed impetuosa della supposta boccia muscolare: lo <lb/>che ammesso, chi non vede quanto riesca felice la spiegazione de'moti mu&shy;<lb/>scolari volontarii? </s>

<s>&rdquo; (Lett. </s>

<s>aggiunte al Comment. </s>

<s>cit., pag. </s>

<s>74). </s></p><p type="main">

<s>Si diceva dianzi che l'avere il Volta rassomigliato a un Elettrometro <lb/>de'pi&ugrave; gelosi le rane preparate a modo del Galvani, lasciate cio&egrave; attaccate <lb/>le loro gambe per i nervi erurali diligentemente snudati, ed infisso uno <lb/>spillo od altro uncinetto metallico nell'asse spinale; conteneva il germe delle <lb/>future contradizioni. </s>

<s>Presto infatti, rimesso il fervore di quelle prime esal&shy;<lb/>tazioni, incominci&ograve; il Volta a riflettere maravigliato &ldquo; come mai una forza <lb/>elettrica inconcepibilmente piccola.... una carica cos&igrave; esile, che non muove <lb/>punto neppure il sommamente delicato Elettroscopio del Bennet, ... basta <lb/>a convellere le gambe della rana preparata nel modo indicato &rdquo; (Op. </s>

<s>cit., <lb/>T. II, P. I, pag. </s>

<s>79). Par che la Natura, egli poco appresso soggiunge, ab&shy;<lb/>bia dotato di tale e tanta sensibilit&agrave; i nervi, di tale e tanta irritabilit&agrave; i mu&shy;<lb/>scoli, che una forza elettrica impercettibile basti ad eccitare i moti musco&shy;<lb/>lari (ivi, pag. </s>

<s>80). Di qui sentesi scoppiar dalla mente il dubbio, e non <lb/>reggendo a reprimerlo, esce nelle parole seguenti: &ldquo; Ma che? </s>

<s>sar&agrave; dunque <lb/>sopra i nervi e non sopra i muscoli che il fluido elettrico agisce <emph type="italics"/>immedia&shy;<lb/>tamente,<emph.end type="italics"/> e la sua azione verr&agrave; limitata ad eccitar quella solamente, allorch&egrave; <lb/>movesi e trapassa per questo o quel membro dall'animale con forza affatto <lb/>insensibile ai pi&ugrave; squisiti Elettrometri? </s>

<s>Cos&igrave; appunto mi conducono a cre&shy;<lb/>dere molte nuove esperienze che ho fatto, e che verr&ograve; tra poco esponendo, <lb/>cio&egrave; che il <emph type="italics"/>primario effetto<emph.end type="italics"/> del fluido elettrico cos&igrave; mosso consista nel met&shy;<lb/>tere in gioco l'<emph type="italics"/>azione nervosa,<emph.end type="italics"/> conseguenza della quale, anzi veri e propri <lb/>effetti della medesima sian poi i moti de'<emph type="italics"/>muscoli volontari &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>81, 82). <lb/>Il principio della rivolta contro le teorie galvaniche oramai &egrave; proclamato: <lb/>Esaminate meglio le cose &ldquo; ho dovuto accorgermi alla fine, che assai pi&ugrave; <lb/>limitato di quel che supponea Galvani, ed io con lui, egli &egrave; il gioco del <lb/>fluido elettrico negli organi animali, terminandosi la sua azione immediata <lb/>nei nervi &rdquo; (ivi, pag. </s>

<s>85). </s></p><p type="main">

<s>L'esperienze, che condussero il Volta a riguardare i nervi, contro l'opi&shy;<lb/>nion del Galvani, come aventi la parte essenziale e primaria ne'moti mu&shy;<lb/>scolari, son varie, e rilevantissime per la novit&agrave; e per l'importanza. </s>

<s>Una di <lb/>queste consisteva nell'applicare due listerelle di foglia metallica, una vicina <lb/>all'estremit&agrave; troncata, e l'altra alcun poco sotto, nel nervo ischiatico di un <lb/>agnello, e nel mostrar che, facendo passare una debole scarica elettrica fra <lb/>le due listerelle, la gamba dibattevasi tutta quanta, bench&egrave; fosse chiaro che <lb/>la detta scarica non vi potesse giungere a un pezzo per la sua debolezza &rdquo; <lb/>(ivi, pag. </s>

<s>87). </s></p><p type="main">

<s>Ma da'nervi motori passando ai sensorii, mostrava il Volta stesso che <lb/>l'elettricit&agrave;, irritando direttamente i nervi, produce le sensazioni, con due <lb/>esperienze insigni. </s>

<s>Consisteva la prima nel riprodurre il gusto dell'acidit&agrave; <lb/>coll'applicar sulla punta della lingua una lamina di stagno, e nel mezzo di <pb xlink:href="020/01/509.jpg" pagenum="490"/>cazione, per mezzo del manico di un cucchiaio (ivi, pag. </s>

<s>94). Consisteva la <lb/>seconda nell'eccitare la sensazion della luce, applicando al bulbo dell'occhio <lb/>l'estremit&agrave; di una listerella di foglia di stagno, messa al contatto del manico <lb/>di un cucchiaio tenuto in bocca (ivi, pag. </s>

<s>164) </s></p><p type="main">

<s>Nel fare la sopra citata esperienza, sul nervo ischiatico di un agnello, <lb/>notava il Volta che, al buon successo di lei, si richiedeva che le due arma&shy;<lb/>ture fossero <emph type="italics"/>dissimili<emph.end type="italics"/> (ivi, pag. </s>

<s>89), e avvertiva come il fatto era stato pure <lb/>osservato dal Galvani come <emph type="italics"/>peculiare atque animadversione dignum.<emph.end type="italics"/> Ma, <lb/>bench&egrave; sia un fatto provato con esperienza diretta, non sa ancora intendere <lb/>il Volta, perch&egrave; quelle armature vogliano esser dissimili, n&egrave; sa pur conce&shy;<lb/>pir troppo bene come si muova il fluido elettrico &ldquo; da un luogo all'altro <lb/>cos&igrave; vicino dell'istesso nervo, per la sola applicazione di quelle armature e <lb/>comunicazione esterna delle medesime &rdquo; (ivi). </s></p><p type="main">

<s>Esponeva cos&igrave; fatti dubbi il Volta nella Memoria seconda <emph type="italics"/>Sull'Elettri&shy;<lb/>cit&agrave; animale,<emph.end type="italics"/> scritta nella primavera del 1792. Verso la fine di quell'anno <lb/>i dubbi erano risoluti, le idee avevano oramai preso un indirizzo proprio, e <lb/>a quelle del Galvani affatto opposto. </s>

<s>Ha trovato che l'Elettricit&agrave; non &egrave; ec&shy;<lb/>citata n&egrave; dai muscoli n&egrave; da'nervi dell'animale, ma dalle virt&ugrave; dei metalli e <lb/>del carbone posti a contatto. </s>

<s>&ldquo; Etiam si tandem electricitas haec animalis <lb/>activa in organis, quam Galvanius tuetur, iterum evanescet, stabit tamen <lb/>incomparabilis ac miranda fibrarum, praecipue nervearum, excitabilitas, ope <lb/>stimuli electrici. </s>

<s>Ex altera quoque parte remanebit novum electricitatis ar&shy;<lb/>tificialis principium, a me detectum, quod maximam huic seientiae lucem <lb/>afferre potest, nempe vis ac virtus metallorum et carbonis concitandi atque <lb/>pellendi fluidum electricum, ope simplicis contactus cum corporibus qui&shy;<lb/>buslibet humidis, ac per hanc ipsorum qualitatem deferentibus, id quod <lb/>experimentis, extra corpora animalia institutis, confirmavi &rdquo; (ibi, pag. </s>

<s>173). </s></p><p type="main">

<s>Nel mentre che il Volta faceva divulgare la novit&agrave; strepitosa di cos&igrave; <lb/>fatte dottrine, nel <emph type="italics"/>Giornale di Lipsia,<emph.end type="italics"/> Giovanni Aldini rendeva nuovamente <lb/>alla luce, in Modena, il Commentario <emph type="italics"/>De viribus electricitatis<emph.end type="italics"/> di suo zio, <lb/>premessavi un'assai dotta ed elegante Dissertazione latina, ed illustrando il <lb/>testo, qua e l&agrave;, con note erudite. </s>

<s>Una Lettera del d&igrave; 22 Ottobre, scritta <lb/>dallo stesso Aldini, avvisava il Volta che gli sarebbe stata trasmessa in Mi&shy;<lb/>lano una copia del libro, che nel d&igrave; 24 Novembre non aveva avuto ancora <lb/>il recapito. </s>

<s>Perci&ograve;, chi ne stava in attesa, cos&igrave; scriveva: &ldquo; Questo libro non <lb/>mi &egrave; pervenuto ancora; ma ho potuto leggerlo per bont&agrave; del mio amico e <lb/>collega Ab. </s>

<s>Spellanzani, che me lo ha prestato, e molto piacere ho avuto <lb/>nello scorrere s&igrave; quelle note, che la Dissertazione sua, erudita non solo, ma <lb/>elegantemente scritta &rdquo; (ivi, pag. </s>

<s>177). </s></p><p type="main">

<s>Cos&igrave; fatte parole non passavano dal Volta all'Aldini per lettera fami&shy;<lb/>liare, ma per la pubblica stampa, in una scrittura che, sotto forma di epi&shy;<lb/>stola, comprendeva la Memoria terza <emph type="italics"/>Sull'Elettricit&agrave; animale.<emph.end type="italics"/> L'intenzione <lb/>precipua, che in iscriver questa terza Memoria si proponeva l'Autore, era <lb/><gap/> o fa-<pb xlink:href="020/01/510.jpg" pagenum="491"/>ceva le viste per ora di non aver compreso quello spirito di rivolta contro <lb/>le teorie galvaniche, suscitato dall'Autore della seconda Memoria. </s>

<s>Nella Dis&shy;<lb/>sertazione infatti al Galvani, al &sect; XXI, rivendicando al Sulzer l'esperienza <lb/>del sapore acido eccitato sopra la lingua dalle due laminette metalliche po&shy;<lb/>satevi sopra e ridotte al contatto; non d&agrave; l'Aldini altro merito al Volta, da <lb/>quello in fuori dell'avere spiegato il fatto curioso per l'applicazione della <lb/>teoria elettrica animale. </s>

<s>&ldquo; Nervi scilicet deferentibus iuncti corporibus electri&shy;<lb/>cum vaporem effundunt, qui si musculis ad quos contendit fuerit restitu&shy;<lb/>tus, aut contractionem aut impressionem excitabit aliquam &rdquo; (Comment. </s>

<s>cit. </s>

<s><lb/>Dissert., pag. </s>

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

<s>Il Volta rest&ograve; sorpreso all'intender che l'esperienza de'sapori metallici <lb/>l'aveva fatta, 25 anni prima di lui, il Sulzer, quell'amabile Filosofo sviz&shy;<lb/>zero, e celebre Accademico di Berlino, che egli dice di aver conosciuto, e <lb/>di aver con esso lui anche familiarmente conversato (Op. </s>

<s>cit., T. II, P. II, <lb/>pag. </s>

<s>183). Ringraziando per&ograve; l'Aldini di avergli dato il primo questa noti&shy;<lb/>zia, protesta energicamente che il suo raziocinio intorno alla ragion del fatto <lb/>sulzeriano &egrave; informato a tutt'altri principii, da quelli ammessi gi&agrave; dal Gal&shy;<lb/>vani. </s>

<s>&ldquo; No, non fu questo il mio raziocinio, n&egrave; tale potea essere, dacch&egrave; <lb/>considerando io le armature, ogni qual volta sono di due metalli diversi, non <lb/>pi&ugrave; quai semplici conduttori, ma quai veri eccitatori e motori del fluido elet&shy;<lb/>trico, teneva che <emph type="italics"/>passivi<emph.end type="italics"/> soltanto fossero gli organi animali e le parti loro <lb/>contigue o vicine a quelle armature dissimili: che niuna mossa cio&egrave; dessero <lb/>per s&egrave; stessi n&egrave; i nervi n&egrave; i muscoli al fluido elettrico, ma bene i metalli, <lb/>per propria virt&ugrave; e forza spingendolo o tirandolo, e s&igrave; l'uno pi&ugrave; dell'al&shy;<lb/>tro, per essere di specie diversa, es. </s>

<s>gr. </s>

<s>stagno e argento, ne lo venissero a <lb/>togliere dal naturale equilibrio e riposo e a mettere in corso &rdquo; (ivi, pag. </s>

<s>187). </s></p><p type="main">

<s>A tali chiare proteste dovette l'Aldini finalmente intendere, e dovettero <lb/>insiem con lui intendere tutti gli altri fautori del Galvani, i quali con ar&shy;<lb/>gomenti nuovi e con nuove esperienze, seguitava il Volta a persuadere, che <lb/>la causa per cui si mettono in convulsione i muscoli consiste in una elet&shy;<lb/>tricit&agrave;, da doversi dir <emph type="italics"/>metallica<emph.end type="italics"/> e non <emph type="italics"/>animale<emph.end type="italics"/> (ivi, pag. </s>

<s>229). Che se alcuno <lb/>dopo l'Aldini, pretendesse ancora di tirar le sue dottrine a consentire con <lb/>quelle del Galvani, egli esce fuori nella Lettera III ad Anton Maria Vassalli, <lb/>dichiarandosi con tali ragionamenti da bastare, egli dice, a mostrar &ldquo; quanto <lb/>sia diversa dalla pretesa Elettricit&agrave; animale, dalle idee del Galvani e suoi <lb/>seguaci, quell'Elettricit&agrave; che sostengo io, la quale non suppone alcuna ca&shy;<lb/>rica o sbilancio, e conseguente scarica degli organi animali, e neppure carica <lb/>o scarica propriamente detta de'conduttori applicati; ma una circolazione, <lb/>ossia corrente continua di fluido elettrico, cagionata e mantenuta da una <lb/>forza arcana, che risulta dal combaciamento di conduttori diversi fra loro, i <lb/>quali in simili circostanze, sono qualche cosa pi&ugrave; che semplici <emph type="italics"/>deferenti,<emph.end type="italics"/> fa&shy;<lb/>cendola da veri <emph type="italics"/>conduttori<emph.end type="italics"/> e <emph type="italics"/>motori &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>234, n.). </s></p><p type="main">

<s>Chi altri mai, fuor del Volta, avrebbe potuto sperare di persuadere al <lb/><gap/> una cosa tanto straordinaria, <pb xlink:href="020/01/511.jpg" pagenum="492"/>qual'era la virt&ugrave; di <emph type="italics"/>mettere in corso<emph.end type="italics"/> o di far <emph type="italics"/>motori<emph.end type="italics"/> dell'Elettricit&agrave; due <lb/>metalli diversi, non per essere confricati, o riscaldati o per aver subito altri <lb/>pi&ugrave; raffinati artifici, ma solamente per esser venuti insieme a misterioso <lb/>contatto! L'Elettricit&agrave; animale parve allo stesso Volta <emph type="italics"/>superiore troppo a <lb/>tutto quello che dell'elettricit&agrave; era noto,<emph.end type="italics"/> eppure, a ricever l'annunzio di <lb/>quella scoperta, gl'ingegni ci eran gi&agrave; preparati dalle idee del Newton, pro&shy;<lb/>mosse fra noi dal Beccaria. </s>

<s>Ma a chi poteva mai venire in testa che la fa&shy;<lb/>ticosa e intermittente elettricit&agrave; eccitata dai macchinamenti del Ramsden, <lb/>s'avesse a veder fluire, in facile corso e ricorso perpetuo, col solo soprapporre <lb/>una lamina, per esempio, di stagno, a un'altra lamina d'argento? </s>

<s>Questo s&igrave; <lb/>che pareva non <emph type="italics"/>superiore,<emph.end type="italics"/> ma <emph type="italics"/>contrario<emph.end type="italics"/> a ci&ograve; che dell'Elettricit&agrave; era noto, <lb/>eppur compiacente il Volta, nell'Ottobre del 1795, incominciava la sopra <lb/>commemorata Lettera al Vassalli, dicendo che <emph type="italics"/>dalla maggior parte de'Fisici, <lb/>massime oltramontani erano state adottate le sue opinioni<emph.end type="italics"/> (ivi, pag. </s>

<s>230). </s></p><p type="main">

<s>Quel nuovo e straordinario <emph type="italics"/>Elettromotore<emph.end type="italics"/> per&ograve;, bench&egrave; fosse dimostrato <lb/>in tanti modi, e <emph type="italics"/>saltasse agli occhi dell'Inventore da tante sue esperienze<emph.end type="italics"/><lb/>(ivi, pag. </s>

<s>215) era tuttavia in potenza, e pener&agrave; ancora cinque anni, prima <lb/>di venir fuori alla luce. </s>

<s>Come riuscisse al genio sperimentatore e specula&shy;<lb/>tore del Volta di salir sulla soglia che apriva il secolo XIX, e di li sollevar <lb/>colla mano in alto la portentosa Lucerna, a illuminare le nuove vie, che <lb/>sarebbe per correre il mondo; &egrave; ci&ograve; che a noi resta a dire, per compimento <lb/>e termine di questa parte di storia. </s></p><p type="main">

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

<s>La somma della teoria, che il Volta contrapponeva a quella del Gal&shy;<lb/>vani, riducevasi a professar che l'elettricit&agrave;, mossa in perpetuo circolo da un <lb/>metallo all'altro, attraverso ai conduttori costituiti dalle parti umide degli <lb/>animali, eccitasse i nervi e venisse, mediante questi, a commovere i muscoli. </s>

<s><lb/>Uno de'primi e principali studi ordinati a illustrare cos&igrave; fatta teoria, e a <lb/>confermar la natura de'nuovi Elettromotori, consisteva nel determinar la di&shy;<lb/>rezione del circolo elettrico; il punto cio&egrave; della sua partenza, e il luogo del <lb/>suo ritorno. </s>

<s>L'importante e delicata ricerca non riusc&igrave; molto difficile al Volta, <lb/>il quale si serv&igrave; di quel medesimo artifizio, e di quello stesso strumento, di <lb/>che erasi gi&agrave; servito per determinare la direzione del circolo galvanico. </s>

<s>Pren&shy;<lb/>deva due piastre di diverso metallo, per esempio una di rame e l'altra di <lb/>zinco, e tenutele per un manico isolatore le applicava insieme, e separatele <lb/>nell'istante faceva, prima all'una poi all'altra, toccar la pallina dell'Elettro&shy;<lb/>metro. </s>

<s>Cos&igrave; trovava che il zinco era elettrizzato in pi&ugrave;, il rame in meno, <lb/>come riscontrava, accostando allo stesso Elettrometro un cannello di cera&shy;<lb/>lacca, ond'&egrave; che, in un Elettromotore composto de'due sopra detti metalli, <lb/>concludeva essere il corso elettrico diretto dal zinco al rame. (Op. </s>

<s>cit., T. II, <lb/>P. II. pag. </s>

<s>155). </s></p><pb xlink:href="020/01/512.jpg" pagenum="493"/><p type="main">

<s>Cos&igrave; fatti studi e importantissime ricerche, nel 1793, erano gi&agrave; state <lb/>fatte: anzi, premessa la distinzione fra conduttori metallici o di prima classe, <lb/>e conduttori umidi o di seconda classe, ne'principii di quello stesso anno, <lb/>aveva, dietro molte esperienze, il Volta <emph type="italics"/>sbozzata,<emph.end type="italics"/> com'egli si esprime, una <lb/>scala o <emph type="italics"/>Tavola de'conduttori della prima classe, che posseggono un diverso <lb/>potere di spingere il fluido elettrico e cacciarlo avanti ne'conduttori umidi, <lb/>ossia di seconda classe<emph.end type="italics"/> (ivi, pag. </s>

<s>236). </s></p><p type="main">

<s>Questi erano, senza dubbio, tali progressi da mettere al sicuro la sco&shy;<lb/>perta dell'Elettricit&agrave; metallica, e da qualificar meglio la natura e l'essere <lb/>de'nuovi Elettromotori. </s>

<s>Ma, poniamo che valessero le esperienze a persua&shy;<lb/>dere la ragion de'Filosofi, non concorrevan o i fatti a persuadere i sensi de'p&igrave;&ugrave; <lb/>valgari, o de'caparbi e degli ostinati, i quali non vedevano la nuova elettri&shy;<lb/>cit&agrave; rivelarsi in quelle scosse e in quelle scintille, con che rivelavasi l'elet&shy;<lb/>tricit&agrave; negli antichi strumenti. </s>

<s>Conosceva perci&ograve; bene il Volta che gli restava <lb/>ancora un gran passo da fare: rendere, co'segnali ordinarii della Macchina, <lb/>la nuova elettricit&agrave; parvente, o, in altre parole, dimostrar l'identit&agrave; fra l'an&shy;<lb/>tico fluido elettrico e il nuovo fluido galvanico. </s>

<s>Ma far ci&ograve; non voleva dir <lb/>altro se non che moltiplicare la virt&ugrave; elettrica nelle coppie metalliche, tro&shy;<lb/>vata sempre fin qui, all'Elettroscopio, cos&igrave; debole, da non incorar nessuna <lb/>speranza di ridur qualcuna di quelle coppie a un Elettromotore, che scota <lb/>e che lampeggi. </s></p><p type="main">

<s>La difficolt&agrave; si presentava grandissima, e chi, per la innumerevole va&shy;<lb/>riet&agrave; de'metalli, si fosse messo a cercare la coppia privilegiata, avrebbe eter&shy;<lb/>namente perduto il tempo e la fatica. </s>

<s>Le speranze del Volta non par che <lb/>s'appuntassero a questo fantasma, ma in ogni modo egli faceva come chi <lb/>va al buio, che pochi passi a diritto lo condurrebbero al termine, e nono&shy;<lb/>stante gira e rigira non vi giunge che per lunga e penosissima via. </s>

<s>Ma gi&agrave;, <lb/>se questa &egrave; la storia di tutte le grandi scoperte, non fa maraviglia che sia <lb/>la storia anche di questa, che, fra tutte le scoperte e le invenzioni, &egrave; la <lb/>grandissima. </s></p><p type="main">

<s>Quella diretta via poi era tanto pi&ugrave; illusoria, in quanto che l'arte, spe&shy;<lb/>cialmente fabbrile, persuadendosi sempre di superar la Natura, raro &egrave; che <lb/>si volga ad imitarla. </s>

<s>Anche il Volta fu per alcun tempo, come tanti altri, <lb/>cos&igrave; sedotto, ma pure all'ultimo, preso miglior consiglio, trov&ograve; ne'magisteri <lb/>della stessa Natura il prodigioso artificio. </s></p><p type="main">

<s>Uno de'pi&ugrave; fini, tra questi magisteri naturali, &egrave; quello, per cui pu&ograve; la <lb/>Torpedine istupidire il braccio dei pescatori. </s>

<s>Il fatto, quanto era ben noto <lb/>agli antichi, tanto alla loro scarsa scienza fisica riusciva misterioso. </s>

<s>Ma quando <lb/>si provarono gli effetti inaspettati della Bottiglia di Leyda, fu allora facile il <lb/>trovare, tra le scosse date dallo strumento e quelle date dal pesce, una stret&shy;<lb/>tissima somiglianza. </s>

<s>Non si dubit&ograve; perci&ograve; allora pi&ugrave; da nessuno che la Tor&shy;<lb/>pedine non contenesse nelle viscere un organo, il quale operasse a quel <lb/>modo che l'Apparato leydese, o il fulminante Quadro frankliniano. </s>

<s>Si inter&shy;<lb/>rog&ograve; l'Anatomia, la quale rispose che quell'organo fulminante della Torpe-<pb xlink:href="020/01/513.jpg" pagenum="494"/>dine consisteva in molti sacchetti membranosi, ripieni di un gran numero <lb/>di pellicole, soprapposte in forma di tanti piccoli dischi, fra l'uno e l'altro <lb/>de'quali stillava un umore acquoso. </s>

<s>Pensarono allora i fisici che cosiffatti <lb/>dischi fossero di una certa materia idoelettrica come il vetro, e che l'ani&shy;<lb/>male, stropicciandoli insieme per forza di muscoli, eccitasse in essi l'eletri&shy;<lb/>cit&agrave; necessaria a caricarne l'organo fulminante. </s>

<s>Il Nicholson pi&ugrave; ingegnosa&shy;<lb/>mente rassomigliava le pellicole o i dischi animali a tante foglie soprapposte <lb/>di talco, di che si componessero altrettanti Elettrofori condensatori. </s></p><p type="main">

<s>Cos&igrave; fatte spiegazioni furono accolte per buone, perch&egrave; si conosceva dal&shy;<lb/>l'altra parte che nulla di meglio sapeva per allora suggerire la scienza. </s>

<s>Ma <lb/>quando il Volta trov&ograve; che nessuna delle parti animali &egrave; coibente, e che tutte <lb/>anzi son conduttrici, specialmente gli umori acquosi, e allora svanirono le <lb/>belle e ingegnose ipotesi, e rest&ograve; tuttavia a sapersi d'onde abbia origine <lb/>l'Elettricit&agrave;, che a loro talento eccitano dentro s&egrave; le Torpedini e simili al&shy;<lb/>tri pesci. </s></p><p type="main">

<s>Il Volta stesso, che aveva rovinato quel primo e seducente edifizio, non <lb/>aveva l&igrave; per l&igrave; saputo suggerire la costruzione di un nuovo, infintanto che <lb/>non occorsero altri notabilissimi fatti concernenti la gran questione dell'Elet&shy;<lb/>tricit&agrave; animale. </s></p><p type="main">

<s>Eusebio Valli, fautore del Galvani, aveva trovato che si contraevano <lb/>tutti i muscoli della rana a pur ripiegare una gamba di lei e ridurla al con&shy;<lb/>tatto de'nervi ischiatici. </s>

<s>Altre esperienze simili a questa consistevano nel te&shy;<lb/>ner sospesa per i piedi la rana con una mano, e coll'altra o colla lingua <lb/>toccare i nervi scoperti, e lasciati penzoloni. </s>

<s>E poich&egrave;, a ridestar ne'mu&shy;<lb/>scoli cos&igrave; fatti mirabili moti, non interveniva nessun'opera di metalli, si <lb/>persuadeva lo Sperimentatore d'aver cos&igrave; decisa la controversia a favor del <lb/>Galvani. </s>

<s>Molti, che avevano disertato, erano per tornar di nuovo sotto gli <lb/>stendardi bolognesi, quando il Volta; non perdutosi di coraggio, confess&ograve; di <lb/>avere asserito non succeder mai le contrazioni senz'alcuno intervento di <lb/>conduttori, che fossero di metallo o di carbone, perch&egrave; non eragli riuscito <lb/>mai di ottener cos&igrave; l'effetto desiderato: ma giacch&egrave; l'ha ora il Valli otte&shy;<lb/>nuto, non dubito, egli dice, &ldquo; di riconoscere che qui pure la diversit&agrave; dei <lb/>conduttori combaciantisi &egrave; necessaria, e che tutto il gioco dipende da que&shy;<lb/>sta diversit&agrave; &rdquo; (Op. </s>

<s>cit, T. II, P. I, pag. </s>

<s>251). Proseguendo il costrutto, <lb/>che qui abbiam lasciato interrotto, chiama il Volta questa sua <emph type="italics"/>una ulteriore <lb/>scoperta;<emph.end type="italics"/> scoperta, la quale consisteva nell'aver trovato da aggiungere alla <lb/>composizione di due metalli e un umido e di due umidi e un metallo, per <lb/>avere un Elettromotore, la composizione di tre umidi contigui fra loro. </s></p><p type="main">

<s>Fu appunto questa nuova scoperta, fu questo progresso di idee, che <lb/>condusse il Volta a riconoscere una somiglianza fra l'&Ograve;rgano elettrico della <lb/>Torpedine, e un Elettromotore, che opera per qualcuna delle sopra notate <lb/>composizioni. </s>

<s>Il porgersi cos&igrave; arrendevoli le nuove teorie ad una spiegazione, <lb/>che era la pi&ugrave; ragionevole di tutte le altre ritrovate ne'principii dell'elet&shy;<lb/><gap/><pb xlink:href="020/01/514.jpg" pagenum="495"/>nell'arte da commentar la Natura. </s>

<s>Ma la compiacenza ineffabilmente si ac&shy;<lb/>crebbe, quando, quasi per ricompensarlo, la Natura stessa gli sugger&igrave; le <lb/>invenzioni dell'arte. </s></p><p type="main">

<s>In mezzo a quel corso e ricorso faticoso di esperienze tendenti tutte a <lb/>cercare il modo di moltiplicare l'intensit&agrave; elettrica delle coppie metalliche, <lb/>venne provvidamente a ingerirsi, nelle speculazioni del Volta, l'organo della <lb/>Torpedine. </s>

<s>Quell'organo scotente e fulminante era appunto ci&ograve; ch'egli cer&shy;<lb/>cava, e giacch&egrave; l'aveva assomigliato a un Elettromotore, in cui le pellicole <lb/>soprapposte o i dischi riferissero una qualche immagine delle coppie de'me&shy;<lb/>talli, e que'dischi vedeva nella Torpedine essere cos&igrave; numerosi; sarebbe <lb/>egli mai, pens&ograve; l'arguto Speculatore, che la mia arte raggiungesse gli ef&shy;<lb/>fetti della Natura col moltiplicar, per soprapposizione, le coppie de'metalli <lb/>alternati? </s></p><p type="main">

<s>Prende una rotella di zinco, le soprappone un'altra simile rotella di <lb/>rame, e cos&igrave; tenendole congiunte fa, ora all'una ora all'altra, toccare il piat&shy;<lb/>tello dell'Elettrometro condensatore. </s>

<s>Trova che il zinco d&agrave; due o tre gradi <lb/>di elettricit&agrave; positiva, il rame due o tre gradi di elettricit&agrave; negativa. </s>

<s>A que&shy;<lb/>sta prima coppia ne soprappone un'altra simile e similmente disposta, ma <lb/>in modo che il rame della inferiore tocchi immediatamente il zinco della su&shy;<lb/>periore, s'aspetta che l'Elettrometro segni, se non il doppio, almeno qualche <lb/>grado di pi&ugrave;: prova, e stupefatto e mortificato vede che l'Elettrometro non <lb/>segna nulla (ivi, T. II, P. II, pag. </s>

<s>157). Fa le coppie di tre pezzi diversi, <lb/>soprappone due di queste coppie come dianzi, e, come dianzi, l'Elettrome&shy;<lb/>tro non si muove (ivi, pag. </s>

<s>189). </s></p><p type="main">

<s>Chi non avesse avuto la pazienza, o diciam meglio il genio sperimen&shy;<lb/>tale del Volta, avrebbe per disperazione lasciato in abbandono ogni cosa. </s>

<s>Ma <lb/>il Nostro pensava che se la Torpedine aveva avuto il suo Elettromotore dalla <lb/>Natura, egli in ogni modo, per imitazione, lo avrebbe ritrovato nell'arte. </s>

<s><lb/>Fermo in questa fiducia, ritorna colla mente sull'anatomia dell'Organo elet&shy;<lb/>trico animale, e attende a un fatto, che ne'fini della sapiente Natura, la <lb/>quale nulla fa a caso, dee esser di non lieve importanza: i dischi membra&shy;<lb/>nosi non si tengono a immediato contatto, ma uno strato umido stilla e <lb/>s'interpone fra l'uno e l'altro. </s></p><p type="main">

<s>Ritorna a far le prove, non trascurata questa parte dal natural magi&shy;<lb/>stero. </s>

<s>La nuova coppia metallica segna all'Elettroscopio a pagliette un ses&shy;<lb/>santesimo di grado. </s>

<s>Taglia, della stessa grandezza e figura delle coppie me&shy;<lb/>talliche, un cartone, lo inzuppa nell'acqua, e, interpostovi questo strato <lb/>d'umido, soprappone alla prima un'altra simil coppia gi&agrave; preparata. </s>

<s>Prova, <lb/>e l'Elettroscopio segna due sessantesimi. </s>

<s>Sopraggiunge, interpostivi i soliti <lb/>cartoni umidi, una terza, una quarta coppia, e l'Elettroscopio solleva le pa&shy;<lb/>gliette a tre, e a quattro sessantesimi di grado (ivi, pag. </s>

<s>187, &sect; XX). </s></p><p type="main">

<s>A questo punto del lungo e fortunoso viaggio, con quella gioia, colla <lb/>quale il pellegrino ricorda il luogo, d'ond'ei prima vide fumare il tetto della <lb/>sua casa, anche il Nostro cos&igrave; scriveva: &ldquo; Questo &egrave; il gran passo da me <pb xlink:href="020/01/515.jpg" pagenum="496"/>fatto sulla fine dell'anno 1799, passo che mi ha condotto ben tosto alla co&shy;<lb/>struzione del nuovo apparato scuotente &rdquo; (ivi). </s></p><p type="main">

<s>Per costruire invero il nuovo apparato, dopo quel gran passo fatto, non <lb/>rimaneva altro al Volta che proseguir nella felicissima imitazione dell'or&shy;<lb/>gano della Torpedine, componendo una colonna di coppie numerose. </s>

<s>Trov&ograve; <lb/>che sessanta all'incirca fatte di zinco e di rame, bastavano perch&egrave; la co&shy;<lb/>lonna stessa potesse dare alcuna scossa &ldquo; quando si toccano le sue due estre&shy;<lb/>mit&agrave; con dita, che non siano asciutte, e assai pi&ugrave; forte se si toccano con <lb/>metalli impugnati per larghe superficie colle mani ben umide, formando cos&igrave; <lb/>una comunicazione assai migliore &rdquo; (ivi, pag. </s>

<s>159, 60). </s></p><p type="main">

<s>S'apriva il secolo XIX, e la gran Lampada che doveva illuminarlo era <lb/>gi&agrave; preparata proprio in quel punto. </s>

<s>L'inventore del portentoso strumento <lb/>non d&agrave; in pazzia per l'allegrezza. </s>

<s>&Egrave; ben sodisfatto e contento, ma non gi&agrave; <lb/>sopraesaltato. </s>

<s>Procedendo di scoperta in scoperta, bevve a sorso a sorso la <lb/>gioia, e gli avvenne perci&ograve; di non inebriarsi come chi non tracanna la coppa <lb/>del vino, ma la centella. </s></p><p type="main">

<s>Nonostante egli sentiva vivissimo il desiderio, e anzi il dovere di diffon&shy;<lb/>dere la notizia della sua invenzione. </s>

<s>Il pi&ugrave; conducevole modo era di rivol&shy;<lb/>gersi alla R. </s>

<s>Societ&agrave; di Londra, e perci&ograve; scrive di langhe pagine, e bench&egrave; <lb/>senta di scriverle malamente, le scrive in francese, <emph type="italics"/>per farsi intendere<emph.end type="italics"/> (ivi, <lb/>pag. </s>

<s>143). Fa poi di queste pagine un trasunto, e sotto forma di lettera, in <lb/>data del d&igrave; 20 Marzo 1800, lo spedisce a Sir Giuseppe Banks, Presidente. </s>

<s><lb/>Incomincia ivi a descrivere il suo <emph type="italics"/>appareil semblable .... &agrave; l'organe &eacute;lectri&shy;<lb/>que naturel de la torpille,<emph.end type="italics"/> per cui non sa per ora chiamarlo con altro nome <lb/>che di <emph type="italics"/>Organo elettrico artificiale,<emph.end type="italics"/> per essere, come poco dopo scriveva al <lb/>Brugnatelli, &ldquo; fondato sopra i medesimi principii e simile anche nella forma, <lb/>secondo la sua prima costruzione, all'organo naturale della Torpedine &rdquo; (ivi, <lb/>pag. </s>

<s>135). Quell'organo poi elettrico artificiale era dal Volta descritto, nella <lb/>sua particolar costruzione, al Banks, nel modo seguente: </s></p><p type="main">

<s>&ldquo; Je me fournis de quelques douzaines de petites plaques rondes ou <lb/>disques, de cuivre, de laiton, ou mieux d'argent, d'un pouce de diam&egrave;tre, <lb/>plus ou moins (par exemple, de monnoyes), et d'un nombre &eacute;gal de plaques <lb/>d'&egrave;tain, ou, ce qui est beacoup mieux, de zinc, de la m&egrave;me figure et gran&shy;<lb/>deur, &agrave;-peu-pr&egrave;s; je dis &agrave;-peu-pr&egrave;s, par ce qu'une precision n'est point re&shy;<lb/>quise, et, en g&eacute;n&eacute;ral, la grandeur, aussi bien que la figure, des pi&egrave;ces m&eacute;&shy;<lb/>talliques, est arbitraire: on doit avoir &eacute;gard soulement qu'on puisse les <lb/>arranger commod&eacute;ment les unes sur les autres, en forme de colonne. </s>

<s>Je <lb/>pr&eacute;pare en outre, un nombre assez grand de rouelles de carton, de pean, <lb/>ou quelque autre mati&egrave;re spongieuse, capable d'imbiber et de retenir beau&shy;<lb/>coup de l'eau, ou de l'humidit&eacute; dont il faudra, pour le succes des exp&eacute;&shy;<lb/>riences, qu'elles soient bien tremp&eacute;es. </s>

<s>Ces tranches ou rouelles, que j'ap&shy;<lb/>pellerai disques movill&eacute;s, je les fais un peu plus petites que les disques ou <lb/>plateaux m&eacute;talliques, &agrave; fin qu'interpos&eacute;es &agrave; ceux de la mani&egrave;re que je dirai </s></p><pb xlink:href="020/01/516.jpg" pagenum="497"/><p type="main">

<s>Descritte cos&igrave; le membra, prosegue il Volta a mostrar, del nuovo Or&shy;<lb/>gano, quasi diremmo la vita, dopo di che soggiunge altri modi di disporre <lb/>quelle medesime membra, uno de'quali, ch'egli chiama <emph type="italics"/>appareil &agrave; gobe&shy;<lb/>lets ou &agrave; couronne de tasses<emph.end type="italics"/> (ivi, pag. </s>

<s>114), consisteva in prendere venti o <lb/>trenta bicchieri pieni d'acqua, facendo comunicare il primo al secondo, il <lb/>secondo al terzo, e cos&igrave; di seguito fino all'ultimo, per mezzo di archi me&shy;<lb/>tallici composti di una lamina di rame e di un'altra di zinco, e disposti tutti <lb/>nel medesimo verso (ivi, pag. </s>

<s>160). </s></p><p type="main">

<s>Gli Accademici di Londra e gli scienziati d'Inghilterra, fra'quali rapi&shy;<lb/>dissima si diffusse la notizia, dato opera a costruire il nuovo Organo elet&shy;<lb/>trico, alla maniera stessa che veniva insegnato in Italia, restarono stupiti, <lb/>quasi paresse loro di vedere un animal mostruoso lavorato dalle mani di un <lb/>uomo, colle membra vive e colle viscere di metallo. </s></p><p type="main">

<s>Tanto romore si fece da quegli Inglesi, che il Volta ebbe a risolversi <lb/>di andare a darne qualche sodisfazione anco ai Padroni. </s>

<s>Stese perci&ograve; e lesse <lb/>all'Istituto Nazionale, in due sedute, ne'd&igrave; 7 e 12 del Novembre 1801, le <lb/>due parti della Memoria <emph type="italics"/>Sull'identit&agrave; del fluido elettrico col fluido galva&shy;<lb/>nico,<emph.end type="italics"/> riscontrando i detti, dopo le sedute, coll'esperienze. </s>

<s>Napoleone, primo <lb/>Console, che ud&igrave; e vide insiem co'pi&ugrave; grandi scienziati convenuti d'ogni <lb/>parte a Parigi, decret&ograve; che fosse coniata una medaglia d'oro commemora&shy;<lb/>tiva del grande avvenimento. </s></p><pb xlink:href="020/01/517.jpg"/><p type="main">

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

<s><emph type="center"/><emph type="bold"/>Di varii altri strumenti<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

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

<s>I. </s>

<s>Degli specilli semplici, o degli occhiali da naso, e del loro modo di operar sul&igrave;a vista. </s>

<s>&mdash; II. </s>

<s>Del <lb/>Microscopio semplice e del Microscopio composto. </s>

<s>&mdash; III. </s>

<s>Del corno acustico. </s>

<s>&mdash; IV. De'primi Igro&shy;<lb/>scopii, degl'Igrometri del Santorio, dell'Igrometro a condensazione del Torricelli, della <emph type="italics"/>Mostra <lb/>umidaria<emph.end type="italics"/> del Folli, della Legge igrometrico-meccanica del Viviani, e dell'Igrometro elettrico del <lb/>Volta. </s>

<s>&mdash; V. Dell'Arcometro e del Pluviometro. </s></p><p type="main">

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

<s>La storia dell'invenzione degli specilli semplici avrebbe dovuto prolu&shy;<lb/>dere alla storia dell'invenzione del Canocchiale: ma perch&egrave;, riguardati gli <lb/>stessi specilli nel loro semplice uso di corregger la vista, specialmente de'vec&shy;<lb/>chi, non appartengono strettamente all'ordine degli strumenti del metodo <lb/>sperimentale; ci contenteremo d'aggiunger qui le seguenti notizie per chi <lb/>desiderasse di averle, come complemento o supplemento di storia alle cose <lb/>gi&agrave; esposte nel Cap. </s>

<s>III. </s></p><p type="main">

<s>Pretendere d'investigare il nome, la patria e il tempo di colui, che ri&shy;<lb/>trov&ograve; l'uso de'cristalli convessi per restituire la bont&agrave; della vista affievolita <lb/>ne'vecchi, &egrave; forse opera assai difficile, e anzi diremmo quasi impossibile, es&shy;<lb/>sendo tante le circostanze e i modi, con che una persona o l'altra pu&ograve; es&shy;<lb/>sersi facilmente accorta che alcuni mezzi diafani soprapposti alla cornea del&shy;<lb/>l'occhio, fanno vedere ingranditi gli oggetti. </s>

<s>Lasciando andar ci&ograve; che Realdo <lb/>Colombo argutamente pens&ograve; della lente cristallina estratta dai cadaveri, la <lb/>quale facendo vedere ingranditi gli oggetti, poteva aver dato la prima oc&shy;<lb/>casione a inventar gli occhiali: le lacrime possono essere state il primo sog&shy;<lb/><gap/><pb xlink:href="020/01/518.jpg" pagenum="499"/>Francesco Redi, in quel suo Discorso che scrisse in forma di Lettera <emph type="italics"/>In&shy;<lb/>torno all'invenzion degli occhiali,<emph.end type="italics"/> riferisce due testi di due medici francesi, <lb/>i quali giusto accennano all'efficacia de'collirii da essi proposti per medi&shy;<lb/>care l'infiammazione degli occhi, dicendo essere di tale e tanta virt&ugrave; da far <lb/>vedere ingranditi gli oggetti, anche senza gli occhiali. </s>

<s>&ldquo; Bernardo Gordoni, <lb/>professore in Monpellieri, nel libro intitolato <emph type="italics"/>Lilium medicinae,<emph.end type="italics"/> principiato <lb/>da lui, come confessa, l'anno 1305 del mese di Luglio, nel capitolo <emph type="italics"/>De subti&shy;<lb/>litate visus,<emph.end type="italics"/> dopo avere insegnato un certo suo collirio, soggiunge con gran <lb/>brio e un po'troppo arditamente: <emph type="italics"/>Et est tantae virtutis quod decrepitum <lb/>faceret legere litteras minutas absque ocularibus.<emph.end type="italics"/> Guido da Caudiac, pro&shy;<lb/>fessore anch'esso di Monpelli&egrave;ri, nella sua <emph type="italics"/>Chirurgia grande,<emph.end type="italics"/> composta <lb/>l'anno 1363, porta in quella alcuni medicamenti buoni alla debolezza degli <lb/>occhi, ed aggiunge di pi&ugrave;, con sincerit&agrave; maggiore di quella del Gordonio: <lb/><emph type="italics"/>Se queste e simili cose non giovano, bisogna ricorrere agli occhiali<emph.end type="italics"/> &rdquo; (Redi, <lb/>Cons. </s>

<s>e opusc., Firenze 1863, pag. </s>

<s>53, 54). </s></p><p type="main">

<s>Forse anche l'osservazione fatta sopra gli effetti di rifrazione, che na&shy;<lb/>turalmente presentano le gocciole della pioggia, le perline di cristallo, e le <lb/>boccie di forma sferoidea, per uso delle mense piene di acqua, dettero oc&shy;<lb/>casione all'arte d'imitar la Natura, con facile persuasione che tutto il se&shy;<lb/>greto consisteva nella curvit&agrave; della superficie del mezzo diafano, ond'&egrave; perci&ograve; <lb/>che prime a ritrovare furon non le lenti concave ma le convesse. </s>

<s>Giova a <lb/>questo proposito riferire una nota apposta dal Canovai al suo <emph type="italics"/>Elogio storico <lb/>di Alessando della Spina.<emph.end type="italics"/> &ldquo; Il p. </s>

<s>Alessandro, ivi egli dice, ebbe in vista <lb/>la sola infermit&agrave; de'presbiti, senza pensare affatto a quella de'miopi. </s>

<s>Tanto <lb/>sembra insinuare Sandro di Pippozzo, allorch&egrave; caratterizza gli occhiali come <lb/><emph type="italics"/>trovati novellamente per comoditae delli poveri veki, quando affiebolano <lb/>dal vedere.<emph.end type="italics"/> Infatti i miopi non si conoscevano quasi punto a quei tempi, e <lb/>potrebbe dirsi che ne &egrave; cresciuto il numero, dopo che si &egrave; inventato un <lb/>rimedio anche per loro. </s>

<s>Son quasi tanto rari i giovani veramente bisognosi <lb/>degli occhiali concavi, quanto lo sono i vecchi, che veramente possan vedere <lb/>senza il soccorso dei convessi. </s>

<s>Del resto, le lenti concave hanno pochissime <lb/>utili propriet&agrave; come ben dimostrano gli Ottici, e l'Astronomia, dopo Gali&shy;<lb/>leo che le combin&ograve; nel suo Telescopio, non ne fa pi&ugrave; alcun uso &rdquo; (Prose <lb/>varie, T. III, Firenze 1817, pag. </s>

<s>36). </s></p><p type="main">

<s>Non tutti certamente acconsentiranno al Canovai che, prima del se&shy;<lb/>colo XIV, non ci fossero <emph type="italics"/>miopi,<emph.end type="italics"/> riman pur nonostante vero che della prima <lb/>invenzione furono le lenti convesse e dopo si fece quella delle concave. </s>

<s>Ci&ograve; <lb/>si spiega ripensando che quelle occorsero pi&ugrave; facilmente a riscontrar negli <lb/>esempii della natura, mentre queste son piuttosto un frutto della specula&shy;<lb/>zione e un portato dell'arte. </s></p><p type="main">

<s>Fermo dunque stando e approvato che primi ad essere inventati furono <lb/>gli occhiali convessi <emph type="italics"/>per comodit&agrave; delli poveri vecchi,<emph.end type="italics"/> e che molti possano <lb/>essere convenuti insieme e concorsi nell'osservazione del fatto naturale rap&shy;<lb/>presentato nelle immagini rifrante dai diafani terminati da superficie curve; <pb xlink:href="020/01/519.jpg" pagenum="500"/>si domanda chi fu il primo, il quale ridusse l'osservazione naturale a sog&shy;<lb/>getto di speculazione o ad esercizio di arte? </s></p><p type="main">

<s>Leopoldo del Migliore, erudito fiorentino del secolo passato, dice essere <lb/>stato costui Salvino degli Armati, come si legge in una epigrafe sepolcrale, <lb/>allora scoperta e ora visibile a tutti nel Chiostro del convento di S. </s>

<s>Maria <lb/>Maggiore di Firenze, dove la famiglia degli Armati ebbe gentilizia sepoltura. </s>

<s><lb/>Quella iscrizione, che soggiace scolpita in marmo bianco al busto di Salvino, <lb/>pure scolpito in marmo, dice cos&igrave;: <emph type="italics"/>Qui diace Salvino d'Armato degli Ar&shy;<lb/>mati di Fir. </s>

<s>inventor degli occhiali. </s>

<s>Dio gli perdoni le peccata. </s>

<s>A. D. 1317.<emph.end type="italics"/></s></p><p type="main">

<s>Dal passo del Gordonio per&ograve; riferito dal Redi, sembra doversi argomen&shy;<lb/>tare che, nel 1305, gli occhiali erano stati gi&agrave; inventati, e il Canovai, in un'al&shy;<lb/>tra Nota al sopra citato Elogio, asserisce non esser punto probabile che un <lb/>tale inventore fosse per patria fiorentino, principalmente, com'egli stesso <lb/>dice, per questa ragione: &ldquo; Se un fiorentino trov&ograve; l'arte di far gli occhiali, <lb/>&egrave; dunque affatto ridicolo il sentimento del B. Giordano, che, predicando pub&shy;<lb/>blicamente in Firenze, si gloria di averlo conosciuto, e dice: <emph type="italics"/>Io vidi colui, <lb/>che prima la trov&ograve; e fece, e favellaili.<emph.end type="italics"/> La pi&ugrave; gran parte degli ascoltanti <lb/>avrebbe potuto rispondergli: <emph type="italics"/>Padre, noi lo abbiamo visto e gli abbiam fa&shy;<lb/>vellato prima di voi<emph.end type="italics"/> &rdquo; (ivi, pag. </s>

<s>35). </s></p><p type="main">

<s>Carlo Dati dunque, in una delle sue <emph type="italics"/>Veglie,<emph.end type="italics"/> dimostr&ograve; che l'inventore <lb/>era pisano, ed era per l'appunto quel frate Alessandro, di cui il Canovai <lb/>tesse l'elogio. </s>

<s>Soggiunse il Dati di pi&ugrave; che l'invenzione occorse pochi anni <lb/>prima del 1300. Finge ivi l'Autor delle <emph type="italics"/>Veglie fiorentine<emph.end type="italics"/> che un giovane <lb/>forestiero venuto apposta a Firenze per veder Galileo, e trattenutovisi al&shy;<lb/>quanti giorni, si ritrovasse una sera, nel giardino del Duca Salviati, a col&shy;<lb/>loquio con alcuni gentiluomini della citt&agrave;, fra'quali Filippo Pandolfini. </s>

<s>Sa&shy;<lb/>ziatosi quel giovane forestiero di rimirar le novit&agrave; celesti con uno de'migliori <lb/>canocchiali di Galileo, armato e diretto dall'esperte mani di quei Signori, <lb/>fu fatto s&igrave; che il discorso cadesse intorno al primo inventore di quel s&igrave; mi&shy;<lb/>rabile strumento, e poi risalendo pi&ugrave; su, intorno al primo inventor degli oc&shy;<lb/>chiali. </s>

<s>Essendo stato dimostrato, da quel dotto ed erudito consesso, che gli <lb/>antichi non conobbero veramente gli occhiali, il giovane forestiero allora cos&igrave; <lb/>prese a dire: &ldquo; Ma giacch&egrave;, secondo il parere di lor signori, gli antichi non <lb/>ebbero occhiali, quando furono egli inventati? </s>

<s>A questa domanda tutti si <lb/>ristrinsero nelle spalle, non sapendo che dirsi, ma il senator Filippo Pan&shy;<lb/>dolfini, il quale fin allora aveva taciuto, dando segno di meditar qualche <lb/>cosa di gran rilievo, risolutamente rispose: Non grandi anni avanti al 1300, <lb/>che tanto afferma fra Giordano da Rivalto, eloquentissimo predicatore del&shy;<lb/>l'Ordine di S. Domenico, il quale fior&igrave; e predic&ograve; in Santa Maria Novella, <lb/>poco dopo a tal tempo. </s>

<s>Dice egli dunque, in una delle sue Prediche citate <lb/>nel nostro Vocabolario da un mio manoscritto: <emph type="italics"/>Non &egrave; ancora 20 anni, che <lb/>si trov&ograve; l'arte di fare occhiali, che fanno veder bene, che &egrave; una delle mi&shy;<lb/>gliori arti e delle pi&ugrave; necessarie, che il mondo abbia.<emph.end type="italics"/> &mdash; Nuova e curiosa <lb/>notizia &egrave; questa, disse il Forestiero, non avendo mai ascoltato particolare <pb xlink:href="020/01/520.jpg" pagenum="501"/>tanto preciso. </s>

<s>Ma dell'inventore? </s>

<s>&mdash; Ella mi ha tolto la parola di bocca, ri&shy;<lb/>spose il Pandolfini, perch&egrave; appunto io mi preparava a dir qualche cosa di <lb/>questo. </s>

<s>Quando io era giovane, andando a Pisa a studiar legge, pi&ugrave; per co&shy;<lb/>mandamento d'altri che per mio genio, il quale era rivolto, piuttosto che <lb/>alla Giurisprudenza romana, a rinvenire le Memorie nostrali; io andava sem&shy;<lb/>pre frugando le librerie manoscritte, dove per ordinario si trova qualche <lb/>erudizione non cos&igrave; esposta alla notizia universale, e particolarmente quella di <lb/>S. </s>

<s>Caterina de'P. P. Predicatori, fornita di buonissimi testi a penna, e mi <lb/>ricordo benissimo, come se fusse ora, di aver letto attentamente e con dili&shy;<lb/>genza sfogliata una Cronaca latina di detto Convento, scritta in cartapecora, <lb/>compilata brevemente, prima da fra Bartolommeo da S. </s>

<s>Concordio Autore <lb/>degli Ammaestramenti antichi, e poi pi&ugrave; largamente continuata da frate Ugo&shy;<lb/>lino di Sernovi, e tutta insieme raccolta e condotta, fino all'anno 1400 in <lb/>circa, da fra Domenico da Peccioli, colla giunta del maestro fra Simone da <lb/>Cascia, figliolo del sopraddetto monastero, la quale non saprei dire fin dove <lb/>arrivassi per mancanza di alquante carte. </s>

<s>Fra le Memorie di questa Cro&shy;<lb/>naca, all'anno 1313, si legge che, in detto convento di S. Caterina, visse e <lb/>mor&igrave; il p. </s>

<s>frate Alessandro Spina, religioso di ottimi costumi e di acutis&shy;<lb/>simo ingegno, apprendendo tutto quello che udiva dire e vedeva fare, e che, <lb/>essendosi dato il caso che un tale fu il primo a inventare gli occhiali, n&egrave; <lb/>volendo comunicare ad altri l'invenzione, egli, da per s&egrave; stesso, gli fabbric&ograve;, <lb/>e a tutti di buon cuore ne fece parte &rdquo; (Targioni, Notiz. </s>

<s>Aggrandim., ediz. </s>

<s><lb/>cit., T. II, P. I, pag. </s>

<s>59, 60). </s></p><p type="main">

<s>A questo frate Alessandro si dovrebbe dunque, circa all'invenzion degli <lb/>occhiali, quel merito stesso che si vuole avere avuto Galileo circa all'inven&shy;<lb/>zione del Canocchiale; ma qualunque sia il valore che vuol darsi ai docu&shy;<lb/>menti storici prodotti dal Pandolfini, &egrave; un fatto che cos&igrave; dell'Occhial piccolo <lb/>come del grande, il ritrovamento &egrave; da attribuirsi all'arte piuttosto che alla <lb/>scienza. </s>

<s>Della scienza diottrica degli specilli narrammo altrove gli Autori; ora <lb/>qui giova mostrar come e quando si riusc&igrave; a intendere il modo d'operar degli <lb/>stessi specilli intorno al correggere e al migliorar la vista de'giovani e <lb/>de'vecchi. </s></p><p type="main">

<s>Il Keplero, nel Cap. </s>

<s>V, proposiz. </s>

<s>XXVIII de'<emph type="italics"/>Paralipomeni a Vitellione,<emph.end type="italics"/><lb/>prim&agrave; di entrare a trattar del nuovo e difficile soggetto, esclama: &ldquo; Quanta <lb/>admiratio rei tantae, tam late propagatum usum et tamen causam ignorari <lb/>hactenus!.... Unus Baptista Porta professus est rationem in Opticis red&shy;<lb/>dere, quae a librariis frustra hactenus requisivi &rdquo; (Francof. </s>

<s>1604, pag. </s>

<s>202). <lb/>Il libro dell'Ottica del Porta, a cui s'accenna in queste parole, a quel che <lb/>pare non diffuso allora in Germania, &egrave; il Trattato <emph type="italics"/>De refractione,<emph.end type="italics"/> stampato <lb/>in Napoli nel 1593, dove giusto l'Autore tratta, nel Libro VIII, <emph type="italics"/>De specillis,<emph.end type="italics"/><lb/>e proemia alla sua trattazione chiamando l'opera, che egli ivi imprende, <emph type="italics"/>res <lb/>ardua, mirabilis, utilis, iucunda, nec ab aliquibus adhuc tentata<emph.end type="italics"/> (pag. </s>

<s>173). </s></p><p type="main">

<s>&Egrave; dunque il Porta, senza dubbio il primo fra gli Ottici, il quale non <lb/>solo dimostra l'andamento de'raggi rifratti attraverso il diafano degli oc-<pb xlink:href="020/01/521.jpg" pagenum="502"/>chiali concavi e de'convessi, ma investiga altres&igrave; la ragione, per cui da quel&shy;<lb/>l'artificioso andamento si viene a correggere il difetto naturale degli occhi. </s>

<s><lb/>Incomincia dal considerar quel che dice Aristotile <emph type="italics"/>senes procul videre, quia <lb/>procul radii non coeunt,<emph.end type="italics"/> e francamente pronunzia che una tale dottrina del <lb/>Filosofo &egrave; falsa, essendo falso il supposto da lui, che cio&egrave;, per vedere, vi <lb/>bisognino ambedue gli occhi, ed essendo di pi&ugrave; la falsit&agrave; manifesta dal fatto <lb/>de'monoculi vecchi, i quali, guardando pur coll'uno, <emph type="italics"/>procul<emph.end type="italics"/> anch'essi <emph type="italics"/>vi&shy;<lb/>dent,<emph.end type="italics"/> come coloro che guardano co'due occhi. </s>

<s>&ldquo; Sed vera ratio est, sog&shy;<lb/>giunge il Porta, quod senibus pupilla deducitur reseraturque, ut caetera quo&shy;<lb/>que membra, non recte suo funguntur officio, humor quoque incrassatur, <lb/>unde maiori luce ad videndum indigent .... necesse enim habent ut quae <lb/>videre velint lucidiora sint, magisque coacta, quod utrumque crystallinis spe&shy;<lb/>cillis emendatur, haec enim refractione radios uniunt et lux multiplicatur <lb/>in eis &rdquo; (pag. </s>

<s>138). </s></p><p type="main">

<s>La presbiopia insomma, pel nostro Ottico napoletano dipende dall'aver <lb/>l'occhio troppo dilatata la pupilla, e dall'esser divenuto, per vecchiezza, ot&shy;<lb/>tuso a sentir l'impressione de'raggi luminosi, a che le lenti convesse soc&shy;<lb/>corrono utilmente condensando quegli stessi raggi, e perci&ograve; moltiplicando la <lb/>luce. </s>

<s>La miopia consiste invece nell'esser la pupilla troppo ristretta e non <lb/>troppo diafano il cristallino; due difetti che s'emendano, secondo il Porta, <lb/>dagli occhiali concavi, i quali fanno al di dietro divergere i raggi, e gli fanno <lb/>convergere dalla parte davanti, e cos&igrave; condensandovi il lume, rischiarano gli <lb/>oggetti. </s>

<s>&ldquo; Juvenes, qui arcta sunt pupilla, ac vitreo humore, qui in oculo <lb/>continetur non claro, duo requirerent, et quae simulacra dilatarent, ut re&shy;<lb/>sarciatur vitium pupillae, et quodammodo unirent; et quod lucem clario&shy;<lb/>rem redderent. </s>

<s>Duo haec praestat concavum specillum, nam et simulacrum <lb/>quodammodo unit ex refractionibus ut intra vitri soliditatem apparet, et quo&shy;<lb/>dammodo aperiret ut videmus lineis in adversam partem refugientibus, et <lb/>lux pertransiens visum multiplicatur &rdquo; (pag. </s>

<s>188). </s></p><p type="main">

<s>Dopo il Porta, a specular la ragione dell'operar gli occhiali sopra la <lb/>vista, venne il De Dominis, nel suo celebre Trattato <emph type="italics"/>De radiis visus et lu&shy;<lb/>cis,<emph.end type="italics"/> in cui, proponendosi di rifiutar come false le dottrine del Fisico napo&shy;<lb/>letano, altre false conseguenze deduce egli stesso in proposito, da pi&ugrave; errati <lb/>principii. </s>

<s>Uno di questi, e de'principali, &egrave; che la visione <emph type="italics"/>proprie et imme&shy;<lb/>diate fit in ipsa pupilla, idest humore chistallino<emph.end type="italics"/> (Venetiis 1611, pag. </s>

<s>6). <lb/>Di qui conclude esser falsa l'opinion di coloro, i quali <emph type="italics"/>defectum oculi se&shy;<lb/>nilis totum reducunt ad dilationem foraminis uvaee<emph.end type="italics"/> (ivi, pag. </s>

<s>15), essendo <lb/>che nell'occhio non avvengono rifrazioni, n&egrave; &egrave; vero che vi si rappresentin <lb/>l'immagini a modo che nella camera oscura, <emph type="italics"/>quia et longe debitiores ibi <lb/>cernuntur rerum colores .... et omnia cernuntur inversa .... quod in <lb/>oculo neque contingit neque contingere potest<emph.end type="italics"/> (ibi). </s></p><p type="main">

<s>Da che dunque dipende per il De Dominis il difetto della vista ne'vec&shy;<lb/>chi? </s>

<s>Da ci&ograve; che <emph type="italics"/>ob diversos axes fiunt quaedam parallaxes visus sive di&shy;<lb/>versitates aspectus<emph.end type="italics"/> (pag. </s>

<s>16). Ora, tali parallassi, prosegue a dire l'Autore, <pb xlink:href="020/01/522.jpg" pagenum="503"/>son tolte via dai vetri convessi, i quali raccolgono tutti insieme, intorno al&shy;<lb/>l'asse della piramide visuale, i raggi che andavan prima disordinati e di&shy;<lb/>spersi. </s>

<s>&ldquo; Visus enim senum invatur appositione vitri rotundi .... Tale enim <lb/>vitrum primo et principaliter aufert parallaxes illas et consequenter confu&shy;<lb/>sionem.... Franguntur enim in tali vitro ad perpendicularem, et consequen&shy;<lb/>ter uniuntur in ipsa perpendiculari, quae est axis verus pyramidis visua&shy;<lb/>lis .... quae unio, et congregatio radiorum aufert omnes parallaxes. </s>

<s>Deinde <lb/>vere iuvat etiam visum, quia tale vitrum ampliat quantitates obiecti visi, et <lb/>facit ut maior appareat quam sit, quia dicta fractio ampliat et dilatat angu&shy;<lb/>lum visivum &rdquo; (ibi, pag. </s>

<s>19). </s></p><p type="main">

<s>Quanto a'miopi il De Dominis ne riconosce il difetto <emph type="italics"/>ex nimia humi&shy;<lb/>ditate et liquiditate humoris crystallini<emph.end type="italics"/> (pag. </s>

<s>19), a togliere il quale giova, <lb/>dic'egli, l'occhiale concavo &ldquo; quia restringit obiectum per angulum strictio&shy;<lb/>rem, quo, etsi res minor appareat quam sub angulo naturali directo, fortius <lb/>tamen agit in oculum, quia virtus unita fortior &rdquo; (pag. </s>

<s>20). </s></p><p type="main">

<s>Resta, da cos&igrave; fatti documenti, provato che n&egrave; il Porta n&egrave; il De Do&shy;<lb/>minis sciolsero il problema degli occhiali, che abbrevian la vista troppo lunga, <lb/>e allungano convenientemente la corta, traendo conclusioni false da non retti <lb/>principii. </s>

<s>Parecchi anni prima per&ograve; che uscissero a mettere in luce le loro <lb/>dottrine i due sopra commemorati Autori, il Maurolico aveva speculato nella <lb/>solitudine, e avea trovato, ne'principii scienziali della Diottrica, quelle verit&agrave;, <lb/>che invano i suoi successori andarono a cercar nella loro fantasia. </s></p><p type="main">

<s>La questione, secondo il Maurolico, dipende tutta dalla forma del cri&shy;<lb/>stallino, che &egrave; per lui riguardato come l'organo essenziale della visione. </s>

<s>&ldquo; In&shy;<lb/>ter ea quae ad visum spectant, dignitatis orcem obtinet glacialis, sive chry&shy;<lb/>stallinus humor, quem et pupillam appellare meo iudicio possumus, in quo <lb/>visiva virtus tanquam in sede consistit.... Ab huius forma dependet quali&shy;<lb/>tas visus, sive brevis sive longi &rdquo; (Diaphan., lib. </s>

<s>III, Neapoli 1611, pag. </s>

<s>69, 70). </s></p><p type="main">

<s>Nel cristallino i raggi si rifrangono con quella legge <emph type="italics"/>quam diaphani <lb/>figura postulat.<emph.end type="italics"/> E perci&ograve; &ldquo; cum perspicui forma variata, variet quoque <lb/>fractionis angulus, iam hinc et visualium radiorum situm diversificari, con&shy;<lb/>cursumque nunc anticipari, nunc differri necesse erit. </s>

<s>Et quoniam quo mi&shy;<lb/>nor est perspicuus globus eo minus spatium coadunat radios; ideo et qui con&shy;<lb/>globatiorem sortiti sunt pupillam breviore sunt visu praediti &rdquo; (ibi, pag. </s>

<s>77). <lb/>Questo &egrave; l'occhio de'miopi, e quello de'vecchi <emph type="italics"/>siquidem in senibus humo&shy;<lb/>ris remissio, remittit non nihil in pupilla tumoris<emph.end type="italics"/> (pag. </s>

<s>78). </s></p><p type="main">

<s>Da ci&ograve; direttamente conclude il Maurolico l'effetto degli occhiali che, <lb/>essendo convessi, abbreviano il troppo lungo concorso de'raggi refratti nella <lb/>pupilla, ed essendo concavi, estendon quello, che per natura sua era troppo <lb/>breve. </s>

<s>Da ci&ograve; si vengono ad emendare gli eccessi, e si fa s&igrave; che vada giu&shy;<lb/>sto ad unirsi e a congregarsi <emph type="italics"/>ad opticum nervum speciem rei.<emph.end type="italics"/> &ldquo; Item con&shy;<lb/>cavis conspicillis brevem oblutum extendi atque convexis longum breviari, <lb/>quoniam seilicet illis collecti dilatantur, his vero dilatati colliguntur radii, <lb/>contrariique defectus contrariis emendantur remediis &rdquo; (pag. </s>

<s>79). </s></p><pb xlink:href="020/01/523.jpg" pagenum="504"/><p type="main">

<s>Si vede chiaro di qui le dottrine del Maurolico avere assai da vicino <lb/>dato nella cruna del vero, se non che ei non conobbe n&egrave; l'organo, n&egrave; il <lb/>modo proprio come si fa la vista. </s>

<s>Quando poi il Keplero dimostr&ograve; niente <lb/>altro essere il cristallino che una lente di rifrangenza, e che le immagini si <lb/>dipingono rovesciate sopra la retina, non bisogn&ograve; fare altro che questa emen&shy;<lb/>dazione alle teorie del Maurolico intorno agli occhiali, per intender, dell'ope&shy;<lb/>rar di questi, la ragion vera. </s></p><p type="main">

<s>Uno de'primi a far ci&ograve; e a pubblicar le emendate dottrine nel suo <emph type="italics"/>Corso <lb/>Matematico,<emph.end type="italics"/> il quale vide nel 1633, per la prima volta la luce, fu l'Heri&shy;<lb/>gonio, cos&igrave; scrivendo: &ldquo; Qui longinqua tantum distincta vident ut senes, hu&shy;<lb/>morem chrystallinum ex siccitate tenuiorem et spirituum penuria nimis <lb/>depressum, nec satis gibbosum habent ad radios divergentes singulorum <lb/>punctorum coaudunandos. </s>

<s>Itaque ii ut radiorum concursus non protendatur <lb/>ultra retinam, longe ab oculo tenent visibile, vel convexis conspicillis, ad <lb/>propius coadunandos radios utuntur. </s>

<s>Myopes contra habent humorem chry&shy;<lb/>stallinum nimis globosum ideoque, nisi visibile fuerit valde proprinquum, <lb/>concursus radiorum fit illis inter humorem chrystallinum et retinam ac <lb/>proinde confusa vident omnia remota indigentque cavis conspicillis ad con&shy;<lb/>cursum radiorum longius propagandum, distincteque videndum &rdquo; (Pari&shy;<lb/>siis 1844, T. V, pag. </s>

<s>182). </s></p><p type="main">

<s>Fra'nostri il Castelli in quel suo <emph type="italics"/>Discorso sopra la vista,<emph.end type="italics"/> raccolto fra <lb/>gli Opuscoli filosofici di lui pubblicati nel 1669, non lasci&ograve; di trattare, fra <lb/>molte altre cose importanti e curiose, anche della Miopia, e della Presbio&shy;<lb/>pia. </s>

<s>Egli pure, emendando, come l'Herigonio, le teorie del Maurolico con <lb/>le dottrine del Keplero, diceva dipendere il difetto de'vecchi dall'essersi con&shy;<lb/>sumato parte degli umori degli occhi, per cui, venendo la retina a esser <lb/>ritirata troppo verso il cristallino, le immagini appariscono annebbiate, e si <lb/>rischiarano coll'artificio degli occhiali convessi. </s>

<s>Ne'miopi al contrario, avendo <lb/>il vitreo e il cristallino maggior convessit&agrave; della necessaria, la retina riman <lb/>troppo lontana dal luogo della visione distinta, e l'arte perci&ograve; con gli oc&shy;<lb/>chiali concavi pu&ograve; facilmente correggere questo difetto della Natura. </s></p><p type="main">

<s>Di questo argomento fece pure soggetto il Baliani in quel suo tratta&shy;<lb/>tello <emph type="italics"/>De visione<emph.end type="italics"/> raccolto fra le <emph type="italics"/>Opere diverse,<emph.end type="italics"/> pubblicate da Giovanni Ca&shy;<lb/>lenzani in Genova nel 1666, ma non avendo accettate le teorie Kepleriane, <lb/>non pot&egrave; perci&ograve; liberarsi da alcuni errori. </s></p><p type="main">

<s>N&egrave; quel Viviani, che discorse per tutte le parti della Fisica, promoven&shy;<lb/>dola nella solitudine col mirabile ingegno, lasci&ograve; indietro di risolvere il pro&shy;<lb/>blema, che &egrave; forse, per il frequente e cos&igrave; comodo uso che si fa degli <lb/>occhiali, fra tutti gli altri, per un ottico, il pi&ugrave; curioso. </s>

<s>A carte 85 del <lb/>Tomo CXXXIII, nella Raccolta de'Manoscritti intitolati <emph type="italics"/>Discepoli di Gali&shy;<lb/>leo,<emph.end type="italics"/> si vedono alcune figure, diligentemente disegnate a penna dallo stesso <lb/>Viviani, rappresentanti la sezione dell'occhio, coll'andamento de'raggi re&shy;<lb/>fratti, che per la pupilla vanno a terminar sulla retina. </s>

<s>Nello spazio, lasciato <lb/>fra la sopraddetta figura e il margine della carta, sotto quest'enunciato di <pb xlink:href="020/01/524.jpg" pagenum="505"/>proposizione <emph type="italics"/>perch&egrave; gli occhi<emph.end type="italics"/> myopes, <emph type="italics"/>cio&egrave; di vista corta vegghino poco, e <lb/>perch&egrave; gli occhiali concavi gli facciano vedere pi&ugrave; di quel che vedevano,<emph.end type="italics"/><lb/>si legge: &ldquo; A questi occhi segue questo quando l'oggetto &egrave; lontano, perch&egrave; <lb/>i raggi, venendo tanto poco divergenti che la sua cornea non serve per <lb/>dargli quella rifrazione che basti, e perci&ograve; concorrono pi&ugrave; presto che non <lb/>dovrebbero; ma essendo vicino, non hanno bisogno di occhiale, perch&egrave; quella <lb/>gran divergenza che hanno dall'oggetto vicino serve per fargli concorrere <lb/>dove bisogna. </s>

<s>E cos&igrave; si vede in che maniera l'occhiale concavo viene a far <lb/>vedere pi&ugrave; di quello si vedeva, perch&egrave; gli occhi <emph type="italics"/>myopes<emph.end type="italics"/> hanno la cornea di <lb/>sfera pi&ugrave; piccola, che non dovrebbero avere, che stante questo i raggi del&shy;<lb/>l'oggetto vengono a concorrere pi&ugrave; presto nella retina, che &egrave; dove si forma <lb/>la vista, ma mettendovi avanti l'occhiale concavo, che ha virt&ugrave; di fare i <lb/>raggi pi&ugrave; divergenti che prima, .... di tal maniera che poi la detta cornea <lb/>viene a fare la refrazione nella retina, &egrave; per&ograve; dunque che l'occhiale con&shy;<lb/>cavo ha virt&ugrave; di far vedere pi&ugrave; di quello che vedeva prima. </s>

<s>&rdquo; </s></p><p type="main">

<s>Poi seguita l'altro enunciato di proposizione, <emph type="italics"/>gli occhi presbiti in che <lb/>maniera vegghino assai di lontano e perch&egrave; per vedere da vicino ci vuol <lb/>gli occhiali convessi,<emph.end type="italics"/> sotto la quale cos&igrave; si legge: &ldquo; Per questa dimostra&shy;<lb/>zione dunque si vedr&agrave; che gli occhi presbiti, che son quelli che avendo la <lb/>cornea di pi&ugrave; grande sfera che non dovrebbero avere, e cos&igrave; battendovi i <lb/>raggi all'oggetto fa maggior rifrazione che non avrebbe a essere, e cos&igrave; <lb/>viene ad essere il punto dove si uniscono i raggi fuori della retina, che <lb/>mettendovi gli occhiali convessi gli toglie di quella divergenza e gli fa con&shy;<lb/>correre pi&ugrave; presto, in maniera tale che viene a stamparsi il punto dell'og&shy;<lb/>getto nella retina, che &egrave; dove si fa la vista. </s>

<s>E questo segue a questi occhi <lb/>quando l'oggetto &egrave; vicino, perch'essendo lontano non hanno bisogno d'oc&shy;<lb/>chiale, perch&egrave; i raggi vengono tanto pi&ugrave; divergenti, che ogni poco di con&shy;<lb/>vessit&agrave; serve per fargli concorrere, e per&ograve; gli serve quella della sua cornea. </s>

<s>&rdquo; </s></p><p type="main">

<s>Cos&igrave; il Maurolico, il Castelli, il Viviani concorsero insieme, e de'primi <lb/>fra'nostri, a trovare il vero di quella dottrina mirabile utile e gioconda a <lb/>sapersi, intorno alla quale invano erasi affaticato il Porta. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>L'invenzione del Microscopio, riguardato nella sua prima semplicit&agrave;, &egrave; <lb/>antica quant'&egrave; antica l'invenzione stessa degli occhiali da naso. </s>

<s>La lente <lb/>convessa da presbiti infatti rappresenta, anche all'occhio normale, le im&shy;<lb/>magini virtuali, ingrandite e diritte degli oggetti vicini. </s>

<s>Ma, forse per la fa&shy;<lb/>cilit&agrave; della costruzione, si ricorse in principio, pi&ugrave; presto che alle lenti, alle <lb/>sfere di vetro o alle boccie ripiene d'acqua, per servirsene ad uso micro&shy;<lb/>scopico in condur miniature o altri minutissimi lavori. </s>

<s>Girolamo Fabrizi <lb/>d'Acquapendente, nel 1600, scriveva cos&igrave; nel suo celebre Trattato <emph type="italics"/>De vi-<emph.end type="italics"/><pb xlink:href="020/01/525.jpg" pagenum="506"/><emph type="italics"/>sione:<emph.end type="italics"/> &ldquo; Quocirca ii, qui vulgo miniatores vocantur, lineas suas tenuissi&shy;<lb/>mas et pene inconspicuas, nonnisi ad lucem refractam ducere possunt. </s>

<s>Unde <lb/>ea dumtaxat luce utuntur, quae post phialam aqua plenam apparet, quasi <lb/>necessitate quadam coacti intelligant eiusmodi lucem refractam caeteris cla&shy;<lb/>riorem esse, robustioremque, ideoque dicebat Vitellio refractionem generare <lb/>lumen, quia adiuvat radios &rdquo; (Venetiis 1600, pag. </s>

<s>70). </s></p><p type="main">

<s>L'effetto dell'ingrandimento microscopico &egrave; qui dall'Acquapendente, <lb/>come da Galileo nel Nunzio Sidereo, spiegato al modo di Vitellione, am&shy;<lb/>mettendo cio&egrave; che i raggi costipati per rifrazione, accrescan lume alla vista, <lb/>ma infin dal 1611 il Keplero e il De Dominis avevan diottricamente dimo&shy;<lb/>strato il modo del rappresentarsi le immagini virtuali e ingrandite nelle lenti <lb/>biconvesse, e il Maurolico aveva, forse con maggior precisione, divisato il <lb/>modo del rappresentarsi le immagini reali nelle lenti stesse e nelle sfere <lb/>cristalline. </s>

<s>Avendo inoltre il Maurolico stesso dimostrato, nel Teorema XVIII <lb/>de'<emph type="italics"/>Diaphanorum partes,<emph.end type="italics"/> che il concorso de'raggi &egrave; tanto pi&ugrave; preciso, e che <lb/>perci&ograve; tanto son minori le aberrazioni di refrangibilit&agrave; e di sfericit&agrave;, quanto <lb/>le sfere son di minor raggio; veniva cos&igrave; a farsi luminosa guida ai futuri <lb/>costruttori dei Microscopi. </s></p><p type="main">

<s>Guidato pi&ugrave; forse dalla propria pratica che non dalla teorica mauroli&shy;<lb/>cana, uno de'primi, fra cos&igrave; fatti costruttori, fu Galileo, il quale gi&agrave;, in fin <lb/>dal 1614, aveva con un segmento di piccola sfera lavorata una lente, e, in&shy;<lb/>seritala dentro un piccolo tubo, per maneggiarla meglio, renderne pi&ugrave; effi&shy;<lb/>cace la visione e applicarla a osservar le cose minute come le esteriori ap&shy;<lb/>parenze degli insetti; ne aveva cos&igrave; composto un Microscopio semplice, a cui <lb/>dava il nome di <emph type="italics"/>Occhialino.<emph.end type="italics"/> Aveva un tale occhialino fatto noto e dispen&shy;<lb/>sato agli amici, e fra questi a Bartolommeo Imperiali, che da Genova gli <lb/>scriveva cos&igrave; in proposito, il d&igrave; 4 d'Ottobre di quell'anno 1614: &ldquo; Ho poi <lb/>fatte alcune osservazioni coll'<emph type="italics"/>Occhialino,<emph.end type="italics"/> e fra le altre ho osservato che le <lb/>mosche femmine hanno minor quantit&agrave; di peli e pi&ugrave; corti assai di quel che <lb/>non abbiano i maschi &rdquo; (MSS. Gal., P. VI, T. IX, c. </s>

<s>206). </s></p><p type="main">

<s>Poi pi&ugrave; tardi lo stesso Galileo pens&ograve; di aggiungere al tubo alcuni altri <lb/>organi per render pi&ugrave; comode le osservazioni. </s>

<s>Cos&igrave; fatti organi, bench&egrave; sem&shy;<lb/>plicissimi, conferiron pure ad esaltar l'Occhialino all'essere e alla dignit&agrave; <lb/>di strumento, e consistevano in una colonnetta posata su un piede, alla <lb/>quale in alto era raccomandato un anello, dentro a cui potesse scorrere il <lb/>tubo o cannoncino, per accostare e discostar la lente dall'oggetto, il quale, <lb/>per osservarlo tutto, posavasi sulla circonferenza di una piccola ruota fissa <lb/>a un asse girevole in un foro della stessa colonnetta, al di sotto del can&shy;<lb/>noncino. </s></p><p type="main">

<s>Noi ci studiammo altrove (Estate in Montagna, Firenze 1884, pag. </s>

<s>230) <lb/>di rappresentare in disegno il nuovo strumento galileiano, pigliando lume <lb/>da un cenno di descrizione, che ne fa al principe Cesi l'Inventore stesso, <lb/>in una sua lettera scritta da Firenze il d&igrave; 23 Settembre 1624: &ldquo; Invio a <lb/>V. E. un Occhialino per vedere da vicino le cose minime, del quale spero <pb xlink:href="020/01/526.jpg" pagenum="507"/>che ella sia per prendersi gusto, e trattenimento non piccolo, che cos&igrave; ac&shy;<lb/>cade a me. </s>

<s>Ho tardato a mandarlo, perch&egrave; non l'ho prima ridotto a per&shy;<lb/>fezione, avendo avuto difficolt&agrave; nel ritrovare il modo di lavor&agrave;re i cristalli <lb/>perfettamente. </s>

<s>L'oggetto si attacca sul cerchio mobile, che &egrave; nella base, e <lb/>si va movendo per vederlo tutto; atteso che quello che si vede in una oc&shy;<lb/>chiata &egrave; piccola parte. </s>

<s>E perch&egrave; la distanza fra la lente e l'oggetto vuol es&shy;<lb/>sere puntualissima, nel guardare gli oggetti che hanno rilievo bisogna potere <lb/>accostare e discostare il vetro, secondo che si guarda questa o quella parte, <lb/>perci&ograve; il cannoncino &egrave; fatto mobile nel suo piede o guida che dir la vo&shy;<lb/>gliamo &rdquo; (Alb. </s>

<s>VI, 297). </s></p><p type="main">

<s>In quel tempo che Galileo si compiaceva cos&igrave;, e dilettavasi della vista <lb/>del suo Occhialino, tre altri simili strumenti, ma costruiti in diverso modo <lb/>dai galileiani, furono d'Oltre monte mandati al Granduca e ai principi della <lb/>corte di Firenze. </s>

<s>La notizia e la descrizione di questo Microscopio oltramon&shy;<lb/>tano l'abbiamo appresa da un <emph type="italics"/>Discorso dell'occhiale detto di moltiplica&shy;<lb/>zione cavato da una lettera scritta di .... dal sig. </s>

<s>Agnolo Marzi Medici.<emph.end type="italics"/><lb/>L'estratto fu ritrovato fra le carte manoscritte della R. </s>

<s>Biblioteca nazionale <lb/>di Firenze, e ci fu mostrato a leggere e ad esaminare dal gentilissimo si&shy;<lb/>gnor Bibliotecario, appena che ei per caso l'ebbe scoperto. </s>

<s>In quel Discorso, <lb/>dop'aver magnificata l'eccellenza dello strumento applicato a veder cose na&shy;<lb/>turalmente invisibili, specie negli insetti, l'Autore soggiunge le parole se&shy;<lb/>guenti: &ldquo; Mi sa male non gli poter mandar l'occhiale, perch&egrave; non &egrave; mio, <lb/>e nemmeno dire come sta, e questo per essermi proibito rispetto al voler <lb/>che si vegga, e se al Galileo d&agrave; il cuore di ritrovarlo, il quale &egrave; un mese <lb/>che ci &egrave; dietro, ma non si &egrave; visto cosa alcuna. </s>

<s>&Egrave; ben vero che con il suo <lb/>mutando i vetri fa una cosa piccola apparir grande, ma non con quella esatta <lb/>distinzione e chiarezza: mostra pi&ugrave; offuscato e questo arriva a perfezion <lb/>tale che l'invisibili fa apparir visibili. </s>

<s>&rdquo; <lb/><figure id="id.020.01.526.1.jpg" xlink:href="020/01/526/1.jpg"/></s></p><p type="caption">

<s>Figura 50.</s></p><p type="main">

<s>Da ci&ograve; si apprende che i Microscopi oltramon&shy;<lb/>tani debbono esser posteriori a quelli descritti da Ga&shy;<lb/>lileo al Cesi, ne'quali per veder dell'oggetto le intere <lb/>parti e il rilievo, i vetri si dovevan <emph type="italics"/>mutare,<emph.end type="italics"/> ossia ora <lb/>avvicinare e ora discostar dall'oggetto stesso, facendo <lb/>scorrere il tubo nell'anello. </s></p><p type="main">

<s>S'apprende di pi&ugrave;, che l'invenzione era confi&shy;<lb/>data in segreto. </s>

<s>Qualunque per&ograve; si fosse il segreto <lb/>imposto all'Autor del Discorso, egli si fa gi&agrave; inten&shy;<lb/>dere abbastanza bene, descrivendo il modo di far uso <lb/>dello strumento. </s>

<s>Ma come ci&ograve; fosse poco, viene in <lb/>calce a dar, con tre disegni che noi rappresentiamo <lb/>nelle tre figure 50, 51, 52, lo spaccato e la pianta <lb/>dello strumento stesso, e, distinte con numeri le <lb/>parti, le dichiara poi cos&igrave; con parole ordinatamente sotto i numeri corri&shy;<lb/>spondenti: </s></p><pb xlink:href="020/01/527.jpg" pagenum="508"/><p type="main">

<s>&ldquo; Figura delle misure e vetri dell'Occhiale sopradescritto, dal medesimo <lb/>signor Marzi mandata. </s>

<s>N.o 1 Profilo del cannone. </s>

<s>N.o 2 Profilo del can&shy;<lb/><figure id="id.020.01.527.1.jpg" xlink:href="020/01/527/1.jpg"/></s></p><p type="caption">

<s>Figura 51.<lb/>none piccolo, che entra nel n.o 1. N.o 3 Pianta del can&shy;<lb/>none 1 per di sopra. </s>

<s>N.o 4 Pianta del cannone 1 per <lb/>di sotto. </s>

<s>N.o 5 Pianta del cannone 2 in bocca. </s>

<s>N.o 6 <lb/>Pianta del cannone 2 in fondo. </s>

<s>N.o 7 dove si mettono <lb/>gli animali cavando il cannone n.o 2. Nel fondo di que&shy;<lb/>sti cannoni, che viene ad essere il n.o 4 e 6, sono i due <lb/>vetri, uno al cannone grande e l'altro al piccolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>La vantata eccellenza di questo Microscopio sopra <lb/>il galileiano dipendeva in primo luogo dal porta oggetti, <lb/>il quale, essendo il vetro piano del cannone n.o 1, lasciava traveder gli og&shy;<lb/>getti investiti per ogni parte di luce, come se fossero liberamente campati <lb/><figure id="id.020.01.527.2.jpg" xlink:href="020/01/527/2.jpg"/></s></p><p type="caption">

<s>Figura 52.<lb/>in aria, mentre il porta oggetti del Microscopio galileiano, <lb/>essendo opaco, lasciava le parti di sotto e da'lati delle piccole <lb/>cose da traguardarsi involte e sbattute nell'ombra. </s>

<s>Dipen&shy;<lb/>deva altres&igrave;, e con miglior ragione, quella eccellenza dall'es&shy;<lb/>ser la lente microscopica incastonatasi nell'anello, in fondo <lb/>al cannone n.o 2, assai conglobata. </s></p><p type="main">

<s>Gli effetti poi de'globuli di vetro ritrovati in pratica, <lb/>conforme alla teoria maurolicana, tanto pi&ugrave; maravigliosi quanto pi&ugrave; i globuli <lb/>stessi erano piccoli, consigliarono i Naturalisti a servirsi di cosiffatti sempli&shy;<lb/>cissimi Microscopii, anche dappoi che furono inventati e divulgati i Micro&shy;<lb/>scopii composti. </s></p><p type="main">

<s>Si chiamarono que'globuli di vetro <emph type="italics"/>Microscopii olandesi,<emph.end type="italics"/> e l'Huyghens <lb/>gli descriveva nel 1678 all'Autor del <emph type="italics"/>Diario parigino<emph.end type="italics"/> in una sua lettera o <lb/>Discorso, a cui premetteva il titolo: <emph type="italics"/>De novo Microscopio ex Hollandia al&shy;<lb/>lato.<emph.end type="italics"/> Di un tal Discorso ugeniano si legge nella Raccolta delle Opere varie <lb/>un estratto, che incomincia: &ldquo; Microscopium hoc ex unico formatur exiguo <lb/>globulo vitreo, simili illis, quibus in Hollandia et Anglia animaleuta fuere <lb/>observata in aqua putcali et pluvia.... &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>764). </s></p><p type="main">

<s>Ritorna anco nella <emph type="italics"/>Diottrica<emph.end type="italics"/> l'Huyghens sopra questo argomento, e rac&shy;<lb/>conta che con uno di cosiffatti Microscopii olandesi una volta il Lewenhoeck <lb/>gli fece veder, nella coda di un'anguilla, come il sangue, <emph type="italics"/>globulis subru&shy;<lb/>bentibus constans, celeri motu per canaliculos arteriarum, qui venis con&shy;<lb/>tinuantur, discurrit<emph.end type="italics"/> (Lugd. </s>

<s>Batav. </s>

<s>1703, pag. </s>

<s>226). </s></p><p type="main">

<s>I Microscopii a globetti di vetro per&ograve;, che intorno al 1678, secondo <lb/>l'Huyghens, s'incominciarono a fabbricare in Olanda, erano infin dal 1644 <lb/>notissimi in Italia, sotto il nome di <emph type="italics"/>Microscopii della perlina.<emph.end type="italics"/> Ne fu inven&shy;<lb/>tore Evangelista Torricelli, il quale sembra non insegnasse ad altri che al <lb/>fratel suo Luca il modo di ridurre in perline i vetri, e di assettarle cos&igrave;, <lb/>da poter traguardar con esse i minutissimi oggetti. </s>

<s>Da Luca Torricelli ebbe <lb/>il segreto il Viviani, che ne lasci&ograve; cos&igrave;, di propia mano ricordo, fra le sue <lb/>carte: <emph type="italics"/>&ldquo; Modo di fare gli occhiali da vedere le cose piccole.<emph.end type="italics"/> Si piglia del <pb xlink:href="020/01/528.jpg" pagenum="509"/>cristallo sottilissimo in filo, e alla lucerna, dove si strugge il vetro o il cri&shy;<lb/>stallo con il soffietto, si soffia in quel filo di cristallo, e cos&igrave; si viene a fare <lb/>una sfera piccola. </s>

<s>Questa si piglia e si accomoda fra due carte, con fare un <lb/>foro nel mezzo, tanto che vi stia la detta sfera, ed incollandole insieme per&shy;<lb/>ch&egrave; tenghino la detta sfera piccola, e poi per il detto foro si guarda al lume <lb/>di lucerna o di altro, quel che si vuol vedere, che si vede con grande ac&shy;<lb/>crescimento &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXIII, c. </s>

<s>12). </s></p><p type="main">

<s>Le perline olandesi poi si costruivano e si assettavano cos&igrave;, secondo <lb/>l'Huyghens, in un modo non molto diverso da quelle del Torricelli: &ldquo; Fra&shy;<lb/>gmina vitri minima ad imam lucernae flammam, qua parte caeruleus color <lb/>conspicitur, admoventur ut candescent atque ita filo ferreo quantum tenuis&shy;<lb/>simum duci potest, excepta, ac porro dextre versata, in globulos abeunt, qui <lb/>satis magni si granum sinapi aequaverint. </s>

<s>Ex pluribus ita paratis aliquos <lb/>probos reperies, idque experieris postquam lamellae aeraee eos incluseris. </s>

<s><lb/>Quod ita fit. </s>

<s>Lamellam ex aere tenuissimo digiti longitudine, longitudine <lb/>dupla complicabis, tum medium hoc rectangulum acus cuspide perforabis; <lb/>foramina opposita coticula levigabis ne quid scabri circa margines adhaereat <lb/>et flammae fuligine inficies, ne quid fulgidum intus remaneat. </s>

<s>Inde sphae&shy;<lb/>rulam adhuc fiilo ferreo haerentem intra lamellam atque ad ipsa foramina <lb/>inseres; pressamque continebis adactis circum aeneis tribus claviculis ex filo <lb/>desectis, malleoque firmatis. </s>

<s>Sic levi opera Microscopia efficies, ex quibus <lb/>quae optima seliges &rdquo; (Dioptr. </s>

<s>Lugd. </s>

<s>1703, pag. </s>

<s>225). </s></p><p type="main">

<s>Ma i Microscopii semplici, e questi stessi squisitissimi delle perline, <lb/>cos&igrave; torricelliani come olandesi, con i quali s'erano gi&agrave; scoperti gli sper&shy;<lb/>matozoi, e le anguillette dell'aceto, e i cos&igrave; detti animalucci delle infusioni, <lb/>erano nonostante ancora assai di lungi dal prestar que'cos&igrave; comodi e cos&igrave; lar&shy;<lb/>ghi servigi alla scienza, che erano ordinati a prestarle i Microscopii composti. </s></p><p type="main">

<s>Nella storia dell'invenzione di questo nuoyo e importantissimo stru&shy;<lb/>mento hanno alcuni dato grande importanza a un fatto, che si dice essere <lb/>stato osservato e considerato da Galileo, ma che non potev&agrave; sfuggire agli <lb/>occhi di molti fra coloro, che si trovavano in mano a trattare un Canoc&shy;<lb/>chiale olandese. </s>

<s>Il fatto consiste nell'osservar che gli oggetti vicini, ritirando <lb/>indietro l'oculare a una notabile distanza dall'obiettivo, appariscono ingran&shy;<lb/>diti. </s>

<s>In qualunque modo per&ograve;, inconsideratamente si crede da costoro che <lb/><emph type="italics"/>il Telescopio accomodato per veder gli oggetti vicinissimi<emph.end type="italics"/> (Alb. </s>

<s>IV, 248), <lb/>come Galileo talvolta per curiosit&agrave; accomodava il suo, possa qualificarsi <lb/>per un vero Microscopio, in cui siasi trasformato lo stesso Telescopio ga&shy;<lb/>lileiano. </s></p><p type="main">

<s>Non dal galileiano, ma dal Telescopio astronomico doveva aspettarsi la <lb/>trasformazione, e il Keplero che aveva dimostrata la teoria diottrica del Mi&shy;<lb/>croscopio semplice, e che, componendo insieme due Microscopii semplici, <lb/>aveva speculata l'invenzione dello stesso Telescopio astronomico, si pu&ograve; dir <lb/>perci&ograve; che fosse nello stesso tempo il primo inventore del Microscopio com&shy;<lb/>posto. </s>

<s>La trasformazione infatti del Telescopio kepleriano in Microscopio si <pb xlink:href="020/01/529.jpg" pagenum="510"/>ottiene immediata, dando contrariamente grandezza e distanza focale alle <lb/>lenti: ci&ograve; vuol dire che se al Telescopio s'applica un obiettivo pi&ugrave; grande <lb/>e d'un fuoco pi&ugrave; lungo, al Microscopio invece s'applica un obiettivo pi&ugrave; <lb/>piccolo e di un fuoco pi&ugrave; corto. </s></p><p type="main">

<s>Ma il Keplero, come non esegu&igrave; il Telescopio, cos&igrave; non pens&ograve; a tra&shy;<lb/>mutar l'obiettivo nell'oculare, e a suggerir la pratica del Microscopio. </s>

<s>Se <lb/>il Matematico alemanno per&ograve; speculava, un nostro ottico italiano operava, <lb/>ed &egrave; quel Francesco Fontana che, essendo stato primo ad eseguire il Tele&shy;<lb/>scopio astronomico, fu primo anche a inventare il Microscopio composto. </s>

<s>Il <lb/>Trattato VIII delle <emph type="italics"/>Novae coelestium terrestriumque rerum observationes<emph.end type="italics"/><lb/>s'intitola <emph type="italics"/>De Microscopio,<emph.end type="italics"/> e l'Autore incomincia cos&igrave; a dire nel capitolo I: <lb/>&ldquo; Inventionem hanc reperi in anno 1618. Duo assero: primo, dictum spe&shy;<lb/>cillum antiqius non esse dicto anno. </s>

<s>Secundo, me fuisse inventorem in hac <lb/>civitate Neapolitana, in qua haec publici iuris fiunt. </s>

<s>Limito dictum quia, ut <lb/>etiam supra in alia mea inventione Telescopii duarum lentium convexarum <lb/>insinuavi, omnes intellectu et operatione praediti sumus, atque adeo Micro&shy;<lb/>scopii inventio, alibi, citato anno antiquior esse potest. </s>

<s>Quoad primum pa&shy;<lb/>tet, quia antea nullum extabat vestigium huiusmodi specilli, nec ullus Au&shy;<lb/>thor, saltem ante recensitum annum, meminerat. </s>

<s>Dixi ante recensitum annum, <lb/>nam in anno 1626 Pater Scheiner e Societate Jesu, in sua Rosa Ursina, <lb/>Lib. </s>

<s>I, Cap. </s>

<s>XXX, asserit: <emph type="italics"/>Eadem arte natum est illud admirabile Mi&shy;<lb/>croscopium, quo musca in elephantem et pulex in camelum amplifica&shy;<lb/>tur.<emph.end type="italics"/> Certum tamen est me prius dicto anno 1626 tale specillum adinvenisse, <lb/>ut fidem facit admodum R. P. </s>

<s>Hieronymus Sirsalis eiusdem Societatis Jesu &rdquo; <lb/>(Neapoli 1646, pag. </s>

<s>145, 46). </s></p><p type="main">

<s>Ma l'Huyghens ebbe qualche scrupolo di accettar per verit&agrave; storiche <lb/>le asserzioni del Fontana, perch&egrave; <emph type="italics"/>testimonium Hier. </s>

<s>Sirsalis quod addu&shy;<lb/>cit, non est antiqius anno 1625<emph.end type="italics"/> (Dioptr. </s>

<s>ibi, pag. </s>

<s>221), perci&ograve; soggiunge: <lb/>&ldquo; Anno autem 1621 apud Drebelium nostratem, conspecta fuisse Microsco&shy;<lb/>pia huiusmodi Londini in Britannia, ipsi qui adfuerant saepe mihi narrave&shy;<lb/>runt, ipsumque primum auctorem eorum tunc habitum &rdquo; (ibi). </s></p><p type="main">

<s>Noi per&ograve; non dubitiamo della verit&agrave; dell'asserto del nostro Ottico na&shy;<lb/>poletano, perch&egrave; &egrave; un fatto che fu egli il primo a costruire il Telescopio <lb/>speculato gi&agrave; dal Keplero, e da questo al Microscopio composto la trasfor&shy;<lb/>mazione &egrave; cos&igrave; naturale, che ci fa anzi gran maraviglia che non gli occor&shy;<lb/>resse di farla prima del 1618. Come, dall'altra parte, fosse condotto il Fon&shy;<lb/>tana, dalla costruzione del tubo astronomico a quello microscopico, lo espone <lb/>al Cap. </s>

<s>II del citato Trattato VIII con s&igrave; lucido processo, da persuader fa&shy;<lb/>cilmente dover esser per quello, come da sicura e diritta scorta, guidato <lb/>alla sua invenzione. </s>

<s>&ldquo; Quia opposita iuxta se posita magis clarescunt, ut in&shy;<lb/>quiunt Philosophi, propterea ipsius specilli melius structura dignoscetur, si <lb/>tubo optico astronomico contrapponetur. </s>

<s>In multis opponuntur astronomicus <lb/>tubus et specillum. </s>

<s>Hoc primo quoad lentem convexam exteriorem: nam tubi <lb/>astronomici quo maioris diametri est lens, eo perfectior est tubus; specilli <pb xlink:href="020/01/530.jpg" pagenum="511"/>vero, quo minoris diametri, eo magis visibile auget, perfectiusque videre <lb/>facit &rdquo; (Novae Observat. </s>

<s>ibi, pag. </s>

<s>146). E prosegue cos&igrave; a contrapporre e a <lb/>rilevar le differenze e le somiglianze che passano fra'due strumenti. </s></p><p type="main">

<s>In far tali riscontri non lascia addietro il Fontana di accennare anche <lb/>all'uso del Telescopio galileiano, in cui le immagini microscopiche si rap&shy;<lb/>presentan diritte: &ldquo; Si autem desiderabis per parvum specillum non inversa <lb/>sed directa videre, adhuc in hoc varietur constructio respectu Tubi astro&shy;<lb/>nomici. </s>

<s>Nam lens exterior parvi specilli eamdem servare debet ab obiecto <lb/>distantiam, ac per inversionem. </s>

<s>Similiter lens concava in hoc specillo qua&shy;<lb/>druplicatam ab obiecto distantiam diametri exterioris lentis servare necesse <lb/>est. </s>

<s>Non sic vero in Tubo astronomico res se habet, ut patet &rdquo; (ibi, pag. </s>

<s>147). </s></p><p type="main">

<s>Qui per&ograve; ben s'intende che l'Autore propone il caso per una semplice <lb/>curiosit&agrave;, come pure lo proponeva Galileo, il quale perci&ograve; nelle sue osser&shy;<lb/>vazioni naturali si serv&igrave; sempre dell'Occhialino. </s>

<s>E in vero, bench&egrave; sia un <lb/>fatto che si pu&ograve; il Telescopio galileiano accomodare a veder cos&igrave; gli oggetti <lb/>vicini come i lontani, nonostante l'immagine reale dell'obiettivo convesso, <lb/>formandosi a gran distanza dal centro della lente, e dovendosi perci&ograve; riti&shy;<lb/>rar molto indietro l'oculare concavo, veniva lo strumento per la sua ecces&shy;<lb/>siva lunghezza a rendersi tanto incomodo nelle osservazioni, tanto si disper&shy;<lb/>deva di luce e tanto si rappresentavano le immagini poco precise, da non <lb/>passar per la mente a nessuno di preferir tanto scapito al meschino gua&shy;<lb/>dagno di veder gli oggetti nella loro posizion naturale. </s>

<s>Da un'altra parte <lb/>poco fa, se nell'osservar un piccolo oggetto, per esempio un animaluccio <lb/>infusorio, apparisce il capo dov'&egrave; la coda. </s></p><p type="main">

<s>Il tutto poi vien suggellato dal fatto che i costruttori de'Microscopii <lb/>composti non hanno poi seguita altra regola, n&egrave; hanno cercata altra com&shy;<lb/>posizione di lenti, ma si son solamente studiati di ridurre a maggior per&shy;<lb/>fezione l'opera del nostro Ottico napoletano. </s></p><p type="main">

<s>Nella grande riforma neutoniana degli strumenti diottrici la mente del <lb/>Filosofo inglese non lasci&ograve; indietro di speculare anche intorno alla perfe&shy;<lb/>zione dei Microscopii. </s>

<s>&ldquo; Saepius, egli scrive, cogitavi de construendo Micro&shy;<lb/><figure id="id.020.01.530.1.jpg" xlink:href="020/01/530/1.jpg"/></s></p><p type="caption">

<s>Figura 53.<lb/>scopio, quod pro vitro <lb/>obiectivo haberet lami&shy;<lb/>nam ex metallo refle&shy;<lb/>ctentem. </s>

<s>Etenim haec <lb/>instrumenta ad maio&shy;<lb/>rem perfectionem, quam <lb/>nunc habent adhuc pos&shy;<lb/>se videntur aeque ac <lb/>Telescopia, et fortasse <lb/>magis, siquidem Micro&shy;<lb/>scopia opus habent una metalli lamina reflectente ut videri potest in Dia&shy;<lb/>grammate (fig. </s>

<s>53) in quo AB est Obiectivum ex metallo; CD vitrum <lb/><gap/> metallo <pb xlink:href="020/01/531.jpg" pagenum="512"/>conflati, ubi obiectum est locatum &rdquo; (Op. </s>

<s>Omn. </s>

<s>Optica, Patavii 1773, Ap&shy;<lb/>pendice, pag. </s>

<s>6). </s></p><p type="main">

<s>I Microscopii per&ograve; non s'aspettarono il loro perfezionamento dagli spec&shy;<lb/>chi del Newton, ma dalle lenti, che riuscirono poi a lavorare squisitissime, <lb/>il Dollond in Inghilterra, e l'Amici in Italia. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Agli strumenti cos&igrave; utilmente inventati per aiutare la vista a veder me&shy;<lb/>glio in chi ne avesse difetto, e per rappresentare i minimi oggetti ingran&shy;<lb/>diti nelle studiose osservazioni di cose naturali, s'aggiunge un'altra inven&shy;<lb/>zione da aiutar la sensibilit&agrave; di quell'organo, che &egrave;, dopo la vista, il pi&ugrave; <lb/>nobile del nostro corpo, e che massimamente conferisce all'educazione del <lb/>nostro intelletto. </s>

<s>Vogliam dire del corno acustico, strumento ordinato ad av&shy;<lb/>viare dentro la concavit&agrave; dell'orecchio le onde sonore per modo, che pi&ugrave; <lb/>intensamente colpiscano il timpano, in chi troppo debole e ottuso avesse <lb/>l'udito. </s></p><p type="main">

<s>Il Porta, nel Libro XX della sua <emph type="italics"/>Magia Naturale,<emph.end type="italics"/> intitola il capitolo V: <lb/><emph type="italics"/>Quomodo instrumentum fieri possit quo longe audiamus.<emph.end type="italics"/> L'invenzione e <lb/>la forma di questo nuovo strumento, dice l'Autore, potersi desumere dalla <lb/>stessa Natura, della quale ha deliberato di seguire, ne'precetti di magia na&shy;<lb/>turale, il sapiente magistero: &ldquo; Sancitum est enim, in magiae naturalis prae&shy;<lb/>ceptis, quum aliqua nova investiganda sunt, naturam perscrutandam et imi&shy;<lb/>tandam censeamus &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1655, pag. </s>

<s>654). Conforme a questo <lb/>verissimo principio, fecondo a chi sa di tante nuove scoperte, il nostro Fi&shy;<lb/>sico osserva che gli animali di udito squisitissimo sopra gli altri, hanno gli <lb/>orecchi sporti esternamente a guisa del padiglion di una tromba, per cui con&shy;<lb/>clude: &ldquo; Forma igitur instrumenti auditus oportet sit ampla et concava et <lb/>aperta, et intus cochlearia duplici de causa: prima, si soni intus recte fer&shy;<lb/>rentur oblaederent sensum; secunda, quia per cochleam circumferuntur, et <lb/>allisa vox per aurium anfractus multiplicatur, ut de echo videmus. </s>

<s>Argu&shy;<lb/>mentum rei esse potest cochlea marina illa, quae auribus admota strepitum <lb/>quaedam leve efficitur &rdquo; (ibi, pag. </s>

<s>656). </s></p><p type="main">

<s>Simili osservazioni e simili idee si possono vedere espresse dall'Acqua&shy;<lb/>pendente, nel Cap. </s>

<s>II della terza Parte del suo Trattato <emph type="italics"/>De aure auditus <lb/>organo,<emph.end type="italics"/> dove discorre, a imitazion del libro <emph type="italics"/>De usu partium<emph.end type="italics"/> di Galeno, <lb/>dell'utilit&agrave; che prestano agli animali gli orecchi esterni. </s>

<s>&ldquo; Exterior autem <lb/>ita anfractuosa tortuosaque est ad bonam auditionem per tres utilitates, ut <lb/>scilicet facile distincteque sonus tum excipiatur, tum intendatur, tum in&shy;<lb/>trorsum deferatur. </s>

<s>Supra enim dictum est sonum facillime et exactissime <lb/>omnium recipi in concavis, duris, et complanatis corporibus, ita ut si etiam <lb/>articulatus sonus veniat, similiter articulatus excipiatur, quae proinde per <lb/><gap/> 1600 pag. </s>

<s>19) </s></p><pb xlink:href="020/01/532.jpg" pagenum="513"/><p type="main">

<s>L'Acquapendente per&ograve;, in quella sua prolissa enumerazione delle uti&shy;<lb/>lit&agrave;, che pu&ograve; ricavar l'animale, per la pi&ugrave; squisita percezione de'suoni, dal <lb/>padiglione esterno degli orecchi; non accenna all'idea di fabbricare uno stru&shy;<lb/>mento configurato a quel modo, per moltiplicare il suono nell'orecchio del&shy;<lb/>l'uomo, ma quella idea &egrave; rivelata per la prima volta, da Paolo Aproino, in <lb/>una lettera scritta a Galileo da Treviso, il d&igrave; 26 Gennaio 1613. Non sa&shy;<lb/>premmo per verit&agrave; dire quali relazioni di idee e di pensieri potessero pas&shy;<lb/>sar fra'due Autori, ma &egrave; notabile in ogni modo che l'Aproino si riscontra <lb/>col Porta nelle accidentali particolarit&agrave; della storia dell'invenzione, e nel&shy;<lb/>l'argomento principale di essa, desunto dal fatto della conca marina appres&shy;<lb/>sata all'orecchio. </s></p><p type="main">

<s>Aveva fatto intenzion l'Aproino, come rilevasi dalla lettera citata, di <lb/>pubblicare la descrizione dello strumento, dedicandola, per l'intermedio di <lb/>Galileo, al Granduca, ma poi, non sapremmo dire per qual motivo, non <lb/>mand&ograve; l'Autore il suo proposito ad effetto, bench&egrave; la descrizione stessa del&shy;<lb/>l'invenzione e la storia si legga in un'altra lettera dell'Aproino al mede&shy;<lb/>simo Galileo, scritta il d&igrave; 27 di Luglio di quell'anno. </s>

<s>&ldquo; Ebbe dunque ori&shy;<lb/>gine la speculazione da questo: che rivedendo io un giorno certe conchiglie, <lb/>che avevo portate meco dal viaggio di mare, che feci l'altr'anno, insieme <lb/>con l'istoria intorno a ci&ograve; di Guglielmo Rondelezio, e vedendomi innanzi <lb/>quella, che egli chiama <emph type="italics"/>Aurita,<emph.end type="italics"/> mi fece saltar capriccio di forare nel fondo <lb/>una turbinata assai grande, ch'io avevo, e metterla nell'orecchio, per ten&shy;<lb/>tar qualche esperimento. </s>

<s>E infatti successe che mi parve di sentir molto <lb/>aggrandirsi la voce, sebben ora che ho l'orecchio avvezzo a cose maggiori, <lb/>pare a me che faccia molto poco, per non dir niente. </s>

<s>Ma per essere accom&shy;<lb/>pagnato quel poco di aggrandire, con un buccinamento grande, mi apparve <lb/>conspicuo, sicch&egrave; ne feci qualche conto. </s>

<s>Allora io, invaghito dalla novit&agrave; <lb/>della cosa, proposi a diversi amici ch'io aveva inteso che uno voleva augu&shy;<lb/>mentare il suono, per sentire com'essi si moveano, ed insieme per iscoprire <lb/>se sapeano che altri avesse osservato questo particolare. </s>

<s>E sebbene da al&shy;<lb/>cuni il problema fu reputato degno di speculazione, fu per&ograve; dagli altri quasi <lb/>tutti deriso e stimato per impossibile. </s>

<s>Onde io mi mossi a meglio conside&shy;<lb/>rare la natura del suono e delle sue differenze, e in ci&ograve; ebbi per fondamento <lb/>principale alcune cose, che io mi ricordo aver imparate da V. S. </s>

<s>Nel resto <lb/>Boezio mi fu scorta per sapere quanto finora ne sia stato detto, sveglian&shy;<lb/>domi intanto in alcune cose quel galantuomo del Maurolico, e in certe altre <lb/>Vetruvio, in quel Capo dove parla del risonar delle scene, sebben, per dire <lb/>il vero, quello che finora se n'&egrave; detto, &egrave; molto poco, e questo poco in gran <lb/>parte malinteso, e parte falso e lontano dagli esperimenti. </s>

<s>Ma chi sa che <lb/>questa nobil parte di Filosofia, tanto interessata con noi, abbandonata da <lb/>tutti e negletta, non sia un d&igrave; per essere suscitata ed accresciuta! &rdquo; (Alb. </s>

<s><lb/>VIII, 277). </s></p><p type="main">

<s>Sembra che in queste parole volesse divinar l'Aproino le presenti sco&shy;<lb/>perte maravigliose dell'elettricit&agrave; applicata, nel Telefono e nel Fonografo, <pb xlink:href="020/01/533.jpg" pagenum="514"/>alla propagazione e fissazione de'suoni, ma &egrave; notabile in ogni modo che fosse <lb/>egli il primo a creder possibile l'invenzione di uno strumento da inacutir <lb/>l'udito, com'era stata gi&agrave; possibile l'invenzione dello strumento da inacu&shy;<lb/>tir la vista; e, non contento a ci&ograve;, la possibilit&agrave; ridusse all'essere, fabbri&shy;<lb/>cando cos&igrave;, com'ei prosegue a descriverlo, il suo Corno acustico: &ldquo; Prima <lb/>dunque fabbricai un cono alto il doppio del suddetto e con sei girate spi&shy;<lb/>rali, e pi&ugrave; aperto forse otto o dieci gradi, per poter fare gli esperimenti pi&ugrave; <lb/>in grande, e far riuscire pi&ugrave; sensibili le differenze. </s>

<s>E fattone un altro eguale <lb/>a questo, in luogo delle spire, che erano alquanto difficili da lavorare, vi ho <lb/>messo dentro sei altri coni successivamente pi&ugrave; piccoli, in modo che sta&shy;<lb/>vano l'un dall'altro separati, il qual modo parve che mi riuscisse piuttosto <lb/>migliore del primo che altri modi. </s>

<s>Ne feci poi anche un semplice della stessa <lb/>misura, che parea a me che giovasse molto meno degli altri &rdquo; (ivi, pag. </s>

<s>278). </s></p><p type="main">

<s>Ricerando in appresso l'Autore altre nuove squisitezze da introdurre <lb/>nello strumento, ei si credette di conseguirle, sciegliendo per materia il ve&shy;<lb/>tro, e facendone eseguir la fabbrica alle Fornaci di Murano. </s></p><p type="main">

<s>Perch&egrave; sperasse ritrovar cos&igrave; fatti vantaggi nel vetro, non &egrave; punto dif&shy;<lb/>ficile l'indovinarlo a chi ripensa alle insufficienti nozioni, che s'avevano a <lb/>que'tempi, intorno alla generazione del suono, e intorno al modo e alle leggi <lb/>del diffondersi di lui nello spazio. </s>

<s>Si credeva che non potessero risonare altro <lb/>che i corpi duri, per collisione, e che l'aria ne portasse tanto pi&ugrave; facilmente <lb/>i tremori, quanto pi&ugrave; libera la via ne lasciassero aperta a'moti di lei le su&shy;<lb/>perficie piane e levigate de'corpi. </s>

<s>Non fa perci&ograve; meraviglia che il vetro pa&shy;<lb/>resse all'Aproino, per la sua durezza e per la sua levigatezza materia attis&shy;<lb/>sima a produr di simili effetti. </s></p><p type="main">

<s>Che s'ignorasse veramente, ai tempi del nostro Trevigiano e alquanto <lb/>dopo, il modo e la legge del diffondersi il suono in onde sferiche, per cui <lb/>l'intensit&agrave; scema a proporzione che crescono i quadrati delle distanze, pu&ograve; <lb/>vedersi da ci&ograve; che ne dice il Cavalieri, ne'capitoli XXXV, XXXVI, e XXXVII <lb/>del suo Specchio Ustorio, ne'quali si parla sempre di <emph type="italics"/>linee sonore,<emph.end type="italics"/> e non <lb/>mai di <emph type="italics"/>onde:<emph.end type="italics"/> per cui, a desumerne di qui le teorie, si direbbe che il Corno <lb/>acustico opera non altrimenti, che lo stesso Specchio Ustorio, condensando <lb/>cio&egrave; i raggi sonori nel fuoco, in cui, per l'ascoltazione, dee trovarsi collo&shy;<lb/>cato puntualmente l'orecchio. </s></p><p type="main">

<s>L'applicazione immediata delle teorie acustiche allo strumento del&shy;<lb/>l'Aproino &egrave; trascurata dal Cavalieri che solo si contenta di render ragione <lb/>del <emph type="italics"/>Portavoce,<emph.end type="italics"/> dicendo che per esso si pu&ograve; parlar di lontano, mantenen&shy;<lb/>dovisi la voce gagliarda, <emph type="italics"/>per la superficie tersa del canale, e per il tremito <lb/>dell'aria, che, senza patire turbamento per la strada, incorrotta perviene <lb/>all'orccchio<emph.end type="italics"/> (Bologna 1650, pag. </s>

<s>81). Quell'applicazione per&ograve;, che sfugg&igrave; al <lb/>Cavalieri, a notizia di cui non era pervenuta l'invenzione dell'Aproino, fu <lb/>fatta dal Viviani, il quale, di sua propria mano, lasci&ograve; disegnato un tubo <lb/>in figura di conoide parabolico, nella cavit&agrave; del quale, per tante linee pa&shy;<lb/>rallele, si rappresentano i raggi sonori, i quali vanno tutti insieme a con-<pb xlink:href="020/01/534.jpg" pagenum="515"/>correre nel foco, presso all'apice spuntato del conoide, che dee chi ascolta <lb/>introdurre nella cavit&agrave; del suo orecchio. </s>

<s>Il disegno &egrave; senz'altro illustrato <lb/>dallo stesso Viviani, sottoscrivendovi le parole: <emph type="italics"/>Strumento per audizione<emph.end type="italics"/><lb/>(MSS. Cim., T. IV, c. </s>

<s>261). &Egrave; anche il Corno acustico insomma una di quelle <lb/>tante invenzioni, a cui furon gli Autori menati dalla pratica, senza alcuna <lb/>scorta di teoria. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Gli Specilli, il Microscopio, il Corno acustico, ordinati dall'arte ad emen&shy;<lb/>dare i difetti naturali della vista e dell'udito, o a renderli pi&ugrave; squisiti, onde <lb/>entrare in pi&ugrave; intime relazioni col mondo creato, primeggiano, per nobilt&agrave; <lb/>ed eccellenza, sopra molti altri strumenti. </s>

<s>Ma l'uomo, che ama di conser&shy;<lb/>var collo stesso mondo creato quelle relazioni costanti, fu sollecito d'inve&shy;<lb/>stigar le cause della mutabilit&agrave; e de'guasti, negli oggetti che lo circondano, <lb/>e nella propria salute, una delle quali cause egli ebbe presto a riconoscerla <lb/>nell'umidit&agrave; dell'aria. </s>

<s>&Egrave; perci&ograve; che antiche sono le osservazioni igroscopi&shy;<lb/>che, le quali, in sul primo nascer dell'arte sperimentale, dettero occasione <lb/>a inventare i primi Igrometri. </s>

<s>Leon Battista Alberti, che professando l'arte <lb/>sua, ebbe a riconoscere i guasti prodotti dall'umidit&agrave; dell'aria sugli edifizi, <lb/>pensando al miglior modo di difenderli e di preservarli, volle veder quali <lb/>fossero i venti pi&ugrave; umidi di tutti gli altri, e vi riusc&igrave; con l'invenzione di <lb/>uno de'primi Igrometri ad assorbimento. </s>

<s>&ldquo; Noi abbiamo provato (egli dice <lb/>nel Cap. </s>

<s>III del X libro dell'Architettura) che una spugna diventa umida <lb/>per la &ugrave;midit&agrave; dell'aria, e di qui caviamo una regola da pesare, con la <lb/>quale noi pesiamo quanto siano gravi e quanto secchi i venti e l'aria &rdquo; (Mi&shy;<lb/>lano 1833, pag. </s>

<s>349). </s></p><p type="main">

<s>A un Igrometro per assorbimento, servendosi egli pure di una Bilan&shy;<lb/>cia ordinari&agrave;, nella quale vien turbato l'equilibrio dal preponderare di un <lb/>corpo facile a imbeversi dell'umidit&agrave; dell'aria, aveva pensato anche quel&shy;<lb/>l'altro fecondissimo ingegno di curiose ed utili invenzioni, Leonardo da Vinci. </s></p><p type="main">

<s>Ma nell'Alberti e in Leonardo la scienza veniva sopraffatta dall'arte, co&shy;<lb/>sicch&egrave; pu&ograve; dirsi che i primi Igrometri fossero introdotti nel metodo speri&shy;<lb/>mentale, dall'ingegno e dall'industria del Santorio. </s>

<s>Egli quasi prolude a <lb/>questo genere d'invenzioni proponendo l'uso di uno strumento, che &egrave; forse <lb/>il primo Igrometro chimico da noi conosciuto. </s>

<s>Nella III Particola infatti, <lb/>capitolo LXXXV del Commentario sull'Arte medica di Galeno, dop'avere ac&shy;<lb/>cennato al Termometro, &ldquo; Insuper nos, egli tosto soggiunge, invenimus mo&shy;<lb/>dum certissimum pro dignoscenda aeris humiditatem, quantam videlicet quo&shy;<lb/>tidie sit, et talis est: sumimus tartarum combustum, quod a vulgo dicitur <lb/>alumen foecis: hoc exponitur aeri, sed antequam exponatur, exactissime <lb/><gap/> enim expositum aeri magis ponderat, nos enim pro <pb xlink:href="020/01/535.jpg" pagenum="516"/>varietate ponderis dicimus maius pondus maiorem humiditatem, et minus <lb/>minorem in aere dominari. </s>

<s>Ex his igitur ultimos gradus activarum et pas&shy;<lb/>sivarum qualitatum exactissime percipere possumus &rdquo; (Op. </s>

<s>Omn, Vene&shy;<lb/>tiis 1660, T. I, pag. </s>

<s>365). </s></p><p type="main">

<s>In questo Igrometro chimico non par che per altro il Santorio pro&shy;<lb/>muova l'invenzion dell'Alberti, che per la scelta del corpo igroscopico. </s>

<s>Ma <lb/>ne'Commentarii sopr'Avicenna esce lo strumento dalla mente dell'Inven&shy;<lb/>tore con organi proprii, i quali saranno quelli, che in sostanza manterr&agrave; <lb/>poi nelle varie forme dategli da'successivi perfezionatori. </s>

<s>Anche in questi <lb/>Commentarii, dopo aver l'Autore, pi&ugrave; diligentemente che altrove, descritto <lb/>il Termometro ad aria e il Pulsilogio &ldquo; deinde habemus, egli soggiunge, <lb/>duos modos dimetiendi siccitatem et humiditatem recedentem a naturali statu, <lb/>de quibus mentionem facimus aphorismo quarto sesundae setionis Staticae <lb/>nostrae &rdquo; (ibi, T. III, pag. </s>

<s>31). </s></p><p type="main">

<s>Consiste il primo di questi modi in una corda tesa fra due chiodi e <lb/>gravata dal peso di una palla, che pende lungo un regolo graduato. </s>

<s>Imbe&shy;<lb/>vendosi di umidit&agrave; pi&ugrave; o meno, la corda si fa pi&ugrave; tirata, la palla pendula <lb/>si solleva con essa, e indica i varii gradi segnati sopra la scala. </s>

<s>&ldquo; Primus <lb/>modus explicatur per figuram tertiam in qua extenditur funis aut, si ma&shy;<lb/>vis, corda testudimis, crassa tamen applicetur corda parieti, vel aliis locis <lb/>et in medio ponatur pila plumbea ac prope signentur gradus. </s>

<s>Dum aer hu&shy;<lb/><figure id="id.020.01.535.1.jpg" xlink:href="020/01/535/1.jpg"/></s></p><p type="caption">

<s>Figura 54.<lb/>mescit corda contrahitur, <lb/>dum vero exiccatur per <lb/>aerem borealem laxatur. </s>

<s><lb/>Aliquando nam aer au&shy;<lb/>strinus ita humectat et <lb/>contrahit cordam, ut at&shy;<lb/>tollatur usque ad litte&shy;<lb/>ram A (fig. </s>

<s>54): dum <lb/>vero spirant venti septen&shy;<lb/>trionales, ita exiccatur ut <lb/>pila perveniat ad ipsum <lb/>B; ita ut licet nulla spiret aura, quotidie gradus siccilatis vel humiditatis <lb/>aeris, quot sint, observari possint &rdquo; (ibi). </s></p><p type="main">

<s>L'altra forma d'Igrometro, che passa a descrivere il Santorio, &egrave; anche <lb/>pi&ugrave; ingegnosa, e si pu&ograve; dir la prima Mostra umidaria. </s>

<s>Consiste in un disco <lb/>o di cartone o di latta, nel centro del quale &egrave; imperniato un leggerissimo <lb/>indice, a cui &egrave; impresso il movimento da una specie di subbio o di verricello, <lb/>attorno al quale &egrave; avvolta una corda di canapa o di lino che, allungandosi <lb/>o scorciandosi, nelle varie vicende o dell'umido o del secco, d&agrave; regola allo <lb/>strumento. </s>

<s>&ldquo; Secundus modus explicatur per quartam figuram (corrispon&shy;<lb/>dente alla nostra fig. </s>

<s>55) quae emulatur Horologium. </s>

<s>Sumitur corda ex lino <lb/>satis crassa et longa, quia, quo crassior et longior, eo melius inservit huic <lb/><gap/><pb xlink:href="020/01/536.jpg" pagenum="517"/>humidum vertit radium ad gradus propositos; dum vero per aerem siccum <lb/>exiccatur, laxatur, et in alios gradus declinat. </s>

<s>Quanti vero momenti sit haec <lb/><figure id="id.020.01.536.1.jpg" xlink:href="020/01/536/1.jpg"/></s></p><p type="caption">

<s>Figura 55.<lb/>observatio sciunt aegrotantes, qui humido et qui sicco <lb/>morbo fuerint oppressi, quos ope istorum instru&shy;<lb/>mentorum ad sanitatem perduximus &rdquo; (ibi, pag. </s>

<s>33). </s></p><p type="main">

<s>Cos&igrave; aveva il Santorio, nel 1625, divulgata l'in&shy;<lb/>venzione di tre varie maniere d'Igrometri. </s>

<s>Ma per&shy;<lb/>ch&egrave; erano quegli strumenti ristretti agli usi medici, <lb/>o per qualche altra pi&ugrave; complicata ragione, non <lb/>par che se ne diffondesse la notizia fra coloro, che, <lb/>seguaci della scuola di Galileo, intendevano a pro&shy;<lb/>movere, per l'universalit&agrave; de'suoi soggetti, la scienza <lb/>sperimentale. </s>

<s>Fatto sta che in Firenze ebbe lo strumento da tutti altri prin&shy;<lb/>cipii la vita, come se fossero quelle prime santoriane invenzioni rimaste ir&shy;<lb/>rigidite o morte in mezzo all'aria mefitica di un ospedale. </s></p><p type="main">

<s>Da una lauta mensa principesca ebbe invece origine il primo Igrome&shy;<lb/>tro fiorentino. </s>

<s>In uno de'pi&ugrave; affannosi giorni estivi del 1645, l&agrave; sulla fine <lb/>del Luglio, vien fatto al Granduca Ferdinando di rivolgere l'attenzione a <lb/>quella sottilissima rugiada, di che vedea velarsi i tersissimi cristalli delle <lb/>bocce piene d'acqua, posate da'coppieri sulla tavola imbandita. </s>

<s>Manda a <lb/>chiamare il Torricelli per saper se il velo rugiadoso era, come dicevano i <lb/>Filosofi, aria convertita in acqua. </s>

<s>Il Torricelli rispose esser quello un er&shy;<lb/>rore de'peripatetici, i quali, fra alcuni altri, adducevano anche un tal fatto <lb/>a provar la trasformazione degli elementi. </s>

<s>Si studiava di persuadere il Gran&shy;<lb/>duca, allegando alcuni passi dalla <emph type="italics"/>Risposta a Lodovico delle Colombe<emph.end type="italics"/> (Alb. </s>

<s><lb/>XII, 347, 467), dove concorrevano insieme a riprovar l'errore peripatetico <lb/>le grandi autorit&agrave; di Galileo e del Castelli. </s></p><p type="main">

<s>&mdash; Da che dunque ha origine questa rugiada? </s>

<s>&mdash; riprese a domandare <lb/>il Granduca, e il Torricelli: &mdash; da quel sottilissimo umido, che &egrave; per l'aria, <lb/>rimasto a poco a poco invischiato al freddo del vetro &mdash; per conferma di <lb/>che, soggiungeva come una di quelle stesse bocce si sarebbe veduta sudar <lb/>pi&ugrave; direttemente, a portarla dalla sala da pranzo gi&ugrave; in qualche cantina. </s>

<s><lb/>Il Granduca si mostr&ograve; allora curioso di vederne la prova, e il Torricelli pro&shy;<lb/>mise che avrebbe pensato al miglior modo di farla. </s>

<s>Torn&ograve; pochi giorni dopo <lb/>collo strumento gi&agrave; preparato, il quale consisteva in un vaso di vetro, in <lb/>figura di cono, co'lati sfuggevoli e colla punta assai acuta. </s>

<s>Infilava cotesto <lb/>vaso dentro un anello sorretto da un tripode, e lo faceva empire di ghiac&shy;<lb/>cio. </s>

<s>Il vetro cominci&ograve; a sudare, e colando gi&ugrave; per la punta, mostrava nella <lb/>sala da pranzo di far tre gocciole al minuto: portato in una cantina, dov'era <lb/>una fonte, delle gocciole ne dava quindici nel medesimo tempo. </s></p><p type="main">

<s>Fece poi il Granduca per suo diletto ripetere l'esperienza, ora all'aria <lb/>aperta in un prato, ora in una ghiacciaia; ora al sole ora al foco di cu&shy;<lb/>cina; ora al vento di Tramontana ora a quello di Scirocco (Targioni, No&shy;<lb/>tizie ecc. </s>

<s>cit., T. II, P. I, pag. </s>

<s>163, 64), e della nuova invenzione si mostrava <pb xlink:href="020/01/537.jpg" pagenum="518"/>assai sodisfatto. </s>

<s>Ma il Torricelli che sentiva di aver ridotto una bagattella <lb/>da putti a uno strumento, il quale sarebbe alla Meteorologia riuscito utilis&shy;<lb/>simo, ne divulgava la notizia ne'suoi amici di Roma, fra'quali il Ricci cos&igrave; <lb/>in tal proposito, per lettera del d&igrave; 13 Agosto 1645, gli rispondeva: &ldquo; Di <lb/>cotesto strumento acqueo per l'umido, &egrave; arrivata la notizia ai padri del Col&shy;<lb/>legio romano, i quali se ne sono fabbricati uno e mi riferisce il sig. </s>

<s>Bonac&shy;<lb/>corsi che vi faccian sopra delle maraviglie grandi. </s>

<s>Veramente non gli si pu&ograve; <lb/>negar molta lode, portando a tanta conseguenza una bagattella maneggiata <lb/>da putti pi&ugrave; che da cerretani &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, c. </s>

<s>147). </s></p><p type="main">

<s>Questo del Torricelli, che &egrave; il primo Igrometro a condensazione di che <lb/>abbia fatto uso la scienza, negletto per alcun tempo, torn&ograve; a rivivere fra le <lb/>mani degli Accademici del Cimento, a cui il Granduca, secondato dall'osse&shy;<lb/>quio de'cortigiani, lo consegn&ograve; come cosa tutta sua. </s>

<s>Nel consegnarlo per&ograve;, <lb/>mostrava il desiderio che aveva di ridurre lo strumento a segnare i gradi <lb/>dell'umido e del secco, a quel modo che il Termometro segnava i gradi <lb/>del caldo e del freddo, ci&ograve; che dette forse occasione al Viviani di pensare <lb/>a raccogliere le gocciole stillate in un bicchiere alto a foggia di cilindro spar&shy;<lb/>tito in gradi, piuttosto che numerarle, come faceva il Torricelli, e lo in&shy;<lb/>dusse a perfezionare il primo strumento torricelliano a quel modo, che fu <lb/>poi descritto nel Libro de'<emph type="italics"/>Saggi<emph.end type="italics"/> (Firenze 1841, pag. </s>

<s>17, 18). </s></p><p type="main">

<s>Intanto era sparsa la voce fra'cortigiani di questo desiderio o di que&shy;<lb/>sto studio, come dicevano essi, che si dava il Granduca, per ridur l'Igro&shy;<lb/>metro a segnare le variazioni dell'umidit&agrave; con regolata misura. </s>

<s>Era fra <lb/>que'cortigiani un tal Paolo Poltri, amico a quel Francesco Folli da Poppi, <lb/>celebre per aver egli il primo pensato alla trasfusione del sangue. </s>

<s>E come <lb/>fosse motivata da questa amicizia la desiderata invenzione, il Folli stesso <lb/>cos&igrave; lo racconta, dop'avere accennato alla notizia del ritrovato olandese, che <lb/>motiv&ograve; l'invenzione del Telescopio. </s>

<s>&ldquo; Il simile occorse a me nel ritrovar lo <lb/>strumento da conoscere i gradi dell'umido e del secco dell'aria, poich&egrave; se <lb/>il signor Paolo Poltri, mentre eramo a caccia poco fuori di Bibbiena, non <lb/>mi avesse motivato che il Serenissimo Granduca andava investigando il modo <lb/>di fare uno strumento da conoscere i gradi dell'umido e del secco, come <lb/>era segu&igrave;to pochi anni avanti il ritrovamento del Termometro; io certo non <lb/>vi avrei pensato. </s>

<s>Eppure la notte seguente lo speculai, ed il giorno dopo <lb/>lo feci e glielo presentai, e ci&ograve; fu l'anno 1664, e quando venni a stare a <lb/>Firenze, che fu l'anno 1665, ne presentai uno al medesimo Serenissimo Pa&shy;<lb/>drone, che mostr&ograve; gradirlo, e ne fece fare alcuni, che subito mand&ograve; a varii <lb/>principi d'Europa &rdquo; (Stadera medica, Firenze 1680, pag. </s>

<s>113, 14). </s></p><p type="main">

<s>Uno ne fu presentato anche al Papa, non dal Granduca per&ograve;, n&egrave; di&shy;<lb/>rettamente dal principe Leopoldo, ma per l'intermedio di mons. </s>

<s>Cesare Ma&shy;<lb/>galotti, a cui il conte Lorenzo, in una Lettera ne descriveva l'adattamento <lb/>e l'uso, accennando a que'perfezionamenti che l'arte squisita del Campani <lb/>avrebbe saputi introdurre nella fabbrica dello strumento (Targ., Notizie cit., <lb/>T. II, P. I, pag. </s>

<s>337, 38). </s></p><pb xlink:href="020/01/538.jpg" pagenum="519"/><p type="main">

<s>Il Granduca per&ograve;, piuttosto che al Campani, aveva pensato a Filippo <lb/>Treffler, dell'arte del quale era tanto rimasto sodisfatto, quando l'ebbe a'suoi <lb/>servigi in Firenze, e perci&ograve; comandava al Viviani scrivesse a lui diretta&shy;<lb/>mente, ordinandogli che pensasse a costruire con maggior perfezione l'Igro&shy;<lb/>metro, per s&egrave; gi&agrave; sensibilissimo, del Folli. </s>

<s>Quella lettera, data da Firenze <lb/>il d&igrave; 21 Novembre 1665, e dallo stesso Viviani spedita ad Augusta, cos&igrave; <lb/>diceva: </s></p><p type="main">

<s>&ldquo; Per l'aggiunto disegno si dimostra un semplicissimo strumento, che <lb/>a'mesi addietro fu presentato al nostro Padron serenissimo, per mezzo del <lb/>quale si conoscono le piccole mutazioni dell'aria dal pi&ugrave; al meno umido <lb/>che vi si trovi. </s>

<s>Tutta l'invenzione si riduce all'avervi ingegnosamente adat&shy;<lb/>tato quell'ordinarissimo effetto che tutti i giorni si vede ne'fogli delle fine&shy;<lb/><figure id="id.020.01.538.1.jpg" xlink:href="020/01/538/1.jpg"/></s></p><p type="caption">

<s>Figura 56.<lb/>stre incartate, che &egrave; di star ben <lb/>tirati ne'tempi asciutti e di al&shy;<lb/>lentare negli umidi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; S'immagini pertanto ABC <lb/>(fig. </s>

<s>56) essere una striscia di <lb/>carta da impannata, a guisa <lb/>d'un nastro, lunga circa due <lb/>terzi di braccio, o pi&ugrave; o meno, <lb/>e larga meno di un dito. </s>

<s>Que&shy;<lb/>sta &egrave; avvolta ne'suoi estremi A, <lb/>C su due subbietti imperniati, <lb/>da potergli ben fermare, ma <lb/>anco girare bisognando, in oc&shy;<lb/>casione di allungare o scor&shy;<lb/>ciare il detto nastro di carta, <lb/>per temperare il suo bench&egrave; <lb/>leggerissimo peso con quello <lb/>di un piccolo contrappeso, che <lb/>deve sempre tenerla tesa, e mi credo che nel fermarvela da principio si <lb/>debba prima privarla interamente dell'umido, con scaldarla, e in tale stato <lb/>immediatamente tirarvela, distendendola per linea retta da A a B. </s>

<s>In mezzo <lb/>di tal nastro nel punto B sta fermato il capo del filo BDE, il quale cavalca <lb/>sopra un piccolissimo rocchetto di ottone, o di legno che sia, col suo asse <lb/>che dentro i fori di due ali sta imperniato sopra i suoi poli, nell'estremit&agrave; <lb/>di uno de'quali sta fissa la lancetta DF, che nel volgersi al moto del detto <lb/>rocchetto dimostra i gradi o minuti sulla circonferenza della sfera stabile o <lb/>mostra FG, avendo per&ograve; riguardo che la detta lancetta e l'imperniatura siano <lb/>agilissimi al moto. </s>

<s>All'altro estremo del filo in E sta pendente un piccol <lb/>peso H, il quale va aggiustato con tal discrezione, che, per ogni minimo al&shy;<lb/>lungamento della suddetta striscia di carta e'sia appunto bastante, senza <lb/>sforzarla, a tenerla ben distesa per le due linee AB, BC. </s>

<s>Cos&igrave; temperato lo <lb/><gap/> nell'operare, che per <pb xlink:href="020/01/539.jpg" pagenum="520"/>ogni poco di alito umido che alla carta s'imprima o che, con qualche ben&shy;<lb/>ch&egrave; debolissimo grado di caldo asciutto le si tolga, si fa subito o all'innanzi <lb/>o all'indietro visibilissima variazione dell'indice sulla mostra, ma rimosse <lb/>queste cagioni alteranti, riducesi quasi immediatamente sul medesimo segno, <lb/>dov'era prima. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Nonostante ci&ograve;, quell'impareggiabile esquisitezza di gusto e nobile <lb/>curiosit&agrave;, con cui V. S. sa che osserva e filosofa il Serenissimo Granduca, <lb/>gli fa desiderare in questo strumento qualche maggior perfezione, e per&ograve; <lb/>mi ha comandato che io lo descriva a V. S., affinch&egrave;, fabbricandone uno, <lb/>ella possa pensare ai modi di migliorarlo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Vorrebbe S. A. primieramente che due di tali strumenti, tenuti in <lb/>un medesimo luogo, andassero, se &egrave; possibile, sempre concordi nel dimo&shy;<lb/>strare i gradi sulle loro mostre; Che nel trasportarsi da un luogo all'altro, <lb/>la lancetta non si movesse di sito come fa adesso, mediante il moto del <lb/>peso H e del medesimo strumento; Che si potesse tenerlo esposto all'aria <lb/>fuori delle stanze, assicurato dalla polvere, dall'acqua e dal vento, ed a que&shy;<lb/>sto effetto era sovvenuto a S. A. di rinchiuderlo, fino al di sotto della mo&shy;<lb/>stra, in cassetta senza coperchio, con le sponde di vetro piane, ben sigillate <lb/>fra di loro e sul fondo, coprendo poi tutto lo strumento con un'altra simile <lb/>cassetta volta all'ingi&ugrave;, ma che lasci, rasente il fondo, tanta apertura, che <lb/>l'aria interna possa con prontezza accomodarsi con l'umido ambiente; Che <lb/>finalmente ella provi se vi sia altra materia pi&ugrave; resistente, ma cos&igrave; pronta <lb/>o pi&ugrave; della carta, a ricevere le varie impressioni dell'aria. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se poi le sovvenisse altra migliore invenzione, per ottenere gli effetti <lb/>sopra accennati, V. S. &egrave; ormai consapevole che tutto sar&agrave; gratissimo all'A. S., <lb/>e di quanto le riuscir&agrave; di conseguire, potr&agrave; ella subito darne parte &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXLII, c. </s>

<s>103). </s></p><p type="main">

<s>A questa lettera il Treffler, dopo pochi giorni rispose da Augusta sotto <lb/>il d&igrave; 4 Dicembre, dicendo al Viviani di aver ricevuto il disegno d'uno stru&shy;<lb/>mento che deve servir per riconoscere le minime differenze del secco e del&shy;<lb/>l'umido. </s>

<s>&ldquo; Ho inteso benissimo, soggiunge, la sua relazione e l'invenzione <lb/>mi piace assai. </s>

<s>Far&ograve; tutto l'istrumento d'ottone che cos&igrave; l'aria non potr&agrave; <lb/>muovere e tirarlo dalla sua perfezione e mi servir&ograve; di carta pecora sottile <lb/>ed in scambio del contrappeso cercher&ograve; di servirmi di una molletta leggera <lb/>per fuggire il moto del pesino ed in tal modo ancora sar&agrave; pi&ugrave; facile di po&shy;<lb/>terlo portare. </s>

<s>Poi penser&ograve; di potere ancora migliorare che per brevit&agrave; del <lb/>tempo non ho potuto considerare tutto quello si potr&agrave; fare &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. CLXIV, c. </s>

<s>287). </s></p><p type="main">

<s>Ma intanto il Viviani, lasciando al Treffler di pensare a dar sodisfazione <lb/>al Granduca, introducendo nello strumento maggior comodit&agrave; ed eleganza, <lb/>egli attendeva, colla semplicit&agrave; e con la precisione, a soccorrere ai bisogni <lb/>della scienza. </s>

<s>La semplicit&agrave; la trov&ograve; facile fissando i due capi d'una lunga <lb/>striscia di cartapecora a un asse di legno, e facendo pender dal mezzo un <pb xlink:href="020/01/540.jpg" pagenum="521"/>inchiodata sull'asse, la qual placca era contrassegnata di gradi, tutti di ugual <lb/>misura. </s>

<s>O sel sapesse il Viviani o no, costruendo questo Igrometro, di cui <lb/>nel R. </s>

<s>Museo di Fisica di Firenze si vede un modello, s'incontrava nello <lb/>stesso Igrometro descritto gi&agrave; dal Santorio, colla sola differenza d'aver so&shy;<lb/>stituito la cartapecora alla corda tesa. </s>

<s>Le scale, cos&igrave; nello strumento del Fi&shy;<lb/>sico fiorentino come in quello del Medico giustinopolitano, erano digradate <lb/>allo stesso modo, e ci&ograve; non conferiva a quella precisione ch'era l'intento <lb/>precipuo del Viviani, e che vale a renderlo per il merito eccellente sopra <lb/>tutti gli altri. </s></p><p type="main">

<s>Infino allora s'erano compartiti, per le scale igrometriche, gli spazi <lb/>uguali, ma ripensando maturamente il Viviani sopra ci&ograve;, ebbe a entrare in <lb/>qualche dubbio, da lui cos&igrave; espresso: &ldquo; Dubito che n&egrave; gli uguali allunga&shy;<lb/>menti, n&egrave; gli uguali abbassamenti sieno fatti da ugual quantit&agrave; di umido &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. CXXXIV, c. </s>

<s>49). A sincerarsi del qual dubbio invo&shy;<lb/>cando per primo aiuto l'esperienza, ebbe a trovar che &ldquo; si ricerca pi&ugrave; umido <lb/>ad abbassare dal secondo al terzo grado, che dal primo al secondo, e maggiore <lb/>dal terzo al quarto che dal secondo al terzo, supposti i gradi uguali &rdquo; (ivi). </s></p><p type="main">

<s>Pure, non essendo ancora contento, voleva di questi abbassamenti, re&shy;<lb/>lativamente agli allungamenti della striscia di carta per effetto dell'umidit&agrave;, <lb/>ritrovare una legge matematica, ed ebbe in ta&igrave;e investigazione a riconoscere <lb/>assai facilmente che il problema igrometrico si riscontrava col problema mec&shy;<lb/>canico della corda tesa e gravata nel mezzo, propostosi a risolvere da Ga&shy;<lb/>lileo dopo la proposizione ultima del IV Dialogo delle Due Nuove Scienze. </s>

<s><lb/>Fu questa l'occasione, che fece rivolgere il Viviani a considerare pi&ugrave; attenta&shy;<lb/>mente quel problema, per cui venne suo malgrado a riconoscere che la so&shy;<lb/>luzione galileiana era sbagliata. </s>

<s>Di ci&ograve; avremo non lieve argomento di trat&shy;<lb/>tazione nella nostra storia della Meccanica, ma intanto basti il dire che lo <lb/>stesso Viviani, in ordine all'Igrometro, riusc&igrave; a formular questa legge: &ldquo; Gli <lb/>allungamenti stanno fra di loro prossimamente nella proporzione de'qua&shy;<lb/>drati deglli abbassamenti, e gli abbassamenti come gli angoli prossimamente, <lb/>ma per&ograve; ne'primi piccoli abbassamenti &rdquo; (ivi, c. </s>

<s>53). </s></p><p type="main">

<s>Sopra questa legge, in un altro Igrometro di forma anche pi&ugrave; sem&shy;<lb/>plice del primo, e maneggevole, perch&egrave; non consisteva in altro che in un <lb/>regolo di ottone, all'estremit&agrave; del quale due colonnette sostenevano in capo <lb/>i due estremi della striscia di carta gravata da un peso, radente una placca <lb/>saldata nel mezzo dello stesso regolo, di che due modelli similissimi si ve&shy;<lb/>dono nel sopra detto Museo; sopra questa legge, per via di esperienze e di <lb/>meccaniche speculazioni scoperta, il Viviani compart&igrave; la scala igrometrica <lb/>del suo nuovo e sventuratamente negletto strumento. </s></p><p type="main">

<s>Diciamo con tanto pi&ugrave; di ragione questo Igrometro sventuratamente ne&shy;<lb/>gletto, ripensando alla sorte ch'ebbe quel balocco ad avena d'esser comme&shy;<lb/>morato da varii Scrittori. </s>

<s>Giorgio Sinclaro, Filosofo per questa parte vera&shy;<lb/>mente curioso, come in dar nel 1669 per cosa nuova l'Orologio a pendolo <lb/><gap/> e il Boyle avessero frugato per <pb xlink:href="020/01/541.jpg" pagenum="522"/>i suoi manoscritti; cos&igrave; dando nel 1669 per cosa nuova l'Igrometro ad avena, <lb/>port&ograve; sull'Hook quel medesimo sospetto pazzamente geloso. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> Creaturam hanc Hygroscopii nomine indigitare statui, eo quod <lb/>acutissime aeris temperiem humidam et siccam manifestet. <emph type="italics"/>Franc.<emph.end type="italics"/> Id no&shy;<lb/>vum videtur inventum, nam non mihi prius innotuit. </s>

<s>Memini tamen me id <lb/>in libro quodam nuper vulgari sermone edito, cui epigraphe <emph type="italics"/>Micrographia<emph.end type="italics"/><lb/>videre. <emph type="italics"/>Alex.<emph.end type="italics"/> Quid? </s>

<s>an Hygroscopii nomine? <emph type="italics"/>Franc.<emph.end type="italics"/> Imo. <emph type="italics"/>Alex.<emph.end type="italics"/> Quam ve&shy;<lb/>reor ne praeter nomen alia nonnulla ex nostro manuscripto mutuatus sit <lb/>auctor. </s>

<s>Sed primus omnium qui illius rei meminit fuit Baptista Porta, verbo <lb/>solum. </s>

<s>Quo ad eius fabricam et structuram attinet, sumatur <emph type="italics"/>grani venacei <lb/>arista,<emph.end type="italics"/> cuius altero extremo corpori alicui plano infixo, indicem transversa&shy;<lb/>rium ex materia aliqua levissima alterum superferet, quem iuxta aeris al&shy;<lb/>terationem, ex siccitate in humiditatem, et ex humiditate in siccitatem con&shy;<lb/>verti videbis &rdquo; (Ars magna ecc., Roterodami 1669, pag. </s>

<s>535). </s></p><p type="main">

<s>Se avesse il Sinclaro potuto sapere che il Moncony vide uno di questi <lb/>Igrometri ad avena, nel 1646, in Firenze appresso il Torricelli (Premier vo&shy;<lb/>yage en Italie, Paris 1695, pag. </s>

<s>229), chi sa che non avesse seguitato ne'suoi <lb/>sospetti, com'a saper che nel 1657 lo Schott aveva nella sua <emph type="italics"/>Mechanica <lb/>hydraulico-pneum.<emph.end type="italics"/> descritto il medesimo strumento come invenzione gi&agrave; <lb/>conosciuta? </s>

<s>&ldquo; Rem totam, egli dice, describit fuse Kirkerius lib. </s>

<s>III Artis <lb/>magnet., pars. </s>

<s>II, cap. </s>

<s>III, Progymnasma I &rdquo; (Herbipoli 1657, pag. </s>

<s>333). <lb/>Anzi si accenna ivi dallo Schott una cosa, per cui renderebbesi molto pro&shy;<lb/>babile che cos&igrave; fatti Igrometri fossero stati conosciuti dal volgo, molto tempo <lb/>prima che venissero descritti dai Filosofi, dicendovisi che le propriet&agrave; igro&shy;<lb/>scopiche dell'avena son comuni a tutte le pianticelle gracili e rampicanti, <lb/>come i convolvoli o i cos&igrave; detti vilucchi. </s>

<s>&ldquo; Eamdem hanc proprietatem ha&shy;<lb/>bent omnes illae herbae et plantae, quae incremento suo in spiras sese na&shy;<lb/>turaliter contorquent, cuiusmodi sunt omnia convolvulorum genera &rdquo; (ibi, <lb/>pag. </s>

<s>234). </s></p><p type="main">

<s>Ma lasciando gli uccellini di carta affissi ad un gambo di avena dar di <lb/>s&egrave; giocondo spettacolo ai visitatori del Museo kirkeriano, gl'Igrometri dot&shy;<lb/>tamente speculati per giovare ai progressi della scienza, rimasero chiusi nel&shy;<lb/>l'officina di Filippo Treffler, e sepolti con le carte manoscritte di Vincenzio <lb/>Viviani. </s>

<s>Perci&ograve; il Folli, che nel 1680 vedeva esser gi&agrave; la sua invenzione nel <lb/>mondo quasi morta, si studi&ograve; di renderla a vita in un libro, da lui stesso <lb/>scritto e intitolato <emph type="italics"/>Stadera medica.<emph.end type="italics"/> Ivi si descrive dall'Inventore, non per&ograve; <lb/>con quella evidenza del Viviani nella Lettera Treffler, il suo nuovo stru&shy;<lb/>mento, a cui &ldquo; per non far questo sfregio alla lingua toscana col dichia&shy;<lb/>rarla fallita e bisognosa d'andar mendicando fra'greci vocaboli &rdquo; (Stad. </s>

<s>med., <lb/>Firenze 1680, pag. </s>

<s>115) dava il nome di <emph type="italics"/>Mostra umidaria.<emph.end type="italics"/></s></p><p type="main">

<s>Cos&igrave;, nel decorso del secolo XVII, avevano gl'Italiani fornito la Meteo&shy;<lb/>rologia di varia maniera d'Igrometri, alcuni de'quali riuscivano sensibilis&shy;<lb/>simi e sufficientemente precisi. </s>

<s>Eppure, nel secolo appresso quando il Saus&shy;<lb/>ssure istitu&igrave; le <gap/><pb xlink:href="020/01/542.jpg" pagenum="523"/>uno strumento, che agli occhi degli scienziati apparve nuovo, e che fu giu&shy;<lb/>dicato dal Volta <emph type="italics"/>eccellente ad ogni riguardo<emph.end type="italics"/> (Op. </s>

<s>cit., T. I, P. II, pag. </s>

<s>84). <lb/>Nonostante, a volere esser giusti, le strisciole di carta del Viviani non pre&shy;<lb/>sentavano maggiori imperfezioni de'famosi capelli, e in ogni modo, chi da <lb/>carte 42 a carte 60 svolge il citato Tomo CXXXIV manoscritto, e considera <lb/>quelle frettolose note interpolate a tanti calcoli laboriosi, &egrave; costretto a con&shy;<lb/>fessar che il Discepolo di Galileo non pose minore studio e diligenza, in re&shy;<lb/>golar le sue scale umidarie, di quel che vi ponesse il Gay-Lussac in costruire <lb/>quelle sue Tavole di correzione. </s></p><p type="main">

<s>Lo stesso Volta per&ograve; che aveva fatto cos&igrave; lieta accoglienza all'Igrome&shy;<lb/>tro saussuriano, non seppe rintuzzare il desiderio che lo frugava di proporne <lb/>uno nuovo, adattando inaspettatamente a quell'uso il Pendolo elettrometrico <lb/>dell'Henley. </s>

<s>Egli e tutti i Fisici avevano dovuto osservare che, se l'aria &egrave; <lb/>molto secca, il pendolo si sostien sul quadrante per parecchi minuti, e tal&shy;<lb/>volta anche per qualche ora; mentre, se l'aria &egrave; umida, non si sostiene il <lb/>pendolo che per qualche minuto secondo. </s></p><p type="main">

<s>Il progetto di stabilir sopra queste osservazioni un Igrometro, era, per <lb/>la novit&agrave; sua, seducente, ma oltre al riuscir l'apparato assai incomodo per <lb/>richiedervisi il concorso della Macchina elettrica o dell'Elettroforo, la scala <lb/>igrometrica, per la sua grandissima estensione, era impraticabile, ond'ebbe <lb/>a confessare lo stesso Volta e a dire: &ldquo; chi mai vorrebbe intraprendere una <lb/>serie di esperienze di questa sorta, che non sono, lo confesso io medesimo, <lb/>di una grandissima importanza? </s>

<s>&rdquo; (ivi, pag. </s>

<s>443). </s></p><p type="main">

<s>Sicch&egrave; l'Igrometro elettrico, bench&egrave; ingegnoso, non potrebbe aversi che <lb/>qual semplice <emph type="italics"/>Elettroscopio.<emph.end type="italics"/> Or che altro hanno dovuto sentenziare i Fisici <lb/>del celebre strumento saussuriano? </s>

<s>Bisogna rassegnarsi, essi dicono, ad usare <lb/>anco l'Igrometro a capello, come si farebbe di qualunque altro elettroscopio <lb/>di quelli anticamente inventati dagli italiani. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Terminandosi da noi, in quest'ultimo paragrafo, la storia de'principali <lb/>strumenti del Metodo sperimentale, non presumiamo, nemmen dentro i ter&shy;<lb/>mini che ci siamo prescritti, d'aver di tutti narrato ci&ograve; che concerne il modo <lb/>e la ragione delle loro invenzioni. </s>

<s>Di parecchi altri ci occorrer&agrave; di parlarne <lb/>in sul punto, che dovremo vedere i varii ordini di scienze sperimentali, pro&shy;<lb/>gredendo via via, provocarli, e reclamarli, come necessaria condizione di <lb/>que'loro progressi. </s>

<s>Solo crediamo di dover aggiunger qui qualche parola, <lb/>per dir dell'Arcometro e del Pluviometro, che, cos&igrave; semplici ambedue nella <lb/>costruzione, son pure altrettanto importanti negli usi. </s></p><p type="main">

<s>L'Areometro o Pesaliquori, ingentilito poi dalla scienza, riconosce la <lb/>prima sua origine da quel rozzo strumento, con cui l'antico Sozione inse-<pb xlink:href="020/01/543.jpg" pagenum="524"/>gnava, secondo riferisce il Porta, a conoscer se il mosto era puro, o s'era <lb/>stato mescolato coll'acqua. </s>

<s>&ldquo; Unde si in mustum mala vel pyra silvestria <lb/>immiseris, et mustum purissimum erit, supernatabunt mala et fluitabunt. </s>

<s>At <lb/>si aquam admistam habuerint, mala fundum petunt introque merguntur. </s>

<s><lb/>Cum enim aqua musto tenuior sit, et levior facit ut malum subsidat. </s>

<s>Quod <lb/>optime a Sotione descriptum est et satis curiose. </s>

<s>Inquit: ut sciamus mustum <lb/>an aquam habeat, pyra silvestria, hoc est crudissima, in mustum coniice, et <lb/>si quidem aquam habuerit ad fundum mergentur. </s>

<s>Nam si vas musto repleas, <lb/>dum sorbum aut pyrum immerges, supernatabit, quanto plus aquae addes, <lb/>plus mergetur malum &rdquo; (Magia Nat, Lugd. </s>

<s>Batav. </s>

<s>1651, pag. </s>

<s>618, 19). </s></p><p type="main">

<s>Galileo, il quale non immeritamente si riconosce per primo inventore <lb/>dell'Areometro, applicato agli usi della scienza, nella I Giornata delle Due <lb/>Nuove Scienze, descrive il seguente dialogo passato fra il Sagredo e il Sal&shy;<lb/>viati: &ldquo; &mdash; Io con un altro artifizio ingannai alcuni amici, appresso i quali <lb/>m'era vantato di ridurre quella palla di cera al giusto equilibrio con l'acqua, <lb/>ed avendo messo nel fondo del vaso una parte d'acqua salata e sopra quella <lb/>della dolce, mostrai loro la palla, che a mezz'acqua si fermava, e spinta nel <lb/>fondo o sospinta ad alto n&egrave; in questo n&egrave; in quel sito restava, ma ritornava <lb/>nel mezzo. </s>

<s>&mdash; Non &egrave; cotesta esperienza priva d'utilit&agrave;, perch&egrave;, trattandosi <lb/>dai medici in particolare, delle diverse qualit&agrave; di acqua e tra l'altre prin&shy;<lb/>cipalmente della leggerezza e gravit&agrave; pi&ugrave; di questa che di quella, con una <lb/>simil palla aggiustata, sicch&egrave; resti ambigua per cos&igrave; dire tra lo scendere e <lb/>il salire in un'acqua, per minima che sia la differenza di peso tra due acque, <lb/>se in una tal palla scender&agrave;, nell'altra che sia pi&ugrave; grave salir&agrave; &rdquo; (Alb. </s>

<s>XIII, 72). </s></p><p type="main">

<s>Dalle citate parole sembra che, rispetto alla invenzione, sieno da distin&shy;<lb/>guere due tempi: il primo, in cui la palla galleggiante non serviva ad altro <lb/>che alla curiosit&agrave; di uno spettacolo, e il secondo in cui si fece di questa <lb/>stessa palla galleggiante l'applicazione all'uso areometrico. </s>

<s>Il primo tempo <lb/><figure id="id.020.01.543.1.jpg" xlink:href="020/01/543/1.jpg"/></s></p><p type="caption">

<s>Figura 57.<lb/>par doversi ridurre intorno al 1604, come si rileva da una lettera <lb/>di Don Antonio de'Medici che fa richiesta a Galieo della palla spet&shy;<lb/>tacolosa. </s>

<s>&ldquo; Intendo (diceva quella lettera che &egrave; del 28 Giugno) che <lb/>V. S. ha una palla, che gettandola nell'acqua sta fra le due acque. </s>

<s><lb/>Vengo con la presente a pregarla vivamente di voler favorirmene <lb/>e consegnarla al P. D. </s>

<s>Antonio Cerrato &rdquo; (Volinski, Lett. </s>

<s>in. </s>

<s>a <lb/>Gal., Firenze 1874, Lett. </s>

<s>IV, pag. </s>

<s>16). </s></p><p type="main">

<s>Quanto al secondo tempo, potrebb'essere che fosse verso il 1612, <lb/>quando pens&ograve; di trovare il peso specifico dell'aria, riducendo il <lb/>galleggiante in figura di quella caraffalla, che fu poi, in quasi <lb/>tutte le varie forme di questo strumento, adottata dai successivi <lb/>inventori. </s>

<s>Cos&igrave; infatti ce ne descrive Galileo la figura e l'uso in <lb/>una Lettera al Nozzolini: &ldquo; Facciasi un vaso di vetro simile al&shy;<lb/>l'ABC (fig. </s>

<s>57) di qualsivoglia grandezza col collo AB lunghetto al&shy;<lb/>quanto ma stretto, e nel fondo C se gli attacchi tanto piombo o altro peso <lb/><gap/> si sommerga, sicch&egrave; solo avanzi fuori del-<pb xlink:href="020/01/544.jpg" pagenum="525"/>l'acqua una parte del collo AB, nel qual collo si noti con diligenza, con <lb/>legarvi un filo sottile, sino a qual parte e'si demerga. </s>

<s>Di poi scaldisi sopra <lb/>la brace accesa il vaso, in guisa che il fuoco scacci tutta o la maggior parte <lb/>dell'aria in esso contenuta, e prima che rimoverlo dal fuoco, serrisi esqui&shy;<lb/>sitamente la bocca A, sicch&egrave; non vi possa rientrar aria. </s>

<s>Levisi di poi dal <lb/>fuoco e lascisi cos&igrave; stare, finch&egrave; si freddi, partendosi per la porosit&agrave; del ve&shy;<lb/>tro quell'esalazione ignea che vi penetr&ograve; e scacci&ograve; l'aria. </s>

<s>Dipoi tornisi a <lb/>metter nell'acqua, e vedrassi galleggiare notabilmente pi&ugrave; che prima, stando <lb/>del collo assai maggior parte fuori, e ci&ograve; per essergli stata rimossa o tutta <lb/>o parte dell'aria, che prima lo riempiva, senza che in luogo di quella sia <lb/>succeduto altro corpo &rdquo; (Alb XII, 114, 15). </s></p><p type="main">

<s>La forma di questo strumento galileiano e l'uso suggerirono facilmente <lb/>al Torricelli l'invenzione di quegli Idrostammi, co'quali s'intendeva di mi&shy;<lb/>surare il peso de'liquidi, nel modo stesso che Galileo aveva misurato quello <lb/>dell'aria. </s>

<s>Perci&ograve; fra gli strumenti attribuiti al Granduca Ferdinando se ne <lb/>trova annoverati e descritti anco alcuni ordinati <emph type="italics"/>a conoscere la gravezza <lb/>e la leggerezza di una cosa liquida<emph.end type="italics"/> (Targioni, Notizie cit., T. I, pag. </s>

<s>153). <lb/>&ldquo; Lo strumento B si deve mettere nel liquido che uno vuol provare, e si <lb/>vede quanto sta all'equilibro appunto: se sopravanza, si deve accrescere di <lb/>peso con anelli segnati C, che sieno d'un grano, mezzo grano, un dodice&shy;<lb/>simo, ventiquattresimo, e quarantottesimo e pi&ugrave; se si vuole, fino resti al&shy;<lb/>l'equilibrio, e torni su appunto, e poi provare agli altri, e vedere la diffe&shy;<lb/>renza del peso, o aggiunto o levato, e da questo cavarne, che dove si metter&agrave; <lb/>pi&ugrave; peso, sar&agrave; pi&ugrave; grave, e dove se ne metter&agrave; meno, sar&agrave; pi&ugrave; leggeri &rdquo; <lb/>(ivi, T. II, P. I, pag. </s>

<s>169). </s></p><p type="main">

<s>&Egrave; facile vedere in questo strumento una grandissima somiglianza colla <lb/><emph type="italics"/>Bilancia areometrica<emph.end type="italics"/> del Nicholson, e con l'Areometro del Fahrenheit, ma <lb/>un altro Idrostammo &egrave; pure annoverato fra gli strumenti del Granduca, il <lb/>quale, consistendo in una bolla di vetro dentrovi migliarole o mercurio, con <lb/>un lungo collo graduato, non par che differisca di nulla o d'assai poco dal&shy;<lb/>l'Areometro, che va comunemente sotto il nome del Baum&egrave;. </s>

<s>&ldquo; Lo stru&shy;<lb/>mento A messo in qualsivoglia liquido si deve osservare quanti gradi re&shy;<lb/>stino fuori di quello a misura, e poi messo negli altri osservare quanti gradi <lb/>medesimamente restino fuori: dove resteranno pi&ugrave; gradi fuori, sar&agrave; pi&ugrave; <lb/>grave, e dove meno, sar&agrave; pi&ugrave; leggeri &rdquo; (ivi). </s></p><p type="main">

<s>Un disegno di questo Idrostammo vedesi abbozzato di mano del Viviani <lb/>ne'MSS Cim., T. XI, c. </s>

<s>105, e a lato si legge: <emph type="italics"/>Strumento per conoscere la <lb/>gravit&agrave; de'fluidi.<emph.end type="italics"/> Di qui parrebbe che fosse questa invenzione dello stesso <lb/>Viviani, intorno a che poi ci rende certi l'Inventore scrivendo: &ldquo; Mio lo <lb/>strumento a palla per la gravit&agrave; in specie de'fluidi, col mettere i pesi den&shy;<lb/>tro la palla &rdquo; (ivi, T. X, c. </s>

<s>259). </s></p><p type="main">

<s>In quella stessa carta, dove abbiamo detto vedersi l'abbozzo di questo <lb/><emph type="italics"/>strumento a palla,<emph.end type="italics"/> vedesi dalla stessa mano abbozzato un altro disegno illu&shy;<lb/><gap/> detto .... <pb xlink:href="020/01/545.jpg" pagenum="526"/>ovvero <emph type="italics"/>Stadera de'liquidi.<emph.end type="italics"/> &rdquo; Rappresenta un tubo barometrico immerso <lb/>nella vaschetta del mercurio, sopra il quale versando un liquido o un altro, <lb/>ne resulta una specie di stadera, per la quale si misurano i pesi dalla virt&ugrave; <lb/>che gli stessi varii liquidi infusi hanno di far sollevare pi&ugrave; o meno il mer&shy;<lb/>curio nel tubo barometrico. </s>

<s>Varii altri strumenti, o dallo stesso Viviani o da <lb/>altri Aceademici, furono inventati <emph type="italics"/>per pesare i liquidi nel vuoto,<emph.end type="italics"/> la descri&shy;<lb/>zion de'quali si legge nel Tomo VI de'citati Manoscritti del Cimento. </s></p><p type="main">

<s>Cos&igrave; la storia dell'invenzion dell'Areometro, che riconosce la sua prima <lb/>origine in una sorba agresta o in una pera galleggiante, ci mostra come tal&shy;<lb/>volta i pi&ugrave; &inodot;ozzi naturali strumenti vengano a trasformarsi, raffinati nelle <lb/>mani dell'arte. </s>

<s>Un altro simile esempio lo abbiamo nel Pluviometro, che fu <lb/>a principio uno di que'vasi di vetro, a cui il Castelli, stato il primo ad usarlo <lb/>per misurare la quantit&agrave; dell'acqua piovuta in un dato tempo, dava, seguendo <lb/>il volgar linguaggio, il nome di orinale. </s>

<s>Narra lo stesso Castelli, in una Let&shy;<lb/>tera a Galileo copiata in calce al Libro I, Della Misura delle acque correnti, <lb/>come ripensando agli effetti prodotti dalla siccit&agrave; nel lago di Perugia, ritor&shy;<lb/>nato che fu dalla visita dell'emissario in citt&agrave;, segui una pioggia non molto <lb/>grossa, ma continuata assai ed uniforme, la quale dur&ograve; per ispazio di otto <lb/>ore in circa. </s>

<s>&ldquo; Allora mi venne in pensiero di volere esaminare, stando in <lb/>Perugia, quanto con quella pioggia poteva essere cresciuto e rialzato il Lago, <lb/>supponendo, come aveva assai del probabile, che la pioggia fosse universale <lb/>sul lago, ed uniforme a quella che cadeva in Perugia, e cos&igrave; preso un vaso <lb/>di vetro di forma cilindrica alto un palmo in circa, e largo mezzo palmo, ed <lb/>avendo infusa un poco d'acqua, tanto che coprisse il fondo del vaso, notai <lb/>diligentemente il segno dell'altezza dell'acqua del vaso, e poi l'esposi al&shy;<lb/>l'aria aperta a ricevere l'acqua della pioggia che ci cascava dentro, e lo la&shy;<lb/>sciai stare per ispazio di un'ora, ed avendo osservato che nel detto tempo <lb/>l'acqua si era alzata nel vaso quanto la seguente linea &mdash;&mdash; considerai <lb/>che se io avessi esposti alla medesima pioggia altri simili ed uguali vasi, in <lb/>ciascuno di essi si sarebbe rialzata l'acqua, secondo la medesima misura, e <lb/>per tanto conclusi che ancora in tutta l'ampiezza del Lago era necessario <lb/>che l'acqua si fosse rialzata nello spazio di un'ora la medesima misura &rdquo; <lb/>(Bologna 1660, pag. </s>

<s>50). </s></p><p type="main">

<s>Di questo stesso vaso di vetro, di cui erasi gi&agrave; servito il Castelli per <lb/>misurare la quantit&agrave; d'acqua piovuta, si serv&igrave; poi per misurare la quantit&agrave; <lb/>d'acqua evaporata, offerendo cos&igrave; come primizia i due nuovi strumenti alla <lb/>nascente Meteorologia. </s></p><pb xlink:href="020/01/546.jpg"/><p type="main">

<s><emph type="center"/>INDICI<emph.end type="center"/><pb xlink:href="020/01/547.jpg"/></s></p><pb xlink:href="020/01/548.jpg"/><p type="main">

<s><emph type="center"/>INDICE DEI CAPITOLI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Discorso Preliminare.<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>PARTE PRIMA<emph.end type="center"/></s></p><p type="main">

<s>I Del primo acquisto delle cognizioni <emph type="italics"/>Pag.<emph.end type="italics"/> 25 </s></p><p type="main">

<s>II Platone e Aristotile &rdquo; 29 </s></p><p type="main">

<s>III Della Filosofia naturale derivata dall'Accademia e dal Peripato &rdquo; 33 </s></p><p type="main">

<s>IV Come le due Filosofie, la platonica e l'aristotelica, venissero a introdursi nella Societ&agrave; <lb/>cristiana &rdquo; 38 </s></p><p type="main">

<s>V De'medici peripatetici; Girolamo Fracastoro; Andrea Cesalpino &rdquo; 42 </s></p><p type="main">

<s>VI Girolamo Cardano, Giuseppe Scaligero, Niccol&ograve; Tartaglia &rdquo; 47 </s></p><p type="main">

<s>VII De'Filosofi razionalisti: Francesco Patrizio, Bernardino Telesio, Giordano Bruno e Toin&shy;<lb/>maso Campanella &rdquo; 54 </s></p><p type="main">

<s>VIII De'frutti di scienza naturale raccolti nel secolo XVI dalle tre Filosofie, accademica, peri&shy;<lb/>patetica e razionalistica &rdquo; 61 </s></p><p type="main">

<s>IX De'cultori dell'arte, veri precursori del metodo sperimentale: Dante Alighieri, Leon Bat&shy;<lb/>tista Alberti, Cristoforo Colombo e Amerigo Vespucci &rdquo; 66 </s></p><p type="main">

<s>X Leonardo da Vinci &rdquo; 74 </s></p><p type="main">

<s>XI Degli anatomici padovani del secolo XVI, e segnatamente di Realdo Colombo &rdquo; 84 </s></p><p type="main">

<s>XII Come nel secolo XVI gli esercizi sperimentali e le notizie dei fatti naturali si diffondes&shy;<lb/>sero dai libri d'uomini letterati: Giovan Battista Porta e Ferrante Imperato &rdquo; 91 </s></p><p type="main">

<s>XIII De'pi&ugrave; immediati precursori e cooperatori alla grande Instaurazione galileiana: Giovan <lb/>Battista Benedetti e Santorre Santorio &rdquo; 101 </s></p><p type="main">

<s>XIV Paolo Sarpi &rdquo; 108 </s></p><p type="main">

<s>XV Dell'Accademia de'Lincei, e di Francesco Bacone &rdquo; 116 </s></p><p type="main">

<s><emph type="italics"/>Nota I<emph.end type="italics"/> &rdquo; 124 </s></p><p type="main">

<s><emph type="italics"/>Nota II<emph.end type="italics"/> &rdquo; 126 </s></p><p type="main">

<s><emph type="center"/>PARTE SECONDA<emph.end type="center"/></s></p><p type="main">

<s>I Di Galileo Galilei e della sua nuova instaurazione scientifica <emph type="italics"/>Pag.<emph.end type="italics"/>127 </s></p><p type="main">

<s>II Si giustificano le cose asserite nel paragrafo precedente &rdquo; 136 </s></p><p type="main">

<s>III Dei benefizi che derivarono alle scienze sperimentali dalla nuova Instaurazione galileiana &rdquo; 143 </s></p><p type="main">

<s>IV Renato Cartesio &rdquo; 150 </s></p><p type="main">

<s>V De'primi e principali Discepoli di Galileo &rdquo; 157 </s></p><p type="main">

<s>VI Della grande esperienza torricelliana dell'argento vivo, e come per lei si diffondessero, <lb/>d'Italia in tutta Europa, l'amore e gli esercizi dell'arte sperimentale &rdquo; 169 </s></p><p type="main">

<s>VII Di Evangelista Torricelli, di Vincenzio Viviani e di ci&ograve; che operassero nelle istituzioni <lb/>della sperimentale Accademia medicea &rdquo; 178 </s></p><p type="main">

<s>VIII Del primo periodo della fiorentina Accademia del Cimento &rdquo; 188 </s></p><p type="main">

<s>IX Del secondo periodo della fiorentina Accademia del Cimento &rdquo; 197 </s></p><p type="main">

<s>X Delle principali Accademie private istituite in Italia a imitazione di quella del Cimento; <lb/>del felico esito della Istituzione medicea, nonostante le rivalit&agrave; degli stranieri, i dis&shy;<lb/><gap/> dei Perinatetici &rdquo; 205 </s></p><pb xlink:href="020/01/549.jpg" pagenum="530"/><p type="main">

<s><emph type="center"/>PARTE TERZA<emph.end type="center"/></s></p><p type="main">

<s>I Isacco Newton <emph type="italics"/>Pag.<emph.end type="italics"/>217 </s></p><p type="main">

<s>II De'principii e de'progressi delle speculazioni neutoniane, e quale efficace concorso v'ab&shy;<lb/>biano avuto le tradizioni scientifiche da'nostri Italiani &rdquo; 224 </s></p><p type="main">

<s>III Delle Istituzioni idrauliche di Domenico Guglielmini, e in che modo i principii della Fi&shy;<lb/>losofia neutoniana, nel secolo XVIII, concorressero a farla progredire &rdquo; 233 </s></p><p type="main">

<s>IV Dell'Elettricismo, della Chimica, dell'Elettro chimica, e come si svolgessero queste nuove <lb/>parti delle scienze dai principii della Filosofia neutoniana &rdquo; 240 </s></p><p type="main">

<s>V Dei progressi della Storia Naturale nel secolo XVIII &rdquo; 249 </s></p><p type="main">

<s>VI Delle condizioni presenti delle scienze sperimentali: qualche parola intorno alla nostra <lb/>Storia &rdquo; 255 </s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>De'principali strumenti del metodo sperimentale.<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>CAPITOLO I.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del Termometro.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Dell'invenzione e degli usi del Termometro santoriano <emph type="italics"/>Pag.<emph.end type="italics"/>265 </s></p><p type="main">

<s>II Delle applicazioni dell'antichissima esperienza eroniana, e segnatamente di quella fatta <lb/>da Daniele Antonini e da Cornelio Drebbellio &rdquo; 270 </s></p><p type="main">

<s>III Della medesima esperienza fatta da Galileo &rdquo; 272 </s></p><p type="main">

<s>IV Se si debba giustamente attribuire a Galileo l'invenzion del Termometro ad aria; de'per&shy;<lb/>fezionamenti che tent&ograve; Giovan Francesco Sagredo d'introdurre nello strumento &rdquo; 274 </s></p><p type="main">

<s>V Della prima invenzione del Termometro a liquido &rdquo; 279 </s></p><p type="main">

<s>VI Della prima scoperta e delle prime ragioni rese del fatto del dilatarsi i liquidi al calore &rdquo; 285 </s></p><p type="main">

<s>VII Della scoperta della dilatazione cubica de'solidi al calore, e delle applicazioni di lei alla <lb/>Termometria &rdquo; 290 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO II.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dell'orologio a pendolo.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I De'primi Orologi a pendolo del Santorio <emph type="italics"/>Pag.<emph.end type="italics"/>299 </s></p><p type="main">

<s>II De'varii modi proposti da Galileo di applicare il pendolo agli Orologi &rdquo; 307 </s></p><p type="main">

<s>III Del primo Orologio descritto da Cristiano Huyghens; della simpatia de'pendoli &rdquo; 313 </s></p><p type="main">

<s>IV Del Cronoscopio di Giorgio Sinclaro e dell'Orologio cicloidale dell'Huyghens &rdquo; 319 </s></p><p type="main">

<s>V Del Cronometro degli Accademici del Cimento &rdquo; 324 </s></p><p type="main">

<s>VI Come probabilmente il Cronometro degli Accademici fiorentini sia invenzione del Vi&shy;<lb/>viani: della ricerca del centro di oscillazione, ne'pendoli degli Orologi &rdquo; 327 </s></p><p type="main">

<s>VII Degli effetti prodotti dal calore negli Orologi: dell'invenzione degli Orologi a bilanciere <lb/>o da tasca: della compensazione de'pendoli &rdquo; 332 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO III.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dell'invenzione e della teoria del Canocchiale.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Del primo inventore del Canocchiale <emph type="italics"/>Pag.<emph.end type="italics"/>339 </s></p><p type="main">

<s>II Di ci&ograve; che, intorno all'invenzione dello Strumento, Galileo dicesse di s&egrave;, e di quel che <lb/>di lui si diceva dagli altri &rdquo; 346 </s></p><pb xlink:href="020/01/550.jpg" pagenum="531"/><p type="main">

<s>III Del primo concetto, e di ci&ograve; che possa aver dato occasione al ritrovamento del Canoc&shy;<lb/>chiale <emph type="italics"/>Pag.<emph.end type="italics"/>351 </s></p><p type="main">

<s>IV Delle prime speculazioni diottriche intorno alla teoria del Canocchiale &rdquo; 356 </s></p><p type="main">

<s>V Di altre vie tentate per risolvere il problema diottrico del Canocchiale, e come fosse final&shy;<lb/>mente risoluto dell'Huyghens: breve conclusione delle cose fin qui discorse &rdquo; 366 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>De'Canocchiali del Fontana, del Torricelli e di altri; <lb/>del Telescopio a riflessione.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I De'Canocchiali di Girolamo Sirturo e di Francesco Fontana <emph type="italics"/>Pag.<emph.end type="italics"/> 374 </s></p><p type="main">

<s>II De'Canocchiali di Evangelista Torricelli &rdquo; 378 </s></p><p type="main">

<s>III Del segreto usato dal Torricelli per lavorare i vetri da Canocchiali &rdquo; 383 </s></p><p type="main">

<s>IV Considerazioni o giudizi intorno al Torricelli come costruttore di Canocchiali, special&shy;<lb/>mente da servire per gli usi astronomici &rdquo; 387 </s></p><p type="main">

<s>V De'Canocchiali di Cristiano Huyghens &rdquo; 391 </s></p><p type="main">

<s>VI De'Canocchiali di Giuseppe Campani, e di Eustachio Divini &rdquo; 394 </s></p><p type="main">

<s>VII De'Telescopii a riflessione &rdquo; 399 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO V.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Degli organi aggiunti, e de'nuovi usi strumentali del Canocchiale.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Del primo Micrometro e delle prime operazioni micrometriche di Galileo <emph type="italics"/>Pag.<emph.end type="italics"/>405 </s></p><p type="main">

<s>II Del Micrometro ugeniano e del Micrometro a reticolo &rdquo; 412 </s></p><p type="main">

<s>III Della Livella diottrica &rdquo; 418 </s></p><p type="main">

<s>IV Del Canocchiale binoculo &rdquo; 424 </s></p><p type="main">

<s>V Dell'Elioscopio, dell'Eliostata, de'Diaframmi de'Canocchiali &rdquo; 429 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del Barometro.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle prime idee, che ebbero i Fisici intorno alla possibilit&agrave; e all'esistenza del vacuo, e <lb/>delle loro prime esperienze intorno al peso e alle pressioni dell'aria <emph type="italics"/>Pag.<emph.end type="italics"/>434 </s></p><p type="main">

<s>II Della celebre esperienza dell'argento vivo: delle esperienze del Pascal e di altri Francesi. </s>

<s>&rdquo; 440 </s></p><p type="main">

<s>III Come l'esperienza dell'argento vivo fosse, per unanime consenso degli stessi stranieri, <lb/>attribuita al Torricelli &rdquo; 447 </s></p><p type="main">

<s>IV Della Lettera torricelliana sull'esperienza dell'argento vivo &rdquo; 451 </s></p><p type="main">

<s>V Come il Torricelli attendesse a costruire lo strumento da misurar le variazioni del peso <lb/>dell'aria, e come non gli riuscisse la sua intenzione &rdquo; 455 </s></p><p type="main">

<s>VI Come e da chi lo strumento torricelliano dell'argento vivo fosse applicato ad uso di <lb/>Barometro &rdquo; 462 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Della Macchina elettrica e della Pila voltaia.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Del globo di zolfo del Guericke, e d&egrave;l globo di vetro dell'Hawksbec: della Macchina elet&shy;<lb/>trica di Lipsia, del Winkler, del Nollet, del Ramsden <emph type="italics"/>Pag.<emph.end type="italics"/>469 </s></p><p type="main">

<s>II Della Bottiglia di Leyda; dell'Elettroforo e del Condensatore del Volta &rdquo; 475 </s></p><p type="main">

<s>III De'primi elettroscopii; dell'Elettroscopio a boccetta, dell'Elettrometro condensatore, e <lb/>dell'Elettrometro a quadrante &rdquo; 479 </s></p><p type="main">

<s>IV Della grande scoperta galvanica dell'Elettricit&agrave; animale, e della nuova elettricit&agrave; me&shy;<lb/>tallica scoperta dal Volta &rdquo; 484 </s></p><p type="main">

<s><gap/> &rdquo; 492 </s></p><pb xlink:href="020/01/551.jpg" pagenum="532"/><p type="main">

<s><emph type="center"/>CAPITOLO VIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Di varii altri strumenti.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Degli specilli semplici o degli occhiali da naso, e del loro modo di operar sulla vista <emph type="italics"/>Pag.<emph.end type="italics"/>498 </s></p><p type="main">

<s>II Del Microscopio semplice e del Microscopio composto &rdquo; 505 </s></p><p type="main">

<s>III Del corno acustico &rdquo; 512 </s></p><p type="main">

<s>IV De'primi Igroscopii, degl'Igrometri del Santorio, dell'Igrometro a condensazione del <lb/>Torricelli, della <emph type="italics"/>Mostra umidaria<emph.end type="italics"/> del Folli, della legge igrometrico meccanica del <lb/>Viviani e dell'Igrometro elettrico del Volta &rdquo; 545 </s></p><p type="main">

<s>V Dell'Areometro e del Pluviometro &rdquo; 523 </s></p><pb xlink:href="020/01/552.jpg"/><p type="main">

<s><emph type="center"/>INDICE ALFABETICO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>DEGLI AUTORI E DELLE COSE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Co'numeri s'accenna alle pagine.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="bold"/>Accademia platonica,<emph.end type="bold"/> carattere filosofico di lei 34, Accad. </s>

<s>napoletana del Conclubet 205. </s></p><p type="main">

<s><emph type="bold"/>Acquapendente (d') Eabrizi Girolamo,<emph.end type="bold"/> anatomico 91. </s></p><p type="main">

<s><emph type="bold"/>Acromatismo<emph.end type="bold"/> delle lenti 394. </s></p><p type="main">

<s><emph type="bold"/>Aggiunti Niccol&ograve;,<emph.end type="bold"/> discepolo di Galileo 163, sue notabili esperienze e ragioni della dilatazione lineare <lb/>de'solidi al calore 288. </s></p><p type="main">

<s><emph type="bold"/>Alberti Leon Battista,<emph.end type="bold"/> sua scienza sperimentale 72. </s></p><p type="main">

<s><emph type="bold"/>Alighieri Dante,<emph.end type="bold"/> sua Filosofia naturale 69. </s></p><p type="main">

<s><emph type="bold"/>Antonini Daniele<emph.end type="bold"/> fa l'esperienza eroniana del Termometro ad aria 271, propone le lenti paraboliche <lb/>per uso de'canocchiali 371. </s></p><p type="main">

<s><emph type="bold"/>Aproino Paolo<emph.end type="bold"/> pensa al modo di aumentare il suono 513, inventa e descrive il corno acustico 514. </s></p><p type="main">

<s><emph type="bold"/>Archimede,<emph.end type="bold"/> sua Fisica 35, suo modo di misurare l'ampiezza della pupilla nelle osservazioni celesti 410. </s></p><p type="main">

<s><emph type="bold"/>Areometro,<emph.end type="bold"/> sua invenzione 524, sua prima forma di caraffa galleggiante datale da Galileo 525. </s></p><p type="main">

<s><emph type="bold"/>Aristotile,<emph.end type="bold"/> sua Filosofia 31. </s></p><p type="main">

<s><emph type="bold"/>Aristotelismo,<emph.end type="bold"/> come s'introducesse nella societ&agrave; Cristiana 40. </s></p><p type="main">

<s><emph type="bold"/>Armati Salvino<emph.end type="bold"/> inventore degli occhiali 500. </s></p><p type="main">

<s><emph type="bold"/>Arrighetti Andrea,<emph.end type="bold"/> discepolo di Galileo, 168. </s></p><p type="main">

<s><emph type="bold"/>Bacone Francesco,<emph.end type="bold"/> tenta nella scienza una nuova e grande Instaurazione 113. </s></p><p type="main">

<s><emph type="bold"/>Baliani Giovan Batista,<emph.end type="bold"/> sue relazioni con Galileo 148, fa la prima esperienza dell'acqua, che ne'canali <lb/>non si sostiene pi&ugrave; su che ad una determinata altezza 437, attribuisce il maraviglioso effetto al <lb/>peso dell'aria esterna 439, rammemora, a'tempi del Torricelli, le sue prime e antiche idee in&shy;<lb/>torno al modo di superare la forza del vacuo 451. </s></p><p type="main">

<s><emph type="bold"/>Barometro,<emph.end type="bold"/> come dai fenomeni di fosforescenza osservati in lui avesse i principii la Scienza elet&shy;<lb/>trica 470. </s></p><p type="main">

<s><emph type="bold"/>Bartoli Giovanni,<emph.end type="bold"/> sue relazioni intorno a ci&ograve; che dicevasi in Venezia dell'inventore del canocchiale 350. </s></p><p type="main">

<s><emph type="bold"/>Beccaria Giovan Batista,<emph.end type="bold"/> sue teorie elettriche 242. </s></p><p type="main">

<s><emph type="bold"/>Benedetti Giovan Batista,<emph.end type="bold"/> suo Libro delle <emph type="italics"/>Speculazioni<emph.end type="italics"/> esaminato 102, maestro a Galileo 131, &egrave; il <lb/>primo a fare e a rendere la ragione dell'esperienza eroniana applicata poi ad uso di Termome&shy;<lb/>tro 278, perfeziona la Camera oscura, e il Porta la divulga 368. </s></p><p type="main">

<s><emph type="bold"/>Bennet,<emph.end type="bold"/> sua invenzione dell'Elettroscopio a foglia di oro 482. </s></p><p type="main">

<s><emph type="bold"/>Beriguardi Claudio,<emph.end type="bold"/> come s'ingannassero il Targioni e l'Antinori in crederlo primo autore dell'espe&shy;<lb/>rienza torricelliana 450. </s></p><p type="main">

<s><emph type="bold"/>Bernoulli Giovanni,<emph.end type="bold"/> osserva e sperimenta intorno alla fosforescenza mercuriale de'Barometri 471. </s></p><p type="main">

<s><emph type="bold"/>Binoculo,<emph.end type="bold"/> non &egrave; invenzione del Galileo 424. </s></p><p type="main">

<s><emph type="bold"/>Borelli Gian Alfonso,<emph.end type="bold"/> accademico del Cimento 189, seguita ad appartenere e a collaborare nell'Acca&shy;<lb/>demia, anco dopo tornato a Messina 202, origine dell'inimicizia di lui col Viviani 296, non com&shy;<lb/>prende il fatto della cos&igrave; detta <emph type="italics"/>simpatia de'pendoli<emph.end type="italics"/> 319, nota sottilmente i difetti della livella ad <lb/>acqua 421, illustra l'esperienza torricelliana 461, forma semplicissima data da lui a'tubi torricel&shy;<lb/>liani, per uso di Barometro 465. </s></p><p type="main">

<s><emph type="bold"/>Bottiglia di Leyda,<emph.end type="bold"/> come e quando fosse stata scoperta 475. </s></p><pb xlink:href="020/01/553.jpg" pagenum="534"/><p type="main">

<s><emph type="bold"/>Boyle Roberto,<emph.end type="bold"/> sua Macchina pneumatica e come facessero uso di lei gli Accademici del Cimento 210, <lb/>ripete l'esperienza del manticetto, che si gonfia via via nel salire un monte 445, perfeziona la <lb/>Macchina pneumatica 446, come s'accorgesse della variabilit&agrave; della pressione ammosferica 464, <lb/>primo costruttore del Barometro portatile 466. </s></p><p type="main">

<s><emph type="bold"/>Boulliaud Ismaele,<emph.end type="bold"/> intermediario fra il principe Leopoldo de'Medici e l'Huyghens nella vertenza <lb/>concernente l'invenzione dell'Orologio a pendolo 315. </s></p><p type="main">

<s><emph type="bold"/>Bruno Giordano,<emph.end type="bold"/> giudizio de'meriti di lui nelle scienze sperimentali 59. </s></p><p type="main">

<s><emph type="bold"/>Camera oscura,<emph.end type="bold"/> inventore e perfezionatore di essa 367. </s></p><p type="main">

<s><emph type="bold"/>Campanella Tommaso,<emph.end type="bold"/> sua Fisiologia 58. </s></p><p type="main">

<s><emph type="bold"/>Campani Giuseppe,<emph.end type="bold"/> suo tornio per lavorare le lenti da Canocchiali 395, suo nuovo Canocchiale de&shy;<lb/>scritto 396. </s></p><p type="main">

<s><emph type="bold"/>Campani Matteo,<emph.end type="bold"/> da opera con suo fratello Giuseppe a perfezionare gli Orologi per gli usi nautici 336. </s></p><p type="main">

<s><emph type="bold"/>Canocchiale<emph.end type="bold"/> astronomico speculato dal Keplero, eseguito dal Fontana 362, a due lenti, una concava e <lb/>l'altra convessa, perch&egrave; dicasi <emph type="italics"/>galileiano<emph.end type="italics"/> 372. </s></p><p type="main">

<s><emph type="bold"/>Capua (da) Leonardo,<emph.end type="bold"/> accademico napoletano 206. </s></p><p type="main">

<s><emph type="bold"/>Carafaggi Cesare,<emph.end type="bold"/> primo a tentar la costruzione de'Telescopii a riflessione 400. </s></p><p type="main">

<s><emph type="bold"/>Cardano Girolamo,<emph.end type="bold"/> sue opposizioni contro Aristotile 47, conosce il principio d'inerzia 48, ha sentore <lb/>delle tra&igrave;ettorie paraboliche, ivi, e della propriet&agrave; de'pendoli 49, veri principii idraulici professati <lb/>da lui 50. Confuta la dottrina della fuga del vacuo 435. </s></p><p type="main">

<s><emph type="bold"/>Cartesio Renato,<emph.end type="bold"/> indole della sua Filosofia sperimentale 151, sua teoria del Canocchiale 369. </s></p><p type="main">

<s><emph type="bold"/>Cassegrain,<emph.end type="bold"/> suo Telescopio a riflessione descritto 403. </s></p><p type="main">

<s><emph type="bold"/>Cassini Gian Domenico<emph.end type="bold"/> non fu accademico del Cimento 194. </s></p><p type="main">

<s><emph type="bold"/>Castelli Benedetto,<emph.end type="bold"/> primo discepolo di Galileo 158, riferisce l'esperienza eroniana del Termometro <lb/>ad aria fatta da Galileo 273. </s></p><p type="main">

<s><emph type="bold"/>Cavalieri Bonaventura,<emph.end type="bold"/> uno de'primi e pi&ugrave; illustri discepoli di Galileo 159, interpetra un passo oscuro <lb/>del Porta relativo allo Specchio ustorio 354, dimostra l'inefficacia delle lenti paraboliche sostituite <lb/>alle sferiche ne'tubi de'Canocchiali 371, sua speculazione intorno al comporre insieme le lenti <lb/>con gli specchi nei Telescopi 401. </s></p><p type="main">

<s><emph type="bold"/>Cavallo Tiberio,<emph.end type="bold"/> suo Elettroscopio a boccetta 480. </s></p><p type="main">

<s><emph type="bold"/>Cesalpino Andrea,<emph.end type="bold"/> carattere della sua Filosofia sperimentale 46. </s></p><p type="main">

<s><emph type="bold"/>Cicloide<emph.end type="bold"/> applicata all'isocronismo del pendolo negli Orologi 323. </s></p><p type="main">

<s><emph type="bold"/>Cigoli Lodovico,<emph.end type="bold"/> suo Trattato manoscritto di Prospettiva 147. </s></p><p type="main">

<s><emph type="bold"/>Cognizione<emph.end type="bold"/> della forma precede a quella della materia 29. </s></p><p type="main">

<s><emph type="bold"/>Cognizioni,<emph.end type="bold"/> primo loro apparire osservato ne'bambini 27. </s></p><p type="main">

<s><emph type="bold"/>Colombo Cristoforo,<emph.end type="bold"/> sue osservazioni naturali 73. </s></p><p type="main">

<s><emph type="bold"/>Colombo Realdo,<emph.end type="bold"/> esame del suo libro <emph type="italics"/>De re anatomica<emph.end type="italics"/> 86. </s></p><p type="main">

<s><emph type="bold"/>Colonna Fabio,<emph.end type="bold"/> accenna al primo <emph type="italics"/>Eliostata<emph.end type="italics"/> 430. </s></p><p type="main">

<s><emph type="bold"/>Compensazioni<emph.end type="bold"/> agli effetti prodotti dal calore ne'pendoli degli orologi 337. </s></p><p type="main">

<s><emph type="bold"/>Condensatori elettrici<emph.end type="bold"/> da chi costruiti 476, condensatori del Volta 478. </s></p><p type="main">

<s><emph type="bold"/>Conduttori elettrici<emph.end type="bold"/> primi scoperti 473. </s></p><p type="main">

<s><emph type="bold"/>Copernico Niccol&ograve;<emph.end type="bold"/> filosofo platonico 63. </s></p><p type="main">

<s><emph type="bold"/>Cordicella<emph.end type="bold"/> tesa ad uso di Micrometro 408. </s></p><p type="main">

<s><emph type="bold"/>Cornelio Tommaso<emph.end type="bold"/> accademico napoletano 207, da un'importante notizia relativa a ci&ograve; che dette oc&shy;<lb/>casione allo sperimento torricelliano 454. </s></p><p type="main">

<s><emph type="bold"/>Corobate<emph.end type="bold"/> vitruviano descritto 416. </s></p><p type="main">

<s><emph type="bold"/>Cotyla,<emph.end type="bold"/> orologio a pendolo del Santorio 302. </s></p><p type="main">

<s><emph type="bold"/>Cronometro<emph.end type="bold"/> degli Accademici del Cimento descritto 326. </s></p><p type="main">

<s><emph type="bold"/>Darwin Carlo,<emph.end type="bold"/> sua nuova Filosofia naturale 256. </s></p><p type="main">

<s><emph type="bold"/>Daviso Urbano,<emph.end type="bold"/> descrizione del suo Termometro a mostra 297. </s></p><p type="main">

<s><emph type="bold"/>De Dominis Marcantonio,<emph.end type="bold"/> suo Trattato diottrico e sue teorie del Canocchiale 360, come spieghi il modo <lb/>dell'operar gli occhiali nella vista 502. </s></p><p type="main">

<s><emph type="bold"/>Del Buono Candido<emph.end type="bold"/> s'incontra coll'Huyghens nella invenzione del Micrometro 413. </s></p><p type="main">

<s><emph type="bold"/>Diaframmi,<emph.end type="bold"/> loro usi ne'Canocchiali 431. </s></p><p type="main">

<s><emph type="bold"/>Divini Eustachio<emph.end type="bold"/> rivaleggia col Campani nella fabbrica de'Canocchiali 397, suo reticolo applicato ad <lb/>uso di Micrometro 414. </s></p><p type="main">

<s><emph type="bold"/>Drebbel Cornelio<emph.end type="bold"/> fa l'esperienza eroniana del Termometro ad aria 272. </s></p><p type="main">

<s><emph type="bold"/>Elettroforo perpetuo<emph.end type="bold"/> inventato e descritto dal Volta 477. </s></p><p type="main">

<s><gap/></s></p><pb xlink:href="020/01/554.jpg" pagenum="535"/><p type="main">

<s><emph type="bold"/>Elioscopio<emph.end type="bold"/> inventato dallo Scheiner 429. </s></p><p type="main">

<s><emph type="bold"/>Eliostata<emph.end type="bold"/> immaginato e proposto dal Borelli 430. </s></p><p type="main">

<s><emph type="bold"/>Esperienze<emph.end type="bold"/> delle membra animali fosforescenti nel vuoto 201, del Torricelli coll'argento vivo, e sua <lb/>grande efficacia ne'progressi delle scienze sperimentali 173 seg. </s></p><p type="main">

<s><emph type="bold"/>Fabry Onorato,<emph.end type="bold"/> corrispondente dell'Accademia del Cimento 213, tenta appropriarsi l'esperimento tor&shy;<lb/>ricelliano 449. </s></p><p type="main">

<s><emph type="bold"/>Falloppio Gabriele<emph.end type="bold"/> anatomico 90. </s></p><p type="main">

<s><emph type="bold"/>Filosofia scolastica,<emph.end type="bold"/> carattere distintivo di lei 41. </s></p><p type="main">

<s><emph type="bold"/>Folli Francesco<emph.end type="bold"/> come inventasse la sua Mostra umidaria 518. </s></p><p type="main">

<s><emph type="bold"/>Fontaua Francesco,<emph.end type="bold"/> suoi Canocchiali 376. </s></p><p type="main">

<s><emph type="bold"/>Fracastoro Girolamo,<emph.end type="bold"/> carattere della sua Filosofia sperimentale 44. </s></p><p type="main">

<s><emph type="bold"/>Galilei Galileo<emph.end type="bold"/> risolve un problema di Astronomia dantesca 124, si contradice in alcune sue dottrine 133, <lb/>come si portasse rispetto alla dimostrazione delle traiettorie paraboliche col Cavalieri 135, non fu <lb/>il primo a dimostrare il Teorema della composizion delle forze 137, profess&ograve; a principio, e poi du&shy;<lb/>bit&ograve; di ammettere le velocit&agrave; virtuali 138, sue savie istituzioni di scienza 144, suoi meriti veri 145, <lb/>prevale in lui l'astrazione matematica all'esperienza de'fatti 170, non e inventor del Termome&shy;<lb/>tro 275, pretende all'invenzione del Canocchiale 347, sua teoria del Canocchiale 357, suoi diversi <lb/>strumenti inventati ad uso di Micrometro 413, a qual causa attribuisse il non potersi sostener <lb/>l'acqua nelle pompe pi&ugrave; su che ad una determinata altezza 438, 441. </s></p><p type="main">

<s><emph type="bold"/>Galleggianti<emph.end type="bold"/> proposti dal Montanari per correggere gli errori della livella a acqua 422. </s></p><p type="main">

<s><emph type="bold"/>Galvani Luigi<emph.end type="bold"/> incomincia a narrar la storia della sua scoperta dell'elettricit&agrave; animale 484. </s></p><p type="main">

<s><emph type="bold"/>Geometria,<emph.end type="bold"/> prima scienza appresa dall'uomo 28. </s></p><p type="main">

<s><emph type="bold"/>Gilberto Guglielmo<emph.end type="bold"/> sua arte sperimentale 156. </s></p><p type="main">

<s><emph type="bold"/>Giocondo Giovanni<emph.end type="bold"/> aveva, secondo riferisce lo Scaligero, dimostrata la forza della percossa 52. </s></p><p type="main">

<s><emph type="bold"/>Grimaldi Francesco Maria,<emph.end type="bold"/> suo Trattato <emph type="italics"/>De Lumine<emph.end type="italics"/> 214. </s></p><p type="main">

<s><emph type="bold"/>Guglielmini Domenico,<emph.end type="bold"/> relazioni fra le dottrine di lui e le neutoniane 236. </s></p><p type="main">

<s><emph type="bold"/>Guericke Ottone<emph.end type="bold"/> inventor della Macchina pneumatica 446. </s></p><p type="main">

<s><emph type="bold"/>Harvey Guglielmo<emph.end type="bold"/> sua acutezza nello speculare 1<gap/>6. </s></p><p type="main">

<s><emph type="bold"/>Hawksbee<emph.end type="bold"/> d&agrave; l'ultima perfezione alla Macchina pneumatica 447, ritrova che la fosforescenza de'Baro&shy;<lb/>metri &egrave; dovuta alla confricazione del mercurio sopra il vetro del tubo 471, cava scintille di foco <lb/>elettrico da un globo di vetro girato attorno 472. </s></p><p type="main">

<s><emph type="bold"/>Hevelio,<emph.end type="bold"/> suoi diafranuni specialmente accomodati alle osservazioni solari 432. </s></p><p type="main">

<s><emph type="bold"/>Horologium,<emph.end type="bold"/> prima invenzione e descrizione dell'Huyghens 314. </s></p><p type="main">

<s><emph type="bold"/>Huyghens Cristiano<emph.end type="bold"/> ripete l'esperienza boileiana del sostenersi l'acqua ne'cannelli stretti sopra il pro&shy;<lb/>prio naturale livello, anche nel vuoto 229, che ne dice dell'Inventore del Canocchiale 345, sua teoria <lb/>dottrica del Canocchiale 370, suo modo di costruire gli oculari per renderli acromatici 392, suo Mi&shy;<lb/>crometro descritto 413, suoi speciali Diaframmi per l'osservazion delle stelle 433. </s></p><p type="main">

<s><emph type="bold"/>Igrometro,<emph.end type="bold"/> sue prime invenzioni 515, Igrometro e corda 516, a mostra 517, Igrometro fiorentino; d'onde <lb/>avesse occasione 517, Igrometro ad avena 522, Igrometro elettrico 523. </s></p><p type="main">

<s><emph type="bold"/>Imperato Ferrante,<emph.end type="bold"/> sua Historia naturale 96, esame di essa 100. </s></p><p type="main">

<s><emph type="bold"/>Imperiali Bartolommeo<emph.end type="bold"/> interpetra un passo oscuro del Porta relativo al Canocchiale 353. </s></p><p type="main">

<s><emph type="bold"/>Keplero Giovanni,<emph.end type="bold"/> sue opinioni intorno all'inventore del Canocchiale 344, suoi Teoremi relativi alle <lb/>immagini rappresentate dalle lenti 361; sue teorie del Canocchiale 362, come pensi, sull'esempio <lb/>di Archimede, ad emendare la visione viziata nelle osservazioni celesti 411, storiella curiosa a pro&shy;<lb/>posito del Binoccolo 425, ammette, contro l'opinione comune, il peso dell'aria 436. </s></p><p type="main">

<s><emph type="bold"/>La Galla Giulio Cesare<emph.end type="bold"/> narra come fosse inventato il Canocchiale 343. </s></p><p type="main">

<s><emph type="bold"/>Lettere torricelliane<emph.end type="bold"/> sull'esperienza dell'argento vivo 452. </s></p><p type="main">

<s><emph type="bold"/>Lincei<emph.end type="bold"/> (Accademia de') fini e frutti della sua istituzione 117. </s></p><p type="main">

<s><emph type="bold"/>Liquidi,<emph.end type="bold"/> ragioni del Noel e del Pacquet del loro dilatarsi per effetto del calore 287. </s></p><p type="main">

<s><emph type="bold"/>Livella ad acqua<emph.end type="bold"/> descritta 419, Livella diottrica descritta 420, Livella a bolla d'aria 422. </s></p><p type="main">

<s><emph type="bold"/>Macchina<emph.end type="bold"/> pneumatica 446, Macchina elettrica di Lipsia descritta da G. M. </s>

<s>Della Torre 474. </s></p><p type="main">

<s><emph type="bold"/>Magalotti Lorenzo<emph.end type="bold"/> accademico e segretario dell'Accademia del Cimento 197. </s></p><p type="main">

<s><emph type="bold"/>Magiotti Raffaello<emph.end type="bold"/> collaboratore al Torricelli nelle esperienze del vuoto 176. </s></p><pb xlink:href="020/01/555.jpg" pagenum="536"/><p type="main">

<s><emph type="bold"/>Magno Valeriano<emph.end type="bold"/> si fa autore dell'esperienza torricelliana dell'argento vivo 418. </s></p><p type="main">

<s><emph type="bold"/>Malpighi Marcello,<emph.end type="bold"/> 200. </s></p><p type="main">

<s><emph type="bold"/>Maurolico Francesco,<emph.end type="bold"/> sue opere di ottica 64, suoi Teoremi diottrici 358, come spieghi l'azione degli <lb/>occhiali in correggere i difetti della vista 503. </s></p><p type="main">

<s><emph type="bold"/>Medici Ferdinando II,<emph.end type="bold"/> Granduca di Toscana, sua curiosit&agrave; per gli studii sperimentali 186. </s></p><p type="main">

<s><emph type="bold"/>Medici Leopoldo,<emph.end type="bold"/> principe di Toscana, suo amore per gli studii sperimentali 186, sua autorit&agrave; di go&shy;<lb/>verno nel principato accademico 215. </s></p><p type="main">

<s><emph type="bold"/>Mersenno Marino,<emph.end type="bold"/> suoi mali portamenti verso gli scienziati italiani 211, diffonde in Francia la notizia <lb/>dello sperimento torricelliano 443. </s></p><p type="main">

<s><emph type="bold"/>Michelini Famiano<emph.end type="bold"/> discepolo di Galileo 162. </s></p><p type="main">

<s><emph type="bold"/>Micrometro<emph.end type="bold"/> primo di Galileo 407. </s></p><p type="main">

<s><emph type="bold"/>Microscopii<emph.end type="bold"/> olandesi 508, loro fabbrica descritta dall'Huyghens 509, microscopii della perlina come <lb/>fossero costruiti dal Torricelli, ivi. </s></p><p type="main">

<s><emph type="bold"/>Microscopio<emph.end type="bold"/> composto &egrave; invenzione di Francesco Fontana 510, Microscopio catottrico 511. </s></p><p type="main">

<s><emph type="bold"/>Montanari Geminiano<emph.end type="bold"/> accademico del Cimento 204, suo reticolo micrometrico descritto 414, rivendic&ograve; <lb/>a s&egrave; sul p. </s>

<s>Lana l'invenzione del Micrometro a reticolo 416, inventore della Livella diottrica 420. </s></p><p type="main">

<s><emph type="bold"/>Moro Lazzero,<emph.end type="bold"/> suo sistema geolo<gap/>co 252. </s></p><p type="main">

<s><emph type="bold"/>Nardi Antonio<emph.end type="bold"/> discepolo di Galileo 167. </s></p><p type="main">

<s><emph type="bold"/>Newton Isacco,<emph.end type="bold"/> metodo della sua Filosofia 220, influsso efficace che sulla Filosofia di lui ebbero gli <lb/>Italiani 224, paragonato col De Dominis nella teoria del flusso marino 232, importanza delle sue <lb/><emph type="italics"/>Questioni<emph.end type="italics"/> 234, descrive il suo Telescopio a riflessione 402, diffonde la notizia dalle scoperte elet&shy;<lb/>triche dell'Hawksbee 472. </s></p><p type="main">

<s><emph type="bold"/>Noferi Cosimo<emph.end type="bold"/> discepolo di Galileo 166. </s></p><p type="main">

<s><emph type="bold"/>Nollet,<emph.end type="bold"/> suoi perfezionamenti introdotti nella macchina elettrica 474. </s></p><p type="main">

<s><emph type="bold"/>Novelli Antonio<emph.end type="bold"/> fabbrica canocchiali 381, sua emulazione col Torricelli 382. </s></p><p type="main">

<s><emph type="bold"/>Occhiale<emph.end type="bold"/> cos&igrave; detto di moltiplicazione venuto d'oltremonti, poco dopo che Galileo avea divulgato il suo <lb/>occhialino 508. </s></p><p type="main">

<s><emph type="bold"/>Occhiall,<emph.end type="bold"/> occasione del loro ritrovato, secondo Realdo Colombo 87. </s></p><p type="main">

<s><emph type="bold"/>Occhialino,<emph.end type="bold"/> microscopio semplice di Galileo 506. </s></p><p type="main">

<s><emph type="bold"/>Orologi da tasca<emph.end type="bold"/> come e da chi inventati 337. </s></p><p type="main">

<s><emph type="bold"/>Orologio a pendolo<emph.end type="bold"/> primo progetto di Galileo 309, orologio ad acqua dello stesso Galileo 311. </s></p><p type="main">

<s><emph type="bold"/>Oscillazione,<emph.end type="bold"/> suo centro ne'pendoli applicati all'orologio 330. </s></p><p type="main">

<s><emph type="bold"/>Pascal Biagio,<emph.end type="bold"/> dimestra il vuoto terricelliano 444, fa l'esperienza del vuoto nel vuoto, e sul Puy de <lb/>Domme 445. </s></p><p type="main">

<s><emph type="bold"/>Patrizio Francesco<emph.end type="bold"/> insorge centro Aristotile 55, suoi sistemi filosofici 57. </s></p><p type="main">

<s><emph type="bold"/>Pendoli,<emph.end type="bold"/> strumento inventato dai Viviani per aggiustare la loro lunghezza ai tempi 328. </s></p><p type="main">

<s><emph type="bold"/>Pendolo conico<emph.end type="bold"/> applicato agli Orologi 321, leggi del pendolo circolare scoperte da Galileo 304, progetti <lb/>di applicarlo agli Orologi a torre 312. </s></p><p type="main">

<s><emph type="bold"/>Peripato,<emph.end type="bold"/> suo carattere filosofico 36. </s></p><p type="main">

<s><emph type="bold"/>Petit<emph.end type="bold"/> descrive il Telescopio calottrico 491. </s></p><p type="main">

<s><emph type="bold"/>Pisani Ottavio<emph.end type="bold"/> primo costruttor del Binoculo 426. </s></p><p type="main">

<s><emph type="bold"/>Platone,<emph.end type="bold"/> sua Filosofia 30. </s></p><p type="main">

<s><emph type="bold"/>Platonismo,<emph.end type="bold"/> come s'introducesse nella Societ&agrave; cristiana 39. </s></p><p type="main">

<s><emph type="bold"/>Pluviometro<emph.end type="bold"/> sua prima origine ed uso fattone dal Castelli 526. </s></p><p type="main">

<s><emph type="bold"/>Polemoscopio<emph.end type="bold"/> 406. </s></p><p type="main">

<s><emph type="bold"/>Porta Glovan Battista,<emph.end type="bold"/> sue opere di Filosofia sperimentale 92, suo trattato delle Rifrazioni 95, esame <lb/>del suo libro degli Spiritali 97, esame del suo trattato delle Rifrazioni 98, fa l'esperienza eroniana, <lb/>d'ond'ebbe origine il Termometro ad aria 270, suoi teoremi intorno alla propriet&agrave; delle lenti ri&shy;<lb/>spetto alle immagini 359, inventore della livella ad acqua 419, primo a investigare il modo come <lb/>sulla vista operano gli occhiali 502, propone uno strumento da udir da lontano 512. </s></p><p type="main">

<s><emph type="bold"/>Portaluce<emph.end type="bold"/> di Leonardo da Vinci 341. </s></p><p type="main">

<s><emph type="bold"/>Porzio Lucantonio<emph.end type="bold"/> accademico napoletano 206. </s></p><p type="main">

<s><emph type="bold"/>Pulsilogio<emph.end type="bold"/> e suo inventore 300. </s></p><p type="main">

<s><emph type="bold"/>Pupilla,<emph.end type="bold"/> misura di lei nelle osservazioni celesti 409. </s></p><p type="main">

<s><emph type="bold"/>Ravaisson Mollien<emph.end type="bold"/> d&agrave; opera a pubblicare i manoscritti vinciani 82, di un passo vinciano da lui in&shy;<lb/>terpetrato 126. </s></p><p type="main">

<s><emph type="bold"/>Razionalisti,<emph.end type="bold"/> loro metodi 60, loro meriti 61. </s></p><pb xlink:href="020/01/556.jpg" pagenum="537"/><p type="main">

<s><emph type="bold"/>Redi Francesco,<emph.end type="bold"/> accademico del Cimento 199. </s></p><p type="main">

<s><emph type="bold"/>Renieri Vincenzio<emph.end type="bold"/> discepolo di Galileo 160, sua osservazione sul moto de'pendoli 308, suo metodo di <lb/>misurare il diametro della pupilla 409. </s></p><p type="main">

<s><emph type="bold"/>Rheita Anton Maria<emph.end type="bold"/> compone il Binoculo di due Canocchiali astronomici accoppiati 427. </s></p><p type="main">

<s><emph type="bold"/>Riccioli Giovan Batista<emph.end type="bold"/> pretende di riformare la scienza 214. </s></p><p type="main">

<s><emph type="bold"/>Richter Giovan Paolo<emph.end type="bold"/> pubblica i manoscritti vinciani 83. </s></p><p type="main">

<s><emph type="bold"/>Rinaldini Carlo<emph.end type="bold"/> accademico del Cimento 192, sue opposizioni contro la ragione di alcuni effetti ope&shy;<lb/>rati dal calore nel dilatare i corpi 294. </s></p><p type="main">

<s><emph type="bold"/>Rossetti Donato<emph.end type="bold"/> accademico del Cimento 204. </s></p><p type="main">

<s><emph type="bold"/>Saggi<emph.end type="bold"/> di naturali esperienze fatte nell'Accademia del Cimento, quando e come fossero pubblicati 195. </s></p><p type="main">

<s><emph type="bold"/>Sagredo Giovan Francesco<emph.end type="bold"/> perfeziona il Termometro 277. </s></p><p type="main">

<s><emph type="bold"/>Salto<emph.end type="bold"/> dell'immersione ne'liquidi posti a ghiacciare e sue ragioni 292. </s></p><p type="main">

<s><emph type="bold"/>Santorio Santorre<emph.end type="bold"/> fisico sperimentale 107, inventor del Termometro ad aria 266, primo ad applicare <lb/>il pendolo alla misura del tempo 305, varie maniere d'Igrometri inventati da lui 516, 517. </s></p><p type="main">

<s><emph type="bold"/>Sarpi Paolo,<emph.end type="bold"/> sua scienza naturale 109, qual parte avesse nelle osservazioni celesti pubblicate da Ga&shy;<lb/>lileo nel suo Nunzio Sidereo 114, ha il primo concetto di uno strumento da veder di lontano 351. </s></p><p type="main">

<s><emph type="bold"/>Scaligero Giuseppe<emph.end type="bold"/> dimostra sperimentalmente il principio d'inerzia 51, ammette la luce diffondersi <lb/>in tempo, e il vacuo come condizione del moto 52, 435. </s></p><p type="main">

<s><emph type="bold"/>Scheiner Cristoforo,<emph.end type="bold"/> sua teoria del Canocchiale 367, descrive il modo di colorire le lenti, ad uso di <lb/>Elioscopio 429. </s></p><p type="main">

<s><emph type="bold"/>Schott Gaspero<emph.end type="bold"/> narra la storia dell'esperienza del vuoto fatta in Roma dal Berti 442. </s></p><p type="main">

<s><emph type="bold"/>Sinclaro Giorgio,<emph.end type="bold"/> suo Orologio a pendolo descritto, 320, si crede essere stato il primo inventore del <lb/>Baroscopio 464. </s></p><p type="main">

<s><emph type="bold"/>Sirturo Girolamo<emph.end type="bold"/> narra come fosse inventato il Canocchiale 342, costruisee egli stesso Canocchiali 375. </s></p><p type="main">

<s><emph type="bold"/>Socrate,<emph.end type="bold"/> sua filosofia 30. </s></p><p type="main">

<s><emph type="bold"/>Spina Alessandro<emph.end type="bold"/> inventor degli occhiali 501. </s></p><p type="main">

<s><emph type="bold"/>Stenone Niccol&ograve;<emph.end type="bold"/> accademico del Cimento 199. </s></p><p type="main">

<s><emph type="bold"/>Stevino Simeone,<emph.end type="bold"/> paradosso idrostatico di lui appropriatosi da Galileo 132. </s></p><p type="main">

<s><emph type="bold"/>Tarde Giovanni,<emph.end type="bold"/> sua teoria del Canocchiale 364. </s></p><p type="main">

<s><emph type="bold"/>Tartaglia Niccol&ograve;<emph.end type="bold"/> 53. </s></p><p type="main">

<s><emph type="bold"/>Telegrafo<emph.end type="bold"/> a galvanometro divinato dal Porta 95. </s></p><p type="main">

<s><emph type="bold"/>Telesio Bernardino,<emph.end type="bold"/> sua filosofia 56, ammette che si possa dare il vacuo in natura, e che sia supe&shy;<lb/>rabile da forza finita 436. </s></p><p type="main">

<s><emph type="bold"/>Termometro<emph.end type="bold"/> applicato a render sensibile il calore de'raggi lunari 268, a liquido, quando fu inven&shy;<lb/>tato 281. </s></p><p type="main">

<s><emph type="bold"/>Termostatici,<emph.end type="bold"/> problemi proposti dal Granduca Ferdinando II a risolvere a varii scienziati, 457. </s></p><p type="main">

<s><emph type="bold"/>Thevenot Melchisedec<emph.end type="bold"/> inventore della Livella a bolla d'aria 423. </s></p><p type="main">

<s><emph type="bold"/>Torpedine,<emph.end type="bold"/> come si spiegasse il modo dell'operare del suo organo elettrico 494. </s></p><p type="main">

<s><emph type="bold"/>Torricelli Evangelista<emph.end type="bold"/> discepolo di Galileo 179, inventore del Termometro a liquido 283, suoi Canoc&shy;<lb/>chiali 379, sua emulazione col Fontana 380, suo segreto per lavorare le lenti de'Canocchiali 383, <lb/>suoi avvertimenti per la buona fabbrica de'cristalli 386, qual fosse la scienza che egli aveva delle <lb/>Rifrazioni 389, come fosse poco esercitato nell'Astronomia 390, come si accorgesse che la pressione <lb/>ammosferica variava da un giorno all'altro 456, risponde alle obiezioni, fattegli dal Ricci, contro <lb/>le ragioni del sostenersi l'argento vivo nello strumento 460, in che trovasse difficolt&agrave; d'applicar <lb/>l'esperienza dell'argento vivo ad uso di Barometro 463, primo inventore dell'Igrometro a con&shy;<lb/>densazione 517, Areometri da lui inventati 525. </s></p><p type="main">

<s><emph type="bold"/>Tradizioni,<emph.end type="bold"/> loro necessit&agrave; 26. </s></p><p type="main">

<s><emph type="bold"/>Treffier Filippo<emph.end type="bold"/> pensa a costruire e a migliorare l'Igrometro del Folli 520. </s></p><p type="main">

<s><emph type="bold"/>Vesalio Andrea<emph.end type="bold"/> anatomico 85. </s></p><p type="main">

<s><emph type="bold"/>Vespucci Amerigo<emph.end type="bold"/> osservatore de'fatti naturali 66. </s></p><p type="main">

<s><emph type="bold"/>Vinci (da) Leonardo,<emph.end type="bold"/> sue osservazioni naturali 77, suo trattato d'idraulica 80, suoi manoscritti 82. </s></p><p type="main">

<s><emph type="bold"/>Virgula<emph.end type="bold"/> ugeniana ad uso di Micrometro 413. </s></p><p type="main">

<s><emph type="bold"/>Visione<emph.end type="bold"/> viziata nelle osservazioni astronomiche 411. </s></p><p type="main">

<s><emph type="bold"/>Viviani Vincenzio<emph.end type="bold"/> discepolo di Galileo 183, accademico del Cimento 191, sue esperienze del dilatarsi <lb/>le corde metalliche al calore 294, origine delle inimicizie di lui col Borelli 296, studia il fatto cu&shy;<lb/>rioso della simpatia de'pendoli 319, qual opera dasse alla fabbrica de'Canocchiali 391, spiega il <lb/><gap/> Treffler l'Igrome-<pb xlink:href="020/01/557.jpg" pagenum="538"/>tro del Folli 519, costruisce un Igrometro semplicissimo, e studia le leggi dell'allungarsi della <lb/>corda e dell'abbassarsi del peso che la tira, per digradare la scala igrometrica 521, inventa un <lb/>areometro simile a quello del Baum&egrave; 525, e la stadera de'liquidi 526. </s></p><p type="main">

<s><emph type="bold"/>Volta Alessandro,<emph.end type="bold"/> suoi principii intorno alla scienza elettrica 243, perfeziona l'Elettroscopio di Tiberio <lb/>Cavallo, e l'accoppia all'Elettroforo 481, rende comparabile l'Elettrometro a quadrante dell'Hen&shy;<lb/>ley 488, legge il Commentario del Galvani e ne rimane esaltato 487, scopre l'error del Galvani, <lb/>dimostrando che il moto del fluido elettrico si fa dal muscolo al nervo 488, trova che l'azione <lb/>immediata del fluido elettrico &egrave; sui nervi 489, sue insigni esperienze per provar che l'elettricit&agrave; <lb/>irritando direttamente i nervi, produce le sensaxioni, ivi, s'accorge finalmente che l'elettricit&agrave; <lb/>detta animale muove dal contatto di due metalli 490, protesta in faccia all'Aldini che le sue dot&shy;<lb/>trine son diverse da quelle del Galvani 491, sue ulteriori scoperte intorno agli organi produttori <lb/>dell'elettricit&agrave; animale 494, sue prime prove colle coppie metalliche soprapposte, non riuscite 495, <lb/>riesce finalmente a costruire il suo Organo elettrico artificiale, e ne diffonde la notizia 496, pro&shy;<lb/>pone un Igrometro elettrico 523. </s></p><p type="main">

<s><emph type="bold"/>Vo<gap/>sle Is<gap/><emph.end type="bold"/> si crede essere stato il primo inventore dell'Aeroscopio 464. </s></p><p type="main">

<s><emph type="bold"/>Wendel<gap/>n<emph.end type="bold"/> &egrave; il primo a notar le differenze del numero delle vibrazioni, fatte da un medesimo pendolo <lb/>nell'estate e nell'inverno 335. </s></p><pb xlink:href="020/01/558.jpg"/><p type="main">

<s>Finito di stampare in Bologna presso la <lb/>Libreria Editrice Forni nel Gennaio 1970 </s></p><pb xlink:href="020/01/559.jpg"/></chap><chap><p type="main">

<s>350478 Storia Del Metodo Sperimentale Italia </s></p><p type="main">

<s><emph type="center"/>THE SOURCES OF SCIENCE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Editor-in-Chief: Harry Woolf<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Willis K. </s>

<s>Shepard Professor of the History of <lb/>Science, The Johns Hopkins University<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="020/01/560.jpg"/><p type="main">

<s><emph type="center"/><emph type="bold"/><emph type="italics"/>Storia del Metodo <lb/>Sperimentale in Italia<emph.end type="italics"/><emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>by RAFFAELLO CAVERNI <lb/>in Six Volumes<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Volume II<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>THE SOURCES OF SCIENCE, NO. 134<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT CORPORATION <lb/>NEW YORK LONDON 1972<emph.end type="center"/></s></p><pb xlink:href="020/01/561.jpg"/><p type="main">

<s>Reproduced here is the Florence edition of 1891-1900. </s></p><p type="main">

<s><emph type="center"/>Copyright &copy; 1972 by Johnson Reprint Corporation All rights reserved <lb/>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT CORPORATION <lb/>111 Fifth Avenue, New York, N.Y. 10003, U.S.A. <lb/>JOHNSON REPRINT COMPANY LTD.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Shipton Group House, 24/28 Oval Road, London, NW1 7DD, England<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Printed in Italy<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="020/01/562.jpg"/><p type="main">

<s><emph type="center"/>DEL METODO SPERIMENTALE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>APPLICATO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>ALLE SCIENZE FISICHE<emph.end type="center"/><pb xlink:href="020/01/563.jpg"/></s></p><pb xlink:href="020/01/564.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO I.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Della luce diretta e della luce riflessa<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. De'primi e principali cultori dell'Ottica. </s>

<s>&mdash; II. </s>

<s>Della legge fondamentale della luce riflessa. </s>

<s>&mdash; <lb/>III. De'corpi diafani e degli opachi; delle ombre e delle penombre. </s>

<s>&mdash; IV. </s>

<s>Di alcune espe&shy;<lb/>rienze singolari sulle ombre: del passaggio della luce attraverso piccoli fori. </s>

<s>&mdash; V. </s>

<s>Delle leggi <lb/>della intensit&aacute; luminosa. </s>

<s>&mdash; VI. </s>

<s>Della velocit&agrave; della luce. </s>

<s>&mdash; VII. </s>

<s>Delle ipotesi delle ondula&shy;<lb/>zioni eterce e dell'emissione. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Un celebre letterato fiorentino del secolo XVI volendo in una Lezione <lb/>accademica dare a intendere ci&ograve; che si volesse da'Filosofi significar per i <lb/>nomi di riflessione e di rifrazione, a proposito della luce, &ldquo; n&egrave; crediate, di&shy;<lb/>ceva a'suoi uditori, che i Latini e i Greci, cio&egrave; quegli che sanno la lingua <lb/>o greca o latina, le possano intendere quantunque dotti, se prima non istu&shy;<lb/>diano, non solo le discipline matematiche, ma ancora la Filosofia naturale, <lb/>perch&egrave; la Prospettiva, avendo per soggetto il razzo visuale ovvero la linea <lb/>radiosa, che &egrave; il medesimo, &egrave; subalternata parte alle Matematiche rispetto <lb/>alle linee, e parte alla Filosofia naturale, rispetto alla radiosit&agrave; &rdquo; (Lez. </s>

<s>su <lb/>Dante di B. Varchi, Firenze 1841, pag. </s>

<s>300). </s></p><p type="main">

<s>Bench&egrave; qui dicasi le linee e la radiosit&agrave; essere una medesima cosa, fa&shy;<lb/>cendole nonostante parte a discipline cos&igrave; varie, quali sono la Filosofia na&shy;<lb/>turale o la Fisica, e la Matematica, s'insinua una notabile distinzione, che <lb/>s'ammetteva allora fra linea e ci&ograve; che chiamavasi radiosit&agrave;, della qual di&shy;<lb/>stinzione possiamo noi dire del Varchi quel che il Boulliaud diceva del Pa&shy;<lb/>trizio, possiamo cio&egrave; dire essere stata suggerita <emph type="italics"/>opticae disciplinae ignoran&shy;<lb/>tia<emph.end type="italics"/> (De natura lucis, Parisiis 1638, pag. </s>

<s>122), non essendo la radiosit&agrave; nulla <lb/>di reale ma una mera affezione dell'occhio. </s></p><pb xlink:href="020/01/565.jpg" pagenum="8"/><p type="main">

<s>Intanto per&ograve; intravedonsi di qui, non le vestigia sole de'progressi, ma <lb/>e le mosse con gli andamenti varii dell'Ottica da'suoi primi e pi&ugrave; antichi <lb/>principii. </s>

<s>Bench&egrave; infatti quella special distinzione insinuata dal Letterato fio&shy;<lb/>rentino e professata dal Filosofo dalmata, non sia che un inganno, pur &egrave; <lb/>vero che la luce si presenta a studiare obiettivamente o nel raggio, e su&shy;<lb/>biettivamente o nell'occhio. </s>

<s>Quella &egrave; subalternata parte alle Matematiche, <lb/>questa alla Filosofia naturale, o come pi&ugrave; propriamente si direbbe oggid&igrave;, <lb/>alla Fisiologia. </s></p><p type="main">

<s>L'importante soggetto non poteva non eccitar le menti di Platone e <lb/>di Aristotile a filosofarvi attorno, e furono, come nelle altre cose, anco in <lb/>ci&ograve; i due grandi Maestri discordi, per cui presero le loro scuole due varii <lb/>indirizzi, e, conforme alle verit&agrave; istituite e professate o agli errori, riusc&igrave; <lb/>ciascuna a variet&agrave; di progressi. </s>

<s>L'aristotelismo ammettendo che l'occhio <lb/>vede per recezione, secondava i progressi nello studio del fenomeno subiet&shy;<lb/>tivo, per cui la teorica della visione fu efficacemente promossa da'settatori <lb/>di quella scuola. </s>

<s>Il platonismo, tutt'al contrario col professare il principio <lb/>dell'emissione delle specie, rendeva affatto impossibile lo studio del feno&shy;<lb/>meno subiettivo, mentre poi da un'altra parte, dando alla luce propriet&agrave; di <lb/>sostanza, dava efficace impulso a ci&ograve; che concerne gli studii del fenomeno <lb/>obiettivo, d'ond'&egrave; che ai platonici, meglio che a nessun'altro, fu facile in&shy;<lb/>trodursi a speculare intorno alle propriet&agrave; della luce. </s></p><p type="main">

<s>Primi infatti a ridurre in ordine di trattato l'Ottica, o come allora di&shy;<lb/>cevasi la Prospettiva, furono Euclide, principe de'Geometri, ed Eliodoro di <lb/>Larissa, ad Herone il meccanico, e Tolomeo e Teone con parecchi alfri ri&shy;<lb/>masti dimenticati, in cos&igrave; lungo decorrere di tempi, e tutti addetti alla scuola <lb/>di Platone. </s>

<s>Della Prospettiva di Euclide, e di quella di Eliodoro, avemmo <lb/>noi italiani, infin dal secolo XVI, una bella traduzione dottamente commen&shy;<lb/>tata da Egnazio Danti, frate domenicano e Cosmografo del Granduca di To&shy;<lb/>scana. </s>

<s>Il principio platonico, di che s'informano e son radicalmente infette <lb/>le speculazioni de'due greci Autori, si rivela, infin dalle prime pagine, in <lb/>quella Prefazione o <emph type="italics"/>Dichiarazione<emph.end type="italics"/> premessa al Trattato di Euclide, e che <lb/>fu, secondo il Danti, dettata da Teone. </s>

<s>Essendosi gi&agrave; dichiarato che i raggi <lb/>visivi escono dall'occhio, soggiunge quest'altre parole per sua ragione: <lb/>&ldquo; Onde, se i corpi che muovono la vista venissero all'occhio senza che da <lb/>esso si partissero i raggi per trovare la cosa veduta, era mestiero nel fab&shy;<lb/>bricare l'occhio di farlo concavo, acci&ograve; fosse pi&ugrave; comodo a ricevere i simu&shy;<lb/>lacri delle cose vedute. </s>

<s>Ma questo veggiamo essere in verit&agrave; altrimenti, per&shy;<lb/>ch&egrave; piuttosto la figura dell'occhio &egrave; tonda e sferica &rdquo; (La Prospettiva di <lb/>Euclide trad. </s>

<s>da E. Danti, Firenze 1573, pag. </s>

<s>4). Similmente il Larisseo, in <lb/>sull'ultimo del suo Trattatello, che lo stesso Danti traduce in poche pagine <lb/>innumerate, e apposte al Trattato di Euclide, cos&igrave; concludeva: &ldquo; Le quali <lb/>cose stando cos&igrave;, non credo che nessuno si vergogner&agrave; di affermare che la <lb/>luce esca dagli occhi nostri, vedendo cos&igrave; gran somiglianza e convenienza <lb/>che &egrave; fra il veder nostro e il sole. </s>

<s>Laonde il gran Platone disse che, fra <pb xlink:href="020/01/566.jpg" pagenum="9"/>tutti gli strumenti de'sensi, solamente quel del vedere era similissimo al <lb/>sole, e che rappresentava principalmente la figura ed immagine sua. </s>

<s>&rdquo; </s></p><p type="main">

<s>In conformit&agrave; di questi principii i due greci Autori s'intrattengono <lb/>molto volentieri intorno allo esaminar, con finezza mirabile d'osservazione, <lb/>e a spiegare alcuni fatti concernenti la vista, come sarebbe per esempio che <lb/>nessuna cosa visibile si pu&ograve; tutta vedere in un tratto. </s>

<s>Lo dimostra Euclide <lb/>da ci&ograve; che si osserva avvenire in colui, che ha per caso perduto un ago, e <lb/>lo va diligentemente cercando. </s>

<s>&ldquo; Dal che chiaro si scorge, egli dice, che non <lb/>si vedendo quel piccolo corpo, che con tanta attenzione si cerca, non si vede <lb/>manco il luogo ove egli luce. </s>

<s>Onde dall'occhio non sono viste in un tratto <lb/>tutte le parti del luogo ove egli mira, perch&egrave; se ci&ograve; fosse che fissando gli <lb/>occhi vedesse ogni parte del luogo, che attentamente riguarda, vedrebbe <lb/>anche l'ago, che s&igrave; accuratamente cerca, e nondimeno non lo vede &rdquo; (ivi, <lb/>pag. </s>

<s>2). Aggiunge poi a conferma di ci&ograve; l'altro esempio di quei che fissa&shy;<lb/>mente guardano sopra un libro aperto, e non possono nemmeno essi veder <lb/>tutte a un tratto le lettere scritte nel libro. </s>

<s>&ldquo; E spesse volte sforzandosi di <lb/>trovare alcune lettere, che radamente nella detta faccia erano scritte, non <lb/>potevano. </s>

<s>E questo avviene perch&egrave; i raggi visuali non si gettano in un tratto <lb/>a ciascuna lettera del foglio, n&egrave; manco sono insieme uniti e congiunti, ma <lb/>distinti e divisi l'uno dall'altro per qualche spazio ed intervallo, dal che <lb/>nasce che ogni lettera del foglio non si pu&ograve; nel medesimo tempo vedere. </s>

<s><lb/>E di qui si manifesta che non si vede tutto il luogo del foglio &rdquo; (ivi, pag. </s>

<s>3). </s></p><p type="main">

<s>La matematica delle linee per&ograve; e de'raggi luminosi, in questi Autori, <lb/>&egrave; impacciata nel suo progredire dal falso principio dell'emissione, ci&ograve; che <lb/>particolarmente si prova per l'esempio di Tolomeo, il pi&ugrave; compiuto autore <lb/>antico di Prospettiva. </s>

<s>Com'era infatti possibile trattar, con precisione di linee <lb/>matematiche, i raggi che non hanno direzion prefinita e forma certa dalla <lb/>posizione e dalla figura immutabile degli oggetti, ma dalla mobilit&agrave; subiet&shy;<lb/>tiva degli occhi? </s>

<s>Com'era possibile avere in considerazione di linee geome&shy;<lb/>triche que'raggi, che uscendo, al dir di Tolomeo, umidi dagli stessi occhi <lb/>si rasciugavano al contatto dell'aria appena usciti fuori? </s></p><p type="main">

<s>Di qui &egrave; che sebbene i Platonici s'avvantaggiassero sopra gli aristote&shy;<lb/>lici in riguardar la luce com'essere sostanziale, per cui l'Ottica matematica <lb/>riusciva cos&igrave; fondata sopra una realt&agrave; e non sopra vaghe accidentalit&agrave; senza <lb/>subietto; tanto nonostante giov&ograve; agli aristotelici l'aver professato il princi&shy;<lb/>pio della recezion de'raggi visivi nell'occhio, ch'ebbe la Prospettiva ad <lb/>aspettarsi un migliore andamento da costoro, primo de'quali fu l'arabo <lb/>Alhazeno. </s>

<s>Il trattato di lui, che riusc&igrave; disordinato e verboso pi&ugrave; forse per <lb/>colpa di chi ebbe in seguito a maneggiarlo, che per difetto dell'Autore, fu <lb/>nel secolo XIII ordinato, e ridotto in parte a compendio, da un matematico <lb/>pollacco di cognome Ciolek, ma pi&ugrave; volgarmente noto sotto il nome di Vi&shy;<lb/>tellione. </s>

<s>Egli solennemente bandiva dall'Ottica l'errore platonico ripetendo <lb/>la sentenza: <emph type="italics"/>Impossibile est visum rebus visis applicari per radios ab ocu&shy;<lb/>lis egressos.<emph.end type="italics"/> (Norimbergae 1535, pag. </s>

<s>55 v.). Provava egli poi la verit&agrave; della <pb xlink:href="020/01/567.jpg" pagenum="10"/>sua sentenza con argomenti, a cui male avrebbero trovato che rispondere i <lb/>Platonici. </s>

<s>I raggi, che voi dite uscire dagli occhi, scriveva Vitellione contro <lb/>essi, o son corporei o no. </s>

<s>Se son corporei, come pu&ograve; dall'occhio, senza pa&shy;<lb/>tirne difetto, uscir tanta materia, che vada a riempire l'universo? </s>

<s>come giu&shy;<lb/>sto avverrebbe, quando l'occhio stesso si trattiene a contemplare un bel <lb/>cielo stellato. </s>

<s>Se sono incorporei, &ldquo; cum sensus non sit nisi in re corporali, <lb/>tunc ipsi radii non sentirent rem visam, ergo nec oculus corporeus, me&shy;<lb/>diante hoc incorporeo non sentiente, poterit sentire &rdquo; (ivi). </s></p><p type="main">

<s>Vitellione riusc&igrave; perci&ograve; nell'Ottica quel Maestro di coloro che sanno, <lb/>che Aristotile era riuscito nella Filosofia universale, per cui, quando s'in&shy;<lb/>sorse contro il venerato idolo greco, ebbe a sentirne offesa anche il vene&shy;<lb/>rato idolo pollacco. </s>

<s>&ldquo; &Egrave; cos&igrave; grande l'autorit&agrave; di Vitellione (scriveva Pietro <lb/>Accolti) unico e principal capo della Scuola de'Prospettivi, che chiunque <lb/>ardisca pronunziare egli aver falsamente o dimostrato o insegnato pu&ograve; di <lb/>facile essere reputato temerario o ardito molto. </s>

<s>Con tuttoci&ograve; sendo la scienza <lb/>delle Matematiche .... fondata meramente e unicamente sopra la evidenza <lb/>delle dimostrazioni e matematiche proposizioni, e non punto sopra l'auto&shy;<lb/>rita del Maestro .... perci&ograve; si &egrave; costumato sempre dar franchezza e libert&agrave; <lb/>di far dimostrazione di quello che, chicchessia, diversamente stimasse &rdquo; (Lo <lb/>inganno degli occhi, Firenze 1625, pag. </s>

<s>116). E prosegue l'Accolti a dire <lb/>come e perch&egrave; sia falso un teorema di Vitellione. </s>

<s>Ma pi&ugrave; di trent'anni prima <lb/>aveva il Porta avventato contro lo stesso Vitellione un giudizio che, se non <lb/>&egrave; calunnioso, non pu&ograve; non sembrare soverchiamente severo. </s>

<s>E quel giudizio <lb/>&egrave; tale: &ldquo; In universo enim opere suo quidquid ex se, supra illud Alhazen <lb/>est, falsum fere est &rdquo; (De refraction. </s>

<s>Neapoli 1593, pag. </s>

<s>64). </s></p><p type="main">

<s>Comunque sia, tanto tempo prima che con s&igrave; libera libert&agrave; si svelas&shy;<lb/>sero in Italia gli errori dell'Ottico pollacco, eravi chi in coltivar nella so&shy;<lb/>litudine la scienza facevasi a s&egrave; stesso maestro. </s>

<s>Leonardo da Vinci avr&agrave; <lb/>senza dubbio appresi dalle tradizioni i fondamenti dell'Ottica, e non &egrave; cre&shy;<lb/>dibile ch'e'non rimanesse anch'egli irretito in parecchi degli antichi errori. </s>

<s><lb/>Nulladimeno &egrave; mirabile il fino giudizio, con cui, riconosciuti quegli errori, <lb/>si studia di cansarli, e cos&igrave; cansati progredire senza altra scorta, e precor&shy;<lb/>rere a chi tanto tempo dopo, sarebbe per riuscire in Ottica solenne mae&shy;<lb/>stro al mondo. </s>

<s>Un mezzo secolo dopo Leonardo, Francesco Maurolico, conse&shy;<lb/>gnava anch'egli a solitari manoscritti i suoi <emph type="italics"/>Photismi<emph.end type="italics"/> e i suoi <emph type="italics"/>Diaphanorum <lb/>Partes,<emph.end type="italics"/> ne'quali, della riflessione e della rifrazione della luce, s'insegnavano <lb/>cose che nessuno degli antichi aveva mai pi&ugrave; pensate. </s></p><p type="main">

<s>Tra il finire del secolo XVI o il cominciar del seguente Giovan Bati&shy;<lb/>sta Porta e Giovanni Keplero iniziarono la scienza delle rifrazioni, l'uno <lb/>mostrando a'troppo creduli gli errori di Vitellione, l'altro promovendo la <lb/>scienza dal punto, dove Vitellione stesso l'aveva lasciata. </s>

<s>L'invenzione poi <lb/>del canocchiale e la viva curiosit&agrave; che frugava tutti d'intendere la ragione <lb/>com'operava il maraviglioso strumento, produssero alla luce i Fotismi e i <lb/>Diafani del Maurolico rimasti per pi&ugrave; di sessant'anni manoscritti: dettero <pb xlink:href="020/01/568.jpg" pagenum="11"/>eccitamento di scrivere la sua <emph type="italics"/>Dioptrica<emph.end type="italics"/> al Keplero, e al De Dominis di ri&shy;<lb/>prendere in mano e condurre a termine il suo <emph type="italics"/>De radiis visus et lucis,<emph.end type="italics"/> cc&shy;<lb/>leberrimo Trattato. </s></p><p type="main">

<s>La storia nel Tomo precedente da noi gi&agrave; narrata, mostra assai chiaro <lb/>come nessuno de'sopra commemorati autori pot&egrave; riuscire a dimostrar la ra&shy;<lb/>gione del Canocchiale olandese, primieramente perch&egrave; ignoravano la legge <lb/>delle relazioni costanti che passano fra gli angoli d'incidenza e quelli di ri&shy;<lb/>frazione, e in secondo luogo perch&egrave; non era facile, anche conosciuta che <lb/>fosse quella legge, il saperla applicare alla composizione delle lenti concave <lb/>e delle convesse. </s>

<s>Willebrod Snellio ne'suoi Manoscritti de'quali s'ebbe poi <lb/>relazione da Isacco Vossio, e Renato Cartesio concorsero insieme a investi&shy;<lb/>gare, a dimostrare sperimentalmente e a divulgare quella celebre legge diot&shy;<lb/>trica, la quale, bench&egrave; fosse il sospiro di tutti i Filosofi, ella fu nonostante <lb/>o accolta con diffidenza o apertamente ripudiata. </s></p><p type="main">

<s>Pi&ugrave; risoluti di tutti gli altri in cos&igrave; fatto ripudio furono i nostri Ita&shy;<lb/>liani, a'quali, per i gravi errori in che incorse Galileo e per la poca cultura <lb/>che raccomand&ograve; alla sua scuola, sarebbe forse mancata ogni scienza ottica, <lb/>se dal gregge avverso al gregge galileiano non fosse col suo celebre trat&shy;<lb/>tato <emph type="italics"/>De lumine<emph.end type="italics"/> uscito fuori Francesco Maria Grimaldi. </s>

<s>Egli discopritore di <lb/>una nuova propriet&agrave; nella luce, oltre alle due notissime della riflessione e <lb/>della rifrazione, ebbe al di fuori d'Italia una gloriosa progenie nell'Huy&shy;<lb/>ghens e nel Newton i quali ambedue perci&ograve; parteciparono, bench&egrave; con pi&ugrave; <lb/>vigoria di natural complessione e di giovent&ugrave;, delle virt&ugrave; paterne. </s>

<s>Il Gri&shy;<lb/>maldi specula intorno alle teorie dell'Ottica, con argomenti fisici e matema&shy;<lb/>tici: l'Huyghens nel Trattato <emph type="italics"/>De la lumiere<emph.end type="italics"/> &egrave; pi&ugrave; fisico che matematico, <lb/>ma nella <emph type="italics"/>Dioptrica,<emph.end type="italics"/> la quale preparata parecchi anni prima non si vide alla <lb/>luce, postuma, che nel 1703, ripudiata ogni fisica ipotesi, prosegue con tutto <lb/>il rigore della Geometria. </s>

<s>Il Newton sa cos&igrave; ben contemperar la Fisica alla <lb/>Matematica, che le ipotesi par s'illustrino d'evidenza matematica anch'esse. </s>

<s><lb/>Per lui cos&igrave; le nuove scoperte grimaldiane, come le altre propriet&agrave; pi&ugrave; an&shy;<lb/>ticamente conasciutesi della luce, trovarono nella Geometria quelle dimo&shy;<lb/>strazioni, che i predecessori invano erano andati cercando desiderosi per <lb/>tante vie. </s></p><p type="main">

<s>Tali sono in brevi tratti i progressi che, per opera e studio de'suoi <lb/>cultori, fece l'Ottica da'suoi principii infino al cominciar del secolo XVIII. </s>

<s><lb/>Ora &egrave; da narrare in che modo si facesse il progredir della scienza ne'suoi <lb/>particolari soggetti. </s>

<s>E perch&egrave; questi tanto son di natura varii e nel com&shy;<lb/>plesso loro cos&igrave; numerosi, non c'intratterremo perci&ograve; che intorno a'princi&shy;<lb/>pali concernenti la luce riflessa, la rifratta e la diffratta, toccando altres&igrave; <lb/>quelle quistioni che pi&ugrave; strettamente s'attengono a queste tre capitali pro&shy;<lb/>priet&agrave; della luce. </s></p><pb xlink:href="020/01/569.jpg" pagenum="12"/><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Che il primo studio de'Filosofi e de'Matematici dovess'esser rivolto a <lb/>ricercar la legge secondo la quale riflettesi la luce dai corpi opachi, s'in&shy;<lb/>tende con assai facilit&agrave;, ripensando esser questo il fenomeno, che pi&ugrave; ov&shy;<lb/>viamente occorre ad osservare. </s>

<s>Gli specchi, d'uso antichissimo, e gli studiosi <lb/>atteggiamenti di chi trattenevasi a rimirare in essi specchiata la propria im&shy;<lb/>magine, suggerirono ai Filosofi il primo strumento da dimostrar che i raggi <lb/>della luce cadono sullo specchio, e risaltano alla parte opposta sempre ugual&shy;<lb/>mente inclinati. </s></p><p type="main">

<s>Euclide infatti pone per fondamento alla sua Calottrica, fra le altre, <lb/>anco questa supposizione, che in ordine per lui &egrave; la terza. </s>

<s>&ldquo; Se lo specchio <lb/>si collocher&agrave; in un piano sopra il quale sia a piombo qualche altezza, la <lb/><figure id="id.020.01.569.1.jpg" xlink:href="020/01/569/1.jpg"/></s></p><p type="caption">

<s>Figura 1.<lb/>ragione che har&agrave; la linea intrapresa fra quel che <lb/>mira e lo specchio alla linea che &egrave; fra lo specchio <lb/>e la gi&agrave; detta altezza, har&agrave; anco l'altezza di quel <lb/>che mira all'altezza della cosa elevata a piombo <lb/>sopra il piano nel quale &egrave; lo specchio &rdquo; (Traduz. </s>

<s><lb/>cit., pag. </s>

<s>77, 78). </s></p><p type="main">

<s>Sia il punto T (fig. </s>

<s>1) lo specchio e CZ il <lb/>piano su cui va collocato. </s>

<s>Sia CT <emph type="italics"/>la linea in&shy;<lb/>trapresa fra quel che mira e lo specchio,<emph.end type="italics"/> e sia <lb/>TZ <emph type="italics"/>la linea che &egrave; fra lo specchio e la gi&agrave; data altezza. </s>

<s>L'altezza di quel <lb/>che mira<emph.end type="italics"/> sia BC, e sia DZ <emph type="italics"/>l'altezza della cosa elevata a piombo sopra il <lb/>piano, nel quale &egrave; lo specchio;<emph.end type="italics"/> suppone Euclide come cosa di fatto che sia <lb/>CT:TZ=BC:DZ. </s></p><p type="main">

<s>Da un tal supposto conclude l'Autore il suo I Teorema cos&igrave; formulato: <lb/><figure id="id.020.01.569.2.jpg" xlink:href="020/01/569/2.jpg"/></s></p><p type="caption">

<s>Figura 2.<lb/>&ldquo; &mdash; I raggi visuali si riflettono ad angoli pari, <lb/>tanto negli specchi piani come anco ne'rotondi <lb/>e ne'concavi. </s>

<s>&mdash; Sia l'occhio nel punto B (fig. </s>

<s>2), <lb/>lo specchio piano sia AG ed esca dall'occhio il <lb/>raggio BC, che si riflette nel punto D: dico che <lb/>l'angolo della riflessione Z &egrave; uguale all'angolo <lb/>della incidenza E. </s>

<s>Imperocch&egrave; tirinsi le due linee <lb/>a piombo BG e DA sopra lo specchio AG: e sar&agrave; <lb/>la BG alla GC com'&egrave; la DA alla AC, per la terza <lb/>supposizione. </s>

<s>Per il che il triangolo BGC sar&agrave; simile al triangolo DAC, tal <lb/>che l'angolo E sar&agrave; uguale all'angolo Z, essendo i triangoli simili di angoli <lb/>uguali &rdquo; (ivi, pag. </s>

<s>80). </s></p><p type="main">

<s>&Egrave; manifesto di qui che la dimostrazione del Teorema euclideo non con&shy;<lb/>sisteva in altro che nell'applicazione del fatto sperimentale supposto, e con <pb xlink:href="020/01/570.jpg" pagenum="13"/>ci&ograve; si dichiarava l'Autore che la legge fondamentale della Calottrica era, <lb/>secondo lui, per via geometrica indimostrabile. </s>

<s>Per non dimostrabile altri&shy;<lb/>menti che dal fatto sperimentato l'ebbe pure Tolomeo, come si par dal Teo&shy;<lb/>rema XLV del I Libro Degli Specchi, e l'ebbe altres&igrave; per tale Alhazeno, <lb/>nelle proposizioni X e XVIII del suo IV Libro. </s>

<s>N&egrave; altra via da'suoi illustri <lb/>predecessori seppe tener Vitellione, il quale si trattiene assai lungamente, <lb/>nella proposizione IX del suo V Libro di Prospettiva, a descrivere lo stru&shy;<lb/>mento <emph type="italics"/>in quo modi omnium reflexionum a quibuscumque regularibus spe&shy;<lb/>culis instrumentaliter declarantur<emph.end type="italics"/> (Edit. </s>

<s>cit., pag. </s>

<s>123). Proponendosi egli <lb/>infatti nel seguente Teorema X, di dimostrar l'uguaglianza che passa tra <lb/>gli angoli dell'incidenza e quelli della riflessione, non sa trovare altra mi&shy;<lb/>glior via della sperimentale, applicandovi lo strumento da s&egrave; prima cos&igrave; mi&shy;<lb/>nutamente descritto: &ldquo; In speculis planis (cos&igrave; viene enunciato quel X Teo&shy;<lb/>rema) radii oblique incidentis, fit ad aliam partem reflexio, semperque <lb/>angulum incidentiae aequale esse angulo reflexionis <emph type="italics"/>experimentaliter<emph.end type="italics"/> com&shy;<lb/>probatur &rdquo; (ibi, pag. </s>

<s>124). </s></p><p type="main">

<s>Lo strumento calottrico di Vitellione, e il modo di farne esperienza, non <lb/>differivano si pu&ograve; dir di niente dallo strumento e dal modo che, per lo stesso <lb/>effetto. </s>

<s>&egrave; tenuto oggid&igrave; dalla Fisica sperimentale. </s>

<s>Consisteva in un semicer&shy;<lb/>chio di ottone diviso in due quadranti da una linea perpendicolare, che bat&shy;<lb/>teva sul centro del semicerchio stesso, a cui soggiaceva applicato lo spec&shy;<lb/>chio. </s>

<s>Uno spiraglio da una parte e un traguardo dall'altra, scorrevoli per <lb/>la curvit&agrave; degli orli sui quadranti graduati, servivano, come servono tutta&shy;<lb/>via ai moderni, per isperimentar che il raggio tanti gradi segna dalla parte <lb/>d'onde cade, quanti dall'altra dove risale. </s></p><p type="main">

<s>Cos&igrave; dimostravansi, con una sola esperienza, le due leggi fondamentali <lb/>della Calottrica, imperocch&egrave; dalla disposizione stessa dello strumento veni&shy;<lb/>vasi a concludere che i due raggi, l'incidente e il riflesso, trovansi sempre <lb/>in un medesimo piano eretto a perpendicolo sulla superficie dello specchio. </s>

<s><lb/>L'Alighieri espose le due leggi calottriche in versi, che sembrano scritti ap&shy;<lb/>posta per persuadere che il bello &egrave; lo splendore del vero. </s>

<s>&ldquo; Come quando, <lb/>dall'acqua o dallo specchio, salta lo raggio all'oppo&shy;<lb/>sita parte, salendo su per lo modo parecchio a quel <lb/><figure id="id.020.01.570.1.jpg" xlink:href="020/01/570/1.jpg"/></s></p><p type="caption">

<s>Figura 3.<lb/>che scende, e, tanto si diparte dal cader della pietra <lb/>in igual tratta, s&igrave; come mostra esperienza ed arte.... &rdquo; <lb/>(Purg. </s>

<s>XV, t. </s>

<s>6, 7). </s></p><p type="main">

<s>In quel dir che il raggio sale per lo modo pa&shy;<lb/>recchio (cio&egrave; pari o nel medesimo piano) a quel che <lb/>scende, esprimesi l'una delle due leggi: l'altra vien <lb/>cos&igrave; dimostrata. </s>

<s>Sia AB (fig. </s>

<s>3) la superficie riflet&shy;<lb/>tente acqua o specchio: CD il cader della pietra, ossia la perpendicolare, <lb/>EC il raggio incidente e CF il riflesso. </s>

<s>Dice che, presa sulla perpendicolare <lb/>un <emph type="italics"/>igual tratta,<emph.end type="italics"/> per esempio CG, tanto si diparte dal punto G il raggio che <lb/>scende, quanto il raggio che sale; ci&ograve; che torna a dire che le due perpen-<pb xlink:href="020/01/571.jpg" pagenum="14"/>dicolari GE, GF, le quali son la giusta misura del dipartirsi i due raggi, sono <lb/>fra loro uguali. </s>

<s>D'onde, essendo i due triangoli EGC, FGC uguali &egrave; facile <lb/>concludere che i due angoli ECB, ACF debbon pure essere uguali. </s></p><p type="main">

<s>Le due leggi, soggiunge ivi Dante essere dimostrate dall'<emph type="italics"/>esperienza<emph.end type="italics"/> e <lb/>dall'<emph type="italics"/>arte,<emph.end type="italics"/> ossia dal ragionamento, il qual ragionamento &egrave; quello che noi ab&shy;<lb/>biamo ora spiegato dai versi del Poeta. </s>

<s>Ma &egrave; facile vedere che anco qui, <lb/>come in Euclide a cui il Cantore de'citati versi tien d'occhio, tutto il fon&shy;<lb/>damento &egrave; nel fatto sperimentale e poco o nulla nell'arte, la quale ancora <lb/>doveva essere attesa assai lungamente. </s></p><p type="main">

<s>Non prima infatti del cominciar del secolo XVII si vide nel Keplero chi <lb/>tentasse di maneggiar quell'arte, invocando la Geometria applicata al moto <lb/>de'corpi, per dimostrar ci&ograve; che Euclide, e tutti gli altri Ottici dopo di lui, <lb/>avevano reputato geometricalmente indimostrabile. </s>

<s>Quel <emph type="italics"/>nescio quid subtile<emph.end type="italics"/><lb/>per cui s'erano l'Alhazen e Vitellione argomentati <emph type="italics"/>motum lucis oblique in&shy;<lb/>cidentis componi ex motu perpendiculari et motu parallelo ad densi su&shy;<lb/>perficiem<emph.end type="italics"/> (Paralipom. </s>

<s>ad Vitell., Francof. </s>

<s>1604, pag. </s>

<s>84), parve al Keplero <lb/>esser uno spiraglio aperto alle nuove speranze d'ostetricare il primo parto <lb/>di quel connubio fra l'Ottica e la Meccanica, da'due commemorati Autori <lb/>felicemente iniziato. </s></p><p type="main">

<s>La proposizione XIX formulata ne'Paralipomeni a Vitellione <emph type="italics"/>Repercus&shy;<lb/>sus fit ad aequales angulos et eius quod oblique incidit ad latus alterum,<emph.end type="italics"/><lb/>&egrave; quella stessa formulata tanti secoli prima nel suo I Teorema di Prospet&shy;<lb/>tiva da Euclide, ma la dimostrazione &egrave; nel Matematico alemanno, dopo tanti <lb/>secoli, nuova, e a chi si diffidava di riuscir nella difficile impresa, si pre&shy;<lb/>senta inaspettata. </s></p><p type="main">

<s>Invocando dunque il Keplero il principio della composizion delle forze <lb/>applicato al moto della luce, cos&igrave; comincia e procede in quella sua dimo&shy;<lb/>strazione: &ldquo; Cum quid oblique movetur ver&shy;<lb/>sus superficiem, motus is componitur ex <lb/><figure id="id.020.01.571.1.jpg" xlink:href="020/01/571/1.jpg"/></s></p><p type="caption">

<s>Figura 4.<lb/>perpendiculari et parallelo superficiei. </s>

<s>Al <lb/>superficies tantum ei parti obiicitur, quae <lb/>est in se perpendicularis, non ei quae est <lb/>sibi parallelos. </s>

<s>Quare nec impedit partem <lb/>sibi parallelon, sed palitur mobile resiliendo <lb/>pergere ad partem alteram sicut advenerat. </s>

<s><lb/>Sit CDF (fig. </s>

<s>4) superficies, BD motus lu&shy;<lb/>cis: continuetur BD in E, secans CDF in <lb/>D, et sit CDE aequalis CDA &rdquo; (ibi, pag. </s>

<s>14). </s></p><p type="main">

<s>La ragione di questa uguaglianza la dimostra il Keplero cos&igrave; argomen&shy;<lb/>tando: Siccome il moto dalla parte D verso C non &egrave; impedito, ma &egrave; impe&shy;<lb/>dito solo quello da C verso E, dunque il raggio riflesso AD deve serbar <lb/>quella medesima inclinazione verso la superficie riflettente CD secondo la <lb/>quale procederebbe il raggio BDE quando non fosse impedito. </s>

<s>In altre pa&shy;<lb/>role, deve esser CDE=CDA. </s>

<s>Ma perch&egrave; CDE &egrave; uguale a BDF &ldquo; ergo (con-<pb xlink:href="020/01/572.jpg" pagenum="15"/>clude il Keplero) BDF incidentiae et ADC reflexionis anguli sunt aequales &rdquo; <lb/>(ibi, pag. </s>

<s>15). </s></p><p type="main">

<s>Questa nuova dimostrazione kepleriana piacque molto al Cartesio, che <lb/>l'accolse nella sua Diottrica ringentilita e con pi&ugrave; lucido ordine condotta. </s>

<s><lb/>Suppone A (fig. </s>

<s>5) essere una palla obliquamente <lb/><figure id="id.020.01.572.1.jpg" xlink:href="020/01/572/1.jpg"/></s></p><p type="caption">

<s>Figura 5.<lb/>cacciata nella direzione AB percotere in B sopra un <lb/>punto della superfice CE, che egli suppone <emph type="italics"/>exacte <lb/>planam duramque esse.<emph.end type="italics"/> Fa altres&igrave; astrazione dalla <lb/>gravezza, peso e misura della palla stessa, cose tutte <lb/>affatto inutili a essere considerate, per non si voler <lb/>d'altro intendere che della luce, <emph type="italics"/>ad quam omnia <lb/>haec referri debent.<emph.end type="italics"/></s></p><p type="main">

<s>Cos&igrave; essendo, si domanda verso qual parte si <lb/>rifletter&agrave; la detta palla scagliata, e si fa via alla ri&shy;<lb/>sposta decomponendo, a imitazione del Keplero, il <lb/>moto obliquo AB nell'orizzontale AH e nel perpendicolare AC, osservando <lb/>che questo solo &egrave; quello, a cui fa impedimento il piano del rimbalzo. </s>

<s>Dopo <lb/>di che il Cartesio, cos&igrave; prosegue nella dimostrazione: </s></p><p type="main">

<s>&ldquo; Ut accurate igitur inquiramus ad quam partem pila illisa debeat re&shy;<lb/>silire, describamus circulum ex centro B, qui transeat per punctum A, et <lb/>dicamus: spatio temporis eodem quo progressa est ab A ad B, necessario <lb/>illam a B ad aliquod punctum huius circuli circumferentiae reverti debere. </s>

<s><lb/>Nam omnia puncta quae eodem intervallo distant a B, quo distat A, in hac <lb/>circumferentia occurrunt, et pilae motum iam supra aeque velocem finxi&shy;<lb/>mus. </s>

<s>Tandem ad designandum ipsum punctum, quod ex omnibus huius <lb/>circumferentiae tangere debet, erigamus ad normam tres rectas AC, HB et <lb/>FE, supra CE, hac ratione ut nec maius nec minus spatium interiaciat AC <lb/>et HB, quam HB et FE. </s>

<s>Deinde dicamus: idem tempus quod pilam dextror&shy;<lb/>sum porrexit ab A uno punctorum linaee AC, usque ad B unum ex punctis <lb/>linaee HB, illam resilientem ab HB sistere debet in aliquo puncto linaee FE. </s>

<s><lb/>Nam singula puncta huius linaee FE eadem distantia hoc respectu ab HB <lb/>remota sunt, et eadem qua singula linaee AC, et ex priori dispositione tan&shy;<lb/>tumdem eo inclinat quantum antea. </s>

<s>Jam eodem momento aliquod punctum <lb/>linaee FE et simul aliquod circumferentiae AFD contingere nequit, nisi in <lb/>puncto D vel F. </s>

<s>Nam extra haec duo nullibi mutuo secantur. </s>

<s>Terra autem <lb/>obstante ad B progredi non potest: sequitur itaque illam necessario tendere <lb/>debere ad F. </s>

<s>Et sic manifestum est qua ratione reflexio fiat, scilicet semper <lb/>ad angulum aequalem illi, quem vulgo incidentiae nominant. </s>

<s>Ut si radius <lb/>ex puncto A emanet in B, superficiem speculi plani CBE resilit ad F, ita <lb/>ut reflexionis angulus FBE, neque cedat, neque exuperet magnitudine al&shy;<lb/>terum illum incidentiae ABC &rdquo; (De Methodo; Dioptrices, Francofurti 1692, <lb/>pag. </s>

<s>48). </s></p><p type="main">

<s>Nella dimostrazione condotta dal'Keplero supponevasi implicita la con&shy;<lb/>dizione che il raggio fosse ugualmente veloce al raggio incidente, ma il Car-<pb xlink:href="020/01/573.jpg" pagenum="16"/>tesio richiede quella stessa condizione esplicita, ben conoscendo come di l&igrave; <lb/>derivasse tutta la forza all'argomento. </s>

<s>&ldquo; Hinc etiam planum minime cre&shy;<lb/>dendum esse necessario pilam aliquo momento haerere puncto B, pruisquam <lb/>digrediatur ad F, iuxta quorumdam Philosophorum opinionem. </s>

<s>Nam inter&shy;<lb/>rupto hoc motu exigua tantummodo mora, nulla extaret causa, qua inci&shy;<lb/>tante, vires resumere posset &rdquo; (ibi, pag. </s>

<s>47). </s></p><p type="main">

<s>L'applicazione del principio d'inerzia alla forza della percossa, fu sog&shy;<lb/>getto di grandi controversie fra'cultori della scienza del moto, ma pur, fuori <lb/>di ogni controversia, &egrave; un errore manifesto il supposto qui dal Cartesio che <lb/>cio&egrave; un corpo duro e privo affatto d'ogni elaterio, com'ei professa ossere <lb/>un atomo di luce, mantenga dopo l'urto la medesima velocit&agrave; di prima e <lb/>la stessa quantit&agrave; di moto. </s>

<s>&Egrave; perci&ograve; impossibile, nella ipotesi cartesiana, che <lb/>un raggio di luce salti all'opposta parte con angolo precisamente pari a <lb/>quel che scende. </s>

<s>Se con V si rappresenta la velocit&agrave; perduta nel'urto e con <lb/><foreign lang="greek">n</foreign> la velocit&agrave;, o istantaneamente come esigeva il Cartesio o con succesione <lb/>di minimo tempo com'altri permettevano, riacquistata nel verso opposto <lb/>dopo l'urto, e s'intenda per <foreign lang="greek">b</foreign> l'angolo di riflessione e per <foreign lang="greek">a</foreign> quello dell'in&shy;<lb/>cidenza, i Meccanici riescono all'equazione tang. <foreign lang="greek">b</foreign>=V/<foreign lang="greek">n</foreign> tang. <foreign lang="greek">a</foreign>, per la quale <lb/>si dimostra assai chiaramente non potersi verificare la legge fondamentale <lb/>della Calottrica, se non a patto che la luce sia dotata di una elasticit&agrave; <lb/>perfetta. </s></p><p type="main">

<s>Il Cartesio perci&ograve; allucinato dalle splendide vie meccaniche apertegli <lb/>innanzi dal Keplero non s'avvide che la severit&agrave; matematica assai male si <lb/>confaceva al suo immaginario sistema, e o non pens&ograve; o non seppe salvar <lb/>le mendicate calottriche dottrine da un'aperta contradizione. </s></p><p type="main">

<s>Esperto de'pericoli che s'incontravano in volere applicare alla luce le <lb/>propriet&agrave; meccaniche de'corpi ponderosi, il Grimaldi, con miglior giudizio, <lb/>si rivolse a cercar nel campo della fisica la desiderata dimostrazione calot&shy;<lb/>trica e la trov&ograve; semplice e tutto insieme ingegnosa. </s>

<s>Potrebbe dirsi altres&igrave; <lb/><figure id="id.020.01.573.1.jpg" xlink:href="020/01/573/1.jpg"/></s></p><p type="caption">

<s>Figura 6.<lb/>concludente se gli si conceda una sup&shy;<lb/>posizione fondamentale, la qual consiste <lb/>nell'ammetter che il raggio luminoso <lb/>abbia &ldquo; aliqua crassities, insensibilis <lb/>quidem sed tamen physica, ita ut in eo <lb/>concipi queant plures linaee tum extre&shy;<lb/>mae, tum mediae, secundum longitudi&shy;<lb/>nem illius extensae &rdquo; (De Lumine, Bo&shy;<lb/>noniae 1665, pag. </s>

<s>166). </s></p><p type="main">

<s>Concessa questa supposizione, &egrave; ne&shy;<lb/>cessit&agrave; concedergli insieme ci&ograve; che ne <lb/>consegue ed &egrave; che, mantenendosi sem&shy;<lb/>pre il raggio nel medesimo mezzo, non ci &egrave; ragione perch&egrave; debba, dopo <lb/>essere stato riflesso, alterarsi in pi&ugrave; o in meno dalla sua prima crassizie. <pb xlink:href="020/01/574.jpg" pagenum="17"/>Supposto ci&ograve;, rappresenti CH (fig. </s>

<s>6) lo specchio e le due strisce KLDF, <lb/>GDFE rappresentino i due raggi. </s>

<s>Se la loro crassizie, dice il Grimaldi, dee, <lb/>com'&egrave; ragionevole, mantenersi uguale, necessario &egrave; che l'angolo dell'inci&shy;<lb/>denza EFH sia uguale ad LFD angolo della riflessione. </s>

<s>Si dimostra cos&igrave; dal&shy;<lb/>l'Autore in poche parole: </s></p><p type="main">

<s>Condotte le OF, DP perpendicolari alle DG, LF ne'punti O, P, saranno <lb/>queste le misure giuste della crassizie de'raggi. </s>

<s>I triangoli poi ODF, PFD <lb/>rettangoli, daranno le due proporzioni OF:DF=sen ODF:1, DP:DF= <lb/>sen PFD:1, onde OF:DP=sen ODF:sen PFD, ma OF &egrave; uguale a DP <lb/>per esser, secondo il supposto, le misure delle due crassizie uguali; dunque <lb/>ODF=PFD. &ldquo; Proinde non possunt non esse aequales anguli incidentiae <lb/>ac reflexionis, si eadem debet esse crassities in radio reflexo ac in directo, <lb/>quod erat ostendendum &rdquo; (ibi, pag. </s>

<s>167). </s></p><p type="main">

<s>Abbiam conceduto al Grimaldi questo supposto, che &egrave; tutto il fonda&shy;<lb/>mento su cui posa la sua bella dimostrazione, ma poi ci soprapprende uno <lb/>scrupolo d'essere stati forse troppo solleciti e liberali con esso. </s>

<s>Diasi pure <lb/>al raggio una qualche insensibile crassizie: questa per&ograve; non pu&ograve; aver pro&shy;<lb/>porzione alcuna fisicamente determinabile, con quelle eminenze e cavit&agrave;, di <lb/>che il Microscopio ci rivela essere aspera qualunque superficie, la quale sem&shy;<lb/>bri al tatto pi&ugrave; levigata. </s>

<s>Di qui &egrave; che il raggio deve dopo l'urto subire una <lb/>certa dispersione per cui venga ad alterarsi notabilmente quella sua prima <lb/>crassizie. </s></p><p type="main">

<s>A rimuovere un tale scrupolo dalle menti d&egrave;tte opera il Newton, il <lb/>quale, esperto oramai delle contradizioni a cui furon fatte segno la dimo&shy;<lb/>strazion meccanica del Keplero e la fisica del Grimaldi, si studi&ograve; di proce&shy;<lb/>dere in modo da non offendere n&egrave; contro uno scoglio n&egrave; contro l'altro. </s>

<s>Egli <lb/>chiede gli si conceda per prima cosa, ci&ograve; che per verit&agrave; nessuno gli potrebbe <lb/>negare, esser gli atomi della luce corpi duri, soggetti alle leggi dell'attra&shy;<lb/>zione, e ch'essendo cos&igrave; attratti da'mezzi attraversati sieno perci&ograve; deviati <lb/>dalla dirittura de'loro moti. </s>

<s>Vuole altres&igrave; gli si conceda, in secondo luogo, <lb/>ch'esali dalle superficie riflettenti, acqua o vetro o cristallo, una sottilissima <lb/>aura eterea, la quale vada soprapponendosi in strati via via pi&ugrave; densi come <lb/>pi&ugrave; si dilungano dalle dette superficie. </s>

<s>&ldquo; Annon medium hoc aethereum pro <lb/>eo ut ex aqua, vitro, crystallo, aliisque crassis densisque corporibus in spa&shy;<lb/>tia vacua eatur, densius evadit paulatim, eoque pacto radios luminis refrin&shy;<lb/>git, non simul et semel in uno puncto, sed gradatim eos in curvas lineas <lb/>flectendo? </s>

<s>Et annon medii huius condensatio, quae ita gradatim ad usque <lb/>intervalla aliqua a corporibus porrigitur, eoque pacto in causa est quamo&shy;<lb/>brem radii luminis, qui prope corporum densorum extrema interiecto aliquo <lb/>intervallo transeunt, inflectantur? </s>

<s>&rdquo; (Optices, Lib. </s>

<s>III, Patavii 1773, pag. </s>

<s>143). </s></p><p type="main">

<s>Come poi que'raggi, cos&igrave;, senza toccar la superficie dello specchio s'in&shy;<lb/>flettano, in modo che il secondo angolo riesca al primo ugualmente incli&shy;<lb/>nato, lo dimostra il Newton, dietro que'supposti, procedendo cos&igrave; per le vie <lb/>della Meccanica, a passo franco e sicuro: </s></p><pb xlink:href="020/01/575.jpg" pagenum="18"/><p type="main">

<s>Sieno Aa, Bb (fig. </s>

<s>7) le due linee conterminanti il mezzo diafano at&shy;<lb/>traversato dall'atomo di luce G nel punto H: se sia quel mezzo meno denso <lb/>dell'altro d'onde il raggio GH &egrave; venuto &ldquo; et si attractio vel impulsus po&shy;<lb/><figure id="id.020.01.575.1.jpg" xlink:href="020/01/575/1.jpg"/></s></p><p type="caption">

<s>Figura 7<lb/>natur uniformis, erit ex demon&shy;<lb/>stratis Galilaei curva HP parabola <lb/>&ldquo; (Principia mathem., Genevae <lb/>1739, T. I, pag. </s>

<s>534). Soggiaccia <lb/>allo strato etereo Ab, un altro si&shy;<lb/>mile strato etereo Bc, ma alquanto <lb/>meno denso del primo, nel quale <lb/>entri, emergendo dal punto P il <lb/>raggio <expan abbr="Pq.">Pque</expan> Si dimostra con gran <lb/>facilit&agrave; dal Newton che la velocit&agrave; <lb/>del raggio avanti l'incidenza &egrave; alla <lb/>velocit&agrave; dello stesso raggio dopo <lb/>l'emergenza, come il seno del&shy;<lb/>l'emergenza al seno dell'incidenza <lb/>(Propositio XCV, ibi, pag. </s>

<s>536), <lb/>e il detto raggio PQ proceder&agrave; <lb/>per le stesse ragioni in arco pa&shy;<lb/>rabolico; cosicch&egrave;, avendo in Q raggiunto l'angolo limite, subir&agrave; in R la <lb/>riflessione interna, e come i gravi proiettili attratti al centro della Terra si <lb/>trover&agrave; aver descritta la traiettoria HPQR semiparabolica. </s></p><p type="main">

<s>&ldquo; Perveniat corpus (giacch&egrave; l'atomo luminoso &egrave; pel Newton un corpo <lb/>qualunque) ad hoc planum in puncto R et quoniam linea emergentiae coin&shy;<lb/>cidit cum eodem plano, perspicuum est quod corpus non potest ultra per&shy;<lb/>gere versus planum Ee. </s>

<s>Sed nec potest idem pergere in linea emergentiae <lb/>Rd, propterea quod perpetuo attrahitur vel impellitur versus medium inci&shy;<lb/>dentiae. </s>

<s>Revertetur itaque inter plana Cc, Dd, describendo arcum parabolae <lb/>QRq cuius vertex principalis, iuxta demonstrata Galilaei, est in R; secabit <lb/>planum Cc in eodem angulo in q ac prius in <expan abbr="q;">que</expan> dein pergendo in arcubus <lb/>parabolicis qp, ph etc. </s>

<s>arcubus prioribus QP, PH, similibus et aequalibus, <lb/>secabit reliqua plana in iisdem angulis in p, h etc. </s>

<s>ac prius in P, H etc. </s>

<s><lb/>emergetque tandem eadem obliquitate in h, qua incidit in H &rdquo; (ibi, pag. </s>

<s>538). </s></p><p type="main">

<s>Il Newton, che nelle speculazioni sue era originale, procede per le vie <lb/>della Meccanica con passo pi&ugrave; sicuro di quel che non facesse il Cartesio <lb/>imitator del Keplero. </s>

<s>Ma il forte si &egrave; che non &egrave; questione di Meccanica pura. </s>

<s><lb/>Nessuno pu&ograve; revocare in dubbio i Teoremi XLVIII, XLIX e L del Tomo I <lb/>de'<emph type="italics"/>Principii,<emph.end type="italics"/> ne'quali nulla osta a supporre un proiettile qualunque che at&shy;<lb/>traversi mezzi via via meno densi. </s>

<s>Si pu&ograve; dubitar per&ograve; se l'etere neuto&shy;<lb/>niano si trovi in cos&igrave; fatte condizioni. </s>

<s>Chi non direbbe piuttosto che le den&shy;<lb/>sit&agrave; di lui crescono via via perch&egrave; pi&ugrave; fortemente attratto verso la superficie <lb/>del riflettente? </s></p><p type="main">

<s>Ma lasciamo un po'da parte questo mezzo etereo, il quale non esiste <pb xlink:href="020/01/576.jpg" pagenum="19"/>forse che nella immaginazione de'Filosofi: consideriamo l'aria, per la quale <lb/>siam certificati dai fatti che ella &egrave; pi&ugrave; fortemente attratta presso alla super&shy;<lb/>ficie de'corpi, i quali perci&ograve; tutto intorno circonda di un'ammosfera via via <lb/>sempre pi&ugrave; densa. </s>

<s>E poich&egrave;, nelle ottiche neutoniane speculazioni, concorre <lb/>anco l'aria a incurvare i raggi dicendosi dal Filosofo matematico che cos&igrave; <lb/>le rifrazioni come le riflessioni non avvengono nel punto dell'incidenza sul <lb/>vetro, <emph type="italics"/>sed paulatim per continuam incurvationem radiorum factam par&shy;<lb/>tim in aere antequam attingunt vitrum<emph.end type="italics"/> (ibi, pag. </s>

<s>540, 4) si vede che se <lb/>la densit&agrave; di essa aria, piuttosto che scemare ella cresce, &egrave; del tutto impos&shy;<lb/>sibile che avvenga la riflessione. </s>

<s>Sia infatti nella precedente figura 7 lo <lb/>strato Bc pi&ugrave; denso dell'Ab e sia questo, anche pi&ugrave; denso dell'altro da cui <lb/>viene il raggio, e allora HP, PQ ecc. </s>

<s>invece di rifrangersi dalla perpendi&shy;<lb/>colare, si rifrangeranno alla perpendicolare, e tutto insieme il raggio HPQ <lb/>non s'avvier&agrave; per riflettersi alla parte opposta, ma si ritorcer&agrave; verso la me&shy;<lb/>desima parte. </s></p><p type="main">

<s>Le speculazioni per&ograve; del Newton si verificano in alcuni fatti naturali, <lb/>quando una superficie &egrave; fortemente riscaldata. </s>

<s>Allora gli strati dell'aria di&shy;<lb/>minuiscono veramente in densit&agrave; secondo l'ipotesi neutoniana dell'etere, <lb/>ch'esala dai corpi, ed &egrave; veramente allora la riflessione indipendente dalla <lb/>levigatezza della superficie. </s>

<s>Qualunque piano pi&ugrave; scabro, e meno atto a ri&shy;<lb/>fletter la luce nelle condizioni ordinarie, come sarebbe per esempio una <lb/>landa arenosa, pu&ograve;, sotto i raggi ardenti del sole, far di s&egrave; specchio agli <lb/>oggetti circostanti, come un lago di chiara acqua tranquilla. </s></p><p type="main">

<s>Cos&igrave;, tornando alla nostra figura 7, se rappresenta Ee quesla landa are&shy;<lb/>nosa infocata, l'occhio che fosse in g vedrebbe in G'il punto G dell'og&shy;<lb/>getto GM, e tutto l'oggetto stesso dipingersi in un'immagine rovesciata nel <lb/>concorso de'raggi visuali col cateto, precisamente come in uno specchio or&shy;<lb/>dinario. </s>

<s>Fu per l'applicazione diretta di questo Teorema neutoniano che An&shy;<lb/>tonio Minasi e Jacopo Pignattari, verso il 1750, usi ad osservar lo spettacolo <lb/>sulle patrie rive marine di Reggio di Calabria, intesero il magico artifizio <lb/>della <emph type="italics"/>Fata Morgana<emph.end type="italics"/> e il Monge toglieva cos&igrave; d'illusione gli assetati com&shy;<lb/>pagni di viaggio in Egitto, dando loro a intender, come, secondo il Newton, <lb/>riflettan la luce allo stesso modo le fresche acque e le aride sabbie. </s></p><p type="main">

<s>Ma ritornando al principale argomento, e ripensando come per nessuna <lb/>delle varie vie tentate e percorse dagli Ottici si riesce a dimostrar la legge <lb/>delle riflessioni, senza contrariet&agrave;, e in modo che ne sien d'ogni parte so&shy;<lb/>disfatti gl'ingegni speculativi; chi non direbbe che da Euclide in poi la Spe&shy;<lb/>cularia non ha fatto progressi, o chi non reputerebbe savi gli antichi, i quali, <lb/>senza travagliarsi in sottili ipotesi o in calcoli faticosi, ritennero quella legge <lb/>come un fatto, non bisognoso, e n&egrave; suscettibile di alcuna dimostrazione? </s></p><p type="main">

<s>Se n&egrave; la Fisica dunque n&egrave; la Geometria sodisfano pienamente, &egrave; forse <lb/>da sperar qualche cosa nella Morale? </s>

<s>Bench&egrave; per verit&agrave; non s'intenda come <lb/>un fatto fisico possa derivare la sua ragion naturale dalla moralit&agrave; delle cose, <lb/>nonostante il Fermat e l'Huyghens invocarono nella Diottrica il principio <pb xlink:href="020/01/577.jpg" pagenum="20"/>delle cause finali. </s>

<s>Il Leibniz estese, con pi&ugrave; zelo che mai, quello stesso prin&shy;<lb/>cipio all'Ottica, alla Catottrica e alla Diottrica, e in una sua scrittura inse&shy;<lb/>rita, nel 1682, negli Atti degli Eruditi di Lipsia, e raccolta poi da pag. </s>

<s>145-50 <lb/>del Tomo III di tutte le opere stampate nel 1768 a Ginevra, incomincia cos&igrave; <lb/>dal dimostrar la legge delle riflessioni sul fondamento dell'unica ipotesi da <lb/>lui costituito: <emph type="italics"/>Lumen a puncto radiante ad punctum illustrandum per&shy;<lb/>venit via omnium facillima.<emph.end type="italics"/> La dimostrazione &egrave; semplicissima e non s'aiuta <lb/>che della Geometria pi&ugrave; elementare. </s></p><p type="main">

<s>&ldquo; Sit enim punctum radians C (fig. </s>

<s>8) illustrandum D, speculum pla&shy;<lb/>num AB. </s>

<s>Quaeritur punctum speculi E radium ad D reflectens. </s>

<s>Dico id esse <lb/><figure id="id.020.01.577.1.jpg" xlink:href="020/01/577/1.jpg"/></s></p><p type="caption">

<s>Figura 8.<lb/>tale ut tota via CE+ED fiat omnium <lb/>minima, seu minor quam CF+FD, si <lb/>nimirum aliud quodcumque speculi pun&shy;<lb/>ctum F fuisset assumptum. </s>

<s>Hoc obtinet <lb/>si E sumatur tale ut anguli CEA et DEB <lb/>sint aequales ut ex Geometria constat &rdquo; <lb/>(pag. </s>

<s>145). </s></p><p type="main">

<s>I Cartesiani, giustamente avversi al <lb/>principio delle cause finali, si ridevano <lb/>del Leibniz, quasi avesse dato al raggio uno spirito di consultazione da eleg&shy;<lb/>ger, fra le infinite che gli si parano innanzi, la pi&ugrave; facile via e la pi&ugrave; breve. </s>

<s><lb/>A costoro il Leibniz stesso cos&igrave; rispondeva: &ldquo; Neque enim radius a C egre&shy;<lb/>diens consultat quomodo ad punctum E vel D, vel G pervenire quam facil&shy;<lb/>lime possit.... sed ipse Creator rerum ita creavit lucem ut ex eius natura <lb/>pulcherrimus ille eventus nasceretur. </s>

<s>Itaque errant, valde, ne quid gravius <lb/>dicam, qui causas finales cum Cartesio in physica reiiciunt &rdquo; (ibi, pag. </s>

<s>146). </s></p><p type="main">

<s>Questa arringheria per&ograve; non ha virt&ugrave; di rimuovere la sentenza di co&shy;<lb/>loro, i quali affermano che la Speculeria, anche senza alcuna dimostrazione <lb/>fisica, o matematica o morale della legge della riflessione, progred&igrave;, come si <lb/>dimostra per l'esempio di tutti gli Autori fioriti da Euclide infino al Ke&shy;<lb/>plero, i quali Autori certificati per l'esperienza essere, il raggio che va, <lb/>ugualmente inclinato a quello che viene, disegnarono con precisione le im&shy;<lb/>magini in ogni configurazione di specchi e dettero ragioni certe di tutti <lb/>questi varii ordini di apparenze. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Conosciute cos&igrave; le leggi del riflettersi la luce negli specchi artificiali, <lb/>risalirono i Filosofi colla contemplazione ad applicarle alle apparenze cele&shy;<lb/>sti, specialmente in quello specchio naturale che, riflettendo a noi i raggi <lb/>del sole, illumina le tenebre delle nostre notti. </s>

<s>Plutarco aveva felicemente <lb/>diffusa l'opinione di coloro, che rassomigliando la Luna alla Terra dicevano <pb xlink:href="020/01/578.jpg" pagenum="21"/>le macchie di lei essere in parte dovute all'ombre proiettate da'monti, e in <lb/>parte dal riflesso de'mari. </s>

<s>Ci&ograve; dette occasione a dispute fra gli stessi se&shy;<lb/>guaci di questa opinione, alcuni de'quali, come il Keplero, ingannati dalla <lb/>natural chiarezza dell'acqua, attribuivano le ombre non mutabili della Luna <lb/>piuttosto ai continenti. </s>

<s>Galileo che, nel Nunzio Sidereo, aveva sentenziato <lb/>senza prove ed avea affermato come cosa da non mettersi in dubbio dover <lb/>l'acqua, a'riflessi del sole, apparir pi&ugrave; buia della terra, nel I Dialogo de'Mas&shy;<lb/>simi Sistemi si studia di persuaderne Simplicio con facili ragionamenti con&shy;<lb/>fortati dall'esperienza. </s></p><p type="main">

<s>&ldquo; Pigliate (cos&igrave; dice allo stesso Simplicio il Salviati) in cortesia quello <lb/>specchio, che &egrave; attaccato a quel muro, e usciamo qua nella corte.... At&shy;<lb/>taccate lo specchio l&agrave; a quel muro, dove batte il sole: discostiamoci e riti&shy;<lb/>riamoci qua all'ombra. </s>

<s>Ecco l&agrave; due superficie percosse dal sole, cio&egrave; il muro <lb/>e lo specchio. </s>

<s>Ditemi ora qual vi si presenta pi&ugrave; chiara quella del muro o <lb/>quella dello specchio? </s>

<s>Voi non rispondete?.... (Alb. </s>

<s>I, pag. </s>

<s>81). Voi ve&shy;<lb/>dete la differenza che cade tra le due reflessioni fatte dalle due superficie <lb/>del muro e dello specchio, percosse nell'istesso modo per l'appunto dai raggi <lb/>solari, e vedete come la reflession che vien dal muro si diffonda verso tutte <lb/>le parti opposteli, ma quella dello specchio va verso una parte sola, non <lb/>punto maggiore dello specchio medesimo; vedete parimente come la super&shy;<lb/>ficie del muro riguardata da qualsivoglia luogo, si mostra chiara sempre <lb/>ugualmente a s&egrave; stessa; e per tutto assai pi&ugrave; chiara che quella dello spec&shy;<lb/>chio, eccettuatone quel piccolo luogo solamente, dove batte il riflesso dello <lb/>specchio, che di l&igrave; apparisce lo specchio molto pi&ugrave; chiaro del muro &rdquo; (ivi, <lb/>pag. </s>

<s>83). </s></p><p type="main">

<s>Qui prosegue il Salviati ad applicar l'esperienza alle riflessioni della <lb/>Luna, ma a persuader meglio Simplicio non trascura di rendere appresso <lb/>la ragione perch&egrave;, conforme alla detta esperienza, il muro apparisce al sole <lb/>pi&ugrave; luminoso dello specchio. </s>

<s>&ldquo; E se voi desiderate intendere l'intero di que&shy;<lb/>sto negozio, considerate come l'esser la superficie di quel muro aspra, &egrave; <lb/>l'istesso che l'esser composta d'innumerabili superficie piccolissime, dispo&shy;<lb/>ste secondo innumerabili diversit&agrave; d'inclinazioni, tra le quali di necessit&agrave; <lb/>accade, che ne sieno molte disposte a mandare i raggi reflessi da loro in <lb/>un tal luogo, molte altre in altro, e insomma non &egrave; luogo alcuno al quale <lb/>non arrivino moltissimi raggi reflessi da moltissime superficiette sparse per <lb/>tutta l'intera superficie del corpo scabroso, sopra il quale cascano i raggi <lb/>luminosi. </s>

<s>Dal che segue di necessit&agrave; che sopra qualsivoglia parte di qua&shy;<lb/>lunque superficie opposta a quella che riceve i raggi primarii incidenti, per&shy;<lb/>vengano raggi reflessi, e in conseguenza l'illuminazione. </s>

<s>Segueno ancora, <lb/>che il medesimo corpo, sul quale vengono i raggi illuminanti, rimirato da <lb/>qualsivoglia luogo, si mostri tutto illuminato e chiaro &rdquo; (ivi, pag. </s>

<s>87, 88). </s></p><p type="main">

<s>Se per&ograve; questa dottrina galileiana, intorno alla maggior riflessione delle <lb/>superficie aspre rispetto alle levigate, sia veramente originale o se sia stata <lb/>insegnata prima da altri, darebbe a noi luogo di dubitare, attendendo a ci&ograve; <pb xlink:href="020/01/579.jpg" pagenum="22"/>che il Baliani scrive in una sua lettera indirizzata al medesimo Galileo, sotto <lb/>il di 31 Gennaio 1614. In essa, fra le altre cose, confessa di essersi ricre&shy;<lb/>duto, per le argomentazioni di Filippo Salviati, di una falsa opinione ch'egli <lb/>aveva intorno alla natura del ghiaccio, stimando ch'egli fosse acqua non ra&shy;<lb/>refatta ma condensata, e che dovesse perci&ograve;, per la sua maggior gravit&agrave; spe&shy;<lb/>cifica, andare a fondo. </s></p><p type="main">

<s>&ldquo; Del quale errore (son parole dello stesso Baliani) mi ha tolto il si&shy;<lb/>gnor Filippo, dicendomi che il ghiaccio occupa maggior luogo dell'acqua, <lb/>il che poi anche provai per esperienza, e gli dissi la mia opinione come possa <lb/>essere che il ghiaccio si faccia dal freddo che condensi l'acqua, e che ad <lb/>ogni modo egli occupi maggior luogo, perch&egrave; si condensa non uniforme&shy;<lb/>mente, ma piuttosto in diverse parti, fra le quali restano delle parti pi&ugrave; <lb/>rare, ond'egli tutto insieme viene ad essere pi&ugrave; raro dell'acqua. </s>

<s>La qual <lb/>difformit&agrave; di parti &egrave; cagione che il ghiaccio perda in gran parte la diafa&shy;<lb/>neit&agrave;, e io credo avere abbastanza provato al detto signor Filippo che tutti <lb/>i corpi son diafani, la cui natura &egrave; totalmente conforme, cio&egrave; non pi&ugrave; rara <lb/>da una parte che dall'altra &rdquo; (Alb. </s>

<s>VIII, 300, 1). </s></p><p type="main">

<s>Le prove che il Baliani aveva per confermare questa sua teorica de'corpi <lb/>opachi e de'diafani, si riducono a quelle stesse, che adducevansi dianzi da <lb/>Galileo, per provar come il muro aspro ed opaco apparisca pi&ugrave; luminoso <lb/>dello specchio di cristallo diafano e levigato. </s>

<s>Di ci&ograve; abbiamo il documento <lb/>certo in alcuni passi del <emph type="italics"/>Trattato della Pestilenza,<emph.end type="italics"/> dove rendesi la ragione <lb/>dell'opacit&agrave;, che presentano alcuni corpi diafani nel raffreddarsi, qual sa&shy;<lb/>rebbe per esempio la cera o lo stesso ghiaccio. </s>

<s>&ldquo; N&egrave; in altra guisa, egli <lb/>dice, credo io che induri, non solo la cera o la pece e tuttoci&ograve; che &egrave; strutto <lb/>a forza di calore, ma l'acqua eziandio, qualora divien ghiaccio, e la pioggia <lb/>e la grandine e l'olio ed altri liquori, quando si congelano. </s>

<s>Quindi &egrave; che <lb/>ognuno di loro ovvero diviene opaco, ovvero perde o tanto o quanto di tra&shy;<lb/>sparenza, perciocch&egrave; le parti, che nel liquido erano uniformi, si variano in <lb/>figura e densit&agrave;, onde il lume, nel penetrarvi, costretto a far pi&ugrave; riflessioni <lb/>e rifrazioni, non pu&ograve; trapassar dirittamente &rdquo; (Savona 1647, pag. </s>

<s>52). </s></p><p type="main">

<s>Conforme a tali principii rende il Baliani la ragione perch&egrave; l'acqua si <lb/>mostri cerulea e diafana, e la spuma invece bianchissima e opaca. </s>

<s>&ldquo; Bianca <lb/>per riflettersi da ognuna di loro bollicelle il lume verso di noi, onde tanto <lb/>lume vediamo quante sono le bollette esterne della spuma, che quasi tanti <lb/>specchi tante volte ci rappresentano il lume quante elle sono. </s>

<s>Non ha tra&shy;<lb/>sparenza (la spuma) come quella che dipende non dalla rarit&agrave;, ma dalla uni&shy;<lb/>formit&agrave; del mezzo, onde entrativi i raggi n&egrave; trovando chi gli sforzi a pie&shy;<lb/>garsi, e perci&ograve; camminando diritti verso gli occhi, rappresentano loro l'oggetto <lb/>onde sono partiti. </s>

<s>Dovecch&egrave; nella spuma, le cui parti sono si diverse in den&shy;<lb/>sit&agrave; e figura, son costretti pi&ugrave; volte a riflettersi, e perci&ograve; spesso a non pe&shy;<lb/>netrarla, ed a rifrangersi, e per questo a non rappresentar l'oggetto se non <lb/>se molto confuso &rdquo; (ivi, pag. </s>

<s>24, 25). </s></p><p type="main">

<s>Quasi nel medesimo tempo dottrine ottiche similissime a queste erano <pb xlink:href="020/01/580.jpg" pagenum="23"/>professate dall'Hodierna, il quale, in uno de'suoi opuscoli intitolato <emph type="italics"/>La Nu&shy;<lb/>vola pendente,<emph.end type="italics"/> cos&igrave; scriveva: &ldquo; Causa della cui diafaneit&agrave; (cio&egrave; dell'aria) &egrave; <lb/>la conservazione di quei atomi nella loro minimeit&agrave;, e l'esser quasi conti&shy;<lb/>nuati con l'aria, nella guisa che il vetro ridotto in sottilissima polvere e <lb/>quella immersa nell'acqua, si rende transpicua e insensibile &rdquo; (Palermo 1644, <lb/>pag. </s>

<s>12). E pi&ugrave; sotto, per ispiegar come l'acqua apparisca bianca sotto <lb/>l'aspetto di neve, cos&igrave; dice: &ldquo; La causa della bianchezza della neve &egrave; la <lb/>massa scontinuata o congregata di moltissime goccioline; l'efficiente la luce <lb/>che illumina tutte e ciascheduna gocciola, che li sta nel cospetto; la causa <lb/>formale &egrave; la specie della luce moltiplicata dalle parti innumerabili e confu&shy;<lb/>samente all'occhio rappresentate &rdquo; (ivi, pag. </s>

<s>21). </s></p><p type="main">

<s>Cos&igrave;, in Italia, nella fisica delle riflessioni, si cercava ingegnosamente <lb/>di render la ragione dell'essere e della natura de'corpi diafani e degli opa&shy;<lb/>chi, mentre i Cartesiani si pascevano d'immaginazioni, e comprendendo i <lb/>Nostri in un'unica speculazione il cielo e la terra, le minime e le grandis&shy;<lb/>sime cose, a una causa unica, a quella cio&egrave; de'moltiplicati riflessi, riducevasi <lb/>il candor della spuma e della neve e il candor della Luna. </s>

<s>Ma se questa <lb/>sovente ne'suoi mensili ritorni, alla luce del sole fa specchio e ci illumina <lb/>le notti, fa anche talvolta da riparo e ci ottenebra i giorni. </s>

<s>L'ecclissi tro&shy;<lb/>varono una facile spiegazione nelle propriet&agrave; che hanno i corpi opachi d'im&shy;<lb/>pedire il libero passaggio alla luce, e di gettar dietro a s&egrave; l'ombre. </s>

<s>N&egrave; fu <lb/>difficile intendere come dipendendo esse ombre dalla figura del corpo opaco <lb/>e dalle relative distanze di questo al corpo illuminante, se ne poteva trat&shy;<lb/>tare applicandovi le regole geometriche. </s>

<s>Ma in progresso dov&egrave; accorgersi la <lb/>scienza che le tenebre erano anch'esse misteriose quanto forse la stessa <lb/>luce, e rimase maravigliata in veder che tanto capricciosamente alle leggi <lb/>della Geometria recalcitravano i fatti osservati. </s></p><p type="main">

<s>Bench&egrave; fosse per&ograve; lo studio dell'ombre posteriore allo studio della luce, <lb/>e penasse alquanto la scienza ad accorgersi che non troppo bene si corri&shy;<lb/>spondevano la Fisica e la Geometria, come dagli Ottici s'era creduto, senza <lb/>troppo travagliarsi d'investigare, in tal proposito, il vero; s'ingann&ograve; nono&shy;<lb/>stante Isacco Vossio quando, uscendo fuori nel 1662 col suo libro <emph type="italics"/>De na&shy;<lb/>tura lucis et proprietate<emph.end type="italics"/> si lusingava d'essere stato egli il primo a inse&shy;<lb/>gnare la teoria dell'ombre. </s>

<s>&ldquo; Sed vero qui sic existimant, graviter errant, <lb/>nec satis intelligunt umbrarum rationem. </s>

<s>Nullum quippe corpus est quam&shy;<lb/>tumvis magnum, sive etiam quamtumvis exiguum, quod non infinitas spar&shy;<lb/>gat umbras. </s>

<s>Verum quidem est ex circumferentia solis progredi radios, qui <lb/>umbram faciant desinentem in conum, sed, cum ex omni solis puncto ad <lb/>omne punctum ferantur radii, necessarium quoque est ut ab codem extremo <lb/>solis ambitu exeant radii &rdquo; (Hagae Comitis, pag. </s>

<s>80, 81). D'onde egli con&shy;<lb/>clude esser due le parti da considerarsi, una dov'&egrave; l'ombra assoluta, l'al&shy;<lb/>tra dove <emph type="italics"/>est umbra dubia sive umbra cum luce permixta.<emph.end type="italics"/></s></p><p type="main">

<s>Fatta una tal considerazione, che l'Autore ci d&agrave; come cosa nuova, cos&igrave; <lb/>immediatamente soggiunge: &ldquo; Quamvis vero nesciam an alii, qui de luce <pb xlink:href="020/01/581.jpg" pagenum="24"/>scripsere, duplicis huius umbrae fecerint mentionem, non ideo tamen minus <lb/>vera esse quae scribimus libenter, ut puto fatebitur si quis vel digiti vel <lb/>cuiuscumque alius corpusculi umbram ad solem vel lucernam examinave&shy;<lb/>rit. </s>

<s>Discrepantes quidem fient umbrae pro ratione intervalli et magnitudine <lb/>corporis lucentis et interpositi opaci.... una interior et ubique sibi simi&shy;<lb/>lis, altera mixta et paulatim imbecillior &rdquo; (ibi, pag. </s>

<s>82). </s></p><p type="main">

<s>Sar&agrave; stato forse vero che nel 1662 s'incominciasse in Olanda a notar <lb/>la differenza fra l'ombra e la penombra, facendo la filosofica esperienza del <lb/>dito suggerita dal Vossio, ma in Italia quell'osservazione &egrave; ben assai pi&ugrave; <lb/>antica, e l'avevan fatta i Pittori, e Leonardo ne aveva dato regola desunta <lb/>dalla pratica e dalla Geometria. </s>

<s>Nel 1625 Pietro Accolti dedic&ograve; la sua III Parte <lb/>della Prospettiva a trattar <emph type="italics"/>De'lumi et ombre<emph.end type="italics"/> e incomincia il Capitolo XII col <lb/>notar che &ldquo; non solamente le ombre propagandosi fanno mutazione quanto <lb/>alle naturali loro intensioni, ma anche, siccome diversamente si contermi&shy;<lb/>nano col lume ne'progressi loro, cos&igrave; ancora variamente e diversamente de&shy;<lb/>vono rappresentarsi &rdquo; (Firenze, pag. </s>

<s>108). Ma perch&egrave; intorno al modo del <lb/>conterminarsi dell'ombre ne'progressi loro sentiva l'Accolti il bisogno di <lb/>spiegarsi co'Pittori, che al loro pratico esercizio attendevano dalla scienza i <lb/>precetti; cos&igrave; appresso scrivava in forma di proposizione: </s></p><p type="main">

<s>&ldquo; Dico dunque che l'ombre, siccome vanno costipate da'lumi, che suc&shy;<lb/>cessivamente le accompagnano fino ne'loro posamenti, ove vanno finalmente <lb/>a terminare; cos&igrave; in tal loro concorde progresso quanto pi&ugrave; sempre dal corpo <lb/>opaco si allontanano, tanto pi&ugrave; ancora l'ombra col lume ed il lume con <lb/>l'ombra si concilia, e pare che gli estremi loro facciano passaggio dentro i <lb/>confini, e termini l'uno dell'altro per qualche poco di spazio, la qual co&shy;<lb/>mune loro mistione i Pittori chiamano unione e sfumamento. </s>

<s>Ci&ograve; apparisce <lb/>in ogni ombra, ma notabilmente in quella, che &egrave; fatta derivante dal diurno <lb/>luminare del sole. </s>

<s>La causa di tale apparenza ed effetto deriva, non dal&shy;<lb/>l'aere ambiente il corpo luminoso, come alcuni credono, ma onninamente <lb/>dalla ampiezza diametrale di esso corpo luminoso, qualunque egli si sia, il <lb/>che meglio apparir&agrave; dalla seguente figura &rdquo; (ivi). E passa di qui l'Accolti <lb/>a dare alla sua proposizione evidenza di prova geometrica, la quale noi lta&shy;<lb/>liani avemmo dall'altra parte, un secolo prima che scrivesse il Vossio il suo <lb/>libro, ne'Fotismi del Maurolico. </s>

<s>Il teorema XVIII infatti del nostro Siciliano <lb/>&egrave; cos&igrave; formulato: &ldquo; Quo maius fuerit lucidum, quoque magis illuminatum <lb/>a plano in quod umbra proiicitur, distiterit, eo maiores atque intensiores <lb/>umbrae termini videntur &rdquo; (Neapoli 1611, pag. </s>

<s>13). </s></p><p type="main">

<s>Supposto che sia AB (fig. </s>

<s>9) il lucido, e CD l'illuminato, condotte le <lb/>linee AK, BL e AF, BE, prosegue l'Autore la sua dimostrazione, che egli <lb/>poi conclude nel corollario seguente: &ldquo; Aut igitur umbra est spatium in <lb/>quod nullum lucidi signum radiat aut id spatium, in quo nullum signum <lb/>est, quod ab unoquoque lucidi signo illuminatur. </s>

<s>Secundum ergo primam <lb/>differentiam ipsius CD umbra est spatium KL: secundum vero reliquam <lb/>ipsius CD umbra est totum EF spatium. </s>

<s>Nam spatium KL, a nullo lucidi <pb xlink:href="020/01/582.jpg" pagenum="25"/>AB signo illuminatur. </s>

<s>Spatium vero EF nullum habet punctum quod ab <lb/>unoquoque lucidi AB puncto illuminetur &rdquo; (ibi, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Che il libro del nostro Maurolico fosse ignorato dal Vossio &egrave; un fatto <lb/><figure id="id.020.01.582.1.jpg" xlink:href="020/01/582/1.jpg"/></s></p><p type="caption">

<s>Figura 9.<lb/>notabile s&igrave;, perch'ebbe da quel celebre Au&shy;<lb/>tore i primi ed efficaci impulsi a risorgere <lb/>l'Ottica matematica in Europa, ma &egrave; ben <lb/>pi&ugrave; notabile che l'Olandese ignorasse i <emph type="italics"/>Pa&shy;<lb/>ralipomeni<emph.end type="italics"/> di quel Keplero, che egli, in <lb/>proposito dell'ombre negli ecclissi, prende <lb/>occasione di confutare. </s>

<s>Nel 1666 arricchiva <lb/>lo stesso Vossio la letteratura scientifica con <lb/>un altro libro intitolato <emph type="italics"/>De Nili origine,<emph.end type="italics"/> in <lb/>appendice al quale torna a trattare della <lb/>penombra negli ecclissi di Luna, e al tro&shy;<lb/>varsi immersa in essa penombra attribui&shy;<lb/>sce, contro l'opinion del Keplero, i rossori, <lb/>che rendon fra le tenebre parvente la stessa <lb/>Luna ecclissata. </s>

<s>&ldquo; Intempestiva est enim ratio Kepleri, eorumque qui illum <lb/>secuti sunt, qui putant ruborem seu dilutiorem umbram quae in Lunae ap&shy;<lb/>paret deliquiis, effici a radiis in hoc nostro aere refractis. </s>

<s>Fieri enim mi&shy;<lb/>nime posse ut illi Solis radii hunc nostrum aerem ingrediantur, et vicissim <lb/>exeant.... Cum enim omnis refractio fiat a rariori ad densius, et aer ter&shy;<lb/>ris vicinus densior sit illo superiore, necesse est ut quotquot radii aerem <lb/>ingrediuntur, in terram impingentes deficiant &rdquo; (Hagae Comitis, pag. </s>

<s>143). </s></p><p type="main">

<s>Intorno a ci&ograve; aveva senza dubbio ragione il Vossio, come si notava da <lb/>noi di sopra a proposito della teoria neutoniana dell'etere esalato dalle su&shy;<lb/>perficie riflettenti, il qual etere, se diminuisse in densit&agrave;, come diminuisce <lb/>l'aria intorno alla Terra, un raggio di luce che vi s'immergesse non po&shy;<lb/>trebbe risaltare al di fuori. </s>

<s>Non aveva per&ograve; ragione di tornar colla sua <emph type="italics"/>Ap&shy;<lb/>pendice<emph.end type="italics"/> a dubitar che prima di lui nessuno avesse atteso alla penombra, la <lb/>quale negli ecclissi accompagna l'ombra proiettata dalla Terra: vi aveva at&shy;<lb/>teso sessantadue anni prima quel Keplero, censurato dal Vossio, il qual Vos&shy;<lb/>sio, entrando a trattare di un tal soggetto avrebbe dovuto leggere nel ca&shy;<lb/>pitolo VI il &sect; 7 che s'intitola <emph type="italics"/>De penumbra Terrae.<emph.end type="italics"/></s></p><p type="main">

<s>Comunque sia, non si pu&ograve; negar che l'Ottico olandese non fosse de'primi <lb/>a risolvere alcuni capitali problemi dell'ombre negli ecclissi. </s>

<s>Se non che <lb/>troppo si confidava che le sue linee condotte sulla carta a prefinire i limiti <lb/>della luce assoluta e della luce incerta, dietro i corpi opachi illuminati, aves&shy;<lb/>sero a rispondere puntualmente ai fatti. </s>

<s>Egli desiderava che gli Astronomi <lb/>&ldquo; accuratius annotassent terminos tam interioris quam exterioris umbrae, <lb/>nam sane si haec differentia nota esset, utique etiam notum fieret interval&shy;<lb/>lum Solis, nec quaeremus utrum Sol 700 an vero 15000 terrae semidiame&shy;<lb/>tris a nobis absit &rdquo; (ibi, pag. </s>

<s>144). </s></p><p type="main">

<s>Il desiderio del Vossio, generoso certamente in s&egrave;, avrebbe per quelle <pb xlink:href="020/01/583.jpg" pagenum="26"/>vie potuto condurre gli Astronomi all'intento, quando fosse stato facile no&shy;<lb/>tare i termini tanto interiori quanto esteriori dell'ombra. </s>

<s>Ma non s'era an&shy;<lb/>cora incontrata la scienza a doversi arretrare incerta innanzi a nessuno di <lb/>que'misteri, che dicemmo le tenebre presentare allo studio de'Filosofi; mi&shy;<lb/>steri non meno impenetrabili forse di quelli della luce. </s>

<s>Come e quando oc&shy;<lb/>corresse il primo, e perch&egrave; inaspettato, rumoroso fatto di que'misteri pre&shy;<lb/>sentati dall'ombre, sar&agrave; non ignobile parte del seguente paragrafo di storia. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Il celebre Filosofo francese Pietro Gassendi, facendo alcune esperienze <lb/>intorno all'ombre proiettate da una palla opaca esposta al sole, e tornando <lb/>a osservare a varie ore del giorno, cred&egrave; di aver trovato, con sua gran ma&shy;<lb/>raviglia che, in sul mattino e in sul tramonto, quelle ombre riuscissero pi&ugrave; <lb/>larghe e pi&ugrave; lunghe, che quando il sole era presso al meridiano. </s>

<s>Frugato <lb/>dalla novit&agrave; della cosa, ripet&egrave;, con pi&ugrave; diligenza che mai, quelle esperienze e <lb/>confermatosi le novit&agrave; osservate esser vere, divulg&ograve; la notizia del fatto, che <lb/>lev&ograve; gran rumore specialmente in Italia. </s>

<s>Il Gassendi per&ograve;, come dava per <lb/>certo quel fatto, cos&igrave; confessava di esser dubbioso delle ragioni, laonde Fi&shy;<lb/>losofi e dilettanti, discepoli e amici si rivolgevano a Galileo che, nella pro&shy;<lb/>fondit&agrave; della sua scienza, ripescasse la chiave di quel mistero. </s>

<s>Fra'Filosofi <lb/>e i discepoli s'annovera il Cavalieri, e fra'dilettanti e gli amici Girolamo <lb/>Bardi, le lettere de'quali son rimaste fra'manoscritti galileiani. </s></p><p type="main">

<s>&ldquo; Discorressimo lungamente (dice il Cavalieri in una lettera scritta da <lb/>Bologna il d&igrave; 8 Giugno 1638) sopra una osservazione fatta da un Francese <lb/>amico suo (di Fortunio Liceti), circa le ombre del sole poste in due siti, <lb/>cio&egrave; alto sopra l'orizzonte e basso intorno al detto orizzonte, al quale, se si <lb/>supponer&agrave; un corpo ombroso, come per esempio una palia che mandi la sua <lb/>ombra in un piano, dal quale ella sia ugualmente lontana nel sito basso e <lb/>alto del sole; dice che l'ombra causata dal sole vicino all'orizzonte &egrave; mag&shy;<lb/>giore dell'ombra cagionata da esso nel sito alto, cio&egrave; che osserva che la <lb/>lunghezza delle ombre fatte dal sole nato di poco, e che poco dopo tra&shy;<lb/>monta, nel qual sito appare maggiore per vapori ecc. </s>

<s>sono maggiori della <lb/>lunghezza delle ombre causate dal sole nel sito alto, stante l'istesso corpo <lb/>ombroso e l'istessa distanza dal piano, nel quale la sbatte; cosa che par <lb/>che debba essere al contrario, poich&egrave;, facendosi il sole apparentemente mag&shy;<lb/>giore, pare che venga a tosare l'ombra attorno attorno che sar&igrave;a fatta da <lb/>esso apparentemente minore, e che perci&ograve; quella dovr&agrave; essere minore nel <lb/>sito pi&ugrave; basso. </s>

<s>Ho bene considerato che se non si parla dell'ombra totale, <lb/>ma dell'ombra con la chioma, dir&ograve;, o con quella parte, che credo i pittori <lb/>chiamino <emph type="italics"/>sbattimento,<emph.end type="italics"/> nella quale si va digradando continuamente dall'om&shy;<lb/>bra totale della luce totale: che l'aggregato dell'ombra totale e della chioma <pb xlink:href="020/01/584.jpg" pagenum="27"/>fatta dal sole basso cio&egrave; maggiore in apparenza, deva esser maggiore del&shy;<lb/>l'aggregato dell'ombra totale e della chioma fatta dal sole alto, cio&egrave; minore, <lb/>come anco V. S. Ecc.ma facilmente intender&agrave; esser vero, ma che la sola om&shy;<lb/>bra totale del sole maggiore deva esser maggiore dell'ombra del sole mi&shy;<lb/>nore, il che afferma ancora della Luna alta e bassa, credo che ci&ograve; sia im&shy;<lb/>possibile, s'io non m'inganno. </s>

<s>Tuttavia mi rimetto alla sottigliezza sua, che <lb/>subito intender&agrave; qual sia la verit&agrave; in questo fatto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ho voluto formare un poco d'esperienza con una riga parallela ad <lb/>una tavoletta, nella quale ricevendo l'ombra dal sole nel mezzod&igrave; e vicino <lb/>al tramontare non ci ho conosciuto differenza di ombra. </s>

<s>Vero &egrave; che la riga, <lb/>che &egrave; lunga poco pi&ugrave; d'un palmo e mezzo, e lontana solo un palmo dalla <lb/>tavoletta, non faceva forse distinguere bene essa ombra, onde la voglio <lb/>fare con metterla assai lontana dalla tavoletta, per vedere pure se pu&ograve; es&shy;<lb/>sere questo che dice avere osservato detto Francese &rdquo; (MSS. Gal., P. VI, <lb/>T. XIII, c. </s>

<s>100). </s></p><p type="main">

<s>Quasi un anno dopo, non sapendosi altro dell'esperienza che aveva in <lb/>animo di ripetere il Cavalieri, la curiosit&agrave; seguitava a frugare gl'ingegni, e <lb/>Girolamo Bardi, cos&igrave;, nel di 24 Agosto 1639, scriveva a Galileo, sperando <lb/>d'esserne sodisfatto. </s>

<s>&ldquo; Vien proposto dal signor Gassendi un problema che <lb/>l'ombra da un corpo opaco resta maggiore dal sole orizzontale che dal me&shy;<lb/>desimo verticale. </s>

<s>Vorrei che V. S. me ne desse la cagione, perch&egrave; la lon&shy;<lb/>tananza del semidiametro dovr&agrave; di ragione fare insensibile mutazione ed egli <lb/>apparisce essere grandissima &rdquo; (ivi, c. </s>

<s>161). </s></p><p type="main">

<s>Qual risposta per&ograve; avessero il Cavalieri e il Bardi alle loro desiderose <lb/>richieste, noi non siamo in grado di dirlo ai nostri lettori, non essendoci <lb/>note le responsive, le quali forse non furono scritte, o se furono scritte par <lb/>che del problema gassendistico Galileo confessasse di non saper che se ne <lb/>dire. </s>

<s>Cos&igrave; per noi s'argomenta da quel che leggesi nella <emph type="italics"/>Lettera sul Can&shy;<lb/>dore lunare,<emph.end type="italics"/> verso la fine, in risposta a Fortunio Liceti, il quale, amico al <lb/>Gassendi, fu da questi, per mezzo del Naudeo, richiesto della spiegazione <lb/>del fatto dell'ombre, non saputa trovar da s&egrave; tale, che se ne potesse sodi&shy;<lb/>sfare un filosofo. </s>

<s>Il Liceti per&ograve;, il quale apparteneva a quella s&egrave;tta di Fi&shy;<lb/>losofi, che sanno con gran facilit&agrave; trovar nel loro cervello una ragion cal&shy;<lb/>zante a qualunque fatto pi&ugrave; strano, ebbe anche una risposta pronta da dare <lb/>al Gassendi, e gliela fece in una lettera, a cui il Gassendi stesso rispose con <lb/>un'altra <emph type="italics"/>lunghissima lettera di sedici fogli interi<emph.end type="italics"/> (Alb. </s>

<s>VII, 346). E per&shy;<lb/>ch&egrave; tanto il Peripatetico si compiaceva d'essersi fatto maestro all'inclito <lb/>Gassendi, dette solennit&agrave; alla risposta fatta al problema dell'ombre nel fa&shy;<lb/>moso capitolo L del <emph type="italics"/>Liteosforo.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sed et partes aetheris (egli ivi scrisse) contermini solaribus affectae <lb/>radiis in lunare corpus opacum et obscurum natura sua repercutere pos&shy;<lb/>sunt exiguum lumen quod et in deliquiis et prope coniunctiones languere <lb/>conspicitur, ac utcumque minuere nativam lunaris corporis obscuritatem. </s>

<s><lb/>Quemadmodum et apud nos aer umbrae conterminus radiis solaribus in me-<pb xlink:href="020/01/585.jpg" pagenum="28"/>ridie laterales umbrae partes abrodit, in eas vividiori lumine repercusso, <lb/>proindeque reddit umbram angustioris latitudinis, quod efficere non potest <lb/>aer matutinus, nec vespertinus, mitioribus radiis, imbecilliorique solis tum <lb/>orientis, tum occidentis lumine perfusus, ut non ita pridem scripsimus ad <lb/>Cl. </s>

<s>Naudaeum, qui nos inclyti Gassendi nomine rogavit causam, ob quam <lb/>opaci corporis umbra latior appareat sole prope finitorem humili, strictior <lb/>e contra editiore sole procul ab horizonte verticalem regionem perambu&shy;<lb/>lante, cuius rei certas observationes, ac indubitata prorsus experimenta se <lb/>dicit habere Cl. </s>

<s>Mathematicus: verum hac de re late perscripsimus ad exi&shy;<lb/>mium virum &rdquo; (Alb. </s>

<s>III, 188). </s></p><p type="main">

<s>Di questa soluzione, data dal Liceti al problema delle ombre, scriveva <lb/>cos&igrave; Galileo nella sopra citata Lettera sul Candore lunare: &ldquo; Circa a quello <lb/>che in ultimo soggiugne del farsi l'ombre maggiori dal sole basso che dal&shy;<lb/>l'alto, non ho che dirci altro, se non che mi pare, che egli altra volta ne&shy;<lb/>gasse cotal effetto &rdquo; (ivi, pag. </s>

<s>236), d'onde s'argomentava da noi di sopra <lb/>che Galileo si fosse astenuto dal dir la sua opinione al Cavalieri e al Bardi, <lb/>e a parecchi altri forse che se ne mostravano desiderosi. </s></p><p type="main">

<s>Le speculazioni del Cavalieri, le quali per verit&agrave; si posson tener nello <lb/>stesso pregio di quelle del Liceti, attribuendo il grand'uomo un effetto reale <lb/>al variare il diametro del sole, secondo le altezze sue varie sull'orizzonte, <lb/>ci&ograve; che non &egrave; realt&agrave;, ma un inganno dell'occhio; non che il tacersi di Ga&shy;<lb/>lileo parrebbero una confessione delle difficolt&agrave; che incontravansi nel risol&shy;<lb/>vere il problema venuto di Francia, la qual confessione toglievasi forse, come <lb/>peso importuno dalla coscienza, col negare, secondo accennava lo stesso Ca&shy;<lb/>valieri, la verit&agrave; del fatto osservato dal Gassendi. </s>

<s>Da ci&ograve; forse provenne che, <lb/>quietato quel subitaneo rumore, non se ne parl&ograve; pi&ugrave; per quasi un secolo, <lb/>infintantoch&egrave; non si sent&igrave; il bisogno di ricorrere allo studio pi&ugrave; diligente <lb/>dell'ombre fatte dai nostri piccoli oggetti, per interpetrare i misteri dell'om&shy;<lb/>bre proiettate negli spazii celesti. </s></p><p type="main">

<s>Quel misterioso apparir tuttavia rubiconda la Luna, anche immersa nel&shy;<lb/>l'ombra della Terra, avea tenuto e tuttavia teneva in gran travaglio l'in&shy;<lb/>gegno degli Astronomi, fra'quali, prima del risorgere della scienza per la <lb/>fortunata invenzione del Canocchiale, &egrave; notabile, quel che cos&igrave; ne speculava <lb/>in proposito il Benedetti: </s></p><p type="main">

<s>&ldquo; Quod vero Luna nullum ex se habeat lumen, sufficiens inditium est <lb/>nos ipsam tanto magis obscuram videre, quanto magis in cono umbrae Ter&shy;<lb/>rae immergitur, et si eo tempore ipsam videmus rubeo colore affectam, hoc <lb/>enim accidit quia radii solares undequaque refranguntur a vaporibus ipsam <lb/>terram circumdantibus, quae quidem refractio fit versus axem coni umbrae <lb/>Terrae, et propterea umbra dicti coni non est aequaliter obscura sed tene&shy;<lb/>brosa. </s>

<s>Circa vero axem ipsius coni magis quam circa eius circumferentiam <lb/>obscuratur, et quia corpus lunare tale est ut facillime recipiat qualecumque <lb/>lumen, quod etiam manifeste videtur dum ipsa Luna reperitur secundum <lb/>longitudinem inter solem et Venerem, quod pars Lunae lumine solis desti-<pb xlink:href="020/01/586.jpg" pagenum="29"/>tuta, a lumine Veneris aliquantulum illustratur, quod ego saepe vidi et mul&shy;<lb/>tis ostendi; propterea dum ipsa Luna in cono umbrae Terrae reperitur adhuc <lb/>videtur &rdquo; (Liber speculationum, Venetiis 1599, pag. </s>

<s>257). </s></p><p type="main">

<s>Ebbero, da queste speculazioni del celebre Veneziano, origine e l'ipo&shy;<lb/>tesi delle rifrazioni professata dal Keplero e quella della fosforescenza in&shy;<lb/>nata nella Luna, a somiglianza della Pietra bolognese immaginata dal Liceti, <lb/>e le altre seguite da varii della illuminazion partecipata da Venere e riflessa <lb/>a noi dal disco lunare, non che quella dell'etere ambiente professata da Ga&shy;<lb/>lileo (Alb. </s>

<s>VII, 276). E bench&egrave; si mantenga in onore appresso i pi&ugrave; degli <lb/>Astronomi l'ipotesi kepleriana, furono tutte le altre dimostrate apertamente <lb/>false: anzi la stessa ipotesi del Keplero fu come vedemmo contraddetta, non <lb/>forse senza ragione, dal Vossio, il quale non alle rifrazioni attribuiva il fe&shy;<lb/>nomeno, ma s&igrave; all'esser la Luna immersa nella penombra della Terra. </s></p><p type="main">

<s>Anche questa ipotesi per&ograve;, che sembra esser pi&ugrave; naturale e accettabile <lb/>delle altre, fu trovata andare incontro a gravissime difficolt&agrave;. </s>

<s>L'ombra as&shy;<lb/>soluta della Terra dovrebbe, secondo i calcoli, distendersi per 110 de'suoi <lb/>diametri, e perch&egrave; la Luna non ne &egrave; distante che 60 semidiametri in circa, <lb/>dovrebbe negli ecclissi trovarsi immersa o totalmente o parzialmente nel&shy;<lb/>l'ombra, e perci&ograve; o disparire del tutto, o mostrarsi falcata, fenomeno che <lb/>nessuno ha mai osservato. </s>

<s>Di qui se n'ebbe a concludere non potersi il <lb/>trasparir fra le tenebre la Luna attribuirsi all'essere immersa nella pe&shy;<lb/>nombra. </s></p><p type="main">

<s>Il Maraldi per&ograve; saviamente considerando che la Natura opera spesso al&shy;<lb/>trimenti da quel che le vorrebbero prescrivere i nostri calcoli artificiosi, <lb/>pens&ograve; di ricorrere alla esperienza, e fu a questa occasione che torn&ograve; in <lb/>campo il problema del Gassendi. </s>

<s>Il valoroso nepote di Gian Domenico Cas&shy;<lb/>sini (e di ci&ograve; lasci&ograve; Memoria negli Atti della R. </s>

<s>Accademia parigina del 1721) <lb/>trov&ograve; esser vero che le ombre proiettate da una sfera opaca o da un cilin&shy;<lb/>dro son pi&ugrave; lunghe, quando in sul mattino il sole o in sul tramonto &egrave; <lb/>alquanto men luminoso. </s>

<s>Trov&ograve; altres&igrave; che una sfera, la quale avrebbe do&shy;<lb/>vuto gittar secondo il calcolo l'ombra a 110 de'suoi diametri, non raggiun&shy;<lb/>geva appena i 41. Il Maraldi speriment&ograve; in questa occasione altri fatti sul&shy;<lb/>l'ombre, con intenzione di illustrar l'Astronomia delle ecclissi, tenendo anche <lb/>conto delle diffrazioni, essendo che il sole pu&ograve; rassomigliarsi al foro e la <lb/>Terra al capello o altro corpicciolo attraversato al raggio lucido nel celebre <lb/>esperimento grimaldiano. </s>

<s>Ma con tuttoci&ograve; le ombre osservate nelle sue pic&shy;<lb/>cole sfere dal Gassendi, e quelle osservate dagli astronomi nelle grandissime <lb/>sfere celesti, rimasero tuttavia se non ombre, certamente penombre nelle <lb/>menti de'Filosofi. </s></p><p type="main">

<s>Dietro questi fatti la storia c'insegna che i Filosofi hanno bene spesso <lb/>trovate difficolt&agrave; dove meno se l'aspettavano. </s>

<s>Ma come si sarebbe aspettato <lb/>Aristotile di dovere arrestarsi dubitoso innanzi a un forellino, per cui passa <lb/>un raggio di sole? </s>

<s>Eppure &egrave; cos&igrave;: nella Sezione XV de'Problemi la Que&shy;<lb/>stione V &egrave; dal Filosofo posta in tal forma: &ldquo; Cur sol per quadrilatera pro-<pb xlink:href="020/01/587.jpg" pagenum="30"/>fluens non rectis lineis figuram decribit, sed circulum format, ut in crati&shy;<lb/>bus patet? </s>

<s>&rdquo; e la risposta che d&agrave; il gran Maestro di coloro che sanno, si <lb/>riduce a dire: &ldquo; An quod aspectuum procidentia turbine agitur, turbinis au&shy;<lb/>tem basis in orbem se colligit, quamobrem quocumque radii Solis incurre&shy;<lb/>rint nimirum circulares appareant? </s>

<s>An quod Solis quoque figuram rectis <lb/>lineis contineri necesse est, siquidem radii recti proveniunt? </s>

<s>&rdquo; (Aristotelis. </s>

<s><lb/>Colliget, Venetiis 1610, T. IX, c. </s>

<s>298). </s></p><p type="main">

<s>Quel solenne maestro d'Ottica, Vitellione che ebbe tanta autorit&agrave; di <lb/>magistero nel mondo, quanta forse ne pot&egrave; avere lo stesso Aristotile, per <lb/>provar la proposizione XXXIX del libro II <emph type="italics"/>Omne lumen per foramina an&shy;<lb/>gularia incidens rotundatur<emph.end type="italics"/> (Perspectiva, edit. </s>

<s>cit., c. </s>

<s>47) introduce il prin&shy;<lb/>cipio che i raggi quanto pi&ugrave; si dilungano dal luminoso e tanto pi&ugrave; si avvi&shy;<lb/>cinano alla equidistanza (propos. </s>

<s>XXXV, c. </s>

<s>46) ond'&egrave; che il lume cadendo <lb/>sulla superficie del foro s'incomincia a rotondare. </s></p><p type="main">

<s>Ma il Cantuariense ne'<emph type="italics"/>Tre Libri della Perspettiva<emph.end type="italics"/> tradotti dal Gallucci <lb/>fa almeno intendere qual sia la sua spiegazione, la quale si fonda principal&shy;<lb/>mente sopra un'ipotesi metafisica, ed &egrave; che gli atomi della luce dovendo <lb/>essere di natura perfettissima non possono essere altrimenti configurati che <lb/>in sfera. </s>

<s>&ldquo; Ora perch&egrave; la figura sferica &egrave; vicina alla luce ed accomodata a <lb/>tutti i corpi del mondo, come perfettissima e molto conservativa della na&shy;<lb/>tura, e che congiunge tutte le parti compitissimamente nel suo intimo; la <lb/>luce dunque si muove naturalmente a questi, ed acquista quella alla di&shy;<lb/>stanza terminata. </s>

<s>Si vede dunque manifestamente da queste due cause che <lb/>il lume che passa per un forame si fa rotondo a poco a poco &rdquo; (Vene&shy;<lb/>zia 1593, c. </s>

<s>3, B). </s></p><p type="main">

<s>Contro cos&igrave; fatti errori del principe de'Filosofi, e di coloro che gli fanno <lb/>intorno corona, insorgeva il Keplero a dimostrar che il fatto era a tutt'al&shy;<lb/>tro da attribuirsi che alla rotondit&agrave; de'raggi o alla perfetta figura sferica <lb/>degli atomi luminosi. </s>

<s>&rdquo; Patuit itaque concurrere ad problema demonstran&shy;<lb/>dum non radii visorii, sed ipsius solis, non quia haec perfectissima sit figura, <lb/>sed quia haec lucentis corporis figura sit in genere &rdquo; (Paralip. </s>

<s>ad Vitell, <lb/>Francofurti 1604, pag. </s>

<s>39). E la proposizione III di questo stesso cap. </s>

<s>II, <lb/>ordinata dall'Autore a dimostrar la ragione che ha la figura dello spettro alla <lb/>figura del foro aperto nell'imposta chiusa di una finestra, va seguita da que&shy;<lb/>sto corollario: &ldquo; Sequitur hinc per singulas fenestrae alicuius puncta quo&shy;<lb/>rum infinita sunt singulas adeoque infinitas transmitti in superficiem illu&shy;<lb/>stratam imagines lucentis inversas, eodem ordine se mutuo consequentes, <lb/>quem tenent ipsa puncta fenestrae &rdquo; (ibi, pag. </s>

<s>44). </s></p><p type="main">

<s>Ma, prima che il Keplero sarebbe stato bello contrapporre al principe <lb/>de'Filosofi e a'veneratori di lui un uomo tutto alieno dal far professione <lb/>di Filosofia, e che seppe imparar da s&egrave; quel che, dopo faticosi studii, non <lb/>avevan saputo insegnare i Maestri. </s>

<s>Leonardo da Vinci, nella sua Ottica di&shy;<lb/>spersa per le note manoscritte, non lasci&ograve; indietro di risolvere il problema <lb/>proposto da Aristotile nella sopra citata sezione, e sicuro di s&egrave;, e non come <pb xlink:href="020/01/588.jpg" pagenum="31"/>Aristotile stesso, dubbioso, frettolosamente scriveva: &ldquo; Nessuno spiracolo <lb/>pu&ograve; trasmutare il concorso de'razzi luminosi in modo che per la lunga di&shy;<lb/>stanzia non porghino all'obietto la similitudine della sua cagione. </s>

<s>&mdash; Impos&shy;<lb/>sibile &egrave; che i razzi luminosi passati per parallelo, dimostrino nell'obbietto <lb/>la forma della loro cagione, poich&egrave; tutti gli effetti de'corpi luminosi sono <lb/>dimostrativi delle loro cagioni. </s>

<s>La Luna di forma naviculare passata dallo <lb/>spiracolo figurer&agrave; nell'obietto un corpo naviculare &rdquo; (Ravaisson-Mollien, Ma&shy;<lb/>nus. </s>

<s>de Leonard. </s>

<s>A fol. </s>

<s>64, v.). </s></p><p type="main">

<s>Il concetto di Leonardo &egrave; in bel modo illustrato dall'Accolti, il quale, <lb/>imbevuto dell'Ottica kepleriana, proponendosi di risolvere il problema dello <lb/>spettro rotondo attraverso allo spiraglio di tutt'altra figura &ldquo; stimo, egli <lb/>scrive, la intrinseca causa di tale effetto essere la circolarit&agrave; dell'istesso corpo <lb/>sferico luminoso del sole, e congiuntamente la distanza dell'opposto piano <lb/>del foro, per il quale fanno passaggio s&igrave; bene tutti i raggi enascenti da cia&shy;<lb/>scun punto del corpo solare, ma non gi&agrave; tutti unitamente, e senza disgre&shy;<lb/>garsi, in detto illuminato piano pervengano &rdquo; (Prospett. </s>

<s>prat. </s>

<s>cit., pag. </s>

<s>113). </s></p><p type="main">

<s>L'asserto, che contien concetti sottili quanto la luce, si studia l'Autore <lb/>di render chiaro per la seguente dottrina: &ldquo; Sia per esempio il sferico corpo <lb/>luminoso del sole, di cui tanta parte di azione illuminante faccia passaggio <lb/>ad illustrare il piano sottopostoli, quanta capisce un dato aperto e quadrato <lb/>foro. </s>

<s>E perch&egrave; da ciascun punto di esso luminoso si spicca piramidalmente <lb/>la suddetta sferale azione del lume, ne seguir&agrave; che quanti punti si pigliano <lb/>a considerare in detto sferico, tante ancora in numero eguali, punte pira&shy;<lb/>midali si costituischino; adunque altrettante loro basi di splendore simili <lb/>tutte di figura al foro, dal quale passando sono formate, ma in tanto diverse <lb/>fra loro di sito, quanto da diversi punti del corpo sferico.... sono dette <lb/>basi qua e l&agrave; costituite. </s>

<s>Onde, perch&egrave; da ciascun punto del luminoso corpo <lb/>si fa passaggio per il dato qual si sia foro, e per ciascuna parte di esso, <lb/>molto bene intendiamo non solo il termine e confino di ciascuno splendore <lb/>dover esser causato sul piano del termine e confino del corpo luminoso.... <lb/>ma che la suddetta figura di splendore sul detto piano esistente, sar&agrave; com&shy;<lb/>posta e rester&agrave; dintornata da tante multiplici base quadrate, in giro dispo&shy;<lb/>ste, da quanti punti dell'estremit&agrave; circolare del raggiante corpo luminoso <lb/>del sole possono formarsi, i quali, perch&egrave; sono infiniti, cos&igrave; da infinite basi <lb/>rester&agrave; composta l'apparenza dello splendore suddetto. </s>

<s>Adunque se il con&shy;<lb/>fino o dintorno del luminoso sia circolare, com'&egrave; quello del sole, cos&igrave; cir&shy;<lb/>colarmente ed in giro si andranno buttando sul piano e disponendo dette <lb/>infinite basi e giuntamente con loro quella infinita multiplicit&agrave; de'respettivi <lb/>angoli di ciascheduna base, li quali unicamente lasciano dintornata sul piano <lb/>la figura d'illuminazione, come parti pi&ugrave; remote e le pi&ugrave; estreme che pos&shy;<lb/>sono considerarsi ne'dintorni delle suddette basi piramidali. </s>

<s>Onde per s&egrave; <lb/>stessa si rende molto ben nota all'intelligenza la cagione, per la quale cia&shy;<lb/>scuna apparente illuminazione passante per foro di qualsivoglia figura, sem&shy;<lb/>pre circoleggi &rdquo; (ivi, pag. </s>

<s>113, 14) </s></p><pb xlink:href="020/01/589.jpg" pagenum="32"/><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>L'Ottica non &egrave; una di quelle scienze che finisca in s&egrave; stessa, non si <lb/>limita cio&egrave; a studiare le propriet&agrave; della luce in quegli effetti, che pi&ugrave; d'ap&shy;<lb/>presso operano sui nostri sensi, ma essendo ella quasi lo spirito animatore <lb/>dell'Universo invita a investigarne i misteri, nel lontano e splendido cielo, <lb/>l'affetto e l'intelligenza dell'uomo. </s>

<s>Le ombre osservate nelle sfere di legno <lb/>o di altra materia opaca fecero intender meglio con qual legge, diversa da <lb/>quella prescritta da'calcoli, si proiettino le ombre dalla Terra, dalla Luna <lb/>e dagli altri pianeti. </s>

<s>Le osservazioni attente e le argute speculazioni intorno <lb/>ai raggi di sole passati attraverso un piccolo foro, che avevan aria di mera <lb/>filosofica curiosit&agrave;, s'accomodarono anch'esse, testimone il Keplero, a pi&ugrave; <lb/>nobile astronomico uso. </s>

<s>&ldquo; Caeterum et Aristotiles et is quem dixi Pisanus <lb/>ad emendationem argumenti pulcherrimum experimentum afferens de Solis <lb/>deficientis radio similiter deficiente, cum is per angustum foramen recipi&shy;<lb/>tur, occasionem Reinholdo, Gemmae et Maestlino praeceptori meo submi&shy;<lb/>nistravit accomodandi theorema ad usum non minus nobilem &rdquo; (Paralip. </s>

<s><lb/>cit., pag. </s>

<s>39). </s></p><p type="main">

<s>Di nessuna propriet&agrave; per&ograve; speculata intorno alla luce si fece pi&ugrave; no&shy;<lb/>bile applicazione all'Astronomia, di quella che concerne la legge dell'intensit&agrave; <lb/>del suo splendore. </s>

<s>Per essa legge, come vedremo, ebbe principio l'Astro&shy;<lb/>nomia matematica, e s'intesero per essa le altre leggi, che governano i moti <lb/>dell'Universo. </s>

<s>Per quali vie tortuose e lunghe si giungesse a dimostrare il <lb/>modo come si diffonde la luce, e come e quando la scienza ottica, dubbiosa <lb/>e diffidente, s'acquietasse all'ultimo in quelle verit&agrave;, che per la Geometria <lb/>e per l'esperienza s'erano da lungo tempo gi&agrave; dimostrate, &egrave; ci&ograve; che noi <lb/>passiamo ora a narrare. </s></p><p type="main">

<s>Primo fra gli Autori d'Ottica pi&ugrave; conosciuti a speculare intorno all'in&shy;<lb/>tensit&agrave; della luce fu il Maurolico, il quale dimostra ne'suoi Fotismi i due <lb/>Teoremi seguenti: <emph type="italics"/>&ldquo; Theorema II.<emph.end type="italics"/> Aequaliter inclinati radii, aequaliter, ere&shy;<lb/>ctiores autem magis, perpendiculares vero maxime illuminant &rdquo; (Neapoli 1611, <lb/>pag. </s>

<s>2). <emph type="italics"/>&ldquo; Theorema III.<emph.end type="italics"/> Aeque remota signa aequaliter; propriora vero <lb/>magis illuminant &rdquo; (ibi, pag. </s>

<s>3). </s></p><p type="main">

<s>I due Teoremi fotometrici limitati cos&igrave; a ci&ograve; che ne porgeva di pi&ugrave; <lb/>certo ogni ovvia esperienza, son con facilit&agrave; dimostrati, essendo evidente&shy;<lb/>mente veri, ma provandosi poi il Maurolico ad allargarsi nel periglioso <lb/>mare inesplorato, smarrisce assai presto la diritta via, come si par dal pros&shy;<lb/>simo V Teorema: &ldquo; Possibile est signa ad inaequales distantias, spacium ali&shy;<lb/>quod aequaliter illustrare &rdquo; (ibi, pag. </s>

<s>4). </s></p><p type="main">

<s>Nel circolo ABD (fig. </s>

<s>10) suppone che A e B sieno due lucenti (signa) <lb/>che illuminino l'oggetto CD: crede che, sebbene i due segni sieno diver&shy;<lb/>samente lontani, possan nulladimeno illuminar con intensit&agrave; uguale l'oggetto. <pb xlink:href="020/01/590.jpg" pagenum="33"/>Crede egli cos&igrave;, perch&egrave; gli angoli CAD, CBD essendo uguali, comprendono <lb/>quantit&agrave; uguale di raggi luminosi, e avendo supposto <emph type="italics"/>plures radios inten&shy;<lb/><figure id="id.020.01.590.1.jpg" xlink:href="020/01/590/1.jpg"/></s></p><p type="caption">

<s>Figura 10.<lb/>sius, aequales vero aequaliter illuminare<emph.end type="italics"/> (ibi, pag. </s>

<s>1) <lb/>ne conclude perci&ograve; che debba esser l'oggetto illumi&shy;<lb/>nato da ugual quantit&agrave; di luce o sia vicino il lucido <lb/>o sia piu&ugrave; lontano. </s></p><p type="main">

<s>Il paralogismo era atto a sedurre qualunque pi&ugrave; <lb/>acuto ingegno, e anche Galileo, come fra poco ve&shy;<lb/>dremo, ne fu sedotto. </s>

<s>La radice occulta poi dell'er&shy;<lb/>ror seducente stava in ci&ograve; che si considerava la luce <lb/>diffondersi non per la solidit&agrave; sferica ma per la su&shy;<lb/>perficialit&agrave; circolare. </s>

<s>Questo errore nel Maurolico <lb/>non apparisce espresso, ma il Keplero che rifuggiva <lb/>dall'ammetter la diffusione sferica della luce, perch&egrave; essendo la trina dimen&shy;<lb/>sione propria de'solidi non faceva possibile intendere come potesse la stessa <lb/>luce penetrare altri corpi e diffondersi in istante; apertamente profess&ograve; nelle <lb/>proposizioni VI e VII del cap. </s>

<s>I de'Paralipomeni a Vitellione la diffusione <lb/>superficiale. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Prop. </s>

<s>VI.<emph.end type="italics"/> Luci cum discessu a centro accidit aliqua attenuatio in <lb/>latum. <emph type="italics"/>Prop. </s>

<s>VII.<emph.end type="italics"/> Lucis radio cum discessu a centro nulla accidit attenua&shy;<lb/>tio in longum: hoc est non quo longior radius hoc rarior seu sparsior, pro&shy;<lb/>pter quidem hanc ipsam longitudinem &rdquo; (edit. </s>

<s>cit., pag. </s>

<s>9). Di qui &egrave;, se&shy;<lb/>condo il Keplero, che, considerato un raggio solo, egli &egrave; ugualmente vigoroso <lb/>a principio e a termine della sua diffusione: considerati pi&ugrave; raggi insieme, <lb/>perciocch&egrave; essi non si attenuano che <emph type="italics"/>in latum,<emph.end type="italics"/> deve dunque la loro inten&shy;<lb/>sit&agrave; scemare a proposizione che crescono le semplici distanze. </s></p><p type="main">

<s>L'Aguilonio, bench&egrave; tenesse anch'egli la diffusione istantanea della luce <lb/>e le attribuisse propriet&agrave; di spirituale sostanza, non ebbe nulladimeno il co&shy;<lb/>raggio di negare una cosa tanto patente al senso, qual'&egrave; che i raggi lumi&shy;<lb/>nosi diffondonsi d'ogni parte per la solidit&agrave; della sfera. </s>

<s>Egli perci&ograve; nell'<emph type="italics"/>Ot&shy;<lb/>tica,<emph.end type="italics"/> trattando al Libro V <emph type="italics"/>De luminis profusione,<emph.end type="italics"/> non dubita di asserire e <lb/>di provare &ldquo; Lumen effusum circumquaque in spherae modum distenditur &rdquo; <lb/>(Antuerpiae 1613, pag. </s>

<s>373). </s></p><p type="main">

<s>Dietro un tal verissimo principio l'Aguilonio, primo fra gli Ottici, s'av&shy;<lb/>via a risolvere con buon indirizzo il problema dell'intensit&agrave; della luce. </s>

<s>&ldquo; Fors <lb/>quisquam hanc idoneam esse causam arbitrabitur, cur lumen progressione <lb/>languescat, quod lumen in spherae modum diffundat sese, ut prop. </s>

<s>III osten&shy;<lb/>sum est. </s>

<s>Erit itaque corpus lucidum velut centrum eius sphaerae, quam <lb/>activitatis vocant, cuius circumferentia erit illa superficies ad quam actio <lb/>corporis lucentis terminatur. </s>

<s>Ab hoc ergo centro, sive corpore lucido, si re&shy;<lb/>ctos undique radios ad circumferentiam protensos animo concipias, ani&shy;<lb/>madvertes eos quo longuis a medio progrediuntur, eo semper ampliori in&shy;<lb/>tervallo ab invicem divaricari. </s>

<s>E converso autem eo semper arctius stringi, <lb/>quo propius ad centrum accesserint, quoad tandem in unum simul omnes <pb xlink:href="020/01/591.jpg" pagenum="34"/>conveniant, seque mutuo amplectantur. </s>

<s>At coniunctum lumen efficacius ex&shy;<lb/>cellentiusque est disperso, per communem notionem, igitur, iuxta sphaerae <lb/>centrum, intensissimum est lumen, inde vero, quo longius provehitur, eo <lb/>semper rarius segniusque evadit &rdquo; (ibi, pag. </s>

<s>375). </s></p><p type="main">

<s>Chi si trova nel leggere condotto a questo punto, s'aspetta che l'Au&shy;<lb/>tore abbia presto a concluderne, proseguendo la diritta via presa, che l'in&shy;<lb/>tensit&agrave; della luce non &egrave; in ragion reciproca delle semplici distanze, come <lb/>conseguiva dai falsi principii del Keplero, ma s&igrave; veramente ch'ella &egrave; in re&shy;<lb/>ciproca ragione de'quadrati delle distanze. </s>

<s>Con sorpresa dolorosa per&ograve; chi <lb/>legge, come chi vedesse uno tornare indietro, quando pochi passi pi&ugrave; oltre <lb/>era per vincere il palio, sente cos&igrave; tosto soggiungere: &ldquo; Haec ratio, licet ex <lb/>necessariis concludere videatur, facile tamen convelli potest &rdquo; (ibi). E perch&egrave; <lb/>si dee cos&igrave; svegliere la radice a un vero tanto felicemente germogliato? </s>

<s>Per <lb/>pi&ugrave; ragioni, risponde l'Aguilonio. </s>

<s>Prima, perch&egrave; la virt&ugrave; del magnete non si <lb/>diffonde in sfera ma in linea retta; poi, perch&egrave; sebben la luce si diffonda <lb/>in lungo e in largo, non ha luogo ci&ograve; nel raggio solitario, in cui pure l'in&shy;<lb/>tensit&agrave; diminuisce colla distanza. </s>

<s>&ldquo; Deinde, si ea esset decrementi causa, se&shy;<lb/>queretur aequalibus spatiis aequalia fieri luminis decrementa &rdquo; (ibi). </s></p><p type="main">

<s>L'allucinazione dell'Autore &egrave; qui veramente singolare Se l'intensit&agrave; <lb/>luminosa diminuisse in ragione della diffusione superficiale della sfera, non <lb/>ne seguirebbe che in spazii uguali i decrementi fossero uguali, ma sareb&shy;<lb/>bero que'decrementi come i quadrati degli spazii uguali. </s>

<s>Tutto l'inganno <lb/>consiste nel considerar quegli stessi decrementi farsi a proporzion che cre&shy;<lb/>scono le circonferenze de'cerchi e non le superficie delle sfere. </s>

<s>&ldquo; Esto (cos&igrave; <lb/>prosegue l'Autore a concludere una verit&agrave;, per farla poi ministra a un pa&shy;<lb/>ralogismo) corpus luminosum A (fig. </s>

<s>11), radiique ab A profusi AB et AC, <lb/><figure id="id.020.01.591.1.jpg" xlink:href="020/01/591/1.jpg"/></s></p><p type="caption">

<s>Figura 11.<lb/>a quibus aequales par&shy;<lb/>tes obscindantur per <lb/>arcus BC, DE, FG et <lb/>HK, ex eodem centro <lb/>A descriptos. </s>

<s>His vero <lb/>arcubus subtendantur <lb/>chordae, quas dico pa&shy;<lb/>rallelas esse.... Tanto <lb/>enim remissus est lu&shy;<lb/>men in loco BC, quanto <lb/>BC maior est ipsa DE, <lb/>aut quanto DE ipsa BC est minor. </s>

<s>Sequitur igitur, si eam ob causam lu&shy;<lb/>men protensum languescit, quod radii a corpore luminoso evibrati magis <lb/>ac magis divaricantur, lumina aequalibus spatiis aequalia pati decrementa &rdquo; <lb/>(ibi, pag. </s>

<s>376). Ma ci&ograve; non pu&ograve; essere, conclude l'Aguilonio, dunque &egrave; falso <lb/>che diminuisca il lume per la sua sferica diffusione. </s></p><p type="main">

<s>Che non possa esser che il lume diminuisca in proporzion che crescono <lb/>le semplici distanze, l'Aguilonio lo dimostra cos&igrave; con un ingegnoso ragio-<pb xlink:href="020/01/592.jpg" pagenum="35"/>namento fondato sull'esperienza. </s>

<s>Sia A (fig. </s>

<s>12) un luminare splendente con <lb/>4 gradi d'intensit&agrave;, che diffonda nel prossimo spazio il suo lume, diventando <lb/>in spazii uguali 3, 2, 1, e finalmente riducendosi a zero. </s>

<s>Sia B un altro si&shy;<lb/><figure id="id.020.01.592.1.jpg" xlink:href="020/01/592/1.jpg"/></s></p><p type="caption">

<s>Figura 12.<lb/>mile luminare, che si diffonda <lb/>con la medesima legge. </s>

<s>Se ve&shy;<lb/>ramente i decrementi de'lumi <lb/>in uguali spazii si facessero <lb/>uguali, ne verrebbe che lo spa&shy;<lb/>zio interposto fra'due luminari <lb/>dovess'essere ugualmente lu&shy;<lb/>minoso, avendosi quattro gradi <lb/>di lume per tutto. </s>

<s>&ldquo; Quis enim <lb/>adeo luminibus destitutus est, qui non videat inter duas lucernas centum <lb/>stadiis ab invecem disiunctas, minus luminis circa medium esse quam circa <lb/>extrema? </s>

<s>Esset autem aequale si aequalibus spatiis aequalia fierent decre&shy;<lb/>menta, ut ex apposito schemate conspici potest &rdquo; (ibi, pag. </s>

<s>377). </s></p><p type="main">

<s>Lasciatosi miseramente aggirar l'Aguilonio, dopo aver corso un buon <lb/>tratto per la diretta via, non ebbe la felicit&agrave; di toccar la meta, ma come <lb/>segno dell'esservisi molto avvicinato, lasci&ograve; nel citato libro V dell'Ottica di&shy;<lb/>mostrate le seguenti proposizioni: <emph type="italics"/>&ldquo; Prop. </s>

<s>V.<emph.end type="italics"/> Lumen longius proiectum <lb/>sensim languescit (pag. </s>

<s>375). <emph type="italics"/>Prop. </s>

<s>VI.<emph.end type="italics"/> Aequalibus spatiis inaequalia fiunt <lb/>luminis decrementa (pag. </s>

<s>376). <emph type="italics"/>Prop. </s>

<s>VII.<emph.end type="italics"/> Aequalium spatiorum quae longius <lb/>absunt, minora efficiunt defectionum momenta (pag. </s>

<s>377). <emph type="italics"/>Prop. </s>

<s>VIII.<emph.end type="italics"/> Lu&shy;<lb/>men aequalibus spatiis proportionalibus decrementis languescit (pag. </s>

<s>379). <lb/><emph type="italics"/>Prop. </s>

<s>IX.<emph.end type="italics"/> Lumen uniformi difformitati decrescit &rdquo; (pag. </s>

<s>379). </s></p><p type="main">

<s>Otto anni dopo che l'Aguilonio aveva dimostrate queste sue proposizioni, <lb/>il Keplero pubblicava di nuovo il Misterio Cosmografico <emph type="italics"/>De admirabili pro&shy;<lb/>portione orbium coe&igrave;estium,<emph.end type="italics"/> dove il perpetuarsi de'pianeti nel loro moto <lb/>s'attribuiva agl'impulsi radiosi del sole. </s>

<s>&ldquo; Ponamus igitur id quod valde <lb/>verisimile est, eadem ratione motum a Sole dispensari qua lucem. </s>

<s>Lucis <lb/>autem ex centro prorogatae debilitatio qua proportione fiat docent Optici &rdquo; <lb/>(Francofurti 1621, pag. </s>

<s>76). </s></p><p type="main">

<s>Fra gli Ottici era da annoverarsi, a quel tempo, anche l'Aguilonio, il <lb/>quale anzi era divenuto il pi&ugrave; autorevole di tutti. </s>

<s>Ora, perch&egrave; questo Au&shy;<lb/>tore aveva dimostrato che il lume decresce con difformit&agrave; uniforme, forse <lb/>il Keplero si crederebbe che avesse corrette quelle sue opinioni, e che la <lb/>bella dimostrazione sperimentale dell'Ottico belga lo avesse persuaso non <lb/>patir il lume decrementi uniformemente uniformi. </s>

<s>Tutt'altrimenti per&ograve; l'Au&shy;<lb/>tore de'Paralipomeni a Vitellione non s'&egrave; niente rimosso da'suoi instituti e <lb/>gli Ottici che egli dianzi citava son quegli che si uniformano a cos&igrave; fatti <lb/>istituti, secondo i quali la luce s'attenua nel circolo o n&ograve; nella sfera, e per&shy;<lb/>ci&ograve; il decrescere dell'intensit&agrave; luminosa &egrave; da misurarsi non dal crescere delle <lb/>superficie sferali, ma delle circonferenze de'cerchi. </s>

<s>&ldquo; Nam quantum lucis <lb/>est in parvo circulo, tantundem etiam lucis sive radiorum solarium est in <pb xlink:href="020/01/593.jpg" pagenum="36"/>magno. </s>

<s>Hinc cum sit in parvo stipatior, in magno tenuior mensura huius <lb/>attenuationis ex ipsa circulorum proportione petenda erit, idque tam in luce, <lb/>quam in motrice virtute &rdquo; (ibi). </s></p><p type="main">

<s>L'errore preso qui dal Keplero, fu infausto, come vedremo ai pro&shy;<lb/>gressi dell'Astronomia matematica, ma perch&egrave; non dovesse un simil danno <lb/>ricevere l'arte del disegno, l'Accolti fu sollecito di avvertire gli artisti del&shy;<lb/>l'errore in ch'erano incorsi alcuni Pittori del maggior grido &ldquo; i quali hanno <lb/>stimato poter conoscere matematicamente e proferire la quantit&agrave; dell'inten&shy;<lb/>sione del lume, dovuto a ciascun oggetto in pittura, rappresentati da loro <lb/>in diverse parti e siti dei loro piani degradati, con misurare e partire in pi&ugrave; <lb/>parti perspettivamente eguali il raggio luminoso o spazio, che si frappone <lb/>tra l'oggetto illuminato ed il corpo luminoso &rdquo; (Prospettiva cit., pag. </s>

<s>98). <lb/>E affine che il Pittore, nella rappresentazione di diversi oggetti da illumi&shy;<lb/>narsi in diverse lontananze sappia come contenersi nel lumeggiare, dimo&shy;<lb/>stra, traducendo quasi a parola l'Aguilonio, com'&egrave; contrario all'esperienza <lb/>il digradar la diminuzione de'lumi in prospettiva a proporzione che cre&shy;<lb/>scono le semplici distanze (ivi, pag. </s>

<s>98, 99). </s></p><p type="main">

<s>Nel 1632 Galileo pubblicava i Dialoghi De'due Massimi Sistemi, e in <lb/>quell'Opera cos&igrave; celebre, dove tanto promovevasi la Filosofia naturale, l'Ot&shy;<lb/>tica non fa nemmeno un passo pi&ugrave; avanti. </s>

<s>Nel I di que'Dialoghi ha l'Au&shy;<lb/>tore occasione di toccare un soggetto di Fotometria, ma pronunziando che <lb/>&ldquo; le medesime superficie vengono dal medesimo lume pi&ugrave; o meno illumi&shy;<lb/>nate, secondo che i raggi illuminanti vi cascano sopra pi&ugrave; o meno obliqua&shy;<lb/>mente, sicch&egrave; la massima illuminazione &egrave; dove i raggi sono perpendicolari &rdquo; <lb/>(Alb. </s>

<s>I, 91); non faceva altro che tradurre il Teorema II del Maurolico <lb/>ne'citati Fotismi. </s>

<s>La prima dimostrazione sperimentale, che Galileo d&agrave; &egrave; <lb/>ovvia al senso di tutti; la seconda dimostrazione geometrica &egrave; quella stessa, <lb/>che il Benedetti dava, come vedremo, per dimostrare il vario grado d'in&shy;<lb/>tensit&agrave; calorifica ricevuta dalla superficie o tenuta obbliqua o perpendico&shy;<lb/>larmente opposta all'irradiazione della sorgente. </s></p><p type="main">

<s>La dimostrazione galileiana per&ograve; &egrave; molto meno elaborata. </s>

<s>Fate conto <lb/>che tutte le linee parallele, che voi vedete partirsi dai termini A, B (fig. </s>

<s>13) <lb/><figure id="id.020.01.593.1.jpg" xlink:href="020/01/593/1.jpg"/></s></p><p type="caption">

<s>Figura 13.<lb/>siano i raggi, che sopra la linea CD ven&shy;<lb/>gono ad angoli retti: inclinate ora la me&shy;<lb/>desima CD, sicch&egrave; penda come DO, non <lb/>vedete voi che buona parte di quei raggi <lb/>che ferivano la CD, passano senza toccare <lb/>la DO? Adunque, se la DO &egrave; illuminata <lb/>da manco raggi, &egrave; ben ragionevole che il <lb/>lume ricevuto da lei sia pi&ugrave; debole &rdquo; (ivi, <lb/>pag. </s>

<s>92). </s></p><p type="main">

<s>N&egrave; il Benedetti nulladimeno n&egrave; Galileo dimostrarono che la intensit&agrave; <lb/>della luce o del calore, ricevuti obliquamente sopra una superficie, &egrave; pro&shy;<lb/>porzionale al seno dell'angolo dell'incidenza; Teorema che in generale, di <pb xlink:href="020/01/594.jpg" pagenum="37"/>qualunque natura sia il corpo che percote, non fu da nessuno, come vedremo <lb/>in altra parte di questa storia, dimostrato prima che dal Torricelli. </s></p><p type="main">

<s>Intanto, anche dopo quel fervore di studii di cose naturali eccitato dalla <lb/>pubblicazione de'<emph type="italics"/>Massimi Sistemi,<emph.end type="italics"/> gli Ottici, della profusione del lume, non <lb/>avevan saputo ancora nulla di pi&ugrave; di quel che aveva loro insegnato l'Agui&shy;<lb/>lonio. </s>

<s>Sapevan che in quella profusione l'intensit&agrave; diminuisce con pi&ugrave; rapide <lb/>proporzioni di quelle delle semplici distanze, ma non sapevan per&ograve; definire <lb/>quali fossero quelle proporzioni. </s></p><p type="main">

<s>Una sera di estate del 1634 il Castelli a Roma conversava con alcuni <lb/>amici suoi letterati, mentre la Luna nuova appariva pel sereno del cielo <lb/>nella sua sottilissima falce, e il resto si mostrava di una luce cinerea leg&shy;<lb/>germente incandito. </s>

<s>Sollevando que'letterati gli occhi alla Luna, e persuasi, <lb/>dagli argomenti del padre don Benedetto, che quel candore era dovuto a'ri&shy;<lb/>flessi della Terra, facevan nulladimeno difficolt&agrave; come potesse la Terra illu&shy;<lb/>minare pi&ugrave; la Luna di quello che fa la Luna la Terra. </s>

<s>Si proponeva cos&igrave; <lb/>un problema di Fotometria, e il Castelli, per sodisfare a que'suoi amici, <lb/>torn&ograve; poche sere dopo, applicando a risolvere le difficolt&agrave; il Teorema cos&igrave; <lb/>da lui formulato: </s></p><p type="main">

<s>&ldquo; Se saranno due lumi, ineguali in specie ed in grandezza, illuminanti <lb/>la medesima sorta di oggetti in distanze ineguali, l'illuminazione assoluta <lb/>del primo all'illuminazione assoluta del secondo avr&agrave; la proporzione com&shy;<lb/>posta del lume in specie del primo al lume in specie del secondo, della <lb/>grandezza della superficie del primo alla grandezza della superficie del se&shy;<lb/>condo, e della proporzion duplicata della lontananza del secondo dall'og&shy;<lb/>getto illuminato alla lontananza del primo dall'oggetto da lui illuminato &rdquo; <lb/>(Alb. </s>

<s>X, 50). </s></p><p type="main">

<s>Ecco finalmente la vera legge fotometrica scoperta: l'intensit&agrave; del lume <lb/>scema a proporzione che crescono i quadrati delle distanze. </s>

<s>Come proce&shy;<lb/>desse il Castelli nella dimostrazione del suo fotometrico Teorema sarebbe <lb/>bello a sapere, ma perch&egrave; non &egrave; rimasto di ci&ograve;, almeno che sia noto a noi, <lb/>altra memoria da quella lettera a Galileo scritta il d&igrave; 12 Agosto 1634, in <lb/>essa, dopo aver formulato il sopraddetto Teorema, dice solo cos&igrave; in gene&shy;<lb/>rale: &ldquo; Tutto dimostro premesse alcune definizioni e supposizioni manifeste, <lb/>dal che si pu&ograve; discorrere di quella tanto varia riflessione di lumi de'Pia&shy;<lb/>neti alla Terra. </s>

<s>Per&ograve; lascio stare il tutto in riposo per poterlo rivedere senza <lb/>passione &rdquo; (ivi). </s></p><p type="main">

<s>Forse disanimato dalla poca accoglienza fatta da Galileo, il quale non <lb/>seppe riconoscere n&egrave; perci&ograve; debitamente pregiare la verit&agrave; feconda che si <lb/>ascondeva nel Teorema fotometrico del suo discepolo, il Castelli non torn&ograve; <lb/>a rivedere la sua dimostrazione, che rimase in perpetuo riposo. </s>

<s>Cos&igrave; lasciava <lb/>il merito di pubblicarla, a benefizio universale della scienza e a gloria della <lb/>patria, a un Francese. </s></p><p type="main">

<s>Quattro anni dopo che il Castelli aveva annunziato il suo Teorema a <lb/>Galileo, Ismaele Boulliaud pubblicava in Parigi, nel 1638, un suo Trattato <pb xlink:href="020/01/595.jpg" pagenum="38"/><emph type="italics"/>De natura lucis.<emph.end type="italics"/> Avendo egli troppo ben riconosciuto quanto errasse il <lb/>Keplero a negare la diffusione sferica alla luce, e quanto infelicemente si <lb/>fosse ritirato indietro l'Aguilonio dalla diritta via, per la quale s'era cos&igrave; <lb/>bene incamminato, liberamente in questa forma scriveva nella sua IV pro&shy;<lb/>posizione: &ldquo; Ut sphaerae incrementum dimensionum suscipiunt a digressu <lb/>linearum infinitarum aequalium a centro ad unam aliquam superficiem, <lb/>ubique a centro aequaliter distantem; ita lux incrementum dimensionum <lb/>suscipit a digressu radiorum infinitorum a corpore lucido ad aliquam su&shy;<lb/>perficiem sphaericam ubivis terminatam.... Superficies sunt ad invicem ut <lb/>ratio diametrorum ad invicem dupla: crescit ergo sphaera iuxta modum <lb/>incrementi dimetientis suae. </s>

<s>Lux vero sphaericam figuram in effluxu obser&shy;<lb/>vat; ergo lucis dimensiones crescunt porrecto radio, idest quo longius a lu&shy;<lb/>cido radii defluent, eo ampliores erunt lucis dimensiones ut in sphaera &rdquo; <lb/>(pag. </s>

<s>9). </s></p><p type="main">

<s>Di qui veniva l'Autore per diritta via condotto a formulare e a dimo&shy;<lb/>strare la sua XXVII proposizione: &ldquo; Densitate superficierum luminis sunt <lb/>ad invicem ut rationes duplae distantiarum superficierum a corpore lucido &rdquo; <lb/>(pag. </s>

<s>42). </s></p><p type="main">

<s>Il libro <emph type="italics"/>De natura lucis<emph.end type="italics"/> fu da Parigi, accompagnato con lettera del d&igrave; <lb/>30 Ottobre 1637, spedito dal Boulliaud a Galileo, a cui scriveva l'Autore <lb/>spero <emph type="italics"/>de illo opusculo iudicium tuum intelligam<emph.end type="italics"/> (Alb. </s>

<s>X, 242). Galileo ri&shy;<lb/>spondeva il d&igrave; 1&deg; Gennaio dell'anno seguente dicendo che la cecit&agrave;, sven&shy;<lb/>turatamente sopravvenutagli, gl'impediva di capir bene quelle dimostrazioni <lb/>&ldquo; quae ex figurarum dependent usu .... ea tamen quae capere auribus po&shy;<lb/>tui, summa cum delectatione audivi &rdquo; (Alb. </s>

<s>VII, 206). </s></p><p type="main">

<s>Per la dimostrazione fotometrica per&ograve; non c'era bisogno delle figure e <lb/>bastava persuadersi della diffusione sferica della luce perch&egrave; del resto, con&shy;<lb/>tentandosi di citarli, il Boulliaud rimanda ai notissimi teoremi geometrici <lb/>di Euclide Ma Galileo non pare che avesse quella persuasione, per cui di&shy;<lb/>cevasi da noi pi&ugrave; sopra che non fece buona accoglienza a quel Teorema del <lb/>Castelli, il quale fa perfettissimo riscontro con la proposizione XXVII del&shy;<lb/>l'Astronomo di Parigi. </s></p><p type="main">

<s>Che Galileo non approvasse i Teoremi dimostrati successivamente da'due <lb/>Autori, e che non sentisse la verit&agrave; feconda che s'annunziava con essi, non <lb/>&egrave; poi una nostra congettura ma un fatto. </s>

<s>Nel 1640, sei anni cio&egrave; dopo l'enun&shy;<lb/>ciato dal Castelli, e due anni dopo la pubblicazione del Boulliaud, occorse <lb/>a Galileo di risolvere un problema di Fotometria simile a quello proposto <lb/>al p. </s>

<s>d. </s>

<s>Benedetto da'suoi amici di Roma. </s>

<s>L'occasione fu a proposito della <lb/>controversia con Fortunio Liceti, il quale, per negar che il candore lunare <lb/>era un riflesso della Terra simile al riflesso della Luna, notava che fra le <lb/>due riflessioni era in intensit&agrave; tanta differenza da non si poter l'una ras&shy;<lb/>somigliare con l'altra. </s>

<s>Qui Galileo poteva applicare il Teorema fotometrico <lb/>del Castelli o la proposizione XXVII <emph type="italics"/>De Natura lucis,<emph.end type="italics"/> e il problema veniva <lb/>con verit&agrave; scientifica risoluto. </s>

<s>Ma egli &egrave; ancora col Maurolico: l'intensit&agrave; <pb xlink:href="020/01/596.jpg" pagenum="39"/>luminosa ei col Maurolico la misura dalla quantit&agrave; de'raggi luminosi com&shy;<lb/>presi dentro l'angolo che s'appunta nell'occhio. </s></p><p type="main">

<s>&ldquo; Di due oggetti visibili, ma in grandezza disuguali il minore ingom&shy;<lb/>bra l'occhio pi&ugrave; di luce che il maggiore, ancorch&egrave; ambedue fossero del&shy;<lb/>l'istesso splendore in spezie. </s>

<s>Ora notisi che il disco lunare vien compreso <lb/>sotto un angolo acutissimo, avvengach&egrave; la sua base non sottenda pi&ugrave; che <lb/>mezzo grado; ma l'angolo, che dalla massima divaricazione de'raggi visivi <lb/>si costituisce nell'occhio, essendo pi&ugrave; grande che retto, sottende a pi&ugrave; di <lb/>90 gradi interi, e questo viene tutto ingombrato dall'aria e piazza luminosa <lb/>della Terra, mentre che da vicino la rimiriamo. </s>

<s>Essendo dunque l'ampiezza <lb/>di questo grande angolo 200 volte maggiore dell'altro acuto che comprende <lb/>il disco lunare, maraviglia non dobbiamo prendere dell'apparente maggio&shy;<lb/>ranza di luce nel rimirar la Terra che la Luna incandita &rdquo; (Alb. </s>

<s>VII, <lb/>pag. </s>

<s>279, 80). </s></p><p type="main">

<s>Essendo cos&igrave;, non fa maraviglia che il Borelli nel 1665 stia ancor col <lb/>Keplero e desumendo la proporzione degl'impulsi radiosi del sole sui pia&shy;<lb/>neti pi&ugrave; o meno lontani, dalla proporzione come nell'intensit&agrave; diminuisce <lb/>la luce, conclude con pi&ugrave; tardo moto sospingere il Sole stesso i globi che <lb/>lo circondano <emph type="italics"/>ea proportione quam reciproce habent resistentiae seu distan&shy;<lb/>tiae<emph.end type="italics"/> (Theor. </s>

<s>medic., Florentiae 1665, pag. </s>

<s>65). </s></p><p type="main">

<s>Nel 1673 era ancora questa kepleriana la legge dell'intensit&agrave; della luce <lb/>professata dal Newton, quando istitu&igrave; il primo calcolo della velocit&agrave; con cui <lb/>sarebbe sulla Terra caduta la Luna. </s>

<s>Le celebri leggi neutoniane dell'attra&shy;<lb/>zione universale furono finalmente quelle che persuasero esser senza ecce&shy;<lb/>zione vero il Teorema fotometrico tanti anni prima dimostrato dal Castelli <lb/>e dal Boulliaud pubblicato, ma in Italia v'era pure chi, anche senza le sco&shy;<lb/>perte del grande Inglese, erasi assai per tempo assicurato, coll'esperienza, <lb/>della vera legge della Fotometria. </s></p><p type="main">

<s>Nel 1672 Geminiano Montanari cos&igrave; scriveva in una sua operetta inti&shy;<lb/>tolata <emph type="italics"/>La Fiamma volante:<emph.end type="italics"/> &ldquo; Ho pi&ugrave; volte sperimentato nella nostra Ac&shy;<lb/>cademia della Traccia che se con un lume di candela ordinaria io vedo con <lb/>una determinata chiarezza a leggere un dato carattere, per esempio alla di&shy;<lb/>stanza di un piede e mezzo dal medesimo lume; con quattro tali lumi ve&shy;<lb/>dr&ograve; con pari chiarezza alla distanza di tre piedi; con nove candele alla di&shy;<lb/>stanza di quattro piedi e mezzo; con sedici candele, a quella di sei piedi, e <lb/>cos&igrave; con quest'ordine, che vuol dire che il numero delle candele sia sem&shy;<lb/>pre il quadrato delle distanze &rdquo; (Bologna, pag. </s>

<s>42). </s></p><p type="main">

<s><emph type="center"/>VI.<emph.end type="center"/></s></p><p type="main">

<s>I moderni, che sanno con qual certezza ritengano oggidi gli Ottici e <lb/>con quanta facilit&agrave; di geometrica precisione dimostrino diffondersi il lume <lb/>sulle superficie di sfere concentriche, le quali crescono in ragione de'qua-<pb xlink:href="020/01/597.jpg" pagenum="40"/>drati de'raggi, conforme ai pi&ugrave; antichi documenti di Euclide; non possono <lb/>non far le maraviglie delle tante difficolt&agrave;, che trovarono gli antichi in in&shy;<lb/>vestigar quella legge, e non sanno persuadersi come, per cos&igrave; poco, si la&shy;<lb/>sciassero indur nell'errore. </s>

<s>Come mai, domanderanno, il gran Keplero perfidi&ograve; <lb/>nel negare alla luce una propriet&agrave; cos&igrave; patente qual'&egrave; quella del diffondersi <lb/>di lei per ogni verso? </s>

<s>E bench&egrave; alla domanda si sia gi&agrave; risposto, ripetiamo <lb/>che ci&ograve; fu per salvare i principii comunemente professati allora intorno al&shy;<lb/>l'essere e alla natura della luce, secondo i quali principii reputavasi che <lb/>l'agente cos&igrave; impercettibile alla crassizie de'sensi, non dovesse soggiacere <lb/>alle passioni degli altri corpi. </s>

<s>Si vede bene insomma che l'origine di quello <lb/>e di parecchi altri simili errori vien dal non essersi ancora ben definito il <lb/>concetto della natura di quel misterioso intangibile elemento, per cui noi <lb/>vediamo. </s></p><p type="main">

<s>Il bisogno di ben definir quel concetto fu sentito dal Boulliaud, il quale <lb/>a tale intento dette opera a scrivere il suo trattato <emph type="italics"/>De natura lucis.<emph.end type="italics"/> Egli <lb/>osserva ivi che gli antichi Euclide, Alhazeno, Vitellione non pensarono per <lb/>niente a definir la natura della luce: e soggiunge che il Keplero, bench&egrave; <lb/>abbia il gran merito di aver coniugato il primo l'Ottica alla Fisica, <emph type="italics"/>saepius <lb/>tamen pungere videtur quam perforare<emph.end type="italics"/> (Editio cit. </s>

<s>pag. </s>

<s>121). </s></p><p type="main">

<s>Primo, secondo il Boulliaud, a tentare la difficile questione fu il nostro <lb/>Dalmata Francesco Patrizio, nel I dei dieci libri della sua <emph type="italics"/>Panurgia,<emph.end type="italics"/> dov'egli <lb/>asserisce la luce essere un che di mezzo tra il corporeo e l'incorporeo nel <lb/>sole e negli astri. </s>

<s>&ldquo; Corpus est quia in his habet molem et trinam dimen&shy;<lb/>sionem, incorporea est, quia est forma solis &rdquo; (ibi) e soggiunge in oltre la <lb/>luce stessa <emph type="italics"/>in instanti moveri.<emph.end type="italics"/> L'Astronomo francese rifiutata solo la di&shy;<lb/>stinzione fra lume e raggi, i quali non son realt&agrave; ma affezioni dell'occhio, <lb/>segue in tutto i placiti del Filosofo nostro razionalista. </s></p><p type="main">

<s>Indipendentemente per&ograve; dalle sottili speculazioni del Patrizio, nel I libro <lb/>dell'Ottica, sentenziava cos&igrave; l'Aguilonio nella proposizione XXXIII &ldquo; Male <lb/>Empedocles lumen corpus esse dixit.... Lumen igitur non est corpus, cum <lb/>illud videamus ocissime et velut momento temporis longissima spatia eme&shy;<lb/>tiri &rdquo; (Edit. </s>

<s>cit., pag. </s>

<s>33), e pi&ugrave; espresso nella proposizione seguente: &ldquo; Sed <lb/>neque lumen corporea est qualitas: recte autem intentionalis vocari po&shy;<lb/>test.... Modus existendi luminis intentionalis est, quo extra proprium su&shy;<lb/>biectum, instar spiritualis substantiae totum existit simul ut in aere, aliove <lb/>corpore impune pervio, in quo sese plura lumina penetrant, et momento <lb/>temporis immensa spatia transcurrunt, more spirituum &rdquo; (ibi, pag. </s>

<s>34). </s></p><p type="main">

<s>Isacco Vossio che, dopo essersi istituita la scienza delle rifrazioni, stim&ograve; <lb/>doversi compiere quello del Boulliaud con un altro trattato <emph type="italics"/>De natura lu&shy;<lb/>cis et proprietate,<emph.end type="italics"/> dimostrava la sua proposizione &ldquo; Radios lucis non esse <lb/>corporeos &rdquo; dal fatto che infinite particelle diffuse ne'raggi lucidi possono <lb/>capire in un punto matematico, qual'&egrave; il foco di uno specchio parabolico. </s>

<s><lb/>Incorona poi cos&igrave; dicendo quella sua proposizione: &ldquo; Ipsum hoc confirmat <lb/>motus lucis. </s>

<s>Cum enim omnia corpora moveantur in tempore, lucis vero <pb xlink:href="020/01/598.jpg" pagenum="41"/>motus sit istantaneus, et hinc quoque patet lucem non esse corporeum &rdquo; <lb/>(Amstelodami 1662, pag. </s>

<s>16). </s></p><p type="main">

<s>&Egrave; manifesto da ci&ograve; che la natura incorporea della luce s'argomentava <lb/>dal diffondersi di lei, come gli spiriti, nell'istante. </s>

<s>Anche tutti i falsi con&shy;<lb/>cetti del Keplero movevano dal supposto che la luce fosse istantanea, d'onde <lb/>egli ne concludeva ch'ella dovess'essere assolutamente imponderabile e perci&ograve; <lb/>incorporea, e perci&ograve; non diffusibile per quelle tre dimensioni, in che si dif&shy;<lb/>fonde la crassizie de'corpi. </s>

<s>Quel supposto da un'altra parte, con circolo ine&shy;<lb/>vitabile, il Keplero stesso lo dimostra col suppor che la luce sia imponde&shy;<lb/>rante, imperocch&egrave; se l'impeto sta in ragione composta della celerit&agrave; e del <lb/>peso, e se questo &egrave; zero, la velocit&agrave; necessariamente ne risulta infinita. </s>

<s>&ldquo; Sed <lb/>hic, vis movens ad lucem movendam infinitam habet proportionem, quia luci <lb/>nulla materia, quare neque pondus. </s>

<s>Ita medium luci nihil resistit, quia lux <lb/>materia caret, per quam fiat resistentia. </s>

<s>Ergo lucis infinita celeritas est &rdquo; <lb/>(Paralip. </s>

<s>cit., pag. </s>

<s>3). </s></p><p type="main">

<s>Quanto a Galileo, essendo egli solito chiamar la luce <emph type="italics"/>l'ultimo spolve&shy;<lb/>ramento de'corpi,<emph.end type="italics"/> par che non dubitasse della natura corporea di lei, ma <lb/>convien pure che potrebb'esser vera la sentenza di chi credeva altrimenti. <lb/></s>

<s>&ldquo; Che la luce sia incorporea ed istantanea si potrebbe dire .... poich&egrave;, <lb/>avendo un pugnello di polvere e dandogli fuoco, ella si spande in immenso, <lb/>e si pu&ograve; vedere com'&egrave; che ella sia ridotta a'suoi indivisibili componenti e <lb/>fatta senza introduzione di corpi o di posizione di vacui quanti, ma bene <lb/>d'infiniti indivisibili vacui, e cos&igrave; non occupa luogo e non ricerca tempo di <lb/>andare da un luogo a un altro &rdquo; (MSS. Gal., P. V, T. IV, c. </s>

<s>28), sentenza <lb/>conforme a quella che leggesi nel <emph type="italics"/>Saggiatore<emph.end type="italics"/> (Alb. </s>

<s>IV, 338). </s></p><p type="main">

<s>Conoscendo per&ograve; Galileo la grande importanza che ha il moto in defi&shy;<lb/>nir la cos&igrave; dubbia e cos&igrave; controversa natura della luce, egli &egrave; il primo che, <lb/>a decidere se quel moto &egrave; in tempo o in istante, e se perci&ograve; la luce &egrave; spi&shy;<lb/>rito o corpo, abbia pensato di ricorrere alle esperienze. </s></p><p type="main">

<s>&ldquo; La poca concludenza di queste e di altre simili osservazioni mi fece <lb/>una volta pensare a qualche modo di poterci senza errore accertare se l'il&shy;<lb/>luminazione, cio&egrave; se la espansion del lume fosse veramente instantanea; <lb/>poich&egrave; il moto assai veloce del suono ci assicura quello della luce non po&shy;<lb/>ter esser se non velocissimo. </s>

<s>E l'esperienza che mi sovvenne fu tale. </s>

<s>Voglio <lb/>che due piglino un lume per uno, il quale, tenendolo dentro la lanterna o <lb/>altro ricetto, possino andar coprendo e scoprendo con l'interposizion della <lb/>mano alla vista del compagno, e che ponendosi l'uno incontro all'altro in <lb/>distanza di poche braccia, vadano addestrandosi nello scoprire ed occultare <lb/>il lor lume alla vista del compagno, sicch&egrave;, quando l'uno vede il lume del&shy;<lb/>l'altro, immediatamente scopra il suo, la qual corrispondenza, dopo alcune <lb/>risposte fattesi scambievolmente, verr&agrave; loro talmente aggiustata, che senza <lb/>sensibile svario, alla scoperta dell'uno risponder&agrave; immediatamente la sco&shy;<lb/>perta dell'altro, s&igrave; che quando l'uno scopre il suo lume vedr&agrave; nell'istesso <lb/>tempo comparire alla sua vista il lume dell'altro. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/599.jpg" pagenum="42"/><p type="main">

<s>&ldquo; Aggiustata cotal pratica in questa piccolissima distanza, pongansi i <lb/>due medesimi compagni con due simili lumi in lontananza di due o tre <lb/>miglia, e tornando di notte a far l'istessa esperienza, vadano osservando at&shy;<lb/>tentamente se le risposte delle loro scoperte e occultazioni seguono secondo <lb/>l'istesso tenore che facevano da vicino; che seguendo, si potr&agrave; assai sicu&shy;<lb/>ramente concludere l'espansion del lume essere instantanea; che quando <lb/>ella ricercasse tempo, in una lontananza di tre miglia, che importano sei, <lb/>per l'andata di un lume e venuta dall'altro, la dimora dovrebb'essere assai <lb/>osservabile &rdquo; (Alb. </s>

<s>XIII, 46, 47). </s></p><p type="main">

<s>Queste parole son nel Dialogo poste in bocca al Salviati, a cui doman&shy;<lb/>dando il Sagredo ci&ograve; che nel praticare un'invenzione non men sicura che <lb/>ingegnosa avesse concluso, il Salviati stesso risponde: &ldquo; Veramente non l'ho <lb/>sperimentata, salvo che in lontananza piccola, cio&egrave; manco d'un miglio, dal <lb/>che non ho potuto assicurarmi se veramente la comparsa del lume opposto <lb/>sia instantanea &rdquo; (ivi, pag. </s>

<s>47). </s></p><p type="main">

<s>L'esperienza fu poi ripetuta dagli Accademici fiorentini, i quali, per la <lb/>lontananza di un miglio, che per l'andar di un lume e la venuta dell'altro <lb/>vuol dir due, non vi seppero trovar differenza. </s>

<s>&ldquo; Se poi, si soggiunge nei <lb/><emph type="italics"/>Saggi di Naturali esperienze,<emph.end type="italics"/> in distanza maggiore sia possibile l'arrivare <lb/>a scorgervi qualche sensibile indugio, questo non c'&egrave; per anche riuscito di <lb/>sperimentare &rdquo; (Firenze 1841, pag. </s>

<s>173). </s></p><p type="main">

<s>Con tali brevi parole se ne spedisce il Segretario Magalotti, ma tanta <lb/>fu la sollecitudine, l'ingegno e l'industriosa variet&agrave; de'modi, con che que'tre <lb/>primi concorsi felicemente insieme nel secondo periodo della sperimentale <lb/>Accademia medica si studiarono di riuscir, bench&egrave; invano, nel difficile in&shy;<lb/>tento, che per l'onore della scienza italiana non vogliono esser taciuti nella <lb/>nostra Storia. </s></p><p type="main">

<s>Principale fra que'tre sappiamo oramai essere stato il Viviani, il quale <lb/>ritessendo, come Galileo, fra l'Ottica e la Meccanica le sue speculazioni, cos&igrave; <lb/>lasci&ograve; in una nota scritto della luce: &ldquo; Un corpo mobile per un mezzo cor&shy;<lb/>poreo vuol tempo a muoversi, perch&egrave; occupandovi luogo e dovendogli ce&shy;<lb/>dere il mezzo ne lo trattiene, ed il medesimo corpo mobile per un mezzo <lb/>incorporeo, come per vacuo, non ricerca tempo, anzi vi si muove in istante, <lb/>e tutto questo dice Aristotile. </s>

<s>Ma io soggiungo che tanto &egrave; muoversi un <lb/>corpo per un mezzo incorporeo, che un mobile incorporeo per un mezzo <lb/>corporeo, sendoch&egrave; l'uno per il mezzo non si tratterrebbe, n&egrave; l'altro sa&shy;<lb/>rebbe trattenuto dal mezzo. </s>

<s>Adunque la luce, che per Aristotile &egrave; incorpo&shy;<lb/>rea, per un mezzo corporeo qual'&egrave; l'aria passerebbe in istante, ma se si <lb/>provasse questa muoversi in tempo, ne seguirebbe che ella fosse corporea. <lb/>(MSS. Gal. </s>

<s>Disc, T. CXXXV, c. </s>

<s>27). </s></p><p type="main">

<s>Tanto conosceva il Viviani essere ai progressi dell'Ottica importante la <lb/>conclusione, che per provarne il principio gli balen&ograve; in mente un concetto <lb/>singolare, di che troviamo fatto ricordo in un'altra delle sue note: &ldquo; Sit <lb/>filum ferreum clavis A, B (fig. </s>

<s>14) longe dissitas religatum. </s>

<s>Constat quod <pb xlink:href="020/01/600.jpg" pagenum="43"/>si percutiatur in B resonabit A in eodem instanti, et sonus ex B in A in <lb/>non tempore tunc ferretur, ex quo patet si quo tempore fit ictus in B de&shy;<lb/>tegatur lumen dignosci ex A num illuminatio fiat in instanti &rdquo; (ibi, c. </s>

<s>14). <lb/><figure id="id.020.01.600.1.jpg" xlink:href="020/01/600/1.jpg"/></s></p><p type="caption">

<s>Figura 14.</s></p><p type="main">

<s>Ma perch&egrave; per troppo breve di&shy;<lb/>stanza pativa d'esser teso fra'due <lb/>anelli quel fil di ferro sonoro, per <lb/>avere spazii pi&ugrave; ampii si rivolse il <lb/>Viviani a praticare i metodi gi&agrave; proposti da Galileo, e sotto il d&igrave; 14 Aprile 1657 <lb/>si trova di sua propria mano scritto questo ricordo: &ldquo; Feci giorni sono l'espe&shy;<lb/>rienza della luce nel modo insegnato da Galileo &rdquo; (MSS. Cim., T. X, c. </s>

<s>181) <lb/>e si scelsero per le due stazioni il monte della Verrucola e il campanile di <lb/>Pisa (Targioni, Notiz. </s>

<s>cit., T. II, P. II, pag 585, 86). </s></p><p type="main">

<s>Fu a questa occasione che avendo risaputo il Borelli, professore di Ma&shy;<lb/>tematiche in quello studio, de'preparativi che si facevano per l'esperienza, <lb/>si sent&igrave; eccitato a speculare un pi&ugrave; facile e pi&ugrave; squisito modo di praticarla. </s>

<s><lb/>Di ci&ograve; Cosimo Galilei, giovane, e che per ragione di studii soggiornava al&shy;<lb/>lora in Pisa, dava conto, con lettera del d&igrave; 4 Aprile 1657, al Viviani. </s></p><p type="main">

<s>&ldquo; Qui in Pisa vo godendo la conversazione dell'Ecc.mo sig. </s>

<s>Borelli e <lb/>dell'Illustriss. </s>

<s>signor Visconte D. </s>

<s>Giacomo Ruffo, suo camerata ... In pro&shy;<lb/>posito del moto della luce ha escogitato il sig. </s>

<s>Dottore una bellissima espe&shy;<lb/>rienza, per conoscere se questa cammina istantaneamente. </s>

<s>Pensa egli di ac&shy;<lb/>comodare molti specchi disposti con quest'ordine, come vede V. S., A, B, <lb/><figure id="id.020.01.600.2.jpg" xlink:href="020/01/600/2.jpg"/></s></p><p type="caption">

<s>Figura 15<lb/>C, D.... (fig. </s>

<s>15) in maniera tale che il raggio del sole <lb/>da A si rifletta in E, e da E in B ecc. </s>

<s>ed alla fine da Q <lb/>di nuovo se ne ritorni in E. </s>

<s>Certa cosa sar&agrave;, se gli spazii <lb/>da uno specchio all'altro saranno grandi, che potr&agrave; asso&shy;<lb/>lutamente, se la luce non cammina instantaneamente, l'os&shy;<lb/>servatore posto in E conoscer qualche differenza dall'ap&shy;<lb/>parire il riflesso di A da quello di <expan abbr="q.">que</expan> Sopra della qual <lb/>cosa vi ha egli ritrovate alcune belle proposizioni, che io <lb/>adesso a V. S. significare non posso per la scarsit&agrave; del <lb/>tempo. </s>

<s>Pensa ancora di servirsi di questa esperienza per <lb/>vedere se veramente sia quella rifrazione nella region va&shy;<lb/>porosa addotta per causa dagli Astronomi di tante e tante <lb/>novit&agrave; contro ogni aspettazione seguite &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. CXLIV, c. </s>

<s>32). </s></p><p type="main">

<s>Dieci giorni dopo, lo stesso Borelli rendendo conto <lb/>de'suoi studii al principe Leopoldo, gli descriveva il nuovo <lb/>modo escogitato per esperimentare la velocit&agrave; della luce, <lb/>cos&igrave; concludendo: &ldquo; Questa sperienza, come vede V. A. S., <lb/>se nel praticarla non s'incontra qualche nuova difficolt&agrave;, oltre a quelle che <lb/>io ho preveduto, &egrave; la pi&ugrave; squisita che si possa immaginare in questo pro&shy;<lb/>posito, se io non m'inganno, e per&ograve; spero questa state, coll'aiuto e favore <lb/>di V. A. S., poterla mettere in opra, per assicurarmi d'un problema tanto <pb xlink:href="020/01/601.jpg" pagenum="44"/>importante e desiderato da tutti i Filosofi &rdquo; (Fabbroni, Lett. </s>

<s>ecc., T. II, <lb/>pag. </s>

<s>61, 62). </s></p><p type="main">

<s>Non par per&ograve; che nell'estate s'operasse nulla in proposito, come pu&ograve; <lb/>congetturarsi da ci&ograve; che Cosimo Galilei tornava a scrivere al Viviani, quasi <lb/>a mezzo Novembre. </s>

<s>&ldquo; Devo in nome ancora del sig. </s>

<s>Dottore avvisargli <lb/>com'esso ha proposto al sig. </s>

<s>Principe Leopoldo il modo di chiarirsi se la <lb/>luce proceda in istante, come feci palese a V. S. nell'ultima mia. </s>

<s>Ora non <lb/>pu&ograve; essere che in corte non se ne discorra, perci&ograve; &egrave; pregata avvisarci quello <lb/>che se ne dica. </s>

<s>Inoltre si &egrave; trovato chi ha opposto a questa esperienza con <lb/>dire che, movendosi il sole, vengono ancora a mutarsi gli angoli della ri&shy;<lb/>flessione &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLIV, c. </s>

<s>101), e prosegue a dir come il <lb/>Borelli ovviasse alla difficolt&agrave;, applicando l'<emph type="italics"/>Eliostata.<emph.end type="italics"/></s></p><p type="main">

<s>Il Rinaldini, per non rimanere indietro a'suoi Colleghi, usciva anch'egli, <lb/>nel Novembre di quell'anno 1657, a proporre un nuovo modo d'esperimen&shy;<lb/>tare il moto della luce, e se si potesse intendere in che maniera egli voleva <lb/>praticare quel suo mulinello, si direbbe che forse egli era men lontano degli <lb/>altri dal conseguire l'intento desiderato, prevenendo il metodo delle ecclissi <lb/>attraverso ai fusi di una lanterna velocissimamente girata attorno, e ritro&shy;<lb/>vata efficace da alcuni fisici moderni: &ldquo; Finir&ograve;, scriveva di Pisa al principe <lb/>Leopoldo, quell'esperienza della velocit&agrave; del vento incominciata, cos&igrave; subito <lb/>che il tempo lo permetta, e che sia venuto il bindolo somigliante a quello <lb/>del Sereniss. </s>

<s>Granduca, del quale mi vorrei parimente servire nell'esperi&shy;<lb/>mentare se il lume si diffonda in tempo oppure in istante &rdquo; (Fabbroni, <lb/>Lett. </s>

<s>ecc., T. I, pag. </s>

<s>186). </s></p><p type="main">

<s>O sia stata o no messa ad effetto, non poteva nemmen questa espe&shy;<lb/>rienza del Rinaldini decider nulla in proposito, persuasi com'erano tutti al&shy;<lb/>lora che la velocit&agrave; della luce non dovesse tanto sproporzionatamente ecce&shy;<lb/>dere quella del suono. </s>

<s>Ma il Viviani non poteva darsi pace che fossero gli altri <lb/>metodi, per quanto ingegnosi, migliori di quel primo proposto da Galileo, e <lb/>ne attribuiva l'inefficacia alle troppo brevi distanze, tra le quali s'era fino al&shy;<lb/>lora sperimentato. </s>

<s>Perci&ograve;, nell'occasione ch'egli ebbe d'andare a Pistoia, per <lb/>servigio del Granduca &ldquo; la mattina de'14 Luglio 1663 si pens&ograve; di valersi <lb/>di quella congiuntura per fare una prova se, nella distanza di 20 miglia <lb/>qual'&egrave; da Firenze a Pistoia, di notte si scoprisse un fuoco, di qual grandezza <lb/>e qual sorta di fuoco pi&ugrave; chiaramente si distinguesse, tutto affine di servirsi <lb/>di quei luoghi che in quella lontananza si fossero potuti vedere, per far <lb/>l'esperienza del movimento della luce &rdquo; (Targioni, cit., T. II, P. II, pag. </s>

<s>587). </s></p><p type="main">

<s>Fatta questa prova, la sera di quel medesimo giorno, il Viviani sul Ma&shy;<lb/>schio della fortezza di Pistoia, e il Magalotti sul campanile del Duomo di <lb/>Firenze, aiutati, per la pi&ugrave; chiara vista de'lumi, da Canocchiali, eseguirono <lb/>l'esperienza di Galileo, e com'era da aspettarsi non fu possibile nemmen <lb/>di qui decider nulla di certo, cos&igrave; per essere la distanza creduta dagli spe&shy;<lb/>rimentatori notabile, invece minima, e per le difficolt&agrave; trovate nella puntua&shy;<lb/>lit&agrave; delle osservazioni. </s></p><pb xlink:href="020/01/602.jpg" pagenum="45"/><p type="main">

<s>Cos&igrave;, dopo tanto laborioso cimento, rimaneva l'Ottica tuttavia incerta <lb/>della velocit&agrave; della luce. </s>

<s>Nulladimeno i vecchi e i nuovi Aristotelici, vogliam <lb/>dire i Peripatetici e i Cartesiani con molti altri sedotti dalle astratte specu&shy;<lb/>lazioni di alcuni Filosofi, come da quelle del Patrizio, attribuendo alla luce <lb/>o una accidentalit&agrave; senza sostanza o una natura partecipante di qualit&agrave; spi&shy;<lb/>rituali, non dubitaron di credere che fosse quel della luce un moto in istante. </s>

<s><lb/>Alcuni altri per&ograve; pi&ugrave; savi ben persuasi dover ci&ograve; che agisce sui sensi esser <lb/>sostanza, e sostanza corporea, ne inferivano per legittima conclusione che <lb/>movendosi la luce da luogo a luogo non pu&ograve; non muoversi con qualche, <lb/>e sia pure insensibile, misura di tempo. </s>

<s>&ldquo; Lumen, ragionava il Grimaldi, <lb/>utpote sensibile, non est quid spirituale, sed est aliquid corporeum: ergo <lb/>iuxta leges omnium corporum vel corporeorum, non potest per vires natu&shy;<lb/>rae esse de novo ubi non producitur, nisi illuc transferatur per motum lo&shy;<lb/>calem, relinquendo seilicet unum locum et transeundo in alium &rdquo; (De lu&shy;<lb/>mine ecc., Bononiae 1665, pag. </s>

<s>153). </s></p><p type="main">

<s>Da simili principii era stato condotto qualche anno prima ad affermare <lb/>la medesima conclusione il Fermat, il quale, nella controversia coi Carte&shy;<lb/>siani, diceva che potevan bene negare il moto successivo nella luce, ma es&shy;<lb/>sendo costretti in ogni modo ad ammettere <emph type="italics"/>aut facilitas aut fuga aut re&shy;<lb/>sistentia maior aut minor, prout media variant,<emph.end type="italics"/> venivano a conceder di <lb/>fatto alla stessa luce quel che apparentemente le negavano colle parole. <lb/>(Descartes, Epistolae, P. III, Francof. </s>

<s>1692, pag. </s>

<s>132). </s></p><p type="main">

<s>Notabile che il Grimaldi chiamava <emph type="italics"/>intrepida<emph.end type="italics"/> quella sua asserzione. <lb/></s>

<s>&ldquo; Ergo intrepide asseri potest lumen spargi cum tempore, quod multi vel <lb/>non audent prae nimium meticulosa cautione, vel non examinant securitate <lb/>nimia confisi quod supponi potius id debeat, quam in dubium ab ullo unquam <lb/>revocari &rdquo; (Op. </s>

<s>cit., pag. </s>

<s>158). Se per&ograve; volevaci intrepidezza per un gesuita <lb/>a professare quella opinione, non minore intrepidezza richiedevasi a un Pe&shy;<lb/>ripatetico, il quale erasi gi&agrave; francato da quella meticolosa cauzione quasi un <lb/>secolo avanti, quando a professar che la luce muovesi in tempo era lo stesso <lb/>che rovesciare all'edifizio aristotelico una delle pi&ugrave; solide parti del suo fon&shy;<lb/>damento. </s>

<s>Lo Scaligero dunque, disputando nell'articolo II della CCXCVIII <lb/>Esercitazione <emph type="italics"/>De Subtilitate<emph.end type="italics"/> &ldquo; An lucis motus sit in tempore &rdquo; cos&igrave; scriveva: </s></p><p type="main">

<s>&ldquo; Memini praeceptores meos in Secundo <emph type="italics"/>De Anima<emph.end type="italics"/> ex vetustis recen&shy;<lb/>tioribusque philosophis, ad probandum repentinam lucis celeritatem identi&shy;<lb/>dem id iactare: Lux in instanti fertur ab oriente in occidentem. </s>

<s>Quod ego <lb/>cum me neutiquam intelligere conquererer, nunquam eos adducere potui ut <lb/>me docerent. </s>

<s>Id namque nonnisi Solis motu percipi potest. </s>

<s>Solus enim autor <lb/>eiusmodi lucis est, quae ab oriente in occidentem ferri videtur. </s>

<s>At illius <lb/>fulgor quaenam spatia repente occupat? </s>

<s>Profecto nulla. </s>

<s>Nonne semper illu&shy;<lb/>minari aiunt orbis huius semissem? </s>

<s>Quam illustrationem adeo sensim re&shy;<lb/>pere atque procedere videmus, ut nihil ad hanc persuasionem. </s>

<s>Haud enim <lb/>aliter sibi succedit radius, atque id loci, quae ante se est subit ac capit, <lb/>quam si baculus esset circumactus. </s>

<s>An vero id ita fit ut idem radius qui <pb xlink:href="020/01/603.jpg" pagenum="46"/>est supra Romam, idem sit cum eo qui est, exempli gratia, supra Hispa&shy;<lb/>lim, ut a Roma Hispalim motus sit? </s>

<s>Non est, sed perpetua successio alia <lb/>atque alia pars illius speciei progeneretur. </s>

<s>Quamobrem rectius quaesissent <lb/>illi: an sine tempore a corpore illo lucido demittatur in terras lumen. </s>

<s>Vi&shy;<lb/>detur enim hoc argumento non illo, momentaneam illam deprehendi posse <lb/>motionem. </s>

<s>Et fortasse verum non est. </s>

<s>Non enim ab immaterialitate ductum <lb/>argumentum satis validum est. </s>

<s>Nam neque soni species, quae aeque imma&shy;<lb/>terialis est, sine tempore defertur. </s>

<s>Dicent esse in moto aere tamquam in <lb/>subiecto. </s>

<s>Quid tum? </s>

<s>Etiam lux in aere est. </s>

<s>Quem tametsi non oporteat mo&shy;<lb/>veri propter illius specici delationem, tamen quantitatem habet in dimen&shy;<lb/>sionibus. </s>

<s>Omnino sane valde ambigua res est &rdquo; (Francof. </s>

<s>1592, pag. </s>

<s>873). </s></p><p type="main">

<s>Ma l'ambiguit&agrave;, dopo tante trepidazioni e dopo tanti affanni, fu tolta, <lb/>quando, a misurare i suoi rapidissimi passi, ebbe la luce a distendersi per <lb/>spazii sufficienti. </s>

<s>Verso il 1678, per opera specialmente del Cassini, erano <lb/>state ridotte quasi alla desiderata perfezione le tavole de'moti delle Medicee <lb/>per uso della navigazione. </s>

<s>Il Roemer dava opera diligentissima in riscontrar <lb/>quelle Tavole con le osservazioni, e trov&ograve; che, quando la Terra restava op&shy;<lb/>posta a Giove al di l&agrave; del Sole, le ecclissi de'circumgioviali avvenivano qual&shy;<lb/>che minuto pi&ugrave; tardi, che quando la Terra stessa rimanevasi apposta a Giove, <lb/>al di qua del Sole. </s>

<s>Gli balen&ograve; la felice idea che ci&ograve; provenisse dal dover nel <lb/>primo caso la luce percorrere tanto pi&ugrave; lungo spazio, per rivelarsi all'oc&shy;<lb/>chio dell'osservatore, quant'era il diametr&ograve; dell'orbe terrestre, e bench&egrave; il <lb/>gran Cassini e il Maraldi fossero entrati in qualche dubbio, se dovesse in&shy;<lb/>vece attribuirsi il fatto alle ineguaglianze de'moti, nonostante altri osserva&shy;<lb/>tori confermarono la scoperta del Roemer, e il Bradley la incoron&ograve; dell'altra <lb/>non meno insigne scoperta dell'<emph type="italics"/>aberrazion della luce<emph.end type="italics"/> nelle stelle fisse. </s>

<s>Cos&igrave; <lb/>l'Ottica pot&egrave;, fra le sue pi&ugrave; certe proposizioni, scrivere anche questa: &ldquo; Lu&shy;<lb/>men propagatur spatio temporis, a corporibus lucidis, impenditque in tran&shy;<lb/>situ suo de Sole in Terram ad septem circiter vel octo minuta &rdquo; (Newton <lb/>Optices, Lib. </s>

<s>II, P. III, prop. </s>

<s>XI, Patavii 1772, pag. </s>

<s>109). </s></p><p type="main">

<s><emph type="center"/>VII.<emph.end type="center"/></s></p><p type="main">

<s>La grande scoperta roemeriana veniva a dar solidi fondamenti all'Ot&shy;<lb/>tica del Grimaldi e preparava a quella del Newton le vie de'lieti e lunghi <lb/>progressi. </s>

<s>Ma intanto ella dava occasione d'investigare in che modo si dif&shy;<lb/>fondesse la luce. </s>

<s>L'Aguilonio se n'era spedito colla sua IV proposizione <lb/>&ldquo; Lumen temporis momento totam virtutis sphaeram complet &rdquo; (Optica cit., <lb/>pag. </s>

<s>374). Ma il Cartesio, e i cartesiani che con s&igrave; amorosa laboriosit&agrave; ne <lb/>illustrarono le dottrine, fecero anche le teorie della diffusion della luce rien&shy;<lb/>trare nell'ordine generale del loro sistema. </s>

<s>La luce per essi &egrave; un moto pro&shy;<lb/>pagatosi dal pulsare in metro di sistole e di diastole del corpo luminoso <pb xlink:href="020/01/604.jpg" pagenum="47"/>contro gli atomi del secondo elemento, i quali, essendo perfettissimamente <lb/>duri, fanno che quel moto si propaghi dal lucido all'occhio senza alcun <lb/>tempo. </s>

<s>&ldquo; Lumen, dice il Cartesio, hoc est actionem qua sol aut aliud cor&shy;<lb/>pus luminosum materiam quandam subtilissimam, quae in omnibus pellu&shy;<lb/>cidis corporibus reperitur, propellit &rdquo; (Dioptr. </s>

<s>cit., pag. </s>

<s>61). </s></p><p type="main">

<s>Il Mersenno che fu il pi&ugrave; operoso commentatore e banditore delle dot&shy;<lb/>trine cartesiane, &ldquo; Omne lucidum, scriveva, dilatat se, tumescitque in molem <lb/>maiorem iterumque contrahit se, perpetuam habens systolem et diastolem &rdquo; <lb/>(Opticae, Lib. </s>

<s>VII, Parisiis 1644, pag. </s>

<s>568). </s></p><p type="main">

<s>Pi&ugrave; particolarmente poi come si diffonda questo moto di sistole e di <lb/>diastole in che consiste il lume, lo descrive lo stesso Mersenno al modo se&shy;<lb/>guente: &ldquo; Sit propositum lucidum corpus solare cuius centrum A (fig. </s>

<s>16) <lb/>semidiameter AB, cui circum scribatur orbis concentricus cuius crassities <lb/>BC.... Rursus orbi BC circumponatur orbis alius concentricus CD, et huic <lb/><figure id="id.020.01.604.1.jpg" xlink:href="020/01/604/1.jpg"/></s></p><p type="caption">

<s>Figura 16.<lb/>alter DE, et eodem modo quotcumque <lb/>alii, quilibet cuilibet aequalis Quoniam <lb/>ergo exteriores circumferentiae semper <lb/>maiores sunt interioribus, erunt reciproce <lb/>crassities interiorum orbium maiores <lb/>quam exteriorum, quare maior est BC, <lb/>quam CD, et CD quam DE. Quoniam, <lb/>iam, per primam, Sol dilatat se et tu&shy;<lb/>mescit in molem maiorem, supponamus <lb/>solem in diastole, sive tumescentia, ae&shy;<lb/>quare totam sphaeram cuius semidiame&shy;<lb/>ter est AC: necesse ergo est ut medii <lb/>pars quae erat in orbe BC exeat in lo&shy;<lb/>cum sibi aequalem proximum, nempe in <lb/>orbem CD, idque eodem tempore, nam <lb/>quo instante incipit motus a B versus C necesse est ut incipiat motus a C <lb/>versus D, et a D versus E, et ab E prorsum, quare si statuatur oculus in <lb/>qualibet distantia a sole puta in E, quo instante incipit Sol dilatare se in B, <lb/>eodem ferietur oculus in E unde propagabitur motus ad retinam et inde <lb/>per connatum retinae nervum opticum usque ad cerebrum &rdquo; (ibi, pag. </s>

<s>569). </s></p><p type="main">

<s>Da cos&igrave; fatte dottrine seguiva che il lume si cagionasse dall'urto pro&shy;<lb/>dotto sopra la retina e sopra il nervo ottico per l'instancabile pulsare del <lb/>lucido, e con ci&ograve; venivasi a spiegar benissimo come nelle percussioni e ne&shy;<lb/>gli urti violenti si produce il fosfeno. </s>

<s>&ldquo; Confirmatur autem etiam experien&shy;<lb/>tia, eo quod in omni concussione cerebri, quo fit motus aliquis per nervum <lb/>opticum extrorsum, ut quando oculus percutitur, apparet lumen quoddam <lb/>ante oculos &rdquo; (pag. </s>

<s>570). </s></p><p type="main">

<s>Il fatto del fosfeno difficilmente spiegabile in altro modo, e l'esistenza <lb/>di un etere pi&ugrave; ponderoso dell'aria, di che sentiva l'Huyghens il bisogno <lb/>per ispiegar come mai due marmi rimangano adesi e l'acqua si sostenga al <pb xlink:href="020/01/605.jpg" pagenum="48"/>di sopra del natural livello ne'tubi collocati nel vuoto; disposero l'ingegno <lb/>del grande Olandese ad accomodarsi all'ipotesi del lucido che vibra ne'moti <lb/>di sistole e di diastole, i quali moti si comunicano al circostante etere, che <lb/>diffondesi in onde sferiche, e percote la retina come si percote il timpano <lb/>dalle onde sonore. </s>

<s>L'ipotesi, che in sostanza &egrave; la cartesiana, ridotta a mag&shy;<lb/>gior propriet&agrave; matematica, e ripurgata dall'errore della diffusione istanta&shy;<lb/>nea, fu dall'Huyghens pubblicata nel 1678 nel suo Trattato <emph type="italics"/>De la lumiere.<emph.end type="italics"/></s></p><p type="main">

<s>Qualunque si fosse l'accoglienza che si fece a questa ipotesi, la quale, <lb/>per essersi originata da quella del loro maestro, allettava i Cartesiani, il <lb/>Newton v'ebbe qualche difficolt&agrave;, e si mostr&ograve; inclinato a seguire un'altra <lb/>ipotesi pi&ugrave; semplice e pi&ugrave; naturale. </s>

<s>Chi fa del grande Ottico inglese l'Au&shy;<lb/>tore di un sistema nuovo, in opposizione a quello delle onde eteree, non co&shy;<lb/>nosce bene l'indole di quell'ingegno severo, il quale non posava le sue per&shy;<lb/>suasioni altro che sopra la fermezza di fatti matematicamente dimostrati. </s>

<s>Egli <lb/>non rifiuta l'ipotesi delle ondulazioni per preferire la sua della emissione, <lb/>ma questiona cos&igrave; dell'una come dell'altra e mostra che se a spiegare molti <lb/>fenomeni si porge docile quella, questa non si porge men docile a spiegarli <lb/>tutti con molto minori difficolt&agrave;, e con pi&ugrave; naturalezza. </s>

<s>Tale, a chi medita <lb/>le XXXI Questioni apposte al III Libro dell'Ottica, si rivela l'indole del&shy;<lb/>l'Autore. </s></p><p type="main">

<s>Solo una cosa &egrave; risoluto il Newton di negare all'Huyghens, ed &egrave; la <lb/>ponderosit&agrave; dell'etere, il quale indugerebbe e impedirebbe i liberi moti ai <lb/>pianeti e metterebbe il languore in ogni ordine naturale. </s>

<s>&ldquo; Quo itaque lo&shy;<lb/>cus sit diuturnis et regularibus planetarum cometarumque motibus, omnino <lb/>necesse est ut spatia coelestia omni materia sint vacua.... Fluidum densum, <lb/>nullo modo utile esse potest ad explicanda phaenomena naturae.... Nihil <lb/>facere posset istuismodi fluidum nisi ut magnorum illorum corporum mo&shy;<lb/>tus interturbaret, et retardaret efficeretque ut naturae ordo languesceret &rdquo; <lb/>(Quaestio XXVIII, ed. </s>

<s>cit., pag. </s>

<s>150). </s></p><p type="main">

<s>Se gli Ugeniani persistono in ammettere questa ponderosa densit&agrave; del <lb/>fluido etereo, il Newton protesta di esser contro a loro, e rigettato questo <lb/>&ldquo; reiicientur simul hypotheses eae quibus lumen in pressu vel motu per <lb/>istiusmodi medium propagato consistere fingitur &rdquo; (ibi). Ma se si ammette <lb/>un etere constare &ldquo; ex particulis a se invicem recedere conantibus .... et eius <lb/>particulas longe tenuiores esse quam aeris, vel etiam luminis &rdquo; (Quaest. </s>

<s>XXI, <lb/>pag. </s>

<s>144) e allora dice il Newton potrebbero anche forse spiegarsi alcuni <lb/>fenomeni e fatti per via del vibrar di questo mezzo etereo. </s></p><p type="main">

<s>Si potrebbe dalle varie grandezze di queste vibrazioni, spiegar la va&shy;<lb/>riet&agrave; de'colori (quaest. </s>

<s>XIII) si potrebbe spiegare, come mai al buio com&shy;<lb/>primendo il nostro occhio si veda quel cerchietto &ldquo; coloribus variegatum <lb/>eorum similibus qui in pluma caudae pavonis conspiciuntur &rdquo; (quaest. </s>

<s>XVI), <lb/>s'intenderebbe come per le vibrazioni di questo sottilissimo mezzo etereo <lb/>si potesse il calore trasmettere e rendersi sensibile a un Termometro col&shy;<lb/>locato nel vuoto (quest. </s>

<s>XVIII); si potrebbe altres&igrave; ammettere che questo <pb xlink:href="020/01/606.jpg" pagenum="49"/>mezzo etereo sia pi&ugrave; raro intra i corpi densi del sole, delle stelle, de'pia&shy;<lb/>neti e delle comete, e che da questi corpi infino a'pi&ugrave; grandi intervalli, vada <lb/>a farsi via via sempre pi&ugrave; denso, e cos&igrave; spiegare come mai que'corpi cele&shy;<lb/>sti gravitino l'uno sopra l'altro (quaestio XXI). </s></p><p type="main">

<s>Ma dopo avere ammesse tutte queste possibilit&agrave; esce a dire in princi&shy;<lb/>pio della Questione XXVIII: &ldquo; Annon errantes sunt, hypotheses illae omnes <lb/>quibus lumen in pressu quodam seu motu per medium fluidum propagato <lb/>consistere fingitur? </s>

<s>Nam in his omnibus hypothesibus phaenomena luminis <lb/>usque adhuc ita explicarunt Philosophi, ut ea ex novis quibusdam radiorum <lb/>modificationibus oriri posuerint. </s>

<s>Quae est opinio errans &rdquo; (pag. </s>

<s>148) di che <lb/>reca per principale esempio la spiegazione data dall'Huyghens alla doppia <lb/>rifrangenza dello spato islandico, scoperta da Erasmo Bartholin, e per que&shy;<lb/>sto giudica essere l'opinione ugeniana, de'due varii mezzi vibranti nel mede&shy;<lb/>simo cristallo, erronea, perch&egrave; la rifrazione straordinaria nello stesso cristallo, <lb/>non dipende &ldquo; ex novis modificationibus, sed ex congenitis et immutabilibus <lb/>radiorum proprietatibus &rdquo; (ibi). </s></p><p type="main">

<s>Perci&ograve;, dimostrata l'insufficienza delle pulsazioni eteree a spiegare il <lb/>fenomeno bartoliniano, apre la seguente Questione XXIX, cos&igrave;, bench&egrave; sotto <lb/>le solite modeste forme del dubbio: &ldquo; Annon radii luminis exigua sunt cor&shy;<lb/>puscula a corporibus lucentibus emissa? </s>

<s>&rdquo; (ibi, pag. </s>

<s>151). E con questa <lb/>ipotesi cos&igrave; naturale prosegue il Newton a dire potersi facilmente spiegare <lb/>le principali propriet&agrave; e i fenomeni della luce, imperocch&egrave; per la teoria de'co&shy;<lb/>lori, per esempio, niente altro pi&ugrave; si richiede &ldquo; quam ut radii luminis sint <lb/>corpuscula diversis magnitudinibus, quorum quidem ea, quae sint minima, <lb/>colorem constituant violaceum, utique tenebrosissimum, et languidissimum <lb/>colorum .... reliqua autem, ut eorum quodque in magnitudinem excedit, <lb/>ita colores exhibeant fortiores et clariores &rdquo; (pag. </s>

<s>152). Per ispiegar le vi&shy;<lb/>cende alternative della pi&ugrave; facile riflessione e della pi&ugrave; facile trasmissione <lb/>&ldquo; nihil aliud opus est, quam ut ii exigua sint corpuscula, quae vel attractione <lb/>sua, vel alia aliqua vi, vibrationes quasdam in medio, in quod agunt, exci&shy;<lb/>tent, quae quidem vibrationes radiis celeriores existentes, praevertant eos <lb/>successive, et ita agitent, ut velocitatem ipsorum augeant, imminuantque al&shy;<lb/>ternis, adeoque vices illas in ipsis generent &rdquo; (ibi). </s></p><p type="main">

<s>Quanto poi all'inusitata rifrazione dello spato d'Islanda, &egrave; verosimile, <lb/>dice il Newton, che ci&ograve; avvenga per qualche virt&ugrave; attrattiva fra certi lati <lb/>de'raggi e delle particelle del cristallo di rifrangenza; virt&ugrave; da potersi in <lb/>qualche modo rassomigliare alla polarit&agrave; magnetica. </s>

<s>&ldquo; Et quoniam crystal&shy;<lb/>lus, ista vi sua, non agit in radios, nisi tum cum et radiorum latera inusi&shy;<lb/>tatae refractionis altera, ad plagam istam crystalli sint conversa; apparet in <lb/>radiorum quoque lateribus illis inesse vim sive virtutem aliquam, quae cor&shy;<lb/>respondeat vi isti quae est in crystallo, eo fere modo quo binorum magne&shy;<lb/>tum poli sibi invicem respondent &rdquo; (ibi). </s></p><p type="main">

<s>L'ipotesi della emissione venne per la sua naturalezza e per la grande <lb/>autorit&agrave;, fatta pi&ugrave; potente dalla modestia di Colui che la preferiva all'altra <pb xlink:href="020/01/607.jpg" pagenum="50"/>ugeniana, segu&igrave;ta da molti, ai quali sembrava di pi&ugrave; che le scoperte del <lb/>Roemer e del Bradley fossero di quella ipotesi neutoniana la pi&ugrave; eloquente <lb/>conferma. </s>

<s>Cos&igrave;, tra l'opinione delle pulsazioni eteree e delle eiaculazioni della <lb/>sostanza luminosa, tergivers&ograve; e seguita tuttavia a tergiversare l'Ottica: e ora <lb/>&egrave; bene vedere che cosa, in tal proposito di cos&igrave; grande importanza, se ne <lb/>pensasse particolarmente in Italia. </s></p><p type="main">

<s>Tommaso Cornelio, sulla fine del suo Proginnasma IV <emph type="italics"/>De sole<emph.end type="italics"/> dedicato <lb/>a Daniele Spinola, con lettera che ha la data del 1661, accingendosi a spie&shy;<lb/>gar la natura della luce, scriveva: &ldquo; Longe autem falluntur qui censent lu&shy;<lb/>men extra oculos existere, et quicquam tale esse, quale visu percipitur. </s>

<s><lb/>Enimvero nusquam alibi lumen est, quam in ipsomet videntis oculo. </s>

<s>Nam <lb/>gignitur illud ex motu appulsuque aetheris ad eam oculi partem, quae re&shy;<lb/>ticulatam tunicam format, ubi spiritus externo et adventitio pulsu agitatus <lb/>luminis ideam menti percipiendam indipiscit &rdquo; (Neapoli 1688, pag. </s>

<s>150). </s></p><p type="main">

<s>E dopo aver confermata questa sua dottrina col fatto del fosfeno nel&shy;<lb/>l'occhio vellicato, o compresso. </s>

<s>&ldquo; Fit igitur, conclude, lumen ex motu aethe&shy;<lb/>ris, seu subtilis materiae a lucido corpore per spat&igrave;a diaphana oculis com&shy;<lb/>municato. </s>

<s>Ea enim est lucis natura ut perenni pulsu, et veluti systole quadam <lb/>atque diastole circumiectum aethera propellat &rdquo; (ibi, pag. </s>

<s>149). </s></p><p type="main">

<s>Si sente bene che non &egrave; in queste dottrine, professate dal Medico na&shy;<lb/>poletano, nulla di originale, e sembrano anzi troppo fedelmente ritrarre il <lb/>senso e comporsi al suono delle sopra citate parole del Mersenno. </s>

<s>Il Cor&shy;<lb/>nelio, insieme con gli altri suoi colleghi nell'Accademia del Conclubet, con&shy;<lb/>tro le pi&ugrave; lodevoli intenzioni del Borelli e degli altri addetti all'Accademia <lb/>dei Medici, cooperarono a introdurre il cartesianismo in Italia. </s></p><p type="main">

<s>Ben pi&ugrave; italiano &egrave; nell'ingegno il gesuita Grimaldi, che alcuni hanno <lb/>annoverato fra coloro, i quali professarono l'ipotesi delle ondulazioni. </s>

<s>Ma le <lb/>ondulazioni grimaldiane, nel significato proprio in che le intese l'Autore, <lb/>differiscono notabilmente da quelle dell'Huyghens. </s>

<s>Il Nostro, riguardando la <lb/>luce diffondersi al modo comune de'fluidi, come sarebbe l'acqua, oltre al <lb/>moto locale vi considera un moto ondoso e d'increspamento che l'accom&shy;<lb/>pagna nel suo viaggio, come quando per esempio si getta una pietra in un <lb/>fiume; in ci&ograve; differente, nella luce, dal moto ondoso nell'acqua, in quanto <lb/>che questo affetta la figura circolare, e quello si estende solamente in lato <lb/>e si spiega per lo lungo. </s></p><p type="main">

<s>&ldquo; Sicut aqua in quam violenter immersus fuerit lapis, statim formatur <lb/>in tenues fluctus circulares, qui successive unus post alium magis ac ma&shy;<lb/>gis dilatantur, nec cessant sic dilatari sibique succedere, quamvis aqua tota <lb/>cum illis deorsum fluat per alveum fluminis; ita in lumine agnoscenda est <lb/>similis agitatio undosa .... cum hoc tamen discrimine quod dilatatio illa <lb/>circulorum in aqua est motus aliquo modo sensibilis ob tarditatem suam, in <lb/>lumine autem fluitatio iam explicata de novo resultans est citissima, et per <lb/>motum insensibilem facta. </s>

<s>Praeterea motus ille in aqua fit per spatium valde <lb/>magnum et circulariter, si aqua fuerit stagnans, vel saltem in latum cum <pb xlink:href="020/01/608.jpg" pagenum="51"/>affectatione figurae circularis, si aqua fluat. </s>

<s>At in lumine agitatio praedicta <lb/>modicum se extendit in latum, et tota fere in longum se explicat &rdquo; (De <lb/>Lumine cit., pag. </s>

<s>197, 98). </s></p><p type="main">

<s>Ma l'ipotesi delle ondulazioni al modo stesso che la speculava l'Huy&shy;<lb/>ghens, era stata insegnata e divulgata, in una delle modeste ma fiorenti <lb/>scuole italiane, qualche anno prima che l'avesse fatta pubblicamente nota <lb/>il grande Ottico olandese. </s>

<s>Quella scuola erasi instituita in Bologna, sotto il <lb/>magistero di quel Geminiano Montanari, che vedemmo essere stato il primo <lb/>a dimostrare sperimentalmente la legge del decrescere, al successivo pro&shy;<lb/>gredire delle distanze, l'intensit&agrave; luminosa. </s>

<s>Aveva appena l'Accademico della <lb/>Traccia conclusa quella legge, che immediatamente cos&igrave; soggiunge: </s></p><p type="main">

<s>&ldquo; Tralascio di rifletter qui a un argomento ch'io credo non sia stato <lb/>avvertito sinora da altri, contro quelli che vogliono che il lume sia una so&shy;<lb/>stanza, la quale dal corpo luminoso, quasi in un istante si diffonda pel <lb/>mezzo, e con la sua presenza lo illumini, con l'assenza lo lasci tenebroso, <lb/>perciocch&egrave; se ci&ograve; fosse, sarebbe d'uopo che l'intensioni dell'illuminazione <lb/>seguitassero la proporzione de'cubi delle distanze, non quella de'quadrati <lb/>come fanno. </s>

<s>Conciossiach&egrave;, se una quantit&agrave; di luce, quella per esempio che <lb/>esce da una fiamma di candela, basta per illuminare a una tale intensione <lb/>una sfera d'un braccio di semidiametro, per una sfera di due braccia, che <lb/>&egrave; 8 volte pi&ugrave; capace, vi vorrebbero 8 lumi, eppure bastano 4; per una di <lb/>tre braccia 27 lumi, per una di quattro braccia 64 lumi, e no nove e se&shy;<lb/>dici come pure vediamo che bastano, cio&egrave; tanti di pi&ugrave;, quanto &egrave; pi&ugrave; grande <lb/>la superficie non gi&agrave; il corpo. </s>

<s>&rdquo; </s></p><p type="main">

<s>L'argomento del Montanari che &egrave; forse uno de'pi&ugrave; validi contro l'ipo&shy;<lb/>tesi dell'emissione, conducendolo a concludere che la materia luminosa pro&shy;<lb/>cede nel suo moto in superficie e non in corpo, cos&igrave; come si vede procedere <lb/>anche il suono, veniva a suggerirgli spontanea l'ipotesi delle ondulazioni. </s>

<s><lb/>Soggiunge l'Autore in fine delle parole sopra citate che di ci&ograve; avrebbe avuto <lb/>campo di discorrerne in altra occasione, e non avr&agrave; certo mancato quel&shy;<lb/>l'uomo cos&igrave; attivo e zelante in promuovere la scienza, di mantenere le sue <lb/>promesse, bench&egrave;, fra le disperse e numerose scritture di lui, non siamo <lb/>noi in grado di dire a'nostri lettori in quali di quelle ci ci&ograve; particolarmente <lb/>facesse. </s>

<s>Ma che non mancasse il Montanari di diffondere nella sua scuola la <lb/>nuova ipotesi speculata, n'abbiamo argomento, si potrebbe dir certo, in colui <lb/>che fu il pi&ugrave; valoroso de'discepoli usciti di l&igrave;, e che ritrae pi&ugrave; al vivo, nel&shy;<lb/>l'ingegno e nelle dottrine, le qualit&agrave; del suo insigne maestro. </s></p><p type="main">

<s>Domenico Guglielmini, nel suo libro <emph type="italics"/>De sanguinis natura,<emph.end type="italics"/> per confu&shy;<lb/>tar l'errore dell'innata fiamma vitale, e per provar che il calore del sangue <lb/>pu&ograve; esser prodotto da tutt'altre cause da quelle consuete d'operare nelle <lb/>cucine, cos&igrave; scriveva: &ldquo; Quid enim impedit quominus undulationes iis si&shy;<lb/>miles quae ab ignis agitatione proficiscuntur etiam ab aliis motibus aetheri <lb/>imprimantur? </s>

<s>An excitabitur in retina igniculus, cum presso exterius oculo <lb/>lucis scintillae videntur observari? </s>

<s>&rdquo; (Venetiis 1701, pag. </s>

<s>92). </s></p><pb xlink:href="020/01/609.jpg" pagenum="52"/><p type="main">

<s>E nella Dissertazione <emph type="italics"/>De salibus,<emph.end type="italics"/> dop'aver co'principii idrostatici di&shy;<lb/>mostrato che le particelle saline sciolte ne'liquidi son cos&igrave; equilibrate, che <lb/>qualunque minima forza &egrave; capace di turbarle da quel loro riposo; assegna <lb/>fra queste minime forze anche l'urto, che pu&ograve; una delle cos&igrave; fatte parti&shy;<lb/>celle ricevere dall'ondata eterea o dalla pulsazion della luce. </s>

<s>&ldquo; Cumque tales <lb/>potentiae motrices plures adsint, aether praeter fluens, <emph type="italics"/>lucis pressio<emph.end type="italics"/> et <lb/>praecipue calor .... &rdquo; (Venetiis 1705, pag. </s>

<s>98): e con ci&ograve; veniva alla scienza <lb/>la prima idea e il primo esempio di un <emph type="italics"/>Radiometro,<emph.end type="italics"/> misterioso strumento, <lb/>per cui fu creduto di render sensibile il moto, e il meccanico operar della <lb/>luce su gli altri corpi. </s></p><p type="main">

<s>Or perch&egrave; le recenti scoperte di nuove propriet&agrave; nella luce, le quali si <lb/>dice non potersi spiegare altrimenti che nell'ipotesi delle ondulazioni, hanno <lb/>a quella ipotesi gli Ottici fatto grande onore, e cos&igrave; gran lode hanno dato <lb/>all'Huyghens, che la specul&ograve; e la diffuse; sarebbe di non lieve importanza <lb/>l'addurre altri documenti a confermare il fatto che quella ipotesi era pro&shy;<lb/>fessata in Italia qualche anno prima, e indipendentemente dall'insegnamento <lb/>di maestri stranieri. </s>

<s>Ma di troppo oramai abbiam trapassati i limiti, che dal&shy;<lb/>l'ampiezza de'soggetti di questa storia ci sono prescritti. </s></p><pb xlink:href="020/01/610.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO II.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Della luce rifratta<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle prime teorie speculate intorno alla natura delle rifrazioni, e de'primi tentativi fatti per isco&shy;<lb/>prirne le leggi. </s>

<s>&mdash; II. </s>

<s>Del Teorema dello Snellio e della legge diottrica indi formulatane dal Car&shy;<lb/>tesio. </s>

<s>&mdash; III. </s>

<s>Della legge diottrica dimostrata dall'Herigonio; del principio delle cause finali <lb/>introdotto in quella dimostrazione, e come il Newton ritornasse ai principii meccanici. </s>

<s>&mdash; <lb/>IV. </s>

<s>Della scienza delle rifrazioni in Italia. </s>

<s>&mdash; V. </s>

<s>Delle rifrazioni astronomiche. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>La propriet&agrave; che ha la luce di rompere la dirittura del suo primo cam&shy;<lb/>mino, quando entri da uno in un altro mezzo di varia densit&agrave;, fu conosciuta <lb/>infino da'pi&ugrave; antichi Ottici, e non poteva non esser ci&ograve; facilmente avvertito <lb/>per la cos&igrave; frequente occorrenza de'fatti naturali. </s>

<s>Euclide fu il primo a con&shy;<lb/>fermare quella propriet&agrave; per mezzo dell'esperienza, ch'egli cos&igrave; descriveva <lb/>nel IV de'<emph type="italics"/>Fenomeni<emph.end type="italics"/> premessi alla sua Prospettiva: &ldquo; Se si porr&agrave; qualsivo&shy;<lb/>glia cosa nel fondo d'un vaso, e poi si discosti tanto dall'occhio che la cosa <lb/>gi&agrave; detta non si veda pi&ugrave;, dico che tal cosa si potr&agrave; vedere in questo luogo <lb/>se il vaso si empier&agrave; d'acqua.... Si vedr&agrave; per i raggi rotti che si rom&shy;<lb/>pono nella superficie dell'acqua, che prima per i raggi retti non si potea <lb/>vedere &rdquo; (Traduz. </s>

<s>di E. Danti, Fiorenza 1573, pag. </s>

<s>80). </s></p><p type="main">

<s>Tolomeo, Alhazeno e Vitellione, troppo ben conoscendo che il fatto del <lb/>rifrangersi la luce ne'mezzi di varia densit&agrave; <emph type="italics"/>plus experientiae instrumen&shy;<lb/>torum innititur quam alteri demonstrationum<emph.end type="italics"/> (Persp. </s>

<s>Vitell. </s>

<s>cit., pag. </s>

<s>47 v.), <lb/>attesero a perfezionare quel semplice strumento euclideo, applicandovi un <lb/>cerchio graduato e discriminando il raggio cos&igrave; incidente come rifratto con <lb/>farlo passare attraverso a sottilissimi fori, i quali per sottilissime linee en-<pb xlink:href="020/01/611.jpg" pagenum="54"/>trando e procedendo dentro il mezzo refringente o acqua o vetro o altro <lb/>diafano, segnassero i gradi precisi degli angoli dell'incidenza e della ri&shy;<lb/>frazione. </s></p><p type="main">

<s>Cos&igrave; poteronsi strumentalmente dimostrare alcune diottriche proposi&shy;<lb/>zioni, di cui le principali sono in Vitellione per tal modo formulate: &ldquo; Per <lb/>medium secundi diafoni densioris primo radius perpendicularis ductus a cen&shy;<lb/>tro corporis luminosi super superficiem obiecti corporis, semper penetrat ir&shy;<lb/>refractus &rdquo; (Lib. </s>

<s>II, prop. </s>

<s>XLII). &mdash; &ldquo; Radio perpendiculari omne corpus <lb/>diafonum penetrante, radius oblique incidens in medio secundi diafoni den&shy;<lb/>sioris refringitur ad perpendicularem ductam a puncto incidentiae super se&shy;<lb/>cundi diaphoni superficiem, et in medio secundi diafoni rarioris refringitur <lb/>ab eadem &rdquo; (Lib II, prop. </s>

<s>XLVII). </s></p><p type="main">

<s>Ma perch&egrave; il fatto per s&egrave; stesso non costituisce la scienza, ufficio della <lb/>quale &egrave; rendere la ragione del fatto, si domandava a Vitellione: perch&egrave; mai <lb/>il raggio perpendicolare procede irrefratto, e perch&egrave; mai il raggio obliquo, <lb/>avendo a penetrare un mezzo pi&ugrave; denso, si accosta pi&ugrave; d'appresso alla per&shy;<lb/>pendicolare? </s>

<s>E il gran Maestro della Prospettiva rispondeva che le linee <lb/>perpendicolari son le pi&ugrave; forti di tutte <emph type="italics"/>quoniam coadunantur virtute uni&shy;<lb/>versali coelesti secundum lineam rectam brevissimam, omni subiecto cor&shy;<lb/>pori influente<emph.end type="italics"/> (Editio cit., pag. </s>

<s>31 v.). Di pi&ugrave; si osserva, soggiunge Vitel&shy;<lb/>lione, che in tutti i moti, tanto son le percussioni oblique pi&ugrave; forti quanto <lb/>pi&ugrave; si avvicinano alla perpendicolare, la quale &egrave; la fortissima di tutte. </s>

<s>Ora <lb/>la luce &egrave; un corpo in velocissimo moto a cui resiste pi&ugrave; o meno la crassi&shy;<lb/>zie del diafano, e perci&ograve;, a rifarsi del danno ricevuto si studia la luce di <lb/>deviare dalla sua obliquit&agrave;, accostandosi alla fortezza della perpendicolare. </s></p><p type="main">

<s>Si vede bene come qui la ragione, piuttosto che dalla scienza &egrave; sug&shy;<lb/>gerita dalla poesia, la quale &egrave; cos&igrave;, dal nostro Varchi fiorentino, molto pi&ugrave; <lb/>gentilmente infiorata che non dal ruvido ottico di Polonia. </s>

<s>&ldquo; Tutti i razzi <lb/>che sono intorno a quella linea forte e perpendicolare che si chiama lo asse, <lb/>i quali erano prima diffusi e disgregati, essendo in un mezzo rado, si con&shy;<lb/>gregano ed uniscono insieme d'intorno allo asse per essere pi&ugrave; forti e pi&ugrave; <lb/>possenti, dovendo passare e penetrare un mezzo pi&ugrave; denso, e questo si chiama <lb/>perfrangersi alla perpendicolare, e di qui &egrave; detto cotal razzo, non altrimenti <lb/>quasi che uno esercito, il quale lontano dal nemico e per paese sicuro va <lb/>sparso e vagabondo, ma vicino al nemico e per paese sospetto si restringe <lb/>ed unisce insieme d'intorno al suo asse, cio&egrave;, al capitano &rdquo; (Lezioni cit., <lb/>pag. </s>

<s>301). </s></p><p type="main">

<s>N&egrave; men fragranti fiori di poesia sa spargere sopra questo sentiero di <lb/>luce nel Trattato suo <emph type="italics"/>De visione<emph.end type="italics"/> il Fabrizi d'Acquapendente. </s>

<s>&ldquo; Optima vero <lb/>ratione accidit in prima refractione quae apparet luce per secundum me&shy;<lb/>dium crassius pertranseunte omnes obliquos radios ad perpendicularem frangi <lb/>et ad eam accedere. </s>

<s>Quoniam cum crassius diaphanum lucis liberum tran&shy;<lb/>situm haberet, propter suam opacitatem, evenit ut lux libere recteque ut <lb/>prius non amplius possit permeare, sed mutationem aliquam subeat, quae <pb xlink:href="020/01/612.jpg" pagenum="55"/>sane mutatio nulla alia est, quam inclinatio seu accesio seu refugium lucis <lb/>veluti ad arcem, et ad id quod potest ipsam roborare ac proinde tueri et <lb/>conservare. </s>

<s>Haec autem arx est radius seu linea perpendicularis, quae uti <lb/>dictum est quocumque progrediatur robustissima et irrefracta progreditur. </s>

<s><lb/>Contra accidit cum lux e denso in rarius diaphanum permeat. </s>

<s>Siquidem, <lb/>cum inveniat minorem diaphani resistentiam merito a perpendiculari rece&shy;<lb/>dit, tamquam eius auxilio non amplius pro sui conservatione indigens &rdquo; (Ve&shy;<lb/>netiis 1600, pag. </s>

<s>70). </s></p><p type="main">

<s>A rimproverar la scienza scesa a fanciulleggiare cos&igrave; tra i fiori della <lb/>poesia insorse con gran severit&agrave; il Keplero &ldquo; quasi lucis species mente prae&shy;<lb/>dita esset, qua et densitatem medii et suum damnum aextimaret et proprio <lb/>arbitratu non extranea vi agendo, non patiendo sese ipsam infringeret &rdquo; <lb/>(Paralip. </s>

<s>cit., pag. </s>

<s>84). Ma egli aveva notato per&ograve; fra le leggerezze di Vi&shy;<lb/>tellione <emph type="italics"/>nescio quid subtile,<emph.end type="italics"/> una sottigliezza di grande importanza ai pro&shy;<lb/>gressi dell'Ottica, la quale consiste nell'applicare al moto della luce il prin&shy;<lb/>cipio meccanico della composizione delle forze. </s></p><p type="main">

<s>Sia AC (fig. </s>

<s>17) un raggio, che obliquamente discende, e nel punto C <lb/><figure id="id.020.01.612.1.jpg" xlink:href="020/01/612/1.jpg"/></s></p><p type="caption">

<s>Figura 17.<lb/>incontra la superfice BE di un dia&shy;<lb/>fano di varia densit&agrave; da quello per <lb/>cui egli &egrave; venuto, fuori del qual caso <lb/>procederebbe per la linea CQ a di&shy;<lb/>ritto. </s>

<s>Conducasi nel punto C la GH <lb/>perpendicolare a BE. &ldquo; Motus radii <lb/>incidentis oblique secundum lineam <lb/>AC, dice Vitellione, componitur ex <lb/>motu in partem perpendicularis CG <lb/>et ex motu facto super lineam quae <lb/>est perpendicularis super lineam CG &rdquo; <lb/>(Perspectiva cit., pag. </s>

<s>52). O altri&shy;<lb/>menti essendo l'atomo lucido C spinto <lb/>per la direzione CE e per la direzione <lb/>CG, n&egrave; potendo ubbidire nello stesso <lb/>tempo all'uno impulso e all'altro, prender&agrave; una via di mezzo, e secondo il <lb/>bisogno o si accoster&agrave; di pi&ugrave; a CG o si accoster&agrave; di pi&ugrave; a CE. </s>

<s>Il bisogno poi <lb/>sar&agrave; dichiarato dalla natura del diafano, il quale se &egrave; pi&ugrave; denso di quello da <lb/>cui il raggio &egrave; venuto, e allora avendo bisogno di maggior fortezza, per su&shy;<lb/>perare l'impedimento, il raggio stesso si accoster&agrave; alla linea CG perpendi&shy;<lb/>colare: cessando poi questo bisogno, per essere il diafano pi&ugrave; raro, si far&agrave; <lb/>invece l'accostamento alla linea CE, e insomma il raggio rifratto ne'due casi <lb/>diversi o sar&agrave; CI, o sar&agrave; CK. </s></p><p type="main">

<s>Ma pur nemmeno procedendo per questa via non s'evitava quel fan&shy;<lb/>tastico supposto che attribuiva alla luce un senso d'andare a cercar presso <lb/>alla perpendicolare il rifugio e il conforto alla sua debolezza. </s>

<s>Perci&ograve; il Ke&shy;<lb/>plero si studiava, cos&igrave; ragionando altrimenti, di giungere alla medesima con-<pb xlink:href="020/01/613.jpg" pagenum="56"/>clusione. </s>

<s>Il moto &egrave; causa della dispersion della luce: argomento poi di tal <lb/>dispersione &egrave; l'incidenza obliqua, ond'&egrave; che tra il moto retto e lo stesso <lb/>obliquo intercede sempre l'angolo, dentro cui si contermina la luce dispersa. </s>

<s><lb/>Suppongasi ora esser quel raggio obliquo AB (fig. </s>

<s>18) il moto retto AC, e <lb/>BAC l'angolo ora detto. </s>

<s>Incontri il moto della dispersione la superficie BC <lb/>del mezzo diafano pi&ugrave; denso. </s>

<s>Se non facesse questo mezzo nessuno impedi&shy;<lb/>mento alla dispersione, proseguendo in D e in E, occuperebbe tutto lo spa&shy;<lb/><figure id="id.020.01.613.1.jpg" xlink:href="020/01/613/1.jpg"/></s></p><p type="caption">

<s>Figura 18.<lb/>zio DE: se poi impedisse affatto quella stessa disper&shy;<lb/>sione lo spazio occupato sarebbe FE uguale a BC. </s>

<s>Ma <lb/>non essendo n&egrave; libera n&egrave; assolutamente quella disper&shy;<lb/>sione impedita, sar&agrave; lo spazio occupato qualche cosa <lb/>di mezzo fra DE ed FE, per esempio EG. &ldquo; Lux igitur <lb/>sine ulla dispersione usque ad ED veniens, occuparet <lb/>spatium EF; eadem, sine ulla perturbatione eousque <lb/>descendens, occuparet spatium ED, spargens et exte&shy;<lb/>nuans se eadem proportione. </s>

<s>Ergo cum intervenit me&shy;<lb/>dium BC densius id dispersionem impediens facit ut <lb/>lux medium spatium occupet inter EF et ED. </s>

<s>Sit illud <lb/>EG. </s>

<s>Radius ergo AB refringitur in B et infra super&shy;<lb/>ficiem densioris medii fiet BG accedens ad perpendicularem BF &rdquo; (Paralip. </s>

<s><lb/>ad Vitell., Francof. </s>

<s>1604, pag. </s>

<s>16). </s></p><p type="main">

<s>Bench&egrave; questa nuova argomentazione cessasse in qualche modo i difetti, <lb/>in ch'erano incorsi gli Ottici suoi predecessori, conosceva nonostante bene <lb/>il Keplero com'ella fosse tuttavia lontana da quella severit&agrave; matematica, che <lb/>si sarebbe desiderata. </s>

<s>Quel <emph type="italics"/>nescio quid subtile<emph.end type="italics"/> della composizione del moto <lb/>si rappresentava dall'altra parte per l'unica via geometrica da potersi se&shy;<lb/>guire con sicurezza, ma bisognava maneggiar l'argomento in altro modo da <lb/>quel che avean fatto Alhazeno e Vitellione, senza mescolarvi cio&egrave; il princi&shy;<lb/>pio delle cause intenzionali. </s>

<s>Giacch&egrave; dunque conveniva non deviar dalle leggi <lb/>della Meccanica, il Keplero rassomiglia la luce a un proiettile, per esempio <lb/>a un globo gettato nell'acqua. </s>

<s>Avviene perci&ograve;, egli dice, nel lume quel che <lb/>ne'mobili fisici, &ldquo; quoties globus in aquam torquetur, dummodo subeat <lb/>aquam. </s>

<s>Patet sic; liceat enim hic mihi verba Opticorum contra mentem <lb/>ipsorum usurpare et in meliorem sensum adducere: Sit BC (nella figura <lb/>preced.) aqua. </s>

<s>AB motus sphaerulae. </s>

<s>Continuetur BC in H et FB in I. </s>

<s>Cum <lb/>ergo motus sphaerulae AB sit quodammodo compositus ex IB in BH, acci&shy;<lb/>det etiam, ut resistat illi tam profunditas BF, quam BH crassities lateralis. </s>

<s><lb/>Prius impedimentum tardiorem efficit eius descensum et retundit, dummodo <lb/>descendat. </s>

<s>Posterius vero repellit ipsam a sua linea, ut quia motus erat BD <lb/>futurus repellatur a BH et fiat BG &rdquo; (ibi). Supposto che la luce non pati&shy;<lb/>sca altra attenuazione che <emph type="italics"/>in latum<emph.end type="italics"/> e non dalla parte della rettitudine ma <lb/>dell'obliquit&agrave;, il simile che ne'proietti dice il Keplero avvenir nella luce, <lb/>ond'&egrave; che il moto di lei non riceve impedimento dalla parte BC, ma dalla <lb/>parte BH. &ldquo; Ergo superficies ex parte BH resistit hinc motui existitque <pb xlink:href="020/01/614.jpg" pagenum="57"/>hinc quasi quaedam reflexio AB in BG plane similis illis quae fiunt in cor&shy;<lb/>poribus naturalibus proiectis &rdquo; (ibi, pag. </s>

<s>17). </s></p><p type="main">

<s>Chiunque per&ograve; s&igrave;a pi&ugrave; largo di concessioni al Keplero non gli potr&agrave; mai <lb/>concedere che avvenga nella luce quel che nel globo gettato nell'acqua, es&shy;<lb/>sendo che questo si allontana dalla perpendicolare e quella invece se le av&shy;<lb/>vicina. </s>

<s>Sia stato l'Autore condotto ad ammetter quella similitudine per di&shy;<lb/>fetto di osservazione, o per aver supposto che l'impedimento al moto, cos&igrave; <lb/>nella luce come nel proietto, non sia fatto altro che dalla superficie del <lb/>mezzo; &egrave; notabile che prima del Matematico alemanno l'Acquapendente ras&shy;<lb/>somigliasse le ottiche rifrazioni alle meccaniche, asserendo anch'egli che si <lb/>facevano ambedue nel medesimo verso. </s>

<s>&ldquo; Nam globulus in aere cum sit et <lb/>extra aquam et in aquam intret, ad perpendiculum refrangetur et accedet &rdquo; <lb/>(De Vis. </s>

<s>cit., pag. </s>

<s>71). </s></p><p type="main">

<s>Nel Keplero per&ograve; s'intende com'egli ammette che il globo pieghi alla <lb/>perpendicolare, concessagli l'ipotesi che l'urto si faccia in un punto solo <lb/>della superficie qual sarebbe per esempio B, nella precedente figura, e che <lb/>perci&ograve; non sia la rifrazione, com'egli professa, altro che un caso particolare <lb/>di riflessione. </s>

<s>Ci&ograve; dall'altra parte &egrave; conforme all'esperienza, perch&egrave;, se il <lb/>diafano non impedisce il moto altro che nella superficie, si pu&ograve; BC riguardar <lb/>come un piano resistente, e B come un punto del suo orlo, contro il quale <lb/>urtando una palla nella direzione AB, nel punto B veramente si piega verso <lb/>la perpendicolare. </s>

<s>Ma non s'intende in ogni modo come si concilii questa <lb/>ipotesi del Keplero con quell'altra da lui medesimo espressa, la quale &egrave; che <lb/>il globo <emph type="italics"/>subeat aquam,<emph.end type="italics"/> nel qual caso il supposto stesso &egrave; manifestamento <lb/>contrario a ci&ograve; che si vede avvenire di fatto. </s></p><p type="main">

<s>Comunque sia, eran tali quali le abbiamo esposte fin qui, le ragioni <lb/>che specularono gli Ottici da Vitellione al Keplero intorno ai raggi rifratti. </s>

<s><lb/>In quelle ragioni, se fossero state vere, ci si doveva trovare compresa la <lb/>legge delle relazioni che passano fra gli angoli dell'incidenza e quelli della <lb/>rifrazione, ma perch&egrave; oramai era l'Ottica esperta, per l'esempio delle rifles&shy;<lb/>sioni non potersi in ci&ograve; far altro fondamento che dell'esperienza, all'espe&shy;<lb/>rienza si rivolsero Alhazeno e Vitellione. </s>

<s>Trovarono che crescendo o sce&shy;<lb/>mando gli angoli dell'inclinazione, gli angoli rifratti non rispondevano in <lb/>esatta ragione geometrica, e si assicurarono che il poter rifrangente variava <lb/>dall'acqua al vetro. </s>

<s>Costrussero di questi loro resultati sperimentali alcune <lb/>Tavole che Vitellione impresse nel libro X Della Prospettiva al Teorema VIII, <lb/>in cui &ldquo; Anguli omnium refractionum per Tabulas declarantur &rdquo; (Edit. </s>

<s>cit., <lb/>pag. </s>

<s>257). </s></p><p type="main">

<s>Qualunque sia l'esattezza di queste Tavole, il Maurolico ebbe torto a <lb/>non farne nessun conto, formulando il suo X Teorema <emph type="italics"/>Diaphanorum:<emph.end type="italics"/> &ldquo; An&shy;<lb/>guli inclinationum sunt fractionum angulis proportionales &rdquo; (Neapoli 1611, <lb/>pag. </s>

<s>35). L'indice di rifrazione per le sfere cristalline lo ritrov&ograve; otto terzi, <lb/>e tale egli stimava esser l'indice, senza differenza, di tutti gli altri mezzi <lb/>refringenti. </s>

<s>&ldquo; Ergo et angulus inclinationis ad angulum suae fractionis sem-<pb xlink:href="020/01/615.jpg" pagenum="58"/>per unam servat rationem estque dupla et duas tertias superpatiens, sicut <lb/>experimento in crystallina sphaera probabimus &rdquo; (ibi, pag. </s>

<s>36). </s></p><p type="main">

<s>Per&ograve; il nostro Ottico siciliano fu nelle applicazioni diottriche molto pi&ugrave; <lb/>esatto dell'Arabo e del Pollacco, come si par comparando i Teoremi XVIII <lb/>e XXIII dei <emph type="italics"/>Diaphanorum Partes<emph.end type="italics"/> colla proposizione XIV del libro X di <lb/>Prospettiva. </s>

<s>In questa proponevasi Vitellione di dimostrare che quanto il <lb/>raggio &egrave; pi&ugrave; obliquo tanto pi&ugrave; crescono gli effetti delle rifrazioni. </s>

<s>&ldquo; Omnium <lb/>formarum punctorum rei visae plus distantium a linea perpendiculari, ducta <lb/>a centro visus super superficiem corporis diafoni a qua fit refractio, maior <lb/>est refractio quam punctorum minus distantium ab illa &rdquo; (Edit. </s>

<s>cit., pag. </s>

<s>259). </s></p><p type="main">

<s>Il Teorema propostosi a dimostrar qui da Vitellione si capisce bene <lb/>com'&egrave; il capitale della Diottrica, ma il Porta fu il primo a notar che l'Au&shy;<lb/>tore in dimostrar quel suo assunto dava nel falso. </s>

<s>La proposizione VIII del <lb/>Lib. </s>

<s>I <emph type="italics"/>De refractione<emph.end type="italics"/> &egrave; dal nostro Ottico napoletano formulata cos&igrave; in modo <lb/>simile all'Ottico pollacco. </s>

<s>&ldquo; Res sub aquis refracta visa, quo magis ab oculo <lb/>distat, eo sublimior videtur &rdquo; (Neapoli 1593, pag. </s>

<s>16). Sia FBEK (fig. </s>

<s>19) <lb/><figure id="id.020.01.615.1.jpg" xlink:href="020/01/615/1.jpg"/></s></p><p type="caption">

<s>Figura 19.<lb/>un vaso pien d'acqua sul <lb/>fondo del quale giacciano <lb/>ad ugual distanza gli og&shy;<lb/>getti C, D, E: dopo aver <lb/>dimostrato che maggior <lb/>rifrazione subisce il punto <lb/>E del punto D, e il punto <lb/>D maggiore del punto C, <lb/>il Porta soggiunge: &ldquo; Sed <lb/>Vitellio in hoc falsus est <lb/>quod etsi aequaliter inter <lb/>se distent in fundo iacentia colorata C, D, E, non ob id aequaliter distant <lb/>in aquae summo puncta refractionum G, T, I &rdquo; (ibi, pag. </s>

<s>17). </s></p><p type="main">

<s>L'osservazione &egrave; notabile, perch&egrave; di qui ebbero principio i progressi <lb/>alla scienza delle rifrazioni. </s>

<s>Venne poi il Keplero, il quale confermando la <lb/><figure id="id.020.01.615.2.jpg" xlink:href="020/01/615/2.jpg"/></s></p><p type="caption">

<s>Figura 20.<lb/>XIV del X di Vitellione esser <emph type="italics"/>vitiose et <lb/>obscure demonstrata,<emph.end type="italics"/> pens&ograve; che fosse <lb/>da tentare altra via. </s>

<s>Considerava che <lb/>tutto il fatto dipende dall'obliquit&agrave; del&shy;<lb/>l'incidenza, e che sempre l'angolo della <lb/>dispersione cresce in ragion di quella <lb/>obliquit&agrave;. </s>

<s>&ldquo; Hinc corollarium: si medium <lb/>ipsum causa suae densitatis considera&shy;<lb/>tur solitarie, anguli refractionum pro&shy;<lb/>portionales fierent angulis incidentiae &rdquo; <lb/>(Paralip. </s>

<s>ad Vitell. </s>

<s>cit., pag. </s>

<s>110). </s></p><p type="main">

<s>Ma &egrave; inoltre da considerare, proseguiva nel suo ragionamento il Ke&shy;<lb/>plero, anche il raggio in s&egrave; stesso, il quale patisce, nel mezzo ch'egli in-<pb xlink:href="020/01/616.jpg" pagenum="59"/>contra, tanto maggior resistenza, quanto vi scende sopra pi&ugrave; obliquo. </s>

<s>Ci&ograve; <lb/>si dimostra dall'Autore nel modo seguente: &ldquo; Sit A (fig. </s>

<s>20) lux, BC me&shy;<lb/>dium densius, AB, KM paralleli vel quasi ex sole: distantia eorum in per&shy;<lb/>pendiculari ML. </s>

<s>Cum igitur BLM rectus sit, et LBM ponatur obliquus, acutus <lb/>erit, igitur LBM minor quam BLM et LM latus minori angulo B oppositum, <lb/>minus erit BM latere, quod maiori angulo L opponitur. </s>

<s>Sed LM metitur la&shy;<lb/>titudinem medii occurrentis luci recte illapsae, quia BLM est rectus, BM vero <lb/>latitudinem occurrentis luci ex obliquo; plus igitur densitatis est in BM, quam <lb/>in LM. </s>

<s>Maior igitur resistentia hoc respectu &rdquo; (ibi, pag. </s>

<s>111). </s></p><p type="main">

<s>Di qui ne concludeva il Keplero che la resistenza, opposta dalla densit&agrave; <lb/>del mezzo all'obliquit&agrave; via via crescente del raggio, &egrave; proporzionale alla se&shy;<lb/>cante BM. Ond'&egrave; che, parte dell'angolo di refrazione, cresce colla semplice <lb/>incidenza, parte cresce in proporzion maggiore della semplice incidenza; dun&shy;<lb/>que anche tutto l'angolo crescer&agrave; con maggiori incrementi della semplice <lb/>obliquit&agrave; dell'incidenza. </s>

<s>&ldquo; Ergo pars anguli refractionum proportionatur in&shy;<lb/>cidentiis, pars maioribus rationis incrementis crescit. </s>

<s>Totus igitur angulus <lb/>maioribus incrementis crescit &rdquo; (ibi, pag. </s>

<s>111). </s></p><p type="main">

<s>Cos&igrave; veniva la Diottrica a ripigliare il vantaggio su quei regressi, verso <lb/>cui era stata sospinta pel Teorema X del Maurolico sopra citato. </s>

<s>Ma pur <lb/>conveniva determinare secondo qual precisa proporzione si facessero quegli <lb/>incrementi maggiori dagli angoli di refrazione, sopra quelli dell'incidenza. <lb/></s>

<s>&ldquo; Non intentatum nec hoc, dice il Keplero, reliqui utrum semel constituta <lb/>horizontali refractione ex densitate medii, caeterae sinubus distantiarum a <lb/>vertice responderent. </s>

<s>Sed nec calculus id approbavit, nec sane opus erat <lb/>inquirere, nam eadem forma crescerent refractiones in omnibus mediis quod <lb/>repugnat experientiae (ibi, pag. </s>

<s>84). Rursum quaesivi .... an ascendant <lb/>imagines in proportione sinuum inclinationum: minime; nam eadem ratio <lb/>esset ascensus in omnibus mediis &rdquo; (ibi, pag. </s>

<s>89). </s></p><p type="main">

<s>In quello stesso anno 1611 il De Dominis pubblicava il suo celebre <lb/>Trattato <emph type="italics"/>De radiis visus et lucis,<emph.end type="italics"/> dove ritornavasi indietro a professar col <lb/>Maurolico la proporzionalit&agrave; fra gli angoli d'incidenza e quelli di rifrazione. </s>

<s><lb/>Vi si professano poi dall'Autore idee che, per non chiamarle strane, si di&shy;<lb/>ranno da noi singolari, come sarebbe per esempio che la luce non si ri&shy;<lb/>frange, se il mezzo &egrave; in piccola quantit&agrave; o di uniforme crassizie. </s>

<s>&ldquo; Fractio <lb/>haec seu refractio radiorum non fit ubi interponitur corpus diaphanum den&shy;<lb/>sius aut rarius reliquo medio, si sit in pauca quantitate et aequalis crassi&shy;<lb/>tiei, ut in exigua aqua altitudinis unius digiti uniformis exiguae crassitiei, <lb/>omnes radii tam luminosi quam visuales penetrant recta et irrefracta absque <lb/>ulla alteratione visus aut luminis &rdquo; (Venetiis, pag. </s>

<s>5). </s></p><p type="main">

<s>Si potrebbe credere che ci&ograve; fosse per opporsi all'error del Keplero, il <lb/>quale ammetteva non refrangersi il raggio altro che nella superficie. </s>

<s>Ma <lb/>intenzion dell'Autore era di apparecchiarsi la via a trattar della rifrazion <lb/>nelle lenti, affermando che elle non per altro rompono i raggi che per la <lb/>loro difforme crassizie, e che sempre si fa la frattura non verso la pi&ugrave; sot-<pb xlink:href="020/01/617.jpg" pagenum="60"/>tile ma verso la parte pi&ugrave; crassa del vetro. </s>

<s>&ldquo; Tunc fractiones semper fient <lb/>versus partem crassiorem, ut si vitrum rotundum sit in medio crassius et <lb/>convexum ac versus extrema et circumferentiam semper tenuius et graci&shy;<lb/>lius, fractiones fient ad perpendicularem, idest versus axem per centrum vi&shy;<lb/>tri transeuntem: contrarium continget si vitrum sit in medio gracilius et <lb/>versus circumferentiam crassius: perpendicularis tamen penetrat recta absque <lb/>sui refractione &rdquo; (ibi). </s></p><p type="main">

<s>Con s&igrave; lieve armatura non era da sperar di venire a quella conquista, <lb/>dalla quale erasi arretrato lo stesso Keplero. </s>

<s>Altre coti s&igrave; richiedevano ad <lb/>affilare quelle armi, altre avventure, le quali ora noi passeremo a narrare. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>L'Autore de'Paralipomeni a Vitellione, lasciando a mezzo quelle sue <lb/>sollecite investigazioni intorno alla legge degli angoli dell'incidenza rispetto <lb/>agli angoli formati dai raggi refratti, mentre da una parte disanimava gli <lb/>Ottici, che vedevano essere la difficolt&agrave; rimasta inespugnata da tanto ardore <lb/>e da tanta possa, additava dall'altra la via, proseguendo la quale si sarebbe <lb/>riusciti alla vittoria. </s>

<s>Egli parve insinuare, nel &sect; II del Cap. </s>

<s>IV, che si do&shy;<lb/>vesse ritrovare ne'calcoli uno de'pi&ugrave; validi argomenti per quella riuscita, <lb/>e in ogni modo accennava chiaro che la legge diottrica sarebbe espressa o <lb/>per le secanti degli angoli o per i seni o in somma per qualche funzione <lb/>trigonometrica. </s></p><p type="main">

<s>Come ad opera di calcolo dunque si rivolse a investigar quella legge <lb/>il Cartesio, che si sentiva esser divenuto pi&ugrave; valoroso degli altri, per la fe&shy;<lb/>lice applicazione dell'Algebra alla Geometria. </s>

<s>Ma i calcoli, in argomento <lb/>fisico qual era quello di che si trattava, volevano avere il lor fondamento <lb/>sull'esperienza, dalla quale nient'altro ancora s'era imparato, se non che gli <lb/>angoli delle rifrazioni crescono con maggior ragion d'incrementi che l'obli&shy;<lb/>quit&agrave; dell'incidenza. </s>

<s>I calcoli cartesiani perci&ograve; si ritrovarono inefficaci, e sa&shy;<lb/>rebbe per l'Autore rimasta l'impresa al punto dove l'aveva lasciata il Ke&shy;<lb/>plero, se per fortuna non avesse trovato a quegli stessi suoi calcoli laboriosi <lb/>il Cartesio, nell'esperienza, sicurt&agrave; di guida e saldezza di fondamento. </s></p><p type="main">

<s>Quando la maravigliosa invenzione del Canocchiale frugava cos&igrave; viva&shy;<lb/>mente gli Ottici per trovar nella scienza delle rifrazioni la ragion di que'mi&shy;<lb/>rabili effetti, e il Maurolico e il Porta, il De Dominis e il Keplero, il Tarde <lb/>e lo Scheiner tanto v'assottigliaron dietro l'ingegno, che riuscirono a pun&shy;<lb/>gere, ma no a perforare, Willebrod Snellio, con miglior giudizio di tutti gli <lb/>altri, s'avvide che non era da confidar nella Geometria o nelle astratte spe&shy;<lb/>culazioni, ma principalmente nell'esperienza. </s>

<s>Perci&ograve; rivolse attentamente gli <lb/>studii sulla XIV proposizione del libro X di Vitellione, e giacch&egrave; il Porta <lb/>l'aveva trovata falsa e il Keplero l'avea dichiarata viziosa ed oscura, n&egrave; il <pb xlink:href="020/01/618.jpg" pagenum="61"/>difetto da'due Autori scoperto gli pareva che fosse lodevolmente emendato, <lb/>egli misuratore insigne del grado del meridiano terrestre, volle sottoporre <lb/>alle pi&ugrave; esatte misure il sollevarsi delle immagini giacenti sul fondo del <lb/>vaso, nella figura e nell'esempio proposto da Vitellione al luogo ora citato. </s></p><p type="main">

<s>Sia per esempio quel vaso pien d'acqua AEYD (fig. </s>

<s>21) e gli oggetti <lb/><figure id="id.020.01.618.1.jpg" xlink:href="020/01/618/1.jpg"/></s></p><p type="caption">

<s>Figura 21.<lb/>posati sul suo fondo a di&shy;<lb/>stanze uguali fra loro R, <lb/>P, Y. </s>

<s>Il raggio refratto RSO <lb/>mostra all'occhio O solle&shy;<lb/>vato l'oggetto R in L, e <lb/>gli altri in Q e in D. </s>

<s>Chia&shy;<lb/>ma lo Snellio OSR, ONP, <lb/>OFY raggi veri dell'inci&shy;<lb/>denza, OSL, ONQ, OFD <lb/>raggi apparenti e dalle mi&shy;<lb/>sure collazionate in mol&shy;<lb/>tissimi casi riusc&igrave; a for&shy;<lb/>mulare la legge seguente: <lb/>&ldquo; Radius incidentiae verus ad adparentem, in eiusdem generis medio, ratio&shy;<lb/>nem semper habet eamdem. </s>

<s>&rdquo; </s></p><p type="main">

<s>Questo Teorema, coi calcoli delle misure e con la descrizione degli stru&shy;<lb/>menti squisitissimi da ritrovarle pi&ugrave; giuste, il celebre Matematico olandese <lb/>avevale esposte in un suo compitissimo trattato di Ottica diviso in tre Libri, <lb/>che alla sua morte avvenuta nel 1626 lasci&ograve; manoscritto. </s>

<s>Il figlio, non com&shy;<lb/>portando forse la spesa della stampa, era liberale co'dotti che ne lo aves&shy;<lb/>sero richiesto, e uno de'primi fra questi fu il Cartesio, il quale in quel <lb/>Teorema al modo detto di sopra formulato, vedeva d'ogni parte risplendere <lb/>la certezza del fatto. </s>

<s>Ma egli voleva in quello stesso Teorema aver espressa la <lb/><figure id="id.020.01.618.2.jpg" xlink:href="020/01/618/2.jpg"/></s></p><p type="caption">

<s>Figura 22.<lb/>legge diottrica per qual&shy;<lb/>che funzione trigonome&shy;<lb/>trica degli angoli, e cos&igrave; <lb/>veder qual corrisponden&shy;<lb/>za avesse il fatto speri&shy;<lb/>mentale dello Snellio, e <lb/>come dovess'essere for&shy;<lb/>mulato conforme al cal&shy;<lb/>colo kepleriano. </s>

<s>La cosa <lb/>era per s&egrave; facilissima e <lb/>il Cartesio vi fu condotto <lb/>per una via che presso <lb/>a poco era questa. </s></p><p type="main">

<s>Rivolgendo lo sguar&shy;<lb/>do sopra la figura 22 dove RM rappresenta la superficie del diafano, FQ, <lb/>GD, IP, KO le perpendicolari ad essa superficie, ABD, HLO i raggi del-<pb xlink:href="020/01/619.jpg" pagenum="62"/>l'incidenza vera, ABC, HLN i raggi apparenti, dal Teorema dello Snellio si ha <lb/>BD:BC=LO:LN, e dalla Trigonometria BD:BC=sen BCD:sen BDC; <lb/>LO:LN=sen LNO:sen LON. </s>

<s>Ma sen BCD=sen (180&mdash;BCE)=sen (90 <lb/>&mdash;CBE)=sen (90&mdash;ABR)=sen ABF; e nello stesso modo avremo pure <lb/>sen LNO=sen HLI, sen BDC=sen DBQ, sen LON=sen OLP. </s>

<s>Sar&agrave; <lb/>perci&ograve; sen ABF:sen DBQ=sen HLI:sen OLP, che vuol dire <emph type="italics"/>i seni degli <lb/>angoli dell'incidenza son proporzionali ai seni degli angoli delle rifra&shy;<lb/>zioni.<emph.end type="italics"/> Ed ecco cos&igrave; trovato come doveva essere espresso, conforme alla <lb/>mente del Keplero, il fatto delle relazioni fra l'immagine vera e l'apparente, <lb/>scoperto dallo Snellio. </s></p><p type="main">

<s>Era venuta cos&igrave; inaspettatamente alle mani del Cartesio quella scoperta <lb/>con tanto vivo desiderio cercata da tutti, e che nessuno ancora si confidava <lb/>d'aver trovata. </s>

<s>Ei n'esult&ograve; apparecchiandosi a pubblicarla, e lasciandosi tra&shy;<lb/>sportare all'aura dell'ambizione, piuttostoch&egrave; all'amore del vero, l'orgoglioso <lb/>Filosofo, che pretendeva far tutta la scienza scaturire dal proprio cervello, <lb/>disprezzata ogni tradizione de'suoi maggiori, tacque d'aver veduto lo Snel&shy;<lb/>lio, e d'essere stato inspirato alle speculazioni diottriche del Keplero. </s>

<s>Come <lb/>poi fosse dal suo stesso orgoglio tradito e come venisse insieme a esser tra&shy;<lb/>dita la scienza, ci verr&agrave; tra poco mostrato dalla storia, ma intanto &egrave; da ve&shy;<lb/>der con quale studio il Cartesio, nel capitolo II della sua Diottrica, pubbli&shy;<lb/>cata in francese nel 1637, cercasse di persuadere al mondo che la legge <lb/>delle relazioni costanti fra i seni degli angoli d'incidenza e i seni degli an&shy;<lb/>goli di rifrazione fosse un legittimo parto e uno spontaneo portato della sua <lb/>nuova Filosofia. </s></p><p type="main">

<s>Dop'avere ne'primi tre paragrafi applicato il principio della composi&shy;<lb/>zione del moto a dimostrar la legge delle riflessioni, come si narr&ograve; nel Ca&shy;<lb/>pitolo precedente, <emph type="italics"/>Hinc progrediamur,<emph.end type="italics"/> incomincia cos&igrave; il &sect; IV, <emph type="italics"/>ad refractio&shy;<lb/>nem.<emph.end type="italics"/> Sia A (fig. </s>

<s>23) la solita palla gettata nella <lb/><figure id="id.020.01.619.1.jpg" xlink:href="020/01/619/1.jpg"/></s></p><p type="caption">

<s>Figura 23.<lb/>direzione obliqua AB, non come dianzi sopra la <lb/>terra dura CE, ma sopra un panno, ch'ella possa <lb/>facilmente squarciare e passar di sotto, bench&egrave; con <lb/>perdita notabile della prima velocit&agrave;, la quale sia <lb/>per esempio ridotta a mezzo. </s>

<s>Decomposto anche <lb/>questo secondo moto nell'orizzontale e nel verti&shy;<lb/>cale, quello per non ricevere offesa dal panno teso <lb/>rimarr&agrave; inalterato, cosicch&egrave; per quel verso passer&agrave; <lb/>nello stesso tempo uno spazio doppio. </s></p><p type="main">

<s>Ci&ograve; supposto e considerato &ldquo; ducto circulo AFD <lb/>ex centro B, et impositis C, B, E ad perpendiculum tribus lineis rectis AC, <lb/>HB, FE, hac ratione ut spatium interiacens FE et HB duplum illius sit quod <lb/>est inter HB et AC, videbimus hanc pilam ituram ad punctum I. </s>

<s>Cum enim <lb/>perrumpendo linteum CBE dimidiam suae velocitatis partem amittat, duplum <lb/>temporis ei impendendum est ut infra ex B ad aliquod punctum circumferen&shy;<lb/>tiae AFD pertingat, eius quod insunsit superne ut accederet ab A ad B. </s>

<s>Et cum <pb xlink:href="020/01/620.jpg" pagenum="63"/>nihil ex dispositione, qua dextrorsum ferebatur intereat, in duplo illius tem&shy;<lb/>poris, quo a linea AC devenit ad HB, duplum eiusdem itineris in eamdem <lb/>partem conficere debet, et consequenter accedere ad aliquod punctum rectae <lb/>FE, eodem momento quo accedit ad aliquod circumferentiae circuli AFD, <lb/>quod factu impossibile foret, nisi progrediatur ad I. </s>

<s>Nam in unico illo puncto <lb/>recta FE et circulus AFD sub linteo sese invicem secant &rdquo; (Francofurti 1692, <lb/>pag. </s>

<s>49). </s></p><p type="main">

<s>Il medesimo fatto prosegue a dimostrare il Cartesio che avverrebbe nella <lb/>palla, se CE, non un panno teso, ma fosse la superfice d'un'acqua. </s>

<s>Passa <lb/>poi nel &sect; VI a fare un'altra supposizione ed &egrave; che, giunta la palla nel <lb/>punto B, invece di ricevere impedimento le sopravvenga nuovo impeto al <lb/><figure id="id.020.01.620.1.jpg" xlink:href="020/01/620/1.jpg"/></s></p><p type="caption">

<s>Figura 24.<lb/>moto, cosicch&egrave; questo divenga per esempio un terzo <lb/>pi&ugrave; veloce del primo. </s>

<s>Dalle cose nel &sect; IV dimostrate, <lb/>segue manifestamente, dice l'Autore, che descritto <lb/>il cerchio AFD (fig. </s>

<s>24) e condotte le perpendico&shy;<lb/>lari AC, HB, FE, con tal ragione che la distanza tra <lb/>FE ed HB sia una terza parte di quella che &egrave; fra <lb/>HB ed AC, il punto I, comune al cerchio e alla <lb/>perpendicolare FI, designer&agrave; il luogo dove s'addi&shy;<lb/>rizza la palla, e la forza che erompe prima della <lb/>incidenza star&agrave; alla forza che erompe dopo la rifra&shy;<lb/>zione come CB:BE, o come AH:GI. </s></p><p type="main">

<s>&ldquo; Tandem vero, prosegue a ragionare il Cartesio nel &sect; VII, quoniam <lb/>lucis actio sequitur hac in re easdem leges, quas pilae motus, dicendum quo&shy;<lb/>ties radii illius obliquo motu ex pellucido corpore in aliud transferuntur, <lb/>quod magis aut minus facile illos admittit, quamprimum ibi ita detorqueri, <lb/>ut semper minus inclinent in superficie quae his corporibus est communis, <lb/>ea parte in qua est illud corpus quod eas facilius recipit, quam ea in qua <lb/>alterum positum est, idque exacte ea proportione qua facilius prius quam <lb/>posterius illos recipit.... Ut ex. </s>

<s>gr. </s>

<s>si radius aerem permeans ab A (fig. </s>

<s>25) <lb/><figure id="id.020.01.620.2.jpg" xlink:href="020/01/620/2.jpg"/></s></p><p type="caption">

<s>Figura 25.<lb/>ad B, tacta in punto B superficie vitri CBR, <lb/>digrediatur ab I in hoc vitro: veniat deinde alius <lb/>a K ad B qui decedat ad L .... eadem ratio li&shy;<lb/>nearum KM et LN esse debet ad invicem quae <lb/>est linearum AH et IG &rdquo; (ibi, pag. </s>

<s>51). </s></p><p type="main">

<s>Pubblicata la Diottrica nella celebre Dis&shy;<lb/>sertazione <emph type="italics"/>Del Metodo<emph.end type="italics"/> i Cartesiani si pu&ograve; cre&shy;<lb/>dere se l'accolsero a grande onore, ma negli <lb/>altri che non erano stati sedotti dal Bretone <lb/>eloquente o insorsero vive le contradizioni o <lb/>si ritrassero da parte dubitosi delle novit&agrave; e <lb/>diffidenti. </s>

<s>Quella diffidenza poi era inevitabile, e bench&egrave; possa apparir come <lb/>indizio di ritrosa caparbie negli animi, era invece argomento di senno ne&shy;<lb/>gl'ingegni, che ragionavano non potersi la Fisica e specialmente l'Ottica <pb xlink:href="020/01/621.jpg" pagenum="64"/>investigare a priori, per via delle sottili speculazioni. </s>

<s>Se fosse stato il Car&shy;<lb/>tesio pi&ugrave; sincero, e avesse dato la legge diottrica, qual ei l'ebbe dallo Snellio, <lb/>come un fatto sperimentato, la diffidenza era tolta, e perci&ograve; si diceva dianzi <lb/>che l'orgoglio cartesiano, ponendo ostacolo al libero accoglimento del vero, <lb/>avea tradita la scienza nei suoi progressi. </s></p><p type="main">

<s>Ma &egrave; pure un fatto che il Filosofo, il quale volle orgogliosamente sol&shy;<lb/>levarsi sopra le conculcate cervici de'suoi maggiori fratelli, trad&igrave; anche in&shy;<lb/>sieme la sua propria reputazione, quando giudici imparzialmente severi si <lb/>misero dietro a esaminare il processo delle seducenti speculazioni. </s>

<s>Il Fer&shy;<lb/>mat richiesto del suo giudizio, intorno alla nuova Diottrica, dal Marsenno, <lb/>si maravigliava come mai l'Autore, tra gl'infiniti modi di decomporre in <lb/>due un moto solo avesse precisamente scelto quello, ch'era meglio accomo&shy;<lb/>dato alla sua conclusione, la quale perci&ograve; non dubita di averla come cosa <lb/>immaginaria. </s>

<s>La scienza ne sa ora quanto prima, soggiunge l'arguto Mate&shy;<lb/>matico francese, e per Bacco, nessuno mi dar&agrave; mai ad intendere che da una <lb/>fantasia possa, come da causa vera, esser derivato un effetto reale. </s>

<s>&ldquo; Patet <lb/>itaque quod ex omnibus divisionibus determinationis ad motum, quae infi&shy;<lb/>nitae sunt multitudinis, author non nisi eam delegit quae ad conclusionem <lb/>suam firmandam conducebat, atque ideo medium suum ad conclusionem <lb/>suam accommodavit, nobisque de eo aeque parum constat ac antea. </s>

<s>Et hercle <lb/>non videtur immaginaria divisio, quae in infinitis formis diversificari potest, <lb/>effectus cuiusdam realis causa esse posse &rdquo; (Des. </s>

<s>Cartes. </s>

<s>Epistolae, P. III, <lb/>Francof. </s>

<s>ad M. 1692, pag. </s>

<s>78). </s></p><p type="main">

<s>Notandosi ivi dal Fermat che il Cartesio andava accomodando la dimo&shy;<lb/>strazione alle sue conclusioni, veniva cos&igrave; tacitamente insinuando nell'animo <lb/>del Mersenno e di coloro i quali sarebbero poi tornati a meditare sul fatto, <lb/>che non fu la speculativa che condusse a ritrovare la legge delle rifrazioni, <lb/>ma che, conosciutasi questa legge, la speculazione si accomod&ograve; le vie da <lb/>scendere addirittura verso quel termine gi&agrave; prima designato. </s>

<s>Cos&igrave; il Filo&shy;<lb/>sofo, che pretendeva d'aver fatto conseguire l'Ottica dalla speculata Geo&shy;<lb/>metria, veniva a tradire il suo ingannevole intanto e a porger motivo ragio&shy;<lb/>nevole ai critici sospettosi di pronunziar per sentenza finale l'accusa d'aver <lb/>furato lo Snellio. </s></p><p type="main">

<s>Altre contradizioni ebbe poi a patire il Cartesio per essersi fatto imi&shy;<lb/>tatore al Keplero troppo inconsiderato. </s>

<s>Si sa che l'Autore de'Paralipomeni <lb/>a Vitellione, professando la diffusion luminosa in superficie, ammetteva che <lb/>sulla sola superficie del mezzo si facesse la rifrazione, e su questa ipotesi <lb/>son condotte le dimostrazioni di quegli Ottici Teoremi, che il Cartesio si <lb/>dette a imitare, non curandosi di sceverar giudiziosamente il vero dal falso. </s>

<s><lb/>Da questa parte vennero all'Autor della nuova Diottrica i rimproveri e le <lb/>redarguizioni per opera d'Isacco Vossio, a cui dee la scienza delle rifrazioni <lb/>l'essere stato tolto di mezzo il pernicioso error kepleriano. </s></p><p type="main">

<s>&ldquo; Altera similitudo, scriveva lo stesso Vossio, qua lucis naturam expli&shy;<lb/>care conatur, desumta est ex motu pilae: prout enim huius inclinatio re-<pb xlink:href="020/01/622.jpg" pagenum="65"/>gitur ad modum superficiei quam vel attingit vel penetrat, eodem modo putat <lb/>vel reflecti vel refringi lumen. </s>

<s>Hac comparatione, quamvis ante Cartesium <lb/>usus quoque sit Keplerus, multis tamen nominibus peccat, nulloque pror&shy;<lb/>sus modo potest defendi. </s>

<s>Licet enim supponamus pilae motum semper ae&shy;<lb/>qualem, hoc est infinitum, nihil tamen habebit simile cum radiis lucis non <lb/>successive sed in instanti promanantibus. </s>

<s>Modum praeterea et rationem re&shy;<lb/>fractionis adsecutus non est, cum in sola superficie refractionem fieri exi&shy;<lb/>stimat, ac linteo supra aquam vel aerem extenso comparat. </s>

<s>Scio quidem <lb/>communem omnium opticorum esse opinionem lucem in superficie tantum <lb/>frangi, quia nempe radii refracti a radiis veris quoad oculum separari vi&shy;<lb/>dentur simul ac densius diaphanum ingrediuntur, tantum tamen abest ut <lb/>hoc ita sese habeat ut potius contrarium verum sit nihilque omnino in su&shy;<lb/>perficie corporis diaphani patiantur radii &rdquo; (De Nat. </s>

<s>lucis., Amstelodami 1662, <lb/>pag. </s>

<s>33), e seguita a dimostrar che i raggi non si refrangono alla superfi&shy;<lb/>cie ma dentro il mezzo con argomenti, a cui non si potrebbe nulla apporre <lb/>in contrario. </s></p><p type="main">

<s>Il Vossio fu forse il primo a far pubblicamente accorti gli Ottici che <lb/>il processo dimostrativo del Cartesio era stato prima tenuto dal Keplero: <lb/>ma dello Snellio tutti per ora stanno in silenzio, anche il Fermat, bench&egrave; <lb/>faccia trasparir qua e l&agrave; nelle sue Lettere d'essere entrato in qualche so&shy;<lb/>spetto. </s>

<s>Il rumore incominci&ograve; dopo il 1703 e fu il Newton il pi&ugrave; sollecito a <lb/>secondarlo. </s>

<s>Nelle Lezioni d'Ottica, dop'avere accennato all'incertezza degli <lb/>antichi intorno alla regola delle rifrazioni, soggiunge: &ldquo; at Cartesius aliam <lb/>regulam primus excogitavit qua illud exactius determinaretur, ponendo dicto&shy;<lb/>rum angulorum sinus esse in ratione data &rdquo; (Patavii 1773, pag. </s>

<s>13, 14). Ma <lb/>nello Scolio alla propos. </s>

<s>XCVI del Lib. </s>

<s>I de'<emph type="italics"/>Principii,<emph.end type="italics"/> nella seconda edi&shy;<lb/>zione, cos&igrave; tornava a scrivere in diversa sentenza: &ldquo; Harum attractionum <lb/>haud multum dissimiles sunt lucis reflexiones et refractiones, factae secun&shy;<lb/>dum datam secantium rationem ut invenit Snellius, et per consequens se&shy;<lb/>cundum datam sinuum rationem, ut exposuit Cartesius &rdquo; (Genevae 1739, <lb/>pag. </s>

<s>539). </s></p><p type="main">

<s>La ragione dell'aver cos&igrave; il Newton cambiata sentenza dal 1670, anno <lb/>in cui dettava le ultime Lezioni di Ottica, al 1713, anno in cui compar&igrave; la <lb/>seconda edizione de'<emph type="italics"/>Principii,<emph.end type="italics"/> &egrave; da attribuirsi alla lettura della Diottrica <lb/>dell'Huyghens pubblicata postuma nel 1703 in Leyda, nell'introduzione alla <lb/>quale il celebre Autore scriveva: &ldquo; Haec autem refractionum mensura non <lb/>sinuum, sed angulorum ipsorum proportione ab Alhaseno arabe et Vitel&shy;<lb/>lione olim definita fuerat, et experimentis quibusdam utcumque confirmata. </s>

<s><lb/>Sed cum in maioribus radiorum inclinationibus a vero discrepare propor&shy;<lb/>tio illa reperiretur, diligentius sibi Recentiores investigandam existimarunt, <lb/>in quibus Keplerus, plurimis frustra tentatis, ipsam quidem rei veritatem <lb/>non est assecutus, coniecturis tamen suis, variisque molitionibus non parum <lb/>sequentium studia adiuvit. </s>

<s>Post eum vero Willebrordus Snellius, cum iam <lb/>maius operae pretium appareret, quippe exorto Telescopii invento, multo la-<pb xlink:href="020/01/623.jpg" pagenum="66"/>bore, mullisque experimentis eo pervenit ut veras quidem refractionum men&shy;<lb/>suras teneret &rdquo; (pag. </s>

<s>2). </s></p><p type="main">

<s>L'Huyghens era mosso a rivelar questi fatti e a pronunziare questi <lb/>giudizii dall'amor della verit&agrave; e della patria, essendo lo Snellio suo conna&shy;<lb/>zionale. </s>

<s>Ma un altro Olandese lo aveva in ci&ograve; preceduto ed era quell'Isacco <lb/>Vossio, il quale parve avere avuto per principale intenzione in pubblicare <lb/>il suo Trattato <emph type="italics"/>De lucis Natura et proprietate<emph.end type="italics"/> quella di divulgare le diot&shy;<lb/>triche dottrine snelliane rimaste immeritamente sconosciute in un libro che <lb/>egli ebbe per grazia di veder manoscritto. </s>

<s>&ldquo; Porro priusquam ad alia re&shy;<lb/>fractionis pergam phaenomena, praeterire non possum insignem Willebrordi <lb/>Snellii observationem, quae unice sententiam nostram confirmat. </s>

<s>Quantus vir <lb/>ille fuerit in universa Mathesi, quamvis ex iis quae palam prostant scriptis <lb/>satis colligi possit, multo tamen idipsum clarius constaret, si fata permisis&shy;<lb/>sent illa quoque perficere, quae utique perfecisset, si vel paulo diuturnio&shy;<lb/>rem Deus vitam indulsisset. </s>

<s>Inter alia vero praeclara quae reliquit monu&shy;<lb/>menta supersunt quoque tres Libri optici quorum usuram superiori hyeme <lb/>concessit mihi filius eius. </s>

<s>Quia illi necdum prodierunt in lucem, dignissimi <lb/>tamen qui prodeant, adponam hic Theorema, quo nullum in tota optica no&shy;<lb/>bilius et utilius extat. </s>

<s>Sic vero se habet: Radius incidentiae verus ad adpa&shy;<lb/>rentem, in eiusdem generis medio, rationem semper habet eamdem &rdquo; (Amste&shy;<lb/>lodami 1662, pag. </s>

<s>36). </s></p><p type="main">

<s>&Egrave; cosa assai singolare per&ograve; che il Vossio, cos&igrave; arguto censor del Cartesio <lb/>e che non lascia mai l'occasion di notare i molti errori di lui, per contrap&shy;<lb/>porgli alle verit&agrave; dimostrate dallo Snellio, non faccia una parola intorno alla <lb/>legge delle rifrazioni, per dir quanto fosse l'Autore della Dissertazione del <lb/>Metodo debitor verso l'Autore dell'Ottica manoscritta. </s>

<s>La singolarit&agrave; per&ograve; <lb/>si spiega avvertendo a un'altra singolarit&agrave;, ed &egrave; che il Vossio non s'accorse <lb/>che il Teorema snelliano e il cartesiano erano in sostanza la medesima cosa. </s>

<s><lb/>Il facilissimo calcolo che dal supporre il raggio vero dell'incidenza propor&shy;<lb/>zionale al raggio apparente conduceva a trovar la costante proporzionalit&agrave; <lb/>fra il seno dell'angolo dell'incidenza e il seno dell'angolo di refrazione, fu <lb/>trascurato affatto dal Vossio, il quale perci&ograve; rimase nella persuasione che <lb/>tutt'altra fosse la legge dello Snellio da quella del Cartesio. </s>

<s>Di qui &egrave; che <lb/>l'Huyghens, dop'aver detto che lo stesso Snellio aveva ritrovata la vera legge <lb/>diottrica, <emph type="italics"/>nec tamen,<emph.end type="italics"/> soggiunge, <emph type="italics"/>quod invenerat intelligeret.<emph.end type="italics"/> &Egrave; un fatto, <lb/>prosegue pi&ugrave; avanti a dire il medesimo Huyghens, che &ldquo; ad hanc sinuum <lb/>proportionem nequaquam attendit Snellius, et usque adeo ab apparente ima&shy;<lb/>gine rem omnem pendere existimavit, ut etiam in radio perpendiculari, ef&shy;<lb/>fectum refractionis, seu ut falso opinatur, decurtationem radii visorii agno&shy;<lb/>scat, deceptus eo, quod etiam recta desuper in vas aqua plenum inspicienti <lb/>fundus omni parte attolli videtur &rdquo; (Dioptr. </s>

<s>cit., pag. </s>

<s>3). </s></p><p type="main">

<s>Dal medesimo inganno si lasci&ograve; pur sedurre il Vossio seguace in tutto <lb/>fedelissimo dello Snellio, ond'&egrave; che tutta l'utilit&agrave; della insigne scoperta non <lb/>seppero ambedue questi autori in altro riconoscerla che nell'aver finalmente <pb xlink:href="020/01/624.jpg" pagenum="67"/>ritrovata la linea del perfetto concorso, la quale non &egrave; parabolica n&egrave; iper&shy;<lb/>bolica, ma &egrave; una concoide <emph type="italics"/>non quidem nicomedeam, aut antinicomedeam, <lb/>sed aliam sui generis.<emph.end type="italics"/> (I. Voss. </s>

<s>De nat. </s>

<s>lucis cit., pag. </s>

<s>38). </s></p><p type="main">

<s>Fu insomma l'Huyghens il primo ad avvertir che il Cartesio aveva con&shy;<lb/>clusa la legge de'seni dalla misura che lo Snellio aveva ritrovata fra i raggi <lb/>veri e i raggi apparenti, intorno a che giova attendere a quel che l'Huy&shy;<lb/>ghens stesso scriveva in questo particolare. </s>

<s>&ldquo; Haec autem omnia quae de <lb/>refractionis inquisitione volumine integro Snellius exposuerat, inedita man&shy;<lb/>sere, quae et nos vidimus aliquando, et Cartesium quoque vidisse accepi&shy;<lb/>mus ut hinc fortasse mensuram illam, quae in sinibus consistit, elicuerit &rdquo; <lb/>(Dioptr. </s>

<s>cit., pag. </s>

<s>3). </s></p><p type="main">

<s>Cosicch&egrave; l'argomento del celebre furto del Cartesio dal manoscritto dello <lb/>Snellio si riduce a non pi&ugrave; che a un <emph type="italics"/>si dice,<emph.end type="italics"/> e dietro ci&ograve; dette il Newton <lb/>il caso per fatto certo, e per fatto certo moltissimi l'hanno ripetuto sull'au&shy;<lb/>torevole testimonianza di lui. </s>

<s>Che se quel perfetto giudizio volse il dubbio <lb/>dell'Huyghens a certezza, non &egrave; da creder che ci&ograve; fosse senza la sua ra&shy;<lb/>gione. </s>

<s>Cos&igrave; la legge diottrica de'seni come la calottrica degli angoli son fatti <lb/>de'quali &egrave; impossibile il dar la dimostrazione. </s>

<s>Ora, &egrave; egli mai da credere <lb/>che la dimostrazione sia stata quella che guid&ograve; il Filosofo alla scoperta del <lb/>fatto? </s>

<s>Quella credibilit&agrave; da un'altra parte vien naturalissima ammettendo <lb/>che al fatto sperimentale scoperto dallo Snellio si venisse accomodando la <lb/>speculata dimostrazion del Cartesio. </s>

<s>Che questi poi potesse avere per le <lb/>esperienze sue proprie fatta quella scoperta, non sapr&agrave; persuadersene nes&shy;<lb/>suno che conosce l'indole di quell'ingegno, e attende a quel gloriarsi che <lb/>e'fa bene spesso d'avere indovinati i fatti stessi dietro la speculativa. </s>

<s>Un <lb/>esempio calzante di ci&ograve; lo abbiamo in que'due strumenti ch'egli ammagin&ograve; <lb/>per la misura delle rifrazioni e de'quali parla nella Lettera LXX della <lb/>Parte II. Dop'aver detto che cos&igrave; fatti strumenti riescono, di quello di Vi&shy;<lb/>tellione, pi&ugrave; comodi e pi&ugrave; precisi &ldquo; Nihilominus fieri potest, soggiunge, ut <lb/>decipiant, neutro enim sum usus neque aliud unquam in hac materie expe&shy;<lb/>rimentum feci, nisi quod quinquennio aut sexennio abhinc curaverim effor&shy;<lb/>mandum vitrum cuius figuram Dom. </s>

<s>Mygdorgius delineaverat, quo perfecte <lb/>radii solis omnes in punctum unum conveniebant exacte quam praedixeram <lb/>distantiam &rdquo; (Francof. </s>

<s>ad M. 1692, pag. </s>

<s>209). </s></p><p type="main">

<s>Ed ecco a confermare il vizio della radice venire l'insipidezza de'frutti, <lb/>qual si dimostra in quelli che seppe dalle sue scoperte raccogliere il Carte&shy;<lb/>sio. </s>

<s>Egli &egrave; ancora dietro con coloro che sono affaccendati a cercar la linea <lb/>del perfetto concorso nelle lenti, la figura prestabilita alle quali &egrave;, giudice <lb/>il Fermat, una lepidezza (ivi, P. III, pag. </s>

<s>78). Dietro tutto ci&ograve; noi teniam <lb/>per certo col Newton quel che il prudentissimo Huyghens si content&ograve; di <lb/>mettere in dubbio, e abbiamo posto questa certezza per fondamento alla <lb/>presente parte di storia. </s></p><pb xlink:href="020/01/625.jpg" pagenum="68"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Il merito di un Filosofo non consiste solamente nell'avere scoperto il <lb/>vero, ma nella virt&ugrave; e nell'efficacia del diffonderlo. </s>

<s>La vera regola delle ri&shy;<lb/>frazioni era stata bene dimostrata dal Cartesio, ma da'suoi ciechi ammira&shy;<lb/>tori in fuori, fu difficile persuaderla a chi in un fatto fisico non aveva fede <lb/>alle speculazioni. </s>

<s>Abbiamo nel paragrafo precedente accennato a queste dif&shy;<lb/>ficolt&agrave;, ma ora &egrave; tempo di considerarle pi&ugrave; attentamente, e di mostrar come <lb/>alla fine si giunse a superarle. </s></p><p type="main">

<s>L'anno dopo che fu venuta alla luce in Parigi la Diottrica cartesiana, <lb/>il Boulliaud pubblicava il suo Trattato <emph type="italics"/>De natura lucis.<emph.end type="italics"/> Forse l'Autore spe&shy;<lb/>culava intorno al difficile soggetto, senza nulla aver sentito delle nuove dot&shy;<lb/>trine del Cartesio, e il libro dell'Astronomo era tuttavia sotto i torchi, quando <lb/>quello del Filosofo n'era uscito di poco. </s>

<s>Comunque sia, nel Boulliaud non <lb/>si trova fatto il minimo accenno alle novit&agrave; diottriche, che gli erano nel me&shy;<lb/>desimo tempo pullulate fra'piedi. </s>

<s>Egli non riconosce altro predecessore a'suoi <lb/>studii pi&ugrave; prossimo del Keplero, di cui non approva le dottrine, n&egrave; l'ana&shy;<lb/>logia del moto della palla gettata, che si piega alla perpendicolare. </s>

<s>La rifra&shy;<lb/>zione per lui &ldquo; nihil aliud est quam repercussio, seu ut vulgus Opticorum <lb/>loquitur, reflexio interna &rdquo; (Parisiis 1638, pag. </s>

<s>37), e la pi&ugrave; giusta e rego&shy;<lb/>lata misura degli angoli non sa in altro meglio trovarla che nella propor&shy;<lb/>zionalit&agrave; de'segmenti iperbolici, come glie lo ha insegnato la stessa espe&shy;<lb/>rienza. </s>

<s>&ldquo; Hiperbolis mensurari docuit experientia &rdquo; (ibi, pag. </s>

<s>38). </s></p><p type="main">

<s>Primo ad accogliere la legge cartesiana de'seni fu l'Herigonio, benemerito <lb/>della Matematica e della Fisica matematica per aver, tuttoci&ograve; ch'era stato <lb/>speculato e scoperto in que'soggetti, raccolto con gran criterio e in bell'or&shy;<lb/>dine disposto nel suo <emph type="italics"/>Corso.<emph.end type="italics"/> E qui l'amore della verit&agrave; e il dovere della <lb/>coscienza ci costringono a ritrattare una nostra opinione, che i Lettori hanno <lb/>oramai notata nel primo Tomo di questa Storia, dove, persuasi che l'edi&shy;<lb/>zione del <emph type="italics"/>Cursus mathematicus<emph.end type="italics"/> fatta nel 1633 fosse in tutto identica a quella <lb/>del 1644, facemmo l'Herigonio precedere al Cartesio. </s>

<s>Fummo tratti in in&shy;<lb/>ganno dal veder ripetuta anche in questa edizione seconda la dedica al Mar&shy;<lb/>chese Bassompierre data <emph type="italics"/>Lutetiae parisiorum ineunte anno a salutifero <lb/>partu M.DC.XXXIV,<emph.end type="italics"/> e dal vedervi riportato il Privileglo reale <emph type="italics"/>donn&eacute; a <lb/>Paris le 29 iour de Decembre l'an de Grace mil six cens trente-trois,<emph.end type="italics"/><lb/>senza dall'altra parte, per esser la prima divenuta s&igrave; rara, aver potuto porre <lb/>a riscontro le due varie edizioni. </s>

<s>Ma poi ci siamo assicurati che nel 1633 <lb/>fu veramente pubblicato il Corso matematico in cinque Tomi, i primi quat&shy;<lb/>tro de'quali furono prestati da Galileo al Cavalieri (Alb. </s>

<s>X, 211, 28) e nel 1644 <lb/>fu nuovamente impresso quel <emph type="italics"/>Corso<emph.end type="italics"/> con molte aggiunte e con pi&ugrave; un sesto <lb/>Tomo per appendice. </s></p><pb xlink:href="020/01/626.jpg" pagenum="69"/><p type="main">

<s>Fra quelle aggiunte notabilissima &egrave; la proposizione II della Diottrica <lb/>cos&igrave; formulata: &ldquo; Sinus inclinationum radiorum oblique incidentium eam&shy;<lb/>dem inter se habent proportionem quam sinus inclinationum radiorum re&shy;<lb/>fractorum &rdquo; (Cursus mathem., T. V, Parisiis 1644, pag. </s>

<s>132). L'Autore tiene <lb/>un'ipotesi pi&ugrave; conforme all'esperienza di quella tenuta dal Cartesio, la quale <lb/>ipotesi &egrave; che i raggi non sieno velocitati ma impediti dalla maggiore den&shy;<lb/>sit&agrave; del mezzo. </s>

<s>Ad evitare poi le contrariet&agrave; che sentiva avere di gi&agrave; incon&shy;<lb/>trate lo stesso Cartesio, al principio della composizione del moto pens&ograve; di <lb/>sostituire quello degli equiponderanti. </s>

<s>Premessi quattro altri assiomi appro&shy;<lb/>vati dagli Ottici suoi predecessori, nel V in particolare s'ammette che le <lb/>virt&ugrave; che hanno i raggi luminosi di penetrare attraverso a varii mezzi dia&shy;<lb/>fani s'accrescono o diminuiscono secondo la mutazione de'mezzi. </s>

<s>Fra que&shy;<lb/>ste virt&ugrave; poi che hanno i diversi raggi di penetrare attraverso ai vari mezzi <lb/>diafani, intercede la proporzione medesima che &egrave; fra i momenti di un grave <lb/>sopra piani variamente inclinati. </s></p><p type="main">

<s>Sia per esempio O (fig. </s>

<s>26) un atomo di luce appartenente al raggio <lb/>AC, che scende obliquo sul diafano BC e sia pure I un altro simile atomo <lb/>appartenente al raggio AD, che per vie pi&ugrave; oblique va a cadere sul mede&shy;<lb/>simo diafano refringente. </s>

<s>Si domanda con qual diverso impeto i due atomi, <lb/><figure id="id.020.01.626.1.jpg" xlink:href="020/01/626/1.jpg"/></s></p><p type="caption">

<s>Figura 26<lb/>per la diversa loro obliquit&agrave;, an&shy;<lb/>deranno a penetrare sotto la su&shy;<lb/>perficie BD. L'Herigonio non <lb/>esita punto a rispondere, appli&shy;<lb/>cando all'Ottica i principii della <lb/>Meccanica, riguardando cio&egrave; i <lb/>due atomi quali precisamente due <lb/>gravi, ambedue di ugual peso, e <lb/>l'uno scendente per il piano in&shy;<lb/>clinato AC e l'altro per il pi&ugrave; <lb/>obliquo AD. </s>

<s>Supposto dunque <lb/>che sia X il peso assoluto dei due <lb/>atomi di luce, il peso cio&egrave; col <lb/>momento del quale scenderebbero nel perpendicolo, i relativi momenti O, I, <lb/>co'quali scendono lungo i due piani inclinati, si hanno, per la Meccanica, <lb/>dalle due seguenti equazioni: X:O=AC:BC e X:I=AD:BD. </s></p><p type="main">

<s>Si considerino ora, prosegue a ragionar l'Herigonio, i raggi AC, AD <lb/>che venendo dall'aria s'abbattono in C e in D a dover penetrare attraverso <lb/>a un diafano pi&ugrave; denso, per esempio acqua o cristallo. </s>

<s>Secondo le leggi <lb/>della Meccanica &egrave; naturale che gli atomi O, I, in mezzo all'acqua o al cri&shy;<lb/>stallo, diventino pi&ugrave; leggeri. </s>

<s>Ma per questo appunto verrebbero a perdere <lb/>del loro impeto e di quella prima virt&ugrave; che avevano di penetrare il mezzo, <lb/>ond'&egrave; che ben s'intende come sia necessario che la natura soccorra al di&shy;<lb/>fetto, perch&egrave; i raggi di luce, che non possono arrestarsi nel loro viaggio, <lb/>hanno bisogno di serbar sempre impeto uguale proporzionato alle resistenze <pb xlink:href="020/01/627.jpg" pagenum="70"/>e agl'impedimenti incontrati nel mezzo. </s>

<s>I rimedii della natura son sempre <lb/>i pi&ugrave; facili e i pi&ugrave; pronti, e nel medesimo tempo i pi&ugrave; efficaci. </s>

<s>Or qual <lb/>pi&ugrave; pronto e pi&ugrave; facile rimedio, a ristorare gl'impeti perduti dagli atomi <lb/>O, I, per l'impedimento del mezzo, di quello che rendere a proporzione pi&ugrave; <lb/>inclinato il loro viaggio? </s>

<s>Supponiamo infatti che giunti i due atomi in C e <lb/>in D non seguitino a scendere per le due prime obliquit&agrave; AC, AD, ma per <lb/>le altre due CF, DH, le quali sieno tanto maggiori delle prime, quanto il <lb/>cristallo e l'acqua son pi&ugrave; densi dell'aria: &egrave; chiaro allora che i due atomi, <lb/>lungo i due nuovi piani inclinati CF, DH, in mezzo all'acqua o al cristallo, <lb/>si moveranno con quell'impeto stesso che si movevano scendendo per i piani <lb/>meno inclinati AC, AD, nel mezzo dell'aria. </s>

<s>Cos&igrave; infatti opera la Natura. </s>

<s><lb/>Giunti in C e in D i raggi d'incidenza non seguitano a dirittura il loro <lb/>viaggio, ma s'inflettono o si frangono pi&ugrave; o meno, secondo la varia densit&agrave; <lb/>del mezzo. </s></p><p type="main">

<s>Da queste premesse concludesi facilmente dall'Herigonio la proporzio&shy;<lb/>nalit&agrave; che passa fra i seni degli angoli d'incidenza e quelli degli angoli di <lb/>rifrazione. </s>

<s>Si conducano infatti le perpendicolari MCE, NDZ. </s>

<s>Avremo per gli <lb/>atomi scendenti lungo i piani CF, DH la proporzionalit&agrave; stessa che per i <lb/>primi, avremo cio&egrave; X:T=CF:EF; X:V=DH:HZ. </s>

<s>Queste quattro pro&shy;<lb/>porzioni si trasformano facilmente nelle altre quattro seguenti: X:O= <lb/>1:sen ACM; X:I=1:sen ADN; X:T=1:sen ECF; X:V=1:sen ZDH, <lb/>d'onde se ne deduce sen ACM:sen ADN=sen ECF:ZDH, che &egrave; ci&ograve; ap&shy;<lb/>punto che l'Autore proponevasi di dimostrare. </s></p><p type="main">

<s>Altri Cartesiani, procedendo per vie alquanto diverse, elaborarono altre <lb/>dimostrazioni delle quali tutte, compresavi quella stessa del Cartesio, il Fer&shy;<lb/>mat dava il seguente giudizio: &ldquo; Hoc saltem addam quod viderim illud <lb/>ipsum D. </s>

<s>Cartesii principium in pluribus authoribus qui post ipsum scripse&shy;<lb/>runt. </s>

<s>Eorum tamen demonstrationes haud magis quam ipsius D. </s>

<s>Cartesii <lb/>recipiendae, aut nomen istud mereri videntur. </s>

<s>Herigonius utitur ad illum <lb/>demonstrandum aequiponderantibus, et ratione ponderum super planis in&shy;<lb/>clinatis; P. </s>

<s>Maignan alia via eo pervenire conatur, sed visu facile est eos <lb/>neutrum demonstrare, et lectis examinatisque studiose eorum demonstratio&shy;<lb/>nibus, nos aeque incertos esse de veritate principii ac lectis iis quae scripsit <lb/>D. </s>

<s>Cartesius &rdquo; (Des Cartes Epist., P. III, Francof. </s>

<s>ad M. 1692, pag. </s>

<s>128). </s></p><p type="main">

<s>Cos&igrave; i Francesi stessi pi&ugrave; giudiziosi confessavano di saper di Diottrica, <lb/>dopo gl'insegnamenti cartesiani, quanto ne sapevano prima, e perch&egrave;, se&shy;<lb/>condo il Fermat, tutta l'incertezza dipendeva dal veder che il Cartesio aveva <lb/>accomodati i mezzi alla conclusione, la quale come si fosse rivelata alla mente <lb/>del Filosofo era un mistero, il Fermat stesso pens&ograve; di ricorrere a un argo&shy;<lb/>mento tutto diverso, per veder dove fosse portato ad approdare spiegate <lb/>all'aria incerta le vele </s></p><p type="main">

<s>Quel nuovo argomento eletto dal Matematico di Tolosa era il principio <lb/>delle cause finali, conforme al quale s'ammetteva <emph type="italics"/>Naturam semper agere <lb/>per vias quam maxime compendiosas.<emph.end type="italics"/> Il carattere morale di questo stesso <pb xlink:href="020/01/628.jpg" pagenum="71"/>principio veniva ad esser diciamo cos&igrave; matematicato nella teoria de'Massimi <lb/>e de'Minimi, intorno alla quale il Fermat aveva metodi suoi proprii. </s>

<s>Era <lb/>tutto ardore per dar mano all'impresa, quando a distrarnelo gli si fecero <lb/>incontro due ostacoli. </s>

<s>Il Petit, uomo di grande autorit&agrave;, lo aveva avvertito <lb/>che l'esperienze confermavano la legge de'seni prescritta dal Cartesio, ond'io <lb/>temo, pensava il Fermat, &ldquo; ne frustra coner introducere proportionem pro&shy;<lb/>portioni eius contrariam, quodque experimenta post publicationem inventi <lb/>mei facienda, ipsam a vestigio destruere possent &rdquo; (ibi, pag. </s>

<s>130). Il se&shy;<lb/>condo ostacolo era il tedio e la difficolt&agrave; del calcolo, in cui bisognava im&shy;<lb/>barcarsi per correre il nuovo pelago periglioso. </s>

<s>Poi rimosse il primo osta&shy;<lb/>colo ripensando che, anche un esattissimo e industrioso osservatore, pu&ograve; <lb/>esser tratto in inganno, e vinse il secondo con invocare, invece dell'ispido <lb/>calcolo, l'amabile Geometria. </s>

<s>Cos&igrave; ripreso il primo ardore, si dette all'opera <lb/>che fu coronata di un esito felice e inaspettato. </s>

<s>&ldquo; Pretium autem laboris <lb/>mei fuit maxime insolitum, inopinatum atque omnium felicissimum. </s>

<s>Post&shy;<lb/>quam enim omnes aequationes, multiplicationes, antitheses et alias opera&shy;<lb/>tiones methodi meae percurrissem, tandemque conclusissem Problema quod <lb/>in schedula separata accipies, deprehendi principium meum plane et prae&shy;<lb/>cise eandem refractionibus dare proportionem quam D. </s>

<s>Cartesius stabilive&shy;<lb/>rat. </s>

<s>Tam insperato successu magnopere commotus et admiratione perculsus <lb/>fui. </s>

<s>Reiteravi saepius algebraicas meas operationes eodem semper successu, <lb/>quamvis demonstratio mea supponat transitum luminis per corpora densa <lb/>difficiliorem esse quam per rara; quod verissimum esse credo et contradi&shy;<lb/>tionem non pati. </s>

<s>D. </s>

<s>Cartesius vero contrarium asseruit. </s>

<s>Quidnam ex omni&shy;<lb/>bus istis nobis concludendum est? </s>

<s>Numquid id amici D. </s>

<s>Cartesii non satis <lb/>habebunt quod ipsi possessionem sui Theorematis liberam relinquam? </s>

<s>An&shy;<lb/>non magnae ipsi gloriae erit cognovisse processum Naturae primo intuitu, <lb/>et absque ulla demonstratione? </s>

<s>Itaque palmam ipsi relinquo, sufficit mihi <lb/>quod D. </s>

<s>Clerselier admittat me in societatem probationis tanti ponderis ve&shy;<lb/>ritatis, quae tam mirabiles consequentias producere debet &rdquo; (ibi, pag. </s>

<s>131). </s></p><p type="main">

<s>Tutta la gran maraviglia che dovette soprapprendere il Fermat dipen&shy;<lb/>deva dall'ignorare la storia gelosamente tenuta occulta dal Cartesio, il quale <lb/>non prescrisse la legge de'seni <emph type="italics"/>primo intuitu et absque ulla demonstra&shy;<lb/>tione,<emph.end type="italics"/> ma dietro i fatti che lo Snellio aveva sperimentalmente gi&agrave; dimostrati. </s>

<s><lb/>Comunque sia, in sul primo entrar dell'anno 1662, che tale &egrave; la data della <lb/>Lettera al De-la-Chambre, dove il Fermat scrive i fatti da noi sopra nar&shy;<lb/>rati, cess&ograve; in Francia quella diffidenza che aveva tenuti gli animi incerti <lb/>intorno alla Diottrica cartesiana. </s></p><p type="main">

<s>Si potrebbe creder forse che, in stabilir la scienza delle rifrazioni, la <lb/>Matematica dello stesso Fermat avesse avuto grande efficacia, ma poi viene <lb/>a rendere vacillante questo giudizio una considerazione ed &egrave; che il Carte&shy;<lb/>sio e il Fermat riuscirono a concludere lo stesso dietro ipotesi fra loro con&shy;<lb/>trarie, l'uno ammettendo che il mezzo pi&ugrave; denso impedisce, l'altro invece <lb/>dicendo che facilita il moto della luce. </s>

<s>Essendo questa seconda ipolesi tanto <pb xlink:href="020/01/629.jpg" pagenum="72"/>contraria al modo consueto d'operare della Natura, ebbe intorno a ci&ograve; il <lb/>Cartesio a patire una delle pi&ugrave; forti opposizioni, dalle quali troppo debol&shy;<lb/>mente per verit&agrave; si difendeva col dir ch'ei non faceva distinzione fra corpi <lb/>densi e rari, ma fra duri e molli, ne'primi de'quali il moto della luce &egrave; <lb/>facilitato, perch&egrave; non si comunica, n&egrave; perci&ograve; si disperde attraverso alle ce&shy;<lb/>devoli pareti de'pori. </s>

<s>&ldquo; Non enim dico lumen facilius propagari in denso <lb/>quam in raro, sed in duro, in quo scilicet materia substilis non communi&shy;<lb/>cat motum suum parietibus meatuum quibus inest, quam in molli, sive hoc <lb/>sit rarius, sive densius &rdquo; (Epistolae, Pars. </s>

<s>III, edit. </s>

<s>cit., pag. </s>

<s>61). </s></p><p type="main">

<s>In qualunque modo per&ograve; il veder che per due vie diverse e anzi op&shy;<lb/>poste si giungeva al medesimo intento inger&igrave; ne'Filosofi poca fiduci&agrave; delle <lb/>dimostrazioni, e se fu stabilita la nuova scienza diottrica ci&ograve; si dee alle espe&shy;<lb/>rienze del Petit e degli altri investigatori de'fatti, piuttosto che alle specu&shy;<lb/>lazioni del Matematico di Tolosa. </s>

<s>Quando poi l'Huyghens, interpetrando il <lb/>Vossio, svel&ograve; al mondo il mistero, e s'intese che quella del Cartesio non <lb/>era una sua intuizione, ma un fatto dimostrato dallo Snellio, e allora la Diot&shy;<lb/>trica si conferm&ograve; per sempre sulla stabilit&agrave; del suo fondamento. </s></p><p type="main">

<s>Ma pur se i fatti son la materia, le speculazioni son la forma della <lb/>scienza, ond'&egrave; che, dovendosi in ogni modo speculare, e avendo gli Ottici <lb/>innanzi i due diversi esempii del Cartesio e del Fermat, si cred&egrave; pi&ugrave; sicuro <lb/>il proceder dietro le orme di questo che non di quello. </s>

<s>Perci&ograve;, sopra le di&shy;<lb/>mostrazioni derivate dai principii meccanici rimasero in onore quelle fon&shy;<lb/>date sul principio delle cause finali, di che son l'Huyghens e il Leibniz i <lb/>primi e principali Autori. </s></p><p type="main">

<s>Il grande Ottico olandese inser&igrave; quella sua dimostrazione diottrica nel <lb/>Trattato <emph type="italics"/>De la lumiere<emph.end type="italics"/> e perch&egrave; l'abbiamo inoculata sull'albero della scienza <lb/>italiana, da questo pensiamo di cogliere i saggi del frutto. </s>

<s>Guido Grandi, <lb/>che volle applicare al moto delle acque il principio delle cause finali, si trov&ograve; <lb/>alle mani il Teorema ugeniano delle stesse cause finali applicato al moto <lb/>della luce, e lo rese compiuto e con forse maggior facilit&agrave; dimostrato. </s>

<s>&ldquo; Con&shy;<lb/>vien premettere, scrive il Nostro, a modo di lemma la soluzione del seguente <lb/>problema, il quale in parte fu gi&agrave; dimostrato dal signor Cristiano Ugenio <lb/>nel suo Trattato <emph type="italics"/>Del Lume,<emph.end type="italics"/> servendosene a dimostrare la ragione delle re&shy;<lb/>frazioni della luce, qualora passa da un mezzo in un altro di densit&agrave; di&shy;<lb/>versa, come sarebbe dall'aria nel cristallo, o dal vetro nell'acqua, ma qui <lb/>da me viene steso questo problema all'attraversamento di pi&ugrave; e diversi <lb/>mezzi &rdquo; (Alb. </s>

<s>XIV, 135). </s></p><p type="main">

<s>Questa maggiore estensione fu data dal Grandi al Teorema ugeniano <lb/>per mezzo della seguente proposizione da lui stesso cos&igrave; formulata: &ldquo; Debba <lb/>un mobile portarsi da A in B (fig. </s>

<s>27) pi&ugrave; speditamente che sia possibile, <lb/>andando dal punto A verso la linea CG, colla velocit&agrave; FC, e nello spazio <lb/>interposto fra le due parallele CG, DH colla velocit&agrave; Z, e nello spazio in&shy;<lb/>tercetto fra le parallele DH, EX colla velocit&agrave; Y, e quindi fino in B colla <lb/>velocit&agrave; BX: si cerca per quale strada dover&agrave; andare. </s>

<s>Si dispongano le rette <pb xlink:href="020/01/630.jpg" pagenum="73"/>AC, CD, DE, EB, talmente che i seni de'loro angoli colle perpendicolari <lb/>tirate sopra le date parallele, quali sono ACF, CDG, DEH, EBX, siano per <lb/><figure id="id.020.01.630.1.jpg" xlink:href="020/01/630/1.jpg"/></s></p><p type="caption">

<s>Figura 27.<lb/>ordine come le velocit&agrave; FC, Z, Y, BX; dico che <lb/>per la strada ACDEB verr&agrave; il mobile da A in B <lb/>in minor tempo, che per qualsivoglia altra <lb/>strada, ritenute ne'siti suddetti le stesse velo&shy;<lb/>cit&agrave; &rdquo; (ivi, pag. </s>

<s>135, 36). </s></p><p type="main">

<s>La dimostrazione geometrica assai facile e <lb/>chiara &egrave; applicata fisicamente al caso della ri&shy;<lb/>frazion della luce, nel seguente corollario, che <lb/>il Grandi fa in primo luogo seguitare alla sua <lb/>proposizione: &ldquo; Quindi &egrave; manifesto che la via <lb/>da spedirsi in pi&ugrave; breve tempo, andando da un <lb/>punto a un altro, non &egrave; la retta, se non quando <lb/>si ha da mantenere in tutto il viaggio la mede&shy;<lb/>sima velocit&agrave;; onde, se si hanno da attraversare diversi mezzi, che diver&shy;<lb/>samente resistano al moto, come dovendo attraversare varii campi, altri <lb/>nudi, altri vestiti d'erbe, altri imbarazzati da spighe, e passare varie strade <lb/>ingombrate da un flusso e reflusso di popolo, non sarebbe buon consiglio <lb/>l'andare verso il termine destinato in via retta, ma sar&agrave; meglio fare tali <lb/>gomiti e svolte, che i seni degli angoli delle loro inclinazioni siano come le <lb/>facilit&agrave; che si hanno ad attraversare que'varii mezzi, come pratica ancora <lb/>la Natura nelle rifrazioni. </s>

<s>Come se un oggetto posto in A dover&agrave; mandare <lb/>un raggio che lo renda visibile all'occhio posto in B, per varii mezzi AG, <lb/>CH, DX, EB, tutti diafani, ma di varia rarit&agrave;, sicch&egrave; abbia in essi pi&ugrave; fa&shy;<lb/>cile il passaggio di mano in mano nella stessa misura in cui crescono i seni <lb/>degli angoli ACF, CDG, DEH, EBX; di fatto la via del raggio trasmesso <lb/>sar&agrave; il flessilineo ACDEB, e non una retta immediatamente tirata dal punto A <lb/>al punto B &rdquo; (ivi, pag. </s>

<s>136, 37). </s></p><p type="main">

<s>L'Huyghens per&ograve;, di cui la dimostrazione &egrave; stata cos&igrave; bene illustrata <lb/>e compiuta dal Grandi, &egrave; pi&ugrave; originale del Leibniz, che imita pi&ugrave; d'appresso <lb/>il Fermat e lo compendia. </s>

<s>Professando anch'egli il principio che la Natura <lb/><figure id="id.020.01.630.2.jpg" xlink:href="020/01/630/2.jpg"/></s></p><p type="caption">

<s>Figura 28.<lb/>procede sempre per le vie pi&ugrave; facili, a proposito <lb/>de'raggi di luce ammette che le difficolt&agrave; opposte <lb/>al loro viaggio sieno in ragion composta della lun&shy;<lb/>ghezza e della resistenza de'mezzi. </s>

<s>&ldquo; Sint rectae M, <lb/>et N repraesentantes resistentiam repectu luminis, <lb/>illa aeris, haec aquae: erit difficultas viae a C ad E <lb/>(fig. </s>

<s>28) ut rectangulum CE.M; ab E ad G ut re&shy;<lb/>ctangulum EG.N. </s>

<s>Ergo ut difficultas viae CEG <lb/>sit omnium minima debet summa rectangulorum <lb/>CE.M+EG.N esse omnium possibilium minima, <lb/>seu minor quam CF.M+FG.N &rdquo; (Op. </s>

<s>Omn., Genevae 1768, T. III, <lb/>pag. </s>

<s>145, 46). </s></p><pb xlink:href="020/01/631.jpg" pagenum="74"/><p type="main">

<s>Applicando poi il Leibniz la sua teoria de'Massimi e de'Minimi alla <lb/>presente ricerca, prova CE.N:EG.M=EN:EL. &ldquo; Ergo, positis CE et EG <lb/>aequalibus, erit N resistentia aquae respectu luminis ad M resistentiam ae&shy;<lb/>ris, ut EH sinus complementi anguli incidentiae in aere ad EL sinum com&shy;<lb/>plementi anguli refractionis in aqua; seu sinus complementorum erunt in <lb/>reciproca resistentiae mediorum ratione &rdquo; (ibi, pag. </s>

<s>146). </s></p><p type="main">

<s>Per quanto sieno queste dimostrazioni ingegnose e, cos&igrave; confortate di <lb/>calcolo e di Geometria, facciano quasi violenza alla persuasione di chi le <lb/>medita e intende, nonostante si promuovono contro l'Huyghens e il Leibniz <lb/>quelle medesime opposizioni che il Clerselier promoveva contro il Fermat, <lb/>quando prima introdusse nella Diottrica il principio delle cause finali. </s>

<s>&ldquo; Prin&shy;<lb/>cipium quod statuis pro fundamento tuae demonstrationis, nimirum Natu&shy;<lb/>ram semper agere via aut modo quam maxime brevi et simplici, non phy&shy;<lb/>sicum sed morale saltem principium est, quod nunquam est aut esse potest <lb/>causa ullius effectus naturae.... Non potest esse causa: hoc enim posito <lb/>praesupponeremus cognitionem in Natura, hic autem per Naturam nihil aliud <lb/>intelligimus quam ordinem istum et sedem istam in mundo stabilitam talem <lb/>qualis est, quae non agit ex praeviso, aut cum electione, aut determinatione <lb/>aliqua necessaria &rdquo; (Des Cartes. </s>

<s>Epist., Pars. </s>

<s>III cit., pag. </s>

<s>138). </s></p><p type="main">

<s>L'opposizione fatta dal Clerselier e dagli altri cartesiani contro chi nelle <lb/>fisiche dimostrazioni introduceva un principio morale, era tanto ragionevole <lb/>e giusta che si dov&egrave; abbandonare anco questa via, la quale erasi pure mo&shy;<lb/>strata a principio tanto lusinghiera, cosicch&egrave; pu&ograve; dirsi che, nonostante l'opera <lb/>di s&igrave; valorosi ingegni, la legge fondamentale della Diottrica, verso la fine del <lb/>secolo XVII mancava ancora della sua dimostrazione. </s>

<s>I pi&ugrave; savi avranno <lb/>pensato d'applicare anche qui il caso della Calottrica di Euclide, il quale <lb/>confess&ograve; essere la legge di lei indimostrabile, com'&egrave; stato confermato da <lb/>tanti secoli di progressi. </s>

<s>Ma in ogni modo, come dianzi da noi si diceva, <lb/>non potendo consister la scienza ne'semplici fatti e non potendosi dall'al&shy;<lb/>tra parte aver perfette le speculazioni, si riduceva ogni studio de'Filosofi a <lb/>scansarne quanto fosse possibile i difetti. </s></p><p type="main">

<s>A ci&ograve; dette opera e riusci da par suo il Newton, che torn&ograve; ad appli&shy;<lb/>care alla luce le leggi del moto de'gravi. </s>

<s>L'applicazion neutoniana per&ograve; era <lb/>molto pi&ugrave; ragionevole di quella fattane gi&agrave; dal Keplero e dal Cartesio, i quali <lb/>non si comprende come potessero sottoporre alle leggi della Meccanica e as&shy;<lb/>segnare una maggiore o minore velocit&agrave; a un moto, che per essi era istan&shy;<lb/>taneo e senza tempo. </s>

<s>Inoltre, anco concessa quella maggiore o minore ve&shy;<lb/>locit&agrave;, nessuno degli ottici ne sapeva assegnare una causa fisica, e da tutti, <lb/>in cosa di s&igrave; grande importanza, si giocava di fantasia. </s></p><p type="main">

<s>Il Newton riguardando la luce come composta di atomi duri proiettati <lb/>con grande impeto dal corpo luminoso, e considerando la densit&agrave; de'mezzi <lb/>avere una virt&ugrave; attrattiva su quegli stessi atomi, procedeva con tutta ragione <lb/>ad applicare all'Ottica le leggi meccaniche benissimo allora note de'corpi <lb/>gravi proietti. </s>

<s>N&egrave; in quel suo modo di procedere era nulla che non fosse o <pb xlink:href="020/01/632.jpg" pagenum="75"/>dimostrato direttamente o per induzione. </s>

<s>Dimostrato direttamente era che la <lb/>luce si muove in tempo come tutti gli altri corpi: dimostrato per induzione <lb/>dal fenomeno grimaldiano, era che gli atomi luminosi vengono attratti, come <lb/>si attraggono a vicenda le minime particelle materiali in tutti i composti. </s></p><p type="main">

<s>Nell'ultima Sezione perci&ograve; del I Libro de'<emph type="italics"/>Principii<emph.end type="italics"/> applica alla luce <lb/>le leggi del moto de'minimi corpi <emph type="italics"/>quae viribus centripetis ad singulas ma&shy;<lb/>gni alicuius corporis partes tendentibus agitantur,<emph.end type="italics"/> e dimostrato nel Teo&shy;<lb/>rema XLVIII che questi minimi corpicelli attratti da un mezzo, sempre con <lb/>la medesima forza, vi descrivono una linea parabolica, come i gravi proietti <lb/>attratti dal centro della Terra; dalle propriet&agrave; della stessa parabola ne con&shy;<lb/>clude che il seno dell'incidenza ha una determinata proporzione col seno <lb/>dell'emergenza. </s>

<s>Passa poi, nel seguente Teorema, a dimostrar che la velo&shy;<lb/>cit&agrave; del proietto avanti l'incidenza &egrave; alla velocit&agrave; di lui dopo l'emergenza, <lb/>come il seno dell'emergenza &egrave; al seno dell'incidenza. </s></p><p type="main">

<s>I Teoremi neutoniani, come son certissimi nella Meccanica, sarebbero <lb/>cos&igrave; certissimi nell'Ottica, quando si potesse ritener come cosa certa che gli <lb/>atomi impalpabili della luce non differiscono sostanzialmente dalle molecole <lb/>componenti gli altri trattabili corpi. </s>

<s>Ma perch&egrave; questo certo non &egrave;, perci&ograve; <lb/>il Newton non pretende che i suoi Teoremi, i quali applicati alla luce da&shy;<lb/>rebbero una dimostrazione matematicamente certa delle rifrazioni, sieno come <lb/>cose matematicamente dimostrate accolte dagli Ottici. </s>

<s>Solamente egli intende <lb/>di determinare la somiglianza che passa fra le traiettorie descritte da'mi&shy;<lb/>nimi proietti attraverso un mezzo attraente, e le traiettorie descritte dagli <lb/>atomi della luce attraverso ai diafani. </s>

<s>&ldquo; Visum est propositiones sequentes <lb/>in usus opticos subiungere, interea de natura radiorum utrum sint corpora <lb/>necne, nihil omnino disputans, sed traiectorias corporum traiectoriis radio&shy;<lb/>rum persimiles solummodo determinans &ldquo; (Genevae 1739, pag. </s>

<s>541). </s></p><p type="main">

<s>Cos&igrave; il grande Filosofo e Matematico dava a que'sapienti, che troppo <lb/>si confidavan di s&egrave;, un bel documento, il quale riducevasi a dire che, in&shy;<lb/>fino a tanto che si sar&agrave; incerti della natura della luce, la legge delle rifra&shy;<lb/>zioni, che pure &egrave; certa come un fatto fisico, non sar&agrave; mai matematicamente <lb/>dimostrabile. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Abbiamo percorso nel paragrafo precedente due buone terze parti del <lb/>secolo XVII, dal Cartesio al Newton, e fra coloro che attesero allo studio <lb/>delle rifrazioni, non abbiamo avuto da commemorare nessuno dei nostri Ita&shy;<lb/>liani. </s>

<s>Chi volesse argomentare da ci&ograve; che poca parte dovettero i Nostri aver <lb/>presa in que'diottrici studii, forse non in tutto s'ingannerebbe, ma ab&shy;<lb/>biamo in ogni modo l&agrave; taciuto, per narrar qui tutti insieme i fatti, che pi&ugrave; <pb xlink:href="020/01/633.jpg" pagenum="76"/>importano alla nostra Storia rimasta sopra, nel Maurolico, nel Porta e nel <lb/>De Dominis, interrotta. </s></p><p type="main">

<s>Il filo si riappicca alla scienza di Galileo, la quale, da chi ha letto il <lb/>Cap. </s>

<s>III del Tomo precedente, si sa troppo bene oramai, quant'ella fosse <lb/>scarsa. </s>

<s>Quel ch'egli poi sa in tal soggetto &egrave; appreso dagli Ottici, de'quali <lb/>pure, insiem con le poche verit&agrave;, si ripetono i molti errori. </s>

<s>Pu&ograve; servir <lb/>d'esempio il concetto che avevasi dell'essenza e della natura delle rifrazioni. </s>

<s><lb/>Il Keplero, come notammo, le riduceva a una riflessione <emph type="italics"/>plane similis illis <lb/>quae fiunt in corporibus naturalibus proiectis,<emph.end type="italics"/> e il Boulliaud, che pur non <lb/>consente con l'error kepleriano della diffusione superficiale, d'ond'ebbe oc&shy;<lb/>casione quella similitudine; non altrimenti qualifica la rifrazione che per una <lb/>riflessione interna. </s></p><p type="main">

<s>Tale &egrave; pure il concetto di Galileo, il quale, se parla di refrazioni, cause <lb/>de'crepuscoli, delle aurore boreali, e degli effetti osservati da Ticone nelle <lb/>apparenze degli astri, non intende quelle stesse rifrazioni per altro modo, <lb/>che per riflessioni fatte da'raggi luminosi, mentre incontran per la loro via <lb/>le vescicole del vapore acquoso, o le tenuissime particelle delle terrestri esa&shy;<lb/>lazioni. </s>

<s>Perci&ograve; l'aria purissima e l'etere e qualunque materia, che non sia <lb/>atta a riflettere, non &egrave;, secondo Galileo, nemmeno atta a rifrangere i raggi <lb/>della luce. </s>

<s>Non volendo il Sarsi e il suo Maestro, cos&igrave; scrive nel <emph type="italics"/>Saggia&shy;<lb/>tore<emph.end type="italics"/> &ldquo; che la Cometa sia un incendio ma inclinando a credere, s'io non <lb/>erro, che almeno la sua coda sia una refrazione dei raggi solari, io gli do&shy;<lb/>mander&ograve; se ei credono che la materia, nella quale si fa tal refrazione, sia <lb/>tagliata appunto alla misura di essa chioma, o pur che di qua e di l&agrave; e di <lb/>ogni intorno ve ne avanzi, e se ve ne avanza, come credo che sar&agrave; rispo&shy;<lb/>sto, perch&egrave; non si vede, essendo tocca dal Sole? </s>

<s>Qui non si pu&ograve; dire che <lb/>la refrazione si faccia nella sostanza dell'etere, la quale come diafanissima <lb/>non &egrave; potente a ci&ograve; fare, n&egrave; meno in altra materia, la quale, quando fosse <lb/>atta a rifrangere, sarebbe ancora atta a riflettere i raggi solari &rdquo; (Alb IV, 247). </s></p><p type="main">

<s>Chi vuole, pu&ograve; svolgendo anche il solo <emph type="italics"/>Saggiatore,<emph.end type="italics"/> notare moltissimi <lb/>altri passi, da'quali si rivela il medesimo concetto, e perci&ograve;, intesa intorno <lb/>a questo punto la mente di Galileo, ci spinge la curiosit&agrave; a saper quel ch'ei <lb/>ne pensasse della legge relativa alle proporzioni che passano tra gli angoli <lb/>incidenti e i refratti. </s></p><p type="main">

<s>Sappiamo per cosa certa che in sulla fine dell'anno 1637 egli ebbe, <lb/>per cura del Cartesio, la Diottrica, a leggere o a farsi leggere il qual libro, <lb/>in quella parte specialmente dove si tratta del Telescopio, Galileo s'ebbe <lb/>molto a male di non trovarvisi nominato. </s>

<s>Con chi facesse direttamente que&shy;<lb/>sti rammarichi non sappiamo di certo, ma forse con Elia Diodati, per mezzo <lb/>del quale il Mersenno, che ne aveva avuta commission dal Cartesio, invi&ograve; <lb/>il volume da Parigi ad Arcetri. </s>

<s>Fatto si &egrave; che di que'rammarichi il Mer&shy;<lb/>senno stesso faceva, per lettera scritta il di 8 Gennaio 1638, consapevole il <lb/>Cartesio, il quale cos&igrave; rispondeva: &ldquo; Quantum ad illum quam me culpare <lb/>dicis, quod Galilaeum non nominaverim, apparet eum quaerere quod re-<pb xlink:href="020/01/634.jpg" pagenum="77"/>prehendat, nec tamen eius invenire causam. </s>

<s>Neque enim ipse Galilaeus sibi <lb/>perspicillorum inventionem attribuit, mihi autem non nisi de eorum inven&shy;<lb/>tore dicendum fuit &rdquo; (Epist. </s>

<s>cit., pag. </s>

<s>88). </s></p><p type="main">

<s>Passa poi a dir perch&egrave; non nominasse nemmeno gli Autori d'Ottica, <lb/>che lo avevano preceduto. </s>

<s>Noi sappiam bene qual si fosse di ci&ograve; la segreta <lb/>ragione, ma il Cartesio trova certe scuse, ripensando alle quali ci confer&shy;<lb/>miam sempre pi&ugrave; nell'opinione che fossero in lui maggiori della scienza, <lb/>l'astuzia e l'orgoglio. </s>

<s>&ldquo; Neque etiam nominandi mihi fuerunt, qui ante me <lb/>de Optica scripserunt. </s>

<s>Neque enim scribere historiam animus erat, satisque <lb/>habui in genere asseruisse etiamnum fuisse qui plurima invenerint, nec pos&shy;<lb/>sem argui me aliorum inventionem mihi attribuere voluisse, in quo plus <lb/>mihi metipsi iniuriae feci, quam illis quorum nomina omisi. </s>

<s>Cogitari quippe <lb/>potest eos multo plura fecisse, quam fortasse eos fecisse deprehenderetur, <lb/>si dixissem quinam illi essent &rdquo; (ibi). </s></p><p type="main">

<s>Il di 2 di Gennaio di quello stesso anno 1638, Elia Diodati riceve da <lb/>Arcetri una lettera, nella quale si diceva: &ldquo; Signor mio, il Galileo vostro <lb/>caro amico e servitore, da un mese in qua &egrave; fatto irreparabilmente del tutto <lb/>cieco &rdquo; (Alb. </s>

<s>VII, 207). La triste nuova fu dal Diodati partecipata al Mer&shy;<lb/>senno, e questi, con lettera del d&igrave; 12 di Febbraio, l'annunzi&ograve; al Cartesio, <lb/>il quale dispiacente gli rispondeva: &ldquo; Doleo Galilaeum usum oculorum ami&shy;<lb/>sisse, quamquam enim eum non nominatum exprimam, persuasum habeo <lb/>ipsum Dioptricam meam non habiturum fuisse contemtui &rdquo; (ibi, pag. </s>

<s>90). </s></p><p type="main">

<s>Noi possiamo per&ograve; con tutta la probabilit&agrave; asseverare che le persuasioni <lb/>del Cartesio riusciron fallaci. </s>

<s>Se in ogni modo Galileo non disprezz&ograve; la Diot&shy;<lb/>trica, &egrave; certo ch'ei non se ne cur&ograve;, n&egrave; si rimosse, per le novit&agrave; cartesiane, <lb/>dalle sue opinioni antiche. </s>

<s>Pi&ugrave; che la non curanza per&ograve; si direbbe che fu <lb/>dal Torricelli ereditato il disprezzo, secondo lo proverebbe il modo, com'ei <lb/>rispose al Mersenno, che lo sollecitava a leggere la Diottrica in francese, e <lb/>poco di poi, per levargli ogni scusa, nella diffusissima traduzione latina. </s></p><p type="main">

<s>Anche il Cavalieri se sa nulla della legge ritrovata fra i seni delle in&shy;<lb/>clinazioni e i seni delle rifrazioni, non l'ha avuto dal Cartesio ma indiret&shy;<lb/>tamente dall'Herigonio. </s>

<s>L'amico e il maestro del Torricelli per&ograve; non volt&ograve; <lb/>con dispetto le spalle a colui, che formul&ograve; quella legge n&egrave; la rifiuta per <lb/>falsa: ne riman soltanto dubitoso e diffidente, perch&egrave; questo principio, egli <lb/>dice, lo prova l'Herigonio &ldquo; solo facendo un trapasso dalla Meccanica alla <lb/>Diottrica, con dire che l'impulso del raggio cadente per un piano eretto o <lb/>inclinato sopra l'orizzonte, ha la medesima inclinazione che ha il raggio sopra <lb/>la superficie del diafano, e di questo non porta altra ragione, e per questo <lb/>sono stato sempre dubitoso &rdquo; (Pref. </s>

<s>alle Lez. </s>

<s>del Torricelli, Milano 1823, <lb/>pag. </s>

<s>25). </s></p><p type="main">

<s>Si pu&ograve; dire che in questa e in poche altre Lettere del Cavalieri, scritte <lb/>nel 1644, sia dal 1637 al 1660, concluso tuttoci&ograve; che fu pensato e scritto <lb/>intorno alla legge delle rifrazioni in Italia, la quale perci&ograve; ne rimase in una <lb/>piena ignoranza In Francia invece si discuteva, con grande ardore: i Fi-<pb xlink:href="020/01/635.jpg" pagenum="78"/>sici pi&ugrave; esperti e i Matematici pi&ugrave; valorosi insorgevano contro il Cartesio, <lb/>il quale stizzito appellava que'rivoltosi calunniatori malevoli, che non discu&shy;<lb/>tono, ma fanno baccano, gente da esser guardate col ghigno della compas&shy;<lb/>sione, perch&egrave; hanno perduto il bene dell'intelletto. </s>

<s>&ldquo; Tibi ultro declaraverim, <lb/>scriveva al Mersenno, tantum abesse ut calumniis, quae de me sparguntur, <lb/>excandescam, ut etiam ultro gaudeam, existimando eas quo magis enormes <lb/>et extravagantes sunt, quippe tanto minus me feriunt, eo magis mihi hono&shy;<lb/>rifices fore, atque ob ideo gratiores. </s>

<s>Et persuasum habeo malevolos non <lb/>tanta sollicitudine in me debacchaturos, nisi simul essent, qui de me hono&shy;<lb/>rifice loquerentur sentirentque, praeterquam quod veritas interdum contra&shy;<lb/>dictione opus babeat, quo magis elucescat. </s>

<s>Verum cachinno excipiendi sunt <lb/>illi, qui ratione et fundamentis destituti loquuntur &rdquo; (Epist. </s>

<s>cit., pag. </s>

<s>87). </s></p><p type="main">

<s>Morto il Cartesio, non cessarono le controversie n&egrave; l'ardore delle in&shy;<lb/>vestigazioni, le quali si fecero saviamente passare, dalle Matematiche astratte <lb/>e dalle aeree speculazioni, al severo giudizio delle esperienze. </s>

<s>Il Petit pro&shy;<lb/>nunzi&ograve; che la legge prescritta dal Cartesio riscontrava co'fatti; l'Autore della <lb/>Dottrica ritorn&ograve; in onore, e in Francia erasi oramai stabilita la scienza delle <lb/>rifrazioni. </s>

<s>Ci&ograve; fu verso il 1660, quando ancora in Italia nessuno aveva ve&shy;<lb/>duto o ripensato a quel che della Diottrica era stato scritto nella famosa <lb/>Dissertazione <emph type="italics"/>Del Metodo.<emph.end type="italics"/></s></p><p type="main">

<s>La prima copia del libro capitata in Firenze venne alle mani del priore <lb/>Orazio Ricasoli Rucellai, il quale, ne'primi giorni di Aprile dell'anno 1660, <lb/>si mette una mattina il libro sotto il braccio, e va a trovare l'amico suo <lb/>Vincenzio Viviani. </s>

<s>Lo trov&ograve; nel suo studio seduto al banco, sopra il quale <lb/>gli pose innanzi il libro della Diottrica aperto al paragrafo IV del capitolo II. </s>

<s><lb/>Incomincia a leggere il Viviani: &ldquo; Hinc progrediamur ad refractionem et <lb/>primo fingamus pilam ab A ad B expulsam offendere non terram sed lin&shy;<lb/>teum CBE.... &rdquo; E finito di leggere il paragrafo, il Rucellai gli chiude sotto <lb/>gli occhi per riprendersi il libro. </s>

<s>Il meditativo lettore rimase dubbioso. </s>

<s>&mdash; Ma <lb/>le rifrazioni della luce, diceva verso l'amico, si fanno in modo contrario a <lb/>quello della palla; or come mai .... &mdash; n&egrave; l'amico sapeva che si rispon&shy;<lb/>dere. </s>

<s>Lo prega gli renda il libro, glielo lasci; il Rucellai ha fretta, vuol ri&shy;<lb/>portare il libro con s&egrave;, gli stringe amichevolmente la mano, e addio. </s></p><p type="main">

<s>Il Viviani rimasto in quel dubbio penoso che lo tormentava, parendogli <lb/>esser certo che quello della palla grave, la quale incontra il velo o &egrave; get&shy;<lb/>tata nell'acqua, non era il modo delle ottiche rifrazioni, e non potendo cre&shy;<lb/>dere che l'Autore avesse potuto dimostrare un effetto contrario a quello che <lb/>si osserva in natura; non ebbe pace in fin tanto che non torn&ograve; a rileggere, <lb/>per veder meglio come stavan le cose. </s>

<s>Un altro suo amico, eccitato dall'esem&shy;<lb/>pio del Rucellai, s'era fatto venire il libro, e da lui il Viviani, con pi&ugrave; libe&shy;<lb/>ralit&agrave; l'ebbe in prestito. </s>

<s>Lesse tutto per ordine e ne rimase cos&igrave; sodisfatto, <lb/>che subito, la mattina del d&igrave; 12 Aprile, prese la penna in mano per scri&shy;<lb/>vere al Rucellai il seguente biglietto: </s></p><p type="main">

<s>&ldquo; In questo punto ho ricevuto in presto da un amico .... la Diottrica <pb xlink:href="020/01/636.jpg" pagenum="79"/>del Cartesio .... ed ho trovato che non senza cagione intoppai al numero IV <lb/>del II capitolo, dove V. S. Ill.ma mi fece leggere, perch&egrave; era necessario che <lb/>io vedessi innanzi le supposizioni e progressi dell'Autore. </s>

<s>Ora letto il tutto, <lb/>&egrave; forza confessare che il modo di salvare gli effetti della riflessione e delle <lb/>rifrazioni &egrave; bellissimo, ingegnosissimo, e maravigliosissimo. </s>

<s>Ricordo bene a <lb/>V. S. che, quanto alle rifrazioni, il negozio procede sicuramente nel modo <lb/>che io le accennai l'altro giorno, cio&egrave; che i raggi, passando da un corpo <lb/>raro per uno men raro, si refrangono verso la perpendicolare e non verso <lb/>la superficie, come segue del moto della palla dopo l'incontro nel panno o <lb/>velo, essendo questo un esempio dato dal Cartesio di un effetto contrario <lb/>per contrarie cagioni &rdquo; (MSS. Gal. </s>

<s>Disc, T. CXLII, c. </s>

<s>61). </s></p><p type="main">

<s>Quel Viviani dunque succeduto a Galileo e al Torricelli a rappresentare <lb/>la scienza sperimentale in Italia, non ha, come il Fermat e altri insigni <lb/>Francesi, che ridir nulla contro i processi dimostrativi del Cartesio: tutto &egrave; <lb/>in lui <emph type="italics"/>bellissimo, ingegnosissimo, maravigliosissimo.<emph.end type="italics"/> Dietro la lettura delle <lb/>seducenti pagine cartesiane ritiene come per cosa certa la costante propor&shy;<lb/>zione, non fra gli angoli, come professavano col Maurolico gli Italiani, ma <lb/>fra i seni degli angoli fatti colla perpendicolare dai raggi incidenti e dai re&shy;<lb/>fratti. </s>

<s>Cos&igrave; la scienza diottrica veniva fra noi, dopo lungo indugio accolta <lb/>senza contradizioni, ci&ograve; che, se in quel primo fervore si dee alle attrattive <lb/>che presentava il lucido orpello cartesiano, il finale motivo per cui si per&shy;<lb/>suase il Viviani della verit&agrave; delle nuove dottrine fu tutto frutto delle espe&shy;<lb/>rienze. </s></p><p type="main">

<s>A lui infatti &egrave; dovuta l'invenzione di quella <emph type="italics"/>Scatola delle rifrazioni,<emph.end type="italics"/><lb/>che si trova descrittta dai Fisici in quasi tutti i loro Trattati, nei quali per&ograve; <lb/>si tace l'Autore, che da alcuni erroneamente si crede essere stato il Carte&shy;<lb/>sio. </s>

<s>Il Viviani ha di quella Scatola varii disegni abbozzati, il pi&ugrave; finito de'quali <lb/>pu&ograve; vedersi a carte 261 del IV Tomo de'MSS. del Cimento. </s>

<s>Di ci&ograve; poi s'ha <lb/>la conferma in quella Nota d'invenzioni, altra volta citata, nella quale si <lb/>legge di mano propria dello stesso Viviani: <emph type="italics"/>Mia la scatola per le rifrazioni <lb/>de'fluidi<emph.end type="italics"/> (MSS. Cim., T. X, c. </s>

<s>259). </s></p><p type="main">

<s>Quando il Newton ebbe scoperta la varia refrangibilit&agrave; de'raggi com&shy;<lb/>ponenti la luce, venne a metter negli Ottici uno scrupolo intorno al modo <lb/>di misurar, colla scatola del Viviani, le rifrazioni. </s>

<s>&ldquo; Credo enim illos qui <lb/>refractiones antehac mensuravere, sive id factum sit, ut iam dicta hypothe&shy;<lb/>sis Cartesii probaretur, sive aliis de causis, credo illos inquam mensuram <lb/>instituisse ad medietatem refractae lucis, hoc est si spatium a coloribus oc&shy;<lb/>cupatum spectemus ad confinium viridis et coerulei.... Porro cum forte <lb/>desideretur accuratius examen dictae regulae cartesianae, quam antehac insti&shy;<lb/>tuebatur, dum varia radiorum refrangibilitas experientes latuit, primo dicam <lb/>quo pacto id non incommode fiat &rdquo; (Lectiones opt., Patavii 1773, pag. </s>

<s>15). <lb/>E segue appresso a descrivere un macchinamento di scrupolosa precisione, <lb/>ma da non venire a confronto, per la comoda facilit&agrave;, colla Scatola del Vi&shy;<lb/>viani, la quale perci&ograve; serve ancora a sperimentar nelle Scuole. </s></p><pb xlink:href="020/01/637.jpg" pagenum="80"/><p type="main">

<s>Sedotto dall'esempio della palla che incontra l'acqua, esempio che a <lb/>lui parve maravigliosissimo, il Viviani non lo lasci&ograve; sterile ricevendolo dal <lb/>Cartesio, come sterile l'avea lasciato il Cartesio ricevendolo dal Keplero, ma <lb/>pens&ograve; di fecondarlo in modo, che s'accostasse pi&ugrave; strettamente il fatto mec&shy;<lb/>canico a fiancheggiare il diottrico. </s>

<s>Consisteva quel pensiero nel volere spe&shy;<lb/><figure id="id.020.01.637.1.jpg" xlink:href="020/01/637/1.jpg"/></s></p><p type="caption">

<s>Figura 29.<lb/>rimentare quali mutazioni, per le varie obliquit&agrave;, <lb/>faceva la direzione della palla entrata nell'acqua, <lb/>forse per veder se avveravasi anco in questo caso, <lb/>come per la luce, la legge de'seni. </s>

<s>Abbiamo di <lb/>questo pensiero le vestigie nella seguente nota au&shy;<lb/>tografa: &ldquo; Diverse prove da farsi, tra le quali que&shy;<lb/>sta: se nel vaso AB (fig. </s>

<s>29) pien d'acqua, la&shy;<lb/>sciando scorrere gi&ugrave; per un'assicella DF una pallina <lb/>per aria, che poi entri nell'acqua; se, nell'entrare <lb/>nell'acqua, muti direzione di moto con alzarsi del&shy;<lb/>l'assicella, come io credo &rdquo; (MSS. Cim., T. IV, <lb/>c. </s>

<s>244). </s></p><p type="main">

<s>Non contento il Viviani di starsene ai modi di sperimentare da s&egrave; in&shy;<lb/>ventati, faceva saggio de'modi proposti anche dagli altri, e a carte 101 del <lb/>Tomo XI de'citati MSS. del Cimento, si vede di sua propria mano abboz&shy;<lb/>zato un disegno, allato al quale si legge: &ldquo; Strumento del Keplero per os&shy;<lb/>servare gli angoli delle refrazioni. </s>

<s>&rdquo; Questo strumento kepleriano &egrave; quello <lb/>che vedesi disegnato a principio della Diottrica, e per mezzo del quale pro&shy;<lb/>ponevasi l'Autore di sciogliere il seguente problema: &ldquo; Pellucidi corporis <lb/>duri refractiones artificiose metiri in omni radiorum inclinatione &rdquo; (Aug. </s>

<s><lb/>Vindel. </s>

<s>1611, pag. </s>

<s>1). </s></p><p type="main">

<s>Cos&igrave;, mentre il Viviani con la sua Scatola sperimentava le rifrazioni <lb/>ne'liquidi, collo strumenlo kepleriano le sperimentava ne'cristalli, non la&shy;<lb/>sciando per nessuna parte il nuovo campo diottrico inesplorato. </s>

<s>Queste no&shy;<lb/>stre investigazioni riuscite non affatto infelici accesero in noi il desiderio di <lb/>procedere a investigare se il Viviani avesse tertato nessuna applicazione di <lb/>que'suoi studii alla diottrica delle lenti. </s>

<s>Com'a splendido segno fra le te&shy;<lb/>nebre si teneva da noi collo sguardo dietro alle relazioni che passarono tra <lb/>l'Huyghens e l'Accademia fiorentina, a proposito della Diottrica. </s></p><p type="main">

<s>Nella <emph type="italics"/>Brevis assertio Systematis sui<emph.end type="italics"/> prometteva l'Autore della scoperta <lb/>dell'Anello saturnio &ldquo; quae ad theoriam Dioptrices spectant propediem in <lb/>lucem mittere &rdquo; (Op. </s>

<s>varia, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>627), promessa che, <lb/>ripetuta per lettera privata al principe Leopoldo, moveva questi a stringere <lb/>il promittente a mantenere, scrivendogli il d&igrave; 19 Novembre 1660: &ldquo; Intanto <lb/>star&ograve; attendendo l'invenzione del suo nuovo modo di Canocchiali, e dopo <lb/>il suo ritorno in Olanda quell'Opera che ella ne promette &rdquo; (MSS. Cim., <lb/>T. XXIII, c. </s>

<s>44). </s></p><p type="main">

<s>Sei anni dopo, nel Giugno, tornava l'Huyghens a concluder cos&igrave; un'al&shy;<lb/>tra sua Lettera indirizzata al medesimo principe Leopoldo: &ldquo; Certo che per <pb xlink:href="020/01/638.jpg" pagenum="81"/>la mia parte, siccome da pi&ugrave; anni in qua ho fortemente amato questo stu&shy;<lb/>dio (della Diottrica), cos&igrave; ho pensiero di non tralasciarlo per l'avvenire, e <lb/>spero che un giorno si stamper&agrave; quello che in questo genere ho speculato, <lb/>e che anche la pratica stessa di quest'arte ricever&agrave; qualche aiuto dalle mie <lb/>nuove speculazioni ed esperienze &rdquo; (ivi, T. XVIII, c. </s>

<s>316). Le speranze si <lb/>sarebbero colorite assai presto, giacch&egrave; l'anno appresso mandava a dire a <lb/>Firenze che le figure erano gi&agrave; intagliate, cosicch&egrave; in breve la Diottrica de&shy;<lb/>siderata si pubblicherebbe. </s></p><p type="main">

<s>&ldquo; Cristiano Ugenio nella sua de'18 Novembre 1667, dopo aver rese <lb/>all'A. V. le dovute grazie, per una mano d'opere nuove matematiche sta&shy;<lb/>tegli inviate da V. A. di tempo in tempo, passa a sodisfare alla richiesta di <lb/>lei col darle contezza de'proprii studii, e in particolare del Trattato della <lb/>Diottrica, il quale stava in breve per pubblicare, essendo gi&agrave; intagliate tutte <lb/>le figure &rdquo; (ivi, T. XXI, c. </s>

<s>99). </s></p><p type="main">

<s>Questa scrittura che leggesi ripetuta a carte 135 del T. CXXXIII de'Di&shy;<lb/>scepoli di Galileo, indirizzata al principe Leopoldo, &egrave; autografa del Viviani, <lb/>ma la pubblicazione che par cos&igrave; prossima del Libro tante volte promesso <lb/>e con tanto desiderio aspettato, bench&egrave; il Cassini abbia sentito dire ch'era <lb/>gi&agrave; stata fatta (MSS. Cim., T. XIV, c. </s>

<s>51), indugi&ograve; ancora, non sappiamo <lb/>dire il perch&egrave;, 36 anni intieri, e avvenne in Leyda nel 1703, quando il Vi&shy;<lb/>viani moriva, e quando gi&agrave; di alquanti anni il principe Leopoldo e l'Huy&shy;<lb/>ghens lo avevano preceduto nel sepolcro. </s></p><p type="main">

<s>Le notizie di queste relazioni passate fra il celebre Autore olandese <lb/>della Diottrica e la nostra Accademia, non son certamente prive d'impor&shy;<lb/>tanza storica, ma tornaron prive di effetto per la nostra intenzione, perch&egrave; <lb/>non s'&egrave; trovato che l'Huyghens comunicasse o proponesse a speculare nes&shy;<lb/>suno di que'diottrici teoremi da pubblicarsi, al Viviani. </s>

<s>N&egrave; ci &egrave; riuscito di <lb/>trovare altri documenti o di esperienze fatte o di teorie speculate nella fio&shy;<lb/>rentina Accademia intorno alla ragione e al modo delle ottiche rifrazioni. </s>

<s><lb/>Solo ha il Rinaldini una Lettera indirizzata ad Anonimo, nella quale riprova <lb/>il processo del Maurolico di ricorrere all'esperienza per prender le propor&shy;<lb/>zioni fra gli angoli: egli vuol aver motivo piuttosto da filosofare, e perci&ograve; <lb/>dice di essersi rivolto a cercare i principii dottrinali. </s>

<s>Ma quali fossero que&shy;<lb/>sti principii si pu&ograve; argomentar dalla leggerezza che si trova in quella stessa <lb/>sua Lettera, tutta la scienza contenuta nella quale si riduce a dar grande <lb/>importanza, e a discutere intorno a ci&ograve; che il semplice sguardo decide, ri&shy;<lb/>volgendolo sulla figura che, ne'<emph type="italics"/>Diafani<emph.end type="italics"/> del Maurolico, &egrave; impressa a illu&shy;<lb/>strare il X Teorema. </s></p><p type="main">

<s>&ldquo; Mi convien dirle che, quando in quella mia lettera, che ella dice ritro&shy;<lb/>varsi presso il sig. </s>

<s>Cassini, io dico che il Maurolico asserisce la proporzione <lb/>tra l'aria ed il cristallo esser come 8 a 3, si deve intendere, com'io intendo <lb/>con esso lui, tra l'angolo dell'inclinazione e non dell'incidenza con quello <lb/>della rifrazione. </s>

<s>Ma perch&egrave;, o facciasi comparazione tra l'angolo dell'incli&shy;<lb/>nazione con quello della rifrazione, o tra l'angolo dell'incidenza col mede-<pb xlink:href="020/01/639.jpg" pagenum="82"/>simo angolo della rifrazione, prender la proporzione dall'esperienza non mi <lb/>pare il dovere, conciossiach&egrave; da quella pu&ograve; ben cavarsi motivo da filosofare, <lb/>ma non gi&agrave; da stabilire una precisa proporzione; perci&ograve; dovendo dimostrar <lb/>quel Teorema che in quella lettera accenno mi &egrave; parso gittarmi ad altro <lb/>principio. </s>

<s>Il che ho voluto significare a V. S. perch&egrave; lo conferisca anche al <lb/>sig. </s>

<s>Cassini, ad effetto che non credino da me essere stato detto che il Mau&shy;<lb/>rolico parli della proporzione tra l'angolo dell'incidenza e della rifrazione, <lb/>perciocch&egrave;, come dissi, deve intendersi tra l'angolo dell'inclinazione e della <lb/>sua rifrazione. </s>

<s>Gli angoli poi d'inclinazione vengono dal suddetto presi per <lb/>quelli che son formati da'raggi retti con la linea perpendicolare, come in <lb/>quel luogo viene avvertito dal Clavio nelle sue Annotazioni &rdquo; (MSS. Cim., <lb/>T. XXV, c. </s>

<s>4). </s></p><p type="main">

<s>I principii diottrici insomma professati dai nostri Accademici del Ci&shy;<lb/>mento rimangono ancora que'<emph type="italics"/>bellissimi, ingegnosissimi, maravigliosissimi<emph.end type="italics"/><lb/>del Cartesio. </s>

<s>Pare impossibile che il Viviani rimeditando poi pi&ugrave; riposata&shy;<lb/>mente sopra quegli stessi principii non v'avesse incontrata qualche difficolt&agrave; <lb/>in seguitare a passare per maravigliosissima quella ipotesi cartesiana, tanto <lb/>contraria all'esperienza, de'mezzi pi&ugrave; densi che, invece d'impedire, facili&shy;<lb/>tano il moto alla luce. </s>

<s>L'errore meccanico, cos&igrave; caratteristico della scuola <lb/>galileiana, che cio&egrave; un moto obliquo non si possa altrimenti decomporre che <lb/>in due ortogonali, non fece veder chiari al Viviani que'difetti, nella dimo&shy;<lb/>strazion cartesiana, dal Fermat, cos&igrave; sottilmente notati; ma non par vero <lb/>che il gran Fisico fiorentino non s'avesse una volta a persuadere, per quelle <lb/>sue diottriche esperienze, che Galileo e il Cartesio si conformavano piuttosto <lb/>a una capricciosa ipotesi kepleriana che all'evidenza de'fatti naturali, quando <lb/>supponevano che le refrazioni non si facessero equabilmente per entro il <lb/>mezzo, ma nella sola superficie. </s></p><p type="main">

<s>A restaurar l'onore della scienza italiana, che s'era cos&igrave; servilmente <lb/>infrancesata, sorse da tutt'altro gregge che da quello adunato nelle sale me&shy;<lb/>dicee, nel 1665, il Grimaldi col suo celebre trattato <emph type="italics"/>De lumine, coloribus et <lb/>iride.<emph.end type="italics"/> Egli prende a esaminar sottilmente nella proposizione XIX l'opinion <lb/>del Cartesio, nella quale s'ammette che maggior resistenza faccia al moto <lb/>della luce un mezzo raro che un denso. </s>

<s>&ldquo; Quin immo in contrarium ma&shy;<lb/>nifeste reclamat experientia, qua videmus corpora proiecta facilius moveri <lb/>per aerem, quam per aquam, et universaliter ea ferri velocius per medium <lb/>rarius, caeteris paribus, quoad impetum et conatum quo impelluntur &rdquo; (Bo&shy;<lb/>noniae, pag. </s>

<s>176). </s></p><p type="main">

<s>Soggiunge poi il Grimaldi un'acutissima osservazione, sfuggita forse agli <lb/>stessi acuti censori francesi, ed &egrave; che al Cartesio conveniva provare e non <lb/>gratuitamente asserire che il raggio, dop'aver penetrato il diafano resistente, <lb/>patisce difficolt&agrave; secondo una sola delle due direzioni, in che s'immagina <lb/>esser decomposto il suo moto. </s>

<s>&ldquo; Dato enim quod superficies talis corporis <lb/>resistat motui luminis quoad solum ingressum, reliquum tamen corporis infra <lb/>superficiem si resistit, utique aequaliter resistit secundum omnes sui partes: <pb xlink:href="020/01/640.jpg" pagenum="83"/>ac proinde tam quoad descensum quam quoad progressum ipsi superficiei <lb/>coextensum debet intelligi retardatum lumen infra superficiem illam decur&shy;<lb/>rens, neque est potior ratio quod ad unam potius quam ad aliam partem <lb/>deflectat &rdquo; (ibi). Ma il Grimaldi s'&egrave; presto infastidito dell'esame di questa <lb/>opinion cartesiana, che crolla tentata per tutti i versi. </s>

<s>&ldquo; Alia multa possent <lb/>obiici contra hanc opinionem, sed satius est eam et illa dimittere &rdquo; (ibi). <lb/>Cos&igrave; lascia la ipotesi del Cartesio per venire a dire la sua. </s></p><p type="main">

<s>Della costante uniformit&agrave; fra i seni degli angoli dell'incidenza e i seni <lb/>degli angoli di rifrazione dice il Grimaldi &ldquo; posse reddi congruentem ratio&shy;<lb/>nem si attendamus refractionem moderari et distribui dependenter a radii <lb/>dilatatione vel restrictione &rdquo; (ibi, pag. </s>

<s>184). Egli professa che la luce si re&shy;<lb/>frange dalla perpendicolare mentre passa obliquamente da un pi&ugrave; denso <lb/>mezzo a un pi&ugrave; raro, <emph type="italics"/>quia cogitur diffundi pressius.<emph.end type="italics"/> Ma da un'altra parte <lb/>il moto dee sempre serbarsi equabile, perch&egrave; altrimenti <emph type="italics"/>fluxus acceleratio <lb/>inferret periculum discontinuationis inter velociores partes luminis et tar&shy;<lb/>diores.<emph.end type="italics"/> E in che modo si pu&ograve; mantenere questa equabilit&agrave;? </s>

<s>Col rattempe&shy;<lb/>rare il moto troppo veloce, risponde l'Autore, e col velocitare il troppo tardo. </s>

<s><lb/>Or l'artificio della Natura consiste in ci&ograve; che nel passar, per esempio, il <lb/>raggio dell'aria nel cristallo, incontrandovi una maggior resistenza, acquista <lb/>nuovo impulso al suo moto, ingrossando. </s>

<s>N&egrave; ci&ograve; pu&ograve; avvenire, dice il Gri&shy;<lb/>maldi, se non che rifrangendosi alla perpendicolare, e lo dimostra al modo <lb/>che segue: </s></p><p type="main">

<s>&ldquo; Incidat superficici planae AB (fig. </s>

<s>30) radius CDE subtilissimus, et <lb/>crassitiei ad sensum nostrum indivisibilis, quae tamen aliqua sit, et geome&shy;<lb/>trice divisibilis in partes quam plurimas. </s>

<s>Immo etiam tanta, ut non tam <lb/>radius ille dicendus sit quam radiatio, seu radiorum aggregatum, qui cum <lb/><figure id="id.020.01.640.1.jpg" xlink:href="020/01/640/1.jpg"/></s></p><p type="caption">

<s>Figura 30<lb/>veniant ab uno eodemque puncto <lb/>C remotissimo, poterunt conside&shy;<lb/>rari tanquam paralleli saltem ad <lb/>sensum. </s>

<s>Ex illis autem conside&shy;<lb/>rentur nunc duo tantum extremi <lb/>CD, et CE, qui cum oblique in&shy;<lb/>currant in superficiem AB medii <lb/>densioris refringuntur versus per&shy;<lb/>pendicularem ductam per punctum <lb/>incidentiae nempe CD versus DF <lb/>et CE versus EG, ita ut radii di&shy;<lb/>recti CD refractus sit DH, et radii <lb/>CE refractus sit EI. </s>

<s>Totum ergo <lb/>lumen, quod intra duos radios CD, CE continebatur, dum per aerem exempli <lb/>gratia decurrebat, continetur deinde post refractionem intra duos DH, et EI <lb/>dum procedit per corpus aere densius, puta, per crystallum cuius plana <lb/>superficies est AB. &rdquo; </s></p><p type="main">

<s>&ldquo; Dico igitur lumen quod continetur in radio CDE, si velit dilatari de-<pb xlink:href="020/01/641.jpg" pagenum="84"/>bere flecti versus praedictas perpendiculares et per hanc solam refractionem <lb/>haberi intentum. </s>

<s>Si enim recta procedunt in L dubium non est quod non <lb/>mutaret latitudinem seu crassitiem, sed conservaret eam prorsus quam ha&shy;<lb/>bebat in aere. </s>

<s>Et si diverteret versus AD recedendo a perpendiculari, mi&shy;<lb/>nueret antiquam crassitiem.... At si per refractionem modo dicto flectatur <lb/>versus perpendicularem, ut de facto flectitur, latitudo radii, quae prius erat <lb/>ME, evadit DO, scilicet mensurata per transversalem lineam utrique lateri <lb/>radii orthogonam. </s>

<s>Est autem DO maior quam ME quia sumpto eodem ra&shy;<lb/>dio seu sinu toto DE, recta DO est sinus anguli DEO, et recta ME est si&shy;<lb/>nus anguli MDE; sed angulus DEO maior est angulo MDE, quia hic per <lb/>XXIX primi Euclidis aequatur alterno DEL (non MDL come per errore tra&shy;<lb/>scorso si legge nella stampa) qui est pars totius anguli DEO. </s>

<s>Ergo et sinus <lb/>anguli DEO nempe DO, maior est quam sinus anguli MDE nempe ME, <lb/><figure id="id.020.01.641.1.jpg" xlink:href="020/01/641/1.jpg"/></s></p><p type="caption">

<s>Figura 31.<lb/>quod erat ostendendum &rdquo; <lb/>(ibi, pag. </s>

<s>180, 81). </s></p><p type="main">

<s>In un modo simile a <lb/>questo prova il Grimaldi <lb/>che se il raggio passa da <lb/>un mezzo pi&ugrave; denso in un <lb/>pi&ugrave; raro, come per esem&shy;<lb/>pio dal cristallo nell'aria, <lb/>il troppo veloce moto del <lb/>raggio si rattempera as&shy;<lb/>sottigliandosi nella sezione <lb/>e perci&ograve; rifrangendosi dal&shy;<lb/>la perpendicolare. </s></p><p type="main">

<s>Da cos&igrave; fatti principii, o diciam meglio ipotesi, fa conseguir l'Autor <lb/><emph type="italics"/>De Lumine<emph.end type="italics"/> la dimostrazione della legge diottrica de'seni, dimostrazione la <lb/>quale si pu&ograve; compendiare e ridurre alla forma seguente: </s></p><p type="main">

<s>Sia LE (fig. </s>

<s>31) la superficie che termina il mezzo pi&ugrave; denso, per esem&shy;<lb/>pio il cristallo, attraversato dal cilindro radioso ABCD, il quale uscendo nel&shy;<lb/>l'aria si rifrange dalla perpendicolare assottigliando la sua sezione come si <lb/>disse, e riducendosi perci&ograve; nel cilindro radioso BHIC. </s>

<s>Dai punti C e B, con&shy;<lb/>dotte le FC, BG perpendicolari, queste misureranno la base o l'ampiezza <lb/>de'due cilindri radiosi, e i due triangoli rettangoli BFC, BCG daranno BC2= <lb/>BF2+FC2=BG2+CG2; e anche BC2&mdash;FC2=BF2, e BC2&mdash;BG2=GC2, <lb/>e perci&ograve; BF:CG=&radic;BC2&mdash;FC2:&radic;BC2&mdash;BG2. </s>

<s>Dall'altra parte que'due <lb/>medesimi triangoli danno le relazioni trigonometriche BC:BF=1:sen BCF, <lb/>e anche BC:CG=1:sen CBG, per cui BF:CG=sen BCF:sen CBG. </s>

<s>Ma <lb/>la relazione fra BF e CG ritrovata di sopra &egrave; costante per qualunque in&shy;<lb/>clinazione del raggio e BCF &egrave; uguale all'angolo dell'incidenza, CBG &egrave; uguale <lb/>all'angolo della rifrazione, dunque la relazione trovata fra'loro seni, per <lb/>qualunque obliquit&agrave; di raggi, &egrave; costante, come volevasi dimostrare. </s></p><p type="main">

<s>&ldquo; Poterit ergo a quadrato longitudinis baseos BC singillatim subtraih, <pb xlink:href="020/01/642.jpg" pagenum="85"/>tum quadratum diametri FC radii incidentis, tum quadratum diametri BG <lb/>radii refracti. </s>

<s>Subtrahantur iam et differentiarum, seu residuorum radices <lb/>quadratae, si simul comparentur, invenientur semper habere eamdem pro&shy;<lb/>portionem quaecumque fuerit inclinatio radii ABCD incidentis in subiectam <lb/>eamdem superficiem LE, ex eodem superiori medio. </s>

<s>Siquidem huiusmodi <lb/>radices sunt reliqua latera BF et CG praedictis triangulis rectangulis, ut pa&shy;<lb/>tet per XLVII primi Euclidis, et praeterea haec ipsa latera sunt sinus illi <lb/>qui praedictam eamdem proportionem conservant. </s>

<s>Sumpto enim BC pro sinu <lb/>toto, evadit BF sinus anguli BCF et CG sinus anguli CBG. </s>

<s>At angulus BCF <lb/>aequatur angulo inclinationis radii ABCD, uterque enim complet rectum cum <lb/>incidentiae angulo DCE, et angulus CBG aequatur angulo refracto, cum uterque <lb/>compleat rectum cum angulo LBH.... Itaque mirum non est, quod in iisdem <lb/>mediis ad quamcumque radii inclinationem refractio ita administretur ut ea&shy;<lb/>dem sit semper proportio inter sinum anguli inclinationis et sinum anguli re&shy;<lb/>fracti, si huiusmodi sinus ipsis diametris et crassitiebus radiorum directi ac re&shy;<lb/>fracti ita alligantur, ut compleant cum ipsis eamdem potentiam &rdquo; (ibi, pag. </s>

<s>185). </s></p><p type="main">

<s>Questa dimostrazion del Grimaldi ha un carattere tutto suo originale, <lb/>non vedendovici nessun vestigio di que'principii meccanici derivati dagli an&shy;<lb/>tichi Ottici nel Keplero, e da questo trasfusi nella numerosa sequela succe&shy;<lb/>dutasi dal Cartesio al Newton. </s>

<s>Si direbbe che il Nostro, riguardando il moto <lb/>della luce come un flusso, si fosse piuttosto aiutato da'principii dell'Idrau&shy;<lb/>lica, se non si trovassero con essi principii le sue ipotesi apertamente di&shy;<lb/>scordi. </s>

<s>Imperocch&egrave; parrebbe che attraversando la luce un mezzo pi&ugrave; denso <lb/>ed entrando per le angustie de'pori di lui, dovesse far come l'acqua che <lb/>velocita il corso restringendo la sua sezione. </s>

<s>Ma allora ne verrebbe che il <lb/>raggio si dovesse rifrangere non alla perpendicolare, com'&egrave; di fatto, ma dalla <lb/>perpendicolare, secondo i placiti del Grimaldi. </s>

<s>Da un'altra parte poi non <lb/>s'intende come possa serbare un fluido, conforme al supposto grimaldiano, <lb/>sempre la medesima quantit&agrave; di moto sia che restringasi, o sia che s'allar&shy;<lb/>ghi indifferentemente la sezione. </s></p><p type="main">

<s>N&egrave; quel che dice l'Autore al numero 7 della proposizione XX, per pre&shy;<lb/>venire una tale difficolt&agrave;, sodisfa punto a coloro che desidererebbero, nella <lb/>dimostrazion diottrica una maggior precisione, imperocch&egrave; sembra un ritor&shy;<lb/>nare a coloro che ammettevano nella luce un senso e quasi una discrezione <lb/>da sapere gl'impedimenti e da trovar la pi&ugrave; facile via di scansarli, quando <lb/>il Grimaldi dice che i raggi fan come noi, che per durar meno fatica ci <lb/>pieghiamo nel nostro cammino piuttosto che affrettare il passo. </s>

<s>&ldquo; Quemad&shy;<lb/>modum et nos ipsi minorem conatum experimur in flectendo nostro cursu, <lb/>quam in accelerando &rdquo; (ibi, pag. </s>

<s>180). Il Grimaldi, se si vuole, avrebbe po&shy;<lb/>tuto suggerire un bello strattagemma al Cartesio per levarsi d'impaccio da <lb/>chi gli opponeva, con lo stesso Grimaldi, esser contrario a quel che s'espe&shy;<lb/>rimenta di fatto, che cio&egrave; la luce si velociti ne'mezzi pi&ugrave; densi, imperocch&egrave; <lb/>poteva rispondere che ella nelle angustie de'pori si velocita come l'acqua <lb/>al restringersi delle sezioni. </s></p><pb xlink:href="020/01/643.jpg" pagenum="86"/><p type="main">

<s>Da ci&ograve; si conferma quel che s'&egrave; da noi altre volte asserito, che cio&egrave; <lb/>la legge diottrica, per qualunque via si tenti, &egrave; a tutto rigore <expan abbr="i&ntilde;dimostra-bile">inndimostra&shy;<lb/>bile</expan>. </s>

<s>E si pu&ograve; da un'altra parte soggiungere che, sebben tardi, ebbero gli <lb/>Italiani nel Grimaldi una qualche dimostrazione di quella legge che, per <lb/>quanto non vada esente da gravissime difficolt&agrave;, pur pu&ograve; stare a con&shy;<lb/>fronto e anzi da qualche parte sopraeccellere a quelle stesse speculate dagli <lb/>stranieri. </s></p><p type="main">

<s>Parrebbe fosse insomma da concludersi che fu pel pubblico magistero <lb/>del Grimaldi che s'introdusse finalmente in Italia la scienza delle rifrazioni. </s>

<s><lb/>Ma forse &egrave; una tal conclusione troppo affrettata, perch&egrave; l'eccellenza del trat&shy;<lb/>tato <emph type="italics"/>De Lumine<emph.end type="italics"/> non fu veramente riconosciuta, e in Italia e altrove, se <lb/>non dappoi che se ne videro derivare le insigni scoperte neutoniane. </s>

<s>La ra&shy;<lb/>gion di ci&ograve;, specialmente per quel che riguarda noi Italiani, &egrave; da attribuirsi <lb/>al non essere appartenuto il Grimaldi alla scuola galileiana, la quale, quanto <lb/>fosse rimasta inferiore a s&egrave; stessa nella cultura dell'Ottica, se vien mostrato <lb/>dai fatti narrati, si conferma altres&igrave; da quel poco, che, negli angusti termini <lb/>a noi prescritti, ci rimane a dire intorno all'importantissimo soggetto delle <lb/>astronomiche rifrazioni. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>La storia, da'pi&ugrave; antichi principii, ce l'ha lasciata scritta il Keplero, <lb/>nel paragrafo primo del Cap. </s>

<s>IV de'Paralipomeni a Vitellione, in modo che <lb/>si pu&ograve; andar dietro a lui sicuri, narrando egli il processo di quelle specula&shy;<lb/>zioni che, per la massima parte, udi dalla bocca del suo maestro, e poi lesse <lb/>e medit&ograve; ne'libri pubblicati da lui stesso e da'suoi contradittori. </s></p><p type="main">

<s>&ldquo; Iamdudum Alhazen arabs, et ex eo Vitellio refractionum materiam <lb/>diligentius quam consuevere Veteres, explicare sunt aggressi. </s>

<s>Ac, cum omnis <lb/>nostra cognitio primum ab experientia proficiscatur, primum eorum angu&shy;<lb/>lorum quantitates instrumentis explorarunt, quibus radii ex aere in aquam <lb/>ingressi refringuntur; tum et eorum qui ex aere in vitrum et qui ex aqua <lb/>in vitrum. </s>

<s>Cumque coelorum materia de veterum sententia pene vitrea, hoc <lb/>est, crystallina crederetur, aer vero aquae esset affinis, audacia subvecti au&shy;<lb/>thores, adminiculo refractionum in coelorum arcana inquirere coeperunt. </s>

<s><lb/>Favit ipsorum conatibus experientia: deprehensa est aliqua etiam in stellis <lb/>refractionis ratio, eaque talis, ex qua per ea experimenta, quae in aqua et <lb/>vitro iam comprebata fuerant, aether non densior aere, sed hoc multo te&shy;<lb/>nuior pronunciari posse videretur. </s>

<s>Diu neglecta haec cura, post aliquot se&shy;<lb/>cula Tychonem Brahe incessit, qui subtilissimis instrumentis angulos refrac&shy;<lb/>tionum in aere, quod Vitellio neglexerat, metiri est aggressus. </s>

<s>Certarunt <lb/>cum hoc tum plurimis aliis inventis is, quem dixi Tycho et Rothmannus <lb/>Hassiae Landgravii mathematicus. </s>

<s>Controversia de refractionibus multa est <pb xlink:href="020/01/644.jpg" pagenum="87"/>in tomo I Epistol. </s>

<s>astronomic. </s>

<s>quas anno 97 Tycho edidit: hanc qui volet <lb/>inde petat. </s>

<s>In praesentia summa ascribam &rdquo; (Francof. </s>

<s>1604, pag. </s>

<s>77). </s></p><p type="main">

<s>La somma &egrave; questa: Ticone s'accorse degli effetti delle rifrazioni in <lb/>misurar le altezze del sole e ne attribu&igrave; la causa, come in Vitellione avea <lb/>letto, alla differenza che passa fra l'etere diffuso negli spazii celesti e que&shy;<lb/>sta nostra aria pi&ugrave; bassa. </s>

<s>Insorse contro lui il Rothmann, il quale avendo <lb/>osservato che gli effetti delle rifrazioni cessano a una data altezza da lui <lb/>stesso, dietro l'osservazion de'crepuscoli, ridotta intorno a venti gradi, as&shy;<lb/>ser&igrave; che il fenomeno era prodotto dalla pi&ugrave; bassa ammosfera vaporosa. </s></p><p type="main">

<s>Ticone allora si ridusse ad ammettere due ammosfere concentriche, una <lb/>aerea e l'altra vaporosa, alla quale principalmente egli attribuiva quel pre&shy;<lb/>cipitoso variar delle refrazioni presso all'orizzonte. </s>

<s>Il Rothmann per&ograve; non <lb/>si mostr&ograve; contento di questa ticoniana condiscendenza, e sostenne che l'am&shy;<lb/>mosfera vaporosa opera tutt'altrimenti da quel che avea prescritto Ticone. </s>

<s><lb/>Se i raggi degli astri, ei ragionava, entrando obliquamente e per pi&ugrave; lungo <lb/>cammino dentro la sfera de'vapori grossi si refrangono, e poi abbreviando <lb/>quella via col diminuir l'obliquit&agrave; non si refrangono altrimenti, ci&ograve; vuol <lb/>dire che a quegli stessi raggi &egrave; stabilito un termine, oltre il quale, sosten&shy;<lb/>gono la dirittura del loro viaggio imperturbati. </s></p><p type="main">

<s>&ldquo; Qua in sententia post hanc cum Rothmanno dissertationem, Tycho <lb/>manserit, habes in Progymn., tomo I, folio 92. Caeterum, quod inter prin&shy;<lb/>cipia rerum constituendarum fieri solet, utrique aquae haesit. </s>

<s>Nam si ge&shy;<lb/>nuinam refractionum mensuram adhibuissent, neque Tychoni opus fuisset <lb/>allegare genuinam refractionum causam geminata inquam corpora, alterum <lb/>aeris, alterum vaporum, neque Rothmannus negasset insensibile quippiam <lb/>refringi lucem etiam versus verticem. </s>

<s>Denique apparuisset superficiem quae <lb/>frangit radios neque vaporum esse temere oberrantium, neque corporis ali&shy;<lb/>cuius sublimis ad Lunae confinia sed plane aeris eius in quo nos homines <lb/>spiritum eum in modum trahimus quo pisces trahunt aquam. </s>

<s>Statuisset ita&shy;<lb/>que Tycho non successivam attenuationem aeris in aetherem, et obliteratio&shy;<lb/>nem densitatis aeriae, sed manifestum et evidens discrimen, quod si quis <lb/>supra consisteret non minus ipsi in oculos esset incursum ac iam superfi&shy;<lb/>cies quae aerem ab aqua separat in oculos incurrit. </s>

<s>Rothmannus contra non <lb/>impegisset in principio optico feriri a luce superficiem densioris medii, nec <lb/>tamen mutuum quicquam pati nec refringi, quodque non est in singulis <lb/>partibus, in conduplicatis inesse et profunditate mediorum refringit radios <lb/>non superficiebus quae omnia absurda sunt &rdquo; (ibi, pag. </s>

<s>79). </s></p><p type="main">

<s>Il Keplero dunque, entrando cos&igrave; di mezzo nella controversia insorta fra <lb/>Ticone e il Rothmann, intorno alla causa delle rifrazioni astronomiche, dopo <lb/>aver liberamente scoperte le fallacie ch'erano nell'una e nell'altra opinione, <lb/>bench&egrave; non siasi egli stesso francato da tutti gli errori, pronunzia nulladi&shy;<lb/>meno alcune verit&agrave; tanto importanti, che, se fossero state accolte da'succes&shy;<lb/>sori, avrebbero potuto far progredire la scienza a gran passi. </s>

<s>Egli prima di <lb/>tutto asserisce che qualche rifrazione, bench&egrave; non tanto sensibile, si fa an-<pb xlink:href="020/01/645.jpg" pagenum="88"/>che verso il vertice: nega in secondo luogo che causa unica ed efficiente <lb/>del fenomeno sia l'ammosfera, e fra l'etere e l'aria pone un deciso tra&shy;<lb/>passo e una distinzione, come fra l'aria stessa e l'acqua. </s>

<s>Vedremo tra poco <lb/>come quest'ultima verit&agrave; specialmente conferisse a stabilire la scienza, quando <lb/>il concetto vago e incerto del Keplero intorno ai limiti dell'ammosfera e al <lb/>peso dell'aria, fu reso evidente dall'uso del Barometro e della Macchina pneu&shy;<lb/>matica, ma intanto altri fatti, bench&egrave; non cos&igrave; dimostrativi, aprono il terreno <lb/>a ricevere le radicelle di quegli stessi kepleriani concetti da'quali, coltivan&shy;<lb/>doli poi gli Ottici e gli Astronomi, se ne sarebbero colti i frutti desiderati. </s></p><p type="main">

<s>Que'fatti, de'quali intendiamo parlare, consistono in alcune astronomi&shy;<lb/>che osservazioni, che fecero rimanere attonito lo Scheiner, a cui tocc&ograve; d'es&shy;<lb/>sere il primo a veder lo spettacolo. </s>

<s>Tornato da Monaco in Ingolstad, un <lb/>giorno dell'anno 1612, gli vien riferito che alcuni suoi scolari avevan no&shy;<lb/>tate alcune macchie del sole ad occhio nudo. </s>

<s>V&agrave; di buon mattino in cam&shy;<lb/>pagna, per sincerarsi del fatto, ed egli e il suo compagno avvertono che il <lb/>sole &egrave; ovale e non rotondo. </s>

<s>Dubita a principio che ci&ograve; sia qualche inganno <lb/>dell'occhio, osserva col Canocchiale e il sole si mostra pi&ugrave; distintamente che <lb/>mai contratto, n&egrave; per mutar posizione nell'osservare quella figura si muta. </s></p><p type="main">

<s>&ldquo; Quapropter, anno 1612, die Novembris decimo hora pomeridiana ve&shy;<lb/>luti quarta, cum obverterem soli Tubum modo nominatum ut in chartam <lb/>illius traducerem maculas solares, conspexi ipsum protinus solem luculenta <lb/>affectum systasi secundum attitudinem ita ut deficeret ea a longitudine nona <lb/>minimum diametri solaris visualis parte. </s>

<s>Haesi attonitus inopinato rei specta&shy;<lb/>culo, etenim contractionis illo tempore immemor solas indagabam maculas, <lb/>quas ut ellipsi non circulo inclusas animadverti &rdquo; (Sol ellipticus, Augustae <lb/>Vindelic. </s>

<s>1615, pag. </s>

<s>3). </s></p><p type="main">

<s>E prosegue a dire che, acceso <emph type="italics"/>incredibili studio rei ulterius inquiren&shy;<lb/>dae,<emph.end type="italics"/> spese tutto quel rimanente Novembre e una buona parte del Dicembre <lb/>appresso in misurar mattina e sera l'ellitticit&agrave; del sole. </s>

<s>Concluse dalle sue <lb/>osservazioni i fatti seguenti: che l'ellitticit&agrave; della mattina non &egrave; sempre <lb/>uguale a quella della sera; che la variabilit&agrave; &egrave; notabile da un giorno all'al&shy;<lb/>tro, e anche da un luogo altro. </s></p><p type="main">

<s>Osservati cos&igrave; diligentemente i fatti lo Scheiner passa a investigarne le <lb/>ragioni, le quali egli brevemente conclude nelle parole seguenti: &ldquo; Con&shy;<lb/>tractio haec solis est defectus, quo diametrus altitudinis, latitudinis diame&shy;<lb/>trum relinquit, defectus autem iste generatur a duabus refractionibus, in <lb/>solis summa et una abside fieri solitis, quae absides diametro solari a se <lb/>distant: est igitur haec contractio quasi differentia duarum eiusmodi re&shy;<lb/>fractionum &rdquo; (ibi, pag. </s>

<s>13). </s></p><p type="main">

<s>Che poi veramente il fenomeno sia dovuto alle rifrazioni, l'argomenta <lb/>saggiamente lo Scheiner dal veder che l'ellitticit&agrave; varia a tenor che variano <lb/>le stesse rifrazioni, secondo l'altezza. </s>

<s>&ldquo; Unde cum pateat ipsa quotidiana <lb/>experientia, hanc solis contractionem paulatim augeri cum eiusdem descensu, <lb/>imminui ascensu, quemadmodum et refractio solet, insuper cum certum sit <pb xlink:href="020/01/646.jpg" pagenum="89"/>ipsam circa horizontem brevissimo tempore, minimo spatio incrementa maxima <lb/>sumere, uti in refractione accidit, plus quam probabile, imo fere certum <lb/>mihi est esse proportionem inter refractiones et hasce contractiones &rdquo; (ibi). </s></p><p type="main">

<s>Cosi, mentre trovava lo Scheiner nelle rifrazioni la ragion certissima <lb/>del sole ellittico, proponeva l'osservazione del sole ellittico come la pi&ugrave; <lb/>certa prova delle rifrazioni messe in dubbio e ripudiate da tanti. </s>

<s>Egli am&shy;<lb/>mira perci&ograve; Ticone, ammira il Keplero, i quali ebbero fede nella verit&agrave;, an&shy;<lb/>che prima di averne veduta qualche prova sperimentale. </s>

<s>Che poi non va&shy;<lb/>lessero gl'ingegni comunali a penetrare le sottili ragioni s'intende, dice lo <lb/>Scheiner, ma or&agrave; come potranno negare un fatto cos&igrave; visibile? </s></p><p type="main">

<s>Si lusingava insomma l'Autore del Sole ellittico d'aver cacciato ogni <lb/>ombra di dubbio dalle menti. </s>

<s>Ma vediamo quali fossero di questo nuovo fer&shy;<lb/>vente magistero i frutti, e vediamolo nella persona che a noi pi&ugrave; importa, <lb/>e che pi&ugrave; muove la nostra curiosit&agrave;, nella persona di Galileo. </s>

<s>Egli &egrave; senza <lb/>dubbio nel numero di quei molti che negaron fede alle nuove dottrine pro&shy;<lb/>fessate ne'suoi Proginnasmi da Ticone. </s>

<s>Ci&ograve; era ben da aspettarsi, pensando <lb/>che Galileo, il quale aveva cos&igrave; scarse e cos&igrave; false idee delle rifrazioni ordi&shy;<lb/>narie, non sarebbe penetrato a conoscere il vero di quelle stesse refrazioni <lb/>ne'fatti astronomici. </s>

<s>Se ne persuase egli forse, quando lo Scheiner pubblic&ograve; <lb/>nel 1615 il suo <emph type="italics"/>Sol ellipticus,<emph.end type="italics"/> e due anni dopo torn&ograve;, in Ingolstad, a trat&shy;<lb/>tare del medesimo soggetto nell'altro libro <emph type="italics"/>Refractiones coelestes?<emph.end type="italics"/></s></p><p type="main">

<s>In generale dobbiam dire che il Gesuita tedesco non aveva l'amabile <lb/>virt&ugrave; d'insinuarsi negli animi, per andare a illuminare le menti. </s>

<s>Quel gi&shy;<lb/>rare e rigirare sempre intorno al medesimo soggetto, e il mostrar della cosa <lb/>sempre la medesima faccia, dopo averla cos&igrave; lungamente maneggiata, riesce <lb/>tedioso: quel dar tanta importanza alla sua scoperta, quasi ella dovess'es&shy;<lb/>sere la nuova luce venuta a illuminare il mondo, rende l'Autore esoso. </s>

<s>Dal&shy;<lb/>l'altra parte l'osservazione del sole ovale &egrave; ovvia a tutti coloro, che rivol&shy;<lb/>gon sulla sera lo sguardo al sole, quando egli traspare attraverso a un velo <lb/>di rubicondi e spessi vapori. </s>

<s>N&egrave; pure la ragion del fatto &egrave; merito dello Schei&shy;<lb/>ner, confessando egli stesso di averla letta gi&agrave; nel Keplero: &ldquo; E quo rursus <lb/>suam meretur laudem Kepleri perspicacia, qui, licet novae huius phaseos <lb/>sensum plane nullum experientiamve habuerit, solem tamen a sola data re&shy;<lb/>fractione in ellipticam speciem conformari, contra Vitellionem et antiquos <lb/>astruere non est veritus, quod ego his omnibus iam habitis experientiis in <lb/>ipso libenter legi &rdquo; (Sol ellipticus cit., pag. </s>

<s>22). </s></p><p type="main">

<s>Lo spiegar poi il sole ellittico per mezzo delle rifrazioni, e il far del <lb/>sole ellittico un argomento a provare quelle stesse rifrazioni &egrave; una specie <lb/>di circolo vizioso, n&egrave; si sa dove consista la forza di questo argomento, a cui <lb/>d&agrave; lo Scheiner un valore sperimentale. </s>

<s>A ragion di esperienza si pu&ograve; dire <lb/>che lo ridusse il Vossio, il quale immaginando di avere un vaso rappresen&shy;<lb/>tato dalla figura 32 mostrava che, se nella parete VA &egrave; dipinto un cerchio, <lb/>infusa acqua nello stesso vaso, l'occhio costituito in O vedrebbe quello stesso <lb/>cerchio contratto in ellisse. </s>

<s>Ma tutto l'argomento sperimentale del Gesuita <pb xlink:href="020/01/647.jpg" pagenum="90"/>consisteva nell'aver preparato il Telescopio a mostrare il disco del sole proiet&shy;<lb/>tato sopra una carta, com'usa farsi per descriver le macchie. <lb/><figure id="id.020.01.647.1.jpg" xlink:href="020/01/647/1.jpg"/></s></p><p type="caption">

<s>Figura 32.</s></p><p type="main">

<s>Non vogliam per&ograve; lasciar di notare che il Vossio <lb/>non giudic&ograve; rettamente dello Scheiner, n&egrave; par che <lb/>avesse letti i due Trattati di lui, quando, dopo aver <lb/>descritta la sopra citata esperienza, soggiunge: &ldquo; Et <lb/>hinc petenda est ratio quamobrem sol oriens et oc&shy;<lb/>cidens sub ellipsis figura spectandum se praebeat, <lb/>quam non satis assecutus est Scheinerus, dum a <lb/>speculis cavis huius rei causam adstruere conatur, <lb/>in quibus refractio locum non habet &rdquo; (De Nili orig. </s>

<s><lb/>appendix. </s>

<s>Hagae Comitis 1666, pag. </s>

<s>112). </s></p><p type="main">

<s>Ripigliando il filo del nostro discorso, se queste considerazioni intorno <lb/>allo Scheiner valgono in generale, a pi&ugrave; forte ragione valevano per Galileo, <lb/>che aveva tanta avversione contro il gesuita travestito in <emph type="italics"/>Apelle.<emph.end type="italics"/> Perci&ograve; se <lb/>tutti avevano scuse di negar l'argomento delle rifrazioni, attribuendo il Sole <lb/>ellittico ad altre cause, fu tra questi principale Galileo, come si vede che <lb/>fece alla prima occasione presentatasi, e fu quella di pubblicare il suo <emph type="italics"/>Sag&shy;<lb/>giatore.<emph.end type="italics"/> Qui un altro Gesuita sosteneva che il Sole e la Luna appariscono <lb/>pi&ugrave; grandi all'orizzonte, perch&egrave;, mediante la sfera vaporosa, vengono ad es&shy;<lb/>sere maggiormente illuminati. </s>

<s>Ma Galileo dice a quel Gesuita che egli era <lb/>in inganno &ldquo; imperocch&egrave; non pel lume de'vapori, ma per la figura sferica <lb/>dell'esterna loro superficie, e per la lontananza maggiore di quella dall'oc&shy;<lb/>chio nostro, quando gli oggetti son pi&ugrave; verso l'orizzonte, appariscono essi <lb/>oggetti maggiori della lor comune apparente grandezza, e non i luminosi <lb/>solamente, ma qualunque altro posto fuor di tal regione. </s>

<s>Traponete tra l'oc&shy;<lb/>chio vostro e qualsivoglia oggetto una lente convessa cristallina in varie lon&shy;<lb/>tananze; vedrete che, quando essa lente sar&agrave; vicina all'occhio, poco si accre&shy;<lb/>scer&agrave; la specie dell'oggetto veduto, ma discostandola, vedrete successivamente <lb/>andar quella ingrandendosi. </s>

<s>E perch&egrave; la region vaporosa termina in una <lb/>superficie sferica, non molto elevata sopra il convesso della Terra, le linee <lb/>rette, che tirate dall'occhio nostro arrivano alla detta superficie, sono disu&shy;<lb/>guali, e minima di tutte la perpendicolare verso il vertice, e delle altre di <lb/>mano in mano maggiori sono le pi&ugrave; inchinate verso l'orizzonte che verso <lb/>il zenit &rdquo; (Alb. </s>

<s>IV, 344). </s></p><p type="main">

<s>Questa speculazione fu poi, senz'ombra di dubbio, accolta dal Renieri, <lb/>il quale la proponeva, per servire al medesimo intento di Galileo, al prin&shy;<lb/>cipe Leopoldo. </s>

<s>&Egrave; notabile che il Principe, sinceramente confessando di aver <lb/><emph type="italics"/>poca cognizione di simili materie<emph.end type="italics"/> (Targioni, Notizie ecc., ediz. </s>

<s>cit., T. II, <lb/>P. II, pag. </s>

<s>751), pur sentisse quanto quelle speculazioni di Galileo e del <lb/>Renieri avessero dello strano, e fossero contradette dalle pi&ugrave; volgari espe&shy;<lb/>rienze. </s>

<s>Ed &egrave; a notare altres&igrave; che il Principe fosse da tanto tempo prevenuto <lb/>da Leonardo da Vinci, il quale risolse da maestro il problema cos&igrave; infelice&shy;<lb/>mente tentato da Galileo e dal Renieri, professando principii ottici, che emen-<pb xlink:href="020/01/648.jpg" pagenum="91"/>dano gli errori del Maurolico, del Fracastoro e di tanti altri, i quali dicevano <lb/>le superficie piane de'diafani ingrandir per rifrazione gli oggetti. </s></p><p type="main">

<s>&ldquo; Prova dell'accrescimento del Sole nell'occidente. </s>

<s>&mdash; Alcuni matema&shy;<lb/>tici dimostrano il Sole crescere nel ponente, perch&egrave; l'occhio sempre lo vede <lb/>per aria di maggior grossezza, allegando che le cose viste nella nebbia e <lb/>nell'acqua paron maggiori. </s>

<s>Io rispondo di no, imperocch&egrave; le cose viste in <lb/>fra la nebbia son simili per colore alle lontane, e non essendo simili per <lb/>diminuzione appariscono di maggior grandezza. </s>

<s>Ancora nessuna cosa cresce <lb/>in acqua piana e la prova ne farai a lucidare un'asse mezza (ma dee dir <lb/><emph type="italics"/>messa<emph.end type="italics"/>) nell'acqua. </s>

<s>Ma la ragione che il Sol cresce si &egrave; che ogni corpo lu&shy;<lb/>minoso quanto pi&ugrave; s'allontana, pi&ugrave; pare grande &rdquo; (Rav. </s>

<s>Mollien Manus. </s>

<s>de <lb/>Leonard, MSS. A, fol. </s>

<s>64 v.). </s></p><p type="main">

<s>Quel che poi, ritornando alla speculazione sopra esposta da Galileo, &egrave; <lb/>anco pi&ugrave; strano, si &egrave; che e'vuole applicarla a spiegare il Sole ellittico. <lb/></s>

<s>&ldquo; Quindi anco, e sia detto per transito, si pu&ograve; facilmente raccorre la causa <lb/>dell'apparente figura ovata del Sole e della Luna presso all'orizzonte, con&shy;<lb/>siderando la gran lontananza dell'occhio nostro dal centro della Terra, che &egrave; <lb/>lo stesso che quello della sfera vaporosa, della quale apparenza, come credo <lb/>che sappiate, ne sono stati scritti, come di problema molto astruso, interi <lb/>trattati, ancorch&egrave; tutto il misterio non ricerchi maggior profondit&agrave; di dot&shy;<lb/>trina che l'intender per qual ragione un cerchio veduto in maest&agrave; ci paia <lb/>rotondo, ma guardato in iscorcio ci apparisca ovato &rdquo; (Alb. </s>

<s>IV, 344). </s></p><p type="main">

<s>Chi rimedita sopra questo dottrine galileiane, specialmente se fosse stato <lb/>sedotto da coloro, i quali insegnano a venerar in tutto Galileo come un ora&shy;<lb/>colo; rimane stupefatto ritrovandolo qui tanto inferiore a s&egrave; stesso. </s>

<s>Atten&shy;<lb/>diamo bene: la ragione dell'apparir maggiori gli astri all'orizzonte, quale <lb/>l'abbiamo ora letta nel <emph type="italics"/>Saggiatore,<emph.end type="italics"/> &egrave; strana, ma pure &egrave; derivata dalle an&shy;<lb/>tiche tradizioni della scienza. </s>

<s>Il Fracastoro nel Cap. </s>

<s>VIII della Sezione II <lb/>degli <emph type="italics"/>Omocentrici<emph.end type="italics"/> aveva professato il principio che, moltiplican dosi il mezzo, <lb/>s'ingrandiscono a proporzione le specie, e l'avea applicato a risolvere il pro&shy;<lb/>blema dell'apparente variabile grandezza degli astri. </s>

<s>&ldquo; Sicut autem si cras&shy;<lb/>sum medium sit, maiora et proprinquiora videri facit, ita et si idem multum <lb/>fuerit idem facit. </s>

<s>Quae nam per plus densi medii veniunt species, illa maiora <lb/>omnia repraesentant. </s>

<s>Qua de causa in eadem aqua quae in summo cernun&shy;<lb/>tur minora apparent, quae in fundo maiora, et per duo specilla ocularia si <lb/>quis perspiciat altero alteri superposito, maiora multo et proprinquiora vi&shy;<lb/>debit omnia. </s>

<s>Hac de causa quaecumque stellarum prope horizontem sunt <lb/>maiores et propinquiores videntur. </s>

<s>In medio coeli minores et remotiores. </s>

<s><lb/>Species nam prope horizontem per medium crassum venit, et per aerem <lb/>vaporibus multis plenum, qui circa terram semper sunt. </s>

<s>Sed hoc non suf&shy;<lb/>ficit, nam et e medio coeli species tandem per eosdem vapores venit, cum <lb/>iuxta terram est, verum illud interest, quod prope horizontem per plus il&shy;<lb/>lius aeris defertur species, e medio coeli per minus &rdquo; (Opera omnia, Ve&shy;<lb/>netiis 1584, c. </s>

<s>13 v.). Il Maurolico dall'altra parte aveva nel I Libro <emph type="italics"/>De'dia-<emph.end type="italics"/><pb xlink:href="020/01/649.jpg" pagenum="92"/><emph type="italics"/>fani<emph.end type="italics"/> formulato il Teorema I. &ldquo; Quod per diaphanum planum transparet <lb/>maius quam sit ac propinqius videtur, eo magis, quo propius plano dia&shy;<lb/>phani &rdquo; (Neapoli 1611, pag. </s>

<s>31). </s></p><p type="main">

<s>Leonardo da Vinci aveva antiveduto e confutato gi&agrave; questo errore mau&shy;<lb/>rolicano, rinnovato dallo Snellio e dal Vossio, i quali ne conclusero le ri&shy;<lb/>frazioni anche nel raggio perpendicolare. </s>

<s>Galileo pure cans&ograve; quell'errore, e <lb/>richiedendo per condizione essenziale non la planizie, ma la curvit&agrave; del <lb/>mezzo accett&ograve; del resto a spiegare il fatto della maggior grandezza appa&shy;<lb/>rente degli astri all'orizzonte le dottrine del Fracastoro. </s>

<s>Il principe Leopoldo <lb/>per&ograve; faceva notare, nella persona del Renieri, alla venerata memoria del suo <lb/><figure id="id.020.01.649.1.jpg" xlink:href="020/01/649/1.jpg"/></s></p><p type="caption">

<s>Figura 33.<lb/>Galileo, com'anche ammessa la curvit&agrave; del mezzo le <lb/>rinnovate dottrine fracastoriane venivano dimostrate <lb/>false dall'esperienza. </s>

<s>&ldquo; Piglisi un vaso di vetro con&shy;<lb/>cavo di figura pi&ugrave; rotonda che sia possibile, quale <lb/>sarebbe appunto la met&agrave; d'un fiasco tagliato, ed em&shy;<lb/>piendolo d'acqua sino a un determinato segno e sia <lb/>v. </s>

<s>g. </s>

<s>AB (fig. </s>

<s>33) e sotto ponendovi l'oggetto C, se si <lb/>guarder&agrave; coll'occhio dal punto D, ancorch&egrave; io accre&shy;<lb/>sca la quantit&agrave; dell'acqua al livello EF, non per&ograve; <lb/>mi cresce punto l'oggetto C &rdquo; (Targioni, loc. </s>

<s>cit.). </s></p><p type="main">

<s>Quelle dottrine insomma son dimostrate false nel <emph type="italics"/>Saggiatore,<emph.end type="italics"/> non meno <lb/>di quel che sieno negli <emph type="italics"/>Omocentrici,<emph.end type="italics"/> e s'intende come e d'onde abbia avuto <lb/>origine l'inganno. </s>

<s>Ma passando all'applicazione, che Galileo stesso ne fa a <lb/>render la ragione del Sole ellittico, chi pu&ograve; comprendere come c'entrino i <lb/>cerchi o veduti in maest&agrave; o in iscorcio, se si tratta del Sole e della Luna <lb/>che sono sfere? </s>

<s>Lo Scheiner ne'suoi due trattati ha senza dubbio difetti, <lb/>ma non errori cos&igrave; grossolani, e mentre le parole del <emph type="italics"/>Saggiatore<emph.end type="italics"/> si vorreb&shy;<lb/>bero, per onor di Galileo, sopprimere dal suo Libro, si ripete anche oggidi <lb/>da tutti gli Astronomi, come verit&agrave; provata, la sentenza espressa in princi&shy;<lb/>pio del Cap. </s>

<s>XXIII delle <emph type="italics"/>Refractiones coelestes:<emph.end type="italics"/> &ldquo; Contractio solis enascitur <lb/>ex inaequali partium ipsius supremarum mediarum et infimarum supra <lb/>horizontem elevatione: haec autem ex eo dimanat quod eae inaequaliter ad <lb/>perpendiculares suas refringantur &rdquo; (Ingolstadii 1617, pag. </s>

<s>34). </s></p><p type="main">

<s>Ma il fatto pi&ugrave; singolare in questa Storia &egrave; che a quelle medesime ve&shy;<lb/>rit&agrave; disprezzate dovette poco dipoi convertirsi anche Galileo, bench&egrave; voglia <lb/>fare apparire che ci&ograve; sia stato per sua spontanea deliberazione, e di sua <lb/>propria scienza, n&ograve; persuaso dagl'insegnamenti dell'odiato Gesuita. </s>

<s>A lui in <lb/>ogni modo pienamente si conformava, ravvedutosi delle stranezze lasciate <lb/>trascorrer nel <emph type="italics"/>Saggiatore,<emph.end type="italics"/> quando nel 1637 (Alb. </s>

<s>VII, 193) dettando le <emph type="italics"/>Ope&shy;<lb/>razioni Astronomiche,<emph.end type="italics"/> recava il Sole ellittico per argomento dimostrativo <lb/>delle rifrazioni celesti. </s>

<s>&ldquo; Posto che sia vero, che merc&egrave; della Rifrazione l'og&shy;<lb/>getto lucido e non molto remoto dall'orizzonte, venga sollevato, che tal sol&shy;<lb/>levamento sia in diversi tempi molto disuguale, ce lo mostra il solar disco, <lb/>il quale alcune fiate trovandosi circa un grado elevato dall'orizzonte, si mo-<pb xlink:href="020/01/650.jpg" pagenum="93"/>stra non in figura circolare, ma bislunga, cio&egrave; d'altezza notabilmente minore <lb/>della lunghezza, il che credo io veramente accadere, perch&egrave; merc&egrave; dei vapori <lb/>bassi l'inferior parte del disco solare viene pi&ugrave; inalzata che la superiore, <lb/>restando l'altra dimensione, cio&egrave; la lunghezza, inalterata &rdquo; (Alb. </s>

<s>V, 383, 84). </s></p><p type="main">

<s>Dal 1622 dunque, anno in cui fu disteso e preparato per le stampe il <lb/><emph type="italics"/>Saggiatore,<emph.end type="italics"/> Galileo s'&egrave; alquanto addimesticato colle dottrine diottriche di <lb/>Ticone, del Keplero e dello Scheiner, per conferma di che pu&ograve; citarsi una <lb/>nota, la quale essendo autografa e portando i segni che lo scrivente aveva <lb/>il libero esercizio della vista, dee essere anteriore al 1637, anno in cui co&shy;<lb/>minci&ograve; a sentire la necessit&agrave; di fare scrivere perpetuamente, non solo per <lb/>rispondere alle lettere numerose, ma per <emph type="italics"/>deporre varii suoi pensieri e con&shy;<lb/>cetti<emph.end type="italics"/> (Alb. </s>

<s>VII, 193). Quella nota galileiana dunque dice cos&igrave;: &ldquo; Incertum <lb/>esse numquid coeli medietas appareat supra horizontem nec ne, ex pluri&shy;<lb/>bus causis contingit, maxime autem ex refractionibus stellas efferentibus, <lb/>praeter quam quod ipsaemet stellae circa orizontem inconspicuae sunt &rdquo; <lb/>(MSS. Gal., P. III, T. III, c. </s>

<s>36). </s></p><p type="main">

<s>Non &egrave; da creder per qu&egrave;sto che Galileo fosse in quella ferma persua&shy;<lb/>sione, ch'erano il Brahe, il Kepler, lo Scheiner: anzi ei non pot&egrave; mai li&shy;<lb/>berarsi in tutto da un dubbio, che apertamente confessa nel principio di <lb/>quella V Operazione astronomica, nella quale si legge il passo da noi sopra <lb/>allegato. </s>

<s>&ldquo; Il negozio delle refrazioni resta per ancora appresso di me assai <lb/>ambiguo, n&egrave; ci so discernere precisione alcuna fondata sopra stabili e certe <lb/>osservazioni. </s>

<s>E veramente confesso di non esser capace come la struttura <lb/>delle Tavole di esse refrazioni, portata come assai risoluta in particolare da <lb/>Ticone, sia veramente tanto sicura, che di essa si possa fare assoluto capi&shy;<lb/>tale nel calcolare le elevazioni delle stelle, in particolare ne'luoghi non molto <lb/>alti sopra l'orizzonte &rdquo; (Alb. </s>

<s>V, 383). </s></p><p type="main">

<s>La poca precisione per&ograve; delle Tavole ticoniane poteva attribuirsi piut&shy;<lb/>tosto alla difficolt&agrave; delle osservazioni, e alla imperfezione degli strumenti, e <lb/>se Galileo avesse ripensato a ci&ograve;, si sarebbe potuto almeno in parte delibe&shy;<lb/>rare dalle pene del dubbio. </s>

<s>Ma egli non sapeva persuadersi che gli astri <lb/>avessero a mutar vista per la ragione che, secondo l'antichissima esperienza <lb/>euclidea, invocata in proposito dal Brahe, muta vista, infusa l'acqua nel <lb/>vaso, la moneta posata sul suo fondo. </s>

<s>Il negozio delle astronomiche refra&shy;<lb/>zioni, cos&igrave; esprimesi lo stesso Galileo, &ldquo; mi pare differentissimo da quello <lb/>del vaso e dell'acqua, essendo che in questo l'occhio &egrave; in un diafano di&shy;<lb/>versissimo da quello, nel quale si trova la moneta. </s>

<s>Ma nel nostro caso l'oc&shy;<lb/>chio &egrave; immerso nei medesimi vapori per li quali ha da passare la spazie. </s>

<s><lb/>Che se l'occhio, il catino e la moneta fossero tutti nell'acqua, la refra&shy;<lb/>zione non vi sarebbe &rdquo; (ivi, pag. </s>

<s>385). </s></p><p type="main">

<s>Galileo non giunse a comprendere che, se l'occhio fosse stato nel luogo <lb/>della moneta e la moneta nel luogo dell'occhio, si sarebbe nulladimeno rap&shy;<lb/>presentata una simile illusione, e non valse a comprender ci&ograve; perch&egrave; non <lb/>seppe convenientemente apprezzare il Keplero il quale, ammettendo un de-<pb xlink:href="020/01/651.jpg" pagenum="94"/>ciso passaggio dall'etere all'aria, e una diversa densit&agrave; fra'due elementi, <lb/>come fra l'aria stessa e l'acqua, veniva a costituir l'esempio ne'precisi ter&shy;<lb/>mini dell'occhio collocato nell'acqua, che vedesse la moneta sospesa fuori <lb/>nell'aria. </s>

<s>Nel caso particolare delle refrazioni astronomiche, l'occhio &egrave; som&shy;<lb/>merso nell'aria, che &egrave; un mezzo pi&ugrave; denso dell'etere, da cui gli astri gli <lb/>mandan la luce. </s></p><p type="main">

<s>Il Barometro, presentito dal Keplero, venne a precisare alquanto le idee <lb/>intorno ai confini dell'ammosfera, ma perch&egrave; mancavano ancora esperienze <lb/>dirette, che dimostrassero rifrangersi di fatto i raggi nel passar dall'etere <lb/>nell'aria, e non s'era bene inteso in che propriamente consistessero le ri&shy;<lb/>frazioni ordinarie, le quali si riducevano a un caso particolare di riflessione; <lb/>e perci&ograve; le rifrazioni astronomiche s'ammettevano come un nome dato alla <lb/>causa, qualunque ella poi si fosse, produttrice di effetti realmente osser&shy;<lb/>vati, e de'quali perci&ograve; non si poteva oramai pi&ugrave; dubitare. </s>

<s>Il Cassini, verso <lb/>l'anno 1655, dava opera a costruire Tavole delle Rifrazioni astronomiche <lb/>assai pi&ugrave; precise delle antiche, e tutti gli Astronomi, primi fra'quali i nostri <lb/>Accademici del Cimento, erano in faccenda di misurare con la pi&ugrave; squisita <lb/>esattezza le rifrazioni orizzontali del Sole e della Luna, per riscontrarle con <lb/>quelle stesse ritrovate gi&agrave; da Ticone. (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>755). </s></p><p type="main">

<s>Tutte queste insomma erano pratiche osservazioni, senz'aver fonda&shy;<lb/>mento di scienza, la quale tutta si riduceva a verificare i concetti keple&shy;<lb/>riani, ci&ograve; ch'era riserbato a farsi dalle sole esperienze. </s>

<s>A queste appunto <lb/>aveva pensato il Borelli, il quale, secondo riferiva Cosimo Galilei al Viviani, <lb/>in una sua Lettera trascritta in parte nel capitolo precedente; voleva ser&shy;<lb/>virsi di quelli specchi ordinati a sperimentar la velocit&agrave; della luce &ldquo; per ve&shy;<lb/>dere se veramente sia quella refrazione, nella region vaporosa, addotta per <lb/>causa dagli Astronomi di tante e tante novit&agrave; contro ogni aspettazione se&shy;<lb/>guite &rdquo; (MSS. Galil. </s>

<s>Disc., T. CXLIV, c. </s>

<s>32). </s></p><p type="main">

<s>Ma come potesse accomodarsi l'esperienza borelliana a riuscir nell'in&shy;<lb/>tento, si capisce difficilmente. </s>

<s>In ogni modo, la prova diretta per verificare <lb/>il conceito del Keplero era quella di veder se la luce si refrange, trapas&shy;<lb/>sando, dall'aria nell'etere o nel vuoto torricelliano. </s>

<s>L'importantissimo e <lb/>nuovo esperimento fu fatto, o diciam meglio, fu tentato nell'Accademia fio&shy;<lb/>rentina dal Viviani, di mano del quale si vede abbozzato in disegno uno <lb/>de'soliti tubi di vetro terminati in un pallone, da fare il vuoto col mercu&shy;<lb/>rio, allato al qual disegno in penna il Viviani stesso lasci&ograve; scritto di pro&shy;<lb/>pria mano, cos&igrave; senz'altro: &ldquo; Strumento per conoscer se il raggio del Sole, <lb/>passando per il luogo privo di aria, far&agrave; differenza dal passar per l'aria &rdquo; <lb/>(MSS. Cim., T. XI, c. </s>

<s>195). </s></p><p type="main">

<s>Noi non siamo in grado di render conto ai nostri Lettori, che ne sa&shy;<lb/>ranno desiderosissimi, del resultato della esperienza, dalla quale forse non <lb/>si decise nulla in proposito, per non esser riuscita cos&igrave; scrupolosa. </s>

<s>Dopo pa&shy;<lb/>recchi anni, il bel pensiero del Viviani ebbe esito fortunatissimo per opera <lb/>dell'inglese Giovanni Lowthorp, ma perch&egrave; i Francesi diffusero la notizia <pb xlink:href="020/01/652.jpg" pagenum="95"/>che l'esperienza invece non era riuscita, la R. </s>

<s>Societ&agrave; di Londra ordin&ograve; <lb/>all'Hawksbee che ripetesse la stessa esperienza, operando il vuoto per mezzo <lb/>della sua perfettissima Macchina pneumatica. </s>

<s>L'Hawksbee esegu&igrave;, e divulg&ograve; <lb/>del fatto in questa forma la storia: </s></p><p type="main">

<s>&ldquo; Giovanni Lowthorp invent&ograve; un apparato per dimostrar la refrazione <lb/>dell'aria.... Egli fece un vuoto tra due piani di vetro inclinati, coll'aiuto <lb/>dell'argento vivo, per entro il quale si poteva vedere che un oggetto guar&shy;<lb/>dato col Canocchiale mutava sensibilmente luogo, quando s'introduceva <lb/>l'aria.... Il signor Cassini figliolo, essendo stato presente quando il Low&shy;<lb/>thorp fece la sua esperienza, .... ne fece un rapporto alla R. </s>

<s>Accademia <lb/>di Francia nella storia della quale dell'anno 1700 lasciarono scritto che <lb/>l'esperienza inglese non riusc&igrave;.... La Societ&agrave; regia di Londra mi ordin&ograve; <lb/>che io facessi uno strumento a proposito colla direzione del signor Halley.... <lb/>Consisteva questo in un gagliardo prisma di ottone due lati del quale ave&shy;<lb/>vano delle padellette da ricever vetri piani ed esattamente lisci, e il terzo <lb/>lato aveva un condotto con una chiave da serrare e aprire, a cui si potesse <lb/>applicar la macchina tanto da cavare. </s>

<s>quanto da condensare l'aria.... Que&shy;<lb/>sto strumento cos&igrave; preparato si accomod&ograve; a un Canocchiale lungo circa <lb/>10 piedi geometrici, in maniera che l'asse del Canocchiale potesse passare <lb/>per entro il mezzo del prisma, e nel foco del Canocchiale fu adattato un ca&shy;<lb/>pello sottilissimo, per dirigere la vista. </s>

<s>Avendo scelto un oggetto assai pro&shy;<lb/>prio distintissimo ed eretto .... noi prima cavammo l'aria dal prisma, e poi <lb/>applicandolo al Canocchiale, il capello orizzontale nel foco copriva un segno <lb/>sopra il nostro oggetto, che si vedeva distintamente per entro il vuoto, i due <lb/>vetri essendo ugualmente piegati verso il raggio visivo, poi, lasciando en&shy;<lb/>trar l'aria nel prisma si scorgeva l'oggetto salire gradualmente sopra il ca&shy;<lb/>pello a misura che entrava l'aria, e in fine fu trovato che il capello nascon&shy;<lb/>deva un segno dita dieci e un quarto sotto l'antecedente segno &rdquo; (Esper. </s>

<s><lb/>fisico meccan., trad. </s>

<s>ital., Firenze 1716, pag. </s>

<s>143-45). </s></p><p type="main">

<s>Cosi, dopo un secolo, l'esperienza dimostrava quella refrazione dall'etere <lb/>nell'aria predicata gi&agrave; dal Keplero, come causa efficiente del mutar vista <lb/>che si vede fare agli astri, nell'attraversar l'aria in direzione ora pi&ugrave; ora <lb/>meno obliqua. </s>

<s>Quasi in quel medesimo tempo il Newton, sottoponendo alle <lb/>leggi universali dell'attrazione anche la luce, aveva dimostrato che il raggio <lb/>non si refrange per una meccanica riflessione effettuata dall'urto contro le <lb/>particelle resistenti alla superficie del mezzo pi&ugrave; denso, ma che la virt&ugrave; di <lb/>quello stesso mezzo, operando uniformemente per tutta la lunghezza del raggio <lb/>entrovi immerso, era quella che lo faceva inflettere dalla sua prima direzione. </s>

<s><lb/>Cosi finalmente s'intese che c'era una causa fisica operatrice del fenomeno <lb/>delle rifrazioni distinta da quella da cui si fanno le riflessioni, e s'ebbe cosi <lb/>pi&ugrave; chiara idea di ci&ograve; che rappresenta la luce, ossia che passi dall'aria ne'dia&shy;<lb/>fani pi&ugrave; densi sparsi sulla superficie terrestre, ossia che per gli spazii eterei <lb/>giunga attraverso all'aria, dagli astri pi&ugrave; lontani, ad approdare a'nostri occhi. </s></p><pb xlink:href="020/01/653.jpg" pagenum="96"/><p type="main">

<s><emph type="center"/>CAPITOLO III.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Della luce diffratta e de'colori<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. Dell'esperienze, da cui fu condotto il Grimaldi a professar che la luce, come i liquidi, si diffrange. <lb/></s>

<s>&mdash; II. </s>

<s>Come il Newton confermasse le verit&agrave; de'fenomeni grimaldiani, e come v'applicasse a <lb/>spiegarli il principio dell'attrazione. </s>

<s>&mdash; III. </s>

<s>Delle teorie de'colori. </s>

<s>&mdash; IV. De'colori e delle varie <lb/>apparenze dell'Iride celeste. </s>

<s>&mdash; V. </s>

<s>Delle Corone e de'Parelii. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>La Storia, ne'due precedenti Capitoli narrata, ci dimostra coi fatti che <lb/>la ragione, per cui l'Ottica, da'suoi principii infino alla prima met&agrave; del se&shy;<lb/>colo XVI, ebbe cos&igrave; impacciati e lenti i suoi incerti progressi, dipendeva <lb/>principalmente dal non essersi saputo ben definire la natura e l'essere della <lb/>luce. </s>

<s>E se l'essenze delle cose son per s&egrave; tutte impenetrabili, si pu&ograve; a pi&ugrave; <lb/>forte ragione asserir ci&ograve; della luce, che sfugge, per la sua sottigliezza, alla <lb/>percezion di que'sensi, da cui ci si rivelano le qualit&agrave; della materia. </s>

<s>Imma&shy;<lb/>teriale perci&ograve; reputarono la luce gli Ottici antichi, e solo alcuni pochi altri <lb/>condiscesero ad ammetter ch'ella fosse qualche cosa di mezzo tra gli spi&shy;<lb/>riti e i corpi, tra la forma e la materia. </s>

<s>Professando cos&igrave; fatti principii s'in&shy;<lb/>tende bene come fosse impossibile salvar le riflessioni e le rifrazioni, le quali <lb/>perci&ograve;, non si ammettevano, se non perch&egrave; venivano dimostrate dai fatti. </s></p><p type="main">

<s>Bench&egrave; dunque non fosse da sperar per nessuno di penetrare addentro <lb/>all'essenza della luce, pur si fece un gran passo, quando si pronunzi&ograve; che <lb/>ell'era sostanza puramente corporea, e perci&ograve; soggetta alle passioni stesse <lb/>di tutta l'altra materia. </s>

<s>Anco il Keplero e il Cartesio &egrave; vero avevano da <lb/>qualche parte riguardata la luce come tale, ma si faceva da essi con ma&shy;<lb/>nifesta violenza ai principii gi&agrave; professati. </s>

<s>Cos&igrave; per non ripetere l'osserva-<pb xlink:href="020/01/654.jpg" pagenum="97"/>zione, che da que'Filosofi un moto infinito si decompone in due e gli si <lb/>prefiniscono, per lunghezza di linee, i limiti nello spazio; non s'intende, <lb/>nella proposizione II del Cap. </s>

<s>IV de'Paralipomeni a Vitellione, come il dif&shy;<lb/>fondersi istantaneo e superficiale si possa conciliar coll'ipotesi che riguarda <lb/>i raggi terminati in grossezza fra due linee parallele, in modo che il cre&shy;<lb/><figure id="id.020.01.654.1.jpg" xlink:href="020/01/654/1.jpg"/></s></p><p type="caption">

<s>Figura 34.<lb/>scer della sezione alla striscia luminosa proporzionato al crescere <lb/>dell'obliquit&agrave; incidente, sia sensibile al resister che fa in contro <lb/>al moto di lei la densit&agrave; maggiore del mezzo in che offende. </s>

<s>Mag&shy;<lb/>gior contradizione poi si nota nel Mersenno, ch'&egrave; il pi&ugrave; affac&shy;<lb/>cendato seguace del Cartesio, il qual Mersenno riguarda il raggio <lb/>perpendicolare come una linea matematica, e il raggio obliquo <lb/>come avente sensibile larghezza, quasi fosse l'accidentale inci&shy;<lb/>denza quella che fa al raggio luminoso cangiar natura. </s>

<s>&ldquo; Possumus ergo <lb/>considerare radium ABCD (fig. </s>

<s>34) sine latitudine, hoc est ut linea mathe&shy;<lb/>matica. </s>

<s>Sed in incidentia obliqua, ubi operatio ab F (fig. </s>

<s>35) ad planum <lb/><figure id="id.020.01.654.2.jpg" xlink:href="020/01/654/2.jpg"/></s></p><p type="caption">

<s>Figura 35.<lb/>in H, in maiori est distantia quam ab E in G, non <lb/>potest considerari EFGH ut linea mathematica, <lb/>quia sic consideraretur EF ut punctum mathe&shy;<lb/>maticum, quod tamen consideratur uno termino <lb/>operari longius quam altero, hoc est consideratur <lb/>ut habens terminos, hoc est non ut punctum &rdquo; <lb/>(Univ. </s>

<s>geom. </s>

<s>Synopsis, Parisiis 1644, pag. </s>

<s>573). </s></p><p type="main">

<s>Dietro queste considerazioni s'intender&agrave; bene quanto dovesse giovare <lb/>ai progressi dell'Ottica il tor via quel mostruoso contrasto, che nasce dal <lb/>plasmar, diciamo cos&igrave;, la luce di spirito e di materia. </s>

<s>L'arrischiata impresa <lb/>se l'assunse il Grimaldi, il quale confessa essergli bisognato a ci&ograve; animo <lb/>intrepido. </s>

<s>L'intrepidezza poi in un Gesuita, che contradiceva non solo alla <lb/>corrente opinion de'Filosofi, ma che toglieva di pi&ugrave; a'Mistici la consolazione <lb/>di riguardar la luce quale ala e veste degli spiriti celesti, era tanto pi&ugrave; ne&shy;<lb/>cessaria, in quanto che egli sentenziava la luce esser corporea sull'ipotesi, <lb/>non potutasi mai dopo tante prove verificare, ch'ella si muova in tempo <lb/>come si vedon muovere tutti i corpi. </s>

<s>Forse, delle due facce contrarie del <lb/>libro del Grimaldi si sarebbe comunemente creduto essere stato il vero scritto <lb/>nella seconda, se l'ipotesi del moto della luce in tempo non fosse stata so&shy;<lb/>lennemente confermata dai fatti, e se non ne fosse legittimamente conse&shy;<lb/>guito da ci&ograve; l'argomento, con cui il Grimaldi provava la materialit&agrave; della <lb/>luce stessa. </s></p><p type="main">

<s>Cos&igrave;, dal fortunato riscontro ritrovato fra le speculazioni del nostro Fi&shy;<lb/>losofo italiano e le osservazioni dell'Astronomo danese, essendosi dimostrato <lb/>dover esser gli atomi componenti la luce sostanze materiali; come il Gri&shy;<lb/>maldi stesso aveva mirabilmente promossa la scienza, applicando alla luce <lb/>la propriet&agrave; de'corpi fluidi in moto, cos&igrave; il Newton non la promosse poi <lb/>meno efficacemente applicando ad essa luce le propriet&agrave; generali del moto <lb/>de'gravi. </s>

<s>L'Autore inglese &egrave; pi&ugrave; matematico, l'Italiano &egrave; pi&ugrave; fisico, ma alla <pb xlink:href="020/01/655.jpg" pagenum="98"/>concorde opera loro v&agrave; debitrice l'Ottica d'aver posato il pi&egrave; sopra pi&ugrave; sta&shy;<lb/>bili fondamenti, e d'essersi arricchita di nuove insigni scoperte, delle quali <lb/>si fa principal soggetto storico al capitolo presente. </s>

<s>E perch&egrave; per tempo e <lb/>per dignit&agrave; vengono prima le scoperte del Grimaldi, che dettero occasione <lb/>e aprirono le vie filosofiche al Newton, ragion vuole che la nostra Storia in&shy;<lb/>cominci da quelle. </s></p><p type="main">

<s>Noi siam tornati pi&ugrave; volte a leggere e ripensare su quella nota XVIII, <lb/>che il Libri trascrive da'Manoscritti di Leonardo da Vinci, nella pagina 234 <lb/>del III Tomo della sua <emph type="italics"/>Histoire des Sciences mathematiques<emph.end type="italics"/> &ldquo; Lo spira&shy;<lb/>colo luminoso, dice quella Nota, veduto di loco ombroso, ancora ch'esso sia <lb/>d'uniforme larghezza, e'parr&agrave; forte restringersi vicino qualunque obbietto <lb/>fia interposto infra l'occhio e tale spiracolo. </s>

<s>&rdquo; L'osservazione ottica ha per <lb/>noi qualche cosa di singolare, e i lettori giudicheranno se ell'abbia davvero <lb/>qualche somiglianza con quest'altra che il Grimaldi descrive nel suo primo <lb/>Esperimento. </s></p><p type="main">

<s>&ldquo; Aperto in fenestra foraminulo per quam parvo AB (fig. </s>

<s>36) introdu&shy;<lb/>catur per illud in cubiculum, alioqui valde obscurum, lumen solis coelo se&shy;<lb/>renissimo, cuius diffusio erit per conum, vel quasi conum ACDB visibilem, <lb/>si aer fuerit refertus atomis pulvureis, vel si in eo excitetur aliquis fumus. <lb/><figure id="id.020.01.655.1.jpg" xlink:href="020/01/655/1.jpg"/></s></p><p type="caption">

<s>Figura 36.<lb/>Huic cono inseratur aliquod <lb/>corpus opacum EF, in magna <lb/>distantia a foramine AB, et <lb/>ita ut saltem unum extremum <lb/>corporis opaci illuminetur. </s>

<s><lb/>Excipiatur deinde in tabella <lb/>candida, vel in folio chartae <lb/>albae super pavimento exten&shy;<lb/>sae, conus praedictus, seu ba&shy;<lb/>sis eius lucida CD cum umbra <lb/>GH, quam proiicit opacum <lb/>EF insertum cono, et illumi&shy;<lb/>natum in utroque sui extremo <lb/>E et F: quae tamen umbra <lb/>secundum leges opticas non erit exactissima praecisa et terminata in uno <lb/>puncto G versus unam partem, et in uno alio puncto H versus aliam; sed <lb/>ratione foraminis AB, aliquam tandem latitudinem habentis simulque ratione <lb/>solis in latum extensi, aliave de causa, erit confinium umbrae aliquo modo <lb/>incertum propter penumbram quandam, et cum sensibili decremento, seu ut <lb/>vocant exsumatione luminis per spatium IG inter certam umbram et nitidum <lb/>lumen ad unam partem praedictae basis, et per spatium HL ad aliam partem &rdquo; <lb/>(De lumine, Bononiae 1665, pag. </s>

<s>2). </s></p><p type="main">

<s>Due cose, prosegue a dire il Grimaldi, son notabili nell'osservazione di <lb/>questo fatto, la prima delle quali &egrave; che calcolati i limiti dell'ombra e della <lb/>penombra, dietro le misure date del foro AB e della grossezza del corpo opaco <pb xlink:href="020/01/656.jpg" pagenum="99"/>EF, non che delle distanze BF, FI, si trovan quegli stessi limiti di fatto ec&shy;<lb/>cedere notabilmente le misure date dal calcolo. </s>

<s>In altre parole, mentre la <lb/>legge geometrica prefinirebbe all'ombra lo spazio IL, si osserva che in realt&agrave; <lb/>si allarga pi&ugrave; oltre fino in MN. </s></p><p type="main">

<s>&ldquo; Praeterea observetur super lucidae basis parte CM et ND, nitide ac <lb/>fortiter illustrata spargi et distingui tractus aliquos, seu series luminis co&shy;<lb/>lorati, ita ut in qualibet serie sit in medio quidem lux valde pura et sin&shy;<lb/>cera, in extremis autem sit color aliquis, nempe caeruleus in extremo ipsi <lb/>umbrae MN proprinquiore, et rubeus in extremo remotiore: quae series lu&shy;<lb/>cidae, licet dependeant a quantitate foraminis AB, quia non apparent si il&shy;<lb/>lud esset maiusculum, non sunt tamen ab eo determinatae, sicut nec deter&shy;<lb/>minantur a quantitate diametri solaris. </s>

<s>Ulterius observatur tractus praedictos <lb/>seu series luminis colorati ita se extendere ab M versus C, et idem dic de <lb/>aliis ab N versus D, ut prima latior sit quam secunda, et haec latior quam <lb/>tertia, neque vero contigit unquam videre plus quam tres, decrescente etiam <lb/>in illis intensione luminis et colorum eodem ordine quo illae recedunt ab <lb/>umbra &rdquo; (ibi, pag. </s>

<s>3). </s></p><p type="main">

<s>Il Grimaldi, esaminato cos&igrave; diligentemente il fatto, ne andava cercando <lb/>la spiegazione, ma volle prima rappresentarsi quello stesso fatto sotto un <lb/>aspetto alquanto diverso, variando cos&igrave; e rendendo tutt'insieme pi&ugrave; efficace <lb/>il singolarissimo esperimento: </s></p><p type="main">

<s>&ldquo; Aperto in fenestra lignea cubiculi bene obscurati foramine fere digi&shy;<lb/>talis crassitiei, applicetur ei lamina opaca subtilis AB (fig. </s>

<s>37) per cuius <lb/><figure id="id.020.01.656.1.jpg" xlink:href="020/01/656/1.jpg"/></s></p><p type="caption">

<s>Figura 37.<lb/>foraminulum arctissimum CD solis lumen ad&shy;<lb/>missum formabit se in conum. </s>

<s>Hic vero in ma&shy;<lb/>gna distantia post laminam AB ad rectos an&shy;<lb/>gulos secetur ab alia lamella EF, habente pariter <lb/>foramen parvum GH, per quod excipiatur ali&shy;<lb/>quid de praedicto luminoso cono secto a la&shy;<lb/>mina EF, utique in loco ubi eius basis valde <lb/>superat amplitudinem foraminis GH, ut ita fo&shy;<lb/>ramen hoc totum illustretur, seu lumine com&shy;<lb/>pleatur. </s>

<s>Rursus ergo hoc ipsum luminis quod <lb/>ingreditur secundum foramen GH, formabitur <lb/>seu procedet formatum in conum, vel quasi co&shy;<lb/>num, qui sectus orthogonaliter ac terminatus ab <lb/>aliquo plano mundo et candido, exhibebit in illo <lb/>suam basem lucidam IL notabiliter maiorem, <lb/>quam ferant radii per utrumque foramen recta transmissi et non solum tran&shy;<lb/>seuntes per extrema foraminum ad easdem partes spectantia, ut sunt radii <lb/>CGL et DHM, sed etiam ad partes contrarias ut sunt radii DGN et CHO &rdquo; <lb/>(ibi, pag. </s>

<s>9). </s></p><p type="main">

<s>Anco qui si nota un fatto simile a quello che osservasi nell'esperienza <lb/>precedente: il cono radioso GIKH &egrave; realmente pi&ugrave; grande del cono geome-<pb xlink:href="020/01/657.jpg" pagenum="100"/>trico GNOH: si osserva inoltre che la base di esso cono &egrave; circumcinta di <lb/>un lume, dice il Grimaldi, in parte di color rosso e in parte di ceruleo. </s></p><p type="main">

<s>Cos&igrave; stando le cose, l'intento osservatore domandava a s&egrave; stesso come <lb/>mai l'ombra nel primo esperimento e il cono radioso del secondo avessero <lb/>in ogni caso a tornare notabilmente pi&ugrave; grandi del dovere. </s>

<s>I sottili lati del <lb/>corpo opaco interposto e gli orli taglienti del secondo foro, inetti cos&igrave; a ri&shy;<lb/>flettere com'a rifrangere la luce, non davano speranza di riuscire a trovar <lb/>la ragione del fenomeno nelle propriet&agrave; ottiche pi&ugrave; comunemente note, e <lb/>dall'altra parte era chiaro che il deviar del raggio rasente gli orli del corpo <lb/>opaco osservava tutt'altre leggi da quelle diottriche e calottriche ordinarie. </s>

<s><lb/>Pareva al Grimaldi che piuttosto la luce imitasse, in quel fatto singolare, <lb/>un filo di fluido, che si sparpaglia fatto passar rasente al sottile orlo di un <lb/>corpo, come si vede gettando l'acqua con forza dal cannello forato di uno <lb/>schizzetto. </s>

<s>&ldquo; Quod si fluidum per quam valido impetu diffundatur, fieri po&shy;<lb/>test ut pars illa quae uni extremo obstaculi allabitur, ac deinde ulterius <lb/>procedit, multipliciter frangatur, et huc illuc divisim dispergatur. </s>

<s>Videmus <lb/>hoc reipsa clarissime, dum aquae per fistulam violenter emissae, applicamus <lb/>aut etiam modice immergimus cuspidem alicuius solidi corporis, observando <lb/>quomodo aqua illa sic fracta disiiciatur &rdquo; (ibi, pag. </s>

<s>13, n.o 4). </s></p><p type="main">

<s>Persuaso perci&ograve; il Grimaldi che dovendo essere la luce sostanza corpo&shy;<lb/>rea in moto non poteva meglio paragonarsi che al flusso di un liquido, non <lb/>esit&ograve; a spiegare i fenomeni presentati da'suoi due esperimenti, ammettendo <lb/>che il raggio nel rasentar l'orlo del corpo intercettante il suo cammino si <lb/>sparpagli, o com'egli diceva si <emph type="italics"/>diffranga,<emph.end type="italics"/> e perci&ograve; l'ombra apparisca pi&ugrave; <lb/>larga di quel che non dovrebbe, se il raggio stesso andasse unito e in linea <lb/>retta. </s>

<s>Cos&igrave; ai tre modi ordinarii del propagarsi la luce, per via diretta, o per <lb/>riflessione o per rifrazione, ne aggiunse, il nostro Autore, un quarto, a cui <lb/>d&agrave; il nome proprio di <emph type="italics"/>Diffrazione.<emph.end type="italics"/> &ldquo; Hactenus quidem putaverunt Optici lu&shy;<lb/>minis propagationem his tribus dumtaxat modis perfici directe, refracte ac <lb/>riflexe .... nobis alius quartus modus illuxit, quem nunc proponimus, voca&shy;<lb/>musque <emph type="italics"/>Diffractionem &rdquo;<emph.end type="italics"/> (ibi, pag. </s>

<s>2, n.o 5). </s></p><p type="main">

<s>In quella stessa rassomiglianza intraveduta fra la luce e un fluido in <lb/>moto, trovava altres&igrave; il Grimaldi la ragione delle frange colorite, che ter&shy;<lb/>minano l'ombra nel primo esperimento, e che nel secondo precingono la <lb/>base al cono radioso. </s>

<s>Imperocch&egrave; egli ammetteva che que'colori nascessero <lb/>dall'increspamento ondoso del raggio, in conseguenza dell'urto ricevuto dal&shy;<lb/>l'incontro nel corpo duro, come si vede avvenir di fatto in qualunque fluido <lb/>anche in moto, percosso per esempio dal cadere di un sasso. </s>

<s>&ldquo; At longe <lb/>maior inaequalitas motus contingit in fluido, si undose agitetur, estque in <lb/>hoc genere motus tam multiplex et adeo mira varietas, ut eam persequi sit <lb/>labyrintum desperationis intrare. </s>

<s>Unum tamen prae aliis facillimum hoc <lb/>adverto, videlicet posse dari undas seu fluctus in fluido, sive illud actu to&shy;<lb/>tum fluat, sive in modum stagni quiescat. </s>

<s>Experire proiecto similiter lapide <lb/>in aquam stagnantem et in defluentem, videbis enim similes circulos unda-<pb xlink:href="020/01/658.jpg" pagenum="101"/>rum in utroque casu elevari ac dilatari aliis post alios succedentibus &rdquo; (ibi, <lb/>pag. </s>

<s>12, 13). </s></p><p type="main">

<s>A questo modo fluttuando il raggio luminoso per l'urto ricevuto, nel <lb/>rasentare o il corpo opaco intraversato o gli orli del foro, si vengono a pro&shy;<lb/>durre secondo il Grimaldi le frange alterne e colorate che si osservano <lb/>ne'due sopra citati esperimenti. </s>

<s>&ldquo; Quid enim aliud est multiplex illa con&shy;<lb/>geries luminis per series lucidas multiformiter collecti, nisi effectus agita&shy;<lb/>tionis qua lumen undose glomeratum amittit uniformem illam sui diffusio&shy;<lb/>nem, qua solet aequabiliter spargi, ideoque dum terminatur super tabella <lb/>candida non exhibet amplius illustrationem uniformiter expansam, immo vero <lb/>illam reddit tractibus dissimilibus intercisam et diversis gradibus lucis di&shy;<lb/>scriminatam? </s>

<s>&rdquo; (ibi, pag. </s>

<s>17, 18). </s></p><p type="main">

<s>Cos&igrave; veniva il Grimaldi ad adempiere tutt'insieme l'ufficio di osserva&shy;<lb/>tore attentissimo e di Filosofo, non contentandosi di descrivere solamente <lb/>il fatto, ma studiandosi di pi&ugrave; di rendere qualunque ella si fosse, una ra&shy;<lb/>gione del fatto. </s>

<s>Ripensando che la camera oscura era forse lo strumento ot&shy;<lb/>tico pi&ugrave; maneggiato e del pi&ugrave; semplice artificio di tutti gli altri, e che no&shy;<lb/>nostante a nessuno era riuscito di assottigliar cos&igrave; il senso e di aguzzare <lb/>l'ingegno a vedervi quel che il Grimaldi ci vide, n&ograve; nelle immagini spet&shy;<lb/>tacolose, ma nel semplice raggio, si riconoscer&agrave; nel nostro Autor bolognese <lb/>l'iniziatore di quella nuova arte di finissimi ottici esperimenti, che dovevan <lb/>di tanta gloria circondare il Newton e poi pi&ugrave; tardi l'Young, il Malus, il <lb/>Fresnel. </s>

<s>Ma a dover riguardare il Grimaldi come tale e a confermargli il <lb/>merito insigne d'avere aperto all'Ottica nuovi larghi campi, ne'quali si sa&shy;<lb/>rebbero tanto gloriosamente esercitati i sopra detti stranieri, s'aggiunge alle <lb/>descritte un'altra scoperta, simile nella natura, e di pari novit&agrave; ma supe&shy;<lb/>riore nella maraviglia. </s></p><p type="main">

<s>&ldquo; Aperiantur in fenestra cubiculi obscurati duo parva foraminula tanto <lb/>intervallo disiuncta ut duo luminosi coni a Sole per ipsa illabentes in ma&shy;<lb/>gna distantia post fenestram concurrant solum ex parte, ideoque in candida <lb/>tabella illos ibi orthogonaliter secante appareant circulares bases conorum <lb/>invicem ex parte permixtae, ut sunt in adiecta figura 38 circuli duo ABCD, <lb/><figure id="id.020.01.658.1.jpg" xlink:href="020/01/658/1.jpg"/></s></p><p type="caption">

<s>Figura 38.<lb/>et AECF se intersecantes, ha&shy;<lb/>bentesque commune segmen&shy;<lb/>tum ADCF. </s>

<s>Claudatur deinde <lb/>unum ex foraminibus et obser&shy;<lb/>vetur conus per alterum intro&shy;<lb/>missus, quomodo scilicet basis <lb/>illius terminetur. </s>

<s>Apparebit <lb/>enim in eius circulo ambitus <lb/>ABCD obscurus in comparatio&shy;<lb/>ne luminis cadentis super me&shy;<lb/>dias partes eiusdem circuli, ita ut circa ipsum manifeste videatur velut armilla <lb/>obscura minus ac minus habens luminis in sui partibus magis accedenti-<pb xlink:href="020/01/659.jpg" pagenum="102"/>bus ad extremam peripheriam; quae tamen armilla seu circellus obscurus <lb/>nihil aliud esse potest quam lumen debile ut revera cognoscitur si compa&shy;<lb/>retur ad partes tabellae extra totum circulum ABC adiacentes et omnino <lb/>obscuras. </s>

<s>Idem plane observabitur in base AECF, aperto altero foramine et <lb/>clauso priore, ita ut non appareat basis ABCD sed sola spectetur AECF. </s>

<s>At <lb/>si aperto utroque foramine observetur utraque simul basis in loco ubi se <lb/>intersecant .... et si commune segmentum ADCF fuerit parvum eo quod <lb/>tabella candida illud excipiens secet utrumque conum valde prope foramina, <lb/>arcus uterque ADC et AFC videbitur rubescere. </s>

<s>At si tabella excipiens lu&shy;<lb/>cidas bases magis distiterit a foraminibus, fueritque propterea maius com&shy;<lb/>mune illud segmentum, erit circellus uterque ADC, AFC magis notabiliter <lb/>obscurus &rdquo; (ibi, pag. </s>

<s>187). </s></p><p type="main">

<s>Da ci&ograve; ne concludeva il Grimaldi un effetto, il quale, piuttostoch&egrave; nuovo <lb/>e maraviglioso, direbbesi addirittura paradossastico, ed &egrave; che luce aggiunta <lb/>a luce non rischiara maggiormente l'oggetto, ma talvolta l'oscura. </s>

<s>&ldquo; Ex his <lb/>quae indubitanter apparent et quae facile quivis poterit experiri, probatur <lb/>propositio: lumen aliquando per sui communicationem reddit obscuriorem <lb/>superficiem corporis aliunde et prius illustratam &rdquo; (ibi). </s></p><p type="main">

<s>Ma come si pu&ograve; ridurre a termini di ragionevolezza il fatto, che ha cos&igrave; <lb/>tanto dello strano? </s>

<s>E il Grimaldi risponde che l'oscurit&agrave; prodotta dall'ag&shy;<lb/>giunta del lume si salva osservando che ogni colorazione &egrave; un principio di <lb/>oscuramento, e la colorazione non da altro dipende se non dal fluitar che <lb/>sopravvien nella luce, per effetto della diffrazione. </s>

<s>Cos&igrave; i cerchietti proiettati <lb/>sulla tavoletta candida, secondo il descritto esperimento, si vedono tutt'in&shy;<lb/>torno rosseggiare negli orli per la luce che entrando nella camera oscura <lb/>si diffrange in passare attraverso alle angustie de'fori, &ldquo; sed haec interim <lb/>vix indicasse sufficiat ut constet luculentius posse aliquid habere circa se <lb/>plus luminis, et tamen reddi obscurius, quatenus lumen alteri lumini im&shy;<lb/>perfecte admixtum minus aptum est illustrare corpus in quod incidit, ob <lb/>suam diffractionem et agitatam diffusionem, per quam positive etiam reprae&shy;<lb/>sentat illud tanquam obscurius &rdquo; (ibi, pag. </s>

<s>189). </s></p><p type="main">

<s>Le ragioni che il Grimaldi rendeva de'fenomeni cos&igrave; nuovi da lui stesso <lb/>prima osservati, e com'abbiamo inteso cos&igrave; diligentemente descritti, erano <lb/>quelle che si potevano avere a que'tempi, e che venivano suggerite dal pa&shy;<lb/>ragonare il moto della luce al flusso di un liquido, che percosso ondeggia <lb/>e, percotendo, in minuti e larghi spruzzoli si diffrange. </s>

<s>In cose tanto remote <lb/>dai sensi com'&egrave; impossibile a penetrare il vero, cos&igrave; anche &egrave; difficilissimo in&shy;<lb/>contrarsi in quel probabile che sodisfaccia agl'ingegni, liberi di pensare al&shy;<lb/>trimenti, e facili a cavar dal loro proprio cervello altre diverse opinioni. </s>

<s>Ma <lb/>lasciando questi cos&igrave; fatti da parte dobbiam dir di que'pochi, i quali cre&shy;<lb/>deron di non dover conformar le loro alle speculazioni ottiche del Grimaldi, <lb/>non pervertiti da pregiudizii di scuola o dai proprii capricci, ma mossi dal <lb/>pi&ugrave; attento esame dei fatti, e dalla pi&ugrave; ingegnosa variet&agrave; data agli espe&shy;<lb/>rimenti. </s></p><pb xlink:href="020/01/660.jpg" pagenum="103"/><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Primo e principale fra questi ci occorre a commemorare il Newton, il <lb/>quale iniziava allora i suoi studii ottici, quando comparve alla luce il libro <lb/><emph type="italics"/>De lumine coloribus et iride<emph.end type="italics"/> del Grimaldi. </s>

<s>Ma non era facile che questo <lb/>Libro, cos&igrave; freddamente accolto nella stessa Italia, e a quel che pare po&shy;<lb/>chissimo letto e compreso, avesse potuto varcar mari e monti per giungere <lb/>infino a Londra, se l'occasione non avesse procacciato alla scienza questa <lb/>buona ventura. </s>

<s>Qual fosse poi l'occasione, per cui il Newton rivolse sopra <lb/>i nuovi fenomeni grimaldiani i suoi studii, &egrave; ci&ograve; che noi dobbiamo per prima <lb/>cosa narrare, e anzi &egrave; il Newton stesso che cos&igrave; ne esordisce la Storia. </s></p><p type="main">

<s>&ldquo; Ineunte anno 1666, quo tempore operam dabam conficiendis opticis <lb/>vitris figurarum a sphaerica diversarum, mihi vitreum Prisma triangulare <lb/>paravi, eo notissima phaenomena colorum experturus. </s>

<s>Cum idcirco cubicu&shy;<lb/>lum meum obscurum raddidissem, parvoque foramine ligneam fenestram <lb/>pertusissem, quo satis lucis a sole venientis intrare posset, illam ingredien&shy;<lb/>tem Prismate excepi, quo refracta fuit in parietem oppositum. </s>

<s>Et primo <lb/>quidem me non parva voluptate affecerunt vividi et intensi colores ita pro&shy;<lb/>deuntes. </s>

<s>Paulo post vero, cum eos maiori cura et attentione considerarem, <lb/>in oblongam figuram diductos miratus sum, siquidem putabam fore, ut iuxta <lb/>receptas refractionum leges in circularem sese contraherent. </s>

<s>Utrinque rectis <lb/>lineis terminabantur, sed difficile fuisset, ob lucem gradatim evanescentem, <lb/>extremitatum figuram accurate definire quae tamen visa est semicircularis &rdquo; <lb/>(Op. </s>

<s>opt. </s>

<s>omnia, Patavii 1773, Appendix, pag. </s>

<s>3). </s></p><p type="main">

<s>Misura la lunghezza dello spettro relativamente alla larghezza, e trova <lb/>quella presso a poco cinque volte maggiore di questa &ldquo; quae tanta inae&shy;<lb/>qualitas maximam mihi cupiditatem iniecit requirendi unde nam orire&shy;<lb/>tur &rdquo; (ibi). Dubita che ci&ograve; dipenda dalla varia grossezza del prisma, il quale <lb/>va dal suo massiccio a terminare in tre spigoli acuti, o che sia in qualche <lb/>parte difettoso il prisma stesso usato per l'esperienza. </s>

<s>Pensa in ogni modo <lb/>che i difetti del primo sarebbero emendati da un altro simile vetro che ri&shy;<lb/>franga i raggi in verso contrario. </s>

<s>Ripete l'esperienza e trova che i due cri&shy;<lb/>stalli prismatici accoppiati non danno pi&ugrave; il solito spettro oblungo e colo&shy;<lb/>rato, ma dipingono un'immagine bianca e circolare, come se fossero i raggi <lb/>liberamente passati attraverso all'aria. </s>

<s>&ldquo; Tunc suspicatus sum colores ita di&shy;<lb/>latari, quod vitrum esset inaequale, aut quavis alia ratione fortuito vitiosum. </s>

<s><lb/>Experturus an id verum esset, sumpsi aliud Prisma primo simile, quod ita <lb/>statui ut lux per utrumque transiens refringi posset ad contrarias partes, <lb/>et hoc pacto a secundo redigi in viam, a qua primum illum detorserat. </s>

<s>Sic <lb/>enim futurum existimabam, ut quae primum Prisma secundum naturae le&shy;<lb/>ges effecerat, a secundo Prismate destruerentur, augescerent autem ob plu-<pb xlink:href="020/01/661.jpg" pagenum="104"/>res refractiones, quae contra has leges accidissent. </s>

<s>Exitus vero fuit quod lux <lb/>quae a primo Prismate in oblongum spatium diffusa fuerat, a secundo in <lb/>orbiculare coercita fuit accuratius, quam si per neutrum transmeasset. </s>

<s>Igi&shy;<lb/>tur, quaecumque demum sit huius longitudinis causa, ea certe non est for&shy;<lb/>tuita quaedam anomalia &rdquo; (ibi, pag. </s>

<s>3, 4). </s></p><p type="main">

<s>Se non &egrave; dunque l'allungamento dello spettro un'anomalia, n&egrave; una illu&shy;<lb/>sione, si domandava pensosamente il Newton, qual'&egrave; di questo effetto reale <lb/>la causa vera? </s>

<s>e dopo lunghe e accuratissime esperienze ebbe a rispondere: <lb/>&ldquo; Unde patet veram imaginis sic exporrectae causam hanc unam esse quod <lb/>scilicet <emph type="italics"/>Lux constat ex radiis quorum alii aliis magis refrangibiles sunt,<emph.end type="italics"/><lb/>qui nulla incidentiae ratione habita pro <emph type="italics"/>peculiaribus refrangibilitatis gra&shy;<lb/>dibus,<emph.end type="italics"/> ad diversas oppositi parietis partes transmittuntur &rdquo; (ibi, pag. </s>

<s>5). </s></p><p type="main">

<s>Questa storia della scoperta de'varii gradi di refrangibilit&agrave; della luce <lb/>eterogenea attraverso il Prisma la partecipava solennemente il Newton alla <lb/>R. </s>

<s>Societ&agrave; di Londra, con lettera data da Cambridge il di 6 Febbraio 1672, <lb/>e la R. </s>

<s>Societ&agrave; ne diffondeva la notizia nel num. </s>

<s>80 delle Transazioni filo&shy;<lb/>sofiche, sotto il di 19 di quel medesimo mese. </s>

<s>Non mancarono, com'era da <lb/>aspettarsi, contradittori, fra'quali il gesuita Ignazio Gastone Pardies, profes&shy;<lb/>sor nel Collegio di Parigi, a cui, parendo che la nuova scoperta neutoniana <lb/>sovvertisse la Diottrica dalle fondamenta, soccorse in pensiero di ovviarvi <lb/>con dire che per questo si refrangono attraverso il prisma variamente i raggi <lb/>solari, e lo spettro ne apparisce bislungo, perch&egrave; le parti estese del disco <lb/>solare cadono sulla superficie del cristallo variamente inclinate (ivi, pag. </s>

<s>22). <lb/>Al Pardies che, per mezzo delle Transazioni filosofiche, faceva note al pub&shy;<lb/>blico nel Giugno di quel medesimo anno 1672 le sue opposizioni, rispondeva <lb/>il Newton nell'Aprile dell'anno seguente, dicendo che il reverendo Padre <lb/>era allucinato, per non avere atteso che, cos&igrave; nel far l'esperienza come nel&shy;<lb/>l'istituire il calcolo della varia refrangibilit&agrave; de'raggi, s'erano anzi adoperate <lb/>le uguali inclinazioni. </s>

<s>&ldquo; Sed hallucinatus est Rever. </s>

<s>Pater, nam refractiones <lb/>a diversa parte Prismatis, quantum potest inaequales statuit R. P. Pardies, <lb/>cum tamen ergo tum in experimentis, tum in calculo de experimentis illis <lb/>inito, aequales adhibuerim &rdquo; (ibi, pag. </s>

<s>24). </s></p><p type="main">

<s>Confessando il reverendo Padre che la risposta fattagli era ingegnosis&shy;<lb/>sima non per questo si assoggetta a consentir che, per le varie refrangibi&shy;<lb/>lit&agrave; de'raggi, l'immagine del Sole attraverso al prisma, debba riuscire cos&igrave; <lb/>allungata. </s>

<s>Pensa che ci&ograve; possa essere per qualche somiglianza che abbia <lb/>questo coll'altro fenomeno grimaldiano. </s>

<s>&ldquo; Etenim in ea hypothesi, quam fuse <lb/>explicat noster Grimaldus, in qua supponitur lumen ease substantia quae&shy;<lb/>dam rapidissime mota, posset fieri aliqua diffusio luminis post transitum fo&shy;<lb/>raminis et decussationem radiorum. </s>

<s>Item in ea hypothesi, qua lumen poni&shy;<lb/>tur progredi per certas quasdam materiae subtilis undulatione, ut explicat <lb/>subtilissimus Hookius, possunt explicari colores per certam quandam diffu&shy;<lb/>sionem atque expansionem undulationuum, quae fiat ad latera radiorum <lb/>ultra foramen, ipso contagio ipsaque materiae continuatione &rdquo; (ibi, pag. </s>

<s>28). </s></p><pb xlink:href="020/01/662.jpg" pagenum="105"/><p type="main">

<s>Ecco la prima volta che risuona all'orecchio del Newton il nome del <lb/>Grimaldi. </s>

<s>Della scoperta di lui non par ne sappia pi&ugrave; avanti di quel che ne <lb/>accenna ivi il Pardies, e risponde che quella dell'Hook niente altro &egrave; che <lb/>un'ipotesi, la quale non ha nulla che rivedere coi fatti. </s>

<s>Io, dice il Newton, <lb/>professo i varii gradi di refrangibilit&agrave; della luce come un fatto da me sco&shy;<lb/>perto, e in varii e diligentissimi modi sperimentato, non come un'ipotesi, <lb/>ch'io mi sia cavata dal mio proprio cervello: e non &egrave; buona regola di filo&shy;<lb/>sofare il concluder che una cosa &egrave;, dal supporre che potrebb'essere. </s>

<s>&ldquo; Opti&shy;<lb/>mus enim et tutissimus philosophandi modus videtur, ut in primis verum <lb/>proprietates diligenter inquiramus et per experimenta stabiliamus, ac dein <lb/>tardius contendamus ad hypotheses per earum explicatione. </s>

<s>Nam hypotheses <lb/>ad explicandas rerum proprietates tantum accommodari debent et non ad <lb/>determinandas usurpari &rdquo; (ibi, pag. </s>

<s>29). E prosegue a dir che non nega po&shy;<lb/>tersi lo spettro allungato e i suoi colori spiegare per mezzo della teoria delle <lb/>ondulazioni dell'Hook e anche per via del moto rotatorio de'globuli del Car&shy;<lb/>tesio, ma comunque vogliasi dar ragione del fatto a lui basta si ammetta la <lb/>verit&agrave; del fatto, la quale consiste ne'varii gradi di refrangibilit&agrave; della luce. </s></p><p type="main">

<s>Qui termina la controversia col Pardies, il quale confess&ograve; di essere pie&shy;<lb/>namente sodisfatto delle ragioni del Newton, ma questi ripensava tuttavia a <lb/>quel <emph type="italics"/>Grimaldus noster<emph.end type="italics"/> e a quella diffusione del lume dop'avere attraver&shy;<lb/>sato il foro della camera oscura, di che gli parlava dianzi quel suo opposi&shy;<lb/>tore. </s>

<s>Ed ecco di qui l'occasione e il motivo ch'ebbe il Filosofo inglese d'in&shy;<lb/>formarsi meglio degli sperimenti, e di rivolger la sua mente alle speculazioni <lb/>del nostro Ottico di Bologna. </s></p><p type="main">

<s>Quanto al fatto, ritrov&ograve; che, adoprando per corpo opaco attraversato al <lb/>raggio, un capello, l'ombra era veramente maggiore, e si vedevano le tre <lb/>frange colorite precisamente a quel modo che le aveva descritte l'Autore <lb/><emph type="italics"/>De Lumine.<emph.end type="italics"/> Quanto alla teoria, trov&ograve; che l'ipotesi della diffrazione non era <lb/>comunemente accettata: i pi&ugrave; sostenevano che il raggio si piega rasente il <lb/>sottilissimo corpo opaco, per la ragione delle rifrazioni ordinarie nell'aria. </s>

<s><lb/>Ma il Newton dimostr&ograve; che la rifrazione ordinaria non aveva alcuna parte <lb/>nel fenomeno, e ci&ograve; fece stringendo il capello fra due lamine di tersissimo <lb/>vetro, fra le quali si distendeva ugualmente, per effetto di capillarit&agrave;, un <lb/>velo sottilissimo di acqua. </s>

<s>Misurata la larghezza dell'ombra del capello in <lb/>aria e in acqua, trov&ograve; che sempre si manteneva la stessa: &ldquo; Cum laminam <lb/>vitream perpolitam madefecissem, capillumque in aqua super id vitrum po&shy;<lb/>suissem, aliamque deinde laminam vitream perpolitam superimposuissem, ut <lb/>adeo aqua repleret id omne spatii quod inter vitra interiaceret, tenui lami&shy;<lb/>nas hasce in radio luminis antedicto, ita ut lumen per vitra ad perpendicu&shy;<lb/>lum transiret, iamque umbra capilli, iisdem iterum interiectis intervallis, <lb/>eandem, ac ante, magnitudinem habebat. </s>

<s>Porro rasurae, quae forte in poli&shy;<lb/>tis vitri laminis inessent, umbras itidem proiiciebant, multo utique quam <lb/>fieri debuit latiores: itemque venae in eiusmodi politis vitri laminis, um&shy;<lb/>beas latiores similiter proiiciebant. </s>

<s>Quare nimia harum umbrarum latitudo, <pb xlink:href="020/01/663.jpg" pagenum="106"/>non ex aeris scilicet refractione, sed omnino ex alia aliqua causa oriatur ne&shy;<lb/>cesse est &rdquo; (Optices, Lib. </s>

<s>III, Observ. </s>

<s>I, Paduae 1773, pag. </s>

<s>127). </s></p><p type="main">

<s>&Egrave; ella dunque la diffrazion grimaldiana la causa del fenomeno? </s>

<s>Il Newton <lb/>non risponde ancora, ma seguita a sperimentare con pi&ugrave; esattezza che mai, <lb/>variando ingegnosamente modi e osservando con pi&ugrave; grande attenzione. </s>

<s><lb/>Prende un pezzetto di cartone, lo tinge da tutt'e due le parti di nero, vi <lb/>fa nel mezzo un forellino quadrato, e v'incolla una lama sottilissima e acu&shy;<lb/>tissima in modo, che esca fuori dell'orlo del quadretto, e ne intercetti qual&shy;<lb/>che poco la luce. </s>

<s>Attraversa il cartone cos&igrave; preparato al raggio del sole ri&shy;<lb/>cevuto dentro la camera oscura, osserva il solito piegarsi di quel raggio nel <lb/>rasentar la punta metallica, e gli par che sia quel piegarsi quasi come se <lb/>fosse il raggio misteriosamente attratto verso la stessa punta per una nuova <lb/>magnetica simpatia. </s>

<s>Nota inoltre che i raggi sembrano essere attratti pi&ugrave; o <lb/>men fortemente secondo che passano dalla punta della lamina o dal sotti&shy;<lb/>lissimo coltro pi&ugrave; o meno lontani. </s></p><p type="main">

<s>La questione dall'Ottica era fatta passare cos&igrave; ad esser parte de'prin&shy;<lb/>cipii filosofici, che rendono le ragioni matematiche delle propriet&agrave; universali <lb/>della materia, e l'Autore ridusse perci&ograve; queste speculazioni nel Libro immor&shy;<lb/>tale dove scrisse quegli stessi <emph type="italics"/>Principii.<emph.end type="italics"/> &ldquo; Radii autem in aere existentes, <lb/>uti dudum Grimaldus, luce per foramen in tenebrosum cubiculum admissa, <lb/>invenit et ipse quoque expertus sum, in transitu suo prope corporum vel <lb/>opacorum vet perspicuorum angulos, quales sunt nummorum ex auro, ar&shy;<lb/>gento et aere cusorum termini rectanguli circulares, et cultrorum, lapidum, <lb/>aut fractorum vitrorum acies, incurvantur circum corpora quasi attracti in <lb/>eadem; et ex his radiis qui in transitu illo propius accedunt ad corpora in&shy;<lb/>curvantur magis quasi magis attracti ut ipse etiam diligenter observavi. </s>

<s>Et <lb/>qui transeunt ad maiores distantias adhuc maiores incurvantur aliquantulum <lb/>ad partes contrarias, et tres colorum fascias efformant &rdquo; (Lib. </s>

<s>I, Genevae 1739, <lb/>pag. </s>

<s>539, 40). </s></p><p type="main">

<s>Il modo particolare poi come il Newton immaginava che si formassero <lb/>le tre fasce de'colori nel fenomeno grimaldiano lo aveva scritto gi&agrave; nella <lb/>Questione II e III del III Libro dell'Ottica, cos&igrave; dicendo: &ldquo; Annon radii qui <lb/>differunt inter se refrangibilitate, iidem flexibilitate quoque inter se diffe&shy;<lb/>runt? </s>

<s>Et diversis suis singolurum inflexionibus ita porro a se invicem se&shy;<lb/>parantur, ut ordinatim exinde in ternas illas finibrias coloratas digerantur? <lb/></s>

<s>&mdash; Annon radii luminis inter transeundum prope corporum extremitates <lb/>inflectuntur ultro citroque, motu quodam undante ac sinuoso instar anguil&shy;<lb/>lae? </s>

<s>Ternaeque luminis colorati fimbriae supra memoratae ex ternis istius&shy;<lb/>modi inflexionibus oriuntur? (ediz. </s>

<s>cit., pag. </s>

<s>138). </s></p><p type="main">

<s>Queste fantasie, nelle quali veramente non si riconosce pi&ugrave; il Newton, <lb/>che pare essersi rifugiato per un momento sotto le tende del Cartesio o del <lb/>Gassendo, porsero occasione e dettero poi motivo di far sentenziare agli Ot&shy;<lb/>tici, che le frange grimaldiane non erano altrimenti possibili a essere spie&shy;<lb/>gate che nell'ipotesi delle ondulazioni. </s>

<s>Il Pardies fu de'primi fra costoro e <pb xlink:href="020/01/664.jpg" pagenum="107"/>de'pi&ugrave; antichi, n&egrave; &egrave; da passare a questo proposito sotto silenzio che il Ge&shy;<lb/>suita parigino citi l'Hook e non il confratello suo Bolognese, di cui piut&shy;<lb/>tosto egli segue con fedelt&agrave; le dottrine. </s>

<s>Imperocch&egrave; mentre il famoso con&shy;<lb/>cittadino del Newton professa l'ipotesi della diffusione delle onde eteree <lb/>eccitate per ogni verso dal vibrare del corpo luminoso, il Pardies ammet&shy;<lb/>teva quegli increspamenti superficiali e quelle ondose diffrazioni, che si co&shy;<lb/>municano lateralmente all'altra parte del lume diffuso, conforme a ci&ograve; che <lb/>leggemmo nel Trattato <emph type="italics"/>De lumine.<emph.end type="italics"/></s></p><p type="main">

<s>Ci&ograve; sarebbe argomento che l'Ottica del Grimaldi non fosse tenuta al&shy;<lb/>lora in grande onore, nemmeno appresso i suoi stessi confratelli, a riconci&shy;<lb/>liarsi co'pi&ugrave; cocciuti de'quali par che non bastasse all'Autore l'essersi con <lb/>strana risoluzione disdetto nelle sei proposizioni peripatetiche, contenute nel <lb/>Libro II. </s>

<s>Stanno in ogni modo queste cose a confermare quel che altrove <lb/>dicemmo che cio&egrave; n&egrave; in Italia n&egrave; fuori, non prima si apprezzarono le sco&shy;<lb/>perte grimaldiane che il Newton venisse a confermarle, dimostrando altres&igrave; <lb/>che i fatti nuovi come dipendevano da cause non ancora ben conosciute, <lb/>cos&igrave; volevano a spiegarli anche nuove ragioni. </s></p><p type="main">

<s>Queste nuove ragioni che secondo gli Ottici, specialmente moderni, non <lb/>s'hanno da'principii matematici neutoniani, da'pi&ugrave; si crede che vengan som&shy;<lb/>ministrate da quell'ipotesi dell'onde eteree, che l'Hook, nella patria del <lb/>Newton speculava, e che l'Huyghens poco dopo ridusse a maggior preci&shy;<lb/>sione geometrica. </s>

<s>Tanto hanno anzi cotesti ottici neoterici ferma fede nella <lb/>dottrina delle onde eteree diffusive del lume, che la professano, non come <lb/>probabile ipotesi, ma come certo e dimostrato sistema. </s>

<s>Su da que'calcoli, <lb/>che tanto ben rispondono alle speculazioni, si vede bollicare lo spirito car&shy;<lb/>tesiano, il quale, dopo quasi tre secoli, non ha smentita la sua natura, ch'&egrave; <lb/>di allettare anzi di affascinare le menti. </s>

<s>Ma non si vede come, seguendo col <lb/>Newton idee pi&ugrave; semplici e pi&ugrave; naturali, non s'abbia a dar quella sodisfa&shy;<lb/>zione agli intelletti, che si vuole esser data a loro da'soli eteristi. </s>

<s>Cos&igrave;, am&shy;<lb/>mettendo che gli atomi eterogenei del raggio sieno con varia forza attratti <lb/>verso il capello, e verso la punta acuta del coltro, si spiega come debba av&shy;<lb/>venire nel raggio stesso composto una dispersione, dalla quale hanno ori&shy;<lb/>gine gli iridescenti colori delle frange. </s>

<s>E se i raggi son tanto men forte&shy;<lb/>mente attratti quanto pi&ugrave; son lontani, s'intende come la seconda frangia si <lb/>mostri men vivamente accesa della prima, ma per&ograve; anche meno sbiadita <lb/>della terza. </s>

<s>E se all'ultimo quella virt&ugrave; attrattiva, dopo l'intervallo occupato <lb/>da tre raggi l'uno dietro l'altro, &egrave; per riuscire insensibile, s'intende come <lb/>tre sole e non pi&ugrave; sieno le frange colorate. </s></p><p type="main">

<s>Anche l'altro cos&igrave; singolare fenomeno che fece dire al Grimaldi luce <lb/>sopraggiunta a luce produrre oscurit&agrave;, non si vede come sia impossibile spie&shy;<lb/>garlo senza ricorrere all'ipotesi delle <emph type="italics"/>Interferenze.<emph.end type="italics"/> Disposto pure l'esperi&shy;<lb/>mento a modo del Fresnel, gli atomi dell'un raggio, che obliquamente in&shy;<lb/>contrano gli atomi dell'altro, urtandosi con vario impeto, secondo la variet&agrave; <lb/>della loro natura, possono esser sufficienti a produr quella dispersione, per <pb xlink:href="020/01/665.jpg" pagenum="108"/>cui si veggano apparire i colori col&agrave; dove si credeva che ci dovesse brillar <lb/>pi&ugrave; che mai vivo e schietto il candor della luce. </s></p><p type="main">

<s>Queste son senza dubbio ipotesi soggette a molte difficolt&agrave;, ma son pure <lb/>ipotesi anche quelle degli eteristi, che non vanno esenti da difficolt&agrave; forse <lb/>maggiori. </s>

<s>Ma perch&egrave; ufficio nostro &egrave; non di giudicar direttamente, ma dai <lb/>fatti narrati far resultare spontanei i giudizii, potranno questi stessi giudizii <lb/>intorno alla pi&ugrave; probabile ipotesi della natura e del modo di diffondersi la <lb/>luce, nella mente di coloro a cui gli lasciamo, resultare pi&ugrave; retti, dal nar&shy;<lb/>rar ci&ograve; che fu immaginato e pensato dai Filosofi per intendere la natura e <lb/>l'origine de'colori. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>I Peripatetici, i quali dicevano la luce non essere sostanza, ma qualit&agrave; <lb/>accidentale, interrogati intorno alla natura de'colori rispondevano essere una <lb/>qualit&agrave; della luce, cosicch&egrave; venivano a definirli un'accidentalit&agrave; di una ac&shy;<lb/>cidentalit&agrave;, ossia una vana apparenza e un puro nome. </s>

<s>Coloro per&ograve;, che pi&ugrave; <lb/>particolarmente si dettero allo studio dell'Ottica, definirono in qualche modo <lb/>le idee, e comunque venisse lor fatto le confortarono dell'esperienza. </s>

<s>Se&shy;<lb/>condo Alhazeno e Vitellione i colori permanenti son propriet&agrave; de'corpi e la <lb/>luce che gli tocca o gli attraversa si riveste delle loro forme, ci&ograve; che dice&shy;<lb/>vano esser patente da quel che di fatto si osserva, quando passa un raggio <lb/>di sole attraverso ai vetri di una finestra. </s>

<s>&ldquo; Item lucem res coloratas per&shy;<lb/>transeuntem illarum coloribus colorari, ut patet de luce transeunte vitrias <lb/>fenestras, quae illorum vitrorum coloribus informatur, secum formas illorum <lb/>colorum super obiecta corpora deferendo &rdquo; (Vitellionis Perspectiva, Norim&shy;<lb/>bergae 1535, pag. </s>

<s>38, v.). </s></p><p type="main">

<s>Ben assai pi&ugrave; difficile rimaneva l'investigar l'origine de'colori evane&shy;<lb/>scenti, che si producono per rifrazione o attraverso alle gocciole dell'acqua, <lb/>come nell'iride o attraverso ai prismi cristallini esposti al sole, a che Vi&shy;<lb/>tellione confessa di non esser giunto se non che <emph type="italics"/>post multos cogitatus et <lb/>experientias<emph.end type="italics"/> (ibi, pag. </s>

<s>287, v.). Frutto di quelle speculazioni e di quelle <lb/>esperienze fu la conclusione che i colori iridescenti sono generati dal mi&shy;<lb/>schiarsi che fa il bianco della luce colla negrezza propria dell'acqua e del <lb/>cristallo. </s>

<s>Dov'&egrave; men ombra ivi il colore &egrave; rosso, dove l'ombra &egrave; massima, <lb/>azzurro; il verde si genera nel mezzo dove si contempera l'ombra alla luce. <lb/></s>

<s>&ldquo; Apparent autem colores in istis luminibus sic reflexis vel refractis propter <lb/>mixtionem nigredinis coloris cristallini cum lumine penetrante, et propter <lb/>ammixtiones umbrarum partium ipsius cristalli praeminentium secundum <lb/>acumen suorum angulorum &rdquo; (ibi, pag. </s>

<s>296). </s></p><p type="main">

<s>Queste dottrine di Vitellione si ripeterono poi per lungo tempo quasi <lb/>da tutti i Filosofi, e non si dubitava di professarle in quell'et&agrave;, in cui gi&agrave; <pb xlink:href="020/01/666.jpg" pagenum="109"/>l'Ottica prometteva di progredire a pari delle altre scienze sperimentali. </s>

<s>Ecco <lb/>quel che il De Dominis, spiegando meglio i concetti dell'antico Maestro, <lb/>scriveva in sul finir del secolo XVI intorno alla natura e all'origine de'co&shy;<lb/>lori: &ldquo; Praeter colores proprios corporum in ipsis corporibus permanentes, <lb/>ex quacumque tandem causa illi resultent et oriantur, dantur in natura co&shy;<lb/>lores aliqui mutabiles et variabiles, qui dicuntur emphatici et apparentes, <lb/>quos ego colores splendidos soleo vocare. </s>

<s>Hos colores ex luce oriri mihi non <lb/>est dubium, imo nihil aliud sunt quam ipsamet lux, nam si in aliquo cor&shy;<lb/>pore pura sit lux, ut in astris et igne, et ex aliqua causa scintillationem <lb/>amittat, tale corpus fit nobis album. </s>

<s>Quod si luci admisceatur opacitas ali&shy;<lb/>qua, quae tamen lucem totam non impediat aut extinguat, intermedii colo&shy;<lb/>res oriuntur. </s>

<s>Idcirco enim ignis noster rubescit quoniam admistos habet <lb/>fumos qui ipsum opacant. </s>

<s>Idcirco etiam sol et astra rubescunt prope hori&shy;<lb/>zontem, quia vapores interpositi illa opacant. </s>

<s>Atque hos intermedios colores <lb/>tres proprie possumus enumerare: prima enim opacitatis admistio, quae albe&shy;<lb/>dinis candorem aliquantum offuscat, facit ipsam lucem puniceam seu ru&shy;<lb/>beam; puniceus enim, seu rubeus color, est maxime lucidus ex intermediis; <lb/>inter extremos, album et nigrum, ut patet manifeste in vitro oblongo trian&shy;<lb/>gulari. </s>

<s>Radius enim solis qui penetrat vitrum prope angulos, ubi minima <lb/>est crassities, et consequenter minima opacitas, puniceus egreditur. </s>

<s>Proxime <lb/>sequitur viridis ex maiori crassitie, ultimus purpureus, quem pavonaceum <lb/>vocamus ex maiori adhuc crassitie, nam pro quantitate crassitiei opacitas <lb/>intenditur et remittitur. </s>

<s>Paulo maior itaque opacitas facit colorem viridem, <lb/>quod si adsit adhuc maior opacitas color erit coeruleus seu purpureus, qui <lb/>ex intermediis est maxime obscurus. </s>

<s>Si demum adhuc magis opacitas inten&shy;<lb/>datur, extinguit totam lucem, et remanet nigredo; quamvis nigredo sit po&shy;<lb/>tius privatio lucis quam color positivus, unde et sensus eodem modo indicat <lb/>meras tenebras atque corpora maxime nigra. </s>

<s>Reliqui vero colores sunt ex <lb/>his misti &rdquo; (De radiis visus et lucis, Venetiis 1611, pag. </s>

<s>9, 10). </s></p><p type="main">

<s>Il De Dominis fece senza dubbio un gran passo, quando, tolte di mezzo <lb/>le forme e le qualit&agrave; accidentali, sentenzi&ograve; che i colori enfatici <emph type="italics"/>nihil aliud <lb/>sunt quam ipsamet lux,<emph.end type="italics"/> ma soggiogato del resto dall'autorit&agrave; di Vitellione <lb/>non seppe veder che la causa efficiente del fenomeno non consisteva nella <lb/>crassizie del mezzo, ma nelle rifrazioni. </s>

<s>Uno de'primi a riconoscere questa <lb/>verit&agrave; e a professarla contro l'errore antico, fu quel Ferrante Imperato, che <lb/>quasi in quello stesso tempo, in cui il celebre Spalatrese meditava i suoi <lb/>diottrici teoremi, dava opera a descrivere la <emph type="italics"/>Historia naturale.<emph.end type="italics"/> L'Autore di <lb/>questa ben si avvide che lo spettro nel prisma era un effetto della rifra&shy;<lb/>zione, e, presentendo la scoperta neutoniana della luce composta, disse che <lb/>l'oscurit&agrave;, pel mescolamento della quale si generano i colori, non era nel <lb/>mezzo, ma ne'raggi della luce stessa. </s>

<s>&ldquo; Veggiamo e con l'uso e con la ra&shy;<lb/>gione tutte le differenze de'colori distintissimamente esser rappresentate da <lb/>corpi di sostanza ugualissima, purch&egrave; vi sia rifrangimento de'raggi tale, che <lb/>gli lucidi ed opachi si meschino, come si vede ne'globi ed ampolle chiaris-<pb xlink:href="020/01/667.jpg" pagenum="110"/>sime di vetro, e nelle colonne triangolari, istrumento di rifrazione all'os&shy;<lb/>servazione della generazion de'colori tra gli altri tutti ottimo &rdquo; (Cap. </s>

<s>XVI, <lb/>Venezia 1672, pag. </s>

<s>294). </s></p><p type="main">

<s>Ma perch&egrave; le idee dell'Imperato non ebbero grande efficacia ne'pro&shy;<lb/>gressi dell'Ottica, e il gran Padre della scienza risorta, Giov. </s>

<s>Keplero, si <lb/>mostr&ograve; per questa parte inferiore a s&egrave; stesso, dicendo che i colori eran luce <lb/>in potenza e nella materia de'diafani consepolta; l'efficienza delle rifrazioni, <lb/>in produrre i colori enfatici, non fu riconosciuta n&egrave; professata dagli Ottici, <lb/>prima che si divulgassero gl'insegnamenti del Maurolico. </s></p><p type="main">

<s>Nel Teorema XXIX del II, in cui proponesi di dimostrar che i colori <lb/>principali dell'iride son quattro, cio&egrave; rosso, verde, azzurro e violetto, l'Autor <lb/>de'libri <emph type="italics"/>Diaphanorum partes<emph.end type="italics"/> procede a questo modo: Nella sfera ED (fig. </s>

<s>39) <lb/>che rappresenta il Sole, prende quattro piccoli cerchi uguali EO, ON, NM, <lb/>MD, e da ciascun punto delle divisioni fa muovere i raggi EF, OF, NF, <lb/><figure id="id.020.01.667.1.jpg" xlink:href="020/01/667/1.jpg"/></s></p><p type="caption">

<s>Figura 39.<lb/>MF, DF, i quali nel pun&shy;<lb/>to F di una gocciola di <lb/>acqua FBC si refran&shy;<lb/>gono in FC, FL, FK, FH, <lb/>FB. </s>

<s>Cos&igrave; fatto, a provar <lb/>che in BH deve essere il <lb/>rosso e in HK il verde, <lb/>il Maurolico dice: &ldquo; A <lb/>maiori solis superficie il&shy;<lb/>luminatur BH quam HK, et ideo necesse est ut color qui in BH, cui plus lucis <lb/>admiscetur, ipsi luci conformior sit: color vero qui in HK, cui plus aquae <lb/>inest quam lucis, sit aquae similior, atque ideo color qui in BH flammeus <lb/>sive croceus, qui vero in HK, viridis videtur &rdquo; (Neapoli 1611, pag. </s>

<s>54, 55). A <lb/>provar poi che in LK dee essere il colore azzurro e in LC il violetto, il no&shy;<lb/>stro Autore cos&igrave; prosegue: &ldquo; Et quamvis LC a superficie EO, quae ipsi DM <lb/>ipsam BH illuminanti, aequalis est, illuminetur, et ideo color qui in LC, si&shy;<lb/>milis ei qui in BH videri oporteat, tamen, quia gyrus Iridis in LC minor <lb/>est quam in BH, ideo radii in LC densiores sunt quam in BH, quare color, <lb/>qui in LC fortior ac coloratior eo qui in BH, croceus videtur, in LC rufus, <lb/>sive purpureus generabitur. </s>

<s>Similiter, quamvis LK a superficie NO .... illu&shy;<lb/>minetur, ideoque, qui in LK, ei qui in KH similem videri oporteret; tamen, <lb/>quia gyrus Iridis in LK minor est quam in KH, ideo radii in LK densiores <lb/>sunt quam in KH, quare color, qui in LK, fortior ac coloratior eo, qui in <lb/>KH videtur. </s>

<s>Sed cum in KH viridis, qui levis ac sobrius est, videatur, in KL <lb/>ceruleus, qui fortior ac saturior est, videbitur &rdquo; (ibi, pag. </s>

<s>55). </s></p><p type="main">

<s>Qualunque sia per&ograve; il giudizio che si vuol dare di queste maurolicane <lb/>speculazioni, non si pu&ograve; negar che non sia strano ammetter che, l&agrave; dove &egrave; <lb/>pi&ugrave; condensata la luce, ivi il colore debba apparir pi&ugrave; fosco. </s>

<s>Il Maurolico <lb/>fu condotto a dir ci&ograve; sull'esempio del color della fiamma e de'carboni ac&shy;<lb/>cesi. </s>

<s>&ldquo; Et notandum quod, sicut ignis levis ac rarus flammeum ac croceum <pb xlink:href="020/01/668.jpg" pagenum="111"/>efficit colorem, velut flamma lenem fumum comburens, densus vero ac for&shy;<lb/>tis ebrium ac rufum gignit colorem, velut in carbonibus &rdquo; (ibi). Ma non <lb/>per questo fu poi l'Autore seguito dagli Ottici, i quali pi&ugrave; ragionevolmente <lb/>ritennero che, l&agrave; dove la luce &egrave; pi&ugrave; condensata, ivi debbano i colori esser <lb/>pi&ugrave; risplendenti. </s></p><p type="main">

<s>Il Boulliaud, nella proposizione XXIX del suo Trattato <emph type="italics"/>De natura lu&shy;<lb/>cis,<emph.end type="italics"/> cos&igrave; scriveva della luce, che refratta nelle lenti cristalline o ne'prismi, <lb/>genera la variet&agrave; de'colori: &ldquo; Fortis lux et condensata coloribus splenden&shy;<lb/>tibus tinguit. </s>

<s>Si enim lentem vitream soli opponas et radios post traiectio&shy;<lb/>nem in alba charta excipias, in medio illuminationis color maxime vividus <lb/>coruscat, in confinio umbrae colores paulatim infuscantur. </s>

<s>Hic vero colores <lb/>papyro albae aut chartae non insunt, neque in vitrea lente, sed a lumine <lb/>deferuntur, cui insunt, et pro luminis fortitudinem et extenuationem mu&shy;<lb/>tantur &rdquo; (Parisiis 1638, pag. </s>

<s>43). </s></p><p type="main">

<s>Il Grimaldi nonostante, il quale ben riconobbe l'importanza del sog&shy;<lb/>getto, e presenti che dal diligente esame dello spettro solare sarebbe uscita <lb/>la vera teoria de'colori, fu colui che dimostr&ograve; come i pi&ugrave; risplendenti erano <lb/>quelli davvero, dove i raggi, nella ineguale dispersione spettrale attraverso <lb/>all'acqua o &agrave;l cristallo, riuscivano pi&ugrave; costipati. </s>

<s>Sia RBCD (fig. </s>

<s>40) un vaso <lb/><figure id="id.020.01.668.1.jpg" xlink:href="020/01/668/1.jpg"/></s></p><p type="caption">

<s>Figura 40.<lb/>di porcellana, il candido fondo del quale sia rico&shy;<lb/>perto d'acqua infino al livello EP. Sia, nel punto A <lb/>della sponda di esso vaso, un'apertura, attraverso <lb/>alla quale, decussati i raggi che vengon dal sole, <lb/>cadano a illuminare ugualmente la superficie MN <lb/>dell'acqua, ma variamente il fondo OPQ del vaso, <lb/>che brilla di tre pi&ugrave; distinti colori. </s>

<s>Dice il Grimaldi <lb/>che questi colori son dovuti alla varia costipazione <lb/>de'raggi, dopo aver subite nell'acqua le rifrazioni. </s>

<s><lb/>Verso NQ quegli stessi raggi son pi&ugrave; costipati, e <lb/>il colore ivi perci&ograve; &egrave; il pi&ugrave; vivamente splendido <lb/>o il rosso: verso MO i raggi son pi&ugrave; dissipati, <lb/>e perci&ograve; il colore &egrave; ivi il pi&ugrave; fosco o il violetto. </s>

<s>Che poi verso NQ i raggi <lb/>sien pi&ugrave; costipati, si prova dall'Autore in questo facile modo: Divide il fa&shy;<lb/>scio incidente AMN in due parti uguali, colla bissettrice AI, la quale si ri&shy;<lb/>frange in IP, cosicch&egrave;, nello spazio occupato dalla luce refratta IQ, debbasi <lb/>ritrovar la medesima copia di raggi che nell'altro spazio MP. </s>

<s>Ma questo, per <lb/>la legge delle rifrazioni, risulta di maggior misura e capacit&agrave; di quello, dun&shy;<lb/>que in IQ i raggi convien che veramente vi stieno pi&ugrave; condensati. </s>

<s>&ldquo; Siqui&shy;<lb/>dem tantumdem radiorum debet intelligi inter duos refractos IP et NQ quan&shy;<lb/>tum intelligitur inter duos IP et MO item refractos, quemadmodum aequalis <lb/>portio luminis ac radiorum continatur inter duos directos GI, LN, ac inter <lb/>duos directos GI, HM, quia nimirum aequalis portio solis radiat per fora&shy;<lb/>men A ad aquae superficiei partem IN, atque ad partem IM. </s>

<s>Cum ergo an&shy;<lb/>gustius sit spatium inter refractos NQ et IP contentum, quam contentum <pb xlink:href="020/01/669.jpg" pagenum="112"/>inter duos IP et MO, ob maiora incrementa refractionum in radiis magis <lb/>inclinatis, ut supra advertebamus ex Optica, sequitur necessario constipari <lb/>magis radios in spatio IPQN, quam in spatio IPOM, quia aequales numero <lb/>radii non possunt non esse magis conferti in spatio angustiore quam in la&shy;<lb/>xiore. </s>

<s>Praeterea in huiusmodi radiatione terminata super candido vasis fundo <lb/>BC videmus colorem subrubeum aut flavum ad partes Q, ubi lumen magis <lb/>densatur, ad partes autem O, ubi lumen laxius diffusum est, observamus co&shy;<lb/>lorem caeruleum, qui sane obscurior est praedictis duobus in parte oppo&shy;<lb/>sita observatis &rdquo; (De lum., Bononiae 1665, pag. </s>

<s>256). </s></p><p type="main">

<s>In tutte queste speculazioni per&ograve; i colori non son riguardati se non che <lb/>obiettivamente, come una modificazione sopravvenuta nel suo refrangersi alla <lb/>luce. </s>

<s>Ma pure &egrave; un fatto che dee l'occhio subiettivamente percepire le va&shy;<lb/>riet&agrave; di cos&igrave; fatte modificazioni, e per esse aver senso e discrezione delle <lb/>variet&agrave; degli stessi colori. </s>

<s>Il Cartesio attese a risolvere, per ci&ograve; che princi&shy;<lb/>palmente riguarda il lato subiettivo, il difficile e curioso problema, e ben&shy;<lb/>ch&egrave;, per le sue troppo capricciose e incongruenti ipotesi, non riuscisse a dar <lb/>sodisfazione a'pi&ugrave; giudiziosi, apr&igrave; nulladimeno nuove splendide vie di filo&shy;<lb/>sofare agl'ingegni. </s></p><p type="main">

<s>Riducendo il senso della vista a una impressione tattile prodotta sulla <lb/>retina dai corpuscoli duri messi in moto dalla sistole e dalla diastole del <lb/>corpo luminoso, il Cartesio immagin&ograve; che quegli stessi corpuscoli duri, nel <lb/>penetrar per la porosit&agrave; de'corpi diafani, urtati pi&ugrave; o men fortemente e ora <lb/>da una parte ora dall'altra, venissero a ricevere e a far sentire alla retina <lb/>l'impressione di un moto rotatorio pi&ugrave; o meno veloce, cosicch&egrave;, da questa <lb/>maggiore o minore velocit&agrave;, ne risultasse il senso del colore o pi&ugrave; splendido <lb/>e vivace o pi&ugrave; fosco e abbacinato. </s>

<s>&ldquo; Et mea quidem sententia manifeste ex <lb/>his omnibus liquet naturam colorum tantum in eo consistere quod particu&shy;<lb/>lae materiae subtilis, actionem luminis transmittentes, maiori impetu et vi <lb/>rotari nitantur quam secundum lineam rectam moveri, ita ut, qui multo va&shy;<lb/>lidius rotari nituntur, rubicundum colorem efficiant, et qui non nisi paulo <lb/>validius flavum &rdquo; e prosegue ad applicare agli altri colori dello spettro le <lb/>medesime dottrine. (Metereor., Cap. </s>

<s>VIII, Francof. </s>

<s>ad M. 1692, pag. </s>

<s>178). </s></p><p type="main">

<s>Questa dottrina del Cartesio parve al Grimaldi ingegnosa, e perci&ograve; si <lb/>volse a professarla, sostituendo, all'ipotesi del moto o dell'inclinazione al <lb/>moto de'corpuscoli duri, quella delle fluitazioni ondose del lume. </s>

<s>&ldquo; Itaque <lb/>dicimus tot notabiliter diversos colores ideo nobis apparere quia lumen tot <lb/>pariter diversas fluitationes recipit ac per eas diverso et proportionato illis <lb/>modo afficit sensorium visionis &rdquo; (De Lum. </s>

<s>cit., pag. </s>

<s>347). Cos&igrave; veniva a ri&shy;<lb/>trovare una nuova e splendida analogia fra la retina, che percossa dall'onda <lb/>luminosa d&agrave; il senso della vista, e il timpano che, percosso dall'onda so&shy;<lb/>nora, d&agrave; il senso dell'udito, intorno a che l'Autore si diffonde prolissamente <lb/>nella XLIV sua proposizione, bench&egrave; la miglior sostanza di lei si concluda <lb/>in queste parole: &ldquo; Cum ergo pro auditu admittenda sit in aere agitatio <lb/>adeo minute crispata, ut eius tremor omnem tactus sensationem subtilitate <pb xlink:href="020/01/670.jpg" pagenum="113"/>sua fugiat, cumque huiusmodi tremor debeat praeterea dici adeo varius ac <lb/>multiplex ut omnibus vocium et sonorum differentiis satisfaciat; multo ma&shy;<lb/>gis in luminis diffusione poterit concipi subtilissima illa et per quam varia <lb/>fluitatio, quae omnibus colorum speciebus in visione determinandis inser&shy;<lb/>vire debet, absque confusione radiorum a diversis obiectis vel obiectorum <lb/>particulis reflexorum &rdquo; (ibi, pag. </s>

<s>392). </s></p><p type="main">

<s>L'Hook e l'Huyghens poi ridussero a maggior precisione queste ipo&shy;<lb/>tesi, sostituendo ai globuli duri del Cartesio, il mobilissimo etere, e agli in&shy;<lb/>crespamenti superficiali del Grimaldi le onde sferiche mosse nell'etere stesso <lb/>dal vibrar del corpo luminoso, in quel modo che si muovono le onde aeree <lb/>eccitate dal tremor del corpo sonoro. </s></p><p type="main">

<s>Son tali i principii e i progressi delle dottrine tanto applaudite dagli <lb/>Ottici moderni, il germe delle quali si trova nulladimeno latente nelle spe&shy;<lb/>culazioni del primo discepolo di Galileo. </s>

<s>Benedetto Castelli professava in&shy;<lb/>torno alla luce la pi&ugrave; semplice e pi&ugrave; naturale delle ipotesi, che &egrave; quella <lb/>dell'emissione. </s>

<s>Ei non dubita perci&ograve; di asserire che gli atomi lucidi, come <lb/>tutti i corpi proietti, acquistano velocit&agrave; col tempo, e non producono la sen&shy;<lb/>sazione della luce bianca, se non che quando hanno raggiunto la massima <lb/>velocit&agrave; del loro moto: gli atomi men veloci danno l'apparenza dell'oscurit&agrave; <lb/>e dei colori. </s>

<s>Queste speculazioni l'applicava il Castelli a dimostrar non solo <lb/>la possibilit&agrave;, ma la necessit&agrave; delle macchie nel sole, e cos&igrave; in una lettera, <lb/>indirizzata a Galileo il d&igrave; 8 Maggio 1612, esprimeva quelle sue idee: </s></p><p type="main">

<s>&ldquo; Mosso poi da s&igrave; bella occasione di filosofare, dico prima che, se mi <lb/>fosse lecito filosofare del corpo lucido solare dai corpi luminosi nostri, direi <lb/>che non solo &egrave; necessario che queste macchie sieno nel corpo solare, ma <lb/>che io non posso pensare altrimenti. </s>

<s>Per dichiararmi meglio, piglio il lume <lb/>che si fa dalla carta bianca accesa dal fuoco. </s>

<s>Chiaro &egrave; che quella lucidezza <lb/>precede una negrezza o dir&ograve; oscurezza del pabulo di quella luce, quale a <lb/>poco a poco passando per l'azzurro e poi al rosso, finalmente diventa luce, <lb/>e quest'accidente &egrave; comunissimo a tutti que'corpi che spandono per s&egrave; stessi <lb/>luce. </s>

<s>Se dunque dal sole si spande luce, non &egrave; maraviglia se si ha il pas&shy;<lb/>saggio dal nero ed oscuro, ed appariscano quelle macchie. </s>

<s>Aggiungo, a con&shy;<lb/>ferma delle mie supposizioni della luce, che non essendo altro corpo lucido <lb/>che un corpo che vibra di continuo e scaglia corpuscoli velocissimi, ed es&shy;<lb/>sendo il sole lucido e conseguentemente saettando di continuo corpuscoli <lb/>velocissimamente, e non potendo i corpi principiare a partirsi con somma <lb/>velocit&agrave;, non mi faranno al sicuro quella apparenza che io chiamo luce, men&shy;<lb/>tre con tardit&agrave; si muovono. </s>

<s>Saranno dunque di necessit&agrave; le macchie nel sole, <lb/>che &egrave; quello che noi vediamo &rdquo; (MSS. Gal., T. III, P. X, c. </s>

<s>55). </s></p><p type="main">

<s>Le belle e sottili speculazioni per&ograve;, fatte intorno ai colori dal Castelli <lb/>al Cartesio, e dal Grimaldi all'Huyghens, accolte con tanto plauso dagli Ot&shy;<lb/>tici moderni, furono dal Newton messe a pari con quelle di Vitellione e del <lb/>De Dominis, e da lui tutte rifiutate ugualmente, <emph type="italics"/>cum omnes in communi <lb/>quodam errore consentiant, scilicet quod modificatio lucis qua singulos<emph.end type="italics"/><pb xlink:href="020/01/671.jpg" pagenum="114"/><emph type="italics"/>colores exhibet, ei non sit insita ab origine sua, sed inter reflectendum <lb/>vel refringendum acquiratur.<emph.end type="italics"/> (Lectiones opt., Paduae 1773, pag. </s>

<s>62). </s></p><p type="main">

<s>Scoperta ch'ebbe il Newton la varia refrangibilit&agrave; de'raggi, di che la <lb/>luce del sole gli result&ograve; composta, ne concluse indi immediatamente la sua <lb/>teoria de'colori. </s>

<s>&ldquo; Ut radii lucis inter se refrangibilitate discrepant, ita dif&shy;<lb/>ferunt insita quadam aptitudine ad exhibendum hunc vel illum certum co&shy;<lb/>lorem. </s>

<s>Colores non sunt lucis qualificationes ortae ex naturalium corporum <lb/>refractionibus, aut reflexionibus, ut vulgo creditur, sed primigeniae et con&shy;<lb/>genitae proprietates in diversis radiis diversae. </s>

<s>Aliqui radii tantum ad ru&shy;<lb/>brum, alii solum ad flavum, alii dumtaxat ad viridem colorem effingendum <lb/>apti sunt &rdquo; (Epistola De luce et color., Paduae 1773, pag. </s>

<s>6). </s></p><p type="main">

<s>Due, soggiunge il Newton, sono i generi dei colori, alcuni semplici e <lb/>primigenii, altri composti. </s>

<s>&ldquo; Colores primigenii sunt <emph type="italics"/>Ruber, Flavus, Viri&shy;<lb/>dis, Coeruleus<emph.end type="italics"/> et <emph type="italics"/>Violaceo-purpureus,<emph.end type="italics"/> una cum <emph type="italics"/>Aureo<emph.end type="italics"/> et <emph type="italics"/>Indico.<emph.end type="italics"/> Il bianco <lb/>&egrave; colore sempre composto e ci bisognano per comporlo tutt'e sette i colori <lb/>primigenii mescolati insieme con certa proporzione. </s>

<s>&ldquo; Saepius admirabun&shy;<lb/>dus observavi quod colores omnes a Prismate detecti, cum convergentes <lb/>redduntur, et hoc pacto rursus miscentur ita ut erant in luce, antequam in <lb/>Prisma incideret, iterum exhibent lucem prorsus et perfecte candidam et <lb/>nihil omnino, sensu indice, diversam a directa luce solari &rdquo; (ibi, pag. </s>

<s>8). </s></p><p type="main">

<s>I colori poi naturali, che s'appresentano alla superficie di tutti i corpi, <lb/>da null'altro, secondo il Newton, dipendono, se non da ci&ograve; che quelle stesse <lb/>superficie son costituite e disposte a rifletter pi&ugrave; copiosamente uno, che un'al&shy;<lb/>tro genere di raggi. </s>

<s>&ldquo; Cuius rei periculum feci in obscuro cubiculo super <lb/>haec corpora coniiciens radios simplices, at coloribus diversos. </s>

<s>Etenim hoc <lb/>pacto quodvis corpus quovis colore donari potest. </s>

<s>Tunc non habent colorem <lb/>proprium, sed semper illum adoptant, quo lux superiniecta praedita est &rdquo; <lb/>(ibi, pag. </s>

<s>9). </s></p><p type="main">

<s>Queste neutoniane dottrine erano cos&igrave; semplici e naturali e, indipen&shy;<lb/>dentemente da qualunque fantasticata ipotesi, cos&igrave; bene dimostrate dai fatti, <lb/>che quasi tutti gli Ottici si rivolsero a professarle, parendo ad essi che, in <lb/>cosa tanto lungamente desiderata, si fosse all'ultimo scoperta la faccia del <lb/>vero. </s>

<s>In Londra l'Epistola <emph type="italics"/>De luce et coloribus<emph.end type="italics"/> fu divulgata nel 1672; fra <lb/>noi &egrave; difficile il precisare quando s'introdussero quelle nuove ottiche dot&shy;<lb/>trine neutoniane, ma si pu&ograve; con gran probabilit&agrave; asserire che ci&ograve; non av&shy;<lb/>venisse prima del cominciar del secolo XVIII. </s></p><p type="main">

<s>Non sar&agrave; perci&ograve; senza una qualche importanza il chiudere questo pa&shy;<lb/>ragrafo di storia citando alcuni pensieri di Geminiano Montanari, a cui si <lb/>pu&ograve; credere che le novit&agrave; inglesi non fossero ancora approdate alle orec&shy;<lb/>chie; pensieri, che si leggono in una lettera di lui pubblicata da France&shy;<lb/>sco Bianchini nell'Introduzione al Dialogo postumo intitolato <emph type="italics"/>Le forze di <lb/>Eolo.<emph.end type="italics"/> Ivi il Montanari, dop'aver dimostrato che il minimo angolo visibile &egrave; <lb/>comunemente quello di un minuto, soggiunge: &ldquo; Quindi avviene perci&ograve; che, <lb/>mescolando insieme due o pi&ugrave; polveri di colore diverso, se ne produce un <pb xlink:href="020/01/672.jpg" pagenum="115"/>terzo color misto, non perch&egrave; ciascuna polvere partecipi intrinsecamente al&shy;<lb/>l'altra le sue qualit&agrave; come dissero alcuni, ma perch&egrave; le parti minute di <lb/>esse polveri sono cos&igrave; piccole, che non sottendendo un minuto ciascuna da <lb/>s&egrave; all'occhio, ne vanno a ciascun filamento i raggi di pi&ugrave; granella, e per&shy;<lb/>ci&ograve; le specie miste di pi&ugrave; colori, e producono nell'occhio la sensazione d'un <lb/>terzo colore da ciascun d'essi distinto. </s>

<s>Quindi &egrave; ancora che veduta in molta <lb/>distanza una fabbrica dipinta, ci si rappresenta d'un sol colore, ma misto <lb/>di tutti quelli che da vicino poi dipinti si scorgono &rdquo; (Parma 1694). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>I cenni storici che resultano dai documenti, da noi raccolti nel para&shy;<lb/>grafo precedente, mostrano che la prima e principale occasione, che mosse <lb/>e fece rivolgere gli Ottici a speculare intorno all'essere e alla generazion <lb/>de'colori, fu quel magnifico arco che il sole oriente od occidente cos&igrave; spesso <lb/>dipinge ai nostri occhi maravigliati sulla bassa volta di un ciel nuvoloso. </s>

<s>I <lb/>Filosofi antichi non lasciarono di esercitarvi attorno l'ingegno, e da quel <lb/>che si legge nel III Libro <emph type="italics"/>De placitis philosophorum<emph.end type="italics"/> di Plutarco par che <lb/>alcuni di essi fossero imboccati per quella diretta via, proseguendo per la <lb/>quale all'ultimo si sarebbe riusciti a intendere la ragione del fenomeno stu&shy;<lb/>pendo. </s>

<s>C'intravidero sagacemente l'opera delle rifrazioni de'raggi solari av&shy;<lb/>versi nelle stile roride della nube. </s>

<s>&ldquo; Siquidem animadvertere oportet umidam <lb/>exalationem in nubem verti subindeque in exiguas sensim stillas rorantes: <lb/>proinde in occiduales vergente sole partes necesse est arcum totum ex ad&shy;<lb/>verso soli visitari, quandoquidem visus stillis offensis refringitur, ox quo fit <lb/>arcus &rdquo; (Romae 1510, fol. </s>

<s>XXI). </s></p><p type="main">

<s>Che poi fosse veramente cos&igrave; lo confermarono que'Filosofi coll'espe&shy;<lb/>rienza: &ldquo; Hoc reipsa sic probare licet: si quis enim soli adversus aquam <lb/>ore sumat et ita insputet ut stillicidia repercussum in solem habeant, actu&shy;<lb/>tum comperit arcus imaginem factam &rdquo; (ibi). </s></p><p type="main">

<s>Anche l'Alighieri, seguendo i placiti di cos&igrave; fatti Filosofi, perch&egrave; l'aere <lb/>si mostri adorno di diversi colori, ammette come condizion necessaria che <lb/>egli sia <emph type="italics"/>ben piorno<emph.end type="italics"/> (Purg., XXV, v. </s>

<s>91) e per via delle riflessioni della luce, <lb/>simili a quelle del suono da cui nasce l'Eco, intende che nasca da quella <lb/>di dentro l'iride di fuori, quando vedonsi talvolta volgere per <emph type="italics"/>tenera<emph.end type="italics"/> nube <lb/>due archi paralleli e concolori (Par., XII, t. </s>

<s>4, 5). </s></p><p type="main">

<s>I placiti filosofici per&ograve; riferitici da Plutarco e cantati divinamente dal&shy;<lb/>l'Alighieri non sodisfacevano punto all'orgoglio peripatetico, a cui pareva <lb/>proprio una meschinit&agrave; ricorrere all'esperienza dell'acqua spruzzagliata dallo <lb/>sputo delle labbra per aria. </s>

<s>Ricorsero perci&ograve; a qualche cosa di pi&ugrave; pelle&shy;<lb/>grino, e immaginarono le nubi configurate in speechi o concavi o convessi, <lb/>secondo bisognava accomodarli meglio a produrre in cielo per riflessione le <lb/>mirabili apparenze dell'Arco. </s></p><pb xlink:href="020/01/673.jpg" pagenum="116"/><p type="main">

<s>Di cos&igrave; fatta forfora peripatetica aspersi uscirono fuori Alhazeno e Vi&shy;<lb/>tellione, in que'loro Trattati, da'quali si attingevano comunemente i responsi <lb/>a ogni sorta di ottiche dottrine, come da oracoli. </s>

<s>Cos&igrave; l'arabo Autore come <lb/>il pollacco riconoscono la primaria efficienza dell'Iride dalle riflessioni dei <lb/>raggi solari sulle stille roride, che compongon la nube, i quali raggi, se&shy;<lb/>condo che vengono riflessi da maggiore o minor profondit&agrave; della nube stessa, <lb/>uscendone fuori mescolati con pi&ugrave; o meno ombra, producono perci&ograve; la splen&shy;<lb/>dida variet&agrave; de'colori. </s>

<s>&ldquo; Item, quoniam a remotiori videtur, tale lumen ideo <lb/>debilius videtur: remotio enim sive protensio visibilis a visu est causa de&shy;<lb/>b&igrave;litatis visus. </s>

<s>Item quia vapor remotior a corpore luminoso grossior est et <lb/>nigrior, et magis aqueus, unde nigredo, vaporis lumini incorporatum plus <lb/>denigrat et magis ipsum visui obscuratum penetrat, et hoc quidem in co&shy;<lb/>loribus iridis aliquam causalitatem habent. </s>

<s>Totalis vero causa omnibus huius <lb/>coloribus universalis immixtio umbrarum ipsi fulgori luminis, quoniam enim, <lb/>ut patet per premissam, vapor roridus est materia iridis a cuius corpuscu&shy;<lb/>lis fit reflexio luminis ad visum, omnia corpora densa in parte luminoso cor&shy;<lb/>pori adversam umbram proiiciunt, patet quod radii reflexi a remotiorum <lb/>corpusculorum superficiebus, umbrarum anteriorum corpusculorum nigre&shy;<lb/>dini se immiscent, et sic permixti colore nigro umbrarum perveniunt re&shy;<lb/>flexi ad visum, et secundum quod plus vel minus umbrarum nigredine per&shy;<lb/>miscentur, secundum hoc diversificant actum suae luminositatis in varios <lb/>colores. </s>

<s>&rdquo; Alle quali sue teorie cerca l'Autore il conforto dell'esperienza in <lb/>un fenomeno di diffrazione in cui veramente l'iridescenza trasparisce di <lb/>mezzo alle ombre. </s>

<s>&rdquo; Et huius rei signum est in coloribus similibus iridi, <lb/>qui obducto visu ipsa manu vel alio umbroso de sub manu in fenestrarum <lb/>periferiis videntur &rdquo; (Vitellionis Perspectiva, edit. </s>

<s>cit., pag. </s>

<s>288). </s></p><p type="main">

<s>L'Iride secondaria, ne'placiti di alcuni di que'Filosofi citati da Plu&shy;<lb/>tarco, come abbiamo veduto in Dante, si faceva nascere per riflessione dalla <lb/>primaria, e bench&egrave; ci&ograve; non fosse punto conforme alla verit&agrave; delle cose, so&shy;<lb/>disfaceva nulladimeno agl'ingegni per l'esempio di ci&ograve; che vedesi negli spec&shy;<lb/>chi, ne'quali le immagini si rappresentano contrapposte, come contrapposti <lb/>si dipingono nella stessa Iride secondaria i colori. </s>

<s>A Vitellione per&ograve; questo <lb/>modo di salvar l'iride esterna, come troppo semplice, non piacque: crede <lb/>piuttosto ch'ella si faccia in una superficie gibbosa <emph type="italics"/>(Sic ergo in vapore ir&shy;<lb/>radiato fit quaedam gibbositas)<emph.end type="italics"/> pi&ugrave; lontana dall'occhio, e che perci&ograve; e per <lb/>esser maggiori gli angoli dell'incidenza, oltre al venir contrapposti i colori, <lb/>appariscano pi&ugrave; dilavati. </s>

<s>&ldquo; Omnes autem colores secundae iridis sunt debi&shy;<lb/>liores necessario coloribus primae Iridis, quoniam fiunt a radiis magis di&shy;<lb/>stantibus a perpendiculari, et secundum maiores angulos ad visum reflexis, <lb/>propter quod isti radii cum radiis incidentibus minus aggregantur, unde mi&shy;<lb/>nus efficiunt luminis et coloris &rdquo; (ibi, pag. </s>

<s>291). </s></p><p type="main">

<s>Tali erano le dottrine divulgate intorno all'Iride dal Maestro universale <lb/>della Scienza ottica, e sull'autorit&agrave; di lui da tutti approvate per vere, quando <lb/>gl'ingegni, riconosciuto all'ultimo essere una grande temerit&agrave; professare una <pb xlink:href="020/01/674.jpg" pagenum="117"/>cosa per vera, perch&egrave; un uomo reputato da tutti sapiente l'aveva insegnata, <lb/>si persuasero che maestra unica di verit&agrave; dev'esser piuttosto la Natura. </s>

<s>Fra <lb/>que'savi, che cos&igrave; la pensarono, fu quel Ferrante Imperato, che i nostri Let&shy;<lb/>tori oramai ben conoscono come uno de'pi&ugrave; valorosi fisici, che precorsero <lb/>all'istituzione del Metodo sperimentale. </s>

<s>Egli che pubblicava la sua <emph type="italics"/>Historia <lb/>naturale<emph.end type="italics"/> nell'ultimo anno del secolo XVI non leggendo i libri di Aristotile <lb/>e di Vitellione per altro, che per riconoscervi gli errori, ma osservando i <lb/>fatti naturali e sopr'essi speculando, ritrov&ograve; le vere ragioni del dipingersi <lb/>l'iride primaria e la secondaria, quasi quarant'anni prima che fosse pub&shy;<lb/>blicato il libro delle Meteore del Cartesio. </s>

<s>&ldquo; Venendo dunque all'area e <lb/>l'iride, diciamo l'una e l'altra farsi con raggi infratti, ma nell'Iride spe&shy;<lb/>zialmente intervenirvi la riflessione.... Nell'Iride la riflessione &egrave; dalla nube <lb/>opposta. </s>

<s>Gi&agrave; ho detto che con detta riflessione sia aggiunta <emph type="italics"/>l'infrazione <lb/>doppia, dico e nell'introito e nell'esito del raggio &rdquo;<emph.end type="italics"/> (Hist. </s>

<s>nat., Venetia 1672, <lb/>pag. </s>

<s>288). </s></p><p type="main">

<s>Nel prescriver l'Iride secondaria l'Imperato non &egrave; cos&igrave; preciso, ma pro&shy;<lb/>fessando la dottrina platonica dell'emissione de'raggi dall'occhio non &egrave; lon&shy;<lb/>tano dal vero, quando riconosce la ragion del fenomeno dalla molta infra&shy;<lb/>zione, per la quale <emph type="italics"/>il raggio che esce e va al sole si taglia col raggio della <lb/>vista che entra<emph.end type="italics"/> (ivi, pag. </s>

<s>290). Cos&igrave; compiacesi il Nostro di aver <emph type="italics"/>la gene&shy;<lb/>razione de'colori nell'una e nell'altra Iride dedutta dagli proprii prin&shy;<lb/>cipii,<emph.end type="italics"/> e non dall'autorit&agrave; di Aristotile, il quale, quantunque prometta di farlo, <lb/>nondimeno ci&ograve; da lui o <emph type="italics"/>non &egrave; trattato o &egrave; ridotto a cause vane<emph.end type="italics"/> (ivi). </s></p><p type="main">

<s>Ma cos&igrave; queste come altre simili dottrine dell'Imperato non ebbero <lb/>ne'progressi dell'Ottica nessuna efficacia, e le speculazioni dello Speziale <lb/>napoletano intorno all'Iride passarono inosservate. </s>

<s>Il Keplero aveva pensato <lb/>di scrivere un Trattatello &ldquo; quod supplementum esset aristotelicae super <lb/>Iride disquisitionis.... itaque in presens hoc negocium deserui &rdquo; (Dioptrice, <lb/>Augustae Vindelic 1611, pag. </s>

<s>10, 11). Mentre per&ograve; il grande Restauratore <lb/>dell'Ottica scriveva cos&igrave; fatte parole in Germania, l'Italia vedeva apparire <lb/>i due Trattati del Maurolico e del De Dominis. </s>

<s>Il maraviglioso fenomeno ve&shy;<lb/>niva dall'uno de'due insigni Autori illustrato co'principii matematici, e dal&shy;<lb/>l'altro coll'esperienza. </s></p><p type="main">

<s>Il secondo libro <emph type="italics"/>Diaphanorum<emph.end type="italics"/> del nostro Ottico messinese, intitolasi <lb/><emph type="italics"/>De iride,<emph.end type="italics"/> e procedendo in esso con ordine tutto geometrico incomincia a <lb/>determinare la posizione e la forma della portentosa apparenza celeste, di&shy;<lb/>cendo che i centri del sole e dell'occhio e dell'iride sono costituiti in una <lb/>medesima linea retta, e che l'iride stessa viene a rappresentarsi sotto figura <lb/>di un cono retto, il vertice del quale s'appunta nell'occhio di chi osserva <lb/>(Theor. </s>

<s>XXV). I colori dell'iride primaria generati dai raggi solari nella nube <lb/>rorida vengono refratti all'occhio sotto un angolo di 45 gradi (additio ad <lb/>Theor. </s>

<s>cit.), cosicch&egrave;, essendo il sole sull'orizzonte, l'iride disegnerebbe in <lb/>cielo un semicerchio completo, ed essendo il sole stesso elevato per mezzo <lb/>angolo retto, dell'Iride nulla ne apparirebbe (Theor. </s>

<s>XXVI). La larghezza <pb xlink:href="020/01/675.jpg" pagenum="118"/>de'colori dell'Iride sottende nell'occhio un angolo uguale a quello, sotto cui <lb/>si vedrebbe il diametro apparente del sole (Theor. </s>

<s>XXVII). I colori princi&shy;<lb/>pali dell'Iride son quattro: rosso, verde, ceruleo e violetto, ma dall'uno al&shy;<lb/>tro si fa passaggio per un colore intermedio, cosicch&egrave; in tutti i colori son <lb/>sette &ldquo; quambrem Iris septicolor iure dici potest. </s>

<s>&rdquo; Lo spettro colorato di&shy;<lb/>pende dalla dispersione che i raggi solari subiscono dentro la gocciola del&shy;<lb/>l'acqua, e, dove i raggi stessi sono pi&ugrave; condensati, il colore &egrave; pi&ugrave; cupo. </s>

<s>Di <lb/>qui s'intende perch&egrave; l'azzurro sia nell'interno dell'arco e il rosso all'esterno <lb/>(Theor. </s>

<s>XXIX). L'iride esterna non nasce per riflessione dall'iride interna <lb/>come dai pi&ugrave; s'&egrave; creduto, ma per effetto de'raggi che vengono rifratti al&shy;<lb/>l'occhio sotto un angolo di un mezzo con pi&ugrave; l'ottava parte di un angolo <lb/>retto, ossia di 56 gradi e un quarto (Additio I ad Theor. </s>

<s>XXX). </s></p><p type="main">

<s>Tali sono i Teoremi ordinatamente dimostrati dal Maurolico intorno al&shy;<lb/>l'Iride, e poniamo che, verso quel che ne lasci&ograve; scritto Vitellione o qual&shy;<lb/>cun altro degli antichi, segnino in questa parte di scienza ottica un nota&shy;<lb/>bile progresso, l'insigne Autor s'ingannava credendo di dover ritrovare il <lb/>vero per la sola via matematica. </s>

<s>Egli par che voglia, co'suoi numeri pre&shy;<lb/>scriver le leggi alla Natura, come fa per esempio quando contro le osser&shy;<lb/>vazioni de'fatti conclude <emph type="italics"/>a priori,<emph.end type="italics"/> dalle dignit&agrave; matematiche, che l'altezza <lb/>dell'Iride primaria dev'esser per l'appunto di 45 gradi, e quella della se&shy;<lb/>condaria di 56 e un quarto. </s></p><p type="main">

<s>&ldquo; Itaque ut omnia paucis concludam, cum reflexio solaris radii a ro&shy;<lb/>rida nube ad oculum sub dimidio recti anguli facta, per dictam octogoni <lb/>radiationem per octo puncta repetitam in singulis globulis generat prima&shy;<lb/>riam atque coloratissimam Iridem. </s>

<s>Iam nulla alia reflexio, nisi quae ad dic&shy;<lb/>tam anguli quantitatem accedens octogoni divisionem suscipiat, aliqualem <lb/>Iridem facere potest, sed talis reflexio non est nisi quae suscipit quinque <lb/>tantum octonas recti, hoc est angulum 56 1/4 graduum. </s>

<s>Igitur ipsa faciet <lb/>secundariam Iridem, nam si talis angulus habet 5/8 recti unius, oportebit <lb/>quatuor rectos singulos in 8 partes et ideo totum ambitum in 32 partes di&shy;<lb/>stingi, in qua distinctione includitur octogoni divisio, nam 32 in octonas par&shy;<lb/>tes secatur. </s>

<s>Hanc autem dignitatem non habet angulus 60 graduum, quia <lb/>postulat ambitum secari in senas partes, et proinde octagonum non susci&shy;<lb/>pit. </s>

<s>Non angulus 50 graduum, quippe qui habet quinque nonas unius recti <lb/>et requirit divisionem totius ambitus in 36 partes, a qua excluditur octogo&shy;<lb/>nus. </s>

<s>Non angulus 40 graduum habens quatuor nonas unius recti, hoc est <lb/>nonam partem totius ambitus, et ob id octogonum non admittit. </s>

<s>Non ceteri <lb/>anguli neque maiores neque minores praedictis, quoniam maiores quidem, <lb/>propter nimiam expansionem, minores vero propter vicinitatem radii primarii <lb/>debilitant omnem reflexionem. </s>

<s>Superest igitur angulus praedictus 56 1/4 gra&shy;<lb/>duum &rdquo; (Neapoli 1611, pag. </s>

<s>60, 61). </s></p><p type="main">

<s>Ma che in queste sottili e astratte speculazioni la Matematica sia in op&shy;<lb/>posizione co'fatti, si comprende assai facilmente ripensando che le molteplici <lb/>riflessioni dentro la gocciola, tutt'altro che rinforzare i raggi, secondo che <pb xlink:href="020/01/676.jpg" pagenum="119"/>dal Maurolico si suppone, gli debilitano anzi, come &egrave; dall'altra parte chiaris&shy;<lb/>simo per la ragione e per l'esperienza. </s>

<s>Che se veramente son le molteplici <lb/>riflessioni che accendono i colori, essendo nell'Iride primaria quelle rifles&shy;<lb/>sioni 8, e nella secondaria 32, questa dovrebbe splendere in pi&ugrave; vivaci co&shy;<lb/>lori di quella. </s>

<s>Or perch&egrave; si vede esser tutto il contrario, avrebbe dovuto ser&shy;<lb/>vire ci&ograve; al Maurolico d'argomento, a persuadersi che quella presa a trattare <lb/>da lui non era questione di sola matemat&igrave;ca. </s></p><p type="main">

<s>Con miglior consiglio il De Dominis ebbe ricorso all'esperienza, e os&shy;<lb/>servando i colori in sfere piene di acqua o in globi di vetro, opportuna&shy;<lb/>mente contrapposti ai raggi del sole, si studi&ograve; per questa via d'investigare <lb/>il mistero. </s>

<s>La via diritta, senza dubbio, e pi&ugrave; sicura era quella, ma troppo <lb/>imperfette idee aveva delle rifrazioni lo Spalatrese, e intorno alla generazion <lb/>de'colori troppo cieca fede ebbe agl'insegnamenti di Vitellione. </s>

<s>In ogni modo, <lb/>lasciata da parte ogni matematica dimostrazione, ecco ci&ograve; che il De Domi&shy;<lb/>nis dice di avere scoperto dalle sue osservazioni sperimentali: </s></p><p type="main">

<s>&ldquo; Quam varietatem nunc explicare demonstrationibus non est operae <lb/>praetium. </s>

<s>Satis est me experimentis clarissimis comperisse in phiala aqua <lb/>plena et globulis vitreis aqua similiter plenis, a me ad hunc tantum effectum <lb/>perfici curatis, ex fundo G (fig. </s>

<s>41) opposito soli directe, praeter refractio&shy;<lb/><figure id="id.020.01.676.1.jpg" xlink:href="020/01/676/1.jpg"/></s></p><p type="caption">

<s>Figura 41.<lb/>nem quae fit in V, duplices fieri reflexiones, alias statim per latera versus <lb/>F et E circulariter, alias vero versus solem prope perpendiculorem BA ad <lb/>partem anteriorem versus H et I similiter circulariter, et non per unam so&shy;<lb/>lam lineam indivisibilem, sed per plures utrobique, cum aliqua latitudine, <lb/>ut sunt in priori reflexione GF, GN, GM; in altera vero GI, GK, GL, quae <lb/>latitudo oritur partim ex refractionibus, quae intra globum fiunt cum ag&shy;<lb/>gregatione plurium radiorum, partim ex magna latitudine corporis lumi&shy;<lb/>nosi PQT &rdquo; (De radiis ecc., Venetiis 1611, pag. </s>

<s>14). </s></p><p type="main">

<s>Ci&ograve; che sperimentalmente rappresentasi nel globo di vetro pien d'acqua, <lb/>rappresentasi naturalmente, secondo il De Dominis, nel vapore <emph type="italics"/>roridus<emph.end type="italics"/> et <lb/><emph type="italics"/>stillans,<emph.end type="italics"/> di ch'&egrave; composta la nube. </s>

<s>Da'fascetti MF si produce l'iride pri&shy;<lb/>maria; dai fascetti IL la secondaria. </s>

<s>I colori sono via via sempre pi&ugrave; oscuri, <lb/>secondo che maggiore opacit&agrave; si aggiunge alla chiarezza. </s>

<s>Cos&igrave; GM, dovendo <lb/>attraversar maggior parte corporea della palla vitrea, esce mescolato con <pb xlink:href="020/01/677.jpg" pagenum="120"/>maggior ombra degli altri, e perci&ograve; sar&agrave; di colore pi&ugrave; oscuro di tutti gli al&shy;<lb/>tri, ossia violetto. </s>

<s>Per la stessa ragione GF, sar&agrave; il pi&ugrave; lucido di tutti gli <lb/>altri, ossia rosso. </s>

<s>&ldquo; Dicimus radium GF esse omnium lucidissimum, quia <lb/>pertransit minimam crassitiem corpusculi A, radium vero sequentem GN esse <lb/>paulo obscuriorem, quia paulo maior ei est globuli A penetranda crassities, <lb/>ac demum radium GM esse obscurissimum quia adhuc maiorem penetrat cras&shy;<lb/>sitiem. </s>

<s>Itaque radius GF erit puniceus, GN viridis, GM purpureus &rdquo; (ibi, <lb/>pag. </s>

<s>56). </s></p><p type="main">

<s>Secondo un tal principio per&ograve; i colori I, K, L dovrebbero rappresen&shy;<lb/>tarsi nel medesimo ordine de'colori F, N, M essendo chiaro che GL attra&shy;<lb/>versando minor parte corporea della gocciola, ed uscendo fuori perci&ograve; me&shy;<lb/>scolato con minor parte d'ombra, dee essere il pi&ugrave; lucido di tutti gli altri, <lb/>cio&egrave; il rosso, mentre al contrario egli &egrave; il pi&ugrave; oscuro, cio&egrave; il violetto. </s>

<s>Ond'&egrave; <lb/>che, per salvare il fenomeno, dovette l'Autore ricorrere ad altro principio, <lb/>ed &egrave; che i raggi sien tanto pi&ugrave; lucidi, quanto a penetrare il mezzo si sen&shy;<lb/>ton pi&ugrave; forti. </s>

<s>Ma perch&egrave; tanto si senton pi&ugrave; forti, quanto pi&ugrave; si accostano <lb/>alla perpendicolare, e perci&ograve; s'intende come GI debba esser, non come prima, <lb/>il violetto ma il rosso, che &egrave; il pi&ugrave; lucido di tutti gli altri colori. </s>

<s>&ldquo; A luce <lb/>igitur fortiori radius fortior et lucidior reflectetur prope perpendicularem, <lb/>cuiusmodi est radius GI, a qua luce iam deflectunt radii, non ex ipso cen&shy;<lb/>tro lucidissimo G prodeuntes per reflexionem, sed paulo remotiores, ut sunt <lb/>radii GK, GL. </s>

<s>Propterea radius GI erit lucidissimus, hoc est puniceus, GK <lb/>erit viridis, GL erit purpureus &rdquo; (ibi, pag. </s>

<s>63). </s></p><p type="main">

<s>La via sperimentale presa dal De Dominis era la retta, ma, per man&shy;<lb/>canza di cognizioni diottriche, hanno veduto i lettori quanto infelice ne sia <lb/>stata la riuscita. </s>

<s>I due insigni Ottici italiani insomma, il Dalmata e il Sici&shy;<lb/>liano, con tutta la loro esperienza e la loro matematica non riuscirono a dar <lb/>nella cruna del vero, come pure vi dette l'Imperato, i concetti del quale <lb/>ebbero la pi&ugrave; splendida illustrazione dal Capitolo VIII delle <emph type="italics"/>Meteore<emph.end type="italics"/> del <lb/>Cartesio. </s></p><p type="main">

<s>Tornato l'Autore ad osservar la palla vitrea preparata a modo del De <lb/>Dominis, e costituita di contro al sole in modo che i raggi di lui si riflet&shy;<lb/>tessero dalla palla stessa alla vista sotto un angolo presso a poco di 42 gradi, <lb/>ne'punti D e K (fig. </s>

<s>42) vedeva apparire un vivace color rubicondo, e va&shy;<lb/>riando alquanto posizione, vedeva, dietro a que'due punti rossi, succedersi <lb/>e contrapporsi via via gli altri colori, se non che verso K erano alquanto pi&ugrave; <lb/>sbiaditi. </s>

<s>Riconosciuta in questa esperienza, come lo stesso De Dominis l'aveva <lb/>gi&agrave; riconosciuta, la viva rappresentazione delle due Iridi celesti, il Cartesio <lb/>passa cos&igrave; a descrivere l'andamento de'raggi dentro la palla vitrea, imma&shy;<lb/>gine della gocciola della pioggia, da'quali raggi variamente refratti hanno <lb/>origine le varie apparenze de'colori: </s></p><p type="main">

<s>&ldquo; Postea cum accuratius examinarem in pila BCD unde rubeus color <lb/>in eius parte D conspicuus oriretur, notavi illum pendere a radiis Solis, qui <lb/>venientes ex A ad B aquam ingrediendo frangebantur in puncto B, et ibant <pb xlink:href="020/01/678.jpg" pagenum="121"/>ad C, unde reflexi ad D et ibi aquam egrediendo iterum fracti tendebant <lb/>ad E. </s>

<s>Nam simul ac corpus aliquod opacum et obscurum alicui linearum <lb/>AB, BC, CD, vel DE opponebam, rubicundus color evanescebat, et licet to&shy;<lb/>tam pilam, exceptis duobus punctis B et D obnuberem, et corpora obscura <lb/>ubivis circumponerem, dummodo nihil actionem radiorum ABCD impediret, <lb/>lucide tamen ille refulgebat. </s>

<s>Postea eodem modo investigata causa rubri il&shy;<lb/>lius coloris, qui apparebat in K inveni illum esse a radiis solis, qui venien&shy;<lb/>tes ab F ad G, ibi refringebantur versus H, et in H reflexi ad I, rursusque <lb/>ab I reflexi ad K, tandemque iterum fracti in puncto K, tendebant ad E. </s>

<s><lb/>Atque ita primaria Iris fit a radiis post duas refractiones et unam reflexio&shy;<lb/><figure id="id.020.01.678.1.jpg" xlink:href="020/01/678/1.jpg"/></s></p><p type="caption">

<s>Figura 42.<lb/>nem ad oculum venientibus; secundaria vero a radiis qui nonnisi post duas <lb/>refractiones et duas reflexiones eodem pertingunt. </s>

<s>Ideoque haec semper al&shy;<lb/>tera minus est conspicua &rdquo; (Ibi, Francofurti ad M. 1692, pag. </s>

<s>175). </s></p><p type="main">

<s>Il problema che aveva per s&igrave; lungo tempo frugata la curiosit&agrave; degli Ot&shy;<lb/>tici e de'Meteorologi veniva cos&igrave; finalmente risoluto, almeno nella parte sua <lb/>pi&ugrave; sostanziale. </s>

<s>Il Grimaldi poi nelle ultime XV proposizioni del 1 Libro <emph type="italics"/>De <lb/>lumine<emph.end type="italics"/> tratt&ograve; largamente e sottilmente dello stesso soggetto, apparecchian&shy;<lb/>dovisi coll'insegnare un modo di rappresentare artificialmente l'Iride in una <lb/>camera oscura, spruzzandovi dentro l'acqua scossa da una spazzola di scopa. <lb/>(Propos. </s>

<s>XLVII, n.&deg; 4). </s></p><p type="main">

<s>Condotta infino a questo punto trovava dunque il Newton questa no-<pb xlink:href="020/01/679.jpg" pagenum="122"/>bile parte di scienza, quando, nel 1671, dettava l'ultima delle sue <emph type="italics"/>Lezioni <lb/>di Ottica<emph.end type="italics"/> dalla cattedra leucasiana. </s>

<s>Termina l'Autore quella sua Lezione <emph type="italics"/>De <lb/>variis colorum phaenomenis<emph.end type="italics"/> cos&igrave; scrivendo: &ldquo; Superest iam mirum illud <lb/>caelestis arcus spectaculum, ad cuius explicationem Cartesius viam stravit. </s>

<s><lb/>Huic enim debetur quod in guttis aquae pluvialis decidentibus efformari co&shy;<lb/>gnoscimus. </s>

<s>Quemadmodum ex eo constat quod nunquam videtur nisi coelo <lb/>pluente; quod, sole pluviam decidentem illustrante, in vicis nonnunquam <lb/>apparuit, quasi non in coelo collocatus, sed in aere vicino, super opposita&shy;<lb/>rum domuum parietibus affixus vel potius interiectus; quod aqua per arti&shy;<lb/>ficium aliquod sparsim eiaculata iridem ostendit, et quod gramen rore ma&shy;<lb/>tutino, quasi guttulis minutissimis conspersum colores etiam Iridis exhibet. </s>

<s><lb/>Huic etiam debetur ingeniosissima de refractionibus guttae et eorum limi&shy;<lb/>tibus inventio, sed causam physicam minus feliciter aggressus est &rdquo; (Edit. </s>

<s><lb/>cit., pag. </s>

<s>127, 28). </s></p><p type="main">

<s>In questi brevi cenni storici i nostri lettori, che si rammentano del&shy;<lb/>l'esperienza antichissima proposta da Plutarco, riconoscono parecchie impro&shy;<lb/>priet&agrave; storiche, e mentre da una parte par poco il dir del Cartesio che <emph type="italics"/>viam <lb/>stravit,<emph.end type="italics"/> sembrer&agrave; dall'altra un'esagerazione il fargli merito di un artificio <lb/>ovvio a'pescatori che battono i remi in acqua, o a'contemplanti, illuminato <lb/>dal sole, lo spettacolo di una cascata. </s></p><p type="main">

<s>Un altro difetto storico reputato pi&ugrave; notabile &egrave; accennato qui a pi&egrave; di <lb/>pagina dall'Editore: &ldquo; Neutonus postea <emph type="italics"/>intellexit<emph.end type="italics"/> alios ante Cartesium huius <lb/>phaenomeni causam invenisse ut verba eius sequentia testantur: <emph type="italics"/>Hodie con&shy;<lb/>venit inter omnes arcum istum refractione luminis solaris in guttulis plu&shy;<lb/>viae cadentis effici. </s>

<s>Intellexerunt hoc etiam antiquorum nonnulli: inter <lb/>recentiores autem plenius id invenit uberiusque explicavit celeberrimus <lb/>Antonius De Dominis Archiepiscopus spalatensis, in libro suo<emph.end type="italics"/> De radiis vi&shy;<lb/>sus et lucis, <emph type="italics"/>quem ante annos amplius viginti scriptum in lucem tandem <lb/>edidit amicus suus Bartolus, Venetiis anno 1611. In eo enim libro osten&shy;<lb/>dit vir celeberrimus quemadmodum arcus interior, binis refractionibus ra&shy;<lb/>diorum solis, singulisque reflexionibus inter binas istas refractiones inter&shy;<lb/>venientibus, in rotundis pluviae guttis effingatur, exterior autem arcus <lb/>binis refractionibus binisque itidem reflexionibus interiectis, in similibus <lb/>aquae guttis efficiatur. </s>

<s>Suamque is explicandi rationem experimentis com&shy;<lb/>probavit in phiala aquae plena et globis vitreis aquae plenis in sole col&shy;<lb/>locatis, quo duorum arcuum istorum colores in illis se exhiberent contem&shy;<lb/>plandos. </s>

<s>Porro eandem explicandi rationem persecutus est Cartesius in <lb/>Meteoris suis, eamque quae est de arcu exteriori insuper emendavit &rdquo;<emph.end type="italics"/><lb/>(Optic., Lib. </s>

<s>I, P. II, prop. </s>

<s>IX). </s></p><p type="main">

<s>Dev'esser proprio vero che queste cose del De Dominis il Newton le <lb/><emph type="italics"/>sent&igrave; dire,<emph.end type="italics"/> perch&egrave; se avesse consultato il libro <emph type="italics"/>De radiis visus et lucis<emph.end type="italics"/> non <lb/>era possibile che non si fosse accorto come le <emph type="italics"/>bine rifrazioni<emph.end type="italics"/> e le <emph type="italics"/>bine ri&shy;<lb/>flessioni,<emph.end type="italics"/> nell'intenzion dello Spalatrese, non erano altro che un nome ri&shy;<lb/>spondente per caso a quello scelto poi a significare le verit&agrave; diottriche. </s>

<s>N&egrave; <pb xlink:href="020/01/680.jpg" pagenum="123"/>pure &egrave; secondo giustizia l'attribuire al Cartesio il merito di aver solamente <lb/>emendato le dottrine del De Dominis, per ci&ograve; che riguardi l'arco esteriore: <lb/>egli non emend&ograve;, ma dimostr&ograve; da'principii, non ad altri prima noti che a <lb/>Ferrante Imperato, gli andamenti de'raggi atti a produrre per riflessione e <lb/>per rifrazione i due Archi paralleli e concolori. </s>

<s>Cosicch&egrave;, secondo il giudi&shy;<lb/>zio imparziale della Storia, rimane al Nostro un merito unico ma pur as&shy;<lb/>sai notabile, ed &egrave; quello di avere apparecchiate al Francese le vie del&shy;<lb/>l'esperienza. </s></p><p type="main">

<s>Il Newton soggiungeva al passo ora ultimamente citato che il De Dominis <lb/>e il Cartesio lasciarono imperfetta la teoria dell'Iride, perch&egrave; ignoravano la <lb/>vera generazion de'colori, e perci&ograve; si compiace che il dar l'ultima mano a <lb/>cos&igrave; nobile opera sia stato riserbato a lui. </s>

<s>La scoperta de'varii gradi di re&shy;<lb/>frangibilit&agrave; non solo dette al grande Ottico inglese modo a divisar le ragioni <lb/>de'colori nell'Arco, ma a precisarne altres&igrave; le misure concluse a priori dal <lb/>Maurolico, e stabilite cos&igrave; all'incirca dal Cartesio e dal Grimaldi. </s>

<s>&ldquo; Itaque (ri&shy;<lb/>trovava il Newton per l'Iride interna) maxima eius semidiameter est 43&deg;, 6&prime;. </s>

<s><lb/>A qua, si auferatur minima semidiameter 41&deg;, 0&prime;, emergit Iridis crassities 2&deg;, 0&prime; <lb/>circiter, vel potius 2&deg;, 37&prime; addita diametro Solis &rdquo; (Letiones Optic. </s>

<s>cit., pag. </s>

<s>109). <lb/>Per l'Iride esterna trov&ograve; il massimo semidiametro 52&deg;, 51&prime;, dalla quale &ldquo; si <lb/>auferatur minima 49&deg;, 2&prime; et residuo addatur diameter Solis 31&prime;, emerget huius <lb/>Iridis crassities 4&deg;, 20&prime;. </s>

<s>Sed propter maiorem huius, quam interioris Iridis <lb/>obscuritatem, colores vix ultra crassitiem trium graduum vel trium et se&shy;<lb/>missis, videri posse coniicio &rdquo; (ibi). </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Le Corone e i Parelii, con altri simili fenomeni spettacolosi che, seb&shy;<lb/>bene non s&igrave; frequentemente, si osservano intorno al Sole e alla Luna, fu&shy;<lb/>rono creduti dagli antichi avere cos&igrave; strette relazioni coll'Iride, che non <lb/>dubitarono di riguardar quelle apparenze come un effetto di somiglianti, se <lb/>non affatto uguali, cagioni. </s>

<s>Vitellione si prov&ograve; a sfiorar qualche cosa del dif&shy;<lb/>ficile campo inesplorato nelle proposizioni LXXXI e LXXXII del suo X Li&shy;<lb/>bro di Prospettiva, e anche quando, specialmente in Italia, s'incominci&ograve; a <lb/>specular della scienza della Natura con libert&agrave; di pensiero, non si seppe, per <lb/>la spiegazione di quelle recondite apparenze celesti, aggiunger nulla di me&shy;<lb/>glio e di nuovo ai detti dell'Ottico pollacco. </s></p><p type="main">

<s>Ferrante Imperato, che cos&igrave; bene indovin&ograve; gli andamenti de'raggi re&shy;<lb/>fratti e riflessi nella nube rorida, a produr le due Iridi, trovava la ragione <lb/>delle Corone o delle Aree, com'ei le chiama, che talvolta come l'Iride stessa <lb/>appariscono colorate, nelle refrazioni fatte dai raggi solari in mezzo ai cor&shy;<lb/>picciuoli, che compongono la consistenza della nube vaporosa o della cali&shy;<lb/>gine: &ldquo; Venendo dunque all'Area e l'Iride, diciamo l'una e l'altra farsi <pb xlink:href="020/01/681.jpg" pagenum="124"/>con raggi infratti, ma nell'Iride spezialmente intervenirvi la riflessione. </s>

<s>Di&shy;<lb/>ciamo inoltre le dette infrazioni e riflessioni farsi da'corpiccioli, che com&shy;<lb/>pongono la consistenza della nube e della caligine. </s>

<s>Intenderemo dunque una <lb/>linea dal corpo lucido al punto, principio visivo come asse, e nel soggetto <lb/>dell'area intenderemo intorno detto asse li raggi visivi infratti dagli corpu&shy;<lb/>scoli delle gocce andar dalla vista al luminare. </s>

<s>Se dunque da corpi simili <lb/>posti similmente dobbiamo avere effetti simili, saranno le infrazioni fatte in <lb/>egual distanza dall'asse, e per conseguenza in circolo d'intorno detto asse. </s>

<s><lb/>Quivi dunque la infrazione &egrave; dalla nube tramezza, ma nell'Iride la ri&shy;<lb/>flessione &egrave; dalla nube opposta &rdquo; (Historia Natur., Lib. </s>

<s>XI, Venezia 1672, <lb/>pag. </s>

<s>288). </s></p><p type="main">

<s>De'tre Autori poi, che tanto efficacemente concorsero a promuover l'Ot&shy;<lb/>tica nel primo risorgere del Metodo sperimentale, il Maurolico e il De Do&shy;<lb/>minis lasciarono intatto il tema delle Corone e dei Parelii, o arretrati dalla <lb/>difficolt&agrave; di divisarne i pi&ugrave; minuti particolari, o forse persuasi che ritornas&shy;<lb/>sero le ragioni di quegli stessi particolari nelle generali ragioni diottriche <lb/>date da loro delle apparenze dell'Iride. </s>

<s>Il Keplero fu tentato dalla voglia di <lb/>applicare le Ottiche discipline a spiegar quegli spettacoli celesti, che fruga&shy;<lb/>vano le menti de'Filosofi e gli animi de'curiosi, ma poi abbandon&ograve; l'im&shy;<lb/>presa, e fece bene, perch&egrave; colle false idee che aveva dell'essere e della na&shy;<lb/>tura de'colori, si rendeva il meno atto, non solo a condurre in porto, ma <lb/>pure a sospingere innanzi la barca. </s>

<s>&ldquo; Explicationem Halonis, Iridis, Pare&shy;<lb/>liorum, Paraselenarumque ex Optica disciplina petendam iam olim vidit <lb/>Aristoteles, neque ea quae adhuc desiderantur in Meteorologicis Aristotelis <lb/>aliunde suppleri possunt. </s>

<s>Cogitaveram et ego hic libellum de Iride subiun&shy;<lb/>gere, quod supplementum esset aristotelicae super Iride disquisitionis, sed <lb/>desiderantur adhuc Pareliorum genuinae causae, quae sunt causis portento&shy;<lb/>sarum Iridum implexae: itaque in praesens hoc negocium deserui &rdquo; (Diop&shy;<lb/>trice, Augustae Vindelic. </s>

<s>1611, pag. </s>

<s>10, 11). </s></p><p type="main">

<s>Non mancarono nonostante, poco appresso i tre celebri Ottici comme&shy;<lb/>morati, alcuni i quali, bench&egrave; fossero persuasi che a produr le Corone talvolta <lb/>iridescenti e i Parelii dovessero necessariamente intervenire quelle rifles&shy;<lb/>sioni, e quelle rifrazioni, alle quali erano gi&agrave; ricorsi Vitellione e i seguaci <lb/>di lui; s'avvidero nulladimeno che simili riflessioni e rifrazioni non era pos&shy;<lb/>sibile che si facessero in mezzo alle stille della nube rorida, come nell'Iride <lb/>celeste. </s>

<s>N&egrave; dall'altra parte era difficile avvedersi di ci&ograve;, avendo osservato <lb/>che, mentre essa Iride non si fa mai che sotto il cielo piovoso, gli Aloni e <lb/>i Parelii invece si vedono sempre apparire quando non piove. </s>

<s>Dove in altro <lb/>dunque se no nelle gocciole piovose ritrovare il soggetto di quelle riflessioni <lb/>e di quelle refrazioni, riconosciute indispensabili a salvare cos&igrave; fatta ap&shy;<lb/>parenza? </s></p><p type="main">

<s>Lo Scheiner, che senti vivo il bisogno di rispondere alla domanda, av&shy;<lb/>vent&ograve; certe sue idee che riconosciute da lui stesso per enimmatiche, lasci&ograve; <lb/>a decifrare ai Filosofi in faccia a'quali pronunziava il motto: <emph type="italics"/>sapientibus<emph.end type="italics"/><pb xlink:href="020/01/682.jpg" pagenum="125"/><emph type="italics"/>pauca.<emph.end type="italics"/> Ecco quali sono quelle idee, che vedonsi lampeggiar dal contesto <lb/>delle seguenti parole: &ldquo; Transferunt autem haec vitra (utrinque convexa et <lb/>utrinque concava) visas res a veris locis mirum in modum, sursum, deor&shy;<lb/>sum dextrorsum sinistrorsum ecc. </s>

<s>Quod etiam in sole experiri potes per vi&shy;<lb/>trum simile coloribus tinetum, aut in Luna plena vitro liquido. </s>

<s>Videbis enim <lb/>utrumlibet sidus in ellipsim configurari et loco transferri, pro situ et statu <lb/>vitri. </s>

<s>Et si eiusmodi duo aut plura vitra diversis locis inter visum et sidera <lb/>dicta statueris, multiplicabis eadem sidera. </s>

<s>E quibus rationem Pareliorum <lb/>Paraselenarumque eruere addisces. </s>

<s>Quod idem specilla polyedra edocebunt. </s>

<s><lb/>Sed et homocentrice convexo concava vitra eadem praestant. </s>

<s>Unde si ex <lb/>hisce humilibus in alia ascendere, tanquam gradibus quibusdam non pige&shy;<lb/>bit, dicemus obiectu vel nobis vel vaporis, aut similis meteori diaphani re&shy;<lb/>fractui et uno istorum modorum multipliciter figurati ecc. </s>

<s>solem saepuiscule <lb/>videri et Parelia ita gigni. </s>

<s>Sed haec ex occasione stringo non instituto enu&shy;<lb/>cleo. </s>

<s>Sapientibus pauca &rdquo; (Refractiones coelestes, Ingolstadii 1617, pag. </s>

<s>40). </s></p><p type="main">

<s>Questo sfolgorar del pensiero at&shy;<lb/><figure id="id.020.01.682.1.jpg" xlink:href="020/01/682/1.jpg"/></s></p><p type="caption">

<s>Figura 43.<lb/>traverso alle parole, cos&igrave; in fretta <lb/>dallo Scheiner pronunziate, era senza <lb/>dubbio assai seducente, ma dove tro&shy;<lb/>vare in cielo que'vetri cristallini e <lb/>que'prismi atti a rifrangere in modo <lb/>i raggi del sole da rappresentare i <lb/>Parelii e le Corone? </s>

<s>Fra i Sapienti <lb/>che ripensavano a queste cose si trov&ograve; <lb/>per avventura il Cartesio, il quale, <lb/>nell'inverno del 1635, trovandosi in <lb/>Amsterdam, si dette ad osservare di&shy;<lb/>ligentissimamente le varie figure cri&shy;<lb/>stalline della neve, in che, sotto l'aria <lb/>freddissima, si trasformavano le goc&shy;<lb/>ciole della pioggia. </s>

<s>Uscito da quella <lb/>contemplazione, che a lui sembr&ograve; nuo&shy;<lb/>va, e ripensando che simili cristallini <lb/>di ghiaccio, pi&ugrave; presto che in terra, <lb/>si formano in aria, dove per qualche <lb/>tempo vi possono rimaner sostenuti <lb/>dai venti; ecco, disse, i vetri lenti&shy;<lb/>colari e i prismi, atti per rifrazione <lb/>a dipingere all'occhio di noi riguar&shy;<lb/>danti in Terra le Corone e gli Aloni. </s></p><p type="main">

<s>&ldquo; Sit ABC (fig. </s>

<s>43) ex. </s>

<s>gr. </s>

<s>Sol, <lb/>D oculus, EFG plurimae glaciei par&shy;<lb/>ticulae pellucidae aliae iuxta alias iacientes, plane quemadmodum esse de&shy;<lb/>bent ut in stellulas formentur, et quarum convexitas talis est ut radius <pb xlink:href="020/01/683.jpg" pagenum="126"/>ex. </s>

<s>gr. </s>

<s>ex puncto A ad extremitatem stellulae G perveniens, et radius ex <lb/>puncto C ad extremitatem stellulae F refringantur vesus D et ut etiam alii <lb/>plures radii perveniant ad D, ex iis qui in illas incidunt quae sunt extra <lb/>circulum GG. </s>

<s>Manifestum est praeter radios AD, CD et similes qui recta <lb/>linea tendentes solem naturali magnitudine repraesentant, alios refractos in <lb/>FE aerem comprehensum hoc circulo FF, satis lucidum reddituros, et cir&shy;<lb/>cumferentiam illius inter circulos FF, et GG, specie coronae Iridis colori&shy;<lb/>bus variegatae exhibituros. </s>

<s>Ipsum etiam rubrum intrinsecus ad F et caeru&shy;<lb/>leum extrinsecus ad G visum iri plane quemadmodum observatur. </s>

<s>Et si <lb/>duo aut plures ordines particularum glaciei congesti sint, dummodo radios <lb/>solares non ideo plane excludant, illi radiorum qui per duos ordines in <lb/>stellarum extremitatibus penetrant bis fere tantumdem incurvati, quan&shy;<lb/>tum alii qui per unum tantum, alium circulum coloratum producent ambitu <lb/>quidem priori longe maiorem sed minus lucidum ita ut tum duae coronae <lb/>quarum una alteram cingat, et quarum exterior interiori minus picta sit, <lb/>appareant, ut etiam interdum fuit observatum &rdquo; (Cap. </s>

<s>IX, Metereorum cit., <lb/>pag. </s>

<s>188, 89). </s></p><p type="main">

<s>Quanto a'Parelli parve al Cartesio non gli poter salvare col ricorso alle <lb/>rifrazioni fatte nelle stelline ghiacciate, e non vedendosi, come dianzi, da <lb/>nessuna parte aperta la via dell'esperienza, ritorna al gioco delle sue solite <lb/><figure id="id.020.01.683.1.jpg" xlink:href="020/01/683/1.jpg"/></s></p><p type="caption">

<s>Figura 44.<lb/>fantasie. </s>

<s>Come tipo generale e rappresentativo del <lb/>fenomeno, prese in mancanza di osservazioni proprie <lb/>la descrizione de'Parelii osservati in Roma, il di <lb/>20 Marzo 1629, nella quale descrizione si diceva che <lb/>cinque soli apparvero, incastonati come gemme in <lb/>anello, in un gran circolo di color bianco. </s>

<s>L'ap&shy;<lb/>parenza di quel circolo, secondo il Cartesio, era do&shy;<lb/>vuta alle riflessioni del sole in un anello di ghiaccio, <lb/>il quale, nella fantasia del Filosofo, aveva avuto ori&shy;<lb/>gine a questo modo: </s></p><p type="main">

<s>&ldquo; Sit ex. </s>

<s>gr. </s>

<s>A (fig. </s>

<s>44) meridies ubi Sol con&shy;<lb/>sistit comitatus vento calido tendente ad B et C Sep&shy;<lb/>tentrio, unde ventus frigidus etiam ad B nititur, et <lb/>ibi suppono hos duos ventos vel invenire, vel cogere <lb/>nubem, ex glaciei particulis compositam, quae tam <lb/>lata est et profunda ut non possint unus super, alius <lb/>subter, vel per eius medium labi, quemadmodum <lb/>alias solent, sed cursum suum circumcirca tenere <lb/>cogantur, qua opera non tantum illam circumdant, <lb/>sed etiam qui a Meridie calidus spirat, nivem eius <lb/>ambitus paululum liquefacit, quae statim iterum gelata, tam frigore venti <lb/>borealis, quam vicinia nivis interioris nondum liquefactae, magnum quen&shy;<lb/>dam velut annulum, ex glacie continua et pellucida, componit &rdquo; (ibi, <lb/>pag. </s>

<s>191). </s></p><pb xlink:href="020/01/684.jpg" pagenum="127"/><p type="main">

<s>E perciocch&egrave; dicevasi che il re di Polonia avesse, nel 1625, veduto infino <lb/>a sei soli incastonati nel grande anello, e i due pi&ugrave; prossimi al sole vero <lb/>nell'apparenza romana si diceva che rappresentassero certe frange iride&shy;<lb/>scenti negli orli, e non mostrassero cos&igrave; bene rotondi da far supporre che <lb/>non fossero come gli altri, generati per riflessione, ma per rifrazione; ac&shy;<lb/>comodando il Cartesio le sue speculazioni a questi fatti osservati, disegn&ograve; <lb/>nell'iconismo ora citato i raggi venienti dal Sole all'occhio dello spettatore <lb/>in modo, che rappresentassero le immagini di sei soli, quattro per rifles&shy;<lb/>sione e due per refrazione. </s>

<s>&ldquo; Possunt etiam apparere stantibus in Terra <lb/>circa punctum K (fig. </s>

<s>preced.) usque ad sex Soles, qui circulo albo, tan&shy;<lb/>quam annulo totidem adamantes inserti sint. </s>

<s>Primus scilicet in E, ob ra&shy;<lb/>dios directe fluentes a Sole quem suppono in A: duo sequentes in D et F, <lb/>per refractionem radiorum qui glaciem iis in locis permeant, ubi crassitie <lb/>illius paulatim decrescente, introrsum ab utraque parte incurvantur, que&shy;<lb/>madmodum ii qui prisma crystallinum perlabuntur. </s>

<s>Et propterea hi duo So&shy;<lb/>les in oris rubrum colorem ostentant, ea parte qua E respiciunt, ubi gla&shy;<lb/>cies crassior est, et coeruleum in altera ubi tenuior. </s>

<s>Quartus in H per <lb/>reflexionem apparet, duo itidem postremi per reflexionem in G et I &rdquo; (ibi, <lb/>pag. </s>

<s>192). </s></p><p type="main">

<s>Queste cartesiane ipotesi intorno all'origine de'Parelii era facile che si <lb/>mettessero in dubbio da tutti coloro, i quali non credevano che potessero <lb/>avere i venti tant'arte da girare a tornio cos&igrave; puntualmente le nubi, ma a <lb/>sostituirne delle migliori mancavano le osservazioni dirette, non presentan&shy;<lb/>dosi que'fenomeni cos&igrave; frequenti. </s></p><p type="main">

<s>Dopo trent'anni interi, da che fu pubblicata la Meteorologia del Car&shy;<lb/>tesio, volle la buona ventura che uno di costoro, a cui tocc&ograve; di osservar lo <lb/>spettacolo, fosse l'Ugenio. </s>

<s>il di 12 maggio 1668, sulle ore nove della mat&shy;<lb/>tina, apparve agli abitanti di Parigi un Alone o corona intorno al Sole, e <lb/>l'Huyghens l'osservava attentissimamente dalle finestre della Libreria del <lb/>Re. </s>

<s>Un cos&igrave; strenuo cultore e promotore della Diottrica non lasci&ograve; di spe&shy;<lb/>culare intorno alle nuove cose osservate, e intanto che faceva esperienze e <lb/>instaurava calcoli per comporre la Dissertazione <emph type="italics"/>De Coronis<emph.end type="italics"/> et <emph type="italics"/>Pareliis,<emph.end type="italics"/> di&shy;<lb/>stese una breve scrittura in francese, nella quale, nascondendosi come Au&shy;<lb/>tore e prendendo l'ufficio di semplice Relatore, descriveva il fenomeno e <lb/>proponeva la ipotesi per ispiegarlo. </s>

<s>Quella Relazione fu stampata, dentro il <lb/>medesimo anno 1667, da Giovanni Cusson a Parigi, ed ha qualche impor&shy;<lb/>tanza il saper com'ella venisse di Francia a farsi nota fra noi. </s></p><p type="main">

<s>Le relazioni passate fra l'Huyghens e la nostra Accademia fiorentina <lb/>son ben note oramai ai lettori di questa Storia, e dopo lo screzio avvenuto <lb/>a cagion dell'Orologio a pendolo, ricomposti gli animi in quiete, il prin&shy;<lb/>cipe Leopoldo regalava l'illustre Olandese de'libri migliori che uscivano di <lb/>mano in mano da'suoi Accademici, e lo pregava a volerne dare particolare <lb/>informazione de'suoi studii e specialmente di quelli concernenti la Diot&shy;<lb/>trica. </s>

<s>L'Huyghens rispondeva in proposito con lettera del di 18 Novem-<pb xlink:href="020/01/685.jpg" pagenum="128"/>bre 1667, accompagnando al Principe la detta Relazione dell'Alone osservato <lb/>a Parigi. </s></p><p type="main">

<s>Leopoldo de'Medici non richiedeva quelle scientifiche informazioni per <lb/>sua privata curiosit&agrave;, ma per diffonderle nella sua Accademia, alla quale, <lb/>cos&igrave; Cardinale com'era diventato, attendeva con maggiore operosit&agrave; e con <lb/>affetto pi&ugrave; vivo. </s>

<s>E perch&egrave; non era allora la lingua francese d'intelligenza <lb/>comune, ordin&ograve; al Viviani che traducesse la <emph type="italics"/>Relazione<emph.end type="italics"/> in lingua italiana, e <lb/>gli ordin&ograve; altres&igrave; ne facesse un sunto, da diffonderne con pi&ugrave; facilit&agrave; la no&shy;<lb/>tizia, e da conservarsi fra'documenti dell'Accademia. </s>

<s>Il Viviani esegui pun&shy;<lb/>tualmente i due comandi, e quanto al primo lasci&ograve; notato alla fine del ma&shy;<lb/>noscritto inserito da c. </s>

<s>137-44 nel Tomo CXXXIII de'Discepoli di Galileo: <lb/>&ldquo; Mal tradotta da me dal francese, a'di 21 Dicembre 1667, e correttami dal <lb/>signor Francesco Pandolfini. </s>

<s>&rdquo; Quanto al secondo, ivi a c. </s>

<s>135: &ldquo; Datone <lb/>copia al Serenissimo Cardinale Leopoldo, che mi aveva richiesto del sunto. </s>

<s>&rdquo; <lb/>Nonostante per&ograve; che il Viviani dica di aver mal tradotto, noi preferiremo la <lb/>versione di lui a quella latina fatta dal Dausmenil, e inserita da pag. </s>

<s>348-58 <lb/>(Lugd. </s>

<s>Batav. </s>

<s>1703) degli Opuscoli postumi di Cristiano Huyghens, per le <lb/>citazioni che occorreranno nel passar a dar brevemente conto della ipotesi <lb/>proposta dal celebre Autore, per salvar le Corone e i Parelii. </s></p><p type="main">

<s>L'osservazione sensata gli avea dimostrato un error capitale, in ch'era <lb/>incorso il Cartesio, e che consisteva nel dire che lo spazio rinchiuso dentro <lb/>la Corona fosse pi&ugrave; chiaro dell'aria all'intorno. </s>

<s>L'Huyghens osserv&ograve; che <lb/>invece era pi&ugrave; oscuro, e indi ne trasse una conclusione importante, che cio&egrave; <lb/>i ghiaccioli, a cui era stato commesso il gioco di rischiarar quello spazio, <lb/>non fossero altrimenti diafani ma opachi. </s>

<s>E perch&egrave; dall'altra parte una certa <lb/>tal qual trasparenza superficiale era necessaria a produrre le rifrazioni, si <lb/>ridusse l'Huyghens a trasformar le stelline cartesiane in cilindretti di ghiac&shy;<lb/>cio, trasparenti alla superficie e col nocciolo opaco. </s>

<s>Per mezzo di cos&igrave; fatti <lb/>cilindretti trasportati e sostenuti per l'aria, non ritti n&egrave; a diacere, ma in&shy;<lb/>clinati al piano dell'orizzonte per un angolo vicino al mezzo retto, pens&ograve; <lb/>che si potessero salvare altresi le apparenze de'Parelii, e tuttoci&ograve; si studi&ograve; <lb/>di confermare per l'esperienza, costruendo alcuni di cos&igrave; fatti cilindretti ar&shy;<lb/>tificiali, e mostrando che collocati opportunamente innanzi all'occhio ripro&shy;<lb/>ducevano le sembianze de'fenomeni celesti. </s></p><p type="main">

<s>&ldquo; Per far vedere all'occhio tutti questi differenti effetti de'ci&shy;<lb/>lindri, leggesi in fine alla citata <emph type="italics"/>Relazione<emph.end type="italics"/> tradotta dal Viviani, <lb/>egli ne ha portato uno di vetro lungo un piede, della forma della <lb/><figure id="id.020.01.685.1.jpg" xlink:href="020/01/685/1.jpg"/></s></p><p type="caption">

<s>Fig. </s>

<s>45.<lb/>45a figura, con un cilindro di legno nel mezzo, invece di nocciolo <lb/>opaco, e con lo spazio fra esso ripieno d'acqua, in luogo di ghiaccio <lb/>trasparente. </s>

<s>Tal cilindro, stando esposto al sole e situato l'occhio in <lb/>luogo a proposito, si vedevano successivamente tutte quelle rifles&shy;<lb/>sioni e rifrazioni, delle quali si &egrave; parlato. </s>

<s>Dal che si poteva con&shy;<lb/>cludere che, dandosi una grande quantit&agrave; di simili cilindri, ma piccolissimi <lb/>in comparazione di questo, occupando l'aria e con quelle diverse positure <pb xlink:href="020/01/686.jpg" pagenum="129"/>che si sono supposte, ne dovrebbero seguire precisamente tutte le apparenze <lb/>de'Parelii e de'cerchi loro. </s>

<s>Si desider&ograve;, per maggior confermazione delle <lb/>verit&agrave; del supposto, di poter osservare di questi piccoli cilindri caduti in <lb/>terra, nel tempo de'Parelii, il che egli mostr&ograve; non potersi fare facilmente, <lb/>perch&egrave; i vapori che allora ascendono da terra e che son cagione delle loro <lb/>figure cilindriche, gli tengon cos&igrave; in aria sospesi, ed aggiunse non dover pa&shy;<lb/>rere strano che dei piccolissimi grani di gragnuola fossero in tal guisa so&shy;<lb/>stenuti dai vapori, i quali, nel rarefarsi ed estendersi per all'insu, potevano <lb/>aver gran movimento per questo effetto. </s>

<s>Che questo era ben molto pi&ugrave; fa&shy;<lb/>cile a concepirsi che l'immaginarsi come questi medesimi vapori potrebbero <lb/>tener sospeso un grandissimo e pesantissimo cerchio di ghiaccio, e tale quale <lb/>l'ha supposto Renato Des Cartes, per dichiarare la cagion de'Parelii e del <lb/>gran cerchio bianco dell'apparenza di Roma. </s>

<s>In questo supposto erano an&shy;<lb/>cora da notarsi le seguenti difficolt&agrave;, cio&egrave; che non vi si trova ragione per&shy;<lb/>ch&egrave; il cerchio bianco debba passar per il sole, come sempre si osserva, e <lb/>lo seguiti secondo che muta altezza, bench&egrave; l'apparenza duri qualche volta <lb/>tre o quattr'ore. </s>

<s>Che questo medesimo cerchio bianco fatto di ghiaccio, es&shy;<lb/>sendo veduto da spettatori lontanissimi tra di loro, non potrebbe mai parere <lb/>tondo a tutti, com'ei fa, e attraversare il sole. </s>

<s>Che quando si osservano i <lb/>Parelii non si vede per modo alcuno questa nuvola tonda circondata da un <lb/>cerchio di ghiaccio, la quale per la sua densit&agrave; dovrebbe ascondere una <lb/>parte del cielo, ma che il tempo par quasi tutto sereno, non avendovi che <lb/>piccole nuvole, le quali si vedono mutar luogo, mentre che il gran cerchio <lb/>ed i Parelii stanno fermi. </s>

<s>Che in questo supposto non viene se non per for&shy;<lb/>tuna che i Parelii, che sono accanto al Sole, apparischino nel segamento <lb/>d'una Corona e del gran cerchio bianco, come quasi sempre si osserva, <lb/>cos&igrave; facendo ben vedere che le cause de'Parelii e delle Corone son molto <lb/>poco differenti, contro l'opinione di Monsu Des Cartes &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. CXXXIII, c. </s>

<s>144). </s></p><p type="main">

<s>Quello che il Viviani rimesse al principe Leopoldo, piuttosto che un <lb/>sunto di questa Relazione, si direbbe un assennatissimo giudizio delle ipo&shy;<lb/>tesi ivi proposte a dichiarar la ragione di apparenze prodotte in luoghi e da <lb/>cause tanto remote e inaccessibili a noi. </s>

<s>E perch&egrave; il giudizio di un tanto <lb/>uomo, in cosa di tanta curiosit&agrave; ed importanza, vuol tenersi in gran pregio, <lb/>da noi si crede esser ben fatto il riferirlo: </s></p><p type="main">

<s>&ldquo; In essa Relazione promuove e tocca leggermente sistemi oltre a modo <lb/>ingegnosi per salvar quelle (le Corone apparse in Parigi) ed altre simili ap&shy;<lb/>parenze meteorologiche. </s>

<s>Da questo saporitissimo saggio, bench&egrave; senza dimo&shy;<lb/>strazioni matematiche, si pu&ograve; risolutamente affermare che se tali fenomeni <lb/>realmente non seguono nei modi immaginati dall'Ugenio (che pur non hanno <lb/>in s&egrave; dell'impossibile, anzi assaissimo del verisimile) questo almeno (con&shy;<lb/>ceduti sospesi e vaganti per l'aria que'piccoli grani di diaccio o tondi o <lb/>bislunghi, o tutti trasparenti o mezzi opachi o in uno o in altro modo si&shy;<lb/>tuati) sono valevoli per s&egrave; soli a salvare quelle apparenze esplicate dall'Uge-<pb xlink:href="020/01/687.jpg" pagenum="130"/>nio, poich&egrave; tanto necessitano a confessare le leggi infallibili della Geometria. </s>

<s><lb/>Se poi la Natura opera in ci&ograve; diversamente, ha nondimeno questo Autore <lb/>adempiuta la parte di ottimo fisico e di matematico senza pari. </s>

<s>E di vero <lb/>questi ed altri maravigliosi effetti intorno a materia si vasta e cotanto astrusa, <lb/>quanto &egrave; questa delle riflessioni e delle rifrazioni della luce, non si poteva <lb/>pretendere che venissero penetrati giammai da alcun Filosofo, che insieme <lb/>non fosse e Filosofo e Geometra sottilissimo; e siccome i passati secoli son <lb/>rimasti privi di notizie tanto sublimi, cos&igrave; il presente pu&ograve; gloriarsi di es&shy;<lb/>ser giunto ad intender, per mezzo prima del Galileo ed ora di si alto inge&shy;<lb/>gno, che nell'oscurit&agrave; della Fisica non si vedr&agrave; mai lume o certezza di co&shy;<lb/>gnizione, senza la chiara scorta della purissima Geometria, che &egrave; quella che <lb/><emph type="italics"/>puote disnebbiar nostro intelletto &rdquo;<emph.end type="italics"/> (MSS. Cim., T. XXI, c. </s>

<s>100). </s></p><p type="main">

<s>Invitato a riferire al principe dell'Accademia fiorentina intorno all'ipo&shy;<lb/>tesi ugeniana, che cosa il Viviani avrebbe potuto dire di pi&ugrave; giudizioso? </s>

<s><lb/>Nessuno pu&ograve; decidere se la Natura operi veramente a quel modo, ma poi&shy;<lb/>ch&egrave; ella in tutte le operazioni sue geometrizza, &egrave; conforme agl'istituti e al <lb/>magistero di lei il modo che vien proposto dall'ingegnosissimo Ugenio. </s></p><p type="main">

<s>Specul&ograve; poco dopo anche il Newton sulle ragioni delle spettacolose <lb/>apparenze celesti, ma a che poteva egli risolversi un uomo di quell'indole, <lb/>che professava il principio non doversi filosofar della Natura, se non che <lb/>sui fatti prima bene osservati? </s>

<s>Egli stesso risponde nell'Avvertimento alla <lb/>prima edizione dell'Ottica: &ldquo; Coronas colorum, quae circum solem et <lb/>lunam nonnumquam videntur, conatus sum quadatenus explicare; verum, <lb/>inopia plurium observationum, materiam illam aliis penitius explorandam <lb/>relinquo. </s>

<s>&rdquo; </s></p><p type="main">

<s>Perci&ograve; nel libro I, parte II, dell'opera che segue, accennando il Newton <lb/>agli Aloni, commenta le ipotesi dell'Huyghens, concludendo come aveva gi&agrave; <lb/>concluso il Viviani che, sebbene non possa dimostrarsi come cosa di fatto, <lb/>pur &egrave; possibile che la Natura operi a quel modo. </s>

<s>&ldquo; Quae porro Halos, quo&shy;<lb/>ties grando apta sit figura, colorata esse poterit: tumque intra rubra erit <lb/>facta, radiis minime refrangibilibus, et caerulea extra radiis maxime refran&shy;<lb/>gibilibus, praesertim si grandinis particulae habeant forte in centris suis <lb/>opacos nivis globulos, qui lumen intra Halo intercipientes, quomodo Huge&shy;<lb/>nius observavit, efficere possint ut interior ipsius pars distinctius, quam alio&shy;<lb/>qui futurum esset, definita sit. </s>

<s>Etenim huiusmodi grandinis particulae, quam&shy;<lb/>vis globosae, tamen terminando lumen inclusa sua nive exhibere poterunt <lb/>Halo rubram intra, et coloris expertem extra, atque etiam obscuriorem in&shy;<lb/>tra rubram sui partem, quam extra, uti plerumque fieri solet. </s>

<s>Etenim ex <lb/>radiis qui proxime nivem praeterferuntur rubri refringentur minime, adeo&shy;<lb/>que ad oculum in lineis directissimis pervenient. </s>

<s>Lumen quod a pluviae <lb/>gutta post duas refractiones et tres pluresve reflexiones egreditur, vix satis <lb/>forte est ad arcum efficiendum qui sub sensum cadat, at in glaciei parti&shy;<lb/>culis illis cylindraceis, quarum ope Hugenius rationem Parheliorum expli&shy;<lb/>cal, poterit fortasse sensu percipi &rdquo; (Edit. </s>

<s>cit., pag. </s>

<s>65). </s></p><pb xlink:href="020/01/688.jpg" pagenum="131"/><p type="main">

<s>Cosi il Newton gran Maestro dell'Ottica, dando un bell'esempio ad al&shy;<lb/>cuni orgogliosi sapienti, confessava che delle Corone e de'Parelii la Diottrica <lb/>e la Meteorologia non avrebbero saputo dire nulla di meglio, di quel che <lb/>l'Huyghens ne scrisse, fra gli Opuscoli postumi, nella sua <emph type="italics"/>Dissertazione,<emph.end type="italics"/> e <lb/>la stessa scienza moderna, bench&egrave; abbia trovato modo di salvar qualche ap&shy;<lb/>parenza, ricorrendo alle diffrazioni, per le grandi Corone e i Parelii invoca <lb/>ancora l'efficacia de'cilindretti ugeniani. </s></p><pb xlink:href="020/01/689.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Del calore<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. Dell'antica teoria degl'ignicoli rinnovata da Galileo: della questione del freddo positive o priva&shy;<lb/>tivo. </s>

<s>&mdash; II. </s>

<s>Di alcune speculazioni e sperienze meno note fatte intorno al calore dagli Accade&shy;<lb/>mici del Cimento. </s>

<s>&mdash; III. </s>

<s>Del calore di comunicazione, e del calorico raggiante. </s>

<s>&mdash; IV. </s>

<s>Degli <lb/>effetti del calore negli agghiacciamenti. </s>

<s>&mdash; V. </s>

<s>Degli effetti del calore nelle evaporazioni. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>La lampada ardente del Sole e le nostre fiamme artificiali conferma&shy;<lb/>rono cos&igrave; nelle menti degli uomini l'opinione della concomitanza della luce <lb/>col calore, che furono per lungo tempo credute inseparabili, cosicch&egrave; sola&shy;<lb/>mente sopite, per causa estrinseca e violenta, si credeva esser rimasta la <lb/>luce stessa, quando in un corpo incalorito non si mostra parvente. </s>

<s>Comun&shy;<lb/>que sia quella concomitanza de'due elementi, ministri principali della Na&shy;<lb/>tura, &egrave; cos&igrave; frequente, e per la comune consuetudine hanno propriet&agrave; tal&shy;<lb/>mente comuni, che non si pu&ograve; alla storia della scienza della luce non far <lb/>immediatamente succedere la storia della scienza del calore. </s></p><p type="main">

<s>Resa quella scienza impossibile da'Peripatetici, che reputarono essere <lb/>il calore stesso qualit&agrave; e non sostanza, Leucippo, Democrito ed Epicuro, con <lb/>altri antichi Filosofi seguaci di Platone, dissero, avviando le loro specula&shy;<lb/>zioni per miglior sentiero, il caldo essere una mera affezione de'nostri sensi, <lb/>la quale non d'altronde derivi che dall'insinuarsi ne'pori delle nostre carni, <lb/>uscendo con moto velocissimo, da'corpi detti calidi, alcuni atomi sottilissimi <lb/>e perci&ograve; atti a penetrare dovunque. </s>

<s>Il veder poi che il calore era bene spesso <lb/>eccitato dal moto, e ch'era effetto naturale di lui il rarefare i corpi, serviva <lb/>di conferma a quelle dottrine, che perci&ograve;, in sul primo risorgere della scienza <pb xlink:href="020/01/690.jpg" pagenum="133"/>fisica fra noi, si seguitarono anche da alcuni volutisi serbare dall'altra parte <lb/>ad Aristotile sempre devoti. </s>

<s>Scriveva Andrea Cesalpino, nel libro V delle <lb/>sue Questioni peripatetiche: &ldquo; Caliditas igitur raritatem sequitur, quia affi&shy;<lb/>nis quaedam naturae sunt: idcirco ubi una in materia oritur et altera se&shy;<lb/>quitur. </s>

<s>Simul enim quid incalescit rarius etiam fit, locum ampliorem quae&shy;<lb/>rens, et e converso, quod enim unum efficit alterum quoque. </s>

<s>Motus igitur <lb/>disgregando simul rarefacit, et caliditatem in materia educit. </s>

<s>Quies autem <lb/>contraria praestat, condensationem scilicet et frigiditatem, quae omnia pri&shy;<lb/>vationes quaedam sunt &rdquo; (Venetiis 1571, pag. </s>

<s>70). E nel Trattato <emph type="italics"/>De plan&shy;<lb/>tis:<emph.end type="italics"/> &ldquo; Quamvis autem sensui manifestus sit calor, non ob id negandum est: <lb/>quae enim minus calida sunt quam tactus nostri, frigida indicantur &rdquo; (Flo&shy;<lb/>rentiae 1583, pag. </s>

<s>4). </s></p><p type="main">

<s>Dal raro e dal denso, come da effetti essenzialmente indicativi, argo&shy;<lb/>mentava la natura e le propriet&agrave; del calore anche quel Giovan Batista Bene&shy;<lb/>detti, primo Maestro della scienza fisica in Italia, e di cui dovremo nel <lb/>presente soggetto ammirar le dottrine cos&igrave; dalla lontana splendenti nella lieta <lb/>luce del vero, in mezzo alla profonda caligine peripatetica. </s>

<s>Se avesse Gali&shy;<lb/>leo prese le Speculazioni di lui ad esempio del suo filosofare, avrebbe po&shy;<lb/>tuto senza scapito, ed anzi con qualche avvantaggio della verit&agrave; raffinare le <lb/>proprie, ringentilendole della grossolana materialit&agrave; delle dottrine democri&shy;<lb/>tiche ed epicuree, ch'egli mette nuovamente in corso come monete cavate <lb/>dall'erario dell'antica Filosofia, senz'essere state rifuse. </s>

<s>E se nel maneg&shy;<lb/>giarle par che perdano alquanto di quella ruggine, ci&ograve; non fa veramente <lb/>altro effetto che di mostrar pi&ugrave; chiara e pi&ugrave; scolpita la poco fina arte che <lb/>ebbe il monetario in coniarle. </s></p><p type="main">

<s>Nel <emph type="italics"/>Saggiatore<emph.end type="italics"/> trattiensi lungamente a dare al Sarsi una lezione pla&shy;<lb/>tonica intorno alle qualit&agrave; secondarie della materia, che non riseggono real&shy;<lb/>mente in essa, ma ne'nostri sensi, fuor de'quali non sono altro che nomi. </s>

<s><lb/>Com'avean fatto gi&agrave; Democrito ed Epicuro, applicando quelle antiche e ve&shy;<lb/>rissime dottrine platoniche al calore, Galileo cos&igrave; scrive: &ldquo; E tornando al <lb/>primo mio proposito in questo luogo, avendo gi&agrave; veduto come molte affe&shy;<lb/>zioni, che sono riputate qualit&agrave; risedenti ne'soggetti esterni, non hanno ve&shy;<lb/>ramente altra esistenza che in noi, e fuor di noi, non sono altro che nomi; <lb/>dico che inchino assai a credere che il calore sia di questo genere, e che <lb/>quelle materie che in noi producono o fanno sentire il caldo, le quali noi <lb/>chiamiamo col nome generale fuoco, siano una moltitudine di corpiccioli mi&shy;<lb/>nimi in tal e tal modo figurati, mossi con tanta e tanta velocit&agrave;, li quali <lb/>incontrando il nostro corpo lo penetrino colla lor somma sottilit&agrave;, e che il <lb/>lor toccamento, fatto nel lor passaggio per la nostra sostanza e sentito da <lb/>noi, sia l'affezione che noi chiamiamo caldo &rdquo; (Alb. </s>

<s>IV, 333). </s></p><p type="main">

<s>Que'corpiccioli ignei riputati da tutti cos&igrave; minimi da rendersi anco agli <lb/>occhi pi&ugrave; acuti invisibili, Galileo fu il primo a vederli penetrare attraverso <lb/>il vetro di una caraffa posta a fuoco lento, e mescendosi all'acqua ivi den&shy;<lb/>tro rinchiusa, farla notabilmente crescere di volume, come dimostrava ve-<pb xlink:href="020/01/691.jpg" pagenum="134"/>dersi per esperienza a Lodovico delle Colombe. </s>

<s>&ldquo; Volendo poi vedere sensa&shy;<lb/>tamente da che derivi questo ricrescimento, andate con diligenza osservando <lb/>e vedrete che, secondo che gli atomi di fuoco si vanno moltiplicando per <lb/>l'acqua, ed aggregandosi molti insieme, formano alcuni piccoli globettini, <lb/>li quali in gran numero vanno ascendendo per l'acqua e scappando fuori <lb/>della sua superficie &rdquo; (Alb. </s>

<s>XII, 466, 67). </s></p><p type="main">

<s>Come poi que'globetti o quelle <emph type="italics"/>sferette di fuoco<emph.end type="italics"/> notassero salvi e si&shy;<lb/>curi in mezzo all'acqua, senza affogarvi dentro, era un mistero che il Co&shy;<lb/>lombo non sapeva intendere, e che a Galileo non riusc&igrave; di spiegare. </s>

<s>Nono&shy;<lb/>stante, dietro questa fede che aveva agli atomi ignei di Democrito resi agli <lb/>occhi suoi cos&igrave; visibili, scioglie alcuni problemi termici de'pi&ugrave; curiosi, uno <lb/>de'quali &egrave; questo che si legge nella raccolta de'<emph type="italics"/>Pensieri varii:<emph.end type="italics"/> &ldquo; Che una <lb/>mano che tenuta in aria ti par calda, poi posta nell'acqua si raffredda; que&shy;<lb/>sta ne &egrave; la cagione considerandosi il caldo esterno e l'interno, che mentre <lb/>resta in aria, gli atomi ignei suoi proprii hanno luogo di uscire, che son <lb/>quelli che cagionano il caldo, ma posta in acqua, le particole d'essa tornano <lb/>e serrano gli aditi onde escono i detti atomi, essendo le parti dell'acqua <lb/>maggiori delle porosit&agrave;, per le quali scappano fuori: il che non avviene del&shy;<lb/>l'aria trovando il campo libero, come quelli che non son tenuti dalle parti <lb/>dell'aria per esser minori de'pori onde <emph type="italics"/>erumpunt,<emph.end type="italics"/> essendo che il caldo non <lb/>sia altro che il contatto e solleticamento di quegli atomi calidi, i quali nello <lb/>scappar fuora trovano le membra del corpo &rdquo; (Alb. </s>

<s>XIV. 334). </s></p><p type="main">

<s>Un altro problema di simil genere fu proposto a risolvere a Galileo dal <lb/>conte Pietro de'Bardi, il quale era venuto in gran curiosit&agrave; di sapere come <lb/>mai coloro che vanno a bagnarsi la state in Arno, al primo entrar nel&shy;<lb/>l'acqua, provino un senso molesto di freddo: poi usciti fuori alla riva e <lb/>tornati a tuffarsi di nuovo, quella stessa acqua dia invece un senso di te&shy;<lb/>pore giocondo. </s>

<s>Quanto alla prima parte Galileo, nella soluzione del problema <lb/>precedente aveva la risposta pronta, ma per&ograve; non si sodisfaceva con essa <lb/>alla seconda parte di questo nuovo quesito, che &egrave; come mai l'acqua sentita <lb/>dianzi cos&igrave; fredda, ora invece si trovi calda. </s>

<s>Ebbe a ricorrer perci&ograve; ad am&shy;<lb/>metter per fondamento del suo discorso il principio che l'acqua d'Arno sotto <lb/>i raggi del sole sia realmente pi&ugrave; fredda dell'aria. </s>

<s>Avrebbe potuto assicu&shy;<lb/>rarsi della verit&agrave; o della falsit&agrave; di un tal principio assunto, per l'esperienza <lb/>del Termometro, ma o non seppe o non volle, o tanto poca pratica aveva <lb/>dello strumento, che non gli sovvenne di farlo. </s></p><p type="main">

<s>La soluzione del problema termico proposto dal conte Bardi si legge <lb/>stampa ta fra le opere di Galileo e, nell'edizione dell'Alberi segnatamente, <lb/>al T. XIV da pag. </s>

<s>297-99. Noi la porgeremo a leggere sotto forma men <lb/>conosciuta, ed &egrave; quella che le dava il Viviani dietro la dettatura dello stesso <lb/>Galileo, il quale voleva anche questa raccogliere fra le soluzioni degli altri <lb/><emph type="italics"/>Problemi Naturali.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Problema II. &mdash; Uno va per bagnarsi in Arno, si spoglia e si mette <lb/>a sedere all'ombra. </s>

<s>Stando cos&igrave;, sente un fresco comportabile e temperato: <pb xlink:href="020/01/692.jpg" pagenum="135"/>entra poi nell'acqua, e gli par di sentirla assai fredda. </s>

<s>Statoci un pezzo, ne <lb/>esce, torna all'ombra e sente un freddo estremo: di nuovo si tuffa nel&shy;<lb/>l'acqua, e dove la prima volta gli parve molto fredda, la seconda gli appa&shy;<lb/>risce piuttosto temperata e calda. </s>

<s>Si domanda adesso la cagione di tal di&shy;<lb/>versit&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il Problema si risolve cos&igrave;: Noi abbiamo in una stanza una tinozza <lb/>piena d'acqua e ci &egrave; stata v. </s>

<s>g. </s>

<s>15 di freddezza. </s>

<s>Vien uno, si spoglia e en&shy;<lb/>tra nella tinozza. </s>

<s>Chiara cosa &egrave; ch'ei sentir&agrave; assai pi&ugrave; freddo in quell'acqua, <lb/>ch'ei non sentiva innanzi ch'ei vi entrassse, dal che si pu&ograve; concludere che, <lb/>stando l'aria e l'acqua in un medesimo luogo, cio&egrave; ad un istesso caldo o <lb/>ad un istesso freddo, sempre l'acqua apparir&agrave; assai pi&ugrave; fredda dell'aria. </s>

<s>Di&shy;<lb/>ciamo adunque che dei gradi di freddezza, de'quali l'aria ne ha per es. </s>

<s>2, <lb/>l'acqua ne abbia 10. Adunque un'altr'acqua, che ne abbia 6 soli, apparir&agrave; <lb/>fredda, in comparazione dell'aria che ne ha 2, ma ben calda in relazione <lb/>dell'acqua che ne ha 10. Ora, stante questo, colui che si va a bagnare in <lb/>Arno, mentre sta ignudo all'ombra, gode il fresco temperato dell'aria, che <lb/>ha 2 soli gradi di freddezza. </s>

<s>Ma quando entra nell'acqua d'Arno, sente la <lb/>freddezza sua che &egrave; di 6 gradi; di 6 gradi dico e non di 10, perch&egrave; il sole <lb/>ardente, che l'ha percossa per lo spazio di molte miglia, glie ne viene aver <lb/>levati 4, e per&ograve;, in rispetto dell'aria che ne ha 2 soli, gli pare assai fredda. </s>

<s><lb/>Esce poi costui d'Arno, e torna all'ombra bagnato e coperto da un sotti&shy;<lb/>lissimo velo d'acqua, la quale, per esser pochissima, non s&igrave; tosto &egrave; condotta <lb/>sotto l'albero all'ombra, che viene ad acquistare i 4 gradi di freddezza tol&shy;<lb/>tigli dal sole; onde, di 6 che ella ne aveva innanzi, si riduce ad un tratto <lb/>ad averne 10. Sicch&egrave; colui che si bagna non sente pi&ugrave; 6 gradi di freddezza <lb/>ma 10, e perci&ograve;, mentre sta sotto l'albero bagnato, sente freddo estremo, <lb/>ma se si torna po&igrave; a tuffarsi entra nell'acqua che ha 6 gradi soli di fred&shy;<lb/>dezza, onde, perdendo 4 gradi di freddo, gli pare di essere entrato in un <lb/>bagno temperato &rdquo; (MSS. Gal., P. VI, T. III, c. </s>

<s>29). </s></p><p type="main">

<s>Essendo falso il principio da cui muove, &egrave; naturale che fosse falso que&shy;<lb/>sto discorso di Galileo, nel suo processo e nella sua conclusione. </s>

<s>Ad accor&shy;<lb/>gersi della qual falsit&agrave; e a palesarla al mondo par che fosse primo Tom&shy;<lb/>maso Cornelio, il quale cos&igrave; in un suo Proginnasma dice del principio <lb/>galileiano, che ammette l'acqua insolata ritener maggior freddezza dell'aria <lb/>circunfusa: &ldquo; Atqui de hoc fortasse quis ambiget qui observaverit aquam <lb/>immobilem aestivo soli diutius expositam maiori calore tangendi sensum ef&shy;<lb/>ficere quam circumpositum aerem. </s>

<s>At vero in aqua, cuius natura crassior <lb/>est, calor a sole excitatus magis intenditur quam in aere, qui est natura <lb/>tenuior, et perpetua mobilitate rarius suique dissimilis &rdquo; (Oper. </s>

<s>posth., <lb/>Neap. </s>

<s>1688, pag. </s>

<s>38). </s></p><p type="main">

<s>Perci&ograve;, mettendosi il Cornelio a risolvere quello stesso problema, e stu&shy;<lb/>diandosi di cansar le false vie tenute da Galileo, assume per fondamento <lb/>del suo discorso un fatto sperimentale, ch'&egrave; pure anch'esso manifestamente <lb/>falso. </s>

<s>Il fatto &egrave; che l'acqua nell'aria rarefatta si riscalda, e nella compressa <pb xlink:href="020/01/693.jpg" pagenum="136"/>e condensata si raffredda, <emph type="italics"/>quod nos,<emph.end type="italics"/> afferma l'Autore, <emph type="italics"/>comparata ad id <lb/>opus peculiari machina quotidie experimur<emph.end type="italics"/> (ibi, pag. </s>

<s>36). </s></p><p type="main">

<s>Quella Macchina dee esser senza dubbio la Pneumatica, e il Cornelio <lb/>dee esser rimasto certamente ingannato da quell'effetto maraviglioso descritto <lb/>gi&agrave; dal Boyle, dell'acqua tiepida che, nel vuoto o nell'aria molto rarefatta, <lb/>si leva a bollore. </s>

<s>I nostri Accademici del Cimento per&ograve; s'erano sgannati <lb/>aprendo la palla del vuoto torricelliano, e cavandone fuori il vasetto del&shy;<lb/>l'acqua, alla quale <emph type="italics"/>non parve che da tal bollimento se le fosse accresciuto <lb/>calore<emph.end type="italics"/> (Saggi ecc., Firenze 1841, pag. </s>

<s>64). Che se anzi avessero con pi&ugrave; di&shy;<lb/>ligenza osservato si sarebbe in essi accresciuta la maraviglia, ritrovando che <lb/>in que'casi la temperatura invece diminuisce, come pure si sarebbe il Cor&shy;<lb/>nelio persuaso con facilissima esperienza che in ogni compressione e nella <lb/>percossa, di che offrono cos&igrave; ovvii esempi i martelli, i corpi tutt'altro che <lb/>raffreddarsi acquistan calore. </s>

<s>Comunque sia, l'Autor de'Proginnasmi profes&shy;<lb/>sando dottrine in aperta contradizione de'fatti, asserisce che il freddo sen&shy;<lb/>tito da chi si espone colla pelle umida al vento dipende da ci&ograve;, che il vento <lb/>stesso percotendo e comprimendo rintuzza il moto agl'ignicoli che, rimasti <lb/>li inerti, vi producono perci&ograve; il senso della freddezza. </s></p><p type="main">

<s>&ldquo; Ex his ut arbitror perspicuum videri potest cur aestatis tempore la&shy;<lb/>vaturi ut primum nudati corpore in maris aut fluminis aquas quamquam <lb/>calore solis quodammodo tepefactas merguntur, statim molesto frigoris sensu <lb/>afficiantur: mox autem brevi mora interposita suaviter degant. </s>

<s>At interea <lb/>si humentia membra supra aquas exerant, vel in litus ripamve exiliant, rur&shy;<lb/>sus novo ingratoque frigore corripiuntur. </s>

<s>Verum ad easdem subinde aquas <lb/>reversi, iucundo quodam teporis sensu recreari videantur. </s>

<s>Nimirum quo&shy;<lb/>tiescumque aestuantes aquas minus calidas subeunt, frigoris sensum perci&shy;<lb/>piunt, donec infracto caloris excessu eorumdem corpora cum contiguis aquis <lb/>aequaliter temperentur: tum vero cessat frigoris sensus. </s>

<s>Sed ubi primum <lb/>ex aquis madentes fuerint egressi, quoniam circumfusus corpori humor a <lb/>quovis vento aurave protinus frigescit, subiti frigoris molestiam perpetiun&shy;<lb/>tur. </s>

<s>Neque vero id unquam solet contingere nisi ubi madens corpus ventus <lb/>aliquis perflaverit &rdquo; (ibi, pag. </s>

<s>37). </s></p><p type="main">

<s>Cos&igrave; il Problema del conte Bardi non riusciva ancora ben risoluto, spe&shy;<lb/>cie per quel che riguarda la seconda parte, essendo chiaro che sempre si <lb/>sente freddo alle membra umide esposte anco all'aria quietissima, come sa&shy;<lb/>rebbe nel chiuso di una stanza. </s></p><p type="main">

<s>Giuseppe Del Papa saviamente avendo riconosciuto quello essere un pro&shy;<lb/>blema di Termometria, ricorse all'uso degli strumenti, e bench&egrave; anche il <lb/>Cornelio avesse giudicato dall'impressione subiettiva del senso non esser al&shy;<lb/>trimenti vero l'assunto di Galileo, che cio&egrave; l'acqua sia pi&ugrave; fredda dell'aria <lb/>circunfusa; ei fu nonostante il primo a farne esperienze nell'Arno co'ter&shy;<lb/>mometri fiorentini. </s>

<s>&ldquo; Ella supponga dunque (cos&igrave; scriveva al Redi nella Let&shy;<lb/>tera dell'Umido e del Secco) per cosa infallibile e da me pi&ugrave; e pi&ugrave; volte <lb/>ed in varie guise esperimentata, che ogni sorta d'acqua tenuta al sole per <pb xlink:href="020/01/694.jpg" pagenum="137"/>una considerabile lunghezza di tempo, si riscalda assai pi&ugrave; ed in s&egrave; stessa <lb/>ritiene maggior caldezza di quella che si ritenga dall'aria, la quale sia stata <lb/>per altrettanto e pi&ugrave; tempo esposta ai medesimi raggi solari &rdquo; (Firenze 1681, <lb/>pag. </s>

<s>89). </s></p><p type="main">

<s>Dietro questo infallibile supposto e dietro la considerazione dell'aria, <lb/>che &egrave; a contatto della pelle ignuda attemperata al calor naturale esalato da <lb/>lei, rimossa la quale aria ne sottentra altra in suo luogo, che sottraendo <lb/>nuovo calor al contatto &egrave; causa del refrigerio prodotto dal vento; il Del Papa <lb/>scioglie cos&igrave; concludendo la prima parte del proposto problema: &ldquo; Insomma <lb/>evidente cosa &egrave; che l'acqua d'Arno, bench&egrave; in realt&agrave; sia notabilmente pi&ugrave; <lb/>calda dell'aere, ci apparisce fredda nel primo ingresso, perch&egrave; toglie da noi <lb/>quel nostro proprio vapore ed in questo caso l'acqua fa l'opra istessa che <lb/>ci fa in aria il vento, il quale parimente, perch&egrave; lungi da noi sospinge l'aria <lb/>dalla nostra esalazione riscaldata, e in luogo di quella ci porta attorno altra <lb/>ed altra aria; perci&ograve; viene a privarci di una parte di caldo, ed in tal guisa <lb/>apportarci refrigerio e freddezza &rdquo; (ivi, pag. </s>

<s>91). </s></p><p type="main">

<s>Quanto al secondo effetto poi preso a spiegare dal Galileo, cio&egrave; che <lb/>dopo esserci noi trattenuti nell'acqua, se ritorniamo nell'aria sentiamo un <lb/>freddo molto notabile, dimodoch&egrave; allora l'acqua ci sembra assai pi&ugrave; calda <lb/>dell'aria; &ldquo; di tutto ci&ograve;, soggiunge il Del Papa, evidentissima cagione si &egrave; <lb/>l'eccesso della caldezza con cui in realt&agrave; l'acqua supera e vince l'aere, onde <lb/>uscendo d'un mezzo pi&ugrave; caldo di quello nel quale entriamo novellamente, <lb/>dobbiamo bene per necessit&agrave; sentir freddo, non essendo altro il freddo che <lb/>mancanza o scemamento di caldo &rdquo; (ivi, pag. </s>

<s>92). </s></p><p type="main">

<s>Nemmen questa, bench&egrave; fosse la miglior soluzione che si potesse a <lb/>que'tempi dare al Problema, sodisfece poi pienamente agl'ingegni, i quali <lb/>trovarono pi&ugrave; opportuno d'applicarvi la teoria del calorico latente, oggid&igrave; <lb/>levata anch'essa di seggio da nuove altre teorie. </s>

<s>Perci&ograve; bastando allo scopo <lb/>nostro di aver mostrato a quali gradi fosse giunto il processo di questo ge&shy;<lb/>nere di speculazioni termiche, in sulla fine del secolo XVII, le ultime pa&shy;<lb/>role sopra citate da Giuseppe Del Papa ci aprono la via alla storia di una <lb/>questione, che se non &egrave; per s&egrave; di grande importanza serve pure a dichia&shy;<lb/>rar meglio il soggetto che abbiamo preso a trattare. </s></p><p type="main">

<s>Diceva dianzi l'Autor della Lettera al Redi nient'altro essere il freddo <lb/>che <emph type="italics"/>mancanza<emph.end type="italics"/> o <emph type="italics"/>scemamento di caldo:<emph.end type="italics"/> sentenza che sebbene sia oggid&igrave; <lb/>da tutti senza controversia tenuta per vera, fu nonostante a'tempi del Del <lb/>Papa, specialmente in Firenze, assai disputata. </s>

<s>La disputa ebbe origine dal <lb/>Gassendo, il quale, nelle sue <emph type="italics"/>Animadversiones in Decimum Librum Dio&shy;<lb/>genis Laertii,<emph.end type="italics"/> rinnovando gli antichi placiti filosofici di Epicuro, professava <lb/>che come il caldo &egrave; prodotto dagli atomi ignei, cos&igrave; il freddo &egrave; prodotto da <lb/>altri atomi di natura opposta, e ch'egli perci&ograve; appella frigorifici. </s>

<s>Quegli atomi <lb/>son di necessit&agrave; in continua lotta fra loro e ora vincono gli uni, ora vin&shy;<lb/>cono gli altri, per cui si vede un corpo, con ripetuta incessante vicenda, <lb/>passare dal freddo al caldo e dal caldo al freddo. </s></p><pb xlink:href="020/01/695.jpg" pagenum="138"/><p type="main">

<s>&ldquo; Atque ex his demum (scrive il Gassendo nel vol. </s>

<s>I dell'opera citata) <lb/>intelligitur dum quaerunt vulgo an frigus sit qualitas vera et positiva, an <lb/>mera caloris privatio. </s>

<s>Videri omnino esse frigus veram et positivam quali&shy;<lb/>tatem eo modo quo calor et caeterae sunt. </s>

<s>Tametsi enim multa videantur <lb/>ex sola caloris absentia frigescere, nihilominus, nisi frigus extrinsecus intro&shy;<lb/>ducatur, non tam profecto frigescere quam decalescere sunt censenda. </s>

<s>Esto <lb/>enim lapis, lignum aut aliquid aliud, quod nec calidum nec frigidum sit: id <lb/>ubi fuerit admotum igni calefiat sane at cum deinceps calor excedet, neque <lb/>frigidum ullum circumstabit, non erit cur dicas ipsum frigefieri, potius quam <lb/>minus calidum fieri redireve in suum statum. </s>

<s>Profecto ii sunt frigoris ef&shy;<lb/>fectus qualeis habere privatio, quae actionis est incapax, non potest. </s>

<s>Siqui&shy;<lb/>dem cum per hyemem immittimus manum in labentem fluminis aquam, quod <lb/>frigus in ea sentitur non potest dici mera privatio, aliudque prorsus esse ap&shy;<lb/>paret sentiri aquam frigidam et sentiri non calidam &rdquo; (Lugduni 1675, pag. </s>

<s>176). </s></p><p type="main">

<s>Il Gassendo fu filosofo a'suoi tempi di gran reputazione, per cui le rin&shy;<lb/>novate dottrine di lui si diffusero nell'universale degli scienziati, come lo <lb/>prova il fatto che dal 1646 al 1675 furon fatte, delle <emph type="italics"/>Animadversiones in <lb/>X Laertii,<emph.end type="italics"/> tre edizioni, e si diffusero particolarmente fra'nostri Accademici <lb/>del Cimento, come si vede qua e l&agrave; dalle citazioni de'<emph type="italics"/>Saggi,<emph.end type="italics"/> e pi&ugrave; frequen&shy;<lb/>temente da quelle de'Manoscritti. </s></p><p type="main">

<s>Professando cos&igrave; i Nostri dottrine introdotte da uno straniero non so&shy;<lb/>spettavano di contrapporsi agli insegnamenti di Galileo, i quali intorno a <lb/>questo proposito, oltre ad essere scarsi, apparivano alquanto dubbiosi. </s>

<s>Seb&shy;<lb/>bene infatti cos&igrave; concluda la ragion dell'operare del Termometro ad aria: <lb/><emph type="italics"/>onde ne segue che il freddo non sia altro che privazione di caldo<emph.end type="italics"/> (Alb. </s>

<s><lb/>XIV, 334), nel risolver poi il Problema del conte Bardi par che ammetta il <lb/>freddo positivo, e come il caldo stesso misurabile in gradi. </s>

<s>Questi dubbii <lb/>per&ograve; veniva a toglierli di mezzo il priore Orazio Ricasoli-Rucellai, il quale <lb/>gloriandosene affermava di avere <emph type="italics"/>visitato nella sua villa d'Arcetri e udito <lb/>pi&ugrave; e pi&ugrave; volte discorrere Galileo Galilei<emph.end type="italics"/> di questo soggetto, e di avergli <lb/>sentito dire: &ldquo; che il freddo non sia veramente cosa positiva nella natura, <lb/>ma solamente privazione del caldo e che per&ograve; non abbia per s&egrave; moto ed <lb/>azione &rdquo; (Prose e rime, Firenze 1822, pag. </s>

<s>60, 62). </s></p><p type="main">

<s>Perci&ograve; il Rucellai acceso di patrio zelo pretendeva che i suoi Fiorentini <lb/>disertassero dalle bandiere francesi del Gassendo, per tornare a ricoverarsi <lb/>sotto quelle di Galileo. </s>

<s>S'incontra una mattina con Carlo Dati nel cortile <lb/>del palazzo Pitti, e gli entra all'improvviso di questo freddo epicureo gas&shy;<lb/>sendistico, giurandogli sulla fede di Galileo ch'egli era una mera privazione, <lb/>e perci&ograve; un nulla. </s>

<s>Il Dati per l'appunto aveva allora l'appalto del Ghiac&shy;<lb/>cio, e a sentir ch'e'pagava per nulla e ch'e'vendeva il nulla, sbalordito <lb/>prega il Priore che ci pensi un po'meglio, perch&egrave; quella era una tal Filo&shy;<lb/>sofia da rovinarlo. </s>

<s>La storia ha del comico, ma &egrave; pur cos&igrave; come il Dati la <lb/>scrisse di sua propria mano: </s></p><p type="main">

<s>&ldquo; Se io devo parlare alla libera, o signor Priore, l'altra mattina io re-<pb xlink:href="020/01/696.jpg" pagenum="139"/>stai sbalordito, quand'ella mi affront&ograve; nel cortile del Palazzo, e mi domand&ograve; <lb/>all'improvviso quel ch'io sentivo di que'cosi che V. S. chiama <emph type="italics"/>atomi frigo&shy;<lb/>rifici<emph.end type="italics"/> e del freddo positivo, perch&egrave; non solamente non intesi lisca quant'ella <lb/>mi diceva, ma mi messi nel capo di non poterla mai intendere, onde la prego <lb/>a perdonarmi se non le risposi n&egrave; bene n&egrave; male, e mi fuggii come se io <lb/>avessi avuto i birri dietro. </s>

<s>Ma poi avendovi dormito sopra, conobbi che que&shy;<lb/>sta sua Filosofia non &egrave; tanto strana cosa quant'io mi credevo, e quanto certi <lb/>la fanno per tenerla in reputazione, e per&ograve; mi sono ardito di scriverle il <lb/>mio parere cos&igrave; alla buona. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In conclusione e'mi pare che V. S. voglia sapere da me se vera&shy;<lb/>mente il freddo &egrave; qualche cosa effettiva oppure un nulla, cio&egrave; uno sperpe&shy;<lb/>ramento, un totale scacciamento del caldo, e dico che, secondo il mio poco <lb/>sapere il freddo &egrave; qualche cosa, e certo s'e'non fosse qualche cosa, non mi <lb/>toccherebbe a pagare parecchi centi di scudi per avere l'appalto del nulla, <lb/>n&egrave; la gente verrebbe a comperare da me una cosa che non &egrave;, n&egrave; del niente <lb/>farebbero tanto schiamazzo queste putte scodate de'cortigiani quando non <lb/>l'hanno. </s>

<s>Per&ograve;, signor Priore, di grazia V. S. studii bene questo punto prima <lb/>di risolvere che il freddo non sia cosa alcuna, perch'ella sarebbe la mia ro&shy;<lb/>vina, e si compiaccia di ascoltare queste mie ragioni quali elle sono &rdquo; (MSS. <lb/>Cim., T. XXXIV, c. </s>

<s>32). </s></p><p type="main">

<s>Le ragioni che prosegue a esporre qui il Dati son quelle stesse in suc&shy;<lb/>cinto che si leggono nell'Opuscolo di Plutarco <emph type="italics"/>De primo frigido:<emph.end type="italics"/> e anzi, <lb/>non essendo a quel tempo nota la bella traduzione che ne aveva fatta Mar&shy;<lb/>cello Adriani, inserita poi da pag. </s>

<s>379-403 del Tomo V insieme con gli altri <lb/>Opuscoli del Filosofo greco, pubblicati in Milano, dopo il primo ventennio <lb/>di questo presente secolo da Francesco Ambrosoli; il Dati stesso aveva fatto <lb/>pensiero di pigliare occasione dal tradurre il detto Opuscolo <emph type="italics"/>Del freddo <lb/>principale,<emph.end type="italics"/> per aggiungervi le speculazioni sue proprie. </s>

<s>Ci&ograve; rilevasi da que&shy;<lb/>sta nota autografa, che segue alla sopra citata Lettera indirizzata al prior <lb/>Rucellai: &ldquo; Del Freddo positivo e privativo vedi l'Opuscolo di Plutarco <emph type="italics"/>De <lb/>primo frigido,<emph.end type="italics"/> che altro non &egrave; che una prova del freddo positivo o priva&shy;<lb/>tivo: questo mi parrebbe bene tradurre in toscano, e con occasione di esso <lb/>soggiungere quanto &egrave; da dirsi in questa materia &rdquo; (ivi, c. </s>

<s>35). </s></p><p type="main">

<s>L'argomento principale addotto da Plutarco a provare l'assunto di quei <lb/>Filosofi di cui riferisce l'opinione, si riduceva a dire ch'essendo il freddo un <lb/>agente operativo di tali e tali altri effetti, come il caldo, non poteva essere <lb/>perci&ograve; una semplice privazione. </s>

<s>&ldquo; Ma se nella guisa che il caldo per la te&shy;<lb/>pidezza e rarit&agrave; del corpo si sente, cos&igrave; parimente il freddo per lo stringi&shy;<lb/>mento e la condensazione dell'istesso si fa sentire; gi&agrave; si vede che siccome <lb/>il caldo cos&igrave; il freddo ha il suo proprio principio e il suo fonte &rdquo; (Opusc. </s>

<s><lb/>cit., T. V, Milano 1829, pag. </s>

<s>382). Passando poi a considerar la natura delle <lb/>vere privazioni, come per esempio del silenzio, ch'&egrave; privazione della voce o <lb/>de'suoni, il Filosofo cheronese conclude: &ldquo; Par dunque che il freddo sia <lb/>simile a tali privazioni e che non disponga altrimenti? </s>

<s>Anzi per lo contra-<pb xlink:href="020/01/697.jpg" pagenum="140"/>rio molti i gran piaceri sono dal freddo cagionati al corpo, e molti danni, <lb/>dolori e gravezze &rdquo; (ivi). </s></p><p type="main">

<s>Quel che poi intendeva di aggiungere il Dati a cos&igrave; fatti argomenti di <lb/>ragione, consisteva in esperienze da farsi, dell'opportunit&agrave; delle quali e della <lb/>loro concludenza giudicheranno, dalla seguente nota autografa, i nostri Let&shy;<lb/>tori: &ldquo; Osservisi se lo Strumentino del caldo e del freddo nel massimo freddo <lb/>sale o no, e questo non solo nell'inverno, ma con diaccio e salnitro e sale <lb/>e freddo veemente. </s>

<s>Notisi se posto in tal freddo lo Strumento scoppia come <lb/>fa col gran caldo. </s>

<s>Pongasi la palla di rame o di oro per la esperienza della <lb/>compressione anche nell'acqua bollentissima per molto tempo, e veggasi <lb/>quello fa, e se l'acqua scemi per trasudazione, che si conoscer&agrave; nell'agi&shy;<lb/>tarla. </s>

<s>La medesima si ponga a diacciare nel diaccio, salnitro, ecc., e se ne <lb/>osservi l'effetto &rdquo; (MSS. Cim., T. XXXIV, c. </s>

<s>36). </s></p><p type="main">

<s>Mentre che il Dati meditava cos&igrave; fra s&egrave; queste cose, il prior di Firenze <lb/>che aveva bene ripensato al fatto suo, attendeva a scrivere un <emph type="italics"/>Discorso con&shy;<lb/>tro il freddo positivo,<emph.end type="italics"/> che ne'primi giorni dell'Aprile 1666 lesse in Firenze, <lb/>in una solenne adunanza accademica, alla presenza del cardinal Delfino e <lb/>del principe Leopoldo. </s>

<s>Il moto, secondo l'Autore, &egrave; l'effetto del fuoco e <lb/>l'inerzia &egrave; la natura del freddo (Prose e rime cit., pag. </s>

<s>64, 65). La nostra <lb/>sensazione &egrave; quella, la quale piglia le sue misure dal caldo e dal freddo, <lb/>non da un freddo assoluto da s&egrave;, ma dalla comparazione per rispetto al pi&ugrave; <lb/>caldo (pag. </s>

<s>69). L'argomento di Plutarco che cio&egrave; la privazione non operi <lb/>cosa che sia non vale, essendoch&egrave; un nulla &egrave; solamente il vuoto, e il buio <lb/>per esempio contiene corpiccioli ch'empiono quegli spazi, senza mescola&shy;<lb/>mento di corpi lucidi (pag. </s>

<s>71). N&egrave; &egrave; poi vero che il freddo e il caldo sieno <lb/>contrarii assoluti, come pure cos&igrave; contrarii non sono, come dicono gli av&shy;<lb/>versarii, l'acqua e il fuoco, conciossiach&egrave; e'non potrebbero mai accozzarsi <lb/>insieme (pag. </s>

<s>78). Conclude all'ultimo il verboso Discorso: &ldquo; Che il moto <lb/>anzi sia effetto che cagione del caldo, e che siccome questo non si trova <lb/>salvo che nelle nostre sensazioni per lo sfregamento con esso le parti sen&shy;<lb/>sibili; cos&igrave; quello fuori del fuoco non avere veruna agitazione per s&egrave;, e che <lb/>per l'opposito infingardo e senza movimento sia il freddo, il quale in qua&shy;<lb/>lunque altra cosa risegga che non abbia mischianza col fuoco. </s>

<s>Con tal sup&shy;<lb/>posto dunque io reputo pi&ugrave; agevole di credere che anche tutte le azioni e <lb/>movimenti, che ci paion nel freddo o dal freddo, da impulsi invisibili deri&shy;<lb/>varsi del caldo, e dove faville o corpuscoli di fuoco non sono, tutto esser <lb/>freddo, senza che di questo ci sia veruna sostanza speciale da se n&egrave; atomi <lb/>frigorifici fatti apposta dalla Natura per ci&ograve;, come i calorifici ci sono, e per&ograve; <lb/>conchiudo altro non essere il freddo che privazione del caldo &rdquo; (pag. </s>

<s>94). </s></p><p type="main">

<s>Dall'eloquenza per&ograve; del gran prior di Firenze non par che il Dati re&shy;<lb/>stasse persuaso, ma perch&egrave; forse comprendeva bene che alle due parti man&shy;<lb/>cava a que'tempi la scienza necessaria a risolvere la questione, che sareb&shy;<lb/>besi, come tant'altre, noiosamente prolungata in parole; a volger la cosa in <lb/>scherzo s'aggiunse a lui il Magalotti. </s>

<s>Chi vuole, vada a carte 38 del citato <pb xlink:href="020/01/698.jpg" pagenum="141"/>Manoscritto e vi legger&agrave; autografa una Lettera del Dati firmato <emph type="italics"/>Rovaio.<emph.end type="italics"/> &ldquo; Al <lb/>freddissimo, rigidissimo, grandinevoso e tre volte agghiacciato Lorenzo Ma&shy;<lb/>galotti, scitico, caucaseo, islandico, Re degl'Iperborei, Monarca de'Rifei, Si&shy;<lb/>gnor delli Appennini, Principe del Mar gelato, Imperator dell'inverno, difen&shy;<lb/>sore, inventor della gelatina, restauratore, mantenitore degli atomi frigorifici. </s>

<s>&rdquo; <lb/>E ivi pure da c. </s>

<s>39-41, trover&agrave; la risposta, pur essa autografa di &ldquo; Lorenzo <lb/>Magalotti, per la Dio grazia, Imperator dell'Inverno, Monarca della Gelatina, <lb/>restauratore, mantenitore, difensore degli atomi frigorifici &rdquo; data &ldquo; Nella no&shy;<lb/>stra regal Ghiacciaia dal punto polare, la Notte della gran freddura. </s>

<s>&rdquo; </s></p><p type="main">

<s>Noi, lasciando lo scherzare a chi piace e tornando alle cose serie, di&shy;<lb/>ciamo che sotto quella nota a c. </s>

<s>35, nella quale il Dati scriveva di voler <lb/>tradurre l'Opuscolo di Plutarco <emph type="italics"/>De primo frigido,<emph.end type="italics"/> e di li cogliere l'occa&shy;<lb/>sione a svolgere pi&ugrave; ampiamente la materia, d'altra mano a noi ignota &egrave; <lb/>soggiunto: &ldquo; Quello che voleva fare C. D. (Carlo Dati) l'ademp&igrave; quasi ne'me&shy;<lb/>desimi tempi il signor Giuseppe Del Papa. </s>

<s>&Egrave; ben vero che tiene l'op&igrave;nione <lb/>contraria e la prova con saldissimi argomenti e con esperienze irrefragabili; <lb/>&egrave; ben vero che ci sarebbe molto da poter aggiungere.... &rdquo; </s></p><p type="main">

<s>Giuseppe Del Papa pubblicava nel 1674 in Firenze una lettera <emph type="italics"/>Intorno <lb/>alla natura del caldo e del freddo,<emph.end type="italics"/> scritta a Francesco Redi, nella quale <lb/>compensavasi largamente la dimenticanza, in che giaceva oramai il Discorso <lb/>manoscritto d'Orazio Ricasoli-Rucellai, edito nel 1822 dall'erudito Moreni. </s>

<s><lb/>La principale intenzione de'due Autori &egrave; la stessa, ed &egrave; quella di dimostrar <lb/>la verit&agrave; delle dottrine professate da Galileo. </s>

<s>Ma pur troppo anche il Del <lb/>Papa affoga in un mar d'artificiose parole i concetti, e le argute esperienze <lb/>non concludono, perch'erano anco a lui ignoti i fatti da cui poi la Termo&shy;<lb/>metria piglierebbe i principii. </s></p><p type="main">

<s>Fra l'esperienze per&ograve; del Del Papa e di tutti coloro che si propone&shy;<lb/>vano di dimostrare esser falsa la dottrina del freddo positivo, non ve ne ha <lb/>una che per la novit&agrave; e per la raffinatezza si possa assomigliare a quella <lb/>immaginata e praticata da Carlo Rinaldini. </s>

<s>Un corpo caldo, ragionava egli, <lb/>collocato di faccia a uno specchio concavo, rende pi&ugrave; intensa la sua azione <lb/>sullo spirito di vino (passum) chiuso nel Termometro: cos&igrave; pure un pezzo <lb/>di ghiaccio dovrebbe dimostrare maggiore intensit&agrave; del suo freddo, ma fatta <lb/>l'esperienza, dice il Rinaldini, non se ne vide l'effetto. </s>

<s>&ldquo; Inditium porro in <lb/>eo positum quod per speculum concavum reflexis radiis calor in Passo ap&shy;<lb/>posite applicato potest iutendi, ut constat cum illud solaribus radiis expo&shy;<lb/>nitur, eousque calor enim intenditur, ut ignis etiam procreetur. </s>

<s>At eiusdem <lb/>speculi expositione facta ad frigidissimum corpus, cuiusmodi est glacies, in <lb/>Passo quantumvis, ut par est, applicato, frigiditatis nunquam incrementum <lb/>experti sumus &rdquo; (Philos. </s>

<s>ration., Paravii 1681, pag. </s>

<s>320). </s></p><p type="main">

<s>Se fosse stato il Rinaldini in sperimentare pi&ugrave; destro, o se avesse avuto <lb/>il Termometro pi&ugrave; geloso, avrebbe dovuto avvertire, con sua gran sorpresa, <lb/>che anzi il ghiaccio dava manifesto indizio di calore piuttosto che di freddo. </s>

<s><lb/>Sarebbe di qui uscita pi&ugrave; concludente la sua dimostrazione, e l'effetto straor-<pb xlink:href="020/01/699.jpg" pagenum="142"/>dinario, ch'egli sarebbe stato il primo ad osservare, lo avrebbe anche reso <lb/>il primo abile a risolver la controversia che, ne'termini in ch'erasi posta in <lb/>campo, riusciva interminabile. </s>

<s>Considerando bene, infatti, tutto il nodo s'an&shy;<lb/>dava ad aggroppar nel ghiaccio, in cui i seguaci dell'opinione di Galileo cre&shy;<lb/>devano che gl'ignicoli fossero spenti del tutto, e che fosse il ghiaccio stesso, <lb/>come direbbero i Fisici odierni, della scala termometrica lo zero assoluto. </s>

<s><lb/>Cos&igrave; riducevansi nell'impossibilit&agrave; di spiegare alcuni fatti da loro stessi os&shy;<lb/>servati, come sarebbe che <emph type="italics"/>l'aria freddissima per tramontana &egrave; pi&ugrave; fredda <lb/>del ghiaccio e della neve,<emph.end type="italics"/> fatto sperimentato da Galileo (Alb. </s>

<s>XIV, 334) col <lb/>Termometro alla mano. </s>

<s>Il Viviani pure argomentava che <emph type="italics"/>l'aria pu&ograve; venire <lb/>in stato d'assai maggior freddezza del medesimo ghiaccio,<emph.end type="italics"/> dal veder che <lb/><emph type="italics"/>ne'freddi dell'inverno l'acqua ghiaccia nell'aria e non ghiaccia nel ghiac&shy;<lb/>cio<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>5). Di questi fatti sperimentati n&egrave; Ga&shy;<lb/>lileo n&egrave; il Viviani potevano ritrovar la ragione nei loro principii, mentre ve <lb/>la trovavano chiarissima i Gassendisti, dicendo che l'aria fredda per tramon&shy;<lb/>tana &egrave; invasa da pi&ugrave; gran numero di atomi frigorifici, d&igrave; quel che non sia <lb/>lo stesso ghiaccio. </s></p><p type="main">

<s>E che cosa poteva ragionevolmente rispondere il Rinaldini al Gassendo, <lb/>il quale diceva che le privazioni non son capaci d'effetti reali? </s>

<s>Se fosse riu&shy;<lb/>scito a veder nel ghiaccio gli effetti del calore la risposta l'avrebbe avuta <lb/>pronta e verissima, dicendo che anche il freddo stesso prodotto da'miscu&shy;<lb/>gli frigorifici &egrave; operativo de'suoi effetti, dipendenti dal calore che pur in essi <lb/>risiede, bench&egrave; ridotto a cos&igrave; minimi gradi. </s>

<s>Ma non poteva il Rinaldini altro <lb/>concludere da quella sua esperienza ingegnosissima s&igrave;, ma rimasta sventu&shy;<lb/>ratamente imperfetta, se non che il freddo rimasto nel ghiaccio &egrave; un'asso&shy;<lb/>luta privazion del calore e in altri termini un nulla. </s></p><p type="main">

<s>La questione insomma agitata in Firenze a proposito del freddo o po&shy;<lb/>sitivo o privativo fecero bene il Magalotti e il Dati a volgerla in scherzo e <lb/>finirla, perch&egrave; non si poteva risolvere co'principii della Termometria pro&shy;<lb/>fessati a que'tempi. </s>

<s>I moderni insegnano il freddo non essere positivo ma <lb/>una privazione o diminuzione del calore come dicevano il Rucellai e il Del <lb/>Papa, ma pigliano il fondamento alle loro dottrine da un principio che nel <lb/>secolo XVII sarebbe sembrato strano. </s>

<s>Quel principio &egrave; che nessun corpo, <lb/>qualunque sia il senso o l'apparente effetto della sua freddezza, &egrave; privo af&shy;<lb/>fatto di calore. </s>

<s>Un tal principio poi ch'&egrave; verissimo non si salva altrimenti <lb/>che per la teoria dinamica perch&egrave; un atomo di materia senza calore sarebbe <lb/>un atomo senza moto, e perci&ograve; senz'essere e senza vita. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>La questione del freddo positivo o privativo, forse perch&egrave; vi presero <lb/>gran parte il Magalotti e il Dati, fu creduto che s'agitasse nell'Accademia <lb/>del Cimento, e poniamo che qualche poco pure vi se ne discorresse e spe-<pb xlink:href="020/01/700.jpg" pagenum="143"/>rimentasse (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>578), &egrave; certo per&ograve; che <lb/>il Rucellai lesse il suo <emph type="italics"/>Discorso<emph.end type="italics"/> in un'altra Accademia, i socii della quale <lb/>attendevano, non a discutere intorno alla verit&agrave; delle cose naturali, ma in&shy;<lb/>torno alla propriet&agrave; delle parole toscane. </s>

<s>Quel che del calore fu trattato nella <lb/>fiorentina Accademia Sperimentale non &egrave; pubblicamente noto, se non da quel <lb/>che se ne legge nel libro de'<emph type="italics"/>Saggi,<emph.end type="italics"/> d'onde s'inferirebbe che ivi, lasciate <lb/>addietro le ipotesi argute e le sottili speculazioni, non si badasse ad altro <lb/>che a sincerarsi de'fatti. </s>

<s>Ma bench&egrave; evitassero da savi, per le ragioni gi&agrave; <lb/>dette, d'entrar nella questione in che voleva tirarli il Rucellai, non &egrave; per <lb/>questo che, tutti intenti i nostri Accademici a sperimentare, trascurassero o <lb/>reputassero inutile e spregevole cosa lo speculare. </s>

<s>Vero &egrave; bene che cos&igrave; fatte <lb/>speculazioni, dovute principalmente al Viviani e al Borelli, rimasero per la <lb/>massima parte sconosciute, ond'&egrave; che non riuscir&agrave; forse discaro ai lettori il <lb/>proposito nostro di far qui di quelle stesse speculazioni particolare soggetto <lb/>storico. </s></p><p type="main">

<s>A saper solamente che si tratta dell'Accademia del Cimento e del Vi&shy;<lb/>viani, si giurerebbe che le opinioni ivi seguitate intorno all'essere e alla na&shy;<lb/>tura del calore son quelle stesse pure e prette gi&agrave; professate da Galileo. </s>

<s>A <lb/>confermar che giurerebbesi il vero, ecco infatti rappresentarsi a'nostri oc&shy;<lb/>chi una scrittura dello stesso Viviani, che ha per titolo: <emph type="italics"/>Opinione di De&shy;<lb/>mocrito circa il modo che tiene il fuoco nello scaldare.<emph.end type="italics"/> In essa non ha <lb/>l'Autore altra intenzione che di esplicare i concetti galileiani espressi nella <lb/><emph type="italics"/>Risposta a Lodovico delle Colombe,<emph.end type="italics"/> e di salvar quegli stessi concetti da ogni <lb/>attentato di straniere aggressioni, come ognuno vedr&agrave; che qui appresso <lb/>legge: </s></p><p type="main">

<s>&ldquo; Tra gli effetti maravigliosissimi della Natura, la quale in tutte le cose <lb/>ci si mostra sempre miracolosa, uno per certo ve ne ha non men utile che <lb/>curioso, e questo &egrave; come il fuoco introdur possa cos&igrave; violentemente e facil&shy;<lb/>mente in un corpo, anco da lui per qualche spazio di braccio distante, il <lb/>calore, ed anco, se sar&agrave; in gran quantit&agrave;, l'abbruciamento. </s>

<s>Sopra cotal ef&shy;<lb/>fetto, come all'umano intendimento molto recondito, filosofarono non pochi <lb/>desiderosi d'intendere, in questo gran Libro del Mondo tutto ripieno di ma&shy;<lb/>raviglie, qualche piccola particolarit&agrave; per capacitarne l'intelletto. </s>

<s>Fra'quali <lb/>lasci&ograve; scritto Democrito che il fuoco, facendo una vastissima e numerosis&shy;<lb/>sima espansione de'corpuscoli ignei, i quali, penetrando in un corpo, se&shy;<lb/>condo l'attivit&agrave; o quantit&agrave;, lo riscaldano o l'abbruciano. </s>

<s>Per lo che, giun&shy;<lb/>gendo questi tali corpuscoli alla testura della nostra pelle, essendo di tal <lb/>figura atta facilmente alla penetrazione, penetrano a poco a poco nel nostro <lb/>corpo, facendoci nel primo moto sentire quello che noi chiamiamo calore: <lb/>accrescendosi poi e la velocit&agrave; e la quantit&agrave; delle medesime particelle o cor&shy;<lb/>puscoli, si va crescendo la sensazione o calore generando prima lo scotta&shy;<lb/>mento, e poi l'arsione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In confermazione di che pu&ograve; addursi una esperienza molto esatta. </s>

<s><lb/>Piglisi una boccia o caraffa con il collo molto lungo e stretto, la quale v. </s>

<s>g. <pb xlink:href="020/01/701.jpg" pagenum="144"/>sia piena d'acqua, fino al giro H (fig. </s>

<s>46). Poi sotto questa caraffa, nel <lb/>luogo EF, pongasi del fuoco molto lento: si vedr&agrave; a poco a poco crescer <lb/>l'acqua fino in G, e nel fondo della caraffa si vedranno alcuni campanelletti, <lb/>li quali di quando in quando partendosi dal fondo ascenderanno per l'acqua <lb/>fino alla sommit&agrave; del suo livello in G, dove rompendosi si risolveranno. <lb/><figure id="id.020.01.701.1.jpg" xlink:href="020/01/701/1.jpg"/></s></p><p type="caption">

<s>Figura 46.<lb/>Fredda che sar&agrave; la medesima acqua, si vedr&agrave; tornare al suo primo <lb/>livello in H, e non esser punto scemata, ma noi per l'addotta <lb/>esperienza ricerchiamo fuoco lento come s'&egrave; detto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si potr&agrave; dunque adesso domandare che cosa sia stato <lb/>ch'abbia dato causa al crescer di quell'acqua. </s>

<s>So che mi po&shy;<lb/>trebb'esser risposto che, avendo il fuoco virt&ugrave; di rarefare, abbia <lb/>rarefatto quell'acqua. </s>

<s>Ma io domando che cosa fosse in que'cam&shy;<lb/>panelli che, spinti di quando in quando all'in su, svaporano. </s>

<s>Io <lb/>veramente non so qual risposta mi potrebbe esser data, ma sento <lb/>bene astringermi a confessare esser quelli diversi aggregati di <lb/>corpuscoli ignei, che sormontando per l'acqua, come leggeris&shy;<lb/>simi, svaporassero. </s>

<s>Quindi &egrave; ch'essendone ancora gran quantit&agrave; <lb/>mescolata nell'acqua, la fanno crescere in mole; onde partendosi essi torna <lb/>essa allo stato di prima, il che parmi che apertamente dimostri questo che <lb/>noi chiamiamo calore prodursi per mezzo di questi tali corpuscoli &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXXXIV, c. </s>

<s>22). </s></p><p type="main">

<s>Bench&egrave; cos&igrave; fatte dottrine che si derivarono dagli Antichi fossero, come <lb/>vedemmo, sanzionate dall'autorit&agrave; di Galileo, cos&igrave; potente sull'animo e sul&shy;<lb/>l'ingegno de'nostri Accademici, sorse, per amor del vero, alcuno in mezzo <lb/>di essi che, se non ebbe la perspicacia di riconoscervi il falso, ebbe nono&shy;<lb/>stante la franchezza di mettervi il dubbio. </s></p><p type="main">

<s>&ldquo; Fu addotta per&ograve;, soggiunge il Viviani, in confutazione di simil parere <lb/>un'altra esattissima prova dal signor dottor Rinaldini, la quale &egrave; che, se <lb/>noi piglieremo due palle di egual grandezza, l'una d'ebano legno durissimo, <lb/>l'altra di sughero, e poste tutt'e due in egual distanza dal fuoco e tenute <lb/>per qualche tempo, levate che saranno le dette palle si trover&agrave; molto pi&ugrave; <lb/>calda quella di ebano che quella di sughero. </s>

<s>Di qui pareva di potersi pro&shy;<lb/>durre il calore non altrimenti potersi generare per via di questi corpuscoli, <lb/>poich&egrave;, essendo il legno del sughero molto poroso, e per conseguenza pi&ugrave; <lb/>atto a ricevere i medesimi corpuscoli, doveva trovarsi pi&ugrave; caldo dell'ebano <lb/>assai pi&ugrave; nelle sue parti costipato. </s>

<s>Eppure per l'esperienza tutto il contra&shy;<lb/>rio succede: adunque par forza confessare il calore non prodursi in tal ma&shy;<lb/>niera &rdquo; (ivi). </s></p><p type="main">

<s>Avrebbe potuto rispondere il Viviani che la superficie nera dell'ebano <lb/>tiene, come il Castelli s'immaginava, cos&igrave; disposti i suoi pori da introdurvi <lb/>pi&ugrave; gran numero d'ignicoli di quel che la superficie del sughero non fac&shy;<lb/>cia, ma egli cos&igrave; cerca pi&ugrave; sottili argomenti alla sua risposta, ricorrendo alla <lb/>varia capacit&agrave; del calore, secondo la varia costituzione de'corpi. </s></p><p type="main">

<s>&ldquo; L'esperienza veramente, prima per essere stata addotta da eccellen-<pb xlink:href="020/01/702.jpg" pagenum="145"/>tissimo uomo e versatissimo in queste filosofiche scienze, secondo per l'uti&shy;<lb/>lit&agrave; che da questa medesima pu&ograve; aversi circa la speculazione di effetto cos&igrave; <lb/>recondito; si deve diligentemente esaminare, e dedurre, se non quella ne&shy;<lb/>cessaria condizione, almeno qualche apparente congruenza, che in qualche <lb/>parte il nostro annebbiato intelletto capaciti e illumini. </s>

<s>E prima &egrave; necessa&shy;<lb/>rio fermare un principio dal qual, come da particolar fondamento, dipenda <lb/>l'intelligenza di tutto il resto. </s>

<s>Vedo dunque, e di questo mio vedere &egrave; ca&shy;<lb/>gione l'esperienza, che quel corpo, che si rende molto facile per ricevere <lb/>il calore, sia ancora molto facile a perderlo, per lo che veggo io che l'aria <lb/>facilissima a ricevere in s&egrave; il calore &egrave; anco facilissima a perderlo, onde fu <lb/>opinione ancora del Galileo che non si scaldasse punto. </s>

<s>L'acqua men facile <lb/>dell'aria a scaldarsi &egrave; men facile a perdere il calore e il sasso e il ferro, <lb/>che via pi&ugrave; sempre hanno pi&ugrave; difficolt&agrave; a scaldarsi, hanno ancora la mede&shy;<lb/>sima maggior difficolt&agrave; a freddarsi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto poi all'esperienza che prima si scaldi, oppure maggiormente <lb/>riceva il calore la palla d'ebano che quella di sughero, io certamente lo <lb/>credo, poich&egrave; del calore che riceve l'ebano in que'corpuscoli punto o po&shy;<lb/>chissimo ne tramanda fuori, poich&egrave;, imprigionandosi quelli tra le di lui parti <lb/>molto ben costipate, non hanno cos&igrave; facile l'esito come in un legno poroso, <lb/>qual'&egrave; il sughero, il quale &egrave; vero che facilmente riceve il calore, ma &egrave; anco <lb/>verissimo, per quel che di sopra s'&egrave; detto, che facilmente lo perde. </s>

<s>Onde <lb/>in uno spazio d'un tal tempo, nel quale ambe le palle sono state al fuoco, <lb/>essendo esse d'ugual mole, e in distanza da esso fuoco uguale, la medesima <lb/>quantit&agrave; di corpuscoli saranno rappresentati all'ebano che al sughero. </s>

<s>L'ebano <lb/>per&ograve; de'corpuscoli ignei che ha in s&egrave; ricevuto, una particella molto minore <lb/>n'ha tramandata di quella del sughero; onde se da cose eguali, cio&egrave; da cor&shy;<lb/>puscoli in quantit&agrave; uguali ricevuti da ambe le palle, se ne levano diseguali <lb/>quantit&agrave;, non v'&egrave; dubbio alcuno che, di dove ne saranno levati meno, pi&ugrave; <lb/>ne rimarranno. </s>

<s>Onde l'ebano, che assai meno ne ha mandati fuora del su&shy;<lb/>ghero, pi&ugrave; in s&egrave; ne aver&agrave; ritenuti, e perci&ograve; dovr&agrave; esser pi&ugrave; caldo del me&shy;<lb/>desimo sughero. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il soggiunger poi che, mediante l'espansione si fa e si genera il ca&shy;<lb/>lore asserito per sentenza di Democrito, e per&ograve; il sughero, conforme si dice, <lb/>avendo maggiore espansione dover&agrave; avere maggior calore; a questo io ve&shy;<lb/>ramente direi prima non aver letto l'opinione di Democrito, ma che dubito <lb/>grandemente che simile espansione deva piuttosto ritrovarsi nell'agente, cio&egrave; <lb/>nel corpo che ha da scaldare, non in quello che ha da essere scaldato, poi&shy;<lb/>ch&egrave; giudicherei io che l'espansione de'corpuscoli sia piuttosto un deperdi&shy;<lb/>mento di calore che accrescimento, e ci&ograve; mi vien persuaso, poich&egrave; molto pi&ugrave; <lb/>facilmente si scalder&agrave; un liquore appresentato al fuoco, e posto dentro ad un <lb/>vaso coperto, che ad uno senza coperchio, il quale altro alla fine non fa che <lb/>impedire l'espansione de'corpuscoli, che &egrave; forza confessar causa del riscal&shy;<lb/>damento &rdquo; (ivi, c. </s>

<s>24, 25). </s></p><p type="main">

<s>Le illustrazioni, che alle dottrine professate da Galileo intorno al calore <pb xlink:href="020/01/703.jpg" pagenum="146"/>derivarono dal Discorso del Viviani da noi riferito, bench&egrave; abbiano per noi <lb/>non lieve importanza storica, pur &egrave; un fatto che, versando intorno a una <lb/>fallace osservazione, in cui scambiavansi le gallozzole dell'aria in globetti di <lb/>fuoco, riuscirono a'progressi della scienza d'assai poco profitto. </s>

<s>Con ci&ograve; pa&shy;<lb/>gavasi senza dubbio il consueto tributo alla debolezza umana, ma perch&egrave; i <lb/>forti non hanno appena piegate per cader le ginocchia che risorgono pi&ugrave; <lb/>diritti, ecco da queste stesse carte manoscritte che svolgiamo porgercisi di <lb/>un tal risorgimento i pi&ugrave; belli esempi. </s></p><p type="main">

<s>Nel primo Dialogo delle Due nuove scienze ha Galileo l'esperienza di <lb/>quella palla di cera immersa nell'acqua, dalla quale il Torricelli, e poi i se&shy;<lb/>guaci di lui nella sperimentale Accademia medicea, trassero cos&igrave; largo par&shy;<lb/>tito per l'invenzione de'loro Idrostammi e di alcuni Termostammi di nuovo <lb/>genere, i quali ebbero particolarmente origine da ci&ograve; che ivi osserva Gali&shy;<lb/>leo potersi far variar l'equilibrio alla palla di cera col riscaldare un poco <lb/>o raffireddar l'acqua, cosicch&egrave; &ldquo; l'infonder quattro gocciole d'altra acqua un <lb/>poco pi&ugrave; calda o un poco pi&ugrave; fredda .... far&agrave; che la palla vi scenda o vi <lb/>sormonti: vi scender&agrave; infondendovi la calda, e monter&agrave; per l'infusione della <lb/>fredda &rdquo; (Alb. </s>

<s>XIII, 72). </s></p><p type="main">

<s>Intorno a tal proposito il Salviati, in bocca al quale son poste queste <lb/>parole, non ne dice pi&ugrave; avanti, e perci&ograve;, poniamo che non lasciasse nulla a <lb/>dubitare della verit&agrave; e della precisione dell'esperienza, rimaneva pure agli <lb/>altri un certo tal qual dovere filosofico di ripeterla variandone la maniera <lb/>e, ch'era pi&ugrave; importante, di trovar, de'nuovi fatti sperimentati, la ragion <lb/>fisica e i modi. </s>

<s>Fu questo appunto l'ufficio che si assunse il Viviani, quasi <lb/>pigliando il sopraccitato passo galileiano per testo de'suoi studii, i quali per <lb/>la storia della Termologia, pi&ugrave; che per quella dell'Accademia del Cimento, <lb/>saranno da chi appresso legge reputati importanti. </s></p><p type="main">

<s>&ldquo; Se una migliarola di piombo si circonder&agrave; di cera bianca, in modo <lb/>che se ne formi una pallina, che immersa in una tal acqua comune o altro <lb/>liquido vadia lentissimamente al fondo; ho provato che non solo collo scal&shy;<lb/>darla alquanto al lume o al fuoco, ma col solo stropicciarsela tra le palme <lb/>delle mani calde naturalmente, si riduce galleggiante, perch&egrave;, spingendola <lb/>con alquanto impeto sotto la superficie dell'acqua del bicchiere, se ne va al <lb/>basso per quello spazio che importa l'impeto impresso, ma con moto ritar&shy;<lb/>dato, come non naturale, e quando si fa l'equilibrio tra detto impeto e il <lb/>momento interno di salire, apparisce fermarsi, bench&egrave; non si trattenga per <lb/>minimo momento, e comincia il suo moto all'insu fino alla superficie, dove <lb/>si ferma per tanto tempo che si parta da detta pallina tanto del calore in&shy;<lb/>trodottovi, che si faccia grave in specie quanto l'acqua, e di poi diventi pi&ugrave; <lb/>grave tornando a immergersi e a scendere pian piano sino al fondo come <lb/>prima, il che si conosce col bagnare d'acqua quella minima cuspide che <lb/>avanza sopra la superficie, mentre la palla galleggia, perch&egrave; replicando pi&ugrave; <lb/>volte e spingendola leggermente sott'acqua, finalmente se ne va in fondo, <lb/>e spesse volte si osserva che il detto equilibrio ed equipondio in specie con <pb xlink:href="020/01/704.jpg" pagenum="147"/>l'acqua, mentre il detto calore si parte, si fa nel salire della detta pallina <lb/>avanti arrivi alla superficie, nel qual caso si osserva con gusto mirabile che <lb/>per tempo notabile si vede la pallina star ferma, e poi si vede risolvere a <lb/>scendere &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>6). </s></p><p type="main">

<s>Fatte queste diligentissime osservazioni il Viviani pensa a ci&ograve; che possa <lb/>essere ragione esplicitiva di esse, e non assicurandosi bene ancora, per man&shy;<lb/>canza di altre esperienze, si esprime cos&igrave; sotto forma di dubbio: </s></p><p type="main">

<s>&ldquo; La ragione di ci&ograve; credo che sia o perch&egrave; per l'introduzione de'mi&shy;<lb/>nimi ignei la cera si rarefaccia e cos&igrave; cresca di mole, stando ferma la me&shy;<lb/>desima materia, e per conseguenza si faccia men grave in specie di prima, <lb/>e questo per doppia ragione: Prima, perch&egrave;, com'ho detto, cresce la mole <lb/>e non la materia; seconda, perch&egrave; s'introduce ne'pori della cera e del <lb/>piombo una materia incomparabilmente pi&ugrave; leggera in specie non solo del <lb/>piombo, ma dell'acqua e della cera qual'&egrave; il calore, oppure, perch&egrave; stando <lb/>ferma la mole senza rarefarsi la cera, diventi nondimeno men grave in spe&shy;<lb/>cie di prima, mediante l'esservisi introdotto il detto calore composto di atomi <lb/>tanto pi&ugrave; leggeri di qualunque di detta materia. </s>

<s>&rdquo; </s></p><p type="main">

<s>La risoluzione del dubbio, in che ondeggiava cos&igrave; la mente del Viviani, <lb/>era importantissima a decidere dagli effetti la propria natura del calore, il <lb/>quale se avesse veramente resa pi&ugrave; leggera in specie la pallina aggiungen&shy;<lb/>dosi a lei, come fanno i sonagli dell'aria che tornano e tengono a galla an&shy;<lb/>che i corpi pi&ugrave; gravi dell'acqua; non era dubbio che ci&ograve; valeva a confer&shy;<lb/>mar l'opinione che fossero veramente sferette di fuoco quelle che si vedevano <lb/>ascender e gallozzolare su pel collo sottile della caraffa. </s>

<s>Bisognava dunque <lb/>risolvere in ogni modo quel dubbio, ma intanto che l'Autore del Mano&shy;<lb/>scritto va rimeditandovi sopra, prosegue a illustrare il testo galileiano per ci&ograve; <lb/>che riguarda il variar dell'equilibrio idrostatico della migliarola incerata, al <lb/>variar la densit&agrave; dell'acqua o mescolandovi il sale o infondendovi spirito di <lb/>zolfo o di vetriolo. </s></p><p type="main">

<s>Venne per&ograve; il tempo in cui l'esperienze decisero al Viviani che non <lb/>rendeva il calore pi&ugrave; leggere in specie le palline incerate con aggiungersi <lb/>ad esse come i sonagli dell'aria a'galleggianti pi&ugrave; gravi dell'acqua, ma col <lb/>rarefarle rimanendo ad esse palline la medesima quantit&agrave; di materia. </s></p><p type="main">

<s>&ldquo; Mi son finalmente accertato che la cera si raref&agrave; e si condensa se&shy;<lb/>condo che cresce il calore nell'ambiente, poich&egrave;, prese pi&ugrave; palline aggiustate <lb/>e temperate con piombo e cera, come si &egrave; detto, in modo che alcune di loro <lb/>in una tale costituzione o temperie di calore di una tale acqua con gran <lb/>difficolt&agrave; vi galleggino, ed altre con difficolt&agrave; stiano in fondo; ho veduto con <lb/>replicate esperienze che nel riscaldar l'ambiente dell'aria si riscalda l'acqua <lb/>ancora del vaso, perci&ograve; si raref&agrave; e diventa men grave in specie di prima, <lb/>onde per conseguenza pareva che le palline di fondo, in mezzo pi&ugrave; leggeri, <lb/>dovessero acquistar maggior gravit&agrave; e starsene in fondo pi&ugrave; facilmente e con <lb/>pi&ugrave; momento, ed all'incontro che le palline galleggianti dovessero, almeno <lb/>alcune di loro, discendere per l'acqua gi&agrave; fatta pi&ugrave; rara, ma segue tutto <pb xlink:href="020/01/705.jpg" pagenum="148"/>l'opposito, perch&egrave; non solo non discende alcuna delle galleggianti, ma ne <lb/>sormonta dal fondo alla superficie dove si fermano, e crescendo il calore <lb/>ambiente se ne vedono salire altre e altre di mano in mano, e prima quelle <lb/>che prima si fanno di egual gravit&agrave; in specie con l'acqua, e poi di minore, <lb/>ma tutte con moto tardissimo ed impercettibile dalla vista, che alcune volte <lb/>appariscono starsene ferme in mezzo l'acqua per lunghissimo tempo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Tornando poi a raffreddarsi l'aria e insieme l'acqua del vaso, si <lb/>vede non solo discendere quelle palline che prima per il calore sormonta&shy;<lb/>vano, e queste con ordine prepostero, perch&egrave; quelle che furono le ultime a <lb/>salire son le prime a calare a basso, e di mano in mano descendono quelle <lb/>che anticipavano le altre nel salire, ma ancora di quelle che nel primo stato <lb/>dell'acqua stavano a galla, e che crescendo il freddo, cio&egrave; scemando sem&shy;<lb/>pre pi&ugrave; il calore dell'acqua, si riducono tutte le palline galleggianti a toc&shy;<lb/>care il fondo del vaso, effetto di cui altra non pu&ograve; essere la cagione se non <lb/>che il calore che s'introdusse nell'acqua per mezzo dell'aria ambiente pi&ugrave; <lb/>e con maggior proporzione raref&agrave; la cera che l'acqua, cio&egrave; con maggior <lb/>proporzione si scema la gravit&agrave; in specie della cera che dell'acqua, e per <lb/>il contrario, partendosi il calore, cio&egrave; raffreddandosi l'acqua, pi&ugrave; e con <lb/>maggior proporzione si condensa e si fa pi&ugrave; grave in specie la cera che <lb/>l'acqua. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che l'acqua in questa esperienza si riscaldasse o si raffreddasse me <lb/>ne sono accertato per mezzo de'gradi del Termometro, che ho tenuto im&shy;<lb/>merso nella medesima acqua, quale mi mostrava che, quando cresceva il <lb/>numero de'gradi sopra il primo stato dell'aggiustamento delle palline, al&shy;<lb/>cune di quelle che erano in fondo salivano a galla, e che quando il numero <lb/>de'gradi si faccia minore del primo stato alcune di quelle che prima gal&shy;<lb/>leggiavano se ne andranno in fondo &rdquo; (ivi, c. </s>

<s>7). </s></p><p type="main">

<s>Tra le prime osservazioni e queste esperienze, colle quali il Viviani <lb/>s'accert&ograve; che la cera vien rarefatta dal calore, pass&ograve; qualche spazio di tempo, <lb/>che quell'avverbio <emph type="italics"/>finalmente<emph.end type="italics"/> dice dover essere stato non breve e anzi al&shy;<lb/>quanto penoso. </s>

<s>Il definir con misura certa lo spazio di quel tempo non sa&shy;<lb/>rebbe possibile, ma non si erra dal vero dicendo che quelle prime osserva&shy;<lb/>zioni appartengono al secondo periodo della sperimentale Accademia medicea <lb/>e che queste esperienze appartengono a'primi anni del terzo periodo. </s></p><p type="main">

<s>Il Viviani succeduto al Torricelli in rappresentar quella seconda et&agrave; di <lb/>essa Accademia, conferiva le sue osservazioni termostatiche con i colleghi <lb/>Borelli e Rinaldini, al primo de'quali venne in pensiero di poter adattar <lb/>simili palline fatte di vetro temperate con migliarole a <emph type="italics"/>pesar,<emph.end type="italics"/> com'ei diceva, <lb/>il caldo e il freddo, desumendo quel peso dal grado dell'immersione indi&shy;<lb/>cato da un'asticella divisa in parti e congiunta al vetro che affiori il liquido <lb/>ora pi&ugrave; alto ora basso, secondo che cresce o scema all'ambiente la tempe&shy;<lb/>ratura. </s>

<s>Di ci&ograve; faceva motto il Borelli stesso al principe Leopoldo in una let&shy;<lb/>tera scrittagli il di 17 Gennaio 1660 da Pisa. </s>

<s>&ldquo; Non veggo far menzione di <lb/>alcune scritture che inviai a V. A. li giorni passati di non so che capricci <pb xlink:href="020/01/706.jpg" pagenum="149"/>sovvenutimi intorno al peso dell'aria ed il modo di pesare il caldo e il freddo, <lb/>per mezzo di quello stesso strumento, che io lasciai in nota quattro anni <lb/>sono all'A. V., che &egrave; una palla di vetro con un filo sottilissimo di rame <lb/>distinto in gradi &rdquo; (MSS. Cim., T. XVII, c. </s>

<s>1). </s></p><p type="main">

<s>Il disegno di questo <emph type="italics"/>Termostatico<emph.end type="italics"/> ingegnosamente applicato dal suo <lb/>stesso inventore a ritrovare la differenza della gravit&agrave; dell'aria, in diversi <lb/>luoghi e in diversi paesi, pu&ograve; vedersi a pag. </s>

<s>250 del Libro <emph type="italics"/>De motionibus <lb/>naturalibus,<emph.end type="italics"/> dov'&egrave; posto a illustrare la propos. </s>

<s>CXIX cos&igrave; formulata: &ldquo; Po&shy;<lb/>stea, omissis quamplurimis Termostaticis a me inventis, afferam instrumen&shy;<lb/>tum quo pondus absolutum aeris in diversis locis elevatis ac depressis et <lb/>varie temperatis reperiri potest. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il Borelli chiama questi suoi Termostatici <emph type="italics"/>pesatori del caldo,<emph.end type="italics"/> a quel <lb/>modo e per quelle stesse ragioni che gli Areometri si chiamano pesatori <lb/>de'liquidi, ma al Viviani sovvenne un concetto anche pi&ugrave; nuovo, e fu quello <lb/>di pesare addirittura il caldo per mezzo di una stadera. </s></p><p type="main">

<s>&ldquo; Si faccia una libbra di braccia disuguali che sia bilicata esquisitissi&shy;<lb/>mamente sopra un pezzo di legno duro o di altra materia di figura di prisma <lb/>triangolare.... Attorno al braccio pi&ugrave; lungo si avvolti una sottilissima corda <lb/>da cetera, come di rame o di ottone, nel modo che insegna il Galileo nella <lb/>sua Bilancia per conoscere i misti, sicch&egrave; tutto il braccio venga diviso per <lb/>esempio in 200 particelle. </s>

<s>Nell'estremit&agrave; del braccio pi&ugrave; corto si appenda <lb/>un vaso di vetro sottile, con il collo sottilissimo volto all'ingi&ugrave;, e sia tale <lb/>che stia in equilibrio con il peso del braccio pi&ugrave; lungo. </s>

<s>Di poi si empia il <lb/>vaso, e perch&egrave; si guaster&agrave; l'equilibrio per l'aggiunta dell'acqua nel vaso, <lb/>si trovi un peso che posto nell'estremit&agrave; appunto del maggior braccio equi&shy;<lb/>pondii con detto vaso con l'acqua. </s>

<s>Qui non &egrave; dubbio che, rarefacendosi poi <lb/>per maggior caldo dallo stato primiero l'aria del vaso, tanto scemer&agrave; l'acqua <lb/>cio&egrave; il peso quanto crescer&agrave; la mole dell'aria, e diminuendosi il peso del&shy;<lb/>l'acqua bisogner&agrave; accostare il contrappeso al sostegno, acci&ograve; si mantenga <lb/>l'equilibrio. </s>

<s>Si accosti dunque e torni v. </s>

<s>g. </s>

<s>pi&ugrave; vicino di prima 15 parti: <lb/>dico che il calore del primo stato al calore di adesso sta come la distanza <lb/>del primo contrappeso alla distanza del secondo &rdquo; (MSS. Cim., T. X, c. </s>

<s>103). </s></p><p type="main">

<s>La dimostrazione la fa il Viviani dipendere da proposizioni anteceden&shy;<lb/>temente dimostrate e importantissime per la storia della Termometria, im&shy;<lb/>perocch&egrave; di li ebbe il suo principio la razionale digradazione dello Stru&shy;<lb/>mento. </s>

<s>Vedemmo a suo luogo come una scala fosse anche applicata ai <lb/>Termometri del Santorio e del Sagredo, ma era una pura pratica senza al&shy;<lb/>cuna scorta di teoria. </s>

<s>Il Viviani &egrave; il primo che ponga per fondamento alla <lb/>digradazione del Termometro ad aria il principio che i ricrescimenti di vo&shy;<lb/>lume dell'aria stessa son proporzionali all'intensit&agrave; del calore, e che dimo&shy;<lb/>stri come quella proporzionalit&agrave; si pu&ograve; esprimere in numeri. </s>

<s>Non &egrave; per <lb/>questo che riuscisse a dare Misuratori assoluti del calore e comparabili, per&shy;<lb/>ch&egrave; anch'egli seguiva l'opinion di que'tempi, che cio&egrave; fosse il ghiaccio la <lb/>privazione totale degl'ignicoli, ma non &egrave; per questo che il documento da <pb xlink:href="020/01/707.jpg" pagenum="150"/>noi posto qui appresso non abbia il pregio di dimostrare d'onde avesse la <lb/>scienza termometrica il suo primo principio. </s></p><p type="main">

<s>&ldquo; Circa il trovar modo di misurare con che proporzione vadi crescendo <lb/>e decrescendo il calore della medesima aria, e far s&igrave; che tal proporzione sia <lb/>effabile e si possa esplicare in numeri, parmi ci&ograve; esser facile a conseguire, <lb/>supposto questo principio: cio&egrave; che il calore d'una mole d'aria ridotta alla <lb/>minima condensazione, che per mezzo del maggior freddo ridur si possa, <lb/>sia nulla, cio&egrave; come zero; onde si possa dire: il calore di una quantit&agrave; <lb/>d'aria &egrave; tanto quanto l'eccesso della mole di detta aria in quello stato di <lb/>caldezza che si trova, sopra la mole della medesima aria priva totalmente di <lb/>calore, cio&egrave; ridotta alla massima condensazione con la massima freddezza, o <lb/>per meglio dire con la total privazione di calore, a cui ridur si possa per <lb/>mezzo del ghiaccio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per esempio sia un vaso di vetro come si vede (fig. </s>

<s>47) con il collo <lb/>assai lungo, dentro il quale si metta tant'acqua, che volto poi con il collo <lb/><figure id="id.020.01.707.1.jpg" xlink:href="020/01/707/1.jpg"/></s></p><p type="caption">

<s>Figura 47.<lb/>all'ingi&ugrave; arrivi all'altezza A, ed il rimanente AB sia pieno d'aria: <lb/>dico che se si esporr&agrave; al maggior rigor d'aria dell'inverno nel <lb/>nostro clima la parte AB, e che la bocca del collo sia immersa <lb/>nell'acqua, l'aria del vaso si condenser&agrave;, potendovi succedere per <lb/>di sotto dell'acqua. </s>

<s>Nel condensarsi l'aria ed alzarsi l'acqua su il <lb/>collo, alla fine arriver&agrave; quella alla massima condensazione, che per <lb/>tal mezzo conseguire si possa, e questa alla massima altezza, e sia <lb/>v. </s>

<s>g. </s>

<s>arrivata all'altezza C. </s>

<s>Supposto dunque il calore della den&shy;<lb/>sissima aria BC esser zero, avendonela privata con la maggior <lb/>freddezza dell'ambiente e scacciati fuori i minimi del calore, ma <lb/>il calore della mole BA della medesima aria men densa esser quanto CA, <lb/>che &egrave; l'eccesso della mole dell'aria BA della prima costituzione sopra la <lb/><figure id="id.020.01.707.2.jpg" xlink:href="020/01/707/2.jpg"/></s></p><p type="caption">

<s>Figura 48.<lb/>mole BC di detta aria della massima densit&agrave;; supposto questo, <lb/>averemo l'intento con ciascuno de'due soliti Termoscopii del <lb/>Galileo ma preparati in questo modo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia un vaso di vetro come AB (fig. </s>

<s>48) dentro al quale sia <lb/>tant'acqua che non sia meno della capacit&agrave; del lunghissimo can&shy;<lb/>nello CD, qual bisogna che nel vano sia d'uniforme grossezza <lb/>per tutto, e sia diviso e contrassegnato in minutissime particelle <lb/>eguali, facendo ad ogni cinque posti o ad ogni dieci un segno <lb/>differente dagli altri. </s>

<s>Questo cannello s'immerga nel vaso, fin&shy;<lb/>ch&egrave; la bocca tocchi il fondo, e poi si sigilli benissimo attorno <lb/>la bocca A, e per la bocca del cannello C s'infonda piano piano <lb/>dell'acqua fino all'altezza E. </s>

<s>Dopo mettasi il vaso nell'acqua con <lb/>molto ghiaccio, o nel solo ghiaccio spezzato in piccole particelle, <lb/>e si lasci tanto, finch&egrave; l'aria del vaso condensata al possibile, <lb/>abbi perso tutto il calore, come si disse nel supposto. </s>

<s>&Egrave; chiaro <lb/>che nel luogo dov'era il calore vi subentrer&agrave; dell'acqua del cannello e sar&agrave; <lb/>calata v. </s>

<s>g. </s>

<s>fino al segno F, oltre al quale il ghiaccio non abbi facolt&agrave; di <pb xlink:href="020/01/708.jpg" pagenum="151"/>farla abbassare di pi&ugrave;, e fatto qui un segno differente da tutti gli altri, e <lb/>levato il ghiaccio, l'aria di dentro torner&agrave; a riscaldarsi, e tanto quanto calore <lb/>vi entrer&agrave; (per ridursi allo stato dell'aria ambiente il vaso) tant'acqua ap&shy;<lb/>punto s'alza nel cannello sopra il segno F. </s>

<s>Sia per esempio tornata al se&shy;<lb/>gno E, che il numero delle particelle che saranno tra F ed E ci danno i <lb/>gradi del calore dell'aria del vaso, per conseguenza dell'ambiente, e segui&shy;<lb/>tando a riscaldarsi, cio&egrave; ad occupar pi&ugrave; luogo, per altrettanto luogo si alzer&agrave; <lb/>l'acqua sopra F, come sino in C, sicch&egrave;, se tra F ed E saranno 20, e tra F <lb/>e C 35, diremo il calor dell'aria del primo stato naturale, al calor della me&shy;<lb/>desima aria nel secondo stato, esser come 20 a 35 secondo il supposto. </s>

<s>Ma <lb/>gli stati dell'aria dentro il vaso sono i medesimi dell'aria ambiente, adun&shy;<lb/>que con tale Strumento potr&ograve; sapere in numeri il caldo dell'aria in diversi <lb/>tempi ed in diversi luoghi, perch&egrave; se alli 25 di Marzo per esempio il nu&shy;<lb/>mero de'posti sopra F sar&agrave; 12, e sia 12 ancora alli 22 di Settembre, dir&ograve; <lb/>che in questi giorni &egrave; stato il medesimo caldo, ancora potr&ograve; sapere di tutto <lb/>l'anno il massimo caldo ed il minimo, che noi chiamiamo il maggior freddo, <lb/>e quanto sia il calor d'una stanza rispetto a quello d'un'altra &rdquo; (ivi, c. </s>

<s>100). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Se potessimo sperare che fossero queste pagine lette da qualche Fisico <lb/>de'nostri giorni, il quale va riguardando com'un'anticaglia oramai insop&shy;<lb/>portabile l'opinion di coloro che ammettono essere il calore un agente im&shy;<lb/>ponderoso, tutto compiacendosi nelle moderne teorie del moto vibratorio e <lb/>dell'unit&agrave; delle forze; a sentire il Borelli e il Viviani proporre strumenti da <lb/>pesare il caldo e il freddo, e a vedere i seguaci di Galileo additare gl'igni&shy;<lb/>coli ch'entrano ed escono dal vetro di un'ampolla piena d'acqua posata sul <lb/>fuoco, direbbero senza dubbio ch'era impossibile riuscisse quella gente a <lb/>intender nulla delle propriet&agrave; del calore. </s>

<s>Eppure &egrave; un fatto che se ne in&shy;<lb/>tesero tanto da trasmettere agli sconoscenti nepoti un'eredit&agrave; di scienza ter&shy;<lb/>mica da giudicarsi non troppo scarsa, riguardata in s&egrave;, ma che riguardata <lb/>in comparazione della boriosa scienza moderna, dovrebbesi dire una dovi&shy;<lb/>zia. </s>

<s>Per quel che infatti concerne il cos&igrave; detto calorico di stato o di comu&shy;<lb/>nicazione le vecchie ipotesi degl'ignicoli erano, nella loro semplicit&agrave; e na&shy;<lb/>turalezza, atte a spiegare i fatti forse meglio delle teorie presenti, e quanto <lb/>al calorico raggiante riguardandolo nel maggior numero de'casi inseparabile <lb/>dalla luce v'applicarono le stesse leggi di lei nel diffondersi e nel riflettersi <lb/>dalla superficie de'corpi, ond'&egrave; che si possono dagli stessi trattati di Ot&shy;<lb/>tica argomentare, di questa parte della scienza termica degli antichi, le ve&shy;<lb/>rit&agrave; e gli errori. </s></p><p type="main">

<s>Una delle prime e principali propriet&agrave; conosciute da'discepoli di Galileo <lb/>fu la varia capacit&agrave; che hanno i corpi di condurre il calore, secondo la loro <pb xlink:href="020/01/709.jpg" pagenum="152"/>varia natura. </s>

<s>Benedetto Castelli fu il primo che pensasse d'applicare util&shy;<lb/>mente quella propriet&agrave; alla buona conservazione de'grani, intorno a che <lb/>scrisse un breve ma notabile <emph type="italics"/>Discorso<emph.end type="italics"/> raccolto insiem con gli altri <emph type="italics"/>Opuscoli <lb/>filosofici<emph.end type="italics"/> di lui postumi stampati dal Dozza di Bologna nel 1669. &ldquo; Avendo <lb/>osservato (egli ivi scrisse) che diversi corpi di diverse materie ricevono molto <lb/>diversamente le impressioni esterne dell'ambiente, cio&egrave; chi pi&ugrave; e chi meno, <lb/>imperocch&egrave; esponendo noi al sole diversi corpi come sarebbero marmi, le&shy;<lb/>gni, bronzi, terra, ecc., e lasciandogli stare eguale spazio di tempo, il me&shy;<lb/>tallo si riscalda assai pi&ugrave; che la pietra, e la pietra pi&ugrave; della terra, e questa <lb/>pi&ugrave; del legno; stimai che dovendo noi conservare il grano con difenderlo <lb/>dall'umido e dalle mutazioni ed alterazioni esterne, tutto ci sarebbe riuscito <lb/>con rinserrarlo in vasi fatti di quella materia, la quale mantenendosi asciutta <lb/>fosse ancora meno capace di freddo e di altre impressioni &rdquo; (ivi, pag. </s>

<s>42). <lb/>Questa materia, secondo il Castelli sarebbe il sughero, la virt&ugrave; coibente del <lb/>quale &egrave; mostrata, seguita egli a dire &ldquo; nel conservare la neve lungo tempo <lb/>per rinfrescare il vino e l'acqua nel tempo dell'estate, ed io ho sperimen&shy;<lb/>tato che la neve si mantiene nei gran caldi in simili vasi di sughero pi&ugrave; <lb/>che in altri di altra materia. </s>

<s>E le scarpe stesse nostre solettate di sughero <lb/>ci difendono i piedi nel tempo dell'estate dal caldo, e nell'inverno dal freddo <lb/>e dall'umido &rdquo; (ivi, pag. </s>

<s>43). </s></p><p type="main">

<s>Queste esperienze che, sebben tardi fossero venute a notizia del pub&shy;<lb/>blico, nonostante il Castelli avevale gi&agrave; divulgate nell'insegnamento orale <lb/>della sua scuola, accesero in desiderio il Torricelli di veder con che ordine <lb/>si succedessero i varii corpi, specialmente i metalli, nella virt&ugrave; di conservar <lb/>pi&ugrave; a lungo il ghiaccio, e perci&ograve; nel Registro delle esperienze che oramai <lb/>ben sappiamo esser dovute a lui, al num. </s>

<s>III si legge: &ldquo; Si fecero pi&ugrave; vasi <lb/>di varie sorti di metallo e di legno, e si empirono di diaccio pesto, e si os&shy;<lb/>serv&ograve; come il diaccio si consumasse e si vedde che li vasi consumavano dif&shy;<lb/>ferentemente, secondo la qualit&agrave;. </s>

<s>&rdquo; E segue una Tavola in cui per migliori <lb/>conduttori figurano l'oro e l'argento, e per maggiori coibenti di tutti gli <lb/>altri metalli messi alla prova, lo stagno e il ferro. (Targioni, Notizie ecc., <lb/>Firenze 1780, T. II, P. II, pag. </s>

<s>164). </s></p><p type="main">

<s>Seguita in quel Registro d'esperienze torricelliane un'altra che ha l'in&shy;<lb/>tento medesimo di questa, ma disposta e accomodata in nuovo elegantissimo <lb/>modo: &ldquo; Si fece piana una lastra di diaccio d'egual grossezza e si messero <lb/>sopra palle fatte delli soprascritti metalli, e detto diaccio si era messo egual&shy;<lb/>mente lontano dal piano, dove era posato sopra, e si trov&ograve; che le palle sfon&shy;<lb/>davano secondo avevano fatto i vasi nel consumare &rdquo; (ivi). Si vollero poi <lb/>l'esperienze della varia conducibilit&agrave; calorifica de'corpi desunta dal consu&shy;<lb/>marsi pi&ugrave; o meno presto il ghiaccio, ripetere dagli Accademici del Cimento, i <lb/>quali confessarono che <emph type="italics"/>nulla ne avevano cavato di certo<emph.end type="italics"/> (Saggi, Firenze 1841, <lb/>pag. </s>

<s>112), ben riconoscendo che quella della fusione col ghiaccio non era la <lb/>via da tenersi per la pi&ugrave; sicura. </s></p><p type="main">

<s>Maggior variet&agrave; di effetti e perci&ograve; pi&ugrave; largo campo a filosofare ne of-<pb xlink:href="020/01/710.jpg" pagenum="153"/>feriva il calorico raggiante, la riflession del quale sopra gli specchi concavi, <lb/>per condensarne i raggi dispersi, ebbe tanta efficacia in promuovere la Geo&shy;<lb/>metria delle sezioni coniche appresso gli antichi. </s>

<s>Narra Plutarco nella vita <lb/>di Numa come il foco gelosamente custodito dalle Vestali, se per caso si <lb/>fosse spento, non in altro modo era ordinato si dovesse riaccendere, che de&shy;<lb/>rivandolo direttamente dal cielo, e ci&ograve; con esporre al sole uno specchio in&shy;<lb/>cavato in figura di parabola. </s>

<s>Cos&igrave; pure lasci&ograve; scritto Oronzio nella prefazione <lb/>al trattato <emph type="italics"/>De speculo ustorio,<emph.end type="italics"/> e tra'meno antichi ch'esercitarono nella scienza <lb/>pi&ugrave; autorevole il magistero, abbiam Vitellione, che formulava cos&igrave; il Teo&shy;<lb/>rema XLIII del IX libro della sua Prospettiva: &ldquo; Speculo concavo conca&shy;<lb/>vitatis sectionis parabolae soli opposito, ita ut axis ipsius sit in directo cor&shy;<lb/>poris solaris, omnes radii incidentes speculo aeque distanter axi reflectuntur <lb/>ad punctum unum axis distantem a superficie speculi, secundum quartam <lb/>lateris recti ipsius sectionis parabolae speculi superficiem causantis, ex quo <lb/>patet quod a superficie talium speculorum ignem est possibile accendi &rdquo; <lb/>(Norimbergae 1535, pag. </s>

<s>250). </s></p><p type="main">

<s>Dalla lettura di questi Autori, dice Marino Ghetaldo, essersi sentito ac&shy;<lb/>cendere il desiderio di fare esperienza di quegli spettacoli &ldquo; qua in re cum <lb/>a me ea opera esset navata, ut tandem aliquando anno superiori (1602) pro&shy;<lb/>positum sim assecutus, illud praeterea commodi accidit, ut ex accurata con&shy;<lb/>sideratione repererim id non solum ei accidere speculo quod in formam pa&shy;<lb/>rabolae recti atque rectanguli coni est excavatum, sed praeterea his, quae <lb/>a parabola coni acutanguli, obtusiangoli et scaleni etiam fuerint descripta &rdquo; <lb/>(De Parabola, Romae 1603, praef.), ond'egli pot&egrave; cos&igrave; formulare, estendendo <lb/>le propriet&agrave; ustorie a ogni genere di parabola, il suo Teorema: &ldquo; Omnes <lb/>radii solares in speculum concavum a quacumque parabola circa manentem <lb/>axem circumducta descriptum incidentes, ita ut axi aequidistent, reflectun&shy;<lb/>tur ad unum idemque axis punctum quod scilicet a vertice speculi distat <lb/>intervallo quartae partis lateris recti parabolae ipsum speculum describen&shy;<lb/>tis &rdquo; (ibi, pag. </s>

<s>17). </s></p><p type="main">

<s>Il Maurolico dop'aver dimostrato, nel Teorema XXIV del libro I <emph type="italics"/>Dia&shy;<lb/>phanorum,<emph.end type="italics"/> come si pu&ograve; accendere il fuoco per la refrazione de'raggi solari <lb/>attraverso a una sfera di vetro, torna col pensiero allo Specchio ustorio pa&shy;<lb/>rabolico, che si dice da alcuni essere stato fabbricato da Tolomeo, e crede <lb/>possibile che s'otterrebbe il medesimo effetto per rifrazione da una lente <lb/>parabolica di cristallo. </s>

<s>&ldquo; Ita fortasse liceret fabricare ex vitro, chrystallo, <lb/>aliove perspicuo lapide, convexum talis figurae diaphanum, per quod fracti <lb/>radii in unum punctum congressi, efficacissimi essent ad ignis generatio&shy;<lb/>nem. </s>

<s>Sed hoc, quoniam plus curiositatis habet, perspicacioribus ingeniis <lb/>perscrutandum relinquo &rdquo; (Neap. </s>

<s>1611, pag. </s>

<s>80). Quando poi le speculazioni <lb/>del Sarpi e del Porta si videro confermate da queste del Maurolico, dagli <lb/>insegnamenti del quale si sperava di attingere la scienza del Telescopio, la <lb/>curiosit&agrave; per gli Ottici divenne un'occupazione seria, di che vedemmo al&shy;<lb/>trove l'Antonini e l'Imperiali darci il pi&ugrave; notabile esempio. </s></p><pb xlink:href="020/01/711.jpg" pagenum="154"/><p type="main">

<s>In queste esperienze degli specchi e delle lenti ustorie i raggi calorifici <lb/>si mostrano cos&igrave; strettamente congiunti co'luminosi, che le questioni di Ter&shy;<lb/>mologia si riducono a pure questioni di Ottica. </s>

<s>Chi volesse perci&ograve; sapere <lb/>che cosa conoscessero gli antichi delle leggi della diffusione del calore nello <lb/>spazio, pu&ograve; rammemorarsi la storia della diffusion della luce. </s>

<s>Se non che <lb/>sembra che debba in questo particolare farsi un'eccezione per rispetto a <lb/>Leonardo da Vinci, nelle note manoscritte del quale noi vediamo chiara&shy;<lb/>mente dimostrata la legge dell'intensit&agrave; del riscaldamento in ragion reci&shy;<lb/>proca de'quadrati delle distanze. </s>

<s>&ldquo; Il caldo del sole, che si ritrover&agrave; sulla <lb/>superficie dello specchio concavo, il quale calore si partir&agrave; per li razzi pi&shy;<lb/>ramidali concorrenti a uno solo punto, il qual punto quanto entrer&agrave; nella <lb/><figure id="id.020.01.711.1.jpg" xlink:href="020/01/711/1.jpg"/></s></p><p type="caption">

<s>Figura 40.<lb/>superficie tante volte fia pi&ugrave; caldo del <lb/>caldo, che si trova sopra lo specchio, <lb/>e cos&igrave; quanto AB (fig. </s>

<s>49) o vuoi CD <lb/>entra nello specchio, tante volte il <lb/>suo calore &egrave; pi&ugrave; potente che quello <lb/>dello specchio &rdquo; (Manuscr. </s>

<s>A, Mollien, <lb/>fol. </s>

<s>20 r.). E pi&ugrave; compendiosamente <lb/>altrove si legge: &ldquo; Tanto quanto la <lb/>punta della piramide solare tagliata in <lb/>qualunque parte entra nella sua base, <lb/>tante volte fia pi&ugrave; calda che essa base &rdquo; (ivi, fol. </s>

<s>54 r.). </s></p><p type="main">

<s>I Maestri della scienza per&ograve; non solo ignorarono questa legge della dif&shy;<lb/>fusion del calore, com'avevano ignorato quella della diffusion della luce, ma <lb/>sopra pi&ugrave; rimasero in dubbio se il calore stesso uniformemente si diffon&shy;<lb/>desse in sfera. </s>

<s>Anzi che i raggi calorifici non si diffondessero cos&igrave;, come si <lb/>diffondono i luminosi, Galileo si cred&egrave; che servisse a dimostrarlo questa espe&shy;<lb/>rienza: &ldquo; Accosti chi si voglia il dito cos&igrave; per fianco alla fiammella di una <lb/>candela accesa: certo non sentir&agrave; offendersi dal caldo, sinch&egrave; per un bre&shy;<lb/>vissimo spazio non se le accosta, e che poco meno che non la tocchi. </s>

<s>Ma <lb/>per l'opposito esponga la mano sopra la medesima fiammella, sentir&agrave; l'of&shy;<lb/>fesa del caldo per distanza ben mille volte maggiore di quell'altra per fianco, <lb/>mentre l'illuminazione, che dalla medesima fiammella deriva, per tutti i <lb/>versi si diffonde, in cio&egrave; s&ugrave;, in gi&ugrave;, lateralmente, ed in somma per tutto, <lb/>ed in gran lontananza sfericamente si distende &rdquo; (Alb. </s>

<s>VII, 304). </s></p><p type="main">

<s>Non parve agli Accademici del Cimento che questa volgare esperienza <lb/>addotta da Galileo fosse decisiva, e perci&ograve; ne fecero soggetto de'loro primi <lb/>studii come s'ha da uno de'Diarii in cui sotto il d&igrave; 10 di Settembre 1657, <lb/>&egrave; registrata l'esperienza C &ldquo; per riconoscere se l'espansione del caldo e del <lb/>freddo fosse sfericamente uniforme &rdquo; (MSS. Cim, T. II, c. </s>

<s>263). I modi <lb/>d'eseguirla furono varii, uno de'quali, proposto dal Rinaldini, consisteva nel&shy;<lb/>l'applicar due Termometri simili, nel medesimo momento di tempo e in di&shy;<lb/>stanze uguali, uno sotto e uno sopra una palla di ferro molto ben riscaldata. </s>

<s><lb/>Era naturale che il Termometro superiore mostrasse d'aver ricevuta mag-<pb xlink:href="020/01/712.jpg" pagenum="155"/>giore impressione e &ldquo; di qui parve che si potesse raccorre che il calore <lb/>non si diffonda egualmente per ogni parte, ma pi&ugrave; all'in s&ugrave; che all'in gi&ugrave; &rdquo; <lb/>(Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>703). </s></p><p type="main">

<s>Non mancarono di avvertire alcuni fra quegli Accademici che, cos&igrave; in <lb/>questa esperienza come e nell'altra di Galileo, la differente diffusion calo&shy;<lb/>rifica dipendeva dal vario riscaldamento dell'aria ambiente, per cui fu de&shy;<lb/>liberato all'ultimo di sperimentare nel vuoto. </s>

<s>Chi per&ograve; legge nel libro dei <lb/><emph type="italics"/>Saggi<emph.end type="italics"/> fra l'<emph type="italics"/>Esperienze fatte nel vuoto<emph.end type="italics"/> questa de'due Termometri cos&igrave; de&shy;<lb/>stramente introdotti nel chiuso della camera barometrica, e ne attende il <lb/>resultato, riman sorpreso da maraviglia in trovar ancora gli sperimentatori <lb/>indecisi se la differenza de'gradi segnati dallo strumentino di sotto e da <lb/>quello di sopra dipendesse o dalla irregolare diffusion del calore o dal vario <lb/>riscaldamento degli strati dell'aria. </s>

<s>La maraviglia cessa in ogni modo per <lb/>coloro, i quali considerano come professando i nostri Accademici tutti in&shy;<lb/>sieme concordi l'opinion degl'ignicoli materiali, che a Galileo e al Viviani <lb/>si rendevano visibili nell'acqua posta al fuoco, e si rappresentavano ai sensi <lb/>del Borelli in que'cunei che inzeppandosi dentro i pori de'corpi ne dila&shy;<lb/>tano cos&igrave; evidentemente i volumi; non era possibile riuscissero a persua&shy;<lb/>dersi che soggiacendo quegli stessi ignicoli alla circumpulsione degli altri <lb/>corpi gravi, non fossero meglio disposti a salire che a moversi indifferen&shy;<lb/>temente per tutti i versi. </s></p><p type="main">

<s>Quando queste idee, derivate dall'antica Filosofia greca nell'insegna&shy;<lb/>mento galileiano, si abbandonarono, per seguitar pi&ugrave; ragionevolmente i nuovi <lb/>placiti degli atomi calorifici imponderabili, e allora fu che s'intese come do&shy;<lb/>vesse anche il calore diffondersi uniformemente in isfera, imitando la luce. </s></p><p type="main">

<s>Ma pur la stessa diffusione termica per emissione implicava i fisici in <lb/>quelle medesime difficolt&agrave; che l'emission luminosa, e perci&ograve; il Montanari <lb/>discorrendo cos&igrave; del calore come del lume, per salvare la legge sperimen&shy;<lb/>tale della ragion reciproca de'quadrati delle distanze e non de'cubi, si volse <lb/>a professar l'ipotesi dell'onde eteree messe in vibrazione dalle molecole del <lb/>corpo calescente. </s>

<s>Questa ipotesi, di che si fa gran merito ad alcuni Fisici <lb/>stranieri assai pi&ugrave; recenti, era gi&agrave; diffusa in sul finir del secolo XVII nella <lb/>Scuola sperimentale bolognese istituita dal medesimo Montanari, e il Gu&shy;<lb/>glielmini, uno de'pi&ugrave; celebri usciti di quella Scuola, la professava nel suo <lb/>trattato <emph type="italics"/>De sanguinis natura et proprietate,<emph.end type="italics"/> ricavandone uno de'pi&ugrave; validi <lb/>argomenti per confutar l'errore della fiamma vitale. </s>

<s>&ldquo; Non minus pariter <lb/>falluntur vitalis flammae assertores, cum eius existentiam a luce, quae in <lb/>piscibus putrescentibus, ovis lacertorum, noctilucis ecc. </s>

<s>observatur, dedu&shy;<lb/>cunt. </s>

<s>Quamvis enim lux inter ignis proprietates et effectus recenseatur, non <lb/>ea tamen est, ut absque igne esse nequeat. </s>

<s>Quid enim impedit quominus <lb/><emph type="italics"/>undulationes iis similes, quae ab ignis agitatione proficiscuntur etiam ab <lb/>aliis motibus aetheri imprimantur?<emph.end type="italics"/> An excitabitur in retina igniculus, cum <lb/>presso exterius oculo lucis scintillae videntur observari? </s>

<s>&rdquo; (Venetiis 1701, <lb/>pag. </s>

<s>93). </s></p><pb xlink:href="020/01/713.jpg" pagenum="156"/><p type="main">

<s>Pochi anni appresso riscontravasi in questi medesimi pensieri anche il <lb/>Newton, mosso dalla considerazione del vedersi diffondere il calore anche <lb/>nel vuoto. </s>

<s>&ldquo; Si in duobus amplis altisque vitris cylindraceis inversis duo <lb/>parva Thermometra ita sint suspensa, ut vitrum non contingant: aerque ex <lb/>horum vitrorum altero sit exhaustus, vitraque hoc modo comparata e loco <lb/>frigido in calidum deferantur, utique Thermometrorum id quod erit in va&shy;<lb/>cuo incalescet nihilo minus, neque fere tardius quam id quod non sit in <lb/>vacuo. </s>

<s>Annon iam calor ille exterior trans vacuum defertur, vibrationibus <lb/>medii cuiusdam longe quam est aer subtilioris, quod quidem medium, exhau&shy;<lb/>sto aere, tamen adhuc in vacuo supersit?... Huiusque medii vibrationes <lb/>annon in corporibus calidis, ut eorum calor intensior sit et durabilior effi&shy;<lb/>ciunt? </s>

<s>Et corpera calida annon calorem suum in frigida contigua transfe&shy;<lb/>runt, vibrationibus huiusce medii e calidis in frigida propagatis? </s>

<s>&rdquo; (Optices, <lb/>Lib. </s>

<s>III, <expan abbr="q.">que</expan> XVIII, Patavii 1773, pag. </s>

<s>142). </s></p><p type="main">

<s>La legge della varia intensit&agrave; calorifica al variare della distanza, che <lb/>ritrov&ograve; pi&ugrave; facile la sua dimostrazione dappoich&egrave; s'introdussero nella scienza <lb/>le ipotesi prima professate da'nostri Bolognesi e poi dal Newton, era una <lb/>delle principali che concernessero il calorico raggiante, ma ve n'erano altre <lb/>pure che avevano richiamato a s&egrave; lo studio de'Filosofi con maggiore atten&shy;<lb/>zione. </s>

<s>Fra questi &egrave; da annoverarsi la legge del vario riscaldamento de'corpi <lb/>dipendente dalle varie inclinazioni de'raggi calorifici emessi. </s>

<s>Al problema <lb/>proposto a risolvere da lungo tempo alla scienza perch&egrave; l'estate sia pi&ugrave; <lb/>calda dell'inverno, non era difficile rispondere attribuendo l'effetto naturale <lb/>al Sole, che si volge intorno alla Terra con guardo ora pi&ugrave; ora meno obli&shy;<lb/>quo. </s>

<s>Ma restava a dimostrar come mai e con qual proporzione l'intensit&agrave; <lb/>calorifica sopra una data superficie scemi, crescendo l'obliquit&agrave; del raggio <lb/>incidente. </s></p><p type="main">

<s>La dimostrazione del Teorema fu de'primi a tentarla Giovan Batista <lb/>Benedetti, studiandosi d'esplicare un concetto espresso cos&igrave; nella LVII del <lb/>X libro di Vitellione: &ldquo; Radios corporis luminosi per reflexionem vel re&shy;<lb/>fractionem aggregari palam est &rdquo; (Perspectiva cit., pag. </s>

<s>281). Sieno QP, BD <lb/>(fig. </s>

<s>50, 51), dice il Benedetti, due superficie uguali, e sopra la prima cada <lb/><figure id="id.020.01.713.1.jpg" xlink:href="020/01/713/1.jpg"/></s></p><p type="caption">

<s>Figura 50.<lb/><figure id="id.020.01.713.2.jpg" xlink:href="020/01/713/2.jpg"/></s></p><p type="caption">

<s>Figura 51.<lb/>il raggio AP, con l'obliquit&agrave; AQP, sopra la seconda cada UB con l'obli&shy;<lb/>quit&agrave; UBD minore della prima. </s>

<s>Riflettendosi i raggi in ambedue i casi in <lb/>modo da far gli angoli d'incidenza uguali agli angoli di riflessione, gli ag-<pb xlink:href="020/01/714.jpg" pagenum="157"/>gregati de'raggi nelle riflessioni sopra le superficie QP e BD saranno pro&shy;<lb/>porzionali ai triangoli OQP, IBD &ldquo; quorum duorum triangulorum nullus <lb/>unquam erit qui dubitari possit QOP non esse minorem BID, cum anguli <lb/>Q e P trianguli QOP acutiores sint angulis B et D trianguli BID, ex sup&shy;<lb/>posito &rdquo; (Speculat. </s>

<s>lib., Venetiis 1599, pag. </s>

<s>188). E perci&ograve; la superficie QP <lb/>sar&agrave; meno riscaldata della superficie BD. </s></p><p type="main">

<s>Il Boulliaud poi segu&igrave; queste stesse norme nella proposizione XXXVI <lb/>del suo trattato <emph type="italics"/>De natura lucis,<emph.end type="italics"/> che &egrave; cos&igrave; formulata ed &egrave; un eco di quella <lb/>di Vitellione: &ldquo; Lux primaria cum secundaria idest, incidens cum repercussa <lb/>coniuncta plus calescunt &rdquo; (Parisiis 1638, pag. </s>

<s>55). D'onde ne conclude che <lb/>nell'estate il lume secondario si unisce col primario come nella figura 51, <lb/>e nell'inverno si separano a vicenda come si vede nel figura 50. &ldquo; Ae&shy;<lb/>state enim lumen secundarium cum primario unitur.... hieme separantur <lb/>ad invicem &rdquo; (ibi). </s></p><p type="main">

<s>Ma il Benedetti procede pi&ugrave; oltre nella sua dimostrazione, ed &egrave; qui dove <lb/>incomincia a specular da s&egrave; stesso lasciandosi lungamente indietro il pol&shy;<lb/>lacco Autore della Prospettiva pi&ugrave; antico. </s>

<s>&ldquo; Quod vero attinet ad maiorem <lb/>quantitatem luminis super Terrae superficiem imaginemur radium AQ (fig. </s>

<s>52) <lb/><figure id="id.020.01.714.1.jpg" xlink:href="020/01/714/1.jpg"/></s></p><p type="caption">

<s>Figura 52.<lb/>cuius respectu etiam imaginemur duos super&shy;<lb/>ficiei Terrae situs, quorum unus sit QO, cui <lb/>dictus radius sit perpendicularis, et alter QP <lb/>cui radius AQ ex obliquo incidat. </s>

<s>Imaginemur <lb/>ergo triangulum QOP, cuius angulus O rectus <lb/>est ex supposito, unde QO minor erit QP, <lb/>ex XVIII primi Euclidis. </s>

<s>Hinc fit ut super QO <lb/>cadat universum lumen quod super QP diffun&shy;<lb/>ditur. </s>

<s>Sit QU aequalis QO et sit imaginatione <lb/>protracta UN aequidistans POA, unde QU il&shy;<lb/>luminata erit a radio NQ minore radio <expan abbr="Aq;">Aque</expan> <lb/>ergo minus calida erit superficies QU ipsius <lb/>terrae, quam QO, quia maius lumen in se maiorem calorem includit quod <lb/>manifeste apparet in radiorum unione mediante reflexione aut refractione &rdquo; <lb/>(Speculat. </s>

<s>lib. </s>

<s>cit., pag. </s>

<s>188). </s></p><p type="main">

<s>Galileo poi compendi&ograve; e ridusse all'intelligenza di Simplicio questa dimo&shy;<lb/>strazione del Benedetti, nella Giornata I de'<emph type="italics"/>Due Massimi Sistemi<emph.end type="italics"/> (Alb. </s>

<s>I, 91) <lb/>ma nessuno de'due grandi Maestri riusc&igrave; a formulare la legge dell'inten&shy;<lb/>sit&agrave; proporzionale al seno dell'angolo dell'incidenza. </s>

<s>Questo teorema, cos&igrave; <lb/>l'Ottica che la Termologia, lo derivarono dalla legge meccanica della per&shy;<lb/>cossa, non dimostrata prima del 1644. </s></p><p type="main">

<s>Il considerar che s'ebbe a fare allora come un raggio incidente o di <lb/>luce o di calore serba nell'illuminare e nel riscaldare le medesime leggi di <lb/>un grave che percotesse con quella stessa incidenza una superficie, confer&igrave; <lb/>moltissimo a confermare i discepoli di Galileo, a'quali si deve la dimostra&shy;<lb/>zione di quel Teorema della percossa, nell'opinione degli ignicoli materiali, <pb xlink:href="020/01/715.jpg" pagenum="158"/>tanto pi&ugrave; che per essi ignicoli insinuantisi pi&ugrave; o men facilmente dentro i <lb/>pori de'corpi, erasi ritrovato da sodisfar convenientemente a una curiosit&agrave; <lb/>singolare qual'era quella della varia quantit&agrave; di calore assorbito dalle su&shy;<lb/>perficie bianche e dalle nere esposte per lo stesso spazio di tempo all'irrag&shy;<lb/>giamento del medesimo corpo calescente. </s></p><p type="main">

<s>Quella curiosit&agrave; non era sfuggita alla considerazion del Keplero, il quale <lb/>nella proposizione XXXVIII del I libro de'Paralipomeni a Vitellione si pro&shy;<lb/>poneva di spiegare in che modo <emph type="italics"/>Lux nigra facilius inflammet quam alba,<emph.end type="italics"/><lb/>e ritrovava quella spiegazione in ci&ograve;, ch'essendo della natura della luce il <lb/>distruggere e il consumare, i corpi neri, che minor quantit&agrave; di luce riflet&shy;<lb/>tono de'bianchi, vengon perci&ograve; pi&ugrave; facilmente impregnati di calor&egrave; e pi&ugrave; <lb/>pronti a infiammarsi. </s>

<s>&ldquo; Hinc orta est opinio, conclude il Keplero, nigris cogi <lb/>radios, albis dissipari &rdquo; (Francof. </s>

<s>1604, pag. </s>

<s>28). </s></p><p type="main">

<s>Il Castelli per&ograve; ne fece particolar soggetto di esperienze e di specula&shy;<lb/>zioni, ch'egli espose in una sua scrittura sotto forma di lettera indirizzata <lb/>a Galileo, e alla quale si dava il nome di <emph type="italics"/>Mattonata.<emph.end type="italics"/> Venne un tal nome <lb/>alla detta scrittura dall'essersi fatta l'esperienza sopra un mattone mezzo <lb/>tinto di bianco e mezzo di nero, che esposto al sole di estate e poi appres&shy;<lb/>sata ora all'una parte ora all'altra una mano, nella parte nera sentivasi <lb/>molto pi&ugrave; bruciante. </s>

<s>Narra il Castelli stesso com'avesse dato ad intendere <lb/>un tal effetto naturale a un signorino di casa Martinenghi, supposto che i <lb/>corpi bianchi riflettano la luce in maggior copia de'neri, e immaginandosi <lb/>che gl'ignicoli scendessero dal sole a percotere nel mattone, come tante <lb/>palle infocate esplose da una pistola. </s>

<s>&ldquo; Se noi sparassimo venticinque colpi <lb/>di pistola con palle infocate nella parte nera, e venticinque nella parte <lb/>bianca, senza esporre il mattone al lume del sole, e di quelle sparate dalla <lb/>nera ritornassero indietro venti, ma di quelle che fossero sparate nella bianca <lb/>ne ritornassero indietro solamente cinque; in qual parte sarebbero restate <lb/>pi&ugrave; palle infocate, nella nera ovvero nella bianca? </s>

<s>pensateci bene. </s>

<s>Ed egli <lb/>senza molto pensarci francamente rispose: nella bianca. </s>

<s>Mi piacque fuor di <lb/>modo quella prontezza e vivacit&agrave; di spirito, e soggiunsi: Ma la verit&agrave; &egrave;, si&shy;<lb/>gnor marchese, che V. S. mi ha detto poco fa che, spargendosi egualmente <lb/>il lume del sole sopra il nero e sopra il bianco, ritorna indietro agli occhi <lb/>nostri pi&ugrave; lume dal bianco che dal nero, non &egrave; cos&igrave;? </s>

<s>&mdash; Padre s&igrave; &mdash; ri&shy;<lb/>spose. </s>

<s>&mdash; E di pi&ugrave; V. S. ha confessato che il lume del sole &egrave; caldo, non &egrave; <lb/>vero? </s>

<s>&mdash; &Egrave; verissimo &mdash; disse. </s>

<s>&mdash; Adunque, soggiunsi io, non &egrave; da far ma&shy;<lb/>raviglia nessuna che essendo vero che nella parte nera sono restate molto <lb/>maggiori moltitudini di palline calde, che nella parte bianca, quando noi ci <lb/>applichiamo le mani si senta maggior caldo nella parte nera che nella bianca, <lb/>ed ecco che il signor marchese ha saputo rispondere esquisitamente &rdquo; (Opusc. </s>

<s><lb/>Filos., Bologna 1669, pag. </s>

<s>60). </s></p><p type="main">

<s>In che modo fossero nella parte nera rimasti presi pi&ugrave; ignicoli che nella <lb/>bianca lo dava il Castelli a intendere a quel signorino rappresentandogli al&shy;<lb/>l'immaginazione un certo artificio usato dalla Natura nel costruire i pori <pb xlink:href="020/01/716.jpg" pagenum="159"/>alle superficie nere de'corpi. </s>

<s>Il Magalotti che applaud&igrave; a quel bene imma&shy;<lb/>ginato artificio, e l'applic&ograve; a spiegar come i raggi del sole entrino dentro <lb/>i chicchi dell'uva a fin di dimostrar quanto fosse vero il detto galileiano <lb/>non esser cio&egrave; altro il vino che un composto di umore e di luce; rendeva <lb/>in questa forma evidenti le cose immaginate dallo stesso Castelli: &ldquo; Figu&shy;<lb/>ratevi che sieno i pori di que'corpi, che si chiamano neri sepolchri artifi&shy;<lb/>ziosissimi della luce, talmente disposti che i raggi che gli feriscono abbian <lb/>sempre le loro fughe verso le parti pi&ugrave; interne, e tutte le novelle direzioni <lb/>che acquistano dagli scontri di quelle facce, gl'impegnino sempre pi&ugrave; ad&shy;<lb/>dentro, e in cos&igrave; fatto modo vi rimangan sepolti. </s>

<s>Dove per lo contrario delle <lb/>superficie di que'corpi che si chiaman bianchi diremo ch'elle sieno d'un <lb/>cos&igrave; fatto lavoro, che tutti o la maggior parte de'lumi che le feriscono si <lb/>rifondano agli occhi nostri &rdquo; (Lettere scientifiche, Firenze 1721, pag. </s>

<s>49). </s></p><p type="main">

<s>Queste per&ograve;, convien confessarlo, piuttosto che speculazioni scientifiche, <lb/>si direbbero giochi di fantasia, conformi dall'altra parte alle opinioni di quel <lb/>Castelli, che mostrava insieme con Galileo, e rendeva visibili a Lodovico <lb/>delle Colombe gli atomi del foco dentro l'acqua delle ampolle di vetro ri&shy;<lb/>scaldate. </s>

<s>E bench&egrave; il Magalotti non solo ma il Borelli e il Viviani si com&shy;<lb/>piacessero di quelle fantasie, il Grimaldi per&ograve; scioglieva questi stessi pro&shy;<lb/>blemi termici in modo assai pi&ugrave; conveniente alla natura del calore, che <lb/>nessuno oramai pi&ugrave; crede di veder con gli occhi e di pesare sulle stadere. <lb/></s>

<s>&ldquo; Sufficiat observare ideo corpora quae dicuntur alba reflectere multum <expan abbr="lu-min&imacr;s">lu&shy;<lb/>minins</expan>, quia illud quam minime debilitant per novam aliquam fluitationem <lb/>in eo inductam, et ex opposito nigra corpora parum luminis reflectere, quia <lb/>illud maxime enervant, ac fere extinguunt, obtundentes eius celeritatem ac <lb/>vim impetus in profusione certis ondulationibus turbata. </s>

<s>Hinc etiam pote&shy;<lb/>rit reddi ratio cur alba difficilius calefiant a lumine, nigra vero facilius cae&shy;<lb/>teris paribus, quia nimirum lumen ab abis expedite reflexum vix habet in <lb/>eorum poris luctam ullam et agitationem radiorum. </s>

<s>At dum lumen etiamsi <lb/>eiusdem intensionis seu densitatis incurrit in corpus nigrum, seque inter <lb/>poros illius insinuat, non ita expedite potest ab illis egredi, ideoque non nisi <lb/>cum multa lucta et post multas agitationes revertitur, quidus necessario <lb/>debuit impetum facere intra poros illos, simulque calorem excitare &rdquo; (De <lb/>Lum. </s>

<s>cit., pag. </s>

<s>361). </s></p><p type="main">

<s>Parve approvare questa ipotesi del Grimaldi anche il Newton, quando <lb/>cos&igrave; scriveva nella VI Questione: &ldquo; Annon corpora nigra calorem de lumine <lb/>ideo facilius quam corpora colorata concipiunt quia luminis id quod in illa <lb/>incidit non reflectitur extra, sed ingreditur &igrave;n ipsa corpora, intraque ea re&shy;<lb/>flectitur ac refringitur saepius atque iterum usque eo donec restinguatur <lb/>penitus et intercidat? </s>

<s>&rdquo; (Optic, lib. </s>

<s>III cit., pag. </s>

<s>138). </s></p><p type="main">

<s>Considerando ora da qual parte la soluzione del Grimaldi e del Newton <lb/>s'avvantaggi sopra quella del Castelli, si vede che un tal vantaggio in ci&ograve; <lb/>principalmente consiste, che il Castelli attribuisce il maggior riscaldamento <lb/>alla maggior quantit&agrave; degl'ignicoli rimasti presi alla trappola de'pori neri, <pb xlink:href="020/01/717.jpg" pagenum="160"/>mentre il Grimaldi e il Newton l'attribuiscono all'agitamento e al moto <lb/>degli atomi luminosi, i quali mettono poi in moto vibratorio le molecole <lb/>de'corpi <emph type="italics"/>in quo calor consistit<emph.end type="italics"/> (Optic. </s>

<s>lib. </s>

<s>III, <expan abbr="q.">que</expan> V). In sostanza per&ograve; non <lb/>era questa dottrina nuova. </s>

<s>Galileo fu dall'esperienza condotto a dire che <emph type="italics"/>ad <lb/>eccitare il caldo non basta la presenza degli ignicoli ma ci vuole il loro <lb/>movimento ancora<emph.end type="italics"/> (Alb. </s>

<s>IV, 337) e insegnava che due corpi confricati in&shy;<lb/>sieme per questo si riscaldano perch&egrave; lo stripicciamento <emph type="italics"/>coll'aprir l'uscita <lb/>agl'ignicoli contenuti gli riduce finalmente in moto<emph.end type="italics"/> (ivi, pag. </s>

<s>338). </s></p><p type="main">

<s>Ma il Grimaldi e il Newton, rivolgendosi pi&ugrave; attentamente a considerar <lb/>le relazioni che passano fra il moto e il calore, dettero apparecchiamento <lb/>pi&ugrave; prossimo a quelle teorie, che formano la compiacenza e la gloria della <lb/>Fisica moderna. </s>

<s>Dissero gli antichi: il moto eccita il calore. </s>

<s>Poi quando si <lb/>videro le macchine esser mosse dal foco, si not&ograve; che il calore produceva il <lb/>moto, e si fin&igrave; col dire essere una medesima cosa, sotto forma e apparenza <lb/>diversa, il moto e il calore. </s>

<s>Cos&igrave; credono d'aver menato finalmente trionfo <lb/>sopra la crassa ignoranza di chi ammetteva gl'ignicoli materiali o gli atomi <lb/>imponderabili, e si lusingano dolcemente questi beati sapienti d'avere sco&shy;<lb/>perta la natura del calore, dicendo ch'egli &egrave; una forza. </s>

<s>Ma che cosa &egrave; la <lb/>forza, che cosa &egrave; il moto? </s>

<s>Quando i Fisici sapranno rispondere, ci sapranno <lb/>anche insegnare che cosa &egrave; il calore, ma per ora i vantati progressi della <lb/>scienza non par che in altro sien fatti consistere da molti che in calcoli <lb/>facilissimi a far colla penna, e inspirati a quel sentimento peripatetico car&shy;<lb/>tesiano, col quale si presume il Filosofo di farsi legislatore e non alunno <lb/>della Natura. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>In qualunque modo, poich&egrave; sempre riuscir&agrave; misteriosa al nostro debole <lb/>intelletto la cognizione di quella causa operatrice degli effetti, che da noi <lb/>s'attribuiscono al calore, per non seguitare a provocarci lo sdegno di coloro <lb/>che si compiacciono d'aver finalmente scoperta quella recondita causa, te&shy;<lb/>niam dietro a que'pi&ugrave; modesti che si contentarono di considerarne gli effetti. </s></p><p type="main">

<s>Tra gli effetti del calore, ch'essendo cos&igrave; comuni, furono perci&ograve; de'primi <lb/>a richiamare a s&egrave; l'attenzione e lo studio de'Filosofi, son da annoverar gli <lb/>agghiacciamenti e l'evaporazioni. </s>

<s>Ne'primi anni del secolo XVII applican&shy;<lb/>dosi da Peripatetici quel general principio approvato dalla loro Filosofia che <lb/>sia propriet&agrave; del freddo il condensare, si diceva senza timor di dubbio che <lb/>anche il ghiaccio era acqua condensata. </s>

<s>Galileo fu il primo che si oppose a <lb/>cos&igrave; fatta sentenza pronunziando ch'egli avrebbe creduto &ldquo; piuttosto il ghiac&shy;<lb/>cio esser acqua rarefatta che condensata, poich&egrave; la condensazione partorisce <lb/>diminuzione di mole e augumento di gravit&agrave;, e la rarefazione maggior leg-<pb xlink:href="020/01/718.jpg" pagenum="161"/>gerezza e augumento di mole; e l'acqua nel ghiacciarsi cresce di mole e il <lb/>ghiaccio gi&agrave; fatto &egrave; pi&ugrave; legger dell'acqua standovi a galla &rdquo; (Alb. </s>

<s>XII, 12). </s></p><p type="main">

<s>Rispondevano i Peripatetici che il ghiaccio galleggia per ragion della <lb/>figura sua larga e piana, n&ograve; per esser pi&ugrave; leggero dell'acqua, ond'&egrave; che <lb/>pigliando Galileo di qui occasione a trattar delle galleggianti, lasci&ograve; il ca&shy;<lb/>rico ad altri di dimostrar come l'acqua sola non partecipi agli effetti di <lb/>condensazione consueti operarsi dal freddo in tutti gli altri corpi. </s></p><p type="main">

<s>I seguaci del Gassendo dicevano essere gli atomi frigorifici che insi&shy;<lb/>nuandosi dentro l'acqua ne fanno ricrescere la mole e la induriscono ce&shy;<lb/>mentandone insieme le particelle. </s>

<s>Ma a costoro era facile rispondere che <lb/>sottentrando gli atomi frigorifici in luogo de'calorifici sarebbero dovute cos&igrave; <lb/>la mole come la gravit&agrave; rimaner le medesime, non vedendosi ragione perch&egrave; <lb/>debban gli atomi del freddo riuscir pi&ugrave; leggeri e pi&ugrave; voluminosi di quelli <lb/>del caldo. </s></p><p type="main">

<s>I seguaci di Galileo ammettendo che i vacui dell'acqua liquida sien <lb/>pieni di un vapore igneo, fatto esalar questo dal freddo, l'acqua stessa per <lb/>dir cos&igrave; si secca, e diventa pi&ugrave; leggera. </s>

<s>&ldquo; Mirabile quidem, lasci&ograve; scritto di <lb/>propria mano il Viviani, est magni Galilaei praeceptoris mei amatissimi ef&shy;<lb/>fatum.... Soliditatem nempe et consistentiam metallorum non ex alia forsan <lb/>pendere causa quam ex vacuo .... Aqua vero semper fluit cum ipsius athomi <lb/>semper sint admistae vapore, qui vacuum replet, qui tamen vapor interdum <lb/>ob nimium frigus expellitur et aqua, ut ita dicam, siccatur et fit glacies, <lb/>cum inter ipsius athomos remaneant vacua ac propterea glacies aquae su&shy;<lb/>pernatat &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>17). </s></p><p type="main">

<s>Cos&igrave; per&ograve; non rendevasi ragione del ricrescimento di mole, per cui il <lb/>Dati ebbe a dire che un tal fatto, il quale sempre si osserva negli agghiac&shy;<lb/>ciamenti dell'acqua, faceva cadere tutta quella speculazione. </s>

<s>&ldquo; E'fu un tempo <lb/>che io credetti che partendosi le minime particelle del foco totalmente dal&shy;<lb/>l'acqua ne seguisse che restando l'acqua in tutto priva di calore cio&egrave; di <lb/>foco diventasse freddissima. </s>

<s>E perch&egrave; in quegli ultimi spazii ripieni dal fuoco <lb/>non potesse entrare altro (perciocch&egrave; piccolissimi fossero ed impermeabili ad <lb/>ogni altro corpo) detti spazii restassero voti e per cos&igrave; dire pieni di vacui, <lb/>i quali vacui disseminati fossero cagione s&igrave; dell'agghiacciamento .... s&igrave; della <lb/>leggerezza del ghiaccio sopra l'acqua, essendone partito il foco ponderoso e <lb/>rimastovi il vacuo senza pro niuno. </s>

<s>Ma veggendosi che l'acqua agghiac&shy;<lb/>ciando cresce di mole, cade a terra tutta questa speculazione, ed &egrave; neces&shy;<lb/>sario vedere che cosa sia quella che entra nell'acqua a farla coagulare e <lb/>crescere insieme, vedendosi chiaro non potersi dare agghiacciamento senza <lb/>augumento, onde quello che fa crescere certo &egrave; che &egrave; anche la necessaria <lb/>cagione dell'agghiacciamento &rdquo; (MSS. Cim., T. XXXIV, c. </s>

<s>37). </s></p><p type="main">

<s>Nessuno aveva ancora badato a quelle bolle disseminate per la mole <lb/>del ghiaccio rimaste ivi dentro prese, per cos&igrave; dire, alle reti del freddo. </s>

<s>Il <lb/>Gassendo &egrave; vero ne aveva fatto qualche cenno, ma non essendosi troppo <lb/>chiaramente espresso, sfugg&igrave; per qualche tempo all'accortezza degli stessi <pb xlink:href="020/01/719.jpg" pagenum="162"/>gassendisti quel cos&igrave; comodo refugio. </s>

<s>&ldquo; Cum verum sit aquam calefactam <lb/>refrigescendo citius fortiusque conglaciare quam frigidam, ecquam aliam pu&shy;<lb/>temus causam quam quia facta maiore quodam partium aquae laxitate ipsae <lb/>aer facilius subingreditur et vehementius stringit particulas aquae quibus <lb/>commiscetur? </s>

<s>&rdquo; (Animadversiones in X Laertii, Lugduni 1675, T. I, pag. </s>

<s>573). </s></p><p type="main">

<s>Poi dopo si avvidero i seguaci del Gassendo del buon partito che avreb&shy;<lb/>bero potuto trarne esplicando quegl'involuti concetti del loro Maestro, e ap&shy;<lb/>plicandoli particolarmente al fatto in questione dissero esser causa del ri&shy;<lb/>crescimento del ghiaccio l'aria, la quale introducendosi dal di fuori vi riman <lb/>presa e come agghiacciata. </s>

<s>L'esperienza per&ograve; degli agghiacciamenti dentro <lb/>i vasi di metallo pieni d'acqua e benissimo chiusi, faceva cader d'un tratto <lb/>cos&igrave; nuova e assai bella speculazione. </s>

<s>Si sarebbe essa potuta facilmente sal&shy;<lb/>vare supponendo che l'aria, invece di sopravvenir dal di fuori, preesistesse <lb/>gi&agrave; in mezzo all'acqua, ma erano molto alieni dal suppor ci&ograve; come possi&shy;<lb/>bile, specie i Fisici della scuola galileiana. </s></p><p type="main">

<s>L'esperienza delle bollicelle che per effetto del calore si sciolgon dal <lb/>liquido, esperienza che avrebbe potuto ridurre quella possibilit&agrave; a una prova <lb/>di fatto, si sa bene come fosse intesa da Galileo e dal Castelli, e come fos&shy;<lb/>sero dal Viviani nel <emph type="italics"/>Discorso sopra Democrito<emph.end type="italics"/> confermate le illusioni de'due <lb/>grandi Maestri. </s></p><p type="main">

<s>Abbiamo detto che alieni da quella supposizione erano particolarmente <lb/>i discepoli di Galileo, perch&egrave; per aria e non per globetti di fuoco erano stati <lb/>riconosciuti, que'sonagli che si vedono salir su per l'acqua riscaldata, dal <lb/>Noel, dal Pecquet e da tutti coloro che alla dilatazione immediata di quella <lb/>stessa aria annidatavi dentro attribuivano la dilatazione termometrica del&shy;<lb/>l'acqua. </s>

<s>Non si potrebbe affermare perci&ograve; che avessero conosciuta la pro&shy;<lb/>priet&agrave; de'liquidi di sciogliere i corpi gassosi: forse essi credevano che il <lb/>calore facesse convertire il liquido in gasse, e che perci&ograve; avvenisse di ritro&shy;<lb/>var cos&igrave; sempre l'aria in mezzo all'acqua riscaldata. </s></p><p type="main">

<s>Questo anzi &egrave; certo per quel che riguarda un nostro Italiano, a cui <lb/>giov&ograve; l'aver bevuto alle fonti cartesiane per non farsi cieco ammiratore di <lb/>ogni dottrina di Galileo. </s>

<s>Tommaso Cornelio osservando il gallozzolar del&shy;<lb/>l'acqua di un'ampolla esposta ai raggi del sole, non dubit&ograve; di asserir che <lb/>quella era aura vaporosa in che trasformavasi l'acqua stessa per opera del <lb/>calore. </s>

<s>&ldquo; Si vitream ampullam aquae plenam solaribus radiis exponemus, <lb/>videbimus infra ipsam aquam passim gigni plurimas aeris bullas margari&shy;<lb/>tularum speciem gerentes.... Id autem aestate frequentius contingit, propte&shy;<lb/>rea quod calor aquam in vapores facile solvit atque idcirco complures ae&shy;<lb/>raee bullae progignuntur &rdquo; (Progymnasmata phisica, Neapoli 1688, pag. </s>

<s>398). </s></p><p type="main">

<s>La particolare scrittura fra'Proginnasmi citati, dalla quale abbiamo tra&shy;<lb/>scritte queste parole, &egrave; un'Epistola intitolata <emph type="italics"/>De cognatione aeris et aquae<emph.end type="italics"/><lb/>diretta a M. </s>

<s>Aurelio Severino da Roma nel 1649. Ivi soggiornava allora <lb/>l'Autore familiarmente conversando con Michelangiolo Ricci, dalla bocca del <lb/>quale ebbe la notizia dell'esperienze fatte dal Torricelli e dal Magiotti in-<pb xlink:href="020/01/720.jpg" pagenum="163"/>torno alla renitenza certissima dell'acqua alla compressione. </s>

<s>La prima espe&shy;<lb/>rienza fu fatta dal Verulamio e da lui stesso descritta nel &sect; XLV del secondo <lb/>libro del <emph type="italics"/>Nuovo Organo.<emph.end type="italics"/> Venne al Torricelli voglia di ripeterla nelle sale <lb/>de'Pitti, per confermare l'importantissima verit&agrave; del fatto, e per dar gusto <lb/>al Granduca, il quale fece con regia liberalit&agrave; tornire esquisitamente sfere <lb/>gettate di argento, di rame e di ottone, per servire a quest'unico intento. </s>

<s><lb/>Chi volesse aver di ci&ograve; pi&ugrave; particolar notizia e pi&ugrave; compiuta, legga, invece <lb/>della descrizione fatta nel libro de'<emph type="italics"/>Saggi di naturali esperienze<emph.end type="italics"/> (Firenze 1841, <lb/>pag. </s>

<s>130), la seguente nota scritta di propria mano da Vincenzio Viviani: </s></p><p type="main">

<s>&ldquo; Che l'acqua come acqua non si possa nemmeno con qualsivoglia vio&shy;<lb/>lenza condensare per minima parte, l'ha sperimentato il Serenissimo Gran&shy;<lb/>duca. </s>

<s>Ha fatto gettare d'ogni metallo com'argento, rame, ottone ecc. </s>

<s>pi&ugrave; <lb/>palle vuote per di dentro e di grossezza di orlo intorno a quella di una pia&shy;<lb/>stra d'argento, quali poi per un foro fattovi a vite ha fatto empir d'acqua <lb/>e serrato con vite di simili metalli strettissimamente il foro di dette palle <lb/>le ha poi fatte posare sopra un'incudine e fattegli dare colpi gagliardi con <lb/>un martello d'acciaio e ha osservato S. A. che l'acqua inclusa per non pa&shy;<lb/>tire condensazione alla violenza de'colpi trasudava fuori della palla per i pori <lb/>del metallo &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>5). </s></p><p type="main">

<s>Il resultato di queste esperienze, come di tutte le altre fatte nella Corte <lb/>medicea, le partecipava il Torricelli a Raffaello Magiotti, il quale nel risol&shy;<lb/>vere poi que'problemi idrostatici mandati da Firenze e descritti a Don Lo&shy;<lb/>renzo de'Medici, conferm&ograve; quella renitenza dell'acqua alla impressione con <lb/>altre nuove spettacolose esperienze. </s>

<s>Il Cornelio dunque informato di tutto <lb/>ci&ograve; come abbiamo detto dal Ricci, ne ricavava di qui un valido argomento <lb/>a provar che l'aria non pu&ograve; in nessun modo ospitare nell'acqua, perch&egrave; <lb/>essendo questa fortemente compressa, dovrebbe almeno cedere per la cede&shy;<lb/>volezza dell'aria, se facesse veramente parte della sua mole. </s></p><p type="main">

<s>L'argomento del Cornelio era ragionevole che potesse altres&igrave; sulle menti <lb/>de'nostri Fiorentini in non farle andar cos&igrave; facilmente a supporre che l'aria <lb/>si rannidasse naturalmente nell'acqua. </s>

<s>Non avevano pensato mai per&ograve; di <lb/>farne particolare e diligente esperienza, quando Paolo Del Buono, con let&shy;<lb/>tera del d&igrave; 6 Ottobre 1657 scritta da Vienna, annunziava a Leopoldo de'Me&shy;<lb/>dici che s'era da pochi mesi dichiarato principe dell'Accademia del Cimento, <lb/>uno de'pi&ugrave; fantastici effetti che gli fosse a suo credere occorso di trovare <lb/>nella Natura. </s>

<s>Consisteva un tal effetto nel veder che dall'acqua rinchiusa in <lb/>ampollette di vetro con sottilissimo collo, sempre si generava aria, bench&egrave; <lb/>in pi&ugrave; o meno copia secondo che maggiore o minore era il caldo della sta&shy;<lb/>gione. </s>

<s>Diceva in proporre quelle sue esperienze che, sebben non fosse riu&shy;<lb/>scito a investigar le cause di effetti tanto stravaganti, sperava nulladimeno <lb/>che sarebbero &ldquo; ai signori Accademici occasioni di assai curiose speculazioni <lb/>non solo, ma di trarne la certezza di qualche occulta fin'ora verit&agrave; nelle <lb/>cose naturali &rdquo; (Targion&igrave;, Notizie cit., T. II, P. I, pag. </s>

<s>312). </s></p><p type="main">

<s>Proposte l'esperienze del Del Buono nell'Accademia e riscontratesi ve-<pb xlink:href="020/01/721.jpg" pagenum="164"/>rissime, il Borelli forse compiacente di non andare in tutto ai versi del Vi&shy;<lb/>viani tenace di quel vapore igneo circondante gli atomi dell'acqua, se&shy;<lb/>condo l'opinione del suo amatissimo Galileo; non dubit&ograve; di affermare che <lb/>l'aria generatasi dall'acqua nel collo delle ampolle preesistesse nell'acqua <lb/>stessa sceveratavi dal calore. </s>

<s>Non decideva se ci&ograve; avvenisse per insinuazione <lb/>delle particelle aereose esterne o per sotterranee esalazioni, ma supposto in <lb/>ogni modo questo fatto per vero, spiegava il Borelli in una sua scrittura <lb/>indirizzata al principe dell'Accademia da Roma il d&igrave; 21 di Settembre 1658, <lb/>il ricrescimento della mole del ghiaccio. </s>

<s>Supposto ci&ograve;, e accettando da Ga&shy;<lb/>lileo quel che con filosofica libert&agrave; credeva di accettare, supposto di pi&ugrave; che <lb/>esalato il vapor igneo d'intorno agli atomi dell'acqua, questi venissero pi&ugrave; <lb/>prontamente a esercitare la reciproca attrazion magnetica, o molecolare come <lb/>si direbbe oggid&igrave;, e fossero perci&ograve; la causa dell'indurirsi la mole; cos&igrave; l'in&shy;<lb/>gegnoso Fisico dimostrava il suo assunto: </s></p><p type="main">

<s>&ldquo; Supponendo il freddo esser privazione di calore, allorch&egrave; l'acqua si <lb/>raffredda, &egrave; necessario che traspiri dalla detta acqua moltitudine grande di <lb/>atomi ignei. </s>

<s>Ma all'assenza di detti atomi ignei segue l'unione e contatto <lb/>delle parti acquee e libert&agrave; di esercitare la virt&ugrave; magnetica, e quel moto che <lb/>&egrave; necessario per unirsi e scappar fuori dai buchetti degli atomi aerei, i quali <lb/>impedivano l'unione di detti atomi, e dentro dei quali gli atomi acquei per <lb/>la necessit&agrave; del sito stavano pravamente collocati, e fuor del loro sito na&shy;<lb/>turale. </s>

<s>Adunque &egrave; necessario che tutti quegli atomi aerei, i quali son di&shy;<lb/>spersi dentro la sostanza dell'acqua rimangano voti d'acqua.... E perch&egrave; <lb/>gli spazietti occupati dal foco allorch&egrave; l'acqua era fluida sono incompara&shy;<lb/>bilmente minori di quelli spazii vacui della concavit&agrave; degli atomi aerei, per <lb/>esser gli atomi ignei assai pi&ugrave; piccoli che non sono gli atomi aerei, adun&shy;<lb/>que necessariamente nell'atto dell'addiacciamento dee ampliarsi la mole del&shy;<lb/>l'acqua &rdquo; (Fabbroni, Lett. </s>

<s>in., Firenze 1773, T. I, pag. </s>

<s>105, 6). </s></p><p type="main">

<s>Il Viviani per&ograve; che voleva in tutto e per tutto salvar le dottrine di Ga&shy;<lb/>lileo non approvava l'ipotesi dell'aria ospitante in mezzo all'acqua, sopra <lb/>la quale principalmente il Borelli fondava la sua dimostrazione. </s>

<s>E tanto era <lb/>persuaso di ci&ograve; che, non avendo potuto liberarsi da quel bollimento che fa&shy;<lb/>ceva sempre il mercurio nel tubo torricelliano, propose &ldquo; di fare un can&shy;<lb/>none di stagno lungo sedici braccia e supplire sino in venti con canne di <lb/>vetro per aver campo di fare il vuoto con l'acqua e per osservare se ve&shy;<lb/>ramente queste bollicine ascendenti dall'argento vivo sian particelle di aria &rdquo; <lb/>(Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>439). </s></p><p type="main">

<s>Questa esperienza, eseguita nel d&igrave; 18 Agosto 1660, &egrave; la prima colla <lb/>quale i nostri Fiorentini operarono il vuoto con tubi pieni di acqua, come <lb/>avevano fatto gi&agrave; il Berti a Roma e il Pascal a Roano ritornando cos&igrave; a fare <lb/>quel ch'erasi fatto tanti anni indietro, per questo fine singolare; per aver <lb/>cio&egrave; uno spazio perfettamente vuoto di quelle esalazioni, che sempre si <lb/>vedevano uscir dal mercurio. </s>

<s>Ma come sar&agrave; rimasto il Viviani a veder nel&shy;<lb/>l'acqua un tal fervore di effluvii, che il mercurio al confronto era un nulla! <pb xlink:href="020/01/722.jpg" pagenum="165"/>Non si volle per&ograve; dar vinto: fece scrivere nel Diario che l'esperienza del <lb/>vuoto con l'acqua non era riuscita, <emph type="italics"/>per difetto dell'istrumento<emph.end type="italics"/> (ivi, pag. </s>

<s>442); <lb/>immagin&ograve; un apparecchio nuovo, e per dimostrar che gli effluvii dell'acqua <lb/>non erano bolle aeree secondo voleva il Borelli, ma ignee come insegnava <lb/>Galileo, applic&ograve; al vaso dell'immersione alquanti carboni accesi, che faces&shy;<lb/>sero indizio certo del crescer per essi le ignee esalazioni nel vuoto. </s>

<s>&ldquo; Fu <lb/>collocato poi il vaso tutto in un luogo a parte, per vedere se in progresso <lb/>di tempo l'acqua col sollevarsi a riempier tutta la palla dia a vedere la ma&shy;<lb/>teria delle gallozzole non essere altrimenti aria, ma o fuoco o altra sostanza <lb/>tenuissima &rdquo; (ivi, pag. </s>

<s>443). </s></p><p type="main">

<s>Che cosa risolvesse il Viviani da queste esperienze non abbiam docu&shy;<lb/>menti da informarne i lettori. </s>

<s>Ma quanto egli &egrave; certo che riconobbe l'aria <lb/>in mezzo al mercurio, altrettanto &egrave; incerto se s'inducesse poi ad ammet&shy;<lb/>terla in mezzo all'acqua. </s>

<s>In ogni modo, d'onde avesse origine l'aria nel <lb/>mercurio rimase al Viviani stesso un mistero. </s>

<s>Geminiano Montanari scrive&shy;<lb/>vagli cos&igrave; nel Settembre del 1671 da Bologna: &ldquo; Adesso mi va incontrando <lb/>una burla bellissima col Baroscopio che non ne trovo n&egrave; regola n&egrave; cagione. </s>

<s><lb/>Ho tenuto tutto il verno passato il Baroscopio ed osservatone in pi&ugrave; mesi <lb/>il moto giornale, n&egrave; mai ha fatte stravaganze come da mezzo Luglio in qua. </s>

<s><lb/>Cominci&ograve; di questo tempo a ribollire cos&igrave; forte il mercurio, generando ogni <lb/>d&igrave; nuova aria che nel corso di una settimana era scemato ben sei once, e <lb/>scotendolo un poco lo vedevo come ribollire e vomitar verso il vuoto gal&shy;<lb/>lozzolette d'aria. </s>

<s>Dubitai si fosse fesso il vetro, onde estrattone il mercurio <lb/>lo riconobbi e feci riconoscere da occhi migliori ben bene n&egrave; vi fu trovato <lb/>difetto &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXXV, c. </s>

<s>185). </s></p><p type="main">

<s>Pochi mesi dopo tornava nel Dicembre su questo fatto il Montanari, <lb/>che confessava di avergli fatto perdere la pazienza. </s>

<s>Tutti i giorni era a vo&shy;<lb/>tar d'aria il tubo del suo Barometro e sempre ce ne rimaneva dell'altra <lb/>senza saper d'ond'ella ci fosse entrata, o dove diamine mai si fosse nasco&shy;<lb/>sta, e rivolto al Viviani a cui raccontava queste cose, all'ultimo conclude: <lb/>&ldquo; Perch&egrave; dunque oramai non &egrave; finita di uscire e perch&egrave; anzi alcuna volta <lb/>ve ne trovo maggior quantit&agrave; di prima, che certo quella che sinora n'ho <lb/>estratta &egrave; molto pi&ugrave; che non bisognerebbe per empir d'aria sola tutta la <lb/>canna; V. S. Ecc.ma mi aiuti col sottilissimo suo intelletto a capir questo <lb/>imbroglio che per me sono intrigato &rdquo; (ivi, c. </s>

<s>210). </s></p><p type="main">

<s>E poich&egrave; siam certi che non venne dal Viviani nessuno aiuto, e che <lb/>rimasero anzi ambedue in quell'imbroglio, ritorniamo al Borelli che nel&shy;<lb/>l'esperienza del vuoto operato coll'acqua, in che il Viviani aveva fatto nau&shy;<lb/>fragio, egli ritrovava alla sua ipotesi dell'aria rimasta dentro il ghiaccio la <lb/>pi&ugrave; bella conferma. </s>

<s>Cos&igrave; infatti scriveva nel libro <emph type="italics"/>De motionibus naturali&shy;<lb/>bus,<emph.end type="italics"/> dove inser&igrave; quelle sue tre proposizioni dimostrate con gli stessi prin&shy;<lb/>cipii e dietro le medesime cose supposte gi&agrave; nella sopra citata scrittura al <lb/>principe Leopoldo, dodici anni avanti: &ldquo; Quod confirmari potest pulcher&shy;<lb/>rimo instrumento torricelliano, in quo vacuum mediante aqua efficitur. </s>

<s>Nam <pb xlink:href="020/01/723.jpg" pagenum="166"/>dum aqua descendit ad solitam depressionem 17 cubitorum proxime, tunc <lb/>videmus ab aqua tantam copiam ampullarum aerearum egredi, ut reprae&shy;<lb/>sentet ebullitionem quam efficere solet fervor ignis in eadem aqua &rdquo; (Regio <lb/>Julio 1670, pag. </s>

<s>552). </s></p><p type="main">

<s>E perch&egrave;, in quel che fu quivi speculato dal Borelli, si conclude quella <lb/>parte di storia che narra come si travagliassero i Fisici per intendere il fatto <lb/>de'naturali agghiacciamenti nella mole liquida, ci rimane a narrar breve&shy;<lb/>mente di altri loro travagli durati per ritrovar la ragione di quella squisita <lb/>regolarit&agrave; di forme geometriche, in che si dispongono le minute gocciole <lb/>dell'acqua stessa ghiacciata sotto le apparenze di neve o di brina. </s></p><p type="main">

<s>Passeggiava tutto solo e pensoso per le vie della citt&agrave; Giovanni Keplero, <lb/>serrandosi bene addosso il mantello per ripararsi da un vento freddissimo <lb/>che spirava dalla parte di Tramontana, quando incominciarono a cader dal <lb/>cielo rannuvolato alcune squamette biancheggianti di ghiaccio. </s>

<s>Cadevano <lb/>quelle squamette sul panno di color nero, di cui il Matematico dell'Impe&shy;<lb/>ratore era coperto, ed egli, rimanendovi attaccate sopra e distese, le osser&shy;<lb/>vava attentissimamente. </s>

<s>Avevano tutte la figura di una piccola stella a sei <lb/>punte. </s>

<s>Scuote il mantello per ricevervene sopra altre che seguitavano a ca&shy;<lb/>dere, e tutte si rassomigliano puntualmente nella figura sessangolare. </s>

<s>&ldquo; Cum <lb/>perpetuum hoc sit, egli allora fra s&egrave; conclude, quoties ningere incipit, ut <lb/>prima illa nivis elementa figuram praeseferant asterisci sexanguli, causam <lb/>certam esse necesse est &rdquo; (De nive sexangula, Francof. </s>

<s>ad M. 1611, pag. </s>

<s>5). </s></p><p type="main">

<s>Ripensa che pur anch'essi sessangolari sono i favi dell'api e ne rico&shy;<lb/>nosce l'origine da un provvido istinto ingerito in quegl'industriosi insetti <lb/>dalla Natura, perch&egrave;, dentro il minimo circuito, le celle costruite a riporvi <lb/>il miele, pi&ugrave; che sia possibile, riescan capaci. </s>

<s>&ldquo; Vulgare est apud Physicos, <lb/>qui ad solam quidem sexangularem structuram respiciunt, ut illa cum hia&shy;<lb/>tibus extrinsecus sese repraesentet. </s>

<s>Cum enim locum planum impleant ex&shy;<lb/>cluso vacuo, tantum hae figurae triangulum, quadrangulum, sexangulum, <lb/>ex iis sexangulum capacissima est figura. </s>

<s>Capacitatem autem sibi parant <lb/>apes ad mella condenda &rdquo; (ibi, pag. </s>

<s>11). </s></p><p type="main">

<s>Ripensa inoltre tal'esser pure la figura de'chicchi de'meli granati, e <lb/>ne riconosce l'origine dalle pressioni per le quali, crescendo la mela, cos&igrave; <lb/>provvede la Natura a far s&igrave; che di que'chicchi sia massimamente capace <lb/>l'interna cavit&agrave; del frutto, senza accrescerne soverchiamente la mole. </s>

<s>Un <lb/>simile effetto di pressione per ristringimento dee esser, seguita a ragionare <lb/>il Keplero, operato dal freddo, propriet&agrave; del quale &egrave; il ristringere e il con&shy;<lb/>densare, ond'&egrave; che, fra le cause estrinseche della neve sessangolare, una <lb/>senza dubbio potrebb'essere anche questa. </s>

<s>&ldquo; Cum enim proposuissemus <lb/>inquirere originem figurae huius in nive inter causas extrinsecas et intrin&shy;<lb/>secas, inter externas primum sese offerebat frigus. </s>

<s>Condensatio sane est a <lb/>frigore: per condensationem vero vapor erit in figuram stellae: videbatur <lb/>igitur frigus illi figuram praestare stellae &rdquo; (ibi, pag. </s>

<s>12). </s></p><p type="main">

<s>Ma non vedeva l'arguto speculatore come questa causa puramente <pb xlink:href="020/01/724.jpg" pagenum="167"/>estrinseca potesse produrre effetti cos&igrave; costanti, e cos&igrave; regolari, per cui si <lb/>rivolge a pensar sopra qualche altra cosa, da cui intrinsecamente dipenda <lb/>quell'ammirabile opera della geometrizzante Natura. </s>

<s>E dopo varii pensieri <lb/>passatigli per la mente &ldquo; An denique, conclude, ipsa huius formatricis na&shy;<lb/>tura in intimo sinu suae essentiae particeps est sexanguli? </s>

<s>&rdquo; (ibi, pag. </s>

<s>22). <lb/>Confermerebbe questa mia congettura, prosegue a dire il Keplero, &ldquo; opera <lb/>huius formatricis facultatis alia ut chrystalli omnes sexangulae, cum ada&shy;<lb/>mantes octaedrici sint rarissimi. </s>

<s>Sed formatrix telluris facultas non unam <lb/>amplectitur figuram, gnara totius Geometricae et in ea exercita. </s>

<s>Vidi enim <lb/>Dresdae in aede regia cui Stabulo nomen, exornatum abacum aere argen&shy;<lb/>toso, ex quo quasi efflorescebat dodecaedron avellanae parvae magnitudine, <lb/>dimidia parte extans. </s>

<s>Extat et in descriptione Thermarum bollensium ico&shy;<lb/>saedri pars anterior inter fossilia. </s>

<s>Itaque verisimile est hanc facultatem for&shy;<lb/>matricem pro diverso humore diversam fieri. </s>

<s>In vitriolo crebra est figura <lb/>cubica, rhombica in nitro sua est figura. </s>

<s>Dicant igitur Chymici an in nive <lb/>sit aliquid salis, et quodnam salis genus, et quam illud alias induat figu&shy;<lb/>ram. </s>

<s>Ego namque, pulsatis Chymiae foribus, cum videam quantum restet <lb/>dicendum ut causa rei habeatur, malo abs te. </s>

<s>Vir solertissime, quid sentias <lb/>audire quam disserendo amplius fatigari &rdquo; (ibi, pag. </s>

<s>23, 24). </s></p><p type="main">

<s>Cos&igrave; termina la Dissertazione <emph type="italics"/>De nive sexangula,<emph.end type="italics"/> che l'Autore indi&shy;<lb/>rizza per <emph type="italics"/>Strenna<emph.end type="italics"/> all'amico suo Giovan Matteo Wackero, e cos&igrave; terminando <lb/>lasciava a'suoi successori a correre un breve tratto di via, per giungere alla <lb/>finale soluzion del problema. </s>

<s>Quella via per&ograve;, bench&egrave; breve, fu trovata cos&igrave; <lb/>difficile e penosa, che ci vollero ancora quasi due secoli prima che si rico&shy;<lb/>noscesse nell'acqua quella intrinseca virt&ugrave; formatrice, che il Keplero non <lb/>vedeva risedere in altro, che nelle soluzioni de'sali. </s>

<s>In tutto quel frattempo <lb/>o si folleggi&ograve; o non si seppe delle ragioni pensate dal Keplero accettar che <lb/>quelle riguardanti le azioni estrinseche operatrici della sessangolar forma&shy;<lb/>zione, invocando in proposito la Geometria de'massimi e de'minimi, e l'esem&shy;<lb/>pio de'favi melliferi e de'meli granati. </s></p><p type="main">

<s>Il Cartesio, come se fosse stato il primo a entrare in questa specula&shy;<lb/>zione, narra nel cap. </s>

<s>VI delle <emph type="italics"/>Meteore<emph.end type="italics"/> come gli occorresse d'osservar la <lb/>figura sessangolare, in che si conformano ghiacciando le gocciole della piog&shy;<lb/>gia. </s>

<s>&ldquo; Referam ea quae proxima hyeme anni 1635 Amstelodami, ubi tunc <lb/>eram, circa hanc rem observavi. </s>

<s>Quarto februarii, quum dies admodum fri&shy;<lb/>gida praecessisset, vesperi paululum pluviae decidit, quae in glaciem verte&shy;<lb/>batur simul ac terram contingebat.... Sed omnium maxime admirabar quae&shy;<lb/>dam ex his granis, quae postrema deciderunt parvos sex dentes circa se <lb/>habere, similes iis qui in horologiorum rotis &rdquo; (Francof. </s>

<s>ad M. 1692, pag. </s>

<s>158). </s></p><p type="main">

<s>O fosse per secondar quel suo genio che lo portava a disprezzare ogni <lb/>scientifica tradizione, o fosse veramente perch&egrave; non fosse capitata in man <lb/>del Cartesio la Strenna kepleriana, fatto &egrave; che, in contemplar la novit&agrave; di <lb/>quelle squisite figure sessangolari, rimase il Filosofo sorpreso di maraviglia, <lb/>e badava a pensare fra s&egrave; e s&egrave; come si potessero que'granelli di ghiaccio <pb xlink:href="020/01/725.jpg" pagenum="168"/>ridurre a pigliar forme cotanto regolari, in mezzo al disordinato imperver&shy;<lb/>sare de'venti. </s>

<s>&ldquo; Aegre tantummodo poteram coniicere quidnam in aere li&shy;<lb/>bero, turbantibus ventis, adeo accurate hos sex dentes formare, et circa sin&shy;<lb/>gula grana disponere potuisset, donec tandem in mentem venit facillime fieri <lb/>potuisse ut ventos nonnulla ex his granis versus alquam nubem expulerit, <lb/>eaque infra illam vel ultra suspensa aliquamdiu detinuerit, satis enim exi&shy;<lb/>gua erant. </s>

<s>Atque ibi procul dubio ita disponi debuisse, ut singula sex aliis <lb/>in eodem plano sitis cingerentur, quia talis est ordo naturae &rdquo; (ibi, pag. </s>

<s>159). </s></p><p type="main">

<s>Nonostante per&ograve; che il Cartesio pretendesse cos&igrave; di farsi primo mae&shy;<lb/>stro a coloro, che desideravano d'aver la ragione della neve sessangolare, <lb/>si riconosceva da'pi&ugrave; e si seguiva come pi&ugrave; autorevole il magisterio di co&shy;<lb/>lui, che 26 anni avanti aveva speculato di quelle cose. </s>

<s>Il Baliani fra'Nostri <lb/>irraggiando di luce propria i concetti del Keplero, cos&igrave; scriveva: &ldquo; Forse <lb/>pu&ograve; essere che le bollette delle nuvole, in luogo ove sono abbandonate dal <lb/>calore, cominciando a congelarsi acquistino una certa tenacit&agrave; e spessezza, e <lb/>perci&ograve; maggior gravit&agrave;, onde aggravatene e compresse le inferiori e perci&ograve; <lb/>schiacciatesi, di sfere divengan circoli, e premute poi ognuna di loro dalle <lb/>collaterali si riducano in figure esagone, come avviene al favo del mele, al <lb/>vespaio, a'granelli della mela grana, a'cristalli, a tutt&egrave; quelle cose che hanno <lb/>figura circolare, qualora si premano e calchino fra loro per l'uguaglianza <lb/>ch'&egrave; fra il semidiametro e il lato dell'esagono &rdquo; (Tratt. </s>

<s>della pestil., Sa&shy;<lb/>vona 1647, pag. </s>

<s>44). </s></p><p type="main">

<s>Il Borelli per&ograve;, mentre sembra che a prima vista si riscontri col Car&shy;<lb/>tesio, si scopre poi aver concetti suoi originali, e anche al vero in certo modo <lb/>conformi, quando congettura che la figura sessangola sia originaria all'ele&shy;<lb/>mento dell'acqua. </s>

<s>&ldquo; Si pu&ograve; supporre, egli dice, che gli atomi acquei sieno <lb/>corpi composti di altri minutissimi corpi primi e semplici.... &Egrave; tal supposi&shy;<lb/>zione assai conforme all'ordine della natura, poich&egrave; intorno a ciaschedun <lb/>corpo rotondo non possono in una superficie piana collocarsi pi&ugrave; che sei <lb/>altri corpi rotondi della medesima grandezza, in maniera per&ograve; che tutti vi&shy;<lb/>cendevolmente si tocchino, come facilmente si pu&ograve; dimostrare. </s>

<s>Di pi&ugrave; l'espe&shy;<lb/>rienza mostra che i minutissimi granellini della neve banno la detta figura <lb/>di stella esagonale con le punte crinite, e perch&egrave; la neve &egrave; un aggregato <lb/>di certa determinata moltitudine di atomi acquei uniti insieme, assai pro&shy;<lb/>babilmente dalla figura di detta neve possiamo congetturare esser tale <lb/>ancora la figura originaria di detta acqua &rdquo; (Fabbroni, Lett. </s>

<s>cit., T. I, <lb/>pag. </s>

<s>110). </s></p><p type="main">

<s>Queste non sono altro che supposizioni e probabilit&agrave;, ben lo riconosce <lb/>il Borelli da s&egrave;, e lo confessa, ma pur &egrave; cosa da non lasciarsi senza consi&shy;<lb/>derazione che cos&igrave; speculavasi in Italia, mentre i pi&ugrave; insigni fisici stranieri, <lb/>fra'quali il Willis, seguitati da alcuni de'Nostri imbevuti de'principii pe&shy;<lb/>ripatetici, ritenevan per cosa certa &ldquo; che il sale volatile delle piante nelle <lb/>fredde notti del verno fa una foglia di ghiaccio su'vetri delle finestre col&shy;<lb/>l'umido accidentale, che seco esce da'rami verdi che si ardono, e in esso <pb xlink:href="020/01/726.jpg" pagenum="169"/>stampa e figura l'immagine dell'albero onde &egrave; tratto &rdquo; (Bartoli, Del ghiac&shy;<lb/>cio, Roma 1681, pag. </s>

<s>118). </s></p><p type="main">

<s>Anzi in quel medesimo che da costoro si professavano simili puerilit&agrave; <lb/>come fatti certissimi e dimostrati, un discepolo del Borelli attendeva ad os&shy;<lb/>servar diligentissimamente col Microscopio i cristallini del ghiaccio, e rasso&shy;<lb/>migliandoli ai cristalli precipitati dalla soluzione de'sali, attribuiva il loro <lb/>formarsi a una virt&ugrave; di attrazione magnetica, che facesse, nel riordinamento <lb/>delle particelle saline gi&agrave; prima dissolute, da necessaria guida ideale. </s></p><p type="main">

<s>Essendo il d&igrave; 19 Dicembre del 1674 caduta a Torino, dove allora di&shy;<lb/>morava Donato Rossetti, gran copia di neve, e ne'seguenti giorni essendosi <lb/>il cielo tutto rasserenato &ldquo; sopra detta neve, scrive lo stesso Rossetti, in <lb/>andando a spasso l'ultimo d&igrave; dell'anno per il nuovo accrescimento della <lb/>citt&agrave;, mi venne osservato che la brinata caduta nelle quattro notti antece&shy;<lb/>denti vi s'era da per tutto distribuita in alcune masserelle simili. </s>

<s>Il che <lb/>messemi in dubbio quello che fermamente credeva, cio&egrave; che la brinata nel <lb/>cadere non obbedisse se non al moto di propensione al centro della Terra, <lb/>e a'moti che le imprimono gl'incontri e gli urti che si avesse nella discesa, <lb/>e mossemi il dubbio che da per tutto si ammassasse nella stessa figura, per <lb/>quelle cagioni, per le quali io mi d&ograve; ad intendere che nella stessa figura <lb/>sempre si vedano, dopo giorni, rimessi insieme i sali che pesti e triti si di&shy;<lb/>spergono nell'acqua. </s>

<s>Movemi il dubbio, voglio dir io, che la brinata si am&shy;<lb/>massasse da per tutto nella stessa figura, perch&egrave; le di lei particelle, nel ca&shy;<lb/>dere una vicina all'altra, fossero guidate a congiungersi per una qualche <lb/>virt&ugrave; magnetica od appetenza e a congiungersi in certi punti come per una <lb/>qualche necessit&agrave; ideale. </s>

<s>E questo dubbio mi ridusse a fare le seguenti os&shy;<lb/>servazioni. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Misi sopra una tavola neve, diaccio d'acqua ordinaria, diaccio di neve <lb/>distrutta, diaccio di brinata strutta, pietra lavagna, ebano, panno nero di <lb/>lana, tela bianca di lino, carta da scrivere, mattone cotto, ed altre coserelle, <lb/>ed il tutto esposi al sereno sopra il tetto di casa la notte seguente il d&igrave; <lb/>primo di Gennaio. </s>

<s>La mattina de'2 l'ebano, la lavagna, e tutte le altre cose <lb/>non bianche, se ne eccettuiamo il mattone cotto, sopra il quale non trovai <lb/>mai segno di brinata, si vedevano col nudo occhio ricoperte di brinata in <lb/>modo, che parevano punteggiate di bianco.... Ma guardando con un Micro&shy;<lb/>scopio di tre lenti molto buono, riscontrai che i punti erano ciascuno una <lb/>rosetta di tre, quattro e fino in sette fogliucce.... Ogni fogliuccia era come <lb/>sottilissima scaglietta da giudicarsi piana, nel mezzo trasparente come un <lb/>diaccio il pi&ugrave; cristallino, ma terminato da una listarella bianca e opaca come <lb/>di neve, e tal listarella la stimai larga la terza parte de'semidiametri di <lb/>quelle fogliucce, che poi si accostavano nella figura al cerchio &rdquo; (MSS. Cim., <lb/>T. XX, c. </s>

<s>192). </s></p><p type="main">

<s>Prosegue il nostro Autore a fare e a descrivere ivi altre diligentissime <lb/>osservazioni, <emph type="italics"/>per venire,<emph.end type="italics"/> com'egli stesso si esprime, <emph type="italics"/>in chiaro di alcuni <lb/>particolari senza la cognizione de'quali stimo non potervisi intorno di-<emph.end type="italics"/><pb xlink:href="020/01/727.jpg" pagenum="170"/><emph type="italics"/>scorrere fisico matematicamente<emph.end type="italics"/> (ivi, c. </s>

<s>194). Se poi in questi discorsi non <lb/>vide il vero con quella chiarezza che lo videro poi tutti quelli, a cui furono <lb/>aperti gli occhi dalla <emph type="italics"/>Cristallografia,<emph.end type="italics"/> non si pu&ograve; per&ograve; negar che il Rossetti <lb/>non fosse uno de'primi ad aprir le vie, per le quali, incamminandosi la <lb/>nuova scienza, avrebbe un secolo dopo fatti cos&igrave; grandi e cos&igrave; veloci pro&shy;<lb/>gressi. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Gli effetti del calore negli agghiacciamenti, come hanno dimostrato i <lb/>fatti precedentemente narrati, non furono intesi n&egrave; perci&ograve; bene spiegati da <lb/>coloro che vi studiarono attorno nel secolo XVII, n&egrave; si pu&ograve; dire che molto <lb/>di pi&ugrave; ne sapessero i fisici succeduti a loro infino a'tempi moderni, trat&shy;<lb/>tandosi di un problema a risolver completamente il quale converrebbe pe&shy;<lb/>netrare addentro a veder la pi&ugrave; intima composizione de'corpi. </s>

<s>Gli altri effetti <lb/>prodotti dal calore stesso nelle evaporazioni sembravano implicare minori <lb/>difficolt&agrave;, ma pure anche qui le difficolt&agrave; non mancarono e gravi, anzi come <lb/>suole spesso avvenire queste nascevano in gran parte dal presentarsi sotto <lb/>troppo facile aspetto il problema, alla soluzion del quale in mancanza di <lb/>ragioni soccorreva pronta la fantasia. </s></p><p type="main">

<s>Un chiaro esempio di ci&ograve; si trova nella Filosofia peripatetica, alle fan&shy;<lb/>tasie della quale un nostro insigne Italiano, a cui si dee l'avere apparec&shy;<lb/>chiate, bench&egrave; cos&igrave; dalla lontana le vie alla Fisica come scienza, sostituiva <lb/>tali ragioni che furon dopo varie vicende all'ultimo riconosciute, in gran parte <lb/>almeno, per vere. </s></p><p type="main">

<s>Una di queste dispute peripatetiche in soggetto di vapori s'aggirava in&shy;<lb/>torno al render la ragione del perch&egrave; nell'inverno si vede esalare una nu&shy;<lb/>vola di fumo dalla bocca e dalle narici degli animali. </s>

<s>Giovan Batista Bene&shy;<lb/>detti riconosciuto quanto stoltamente si disputasse, entr&ograve; in mezzo per il <lb/>primo a render cos&igrave; la ragion fisica del fatto. </s>

<s>&ldquo; Antiqui peripatetici de vi&shy;<lb/>dendo in hyeme animalium halitu, id quod in aestate non evenit, male di&shy;<lb/>sputaverunt quia hoc nascitur a condensatione halitus quae ab ambiente fri&shy;<lb/>gore fit, quia halitus is ab ore aut naso animalis exiens non est purus aer <lb/>attractus primo, sed mixtus est cum quodam vapore excrementitio et subtili, <lb/>quo semper ab ea parte evacuatur corpus, qui statim ab aere frigido cir&shy;<lb/>cumdatur et densatur, quam ob causam ab ipso ea luminis pars reflect&igrave;tur <lb/>quae eum penetrare non potest &rdquo; (Speculat. </s>

<s>Lib., Venetiis 1599, pag. </s>

<s>191). <lb/>E prosegue, applicando questi principii a render la ragione di un altro fatto <lb/>simile, ch'&egrave; del vedersi fumar l'acqua l'inverno appena attinta dal pozzo. </s></p><p type="main">

<s>Cos&igrave; avviatosi il nostro Autore a insegnare a'Peripatetici da quali vere <lb/>cause abbiano effetto le condensazioni de'vapori, passa a dir della rugiada <lb/>che si vede velar l'estate i tersi cristalli delle bocce piene d'acqua ghiac-<pb xlink:href="020/01/728.jpg" pagenum="171"/>ciata; rugiada che i peripatetici dicevano essere umor trasudato da'pori dello <lb/>stesso cristallo. </s>

<s>&ldquo; Neque etiam iidem noverunt causam unde fiat ut in ae&shy;<lb/>state, impleto vaso vitreo aut argenteo, aut ex materia non porosa constante <lb/>aqua frigida, vas sudet, quod tempore hyemis, nonnisi in calidis locis eve&shy;<lb/>nit, quem sudorem dicebant ipsi esse eamdem aquam, quae per poros vasis <lb/>exiret, quod falsissimum est, quia si per poros aqua frigida exiret, multo <lb/>magis exiret calida, cum subtilior sit et ad penetrandum aptior. </s>

<s>Sed hoc non <lb/>aliunde oritur quam a condensatione aeris vas circumdantis causata a fri&shy;<lb/>giditate vasis refrigerati ab aqua, quemadmodum tempore hyberno clare vi&shy;<lb/>demus mane superficies interioris vitri fenestrarum sudare, quia extrinse&shy;<lb/>cum frigus refrigerando vitrum intrinsecum aerem sibi contiguum congelat &rdquo; <lb/>(ibi, pag. </s>

<s>192). </s></p><p type="main">

<s>Ma nel lasciar che si fa dall'Autore, di discorrere sopra questo soggetto, <lb/>fra tutti gli errori scoperti e la sostituzione di altrettante verit&agrave; per la prima <lb/>volta annunziate, notabile in tal proposito &egrave; la seguente, che ha pi&ugrave; imme&shy;<lb/>diato riguardo all'evaporazione. </s>

<s>&ldquo; Nec proprie locutus est Aristoteles (sog&shy;<lb/>giunge il Benedetti) cum dixerit calorem solis eum esse qui sursum humo&shy;<lb/>res vaporesque evehat, quia sol nil aliud facit, quam calefacere, cuius caloris <lb/>ratione ea materia rarefit, et ob rarefationem levior facta ascendit, non quia <lb/>sursum a sole feratur &rdquo; (ibi, pag. </s>

<s>194). </s></p><p type="main">

<s>Cos&igrave; veniva il Benedetti molto per tempo a dimostrare la insufficienza <lb/>e anzi la falsit&agrave; delle dottrine aristoteliche, mentre Galileo parecchi anni <lb/>dopo tornava a ricacciar la fisica dell'evaporazioni nel buio di quegli anti&shy;<lb/>chi peripatetici errori. </s>

<s>&ldquo; Se noi volessimo ancora, si legge nella <emph type="italics"/>Risposta a <lb/>Lodovico delle Colombe<emph.end type="italics"/> strumenti pi&ugrave; sottili e operazione pi&ugrave; esquisita, direi <lb/>che guardassimo i raggi del sole osservando con quanta diligenza vanno se&shy;<lb/>parando le supreme e minime particelle dell'acqua, le quali dall'esalazione <lb/>ascendente vengono sublimate, ed essendo ridotte forse ne'primi corpicelli <lb/>componenti sono a noi invisibili a una a una e solo ci si manifestano mol&shy;<lb/>tissime insieme sotto specie di quello che noi chiamiamo vapore o nebbia o <lb/>nuvola o fumi o cose tali &rdquo; (Alb. </s>

<s>XII, 328) </s></p><p type="main">

<s>Cos&igrave;, insieme con Galileo, si seguit&ograve; da'Fisici e nostrali e stranieri a <lb/>fornicare coll'errore antico, e il Roberval, secondo riferisce l'Huyghens, dopo <lb/>la prima met&agrave; del secolo XVII, ripetendo le dottrine stesse e le espressioni <lb/>usate da Aristotile nel IX e X capitolo del I e II libro delle Meteore, am&shy;<lb/>metteva che il sole sollevasse vapori tutt'intorno al globo di Saturno, ec&shy;<lb/>cettuato che verso i poli &ldquo; ubi fortassis intensum frigus eos <emph type="italics"/>a sole attrahi<emph.end type="italics"/><lb/>prohibeat (Syst. </s>

<s>Saturnium, Op. </s>

<s>varie, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>561). L'Huy&shy;<lb/>ghens stesso argomentando dal variabile aspetto della fascia di Giove l'esi&shy;<lb/>stenza di vapori ora pi&ugrave; ora men condensati, e perci&ograve; la generazione sulla <lb/>superficie di quel pianeta, come sulla nostra Terra, di piogge e di venti <lb/>&ldquo; erunt ergo, si esprime, et imbres et venti quia <emph type="italics"/>attractum a sole<emph.end type="italics"/> humo&shy;<lb/>rem incidere in terram necesse est, et calore soluti vapores ventorum causa <lb/>sunt &rdquo; (Cosmot. </s>

<s>Lib. </s>

<s>I, Op. </s>

<s>v. </s>

<s>cit., pag. </s>

<s>681). </s></p><pb xlink:href="020/01/729.jpg" pagenum="172"/><p type="main">

<s>Ma per tornare al nostro Galileo, bench&egrave; avesse il Benedetti, nelle ra&shy;<lb/>refazioni operate dal calore, riconosciuta la ragione del separarsi dalla ri&shy;<lb/>manente mole liquida e del sollevarsi in alto i vapori; pur riducendosi noi <lb/>alla memoria le parole dianzi trascritte dalla Risposta a Lodovico delle Co&shy;<lb/>lombe, si trova essere dall'Autore invocate l'<emph type="italics"/>esalazioni ascendenti<emph.end type="italics"/> com'ef&shy;<lb/>ficacissima causa dell'evaporazioni. </s>

<s>Che cosa intendesse poi per quelle esa&shy;<lb/>lazioni ascendenti &egrave; dichiarato meglio da ci&ograve; che altrove si legge nella detta <lb/><emph type="italics"/>Risposta.<emph.end type="italics"/> &ldquo; E in cotal guisa (cio&egrave; congiunte le bollicelle dell'aria nell'acqua) <lb/>resterebbero lungo tempo, se l'esalazioni ignee e molto pi&ugrave; sottili dell'aria, <lb/>ascendendo continuamente non passassero pel velo di esse bolle e le dissol&shy;<lb/>vessero, sublimando e portando via parte dei corpicelli dell'acqua, perch&egrave; <lb/>mostrandoci la continua esperienza che l'acqua de'vasi scoperti e pi&ugrave; sen&shy;<lb/>sibilmente de'panni bagnati, se ne va ascendendo, non credo che per dire <lb/>conforme al vero si possa dir altro se non che ella viene portata via dai <lb/>detti corpuscoli caldi, come la polvere dal vento &rdquo; (Alb. </s>

<s>XII, 345). </s></p><p type="main">

<s>L'efficacia poi di queste esalazioni ignee in sollevar l'acqua e le bol&shy;<lb/>licelle di lei &egrave; resa pi&ugrave; manifesta secondo Galileo, ne'vasi larghi ed aperti <lb/>posti in sul fuoco a bollire. </s>

<s>&ldquo; Ma se poi voi piglierete vasi larghi ed aperti, <lb/>e scalderete l'acqua assai, allora la grandissima copia del fuoco, &igrave;l quale <lb/>dal fondo del vaso voi vedrete salire, s'aggregher&agrave; in globi molto grandi, li <lb/>quali con impeto maggiore ascenderanno e cagioneranno quell'effetto che <lb/>noi chiamiamo bollore, e nello scappare fuori solleveranno e porteranno seco <lb/>molti atomi d'acqua nel modo che aliti gagliardi sollevano la polvere e seco <lb/>ne portano le parti pi&ugrave; sottili &rdquo; (ivi, pag. </s>

<s>467). </s></p><p type="main">

<s>Sembrerebbe da una parte che queste di Galileo e del Castelli fossero <lb/>pi&ugrave; perfette ragioni di quelle date dal Benedetti, il quale attribuendo il fatto <lb/>alla semplice rarefazione non sodisfaceva a coloro, che non sapevano inten&shy;<lb/>dere come l'acqua pi&ugrave; grave in specie potesse cos&igrave; lievemente ascender per <lb/>l'aria. </s>

<s>Di questo diremo altrove, ma per ora ci contenterem di notare che <lb/>le dottrine professate da Galileo erano difettose da due lati: dal creder cio&egrave; <lb/>che le bollicelle d'aria fossero ignee esalazioni, e dall'attribuire ad esse bol&shy;<lb/>licelle la causa, mentre in verit&agrave; non son altro che l'effetto di ci&ograve; che &egrave; <lb/>causa vera dell'ebullizione. </s></p><p type="main">

<s>Questa vera causa non fu prima riconosciuta che il Boyle facesse quella <lb/>sua bellissima esperienza dell'acqua tiepida che bolle nel vuoto, esperienza <lb/>nella quale, prima che fossero fra noi divulgati i <emph type="italics"/>Nuovi esperimenti fisico&shy;<lb/>meccanici,<emph.end type="italics"/> s'erano incontrati i nostri Accademici fiorentini, quando osser&shy;<lb/>varono il bollir dell'acqua nello strumento torricelliano, di che nell'altro <lb/>paragrafo da noi fu narrato. </s>

<s>Al&igrave;ora si comprese che il bollimento de'liquidi <lb/>dipende men dal calore che dall'ammosfera sopraincombente alla superficie <lb/>del liquido, alla pression della quale anzi attempera i suoi gradi lo stesso <lb/>conceputo calore. </s>

<s>Sopra questo principio il Papin, che i fecondi concetti <lb/>boileiani incarnava in macchine esquisitissime, costru&igrave; quel suo <emph type="italics"/>Digestore,<emph.end type="italics"/><lb/>del quale il Newton nella Questione XI del III Libro dell'Ottica divulgava <pb xlink:href="020/01/730.jpg" pagenum="173"/>cos&igrave; la teoria: &ldquo; Etenim si aqua in vase aliquo pellucido tepescat, et aer <lb/>deinde e vase exhauriatur, aqua illa in vacuo ebulliet nihilo minus vehe&shy;<lb/>menter, quam si in vase igni imposito calorem multo maiorem in aperto aere <lb/>concepisset. </s>

<s>Nam atmosphaerae incumbentis pondus vapores deprimit impe&shy;<lb/>ditque quominus aqua ebulliat, donec calorem contraxerit multo maiorem, <lb/>quam quo ad eiusdem in vacuo ebullitionem excitandam opus sit &rdquo; (Pata&shy;<lb/>vii 1773, pag. </s>

<s>140). </s></p><p type="main">

<s>Il Papin col suo Digestore e con altre macchine ingegnosamente co&shy;<lb/>struite, nelle quali il vapore acqueo veniva applicato come forza motrice, <lb/>torn&ograve; a sollevare la fronte dall'oblio, quando gli eruditi si misero dietro a <lb/>ricercare i nomi e le opere di tutti coloro che, come stille d'acqua concorse <lb/>a una fonte, scaturirono dall'ingegno del Watt nel portentoso macchina&shy;<lb/>mento. </s>

<s>Scavate dagli stili acuti di quegli infaticabili eruditi esultaron le ossa <lb/>del Porta e di Giovanni Branca, con parecchi altri venuti fuori a progettar <lb/>macchine da sedurre i semplici con gli strani effetti promessi, e da accen&shy;<lb/>der contro s&igrave; sfacciate imposture l'ira degli intelligenti. </s>

<s>Chi volesse per sua <lb/>ricreazione aver di ci&ograve; qualche esempio, converrebbe che cercasse nella R. </s>

<s>Bi&shy;<lb/>blioteca Marucelliana di Firenze <emph type="italics"/>Le Machine, volume nuovo e di molto ar&shy;<lb/>tifizio, da fare effetti maravigliosi tanto spiritali che animali di Giovanni <lb/>Branca,<emph.end type="italics"/> libro stampato in Roma nel 1629, e leggesse quelle postille, che <lb/>condite di sale, misto a un po'di aceto e di pepe, scrisse in margine un <lb/>certo fiorentino. </s>

<s>Nell'ultima a c. </s>

<s>17 e che appella alla XVII fra le XXV <lb/><emph type="italics"/>figure di Machine fondate sugli effetti del vuoto,<emph.end type="italics"/> cos&igrave; scrive il postillatore: <lb/>&ldquo; Ti rispondo che &egrave; falso e peggio non si pu&ograve; dire: addio pazzo. </s>

<s>&rdquo; </s></p><p type="main">

<s>E in verit&agrave; non ha nulla il Branca che non si possa dire una pazzia, <lb/>da quella testa vuota in fuori, la quale sputando per un cannello il vapore <lb/>dalla bocca sopra le alette di una ruota orizzontale, la fa volgere in giro a <lb/>produr qualche debole effetto di moto. </s>

<s>Di bene altra importanza &egrave; per la <lb/>storia italiana delle Macchine a vapore quella, che vedesi disegnata in alcune <lb/>carte manoscritte ritrovate nella R. </s>

<s>Biblioteca nazionale di Firenze, secondo <lb/>l'invenzione di Alessandro Galilei architetto fiorentino, che nel 1716 l'aveva <lb/>messa in pratica a Londra per sollevar l'acqua, con gran vantaggio sopra <lb/>le trombe ordinarie. </s>

<s>Noi per sodisfare ai curiosi citeremo la descrizione del&shy;<lb/>l'ingegnoso macchinamento, come la lasci&ograve; distesa nelle dette carte il pro&shy;<lb/>prio inventore, ma convien prima soggiungere qualche altra notizia alla sto&shy;<lb/>ria dell'evaporazione, che c'&egrave; rimasta sopra interrotta. </s></p><p type="main">

<s>Era facile accorgersi, per le quotidiane esperienze, che il vento concorre <lb/>a far evaporar l'acqua pi&ugrave; sollecitamente talvolta di quel che non faccia lo <lb/>stesso calore, come vedesi per esempio l'inverno venir pi&ugrave; presto rasciugate <lb/>le strade dal vento di tramontana che non da'raggi del sole. </s>

<s>Galileo rasso&shy;<lb/>migliava l'effetto al rapir che lo stesso vento fa la polvere delle strade, sol&shy;<lb/>levandola in aria come le vescicole del vapore. </s>

<s>&ldquo; Siccome (leggesi nella so&shy;<lb/>pracitata Risposta a Lodovico delle Colombe) in un monte di sottilissima <lb/>polvere si vede un leggero venticello andarne superficialmente levando molte <pb xlink:href="020/01/731.jpg" pagenum="174"/>particelle, lasciando l'altre immote; cos&igrave; creder&ograve; io che i medesimi venti <lb/>vadano portando via con li loro sottilissimi aliti le supreme particelle del&shy;<lb/>l'acqua da un panno o da una pietra bagnata o dall'acqua contenuta in un <lb/>vaso, non movendo altre parti che le sole che si separano da quelle che re&shy;<lb/>stano &rdquo; (Alb. </s>

<s>XII, 327, 28). </s></p><p type="main">

<s>Cos&igrave; presso a poco la pensava anco il Borelli, il quale, come fu de'primi <lb/>a riconoscer l'aria ospitante in mezzo all'acqua, fu cos&igrave; de'primi a trovar <lb/>la ragione meccan&igrave;ca dell'insinuarsi fra le liquide, le particelle aerose cac&shy;<lb/>ciate ivi dentro e quasi confittevi dal vento. </s>

<s>&ldquo; Et summopere advertendum <lb/>quod minor copia aeris reperitur intra aquam glaciatam in vase clauso, quam <lb/>includatur in aqua stagni, quae aeri contigua est, dum gelat. </s>

<s>In illa enim <lb/>paucissimae bullae aeraee reperiuntur, in hac copiosissimae et grandiores. </s>

<s><lb/>Ratio huius discriminis est quia aer sicut facile abradit aqueas particulas ab <lb/>eius superficie, sic aeraee spirulae insinuantur intra aquam. </s>

<s>Hoc suadetur <lb/>quia videmus linteum madidum in loco umbroso expansum etiam hyeme <lb/>exiccari, et spirante vento citissime arefieri. </s>

<s>Hoc certe contingit quia aeris <lb/>particulae a vento agitatae abradunt aquea granula et eadem violentia pluri&shy;<lb/>mae aeris particulae insinuari debent intra aquam, a qua vinciuntur, ut inde <lb/>effugere non possint &rdquo; (De motu anim., Pars. </s>

<s>II, Romae 1681, pag. </s>

<s>218). </s></p><p type="main">

<s>Le spire aeree secondo immaginava il Borelli rimangon prese al visco <lb/>dell'acqua, al qual visco giusto il Del Papa attribuiva una grande efficacia <lb/>negli effetti dell'evaporazione sollecitata dal vento. </s>

<s>&ldquo; Perocch&egrave; sebbene anco <lb/>il vento sferzando e radendo la superficie dell'acqua &egrave; potente egli stesso <lb/>a sospingere in alto l'acqua medesima, egli &egrave; per&ograve; ragionevole che in que&shy;<lb/>sto effetto ancora gran parte abbia l'acquea viscosit&agrave;, cio&egrave; a dire quelle te&shy;<lb/>nui membrane nell'acqua istessa disseminate, nelle quali il vento urtando <lb/>e intrigandosi possa in tal modo con agevol rapina seco portare l'acquee <lb/>sostanze &rdquo; (Della natura dell'umido e del secco, Firenze 1681, pag. </s>

<s>133). </s></p><p type="main">

<s>Cos&igrave; fatte dottrine hanno per verit&agrave; troppo del meccanico e del mate&shy;<lb/>riale, e non si tien conto alcuno del grado di saturit&agrave; dell'aria soprastante <lb/>al liquido, la quale rinnovata via via &egrave; principalissima causa dell'efficacia <lb/>del vento nelle evaporazioni. </s>

<s>Il Montanari &egrave; forse l'unico che prima dello <lb/>stesso Borelli scrivesse intorno a ci&ograve; cose, che hanno pi&ugrave; sembianza di vere. <lb/></s>

<s>&ldquo; Si vede che il vento, egli dice, ha cos&igrave; gran parte nell'essiccare le cose <lb/>bagnate .... posciach&egrave; quelle particole dell'umido, a causa della pressione <lb/>dell'aria, come gi&agrave; dissi, si sollevano fra le particole dell'aria medesima lor <lb/>vicina, portate via d'un subito dal vento danno luogo ad altre di sollevarsi, <lb/>e di cos&igrave; successivamente svaporare &rdquo; (Lett. </s>

<s>al Sampieri, Bologna 1667, <lb/>pag. </s>

<s>83). </s></p><p type="main">

<s>E dalle teorie fisiche ch'ebbero cos&igrave; nel Montanari quella maggior per&shy;<lb/>fezione desiderabile a que'tempi, passando alle applicazioni meccaniche da <lb/>noi sopra promesse, ecco la descrizione della macchina di Alessandro Ga&shy;<lb/>lilei, nella quale il vapore per elasticit&agrave; preme e per condensazione aspira <lb/>l'acqua, operando con facilit&agrave; quel che operano gli stantuffi mossi su e giu <pb xlink:href="020/01/732.jpg" pagenum="175"/>per i corpi delle trombe ordinarie, con gran pena e fatica. </s>

<s>&ldquo; Infondasi nel <lb/>vaso A (fig. </s>

<s>53) l'acqua per il foro B fino a tre quarti della sua altezza, e <lb/>facendo fuoco sotto il vaso la medesima bollendo si raref&agrave; in vapori, i quali <lb/>quando si gira il regolatore C verso D se ne passano per la canna E den&shy;<lb/>tro il recipiente F, e chiudono una valvola che &egrave; dentro la canna in G, e <lb/>forzano l'aria a sortire per una valvola che &egrave; in H fuori della canna I. </s>

<s><lb/>Quando il recipiente F &egrave; del tutto pieno di vapori, allora si torna a rigi&shy;<lb/>rare il regolatore C verso E ed i medesimi vapori se ne passano per la <lb/><figure id="id.020.01.732.1.jpg" xlink:href="020/01/732/1.jpg"/></s></p><p type="caption">

<s>Figura 53.<lb/>canna D dentro il recipiente K, il quale &egrave; simile ed uguale all'altro F, e <lb/>costruito nell'istesso modo, e con l'istesse valvole dentro la canna in G <lb/>ed H. </s>

<s>Subito che i vapori sono fermi in F, mentre che se ne passano per D <lb/>ad empire il recipiente K, si deve girar la chiave L e lasciare cadere un <lb/>poco d'acqua fredda dentro il recipiente F, la quale subito condensa que'va&shy;<lb/>pori, di maniera che il suddetto recipiente rimane del tutto esausto onde <lb/>l'ammosfera, premendo sopra l'acqua M la forza ad ascendere per la canna <lb/>G ed a riempire il recipiente F. </s>

<s>Allora fermando i vapori in D, essendo che <pb xlink:href="020/01/733.jpg" pagenum="176"/>il recipiente K sar&agrave; gi&agrave; pieno, si lasceranno di nuovo entrare in F, i quali <lb/>immediatamente forzeranno tutta l'acqua ad uscire per la canna I, come <lb/>fece prima l'aria, e di nuovo il recipiente F sar&agrave; ripieno di vapori, e gi&shy;<lb/>rando la chiave N, si condenseranno i vapori che sono in K e l'acqua M <lb/>ascender&agrave; per la canna G, come fece nell'altro recipiente, onde fermati i <lb/>vapori in E si lasceranno entrare dentro il recipiente K e similmente l'acqua <lb/>se ne sortir&agrave; fuori dalla canna I, ed il recipiente rimarr&agrave; pieno di vapori, e <lb/>cos&igrave; successivamente tornando a condensare e lasciare entrare i vapori den&shy;<lb/>tro i recipienti, si potr&agrave; continuare ad alzar l'acqua a piacere. </s>

<s>Il presente <lb/>modello alza in circa cinquanta barili d'acqua in un'ora. </s>

<s>Londra 20 Feb&shy;<lb/>braio 17 15/16. Alessandro Galilei archit. </s>

<s>fiorentino. (Lavori per servire alla <lb/>vita di Galileo raccolti dal Viviani e dal Nelli, Filza IX, c. </s>

<s>311). </s></p><pb xlink:href="020/01/734.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO V.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Del suono<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della diffusione del suono per l'aria. </s>

<s>&mdash; II. </s>

<s>Delle varie esperienze ordinate a dimostrar la diffu&shy;<lb/>sione, e a misurar la velocit&agrave; del suono per l'aria. </s>

<s>&mdash; III. </s>

<s>Delle prime fisiche ragioni date delle <lb/>consonanze. </s>

<s>&mdash; IV. </s>

<s>Di ci&ograve; che intorno al risonar delle corde fu dimostrato da Galileo. </s>

<s>&mdash; V. </s>

<s>Di <lb/>un Trattato fisico matematico, che preparava Niccol&ograve; Aggiunti sui tremori armonici nelle corde. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Alla luce e al calore aggiunsero i Pitagorici l'armonia a intreare quei <lb/>vivifici influssi, che piovon su noi dall'alto delle sfere celesti. </s>

<s>Ma perch&egrave; <lb/>quell'armonia, insensibile all'ottusit&agrave; del nostro udito, non si faceva consi&shy;<lb/>stere in altro che in un bell'ordine di numeri, si vede qui pure verificarsi <lb/>la legge storica altre volte da noi avvertita, ed &egrave; che la matematica preced&egrave; <lb/>la fisica anche nel filosofare intorno alla natura e alla propriet&agrave; de'suoni. </s>

<s><lb/>Le dottrine pitagoriche per&ograve; e le platoniche son come fior di bellezza, che <lb/>aprendo leggero all'aria il suo seno, col progredir del tempo allegando in <lb/>frutto, convien che anch'egli si pieghi a terra trattovi dal proprio peso. </s>

<s>Quel <lb/>tornar cos&igrave; a soggiacere alle passioni comuni a tutti gli altri corpi, signifi&shy;<lb/>cava, traducendo il simbolo a senso proprio, il passar dalle matematiche con&shy;<lb/>templazioni alle fisiche realt&agrave;, che facevano le antiche dottrine; passaggio che <lb/>avvenne per opera della Filosofia stoica succeduta, propriamente come frutto <lb/>maturato, al fiore della Filosofia pitagorica. </s></p><p type="main">

<s>Agli Stoici si deve l'avere avvertita quella somiglianza che passa fra <lb/>gl'increspamenti dell'aria alle vibrazioni del corpo risonante, e i cerchi che <lb/>si diffondono intorno a un sasso gittato sulla superficie di un'acqua tran-<pb xlink:href="020/01/735.jpg" pagenum="178"/>quilla; somiglianza che si ripete anche oggid&igrave; nelle scuole propagatasi di <lb/>bocca in bocca, quasi come i cerchi stessi di quell'acqua, i quali avendo il <lb/>loro centro nella Stoa si son tanto diffusi al largo, da giungere in fin presso <lb/>a toccare la nostra riva. </s>

<s>&ldquo; Dicono questi (cos&igrave; nel bel linguaggio del loro <lb/>Segretario commemorano le dottrine degli Stoici i nostri Accademici fioren&shy;<lb/>tini) che, siccome veggiamo l'acqua stagnante incresparsi in giro per una <lb/>pietruzza che in lei si getti, e tali increspamenti andarsi via via propagando <lb/>in cerchi successivamente maggiori, tanto ch'e'giungano stracchi alla riva <lb/>e vi muoiono, e che percotendola con impeto, da essa per all'in l&agrave; si ri&shy;<lb/>flettono; cos&igrave; per appunto asseriscono la sottilissima aria dintorno al corpo <lb/>sonoro andarsi minutamente increspando per immenso tratto, onde incon&shy;<lb/>trandosi con tali ondeggiamenti nell'organo del nostro udito, e quello tro&shy;<lb/>vando molle e arrendevole, gl'imprime un certo tremore che noi suono ap&shy;<lb/>pelliamo &rdquo; (Saggi di natur. </s>

<s>esper., Firenze 1841, pag. </s>

<s>156). </s></p><p type="main">

<s>Il modo di rappresentar cos&igrave; all'occhio nell'acqua ci&ograve; che &egrave; affatto <lb/>invisibile nell'aria, e la semplice facilit&agrave; e naturalezza della dimostrazione <lb/>sedussero tanto gl'ingegni, che fu creduto di aver fatto un gran progresso <lb/>nell'Ottica, quando introdotte le ondulazioni eteree si poteron ridurre a <lb/>quella stessa facilit&agrave; e naturalezza i modi dell'operar sull'occhio la luce. </s>

<s>Che <lb/>fosse veramente quella una seduzione lo prova l'esser rimasti tuttavia mi&shy;<lb/>steriosi molti fatti ottici ritrosi a secondare i moti ondulatori dell'etere, ma <lb/>ben pi&ugrave; seduttrice fu quella facilit&agrave; in coloro, che, nel primo risorgere della <lb/>scienza sperimentale, dall'esempio stoico de'circoli nell'acqua passarono a <lb/>filosofare intorno al modo del diffondersi il suono nell'aria, attribuendo a <lb/>questa le qualit&agrave; proprie a solo il liquido elemento. </s></p><p type="main">

<s>Galileo, che tanta parte ebbe al risorgimento di quella scienza speri&shy;<lb/>mentale, com'aveva accolti i placiti dell'antica Filosofia stoica rispetto al ca&shy;<lb/>lore e alle altre qualit&agrave; secondarie de'corpi, cos&igrave; ripet&egrave; le stesse stoiche <lb/>dottrine relative ai suoni. </s>

<s>&ldquo; Resta poi (scrive nel <emph type="italics"/>Saggiatore<emph.end type="italics"/>) l'elemento <lb/>dell'aria per li suoni, i quali indifferentemente vengono a noi dalle parti <lb/>basse e dall'alte e dalle laterali, essendo noi costituiti nell'aria, il cui mo&shy;<lb/>vimento in s&egrave; stessa, cio&egrave; nella propria regione, &egrave; ugualmente disposto per <lb/>tutti i versi, e la situazion dell'orecchio &egrave; accomodata, il pi&ugrave; che sia pos&shy;<lb/>sibile, a tutte le positure di luogo, ed i suoni allora son fatti e sentiti da <lb/>noi, quando (senz'altre qualit&agrave; sonore e transonore) un frequente tremor <lb/>dell'aria, in minutissime onde increspata, muove una certa cartilagine di <lb/>certo timpano che &egrave; nel nostro orecchio. </s>

<s>Le maniere poi esterne potenti a <lb/>far questo increspamento nell'aria sono moltissime, le quali forse si ridu&shy;<lb/>cono in gran parte al tremore di qualche corpo, che urtando nell'aria l'in&shy;<lb/>crespa, e per essa con gran velocit&agrave; si distendono l'onde dalla frequenza <lb/>delle quali nasce l'acutezza del suono e la gravit&agrave; dalla rarit&agrave; &rdquo; (Alb. </s>

<s>IV, 336). </s></p><p type="main">

<s>Bench&egrave; a ritrar pi&ugrave; perfettamente le dottrine stoiche manchi in queste <lb/>parole di Galileo la similitudine espressa degli ondeggiamenti dell'acqua, &egrave; <lb/>certo nulladimeno, da quel che altrove e segnatamente nel I Dialogo delle <pb xlink:href="020/01/736.jpg" pagenum="179"/>Due Nuove Scienze scrive del suono, e meglio dalle teorie acustiche da lui <lb/>stesso professate, che riguard&ograve; le onde sonore diffondersi meccanicamente a <lb/>quel modo che si diffondono gl'increspamenti sulla superficie di un'acqua <lb/>tranquilla intorno al centro della percossa. </s>

<s>La somiglianza per&ograve; (e da que&shy;<lb/>sto principalmente nacque l'inganno di Galileo e de'suoi discendenti) non <lb/>&egrave; che apparente, perch&egrave; mentre nell'acqua l'impulso al moto consiste nel <lb/>peso, nell'aria invece consiste tutto nell'elaterio. </s></p><p type="main">

<s>Il Frisi, ch'&egrave; pure il pi&ugrave; assennato fra quanti scrissero l'Elogio di Ga&shy;<lb/>lileo, fu primo a notare che nel I Dialogo delle Nuove Scienze l'Autore, <lb/>come non aveva ben conosciuto n&egrave; la pressione n&egrave; il peso dell'aria, <emph type="italics"/>cos&igrave; <lb/>non parve che si fosse formata una giusta idea neppure dell'elasticit&agrave;.<emph.end type="italics"/><lb/>(Elog. </s>

<s>del Gal., Livorno 1775, pag. </s>

<s>76). Non par credibile che cos&igrave; fatti giu&shy;<lb/>dizi sieno usciti dalla penna di chi, citando quel I Dialogo galileiano, doveva <lb/>aver letta l'esperienza del fiasco di vetro, dentro al quale condensata l'aria <lb/>con uno schizzatoio, diceva il Salviati di aver trovato lo stesso fiasco sulla <lb/>bilancia esser notabilmente cresciuto di peso (Alb. </s>

<s>XIII, 81). Quanto &egrave; falso <lb/>per&ograve; quel che asserisce il Frisi rispetto alla pressione e al peso dell'aria, <lb/>altrettanto &egrave; giusto per quel che riguarda l'elasticit&agrave;, la quale non par che <lb/>fosse veramente conosciuta, e in ogni modo &egrave; certo che non fu applicata, <lb/>n&egrave; da Galileo n&egrave; da'Discepoli di lui pi&ugrave; prossimi, al moto e alla diffusione <lb/>ondosa del suono. </s></p><p type="main">

<s>Il Porta, nel suo libro I degli Spiritali, descrive fra le altre esperienze <lb/>pneumatiche quella dell'archibugio di ferro, dentro il quale &ldquo; se alcuno <lb/>metter&agrave; la verga nel suo cavo di mezzo, la cui punta sia bagnata d'olio .... <lb/>e col suo dito si otturi lo spiraglio per dove si d&agrave; foco che non fugga l'aria, <lb/>di l&agrave; vedremo per esperienza che con molta forza ci ficcaremo la verga den&shy;<lb/>tro, perch&egrave; l'aria si viene a condensare e a restringere in s&egrave; medesima, e <lb/>quando per forza non vi potr&agrave; pi&ugrave; entrar dentro lascieremo libera la verga, <lb/>allora verr&agrave; fuori con grande strepito e violenza e balzer&agrave; di molto di lon&shy;<lb/>tano &rdquo; (Napoli 1606, pag. </s>

<s>17). Il Castelli poi, nel corollario XI al I Trat&shy;<lb/>tato della <emph type="italics"/>Misura <gap/>elle acque correnti,<emph.end type="italics"/> dop'aver detto che l'acqua non si <lb/>comprime n&egrave; ha molla da ritornare come la bambagia o la lana o come <lb/>l'aria, cita l'<emph type="italics"/>Archibugio a vento inventato a'nostri tempi da M. </s>

<s>Vincenzo <lb/>Vincenti urbinate<emph.end type="italics"/> (Bologna 1660, pag. </s>

<s>19) che &egrave; l'applicazione immediata <lb/>dell'esperienza descritta dal Porta. </s></p><p type="main">

<s>Nonostante tutto questo, quando il Pecquet pubblic&ograve; insiem con le sue <lb/>l'esperienze fatte dall'Auzout e dal Robervall nel vuoto torricelliano, si com&shy;<lb/>piacque di aver egli e i suoi illustri colleghi dimostrato per i primi riseder <lb/>nell'aria un'innata e spontanea tendenza d'espander la sua mole, diminuita <lb/>la pressione esterna; tendenza e sforzo da essi chiamato <emph type="italics"/>forza elastica.<emph.end type="italics"/> Re&shy;<lb/>clam&ograve; contro i vanti del Pecquet il nostro Tommaso Cornelio rivendicando <lb/>a s&egrave; l'anteriorit&agrave; di quella scoperta, n&egrave; concedendo altro merito ai fisici pa&shy;<lb/>rigini da quello in fuori di aver trovato il nome da significare quella innata <lb/>propriet&agrave; dell'aria. </s>

<s>&ldquo; Memini me olim (scriveva lo stesso Cornelio nel 1682) <pb xlink:href="020/01/737.jpg" pagenum="180"/>ante annos ferme quatuor supra triginta in hanc considerationem incidisse, <lb/>eiusque rude aliquod specimen exhibuisse in Epistola <emph type="italics"/>De platonica circum&shy;<lb/>pulsione,<emph.end type="italics"/> quam sub idem tempus nimium festinanter scripseram. </s>

<s>Sed ecce <lb/>post exactos ab edita Dissertatione nostra tres annos prodit Libellus Johan&shy;<lb/>nis Pecqueti, ex quo palam factum est ingeniosissimum Robervallium ad <lb/>exquirendam hanc spontaneam aeris distractionem dilatationemque sedulo <lb/>incubuisse, eamque pluribus argumentis ab experientia deductis evidentis&shy;<lb/>sime demonstrasse. </s>

<s>Tum vero primum, ni fallor, in usu fuere verba illa <lb/><emph type="italics"/>elater<emph.end type="italics"/> seu <emph type="italics"/>vis elastica,<emph.end type="italics"/> quae respondere iis videntur, quibus usus est Lu&shy;<lb/>cretius, qui saepe memoravit a circumfuso aere res agitari et verberari &rdquo; <lb/>(Progymnasm. </s>

<s>post., Neapoli 1688, pag. </s>

<s>11). </s></p><p type="main">

<s>Comunque sia &egrave; un fatto che, poco dopo la met&agrave; del secolo XVII, si <lb/>riteneva che l'elaterio fosse una propriet&agrave; recentemente scoperta o dimo&shy;<lb/>strata nell'aria. </s>

<s>Lo Schott, per esempio, pubblicando nel 1664 la sua <emph type="italics"/>Tecnica <lb/>curiosa,<emph.end type="italics"/> discute nel cap. </s>

<s>X del lib. </s>

<s>IV la questione di questa elasticit&agrave; come <lb/>controversa, e incomincia: &ldquo; Recentiores pneumaticorum experimentorum <lb/>scriptores aeri non tantum pondus sed elaterem quoque, seu vim ac pote&shy;<lb/>statem elasticam attribuunt, hoc est innatum ac spontaneum nisum ad sese <lb/>rarefaciendum ac dilatandum, quo prementibus circum se corporibus resistat, <lb/>et ubi liber ab eorum pressione est spontanea dilatatione sese ad statum sibi <lb/>naturaliter debitum reducat &rdquo; (Norimbergae, pag. </s>

<s>292). E proseguendo ivi <lb/>nel &sect; I a esporre in che modo que'recenti Pneumatici dimostrassero la pro&shy;<lb/>priet&agrave; innata che ha l'aria di restituirsi al suo primo volume, cita gli Espe&shy;<lb/>rimenti nuovi del Boyle, che ricorre agli esempi della spugna &ldquo; quae com&shy;<lb/>pressa constringitur et a pressione libera sponte se se iterum dilatat, et ad <lb/>pristinam suam molem reducit &rdquo; (ibi, pag. </s>

<s>293) come gi&agrave; il Castelli era pa&shy;<lb/>recchi anni prima ricorso all'esempio della lana e della bambagia. </s></p><p type="main">

<s>Rimeditando sopra questi fatti occorre a distinguere fra l'elasticit&agrave; del&shy;<lb/>l'aria dimostrata dalla pressione di pesi esterni e dalla pressione in s&egrave; stessa. </s>

<s><lb/>Quanto al primo caso non ci &egrave; dubbio che l'esperienza del Porta e l'appli&shy;<lb/>cazione che ne fece il Vincenti al Fucile pneumatico, non che l'esperienza <lb/>di Galileo sulla compressione dell'aria, non dimostrassero sufficientemente <lb/>l'elaterio di lei. </s>

<s>Quanto al secondo caso occorreva sperimentare nel vuoto <lb/>torricelliano, come fece il Robervall, o come il Boyle sotto la campana della <lb/>Macchina pneumatica. </s>

<s>Cos&igrave; a parer nostro si spiega come potessero appresso <lb/>gli stranieri apparir nuove le cose che avevano i Nostri molto prima spe&shy;<lb/>rimentate. </s></p><p type="main">

<s>Ne avremo di ci&ograve; una conferma confrontando insieme l'illustrazione data <lb/>da Galileo (Alb. </s>

<s>VI, pag. </s>

<s>10, 11) e dallo Schott (Mechanica hydraulico-pneu&shy;<lb/>matica, Herbipoli 1657, pag. </s>

<s>50-52) intorno al modo di operare della <emph type="italics"/>Lu&shy;<lb/>cerna eroniana.<emph.end type="italics"/> Il Fisico tedesco avvertendo che il tubo, il quale attraversa <lb/>il diaframma e scende nella cavit&agrave; inferiore che fa da piede alla Lucerna, <lb/>deve essere munito di chiavetta, determina la lunghezza di esso tubo rispetto <lb/>alla lunghezza dell'altro tubo, che dalla coppa sale a portar l'olio su al boc-<pb xlink:href="020/01/738.jpg" pagenum="181"/>ciolo del lucignolo, quasi che il volume dell'aria dovess'essere uguale al vo&shy;<lb/>lume dell'aria espulsa, e l'aria stessa non operasse che per solo effetto di <lb/>impenetrabilit&agrave;, e nulla per forza elastica. </s>

<s>Galileo invece contentandosi di <lb/>ammetter, qualunque sia la lunghezza del tubo, una comunicazione fra il <lb/>recipiente superiore e l'inferiore della Lucerna, mostra al contrario dello <lb/>Schott di credere che l'aria nella coppa dell'olio prema per forza elastica <lb/>sull'olio stesso, da farlo risalir per tale impulsione infino al bocciolo del lu&shy;<lb/>cignolo a farlo ardere in fiamma. </s></p><p type="main">

<s>Se per&ograve; dall'esperienza descritta negli Spiritali dal Porta, Galileo allora <lb/>giovane fu persuaso dell'elasticit&agrave; dell'aria, e l'applic&ograve; a spiegare ad Alvise <lb/>Mocenigo che n'era curioso il modo della Lucerna eroniana, non seppe ap&shy;<lb/>plicarla, ci&ograve; che sarebbe stato assai pi&ugrave; importante, alle onde sonore, le quali <lb/>non si diffondono per pressione idrostatica come quelle dell'acqua, ma per <lb/>condensazione e per rarefazione. </s>

<s>Da questo ostacolo rimase chiusa per lungo <lb/>tempo la via da conoscere la verit&agrave;, come vedesi confermato dall'esame delle <lb/>dottrine acustiche professate da tutti i Fisici infino al Newton, i quali ben&shy;<lb/>ch&egrave; fossero oramai fatti certi per tante ripetute prove dell'elasticit&agrave; dell'aria, <lb/>pur sedotti dalle dottrine stoiche non seppero, come Galileo non seppe, ap&shy;<lb/>plicarla alla generazione del suono. </s></p><p type="main">

<s>Dall'ammettere la diffusione delle onde aeree farsi a quel modo stesso <lb/>delle acquee veniva per prima conseguenza che non si potessero i suoni pro&shy;<lb/>dur che dall'urto e dalla collisione de'corpi, in modo che ne venisse l'aria <lb/>percossa e flagellata. </s>

<s>Di qui &egrave; che il Grimaldi, per citar uno de'pi&ugrave; autore&shy;<lb/>voli esempi, asseriva esser da tutti i fatti universalmente provato <emph type="italics"/>omnia so&shy;<lb/>nora debere tremere et observamus ipsam percussionem vel collisionem <lb/>corporum ad sonum necessariam.<emph.end type="italics"/> (De Lum., Bononiae 1665, pag. </s>

<s>374). </s></p><p type="main">

<s>Un altro esempio di Fisico non meno autorevole lo abbiamo nel Mon&shy;<lb/>tanari, il quale nel suo Dialogo intitolato <emph type="italics"/>Le forze d'Eolo,<emph.end type="italics"/> volendo dare ad <lb/>intendere in che modo si faccia il chiocco della frusta, dop'aver sottilmente <lb/>dimostrato, per l'applicazione delle leggi meccaniche, che tutto dipende dalla <lb/>velocit&agrave; con che il cordone ficca nell'aria la punta, e dalla sollecitudine con <lb/>che dal braccio la punta stessa &egrave; ritirata, conclude la ragion dell'effetto col <lb/>dire che si fa il chiocco perch&egrave; la punta della frusta &ldquo; percote l'aria con <lb/>strepito, e si va stracciando nell'istessa pi&ugrave; debole estremit&agrave; &rdquo; (Parma 1694, <lb/>pag. </s>

<s>151). Or &egrave; chiaro che il chiocco si produce dal violento irrompere del&shy;<lb/>l'aria circostante dentro il vuoto lasciato nel repentino ritirar della punta <lb/>della frusta; chiocco simile a quello che si ode stappando, per esempio, la <lb/>bocca a una bottiglia. </s>

<s>Qui e in tanti altri esempii che ci porgono gli stru&shy;<lb/>menti a fiato non ci &egrave; collisione di corpi, n&egrave; l'aria &egrave; flagellata o percossa, <lb/>ma entrando a riempire il vuoto per elasticit&agrave;, per elasticit&agrave; si commuove <lb/>in s&egrave; stessa e suona. </s></p><p type="main">

<s>A questo punto non possiamo non trattenerci a considerare che, men&shy;<lb/>tre da tali insigni Autori s'ignoravano le ragioni di simili fatti acustici, il <lb/>Benedetti, morto quasi un secolo avanti, avesse intravedute, e, condensate <pb xlink:href="020/01/739.jpg" pagenum="182"/>in poche parole, avesse annunziate le verit&agrave; di quelle dottrine, alle quali il <lb/>Newton un secolo dopo dette la pi&ugrave; solenne e splendida esplicazione. </s>

<s>L'Au&shy;<lb/>tor del libro delle <emph type="italics"/>Speculazioni,<emph.end type="italics"/> dietro esperienze simili a quelle ora da noi <lb/>citate, concluse come cosa nuova e da nessun altro prima avvertita, che il <lb/>suono &egrave; generato dall'aria mossa velocemente a riempire il vuoto. </s>

<s>E bench&egrave; <lb/>riconosca ne'casi pi&ugrave; ordinarii la necessit&agrave; di avere un corpo che tremi, <lb/>que'tremori nonostante mettono secondo il Benedetti l'aria in moto, per&shy;<lb/>ch'ella velocemente sottentra a riempir il vacuo lasciato dietro a s&egrave; via via <lb/>dal vibrare del corpo sonoro. </s></p><p type="main">

<s>&ldquo; Posse sonum corpus aliquod quod sensu sit destitutum, ut Aristoti&shy;<lb/>les IX cap. </s>

<s>lib. </s>

<s>I <emph type="italics"/>De coelo<emph.end type="italics"/> putavit, ostendere est falsum. </s>

<s>Corpus enim non <lb/>nisi a corpore potest laedi, non ergo a sono, cum sonus corpus non sit. </s>

<s>Sed <lb/>aer et ignis cum e contra sint corpora hoc facile praestare possunt implendo <lb/>aliquem locum velociter ad excludendum vacuum, unde generatur sonus, <lb/>quod hucusque a nemine animadversum fuisse comperio &rdquo; (Venetiis 1599, <lb/>pag. </s>

<s>289). E altrove: &ldquo; Necessarium quoque est ut tremat sive trepidet cor&shy;<lb/>pus quod sonum edere debet. </s>

<s>Neque etiam absque aere sonus effici potest <lb/>quia aer sonat ingrediendo velociter ad implendum locum ut non remaneat <lb/>vacuus &rdquo; (ibi, pag. </s>

<s>190). </s></p><p type="main">

<s>Cos&igrave; fatte dottrine per&ograve; non furono comprese per essere ancora troppo <lb/>precoci, e seguitando a insistere i Fisici sull'esempio delle onde nell'acqua, <lb/>un'altra delle perniciose conseguenze derivatene si fu quella di non aver <lb/>riconosciuto che, per effetto dell'elasticit&agrave;, dovevano diffondersi le onde in&shy;<lb/>torno al corpo risonante regolarmente in sfera. </s>

<s>L'aver notato che i suoni <lb/>ci vengono indifferentemente da tutte le parti, essendo noi costituiti nell'aria <lb/>il cui movimento in s&egrave; stessa &egrave; ugualmente disposto per tutti i versi, e <lb/>l'aver considerato che la situazion dell'orecchio &egrave; accomodata il pi&ugrave; che sia <lb/>possibile a tutte le positure del luogo, non furono sufficiente avviso di quella <lb/>sferica diffusione de'suoni a Galileo. </s>

<s>Se n'ebbe poi qualche sentore dagli <lb/>Accademici del Cimento, ma l'esperienza proposta dal Rinaldini ed eseguita <lb/>il d&igrave; 30 Agosto 1662 (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>564) lasci&ograve; i <lb/>desiderosi d'intendere il vero in quella loro prima incertezza. </s></p><p type="main">

<s>E fu appunto questa stessa incertezza che port&ograve; a dubitar della legge <lb/>secondo la quale diminuisce l'intensit&agrave; del suono col crescere delle distanze. </s>

<s><lb/>Vedemmo che la dimostrazione certa di ci&ograve;, rispetto alla luce, non s'ebbe <lb/>prima che si pensasse all'ipotesi delle onde eteree o della diffusione sferica <lb/>di essa luce, ond'&egrave; chiaro che, se tale ipotesi fosse stata ammessa anche per <lb/>la diffusione del suono, non restava nulla a dubitare che, siccome le super&shy;<lb/>ficie delle sfere concentriche crescono a proporzione de'quadrati de'raggi, <lb/>cos&igrave; con la medesima proporzione avrebbe pur dovuto diminuire l'attivit&agrave; <lb/>dell'onda sonora. </s>

<s>Eppure noi leggiamo negli Autori di Acustica di que'tempi <lb/>esser detto del suono &ldquo; che egli procede con Iddio sa qual misura di pro&shy;<lb/>porzione fra il distendersi nello spazio e il diminuirsi nel grado &rdquo; (Bartoli, <lb/>Del suono, Roma 1679, pag. </s>

<s>44). </s></p><pb xlink:href="020/01/740.jpg" pagenum="183"/><p type="main">

<s>Dal non aver riconosciuta la diffusione sferica delle onde sonore dipen&shy;<lb/>deva inoltre la difficolt&agrave; d'intendere come mai, per esempio, una voce si <lb/>ascolti anco dopo un muro o s'oda anche dietro un monte lo squillo delle <lb/>campane, per cui furono indotti i Fisici a credere e a dire che il suono, a <lb/>differenza della luce, proceda indifferentemente cos&igrave; per linee rette come per <lb/>linee flessuose. </s>

<s>&ldquo; Il suono, scriveva il Cavalieri, non soggiace cos&igrave; a queste <lb/>leggi come il lume, propagandosi quello anco per linee flessuose, cagionan&shy;<lb/>dosi egli dalla pulsazione nell'organo dell'udito fatta dall'aria tremante di <lb/>pi&ugrave; o men veloci tremori, che fanno l'alto e il basso, il grave e l'acuto nel <lb/>suono, il qual tremore comincia col corpo sonoro e ad ogni posizione si va <lb/>continuamente diffondendo per diritta linea, quando non trovi ostacoli, ma <lb/>per diritta linea e per flessuosa, quando ritrovi impedimenti &rdquo; (Specchio <lb/>Ustorio, Bologna 1650, pag. </s>

<s>79). </s></p><p type="main">

<s>E giacch&egrave; il Cavalieri, fra gli Autori che si possono citare al presente <lb/>proposito, &egrave; uno de'principali, si noti inoltre come l'aver egli ignorata la <lb/>diffusione sferica delle onde sonore l'avesse condotto a dare una spiegazione <lb/>falsa de'tubi parlanti e del Portavoce. </s>

<s>&ldquo; Per canali rinchiusi so molto bene <lb/>potersi parlar di lontano, ma in questi non vi &egrave; artificio per conto di rifles&shy;<lb/>sione, ma semplicemente mantengono la voce gagliarda per la superficie <lb/>tersa del canale, e per il tremito dell'aria che, senza patir turbamento per <lb/>la strada, incorrotto perviene all'orecchio &rdquo; (ivi, pag. </s>

<s>80). </s></p><p type="main">

<s>La ragion fisica del diffondersi i suoni per l'aria dipendente dall'altra <lb/>ragione del loro procedere in onde rarefatte e condensate, come sagacemente <lb/>aveva avvertito gi&agrave; il Benedetti, l'ebbe finalmente l'Acustica ordinata in pro&shy;<lb/>posizioni dimostrate con rigore geometrico nel II libro de'Principii di Filo&shy;<lb/>sofia neutoniana. </s>

<s>La XLIII di quelle proposizioni fu che cacci&ograve; dall'Acustica <lb/>il dannoso errore stoico delle onde sonore propagate nell'aria dalla percus&shy;<lb/>sione de'corpi, a quel modo che si propagano le onde circolari nell'acqua <lb/>percossa, per esempio, dal cader di una pietra. </s>

<s>&ldquo; Nam partes corporis tre&shy;<lb/>muli, dice ivi il Newton spiegando il concetto antico del Benedetti, vicibus <lb/>alternis eundo et redeundo, itu suo urgebunt et propollent partes medii sibi <lb/>proximas, et urgendo compriment easdem et condensabunt: dein reditu suo <lb/>sinent partes compressas recedere et sese expandere. </s>

<s>Igitur partes medii <lb/>corpori tremulo proximae ibunt et redibunt per vices, ad instar partium <lb/>corporis illius tremuli, et qua ratione partes corporis huius agitabant hasce <lb/>medii partes, hae similibus tremoribus agitatae agitabunt partes sibi proxi&shy;<lb/>mas, eaeque similiter agitatae agitabunt ulteriores, et sic deinceps in infi&shy;<lb/>nitum &rdquo; (Genevae 1740, pag. </s>

<s>353). </s></p><p type="main">

<s>Avendo cos&igrave; spiegato in questa come nella precedente proposizione il <lb/>moto progressivo dell'onda aerea, che riceve i suoi impulsi dal continuo di&shy;<lb/>latarsi delle parti addensate verso i precedenti e successivi intervalli rima&shy;<lb/>sti rarefatti; dimostra il Newton in che modo, supposto che in A (fig. </s>

<s>54) <lb/>sia un corpo sonoro, ed RS un ostacolo, in mezzo al quale sia aperto un <lb/>piccolo foro BC, s'oda il suono non solo dentro il cono APQ, com'avver-<pb xlink:href="020/01/741.jpg" pagenum="184"/>rebbe se A fosse un corpo luminoso, ma per ogni parte anche pi&ugrave; riposta, <lb/>come sarebbe in NO, KL. &ldquo; Et quoniam pulsuum progressivus motus ori&shy;<lb/><figure id="id.020.01.741.1.jpg" xlink:href="020/01/741/1.jpg"/></s></p><p type="caption">

<s>Figura 54.<lb/>tur a perpetua re&shy;<lb/>laxatione partium <lb/>densiorum versus <lb/>antecedentia inter&shy;<lb/>valla rariora, et pul&shy;<lb/>sus eadem fere ce&shy;<lb/>leritate sese in me&shy;<lb/>dii partes quietas <lb/>KL, NO, hinc inde <lb/>relaxare debent; <lb/>pulsus illi eadem <lb/>fere celeritate sese <lb/>dilatabunt undique <lb/>in spatia immota <lb/>KL, NO, qua pro&shy;<lb/>pagantur directe a <lb/>centro A, ideoque <lb/>spatium totum KLNO occupabunt. </s>

<s>Hoc experimur in sonis, qui vel monte <lb/>interposito audiuntur, vel in cubiculum per fenestram admissi sese in omnes <lb/>cubiculi partes dilatant, inque angulis omnibus audiuntur, non tam reflexi <lb/>a parietibus oppositis, quam a fenestra directe propagati, quantum ex sensu <lb/>iudicare licet &rdquo; (ibi, pag. </s>

<s>345, 46). </s></p><p type="main">

<s>Qui cadrebbe opportuno osservare che fu dalla dimostrazione di questo <lb/>Teorema condotto il Newton a negar l'ipotesi delle onde eteree nella dif&shy;<lb/>fusione del lume, perch'egli ragionava che siccome, costituito in A, per <lb/>esempio, un campanello, si sente per la diffusione dell'onda aerea in ogni <lb/>verso il suono anche nelle parti pi&ugrave; riparate quali sarebbero KL, NO; cos&igrave; <lb/>per una simile diffusione dell'onda eterea, si dovrebbero veder dietro l'osta&shy;<lb/>colo quelle stesse parti KL, NO, illuminate se fosse in A collocata la fiamma <lb/>di una candela. </s></p><p type="main">

<s>Ma perch&egrave; non &egrave; tempo oramai di tornare indietro sopra le cose gi&agrave; <lb/>prima discorse, ecco, procedendo a diritto per la nostra via, com'applicando <lb/>il principio della diffusione sferica delle onde sonore spieghi il Newton il <lb/>vero modo come procedono esse onde a rinforzare il suono nel Portavoce: <lb/>&ldquo; Sed et cur soni in Tubis stentorophonicis valde augentur ex allatis prin&shy;<lb/>cipiis manifestum est. </s>

<s>Motus enim omnis reciprocus singulis recursibus a <lb/>causa generante augeri solet. </s>

<s>Motus autem in tubis dilatationem sonorum <lb/>impedientibus, tardius amittitur et fortius recurrit et propterea a motu novo <lb/>singulis recursibus impresso magis augetur. </s>

<s>Et haec sunt praecipua phae&shy;<lb/>nomena sonorum &rdquo; (ibi, pag. </s>

<s>396). </s></p><p type="main">

<s>Fra questi fenomeni per&ograve; n'&egrave; uno che se non &egrave; de'precipui, &egrave; certo <lb/>de'pi&ugrave; curiosi. </s>

<s>Il Newton spieg&ograve; bene il modo come il suono si diffonde per <pb xlink:href="020/01/742.jpg" pagenum="185"/>tutto in una stanza, bench&egrave; non v'abbia adito che per una piccola finestra <lb/>aperta, perch&egrave; comunicandosi insieme l'aria le onde interne ricevono i primi <lb/>impulsi al moto da quelle che v'entrano dal di fuori. </s>

<s>Ma se la finestra &egrave; <lb/>chiusa? </s>

<s>se anzi &egrave; murata? </s>

<s>il suono, bench&egrave; sia interclusa ogni comunica&shy;<lb/>zione fra l'aria interna e l'esterna, passa ancora attraverso il muro, n&egrave; si <lb/>trova detta di ci&ograve; la ragione in nessun de'Teoremi neutoniani. </s>

<s>Eppure si <lb/>mostrarono curiosi di saperla anche gli antichi, e Seneca fra gli altri, con&shy;<lb/>siderando che il muro &egrave; poroso e che l'aria, sottilissimo spirito, vi s'insi&shy;<lb/>nua assai facilmente, trov&ograve; nell'aria stessa ivi dentro insinuata la continuit&agrave; <lb/>necessaria al libero trapassare del suono. </s>

<s>&ldquo; Vox, qua ratione per parietum <lb/>munimenta transmittitur? </s>

<s>nisi quod solido quoque aer inest, qui sonum <lb/>extrinsecus missum et accipit et remittit &rdquo; (Naturalium quaestionum li&shy;<lb/>bri VII, Aldus Venetiis 1522, c. </s>

<s>13). </s></p><p type="main">

<s>Era facile per&ograve; avvedersi che non poteva esser questa addotta da Se&shy;<lb/>neca la ragion vera del fatto, perch&egrave; il suono dovrebbe tanto pi&ugrave; facilmente <lb/>avere il transito, quanto l'ostacolo fosse pi&ugrave; poroso, o contenesse maggior <lb/>copia d'aria rinchiusa, ci&ograve; che l'esperienze dimostrano esser falso. </s>

<s>Persuaso <lb/>di ci&ograve; il Grimaldi ebbe a concluderne che non era possibile spiegare il fatto <lb/>altrimenti, che ammettendo nella voce di un che parla dentro una stanza <lb/>la virt&ugrave; di far vibrare il muro e di trasmettere all'aria dell'altra stanza at&shy;<lb/>tigua le vibrazioni sincrone a quelle ricevute e produttrici perci&ograve; de'mede&shy;<lb/>simi suoni. </s>

<s>&ldquo; Si non admittatur aliquis motus in muris praedictis, vel in <lb/>substantia per eos diffusa, non video quomodo concipiendus sit fieri alius <lb/>motus in aere post murum consequente. </s>

<s>Motus enim non communicatur <lb/>mobili nisi per motum medii si hoc intercedat &rdquo; (De lum. </s>

<s>cit., pag. </s>

<s>391). </s></p><p type="main">

<s>Queste dottrine, che non fa maraviglia se parvero strane ai tempi del&shy;<lb/>l'Autore, avrebbero trovato ora la pi&ugrave; bella dimostrazione e la pi&ugrave; valida <lb/>conferma ne'modi d'operar del Telefono e del Fonografo, se come una sot&shy;<lb/>tile laminetta metallica fosse cos&igrave; gelosa in sentire i tremori leggerissimi del&shy;<lb/>l'aria la mole solidissima di un muro. </s>

<s>&Egrave; perci&ograve; che il Grimaldi raccoglie <lb/>insieme le forze a difender le sue dottrine, le quali prevedeva che sareb&shy;<lb/>bero assalite da questa parte, facendo opportunamente osservare che basta <lb/>una minima forza ad eccitare e a diffondere i tremori armonici nel pi&ugrave; pon&shy;<lb/>deroso corpo, e nel pi&ugrave; duro che sia. </s>

<s>Cos&igrave; a solo strisciar la punta di uno <lb/>spillo s'ode fremer nel suono il bronzo di una campana, e le barbe di una <lb/>penna fregate in capo a una lunghissima trave fan sentire il fruscio a chi <lb/>tiene applicato l'orecchio all'estremit&agrave; opposta. </s></p><p type="main">

<s>Altro esempio di questa maravigliosa facilit&agrave; di trasmettere i suoni, da <lb/>una forza debolissima, lo ritrova il Grimaldi in un fatto, di che dice esser <lb/>soliti di pigliare esperienza i soldati, i quali argomentano dal vibrar di un <lb/>pendolo posato sopra la pelle di un tamburo, il calpestar de'cavalli dell'eser&shy;<lb/>cito nemico, che s'avanzano talvolta parecchie miglia di lontano. </s>

<s>&ldquo; Plura in <lb/>rem praesentem experimenta afferre censeo.... Unum tamen prae caeteris <lb/>non possum non indicare. </s>

<s>Fertur consuetum esse militibus ut, si quando <pb xlink:href="020/01/743.jpg" pagenum="186"/>explorare voluerint adventum hostilis equitatus, tympanum in plano terrestri <lb/>erectum observant, animadvertentes utrum talus aut aliud quid impositum <lb/>pelli tympani subsultet ob tremorem scilicet ipsius pellis in tympano bene <lb/>tensae, quia nimirum id eis signum est terram equorum advenentium pedi&shy;<lb/>bus pulsatam et tremere ipsam et tremorem consequenter impertiri tym&shy;<lb/>pano ipsi terrae imposito &rdquo; (ibi, pag. </s>

<s>387). </s></p><p type="main">

<s>Questo tamburo da militari dette poi occasione al Grimaldi d'inventare <lb/>il primo <emph type="italics"/>Sismometro<emph.end type="italics"/> o <emph type="italics"/>Sismoscopio<emph.end type="italics"/> che si debba chiamare e di applicarlo <lb/>a riconoscere i minimi tremori comunicati a ogni parte di qualche vastis&shy;<lb/>simo edifizio bench&egrave; prodotti da non pi&ugrave; validi colpi di quelli dati da un <lb/>maglio di legno. </s>

<s>&ldquo; Solum adverto posse subtilius agnosci tremorem prae&shy;<lb/>dictae pellis in tympano, si illi imponatur aliquod speculum, a quo lumen <lb/>aliquod reflectatur ad magnam distantiam, huiusmodi enim lumen reflexum <lb/>et super aliquo corpore distante praesertim candido terminatum, suo tre&shy;<lb/>more notabilius indicabit tremorem speculi, et consequenter etiam tympani. </s>

<s><lb/>Hoc artificio usus agnovi totum aliquod ingens aedificium tremere eo ipso <lb/>quod tellus in aliqua notabili ab eo distantia percutiebatur gravi quodam <lb/>malleo ex ligno, qualis adhiberi solet dum ligna scinduntur cuneis ferreis <lb/>per vim intrusis &rdquo; (ibi, pag. </s>

<s>387, 88). </s></p><p type="main">

<s>Ma n&egrave; cos&igrave; belle e argute prove sperimentali valsero a persuadere i ri&shy;<lb/>trosi, i quali andavano dicendo che sarebbero allora state concludenti, quando <lb/>la voce avesse virt&ugrave; di mettere in tremore un edifizio o di far vibrare una <lb/>campana o fremere una lunga trave. </s>

<s>Contrapponevano anzi cotesti opposi&shy;<lb/>tori, come vedremo, all'esperienze del Grimaldi altre esperienze dimostra&shy;<lb/>tive dell'insufficienza delle onde aeree a muovere co'loro impulsi, nonch&egrave; <lb/>un solido muro, una sottilissima corda tesa. </s>

<s>E per verit&agrave; non par che cos&igrave; <lb/>fatte opposizioni trovassero pronta la risposta, ma perch&egrave; in ogni modo il <lb/>trapassar del suono attraverso ai corpi non si pu&ograve; spiegare altrimenti che <lb/>con le ipotesi del Grimaldi, si potrebbe dir per salvarle che l'aria mette in <lb/>vibrazione non immediatamente il muro, ma gli oggetti pi&ugrave; leggeri o che <lb/>siano a vibrare meglio disposti, i quali, bench&egrave; con tenui impulsi, bastano, <lb/>come l'esperienza dimostra, a comunicare il moto anche alle pi&ugrave; solide <lb/>pareti. </s></p><p type="main">

<s>Comunque sia, essendo nostro unico fine quello di narrar la Storia, <lb/>abbiam veduto come e quanto penasse la scienza a intendere le ragioni del <lb/>moto ondoso e diffusivo del suono. </s>

<s>Eppure ella v'era bene arrivata dalla Fi&shy;<lb/>losofia stoica, alla quale fra gli altri benefizi dobbiamo l'aver sostituito al&shy;<lb/>l'errore peripatetico delle specie intenzionali un real moto ondulatorio nel&shy;<lb/>l'aria, la quale perci&ograve; supponevasi allora mezzo necessario a mettere in <lb/>comunicazione il corpo risonante con l'organo dell'udito. </s>

<s>E bench&egrave; fosse <lb/>una tal supposizione cos&igrave; ragionevole, da non trovar contradittori, pur per <lb/>non fondar la miglior parte dell'Acustica sopra un supposto, conveniva as&shy;<lb/>sicurarsene in qualche modo, e di qui ebbero occasione quelle varie espe&shy;<lb/>rienze, delle quali ora passiamo a narrar brevemente il successo. </s></p><pb xlink:href="020/01/744.jpg" pagenum="187"/><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Sembrava che cos&igrave; fatte nuove e curiose esperienze non fosse possibile <lb/>d'eseguirle, senza l'uso della Macchina pneumatica, o almeno dello stru&shy;<lb/>mento torricelliano: eppure, in quel tempo che disputavasi ancora con tanto <lb/>ardore se si dava o no il vuoto in Natura, e che si credeva da'Filosofi do&shy;<lb/>ver senza il mezzo dell'aria tutto il mondo creato rimanersi fra le tenebre <lb/>e immoto; un gentiluomo veneziano che dilettavasi di questi studii, traspor&shy;<lb/>tatovi dal proprio genio e dall'amicizia che teneva con Galileo, riusci a di&shy;<lb/>mostrare sperimentalmente e senz'uso degli strumenti inventati poi per <lb/>fare il vuoto, che senz'aria nella Natura veramente regnerebbe il pi&ugrave; alto <lb/>silenzio. </s></p><p type="main">

<s>L'inaspettato esperimento non veniva suggerito dal caso, ma da una <lb/>speculazione condotta a fil di severa logica, bench&egrave; avesse per fondamento <lb/>la immaginata teoria degl'ignicoli, i quali in uno spazio riscaldato sotten&shy;<lb/>trano d'ogni parte a riempirlo in luogo dell'aria. </s>

<s>Giovan Francesco Sagredo, <lb/>cos&igrave; dunque scriveva il d&igrave; 11 Aprile 1615 a Galileo, in proposito della co&shy;<lb/>struzione e del modo d'operar de'tubi termometrici: &ldquo; Alle fornaci di Mu&shy;<lb/>rano ho fatto fare un vaso di vetro con un palmo di collo, ed essendo ben <lb/>caldo, l'ho fatto richiudere, sicch&egrave; tutto l'aere, che v'era dentro rinchiuso <lb/>pieno di calore, non potesse pi&ugrave; uscire dopo raffreddato. </s>

<s>E per conseguenza, <lb/>uscito lo spirito igneo e restatoci dentro l'aere di ugual temperamento al&shy;<lb/>l'ambiente, persuasi chi erano presenti che dentro vi fosse pochissima aria <lb/>siccome al senso era manifesto che non vi fosse spirito igneo. </s>

<s>Le prove fu&shy;<lb/>rono due: la prima che avendovi fatto rinchiudere dentro un sonaglio da <lb/>sparviero, questo mosso non faceva un suono esterno se non quanto per&shy;<lb/>coteva nel vetro, e per conseguenza faceva un suono esterno, il che fu as&shy;<lb/>sai facilmente creduto che non avvenisse per altro, che per lo mancamento <lb/>dell'aere nel vaso suddetto, e tanto pi&ugrave; ch'essendosi rotto detto vaso si <lb/>trov&ograve; il sonaglio sonoro, secondo l'ordinario. </s>

<s>La seconda perch&egrave;, avendo io <lb/>posto esso vaso col collo in una mastella d'acqua, con un ferro gentilmente <lb/>apersi la bocca, per la quale salendo entr&ograve; tant'acqua che pareva che vo&shy;<lb/>lesse riempire tutto il detto vaso &rdquo; (Alb. </s>

<s>VIII, 372). </s></p><p type="main">

<s>La bella esperienza, cos&igrave; ben riuscita al Sagredo con tanto semplice <lb/>artificio, &egrave; notabile ripensando alle incertezze e ai tanti dubbii penosi, in che <lb/>lo Strumento torricelliano e la stessa Macchina pneumatica lasciarono poi i <lb/>Fisici, che si dettero cos&igrave; industriosamente a investigar que'medesimi ef&shy;<lb/>fetti. </s>

<s>&Egrave; celebre nella storia da noi gi&agrave; narrata la prima di cos&igrave; fatte inve&shy;<lb/>stigazioni tentata nel vuoto torricelliano da Gaspero Berti in Roma, investi&shy;<lb/>gazione che riusc&igrave;, come sappiamo, priva di effetto, perch&egrave;, ritirata la calamita <lb/>e cadendo perci&ograve; il martellino di ferro sul campanello, questo <emph type="italics"/>limpidissi-<emph.end type="italics"/><pb xlink:href="020/01/745.jpg" pagenum="188"/><emph type="italics"/>mum edidit sonum ab omnibus experimento spectatoribus auditum.<emph.end type="italics"/> Non <lb/>si pu&ograve; credere che il Magiotti, il quale era uno di quegli spettatori non ri&shy;<lb/>conoscesse, com'aveva gi&agrave; riconosciuto il Sagredo, che il suono era esterno, <lb/>essendo la codetta del campanello cos&igrave; saldata col tubo di piombo, da co&shy;<lb/>municargli assai facilmente i conceputi suoi tremori sonori, ma non si ve&shy;<lb/>deva dall'altra parte come si potesse interrompere quella inevitabile comu&shy;<lb/>nicazione. </s></p><p type="main">

<s>Furono da questa difficolt&agrave; sopraffatti gli Accademici del Cimento, i quali <lb/>ripeterono l'esperienza del sonaglio (Saggi ecc., Firenze 1841, pag. </s>

<s>57, 58) <lb/>cos&igrave; bene riuscita al Sagredo, e credendo che si potesse quella difficolt&agrave; no&shy;<lb/>tabilmente diminuire, si dettero con incredibile industria a sperimentar con <lb/>uno strumento a fiato, conforme a ci&ograve; che aveva progettato il Boyle nel <lb/>XXVII de'suoi nuovi esperimenti (Op. </s>

<s>Omnia, Venetiis 1697, T. I, pag. </s>

<s>62-64). <lb/>Con tale occasione furono i nostri Accademici i primi a far l'esperienza del <lb/>suono anche nell'aria compressa, ma tutti questi cos&igrave; laboriosi tentativi eb&shy;<lb/>bero un infelice successo, e fu quel che se n'ebbe a concludere uno scherzo <lb/>espresso in tali parole: &ldquo; O l'aria non ha che far col suono, o ella vale <lb/>in qualunque stato (o rarefatta o compressa) ad ugualmente produrlo &rdquo; <lb/>(Saggi cit., pag. </s>

<s>59). </s></p><p type="main">

<s>Questo era come il sorriso amaro di chi dispera di conseguire un in&shy;<lb/>tento vivamente desiderato; disperazione alla quale s'abbandonarono total&shy;<lb/>mente gli Accademici fiorentini, quando persuasi gi&agrave; che il buon successo <lb/>dell'esperienza dipendeva tutto dal far s&igrave; che il corpo sonoro non comuni&shy;<lb/>chi col vaso di vetro, essendo a loro sovvenuto il pensiero di una sospen&shy;<lb/>sione magnetica, riconobbero che non era effettuabile il lusinghiero progetto. <lb/></s>

<s>&ldquo; Si tratta di disporre il corpo sonoro (leggesi in uno de'Diari dell'Ac&shy;<lb/>cademia) in modo che non comunichi col vaso di vetro, come per esempio <lb/>tenendolo sospeso senza contatto per sola virt&ugrave; magnetica &rdquo; (MSS. Cim., <lb/>T. IV, c. </s>

<s>107). </s></p><p type="main">

<s>Anche questa storia per&ograve; ne porge un altro de'tanti esempi che s'hanno <lb/>di difficolt&agrave; credute insuperabili, e di faticosi tentativi tornati sempre inu&shy;<lb/>tili, che si son veduti poi riuscire con massima facilit&agrave;, facendo rimanere <lb/>quei che s'erano ritirati indietro maravigliati. </s>

<s>Per far s&igrave; che il corpo sonoro <lb/>non comunichi le sue vibrazioni al recipiente del vuoto fu trovato che ba&shy;<lb/>stava posare una sveglia sopra una coltricetta di lana o di ovatta. </s>

<s>L'espe&shy;<lb/>rienza del suono nel vuoto divenne allora cos&igrave; facile e tanto comune, da non <lb/>parer credibili le difficolt&agrave; incontrate dal Boyle e da'nostri Accademici di <lb/>Firenze, ond'&egrave; che il Musschenbroek non ripensando forse a queste cose, <lb/>ebbe ad accusare gli stessi nostri Accademici di poco accurati nell'eseguire <lb/>le delicate esperienze. </s>

<s>&ldquo; Experimenta quae hic a florentinis Philosophis tra&shy;<lb/>duntur .... non videntur tanta accuratione capta ac desiderare posset. </s>

<s>Ma&shy;<lb/>gnus compositusque instrumentorum apparatus plerumque vitiis obnoxius <lb/>hos perspicacissimos caeteroquin viros illusisse et in errorem coniecisse ve&shy;<lb/>risimile est &rdquo; (Tentamina Experim. </s>

<s>natur., Viennae 1756, Pars I, pag. </s>

<s>88). <pb xlink:href="020/01/746.jpg" pagenum="189"/>Ma &egrave; falso che gli Accademici si fossero mai lusingati, come l'Olandese as&shy;<lb/>serisce, avendo anzi sinceramente confessato l'infelice successo de'loro stu&shy;<lb/>dii, la quale infelicit&agrave; di successo non fu occasionata dal grande e compli&shy;<lb/>cato apparecchio degli strumenti, ma dal creder che si dovesse o si potesse <lb/>tener assolutamente separato il corpo sonoro dal recipiente del vuoto, e dal <lb/>non aver pensato che bastava frapporvi un corpo anelastico, il quale impe&shy;<lb/>disse al tremore di comunicarsi e tradursi dal di dentro al di fuori. </s></p><p type="main">

<s>Cos&igrave; insomma con maravigliosa facilit&agrave; riuscita la bella esperienza, che <lb/>erasi in principio rappresentata come non superabile ad ogni argomento del&shy;<lb/>l'arte, venivasi con essa a dimostrar che l'etere, sottilissimo mezzo propor&shy;<lb/>zionato ad operar sensibilmente sopra l'organo della vista, sfuggiva per quella <lb/>sua sottigliezza alle percezioni dell'organo dell'udito accomodato a non rice&shy;<lb/>ver che le impressioni dell'aria o di qualche altro corpo pi&ugrave; crasso. </s>

<s>Que&shy;<lb/>sto principalmente tendeva a dimostrar l'esperienza del timpano o del cam&shy;<lb/>panellino nel vuoto diffusa oramai, in sul cominciar del secolo XVIII, in <lb/>tutte le scuole, ma il Nollet notava ch'era la gentile esperienza tirata ge&shy;<lb/>neralmente a diversa intenzione, a servir d'argomento cio&egrave; a concludere <emph type="italics"/>che <lb/>l'aria &egrave; il solo mezzo idoneo alla propagazione del suono<emph.end type="italics"/> (Lezioni di Fi&shy;<lb/>sica, trad. </s>

<s>ital., T. III, Venezia 1762, pag. </s>

<s>273). Aveva inoltre il francese <lb/>Autore delle Lezioni di Fisica precedentemente notato che da nessuno si <lb/>pensava a que'tempi potersi altresi diffondere il suono ne'solidi e ne'li&shy;<lb/>quidi, ond'&egrave; ch'e'crede essere stato egli il primo a far l'esperienza della <lb/>diffusion del suono per l'acqua, sommergendo una sveglia chiusa dentro una <lb/>cassetta in un gran vaso cilindrico pieno d'acqua ripurgata dall'aria (ivi, <lb/>pag. </s>

<s>272). </s></p><p type="main">

<s>Bench&egrave; sia questa veramente l'opinion comune che avevano i Fisici <lb/>a'tempi del Nollet in Francia, non &egrave; da tacer che in Italia, un secolo prima, <lb/>Niccol&ograve; Aggiunti, rigoglioso e ubertoso ramo che troppo presto la morte re&shy;<lb/>cise dall'albero della scienza, aveva avvertito come talora il suono si diffonde <lb/>con pi&ugrave; intensit&agrave; ne'solidi che nell'aria, e l'argoment&ograve; da due varie espe&shy;<lb/>rienze tolte dal ricco armario de'fanciulleschi trastulli e da lui stesso scelte <lb/>e applicate al proposito con filosofico acume. </s>

<s>Fu pure il medesimo Aggiunti <lb/>il primo a dimostrar con facili esperienze che il suono si diffonde anco per <lb/>l'acqua, e a congetturar che diffonderebbesi pure, bench&egrave; con tenor vario <lb/>anco nell'olio, di che e di molte altre dottrine acustiche ben pi&ugrave; importanti, <lb/>recheremo in fine del presente capitolo i documenti. </s></p><p type="main">

<s>Non si vuol tacere altres&igrave; che nell'esperienza della diffusion del suono <lb/>per l'acqua il Nollet, il quale credette essere stato il primo a farla, fu pre&shy;<lb/>venuto dagli Accademici del Cimento, bench&egrave; la loro intenzion principale <lb/>fosse alquanto diversa, e bench&egrave; solamente parecchi anni dopo, il Targioni, <lb/>togliendola da'Diarii ne divulgasse la notizia nel suo T. II, P. II, dove ap&shy;<lb/>punto si legge: &ldquo; A'd&igrave; 5 Luglio 1657. Per usare ogni possibil diligenza nel <lb/>riconoscere se potessero scorgersi quei cerchi nell'acqua, per suono che esce <lb/>di sotto di essa, come si presuppone che si facciano nell'aria, si pose in un <pb xlink:href="020/01/747.jpg" pagenum="190"/>vaso di vetro un Orivolo carico con la sveglia, ed essendosi ben chiuso si <lb/>seppell&igrave; in un altro vaso pieno d'acqua, ma cominciando a sonare l'Oriolo <lb/>non si poteva riconoscere increspamento alcuno nell'acqua circonfusa al vaso <lb/>contenente detto suono: solo fu casualmente osservato che, accostandosi un <lb/>par di cisoie all'ultimo vaso, queste erano fatte tremare, forse dall'impulso <lb/>dell'istesso suono che usciva &rdquo; (pag. </s>

<s>562, 63). </s></p><p type="main">

<s>L'osservazione fatta dal Nollet a proposito del suono nell'acqua, che <lb/>non &egrave; vera, secondo abbiamo veduto, rispetto alla diffusione, &egrave; verissima ri&shy;<lb/>spetto alla velocit&agrave; del suono, l'esperienze della quale velocit&agrave; furono prima <lb/>tentate nell'aria riguardata come il pi&ugrave; natural mezzo ordinato a trasmet&shy;<lb/>tere i tremori armonici d'ogni parte al timpano dell'orecchio. </s>

<s>Perciocch&egrave; i <lb/>suoni non si trasmettono al nostro organo per mezzo dell'acqua, se non che <lb/>in qualche costituzione straordinaria, come sarebbe in chi per qualche mo&shy;<lb/>mento vi rimanga sommerso bagnandosi in un fiume o nel mare, e perch&egrave; <lb/>non si trasmettono per gli altri liquidi, se non in una costituzione ben pi&ugrave; <lb/>artificiosa e diremmo quasi violenta; non fu prima pensato a sperimentar <lb/>la velocit&agrave; del suono in mezzo a quegli stessi liquidi, se non che quando la <lb/>scienza si senti frugata dalla curiosit&agrave; di saper tutto, ed ebbe il modo a vin&shy;<lb/>cere le difficolt&agrave; dall'arte pi&ugrave; raffinata e dalla squisitezza degli strumenti. </s>

<s>Di <lb/>qui &egrave; che l'esperienze della velocit&agrave; del suono in mezzo ai liquidi si pu&ograve; dir <lb/>che sieno opera de'nostri giorni, mentre l'esperienze della velocit&agrave; del suono <lb/>nell'aria, la quale per ogni parte circonda il nostro corpo, e lasciandoci liberi <lb/>ne'nostri proprii moti ci mette in comunicazione diretta con gli altri corpi, <lb/>incominciarono fin quasi da'primi anni che l'Acustica inizi&ograve; i suoi progressi. </s></p><p type="main">

<s>Nel 1644 usciva in Parigi dall'officina di Antonio Bertier la <emph type="italics"/>Ballistica<emph.end type="italics"/><lb/>di Marino Mersenno, nella quale si leggeva per la prima volta una propo&shy;<lb/>sizione, che &egrave; la XXXV del libro, e che veniva dall'Autore annunziata sotto <lb/>questa forma: &ldquo; Soni velocitas maior est globorum explosorum velocitate, <lb/>et 230 sexpedas, spatio unius secundi minuti, conficit &rdquo; (pag. </s>

<s>138). La di&shy;<lb/>mostrazione, com'&egrave; facile prevedere, &egrave; tutta sperimentale e il Mersenno pro&shy;<lb/>mette a chiunque voglia tornare a far esperienza della velocit&agrave; di qualunque <lb/>suono che &ldquo; noctu diuque, sive in vallibus, sylvis, aut montibus, sive <lb/>adverso, sive favente vento, sive aeris facie pluvia vel serena .... semper <lb/>eamdem soni velocitatem inveniet &rdquo; (ibi). </s></p><p type="main">

<s>Trov&ograve; lo stesso Mersenno anche un'altra propriet&agrave; singolare nel movi&shy;<lb/>mento del suono, ed &egrave; che la velocit&agrave; di lui non diminuisce con l'intensit&agrave;, <lb/>ma sempre si serba equabile, cosicch&egrave; in un tempo doppio o quintuplo, per <lb/>esempio, percorre imperturbatamente un doppio o un quintuplo spazio. <lb/></s>

<s>&ldquo; Postquam vero per 230 sexpedas secundum exploraveris, qui minus tor&shy;<lb/>mentum explodit, iterum per alias 230 sexpedas recedat, ut abs te 460 sex&shy;<lb/>pedas recesserit, idem vel aequalis sonus duo secunda in illo itinere percur&shy;<lb/>rendo consumet; quod cum quinquies a nobis fuerit multiplicatum, ut ex 1150 <lb/>hexapedis fragorem audiremus, ignis ex ore tormenti noctu erumpere sem&shy;<lb/>per quinque secundis minutis fragorem praevertit &rdquo; (ibi). </s></p><pb xlink:href="020/01/748.jpg" pagenum="191"/><p type="main">

<s>Da questa bella propriet&agrave; scoperta ne deduce il Mersenno una conse&shy;<lb/>guenza nuova, ed &egrave; che si possono per via del suono misurare esattamente <lb/>le distanze, quanto per esempio &ldquo; tormenta in obsessos aut obsidentes <lb/>explosa distent .... ex tonitrui fragore audito visoque fulgore praecedente <lb/>sciri quantum illud absit &rdquo; (ibi, pag. </s>

<s>139). S'erano anche gli antichi, per <lb/>volgari ed ovvie esperienze, accorti ch'essendo l'apparir della luce istanta&shy;<lb/>neo il suono la seconda con tempo; ond'&egrave; che Galileo, dal piccolo intervallo <lb/>che resta tra il veder noi il baleno e il sentire il tuono, argomentava che le <lb/>folgori non si fanno alte da terra neanco un miglio (Alb. </s>

<s>IV, 333). In que&shy;<lb/>sta argomentazione si trova applicata la velocit&agrave; del suono alla misura della <lb/>distanza, presa per&ograve; cos&igrave; all'ingrosso, ignorandosi da Galileo e da'predeces&shy;<lb/>sori di lui di quella stessa velocit&agrave; il grado. </s></p><p type="main">

<s>La Ballistica del Mersenno, il quale fu de'primi ad annunziare al pub&shy;<lb/>blico la sperimentata misura di quel grado di velocit&agrave;, non s'introdusse n&egrave; <lb/>cos&igrave; facile n&egrave; cos&igrave; pronta in Italia, dove non facevasi dell'Autor di lei troppo <lb/>grande stima. </s>

<s>E chi sa quanto ancora avrebbero indugiato i Nostri ad aver <lb/>notizia dell'esperienze e delle scoperte francesi, se non fossero approdate qua <lb/>nel libro delle Considerazioni sopra Diogene Laerzio di Pietro Gassendi. </s>

<s>Il <lb/>Gassendi, sincero estimatore, promotore e difensore in Francia delle dottrine <lb/>di Galileo era dagli Italiani amato pi&ugrave; forse di tutti gli altri stranieri, e la <lb/>teoria atomistica rinnovellata da lui piacque principalmente al Borelli. </s>

<s>Fu <lb/>primo infatti il Borelli ad annunziar ne'medicei consessi quel che aveva spe&shy;<lb/>rimentato e dimostrato il Gassendo, e fu che si diffondono con eguale ve&shy;<lb/>locit&agrave; i tuoni o grandi come quello di un cannone o piccoli come quel d'un <lb/>moschetto. </s>

<s>Non era questa la pi&ugrave; difficile tra l'esperienze fatte gi&agrave; dal Mar&shy;<lb/>senno, e il Grimaldi citava il fatto ovvio delle campane che mantengono <lb/>sempre la medesima armonia fra le piccole e le grandi, per qualunque va&shy;<lb/>riar di distanze (De lum. </s>

<s>cit., pag. </s>

<s>377), ma pur parve al Roberval, e lo <lb/>rifer&igrave; allo stesso Mersenno, di aver trovato qualche differenza tra il diffon&shy;<lb/>dersi de'grandi e de'piccoli rumori; diversit&agrave; che senza dubbio dipendeva <lb/>dalla poca esattezza dell'esperienza e di che venne ad assicurarne il Gassendo. </s></p><p type="main">

<s>Il Borelli pure, non contento al dire ma pronto all'operare, conferm&ograve; <lb/>il fatto asserito nelle Considerazioni sopra Laerzio, e lo riguard&ograve; sotto un <lb/>aspetto nuovo sfuggito alla considerazione de'Fisici francesi. </s>

<s>Proponeva la <lb/>questione alla presenza del Granduca e del Rinaldini se la velocit&agrave; del tuono <lb/>d'un cannone crescesse a proporzion della quantit&agrave; della polvere o rima&shy;<lb/>nesse sempre la medesima. </s>

<s>Il Rinaldini asseriva che sarebbe cresciuta, il <lb/>Borelli negava; ond'&egrave; che a decidere s'invocarono l'esperienze, la curiosa <lb/>storia delle quali &egrave; cos&igrave; narrata dal Magalotti: &ldquo; Ho trovato grandissima di&shy;<lb/>scordia tra il Borelli e il Rinaldini sopra la velocit&agrave; del suono. </s>

<s>Diceva que&shy;<lb/>sti che la prestezza dell'arrivare il rumore d'un'artiglieria sarebbe cresciuta <lb/>a proporzione della maggior quantit&agrave; della polvere.... Il Borelli diceva che <lb/>tutti sarebbero arrivati in tempi eguali, bench&egrave; la polvere dell'uno fosse <lb/>stata millionecupla a quella dell'altro. </s>

<s>Ciascuno port&ograve; i suoi pensieri al Gran-<pb xlink:href="020/01/749.jpg" pagenum="192"/>duca, il quale comand&ograve; che mercoled&igrave; sera dopo l'unora di notte si facesse <lb/>l'esperienza.... Per conoscere i tempi avevano aggiustato un funependolo <lb/>al suo libramento ed ei, quando si vedeva il lampo che era segno di gi&agrave; <lb/>essere sparato il pezzo, lasciavano cadere, e tanto allo sparo dello smeriglio, <lb/>quanto della spingarda e del mezzo cannone si contarono l'istesse vibrazioni <lb/>a capello &rdquo; (MSS. Cim., T. XXV, c. </s>

<s>181). </s></p><p type="main">

<s>In quel capitolo del Gassendo, in che il Borelli aveva letta l'esperienza <lb/>della ugual velocit&agrave; de'suoni o piccoli o grandi, trov&ograve; citate anche le osser&shy;<lb/>vazioni rese note al pubblico dal Mersenno due anni avanti. </s>

<s>Fu questa ci&shy;<lb/>tazione che invi&ograve; il Nostro a ricercar la <emph type="italics"/>Ballistica<emph.end type="italics"/> dell'Autore francese, e <lb/>trovatevi quella nuove esperienze sulla velocit&agrave; del suono, e quelle applica&shy;<lb/>zioni alla misura delle distanze delle quali dianzi dicemmo, confer&igrave; il tutto <lb/>privatamente col Granduca, il quale volle per sua curiosit&agrave; gli scrivesse di <lb/>quelle cose un sunto, o gliene distendesse una nota. </s></p><p type="main">

<s>In quella Nota rimessa dal Borelli al Granduca l'esperienze del Mer&shy;<lb/>senno si assommavano ne'quattro capi seguenti: I. </s>

<s>I suoni o piccoli o grandi <lb/>arrivano tutti all'orecchio nel medesimo tempo. </s>

<s>II. </s>

<s>Il vento anche avverso <lb/>non impedisce nulla il moto del suono. </s>

<s>III. All'orecchio di chi sta ad os&shy;<lb/>servare (&egrave; questa l'espression propria dello stesso Mersenno) <emph type="italics"/>sive distantia <lb/>fuerit verticalis, sive lateralis sive obliqua, nil interest.<emph.end type="italics"/> IV. </s>

<s>I tempi di due <lb/>suoni qualunque sono direttamente proporzionali alle distanze. </s></p><p type="main">

<s>Sapeva bene il Granduca ch'erano tutte queste particolarit&agrave; ignote al <lb/>Viviani, non intervenuto alle esperienze fatte alla Petraia, e di ci&ograve; veniva <lb/>anche meglio rassicurato dal Borelli, il quale discorrendo col suo Collega <lb/>s'era bene avveduto che in questo negozio non aveva altro sentito dire, se <lb/>non che il Gassendi asseriva farsi in tempi uguali tanto il colpo di un mo&shy;<lb/>schetto quanto il tuono di una bombarda. </s>

<s>Perci&ograve; indulgendo a quel suo ge&shy;<lb/>nio di comparire in cose fisiche a'suoi sudditi primo maestro, avuto un <lb/>giorno il Granduca a s&egrave; il Viviani lo incominci&ograve; a tentare di quel che sa&shy;<lb/>pesse rispondere intorno a quei quattro quesiti risoluti dall'esperienze mer&shy;<lb/>senniane, conforme alla nota trasmessagli dal Borelli. </s>

<s>Il curioso esame &egrave; cos&igrave; <lb/>candidamente descritto dallo stesso Viviani, il quale racconta come, trovan&shy;<lb/>dosi un giorno a'Pitti nelle stanze de'Paggi, fosse mandato a chiamar dal <lb/>Serenissimo Granduca per fargli queste domande: </s></p><p type="main">

<s>&ldquo; Prima quale de'due suoni, il grande o il piccolo arrivasse in meno <lb/>tempo all'orecchio, al che risposi che in tempi eguali l'uno e l'altro. </s>

<s>Se&shy;<lb/>conda, quale impedimento potesse apportare il vento al moto del suono. </s>

<s>Ri&shy;<lb/>sposi: nessuno; e fin qui risposi guidato non solo dal discorso e dalle ra&shy;<lb/>gioni che ne avevo, ma ancora avvalorato da ci&ograve; che ne dice il Gassendi, e <lb/>mi conferm&ograve; il sig. </s>

<s>Borelli. </s>

<s>Pass&ograve; poi pi&ugrave; oltre con le domande e dissemi <lb/>qual differenza di tempo io credevo che si intermettessi nel moto del suono <lb/>dallo sparare una volta il pezzo con la bocca verso l'orecchio di chi sta ad <lb/>osservare o volta all'ins&ugrave; perpendicolarmente o volta per il contrario, al che <lb/>risposi subito, con tutto che mi giungesse nuovo il quesito, che averei cre-<pb xlink:href="020/01/750.jpg" pagenum="193"/>duto questi tempi ugualissimi tra di loro. </s>

<s>S. A. allora non mi disse se io <lb/>avevo risposto a'quesiti bene o male, ma la sera poi .... mi accert&ograve; che <lb/>nelle esperienze fatte e replicate due sere avanti con un pezzo a spingarda, <lb/>dalla Petraia, si era trovato seguire puntualmente che i tempi del piccolo <lb/>suono erano uguali a quelli del grande; che il vento che la seconda sera <lb/>tirava per scirocco non impediva o alterava di niente, e che gli spari fatti <lb/>per qualunque verso non facevano variazione nel tempo del moto di detti <lb/>suoni. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Non finirono qui l'instanze fattemi da S. A. che avanti io mi par&shy;<lb/>tissi .... mi domand&ograve; in ultimo quello che io avrei creduto che fossero per <lb/>riuscire i tempi di due suoni, cio&egrave; d'uno fatto in distanza di due miglia, e <lb/>di un altro fatto in doppia distanza. </s>

<s>Risposi a questo che io ancora avevo <lb/>un tempo curiosit&agrave; di chiarirmi se il moto del suono era in s&egrave; stesso di <lb/>velocit&agrave; continuamente ritardata oppure equabile, perch&egrave; se si trovasse tale <lb/>mi pareva di cavarne conseguenze assai curiose e grandissime utilit&agrave;. </s>

<s>Su <lb/>questo mi astrinse a dirne quel ch'io ne credevo, perch&egrave; poi voleva farne <lb/>la prova. </s>

<s>Risposi, veramente con troppo ardire, che in doppia distanza si <lb/>ricercherebbe doppio tempo per appunto, tenendo che il moto del suono in <lb/>s&egrave; stesso sia uniforme, cio&egrave; che, in quali si siano tempi uguali, passi spazii <lb/>uguali. </s>

<s>Ma perch&egrave; sopra questo particolare ci avevo di nuovo speculato il <lb/>giorno avanti, e mi pareva d'aver pi&ugrave; ragioni che mi persuadessero questo <lb/>che il contrario; per&ograve; non messi in dubbio la risposta, e qui per allora fin&igrave; <lb/>il discorso. </s>

<s>&rdquo; (Antinori, Notizie Stor. </s>

<s>relative all'Accad. </s>

<s>del Cimento, Fi&shy;<lb/>renze 1841, pag. </s>

<s>51, 52). </s></p><p type="main">

<s>Proseguendo il racconto importante di questa storia soggiunge ivi il <lb/>Viviani che supposta l'equabilit&agrave; del suono se ne caverebbero conseguenze <lb/>curiosissime e utilissime, delle quali fece per sua memoria una nota, ch'ei <lb/>lesse al principe Leopoldo e al Granduca. </s>

<s>Questa nota autografa fu pure <lb/>pubblicata dall'Antinori a pag. </s>

<s>53 del Discorso citato, e porta scritta la data <lb/>del d&igrave; 10 Ottobre 1656. Ci&ograve; vuol dir che il Viviani suppone ancora quel che <lb/>dodici anni prima aveva dimostrato il Mersenno, e d&agrave; come invenzione re&shy;<lb/>pentinamente cadutagli in pensiero la soluzione di que'problemi relativi alla <lb/>misura delle distanze, ch'eran pur dodici anni prima, non solamente caduti <lb/>in pensiero, ma divulgati dallo stesso Mersenno. </s>

<s>Questo sol si pu&ograve; dire che <lb/>a'tre problemi proposti come risolubili per via della velocit&agrave; de'suoni a <lb/>pag. </s>

<s>139 della Ballistica mersenniana, il Viviani in quella sua Nota aveva <lb/>pensato di aggiungervene alcuni altri utili particolarmente alla Geografia. </s></p><p type="main">

<s>Chi conosce l'indole di quell'uomo &egrave; ben persuaso ch'ei doveva es&shy;<lb/>sersi veramente incontrato ne'medesimi pensieri del Mersenno, senz'aver <lb/>letto il suo libro. </s>

<s>In questa tranquilla persuasione d'essere stato il primo <lb/>ad applicare i suoni alla misura delle distanze, rimase il Viviani anche dieci <lb/>e pi&ugrave; anni dopo avere scritta la sopra detta Nota, e ci&ograve; risulta non solo da <lb/>quel ch'egli afferm&ograve; <emph type="italics"/>suo essere il concetto dell'equabilit&agrave; de'suoni e de'loro <lb/>usi; suo il nuovo modo di misurare le distanze senza la vampa<emph.end type="italics"/> (MSS. <pb xlink:href="020/01/751.jpg" pagenum="194"/>Cim., T. X, c. </s>

<s>259), ma da quel che fece scrivere al Segretario degli Ac&shy;<lb/>cademici del Cimento, i quali accolsero l'esperienze del suono fatte nel se&shy;<lb/>condo periodo dell'Accademia medicea fra quelle particolarmente eseguite da <lb/>loro e descritte insiem colle altre nel loro Libro. </s>

<s>&Egrave; probabile per&ograve; che quelle <lb/>stesse esperienze fossero ripetute, e anzi abbiamo argomenti da dar ci&ograve; per <lb/>cosa certa, nella qual certezza occorre a notare che gli Accademici fioren&shy;<lb/>tini non fanno alcuna menzion del Mersenno, unicamente proponendosi, quasi <lb/>come programma a'loro studii, di verificar ci&ograve; che de'suoni aveva nelle Con&shy;<lb/>siderazioni sopra Diogene Laerzio scritto il Gassendi; programma che tro&shy;<lb/>vasi inserito nel T. XXIV, de'MSS. del Cimento, dove a carte 293, copiati <lb/>dalla detta Opera stampata la prima volta a Parigi nel 1646, si leggono i <lb/>passi seguenti: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Gassendus pag. </s>

<s>279 in Philosophia epicurea.<emph.end type="italics"/> Quod spectat ad mo&shy;<lb/>tum aeris ipsius a corpore usque sonante versus aurem tendentes, id per&shy;<lb/>mirum est: quaecumque sit tandem sive vehementia, sive remissio impetus, <lb/>quo a sonante exagitatur, translationem eius per spatium esse semper ae&shy;<lb/>quivelocem. </s>

<s>Siquidem constat experientia quoslibet sonos seu parvos, seu <lb/>magnos, in eodem loco excitatos aequali ferri tempore in eumdem locum e <lb/>quo exaudiuntur. </s>

<s>Id facile nempe observatur in sonis bellicorum tormento&shy;<lb/>rum uno, alterove, aut tribus passuum millibus dissitorum, dum adnotato <lb/>momento, quo creata simul cum sono flammula oculis apparet, numerantur <lb/>pulsus arteriae, aut itus reditusque chordulae pondere appenso, quousque <lb/>sonus ad aurem perveniat. </s>

<s>Deprehenduntur enim huiusmodi pulsus sive itus <lb/>ac reditus, qui aliunde sunt aequitemporanei, aequales esse numero, sive <lb/>sonus sit machinae ingentis, ut puta dicti <emph type="italics"/>Canonis,<emph.end type="italics"/> sive parvae ut vocati <lb/><emph type="italics"/>Mosqueti.<emph.end type="italics"/> Qua ratione porro id fiat insinuatur a Stoicis quatenus docent, ut <lb/>Plutarchus et Laertius memorant, aerem percussum quod continuus sit pe&shy;<lb/>rinde formari in orbeis ac placida aqua, lapide iniecto, formatur in circu&shy;<lb/>los. </s>

<s>Quippe haec in aqua circulorum formatio nihilo segnius aut velocius <lb/>fit, sed ad ripam usque pari tenore continuatur, seu lapis magnus seu par&shy;<lb/>vus sit, et seu magna vi seu parva incidat in aquam. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Ibidem subiungit pag. </s>

<s>280:<emph.end type="italics"/> Quo loco tacenda non est Mersenni no&shy;<lb/>stri observatio, qui velocitatem soni studiose emensus deprehendit ipsum <lb/>uno horae secundo pervadere ducentas triginta parisinas orgyas, seu hexa&shy;<lb/>podas, ac uno proinde minuto horae primo, seu sexagesima horae parte su&shy;<lb/>pra orgyarum quatordecim millia. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Idem ibidem:<emph.end type="italics"/> Mirabile aliud circa motum soni illud est quod nec <lb/>secundo flante vento acceleretur, neque adverso reflante retardetur, sed fe&shy;<lb/>ratur semper aequabiliter, sive aequali tempore ex eodem loco, in eumdem <lb/>perveniat. </s>

<s>Sed nempe et secundus ventus est incomparabiliter segnior sono <lb/>(ut vel ex nubibus segetumque vel ramorum in sylvis succedentibus moti&shy;<lb/>bus undulationibusque apparet) adeo ut promovere illum sensibiliter admo&shy;<lb/>dum non possit. </s>

<s>&rdquo; </s></p><p type="main">

<s>Tenendo a riscontro questi tre passi cos&igrave; trascritti con le descrizioni <pb xlink:href="020/01/752.jpg" pagenum="195"/>della prima e della seconda dell'esperienze fatte dagli Accademici del Ci&shy;<lb/>mento intorno ai movimenti del suono (Saggi ecc., Firenze 1841, pag. </s>

<s>156, 57) <lb/>si vede come, verificati in ogni altra parte i detti del Gassendi, lo trovarono <lb/>solamente falso in ci&ograve; ch'egli dice di avere osservato essere gl'increspa&shy;<lb/>menti equiveloci o cada naturalmente il sasso nell'acqua, o vengavi scagliato <lb/>con grandissima forza. </s>

<s>Ma nella Esperienza terza, sotto la quale si descri&shy;<lb/>vono le applicazioni della ugual velocit&agrave; del suono alla misura delle distanze, <lb/>si dice che il potersi far ci&ograve; <emph type="italics"/>cadde in animo a un nostro Accademico,<emph.end type="italics"/> in <lb/>occasione del verificarsi le sopraddette esperienze. </s>

<s>Ond'&egrave; chiaro di qui che <lb/>non solo il Viviani ma tutta l'Accademia era persuasa che quello del mi&shy;<lb/>surar le distanze per via de'suoni fosse un concetto nuovo, bench&egrave; a voler <lb/>esser giusti la novit&agrave; non consistesse in altro che nell'aver pensato a con&shy;<lb/>seguir quelle stesse misure anco quando, per l'interposizione di menti o di <lb/>altri ostacoli, non si potesse vedere la vampa, servendo a ci&ograve; di scala &ldquo; il <lb/>tempo che il suono pena a correre una distanza nota di un miglio trovato <lb/>da noi essere cinque minuti secondi &rdquo; (ivi, pag. </s>

<s>159). </s></p><p type="main">

<s>Gli Accademici fiorentini, cos&igrave; come il Mersenno prima di loro, avevano <lb/>ritrovate quelle misure pi&ugrave; o meno esatte per via di esperienze dirette, e <lb/>ci&ograve; fu come se avessero ricevuto un dono dalle braccia sporte della Natura. </s>

<s><lb/>Ma il Newton, con mirabile novit&agrave; d'esempio, consegu&igrave; quel medesimo dono <lb/>come parto ostetricato con le sue proprie mani dal pi&ugrave; intimo e fecondo <lb/>seno delle verit&agrave; naturali. </s></p><p type="main">

<s>Il principal fondamento di questa nuova e pellegrina speculazione &egrave; po&shy;<lb/>sto nel Teorema XXXVII del II Libro de'Principii matematici di Filosofia <lb/>naturale, cos&igrave; formulato: &ldquo; Pulsibus per fluidum progagatis, singulae fluidi <lb/>particulae, motu reciproco brevissimo euntes et redeuntes, accelerantur sem&shy;<lb/>per et retardantur pro lege oscillantis penduli &rdquo; (Genevae 1740, pag. </s>

<s>360). </s></p><p type="main">

<s>Cercar dunque il tempo di una pulsazione aerea e sonora si riduce pel <lb/>Newton a cercare il tempo dell'oscillazione di un pendolo di lunghezza <lb/>uguale all'altezza di un mezzo omogeneo, il peso di cui adegui il peso so&shy;<lb/>praincombente, e la densit&agrave; sia per tutto uguale a quella del mezzo stesso, <lb/>in che si fa la pulsazione. </s>

<s>&ldquo; Fingamus medium ab incumbente pondere pro <lb/>more aeris nostri comprimi, sitque A altitudo medii homogenei, cuius pon&shy;<lb/>dus adaequet pondus incumbens et cuius densitas eadem sit cum densitate <lb/>medii compressi, in quo pulsus propagantur. </s>

<s>Constitui autem intelligatur <lb/>pendulum cuius longitudo inter punctum suspensionis et centrum oscillatio&shy;<lb/>nis sit A.... &rdquo; (ibi, pag. </s>

<s>387). Supposto ci&ograve; e invocando il Teorema uge&shy;<lb/>niano relativo alle propriet&agrave; meccaniche della Cicloide, che cio&egrave; il tempo <lb/>della caduta per la perpendicolare &egrave; al tempo dell'oscillazione come il rag&shy;<lb/>gio del circolo alla circonferenza di lui, dimostra il Newton che &ldquo; quo tem&shy;<lb/>pore pendulum illud oscillationem integram ex itu et reditu compositam <lb/>peragit, eodem pulsus eundo conficiet spatium circumferentiae circuli radio A <lb/>descripti aequale &rdquo; (ibi) </s></p><p type="main">

<s>Per far poi l'applicazione di questi principii matematici al caso parti-<pb xlink:href="020/01/753.jpg" pagenum="196"/>colare dell'aria, in mezzo alla quale si diffondono i suoni, conveniva per <lb/>prima cosa trovar la lunghezza A del pendolo, ossia l'altezza di quell'aria <lb/>di uniforme densit&agrave; capace di comprimere quell'altra a s&egrave; sottoposta, che <lb/>supponesi dover esser messa in vibrazione sonora. </s>

<s>Essendo il peso specifico <lb/>dell'aria a quello del mercurio come 1:11,890 prossimamente, e l'altezza <lb/>media del mercurio nel tubo barometrico 30 digiti inglesi, la lunghezza del <lb/>pendolo che si cerca, o il raggio del cerchio si trova essere 356,700 di <lb/>que'digiti, ossia di piedi 29,725, e perci&ograve; la circonferenza da esso raggio de&shy;<lb/>scritta, piedi 186,768. &ldquo; Et cum pendulum digitos 39 1/5 longum oscillatio&shy;<lb/>nem ex itu et reditu compositam tempore minutorum duorum, uti notum <lb/>est, absolvat, pendulum pedes 29,725 seu digitos 356,700 longum oscillatio&shy;<lb/>nem consimilem tempore minutorum secundorum 190 1/4 absolvere debebit &rdquo; <lb/>(ibi, pag. </s>

<s>392). Dunque per il citato Teorema ugeniano: &rdquo; eo tempore so&shy;<lb/>nus progrediendo conficiet pedes 186,768, ideoque tempore minuti unius <lb/>secundi pedes 979 &rdquo; (ibi). </s></p><p type="main">

<s>Tale si &egrave; la velocit&agrave; del suono, supposto che sia l'aria sgombra d'estra&shy;<lb/>nee materie come di particelle solide o di vapori, e che rispetto all'elasticit&agrave; <lb/>rimanga sempre nella medesima costituzione. </s>

<s>Ma perch&egrave; un tal supposto, <lb/>dice il Newton, non si verifica mai, essendo volitanti per l'aria particelle <lb/>saline attraverso alle quali il suono si diffonderebbe in istante, calcola per&shy;<lb/>ci&ograve; un aumento di velocit&agrave; di 109 piedi all'incirca &ldquo; ob crassitudinem par&shy;<lb/>ticularum aeris, et sic sonus tempore minuti unius secundi conficiet pe&shy;<lb/>des 1088 circiter &rdquo; (ibi, pag. </s>

<s>393). Ci sono inoltre nell'aria disciolti i vapori <lb/>acquosi attraverso ai quali il suono propagasi pi&ugrave; veloce, e una tal maggiore <lb/>velocit&agrave; vien dal Newton calcolata in modo che la misura ultimamente de&shy;<lb/>finita vien ridotta a piedi 1142. </s></p><p type="main">

<s>A queste due nuove considerazioni, trascurate gi&agrave; dal Mersenno e dai <lb/>nostri Accademici fiorentini, i quali misurarono la velocit&agrave; de'suoni, non so&shy;<lb/>spettando che per variar delle condizioni ammosferiche si potessero in qual&shy;<lb/>che modo alterare, ne soggiunge il Newton una terza, ben assai pi&ugrave; impor&shy;<lb/>tante ed espressa da lui in questa forma: &ldquo; Haec ita se habere debent tem&shy;<lb/>pore verno et autumnali ubi aer per calorem temperatum rarescit et eius <lb/>vis clastica nonnihil intenditur. </s>

<s>At hyberno tempore, ubi aer per frigus con&shy;<lb/>densatur et eius vis elastica remittitur, motus sonorum tardior esse debet <lb/>in subduplicata ratione densitatis et vicissim aestivo tempore debet esse ve&shy;<lb/>locior &rdquo; (ibi, pag. </s>

<s>394). </s></p><p type="main">

<s>Dell'aumento di velocit&agrave; del suono prodotto dal trovarsi sollevati per <lb/>l'aria gli umidi vapori, e dal trovarvisi sempre in mezzo particelle solide <lb/>volitanti, non par che ne facessero troppo gran conto i Fisici, giudicando <lb/>cos&igrave; fatte avvertenze quasi come sottigliezze di matematica neutoniana. </s>

<s>Ma <lb/>quel che argutamente il Newton stesso avvertiva dover esser cio&egrave; la velo&shy;<lb/>cit&agrave; del suono maggiore nell'estate che nell'inverno persuadeva, per la buona <lb/>ragione del variabile elaterio dell'aria col variare della temperatura. </s>

<s>Lasciava <lb/>perci&ograve; l'Autore de'Principii di Filosofia naturale a verificar le sue dimo-<pb xlink:href="020/01/754.jpg" pagenum="197"/>strate proposizioni matematiche coll'esperienza, e non mancarono i Fisici di <lb/>ricorrere ai fatti per decider se veramente questi confermavano le ragioni. </s></p><p type="main">

<s>Pi&ugrave; solleciti di tutti fra coloro che dettero mano all'opera &egrave; naturale <lb/>che fossero gl'Inglesi, e il Flamsteed e l'Halley instituirono le loro espe&shy;<lb/>rienze in una campagna vicino a Londra. </s>

<s>Dietro a loro, dopo trent'anni, <lb/>mossi dal medesimo desiderio vi si provarono i Francesi, che scelsero a far <lb/>le opportune esperienze il La Caille, il Cassini giovane, e il Maraldi dal seno <lb/>della loro Accademia. </s>

<s>Notabile cosa &egrave; che Inglesi e Francesi non trovassero <lb/>differenza nella velocit&agrave; del suono o si diffondesse per l'aria caldissima del&shy;<lb/>l'estate o per la freddissima dell'inverno. </s></p><p type="main">

<s>Esperienze cos&igrave; solenni eseguite da tanto celebri sperimentatori erano <lb/>per far concludere che alle ragioni del Newton belle e buone in s&egrave; non ri&shy;<lb/>spondevano i fatti, quando un nostro Italiano ripensando sopra ci&ograve; conclu&shy;<lb/>deva non poter cause vere e reali essere inefficaci in produrre i loro effetti. </s>

<s><lb/>Persuaso perci&ograve; Lodovico Bianconi che l'esperienze degl'Inglesi e de'Fran&shy;<lb/>cesi dovevano essere in ogni modo o da qualsivoglia parte riuscite difettose, <lb/>volle egli stesso, aiutato da due suoi valentissimi amici, ripeterle con gran <lb/>diligenza ed ebbe il merito d'aver dimostrato per il primo che i fatti fisici <lb/>confermavano le verit&agrave; de'principii matematici neutoniani. </s></p><p type="main">

<s>L'esperienze furono dall'Autore stesso descritte in una lettera indiriz&shy;<lb/>zata a Scipione Maffei e che s'intitola <emph type="italics"/>Della diversa velocit&agrave; del suono.<emph.end type="italics"/> In&shy;<lb/>comincia in essa a far la storia delle tentate prove in proposito, incomin&shy;<lb/>ciando da quelle degli Accademici di Firenze, infino a quelle eseguitesi <lb/>presso Londra dal Flamsteed e dall'Halley, nel 1708, e alle altre nel 1738 <lb/>eseguitesi dal Cassini e dal Maraldi presso Parigi. </s></p><p type="main">

<s>&ldquo; Prima che a noi in Italia, soggiunge poi il nostro Bianconi, giun&shy;<lb/>gesse questa notizia che solo giunseci dopo la stampa degli Atti di quell'Ac&shy;<lb/>cademia, avendo io lette le Transazioni anglicane, vennemi voglia l'anno 1740 <lb/>di provare in Bologna alcune delle osservazioni che fecero a Londra, e spe&shy;<lb/>cialmente quella per cui dicono non aver essi trovato divario alcuno tra la <lb/>celerit&agrave; del suono nell'inverno e nell'estate. </s>

<s>Parevami strano che essendo <lb/>nel rigido freddo l'aria condensatissima, rispetto alla rarefazione che aver <lb/>dee nel caldo dell'estate; parevami strano, dico, che nessuna differenza do&shy;<lb/>vesse poi trovarsi nel suono, che dai di lei tremori &egrave; propagato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La stagione caldissima che gi&agrave; incominciava a farsi sentire, parve in&shy;<lb/>vitarmi a mettere all'opera il gi&agrave; divisato pensiero, cio&egrave; a provare quale <lb/>celerit&agrave; avesse il suono nell'estate per paragonarlo poi con quello che avrei <lb/>trovato nell'inverno venturo. </s>

<s>Eccole i luoghi che determinai per fare le os&shy;<lb/>servazioni: la fortezza urbana posta sulle frontiere del modanese fu l'uno, <lb/>l'altro fu il Convento dei Padri zoccolanti dell'Osservanza.... Pregati il si&shy;<lb/>gnor Eustachio Zanotti e il signor abate Petronio Matteucci, ambo astronomi <lb/>dell'Osservatorio nostro dell'Istituto ed amici miei ornatissimi, a venir meco <lb/>verso la sera al Convento stabilito, vi portammo un orologio astronomico a <lb/>cicloide che batteva esattissimamente i secondi.... Aspettavamo l'ora del <pb xlink:href="020/01/755.jpg" pagenum="198"/>primo strepito del cannone, giunto il quale .... incominciaronsi allora a con&shy;<lb/>tare i secondi, n&egrave; arriv&ograve; a noi il suono, prima che, contando, al sessante&shy;<lb/>simosesto non fossimo giunti. </s>

<s>Replicossi per quattro volte in quella sera l'os&shy;<lb/>servazione e in tutte vedemmo esser costante la celerit&agrave; del suono, ed <lb/>impiegare un minuto e sedici secondi esattissimi per venire dalla fortezza <lb/>urbana al Convento.... &rdquo; </s></p><p type="main">

<s>&ldquo; Altro pi&ugrave; non restavaci a fare che aspettar l'inverno, per replicare <lb/>in quella stagione le nostre osservazioni.... La notte precedente i sette di <lb/>Febbraio dell'anno 1741 fu la determinata da noi per le nostre esperienze.... <lb/>Tenendo tutti noi gli occhi immobili all'Occidente vedemmo, all'ora accor&shy;<lb/>data, il lampo del fuoco alla fortezza, nel qual momento cominciammo a nu&shy;<lb/>merare i secondi dell'orologio. </s>

<s>Questi non furono gi&agrave; sessantasei come l'anno <lb/>avanti, ma furono settanta otto e mezzo costantemente, per tutte quattro le <lb/>volte che replicossi l'esperienza.... Queste due osservazioni adunque, che <lb/>io le do per esattissime, dovrebbero farci credere esservi qualche divario tra <lb/>la velocit&agrave; del suono nell'estate e nell'inverno. </s>

<s>&rdquo; (Venezia 1746, pag. </s>

<s>82-90). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Come mai dalla sublime contemplazione delle armonie pitagoriche, d'onde <lb/>mosse il presente capitolo, siam, procedendo di discorso in discorso, caduti <lb/>ne'freddi calcoli matematici del Newton e nelle aride esperienze di Lodovico <lb/>Bianconi, potrebbe in chi a considerar ci&ograve; soffermasse il passo recare al&shy;<lb/>quanto di maraviglia, se non gli occorresse poi facilmente in pensiero che <lb/>anzi i numeri calcolati dal Matematico di Cambridge e sperimentati dal Fi&shy;<lb/>sico di Bologna mirabilmente confermano quelle speculazioni intorno ai nu&shy;<lb/>meri, nella ragion de'quali riconosceva il Filosofo antico le misteriose ori&shy;<lb/>gini dell'armonia. </s></p><p type="main">

<s>Ma in ogni modo il rimbombo de'cannoni e il fragor de'moschetti, in <lb/>mezzo ai quali s'&egrave; aggirata fin qui la nostra storia, sembrerebbe meglio che <lb/>suoni si dovessero dir dissonanze, e che avessero perci&ograve; quella relazione alle <lb/>vere armonie che le ombre hanno alla luce. </s>

<s>&Egrave; da risalir dunque su alla <lb/>storia di que'pitagorici musicali concenti, d'onde troppo affrettatamente siamo <lb/>discesi, quasi trasportati dietro a quell'onda che commoveva l'aria ne'disor&shy;<lb/>dinati fragori. </s></p><p type="main">

<s>Racconta Giamblico che passando un giorno Pitagora presso all'officina <lb/>di un fabbro ferraio, in sul punto che il maestro e i garzoni battevano il <lb/>ferro sull'incudine co'martelli menati con vicenda misurata di tempi, sof&shy;<lb/>fermasse ivi il piede e vi si trattenesse ad ascoltar quel semplice eppure ar&shy;<lb/>monioso concerto. </s>

<s>Pens&ograve; che la differenza de'suoni gravi ed acuti era fatta <lb/>dal differente peso degli stessi martelli, e gli cadde allora in animo di poter <lb/>per via di que'pesi ritrovar le leggi delle relazioni che passano tra le varie <pb xlink:href="020/01/756.jpg" pagenum="199"/>intensit&agrave; degl'impulsi sonori. </s>

<s>Ritrov&ograve; che il peso, il quale dava la nota di <lb/>chiave a quelli che davano la quarta, la quinta, e l'ottava era come 1 a 4/3, <lb/>a 3/2, a 2. Seguitando cos&igrave; a speculare pens&ograve; che la medesima legge doveva <lb/>pure verificarsi nelle corde, e pizzicatane una, che tirata da un certo peso <lb/>dava la chiave, trov&ograve; che riducendo quel peso a 4/3 a 3/2, al doppio si otte&shy;<lb/>nevano via via per ordine le varie altre note. </s></p><p type="main">

<s>La storia di Giamblico non ha punto aria di alcuna verosomiglianza, e <lb/>parrebbe anzi strano che da un principio falso, qual'&egrave; che tra'pesi de'mar&shy;<lb/>telli passino le riferite proporzioni colle note sonate dalle incudini, potess'es&shy;<lb/>ser condotto il Filosofo a una conclusione vera concernente le corde. </s>

<s>&Egrave; a <lb/>notar per&ograve; che la conclusione, alla quale fu condotto propriamente Pitagora, <lb/>non &egrave; quella che riferisce Giamblico, essendoch&egrave; le sopra riferite propor&shy;<lb/>zioni non passano fra i pesi tendenti le corde ma fra le lunghezze di esse <lb/>corde sonore. </s></p><p type="main">

<s>Apparisce in ogni modo di qui essere state antichissime le prime spe&shy;<lb/>culazioni intorno alla ragione degl'intervalli armonici, bench&egrave; poco pi&ugrave; oltre <lb/>si progredisse dagl'insegnamenti pitagorici e dalle prime scoperte nel lungo <lb/>decorrere di duemila anni. </s>

<s>Scriveva perci&ograve; il Keplero, poco dopo il comin&shy;<lb/>ciar del secolo XVII: &ldquo; Utcumque tamen antiqua sit cantus humani forma, <lb/>ex intervallis consonis vel concinnis composita, causae tamen intervallorum <lb/>latuerunt homines adeo ut ante Pythagoram ne quaererentur quidem, et <lb/>quaesitas per duo millia annorum, primus ego, nisi fallor, exactissime pro&shy;<lb/>feram &rdquo; (Harmonices mundi lib III, Lincii Austriae 1619, pag. </s>

<s>3). </s></p><p type="main">

<s>&Egrave; egli vero quel che il Kepler si lusingava cos&igrave; d'essere stato il primo <lb/>a trattar della teoria della Musica? </s>

<s>Convien per risponder con fondamento <lb/>alla domanda che si distingua una duplice teoria, essendo che la Musica si <lb/>pu&ograve; riguardare o in quanto &egrave; sentita nell'anima o in quanto &egrave; un effetto <lb/>del vibrar de'corpi secondo una legge determinata. </s>

<s>Trattar delle ragioni del&shy;<lb/>l'armonia musicale nel suggetto senziente &egrave; opera de'Filosofi speculativi, i <lb/>quali bench&egrave; sollevino i voli della mente sublimi, e largamente spaziino per <lb/>le aeree regioni, profitterebbero forse meglio contentandosi di dire che l'ar&shy;<lb/>monia nell'anima &egrave; una misteriosa estasi dell'intelletto dell'uomo e del&shy;<lb/>l'amore. </s>

<s>Ma non &egrave; troppo comune ai Filosofi la virt&ugrave; del tacere innanzi ai <lb/>misteri, n&egrave; ebbe questa virt&ugrave; nemmeno il Keplero, il quale avrebbe avuto <lb/>senza dubbio miglior ragion di credersi primo Autore di questa nuova Fi&shy;<lb/>losofia musicale, se avesse usato la Matematica e l'avesse fatta servire a il&shy;<lb/>lustrar le attente osservazioni de'fatti. </s>

<s>Ma la Matematica per lui, tutt'altro <lb/>ch'essere ancella dell'Armonia, &egrave; sorella di Lei nata dalla Divina Mente <lb/>Creatrice a un medesimo parto. </s></p><p type="main">

<s>Pubblicando nel 1596 per la prima volta il <emph type="italics"/>Mysterium Cosmographi&shy;<lb/>cum<emph.end type="italics"/> aveva asserito esser cinque le consonanze musiche, perch&egrave; cinque son <lb/>le consonanze geometriche rappresentate dalle cinque forme regolari de'corpi <lb/>solidi. </s>

<s>Vent'anni dopo, ne'V libri <emph type="italics"/>Armonices mundi<emph.end type="italics"/> annunziava di aver ri&shy;<lb/>dotte quelle consonanze a sette, essendo veramente sette e non pi&ugrave; le se-<pb xlink:href="020/01/757.jpg" pagenum="200"/>zioni armoniche di una corda armonica. </s>

<s>Una mente libera dall'amor de'si&shy;<lb/>stemi avrebbe incominciato a dubitar se la supposta corrispondenza fra le <lb/>note musicali e le figure geometriche era vera, ma il Keplero, tutt'altro che <lb/>mettere ombra di dubbio ne'principii, attribuisce a una allucinazione della <lb/>sua propria mente la variet&agrave; delle conclusioni, alle quali era venuto in quella <lb/>differenza di tempi. </s>

<s>Io ricercai da principio, egli dice, le consonanze nella <lb/>regolarit&agrave; delle figure solide, mentre invece conveniva cercarle nella rego&shy;<lb/>larit&agrave; geometrica delle figure piane. </s>

<s>&ldquo; Legat curiosus lector quae de his <lb/>sectionibus ante annos XXII scripsi in Mysterio Cosmographico, capite XII, <lb/>et perpendat quomodo fuerim illo loco hallucinatus super causis sectionum <lb/>et harmoniarum: perperam nisus eorum numerum et rationes deducere ex <lb/>numero quinque corporum regularium solidorum, cum verum sit hoc potius <lb/>tam quinque figuras solidas, quam harmonias musicas et chordae sectiones <lb/>communem habere originem ex figuris regularibus planis &rdquo; (ibi, pag. </s>

<s>27). </s></p><p type="main">

<s>Questo indirizzo puramente geometrico, preso in investigar le ragioni <lb/>dell'armonia, riusc&igrave; provvidamente benefico alla scienza, perch&egrave; condusse il <lb/>Keplero alla scoperta delle celebri leggi cosmografiche conosciute sotto il nome <lb/>di lui. </s>

<s>L'Acustica per&ograve; non ebbe uguale fortuna, anzi ella par come sementa <lb/>nata in ben disposto terreno, che poi intristisce aduggiata dalle fronde e sof&shy;<lb/>focata dalle spine. </s>

<s>Ma pur perch&egrave; udimmo dianzi il Keplero stesso asserir <lb/>che nessun altro prima di lui aveva investigata la causa de'musici intervalli, <lb/>ed egli promette di profferirla <emph type="italics"/>exactissime<emph.end type="italics"/> giova veder in che modo egli poi <lb/>riuscisse a mantenere le sue promesse. </s></p><p type="main">

<s>La questione intorno all'origine dell'Armonia propostasi a risolvere dal <lb/>Keplero &egrave; da lui stesso formulata al modo seguente: &ldquo; Unde existat illa <lb/>suavitas, quae auribus allabitur ex proportione vocum, qua suavitate conso&shy;<lb/>nantias definimus &rdquo; (ibi, pag. </s>

<s>14). E perch&egrave; dice che la questione non era <lb/>nuova, ma che anzi ella fu tra'Filosofi lungamente disputata, incomincia ad <lb/>esaminar le loro varie opinioni. </s>

<s>&ldquo; Qui ad materiam et motum elemontorum <lb/>inclinant, exemplum afferunt hoc per se quidem sane quam mirabile, quod <lb/>chorda pulsata chordam aliam non pulsatam secum in sonitum trahit, si <lb/>tensa fuerit sibi consone, dissone tensam immotam relinquit &rdquo; (ibi). </s></p><p type="main">

<s>Riconosce dunque il Keplero che la teoria de'suoni armonici ebbe i <lb/>suoi primi principi dalle osservazioni e dalle speculazioni di quel fatto sin&shy;<lb/>golare che cio&egrave; una corda immota spontaneamente si commove all'unisono <lb/>di un'altra corda fatta a lei vibrare da presso. </s>

<s>Gli Autori perci&ograve; che pre&shy;<lb/>corsero in questa nuova Filosofia all'Alemanno essendo que'che osservarono <lb/>e specularono intorno alla singolarit&agrave; di questo fatto, giova prima di tutto <lb/>che si ricerchi da noi chi fossero e che ne pensassero. </s></p><p type="main">

<s>I Musici e i Lituai chi sa quante volte avranno osservato che a sonar <lb/>la corda di uno strumento risonava all'unisono quella di un altro simile <lb/>strumento immoto, ma del diligente esame sperimentale del fatto uno de'pi&ugrave; <lb/>antichi documenti &egrave; quello forse che lasci&ograve; scritto nelle sue carte solitarie <lb/>Leonardo da Vinci. </s>

<s>&ldquo; Il colpo dato nella campana risponder&agrave; e mover&agrave; al-<pb xlink:href="020/01/758.jpg" pagenum="201"/>quanto una campana simile a s&egrave;, e la corda sonata di un liuto risponder&agrave; <lb/>e mover&agrave; un'altra simile corda di simile boce in un altro liuto, e questo <lb/>vedrai con porre una paglia sopra una corda simile alla sonata &rdquo; (Mollien <lb/>MSS. </s>

<s>A fol. </s>

<s>22 v.). </s></p><p type="main">

<s>N&egrave; Leonardo per&ograve; n&egrave; altri prima di lui si sa che speculassero la ra&shy;<lb/>gione del fatto, cos&igrave; bene sperimentato, e i Filosofi <emph type="italics"/>in libris<emph.end type="italics"/> se ne spaccia&shy;<lb/>vano assai facilmente attribuendolo a un'occulta e misteriosa virt&ugrave; di sim&shy;<lb/>patia. </s>

<s>Primo a toglier la bella esperienza da questo tenebroso regno e a <lb/>renderla alla luce filosofica fu il Fracastoro, il quale giusto nel trattar <emph type="italics"/>De <lb/>sympathia et antipathia rerum<emph.end type="italics"/> cos&igrave; scriveva: &ldquo; Unisonum aliud unisonum <lb/>commotat, quoniam quae similiter tensae sunt chordae consimiles aeris un&shy;<lb/>dationes, et facere et recipere natae sunt: quae vero dissimiliter sunt ten&shy;<lb/>sae non eisdem circulationibus natae sunt moveri, sed una circulatio aliam <lb/>impedit. </s>

<s>Ictus enim chordae est motus compositus ex duobus motibus, uno <lb/>quidem quo chorda pellitur ante, hoc est versus aeris circulationes, alio vero <lb/>qui retro fit, chorda redeunte sese ad situm proprium. </s>

<s>Si igitur mota una <lb/>chorda debet et alia moveri oportet ut in secunda talis proportio sit ut <lb/>undationes et circulationes aeris, quae impellunt et faciunt motum ante, non <lb/>impediant motum qui retro fit a chorda. </s>

<s>Quam proportionem solum eae <lb/>chordae habent quae etiam consimilem tensionem habent. </s>

<s>Quae vero dissi&shy;<lb/>milem sortitae sunt tensionem non sese commotant, quoniam dum secun&shy;<lb/>dus fit motus idest reditus chordae circulatio secunda illi obviat et se se <lb/>impediunt, unde nec motus fit ullus praeter primam impulsationem quae <lb/>insensibilis est &rdquo; (Opera omnia, Venetiis 1584, c. </s>

<s>66). </s></p><p type="main">

<s>O avesse o no veduto il Trattato del Fracastoro, si riscontr&ograve; molto da <lb/>presso nelle speculazioni di lui un altro eletto ingegno Italiano, consegnando <lb/>quelle sue solitarie speculazioni a carte manoscritte, che da non molti anni <lb/>in qua furon date alla luce. </s>

<s>Il titolo di quel Manoscritto, pubblicato dal Li&shy;<lb/>bri nel III Tomo della sua <emph type="italics"/>Histoire des Sciences math&eacute;matiques,<emph.end type="italics"/> &egrave; <emph type="italics"/>Medi&shy;<lb/>tatiunculae Guidi Ubaldi e Marchionibus Montis Sanctae Mariae de rebus <lb/>mathematicis.<emph.end type="italics"/> Fra quelle Meditaziuncule, parte scritte in latino e parte in <lb/>italiano, ve n'ha alcune che riguardano le propriet&agrave; delle corde sonore, dalle <lb/>quali propriet&agrave; cos&igrave; concludesi la soluzion del problema acustico data prima <lb/>dal Fracastoro: </s></p><p type="main">

<s>&ldquo; Di qui ancora si p&ograve; render ragione perch&egrave; causa se saranno due istru&shy;<lb/>menti vicini et habbino pi&ugrave; corde e posta una paglia sopra le corde di uno <lb/>e con l'altro si tocchi una corda si senta che quella corda dell'altro instru&shy;<lb/>mento che sar&agrave; unisono ad quella che si tocca suona ancor lei e le altre <lb/>non suonano, e questo potrebbe nascer da questo che l'aere della corda <lb/>ch'&egrave; sonata per la sua agitazione muove tutte le altre corde, ma perch&egrave; <lb/>quelle che non sono in unisono non possono ricevere il medesimo moto di <lb/>quella ch'&egrave; sonata, e quella ch'&egrave; in unisono lo p&ograve; ricevere, per&ograve; ancor ella <lb/>suona e le altre non suonano. </s>

<s>La paglia poi che se gli mette sopra fa che <lb/>movendosi la corda urta nella paglia spesso e si sente al suono. </s>

<s>Favorisce <pb xlink:href="020/01/759.jpg" pagenum="202"/>questa ragione che bisogna che gl'instrumenti siano fra loro vicini, che come <lb/>sono lontani non segue l'effetto &rdquo; (A Paris 1841, pag. </s>

<s>396). </s></p><p type="main">

<s>La spiegazione del Fracastoro &egrave; pi&ugrave; sottilmente condotta di questa di <lb/>Guidubaldo, il quale per&ograve; s'avvantaggia sopra l'altro per aver suggerita <lb/>l'esperienza che prova come i corsi e i ricorsi delle due corde sono isocroni <lb/>e non s'impediscono perci&ograve;, ma si secondano i moti. </s>

<s>&ldquo; Di qui &egrave; che due <lb/>corde in unisono vanno bene insieme e non si percotono fra loro, mentre <lb/>sonano, che nasce perch&egrave; hanno il medesimo moto nell'andare e tornare: <lb/>che se se ne scorda et muove una non sonano bene insieme, ma si perco&shy;<lb/>tono et urtano insieme l'una ed l'altra, perch&egrave; il moto dell'una non &egrave; come <lb/>il moto dell'altra, che per essere un moto pi&ugrave; veloce dell'altro &egrave; causa che <lb/>si urtano, come si sente per esperienza con due corde di leuto vicine &rdquo; (ivi, <lb/>pag. </s>

<s>395, 96). </s></p><p type="main">

<s>Non &egrave; presumibile che il Keplero avesse inteso di queste speculazioni <lb/>di Guidubaldo rimaste sconosciute al pubblico e non note forse che al solo <lb/>Galileo, il quale ebbe da giovane cos&igrave; intimo privato commercio d'idee col <lb/>Marchese del Monte. </s>

<s>Quando per&ograve; si pubblicarono i V libri <emph type="italics"/>Harmonices <lb/>mundi<emph.end type="italics"/> il libro unico <emph type="italics"/>De sympathia et antipathia rerum<emph.end type="italics"/> era da un mezzo <lb/>secolo di gi&agrave; pubblicato, e per la celebrit&agrave; dell'Autore &egrave; probabile che se <lb/>ne fosse diffusa la notizia anche in Germania. </s>

<s>In qualunque modo, propo&shy;<lb/>nendosi il Keplero di risolvere il problema <emph type="italics"/>quod chorda pulsata chordam <lb/>aliam non pulsatam secum in sonitum trahit si tensa fuerit sibi consone,<emph.end type="italics"/><lb/>cos&igrave; scrive come speculazione sua nuova, bench&egrave; di nuovo propriamente non <lb/>abbia che il rinnovato errore peripatetico delle specie immateriate, che si <lb/>diffondono dal corpo della corda: </s></p><p type="main">

<s>&ldquo; Cum igitur duarum chordarum fuerit eadem tensio, sic ut unisonum <lb/>reddere possint tunc sonus unius idest species immateriata corporis chor&shy;<lb/>dae constitutae in vibratione, delapsa a sua chorda ferit chordam alteram, <lb/>sicut si quis boatum edat versus Chelyn aut aliquod cavum eo boatu per&shy;<lb/>cutit id cavum facitque resonare chordas eius omnes. </s>

<s>Ferit autem illa vi&shy;<lb/>brationis species chordam alteram eodem rhytmo celeritatis quo movetur et <lb/>haec, quia aeque tensa; ut ita singuli ictus, in quos vibratio divisa esse in&shy;<lb/>telligitur, in singulas percussae alterius chordae cessiunculas perpetuo inci&shy;<lb/>dant. </s>

<s>Ita fit ut omnium maxime moveatur illa chorda quae ad unisonum <lb/>est tensa cum prima &rdquo; (Harmonices mundi lib. </s>

<s>cit., pag. </s>

<s>14). </s></p><p type="main">

<s>Conclude poi il Keplero questa sua speculazione dicendo: &ldquo; Haec mihi <lb/>videtur causa mirabilis huius experimenti: qui me foelicior est indagine <lb/>mentis ei palmam dabo &rdquo; (ibi, pag. </s>

<s>15). Ma la palma era gi&agrave; stata data un <lb/>mezzo secolo prima al Fracastoro, e all'Autore dell'Armonia del mondo com&shy;<lb/>peterebbe solo il merito di avere estesa la teoria fracastoriana anche alle <lb/>altre consonanze, se alcuni fatti di cui tra poco diremo non dimostrassero <lb/>essere stato pi&ugrave; giudizioso il Nostro in restringere, che l'Alemanno in al&shy;<lb/>largare cos&igrave; il campo alla speculazione. </s></p><p type="main">

<s>&ldquo; Movetur vero et illa chorda quae duplae est aut subduplae celerita-<pb xlink:href="020/01/760.jpg" pagenum="203"/>tis, quia duo vibrationis ictus in una chordae cessiuncula absolvuntur, et <lb/>sic semper ictus a priori tertius quisque congruit in unius cessiunculae <lb/>extremum. </s>

<s>Movetur denique et illa chorda nonnihil quae est sesquialterae <lb/>celeritatis, quia tres ictiunculae fiunt in duabus huius cessiunculis. </s>

<s>Sed iam <lb/>incipiunt invicem obviare crebrius illi ictus et hae cessiunculae seque mu&shy;<lb/>tuo impedire dum duo illius ictus a fine cessiunculae huius aberrant, unus <lb/>solus incidit congrue. </s>

<s>Quo occursu motus chordarum caeterarum sistitur non <lb/>secus ac si quis digitum vibratae admovisset &rdquo; (ibi, pag. </s>

<s>15). </s></p><p type="main">

<s>Le cose fin qui discorse somministrano gli argomenti da rispondere a <lb/>chi voleva sapere se avesse con ragione affermato il Keplero a proposito <lb/>della teoria fisica della Musica: <emph type="italics"/>primus ego ni fallor exactissime proferam.<emph.end type="italics"/><lb/>Giova nonostante, affinch&egrave; la risposta sia piena, tornare ancora sopra quella <lb/>distinzione che si faceva tra l'armonia nel sentimento o nel subietto, e l'ar&shy;<lb/>monia nelle cause naturali o nell'obietto: distinzione che poi corrisponde <lb/>all'altra fatta dallo stesso Keplero tra l'armonia <emph type="italics"/>quae est mentis opus,<emph.end type="italics"/> e <lb/>l'armonia <emph type="italics"/>quae Naturae elementorum materiaeque necessitate fiat.<emph.end type="italics"/></s></p><p type="main">

<s>Ma sia pure che fatta questa distinzione il Fracastoro e il Del Monte <lb/>abbian, risolvendo il problema delle consonanze a quel modo, colte le prime <lb/>palme: non &egrave; questo, dice il Keplero, il fondamento a ragionar delle cause <lb/>degl'intervalli musici e de'principii dell'Armonia. </s>

<s>&ldquo; Quid igitur? </s>

<s>Si celeri&shy;<lb/>tas chordae unius valet ad motum chordae alterius proportionatae quae, <lb/>quoad visum manet intacta, an non eaedem celeritates duarum chordarum <lb/>inter se valebunt ad titillationem auditus suavem, propterea quod is quo&shy;<lb/>dammodo uniformiter ab utraque chorda movetur, duoque ictus a duobus <lb/>sonis seu vibrationibus in idem momentum competunt? </s>

<s>Nequaquam vero, <lb/>inquam ego &rdquo; (ibi) perch&egrave; queste non son ragioni da sodisfare un profon&shy;<lb/>dissimo Filosofo. </s></p><p type="main">

<s>In ben pi&ugrave; recondite cause, prosegue a dire il Keplero, che nella soave <lb/>titillazion degli orecchi, consiste l'armonia. </s>

<s>Ella non risiede nel semplice <lb/>senso ma principalmente nell'intelletto, il quale allora percepisce e gusta le <lb/>melodie, quando le specie de'suoni immateriate si conformano alla regola&shy;<lb/>rit&agrave; di quelle geometriche figure sulle quali &egrave; condotta l'architettura del <lb/>Mondo. </s>

<s>I concerti musicali insomma son pel Keplero una soave espressione <lb/>e una sentita corrispondenza colla generale Armonia dell'Universo. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Erano a questo punto pervenute le speculazioni de'Filosofi alquanti <lb/>anni prima che Galileo rivolgesse intorno al medesimo soggetto i suoi stu&shy;<lb/>dii. </s>

<s>Il <emph type="italics"/>nequaquam vero<emph.end type="italics"/> del Keplero fu per lui come se non fosse pronun&shy;<lb/>ziato, e tenendo per profondissimi solamente coloro, che filosofano sopra i <lb/>fatti senza voler trascendere a ricercar le altissime ragioni, stabilisce i prin-<pb xlink:href="020/01/761.jpg" pagenum="204"/>cipii dell'armonia nelle teorie fisiche del Fracastoro. </s>

<s>Egli nelle appassite <lb/>membra del Medico veronese infonde cos&igrave; nuovo e lieto vigore di vita: </s></p><p type="main">

<s>&ldquo; Dico che non &egrave; la ragion prossima ed immediata della forma degl'in&shy;<lb/>tervalli musici la lunghezza delle corde, non la tensione, non la grossezza o <lb/>per meglio dire non il peso, ma s&igrave; ben la proporzione dei numeri delle vi&shy;<lb/>brazioni e percosse dell'onde dell'aria che vanno a ferire il timpano del <lb/>nostro orecchio, il quale esso ancora sotto le medesime misure di tempi vien <lb/>fatto tremare. </s>

<s>Fermato questo punto, potremo per avventura assegnare assai <lb/>congrua ragione onde avvenga che di essi suoni differenti di tuono alcune <lb/>coppie siano con gran diletto ricevute dal nostro sensorio, altre con minore, <lb/>ed altre ci feriscano con grandissima molestia; che &egrave; il cercare la ragione <lb/>delle consonanze pi&ugrave; o men perfette, e delle dissonanze. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La molestia di queste nascer&agrave;, credo io, dalle discordi pulsazioni di <lb/>due diversi tuoni, che sproporzionatamente colpeggiano sopra il nostro tim&shy;<lb/>pano, e crudissime saranno le dissonanze, quando i tempi delle vibrazioni <lb/>fossero incommensurabili.... Consonanti e con diletto ricevute saranno quelle <lb/>coppie di suoni, che verranno a percuotere con qualche ordine sopra il tim&shy;<lb/>pano, il quale ordine ricerca prima che le percosse fatte dentro all'istesso <lb/>tempo siano commensurabili di numero, acciocch&egrave; la cartilagine del timpano <lb/>non abbia a stare in un perpetuo tormento d'inflettersi in due diverse ma&shy;<lb/>niere per acconsentire e ubbidire alle sempre discordi battiture. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sar&agrave; dunque la prima e pi&ugrave; grata consonanza l'ottava, essendo che <lb/>per ogni percossa, che dia la corda grave su il timpano, l'acuta ne d&agrave; due, <lb/>talch&egrave; amendue vanno a ferire unitamente in una si e nell'altra no delle <lb/>vibrazioni della corda acuta, sicch&egrave; di tutto il numero delle percosse la met&agrave; <lb/>si accordano a battere unitamente, ma i colpi delle corde unisone giungono <lb/>sempre tutti insieme, e per&ograve; son come di una corda sola, n&egrave; fanno conso&shy;<lb/>nanza. </s>

<s>La quinta diletta ancora, attesoch&egrave; per ogni due pulsazioni della corda <lb/>grave l'acuta ne d&agrave; tre, dal che ne seguita che, numerando le vibrazioni <lb/>della corda acuta, la terza parte di tutte si accordano a battere insieme, cio&egrave; <lb/>due solitarie s'interpongono tra ogni coppia delle concordi, e nella Diates&shy;<lb/>saron se n'interpongon tre. </s>

<s>Nella seconda, cio&egrave; nel tuono sesquiottavo, per <lb/>ogni nove pulsazioni una sola arriva concordemente a percotere con l'altra <lb/>della corda pi&ugrave; grave; tutte l'altre sono discordi e con molestia ricevute <lb/>su il timpano e giudicate dissonanti dall'udito &rdquo; (Alb. </s>

<s>XIII, 106, 7). </s></p><p type="main">

<s>E perciocch&egrave; le speculazioni di Galileo intorno al vibrar delle corde so&shy;<lb/>nore ebbero occasione dallo studio delle propriet&agrave; de'pendoli, s'incontr&ograve; fa&shy;<lb/>cilmente in quell'elegantissimo pensiero di render visibile e dilettevole al&shy;<lb/>l'occhio quel che dilettevolmente percepisce l'udito, sospendendo palle di <lb/>piombo o altri simili gravi da tre fili di lunghezze diverse, ma tali che, nel <lb/>tempo che il pi&ugrave; lungo fa due vibrazioni, il pi&ugrave; corto ne faccia quattro e il <lb/>mezzano tre. </s>

<s>Rimossi tutti insieme i tre pendoli dal perpendicolo, e poi la&shy;<lb/>sciatigli andare, si vedr&agrave; un intrecciamento vago di essi fili con incontri <lb/>vari, ma tali che ad ogni quarta vibrazione del pi&ugrave; lungo tutti e tre arri-<pb xlink:href="020/01/762.jpg" pagenum="205"/>veranho al medesimo tempo unitamente, e da quello poi si partiranno rei&shy;<lb/>terando di nuovo lo stesso periodo. </s>

<s>La mistione di tali vibrazioni rappresen&shy;<lb/>tata cos&igrave; all'occhio &egrave; quella che fatta dalla corda rende all'udito l'ottava <lb/>con la quinta in mezzo (ivi, pag. </s>

<s>109, 10). </s></p><p type="main">

<s>Si diceva dianzi che questa teoria galileiana delle consonanze musiche <lb/>era quella derivata dalle dottrine del Fracastoro, le quali negavasi dal Ke&shy;<lb/>plero che potessero servir di fondamento a specular le ragioni altissime del&shy;<lb/>l'armonia. </s>

<s>Galileo, come abbiamo veduto, la pensava assai diversamente, e <lb/>anzi a noi sembra questo uno de'punti pi&ugrave; notabili che rivelano la varia <lb/>indole de'due grandissimi ingegni. </s>

<s>&Egrave; ragionevole dunque che quel fonda&shy;<lb/>mento non fosse trascurato dall'Autor de'Dialoghi intorno alle Due Scienze <lb/>Nuove, il quale perci&ograve;, prende le mosse a trattar della Musica fisica col ren&shy;<lb/>der ragione del maraviglioso problema della corda della cetera o del cim&shy;<lb/>balo, che nuove e fa realmente sonare quella non solo che all'unisono gli <lb/>&egrave; concorde, ma anco all'ottava e alla quinta. </s></p><p type="main">

<s>Udiamo come, dopo il Fracastoro, il Del Monte e il Keplero, torni Gali&shy;<lb/>leo a render la ragione di quel problema cos&igrave; maraviglioso. </s>

<s>&ldquo; Toccata la <lb/>corda, egli dice, comincia e continua le sue vibrazioni per tutto il tempo al&shy;<lb/>meno che da'nostri orecchi si sente durar la sua risonanza. </s>

<s>Queste vibra&shy;<lb/>zioni fanno vibrare e tremare l'aria che gli &egrave; appresso, i cui tremori e in&shy;<lb/>crespamenti si distendono per grande spazio e vanno a urtare in tutte le <lb/>corde del medesimo strumento, ed anco di altri vicini. </s>

<s>La corda, che &egrave; tesa <lb/>all'unisono con la tocca, essendo disposta a far le sue vibrazioni sotto il <lb/>medesimo tempo, comincia al primo impulso a muoversi un poco, e soprag&shy;<lb/>giungendogli il secondo, il terzo, il ventesimo e pi&ugrave; altri, e tutti negli ag&shy;<lb/>giustati e periodici tempi, riceve finalmente il medesimo tremore che la prima <lb/>tocca, e si vede chiarissimamente andar dilatando le sue vibrazioni giusto <lb/>allo spazio della sua motrice &rdquo; (ivi, pag. </s>

<s>101). </s></p><p type="main">

<s>I nostri lettori, in mente ai quali risuonano ancora le parole riferite di <lb/>sopra dal libro <emph type="italics"/>De sympathia et antipathia rerum,<emph.end type="italics"/> sentono che questa ga&shy;<lb/>lileiana teoria &egrave; una ripetizion fedelissima di quella del Fracastoro, bench&egrave; <lb/>in qualche parte notabilmente illustrata. </s>

<s>In quella fracastoriana spiegazione <lb/>infatti recava qualche difficolt&agrave; l'intendere come mai i cos&igrave; deboli impulsi <lb/>dell'onda aerea potessero aver virt&ugrave; di muovere una corda tesa con forza. </s>

<s><lb/>L'Autore aveva in qualche modo ovviato alla difficolt&agrave; col dire <emph type="italics"/>unde nec <lb/>motus fit ullus praeter primam impulsationem, quae insensibilis est;<emph.end type="italics"/> ma <lb/>queste parole avevano bisogno di spiegazione, che poi fu data da Galileo, il <lb/>quale ricorse a'principii della Meccanica, e all'esperienza de'pendoli per di&shy;<lb/>mostrar come debolissimi impulsi ripetuti possono accumular tanta forza da <lb/>mover qualunque peso. </s>

<s>&ldquo; Ad un pendolo, fa dire al Salviati, ancorch&egrave; grave <lb/>e posto in quiete, col solo soffiarvi dentro conferiremo noi moto a moto assai <lb/>grande col reiterare i soffi, ma sotto il tempo che &egrave; proprio quel delle sue <lb/>vibrazioni. </s>

<s>Che se al primo soffio l'avremo rimosso dal perpendicolo mezzo <lb/>dito, aggiungendogli il secondo dopo che, sendo ritornato verso noi, comin-<pb xlink:href="020/01/763.jpg" pagenum="206"/>cerebbe la seconda vibrazione, gli conferiremo nuovo moto, e cos&igrave; successi&shy;<lb/>vamente con altri soffi, ma dati a tempo e non quando il pendolo ci viene <lb/>incontro, che cos&igrave; gl'impediremo e non aiuteremo il moto, e seguendo con <lb/>molti impulsi gli conferiremo impeto tale, che maggior forza assai che quella <lb/>d'un soffio ci bisogner&agrave; a cessarlo &rdquo; (ivi, pag. </s>

<s>100, 1). </s></p><p type="main">

<s>Cos&igrave; Galileo si godeva il merito di aver posta in sicuro da tutte le dif&shy;<lb/>ficolt&agrave; la dottrina del Fracastoro, e di aver perci&ograve; pi&ugrave; compiutamente di <lb/>tutti risoluto il maraviglioso problema del risonar delle corde non tocche, <lb/>quando rigidi censori lo colsero in contradizione con s&egrave; medesimo e lo ac&shy;<lb/>cusarono d'incauto nell'aver segu&igrave;to gli esempi del Keplero, il quale volle <lb/>estendere la spiegazione fracastoriana non all'unisono solo, ma a tutte le <lb/>altre consonanze. </s></p><p type="main">

<s>&ldquo; ABC, dice uno di questi censori, sia lo spazio che corre la vibra&shy;<lb/>zione della corda grave d'un'ottava mossa da A (fig. </s>

<s>55) e B ne sia il punto <lb/><figure id="id.020.01.763.1.jpg" xlink:href="020/01/763/1.jpg"/></s></p><p type="caption">

<s>Figura 55.<lb/>di mezzo, cio&egrave; quello che la parte in <lb/>due met&agrave;. </s>

<s>Similmente DE sia lo spa&shy;<lb/>zio che corre la vibrazione della corda <lb/>acuta della medesima ottava, e D sia <lb/>il punto di mezzo ond'ella &egrave; mossa. </s>

<s>Facciamo ora che nel medesimo istante <lb/>si muovano a far le loro vibrazioni i punti A, D e discorriamo cos&igrave;: Men&shy;<lb/>tre A va in B, D viene in E e riceve a seconda la sospinta e l'impulso fa&shy;<lb/>vorevole d'A. </s>

<s>Ma mentre B prosegue il suo andare in C non torna E in D? <lb/>e nello scontrarsi che fanno in que'lor due moti contrarii non si cozzano? </s>

<s><lb/>non si urtano insieme l'aria BC con la corda ED? &rdquo; (Bartoli, Del suono, <lb/>Roma 1679, pag. </s>

<s>161). </s></p><p type="main">

<s>Se fosse stata fatta una simile interrogazione a Galileo in persona avrebbe <lb/>dovuto confessare che cos&igrave; dee n&egrave; pi&ugrave; n&egrave; meno avvenire in due corde, una <lb/>del&igrave;e quali fosse tesa all'ottava, essendo questo proprio il caso de'soffi dati <lb/>ad un pendolo non a tempo, ma quando il pendolo stesso ci viene incon&shy;<lb/>tro, <emph type="italics"/>che cos&igrave; gl'impediremo e non aiuteremo il moto.<emph.end type="italics"/> E perch&egrave; lo stesso <lb/>ragionamento di quel censore, pu&ograve; applicarsi a tutte le altre consonanze, &egrave; <lb/>perci&ograve; che Galileo medesimo da s&egrave; confessa non potersi applicare il princi&shy;<lb/>pio de'piccoli urti accumulati a muover le corde tese, non verificandosi il <lb/>caso di cos&igrave; fatti accumulamenti altro che nell'unisono. </s>

<s>Di qui si prese oc&shy;<lb/>casion d'ammirare l'accortezza del Fracastoro, che giusto al solo unisono <lb/>ristrinse la sua spiegazione, e s'ebbe giusto motivo di tacciar d'inconsiderati <lb/>il Keplero e Galileo, i quali estendendo quella spiegazione all'Ottava e alla <lb/>Quinta non si avvidero come ci&ograve; non poteva farsi, perch&egrave; contradiceva a quel <lb/>verissimo principio e a quella sicura norma posta gi&agrave; dal medesimo Fracastoro, <lb/>e ne'Dialoghi galileiani sperimentalmente confermata: <emph type="italics"/>oportet ut quae im&shy;<lb/>pellunt et faciunt motum ante non impediant motum qui retro fit a chorda.<emph.end type="italics"/></s></p><p type="main">

<s>Sopra il Keplero e il Galileo rimaneva cos&igrave; salvo'dalle censure il solo <lb/>Fracastoro, quando avventati i colpi anche contro a lui cadde travolgendo <lb/>pi&ugrave; abbasso nella sua propria ruina anche gli altri due grandi, che gli gia-<pb xlink:href="020/01/764.jpg" pagenum="207"/>cevan di sotto. </s>

<s>I colpi venivano avventati da que'medesimi contradittori del <lb/>Grimaldi, i quali come dicemmo reputando che i leggerissimi increspamenti <lb/>di un'onda sonora non potessero aver momento alcuno di forza in un corpo <lb/>solido, negavano perci&ograve; che la causa del risonar una corda non tocca, ri&shy;<lb/>siedesse negli urti dell'aria messa in moto da una simile altra corda so&shy;<lb/>nata. </s>

<s>Cotesti contradittori nel proporsi a risolvere il maraviglioso problema, <lb/>risoluto con s&igrave; gran compiacenza dal Keplero e da Galileo, piuttosto che alle <lb/>speculazioni ebbero fede nelle esperienze, le quali rivelarono tosto a loro <lb/>questo fatto importante: che cio&egrave; una corda vibrata non fa risonar l'altra <lb/>corda non tocca se non che in certe particolari condizioni, in che par che <lb/>vogliano trovarsi collocati i due strumenti. </s></p><p type="main">

<s>&ldquo; Temperate dunque all'unisono due eccellenti chitarre spagnuole (dice <lb/>quel solito contradittore citato poco avanti) e posate con quel loro fondo <lb/>piano sopra una tavola in competente distanza, seguiva indubitatamente il <lb/>tremar delle corde dell'una in toccando quelle dell'altra. </s>

<s>Ci&ograve; fatto le por&shy;<lb/>tai a posare, con la medesima distanza fra loro, sopra non mi ricordo se <lb/>una coltre o che che altro si fosse, solamente che cosa soffice e morbidis&shy;<lb/>sima, e quivi rifatta la sperienza del toccare le corde dell'una trovai che <lb/>quelle dell'altra, che giacendo sopra la tavola eran s&igrave; vive al muoversi e <lb/>s&igrave; spiritose al guizzare, ora si stavano insensibili e immobili come morte, n&egrave; <lb/>mai segu&igrave; altramente se non solo al far che le chitarre si toccassero l'una <lb/>l'altra &rdquo; (ivi, pag. </s>

<s>165). </s></p><p type="main">

<s>Se ne volle inferir da questa, e da simili altre esperienze tutte istituite <lb/>a tal proposito, che il pulsar di una corda non si comunica all'altra per <lb/>l'intermedio dell'aria, ma de'corpi solidi interposti, i quali intanto trasmet&shy;<lb/>tono il moto, in quanto son atti a vibrare a tenor del corpo risonante a cui <lb/>sono congiunti. </s>

<s>La conclusione par che non si possa negare se l'esperienze <lb/>son vere. </s>

<s>Or chi pu&ograve; mettere in dubbio che il fatto delle due chitarre non <lb/>avvenga propriamente a quel modo che l'Autor lo descrive? </s>

<s>Riscontra dal&shy;<lb/>l'altra parte con questa l'esperienza degli Accademici fiorentini, bench&egrave; <lb/>instituita ad intento alquanto diverso. </s>

<s>&ldquo; Si messero due Viole in ugual di&shy;<lb/>stanza da una di mezzo e tutte collocate orizzontalmente. </s>

<s>Indi accordate tutte <lb/>all'unisono, data un'arcata a quella di mezzo, si osserv&ograve; in qual distanza <lb/>risonassero l'altre due, per via del tremolio di un ballerino di paglia acca&shy;<lb/>vallato ad una delle loro corde. </s>

<s>Si fece questa esperienza la prima volta in <lb/>una stanza terrena in volta, e si trov&ograve; che toccatane una ne rispondeva <lb/>un'altra in distanza di braccia sette. </s>

<s>Trasportate poi in un giardino all'aria <lb/>aperta, lontane poco pi&ugrave; di un braccio non si movevano &rdquo; (Targioni, Noti&shy;<lb/>zie cit., T. II, P. II, pag. </s>

<s>564). </s></p><p type="main">

<s>Or &egrave; chiaro di qui che se fosse veramente l'aria il mezzo della tra&shy;<lb/>smissione de'moti avrebbero dovuto le due viole risonar meglio all'eperto <lb/>che non nel chiuso di una stanza, dove segu&igrave; l'effetto perch&egrave; furono i due <lb/>strumenti posati sopra una medesima tavola, mentre nel giardino si tenevan <lb/>sospesi a'rami degli alberi o alle stecche di qualche pergolato. </s></p><pb xlink:href="020/01/765.jpg" pagenum="208"/><p type="main">

<s>Aveva anche Galileo avvertito che quell'ondeggiamento che si va di&shy;<lb/>stendendo per l'aria muove e fa vibrare non solamente le corde, ma qual&shy;<lb/>sivoglia altro corpo disposto a tremare e vibrarsi sotto quel tempo della tre&shy;<lb/>mante corda, ma l'esperienza ch'egli adduce per provar ci&ograve; o &egrave; mal descritta <lb/>o &egrave; un inganno. </s>

<s>&ldquo; Se si ficcheranno, egli dice, nelle sponde dello strumento <lb/>diversi pezzetti di setole o di altre materie flessibili, si vedr&agrave; nel suonare il <lb/>cimbalo tremare or questo or quel corpuscolo, secondo che verr&agrave; toccata <lb/>quella corda, le cui vibrazioni van sotto il medesimo tempo: gli altri non <lb/>si muoveranno al suono di questa corda, n&egrave; quella tremer&agrave; al suono d'altra <lb/>corda &rdquo; (Alb. </s>

<s>XIII, 102). </s></p><p type="main">

<s>Or com'&egrave; a credere che un corpo flessibile e lasso, n&egrave; perci&ograve; disposto <lb/>a risentirsi in que'leggeri e velocissimi tremori, in ch'entran le corde so&shy;<lb/>nore, possa mettersi in misurata danza con queste? </s>

<s>Se una setola si vedeva <lb/>vibrare sonando una corda, ci&ograve; doveva essere, senza dubbio, per aver qual&shy;<lb/>che comunicazione diretta colla corda stessa, cosicch&egrave; quello che a Galileo <lb/>sembrava un effetto acustico di risonanza non era altro in verit&agrave; che un <lb/>gioco meccanico. </s>

<s>In qualunque modo non solo il Bartoli (Del suonc cit., <lb/>pag. </s>

<s>135) ma altri forse pi&ugrave; valenti di lui provatisi a ripetere l'esperienza <lb/>galileiana, trovarono che non seguiva come non era possibile che ne seguisse <lb/>l'effetto. </s></p><p type="main">

<s>E perch&egrave; il risonar di una corda non tocca e tesa all'unisono di un'al&shy;<lb/>tra corda sonata fu esperienza spontaneamente in fin dai tempi pi&ugrave; antichi <lb/>offerta dal caso, si pu&ograve; dir che questa della setola infilata nelle sponde del <lb/>cimbalo &egrave; la prima fra l'esperienze che siano state fatte a studio, e in che <lb/>s'incontri la storia dell'Acustica. </s>

<s>La poca precisione di lei sarebbe non lieto <lb/>augurio ai progressi della scienza, se non pensassimo che a que'tempi, e <lb/>particolarmente negli istituti galileiani, l'arte sperimentale era in que'suoi <lb/>primi principii cos&igrave; ancora inesperta, da non valere a scoprir nuove verit&agrave; <lb/>ma da servir di qualche riscontro piuttosto che di conferma a quelle che <lb/>s'erano speculate gi&agrave; per ragion matematica. </s></p><p type="main">

<s>Tornan perci&ograve; quegli infausti auguri scongiurati dal ripen&sacute;ar che l'Acu&shy;<lb/>stica &egrave; fondata meglio nelle matematiche ragioni che nell'esperienze de'fatti, <lb/>ond'avvenne che Galileo riusc&igrave; a promuoverla indipendentemente da quelle <lb/>pi&ugrave; difficili e pi&ugrave; gelose esperienze, le quali se talvolta sono a studio invo&shy;<lb/>cate per conferma o riscontro delle matematiche conclusioni, riescono in Ga&shy;<lb/>lileo stesso, come, oltre al citato, dimostreranno altri esempii, immaginarie <lb/>e tutt'affatto ideali. </s></p><p type="main">

<s>A mostrar d'onde Galileo incominciasse a promovere questa importan&shy;<lb/>tissima parte della scienza de'suoni giova prima vedere fino a che punto <lb/>l'avessero lasciata i suoi predecessori da'pi&ugrave; antichi infino al Keplero. </s>

<s>Che <lb/>i suoni acuti dipendessero dal pi&ugrave; veloce vibrar delle corde, e che dal loro <lb/>pi&ugrave; lento moto si producessero i suoni gravi, fu dottrina universalmente <lb/>conosciuta perch&egrave; trasmessa dagl'insegnamenti concordi di Aristotile e di <lb/>Platone, dal Timeo del quale quasi come aforismo citavasi la sentenza: <emph type="italics"/>Mo-<emph.end type="italics"/><pb xlink:href="020/01/766.jpg" pagenum="209"/><emph type="italics"/>tio quidem velox acuta provenit, tarda gravis.<emph.end type="italics"/> Il facile uso poi del Mono&shy;<lb/>cordo, nel quale si poteva a piacere far vibrare una parte sola di tutta la <lb/>corda, e da un musico orecchio apprezzarsene il vario suono ch'ella ren&shy;<lb/>deva, fece riconoscere che dimezzata la corda stessa rendeva l'ottava, e dette <lb/>modo a congetturare che la ragione di ci&ograve; consistesse nella velocit&agrave; raddop&shy;<lb/>piata. </s>

<s>Di qui &egrave; che ripetevasi come altro aforismo quel di Boezio nel libro IV <lb/><emph type="italics"/>De harmonia: Dimidia in quantitate duplex est in acumine,<emph.end type="italics"/> e sotto altra <lb/>forma dicevasi <emph type="italics"/>l'ottava esser contenuta dalla dupla.<emph.end type="italics"/></s></p><p type="main">

<s>Ma le variet&agrave; del suono fatte dalle corde, secondo il variar del peso che <lb/>le tende e della loro propria gravezza, rimasero appresso tutti prima di Ga&shy;<lb/>lileo inconsiderate. </s>

<s>Solo Guidubaldo del Monte avvertiva, nelle citate sue <lb/><emph type="italics"/>Meditaziuncule,<emph.end type="italics"/> che di due corde ugualmente lunghe e ugualmente tese <lb/>quella che d&agrave; il suono pi&ugrave; acuto &egrave; la pi&ugrave; leggera, ma egli non sa con qual <lb/>legge voglia quella leggerezza esser variamente dispensata. </s>

<s>&ldquo; Le corde ti&shy;<lb/>rate ugualmente, quella ch'&egrave; pi&ugrave; leggera fa il suono pi&ugrave; acuto essendo lun&shy;<lb/>ghe ugualmente, come per esperienza si prova una corda di ottone o ac&shy;<lb/>ciaro ed una di leuto, alle quali se gli pu&ograve; attaccar due pesi eguali, essendo <lb/>gl'intervalli eguali, se quella di leuto sar&agrave; pi&ugrave; leggera ancorch&egrave; pi&ugrave; grossa <lb/>dell'altra, far&agrave; il suono pi&ugrave; acuto. </s>

<s>La ragione &egrave; che percotendole tutte due <lb/>quella pi&ugrave; leggera riceve il moto pi&ugrave; veloce nell'andare e tornar che fa la <lb/>corda e per&ograve; fa il suono pi&ugrave; acuto &rdquo; (Libri, <emph type="italics"/>Histoire<emph.end type="italics"/> ecc. </s>

<s>loc. </s>

<s>cit., pag. </s>

<s>395). </s></p><p type="main">

<s>Il Keplero appositamente riserba il cap. </s>

<s>II del libro III <emph type="italics"/>Harmonices <lb/>mundi<emph.end type="italics"/> a trattar <emph type="italics"/>De sectione harmonica chordae,<emph.end type="italics"/> ma contento solo a ma&shy;<lb/>tematicar le dottrine di Boezio sull'armonia non tocca poi nulla che con&shy;<lb/>cerna il vario vibrar delle corde stesse al variar loro il peso o la tensione. </s></p><p type="main">

<s>Galileo fu dunque il primo ad avvertir che la formula di Boezio, <emph type="italics"/>dimi&shy;<lb/>dia in quantitate duplex est in acumine,<emph.end type="italics"/> se non addirittura falsa era in <lb/>ogni modo in s&egrave; difettosa, perch&egrave; l'acume non varia solamente al variare <lb/>della lunghezza, ma e del peso e della trazione, e varia altres&igrave; con legge <lb/>diversa, la quale non &egrave; del doppio ma del quadruplo, cosicch&egrave;, a voler che <lb/>una corda tesa renda l'ottava pi&ugrave; acuta, convien tirarla non con un peso <lb/>doppio ma quadruplo, come del quadruplo e non del semplice doppio &egrave; pur <lb/>necessario l'alleggerirla. </s>

<s>E per usare il linguaggio de'Fisici moderni Gali&shy;<lb/>leo fu il primo a dimostrar che le tensioni variavano direttamente e i pesi <lb/>inversamente come i quadrati. </s>

<s>Ma giova udire in qual forma propria espo&shy;<lb/>nesse Galileo stesso le leggi da s&egrave; prima scoperte intorno al vario risonar <lb/>delle corde. </s></p><p type="main">

<s>&ldquo; Stetti lungo tempo perplesso, egli dice per bocca del suo caro Sa&shy;<lb/>gredo, intorno a queste forme delle consonanze, non mi parendo che la ra&shy;<lb/>gione che comunemente se ne adduce dagli Autori, che sin qui hanno scritto <lb/>dottamente della Musica, fosse concludente abbastanza. </s>

<s>Dicono essi la Dia&shy;<lb/>pason, cio&egrave; l'ottava, esser contenuta dalla doppia, la Diapente, che noi di&shy;<lb/>ciamo la quinta, dalla sesquialtera, perch&egrave; distesa sopra il Monocordo una <lb/>corda, sonandola tutta e poi sonandone la met&agrave;, col mettere un ponticello <pb xlink:href="020/01/767.jpg" pagenum="210"/>in mezzo, si sente l'ottava, e se il ponticello si metter&agrave; al terzo di tutta la <lb/>corda, toccando l'intera e poi li due terzi, ci rende la quinta; per lo che <lb/>l'ottava dicono esser contenuta tra il due e l'uno, e la quinta tra il tre <lb/>e il due. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Questa ragione, dico, non mi pareva concludente per poter assegnare <lb/>iuridicamente la dupla e la sesquialtera per forme naturali della Diapason <lb/>e della Diapente; e il mio motivo era tale: Tre sono le maniere colle quali <lb/>noi possiamo inacutire il tuono a una corda; l'una &egrave; lo scorciarla, l'altra <lb/>il tenderla pi&ugrave;, o vogliam dir tirarla, il terzo &egrave; l'assottigliarla. </s>

<s>Ritenendo la <lb/>medesima tiratezza e grossezza della corda, se vorremo sentir l'ottava, bi&shy;<lb/>sogna scorciarla la met&agrave;, cio&egrave; toccarla tutta e poi mezza. </s>

<s>Ma se ritenendo <lb/>la medesima lunghezza e grossezza vorremo farla montare all'ottava col ti&shy;<lb/>rarla pi&ugrave;, non basta tirarla il doppio pi&ugrave; ma ci bisogna il quadruplo, sic&shy;<lb/>ch&egrave; se prima era tirata dal peso d'una libbra converr&agrave; attaccarvene quattro <lb/>per inacutirla all'ottava. </s>

<s>E finalmente, se stante la medesima lunghezza e <lb/>tiratezza vorremo una corda che per esser pi&ugrave; sottile renda l'ottava, sar&agrave; <lb/>necessario che ritenga solo la quarta parte della grossezza dell'altra pi&ugrave; <lb/>grave. </s>

<s>E questo che dico dell'ottava, cio&egrave; che la sua forma presa dalla ten&shy;<lb/>sione o dalla grossezza della corda &egrave; in duplicata proporzione di quella che <lb/>si ha dalla lunghezza, intendasi di tutti gli altri intervalli musici &rdquo; (Alb. </s>

<s><lb/>XIII, 102, 3). </s></p><p type="main">

<s>Co&mgrave;e riuscisse Galileo a scoprir questa legge ei lo tace, perch'era fa&shy;<lb/>cile argomentare non poter essergli aperta altra via da quella in fuori del&shy;<lb/>l'esperienza: e lo tace anche forse perch&egrave; il comune uso che facevasi del <lb/>Monocordo rendeva non difficile a chi avesse saputo usarvi qualche diligenza <lb/>quelle stesse esperienze. </s>

<s>Ben pi&ugrave; difficile era il dimostrar quel principio fon&shy;<lb/>damentale, che s'ammetteva da tutti per congettura e che consisteva in ci&ograve; <lb/>che nell'ottava pi&ugrave; acuta sia raddoppiato il numero delle vibrazioni che fa <lb/>la corda. </s>

<s>In che modo infatti sarebb'egli stato possibile riscontrar quel nu&shy;<lb/>mero a que'tempi, quando la <emph type="italics"/>Ruota<emph.end type="italics"/> del Savart, e la <emph type="italics"/>Sirena<emph.end type="italics"/> del Cagnard&shy;<lb/>Latour erano ancora lontane quasi due secoli? </s>

<s>Eppure Galileo cred&egrave; d'es&shy;<lb/>ser riuscito il primo a dimostrare ci&ograve; per l'esperienza volgarissima del <lb/>bicchier pieno d'acqua, fregati gli orli col polpastrello del dito, facendo os&shy;<lb/>servar com'accadendo talvolta che il tuono salti all'ottava si vedon nel&shy;<lb/>l'istante le onde dell'acqua dividersi in due. </s>

<s>&ldquo; Ma perch&egrave; il numerare le <lb/>vibrazioni d'una corda, che nel render la voce le fa frequentissime, &egrave; del <lb/>tutto impossibile, sarei, dice Galileo, restato sempre ambiguo se vero fosse <lb/>che la corda dell'ottava pi&ugrave; acuta facesse nel medesimo tempo doppio nu&shy;<lb/>mero di vibrazioni di quelle della pi&ugrave; grave, se le onde permanenti per <lb/>quanto tempo ei piace nel far sonare e vibrare il bicchiere non m'avessero <lb/>sensatamente mostrato come, nell'istesso momento che alcuna volta si sente <lb/>il tuono saltare all'ottava, si vedono nascere altre onde pi&ugrave; minute, le quali <lb/>con infinita pulitezza tagliano in mezzo ciascuna di quelle prime &rdquo; (ivi, <lb/>pag. </s>

<s>104). </s></p><pb xlink:href="020/01/768.jpg" pagenum="211"/><p type="main">

<s>Fu provato da alcuni a ripetere questa esperienza di Galileo e segu&igrave; a <lb/>loro quel ch'era segu&igrave;to al Bartoli; segu&igrave; cio&egrave; che alla descrizione galileiana <lb/>non si videro punto corrispondere i fatti osservati. </s>

<s>Intorno al circuito inte&shy;<lb/>rior del bicchiere non si osserva altro che una fascia o ghirlanda di crespe <lb/>da non si saper a chi altro meglio rassomigliarle che ai processi ciliari che <lb/>stanno intorno al cristallino dell'occhio &rdquo; (De'suoni cit., pag. </s>

<s>140). </s></p><p type="main">

<s>Forse meno ideale e immaginaria di questa &egrave; l'altra esperienza che ivi <lb/>appresso soggiungesi delle virgolette rimaste incise sopra una lamina metal&shy;<lb/>lica raschiata collo strisciarvi sopra velocemente la punta di uno scarpello. <lb/></s>

<s>&ldquo; L'invenzione fu del caso e mia, fa dire Galileo al Salviati, fu solamente <lb/>l'osservazione e il far di essa capitale e stima come di riprova di nobil con&shy;<lb/>templazione ancorch&egrave; fattura in s&egrave; stessa assai vile. </s>

<s>Raschiando con uno <lb/>scarpello di ferro tagliente una piastra di ottone per levarle alcune macchie, <lb/>nel muovervi sopra lo scarpello con velocit&agrave;, sentii una volta e due tra molte <lb/>strisciate fischiarne e uscirne un sibilo molto gagliardo e chiaro, e guar&shy;<lb/>dando sopra la piastra vidi un lungo ordine di virgolette sottili tra di loro <lb/>parallele e per egualissimi intervalli l'una dall'altra distanti. </s>

<s>Tornando a <lb/>raschiar di nuovo pi&ugrave; e pi&ugrave; volte, mi accorsi che solamente nelle raschiate <lb/>che fischiavano lasciava lo scarpello le intaccature sopra la piastra, ma <lb/>quando la strisciata passava senza sibilo, non restava pur minima ombra di <lb/>tali virgolette. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Replicando poi altre volte lo scherzo, strisciando ora con maggiore <lb/>ed ora con minore velocit&agrave;, il sibilo riusciva di tuono or pi&ugrave; acuto ed or <lb/>pi&ugrave; grave, ed osservai i segni fatti nel suono pi&ugrave; acuto esser pi&ugrave; spessi, e <lb/>quelli del pi&ugrave; grave pi&ugrave; radi, e talora ancora, secondo che la strisciata me&shy;<lb/>desima era fatta verso il fine con maggiore velocit&agrave; che nel principio, si <lb/>sentiva il suono andarsi inacutendo, e le virgolette si vedeva essere andate <lb/>inspessendosi, ma sempre con estrema lindura e con assoluta equidistanza <lb/>segnate.... Ho anco talvolta tra le corde del cimbalo notatone due unisone <lb/>alli due sibili fatti strisciando al modo detto e di pi&ugrave; differenti di tuono, dei <lb/>quali due precisamente distavano per una quinta perfetta, e misurando poi <lb/>gl'intervalli delle virgolette dell'una e dell'altra strisciata si vedeva la di&shy;<lb/>stanza che conteneva quarantacinque spazii dell'una contenere trenta del&shy;<lb/>l'altra quale veramente &egrave; la forma che si attribuisce alla Diapente &rdquo; (Alb. </s>

<s><lb/>XIII, 104, 5). </s></p><p type="main">

<s>Chiunque avesse per&ograve; pi&ugrave; ferma fede nella sincerit&agrave; di Galileo, direbbe <lb/>che il riconoscer que'segni cos&igrave; assolutamente equidistanti e il saperne in&shy;<lb/>ferir di l&igrave; la frequenza e il numero delle vibrazioni corrispondenti all'acu&shy;<lb/>tezza de'sibili della piastra strisciata; il misurar cos&igrave; precisamente gli spazii <lb/>compresi da una serie di virgolette e il trovar che tornavano a proporzione <lb/>degl'intervalli musici delle due corde del cembalo; non doveva esser cosa <lb/>tanto facile e piana come voleva farla credere lo stesso Galileo, il quale ve&shy;<lb/>deva la proporzione di quegli spazii perch&egrave; prestabilita gi&agrave; nella sua mente <lb/>a quel modo che le matematiche ragioni, gli persuadevano, anche contro <pb xlink:href="020/01/769.jpg" pagenum="212"/>l'esperienza de'fatti, l'isocronismo ne'pendoli oscillanti. </s>

<s>Chi credesse altri&shy;<lb/>menti e volesse salvar la reputazione di Galileo rendendola anche da que&shy;<lb/>sta parte immacolata, si studii e veda se il noverar quelle galileiane virgo&shy;<lb/>lette cos&igrave; ben compassate, lo dispensi dall'uso e dalla spesa della Ruota <lb/>dentata o della Sirena. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Un certo tal qual sussulto, che dee necessariamente toccare il cuore <lb/>de'ciechi ammiratori di Galileo, e che gli mover&agrave; forse ad ira contro di noi, <lb/>come contro Galileo stesso che notava gli errori di Aristotile si commove&shy;<lb/>vano d'ira furiosa i Peripatetici, ne porge opportuna occasione di tratte&shy;<lb/>nerci a ripensar sopra queste esperienze descritte, secondo abbiamo veduto, <lb/>dall'Autore del I Dialogo delle Due nuove Scienze. </s>

<s>C'intravedono anche i <lb/>meno sagaci una certa compiacenza e una ostentazione di novit&agrave; spettaco&shy;<lb/>lose, d'onde viene a spiegarsi come Galileo taccia di quelle facili esperienze <lb/>sul Monocordo dalle quali fu condotto a scoprir le leggi della proporziona&shy;<lb/>lit&agrave; delle forze traenti e de'pesi delle corde, in variare il tuono de'loro tre&shy;<lb/>mori, e s'intrattenga cos&igrave; minuziosamente a descriver le setole infilate nella <lb/>sponda del cimbalo e le onde sdoppiate nel fregar col polpastrello del dito <lb/>l'orlo del bicchiere, e l'ordine delle virgolette sulla piastra strisciata colla <lb/>punta dello scarpello; esperienze tutte che non riuscendo alle prove noi ab&shy;<lb/>biam qualificate addirittura per cose immaginarie. </s></p><p type="main">

<s>Ma noi siamo stati forse i primi a sentenziar cos&igrave; con tale franchezza, <lb/>che ci viene imputata ad audacia: nessuno avrebbe osato di mettere in dub&shy;<lb/>bio quelle acustiche esperienze, e bastava per crederle vere, il saper ch'erano <lb/>state fatte da Galileo. </s>

<s>Il Bartoli stesso, dop'aver trascritta l'esperienza delle <lb/>setole infilate nella sponda del cimbalo, e aver detto dolergli il non poter <lb/>allegare in confermazione del fatto la testimonianza ancor de'suoi occhi, con&shy;<lb/>clude: <emph type="italics"/>ci&ograve; nonostante io lo prendo per indubitato.<emph.end type="italics"/> (Del suono cit., pag. </s>

<s>135). <lb/>E dop'aver citata l'esperienza dello sdoppiamento delle onde nel bicchiere <lb/>fregato, lo stesso Bartoli soggiunge: &ldquo; E senza bisognarmi altra pruova il <lb/>credo fatto non altrimenti che se io stesso l'avessi veduto con gli occhi del <lb/>Salviati; e ci&ograve; nulla ostante il non aver risposto a me in tutto l'esperienza, <lb/>come io mi prometteva &rdquo; (ivi, pag. </s>

<s>140). </s></p><p type="main">

<s>Che se tanto pesava l'autorit&agrave; di Galileo sull'animo di un gesuita, pen&shy;<lb/>siamo ci&ograve; che dovess'essere sopra que'suoi discepoli, i quali attingevan da <lb/>lui come ad unica sorgente, in che, raccolti d'ogni parte di sotto terra e <lb/>purificati, si mescevano i rivi della scienza. </s>

<s>In ci&ograve; noi principalmente rico&shy;<lb/>noscemmo la maravigliosa efficacia della grande Instaurazione galileiana, per <lb/>conferma di che ci occorre ora opportuno a citar l'esempio di Niccol&ograve; Ag&shy;<lb/>giunti, a cui andrebbe debitrice l'Acustica del primo Trattato matematico <pb xlink:href="020/01/770.jpg" pagenum="213"/>sulle corde sonore, se non gli fosse stato tolto il condur l'opera egregia <lb/>dalla troppo sollecita morte. </s></p><p type="main">

<s>L'Aggiunti non va a imparar che cosa &egrave; il suono n&egrave; da Platone n&egrave; <lb/>da'Filosofi pitagorici o dagli stoici: egli lo apprende da Galileo, il quale fa <lb/>sulla sua propria bocca rivivere e quasi germogliar sul nuovo albero della <lb/>scienza quelle antiche e verissime dottrine. </s>

<s>&ldquo; Galilaeum sequar auctorem qui <lb/>primus a condita Philosophia in soni contemplatione veritatis sonum emisit. </s>

<s>&rdquo; </s></p><p type="main">

<s>E che cosa nel 1633 o 34, in che dee aver l'Aggiunti scritte queste <lb/>parole, che cosa aveva filosofato e contemplato Galileo circa i suoni? </s>

<s>Quel <lb/>che leggesi nel <emph type="italics"/>Saggiatore,<emph.end type="italics"/> e che noi abbiam riferito ne'principii del pre&shy;<lb/>sente capitolo, dove si ripetono dall'Autore gl'insegnamenti platonici del&shy;<lb/>l'ondeggiar dell'aria che percotendo la cartilagine dell'orecchio v'eccita la <lb/>sensazion dell'udito, e dove, pur ripetendo antiche dottrine e dalla corrente <lb/>Filosofia approvate, si dice che dalla frequenza delle onde sonore nasce l'acu&shy;<lb/>tezza del suono e la gravit&agrave; dalla rarit&agrave; (Alb. </s>

<s>IV, 336). </s></p><p type="main">

<s>Singolar cosa &egrave; che avendo l'Aggiunti per concluder, come vedremo, <lb/>una sua Proposizione, bisogno d'invocar questo principio che cio&egrave; <emph type="italics"/>cordae <lb/>quae tardius suas expediunt vibrationes graviorem sonum edunt,<emph.end type="italics"/> imme&shy;<lb/>diatamente soggiunge: <emph type="italics"/>ut Galileus probat.<emph.end type="italics"/> Ma nel <emph type="italics"/>Saggiatore<emph.end type="italics"/> non ha nem&shy;<lb/>meno un cenno Galileo di queste prove, e l'esperienza delle virgolette ri&shy;<lb/>maste impresse sulla piastra d'ottone raschiata collo scarpello non ricorre <lb/>altrove che nel I Dialogo delle Due Nuove Scienze, pubblicate quasi tre anni <lb/>dopo che l'Aggiunti era morto. </s>

<s>Potrebbesi pensare che il Maestro avesse al <lb/>suo giovane e diletto discepolo comunicato a voce e in privata conversa&shy;<lb/>zione quelle esperienze, prima di pubblicarle, se le Proposizioni acustiche, <lb/>che lasci&ograve; manoscritte lo stesso Aggiunti, e delle quali fra poco diremo, non <lb/>facessero certo argomento che l'Autore di quelle proposizioni ignorava quel <lb/>che di nuovo aveva scoperto sul risonar delle corde il Galileo, o che que&shy;<lb/>sti non avesse fatto ancora, quando l'Aggiunti scriveva, quelle scoperte, o <lb/>che volesse riserbarsele in petto, affinch&egrave; ne'Dialoghi comparissero a tutti <lb/>nuove. </s>

<s>In ogni modo non si pu&ograve; intender quell'<emph type="italics"/>ut Galileus probat<emph.end type="italics"/> se non che <lb/>l'aver professate Galileo quelle dottrine serviva all'Aggiunti come di prova. </s></p><p type="main">

<s>Se cos&igrave; spesso &egrave; dato a Galileo il titolo di divino per questa parte sola <lb/>si riconosce come non immeritato, per aversi cio&egrave; acquistata tanta virt&ugrave; da <lb/>farsi rassomigliare a Dio, a cui si crede una cosa esser vera perch'Egli l'ha <lb/>detta. </s>

<s>S'era molti secoli prima acquistata quella medesima virt&ugrave; anche Ari&shy;<lb/>stotile, ma egli ne abus&ograve; torcendo i suoi seguaci nella Filosofia naturale per <lb/>le vie dell'errore, mentre invece altra ragione d'appellar Galileo uomo divino <lb/>&egrave; quella dell'avere egli addirizzato e additato il metodo delle verit&agrave; natu&shy;<lb/>rali, a cui rivolti que'discepoli che avevano il pi&egrave; valido per s&egrave; medesimi, <lb/>per s&egrave; medesimi pure correndo la gloriosa palestra riuscirono a precorrere <lb/>e talvolta a superare lo stesso Maestro. </s>

<s>Anche di ci&ograve; ne porge opportunis&shy;<lb/>simo esempio il medesimo Aggiunti delle Proposizioni meccanico acustiche <lb/>del quale &egrave; tempo che rendiam conto ai Lettori, incominciando dal narrar <pb xlink:href="020/01/771.jpg" pagenum="214"/>come avessero nella mente di lui l'occasione dagl'insegnamenti e dalle fa&shy;<lb/>miliari consuetudini ch'egli ebbe con Galileo. </s></p><p type="main">

<s>Quando ricoverato a Siena, come chi uscito fuor del pelago alla riva si <lb/>rivolge indietro a guardar l'onda pericolosa, Galileo deliber&ograve; di abbandonare <lb/>le contemplazioni del cielo per tornar tutto a specular quel che accade sopra <lb/>la terra, specialmente ne'gravi che son tirati al centro di essa; quasi si <lb/>sentisse trascinar la mente da quella forza e seguirla docile il desiderio di <lb/>nascondersi agli occhi degli uomini, rivolse i suoi studii a penetrare adden&shy;<lb/>tro alla pi&ugrave; intima compagine de'corpi. </s>

<s>Ricercando la natura di quel glu&shy;<lb/>tine, che ne tiene unite le particelle componenti, le ridusse alla forza del <lb/>vacuo, e pens&ograve; allora a quello strumento, ch'e descrisse poi nel I Dialogo <lb/>delle Nuove Scienze (Alb. </s>

<s>XIII, 18, 19) per misurar quella forza, e per con&shy;<lb/>cluderne di l&igrave; le ragioni della resistenza che fanno le verghe solide allo spez&shy;<lb/>zarsi. </s>

<s>Tanto si compiacque di questo primo principio dato al secondo di <lb/>que'Trattati nuovi, di che proponevasi gi&agrave; di arricchire la scienza, che par&shy;<lb/>tecip&ograve; la notizia delle nuove meditazioni agli amici e agli scolari, fra quali <lb/>era de'primi Niccol&ograve; Aggiunti. </s>

<s>Questi, il d&igrave; 10 Settembre 1633, dopo su&shy;<lb/>bito aver avuto quella bella notizia rispondeva cos&igrave; al venerato suo Maestro <lb/>a Siena: </s></p><p type="main">

<s>&ldquo; Io non potevo ricevere da V. S. </s>

<s>Eccellentissima maggior onore che <lb/>esser fatto partecipe dell'ambrosia degli Dei, che tale a mio giudizio e gu&shy;<lb/>sto deve chiamarsi ogni speculazione del suo sovrano ingegno. </s>

<s>Quest'ultima <lb/>sua meditazione mi ha arrecato gusto grandissimo non solo perch&egrave; ho ve&shy;<lb/>duto in essa risoluto con tanta facilit&agrave; ed evidenza un quesito cos&igrave; bello e <lb/>curioso, ma ancora per l'importante considerazione, che appresso ella ne fa, <lb/>deducendone quella mirabile necessit&agrave; che nella struttura delle fabbriche <lb/>tanto artificiali quanto naturali si ritrova, di esserci una limitata grandezza, <lb/>oltre la quale l'arte e la natura, tentando di fabbricare, piuttosto demoli&shy;<lb/>rebbero e distruggerebbero &rdquo; (Alb. </s>

<s>IX, 393). </s></p><p type="main">

<s>Ma l'Aggiunti era rimasto preso di maraviglia a considerar quel ci&shy;<lb/>lindro di vetro, con quello zaffo scorrevole dentro, che tirato indietro con <lb/>forza dava la misura del vacuo, e nello stesso tempo della resistenza de'so&shy;<lb/>lidi allo spezzarsi, e gli pareva avere in mano in quello strumento la chiave <lb/>da aprire infiniti segreti della Natura, ond'&egrave; che, una settimana dopo la <lb/>precedente, tornava cos&igrave; a scrivere a Galileo da Firenze: &ldquo; Ho voluto ve&shy;<lb/>dere se mi riusciva d'adoperare la chiave, che a questi giorni V. S. ci ha <lb/>data attissima ad aprire infiniti segreti di spezzamenti ecc., e perci&ograve; ho ten&shy;<lb/>tato di risolvere il problema da lei accennatomi: glielo mando acci&ograve; veda se <lb/>io ho preso un granchio. </s>

<s>Sto poi attendendo con desiderio grande la sua di&shy;<lb/>mostrazione &rdquo; (Targioni, Notizie cit., T. II, P. I, pag. </s>

<s>130). </s></p><p type="main">

<s>Saper qual sia questa particolar dimostrazione e questo particolar pro&shy;<lb/>blema non occorre per ora: basta che fra'Manoscritti dell'Aggiunti si trovan <lb/>distese varie proposizioni, nelle quali tutte gioca per fondamento della spe&shy;<lb/>culazione lo strumento proposto da Galileo per misurare la forza del vacuo. <pb xlink:href="020/01/772.jpg" pagenum="215"/>L'uso fatto di un tale strumento dal valoroso Discepolo non dee tornar <lb/>nuovo ai Lettori di questa Storia, a'quali descrivemmo nel cap. </s>

<s>I del Tomo I <lb/>quel <emph type="italics"/>poculus vel syphunculus, eiusque manubrium, cui annexum sit opti&shy;<lb/>mum obturamentum<emph.end type="italics"/> applicato dall'Autore a dimostrar come le corde me&shy;<lb/>talliche, quali sarebbero quelle degli strumenti musici, si allunghino o si <lb/>accorcino al variar dell'ambiente temperatura. </s>

<s>Cotesto <emph type="italics"/>poculus<emph.end type="italics"/> galileiano &egrave; <lb/>quello appunto che si diceva servir di fondamento, o come l'Aggiunti stesso <lb/>esprimevasi, di chiave da aprir la via a dimostrar fra le altre queste sue <lb/>nuove meccaniche proposizioni. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Propositio V.<emph.end type="italics"/> Si fuerint duae cordae extensae, et illarum duas so&shy;<lb/>lummodo partes norimus tum remissas tum extensas inter se aequales esse, <lb/>erunt totae inter se aequaliter extensae &rdquo; (MSS. Gal. </s>

<s>Disc., T. XVIII, c. </s>

<s>65 v.). </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Prop. </s>

<s>VI.<emph.end type="italics"/> Partes quaecumque aequales cuiusvis cordae extensae, vi&shy;<lb/>ribus aequalibus extensae sunt &rdquo; (ibi, c. </s>

<s>66). </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Prop. </s>

<s>VIII.<emph.end type="italics"/> Si fuerint cordae similes inter se aequaliter extensae, <lb/>vires quibus extenduntur eamdem habent rationem quam longitudines ex&shy;<lb/>tensarum &rdquo; (ibi, c. </s>

<s>66 v.). </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Prop. </s>

<s>IX.<emph.end type="italics"/> Si corda brevissima, quanta maxima potest extensione <lb/>extensa fuerit nec abrupta, corda quaevis similis, quamquam longissima, <lb/>aequaliter et eodem quo illa modo extensa, non abrumpetur &rdquo; (ibi, c. </s>

<s>67 v.). </s></p><p type="main">

<s>Apparisce da questi enunciati di proposizione come si vedesse l'Ag&shy;<lb/>giunti aperto a speculare un pi&ugrave; largo campo di quello, che non gli era <lb/>accennato dallo stesso Galileo, e come, oltre alla ragion dello strapparsi le <lb/>corde, si fosse messo dietro a investigarne altre nuove concernenti le pro&shy;<lb/>priet&agrave; meccaniche delle loro tensioni. </s>

<s>Si domandava per esempio se una <lb/>corda sia tesa ugualmente nelle sue estremit&agrave; e nel mezzo; se un mede&shy;<lb/>simo peso tenda con ugual forza una corda lunga e una corta: domande <lb/>tutte alle quali, anche un mezzo secolo dopo, variamente si rispondeva e to&shy;<lb/>glievasi l'argomento alla risposta dalla sola esperienza. </s>

<s>L'Aggiunti aveva <lb/>tanto tempo prima invocate le ragioni matematiche, delle quali fece uso prin&shy;<lb/>cipalmente nelle Proposizioni sopra citate. </s>

<s>Non &egrave; questo il luogo da tratte&shy;<lb/>nersi in un soggetto di Meccanica, ma perch&egrave; fu da ci&ograve; condotto il Nostro <lb/>a trattar de'tremori armonici nelle corde, e perch&egrave; abbiano intanto i Lettori <lb/>un saggio del modo come il Discepolo di Galileo fece uso dello <emph type="italics"/>Strumento<emph.end type="italics"/><lb/>galileiano, abbiam creduto opportuno trascriver qui la prima dimostrata parte <lb/>della seguente proposizione: </s></p><p type="main">

<s>&ldquo; Si duae quaevis cordae similes eadem vel aequali vi extendantur, in&shy;<lb/>ter se aequaliter extendentur, etiamsi illarum altera brevissima, altera vero <lb/>longissima fuerit. </s>

<s>&mdash; Proponamus nobis ob oculos <emph type="italics"/>Instrumentum,<emph.end type="italics"/> cuius paulo <lb/>ante meminimus, et quod, ut descripsimus, e cylindricis vasculis et opercu&shy;<lb/>lis aequalibus et se mutuo congrue excipientibus coagmentatur. </s>

<s>Ac primo <lb/>quidem manu vel quovis alio modo ita retineatur, ut totum Instrumentum <lb/>suis urgentibus nutibus ad perpendiculum turris impendeat. </s>

<s>Deinde sit pon&shy;<lb/>dus aliquod E (fig. </s>

<s>56) appensum uncinato claviculo, qui fundo tubuli AB <pb xlink:href="020/01/773.jpg" pagenum="216"/>fuerit applumbatus. </s>

<s>In Intrumentum autem aequalia spatia RQ, NM, HG, CB, <lb/>imis operculi et fundi basibus interiecta eiusdem generis materiam conti&shy;<lb/>neant, quae tractioni obsequens rarior fiat. </s>

<s>Quoniam igitur gravitate ponde&shy;<lb/><figure id="id.020.01.773.1.jpg" xlink:href="020/01/773/1.jpg"/></s></p><p type="caption">

<s>Fig. </s>

<s>56.<lb/>ris E tubulus AB deorsum trahitur, materies inclusa <lb/>spatio CB rarescat necesse est. </s>

<s>Interea, dum tubulus <lb/>AB deorsum fertur, et intervallum CB amplificatur. </s>

<s><lb/>Quia vero eadem materies quanto maiorem ad rarita&shy;<lb/>tem distrahi debet, tanto maiori vi trahenda est, sit <lb/>ponderis E eiusmodi gravitas ut eius vi materies CB <lb/>rarior facta non impleat universam cavitatem tubuli <lb/>AB, sed dilatetur in grandiusculum spatium CB quale <lb/>ostendit altera figura 57. &rdquo; <lb/><figure id="id.020.01.773.2.jpg" xlink:href="020/01/773/2.jpg"/></s></p><p type="caption">

<s>Fig. </s>

<s>57.</s></p><p type="main">

<s>&ldquo; His ita se habentibus, postquam desierit rare&shy;<lb/>scere materies CB, manus vel quicquid retinet tubulum <lb/>FG sentiet vim ponderis E, et quicquid sustinet In&shy;<lb/>strumentum FB sustinebit etiam pondus E, quod qui&shy;<lb/>dem conatur pessum trahere cylindrum FG, sed frustra, <lb/>quia manu vel alio retinaculo retinetur. </s>

<s>Quamobrem <lb/>si, omisso tubulo FG manu, comprehenderemus cylin&shy;<lb/>drum LM, tum pondus trahens FG ipsum etiam per&shy;<lb/>trahet, quia non amplius praepeditur aut retinetur. </s>

<s>Et <lb/>quoniam pondus E ita tubulo FG grave est, ut si ex <lb/>T penderet; quo igitur modo, cum pondus E depende&shy;<lb/>bat ex Z et vasculum FG retinebatur, eius ponderis vi <lb/>distrahebatur materies CB; ita nunc retento LM idem <lb/>pondus velut appensum ad T distrahet materiem HG <lb/>et subsidenti vasculo FG laxabitur spatium HG, ut per&shy;<lb/>spicuum est in altera figura. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Porro autem, si detento PQ missum facias LM, pondus E cum one&shy;<lb/>ret LM, qui a nullo detinetur, deferet illum deorsum, et spatium NM tam <lb/>late patescet quam HG et CB, et postremo manubrii S apprehensa estre&shy;<lb/>mitate K et relicto PQ, pondus E, perinde quasi in X appensum, vim affe&shy;<lb/>ret cylindro PQ, qui cum iam non ut antea inhibeatur descendet et spatium <lb/>RQ pari laxitate hiabit ut reliqua NM, HG, CB. </s>

<s>Etsi enim spatia quae su&shy;<lb/>binde altiora sunt, subinde etiam ampliora fieri deberent ob maiorem acces&shy;<lb/>sionem ponderis ipsius Instrumenti supra pondus appensum E, nos tamen <lb/>in praesens Instrumenti pondus non advertimus sed solum inquirimus id <lb/>quod provenit ab eppensi ponderis vi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Hactenus vidimus quomodo ab eodem pondere infime appenso aequa&shy;<lb/>liter distrahantur aequales quotcumque materiae dissipabilis portiunculae, <lb/>sive plurimae sive paucissimae in Instrumento reperiantur. </s>

<s>Modo ponamus <lb/>duo Instrumenta consimili modo constructa hoc est aequalibus vasculis, ma&shy;<lb/>nubriis et spatiis eadem materia refertis, quae sint.... &rdquo; (ibi, c. </s>

<s>74). </s></p><p type="main">

<s>Abbiamo detto di sopra che cos&igrave; fatte proposizioni meccaniche condus-<pb xlink:href="020/01/774.jpg" pagenum="217"/>sero l'Aggiunti a trattar delle corde musicali, facilmente trapassando dai <lb/>semplici moti a speculare in esse corde il tenore armonico de'loro tremori. </s>

<s><lb/>Come corollario infatti di queste e delle altre sopra enunciate deduceva un <lb/>argomento da confutar l'errore di alcuni, i quali dicevano che perci&ograve; le <lb/>corde pi&ugrave; lunghe rendono i suoni pi&ugrave; gravi, perch&egrave; son pi&ugrave; fortemente ri&shy;<lb/>tese fra'loro sostegni. </s></p><p type="main">

<s>&ldquo; Sed vel inde perspicuum fiet longiores cordas graviorem sonum edere, <lb/>quia retensiores sint quam breviores, nam corda AB (fig. </s>

<s>58) si duobus cla&shy;<lb/><figure id="id.020.01.774.1.jpg" xlink:href="020/01/774/1.jpg"/></s></p><p type="caption">

<s>Figura 58.<lb/>viculis A, B utroquo extremo religata <lb/>atque extensa fuerit sub plano FG, dein&shy;<lb/>de autem asserculo LM, ita introacto ut <lb/>nulla vi adhibita probe congruat spatio <lb/>interiecto intra planum et cordam, si <lb/>dirimatur in partes AC, CB, quarum <lb/>utravis percussa altera sileat; ex Pro&shy;<lb/>positione.... planum est cordas BA, <lb/>CA aequaliter esse extensas. </s>

<s>Sed pulsata corda breviori CA acutior exit sonus <lb/>quam pulsata longiori BA, ut auritum docet experimentum, non ergo ab <lb/>extensionis inaequalitate soni discrimen proficiscitur &rdquo; (ibi, c. </s>

<s>68). </s></p><p type="main">

<s>Di qui coglie l'occasione l'Aggiunti di passare addirittura a trattar <lb/>de'suoni, pigliando per fondamento quel po'di principio, che ne aveva letto <lb/>nel <emph type="italics"/>Saggiatore,<emph.end type="italics"/> e ch'ei fecondava con singolari osservazioni sue proprie. </s></p><p type="main">

<s>&ldquo; Ut ergo id vera ex causa cognoscamur (cos&igrave; ripiglia il costrutto la&shy;<lb/>sciato da noi interrotto nelle sopra citate parole) peropportunum fuerit et <lb/>generatim quid sonum efficiat et speciatim quid gravem, quid acutum so&shy;<lb/>num producat pervidere, quo loco Galilaeum sequar auctorem, qui primus <lb/>a condita Philosophia in soni contemplatione veritatis sonum emisit, et su&shy;<lb/>per hac re suam aperuit sententiam in auri libratrice <emph type="italics"/>Simbella,<emph.end type="italics"/> seu veri&shy;<lb/>tatis staterula, delibatione vel pensitatione.... pag..... Haec autem est il&shy;<lb/>lius sententia: <emph type="italics"/>Cum nostri timpani auricularis cartilago quaedam tremore <lb/>succussu vibratur, id quod sentimus et quo afficimur in eiusmodi tremore <lb/>sonum vocitamus, cuius intrinsecus effectus est tremor ille cartilagineus, <lb/>sensus autem qui efficitur et quo sonum percipimus appellamus auditum. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Quia vero cartilago illa, quae tremula inhorruit, non ipsa seipsam <lb/>commovet, sed potius commota paulatim se quieti componit, adeo ut tre&shy;<lb/>mula fiat, extimo aliquo pulsu eget. </s>

<s>Cum ergo externum aliquod corpus <lb/>erebra succussatione agitatum cogit ipsam quoque tremescere aurium car&shy;<lb/>tilaginem, tunc sonus gignitur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Plerumque autem fit ut trementis corporis concussu conterminus aer, <lb/>crispatim et consimili modo illa concussione fluitans, nostrarum aurium <lb/>tympanum pulset, et cartilaginem illam sua vi tremulam faciat sonumque <lb/>progignat. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Hoc tamen semper, ut ego ostendam, undatim crispati tremuleque <lb/>contorti aeris appulsu ad aures fit sonus, sed caput ipsum, tremore concus-<pb xlink:href="020/01/775.jpg" pagenum="218"/>sum a vi aliqua, concutit ac tremere cogit aurium cartilaginem sonumque <lb/>efficit, nam si ori mordicus detineris cordae caput alterum, alterum vero <lb/>dextrae digitis cordam hanc percusseris, maiorem hauries sonum quam si <lb/>eadem distenta corda inter os et digitum alterius sonuerit, ac tu ad idem <lb/>intervallum aures admoveris; quod iccirco accidit quia cordae tremor, prae&shy;<lb/>ter aurem, caput ipsum concutit, a quo rursus aurium cartilago in tremo&shy;<lb/>rem compellitur et maiorem fert sonum, qua si solo aeris tremore ageretur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sic etiam, si virga ferrea vinclo quodam lineo adstricta levae dex&shy;<lb/>traeque manus digitum bina staminis capita illigent, et geminos digitos sta&shy;<lb/>mine religatos in geminas aures tuas inseras, si obseratis hoc modo auribus <lb/>virgam ferream in lapidem aut tale quippiam impingas ut resonet, vehe&shy;<lb/>mentiorem, occlusis auribus sonitum percipies, quam si reseratis auribus ac&shy;<lb/>cipias, quippe virga ferrea cum ictu percussa intremit stamen et iunctos <lb/>stamini digitos pari tremore concutit, et vicissim digiti concussi caput et <lb/>cartilaginem vehementius tremere cogunt quam si aeris solo tremore illa <lb/>adigerentur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Interdum etiam non aeris, sed cuiuscumque fluidi caput ambientis <lb/>tremore, fit sonus. </s>

<s>Itaque si caput aquis merseris et lapides manu subter <lb/>aquas mutuo affligas, ingentem percipies sonitum: in oleo gravior fortasse <lb/>sonitus foret ob eius liquoris lentum gluten et viscidum crassamentum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Plerumque tamen sonus fit ea qua diximus ratione, cum scilicet cor&shy;<lb/>pus aliquod durum ac rigens concussum tremit et eius succussatione aer <lb/>circumfusus in tenues undulas crispatus, eaque rugosa crispatione orbicu&shy;<lb/>latim fusus, ad aures pertingit et cartilaginem illam tremebundo pulsu con&shy;<lb/>cutit ac sonum facit. </s>

<s>Hac de causa..... &rdquo; (ibi, c. </s>

<s>68, 69). </s></p><p type="main">

<s>A questo punto la scrittura autografa del nostro Autore si rimane in&shy;<lb/>terrotta, n&egrave; abbiam trovato che ei la riprenda altrove in nessuna parte del <lb/>Manoscritto disordinato e confuso. </s>

<s>Con quelle considerazioni in ogni modo <lb/>sopra la natura, la generazione e la diffusion del suono ne'varii mezzi so&shy;<lb/>disfaceva al primo de'propositi espressi: rimaneva l'altro che si riduceva <lb/>per lui a vedere <emph type="italics"/>quid gravem quid acutum sonum producat,<emph.end type="italics"/> e lo fa di&shy;<lb/>mostrando una serie di proposizioni, la prima delle quali &egrave; in ordine la XII, <lb/>dopo quelle meccaniche di cui parlammo di sopra, e che servivano a que&shy;<lb/>ste acustiche quasi come di Lemma. </s>

<s>L'enunciato di ciascuna di quelle acu&shy;<lb/>stiche Proposizioni dimostrate dall'Aggiunti &egrave; il seguente: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Propositio XII.<emph.end type="italics"/> Cordae similes, sed inaequales et inter se aequaliter <lb/>extensae, inaequale sonum reddunt, et longior graviorem brevior acutio&shy;<lb/>rem &rdquo; (ibi, c. </s>

<s>78). </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Prop. </s>

<s>XIII.<emph.end type="italics"/> Ex duabus cordis similibus et aequalibus, sed inter se <lb/>inaequaliter tensis, remissior gravior, tensior acutius sonat &rdquo; (ibi, c. </s>

<s>80). </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Prop. </s>

<s>XIV.<emph.end type="italics"/> Si cordae similes, sed crassitudine inaequales, a qui&shy;<lb/>busdam ponderibus sint inter se aequaliter extensae, pondera inter se eam&shy;<lb/>dem habebunt rationem ac crassitudines vel bases cordarum: nihil autem <lb/>refert an aequales vel inaequales longitudine cordae fuerint &rdquo; (ibi, c. </s>

<s>81). </s></p><pb xlink:href="020/01/776.jpg" pagenum="219"/><p type="main">

<s><emph type="italics"/>&ldquo; Prop. </s>

<s>XV.<emph.end type="italics"/> Cordae similes, aequales et aequaliter tensae, quamquam <lb/>crassitudine inaequales, sonum efficiunt aeque acutum &rdquo; (ibi, c. </s>

<s>82). </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Prop. </s>

<s>XVI.<emph.end type="italics"/> Corda crassior, aequalibus viribus extensa ac altera te&shy;<lb/>nuior illi similis et aequalis longitudine, graviorem sonum edit &rdquo; (ibi, c. </s>

<s>83). </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Prop. </s>

<s>XVII.<emph.end type="italics"/> Si cordae fuerint eiusdem longitudinis, crassitudinis, ac <lb/>tenacitatis, sed diversi ponderis, hae viribus aequalibus aequaliter extensae <lb/>inaequaliter resonabunt, et pondere gravior graviorem etiam sonum reddet &rdquo; <lb/>(ibi, c. </s>

<s>83 v.). </s></p><p type="main">

<s>Diceva l'Aggiunti, come udimmo nell'introdursi in questa sua tratta&shy;<lb/>zione, che e'seguiva Galileo per suo autore, il qual Galileo non aveva an&shy;<lb/>cora per verit&agrave; in Acustica scoperto nulla di nuovo. </s>

<s>Le nuove dottrine, pub&shy;<lb/>blicate nel I Dialogo delle Scienze Nuove, l'Aggiunti non fu sventuratamente <lb/>a tempo a vederle, e di qu&igrave; nacque che alcune delle sopra enunciate pro&shy;<lb/>posizioni di lui son difettose, e altre peggio son false. </s>

<s>Ei non sa veder quanto <lb/>diversamente operi, nell'acutire il suono alle corde, la crassizie dal peso, e <lb/>la fallacia, che perci&ograve; si asconde nelle due prop. </s>

<s>XV e XVI, lo fa cos&igrave; con&shy;<lb/>cludere nel corollario II alla XVII seguente: &ldquo; Hinc etiam manifestum est <lb/>maius pondus non esse caussam maioris gravitatis soni, quandoquidem vi&shy;<lb/>dimus cordam, maioris ponderis quam altera corda aequaliter tensa et aeque <lb/>longa, nihilominus modo graviorem modo non graviorem illius sono sonum <lb/>excitare &rdquo; (ibi, c. </s>

<s>84 v.). </s></p><p type="main">

<s>La proposizione XIII &egrave; consenziente alle dottrine professate da'Filosofi <lb/>antichi, e confermate da facilissime esperienze, ma non sa definire l'Ag&shy;<lb/>giunti con qual proporzione, e secondo qual legge, vogliano esser propria&shy;<lb/>mente cresciute le tensioni. </s>

<s>Ingannato anch'egli dal comune errore che <lb/>la forma dell'Ottava sia quella desunta dalla lunghezza, ossia della dupla, <lb/>crede che uno strumento incordato, per esempio, di ottone dia il diapa&shy;<lb/>son di un altro incordato d'oro, perch&egrave; questo metallo &egrave; il doppio pi&ugrave; <lb/>peso di quello, mentre &egrave; il vero, secondo Galileo dimostra e confermano i <lb/>fatti, che l'incordatura d'oro d&agrave; suono non di un'ottava pi&ugrave; grave, ma di <lb/>circa una quinta. </s>

<s>&ldquo; Hinc colligere licet (scrive l'Aggiunti per coroll. </s>

<s>I alla <lb/>XVII proposizione) cur aereae et aureae cordae similes et aequales et ae&shy;<lb/>qualibus viribus extensae propemodum diapason consonantiam efficiunt. </s>

<s>Cum <lb/>enim utraque aequali vi aequaliter propemodum extendatur, et aureum pon&shy;<lb/>dus aerei ponderis sit fere duplum, necesse est ut aurea corda duplo tardius <lb/>quam aerea se vicissim corrigat et inflectat, seu duplo tardiores tremulae <lb/>concussionis peragat vices, ex quo oritur consonantia Diapason &rdquo; (ibi, c. </s>

<s>84). </s></p><p type="main">

<s>Gli errori insomma, di che riuscivano infelicemente viziate le proposi&shy;<lb/>zioni del nostro Aggiunti, venivano cos&igrave; tutti emendati dalle dottrine gali&shy;<lb/>leiane: &ldquo; Ma qui, prima di passare pi&ugrave; avanti, voglio avvertirvi che delle <lb/>tre maniere d'inacutire il suono quella che voi riferite alla sottigliezza della <lb/>corda con pi&ugrave; verit&agrave; deve attribuirsi al peso. </s>

<s>Imperocch&egrave; l'alterazione presa <lb/>dalla grossezza risponde solo quando le corde siano della medesima materia, <lb/>e cos&igrave; una minugia, per far l'ottava, deve esser pi&ugrave; grossa quattro volte <pb xlink:href="020/01/777.jpg" pagenum="220"/>dell'altra pur di minugia, che sia egualmente lunga ed egualmente tirata, <lb/>ed una di ottone pi&ugrave; grossa quattro volte di un'altra di ottone. </s>

<s>Ma se io <lb/>vorr&ograve; far l'ottava, con una di ottone ed una di minugia di egual lunghezza <lb/>e tensione, non si ha da ingrossar quattro volte ma s&igrave; ben farla quattro <lb/>volte pi&ugrave; grave, sicch&egrave;, quanto alla grossezza, questa di metallo non sar&agrave; <lb/>altrimenti quattro volte pi&ugrave; grossa, ma ben quadrupla in gravit&agrave;, che tal&shy;<lb/>volta sar&agrave; pi&ugrave; sottile che la sua rispondente all'ottava pi&ugrave; acuta, che sia di <lb/>minugia. </s>

<s>Onde accade che, incordandosi un cimbalo di corde di oro ed un <lb/>altro di ottone, se saranno della medesima lunghezza, grossezza e tensione, <lb/>per esser l'oro quasi il doppio pi&ugrave; grave riuscir&agrave; l'accordatura circa una <lb/>quinta pi&ugrave; grave &rdquo; (Alb. </s>

<s>XIII, 105, 6). </s></p><p type="main">

<s>Fu veramente una sventura l'aver trovato l'Aggiunti l'Acustica non <lb/>isnebbiata ancora dal sole galileiano, e fu un'altra sventura il non posse&shy;<lb/>der Galileo l'acume matematico del suo Discepolo. </s>

<s>Da quelle due virt&ugrave; con&shy;<lb/>giunte sarebbe cos&igrave; per tempo uscita di mezzo a noi la scienza matematica <lb/>de'suoni. </s></p><p type="main">

<s>Le proposizioni dell'Aggiunti non hanno certo n&egrave; la profondit&agrave; n&egrave; la <lb/>finezza di quelle del Taylor, del Newton, o di Daniele Bernoulli, ma un se&shy;<lb/>colo prima che fiorissero questi, quando l'analisi era affatto sconosciusta e <lb/>cos&igrave; rari erano della matematica applicata alla Fisica gli esempi, chi avrebbe <lb/>pensato mai che si potesse matematicamente dimostrar che di due corde la <lb/>pi&ugrave; lunga rende il suono pi&ugrave; grave? </s>

<s>Ci&ograve; si teneva da tutti per esperienza, <lb/>e n&egrave; anco a Galileo pass&ograve; per la mente che si potesse dimostrare per altra <lb/>via. </s>

<s>Eppure vi riusc&igrave; l'Aggiunti nella sua XII proposizione, il processo di&shy;<lb/>mostrativo della quale, non vogliam terminare il presente capitolo senza tra&shy;<lb/>scriverlo ai nostri Lettori, lieti di veder allegati cos&igrave; primaticci in Italia <lb/>que'frutti, che si videro poi maturare in terra straniera. </s></p><p type="main">

<s>&ldquo; Sint cordae, ut dictum est, longior AB (fig. </s>

<s>59) CD brevior (fig. </s>

<s>60), <lb/><figure id="id.020.01.777.1.jpg" xlink:href="020/01/777/1.jpg"/></s></p><p type="caption">

<s>Figura 59.<lb/>quarum media puncta E,F, ae&shy;<lb/>qualibus percussa vel impulsa <lb/>viribus, deducta sint ad G, H. </s>

<s><lb/>Iam ex superioribus constat li&shy;<lb/>neas AGB, CHD et sibi ipsis <lb/>et mutuo inter sese esse ae&shy;<lb/>qualiter extensas. </s>

<s>Quoniam vero <lb/>punctum E pertractum est in G, simulac dempta vi cordam AGB libere <lb/>abire sinas, corriget illa sese et recta AEB rursus evadet, et quanta fuit vis <lb/><figure id="id.020.01.777.2.jpg" xlink:href="020/01/777/2.jpg"/></s></p><p type="caption">

<s>Figura 60.<lb/>illam extendens in AGB, tantus erit impetus quo se <lb/>contrahet in AEB. </s>

<s>Et quia cordae GB singulae par&shy;<lb/>tes sunt inter se aequaliter et per consequens ae&shy;<lb/>qualibus viribus extensae, iccirco aequalibus singu&shy;<lb/>lae viribus contrahentur, et ob id inter contrahendum <lb/>aequaliter etiam inter se contrahentur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Praeterea cum GB contrahi nequeat in EB, nisi transmoveatur a po-<pb xlink:href="020/01/778.jpg" pagenum="221"/>sitione GB in positionem EB, atque insuper cum GB, dum contrahitur, par&shy;<lb/>tes omnes inter sese aequaliter contractas habere debeat; necesse est ut, <lb/>dum contrahitur GB in EB, pars cordae G deferatur per perpendiculare GE, <lb/>et caeterae omnes partes I, K, L, R, T decurrant lineas quae ab eisdem <lb/>punctis ducuntur aequidistantes ipsi GE. </s>

<s>Hac enim sola ratione linea AGB, <lb/>partes omnes dum remiserit, habebit aequaliter remissas vel aequaliter <lb/>tensas. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Rursusque, quoniam cum GB fit contractior et simulac G est in E, <lb/>partes omnes inter GB in arctius coactae sunt inter EB, ut igitur GB con&shy;<lb/>trahatur in EB, quo tempore pars G delata est in E, per totam GE, eodem <lb/>simul pars I deferri debuit per IN ipsi EG parallelam. </s>

<s>Quare, cum sint par&shy;<lb/>tes G, I similes et aequales et eodem tempore deferri debeant per spatia inae&shy;<lb/>qualia GE, IN, vis deferens partem G ad vim deducentem partem I, ita se <lb/>haberi debet ut GE ad IN, et si a quotcumque aliis partibus cordae GB <lb/>ductae concipiantur parallelae ipsi EG, huiusmodi parallelae repraesentabunt <lb/>vires, quibus eae partes transferuntur in EB. Quamobrem, si ab omnibus <lb/>partibus cordae GB ductae intelligantur omnes parallelae lineae ipsi EG, eae <lb/>simul acceptae ostendent omnes vires quibus tota GB traducitur in EB. </s>

<s>Quod <lb/>si, ex GB dematur pars LB aequalis cordae HD, parallelae omnes, quae ab <lb/>omnibus partibus ipsius LB ductae intelligentur, denotarent vires omnes, <lb/>quibus tota BL in MB transponeretur. </s>

<s>Quamobrem vires deducentes BG <lb/>in BE, ad vires quae tempore eodem transferunt BL in MB, eam habent <lb/>rationem quam lineae omnes ductae a punctis omnibus lineae GB, paral&shy;<lb/>lelae ipsi GE, ad lineas omnes ductas a punctis omnibus lineae BL aequi&shy;<lb/>distantes lineae LM, vel GE. </s>

<s>Sed lineae omnes, quae duci possunt in trian&shy;<lb/>gulo GBE parallelae ipsi GE, explent ipsum triangulum GBE, universae <lb/>autem parallelae ipsi LM ductae in triangulo LBM conficiunt triangulum <lb/>ipsum LBM; ergo vires, quibus eodem tempore GB in BE, ad vires omnes <lb/>quibus BL in BM, hoc est HD in DF deducitur, eam habent rationem quam <lb/>triangulus GBE ad triangulum LBM, sive triangulum HDF. </s>

<s>Ut ergo eodem <lb/>tempore orda BG transferatur in EB, et DH in FD, oportet vim deducen&shy;<lb/>tem GB, ad vim quae impellit HD, ita esse, ut triangulus GBE ad trian&shy;<lb/>gulum HDF. </s>

<s>Sed cum dimittimus partem G, vis deducens ipsam GB in EB <lb/>nihil aliud est quam vis contrahens ipsam GB, quae aequalis est vi exten&shy;<lb/>denti eamdem, et amissa parte H vis quae contrahit HD illam transferri co&shy;<lb/>git in FD. </s>

<s>Vires igitur deducentes sunt eiusdem momenti ac vires con&shy;<lb/>trahentes. </s>

<s>Hae vero sunt aequales viribus extendentibus cordas, quare et <lb/>deducentes erunt eisdem aequales. </s>

<s>Sed momentum vis extendentis BG, ad <lb/>momentum vis extendentis HD, eam habet rationem quam longitudo EB ad <lb/>longitudinem FD, quae subduplicata proportio est eius, quam habet trian&shy;<lb/>gulus GBE ad triangulum HDF; ergo vis deducens GB, ad vim deducen&shy;<lb/>tem HD, minorem habet rationem quam ut eodem tempore esse posset GB <lb/>in EB, et HD in DF translata. </s>

<s>Serius ergo deveniet BG in EB, et quia tam <lb/>corda AB quam CD, ad quodvis aliud punctum extensa et inde dimissa, <pb xlink:href="020/01/779.jpg" pagenum="222"/>utraque tamen aequalibus intervallis temporum suas obit reciprocationes, <lb/>(cuius rei argumentum habemus quod eadem corda quomodocumque pul&shy;<lb/>sata eumdem vocis gradum obtinet sibique ipsi unisona semper est) iccirco <lb/>corda AB suos excursus ac recursus semper tardius absolvet quam CD, et <lb/>ob id eodem tempore minus frequentior ibit ac redibit quam CD. </s>

<s>Sed cor&shy;<lb/>dae quae tardius suas expediunt vibrationes graviorem sonum edunt, ut Ga&shy;<lb/>lilaeus probat, ergo corda longior AB, licet aequaliter tensa ac CD, nihilo&shy;<lb/>minus gravius sonat quam CD, quod probare voluimus &rdquo; (ibi, c. </s>

<s>78-80). </s></p><pb xlink:href="020/01/780.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Del Magnete<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I Delle pi&ugrave; antiche osservazioni e delle prime esperienze fatte intorno al Magnete. </s>

<s>&mdash; II. </s>

<s>Di ci&ograve; che <lb/>a promovere la Filosofia magnetica si cooper&ograve; dal Gilberto, dal Sarpi e da Galileo. </s>

<s>&mdash; III. </s>

<s>Delle <lb/>teorie magnetiche, e di ci&ograve; che particolarmente ne pensarono i Filosofi inglesi. </s>

<s>&mdash; IV. Dell'ipo&shy;<lb/>tesi dei due fiuidi essenziali, e del loro modo di operar sul Magnete, secondo A. </s>

<s>Nardi e se&shy;<lb/>condo F. M. Grimaldi. </s>

<s>&mdash; V. </s>

<s>Delle variazioni della declinazione magnetica. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Bench&egrave; le ragioni altissime dell'armonia musicale rimanessero appresso <lb/>i Filosofi antichi, e rimangano tuttavia involte nel mistero ai moderni, lo <lb/>studio nonostante possibile a farsene sul soggetto fisico e particolare delle <lb/>corde vibranti porgeva qualche pascolo da quietare almeno, se non da sa&shy;<lb/>ziare le menti. </s>

<s>Dall'altra parte il pi&ugrave; ordinario e consueto modo del diffon&shy;<lb/>dersi il suono per l'aria, e l'aver quasi rese visibili le onde aeree nella so&shy;<lb/>miglianza coll'onde, che si diffondono circolarmente al largo nell'acqua, <lb/>lusingava e lusinga ancora l'intelletto per modo, da non accorgersi o da <lb/>passar facilmente sopra a que'tanti misteri, che s'ascondono sotto l'incre&shy;<lb/>spato velo di un'onda sonora. </s></p><p type="main">

<s>Ma che sodisfazione rendeva la Scienza alle curiosit&agrave; de'Filosofi, quando <lb/>si mostrarono tanto desiderosi d'intendere la ragione perch&egrave; il Magnete ap&shy;<lb/>petisca di ricongiungersi al ferro con tanto ardore, e con tanta costanza, <lb/>allungato in ago, s'appunti al segno della sua stella? </s>

<s>Migliaia di anni son <lb/>gi&agrave; passati dalla scoperta di quel primo fatto, centinaia son passati dall'os-<pb xlink:href="020/01/781.jpg" pagenum="224"/>servazione, che del secondo ne fecero i naviganti, e i Filosofi non hanno <lb/>saputo far altro che immaginare un alito, il quale esali dalle occulte vene <lb/>della pietra misteriosa, alito invisibile in s&egrave; e da non avere a rassomigliarlo <lb/>a nessun fatto visibile, o a nessun sensibile respiro della silenziosa Natura. </s></p><p type="main">

<s>&Egrave; perci&ograve; che della scienza magnetica pochi si hanno da contare i pro&shy;<lb/>gressi dalla Storia, alla quale non molto pi&ugrave; resta a dire dopo quelle spe&shy;<lb/>culazioni, in che s'assottigliarono i Filosofi intorno alle ragioni degli anti&shy;<lb/>chissimi fatti osservati o di qualcun altro de'nuovi scoperti. </s>

<s>Comunque sia, <lb/>&egrave; riserbato da noi il presente Capitolo a dar breve conto ai lettori di quei <lb/>fatti naturali e di quelle filosofiche speculazioni. </s></p><p type="main">

<s>Volere andare a ricercar chi fosse quel cos&igrave; esperto piloto, che si ab&shy;<lb/>batt&egrave; a riconoscere la direzione costante verso cui si volge un ago calami&shy;<lb/>tato, oltre che sarebbe un trascorrere troppo fuor de'termini assegnati alla <lb/>nostra Storia, non si potrebbe far con sodisfazione de'nostri Lettori, a'quali <lb/>non abbiamo da mettere innanzi in tal proposito nessuna certezza di docu&shy;<lb/>menti. </s>

<s>Concedendo perci&ograve; di buon grado che la verticit&agrave; dell'ago magne&shy;<lb/>tico sia stata osservata infino dagli antichi Cinesi, proseguiamo la pi&ugrave; con&shy;<lb/>corde opinione, che cio&egrave; quell'utilissimo ritrovato fossero i primi in Italia, <lb/>e forse in Europa, a metterlo in pratica i naviganti amalfitani. </s>

<s>Quasi tutti <lb/>gli scrittori, cos&igrave; antichi come moderni, s'accordano, da qualche particolare <lb/>in fuori di non molto rilievo, ad approvare quel che ne lasci&ograve; scritto il Porta <lb/>nel cap. </s>

<s>XXXII del Libro VII della <emph type="italics"/>Magia naturale<emph.end type="italics"/> dove, dopo aver ma&shy;<lb/>gnificati i vantaggi che arrec&ograve; l'uso della pisside magnetica all'arte naviga&shy;<lb/>toria, cos&igrave; soggiungeva: &ldquo; Cuius inventio Itali fuit Amalphi oriundi nostra <lb/>Campania, ut a Flavio traditur. </s>

<s>Qui nauticam totam ignorans acum paleae <lb/>vel ligno infigebat per transversum, et in lance aqua pleno mergebat acus, <lb/>ut natarent libere. </s>

<s>Dein magnetem circum ducendo acus eum sequebantur <lb/>quo subtracto, quasi quodam naturali motu, cuspides acu'<gap/>m polo arctico ver&shy;<lb/>tebantur, eoque invento quiescebant. </s>

<s>Praecognito igitur loco ad sua vota iter <lb/>dirigebat &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1651, pag. </s>

<s>316). </s></p><p type="main">

<s>Pi&ugrave; completa &egrave; la Storia, che in brevi parole ci tratteggia, al cap. </s>

<s>I <lb/>del I Libro del suo celebre Trattato, Guglielmo Gilberto: &ldquo; In Regno nea&shy;<lb/>politano Melphitani omnium primi, ut ferunt, pyxidem instruebant nauticam, <lb/>utque Flavius Blondus melphitanus haud perperam gloriari prodit, edocti a <lb/>cive quodam Johanne Goia, anno post natum Christum millesimo trecen&shy;<lb/>tesimo. </s>

<s>Oppidum illud in Regno neapolitano, non procul a Salerno, iuxta <lb/>promontorium Minervae situm, cuius principatu Carolus V Andream Doriam <lb/>magnum illum classicum Ducem, propter egregiam navatem operam, dona&shy;<lb/>vit. </s>

<s>Atque illa quidem pyxide nihil umquam humanis excogitatum artibus <lb/>humano generi profuisse magis constat. </s>

<s>Inventam tamen ante ab aliis, et <lb/>in marinis artibus admissam, ex veteribus scriptis, et quibusdam argumen&shy;<lb/>tis et coniecturis existimant nonnulli. </s>

<s>Scientia nauticae pyxidulae traducta <lb/>videtur in Italiam per Paulum Venetum, qui circa annum MCCLX apud <lb/>Chinas artem pyxidis didicit. </s>

<s>Nolim temen Melphitanos tanto honore privari, <pb xlink:href="020/01/782.jpg" pagenum="225"/>quod ab iis in mari Mediterraneo primum vulgariter fabricata fuerit &rdquo; (De <lb/>Magnete, Londini 1600, pag. </s>

<s>4). </s></p><p type="main">

<s>Nelle ristrette navigazioni del nostro Mediterraneo per&ograve; era difficile, per <lb/>non dire affatto impossibile, accorgersi delle variazioni che fa l'ago magne&shy;<lb/>tico sotto diversi meridiani e per distanze notabili fra s&egrave; divisi. </s>

<s>Ma quando <lb/>si prese pi&ugrave; alla larga il cammino, quel primo animoso che affid&ograve; la nave <lb/>allo sconfinato Oceano fu altres&igrave; il primo ad accorgersi di quella variazione <lb/>e a tenerne conto per dirigere pi&ugrave; cautamente il suo viaggio. </s>

<s>Fa testimo&shy;<lb/>nianza di ci&ograve; Ferdinando Colombo nel cap. </s>

<s>XVII della Vita che scrisse di <lb/>suo padre: &ldquo; Ma essendo poi corsi oltre cinquanta leghe verso ponente, ai <lb/>13 di Settembre (1482) trov&ograve; che da prima notte norvestavano le calamite <lb/>ne'bussoli per mezza quarta, e l'alba norvestava poco pi&ugrave; d'altra mezza, <lb/>da che conobbe che l'agucchia non andava a ferire la stella che chiamano <lb/>Tramontana, ma un altro punto fisso e invisibile. </s>

<s>La qual variet&agrave; fino al&shy;<lb/>lora mai non aveva conosciuto alcuno, e per&ograve; ebbe giusta causa di maravi&shy;<lb/>gliarsi di ci&ograve; &rdquo; (Traduzione di A. Ulloa, Londra 1867, pag. </s>

<s>52). </s></p><p type="main">

<s>Dalla stessa maraviglia fu preso anche l'altro illustre navigatore Gio&shy;<lb/>vanni da Empoli, il quale forse ignorava le osservazioni fatte gi&agrave; sul vario <lb/>declinar dell'ago al variare de'meridiani, da Cristoforo Colombo. </s>

<s>&ldquo; Maravi&shy;<lb/>glia mi fu assai, egli scrive, il variar delle Bussole, non solo della nostra <lb/>ma di tutte le altre dell'armata, che la fiamma della Tramontana, passando <lb/>noi di Ghinea cominci&ograve; ad inclinare, secondo &egrave; il parere di tutti noi e mas&shy;<lb/>sime de'Piloti, una quarta verso Libeccio, et als&igrave; (altres&igrave;) passando al Capo <lb/>di Buona Speranza per alla Ghinea, a Scirocco. </s>

<s>Io confesso non aver tanto <lb/>discorso o di scienza, che io sappia ritrattare se dalla calamita o dal Sole <lb/>o dalla regione proceda tal cosa, ma se Iddio, la salute e la tornata mi con&shy;<lb/>cede, vedr&ograve; se tanto porter&agrave; mio ingegno a sapere e tirerollo pi&ugrave; al netto <lb/>potr&ograve; &rdquo; (Vieusseux, Archivio Stor. </s>

<s>Append., T. III, pag. </s>

<s>91). </s></p><p type="main">

<s>Ecco il primo Navigatore filosofo, il quale aspetta quiete e tranquillit&agrave; <lb/>per speculare intorno ad un fatto, che il Colombo si stette solamente con&shy;<lb/>tento ad osservare. </s>

<s>Se veramente Giovanni attese, tornato in patria, a sodi&shy;<lb/>sfare a quel suo scientifico desiderio sar&agrave; senza dubbio dovuto tornar di&shy;<lb/>giuno e disperato di conseguire il suo intento, come avvenne a un altro <lb/>Navigatore filosofo nostro italiano. </s>

<s>Filippo Sassetti, prima d'intraprendere il <lb/>suo viaggio per l'Indie, cos&igrave; scriveva il d&igrave; 18 di Dicembre 1581 da Lisbona <lb/>al fiorentino amico suo Baccio Valori: &ldquo; Vedr&ograve; nel viaggio la declinazione, <lb/>che e'dicono della calamita, come ora sta sopra la linea meridiana, ora se <lb/>ne allontana e va discostandosi fino ad un certo che, e poi si viene a rap&shy;<lb/>pressare e torna sopra mezzogiorno un'altra volta; cosa che i Portoghesi la <lb/>sanno, ma confusamente, sicch&egrave; non si pu&ograve; fermare con effetto certo per <lb/>andare discorrendo intorno alla cagione &rdquo; (Lettere, Milano 1874, pag. </s>

<s>162). </s></p><p type="main">

<s>Voleva dunque il Sassetti far pi&ugrave; diligenti osservazioni di quelle che <lb/>non avessero fatto i Portoghesi, dietro gli ammaestramenti e gli esempi di <lb/>Cristoforo Colombo, e da vero Filosofo, che presente le rette regole del me-<pb xlink:href="020/01/783.jpg" pagenum="226"/>todo sperimentale, sopra quelle osservazioni de'fatti specularne le ragioni. </s>

<s><lb/>Tali erano le generose speranze concepute dal Sassetti, ma tornando nel <lb/>Settembre dell'anno dopo (1582) a scrivere allo stesso Valori, cos&igrave; gli con&shy;<lb/>clude: &ldquo; La calamita &egrave; uno strano strumento per la sua variet&agrave;, della quale <lb/>&egrave; difficil cosa trovare la causa. </s>

<s>N&egrave; anche la minima parte degli accidenti si <lb/>conoscono, volgendosi in certi luoghi a Tramontana direttamente, in altri <lb/>va da Tramontana a Greco fino a 14 gradi di tutta la circonferenza del&shy;<lb/>l'Orizzonte. </s>

<s>Altre volte va verso Maestro e fa tutte queste differenze a grado <lb/>a grado, c&agrave;mminando da Levante a Ponente ed anche da Mezzogiorno a Tra&shy;<lb/>montana &rdquo; (ivi, pag. </s>

<s>182). </s></p><p type="main">

<s>Sei anni dopo di aver per ripetute esperienze osservato ne'suoi viaggi <lb/>orientali il vario declinare dell'ago, scrive il Sassetti da Coccino a Lorenzo <lb/>Giacomini a Firenze, discutendo sopra una spiegazione che, del misterioso <lb/>fatto del cos&igrave; variamente declinare la Calamita, proponeva un tal Lupicino. <lb/></s>

<s>&ldquo; Ho bene inteso, scrive il nostro Fiorentino viaggiatore, con molto contento <lb/>l'effetto che fa la Calamita avvicinandosi i navili all'Elba. </s>

<s>Vorrei sapere io <lb/>che effetti ella faccia a coloro che si avvicinano al Polo, cio&egrave; che vanno in <lb/>que'paesi freddissimi, perch&egrave; l'avvertimento del Lupicino d&agrave; per ragione <lb/>del volgersi in alcuna parte pi&ugrave; che in un'altra, la posizione della medesima <lb/>pietra in.... parte del Globo terrestre, cosa che noi possiamo credere, <lb/>perch&egrave; se si va dintorno ad alcuno oriolo con un pezzo di Calamita, ella <lb/>inebria l'ago in maniera che la punta della lancetta si volge ora a Levante, <lb/>per calamitato ch'e'sia, ora a Ponente, ed ora a Mezzogiorno conforme alla <lb/>posizione della calamita che gli sta presso. </s>

<s>Ma in tanta distanza di paese <lb/>quanta pu&ograve; essere da questi monti non saputi fino al Capo di Buona Spe&shy;<lb/>ranza, che sono per lo meno cento gradi di latitudine, variato il mezzo che <lb/>ha ad essere il veicolo di questa virt&ugrave; da tante piagge e tanti venti e tante <lb/>e s&igrave; diverse costituzioni di aria, io non posso inclinare a far causa efficiente <lb/>di questo moto questa simpatia che &egrave; tra que'monti e l'ago calamitato. </s>

<s>Ag&shy;<lb/>giugnete che ogni pezzo di calamita ha il suo sito di mezzogiorno e tra&shy;<lb/>montana, e ciascuna parte tira la parte dell'ago che &egrave; calamitato con esso, <lb/>cio&egrave; la parte di Tramontana della Calamita tira l'ago per la lancetta della <lb/>freccia, e la parte di Mezzogiorno tira l'ago dalla parte opposta alla lancetta. </s>

<s><lb/>Ora questi monti, che si suppongono sotto e presso alla Tramontana risguar&shy;<lb/>dano la nostra Bussola con la parte di Mezzogiorno, in maniera che ella <lb/>avrebbe a tirare quella parte dell'ago, che &egrave; opposta alla lancetta, e non la <lb/>lancetta che &egrave; calamitata con la parte opposta di Tramontana; argomento <lb/>che mi pare insolubile, e quanto a me inclinerei a mescolarci qualche virt&ugrave; <lb/>celeste, quale ella si fosse &rdquo; (ivi, pag. </s>

<s>337, 38). </s></p><p type="main">

<s>Attendendo al significato di queste parole del Sassetti si rileva come, <lb/>speculando sopra le ragioni addotte dal Lupicino, egli avesse fatto ricerca <lb/>di riscontrare la nuova teoria proposta col fatto di ci&ograve; che avviene all'ago, <lb/>avvicinandosi i vascelli all'isola ferrifera dell'Elba, e sembrerebbe che le <lb/>osservazioni fatte da'marinari in proposito, e riferite al Sassetti, confermas-<pb xlink:href="020/01/784.jpg" pagenum="227"/>sero l'opinione del Lupicino, che cio&egrave; avvicinandosi a quell'Isola fosse tro&shy;<lb/>vato l'ago deviare notabilmente dalla direzione sua prima. </s>

<s>Questo era anzi <lb/>senza dubbio tale argomento da favorire il pensier di coloro i quali ricono&shy;<lb/>scevano le ragioni di quella deviazione da'ferriferi monti incogniti collocati <lb/>verso il polo Boreale. </s></p><p type="main">

<s>L'avvertimento che il Sassetti dice essere stato dato dal Lupicino, au&shy;<lb/>tore oscuro, era stato ridotto a teoria dal Fracastoro, teoria che il Gilberto <lb/>rifiuta, come il Sassetti stesso l'aveva gi&agrave; rifiutata, dicendo esser ci&ograve; con&shy;<lb/>trario a quel che si osserva di fatto. </s>

<s>&ldquo; Reiicienda est vulgaris illa recentio&shy;<lb/>rum opinio de montibus magneticis, aut rupe aliqua magnetica aut polo <lb/>phantastico a polo mundi distante, quibus motus pyxidis aut versorii com&shy;<lb/>poneretur. </s>

<s>Quam opinionem Fracastorius, ab aliis ante inventam ipse coluit <lb/>et auxit, omnino tamen cum experimentis non consentit. </s>

<s>Nam ad propor&shy;<lb/>tionem et aequalitatem geometricam in variis locis per mare, per terras va&shy;<lb/>riationis punctum mutaretur in Eurum aut occidentem semperque polum <lb/>magneticum versorium observaret, sed experientia docet nullum certum <lb/>esse polum aut terminum Tellure pro variatione fixum &rdquo; (De Magnete cit., <lb/>pag. </s>

<s>152) </s></p><p type="main">

<s>Cita anche il Gilberto il fatto dell'isola dell'Elba, ma le osservazioni sem&shy;<lb/>brano aver risposto al Filosofo inglese tutto al contrario di quel che fu ri&shy;<lb/>ferito al Navigator fiorentino, imperocch&egrave; servesi l'Autor <emph type="italics"/>De Magnete<emph.end type="italics"/> di <lb/>quelle stesse osservazioni a dimostrare e a confermare il suo asserto: <emph type="italics"/>Insula <lb/>in Oceano variationem non mutat.<emph.end type="italics"/> Ecco le parole proprie del Gilberto, che <lb/>fanno a questo proposito: &ldquo; Quod de Ilva insula mirantur nonnulli, quae <lb/>licet magnetum ferax sit, tamen versorium sive nautica pyxidula nullam fa&shy;<lb/>cit in illam peculiarem inclinationem cum prope navigia in Thyrreno pelago <lb/>feruntur, ut iam ostensa causa, sufficere posset, ita etiam hae causae pu&shy;<lb/>tandae sunt quod virtus magneticorum minorum ex se parum aut nihil extra <lb/>sua metalla extendatur &rdquo; (ibi, pag. </s>

<s>161). </s></p><p type="main">

<s>Quest'ultimo argomento del Gilberto si riduceva infine a quello del no&shy;<lb/>stro Sassetti, il quale per&ograve; non ebbe il coraggio di filosofare pi&ugrave; oltre, e <lb/>atterrito dalle tante difficolt&agrave;, che gli si paravano innanzi, fin&igrave; per risolvere <lb/>l'astruso problema, come il Cardano, il Ficino, lo Scaligero, ricorrendo ai <lb/>superni influssi celesti. </s></p><p type="main">

<s>Fra'viaggiatori filosofi, che rivolsero l'occhio e la mente al misterioso <lb/>fatto della declinazione magnetica, non &egrave; a tacer di Giovan Francesco Sa&shy;<lb/>gredo, il quale cos&igrave; scriveva da Aleppo in una sua lettera diretta a Galileo: <lb/>&ldquo; Ho fatto l'osservazione della Calamita, la quale certissimamente qui de&shy;<lb/>clina sette gradi e mezzo verso maestro, tanto che da Venezia a qui la dif&shy;<lb/>ferenza sarebbe di quindici: ne vada V. S. investigando la ragione &rdquo; (Alb. </s>

<s><lb/>VIII, 50) persuaso che dovesse riuscir d'intendere a Galileo quel che non <lb/>era potuto riuscire a nessun altro, non eccettuato lo stesso grande Gilberto. </s></p><p type="main">

<s>E anche prima di averne avuto l'invito dal gentiluomo veneziano avr&agrave;, <lb/>per sua propria curiosit&agrave;, Galileo investigata la ragione d&igrave; quel vario decli-<pb xlink:href="020/01/785.jpg" pagenum="228"/>nar del Versorio magnetico, ma per acuto e forte che si sentisse l'ingegno <lb/>troppo sproporzionata ritrovava quella sua virt&ugrave; alla durezza adamantina di <lb/>ci&ograve; che avevasi a penetrare. </s>

<s>N&egrave; di penetrarvi &egrave; a nessuno riuscito ancora <lb/>dopo tanti conati, cosicch&egrave; la scienza magnetica da questa parte &egrave; rimasta <lb/>alle prime osservazioni di Cristoforo Colombo, senz'aver fatto progressi. </s></p><p type="main">

<s>Restavano per&ograve; nella misteriosa pietra d'Ercole altre propriet&agrave; da sco&shy;<lb/>prire e, trovata chiusa l'una delle vie, si tent&ograve; di progredire per le altre, <lb/>tanto che della sua propria Filosofia non mancasse il Magnete. </s>

<s>Dettero mano <lb/>a coltivar la nuova scienza, fra noi, il Cardano e lo Scaligero, e con pi&ugrave; <lb/>senno d'ambedue il Fracastoro, ma primo ad abbandonare i giochi della <lb/>fantasia e a seguir le regole del Metodo sperimentale par che sia stato il <lb/>Sarpi, le speculazioni del quale e l'esperienze, che lo condussero a non po&shy;<lb/>che e assai notabili scoperte, furono ridotte come in ordine di Trattato dal <lb/>Porta e inserite a comporre il VII Libro della Magia Naturale. </s></p><p type="main">

<s>Premesse a quello stesso libro l'Autore una prefazioncella, nella quale <lb/>fra le altre si leggono le seguenti parole: &ldquo; Venetiis eidem studio invigi&shy;<lb/>lantem cognovimus R. M. </s>

<s>Paulum venetum Ordinis Servorum tunc provin&shy;<lb/>cialem, nunc dignissimum procuratorem, a quo aliqua didicisse non solum <lb/>fateri non erubescimus, sed gloriamur, quum eo doctiorem subtilioremque <lb/>quotquot adhuc videre contigerit neminem cognoverimus, natum ad Enci&shy;<lb/>clopediam, non tantum Venetae urbis et Italiae sed orbis splendor et or&shy;<lb/>namentum &rdquo; (Editio cit., pag. </s>

<s>287). </s></p><p type="main">

<s>Il Gilberto perci&ograve;, apparecchiandosi a scrivere il suo celebre Trattato, <lb/>trov&ograve; nel Porta il solo e unico precursore, di cui fa il seguente giudizio: <lb/>&ldquo; Novissime Baptista Porta, philosophus non vulgaris, in sua Magia natu&shy;<lb/>rali Librum septimum fecit condum et promum mirabilium Magnetis, sed <lb/>pauca illa de magneticis novit motionibus aut vidit unquam, et nonnulla de <lb/>manifestis viribus quae, vel ipse a R. M. </s>

<s>Paulo veneto didicit, vel suis vi&shy;<lb/>giliis deprompsit, non ita bene inventa et observata sunt, sed falsissimis <lb/>experimentis scatent &rdquo; (De Magnete cit., pag. </s>

<s>6) </s></p><p type="main">

<s>Il giudizio, che fa qui del Porta il Gilberto, a noi sembra per verit&agrave; <lb/>troppo severo, perch&egrave;, se non c'inganniamo, ha quel VII Libro qualit&agrave; pro&shy;<lb/>prie, che lo distinguono sopra gli altri, e tali in ogni modo da non meri&shy;<lb/>tarsi di essere accolto in fascio con essi sotto il titolo di Magia, divenuto <lb/>oramai meritamente obbrobrioso. </s>

<s>Non si vuol disputare qual parte abbia <lb/>avuto l'Autore in compor quel primo Trattato di Filosofia magnetica, e quale <lb/>il Sarpi; noi crediamo per&ograve; che da que'giochetti in fuori, immaginati spesso <lb/>scapestratamente per dar pascolo agli sfaccendati e a'curiosi, tutto quel che <lb/>v'ha di Fisica sperimentale propriamente appartenga al Sarpi. </s></p><p type="main">

<s>Quel fatto osservato gi&agrave; infin dagli antichi, e di cui fa tra gli altri men&shy;<lb/>zione anche S. </s>

<s>Agostino nella <emph type="italics"/>Citt&agrave; di Dio,<emph.end type="italics"/> il fatto cio&egrave; che il Magnete at&shy;<lb/>trae il ferro o altro simile Magnete, anche attraverso a una tavola di legno, <lb/>a una carta, a una tela, a una lamina di qualunque altro metallo che non <lb/>sia ferro o mescolato con ferro, d&agrave; occasione al Porta di pensare alla danza <pb xlink:href="020/01/786.jpg" pagenum="229"/>degli aghi, o, per accrescer lo spettacolo, di figurine di cartone infilate in <lb/>quegli aghi; danza magicamente governata dall'invisibile Magnete, che si <lb/>muove nascosto sotto una tavola. </s>

<s>Ma il Sarpi d&agrave; in persona dello Scrittore <lb/>le prime descrizioni di due esperienze, che dimostrano il magnetizzamento <lb/>per influenza e quello che pu&ograve; chiamarsi irraggiamento magnetico. </s></p><p type="main">

<s>L'esperienza del magnetizzamento per influenza ecco in che modo ci <lb/>vien descritta: &ldquo; Alia enim dote lapis idem apud nos commendandus venit, <lb/>nam cum alium lapidem apprehendit, non solum eum pertinaciter complecti&shy;<lb/>tur, sed in eius corpus suarum virium effluvium eructat expuitque, sed is <lb/>ubi uberiores vires sibi vindicavit, alium perinde manibus comprehendens, <lb/>facultatem eamdem expuit et diffundit; hic tertius eadem ut illa effectus, <lb/>undecumque ex proximo, vel longinquo alios rapit, eamdemque virtutem <lb/>iaculatur et vibrat, et hic alios, ut reciproco iaculatu, eadem qua tenetur <lb/>alios teneat, et ex unoquoque quasi iacula virtutis delibuta in alterum pro&shy;<lb/>ruant, et in altum elevati quasi concatenati pendere videntur &rdquo; (Magia natur. </s>

<s><lb/>cit., pag. </s>

<s>301). </s></p><p type="main">

<s>Col principio del Magnetismo per influenza passa nel capitolo appresso <lb/>il Porta a spiegare il fatto curioso di que'capillamenti in che si dirizza la <lb/>limatura del ferro, di che sia aspersa una verga o un globo magnetico; espe&shy;<lb/>rienza affatto nuova, la quale probabilmente si deve al Sarpi, com'a lui senza <lb/>dubbio si deve la teoria di questo, per cos&igrave; dire, irraggiamento magnetico. </s></p><p type="main">

<s>Un'altra notabilissima esperienza &egrave; quella che il nostro Autore ci de&shy;<lb/>scrive al cap. </s>

<s>XLVII del citato settimo Libro della <emph type="italics"/>Magia<emph.end type="italics"/> con queste pa&shy;<lb/>role: &ldquo; Ferream scobem si in papyrum convolutam posuerimus, quomodo <lb/>seplassarii efformari solent in conum, Magnetem ei propius admoverimus, <lb/>tota simul universa scobs eamdem vim recipit ac longum trahit ferrum ei&shy;<lb/>que vim conciliat, ut integro ferro. </s>

<s>At si scobem agitabis et iterum papyro <lb/>impones, vis illa confunditur et disperditur et nil operatur &rdquo; (ibi, pag. </s>

<s>324). <lb/>Questa stessa esperienza la troviamo citata, senza che nessuno faccia men&shy;<lb/>zione di chi prima la istitu&igrave; e la descrisse, da'due pi&ugrave; insigni Autori della <lb/>Filosofia magnetica, il Gilberto e il Grimaldi, per servirsene ambedue a con&shy;<lb/>fermare le loro speculate magnetiche teorie. </s>

<s>Il primo infatti la cita nel ca&shy;<lb/>pitolo XXIII, libro II, del suo Trattato per dimostrare in che modo, am&shy;<lb/>messo che tutto insieme il Globo terrestre sia un gran Magnete, <emph type="italics"/>terrarum <lb/>fundamenta connectuntur, coniunguntur, ferruminantur<emph.end type="italics"/> (De Magn. </s>

<s>cit, <lb/>pag. </s>

<s>91). Il secondo se ne serve per dimostrare, come tra poco si vedr&agrave; <lb/>meglio, che la virt&ugrave; magnetica dipende da un certo orientamento moleco&shy;<lb/>lare che, turbato, guasta e dissolve la virt&ugrave; stessa. </s></p><p type="main">

<s>Questi fatti, e altri simili che si potrebbero aggiungere, sembrano a noi <lb/>sufficienti a giustificare il nostro asserto parerci cio&egrave; troppo severo il giu&shy;<lb/>dizio, che il Gilberto faceva del suo predecessore nella Scienza magnetica, <lb/>Giovan Batista Porta. </s>

<s>Che non tutti gli sperimenti descritti dal nostro Fi&shy;<lb/>sico napoletano siano esatti, questo lo concediamo facilmente, comprendendo <lb/>assai bene che non poteva non esser cos&igrave; per qualche fretta, che nello spe-<pb xlink:href="020/01/787.jpg" pagenum="230"/>rimentare ebbe il Sarpi, e per non aver sempre il Porta appresa la verit&agrave; <lb/>de'veduti o riferiti esperimenti. </s>

<s>Ma se si bada bene allo spirito, che in dar <lb/>quel giudizio informava l'animo del Filosofo inglese, non sar&agrave; difficile il ri&shy;<lb/>trovar che, secondo lui, il gran difetto del Porta consisteva in non aver sa&shy;<lb/>puto investigar l'universal ragione de'moti magnetici, e nell'avere ammesso <lb/>un fluido invisibile come causa di quegli stessi occulti moti. </s></p><p type="main">

<s>Per quel che riguarda la prima parte di cos&igrave; fatti principii dottrinali <lb/>sopra cui, quasi come sopra fondamento si posa la Filosofia magnetica, po&shy;<lb/>teva senza dubbio il Gilberto vantarsi di aver superato il Porta, o il Sarpi <lb/>che voglia dirsi, ma, quanto all'altra parte, il Gilberto riman di gran lunga <lb/>inferiore ai due nostri Italiani, essendo stati essi i primi che, proscrivendo <lb/>quelle insignificanti parole di simpatia e di antipatia, introdussero i fluidi <lb/>magnetici per ispiegarne gli occulti e maravigliosi effetti della natura. </s></p><p type="main">

<s>Il Gilberto &egrave; nemico de'fluidi corporei: la virt&ugrave; magnetica egli vorrebbe <lb/>quasi ridurla a una propriet&agrave; metafisica, per cui vagheggi&ograve; le idee di Ta&shy;<lb/>lete Milesio e dello Scaligero, che alla pietra magnetica concessero un'anima. <lb/></s>

<s>&ldquo; Non est igitur corporeum quod defluit a Magnete, aut quod ferrum in&shy;<lb/>greditur .... sed ille est, ne mundus rueret, concentus, partium nempe glo&shy;<lb/>borum mundi perfectarum et homogenearum ad totum analogia.... Quare <lb/>in tam admirabili effectu et stupendo, ab aliis naturis diverso, vigore insito, <lb/>Thaletis Milesii non absurda admodum opinio, nec vehemens delirium Sca&shy;<lb/>ligeri censura, quia animam Magneti concessit &rdquo; (ibi, pag. </s>

<s>67, 68). Ma la <lb/>Filosofia moderna ha condannato oramai l'opinion del G&igrave;lberto per assurda <lb/>o almeno per immaginaria, ed ha accolta l'ipotesi de'fluidi introdotta gi&agrave; <lb/>dal Sarpi e dal Porta, e sopra questa ipotesi ha posato anzi il fondamento <lb/>al grande edifizio della nuova scienza magnetico-elettrica. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>L'aver ridotto il Gilberto i varii e cos&igrave; apparentemente discordi moti <lb/>magnetici a una causa unica universale, &egrave; senza dubbio il precipuo e mas&shy;<lb/>simo merito della sua <emph type="italics"/>Fisiologia nuova del Magnete.<emph.end type="italics"/> &ldquo; Io sommamente <lb/>laudo, scriveva Galileo, ammiro e invidio questo Autore per essergli caduto <lb/>in mente concetto tanto stupendo circa a cosa maneggiata da infiniti inge&shy;<lb/>gni sublimi, n&egrave; da alcuno avvertita. </s>

<s>Parmi anco degno di grandissima laude <lb/>per le molte nuove e vere osservazioni fatte da lui, in vergogna di tanti <lb/>autori mendaci e vani &rdquo; (Alb. </s>

<s>I, 439). </s></p><p type="main">

<s>Il concetto tanto stupendo, che Galileo ammira e invidia al Gilberto, &egrave; <lb/>che il Globo terrestre sia una gran calamita e che un globo di calamita sia <lb/>una piccola Terra. </s>

<s>Mario Guiducci, in una sua Lezione accademica, com&shy;<lb/>pendia in cos&igrave; belle ed eleganti parole lo svolgimento che fa di quel con&shy;<lb/>cetto l'Autore nel celeberrimo libro <emph type="italics"/>De Magnete,<emph.end type="italics"/> che i nostri Lettori con-<pb xlink:href="020/01/788.jpg" pagenum="231"/>sentiranno volentieri si lasci libert&agrave; di parlare intorno a cos&igrave; importante <lb/>soggetto storico all'eloquentissimo discepolo di Galileo. </s></p><p type="main">

<s>&ldquo; Ma perch&egrave; lungo sarebbe, dice egli a'suoi Uditori, e per avventura <lb/>noioso l'addurre tutte le ragioni e i discorsi, onde a cos&igrave; affermare si mosse <lb/>questo grand'uomo, per&ograve; al suo Libro rimettendo chiunque pi&ugrave; chiara e <lb/>squisita contezza bramasse in tal materia, mi baster&agrave; solo, per non passarmi <lb/>affatto digiuno in conclusione cos&igrave; nobile e cotanto lontana dai pareri popo&shy;<lb/>lari e comuni, rappresentarvi in generale la maniera, colla quale procede e <lb/>discorre questo Filosofo, e secondariamente, di secento e pi&ugrave; esperienze ma&shy;<lb/>ravigliose, colle quali e'v&agrave; confermando il suo intento, addurne due o tre <lb/>delle pi&ugrave; notabili. </s>

<s>Il modo dunque con cui procede il Gilberto &egrave; questo. </s>

<s><lb/>Dopo d'aver diligentemente e minutamente osservato varie e diverse pro&shy;<lb/>priet&agrave; d'un piccol Globo di calamita; dopo d'avere esattamente considerato <lb/>con quali forze e con quali ordinate e determinate regole vada movendo e <lb/>disponendo il ferro posato sopra il suo convesso; dopo d'avere scoperta ed <lb/>esaminata la maravigliosa disposizione della sua virt&ugrave; variamente per le varie <lb/>sue parti disposta, e finalmente notata la perpetua inclinazione che ha di <lb/>conformarsi con infallibile regola alla posizione e sito dell'Universo; passa <lb/>alla considerazione del gran Globo terrestre. </s>

<s>E non avendo perdonato n&egrave; a <lb/>fatica n&egrave; a diligenza n&egrave; a spesa niuna, va rincontrando minutamente tutte <lb/>le medesime propriet&agrave;, inclinazione, disposizione e virt&ugrave; ed il tutto cos&igrave; ag&shy;<lb/>giustatamente e a capello rispondere, che con molta ragione chiama egli <lb/><emph type="italics"/>Terrella<emph.end type="italics"/> il piccol globo di calamita, siccome <emph type="italics"/>Gran calamita<emph.end type="italics"/> il globo terre&shy;<lb/>stre, non riconoscendo in effetto tra essi altra differenza che di grandezza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto al secondo, fra le molte e sensate prove, per confermazione <lb/>di tal verit&agrave;, osserva il Gilberto in qualsivoglia piccola palla di calamita due <lb/>principali punti, diametralmente tra loro opposti, e segnalati di propria virt&ugrave;, <lb/>i quali dispongono e indirizzano il globo conforme alla situazione e posi&shy;<lb/>zione dell'Universo; uno de'quali perpetuamente si rivolge a settentrione, <lb/>l'altro a mezzogiorno. </s>

<s>E questi, per la loro conformit&agrave; co'poli del mondo, <lb/>chiama egli poli della calamita. </s>

<s>E siccome ugualmente remoto dall'uno e <lb/>dall'altro polo della Terra &egrave; da Cosmografi assegnato il circolo equinoziale; <lb/>cos&igrave; ancora tra questi due poli magnetici dimostra il Gilberto ritrovarsi il <lb/>suo equatore di sito e d'operazione altres&igrave; corrispondente all'equinoziale della <lb/>gran Terra. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma per venire a maggior particolarit&agrave;, l'esperienza ci mostra che, se <lb/>si toccher&agrave; colla punta d'uno stile di ferro la palla di Calamita in alcun <lb/>de'detti poli, v. </s>

<s>g. </s>

<s>nel settentrionale, si conferisce a tal ferro una virt&ugrave;, me&shy;<lb/>diante la quale, o sospeso da un sottil filo o posato sull'acqua, sopra una <lb/>tavoletta di suvero o in altra guisa lasciato in libert&agrave; e indifferenza a rivol&shy;<lb/>gersi verso qualunque parte, rivolge subito a settentrione la cuspide che &egrave; <lb/>stata toccata. </s>

<s>E la medesima, presentata al polo australe della calamita, tosto <lb/>ne vien respinta e indietro scacciata. </s>

<s>Il medesimo effetto si vede per l'ap&shy;<lb/>punto accader nei ferri, che hanno avuto per lungo tempo una continuata <pb xlink:href="020/01/789.jpg" pagenum="232"/>postura di riguardare con alcuno de'loro termini o verso Borea o verso Au&shy;<lb/>stro, i quali acquistano l'istessa virt&ugrave; dal Gilberto chiamata <emph type="italics"/>verticit&agrave;<emph.end type="italics"/> d'in&shy;<lb/>dirizzarsi a quella medesima plaga, ove han rimirato per lungo tempo, siccome <lb/>parimente di rivolgersi addietro e d'esser ributtati dalla contraria ed opposta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; N&egrave; paia ad alcuno incredibile che il globo terrestre abbia facolt&agrave; di <lb/>calamitare i ferri e di conferire ad essi questa medesima verticit&agrave;, poich&egrave; <lb/>la Calamita stessa non altronde trae questa propriet&agrave; d'indirizzarsi determi&shy;<lb/>natamente con una sua parte all'uno con l'altra all'opposto polo, che dalla <lb/>situazione o postura, che per gran tempo ebbe nella sua miniera, imperoc&shy;<lb/>ch&egrave; la lunga assuefazione a un determinato sito si converte in natura &rdquo; (Lez. </s>

<s><lb/>accad. </s>

<s>premesse alle Rime di M. Bonarroti, Firenze 1863, pag. </s>

<s>CXXV, VI). </s></p><p type="main">

<s>Questa nuova e stupenda teoria della verticit&agrave; per assuefazione vien <lb/>confermata da un fatto che il Gilberto dice di avere appreso dalla lettura <lb/>di un libro scritto da maestro Filippo Costa da Mantova, il qual fatto &egrave; che <lb/>una staffa di ferro, la quale da lungo tempo serviva a sostenere le pietre <lb/>del campanile alla Chiesa di S. Agostino, essendosi torta e portatasi al fab&shy;<lb/>bro ferraio per raddirizzarla, fu dall'artefice trovato cos&igrave; per caso che at&shy;<lb/>traeva il ferro come la Calamita. </s>

<s>Ma la prova diretta di questa verticit&agrave; la <lb/>desume l'Autor <emph type="italics"/>De Magnete<emph.end type="italics"/> dal fatto che, messo un ferro nella fucina e <lb/>poi battutolo sull'incudine, avendo cura di tenerlo rivolto in direzione co&shy;<lb/>stante da Borea ad Ostro, nel raffreddarsi, acquista la virt&ugrave;, come la Cala&shy;<lb/>mita stessa, di dirigersi al Polo (Lib. </s>

<s>III, cap. </s>

<s>XII, pag. </s>

<s>139-42). </s></p><p type="main">

<s>Gli encomii dati all'opera del Gilberto, da Galileo e dai discepoli di lui <lb/>rappresentati in Mario Guiducci, sono informati dalla coscienza del vero e <lb/>come usciti da gente, che ha meditato sulle dottrine della Fisiologia del Ma&shy;<lb/>gnete, e ne ha saputo trarre profitto all'ingegno. </s>

<s>Non cos&igrave; pu&ograve; dirsi de'giu&shy;<lb/>dizi enfatici di alcuni moderni, i quali, quando si metton dietro ad Autori <lb/>antichi, ne parlano quasi sempre senz'averli mai letti. </s>

<s>Ci serva per esem&shy;<lb/>pio di ci&ograve; l'Humboldt, il quale, nel Tomo II del suo celebre <emph type="italics"/>Cosmo,<emph.end type="italics"/> encomia <lb/>la Fisiologia nuova del Magnete come l'opera pi&ugrave; ingegnosa e importante <lb/>che sia stata mai scritta intorno alle teorie magnetoelettriche, soggiugendo <lb/>essere stata opinion del Gilberto che il Magnetismo e l'Elettricit&agrave; sieno due <lb/>diverse emanazioni di una medesima forza della materia, ond'&egrave; ch'ei fa sog&shy;<lb/>getto d'ambedue insieme alla sua trattazione (Traduz. </s>

<s>di V. Uberti, Na&shy;<lb/>poli 1850, pag. </s>

<s>438). Ora basta leggere solamente il principio del Cap. </s>

<s>II <lb/>del secondo libro <emph type="italics"/>De Magnete<emph.end type="italics"/> per sentir come il Gilberto ridasi di coloro <lb/>che l'attrazion dell'ambra rassomigliavano a quella del Magnete, mostrando <lb/>com'ei sien rimasti ingannati dall'apparenza. </s>

<s>&ldquo; Nam in aliis corporibus, <lb/>egli cos&igrave; propriamente si esprime, aliter quam in Magnete attrahendi etiam <lb/>vis conspicua videtur, quaemadmodum in Succino, de quo nonnulla prius <lb/>dicenda sunt, ut qualis illa corporum applicatio, et quam diversa a magne&shy;<lb/>ticis actionibus et aliena sit, insciis adhuc mortalibus, qui illam inclinatio&shy;<lb/>nem attractionem esse putant et cum magneticis coitionibus conferunt, ap&shy;<lb/>pareat &rdquo; (ibi, pag. </s>

<s>47). </s></p><pb xlink:href="020/01/790.jpg" pagenum="233"/><p type="main">

<s>L'ammirazione sincera, che Galileo prese delle nuove speculazioni ma&shy;<lb/>gnetiche del Gilberto, non poteva non accendere in lui il desiderio di rivolger <lb/>la mente a coltivar quegli studii, a'quali aveva l'arguto Britanno aperto un <lb/>cos&igrave; largo campo, e che prometteva d'esser di ritrovati nuovi tanto fecondo. </s>

<s><lb/>E chi sa quali sensi ridestasse quel libro nell'animo del Sarpi, che solen&shy;<lb/>nemente sentivasi proclamare ivi per primo istitutore de'magnetici esperi&shy;<lb/>menti e si trovava in persona del Porta accusato per quelle pagine con ra&shy;<lb/>gioni, che non apparivano vere al giudizio degli imparziali. </s></p><p type="main">

<s>&Egrave; naturale perci&ograve; che critici acuti e saggiatori finissimi della bont&agrave; degli <lb/>argomenti sperimentali promossi dal Filosofo inglese, fossero i due sommi <lb/>nostri Italiani Galileo e il Sarpi, ed &egrave; cosa naturalissima che soggetto a'loro <lb/>commerci scientifici dovessero fare anco queste nuove magnetiche questioni. </s>

<s><lb/>Era infatti da non bene ancora interamente due anni stata pubblicata in <lb/>Londra la Fisiologia magnetica del Gilberto, e il Sarpi, sotto il d&igrave; 2 Settem&shy;<lb/>bre 1602, cos&igrave; incomincia una sua lettera da Venezia indirizzata a Padova <lb/>a Galileo: &ldquo; Poich&egrave; li 25 miglia, per quanto siamo distanti m'impedisce il <lb/>discorrere con V. S., cosa che desidero sopra tutte le altre, voglio tentare <lb/>di farlo con intermedio delle lettere, e al presente, nel proposito ch'inco&shy;<lb/>minciai trattare con esso lei, quando l'altro giorno fummo insieme, della <lb/>inclinazione della calamita con l'orizzonte &rdquo; (Lettere, Firenze 1863, Vol. </s>

<s>I, <lb/>pag. </s>

<s>7, 8). L'inclinazione dell'ago, che faceva il soggetto del colloquio e del <lb/>carteggio passato fra due grandi uomini, &egrave; uno de'movimenti della Cala&shy;<lb/>mita, che Galileo, verso la fine della III Giornata de'Massimi Sistemi, dice <lb/>essere stato <emph type="italics"/>nuovamente scoperto dal Gilberto<emph.end type="italics"/> (Alb. </s>

<s>I, 445). &Egrave; il vero per&ograve; <lb/>che non si fa il Gilberto nuovo scopritore della <emph type="italics"/>inclinazione<emph.end type="italics"/> dell'ago, chia&shy;<lb/>mata da lui col comun nome di <emph type="italics"/>Declinazione,<emph.end type="italics"/> ma ne fa autore Roberto <lb/>Normann, di cui cos&igrave; scrive sulla fine del cap. </s>

<s>I del primo libro, dopo averlo <lb/>annoverato fra gl'inventori di nuovi strumenti nautici: &ldquo; Atque hic est ille <lb/>Robertus Normannus, navita peritus et ingeniosus artifex, qui primum de&shy;<lb/>clinationem magnetici ferri invenit &rdquo; (De Magn. </s>

<s>cit., pag. </s>

<s>7, 8). </s></p><p type="main">

<s>Ai moti dell'inclinazione dell'ago consacra il Gilberto tutto il suo li&shy;<lb/>bro V, che perci&ograve; egli intitola <emph type="italics"/>De declinatione.<emph.end type="italics"/> Sull'argomento stesso, di <lb/>che tratta l'Autore in questo suo V libro, s'intrattiene il soggetto della ci&shy;<lb/>tata lettera del Sarpi a Galileo, la qual lettera parve prima all'Alberi e poi <lb/>al Polidori tanto oscura. </s>

<s>Ed &egrave; veramente tale, ma l'oscurit&agrave; dipende in gran <lb/>parte dal non essersi curati i due egregi uomini di commentarla col testo <lb/>gilbertiano, a cui forse non sospettaron nemmeno che avesse relazione, e <lb/>ad ambedue in ogni modo troppo faceva difetto la scienza necessaria a ca&shy;<lb/>pir ci&ograve; che in quella oscura pagina si trattava. </s></p><p type="main">

<s>Incomincia dunque il Filosofo inglese nel cap. </s>

<s>I a descrivere lo stru&shy;<lb/>mento inclinatorio, e dopo avere insegnato il modo di costruirlo cos&igrave; sog&shy;<lb/>giunge: &ldquo; Cum in aliis magneticis motionibus telluris et lapidis iusta <lb/>convenientia sit et manifeste sensibus nostris apparens consensus per de&shy;<lb/>monstrationes nostras; ita in hac declinatione globi terrestris cum Magnete, <pb xlink:href="020/01/791.jpg" pagenum="234"/>certa et perspicua est concordantia. </s>

<s>Huius tanti et tamdiu omnibus morta&shy;<lb/>libus incogniti effectus talis causa certa et verissima existit &rdquo; (ibi, pag. </s>

<s>187). </s></p><p type="main">

<s>Al Sarpi per&ograve; sembrava di vederci tutt'altro che certezza, per cui scri&shy;<lb/>veva: &ldquo; Non veggo come e a che fine, n&egrave; quali parti o quale vogli situare. </s>

<s><lb/>Ma egli come ha trovato il suo modo? </s>

<s>Per esperienza o per ragione? </s>

<s>Non <lb/>per esperienza, perch&egrave;, o con la terra, e questo ricercherebbe viaggio re&shy;<lb/>golato per una quarta. </s>

<s>Non con la terrella, perch&egrave; si ricerca che il Versorio <lb/>non abbia sensibile proporzione con la terrella, acci&ograve; nell'istesso luoco sii <lb/>il centro e la cuspide: altrimenti non ha fatto niente. </s>

<s>Non mi par manco <lb/>che per ragione, imperocch&egrave; bisogna render causa della descrizione di quei <lb/>cerchi, che lui chiama <emph type="italics"/>conversionis,<emph.end type="italics"/> che nella piccola designazione (non <emph type="italics"/>di&shy;<lb/>chiarazione,<emph.end type="italics"/> come interpetra il Polidori, perch&egrave; <emph type="italics"/>disegnazione<emph.end type="italics"/> o <emph type="italics"/>designa&shy;<lb/>zione<emph.end type="italics"/> &egrave; la traduzione della parola <emph type="italics"/>diagramma<emph.end type="italics"/> usata dal Gilberto) ne de&shy;<lb/>scrive tre &rdquo; (Lett. </s>

<s>cit., pag. </s>

<s>8, 9). </s></p><p type="main">

<s>Le parole che seguono appresso a queste nella tanto oscura Lettera del <lb/>Sarpi possono essere facilmente illustrate dalla <emph type="italics"/>piccola designazione,<emph.end type="italics"/> come <lb/>il Sarpi stesso la chiamava, o diagramma, come la chiamava il Gilberto, o <lb/>figura, come comunemente si chiama da noi, intercalata nel testo a pag. </s>

<s>198 <lb/>della citata edizion del Gilberto, e anche insieme dall'altra pi&ugrave; grande de&shy;<lb/>signazione, o diagramma o figura interfogliata ivi tra pag. </s>

<s>200 e pag. </s>

<s>201. <lb/>Ma molto meglio delle figure gioveranno a interpetrar le parole del Sarpi <lb/>le parole proprie con che il Gilberto stesso incomincia il capitolo VIII. &ldquo; In <lb/>superiore diagrammate ad corpus telluris vel terrellae circulus conversionum <lb/>et circulus declinationum coaptantur, cum primo, ultimo, et medio arcu con&shy;<lb/>versionum et declinationum. </s>

<s>Nunc a quinta quoque parte arcus illius qui <lb/>conversionis arcus omnes terminat, quique in 99 partes aequales dividi <lb/>subintelligitur, arcus ducuntur ad polum, et a quinto quolibet gradu arcus <lb/>terminantis quadrantis declinationum, quadrantes ducuntur ad centrum, et <lb/>simul ducit linea spiralis declinationem in omni latitudine, quadrantis mo&shy;<lb/>bilis adminiculo, indicans &rdquo; (De Magnete cit., pag. </s>

<s>200). </s></p><p type="main">

<s>Delle quali parole del Gilberto, ripigliando il Sarpi il costrutto, cos&igrave; se&shy;<lb/>guita nella sopra citata lettera a scrivere a Galileo: &ldquo; Della spirale non ho <lb/>difficolt&agrave; alcuna, ma &egrave; un bel genere di elica, generandosi di due moti cir&shy;<lb/>colari. </s>

<s>Prego V. S. che abbia un poco di considerazione sopra le mie diffi&shy;<lb/>colt&agrave;, e supplisca al mancamento del mio Autore, il quale ha lasciate le <lb/>cause delle pi&ugrave; oscure cose che siano. </s>

<s>Almeno avesse detto come ne &egrave; ve&shy;<lb/>nuto in cognizione! Appresso, perch&egrave; desidero far isperienza di questa in&shy;<lb/>clinazione, per levarmi la fatica, prego V. S. scrivermi il modo tenuto in <lb/>fare il Versorio, con che li applica li perni, se con fuoco o con colla, e come <lb/>e di che materia li fa, e sopra che li appoggia, e insomma ogni particolare, <lb/>perch&egrave; non vorrei consumar tempo in sperimentar molte cose, poich&egrave; ella <lb/>ha fatto la fatica &rdquo; (Lettere cit., pag. </s>

<s>9, 10). </s></p><p type="main">

<s>Galileo non rispose per lettera al Sarpi, n&egrave; direttamente mand&ograve; la Bus&shy;<lb/>sola di declinazione, ch'egli aveva gi&agrave; costruita, interpetrando la descrizione <pb xlink:href="020/01/792.jpg" pagenum="235"/>alquanto monca ed oscura, che ne aveva fatta il Gilberto, e forse miglio&shy;<lb/>randone la costruzione, ma glie la sped&igrave; per mezzo del Sagredo, a cui com&shy;<lb/>mise anche insieme di rispondere alle domande fatte dal padre Maestro <lb/>intorno ai dubbii incontrati nel rimeditare il libro V <emph type="italics"/>De Magnete.<emph.end type="italics"/> Il d&igrave; <lb/>18 Ottobre infatti di quello stesso anno 1602 cos&igrave; il Sagredo incominciava <lb/>una sua lettera, che doveva da Venezia recapitare in Padova a Galileo: <lb/>&ldquo; Ringrazio V. S. Ecc.ma de'ferri. </s>

<s>Dar&ograve; al P. M. </s>

<s>Paolo il Declinatorio, e <lb/>far&ograve; l'ambasciata com'ella mi comanda. </s>

<s>Ho provato il Declinatorio al modo <lb/>com'ella mi mostr&ograve; cost&igrave;. </s>

<s>L'effetto di star perpendicolare, posto il suo as&shy;<lb/>setto sotto la meridiana, m'&egrave; riuscito molto bene, e situato sotto il paral&shy;<lb/>lelo ho veduto la declinazione, ma sopra il pi&ugrave; e meno a me pare che sia <lb/>materia da filosofare &rdquo; (Campori, Carteggio gal. </s>

<s>ined., Modena 1881, pag. </s>

<s>6). </s></p><p type="main">

<s>Ecco che il Sagredo pure sente come il Sarpi, il bisogno di portare in <lb/>queste dottrine un po'di Filosofia, di che pareva essere il lettore lasciato <lb/>in difetto dal Gilberto, e tale &egrave; pure il sentimento di Galileo, il quale, dopo <lb/>d'aver tanto esaltati i meriti del Filosofo inglese e averne ammirato e in&shy;<lb/>vidiato lo stupendo concetto, di che &egrave; informato il suo libro, cos&igrave; soggiunge: <lb/>Quello che avrei desiderato nel Gilberti &egrave; che fosse stato un poco maggior <lb/>matematico e in particolare ben fondato nella Geometria, la pratica della <lb/>quale l'avrebbe reso men risoluto nell'accettare per concludenti dimostra&shy;<lb/>zioni quelle ragioni, ch'ei produce per vere cause delle vere conclusioni <lb/>da s&egrave; osservate. </s>

<s>Le quali ragioni, liberamente parlando, non annodano e <lb/>stringono con quelle forze che indubitabilmente debbon fare quelle, che di <lb/>conclusioni naturali necessarie ed eterne, si possono addurre &rdquo; (Alb. </s>

<s>I, <lb/>439, 40). </s></p><p type="main">

<s>Prosegue ivi a dir Galileo di avere speranza che col progresso del tempo <lb/>si avesse a perfezionare quella nuova scienza magnetica, per via di altre <lb/>nuove osservazioni, e intanto egli stesso avr&agrave; cercato, co'suoi proprii stu&shy;<lb/>dii e con le sue proprie esperienze, che quella generosa speranza avesse il <lb/>desiderato suo effetto. </s>

<s>L'occasione gli si offerse propizia a proposito che, <lb/>desiderando il Granduca di fare acquisto di un buon pezzo di calamita ga&shy;<lb/>gliarda, egli ne propose il contratto con Giovan Francesco Sagredo che la <lb/>possedeva, e il contratto stesso per la sua mediazione ne fu stipulato. </s>

<s>Data <lb/>dalla munificenza del Sovrano facolt&agrave; a Galileo di poter far uso di questa <lb/>pietra calamitica a suo piacere, volle sperimentarne la magnificata virt&ugrave;, e <lb/>tanto seppe aiutare la Natura con l'arte, che giunse a farle sostenere una <lb/>libbra di peso sopra quello che sosteneva, essendo in mano del suo primo <lb/>padrone. </s>

<s>L'arte usata attorno alla Calamita da Galileo consisteva nella scelta <lb/>del ferro del contatto e nella pi&ugrave; opportuna disposizione delle parti di lui. </s></p><p type="main">

<s>&ldquo; N&egrave; si maravigli V. S. </s>

<s>Illustrissima (scriveva il d&igrave; 8 di Febbraio 1608 <lb/>a Belisario Vinta) che ci sia bisogno di esperienze e investigazioni per sco&shy;<lb/>prir la sua forza, perch&egrave;, prima i punti nella pietra, dove la virt&ugrave; &egrave; robu&shy;<lb/>stissima, sono due soli poli e questi bisogna con diligenza ritrovare. </s>

<s>Inoltre <lb/>la virt&ugrave; del sostenere non &egrave; meno del ferro che della calamita, sicch&egrave; non <pb xlink:href="020/01/793.jpg" pagenum="236"/>ogni ferro n&egrave; di ogni grandezza e figura &egrave; ugualmente sostenuto, ma l'ac&shy;<lb/>ciaio elaboratissimo e di una particolare figura e grandezza pi&ugrave; gagliarda&shy;<lb/>mente si attacca. </s>

<s>Inoltre, le armature dei poli, attaccate un poco pi&ugrave; qua o <lb/>l&agrave;, possono far gran variazione: e io in questi quattro giorni che l'ho te&shy;<lb/>nuta nelle mani, e che mi ci sono occupato intorno, l'ho fatta reggere quasi <lb/>una libbra di pi&ugrave; di quello, che il padrone della pietra abbia mai veduto <lb/>sostenergli, e sono in speranza, facendo io fabbricare alcuni pezzi d'acciaio <lb/>finissimo, di ridurla a sostenere ancora molto pi&ugrave; &rdquo; (Alb. </s>

<s>VI, 46). </s></p><p type="main">

<s>Il d&igrave; 4 d'Aprile infatti, tornando a scrivere allo stesso Vinta, gli dice <lb/>di aver ridotto la Calamita a sostenere il doppio del suo proprio peso, e <lb/>scrivendogli il di 3 Maggio di nuovo annunzia di esser progredito di qual&shy;<lb/>che altro poco, riducendo la stessa calamita a sostener qualche cosa pi&ugrave; del <lb/>doppio. </s>

<s>In questa lettera dice Galileo di aver fatto fabbricare i ferri in forma <lb/>di <emph type="italics"/>ancorette,<emph.end type="italics"/> e di qui deriv&ograve; il nome di <emph type="italics"/>ancora,<emph.end type="italics"/> che si d&agrave; tuttavia al ferro <lb/>che combacia co'poli dell'armatura. </s>

<s>&ldquo; Ho fatto fabbricare questi due ferri <lb/>in forma di due ancorette, s&igrave; per dar loro qualche forma, come per allu&shy;<lb/>dere a quello che forse favolosamente si scrive essersi trovato un pezzo di <lb/>calamita s&igrave; vasto e robusto, che sosteneva un'anc&ograve;ra di nave, e s&igrave; ancora <lb/>per la comodit&agrave; di queste branche, alle quali si possono andare attaccando <lb/>altri diversi pezzetti fino all'ultimo tentativo della sua gagliardezza &rdquo; (ivi, <lb/>pag. </s>

<s>54, 52). </s></p><p type="main">

<s>In questa stessa lettera Galileo manifesta una sua opinione, ed &egrave; che il <lb/>medesimo pezzo non sostenga con egual forza in qualunque luogo della <lb/>terra, ma che varii d'intensit&agrave; secondo la latitudine, e ci&ograve; desidererebbe egli <lb/>che fosse osservato con diligenza. </s>

<s>Arguta ipotesi &egrave; questa, la quale se fosse <lb/>stata vera avrebbe aggiunto ai tanti servigii prestati dalla Bussola, quello <lb/>di ritrovar con grandissima facilit&agrave; le latitudini geografiche, senz'altro bi&shy;<lb/>sogno di ricorrere alle osservazioni celesti. </s></p><p type="main">

<s>Distratto dalle maravigliose scoperte fatte col Canocchiale e tutto im&shy;<lb/>merso nelle astronomiche contemplazioni, Galileo non torn&ograve; sulla Calamita <lb/>se non che dopo diciott'anni, dando effetto alle gi&agrave; concepute speranze di <lb/>moltiplicarne la virt&ugrave; perfezionandone l'armatura. </s>

<s>Scriveva in fatti cos&igrave; il <lb/>d&igrave; 27 di Giugno 1626, in una sua lettera indirizzata a Cesare Marsigli: &ldquo; Io <lb/>sono da tre mesi in qua sopra un maneggio ammirabile, che &egrave; di moltipli&shy;<lb/>plicar con artificio estremamente la virt&ugrave; della Calamita in sostenere il ferro. </s>

<s><lb/>Gi&agrave; sono arrivato a fare che un pezzetto di sei once, che per sua forza na&shy;<lb/>turale non sostiene pi&ugrave; di un'oncia di ferro, ne sostiene con arte once 150, <lb/>e spero di avere a passare ancora a maggior quantit&agrave;, e ne dar&ograve; conto a <lb/>V. S. come a persona speculativa, e che gusta di simili accidenti, dei quali <lb/>io non posso abbastanza stupirmi, mentre veggo farsi tanto arrabbiatamente <lb/>una congiunzione con una semplice virt&ugrave; immateriale, e tanto pi&ugrave; mi pre&shy;<lb/>gio in questo affare quanto che io veggo che il Gilberto, che tanto si pro&shy;<lb/>fond&ograve; in questa speculazione e tanto speriment&ograve;, e con tanta diligenza scrisse, <lb/>non pass&ograve; a far che un simil pezzo di calamita, che per s&egrave; stesso reggesse <pb xlink:href="020/01/794.jpg" pagenum="237"/>non pi&ugrave; di un'oncia, con l'artificio poi potesse regger pi&ugrave; di once tre, come <lb/>si legge nel secondo libro suo <emph type="italics"/>De Magnete<emph.end type="italics"/> al capo 17 &rdquo; (ivi, pag. </s>

<s>314). </s></p><p type="main">

<s>A questa lettera risponde il Marsigli ringraziando Galileo dell'onore fat&shy;<lb/>togli nell'avergli dato parte delle sue glorie in proposito dello straordinario <lb/>augumento della virt&ugrave; della Calamita &ldquo; e tanto pi&ugrave;, soggiunge, quanto sen&shy;<lb/>tivo predicare per ammirabile l'invenzione di Bartolommeo Sovero svizzero, <lb/>il quale si vantava con un cappelletto d'acciaio finissimo sopra una sferetta <lb/>di Calamita farle moltiplicare la virt&ugrave; sessanta volte pi&ugrave; dell'innata &rdquo; (Cam&shy;<lb/>pori, Carteggio cit., pag. </s>

<s>246). </s></p><p type="main">

<s>Quella del Sovero non era dunque un'invenzione sua propria, essen&shy;<lb/>doch&egrave; i cappelletti di acciaio o i <emph type="italics"/>nasi<emph.end type="italics"/> ferrei, com'ei gli chiama, furono prima <lb/>usati per armature dal Gilberto, che cos&igrave; gli descrive: &ldquo; Concava lamella <lb/>rotunda latitudinis digiti applicatur convexae Magnetis superficiei polari et <lb/>artificiose connectitur. </s>

<s>Aut glans ferrea basi in conum obtusum assurgens <lb/>excavata paululum et lapidis superficiei coaptata alligatur magneti. </s>

<s>Ferrum <lb/>sit optimum acciarum levigatum splendens et aequali. </s>

<s>Tali instrumento Ma&shy;<lb/>gnes qui antea tantum uncias 4 ferri sustulit, nunc uncias 12 attollit &rdquo; (De <lb/>Magn. </s>

<s>cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Ora che il Sovero, usando lo stesso metodo, potesse aver moltiplicata <lb/>sessanta volte quella virt&ugrave; del Magnete che al Gilberto era riuscito appena <lb/>di ridurre al triplo, non par credibile. </s>

<s>Galileo perci&ograve; trovando difettoso il <lb/>metodo delle armature usato dal Gilberto, e pedantescamente imitato dal <lb/>Sovero, lo corresse e lo perfezion&ograve; coll'aumentar la superficie del contatto, <lb/>e cos&igrave; venne giustamente ad acquistarsi il merito di aver egli trovato il modo <lb/>d'armar validamente la Calamita. </s>

<s>&ldquo; Questa osservazione, egli dice, di spia&shy;<lb/>nar la superficie de'ferri che si hanno a toccare, non fu avvertita dal Gil&shy;<lb/>berto, anzi egli fa i ferri colmi, sicch&egrave; piccolo &egrave; il loro contatto, onde av&shy;<lb/>viene che minore assai sia la tenacit&agrave; con la quale essi ferri si attaccano &rdquo; <lb/>(Alb. </s>

<s>I, 443). </s></p><p type="main">

<s>A una tal pratica di armare la Calamita giunse Galileo, non gi&agrave; per <lb/>caso, ma guidatovi dal ragionamento fondato sull'esperienza. </s>

<s>Assicuratosi di <lb/>fatto essere le particelle magnetiche nella pietra pi&ugrave; rare assai di quelle del <lb/>ferro, da ci&ograve; ne concludeva che, facendosi toccar ferro con ferro, gl'infiniti <lb/>punti dell'uno s'incontrano con gl'infiniti punti dell'altro, sicch&egrave; i filamenti <lb/>che collegano insieme i due ferri son molti pi&ugrave; di quelli che collegano la <lb/>calamita col ferro, per essere la sostanza della calamita stessa assai pi&ugrave; po&shy;<lb/>rosa, e molto meno sincera. </s>

<s>Ond'&egrave; ch'ei conclude con s&igrave; fatte parole: &ldquo; Ap&shy;<lb/>plicando la superficie del ferro alla superficie della calamita, le minime par&shy;<lb/>ticelle del ferro, bench&egrave; continuatissime forse pi&ugrave; di quelle di qualsivoglia <lb/>altro corpo (siccome ci mostra il lustrarsi egli pi&ugrave; di qualsivoglia altra ma&shy;<lb/>teria) non tutte, anzi poche, incontrano sincera calamita, ed essendo pochi <lb/>i contatti debile &egrave; l'attraimento. </s>

<s>Ma perch&egrave; l'armatura della Calamita, oltre <lb/>al toccar gran parte della sua superficie, si veste anco della virt&ugrave; delle parti <lb/>vicine, ancorch&egrave; non tocche, essendo esattamente spianata quella sua faccia <pb xlink:href="020/01/795.jpg" pagenum="238"/>alla quale s'applica l'altra pur similmente bene spianata del ferro da esser <lb/>sostenuto; il toccamento si fa d'innumerabili minime particelle, se non forse <lb/>degl'infiniti punti di amendue le superficie, per lo che l'attaccamento ne <lb/>riesce gagliardissimo &rdquo; (ivi, pag. </s>

<s>443). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Era nelle generose speranze di Galileo, come fu gi&agrave; accennato di sopra, <lb/>che la nuova Scienza magnetica dovesse progredire, non tanto per la sco&shy;<lb/>perta di nuovi fatti, quanto per venir confermata con vere e necessarie di&shy;<lb/>mostrazicni. </s>

<s>Ecco il punto della gran difficolt&agrave;, e dove Galileo sentiva riseder <lb/>davvero la vita di quella scienza: dimostrarne le proposizioni concludendole <lb/>da veri e necessarii principii. </s>

<s>Bench&egrave; fosse ci&ograve;, in soggetto fisico, un pre&shy;<lb/>tender l'impossibile, il Castelli nondimeno vi si volle provare, e lo fece in <lb/>un suo Discorso rimasto inedito e sconosciuto infino a questi ultimi giorni. </s>

<s><lb/>Qualche frammento che noi scegliemmo a infiorar la raccolta di <emph type="italics"/>Problemi <lb/>naturali<emph.end type="italics"/> stampata in Firenze nel 1874 da Giulio Cesare Sansoni, invogli&ograve; <lb/>altri a pubblicarlo nella sua integrit&agrave;, inserendolo nel Tomo XVI del Bul&shy;<lb/>lettino di scienze fisiche e matematiche di Roma, fascicolo dell'Ottobre 1883. <lb/>Che debba un tal Discorso essere stato scritto dal Castelli nel 1639, s'ar&shy;<lb/>gomenta da una lettera di Galileo del 18 Dicembre di quello stesso anno, <lb/>nella quale gli dice che stava aspettando con ansiet&agrave; sue scritture promesse <lb/>della Calamita, del terremoto, e dell'origine de'fiumi (Alb. </s>

<s>VII, 242). </s></p><p type="main">

<s>Il Discorso procede ordinatamente con rigoroso metodo geometrico, di&shy;<lb/>stinto in proposizioni coll'aggiunta di scolii e di corollarii e colla premessa <lb/>di definizioni e di supposti. </s>

<s>Ma a chi domandasse se veramente il Castelli <lb/>fosse con questa sua operetta riuscito a colorire le generose speranze di Ga&shy;<lb/>lileo, risponderebbe candidamente il Castelli stesso colle seguenti parole: <lb/>&ldquo; Voglio per&ograve;, avanti di passare pi&ugrave; oltre, significarle qualmente facendo ri&shy;<lb/>flessione a questo mio Discorso, ero precipitato in qualche mestizia, poich&egrave;, <lb/>a dire il vero schiettamente, con questi progressi di sopra spiegati non tro&shy;<lb/>vavo d'aver fatto altro che, dopo avermi accomodate alcune cosucce e sup&shy;<lb/>posizioni per vere, ero poi trapassato avanti, ma mostrando sempre le me&shy;<lb/>desime cose, solamente per modo di dire sotto diverse vedute, le quali poi <lb/>in realt&agrave; sono le medesime che quelle prime debolezze, come facilmente si <lb/>pu&ograve; comprendere &rdquo; (Bullettino cit., pag. </s>

<s>17). N&egrave; il giudizio &egrave; inspirato dalla <lb/>modestia: quella lucida coscienza erasi, caso raro, severamente giudicata da <lb/>s&egrave; medesima. </s>

<s>Alcuni vorrebbero riconoscer qui come nuova l'esperienza della <lb/>limatura del ferro o della calamita pestata, che si dispone in filamenti e <lb/>quasi imbarba i due poli della stessa calamita intera; esperienza che si legge <lb/>descritta, come vedemmo, tanti anni prima nella Magia Naturale del Porta. </s></p><p type="main">

<s>Aveva il nostro Autore per&ograve; nel citato Discorso proposta la soluzione <pb xlink:href="020/01/796.jpg" pagenum="239"/>di un problema importantissimo e principalissimo in questa scienza nuova, <lb/>il qual problema era: come la Calamita potesse operare in distanza e at&shy;<lb/>traverso a corpi amagnetici, che vi fossero in mezzo frapposti. </s>

<s>A tale in&shy;<lb/>tento egli presupponeva che tutti i corpi, di qualunque natura si fossero, <lb/>tenessero nella loro sostanza disseminate particelle di calamita, le quali mo&shy;<lb/>bilissime per la loro piccolezza fossero disposte a rivolgersi facilmente per <lb/>quel verso, a cui fossero dirette dalla forza del Magnete. </s>

<s>Cos&igrave; fatti corpu&shy;<lb/>scoli, disordinatamente disseminati, costituiscono secondo il Castelli i corpi <lb/>magnetici, ch'ei chiama di <emph type="italics"/>second'ordine.<emph.end type="italics"/> Presupposte le quali cose &ldquo; si <lb/>apre, segue a dire l'Autore, spaziosa strada di render la ragione come pare <lb/>che la virt&ugrave; della Calamita penetri in certo modo quasi in istante ogni sorta <lb/>di corpo, e che si faccia la sua operazione come in un momento con le altre <lb/>calamite e con i ferri senza toccarli, in distanza molto notabile, imperocch&egrave; <lb/>quando si vedr&agrave; v. </s>

<s>g. </s>

<s>che la Calamita operi trapassando il vetro, il legno, <lb/>l'argento, ecc., noi possiam dire che i corpuscoli di second'ordine sparsi per <lb/>la sostanza de'suddetti corpi, con la presenza della Calamita, subito vengono <lb/>ordinati calamiticamente, e per&ograve; essi, senza introdurre altra penetrazione di <lb/>virt&ugrave;, sono quelli che operano con i loro ordinati toccamenti, e rimossa la <lb/>Calamita, ritornando nella loro primiera costituzione, mancano di quella <lb/>forza &rdquo; (ivi, pag. </s>

<s>21). </s></p><p type="main">

<s>Il Grimaldi riprese poi il filo delle idee del Castelli e intess&egrave; forse la <lb/>pi&ugrave; compiuta teoria che si potesse desiderare a que'tempi. </s>

<s>A render conto <lb/>di quelle grimaldiane teorie ci porterebbe ora l'ordine del nostro discorso, <lb/>ma tanta &egrave; l'importanza della presente parte di Storia che giova, invece di <lb/>seguir dietro a quell'ordine, risalir su a'primi principii, riferendo ci&ograve; che <lb/>specularono i Filosofi per ritrovar qualche ragione a'magnetici misteri. </s>

<s>E <lb/>perch&egrave; non vogliam divagarci in cercar notizie, le quali ci farebbero uscir <lb/>de'limiti che ci siamo prescritti, e abbiamo dall'altra parte quelle erudite <lb/>notizie compendiate e raccolte dal Gassendo, terrem dietro a ci&ograve; ch'egli <lb/>scrive nel X libro delle sue Considerazioni su Diogene Laerzio. </s></p><p type="main">

<s>Dop'aver ivi distinto una duplice virt&ugrave; magnetica, quella di attrarre il <lb/>ferro e l'altra di dirigersi al polo &ldquo; cum ab antiquis, egli tosto soggiunge, <lb/>disquisita causa prioris.... nihil extat tamen de posterioris, sive directricis <lb/>causa disputatum.... Recentiores dumtaxat fuere qui hanc edisseruerint, ut <lb/>idem Peregrinus opinatus ipsam a coeli polis pendere, et Ficinus nomina&shy;<lb/>tim ab Austro, dum Cardanus a cauda Ursae.... Fracastorus a montibus <lb/>quibustam magneticis.... et Maurolicus a quadam magnetica insula.... <lb/>dum Gulielmus Gilbertus demum et qui illum imitati sunt, ab ipsamet Terra, <lb/>quae et ingens Magnes, Magnetem quasi parvam Terram et ferrum ut ipsius <lb/>prolem in nativum situm hoc est in Boream Austrumque conformat. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ad quod attinet ad priorem,... Cardanus innuit appetitum quemdam <lb/>nutritionis esse quo Magnes ferrum corripiat.... Democritus ad effluxiones <lb/>atomorum.... Cohaeret cum istis ex parte Platonis sententia: temetsi enim <lb/>ille videatur non satis perspicue se se explicare, ex Plutarchi tamen inter-<pb xlink:href="020/01/797.jpg" pagenum="240"/>petratione admisit quoque effluxiones quasdam, a quibus aer Magneti vici&shy;<lb/>nus in orbem propulsus, dum redit ad implendum vacuum secum una cor&shy;<lb/>ripiat ferrum.... Fracastorus autem cum effluvium quoque atomorum non <lb/>abnuat, censet tamen ferri motionem versus Magnetem fieri, non ut vacuum <lb/>impediatur, sed ut amotae loculis suis particulae connaturalem obtineant si&shy;<lb/>tum, quod dum nituntur, sua quoque subiecta continentia moveunt. </s>

<s>&rdquo; E <lb/>prosegue a dir del Gilberto, e com'egli negasse al Magnete ogni sorta di <lb/>effluvi corporei e sostanziali (Lugduni 1675, T. I, pag. </s>

<s>193, 94). </s></p><p type="main">

<s>Venne dopo il Gilberto, tra'Filosofi che fecero pi&ugrave; romore, il Cartesio, <lb/>il quale, avendo ridotte a XXXIV le Questioni, che si possono fare intorno <lb/>al Magnete, prese tutte a risolverle con un'ipotesi sola, dedotta come per <lb/>corollario dal suo fantastico sistema. </s>

<s>Egli non solo ammette, contro l'opi&shy;<lb/>nion del Gilberto, i magnetici efflussi corporei, ma alle particelle compo&shy;<lb/>nenti que'magnetici efflussi assegna la particolar figura cocleare, colle spire, <lb/>in quelle che vengon da Borea, in altro verso intorte da quelle che vengono <lb/>d'Ostro. </s>

<s>E perch&egrave; cos&igrave; fatte particelle, chiamate dal Cartesio <emph type="italics"/>Striate,<emph.end type="italics"/> ve&shy;<lb/>nendo dalle regioni celesti attraversan la Terra e n'escon da per tutte le <lb/>parti, non c'&egrave; pericolo che scambino mai direzione, perch&egrave; da Borea, per <lb/>esempio, non possono entrar ne'pori aperti se non le particelle, che hanno <lb/>le avvitature disposte secondo la madrevite, in che si rigirano da quella <lb/>parte gl'interni canaletti, dentro cui fanno quelle stesse particelle striate, <lb/>attraverso alla Terra, i loro continui corsi e ricorsi. </s>

<s>&ldquo; Ad quarum proprie&shy;<lb/>tatum causas intelligendas, proponamus nobis ob oculos Terram.... note&shy;<lb/>musque particulas striatas ab australi coeli parte venientes, alio plane modo <lb/>intortas esse quam venientes a Boreali, quo fit ut unae aliarum meatus in&shy;<lb/>gredi plane non possint. </s>

<s>Notemus etiam australes quidem recta pergere.... <lb/>per mediam Terram.... quia meatus, per quos ab una parte ad aliam ve&shy;<lb/>nerant, sunt tales ut per ipsos regredi non possint &rdquo; (Principia Philosophiae, <lb/>Amstelodami 1650, pag. </s>

<s>265). </s></p><p type="main">

<s>Di s&igrave; fatte goffaggini si potevano contentare i semplici, ma non sodisfar&shy;<lb/>sene i Filosofi, i quali n&ograve; nelle finzioni della mente cercav<gap/> le cause na&shy;<lb/>turali, ma ne'principii matematici e negli sperimenti. </s>

<s>Necessariamente av&shy;<lb/>versa alla Filosofia cartesiana era quella che il Newton aveva istituita nella <lb/>sua patria, dove dalle teorie sull'attrazione universale si concep&igrave; la speranza <lb/>di derivar lume a intendere i misteri dell'attrazion del Magnete. </s>

<s>Ma tor&shy;<lb/>narono cos&igrave; belle speranze deluse, essendo l'intima causa, per cui le par&shy;<lb/>ticelle della materia s'attraggono e si respingono a vicenda, rimasta allo <lb/>stesso Newton occulta. </s></p><p type="main">

<s>Non manc&ograve; nonostante la nuova Filosofia matematica di rifletter qual&shy;<lb/>cuno de'suoi splendidi raggi sulla Filosofia magnetica, la quale parve allora <lb/>che ripigliasse in Inghilterra il vigore infusole dal Gilberto, quando pi&ugrave; ac&shy;<lb/>curate osservazioni confermarono una scoperta fatta parecchi anni prima dal <lb/>Gillibrando. </s>

<s>Concorrevano a coltivar quegli studii, insiem col Newton, due <lb/>altri valorosi ingegni, l'Hook e l'Halley, che sorgevano in splendida Pleiade <pb xlink:href="020/01/798.jpg" pagenum="241"/>sull'orizzonte di Londra, quando in Firenze eran gi&agrave;, dietro il sole di Ga&shy;<lb/>lileo, tramontati i numerosi pianeti che gli facevan corona. </s>

<s>Uno solo rima&shy;<lb/>neva ancora a consolar della sua luce il vedovo cielo d'Italia, l'astro di <lb/>Vincenzio Viviani. </s></p><p type="main">

<s>Vecchio di pi&ugrave; che sett'anni si trovava il Viviani a rappresentar la per&shy;<lb/>sona dell'ultimo Principe rimasto d'una dinastia gi&agrave; trapassata, e che si <lb/>vede sorgere a petto una nuova dominazione straniera. </s>

<s>Altri forse si sarebbe <lb/>ritirato in s&egrave; stesso a compiacersi delle glorie antiche, non superabili dalle <lb/>nuove, e ad ostentare il fasto delle antiquate divise, ma il Discepolo di Ga&shy;<lb/>lileo, messo da parte l'orgoglio impotente e dispettoso, compiacevasi mesta&shy;<lb/>mente di veder che il buon seme delle dottrine sparso dal suo Maestro, <lb/>sfruttato oramai il proprio campo, andasse rigogliose a crescere e a frutti&shy;<lb/>ficare in campi vergini, e per piagge remote. </s>

<s>A que'nuovi cultori inglesi <lb/>si rivolse con desiderio il vecchio Italiano, chiedendo a loro notizia de'loro <lb/>studii, ed essi da Londra corrispondevano ossequiosi con Firenze, quasi <lb/>com'aura che ritorna profumata da quel pomario, ch'ella and&ograve; a fecondare. </s></p><p type="main">

<s>Il d&igrave; 27 Dicembre dell'anno 1695 il Viviani, che aveva sentito dire di <lb/>quel fervore di studii con che l'Hook e l'Halley s'erano dati a sperimentare <lb/>e a speculare intorno al Magnete, scriveva una lettera a Roberto Southvell, <lb/>allora presidente della R. Accademia, per esser particolarmente informato <lb/>delle scoperte, delle ipotesi, delle teorie, di tutto insomma che s'era scritto <lb/>intorno alla natura e alle propriet&agrave; della Calamita. </s>

<s>La mal ferma salute e <lb/>l'ufficio non permisero al Southvell di rispondere con sollecitudine, e dopo <lb/>otto mesi il Viviani disperava oramai di esser degnato delle desiderate no&shy;<lb/>tizie, quando un giorno dell'Agosto del 1696 gli agenti in Firenze di Giu&shy;<lb/>seppe Cagnoni, ch'esercitava la mercatura a Londra, portano a casa dello <lb/>stesso Viviani e gli consegnano una cassetta approdata pochi giorni prima <lb/>a Livorno colla nave <emph type="italics"/>Regina coeli<emph.end type="italics"/> capitanata da Alessandro Polino. </s>

<s>Apre <lb/>con cuor trepidante quella cassetta, e vi trova dentro varie carte manoscritte, <lb/>due fascicoli e due grossi volumi stampati. </s>

<s>Gli bast&ograve; un semplice sguardo <lb/>per saper che si contenevano tutte insieme raccolte in que'due gran volumi <lb/>le opere matematiche del Wallis, e un'altro semplice sguardo bast&ograve; per <lb/>capir che que'due fascicoli contenevano due Dissertazioni magnetiche del&shy;<lb/>l'Halley. </s></p><p type="main">

<s>Maggior curiosit&agrave; lo frugava di veder ci&ograve; che riferissero quelle carte <lb/>manoscritte, per prima delle quali gli venne a mano il Diploma, che lo di&shy;<lb/>chiarava socio nuovamente eletto della R. </s>

<s>Accademia di Londra. </s>

<s>Erano in <lb/>quella stessa cassetta, insiem col Diploma, accluse due lettere, una di Ric&shy;<lb/>cardo Waller, segretario, e un'altra di Giovanni Wallis, sopra la quale il <lb/>Viviani, quietato a un tratto l'animo fra quel tumulto di pensieri e di af&shy;<lb/>fetti, si tratteneva a leggere ci&ograve; che, dopo essersi scusato il celebre Mate&shy;<lb/>matico inglese per non ricordarsi di quel che aveva scritto allo stesso Vi&shy;<lb/>viani in una lettera andata smarrita, cos&igrave; soggiungeva: &ldquo; Quod autem iam <lb/>expetis, ut earum exemplar ad te mittam praestare non valeo, quoniam <pb xlink:href="020/01/799.jpg" pagenum="242"/>carum exemplar vel apud me non retinui, vel nunc non possum invenire. </s>

<s><lb/>Sed neque satis memini quid inibi contineretur praeter officiosam saluta&shy;<lb/>tionem meique in te amoris et observantiae testificationem, iustaeque de te <lb/>conceptae aestimationis et de Galilaeo tuo, quem ego semper magni aesti&shy;<lb/>mavi, et etiam nunc veneror et cui debemus, non modo Cavalierium, Tor&shy;<lb/>ricellium, Vivianum aliosque magnos viros, sed et totam quam dicimus no&shy;<lb/>vam Philosophiam, quo praelucente, caeteri suas accenderunt faces &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXLVIII, c. </s>

<s>87). </s></p><p type="main">

<s>Rest&ograve; commosso il buon vecchio alla lettura di queste parole, compia&shy;<lb/>cendosi che quegli Inglesi inchinassero cos&igrave; innanzi al suo Galileo la fronte <lb/>baldanzosa, e gli pareva che in quel Diploma avessero gli Accademici di <lb/>Londra mandato a Firenze a riconoscere i diritti del principato antico della <lb/>scienza italiana. </s></p><p type="main">

<s>Ricomposto poi l'animo, seguit&ograve; il Viviani a svolgere quelle altre carte <lb/>rimaste e lesse in fronte alla prima scritta di propria mano del Southvell: <lb/>&ldquo; Londini 20 Martii 169 5/6. Sententia excerpta ex authographo Domini Hal&shy;<lb/>ley circa Magnetem, pro Domino Viviano conscripta. </s>

<s>&rdquo; Lesse poi in fronte <lb/>a una seconda carta aggiunta e ripiegata con quella prima: &ldquo; De Gresham <lb/>Colledge a Londres le 9 Mar. </s>

<s>169 5/6. Opinion de Mons.r le D.r Hook tou&shy;<lb/>chant le pierre d'Aimant pour Mons.r Viviani. </s>

<s>&rdquo; </s></p><p type="main">

<s>Le due scritture son, secondo noi, documento cos&igrave; importante di storia, <lb/>da non defraudarne della notizia i Lettori, alla maggior parte de'quali non <lb/>sar&agrave; forse noto questo scientifico commercio ch'ebbero i Colleghi del Newton <lb/>coll'ultimo rimasto fra i Discepoli di Galileo. </s></p><p type="main">

<s>&ldquo; Authores Philosophiae magneticae quod spectat, scriveva il Southvell, <lb/>post Cartesium, non est quod sciam qui rem adeo difficilem aggredi ausus <lb/>sit novamve aliquam hypothesim comminisci, etiamsi a multis iam annis <lb/>apud eruditos cartesianae illae particulae striatae pro ingenioso figmento po&shy;<lb/>tius quam pro vera et adaequata attractionis ac directionis magneticae causa <lb/>efficiente merito censeatur. </s>

<s>Latet igitur horum causa inter ardua Philoso&shy;<lb/>phiae, qualia sunt causae gravitatis ac particularum materialium cohaesionis <lb/>ac mutui coalitus, quae, cum ipsius materiae intimam cognitionem requi&shy;<lb/>rere videantur, fortasse prae tenuitate humani ingenii captum nostrum ef&shy;<lb/>fugiunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Gravitatis autem phaenomena explicuit celeberrimus noster Newtonus <lb/>ex sola hypothesi quod unaquaeque materiae particula gravis, sit in aliam <lb/>gravius particulam pro ratione distantiae ac quantitatis suae, inde demonstra&shy;<lb/>vit vires attractionis vel, ut vocat centripetas corporum coelestium a summa <lb/>sive mole omnium particularum in illis corporibus collectarum oriri, eique <lb/>semper proportionatas esse; cuius quidem inventi veritas per totum mundi <lb/>systema elucescit. </s>

<s>Causam autem huius vis congregativae ne coniectura qui&shy;<lb/>dem probabili assequi valemus. </s>

<s>Periter si lapis supponamus ex atomis ma&shy;<lb/>gneticis similiter positis conflari, quarum qualibet sit axe suo ac polis prae&shy;<lb/>dita, totum compositum foret etiam Magnes, qui iunctis viribus traheret <pb xlink:href="020/01/800.jpg" pagenum="243"/>secundum axem communem per earum medium tendentem, quo supposito, <lb/>plurima solvuntur Magnetis phaenomena alias satis difficilia explicatu. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Acus autem magnetica, a quovis Magnete impregnata, in eodem loco <lb/>tandem semper acquirit positionem, nisi quod longo temporis intervallo <lb/>omnes ubique deviant, gradatim quidem ac regulariter apud nos in Occi&shy;<lb/>dentem fertur per unum circiter gradum spatio sexennii, ac in eamdem <lb/>semper plagam deflexit per CXV annos, ex quo primum Londini observa&shy;<lb/>tum est, quo temporis spatio plus quam XVII gradus continuo motu pro&shy;<lb/>cessit. </s>

<s>Olim enim in Ortum XI gradus declinavit, hodie vero prope VII gra&shy;<lb/>dus in Occasum, uti assiduis observationibus experimur. </s>

<s>Ac procul dubio <lb/>multo ulterius progressura est, antequam stationaria facta, iterum in Ortum <lb/>pedem referre incipiat. </s>

<s>Multorum enim saeculorum est periodus, nec nisi <lb/>longa et accurata observationum serie enucleanda uti recte observat Vir cla&shy;<lb/>rissimus. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; A centrali vero causa per totum Terrarum orbem operanti, acumque <lb/>magneticam ubique locorum simul agitante, hae deflectiones oriuntur, quod <lb/>quidem summo studio explicare conatus est Halleus noster duabus Disser&shy;<lb/>tationibus in Actis nostris philosophicis ea de re editis. </s>

<s>In priore quatuor <lb/>esse polos magneticos contendit, iisque loca in globi superficie designat, ex <lb/>quorum viribus varie compositis directionem Acus per totum Orbem gu&shy;<lb/>bernari credit. </s>

<s>In posteriori causas varietatis deflectionis inquirit, globum&shy;<lb/>que hunc terraqueum concavum supponit incluso vel uno vel forzam pluribus <lb/>minoribus globis eodem communi gravitatis centro innixis. </s>

<s>Quemadmodum <lb/>videmus Saturnum intra circulum sibi concentricum collocari, atque una <lb/>moveri. </s>

<s>Cumque globus interior possit vim Magnetis habere, simulque len&shy;<lb/>tissimo motu situs eius respectu interioris possit immutari, hoc modo putat <lb/>omnibus totius sistematis magnetici phaenomenis satisfactum iri. </s>

<s>Quo rectius <lb/>possis de his hypothesibus iudicium ferre, utramque Dissertationem tibi tra&shy;<lb/>smittendam curavi &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXIV, c. </s>

<s>28). </s></p><p type="main">

<s>L'altra scrittura dell'Hook, come dal titolo riferito di sopra si saranno <lb/>accorti i lettori, era dettata in francese, e trovasi inserita a c. </s>

<s>32 del citato <lb/>Tomo CXXXIV. </s>

<s>Il nitido carattere e l'accurata ortografia ci fanno presup&shy;<lb/>porre che non sia autografa. </s>

<s>Forse il Southvell ne fece, dall'autografo stesso <lb/>dell'Hook, far quella copia, perch&egrave; riuscisse pi&ugrave; comodamente leggibile e <lb/>con minor difficolt&agrave; ne potess'essere intesa la lingua. </s>

<s>Bench&egrave; confessi a pi&ugrave; <lb/>occasioni il Viviani di non aver gran pratica in tradur dal francese, tradusse <lb/>nonostante, a nostro giudizio, assai bene quella scrittura dell'Hook, ond'&egrave; <lb/>che noi, lasciato l'originale, trascriveremo qui la traduzione italiana fatta <lb/>forse per divulgarne fra i discepoli e gli amici la notizia. </s></p><p type="main">

<s>&ldquo; Per rispondere alle questioni e domande del saggio signor Viviani in&shy;<lb/>torno agli Autori, che hanno scritto sopra la Calamita, loro osservazioni, sco&shy;<lb/>perte, ipotesi, teoriche, ecc., non posso al presente dir molto, poich&egrave;, per <lb/>quanto ho veduto finora nelle scritture e libri trattare della Calamita, io non <lb/>trovo cosa alcuna di considerabile per quel che riguarda a nuove scoperte <pb xlink:href="020/01/801.jpg" pagenum="244"/>o teoriche appartenenti a questa maravigliosa operazione della Natura, dopo <lb/>il Gilberti, se ci&ograve; non &egrave; nel libro del sig. </s>

<s>Gillibrand, gi&agrave; professore in que&shy;<lb/>sto Collegio, il quale nell'anno 1634 scoperse e prov&ograve; il primo la variazione <lb/>della variazione della direzione dell'ago magnetico. </s>

<s>Egli trov&ograve; allora in <lb/>un luogo poco lontano da Londra la variazione esser circa quattro gradi <lb/>verso Oriente, nonostante che un tal sig. </s>

<s>Burrocus, nell'anno 1580, l'avesse <lb/>trovata nel medesimo luogo esser tredici gradi e venti minuti verso Oriente, <lb/>e che un tal sig. </s>

<s>Gunter, altro professore in questo Collegio, l'anno 1622, <lb/>ve l'avesse trovata di sei gradi e tredici minuti, senz'allora immaginarsi che <lb/>vi fosse alcuna variazione di variazione, ma attribuendo ci&ograve; piuttosto a qual&shy;<lb/>che mancamento nelle osservazioni del sig. </s>

<s>Burrocus. </s>

<s>E per questa ragione <lb/>il sig. </s>

<s>Gillibrand, facendo comparazione di queste osservazioni con le sue <lb/>proprie, suppose il primo e sostenne la variazione della variazione, e pub&shy;<lb/>blic&ograve; un piccol Trattato, in cui d&agrave; ragguaglio delle dette sue osservazioni e <lb/>delle sopraddette sue opinioni. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; L'anno 1657 un tal chiamato il sig. </s>

<s>Bond fece nuove osservazioni, <lb/>ch'ei parimente pubblic&ograve; in un Trattato di maggior considerazione, e trov&ograve; <lb/>solamente che l'ago segnava la vera meridiana, senza variar n&egrave; verso Oriente <lb/>n&egrave; verso Occidente. </s>

<s>E dopo il suddetto tempo &egrave; stato spesse volte osser&shy;<lb/>vato, e da me e da altri signori della Societ&agrave; Reale, che l'ago continua a <lb/>variar sempre pi&ugrave; verso Occidente, di modo che al presente ell'&egrave; qui circa <lb/>sette gradi verso Occidente. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si son viste proporre differenti ipotesi per la soluzione di tali appa&shy;<lb/>renze, ma io confesso di non aver ancora veduto chi ne abbia dato la so&shy;<lb/>disfazione ricercata. </s>

<s>Certo si &egrave; che quelle non convengono punto con una <lb/>teorica, che io ne feci gran tempo fa, e che io pretendo fra poco di pub&shy;<lb/>blicarla, quando le altre occupazioni mi permetteranno il tempo e la libert&agrave; <lb/>di porla in ordine per farla stampare, e allora io spero di provar con la <lb/>sperienza, nell'istesso modo che con le regole della Geometria, tutte le ap&shy;<lb/>parenze riguardanti la Calamita state comunemente conosciute fin ad ora, <lb/>con le cause probabili, almeno se non vere, e le ragioni che ne possono <lb/>essere assegnate. </s>

<s>Questa teoria sar&agrave; differente da quante io ne ho vedute, <lb/>e sar&agrave; una parte di una nuova Teorica della Fisica in generale, di cui ho <lb/>anche fatto il concetto differente da tutti gli altri che ho visto, ed il quale, <lb/>per quanto io spero, spiegher&agrave; la maggior parte delle apparenze e pi&ugrave; chia&shy;<lb/>ramente di quanti se ne son veduti fin ora. </s>

<s>E per questa ragione io mi ri&shy;<lb/>guarder&ograve; di fare abortire i miei proprii parti con lo stroppiargli prima di <lb/>fargli nascere &rdquo; (ivi). </s></p><p type="main">

<s>Se i parti, a'quali accennano queste ultime parole profferite dall'Hook, <lb/>veramente sian nati, ce lo dir&agrave; qualche erudito Inglese, che meglio di noi <lb/>conosca la vita letteraria del suo celebre connazionale: noi crediamo che <lb/>fossero anche questi abortiti insiem con tanti altri concepiti da quell'inge&shy;<lb/>gno mirabilmente fecondo. </s>

<s>Che cosa insomma aveva il Viviani, circa alla Fi&shy;<lb/>losofia magnetica, imparato da quegli Inglesi di nuovo? </s>

<s>Nulla di pi&ugrave; di quel <pb xlink:href="020/01/802.jpg" pagenum="245"/>che ne aveva scritto il Cartesio alle strane ipotesi del quale potevansi in <lb/>certo modo rassomigliare le ipotesi dell'Halley. </s></p><p type="main">

<s>Se qualche cosa di nuovo ci era, e di meglio di quel che fosse uscito <lb/>dalla fantasia del Cartesio, era stato consegnato a manoscritti o divulgato in <lb/>libri nostrali, a'quali ricorrendo il Viviani avrebbe trovato da sodisfar, quan&shy;<lb/>t'era possibile, i suoi desiderii. </s>

<s>&Egrave; perci&ograve; dover nostro render conto ai Let&shy;<lb/>tori di quelle ipotesi e di quelle teorie magnetiche ignorate dal Discepolo <lb/>di Galileo, bench&egrave; fossero state professate in Italia tanti anni prima, che il <lb/>Southvell scrivesse essersi innanzi alle grandi difficolt&agrave; arretrati gli Accade&shy;<lb/>mici suoi Londinesi. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>In quel tempo, presso a poco, che il Cartesio pubblicava i Principii <lb/>della Filosofia, il Castelli meditava nel suo Discorso sopra la Calamita. </s>

<s>I di&shy;<lb/>fetti del Francese si qualificano in breve dicendo ch'egli &egrave; un romanziere <lb/>e no un filosofo; i difetti del Nostro si compendiano pure in breve dicendo <lb/>che egli tratt&ograve; del Magnete non da fisico, ma da matematico. </s>

<s>Le teorie fisi&shy;<lb/>che del Magnete a noi par che cominciasse a specularle Antonio Nardi in <lb/>quelle <emph type="italics"/>Scene Accademiche<emph.end type="italics"/> dove s'ha, con mirabile variet&agrave;, tutta insieme e <lb/>in un ampio teatro rappresentata l'erudizione e la scienza italiana ai tempi <lb/>di Galileo. </s></p><p type="main">

<s>I flussi magnetici, secondo il Nardi, son due: differenti non tanto di <lb/>sito e di direzione, ma di qualit&agrave;, e con essi in gioco spiega, a quel modo <lb/>presso a poco che i fisici moderni, la scambievole azione fra due Calamite, <lb/>e gli effetti loro naturali. </s>

<s>Principale fra questi effetti &egrave; che si attraggono i <lb/>poli di nome contrario, ci&ograve; che dal Nardi si spiega dicendo che nelle estre&shy;<lb/>mit&agrave; prevalgono i flussi, i quali si diffondono dal centro della Pietra, e per&shy;<lb/>ci&ograve; a Borea per esempio sograggiungono quelli spirati dalla parte contraria <lb/>di Ostro. </s></p><p type="main">

<s>&ldquo; Ora il punto sta (dice l'Autore nella Veduta XVIII della Scena IV) <lb/>nel cercar l'origine onde avvenga che l'ago verso il suo principio tirato sia <lb/>e si raddrizzi sempre pi&ugrave;, quanto pi&ugrave; al magnetico polo si accosti. </s>

<s>Stima il <lb/>Gilberto che dal centro della Calamita si diffonda principalmente la virt&ugrave;, <lb/>e che termini il suo maggiore ne'poli, e quindi procedendo cominci a lan&shy;<lb/>guire. </s>

<s>Repugna alcuno e vuole che dai poli diffondasi: quindi cerca render <lb/>ragione perch&egrave; nell'Equinoziale valido sia il dirigersi e nullo sia l'erigersi. </s>

<s><lb/>Per il contrario, nel polo questo si trovi e non quello, e finalmente nelle <lb/>altre parti si trovi l'uno e l'altro composto delle proposizioni delle distanze <lb/>dai poli; ed altre cose che lungo il riferirle saria. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pensomi che se sia la Calamita ACB (fig. </s>

<s>61) di cui A il polo Bo&shy;<lb/>reale, B l'Australe, C il mezzo, non poter essere A principio di guardar <pb xlink:href="020/01/803.jpg" pagenum="246"/>Ostro ai ferri che quello tocchino, e niuna forza ivi risiedere, perch&egrave; inco&shy;<lb/>minciando un empito reale, o eminenziale come nel caso nostro, da un punto, <lb/><figure id="id.020.01.803.1.jpg" xlink:href="020/01/803/1.jpg"/></s></p><p type="caption">

<s>Figura 61.<lb/>&egrave; necessario che per arrivare <lb/>all'altro termine, nel quale si <lb/>finisse di comunicar l'impeto, <lb/>si passi per mezzi infiniti e cos&igrave; <lb/>il punto A nulla forza otterr&agrave; <lb/>verso CB. &rdquo; </s></p><p type="main">

<s>&ldquo; Se dunque ad A s'applichi la punta d'un ago, ricever&agrave; la diffusione <lb/>valida dal punto C, di maniera che per la comune forma diventeranno un <lb/>sol corpo l'ago e la pietra. </s>

<s>E per&ograve;, supponiamo che in ogni punto dentro <lb/>alla Calamita si faccia simile diffusione in retto ed a tale che empia tutta <lb/>la sfera della sua attivit&agrave;, con tal ragione che, non come la luce abbia re&shy;<lb/>lazione ad un solo principio, ma a due estremi ove concorrono dal centro <lb/>due principali linee; quindi nasce che nei punti boreali magnetici preval&shy;<lb/>ghino flussi dalla parte opposta. </s>

<s>E per&ograve;, se spezzeremo la Calamita, vedremo <lb/>cambiarsi il modo di comunicar la virt&ugrave;, ma non gi&agrave; avverr&agrave; che la parte, <lb/>quale nella Calamita congiunta guardava Ostro, guardi disgiunta Borea, poi&shy;<lb/>ch&egrave; rimane come prima il flusso della virt&ugrave; sua congiunto col flusso per&shy;<lb/>petuo del Magnete universale. </s>

<s>Qui dunque alcuni forse s'ingannano, i quali <lb/>vedendo come dal boreale toccamento acquisti l'ago la direzione australe, <lb/>non considerano che la virt&ugrave; si comunica nel punto del toccamento, ma per&ograve; <lb/>non indi procedeva. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, non &egrave; maraviglia, se avendo l'ago la virt&ugrave; concepita in una <lb/>parte della Pietra dove prevale la opposta diffusione, venga poi a congiun&shy;<lb/>gersi allo stesso e simil principio, perch&egrave; altrimenti non lo potrebbero in&shy;<lb/>sieme unire le contrarie flussioni magnetiche, delle quali il comun termine <lb/>&egrave; la punta dell'ago, e perch&egrave; mescolate sono nel mezzo della Pietra le flus&shy;<lb/>sioni, e sincere assai negli estremi; quindi ancora si apre la strada al filo&shy;<lb/>sofare intorno alla cagione, perch&egrave; negli angoli sia pi&ugrave; efficace la calamita <lb/>che nel mezzo &rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, c. </s>

<s>603). </s></p><p type="main">

<s>Bench&egrave; a parole non se ne trovi fatto alcun cenno, si vede nulladimeno <lb/>che qui il Nardi tien d'occhio al Gilberto nel Cap. </s>

<s>IV del Libro III <emph type="italics"/>De <lb/>Magnete,<emph.end type="italics"/> dove proponesi di risolvere la questione: <emph type="italics"/>Cur ferrum tactum <lb/>acquirit contrariam verticitatem<emph.end type="italics"/> (Edit. </s>

<s>cit., pag. </s>

<s>125). E tanto &egrave; vero che <lb/>intende il nostro a infondere un qualche spirito di Filosofia nelle aride dot&shy;<lb/>trine dell'Inglese, che usa il linguaggio medesimo di lu&igrave; nel trattar della <lb/>Calamita, ora segata secondo il parallelo, ossia da un piano perpendicolare <lb/>all'asse, ora segata invece secondo il meridiano, ossia da un piano parallelo <lb/>allo stesso asse. </s></p><p type="main">

<s>&ldquo; Sia la Calamita, prosegue il Nardi, ACB (fig. </s>

<s>prec.) come sopra, e <lb/>s'intenda diviso il suo asse in due parti ADE, BED: dico che ADE si riu&shy;<lb/>nir&agrave; con BED, quando insieme s'accostino, perch'essendo la sezione DE co&shy;<lb/>mune all'uno ed all'altro pezzo, la stessa virt&ugrave; corre e ricorre da B verso A <pb xlink:href="020/01/804.jpg" pagenum="247"/>e da A verso B, onde anco A e B si possono congiungere per esser ter&shy;<lb/>mini e principii scambievolmente di virt&ugrave;, che riunirsi tenta per la somi&shy;<lb/>glianza del corso. </s>

<s>E sebbene DE, rispetto ad A, riguardi Ostro, rispetto poi <lb/>a B riguarda &Bacute;orea, e se disgiunto &egrave; in ADE australe o in BED boreale, <lb/>congiunto poi &egrave; comune. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora se la medesima Pietra si tagli, non secondo il parallelo, ma se&shy;<lb/>condo il meridiano, avverr&agrave; che soprapposto il pezzo C (fig. </s>

<s>62) al pezzo D <lb/><figure id="id.020.01.804.1.jpg" xlink:href="020/01/804/1.jpg"/></s></p><p type="caption">

<s>Figura 62.<lb/>non si ricongiungeranno nel modo <lb/>che stavano prima, ma la parte che <lb/>guarder&agrave; Borea si volger&agrave; in Ostro, <lb/>perch&egrave; noi detto abbiamo che l'ago <lb/>si volta ad Ostro con la lancetta, <lb/>mentre sia posto sopra la Calamita, <lb/>per ricongiungersi al suo principio, e lo stesso avvenir forse bisogna nel <lb/>caso nostro, perch&egrave;, se nel pezzo ACB il punto A prese la virt&ugrave; congiunto <lb/>dal toccamento nel pezzo ADB, dovrebbe ancora disgiunto aspirare allo stesso <lb/>toccamento, ed aver&agrave; forse per tal causa il punto A nella Pietra la propria <lb/>sua virt&ugrave; congiunta a quella dell'opposto polo B, e con ogni punto australe, <lb/>d'onde ha il principio ed a cui separata riunir circolarmente si vuole, perch&egrave; <lb/>la pietra &egrave; contenuta da un solo abito che in s&egrave; circolarmente ricorre &rdquo; (ivi). </s></p><p type="main">

<s>Le teorie magnetiche del Nardi, di cui abbiamo accennato alle princi&shy;<lb/>pali, non son certamente compiute, e non sempre derivano da principii o <lb/>espressi con chiarezza o definiti con precisione filosofica. </s>

<s>Ci&ograve; non compor&shy;<lb/>tavasi dall'altra parte, n&egrave; era conforme all'indole del suo Libro, il quale <lb/>non era un libro di Filosofia, ma una specie di Giornale enciclopedico, come <lb/>altra volta dicemmo, e che doveva servir non da face posata sul candelabro <lb/>a illuminare le menti, ma da cote percossa in fretta a dare scintille infiam&shy;<lb/>matrici dell'esca che ritrovan meglio disposta. </s>

<s>L'esser rimaste quelle pa&shy;<lb/>gine occulte, e per&ograve; il fuoco nella cote stessa latente, imped&igrave; che si produ&shy;<lb/>cessero que'benefici effetti nelle menti dei lettori, di che sarebbe anche <lb/>maggiormente a dolersi, se a supplire al difetto delle Scene del Nardi non <lb/>fosse uscito in Italia il Libro <emph type="italics"/>De Lumine<emph.end type="italics"/> del Grimaldi. </s></p><p type="main">

<s>Come c'entri il trattar del Magnete, dove il proposito era di trattar <lb/>della luce, potrebbe frugare alcuno di una certa curiosit&agrave;, la quale poi cos&igrave; <lb/>si acquieta in poche parole. </s>

<s>Tanto la luce quanto gli effluvii magnetici erano <lb/>da'Filosofi riguardati come qualit&agrave; accidentali. </s>

<s>Proponendosi perci&ograve; il Gri&shy;<lb/>maldi di dimostrar che la luce era un essere sostanziale, piglia occasione di <lb/>confermare il suo assunto col dimostrar l'essere sostanziale del magnetico <lb/>effluvio. </s>

<s>Il pernicioso errore dell'immaterialit&agrave; di questo effluvio era stato, <lb/>come vedemmo, introdotto nella Filosofia magnetica dallo stesso Gilberto, <lb/>dall'autorit&agrave; del quale rimase soggiogato il Castelli, che s'indusse a negare <lb/>il principio corporeo alla virt&ugrave; magnetica dal veder ch'ella, anche attraverso <lb/>a qualunque ostacolo che non fosse di ferro, operava in distanza. </s>

<s>Il Gri&shy;<lb/>maldi dunque, contro quelle false e ai progressi della Scienza cos&igrave; dannose <pb xlink:href="020/01/805.jpg" pagenum="248"/>dottrine, dimostrava la seguente proposizione: &ldquo; Si dicatur virtutem a Ma&shy;<lb/>gnete diffusam esse aliquid substantiale, per modum tenuissimae expiratio&shy;<lb/>nis, multo melius intelliguntur et explicantur experimenta, quibus aliquid <lb/>cognoscimus de proprietatibus Magnetis &rdquo; (De Lumine, Bononiae 1665, pag. </s>

<s>65). </s></p><p type="main">

<s>Ammesso un tal sostanziale effluvio risolveva il Grimaldi il problema che <lb/>rest&ograve; irresoluto alle mani del Castelli, dicendo che la Calamita opera sul ferro <lb/>a distanza attraverso a un'asse di legno, a una lamina di metallo o di ve&shy;<lb/>tro, perch&egrave; tutti i corpi son porosi e si lascian perci&ograve; attraversare ai ma&shy;<lb/>gnetici effluvii. </s>

<s>Secondo il nostro Fisico dunque, non consiste la virt&ugrave; cala&shy;<lb/>mitica in qualche forza inconsapevole e immaginaria, come il Castelli stesso <lb/>ammetteva, e tanto meno in un principio animale, come stranamente opi&shy;<lb/>nava il Gilberto, ma risiede in un fluido essenziale che riempie i pori della <lb/>Calamita e scorre con certa direzione segnata dai punti de'poli, cosicch&egrave; i <lb/>profluvii son due apparentemente diversi, per quella loro direzione diversa, <lb/>ma sostanzialmente son della stessa natura. </s>

<s>Il ferro dolce che si calamita <lb/>contiene in s&egrave; questo fluido magnetico, ma disordinato, e acquista la virt&ugrave; <lb/>calamitica per via di un'orientazione dello stesso fluido che gi&agrave; conteneva, <lb/>orientazione indotta dagl'influssi attivi e naturali della Pietra. </s></p><p type="main">

<s>Queste sue teorie le illustrava il Grimaldi e le confermava con le se&shy;<lb/>guenti esperienze: Un ferro infocato o battuto perde la sua verticit&agrave; e la <lb/>perde pure un ferro torto, che sia violentemente addirizzato o che venga in <lb/>qualunque modo ridotto a una forma diversa da quella sua prima. </s>

<s>&ldquo; Ex his <lb/>omnibus, prosegue a dire il Grimaldi, duo certissima inferuntur: Primo, <lb/>destructionem illam virtutis magneticae in ferro ignito, sive tunso, sive vio&shy;<lb/>lenter ut supra inflexo et fricato, tribuendum esse non calori immediate, sed <lb/>mutuae dispositioni locali particularum in ferro et alicui pororum perturba&shy;<lb/>tioni, hoc est diductioni simul et constrictioni. </s>

<s>Secundo, consequenter virtu&shy;<lb/>tem magneticam pendere in sui diffusione, vel permanentia a porositate et <lb/>certa cohordinatione particularum in ferro, ac proinde esse corporeum ali&shy;<lb/>quod et substantiale effluvium a Magnete trasmissum, aptumque recipi in <lb/>ferro et a ferro item expelli, per quamdam partium impressionem &rdquo; (ibi, <lb/>pag. </s>

<s>66, &sect; 45). </s></p><p type="main">

<s>Che la verticit&agrave; poi dipenda dall'orientamento delle sferette magnetiche, <lb/>il Grimaldi lo prova con questa bella esperienza, fatta gi&agrave; come dicemmo <lb/>dal Sarpi e divulgata dal Porta nel cap. </s>

<s>XLVII del suo VII libro della Ma&shy;<lb/>gia, e della quale si serv&igrave; pure il Gilberto a provar nel cap. </s>

<s>XXIII del Li&shy;<lb/>bro II la proposizione: &ldquo; Magnetica vis motum facit ad unitatem et unita <lb/>firmiter connectit &rdquo; (pag. </s>

<s>90); esperienza la quale consiste nel mostrar che <lb/>un cartoccio di foglio o un tubo di argento ripieni di limatura di ferro ma&shy;<lb/>gnetizzata, subito perdon la loro verticit&agrave;, che le particelle ferree vengano <lb/>disordinate col votarli e poi riempirli di nuovo. </s>

<s>&ldquo; Et ratio est, soggiunge il <lb/>Grimaldi, quia singula ramenta ferri habent quidem adhuc suam longitudi&shy;<lb/>nem, secundum quam in illis disposita fuerat virtus magnetica, sed non or&shy;<lb/>dinantur similiter omnia ut prius, immo temere huc illuc conversa, vel non <pb xlink:href="020/01/806.jpg" pagenum="249"/>possunt simul et per modum unius magnetici exercere virtutem quae in <lb/>illis remanet, vel tandem inter se conflictando mutua contrarietate illam vi&shy;<lb/>cissim extingunt &rdquo; (ibi, pag. </s>

<s>68, &sect; 47). </s></p><p type="main">

<s>In che modo si dispensi questo sostanziale magnetico effluvio, &egrave; vera&shy;<lb/>mente cosa mirabile e non potendosene avere esperienza per mezzo dei sensi <lb/>&egrave; da confessare ingenuamente, dice il Grimaldi, che non se ne pu&ograve; dare <lb/>certezza di scienza. </s>

<s>N&egrave; per questo, egli prosegue ivi a dire, &egrave; da ricorrere <lb/>alle qualit&agrave; occulte che non son poi altro che un nome, ma &egrave; da ripensar <lb/>tra le fisiche, qual possa essere la pi&ugrave; probabile ragione. </s>

<s>&ldquo; Itaque dicimus <lb/>valde probabile esse quod ab utroque polo terrestri versus alterum et ver&shy;<lb/>sus totam superficiem telluris continue fluxus accurrat aliquid substantiale <lb/>valde tenuis, ob eam potissimum rationem qua Sol perpetuo attenuat ma&shy;<lb/>gis medias partes ipsius Telluris positas intra Zonam torridam, quarum sci&shy;<lb/>licet resolutio melius compensari non potest, quam per continuum affluxum <lb/>vicinarum. </s>

<s>Coepto autem praedicto affluxu vicinarum, facile est subinde aliae <lb/>atque aliac etiam remotiores occurrant &rdquo; (ibi, pag. </s>

<s>73, &sect; 61). </s></p><p type="main">

<s>Coll'ipotesi di questi due fluidi sostanziali, che corrono e ricorrono dai <lb/>due poli, spiega mirabilmente il Grimaldi i fatti osservati nel Magnete prima <lb/>di lui e quelli altres&igrave; ch'egli stesso scopr&igrave; come nuovi. </s>

<s>Fra questi &egrave; nota&shy;<lb/>bile il fatto della polarit&agrave; magnetica, che spontaneamente s'induce in una <lb/>sottile e lunga verga di ferro tenuta un istante in direzione perpendicolare <lb/>al piano dell'orizzonte; fatto che fu poi osservato dal Boyle e da altri, e <lb/>del quale all'ultimo il Musschenbroek, nella Dissertazion <emph type="italics"/>De Magnete,<emph.end type="italics"/> fece <lb/>soggetto a'suoi diligentissimi esperimenti. </s>

<s>&ldquo; Observandum est, dice il no&shy;<lb/>stro Grimaldi, virgam ferream uniformis crassitici et rectitudinis, et quae <lb/>nunquam a Magnete fuerit excitata, si sursum erecta vel parum omnino in&shy;<lb/>clinata a situ perpendiculari applicetur Versorio parte sui infima, ita allicere <lb/>Versorium nostris hisce regionibus borealibus, ut ad eam accurrat extre&shy;<lb/>mum illud Versorii quod solet converti ad Austrum. </s>

<s>At si virga eadem ap&shy;<lb/>plicetur Versorio, parte sui suprema, accurrere extremum, quod de se con&shy;<lb/>vertitur ad Boream, quaecumque sit ea pars virgae, quae modo ponitur in <lb/>imo, modo in summo &rdquo; (ibi, pag. </s>

<s>69, &sect; 51). </s></p><p type="main">

<s>Chi in conclusione medita attentamente sopra que'LXVI paragrafi, che <lb/>il Grimaldi aggiunse come appendice alla proposizione sua VI <emph type="italics"/>De lumine,<emph.end type="italics"/><lb/>si persuade con facilit&agrave; che ivi, delle esperienze del Gilberto si trova per la <lb/>prima volta suggerita una qualche probabile ragione. </s>

<s>Se l'Inglese dette la <lb/>Fisiologia del Magnete, si pu&ograve; dir che il Nostro ne abbia data la Filosofia, <lb/>che &egrave; quella in sostanza professata universalmente nelle scuole infino a que&shy;<lb/>sti ultimi tempi. </s>

<s>L'ipotesi de'due fluidi essenziali infatti, immaginata prima <lb/>dal Nardi, e illustrata poi dal Grimaldi con tanta variet&agrave; di sottili argomenti, <lb/>&egrave; quella ch'&egrave; tuttavia rimasta a spiegare in qualche modo le attrazioni, le <lb/>direzioni e tutti gli altri magnetici misteri. </s></p><p type="main">

<s>Quella ipotesi del flusso che si dirige da un polo verso il polo opposto <lb/>per ritornarvi con circolo perpetuo, d'onde sono, secondo il Nardi e il Gri-<pb xlink:href="020/01/807.jpg" pagenum="250"/>maldi, rapiti e volti i corpi magnetici, come i galleggianti nell'acqua son <lb/>rapiti e volti nella direzione della corrente, si potrebbe credere a prima vi&shy;<lb/>sta che fosse suggerita ai Nostri dall'ipotesi cartesiana. </s>

<s>Ma le particelle <lb/>striate operanti come le punte de'succhielli, e che discese dalle regioni ete&shy;<lb/>ree ronzano intorno al nostro globo e v'entrano ed escono, come da'loro <lb/>nidi le vespe, presentano delle virt&ugrave; magnetiche altra immagine da quel&shy;<lb/>l'aura invisibile e spiritosa, che secondo il Nardi circola nella Pietra e che <lb/>ha origine, secondo il Grimaldi, dall'azione del Sole sopra la Terra. </s>

<s>Sublime <lb/>concetto &egrave; questo con cui il nostro Filosofo bolognese apr&igrave;, a veder le cor&shy;<lb/>renti elettro-magnetiche sulla superficie terrestre, gli occhi ad alcuni cele&shy;<lb/>brati fisici de'nostri giorni. </s></p><p type="main">

<s>Chi ritorni ora col pensiero sopra le cose narrate non pu&ograve; non mara&shy;<lb/>vigliarsi come il Viviani, che aveva in Italia ci&ograve; che s'era meglio speculato <lb/>intorno al Magnete, fosse nonostante ricorso a interpellarne gli Accademici di <lb/>Londra, n&egrave; s'intende come potesse quietarsi alla loro risposta, che cio&egrave; nes&shy;<lb/>suno dopo il Cartesio aveva osato di suggerire, in mezzo a tante difficolt&agrave;, <lb/>qualche ipotesi nuova. </s>

<s>Pu&ograve; esser che fosse al Viviani ignoto ci&ograve; che lasci&ograve; <lb/>Antonio Nardi manoscritto in quel Volume, conosciuto da molti in Toscana, <lb/>bench&egrave; letto da pochi, ma come si pu&ograve; scusare del non aver tenuto in nes&shy;<lb/>sun conto le speculazioni magnetiche divulgate nel libro del Grimaldi? </s></p><p type="main">

<s>Il fatto ch'&egrave; pur degno di qualche considerazione conferma quel che <lb/>fu osservato da noi ad altro proposito, ed &egrave; che il Grimaldi rimase solita&shy;<lb/>rio e come fuori di strada a chi, senza rivolgersi n&egrave; da una parte n&egrave; da <lb/>un'altra, teneva dietro sicuro alla Filosofia galileiana. </s>

<s>Quel che il Gesuita <lb/>bolognese scopr&igrave; intorno alle propriet&agrave; della luce si diffuse pel magisterio, <lb/>e si pregi&ograve; per l'autorit&agrave; del Newton, il quale, perch&egrave; non ebbe occasione <lb/>di considerare le magnetiche speculazioni grimaldiane, queste rimasero in <lb/>dimenticanza cos&igrave; appresso gl'Inglesi come appresso i nostri Italiani. </s></p><p type="main">

<s>Ma se il discepolo prediletto e gli altri sviscerati ammiratori di Galileo <lb/>avessero pensato che la verit&agrave; poteva essere stata rivelata anche a chi non <lb/>fosse andato allo studio di Padova, o fosse intervenuto a'coloqui di Arcetri, <lb/>avrebbero potuto promuover pi&ugrave; oltre la Filosofia magnetica da quel segn o <lb/>a che la condussero nella loro fiorentina Accademia. </s>

<s>Quel segno dall'altra <lb/>parte &egrave; poco pi&ugrave; qua remosso dal punto dove lo fissarono il Gilberto, il <lb/>Gassendo o qualcun altro, e gli Accademici lo conobbero bene e lo confes&shy;<lb/>sarono, facendo dire al loro Segretario esser quelle notizie date ne'Saggi di <lb/>Naturali esperienze <emph type="italics"/>assai ordinarie, e per avventura non del tutto nuove.<emph.end type="italics"/><lb/>(Firenze 1841, pag. </s>

<s>137). </s></p><p type="main">

<s>Ma pur, per la verit&agrave;, convien dire che qualche cosa tentassero di nuovo, <lb/>di che non tennero conto nel sopra detto Libro de'Saggi, forse per non <lb/>averne potuto ricavare nulla di certo. </s>

<s>Lasciamo per ora da parte l'espe&shy;<lb/>rienza istituita per determinare secondo qual legge diminuisca la forza del&shy;<lb/>l'attrazion magnetica al crescere della distanza, di che diremo altrove, ma <lb/>furono essi i nostri Accademici de'primi a sperimentare le operazioni della <pb xlink:href="020/01/808.jpg" pagenum="251"/>Calamita nel vuoto. </s>

<s>Si sa come rimanessero intorno a ci&ograve; ingannati l'Hart&shy;<lb/>foeker, lo Sturm e lo stesso Boyle, non facendo considerazione sopra la re&shy;<lb/>sistenza che variamente oppone al Versorio l'aria pi&ugrave; e meno densa, n&egrave; <lb/>sopra le alterazioni della gravit&agrave;, che i corpi subiscon nel vuoto, per le quali <lb/>considerazioni s'intende come, sotto la campana della Macchina pneumatica, <lb/>pi&ugrave; facilmente volubile debba esser l'ago, e una calamita ivi dentro non <lb/>sostenti tutto quel peso, che sosteneva nell'aria, dove il Banoscopio dimo&shy;<lb/>stra essere alquanto pi&ugrave; leggero. </s></p><p type="main">

<s>Forse sfuggirono cos&igrave; fatte considerazioni anche ai nostri Accademici, <lb/>come s'argomenta dall'incertezza in che gli lasciarono due conclusioni spe&shy;<lb/>rimentali fra s&egrave; discordi. </s>

<s>Nel libro de'<emph type="italics"/>Saggi,<emph.end type="italics"/> per esempio, trovarono che <lb/>nel vuoto la Calamita tira l'ago alla distanza medesima che nell'aria (pag. </s>

<s>60) <lb/>ma in una <emph type="italics"/>Nota d'osservazioni e sperienze da farsi nel gran vacuo,<emph.end type="italics"/> di <lb/>contro all'articolo che dice: <emph type="italics"/>Attrazioni magnetiche, se venghin tolte, im&shy;<lb/>pedite o facilitate,<emph.end type="italics"/> il Viviani accenn&ograve; in margine il resultato avutone, scri&shy;<lb/>vendo di sua propria mano: <emph type="italics"/>Facilitate.<emph.end type="italics"/> (MSS. Cim., T. X, c. </s>

<s>253). </s></p><p type="main">

<s>Ma comunque sia, non perci&ograve; si pu&ograve; dir, come da s&egrave; medesimi con&shy;<lb/>fessarono i nostri Accademici, che avessero <emph type="italics"/>arrecato qualche gran lume <lb/>nella Filosofia magnetica<emph.end type="italics"/> (Saggi cit., pag. </s>

<s>137); merito che unicamente <lb/>rimane al Grimaldi e in Italia e fuori, dove, piuttosto che alle generali pro&shy;<lb/>priet&agrave; del Magnete, s'attese a un fatto particolare, di che dobbiamo ora pas&shy;<lb/>sare a narrar la storia. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Il fatto particolare, che rivolse a s&egrave; l'attenzione de'cultori della Filo&shy;<lb/>sofia magnetica, specialmente in Inghilterra e in Francia, fu quello della <lb/>variabile declinazione della Calamita. </s>

<s>Udimmo l'Hook di sopra narrare al <lb/>Viviani come al Gillibrand occorresse di fare l'inaspettata scoperta, e come <lb/>nel 1634 si studiasse l'Autore, per mezzo di un Trattato scritto in tal pro&shy;<lb/>posito, di divulgarla. </s>

<s>Ma come sempre avviene alle cose nuove e che hanno <lb/>dello straordinario, non trov&ograve; quella opinione del professor di Gresham troppo <lb/>facile accoglienza. </s>

<s>Molti anche fra gl'Inglesi recalcitrarono, allegando l'Ora&shy;<lb/>colo del Gilberto, il quale aveva sentenziato <emph type="italics"/>Variatio unius cuiusque loci <lb/>constans est.<emph.end type="italics"/> (De Magn., Lib. </s>

<s>IV, cap. </s>

<s>IV, pag. </s>

<s>159). Altri fra'pi&ugrave; giudi&shy;<lb/>ziosi se ne spacciavano con un <emph type="italics"/>pu&ograve; cssere,<emph.end type="italics"/> cosicch&egrave;, dopo qualche anno, <lb/>nessuno pi&ugrave; ci pensava. </s></p><p type="main">

<s>Il Cartesio, alle orecchie del quale era pervenuto qualche romore, pose <lb/>nel IV libro de'<emph type="italics"/>Principii della Filosofia,<emph.end type="italics"/> fra i problemi da risolversi intorno <lb/>al Magnete, anche il XX. <emph type="italics"/>Quod ista declinatio cum tempore mutari pos&shy;<lb/>sit<emph.end type="italics"/> (pag. </s>

<s>264). Ma perch&egrave; i seguaci del retto metodo sperimentale, anche in <lb/>Francia, non tenevano in nessun conto quelle strane particelle striate, pass&ograve; <pb xlink:href="020/01/809.jpg" pagenum="252"/>insiem con esse inosservato anche ci&ograve; che il Cartesio aveva detto della pos&shy;<lb/>sibile variabilit&agrave; della declinazione magnetica, cosicch&egrave; nel 1654 giunse al <lb/>Petit e agli altri Fisici parigini la notizia di questa scoperta come cosa del <lb/>tutto nuova. </s>

<s>In che modo poi occorresse una tal notizia a quel Petit, che <lb/>doveva promoverla con tanto studio e diffonderla con tanto zelo, ci &egrave; nar&shy;<lb/>rato da lui stesso nella Dissertazione <emph type="italics"/>De latitudine parisiensi<emph.end type="italics"/> aggiunta, in&shy;<lb/>siem con altre Dissertazioni astronomiche, all'Astronomia fisica del Du-Hamel. </s></p><p type="main">

<s>Studiosissimo il Petit, sopra quanti altri mai, della Filosofia magnetica, <lb/>s'era proposto di sperimentare se le Calamite facessero differente declina&shy;<lb/>zione secondo che, nella loro nativa miniera, giacevano pi&ugrave; o meno vicino <lb/>al punto del Polo. </s>

<s>Con tre pietre, avute da varie parti della Terra, calamit&ograve; <lb/>tre aghi di varia lunghezza, e per esplorare il grado della loro declinazione <lb/>costru&igrave; colla massima accuratezza tre linee meridiane in varii luoghi della <lb/>citt&agrave; di Parigi, e trov&ograve; che dovunque gli aghi soprapposti declinavano di <lb/>quattro gradi in Oriente. </s>

<s>Rimase il Petit sorpreso di gran maraviglia, aspet&shy;<lb/>tandosi che, non facendo i tre aghi variet&agrave; fra loro, dovessero in quella im&shy;<lb/>perturbata concordia declinare fra i nove o i dieci gradi, come si teneva <lb/>allora da tutti in Parigi, dietro le accuratissime osservazioni dell'Oronzio e <lb/>del Castelfranco. </s></p><p type="main">

<s>Divulgatasi la notizia che la Declinazione magnetica in Parigi non era <lb/>altrimenti di dieci gradi, ma di soli quattro, i Fisici e gli Astronomi fran&shy;<lb/>cesi si riscossero, e premurosi concorsero da varie parti a confermare colle <lb/>loro particolari osservazioni la verit&agrave; del fatto scoperto. </s>

<s>Tanto rimasero a <lb/>quella inaspettata novit&agrave; commossi, che ne giunse il rumore in Inghilterra, <lb/>e allora si sovvennero quegli Inglesi del loro Gillibrando, e riconobbero nei <lb/>fatti osservati a Parigi la pi&ugrave; bella conferma di ci&ograve; che vent'anni prima era <lb/>stato scoperto nella loro citt&agrave; di Londra. </s>

<s>Dettero subito di ci&ograve; avviso al Pe&shy;<lb/>tit, in quel ch'egli stava per sentenziar che senz'altro le osservazioni del&shy;<lb/>l'Oronzio dovevano essere sbagliate, come il Gunter aveva creduto che fos&shy;<lb/>sero sbagliate le osservazioni del Burrosio. </s></p><p type="main">

<s>&ldquo; Tum fuimus (cos&igrave; il Petit colle sue proprie parole prosegue la nar&shy;<lb/>razione) omnes in ea sententia ut putaremus ab antiquis peccatum hic fuisse, <lb/>nec alias declinationis magneticae aliam extitisse positionem, cum ecce nobis <lb/>ab Anglia allatae sunt literae, quibus accepimus hanc dubio procul haud <lb/>esse constantem, quando quidem olim, anno scilicet 1580, Burrosius in ma&shy;<lb/>thematicis eximius, ex observationibus Solis azimuthorum accuratissimis, <lb/>mense Octobri prope Londinum, acum Magnete illitam a Meridie in Ortum <lb/>11 grad. </s>

<s>15 min. </s>

<s>deflectere compererit: anno vero 1622, mense Junio, Gon&shy;<lb/>therus metheseos professor in eodem loco declinationem multum imminu&shy;<lb/>tam nempe 6 gr. </s>

<s>tantum invenerit. </s>

<s>Postremo, annis 1633 et 1634, Geli&shy;<lb/>brandus Gontheri successor eamdem observationem, eodem in loco, atque <lb/>eadem prorsus methodo instituens, cum acus 12 digitis longas adhibuisset, <lb/>4 dumtaxat gradus a Meridie deflectere cognovit. </s>

<s>Quae omnia, cum in lu&shy;<lb/>cem is dederit, nullus dubitandi locus relinquitur Mugnetis declinationem <pb xlink:href="020/01/810.jpg" pagenum="253"/>variasse, quod et nos experti sumus et quivis alius experiri facile potest &rdquo; <lb/>(Parisiis 1660, pag. </s>

<s>30). </s></p><p type="main">

<s>La scoperta dunque del Gillibrando veniva cos&igrave; confermata, secondo il <lb/>Petit, dai fatti per modo, che nessuno aveva oramai pi&ugrave; ragione di metterla <lb/>in dubbio. </s>

<s>Ma dover de'Filosofi era quello d'investigarne le cause, la pro&shy;<lb/>babilit&agrave; delle quali, se non la verit&agrave;, avrebbe giovato a persuader meglio la <lb/>mente dei ritrosi. </s>

<s>Or dove si sarebbero potute rinvenir queste cause, che <lb/>avessero almeno apparenza d'esser produttrici di effetti tanto straordinari? </s>

<s><lb/>Il Problema per&ograve; non era del tutto nuovo: ei dipendeva da un altro primo <lb/>problema, che tenevasi per risoluto gi&agrave; dal Gilberto, quando nel cap. </s>

<s>I del <lb/>Libro IV, rifiutate le opinioni del Ficino, del Cardano, del Maurolico, dello <lb/>Scaligero e di altri, attribu&igrave; all'inegualit&agrave; della superficie terrestre il variar <lb/>della Declinazione sotto i varii meridiani. </s></p><p type="main">

<s>&ldquo; Cum vero globus telluris in superficie sua mancus sit et inaequalis, <lb/>varia natura deformatus, summasque habeat et convexas partes, ad aliquot <lb/>milliariorum profunditatem, nec natura nec corpore uniformes, sed contra&shy;<lb/>rias et dissimiles; fit ut vis illa tota telluris divertat in eius peripheria ma&shy;<lb/>gnetica corpora versus robustiores et eminentiores continentes magneticas <lb/>partes. </s>

<s>Quare in superna telluris superficie a vero meridiano magnetica pau&shy;<lb/>lulum perventuntur. </s>

<s>Etiam, cum globi superficies distincta sit in terrestres <lb/>et aqueas eminentias, in magnas terras continentes, in oceanum et maria <lb/>vastissima, vis vero omnium motuum magneticorum a terrestri sit natura <lb/>constante et magnetica, quae in maiore continente magis praevalet, non in <lb/>aquosa, fluida, et incerta; sequitur quod versus terram magnam, sive con&shy;<lb/>tinentem magis eminentem, a quovis meridiano, sive per maria sive per <lb/>insulas transeunte, orientem versus aut occidentem, a vero polo inclinatio <lb/>magnetica partibus quibusdam fiat, ad fortiorem nempe, sive altiorem et <lb/>eminentiorem globi terrestris magneticam partem &rdquo; (De Magn. </s>

<s>cit., pag. </s>

<s>153). </s></p><p type="main">

<s>Se questa &egrave; dunque la causa della variazione, ammettendo che col tempo, <lb/>o per opera dell'arte o della Natura, si trasformi in qualche modo l'abito <lb/>della Terra, s'intender&agrave; d'onde abbia origine la variazione della variazione <lb/>che l'esperienza ci ha dimostrata. </s>

<s>Di qui infatti s'attinse quella prima ra&shy;<lb/>gione, che il Cartesio sugger&igrave; ai Filosofi nella forma seguente: &ldquo; Sunt qui <lb/>dicunt istam declinationem non semper in iisdem terrae locis eandem ma&shy;<lb/>nere, sed cum tempore mutari, quod minime mirum videri debet. </s>

<s>Non modo <lb/>quia ferrum quotidie ex unis terrae partibus in alias ab hominibus transfer&shy;<lb/>tur, sed etiam quia eius glebae quae sunt in hac terra exteriore, quibusdam <lb/>in locis cum tempore corrumpi possunt, et aliae in aliis generari, sive ab <lb/>interiore terra submitti &rdquo; (Principi Philos. </s>

<s>cit., pag. </s>

<s>278). </s></p><p type="main">

<s>Ma questa ragion del Cartesio, bench&egrave; legittimamente derivata dalle <lb/>dottrine del Gilberto, fu non curata da chi seguiva altri pi&ugrave; sani principii <lb/>di Filosofia naturale, e i Cartesiani stessi par che pretendessero qualche cosa <lb/>di meglio. </s>

<s>Il Mersenno infatti, appena che per le lettere venute al Petit <lb/>d'Inghilterra, si diffuse in Parigi la notizia della scoperta del Gillibrando, <pb xlink:href="020/01/811.jpg" pagenum="254"/>fu sollecito di avvertire il Kircher che dava in quel tempo opera in Roma <lb/>a scrivere il suo libro <emph type="italics"/>De arte magnetica,<emph.end type="italics"/> aspettandosi da lui in tal con&shy;<lb/>giuntura qualche bella e ingegnosa spiegazione del fatto maraviglioso. </s>

<s>&ldquo; Gau&shy;<lb/>deo vehementer, mi Pater, te nondum postremam manum operi magneti&shy;<lb/>cae adhibuisse, cuius titulo plurimum me recreasti. </s>

<s>Enimvero iam ad te <lb/>quaedam admodum stupenda scripturus sum quorum, si vel probabiles ra&shy;<lb/>tiones afferas, viros magneticos tibi solide obstrinxeris &rdquo; (Kircheri Magnes, <lb/>Romae 1654, pag. </s>

<s>340). </s></p><p type="main">

<s>N&egrave; in mezzo a tale e a tanta commozione, di ch'eran presi gli scien&shy;<lb/>ziati parigini, non era credibile che se ne stesse il Gassendo, il quale, per&shy;<lb/>ch&egrave; non ritrovava nelle dottrine del Copernico, n&egrave; in quelle del Keplero e <lb/>del Gilberto, una ragione sodisfacente del fatto, aveva anch'egli fiducia nella <lb/>solerzia ingegnosa del padre Kircher, a cui scriveva: &ldquo; De causa nihil adhuc <lb/>potui quod satisfaciat comminisci, tametsi varie versaverim et copernicanam <lb/>anticipationem, et gilbertinam verticitatem, et Keplericos nucleos, et demo&shy;<lb/>criticos tramites catenulasque, et alia id genus oppido quam multa. </s>

<s>Expecto <lb/>quid censueris ipse qui praeter insignem solertiam perfecisti haud dubia expe&shy;<lb/>rimenta longe plura &rdquo; (ibi, pag. </s>

<s>345). </s></p><p type="main">

<s>Punto da questi stimoli acuti, non rispondendo ai quali ne andava della <lb/>sua riputazione, il Kircher assottigli&ograve; l'ingegno, ma non seppe far altro che <lb/>sminuzzare e stemperare, con un'arte ch'era tutta sua propria, l'argomento <lb/>pensato gi&agrave; dal Cartesio. </s>

<s>&ldquo; Altera ratio dependet ab immutatione terrestrum <lb/>partium &rdquo; (ibi, pag. </s>

<s>346) della qual mutazione riconosce i pi&ugrave; validi effi&shy;<lb/>cienti ne'fochi sotterranei e nei terremoti. </s></p><p type="main">

<s>Il Petit fu il primo a uscir fuori con un'ipotesi, la quale tanto si mo&shy;<lb/>str&ograve; pi&ugrave; nuova, quanto parve pi&ugrave; ardita. </s>

<s>O non sempre, egli ragionava, l'ago <lb/>riguarda lo stesso punto del polo terrestre, o il polo terrestre non riguarda <lb/>sempre lo stesso punto del cielo. </s>

<s>&ldquo; Cum vero longe probabilius videatur hanc <lb/>varietatem prodire potius ex telluris axe, qui situm mutet, neque semper ad <lb/>eadem coeli puncta dirigatur, quam ex axe magnetis qui velut sub iure ac <lb/>dominio globi terrestris, extra controversiam positus est &rdquo; (Dissert. </s>

<s>cit., <lb/>pag. </s>

<s>30). A creder cos&igrave; fu condotto l'Autore dal veder che variava col tempo <lb/>la latitudine de'paesi, com'egli stesso riscontrava di fatto, confrontando la <lb/>latitudine di Parigi, da s&egrave; trovata, con quella posta dall'Oronzio, dal Fer&shy;<lb/>nelio e dal Vieta. </s></p><p type="main">

<s>Persuaso perci&ograve; che la pi&ugrave; probabile causa della variabilit&agrave; della decli&shy;<lb/>nazione magnetica consistesse nel variar che fa la linea meridiana, era il <lb/>Petit vivamente desideroso d'osservare il fatto in meridiane diligentemente <lb/>descritte, e da assai lungo tempo. </s>

<s>Ma in Parigi e nelle sue vicinanze non <lb/>si trovava altro che Orologi scioterici, ordinati a segnar l'ore, tanto da ser&shy;<lb/>vire agli usi domestici o civili. </s>

<s>In questo tempo venne a saper che in Bo&shy;<lb/>logna, sul pavimento della Chiesa di S. Petronio, era stata disegnata una <lb/>meridiana da servire agli usi proprii della scienza, e credette il Petit che, <lb/>diffusasi anche in Italia la notizia di ci&ograve; ch'era stato osservato prima a Lon-<pb xlink:href="020/01/812.jpg" pagenum="255"/>dra e poi a Parigi, fosse la principale intenzione dell'opera egregia quella <lb/>di verificare la variabilit&agrave; della declinazione magnetica. </s>

<s>Il nome di Gian Do&shy;<lb/>menico Cassini non par che fosse allora conosciuto in Francia, n&egrave; si sapeva <lb/>che la vera intenzione di lui, nel dar opera a descriver la Meridiana di <lb/>S. Petronio, era quella, non di giovar particolarmente alla scienza del Ma&shy;<lb/>gnete, ma di erigere un monumento solenne ai progressi dell'Astronomia. </s></p><p type="main">

<s>Pi&ugrave; tardi s'intese troppo chiaro anche a Parigi quale uomo fosse il <lb/>Cassini, ma intanto il Petit sperava di ritrovar nelle diligenti osservazioni di <lb/>lui la pi&ugrave; valida conferma alla sua ipotesi. </s>

<s>Preparato perci&ograve; un esemplare <lb/>della dissertazione <emph type="italics"/>De latitudine parisiensi,<emph.end type="italics"/> la spediva a Bologna accompa&shy;<lb/>gnata con una lettera, nella quale pregava il Cassini a verificar la declina&shy;<lb/>zione magnetica sopra la sua esattissima Meridiana, e lo richiedeva nello <lb/>stesso tempo del suo giudizio intorno al decider se la ragione del variar del <lb/>declinatorio da un tempo a un altro dipendesse dal variar postura il Cielo o <lb/>la Terra. </s>

<s>Le risposte, qualunque fosse di ci&ograve; la ragione, indugiavano, ond'&egrave; <lb/>che ritrovandosi a viaggiare fra noi quel Sauval, autore del libro sull'anti&shy;<lb/>chit&agrave; di Parigi, e a richiesta del quale il Petit aveva misurata la precisa la&shy;<lb/>titudine di quella citt&agrave;, e ne avea scritta la sopra citata Dissertazione; a lui <lb/>si rivolse come ad amico suo e a suo concittadino, per lagnarsi della poca <lb/>corrispondenza e della poca sincerit&agrave; trovata in certi scienziati, a cui s'era <lb/>rivolto in Italia, e per commettergli alcuni ufficii e negozi da trattarsi col <lb/>principe Leopoldo di Toscana. </s>

<s>Abbiamo di tutto ci&ograve; il documento in una <lb/>lettera, che il Petit stesso da Parigi indirizzava al Sauval a Firenze; lettera, <lb/>della quale il Viviani fece cos&igrave; la traduzione, e ne conserv&ograve; l'estratto di sua <lb/>propria mano. </s></p><p type="main">

<s>&ldquo; ....... di S. A. alla quale io pregavo di mandare i miei Discorsi, <lb/>che ultimamente il signor Du-Hamel ha fatto stampare con la sua Astro&shy;<lb/>nomia fisica, de'quali voi sapete che ve n'&egrave; uno appartenente alla latitu&shy;<lb/>dine di Parigi e la declinazione della Calamita fatta per voi e nell'occasione <lb/>della vostra bell'Opera <emph type="italics"/>Dell'antichit&agrave; di Parigi.<emph.end type="italics"/> Io aver&ograve; ben dispiacere <lb/>se, per la negligenza del nostro amico Thevenot, S. A. non avesse ancora <lb/>ricevuto le attestazioni della mia reverenza, e li detti Discorsi, de'quali vi <lb/>prego d'informarvene e di giustificarmene. </s>

<s>Io ne mandai ancora qualche <lb/>esemplare al sig. </s>

<s>Settala a Milano, ed al sig. </s>

<s>Cassini a Bologna, da'quali <lb/>non ho avuto risposta sodisfacevole, in che io gli pregavo di verificare la <lb/>declinazione della Calamita sopra di qualche mer&igrave;diana esattamente descritta, <lb/>perch&egrave;, avendola fatta quest'anno a Parigi in casa di Mons. </s>

<s>Thevenot, in <lb/>campagna, noi aviamo trovato che non vi era alcuna declinazione, e che la <lb/>lancetta &egrave; propriamente sulla linea meridiana, e per quel ch'&egrave; mio parere, <lb/>&egrave; che questa pu&ograve; procedere da un moto della propensione della Terra nel <lb/>suo centro, che fa cambiare la meridiana e non la virt&ugrave; magnetica, che se&shy;<lb/>guita sempre il polo della Terra. </s>

<s>Io lo avevo pregato di provarlo e di ve&shy;<lb/>rificarlo sopra qualche linea antica meridiana, descritta da cinquanta o ses&shy;<lb/>sant'anni in qua da qualche persona diligente, se ci fosse mutazione al <pb xlink:href="020/01/813.jpg" pagenum="256"/>presente, e se quella che si descrivesse adesso convenisse coll'antica e gli <lb/>fusse parallela o facesse il medesimo angolo, che la declinazione della lan&shy;<lb/>cetta di que'tempi fa in questi tempi. </s>

<s>Ma di tutto questo non ho avuto ri&shy;<lb/>sposta alcuna da veruna parte dove ho scritto, perch&egrave; forse pu&ograve; essere che <lb/>non abbiano potuto trovare nessuna linea meridiana antica assai giusta, e <lb/>della quale possano esser ben certi per compararla con queste che si fanno <lb/>di presente, e questo &egrave; quello di ch noi doviamo dolerci, che nessuno abbia <lb/>pensato, da cent'anni in qua, a la<gap/>ciarci questa linea descritta in qualche <lb/>luogo invariabile ed immobile, come s'&egrave; fatto da poco in qua in S. </s>

<s>Petro&shy;<lb/>nio di Bologna, che servir&agrave; tra qualche tempo a rettificare molte cose pel <lb/>cielo e per la Terra. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma poich&egrave; sono sopra la Calamita, e tratto con voi dell'isola del&shy;<lb/>l'Elba attenente a S. A., io vi prego d'assicurarvi se &egrave; vero che la lancetta <lb/>declina diversamente in quell'Isola, e se vi &egrave; qualche parte, dove ella de&shy;<lb/>clina fino a venti gradi, cosa che io non credo, come nemmeno credo quel <lb/>che mi ha scritto altre volte il Settala, che aveva due o tre Pietre, che non <lb/>pesavano due once, che alzavano, coperte di ferro, cinquanta o sessanta lib&shy;<lb/>bre. </s>

<s>Ma quand'io l'ho stimolato e fatto stimolare da persone di qualit&agrave; di <lb/>trovarmene, vendermene, o prestar qualcuna sotto buona sicurezza, non ci <lb/>ha fatto veruna risposta. </s>

<s>Vedete quel che se ne pu&ograve; credere, e se voi pas&shy;<lb/>sate a Milano, assicuratevene, ed attestateli che non siamo burlati a l'arigi. </s>

<s><lb/>E se nel vostro viaggio ed in Fiorenza, dove ne deve esser molte, voi ne <lb/>trovassi qualcheduna buona, disarmata, e dalla quale si possa cavarne un <lb/>globo di due, tre o quattro dita grosso, voi mi obbligheresti infinitamente <lb/>a comprarla per me. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io ho qualche bell'esperienza da fare, che io non finisco per man&shy;<lb/>canza di quella, ancorch&egrave; voi sapete che ne ho molte altre, e per questo la <lb/>mia opera contro di Monsu Des Cartes resta imperfetta. </s>

<s>Me ne fanno spe&shy;<lb/>rare di Norvegia, cavate secondo la mia maniera, dalla scoria o dalla mi&shy;<lb/>niera, e segnate da quattro parti del mondo che le occupavano, essendovi <lb/>attaccate, ma se io potessi avere la medesima cosa dall'Isola dell'Elba, che <lb/>&egrave; pi&ugrave; vicina a noi, quanto sarei obbligato a chi me ne facesse questa gra&shy;<lb/>zia, ed acciocch&egrave; me le procurasse per l'avanzamento di questa Filosofia <lb/>magnetica!.... &rdquo; (MSS. Cim., T. XXV, c. </s>

<s>154, 55). </s></p><p type="main">

<s>Ritornando ora addietro a considerar parte per parte questo, come lo <lb/>chiamava il Viviani, <emph type="italics"/>capitolo di lettera,<emph.end type="italics"/> non par che avesse il Petit ragione <lb/>di rammaricarsi del Thevenot, avendo egli adempiuto, sebben forse con qual&shy;<lb/>che indugio, di far l'ufficio col principe Leopoldo, il quale, dopo aver ri&shy;<lb/>cevuto il Discorso Della Latitudine di Parigi, rispose in proposito all'Autore <lb/>con lettera del di 2 Novembre 1665: &ldquo; Curiosa non meno che utile &egrave; stata <lb/>l'esperienza, che V. S. ha fatto intorno alla Calamita, tanto pi&ugrave; che nel farla <lb/>esattamente, ciascheduno che intende, sa ancora le difficolt&agrave;, che V. S. potr&agrave; <lb/>avere incontrate &rdquo; (ivi, T. XXIII, c. </s>

<s>127). </s></p><p type="main">

<s>Quanto agli incaricati di verificare la declinazione dell'ago sopra meri-<pb xlink:href="020/01/814.jpg" pagenum="257"/>diane, che fossero state disegnate in Italia almeno da un mezzo secolo, aveva <lb/>ragione il Petit di scusarli, col pensar che non si saranno fidati della pre&shy;<lb/>cisione di quelle linee descritte o da artefici inesperti, o con poco esatti <lb/>strumenti. </s>

<s>Ma non indovinava forse l'Astronomo parigino che s'aveva in <lb/>Italia un'idea, che fosse difficilissimo, anzi quasi impossibile, tracciar la di&shy;<lb/>rittura del meridiano, qualunque fosse la precisione degli strumenti o la <lb/>perizia dell'arte. </s>

<s>Era stata una tale idea ingerita nelle menti da quel Nic&shy;<lb/>col&ograve; Cabeo, che fu tenuto per diligentissimo e pazientissimo sperimentatore <lb/>dal Castelli e dal Baliani. </s></p><p type="main">

<s>Narra esso Cabeo, nel cap. </s>

<s>XV del III Libro della <emph type="italics"/>Filosofia magnetica,<emph.end type="italics"/><lb/>com'essendosi tante volte provato a descriver, con una Bussola squisitissima, <lb/>due linee meridiane, l'una poco distante dall'altra, sulla soglia di una fine&shy;<lb/>stra, non ci fu caso che gli volessero mai riuscir parallele, come sarebbe <lb/>dovuto avvenire se l'ago, nelle due stazioni, avesse segnato sempre la me&shy;<lb/>desima declinazione. </s>

<s>Maravigliato di questo fatto e datosi a investigarne la <lb/>causa, ritrov&ograve; che dipendeva dai mattoni troppo cotti, o come fra noi si dice <lb/><emph type="italics"/>inferrettati,<emph.end type="italics"/> di ch'era costruito il muro della finestra, dall'azione magnetica <lb/>de'quali mattoni la direzion generale del Magnete era notabilmente alterata. <lb/></s>

<s>&ldquo; Causa igitur cur Versorium in parietibus sic incostanter meridianum re&shy;<lb/>spiciat, sunt lateres nimium excocti, qui in tali pariete saepe delitescunt. </s>

<s><lb/>Ex longa enim commoratione in tali situ, virtute telluris, magneticam con&shy;<lb/>trahunt naturam, ac proinde cogunt sibi etiam aliqua saltem ratione Verso&shy;<lb/>rum obtemperare &rdquo; (Coloniae 1629, pag. </s>

<s>234). </s></p><p type="main">

<s>La curiosa esperienza fu confermata poi dal Cassini, per la mente del <lb/>quale, nell'atto che apparecchiavasi a rispondere al Petit, passavano queste <lb/>parole, con che il Cabeo stesso concludeva quel suo capitolo sopra citato: <lb/>&ldquo; Hinc vides quam incerto effectu solaria horologia, si magnetico dirigan&shy;<lb/>tur cuspide, collocentur supra parietes aut fenestras &rdquo; (ibi). </s></p><p type="main">

<s>Par che dunque troppo si mostrasse impaziente il Petit, lagnandosi che <lb/>dal Cassini non aveva avuto risposta. </s>

<s>Voleva il Cassini tempo a pensarci, <lb/>essendo cosa tanto nuova e di tanta importanza, e dopo averci lungamente <lb/>pensato rispose dubitando se i fatti osservati a Londra e a Parigi potessero <lb/>essere argomento sicuro, e prova dimostrativa della mobilit&agrave; del cielo o della <lb/>terra. </s>

<s>La scrittura ci fu diligentemente conservata dal Viviani, che la copi&ograve; <lb/>di seguito al capitolo di Lettera del Petit, alla quale, in questa del Cassini, <lb/>si fa cos&igrave; la risposta. </s></p><p type="main">

<s>&ldquo; L'esatta descrizione della meridiana richiede tante circospezioni, che, <lb/>non essendo di volgar perspicacia l'osservarle, malamente potiam fidarci che <lb/>quelle che troviam descritte da altri, senza sapere il modo e la diligenza in <lb/>esse adoprata, non svarino alquanti minuti dal vero sito. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quelle che si descrivono per mezzo dell'ombre di uno stile, che &egrave; il <lb/>modo pi&ugrave; usitato, ancorch&egrave; si faccia elezione del tempo solstiziale, per la <lb/>perplessit&agrave; nell'esatta terminazione dell'ombra, e per la brevit&agrave; dello stile, <lb/>per qualsisia inegualit&agrave; o scabrosit&agrave; o inclinazione del piano, soggiacciono a <pb xlink:href="020/01/815.jpg" pagenum="258"/>svarii di gradi interi. </s>

<s>Quelle, che si descrivono per mezzo di un'altezza del <lb/>sole presa con istrumenti ancorch&egrave; esatti, restano con molta ambiguit&agrave;, <lb/>quando il sole, con poca mutazione d'altezza, fa notabile mutazione di sito <lb/>orizzontale, com'avviene qualche ora innanzi e dopo mezzogiorno, e presup&shy;<lb/>pongono sempre molti elementi, cio&egrave; l'altezza del polo, il vero luogo del <lb/>sole, l'obliquit&agrave; del Zodiaco, oltre alle rifrazioni e parallassi, e perci&ograve;, come <lb/>descritte con metodo troppo composto, non sogliono riuscire esatte. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Con due altezze delle stelle uguali, una innanzi l'altra dopo mezzo&shy;<lb/>giorno, in notabil distanza dal meridiano e dal sole, ne'giorni solstiziali, rie&shy;<lb/>scono pi&ugrave; accertate, siccome anco ha evidenza la descrizione della via della <lb/>specie del sole introdotta per un buco rotondo orizzontale molto alto in un <lb/>piano esattamente orizzontale, nel giorno solstiziale, per trovare, per mezzo <lb/>di esso e del punto verticale esattamente stabilito, la meridiana, come s'&egrave; <lb/>fatto in S. </s>

<s>Petronio di Bologna, ed evidentissima &egrave; quella, che si cava dalle <lb/>due massime declinazioni diurne della Stella polare, che pigliano per mezzo <lb/>la meridiana, massime con istrumenti molto grandi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma perch&egrave; simili diligenze non si fanno che da peritissimi Astronomi, <lb/>per valersene di fondamento nelle osservazioni celesti, non &egrave; cos&igrave; in pronto <lb/>avere meridiane antiche di questa sorta, n&egrave; devonsi le altre meridiane, fatte <lb/>in alcuno de'primi modi, mettere ad altro capitale che ad uso di Orologi <lb/>solari, ne'quali si trascurano simili esattezze. </s>

<s>N&egrave; &egrave; cosa da maravigliarsi se <lb/>nello stesso piano, in diversi tempi, venga la meridiana un poco diversa&shy;<lb/>mente descritta, mentre ogni tal descrizione &egrave; per natura soggetta a qual&shy;<lb/>che svario, e chi ne far&agrave; l'esperienza trover&agrave; non poca difficolt&agrave; in descri&shy;<lb/>vere, nel giorno stesso non che in diversi tempi, due lunghe meridiane <lb/>nello stesso piano, senza sensibile declinazione di una all'altra. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Non par dunque che un poco di svario, trovato fra due meridiane <lb/>descritte in diversi tempi, debba esser sufficiente fondamento di sospicare <lb/>che, da un tempo all'altro, sia segu&igrave;ta reale mutazione della meridiana per <lb/>moto del Cielo e della Terra, essendo pi&ugrave; pronto attribuirlo alla somma dif&shy;<lb/>ficolt&agrave; di descrivere con esattissimo confronto due meridiane. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quando da un tempo all'altro si trovasse differenza notabilmente mag&shy;<lb/>giore di quella, che possa portare la difficolt&agrave; dell'esatta descrizione, e que&shy;<lb/>sta si trovasse, in luoghi diversi e in diversi tempi, con certe proporzioni <lb/>corrispondenti a'luoghi e tempi; allora potrebbesi cominciare a dubitare di <lb/>tal reale mutazione. </s>

<s>Ma sinora le differenze, che si presuppongono per fon&shy;<lb/>damento, son cos&igrave; piccole, che quando tutto quello svario si attribuisse alle <lb/>difficolt&agrave; delle descrizioni, ancor rimane alle descrizioni stesse la lode di pi&ugrave; <lb/>che mediocremente diligenti, essendo difficile a non commettere svarii mag&shy;<lb/>giori con somiglianti metodi in due meridiane, nell'istesso giorno e nel&shy;<lb/>l'istesso luogo descritte. </s>

<s>Onde tanto &egrave; lontano che le osservazioni esposte <lb/>debbano dar motivo d'entrare in questo dubbio e di farne perquisizione, che <lb/>piuttosto, quando altronde vi fosse dubbio, basterebbero queste a farlo de&shy;<lb/>porre, mentre le differenze sono dentro i termini di quelle, a'quali soggiac-<pb xlink:href="020/01/816.jpg" pagenum="259"/>ciono per s&egrave; stesse le osservazioni. </s>

<s>Onde almeno potiam concludere non es&shy;<lb/>servi mutazione evidentemente sensibile, ci&ograve; che siasi d'una insensibile <lb/>mutazione, di cui non &egrave; sicuro il far prova con antiche meridiane, delle <lb/>quali non sappiamo che siano con straordinaria diligenza e circospezione de&shy;<lb/>scritte. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; &Egrave; difficile il trovar altre antiche meridiane che degli Orologi solari, <lb/>ne'quali non si presuppone tanta squisitezza. </s>

<s>Tra queste, la meridiana del&shy;<lb/>l'Orologio della piazza di Bologna, nella faccia meridionale della Torre del <lb/>palazzo del Potest&agrave;, che si suppone molto antica, concorre con la gran me&shy;<lb/>ridiana di S. </s>

<s>Petronio descritta con ogni diligenza nel solstizio estivo del 1656. <lb/>Chi avesse certezza della retta descrizione di quella, come abbiamo di que&shy;<lb/>sta, potrebbe concludere non apparire per gran lunghezza di tempo sensi&shy;<lb/>bile mutazione di meridiana. </s>

<s>Resta per&ograve; per mezzo di questa molto maggior <lb/>probabilit&agrave; dell'immutabilit&agrave; sensibile, e dalla meridiana di S. Petronio, per <lb/>essere molto grande ed esatta, esaminata dopo qualche lunghezza di tempo, <lb/>si aver&agrave; maggiore evidenza della verit&agrave; di questo fatto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Una insensibile mutazione del centro dell'asse e de'poli della Terra <lb/>par che si potesse presupporre dalla variazione a noi sensibile della super&shy;<lb/>ficie della Terra, che si fa continuamente con abbassarsi e dimagrirsi i <lb/>monti e riempiersi le valli: ma siccome l'inegualit&agrave; della superficie della <lb/>Terra &egrave; molto poca, in proporzione di tutta la di lei grandezza; cos&igrave; questa <lb/>sola, nel ridursi ad ugualit&agrave; non far&agrave; giammai mutazione che possa discer&shy;<lb/>nersi nella meridiana, che si mutasse in diversi luoghi diversamente con la <lb/>mutazione de'poli. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto alla mutazione della direzione magnetica, che in progresso di <lb/>tempo si vada facendo, nemmeno di questa pare sufficiente motivo di so&shy;<lb/>spettare l'avere in diversi tempi a diverse meridiane osservato alquanti mi&shy;<lb/>nuti di diversit&agrave; di declinazione, s&igrave; perch&egrave;, per le ragioni predette, non ab&shy;<lb/>biamo certezza dell'esatta descrizione di quelle meridiane, nel termine di <lb/>quei pochi minuti, s&igrave; perch&egrave; riesce sommamente difficile, anco ad una me&shy;<lb/>ridiana giustissima, determinar la declinazione stessa cos&igrave; sottilmente, che <lb/>non segua svario di pochi minuti, poich&egrave;, richiedendosi in un circolo che <lb/>possa distinguere tutti i minuti, il diametro di lunghezza almeno di quattro <lb/>piedi, la lunghezza della lancetta di quattro o cinqu'once, fatta diametro <lb/>d'un circolo, appena potr&agrave; dare in esso nemmeno le diecine di minuti di&shy;<lb/>stintamente. </s>

<s>N&egrave; questa difficolt&agrave; &egrave; superabile col prolungar la linea a segno, <lb/>che diventi diametro d'un circolo, in cui si possano distinguere i minuti, <lb/>perch&egrave; simili prolungazioni di linee brevi in pratica non si fanno con evi&shy;<lb/>dente esattezza, e massime quelle di queste lancette, che non sono senza <lb/>grossezza sensibile, n&egrave; &egrave; facile sottilizzare in esse sino a questo segno con <lb/>l'occhio l'aerea linea immaginaria indivisibile della direzione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Chi far&agrave; prova di prolungare in diverse parti dello stesso piano si&shy;<lb/>mili linee di quattro o cinque piedi, s'accorger&agrave; facilmente quanto sia dif&shy;<lb/>ficile descriverle esattamente parallele. </s>

<s>Ond'&egrave; che alcuni, avendo trovato de-<pb xlink:href="020/01/817.jpg" pagenum="260"/>clinar l'una dall'altra simili linee con diversi aghi descritte, non riflettendo <lb/>quanto facilmente ci&ograve; possa procedere dalla difficolt&agrave; d'operare con tale esat&shy;<lb/>tezza, l'hanno attribuito a diversa inclinazione, che abbiano diverse calamite, <lb/>la quale forse non &egrave; improbabile, ma non per&ograve; con simile esame a suffi&shy;<lb/>cienza provata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Tralascio la circospezione, con cui bisogna in simili osservazioni guar&shy;<lb/>darsi, non solo dal ferro, ma anco da certi altri corpi vicini, avendo speri&shy;<lb/>mentato pi&ugrave; d'una volta che la vicinanza a mattoni pi&ugrave; o meno cotti la <lb/>fanno pi&ugrave; o meno declinare. </s>

<s>E siccome conosciam questi, cos&igrave; niuna cer&shy;<lb/>tezza abbiamo che altri non ce ne sieno di simili facult&agrave; a noi ignote, che <lb/>nelle operazioni ponno per accidente incontrarsi. </s>

<s>Onde, dato ancora che fosse <lb/>oltre ogni speranza esattissimo il modo d'operare, a tante altre cause par&shy;<lb/>ziali si pu&ograve; attribuire simile diversit&agrave; che s'osservasse, che parrebbe dover <lb/>esser sempre l'ultima la mutazione universale della direzione magnetica. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma simili diversit&agrave;, che da pochi minuti procedono, mentre stanno <lb/>ne'termini della perplessit&agrave; a cui di natura sua &egrave; soggetta l'osservazione, <lb/>non par che debban servire di fondamento d'investigar altra causa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Gli anni passati, nella campagna di Bologna e di Ferrara, fu tirata una <lb/>linea secondo la direzione magnetica per alquante miglia, e dopo due anni <lb/>tiratane un'altra dall'istesso principio, fu trovato nel fine discostarsi dalla <lb/>precedente alquanti passi, ma non perci&ograve; tale accidente fu attribuito a mu&shy;<lb/>tazione della linea magnetica, ma all'estrema difficolt&agrave; di prolungar giusta&shy;<lb/>mente a tanta distanza una linea s&igrave; corta, quanto &egrave; quella di una lancetta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Insomma, se maggior fondamento non abbiamo della mutazione della <lb/>meridiana o della direzione magnetica, che la differenza di pochi minuti ve&shy;<lb/>nuta nelle osservazioni, pare piuttosto che venga stabilita l'immutabilit&agrave; del&shy;<lb/>l'una e dell'altra, che posta alcuna di esse in sospetto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In Bologna la Calamita non declina sensibilmente dalla meridiana, <lb/>ancorch&egrave; alcuni abbian pubblicato che declini tre gradi, e sebbene si pu&ograve; <lb/>attribuire questa differenza al modo di osservare, non per questo vien reso <lb/>probabile il perpetuo concorso della meridiana con la linea della direzione <lb/>magnetica, ancorch&egrave; in alcuni altri luoghi sia stato con diligente metodo os&shy;<lb/>servato, poich&egrave;, pubblicandosi in molti luoghi simili declinazioni di molti <lb/>gradi, sarebbe un tacciare di troppo grossolane tali osservazioni, e quali sono <lb/>state stabilite, se allo svario di esse si attribuisse tanta differenza. </s>

<s>E si pas&shy;<lb/>serebbe da un estremo all'altro nel fondare su pochi minuti di differenza <lb/>una reale mutazione, e poi non far caso della differenza di molti gradi, per <lb/>istabilire l'uniformit&agrave; delle declinazioni. </s>

<s>N&egrave; per&ograve; deve defraudarsi della do&shy;<lb/>vuta lode chi dell'uno e dell'altro su tali fondamenti ha dubitato, mentre <lb/>porge occasione e stimolo di rintracciare con maggior diligenza ed accura&shy;<lb/>tezza la verit&agrave; del fatto &rdquo; (ivi, c. </s>

<s>156-59). </s></p><p type="main">

<s>I lettori vedono in questo Discorso del Cassini lucidamente riflessa l'in&shy;<lb/>dole dell'ingegno italiano, alieno dalle arrischiate ipotesi e dai facili archi&shy;<lb/>tettati sistemi, e che se non &egrave; sicuro non fa progressi. </s>

<s>Quella maggior <pb xlink:href="020/01/818.jpg" pagenum="261"/>diligenza e accuratezza, aspettata dal Cassini, poi venne e fu confermata la <lb/>verit&agrave; non del fatto solo osservato dal Gillibrando, ma di altri simili a quello. </s>

<s><lb/>Fu osservato cio&egrave; e confermato per vero che la declinazione dell'ago varia, <lb/>non solamente di anno in anno, ma di mese in mese, e anche di giorno in <lb/>giorno. </s>

<s>&ldquo; Monui autem superius (dice il Musschenbroek nella Dissertazione <lb/>sua <emph type="italics"/>De Magnete<emph.end type="italics"/>) non modo singulo anno sed singulo mense et die decli&shy;<lb/>nationem esse diversam, quod constat ex observationibus a patre Guy Ta&shy;<lb/>chart factis anno 1682.... Nescio an ante hunc patrem aliquis hanc quo&shy;<lb/>tidianam mutationem observaverit: eamdem confirmare possum propria <lb/>experentia &rdquo; (Viennae 1756, pag. </s>

<s>156). </s></p><pb xlink:href="020/01/819.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dell'Elettro<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle prime esperienze elettriche e delle ipotesi del Gilberto e del Cabeo; delle esperienze del Gue&shy;<lb/>ricke e degli Accademici del Cimento. </s>

<s>&mdash; II. De'fuochi elettrici dell'Hawksbee; dell'elettricit&agrave; <lb/>per comunicazione; dell'elettricit&agrave; vitrea e resinosa, e dell'elettricit&agrave; positiva e negativa. </s>

<s>&mdash; <lb/>III. </s>

<s>Di ci&ograve; che a promuovere la scienza elettrica, fu cooperato in Italia, principalmente dal Bec&shy;<lb/>caria e dal Volta. </s>

<s>&mdash; IV. Dell'elettricit&agrave; e degli effetti di lei nell'ammosfera. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Il Magnete e l'Elettro, nella loro vita avventurosa, non andarono mai <lb/>fra s&egrave; disgiunti. </s>

<s>Celebre fu sempre la loro fama, dice il Gilberto, nelle com&shy;<lb/>memorazioni dei dotti. </s>

<s>Il Magnete e l'Elettro sono invocati da alcuni Filo&shy;<lb/>sofi, quando, a investigar molti effetti della Natura, riescono infermi i sensi, <lb/>e la ragione dietro a loro ha corte le ali. </s>

<s>Anche i Teologi curiosi, per mezzo <lb/>del Magnete e dell'Elettro, illustrano i divini misteri e la boria de'Metafi&shy;<lb/>sici se ne serve come della spada di Delfo, nelle sue fantasticate battaglie, <lb/>a penetrare le armature pi&ugrave; forti. </s>

<s>E che? </s>

<s>i medici stessi, sull'autorevole <lb/>esempio di Galeno, per confermare il fatto dell'attrazion de'succhi nell'opera <lb/>de'purganti o nell'uso degli altri medicamenti, invocano per testimonianza <lb/>il Magnete <emph type="italics"/>magnae authoritatis et efficentiae conspicuae naturam, corpus&shy;<lb/>que inclytum!<emph.end type="italics"/> (De Magn. </s>

<s>cit., pag. </s>

<s>47). Dovunque insomma si tratta di <lb/>qualche causa, della quale non si sa far la ragione, si rimanda i clienti, <lb/><emph type="italics"/>tamquam personatos advocatos,<emph.end type="italics"/> all'Elettro e al Magnete. </s></p><p type="main">

<s>Consorti nelle avventure le due materiali sostanze, nel far caro a'Filo&shy;<lb/>sofi de'loro gelosi misteri si trovarono pure insieme consorti. </s>

<s>Com'aveva <lb/>Plutarco ostetricata dalla divina mente platonica l'ipotesi che il Magnete at-<pb xlink:href="020/01/820.jpg" pagenum="263"/>traesse il ferro, perch&egrave; sospintogli incontro dal vortice dell'aria, cos&igrave; fu cre&shy;<lb/>duto che venissero dall'Elettro nel medesimo modo attratti i tritumi della <lb/>paglia. </s>

<s>I Filosofi, specialmente italiani del secolo XVI, avendo osservato che <lb/>l'Ambra e il Gagate, per attrarre i minuzzoli de'corpi, volevano esser prima <lb/>ben confricati, e credendo che fosse quella confricazione a questo sol ne&shy;<lb/>cessaria per promuover in essi il calore, al calore stesso, e non all'Ambra <lb/>o <gap/> Gagate, attribuivano la virt&ugrave; di attrarre. </s>

<s>Gli esempi delle cucurbite me&shy;<lb/>di<gap/> de'tanti altri giochetti pneumatici descritti da Herone servivano a <lb/>que'Filosofi per prova degli effetti da essi riconosciuti come naturale pro&shy;<lb/>priet&agrave; del calore. </s>

<s>E bench&egrave; a rimovere dalla Fisica un tal dannosissimo er&shy;<lb/>rore uscisse, come altrove dicemmo, il Benedetti a dimostrar contro il Car&shy;<lb/>dano e il Tartaglia che propriet&agrave; del calore &egrave; il condensar non l'attrarre, <lb/>pur fu cos&igrave; quell'errore tenace, che Fisici insigni durarono per tutto il se&shy;<lb/>colo XVII a credere e a dire che i vapori erano dalla superficie terrestre <lb/>attirati in alto dalla forza de'raggi del Sole. </s></p><p type="main">

<s>Cos&igrave; essendo, aveva ragione il Gilberto a rimproverar tutti i Filosofi <lb/>suoi predecessori che si fossero messi a ragionar delle propriet&agrave; elettriche <lb/><emph type="italics"/>nullis rationibus ab experimentis et demonstrationibus inventis.<emph.end type="italics"/> &ldquo; Tantum, <lb/>prosegue a dire, agunt verbis, rebus ipsis maiorem culiginem inducenti&shy;<lb/>bus &rdquo; (ibi, pag. </s>

<s>48). Tanto poi queste cose son vere, che nessuno ha potuto <lb/>ancora negare al Filosofo inglese il merito di aver egli il primo dato ini&shy;<lb/>zio alla scienza elettrica, fugando le tenebrose parole de'suoi predecessori, <lb/>colla luce de'suoi nuovi esperimenti. </s></p><p type="main">

<s>Apre il Gilberto il campo alla nuova Filosofia e n'estende ampiamente <lb/>la provincia, incominciando dal dimostrar che la virt&ugrave; di attrarre non &egrave; pro&shy;<lb/>pria di sola l'Ambra o il Gagate, com'era stato creduto fin'allora, ma di <lb/>moltissimi altri corpi, cos&igrave; naturali, come artefatti. </s>

<s>&ldquo; Non solum succinum <lb/>et Gagates, ut illi putant allectant corpuscula, sed Adamas, Sapphirus, Car&shy;<lb/>bunculus, Iris gemma, Opalus, Amethystus, Vincentina et Bristolla, Beril&shy;<lb/>lus et Crystallus idem faciunt. </s>

<s>Similes etiam attrahendi vires habere videntur <lb/>vitrum, praesertim clarum et lucidum, tum ex vitro aut crystallo adultera&shy;<lb/>tae gemmae, vitrum antimonii, et fluores plurimi ex fodinis et Belemnites. </s>

<s><lb/>Allicit etiam sulphur, mastix, et cera dura sigillaris ex lacca variis colori&shy;<lb/>bus tincta et composita. </s>

<s>Allicit resina durior, ut Arsenicum, sed imbecillius; <lb/>aegre etiam et obscure in convenienti coelo sicco Sal gemma, Lapis specu&shy;<lb/>laris, et Alumen rupeum &rdquo; (ibi). </s></p><p type="main">

<s>E come aveva il Gilberto esteso il numero de'corpi attraenti, cos&igrave;, sopra <lb/>quel che tenevasi prima di lui, estese il numero de'corpi attratti, i quali <lb/>dalle uniche festuche ridusse ai metalli, alle pietre, ai legni e anzi ad ogni <lb/>sorta di cose, <emph type="italics"/>quae sensibus nostris subiiciuntur.<emph.end type="italics"/> Provocava chiunque vo&shy;<lb/>lesse a pigliare esperienza di ci&ograve;, insegnando a farla con un Versorio, che <lb/>portasse nella sua punta qualunque specie di metallo, con che intanto do&shy;<lb/>tava la scienza elettrica del suo primo e semplicissimo strumento, che &egrave; una <lb/>specie di Elettroscopio. </s></p><pb xlink:href="020/01/821.jpg" pagenum="264"/><p type="main">

<s>Ma perch&egrave; la scienza non consiste solo nello sperimentare i fatti, si <lb/>principalmente nello specularne le recondite ragioni, il Gilberto vuol da vero <lb/>filosofo investigar le ragioni di quegli elettrici misteri. </s>

<s>Dicemmo che si ri&shy;<lb/>ducevano quelle ragioni ai vortici dell'aria e al calore, ma il nuovo Filosofo <lb/>crede falsa l'una e l'altra di queste ipotesi professate da'Filosofi suoi pre&shy;<lb/>decessori. </s>

<s>E quanto al dir che l'Ambra attrae per effetto del calore eccitato <lb/>colle frizioni, il Gilberto ne mostrava la falsit&agrave; con questa semplice e con&shy;<lb/>cludentissima osservazione: &ldquo; Si a calore fit attractio, cur alia etiam plu&shy;<lb/>rima corpora, sive igne, sole aut attritu excalefacta non attraherent? </s>

<s>&rdquo; (ibi, <lb/>pag. </s>

<s>49). </s></p><p type="main">

<s>L'altra ipotesi de'vortici dell'aria, come pi&ugrave; radicata nelle menti, per <lb/>la lunghezza del tempo e per la grande autorit&agrave; di Platone, e come pi&ugrave; se&shy;<lb/>ducente per la facilit&agrave; del modo, con cui si dava per essa a intendere il <lb/>fatto elettrico; voleva esser confutata con pi&ugrave; diretti argomenti, che piglias&shy;<lb/>sero valore dall'esperienza. </s>

<s>Due furono gli argomenti sperimentali pensati <lb/>in proposito dal Gilberto: il primo desunto dalla figura conica, in che si <lb/>assottiglia e s'appunta verso l'ambra una gocciola d'acqua attirata: il se&shy;<lb/>condo concluso dal veder che l'ambra stessa non pu&ograve; far s&igrave; che con l'aria <lb/>si pieghi, verso il centro dell'attrazione, la fiamma di una candela. </s>

<s>&ldquo; Cor&shy;<lb/>pus vero ducit ipsum manifesto in aquae globosa gutta posita supra siccum, <lb/>nam succinum appositum in convenienti distantia, proximas convellit par&shy;<lb/>tes, et educit in conum: alioquin si ab aer&egrave; ruente adduceretur, gutta <lb/>tota inclinaret. </s>

<s>Quod vero aerem non trahit, sic demonstratur: Sit tenuis&shy;<lb/>sima candela cerea, quae flammam minimam et claram concipiat: appone <lb/>huic succinum vel gagatem planum, latum, bene praeparatum, et fricatum <lb/>secundum artem, intra duos digitos, vel quamvis distantiam convenientem; <lb/>succinum tale quod longe lateque alliceret corpora, flammam tamen non <lb/>commovet, quod fieri, si commoveretur aer, necessum esset, flamma enim <lb/>fluentem aerem sequeretur &rdquo; (ibi, pag. </s>

<s>55). </s></p><p type="main">

<s>Ma l'argomento pi&ugrave; sottile e pi&ugrave; concludente lo ritrae il Gilberto in <lb/>fare osservar che, per mezzo de'vortici dell'aria, si potrebbero bene spie&shy;<lb/>gar l'impeto e la veemenza, con cui le festuche son trascinate verso l'am&shy;<lb/>bra, ma non s'intenderebbe come vi potessero essere altres&igrave; trattenute. </s>

<s>Or <lb/>perch&egrave; &egrave; un fatto che trattenute vi sono, dopo esservi state sospinte, la virt&ugrave; <lb/>dunque dell'ambra consiste in una vera e propria attrazione, similissima a <lb/>quella del Magnete e che, come quella del Magnete, s'attenua essa pure col <lb/>crescere delle distanze. </s></p><p type="main">

<s>Qual'esser pu&ograve; dunque, secondo il Gilberto, la causa efficiente e il prin&shy;<lb/>cipio di cos&igrave; misteriosa attrazione? </s>

<s>&ldquo; Verisimile est, egli risponde, succinum <lb/>expirare aliquid peculiare quod corpora ipsa alliciat &rdquo; (ibi). Quest'alito &egrave; <lb/>sottilissimo ne'corpi elettrici; rapido e crasso ne'non elettrici: in quegli si <lb/>ridesta per via di affrizioni leggere e sottilissime; &ldquo; ita enim tenuissima <lb/>evocantur effluvia &rdquo; (ibi, pag. </s>

<s>56). </s></p><p type="main">

<s>Ma come possono i corpi elettrici, per via di queste tenuissime esala-<pb xlink:href="020/01/822.jpg" pagenum="265"/>zioni, copulare a s&egrave; gli altri corpi? </s>

<s>&ldquo; Effluvia, risponde il Gilberto, ex subtili <lb/>fusione humoris existunt &rdquo; (ibi) e tutti quanti i corpi <emph type="italics"/>uniuntur,<emph.end type="italics"/> secondo <lb/>lui, <emph type="italics"/>et quasi ferruminantur quodammodo humore.<emph.end type="italics"/> Invoca a provar questo <lb/>suo assunto le attrazioni de'corpuscoli galleggianti sull'acqua. </s>

<s>Non ch'egli <lb/>attribuisca il fenomeno di capillarit&agrave; ad un fatto elettrico, ma lo adduce cos&igrave; <lb/>come per via di esempio, e per concluder l'argomento dall'analogia. </s>

<s>Pur <lb/>per&ograve; confessando essere gli effluvii elettrici molto pi&ugrave; sottili di quelli del&shy;<lb/>l'acqua, non si rimane il Gilberto dal generalizzare cos&igrave; la teoria dell'umido <lb/>copulatore: &ldquo; Omnis attractio electrica fit mediante humido, ita propter hu&shy;<lb/>morem omnia mutuo conveniunt &rdquo; (ibi, pag. </s>

<s>58). </s></p><p type="main">

<s>In queste speculazioni e in queste esperienze si conclude in sostanza <lb/>ci&ograve; che dal Gilberto, primo Autore, si tratt&ograve; dell'Elettro. </s>

<s>Fa maraviglia che, <lb/>tanto ritroso in consentire un fluido nel Magnete, a cui s'attribuisce per lui <lb/>una virt&ugrave; incorporea e immateriale, scenda a materiar poi gli effluvii elet&shy;<lb/>trici da rassomigliarli alle umide esalazioni. </s>

<s>Ma la maraviglia cessa in pen&shy;<lb/>sare a quali varii ufficii sieno ordinate, secondo il Filosofo, ne'magisteri della <lb/>Natura le due diverse virt&ugrave; operanti, e quale ne resulti da essa variet&agrave; di <lb/>moti. </s>

<s>&ldquo; Motus electricus est motus coacervationis materiae, magneticus est <lb/>dispositionis et conformationis. </s>

<s>Globus telluris per se electrice congregatur <lb/>et cohaeret, globus Telluris magnetice dirigitur et convertitur &rdquo; (ibi, pag. </s>

<s>60). </s></p><p type="main">

<s>Or &egrave; da vedere quale efficacia avessero le nuove elettriche dottrine sulla <lb/>mente de'Filosofi curiosi d'intendere la ragione di s&igrave; occulti misteri. </s>

<s>E spac&shy;<lb/>ciandosene in breve, diciamo che l'ipotesi gilbertina del fluido copulatore a <lb/>s&egrave;, per l'intermedio dell'umido, non sodisfece a nessuno, ond'&egrave; che, non <lb/>vedendosi esser detto nulla di meglio, si stette all'antica ipotesi di Platone. </s>

<s><lb/>Ne abbiamo di ci&ograve; un esempio insigne in Galileo, al quale occorrendo di do&shy;<lb/>ver rendere qualche ragione delle attrazioni elettriche, le attribu&igrave; senz'altro <lb/>all'aria, che trascina nel suo vortice i corpiccioli, mostrando cos&igrave; di non far <lb/>nessun conto dell'esperienze e degli argomenti che ci fond&ograve; sopra il Gilberto. <lb/></s>

<s>&ldquo; L'ambra, egli dice, il diamante, l'altre gioie e materie molto dense, ri&shy;<lb/>scaldate attraggono i corpuscoli leggeri, e ci&ograve; perch&egrave; attraggono l'aria nel <lb/>raffreddarsi, e l'aria fa vento ai corpuscoli &rdquo; (Alb. </s>

<s>III, 365). </s></p><p type="main">

<s>Non avendo avuto occasion Galileo o non essendo voluto entrare in una <lb/>cos&igrave; oscura materia, all'intelligenza della quale non preluceva l'amabile Geo&shy;<lb/>metria, non sappiamo da quali ragioni egli fosse mosso ad abbandonar nella <lb/>Filosofia elettrica quel Gilberto, che nella Magnetica aveva, unico fra'con&shy;<lb/>temporanei, cos&igrave; con grande ammirazion proseguito. </s>

<s>Il primo a esporre so&shy;<lb/>lennemente quelle ragioni contro il gran Filosofo inglese fu Niccol&ograve; Cabeo. </s>

<s><lb/>Ei comincia con gran sottigliezza a discutere l'ipotesi dell'umido copulatore <lb/>in que'fenomeni di capillarit&agrave;, che male a nostro giudizio egli dice essere <lb/>stati dal Gilberto attribuiti a fenomeni elettrici. </s>

<s>Le ragioni per&ograve; che ebbe <lb/>il nostro Ferrarese di contradire alle dottrine del Medico di Londra, pog&shy;<lb/>giavano sopra pi&ugrave; saldi fondamenti, che non sul negare l'identit&agrave; che passa <lb/>fra la causa delle attrazioni elettriche e quella dell'andarsi a incontrare e a <pb xlink:href="020/01/823.jpg" pagenum="266"/>copularsi le festuche galleggianti sull'acqua. </s>

<s>Il Cabeo, sottilissimo osserva&shy;<lb/>tore, aveva a citare altri fatti che non era possibile al Gilberto spiegarli. </s></p><p type="main">

<s>Preso un pezzo d'ambra e strofinatolo ben bene l'applicava ad attrarre <lb/>la segatura del legno. </s>

<s>Osservava l'attentissimo Cabeo que'corpiccioli, e gli <lb/>vedeva dirizzarsi sulla superficie dell'ambra come tanti rigidissimi peli. </s>

<s>Non <lb/>piegando, non cadendo, gli vedeva titubare, e dopo essere stati cos&igrave; alquanto <lb/>quasi dubbiosi, risolversi e spiccare un agilissimo salto. </s>

<s>&ldquo; Observavi autem <lb/>semper fere extremitates illorum pilorum fluctuare, nutare, et subinde non <lb/>tam decidebant extremitates illorum pilorum quam proiiciebantur procul, ut <lb/>manifesto observavi aliis etiam spectantibus. </s>

<s>Post aliqualem enim nutatio&shy;<lb/>nem videbamus aliquas ligni particulas proiici &rdquo; (Philos. </s>

<s>magnetica, Colo&shy;<lb/>niae 1629, pag. </s>

<s>194). </s></p><p type="main">

<s>Il Cabeo dunque aveva fatta una scoperta nuova e rilevantissima: aveva <lb/>scoperto, cio&egrave;, che non &egrave; sola propriet&agrave; dell'Ambra, com'aveva creduto il <lb/>Gilberto, quella di attrarre e di copulare, ma quella altres&igrave; di respingere e <lb/>separare. </s>

<s>Il fatto era per s&egrave; medesimo sufficiente a dimostrar che l'ipotesi <lb/>gilbertina era per lo men difettosa. </s>

<s>E come potevasi dall'altra parte pen&shy;<lb/>sare che avesse un medesimo fluido, nello stesso tempo, due virt&ugrave; cos&igrave; tra <lb/>loro contrarie, quella di attrarre e l'altra di respingere? </s>

<s>Fu da ci&ograve; condotto <lb/>il Cabeo a negar che le due contrarie virt&ugrave; fossero inerenti all'ambra, ond'&egrave; <lb/>ch'ei rassomigliava quelle osservate repulsioni al rimbalzar di un corpo ela&shy;<lb/>stico proiettato da qualche estrinseca forza contro un corpo duro. </s>

<s>Or dove <lb/>pu&ograve; riseder mai questa forza proiiciente? </s>

<s>E rispondeva il Cabeo: nell'aria. <lb/></s>

<s>&ldquo; Dico igitur ex electro, seu ex quolibet corpore attrahente electrice, quando <lb/>sic attrahit, effluere effluvium tenuissimum, quod aerem attenuat, et disiicit, <lb/>imo et incitatissime impellit sed tenuiter. </s>

<s>Tum vero attenuatus et impulsus <lb/>aer vevertitur ad corpus electricum, secumque una rapit paleas et quae&shy;<lb/>cumque obvia corpuscula &rdquo; (ibi, pag. </s>

<s>192). Cos&igrave;, mentre si scoprivano fatti <lb/>nuovi, le teorie si riducevano a quelle professate gi&agrave; da'Filosofi antichi. </s>

<s>Un <lb/>secolo ancora dovr&agrave; decorrere prima che si veda la scienza uscir fuori ad <lb/>immaginar qualche pi&ugrave; probabile ipotesi, a preparar la quale concorrevano <lb/>intanto altri nuovi e importantissimi fatti scoperti. </s></p><p type="main">

<s>La scoperta di questi nuovi fatti, che tanto poi dovevano conferire ai <lb/>progressi della scienza elettrica, &egrave; dovuta ad Ottone di Guericke. </s>

<s>Egli non <lb/>&egrave; come il Cabeo ritroso ad accettare i documenti di Filosofia magnetica del <lb/>Gilberto, ma gli accoglie anzi con grande amore e se ne trova mirabilmente <lb/>fecondato l'ingegno. </s>

<s>Rimeditando su quelle parole che aveva lette: <emph type="italics"/>Globus <lb/>telluris per se electrice congregatur et cohaeret; globus telluris magnetice <lb/>dirigitur et convertitur,<emph.end type="italics"/> ne concludeva il Filosofo di Magdeburgo, che come <lb/>v'&egrave; una Terrella, la quale rappresenta e imita la virt&ugrave; direttrice della gran <lb/>Terra; cos&igrave; dee esservi un'altra simile Terrella, che ne rappresenti e imiti <lb/>la virt&ugrave; conservatrice, la quale principalmente dipende dalla virt&ugrave; attrattiva <lb/>e dalla repulsiva. </s>

<s>Come il Gilberto insomma aveva ritrovata la <emph type="italics"/>Terrella ma&shy;<lb/>gnetica,<emph.end type="italics"/> il Guericke si studiava con grande ardore di ritrovar la <emph type="italics"/>Terrella<emph.end type="italics"/><pb xlink:href="020/01/824.jpg" pagenum="267"/><emph type="italics"/>elettrica,<emph.end type="italics"/> la quale gli si offerse felicemente nel Zolzo, come la Terra confi&shy;<lb/>gurato in globo, fatto come la Terra stessa girare attorno. </s>

<s>&ldquo; Hic globus gut&shy;<lb/>tis aquarum propius admotus illas tumescentes, et turgescentes facit, pariter <lb/>aerem et fumum attrahit. </s>

<s>Ex quibus perspiciendum eiusmodi virtutem in <lb/>Tellure ad sui conservationem existere, quae etiam per attritum in singulari <lb/>corpore habili, videlicet hoc globulo, excitari possit &rdquo; (Experim. </s>

<s>Magdeburg. </s>

<s><lb/>Amstelodami 1672, pag. </s>

<s>147). </s></p><p type="main">

<s>L'attrito esercitato colla mano in questo globo di zolfo fu cagione che <lb/>si rappresentassero agli occhi dell'attento sperimentatore i fatti spettacolosi <lb/>da nessuno innanzi avvertiti. </s>

<s>E prima di tutto, tenne dietro a quelle repul&shy;<lb/>sioni, che dal Cabeo erano state credute un puro gioco meccanico. </s>

<s>Che v'in&shy;<lb/>tervenisse per&ograve;, non l'azione esterna dell'aria, ma l'intrinseca virt&ugrave; propria <lb/>del corpo elettrizzato, lo argoment&ograve; il sagace Filosofo dal fatto notabilissimo <lb/>che i corpuscoli attratti, e poi respinti, non tornavano ad essere attratti dal <lb/>globo, se non avevano prima toccato qualche altro corpo straniero. </s>

<s>S'ac&shy;<lb/>corse di ci&ograve; il Guericke osservando le attrazioni e le ripulsioni ne'corpi <lb/>leggerissimi, che rimangon facilmente sospesi nell'aria, fra'quali corpi trov&ograve; <lb/>attissime alle sue esperienze le piume lanuginose e molli. </s>

<s>&rdquo; Haec virtus au&shy;<lb/>tem in plumis mollioribus et levioribus, omnium optime cognoscenda est, <lb/>quia in terram non eo citius cadunt quam alia frustula, exinde illae sur&shy;<lb/>sum propulsae, in orbe virtutis huius globi pendulae, diutius sustineri, et sic <lb/>cum globo, eo quo velis, in toto conclavi circumagi possunt &rdquo; (ibi, pag. </s>

<s>147). </s></p><p type="main">

<s>E qui la Terrella elettrica non &egrave; in rappresentar nuovi cospicui fatti al <lb/>Guericke, men feconda di quel che si fosse la Terrella magnetica al Gil&shy;<lb/>berto. </s>

<s>&ldquo; Circa quod praeterea notanda sunt: I. </s>

<s>Che la piuma, tanto sul globo <lb/>quanto per aria, distende la sua molle lanugine, come se fosse viva, e, ri&shy;<lb/>manendo cos&igrave; sospesa, ora i corpiccioli notanti si muovono ad essa, ora &egrave; <lb/>proprio lei che va a cercare i corpi stabili, posandosi sopra le loro punte <lb/>pi&ugrave; volentieri. </s>

<s>Appressandole una fiamma, per esempio quella di una can&shy;<lb/>dela, subito rifugge al Globo, <emph type="italics"/>atque penes illum quasi praesidium quaerit.<emph.end type="italics"/><lb/>II. </s>

<s>La piuma si volge al Globo sempre dalla medesima parte, a quel modo <lb/>che tien sempre rivolta verso la Terra la medesima faccia la Luna. </s>

<s>III. </s>

<s>Se <lb/>mentre che la piuma &egrave; attaccata al Globo le si presenta la punta di un dito, <lb/>vi corre subito desiderosa, e poi ritorna al Globo stesso, ripetendo cos&igrave; lun&shy;<lb/>gamente il medesimo gioco. </s>

<s>IV. </s>

<s>Se un filo di lino sospeso in alto scende a <lb/>toccare il Globo, rifugge indietro appuntandogli un dito. </s>

<s>V. </s>

<s>La virt&ugrave; del <lb/>Globo si comunica a un fil di lino lungo circa un braccio in modo, che pu&ograve; <lb/>tirare il capo di un altro filo che se gli accosti, e quasi rannodarsi con esso. </s>

<s><lb/>VI. </s>

<s>Sottoposta la piuma al Globo confricato, sul piano della Macchina, viene <lb/>attratta e respinta con lunga vicenda. </s>

<s>VII. </s>

<s>Posto il medesimo Globo in una <lb/>stanza al buio, si mostra splendere in quella luce, che suole il zucchero <lb/>stritolato col pestello &rdquo; (ivi). </s></p><p type="main">

<s>Il concetto, che s'era il Guericke formato della Terrella elettrica, la <lb/>quale rappresenta tutte insieme unite le virt&ugrave; della gran Terra, serviva al <pb xlink:href="020/01/825.jpg" pagenum="268"/>Filosofo di fondamento a una teoria generale, che pareva dispensarlo dal&shy;<lb/>l'investigare altre teorie particolari. </s>

<s>Ma bench&egrave; di queste particolari teorie, <lb/>il valoroso Magdeburgese, non si travagli, non lascia per&ograve; di confutare il <lb/>Cabeo, l'ipotesi del quale ei giudica che sia forse men ragionevole di quella <lb/>del Gilberto. </s>

<s>&ldquo; Non possumus concedere hanc attractionem mediante aere <lb/>fieri, quia experimenta oculariter monstrant hunc sulphureum Globum, at&shy;<lb/>tritione antea excitatum, suam quoque virtutem per filum lineum, ulnam <lb/>et ultra longum, posse exercere, et ibi aliquid attrahere &rdquo; (ibi). </s></p><p type="main">

<s>Cos&igrave; veniva la nuova Scienza ad arricchirsi di fatti, de'quali per&ograve; non <lb/>si penetravano le ragioni, essendo manifestamente le ipotesi del Gilberto e <lb/>del Cabeo insufficienti a spiegarli. </s>

<s>Nonostante, non s'era ancora di quelle <lb/>ipotesi trovata una confutazione diretta, per la quale sarebbe stato conclu&shy;<lb/>dentissimo il provar che l'ambra e lo zolfo attraggono anche senza l'inter&shy;<lb/>vento dell'aria in uno spazio vuoto. </s>

<s>Lo zelo de'nostri Accademici fiorentini <lb/>gli indusse a tentar, con mirabile industria, la prova nel vuoto torricelliano, <lb/>ma le pretese ch'ebbero di esercitar la confricazione in esso vuoto, riusci&shy;<lb/>rono per far confessare al loro Segretario che l'esperienza <emph type="italics"/>fu tentata per <lb/>tante vie inutilmente<emph.end type="italics"/> (Saggi ecc., Firenze 1841, pag. </s>

<s>54). </s></p><p type="main">

<s>Disanimati cos&igrave; in sulle prime, poco frutto per verit&agrave; raccolsero nel <lb/>campo delle esperienze elettriche i Nostri. </s>

<s>Con facile trasformazione del Ver&shy;<lb/>sorio gilbertino dimostrarono che la virt&ugrave; dell'Ambra di tirare a s&egrave; i corpi <lb/>&ldquo; &egrave; un'azione scambievole e niente pi&ugrave; propria dell'Ambra che de'mede&shy;<lb/>simi corpi, da'quali anch'essa &egrave; tirata &rdquo; (ivi, pag. </s>

<s>146). Avvertirono altresi <lb/>che <emph type="italics"/>la seta sfilaccicata corre alla mano,<emph.end type="italics"/> e s'erano proposto anco questo <lb/>fra alcuni altri <emph type="italics"/>curiosi problemi da esplorare<emph.end type="italics"/> (MSS. Cim., T. II, P. I, c. </s>

<s>178), <lb/>ma sventuratamente abbandonarono il proposito, che gli avrebbe potuti con&shy;<lb/>durre alla scoperta fatta poi dal Symmer e da altri Fisici inglesi. </s></p><p type="main">

<s>Del resto, gli Accademici del Cimento non fecero altro che confermare, <lb/>e in qualche parte illustrare, l'esperienze del Gilberto. </s>

<s>&ldquo; Ruunt ad electria, <lb/>aveva egli lasciato scritto, omnia praeter flammam et inflammata, et aerem <lb/>tenuissimum, sicut flammam non ducunt .... manifestum enim est quod <lb/>effluvia destruuntur a flamma et calore igneo, quare nec flammam nec cor&shy;<lb/>pora flammae propinquiora provocant.... Fumum tamen excitatum extincto <lb/>lumine allectant, et quanto magis fumus ille superiora petens extenuatur, <lb/>tanto infirmius inclinat, nimis enim rara non deducuntur, tandemque, cum <lb/>iam fere evanuit, nihil inclinat, quod versus lucem facile cernitur &rdquo; (De Ma&shy;<lb/>gnete cit., pag. </s>

<s>59). </s></p><p type="main">

<s>I nostri Accademici pure sperimentarono che la fiamma non solo non <lb/>si lascia tirar per s&egrave; &ldquo; ma se l'Ambra dopo strofinata le rigira punto dat&shy;<lb/>torno, spegne la virt&ugrave; sua, onde vi bisogna nuovo strofinamento per farla <lb/>tirare &rdquo; (Saggi cit., pag. </s>

<s>145). Quanto al fumo, sperimentarono ch'esso pure <lb/>viene attratto &ldquo; anzi assai curioso, soggiungono, &egrave; il vedere come accostan&shy;<lb/>dosi l'Ambra gi&agrave; strofinata e calda a quel fumo, che sorge da una candela <lb/>allora spenta, questo piega subito alla volta dell'Ambra. </s>

<s>Quivi dunque parte <pb xlink:href="020/01/826.jpg" pagenum="269"/>ne riman preso e parte come riflesso da specchio si leva in alto, mentre <lb/>quello che vi rimane si raguna in sembianza di una piccola nuvoletta, la <lb/>quale, secondo che l'Ambra va raffreddandosi, si discioglie novamente in <lb/>fumo e si parte &rdquo; (ivi, pag. </s>

<s>144). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Dopo l'esperienze del Guericke e de'nostri Accademici del Cimento, <lb/>parve avvenisse alla Scienza elettrica quel che suole avvenire a una sementa, <lb/>che germogliata lietamente in Autunno arresta i suoi progressi, e quasi as&shy;<lb/>siderata, intristisce sotto il cielo invernale, infin tanto che non le soprav&shy;<lb/>vengano i dolci tepori e le roride piogge di Primavera. </s>

<s>Incominci&ograve; la lieta <lb/>stagione novella coll'entrar del secolo XVIII, quando la fosforescenza osser&shy;<lb/>vata nella camera barometrica, facendo risovvenir l'Hawksbee della fosfo&shy;<lb/>rescenza nel Globo sulfureo di Magdeburgo, lo condusse a derivare il foco <lb/>elettrico dai globi tornatili di vetro. </s></p><p type="main">

<s>Furono principalmente rivolte le attenzioni del Fisico inglese alla diffe&shy;<lb/>rente emanazione di luce osservata, o quando il globo vitreo era vuoto, o <lb/>quando gli veniva riammessa la prim'aria. </s>

<s>&ldquo; In questo caso &egrave; da notarsi, <lb/>scrive l'Autore, che riscaldatosi il vetro, la mano veniva continuamente se&shy;<lb/>guitata nel suo moto da una luce o lume, che andava innanzi e indietro. </s>

<s>E <lb/>nello stesso tempo, se un'altra mano era tenuta vicino al tubo, spuntava <lb/>una luce evidente da quello, e questa accompagnata da uno strepito simile <lb/>a quello dello scoppiettare nel fuoco d'una foglia verde, ma non cos&igrave; forte.... <lb/>Ma quando fu cavata l'aria dal tubo, vi comparve una differenza notabile, <lb/>tanto in riguardo alla luce che a'suoi effetti. </s>

<s>Conciossiach&egrave; alla prima con&shy;<lb/>fricazione del vetro ne insorse in vero una maggior luce, ma pareva bensi <lb/>del tutto perduta la qualit&agrave; di dar luce ad un corpo, che gli fosse tenuto <lb/>vicino. </s>

<s>E la luce (che &egrave; un'altra non meno notabile differenza, prodotta dalla <lb/>confricazione dell'esausto tubo) appariva totalmente per entro di quello. </s>

<s>Dove <lb/>che quella discoperta, quando il tubo era pieno d'aria, pareva che fosse to&shy;<lb/>talmente al di fuori &rdquo; (Esperienze fisico-meccaniche, traduz. </s>

<s>ital., Firenze 1716, <lb/>pag. </s>

<s>40). </s></p><p type="main">

<s>La differenza de'fenomeni osservati per&ograve; non distolse l'Hawksbee dalla <lb/>persuasione che non fosse quella luce effluita dal vetro, e anzi riconobbe la <lb/>ragione di una tal differenza da'varii impedimenti opposti dall'aria al libero <lb/>passaggio di quegli effluvii. </s>

<s>Ma di qual natura &egrave; quel fuoco elettrico esa&shy;<lb/>lato dal vetro, o qual relazione ha col foco ordinario? </s>

<s>La prima esperienza <lb/>istituita non a risponder direttamente ma a preparar le vie da rispondere <lb/>alla domanda, fu quella della pietra focaia, che si trov&ograve; non scintillare nel <lb/>vuoto, d'onde se ne trasse la conclusione importante &ldquo; che la presenza del&shy;<lb/>l'aria sia assolutamente necessaria per quel vigoroso moto espansivo delle <lb/>parti de'corpi, i quali costano della natura stessa del foco di cucina &rdquo; (ivi, <pb xlink:href="020/01/827.jpg" pagenum="270"/>pag. </s>

<s>19). Ora poich&egrave; producesi il foco elettrico anco nel vuoto, pareva se ne <lb/>potesse concluder di qui la differente natura di lui dal foco ordinario. </s></p><p type="main">

<s>Una dimostrazione diretta per&ograve; della differente natura di questi due <lb/>fochi veniva dal veder che l'elettrico si produceva anche nell'acqua, con&shy;<lb/>fricando sott'essa insieme due vetri. </s>

<s>&ldquo; Vediamo dunque che la luce &egrave; pro&shy;<lb/>ducibile dalla confricazione di vetro sopra vetro, non solamente in voto e in <lb/>aria aperta, ma nell'acqua ancora. </s>

<s>Quinci evidente si &egrave; di pi&ugrave; che i vetri <lb/>non sono infocati dalla confricazione qualunque si sia la somiglianza che ne <lb/>porta seco il colore &rdquo; (ivi, pag. </s>

<s>29). </s></p><p type="main">

<s>Venendo chiaramente dimostrato di qui che il foco elettrico &egrave; di diversa <lb/>natura da quello, che si produce dal calore ordinario, sarebb'egli mai piut&shy;<lb/>tosto identico a quello che induce la fosforescenza ne'legni umidi o in altri <lb/>simili corpi? </s>

<s>Per rispondere a ci&ograve; &ldquo; presi, dice l'Autore, un pezzo di legno, <lb/>il quale mi suppongo che fosse stato lungo tempo sotto terra, molto umido <lb/>ma non infracidito. </s>

<s>Al buio appariva vivacissimamente di color di foco, ma <lb/>avendolo rinchiuso in un recipiente sopra la Tromba, trovai che, a misura <lb/>che se ne traeva l'aria, smontava a proporzione l'apparenza di somiglianza <lb/>di foco, e da ultimo nel voto diveniva affatto privo di luce &rdquo; (ivi, pag. </s>

<s>34). <lb/>Agli effetti dunque non appariva nessuna corrispondenza fra i fenomeni elet&shy;<lb/>trici e i fosforescenti. </s></p><p type="main">

<s>Cos&igrave; lasciava l'Hawksbee indecisa la questione della natura del foco <lb/>elettrico, come il gran Newton poco di poi lasciava indecisa la questione <lb/>della natura e dell'origine di qualunque altra sorta di foco. </s>

<s>&ldquo; Annon cor&shy;<lb/>pora omnia fixa, quum sint ultra certum gradum calafacta, emittunt lumen <lb/>et splendent? </s>

<s>Eaque luminis emissio per motus vibrantes partium suarum <lb/>efficitur? </s>

<s>Et annon corpora omnia, quae partibus abundant terrestribus et <lb/>praesertim sulphorosis, lumen emittunt, quotiescumque partes illae satis sint <lb/>agitatae, sive id calore fiat, sive attritu, sive percussu, sive putrescendo, sive <lb/>motu aliquo vitali, sive alia quavis de causa? </s>

<s>ut aqua marina saeviente pro&shy;<lb/>cella, argentum vivum in vacuo agitatum, felis dorsum vel equi collum manu <lb/>oblique in loco tenebricoso affrictum; ligna, carnes et pisces dum putre&shy;<lb/>scunt vapores ex aquis putridis, qui ignes fatui vulgo appellantur, metae <lb/>foeni segetisve subhumidae fermentescentes, cicindulae, et animalium quo&shy;<lb/>rundam oculi, motu quodam vitali; phosphorus bononiensis, radiis luminis <lb/>agitatus; phosphorus vulgaris, corporis cuiusvis attritu, vel acidis aeris par&shy;<lb/>ticulis agitatus; electrum, et adamantes aliqui, feriendo, premendo vel fri&shy;<lb/>cando; chalybis strigmenta, silice decussa; ferrum ictibus malleorum cale&shy;<lb/>factum, donec sulphur sibi iniectum accendat; axes curruum, motu rotarum <lb/>rapidiore incensi; et certi liquores inter se permixti, quorum particulae cum <lb/>impetu concurrunt, ut oleum vitrioli a nitro pari pondere distillatum, dein <lb/>dupla portione mixtum cum oleo caryophillorum, sive anisi. </s>

<s>Similiter glo&shy;<lb/>bus vitreus .... machinae versatili infixus .... qua sui parte vola manus <lb/>apposita, inter volvendum confricatur, lucebit &rdquo; (Optices lib. </s>

<s>III, quaestio VIII, <lb/>Patavii 1773, pag. </s>

<s>138, 39). </s></p><pb xlink:href="020/01/828.jpg" pagenum="271"/><p type="main">

<s>Troppo pi&ugrave; gran progressi doveva fare la scienza, prima di assegnare <lb/>a ciascuna specie di fochi, nel lungo ordine dal Newton annoverati, la causa <lb/>distinta e l'origine propria, e perci&ograve; tornando all'Hawksbee &egrave; da veder quel <lb/>ch'egli pensasse intorno alle ragioni di molti altri fatti da s&egrave; diligentissi&shy;<lb/>mamente sperimentati. </s>

<s>La pi&ugrave; bella riuscita di queste sue esperienze si pot&egrave; <lb/>facilmente conseguirla, sostituendo al primo globo un cilindro concavo di <lb/>vetro, e bench&egrave; avesse cos&igrave; col nuovo strumento ottenuto tanto maggiore <lb/>energia elettrica, e tanto pi&ugrave; cospicui gli effetti, ebbe nonostante a notare <lb/>una gran differenza, che non era possibile non attribuire al variar delle <lb/>stagioni. </s></p><p type="main">

<s>Gi&agrave;, infin dal Gilberto, era stato notato che il Sal gemma, la Pietra <lb/>speculare e l'Allume di rocca non tirano, se non <emph type="italics"/>cum aer media hyeme <lb/>rigidus fuerit et clarus tenuisque<emph.end type="italics"/> (De Magn. </s>

<s>cit., pag. </s>

<s>48). Il Cabeo pure <lb/>aveva avvertito che l'esperienze delle attrazioni elettriche volevano esser fatte <lb/><emph type="italics"/>coelo sereno et puro, non humido aut nebuloso<emph.end type="italics"/> (Phil. </s>

<s>magn. </s>

<s>cit., pag. </s>

<s>193). <lb/>E in conformit&agrave; de'due pi&ugrave; antichi Autori veniva ripetendo l'Hawksbee di <lb/>aver sempre osservato <emph type="italics"/>che l'umido &egrave; gran nemico di tutte l'esperienze di <lb/>questa sorta<emph.end type="italics"/> (Esper. </s>

<s>cit., pag, 37). </s></p><p type="main">

<s>E perch&egrave; facile parve a tutt'e tre gli Autori il rinvenir la causa di un <lb/>effetto cos&igrave; costante, il Gilberto l'attribu&igrave; a ci&ograve; che nell'inverno <emph type="italics"/>effluvia <lb/>telluris electrica minus impediunt et electrica firmius indurescunt<emph.end type="italics"/> (De <lb/>Magn. </s>

<s>cit., pag. </s>

<s>48). Il Cabeo poi riconobbe l'umido riuscire a'corpi elet&shy;<lb/>trici cos&igrave; nocivo, perch&egrave; <emph type="italics"/>aere statim obnubilatur corpus quod debet esse <lb/>nitidissimum, et impeditur transpiratio effluvii. </s>

<s>Imo ex hac praecipue <lb/>causa oritur ut electrum non trahat, nisi praeparatum fricatione<emph.end type="italics"/> (Phil. </s>

<s><lb/>magn. </s>

<s>cit., pag. </s>

<s>193). </s></p><p type="main">

<s>N&egrave; dopo un mezzo secolo e alquanti anni di pi&ugrave;, fra tante squisitezze <lb/>di macchine, e fra tanta dovizia di sperimenti, sa dir l'Hawksbee nulla di <lb/>meglio de'due suoi predecessori. </s>

<s>&ldquo; Quando l'aria &egrave; densa o da umide ed <lb/>acquee o da altre pi&ugrave; grosse e solide parti, sollevate dal vasto fondo della <lb/>terrestre materia, quaggi&ugrave; ingombrata; non vi &egrave; dubbio che la resistenza, <lb/>che allora incontrano questi belli effluvii nel loro viaggio, bisogna che sia <lb/>molto pi&ugrave; grande che quando l'aria &egrave; schietta e libera, e che non accadono <lb/>tali impedimenti da opporsi nel suo passaggio. </s>

<s>Poich&egrave; gli effluvii, per quanto <lb/>mai sottili che si possano immaginare, sono tuttavia corpo e materia, e per&ograve; <lb/>debbono esser soggetti alla comune legge dei corpi, quale si &egrave; di dover <lb/>trovare resistenza in qualche proporzione alla forza e densit&agrave; del mezzo &rdquo; <lb/>(Esper. </s>

<s>cit., pag. </s>

<s>36). Crede anzi l'Hawksbee d'aver di ci&ograve; una dimostra&shy;<lb/>zione oculare nell'esperienza di una mussolina, che interposta e tesa fra il <lb/>cilindro confricato e alcuni frammenti di orpello, impedisce a questi di es&shy;<lb/>sere attratti (ivi, pag. </s>

<s>37). </s></p><p type="main">

<s>Ma poniamo che queste ragioni, intorno alle quali i tre primi e prin&shy;<lb/>cipali Autori della Filosofia elettrica si trovarono concordi, quietassero i cu&shy;<lb/>riosi, per avere qualche apparenza d'esser probabili, restavano per&ograve; tuttavia <pb xlink:href="020/01/829.jpg" pagenum="272"/>misteriosi que'molti altri fatti elettrici sperimentati in Magdeburgo. </s>

<s>La chiave <lb/>del mistero era capitata alle mani dello stesso Ottone di Guericke quand'egli <lb/>ebbe trovato che la virt&ugrave; del suo Globo di zolfo si <emph type="italics"/>comunicava,<emph.end type="italics"/> e si dif&shy;<lb/>fondeva per quel braccio e pi&ugrave;, quant'era lungo il filo di lino. </s>

<s>Ma non seppe <lb/>indovinar di quali conseguenze sarebbe stata quella sua esperienza feconda, <lb/>ci&ograve; che un mezzo secolo e pi&ugrave; dopo fu riserbato al fortunatissimo Gray. </s>

<s>Egli <lb/>primo accortosi che l'elettricit&agrave; del globo tornatile si comunicava all'asse di <lb/>metallo, e a'perni della macchina, si condusse di prova in prova a comu&shy;<lb/>nicare e a diffondere l'elettricit&agrave;, no ne'soli fili di lino, bench&egrave; tanto pi&ugrave; <lb/>lunghi di quelli del Guericke, ma nelle verghe di qualunque sorta di me&shy;<lb/>tallo, e anzi in tutti i corpi, eccettuati il vetro, la seta, la resina e tutti quelli <lb/>insomma annoverati di sopra dal Gilberto, i quali avendo la virt&ugrave; di ride&shy;<lb/>starla in s&egrave; stessi, non patiscono che sia l'elettricit&agrave; comunicata a loro dagli <lb/>altri corpi. </s>

<s>Anzi mettendovisi di mezzo, ne impediscono il libero corso, per <lb/>cui, dal contener la nativa elettricit&agrave;, furono detti <emph type="italics"/>idioelettrici,<emph.end type="italics"/> e dall'im&shy;<lb/>pedirne il corso, <emph type="italics"/>coibenti.<emph.end type="italics"/> Per aver poi virt&ugrave; a questi contrarie, tutti gli altri <lb/>corpi si chiamarono <emph type="italics"/>anelettici<emph.end type="italics"/> e <emph type="italics"/>deferenti.<emph.end type="italics"/></s></p><p type="main">

<s>Questa del Gray confermata dal Dufay fu un'insigne scoperta, per la <lb/>quale venne tanto valido impulso al progredir della scienza. </s>

<s>S'intese infatti <lb/>allora che l'umidit&agrave; rintuzza la forza elettrica, perch'essendo l'acqua un <lb/>corpo deferente dissipa il fluido via via ch'esce dall'ambra e dal vetro. </s>

<s>S'in&shy;<lb/>tesero allora i miracoli operati dalla piuma intorno al Globo sulfureo di <lb/>Magdeburgo, e com'essa piuma, elettrizzata gi&agrave; per comunicazione, avendo <lb/>perduta l'elettricit&agrave; sua propria, per averla comunicata al corpo che la toc&shy;<lb/>cava, tornasse nuovamente al Globo per riacquistarla. </s></p><p type="main">

<s>S'intesero gli altri fatti ancora ordinatamente descritti dal Guericke, <lb/>ma pur alcuni rimanevano tuttavia irresoluti, e fra questi quello principal&shy;<lb/>mente della piuma che ritorna al globo dalla fiamma della candela. </s>

<s>La dif&shy;<lb/>ficolt&agrave; pareva venisse tolta dall'osservazion del Gilberto confermata poi dai <lb/>nostri Accademici fiorentini, che cio&egrave; la fiamma spenge la virt&ugrave; elettrica, ma <lb/>ci&ograve; non poteva entrare nell'ordine delle nuove idee, se non ammettendo che <lb/>fosse anche la fiamma un corpo deferente. </s>

<s>Ora n&egrave; il Gray n&egrave; il Dufay ave&shy;<lb/>vano osato di asserir tanto, anzi ebbero a concludere, dalle loro incerte espe&shy;<lb/>rienze, che la materia elettrica o non veniva direttamente comunicata alla <lb/>fiamma, o che non si vedevano operarsi in lei gli effetti consueti. </s></p><p type="main">

<s>Pi&ugrave; tardi il Krugers e il Winkler riuscirono a condur l'elettricit&agrave; at&shy;<lb/>traverso alla fiamma di una candela, e alla vampa dello spirito di vino, ma <lb/>nessun seppe maneggiar la difficile sperienza con pi&ugrave; elegante semplicit&agrave; di <lb/>un nostro Italiano. </s>

<s>Egli &egrave; per noi senza dubbio il Gray degl'Inglesi, e il <lb/>Dufay de'Francesi, e ci duole perci&ograve; il non poterne onorare il nome, avendo <lb/>egli, non si sa perch&egrave;, mandato fuori, prima in Venezia nel 1746 poi l'anno <lb/>dopo in Napoli il suo Libro <emph type="italics"/>Dell'elettricismo,<emph.end type="italics"/> innominato. </s>

<s>Cos&igrave; dunque de&shy;<lb/>scrive l'elegante esperienza quel nostro Innominato: </s></p><p type="main">

<s>&ldquo; Io misi sopra una verga di ferro, sospesa da corde di seta orizzon-<pb xlink:href="020/01/830.jpg" pagenum="273"/>talmente, due piccoli cerini accesi, l'uno assai vicino all'altro, cos&igrave; per&ograve; che <lb/>le loro fiamme si stessero lontane l'una dall'altra per un pollice. </s>

<s>Subito <lb/>che comunicai l'elettricit&agrave; alla verga di ferro le due fiamme, che prima sta&shy;<lb/>vano ritte, si fuggirono l'una dall'altra. </s>

<s>Toccavo con un dito le verghe, ed <lb/>elleno si rimettevano nel luogo; rimovevo il dito, ed elleno ritornavano a <lb/>fuggirsi &rdquo; (Napoli 1647, pag. </s>

<s>144). </s></p><p type="main">

<s>Ma n&egrave; da queste s&igrave; ingegnose esperienze si vedeva ancora uscire un <lb/>raggio di luce all'intelligenza di un altro, ch'&egrave; pur tra i fatti osservati dal <lb/>Guericke, ed &egrave; che la piuma, pi&ugrave; volentieri che altrove, s'andava a posar <lb/>sulle punte dei corpi circostanti. </s>

<s>Ha questo stesso fatto una invisibile rela&shy;<lb/>zione con un assai singolare effetto osservato dagli Accademici fiorentini nei <lb/>diamanti, ed &egrave; che, fra questi, i gruppiti son ricchi di potenza elettrica, men&shy;<lb/>tre riescon, segati in tavole, cos&igrave; deboli e fiacchi (Saggi cit., pag. </s>

<s>147). Ma <lb/>per l'intelligenza di simili effetti si richiedevano nella Filosofia elettrica nuovi <lb/>progressi, prima di venire a'quali giova trattenersi sopra un'altra singolar <lb/>differenza che fu notata, nel modo di attrarre, fra i cos&igrave; detti corpi idioe&shy;<lb/>lettrici. </s></p><p type="main">

<s>Essendo passato l'Hawksbee dalle esperienze elettriche fatte col vetro a <lb/>quelle fatte colla ceralacca, della miglior qualit&agrave; che avesse potuto trovare, <lb/>parvegli aver riscontrato tanta somiglianza in que'loro effetti, da conclu&shy;<lb/>derne che &ldquo; l'elettriche qualit&agrave; di quei due corpi sono le medesime, quanto <lb/>a tutte le pi&ugrave; generali propriet&agrave;: sono solamente discrepanti ne'gradi, gli <lb/>effluvii del vetro producendo effetti pi&ugrave; potenti di quelli della ceralacca &rdquo; <lb/>(Esperienze cit., pag. </s>

<s>95). </s></p><p type="main">

<s>Poco dopo s'osservarono per&ograve; alcuni fatti, da'quali se ne volle conclu&shy;<lb/>dere che questa sentenza dell'Hawksbee non era vera. </s>

<s>Si osserv&ograve; che il ve&shy;<lb/>tro elettrizzato o non tirava a s&egrave;, o debolmente tirava certi minuzzoli di <lb/>vetro, che se gli ponevano appresso: si osserv&ograve; pure che la ceralacca o l'am&shy;<lb/>bra facevano lo stesso verso bricioli della medesima sostanza resinosa, ma <lb/>che al contrario il vetro tirava con avidit&agrave; i minimi corpiccioli della cera&shy;<lb/>lacca, e la ceralacca i minimi corpiccioli del vetro. </s>

<s>Da questi fatti dunque <lb/>il Dufay volle concluderne che, tra la virt&ugrave; elettrica del vetro e quella della <lb/>ceralacca, non passava, come l'Hawksbee aveva asserito, una semplice di&shy;<lb/>screpanza di gradi, ma di natura, e introdusse, egli stesso il Dufay, per de&shy;<lb/>signare una tale essenzial discrepanza, i nomi di elettricit&agrave; <emph type="italics"/>vitrea,<emph.end type="italics"/> e di elet&shy;<lb/>tricit&agrave; <emph type="italics"/>resinosa.<emph.end type="italics"/></s></p><p type="main">

<s>Fu questa distinzione accolta con docilit&agrave; in Francia e per qualche <lb/>tempo anche in Inghilterra, ma il nostro Italiano innominato protest&ograve; con&shy;<lb/>tro una tal distinzione, qualificandola per <emph type="italics"/>un'ipotesi poco o niente verisi&shy;<lb/>mile,<emph.end type="italics"/> e che introdurrebbe <emph type="italics"/>una moltiplicit&agrave; nociva alle semplici maniere, <lb/>colle quali operar suol la Natura.<emph.end type="italics"/> (Dell'Elettric. </s>

<s>cit., pag. </s>

<s>177). </s></p><p type="main">

<s>L'Elettricit&agrave; vitrea non &egrave;, secondo il nostro illustre Italiano, di qualit&agrave; <lb/>e di natura diversa dalla resinosa, ma sono ambedue il medesimo fluido, che <lb/>qu&agrave; opera in un modo, secondo il grado della sua intensit&agrave;, e l&agrave; si vede <pb xlink:href="020/01/831.jpg" pagenum="274"/>invece operare in un altro. </s>

<s>La diversit&agrave; de'modi com'egli crede che l'elet&shy;<lb/>tricit&agrave; operi nelle resine e ne'vetri, &egrave; da lui stesso, dal nostro Autore del <lb/>libro <emph type="italics"/>Dell'elettricismo,<emph.end type="italics"/> descritta colle seguenti parole, nelle quali si con&shy;<lb/>tiene espressa la prima fra le teorie elettriche razionali ch'abbia avuto la <lb/>scienza. </s></p><p type="main">

<s>&ldquo; La ragione del fenomeno qui motivato, riguardo all'elettricit&agrave; <emph type="italics"/>vitrea<emph.end type="italics"/><lb/>e <emph type="italics"/>resinosa,<emph.end type="italics"/> ci apre la strada alla risoluzione ancora di molti altri effetti, che <lb/>sembrano incomprensibili. </s>

<s>Cotesta ragione &egrave; fondata sulla direzione recurva <lb/>che prende la materia elettrica ne'corpi originalmente o per comunicazione <lb/>elettrizzati. </s>

<s>Egli &egrave; certo che i corpi resinosi, per quanto si elettrizzino, non <lb/>diventano mai capaci di render fuori, toccati che siano, luce alcuna fulmi&shy;<lb/>nante, come a suo luogo diremo, ond'&egrave; che il loro vortice anche originario <lb/>tiene un vigore molto inferiore a quello de'corpi vitrei, de quali il vortice <lb/>elettrico gode d'un insigne energia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Colui che intende la dottrina de'vortici sa bene che due vortici di <lb/>ugual vigore, e che si premono con ugual forza l'uno l'altro, non si pos&shy;<lb/>sono alternativamente distruggere, ma ci&ograve; fanno di leggeri allora s&igrave;, quando <lb/>l'uno si trova pi&ugrave; debole dell'altro. </s>

<s>Ora essendo proprio de'corpi facilmente <lb/>elettrizzabili per comunicazione di ricevere e di assorbire in s&egrave; stessi la ma&shy;<lb/>teria elettrica vestendosi d'un vortice, subito che entrano in alcun altro <lb/>vortice mandato e formato da qualche corpo elettrizzato; cos&igrave; una foglia <lb/>d'oro che cadendo dall'alto s'avvia verso la canna di vetro elettrizzata, ap&shy;<lb/>pena entra nell'atmosfera elettrica di essa, ossia nel di lei vortice, ch'ella <lb/>pure si veste di un piccol vortice avente l'energia stessa de'strati del vor&shy;<lb/>tice della canna pe'quali passa, sicch&egrave; per l'uguaglianza delle azioni d'am&shy;<lb/>bedue questi vortici, l'uno maggiore e l'altro minore, la foglietta d'oro &egrave; <lb/>obbligata a star sospesa nell'aria, senz'ardir punto d'avanzarsi pi&ugrave; oltre <lb/>verso la canna stessa. </s>

<s>Ma all'incontro, essendovi due vortici inuguali di <lb/>forze, il pi&ugrave; forte &egrave; quello che superchia il pi&ugrave; debole, ond'&egrave; che avendo <lb/>la stessa foglietta d'oro il suo vortice pi&ugrave; gagliardo del vortice d'un pezzo <lb/>d'ambra o di resina, conviene ch'ella s'avvicini alla resina stessa giacch&egrave; <lb/>la resina, come un pezzo pi&ugrave; grave e grande, non pu&ograve; moversi verso di lei <lb/>ch'&egrave; un corpetto leggerissimo e sciolto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se tal foglietta d'oro corredata del suo piccolo vortice &egrave; toccata da <lb/>un dito, il dito assorbe in s&egrave; esso vortice, e cos&igrave; la foglietta resta in istato <lb/>d'essere attirata da'vortici vicini se ve ne sono. </s>

<s>Peraltro bisogna badare che <lb/>un vortice, quantunque pi&ugrave; grande d'un altro, egli per&ograve; potr&agrave; esser pi&ugrave; de&shy;<lb/>bole di questo, quando la materia del pi&ugrave; grande sia meno densa e veloce. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ogni vortice &egrave; composto come di tanti strati concentrici, de'quali li <lb/>pi&ugrave; vicini al centro sono i pi&ugrave; densi e pi&ugrave; forti. </s>

<s>Li vortici di materia <emph type="italics"/>vitrea<emph.end type="italics"/><lb/>sono in tutti i loro strati pi&ugrave; forti di tutti i strati de'vortici della materia <lb/><emph type="italics"/>resinosa.<emph.end type="italics"/> Ed ecco che non sono queste due specie di elettricit&agrave;, ma solo due <lb/>diversi gradi d'intensione e di vigore. </s>

<s>Immaginatevi, ci&ograve; che punto non si <lb/>discosta dal vero, che il vortice dell'elettricit&agrave; <emph type="italics"/>vitrea<emph.end type="italics"/> sia pi&ugrave; denso di quello <pb xlink:href="020/01/832.jpg" pagenum="275"/>dell'etettricit&agrave; <emph type="italics"/>resinosa,<emph.end type="italics"/> e vi sar&agrave; facile di sciorre ogni difficolt&agrave;, che vi po&shy;<lb/>tesse cadere su questo proposito &rdquo; (ivi, pag. </s>

<s>182-84). </s></p><p type="main">

<s>La teoria del nostro Italiano fu in cos&igrave; bel modo illustrata da Benia&shy;<lb/>mino Frankli&nacute;, che s'introdusse nella scienza universale dell'Elettricismo <lb/>sotto il venerato e autorevole nome di lui. </s>

<s>Ripensava l'Inglese di Pensil&shy;<lb/>vania a quella piuma del Guericke, che s'andava a posar sulle punte pi&ugrave; <lb/>volentieri che sulle parti arrotondate de'corpi, e negli insegnamenti della <lb/>scienza elettrica di allora non trovava tali da sodisfarsene le ragioni. </s>

<s>Era in&shy;<lb/>torno a questa meditazione, in quel tempo che il Krugers e il Pons avevano <lb/>avvertito che l'elettricit&agrave;, tutt'altro che indebolire, pareva anzi crescer d'in&shy;<lb/>tensit&agrave; nelle parti estreme de'lunghi fili da lei percorsi, d'onde appunto <lb/>argoment&ograve; il sagace Filosofo americano che la virt&ugrave; elettrica affluiva con pi&ugrave; <lb/>libero e spontaneo moto verso le punte. </s>

<s>Non era nemmeno questo fatto <lb/>nuovo sfuggito alle osservazioni di quel nostro italiano Innominato, il quale <lb/>trov&ograve; che la luce elettrica era solita <emph type="italics"/>di sortir fuori dalle punte, dagli an&shy;<lb/>goli e dalle pretuberanze de'corpi facilmente elettrizzabili per comunica&shy;<lb/>zione, massime dal ferro<emph.end type="italics"/> (Dell'Elettric. </s>

<s>cit., pag. </s>

<s>262), ma il Franklin os&shy;<lb/>serv&ograve; di pi&ugrave; <emph type="italics"/>l'&eacute;tonnant effet des corps pointus, tant pour tirer que pour <lb/>pouffer le feu &eacute;lectrique<emph.end type="italics"/> (Oeuvres, Paris 1773, T. I, pag. </s>

<s>3). </s></p><p type="main">

<s>L'esalazione da una parte gli faceva necessariamente arguire una ri&shy;<lb/>dondanza, e dall'altra l'attrazione gli faceva arguire un difetto nel fluido <lb/>elettrico, e vedeva in quel moto una tendenza del fluido stesso a ristabilirsi <lb/>nel suo primo e naturale equilibrio. </s>

<s>L'ipotesi cos&igrave; dell'ammosfere pi&ugrave; dense <lb/>e meno dense introdotta dal nostro Innominato veniva pel Franklin ad es&shy;<lb/>ser ridotta a un principio generale, ond'&egrave; ch'egli insegnava tutti i corpi <lb/>non elettrizzarsi, e non potersi artificiosamente elettrizzare che in <emph type="italics"/>pi&ugrave;<emph.end type="italics"/> o in <lb/><emph type="italics"/>meno.<emph.end type="italics"/> &ldquo; De-l&agrave; quelques termes nouveux se sont introduits parmi nous. </s>

<s>Nous <lb/>disons que B (ou tout autre corps dans les m&ecirc;mes circonstances) est &eacute;lectris&eacute; <lb/><emph type="italics"/>posuivement,<emph.end type="italics"/> et A <emph type="italics"/>n&eacute;gativement,<emph.end type="italics"/> ou plut&ograve;t B est &eacute;lectris&eacute; <emph type="italics"/>plus<emph.end type="italics"/> et A l'est <lb/><emph type="italics"/>moins,<emph.end type="italics"/> et tous les jours dans nos exp&eacute;riences nous &eacute;lectrisons les corps en <lb/><emph type="italics"/>plus<emph.end type="italics"/> ou en <emph type="italics"/>moins,<emph.end type="italics"/> suivant que nous le jugeons &agrave; propos. </s>

<s>&mdash; Pour &eacute;lectri&shy;<lb/>ser en plus ou en moins, il faut seulement savoir que les parties du tube <lb/>ou du globe qui sont frott&eacute;es, attirent dans l'instant du frottement le feu <lb/>&eacute;lectrique, et l'enlevent par cons&eacute;quent &agrave; la chose frottante. </s>

<s>Les m&ecirc;mes par&shy;<lb/>ties, aussit&ograve;t que le frottement cesse, sont dispos&eacute;es &agrave; donner le feu qu'elles <lb/>ont re&ccedil;u &agrave; tout corps qui en a moins &rdquo; (l&agrave;, page 8). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>In questa teoria elettrica del Franklin espressa cos&igrave; in semplici parole, <lb/>si conteneva una novit&agrave; di grande importanza, la quale consisteva nell'in&shy;<lb/>segnar che la perenne sorgente elettrica non &egrave; nel vetro tornatile della Mac-<pb xlink:href="020/01/833.jpg" pagenum="276"/>china, come da tutti i Fisici allora si credeva, ma s&igrave; nel suolo, da cui ac&shy;<lb/>corre allo stesso vetro, nell'atto e per via dello strofinamento. </s>

<s>Non avrebbe <lb/>ricevuto forse appresso i Fisici la nuova ipotesi frankliniana cos&igrave; favorevole <lb/>accoglienza, se non avesse dato, quasi come primo saggio del suo valore, la <lb/>spiegazione di un fatto, innanzi al quale il mondo de'Fisici non s'era an&shy;<lb/>cora riavuto dello stupore di che fu colto. </s></p><p type="main">

<s>Riferivasi quel fatto alla virt&ugrave; fulminante, che risedeva in agguato <lb/>dentro la bottiglia di Leyda, il mistero della quale accresceva negli uomini <lb/>la paura. </s>

<s>Parve anche al Franklin quello uno strumento miracoloso e con&shy;<lb/>fess&ograve; che trapassava la sua intelligenza, ma nonostante si studi&ograve; di farne <lb/>intendere l'occulto modo di operare per mezzo del fluido positivo e conden&shy;<lb/>sato sull'una armatura, che nell'andare a ristabilirsi in equilibrio, diffon&shy;<lb/>dendosi sull'altra armatura negativa, irrompe con quella sperimentata gi&agrave; e <lb/>cos&igrave; paurosa violenza. </s></p><p type="main">

<s>&ldquo; La bouteille &eacute;tant &eacute;lectris&eacute;e (cos&igrave; il Franklin descrive al Collinson <lb/>la teoria e l'uso della Bottiglia di Leyda) le feu &eacute;lectrique est accumul&eacute; &agrave; <lb/>sa surface ext&eacute;rieure et forme librement &agrave; l'entour une atmosph&egrave;re &eacute;lectri&shy;<lb/>que d'une &eacute;tendue consid&eacute;rable, au lieu qu'il est resserr&eacute; de toutes parts <lb/>dans l'int&eacute;rieur. </s>

<s>En m&ecirc;me temps que le fil d'archal et le sommet de la bou&shy;<lb/>teille sont &eacute;lectris&eacute;s <emph type="italics"/>positivement,<emph.end type="italics"/> ou <emph type="italics"/>plus,<emph.end type="italics"/> le fond de la bouteille est &eacute;lectris&eacute; <lb/><emph type="italics"/>n&eacute;gativement,<emph.end type="italics"/> ou <emph type="italics"/>moins,<emph.end type="italics"/> dans une exacte proportion.... L'equilibre ne sau&shy;<lb/>roit &egrave;tre r&eacute;tabli par la communication int&eacute;rieure, ou par le contact des par&shy;<lb/>ties, mais seulement par une communication formee au-dehors de la bou&shy;<lb/>teille entre le haut et le bas, par le moyen de quelque corps non &eacute;lectri&shy;<lb/>que qui les touche &rdquo; (l&agrave;, pag. </s>

<s>12, 13). </s></p><p type="main">

<s>Una tale ipotesi del fluido positivo e del fluido negativo applicata a spie&shy;<lb/>gare i misteriosi effetti della Bottiglia, dicemmo che sodisfece allora i Fi&shy;<lb/>sici, i quali non sapevan trovare nella loro scienza elettrica altro migliore <lb/>argomento di questo. </s>

<s>Ma il Franklin non aveva di quella deficienza e so&shy;<lb/>prabbondanza di fluido elettrico avuto altro indizio, da quello in fuori dimo&shy;<lb/>stratogli dalle punte. </s>

<s>Or perch&egrave; questi infine non erano altro che fatti, non <lb/>pareva dicevole che si fondasse sopr'essi una teoria senza renderne qual&shy;<lb/>che ragione. </s></p><p type="main">

<s>L'importante ufficio di supplire in ci&ograve; al difetto della scienza frankli&shy;<lb/>niana se lo assunse un nostro Italiano, il quale ebbe a rivolgere la sua at&shy;<lb/>tenzione sopra certe particolari esperienze eseguite dal Monnier in Parigi. </s>

<s><lb/>Risultava da cos&igrave; fatte esperienze che una lamina di piombo riquadrata, es&shy;<lb/>sendo resa elettrica, scintillava men vivamente di quando, tagliata essa lamina <lb/>in sottili strisce, queste si disponevano per lo lungo l'una dopo l'altra, come <lb/>in ordine di catena. </s>

<s>Aveva inoltre osservato lo stesso Monnier che un lun&shy;<lb/>ghissimo filo di ottone dava alla sua estremit&agrave; scintille pi&ugrave; penetranti di <lb/>quel che non paresse convenire all'intensit&agrave; della carica. </s></p><p type="main">

<s>Come simili fatti osservati gi&agrave; dal Krugers e dal Pons avevano ecci&shy;<lb/>tato a speculare il Franklin, cos&igrave; questi nuovi eccitarono Giovan Batista Bec-<pb xlink:href="020/01/834.jpg" pagenum="277"/>caria, il quale ebbe per prima cosa a concluderne che &ldquo; il vapore con al&shy;<lb/>cuna maggiore forza iscorra secondo la lunghezza, ovvero massima dimensione <lb/>di un corpo, e che scorra con forza maggiore per una lunghezza maggiore &rdquo; <lb/>(Dell'Elettricismo, Torino 1753, pag. </s>

<s>55). </s></p><p type="main">

<s>A questa prima conclusione la feconda mente del nostro Autore ne fa <lb/>conseguire un'altra, ch'egli appresso soggiunge ed esprime in cos&igrave; fatta <lb/>forma: &ldquo; Questo impeto maggiore, secondo la lunghezza, produce un'altra <lb/>propriet&agrave; nello scorrimento dell'elettrico vapore, la quale non so che da altri <lb/>sia stata avvertita. </s>

<s>Essa &egrave; che il vapore elettrico, scorrendo dentro ad una <lb/>sostanza elettrizzabile per comunicazione, dove si restringe lo spessore di <lb/>questa sostanza, ivi a proporzione si condensa e cresce di forza e di atti&shy;<lb/>vit&agrave; &rdquo; (ivi, pag. </s>

<s>57). </s></p><p type="main">

<s>Il nostro Fisico torinese insomma riscontra nel fluido elettrico la legge <lb/>idraulica stessa che governa il moto di tutti gli altri fluidi, ed &egrave; che cor&shy;<lb/>rendo per canali si velocitano reciprocamente alle sezioni. </s>

<s>&ldquo; E in queste pro&shy;<lb/>priet&agrave; discerno tutta l'analogia colla meccanica propriet&agrave; de'fluidi elastici, <lb/>che movendosi da'pi&ugrave; ampi ne'pi&ugrave; ristretti spazii hanno un certo prodotto <lb/>di densit&agrave; e velocit&agrave; reciproco a'spazii medesimi &rdquo; (ivi). </s></p><p type="main">

<s>Veniva cos&igrave; l'Elettro, che non aveva fatto altra mostra di s&egrave; che di <lb/>fatti, e non era stato soggetto altro che d'ipotesi senza dimostrazioni; a pi&shy;<lb/>gliar qualche buon fondamento di scienza, e a confortarsi in quelle leggi, <lb/>di che si sapeva esser pi&ugrave; certamente governato il moto della fluida mate&shy;<lb/>ria. </s>

<s>Nello stesso tempo, quella ridondanza di fluido ammessa gi&agrave; dal Franklin <lb/>in conseguenza degli effetti osservati da lui nelle punte ritrovava nell'espe&shy;<lb/>rienze diligentissime del Beccaria una piena conferma, e nelle speculazioni <lb/>di lui una meccanica dimostrazione, che derivata da fonti sicure e non avendo <lb/>altro da sostituirle, si poteva allora tenere per certa. </s></p><p type="main">

<s>Ma questa stessa dimostrazione cos&igrave; ingegnosamente desunta dalla legge <lb/>idraulica, conosciuta sotto il nome del Castelli, non valeva se non pel caso <lb/>delle punte metalliche, dalle quali il vapore elettrico si disperde. </s>

<s>Era un fatto <lb/>per&ograve; con certezza sperimentato dal Franklin che se quelle stesse punte esa&shy;<lb/>lano il fluido quando ne soprabbondano, son dall'altra parte avidissime di <lb/>assorbirlo, quando per le particolari condizioni, in che si trovano talvolta <lb/>rispetto agli altri corpi elettrizzati, se ne sentano qualche difetto. </s>

<s>A dar com&shy;<lb/>piute perci&ograve; le sue dottrine, e a render d'ogni parte sicura l'ipotesi fran&shy;<lb/>kliniana, conveniva al nostro Beccaria dimostrare in che modo le punte be&shy;<lb/>vano cos&igrave; pi&ugrave; avidamente il fluido elettrico, di quel che non si veda fare <lb/>alle superficie convesse o comunque sia allargate ed espanse. </s></p><p type="main">

<s>Egli dunque da savio si apparecchi&ograve; ia via per mezzo delle esperienze. </s>

<s><lb/>Trov&ograve; per prima cosa che un corpo pi&ugrave; acuto tira a s&egrave; il fluido elettrico <lb/>da distanze maggiori, ma in minor quantit&agrave; e densit&agrave;, che uno meno acuto. </s>

<s><lb/>Trov&ograve; inoltre che un corpo acuto attira a s&egrave; il fluido elettrico da distanze <lb/>maggiori, ma per&ograve; in minor quantit&agrave; e densit&agrave; che un simile altro corpo, <lb/>che invece di aver la sua sommit&agrave; appuntata, l'abbia rotonda. </s>

<s>Trov&ograve; in ul-<pb xlink:href="020/01/835.jpg" pagenum="278"/>timo che un corpo, il quale termina in maggior convessit&agrave;, di bel nuovo tira <lb/>a s&egrave; il fluido da distanza maggiore, ma per&ograve; in minor copia e densit&agrave; di <lb/>un altro simile corpo, l'estrema convessit&agrave; del quale sia invece minore (ivi, <lb/>pag. </s>

<s>64). </s></p><p type="main">

<s>Osservate cos&igrave; diligentemente queste cose, e supposto che l'aria resi&shy;<lb/>sta alla libera diffusione del fluido elettrico, e che questo trapassando per <lb/>un tal mezzo aereo vi si faccia attraverso la via dilatandolo, come poi prova <lb/>con certissime esperienze, ritrova il nostro Autore la ragion facilissima per&shy;<lb/>ch&egrave; lo stesso fluido elettrico abbia pi&ugrave; spedito il suo passaggio in una punta, <lb/>che in una superficie arrotondata ed espansa. </s>

<s>Rendeva per dir cos&igrave; visibile <lb/>la sua spiegazione, osservando nel buio a qual distanza incominciasse a ri&shy;<lb/>splendere la punta di uno spillo avvicinata al conduttore di una Macchina <lb/>elettrica. </s>

<s>Aggiunti insieme due spilli vedeva che, perch&egrave; incominciassero come <lb/>dianzi a risplendere, le loro punte conveniva accostarle al conduttore di pi&ugrave;, <lb/>e di pi&ugrave; ancora se tre erano quelle stesse punte aggiunte insieme. </s>

<s>Da ci&ograve; <lb/>rendevasi, secondo il Beccaria, visibile ci&ograve; ch'egli ragionava intorno alla sin&shy;<lb/>golare propriet&agrave; delle punte, ed era che &ldquo; il vapore pi&ugrave; rado della esteriore <lb/>parte dell'elettrica atmosfera che unitamente correndo ad una punta sola <lb/>pu&ograve; vincere la resistenza d'un filo d'aria, dividendosi e dirigendosi a due <lb/>diverse punte non &egrave; sufficiente a vincere la doppia resistenza de'due fili <lb/>d'aria, onde le due punte si dovranno immergere pi&ugrave; profondamente nella <lb/>pi&ugrave; densa elettrica atmosfera &rdquo; (ivi, pag. </s>

<s>67). </s></p><p type="main">

<s>Cos&igrave; persuadevasi l'illustre Fisico di Torino che, l'esalar con pi&ugrave; fa&shy;<lb/>cilit&agrave; la ridondanza del fluido elettrico e il ristorarne pi&ugrave; prontamente il di&shy;<lb/>fetto, non si potesse altrimenti salvar nelle punte, che per l'applicazione <lb/>de'suoi nuovi principii. </s>

<s>&ldquo; Insomma, egli dice, non m'&egrave; accaduto di riflet&shy;<lb/>tere ad alcuno o che sia stato da altri conosciuto o che abbia io ritrovato <lb/>o semplice o quanto si voglia composto sperimento, che alle punte comun&shy;<lb/>que rilucenti appartenesse, di cui non mi sia paruto di scorgerne la ragione, <lb/>o nella particolare forza che secondo la lunghezza delle punte si propaga, <lb/>ed in esse si condensa, se si tratti di corpi che disperdano il loro vapore; <lb/>o nella maggiore unione che si fa verso una punta che verso pi&ugrave; parti, se <lb/>si tratta di corpi, ne'quali esso si diffonde &rdquo; (ivi). </s></p><p type="main">

<s>Per questi effetti osservati e dimostrati intorno alle punte veniva il Bec&shy;<lb/>caria a porre in salvo la distinzion frankliniana del fluido positivo e del <lb/>fluido negativo, essendo per s&egrave; manifesto che le punte esalanti dovevan es&shy;<lb/>sere elettrizzate in pi&ugrave;, e le assorbenti in meno. </s>

<s>Perci&ograve; aveva nelle spran&shy;<lb/>ghe appuntate uno strumento da riconoscer con certezza se un dato corpo <lb/>era elettrizzato in pi&ugrave; o in meno. </s>

<s>Dall'altra parte il diverso modo d'operar <lb/>di esse spranghe appuntate, secondo che nella ridondanza esalano il foco <lb/>elettrico o lo riassorbono nel difetto, rendevasi patente per la semplice vista <lb/>di quello stesso foco, il quale appariva in forma di un largo fiocco nel primo <lb/>caso, e di una tenue stelletta nel secondo. </s></p><p type="main">

<s>Il Franklin aveva detto che il vetro della Macchina assorbisce il fluido <pb xlink:href="020/01/836.jpg" pagenum="279"/>elettrico dal corpo strofinatore, cosicch&egrave; questo da quello riceve. </s>

<s>Il Beccaria <lb/>quel ch'era stato un semplice detto lo ridusse cos&igrave; alla dimostrazione di un <lb/>fatto: &ldquo; Presentate ad una qualunque parte di lei (della Macchina elettrica) <lb/>la punta di una spranghetta metallica alla distanza di un pollice o pi&ugrave;, e <lb/>vedrete uscire da questa punta, ed indirizzarsi alla parte pi&ugrave; vicina della <lb/>Macchina un fascetto d'innumerabili, minutissimi, tra loro divergenti raggi <lb/>elettrici, che successivamente si suddividono e scompaiono a proporzione che <lb/>pi&ugrave; si allontanano da essa punta &rdquo; (ivi, pag. </s>

<s>9). </s></p><p type="main">

<s>Cos&igrave; la punta nell'apparenza del fiocco elettrico rendeva manifesto in&shy;<lb/>dizio ch'essa dava alla Macchina e non riceveva. </s>

<s>&ldquo; All'incontrario, soggiunge <lb/>l'Autore, se apparecchiate la spranghetta medesima ad una qualunque parte <lb/>della Macchina comunque elettrica, e ne presenterete alla punta di lei o la <lb/>palma della mano o qualunque corpo elettrizzabile per comunicazione, ve&shy;<lb/>drete splendere alcuni punti del corpo, che presentate alla spranghetta e <lb/>vedrete adunarsi una tenue luce sulla punta della spranghetta medesima <lb/>incomparabilmente pi&ugrave; piccola del fiocco elettrico &rdquo; (ivi). Questa tenue stel&shy;<lb/>letta perci&ograve; dava indizio sicuro che la Macchina riceveva dalla palma della <lb/>mano del fluido elettrico anzi che darle nulla del suo. </s></p><p type="main">

<s>Cos&igrave; l'ipotesi frankliniana, per opera dell'Autore <emph type="italics"/>Dell'Elettricismo ar&shy;<lb/>tificiale e naturale,<emph.end type="italics"/> si veniva a trasformare in una teoria dimostrata, la <lb/>quale fu sentito subito quanto fosse per giovare ai progressi, verso cui si <lb/>vedeva lietamente incamminare la scienza. </s>

<s>Il Franklin perci&ograve; se ne com&shy;<lb/>piacque grandemente, e al Dalibard che lo avea richiesto del suo autore&shy;<lb/>vole giudizio intorno al libro del nostro Italiano, cos&igrave; rispondeva il d&igrave; 29 Giu&shy;<lb/>gno del 1755 dalla sua Filadelfia: &ldquo; Vous me demandez mon sentiment sur <lb/>le livre italien du P. Beccaria. </s>

<s>Je l'ai lu avec beaucoup de plaisir, et je le <lb/>regarde comme un des meilleurs ouvrages que j'aye v&ucirc;s, dans aucune lan&shy;<lb/>gue, sur cette mati&egrave;re &rdquo; (Oeuvres cit., pag. </s>

<s>149). </s></p><p type="main">

<s>Il grande Filosofo americano non vedeva dunque in questo libro del <lb/>Beccaria solamente colui, che illustrata prima coll'esperienze e colle ragioni <lb/>aveva data tutta la possibile estensione alla sua teoria, ma riconosceva di <lb/>pi&ugrave; quella essere la miglior opera che fosse stata scritta in materia elet&shy;<lb/>trica. </s>

<s>Il soggetto infatti trattato dal nostro Autore s'estende a tutte quante <lb/>le parti della scienza elettrica d'allora, e tutte le irraggia mirabilmente di <lb/>nuova luce. </s>

<s>Una delle pi&ugrave; importanti fra queste parti era senza dubbio quella <lb/>che riguardava la causa delle attrazioni, rimasta tuttavia incerta, e dopo tante <lb/>fatiche di manifestarsi sempre ritrosa. </s></p><p type="main">

<s>Da che il Symmer aveva proposta l'ipotesi de'due fluidi distinti fra <lb/>loro di natura, com'avevano distinto il loro modo di operare, venne in mente <lb/>al Nollet di salvar le attrazioni e le repulsioni ammettendo che un'aura <lb/><emph type="italics"/>effluisca<emph.end type="italics"/> dal corpo elettrico, e un'altra simile aura v'<emph type="italics"/>affluisca<emph.end type="italics"/> dai corpi cir&shy;<lb/>costanti. </s>

<s>Cos&igrave; per mezzo di queste due contrarie correnti studiavasi di spie&shy;<lb/>gare ogni accostamento e discostamento, che si vede per causa dell'elettri&shy;<lb/>cit&agrave; avvenire ne'piccoli corpi: lo scostamento per l'urto della materia che <pb xlink:href="020/01/837.jpg" pagenum="280"/>esce dal corpo elettrizzato, l'accostamento per l'urto di quella che viene allo <lb/>stesso corpo dovunque dai corpi stranieri. </s></p><p type="main">

<s>A chi poi metteva in dubbio quell'aura affluente rispondeva il Nollet <lb/>mostrandogliela visibile nell'acqua, la quale, essendo elettrizzata, affluisce in <lb/>vapore. </s>

<s>Ma faceva il Beccaria argutamente osservare che causa unica del&shy;<lb/>l'evaporazione dell'acqua &egrave; l'aura effluente, ossia il fluido elettrico esalato dal <lb/>corpo che lo contiene, perch&egrave; operando questo sopra qualsivoglia altro corpo <lb/>vi si diffonde a esercitarvi la sua attivit&agrave; naturale. </s>

<s>&ldquo; Che per&ograve;, soggiunge <lb/>lo stesso Beccaria, alla materia effluente si pu&ograve; attribuire essa evaporazione, <lb/>senza che uopo sia fingerne la affluente, che, come si &egrave; visto qui di passag&shy;<lb/>gio, ed altrove si prover&agrave; pi&ugrave; ampiamente, affatto non esiste &rdquo; (ivi, pag. </s>

<s>33). </s></p><p type="main">

<s>A tutti quelli perci&ograve; a'quali, anche senza le prove del Beccaria, pareva <lb/>quella materia affluente introdotta dal Nollet una cosa del tutto immagina&shy;<lb/>ria; non rimaneva in salvo altra ipotesi che quella dell'azione e della rea&shy;<lb/>zione dell'aria. </s>

<s>Cos&igrave;, dopo un intero secolo e un terzo, dopo tanta dovizia <lb/>di fatti nuovi scoperti, non sapevano i Fisici spiegare il fatto delle elettri&shy;<lb/>che attrazioni punto meglio del Cabeo, anzi di quegli antichissimi Filosofi <lb/>riferitici da Plutarco. </s>

<s>L'esperienze da'nostri Accademici fiorentini tentate <lb/>nel vuoto torricelliano avrebbero potuto risolvere la questione da lungo <lb/>tempo, ma ebbero, come vedemmo, esito sfortunato. </s>

<s>Quelle eseguite poi dal <lb/>Dufay, introducendo corpi elettrici gi&agrave; prima ben confricati sotto la campana <lb/>della Macchina pneumatica, non parvero essere tanto dimostrative quanto ri&shy;<lb/>chiedeva il bisogno. </s></p><p type="main">

<s>Il primo insomma che riuscisse a chiarire la falsit&agrave; di quella ipotesi, la <lb/>quale attribuiva le attrazioni elettriche all'azione dell'aria, dimostrando che <lb/>avvenivano le stesse attrazioni anche nel vuoto il pi&ugrave; squisito che sia pos&shy;<lb/>sibile all'arte; fu il nostro Beccaria. </s>

<s>Essendosi egli primieramente applicato <lb/>ad osservare i cambiamenti che soffre il fiocco elettrico eccitato dentro una <lb/>campana, dalla quale andavasi via via estrando l'aria, rest&ograve; convinto che <lb/>questa resiste al fluido elettrico, sicch&egrave; divide e rompe e fa divergere quei <lb/>raggi luminosi, che vanno liberamente nel vuoto a diritto ed uniti. </s>

<s>Avrebbe <lb/>incominciato di qui a sospettare che veramente conferisse qualche cosa la <lb/>reazione dell'aria alle attrazioni de'corpuscoli elettrizzati, &ldquo; ma ben presto, <lb/>soggiunge il Nostro, mi disingannai.... Appesi all'estremit&agrave; della verga (di <lb/>ottone introdotta attraverso a'dischi di coio, di ch'era otturata la bocca della <lb/>campana della Macchina pneumatica) un filo di refe lungo sei pollici, che <lb/>restava distante un pollice e mezzo dalla superficie interiore della campana, <lb/>e due pollici dal piano della Macchina pneumatica. </s>

<s>Sul piano medesimo al&shy;<lb/>l'altro lato del filo collocai un piccolo piede di ottone con sopra un dado <lb/>similmente di ottone, sicch&egrave; il filo pendeva di mezzo alla cavit&agrave; della cam&shy;<lb/>pana e di questo dado in distanza uguale dall'uno e dall'altro. </s>

<s>Poi fattto <lb/>un esattissimo vuoto ed eccitato l'Elettricismo mi fu giocondissima cosa ve&shy;<lb/>dere il filo, che velocissimamente si vibrava tra il dado e la campana, que&shy;<lb/>sto e quella alternativamente percotendo colla sua estremit&agrave; &rdquo; (ivi, pag. </s>

<s>35). </s></p><pb xlink:href="020/01/838.jpg" pagenum="281"/><p type="main">

<s>Non contento a ci&ograve; prosegu&igrave; di sperimentare in altra maniera, introdu&shy;<lb/>cendo alcune fogliette di oro nel vuoto della campana pneumatica dove os&shy;<lb/>serv&ograve; che, nell'atto del diffondersi il fluido elettrico, alcune di quelle foglie <lb/>sollevavano la loro punta verso la verga, rimanendo coll'altra estremit&agrave; ade&shy;<lb/>renti al piano del piatto. </s>

<s>Osserv&ograve; inoltre con gran compiacenza che, toc&shy;<lb/>cando con un dito il vetro della Campana, quelle stesse fogliette risaltavano <lb/>per accorrere desiderose al punto del contatto. </s>

<s>&ldquo; Questo sensibilissimo mo&shy;<lb/>vimento delle foglie che accorrevano al dito, conclude ivi il Beccaria, mi <lb/>convinse sempre pi&ugrave; che realmente gli elettrici movimenti si facciano indi&shy;<lb/>pendentemente dall'azione dell'aria &rdquo; (pag. </s>

<s>36). </s></p><p type="main">

<s>Cos&igrave; dunque restava dimostrata falsa l'ipotesi degli antichi Filosofi rin&shy;<lb/>novellata dal Cabeo e proseguita dal pi&ugrave; gran numero de'fisici in fino a <lb/>mezzo il secolo XVIII, e poniamo che gli sperimenti del Beccaria avessero <lb/>ben persuaso tutti di quella falsit&agrave;, rimaneva ancora vivissimo il desiderio <lb/>di saper quale altra si potess'essere la causa di quegli elettrici moti. </s>

<s>Il Bec&shy;<lb/>caria stesso sentiva in s&egrave; la necessit&agrave; e il dovere di sodisfare all'universale <lb/>desiderio, e confessava, dopo le sue invitte confutazioni, richiedersi al com&shy;<lb/>pimento dell'opera &ldquo; che si potesse assegnare la individua meccanica ma&shy;<lb/>niera onde ..... debbano necessariamente avvenire i finora descritti mo&shy;<lb/>vimenti &rdquo; (ivi, pag. </s>

<s>40). Ma sentendone la grave difficolt&agrave; se ne spaccia <lb/>appagandosi &ldquo; di avere ridotti ad un solo principio o, se cos&igrave; piaccia, ad una <lb/>sola universalissima legge tutti i movimenti che si eccitano pell'elettricismo, <lb/>cio&egrave; avvenire tutti pella forza dell'elettrico vapore che dal corpo in cui ve <lb/>ne ha pi&ugrave; nel corpo in cui ve ne ha meno ad eguaglianza si espande &rdquo; (ivi). </s></p><p type="main">

<s>Soggiungeva il Beccaria, appena scritte queste parole, che avrebbe la&shy;<lb/>sciato a'pi&ugrave; acuti e meno occupati di lui il piacere di comporre su quel <lb/>principio ch'ei professava nuovi sistemi. </s>

<s>Ma perch&egrave; in verit&agrave; non appariva <lb/>chiaro come si potesse derivar la causa delle attrazioni elettriche da quegli <lb/>stessi principii, s'ebbero perci&ograve; i Fisici a rivolgere ad altri espedienti. </s>

<s>Quel&shy;<lb/>l'Autore Innominato che commemorammo di sopra erasi saviamente studiato <lb/>di ritrovar la occulta causa de'movimenti elettrici ne'principii neutoniani, <lb/>e persuaso che dovesser essere identici nella natura il fluido elettrico e il <lb/>fluido luminoso, cos&igrave; recisamente volle risolvere l'astruso problema. </s>

<s>&ldquo; Circa <lb/>l'attrazione e la ripulsione d'alcuni corpi sopra la materia elettrica, quando <lb/>questa &egrave; la stessa materia che quella della luce, m'appello all'Ottica del <lb/>sig. </s>

<s>Newton &rdquo; (Dell'Elettricismo cit., pag. </s>

<s>257). </s></p><p type="main">

<s>Una tal soluzione sarebbe senza dubbio stata la migliore che potevasi <lb/>desiderare, se si fosse liberamente concesso al nostro Autore quella mede&shy;<lb/>simezza di natura da lui professata fra l'elettrico e la luce. </s>

<s>Ma l'esperienze <lb/>dell'Hawksbee avevano gi&agrave; dimostrato ad evidenza che al foco elettrico non <lb/>competono punto le propriet&agrave; del foco ordinario, e lo stesso Beccaria, nel <lb/>&sect; III del cap. </s>

<s>VIII dell'<emph type="italics"/>Elettricismo artificiale,<emph.end type="italics"/> proponevasi di scoprire <emph type="italics"/>al&shy;<lb/>cune propriet&agrave; che indicano essere differente la natura del vapore elet&shy;<lb/>trico dalla natura della luce e fuoco.<emph.end type="italics"/> (Ediz. </s>

<s>cit., pag. </s>

<s>137). </s></p><pb xlink:href="020/01/839.jpg" pagenum="282"/><p type="main">

<s>Cos&igrave; rimaneva soffocato il buon seme della dottrina, che il nostro In&shy;<lb/>nominato avea sparso nel campo della scienza, quando a coltivarla fra noi <lb/>sorse un tale, a cui nessun altro sarebbe stato simile nella squisitezza dei <lb/>frutti e nell'abbondanza della raccolta. </s>

<s>Fece, nel 1769, in Como sua patria, <lb/>la prima comparsa dirigendosi al Beccaria con una Dissertazione epistolare, <lb/>che avea il titolo <emph type="italics"/>De vi attractiva ignis electrici.<emph.end type="italics"/> L'Autore non decide e <lb/>non gl'importa se l'elettricit&agrave; sia una cosa diversa dalla luce: gli basta si <lb/>conceda esser ella un fluido materiale e perci&ograve; soggetto a que'moti che com&shy;<lb/>petono universalmente alla materia. </s>

<s>Quanto poi all'esistenza di cos&igrave; fatti moti <lb/>molecolari se ne richiama anch'egli al Newton, il quale aveva dimostrate <lb/>le attrazioni e le repulsioni, non della luce sola, ma di qualunque altra sorta <lb/>di corpi, quando vengano le loro minime particelle a'pi&ugrave; intimi contatti. </s></p><p type="main">

<s>&ldquo; Et vero harum virium existentiam vel sola luminis refractio erincit, <lb/>ubi illud, caeteris omissis, notatur radios jam tunc prope corporum super&shy;<lb/>ficiem deflecti, antequam eam attingant. </s>

<s>Sed et alia quamplurima suppetunt <lb/>exempla harum virium, ut in corporibus perfecte laevibus, quae mutuo ad&shy;<lb/>haerent vi pondus atmosphaerae longe excedente, et in duabus aquae gut&shy;<lb/>tis, quae ad minimam distantiam sitae, primo apicem extendunt invicem, <lb/>quo se contingant, tum in unum coeunt, et in suspensione fluidorum in tu&shy;<lb/>bis capillaribus, sive quod adhuc melius visitur in ascensu accelerato gut&shy;<lb/>tae olei inter duas luminas vitreas, ne quid dicam de operationibus Che&shy;<lb/>miae, cuius nulla est pars, in qua praeter inertiam massae et specificam <lb/>gravitatem, alia virium mutuarum genera non ubique se prodant, et vel <lb/>invitis incurrant in oculos, quod quidem vel in sola postrema quaestione <lb/>Opticae Newtoni abunde patet, ubi tam multa virium mutuarum indicia atque <lb/>argumenta proferuntur &rdquo; (A. Volta, Opere, Firenze 1816, T. I, P. I, pag. </s>

<s>7). </s></p><p type="main">

<s>Bench&egrave; la principale intenzione del Volta sia, com'apparisce dal titolo <lb/>stesso di questa Epistola, quella di trattare delle attrazioni elettriche, v'in&shy;<lb/>trattien nonostante buona parte del suo discorso sopra un nuovo genere di <lb/>esperimenti relativi a un'Elettricit&agrave; comparsa sotto altro aspetto dell'ordi&shy;<lb/>naria, e alla quale perci&ograve; si dava il nome proprio e particolare di <emph type="italics"/>Elettri&shy;<lb/>cit&agrave; vindice.<emph.end type="italics"/> Giova accennar brevemente a ci&ograve; che dette occasione alla nuova <lb/>scoperta e all'origine di questo nome. </s></p><p type="main">

<s>La bella esperienza, suggerita all'Epino dall'osservazione fatta da'Ge&shy;<lb/>suiti missionari, del vetro elettrizzato posto sul vetro di una Bussola nau&shy;<lb/>tica; il fatto curiosissimo occorso al Symmer delle propriet&agrave; elettriche delle <lb/>calze di seta, avean condotto il nostro Gian Francesco Cigna a inventare una <lb/>Macchina che, sebbene assai scarsa, era pure una nuova sorgente di elet&shy;<lb/>tricit&agrave; diversa d'origine da quella solita attingersi alla Macchina ordinaria. </s>

<s><lb/>Egli prendeva un nastro di seta fortemente elettrizzato e lo applicava a una <lb/>lamina di piombo isolata, la quale toccata col dito, nell'atto stesso che ri&shy;<lb/>tiravasi il nastro con destrezza, rimaneva essa pure elettrizzata in modo da <lb/>dare una scintilla. </s></p><p type="main">

<s>Il Beccaria, il quale era felicemente riuscito a dar la teorica dell'elet-<pb xlink:href="020/01/840.jpg" pagenum="283"/>tricismo eccitato ne'globi di vetro tornatili e comunicato ai conduttori me&shy;<lb/>tallici, volle illustrare anche questa nuova Macchina del Cigna, derivandone <lb/>la ragione da'pi&ugrave; semplici fatti e pi&ugrave; comuni. </s>

<s>Stropicciando fortemente un <lb/>nastro di seta sopra un piano vi resta aderente; intorno a che si doman&shy;<lb/>dava: ritiene in questo caso il nastro l'elettricit&agrave; sua propria, ovvero la <lb/>smarrisce nel piano ch'e'tocca, per non riprendersela o <emph type="italics"/>rivendicarsela<emph.end type="italics"/> se <lb/>no nell'atto che ne venga staccato? </s>

<s>Il Beccaria sosteneva il caso dell'elet&shy;<lb/>tricit&agrave; <emph type="italics"/>vindice,<emph.end type="italics"/> ch'egli applicava alla Macchina del Cigna, e il Cigna stesso <lb/>lo secondava, infintanto che non sorse a contradire all'uno e all'altro con <lb/>validi argomenti il Volta. </s></p><p type="main">

<s>La disputa fra cos&igrave; grandi uomini, de'quali si studiava ciascuno di so&shy;<lb/>stener la sua parte, escogitando nuovi argomenti, che equivalevano ad al&shy;<lb/>trettante scoperte; frutt&ograve; bene alla scienza. </s>

<s>Il Beccaria, che infino da'suoi <lb/>primi esperimenti sull'Elettricismo artificiale posti per fondamento alla teo&shy;<lb/>ria della Bottiglia di Leyda, aveva riconosciuta la virt&ugrave; che ha il vetro di <lb/>accumulare cos&igrave; gran quantit&agrave; di fluido elettrico, il quale viene ampiamente <lb/>distribuito su tutta la sua superficie per mezzo delle armature; richiamava <lb/>l'attenzione del Volta sopra quel soloo di luce che trasparisce in quell'atto, <lb/>che una lastra di vetro si snuda della sua veste. </s></p><p type="main">

<s>Ma il Volta rispondeva che anzi era quella una prova dell'elettricit&agrave; <lb/><emph type="italics"/>permanente<emph.end type="italics"/> nel vetro, e non ripresa da lui dalla veste che lo abbandona, <lb/>per rivendicarsi di ci&ograve; che la veste stessa gli avea rapito in quel primo con&shy;<lb/>tatto. </s>

<s>&ldquo; Osservai, dice egli, che caricata una lastra di vetro e scaricatala, <lb/>nell'atto indi di alzar con fili di seta la laminetta metallica, che vestiva la <lb/>faccia <emph type="italics"/>ridondante,<emph.end type="italics"/> i piccoli getti di luce non avevano pi&ugrave; la figura di <emph type="italics"/>fioc&shy;<lb/>chi<emph.end type="italics"/> spandentisi dalla lamina di vetro, come esser dovrebbono nella suppo&shy;<lb/>sizione del P. Beccaria, ma quella anzi di luce affluente alla stessa veste con <lb/>apparire pi&ugrave; che altrove distintissime le <emph type="italics"/>stellette<emph.end type="italics"/> agli orli e sugli angoli di <lb/>esse. </s>

<s>Il contrario accadeva snudando l'altra faccia <emph type="italics"/>deficiente<emph.end type="italics"/> del vetro: la <lb/>foglietta metallica divenuta nella scarica, secondo i miei principii, elettrica <lb/>in <emph type="italics"/>pi&ugrave;,<emph.end type="italics"/> tostoch&egrave; alzavasi, spandeva d'attorno bellissimi <emph type="italics"/>fiocchi.<emph.end type="italics"/> Fui dunque <lb/>sicuro, non per conseguenza solo de'meditati principii, ma per dirette os&shy;<lb/>servazioni e prove di fatto, che la faccia della lastra, all'atto dello snuda&shy;<lb/>mento, non ripigliava il suo primo fuoco ridondante a spese, dir&ograve; cos&igrave;, della <lb/>veste, che anzi questa ne tirava a s&egrave; per rifarsi d'un gi&agrave; sofferto spoglia&shy;<lb/>mento .... che dunque la luce trallo disgiungimento mirava non gi&agrave; ad in&shy;<lb/>durre elettricit&agrave; in ambedue, bens&igrave; a dissipar la esistente, segnatamente quella <lb/>della veste &rdquo; (Opere e Tomo cit., pag. </s>

<s>152, 53). </s></p><p type="main">

<s>Come fosse il frutto di cos&igrave; nobile e dignitosa controversia l'invenzione <lb/>dell'Elettroforo perpetuo, d'onde ne consegu&igrave; il Condensatore con altri pre&shy;<lb/>ziosissimi strumenti, che la scienza elettrica ebbe dalle mani del Volta; fu <lb/>da noi narrato altrove, ond'&egrave; che dovendoci arrestar qui, per non oltrepas&shy;<lb/>sare i limiti che ci sono prescritti, diciamo a coloro i quali ammirano gli <lb/>straordinari progressi fatti dalla Fisica sull'Elettricismo in questi ultimi tempi, <pb xlink:href="020/01/841.jpg" pagenum="284"/>e intorno alla storia de'quali si son dovuti scrivere ampli volumi; che ri&shy;<lb/>pensino come nient'altro sono quegli ammirati progressi che l'incremento <lb/>sopravvenuto, per la favorevole stagione, in quel grande albero coltivato, <lb/>dopo il Franklin, massimamente in Italia dal Beccaria e dal Volta. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Quando, per opera de'tre grandi ora commemorati, s'impar&ograve; a cono&shy;<lb/>scer meglio quel fuoco che, con quasi nuov'arte magica, facevasi scaturire <lb/>dalla confricazione de'globi o de'cilindri di vetro; come disegno svanito, che <lb/>rifiorisce ai raggi del Sole, ritorn&ograve; alla mente de'Fisici la Terrella elettrica <lb/>del Guericke dimostrativa tutta insieme delle virt&ugrave; possedute dal globo della <lb/>gran Terra. </s>

<s>Non vi fu allora nessun fatto naturale rappresentatosi o nel&shy;<lb/>l'interiore del globo, o in mezzo all'aria che lo involge, sotto le apparenze <lb/>della luce, che non si credesse vedervi le sembianze della luce elettrica, <lb/>ond'&egrave; che i varii misteri o si tenevano cos&igrave; come per rivelati, o si riduce&shy;<lb/>vano almeno sotto l'ombra di un solo. </s></p><p type="main">

<s>Quante vane cose, da Filosofi solennissimi, non erano state insegnate <lb/>intorno alle folgori! E come potevano dall'altra parte giungere quegli in&shy;<lb/>gegni a capir la generazione del fuoco in mezzo alle umide nubi? </s>

<s>Ma quando <lb/>il Guericke mostr&ograve; generarsi un simile fuoco da un globo di zolfo freddo, <lb/>e in s&egrave; stesso, dall'ordinaria combustione non alterato, e allora soccorse fa&shy;<lb/>cilmente al pensiero di attribuire i lampi e le folgori alle sulfuree esalazioni <lb/>terrestri. </s></p><p type="main">

<s>Il di primo di Maggio del 1669 una saetta aveva colpito due fanciulli <lb/>nelle campagne circostanti a Bologna. </s>

<s>Ebbe occasione di esaminare il fatto <lb/>disgraziatamente occorso Geminiano Montanari, e di renderne conto all'Ac&shy;<lb/>cademia fiorentina, dirigendosi al cardinale Leopoldo che, in quella disper&shy;<lb/>sione de'socii, la rappresentava tutta insieme unita in Firenze, nella sua <lb/>propria persona. </s>

<s>Ne concludeva il Montanari, da ci&ograve; che v'aveva diligente&shy;<lb/>mente osservato, che la materia delle saette dev'essere di natura fluida e <lb/>tale che ardendo si consumi, bench&egrave; confessasse rimanergli oscuro come po&shy;<lb/>tesse una materia fluida rompere le muraglie (Fabbroni, Lett., T. I, Fi&shy;<lb/>renze 1773, pag. </s>

<s>163). A che rispondeva cos&igrave; il Principe dell'Accademia, <lb/>con lettera del di 7 di Maggio: &ldquo; Gratissimo mi &egrave; stato l'udire l'accidente <lb/>occorso de'duoi fanciulli percossi dal fulmine, e per l'opinione che io tengo <lb/>delle operazioni de'fulmini non mi giungon nuovi gli effetti, ch'ella mi a&shy;<lb/>cenna, mentre io tengo per cosa molto probabile che i fulmini si gene&shy;<lb/>rino dalle esalazioni della Terra ed in gran parte sulfuree &rdquo; (MSS. Cim., <lb/>T. XXIII, c. </s>

<s>169). </s></p><p type="main">

<s>Quando queste esalazioni sulfuree presero il nome pi&ugrave; particolare di <lb/>effluvii elettrici, non mancarono il Gray e il nostro Innominato di dir che <pb xlink:href="020/01/842.jpg" pagenum="285"/>il baleno era un fenomeno elettrico, prodotto cio&egrave; da quella stessa materia <lb/>che s'eccita da'macchinamenti artificiali. </s>

<s>Il Nollet insist&egrave; sulla somiglianza <lb/>che passa tra la folgore e la scintilla scoccata dalla Machina, di che poi <lb/>si compiacque, quando vide quella ipotesi cos&igrave; spendidamente confermata <lb/>dai fatti. </s></p><p type="main">

<s>Ma d'onde hanno origine quegli elettrici effluvii nelle nuvole, e quel <lb/>fuoco che dentro vi balena? </s>

<s>si domand&ograve; quando i fatti venivano ogni giorno <lb/>pi&ugrave; confermando quella prima analogia intraveduta fra l'elettricit&agrave; naturale <lb/>e l'artificiale. </s>

<s>La macchina esercitata dalla Natura per lo svolgimento del&shy;<lb/>l'elettricit&agrave; da comunicarsi all'aria, si pens&ograve; da principio che risedesse nel <lb/>mare. </s>

<s>La fosforescenza delle acque di lui, prima e anche qualche tempo <lb/>dopo che il Vianelli dimostrasse esser dovuta ad alcune specie d'insetti, si <lb/>ridusse anch'essa a uno de'soliti fenomeni elettrici, che s'attribuiva parti&shy;<lb/>colarmente ai sali, non essendosi mai veduti fosforeggiare i laghi o simili <lb/>altre acque dolci. </s>

<s>&ldquo; Il bitume e i sali che si trovano nelle acque del mare <lb/>sono, scrive il nostro Innominato, quelli che pi&ugrave; conservar possono la luce <lb/>dell'acqua stessa, perch&egrave; ne'fiumi dove l'acqua &egrave; dolce ci&ograve; non succede. </s>

<s><lb/>Questa luce si sviluppa fuori con maggior empito, quanto pi&ugrave; fredda e umida <lb/>&egrave; l'aria, perch&egrave; in tal modo l'aria stessa fa la funzione di un corpo manco <lb/>originalmente elettrizzato, e con ci&ograve; pi&ugrave; facile ad elettrizzarsi per comuni&shy;<lb/>cazione, cio&egrave; pi&ugrave; pronto a ricevere in s&egrave; la materia elettrica che scappa <lb/>fuori &rdquo; (Dell'Elettric. </s>

<s>cit., pag. </s>

<s>226, 27). </s></p><p type="main">

<s>Nel 1747 seguitava questa opinione del nostro Italiano anche il Fran&shy;<lb/>klin, il quale riguardava &ldquo; la mer comme la grande source des &eacute;clairs, ima&shy;<lb/>ginant que la lumiere qu'on y apper&ccedil;oit venoit du feu &eacute;lectrique produit <lb/>par le frottement des particules de l'eau avec celles du sel &rdquo; (Oeuvres cit., <lb/>pag. </s>

<s>116). Ma nel 1750, avendo avuto occasione di far pi&ugrave; particolari e pi&ugrave; <lb/>diligenti esperienze sopra l'acqua di mare raccolta e chiusa dentro una bot&shy;<lb/>tiglia &ldquo; sur cette observation, egli scrive, e sur ce qu'en agitant une solu&shy;<lb/>tion de sel marin dans de l'eau, je ne pouvois produire aucune lumiere, je <lb/>commen&ccedil;ai d'abord &agrave; douter de ma premiere hypothese et &agrave; soup&ccedil;onner que <lb/>cette lumiere dans l'eau de la mer devoit &egrave;tre attribu&eacute;e &agrave; quelques autres <lb/>principes &rdquo; (l&agrave;). </s></p><p type="main">

<s>Questo diverso principio, da cui sarebbe stata eccitata e comunicata l'elet&shy;<lb/>tricit&agrave; alla gran mole dell'aria, lo riconobbe il Franklin nell'aria stessa, la <lb/>quale &ldquo; &eacute;tant &eacute;lectriques par elles-m&ecirc;mes, tirassent du feu &eacute;lectrique de la <lb/>terre dans les grands coups de vent par leur frottement contre les arbres, <lb/>les montagnes, les b&acirc;timents, etc., comme autant de petits globes &eacute;lettri&shy;<lb/>ques frottants contre des coussins non &eacute;lectriques, et que les vapeurs en <lb/>s'&eacute;levant re&ccedil;&ugrave;ssent de l'air ce feu, et que par ces moyens les nuages de&shy;<lb/>vinssent &eacute;lectris&eacute;s &rdquo; (l&agrave;, pag. </s>

<s>117). </s></p><p type="main">

<s>Persuaso in ogni modo, qualunque poi ne fosse l'origine vera, dell'elet&shy;<lb/>tricismo esistente nell'aria, e comunicato per mezzo di lei alle nuvole, oc&shy;<lb/>corse al Franklin, nel proseguire i suoi prediletti esperimenti sopra la facolt&agrave; <pb xlink:href="020/01/843.jpg" pagenum="286"/>delle punte, di prender due bacini di rame pendenti per cordicelle di seta <lb/>dall'estremit&agrave; di un flagello da bilancia, intorno al quale potevano muoversi <lb/>in giro orizzontale, e anche insieme d'alto in basso. </s>

<s>Elettrizzando uno di <lb/>cotesti bacini e facendolo poi, nel girarlo, passar sopra una punta metallica <lb/>opportunamente collocata sull'estremit&agrave; di una verga infissa sul pavimento, <lb/>vedeva lo stesso bacino scaricare <emph type="italics"/>son feu en silence sur la pointe.<emph.end type="italics"/></s></p><p type="main">

<s>In questo gli balen&ograve; alla mente un pensiero stupendo: &ldquo; Maintenant <lb/>si le feu de l'&eacute;lectricit&eacute; et celui de la foudre sont une seule et m&ecirc;me chose, <lb/>comme j'ai tach&eacute; de le prouver assez amplement, ce tube de carton et ces <lb/>bassins peuvent repr&eacute;senter les nuages &eacute;lectris&eacute;s.... Le mouvement hori&shy;<lb/>sontal des bassins sur le plancher peut repr&eacute;senter le mouvement des nua&shy;<lb/>ges sur la terre et le poin&ccedil;on &eacute;lev&eacute; nous represente les montagnes et les <lb/>plus hauts &eacute;difices, et cela nous fait voir comment les nuages &eacute;lectris&eacute;s pas&shy;<lb/>sant sur le montagnes et sur les b&acirc;timents &agrave; une trop grande hauteur pour <lb/>les frapper, peuvent &egrave;tre attir&eacute;s en bas jusqu'&agrave; la proximit&eacute; qui leur est <lb/>necessaire pour cet effet.... </s></p><p type="main">

<s>Dopo ci&ograve;, ecco lo stupendo concetto che si diceva, e ch'essendo poi <lb/>riuscito nella pratica basterebbe egli solo a far tacere i declamatori contro <lb/>le oziose vanit&agrave; della scienza: &ldquo; Les choses &eacute;tant ainsi, je demande, si la <lb/>connoissance du pouvoir des pointes ne pourroit pas &ecirc;tre de quelque avan&shy;<lb/>tage aux homines pour pr&eacute;server les maisons, les eglises, les vaisseaux etc., <lb/>des coups de la foudre, en nous engageant &agrave; fixer perpendiculairement sur <lb/>les parties les plus &eacute;lev&eacute;es des verges de fer aiguiss&eacute;es par la pointe comme <lb/>des aiguilles, et dor&eacute;es pour pr&eacute;venir la rouille, et &agrave; attacher au pied de <lb/>ces verges un fil d'archal descendant le long du b&acirc;timent dans la terre, ou <lb/>le long d'un des aubans d'un vaisseau et de son bordage jusqu'&agrave; fleur d'eau? </s>

<s><lb/>N'est-il pas probable que ces verges de fer tireroient sans bruit le feu <lb/>&eacute;lectrique du nuage avant qu'il vint assez pr&egrave;s pour frapper, et que par ce <lb/>moyen nous serions pr&eacute;serv&eacute;s de tant de d&eacute;sastres soudains et terribles? </s>

<s>&rdquo; <lb/>(l&agrave;, pag. </s>

<s>61, 62). </s></p><p type="main">

<s>Tutto il fondamento per&ograve; di cos&igrave; bella e generosa proposta consisteva <lb/>nell'assicurarsi se veramente i nuvoli davano segnali elettrici, di che il Fran&shy;<lb/>klin stesso suggeriva ivi appresso il modo servendosi di un lungo palo di <lb/>ferro appuntato, eretto sulla sommit&agrave; di qualche alta torre, dove, dentro una <lb/>specie di casotto da sentinella, invigilasse un uomo co'pi&egrave; posati sopra uno <lb/>sgabello isolatore, per esplorare i segnali elettrici in tempo che le nubi pro&shy;<lb/>cellose gli passavano sopra la testa. </s></p><p type="main">

<s>Il Collinson diffuse con grande ardore in Inghilterra e in Francia il <lb/>progetto frankliniano di riparar da'fulmini i cos&igrave; spesso minacciati edifizi, <lb/>e a una tale inaspettata notizia si commosse tutta Parigi. </s>

<s>Nell'animo del Re <lb/>era entrata cos&igrave; grande curiosit&agrave;, che non gli dette pace infin tanto che non <lb/>ne ebbe veduta la prova, per eseguir la quale il duca d'Ayen offerse a Sua <lb/>Maest&agrave; la suburbana villa di S. Germano. </s>

<s>Ma il Dalibard scelse un giardino <lb/>di Marly-la-ville, a una distanza di sei leghe da Parigi, dove &ldquo; le 10 Mai <pb xlink:href="020/01/844.jpg" pagenum="287"/>dernier, &agrave; 2 heures 20 minutes apr&egrave;s midi, une nu&eacute;e orageuse ayant pass&eacute; <lb/>au-dessus du lieu o&ugrave; la barre &eacute;toit &eacute;lev&eacute;e, ceux que l'on avoit appost&eacute;s <lb/>pour y veiller, s'approcherent et en tirerent des &eacute;tincelles de feu, &eacute;prou&shy;<lb/>vant les m&ecirc;mes especes de commotions que dans les experiences &eacute;lectriques <lb/>ordinaires &rdquo; (Franklin, Oeuvres cit., T. I, pag. </s>

<s>104). </s></p><p type="main">

<s>Lo stesso Dalibard, tre giorni dopo, rendeva solennemente conto alla <lb/>R. </s>

<s>Accademia del fortunato avvenimento del d&igrave; 10 di Maggio 1752, e con <lb/>l'animo esaltato, com'&egrave; facile immaginare, terminava cos&igrave; la sua Relazione: <lb/>&ldquo; L'id&eacute;e qu'en a eu M. </s>

<s>Franklin cesse d'&ecirc;tre d'une coniecture; la voil&aacute; de&shy;<lb/>venue une r&eacute;alit&eacute; et j'ose croire que plus on approfondira tout ce qu'il a <lb/>publi&eacute; sur l'&eacute;lectricit&eacute;, plus on reconno&icirc;tra combien la Physique lui est re&shy;<lb/>devable pour cette partie &rdquo; (l&agrave;, pag. </s>

<s>109, 10). </s></p><p type="main">

<s>Si pu&ograve; facilmente ognuno immaginare quanto si dovesse il Franklin <lb/>compiacere della corrispondenza che le sue idee felicemente trovarono nel&shy;<lb/>l'esperienze eseguite dai Fisici parigini, e fu forse una tal compiacenza, nella <lb/>quale egli cos&igrave; dolcemente riposava, che lo fece indugiare infino al Settem&shy;<lb/>bre a darne sodisfazione a'suoi occhi proprii. </s>

<s>&ldquo; En Septembre 1752 j'&eacute;le&shy;<lb/>vai sur ma maison une verge de fer pour tirer le feu du tonnerre, afin de <lb/>faire quelques exp&eacute;riences sur cela, ayant dispos&eacute; deux petits timbres pour <lb/>m'avertir quand la verge seroit &eacute;lectris&eacute;e, ce qui est une pratique familiere <lb/>a tout &eacute;lectricien &rdquo; (l&agrave;, pag. </s>

<s>117). </s></p><p type="main">

<s>Abbiamo messo in forse questo indugio di quattro mesi, perch&egrave; una <lb/>volgar tradizione avvalorata da gravissimi Autori tien per cosa certa che il <lb/>Franklin, prima di esperimentare l'elettricit&agrave; delle nubi co'pali di ferro, <lb/>com'avevano fatto il Dalibard e il Lor, l'avesse esplorata con maggior fa&shy;<lb/>cilit&agrave;, e con pi&ugrave; semplice e pronto apparecchio, per mezzo del cos&igrave; detto <lb/><emph type="italics"/>Cervo volante.<emph.end type="italics"/> Carlo Barletti, il quale riserb&ograve; il V Articolo de'suoi Saggi <lb/>di Fisica (<emph type="italics"/>Fhysica specimina<emph.end type="italics"/>) a trattar del modo di costruire e di far uso, <lb/>per esplorar l'elettricit&agrave; ammosferica, di quella stessa Macchina volante, si <lb/>cred&egrave; di poter uscire in cos&igrave; fatta sentenza: &ldquo; Certe Franklinus ipse atmo&shy;<lb/>sphaericam electricitatem anno 1572 Cervo prius volante, quam virga explo&shy;<lb/>ravit &rdquo; (Mediolani 1772, pag. </s>

<s>129), ma non reca di tal certezza alcun do&shy;<lb/>cumento, e cercandolo noi per le dissertazioni e per le lettere frankliniane <lb/>non ce lo abbiamo saputo trovare. </s></p><p type="main">

<s>Comunque sia, fa maraviglia che l'infaticabile Sperimentatore ameri&shy;<lb/>cano si lasciasse prevenire in sodisfare a cos&igrave; nobile curiosit&agrave; non sol dai <lb/>Francesi, ma dagli stessi Italiani, appresso i quali la notizia del progetto <lb/>de'parafulmini e della felice riuscita avutane nel Maggio a Parigi, non giunse <lb/>che sulla fine del prossimo Giugno. </s>

<s>&ldquo; Avuta notizia, scrive il Beccaria, sulla <lb/>fine di Giugno della oramai notissima esperienza inventata dal valoroso In&shy;<lb/>glese Beniamino Franklin, abitante in Filadelfia, citt&agrave; della Pensilvania in <lb/>America, ed avverata in Parigi da'signori De Lor, e Dalibard, m'applicai <lb/>immantinente ad effettuarla anch'io qui in Torino. </s>

<s>I. </s>

<s>Feci empire di mastice <lb/>all'altezza di sei pollici una cassa triangolare e la feci sospendere sotto il <pb xlink:href="020/01/845.jpg" pagenum="288"/>tetto in contatto delle tegole. </s>

<s>II. </s>

<s>Tolte alcune tegole, feci collocare sul ma&shy;<lb/>stice della cassa un trepiede che reggeva una spranga di ferro, la quale <lb/>s'alzava da dodici piedi sopra del tetto. </s>

<s>III. </s>

<s>Al basso della spranga avea <lb/>fatto conficcare una spranghetta, che orizzontalmente sporgeva fuora della <lb/>cassa tra essa ed il tetto. </s>

<s>IV. All'estremit&agrave; di questa spranghetta appiccai <lb/>una catena, che per un buco fatto nel solaio calava in una larga stanza e <lb/>reggeva una palla di metallo di due pollici di diametro, in distanza di un <lb/>piede da un tavolato. </s>

<s>V. </s>

<s>Conficcai in questo tavolato due stili, uno con al&shy;<lb/>l'estremit&agrave; un campanello distante tre pollici dalla palla, un altro pi&ugrave; alto <lb/>con all'estremit&agrave; un filo di seta, che reggeva una palletta di metallo tralla <lb/>suddetta palla e il campanello. </s>

<s>VI. </s>

<s>E finalmente adattai in giro della spranga, <lb/>un po'sopra del tetto, una specie d'ombrello, che riparasse il mastice dalla <lb/>pioggia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Disposte cos&igrave; le cose, addi 2 Luglio, alle due ore e mezzo dopo mez&shy;<lb/>zogiorno, nello spandersi verticalmente sulla spranga una nuvola assai bassa, <lb/>spinta da libeccio verso greco, la palla di metallo cominci&ograve; a dare scintille <lb/>assai vive alla distanza di dieci linee in circa e seguit&ograve; a scintillare per <lb/>25 minuti, cio&egrave; finch&egrave; pass&ograve; la nuvola. </s>

<s>In tempo di questo elettrizzamento <lb/>non vi furono n&egrave; lampi n&egrave; tuoni. </s>

<s>Poco prima che esso cominciasse un'al&shy;<lb/>tra nuvola avea dato un poco di pioggia e s'era visto a libeccio alcun lampo <lb/>accompagnato da tuono assai leggero &rdquo; (Dell'Elettric. </s>

<s>natur., Torino 1753, <lb/>pag. </s>

<s>159, 60). </s></p><p type="main">

<s>Prosegue il Beccaria a descrivere colla sua solita diligenza altre simili <lb/>osservazioni fatte ne'susseguenti mesi di Agosto e di Settembre, non tanto <lb/>per verificare l'ipotesi frankliniana, ci&ograve; che oramai non pi&ugrave; bisognava, quanto <lb/>per apparecchiarsi i fondamenti a dimostrar, nel capitolo secondo (ci&ograve; che fu <lb/>trascurato da'Fisici parigini) <emph type="italics"/>la medesimezza de'segni elettrici nell'elettri&shy;<lb/>cismo delle nuvole con i segni elettrici nell'elettricismo artificiale.<emph.end type="italics"/></s></p><p type="main">

<s>Dopo questi diligentissimi studi del nostro Fisico torinese poteva con <lb/>pi&ugrave; ragione che mai asserire il Dalibard che la congettura era felicemente <lb/>tornata nella realt&agrave; de'fatti, e il Franklin aveva cos&igrave; nuovo motivo di com&shy;<lb/>piacersi. </s>

<s>Non era per&ograve; nell'animo di lui quella compiacenza perfetta: egli <lb/>trovato falso il suo primo supposto dell'origine dell'elettricit&agrave; ammosferica <lb/>dalle acque del mare, ebbe, come vedemmo, ricorso agli sfregamenti che su&shy;<lb/>bisce l'aria contro le asprezze superficiali della terra, nelle ventose agita&shy;<lb/>zioni, e l'ipotesi aveva aspetto di probabilit&agrave;, <emph type="italics"/>mais l'experience,<emph.end type="italics"/> ingenua&shy;<lb/>mente confessa il Franklin, <emph type="italics"/>que je tentai dans cette vue ne me r&eacute;ussit <lb/>pas<emph.end type="italics"/> (Oeuvres cit., pag. </s>

<s>117). A render pi&ugrave; che mai vacillante l'ipotesi, non <lb/>potutasi confermare dai fatti, s'aggiunse poi la scoperta del Monnier del&shy;<lb/>l'elettricit&agrave; dell'aria anche a ciel sereno, e la difficolt&agrave; veniva a complicarsi <lb/>anche di pi&ugrave; per le osservazioni elettroscopiche, le quali davano ora una <lb/>elettricit&agrave; positiva, ora una elettricit&agrave; negativa, e ora un passaggio inaspet&shy;<lb/>tato dell'una nell'altra. </s></p><p type="main">

<s>Rassicurare la scienza per questa parte cos&igrave; principale e, lasciate ad-<pb xlink:href="020/01/846.jpg" pagenum="289"/>dietro le congetture, dimostrar l'origine dell'elettricit&agrave; ammosferica per via <lb/>di fatti sperimentati, e in che ritrovasse la causa sua unica e vera la sva&shy;<lb/>riata moltiplicit&agrave; degli effetti; era riserbato al genio di Alessandro Volta. </s></p><p type="main">

<s>Persuasi oramai i Fisici che non dovesse mancare uno svolgimento di <lb/>elettricit&agrave;, dovunque fosse confricamento e collisione fra le particelle de'corpi, <lb/>s'erano dati con sollecito studio a ricercar di quell'occulto elettricismo i <lb/>segnali nell'evaporar che fanno i liquidi, segnatamente, e nelle fermenta&shy;<lb/>zioni. </s>

<s>Il Franklin, il De Saussure, il Wenly, il Cavallo erano de'principali <lb/>fra coloro ch'eransi rivolti a cos&igrave; fatte ricerche, le quali poi presto ebbero ad <lb/>abbandonare, per non aver corrisposto i fatti alle concepute speranze. </s></p><p type="main">

<s>Ma le persuasioni del Volta in tal proposito erano assai pi&ugrave; tenaci: egli <lb/>che ammaestrato dal Newton vedeva in quelle effervescenze de'corpi un <lb/>gioco delle intestine forze molecolari; egli che giovane s'introduceva alla <lb/>Filosofia elettrica dimostrando come le attrazioni de'corpi elettrizzati eran <lb/>dovute a forze di uguale e di simil natura a quelle che attraggono e re&shy;<lb/>spingono le minime particelle, eccitando ne'corpi dissolubili le evaporazioni <lb/>e i fermenti; non si poteva dar pace che l'elettricit&agrave; non si manifestasse <lb/>per alcuno di tali processi, e del non essersene potuti ancora vedere i se&shy;<lb/>gni, ne accagionava l'imperfezione degli strumenti. </s></p><p type="main">

<s>Riuscito perci&ograve; a costruire il suo squisitissimo Elettrometro condensa&shy;<lb/>tore incor&ograve; buona speranza di veder ci&ograve;, che non era a nessuno riuscito di <lb/>vedere prima di lui. </s>

<s>Nella primavera dell'anno 1782 egli era a Parigi, e il <lb/>di 13 d'Aprile, mostr&ograve;, per mezzo del suo eccellentissimo strumento, al La&shy;<lb/>voisier e al La-Place ivi presenti, i segni chiarissimi dell'elettricit&agrave; dall'eva&shy;<lb/>porazione dell'acqua. </s>

<s>L'esperienze per&ograve; gli riuscirono assai meglio a Lon&shy;<lb/>dra alla presenza del Magellan, del Kirwan, del Walker, gli occhi de'quali <lb/>furono testimonii de'segni dell'elettricit&agrave; negativa che, gettate alquante goc&shy;<lb/>ciole d'acqua sui carboni accesi, eran dati da un braciere di rame. </s></p><p type="main">

<s>La scoperta dell'elettricit&agrave; svoltasi cos&igrave; dall'acqua che si trasforma in <lb/>vapori, apr&igrave; la via a scoprire l'elettricit&agrave;, che si svolge nelle multiformi tra&shy;<lb/>sformazioni de'corpi, d'onde tanto largo campo d'aperse ai progressi della <lb/>nuova Scienza chimica, ma intanto il Volta applicava quella sua stessa sco&shy;<lb/>perta a risolvere il problema dell'origine dell'elettricit&agrave; ammosferica, con&shy;<lb/>cludendo cos&igrave; l'<emph type="italics"/>Appendice alla II Parte del Condensatore,<emph.end type="italics"/> dop'aver par&shy;<lb/>ticolarmente descritte l'esperienze in proposito fatte a Parigi e a Londra. </s></p><p type="main">

<s>&ldquo; Le esperienze fatte fin qui e che abbiamo riferite, bench&egrave; non sian <lb/>molte, tutte per&ograve; concorrono a mostrarci che i vapori dell'acqua e general&shy;<lb/>mente le parti d'ogni corpo, che si staccano volatizzandosi, portano via seco <lb/>una quantit&agrave; di fluido elettrico a spese dei corpi fissi che rimangono, la&shy;<lb/>sciandoli perci&ograve; elettrizzati <emph type="italics"/>negativamente,<emph.end type="italics"/> non altrimenti che ne portan via <lb/>una quantit&agrave; di fuoco elementare con ci&ograve; raffreddandoli. </s>

<s>Quindi vuolsi in&shy;<lb/>ferire che i corpi, risolvendosi in vapori, o prendendo l'abito aereo, acqui&shy;<lb/>stino una maggior capacit&agrave; rispetto al fluido elettrico, giusto come l'acqui&shy;<lb/>stano maggiore rispetto al fuoco comune o fluido calorifico. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/847.jpg" pagenum="290"/><p type="main">

<s>&ldquo; Chi non sar&agrave; colpito da cos&igrave; bella analogia, per cui l'elettricit&agrave; porta <lb/>del lume alla novella dottrina del calore e ne riceve a vicenda? </s>

<s>Parlo della <lb/>dottrina del calor <emph type="italics"/>latente<emph.end type="italics"/> o <emph type="italics"/>specifico,<emph.end type="italics"/> come si vuol chiamare, di cui Black e <lb/>Wilke, colle stupende loro scoperte, han gettato i semi e che &egrave; stata ultima&shy;<lb/>mente tanto promossa dal D. Crawford, dietro le esperienze del D. Irwine. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Seguendo questa analogia, siccome i vapori, allorch&egrave; si condensano, <lb/>e ritornano in acqua e conseguentemente alla primiera pi&ugrave; angusta capacit&agrave;, <lb/>perdono il loro calore <emph type="italics"/>latente,<emph.end type="italics"/> ossia depongono il di pi&ugrave; di fuoco che si <lb/>avevano appropriato volatizzandosi; cos&igrave; pure manderan fuori il fluido elet&shy;<lb/>trico divenuto ora ridondante. </s>

<s>Ed ecco come nasce l'<emph type="italics"/>elettricit&agrave; di eccesso,<emph.end type="italics"/><lb/>che domina sempre pi&ugrave; o meno nell'aria anche serena, a quell'altezza in <lb/>cui i vapori cominciano a condensarsi, la quale &egrave; pi&ugrave; sensibile nelle neb&shy;<lb/>bie, ove quelli si condensano maggiormente, e infine fortissima l&agrave; dove le <lb/>folte nebbie si agglomerano in nubi, e gi&agrave; si figurano in gocce. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Fin qui l'elettricit&agrave; dell'ammosfera sar&agrave; sempre <emph type="italics"/>positiva.<emph.end type="italics"/> Ma formata <lb/>che sia una nube potentemente elettrica <emph type="italics"/>in pi&ugrave;<emph.end type="italics"/> ella avr&agrave; una sfera di at&shy;<lb/>tivit&agrave; intorno ad essa, nella quale, se avviene ch'entri un'altra nube, al&shy;<lb/>lora, giusta le note leggi delle <emph type="italics"/>Ammosfere,<emph.end type="italics"/> gran parte del fluido elettrico <lb/>di questa seconda nube si ritirer&agrave; verso l'estremit&agrave; pi&ugrave; lontana dalla prima, <lb/>e potr&agrave; anche uscirne ove incontri o altra nube o vapori o prominenze ter&shy;<lb/>restri che lo possan ricevere, ed ecco una nube elettrizzata <emph type="italics"/>negativamente,<emph.end type="italics"/><lb/>la quale potr&agrave; a sua posta occasionare, coll'influsso della propria ammosfera, <lb/>l'elettricit&agrave; positiva in una terza ecc. </s>

<s>In questa maniera s'intende benissimo <lb/>come si possano avere sovente ne'conduttori ammosferici segni di elettri&shy;<lb/>cit&agrave; <emph type="italics"/>negativa<emph.end type="italics"/> a cielo pi&ugrave; che coperto, e come ne'temporali specialmente, <lb/>ove molte nubi si veggono pensili, e staccate vergere al basso e or ondeg&shy;<lb/>giare per qualche tempo, ora scorrere le une sotto le altre, or trasportarsi <lb/>rapidamente, l'elettricit&agrave; cambi pi&ugrave; volte e spesso a un tratto da <emph type="italics"/>positiva<emph.end type="italics"/> in <lb/><emph type="italics"/>negativa<emph.end type="italics"/> c viceversa. </s>

<s>&rdquo; (Opere cit., T. I, P. I, pag. </s>

<s>275-77). </s></p><p type="main">

<s>L'analogia cos&igrave; felicemente dimostrata fra il fuoco delle folgori e il fuoco <lb/>elettrico allett&ograve; i Fisici ad ammettere una somigliante analogia tra la luce <lb/>emessa dai globi artificialmente confricati, e la luce naturalmente diffusa per <lb/>le altissime regioni dell'aria nelle Aurore Boreali. </s>

<s>Prima che vedesse il Gue&shy;<lb/>ricke fosforeggiare, come suole talvolta il cielo, la sua Terrella, si credeva, <lb/>da'pi&ugrave; savi Filosofi, che l'apparenza delle Aurore Boreali nascesse dalla luce <lb/>del Sole riflessa ne'vapori esalati su dalla Terra. </s></p><p type="main">

<s>&ldquo; Quod circa terram eleventur vapores, scriveva Galileo, qui ascenden&shy;<lb/>tis solis lumen reflectant, saepissime apparet cum media interdum nocte coe&shy;<lb/>lum adeo illustret, ut lumen in terram crepusculinum maius effundat. </s>

<s>Id <lb/>autem a me saepius observatum est et semper talis lux boream versus ap&shy;<lb/>paret et ratio est manifesta, quia ex meridie vel ab ortu vel ab occasu in&shy;<lb/>tra conum umbrae tales complectuntur vapores, quoniam Boream versus, ob <lb/>nostrum in eam partem situm, conspici possunt ut diligentius consideranti <lb/>patet. </s>

<s>Vidi Venetiis circa horam noctis secundam aerem ad Boream adeo <pb xlink:href="020/01/848.jpg" pagenum="291"/>clarum, ut adversus parietes ultra Lunae rotundae lumen illustraret, aversi <lb/>autem tenebrosissimi erant. </s>

<s>Novam autem admirationem afferebat quod viae <lb/>quae proximae ad Septentrionem dirigebantur, utrimque a splendore illu&shy;<lb/>minabantu&racute;, nec tecta umbram in terram demittebant, ut ex illuminatione <lb/>Solis et Lunae contingit, quia in his tamquam ab uno puncto provenit il&shy;<lb/>luminatio tunc vero ex quarta fere anguli parte magna lux emanabat &rdquo; (MSS. <lb/>Gal., P. III, T. II, c. </s>

<s>13. Alb. </s>

<s>V, 393). </s></p><p type="main">

<s>Questa ipotesi galileiana dell'origine delle Aurore boreali cadde insieme, <lb/>e per quelle stesse ragioni che caddero le altre ipotesi professate pure da <lb/>Galileo intorno all'origine delle stelle nuove e delle Comete, essendo per&shy;<lb/>suaso ognuno assai facilmente che cos&igrave; fatte apparenze celesti hanno sede <lb/>in regioni tanto pi&ugrave; alte di quelle, alle quali si possono sublimare i vapori <lb/>o le altre esalazioni terrestri. </s>

<s>A chi prima, osservando la fosforescenza che <lb/>appariva diffondersi sulla superficie del globo sulfureo del Guericke, o me&shy;<lb/>glio nell'interna cavit&agrave; de'vetri tornatili dell'Hawksbee, venisse in mente di <lb/>paragonare quel lume elettrico colle luminose apparenze delle Aurore, non <lb/>&egrave; forse facile a definire, ma dovette senza dubbio aver grande efficacia, in <lb/>confermar gl'ingegni in cos&igrave; fatta opinione, ci&ograve; che ne fu scritto e divul&shy;<lb/>gato per le Lettere frankliniane. </s></p><p type="main">

<s>In una di queste diretta al Collinson immagina il celebre Autore che <lb/>l'aria, fortemente riscaldata e rarefatta dal sole sotto i tropici, si distenda <lb/>verso i poli, dove le due elettricit&agrave; de'vapori equatoriali e polari, comuni&shy;<lb/>candosi insieme, si rendono all'occhio dello spettatore parventi. </s>

<s>Cos&igrave;, ben&shy;<lb/>ch&egrave; paia slanciarsi la luce da settentrione a mezzod&igrave;, il progresso nulladi&shy;<lb/>meno &egrave; realmente in verso contrario, e avviene in ci&ograve; quel che suole avvenire <lb/>de'tubi pieni d'acqua, nell'atto che si votano, ne'quali, bench&egrave; il flusso ap&shy;<lb/>parisca dalla parte di sotto, il principio del moto in realt&agrave; &egrave; dalla parte di <lb/>sopra. </s>

<s>&ldquo; Comme lorsqu'on ouvre &agrave; l'une de ses extr&egrave;mit&eacute;s un long canal <lb/>repli d'eau, pour le vuider, le mouvement de l'eau commence d'abord au&shy;<lb/>pr&egrave;s de l'extr&egrave;mit&eacute; ouverte, et continue vers l'extr&egrave;mit&eacute; ferm&eacute;e, quoique <lb/>l'eau elle-m&ecirc;me avance de l'extr&egrave;mit&eacute; ferm&eacute;e vers l'extr&egrave;mit&eacute; ouverte: ainsi <lb/>le feu &eacute;lectrique d&eacute;charg&eacute; dans les r&eacute;gions polaires, peut &ecirc;tre sur une lon&shy;<lb/>gueur de mille lieves d'air en vapeurs, paro&icirc;t d'abord l&agrave; o&ugrave; il est en mou&shy;<lb/>vement; c'est-&agrave;-dire, dans les parties le plus septentrionales, et l'apparition <lb/>s'&eacute;lance du c&ograve;t&eacute; du midi, quoi que le feu avance r&eacute;ellement du c&ograve;t&eacute; du <lb/>septentrion &rdquo; (Oeuvres cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Non si persuadeva per questo il Franklin d'aver data la soluzione del <lb/>difficile problema, in modo che se n'avessero tutti a sodisfare: era un'ab&shy;<lb/>bozzo, ch'egli stesso rimetteva all'opera di qualche altra mano. <emph type="italics"/>Ceci,<emph.end type="italics"/> con&shy;<lb/>cludevano le sopra riferite parole, <emph type="italics"/>pourroit passer pour une explication de <lb/>l'Aurore Bor&egrave;ale.<emph.end type="italics"/></s></p><p type="main">

<s>La mano che riprese poi quell'opera era una delle pi&ugrave; esperte, che si <lb/>potesse trovare allora; quella, vogliam dire, del nostro Beccaria. </s>

<s>Egli, nel <lb/>&sect; 657 del suo Trattato <emph type="italics"/>Dell'Elettricismo<emph.end type="italics"/> pone con lungo ordine sotto di-<pb xlink:href="020/01/849.jpg" pagenum="292"/>stinti capi le analogie, che passano fra ci&ograve; che si osserva nelle Aurore bo&shy;<lb/>reali e ne'fenomeni elettrici, e pi&ugrave; che in altro insiste sulla somiglianza della <lb/>diffusione della luce nell'opera dell'arte e della Natura. </s>

<s>&ldquo; Della luce appena <lb/>accade parlare: non v'ha chi abbia osservata la luce elettrica nel voto, che <lb/>non vi scorga una somiglianza colle colonne lucenti dell'Aurora boreale, che <lb/>accadono attraverso all'ammosfera pi&ugrave; alta ne'luoghi dell'aria meno densa &rdquo; <lb/>(Ediz. </s>

<s>cit., pag. </s>

<s>220, 21). </s></p><p type="main">

<s>Questa somiglianza era senza dubbio la pi&ugrave; seducente di tutte, ma come <lb/>si dimostrava, dall'analogia degli effetti, l'identit&agrave; delle cause? </s>

<s>E nel prin&shy;<lb/>cipal fondamento dell'ipotesi frankliniana come poteva provarsi che i vapori <lb/>equatoriali abbiano elettricit&agrave; contraria a quella de'vapori che si sollevan <lb/>dalla parte di Borea? </s></p><p type="main">

<s>Il prof. </s>

<s>Pierantonio Bondioli si lusing&ograve; di essersi potuto sottrarre a cos&igrave; <lb/>gravi difficolt&agrave;, dicendo che nelle regioni boreali i vapori si sollevano in pi&ugrave; <lb/>gran copia, e sprigionando nel condensarsi l'elettricit&agrave; latente, secondo le nuove <lb/>dottrine insegnate dal Volta, davano origine perci&ograve; cos&igrave; facilmente alle Aurore. </s></p><p type="main">

<s>La Dissertazione, in che si dimostrava la ragionevolezza di questa ipo&shy;<lb/>tesi, fu inviata dall'Autore allo stesso Volta, il quale rispose che com'egli si <lb/>rideva di coloro, che ogni meteora attribuiscono al fluido elettrico senza crite&shy;<lb/>rio; cos&igrave; dubitava, per mancar la prova opportuna, dell'origine elettrica delle <lb/>Aurore, bench&egrave; fosse inclinato a crederlo principalmente &ldquo; per la non piccola <lb/>somiglianza che ravvisiamo nelle fulgurazioni delle celesti Aurore, coi bei <lb/>getti e lampi e trascorrimenti di fuoco elettrico da noi eccitati artificialmente <lb/>ne'recipienti d'aria molto diradata &rdquo; (Opere cit., T. I, P. II, pag. </s>

<s>431, 32). </s></p><p type="main">

<s>Quanto poi al particolare della dottrina dell'elettricit&agrave; latente espressa <lb/>dal subitaneo condensamento de'vapori straordinariamente affollati verso il <lb/>polo, dubitava il Volta se potesse quella stessa dottrina essere opportuna&shy;<lb/>mente applicata a spiegare il fenomeno delle Aurore boreali, per la ragione <lb/>principalmente che queste si formano in regioni molto pi&ugrave; alte di quelle, <lb/>alle quali possono sollevarsi i vapori terrestri. </s>

<s>&ldquo; Questa pressura per&ograve; di <lb/>vapori, a cos&igrave; spiegarmi, che accader deve, se bene si esaminano le cagioni <lb/>fisiche (e accade infatti se ci riportiamo all'osservazione medesima nella bassa <lb/>e nella mezzana regione dell'ammosfera) veggo bene come debba produrre <lb/>le nebbie foltissime e i nuvoloni, i temporali e le grandi burrasche, che <lb/>sono s&igrave; frequenti e s&igrave; terribili in quelle parti del mondo; ma non com&shy;<lb/>prendo ancora come abbiano ad esser causa delle Aurore boreali, le quali <lb/>tengono la loro sede nell'altissima regione, negli ultimi strati e quasi fuora <lb/>dell'ammosfera terrestre, ove, non che affollarsi, non &egrave; credibile che nep&shy;<lb/>pur giungano gli acquei vapori, e seppur ve ne giungono dispersi e a cos&igrave; <lb/>dire raminghi, debbono esser ben pochi &rdquo; (ivi, pag. </s>

<s>433, 34). </s></p><p type="main">

<s>Cos&igrave; veniva il Volta a mettere la diffidenza anche in questa novella ipo&shy;<lb/>tesi germogliata dalle sue stesse scoperte, ma egli, che pur ridevasi di co&shy;<lb/>loro i quali volevan ridurre all'elettricit&agrave; ogni Meteora, non pot&egrave; liberarsi <lb/>da questa scabbia pruriginosa. </s></p><pb xlink:href="020/01/850.jpg" pagenum="293"/><p type="main">

<s>Nelle sue Lettere di Meteorologia elettrica, e pi&ugrave; di proposito in una <lb/><emph type="italics"/>Memoria divisa in tre parti,<emph.end type="italics"/> si propone l'Autore di risolvere alcune gravi <lb/>difficolt&agrave; sul soggetto della formazione della grandine <emph type="italics"/>che &egrave; uno de'pi&ugrave; in&shy;<lb/>tralciati e difficili della Meteorologia<emph.end type="italics"/> (ivi, pag. </s>

<s>304). Il De-Luc era ricorso <lb/>al supposto de'vapori saliti alle altissime regioni, ed ivi congelati in forma <lb/>di fiocchi di neve pi&ugrave; freddi assai della neve ordinaria, sicch&egrave;, cadendo ed <lb/>aggiungendosi ad altri vapori incontrati per via, venissero cos&igrave; a rivestirsi <lb/>di quella loro dura e grossa crosta di ghiaccio. </s>

<s>Ma poi ebbe egli stesso a <lb/>riconoscer falsa questa sua ipotesi, e a congetturar piuttosto che i fiocchetti <lb/>nevosi, i quali diverranno poi i nuclei della grandine, si formino verso l'alto <lb/>della nuvola medesima, merc&egrave; un subitaneo raffreddamento. </s></p><p type="main">

<s>Questa nuova congettura del De-Luc parve ragionevolissima al Volta, <lb/>che la illustr&ograve;, nella prima parte della <emph type="italics"/>Memoria<emph.end type="italics"/> suddetta, coll'esempio del&shy;<lb/>l'agghiacciamento dell'acqua prodotto dall'evaporazione dell'etere solforico, <lb/>e coll'analogia di ci&ograve; che avviene nella macchina idraulica dell'Hell, nella <lb/>quale per subitanea evaporazione un getto di acqua incrosta un fazzoletto, <lb/>o che altro a cui si diriga (ivi, pag. </s>

<s>339). </s></p><p type="main">

<s>Non sembrava al Volta per&ograve; sufficiente, a potere ingrossarsi nella cro&shy;<lb/>sta di ghiaggio il nucleo nevoso, quel s&igrave; breve tempo del suo frettoloso pas&shy;<lb/>saggio attribuitogli dal De-Luc attraverso allo spessor della nube, e giudi&shy;<lb/>cava dall'altra parte gratuita l'opinion di que'Fisici, che fanno cader la <lb/>grandine da tanta altezza quanto &egrave; necessario perch&egrave; si riduca s&igrave; grossa, <lb/>avendo egli anzi osservato che son le nuvole grandinose delle pi&ugrave; basse. </s>

<s>In&shy;<lb/>voca il Volta perci&ograve; i giochi dell'elettricit&agrave; a render la ragione di un fatto, <lb/>ch'&egrave; in questo genere il pi&ugrave; difficile a intendersi di tutti gli altri. </s></p><p type="main">

<s>&ldquo; Immagino io, egli dice, e tengo oramai per certo, che gli embrioni <lb/>della grandine, i quali soglion essere fiocchetti di neve, indi i grani stessi <lb/>gi&agrave; formati e solidi rimangano per lo pi&ugrave; sospesi e saltellanti fra due strati <lb/>di nuvole collocati un sopra l'altro a conveniente distanza, e contrariamente <lb/>elettrici, e ci&ograve;, se accade, per delle ore: durante la qual danza elettrica va&shy;<lb/>dano essi grani rivestendosi di nuove lamine di ghiaccio, e s'ingrossi cos&igrave; <lb/>mano mano la loro crosta. </s>

<s>Questo bel gioco &egrave; assai curioso dei grani di <lb/>grandine che vanno su e gi&ugrave; frequenti e tumultuosi tra due quasi tavole <lb/>di nubi; gioco da me immaginato per render ragione del pi&ugrave; difficile a in&shy;<lb/>tendersi dei suoi fenomeni, che &egrave; la tanta grossezza a cui pervengono non <lb/>di rado tali grani &rdquo; (ivi, pag. </s>

<s>429). </s></p><p type="main">

<s>Se fosse stato questo bel gioco della danza elettrica fra le nubi una <lb/>realt&agrave;, si sarebbe reso il Volta, co'paragrandini, non men benemerito del <lb/>genere umano, di quel che non si fosse reso benemerito il Franklin co'suoi <lb/>parafulmini; ma essendosi quel gioco ritrovato una immaginazione, riman <lb/>tuttavia a cercar l'origine della grandine, e dove tenda, la nostra crudel <lb/>nemica, e com'ella esca fuori da'suoi freddi agguati. </s></p><pb xlink:href="020/01/851.jpg" pagenum="294"/><p type="main">

<s><emph type="center"/>CAPITOLO VIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle Meteore<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle sublimazioni de'vapori vescicolari e de'loro condensamenti in pioggia. </s>

<s>&mdash; II. Dell'origine <lb/>de'venti in generale, e in particolare de'venti tropicali. </s>

<s>&mdash; III. </s>

<s>Delle variazioni, che subisce il <lb/>Barometro al vario stato del cielo. </s>

<s>&mdash; IV. </s>

<s>Delle Effemeridi meteorologiche del Ramazzini; delle <lb/>variazioni barometriche prodotte dallo spirare dei venti, e dall'appressarsi delle procelle. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Le folgori, le Aurore boreali, i nembi grandinosi, intorno a che eser&shy;<lb/>citarono i loro studi gli elettricisti, appartengono a quell'ordine di fatti na&shy;<lb/>turali, a cui fu dato il nome di Meteore infino da'Filosofi pi&ugrave; antichi. </s>

<s>La <lb/>Meteorologia per&ograve;, bench&egrave; possa vantarsi dell'antichit&agrave; del nome, fu da quegli <lb/>stessi antichi Maestri men coltivata delle altre scienze sorelle, le quali non <lb/>progredirono, per non si saper l'arte, e per non avere strumenti da osser&shy;<lb/>vare i fatti naturall, mentre alla Meteorologia restava, di pi&ugrave;, difficile anche <lb/>l'osservare quegli stessi fatti, i quali avvengono in regioni troppo lontane <lb/>dalla corta apprensiva de'nostri sensi. </s></p><p type="main">

<s>Ma perch&egrave; questa &egrave; una tal difficolt&agrave;, che riman tuttavia e rimarr&agrave; in&shy;<lb/>fintantoch&egrave; l'uomo non impenner&agrave; l'ali per salire a sedersi sul dorso delle <lb/>nubi, non ha perci&ograve; la scienza delle Meteore, a progredire, altro modo che <lb/>quello d'imitar con l'arte, in questi bassi fondi, ci&ograve; che s'opera dalla Na&shy;<lb/>tura ne'suoi sublimi teatri, e d'argomentare all'identit&agrave; della causa dalle <lb/>somiglianze riscontratesi negli effetti. </s>

<s>Tale in vero &egrave; la ragione di tutte le <lb/>meteorologiche scoperte che si son fatte, e tale &egrave; stato sempre il processo <lb/>che tennero i Fisici per farle. </s>

<s>Cos&igrave; i colori prodotti dalle rifrazioni de'raggi <pb xlink:href="020/01/852.jpg" pagenum="295"/>solari, ne'globi di vetro pieni di acqua, dettero facile modo a intender la <lb/>generazione dell'Iride, e i cilindretti di vetro, co'loro nuclei opachi, se non <lb/>valsero a sodisfarla, acquietarono la curiosit&agrave; di coloro, che ardevano di sa&shy;<lb/>pere in che si facessero specchio il Sole e la Luna per incoronarsi di luce <lb/>avventizia, e moltiplicare all'intorno la loro sembianza. </s>

<s>Allo stesso modo, <lb/>nel crepitar della scintilla elettrica, si intravide la ragione de'tuoni e de'ba&shy;<lb/>leni, e l'effusion del lume dentro i globi di vetro, vuoti d'aria ed elettriz&shy;<lb/>zati, pass&ograve;, in mancanza d'altro, per una spiegazione delle misteriose Au&shy;<lb/>rore boreali. </s></p><p type="main">

<s>Di tutte queste, che appartengono alle Meteore elettriche luminose, <lb/>narrammo a parte a parte ne'capitoli precedenti la storia, dalla quale si <lb/>mostra che la difficolt&agrave; d'intendere la ragion di que'fatti dipendeva in parte, <lb/>come dicemmo, dal non se ne poter far soggetto di osservazioni dirette. </s>

<s>Ma <lb/>il forte della difficolt&agrave;, a ripensarla meglio, si riduceva a due capi: a saper <lb/>trovar l'artificio che imiti la Natura, e ad assicurarsi che quel tale artificio <lb/>&egrave; veramente imitativo della Natura. </s>

<s>Che qui principalmente, e n&ograve; nell'im&shy;<lb/>possibilit&agrave; di osservare i fatti in s&egrave; stessi, riseggano le difficolt&agrave; che s'in&shy;<lb/>contrano nel risolvere i problemi di Meteorologia, si mostrer&agrave; da ci&ograve; che <lb/>occorse a pensare e a dire intorno all'origine delle piogge e de'venti. </s>

<s>Que&shy;<lb/>ste che sono delle Meteore pi&ugrave; comuni, bench&egrave; abbiano in alto i loro prin&shy;<lb/>cipii, hanno pure in terra e presso a noi i loro termini e i loro effetti, e <lb/>nonostante, tanto si pen&ograve; a intenderne le ragioni, perch&egrave; non si seppe tro&shy;<lb/>var nell'arte il modo d'imitar la natura, o trovato, non si seppe almeno in <lb/>tutto riscontrarvene la somiglianza. </s></p><p type="main">

<s>La ragione della produzion delle pioggie dipende e si conclude per pi&ugrave; <lb/>altre ragioni, le quali si riducono a saper come mai si sollevino i vapori <lb/>acquosi dalla terra, e come sollevati si condensino, s'accrescano notabilmente <lb/>di mole, e cos&igrave; poi tornino in pioggia. </s>

<s>Il fatto di tali sublimazioni, che de&shy;<lb/>ducevasi con certezza dal vedersi i vapori scender gi&ugrave; d'onde e'non pos&shy;<lb/>sono aver le loro sedi naturali, Galileo lo dimostrava rendendolo visibile at&shy;<lb/>traverso i vetri del Canocchiale, e nella maniera seguente pensava che, giunti <lb/>i vapori stessi a un'altezza ch'&egrave; il termine del purissimo nostro etere am&shy;<lb/>biente, potessero per la loro accresciuta mole cadere in gocciole piovose. <lb/></s>

<s>&ldquo; Essendo che dalla terra si sollevano continuamente esalazioni sottili, tenui, <lb/>ascendenti, e intanto si portano seco vapori pi&ugrave; grossi ed acquei, ed arri&shy;<lb/>vati a un'altezza, che &egrave; il termine dell'etere nostro ambiente e l'aria pu&shy;<lb/>rissima, si dilatano, si distendono e si trattengono o calano abbasso, dopo <lb/>essersi fatta una costipazione o spessitudine di questi vapori, e cos&igrave; si fanno <lb/>le piogge. </s>

<s>Ma non so in che maniera, quando &egrave; un tempo serenissimo, <lb/>chiaro, e's'abbia subitamente a rannuvolare ogni cosa, farsi grande oscurit&agrave; <lb/>e venir milioni di botti d'acqua a basso. </s>

<s>&mdash; Che continuamente si sollevino <lb/>vapori si fa manifesto in pi&ugrave; maniere, poich&egrave; gittando in terra un po'd'acqua, <lb/>e guardando con l'Occhiale, si vede salir con prestezza un fumo, un vapore, <lb/>e si fa manifesto nella fiamma che continuamente, e con gran velocit&agrave;, si <pb xlink:href="020/01/853.jpg" pagenum="296"/>vede salire ad alto, e cos&igrave; nei carboni accesi quel vapore va ad alto &rdquo; (MSS. <lb/>Gal., P. V, T. IV, c. </s>

<s>28). </s></p><p type="main">

<s>Cos&igrave; presumevasi Galileo di render visibili quelle esalazioni umide e <lb/>secche sollevate su dall'acqua e dal fuoco, ch'egli accolse con troppa doci&shy;<lb/>lit&agrave; dalla Filosofia peripatetica, introducendo cos&igrave; nel suo proprio insegna&shy;<lb/>mento dottrine contradittorie. </s>

<s>Egli infatti negava ad Aristotile il principio <lb/>della leggerezza positiva, affermando che tutti i corpi son gravi, e che se <lb/>talvolta, invece di cadere, salgono, ci&ograve; da nient'altro dipende che dalla cir&shy;<lb/>cumpulsione del mezzo. </s>

<s>Ma o Galileo non credeva l'ignee esalazioni appar&shy;<lb/>tenessero alla materia, o faceva per esse esalazioni una particolare eccezione <lb/>dalle propriet&agrave; comuni de'corpi, professando ch'elle son naturalmente di&shy;<lb/>sposte a salire, e che sono anzi esse stesse che sublimano la materia vapo&shy;<lb/>rosa, quasi portandola sulla leggerezza delle ali. </s></p><p type="main">

<s>Si potrebbero forse salvar le dottrine galileiane dicendo che si teneva <lb/>da esso le ignee esalazioni esser di cos&igrave; tenue materia, da riuscire incom&shy;<lb/>parabilmente men gravi in specie dell'etere purissimo o di qual si voglia <lb/>altra sostanza pi&ugrave; sottile, ma non &egrave; possibile, in ogni modo, salvare intorno <lb/>a ci&ograve; Galileo dall'imputazione di avere strascicato per la trita polvere peri&shy;<lb/>patetica il suo dignitoso pallio filosofale. </s>

<s>Pi&ugrave; grave danno si fu che si tra&shy;<lb/>dussero cos&igrave; fatte immaginate dottrine delle esalazioni umide e secche, <lb/>dall'autorit&agrave; di un tanto maestro, nella docilit&agrave; de'discepoli, i quali sul fon&shy;<lb/>damento degl'insegnamenti galileiani elaborarono, intorno alla generazione <lb/>e alla produzion delle piogge, un sistema, che ha molto del singolare. </s></p><p type="main">

<s>S'immaginava dunque il Borelli che le esalazioni ignee, moventisi dalle <lb/>parti centrali del Globo, sollevassero in alto i vapori, e cos&igrave; sotto terra des&shy;<lb/>sero origine alle fonti, e usciti sopra terra producessero le piogge. </s>

<s>Suppo&shy;<lb/>neva inoltre che tali sublimazioni procedessero reciprocamente veloci alla <lb/>densit&agrave; de'mezzi via via attraversati, cosicch&egrave; velocissime fossero col&agrave;, dove <lb/>l'etere &egrave; sottilissimo, e anzi tanto veloci, che, non reggendo dietro a loro <lb/>la gravezza de'vapori, rimanessero ivi abbandonati e perci&ograve; costretti a ca&shy;<lb/>dere, come corpo a cui vien mancando chi lo sostenti. </s>

<s>Pi&ugrave; singolare &egrave; poi, in <lb/>questo filosofico romanzetto, il modo come s'immaginava che le tenui vesci&shy;<lb/>cole vaporose venissero a ingrossarsi in gocciole d'acqua. </s>

<s>Si ricorreva niente <lb/>di meno che al convergere che fanno le fila piovose verso il centro della Terra, <lb/>a cui si studiano di giunger cadendo, andandovi sempre pi&ugrave; fra s&egrave; ristrette <lb/>e condensate. </s>

<s>Ma perch&egrave; tanto hanno cos&igrave; fatte cose dello strano, che difficil&shy;<lb/>mente si crederebbe essere state pensate dal Borelli e accolte dal Viviani e <lb/>dagli altri Accademici fiorentini, trascriveremo qui, nella forma propria in cui <lb/>venne disteso, quello che si qualificava da noi per un filosofico romanzetto: </s></p><p type="main">

<s>&ldquo; Dalla controversia, d'onde l'origine avessero le fonti, pass&ograve; l'Ecc.mo<lb/>signor Borelli a dar la sua opinione circa l'origine delle piogge, e non altra <lb/>essere alla fine concluse che la medesima, la quale dello scaturire le fonti <lb/>&egrave; cagione. </s>

<s>La ragione che egli medesimo, s'io ben mi ricordo, n'adduce &egrave; <lb/>la presente: che cio&egrave; gli artefici, nello scavar che fanno sotto terra per <pb xlink:href="020/01/854.jpg" pagenum="297"/>molte canne per ritrovar la miniera, sanno precisamente quando di sopra <lb/>vuol piovere, ed asseriscono ci&ograve; devenire nel veder loro passare fumi e sen&shy;<lb/>tire caldo non ordinario. </s>

<s>Bisogna dunque dire che quelle esalazioni congiunte <lb/>con particelle acquee sormontino al cielo, e dieno a vedere quel fumo e a <lb/>sentire quel caldo. </s>

<s>Contrariano per&ograve; alcuni Filosofi alla gi&agrave; detta opinione, <lb/>non volendo che l'origine delle piogge sia questa, ma un'altra ne asseri&shy;<lb/>scono ed adducono essi, la quale non sar&agrave; discaro l'esaminarla. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Dicono dunque che il sole, con i suoi raggi, come con una tromba, <lb/>attinge dal mare l'acqua, la quale condotta ad una tal regione dell'aria, co&shy;<lb/>lass&ugrave; in nuvole si riduce, e abbandonata poi dal medesimo sole, cadendo a <lb/>basso, cagiona le piogge. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quante e quali difficolt&agrave; patisca questa opinione ciascuno, anco d'in&shy;<lb/>gegno ordinario, potr&agrave; conoscere, e prima, gi&agrave; di sopra si &egrave; detto che il <lb/>sole &egrave; inabile da per s&egrave; stesso a tirare all'ins&ugrave; particelle acquee, poich&egrave; se <lb/>noi, di state tempo, nel quale il sole ha pi&ugrave; ardenti i suoi raggi, scaveremo <lb/>sotto terra quattro o sei braccia, troveremo la terra di sotto molto pi&ugrave; umida <lb/>che sopra abbondantemente; segno chiaro che il sole con i suoi raggi non <lb/>ci penetra, come nelle cantine e nelle ghiacciaie, dove si conserva la neve <lb/>e il diaccio nel medesimo tempo di state. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma dicono essi che non altrimenti dalla terra, ma dal mare, vien con&shy;<lb/>tribuito al sole l'umido. </s>

<s>Io perci&ograve; non resto consapevole come, ne'paesi lon&shy;<lb/>tanissimi dal mare, s'abbino a veder continuamente le piogge condotte sopra <lb/>le spalle dai raggi del sole quattro o cinquecento miglia, e ne'paesi vicinis&shy;<lb/>simi al mare, e dove il calor del sole &egrave; veementissimo, come nell'Egitto, <lb/>non abbia a piover mai: come di estate non piova molto pi&ugrave; che nell'in&shy;<lb/>verno, nel tempo della quale i raggi sono molto pi&ugrave; cocenti che in verun <lb/>altro tempo, ed insomma per molte e molte altre difficolt&agrave;, che per non per&shy;<lb/>dere tanto male il tempo tralascio, si dovrebbe vedere il contrario di quello <lb/>che alla giornata ne segue. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Tornando dunque al nostro proposito tale esser l'origine delle fonti <lb/>io stimo, quale dal signor dott. </s>

<s>Giov. </s>

<s>Alfonso dimostrata ne viene, ma vedo <lb/>gi&agrave; contro di me inalzarsi un Peripatetico, non volendo partirsi invendicato <lb/>con addurre difficolt&agrave; indissolubili contro l'apportata opinione. </s>

<s>Dice egli che <lb/>se &egrave; la medesima la causa delle piogge, che quella delle fonti, si dovrebbe <lb/>vedere, avanti che cominci la pioggia, sgorgare in maggior profluvio la fonte, <lb/>poich&egrave; le particelle acquee trasportate dalle esalazioni ignee molto pi&ugrave; presto <lb/>arrivano alla fonte che alle supreme regioni dell'aria, d'onde devono poi <lb/>partirsi e cadere in terra, sicch&egrave;, dovendo esse far molto pi&ugrave; lungo viaggio <lb/>in un luogo che in un altro, dovrebbero prima sgorgar pi&ugrave; copiosamente le <lb/>fonti, e poi cagionarsi le piogge. </s>

<s>Difficolt&agrave; invero degna di considerazione e <lb/>adattata, se per&ograve; fosse in campo apportata da chi non avesse veduto ci&ograve; che, <lb/>circa all'origine delle fonti, di sopra si &egrave; detto; cio&egrave; che esse hanno neces&shy;<lb/>sit&agrave; di qualche preminenza che gli sovrasti, non potendo esse nascere in un <lb/>piano lontanissimo da'monti o sopra la cima d'un monte. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/855.jpg" pagenum="298"/><p type="main">

<s>&ldquo; Avvertasi dunque ch'essendo molto spessi gli anfratti del monte, dove <lb/>si generano le fontane, possono le particelle acquee molto veloci nell'aria <lb/>camminare assai pi&ugrave; presto per quel mezzo, che non fanno le particelle <lb/>acquee, per il mezzo della terra, poich&egrave;, se si pone un vaso pieno d'acqua <lb/>e il fondo turato con terra, l'acqua di dentro tardissimamente andr&agrave; pas&shy;<lb/>sando, e quasi incomprensibilmente per la terra, sicch&egrave;, per i molti anfratti <lb/>che si trovano per la terra, queste particelle acquee son ritardate, e ci&ograve; aper&shy;<lb/>tamente si vede, poich&egrave;, nell'istesso tempo che segue la pioggia, si vedono <lb/>crescere le fonti, argomento certissimo essere la medesima la cagione. </s>

<s>N&egrave; <lb/>dicasi che il crescere delle fonti venga dall'acqua che piove, poich&egrave; ci&ograve; ne <lb/>dimostra falso l'esperienza certa. </s>

<s>Imperocch&egrave; se, dopo che sar&agrave; seguita la <lb/>pioggia, in maniera tale che sien cresciute le fonti, cominci a scalzarsi e a <lb/>scortecciarsi la terra per due o tre braccia, si trover&agrave; la terra non essere di <lb/>sotto quasi bagnata. </s>

<s>Adunque, se sotto tre braccia di terra non &egrave; passata <lb/>l'acqua, come pu&ograve; essere che sia passata all'origine delle fonti, la quale <lb/>&egrave; molto pi&ugrave; sotterranea? </s>

<s>Sar&agrave; dunque certissimo argomento questo la me&shy;<lb/>desima esser l'origine delle fonti e delle piogge. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; &mdash; In qual maniera poi queste moli composte d'esalazioni ignee e <lb/>particelle acquee sormontano invisibilmente a noi, e poi tornano a basso in <lb/>s&igrave; gran copia, che ne formino le piogge? </s>

<s>&mdash; Per dunque meglio intendere <lb/>questa naturale operazione, intendasi per la superficie della Terra la linea <lb/>ACDB (fig. </s>

<s>63), dalla quale si partano le moltissime linee CD verso EF. <lb/><figure id="id.020.01.855.1.jpg" xlink:href="020/01/855/1.jpg"/></s></p><p type="caption">

<s>Figura 63.<lb/>Giunte che saranno queste particelle in EF, spazio <lb/>lontano per qualche miglio dalla superficie della Terra; <lb/>onde molto maggiore sar&agrave; la circonferenza della linea EF <lb/>rappresentante le altissime regioni dell'aria, che la su&shy;<lb/>perficie CD. </s>

<s>Per lo che le particelle arrivate alla su&shy;<lb/>perficie EF, nel tornar che faranno, s'andranno restrin&shy;<lb/>gendo, e per conseguenza accrescendosi in mole con <lb/>moltiplicarsi l'una sopra l'altra, talch&egrave; poi, arrivate alla <lb/>superficie terrestre, si saranno fatte a quella mole che <lb/>si vede. </s>

<s>Inoltre, quello che maggiormente convince &egrave; <lb/>che, quando le particelle si partirono dalla superficie <lb/>terrestre, erano piccolissime, e per conseguenza invi&shy;<lb/>sibili, ma nel tornar che fanno, avendone seco dietro <lb/>tirate dell'altre, che si vanno incontrando con quelle, conseguentemente si <lb/>accrescono, e possono accrescersi non solo mille, ma duemila volte e pi&ugrave; an&shy;<lb/>cora, come la linea &egrave; maggior d'un suo punto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Resta solo dunque da investigarsi in qual maniera si faccia la sepa&shy;<lb/>razione delle particelle acquee dalle esalazioni ignee, la quale, acci&ograve; meglio <lb/>da noi esser possa conosciuta, necessario &egrave; fermare due principii: l'uno dei <lb/>quali ancora dagli avversarii &egrave; conceduto, cio&egrave; che, allontanandosi vie pi&ugrave; <lb/>dalla Terra, un elere pi&ugrave; puro si vada incontrando; l'altro che i corpi pi&ugrave; <lb/>duri mantenghino pi&ugrave; lungamente il caldo, come chiaro ne mostra l'espe-<pb xlink:href="020/01/856.jpg" pagenum="299"/>rienza. </s>

<s>Imperocch&egrave;, se noi piglieremo un sasso ed un vaso d'acqua, e ambi <lb/>gli faremo ugualmente caldi, l'acqua durer&agrave; per brevissimo tempo a con&shy;<lb/>servare il suo calore, ma il sasso per un'ora o due l'andr&agrave; conservando. </s>

<s>E <lb/>similmente si dice dell'aria e dell'acqua, e la ragione &egrave; che pi&ugrave; facilmente <lb/>passano gli spiriti ignei, parti minime del fuoco, per un mezzo men duro, <lb/>che per un mezzo pi&ugrave; duro, onde nell'aria velocissimamente traspirano. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Supposte dunque queste cose, chiaramente si conosce la cagione per&shy;<lb/>ch&egrave; e in qual maniera si faccia la separazione delle particelle acquee dalle <lb/>esalazioni ignee, essendoch&egrave; l'aria vicinissima alla terra, come molto vapo&shy;<lb/>rosa e quasi densa, fa che molto lentamente per il di lei mezzo passino <lb/>l'esalazioni ignee, e per conseguenza, movendosi esse tardamente, seco ne <lb/>conducono le particelle acquee, ma arrivando ove l'aria &egrave; pi&ugrave; pura, l'esa&shy;<lb/>lazioni, movendosi pi&ugrave; velocemente, sono abbandonate dalle particelle acquee, <lb/>le quali non possono seguitarle con la medesima velocit&agrave; &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. CXXXVI, c. </s>

<s>6-8). </s></p><p type="main">

<s>Son tali quali gli abbiamo veduti, per queste pagine manoscritte rac&shy;<lb/>colti, i frutti degl'insegnamenti galileiani, n&egrave; quegli altri derivati dalla scuola <lb/>cartesiana son per verit&agrave; punto migliori. </s>

<s>Il cap. </s>

<s>V delle Meteore &egrave; riserbato <lb/>dal Cartesio a trattar <emph type="italics"/>De nubibus,<emph.end type="italics"/> le quali son generate dai vapori coatti e <lb/>condensati. </s>

<s>Si sublimano, secondo il Filosofo, questi vapori, perch&egrave; si dila&shy;<lb/>tano, e la <emph type="italics"/>materia sottile,<emph.end type="italics"/> che gl'involge tutt'intorno e gli preme ugual&shy;<lb/>mente per ogni parte, &egrave; che gli riduce in quella figura di squisitissime sfe&shy;<lb/>rette rotonde. </s>

<s>Sollevate che si sono cos&igrave; fatte sferule vaporose, a farle ricadere <lb/>in terra vi conferisce l'aria, la quale, dilatandosi al di sotto, fa passare at&shy;<lb/>traverso a s&egrave; la pioggia crivellata in minutissime gocciole; gocciole che al <lb/>contrario scendono assai pi&ugrave; grosse, quando l'aria preme solamente al di <lb/>sopra della nube. </s></p><p type="main">

<s>&ldquo; Nunc autem, ex iis quae diximus, facile intelligitur qua ratione nubes <lb/>solis aquae guttis constantes depluant, nempe vel pondere proprio, cum gut&shy;<lb/>tae satis crassae sunt; vel cum aer inferior recessu vel superior incursu illas <lb/>ad descensum invitat, vel etiam quando plures ex his causis simul concur&shy;<lb/>runt. </s>

<s>Atque inferiori aere se contrahente pluvia maxime minuta, et veluti <lb/>rorans generatur; imo aliquando adeo minuta est, ut saepissime delabentem <lb/>non pluviam sed nebulam potius dicamus; magna contra, seu grandibus <lb/>guttis colligitur, quoties nubes solo aere superiori pressa descendit; subli&shy;<lb/>mes enim illius guttarum primo delapsae, alias in via inveniunt quibus <lb/>crassescunt &rdquo; (Francofurti ad M. 1692, pag. </s>

<s>164). </s></p><p type="main">

<s>Mentre per&ograve; la maggior parte de'Fisici seguitava la meteorologia peripa&shy;<lb/>tetica galileiana delle esalazioni umide e secche, e altri, anche in Italia, si <lb/>lasciavano affascinare alle eloquenti fantasie del Cartesio, rimanevano, per <lb/>onor della scienza, alcuni pochi eletti ingegni fra noi che, a'sistemi de'nuovi <lb/>celeberrimi Maestri, preferivano le verit&agrave; dimostrate nelle solitarie Specula&shy;<lb/>zioni del Benedetti. </s>

<s>In conformit&agrave; di queste cos&igrave; pensava il Baliani intorno <lb/>a ci&ograve; che d&agrave; origine e che produce la pioggia: &ldquo; L'acqua &egrave; pi&ugrave; densa, pi&ugrave; <pb xlink:href="020/01/857.jpg" pagenum="300"/>grave, ma &egrave; liquida, cio&egrave; a dire ha le porzioni minime disgiunte fra loro, <lb/>onde il calore, per poco che sia, penetrandola agevolmente la muove, ed in <lb/>piccole vescichette una parte successivamente ne converte, che per farsi <lb/>perci&ograve; pi&ugrave; rara di gran lunga che il rimanente, e perci&ograve; divenuta leggera, <lb/>s'inalza e sale in aria ed &egrave; detta vapore, che non &egrave; altro che una massa di <lb/>bollicine acquee, le quali per esser formate di materia si liquida, agevol&shy;<lb/>mente si spezzano, ondc picciol tempo durano, e di nuovo in acqua, ossia <lb/>in pioggia, si risolvono &rdquo; (Della Pestilenza, Savona 1647, pag. </s>

<s>37). </s></p><p type="main">

<s>L'illustre Genovese, che della Fisica sperimentale e segnatamente della <lb/>Meteorologia &egrave; molto pi&ugrave; benemerito del gran Galileo, conosceva bene che, <lb/>a voler trattar per scienza della pioggia, conveniva dimostrare due cose: <lb/>prima, come mai i vapori acquosi, pi&ugrave; gravi in specie, si sollevino per l'aria, <lb/>e poi in che modo questi stessi vapori si condensino, condensandosi ingros&shy;<lb/>sino, e cos&igrave; ingrossati in gocciole, tornino, per la loro natural gravezza, a <lb/>cadere sotto forma di pioggia. </s>

<s>Ardue al Baliani parvero ambedue queste di&shy;<lb/>mostrazioni, e non osando pur di provarsi intorno alla seconda, tanto lon&shy;<lb/>tano dall'immaginare che si potesse un giorno ridurre a soggetto di espe&shy;<lb/>rienza, cos&igrave; lasciava scritto in che modo egli avrebbe pensato che si potessero <lb/>diminuire le difficolt&agrave; della prima: </s></p><p type="main">

<s>&ldquo; Ma di qual mezzo si vaglia la Natura e qual maniera ella usi, ac&shy;<lb/>ciocch&egrave; la bolla si riduca a tanta leggerezza che possa salir da s&egrave;, non mi <lb/>riesce cos&igrave; facile a comprendere, cio&egrave; a dire com'esser possa pi&ugrave; grave l'aria <lb/>semplice, che un composto d'aria e d'acqua, per quanto ella si assottigli, e <lb/>come possa racchiudersi nell'acqua una sostanza tanto pi&ugrave; dell'aria leggera, <lb/>che la massa d'ambedue, stando non pur nell'acqua ma nell'aria, in su se <lb/>ne vola. </s>

<s>Mi &egrave; caduto nel pensiero cosa, che a prima giunta parr&agrave; strana, <lb/>che tal sostanza sia fuoco o lume che dir vogliamo &rdquo; (ivi, pag. </s>

<s>27). </s></p><p type="main">

<s>Persuaso perci&ograve; il Montanari questa del Fisico genovese essere vera&shy;<lb/>mente un'idea strana, ricorse all'aiuto delle agitazioni dell'aria, per le quali, <lb/>come si vede rimaner sospeso il pulviscolo delle materie terree e degli <lb/>stessi metalli, cos&igrave; argomentava che potessero per ugual ragione rimanervi <lb/>in mezzo sospesi i vapori. </s>

<s>Pi&ugrave; efficace poi, soggiungeva, dover riuscire in <lb/>produrre il misterioso effetto la causa da s&egrave; escogitata, aggiungendo ai tur&shy;<lb/>binamenti intestini la continua irrequieta agitazione dei venti. </s></p><p type="main">

<s>&ldquo; Io mi avveggo di proporre a V. S. </s>

<s>Illustrissima (scriveva al Sampieri <lb/>in una Lettera aggiunta ai <emph type="italics"/>Pensieri fisico-matematici<emph.end type="italics"/>) un paradosso, poich&egrave; <lb/>tale ella lo creder&agrave; facilmente, se per l'avanti ella s'era sodisfatta del modo, <lb/>con che altri spiegano questo sollevarsi delle particelle dell'acqua, come sa&shy;<lb/>rebbe l'acutissimo Cartesio, che le fa aggirare dai globuli di quel suo se&shy;<lb/>condo elemento, oppure il Bagliani, che a guisa d'ampollette le fa gonfiare <lb/>dall'interno calore, o altri che congiungendole con particole di fuoco le fanno <lb/>ascender per l'aria in quel modo, che piombo congiunto al sughero sormon&shy;<lb/>terebbe per l'acqua.... Io non contradico a si grandi uomini; ... dico per <lb/>tanto che, avendo veduto che l'acqua, in fondo della quale sia alcuna sot-<pb xlink:href="020/01/858.jpg" pagenum="301"/>tilissima polvere,.... facilmente la intorbida,.... che le minime particelle <lb/>di quella polvere non hanno di bisogno n&egrave; di gonfiarsi, n&egrave; d'attaccarsi ad <lb/>altre particole dell'acqua pi&ugrave; leggeri,.... e quindi essendomi caduto in <lb/>mente potere in qualche modo simile sollevarsi nell'aria non solo le parti&shy;<lb/>celle dell'acqua, ma le terrestri ancora pi&ugrave; sottili,.... il sollevarsi delle <lb/>quali fu anche osservato doversi al moto dell'aria dal nobilissimo e dottis&shy;<lb/>simo Bagliani, ne'dottissimi opuscoli ultimamente da lui stampati;.... final&shy;<lb/>mente mi posi a speculare alle ragioni perch&egrave; possino cio&egrave; tali minime par&shy;<lb/>ticelle sollevarsi in aria, e quivi dipoi.... trattenersi senza piombare a basso, <lb/>tuttoch&egrave; siano di essa aria pi&ugrave; gravi in specie.... &rdquo; </s></p><p type="main">

<s>&ldquo; Molte considerazioni mi persuadono verisimile che eziandio, senz'al&shy;<lb/>tr'opera del calore, fuor di quella che agita l'acqua in diverse maniere, pos&shy;<lb/>sano le particole de'fluidi andarsi separando lentamente, giusta la viscosit&agrave; <lb/>loro, dalle loro superficie, attaccandosi alle particelle dell'aria che li preme, <lb/>e mediante l'agitazione dell'aria medesima, che vediamo infatti continua&shy;<lb/>mente turbinarsi in mille modi in s&egrave; stessa, sollevarsi con essa lei, &igrave;n quel <lb/>modo appunto che con l'acqua si sollevano i torbidumi, qualora ella viene <lb/>agitata, e sollevati trattenervisi senza potere per la piccolezza loro scendere <lb/>a basso. </s>

<s>E quando pure mi negasse alcuno che fossero questi minimi del&shy;<lb/>l'acqua cos&igrave; piccoli, che non potessero superare la viscosit&agrave; che ha in s&egrave; <lb/>l'aria, io sebbene potrei mostrar loro quegli atomi terrei, che, come dissi, <lb/>si veggono ne'raggi solari, e che pure sono maggiori e pi&ugrave; pesanti degl'in&shy;<lb/>visibili minimi dell'acqua; nulladimeno aggiungerei che, quando pur fosse <lb/>vero ci&ograve; che dicono, a me basterebbe che fossero tali che di poco la supe&shy;<lb/>rassero, posciach&egrave;, aggiuntavi all'incontro la continua agitazione dell'aria <lb/>medesima, l'intenderessimo ascendere non meno che si facciano le vesciche <lb/>dell'acqua saponata..... &rdquo; </s></p><p type="main">

<s>&ldquo; Che se per sorte alla forza che ha l'aria col suo peso ed al moto <lb/>naturale, che tale chiameremo quello con che ella, anco quando &egrave; rinchiusa, <lb/>va in s&egrave; stessa volutandosi, s'aggiungono l'esterne cause, che ponno con&shy;<lb/>correre a questo sollevarsi de'vapori; non ha dubbio che pi&ugrave; facilmente e <lb/>in maggior copia s'alzeranno, onde si vede che il vento ha cos&igrave; gran parte <lb/>nell'essiccare le cose bagnate &rdquo; (Bologna 1667, pag. </s>

<s>67-83). </s></p><p type="main">

<s>Il Guglielmini, secondando gl'insegnamenti del suo illustre Maestro, <lb/>soggiungeva alla ragion fisica addotta da lui l'altra derivata dalla Geometria, <lb/>conforme alla quale attenuandosi le particelle vaporose in modo, che il loro <lb/>peso assoluto scemi con assai minor proporzione di quel che non scemi la <lb/>superficie, vengon per il contatto, cos&igrave; sproporzionatamente divenuto mag&shy;<lb/>giore, a trovar maggiore la resistenza dell'aria che debbon fendere, e cos&igrave; <lb/>con facilit&agrave; vi rimangon sospese. </s>

<s>Condensandosi in gocciole, minore &egrave;, per <lb/>la ragion contraria alla sopra detta, la resistenza che quelle stesse gocciole <lb/>hanno da superare, e perci&ograve; cadono a terra pi&ugrave; facilmente. </s>

<s>&ldquo; Unendosi in&shy;<lb/>sieme pi&ugrave; particelle d'acqua viene il composto a crescere di peso assoluto <lb/>pi&ugrave; di quello s'accresca la di lui superficie, e conseguentemente viene a sce-<pb xlink:href="020/01/859.jpg" pagenum="302"/>marsi in proporzione la resistenza; quindi &egrave; che successivamente accresciuta <lb/>la potenza operante, e scemata maggiormente in proporzione la resistente, <lb/>&egrave; necessario che finalmente la prima superi la seconda, e perci&ograve; che l'acqua <lb/>discenda per l'aria. </s>

<s>Questi effetti della separazione ed unione delle particelle <lb/>dell'acqua sono da noi cotidianamente osservati nell'ascendere che fanno i <lb/>vapori e nel cadere delle piogge &rdquo; (Della Natura de'fiumi, T. I, Milano 1821, <lb/>pag. </s>

<s>146). </s></p><p type="main">

<s>Fu questa, dopo Galileo, la ragione che principalmente s'adduceva dal <lb/>Guglielmini e dagli altri, non solo dell'intorbidamento delle acque de'fiumi <lb/>e del loro chiarificarsi, ma delle soluzioni e delle precipitazioni delle sostanze <lb/>saline e metalliche ne'mestrui liquidi specificamente pi&ugrave; leggeri. </s>

<s>Venne per&ograve; <lb/>presto l'Hawksbee a ingerire un molesto sospetto in quella pace di fede, in <lb/>che tranquillamente riposava la Scienza. </s>

<s>Se il galleggiamento delle parti&shy;<lb/>celle dell'oro, nell'acqua regia, discorreva il grande Fisico inglese, dipende <lb/>da quel grande accrescimento delle superficie ne'piccoli corpi, a propor&shy;<lb/>zione della loro mole &ldquo; avrebbe dovuto necessariamente apparire qualche <lb/>parte di questa grandissima differenza dal pesare quantit&agrave; eguali di mate&shy;<lb/>ria, e perci&ograve; egualmente gravi, ma di superficie molto diseguali, nell'acqua <lb/>o in qualche altro liquido, e allora vedere col&agrave; quanto l'una eccedesse l'altra <lb/>di peso &rdquo; (Esper. </s>

<s>fisico-meccan., Traduz. </s>

<s>ital., Firenze 1716, pag. </s>

<s>148). </s></p><p type="main">

<s>Venuto alle esperienze trov&ograve; che quella differenza stimata da tutti gran&shy;<lb/>dissima era invece cos&igrave; piccola, che non meritava d'esser messa nemmeno <lb/>in conto, ond'egli ebbe a concluderne altra dover esser la causa del gal&shy;<lb/>leggiamento de'corpi gravi ne'mezzi pi&ugrave; leggeri. </s>

<s>Pens&ograve; l'Hawksbee che <lb/>potesse una tal causa risedere nell'attrazione molecolare, saviamente ragio&shy;<lb/>nando che la superficie cresciuta in maggior proporzione nella piccola mole, <lb/>ne rendesse pi&ugrave; esteso il contatto colle particelle del mezzo ambiente, e cos&igrave; <lb/>per l'aumentata intensit&agrave; delle forze attrattive pi&ugrave; difficile si rendesse la se&shy;<lb/>parazione del corpicciolo dissoluto dal suo mezzo solvente. </s></p><p type="main">

<s>Terminava l'Autore il racconto di questa sua Esperienza fisico-mecca&shy;<lb/>nica con le seguenti notabilissime parole: &ldquo; Ma verr&agrave; forse il tempo che <lb/>questa maravigliosa legge dell'attrazione, a misura che prevale nelle pi&ugrave; <lb/>piccole porzioni della materia sar&agrave; pi&ugrave; ampiamente e chiaramente intesa, e <lb/>qualche nuovo effetto di essa si scoprir&agrave; che ora non vien creduto proce&shy;<lb/>dere da quella causa &rdquo; (ivi, pag. </s>

<s>151). Il vaticinio s'avver&ograve; puntualmente <lb/>nel particolar soggetto di questa sloria, imperocch&egrave; trascuratasi l'applica&shy;<lb/>zione delle attrazioni molecolari a spiegar la prevalente leggerezza de'corpi <lb/>gravi sospesi, si torn&ograve; indietro a vagheggiar le idee passate gi&agrave; per la mente <lb/>al Baliani. </s>

<s>Queste avevano avuto intanto un illustratore in Giuseppe Del <lb/>Papa, il quale seppe far apparir meno strana quella mistione del fuoco col&shy;<lb/>l'acqua delle vescicole vaporose, mettendo in gioco il glutine dell'acqua <lb/>stessa, dal quale vien colta e tenuta sotto il suo duttile velo avvinta ia luce <lb/>ardente del sole. </s>

<s>&ldquo; Stariasi l'acqua, egli dice, tutta perpetuamente ferma e <lb/>raccolta nelle pi&ugrave; basse cavit&agrave; della Terra, s'egli non fosse che colta quivi <pb xlink:href="020/01/860.jpg" pagenum="303"/>e ferita dai fervidi raggi solari, ella col proprio glutine parte di essi in s&egrave; <lb/>ritenendo, e divenendo per tale mistione della luce pi&ugrave; rarefatta e men pe&shy;<lb/>sante dell'aria, potesse in tal guisa nelle aeree regioni sormontare e tra&shy;<lb/>scorrere &rdquo; (Dell'Umido ecc., Firenze 1681, pag. </s>

<s>133). </s></p><p type="main">

<s>Se non che potevano queste del Del Papa parere stranezze nuove ag&shy;<lb/>giunte a pi&ugrave; antiche stranezze, quando quell'elettricit&agrave;, che s'incominci&ograve; a <lb/>vedere in tutto e per tutto presente come la nuova vita e l'anima del <lb/>Mondo, parve dispensar dal ricorrere in alto ad attingere la luce e il fuoco <lb/>dal Sole. </s></p><p type="main">

<s>Il De Saussure, dato mano al Microscopio, fece maravigliose osserva&shy;<lb/>zioni intorno alla fisica costituzione de'vapori vescicolari. </s>

<s>Not&ograve; fra le altre <lb/>cose che due tali vescicole non vengono mai a stringersi insieme in intimo <lb/>contatto, e che rimbalzano e rotolano sulla superficie di un'acqua senza toc&shy;<lb/>carla, e pronte anzi a volarsene via come v'eran venute, scosse da un leg&shy;<lb/>gerissimo soffio. </s>

<s>Sorpreso da una tal novit&agrave;, il celebre Autore degli <emph type="italics"/>Essais <lb/>sur l'Hygrometrie<emph.end type="italics"/> sospett&ograve; che il tutto dipendesse dall'esser ciascuna di <lb/>quelle vescicole involte nell'ammosfera di qualche aura sottilissima, da non <lb/>sapere a che altro meglio rassomigliarla che al vapore elettrico. </s>

<s>Ed ecco cos&igrave; <lb/>segnato il progresso che fecero le idee dal Baliani al Saussure: l'elemento <lb/>della leggerezza, che s'aggiunge all'acqua per tenerla sollevata in vapori, &egrave; <lb/>pura elettricit&agrave; terrestre, e non luce o foco di Sole. </s></p><p type="main">

<s>Divulgatesi queste idee nel 1783, quand'era stata gi&agrave; scoperta e con&shy;<lb/>fermata da tante esperienze l'elettricit&agrave; ammosferica, anche a ciel sereno, <lb/>non bisognava andar a cercar d'onde avesse origine l'elettricit&agrave; nelle ammo&shy;<lb/>sfere involgenti le vescicole vaporose sospese nel mezzo dell'aria: potevasi <lb/>per&ograve; domandare com'andasse il vapore elettrico a distribuirsi intorno a cia&shy;<lb/>scuna di esse vescicole, e come potesse rimanervi aderente sotto apparenze <lb/>cos&igrave; tanto trasformate dalle ordinarie. </s></p><p type="main">

<s>La risposta, che non avrebbe saputo darla il Saussure, fu suggerita <lb/>prontamente dal Volta, quand'ebbe scoperta l'elettricit&agrave; latente espressa <lb/>come il calor de'vapori, mentre si trasformano dallo stato elastico allo stato <lb/>vescicolare. </s>

<s>&ldquo; Or chi sa, dice egli, che la ridondanza del fluido elettrico, che <lb/>risulta dalla trasmutazione dei vapori elastici in vescicolari, non sia una <lb/>delle principali cagioni di cotal conformazione singolare? </s>

<s>E non potrebbe <lb/>questo fluido sovrabbondante concorrere ad accrescere la leggerezza specifica <lb/>delle vescichette, gonfiandole, estendendone la pellicola? </s>

<s>Non potrebbe il <lb/>medesimo costituire in gran parte, se non in tutto, quel fluido sottile, di <lb/>cui son piene tali vescichette, o quell'ammosfera onde ciascuna va involta <lb/>come da un velo? (Opere, T. I, P. II, Firenze 1816, pag. </s>

<s>235). </s></p><p type="main">

<s>Cos&igrave; il Saussure e il Volta videro in que'veli vescicolari, e quasi si sa&shy;<lb/>rebbero provati di toccar colle mani le sfere elettriche, come Galileo in si&shy;<lb/>miglianti vescicolette vedeva e avrebbe giurato di toccare gli atomi del fuoco, <lb/>i quali non erano poi altro che aria, come altro che aria non &egrave; quel velo <lb/>involgente le vescicole de'vapori. </s>

<s>La forte aderenza di un tal velo &egrave; per <pb xlink:href="020/01/861.jpg" pagenum="304"/>effetto di attrazione molecolare, la quale &egrave;, secondo le speculazioni neuto&shy;<lb/>niane, confermate dalle belle esperienze dell'Hawksbee, tanto pi&ugrave; forte, <lb/>quanto per la minima divisione a cui si riducono i corpi operano a minori <lb/>distanze. </s>

<s>Che del resto un tal velo sferico d'aria circondante la vescicola, <lb/>come se facesse un corpo solo con lei, conferisca alla leggerezza, nessun <lb/>fisico e nessun geometra avrebbe ragione di dubitarne. </s></p><p type="main">

<s>Dell'avere scambiata l'aria coll'elettricit&agrave; non &egrave; che quel sagace Volta <lb/>non avesse sentito il lubrico, ad assicurarsi dal quale ebbe ricorso alle forze <lb/>molecolari, o <emph type="italics"/>forze mutue,<emph.end type="italics"/> com'ei le chiama. </s>

<s>Queste come operano diver&shy;<lb/>samente su tutti gli altri corpi ridotti in minime parti, ccsi operano diver&shy;<lb/>samente sull'elettricit&agrave; ridotta a minime moli. </s>

<s>In s&igrave; fatto modo davasi a <lb/>intendere e si studiava di persuadere come l'elettrico mobilissimo per sua <lb/>natura ed attivo, quasi avesse perduta la propria effigie, si vedesse l&igrave; stare <lb/>inerte attorno alle vescicole vaporose. </s></p><p type="main">

<s>Non avrebbe il Baliani creduto mai che, dopo tanto progredir della <lb/>scienza, quel concetto suo strano del lume del sole rimasto preso nelle ve&shy;<lb/>scichette dell'acqua si dovesse trasformare in un altro concetto non meno <lb/>strano, per opera di un Saussure e di un Volta. </s>

<s>Eppure questa, del pro&shy;<lb/>blema che il Fisico genovese erasi proposto a risolvere, era la parte men <lb/>difficile. </s>

<s>Pi&ugrave; difficile s'appresentava e doveva naturalmente appresentarsi <lb/>l'altra parte di quello stesso problema concernente il modo come i vapori <lb/>ascesi gi&agrave; in aria tornino in pioggia, perciocch&egrave; se l&agrave; bastavano le specu&shy;<lb/>lazioni, qui bisognavano l'esperienze, le quali tanto ancora ai tempi del Ba&shy;<lb/>liani eran lontane, quant'era lontana l'invenzione della Macchina pneu&shy;<lb/>matica. </s></p><p type="main">

<s>E a Ottone di Guericke appunto occorse a dimostrar per la prima volta <lb/>come faccia il cielo a rannuvolarsi, a piovere, e a tornar poi nuovamente <lb/>sereno. </s>

<s>Prendeva un pallone di vetro munito di chiavetta, e dal quale aveva <lb/>estratto gi&agrave; l'aria: un altro simile pallone, bench&egrave; un po'pi&ugrave; piccolo, era <lb/>pieno d'aria o naturalmente umida o artificialmente inumidita, e congiun&shy;<lb/>geva poi insieme i due palloni avvolgendo l'un sopra l'altro a vite. </s>

<s>Aperte <lb/>le due chiavi in modo che l'aria dal pallone di sopra potesse irrompere vio&shy;<lb/>lente nel pallone vuoto e posto al di sotto &ldquo; ex hac subitanea aeris in su&shy;<lb/>periori vitro dilatione et descensu in inferius, aer residuus valde alteratur <lb/>et minuitur: multum autem aeris plus humiditatis continere potest quam <lb/>parum, ideoque relinquit inibi aer superfluam suam humiditatem, quae ocu&shy;<lb/>lariter videri potest in guttulis minimis, quae pedetentim ad fundum de&shy;<lb/>scendunt.... Ex quibus evidenter constat propter aeris contractionem vel <lb/>diminutionem, aquam quae est in aere se separare ab aere et in nubes con&shy;<lb/>gregare. </s>

<s>Unde si epistomium omnino relaxatur et aer plene intromittitur, <lb/>illico nubes vel nebulae evanescunt, quia ab intrante aere absorbentur &rdquo; <lb/>(Experim. </s>

<s>nova magdeb., Amstelodami 1672, pag. </s>

<s>88, 89). </s></p><p type="main">

<s>Questa esperienza, nella quale si vedeva sotto un piccolo cielo artifi&shy;<lb/>ciale l'aria rannuvolarsi, piovere, e poi rifarsi serena, pareva che dovess'es-<pb xlink:href="020/01/862.jpg" pagenum="305"/>sere ricevuta non con minore applauso di quel che fosse poi ricevuta l'altra <lb/>del Franklin, che in un simile piccolo cielo artificiale rappresentava gli ef&shy;<lb/>fetti del tuono e del baleno. </s>

<s>Eppure la bellissima e importantissima espe&shy;<lb/>rienza guericchiana giacque negletta, e fu per questa negligenza che tanto <lb/>e cos&igrave; penosamente rimase incerta la Meteorologia barometrica, come si nar&shy;<lb/>rer&agrave; appresso dop aver detto dell'origine del vento. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Tutti quanti i Filosofi ripetevano da secoli e secoli i detti di Aristotile <lb/>intorno all'origine de'venti, quando, verso la fine del secolo XVI, un nostro <lb/>insigne italiano soggiungeva dopo di aver ridotti molti fatti fisici, che s'at&shy;<lb/>tribuivano all'antiperistasi, alla ragione del denso e del raro, queste libere <lb/>e franche parole: &ldquo; Neque silentio involvendum est nec Aristotilem neque <lb/>alium ex suis fautoribus animadvertisse densum et rarum esse causam <lb/>ventorum &rdquo; (Joannis Bapt. </s>

<s>Benedicti, Speculationum liber., Venetiis 1599, <lb/>pag. </s>

<s>192). </s></p><p type="main">

<s>Come poi dal rarefarsi e dal condensarsi l'aria, sotto le continue vi&shy;<lb/>cende del caldo e del freddo, si produca quel moto nell'aria che s'appella <lb/>comunemente col nome di vento, cos&igrave; il Benedetti seguita a esporlo, dopo <lb/>aver pronunziate le sopra riferite parole: &ldquo; Rarum autem et densum me&shy;<lb/>diante calore et frigore fit, et si a partibus in omogeneis licet argumentari <lb/>de toto deducat consequentiam qui velit, observans in calidis aestatis die&shy;<lb/>bus, dum aliqua nubecula ad solem cooperiendum incedit, ibi statim agita&shy;<lb/>tionem aeris sentiri: ea vero nubecula praetergressa cum fuerit, et in ea <lb/>parte aer ad pristinam raritatem causatam a calore solis redierit, quiescit. </s>

<s><lb/>Huiusmodi autem aeris agitatio a nulla certe exhalatione proficiscitur, sed a <lb/>motu solum locali, quem dam condensatur facit &rdquo; (ibi). </s></p><p type="main">

<s>Dopo un'esperienza cos&igrave; semplice e un argomento cos&igrave; concludente, <lb/>pareva che dal primo e grande Maestro della Fisica sperimentale in Italia <lb/>fossero cacciate via per sempre le peripatetiche esalazioni, e che si fosse <lb/>stabilita la verace dottrina dell'origine de'venti. </s>

<s>Eppure &egrave; un fatto che reca <lb/>gran maraviglia, ma che ce lo mostrer&agrave; vero la storia, &egrave; un fatto che quella <lb/>dottrina era stata dimenticata da'seguaci di Galileo, i quali o confessavano <lb/>la loro propria ignoranza in tal subietto, o tenevan dietro all'errore un se&shy;<lb/>colo dopo il Benedetti. </s></p><p type="main">

<s>Ebbe intorno a ci&ograve; non piccola colpa lo stesso Galileo, il quale, bench&egrave; <lb/>si lasciasse una volta uscir dalla bocca che &ldquo; dalle regioni scaldate, nel raf&shy;<lb/>freddarsi, si eccitano i venti nelle circonvicine provincie &rdquo; (Alb. </s>

<s>III, 365) <lb/>mette nonostante la cosa in forse, e tanto poi si dilung&ograve; da questi savii in&shy;<lb/>segnamenti del Benedetti, che si volse tutto a professar, co'seguaci di Ari&shy;<lb/>stotile, la falsa ipotesi delle esalazioni ventose, da buon peripatetico invo&shy;<lb/>cando l'antiperistasi, come presto vedremo. </s></p><pb xlink:href="020/01/863.jpg" pagenum="306"/><p type="main">

<s>S'aggiunsero ai danni della Meteorologia le false dottrine cartesiane <lb/>accolte e professate con grande amore dai numerosissimi settatori di quella <lb/>scuola. </s>

<s>Illuso dall'esempio dell'Eolipila, addotto gi&agrave; da Vitruvio, pensava il <lb/>Cartesio che fosse il vento eccitato dal moto de'vapori che si espandono con <lb/>tanta forza all'intorno, essendo riscaldati. </s>

<s>&ldquo; Atque ita aer ex folle elisus vel <lb/>flabello impulsus ventus nominatur, licet venti latius diffusi terrasque et <lb/>maria perflantes nihil sint nisi vapores moti, qui dilatati ex loco arctiori in <lb/>quo erant, in alium ubi facilius expandantur, transeunt &rdquo; (Metereor, Cap. </s>

<s>IV, <lb/>Francof. </s>

<s>1692, pag. </s>

<s>141). </s></p><p type="main">

<s>Dall'esperienza del vento freddo, che sogliono mandar fuori le mesco&shy;<lb/>lanze frigorifere, fu similmente sedotto un altro caposcuola, ch'ebbe in Fran&shy;<lb/>cia e in Italia non forse minore autorit&agrave; dello stesso Cartesio. </s>

<s>Il Gassendo <lb/>insegnava che le commozioni ventose dell'ammosfera venivano suscitate dal&shy;<lb/>l'esalazioni de'sali nitrosi terrestri sollevatisi in aria, e ivi mescolati co'va&shy;<lb/>pori dell'acqua. </s>

<s>Cos&igrave; venivano da Galileo, dal Cartesio e dal Gassendo, so&shy;<lb/>lenni maestri della scienza, dissipati e resi torbidi que'sereni aliti di verit&agrave; <lb/>usciti dalla bocca del Benedetti. </s></p><p type="main">

<s>Primo a rimetter la Meteorologia sopra il retto sentiero, ritornando al <lb/>principio del raro e del denso professato dal Fisico veneziano, fu Francesco <lb/>Bacone, in quel suo libro ch'egli intitol&ograve; <emph type="italics"/>Historia naturalis et experimen&shy;<lb/>talis de'ventis.<emph.end type="italics"/> L'esperienza del vento cagionato dall'ardor de'raggi del <lb/>sole, che vengono riparati per caso da qualche fitta nuvola interposta, la ri&shy;<lb/>dusse Bacone a rappresentarsi a piacere sotto gli occhi di ognuno, imitando <lb/>coll'arte gli effetti della Natura. </s>

<s>&ldquo; Experimentum fecimus, egli scrive, in <lb/>turri rotunda undique clausa, huius generis venti. </s>

<s>Nam foculum in medio <lb/>eius locavimus, cum prunis penitus ignitis ut minus esset fumi, et a latere <lb/>foculi in distantia nonnulla filum suspendimus, cum cruce ex plumis ut fa&shy;<lb/>cile moveretur. </s>

<s>Itaque post parvam moram, aucto calore et dilatato aere, <lb/>agitabatur crux plumea cum filo suo, hinc inde motu vario, quin etiam facto <lb/>foramine in fenestra turris, exibat flatus calidus, neque ille continuus, sed <lb/>per vices et undulatus. </s>

<s>Etiam receptio aeris per frigus a dilatatione creat eius&shy;<lb/>modi ventum sed debiliorem ob minores vires frigoris &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1648, <lb/>pag. </s>

<s>54). </s></p><p type="main">

<s>Questa stessa esperienza fu poi illustrata con pi&ugrave; lucido concetto, e <lb/>con maggior finezza descritta dal nostro Borelli, bench&egrave; la principale inten&shy;<lb/>zione fosse alquanto diversa. </s>

<s>&ldquo; Videmus enim maiores et ampliores flam&shy;<lb/>mas in caminis accensas non vigere nec diutius perseverare, nisi adsit aditus <lb/>aeri de foris advenienti, per quem ingrediatur ventus perpetuus, qui inter <lb/>crura et foemora circumstantium excurrit versus flammam estque evidenter <lb/>sensibilis, nam, si cubiculi ostium claudatur extenso panno vel cortina, ut <lb/>fieri solet, haec inflatur versus ignem camini, ut velum navis, imo in cubi&shy;<lb/>culis undique diligenter clausis, in quibus aer externus subingredi nequeat, <lb/>non poterit flamma sursum impelli ab aere quin cubiculum inane remaneat, <lb/>et tunc ignis camini nullo pacto accendi potest, nec in flammam verti, aut <pb xlink:href="020/01/864.jpg" pagenum="307"/>perdurare nisi ostiolum vel foramen aliquod in ipso camino aperiatur, et <lb/>tunc facile flamma accenditur et perseverat. </s>

<s>Ratio huius effectus pendet ne&shy;<lb/>dum ab impulsu flammae sursum, sed etiam a rarefatione aeris prope ignem <lb/>existentis eumque ambientis per totam camini longitudinem, quia nempe <lb/>aer praedictus ab igne calefactus minus gravis specie redditur quam aer cu&shy;<lb/>biculi et externus qui a camino distat. </s>

<s>Hoc autem necessario advenit in le&shy;<lb/>gibus mechanicis et ex Archimedis demonstrationibus. </s>

<s>Necesse est enim ut <lb/>aer rarior et minus gravitans sursum expellatur exprimaturque a graviore <lb/>aere circumambiente. </s>

<s>Hinc fit ut, post ascensum illius aeris rarefacti per <lb/>caminum, diminuatur moles aeris ipsius cubiculi prope et circa caminum. </s>

<s><lb/>Non ergo mirum est novum aerem profluere ad replendum cubiculi spatium, <lb/>et haec est causa quare percipitur ventus ille et effluvium perpetuum dum <lb/>flamma camini viget &rdquo; (De motion. </s>

<s>natur., Regio Julio 1670, pag. </s>

<s>124, 25). </s></p><p type="main">

<s>Nessun altra esperienza poteva esser meglio di questa accomodata a <lb/>esplicare il concetto del Benedetti, e a dimostrar per la similitudine del <lb/>vento artificiale, che il vento naturale &egrave; veramente prodotto dall'avvicen&shy;<lb/>darsi del denso e del raro nell'aria, per gli effetti del calore del sole. </s>

<s>Ma <lb/>al Borelli non sovvenne un cos&igrave; fatto concetto, e l'intenzione per cui si <lb/>trattenne cos&igrave; a descrivere i moti dell'aria nel cammino ardente, si fu quella <lb/>di provar contro i Peripatetici che la fiamma non sale alto per suo natu&shy;<lb/>rale istinto, ma per circumpulsione del mezzo ambiente, come qualunque <lb/>altro corpo leggero. </s></p><p type="main">

<s>Bacone stesso non prosegu&igrave; quel concetto, come pareva dal suo prin&shy;<lb/>cipio, perch&egrave; il mal vezzo ch'egli ebbe di cincischiare la scienza, riducen&shy;<lb/>dola a categorie, lo port&ograve; a distinguere varie specie di venti, a ciascun <lb/>de'quali assegn&ograve; le sue cause particolari. </s>

<s>Fra queste cause particolari, oltre <lb/>quella del raro e del denso, eravi eziandio l'altra del vapor dilatato ed <lb/>espanso, conforme all'ipotesi del Cartesio, e anco questa causa riduceva il <lb/>Verulamio a soggetto di esperienza, dimostrando che il molinello di piume <lb/>era fatto volgere attorno anche dal vapore esalato dall'acqua di una pen&shy;<lb/>tola che bolla. </s>

<s>&ldquo; Itaque excitationis motus in ventis, di qui ne concludeva, <lb/>causa est praecipua superoneratio aeris ex nova accessione aeris facti ex va&shy;<lb/>poribus &rdquo; (Historie natur. </s>

<s>de ventis cit., pag. </s>

<s>65). </s></p><p type="main">

<s>Cos&igrave;, per non aver saputo Bacone ridur l'origine de'venti a una causa <lb/>unica e generale, rese inefficaci anche quelle vie sperimentali, ch'egli <lb/>avea prese dietro la scorta del Benedetti, e insomma tutti quanti filosofa&shy;<lb/>rono dopo di lui, infin verso il termine del secolo XVII, o seguitarono la <lb/>ipotesi del Cartesio o quella del Gassendo. </s>

<s>L'Huyghens, che pu&ograve; servire per <lb/>esempio di tutti gli altri, cos&igrave; scriveva nel I libro del Cosmoteoro: &ldquo; Erunt <lb/>ergo et imbres et venti, quia attractum a sole humorem recidere in ter&shy;<lb/>ram necesse est, et calore soluti vapores ventorum causa sunt &rdquo; (Lugd. </s>

<s><lb/>Batav. </s>

<s>1724, pag. </s>

<s>681). </s></p><p type="main">

<s>In Italia, dove quel <gap/>roso Borelli aveva saputo sostituire all'autorit&agrave; <lb/>del Cartesio l'autorit&agrave; s<gap/>a propria, si vagheggiava da molti quella proposi-<pb xlink:href="020/01/865.jpg" pagenum="308"/>zione L, che noi di sopra citammo dal Trattato <emph type="italics"/>De motionibus naturali&shy;<lb/>bus,<emph.end type="italics"/> e bench&egrave; non si osasse di estenderla alla causa generale de'venti, si <lb/>confessava nulladimeno che se la Natura non imita l'arte a quel modo, l'ori&shy;<lb/>gine de'venti rimane ancora riposta ne'tesori della Divina Sapienza. </s>

<s>&ldquo; Io <lb/>non so, scriveva in una sua Lettera il Redi, come nel mondo grande si fac&shy;<lb/>cia il vento, e mi accorgo che le cagioni sue stanno nascoste ne'segreti te&shy;<lb/>sori della Divina Sapienza, ma, se io fo alcuni piccoli modelli del vento ar&shy;<lb/>tificiale, veggo che la cagione di quel vento &egrave; sempre il fuoco &rdquo; (Opere, <lb/>T. V, Napoli 1741, pag. </s>

<s>50). </s></p><p type="main">

<s>Quella renitenza, che si provava in applicar lo sperimento borelliano <lb/>de'venti artificiali ai venti naturali, veniva ingerita dall'esempio autorevole <lb/>dello stesso Borelli, il quale inclinatissimo alla Filosofia atomica e dando <lb/>grande efficacia ai sali nitrosi sollevati e sospesi per l'aria, insinuava taci&shy;<lb/>tamente ne'Nostri l'ipotesi del Gassendo a preferenza di quella del Be&shy;<lb/>nedetti, bench&egrave; cos&igrave; ben confermata dalla somiglianza di quel vento, che <lb/>artificialmente si produce dal rarefarsi dell'aria intorno alla fiamma dei <lb/>cammini. </s></p><p type="main">

<s>Giuseppe Del Papa, valente fisico della scuola del Redi, lasci&ograve; scritto <lb/>in proposito le parole seguenti: &ldquo; N&egrave; voglio tacere che per avventura tal&shy;<lb/>volta, ne'tempi d'inverno, non poca freddezza all'aria vien conferita da una <lb/>gran quantit&agrave; di sali, ond'ella &egrave; ripiena, i quali, per essere della stessa na&shy;<lb/>tura e forse anche della medesima sorte del salnitro e del sale armoniaco, <lb/>non avrei gran ripugnanza a dire poter eglino lo stesso effetto nell'aria pro&shy;<lb/>durre circa il raffreddarla, che essi producono nell'acqua.... e quindi na&shy;<lb/>sce che alcune sorti di venti, ed in particolare la Tramontana e general&shy;<lb/>mente tutti quelli, i quali dalla dissoluzione delle nevi e delle grandini hanno <lb/>origine, tanto sensibilmente raffreddino.... E chi sa che queste sorti di <lb/>venti, i quali siccome ho detto hanno origine dalla grandine e dalle nevi, <lb/>non siano il solo sprigionamento de'sali sopraddetti, i quali, all'aria giun&shy;<lb/>gendo, l'urtino e la sospingano al moto? </s>

<s>Ma oh Dio che inavvertentemente <lb/>io entrerei in un pelago immenso, senza speranza di poter cos&igrave; tosto ricon&shy;<lb/>durmi al porto, quando della generazione de'venti a favellare io mi ponessi, <lb/>la quale chiaramente conosco ed ingenuamente confesso che &egrave; da altri omeri <lb/>che da'miei &ldquo; (Del freddo e del caldo, Firenze 1674, pag. </s>

<s>225, 26). </s></p><p type="main">

<s>N&egrave; la difficolt&agrave; di sciogliere il problema si fece sentir minore a un altro <lb/>de'pi&ugrave; valorosi fisici, che avesse l'Italia, il quale, come fu franco e risoluto <lb/>in repudiare l'ipotesi del Cartesio, parve non avversare al gioco di quelle <lb/>fermentazioni salino nitrose descritto dal Del Papa, e introdotto nella pre&shy;<lb/>sente questione meteorologica dalla fantasia del Gassendo. </s>

<s>&ldquo; Il Cartesio ed <lb/>i suoi seguaci, scrive il Montanari nella sua <emph type="italics"/>Astrologia convinta di falso,<emph.end type="italics"/><lb/>vengono alquanto pi&ugrave; alle strette, mentre, supposto quel loro secondo ele&shy;<lb/>mento sottilissimo, che di continuo con velocissima agitazione si muove, as&shy;<lb/>seriscono che il moto di questo vada staccando e dall'acqua e dalla Terra <lb/>e da altri corpi sottilissime particole, le quali agitate in giro da esso ele-<pb xlink:href="020/01/866.jpg" pagenum="309"/>mento, occupino perci&ograve; spazio maggiore, nel modo che una bandiera, che <lb/>prima ripiegata poco luogo teneva, se da braccio di destro e pratico alfiere <lb/>vien maneggiata in giro, si fa intorno ben larga piazza, onde in tal forma <lb/>spiegano poscia il vento che dalle palle di Eolo, riferite e spiegate anche <lb/>copiosamente da Vitruvio, e da'pomi al fuoco scaldati, ed altri simili corpi, <lb/>con s&igrave; grand'empito, e in tanta copia da poca umidit&agrave; scaturisce, mercecch&egrave; <lb/>quelle particelle d'umido, che per la veemenza del fuoco si staccano dalle <lb/>altre, e sono in giro portate, occupano spazio di gran lunga maggiore che <lb/>prima non facevano, onde a furia prorompono da quel foro, da cui vien <lb/>loro permesso d'uscire, ed in questo modo spiegano eziandio i venti, che <lb/>nell'aria, dal moto e calore del sole, son generati, mentre quelle particelle <lb/>de'vapori cos&igrave; da quell'elemento agitate, occupando spazio maggiore di <lb/>prima, spingono l'aria all'intorno per ogni verso e noi il moto di questo <lb/>vento chiamiamo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma oltre tante difficolt&agrave;, ch'io sento nell'ammettere tutta intiera l'ipo&shy;<lb/>tesi cartesiana,.... io non trovo nemmen contento l'intelletto mio in questa <lb/>particolare dottrina, mentre quell'azione del secondo suo elemento suppone <lb/>quel moto stesso ch'egli chiama calore: eppure dalla parte di Tramontana <lb/>spirano anche l'inverno e talora per lungo tempo venti freddissimi.... Al&shy;<lb/>l'incontro il Gassendo ed altri con lui hanno riferite le cause de'venti alla <lb/>varia mistione de'sali o nitrosi o armoniaci o simili, che con altre esalazioni <lb/>dalla terra si levano, e mescolati con i vapori acquei eccitano in tutto quel <lb/>misto d'aria d'esalazioni, vapori e sali una mozione, che altri fermentazione <lb/>direbbero, alla qual serve necessaria rarefazione, e dalla rarefazione il moto &rdquo; <lb/>(Venezia 1685, pag. </s>

<s>18, 19). </s></p><p type="main">

<s>La scoperta della verit&agrave; si riman tante volte lontani dal conseguirla, <lb/>perch&egrave; si presuppone ch'ella debba esser difficile e faticosa, e non si crede <lb/>a colui che dice d'esservi giunto per una via speditissima e piana. </s>

<s>Un sin&shy;<lb/>golare esempio di ci&ograve; lo abbiamo nel soggetto di questa storia, dalla quale <lb/>apparisce che la ragion de'venti data dal Benedetti non fu approvata, per&shy;<lb/>ch&egrave; parve troppo semplice, e perch&egrave; dall'altra parte non si vedeva come <lb/>riducesse la variet&agrave; de'fatti a una causa generale. </s>

<s>Ma mentre in Italia e fuori, <lb/>in fin presso a terminare il secolo XVII, s'erano i fisici lasciati illudere da <lb/>simili pregiudizii, cinquanta o sessant'anni prima, il Torricelli risolveva il <lb/>problema generale de'venti, mirabilmente esplicando quel semplicissimo con&shy;<lb/>cetto del Benedetti. </s>

<s>La Lezione accademica, in cui s'annunziava e si dimo&shy;<lb/>strava quel vero, dietro al quale i Fisici s'erano cos&igrave; lungamente affaticati <lb/>invano, non vide la luce prima del 1715, ma non fa per questo che non <lb/>debbasi al Nostro il merito d'avere alle fantasie cartesiane e gassendistiche <lb/>sostituite le fisiche ragioni, tanti anni prima dell'Halley o di chi altri, a cui <lb/>s'attribuisce l'aver, nelle condensazioni e nelle rarefazioni dell'aria, ricono&shy;<lb/>sciuta la causa generale de'venti. </s></p><p type="main">

<s>&ldquo; Non sarebb'egli, dice il Torricelli a suoi uditori, manifesto segno <lb/>d'avere incontrato la vera cagione dell'origine dei venti, se col medesimo <pb xlink:href="020/01/867.jpg" pagenum="310"/>principio la causa e la necessit&agrave; di tutti ugualmente si dimostrasse? </s>

<s>Questo <lb/>principio altro non &egrave; che quel notissimo e volgarissimo della condensazione <lb/>e rarefazione dell'aria. </s>

<s>Con questo, preso opportunamente, e non a rovescio, <lb/>come da alcuno &egrave; stato fatto, procureremo di sodisfare alla produzione di <lb/>qualsivoglia sorta di vento. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se un grandissimo tempio fosse pieno tutto d'acqua fino alla sua <lb/>pi&ugrave; alta sommit&agrave;, che farebbe? </s>

<s>la risposta &egrave; pronta. </s>

<s>Se le porte fossero <lb/>aperte l'acqua per esse se n'uscirebbe con grandissimo impeto, e per le <lb/>finestre pi&ugrave; sublimi succederebbe nel tempio altrettant'aria per l'appunto, <lb/>quanta acqua per le porte se ne partisse, e se il tempio avesse un'occulta <lb/>virt&ugrave; di convertire subito in acqua quell'aria succeduta, il profluvio delle <lb/>porte sarebbe continuo e non finirebbe mai, fintantoch&egrave; durasse la suppo&shy;<lb/>sta metamorfosi dell'aria in acqua. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quello che abbiamo esemplificato in due elementi diversi si consi&shy;<lb/>deri ora in un elemento solo, non tramutato di spezie ma alterato nelle <lb/>qualit&agrave;. </s>

<s>L'augustissimo tempio di Santa Maria del Fiore, qualche volta, ma <lb/>molto pi&ugrave; spesso la maggior basilica di Roma hanno questa propriet&agrave; di <lb/>esalare, ne'giorni pi&ugrave; caldi della state, un vento assai fresco fuor delle pro&shy;<lb/>prie porte, in tempo per l'appunto, quando l'aria si trova tranquillissima <lb/>e senza vento alcuno. </s>

<s>La ragione &egrave; questa: perch&egrave; l'aria, dentro la vasta <lb/>fabbrica racchiusa, qualunque sia la ragione, si trova pi&ugrave; fresca dell'esterna <lb/>infiammata da tanti raggi e reflessi del sole: per&ograve;, se pi&ugrave; fresca, &egrave; anco pi&ugrave; <lb/>densa; adunque sar&agrave; anco pi&ugrave; grave. </s>

<s>E se questo &egrave; vero, dovr&agrave; dalle porte <lb/>uscir quel profluvio d'aria, che nell'acqua abbiamo esemplificato. </s>

<s>Nel tem&shy;<lb/>pio di Roma il fresco sull'ore meridiane di questi tempi non solo diletta, <lb/>ma anche offende: per&ograve; il vento sulle porte di esso &egrave; tanto impetuoso che <lb/>apporta maraviglia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Applichiamo ora la contemplazione e passiamo dalle cavit&agrave; riserrate <lb/>all'ampiezza aperta de'campi spaziosissimi dell'aria. </s>

<s>Io domando: se la To&shy;<lb/>scana tutta avesse sopra di s&egrave; in cambio d'aria una mole egualmente alta <lb/>d'acqua, che seguirebbe? </s>

<s>Si risponde che questa mole non potrebbe reg&shy;<lb/>gersi, ma con profluvio rapidissimo si spargerebbe, dilatandosi in giro per <lb/>tutte le campagne degli stati circonvicini, spianando col corso impetuoso non <lb/>solamente le piante e gli edifizi, ma forse gli scogli e le muraglie stesse, e <lb/>per di sopra, per riempir la cavit&agrave; che lasciasse l'acqua, succederebbe al&shy;<lb/>trettant'aria. </s>

<s>Ecco dunque la generazione del vento per via di condensa&shy;<lb/>zione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Suppongasi tutto l'emisferio boreale quieto ed in istato di calma <lb/>tranquilla, senza un soffio di vento, senza un alito d'aura. </s>

<s>Venga poi una <lb/>pioggia repentina o qualsivoglia altro accidente, il quale, senza alterar punto <lb/>il rimanente dell'emisfero, accresca pi&ugrave; del dovere il freddo solamente alla <lb/>Germania. </s>

<s>Certo &egrave; che subito l'aria raffreddata di quel vasto regno si con&shy;<lb/>denser&agrave;. </s>

<s>Condensandosi &egrave; necessario che nell'alta regione dell'aria si faccia <lb/>sopra la Germania una cavit&agrave; cagionata dalla predetta condensazione: l'aria <pb xlink:href="020/01/868.jpg" pagenum="311"/>di sopra i regni circonvicini, come fluida e lubrica, scorre a riempier quella <lb/>cavit&agrave; improvvisamente nata, onde, nelle parti sublimi dell'aria, il corso del <lb/>vento sar&agrave; verso la parte raffreddata, ma nell'infima regione, cio&egrave; nell'aria <lb/>conterminante colla terra, il corso andr&agrave; al contrario: avvegnach&egrave; la Ger&shy;<lb/>mania ritrovandosi coperta d'aria condensata e anco accresciuta, e per&ograve; pi&ugrave; <lb/>grave della circonvicina, mander&agrave; per tutti i versi un profluvio di vento, <lb/>nel medesimo modo per appunto come abbiamo esemplificato nella Toscana, <lb/>quando fosse tutta in cambio d'aria ricoperta d'acqua. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In questo modo il vento sarebbe una circolazione, la quale non iscor&shy;<lb/>rerebbe sopra pi&ugrave; che ad una parte terminata della terra, e tanto durerebbe <lb/>l'effetto della circolazione predetta, quanto durasse la causa, cio&egrave; quel freddo <lb/>d'una provincia, maggior che non dovrebb'essere in paragone di quello <lb/>de'luoghi circonvicini. </s>

<s>Circolazione la chiamo, poich&egrave; nella parte superiore <lb/>tutto il moto dell'aria concorre verso il centro della provincia pi&ugrave; del do&shy;<lb/>vere raffreddata. </s>

<s>Quivi poi sentendo quel medesimo freddo accidentale, si <lb/>condensa, si aggrava e discende a terra, ove non reggendosi scorre da tutte <lb/>le parti e cagiona sulla superficie del terreno un vento contrario a quello <lb/>delle regioni sublimi &rdquo; (Lez. </s>

<s>accad., Milano 1823, pag. </s>

<s>158-61). </s></p><p type="main">

<s>Dopo tante strane ipotesi immaginate, quando in sui principii del se&shy;<lb/>colo XVIII si riconobbe la vera causa, che d&agrave; origine ai venti, i Fisici non <lb/>seppero dir nulla di meglio di quel che avesse cos&igrave; tanti anni prima inse&shy;<lb/>gnato il Torricelli, sul fondamento di quel principio notissimo e volgatissimo <lb/>della condensazione e della rarefazione dell'aria. </s>

<s>Ma, infin da quando invalse <lb/>tra'Filosofi l'opinione che la Terra si rivolgesse intorno al suo proprio asse, <lb/>occorse alle loro menti il pensiero che dovesse quel cos&igrave; rapido rivolgimento <lb/>cooperare a commover l'aria, ond'&egrave; che, mentre si fantasticava cos&igrave; strane <lb/>cose intorno all'origine dei venti ordinarii, si riconobbe almeno in parte la <lb/>vera causa di quelli, che spirano sotto i tropici in direzioni costanti. </s></p><p type="main">

<s>Il di 17 Dicembre 1630 il Cavalieri scriveva una lettera a Galileo, nella <lb/>quale gli significava certi suoi concetti di non lieve importanza in questa <lb/>storia. </s>

<s>&ldquo; Desidererei sapere, gli dice, se ha mai pensato alla generazione dei <lb/>venti, e se in qualche modo, nell'ipotesi copernicana, vi potessero aver che <lb/>fare i moti, che egli attribuisce alla Terra, cio&egrave; che nel rivolgersi con quella <lb/>velocit&agrave; che le viene ascritta, mentre qualche materia pi&ugrave; densa dell'etere, <lb/>che riempie questi immensi spazii, si ritrovasse attraversare l'orbe annuo <lb/>con altro moto, oppure in quello stesse quiescente; cio&egrave; dico che soprag&shy;<lb/>giungendo la Terra col suo orbe vaporoso circonfuso sino a quella altezza, <lb/>che si stima costituita in somma velocit&agrave;, che in caso d'urtare in quella <lb/>materia, per dir cos&igrave;, cometaria, si facesse un gagliardissimo contrasto, per <lb/>non ubbidire ella cos&igrave; presto al moto della Terra, e questo fosse causa di <lb/>sentir vento, quale poi, dalla Terra domato, non pi&ugrave; contumace camminasse <lb/>del pari con l'orbe vaporoso, e questo fosse poi il passare del vento; sicch&egrave; <lb/>si potesse formare questo paradosso: che il vento &egrave; una materia talvolta <lb/>quiescente, e che quando si muove non &egrave; pi&ugrave; vento. </s>

<s>So che si possono fare <pb xlink:href="020/01/869.jpg" pagenum="312"/>molte instanze, e tra le altre questa principalissima dell'esser loro cos&igrave; tu&shy;<lb/>multuari e sregolati, che nell'istesso tempo spirano da parti contrarie: ma <lb/>credo che dall'implicamento de'moti di essa Terra, e de'moti, che possono <lb/>avere tali materie, come vaganti per l'etere, si potr&agrave; forse scusare il tutto &rdquo; <lb/>(MSS. Galileo, P. VI, T. XI, c. </s>

<s>152). </s></p><p type="main">

<s>Al desiderio del Cavalieri, anche senza saper la risposta fatta a questa <lb/>sua lettera, possiamo sodisfar noi, dicendo che Galileo doveva aver gi&agrave; pen&shy;<lb/>sato a quel tempo alle relazioni che passano tra certi particolari moti ven&shy;<lb/>tosi dell'aria, e i moti della Terra. </s>

<s>Quando infatti ricev&egrave; quella lettera da <lb/>Bologna i Dialoghi manoscritti de'Due Massimi Sistemi erano pronti gi&agrave; per <lb/>la stampa, e nel IV di que'Dialoghi, com'ora vi si legge, cos&igrave; si leggeva: <lb/>&ldquo; Dicevamo pur ora, e con qualche aggiunta replico, che l'aria, come corpo <lb/>tenue e fluido e non saldamente congiunto alla Terra, pareva che non avesse <lb/>necessit&agrave; d'ubbidire al suo moto, se non in quanto l'asprezza della super&shy;<lb/>ficie terrestre ne rapisce e seco porta una parte a s&egrave; contigua, che di non <lb/>molto intervallo sopravanza le maggiori altezze delle montagne, la qual por&shy;<lb/>zione d'aria tanto meno dovr&agrave; essere renitente alla conversion terrestre, <lb/>quanto che ella &egrave; ripiena di vapori, fumi ed esalazioni, materie tutte par&shy;<lb/>tecipanti delle qualit&agrave; terrene, e per conseguenza atte nate per loro natura <lb/>ai medesimi movimenti. </s>

<s>Ma dove mancassero le cause del moto, cio&egrave;, dove <lb/>la superficie del globo avesse grandi spazii piani e meno vi fosse della m&igrave;&shy;<lb/>stione dei vapori terreni, quivi cesserebbe in parte la causa, per la quale <lb/>l'aria ambiente dovesse totalmente obbedire al rapimento della conversion <lb/>terrestre; sicch&egrave; in tali luoghi, mentre che la Terra si volge verso oriente, <lb/>si dovrebbe sentir continuamente un vento, che ci ferisse spirando da le&shy;<lb/>vante verso ponente, e tale spiramento dovrebbe farsi pi&ugrave; sensibile dove la <lb/>vertigine del globo fosse pi&ugrave; veloce, il che sarebbe nei luoghi pi&ugrave; remoti <lb/>dai poli e vicini al cerchio massimo della diurna conversione. </s>

<s>Ma gi&agrave; <emph type="italics"/>de <lb/>facto<emph.end type="italics"/> l'esperienza applaude molto a questo filosofico discorso, poich&egrave;, negli <lb/>ampii mari e nelle lor parti lontane da terra e sottoposte alla zona torrida, <lb/>cio&egrave; comprese dai tropici, dove ancora l'evaporazioni terrestri mancano, si <lb/>sente una perpetua aura muovere da oriente con tenor tanto costante, che <lb/>le navi, merc&egrave; di quella, prosperamente se ne vanno all'Indie occidentali &rdquo; <lb/>(Alb. </s>

<s>I, 475, 76). </s></p><p type="main">

<s>Questo filosofico discorso &egrave; tessuto dentro all'altro filosofico discorso <lb/>del flusso marino, in ambedue i quali non &egrave; la Filosofia per verit&agrave; cos&igrave; <lb/>schietta e sincera, come presumeva di darcela Galileo. </s>

<s>All'aria, non si sa <lb/>perch&egrave;, ei non concede le qualit&agrave; terrene e la mantien disgiunta, indipen&shy;<lb/>dente e immobile intorno alla Terra contro l'opinione di tutti i Coper&shy;<lb/>nicani, fra'quali udimmo ora che &egrave; poco il Cavalieri. </s>

<s>E il Gilberto prima di <lb/>lui aveva scritto: &ldquo; aer omnis, terrae et aquarum spiramenta, nubes et pen&shy;<lb/>dentia meteora simul cum globo circulariter concitantur &rdquo; (De Magnete, <lb/>Londini 1600, pag. </s>

<s>219). E dall'altra parte non potevano approvar l'opi&shy;<lb/>nione di Galileo se non che i Peripatetici, i quali non tenevan conto del <pb xlink:href="020/01/870.jpg" pagenum="313"/>peso e ammettevan nell'aria una leggerezza innata. </s>

<s>Comunque sia, bevve <lb/>quell'opinione Galileo infino dai primi anni della sua vita scientifica, e la <lb/>mantenne lungamente salda in mezzo alle pi&ugrave; aperte contradizioni. </s>

<s>Il passo <lb/>infatti che noi trascrivemmo di sopra dal IV Dialogo de'Massimi Sistemi, &egrave; <lb/>in sentenza conforme a quello dei <emph type="italics"/>Sermones de'motu gravium,<emph.end type="italics"/> a proposito <lb/>della palla di marmo girevole su'suoi cardini, alla quale, dato il primo im&shy;<lb/>pulso, &ldquo; tunc certo sphaera per longum temporis spatium girabit, et tamen <lb/>nec aer a motore fuerit commotus &rdquo; (Alb. </s>

<s>XI, 16). </s></p><p type="main">

<s>Ma pure quella falsa opinione dell'immobilit&agrave; dell'aria intorno alla Terra <lb/>ebbe origine da questa meccanica esperienza, nella quale era necessario am&shy;<lb/>mettere l'immobilit&agrave; dell'aria stessa intorno alla palla marmorea, perch&egrave; <lb/>fosse l'argomento contro i Peripatetici concludente. </s>

<s>E tutto ebbe origine in <lb/>Galileo dal desiderio di trasformar l'esperienza dello Scaligero per farla sua <lb/>propria. </s>

<s>Lo Scaligero infatti concludeva, contro gli aristotelici, il principio <lb/>intrinseco dell'inerzia della materia, e ne escludeva l'intervento esterno del&shy;<lb/>l'aria, dimostrando che la ruzzola segata nel pezzo dell'assicella di legno se&shy;<lb/>guitava a girar sopra i suoi perni, ricevuto il primo impulso, e che non si <lb/>poteva ci&ograve; attribuire a quella minima quantit&agrave; d'aria rimasta in un solco <lb/>cos&igrave; sottile, quant'esser pu&ograve; sottile la lama di una sega. </s>

<s>Galileo, che aveva <lb/>trasformata l'esperienza nella palla di marmo, girevole in mezzo all'aria <lb/>libera, non poteva concluder l'argomento dello Scaligero, com'era la sua <lb/>intenzione, senz'ammetter che l'aria ambiente, rivolgendosi la palla attorno, <lb/>vi rimanesse immota. </s></p><p type="main">

<s>Gratuita ipotesi in ogni modo era questa, e dubitando delle ragioni, che <lb/>persuadevano del contrario i copernicani, come per esempio il Gilberto e il <lb/>Cavalieri, giovava d'invocare in proposito l'esperienza. </s>

<s>Ma il vento che si <lb/>rende sensibile ed &egrave; menato da un solido ridotto sul torno, Galileo lo at&shy;<lb/>tribuiva <emph type="italics"/>agli urti della sua scabrosit&agrave; e porosit&agrave; che si fanno nel mezzo <lb/>ambiente<emph.end type="italics"/> (Alb. </s>

<s>II, 320), essendo impossibile il togliere affatto simili scabro&shy;<lb/>sit&agrave;, per rotondar quel solido quanto pi&ugrave; perfettamente si possa. </s></p><p type="main">

<s>Nelle controversie col Sarsi, che ammetteva esser l'ammosfera menata <lb/>in volta dal concavo lunare intorno alla Terra immota, Galileo richiamava <lb/>il suo avversario all'esperienza dell'aria ne'vasi giranti, dentro ai quali so&shy;<lb/>steneva l'immobilit&agrave; dell'aria rivelata dal rimanervi quieta la fiammella di <lb/>una candela. </s>

<s>&ldquo; Pigli due candelette accese, ed una ne attacchi dentro al&shy;<lb/>l'istesso vaso, un dito o due lontana dalla superficie, e l'altra ritenga in <lb/>mano, pur dentro al vaso, in simil lontananza dalla medesima superficie. </s>

<s><lb/>Faccia poi con velocit&agrave; girare il vaso, che se in alcun tempo l'aria andr&agrave; <lb/>parimente con quello in volta, senza alcun dubbio, movendosi il vaso, l'aria <lb/>contenuta e la candeletta attaccata, tutto colla medesima velocit&agrave;, la fiam&shy;<lb/>mella di essa candela non si piegher&agrave; punto, ma rester&agrave; come se il tutto <lb/>fosse fermo.... ma l'altra candeletta ferma dar&agrave; segno della circolazion del&shy;<lb/>l'aria, che ferendo in lei la far&agrave; piegare. </s>

<s>Ma se l'evento sar&agrave; al contrario, <lb/>cio&egrave; se l'aria non seguiter&agrave; il moto del vaso, la candela ferma manterr&agrave; la <pb xlink:href="020/01/871.jpg" pagenum="314"/>sua fiammella diritta e quieta, e l'altra portata dall'impeto del vaso, ur&shy;<lb/>tando nell'aria quieta, si piegher&agrave;. </s>

<s>Ora nelle esperienze vedute da me &egrave; ac&shy;<lb/>caduto sempre che la fiammella ferma &egrave; restata accesa e diritta, ma l'altra <lb/>attaccata al vaso si &egrave; sempre grandissimamente piegata e molte volte spenta &rdquo; <lb/>(Alb. </s>

<s>IV, 307). </s></p><p type="main">

<s>Il Venturi (Memorie di Gal., P. II, pag. </s>

<s>50) mostr&ograve; quanto fossero poco <lb/>accurate queste esperienze descritte nel <emph type="italics"/>Saggiatore,<emph.end type="italics"/> per cui Galileo, invece <lb/>di deliberarsene come pareva, si conferm&ograve; nel suo errore di mantenere im&shy;<lb/>mobile l'aria intorno alla Terra, a quel modo ch'ei credette di averla os&shy;<lb/>servata intorno al vaso girante. </s></p><p type="main">

<s>La radice prima di questo errore la riconoscemmo in ci&ograve; che Galileo <lb/>negava all'aria le qualit&agrave; proprie alle materie terracquee, e che perci&ograve; ne <lb/>partecipasse agli effetti, ond'&egrave; ch'ei credeva intanto solo moversi e&sgrave;sa aria <lb/>intorno alla Terra, in quanto ella &egrave; mescolata alle esalazioni terrestri, fra <lb/>le quali si comprendevano anche i vapori acquosi. </s>

<s>Avendo sotto i tropici <lb/>perci&ograve; bisogno di costituire l'ammosfera immobile, e non turbata da nes&shy;<lb/>sun'altra causa accidentale, poneva per condizion necessaria, oltre alla levi&shy;<lb/>gatezza della superficie del mare, la scarsit&agrave; delle evaporazioni di lui. </s></p><p type="main">

<s>Questa seconda condizione per&ograve;, che dai mari, e specialmente da quelli <lb/>che soggiacciono all'Equatore, non esalino vapori in pi&ugrave; gran copia sotto la <lb/>gran ferza de'raggi solari, ha tanto dell'incredibile che non si capisce come <lb/>potess'essere ammessa da Galileo. </s>

<s>Si direbbe anzi, e alcuni ne sospettarono <lb/>davvero (Humboldt Cosmo, traduz. </s>

<s>ital., T. II, Napoli 1850, pag. </s>

<s>447 n.) che <lb/>fosse quel passo di sopra addotto dai <emph type="italics"/>Massimi Sistemi<emph.end type="italics"/> adulterato, se non ci <lb/>fossero i documenti a provare come Galileo, non solo opinava che non eva&shy;<lb/>porassero i mari, altro che poco, ma sapeva di pi&ugrave; trovar la ragione da sal&shy;<lb/>var questo, che per senso comune &egrave; un paradosso. </s></p><p type="main">

<s>Di quella ragione per&ograve; e di altre simili dubitava argutamente il Vi&shy;<lb/>viani, il quale non doveva ancora certamente sapere ch'ell'erano uscite <lb/>dalla divina mente del suo Galileo. </s>

<s>In una <emph type="italics"/>Raccolta di esperienze e di pen&shy;<lb/>sieri diversi,<emph.end type="italics"/> per la massima parte originali, ma alcuni trascritti dalle carte <lb/>disperse di altri Autori, il Viviani stesso scrisse di sua propria mano anche <lb/>questo: &ldquo; Cercasi la cagione onde avvenga che i luoghi montuosi o vicini <lb/>alle gran montagne siano pi&ugrave; delli altri sottoposti alle tempeste, fulmini, <lb/>tuoni, baleni, ecc. </s>

<s>Forse la cagione &egrave; tale, oppure &egrave; una coglio ... ria, la <lb/>quale il Galileo contrassegnerebbe cos&igrave;.... Levansi dalla terra vapori ed esa&shy;<lb/>lazioni ecc. (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>21). </s></p><p type="main">

<s>Che dovessero questi pensieri meteorologici parere al Viviani cosa inde&shy;<lb/>gna di Galileo, e dettatura piuttosto di qualche peripatetico, era naturale, <lb/>vedendovisi messo in gioco il principio delle contrariet&agrave;, e all'<emph type="italics"/>antiperistasi<emph.end type="italics"/><lb/>delle esalazioni attribuita l'origine delle grandini e delle tempeste. </s>

<s>Ma che <lb/>veramente quelle meteorologiche speculazioni appartengano a Galileo, oltre <lb/>all'esservene l'autografo (MSS. Gal., P. VI, T. II, c. </s>

<s>5), per cui gli editori <lb/>accolsero anche questa fra le scritture di lui, si conferma dal ritrovarsi qui <pb xlink:href="020/01/872.jpg" pagenum="315"/>il pi&ugrave; chiaro commento alle idee professate ne'Dialoghi de'Due Massimi <lb/>Sistemi. </s></p><p type="main">

<s>A chi legge infatti nel IV di que'Dialoghi il passo da noi sopra citato, <lb/>e domanda com'esser possa che ivi dicasi da Galileo una cosa tanto contra&shy;<lb/>ria al senso comune, qual'&egrave; che negli ampii mari intertropicali <emph type="italics"/>manchino <lb/>l'evaporazioni,<emph.end type="italics"/> risponde cos&igrave; l'Autore di quel <emph type="italics"/>Pensiero,<emph.end type="italics"/> in margine al quale <lb/>dubitava il Viviani che si potesse imprimere quel bizzarro algoritmo, col <lb/>quale era solito lo stesso Galileo di notar, leggendo, le altrui corbellerie: <lb/>&ldquo; Dico inoltre maggior copia di vapori elevarsi dalla terra umida, che dal&shy;<lb/>l'acqua, perch&egrave; l'acqua come diafana trasmette i raggi del sole e meno si <lb/>riscalda che la terra opaca.... Poco dunque di vapori e meno di esalazioni <lb/>si eleva dal mare &rdquo; (Alb. </s>

<s>XIV, 337, 38). </s></p><p type="main">

<s>Cos&igrave; veniva Galileo a guastarsi, diciamo cos&igrave;, fra le mani quel cos&igrave; bello <lb/>argomento, che porgevano a conferma del sistema copernicano i venti equa&shy;<lb/>toriali, argomento di cui poi si valse il valoroso sperimentatore di Magde&shy;<lb/>burgo. </s>

<s>Dal ponderar dell'aria ne deduceva sicuramente il Guericke che &ldquo; si <lb/>Terra, secundum Copernici sententiam, motum illum vertiginis habeat, to&shy;<lb/>tum quoque aereum systema simul inconcussum procedat cum Terra &rdquo; <lb/>(Experim. </s>

<s>magd. </s>

<s>cit., pag. </s>

<s>167). Ma bench&egrave; sia uniforme quel moto rota&shy;<lb/>torio della sfera dell'aria &ldquo; tamen in locis, nimirum sub Aequatore et Tro&shy;<lb/>picis ubi circumvolutio Terrae, ob maiorem circumferentiam celerior est <lb/>quam alibi, remissio quaedam parva sentitur, ita ut aer raptui conversionis <lb/>terrestris totaliter non obediat &rdquo; (ibi, pag. </s>

<s>168). Hanno di qui origine quei <lb/>venti regolari, che spirano sotto i Tropici, e ci&ograve;, conclude il Guericke, non <lb/>leggero argomento <emph type="italics"/>ad struendum copernicanum systema adfert<emph.end type="italics"/> (ibi). </s></p><p type="main">

<s>L'argomento di Ottone di Guericke per&ograve; non &egrave; assoluto, perch&egrave; i venti <lb/>equatoriali dipendono tutto insieme dalla Terra, che si rivolge in s&egrave; stessa, <lb/>e sotto il Sole che ne dilata l'aria pi&ugrave; o meno, secondo che pi&ugrave; o men di&shy;<lb/>rettamente ne riceve il calore. </s>

<s>Avrebbe del s&igrave; importante problema dato il <lb/>Verulamio la soluzione completa, se, avverso com'era all'ipotesi copernicana, <lb/>non si fosse, co'pi&ugrave; antichi Filosofi e col nostro Alighieri, immaginato che <lb/><emph type="italics"/>in circuito tutto quanto l'aer si volge con la prima volta<emph.end type="italics"/> (Purg., C. XXVIII, <lb/>t. </s>

<s>35), ond'&egrave; che si fa vento dovunque <emph type="italics"/>tal moto percuote.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Quod <emph type="italics"/>Briza<emph.end type="italics"/> illa, si legge nella citata <emph type="italics"/>Historia naturalis et experi&shy;<lb/>mentalis de ventis,<emph.end type="italics"/> inter tropicos luculenter spiret, res certa, causa ambigua. </s>

<s><lb/>Posset ea esse quia aer more coeli movetur. </s>

<s>Sed extra tropicos, quasi imper&shy;<lb/>ceptibile propter circulos minores, intra, manifeste, propter circulos maiores <lb/>quos conficit. </s>

<s>Posset alia esse quia calor omnem aerem dilatat, nec se priori <lb/>loco contineri patitur. </s>

<s>Ex dilatatione autem aeris necessario fit impulsio aeris <lb/>contigui, quo brizam istam pariat prout progreditur sol. </s>

<s>Sed illa intra tro&shy;<lb/>picos, ubi sol est ardentior, insignior est, extra, fere latet &rdquo; (pag. </s>

<s>16, 17). </s></p><p type="main">

<s>Cos&igrave; venivano anche i <emph type="italics"/>Monsoni<emph.end type="italics"/> a ridursi alla causa generale di tutti i <lb/>venti assegnata dal Torricelli, e alla quale dettero poi il pi&ugrave; pieno svolgi&shy;<lb/>mento l'Hook e l'Halley. </s></p><pb xlink:href="020/01/873.jpg" pagenum="316"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Si disse, nel chiuder la prima parte del presente Capitolo, che la Me&shy;<lb/>teorologia barometrica rimase, nel render la ragione delle sue congetture, <lb/>cos&igrave; lungamente incerta, per non aver debitamente atteso a quel bellissimo <lb/>esperimento, per cui rappresentavasi con ingegnoso artifizio dal Guericke, <lb/>ora il cielo piovoso, ora il sereno. </s>

<s>Suppongasi infatti di avere introdotto <lb/>nella cucurbita guericchiana un Barometro: quando l'aria rarefatta si ran&shy;<lb/>nuvola, e il vapor condensato incomincia a cadere in pioggia, la colonna ba&shy;<lb/>rometrica necessariamente si abbassa; quando, riammessa l'aria, questa, <lb/>restituitasi alla sua primiera densit&agrave;, si rasserena, la colonna barometrica non <lb/>men necessariamente si alza. </s></p><p type="main">

<s>Cos&igrave; venivano le vicende del Barometro, per quel che pu&ograve; dipendere <lb/>dall'avvicendarsi delle stagioni, dimostrate, ne'casi pi&ugrave; ordinarii, per modo, <lb/>che sarebbero bastati i fatti sperimentali a rassicurar di ogni dubbio, e a <lb/>togliere alle controversie ogni mendicata occasione. </s>

<s>Tutt'al contrario ha in&shy;<lb/>torno a ci&ograve; la Storia tanta faccenda, che non si pu&ograve; cos&igrave; ridurre negli an&shy;<lb/>gusti termini di questo paragrafo, senza timor che s'abbia, per qualche parte, <lb/>a lasciar da noi difettosa. </s></p><p type="main">

<s>Quel Pascal, che fu il primo a sperimentare le variazioni ipsometriche <lb/>del Barometro, fu il primo altres&igrave; a notare con gran diligenza le variazioni <lb/>che subiva lo strumento al variare delle stagioni. </s>

<s>L'editore del <emph type="italics"/>Traitez de <lb/>l'equilibre des liqueurs<emph.end type="italics"/> pubblic&ograve; nell'Appendice al particolar Trattato <emph type="italics"/>De la <lb/>pesanteur de l'air<emph.end type="italics"/> alcuni frammenti di una lunga opera, o lasciata dallo <lb/>stesso Pascal incompiuta, o andata sventuratamente per la maggior parte <lb/>smarrita. </s>

<s>Fra cotesti frammenti &egrave; un capitolo che s'intitola &ldquo; De la regle <lb/>des variations qui arrivent a ces effects, par la vari&eacute;t&eacute; des temps. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ces vicissitudes, scrive l'Autore, sont sans regles dans les chauge&shy;<lb/>mens du mercure aussi bien que dans l'air: de sorte que quelquefois d'un <lb/>quart d'heure a l'autre il y a grande difference et quelquefois durant qua&shy;<lb/>tre ou cinq'jours il y en a tres peu. </s>

<s>La faison ou le mercure est le plus <lb/>haut pour l'ordinaire est l'Hyver. </s>

<s>Celle ou d'ordinaire il est le plus bas est <lb/>l'Est&eacute;. </s>

<s>Ou il est le moins variable est aux solstices; et ou il est le plus va&shy;<lb/>riable est aux Equinoxes. </s>

<s>Ce n'est pas que le mercure ne foit quelquefois <lb/>haut en Est&eacute;, bas en Hyver, incostant aux solstices, constant aux Equino&shy;<lb/>xes; eat il n'ya point de regle certaine; mais pour l'ordinaire la chose est <lb/>comme nous l'avons dite; parce qu'aussi pour l'ordinaire quoy que non pas <lb/>toujours, l'air est le plus charge en Hyver, le moins en Est&eacute;, le plus in&shy;<lb/>costant en Mars et en Septembre, et le plus constant aux Equinoxes &rdquo; (Pa&shy;<lb/>ris, pag. </s>

<s>153, 54). </s></p><p type="main">

<s>In mezzo a queste osservazioni delle variazioni annuali vedute fare al <lb/>Barometro, occorse al Pascal di notare altre variazioni giornaliere nello stru-<pb xlink:href="020/01/874.jpg" pagenum="317"/>mento, le quali si accorse che dipendevano dall'esser l'aria ora pi&ugrave;, ora <lb/>meno carica di vapori. </s>

<s>Dietro a ci&ograve;, si credeva di poterne concludere che <lb/>&ldquo; la pesanteur de la masse de l'air augmente quand il est plus charg&eacute; de <lb/>vapeur, et diminu&eacute; quand il l'es moins &rdquo; (ivi, pag. </s>

<s>96). </s></p><p type="main">

<s>Altre simili variazioni ebbe a notare il Pascal in ordine al tempo, che, <lb/>s'era bello, l'argento vivo nella canna barometrica rimaneva pi&ugrave; basso, ben&shy;<lb/>ch&egrave; fossesi accorto che non riusciva questa regola sempre infallibile, avendo <lb/>notato che lo stesso argento vivo talvolta si solleva, facendosi il cielo sereno. <lb/></s>

<s>&ldquo; Il arrive aussi peur l'ordinaire que le mercure baisse quand il fait beau <lb/>temps, qu'il hausse quand le temps devient froid ou charg&eacute;; mais cela n'est <lb/>pas infallible; car il hausse quelquefois quand le temps s'embellit, et il baisse <lb/>quelquefois quand le temps se couvre &rdquo; (ivi, pag. </s>

<s>154). </s></p><p type="main">

<s>Queste osservazioni fatte dal Pascal a Parigi, e altre simili fatte a Cler&shy;<lb/>mont dal Perier, negli anni 1649, 50 e 51, rimasero ignote al pubblico in&shy;<lb/>fino al 1663, cosicch&egrave; nulla se ne sapeva ancora in Italia, quando il Gran&shy;<lb/>duca di Firenze ordinava quelle stazioni meteorologiche a notar diligentemente, <lb/>giorno per giorno, lo stato dell'aria, la temperatura, l'intensit&agrave; e la direzione <lb/>de'venti. </s></p><p type="main">

<s>Le osservazioni barometriche furono particolarmente affidate dal Gran&shy;<lb/>duca al Borelli, professore allora nello studio di Pisa, il quale con gran di&shy;<lb/>ligenza le prosegu&igrave; per tutti i giorni dell'anno 1657 e dell'anno appresso. </s>

<s><lb/>Egli ebbe, come il Pascal, a concludere da quelle sue Effemeridi che il Ba&shy;<lb/>rometro si solleva sotto il cielo nuvoloso e si abbassa quando torna sereno. </s>

<s><lb/>Mettendosi dietro a investigar la ragione di ci&ograve;, da nessuno, e nemmeno <lb/>dallo stesso Pascal per lo innanzi tentata, parvegli di riconoscerla negli stessi <lb/>vapori, che aggravano col loro peso il peso dell'aria, e pens&ograve; di riscontrare <lb/>il fatto e di renderlo visibile coll'esperienza. </s></p><p type="main">

<s>Preso un largo vaso cilindrico di cristallo e calato nel suo fondo un <lb/>Barometro, ne riempiva lo stesso vaso d'olio o di altro liquido pi&ugrave; leggero, <lb/>notando il livello a cui il mercurio, per l'infusione del liquido, era salito. </s>

<s><lb/>Poi faceva sull'olio gravare una scodella piena di minutissimi granelli di <lb/>arena, che, aggiungendo nuova pressione alla pressione dell'olio, faceva ri&shy;<lb/>salire alquanto il mercurio. </s>

<s>Riversati i granellini dell'arena dalla scodella <lb/>osservava il Borelli che, nell'atto della discesa, il livello barometrico non si <lb/>moveva, ma scesi i granellini in fondo, quel livello si restituiva a poco a poco <lb/>a quell'altezza precisa, alla quale era giunto per la sola pressione dell'olio <lb/>soprapposto. </s>

<s>I granellini dell'arena contenuti nella scodella rappresentavano, <lb/>secondo il Borelli, i granellini o le vescichette dell'umido, di che si com&shy;<lb/>pone la nuvola; la discesa di que'granellini arenosi rappresentava il cader <lb/>delle gocciole della pioggia, e l'olio rimasto libero da que'corpicelli stra&shy;<lb/>nieri rendeva immagine dell'aria divenuta serena, per esser caduti a terra <lb/>i vapori. </s></p><p type="main">

<s>Nel Novembre dell'anno 1657 riferiva da Pisa queste sue speculazioni, <lb/>e descriveva queste esperienze al principe Leopoldo, il quale rispondeva al <pb xlink:href="020/01/875.jpg" pagenum="318"/>Borelli per lettera, che il Fabbroni pubblic&ograve; senza data, ma che nella copia <lb/>manoscritta &egrave; del d&igrave; 15 di Dicembre dell'anno suddetto (MSS. Cim., T. XXIII, <lb/>c. </s>

<s>2). Incomincia ivi il principe a dire che gratissimo gli era riuscito il pro&shy;<lb/>blema delle variazioni dell'argento vivo, in relazione collo stato del cielo, e <lb/>che ingegnosissima gli era parsa la soluzione: dubitava per&ograve;, per non averne <lb/>fatta esperienza, se fosse vero che, soprastando i nuvoli in alto e non toc&shy;<lb/>cando terra, dovessero <emph type="italics"/>aggravare maggiormente sopra l'argento vivo, e <lb/>conseguentemente alzarlo pi&ugrave; di quando fosse compresso dall'aria am&shy;<lb/>biente purissima.<emph.end type="italics"/> (Fabbroni, Lett. </s>

<s>ecc., T. I, pag. </s>

<s>112). </s></p><p type="main">

<s>Il dubbio era ragionevolissimo e degno di maggior Filosofo, che non <lb/>potess'essere il principe Leopoldo. </s>

<s>Ma le considerazioni di lui dovevano aver <lb/>gran fondamento in altre considerazioni suggeritegli dal Viviani, alla saga&shy;<lb/>cia del quale non potevano essere sfuggiti i difetti dell'esperienza e la fal&shy;<lb/>lacia dell'argomento del Borelli. </s>

<s>E in verit&agrave;, improprio e anzi falso era il <lb/>dire che la scodella piena di granellini di arena, premendo sull'olio, ne au&shy;<lb/>menta la pressione sul fondo del vaso, perch&egrave; la pressione idrostatica non <lb/>pu&ograve; variarsi per altre ragioni, che per variar l'altezza perpendicolare del li&shy;<lb/>vello. </s>

<s>N&egrave; i galleggianti aumentan nulla di peso, equilibrandosi esattamente <lb/>col mezzo: solo pu&ograve; dubitarsi, e l'esperienza dovrebbe decidere, se niuna <lb/>alterazion sopravvenga per la discesa o l'ascesa, che dentro il mezzo si fac&shy;<lb/>cia da qualche corpo straniero. </s></p><p type="main">

<s>&ldquo; Se la nuvola o l'umidit&agrave; sta ferma o sospesa in aria (tali sono le <lb/>parole del Viviani) non si altera la gravit&agrave; in specie dell'aria premente n&egrave; <lb/>l'altezza, in quel modo che non si altera la gravit&agrave; in specie n&egrave; l'altezza <lb/>dell'acqua di un vaso pieno nell'immersione di corpi galleggiantivi o di <lb/>corpi, se pi&ugrave; gravi in specie, tenutivi sospesi da potenza esteriore. </s>

<s>Se le nu&shy;<lb/>vole son discendenti par che deva crescere la pressione, se ascendenti che <lb/>deva scemare. (Esperimentar questo nell'acqua con corpi discendenti ed <lb/>ascendenti). Se toccano terra in modo che sieno tutto un corpo continuato <lb/>come solido, dovrebbe mancar la pressione, perch&egrave; l'aria che &egrave; sopra pose&shy;<lb/>rebbe e graviterebbe sopra detto umido. </s>

<s>Ma se questo umido, che tocca <lb/>terra, &egrave; cedente e condensabile, la pressione dell'aria operer&agrave; sopra esso, e <lb/>per conseguenza sopra l'argento vivo, come opera l'aria sopra l'acqua che <lb/>sia sopra il mercurio &rdquo; (MSS. Cim., T. X, c. </s>

<s>156). </s></p><p type="main">

<s>Persuaso il Viviani, dictro tali considerazioni, che non era la soluzion <lb/>del difficile problema a ricercarla nel galleggiare e nel premere delle nubi, <lb/>un fatto che gli occorse di sperimentare fu quello da cui venne a essere <lb/>indirizzato per una via diversa, che a lui parve, ed era veramente la pi&ugrave; <lb/>sicura. </s>

<s>Il fatto che si diceva &egrave; cos&igrave; dal Viviani stesso notato: &ldquo; Lo stru&shy;<lb/>mento del mercurio portato in stanza, dove si faccia fuoco, abbassa gi&ugrave; per <lb/>il cannello, e pi&ugrave; e pi&ugrave;, secondo che pi&ugrave; s'avvicina al fuoco, eppure per <lb/>due ragioni doverebbe alzare: Prima, per l'ingresso del calore nel mercurio <lb/>che dovrebbe far l'effetto che fa ne'Termometri; seconda, perch&egrave; il mer&shy;<lb/>curio riscaldato si fa pi&ugrave; leggeri in specie, ed i liquidi occupano sempre nel <pb xlink:href="020/01/876.jpg" pagenum="319"/>cannello maggiore altezza, secondo che sono pi&ugrave; leggeri. </s>

<s>Se dunque que&shy;<lb/>ste due cagioni non dimostrano i loro effetti, &egrave; segno che prevale la cagione <lb/>della minor pressione dell'aria ambiente lo strumento, che per esser riscal&shy;<lb/>data pesa meno &rdquo; (ivi, c. </s>

<s>53). </s></p><p type="main">

<s>Di qui fu condotto il Viviani a dar tutta l'importanza e tutta l'effica&shy;<lb/>cia alle rarefazioni e alle condensazioni dell'aria, dalle quali dipendono, e lo <lb/>stato del cielo e le variazioni del Barometro. </s>

<s>&ldquo; L'aria umida dell'inverno, <lb/>pensava, &egrave; pi&ugrave; calda dell'aria asciutta della medesima stagione, e perci&ograve; &egrave; <lb/>pi&ugrave; rara e pi&ugrave; leggera e meno premente. </s>

<s>L'aria umida dell'estate &egrave; pi&ugrave; <lb/>fresca dell'aria asciutta dell'estate, ond'&egrave; pi&ugrave; densa e pi&ugrave; grave e pi&ugrave; pre&shy;<lb/>mente &rdquo; (ivi, c. </s>

<s>156). Di qui ne concludeva, bench&egrave; non sicuro di questi <lb/>suoi argomenti, in ordine alle variazioni barometriche: &ldquo; Forse l'argento <lb/>vivo sar&agrave; pi&ugrave; alto nel cannello in tempo asciutto che umido, e nell'estate <lb/>pi&ugrave; alto in tempo umido che in tempo asciutto, ma ben nell'asciutto del&shy;<lb/>l'estate sar&agrave; forse pi&ugrave; basso che nell'asciutto dell'inverno, e nell'umido <lb/>dell'estate pi&ugrave; basso che nell'umido dell'inverno &rdquo; (ivi). </s></p><p type="main">

<s>Le variet&agrave; degli effetti cos&igrave; saviamente dal Viviani considerati come di&shy;<lb/>pendenti da quella complicanza di cause, in mezzo alle quali si smarrisce il <lb/>Meteorologo, che non arriva colla mente a determinare delle infinite inco&shy;<lb/>gnite del problema altro che poche; mettevano il soggetto intorno a che si <lb/>discuteva, sotto altre forme da quelle che lo presentava il Borelli, a giudi&shy;<lb/>zio del quale il fatto semplice in modo e costante, da potersene dare una <lb/>dimostrazione sperimentale, era questo: l'aria nuvolosa &egrave; sempre pi&ugrave; pe&shy;<lb/>sante della serena. </s></p><p type="main">

<s>Che il principe Leopoldo per levar quella sua confidenza al Borelli gli <lb/>abbia conferiti, oltre a'suoi, anche i dubbi del Viviani, e gli abbia fatto no&shy;<lb/>tar quella incostanza di effetti dipendenti dalle rarefazioni e dai condensa&shy;<lb/>menti dell'aria, che soli hanno efficacia in alterar lo stato del cielo, e in far <lb/>variare il livello al Barometro; &egrave; cosa molto prababile, mentre &egrave; certo dal&shy;<lb/>l'altra parte, perch&egrave; dimostrato dai documenti, che lo stesso Principe, il <lb/>quale era intorno a ci&ograve; inspirato dal senno del Viviani, faceva avvertito il <lb/>Borelli che, a render variabile il livello barometrico, oltre a quello dell'umido <lb/>e del sereno, potevano concorrere altri innumerevoli accidenti. </s>

<s>Di alcuni <lb/>sovvenutigli, e ridotti a otto capi principali, se ne trova nota nel T. XXIII <lb/>de'Manoscritti del Cimento, col titolo: &ldquo; Diversit&agrave; di accidenti che adesso <lb/>sono sovvenuti poter seguire nell'aria sopra l'argento vivo nello strumento <lb/>denominato..... &rdquo; (c. </s>

<s>205). </s></p><p type="main">

<s>Non per questo per&ograve; il Borelli si rimosse dalle sue persuasioni. </s>

<s>Dodici <lb/>anni e pi&ugrave; dopo, quando sotto il titolo <emph type="italics"/>De motionibus naturalibus a gra&shy;<lb/>vitate pendentibus<emph.end type="italics"/> raccolse tutte insieme, e in ordine di Trattato, le sue <lb/>fisiche esperienze, non lasci&ograve; indietro quelle di Meteorologia barometrica, <lb/>presentandole solennemente in pubblico come le avea conferite in privato, <lb/>e senza nulla dubitar della verit&agrave; de'primi fatti osservati, e delle prime spe&shy;<lb/>culate ragioni. </s>

<s>Permettendoci, per levar tedio a chi legge, di ridurre al co-<pb xlink:href="020/01/877.jpg" pagenum="320"/>mun linguaggio l'originale dettato in latino, cos&igrave; narra il Borelli la storia della <lb/>sua scoperta e della esperienza immaginata per confermarla. </s></p><p type="main">

<s>&ldquo; Fu da noi osservato che, pur rimanendo lo Strumento stazionario, il <lb/>livello del mercurio non sempre si mantiene alla medesima altezza. </s>

<s>Ci&ograve; pu&ograve; <lb/>in parte dipendere dalla varia temperatura dell'aria ora calda, ora fredda, <lb/>ma le variazioni prodotte da questa causa per verit&agrave; son piccolissime, spe&shy;<lb/>cialmente se vada aggiunta alla cima della canna di vetro una palla alquanto <lb/>grossa. </s>

<s>Le variazioni per&ograve;, delle quali io intendo parlare, sono notabilissime, <lb/>e che non dipendano propriamente dal caldo e dal freddo me ne persuade <lb/>il vedersi fare simili variazioni tanto nell'estate quanto nell'inverno, cos&igrave; in <lb/>luogo aperto, come in una stanza chiusa riscaldata dal fuoco. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ho delle sopraddette variazioni appresso di me le Effemeridi per gli <lb/>anni 1657 e 58, nelle quali andavo tutti i giorni notando i gradi del Ter&shy;<lb/>mometro e lo stato del cielo, se cio&egrave; era nuvolo o sereno, e da qual parte <lb/>e in quale ora spirasse il vento; osservazioni ch'io feci ai conforti e ai co&shy;<lb/>mandi del Serenissimo Ferdinando granduca di Toscana, sagacissimo esplo&shy;<lb/>ratore dei segreti della Natura. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sembra ora, da tutte queste mie osservazioni comparate insieme, po&shy;<lb/>tersi dedurre che molte volte, essendo imminente qualche lunga e ostinata <lb/>pioggia, il mercurio si solleva di alquanti gradi nella canna al di sopra del&shy;<lb/>l'altezza ordinaria, e al contrario si suole abbassare nell'atto stesso che cade <lb/>la pioggia. </s>

<s>N&egrave; &egrave; da credere che una tal differenza sia piccola, avend'io pi&ugrave; <lb/>volte osservato in Pisa che, in certi temporali di lunga durata, giungevano <lb/>queste variazioni infino a dodici gradi. </s>

<s>E perch&egrave; serbo ancora appresso di <lb/>me l'esemplare di una lettera, che scrissi nel 1657 al serenissimo principe <lb/>Leopoldo, ora cardinale, in tal subietto, vo'riferire qui brevemente quello <lb/><figure id="id.020.01.877.1.jpg" xlink:href="020/01/877/1.jpg"/></s></p><p type="caption">

<s>Figura 64.<lb/>ch'io avevo gi&agrave; speculato per rendere la ragione di <lb/>questo fatto: onde avvenga cio&egrave; che l'aria prema pi&ugrave; <lb/>fortemente il mercurio innanzi, e meno nell'atto del <lb/>cadere e dopo esser caduta la pioggia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Prendasi una canna barometrica AIC (fig. </s>

<s>64) e, <lb/>fatto il vuoto al solito modo, sia F il punto dove ascende <lb/>e si ferma il livello del mercurio. </s>

<s>Poi si cali questa <lb/>stessa canna nel pi&ugrave; cupo fondo del vaso DK di vetro, <lb/>che si empie di olio o di altro liquido pi&ugrave; leggero. </s>

<s>Il <lb/>livello, per la pressione del liquido sopra infuso, ascen&shy;<lb/>der&agrave; da F in H. </s>

<s>Imperniata poi ne'punti D e G si so&shy;<lb/>prapponga all'olio una scodella N, il fondo della quale <lb/>sia pieno di granelli minutissimi di arena o di acqua <lb/>o di qualche altro liquido pi&ugrave; grave in specie dell'olio. </s>

<s><lb/>Il livello nella canna, per la nuova pressione del corpo grave soprastante, <lb/>si sollever&agrave; ancora alquanto di pi&ugrave;, passando da H per esempio in M. &rdquo; </s></p><p type="main">

<s>&ldquo; Cos&igrave; tutto preparato, rovescisi la scodella N, girevole intorno all'asse <lb/>DG, in modo che i granelli dell'arena o le gocciole dell'acqua, di che ell'era <pb xlink:href="020/01/878.jpg" pagenum="321"/>piena, vengano a cader gi&ugrave; in mezzo all'olio, per similitudine di ci&ograve; che av&shy;<lb/>vien nella pioggia. </s>

<s>Si vedr&agrave; che, mentre durano que'granellini o quelle goc&shy;<lb/>ciole a cadere, il mercurio non si rimuove dal punto M, ma cessata la ca&shy;<lb/>duta, il livello nella canna si abbassa via via, per ritornare al punto H, <lb/>dove l'aveva ridotto il premente peso dell'olio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Da questi evidentissimi esperimenti io penso che si possa facilmente <lb/>risolvere il proposto problema. </s>

<s>E in verit&agrave; che altro sono le nuvole piovose <lb/>se non che un aggregato d'innumerevoli minutissimi granellini di acqua? </s>

<s>E <lb/>perci&ograve;, quando alcuna di queste nuvole nuoter&agrave; per le alte regioni dell'aria, <lb/>o quando quelle particelle acquose scenderanno con lentissimo moto, ver&shy;<lb/>ranno a comprimere con maggior forza la superficie terrestre, di quel che <lb/>non facciasi l'aria pura. </s>

<s>Di qui &egrave; che il mercurio nella vaschetta barome&shy;<lb/>trica, essendo costituito nelle pi&ugrave; basse regioni dell'ammosfera, dee neces&shy;<lb/>sariamente esser premuto, non da solo il peso di tutta la soprastante mole <lb/>dell'aria, ma dal peso altresi delle particelle acquee, di che si compone, <lb/>tutte raccolte insieme, la nuvola suprema. </s>

<s>Pu&ograve; perci&ograve; benissimo avvenire, <lb/>alquanto prima che la pioggia discenda, che il livello del mercurio dentro <lb/>la canna aggiunga alla sua massima altezza, e ivi immobilmente rimanga. </s>

<s><lb/>Ci&ograve; pu&ograve; da un'altra parte avvenire, non per sola ragion delle nuvole, ma <lb/>di qualunque altra simile cosa gravitante, perch&egrave; se qualche poco della pol&shy;<lb/>vere terrestre venga sollevata per caso e largamente dispersa dai venti per <lb/>l'aria, non &egrave; a dubitar che ci&ograve; non sia nuova cagione di far gravitar pi&ugrave; <lb/>ponderosamente l'aria stessa sopra la superficie terrestre. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se poi per qualunque causa la nuvola vada dispersa, cadendo in goc&shy;<lb/>ciole che bagnino il terreno, e allora &egrave; chiaro che quelle gocciole stesse po&shy;<lb/>santi in terra, e non aggravantisi perci&ograve; pi&ugrave; nel mezzo dell'aria, non ag&shy;<lb/>giungono ad essa la loro forza di compressione, e il mercurio perci&ograve; pi&ugrave; <lb/>leggermente premuto torna ad abbassarsi o a ridursi al suo pi&ugrave; infimo li&shy;<lb/>vello &rdquo; (Regio Julio 1670, pag. </s>

<s>238-44). </s></p><p type="main">

<s>Nel 1670, quando si pubblicarono cos&igrave; fatte dottrine in Italia, era da <lb/>sette anni pubblicato in Francia il Trattato del Pascal, cosicch&egrave; si avevano <lb/>le due pi&ugrave; grandi autorit&agrave; in fisica meteorologica concordi in asserire che <lb/>l'aria nuvolosa &egrave; men leggera della serena. </s>

<s>Tanta fu poi quella autorit&agrave; che <lb/>si prest&ograve; piena fede alle asserzioni di cos&igrave; esperti osservatori, pochi essendo <lb/>in Francia coloro che sospettavano essersi ingannato un Pascal, pochissimi <lb/>essendo in Italia quegli altri, che sospettavano essersi ingannato un Borelli. </s>

<s><lb/>Fu questa fede che fece passare inosservato lo sperimento guericchiano, ma <lb/>pur non mancarono alcuni, i quali, osservando per s&egrave; medesimi i fatti, tro&shy;<lb/>varono che corrispondevano realmente coll'esperienza del Guericke e non <lb/>con quella del Borelli. </s></p><p type="main">

<s>&Egrave; di questi da annoverar fra principali il Du-Hamel, il quale, dopo aver <lb/>francamente negato <emph type="italics"/>graviorem esse aera pluvio coelo quam sereno, cum <lb/>ipsa experientia contrarium demonstret,<emph.end type="italics"/> e dop'aver messo in dubbio quel <lb/>che alcuni adducevano per ragione di questo fatto, riconoscendola negli aliti <pb xlink:href="020/01/879.jpg" pagenum="322"/>terrestri che tengono sollevati i vapori, quasi sopra la leggerezza delle loro <lb/>ali. </s>

<s>&ldquo; An potius, soggiunge tosto, idem accidit in aere quod cernimus in <lb/>Machina dum exhauritur. </s>

<s>Tum enim saepe vitrum velut nebula obfuscatur <lb/>et rore madidum apparet. </s>

<s>Sic pluvio coelo et nubibus obducto superior aer <lb/>multum dilatatur et permistas aquae seu vaporum partes post se relinquit, <lb/>ex quibus coalescentibus tum nubes tum imbres oriuntur. </s>

<s>Aer enim debi&shy;<lb/>litatus tot aquae velut atomos non potest exsolvere, ac velut aqua fortis <lb/>simplicis aquae affusione fracti metalli pulverem, sic aquae globulos aer <lb/>dimittit et praecipitat &rdquo; (Philosophia vetus et nova, T. IV, Parisiis 1682, <lb/>pag. </s>

<s>377). </s></p><p type="main">

<s>Non ci voleva altro che il fascino dell'autorit&agrave; del Borelli e del Pascal <lb/>a non lasciarsi persuadere che tale essendo la causa, e tale l'origine della <lb/>pioggia, l'aria nuvolosa pi&ugrave; rarefatta deve necessariamente ponderar sul Ba&shy;<lb/>rometro meno della serena. </s>

<s>Ma il Du-Hamel stesso abbiam veduto com'an&shy;<lb/>dasse dubitoso intorno a cosa per s&egrave; tanto evidente, cosicch&egrave;, non sapendosi <lb/>e non osandosi fare una precisa e netta distinzione del vero dal falso, si <lb/>teneva l'opinion di coloro, che asserivano al contrario del Pascal e del Bo&shy;<lb/>relli, come solamente probabile, e da potersi seguitar con buone ragioni, a <lb/>pari di quelle professate da'due celebratissimi Autori. </s>

<s>Giova in tal proposito <lb/>addur le parole, che scriveva il padre Giuseppe Ferroni, professore di Fi&shy;<lb/>sica nel Collegio di Siena, al suo amico e maestro Vincenzio Viviani. </s></p><p type="main">

<s>&ldquo; ..... Nel dettar l'esperienze degli Elementi, sono in quella dell'aria, <lb/>e dopo varii e nuovi Termometri del caldo e del freddo, del secco ed umido <lb/>dell'aria, sono in quella pi&ugrave; bella di tutte per conoscere se il tempo si pre&shy;<lb/>pari alla pioggia, o si disponga al sereno. </s>

<s>Questo &egrave; il famoso barometro del <lb/>Torricelli, in cui il mercurio ora alzandosi, ora abbassandosi, d&agrave; indizio della <lb/>mutazione del tempo, quanto al disporsi in piovoso o sereno. </s>

<s>Ma io trovo <lb/>gli autori sperimentali molto discordi, perch&egrave; Mons&ugrave; di Amontons, accade&shy;<lb/>mico di Parigi, Alfonso Borelli, Giovan Cristoforo Sturmio dicono che, di&shy;<lb/>sponendosi il tempo al piovoso, per esser l'aria pi&ugrave; grave cresce e pi&ugrave; si <lb/>alza nel collo del Barometro il mercurio, ma disponendosi al sereno, per la <lb/>minor pressione dell'aria pi&ugrave; purgata e pi&ugrave; leggera, meno si sostenta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; All'incontro Giovan Batista Du-Hamel, nella sua Filosofia burgun&shy;<lb/>dica, ed il nostro padre Francesco Lana ed il nostro medico ed eruditissimo <lb/>dottor Gabrielli sentono che l'aria torbida e nugolosa, quando il tempo si <lb/>dispone alla pioggia o neve, sia pi&ugrave; leggera e l'aria serena sia pi&ugrave; grave; <lb/>onde vogliono che, quando meno si sostenta il mercurio, sia segno di piog&shy;<lb/>gia; quando pi&ugrave; si sostenta sia per disporsi al sereno. </s>

<s>E che cos&igrave; sia, il no&shy;<lb/>stro Medico si offerisce di farlo vedere nel suo Barometro a chi nol cre&shy;<lb/>desse. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io oggi insegno l'opinione di questi ultimi, ma non mi piace la <lb/>ragione che l'aria torbida e nugolosa disponentesi a pioggia sia pi&ugrave; leggera <lb/>di quello che sia l'aria serena purgata come un cristallo. </s>

<s>Io assegner&ograve; <lb/>un'altra ragione sovvenutami ed &egrave; questa: La causa sostentativa, non sol <pb xlink:href="020/01/880.jpg" pagenum="323"/>del mercurio ma di altri fluidi sopra il loro livello, &egrave; senza dubbio la pres&shy;<lb/>sione dell'aria, ma questa non &egrave; la causa pi&ugrave; prossima ed immediata quale <lb/>io stimo essere la forza elastica, forza di susta, forza di molla, che ha l'aria. </s>

<s><lb/>Dico dunque che, quando l'aria torbida e nugolosa si dispone alla pioggia <lb/>per i vapori acquei che salgono, resta molto inumidita, e questa umidit&agrave; <lb/>snerva la forza elastica dell'aria. </s>

<s>S'io stringo in pugno la lana secca ed <lb/>asciutta, vedo che ella si dilata, quando apro il pugno, ma s'io stringo la <lb/>lana bagnata, vedo che ha debilitato il suo elaterio, e poco dilatasi, aperto <lb/>il pugno. </s>

<s>Or cos&igrave; l'aria serena, bench&egrave; pi&ugrave; leggera, pi&ugrave; sostenta nel Baro&shy;<lb/>metro il mercurio, perch&egrave; d&agrave; maggior forza d'arco, forza di molla. </s>

<s>Ma l'aria <lb/>torbida disponentesi alla pioggia, bench&egrave; pi&ugrave; pesante, sostenta meno il mer&shy;<lb/>curio, perch&egrave;, inumidita dai vapori acquei che salgono, resta la sua forza <lb/>elastica debilitata &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLVII, c. </s>

<s>126). </s></p><p type="main">

<s>Questo suo pensiero lo scriveva il Ferroni nell'Aprile del 1693, pre&shy;<lb/>gando il Viviani a rispondergli se giudicava che si potesse approvare. </s>

<s>Qual <lb/>fosse precisamente la risposta non siamo ora noi in grado di dirlo, non es&shy;<lb/>sendoci capitato sotto gli occhi il documento, ma, da quelle note che tra&shy;<lb/>scrivemmo di sopra, si pu&ograve; facilmente argomentare che l'opinion del Vi&shy;<lb/>viani era molto diversa e assai pi&ugrave; conforme alla verit&agrave; di quella, ch'erasi <lb/>composta il Ferroni nella sua fantasia. </s>

<s>Fu nonostante a quella occasione che <lb/>si risvegli&ograve; nello stesso Viviani il desiderio di fare esperienza di un concetto <lb/>sovvenutogli, dal qual concetto, quand'avesse avuto corrispondenza nei fatti, <lb/>ne sarebbero derivate, in ordine alla causa delle variazioni barometriche, <lb/>conseguenze molto importanti. </s></p><p type="main">

<s>Quel desiderio si legge espresso sotto questa forma: &ldquo; Esperimentare <lb/>se gli archi dell'aria vengano allentati con lo star lungamente compressi, e <lb/>se il vaso, dove si fa la compressione, si dilati e poi ritorni, ovvero anch'egli <lb/>rimanga in progresso di tempo dilatato &rdquo; (MSS. Cim., T. X, c. </s>

<s>11). </s></p><p type="main">

<s>Forse il Ferroni dette con quel suo pensiero al Viviani l'impulso di <lb/>mettere in esecuzione il proposito fatto da qualche tempo, ma non se ne <lb/>ha certezza, e non sappiam dire perci&ograve; ai nostri lettori quali si fossero i <lb/>resultati dell'esperienza. </s>

<s>Questo solo sappiamo che fu di ci&ograve;, pochi anni <lb/>dipoi, pienamente sodisfatta la scienza dal valorosissimo Hawksbee, il quale, <lb/>mandando ad effetto quel che il Viviani si era proposto, raccolse da un suo <lb/>accuratissimo esperimento &ldquo; che le molle dell'aria possono essere in tal modo <lb/>disturbate da violenti impulsi o da gagliarde compressioni, che si richieda <lb/>un tempo considerabile, perch&egrave; elleno ricuperino di nuovo la naturale loro <lb/>tensione o temporamento &rdquo; (Esper. </s>

<s>fisico-meccan. </s>

<s>cit., pag. </s>

<s>71). </s></p><p type="main">

<s>Raccolse di pi&ugrave; che il tempo e la forza della restituzione son proporzio&shy;<lb/>zionali al tempo e alla forza della compressione, e applic&ograve; queste conclu&shy;<lb/>sioni a render pi&ugrave; compiuta la notizia della causa di alcuni effetti naturali. </s>

<s><lb/>Passando dal senso figurato al reale, si comprende quanto il concetto del <lb/>Viviani, illustrato dalle esperienze dell'Hawksbee, dovesse conferire a sta&shy;<lb/>bilir le leggi dell'attrazione molecolare, relative al diminuir dell'intensit&agrave; di <pb xlink:href="020/01/881.jpg" pagenum="324"/>lei col crescere delle distanze, e come venisse da ci&ograve; ingerito ne'fisici il <lb/>sospetto di un'occulta efficacia dell'elaterio dell'aria, pi&ugrave; o meno compressa, <lb/>in produr tante misteriose variazioni che cos&igrave; spesso occorre d'osservar nel <lb/>livello del Barometro. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Bench&egrave; fosse sottile il concetto sovvenuto in mente al Viviani di spe&shy;<lb/>rimentar se l'elaterio dell'aria si smorza, dopo una compressione diuturna; <lb/>bench&egrave; i resultati sperimentali raccolti dall'Hawksbee riuscissero utilissimi <lb/>a investigar le recondite cause di molti effetti della Natura, che special&shy;<lb/>mente concernono la statica vegetabile e animale, e quella che si pu&ograve; per <lb/>similitudine chiamare statica barometrica; erano tutte queste cose per&ograve; fuor <lb/>di proposito a decider la questione se l'aria, quando &egrave; ingombra di vapori <lb/>nuvolosi preme sul mercurio del Barometro pi&ugrave; o meno, che quando &egrave; lim&shy;<lb/>pida e serena. </s>

<s>La decisione dall'altra parte era riserbata ai fatti, i quali, <lb/>quando fossero stati bene accertati, avrebbero avuto virt&ugrave; d'infirmare le <lb/>autorit&agrave;, bench&egrave; grandissime, del Pascal e del Borelli. </s>

<s>E bench&egrave; paresse che <lb/>non dovesse la cosa presentar poi troppo grandi difficolt&agrave;, vedemmo come in <lb/>sul finir del secolo XVII andassero cauti e quasi non sicuri di s&egrave; tutti co&shy;<lb/>loro, che trovarono le variazioni barometriche andar tutto al contrario di <lb/>quel che furono osservate a Parigi e a Pisa. </s></p><p type="main">

<s>L'incertezza fu finalmente tolta fra noi dal Ramazzini, il quale confess&ograve; <lb/>liberamente essere stati, a persuaderlo del vero, pi&ugrave; eloquenti i fatti, che <lb/>non la grande autorit&agrave; del Borelli, amatissimo suo precettore. </s>

<s>Le osserva&shy;<lb/>zioni ramazziniane furono fatte nel 1694, e pubblicate l'anno appresso in <lb/>Modena, col titolo di <emph type="italics"/>Ephemerides barometricae mutinenses.<emph.end type="italics"/></s></p><p type="main">

<s>Incomincia l'Autore il suo Discorso facendo osservar che a principio <lb/>aveva creduto piuttosto alle parole altrui, che ai fatti, d'ond'ebbe a trovarsi <lb/>incautamente aggirato ne'medesimi errori. </s>

<s>&ldquo; Iisdem erroribus aliorum scripta <lb/>me quoque per aliquot tempus transversum egisse fateri non pudet, ratio&shy;<lb/>cinio enim celeberrimi viri I. </s>

<s>Alphonsi Borelli, in opere tam commendato <lb/><emph type="italics"/>De motionibus naturalibus a gravitate pendentibus,<emph.end type="italics"/> nimis fidens putabam. </s>

<s><lb/>Imo cum tanto praeceptore iurassem quod nebuloso coelo et impendente <lb/>pluvia ob auctam, saltem probabiliter, aeris gravitatem, altius in fistula de&shy;<lb/>buisset elevari mercurius, sicuti post pluviam aere repurgato et redeunte <lb/>serenitate deprimi. </s>

<s>Verum ex observationibus singulis diebus in hac urbe, <lb/>per integrum annum, accurate mihi habitis, deprehendi me non leviter de&shy;<lb/>ceptum ac toto coelo errasse: constanter enim, post diuturnam serenitatem, <lb/>coelo nubibus obducto, ac imminenti pluvia, cum aerem quilibet graviorem <lb/>crederet, mercurium in fistula descendere observavi, attolli autem post plu&shy;<lb/>viarum descensum, aere serenato. </s>

<s>Validissima equidem sunt rationum mo-<pb xlink:href="020/01/882.jpg" pagenum="325"/>menta, quibus Vir clarissimus statuminare satagit propositionem suam CXV <lb/>quae sic habet: <emph type="italics"/>Mercurius in fistula torricelliana altius elevatur, dum aer <lb/>nebulis pluviosis impregnata, et postquam pluvia delapsa est, denuo mer&shy;<lb/>curius in fistula deprimitur.<emph.end type="italics"/> Ast in contrarium ipsa reclamat experentia, <lb/>quae ratiociniis nostris persaepe illudit et ingeniosa conficta, sed falsis fun&shy;<lb/>damentis superstructa, facillime diruit &rdquo; (Mutinae 1695, pag. </s>

<s>II, III). </s></p><p type="main">

<s>Nel qualificar cos&igrave; indirettamente il Ramazzini le dottrine borelliane per <lb/>ingegnose finzioni, si sentiva da un'altra parte inclinare alla riverenza verso <lb/>un tanto precettore, e non sapendo far meglio si studiava di dar nuova forma <lb/>a quelle stesse ingegnose finzioni, per accomodarle, quanto fosse possibile, <lb/>alla realt&agrave; de'fatti osservati. </s>

<s>Vedemmo quanto docilmente secondasse il Bo&shy;<lb/>relli i placiti filosofici del Gassendo, il quale affidava al gioco delle parti&shy;<lb/>celle sulfuree e nitrose sollevate dalla terra e disperse per l'aria alcuni par&shy;<lb/>ticolari effetti di Meteorologia. </s>

<s>Anche il Ramazzini dunque, vedendola cos&igrave; <lb/>favorita dal suo Borelli, ebbe ricorso a quella ipotesi. </s>

<s>&ldquo; Suppono itaque e <lb/>globo terraqueo non solum vapores, qui sunt pluviarum materia, sed mul&shy;<lb/>tas exhalationes diversae indolis continuo plus et minus protrudi et aeri com&shy;<lb/>misceri, ut particulas sulphureas, aluminosas, vitriolicas, mercuriales, etc. </s>

<s>&rdquo; <lb/>(ibi, pag. </s>

<s>XLVII). </s></p><p type="main">

<s>Fatta questa supposizione, congettura il Nostro che la maggior gra&shy;<lb/>vezza, che si sperimenta aver l'aria quando il cielo &egrave; sereno, sia dovuta <lb/>principalmente a quelle invisibili particelle saline terrestri, dalle quali poi <lb/>venendo rilavata l'aria stessa, quando i vapori si condensano e cadono in <lb/>pioggia, non &egrave; maraviglia se men leggermente prema sulla superficie della <lb/>Terra. </s>

<s>&ldquo; Et hoc pacto, ob harum partium mineralium et alterius generis <lb/>praecipitationem et exclusionem ab aeris poris, aer ipse redditur levius &rdquo; <lb/>(ibi, pag. </s>

<s>LIV). </s></p><p type="main">

<s>Le osservazioni barometriche del Ramazzini, dalle quali risultava avve&shy;<lb/>nir di fatto tutto al contrario di quel che credevasi di avere osservato e di&shy;<lb/>mostrato il Borelli, trovarono com'&egrave; facile a supporre, contradittori, fra'quali <lb/>un Francesco Torti, che usci fuori con una sua prima Dissertazione, alla <lb/>quale poi soggiunse <emph type="italics"/>Dissertatio epistolaris altera triceps circa mercurii <lb/>motiones in Barometro,<emph.end type="italics"/> stampata da Bartolommeo Soliani in Modena, nel&shy;<lb/>l'anno 1698. Gli argomenti del Torti per&ograve; non son di molta importanza, ri&shy;<lb/>ducendo la loro forza in considerar la grande autorit&agrave; del Borelli, quasi fosse <lb/>incredibile in tant'uomo un cos&igrave; grave errore. </s></p><p type="main">

<s>Altro pi&ugrave; valido oppositore ebbe l'Autor delle Effemeridi Modanesi nello <lb/>Schelhamer, il quale ben persuaso dell'errore preso dal Borelli, e conve&shy;<lb/>nendo che i fatti passavan pure a quel modo che gli aveva osservati il Ra&shy;<lb/>mazzini, negava per&ograve; l'ipotesi ramazziniana, giudicandola inverisimile, e ne <lb/>proponeva una sua propria. </s>

<s>Fece di ci&ograve; il soggetto a un'Epistola stampata <lb/>in Modena nel 1698, e indirizzata a Luca Schroek col titolo seguente: &ldquo; So&shy;<lb/>lutio problematis cur mercurius in tubo torricelliano, seu Barometro, plu&shy;<lb/>vioso tempore descendat cum deberet ascendere. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/883.jpg" pagenum="326"/><p type="main">

<s>Le ragioni per cui lo Schelhamer crede l'ipotesi del Ramazzini inve&shy;<lb/>rosimile, son queste: prima, che non si vede e non s'intende come e d'onde <lb/>abbiano origine le particelle nitrose nell'aria, non trovandosene altro che in <lb/>alcuni luoghi eccezionali assai leggeri vestigi; poi &egrave; da notar che, mentre <lb/>s'intende a levar via con quella ipotesi un paradosso, s'incappa in un altro <lb/>paradosso maggiore, qual sarebbe che un corpo galleggi in un mezzo tanto <lb/>pi&ugrave; leggero in specie. </s>

<s>&ldquo; Admissa ratione cl. </s>

<s>Ramazzini consequens aliud <lb/>absurdum colligeretur. </s>

<s>Hoc enim posito, particulas salinas, nitrosas, terreas <lb/>in aere innatantes plus millies superare necessum foret ipsius aeris pondus <lb/>in quo natant, adeoque graviora corpora in leviori innatare, seu aerem ma&shy;<lb/>ius pondus substinere quam ipse constituat. </s>

<s>Quod facile est ostendere. </s>

<s>Nam <lb/>si aqua eas deprimere et praecipitare ex aere debet, oportet eam replere <lb/>omnes aeris poros illosque totos, nam alias possent utraque in iisdem poris <lb/>simul haerere. </s>

<s>At aqua millies aequat pondus aeris: fit autem ille levior ex <lb/>hypothesi, si aquosae deturbant salinas. </s>

<s>Ergo necessum est eas aqua omni <lb/>in aere contenta fuisse graviores, adeoque plus millies aeris pondus supe&shy;<lb/>rasse &rdquo; Epistola ecc., Mutinae 1698, pag. </s>

<s>4, 5). </s></p><p type="main">

<s>La soluzione, dall'altro canto, che il Medico tedesco proponeva contro <lb/>quella del nostro Italiano, era semplicissima, e ragionevolissima, perch&egrave; cos&igrave; <lb/>ragionava: Se i nuvoli stanno sospesi per l'aria, dunque son pi&ugrave; leggeri <lb/>dell'aria: dunque a ciel nuvoloso il mercurio nel Barometro &egrave; premuto in <lb/>parte dall'aria soprastante, e in parte da una cosa ch'&egrave; pi&ugrave; leggera del&shy;<lb/>l'aria; dunque dev'esser premuto men fortemente che quando la colonna <lb/>&egrave; tutta composta d'aria schietta, ossia, quando il cielo &egrave; tutto sereno. </s></p><p type="main">

<s>Questa spiegazione, che dicemmo essere semplicissima e atta a persua&shy;<lb/>der facilmente, non riusciva per&ograve; compiuta, essendo che il mercurio nello <lb/>strumento seguita a mantenersi basso, anco quando i vapori condensati in <lb/>gocciole divengono talmente pi&ugrave; gravi in specie dell'aria, che sono spinti a <lb/>cader gi&ugrave; in mezzo ad essa. </s>

<s>Dall'altra parte veniva dallo Schelhamer, col&shy;<lb/>l'argomento riferito di sopra, cos&igrave; ben dimostrata l'inverosimiglianza delle <lb/>particelle saline notanti per l'aria, e la loro inefficacia in produr le varia&shy;<lb/>zioni barometriche, da doversene persuadere anche lo stesso Ramazzini, il <lb/>quale, arretratosi innanzi alle grandi difficolt&agrave; che presentava il problema, <lb/>si rivolse al celebre amico suo Gotifredo Leibniz per averne la soluzione. </s></p><p type="main">

<s>Il Leibniz invoc&ograve; l'aiuto della Meccanica, e rappresent&ograve; gli effetti me&shy;<lb/>teorologici per mezzo di uno strumento, che ha grandissima somiglianza con <lb/>quella Bilancia immaginata e descritta da Galileo (Alb. </s>

<s>XIII, 309) per espe&shy;<lb/>rimentare la forza della percossa. </s>

<s>&ldquo; Esto tubus AB (fig. </s>

<s>65) infra clausus <lb/>in B, aqua plenus, erectus, ex librae extremo suspensus, ac cum pondere <lb/>opposito in aequilibrio constitutus. </s>

<s>Ibi in aquae superficie natet cavum ali&shy;<lb/>quod corpus D, ex materia gravi, casurum si aqua intraret. </s>

<s>Ponamus obtu&shy;<lb/>ratum esse eius foramen, sed ita ut paulatim aquae pervium fiat; ergo, ubi <lb/>ea intraverit, descendet corpus D versus fundum B. </s>

<s>His positis, durante de&shy;<lb/>scensu corporis D, cessaturum esse aequilibrium aio, descensurumque pon-<pb xlink:href="020/01/884.jpg" pagenum="327"/>dus C ac totum tubum AB elevatum iri. </s>

<s>Cuius rei ratio est manifesta quod, <lb/>quantum descendit D, in tantum ab aqua tubi libra non sustinetur, et ea&shy;<lb/>tenus non resistit ponderi opposito. </s>

<s>Compara iam pondus C cum hydrar&shy;<lb/><figure id="id.020.01.884.1.jpg" xlink:href="020/01/884/1.jpg"/></s></p><p type="caption">

<s>Figura 65.<lb/>gyro, aquam tubi cum aeris co&shy;<lb/>lumna, corpus natans D guttis plu&shy;<lb/>viae. </s>

<s>Nempe, cum guttae tam gran&shy;<lb/>des fiunt ut amplius ab aere non <lb/>sustineantur, descendereque inci&shy;<lb/>piunt, tota columna aeris levior <lb/>est quam ante, mercuriumque in <lb/>tubo suspensum ad priorem altitu&shy;<lb/>dinem non sustinebit, itaque de&shy;<lb/>scendit nonnihil mercurius. </s>

<s>Con&shy;<lb/>tra, sereno aere, guttae aquae ita <lb/>imminuuntur, et per aerem di&shy;<lb/>sperguntur, ut per se descendere <lb/>non possint &rdquo; (Gotifredi G. </s>

<s>Leib&shy;<lb/>nitii Op. </s>

<s>Omn., T. II, P. II, Ge&shy;<lb/>nevae 1768, pag. </s>

<s>75). </s></p><p type="main">

<s>Ma, anche quando il vapore elastico diffuso nel ciel sereno si condensa <lb/>in nuvola, il Barometro si abbassa, eppur la nuvola non discende, e riman <lb/>tuttavia ad aggiunger peso a quell'aria, sulla quale galleggia; cosicch&egrave;, per <lb/>questa parte, lo sperimento leibniziano riusciva difettoso, e insufficiente a <lb/>rappresentar tutta intiera la verit&agrave; del fatto meteorologico. </s>

<s>Piacque nono&shy;<lb/>stante al Ramazzini quella meccanica dimostrazione, e ne facilit&ograve; la pratica <lb/>sperimentale, tenendo sospeso per un filo al giogo della bilancia un corpo <lb/>grave immerso nell'acqua del tubo; corpo che, reciso il filo, cadeva natu&shy;<lb/>ralmente in fondo trattovi dal proprio peso. </s></p><p type="main">

<s>Il Desaguliers per&ograve; messe in mala fama, nelle Transazioni anglicane <lb/>del 1717, quel che tanti altri avevano applaudito e, o fosse per malizia, o <lb/>fosse per non aver bene atteso ai particolari della descrizione leibniziana, <lb/>supponeva che il peso, invece di gravar sulla bilancia, come il Leibniz di&shy;<lb/>ceva, fosse, prima di cader per l'acqua, sostenuto da qualche forza stra&shy;<lb/>niera. </s>

<s>Quella scrittura del Desaguliers parve una diffamazione al nostro Pie&shy;<lb/>ranton Michelotti, il quale prese perci&ograve; a far del celeberrimo amico suo le <lb/>difese concludendole in queste parole: </s></p><p type="main">

<s>&ldquo; Quare phaenomenon Barometri a celeberrimo Leibnitio optime.... <lb/>explicatur per guttas aqueas primo minores suspensas haerentes in aere, <lb/>quae et atmosphaeram graviorem reddunt, et columnam mercurialem in tubo <lb/>altius elevant; postea vero in grandiores massulas coalescentes, atque iccirco <lb/>superficiebus minoribus quam earum moles exigere videntur, comprehen&shy;<lb/>sas, gravitate sua vim fricationis superantes: quae itaque, quum descendere <lb/>incipiunt, seseque a nexu villorum aereorum, quibus implicabantur, expe<gap/><lb/>diunt, statim ipsa atmosphaera levior redditur, ac proinde mercurius minu<gap/><pb xlink:href="020/01/885.jpg" pagenum="328"/>quam antea pressus protinus in tubo descendit &rdquo; (De separatione liquid., <lb/>Venetiis 1721, pag. </s>

<s>47, 48). </s></p><p type="main">

<s>Che il fenomeno del Barometro per&ograve; fosse dal Leibniz ottimamente spie&shy;<lb/>gato, si sarebbe potuto credere al Michelotti, quando fosse stato vero che il <lb/>livello del mercurio si abbassa dentro la canna, solamente nell'atto che le <lb/>gocciole piovose cadono a terra; ma se l'osservazione dimostra farsi quel&shy;<lb/>l'abbassamento anche nel tempo che le vescicole vaporose stanno sospese e <lb/>galleggianti per l'aria, non si vede con qual ragione si potesse salvare quel&shy;<lb/>l'ingegnoso leibniziano esperimento. </s></p><p type="main">

<s>Chi rimedita intorno ai fatti fin qui narrati, non pu&ograve; non sentirsi preso <lb/>di gran maraviglia vedendo cos&igrave; grandi uomini, e nostrali e forestieri, aver <lb/>tanta fiducia nella soluzion di un problema, che seduceva coll'artifizio dei <lb/>mezzi usati a risolverlo, senz'essere per&ograve; veramente risoluto: e dall'altra <lb/>parte non facevasi nessun conto della vera soluzione sperimentale, che, sul <lb/>principio del raro e del denso, ne aveva data tanti anni prima il Guericke. </s></p><p type="main">

<s>Altro motivo del non s'intender come mai Fisici cos&igrave; illustri non si <lb/>curassero d'invocare il principio delle rarefazioni e de'condensamenti del&shy;<lb/>l'aria, &egrave; che, per questo stesso principio, rendevasi anche di pi&ugrave; la ragione <lb/>del variar che fa di livello il Barometro, nel cos&igrave; volubile moto del vento. <lb/></s>

<s>&ldquo; Mirum, ebbe a esclamare il Ramazzini, tornando a considerare le sue Effe&shy;<lb/>meridi, mirum est autem quomodo australes venti mercurium deprimant, <lb/>boreales vero attollant &rdquo; (Ephaemerides cit., pag. </s>

<s>XXII). </s></p><p type="main">

<s>Pareva che tutta la maraviglia dovesse esser tolta, ripensando che l'aria <lb/>tiepida spirata d'Austro &egrave; pi&ugrave; rarefatta, e quella fredda spirata da Borea &egrave; <lb/>pi&ugrave; condensata. </s>

<s>Era un tal pensiero per verit&agrave; passato in mente al Du-Ha&shy;<lb/>mel, ma e'fece poi pi&ugrave; volentieri accoglienza a un altro pensiero, che lu&shy;<lb/>singhiero gli ragionava essere i venti boreali sul mercurio pi&ugrave; ponderosi, <lb/>perch&egrave; spirano di sopra in gi&ugrave;, e gli australi invece men ponderosi, perch&egrave; <lb/>spirano di traverso. </s>

<s>&ldquo; An potius flante aquilone aer fit densior? </s>

<s>Hinc tubo <lb/>optico velut undis asperior videtur, ac minus pellucet. </s>

<s>Hinc Pyrenaea iuga <lb/>nivibus cana et idem dicendum est de aliis montibus coelo sereno non tam <lb/>distincte eminus cernuntur ac coelo nubibus obducto. </s>

<s>Fieri etiam potest ut <lb/>Aquilo deorsum ruat, et multum materiae secum vehat, cum auster ex <lb/>transverso spiret &rdquo; (Philosophia cit., pag. </s>

<s>378). </s></p><p type="main">

<s>Essendosi cos&igrave; fatte difficolt&agrave;, prosegue ivi a dire il Du-Hamel, poco fa <lb/>proposte nella R. </s>

<s>Accademia parigina, <emph type="italics"/>hanc rationem satis idoneam red&shy;<lb/>didit doctissimus Borellus,<emph.end type="italics"/> ed &egrave; la ragion che l'Autore <emph type="italics"/>De motion. </s>

<s>natur.<emph.end type="italics"/><lb/>rendeva dalle variazioni barometriche, secondo il vario stato del cielo. </s>

<s>In <lb/>proposito di che, lasciando che altri ripensi a quel singolar favore ch'ebbe <lb/>appresso i fisici di Parigi l'ipotesi del Nostro, non &egrave; a tacer di un fatto <lb/>straordinario occorso a osservare in Pisa allo stesso Borelli, n&egrave; di quei che <lb/>faceva, dietro ci&ograve;, stravaganti presagi. </s></p><p type="main">

<s>&ldquo; Questa mattina (cos&igrave; scriveva il d&igrave; 5 marzo 1660 al principe Leo&shy;<lb/>poldo) a caso mi sono accorto che, nel cannello ordinario dell'argento vivo, <pb xlink:href="020/01/886.jpg" pagenum="329"/>si trova il mercurio sollevato intorno a 20 gradi sopra la massima altezza <lb/>osservata da me, quasi per lo spazio di tre anni.... Or questa gran stra&shy;<lb/>vaganza, se &egrave; vero quello che io fin qui fermamente ho creduto, che la gra&shy;<lb/>vezza maggi ore o minore dell'aria sia cagione di tal disuguale sollevamento <lb/>dell'argento vivo n el cannello, mostra che l'aria, che sovrasta all'orizzonte <lb/>di Pisa, sia eccessivamente e straordinariamente pi&ugrave; aggravata di quel che <lb/>sia stato per altri tempi dalla mistura d'altre materie vaporose acquee o ter&shy;<lb/>restri. </s>

<s>A tale inaspettata stravaganza vedremo se ne segue qualche straor&shy;<lb/>dinario effetto di eccessiva ed abbondante pioggia, oppure, quando le ma&shy;<lb/>terie non sieno acquee e non venghino dissipate dai venti, vedremo se per <lb/>avventura ne succedesse qualche apparenza di quelle che sogliono prece&shy;<lb/>dere alle comete &rdquo; (MSS. Cim., T. X, c. </s>

<s>10). </s></p><p type="main">

<s>Al principe Leopoldo non parve poi il fatto tanto straordinario, n&egrave; che <lb/>ne dovessero perci&ograve; seguire gli accennati pronostici, ma credeva che una <lb/>continuazione di venti gagliardi potesse accumulare gran quantit&agrave; d'aria so&shy;<lb/>pra l'orizzonte di Pisa e suoi contorni, dalla qual mole venisse ad accre&shy;<lb/>scersi il peso dell'aria, ed in conseguenza il sollevamento dell'argento vivo <lb/>nel cannello (ivi, c. </s>

<s>12). </s></p><p type="main">

<s>Rispondeva il Borelli parergli difficil cosa che perseverassero i venti per <lb/>tanti giorni, e che potessero i cavalloni dell'aria sostenersi cos&igrave; lungamente, <lb/>senza spianarsi. </s>

<s>Men difficile stimava a intendere &ldquo; che l'aria, senza punto <lb/>alterar la sua sfericit&agrave;, n&egrave; alzarsi sopra il livello estremo dell'oceano aereo, <lb/>possa rendersi pi&ugrave; grave di prima, in virt&ugrave; dell'aggiunta di nuove esalazioni <lb/>terree o acquee pi&ugrave; gravi in spezie della stess'aria &rdquo; (ivi, c. </s>

<s>14). </s></p><p type="main">

<s>Mentre che cos&igrave; in Toscana si disputava delle ragioni, il Guericke in <lb/>Magdeburgo osservava i fatti, e sopr'essi fondava i suoi pronostici. </s>

<s>Aveva <lb/>egli notato tale costanza tra l'abbassarsi del livello barometrico e il segui&shy;<lb/>tarne qualche procella, che si confid&ograve; di presagirla, quasi come necessario <lb/>effetto di una causa gi&agrave; conosciuta. </s>

<s>&ldquo; Ego certe, cum praeterito anno (1660) <lb/>quo ingens ille ventus ac tempestas fuit, ex paulo ante memorato Experi&shy;<lb/>mento singularem et extraordinariam aeris alterationem deprehendi, qui adeo <lb/>levis praeter consuetum alias modum fuit redditus, ut virunculi digitus (che <lb/>segnava il livello nel Barometro) infra infimum etiam in vitreo tubo nota&shy;<lb/>tum punctum descenderit. </s>

<s>Quo viso praesentibus palam dixi magnam sine <lb/>dubio tempestatem alicubi extitisse. </s>

<s>Vix duae clapsae erant horae, cum ven&shy;<lb/>tus ille procellosus in nostram etiam regionem, minus tamen violentus, quam <lb/>in Oceano fuerat, irruit &rdquo; (Esperim. </s>

<s>magdeburg. </s>

<s>cit., pag. </s>

<s>100). </s></p><p type="main">

<s>Questo modo per&ograve; di presagir le procelle, per mezzo del Barometro, <lb/>non fu divulgato che nel 1672, quando pubblic&ograve; il Guericke i suoi Esperi&shy;<lb/>menti nuovi di Magdeburgo. </s>

<s>Ebbe perci&ograve; ragione il Vossio, dando nel 1663 <lb/>alla luce il suo libro <emph type="italics"/>De motu marium et ventorum,<emph.end type="italics"/> di trattar dell'Aero&shy;<lb/>scopio <emph type="italics"/>ad praecognoscendas tempestates,<emph.end type="italics"/> e ch'egli ivi nel cap. </s>

<s>XIX descrive, <lb/>come di uno strumento <emph type="italics"/>a nemine quod sciam hactenus observati.<emph.end type="italics"/></s></p><p type="main">

<s>Il fondamento certo di que'nuovi presagi posava tutto sul fatto che <pb xlink:href="020/01/887.jpg" pagenum="330"/>&ldquo; quandocumque ventus aut procella aliqua a mari oritur, sensim et mani&shy;<lb/>feste deprimitur altitudinem hydrargiri, idque exacte ad legem et mensuram <lb/>ingruentis tempestatis. </s>

<s>Quando vero illa remittit et malacia redit, iterum <lb/>adscendit hydrargyrus.... Porro tantae utilitatis esse existimo hoc experi&shy;<lb/>mentum ut nesciam an ullum aliud aeque tutum et idoneum ad praeviden&shy;<lb/>das tempestates possit excogitari &rdquo; (Hagae Comitis, pag. </s>

<s>122). </s></p><p type="main">

<s>I presagi del Guericke e del Vossio per&ograve; eran fondati sopra osserva&shy;<lb/>zioni, che rendevano probabilissimo esser causa delle variazioni barometriche <lb/>il violento soffiar tempestoso de'venti, ma non se ne aveva ancora una cer&shy;<lb/>tezza sperimentale, che fu quasi un mezzo secolo dopo data dal valorosis&shy;<lb/>simo Hawksbee. </s>

<s>Condensata l'aria in un vaso, da cui facevala uscire in <lb/>soffi, che passassero sopra il mercurio della scodella, nella quale era im&shy;<lb/>mersa la canna barometrica, osservava che a ogni soffio si abbassava nota&shy;<lb/>bilmente nella stessa canna il livello. </s>

<s>Da un tale esperimento, ne conclu&shy;<lb/>deva l'Autore, &ldquo; abbiamo una chiara e naturale riprova della discesa e delle <lb/>vibrazioni del mercurio nelle violenti burrasche e tempeste. </s>

<s>Conciossiach&egrave; <lb/>l'estrema forza di quelle folate di vento indeboliscono la pressione delle so&shy;<lb/>prastanti ammosferiche colonne, da cui dee necessariamente seguire la di&shy;<lb/>scesa del mercurio. </s>

<s>E quell'interrotta ineguale azione di quelle folate, ov&shy;<lb/>vero il presto e subito loro ritorno sono capaci di produrre e continuare i <lb/>moti vibratorii, cio&egrave; le spedite salite e discese di quello &rdquo; (Esperienze cit., <lb/>pag. </s>

<s>74). </s></p><p type="main">

<s>Cos&igrave;, in mezzo e dopo tante vicende, per le quali s'&egrave; dovuta aggirare <lb/>la nostra storia, il Guericke e l'Hawksbee fondavano quegli sperimenti, per <lb/>i quali finalmente s'intese la vera causa delle variazioni barometriche, e si <lb/>ridusse alle giuste ragioni il Barometro in presagir la pioggia o il sereno <lb/>la tranquillit&agrave; dell'aria, e l'imperversar dei venti. </s></p><pb xlink:href="020/01/888.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO IX.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Del sistema del Mondo<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Del sistema del Mondo immaginato dagli antichi Peripatetici: Della Sintassi platonica e della co&shy;<lb/>pernicana, e quali fossero i primi loro incontri appresso gli stranieri. </s>

<s>&mdash; II. </s>

<s>Del Sistema coper&shy;<lb/>nicano in Italia, e segnatamente di Galileo Galilei. </s>

<s>&mdash; III. </s>

<s>Del Dialogo galileiano sopra i due <lb/>Massimi sistemi del Mondo. </s>

<s>&mdash; IV. </s>

<s>Delle avventure del Copernicismo dai tempi di Galileo alla <lb/>fine del secolo XVII. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>I mezzi suggeriti dall'arte sperimentale per lo studio delle Meteore si <lb/>riducono sostanzialmente a quelli, che sugger&igrave; l'arte stessa ai Fisici per lo <lb/>studio degli astri, i quali pure, essendo costituiti in regioni cos&igrave; remote da <lb/>noi, non possono esser soggetto immediato e diretto ai nostri artificiosi espe&shy;<lb/>rimenti. </s>

<s>Come perci&ograve; la storia delle cose passate ci mostrava la Meteorolo&shy;<lb/>gia aiutarsi d'imitare con l'arte la Natura, e cos&igrave; riuscire ad intendere, per <lb/>la similitudine degli effetti osservati, la similitudine delle cause operanti; <lb/>s'aiut&ograve; in pari modo l'Astronomia rappresentando graficamente in mappe o <lb/>con macchine artificiali il moto e le varie apparenze dei pianeti. </s>

<s>I Globi e <lb/>le Sfere armillari son d'uso tanto antico quanto sono antichi i principii della <lb/>scienza astronomica, ma chi volesse avere un esempio dell'efficacia di cos&igrave; <lb/>fatti artificii, i quaii imitando gli effetti ne fanno argomentar sicuramente alle <lb/>cause naturali, ripensi a quella Macchinetta inventata dai nostri Accademici <lb/>del Cimento, per la quale, rappresentandosi tutti i fenomeni dell'anello di <lb/>Saturno, si pot&egrave; dare una fisica dimostrazione del sistema ugeniano. </s></p><p type="main">

<s>Simili in certo modo alle Meteore son, per la studiosa osservazione, gli <lb/>oggetti, i quali, bench&egrave; non si trovino costituiti in aria ma sopra la super-<pb xlink:href="020/01/889.jpg" pagenum="332"/>ficie terrestre, hanno nulladimeno rispetto a noi, o per gl'impedimenti in&shy;<lb/>terposti o per la lontananza, le loro vie inaccessibili. </s>

<s>Dette un s&igrave; fatto stu&shy;<lb/>dio occasione a inventar le diottre e i tubi aperti a diriger la linea di mira, <lb/>e a togliere le irradiazioni avventizie, supplendo opportunamente e secondo <lb/>la loro possibilit&agrave; al difetto de'Canocchiali. </s>

<s>N&egrave; perci&ograve; i Canocchiali stessi <lb/>dispensarono nelle osservazioni celesti dall'arte imitativa delle apparenze na&shy;<lb/>turali, ma dimostrando pi&ugrave; secondo il vero quelle tali apparenze, riuscirono <lb/>efficacissimi a conformar meglio alle imitabili opere della Natura gli artifi&shy;<lb/>ciosi nostri macchinamenti. </s></p><p type="main">

<s>Tutti questi apparati strumentali per&ograve; appartengono all'Astronomia fisica, <lb/>intorno alla quale solamente dovrebbe intrattenersi la nostra storia, ma per&shy;<lb/>ch&egrave; la fisica, senza la matematica, essendo materia senza forma, riuscirebbe <lb/>inintelligibile, non si pu&ograve; lasciar addietro da noi di far qualche cenno del&shy;<lb/>l'Astronomia matematica, la quale precede alla fisica, come sempre per legge <lb/>universale la sintesi precede all'analisi, o come la forma precede alla materia. </s></p><p type="main">

<s>Grande Sintassi perci&ograve; soleva chiamarsi il sistema del mondo dai Filo&shy;<lb/>sofi antichi. </s>

<s>Il luogo da giudicar l'ordine e la particolare disposizione di <lb/>quella Sintassi &egrave; per noi naturalmente la Terra, dalla quale, osservandosi il <lb/>Cielo, in due modi ugualmente bene si salvavano le apparenze di lui: o col <lb/>supporre ch'egli si volga attorno alla terra immota o che la Terra stessa <lb/>ruoti intorno al suo asse. </s>

<s>Era quel primo supposto, senza dubbio, pi&ugrave; con&shy;<lb/>forme alle esteriori apparenze e meglio accomodato all'intelligenza del volgo, <lb/>ma que'pi&ugrave; sottili Filosofi, cos&igrave; esperti dell'inganno che spesso ci fanno i <lb/>sensi, non dubitarono di attenersi al secondo, come pi&ugrave; conforme a una <lb/>meglio ordinata architettura dell'Universo. </s></p><p type="main">

<s>S'annoverano tra cos&igrave; fatti Filosofi quegli antichi italiani discepoli di <lb/>Pitagora, i quali ebbero poi nel gran Platone la pi&ugrave; splendida rappresen&shy;<lb/>tanza. </s>

<s>Si sa essere le dottrine di lui informate da quel principio che non <lb/>si dee credere ai sensi, i quali si limitano alla materia, ma alla mente, nella <lb/>quale irraggia la divina intelligibilit&agrave; della forma. </s>

<s>Platone perci&ograve;, pi&ugrave; che <lb/>con gli occhi del corpo, contempla il cielo con le vedute dell'intelletto, e <lb/>conclude che l'apparir la immensa sfera stellata aggirarsi tutta intorno alla <lb/>nostra piccola Terra &egrave; un inganno degli occhi, e che non pu&ograve; la Sapienza <lb/>del Creatore aver disposte le cose cos&igrave; fuor d'ordine, come si giudicherebbe <lb/>dai primi aspetti. </s></p><p type="main">

<s>La lampada, che d'ogni parte rischiara il mondo, &egrave; il Sole, e il sa&shy;<lb/>pientissimo Ordinatore dev'aver collocata quella lampada ardente nel mezzo <lb/>del bellissimo Tempio. </s>

<s>Intorno al Sole immoto perci&ograve;, e costituito nel cen&shy;<lb/>tro della immota sfera stellata, si rivolgono in orbite circolari Saturno, Giove, <lb/>Marte e la Terra con la sua Luna. </s>

<s>La collocazione cos&igrave; ordinata di questi <lb/>pianeti era per Platone certissima, perch&egrave; venivano a dimostrarla tale i loro <lb/>osservati aspetti: in gran dubbio rimaneva ancora per&ograve; il luogo dove oppor&shy;<lb/>tunamente collocarsi Venere e Mercurio. </s>

<s>Le loro elongazioni tanto pi&ugrave; ri&shy;<lb/>strette di quelle che si fan da Saturno, da Giove, e dallo stesso Marte, e il <pb xlink:href="020/01/890.jpg" pagenum="333"/>non essersi veduti mai Venere e Mercurio nell'opposizione, avrebbero con&shy;<lb/>sigliato il Filosofo a collocarli tra la Terra e il Sole, ma a lui, che teneva <lb/>tutti i pianeti essere per s&egrave; oscuri, se non in quanto gli allumina il Sole, <lb/>si faceva, ad ammettere quell'ordinamento, una grandissima difficolt&agrave;, ed <lb/>era che, costituiti Venere e Mercurio inferiori, avrebbero dovuto mostrar, <lb/>come la Luna, la variet&agrave; delle fasi, le quali, perch&egrave; non furono osservate <lb/>mai, fecero deliberar finalmente Platone a costituir superiori anche quelli, <lb/>che parevano essere i due pi&ugrave; prossimi Pianeti. </s></p><p type="main">

<s>Nel Timeo dunque, dove si leggono queste cose, troviamo cos&igrave; descritta, <lb/>o diciam meglio accennata, la prima gran Sintassi dell'Universo. </s>

<s>Successe <lb/>poco dopo Aristotile, di principii tutt'affatto diversi, come sappiamo. </s>

<s>Egli <lb/>nel II Libro <emph type="italics"/>De coelo<emph.end type="italics"/> discusse la question pitagorica, alla quale, dop'aver <lb/>riferita l'opinion di coloro che stabiliscon la Terra nel mezzo, accenna <lb/>con s&igrave; fatte parole: &ldquo; Pythagorici autem habitantes Italiam contradicunt illis <lb/>et dicunt.... quod Terra est stellarum una et revolvitur circulariter et ex <lb/>motu eius circulari fit nox et dies &rdquo; (Tomus V, Operum, Venetiis 1560, <lb/>c. </s>

<s>151 v.). </s></p><p type="main">

<s>Il Filosofo per&ograve; rifiuta una cos&igrave; fatta ipotesi per pi&ugrave; ragioni: Prima, <lb/>perch&egrave; il moto circolare &egrave; violento e non pu&ograve; perci&ograve; essere eterno; poi, <lb/>perch&egrave; se si movesse la Terra si dovrebbe veder qualche mutazione farsi <lb/>nelle stelle fisse &ldquo; hoc autem non videtur fieri, sed semper eadem apud <lb/>eadem loca ipsius et oriuntur et occidunt &rdquo; (ibi, c. </s>

<s>167 v.). Soggiunge inol&shy;<lb/>tre che, movendosi la Terra, i proietti in gran distanza non tornerebbero <lb/>al luogo preciso d'onde furon partiti, ond'&egrave; che da tutto questo conclude: <lb/>&ldquo; Manifestum est igitur quod necesse est in medio Terram esse et immo&shy;<lb/>bilem &rdquo; (ibi, c. </s>

<s>169). </s></p><p type="main">

<s>Notabile &egrave; quel che dice Aristotile contro i Pitagorici nell'accingersi a <lb/>confutarli, accusandogli di avere sbagliato metodo in filosofar delle cause na&shy;<lb/>turali, imperocch&egrave; non ragionan costoro, secondo lui, sui fatti, come si con&shy;<lb/>verrebbe, ma i fatti accomodano alle loro intenzioni: &ldquo; Et opinantur hanc <lb/>opinionem, quia non quaerunt cognitionem causarum rerum et sermonum <lb/>in eis ex visu, sed mutant visum secundum suam voluntatem, donec labo&shy;<lb/>rant in confirmando illam voluntatem &rdquo; (ibi, c. </s>

<s>151 v.). </s></p><p type="main">

<s>Dicemmo essere quell'accusa notabile, perch&egrave; ci porge motivo d'argo&shy;<lb/>mentare che la questione del moto e della quiete della Terra si risolvesse <lb/>ne'metodi filosofali variamente seguiti da Aristotile e da'Pitagorici precur&shy;<lb/>sori a Platone. </s>

<s>Del resto si pu&ograve; quell'accusa ritorcere contro chi la mosse, <lb/>imperocch&egrave;, non i Pitagorici, ma gli Aristotelici piuttosto accomodavano i <lb/>fatti alle loro intenzioni. </s>

<s>La Terra posta immobile nel mezzo e corteggiata <lb/>tutto intorno dal Cielo configurava il mondo fisico sull'esempio del mondo <lb/>intellettuale, in mezzo a cui, secondo Aristotile, risiede e regna la Ragione <lb/>legislatrice e dea. </s>

<s>Nel sistema pitagorico, al contrario, non &egrave; lo scettro del <lb/>regno posto in mano alla Ragione dell'uomo rappresentata nella Terra, ma <lb/>nelle mani della Sapienza e Onnipotenza di Dio rappresentato nel Sole. </s>

<s>Tanto <pb xlink:href="020/01/891.jpg" pagenum="334"/>&egrave; poi propria questa differenza ai due differenti sistemi filosofici che, in <lb/>mezzo alla lunga e ostinata tirannide aristotelica, sempre si torn&ograve; a cono&shy;<lb/>scere il moto della Terra intorno al Sole, che insorsero gl'intelletti a ricon&shy;<lb/>quistare la loro filosofica libert&agrave; con Platone. </s></p><p type="main">

<s>Nell'ecclettismo enciclopedico della scuola alessandrina Aristarco di <lb/>Samo professa il moto della Terra, e Archimede, nel porre il fondamento a <lb/>quel suo celebre calcolo dell'arena, lo segue, e di lui e della sua ipotesi <lb/>cos&igrave; scrive: &ldquo; Ea vero quae habentur ab astronomis scripta discutiens Ari&shy;<lb/>starchus Samius hypotheses quasdam scriptis prodidit, ex quibus suppositis <lb/>consequitur mundum multiplicem esse eius qui mox praescriptus est. </s>

<s>Sup&shy;<lb/>ponit enim inerrantia sidera et solem non moveri. </s>

<s>Terram vero ferri in gy&shy;<lb/>rum circa solem qui in medio stadio iacet &rdquo; (Opera, Parisiis 1615, pag. </s>

<s>449). </s></p><p type="main">

<s>Tolomeo per&ograve; si volse a professare altre dottrine. </s>

<s>Si potrebbe credere <lb/>che fosse rimasto impaurito delle contradizioni e delle persecuzioni, le quali <lb/>ebbe a sopportare Aristarco, ma forse correvano allora tempi in cui, affie&shy;<lb/>volitasi l'autorit&agrave; di Platone, la tirannide aristotelica soggiogava pi&ugrave; prepo&shy;<lb/>tente gl'ingegni. </s>

<s>In qualunque modo la Grande sintassi tolemaica era la <lb/>pi&ugrave; viva incarnazione di quello spirito, che Aristotile infuse nella sua Fi&shy;<lb/>losofia. </s></p><p type="main">

<s>Chi ben considera infatti &egrave; in quella Sintassi il Filosofo che assetta il <lb/>mondo a suo piacere, e gli prescrive le leggi. </s>

<s>I pianeti sono ora pi&ugrave; vicini <lb/>ora pi&ugrave; lontani alla Terra, perch&egrave; si volgono in orbite eccentriche intorno <lb/>ad essa; e ora si mostran retrogradi, ora stazionarii, perch&egrave; le orbite son <lb/>deferenti ciascuna di bene proporzionati epicicli. </s>

<s>Qui l'orgoglio filosofico <lb/>riman sodisfatto, perch&egrave; pu&ograve; sottilizzare a suo modo intorno all'Architettura <lb/>del mondo, ma no nella Sintassi platonica, la quale esclude ogni sottigliezza, <lb/>non richiedendo altro che la semplice regolarit&agrave; delle forme geometriche, e <lb/>si accora e diffida di s&egrave; il Filosofo, dovunque una tanto desiderata sempli&shy;<lb/>cit&agrave; non gli sia dato di conseguirla. </s></p><p type="main">

<s>Come il vento di quell'orgoglio filosofico spirasse d'Egitto sopra le no&shy;<lb/>stre contrade e vi mantenesse cos&igrave; lungamente il bel sereno del cielo pita&shy;<lb/>gorico rannuvolato, non &egrave; qui luogo a narrare. </s>

<s>Soffi di vento contrario, a <lb/>dissipar quelle nubi, spiravano nel secolo XV da que'libri illustrati e ri&shy;<lb/>messi in onore dai cultori delle lettere umane, come per esempio dalle <emph type="italics"/>Que&shy;<lb/>stioni accademiche<emph.end type="italics"/> di Cicerone, nelle quali rinfrescavasi eloquentemente la <lb/>memoria di Niceta da Siracusa, e dalle <emph type="italics"/>Questioni naturali<emph.end type="italics"/> di Seneca, dove <lb/>proemiando l'Autore rintuzza l'orgoglio degli uomini, considerando essere <lb/>un misero punto quello su cui fieramente combattono, per dividersi i regni, <lb/>e poi nel Cap. </s>

<s>II del VII Libro eccita gagliardamente i Filosofi a rivolgersi <lb/>alle contemplazioni celesti &ldquo; ut sciamus in quo rerum statu simus, piger&shy;<lb/>rimam sortiti an velocissimam sedem; circa nos Deus omnia an nos agat &rdquo; <lb/>(Venetiis 1522, c. </s>

<s>38 v.). </s></p><p type="main">

<s>Ma non era questa una voce, che potessero intenderla i cos&igrave; detti <emph type="italics"/>uma&shy;<lb/>nisti.<emph.end type="italics"/> Cosimo de'Medici e Lorenzo il Magnifico avevano, col loro senno e <pb xlink:href="020/01/892.jpg" pagenum="335"/>co'loro favori, cooperato alla diffusione de'libri e alla illustrazione degl'in&shy;<lb/>segnamenti platonici in Toscana, e di li per tutta l'Italia, e quella che isti&shy;<lb/>tuirono sotto il titolo di <emph type="italics"/>Accademia<emph.end type="italics"/> era una poderosa oste ordinata a insor&shy;<lb/>gere contro la tirannide aristotelica. </s>

<s>Platone allora risorse a rammemorare <lb/>a'Filosofi le sue dottrine cosmografiche negli scritti di Niccol&ograve; da Cusa, e <lb/>negli insegnamenti di Domenico Maria da Novara. </s></p><p type="main">

<s>Scendeva fra noi avventurosamente in quel tempo, di Prussia, Niccol&ograve; <lb/>Copernico, a cui la voce di Seneca si fece pi&ugrave; che ad altri mai sentire po&shy;<lb/>tente. </s>

<s>E giacch&egrave; i rinascenti studi letterarii in Italia gli avevano messi nelle <lb/>mani i libri di Cicerone, dove lesse l'ipotesi di Niceta e i Placiti di Plu&shy;<lb/>tarco gli riferivano essere una simile ipotesi approvata da Filolao; e dal&shy;<lb/>l'altra parte i Filosofi maestri di lui e i dotti italiani suoi familiari lo con&shy;<lb/>sigliavano a veder quella pitagorica ipotesi rivestita della divina eloquenza <lb/>del loro Platone; sulla diritta scorta del Timeo si avvio il Copernico alle <lb/>sue contemplazioni celesti. </s></p><p type="main">

<s>Non esit&ograve; a rispondere dicendo col suo Autore che no <emph type="italics"/>circa nos Deus <lb/>omnia,<emph.end type="italics"/> ma che <emph type="italics"/>nos agit,<emph.end type="italics"/> giudicando di nessun peso gli argomenti, che ad&shy;<lb/>ducevano contro questa sentenza Aristotile e Tolomeo. </s>

<s>Diceva questi che la <lb/>Terra si scompaginerebbe nel suo moto vertiginoso. </s>

<s>&ldquo; Sed cur non illud, <lb/>rispondeva il Copernico, etiam magis de mundo suspicatur, cuius tanto ve&shy;<lb/>lociorem esse motum oportet quanto maius est coelum Terra? </s>

<s>&rdquo; (De revo&shy;<lb/>lutionibus ecc., Norimbergae 1543, c. </s>

<s>5 v.). Soggiungeva l'altro che il moto <lb/>semplice, ossia il retto compete agli elementi semplici, ma no il circolare: <lb/>a cui rispondeva ancora il Copernico che anzi il moto circolare &egrave; pi&ugrave; sem&shy;<lb/>plice del retto, essendo che per la sua causa indeficiente <emph type="italics"/>aequaliter sem&shy;<lb/>per volvitur<emph.end type="italics"/> (ibi, c. </s>

<s>6, v.). </s></p><p type="main">

<s>La Sintassi platonica per&ograve; vide accortamente il Copernico che voleva <lb/>essere riformata, per quel che particolarmente concerne la collocazione di <lb/>Venere e di Mercurio. </s>

<s>Oltre al gran valore che avevano per lui gli argo&shy;<lb/>menti delle elongazioni e del modo costante, che nelle loro congiunzioni <lb/>tengono i due Pianeti, v'erano altre ragioni molto pi&ugrave; concludenti, e ch'ei <lb/>derivava direttamente dagli stessi principii platonici della simmetrica collo&shy;<lb/>cazione delle sfere celesti. </s>

<s>Costituiti Venere e Mercurio superiori, un troppo <lb/>grande intervallo restava vuoto fra la Luna e il Sole, e dall'altra parte irre&shy;<lb/>golarit&agrave; incompatibile col sapiente ordinamento degli altri Pianeti sarebbe <lb/>stata quella di far descrivere a'due suddetti, in tanto minor tempo, orbite <lb/>maggiori di quella della Terra. </s></p><p type="main">

<s>Sent&igrave; il Copernico che tanti e cos&igrave; validi argomenti non potevano es&shy;<lb/>sere n&egrave; distrutti n&egrave; infirmati da quell'unico del non essersi veduti mai Ve&shy;<lb/>nere e Mercurio n&egrave; dicotomi, n&egrave; falcati, perch&egrave; pensava non esser certa&shy;<lb/>mente dimostrato che i pianeti siano per s&egrave; stessi oscuri, ond'eravi luogo <lb/>a congetturare o che anch'essi, i pianeti, abbiano lume proprio, o che per <lb/>tutta la loro mole, qualunque ne sia il riguardo, s'imbevano de'raggi solari. </s></p><p type="main">

<s>Tali erano i sentimenti e i pensieri dell'Autore <emph type="italics"/>Delle rivoluzioni,<emph.end type="italics"/> ben-<pb xlink:href="020/01/893.jpg" pagenum="336"/>che cos<gap/> gn esponga come sovvenuti in mente ad altri. </s>

<s>&ldquo; De Venere vero <lb/>atque Mercurio diversae reperiuntur sententiae, eo quod non omnifariam <lb/>elongantur a Sole ut illi. </s>

<s>Quamobrem alii supra Solem eos collocant, ut <lb/>Patonis Timaeus.... Igitur qui Platonem sequuntur, cum existiment omne s <lb/>stellas, obscura alioqui corpora, lumine solari concepto resplendere, si sub <lb/>Sole essent, ob non multam ab eo divulsionem, dimidia aut certe a rotun&shy;<lb/>ditate deficientes cernerentur. </s>

<s>Nam lumen sursum ferme, hoc est versus So&shy;<lb/>lem, referrent acceptum ut in nova Luna vel desinente videmus.... Contra <lb/>vero qui sub Sole Venerem et Mercurium ponunt, ex amplitudine spatii <lb/>quod inter Solem et Lunam comperiunt, vendicant rationem.... Non ergo <lb/>fatentur in stellis opacitatem esse aliquam lunari similem, sed vel proprio <lb/>lumine, vel solari totis imbutas corporibus fulgere &rdquo; (ibi, c. </s>

<s>7 v.). </s></p><p type="main">

<s>Questa persuasione che dovessero in ogni modo, per le sopra dette ra&shy;<lb/>gioni, essere Venere e Mercurio costituiti inferiori, veniva confermata nel <lb/>Copernico da Marziano Capella &ldquo; qui Encyclopediam scripsit, et quidem alii <lb/>Latinorum percalluerunt. </s>

<s>Existimant enim quod Venus et Mercurius cir&shy;<lb/>cumcurrant Solem in medio existentem et eam ob causam ab illo non ul&shy;<lb/>terius digredi putant, quam suorum convexitas orbium patiatur, quoniam <lb/>Terram non ambiunt ut caeteri sed absidas conversas habent &rdquo; (ibi, c. </s>

<s>8 v.). </s></p><p type="main">

<s>N&egrave; &egrave; a tacere in tal proposito che fu questo sistema, derivato da'pi&ugrave; <lb/>antichi Egiziani nell'Enciclopedia latina del Capella, subodorato per vero, <lb/>tanti anni prima che dal Copernico, dal nostro Alighieri, il quale sgonfiava <lb/>i tumori orgogliosi de'Filosofi peripatetici divinamente traducendo l'espres&shy;<lb/>sione di Seneca &ldquo; Punctum est illud in quo navigatis, in quo bellatis, in <lb/>quo regna disponitis &rdquo; nell'<emph type="italics"/>aiola che ci fa tanto feroci<emph.end type="italics"/> (Par., C. XXII, <lb/>v. </s>

<s>151). Il divino Cantore dunque, rivolgendosi indietro a contemplar le <lb/>sfere, che via via avea trasvolate, dice di aver di l&igrave; sostenuto l'aspetto di <lb/>Iperione e di aver pur di l&igrave; veduto <emph type="italics"/>come si muove circa e vicino a lui <lb/>Maia e Dione<emph.end type="italics"/> (ivi, v. </s>

<s>143, 44). </s></p><p type="main">

<s>Cos&igrave; riformata la Sintassi platonica si riduceva alla seguente descri&shy;<lb/>zione copernicana: &ldquo; Prima et suprema omnium est stellarum fixarum <lb/>sphaera seipsam et omnia continens, ideoque immobilis.... Sequitur erran&shy;<lb/>tium primus Saturnus, qui XXX anno suum complet circuitum. </s>

<s>Post hunc <lb/>Jupiter duodecennali revolutione mobilis. </s>

<s>Deinde Mars, qui biennio circuit. </s>

<s><lb/>Quartum in ordine annua revolutio locum obtinet, in quo Terram cum orbe <lb/>lunari, tanquam Epicyclo, contineri diximus. </s>

<s>Quinto loco Venus nono mense <lb/>reducitur. </s>

<s>Sextum denique locum Mercurius tenet octuaginta dierum spacio <lb/>circumcurrens. </s>

<s>In medio vero omnium residet Sol &rdquo; (De revolut. </s>

<s>cit., c. </s>

<s>9). </s></p><p type="main">

<s>E qui il Copernico, col viso ritornando, come l'Alighieri, per tutte <lb/>quante le sette sfere illuminate dal Ministro maggior della Natura &ldquo; quis <lb/>enim, esclama con enfasi platonica, in hoc pulcherrimo templo lampadem <lb/>hanc in alio vel meliori loco poneret quam unde totum simul possit illu&shy;<lb/>minare? </s>

<s>Siquidem non inepte quidam lucernam mundi, alii mentem, alii <lb/>rectorem vocant &rdquo; (ibi pag. </s>

<s>9. v.). </s></p><pb xlink:href="020/01/894.jpg" pagenum="337"/><p type="main">

<s>Mal si giudicherebbe per&ograve; il merito del Copernico se si volesse tutto <lb/>ridurre all'aver rinnovellata l'ipotesi pitagorica, e all'aver riformata la Sin&shy;<lb/>tassi platonica: ma egli restaur&ograve; le fondamenta all'Astronomia, costituendo <lb/>il Sole per centro da misurare indi la pi&ugrave; giusta distanza de'pianeti da lui, <lb/>e i periodi delle loro circumvoluzioni. </s>

<s>A far ci&ograve;, con tutto il rigore mate&shy;<lb/>matico, e dietro quelle osservazioni possibili allora, per il difetto e per la <lb/>imperfezione degli strumenti astronomici, dedic&ograve; l'Autore gli altri cinque <lb/>libri dell'immortale Opera sua. </s></p><p type="main">

<s>I calcoli laboriosi disposti in Tavole e conclusi in canoni, per adattarli <lb/>all'uso, erano stati da lungo tempo condotti, ed erano gi&agrave; in ordine di <lb/>uscir fuori alle stampe i capitoli e i libri, dove di que'calcoli si espone&shy;<lb/>vano dal Copernico le ragioni, ma non si risolveva ancora l'Autore di pub&shy;<lb/>blicarli. </s>

<s>Sentiva che troppo gagliardo tuttavia durava il vento peripatetico, <lb/>che avrebbe contrastato col suo malefico soffio alla diffusion dell'aura de'suoi <lb/>nuovi concetti. </s>

<s>L'insurrezion de'Platonici, perduti in oziose contemplazioni <lb/>sotto l'ombre deliziose de'platani di Careggi, vedeva esser riuscita ineffi&shy;<lb/>cace, n&egrave; sperava che gli ammiratori di Pico della Mirandola, impugnatore <lb/>dell'Astronomia, avrebbero fatta a lui migliore accoglienza che non a Luca <lb/>Paciolo, a Leonardo da Vinci e ad Amerigo Vespucci. </s></p><p type="main">

<s>Que'calcoli copernicani nonostante, potendosi applicare alla riforma del <lb/>Calendario tanto desiderata, promettevano di aver virt&ugrave;, mostrando l'utilit&agrave; <lb/>de'frutti, di salvare il fiore delle dottrine, ond'&egrave; che Niccol&ograve; Schonberg, <lb/>cardinale di Capua, richiese l'Autore gli rimettesse le carte dottissime e la&shy;<lb/>boriose per farle stampare a sue spese. </s>

<s>&ldquo; Dedi autem negotium Theodorico <lb/>a Reden ut istic, meis sumptibus, omnia describantur atque ad me transfe&shy;<lb/>rantur. </s>

<s>&rdquo; </s></p><p type="main">

<s>L'edizione fu fatta in Norimberga nel 1543 e dedicata a Papa Paolo III <lb/>principe di quella Repubblica ecclesiastica, alla quale sperava il Copernico <lb/>non sarebbero per riuscire inutili le sue fatiche. </s>

<s>&ldquo; Nam non iam multo ante <lb/>sub Leone X cum in Concilio lateranensi vertebatur quaestio de emendando <lb/>Calendario ecclesiastico, quae tum indecisa hanc solummodo ob causam man&shy;<lb/>sit, quod annorum et mensuum magnitudines, atque Solis et Lunae motus <lb/>nondum satis dimensi haberentur. </s>

<s>Ex quo equidem tempore his accuratius <lb/>observandis animum intendi, admonitus a praeclarissimo viro D. </s>

<s>Paulo epi&shy;<lb/>scopo Semprionensi, qui tum isti negotio praeerat. </s>

<s>&rdquo; </s></p><p type="main">

<s>Conforme a queste copernicane osservazioni fu poi veramente, sotto <lb/>Gregorio XIII, regolato il Calendario, e fu tale il frutto che ne raccolse la <lb/>Repubblica ecclesiastica e la civile: ma per salvare i principii, che si ri&shy;<lb/>guardaron da noi come il fiore in che allegarono que'desideratissimi frutti, <lb/>s'ebbero a ingaggiar fierissime battaglie, che tennero per pi&ugrave; di un secolo <lb/>fra s&egrave; divisa la Repubblica letteraria. </s></p><p type="main">

<s>Che i Peripatetici predominanti vedessero di mal occhio il Libro <emph type="italics"/>De re&shy;<lb/>volutionibus orbium,<emph.end type="italics"/> appena uscito fuori, &egrave; cosa naturalissima, e bench&egrave; <lb/>tentassero qua e l&agrave; d'insorgere ad oppugnarlo, si sentivano ancora deboli e <pb xlink:href="020/01/895.jpg" pagenum="338"/>dispersi per la mancanza di qualche valoroso capitano, che finalmente usc&igrave; <lb/>fuori nella persona di Ticon Brahe. </s>

<s>La Sintassi, ch'egli contrappose alla <lb/>copernicana, &egrave; notissima a tutti, e le ragioni, per le quali si condusse a ri&shy;<lb/>pudiar la posizione del Copernico per seguitare la sua, si posson veder com&shy;<lb/>pendiosamente esposte in una Lettera, ch'egli scriveva dall'Uraniburg il <lb/>d&igrave; 24 Novembre 1589 a Cristoforo Rothmann. </s>

<s>A lui, al quale vedeva arri&shy;<lb/>dere il triplice moto dal Copernico attribuito alla Terra, proponeva Ticone, <lb/>contro ciascuno di que'tre moti, qualcun fra'molti <emph type="italics"/>non adeo operosum <lb/>dubium.<emph.end type="italics"/></s></p><p type="main">

<s>Quanto al moto diurno &ldquo; dic mihi, scriveva l'Astronomo danese, qui <lb/>fieri possit ut globulus plumbeus, ex altissima turre iusto modo demissus, <lb/>punctum Terrae infra se positum perpendiculariter ad amussim contingat; <lb/>id enim circumducta interea Terra, cum cursus eius sit velocissimus, fieri <lb/>nequaquam posse te supputatio docebit geometrica. </s>

<s>Siquidem, in uno scru&shy;<lb/>pulo secundo temporis, Terra revolvi debeat, etiam in his borealibus pla&shy;<lb/>gis, sesquicentum passus maiores proxime. </s>

<s>Hinc caetera ratiocinare: neque <lb/>enim casus plumbi aerem concomitatur, sed violenter illum transit &rdquo; (Epistol. </s>

<s><lb/>astromic. </s>

<s>libri, Uraniburgi 1596, pag. </s>

<s>167). </s></p><p type="main">

<s>Quanto al moto annuo, soggiungeva Ticone, quando questo fosse vero, <lb/>e fosse vera la sentenza copernicana che cio&egrave; l'orbe terrestre &egrave; un punto <lb/>rispetto all'ampiezza della sfera stellata, rimarrebbe un immenso spazio vuoto <lb/>affatto di stelle fra Saturno e questa stessa immobile sfera. </s>

<s>&ldquo; Imo tunc quo&shy;<lb/>que stellae fixae tertiae magnitudinis, quae unum minutum in diametro <lb/>habent, necessario erunt aequales toti huic orbi annuo, idest comprehendent <lb/>in diametro 2284 semidiametros Terrae: distabunt enim 7,850,000 iisdem <lb/>semidiametris proxime. </s>

<s>Quid dicemus de stellis primae magnitudinis, qua&shy;<lb/>rum aliquae bina, quaedam fere terna minuta in diametro visibili occupant? </s>

<s><lb/>Et quid si adhuc altior removeatur octava sphaera, ut motus Terrae annuus <lb/>illic prorsus evanescat? </s>

<s>Deduc si lubet haec geometrice, et videbis quanta <lb/>absurda, vel sic inferendo, ut de aliis non dicam, assuntionem hanc conco&shy;<lb/>mitentur. </s>

<s>Tertius, sublato annuo, per se ruit &rdquo; (ibi). </s></p><p type="main">

<s>N&egrave; per questo il Rothmann si lasci&ograve; persuadere. </s>

<s>Diceva che l'argo&shy;<lb/>mento del cader del piombo era stato gi&agrave; enodato dallo stesso Copernico, il <lb/>quale, dal principio verissimo che alle parti convengono le propriet&agrave; del <lb/>tutto ne concludeva, che movendosi attorno la Terra dovevano seguirla di <lb/>pari passo anche i corpi, che son parte di lei. </s>

<s>Che se ci&ograve; non fosse, instava <lb/>il Rothmann, non il piombo solo, ma e la Torre stessa, e anzi tutti quanti <lb/>gli edifizii dovrebbero rovinare, movendosi dal suo luogo la Terra. </s>

<s>&ldquo; Sed <lb/>quid de casu rerum gravium solicitus es, cum omnia quae in superficie ter&shy;<lb/>rae libera et a toto separata iacent, quinimo ipsa Turris, ex qua globus <lb/>plumbeus demittetur, ipsaque aedificia ruerent atque a Terrae motu relin&shy;<lb/>querentur necesse esset, si partes non retinerent motum totius, quod quam <lb/>sit contra Naturae sapientiam nemo non videt &rdquo; (ibi, pag. </s>

<s>185). </s></p><p type="main">

<s>Quanto a quel che poi riguarda gli assurdi che ne conseguirebbero, <pb xlink:href="020/01/896.jpg" pagenum="339"/>secondo Ticone, dall'ammettere il moto annuale, il Rothmann confessava di <lb/>non saper veder quale assurdo implicasse l'ammetter che una stella possa <lb/>essere di diametro tanto grande, quant'&egrave; grande il diametro dell'orbita ter&shy;<lb/>restre. </s>

<s>&ldquo; An id, aut cum voluntate divina pugnat, aut divinae Naturae im&shy;<lb/>possibile est, aut infinitae naturae non competit? </s>

<s>Haec demonstranda omnino <lb/>tibi sunt, si absurdi quid hinc colligere volueris &rdquo; (ibi, pag. </s>

<s>186). </s></p><p type="main">

<s>Gli argomenti per&ograve; del Rothmann, bench&egrave; savissimi, erano nonostante <lb/>negativi, ond'&egrave; che a conforto del sistema copernicano non restavano altri <lb/>argomenti positivi da quelli in fuori che la Matematica aveva suggerito al&shy;<lb/>l'Autor del Libro Delle revoluzioni. </s>

<s>Non stette per&ograve; molto a uscir fuori quel <lb/>Giovanni Keplero, che doveva colla valida mano non solo sostenere, ma dar <lb/>l'ultima perfezione al combattuto edifizio. </s></p><p type="main">

<s>Nel 1590 frequentava in Tubinga la Scuola di Michele Maestlin, dove, <lb/>avendo udito esporre con s&igrave; gran plauso l'opinione copernicana, dice di es&shy;<lb/>sersene dilettato per modo &ldquo; ut non tantum crebro eius placita in physicis <lb/>disputationibus candidatorum defenderem, sed etiam accuratam disputatio&shy;<lb/>nem de motu primo quod Terrae volutione accidat conscriberem. </s>

<s>Tamque <lb/>in eo eram ut eidem etiam Telluri motum solarem, ut Copernicus mathe&shy;<lb/>maticis, sic ego physicis, seu mavis metaphisicis rationibus adscriberem &rdquo; <lb/>(Mysterium cosmogr., Francofurti 1621, pag. </s>

<s>7). </s></p><p type="main">

<s>Lasciamo da parte la Metafisica, la quale poco o nulla giov&ograve; al Keplero, <lb/>ma le ragioni fisiche di lui si ridussero al moto rotatorio del Sole e alla <lb/>scoperta delle orbite ellittiche, per cui le variet&agrave; de'moti planetarii, credute <lb/>dagli Astronomi e dallo stesso Copernico apparenti, furono dimostrate reali. </s>

<s><lb/>Pi&ugrave; che fisiche per&ograve; queste si potevano dir prove dell'ordine matematico, <lb/>ond'&egrave; che affatto nuovi appariscono nella storia que'veri argomenti fisici <lb/>del moto della Terra dati fuori da Guglielmo Gilberto. </s></p><p type="main">

<s>A Tolomeo, che dubitava pel moto suo vertiginoso dover dissolversi la <lb/>Terra, aveva dato buona sicurt&agrave; il Copernico, nel Cap. </s>

<s>VIII del Libro I, e <lb/>una medesima sicurt&agrave; aveva dato a Ticone, come vedemmo, il Rothmann, <lb/>ma erano que'loro argomenti dedotti da principii metafisici e da ragioni di <lb/>congruenza, che intanto avevano peso, in quanto ancora la Fisica si taceva. </s>

<s><lb/>Fu il Gilberto il primo a parlare in nome di lei, e a dire che le parti com&shy;<lb/>ponenti il Globo terrestre non si dissolvono, perch&egrave; alle forze della vertigine <lb/>prevalgono le forze dell'attrazion magnetica, e perci&ograve; rimangono quelle stesse <lb/>parti componenti insieme conglutinate. </s>

<s>&ldquo; Ita etiam magnetice terrarum fun&shy;<lb/>damenta connectuntur, coniunguntur, ferruminantur. </s>

<s>Quo minus Ptolomeus <lb/>Alexandrinus, eiusque sectatores et philosophi nostri, si Terra circulariter <lb/>moveretur, dissolutionem eius urgeant aut inhorroscant &rdquo; (De Magnete, Lon&shy;<lb/>dini 1600, pag. </s>

<s>91). </s></p><p type="main">

<s>Aveva anche francamente il Copernico asserito co'Pitagorici che la Terra <lb/>si rivolge intorno al suo asse, ma chi la tiene cos&igrave; in sito per modo, che <lb/>non divaghi a talento nel libero spazio, o in che risiede la fermezza del suo <lb/>polo? </s>

<s>N&egrave; il Copernico n&egrave; altri, prima e dopo di lui, avevano saputo rispon-<pb xlink:href="020/01/897.jpg" pagenum="340"/>dere infino al Gilberto, il quale riconobbe, nella verticit&agrave; magnetica, la co&shy;<lb/>stante direzione e la fermezza dell'asse terrestre. </s>

<s>&ldquo; Volvitur igitur Terra, <lb/>quae magna quadam necessitate, virtute etiam insita manifesta et conspicua <lb/>convertitur ad Solem circulariter, quo motu solaribus virtutibus et influen&shy;<lb/>tiis gaudet, firmaturque certa sua verticitate, ne vage in omnem coeli re&shy;<lb/>gionem volveretur &rdquo; (ibi, pag. </s>

<s>224). </s></p><p type="main">

<s>All'obiezione aristotelica antica de'proietti, che non ritornerebbero al <lb/>luogo d'onde furon gittati, e alla pi&ugrave; recente ticoniana de'corpi cadenti dal&shy;<lb/>l'alto, che non batterebbero al giusto perpendicolo, movendosi la Terra in <lb/>velocissimo giro, avevano il Copernico e il Rothmann in qualche modo ri&shy;<lb/>sposto, ma fu il Gilberto, che alle attrazioni magnetiche ridusse tutta la <lb/>virt&ugrave; di quel fisico argomento. </s>

<s>Ei precorrendo il. </s>

<s>Newton considerava tutti <lb/>i corpi rimaner congiunti alla Terra sempre che non uscivano fuori di quella, <lb/>ch'ei chiamava orbita degli effluvii terrestri, o sfera attiva dell'attrazione, <lb/>come diremmo noi. </s>

<s>&ldquo; Dubitant nonnulli qui fieri possit ut globus ferreus <lb/>aut plumbeus, ex altissima turri demissus, in punctum Terrae infra se per&shy;<lb/>pendiculariter positum ad amussim incidat, Terra circa suum axem mota. </s>

<s><lb/>Quomodo etiam sphaerulae bombardicae maioris colubrini simili pulveris <lb/>tormentitii quantitate et vigore pari etiam per aerem eumdem directione et <lb/>altitudine eiaculatae, pari intervallo ab uno certo loco et versus Eurum et <lb/>versus Occasum eiacularentur, mota Tellure versus Eurum. </s>

<s>Sed decipiun&shy;<lb/>tur, qui huiusmodi argumenta proferunt, non animadvertentes naturam glo&shy;<lb/>borum primariorum et combinationem partium cum suis globis, etiamsi so&shy;<lb/>lidis partibus non adiungantur. </s>

<s>Terra vero diurna revolutione non movetur <lb/>separatione solidioris circumferentiae eius a circumfusis corporibus, sed cir&shy;<lb/>cumfusa effluvia omnia et in illis gravia quovis modo vi pulsa simul cum <lb/>Tellure generali cohaerentia uniformiter procedunt. </s>

<s>Quod etiam fit in omni&shy;<lb/>bus primariis corporibus, Sole, Luna, Tellure, partibus ad sua principia et <lb/>fontes sese conferentibus, quibus eadem appetentia annectuntur, ut terrena <lb/>Telluri, quae gravia nos nominamus. </s>

<s>Sic lunaria appellunt Lunam, solaria <lb/>Solem, intra effluviorum suorum orbes. </s>

<s>Cohaerent effluvia continuatione <lb/>substantiae, et gravia etiam gravitate sua uniuntur Telluri, et simul cum <lb/>generali motu procedunt, praesertim cum nulla corporum obstet renitentia. </s>

<s><lb/>Ob eamque causam, propter diurnam Telluris revolutionem, nec incitantur <lb/>corpora, nec retardantur, non praeveniunt non subsequuntur versus ortum <lb/>vel occasum emissa violenter.... Minime igitur ab illustri Tychone Brahe <lb/>diurnus motus Telluris talibus argumentis refellitur &rdquo; (ibi, pag 228, 29). </s></p><p type="main">

<s>In questi nuovi concetti del Gilberto sente ognuno alitar le prime aure <lb/>di quel gran vero, che sarebbe stato messo, un secolo dopo, in cos&igrave; chiara <lb/>luce da un altro celebre Filosofo inglese. </s>

<s>Ma intanto avrebbe il nostro Ga&shy;<lb/>lileo fra non molti anni ripresi in mano e largamente svolti, a rimuovere <lb/>ogni difficolt&agrave; contro il moto diurno della Terra, que'fisici e meccanici ar&shy;<lb/>gomenti, de'quali non aveva l'Autor <emph type="italics"/>De Magnete<emph.end type="italics"/> fatto nel suo VI libro <lb/>altro che un cenno. </s>

<s>Ond'&egrave; che siamo da ci&ograve;, dop'aver detto delle vicende, <pb xlink:href="020/01/898.jpg" pagenum="341"/>che sub&igrave; ne'suoi primi tempi il Sistema Pitagorico descritto dal Copernico, <lb/>specialmente appresso gli stranieri; messi in via di narrar, con la solita bre&shy;<lb/>vit&agrave;, ci&ograve; che particolarmente se ne pensasse o se ne disputasse in Italia. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Crediamo anche noi che uno di quegli Italiani, co'quali il Copernico <lb/>familiarmente conversava, e ch'ebbero qualche efficacia in ispirargli i pla&shy;<lb/>tonici concetti, fosse Girolamo Fracastoro. </s>

<s>Vanno per&ograve; i momenti, per dir <lb/>cos&igrave;, di quella efficacia ben ponderati, essendo un fatto che l'Autor <emph type="italics"/>De re&shy;<lb/>volutionibus,<emph.end type="italics"/> infin dalla dedica a papa Paolo III, confessa l'insufficienza del <lb/>sistema omocentrico a comporre ordinatamente i moti celesti. </s></p><p type="main">

<s>&Egrave; a tutti noto che la ragione, per cui Tolomeo ricorse ad ammettere <lb/>il sistema eccentrico, era il veder variar di grandezza gli astri, e special&shy;<lb/>mente la Luna, in due punti diametralmente opposti della loro orbita, che <lb/>perci&ograve; si dissero il perigeo e l'apogeo. </s>

<s>Il Fracastoro sosteneva quella va&shy;<lb/>riet&agrave; essere una semplice apparenza, come quella che da non altro, secondo <lb/>lui, dipende, se non dal passar le specie visibili per mezzi ora pi&ugrave; ora meno <lb/>alti, ora pi&ugrave; e ora meno densi. </s>

<s>&ldquo; Nos autem utramque dictarum causarum <lb/>prorsus auferimus et planetas nunquam altiores, numquam depressiores <lb/>reipsa fieri asseveramus: videri autem propter alias causas, quarum una a <lb/>medio pendet &rdquo; (Homocentricorum liber, Op. </s>

<s>omnia, Venetiis 1584, c. </s>

<s>13). </s></p><p type="main">

<s>Questa singolare ipotesi del Fracastoro (fatto notabilissimo) trov&ograve; pi&ugrave; <lb/>di un secolo dopo un propugnatore zelante in Ottone di Guericke, a cui <lb/>parve di render, delle varie apparenti grandezze del Sole in Cancro e in <lb/>Capricorno, la seguente ragione: &ldquo; Porro quoque reddit diversas Solis et <lb/>Lunae apparentias maior vel minor aeris profunditas. </s>

<s>Nam quando Sol aut <lb/>Luna sunt in signis australibus adeoque humiliores, tunc aspiciuntur a no&shy;<lb/>bis per maiorem aeris profunditatem, consequenter apparent maiores. </s>

<s>Unde, <lb/>tempore hyberno, quando Sol est in Capricorno apparet maior propter ma&shy;<lb/>iorem aeris copiam, quae intermediat inter visum nostrum et corpus Solis <lb/>obiectum. </s>

<s>Quando autem est in Cancro, adeoque versus nostrum zenith <lb/>altior, per minorem aeris copiam adspicitur minor &rdquo; (Experim. </s>

<s>magd. </s>

<s>cit., <lb/>pag. </s>

<s>166). </s></p><p type="main">

<s>Il Copernico per&ograve;, ben persuaso che le varie grandezze del Sole e della <lb/>Luna non sono illusioni ottiche, ma fatti reali, vide come fosse impossibile <lb/>salvar questi stessi fatti nel sistema assolutamente omocentrico, ma che o <lb/>bisognava ammettere gli eccentrici o gli omocentrici con gli epicicli. </s>

<s>&ldquo; Eius <lb/>autem inaeqnalitas demonstratur quod motus centri ac annuae revolutionis <lb/>Terrae non sit omnino circa Solis centrum. </s>

<s>Quod sane duobus modis in&shy;<lb/>telligi potest, vel per eccentrum circulum, idest cuius centrum non sit Solis, <lb/>vel per epicyclum in homocentro &rdquo; (De revolut. </s>

<s>cit., pag. </s>

<s>85). Se l'uno o <pb xlink:href="020/01/899.jpg" pagenum="342"/>l'altro, l'eccentrico cio&egrave;, o l'omocentrico coll'epiciclo, esista nel Cielo, sog&shy;<lb/>giunge il Copernico, <emph type="italics"/>non est facile discernere,<emph.end type="italics"/> ma egli &egrave; in ogni modo af&shy;<lb/>fatto alieno dal partecipare colle idee professate dal Fracastoro, al quale in&shy;<lb/>somma non rimane altro merito, da quello in fuori di aver presentito dalla <lb/>lontana che il sistema vero del mondo sarebbe stato pi&ugrave; conforme alla sem&shy;<lb/>plicit&agrave; platonica, che non alla complicata architettura tolemaica; sentimento <lb/>ch'egli infuse nel grande astronomo prussiano, a cui siamo certi che fu <lb/>amico, e si crede che fosse anche maestro. </s></p><p type="main">

<s>Fra'precursori del Copernico sarebbe da annoverar piuttosto Niccol&ograve; <lb/>da Cusa, a cui in questo particolar proposito compete il merito di avere, in <lb/>mezzo a tanta incredulit&agrave;, avuto fede a quel che di Niceta gli riferiva Ci&shy;<lb/>cerone, o a quel che di Filolao raccontava Plutarco. </s>

<s>In ogni modo, giacch&egrave; <lb/>la preparazione e gl'impulsi, ch'ebbe il libro <emph type="italics"/>De revolutionibus<emph.end type="italics"/> dagl'Ita&shy;<lb/>liani, son noti per i fatti sopra narrati, e ci&ograve; basta alla nostra gloria; senza <lb/>pi&ugrave; perderci dietro ai precursori del Copernico passiamo a dir de'seguaci. </s></p><p type="main">

<s>Non ci d&agrave; il cuore di annoverar fra questi Giordano Bruno, come al&shy;<lb/>cuni, specie in questi ultimi tempi, scapestratamente hanno fatto, essendo <lb/>per avventura il Sistema copernicano assunto fra gli strani e sconvolti me&shy;<lb/>tafisicumi del frate da Nola, come suol talvolta una pagliuzza d'oro venir <lb/>rapita in mezzo al ciarpame, e sostenuta in aria da un vento turbinoso. </s></p><p type="main">

<s>La matematica copernicana voleva essere confortata, non da vane me&shy;<lb/>tafisiche speculazioni, ma da fisiche esperienze, delle quali vide la nostra <lb/>Italia le primizie in un argomento sovvenuto gi&agrave; a Seleuco filosofo antico, <lb/>e a cui dette vigor nuovo di vita, nelle <emph type="italics"/>Questioni peripatetiche,<emph.end type="italics"/> il Cesal&shy;<lb/>pino. </s>

<s>Egli dunque, non saputosi in tutto espedire dai lacci peripatetici, non <lb/>sa prestar fede al suo divino Aristotile, che nega il moto diurno della Terra, <lb/>perch&egrave; vede questo perpetuo moto nel flusso e riflusso marino dimostrato <lb/>con evidenza. </s>

<s>&ldquo; Quoniam autem perpetua est huiusmodi Terrae circumvo&shy;<lb/>lutio, perpetua quoque redditur maris librat&igrave;o. </s>

<s>Quatenus igitur motus iste <lb/>est continentis, per accidens in aqua est, nec secundum eius naturam ne&shy;<lb/>que praeternaturam: quaerit enim semper locum magis declivem, quia non <lb/>pari passu prosequitur Terrae mo&shy;<lb/>tum. </s>

<s>Quod autem in maxima aqua&shy;<lb/>rum congregatione hic motus contin&shy;<lb/>gat, non autem in parvis ut lacubus <lb/>et fluminibus, iustissime evenit. </s>

<s>Cum <lb/>enim Terrae motus minimus sit, non <lb/>potest, nisi in magna aquarum mole <lb/>apparere. </s>

<s>Sit enim AA (fig. </s>

<s>66) su&shy;<lb/><figure id="id.020.01.899.1.jpg" xlink:href="020/01/899/1.jpg"/></s></p><p type="caption">

<s>Figura 66.<lb/>perficies aquae supra perpendicu&shy;<lb/>lum CD; BB autem altera superfi&shy;<lb/>cies dimota super alterum perpendiculum GC: quanto magis protrahitur <lb/>AA, BB, tanto magis apparet seiunctio a se invicem &rdquo; (Venetiis 1571, c. </s>

<s>60 v.). </s></p><p type="main">

<s>Il Cesalpino per&ograve; non seppe tanto riconquistare la propria libert&agrave;, da <pb xlink:href="020/01/900.jpg" pagenum="343"/>professare apertamente il sistema vero del mondo: egli &egrave; un semicoperni&shy;<lb/>cano, che non sa risolversi a far posare il Sole nella sua sede, per man&shy;<lb/>dargli attorno la Terra in perpetuo giro annuale. </s>

<s>Dall'altra parte tanto ri&shy;<lb/>mane ancora il Filosofo aretino devoto al suo Aristotile, che delle poche <lb/>verit&agrave; spicciolate di lui non si fa conto da coloro, i quali seguitano tutt'al&shy;<lb/>tro metodo in filosofare. </s>

<s>Ci&ograve; poi pi&ugrave; distintamente avvenne, quando quel <lb/>metodo ebbe un primo ordinatore in Giovan Batista Benedetti, dalle parole <lb/>del quale, che riferivano l'opinion di Aristarco Samio <emph type="italics"/>divinitus a Nicolao <lb/>Copernico expressam contra quam nil plane valent rationes ab Aristotile <lb/>neque etiam a Ptolomeo propositae,<emph.end type="italics"/> si riconobbe autorevolmente decisa la <lb/>gran sentenza. </s>

<s>&Egrave; perch&egrave;, segnatamente in Italia, i seguaci del retto metodo <lb/>sperimentale riconoscevano il Benedetti solo per primo istitutore e Maestro, <lb/>i Filosofi usciti di quella scuola erano tutti perci&ograve; schiettamente coper&shy;<lb/>nicani. </s></p><p type="main">

<s>Fu il pi&ugrave; insigne di meriti, e il pi&ugrave; famoso tra costoro Galileo Galilei, <lb/>il quale, giovane professore nello studio pisano, ci si rivela di gi&agrave; per fautor <lb/>del Copernico in alcune dispute familiari, ch'egli ebbe con l'amico e col&shy;<lb/>lega suo Jacopo Mazzoni. </s>

<s>Meditavano con pari amore lo <emph type="italics"/>Speculationum liber,<emph.end type="italics"/><lb/>e conferivano insieme i loro pensieri. </s>

<s>Il Mazzoni era ben persuaso di ci&ograve; <lb/>che il Benedetti ivi dimostrava contro Aristotile, riguardo al dir che le velo&shy;<lb/>cit&agrave; nel vacuo sarebbero infinite, e riguardo a tanti altri errori detti dal <lb/>Filosofo intorno alla natura e alle propriet&agrave; del moto. </s>

<s>Si studiava per&ograve; di <lb/>scusare in qualche modo Aristotile, facendo per esempio osservare all'amico <lb/>che non essendo ancora noto il Teorema archimedeo, non era da far le ma&shy;<lb/>raviglie se l'Autor nel <emph type="italics"/>VII Physicorum<emph.end type="italics"/> aveva asserito non potersi dare una <lb/>linea retta uguale alla circolare. </s>

<s>&ldquo; Sed tamen in isto lapsu venia dignus vi&shy;<lb/>detur Aristotiles, nam, ut ait Simplicius, illius tempore nondum inventa fue&shy;<lb/>rant ab Archimede elaborata Theoremata ad hoc attinentia. </s>

<s>Addamus et <lb/>illud quod adhuc proportio circuli et diametri non sit nobis omnino explo&shy;<lb/>rata et cognita &rdquo; (In universam Plat. </s>

<s>et Arist. </s>

<s>philos. </s>

<s>praeludia. </s>

<s>Vene&shy;<lb/>tiis 1597, pag. </s>

<s>194). Ma Galileo pi&ugrave; rigido censore non voleva conoscere <lb/>scuse: &ldquo; Neque dicas hoc latuit Aristotilem quia Archimedes Aristotele est <lb/>multo recentior. </s>

<s>Nam si Aristotelem latuit demonstratio inveniendae rectae <lb/>curvae aequalis, latuit etiam demonstratio probans non dari rectam curvae <lb/>aequalem, quare non debebat temere asserere non dari talem rectam &rdquo; <lb/>(Alb. </s>

<s>XI, 64). </s></p><p type="main">

<s>Dalle questioni meccaniche passavano i due amici alle astronomiche, <lb/>intorno alle quali i dissensi erano pi&ugrave; risoluti. </s>

<s>Galileo sosteneva aver sen&shy;<lb/>tenziato verissimo il Benedetti a dir che non valgono contro il divino Co&shy;<lb/>pernico le obiezioni promosse da Aristotile e da Tolomeo. </s>

<s>Contradiceva il <lb/>Mazzoni, asseverando che se l'altezza del monte Caucaso fa cos&igrave; deprimere <lb/>l'orizzonte, la distanza della Terra dal Sole, quando fosse vera l'ipotesi co&shy;<lb/>pernicana, altererebbe cos&igrave; la posizion dello stesso orizzonte, da non si poter <lb/>mai veder divisa per giusta met&agrave; la sfera stellata. </s></p><pb xlink:href="020/01/901.jpg" pagenum="344"/><p type="main">

<s>Tanto parve al Mazzoni potersi con questa difficolt&agrave; infirmare la sen&shy;<lb/>tenza del Benedetti, che produsse in pubblico, dai familiari colloqui, quella <lb/>stessa difficolt&agrave; nella Sezione III dei sopra citati <emph type="italics"/>Preludi,<emph.end type="italics"/> dove cos&igrave; s'inti&shy;<lb/>tola il cap. </s>

<s>V. &ldquo; Quod Terra sit centrum mundi et quod non moveatur: <lb/>reiicitur commentum Pythagoreorum, Aristarchi Sami et Nicolai Copernici &rdquo; <lb/>(pag. </s>

<s>129). </s></p><p type="main">

<s>Una copia del libro fu dall'Autore inviata immediatamente a Padova a <lb/>Galileo, che l'ebbe appena uscite fuori le stampe, verso la met&agrave; del Mag&shy;<lb/>gio. </s>

<s>Galileo rispose una lettera, in data del d&igrave; 30 di quello stesso mese e <lb/>di quell'anno 1597, dove commemorando i primi dolci anni della loro ami&shy;<lb/>cizia, quando con tanta giocondit&agrave; disputavano insieme, torna a far ora quelle <lb/>risposte in scritto, che aveva allora pronunziate a voce. </s>

<s>Dimostra che l'ar&shy;<lb/>gomento si fonda sopra un inganno ottico, il quale poi facilmente si dis&shy;<lb/>solve, avvertendo la gran differenza che passa, tra il far discostare l'occhio <lb/>posto nella superficie della Terra con tutta la Terra dal centro del Cielo, e <lb/>tra il fare alzare l'occhio sopra la superficie della Terra. </s>

<s>Dalla quale av&shy;<lb/>vertenza conclude: &ldquo; forse minor diversit&agrave;, circa la disegualit&agrave; delle pi&ugrave; <lb/>volte dette divisioni orizzontali, potria cagionare la grandissima lontananza <lb/>ch'&egrave; tra il Sole e la Terra, che la piccola altezza del monte Caucaso &rdquo; <lb/>(Alb. </s>

<s>II, 4). </s></p><p type="main">

<s>Pochi mesi dopo, la fama del Matematico nello studio di Padova era <lb/>giunta in Germania alle orecchie del Keplero, il quale, avendo l'anno <lb/>avanti (1596) pubblicata la prima edizione del suo <emph type="italics"/>Prodromus Dissertatio&shy;<lb/>num cosmographicarum,<emph.end type="italics"/> invi&ograve; da Gratz una copia del libro a Galileo. </s>

<s>Que&shy;<lb/>sti rispondeva da Padova, il d&igrave; 4 Agosto 1597, una lettera, nella quale, <lb/>dop'aver ringraziato l'Autore del dono, ed essersi compiaciuto di vedersi <lb/>onorare dell'amicizia di chi aveva confermato le combattute verit&agrave; con tante <lb/>belle invenzioni, delle quali si congratulava, &ldquo; Id autem, soggiunge, eo li&shy;<lb/>bentius faciam quod in Copernici sententiam multis abhinc annis venerim, <lb/>et ex tali positione multorum etiam naturalium effectuum causae sint a me <lb/>adinventae; quae dubio procul per comunem hypothesim inexplicabiles sunt. </s>

<s><lb/>Multas conscripsi et rationes et argumentorum in contrarium eversiones, <lb/>quas tamen in lucem hucusque proferre non sum ausus, fortuna ipsius Co&shy;<lb/>pernici praeceptoris nostri perterritus, qui licet sibi apud aliquos immorta&shy;<lb/>lem famam paraverit, apud infinitos tamen, tantus enim est stultorum nu&shy;<lb/>merus, ridendus et explodendus prodiit &rdquo; (Alb. </s>

<s>VI, 12). </s></p><p type="main">

<s>Chi ripensa sopra queste parole, e non sa che della lettera scritta al <lb/>Mazzoni, domander&agrave; curioso quali sono que'tanti altri scritti, ne'quali Ga&shy;<lb/>lileo si vanta di aver molte nuove ragioni in favor del Copernico, e molte <lb/>eversioni degli argomenti in contrario. </s>

<s>Risponderanno gli adoratori al solito <lb/>lamentando l'iattura, ma noi che conosciamo l'indole di quell'uomo, sem&shy;<lb/>pre magnificator di s&egrave; stesso, possiamo rassicurare gli animi col persuaderli <lb/>che tutte l'eversioni degli argomenti contro il Copernico, fino a quel tempo, <lb/>si compendiano nella lettera al Mazzoni, e che le cause degli effetti naturali <pb xlink:href="020/01/902.jpg" pagenum="345"/>non esplicabili altrimenti che nella posizione copernicana, e le ragioni che <lb/>escogit&ograve; Galileo per confermarla, si riducono a quella falsa speculazione del <lb/>flusso del mare suggeritagli dalla lettura del Cesalpino. </s></p><p type="main">

<s>Cos&igrave; Seleuco antico, come il pi&ugrave; recente Autore delle Questioni peri&shy;<lb/>patetiche, erano semicopernicani; non attribuivano cio&egrave; alla Terra altro che <lb/>la conversione diurna, e facevano dipendere il flusso marino da quest'unico <lb/>moto. </s>

<s>Voleva Galileo farne argoment&ograve; anco del moto annuo, e cos&igrave; pensando <lb/>fin&igrave; per concludere che anzi era necessario questo secondo moto s'aggiun&shy;<lb/>gesse al primo, senza che non s'intenderebbe come un semplice andamento <lb/>uniforme potesse esser causa di quel perpetuo e regolare avvicendarsi del <lb/>flusso. </s>

<s>Ci voleva una difformit&agrave; nella uniformit&agrave;, la quale Galileo sottilmente <lb/>rinvenne in quel che, supposta vera la posizione copernicana, avviene al moto <lb/>vertiginoso della Terra, che ora aggiunge ora detrae al moto annuale nel&shy;<lb/>l'orbita. </s>

<s>Tanto si compiacque poi, l'inventore, di questa sottigliezza, che <lb/>secondo lui non ci bisognava altro per istabilire il Copernicismo nella scienza <lb/>astronomica, ma pur bisognava ancora mostrar che i fatti rispondevano alle <lb/>speculazioni. </s></p><p type="main">

<s>Mentre intanto, e per le osservazioni sue proprie e per le relazioni al&shy;<lb/>trui attendeva a raccogliere e a sottordinare all'immaginato sistema que'fatti, <lb/>l'apparizione di una stella nuova veniva eccitando un insolito fervore in tutti <lb/>gli Astronomi. </s>

<s>Galileo &egrave; nello Studio padovano de'pi&ugrave; affaccendati, e inter&shy;<lb/>rotto il corso ordinario fa di quella nuova apparizione celeste particolar sog&shy;<lb/>getto alle sue lezioni. </s>

<s>Quali fossero i suoi pensieri lo sappiamo oramai certo <lb/>da quelle note che lasci&ograve; manoscritte, e che son tutte ora venute alla pub&shy;<lb/>blica luce; quali ne fossero i calcoli laboriosi pu&ograve; vedersi nella Giornata III <lb/>de'due Massimi Sistemi. </s></p><p type="main">

<s>Ma fra que'pensieri e que'calcoli della stella nuova Seneca, intorno a <lb/>ci&ograve; consultato, mette in grande ardore il Professor di Padova di darsi a <lb/>contemplare il cielo, per decidere finalmente del sistema del mondo. </s>

<s>E per&shy;<lb/>ch&egrave; gli rimangano le parole del Filosofo morale pi&ugrave; impresse, le trascrive <lb/>di suo proprio pugno a carte 15 del Tomo VI, Parte IV de'manoscritti <lb/>astronomici, fra i pensieri sovvenutigli intorno all'origine della stella nuova. <lb/></s>

<s>&ldquo; Seneca lib. </s>

<s>VII Natur. </s>

<s>quaest. </s>

<s>cap. </s>

<s>II. </s>

<s>Illo quoque pertinebit hoc exau&shy;<lb/>sisse ut sciamus utrum mundus Terra stante circumeat, an mundo stante <lb/>Terra vertatur. </s>

<s>Fuerunt nam qui dicerent nos esse quorum rerum natura <lb/>nescientes ferat, nec coeli motu fieri ortus et occasus, sed ipsos oriri et oc&shy;<lb/>cidere. </s>

<s>Digna res est contemplatione ut sciamus in quo rerum statu si&shy;<lb/>mus, pigerrimam sortiti an velocissimam sedem; circa nos Deus omnia an <lb/>nos agat. </s>

<s>&rdquo; </s></p><p type="main">

<s>E che veramente Galileo si fosse volto con pi&ugrave; ardore che mai a cos&igrave; <lb/>degna contemplazione, s'argomenta da certi pensieri inseriti qua e l&agrave; fra <lb/>que'calcoli disordinati, e relativi alla stella nuova, come per esempio da <lb/>quello che si legge a carte 22 del T. II, P. III. &ldquo; Aggiugni al volar degli <lb/>uccelli che il maggior deviar dalla vertigine della Terra sarebbe il volar con-<pb xlink:href="020/01/903.jpg" pagenum="346"/>tinuamente verso occidente, e cos&igrave; l'uccello doventa come una freccia tirata <lb/>per quel verso, che non fa altro che detrarre alquanto al moto diurno. </s>

<s>&rdquo; </s></p><p type="main">

<s>Avvennero queste cose dopo il 1604, anno in cui comparve quella stella <lb/>nuova. </s>

<s>Dieci anni dopo s'avevano nella vita astronomica di Galileo da con&shy;<lb/>tare ben pi&ugrave; nuovi e pi&ugrave; rumorosi avvenimenti. </s>

<s>Era stato inventato il Te&shy;<lb/>lescopio, e s'erano pubblicate, dopo il Nunzio Sidereo, le lettere velseriane. </s>

<s><lb/>Con tant'arte seppe maneggiarsi quell'uomo intorno a questi negozii, che <lb/>riusc&igrave; veramente, com'era la sua intenzione, a comparire al mondo primo <lb/>e solo Messaggero del cielo, ma vi riusc&igrave; da conquistatore colle solite pre&shy;<lb/>potenze e colle solite stragi, che gli suscitarono contro, in alcuni ire impo&shy;<lb/>tenti, in altri odii vendicativi. </s></p><p type="main">

<s>Primo e solo voleva essere Galileo, primo e solo voleva essere il Col&shy;<lb/>legio de'Gesuiti. </s>

<s>Le spavalde millanterie dell'uno soffiavano, col mantice <lb/>della gelosia, ad accendere le ire negli altri. <emph type="italics"/>Magna longeque admirabilia <lb/>apud me habeo<emph.end type="italics"/> va ricantando a Belisario Vinta, e a quanti altri gli capi&shy;<lb/>tano d'intorno. </s>

<s>Ha a trattare un concetto immenso e pieno di Filosofia, <lb/>Astronomia, Geometria; ha una scienza interamente nuova, non avendo al&shy;<lb/>cun altro scoperto alcuno de'sintomi ammirandi ch'egli dimostra; ha da in&shy;<lb/>segnar cose non pi&ugrave; sapute intorno al suono e alla voce, alla vista e a'co&shy;<lb/>lori, al flusso e riflusso del mare, al moto degli animali.... (Alb. </s>

<s>VI, 97, 98). </s></p><p type="main">

<s>Questo era il linguaggio del Conquistator fortunato, a cui volevasi in <lb/>ogni modo rintuzzare l'orgoglio. </s>

<s>Al Collegio de'Gesuiti, per risorgere nel <lb/>regno della scienza, conveniva opprimere il baldanzoso rivale, e lo fece con <lb/>armi invitte perch&egrave; fatte scendere a ferire dall'alto del Cielo. </s></p><p type="main">

<s>S'erano quelle armi, come un acuto strale, appresentate alla fantasia <lb/>del Copernico, ma a non temerne le offese gli bast&ograve; il pensare che male era <lb/>quello strale <emph type="italics"/>ad suum propositum detortum.<emph.end type="italics"/> Ei non s'era arretrato punto <lb/>per paura de'Teologi, ma de'Peripatetici e del volgo, il quale non si sa&shy;<lb/>rebbe indotto a creder falsa un'opinione confermata <emph type="italics"/>multorum seculorum <lb/>indiciis.<emph.end type="italics"/> Quando poi incominciarono fra gli Astronomi le discussioni, parve <lb/>anche al Rothmann che ci entrassero gli argomenti biblici come i calzari <lb/>degli attori in iscena; similitudine, che Ticone giudic&ograve; irriverente, soggiun&shy;<lb/>gendo rifuggirgli l'animo dal pensare che si potessero nelle Sante Scrit&shy;<lb/>ture propor cose non vere, e avvertendo che, sebbene Mos&egrave; si accomodi <lb/>all'intelligenza del volgo, non per&ograve; dice cose da non si approvar dagli Astro&shy;<lb/>nomi. </s>

<s>&ldquo; Maior enim, scriveva dall'Uraniburgo allo stesso Rothmann, et est <lb/>et esse debet divinarum Literarum autoritas ac reverentia, quam ut sic in <lb/>modum cothurni eas trahi deceat. </s>

<s>Licet enim ipsae in rebus physicis et aliis <lb/>quibusdam, ut plurimum, ad captum vulgi sese attemperent, absit tamen <lb/>ut ob id statuamus eas ita vulgariter loqui quin etiam vera proponere cre&shy;<lb/>damus. </s>

<s>Sic Moses, etsi in primo cap. </s>

<s>Geneseos de Mundi creatione agens <lb/>Astronomiae penetralia non reseret, utpote rudi populo scribens, nihil ta&shy;<lb/>men in medium profert quod non etiam ab ipsis Astronomis concedi queat &rdquo; <lb/>(Epist. </s>

<s>astronomic., libri cit., pag. </s>

<s>147). In ogni modo il Keplero, uomo re-<pb xlink:href="020/01/904.jpg" pagenum="347"/>ligiosissimo e di viva fede alle verit&agrave; rivelate, incomincia il suo <emph type="italics"/>Mysterium <lb/>cosmographicum<emph.end type="italics"/> col dimostrar la ragionevolezza dell'ipotesi copernicana, <lb/>persuaso di non esser per dir nulla <emph type="italics"/>quod in Sacras Literas iniurium sit, <lb/>et si cuius Copernicus mecum convincatur,<emph.end type="italics"/> protesta liberamente, <emph type="italics"/>pro nullo <lb/>habiturum.<emph.end type="italics"/> (Editio cit., pag. </s>

<s>13). </s></p><p type="main">

<s>Tali erano pure questi sentimenti in Italia, quando a un tratto escono <lb/>con gran furia i frati a dire e a predicare che l'ipotesi copernicana &egrave; ere&shy;<lb/>tica, come quella che contradice alla Santa Scrittura. </s>

<s>Dopo settant'anni, <lb/>ch'era uscito un libro scritto da Niccol&ograve; Copernico canonico, pubblicato ad <lb/>istanza di Tidemanno Gisio vescovo, e di Niccol&ograve; Schonberg cardinale, e de&shy;<lb/>dicato a Paolo III Pontefice sommo, insorgere i frati a dichiararlo eretico, <lb/>era un fatto che non sapevasi spiegare nemmen da quello stesso Galileo, <lb/>contro al quale, piuttosto che contro al Copernico, si moveva cos&igrave; aspra <lb/>guerra. </s>

<s>&ldquo; Ora questi buoni frati solo per un sinistro affetto contro di me, <lb/>sapendo ch'io stimo quest'Autore, si vantano di dargli il premio delle sue <lb/>fatiche col farlo dichiarare eretico &rdquo; (ivi, pag. </s>

<s>16). </s></p><p type="main">

<s>Quel che reca poi pi&ugrave; gran maraviglia &egrave; che Galileo, per far le sue <lb/>ragioni, pensa di <emph type="italics"/>battere a'padri Gesuiti<emph.end type="italics"/> (Alb. </s>

<s>II, 17) non comprendendo <lb/>che erano essi che gli facevan nascostamente la guerra, servendosi dello <lb/>strumento degli altri frati. </s>

<s>Essendo chiaro infatti che si combatteva no una <lb/>dottrina ma una persona, qual occasione o qual motivo aveva dato Galileo <lb/>ai frati d'insorgere contro lui? </s>

<s>Ma l'occasione e il motivo l'aveva ben dato <lb/>ai Gesuiti, i quali contendevano non della verit&agrave; del sistema del mondo, ma <lb/>del primato della scienza che si vedevano tolto di mano. </s></p><p type="main">

<s>Si sar&agrave; cominciato Galileo ad avvedere di qualche cosa, quando quel <lb/>Grembergiero <emph type="italics"/>matematico insigne e suo grandissimo amico e padrone<emph.end type="italics"/> (ivi), <lb/>lo trov&ograve; invece suo contradittore, e quando vide Paolo Anton Foscarini, frate <lb/>carmelitano, entrare in quella fatica di accordare e appaciare i luoghi della <lb/>Sant&agrave; Scrittura coll'opinione copernicana, pensando di far <emph type="italics"/>cosa grata agli <lb/>studiosi di queste dottrine ed in particolare alli dottissimi signori Galileo <lb/>Galilei e Giovanni Keplero<emph.end type="italics"/> (Alb. </s>

<s>V, 461). Si sar&agrave; tanto meglio poi lo stesso <lb/>Galileo confermato in questa opinione, quando avr&agrave; risaputo che fu la Let&shy;<lb/>tera del Frate carmelitano pretesto nelle mani de'Gesuiti di fare emanare <lb/>dalla Sacra congregazione de'Cardinali il Decreto del d&igrave; 5 Marzo 1616, cos&igrave; <lb/>dal Riccioli trascritto a pag. </s>

<s>495 della I Parte del suo <emph type="italics"/>Almagesto Nuovo<emph.end type="italics"/><lb/>(Bologna 1651): </s></p><p type="main">

<s>&ldquo; Et quia etiam ad notitiam praefatae Congregationis pervenit falsam <lb/>illam doctrinam pythagoricam divinaeque Scripturae omnino adversantem de <lb/>mobilitate Terrae et immobilitate Soiis, quam Nicolaus Copernicus <emph type="italics"/>De re&shy;<lb/>volutionibus orbium coelestium<emph.end type="italics"/> et Didacus a Stunica <emph type="italics"/>in Job<emph.end type="italics"/> etiam docent, <lb/>iam divulgari et a multis recipi, sicut videri est ex Epistola quadam im&shy;<lb/>pressa cuiusdam patris carmelitae, cui titulus <emph type="italics"/>Lettera del R. P. maestro <lb/>Paolo Antonio Foscarini carmelitano sopra l'opinione dei Pitagorici e del <lb/>Copernico della mobilit&agrave; della Terra e stabilit&agrave; del Sole ed il nuovo Pi-<emph.end type="italics"/><pb xlink:href="020/01/905.jpg" pagenum="348"/><emph type="italics"/>tagorico sistema del mondo; in Napoli, per Lazzero Scorriggio, 1615,<emph.end type="italics"/> in <lb/>qua dictus Pater ostendere conatur praefatam doctrinam de immobilitate <lb/>Solis in centro mundi et mobilitate Terrae consonam esse veritati et non <lb/>adversari Sacrae Scripturae; ideo ne ulterius huiusmodi opinio in perniciem <lb/>catholicae veritatis serpat, censuit dictos Nicolaum Copernicum <emph type="italics"/>De revolu&shy;<lb/>tiodibus orbium,<emph.end type="italics"/> et Didacum a Stunica <emph type="italics"/>in Job<emph.end type="italics"/> suspendendos esse donec cor&shy;<lb/>rigantur; librum vero P. </s>

<s>Pauli Antonii Foscarini carmelitae omnino prohi&shy;<lb/>bendum atque dannandum, aliosque omnes libros pariter idem docentes <lb/>prohibendos, prout praesenti decreto omnes respective prohibet, damnat <lb/>atque suspendit. </s>

<s>&rdquo; </s></p><p type="main">

<s>In questo Decreto non ci &egrave;, come si vede, nulla che tocchi diretta&shy;<lb/>mente Galileo, n&egrave; ci era per verit&agrave; ragione di toccarlo, non avendo negli <lb/>scritti fin allora da lui pubblicati dato altro indizio d'essere copernicano, <lb/>che verso la fine del Nunzio Sidereo, dove dice che non dovrebbe fare dif&shy;<lb/>ficolt&agrave; al moversi della Terra il portarsi dietro la Luna, mentre Giove stesso <lb/>si muove e porta seco, non una sola, ma quattro Lune (Alb. </s>

<s>III, 98). </s></p><p type="main">

<s>Eppure &egrave; certo che fu quel Decreto fatto emanare apposta contro Ga&shy;<lb/>lileo, il quale assordava il mondo colle sue parole, ch'erano agli amici dolci <lb/>promesse, e a'rivali odiose minacce. </s>

<s>Tutte queste promesse poi e queste <lb/>minacce si concludevano in quel vero capriccio del flusso e riflusso, che, <lb/>occorsogli al pensiero parecchi anni avanti, come dicemmo, ora era venuto <lb/>confortandolo di osservazioni procuratesi qua e l&agrave; da'praticanti ne'mari. </s>

<s>In <lb/>quel tempo che i cardinali in Roma meditavano il famoso Decreto, in quel <lb/>tempo dice Galileo (Ald. </s>

<s>VI. 279) di aver dato mano in Roma a distendere <lb/>il Discorso del flusso, avutone comandameuto dal cardinale Orsino. </s>

<s>Fatto sta <lb/>che venne quella scrittura veramente distesa in forma di Lettera indirizzata <lb/>a detto cardinale sotto il di 8 Gennaio 1616. </s></p><p type="main">

<s>Fra'primi ad averne copia, dalle mani del medesimo Autore, fu l'ami&shy;<lb/>cissimo suo Gian Francesco Sagredo, il quale per lettera del d&igrave; 19 Novem&shy;<lb/>bre di quell'anno gli rispondeva cos&igrave; fatte assennate parole: &ldquo; Circa il suo <lb/>Discorso del flusso e riflusso del mare, scorso da me, posso dire, a volo, <lb/>non posso dirle altro, se non che il principio trovato da lei &egrave; sottilissimo, <lb/>verissimo e necessario, con tutte le conseguenze considerate da lei, stante <lb/>l'ipotesi della Terra e sua revoluzione, e stante la natura de'progetti e <lb/>fluidi, per la quale, non pure si verificherebbe il flusso e riflusso sensibile <lb/>de'mari, ma ancora l'insensibile dell'acque, che sono rinchiuse in minime <lb/>caraffine, le quali proporzionatamente alla loro grandezza necessariamente <lb/>devono sentire l'acceleramento e ritardamento del moto della Terra, e per <lb/>conseguenza patire i loro minimi e insensibili flussi e riflussi. </s>

<s>Ma se questa <lb/>dottrina avesse a divulgare, so che l'umana ignoranza di tanti infiniti uo&shy;<lb/>mini incapaci della sottilit&agrave; del vero e della ragione farebbe una bestiale re&shy;<lb/>sistenza. </s>

<s>Con comodit&agrave; di tempo rilegger&ograve; esso Discorso, e l'avviser&ograve; &rdquo; (MSS. <lb/>Gal., P. I, T. VII, c. </s>

<s>265). </s></p><p type="main">

<s>Quando il Sagredo torn&ograve; a dare l'avviso, la notizia del Decreto della <pb xlink:href="020/01/906.jpg" pagenum="349"/>proibizione e della condanna s'era largamente e con gran rumore diffusa, e <lb/>Galileo perci&ograve;, bene intese che conveniva, o volere o no, piegare a quel <lb/>vento le vele. </s>

<s>Ond'&egrave; che accompagnando una copia del Discorso del flusso <lb/>all'arciduca Leopoldo d'Austria, con lettera del d&igrave; 23 Maggio 1618, dopo <lb/>avergli accennato alla sentenza de'Teologi romani contro il moto della Terra <lb/>come repugnante alla Santa Scrittura, cos&igrave; soggiunge: &ldquo; Ora, perch&egrave; io so <lb/>quanto convenga ubbidire e credere alle determinazioni dei superiori, come <lb/>quelli che sono scorti da pi&ugrave; alte cognizioni, alle quali la bassezza del mio <lb/>ingegno per s&egrave; stesso non arriva, reputo questa presente scrittura, che gli <lb/>mando, come quella che &egrave; fondata sopra la mobilit&agrave; della Terra, ovvero che <lb/>&egrave; uno degli argomenti che io produceva in confermazione di essa mobilit&agrave;, <lb/>la reputo, dico, come una poesia, ovvero un sogno, e per tale la riceva <lb/>l'A. V. &rdquo; (Alb. </s>

<s>VI, 280). </s></p><p type="main">

<s>Era in principio di questa scrittura, che Galileo cos&igrave; manoscritta man&shy;<lb/>dava all'Arciduca, accennato che pi&ugrave; diffusamente parlerebbe l'Autore di s&igrave; <lb/>fatta materia nel suo Sistema del mondo (Alb. </s>

<s>II, 388), e perci&ograve;, nella Let&shy;<lb/>tera che l'accompagnava, dop'avere umiliata la fronte innanzi al Decreto <lb/>de'Teologi romani, conclude allo stesso Arciduca, dicendogli che il pensiero <lb/>di ampliarsi sopra quell'argomento, apportandone altri riscontri e riordinan&shy;<lb/>dolo e distinguendolo in altra miglior forma e disposizione, com'avrebbe <lb/>fatto ne'Dialoghi del Sistema del mondo, s'era risoluto in nebbia insiem <lb/>con tutti i suoi confusi e avviluppati fantasmi (Alb. </s>

<s>VI, 280). </s></p><p type="main">

<s>Stette per&ograve; poco che quella nebbia parve alquanto dileguarsi. </s>

<s>Giovanni <lb/>Ciampoli, Ferdinando Cesarini monsignori, Maffeo Barberini e quell'Orsino, <lb/>a cui fu dedicato il Discorso del flusso, cardinali, insiem con altri prelati, <lb/>che inclinavano a favorire i progressi della scienza, sentivano gl'impedi&shy;<lb/>menti che veniva frapponendo il Decreto del d&igrave; 5 Marzo, e come sarebbe <lb/>rimproverata la Repubblica ecclesiastica d'irriverenza e d'ingratitudine, per <lb/>aver condannato un libro scritto da un religiosissimo canonico, pubblicato <lb/>ad istanza di un vescovo e di un cardinale, e dedicato a un Papa, e a cui <lb/>si doveva l'utilissima riforma del Calendario. </s>

<s>Consigliati perci&ograve; dallo zelo <lb/>per l'utilit&agrave; scientifica, e dalla prudenza, promossero nel 1620 l'emanazione <lb/>di quell'altro Decreto, in cui, sebben si riconoscesse giusta dai Cardinali <lb/>la condanna dei libri del Copernico &ldquo; nihilominus, quia in iis multa sunt <lb/>Reipublicae utilissima, unanimi censensu in eam fuerunt sententiam ut Co&shy;<lb/>pernici opera, ad hanc usque diem impressa, permittenda essent, prout per&shy;<lb/>miserunt, iis tamen correctis, iuxta subiectam emendationem, locis in qui&shy;<lb/>bus non ex hypothesi sed asserendo de situ et motu Terrae disputat &rdquo; <lb/>(Riccioli, Almag. </s>

<s>novum, Pars post., T. I, Bononiae 1651, pag. </s>

<s>496). </s></p><p type="main">

<s>Il Cesarini e il Ciampoli particolarmente, nel dargli la notizia di questo <lb/>nuovo Decreto e di quel che i fatti promettevano sopra le parole, solleva&shy;<lb/>rono l'animo di Galileo, il quale, ripreso in mano il Discorso del flusso, <lb/>insinuava all'Aggiunti, per maggior pubblicit&agrave;, che lo rendesse in latino. </s>

<s><lb/>L'ossequioso discepolo teneva nel 1622 preparata per le stampe quella ver-<pb xlink:href="020/01/907.jpg" pagenum="350"/>sione, alla quale aveva premesso un avvertimento ai lettori, dove fra le altre <lb/>leggevansi queste parole: &ldquo; Hanc ego Epistolam per hos dies ex Etruria in <lb/>Latium transtuli, quod a me duplici de causa factum fuit; primum, quia <lb/>Transalpinis nationibus, harum rerum maxime studiosis et Galilaei gloriae <lb/>vehementer deditis, id egregie carum fore existimavi; deinde ut si pluribus <lb/>ille linguis legeretur, qui omnibus linguis omni aevo perpetua celebratione <lb/>luculentissime depraedicari debet; an non debeat qui tot inauditis ac miri&shy;<lb/>ficis inventis haec nostra tempora illnstrat? </s>

<s>&rdquo; (MSS. Gal., P. IV, T. IV, c 68). </s></p><p type="main">

<s>Mentre che si meditava di dar cos&igrave; solenne pubblicit&agrave; a questa versione <lb/>latina, l'animo di Galileo rinverd&igrave; di pi&ugrave; liete e rigogliose speranze. </s>

<s>Quel <lb/>Maffeo Barberini, ch'ebbe tanta parte nell'emanazion del Decreto del 1620, <lb/>in cui si temperava il rigore di quell'altro emesso quattro anni avanti dalla <lb/>Sacra Congregazione de'Cardinali, era stato assunto al soglio pontificio sotto <lb/>il nome di Urbano VIII. </s>

<s>Parve che si potesse sotto un tanto protettore, non <lb/>solo avventurar la pubblicazione del Discorso sul flusso, ma e del Libro da <lb/>s&igrave; lungo tempo meditato del Sistema del mondo, e perci&ograve; il d&igrave; 9 Otto&shy;<lb/>bre 1623 scrive Galileo al principe Cesi che sarebbe voluto venire a Roma <lb/>in tempo opportuno per baciare il piede a Sua Santit&agrave;. </s>

<s>&ldquo; Io raggiro, ivi <lb/>soggiunge, nella mente cose di qualche momento per la Repubblica lette&shy;<lb/>raria, le quali, se non si effettuano in questa mirabil congiuntura, non oc&shy;<lb/>corre, almeno per quel che si aspetta per la parte mia, sperar d'incon&shy;<lb/>trarne mai pi&ugrave; una simile &rdquo; (Alb. </s>

<s>VI, 289, 90). </s></p><p type="main">

<s>La congiuntura fu colta e le speranze ebbero buon effetto. </s>

<s>Eccolo tutto <lb/>in fervore di tessere que'suoi Dialoghi, dai quali tanta luce si diffonderebbe <lb/>sul mondo della materia e sul mondo degl'intelletti. </s>

<s>Ne'principii dell'anno 1625 <lb/>quel fervore gli si rallenta un poco, ma pur procede avanti e l'assiduit&agrave; fa <lb/>crescere il lavoro (Campori, Carteggio galil., Modena 1881, pag. </s>

<s>224): a mezzo <lb/>Febbraio nonostante torna a scrivere alla gagliarda (ivi, pag. </s>

<s>225). </s></p><p type="main">

<s>La notizia che Galileo attende a scrivere in Dialogo del flusso e del Si&shy;<lb/>stema del mondo &egrave; diffusa per tutto, e il p. </s>

<s>Scheiner esprime il desiderio <lb/>vivissimo di veder quello scritto, confessando di essersi convertito al Coper&shy;<lb/>nicanismo (ivi, pag. </s>

<s>233). &Egrave; quella stessa notizia giunta pure in Germania, <lb/>e il Pieroni da Praga scrive il d&igrave; 26 Luglio 1626 a Galileo, pregando lo <lb/>certificasse se era vero ch'egli avesse messo mano a scrivere quell'opera <lb/>della sua mirabile invenzione, che gli aveva detto volere intitolare <emph type="italics"/>Fluxus <lb/>atque refluxus maris<emph.end type="italics"/> (MSS. Gal., P. I, T. IX, c. </s>

<s>43). </s></p><p type="main">

<s>Nel Luglio del 1627 gli amici impazienti sono intorno al Ciampoli, che <lb/>solleciti Galileo a sodisfar pi&ugrave; presto che sia possibile ai loro ardentissimi <lb/>desiderii: &ldquo; Arrivano qua avvisi che il corso de'suoi Dialoghi si muova con <lb/>lentezza, e noi sentendo ci&ograve; sospiriamo la perdita di s&igrave; rari tesori. </s>

<s>Non ve&shy;<lb/>diamo l'ora di leggerne almeno qualche part&igrave;cella, s&igrave; che nel medesimo tempo <lb/>molti suoi amici, e fra questi come capo il p. </s>

<s>d. </s>

<s>Benedetto, uniamo le no&shy;<lb/>stre preghiere e le chiediamo instantemente due grazie: una che ci lasci <lb/>gustare qualche cosa del fatto fin qui; l'altra ch'ella voglia vincere i con-<pb xlink:href="020/01/908.jpg" pagenum="351"/>sigli della quiete con gli stimoli della gloria e con le esortazioni degli amici &rdquo; <lb/>(Campori, Carteggio cit., pag. </s>

<s>258). Un anno e mezzo dopo le grazie furono <lb/>esaudite: in casa del signor canonico Cini si leggono i Dialoghi galileiani <lb/><emph type="italics"/>con stupore ed infinito applauso di chiunque li ode<emph.end type="italics"/> (ivi, pag. </s>

<s>278). </s></p><p type="main">

<s>Mancavano per&ograve; ancora a que'Dialoghi la cerimoniale Introduzione e le <lb/>attaccature de'principii con le materie seguenti, che sebben sieno, dice lo <lb/>stesso Galileo, cose piuttosto oratorie e poetiche che scientifiche, non vuol <lb/>tuttavia trascurarle perch&egrave; l'opera abbia spirito e vaghezza (Alb. </s>

<s>VI, 333). <lb/>Pare nonostante che fosse questo il lavoro di pochi giorni, avendo gi&agrave; il <lb/>d&igrave; 5 di Gennaio 1630 dato avviso al Ciampoli che i Dialoghi erano felice&shy;<lb/>mente terminati (Campori cit., pag. </s>

<s>289). </s></p><p type="main">

<s>Tutto il forte stava in dar quel manoscritto di tanti desiderii e di tante <lb/>trepidazioni alle stampe, per le quali conveniva entrar ne'gelosi trattati della <lb/>licenza ecclesiastica. </s>

<s>Era Maestro del sacro Palazzo allora un tal padre Nic&shy;<lb/>col&ograve; Riccardi, soprannominato il Mostro, assai inclinato a favorir Galileo <lb/>(ivi, pag. </s>

<s>290), il qual Padre aveva nel Novembre di quell'anno 1630 pro&shy;<lb/>messo pi&ugrave; volte al Castelli di <emph type="italics"/>spedir la licenza per i Dialoghi<emph.end type="italics"/> (ivi, pag. </s>

<s>302). <lb/>Il d&igrave; 20 Marzo del seguente anno 1631 n'erano stati stampati sei fogli <lb/>(Alb. </s>

<s>VI, 378) e tutto il lavoro comp&igrave;to alla met&agrave; di Dicembre (Campori, <lb/>pag. </s>

<s>319). Si pubblic&ograve; ne'primi giorni dell'anno appresso 1632, in Firenze, <lb/>dall'Officina di Giovan Batista Landini, col titolo: <emph type="italics"/>Dialogo di Galileo Gali&shy;<lb/>lei Linceo.... dove nei congressi di quattro giornate si discorre sopra i <lb/>due massimi Sistemi del mondo tolemaico e copernicano.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>&Egrave; questo finalmente quel libro con tanta solennit&agrave; promesso da ven&shy;<lb/>tidue anni nell'Avviso sidereo (Alb. </s>

<s>III, 73) e a innumerevoli occasioni dal&shy;<lb/>l'Autore stesso magnificato come quello che darebbe la dimostrazione pi&ugrave; <lb/>certa del Sistema copernicano. </s>

<s>Confidava l'Autore che sarebbe questa nuova <lb/>certezza principalmente derivata dal flusso marino, che nel moto della Terra <lb/>e non in altro riconosceva la sua ragione, ond'&egrave; che, sebben nella prima <lb/>pagina non si conservi altrimenti il titolo di <emph type="italics"/>Fluxus et Refluxus,<emph.end type="italics"/> sotto il <lb/>quale era stato annunziato, occupa nonostante la trattazione di quel soggetto <lb/>la quarta parte di tutto il Libro. </s></p><p type="main">

<s>Che vana fosse quella confidenza, di che tanto s'enfiava l'animo di Ga&shy;<lb/>lileo, si &egrave; subodorato gi&agrave; dal Discorso al cardinale Orsino, ma pur era de&shy;<lb/>gno l'Autore allora di qualche compatimento, ripensando alle puerili ipotesi <lb/>che ricorrevano per i libri filosofici di que'tempi. </s>

<s>Si possono cos&igrave; fatte ipo&shy;<lb/>tesi, senza bisogno di squadernare altri libri, veder raccolte e discusse in un <lb/>Trattato, che Galileo ebbe ad esaminar sotto gli occhi e a confutar ne'suoi <lb/>Dialoghi. </s></p><pb xlink:href="020/01/909.jpg" pagenum="352"/><p type="main">

<s>Girolamo Borro aretino, verso il 1560, aveva scritto alcuni Dialoghi in <lb/>volgare sul flusso e riflusso marino, mandandoli attorno fra gli amici, cosi <lb/>manoscritti. </s>

<s>Girolamo Ghirlanda pens&ograve; a pubblicarli, e gli fece stampare in <lb/>Lucca nel 1561 per il Busdrago, sotto il nome di <emph type="italics"/>Talascopio Alseroforo,<emph.end type="italics"/> in&shy;<lb/>dirizzandoli, per mezzo di una Lettera impressa nelle prime pagine, al me&shy;<lb/>desimo Autore, il quale parve se ne adirasse cos&igrave; un poco, ma poi compia&shy;<lb/>ciutosi del favore incontrato da questa sua opera letteraria, l'ampli&ograve;, la <lb/>corresse in qualche parte, e la stamp&ograve; in Firenze nel 1577 appresso Gior&shy;<lb/>gio Mariscotti col titolo: <emph type="italics"/>Girolamo Borro aretino, Del flusso e riflusso del <lb/>mare ecc.<emph.end type="italics"/></s></p><p type="main">

<s>Il Talascopio Alseroforo dimostra nel suo Trattato questa proposizione <lb/>fondamentale: &ldquo; Come la Luna abbia possanza col suo temperato calore di <lb/>rarefar l'acqua, la quale rarefatta viene a sollevarsi &rdquo; (pag. </s>

<s>35) e cosi con&shy;<lb/>clude la ragione del sollevarsi e deprimersi il mare di sei in sei ore, in or&shy;<lb/>dine al moto circolare della Luna intorno alla Terra. </s></p><p type="main">

<s>Girolamo Borro poi conferma questa sua ipotesi mostrando quant'ella <lb/>sia pi&ugrave; ragionevole di quell'altre professate dai Peripatetici, i quali consi&shy;<lb/>derando che ne'fondi del mare son come sulla Terra asciutta, monti e valli, <lb/>dicevano che &ldquo; l'acque che sono sopra i monti da fondo del mare vi stanno <lb/>per forza e naturalmente cercano di scendere nelle basse valli, dove tro&shy;<lb/>vando le altre acque, n&egrave; con esse potendosi fermare in quel piccolo luogo, <lb/>le cacciano. </s>

<s>Queste cacciate per forza salgono sopra i monti del mare, d'onde <lb/>le prime si partirono.... Il salir delle acque fa il flusso e lo scendere delle <lb/>medesime fa il riflusso, il quale sempre dura perch&egrave; elle sempre salgono e <lb/>sempre scendono &rdquo; (pag. </s>

<s>43). </s></p><p type="main">

<s>Appetto a queste ipotesi doveva a buon diritto sembrare a Galileo una <lb/>peregrina speculazione quella dell'antico Seleuco rinnovellata dal Cesalpino, <lb/>e aveva qualche giusto motivo di compiacersi per averla cos&igrave; sottilmente ri&shy;<lb/>dotta ad essere dimostrativa, non tanto del diurno, quanto del moto annuale <lb/>della Terra. </s>

<s>Ma chi pu&ograve; scusare la vanit&agrave; di colui, che dentro un'arca ri&shy;<lb/>dotta a forma latina dall'Aggiunti voleva riposti i suoi preziosi tesori, per <lb/>ispedirli di l&agrave; dai monti e dai mari, anche dopo che il De Dominis aveva <lb/>pubblicato il suo <emph type="italics"/>Euripus?<emph.end type="italics"/> o chi pu&ograve; sopportare il disprezzo con che l'Au&shy;<lb/>tore de'Due Massimi sistemi deride l'opinione di quel <emph type="italics"/>certo prelato?<emph.end type="italics"/><lb/>(Alb. </s>

<s>I, 455). </s></p><p type="main">

<s>Che fosse quell'opinione conforme alla verit&agrave;, come fu poi dal gran <lb/>Newton dimostrato, non occorre ora a noi ripeterlo: basti dir come, sup&shy;<lb/>posto che il flusso e riflusso marino dipenda dalle attrazioni ora concordi <lb/>ora discordi del Sole e della Luna, risolve il De Dominis tutte le pi&ugrave; astruse <lb/>questioni, che si possono fare intorno a quel cosi complicato soggetto, delle <lb/>quali questioni cos&igrave; magistralmente risolute dall'Autor dell'<emph type="italics"/>Euripus<emph.end type="italics"/> giova <lb/>a noi riferire le principali: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Quaesitum I.<emph.end type="italics"/> Cur aliqua maria multo plus quam aliqua alia, et cur <lb/>aliqua etiam aut nihil, aut parum admodum intumescunt et detumescunt? <pb xlink:href="020/01/910.jpg" pagenum="353"/>Respondeo .... quoniam igitur aliqua maria sunt ampliora, alia angustiora, <lb/>et alia profundioria, alia minus profunda, ideo alia plus habent aquae trahen&shy;<lb/>dae quam alia &rdquo; (Romae 1624, pag. </s>

<s>47). <lb/>&hellip; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Quaesitum III.<emph.end type="italics"/> Cur ordinarie bis in die naturali aquae intumescunt, <lb/>et bis detumescunt per quasi sena horarum spatia, alicubi vero saepius in <lb/>die?... Respondeo .... sic igitur unus ex dictis semicirculis duodecim hora&shy;<lb/>rum spatio percurrit unum hemisphaerium, ascendendo nimirum per sex <lb/>horas quousque vertex cumuli sit in meridiano dicti hemisphaerii, et per <lb/>sex alias descendendo cui alter similiter semicirculus priori diametraliter <lb/>oppositus, per alias 12 horas succedit et sic deinceps.... Quod vero alicubi <lb/>saepius in die id contingit, ego fateor me non posse in mari veram causam <lb/>assignare &rdquo; (ibi, pag. </s>

<s>57). <lb/>&hellip; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Quaesitum V.<emph.end type="italics"/> Cur in eodem etiam loco diversis temporibus intume&shy;<lb/>scentia et detumescentia maris est inaequalis? </s>

<s>Respondeo totum id contin&shy;<lb/>gere ordinarie ex ipsis luminaribus ipsorumque circulis mare attrahentibus <lb/>vel allicientibus. </s>

<s>Cum enim non sola Luna sed etiam Sol pro suo modulo <lb/>suum cumulum, licet minorem, efficiat, ex diversis aspectibus qui sunt in&shy;<lb/>ter Solem et Lunam, maior vel minor fieri debet fluxus et refluxus. </s>

<s>Si lu&shy;<lb/>minaria sint in coniunctione vel oppositione, quia uterque cumulus utriusque <lb/>luminaris simul concurrunt, profecto plus aquae accumulabitur utroque cu&shy;<lb/>mulo simul iuncto, ubi uterque circulus transpolaris aquas trahens, in uni&shy;<lb/>cum circulum conveniunt, quod fit in coniunctione et oppositione lumina&shy;<lb/>rium, quam si in alio aspectu a se invicem circuli illi disiiungantur, et se <lb/>invicem in sua actione impediant &rdquo; (ibi, pag. </s>

<s>59, 60). </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Quaesitum VI.<emph.end type="italics"/> Cur non eadem diei hora aqua fit ubique et altis&shy;<lb/>sima et depressissima sed magna fit in hac horarum diversitas, tum eodem <lb/>loco tum etiam diversis, quoad initium tum fluxus quam refluxus compara&shy;<lb/>tis? </s>

<s>Respondeo ex mea positione sequi finem fluxus, hoc est maximum <lb/>uniuscuiusque diei tumorem aquae, ubique .... deberi contingere quando <lb/>Luna existit circa loci meridianum; hoc est ad horam astronomicam duo&shy;<lb/>decimam solarem tam diurnam quam nocturnam; finem vero refluxus et <lb/>initium fluxus, quando eadem Luna existit circa horam solarem utramque <lb/>sextam.... Et quoniam non eadem hora solari quotidie Luna est aut in me&shy;<lb/>ridiano aut in circulo horae sextae, sed variat plurimum, ideo quotidianus <lb/>hic effectus, finis nimirum et initium fluxus et refluxus, quotidie per totum <lb/>mensem variat horas solares &rdquo; (ibi, pag. </s>

<s>64, 65). </s></p><p type="main">

<s>Se Galileo avesse solamente atteso a questo notissimo fatto risoluto dal <lb/>De Dominis in questo suo ultimo quesito, si sarebbe facilmente persuaso <lb/>della falsit&agrave; della sua ipotesi; cosa che gli fu poi fatta notar dal Baliani, il <lb/>quale giudicando tutto il quarto Dialogo maraviglioso, confessava nonostante <lb/>esservi una gravissima difficolt&agrave;, alla quale non si rispondeva, perch&egrave; do&shy;<lb/>vrebbe, nell'ipotesi galileiana, essere il flusso &ldquo; ogni di alla stess'ora; ep-<pb xlink:href="020/01/911.jpg" pagenum="354"/>pur l'opinione comune &egrave; contraria, cio&egrave; che si anticipi ogni giorno circa quat&shy;<lb/>tro quinti di ora per andar esso seguendo il moto della Luna &rdquo; (Alb. </s>

<s>IX, 266). </s></p><p type="main">

<s>Ma era Galileo tanto pieno di s&egrave;, che non ci ammetteva nessun altro, <lb/>e lo cacciava con orgoglioso dispetto, come fece non solo con Girolamo <lb/>Borro, il quale diceva &ldquo; che la Luna ha possanza col suo temperato calore <lb/>di rarefar l'acqua, la quale rarefatta viene a sollevarsi &rdquo; (Alb. </s>

<s>I 455) ma <lb/>con quel <emph type="italics"/>certo prelato<emph.end type="italics"/> autore di un trattatello dove si legge &ldquo; che la Luna <lb/>vagando per il cielo attrae e solleva verso di s&egrave; un cumulo d'acqua, il quale <lb/>la va continuamente seguitando, sicch&egrave; il mare alto &egrave; sempre in quella parte <lb/>che soggiace alla Luna &rdquo; (ivi). </s></p><p type="main">

<s>Perch&egrave; poi &egrave; un fatto evidentissimo che il flusso ha una certa costante <lb/>relazione con la Luna, ecco in che Galileo fa consistere l'efficienza di lei <lb/>sulla marea. </s>

<s>Considera ch'essendo la stessa Luna ora nella congiunzione ora <lb/>nell'opposizione fa le veci del <emph type="italics"/>tempo,<emph.end type="italics"/> che accomodavano gli art&egrave;fici per re&shy;<lb/>golare il moto agli antichi orologi, e da ci&ograve; ne segue che la Terra intorno <lb/>al Sole ora si muove pi&ugrave;, ora meno veloce con periodi e restituzioni me&shy;<lb/>strue, che son la causa vera efficiente delle alterazioni periodiche mestrue <lb/>e annue de'flussi e refiussi. </s>

<s>&ldquo; Ora vedete, conclude Galileo, come la causa <lb/>del periodo mestruo risiede nel moto annuo, e insieme vedete ci&ograve; che ha <lb/>che far la Luna in questo negozio, e come ella ci entra a parte, senza aver <lb/>che fare niente n&egrave; con mari n&egrave; con acqua &rdquo; (Alb. </s>

<s>I, 491). </s></p><p type="main">

<s>Il concetto galileiano del riguardar la Luna come il contrappeso, che <lb/>ritirato ora pi&ugrave; ora meno dal centro, indugia o velocita il moto alla Terra, <lb/>bench&egrave; sia male appropriato al fatto della marea, avrebbe nonostante il me&shy;<lb/>rito di esser chiamato arguto, se fosse stato originale, ma non fece altro in <lb/>verit&agrave; Galileo che tirare alla sua ipotesi le dottrine, con le quali spiegavano, <lb/>secondo il Copernico, gli Astronomi antichi come mai si muova nell'apogeo <lb/>la Luna pi&ugrave; tarda e nel perigeo pi&ugrave; veloce. </s>

<s>&ldquo; Sub hoc igitur orbe et ipsius <lb/>plano Luna semper in consequentia moveri cernitur, sed aliquando mini&shy;<lb/>mum, aliquando plurimum. </s>

<s>Tanto enim tardior quanto sublimior, velocior <lb/>autem quo Terrae proprinquior. </s>

<s>Quod in ea facilius quam in alio quovis <lb/>sidere ob eius vicinitatem discerni potuit. </s>

<s>Intellexerunt igitur per epicyclum <lb/>fieri quum Luna illum circumcurrens in superna circumferentia detraheret <lb/>aequalitati, in inferna autem promoveret eamdem &rdquo; (De revolut. </s>

<s>cit., c. </s>

<s>98 v.). </s></p><p type="main">

<s>Coloro che affascinati da quell'insolito splendore tutto ammiravano in <lb/>Galileo, dissero maravigliosa anche questa dimostrazione del flusso marino. </s>

<s><lb/>Ma perch&egrave; per le quotidiane osservazioni troppo si rendeva evidente la re&shy;<lb/>golarit&agrave; de'moti del mare e la loro conformit&agrave; ai moti della Luna, smar&shy;<lb/>rita quella diritta via aperta gi&agrave; dal Gilberto e dal De Dominis, molti se&shy;<lb/>guitarono le fantasie del Cartesio, che attribuiva il flusso alla maggiore o <lb/>minor pressione della sostanza eterea interposta fra la Terra e la Luna. </s>

<s>Il <lb/>Fabry, ne'suoi <emph type="italics"/>Dialogi physici De motu Terrae,<emph.end type="italics"/> attribu&igrave; l'effetto non al&shy;<lb/>l'etere cartesiano ma all'aria, la pression della quale prevalendo ora pi&ugrave; da <lb/>una parte che dall'altra, fa s&igrave; che l'umida superficie marina si rigonfi pi&ugrave; <pb xlink:href="020/01/912.jpg" pagenum="355"/>l&agrave;, dove si sente esser meno premuta. </s>

<s>Cos&igrave; senza soggiacerne agl'influssi <lb/>emula il mare il moto della Luna. </s>

<s>&ldquo; Atque ita praedictus aquae tumor mo&shy;<lb/>tum Lunae omnino aemulatur &rdquo; (Lugduni 1665, pag. </s>

<s>108). </s></p><p type="main">

<s>Venne curiosit&agrave; al Wrenn di far della verit&agrave; di queste ipotesi qualche <lb/>esperienza, e perci&ograve; consigliava il Boyle a prendere un lungo tubo barome&shy;<lb/>trico per osservar pi&ugrave; facilmente se, in conformit&agrave; del flusso e riflusso ma&shy;<lb/>rino, vi si fosse potuta notare qualche variet&agrave; di livello. </s>

<s>Quel che rispon&shy;<lb/>desse il celebre Autore degli Sperimenti fisico-meccanici si pu&ograve; vederlo dallo <lb/>Sperimento XVIII, in cui, dopo aver significati i desiderii del Wrenn cos&igrave; <lb/>prosegue a dire a suo nipote: &ldquo; Cum autem comperimus hydrargyrum in <lb/>tubo contentum, prae accidentali, ut videtur aeris mutatione tam incertis <lb/>motibus sursum et deorsum ferri, in ancipiti haereo dubitans altitudinem <lb/>nec ne inveniemus mercurii tam regulariter variari, quam quaestionem in&shy;<lb/>geniose propositam invenimus. </s>

<s>Postquam autem, Deo favente, rem repertus <lb/>fuero, curabo ne te lateat successus &rdquo; (Opera omnia, T. I, Venetiis 1697, <lb/>pag. </s>

<s>39). </s></p><p type="main">

<s>Parecchi anni prima per&ograve; che al gran Fisico inglese, parve quel suc&shy;<lb/>cesso essere stato rivelato a un nostro Italiano. </s>

<s>Cos&igrave; infatti si legge a carte 182 <lb/>del T. IX de'Manoscritti del Cimento: <emph type="italics"/>&ldquo; L'esperimento nuovo osservato da <lb/>don Francesco Tarvigia in Venezia, cavato da una Lettera indirizzata al <lb/>p. </s>

<s>Atanasio Kircher.<emph.end type="italics"/> &mdash; Ho osservato nella fistola o canna di vetro, con la <lb/>quale il Torricelli, Robervallio, Valeriano Magno e Mersenno mostrarono il <lb/>vacuo, che disceso il mercurio fino a quel segno che &egrave; salito di due piedi <lb/>pi&ugrave; o meno, secondo la diversit&agrave; de'paesi, al calar dell'acqua marina il mer&shy;<lb/>curio s'inalza un mezzo dito: nel crescer della medesima acqua si abbassa <lb/>e persevera con questa reciprocazione costantemente con un moto contrario <lb/>al moto del mare. </s>

<s>La mutazione dell'aria altera talvolta l'esperimento, ma <lb/>con la replicata operazione mi sono certificato esservi una invariabile con&shy;<lb/>nessione fra il moto dell'acqua marina e quello che si vede nel vetro. </s>

<s>Di <lb/>questa connessione supplico V. P. rendermi capace della causa fisica &rdquo; </s></p><p type="main">

<s>Ci&ograve; che si rispondesse da quel Kircher, il quale a qualunque pi&ugrave; dif&shy;<lb/>ficile problema proposto aveva pronta la soluzione, non sapremmo noi dire, <lb/>ma &egrave; da creder che facesse tutt'altra risposta dalla vera, la quale sarebbe <lb/>stata che facilmente il Tarvigia s'era ingannato. </s>

<s>L'inganno fu poi in ogni <lb/>modo tolto via dalle diligentissime osservazioni del Ramazzini, dalle quali fu <lb/>concluso essere indipendenti le variazioni barometriche cos&igrave; dalle vicende <lb/>de'pleniluni e de'noviluni, come de'flussi del mare e de'riflussi. </s></p><p type="main">

<s>Ma &egrave; da tornare a Galileo, riguardo al quale ha la storia da notare un <lb/>fatto, per cui si dar&agrave; sempre meglio a conoscere l'indole di quell'uomo. </s>

<s><lb/>Dop'aver tanto accarezzata quella sua dimostrazione del flusso, dop'averle <lb/>dato cos&igrave; precipua e splendida parte ne'Dialoghi de'Massimi Sistemi, dopo <lb/>aver negato fede al gran Gilberto, nel quale aveva letto: <emph type="italics"/>Videmus namque <lb/>quomodo oceanus sub certis quibusdam Lunae positionibus intumescat et <lb/>aestuet<emph.end type="italics"/> (De Magn. </s>

<s>cit., pag. </s>

<s>224), e tutto ci&ograve; per sola virt&ugrave; magnetica; <pb xlink:href="020/01/913.jpg" pagenum="356"/>dop'aver conculcato il De Dominis mettendolo alla pari di Girolamo Borro <lb/>e degli altri Filosofi pi&ugrave; volgari, eccolo, all'occasion di avere osservato la <lb/>titubazione lunare, dar abito tutt'affatto diverso a'suoi pensieri, approvando <lb/>in sostanza ci&ograve; che aveva prima confutato e deriso. </s>

<s>&ldquo; Aggiungesi (scriveva <lb/>al Castelli, dop'avergli significate le tre nuove mutazioni osservate nella fac&shy;<lb/>cia della Luna) di pi&ugrave; una seconda maraviglia, ed &egrave; che queste tre diverse <lb/>mutazioni hanno tre diversi periodi, imperocch&egrave; l'una si muta di giorno in <lb/>giorno e cos&igrave; viene ad avere il suo periodo diurno; la seconda si va mu&shy;<lb/>tando di mese in mese, ed ha il suo periodo mestruo; la terza ha il suo <lb/>periodo aunuo, secondo il quale finisce la sua variazione. </s>

<s>Or che dir&agrave; la <lb/>P. V. R. nel confrontare questi tre periodi lunari co'tre periodi diurno, <lb/>mestruo ed annuo de'movimenti del mare, de'quali per comune consenso <lb/>di tutti la Luna &egrave; arbitra e soprantendente? </s>

<s>&rdquo; (Alb. </s>

<s>VII, 196). A che il Ca&shy;<lb/>stelli non seppe dir altro, se non ch'egli era curioso d'intendere &ldquo; come que&shy;<lb/>ste osservazioni si accordano con le dottrine de'Dialoghi &rdquo; (Alb. </s>

<s>X, 246). </s></p><p type="main">

<s>Cos&igrave; veniva suo malgrado confessato dallo stesso Autore che la quarta <lb/>parte dell'opera de'Massimi Sistemi vacillava sul falso, in cui poi cadde irre&shy;<lb/>parabilmente quando il Newton, svolgendo il germe di que'concetti infusi <lb/>nel lib. </s>

<s>VI <emph type="italics"/>De Magnete<emph.end type="italics"/> conferm&ograve; le dottrine colle quali il De Dominis aveva, <lb/>due terzi di secolo prima, sciolto il problema del flusso e del riflusso del <lb/>mare. </s>

<s>Quella tanto vantata dimostrazione galileiana non era dunque riuscita <lb/>che ad una vanit&agrave;, e non ebbe di qui il sistema copernicano, per opera di <lb/>Galileo, nessun conforto, come non l'ebbe da lui nell'argomento de'venti <lb/>tropicali. </s></p><p type="main">

<s>Passando ora ad esaminare gli altri argomenti, uno de'principali che <lb/>si trovi svolto ne'<emph type="italics"/>Massimi Sistemi<emph.end type="italics"/> &egrave; quello che riguarda la discesa de'gravi <lb/>e il moto de'proietti in relazione col moto vertiginoso della Terra. </s>

<s>Vedemmo <lb/>come alle difficolt&agrave; promosse prima da Aristotile e ripetute poi da Ticone <lb/>avesse risposto il Gilberto nella Fisiologia sua nuova <emph type="italics"/>De Magnete,<emph.end type="italics"/> segnata&shy;<lb/>mente al cap. </s>

<s>V del VI libro, desumendo le prove dal principio delle ma&shy;<lb/>gnetiche forze attrattive, gli effluvii delle quali o la sfera di attivit&agrave; come <lb/>si dice, si estende, secondo il Gilberto, alquanto al di l&agrave; de'limiti superfi&shy;<lb/>ciali del Globo. </s>

<s>Dietro questo luminoso principio le conclusioni del Filosofo <lb/>inglese riescono invitte, e la nuova scienza neutoniana nient'altro in sostanza <lb/>ha fatto pi&ugrave; che stabilir meglio quello stesso principio del Gilberto e svol&shy;<lb/>gerne la conclusione. </s></p><p type="main">

<s>Galileo non seppe riconoscere quanto fosse di vero in quelle forze at&shy;<lb/>trattive, e ammettendo che vengano i proietti trasportati seco nella sua ver&shy;<lb/>tigine dalla Terra, come vien trasportata la Luna, afferm&ograve; un fatto senza <lb/>per&ograve; dir qual ne fosse la causa misteriosa. </s>

<s>Di qui &egrave; che facendosi Galileo <lb/>stesso commentatore al Gilberto, svolge prolissamente nel secondo Dialogo <lb/>gli argomenti di lui in modo, che i Simplicii stessi ne vadan capaci, ma <lb/>non v'infonde que'principii scienziali, che si sarebbero desiderati dai Sa&shy;<lb/>gredi. </s></p><pb xlink:href="020/01/914.jpg" pagenum="357"/><p type="main">

<s>Della perspicuit&agrave; per&ograve; delle galileiane dimostrazioni n'abbiamo l'esem&shy;<lb/>pio in queste note, nelle quali condensa l'Autore ci&ograve; che sciolse poi in quel <lb/>profluvio di parole, che si leggono nel sopra citato Dialogo secondo: &ldquo; Cor&shy;<lb/>rendo una nave velocissimamente, la <lb/>freccia, o palla che sar&agrave; meglio, sca&shy;<lb/>ricata con l'arco a perpendicolo, ve&shy;<lb/>ramente non riceve l'impeto a per&shy;<lb/>pendicolo, ma inclinato verso la parte <lb/>dove cammina la nave, perch&egrave;, mo&shy;<lb/>vendosi per esempio la nave dalla <lb/>sinistra verso la destra, nello scattare <lb/>dell'arco, la palla si trova in A (fig. </s>

<s>67) <lb/><figure id="id.020.01.914.1.jpg" xlink:href="020/01/914/1.jpg"/></s></p><p type="caption">

<s>Figura 67.<lb/>e nel separarsi dalla corda si trova <lb/>in B: adunque l'impeto ricevuto &egrave; <lb/>secondo la linea inclinata AB, e non <lb/>secondo il perpendicolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Parimente, se la Terra stesse ferma, l'artiglieria A (fig. </s>

<s>68) al segno B <lb/>dar&agrave; giusto, movendosi la palla secondo la linea ABF. </s>

<s>Ma se la Terra gi&shy;<lb/><figure id="id.020.01.914.2.jpg" xlink:href="020/01/914/2.jpg"/></s></p><p type="caption">

<s>Figura 68.<lb/>rasse dovria da&shy;<lb/>re alto girando <lb/>verso la destra, <lb/>e cos&igrave; appare a <lb/>chi considera <lb/>poco, ma a chi <lb/>considerer&agrave; che, <lb/>mentre che la <lb/>palla cammina <lb/>dentro il pezzo, <lb/>l'artiglieria vie&shy;<lb/>ne da A in C, <lb/>onde la palla ri&shy;<lb/>ceve l'impeto <lb/>pi&ugrave; inclinato, <lb/>cio&egrave; secondo la linea AD; intender&agrave; benissimo come la botta non dovr&agrave; dar <lb/>alto, ma nell'istesso segno B trasportato dal moto della Terra in D, men&shy;<lb/>tre la palla va per aria da C in D. </s>

<s>E quanto pi&ugrave; il moto sar&agrave; veloce, tanto <lb/>pi&ugrave; grande sar&agrave; la distanza BD, ma anco tanto sar&agrave; maggiore il progresso <lb/>AC e l'inclinazione del CD sotto al tiro primo ABF &rdquo; (MSS. Gal., P. VI, <lb/>T. II, c. </s>

<s>20). </s></p><p type="main">

<s>Nemmeno dunque per questa parte Galileo ha gran merito in confer&shy;<lb/>mare il sistema copernicano, non avendo fatto altro che ridurre all'intelli&shy;<lb/>genza comune, trascurati i principii scientifici, gli argomenti del Gilberto. </s>

<s><lb/>Chi legge nella Giornata III le meraviglie fatte di Aristarco e del Copernico, <lb/>i quali, non essendo riusciti a risolvere le difficolt&agrave; delle fasi di Venere, pur <pb xlink:href="020/01/915.jpg" pagenum="358"/>confidentemente affermarono non poter, da quella ch'essi stessi avevano di&shy;<lb/>segnata, esser altra la struttura dell'universo, e poi legge come il canoc&shy;<lb/>chiale a lui proprio, a Galileo, mostrasse prima che ad ogni altro Venere e <lb/>Marte disuguali a s&egrave; stessi, secondo le proporzioni assegnate gi&agrave; dal Coper&shy;<lb/>nico, e Venere sotto il Sole apparir falcata e mutar le sue forme nello stesso <lb/>modo che fa la Luna (Alb. </s>

<s>I, 365); ecco, dice, l'Autore de'Massimi Sistemi <lb/>essere il primo a dar la pi&ugrave; splendida conferma al sistema copernicano. </s>

<s>E <lb/>di tal gloria veramente si compiacque Galileo, ma la critica crudele svela <lb/>cos&igrave; le occulte fraudi, che l'usurpata gloria si converte finalmente in meri&shy;<lb/>tata ignominia. </s></p><p type="main">

<s>Il d&igrave; 13 di Novembre 1610 il fortunato Autore del Messaggero celeste <lb/>scriveva a Praga a don Giuliano de'Medici che, trovata la corte a Giove e <lb/>due servi al vecchio Saturno che non staccandosegli mai dal fianco lo aiu&shy;<lb/>tino a camminare, <emph type="italics"/>intorno agli altri pianeti non ci &egrave; novit&agrave; alcuna.<emph.end type="italics"/><lb/>(Alb. </s>

<s>VI, 127). </s></p><p type="main">

<s>Aveva appena Galilco spedito questa, senza speranza oramai di pi&ugrave; re&shy;<lb/>cuperarla, quando gli recapita una lettera scritta dal Castelli otto giorni <lb/>prima da Brescia, nella quale, come uno che si risvegli dal sonno, atten&shy;<lb/>deva a leggere queste parole: &ldquo; Essendo, come credo, vera la proposizione <lb/>di Copernico che Venere giri intorno al Sole, &egrave; chiaro che sarebbe neces&shy;<lb/>sario che fosse vista da noi alle volte cornuta, alle volte no, stando pure il <lb/>detto Pianeta in pari remozione dal Sole, ogni volta per&ograve; che la piccolezza <lb/>de'corni e la effusione de'raggi non c'impedissero l'osservazione di questa <lb/>differenza. </s>

<s>Ora desidero saper da V. S. se lei, con l'aiuto de'suoi meravi&shy;<lb/>gliosi occhiali, ha notata simile apparenza, quale senza dubbio saria mezzo <lb/>sicuro di convincer qualsivoglia ostinato ingegno. </s>

<s>Simil cosa vo sospettando <lb/>ancora di Marte circa il quadrato con il Sole, non dico gi&agrave; di apparenza <lb/>cornuta o non cornuta, ma almeno di semicircolare o pi&ugrave; piana. </s>

<s>&rdquo; E con&shy;<lb/>clude supplicandolo di due righe in risposta (Alb. </s>

<s>VIII, 118, 19). </s></p><p type="main">

<s>E che cosa poteva rispondere? </s>

<s>Volendo esser sincero conveniva ripe&shy;<lb/>tesse al Castelli quel che poche ore prima aveva scritto a don Giuliano <lb/>de'Medici, che cio&egrave; non aveva ancora osservato alcuna di quelle novit&agrave; ce&shy;<lb/>lesti. </s>

<s>Ma colla sincerit&agrave; non veniva a secondare que'suoi fermi propositi di <lb/>voler essere in tutto o apparire il primo ed il solo. </s>

<s>Conveniva dunque usare <lb/>ogni arte, e fosse pure anche illecita, per mostrar ch'era a lui sovvenuto <lb/>prima che al Castelli quel cos&igrave; importante concetto, e ch'egli era stato pro&shy;<lb/>priamente il primo a metterlo in atto. </s></p><p type="main">

<s>Mentre pensa ai modi pi&ugrave; scaltri di esercitare quell'arte, gli viene <lb/>scritto allo stesso don Giuliano, il d&igrave; 11 Dicembre, di un altro particolare <lb/>da s&egrave; <emph type="italics"/>nuovamente<emph.end type="italics"/> osservato (Alb. </s>

<s>VI, 128), che &egrave; quello delle fasi di Ve&shy;<lb/>nere dichiarate in cifra per serbare il segreto geloso. </s>

<s>Cos&igrave; insomma resul&shy;<lb/>tava da questa lettera scritta a Praga all'Ambasciatore toscano, che occorse <lb/>l'osservazion del fenomeno tra il d&igrave; 13 di Novembre e l'undici del seguente <lb/>Dicembre 1610. Ma la lettera del Castelli precedeva col suo avviso questi <pb xlink:href="020/01/916.jpg" pagenum="359"/>documenti di otto giorni, ond'&egrave; che il primo partito suggerito dall'astuzia <lb/>a Galileo fu quello di soprapporre un X al 9 precedente al <emph type="italics"/>bre<emph.end type="italics"/> dell'abbre&shy;<lb/>viatura, con la quale il Castelli aveva scritto il mese di Novembre. </s>

<s>Ma l'in&shy;<lb/>chiostro, con cui la mano dello stesso Galileo tir&ograve; quell'X, essendo molto <lb/>pi&ugrave; chiaro, fa trasparir di sotto le forme distintissime del 9 scritto dal Ca&shy;<lb/>stelli con inchiostro pi&ugrave; nero, cosicch&egrave; l'Alberi, come qualunque altro che <lb/>posasse gli occhi in fondo al tergo della c. </s>

<s>164 del T. VII, P. VI de'ma&shy;<lb/>noscritti galileiani, non dubiterebbe di leggervi chiara la data originalmente <lb/>scrittavi del Novembre. </s></p><p type="main">

<s>Riguardando dunque Galileo come un fatto vero quello ch'era una sua <lb/>sottilissima frode, aspett&ograve;, per colorirla meglio, il 30 di Dicembre, giorno in <lb/>cui scrisse cos&igrave; al padre don Benedetto: &ldquo; Alla gratissima di V. S. molto <lb/>rever. <emph type="italics"/>delli 5 Dicembre<emph.end type="italics"/> dar&ograve; breve risposta.... Sappia dunque che io, circa <lb/>tre mesi fa, cominciai ad osservar Venere collo strumento e la vidi di figura <lb/>rotonda ed assai piccola; and&ograve; di giorno in giorno crescendo in mole e man&shy;<lb/>tenendo pure la medesima rotondit&agrave;, finch&egrave; finalmente, venendo in assai <lb/>gran lontananza dal Sole, cominci&ograve; a scemare della rotondit&agrave; dalla parte <lb/>orientale, ed in pochi giorni si ridusse al mezzo cerchio.... Quanto a Marte <lb/>non ardirei di affermare niente di certo, ma osservandolo da quattro mesi <lb/>in qua, parmi che in questi ultimi giorni, sendo in mole appena il terzo di <lb/>quello ch'era il Settembre passato, si mostri da oriente alquanto scemo, se <lb/>gi&agrave; l'effetto non m'inganna, il che non credo.... Oh quante e quali con&shy;<lb/>seguenze ho io dedotto, don Benedetto mio, da questa e da altre osserva&shy;<lb/>zioni! &rdquo; (Alb. </s>

<s>VI, 134, 35). </s></p><p type="main">

<s>Le lettere a don Giuliano, dalle quali manifestamente apparisce che le <lb/>fasi di Venere incominci&ograve; Galileo ad osservarle dopo il d&igrave; 11 di Novembre, <lb/>e dopo l'avviso avutone dal Castelli, tradiscono di menzogna la sopra rife&shy;<lb/>rita asserzione che, dicendo essere incominciate invece <emph type="italics"/>circa tre mesi fa,<emph.end type="italics"/><lb/>le ridurrebbe presso alla fine di Agosto. </s>

<s>Delle contestazioni di don Giuliano <lb/>per&ograve; Galileo non teme, e non ci pensa, n&egrave; teme pure di quel buon uomo <lb/>di don Benedetto, ma pensa ai posteri, appresso ai quali vuole assicurar la <lb/>sua gloria. </s>

<s>Da cos&igrave; fatti pensieri e timori fu pi&ugrave; fortemente che mai so&shy;<lb/>prappreso negli ultimi anni della sua vita, e un giorno, nella sua oscura so&shy;<lb/>litudine di Arcetri, gli torn&ograve; alla memoria quella-lettera ricevuta il d&igrave; 5 del <lb/>Novembre 1610 da Brescia, e sent&igrave; che, con averle alterata la data, non <lb/>veniva in ogni modo ad assicurarsi d'apparire al mondo il primo ed il solo. </s></p><p type="main">

<s>Lacerare quella lettera del Castelli era inutile, rimanendo essa comme&shy;<lb/>morata e viva nella risposta del di 30 Dicembre. </s>

<s>Non ci era altra via che <lb/>riformarla sostituendogliene un'altra, dalla quale apparisse che il concetto <lb/>delle fasi di Venere e delle alterazioni di figura in Marte, per trionfale con&shy;<lb/>ferma del sistema copernicano, sovvenne in mente al Castelli dietro una <lb/>finta lettera scrittagli il di 22 d'Agosto da lui stesso, che meditava questi <lb/>tradimenti, da Galileo. </s></p><p type="main">

<s>E secondo aveva il vecchio Tiranno di Arcetri meditato fra le cupe ge-<pb xlink:href="020/01/917.jpg" pagenum="360"/>losie del suo regno, mand&ograve; ad effetto. </s>

<s>Dette ad intendere al giovane Vi&shy;<lb/>viani, ospite suo, ch'essendosi smarrita la lettera del Castelli, alla quale <lb/>aveva fatto la risposta il d&igrave; 30 Dicembre 1610, voleva perci&ograve; dettargliela, <lb/>affinch&egrave; in luogo dell'originale ne rimanesse almeno la copia. </s>

<s>Lo stesso Vi&shy;<lb/>viani scrisse appunto cos&igrave; con le forme proprie di quel suo carattere cal&shy;<lb/>ligrafico giovanile: </s></p><p type="main">

<s>&ldquo; Da che io ebbi la lettera di V. S. Ecc.ma delli 22 d'Agosto, nella <lb/>quale mi accenna di avere osservato in cielo un'altra novit&agrave; inopinabile, <lb/>quel desiderio che ho sempre avuto di trasferirmi un'altra volta dove Ella <lb/>si ritrovava, per poter con il suo aiuto dare qualche gagliardo principio a <lb/>quello studio di Geometria e Filosofia, al quale, mentre dimoravo in Pa&shy;<lb/>dova, m'incit&ograve;, hora in tal guisa mi s'&egrave; accresciuto, che ho fatto ferma ri&shy;<lb/>soluzione di venire, con buona grazia de'miei Superiori, a stanziare in Fi&shy;<lb/>renze, e credo che dopo Pasqua sar&ograve; consolato. </s>

<s>Dall'istesso avviso che V. S. <lb/>mi d&agrave;, dopo varii pensieri che mi sono passati per il capo, finalmente son <lb/>cascato in questo: che essendo vera, come tengo verissima, la copernicana <lb/>costituzione del mondo, Venere abbia da fare, in pari digressioni dal Sole, <lb/>talvolta apparenza cornuta, talvolta non cornuta, secondo che si ritrover&agrave; o <lb/>di qua o di l&agrave; dal Sole, ma che ne'secoli passati sia stata impossibile simile <lb/>osservazione, per la piccolezza del globo di Venere e lo svanimento della sua <lb/>figura. </s>

<s>Or che V. S. con le sue immortali invenzioni ha osservato tante altre <lb/>maraviglie nelle cose celesti, invisibili alle forze ordinarie, desiderei sapere <lb/>se in questo particolare ha fatto osservazione alcuna, e se &egrave; vero quanto ho <lb/>sospettato. </s>

<s>Nel medesimo desiderio stanno il p. </s>

<s>d. </s>

<s>Serafino di Quinzano, e <lb/>gli signori Ferrante Lana e Francesco Albano affezionatissimi alle dottrine <lb/>di V. S. e filosofi non dozzinali. </s>

<s>Per tanto la supplico a darmene avviso, <lb/>perch&egrave;, oltre che la conclusione, sar&agrave; per s&egrave; stessa di gran conto, e noi <lb/>tutti gliene resteremo obbligatissimi: servir&agrave; parimente per convincere qual&shy;<lb/>sivoglia ostinato ingegno contro Copernico. </s>

<s>Vado sospettando ancora simile <lb/>apparenza in Marte, ma perch&egrave; a questa terminazione si ricercherebbe pi&ugrave; <lb/>esatta cognizione della remozion sua dal Sole, della quale me ne confesso <lb/>ancora ignorante, non dir&ograve; altro, solo che, ricordandomegli obbligatissimo <lb/>servitore e discepolo, li fo riverenza pregandogli da Dio benedetto ogni con&shy;<lb/>tento. </s>

<s>Li soprannominati signori li bacian le mani. </s>

<s>Di Brescia 5 di Xbre 1610. <lb/>Devotiss. </s>

<s>servo e discepolo D. </s>

<s>Benedetto Castelli. </s>

<s>&rdquo; (MSS. Gal., P. VI, <lb/>T. TII, c. </s>

<s>167), </s></p><p type="main">

<s>Questa dunque sarebbe stata la Lettera, che si voleva far comparire <lb/>nell'Epistolario galileiano, ma all'astuto vecchio di Arcetri manc&ograve; un punto <lb/>che l'ha tradito. </s>

<s>Ei non si seppe risolvere a distrugger l'autografo del Ca&shy;<lb/>stelli, il quale venuto alle mani dell'Alberi fu da lui ingenuamente pubbli&shy;<lb/>cato, invece della copia rifatta. </s>

<s>Abbiam detto ingenuamente, perch&egrave; il buon <lb/>uomo editore era mille miglia lontano dal sospettar della tresca, e fu que&shy;<lb/>sta stessa ingenuit&agrave; che non gli fece ricercar come mai dica Galileo a <lb/>pag. </s>

<s>134 del T. VI di far la risposta <emph type="italics"/>alla gratissima delli 5 Dicembre,<emph.end type="italics"/><pb xlink:href="020/01/918.jpg" pagenum="361"/>che poi a pag. </s>

<s>117 del T. VIII lo stesso Alberi pubblic&ograve; colla vera data <lb/><emph type="italics"/>delli 5 Novembre.<emph.end type="italics"/></s></p><p type="main">

<s>La dura necessit&agrave; costrinse Galileo, rispetto alle apparenze di Marte, ad <lb/>essere pi&ugrave; sincero. </s>

<s>Troppo era in verit&agrave; debole a scorgere cos&igrave; fatte sotti&shy;<lb/>gliezze quel suo strumento. </s>

<s>Quando poi il Fontana ebbe costruiti que'suoi <lb/>eccellenti canocchiali, e allora fu possibile osservare le variazioni di figura <lb/>anche in Marte, e fu giusto il Castelli, il quale vide prima di ogni altro, con <lb/>gli occhi corporei, ci&ograve; che aveva divinato gi&agrave; con la sagacia della mente. </s>

<s>Il <lb/>d&igrave; 17 Luglio 1638 cos&igrave; infatti scriveva a Galileo: &ldquo; Ho visto Marte, il quale, <lb/>ora che &egrave; intorno al quadrato del Sole, scema chiaramente dalla parte orien&shy;<lb/>tale, come una Luna di dodici o tredici giorni, e si vede chiaramente che <lb/>la parte di esso Marte occidentale &egrave; vivissima di splendore, dove che la orien&shy;<lb/>tale apparisce a poco a poco sfumata; segno manifesto che in Marte si ri&shy;<lb/>trovano sparse pi&ugrave; ombre nella detta parte orientale, che nella occidentale, <lb/>come parimente si osserva nella Luna &rdquo; (Alb. </s>

<s>X, 307). </s></p><p type="main">

<s>Galileo, avuta una tale notizia, risponde l'osservazione di Marte esser <lb/>bellissima e di gran conseguenza (Alb. </s>

<s>VII, 212) e scrivendo ad Anonimo, <lb/>nel Gennaio dell'anno dopo, cos&igrave; gli dice, studiandosi di tirare a s&egrave; quanto <lb/>fosse possibile i meriti del Castelli: &ldquo; Quanto al pianeta di Marte si &egrave; os&shy;<lb/>servato che, essendo al quadrato col Sole, ei non si vede perfettamente ro&shy;<lb/>tondo, ma alquanto sguanciato, simile alla Luna quando ha dodici o tredici <lb/>giorni: che dalla parte opposta a quella del Sole che &egrave; tocca dai raggi so&shy;<lb/>lari resta non illuminato e per conseguenza non veduto; cosa che io gi&agrave; di&shy;<lb/>cevo dovere apparire, quando Marte fusse poco superiore al Sole. </s>

<s>Ma i no&shy;<lb/>stri Telescopi, come quelli che non ingrandiscono tanto, non ci mostravano <lb/>al senso la rotondit&agrave; non perfetta di esso Marte &rdquo; (Alb. </s>

<s>VII, 227). </s></p><p type="main">

<s>Si possono raccogliere da questi fatti narrati i giusti meriti che, in con&shy;<lb/>fermare il Sistema copernicano, competono all'Autore dei <emph type="italics"/>Massimi Sistemi.<emph.end type="italics"/><lb/>Udimmo Ticone muovere un'altra difficolt&agrave; contro il Copernico, il quale <lb/>aveva asserito essere la Terra rispetto al cielo <emph type="italics"/>ut punctum ad corpus, et <lb/>finitum ad infinitum magnitudine<emph.end type="italics"/> (De Revolut. </s>

<s>cit., c. </s>

<s>4 v.) e nel V ca&shy;<lb/>pitolo appresso, dop'aver descritte le variet&agrave; di aspetto che presentano i Pia&shy;<lb/>neti &ldquo; quod autem, avea soggiunto, nihil eorum apparet in fixis, immensam <lb/>illorum arguit celsitudinem, quae faciat etiam annui motus orbem sive eius <lb/>imaginem ab oculis evanescere &rdquo; (ibi, c. </s>

<s>10). </s></p><p type="main">

<s>&ldquo; Qui si levano su, entra a dire in proposito Galileo, gli avversarii di <lb/>questa opinione, e posta quella nominata insensibilit&agrave; del Copernico come <lb/>presa da lui per cosa che realmente e assolutamente sia nulla, e soggiu&shy;<lb/>gnendo che una stella fissa, anco delle minori, &egrave; pur sensibile, poich&egrave; ella <lb/>cade sotto il senso della vista; vengono calcolando, con l'intervento di altri <lb/>falsi assunti, e concludendo bisognare in dottrina del Copernico ammettere <lb/>che una stella fissa sia maggiore assai che tutto l'Orbe magno. </s>

<s>Ora io, per <lb/>discoprir la vanit&agrave; di tutto questo progresso, mostrer&ograve; che dal porre che una <lb/>stella fissa della sesta grandezza non sia maggior del Sole, si conclude con <pb xlink:href="020/01/919.jpg" pagenum="362"/>dimostrazion verace che la distanza di esse stelle fisse da noi viene ad esser <lb/>tanta, che basta per far che in esse non apparisca notabile il movimento <lb/>annuo della Terra, e che nei Pianeti cagiona s&igrave; grandi e osservabili varia&shy;<lb/>zioni, e insieme particolarmente mostrer&ograve; la gran fallacia negli assunti degli <lb/>avversarii del Copernico &rdquo; (Alb. </s>

<s>I, 390). </s></p><p type="main">

<s>Chi prosegue oltre nella lettura, trova la dimostrazione e la conclusione <lb/>per prima cosa promessa da Galileo in queste parole, ma chi volesse con <lb/>men lungo discorso vedere pi&ugrave; sminuzzata quella stessa dimostrazione, legga <lb/>la nota autografa che qui da noi si trascrive: &ldquo; La corda di un minuto &egrave; 291; <lb/>d'un secondo &egrave; poco meno di 5. Una stella fissa della terza grandezza &egrave; 4&Prime;, <lb/>e la sua sottesa sar&agrave; 20. Il 20 in 100,000 entra 5000 volte. </s>

<s>La circonferenza <lb/>al semidiametro &egrave; come 44 a 7; la corda di un grado, che &egrave; insensibilmente <lb/>minore del suo arco, sar&agrave; contenuta nel semidiametro volte 57 prossima&shy;<lb/>mente. </s>

<s>La corda di un minuto primo entra nel semidiametro 3436 volte; <lb/>la corda di un minuto secondo entra nel semidiametro 208,454; adunque, <lb/>posto il diametro visuale del Sole 30, entrer&agrave; nella sua distanza dalla Terra <lb/>114 volte, ed il diametro intero dell'Orbe magno conterr&agrave; 228 diametri del <lb/>Sole. </s>

<s>E posto che il diametro visuale del Sole contenga 360 diametri vi&shy;<lb/>suali d'una stella della seconda grandezza (che sar&agrave; quando il diametro <lb/>visuale della stella fissa sar&agrave; cinque minuti secondi) adunque, quando si po&shy;<lb/>nesse che le stelle della seconda grandezza fossero grandi quanto il Sole, la <lb/>distanza di tali stelle dalla Terra conterrebbe 82,080 diametri del Sole o di <lb/>esse stelle.... Sar&agrave; dunque la distanza delle stelle fisse 360 diametri del&shy;<lb/>l'Orbe magno &rdquo; (MSS. Gal., P. IV, T. VI, c. </s>

<s>19). </s></p><p type="main">

<s>Le gran fallacie poi, negli assunti degli avversarii del Copernico, che <lb/>prometteva dianzi di scoprir Galileo, consistono nel non avere gli Astronomi <lb/>suoi predecessori avvertito che le stelle fisse e i pianeti s'irraggiano di crini <lb/>lucidi ascitizi in modo, da apparir cento e pi&ugrave; volte maggiori del vero esser <lb/>loro. </s>

<s>Come, anche senza il Telescopio, si possan radere d'attorno agli astri <lb/>que'crini, per determinar la pi&ugrave; giusta misura de'loro diametri apparenti, <lb/>&egrave; ci&ograve; che insegna di far Galileo, concludendo che da simili fallacie ebbero <lb/>occasione le difficolt&agrave; promosse dagli oppositori del Sistema copernicano; <lb/>difficolt&agrave; che, tolte cos&igrave; di mezzo, lasciano mirabilmente confermata la ve&shy;<lb/>rit&agrave; di quello stesso sistema. </s></p><p type="main">

<s>A voler dunque esser giusti, nell'avere scoperte queste fallacie degli <lb/>astronomi antichi consistono tutte le benemerenze che s'acquist&ograve;, verso il <lb/>Copernicanismo, l'Autore de'Massimi Sistemi. </s>

<s>All'aver poi raccolte insieme, <lb/>illustrate e con popolare eloquenza diffuse quelle dottrine; all'esser riuscito <lb/>a comparir di esse unico Maestro al mondo; all'aver saputo apparire inno&shy;<lb/>cente e ingiustamente oppresso nella sventura; v&agrave; debitore Galileo de'me&shy;<lb/>riti insigni che s'acquist&ograve; nella scienza, della gloria del suo nome, della <lb/>fama immortale di questo Dialogo copernicano. </s></p><pb xlink:href="020/01/920.jpg" pagenum="363"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Le declamazioni contro l'ignoranza degli ecclesiastici hanno da due se&shy;<lb/>coli e mezzo assordato il mondo, e poniamo che sempre abbian fatto stre&shy;<lb/>pito nel volgo, non son per&ograve; mai riuscite a persuadere i savi, i quali sanno <lb/>che fu il Copernicismo introdotto nella scienza per opera e virt&ugrave; di soli ec&shy;<lb/>clesiastici, e hanno appreso dalla storia che Galileo ricev&egrave; a larga usura di <lb/>quel che aveva dato al Castelli, al Cavalieri, al Renieri, tutt'e tre monaci e <lb/>insigni astronomi copernicani. </s>

<s>Son le nuove dottrine diffuse da Parigi per <lb/>tutta la Francia da tre zelantissimi uomini addetti agli istituti religiosi, che <lb/>si chiamano Pietro Gassendo, Ismaele Bullialdo e Marino Mersenno. </s></p><p type="main">

<s>Il Gassendo, appena ricevuti in dono i Dialoghi dei Massimi Sistemi, <lb/>risponde lieto all'Autore approvando insiem col Mersenno e congratulando <lb/>ammirato insiem col Morin, di cui particolarmente cos&igrave; gli scrive: &ldquo; Mori&shy;<lb/>nus inter caeteros librum tuum avide legit, teque suspicit ut par est; non <lb/>fatetur tamen se victum, existimatque rationes suas in manuscriptum Pro&shy;<lb/>dromum perseverare illibatas. </s>

<s>Ipse, cum multa alia in tui gratiam, edisse&shy;<lb/>rui, tum praesertim exaggeravi causam abs te redditam de geminata intra <lb/>diem naturalem maris reciprocatione et commendatione dignissimam esse, <lb/>et inconcussam persistere &rdquo; (Alb. </s>

<s>IX, 310). </s></p><p type="main">

<s>Il Bullialdo aveva scritto un'opera astronomica in quattro libri intito&shy;<lb/>lata <emph type="italics"/>Philolai seu Dissertationes de vero systemate mundi,<emph.end type="italics"/> e ch'era sotto i <lb/>torchi in Amsterdam verso la fine dell'anno 1637 (Alb. </s>

<s>X, 242). Tutt'altro <lb/>che patir molestia ebbe lode universale talmente, che torn&ograve; ad ampliare la <lb/>prima opera sua e la pubblic&ograve; in Parigi nel 1645 col titolo di <emph type="italics"/>Astronomia <lb/>philolaica.<emph.end type="italics"/> Per render poi ragione ai lettori di questo titolo, cos&igrave; scrisse <lb/>nella sua Introduzione: &ldquo; Ante quinquennium libros IV de vero systemate <lb/>mundi vulgaveram sub nomine <emph type="italics"/>Philolai,<emph.end type="italics"/> in quibus, Geometrae et Astronomi <lb/>partes agens, per principia cognoscendi Solem in medio mobilium stare, <lb/>Terram inter Martem et Venerem circa Solem ferri, ostenderam. </s>

<s>Philolai <lb/>nomen libello imposueram, quoniam, quod olim dogma Terrae mobilitatis <lb/>Philolaus pythagoricus docuerat, rationibus e Geometria, Optica et Astrono&shy;<lb/>mia petitis, confirmabam et demontrabam &rdquo; (pag. </s>

<s>7). </s></p><p type="main">

<s>Il Mersenno confer&igrave; alla diffusione del Copernicanismo, diffondendo un <lb/>libro sotto il nome di Aristarco di Samo. </s>

<s>Il nome per&ograve; dell'Astronomo an&shy;<lb/>tico non ci entrava, come quello di Filolao nell'opera del Bullialdo, ma ci <lb/>entrava come vero e proprio Autore di quello stesso libro, il manoscritto <lb/>del quale finse il Roberval di averlo avuto da Pietro Brulart, consigliere <lb/>regio, con ordine d'interpetrarlo, di annotarlo, di farne l'apologia e di darne <lb/>il giudizio. </s></p><p type="main">

<s>Il Roberval, nell'accompagnare la finta opera al Brulart, gli dice di <pb xlink:href="020/01/921.jpg" pagenum="364"/>avere eseguiti i comandamenti impostigli di curare il testo e d'illustrarlo <lb/>con note: in questo per&ograve; non l'ha ubbidito, in far cio&egrave; l'apologia, che non <lb/>bisogna, avendola fatta gi&agrave; Archimede nell'Arenario, e in dare al pubblico <lb/>il suo giudizio per le ragioni che dice appresso: &ldquo; Sensum tamdem nostrum <lb/>quaeris? </s>

<s>et an valere iussis Ptolomaeo atque Tychone, soli Aristarcho pe&shy;<lb/>nitus adhaereamus? </s>

<s>Absit: neque enim recte sentientem mathematicum de&shy;<lb/>cet opiniones sequi aut huic adhaerere, illas vero reiiciere, donec evidens <lb/>prodierit vel huius demonstratio vel illarum confutatio. </s>

<s>Sed nec illud con&shy;<lb/>stat quidem an ex tribus authorum ipsorum celeberrimorum diversi syste&shy;<lb/>matis, aliquod verum sit ac genuinum Mundi systema. </s>

<s>Forsan etiam omnia <lb/>tria falsa sunt et verum ignoratur. </s>

<s>Quidquid sit ex tribus illis praedictis <lb/>simplicissimum et naturae legibus apprime conveniens visum est systema <lb/>Aristarchi, ita ut, si non certa scientia in illud abducamur, at graviori longe <lb/>opinione in idem quam in duo reliqua propendamus. </s>

<s>Vale. </s>

<s>Parisiis pridie <lb/>non. </s>

<s>Julii an. </s>

<s>1643. Ae. </s>

<s>P. Roberval. </s>

<s>&rdquo; </s></p><p type="main">

<s>Quest'artificiosa scrittura del Matematico francese, che si voleva far <lb/>passare per originale dell'Astronomo greco, fu divulgata dal Mersenno nel <lb/>T. III delle sue <emph type="italics"/>Novarum Observationum<emph.end type="italics"/> stampate nel 1647 a Parigi, col <lb/>titolo <emph type="italics"/>Aristarchi Samii De mundi systemate.<emph.end type="italics"/> La burla fu creduta univer&shy;<lb/>salmente in Francia, e il Roberval col Mersenno e col Brulart ridevano tutti <lb/>insieme contenti, e solamente stizziti, perch&egrave; non era fra gl'Italiani voluto <lb/>entrare in quella rete il Torricelli. </s>

<s>Il Mersenno lo andava zimbellando con <lb/>sue lettere da Roma, e voleva ad ogni costo sapere ci&ograve; che nell'Aristarco <lb/>gli avesse dato disgusto, non trovandoci il Roberval nulla, che non gli sia <lb/>per ogni parte piaciuto. </s>

<s>&ldquo; Porro quum non omnia tibi satisfacerint quae <lb/>penes Aristarchum legisti, gratum facies si quod minus placens moneas, ac <lb/>aliquam tuae displicentiae rationem innuas, quum nihil in eo fuerit quod <lb/>nostro Robervallio non placuerit &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>52). </s></p><p type="main">

<s>S'aggiunse poi a far da zimbellatore anche il Carcavy, a cui, perduta <lb/>finalmente la pazienza, il Torricelli rispose: &ldquo; Sed quid est cur tantopere <lb/>petatis iudicium meum de Aristarchi libello? </s>

<s>Idem postulavit cl. </s>

<s>Mersen&shy;<lb/>nus dum esset Romae. </s>

<s>Amici mei existimant libellum plane divinum et ab <lb/>Auctore divino compositum. </s>

<s>Ego censeo libellum sub Aristarchi nomine edi&shy;<lb/>tum conscriptum fuisse nostra hac aetate. </s>

<s>Quod attinet ad doctrinam, omnia <lb/>quidem optima credo cum a doctissimis viris probentur, attamen et mihi et <lb/>quibusdam amicis quam plurima non placent, ob ingenii nostri imbecillitate. </s>

<s><lb/>Sed queso ne et rationes postuletis, quemadmodum fecit ipse cl. </s>

<s>Mersen&shy;<lb/>nus, cur ego libellum nuper conscriptum censeam, sive cur in eo multa <lb/>displiceant. </s>

<s>Ridiculum,.... circa negotium quod ad me minime attinet, <lb/>excruciari &rdquo; (ibi, T. XL, c. </s>

<s>38). </s></p><p type="main">

<s>La burla fu poi svelata, e que'francesi ebbero a maravigliarsi del sot&shy;<lb/>til fiuto del Torricelli. </s>

<s>Ma perch&egrave; il fatto &egrave; d'assai maggiore importanza <lb/>che di una semplice curiosit&agrave; letteraria, si domanda: fu veramente l'inten&shy;<lb/>zione del Roberval quella di fare agli Astronomi una burla? </s>

<s>Ma perch&egrave; al-<pb xlink:href="020/01/922.jpg" pagenum="365"/>lora usar tanto riserbo in sentenziare quale de'tre sistemi del mondo pro&shy;<lb/>posti da Aristarco, da Tolomeo e da Ticone fosse da seguitarsi per vero? </s>

<s><lb/>Perch&egrave; il Torricelli scans&ograve; d'entrare e si ritir&ograve; da quella questione come se <lb/>fosse una fiamma che lo scottasse? </s></p><p type="main">

<s>Giova, per rispondere a cos&igrave; fatte domande, considerare che i Decreti <lb/>della Chiesa romana erano a poco a poco entrati a turbar la pace e il se&shy;<lb/>reno delle coscenze. </s>

<s>Il Gassendo, dop'aver mostrato tanto fervore in difen&shy;<lb/>dere i principii di Galileo e in magnificarne la virt&ugrave; degli argomenti, nella <lb/>Epistola II, <emph type="italics"/>Dc motu impresso a motore translato,<emph.end type="italics"/> fin&igrave; per acquietarsi nella <lb/>immobilit&agrave; della Terra, dicendo che, sebben non sia questo un articolo di <lb/>fede, <emph type="italics"/>apud universam Ecclesiam promulgatum atque receptum,<emph.end type="italics"/> non po&shy;<lb/>teva nonostante un tal giudizio emanato da Lei <emph type="italics"/>apud Fideles non maximi <lb/>esse momenti<emph.end type="italics"/> (Op. </s>

<s>omn., T. III, Lugduni 1658, pag. </s>

<s>519). </s></p><p type="main">

<s>Il Mersenno poi, fra l'instabilit&agrave; della sua scienza combattuto dal dub&shy;<lb/>bio, si consol&ograve; col dire che non era l'opera del Copernico condannata come <lb/>eretica. </s>

<s>Cos&igrave; il banditore dell'Aristarco Samio s'opponeva insieme col Gas&shy;<lb/>sendo alla intolleranza di Giusto Lipsio, di Melchior Inchofer e di Giorgio <lb/>Pollacco, i quali dicevano dover tenersi la stabilit&agrave; della Terra come dot&shy;<lb/>trina di fede. </s></p><p type="main">

<s>Il Riccioli allora con duplice autorit&agrave; di Teologo e di Astronomo venne <lb/>ad assicurare le menti dal dubbio e a prescriver le giuste norme alle scru&shy;<lb/>polose coscenze. </s>

<s>Galileo, con forze impari all'arduo soggetto, come faremo <lb/>vedere a suo tempo, s'era messo a investigare le leggi della caduta de'gravi <lb/>in relazione col moto vertiginoso della Terra, e ne aveva concluso l'acce&shy;<lb/>lerazione di essi gravi essere apparente e non reale. </s>

<s>Il Riccioli si oppose <lb/>con dire ch'essendo reale l'incremento della percossa, reale doveva esser <lb/>pure l'accelerazione del corpo cadente, e cos&igrave; ritorcendo l'argomento nelle <lb/>mani stesse di Galileo veniva a concluderne, per la medesima via di lui, <lb/>l'immobilit&agrave; della Terra. </s>

<s>Quest'argomento fisico-matematico del p. </s>

<s>Riccioli <lb/>era <emph type="italics"/>ad hominem<emph.end type="italics"/> contro l'Autore de'<emph type="italics"/>Massimi Sistemi,<emph.end type="italics"/> e bench&egrave; il p. </s>

<s>Ste&shy;<lb/>fano Angeli e il Borelli rispondessero assai lunghe parole, la stessa inurba&shy;<lb/>nit&agrave; de'modi venne a mettere in sospetto la validit&agrave; delle ragioni. </s></p><p type="main">

<s>Di qui si sceverarono gli Astronomi in due ordini distinti. </s>

<s>I convertiti <lb/>dall'eloquenza di Galileo, sentendogli contrapporre un argomento che pa&shy;<lb/>reva non si potesse oppugnare, pensarono nel dubbio di seguire la parte <lb/>pi&ugrave; sicura, avendo come Teologo il Riccioli stesso insegnato che non facendo <lb/>la Sacra Congregazione de'Cardinali, di per s&egrave; senza il Pontefice, proposi&shy;<lb/>zioni <emph type="italics"/>de fide,<emph.end type="italics"/> tutti i buoni Cattolici per&ograve; erano obbligati ad assoggettarsi ai <lb/>Decreti di lei <emph type="italics"/>ex virtute tum Prudentiae tum Obedientiae.<emph.end type="italics"/> Quegli altri poi <lb/>che, nonostante gli argomenti del Riccioli, erano certi della mobilit&agrave; della <lb/>Terra, la professavano con libert&agrave; nella loro coscienza, che veniva francata <lb/>dall'imputazione di eresia, e in pubblico riducevano le virt&ugrave; della Prudenza <lb/>e dell'Obbedienza a tener d'occhio all'Inquisitore. </s></p><p type="main">

<s>Un esempio assai notabile di que'primi lo abbiamo in Giorgio Sinclaro, <pb xlink:href="020/01/923.jpg" pagenum="366"/>il quale all'argomento <emph type="italics"/>ad hominem<emph.end type="italics"/> contro Galileo, che il Riccioli avea de&shy;<lb/>sunto dagl'incrementi della percossa, ne aggiunse un altro dedotto dalle <lb/>leggi del pendolo. </s>

<s>Argomentava ch'essendo i moti del pendolo orizzontale e <lb/>del verticale una sola e medesima cosa, se gl'incrementi della velocit&agrave; del <lb/>primo giusta i seni son reali, reali pure debbon essere gl'incrementi della <lb/>velocit&agrave; del secondo giusta i numeri quadrati. </s>

<s>E qui tra Alessandro, in cui <lb/>s'impersona l'Autore, e Francesco intercede un dialogo, ch'&egrave; al presente <lb/>proposito assai importante. </s></p><p type="main">

<s>Dice Alessandro del suo argomento anticopernicano dedotto dalle leggi <lb/>del pendolo: &ldquo; Pungit nonnihil, at non vereor quin possit solvi, imo non <lb/>modo hoc, sed quodlibet, seposita S. </s>

<s>Scripturae auctoritate. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> &mdash; Quid? </s>

<s>An sententiae tam vertiginosi cerebri patrocinaris? </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> &mdash; Licet eo persuasionis nondum pervenerim, censeo tamen <lb/>Copernici atque Galilaei hypotheses de mundi fabrica viam esse expeditis&shy;<lb/>simam ad pleraque phaenomena coelestia solvenda et explicanda. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> &mdash; Sed tutum non est vel tam haereticam sententiam nomi&shy;<lb/>nare, nedum propugnare, quum aperte tam Sacris repugnet Literis, quam <lb/>Ecclesiae auctoritate. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> &mdash; Qui opinionem de Telluris motu sub mera hypothesi pro&shy;<lb/>movere studet, erroris contra fidem vel contumaciae contra Ecclesiae aucto&shy;<lb/>ritatem infirmandus non est. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> &mdash; Quam itaque ob causam tot passus est mala vir elle in&shy;<lb/>comparabilis ingenii Galilaeus de Galilaeo ab Ecclesia romana? </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> &mdash; Quod monitus a cardinali Bellarmino sacris Ecclesiae cen&shy;<lb/>soribus non paruerit. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> &mdash; At coactus est tamen sententiam suam publice eiurare. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> &mdash; Fateor: at crede mihi crassam Ecclesiae Doctorum ignoran&shy;<lb/>tiam redolevit. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Franc.<emph.end type="italics"/> &mdash; Nil mirum, quum in studia altiora multo continuo in&shy;<lb/>cumbant. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Alex.<emph.end type="italics"/> &mdash; At pudet viros doctos parum vel nihil in Astronomia sa&shy;<lb/>pere &rdquo; (Ars nova et magna, Roterodami 1669, pag. </s>

<s>581, 82). </s></p><p type="main">

<s>Son fra que'secondi, che si diceva aver preso la risoluzion dal Riccioli, <lb/>da annoverare tutti i Discepoli di Galileo, tra'quali come in tutto cos&igrave; anche <lb/>in questo primeggiano il Borelli e il Viviani. </s>

<s>La Lettera <emph type="italics"/>Del moto della <lb/>Cometa<emph.end type="italics"/> scritta sotto il finto nome di Pier Maria Mutoli, e le <emph type="italics"/>Theoricae Me&shy;<lb/>diceorum planetarum<emph.end type="italics"/> bastano a qualificare la profession copernicana del <lb/>primo: il secondo pochissimo si fece conoscere in pubblico, dal quale fu <lb/>perci&ograve; accusato di troppo meticuloso. </s></p><p type="main">

<s>Con quale intendimento incominciasse il Viviani la traduzione dell'Ari&shy;<lb/>starco Samio del Robervallio, che si legge da carte 86-97 del T. CXXXIX <lb/>de'MSS. appartenenti ai Discepoli di Galileo, non sapremmo dire precisa&shy;<lb/>mente, ma forse voleva, ad imitazion de'Francesi, diffondere anche in Ita&shy;<lb/>lia sotto quell'abito le dottrine del suo Maestro, ch'egli teneva per certis-<pb xlink:href="020/01/924.jpg" pagenum="367"/>sime, e le professava in segreto senza timor di offendere la sua propria <lb/>coscienza, per assicurar meglio la quale un giorno prende un foglio, che fu <lb/>inserito a c. </s>

<s>56 del T. IV, P. IV de'manoscritti di Galileo, e ci scrive con <lb/>carattere scolpito cos&igrave; di sua propria mano: &ldquo; In parte prima Tomi primi <lb/>Almagesti Novi Joannis Baptistae Riccioli ferrariensis, e Soc. </s>

<s>Jesu, Philoso&shy;<lb/>phiae, Theologiae et Astronomiae professoris, ad pag. </s>

<s>52 editionis bononien&shy;<lb/>sis anni 1651, Scholio II, haec leguntur: &mdash; Sacra congregatio Cardinalium, <lb/>seorsim sumpta a Summo Pontifice, non facit propositiones de fide, etiamsi <lb/>eas definiat esse de fide vel oppositas esse haereticas. </s>

<s>Quare, cum nondum <lb/>de hac re prodierit definitio Summi Pontificis aut Concilii ab eo directi vel <lb/>approbati, nondum est de fide Solem moveri et Terram stare vi Decreti pre&shy;<lb/>cise illius Congregationis, sed ad summum et solum vi Sacrae Scripturae, <lb/>apud eos quibus est evidens moraliter Deum ita revelasse. </s>

<s>Omnes tamen <lb/>catholici, ex virtute tum Prudentiae tum Obedientiae, obligantur ad tenen&shy;<lb/>dum quod illa Congregatio decrevit, et saltem ad non docendum absolute <lb/>oppositum. </s>

<s>Sed de hac subtilitate theologica egi ex professo in Tractatu <emph type="italics"/>De <lb/>fide,<emph.end type="italics"/> ubi De regulis fidei. </s>

<s>&rdquo; </s></p><p type="main">

<s>Era naturalissimo che il Viviani fosse copernicano al modo di Galileo, <lb/>e perci&ograve; dava una grande importanza all'argomento del flusso e riflusso del <lb/>mare. </s>

<s>Rimeditava un giorno sopra questa conclusione, che aveva letta nel <lb/>Discorso al cardinale Orsino: <emph type="italics"/>sicch&egrave; delle acque che saranno contenute in <lb/>ricetti di uguali lunghezze, ma di disuguali profondit&agrave;, quella che sar&agrave; <lb/>pi&ugrave; profonda far&agrave; le sue librazioni sotto tempi pi&ugrave; brevi, e men frequenti <lb/>saranno le reciprocazioni dell'acque meno profonde<emph.end type="italics"/> (Alb. </s>

<s>II, 394, 95), e <lb/>considerando che il moto ondoso avviene alla superficie, la quale in ogni <lb/>mare &egrave; sempre ad ugual distanza dal centro terrestre, cos&igrave; credette che si <lb/>potesse emendare il concetto galileiano e renderlo, per altra via e con pi&ugrave; <lb/>saldo fondamento di scienza, argomento dimostrativo del moto della Terra: <lb/>&ldquo; Cum pendentia gravia seu pendula habeant statuta tempora suarum reci&shy;<lb/>procationum pro ratione distantiae a puncto suspensionis cui innituntur, exa&shy;<lb/>minandum est num pendula, ex distantia semidiametro Terrae &aelig;quali, suas <lb/>faciant vibrationes h. </s>

<s>6 vel circiter. </s>

<s>Quod si sic esset, non incongrua erit <lb/>causa aestus maris, quam et revolutionis diurnae Telluris, et forsan habe&shy;<lb/>bitur orbium planetarum magnitudo ex ratione temporum revolutionum &rdquo; <lb/>(MSS. Gal. </s>

<s>Dis., T. CXXXV, c. </s>

<s>11). </s></p><p type="main">

<s>Questo arguto pensiero, bench&egrave; sia viziato dai falsi insegnamenti ga&shy;<lb/>lileiani, &egrave; nonostante notabile per l'applicazione che voleva farsi delle <lb/>propriet&agrave; de'pendoli oscillanti a dimostrare il moto della Terra. </s>

<s>Secondo <lb/>questo rispetto si pu&ograve; dire in certo modo che il Viviani precorresse il <lb/>Foucault, ma non come l'intesero e l'intendono tuttavia parecchi scrittori <lb/>moderni. </s></p><p type="main">

<s>Ai visitatori del R. </s>

<s>Museo di Fisica e di Storia naturale in Firenze &egrave; <lb/>richiamata particolarmente l'attenzione verso una tavola rotonda, al centro <lb/>della quale sovrasta una pesante sfera di metallo pendula da un filo, non <pb xlink:href="020/01/925.jpg" pagenum="368"/>pi&ugrave; lungo di cinque o sei metri. </s>

<s>Sta su quella medesima tavola posata una <lb/>cartella scritta, la quale cos&igrave; sommessamente parla ai curiosi, risparmiando <lb/>per un momento la voce all'erudito dimostratore: </s></p><p type="main">

<s>&ldquo; La chiara dimostrazione della rotazione della Terra, che Foucault offri <lb/>nel 1851 per mezzo dalla deviazione del pendolo dal piano di oscillazione, <lb/>fu subito in questo R. </s>

<s>Museo ripetuta e lungamente osservata, adattando <lb/>all'uopo questa Tavola, la quale aveva servito alla grande esperienza degli <lb/>Accademici del Cimento, ai quali, ne'loro molteplici studii sul pendolo, non <lb/>era neppure sfuggito il fatto dello spostamento apparente del piano di oscil&shy;<lb/>lazione, come rilevasi dalla Nota e dal disegno autografo del Viviani che qui <lb/>trascriviamo: <emph type="italics"/>Osservammo che tutti i pendoli da un filo deviano dal piano <lb/>verticale, e sempre per il medesimo verso, cio&egrave; secondo le linee AB, CD, <lb/>EF, da destra verso sinistra, nelle parti anteriori. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Sempre il mistero nell'animo degli uomini ha generato la fede, e fu <lb/>perci&ograve; la misteriosa maniera dell'apparizione di questo documento che illuse <lb/>i troppo facili a credere ai miracoli dell'ingegno. </s></p><p type="main">

<s>A carte 47 del Tomo X de'Manoscritti del Cimento il Viviani tir&ograve; gi&ugrave;, <lb/>come gli eran venute al pensiero, alcune note <emph type="italics"/>De'pendoli,<emph.end type="italics"/> e dopo aver de&shy;<lb/>scritto il fatto delle loro <emph type="italics"/>simpatie,<emph.end type="italics"/> in quel modo che si rifer&igrave; da noi nel <lb/>cap. </s>

<s>II, &sect; III dell'altro Tomo di questa Storia, cos&igrave; prosegue a dire in quel <lb/>medesimo soggetto sperimentale: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Osserveremo<emph.end type="italics"/> che tutti i pendoli da un <emph type="italics"/>sol<emph.end type="italics"/> filo deviano dal piano ver&shy;<lb/>ticale, e sempre per il medesimo verso, cio&egrave; secondo le linee AB, CD, EF, <lb/>(fig. </s>

<s>69) da destra verso sinistra, nelle parti an&shy;<lb/><figure id="id.020.01.925.1.jpg" xlink:href="020/01/925/1.jpg"/></s></p><p type="caption">

<s>Figura 69.<lb/>teriori. </s>

<s>&mdash; Ogni pendolo appeso con due fili ac&shy;<lb/>coppiati insieme devia pochissimo dal verticale, <lb/>e assai meno che con un sol filo. </s>

<s>&mdash; Date le me&shy;<lb/>desime lunghezze di pendoli, pi&ugrave; presto deviano <lb/>dal piano verticale i pi&ugrave; leggeri, che i pi&ugrave; gravi; <lb/>e dati i medesimi pesi e diverse lunghezze, pi&ugrave; <lb/>presto i pi&ugrave; corti che i pi&ugrave; lunghi. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il mistero cos&igrave; facilmente svelato rende chiaro <lb/>e manifesto a ciascuno che il moto della Terra <lb/>non entra, nemmen per sogno, in queste espe&shy;<lb/>rienze, soggetto delle quali era proprio di osservar <lb/>quel traviamento insensibile dalle prime gite, che fa il pendolo verso la fine, <lb/>e di che poi fu reso conto a pag. </s>

<s>20 de'<emph type="italics"/>Saggi di Naturali esperienze<emph.end type="italics"/> (Fi&shy;<lb/>renze 1844); traviamento di cui non vogliono ivi gli Accademici fiorentini <lb/>dir la causa, che probabilmente &egrave; dovuta alla torsione del filo. </s></p><p type="main">

<s>Ma per tornare al primo nostro proposito, ch'era quello di mostrar gli <lb/>effetti della proibizione ecclesiastica nell'esercizio della professione coperni&shy;<lb/>cana, diciamo che sulla fine del secolo XVII non avevano ancora i Peripate&shy;<lb/>tici cessato di prevalersi delle armi della coscienza, per arrestar fra i Cat&shy;<lb/>tolici que'cos&igrave; rapidi progressi, che si vedevan fare alla scienza. </s>

<s>Basti per <pb xlink:href="020/01/926.jpg" pagenum="369"/>esser brevi citar, come prova di ci&ograve;, questo, che noi scegliamo fra molti <lb/>esempi. </s></p><p type="main">

<s>Era Antonio Leeuwenhoek, nella propria casa in Leyda, tutto intento <lb/>alle naturali esperienze, quando un giorno dell'anno 1695 gli capita a visi&shy;<lb/>tarlo un Professore italiano. </s>

<s>Si lamentava questi, entrato in discorso, che <lb/>per avere scritta e pubblicata una Tesi a dimostrare il moto della Terra, <lb/>gli si fossero concitati contro gli animi de'suoi paesani, e particolarmente <lb/>di coloro, che avevano autorit&agrave; di condannarlo. </s>

<s>&ldquo; Quum vero, esclama qui <lb/>con gioia il Leeuwenhoek, nos liberiorem hauriamus in his regionibus ae&shy;<lb/>rem, ubi sententiam suam de Telluris motu libere proponere liceat, saepe <lb/>postea de Professoris eius querelis cogitavi, ac tandem in animum induxi <lb/>hasce meas theses, quibus ante aliquot annos mihi satisfacere conatus fui, <lb/>chartae mandare &rdquo; (Arcana Naturae continuatio, Lugd. </s>

<s>Batav. </s>

<s>1722, pag. </s>

<s>121). </s></p><p type="main">

<s>Il soggetto di queste tesi consisteva nel proporre una nuova esperienza <lb/>appositamente ordinata a dimostrare il moto della Terra, e lo strumento ac&shy;<lb/>comodato a ci&ograve; vien dall'Autore stesso cos&igrave; descritto: &ldquo; Conflari ego mihi <lb/>curavi sphaeras aliquot vitreas. </s>

<s>Has aqua replevi, ac tum sumsi ceram hispa&shy;<lb/>nicam rubram antea malleo frustillatim contritam. </s>

<s>Particulis his sphaerae <lb/>inditis, sumsi globulum plumbeum, cui vitri apertura erat pervia. </s>

<s>Huic glo&shy;<lb/>bulo plumbeo ante indideram foramen exiguum, transmittendo longo ac te&shy;<lb/>nui funiculo ei infixo. </s>

<s>Postea sumsi particulam suberis sphaerae aperturae <lb/>aptatam, atque in ea angustam terebravi aperturam, quam funiculus, cui <lb/>globulus plumbeus erat affixus, aegre transibat &rdquo; (ibi, pag. </s>

<s>122). </s></p><p type="main">

<s>Faceva girare velocemente questa palla di vetro, per la torsion di una <lb/>fune sostenuta all'estremit&agrave; con una mano, e osservava, attentamente guar&shy;<lb/>dando, i fatti seguenti: &ldquo; Dum sphaera illa vitrea ita in gyrum circumage&shy;<lb/>batur, globulus plumbeus lente tantummodo in orbem latus quasi in aequi&shy;<lb/>librio haerebat. </s>

<s>At cerae particulae, quae, dum vitrum quiesceret, circum <lb/>globum plumbeum iacuerant, iam, ubi sphaera ita in orbem circumfereba&shy;<lb/>tur undique sese vitro interiori applicabant, atque ita, quantum per vitri <lb/>angustiam licebat, ab globulo dilatabantur &rdquo; (ibi, pag. </s>

<s>123). </s></p><p type="main">

<s>Fatto poi arrestare il moto alla stessa palla, posandola sopra un guan&shy;<lb/>ciale di piuma &ldquo; videre licet partes cerae hispanicae admodum confuse ac <lb/>irregulariter moveri, cumque eae partes, dum sphaera in orbem ferebatur <lb/>a globulo plumbeo dilatarentur, iam e contrario eae versus globulum fere&shy;<lb/>bantur, imo usque adeo ut globulus iis partibus plane fere tegebatur &rdquo; (ibi). </s></p><p type="main">

<s>Dalla diligente osservazione di questi fatti ecco, applicandoli al caso del <lb/>moto vertiginoso della Terra, ci&ograve; che l'Autor ne conclude: &ldquo; Quemadmo&shy;<lb/>dum autem iam per vitri motum partes cerae hispanicae, quae primo glo&shy;<lb/>bulum plumbeum cingebant, ab eo separantur; ita etiam mihi persuadeo <lb/>nubes per diurnum Telluris nostrae motum sive gyrationem in aere suspen&shy;<lb/>sas retineri. </s>

<s>Ac porro, sicuti ubi vitrum quiescere incipit, partes cerae sese <lb/>circum globum plumbeum locant, atque eum tegunt, idem ut opinor futu&shy;<lb/>rum esset si Tellus quiesceret, et totum hoc Universum circum Tellurem <pb xlink:href="020/01/927.jpg" pagenum="370"/>in orbem ferretur, sic nempe omnes nubes ac partes aquae ceteraeque ma&shy;<lb/>teriae graves inter quas vivimus in aere suspensae manere non possent, sed <lb/>in Tellurem ruerent atque illic quiescerent &rdquo; (ibi, pag. </s>

<s>124). </s></p><p type="main">

<s>Racconta in principio della sua Tesi lo stesso Leeuwenhoeck com'es&shy;<lb/>sendo andato un giorno a fargli visita Cristiano Huyghens, ed essendo en&shy;<lb/>trato seco in discorso del moto della Terra, gli facesse veder quel suo globo <lb/>di vetro, e gli effetti ch'ei dimostrava, di che prese l'Huyghens tanto di&shy;<lb/>letto, che chiese ed ebbe in dono dall'Autore il bello strumento. </s></p><p type="main">

<s>Qual efficacia possa avere avuto questo stesso strumento leuvenoecchio <lb/>sui celeberrimi Teoremi ugeniani <emph type="italics"/>De vi centrifuga,<emph.end type="italics"/> siam costretti a passar&shy;<lb/>cene per la fretta, contentandoci di dire come accomodasse lo stesso Huy&shy;<lb/>ghens l'esperienza del Professore di Leyda a dimostrare secondo qual ra&shy;<lb/>gione, volgendosi la Terra in giro i corpi sulla superficie di lei sien da dir <lb/>gravi e leggeri. </s>

<s>Il documento lo abbiamo nella <emph type="italics"/>Cosmografia<emph.end type="italics"/> di Mons&ugrave; Du <lb/>Rh&ograve;, le parole del quale siamo lieti di riferirle nella traduzione, che del&shy;<lb/>l'Opera francese lasci&ograve; manoscritta il Viviani. </s></p><p type="main">

<s>Il cap. </s>

<s>XXVIII s'intitola <emph type="italics"/>Della gravit&agrave; e della leggerezza,<emph.end type="italics"/> la causa <lb/>fisica de'quali effetti della Natura &egrave; cos&igrave;, dice l'Autore, sperimentalmente <lb/>dimostrata dal signor Hugenio: &ldquo; Egli prende un vaso di maiolica di co&shy;<lb/>lor bianco, di figura tonda, che ha sette o otto pollici di diametro, del quale <lb/>il fondo &egrave; piano e gli argini alti circa tre pollici, ed empie d'acqua questo <lb/>vaso, dopo averci messo un poco di cera di Spagna in polvere, che la sua <lb/>gravit&agrave; la fa andare al fondo, ed il color rosso la rende molto visibile su <lb/>quel fondo bianco. </s>

<s>Egli lo copre con un vetro molto trasparente e lo sug&shy;<lb/>gella, acci&ograve; niente possa scappar fuori, ed attaccando questo vaso sur un <lb/>pernio o sur una macchina, che egli lo possa far girare o fermare quando <lb/>gli piace, e'lo muove in giro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Poich&egrave; questa polvere che tocca il fondo del vaso non sguizza per di <lb/>sopra s&igrave; felicemente come l'acqua, e che per questo ancora ella &egrave; pi&ugrave; fa&shy;<lb/>cilmente strascinata; da ci&ograve; avviene che essa acquista pi&ugrave; moto in giro che <lb/>non fa l'acqua, e questo l'obbliga a discostarsi dal centro in giro del quale <lb/>essa era sparsa, e ad ordinarsi per gli orli del vaso. </s>

<s>Allora facendo arre&shy;<lb/>stare in un subito il moto di quella Macchina, e per conseguenza il vaso <lb/>che ne &egrave; imperniato, la cera di Spagna che gliscia il fondo (della quale le <lb/>particelle sono scabrose) non si muove pi&ugrave; veloce dell'acqua, il moto della <lb/>quale non si rallenta tanto, a cagione della facilit&agrave; che essa ha di glisciare <lb/>sul fondo liscio del vaso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In questo tempo Egli fa vedere che l'acqua rassembra la materia <lb/>fluida che circonda la Terra, e che questa polvere di cera di Spagna ras&shy;<lb/>somiglia alle parti della Terra, ch'&egrave; solito vedersi discendere per aria, per&shy;<lb/>ch&egrave; questa polvere &egrave; sforzata di avvicinarsi al centro del suo moto, verso <lb/>il quale essa &egrave; spinta dalle parti dell'acqua, che tendono a discostarsi con <lb/>maggior forza, e quel centro s'assomiglia ad una piccola massa tonda che <lb/>assomiglia alla Terra &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLI, c. </s>

<s>114). </s></p><pb xlink:href="020/01/928.jpg" pagenum="371"/><p type="main">

<s>Cos&igrave; gli effetti delle forze centrifughe, messi in considerazione dall'Huy&shy;<lb/>ghens, predisposero l'ingegno del Newton a considerar gli effetti contrarii <lb/>delle forze centripete, e ingeritasi finalmente, per queste matematiche di&shy;<lb/>mostrazioni, la persuasione che il Verbo creato e il Verbo scritto non po&shy;<lb/>tevano contradirsi, quella libera gioia, che il Leeuwenhoek si compiaceva <lb/>esser solamente riserbata alla sua patria, si diffuse nella scienza universale. </s></p><pb xlink:href="020/01/929.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO X.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Del Sole e della Luna<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle prime osservazioni intorno alle Macchie solari fatte in Italia, e descritte da Galileo.&mdash; <lb/>II. </s>

<s>Delle controversie insorte fra lo Scheiner e Galileo: dell'essere e della natura delle Mac&shy;<lb/>chie solari.&mdash;III. </s>

<s>Delle macchie, e di varie altre apparenze nel cerchio della Luna.&mdash;IV. </s>

<s>Del <lb/>Candore lunare, e particolarmente della Lettera di Galileo sopra questo argomento.&mdash;V. </s>

<s>Del color <lb/>rosso nelle Ecclissi di Luna. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>La Matematica del Newton l'aveva dunque vinta sopra la Metafisica dei <lb/>Peripatetici, i quali da lungo tempo s'erano compiaciuti d'aver dato fatica <lb/>al Sole d'aggirarsi attorno a illuminare, e a riscaldare co'suoi raggi la loro <lb/>Terra, e avevan trionfato in veder l'immensa sfera stellata andar perpetua&shy;<lb/>mente in volta a farle ricca e splendida corona. </s>

<s>E perch&egrave; fosse sodisfatto <lb/>pi&ugrave; a pieno quel loro orgoglio, pretendevano di aver cos&igrave; fatti onorevoli ser&shy;<lb/>vigi dal cielo, incorruttibile, eterno. </s>

<s>Di qui &egrave; che venne a que'Filosofi altra <lb/>occasione a insorgere contro i progressi dell'Astronomia, quando prima l'ap&shy;<lb/>parizione di una nuova stella pareva accusar l'essere alterabile del puris&shy;<lb/>simo etere, e poi il Canocchiale spi&ograve; ch'era mista a fumi caliginosi la splen&shy;<lb/>dentissima Lampada del mondo, e ch'era anch'essa, l'eterna Margherita, <lb/>composta di vilissimo peltro. </s>

<s>Le macchie scoperte nel Sole perci&ograve; e le om&shy;<lb/>bre vedute in faccia alla Luna succedono, per ordine e per importanza, nel <lb/>soggetto di questa Storia. </s></p><p type="main">

<s>Quando Galileo annunziava pubblicamente e solennemente al mondo le <lb/>sue nuove scoperte fatte col canocchiale nel Cielo in quelle memorabili pa&shy;<lb/>gine, dove si passano in rivista la Luna, le Stelle, le Costellazioni, i Pia&shy;<lb/>neti, non fa nessun cenno del Sole. </s>

<s>La cosa dall'altra parte sembrava na-<pb xlink:href="020/01/930.jpg" pagenum="373"/>turalissima: com'era possibile infatti, senza rimanere accecato, fissare gli <lb/>occhi in quella fulgidissima sfera? </s>

<s>Ci&ograve; bastava per allora a tener lontano <lb/>il nuovo Messaggero dalle osservazioni dirette, e il poco pregio in ch'egli <lb/>aveva la camera oscura, e il professar tutt'altre teorie ottiche da quelle che <lb/>si venivano sperimentalmente a dimostrare per mezzo di essa, non gli la&shy;<lb/>sciavano a pensare che si potessero quelle osservazioni far sopra l'imma&shy;<lb/>gine ricevuta dentro una qualche candida superficie opposta ai raggi proiet&shy;<lb/>tati dal Sole. </s></p><p type="main">

<s>Ma l'adito a quel pensiero dovette venir presto aperto e fecondato da <lb/>simili altri pensieri, che nella sua Dissertazione sul Nuncio Sidereo, gli ve&shy;<lb/>niva significando il Keplero. </s>

<s>Egli, senza Canocchiale, diceva di aver pure <lb/>ossservato il Sole guardando non <emph type="italics"/>converso in coelum vultu, sed averso,<emph.end type="italics"/> e <lb/>in questo modo aver veduto Mercurio proiettar l'ombra come una macchia <lb/>nera sulla faccia stessa del Sole. </s>

<s>&ldquo; Stet igitur Galilaeus iuxta Keplerum. </s>

<s><lb/>Ille Lunam observans converso in coelum vultu, hic Solem aversus in Ta&shy;<lb/>bellam (ne oculum urat specillum) suo utroque artificio .... quin etiam prae&shy;<lb/>ter Lunam Mercurium ipsum in disco solis meo artificio vidi &rdquo; (Alb. </s>

<s>V, 416). </s></p><p type="main">

<s>Poco pi&ugrave; sotto poi dichiara il pensiero di migliorare questo nuovo me&shy;<lb/>todo di osservazione, trasformando l'apparecchio in quell'altro pi&ugrave; compiuto <lb/>strumento della Camera oscura gi&agrave; descritto dal Porta. </s>

<s>&ldquo; Ex eo subit ani&shy;<lb/>mum certare tecum in pervidendis illis minutis maculis a te primum in parte <lb/>lucidiori animadversis. </s>

<s>Id autem hoc pacto me spero perfecturum mea obser&shy;<lb/>vandi ratione vultu a Luna averso; si Lunae lumen per foramen in tabel&shy;<lb/>lam pertica circulatam intromisero, sic tamen ut foramen obvallet lens cry&shy;<lb/>stallina, sphaerico maximi circuli gibbo et tabella ad locum collectionis <lb/>radiorum accomodetur. </s>

<s>Sic in pertica 12 pedes longa, Lunae corpus per&shy;<lb/>fectissime depingetur quantitate monetae argentaee maioris. </s>

<s>Artificium de&shy;<lb/>monstravi prop. </s>

<s>XXIII, fol. </s>

<s>196 et 211 Libri mei; simplicior tamen fuit <lb/>propositum a Porta primo titulo cap. </s>

<s>VI de lente cum ego de integro globo <lb/>demonstraverim &rdquo; (ibi, pag. </s>

<s>416, 17). </s></p><p type="main">

<s>Veniva cos&igrave; suggerito a Galileo il modo di osservare il Sole, <emph type="italics"/>ne ocu&shy;<lb/>lum urat specillum,<emph.end type="italics"/> e varie testimonianze abbiamo che veramente l'osserv&ograve; <lb/>a questo modo, dopo la met&agrave; dell'Aprile 1610, quando fu data fuori questa <lb/>Dissertazione kepleriana. </s></p><p type="main">

<s>Possiamo, per prima di cos&igrave; fatte testimonianze, recar quella del Mi&shy;<lb/>canzio, il quale, dopo insorte le controversie con lo Scheiner, cos&igrave;, per giu&shy;<lb/>stificare la priorit&agrave; della scoperta e assecondare le pertinaci pretese di Ga&shy;<lb/>lileo, gli scriveva: &ldquo; Io ho memoria distintissima che, quando V. S. ebbe <lb/>fabbricato qu&agrave; (in Venezia) il primo occhiale, una delle cose che osserv&ograve; fu <lb/>le macchie del Sole, e saprei dire il luogo ed il punto, ov'ella coll'Oc&shy;<lb/>chiale, su una carta bianca, le mostr&ograve; al Padre (Paolo Sarpi) di gloriosa me&shy;<lb/>moria, e mi ricordo delli discorsi che si facevano: prima se fosse inganno <lb/>dell'Occhiale, se vapori del mezzo, e poi replicate l'esperienze si concludeva <lb/>il fatto apparir tale e doversi filosofarvi sopra &rdquo; (Alb. </s>

<s>IX, 257). </s></p><pb xlink:href="020/01/931.jpg" pagenum="374"/><p type="main">

<s>Si raccoglie dunque da un tal documento che Galileo nel 1610, in Pa&shy;<lb/>dova e in Venezia, osserv&ograve; e fece osservare le macchie <emph type="italics"/>averso vultu,<emph.end type="italics"/> se&shy;<lb/>condo il metodo kepleriano, sostituendo al foro della camera oscura il Ca&shy;<lb/>nocchiale, invece della semplice lente biconvessa, e si rileva di pi&ugrave; come <lb/>non si facesse altro in quel tempo che osservare il puro fatto, senza specu&shy;<lb/>larne o saperne ancora specular la ragione. </s></p><p type="main">

<s>Conformi a questa del Micanzio si posson dire le testimonianze, che fa <lb/>in pi&ugrave; luoghi e a diverse occasioni di s&egrave; medesimo Galileo. </s>

<s>Primo di questi <lb/>luoghi occorre a citare una lettera, scritta da Firenze il d&igrave; 23 Giugno 1612 <lb/>a don Giuliano de'Medici, nella quale cos&igrave; gli dice: &ldquo; Sappia di pi&ugrave; V. S. </s>

<s><lb/>Illustrissima come gli scoprimenti celesti non hanno ancora finito, ma sono <lb/>ancora <emph type="italics"/>quindici<emph.end type="italics"/> mesi e pi&ugrave; che cominciai a vedere nel Sole alcune macchie <lb/>oscure e pur l'anno passato, nel mese d'Aprile, essendo in Roma, le feci <lb/>vedere a diversi prelati e altri signori &rdquo; (Alb. </s>

<s>VI, 188). Cosicch&egrave; parrebbe <lb/>di qui che occorresse a Galileo il primo scoprimento di quelle macchie oscure <lb/>nel Sole verso il mese di Luglio 1610. </s></p><p type="main">

<s>Da un'altra testimonianza per&ograve; dello stesso discopritore si conclude che <lb/>l'osservazione gli occorse invece tre mesi dopo. </s>

<s>Nella prima Lettera al Vel&shy;<lb/>sero infatti dice di avere osservate le macchie <emph type="italics"/>da diciotto mesi in qua<emph.end type="italics"/><lb/>(Alb. </s>

<s>III, 382). Ond'&egrave; che avendo quella Lettera la data del d&igrave; 4 Mag&shy;<lb/>gio 1612, sarebbe stato il principio, che dette Galileo alle osservazioni so&shy;<lb/>lari, no del Luglio ma del Novembre 1610. </s></p><p type="main">

<s>Sarebbe una cos&igrave; fatta incoerenza indizio di poca sincerit&agrave;, di che Ga&shy;<lb/>lileo tanti esempi ne porge nella storia della sua vita scientifica, ma pur si <lb/>pu&ograve; dire che, trattandosi di cose passate e delle quali ancora non se ne <lb/>prevedeva l'importanza, non dovesse far maraviglia se qualche poco, in de&shy;<lb/>terminar la data precisa di quella scoperta, fallisse, in chi intendeva di ri&shy;<lb/>vendicarsela, la memoria, per cui ne'<emph type="italics"/>Massimi Sistemi,<emph.end type="italics"/> senza pretendere di <lb/>precisare il giorno n&egrave; il mese, afferma in ogni modo l'Autore che il fatto <lb/>occorse nel 1610. &ldquo; Fu il primo scopritore e osservatore delle macchie so&shy;<lb/>lari, siccome di tutte le altre novit&agrave; celesti, il nostro Accademico Linceo, e <lb/>queste scoperse egli nel 1610, trovandosi ancora alla lettura delle Matema&shy;<lb/>tiche nello studio di Padova, e quivi e in Venezia ne parl&ograve; con diversi &rdquo; <lb/>(Alb. </s>

<s>I, 375). </s></p><p type="main">

<s>Si conceda dunque a chi in ogni modo, o a ragione o a torto, voleva <lb/>in tutto essere il primo e il solo, ch'egli osservasse le macchie solari dopo <lb/>l'Aprile del 1610. Egli non presentiva per&ograve; nulla ancora dell'importanza di <lb/>quel fatto: per lui era una curiosit&agrave; non punto dissimile da quella di co&shy;<lb/>loro, i quali vedevano le macchie solari nello spettro proiettato dagli spira&shy;<lb/>gli di una finestra sul pavimento di qualche altissimo edifizio; curiosit&agrave; resa <lb/>per mezzo del canocchiale assai meglio sodisfatta, ma ch'era tanto ancora <lb/>lontana dall'aver merito e ragione di una vera scoperta astronomica. </s>

<s>Gali&shy;<lb/>leo stesso non la stim&ograve; per lungo tempo che quale una mera curiosit&agrave;, non <lb/>dandole nessuna importanza in mezzo alle altre sue scoperte celesti, fra le <pb xlink:href="020/01/932.jpg" pagenum="375"/>quali, a tante studiate occasioni, egli eloquente magnificator d'ogni cosa sua, <lb/>non annover&ograve; mai le macchie solari: e facendole egli vedere in Roma e al&shy;<lb/>trove, non si propone altro fine, che <emph type="italics"/>di sodisfar la curiosit&agrave; di que'pre&shy;<lb/>lati e di que'signori<emph.end type="italics"/> (Alb. </s>

<s>III, 183). N&egrave; poteva dall'altra parte pensare al&shy;<lb/>lora seriamente, Galileo, al Sole, essendo infaticabilmente dietro a ritrovare <lb/>i periodi de'satelliti di Giove, e a dar principio a calcolar le Tavole dei loro <lb/>moti (Alb. </s>

<s>XII, 9; VI, 57). </s></p><p type="main">

<s>Sarebbero state forse per rimanere ancora, chi sa quanto tempo, una <lb/>semplice curiosit&agrave; le macchie del Sole nella mente di Galileo, quando non <lb/>fosse provvidamente venuta a risvegliarla una lettera scritta nel d&igrave; 8 Gen&shy;<lb/>naio 1612 da Augusta. </s>

<s>Marco Velseri che la scriveva, dopo altre parole sog&shy;<lb/>giunge le seguenti: &ldquo; Veda ci&ograve; che si &egrave; arrischiato questo mio amico; e se <lb/>a Lei non riuscir&agrave; cosa totalmente nuova, come credo, spero per&ograve; che le <lb/>sar&agrave; di gusto vedendo che ancora da questa banda de'monti non manca chi <lb/>vada dietro alle sue pedate. </s>

<s>Ella faccia, in proposito di queste macchie so&shy;<lb/>lari, di dirmene liberamente il suo parere, se giudica tali materie stelle o <lb/>altro, dove crede sieno situate, e qual sia il lor moto &rdquo; (Alb. </s>

<s>III, 371). </s></p><p type="main">

<s>La Lettera veniva accompagnata da tre epistole latine <emph type="italics"/>De maculis so&shy;<lb/>laribus<emph.end type="italics"/> d'incognito Autore, <emph type="italics"/>post tabulam latentis.<emph.end type="italics"/> Incomincia la prima epi&shy;<lb/>stola col narrare in che modo occorresse all'Autore, che si d&agrave; il nome di <lb/>Apelle, di far le prime osservazioni di quelle macchie. </s>

<s>&ldquo; Phaenomena quae <lb/>circa Solem observavi petenti affero, mi Velsere, nova et pene incredibilia. </s>

<s><lb/>Ea ingentem non solum mihi sed et amicis, primum admirationem, deinde <lb/>etiam animi voluptatem pepererunt; quod eorum ope, plurima, hactenus <lb/>astronomis aut dubitata aut ignorata aut etiam fortassis pernegata, in cla&shy;<lb/>rissimam veritatis lucem, per fontem luminis et astrorum ductorem Solem, <lb/>protrahi posse plane persuasum habeamus. </s>

<s>Ante menses septem, octo cir&shy;<lb/>citer, ego, unaque mecum amicus quidam meus Tubum opticum, quo et <lb/>nunc utor, quique obiectum sexcenties aut etiam octingenties in superficie <lb/>amplificat, in Solem direximus, dimensuri illius ad Lunam magnitudinem <lb/>opticam, invenimusque utriusque fere aequalem. </s>

<s>Et cum huic rei intende&shy;<lb/>remus, notavimus quasdam in Sole nigricantes quodammodo maculas, instar <lb/>guttarum subnigrarum. </s>

<s>Quia vero tum id ex instituto non investigavimus <lb/>parvi rem istam pensitantes distulimus in aliud tempus. </s>

<s>Redivimus ergo ad <lb/>hoc negotium mense praeterito octobri, reperimusque in Sole apparentes <lb/>maculas eo modo fere quo descriptas vides &rdquo; (Alb. </s>

<s>III, 372, 73). Essendo <lb/>questa Lettera di Apelle in data del di 12 Novembre 1611, si risale dunque <lb/>al Febbraio o al Marzo di quello stesso anno a porre i principii delle nuove <lb/>spettacolose osservazioni. </s></p><p type="main">

<s>Prosegue ivi l'Autore a dire in che modo abbia potuto, senz'alcuna <lb/>offesa, tener fissi gli occhi nel Telescopio diretto al Sole: &ldquo; Primo, Sol ma&shy;<lb/>tutinus et vespertinus, vicinus horizonti, per quartam horae partem nudo <lb/>Tubo, bono tamen, apertus et serenus utcumque impune aspicitur. </s>

<s>Secundo, <lb/>Sol ubicumque opertus nebula vel nube debite perspicua, nudo Tubo, sal-<pb xlink:href="020/01/933.jpg" pagenum="376"/>vis oculis videtur. </s>

<s>Tertio, Sol ubicumque apertus per Tubum praeter con&shy;<lb/>vexum et concavum vitrum vitro insuper utrinque plano coeruleo aut viridi <lb/>debite crasso munitum, ea parte qua admovetur oculus, indennes adversus <lb/>servat oculos vel in ipso meridie, et hoc amplius, si ad ipsum coeruleum <lb/>vitrum non satis attemperatum accesserit in aere tenuis vel vapor vel nu&shy;<lb/>becula Solem veli instar subohumbrans. </s>

<s>Quarto, Solis intuitus inchoandus <lb/>a perimetro et paulatim in medium est tendendum, ibique paulisper immo&shy;<lb/>randum; lux enim circum stans umbras non statim admittit &rdquo; (ibi, pag. </s>

<s>375). </s></p><p type="main">

<s>Nella terza Lettera passa l'Autore a dir la sua propria opinione intorno <lb/>all'essere e alla natura di queste Macchie: &ldquo; Sed quid eae tandem sunt? </s>

<s><lb/>Non nubes .... sed neque Cometae.... Reliquum ergo ut sint vel partes <lb/>alicuius Coeli densiores, et sic erunt, secumdum Philosophos, stellae, aut <lb/>sint corpora per se existentia solida et opaca, et hoc ipso erunt stellae non <lb/>minus atque Luna et Venus, quae ex aversa a Sole parte nigrae apparent &rdquo; <lb/>(ibi, pag. </s>

<s>378). </s></p><p type="main">

<s>Entriamo ora addentro a scrutare da quali sentimenti dovess'esser com&shy;<lb/>mosso alla lettura di queste Epistole l'animo di Galileo. </s>

<s>Non nuovo il fatto <lb/>dell'osservazione, prima di tutto, n&egrave; nuovo dovette apparirgli il modo. </s>

<s>Egli <lb/>non s'era attentato ancora mai di fissar gli occhi direttamente nel Sole, ma <lb/>quasi due mesi prima che il Gualdo gli scrivesse esser venuto al Pignoria <lb/>avviso che c'erano in Germania alcuni, che <emph type="italics"/>cominciavano a mirare anco <lb/>nel Sole<emph.end type="italics"/> (Alb. </s>

<s>VIII, 178), il Cigoli, sotto il d&igrave; 16 Settembre di quell'anno 1611, <lb/>gli aveva scritto cos&igrave; da Roma: &ldquo; Volevo scriverli, sino per la passata, come <lb/>il Passignano, avendo avuto da un amico suo in Venezia un Occhiale simile <lb/>a quello di V. S., con il quale dice aver osservato gi&agrave; molte volte il Sole <lb/>la mattina, al mezzogiorno e la sera, e il figliolo e il genero dice che la vista <lb/>non li resiste, n&egrave; io mi sono ardito, oltre al non avere avuto occasione n&egrave; <lb/>tempo, di tentare se la vista mi resiste, dove dice il Passignano che guarda <lb/>e leva l'occhio e per un pezzetto non vede, ma poi tornando vede benis&shy;<lb/>simo e con molta comodit&agrave; &rdquo; (MSS. Gal., P. VI, T. VIII, c. </s>

<s>41). La stessa <lb/>cosa ripete il Cigoli in un altra del d&igrave; 23 di quel mese di Settembre pub&shy;<lb/>blicata da pag. </s>

<s>169-71 nel T. VIII dall'Alb&egrave;ri. </s></p><p type="main">

<s>Nuova non doveva pure tornare a Galileo l'invenzione del vetro colo&shy;<lb/>rato, imperocch&egrave; il Passignano, pochi giorni prima che avesse lo stesso Ga&shy;<lb/>lileo ricevuta la lettera del Velsero con le tre Epistole di Apelle, cosi gli <lb/>mandava a dire da Roma: &ldquo; Credo che il signor Lodovico (Cigoli) li aver&agrave; <lb/>scritto come con un mio Occhiale ho fatto alcune osservazioni di nubi nel <lb/>Sole, delle quali in questa ne mando copia a V. S., dove la vedr&agrave; il giorno e <lb/>l'ora che si sono viste. </s>

<s>Ora io li ho mostri alli Padri Grembergero e Mal&shy;<lb/>colfo, li quali dicono che si vedono e mi hanno detto come posso soffrire la <lb/>vista del Sole? </s>

<s>Li ho detto che avanti il vetro piccolo ci metto un vetro <lb/>oscuro, che modifica il calore del Sole &rdquo; (MSS. Gal., P. VI, T. VIII, c. </s>

<s>75). </s></p><p type="main">

<s>Forse nuova sar&agrave; riuscita a Galileo la osservazione di Apelle delle mac&shy;<lb/>chie vedute andare pi&ugrave; celeri nel mezzo, che verso i lembi della sfera so-<pb xlink:href="020/01/934.jpg" pagenum="377"/>lare, d'onde ne argomentava un moto di circolazione di esse macchie o del <lb/>Globo centrale. </s>

<s>&Egrave; certo in ogni modo che a'quesiti proposti dal Velsero, <lb/>l'Autor del Nunzio Sidereo non ci aveva punto pensato, e ne dovette rima&shy;<lb/>nere sorpreso. </s>

<s>Confessare ingenuamente il fatto non era della sua indole, e <lb/>perci&ograve;, sollecito di cogliere la prima occasione che gli si porgesse, al Di&shy;<lb/>scorso che aveva allora fra mano intorno alle cose che stanno in sull'acqua, <lb/>appiccica, ripetendo le varie opinioni di Apelle e approvando indifferente&shy;<lb/>mente le une e le altre, queste parole: &ldquo; Aggiungo a queste cose, egli dice, <lb/>l'osservazione di alcune macchiette oscure che si scorgono nel corpo solare, <lb/>le quali mutando positura in quello porgono grande argomento o che il Sole <lb/>si rivolga in s&egrave; stesso, o che forse altre stelle, nella guisa di Venere e di <lb/>Mercurio, se gli volgano intorno invisibili in altri tempi, per le piccole di&shy;<lb/>gressioni, minori di quelle di Mercurio, e solo visibili, quando s'interpon&shy;<lb/>gono tra il Sole e l'occhio nostro, oppur danno segno che sia vero e que&shy;<lb/>sto e quello &rdquo; (Alb. </s>

<s>XII, 11). </s></p><p type="main">

<s>Una tale aggiunta dev'essere stata fatta dall'Autore dopo ch'egli ebbe <lb/>ricevuta la Lettera del Velsero, e prima del di 17 Febbraio, per le ragioni <lb/>che si vedranno, quando il Manoscritto gi&agrave; consegnato alla Revisione, non <lb/>dava luogo e tempo da riporvi sopra la mano. </s></p><p type="main">

<s>Intanto il d&igrave; 4 Maggio 1612 usc&igrave; in pubblico la prima Lettera Solare, <lb/>in risposta alla scritta, non tre mesi, come dice in principio l'Autore, ma <lb/>quattro mesi prima, dal Velsero, se si deve stare alla data. </s>

<s>In questa Let&shy;<lb/>tera Galileo professa circa alla costituzion delle macchie, idee in tutto di&shy;<lb/>verse da quelle gi&agrave; significate nel Discorso delle Galleggianti pubblicato nel <lb/>precedente mese di Marzo. </s>

<s>Mentre infatti qui, nel Discorso, ammette che le <lb/>macchie possano anch'essere stelle, l&agrave;, nella Lettera, dimostra come cosa <lb/>certa non aver nulla che alle stelle, veramente e propriamente dette, le ras&shy;<lb/>somigli. </s>

<s>Ma se a qualche cosa pure si volessero rassomigliare, dice che sa&shy;<lb/>rebbero le nuvole, le quali adombrano la superficie della nostra Terra. </s></p><p type="main">

<s>Nella seconda di queste Lettere velseriane, che porta la data del d&igrave; <lb/>11 Agosto 1612, si diffonde pi&ugrave; lungamente Galileo a descrivere i fenomeni <lb/>osservati nelle macchie, dalle quali osservazioni &egrave; condotto a congetturar <lb/>l'esistenza di una sfera vaporosa circondante e menata in volta dal Sole, <lb/>che rapidamente convertesi intorno al suo proprio asse. </s></p><p type="main">

<s>Nella sopra citata Lettera a Giuliano de'Medici sono cos&igrave;, con brevit&agrave; <lb/>da preferirsi alla loquacit&agrave; delle Lettere velseriane, descritte quelle appa&shy;<lb/>renze: &ldquo; Tali macchie sono non pur vicine al Sole, ma contigue alla su&shy;<lb/>perficie di quello, dove continuamente altre se ne producono e altre se ne <lb/>dissolvono, essendo altre di breve e altre di lunga durazione: cio&egrave; alcune <lb/>si disfanno in due, tre o quattro giorni, e altre duran quindici, venti, trenta <lb/>e ancor pi&ugrave;. </s>

<s>Vannosi mutando di figura, le quali figure sono per lo pi&ugrave; irre&shy;<lb/>golarissime, si condensano e si distraggono, sendo talora alcune oscurissime, <lb/>e altre non cos&igrave; negre; spesso una si divide in tre o quattro ed altre volte <lb/>due o tre o pi&ugrave; si aggregano in una sola. </s>

<s>Hanno poi un movimento rego-<pb xlink:href="020/01/935.jpg" pagenum="378"/>lato, secondo il quale uniformemente vengono tutte portate in giro dall'istesso <lb/>corpo solare, il quale si muove in s&egrave; stesso in un mese lunare in circa &rdquo; <lb/>(Alb. </s>

<s>VI, 189). </s></p><p type="main">

<s>Come poi le non possano essere stelle, Galileo lo dim&ograve;stra nella III Vel&shy;<lb/>seriana con matematici argomenti e con fisiche ragioni. </s>

<s>Pu&ograve; chi vuole leg&shy;<lb/>ger quegli argomenti nel Tomo III dell'Alb&egrave;ri, ma quanto alle ragioni fisi&shy;<lb/>che concluse nelle parole che leggonsi a pag. </s>

<s>499, 500, invece delle stampate, <lb/>le trascriveremo ai nostri Lettori quali uscirono di primo getto dalla penna <lb/>stessa di Galileo, meno ordinate s&igrave;, ma pi&ugrave; concise e pi&ugrave; efficaci: </s></p><p type="main">

<s>&ldquo; Io poi metto tanta poca difficolt&agrave; sopra i nomi, anzi pur so che &egrave; in <lb/>arbitrio di ciascheduno d'imporgli a modo loro, che non farei caso a chia&shy;<lb/>marle stelle, e massime chiamandosi con tal nome anco le Comete, li due <lb/>fulgori del 1572 e del 1604, l'esalazioni cadenti e discorrenti per l'aria, ed <lb/>essendo infin conceduto agli amanti e a'poeti chiamare stelle gli occhi delle <lb/>loro donne: <emph type="italics"/>Quando si vidde il successor d'Astolfo sopra apparir quelle <lb/>ridenti stelle.<emph.end type="italics"/> E di pi&ugrave; dire, di un alterato dal vino o stordito da una per&shy;<lb/>cossa, <emph type="italics"/>Vidde mirando in terra alcuna stella. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ma saranno queste stelle solari differenti dalle altre in alcune con&shy;<lb/>dizioni, pur di qualche considerazione, attesoch&egrave; quelle ci si mostrano sem&shy;<lb/>pre di una sola figura, e quella &egrave; la regolarissima fra tutte, e queste d'infiniti <lb/>ed irregolarissimi tratti. </s>

<s>Quelle consistenti n&egrave; mai mutatesi di grandezza e <lb/>di forma, e queste instabili sempre e mutabili. </s>

<s>Quelle l'istesse sempre e di <lb/>permanenza, che supera la memoria di tutti i secoli decorsi, queste gene&shy;<lb/>rabili e dissolubili dall'uno all'altro giorno. </s>

<s>Quelle non mai visibili se non <lb/>piene di luce, queste oscure sempre, e splendide non mai. </s>

<s>Quelle mobili <lb/>ognuna per s&egrave; di moti proprii e regolari e tra di loro differentissimi, que&shy;<lb/>ste mobili di un moto solo comune a tutte, regolare solo in universale, ma <lb/>da infinite particolari disagguaglianze alterato. </s>

<s>Quelle costituite tutte in par&shy;<lb/>ticolari e diverse lontananze dal Sole, e queste tutte contigue e insensibil&shy;<lb/>mente remote dalla sua superficie. </s>

<s>Quelle non mai visibili, se non quando <lb/>sono separate dal Sole, queste non mai vedute se non congiuntegli. </s>

<s>Quelle <lb/>di materia probabilissimamente densa ed opacissima, queste, a guisa di neb&shy;<lb/>bia o fumo, rare. </s>

<s>E chi sar&agrave; quello che le vogli stimar cosa, con la quale <lb/>non hanno pur una minima particolar convenienza, che non l'abbiano con <lb/>cent'altre cose, pi&ugrave; presto che cosa con la quale in ogni particolare con&shy;<lb/>vengono? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io le ho agguagliate alle nostre nuvole o ai fumi, e certo chi le vo&shy;<lb/>lesse con alcuna delle nostre materie imitare, non credo che si trovasse pi&ugrave; <lb/>aggiustata imitazione che lo spruzzare sopra un ferro rovente, in piccole <lb/>stille, qualche bitume di difficile combustione, il quale sul ferro imprime&shy;<lb/>rebbe una macchia negra, dalla quale, come da sua radice, si eleverebbe un <lb/>fumo oscuro, che in figure stravaganti e mutabili si andrebbe spargendo. </s>

<s>&rdquo; <lb/>&hellip; </s></p><p type="main">

<s>&ldquo; Se le fossero stelle, o congerie o drappelli di stelle, che per l'ine-<pb xlink:href="020/01/936.jpg" pagenum="379"/>gualit&agrave; dei lor movimenti si accozzassero insieme, come tali accozzamenti si <lb/>farebbero sempre numerosissimi, e massimi solamente verso il mezzo del <lb/>Sole, ed i medesimi verso la circonferenza sempre si andrebbero dimi&shy;<lb/>nuendo? </s>

<s>e com'essendo alcuna macchia talvolta ben cinquanta volte mag&shy;<lb/>giore in superficie di Venere, non si fa veder luminosa fuori del disco so&shy;<lb/>lare? </s>

<s>&rdquo; (MSS. Gal., P. III, T. X, c. </s>

<s>74). </s></p><p type="main">

<s>In pochi mesi insomma, ripigliando il filo del nostro discorso, Galileo <lb/>aveva fatto, nello studio delle macchie solari, grandissimi progressi. </s>

<s>Il prin&shy;<lb/>cipio dell'anno 1612 lo aveva trovato nuovo di quello studio: nel Giugno <lb/>&egrave; gi&agrave; penetrato addentro ai pi&ugrave; reconditi misteri della fisica costituzione del <lb/>Sole. </s>

<s>Ne ha minutamente osservate e diligentemente descritte le fasi della <lb/>sua superficie, e ha misurato con sufficiente precisione il periodo della con&shy;<lb/>versione in s&egrave; stesso. </s></p><p type="main">

<s>Per giunger per&ograve; con tanta sicurezza a conclusioni cos&igrave; importanti, con&shy;<lb/>veniva aver fatto qualche osservazione diretta sulla faccia del Sole, perch&egrave; <lb/>il metodo delle proiezioni, se non era troppo bene accomodato a rappresen&shy;<lb/>tar con evidenza il fenomeno, tanto era meno sufficiente a ricavar con pre&shy;<lb/>cisione la verit&agrave; di que'si svariati accidenti. </s>

<s>Galileo, il quale, come sappiamo, <lb/>non ammetteva nel Canocchiale l'inversione de'raggi, non si sarebbe facil&shy;<lb/>mente per s&egrave; medesimo accorto nemmen che i punti proiettati dalla parte <lb/>orientale sopra la carta rispondevano alla parte occidentale della sfera so&shy;<lb/>lare; per cui si pu&ograve; comprendere quanto dovess'essere, per sua propria <lb/>scienza ed arte, atto a ritrovare, con quella precisione con cui lo ritrov&ograve; e <lb/>cos&igrave; presto, il periodo della rivoluzione del Sole intorno al suo proprio asse. </s>

<s><lb/>Di qual dunque altra scienza ed arte si giov&ograve; Galileo per risolvere i nuovi <lb/>problemi di Astronomia solare? </s>

<s>E risponderanno alla domanda le seguenti <lb/>notizie. </s></p><p type="main">

<s>Mentre in Roma, nell'Aprile del 1611, faceva esso Galileo, per curio&shy;<lb/>sit&agrave; spettacolosa, osservar le macchie del Sole, fra'curiosi concorsi vi furon <lb/>due celebri artisti venuti di Toscana, Lodovico Cigoli e Domenico Passi&shy;<lb/>gnani. </s>

<s>Gi&agrave; vedemmo come fosse questo Passignani uno de'primi fra noi, <lb/>che senza nulla ancora saper di ci&ograve; che s'era incominciato a fare in Ger&shy;<lb/>mania, osasse di fissare il Sole col Canocchiale scoperto, e poi v'applicasse <lb/>i vetri neri. </s>

<s>Per qualche tempo non si cur&ograve; che delle semplici osservazioni, <lb/>ritraendo in disegno la faccia del Sole, quasi come un nuovo esercizio del&shy;<lb/>l'arte sua, ma venuto a notizia delle Epistole di Aprile, che il Velsero avea <lb/>diffuse in Italia, dall'ufficio di pittore arditamente passando a quello di astro&shy;<lb/>nomo, incominci&ograve; a filosofare intorno alla natura di quelle macchie, e as&shy;<lb/>ser&igrave;, contro l'opinion dello stesso Apelle, che le non erano ombre proiet&shy;<lb/>tate da corpi opachi stellari, che s'aggirassero separati dal Sole, ma che <lb/>ell'erano dentro lo stesso Sole, come oscure voragini approfondatesi nella <lb/>sostanza di lui. </s>

<s>Questa sua opinione, tanto nuova e tanto contraria alle idee <lb/>comunemente invalse della incorruttibile integrit&agrave; del Sole, il Passignani la <lb/>significava cos&igrave; a Galileo, per lettera scritta il d&igrave; 17 Febbraio 1612: </s></p><pb xlink:href="020/01/937.jpg" pagenum="380"/><p type="main">

<s>&ldquo; Avendo visto un Discorso venuto d'Alemagna sopra le macchie, che <lb/>si vedono nel Sole, ed ancora una dimostrazione di alcune osservazioni, ed <lb/>avendone parlato con il p. </s>

<s>Griembergero, il quale &egrave; dell'istesso parere di <lb/>questo che scrive, che &egrave; questo: Dice che le macchie che si vede sieno <lb/>stelle, come quelle che si vedono attorno a Giove. </s>

<s>Io sono di contraria opi&shy;<lb/>nione, perch&egrave;, avendone fatto per cinque mesi osservazione, non ho potuto <lb/>comprendere che sieno fuori del corpo del Sole, perch&egrave; in detto tempo non <lb/>&egrave; possibile che non avessi visto qualcheduna, che non occupassi il dintorno <lb/>del Sole, siccome farebbe se le fossero fuori del corpo del Sole. </s>

<s>Ma non ne <lb/>ho mai viste vicine a detto dintorno, anzi cominciano un poco lontano, e si <lb/>vedono poco, e di mano in mano, quando si avvicinano al mezzo, si vedono <lb/>pi&ugrave;, ed ancora ne ho viste da un giorno all'altro venire appresso al mezzo <lb/>in un tratto, e poi fare il suo corso in pi&ugrave; giorni e svanire, ed ancora ne <lb/>ho viste che, quando sono a mezzo venute, in pochi giorni svanire e non <lb/>si vedere pi&ugrave;, e con queste dimostrazioni non so capire che le sieno stac&shy;<lb/>cate dal Sole. </s>

<s>Se quando in un tratto le si vedono appresso il mezzo e poi <lb/>fare il corso in pi&ugrave; giorni, gi&agrave; avverrebbe che in un tratto venissero e <lb/>poi mutassero corso e se ne andassero adagio, e per contrario ne ho viste <lb/>venire adagio e poi, quando sono vicine al mezzo, sparire. </s>

<s>Di qui avverrebbe <lb/>che avessero corso veloce ed adagio e non seguente, la qual cosa io non <lb/>credo che possa stare, che tengo che tutti i corpi celesti abbino il loro corso <lb/>seguente e che non si muti. </s>

<s>Io tengo che sieno dentro il corpo del Sole, <lb/>non solo in superficie, ma che s'incentrino dentro, e venghino in superfi&shy;<lb/>cie, ed al Rev. </s>

<s>Griembergero ho detto quello che ho veduto, che ha detto <lb/>che si &egrave; risoluto di far le osservazioni, che trover&agrave; tutte queste cose che ho <lb/>detto, e cos&igrave; da lei vorrei sapere se, nelle osservazioni che ha fatte, la ci <lb/>ha trovato queste cose che dico: la mi far&agrave; grazia di dirmi in questo quello <lb/>la ne pensa &rdquo; (MSS. Gal., P. VI, T. VIII, c. </s>

<s>88). </s></p><p type="main">

<s>Galileo per&ograve; non rispose, ci&ograve; che il Passignano se l'ebbe molto a male, <lb/>e <emph type="italics"/>and&ograve; in valigia,<emph.end type="italics"/> come il Cigoli fiorentinescamente si esprime (ivi, c. </s>

<s>128). <lb/>Ma se non rispose colle parole, rispose coi fatti, approvando cos&igrave; l'opinione <lb/>del Passignano da farla sua, e riprovando quell'altra di Apelle che aveva <lb/>dianzi pubblicamente approvata. </s>

<s>E perch&egrave; non rimanesse di ci&ograve; la memo&shy;<lb/>ria, sempre fermo in un proposito di non confessar mai di avere errato, fa <lb/>ristampare il Discorso delle Galleggianti, per l'unico fine di sostituire alle <lb/>parole scritte: <emph type="italics"/>essere argomento le macchie o che il Sole si rivolga in s&egrave; <lb/>stesso, o che forse altre stelle nella guisa di Venere e di Mercurio se gli <lb/>volgano intorno,<emph.end type="italics"/> il periodo seguente: &ldquo; Hannomi finalmente le continuate <lb/>osservazioni accertato tali macchie esser materie contigue alla superficie del <lb/>corpo solare, e quivi continuamente prodursene molte e poi dissolversi: <lb/>altre in pi&ugrave; brevi, altre in pi&ugrave; lunghi tempi, ed esser dalla conversione del <lb/>Sole in s&egrave; stesso, che in un mese lunare in circa finisce il suo periodo, <lb/>portate in giro: accidente per s&egrave; grandissimo e maggiore per le sue con&shy;<lb/>guenze &rdquo; (Firenze, Giunti, 1612, pag. </s>

<s>2, 3). </s></p><pb xlink:href="020/01/938.jpg" pagenum="381"/><p type="main">

<s>La definizione di questo periodo richiedeva osservazioni diligenti, le <lb/>quali dubitiamo se potessero esser fatte da Galileo, tutto intento allora ai <lb/>satelliti gioviali. </s>

<s>Ci dee probabilmente avere avuto gran parte il Castelli, a <lb/>cui l'Autore della II Lettera velseriana non par voglia dare altro merito <lb/>che di avere insegnato il modo di descriver le macchie per proiezione <lb/>(Alb. </s>

<s>III, 419); merito che si doveva piuttosto attribuire al Keplero, il quale <lb/>aveva qualche tempo prima insegnato nella proposizione XXIII dell'Ottica <lb/>e nella CV della Diottrica &ldquo; Visibilia lente cava et convexa pingere super <lb/>papyro maiori quantitate, quam per solam convexam, sed eversa &rdquo; (Augustae <lb/>Vindelic. </s>

<s>1611, pag. </s>

<s>54). </s></p><p type="main">

<s>&Egrave; poi notabile che potesse il Castelli persuadere a Galileo questa ever&shy;<lb/>sione, la quale doveva stare nella mente di lui a dispetto e fare ai cozzi con <lb/>le altre opinioni a cui non volle mai rinunziare, bench&egrave; il Castelli non solo, <lb/>ma l'Antonini, il Sagredo e altri di pi&ugrave; sano giudizio, facessero notare allo <lb/>stesso loro riverito maestro, la irragionevole, e anzi mostruosa incongruenza. </s></p><p type="main">

<s>L'Antonini, che aveva ricevute in Bruxelles le due prime Lettere vel&shy;<lb/>seriane, maravigliato della scoperta e delle osservazioni delle macchie, a lui <lb/>giunte come cosa nuova, scriveva a Galileo ne'termini seguenti: &ldquo; In quanto <lb/>alla speculazione, che V. S. mi d&agrave; della figura, che sopra la carta s'inverte <lb/>e non sopra l'occhio, a me non pare che perci&ograve; ne segua che siano diversi <lb/>que'raggi, che apportan le immagini, da quelli co'quali si fa la vista, e <lb/>prima io nego che quelle immagini, che s'invertono sopra la carta, non <lb/>s'invertano ancora sopra l'occhio &rdquo; (MSS. Gal., P. VI, T. VII, c. </s>

<s>132). </s></p><p type="main">

<s>Similmente il Sagredo, quasi in quegli stessi giorni in che tali parole <lb/>scriveva l'Antonini, cio&egrave; nel d&igrave; 7 Luglio 1612, con filosofica libert&agrave; si op&shy;<lb/>poneva cos&igrave; alle false opinioni di Galileo: &ldquo; Circa a quello che mi scrive <lb/>della inversione delle macchie del Sole, che si vedono nella carta, io non <lb/>metto dubbio che l'istesso non occorra nell'occhio, il quale, per essere avvezzo <lb/>ad apprendere tutte le spezie a rovescio, le guarda diritte &rdquo; (Alb. </s>

<s>XVI, 59). </s></p><p type="main">

<s>Dalle quali notabilissime incongruenze delle dottrine galileiane, e dalle <lb/>altre cose fin qui discorse, ritornando indietro per concludere quel nostro <lb/>ragionamento, non sar&agrave; difficile persuadersi che la Filosofia e la Matematica <lb/>delle Macchie solari, sottentrate in cos&igrave; breve tempo ai primi errori, e cos&igrave; <lb/>largamente trasfuse nelle Lettere velseriane; le attinse, senza troppa fatica, <lb/>Galileo dalle osservazioni del Passignano principalmente, e dalle speculazioni <lb/>del Castelli. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Chi legge attentamente queste Lettere velseriane, fonti di scienza astro&shy;<lb/>nomica e d'italiana eloquenza, ci sente dentro un'amarezza, e anzi un odio <lb/>cupo contro Apelle, quasi fossero quelle sue Epistole una usurpazione della <pb xlink:href="020/01/939.jpg" pagenum="382"/>prima scoperta. </s>

<s>A rispondere alle accuse Cristoforo Scheiner, che tale &egrave; il <lb/>nome vero del finto Apelle, scrisse un libraccione in folio di 784 pagine a <lb/>due colonne, col titolo di <emph type="italics"/>Rosa Ursina,<emph.end type="italics"/> perch&egrave; dedicato a Paolo Gior&shy;<lb/>dano II Orsino, duca di Bracciano, nella qual citt&agrave; il libro, nel 1630, venne <lb/>alla luce. </s>

<s>Tutto, in quel libro, incominciando dal frontespizio, spira antipa&shy;<lb/>tia, ma se si pu&ograve; con ragione ridere dell'impresa delle tre Orse nella ca&shy;<lb/>verna, a noi per verit&agrave; non sembra n&egrave; ragionevole n&egrave; onesto il trattar che <lb/>fa Galileo l'Autore di <emph type="italics"/>porco,<emph.end type="italics"/> e di <emph type="italics"/>maligno asinaccio<emph.end type="italics"/> (Alb. </s>

<s>VII, 59). Vero <lb/>&egrave; che vomitava questi titoli in una lettera familiare al Micanzio, ma pure <lb/>anche in fine al Discorso astronomico Delle montuosit&agrave; della Luna a don <lb/>Giacomo Muti, non lascia di appioppare allo Scheiner i titoli di arrogante, <lb/>d'ignorantissimo, d'insensato (Alb. </s>

<s>III, 182, 83). </s></p><p type="main">

<s>L'Autore della <emph type="italics"/>Rosa Urbina<emph.end type="italics"/> non esce mai cos&igrave; fuori de'termini della <lb/>civilt&agrave;, come il velenoso carcerato di Arcetri. </s>

<s>Ma a che tant'ira eruttata <lb/>in parole cos&igrave; ingiuriose e plebee? </s>

<s>Non perch&egrave; l'odiato rivale gli avesse <lb/>usurpata la teorica delle macchie, o si fosse appropriato il ritrovamento del <lb/>loro periodo, cose anzi che lo Scheiner generosamente concede a Galileo, e <lb/>con le quali riduce a consentire la prima sua dissenziente opinione, ma <lb/>tutta la fiera contesa versava intorno al primato della osservazione semplice <lb/>e materiale, che Galileo, senza pro e senza diritto, voleva ad ogni costo ri&shy;<lb/>vendicare a s&egrave; stesso. </s></p><p type="main">

<s>Diciamo senza pro, perch&egrave; il merito doveva essere propriamente di colui <lb/>che osserv&ograve; prima le Macchie proiettale attraverso a qualche alto spiraglio <lb/>sul pavimento di un tempio, merito che poteva essere offerto a qualunque <lb/>pi&ugrave; volgare e curioso osservatore o dalla fortuna o dal caso. </s>

<s>Senza diritto, <lb/>perch&egrave; se la prima Lettera di Apelle ha la data del d&igrave; 12 Novembre 1611, <lb/>e il Discorso delle Galleggianti ha la data del d&igrave; 3 Marzo 1612, e la Storia <lb/>non giudica se non da ci&ograve; che &egrave; pubblicamente noto, lo Scheiner preced&egrave; <lb/>Galileo nell'annunziare al mondo la sua scoperta di quasi quattro mesi. </s>

<s>Che <lb/>se lo stesso Galileo, avendo gi&agrave; fatta quella medesima scoperta nel 1610, <lb/>com'ei pretese di dimostrare, non la fece pubblicamente nota, sua colpa, <lb/>ci&ograve; non potendo essere che o per negligenza o perch&egrave; egli non dava al fe&shy;<lb/>nomeno nessuna scientifica importanza. </s>

<s>Noi affermammo che dovett'essere <lb/>per questa ultima ragione, e mentre il Nostro si rimase cos&igrave; indifferente, e <lb/>non riguard&ograve; il fatto se non come una nuova curiosit&agrave; spettacolosa, il Ge&shy;<lb/>suita tedesco se ne sent&igrave; talmente commosso da levare a romore tutta l'Ale&shy;<lb/>magna, nella quale s'incominci&ograve; a riguardar da molti nel Sole, e s'inger&igrave; <lb/>nell'animo del Velsero e di altri Filosofi di l&agrave; dai monti il desiderio di sa&shy;<lb/>per l'origine di que'nuovi misteri. </s></p><p type="main">

<s>Quel fervore di osservazioni e di studi ebbe senza dubbio origine dal <lb/>Nunzio Sidereo di Galileo, dentro il quale rileggendo ammirati, e trovan&shy;<lb/>dovi, contro ci&ograve; che si sarebbero aspettato o che paresse a lor conveniente, <lb/>dimenticato il Sole, si sentiron naturalmente frugati dalla curiosit&agrave; di ri&shy;<lb/>cercar se, anche in esso, il Canocchiale svelasse qualche cosa di nuovo a <pb xlink:href="020/01/940.jpg" pagenum="383"/>un pi&ugrave; diligente Messaggero celeste. </s>

<s>Fa di ci&ograve; principalmente fede il Ke&shy;<lb/>plero, il quale cos&igrave; scriveva da Linz il d&igrave; 18 Luglio 1613 a Oddone Mal&shy;<lb/>cozio: </s></p><p type="main">

<s>&ldquo; Primum atque Galilaeus, inventis novis sideribus, plura arcana coe&shy;<lb/>lestia iactavit, de Solis maculis cogitare coepi, si forsan earum indicio motum <lb/>aliquem Telluris circa Solem comprobare possimus, tunc nimirum si Sol <lb/>ipse non fuisset rotatus. </s>

<s>Igitur, lente convexa Telescopii optimi, quod habe&shy;<lb/>bam ex concessu Electoris coloniensis, post meridiem radium Solis excepi, <lb/>et papyrum in puncto concursus radiorum applicavi, remoto concavo vitro. </s>

<s><lb/>Sed fulgor immensus radiorum collectorum, et speciei exilitas mihi obstite&shy;<lb/>runt ut maculas nullas cernerem. </s>

<s>Quare curam inquirendi maculas depo&shy;<lb/>sui. </s>

<s>Assumpsit autem eas quidam Fabricius Witembergae, libellumque su&shy;<lb/>per hac re vulgavit, mense Junii anni 1611, quem sequtus est Augustanus <lb/>quidam anonymus, seu ficto nomine Apellis; quam ad famam ego ad Te&shy;<lb/>lescopium redii, ususque utroque vitro, maculas tamdem et ipse detexi &rdquo; <lb/>(Epistolae, Lipsiae 1718, pag. </s>

<s>555). </s></p><p type="main">

<s>La naturale ingenuit&agrave; di Giovanni Keplero e la serenit&agrave; d'animo, con <lb/>la quale scriveva queste parole, ci assicurano della veracit&agrave; della Storia, <lb/>dalla quale apparisce essere stato esso Keplero il primo a pensare alle Mac&shy;<lb/>chie del Sole, anche innanzi di averle vedute attraverso il Canocchiale, o in <lb/>quel modo ch'ei suggeriva, come dicemmo, a Galileo. </s>

<s>Apparisce inoltre che <lb/>prima dello stesso Apelle ne aveva scritto con intendimento astronomico <lb/>Giovanni Fabricio, il quale, nella sua Narrazione <emph type="italics"/>De maculis in Sole obser&shy;<lb/>vatis et apparente corum cum Sole conversione,<emph.end type="italics"/> incomincia a dire come, <lb/>all'annunzio delle nuove scoperte celesti di Galileo, fosse mosso dalla cu&shy;<lb/>riosit&agrave; di vedere quel che di nuovo avesse a rivelarci la faccia del Sole. </s>

<s><lb/>Racconta come a principio riuscisse la cosa un po'difficile, per la offesa <lb/>degli occhi, ma che poi la difficolt&agrave; fu vinta, approdando a principio la vista <lb/>nel lembo del disco solare, e poi introducendosi a poco a poco a guardare <lb/>nel mezzo. </s>

<s>Pi&ugrave; tardi gli occorse al pensiero di osservar l'immagine del Sole <lb/>proiettata sul diaframma di una camera oscura. </s>

<s>&ldquo; Cogitavimus igitur de ra&shy;<lb/>diis Solis per angustum foramen intromittendis et in obscura clausis fene&shy;<lb/>stris camera observandis. </s>

<s>Notum enim est Opticis, quae foris sunt et agun&shy;<lb/>tur in tenebroso cubiculo possint repraesentari, aperto solum angusto quodam <lb/>foramine, per quod species rerum ipso foramini obiectarum illabantur, et <lb/>pingant parietem in cubiculo oppositum sed omnia inverso situ. </s>

<s>&rdquo; </s></p><p type="main">

<s>N&egrave; a sodisfar oziosamente la pura curiosit&agrave; stette contento il Fabricio, <lb/>ma specul&ograve; altres&igrave;, bench&egrave; ne confessasse la difficolt&agrave;, e non sperasse di sa&shy;<lb/>per nulla di certo, intorno alla natura delle Macchie osservate; e avendone <lb/>avvertito il loro moto, ne fece argomento a dimostrar quella vera conver&shy;<lb/>sione del Sole intorno a s&egrave; stesso, <emph type="italics"/>quam Jordanus Bruno asseruit, et nu&shy;<lb/>per admodum defendit in suis, quos de Martis motibus edidit, Commen&shy;<lb/>tariis, Keplerus.<emph.end type="italics"/></s></p><p type="main">

<s>La Dissertazion kepleriana sul Nunzio Sidereo dunque e questa Narra-<pb xlink:href="020/01/941.jpg" pagenum="384"/>zion del Fabricio, ambedue pubblici documenti anteriori al Discorso delle <lb/>cose che stanno sull'acqua, e alle Lettere velseriane, bastano a dimostrar <lb/>che Galileo non poteva pretendere il primato dell'osservazione strumentale <lb/>delle Macchie dovuto al Keplero, n&egrave; il primato delle speculazioni intorno alla <lb/>natura e al moto delle stesse Macchie dovuto al Keplero medesimo e al Fa&shy;<lb/>bricio. </s>

<s>E nonostante, lasciati in pace que'due trionfanti competitori, non <lb/>muove guerra che contro il solo Apelle. </s>

<s>Son due ambiziosi conquistatori del <lb/>Regno della Scienza, e di una provincia che a loro men si compete si con&shy;<lb/>tendono furiosamente il principato. </s>

<s>In ogni modo &egrave; lo Scheiner quello, che <lb/>ha la ragione, se si ha da lasciar le passioni e giudicare dai fatti, per il pi&ugrave; <lb/>imparziale esame de'quali convien tornare a svolgere le prolisse colonne <lb/>della <emph type="italics"/>Rosa Ursina.<emph.end type="italics"/></s></p><p type="main">

<s>L'Autore d&agrave; le prime testimonianze di s&egrave; cos&igrave; narrando come fosse <lb/>condotto all'osservazione del singolar fenomeno, dietro le sue proprie espe&shy;<lb/>rienze sulla camera oscura. </s>

<s>&ldquo; Cum ea tempestate species rerum visibilium <lb/>in loca tenebrosa immittendarum, iam diu tractatas, satisque perspectas in <lb/>manibus quotidie haberem, .... statim itaque ad Maculas a Sole captandas <lb/>idem artificium transtuli, sicque eumdem, per exile atque rotundum fora&shy;<lb/>men intrare, atque arcana sua patefacere coegi, quae ego in mundissimam <lb/>chartam foramini, seu penicillo solis radioso orthogonos in longissima di&shy;<lb/>stantia oppositam excepi, et quam potui fidelissime depinxi &rdquo; (Bracciani 1630, <lb/>pag. </s>

<s>10). </s></p><p type="main">

<s>Lo Scheiner dunque non manca di render pieno conto di s&egrave; innanzi al <lb/>tribunal della Storia. </s>

<s>Volete sapere a quale occasione gli occorresse di ri&shy;<lb/>volgere il Canocchiale nella spera del Sole? </s>

<s>ed ei ve lo narra. </s>

<s>Volete sa&shy;<lb/>pere come facesse a non ricevere offesa agli occhi? </s>

<s>ed ei vi risponde. </s>

<s>Vo&shy;<lb/>lete sapere a qual proposito gli accadesse di osservare l'immagine del Sole? </s>

<s><lb/>ed ei ve lo descrive e vi rammenta l'esperienze preparatorie della camera <lb/>oscura. </s>

<s>Volete finalmente sapere in compendio tutta la storia di questo ne&shy;<lb/>gozio? </s>

<s>ed ei cos&igrave;, con tutta l'ingenuit&agrave;, ve la racconta: </s></p><p type="main">

<s>&ldquo; Anno Domini millesimo sexcentesimo undecimo, cum in celeberrima <lb/>Universitate Ingolstadiana Scientias mathematicas publice profiterer, et ex <lb/>assidua diuturnaque investigatione praevia maculas in Sole, ope Telescopii, <lb/>primum mense Martio, Sole per nebulam inspecto cuius tunc magnitudinem <lb/>inquirebam, deinde mense Octobri iterum Telescopio per nebulam et sine <lb/>hac Helioscopii, quod ex vitris ad hunc finem coloratis convexis et cavis <lb/>ipsemet elaboraveram, beneficio, animadvertissem earumque tam inter se <lb/>quam ad Solem situm in dies, numerum, figurarum et magnitudinem quam <lb/>potui diligentissime observassem, idque tam immissione naturali per nudum <lb/>exile foramen quam directo intuitu per dictum Helioscopium, et factas obser&shy;<lb/>vationes ex die in diem et ex horis pene in horas circulis observationis <lb/>comprehensas in chartas coniecissem, indeque observationum inter se com&shy;<lb/>paratione facta apparentem macularum motum, multasque in figuris atque <lb/>magnitudinibus nec non sitibus mutationes quotidianas sensim accidere vi-<pb xlink:href="020/01/942.jpg" pagenum="385"/>dissem, alias exire alias de novo Solem subintrare, multas in medio cursu <lb/>deficere et vicissim novas ex ipso Sole exoriri; attonitus tanta rerum no&shy;<lb/>vitate et vicissitudine patefeci ea primum discipulis meis &rdquo; (ibi, pag. </s>

<s>6). </s></p><p type="main">

<s>Poi prosegue a dire com'ei ne desse qualche sentore al Velsero &ldquo; qui <lb/>continuis me literis fatigavit, donec a me phaenomeni inventi novitatem <lb/>extorsit, quo aliqnot epistolis accepto, statim animum ad illius editionem <lb/>adiecit, ne quid de gratiae novitatis, ut ipse aiebat, longa mora deperiret <lb/>aut proinde inventionis laurea aliunde decerperetur. </s>

<s>&rdquo; Ma perch&egrave; poteva una <lb/>tale e tanta novit&agrave; partorire nell'animo de'Filosofi qualche grave dissidio <lb/>&ldquo; censuerunt superiores mei procedendum caute et pedetentim, donec et <lb/>phaenomenon ipsa aliorum quoque experientia accedente corroboraretur, ne&shy;<lb/>que a tritis Philosophorum semitis sine evidentia contraria facile receden&shy;<lb/>dum, neque observata mea in Epistolis ad Velserum destinatis meo nomine <lb/>edendo..... Hisce cautelis factum est ut Epistolae, multo pauciores quam <lb/>ad Velserum exaravissem, in vulgis emanarent ut sub alieno Apellis no&shy;<lb/>mine prodirent &rdquo; (ibi, pag. </s>

<s>7). </s></p><p type="main">

<s>La narrazione, esaminata in s&egrave; stessa e posta a riscontro con l'Epistole <lb/>dello stesso Apelle, non ha nulla che dia qualche sospetto di menzogna, per <lb/>cui nessuno che abbia animo retto e imparziale giudizio non pu&ograve; non chia&shy;<lb/>marsi, del conto che d&agrave; di s&egrave; lo Scheiner, sufficientemente sodisfatto. </s>

<s>Ma <lb/>qual conto rendesi alla Storia da Galileo? </s>

<s>Domandiamo a quale occasione <lb/>rivolgesse il Canocchiale in faccia al Sole e non sa dirlo. </s>

<s>Domandiamogli di <lb/>grazia come fece a vincere le difficolt&agrave; dell'osservazione, o che fu che gli <lb/>sugger&igrave; il partito di guardare il Sole <emph type="italics"/>averso vultu?<emph.end type="italics"/> Noi lo abbiamo con&shy;<lb/>getturato, ma n&egrave; da lui n&egrave; da'suoi amici se ne ricava nulla di certo. </s>

<s>Si <lb/>prova, come vedemmo, a dire quando gli occorresse di far l'ambita sco&shy;<lb/>perta, e ora ne assegna un tempo ora ne assegna un altro, ingerendo cos&igrave; <lb/>il sospetto che sia quello un aggirarsi come di chi vuol dar colore di vero <lb/>alla menzogna. </s></p><p type="main">

<s>Da queste consi.lerazioni e da que'fatti vien decisa fra lo Scheiner e <lb/>Galileo l'antica celebre controversia, soggetto della quale era, come dicemmo, <lb/>il primato delle osservazioni del Sole. </s>

<s>Ma perch&egrave; in ogni modo il merito <lb/>della causa non consisteva qui, ma nel filosofare intorno all'essere di ci&ograve; <lb/>che stranamente vedevasi apparire nella purissima faccia del Sole, &egrave; da av&shy;<lb/>vertir meglio ad alcuni fatti particolari, dai quali verr&agrave; definita la giusta <lb/>parte di quel merito, che intorno a ci&ograve; competesi a Galileo. </s></p><p type="main">

<s>In quel tempo ch'era per uscire alle stampe la prima edizione del Di&shy;<lb/>scorso delle Galleggianti, in cui l'Autore si mostrava cos&igrave; incerto dell'es&shy;<lb/>sere di quell'ombre nell'astro creato a dispensare al mondo la luce, il Ke&shy;<lb/>plero che, come udimmo dianzi dir da s&egrave; stesso, commosso dalla fama della <lb/>Narrazion del Fabricio e delle Lettere di Apelle, era tornato al Telescopio, <lb/>fu il primo che osasse dir la sua opinione intorno all'essere e alla natura <lb/>di quelle strane apparenze nella faccia del Sole. </s>

<s>Esprimeva cos&igrave; un anno <lb/>dopo questa sua opinione, in una Lettera del d&igrave; 10 Novembre 1612, a Simon <pb xlink:href="020/01/943.jpg" pagenum="386"/>Mario: &ldquo; Existimo esse analogon quippiam nubium terrestrium quod Solis <lb/>globus, suopte aestu coctus, excernat materiam forte cometarum qui fere a <lb/>Sole prodeunt &rdquo; (Epistolae, Lipsiae 1718, pag. </s>

<s>552). </s></p><p type="main">

<s>E dopo anche un altr'anno, sempre pi&ugrave; confermatosi in quella sua <lb/>prima opinione, la veniva cos&igrave; pi&ugrave; particolarmente esplicando al Malcozio: <lb/>&ldquo; Scripsi sub finem anni 1611 quid de substantia macularum harum sen&shy;<lb/>tirem, et parum quid mutem ex posterioribus observationibus invenio. </s>

<s>Ni&shy;<lb/>mirum non sunt omnes eiusdem omnino celeritatis, nec viam Ecclipticae <lb/>parallelam incedunt. </s>

<s>Itaque non haerent in superficie corporis solaris, neque <lb/>tamen absunt ab ea visibili intervallo. </s>

<s>Ex his argumentis, et quia in ipsa <lb/>facie Solis oriuntur nonnullae, evanescunt aliac, densantur, rarefiunturque, <lb/>passim schematismos permutant sensibiliter, dum una alia celerior est; fa&shy;<lb/>cile colligitur tale quid esse materiam horum macularum quale sunt in huius <lb/>terrestris Globi superficie nubes et nebulae, motum nonnullum obtinentes <lb/>in aere, qui nullis partibus a rapida gyratione Telluris superatur &rdquo; (ibi, <lb/>pag. </s>

<s>555). </s></p><p type="main">

<s>Ripensando poi all'origine di queste fuliggini credeva che le potessero <lb/>essere esalate <emph type="italics"/>ex ignitissimo illo solaris corporis titione,<emph.end type="italics"/> e giacch&egrave; nel&shy;<lb/>l'Astronomia ottica aveva, alquanti anni prima, approvata l'ipotesi di Dio&shy;<lb/>gene Laerzio, <emph type="italics"/>Solem statuens esse candentem lapidem<emph.end type="italics"/> (Francof. </s>

<s>1604, <lb/>pag. </s>

<s>222), non era alieno dal professar quelle sozze fuliggini <emph type="italics"/>efflorescere, <lb/>ut in candenti ferro, quibus partibus ab umido aere aspiratur<emph.end type="italics"/> (Epist. </s>

<s>cit., <lb/>pag. </s>

<s>558). </s></p><p type="main">

<s>Queste Kepleriane opinioni intorno all'essere e all'origine delle mac&shy;<lb/>chie solari, divulgatesi in Italia, approdarono alle orecchie di Galileo, in quel <lb/>medesimo tempo che il Cigoli gli riferiva da Roma le osservazioni sue pro&shy;<lb/>prie, e il Passignano gli significava il suo pensiero intorno alla natura di <lb/>esse Macchie, dicendo che ell'erano voragini aperte nella sostanza del Sole, <lb/>e che e'le vedeva, secondo l'espression del Cigoli, &ldquo; pi&ugrave; apparenti e pi&ugrave; <lb/>nere ne'lembi che se siano nella superficie di verso noi, e poi girando ora <lb/>verso il mezzo ora verso la circonferenza per linee spirali, s'immergono nel <lb/>corpo luminoso &rdquo; (Alb. </s>

<s>VIII, 170). </s></p><p type="main">

<s>Tutte queste opinioni e quel che lo stesso Cigoli gli riferiva de'suoi <lb/>proprii pensieri, cos&igrave; espressi: &ldquo; non credo siano un cumulo di stelle se <lb/>per&ograve; fra di loro facendo un cerchio non lasciassero uno spazio di spiracolo <lb/>di foro nel corpo solare, ma mi d&agrave; noia quell'esser sempre la parte pi&ugrave; ca&shy;<lb/>rica di scuro verso il centro del corpo solare &rdquo; (MSS. Gal., P. III, T. X, <lb/>c. </s>

<s>61); persuasero intanto Galileo non poter esser, com'aveva prima cre&shy;<lb/>duto, le macchie solari ombre di stelle circondanti il Sole, ci&ograve; che si af&shy;<lb/>frett&ograve; dl pronunziare in pubblico nella seconda edizione delle Galleggianti. </s></p><p type="main">

<s>Venuto poi a pubblicar le Lettere velseriane, e dovendo dir ci&ograve; ch'ei <lb/>pensava dell'essere e dell'origine delle macchie solari, prefer&igrave; all'ipotesi del <lb/>Passignano quella del Keplero, ch'ei ripet&egrave; in tutti i particolari, non eccet&shy;<lb/>tuato l'esempio del fumo esalato, o delle macchie rimaste sopra il ferro ro-<pb xlink:href="020/01/944.jpg" pagenum="387"/>vente. </s>

<s>Di qui &egrave; che lo stesso Keplero, il quale ricev&egrave; il di 18 Luglio 1613 <lb/>le Lettere velseriane (Epist. </s>

<s>cit., pag. </s>

<s>555), chiama quelle un <emph type="italics"/>accurata di&shy;<lb/>scussio,<emph.end type="italics"/> e poi scrivendo al Maestlin gli diceva come, discutendo l'Autor del <lb/>libro italiano intorno alle macchie, <emph type="italics"/>omne tulerit punctum<emph.end type="italics"/> (ibi, pag. </s>

<s>45). </s></p><p type="main">

<s>Il Passignani invece s'ebbe molto per male in veder che Galileo non <lb/>si fosse degnato, nemmen privatamente, di rispondere alla sua del 17 Feb&shy;<lb/>braio da noi riferita di sopra, e che scrivendo per il pubblico la Prima sua <lb/>velseriana, non si fosse curato di nominarlo, professando in parte altra opinion <lb/>dalla sua. </s>

<s>Veniva ci&ograve; significato allo stesso Galileo dal Cigoli, che cos&igrave; gli scri&shy;<lb/>veva da Roma: &ldquo; Il signor Domenico Passignani &egrave; in valigia, s&igrave; perch&egrave; la <lb/>non gli ha dato risposta alla sua, come anco della diversit&agrave; della sua riso&shy;<lb/>luzione delle Macchie del Sole, attesoch&egrave; egli &egrave; uomo molto amico di sua <lb/>opinione &rdquo; (MSS. Gal., P. VI, T. VIII, c. </s>

<s>128). </s></p><p type="main">

<s>Nel Pittore filosofo aveva dunque Galileo ritrovato inaspettatamente un <lb/>competitore, e conveniva perci&ograve;, al modo che tutti gli altri competitori nella <lb/>scoperta, trattarlo col solito disprezzo. </s>

<s>&ldquo; Il Passignano, gli scriveva lo <lb/>stesso Cigoli, fa gran cose e gran rumori e millantamenti, appropriandosi <lb/>del guardare e dell'avere scoperto nel Sole le Macchie e le osservazioni, ed <lb/>inoltre mi disse iersera che ha gran cose per le mani e cor una sua inven&shy;<lb/>zione, qual non mi volse dire, neanco al sig. </s>

<s>Luca (Valerio), che saperr&agrave; <lb/>dire cose minutissime, e che Giove lo vede montuoso &rdquo; (MSS. Gal., P. I, <lb/>T. VII, c. </s>

<s>12). </s></p><p type="main">

<s>Il Cigoli, com'anche trasparisce da queste parole, secondava in disprez&shy;<lb/>zar l'amico suo e collega, il Galileo, a cui scriveva di averne sentite dire <lb/>al Passignano <emph type="italics"/>alle volte di quelle che mi fa ridere solennemente<emph.end type="italics"/> (MSS. <lb/>Gal., P. VI, T. VIII, c. </s>

<s>128), e ch'egli non faceva altro che <emph type="italics"/>lucidare e ri&shy;<lb/>dicolmente storpiare<emph.end type="italics"/> cose sentite gi&agrave; dire a Luca Valerio, e al padre Griem&shy;<lb/>bergero (ivi, c. </s>

<s>117). </s></p><p type="main">

<s>Ma pure era il Cigoli stesso, il quale in altra lettera a Galileo aveva <lb/>fatto notar la differenza grande, che passa fra l'opinion del Griemberger a <lb/>cui parve d'acconsentir che le macchie sien ombre di stelle, e l'opinion del <lb/>Passignano, che attribuiva le stesse macchie a voragini aperte nella corpu&shy;<lb/>lenza del Sole; era il Cigoli stesso che dall'apparirgli sempre <emph type="italics"/>la parte om&shy;<lb/>brosa verso il centro del corpo solare<emph.end type="italics"/> (MSS. Gal., P. III, T. X, c. </s>

<s>61) pi&shy;<lb/>gliava risoluzione di creder meno ai discorsi del Gesuita tedesco, che non <lb/>a quelli del Pittore toscano; era il Cigoli stesso, il quale aveva avuto prove <lb/>non dubbie che il Canocchiale usato dal Passignani era molto pi&ugrave; eccellente <lb/>di quello che aveva Galileo per le sue osservazioni celesti. </s>

<s>Vedremo di que&shy;<lb/>sta superiorit&agrave; fra poco una prova di fatto, ma non sar&agrave; piccola prova in&shy;<lb/>tanto il dire che i resultati delle osservazioni, a null'altro fanno meglio rasso&shy;<lb/>migliar lo strumento e la veggenza del nostro Passignani, che allo strumento <lb/>e alla veggenza dell'Herschel stesso. </s>

<s>A persuadersi di che basta percorrer <lb/>d'un volo la storia delle ipotesi varie intorno alle Macchie solari, fondate <lb/>sulle pi&ugrave; o meno esatte osservazioni. </s></p><pb xlink:href="020/01/945.jpg" pagenum="388"/><p type="main">

<s>Le prime supposizioni kepleriane delle nuvole o de'fumi fuligginosi esa&shy;<lb/>lati dal tizzone infocato del Sole; supposizioni approvate da Galileo, non eb&shy;<lb/>bero grande accoglienza in Germania, dove il Moestlin, persuaso che il Sole <lb/>s'assomigliasse, come la Luna, alla Terra, per avervi scorte alcune montuo&shy;<lb/>sit&agrave;, andava a queste montuosit&agrave; e alle valli attribuendo l'origine delle mac&shy;<lb/>chie solari, ond'&egrave; che cos&igrave; in proposito scriveva allo stesso Keplero: &ldquo; Mihi, <lb/>ut pace tua dicam, non quales in Terra sunt nubes, sed perpetua corpora <lb/>videntur.... Vidimus enim pariter magnas eminentias et notabiles hiatus, <lb/>quales in Terra sunt montes et valles. </s>

<s>Num ergo et Solis corpus rudis ve&shy;<lb/>lut Terra globus est? </s>

<s>Certe Lunam Terrae esse simillimam, prout in Di&shy;<lb/>sputatione probavi, hae novae observationes, non ad credendum invitant, sed <lb/>ut certo asseram, cogunt &rdquo; (Ad Keplerum Epist. </s>

<s>cit., pag. </s>

<s>41). Ma quando <lb/>poi il Keplero fece notare al suo Maestro che la permanenza era contrariata <lb/>dal vedersi cos&igrave; spesso pi&ugrave; Macchie confondersi un una sola, e allora ebbe <lb/>a dire il Moestlin: &ldquo; De maculis in Sole magis magnisque turbor &rdquo; (ivi, <lb/>pag. </s>

<s>44). </s></p><p type="main">

<s>Quella ipotesi moestliniana rifior&igrave; poi in Francia, nel secolo XVIII, dalla <lb/>fantasia del Fontenelle, il quale immagin&ograve;, per salvarle dalle opposizioni del <lb/>Keplero, che le montuosit&agrave; del Sole uscissero fuori da un gran mare di <lb/>fuoco, da cui fossero lasciate ora pi&ugrave; ora meno allo scoperto, per un tal <lb/>perpetuo avvicendarsi del suo flusso e riflusso. </s>

<s>Ma all'Herschel Telescopii <lb/>assai pi&ugrave; squisiti rivelarono esser piuttosto voragini che montuosit&agrave; sul&shy;<lb/>l'ignita faccia del Sole: voragini che parve poi necessario ammettere, per <lb/>salvare alcune delle principali apparenze presentate dalle Macchie solari. </s>

<s><lb/>Ond'&egrave; che, se pu&ograve; dubitarsi della verit&agrave; della posizione Herscelliana, la quale <lb/>ammetteva una fotosfera involgente il nucleo opaco e solido del Sole; se <lb/>pu&ograve; dubitarsi della Wilsoniana, nella quale s'aggiungeva un'ammosfera ne&shy;<lb/>bulosa interposta tra la fotosfera stessa e l'opaco globo centrale; non par <lb/>che possa dubitarsi di quelle voragini vedute in Roma, pi&ugrave; di un secolo <lb/>prima che in Londra, da'due nostri Pittori toscani. </s></p><p type="main">

<s>Aveva dunque, concludendo il nostro discorso, giusta ragione il Passi&shy;<lb/>gnani appropriandosi del guardare e dell'avere scoperto nel Sole l'origine <lb/>delle Macchie, ed ebbe il torto Galileo a disprezzar questa scoperta, che fu <lb/>prima a farlo accorto dell'errore di Apelle, e a posporla alle ipotesi del <lb/>Keplero. </s>

<s>Cosi, non resta all'Autore delle Lettere velseriane nemmeno il me&shy;<lb/>rito della scelta, la quale sebben versasse, non tra il vero e il falso, ma tra <lb/>il pi&ugrave; e il meno probabile, pareva che maggior probabilit&agrave; porgessero le sen&shy;<lb/>sate osservazioni del Pittor nostro da Passignano, che non le ardite fanta&shy;<lb/>sie dell'Astronomo alemanno. </s></p><pb xlink:href="020/01/946.jpg" pagenum="389"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>La faccia del Sole, per la soverchia sua visibilit&agrave;, rimasta invisibile per <lb/>lungo tempo ai Filosofi, non fu potuta con sicura pace guardare, per osser&shy;<lb/>varne le Macchie, infintanto che gli artificii della Camera oscura non inse&shy;<lb/>gnarono a dipingere con precisione l'immagine radiosa, e i Canocchiali, dis&shy;<lb/>sipando la luce e temperando attraverso ai vetri neri gli accecanti fulgori, <lb/>non dettero il modo di avvalorar tutt'insieme la vista, e di difendere gli <lb/>occhi. </s>

<s>Non fu cos&igrave; della Luna, i segni bui della quale fecero, infin dalla pi&ugrave; <lb/>remota antichit&agrave;, favoleggiar di Caino e delle spine. </s>

<s>Che se non rimase a <lb/>quello spettacolo il volgo indifferente, non &egrave; a creder che non volesse fru&shy;<lb/>gare la curiosit&agrave; de'Filosofi antichi, de'quali, se alcuni dissero pazze cose, <lb/>altri indovinarono cos&igrave; il vero, da recare stupore ai moderni. </s></p><p type="main">

<s>Fra gli altri suoi Opuscoli Plutarco ne ha uno, che giusto s'intitola <lb/><emph type="italics"/>Della faccia, che si vede nel cerchio della Luna,<emph.end type="italics"/> dove, a proposito delle <lb/>Macchie, entra a trattar delle principali questioni fisiche intorno a quella, <lb/>ch'egli elegantemente chiama <emph type="italics"/>nostra nutrice e fedel custode e fattrice del <lb/>Giorno e della Notte<emph.end type="italics"/> (Opuscoli volgarizzati, Milano 1829, T. V, pag. </s>

<s>358). <lb/>Dal veder, prima di tutto, ch'ell'&egrave; la pi&ugrave; bassa di tutte le stelle, a propor&shy;<lb/>zion delle quali si dilunga cos&igrave; di poco dalle regioni della nostra Terra, il <lb/>Filosofo di Cheronea ne conclude che non &egrave; la Luna altrimenti cosa cele&shy;<lb/>ste, ma terrena. </s>

<s>N&egrave; per esser grave &egrave; da temer ch'ella cada &ldquo; essendo aiu&shy;<lb/>tata dal moto e dall'impeto suo, nel modo che i sassi posti dentro la fionda &rdquo; <lb/>(ivi, pag. </s>

<s>325). </s></p><p type="main">

<s>Essendo dunque terrena, non &egrave; tersa e pulita come uno specchio, ma <lb/>distinta d'inegualit&agrave; e di asprezze, come di monti e di valli. </s>

<s>Lo prova di&shy;<lb/>cendo che non potrebbe altrimenti mostrarsi tutta illuminata, essendo che <lb/>uno specchio non riflette la luce che da un punto solo, l&agrave; dove le innume&shy;<lb/>revoli asperit&agrave; della superficie &ldquo; possono scambievolmente risplendere, ed <lb/>in ogni modo reflettersi, invilupparsi e continuar fra s&egrave; lo splendore, come <lb/>se a noi venisse da molti specchi &rdquo; (ivi, pag. </s>

<s>342). </s></p><p type="main">

<s>Da questo vero modo d'illuminarsi conclude inoltre il Filosofo che la <lb/>Luna &egrave; un corpo solido, &ldquo; perch&egrave; le riflessioni non si fanno in alcuna cosa <lb/>rara e composta di parti tenui, n&egrave; &egrave; facil cosa l'immaginarsi reverbero del <lb/>fuoco nel fuoco, o del lume nel lume, ma fa di mestieri che solida e densa <lb/>sia quella cosa, dalla quale un'altra deve essere reverberata e reflessa &rdquo; <lb/>(ivi, pag. </s>

<s>343). </s></p><p type="main">

<s>Che poi veramente s'illumini la Luna solida e aspra per riflessione, e <lb/>che non sia per s&egrave; luminosa, lo prova dal fatto delle ecclissi, le quali allora <lb/>succedono &ldquo; quando questi tre corpi, la Terra, il Sole e la Luna si diriz&shy;<lb/>zano ad una retta linea, perch&egrave; la Terra priva la Luna del Sole, o all'in-<pb xlink:href="020/01/947.jpg" pagenum="390"/>contro la Luna ne spoglia la Terra, essendo che s'oscura il Sole, quando <lb/>vi si frammette la Luna, e questa s'ecclissa, quando v'&egrave; di mezzo la Terra: <lb/>l'una di queste ecclissi segue per la congiunzione de'due luminari, l'altra <lb/>per l'opposizione &rdquo; (ivi, pag. </s>

<s>347). Se dunque per queste ecclissi si mostra <lb/>che la Luna nell'ombra perde il suo lume, e lo ricupera quando &egrave; uscita <lb/>dall'ombra, segno certo &egrave; che non ha lume proprio, ma che lo riceve dal <lb/>Sole (ivi, pag. </s>

<s>349). </s></p><p type="main">

<s>N&egrave; fa nulla in contrario il veder la stessa Luna nell'ombra delle ec&shy;<lb/>clissi rosseggiar d'un colore simile a quel della bragia, &ldquo; il quale si pu&ograve; <lb/>dire essere lontanissimo dalla Luna, e chiamarsi piuttosto mistura di lume <lb/>che manchi, e che splenda fra l'ombra, ed affermare che il proprio e na&shy;<lb/>tivo sia il nero e il terrestre &rdquo; (ivi, pag. </s>

<s>351). Una tal mistura, secondo Plu&shy;<lb/>tarco, vien dalle innumerevoli stelle che circondano il Sole e in difetto ne <lb/>suppliscono al lume. </s></p><p type="main">

<s>Premessa cos&igrave; questa vera teoria lunare, e venendo al soggetto proprio <lb/>delle macchie, il grande Astronomo di Cheronea dice che le variabili son <lb/>dovute all'ombre, ora pi&ugrave; ora meno lunghe proiettate da'monti, secondo che <lb/>il Sole ora pi&ugrave; ora men lontano gl'irraggia. </s>

<s>&ldquo; Ma perch&egrave; le distanze dei <lb/>lumi allungano l'ombre de'corpi, considera dunque che il Sole s'ollontana <lb/>dalla Luna per grandissimo spazio, quando ella &egrave; piena, ed esprime chia&shy;<lb/>ramente l'effigie della faccia con l'altezza dell'ombra, perch&egrave; la distanza <lb/>stessa del lume fa l'ombra grande, e non la grandezza delle inegualit&agrave; che <lb/>nella Luna si trovano &rdquo; (ivi, pag. </s>

<s>355). </s></p><p type="main">

<s>Quanto poi alle altre macchie pi&ugrave; permanenti, confutata l'opinion di <lb/>Clearco, che le attribuiva allo specchiarsi del grand'Oceano terrestre nella <lb/>Luna, stima Plutarco che sien piuttosto dovute a grandi cavit&agrave; piene d'acqua <lb/>o d'aria caliginosa. </s>

<s>&ldquo; Siccome la nostra Terra, egli dice, ha alcuni gran seni, <lb/>cos&igrave; stimiamo che la Luna sia aperta da vaste profondit&agrave; e rotture piene <lb/>d'acqua, o d'aria caliginosa, nelle quali il Sole col suo lume non penetri, <lb/>ma lassandole, faccia la reflessione dissipata &rdquo; (ivi, pag. </s>

<s>353). </s></p><p type="main">

<s>Queste pitagoriche dottrine di Plutarco furono contradette a'suoi giorni, <lb/>come furono per le medesime ragioni contradette ai giorni di Galileo, e per&shy;<lb/>ci&ograve;, rimaste per un tempo dimenticate, e poi rifiutate, dovettero soggiacer <lb/>lungamente alla tirannia dell'errore. </s>

<s>L'Alighieri, con argomenti che hanno <lb/>per quel secolo del singolare, confuta l'opinion di coloro, che dicevano nella <lb/>Luna il raro esser cagione di quel bruno (Paradiso, C. II, t. </s>

<s>25-35) e non <lb/>sodisfatto, a quel che pare, di nessuna fisica ragione, v&agrave; sublimandosi a ri&shy;<lb/>trovarla nella Metafisica e nella Teologia. </s></p><p type="main">

<s>Quando poi l'umanismo letterario fece rivivere fra'libri antichi anche <lb/>quelli di Plutarco, e gli diffuse, curandone con diligenza il testo o facen&shy;<lb/>done eleganti versioni latine; mentre alcuni privilegiati ingegni vi sentirono <lb/>il gusto del vero, altri, col palato guasto da'simposii peripatetici, ne prova&shy;<lb/>ron fastidio. </s>

<s>Nel fatto particolare delle apparenze lunari noi possiam di ci&ograve; <lb/>addurre alcuni pochi esempii, che valgano per i tanti altri. </s></p><pb xlink:href="020/01/948.jpg" pagenum="391"/><p type="main">

<s>Al peripatetico nostro Cesalpino, ostinato in mantenere alla Luna la su&shy;<lb/>perficie tersa, arrise, meglio della pitagorica, l'opinion di Clearco. </s>

<s>Se non <lb/>che, invece d'esser le macchie la rappresentanza scolpita de'soli mari ter&shy;<lb/>restri, diceva esser l'immagine specchiata di essi insieme a dei continenti. <lb/></s>

<s>&ldquo; Aliam cogimur.... maculae Lunae rationem excogitare. </s>

<s>An refractio fue&shy;<lb/>rit nostri visus ad Terram? </s>

<s>ut Luna sit speculum quoddam in quo tota Ter&shy;<lb/>rae facies cum latitudine marium appareat? </s>

<s>ut alterum maculae crus occa&shy;<lb/>sum spectans Terrae illam partem repraesentet, quam nostris temporibus <lb/>Hispani, vastum Oceani pelagum transmeantes, invenerunt: alterum vero <lb/>triangulum Africae formam ostendat. </s>

<s>Reliqua autem maculae agglomeratio <lb/>Asiam cum Europa et mari mediterraneo exprimat, non satis distinguente <lb/>visu ob multas eius maris angustias &rdquo; (Peripat. </s>

<s>Quaest., Venetiis 1571, <lb/>pag. </s>

<s>52). </s></p><p type="main">

<s>Quell'altro filosofo poi, Girolamo Borro, che scrisse del flusso e riflusso <lb/>marino, ripudiata con ugual nausea e l'opinion di Clearco e quella di Plu&shy;<lb/>tarco, non sente venir buono odore che dalla peripatetica del denso e del <lb/>raro, confutata dall'Alighieri. </s>

<s>&ldquo; La faccia della Luna, scrive il nostro Are&shy;<lb/>tino, &egrave; meno densa che non &egrave; quella del Sole e delle altre stelle, per&ograve; <lb/>manco riluce. </s>

<s>E nella stessa faccia della Luna sono alcune parti pi&ugrave; rare, <lb/>le quali fanno la macchia che in essa si vede, la quale non &egrave; n&egrave; l'ombra <lb/>de'monti n&egrave; la riverberazione del mare, n&egrave; altra somigliante cosa, ma &egrave; sola <lb/>una parte meno densa, per&ograve; meno rilucente &rdquo; (Lucca 1561, pag. </s>

<s>52). </s></p><p type="main">

<s>Que'semi del vero, che conteneva l'opuscolo di Plutarco, non furono <lb/>riconosciuti, perch&egrave; vi stavano dentro come nella polpa di un frutto colti&shy;<lb/>vato fra'lazzi sorbi dagli avi, e custodito nel chiuso di un vaso, che final&shy;<lb/>mente aprendosi, venne a spander le sue fragranze, e a dar gusto de'suoi <lb/>sapori incorrotti sulla scelta mensa imbandita ai pi&ugrave; tardi nepoti. </s>

<s>Primo a <lb/>sedere a quella mensa era stato il Copernico, poi il Moestlin, che ne fece, <lb/>venutogli a sedere al fianco, gustar soavemente al Keplero. </s>

<s>Leggiam cos&igrave; <lb/>come questi si levasse ebro di una nuova dolcezza da quel filosofico convito: </s></p><p type="main">

<s>&ldquo; Elegantissimum est illud Plutarchi Opusculum et festivissimum, di&shy;<lb/>gnumque quo se Philosophus, depositis aliquando studiis gravioribus, oblectet. </s>

<s><lb/>Quae adeo causa est ut non invitus cum ipso tandem authore in hanc sen&shy;<lb/>tentiam concedam, cuius mihi quidem iam pridem et Moestlinus praeceptor <lb/>meus author fuit, dicamque Lunae tale esse corpus quale haec nostra Terra <lb/>est, ex aquae et continentibus unum globum efficiens. </s>

<s>Id quidem pertendit <lb/>Plutarchius: multis rationibus, et oratorie et argute, communit contra va&shy;<lb/>rias obiectiones, ut merito mirari possit Peripateticus aliquis tam multa et <lb/>solida contra suae sectae placita disserri posse &rdquo; (Paralip. </s>

<s>ad Vitell., Fran&shy;<lb/>cofurti 1604, pag. </s>

<s>248). E prosegue a dire essergli confermata questa opi&shy;<lb/>nione dalle sinuosit&agrave; della Luna bissetta, le quali non possono essere effetto <lb/>d'altro, che di qualche montuosa disuguaglianza. </s>

<s>In una cosa per&ograve; dissente <lb/>dal suo Plutarco, parendogli pi&ugrave; consentaneo &ldquo; quae sunt in Luna partes luci&shy;<lb/>dae maria credi, quae maculosae terras, continentes et insulas &rdquo; (ibi, pag. </s>

<s>251). </s></p><pb xlink:href="020/01/949.jpg" pagenum="392"/><p type="main">

<s>Tanto amore poi prese il Keplero a questa opinion di Plutarco, che ve&shy;<lb/>dendolo per grande antichit&agrave; guasto e corrotto, vi si pose attorno ad emen&shy;<lb/>darlo, a supplirne alquante lacune, a tradurlo in latino, e poi pi&ugrave; tardi a <lb/>illustrarlo con note. </s>

<s>Questo studio, ch'egli intraprese per .sollevarsi <emph type="italics"/>deposi&shy;<lb/>tis aliquando studiis gravioribus,<emph.end type="italics"/> fu pubblicato postumo, insiem col <emph type="italics"/>Sogno <lb/>astronomico,<emph.end type="italics"/> dal figliolo di lui Lodovico in Francfort, nel 1634. </s></p><p type="main">

<s>Ma intanto anche tutti quegli altri dell'antico Plutarco, che parevano <lb/>a molti astronomici sogni, Galileo venne ad annunziare al mondo che si <lb/>erano pienamente avverati. </s>

<s>Guardando col Canocchiale quella linea sinuosa, <lb/>che divide in due parti la Luna, la vide molto pi&ugrave; frastagliata di quel che <lb/>non apparisse naturalmente al Keplero, per cui veniva cos&igrave; quasi di fatto con&shy;<lb/>fermata la congettura, anzi l'argomento dell'Astronomo alemanno. </s>

<s>&ldquo; Quarta <lb/>aut quinta post coniunctionem die, cum splendida Luna sese nobis corni&shy;<lb/>bus offert, iam terminus partem obscuram a luminosa dividens, non aequa&shy;<lb/>liter secundum ovalem lineam extenditur, veluti in solido perfecte sphaerico <lb/>accideret, sed inaequali aspera et admodum sinuosa linea designatur &rdquo; <lb/>(Alb III, 63). D'onde l'Autor del Nunzio Sidereo ne conclude: &ldquo; Lunae <lb/>superficiem non perpolitam, aequabilem, exactissimaeque sphaericitatis exi&shy;<lb/>stere, ut magna Philosophorum cohors de ipsa deque reliquis corporibus <lb/>coelestibus opinata est, sed contra inaequalem, asperam, cavitatibus tumo&shy;<lb/>ribusque confertam, non secus ac ipsamet Telluris facies, quae montium iu&shy;<lb/>gis, valliumque profunditatibus hinc inde distinguitur &rdquo; (ibi). </s></p><p type="main">

<s>Chi pu&ograve; immaginare la compiacenza, che dovette provare questo no&shy;<lb/>stro primo Messaggero celeste? </s>

<s>Se il Keplero sent&igrave; venirsi tanto diletto dalla <lb/>lettura degli Opuscoli di Plutarco, che doveva esser l'animo di Galileo, il <lb/>quale veniva ad annunziar come le congetture eran confermate dal vero? </s>

<s><lb/>Or chi, tutt'al contrario, crederebbe mai, che fra le cupe gelosie del regno <lb/>dovesse l'ombra del sospetto cadere anche su quel buono e amabile vec&shy;<lb/>chio di Cheronea? </s>

<s>Colui che voleva in tutto essere il primo e il solo, avrebbe <lb/>dato chi sa che, se avesse potuto cancellar dalle menti la memoria di Plu&shy;<lb/>tarco. </s>

<s>Il Copernico lo commemora nella prefazione al suo libro; gli fa cosi <lb/>lieta e lunga accoglienza, nell'Astronomia ottica, il Keplero, ma Galileo, ch'&egrave; <lb/>solo maestro a s&egrave; stesso e al mondo, fa vista di non lo conoscere nemmeno <lb/>per nome. </s>

<s>Eppure si sa che da giovane s'esercit&ograve; anch'egli a tradurre gli <lb/>Opuscoli del Filosofo greco (MSS. Gal., Nelli filza VI, c. </s>

<s>52), e di l&igrave; apprese <lb/>i primi pitagorici principii d'astronomia lunare. </s></p><p type="main">

<s>Abbiamo una prova di ci&ograve; dalla sicurezza, con la quale seppe Galileo <lb/>evitare una fallacia, nella quale era incorso il Keplero. </s>

<s>Vedemmo come a <lb/>questi paresse pi&ugrave; conveniente ammettere che le parti pi&ugrave; luminose nel cer&shy;<lb/>chio della Luna fossero mari, ma Galileo non si dilung&ograve; da Plutarco, l'opi&shy;<lb/>nion del quale, anzi la vera sentenza, scrisse cos&igrave; in alcune note di propria <lb/>mano, verso il 1604, quando forse dal latino traduceva gli Opuscoli greci, <lb/>e leggeva Seneca, da'quali Autori senti venirsi i pi&ugrave; forti impulsi all'aperta <lb/>professione copernicana. </s>

<s>&ldquo; Consideretur duplicem esse reflexionem: unam a <pb xlink:href="020/01/950.jpg" pagenum="393"/>tota superficie rudi, alteram a parte superficiei perpolitae sphaerice. </s>

<s>A Luna <lb/>fit, non tamquam a Speculo, quia ab exigua eius parte fieret, cum sit con&shy;<lb/>vexa et esset longe validior &rdquo; (MSS. Gal., P. IV, T. IV, c. </s>

<s>15). Questo pen&shy;<lb/>siero fu poi largamente svolto nella I Giornata dei <emph type="italics"/>Massimi Sistemi,<emph.end type="italics"/> dove, <lb/>chi volesse farne il confronto, troverebbe il pi&ugrave; splendido commento all'Opu&shy;<lb/>scolo di Plutarco. </s></p><p type="main">

<s>Intanto manifestava nel Nunzio Sidereo quella sua sicurt&agrave; di pensiero, <lb/>asserendo coll'Autor antico che se son nella Luna veramente laghi o mari, <lb/>questi dovrebbero apparire pi&ugrave; oscuri dei continenti, com'apparirebbero <lb/>senza dubbio a chi guardasse di molt'alto la nostra Terra: &ldquo; Mihi autem, <lb/>dubium fuit nunquam terrestris globi, a longe conspecti atque a radiis so&shy;<lb/>laribus perfusi, terream superficiem clariorem, obscuriorem vero aqueam <lb/>sese in conspectum daturam &rdquo; (Alb. </s>

<s>III, 65). </s></p><p type="main">

<s>Nella Dissertazione sul Nunzio Sidereo confess&ograve; il Keplero che Galileo <lb/>l'avea convinto del suo primo errore e confermatolo nella vera sentenza di <lb/>Plutarco, ma poi, nella nota 154 al <emph type="italics"/>Sogno Astronomico,<emph.end type="italics"/> soggiunse pi&ugrave; par&shy;<lb/>ticolarmente le ragioni di ci&ograve; suggeritegli dal ragionamento suo proprio e <lb/>dalla esperienza. </s>

<s>&ldquo; Hunc paragraphum allegavi in Dissertatione cum Nuncio <lb/>Galilaei Sidereo, quam edidi Pragae anno 1610, simulque et censuram ad&shy;<lb/>didi necessariam. </s>

<s>Docuit me Galilaeus edita Lunae et aspera non maculas <lb/>esse sed claritatem, fusa vero in depressas partes aequora nigricare, macu&shy;<lb/>larumque speciem induere..... Quod prius in contrariam iveram senten&shy;<lb/>tiam causa haec fuit, quia terrae superficies varios induit colores, aquae co&shy;<lb/>lore vacare censebantur &rdquo; (pag. </s>

<s>62). L'esperienza che lo persuase l'acqua <lb/>invece aver color fosco, gli occorse di farla cos&igrave;, com'egli stesso racconta, <lb/>in Praga, guardando di sul Ponte, insiem con un amico oppositore di Ga&shy;<lb/>lileo, gli edifizi specchiati nell'acque della Moldava: &ldquo; Cum Pragae me <lb/>prope staret Literatus quisquam in Ponte, splendorem mihi aquarum in&shy;<lb/>culcans, ut Galilaei assertionem convelleret, iussi ut imagines domorum in <lb/>undis respiceret, easque cum recto aspectu domuum ipsarum compararet: <lb/>manifestum enim claritatis discrimen est, et imagines in undis obscuriores &rdquo; <lb/>(ibi, pag. </s>

<s>63). </s></p><p type="main">

<s>Tornando ora alle asperit&agrave; montuose riscontrate da Galileo nella Luna, <lb/>&egrave; da creder che i Peripatetici, i quali avevano derisi i sogni di Plutarco, ne <lb/>giudicassero altresi impossibili gli avveramenti. </s>

<s>I Gesuiti del Collegio ro&shy;<lb/>mano al card. </s>

<s>Bellarmino, che domandava s'era vero che la Luna fosse di <lb/>superficie aspra ed ineguale (Alb. </s>

<s>VIII, 160), rispondevano negando, man&shy;<lb/>tenendosi fedeli all'antica opinione peripatetica del denso e del raro (ivi, <lb/>pag. </s>

<s>161). </s></p><p type="main">

<s>I Gesuiti per&ograve; di un altro Collegio negavano esser aspra e montuosa <lb/>la Luna, perch&egrave; guardandola col Canocchiale non si vedevano uscir fuori <lb/>prominenze dal giro luminoso intorno intorno. </s>

<s>&ldquo; Che poi veramente non vi <lb/>sieno monti in quel giro, scriveva il padre Biancani, lo dimostra l'osser&shy;<lb/>vazione, massime quando la Luna &egrave; s&igrave; vicina al plenilunio, che pare tonda, <pb xlink:href="020/01/951.jpg" pagenum="394"/>perch&egrave; allora non si vedono adombrazioni verune, se non poche nella parte <lb/>per&ograve; opposta al Sole, le quali poi poco dopo spariscono, e resta in giro della <lb/>Luna tutto lucido senza alcuna ombra o segno d'inegualit&agrave; &rdquo; (Alb. </s>

<s>III, 147). </s></p><p type="main">

<s>La difficolt&agrave; era stata gi&agrave; presentita dallo stesso Galileo, che nel Nun&shy;<lb/>zio Sidereo cos&igrave; soggiungeva, dop'aver descritte le varie apparenze de'monti <lb/>lunari: &ldquo; Verum magna hic dubitatione complures affici sentio, adeoque <lb/>gravi difficultate occupari ut iam explicatam, et tot apparentiis confirmatam <lb/>conclusionem in dubium revocare cogentur. </s>

<s>Si enim pars illa lunaris su&shy;<lb/>perficiei, quae splendidius solares radios retorquet, anfractibus, tumoribus <lb/>scilicet et lacunis innumeris est repleta; cur in crescenti Luna extrema cir&shy;<lb/>cumferentia, quae occasum versus spectat, in decrescenti vero altera circum&shy;<lb/>ferentia orientalis, se ac in plenilunio tota peripheria non inaequalis, aspera <lb/>et sinuosa, verum exacte rotunda et circinata, nullisque tumoribus aut ca&shy;<lb/>vitatibus corrosa conspicitur? </s>

<s>&rdquo; (ibi, pag. </s>

<s>67). </s></p><p type="main">

<s>Galileo si studi&ograve; di risolvere il dubbio, riducendo il fatto a un caso di <lb/>prospettiva, e ad una illusione ottica occasionata dalle riflessioni de'raggi <lb/>solari dentro l'orbe vaporoso, di che supponeva esser circondato il globo <lb/>della Luna, ma non indovin&ograve; che tutto dipendeva dal Canocchiale inabile, <lb/>per il cos&igrave; piccolo ingrandimento, a tor via l'irradiazione. </s>

<s>Il Passignani in&shy;<lb/>fatti, con Strumento assai pi&ugrave; perfetto, fu il primo ad osservare alcuni ri&shy;<lb/>lievi in figura di merletti nell'orlo della Luna piena, e a fargli vedere in <lb/>Roma agli amici, fra'quali il Cigoli, che ne scrisse cos&igrave; a Galileo, pungen&shy;<lb/>dolo di gelosia con dargli prove di fatto che venivan di fuori, a chi ne avesse <lb/>voluti, Canocchiali pi&ugrave; eccellenti de'suoi. </s>

<s>&ldquo; Vidi bene con il suo Canoc&shy;<lb/>chiale (del Passignani) nel dintorno della Luna due merlature assai evidenti, <lb/>e questo fu l'altra notte (sulla fin del Gennaio 1612) quando ell'era quasi <lb/>piena. </s>

<s>Imper&ograve; me ne ha fatto venir voglia d'uno, e ci &egrave; qui uno che ne <lb/>fa venire, e gli ho dato ordine, ed i padri Gesuiti me lo scerranno &rdquo; (MSS. <lb/>Gal., P. I, T. VII, c. </s>

<s>12). </s></p><p type="main">

<s>Quasi un anno dopo, anche il Keplero scriveva cos&igrave; a Simon Mario: <lb/>&ldquo; Vidi duos colliculos in interiori speciei solaris circulo, quem formabat <lb/>Luna corpore. </s>

<s>Sunt igitur, etiam in circumferentia Lunae, montes quibus <lb/>aegre carere se Galilaeus haud obscure significaverat &rdquo; (Epist. </s>

<s>cit., pag. </s>

<s>552). </s></p><p type="main">

<s>Ma il Canocchiale del Passignani e quel del Keplero non tosavano cos&igrave; <lb/>il cerchio alla Luna, che non apparissero quelle prominenze vedute in giro <lb/>in giro alquanto imbambagiate. </s>

<s>Primo a mostrarle cos&igrave; ben terminate e di&shy;<lb/>stinte, da poterle riportare in disegno, fu un Canocchial del Campani, col <lb/>quale, afferma esso Campani, nel suo <emph type="italics"/>Ragguaglio di due nuove osserva&shy;<lb/>zioni,<emph.end type="italics"/> che il Cassini vide la circonferenza lunare &ldquo; scabrosa e anfrattuosa <lb/>nella forma che, mirato da luogo eminente, apparisce il nostro orizzonte ter&shy;<lb/>minato da monti spessi e lontani &rdquo; (Roma 1664, pag. </s>

<s>40). </s></p><p type="main">

<s>Un'altra difficolt&agrave;, prima che fosse divulgata questa nuova osservazione <lb/>del Cassini, si promoveva contro l'esistenza dei monti della Luna, dietro i <lb/>calcoli galileiani, dai quali risultando essere quegli stessi monti quasi cento <pb xlink:href="020/01/952.jpg" pagenum="395"/>volte pi&ugrave; grandi dei terrestri, non parevano aver possibile proporzione a un <lb/>corpo cos&igrave; esile. </s>

<s>&ldquo; Tantum pondus, scriveva il Vossio nel Trattato <emph type="italics"/>De lucis <lb/>natura,<emph.end type="italics"/> in tam exili corpore, si Telluris vastitatem respiciamus, cum nul&shy;<lb/>lam prorsus rationem habere videatur, non immerito multos promovit ut <lb/>dubitarent de hoc phaenomeno &rdquo; (Amstelodami 1662, pag. </s>

<s>46). </s></p><p type="main">

<s>Lo stesso Vossio fu che risolse una siffatta difficolt&agrave;, dimostrando che <lb/>le misure prese da Galileo venivano esagerate dalle refrazioni, dagli effetti <lb/>delle quali liberando quelle stesse misure, cred&egrave; di averle avute cos&igrave; giuste <lb/>e cos&igrave; bene proporzionate, da doverne concludere: &ldquo; Quanta igitur differen&shy;<lb/>tia est totius Telluris ad totam Lunam, tanta quoque est differentia inter <lb/>montes terrestres et lunares &rdquo; (ibi, pag. </s>

<s>48). </s></p><p type="main">

<s>Lasciando addietro quel che di meno approvato &egrave; nelle persuasioni del <lb/>Vossio, non pu&ograve; Galileo, che ammetteva allora l'esistenza di un'ammosfera <lb/>densa intorno alla Luna, andare in tutto scusato dalla censura dell'Ottico <lb/>olandese. </s>

<s>L'esistenza di quella ammosfera era stata dimostrata dal Moestlin <lb/>nella Disputazione <emph type="italics"/>De passionibus Planetarum,<emph.end type="italics"/> edita in Tubinga nel 1605, <lb/>sul principale argomento delle rifrazioni subite dalle Stelle presso a toccare <lb/>il lembo del disco lunare, e attribuiva pure a un effetto di rifrazione attra&shy;<lb/>verso a una tale sfera vaporosa, il vedersi la Luna nuova chiusa in un cer&shy;<lb/>chio notabilmente minore della circonferenza della sua splendida falce. </s>

<s>Que&shy;<lb/>ste medesime dottrine, apprese dal Moestlin, le professava Galileo nel Nunzio <lb/>Sidereo, dove dice che dell'essere veramente il globo lunare circondato da <lb/>vapori, &ldquo; signum est quod pars Lunae lumine perfusa amplioris circumfe&shy;<lb/>rentiae apparet quam reliquum orbis tenebrosi &rdquo; (Alb. </s>

<s>III, 69). </s></p><p type="main">

<s>Il Keplero per&ograve;, in questa parte men ossequioso al proprio maestro di <lb/>quel che non si fosse mostrato Galileo, accennando, nell'Astronomia ottica, <lb/>al fatto che &ldquo; in prima vel ultima phasi Lunae cornu lucidum longe am&shy;<lb/>pliori circulo claudi videtur quam reliquum corpus lumine Telluris illustra&shy;<lb/>tum et clarissime conspicuum &rdquo; (edit. </s>

<s>cit., pag. </s>

<s>217) aveva detto che questo <lb/>e simili altri fenomeni &ldquo; ex retina tunica trahunt originem &ldquo; perch&egrave; in essa <lb/>non solamente si ampliano, ma quasi si moltiplicano le specie del rilucente <lb/>&ldquo; et id videtur esse vel propter rugas uveae, quae noctu, cum Lunam in&shy;<lb/>tuemur, dilatatur et in se, inque rugas suas coit, vel propter hiatus cilia&shy;<lb/>rium processuum &rdquo; (ibi, pag. </s>

<s>217). </s></p><p type="main">

<s>Vedendo poi come Galileo, invece che all'irradiazione avventizia pro&shy;<lb/>dotta sulla retina, avesse col Moestlin attribuito il fenomeno alle rifrazioni <lb/>nell'orbe vaporoso della Luna, lo stesso Keplero, nella Dissertazione sul <lb/>Nuncio Sidereo, cos&igrave; conferma contro ambedue la verit&agrave; della sua prima <lb/>sentenza: &ldquo; Verum pace vestra mihi liceat ego, etsi aerem Lunae concedo, <lb/>tamen super hoc experimento maneo in sententia: lumen hinc Lunae inde <lb/>Stellae de die etiam se se in oculo ampliare, locumque partis tenebrosae <lb/>carpere, et ea minuita lucida magna putatur &rdquo; (Alb. </s>

<s>V, 423). </s></p><p type="main">

<s>Rimasto a queste ragioni persuaso Galileo, ripudi&ograve; l'opinion moestli&shy;<lb/>niana professata nel <emph type="italics"/>Nuncio,<emph.end type="italics"/> per rivolgersi a questa kepleriana, intorno alla <pb xlink:href="020/01/953.jpg" pagenum="396"/>quale e a'generali effetti delle irradiazioni ascitizie, filosofando al Griember&shy;<lb/>ger, cos&igrave; gli scriveva nel 1611 il d&igrave; primo di Settembre: &ldquo; Ora applicando <lb/>queste considerazioni al nostro proposito, dico che la Luna illuminata dal <lb/>Sole s'irraggia ed incapella di fulgori ella ancora, ma non tanto quanto <lb/>Venere, per esser pi&ugrave; di quella remota dal Sole, e perch&egrave; la sua capella&shy;<lb/>tura non solamente &egrave; pi&ugrave; corta di quella di Venere, ma &egrave; aggiunta ed at&shy;<lb/>taccata intorno a un grandissimo globo, che tale, per la sua vicinanza, ci si <lb/>rappresenta il Corpo lunare, e quindi &egrave; che la figura di essa Luna, non <lb/>solo tra la sua irradiazione non si smarrisce, ma pochissimo e quasi insen&shy;<lb/>sibilmente si altera, e solamente si vede che la circonferenza della parte <lb/>illuminata alquanto si eleva sopra la circonferenza della parte oscura, sicch&egrave; <lb/>questa pare termine di un cerchio minore e quella di uno alquanto mag&shy;<lb/>giore, e questo apparente ricrescimento della parte lucida sopra la oscura <lb/>non &egrave; altro che la irradiazione ascitizia &rdquo; (Alb. </s>

<s>III, 167). </s></p><p type="main">

<s>Ne'<emph type="italics"/>Dialoghi<emph.end type="italics"/> per&ograve;, dove Galileo torna a svolgere ampiamente il sog&shy;<lb/>getto della Luna, non tocca di questo fenomeno, forse per non aver solen&shy;<lb/>nemente a ritrattare ci&ograve; che prima aveva detto nel <emph type="italics"/>Nunzio,<emph.end type="italics"/> ond'&egrave; che il <lb/>Castelli, il quale era allora tutto intorno a meditar su que'Dialoghi. </s>

<s>&ldquo; Mi <lb/>pare d'avere osservato (scriveva allo stesso Autore, quasi per supplire al <lb/>difetto) che la Luna intorno alle congiunzioni si mostri assai maggiore di <lb/>diametro, considerata la grandezza del suo disco in riguardo alla parte illu&shy;<lb/>minata.... e questo eccesso mi pare tanto grande, che senza scrupolo si <lb/>pu&ograve; affermare che ancora la Luna illustrata dal Sole mostra la irradiazione <lb/>avventizia non meno degli altri pianeti &rdquo; (Alb. </s>

<s>IX, 273). </s></p><p type="main">

<s>Nel <emph type="italics"/>Discorso<emph.end type="italics"/> poi <emph type="italics"/>sopra la vista,<emph.end type="italics"/> riscontrandosi colle medesime dottrine <lb/>insegnate gi&agrave; dal Keplero, il Castelli ripete ch'entrando i raggi della luce <lb/>nell'occhio &ldquo; non solo conturbano la tunica retina, ma le parti della me&shy;<lb/>desima retina a loro contigue, adiacenti e circonfuse, e cos&igrave; ci fanno appa&shy;<lb/>rire l'oggetto maggiore di quello che apparire dovrebbe &rdquo; (Bologna 1669, <lb/>pag. </s>

<s>18). Dietro questo principio spiega, insiem con parecchi altri fenomeni <lb/>curiosi e dipendenti dall'irradiazione, in che modo la Luna &ldquo; ci apparisce <lb/>terminata da una circonferenza di cerchio maggiore notabilmente che quella <lb/>rimanente che non &egrave; ancora tocca dai raggi del Sole, la qual rimanente <lb/>mostra di esser terminata da circonferenza di cerchio notabilmente minore <lb/>della circonferenza delle corna risplendenti &rdquo; (ivi, pag. </s>

<s>18). </s></p><p type="main">

<s>Fra le apparenze lunari descritte nel Nunzio Sidereo, oltre a quelle <lb/>delle quali s'&egrave; detto, n'&egrave; una, che fece pi&ugrave; lungamente dell'altre dubitare <lb/>i Saggi, e che concerne quella luce di color cinereo, della quale, presso alle <lb/>congiunzioni, si vede essere leggermente aspersa la faccia tenebrosa della <lb/>luna. </s>

<s>Di quel dubbio converrebbe ora narrar la storia, ma perch&egrave;, per una <lb/>certa sua particolare importanza, siam consigliati di trasferire la narrazione <lb/>al paragrafo seguente, termineremo questo dicendo in qual vario modo ri&shy;<lb/>spondessero gli Astronomi al quesito dell'apparente maggior grandezza della <lb/>Luna all'orizzonte. </s></p><pb xlink:href="020/01/954.jpg" pagenum="397"/><p type="main">

<s>Vedemmo altrove ci&ograve; che ne pensasse in tal proposito il Fracastoro, e <lb/>in modo simile a quel di lu&igrave;, Galileo. </s>

<s>Il Cartesio diceva ch'essendo per la <lb/>pi&ugrave; gran mole de'vapori interposti, la Luna e il Sole e gli astri all'oriz&shy;<lb/>zonte di raggio men vivi, son ricevute le loro immagini dentro a maggior <lb/>ampiezza di pupilla, e perci&ograve; mostran pi&ugrave; grandi. </s>

<s>Questa si fu pure l'opi&shy;<lb/>nion del Gassendo, il quale, nella celebre lettera delle ombre, cos&igrave; scriveva <lb/>a Gabriele Naudeo: &ldquo; Heinc dici posse videtur primo Solem humilem oculo <lb/>spectatum ideo apparere maiorem, quam dum altius egreditur, quia, dum <lb/>vicinus est horizonti, prolixa est series vaporum, atque adeo corpusculorum <lb/>quae Solis radios ita retundunt, ut oculus minus conniveat, et pupilla quasi <lb/>umbrefacta longe magis amplificatur quam dum Sole multum elato rari va&shy;<lb/>pores intercipiuntur, Solque ipse ita splendescit ut pupilla in ipsum spectans <lb/>contractissima efficiatur. </s>

<s>Nempe ex hoc esse videtur cur visibilis species, ex <lb/>Sole procedens et per pupillam amplificatam intromissa in retinam, amplio&shy;<lb/>rem in illa sedem occupet, maioremque proinde creet Solis apparentiam, <lb/>quam dum per contractam pupillam eadem intromissa contendit &rdquo; (Opera, <lb/>T. III, Opuscula, Lugduni 1658, pag. </s>

<s>421). </s></p><p type="main">

<s>Il Vossio per&ograve; fu de'pi&ugrave; liberi e de'pi&ugrave; solleciti a notar contro i Car&shy;<lb/>tesiani come il creder che la grandezza delle immagini vada a proporzion <lb/>della grandezza della pupilla, era un errore dimostrato dal fatto della Ca&shy;<lb/>mera oscura. </s>

<s>&ldquo; Sive enim patulum, sive angustum fuerit cubiculi foramen, <lb/>aequali tamen magnitudine obiecta quaevis in opposito linteo, seu pariete <lb/>depinguntur &rdquo; (De nat. </s>

<s>lucis. </s>

<s>cit., pag. </s>

<s>75). </s></p><p type="main">

<s>Il curioso fenomeno richiam&ograve; a s&egrave; lo studio non de'soli Astronomi, ma <lb/>e degli Antropologi, i pi&ugrave; giudiziosi de'quali concorsero insomma in ci&ograve; che, <lb/>nel sopra citato Discorso, a scoprire altri simili inganni della vista, aveva <lb/>detto il Castelli. </s>

<s>Fermato il principio che sempre nel giudicar della gran&shy;<lb/>dezza di un oggetto ci riferiamo alla grandezza di un altro oggetto a noi <lb/>noto, ne fece una leggiadra applicazione una sera in Roma, essendo lungo <lb/>il Tevere a spasso con alcuni signori e letterati amici suoi, mentre che dal&shy;<lb/>l'Aventino spuntava la Luna piena. </s>

<s>Domandato ad uno di costoro quanto la <lb/>gli paresse grande, veduta sull'orlo del monte, gli par&ograve; innanzi agli occhi <lb/>il suo cappello per modo, che venisse il disco lunare quasi a toccare la <lb/>tesa, sulla quale disse maravigliato comparirgli assai men grande di prima. </s>

<s><lb/>Dietro questa esperienza, ripetuta anche dagli altri via via &ldquo; tutti confes&shy;<lb/>sarono che, mentre noi paragoniamo la Luna col monte, ed apparendoci oc&shy;<lb/>cupare un tratto di esso stimato da noi quattro o cinque braccia, ancora la <lb/>Luna veniva stimata di quella grandezza. </s>

<s>Ma quando, coperta la veduta del <lb/>colle, la medesima Luna era paragonata e riferita all'ala del cappello, che <lb/>corrispondeva alla Luna, veniva stimata tanto minore, ed in ogni modo, con&shy;<lb/>siderando quello che operava la Luna nel nostro occhio sopra la retina, im&shy;<lb/>pressionandola con la sua immagine, sempre ci doveva fare sopra di essa le <lb/>immagini eguali per l'appunto &rdquo; (pag. </s>

<s>31). </s></p><pb xlink:href="020/01/955.jpg" pagenum="398"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Fu il Venturi il primo a richiamar l'attenzione di chi sarebbe per <lb/>scriver la storia dell'Astronomia sopra una nota lasciata da Leonardo da <lb/>Vinci in un suo Manoscritto contrassegnato F: nota che cos&igrave; dice: &ldquo; La <lb/>Terra non &egrave; punto situata nel mezzo dell'orbita del Sole, n&egrave; nel mezzo del <lb/>mondo: ella &egrave; nel mezzo de'suoi elementi che sono a lei associati e ade&shy;<lb/>renti. </s>

<s>Per un uomo che fosse nella Luna, quando nella notte ella &egrave; col Sole <lb/>al di sotto del nostro orizzonte, la Terra e l'oceano produrrebbero sulla <lb/>Luna, a somiglianza del Sole, il medesimo effetto che ella produce sulla <lb/>Terra. </s>

<s>&rdquo; </s></p><p type="main">

<s>Un tale pensiero per&ograve; balenato fra le tante altre mirabili speculazioni <lb/>del Nostro, e rimasto per cos&igrave; lungo tempo nascosto, era in Germania rifio&shy;<lb/>rito nella mente del Moestlin, e come un giovane arbusto dal natio vasello <lb/>l'avea il Keplero trasposto nel campo della scienza ad assodarvi le sue ra&shy;<lb/>dici e a distendere al largo l'ubertosa sua chioma. </s>

<s>Il decimo paragrafo del <lb/>Cap. </s>

<s>VI dell'Astronoma Ottica s'intitola <emph type="italics"/>De illustratione mutua Lunae et <lb/>Terrae,<emph.end type="italics"/> dove, dopo di aver dimostrato che quell'albor cinereo di che si vede <lb/>aspersa ne'primi e negli ultimi giorni la faccia tenebrosa della Luna, non <lb/>pu&ograve; attribuirsi n&egrave; all'essere ella diafana, come dicevano alcuni, n&egrave; al venir <lb/>illuminata da'riflessi di Venere, come volevano altri. </s>

<s>&ldquo; Caeterum veram <lb/>causam, soggiunge, Moestlinus praeceptor meus primus quod sciam invenit, <lb/>meque et totum suum auditorium ante 12 annos docuit, et anno 1596 <lb/>in <emph type="italics"/>Disputatione de ecclipsibus,<emph.end type="italics"/> thesibus 21, 22, 23, pubblice explicavit &rdquo; <lb/>(Edit. </s>

<s>cit., pag. </s>

<s>254). E soggiunge appresso le testuali parole del Moestlin <lb/>usate a dimostrare il suo assunto, la conclusion del quale &egrave; la seguente: <lb/>&ldquo; Dicimus ergo Terram corusco suo, a Sole sibi immisso lumine, opacitatem <lb/>sive noctem in lunari corpore non minus irradiare, quam vicissim, prorsus <lb/>simili modo, Luna plena suis a Sole acceptis radiis nostras in Terra noctes <lb/>illustrat &rdquo; (ibi, pag. </s>

<s>255). </s></p><p type="main">

<s>Nonostante che il problema astronomico avesse avuto cos&igrave; dal Moestlin <lb/>la sua risoluzione completa, e che il Keplero l'avesse cos&igrave; solennemente dif&shy;<lb/>fuso e dottamente illustrato, Galileo nel suo Nunzio Sidereo lo propone come <lb/>cosa che fosse allora apparita nel mondo nuova, e da nessun altro, prima <lb/>di lui, insegnata. </s>

<s>&ldquo; Hic mirabilis fulgor non modicam Philosophantibus in&shy;<lb/>tulit admirationem, pro cuius causa afferenda alii alia in medium protule&shy;<lb/>runt &rdquo; (Alb. </s>

<s>III. 71). Fra queste diverse cause non annovera altro che le <lb/>false per confutarle, tacendo che tra-que'filosofanti, da'quali era stato pre&shy;<lb/>ce<gap/>uto, avevano alcuni prima di lui dimostrata la causa, ch'egli pure ap&shy;<lb/>prova per vera, e parecchi anni prima con autorevole magisterio l'avevano <lb/>gi&agrave; divulgata. </s></p><pb xlink:href="020/01/956.jpg" pagenum="399"/><p type="main">

<s>Di qui &egrave; che il Keplero non pot&egrave; tenersi nella Dissertazione sul Nuncio <lb/>Sidereo di rivendicare al Moestlin e a s&egrave;, su Galileo, il merito d'aver, fra <lb/>tanti errori, dimostrato per i primi la vera origine del candor della Luna, e <lb/>da quel sincero uomo ch'egli era pronunziava in faccia a Galileo queste <lb/>libere parole: &ldquo; Quod vero demonstrationem attinet, quae ostendit hoc lu&shy;<lb/>men ex nostra Tellure effundi, ea iam a viginti annis eoque amplius fuit <lb/>pene Moestlinum, ex cuius doctrina illam transtuli in meam Astronomiae <lb/>partem opticam, cap. </s>

<s>VI, num. </s>

<s>10, fol. </s>

<s>252, plenissimo tractatu: ubi easdem <lb/>etiam opiniones, quod lumen hoc sit a Sole vel a Venere tecum eodem modo <lb/>refuto, nisi quod hanc ultimam merito suo, paulo quam tu mollius excipio &rdquo; <lb/>(Alb. </s>

<s>V, 423). </s></p><p type="main">

<s>Se fosse stato Galileo trattato a quel modo, ch'egli tratt&ograve; il Moestlin e <lb/>il Keplero, avrebbe, come sempre fece anche per pi&ugrave; leggere cagioni, messo <lb/>a romore il mondo: eppure il buono e generoso Alemanno si content&ograve; di <lb/>rinfacciargli quelle parole, per amore e per giustizia del vero, lasciando del <lb/>resto libero Galileo d'esercitar sue arti per consolidarsi nell'usurpato pos&shy;<lb/>sesso. </s>

<s>Lo consolid&ograve; poi nel Dialogo del Mondo, e tanto ben quell'arti se&shy;<lb/>condarono le sue intenzioni d'apparir primo a dir la causa vera della luce <lb/>cinerea, che lui solo fecero oggetto di plauso gli amici, lui solo fecero segno <lb/>di contradizione i nemici. </s></p><p type="main">

<s>Ne porge una singolar prova di questo fatto il peripatetico Fortunio <lb/>Liceti, il quale, cogliendo l'occasione di trattar nel cap. </s>

<s>L del suo Liteo&shy;<lb/>sforo, <emph type="italics"/>De Lunae suboscura luce prope coniunctiones,<emph.end type="italics"/> pens&ograve; di dover asse&shy;<lb/>gnarne altra pi&ugrave; ragionevole causa da quella ch'ei giudic&ograve; essere stata fal&shy;<lb/>samente proferita da Galileo. </s>

<s>&ldquo; Primum existimo lumen illud obscurum non <lb/>esse Solare tunc a Terra revibratum in lunarem superficiem, sed, si qui&shy;<lb/>dem Luna lucem aliquam habet in se congenitam, coniunctum quid ex im&shy;<lb/>becilla Lunae luce nativa et lumine Solis in ipsam repercusso, reflexoque <lb/>ab aetheris alti partibus, lunare corpus ambientibus &rdquo; (Alb. </s>

<s>III, 184). </s></p><p type="main">

<s>Avuta Galileo notizia di questo suo nuovo contradittore, domand&ograve; con&shy;<lb/>siglio al Renieri se fosse bene rispondergli, ed ebbe da Genova, in una let&shy;<lb/>tera del d&igrave; 17 Febbraio 1640, queste parole: &ldquo; Giudico dunque bene che <lb/>V. S. E., mentre non venghino in campo argomenti pi&ugrave; saldi, possa lasciar <lb/>la briga di rispondere; che se pur la non vuole lasciar cos&igrave; trascorrer tal <lb/>opra senza replica, mi offerisco di farlo io a capo per capo coll'ordinario <lb/>seguente e mandarne a V. S. E. la lettera acciocch&egrave;, se giudicher&agrave; che io <lb/>abbia interamente sodisfatto a questo Signore, gli mandi la mia risposta &rdquo; <lb/>(MSS. Gal., P. III, T. VII, c. </s>

<s>180). </s></p><p type="main">

<s>Poco pi&ugrave; di un mese dopo venne a togliere Galileo d'ogni incertezza <lb/>una lettera scrittagli da Pisa dal principe Leopoldo, dove dicendo di aver <lb/>veduto il libro <emph type="italics"/>De lapide bononiensi<emph.end type="italics"/> e di avervi letti alcuni argomenti contro <lb/>quel che del candor lunare avea detto ne'<emph type="italics"/>Massimi Sistemi,<emph.end type="italics"/> desiderava, per <lb/>dar causa al suo ingegno d'insegnar qualche cosa di nuovo &ldquo; che gli avesse <lb/>scritto il suo pensiero intorno a queste nuove opposizioni &rdquo; (Alb. </s>

<s>VII, 254). </s></p><pb xlink:href="020/01/957.jpg" pagenum="400"/><p type="main">

<s>Non potendo mancare di ubbidire al cenno di S. A. S., come scrisse a <lb/>Daniele Spinola, trovandosi cieco e per vecchiezza debole di forze, con l'aiuto <lb/>degli occhi e della mano di Vincenzio Viviani, allora giovanotto ospite e di&shy;<lb/>scepolo suo, ma a cui Galileo d&agrave; il titolo di <emph type="italics"/>suo caro amico<emph.end type="italics"/> (ivi, pag. </s>

<s>257) <lb/>messe in carta quello, che pochi giorni dopo fu mandato al Principe in <lb/>forma di una Lettera a lui stesso diretta, dentro il mese di Aprile 1640. </s></p><p type="main">

<s>Varie copie manoscritte furono mandate agli amici, dal numero de'quali <lb/>non fu escluso il Liceti, ed egli, tutt'altro che offendersene, espresse a Ga&shy;<lb/>lileo il desiderio di stampar quella Lettera al principe Leopoldo insiem con <lb/>le sue risposte. </s>

<s>Galileo si mostr&ograve; docile in assecondar que'desiderii, ma <lb/>perch&egrave; la scrittura era fatta per metterla sotto gli occhi di quattro o sei, <lb/>ora che si trattava di metterla invece sotto milioni di occhi, voleva gli fosse <lb/>conceduto di rivederla e bisognando ripulirla, e senza punto alterare le cose <lb/>scritte distenderla in altra forma. </s>

<s>Soggiungeva allo stesso Liceti un'altra in&shy;<lb/>tenzione, in mandare ad effetto questa, ed era d'indirizzare a lui medesimo <lb/>la scrittura, se cos&igrave; gli piaceva, aggiungendo qualche altra considerazione <lb/>per ampliargli il campo a risolver ci&ograve; che gli sarebbe opposto (Alb. </s>

<s>VII, 333). <lb/>Accett&ograve; volentieri il Liceti e Galileo, consigliatovi anche dagli amici, strinse <lb/>il patto scrivendo: &ldquo; Piacemi grandemente che ella applauda al mio pen&shy;<lb/>siero di ridurre in altra Lettera le mie risposte, inviandole a lei medesima &rdquo; <lb/>(ivi, pag. </s>

<s>343). </s></p><p type="main">

<s>Dato dunque mano a ridur quella prima Lettera, cos&igrave; dettava al Viviani <lb/>il nuovo invocativo e l'introduzione, sotto quest'altra forma: </s></p><p type="main">

<s>&ldquo; All'Illustriss. </s>

<s>ed Eccell.mo signor Fortunio Liceti, Filosofo eminen&shy;<lb/>tissimo, Galileo Galilei vero e cordiale amico, salute. </s>

<s>&mdash; Appena aveva <lb/>V. S. Ecc.ma finito di mandare alla luce il suo Trattato della Pietra luci&shy;<lb/>fera di Bologna, che ella me ne mand&ograve; una copia, accompagnandola con una <lb/>sua lettera piena di affetti di cortesia, nella quale, in segno della stima che <lb/>ella fa del mio giudizio, in poter librare con giusta lance i momenti della <lb/>dottrina che nel suo Trattato si contiene, mi preg&ograve; che io, con quella filo&shy;<lb/>sofica libert&agrave; che tra gl'indagatori del vero si ricerca, sinceramente gli sco&shy;<lb/>prissi e significassi i miei sensi. </s>

<s>Io, per sodisfare a due debiti, nei quali mi <lb/>sentivo obbligato, risposi immediatamente al primo, che era di renderle le <lb/>debite grazie del regalo fattomi in mandarmi il libro, registrandomi nel nu&shy;<lb/>mero dei primi e suoi pi&ugrave; cari amici. </s>

<s>Quanto all'altro obbligo, che &egrave; di <lb/>eseguire il suo cenno circa il liberamente manifestarle il giudizio, che fo <lb/>sopra la dottrina e i concetti in esso libro racchiusi; mi &egrave; stato forza, ri&shy;<lb/>spetto all'infelicit&agrave; della perduta vista, che al servirmi nel leggere e nello <lb/>scrivere degli occhi e della penna di altri mi necessita; differir fino al pre&shy;<lb/>sente di deporre in carta tutto quello, che ho stimato poter dare sodisfa&shy;<lb/>zione alla domanda &rdquo; (MSS. Gal., P. III, T. VII, c. </s>

<s>110). </s></p><p type="main">

<s>Da questo punto prosegue il Manoscritto per alquante pagine, come <lb/>nella stampa, con la differenza che viene il discorso, invece che all'<emph type="italics"/>Altezza <lb/>Serenissima<emph.end type="italics"/> del principe, rivolto alla <emph type="italics"/>Signoria Eccellentissima<emph.end type="italics"/> del dottore. <pb xlink:href="020/01/958.jpg" pagenum="401"/>La dettatura, con parecchie cancellature e con spessi richiami, veniva da <lb/>Arcetri inviata a Firenze a Vincenzio Galilei, che la riduceva a pulito, cos&igrave; <lb/>raccomandandogli lo stesso Viviani per scritto in fronte a c. </s>

<s>119: &ldquo; Signor <lb/>Vincenzio, V. S. abbia cura ad alcuni richiami e segni, che sono qui nel&shy;<lb/>l'ultimo. </s>

<s>&rdquo; </s></p><p type="main">

<s>La copia a pulito di Vincenzio Galilei non va oltre le due carte 110, 111 <lb/>del citato Volume, e nella dettatura originale si prosegue a ridur la prima <lb/>Lettera, tornando a dirigere il discorso al medesimo principe Leopoldo. </s>

<s>A <lb/>render la ragione di un tal cambiamento soccorre opportuna la seguente let&shy;<lb/>tera, che Mario Guiducci scriveva il di 17 Settembre di quell'anno 1640 <lb/>allo stesso Galileo: </s></p><p type="main">

<s>&ldquo; ...... Io dissi alcuni giorni sono al signor Jacopo Soldani il pen&shy;<lb/>siero di V. S. circa allo scrivere a dirittura al signor Liceti, quanto Ella <lb/>aveva scritto al Serenissimo sig. </s>

<s>principe Leopoldo, di che avendone esso <lb/>dato conto a S. A., ha avuto risposta che le piace il pensiero, ma che avrebbe <lb/>desiderato che V. S. avesse levato dal discorso alcune parole, che appari&shy;<lb/>vano pungenti e piccanti, per non irritare un uomo tanto maledico, come <lb/>in altre occasioni si &egrave; scorto il Liceti. </s>

<s>Risposi che V. S. si sarebbe attenuto <lb/>al pensiero di S. A. quando le fosse stato mostrato le punture, le quali non <lb/>aveva avuto intenzione di mettervi come tali. </s>

<s>E perch&egrave; esso signor Jacopo <lb/>si esibi di notarle, insieme col signor Francesco Nerli, non ho ancora ria&shy;<lb/>vuto la scrittura n&egrave; il libro. </s>

<s>Procurer&ograve; bene di riaverli quanto prima, e ver&shy;<lb/>remo il sig. </s>

<s>Jacopo e io a restituirglieli &rdquo; (ivi, c. </s>

<s>176). </s></p><p type="main">

<s>Quella per&ograve; del principe Leopoldo era una scusa, attraverso alla quale <lb/>voleva far trasparire la sua vera intenzione essere che il Discorso, in qua&shy;<lb/>lunque modo fosse stato ridotto, seguitasse ad esser rivolto, non ad altri <lb/>che a lui. </s>

<s>Poco di poi signific&ograve; pi&ugrave; chiaramente quel suo desiderio, ond'&egrave; <lb/>che Galileo mut&ograve; concetto, scusandosi cos&igrave; col Liceti: &ldquo; Pensavo a quest'ora <lb/>di poter inviar le mie risposte sopra il candore della Luna distese in forma <lb/>di lettera a lei medesimo, e gi&agrave; le avevo quasi ridotte al netto, quando mi <lb/>&egrave; venuto avviso che il Serenissimo principe Leopoldo, alla cui Altezza avevo <lb/>in prima scritto, si maraviglia che io avessi mutato concetto..... Onde io <lb/>reputando a mia somma gloria che il mondo senta una testimonianza del&shy;<lb/>l'essere io in buon grado in grazia di tanto principe, e stimando che il <lb/>medesimo possa accadere a V. S., ho risoluto di ritornare in sulla prima <lb/>maniera di scrivere all'A. S. ma con tessitura alquanto pi&ugrave; ampla, per la <lb/>interposizione di varie mie considerazioncelle &rdquo; (Alb. </s>

<s>VII, 345). </s></p><p type="main">

<s>Queste considerazioncelle furono dettate da Galileo al Viviani a parte, <lb/>con segni di richiamo e colla nota: <emph type="italics"/>per inserirli in luogo opportuno.<emph.end type="italics"/> Ma <lb/>non essendo poi inserite altrimenti, rimasero allora e rimangono tuttavia <lb/>da c. </s>

<s>135-41 nel Manoscritto. </s>

<s>I pi&ugrave; importanti fra que'varii pensieri non <lb/>son forse che due: il primo, nel quale dimostra contro il Liceti essere per <lb/>s&egrave; tenebrosi anche i tre pianeti superiori, come si riferir&agrave; nel seguente no&shy;<lb/>stro capitolo, e l'altro, dove svolge ampiamente un suo concetto accennato <pb xlink:href="020/01/959.jpg" pagenum="402"/>gi&agrave; nel Sistema del Mondo. </s>

<s>Aveva nella Giornata I scritto che la luce se&shy;<lb/>condaria si mostra notabilmente pi&ugrave; viva, quando noi vediam la Luna sul&shy;<lb/>l'alba, che quando si vede in sulla sera, attribuendo la differenza all'esser <lb/>la Luna orientale opposta all'Asia, che ha poco mare e assaissima terra <lb/>&ldquo; dovecch&egrave;, quand'ella &egrave; in occidente, riguarda grandissimi mari, cio&egrave; tutto <lb/>l'Oceano atlantico sino alle Americhe &rdquo; (Alb. </s>

<s>I, 111). </s></p><p type="main">

<s>Rimeditando sopra queste parole il Castelli, a cui era occorso di veder <lb/>la luce secondaria assai cospicua nella Luna vicina al primo quarto, bench&egrave; <lb/>avesse letto nel Nunzio Sidereo che <emph type="italics"/>debilis admodum, et incerta conspici&shy;<lb/>tur,<emph.end type="italics"/> giudic&ograve; che, ritrovandosi la Luna meridionale, dovesse essere illustrata <lb/>da qualche esteso tratto di Terra. </s>

<s>&ldquo; E per&ograve;, scrive queste precise parole a <lb/>Galileo, mi venne in mente che le terre meridionali a noi incognite deb&shy;<lb/>bono essere vastissime province, e che per&ograve; riflettino gagliardo lume nella <lb/>Luna. </s>

<s>Se ho detto qualche sproposito me lo perdoni, perch&egrave; confesso di non <lb/>averci pensato abbastanza &rdquo; (Alb. </s>

<s>X, 244). </s></p><p type="main">

<s>Queste parole scritte il d&igrave; 14 Novembre 1637, richiamarono forse pi&ugrave; <lb/>attentamente il pensiero di Galileo nell'occasion ch'egli ebbe a scrivere in&shy;<lb/>torno al Candore lunare, e fu in ogni modo allora che, riconosciutane l'im&shy;<lb/>portanza, si dette a svolgere quel concetto accennato gi&agrave; nel I Dialogo dei <lb/>Due Massimi Sistemi, dettandolo al Viviani, <emph type="italics"/>per metterlo in luogo oppor&shy;<lb/>tuno,<emph.end type="italics"/> in questa forma: </s></p><p type="main">

<s>&ldquo; Non voglio tacere in questo luogo a V. A. S. certa mia particolare <lb/>osservazione fatta nel candore della Luna, dalla quale resulta una nuova <lb/>molto probabil coniettura a favore del riflesso terrestre, per produrre il can&shy;<lb/>dore, la quale non ha luogo nell'etere ambiente, per il medesimo effetto, e <lb/>l'osservazione &egrave; tale: Avendo io, due o tre giorni avanti il Novilunio, po&shy;<lb/>sta diligente cura quale si rappresenti la chiarezza del candor lunare, men&shy;<lb/>tr'ella surgendo dall'oriente fa di s&egrave; mostra nell'Aurora, e dipoi altro e <lb/>tanto tempo dopo il Novilunio attentamente rimirandola in occidente nel cre&shy;<lb/>puscolo vespertino, parmi aver ritrovato non piccola diminuzione nel suo <lb/>medesimo candore, il quale men vivo si dimostra, ed avendo pregato alcuni <lb/>amici che facciano la medesima osservazione, trovo che concordemente af&shy;<lb/>fermano agli occhi loro dimostrarsi quella medesima differenza, che a'miei <lb/>pi&ugrave; volte dimostrata si era. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora se in questo effetto si trova una tal mutazione, bene &egrave; necessa&shy;<lb/>rio che, nella causa di tale effetto produttrice, mutazione si trovi quanto al <lb/>potere or pi&ugrave; vivamente or meno illuminare. </s>

<s>E se la causa, com'io ho sti&shy;<lb/>mato, &egrave; il riflesso dei raggi solari nella terrestre superficie, converr&agrave; che <lb/>ella or pi&ugrave; or meno risplendente si mostri all'emisferio lunare. </s>

<s>Ed essendo <lb/>che, posta la Luna in oriente, a lei si espone delli due emisferi terrestri <lb/>separati dal nostro meridiano lo orientale, ed all'incontro vede ella posta <lb/>in occidente l'emisfero occidentale; bisognerebbe per mantenimento della <lb/>mia opinione, che il terrestre emisfero orientale pi&ugrave; splendidamente riflet&shy;<lb/>tesse i raggi solari che l'altro emisfero occidentale. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/960.jpg" pagenum="403"/><p type="main">

<s>&ldquo; Questa necessit&agrave; m'indusse a pensare se differenza alcuna potesse <lb/>cadere tra i detti due emisferi, per la quale, con qualche disegualit&agrave;, pro&shy;<lb/>cedesse il loro riflesso. </s>

<s>E veramente assai probabile mi pare che ella por <lb/>vi si possa, regolandoci con quella apparenza che nella Luna si scorge, cio&egrave; <lb/>che la sua superficie non &egrave; per tutto egualmente lucida, ma sono in quella <lb/>sparse molte macchie meno del restante lucide. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La superficie del nostro Globo terrestre &egrave; composta di due parti mas&shy;<lb/>sime, dico dei mari e dei continenti. </s>

<s>Queste percosse dai raggi del Sole non <lb/>egualmente illustrano, ma notabilmente pi&ugrave; illuminano le parti terrene, che <lb/>quelle dell'acqua, per lo che pi&ugrave; potenti saranno i raggi reflessi dalla Terra <lb/>che i reflessi dal mare. </s>

<s>Ora, se noi considereremo qual proporzione abbiano <lb/>in grandezza le parti marittime con le terrestri nell'emisferio orientale; se <lb/>parimenti andremo esaminando quello che accaggia tra i mari e continenti <lb/>dell'emisferio occidentale, troveremo senza dubbio, dell'emisferio orientale <lb/>vastissime essere le campagne terrestri, e minori assai quelle dei mari, e <lb/>nell'altro emisferio troveremo accader tutto l'opposto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Tutta l'Asia, parte vastissima sopra le altre, &egrave; a noi orientale, con <lb/>gran parte dell'Europa e dell'Affrica ancora. </s>

<s>In occidente aviamo sola l'Ame&shy;<lb/>rica, con parte dell'Affrica, e qui sono i mari vastissimi, Atlantico e Paci&shy;<lb/>fico, sommamente pi&ugrave; ampli di quelli che restano verso l'Oriente. </s>

<s>Quan&shy;<lb/>dunque sia vero che il riflesso della Terra superi quello del mare, molto <lb/>probabile coniettura averemo per render ragione del candore pi&ugrave; lucido in <lb/>oriente, che in occidente, della qual differenza non si pu&ograve; referir la causa <lb/>all'etere ambiente la Luna, trovandosi egli in ambedue questi casi egual&shy;<lb/>mente lontano dal Sole &rdquo; (MSS. Gal., P. III, T. VII, c. </s>

<s>141). </s></p><p type="main">

<s>&Egrave; questa senza dubbio una delle pi&ugrave; argute ragioni escogitate da Ga&shy;<lb/>lileo a dimostrar, contro il Liceti, che non pu&ograve; la luce secondaria attribuirsi <lb/>alle rifrazioni de'raggi solari nella sfera vaporosa che circonda la Luna, <lb/>come si producono per un simile effetto i crepuscoli qui sulla Terra, e sa&shy;<lb/>rebbe stato degno anche questo argomento d'esser veramente inserito nella <lb/>Lettera riformata. </s>

<s>Non s'intende perci&ograve; il motivo che consigli&ograve; l'Autore a <lb/>lasciarlo indietro, come non s'intende perch&egrave;, avendo Galileo dettato al Vi&shy;<lb/>viani un altro bel tratto di eloquenza <emph type="italics"/>da inserirsi nel fine dell'opera<emph.end type="italics"/> (ivi, <lb/>c. </s>

<s>136), fosse, come membro disutile, lasciato esso pure indietro fra le bozze <lb/>della scrittura. </s></p><p type="main">

<s>Forse, non essendo questo altro che un riepilogo, pens&ograve; Galileo esser <lb/>l'Opera cos&igrave; breve da non averne il Lettore altrimenti bisogno. </s>

<s>Ma se pro&shy;<lb/>priamente non bisogna a chi tutto per disteso ha letto il Discorso sul can&shy;<lb/>dore lunare, non sar&agrave; disutile il trascriver qui le parole, che lasci&ograve; indietro <lb/>l'Autore, e nelle quali, chi non ha tutta presente alla memoria la Let&shy;<lb/>tera al principe Leopoldo, trova conclusi i principali argomenti galileiani <lb/>contro il Liceti: </s></p><p type="main">

<s>&ldquo; Ora, eccellentissimo mio Signore, facciami grazia di considerare con <lb/>quanta bella analogia si rispondano nella Luna e nella Terra le tre diverse <pb xlink:href="020/01/961.jpg" pagenum="404"/>illuminazioni, le quali tutte, come da un istesso fonte, scaturiscono dal ful&shy;<lb/>gore immenso del lucidissimo Sole, senza il quale n&egrave; queste illuminazioni e <lb/>splendori, n&egrave; quello di qualsivoglia dei pianeti erranti resterebbero al mondo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E prima, essendo perpetuamente uno emisferio della Luna esposto <lb/>alla vista del Sole, viene in ogni sua parte egualmente da quello illustrato. </s>

<s><lb/>L'istesso accade dell'emisferio terrestre: dico di essere illuminato tutto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Oltre a questa massima illuminazione, ce n'&egrave; una parziale e secon&shy;<lb/>daria prodotta nella Terra, e pur dai raggi solari riflessa dalla sfera vapo&shy;<lb/>rosa, la quale essa Terra circonda, e secondo che il Sole si abbassa sotto <lb/>l'orizzonte, quella parte di essi vapori illustrati, che sopra l'orizzonte ri&shy;<lb/>mane, riflette i raggi solari sopra la proprinqua parte della superficie ter&shy;<lb/>restre, ma questa illuminazione non molto addentro si distende, per essere <lb/>l'altezza dei vapori non molta, e la superficie della Terra non piana ma <lb/>sfericamente tuberosa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; A questo risponde una simile illaminazione fatta da quella parte del&shy;<lb/>l'etere ambiente la Luna, che per essere alquanto pi&ugrave; denso del resto, che <lb/>per gl'immensi spazi del cielo si diffond&egrave;; &egrave; potente a riflettere i raggi so&shy;<lb/>lari intorno a quella parte dello emisferio tenebroso della Luna, la quale <lb/>con l'altro suo emisferio illuminato dai raggi primarii del Sole &egrave; conter&shy;<lb/>mina. </s>

<s>Ma tale illuminazione &egrave; assai debole, per esser la parte dell'etere am&shy;<lb/>biente assai meno atta a far la riflessione gagliarda sopra la Luna, che non <lb/>&egrave; la parte molto pi&ugrave; densa dei vapori sopra la Terra, e questa parimente <lb/>non candisce tutto l'emisfero tenebroso, ma solo una parte, che confina <lb/>l'emisfero illustrato dal Sole, e di questo ne aviamo la sensata esperienza <lb/>nelle Ecclissi, mentre che, dopo essersi immersa la Luna nel cono dell'om&shy;<lb/>bra terrestre, e persa la primaria illuminazione de'raggi solari, si vede im&shy;<lb/>mediatamente per qualche tempo biancheggiare alquanto quella parte della <lb/>periferia della Luna, che fu l'ultima a entrar nell'ombra. </s>

<s>Ma tal bianchezza <lb/>tosto si perde nel profondarsi la Luna verso il mezzo del cono tenebroso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ci &egrave; la terza e pure ampla illuminazione, prodotta in Terra pur <lb/>da'medesimi raggi solari reflessi nella Luna, ed inviati allo intero emisfero <lb/>terrestre, il quale non tocco dai raggi solari &egrave; esposto alla vista della splen&shy;<lb/>dida Luna. </s>

<s>A questa ultima totale illuminazione risponde il candore della <lb/>Luna, il quale si vede egualmente diffuso nello emisfero della Luna non <lb/>tocco dai raggi solari, e tal candore amplo e massimo si scorge presso alla <lb/>congiunzione di essa Luna col Sole, nel qual tempo viene opposto alla Luna <lb/>il grande emisfero terrestre illuminato dai raggi solari. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, Eccellentissimo Signore, qual ragione pu&ograve; indurla a volere di <lb/>questo gran candore porne la causa nel medesimo etere ambiente, il quale <lb/>aviamo veduto che pochissima parte della Luna tigne di un debole colore, <lb/>piuttosto plumbeo che argenteo, dovecch&egrave;, quando l'etere ambiente fosse <lb/>potente a produrre l'amplo e assai vivo candore, molto pi&ugrave; vivo ci si rap&shy;<lb/>presenterebbe egli nel campo oscuro della notte, che nello assai ben lucido <lb/>del crepuscolo e dell'aurora? </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/962.jpg" pagenum="405"/><p type="main">

<s>&ldquo; Io non mi posso persuadere che, facendo V. S. col suo perspicacis&shy;<lb/>simo ingegno riflessione sopra questa cos&igrave; bella analogia, non sia per pre&shy;<lb/>stargli l'assenso, e massime che io ho grande opinione che tra i fenomeni, <lb/>che indussero grandissimi Filosofi, e Aristotile stesso sommo tra tutti, a <lb/>concedere gran simpatia e corrispondenza tra la Luna e la Terra, non solo <lb/>la similitudine di figura e della faccia maculosa, quale in essa Luna veg&shy;<lb/>giamo e nella Terra si scorgerebbe, cagionata dai mari e dai continenti, <lb/>quando da luogo tenebroso e molto lontano potessimo vedere la faccia ter&shy;<lb/>restre illuminata, gli avesse indotti; ma molto pi&ugrave; la corrispondenza di que&shy;<lb/>sta triplice illuminazione, che non &egrave; credibile che da Aristotile, tanto sagace <lb/>contemplatore degli effetti di Natura, questo s&igrave; bello e nobile restasse inos&shy;<lb/>servato. </s>

<s>E se io avessi quella pratica in tutti i libri fisiologici di Aristotile, <lb/>e che la memoria mi servisse, come di altri sagaci contemplatori accade, <lb/>non diffiderei di poter, con andar sottilmente rintracciando e conferendo <lb/>questa particola con quella, e quella con quell'altra, accozzar tanti luoghi <lb/>insieme, che io mi ritrovassi scritta questa verit&agrave;, che bene &egrave; ragionevole <lb/>che l&agrave; tutte le verit&agrave; si ritrovino, dove le proposizioni che scaturiscono son <lb/>tutte vere &rdquo; (ivi, c. </s>

<s>136, 37). </s></p><p type="main">

<s><emph type="center"/>.V<emph.end type="center"/></s></p><p type="main">

<s>Nella Digressione fisico-matematica, fatta nel capitolo L del Liteosforo, <lb/>ebbe intenzione il Liceti di trattar della luce suboscura della Luna, non solo <lb/>presso alle congiunzioni, ma <emph type="italics"/>et in deliquis observata.<emph.end type="italics"/> Il singolare fenomeno, <lb/>che tanto frug&ograve; la curiosit&agrave; degli Astronomi, e tanto ne mise in travaglio <lb/>la scienza, vedemmo come non isfugg&igrave; alle argute speculazioni dell'antico <lb/>Plutarco, il quale attribu&igrave; la luce, che rende ancora visibile nelle ecclissi il <lb/>disco lunare, allo splendor delle Stelle che circondano il Sole. </s>

<s>Ma, che pi&ugrave; <lb/>importa alla nostra Storia, non isfuggi quella stessa speculazione al primo <lb/>e vero padre della risorgente Scienza sperimentale in Italia, il quale disse <lb/>esser causa della luce rossiccia, di che si vede aspersa nelle ecclissi la fac&shy;<lb/>cia della Luna, le rifrazioni fatte in mezzo alla nostra ammosfera, che ri&shy;<lb/>torcono i raggi del Sole verso l'asse del cono ombroso, dove vanno talvolta <lb/>a riflettersi anco i vivi splendori di Venere. </s></p><p type="main">

<s>&ldquo; Quod vero Luna nullum ex se habeat lumen, sufficiens inditium est <lb/>nos ipsam tanto magis obscuram videre, quanto magis in cono umbrae Ter&shy;<lb/>rae immergitur, et si eo tempore ipsam videmus rubeo colore affectam, hoc <lb/>enim accidit quia radii Solares undequaque refranguntur a vaporibus ipsam <lb/>Terram circumdantibus, quae quidem refractio fit versus axem coni um&shy;<lb/>brae Terrae, et propterea umbra dicti coni non est aequaliter obscura sed <lb/>tenebrosa. </s>

<s>Circa vero axem ipsius coni, magis quam circa eius circumferen&shy;<lb/>tiam obscuratur, et quia Corpus lunare tale est ut facillime recipiat qua-<pb xlink:href="020/01/963.jpg" pagenum="406"/>lecumque lumen, quod etiam manifeste videtur dum ipse Luna reperitur <lb/>secundum longitudinem inter Solem et Venerem, quod pars Lunae lumine <lb/>Solis destituta a lumine Veneris aliquantulum illustratur, quod ego ipse vidi <lb/>et multis ostendi; propterea, dum ipsa Luna in cono umbrae Terrae repe&shy;<lb/>ritur, adhuc videtur &rdquo; (Speculationum Liber, Venetiis 1599, pag. </s>

<s>257). </s></p><p type="main">

<s>Dopo quasi vent'anni, torn&ograve; a parlar <emph type="italics"/>De rubore Lunae deficientis,<emph.end type="italics"/> in <lb/>Germania, l'altro primo e vero Padre dell'Ottica astronomica, e confutata, <lb/>fra le altre, l'ipotesi di Plutarco, che fosse cio&egrave; quel color rosso dovuto a'ri&shy;<lb/>flessi delle stelle e di Venere &ldquo; nam si sidera Solem circumstantia Lu&shy;<lb/>nam ita pinxinssent, totum eius discum aequaliter sibi obiectum pinxissent <lb/>aequaliter &rdquo; (Kepleri Astron. </s>

<s>pars Optica cit., pag, 276); conclude poi cos&igrave;, <lb/>quasi ripetendo a parole quello, che aveva gi&agrave; scritto il nostro Benedetti: <lb/>&ldquo; Causa vero plane est in refractionibus, ut sit nihil aliud rubor iste quam <lb/>illustratio Lunae a Solis radiis, per aeris densitatem transmissis, et intro <lb/>versus axem umbrae refractis, ut ex sequentibus experimentis clarum eva&shy;<lb/>det &rdquo; (ibi, pag. </s>

<s>274). Quelli esperimenti poi si riducono ai fatti diligente&shy;<lb/>mente osservati in varie ecclissi lunari, e qui dal Keplero stesso descritti. </s></p><p type="main">

<s>Il Liceti per&ograve;, o non conoscesse quelle Speculazioni del Benedetti e <lb/>queste astronomiche osservazioni del Keplero, o conoscendole, non credesse <lb/>di dover approvarle per vere, attribu&igrave; la luce, che fa cospicua la Luna nel&shy;<lb/>l'ombra della Terra, a tutt'altra cagione. </s>

<s>&ldquo; Si tamen ex sese Luna penitus <lb/>est obscura et opaca, perinde ac Terra, uti censet Vir clariss, (Galilaeus), <lb/>eam cum Lapide bononiensi magnam et nobilem analogiam habere censeo, <lb/>ut absente Sole ac in umbra, seu Terrae dum deficit, seu sua, dum Soli <lb/>coniungitur in parte lumine Solari non tacta; conservet aliquamdiu lucem, <lb/>quam prius a Sole susceperat &rdquo; (Alb. </s>

<s>III, 188). </s></p><p type="main">

<s>Fu a questa occasione che Galileo, per confutare il Liceti, si dette di <lb/>proposito a rivolgere il pensiero sopra la causa di quel rosso ne'deliqui di <lb/>Luna; causa, intorno alla quale interpellato vent'anni prima dal Cavalieri <lb/>(Alb. </s>

<s>IX, 10), avea col tacere confessato di non saperla. </s>

<s>Di quelle specula&shy;<lb/>zioni poi, che non ebbero nulla n&egrave; di peregrino n&egrave; di nuovo, si compiacque <lb/>al solito Galileo magnificandole al Renieri, il quale rispondeva cos&igrave; in un <lb/>poscritto di lettera: &ldquo; Se V. S. E. mi avviser&agrave; di qualche bel problema in&shy;<lb/>torno a'lumi diretti e riflessi, ecclissi lunari e solari, come mi scrive di <lb/>avere avvertito, mi far&agrave; sommo favore &rdquo; (MSS. Gal., P. III, T. VII, c. </s>

<s>180). </s></p><p type="main">

<s>L'avviso per&ograve; non fu dato allora, perch&egrave; voleva Galileo tutto insieme <lb/>e perfetto far apparire al mondo il suo parto, ma intanto il Renieri stesso <lb/>lo preveniva nelle recondite speculazioni, scrivendogli, a provar che il can&shy;<lb/>dor della Luna era dovuto ai riflessi della Terra, un concetto, che poi Ga&shy;<lb/>lileo benignamente fece suo (Alb. </s>

<s>III, 224), e ricordandogli, rispetto al <lb/>rosso lunare, ci&ograve; che nell'Ottica astronomica aveva insegnato il Keplero. <lb/></s>

<s>&ldquo; Se debbo dire, un tal mio pensiero, scriveva da Genova il d&igrave; 29 Feb&shy;<lb/>braio 1640, mentre mi ricordo che alcuni hanno stimato la Luna corpo <lb/>diafano, perch&egrave; nella solare ecclissi notarono il disco di essa sparso di <pb xlink:href="020/01/964.jpg" pagenum="407"/>qualche luce, v&ograve; dubitando che tal luce fosse per appunto quella, che <lb/>dalle parti della Terra non ecclissata col&agrave; venia ripercossa. </s>

<s>Non &egrave; dunque <lb/>la luce secondaria del disco lunare altro che il riflesso de'raggi del Sole, <lb/>col&agrave; dalla Terra ripercossi: n&egrave; perch&egrave; nell'ecclisse della Luna ella resti <lb/>sparsa di qualche luce, pu&ograve; paragonarsi con la pietra di Bologna, perch&egrave; <lb/>tal lume, come bene avvert&igrave; il Keplero, vien cagionato da'raggi del Sole, <lb/>che battendo nell'aria contermina alla Terra si ripiegano e riflettono verso <lb/>la Luna, e di tal luce la spargono, come nella seguente figura pu&ograve; vedersi. </s>

<s>&rdquo; <lb/>E qui, a tergo della carta 179 del citato Manoscritto, vedesi, con fedel co&shy;<lb/>pia, disegnato l'iconismo impresso a pag. </s>

<s>279 dell'Ottica astronomica ne'Pa&shy;<lb/>ralipomeni a Vitellione. </s></p><p type="main">

<s>Questo, suggerito cos&igrave; a Galileo dal Renieri, sarebbe stato insomma il <lb/>modo, che le tradizioni scientifiche porgevano, a confutar l'error del Liceti. </s>

<s><lb/>Ma Galileo non conosce maestri: la confutazione al Liteosfore &egrave; un <emph type="italics"/>pensiero <lb/>suo nuovo<emph.end type="italics"/> (Alb. </s>

<s>VII, 25). </s></p><p type="main">

<s>Giacch&egrave; dunque &egrave; aperto il cervel di Minerva, da cui &egrave; uscita fuori <lb/>questa bella novit&agrave; di pensiero, ascoltiamo: Venere, Giove e la Canicola <lb/>concorrono insieme, spento il Sole, a illuminare la Luna (Alb. </s>

<s>III, 213, 14). <lb/>Questa novit&agrave; per&ograve; era tanto vecchia, che risaliva a Plutarco, la ipotesi del <lb/>quale si disse come fosse, con invitte ragioni, convinta di falsit&agrave; dal Keplero. </s></p><p type="main">

<s>Or perch&egrave; troppo importa a noi conoscer, meglio di quel che non si <lb/>sia fatto fin qui, un uomo, ch'&egrave; il principale attore di questa Storia, non <lb/>si pu&ograve; senza considerazione passar sopra a certi fatti, che hanno dello straor&shy;<lb/>dinario, anzi del maraviglioso. </s>

<s>Chi altri, dopo la Disputazione del Moestlin <lb/>cos&igrave; solennemente bandita ne'Paralipomeni a Vitellione, e dopo le calme si, <lb/>ma forti rivendicazioni fatte a s&egrave; e al suo proprio maestro dall'Autor della <lb/>Dissertazione sul Nuncio Sidereo, avrebbe osato mai di rinfacciare pubbli&shy;<lb/>camente a que'filosofi, de'quali si ripetevano le dottrine, che <emph type="italics"/>per tanti secoli <lb/>prima di lui erano rimaste occulte agl'ingegni speculativi?<emph.end type="italics"/> (Alb. </s>

<s>III, 203). <lb/>Eppure Galileo lo fece, e principi e privati gli fecero plauso. </s></p><p type="main">

<s>Chi altri mai si sarebbe potuto cos&igrave; compiacentemente gloriare delle <lb/>falsit&agrave; fotometriche, scritte nella Lettera sul Candore lunare, rifiutando, come <lb/>vedemmo altrove, quella vera legge di Fotometria dimostrata dal Castelli? </s>

<s><lb/>o chi altri sarebbesi potuto lusingar di destare ammirazione in chi legge, <lb/>per venire a ripetere, dopo Plutarco e il Benedetti, un errore cos&igrave; facil&shy;<lb/>mente confutato dall'osservazione de'fatti? </s>

<s>Eppure quelle compiacenze e <lb/>queste lusinghe albergarono nel petto di Galileo, come lo attesta il sopra <lb/>citato poscritto di lettera del Renieri. </s></p><p type="main">

<s>Che si vorr&agrave; dunque dire? </s>

<s>che gli occhi, riguardando in quel che a <lb/>loro pareva un Sole, rimanessero abbarbagliati per modo, da non vedere <lb/>altro all'intorno? </s>

<s>Ma s'&egrave; cosa veramente maravigliosa la virt&ugrave; ch'ebbe Ga&shy;<lb/>lileo di apparire unico sole a illuminare il mondo, non fa minor maraviglia <lb/>a vedere occhi s&igrave; acuti pigliare un comun fosforo di terra per un divino <lb/>raggio celeste. </s></p><pb xlink:href="020/01/965.jpg" pagenum="408"/><p type="main">

<s>Comunque sia, non erano un Baliani, un Cavalieri, un Renieri, per esem&shy;<lb/>pio, cos&igrave; abbarbagliati e ritenuti da non conoscer, bench&egrave; attraverso a un <lb/>velo teso, gli errori di Galileo, e da non insorgere, bench&egrave; attraverso a <lb/>un vallo opposto, contro ci&ograve; che indebitamente pretendeva il loro ammirato <lb/>amico e venerato maestro, da cui, quando non dimostrava il vero, diserta&shy;<lb/>vano in punta di piedi. </s></p><p type="main">

<s>Abbiam nominato il Baliani, il Cavalieri e il Renieri, perch&egrave; furono <lb/>questi de'primi a ricevere la Lettera sul Candore lunare, facendo Galileo <lb/>gran conto della loro approvazione. </s>

<s>Il Baliani, cos&igrave; libero e arguto in dire <lb/>il suo parere all'Autor del Saggiatore, de'Massimi Sistemi e delle Due Nuove <lb/>Scienze, quand'&egrave; richiesto della sua opinione su quella Lettera al principe <lb/>Leopoldo, v&agrave; per le generali, contento di plaudire al vero, da Galileo dimo&shy;<lb/>strato contro l'error del Licet&igrave;. </s></p><p type="main">

<s>Non &egrave; a passare inosservato, quel che dice della soluzione data dallo <lb/>stesso Liceti al famoso problema delle ombre. </s>

<s>Quella soluzione del Peripa&shy;<lb/>tetico di Bologna si riduce insomma all'altra del Gassendo, il quale, sul <lb/>fondamento che gli astri all'orizzonte hanno, per la maggior mole de'va&shy;<lb/>pori interposti, difetto di luce, ossia soverchianza d'ombra; ne conclude <lb/>perci&ograve; non dover far maraviglia se le ombre, in quel caso, ci appariscon <lb/>maggiori. </s>

<s>Al Baliani parve vana questa risposta &ldquo; perch&egrave; io (in tal modo <lb/>si esprime con Galileo) non so discerner nell'aria del mezzod&igrave; vivezza di <lb/>luce, che faccia cotal effetto: &egrave; falso il quesito, perch&egrave; l'ombra mandata <lb/>dal medesimo corpo nella medesima lontananza, io stimo che sia la stessa <lb/>ad ogni ora, cos&igrave; dettandomi la ragione &rdquo; (MSS. Gal., P. III, T. VII, c. </s>

<s>171). </s></p><p type="main">

<s>Il Cavalieri ingenuamente rispondeva che s'era vero la Luna talvolta <lb/>nell'ecclissi scomparir tutta, non vedeva come poter altrimenti salvare il <lb/>fatto, che ammettendo l'ipotesi di Galileo. </s>

<s>&ldquo; Mi &egrave; ben giunta nuova la ra&shy;<lb/>gione del vedersi, ne'totali ecclissi lunari, essa Luna talvolta e talvolta no, <lb/>perch&egrave; io credeva prima che sempre si vedesse, come pi&ugrave; volte ho speri&shy;<lb/>mentato, e che quel lume fosse cagionato dai raggi del Sole refratti nel&shy;<lb/>l'ammosfera terrestre. </s>

<s>Ma essendo vero che talvolta resti invisibile la Luna, <lb/>conosco che di tale effetto non pu&ograve; esser cagione tale refrazione, che sem&shy;<lb/>pre &egrave;, o almeno tale lume deve restare insensibile, e perci&ograve; resta che sieno <lb/>veramente cagioni di tal lume Venere, Giove e il Cane principalmente, tro&shy;<lb/>vandosi dalla banda del Sole &rdquo; (Alb. </s>

<s>X, 388). </s></p><p type="main">

<s>Avrebbe volentieri applaudito anche il Renieri a un tal concetto, se l'ar&shy;<lb/>gomento fattogli dal Keplero avverso, e le sue proprie osservazioni non fossero <lb/>venute a metterglielo in dubbio. </s>

<s>&ldquo; Ho notato (scriveva il d&igrave; 13 Aprile 1640 <lb/>allo stesso Galileo) il suo pensiero circa di quel rossore che ha la Luna nelli <lb/>Ecclissi, e sommamente mi piace. </s>

<s>Perch&egrave; in vero, se Venere a noi comu&shy;<lb/>nica talvolta tanta luce, che &egrave; atta a cagionar l'ombra; perch&egrave; non lo dovr&agrave; <lb/>fare, nello stesso modo, nella Luna? </s>

<s>Una sola cosa mi d&agrave; un poco di fa&shy;<lb/>stidio, ed &egrave; la variazione di colori stravagantissimi, ed io ho osservato nel&shy;<lb/>l'Ecclisse dell'anno 1635, a'27 di Agosto, dove appariva la Luna tinta di <pb xlink:href="020/01/966.jpg" pagenum="409"/>macchie pallide, pavonazze e rosse in modo, che mi faceva sovvenire ci&ograve; <lb/>che scrive Cornelio Gemma, <emph type="italics"/>Cosmocritices Lib. </s>

<s>II, Anno 1569, Martii die <lb/>tertia, mane hora tertia, Phoebin vidi ecclipsim horrendam passam diris <lb/>coloribus insignitam. </s>

<s>Primo enim fuscus, inde sanguineus fulsit, mox pu&shy;<lb/>niceus et virens et lividus, ac tandem incredibili varietate difformis,<emph.end type="italics"/> cosa <lb/>degna invero d'ammirazione, e che io difficilissimamente averei creduta, se <lb/>non l'avessi appuntino veduta con questi occhi, in tempo che l'Ecclisse fu <lb/>centrale. </s>

<s>Facciasi per grazia V. S. E. leggere ci&ograve; che in questo proposito <lb/>scrive il Keplero, a carte 271 della sua <emph type="italics"/>Astronomia optica,<emph.end type="italics"/> dove tratta <emph type="italics"/>De <lb/>umbra<emph.end type="italics"/> (ma dice <emph type="italics"/>De rubore<emph.end type="italics"/>) <emph type="italics"/>Lunae deficientis,<emph.end type="italics"/> e dove arreca la cagione <lb/>perch&egrave; non crede in tutto a Ticone, che fu di questo stesso pensiero che <lb/>Venere comunicasse il lume alla Luna, bench&egrave; non nel tempo degli Ecclissi <lb/>ma circa i Plenilunii, e mi faccia grazia di dirmene il suo parere &rdquo; (MSS. <lb/>Gal., P. III, T. VII, c. </s>

<s>184). </s></p><p type="main">

<s>E giacch&egrave; non era punto conforme al genio di Galileo, per dire un suo <lb/>parere, andare alla scuola, alla quale lo consigliava il Renieri, ed &egrave; inutile per&shy;<lb/>ci&ograve; attenderne la risposta; giova qui, delle involte e sparse idee, soffermarci <lb/>a enodare e compilare le fila. </s>

<s>Il Benedetti, a colorir la Luna ecclissata, aveva <lb/>fatto concorrere insieme due cause: i raggi del Sole rifratti nell'ammosfera <lb/>terrestre, e gli splendori di Venere, i quali mancando (per non esser sem&shy;<lb/>pre il Pianeta collocato in luogo opportuno, e per non aver le rifrazioni <lb/>tanta virt&ugrave; da s&egrave; sole) facevan s&igrave; che invisibile si rendesse talvolta nell'om&shy;<lb/>bra lo stesso rubicondo cerchio lunare. </s></p><p type="main">

<s>Il Keplero, dall'altra parte, considerando essere il lume di Venere e <lb/>delle stelle circostanti al Sole sempre eguale, e che perci&ograve;, contrariamente <lb/>alle osservazioni, avrebbe dovuto tinger la faccia della Luna sempre ugual&shy;<lb/>mente, ridusse tutta l'efficienza alla causa unica delle rifrazioni. </s>

<s>Ma perch&egrave; <lb/>queste, che sempre operano, non davan facile modo a spiegar come talvolta <lb/>la Luna sparisca affatto nell'ombra, Galileo le escluse, chiamando, invece di <lb/>esse, a soccorrer la virt&ugrave; di Venere, Giove e altre stelle, fra le quali il Cane <lb/>maggiore. </s>

<s>Implicava per&ograve; questa ipotesi maggiormente nella difficolt&agrave;, che <lb/>cio&egrave; si sarebbe dovuta sempre d'ugual colore veder tinta la faccia alla Luna; <lb/>difficolt&agrave; sentita dal Renieri s&igrave; forte, che lo fece tacitamente confessar la <lb/>cosa rimaner tuttavia involta in un gran mistero. </s></p><p type="main">

<s>I pi&ugrave; sinceri non dubitarono di far questa medesima confessione, ma <lb/>perch&egrave; non &egrave; della dignit&agrave; del Filosofo il dir di non sapere, per dir dun&shy;<lb/>que qualche cosa, attribuivasi alle rifrazioni il color rosso nella Luna adom&shy;<lb/>brata. </s>

<s>Dall'altra parte il totale sperimento di lei era stato osservato da pochi, <lb/>e que'pochi non avevano grande autorit&agrave; nella scienza, potendosi dubitare <lb/>che avessero occhi infermi o strumenti imperfetti. </s>

<s>Cos&igrave; rimaneva, a tolle&shy;<lb/>rato e precario servigio dell'Astronomia, l'ipotesi kepleriana, quando l'ac&shy;<lb/>cusa di falsa e d'inetta venutale dall'autorit&agrave; concorde della scienza specu&shy;<lb/>lativa e della pratica, fece s&igrave; che fosse con pi&ugrave; severo decreto licenziata. </s></p><p type="main">

<s>L'accusa di falsa si deriv&ograve; dai principii dell'Ottica, conforme ai quali, <pb xlink:href="020/01/967.jpg" pagenum="410"/>e secondo quel che si cont&ograve; addietro nel cap. </s>

<s>I, un raggio di luce non si <lb/>ritorce, per descriver la parabola neutoniana nel mezzo rifrangente, se non <lb/>che quando gli strati di quello stesso mezzo scemino in densit&agrave; dall'alto al <lb/>basso. </s>

<s>&ldquo; Intempestiva est enim (disse il Vossio che fu primo a promuovere <lb/>quell'accusa) ratio Kepleri, eorumque qui illum secuti sunt, qui putant ru&shy;<lb/>borem seu dilutiorem umbram, quae in Lunae apparet deliquis, effici a ra&shy;<lb/>diis in hoc nostro aere refractis. </s>

<s>Fieri enim minime posse ut ulli Solis radii <lb/>hunc nostrum aerem ingrediantur, et vicissim exeant, iam ante complures <lb/>annos, monuimus. </s>

<s>Cum enim omnis refractio fiat a rariori ad densius, et <lb/>aer terris vicinus densior sit illo superiore, necesse est, ut quotquot radii <lb/>aerem ingrediuntur, in terram impingentes deficiant &rdquo; (De Nili orig. </s>

<s>Ap&shy;<lb/>pendix, Hagae Com. </s>

<s>1666, pag. </s>

<s>143). </s></p><p type="main">

<s>L'accusa d'insufficiente a spiegare il fatto venne all'ipotesi kepleriana, <lb/>non da osservazioni incerte o da osservatori inesperti, ma da uno de'pi&ugrave; <lb/>valorosi, e perci&ograve; de'pi&ugrave; autorevoli Astronomi italiani del secolo XVII. </s>

<s>Gian <lb/>Alfonso Borelli, avendo osservato il d&igrave; 11 Gennaio 1675 l'ecclisse di tutta <lb/>la Luna, il mezzo della quale avvenne in Roma a ore 8, 2&prime;, 56&Prime;, e aven&shy;<lb/>done minutamente descritte le fasi, per rimetterle al cardinale Leopoldo <lb/>de'Medici, principe della sperimentale Accademia fiorentina, nelle Memorie <lb/>della quale furono inserite a carte 61 e 62 del Tomo XXV; ebbe a notare <lb/>due circostanze non osservate altra volta da lui. </s>

<s>&ldquo; Dopo quella rara nebbia, <lb/>egli dice, in faccia della Luna, la qual suol precedere l'Ecclissi, comparve <lb/>il confine dell'ombra terrena nella faccia lunare, non sfumato e tanto con&shy;<lb/>fuso com'&egrave; solito, ma cos&igrave; terminato, che distintamente si discernevano i <lb/>contatti di tal cerchio terminatore dell'ombra, e delle circoferenze delle mac&shy;<lb/>chie lunari, tanto che si pot&egrave; notare il contatto della Macchia Gassendo, <lb/>presso il Riccioli, occorso, essendo alto il destro umero di Orione dal ver&shy;<lb/>tice 58&deg;, 46&prime;, 25&Prime;, e cos&igrave; altre Macchie. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di pi&ugrave; osservai che la parte intorno al mezzo dell'ombra terrestre <lb/>era cos&igrave; oscura e tenebrosa, che dopo la totale immersione il termine orien&shy;<lb/>tale della Luna non si discerneva, anzi pareva scantonato, e cos&igrave; anche si <lb/>vide prima di uscire dall'ombra dalla parte occidentale, e quando fu nel <lb/>mezzo dell'ombra, comparve intorno al centro del disco lunare una vasta <lb/>macchia pi&ugrave; oscura del resto, e questo occorse essendo l'aria pura ed af&shy;<lb/>fatto serena spazzata dalla Tramontana. </s>

<s>E perch&egrave; tal cosa repugna alle os&shy;<lb/>servazioni passate ed alla ricevuta dottrina del Keplero, mi pare che meriti <lb/>particolar riflessione per intenderne la causa &rdquo; (MSS. Cim., T. XXV, c. </s>

<s>60). </s></p><p type="main">

<s>La causa non fu intesa per&ograve; se non che quando il Maraldi, facendo partico&shy;<lb/>lari esperienze sull'ombre, delle quali si rese conto addietro nel &sect; IV del cap. </s>

<s>I, <lb/>non dimostr&ograve; che la Luna si rende visibile perch&egrave; si trova per lo pi&ugrave; im&shy;<lb/>a mers nella penombra, e talvolta anche sparisce o tutta o parte, perch&egrave; <lb/>s'immerge nell'ombra assoluta, la quale mostr&ograve; che di fatto non risponde <lb/>punto, in larghezza e in lunghezza, alle precise regole della nostra Geometria. </s></p><pb xlink:href="020/01/968.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO XI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Di Giove<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della scoperta de'quattro Pianeti medicei; de'metodi usati da Galileo per definirne i tempi pe&shy;<lb/>riodici e le massimo digressioni. </s>

<s>&mdash; II. </s>

<s>Degli studii intorno al Sistema gioviale proseguiti dal <lb/>Castelli, dal Renieri e dall'Hodierna. </s>

<s>&mdash; III. </s>

<s>Di ci&ograve; che a perfezionare le osservazioni, e a di&shy;<lb/>mostrare le teoriche de'Medicei, cooperarono il Montanari e il Borelli, il Viviani e il Cassini. <lb/></s>

<s>&mdash; IV. Dell'aspetto di Giove, e della fisica costituzione di lui. </s>

<s>&mdash; V. </s>

<s>Del problema delle Longi&shy;<lb/>tudini e della particolar soluzione di lui per mezzo delle Effemeridi gioviali. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Sceso in terra ad annunziare ai mortali ci&ograve; che, sollevato dal suo ma&shy;<lb/>raviglioso strumento, giunse Galileo a veder di stupendo nella visita delle <lb/>varie corti celesti, dop'aver narrato quel che di nuovo ritrov&ograve; nella Luna, <lb/>sotto l'aperto candido padiglione, e in Galassia, che distende in mezzo al <lb/>firmamento la sua argentea benda trapunta d'innumerevoli stelle; e dopo <lb/>aver data una descrizione pi&ugrave; precisa e pi&ugrave; compiuta di varie Costellazioni, <lb/>rivel&ograve; &ldquo; quod maximum in praesenti negotio existimandum videtur &rdquo; quat&shy;<lb/>tro lucide scorte, che s'eran prima tenute ad ogni vista occulte e che sta&shy;<lb/>vano in assidua faccenda intorno al trono di Giove. </s></p><p type="main">

<s>Il principio della memoranda osservazione occorse a Galileo nella prima <lb/>ora della notte seguente al di 7 Gennaio 1610, nel qual tempo vide tre pi&ugrave; <lb/>piccole stelle stare intorno al disco di Giove, due dalla parte orientale, e <lb/>una ad occidente. </s>

<s>La notte consecutiva al di 8, tornando ad osservare, trov&ograve; <lb/>che tutt'e tre le stelle rimanevano dalla parte occidentale del Pianeta, e due <lb/>notti dopo eran passate all'occidente, ma la terza, che pi&ugrave; non si vedeva, <lb/>pens&ograve; che d&ograve;vess'esser rimasta occulta dietro il disco gioviale. </s>

<s>&ldquo; Die decima <pb xlink:href="020/01/969.jpg" pagenum="412"/>apparuerunt stellae in eiusmodi ad Jovem positu: duae enim, et orientales <lb/>ambae aderant: tertia, ut opinatus fui, sub Jove latitante &rdquo; (Alb. </s>

<s>III, 78). </s></p><p type="main">

<s>Credette a principio Galileo che tali variazioni di posizione dipendes&shy;<lb/>sero da Giove, ma poi si accorse esser le stesse stelle che si movevano <lb/>intorno a lui; ond'&egrave; che, sentendosi pi&ugrave; vivamente che mai frugato dalla <lb/>curiosit&agrave; di osservare, trov&ograve; che invece di tre erano quattro stelle &ldquo; vagan&shy;<lb/>tes circa Jovem instar Veneris atque Mercurii circa Solem &rdquo; (ibi). </s></p><p type="main">

<s>Le varie costituzioni di esse stelle, rispetto al centro di Giove, furono <lb/>da Galileo diligentemente osservate per molte notti consecutive, e infino al <lb/>18 Aprile descritte nel Nunzio Sidereo. </s>

<s>Quella descrizione per&ograve; fu elabo&shy;<lb/>rata, per dare alle stampe, sopra gli appunti presi a mente fresca sera per <lb/>sera, i quali, essendo rimasti ne'Manoscritti galileiani, giovano molto a ri&shy;<lb/>velarci in quella loro semplice e negletta veste le prime e pi&ugrave; vive e vere <lb/>impressioni dell'Osservatore. </s>

<s>Oltre a ci&ograve; si trovano alcuni minuti partico&shy;<lb/>lari trascurati nel <emph type="italics"/>Nunzio,<emph.end type="italics"/> e gl'iconismi originali rispondono, molto meglio <lb/>degli artefatti da una e altra mano, alla verit&agrave; delle cose rappresentandole <lb/>tali quali furono osservate. </s></p><p type="main">

<s>Pare una minuzia, ma &egrave; pure di qualche importanza la nota, che si <lb/>legge inserita fra queste Effemeridi manoscritte, e con la quale prescriveva <lb/>Galileo all'artista il modo di riportare fedelmente in disegno quel che avea <lb/>veduto con gli occhi. </s>

<s>&ldquo; Farannosi, dice delle figure quella Nota, intagliare <lb/>in legno tutto d'un pezzo, e le stelle bianche e il resto nero: poi si seghe&shy;<lb/>ranno i pezzi &rdquo; (MSS. Gal., P. III, T. III, c. </s>

<s>30, a tergo). Noi ossequiosi a <lb/>una tal prescrizione diamo di quelle galileiane Effemeridi manoscritte, e che <lb/>si potrebbero utilmente collazionare con <lb/>le stampate nel <emph type="italics"/>Nunzio Sidereo,<emph.end type="italics"/> que&shy;<lb/>sto poco di Saggio ai nostri Lettori: </s></p><p type="main">

<s>&ldquo; A'd&igrave; 7 di Gennaio 1610 Giove <lb/>si vedeva col Cannone con tre st&egrave;lle <lb/>fisse cos&igrave;: <lb/><figure id="id.020.01.969.1.jpg" xlink:href="020/01/969/1.jpg"/><lb/>delle quali senza il Cannone niuna si vedeva (fig. </s>

<s>70). &rdquo; </s></p><p type="main">

<s>&ldquo; A'd&igrave; 8 appariva cos&igrave;: <lb/><figure id="id.020.01.969.2.jpg" xlink:href="020/01/969/2.jpg"/><lb/>Era dunque diritto e <lb/>non retrogrado, co&shy;<lb/>me pongono i cal&shy;<lb/>colatori (fig. </s>

<s>71). &rdquo; </s></p><p type="main">

<s>&ldquo; A'd&igrave; 9 fu nuvolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; A'd&igrave; 10 <lb/>si vedeva cos&igrave;: <lb/><figure id="id.020.01.969.3.jpg" xlink:href="020/01/969/3.jpg"/><lb/>cio&egrave; congiunto con la pi&ugrave; occi&shy;<lb/>dentale, sicch&egrave; si occultava per <lb/>quanto si pu&ograve; credere (fig. </s>

<s>72). &rdquo; </s></p><pb xlink:href="020/01/970.jpg" pagenum="413"/><p type="main">

<s>&ldquo; A'd&igrave; 11 era <lb/>in questa guisa: <lb/><figure id="id.020.01.970.1.jpg" xlink:href="020/01/970/1.jpg"/><lb/>(fig. </s>

<s>73) e la stella pi&ugrave; vicina <lb/>a Giove era la met&agrave; minore <lb/>dell'altra e vicinissima all'al&shy;<lb/>tra, dovecch&egrave; le altre sere erano <lb/>le dette stelle apparite tutt'e <lb/>tre di ugual grandezza, e tre <lb/>di loro ugualmente lontane. </s>

<s>Dal che appare intorno a Giove esser tre altre <lb/>stelle erranti invisibili ad ognune sino a questo tempo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; A'd&igrave; 12 si <lb/>vedde in tale co&shy;<lb/>stituzione: <lb/><figure id="id.020.01.970.2.jpg" xlink:href="020/01/970/2.jpg"/><lb/>Era la stella occidentale poco <lb/>minore della orientale e Giove <lb/>era in mezzo lontano dall'una <lb/>e dall'altra quanto il suo dia&shy;<lb/>metro in circa, e forse era una <lb/>terza piccolissima e vicinissima <lb/>a Giove verso oriente (fig. </s>

<s>74). Anzi pur v'era veramente, avendo io con <lb/>pi&ugrave; diligenza osservato, ed essendo pi&ugrave; imbrunita la notte. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; A'd&igrave; 13, avendo benissimo fermato lo strumento, si veddono vicinis&shy;<lb/>sime a Giove quattro stelle in questa costituzione: <lb/><figure id="id.020.01.970.3.jpg" xlink:href="020/01/970/3.jpg"/><lb/>(fig. </s>

<s>75) o meglio cos&igrave;: <lb/><figure id="id.020.01.970.4.jpg" xlink:href="020/01/970/4.jpg"/><lb/>(fig. </s>

<s>76) e tutte apparivano della medesima grandezza. </s>

<s>Lo spazio delle tre <lb/>occidentali non era maggiore del diametro di Giove, ed erano fra di loro <lb/>notabilmente pi&ugrave; vicine che le altre sere, n&egrave; erano in linea retta esquisita&shy;<lb/>mente come per l'avanti, ma la media delle tre occidentali era un poco ele&shy;<lb/>vata, ovvero la pi&ugrave; occidentale alquanto depressa. </s>

<s>Sono queste stelle tutte <lb/>molto lucide, bench&egrave; piccolissime, ed altre fisse che appariscono della me&shy;<lb/>desima grandezza non sono cos&igrave; splendenti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; A&igrave; di 14 fu nugolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; A'd&igrave; 15 <lb/>era cos&igrave;: <lb/><figure id="id.020.01.970.5.jpg" xlink:href="020/01/970/5.jpg"/><lb/>La prossima a Giove era <lb/>la minore e le altre di <lb/>mano in mano maggiori <lb/>(fig. </s>

<s>77). Gl'interstizi tra <lb/>Giove e le tre seguenti <lb/>erano ciascheduno quan&shy;<lb/>to il diametro di Giove, ma la quarta era distante dalla terza il doppio in <lb/>circa. </s>

<s>Non facevano interamente linea retta, ma come mostra l'esempio. </s>

<s><lb/>Erano al solito lucidissime bench&egrave; piccole e niente scintillavano com'anco <lb/>per l'innanzi &rdquo; (ivi). </s></p><p type="main">

<s>A questo punto l'avventurato Osservatore sent&igrave; che l'importanza della <lb/>sua scoperta avrebbe di grande ammirazione commosso il mondo, a cui do-<pb xlink:href="020/01/971.jpg" pagenum="414"/>vendo annunziarla conveniva usare altro linguaggio. </s>

<s>Perci&ograve; incomincia a <lb/>stendere cos&igrave; le sue note in latino: &ldquo; Fuit praecedens constitutio hora noc&shy;<lb/>tis tertia. </s>

<s>Sed&shy;<lb/>hora septima <lb/>tres tantum a&shy;<lb/>derant stellu&shy;<lb/>lae cum Jove, <lb/>in taliadspectu <lb/><figure id="id.020.01.971.1.jpg" xlink:href="020/01/971/1.jpg"/><lb/>Minima erat Jovi vici&shy;<lb/>nior, parva, reliquae 2 <lb/>maiores duplo et inter <lb/>se aequales. </s>

<s>Distantia <lb/>a Jove ad proximam <lb/>aucta erat: ipsa vicinior <lb/>erat secundae, nempe per dimidium diametri Jovis. </s>

<s>Tertia distabat a se&shy;<lb/>cunda, paulo plus quam ipsa secunda a Jove. </s>

<s>Post vero aliam horam 2 me&shy;<lb/>diae stellulae erant adhuc viciniores, (fig. </s>

<s>78) adeo ut inter ipsas spacium <lb/>mediaret ipsa minima stella minus, scilicet circa minuta secunda 40. &rdquo; </s></p><p type="main">

<s>&ldquo; Die 16, hora <lb/>prima noctis talis <lb/>fuit constitutio, <lb/><figure id="id.020.01.971.2.jpg" xlink:href="020/01/971/2.jpg"/><lb/>tres enim tantum cernebantur <lb/>stellulae: duae Jovi proximae <lb/>per quartam nempe diametri <lb/>ipsius partem ab eo utrimque <lb/>distantes scrup. </s>

<s>1. Tertia vero <lb/>occidentalis per quadruplum <lb/>diametri ipsius ab illo aberat (fig. </s>

<s>79). Proximae Jovi non maiores appa&shy;<lb/>rebant remotiori sed lucidiores &rdquo; (ivi, a tergo). </s></p><p type="main">

<s>Cos&igrave; procede questa prima forma di Effemeride latina infino a tutto il <lb/>18 Aprile, come nel Nunzio Sidereo, dove dalle molteplici osservazioni ne <lb/>conclude Galileo le seguenti importantissime notizie: &ldquo; Ac primo cum Jo&shy;<lb/>vem consimilibus interstitiis modo consequantur, modo praeeant, ab eoque <lb/>tum versus ortum, tum in occasum angustissimis tantum divaricationibus <lb/>elongentur, cundemque retrogradum pariter atque directum concomitentur; <lb/>quin circa illum suas conficiant conversiones, interea dum circa Mundi cen&shy;<lb/>trum omnes una duodecennales periodos absolvunt, nemini dubium esse po&shy;<lb/>test. </s>

<s>Convertuntur insuper in circulis inaequalibus, quod manifeste colligi&shy;<lb/>tur ex eo, quia in maioribus a Jove digressionibus nunquam binos Planetas <lb/>iunctos videre licuit, cum tamen prope Jovem duo, tres et inerdum omnes <lb/>simul constipati reperti sunt. </s>

<s>Deprehenditur insuper velociores esse conver&shy;<lb/>siones Planetarum angustiores circa Jovem circulos describentium; propin&shy;<lb/>quiores enim Jovi stellae saepius spectantur orientales, cum pridie ex occasu <lb/>apparuerint, et e contra &rdquo; (Alb. </s>

<s>III, 97, 98). </s></p><p type="main">

<s>Aveva insomma Galileo raccolto da quelle sue prime osservazioni che <lb/>le nuove stelle scoperte si volgevano intorno a Giove in orbite di varie gran&shy;<lb/>dezze, e che sopra le maggiori andavano via via meno veloci. </s>

<s>A coronare <lb/>perci&ograve; il merito della scoperta, e a ridurla a opera di vera scienza astrono&shy;<lb/>mica, ben comprese che conveniva definir di ciascuna stella i tempi perio&shy;<lb/>dici, e ritrovar le giuste misure delle loro massime digressioni. </s>

<s>Di qui &egrave; che <lb/>in render pubblicamente note, nell'Avviso Sidereo, le sue Effemeridi, faceva <lb/>appello agli Astronomi &ldquo; ut ad illorum periodos inquirendas, atque definien&shy;<lb/>das se conferant, quod nobis in hanc usque diem, ob temporis angustiam, <pb xlink:href="020/01/972.jpg" pagenum="415"/>assequi minime licuit &rdquo; (ivi, pag. </s>

<s>77). Nonostante avendo accuratamente no&shy;<lb/>tato, in mezzo a queste prime osservazioni, in quanto tempo il Pianetino pi&ugrave; <lb/>esterno ritornava a un medesimo punto dell'orbita, gli parve che fosse in <lb/>circa a quattordici giorni. </s>

<s>&ldquo; At Planeta maximum permeans orbem, accurate <lb/>praeadnotatas reversiones perpendenti, restitutiones semimenstruas habere <lb/>videtur &rdquo; (ivi, pag. </s>

<s>98). </s></p><p type="main">

<s>Dal di 18 di Aprile in poi non prosegu&igrave; Galileo le sue osservazioni gio&shy;<lb/>viali con quella prima regolarit&agrave;, ma attendeva di gran proposito a ci&ograve; che <lb/>era pi&ugrave; d'ogni altra cosa importante, a investigar cio&egrave; i periodi pi&ugrave; precisi <lb/>dei quattro nuovi Pianeti &ldquo; materia, scriveva il d&igrave; 7 Maggio 1610 a Belisario <lb/>Vinta, quanto pi&ugrave; vi penso, tanto pi&ugrave; laboriosa, per il non si dissipar mai <lb/>se non per brevi intervalli l'uno dall'altro, e per esser questi, e di colore <lb/>e di grandezza, molto simili &rdquo; (Alb. </s>

<s>VI, 98). Il pi&ugrave; esterno per&ograve;, essendo il <lb/>pi&ugrave; tardo, dava il modo pi&ugrave; facile degli altri, e perci&ograve; ne ritrov&ograve; poco dopo <lb/>il periodo alquanto pi&ugrave; preciso di quello primo assegnato scrivendo che &ldquo; fa <lb/>il suo cerchio in quindici giorni circa &rdquo; (ivi, 102). </s></p><p type="main">

<s>A mezzo Settembre, avendo <emph type="italics"/>perfezionato un poco pi&ugrave; il suo strumento<emph.end type="italics"/><lb/>(ivi, 121) vedeva Giove e la sua corte assai pi&ugrave; lucidi e distint&igrave;, ci&ograve; che <lb/>venne a incorargli una pi&ugrave; ferma speranza &ldquo; di definire i periodi dei quat&shy;<lb/>tro Pianeti medicei, stimati con gran ragione quasi inesplicabili al signor <lb/>Keplero &rdquo; (ivi, 128) tanto pi&ugrave; ch'essendosi allora volto a cercare un me&shy;<lb/>todo, scriveva ivi a don Giuliano de'Medici che sperava di averlo trovato. </s>

<s><lb/>Ond'&egrave; che alla fine di questo anno 1610 concludeva al Castelli che il de&shy;<lb/>finir i periodi di tutti quattro i Satelliti di Giove, se glielo avesse concesso <lb/>la salute, sarebbe stato tra breve (ivi, 136). </s></p><p type="main">

<s>Nel Febbraio per&ograve; dell'anno seguente (ivi, 145) e anche a'principii di <lb/>Aprile, i periodi de'quattro gioviali si trovavano tuttavia chiusi dentro i fiori <lb/>della speranza &ldquo; confidando in Dio Benedetto (cos&igrave; Galileo da Roma scriveva al <lb/>Vinta) che siccome mi ha fatto grazia di essere stato solo a scoprire tante <lb/>nuove maraviglie della sua mano; cos&igrave; sia per concedermi che io abbia a <lb/>ritrovare l'ordine assoluto dei loro rivolgimenti, e forse al mio ritorno avr&ograve; <lb/>ridotto questa mia fatica veramente atlantica a segno di poter predire i siti <lb/>e le disposizioni che essi nuovi Pianeti siano per avere in ogni tempo fu&shy;<lb/>turo, e abbiano anche avuto in ciascun tempo passato &rdquo; (ivi, 156, 57). </s></p><p type="main">

<s>Da queste parole siamo fatti accorti che il metodo, di che dianzi par&shy;<lb/>lavasi da Galileo, consisteva nel dividere i gradi di pi&ugrave; conversioni fatte nel <lb/>tempo di due delle pi&ugrave; certe osservazioni per il numero dell'ore impiegato, <lb/>d'onde veniva a resultarne il moto medio orario, e da ci&ograve; il particolar pe&shy;<lb/>riodo pi&ugrave; assoluto di quel che non si potesse ottenere, misurando il tempo <lb/>passato in una conversione tra il muovere e il ritornare al medesimo punto <lb/>dell'orbita. </s></p><p type="main">

<s>Con questo metodo, i processi del quale si posson veder pubblicati dal&shy;<lb/>l'Alb&egrave;ri (V, 10, 11), le speranze che al principiar dell'Aprile erano in sul <lb/>fiorire, avevano verso la fine del mese allegato in frutto. </s>

<s>I primi indugi che <pb xlink:href="020/01/973.jpg" pagenum="416"/>si potevano attribuire alla sola difficolt&agrave; della cosa, Galileo gli attribuisce <lb/>invece all'avere atteso allo scoprimento di Saturno tricorporeo, e di Venere <lb/>mutabile come la Luna, e ci&ograve; solo fu che lo distrasse dall'investigazion dei <lb/>tempi delle conversioni di ciaschedun de'quattro Pianeti medicei intorno a <lb/>Giove, &ldquo; la quale investigazione (dice lo stesso Galileo in principio del Di&shy;<lb/>scorso intorno alle cose che stanno in sull'acqua) mi succedette l'Aprile <lb/>dell'anno passato 1611, mentre ero in Roma, dove finalmente m'accertai <lb/>che il primo e pi&ugrave; vicino a Giove passa del suo cerchio gradi 8 e m. </s>

<s>29 in <lb/>circa per ora, facendo la intera conversione in giorni naturali 1 e ore 18 e <lb/>quasi mezza. </s>

<s>Il secondo fa nell'orbe suo gr. </s>

<s>4, m. </s>

<s>13 prossimamente per <lb/>ora, e l'intera revoluzione in giorni 3, ore 13 e un terzo in circa. </s>

<s>Il terzo <lb/>passa in un'ora gr. </s>

<s>2, m. </s>

<s>6, in circa, del suo cerchio e lo misura tutto in <lb/>giorni 7 e ore quattro prossimamente. </s>

<s>Il quarto, e pi&ugrave; lontano degli altri, <lb/>passa in ciaschedun'ora gr. </s>

<s>0, m. </s>

<s>54 e quasi mezzo del suo cerchio, e lo <lb/>finisce tutto in giorni 16 e ore 18 prossimamente &rdquo; (Alb. </s>

<s>XII, 9, 10). </s></p><p type="main">

<s>In quel medesimo mese di Aprile 1611 il Keplero, che aveva prima <lb/>stimato la cosa tanto difficile, anzi quasi impossibile, messosi, dietro l'esem&shy;<lb/>pio di Galileo, all'opera, riusc&igrave; con gran fatica a ritrovare il periodo di quella <lb/>seconda Luna gioviale, ch'&egrave; prossima alla tardissima &ldquo; sed maxime omnium <lb/>conspicua &rdquo; la quale egli trov&ograve; avere le sue restituzioni &ldquo; spacio dierum <lb/>octo &rdquo; (Dioptrice, Augustae Vindelic 1611, pag. </s>

<s>14). Quanto alle rimanenti <lb/>due non sa dir altro, se non ch'elle debbono percorrere le loro orbite in <lb/>tempi anche pi&ugrave; brevi, e ci&ograve; in conseguenza e in conformit&agrave; delle leggi dei <lb/>moti rotatorii. </s></p><p type="main">

<s>Fatta tutta intera la scoperta, la quale non era al Keplero riuscita che <lb/>a mezzo, Galileo ne diffuse tra gli amici compiacentissimo la notizia, e l'An&shy;<lb/>tonini rispondendogli da Bruxelles se ne congratulava e stupiva sopra la <lb/>grandezza dell'invenzione &ldquo; tanto pi&ugrave;, egli dice, ch'ero anch'io di quelli che <lb/>ci&ograve; stimavano cosa impossibile &rdquo; (Alb. </s>

<s>VIII, 151). </s></p><p type="main">

<s>Un altro di cotesti amici, a cui aveva in Roma partecipato ne'familiari <lb/>colloqui la bella notizia, fu Giovan Batista Agucchia, il quale essendo stato <lb/>pregato, alquanti mesi dopo, da un Signore di fargli un'<emph type="italics"/>Impresa<emph.end type="italics"/> di cose <lb/>celesti, com'aveva pensato di pigliare da un Autore gravissimo il <emph type="italics"/>motto,<emph.end type="italics"/> cos&igrave; <lb/>aveva, dalla scoperta di Galileo, pensato di pigliare il <emph type="italics"/>corpo.<emph.end type="italics"/> Voleva inoltre <lb/>quel Signore che fosse l'Impresa illustrata da un Discorso, il quale &ldquo; poi&shy;<lb/>ch&egrave;, scriveva a Galileo lo stesso Agucchia, si dee presentare ad un'Accade&shy;<lb/>mia fuori di Roma, io vorrei, con pi&ugrave; sicurezza di quel che la memoria mi <lb/>d&agrave;, poterne formare la figura, ed esprimere la grandezza degli orbi che (i sa&shy;<lb/>telliti) girano. </s>

<s>Perciocch&egrave; mi mostr&ograve; ben V. S. cortesemente la figura di <lb/>quelli e dissemi ancora i minuti del loro diametro, ma come che io possa <lb/>da vicino figurare gli orbi, non mi sovviene per&ograve; quasi punto della misura <lb/>di essi. </s>

<s>Pertanto io la prego a favorirmi di significarlami pi&ugrave; particolar&shy;<lb/>mente, ed aggiungervi oltre a ci&ograve; in quanto spazio di tempo ciascuna stella <lb/>compia suo orbe &rdquo; (ivi, 168). </s></p><pb xlink:href="020/01/974.jpg" pagenum="417"/><p type="main">

<s>Galileo, per quel suo solito timore di non avere a scorbiare i suoi parti <lb/>prima di averli dati alla luce, non rispose con gran chiarezza, per cui l'Aguc&shy;<lb/>chia pens&ograve; di andarci col suo proprio ingegno. </s>

<s>Dai colloqui tenuti in Roma <lb/>aveva appreso il metodo de'moti medii, i quali egli concluse dall'Effemeridi <lb/>che trov&ograve; scritte nel Nunzio Sidereo, e cos&igrave;, dietro a qualche altro barlume, <lb/>riusci a definir da s&egrave; i tempi de'moti periodici di tutt'e quattro le Medi&shy;<lb/>cee con pochissima differenza da'tempi stessi trovati da Galileo. </s></p><p type="main">

<s>&ldquo; Perci&ograve; avendole io riconosciute e distinte tutte quante ad una ad una, <lb/>ho raccolto che la Prima della sfera pi&ugrave; piccola, la quale non pare che si <lb/>allontani mai pi&ugrave; di m. </s>

<s>2, sec. </s>

<s>40 da Giove, fa suo giro in spazio di un <lb/>giorno, e ore diciotto e un terzo o poco pi&ugrave;, parendomi che, in giorni sette <lb/>e ore una e mezza, ella il compia quattro volte con piccola differenza dal <lb/>pi&ugrave; al meno. </s>

<s>E la Seconda mi mostra che il faccia in giorni tre e ore quin&shy;<lb/>dici, due volte girandolo in giorni sette e un quarto o poco manco. </s>

<s>Della <lb/>Terza poi, la quale in quel tempo non diede segno di discostarsi pi&ugrave; di mi&shy;<lb/>nuti otto da Giove, ho stimato che sia il periodo giorni sette e ore quattro <lb/>in circa, sicch&egrave; ella vi spenda quasi il doppio del tempo, che v'impiega la <lb/>Seconda, e per&ograve;, ad ogni sette giorni ed ore quattro o poco pi&ugrave;, si con&shy;<lb/>giungano particolarmente insieme. </s>

<s>L'Ultima finalmente mi sembra che si <lb/>rivolga intorno all'Orbe in giorni sedici e ore venti &rdquo; (ivi, 174, 75). </s></p><p type="main">

<s>Sopra questi elementi del Sistema gioviale disegn&ograve; l'Agucchia l'<emph type="italics"/>Im&shy;<lb/>presa,<emph.end type="italics"/> ch'egli illustr&ograve; veramente, come n'era stato richiesto, con un Di&shy;<lb/>scorso accademico intitolato <emph type="italics"/>Del mezzo,<emph.end type="italics"/> che incomincia con la terzina dan&shy;<lb/>tesca <emph type="italics"/>Nel mezzo del cammin di nostra vita<emph.end type="italics"/> ecc., e termina col disegno di <lb/>Giove collocato in mezzo alle orbite delle sue quattro Lune, scrittovi in giro <lb/>il motto <emph type="italics"/>Medii cupidine victae.<emph.end type="italics"/> Una copia di questo Discorso fu dall'Au&shy;<lb/>tore mandata a Galileo e doveva esser perci&ograve; raccolta fra le carte mano&shy;<lb/>scritte di lui, ma i collettori, forse per inavvertenza, inserirono la scrittura <lb/>del monsignor di Roma fra le carte manoscritte dei <emph type="italics"/>Discepoli,<emph.end type="italics"/> dove ancora <lb/>si trova da c. </s>

<s>95-110 del Tomo CXXXVI. </s></p><p type="main">

<s>Aveva l'Agucchia in quelle sue notabili osservazioni trovato, oltre ai <lb/>periodi, le massime distanze angolari dal centro di Giove per i tre pi&ugrave; pros&shy;<lb/>simi Pianeti, distanze ch'egli certamente misur&ograve; col metodo insegnato da <lb/>Galileo nelle prime pagine del Nunzio Sidereo. </s>

<s>Questo era allora l'unico <lb/>modo micrometrico conosciuto, e Galileo stesso, per mezzo de'fori pi&ugrave; o men <lb/>largamente aperti in una lamina sottile, accomodata alla lente obiettiva del <lb/>Telescopio, misurava gl'interstizii fra una luna gioviale e un'altra. </s>

<s>&ldquo; Inter&shy;<lb/>stitia quoque inter ipsa, per Perspicillum, superius explicata ratione, dime&shy;<lb/>titus sum &rdquo; (Alb. </s>

<s>III, 78). </s></p><p type="main">

<s>Quelle misure angolari per&ograve; non riuscivano assolute, se non che nella <lb/>grandezza definita del raggio, ch'&egrave; naturalmente la distanza da noi a Giove. </s>

<s><lb/>Cos&igrave; tornava possibile il determinar l'apparente grandezza del Pianeta a cui, <lb/>come a unit&agrave;, riferire i varii interstizii fra stellina e stellina, e le misure <lb/>delle loro massime digressioni. </s></p><pb xlink:href="020/01/975.jpg" pagenum="418"/><p type="main">

<s>Nelle ricerche laboriose di cos&igrave; fatti elementi fu questo propriamente il <lb/>processo tenuto da Galileo, del qual processo abbiam l'esempio in una Nota <lb/>pubblicata dall'Alb&egrave;ri, dove le misure del diametro di Giove si desumono <lb/>cos&igrave; variamente da due varie osservazioni: Supposto che AB (fig. </s>

<s>80) rap&shy;<lb/>presenti il diametro di Giove, e CL il diametro del foro della lamina adat&shy;<lb/>tata per l'una delle osservazioni, ch'&egrave; del 21 Gennaio 1612, Galileo trovava <lb/><figure id="id.020.01.975.1.jpg" xlink:href="020/01/975/1.jpg"/></s></p><p type="caption">

<s>Figura 80.<lb/>che tra il diametro del Foro e la lun&shy;<lb/>ghezza dell'asse del Canocchiale pas&shy;<lb/>sava la relazione di 1 a 275: trovava, <lb/>per l'altra osservazione del d&igrave; 9 Giu&shy;<lb/>gno, essere quella proporzione invece <lb/>di 1 a 291. Queste stesse proporzioni <lb/>poi, per la similitudine de'triangoli, <lb/>esiston pure tra AB, diametro di Giove, <lb/>e GE o AE o BE, che tutt'e tre si possono senza errore tener per eguali <lb/>e misuratrici della distanza del Pianeta da noi. </s>

<s>Perci&ograve; l'angolo AEB s'ha <lb/>dalla risoluzione del triangolo AEB, in cui son noti gli elementi a ci&ograve; ne&shy;<lb/>cessarii. </s>

<s>&ldquo; Quia vero (inteso ci&ograve;, dice Galileo) Telescopium lineas multipli&shy;<lb/>cat in rationem 18:1, fuit in prima observatione ratio distantiae a Terra <lb/>ad diametrum Stellae ut 4950:1; in altera vero ut 3238 ad 1. Reperitur ergo <lb/>per Tabulas sinium Jovis diametrum in prima observatione angul. </s>

<s>gr. </s>

<s>0&deg;, 0&prime;, <lb/>41&Prime;, 37&tprime; in secunda vero subtendisse gr. </s>

<s>0&deg;, 0&prime;, 39&Prime;, 24&tprime; (Alb. </s>

<s>V. 176). </s></p><p type="main">

<s>Trovato cos&igrave; il diametro di Giove, riduceva Galileo facilmente le distanze <lb/>angolari delle massime digressioni, misurate per mezzo della lamina micro&shy;<lb/>metrica applicata al Canocchiale, in distanze lineari riferite allo stesso diame&shy;<lb/>tro gioviale. </s>

<s>Cos&igrave; ad esempio, per il Pianeta pi&ugrave; esterno, dice, nella III Let&shy;<lb/>tera velseriana, di aver trovato quella distanza angolare 15 minuti (Alb. </s>

<s><lb/>III, 497, 98), ossia 900&Prime; che divisi per 41 o per 39 davano due varie misure <lb/>delle massime digressioni di quel Satellite in diametri apparenti di Giove. </s></p><p type="main">

<s>Or vediamo come, giunto a tale importantissimo passo, procedesse oltre <lb/>Galileo nelle sue investigazioni. </s>

<s>E per prima cosa &egrave; da osservar che i moti <lb/>de'Medicei non era possibile osservarli altrimenti, che per qualche artificio <lb/>simile a quello con cui gli Astronomi osservano i moti di Venere e di Mer&shy;<lb/>curio, le orbite de'quali sono esterne alla Terra in quel modo che sono <lb/>esterne, perch&egrave; non la comprendono, le orbite de'Pianeti gioviali. </s>

<s>Perci&ograve;, <lb/>come in Venere e in Mercurio non si osservano gli archi delle orbite de&shy;<lb/>scritte ne'loro moti, ma le proiezioni di essi archi o i seni; cos&igrave; misura&shy;<lb/>bili, ne'Medicei, non sono altrimenti gli archi, ma i seni. </s></p><p type="main">

<s>L'artificio dunque suggerito a Galileo dalla pratica degli Astronomi <lb/>precedenti consisteva in ci&ograve;: Posto per esempio 40&Prime; il diametro apparente <lb/>di Giove, quale resultava dalla media delle due sopra riferite osservazioni, <lb/>e posto che la distanza angolare dal centro del Pianeta, nelle massime di&shy;<lb/>gressioni del Satellite pi&ugrave; esterno, fosse di 15&prime;, come s'ha dalla citata Let&shy;<lb/>tera solare, misurata quella massima digressione in diametri gioviali, trovava <pb xlink:href="020/01/976.jpg" pagenum="419"/>che di que'diametri una tal distanza del Satellite da Giove, ne conteneva 22 <lb/>prossimamente, trascurandosi la frazione. </s></p><p type="main">

<s>Perci&ograve; descritto col centro in C (fig. </s>

<s>81) un piccolo cerchio di diame&shy;<lb/><figure id="id.020.01.976.1.jpg" xlink:href="020/01/976/1.jpg"/></s></p><p type="caption">

<s>Figura 81.<lb/>tro ED a rappresentare il disco di Giove, gli <lb/>circoscriveva un altro pi&ugrave; gran cerchio con un <lb/>raggio che contenesse 22 volte il detto dia&shy;<lb/>metro. </s>

<s>Cos&igrave; con quel cerchio si rappresentava <lb/>sott'occhio l'orbita del Satellite, la quale, poi&shy;<lb/>ch&egrave; Galileo supponeva essere squisitamente <lb/>disposta in un piano parallelo all'Ecclittica, <lb/>veniva, per chi l'avesse riguardata dalla Terra, <lb/>a proiettarsi sul suo proprio diametro in esqui&shy;<lb/>sitissima linea retta. </s></p><p type="main">

<s>Dopo ci&ograve;, procedendo in questa pratica, <lb/>da ciascun punto delle 22 divisioni inalzava il <lb/>nostro Astronomo altrettante linee perpendi&shy;<lb/>colari, cosicch&egrave; se, per esempio, il Satellite incomincia in F una sua con&shy;<lb/>versione, giunto in S rappresenter&agrave; in FG proiettato l'arco FS della sua <lb/>orbita e GC ne misurer&agrave; dal disco di Giove la relativa distanza. </s></p><p type="main">

<s>Simili altri di questi <emph type="italics"/>Schematismi<emph.end type="italics"/> disegnava Galileo per gli altri Sa&shy;<lb/>telliti descrivendone le orbite con i raggi misurati dal contener quelle tante <lb/>volte il diametro gioviale. </s>

<s>L'uso poi di cos&igrave; fatti Schematismi era questo: <lb/>Ad ogni osservazione giudicava cos&igrave; ad occhio a qual punto della linea CF <lb/>immaginaria potesse corrispondere la distanza reale del Satellite. </s>

<s>Giudicava <lb/>per esempio che corrispondesse al punto G, da cui contato il numero delle <lb/>segnate divisioni, scriveva senz'altro nelle sue Effemeridi che il Satellite <lb/>stesso si trovava, in quel giorno e in quell'ora, a tanti diametri di distanza <lb/>da Giove. </s></p><p type="main">

<s>Che fosse veramente questo l'uso fatto di tali Schematismi da Galileo, <lb/>nel proseguire quelle sue prime Effemeridi gioviali descritte nel Nunzio Si&shy;<lb/>dereo, ce lo dice da s&egrave; stesso in principio del Discorso intorno alle Galleg&shy;<lb/>leggianti, dove, dopo aver riferiti i tempi periodici de'quattro Medicei, cos&igrave; <lb/>soggiunge: &ldquo; Per simili precisioni non mi bastano le prime osservazioni, <lb/>non solo per li brevi intervalli di tempo, ma perch&egrave; non avendo io allora <lb/>ritrovato modo di misurar con istrumento alcuno le distanze di luogo tra <lb/>essi pianeti, notai tali interstizii con le semplici relazioni al diametro del <lb/>corpo di Giove prese, come diciamo a occhio, le quali, bench&egrave; non ammet&shy;<lb/>tano errore di un minuto primo, non bastano per&ograve; per la determinazione <lb/>delle esquisite grandezze delle sfere di esse stelle. </s>

<s>Ma ora che ho trovato <lb/>modo di prender tali misure, senza errore anche di pochissimi secondi, con&shy;<lb/>tinuer&ograve; l'osservazioni sino all'occultazion di Giove, le quali dovranno essere <lb/>abbastanza per l'intera cognizione de'movimenti e delle grandezze degli orbi <lb/>di essi pianeti, e di alcune altre conseguenze insieme &rdquo; (Alb. </s>

<s>XII, 10). </s></p><p type="main">

<s>Dello strumento, di che qui si tratta, incominci&ograve; Galileo a fare le prime <pb xlink:href="020/01/977.jpg" pagenum="420"/>prove nella seconda osservazione del 31 Gennaio 1612, come si rileva dalla <lb/>seguente Nota interpolata all'Effemeridi: &ldquo; In hac secunda observatione <lb/>primum usus sum Instrumento ad intercapedines exacte accipiendas, ac di&shy;<lb/>stantiam Orientalioris proxime accepi, non enim fuit Instrumentum exactis&shy;<lb/>sime paratum &rdquo; (Alb. </s>

<s>V, 84). </s></p><p type="main">

<s>E qui non possiamo non sentirci frugare da una gran curiosit&agrave; di sapere <lb/>in che consistesse quello Strumento <emph type="italics"/>ad intercapedines exacte accipiendas,<emph.end type="italics"/><lb/>che non pu&ograve; essere il Telescopio colle brattee perforate &ldquo; quorum ope Stel&shy;<lb/>larum intercapedines per aliquot minuta ad invicem dissitarum, citra unius <lb/>aut alterius minuti peccatum commode dimetiri poterimus &rdquo; (Alb. </s>

<s>III, 62). <lb/>Infatti queste brattee micrometriche, delle quali fece uso nelle prime osser&shy;<lb/>vazioni descritte nel Nunzio Sidereo, erano state dallo stesso Galileo trovate <lb/>incomodissime, e non rispondevano oramai pi&ugrave; ai bisogni richiesti da quel <lb/>nuovo ordine intrapreso di osservazioni gioviali. </s></p><p type="main">

<s>Qual'&egrave; insomma quello Strumento, che non era bene ancora all'ordine <lb/>nel 1612 la sera del d&igrave; 31 Gennaio? </s>

<s>Galileo non lo dice, e fu forse il Bo&shy;<lb/>relli il primo a divulgarne la notizia, ch'egli apprese o dal Castelli o dal <lb/>Renieri, a cui, come vedremo, Galileo stesso lo descriveva in una sua let&shy;<lb/>tera, che non &egrave; a noi pervenuta, e nella quale insegnava il modo partico&shy;<lb/>lare di farne uso. </s></p><p type="main">

<s>Nel capitolo IV dunque del II Libro <emph type="italics"/>Theoricae Medicaeorum<emph.end type="italics"/> il Borelli <lb/>presuppone un principio ottico, sopra il quale era fondato il nuovo Stru&shy;<lb/>mento micrometrico di Galileo. </s>

<s>Quel principio cos&igrave; bene illustrato dal Porta, <lb/>nel Libro VI <emph type="italics"/>De refractione,<emph.end type="italics"/> dove scioglie altri curiosi problemi relativi a <lb/>quello <emph type="italics"/>Cur binis oculis rem unam cernamus,<emph.end type="italics"/> consiste nel fatto che, nella <lb/>visione binoculare, gli oggetti si vedon distinti solamente nel piano dove <lb/><figure id="id.020.01.977.1.jpg" xlink:href="020/01/977/1.jpg"/></s></p><p type="caption">

<s>Figura 82.<lb/>vanno a concorrere i <lb/>punti de'due assi ottici, <lb/>oltre il qual piano, decus&shy;<lb/>sandosi gli assi, le imma&shy;<lb/>gini non si confondono <lb/>in una sola chiara e di&shy;<lb/>stinta, ma si dividono <lb/>in due, che per un'abi&shy;<lb/>tudine contratta da noi <lb/>infin dall'infanzia si giu&shy;<lb/>dicano esse pure collo&shy;<lb/>cate sulla medesima su&shy;<lb/>perficie che termina la <lb/>visione. </s></p><p type="main">

<s>&ldquo; His suppositis, pro&shy;<lb/>segue a dire il Borelli, <lb/>conspiciatur iam destro <lb/>oculo A (fig. </s>

<s>82) Jovis <pb xlink:href="020/01/978.jpg" pagenum="421"/>stella J, Telescopio CD: postea, aperto oculo sinistro B, dirigatur axis vi&shy;<lb/>sualis BE ut intersecet reliquum axim AE per Telescopium traductum in <lb/>puncto E, atque per punctum E extendatur Reticulum vel Rastellum ali&shy;<lb/>quod FG perpendiculare ad communem axim oculorum EM. </s>

<s>Patet ex dictis <lb/>in plano FG terminari visionem, et ideo omnia obiecta, quae duobus oculis <lb/>conspiciuntur, visu iudice, collocantur in dicto plano FG. </s>

<s>Et quia dexter <lb/>oculus A videt Stellam Telescopio aucta in E, atque sinister oculus B Re&shy;<lb/>ticulum aut Rastellum FG conspicit, existimabit discum Jovis auctum occu&shy;<lb/>pare interstitium Reticuli aut Rastelli, et ideo mensurari poterit diameter <lb/>Disci iovialis E respective ad amplitudinem Reticuli aut Rastelli FG. </s>

<s>Qua&shy;<lb/>propter si integrum intervallum FG subdivisum fuerit in viginti aequalia <lb/>spatia, sive interstitia, apparebit diameter Jovis Telescopio aucta vigesima <lb/>parte Reticuli. </s>

<s>Postea, quia Telescopio nedum discus Jovis E sed Medicei <lb/>H, O, L, N, una cum suis distantiis a Disco ioviali E eadem proportione <lb/>augentur, et repraesentantur in plano FG, ubi visus terminatur; et auxilio <lb/>alterius oculi mensurari possunt distantiae eorumdem Mediceorum in eodem <lb/>Rastello a limbo vel centro Jovis et ulterius situs et inclinationes eorum&shy;<lb/>dem Mediceorum praecise reperiri et delineari possunt &rdquo; (Florentiae 1665, <lb/>pag. </s>

<s>143, 44). </s></p><p type="main">

<s>Di questo artificio per&ograve; di Galileo, che pure &egrave; <emph type="italics"/>pulcherrimum, dignum <lb/>sane sagacitate et ingenio tanti viri<emph.end type="italics"/> (ibi, pag. </s>

<s>142), confessa il Borelli stesso <lb/>che <emph type="italics"/>nullam fere utilitatem<emph.end type="italics"/> quel grand'Uomo <emph type="italics"/>consequi potuit.<emph.end type="italics"/> Le ragioni <lb/>di ci&ograve; son diverse e due son dal Borelli annoverate fra le principali. </s>

<s>La <lb/>prima: che la troppo debole virt&ugrave; del Telescopio non toglieva in tutto l'ir&shy;<lb/>radiazione avventizia; la seconda, che l'illuminazione, necessaria a render <lb/>visibile il Rastrello o la Righetta micrometrica, impediva la vista de'Me&shy;<lb/>dicei e ingrossava allo stesso Rastrello i fili o alla Righetta i segni delle <lb/>divisioni. </s></p><p type="main">

<s>Tanto &egrave; vero essersi, per queste difficolt&agrave; e per que'difetti, reso inu&shy;<lb/>tile a Galileo quel suo ingegnoso Strumento, che l'us&ograve; per sole ventuna <lb/>notti, dal 31 Gennaio al 20 del Febbraio seguente. </s>

<s>Nell'osservazione del <lb/>21 appresso, <emph type="italics"/>sine Instrumento captae sunt distantiae<emph.end type="italics"/> (Alb. </s>

<s>V, 86). Che poi <lb/>veramente il nostro Osservatore tornasse a misurar quelle distanze a oc&shy;<lb/>chio nello <emph type="italics"/>Schematismo de'seni,<emph.end type="italics"/> ne abbiamo un argomento dal veder nel <lb/>Marzo 1612 costruito lo stesso Schematismo co'nuovi moduli trovati per <lb/>mezzo dello Strumento, che sono per il Satellite pi&ugrave; esterno 24 semidiame&shy;<lb/>tri di Giove, e per gli altri tre interni infino al pi&ugrave; centrale 14, 9, 5, 30 <lb/>(ivi, pag. </s>

<s>176). </s></p><p type="main">

<s>Di que'moduli cos&igrave; nuovamente trovati si giov&ograve; altres&igrave; Galileo, con <lb/>grande industria, per riscontrare la misura del diametro apparente di Giove, <lb/>servendosi del Canocchiale accomodato a quel modo che si disse di sopra, <lb/>quando fu tolta quella stessa misura direttamente dagli angoli sottesi. </s></p><p type="main">

<s>Sia, come nella precedente figura 80, G il centro di Giove e A, B i <lb/>punti delle massime digressioni del pi&ugrave; remoto Satellite, cosicch&egrave; AB rap-<pb xlink:href="020/01/979.jpg" pagenum="422"/>presenti il diametro dell'orbita. </s>

<s>Sia CL il diametro del foro della lamina <lb/>applicata all'obiettivo del Telescopio, della giusta misura che si ricerca per <lb/>questa osservazione. </s>

<s>La similitudine de'triangoli d&agrave; DE:CL=GE:AB. </s>

<s>La <lb/>prima delle due ragioni che &egrave; dell'asse del Canocchiale al diametro della <lb/>lamina perforata trov&ograve; Galileo essere di 100,000 a 10,968, dunque anche la <lb/>seconda ragione che &egrave; della distanza di Giove dalla Terra al diametro del&shy;<lb/>l'orbita del Satellite pi&ugrave; esterno, sar&agrave; la stessa. </s>

<s>&ldquo; Quia vero Telescopium <lb/>longitudines multiplicat in rationem 19 ad 1, si numeri 10,968 undevige&shy;<lb/>sima pars accipiatur, habemus rationem 100,000 ad 577 &rdquo; (ibi, pag. </s>

<s>176 n.). <lb/>Ond'&egrave; che dal triangolo isoscele AEB, con questi dati numerici risoluto, <lb/>s'avr&agrave; l'angolo AEB=0&deg; 2&prime;. </s>

<s>Di qui, supposto che AB sia 24 diametri gio&shy;<lb/>viali, secondo le misure gi&agrave; ritrovate come si avverti per mezzo dello Stru&shy;<lb/>mento, Galileo ne concluse cos&igrave; la misura del diametro apparente di Giove: <lb/>&ldquo; Quod si Jovis diameter est pars 24 ciusdem diametri, ergo diameter Jovis <lb/>subtendit gradus 0&deg;, 0&prime;, 50&Prime; et hoc accidet cum Jovis est Terrae proxi&shy;<lb/>mus &rdquo; (ibi). </s></p><p type="main">

<s>Tali sono insomma i frutti delle vigilie di Galileo intorno al Mondo gio&shy;<lb/>viale, e pu&ograve;, dietro i fatti narrati, un giusto giudice estimarne i meriti e i <lb/>pregi. </s>

<s>Che poi quell'Uomo, magnificator d'ogni cosa sua, magnificasse anche <lb/>questa, non fa maraviglia, come non fa maraviglia che vantandosi della prio&shy;<lb/>rit&agrave; della scoperta si risentisse fieramente contro chi gliel'avesse contesa. </s>

<s><lb/>Sarebbero fra tali contenditori da annoverare quegl'Italiani commemorati <lb/>dal Sarpi, i quali, avuto notizia del Canocchiale olandese, lo ridussero pi&ugrave; <lb/>adatto e perfezionato e <emph type="italics"/>principiarono a valersene per l'Astronomia<emph.end type="italics"/> (Let&shy;<lb/>tere, Vol. </s>

<s>II, Firenze 1863, pag. </s>

<s>41) scoprendo in cielo quel che veniva, <lb/>nello stesso tempo, scoprendo Galileo. </s>

<s>A lui per&ograve; non vollero turbare la com&shy;<lb/>piacenza del primato per certe ragioni, che non valsero a legare la lingua <lb/>in bocca a Simon Mario n&egrave; poi a trattenergli in mano la penna. </s>

<s>Egli ebbe <lb/>perci&ograve; a toccarsi quella lavata di capo, che gli fu fatta senza piet&agrave; nelle <lb/>prime pagine del <emph type="italics"/>Saggiatore,<emph.end type="italics"/> dove l'Autore vuol, con argomenti cronolo&shy;<lb/>gici e astronomici provare ch'esso Mario o non vide mai i Satelliti di Giove <lb/>o che gli vide solo due anni dopo la pubblicazione del Nunzio Sidereo. </s></p><p type="main">

<s>L'Astronomo di Brandeburgo asseriva che il piano delle orbite de'Gio&shy;<lb/>viali &egrave; costantemente inclinato al piano dell'Ecclittica, e che perci&ograve; sempre <lb/>si osservano que'piccoli Pianeti avere una qualche latitudine, la quale ne'se&shy;<lb/>micerchi superiori &egrave; dalla parte di Austro e negl'inferiori da quella di Bo&shy;<lb/>rea. </s>

<s>L'Astronomo di Firenze persisteva nell'opinione dell'esatto paralleli&shy;<lb/>smo tra il piano dell'Ecclittica e il piano dove giacciono le orbite de'quattro <lb/>Medicei, attribuendo le loro latitudini apparenti alla inclinazione dell'orbita <lb/>di Giove, e da queste stesse apparenze argomentando i tempi delle osser&shy;<lb/>vazioni fatte dal suo odiato rivale. </s></p><p type="main">

<s>L'Hodierna si studi&ograve; di comporre la controversia con dire che avendo <lb/>egli scoperto la latitudine de'Medicei esser variabile, Galileo osserv&ograve; quando <lb/>quella latitudine era nulla e Simon Mario quand'era gi&agrave; all'occhio dell'Os-<pb xlink:href="020/01/980.jpg" pagenum="423"/>servatore parvente. </s>

<s>Non perci&ograve; vien l'Hodierna a decider nulla dell'altra <lb/>pi&ugrave; agitata controversia intorno alla priorit&agrave; della scoperta; causa che 44 anni <lb/>prima era stata pregiudicata da un pi&ugrave; competente e imparzial tribunale in <lb/>Germania. </s></p><p type="main">

<s>Noi richiamiamo perci&ograve; la considerazione de'nostri Lettori sopra le se&shy;<lb/>guenti parole, che il Keplero da Praga scriveva il d&igrave; 10 Novembre 1612 allo <lb/>stesso Simon Mario, non a proposito di solo Giove, ma di un'altra delle pi&ugrave; <lb/>rumorose scoperte occorse felicemente all'Astronomia in quei primi tempi: </s></p><p type="main">

<s>&ldquo; Galilaeus rerum suarum sategit; bene sibi consuluit, inquam, quippe <lb/>qui rerum suarum satagebat. </s>

<s>Bene fecit quod mature nos certiores reddidit <lb/>de inventis suis, per gryphos tamen. </s>

<s>Nam, si non mature, tu praevenisses: <lb/>ita Galilaeo laus primae inventionis periisset. </s>

<s>Si non per gryphos, statim <lb/>nos, ad quos ille scripsit, dicere potuissemus nos eodem tempore eadem vi&shy;<lb/>disse vel etiam antea. </s>

<s>Tibi quoque, Mari, bene cessit gryphus, seu anagram&shy;<lb/>matismus iste. </s>

<s>Nam si Galilaeus clare scripsisset tanto antea, nemo facile <lb/>credisset tuam esse secundam huius observationis palmam. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Nunc eodem tempore et Galilaeus Florentiae sua nobis aenigmata <lb/>scripto detexit, et tu in Franconia observare eadem coepisti, ut impossibile <lb/>sit te tua ex Galilaei laboribus habere. </s>

<s>Agnoscis, ni fallor, sensum postremi <lb/>marginis. </s>

<s>Desine igitur te furti insimulatione queri ab eo loco, qui te furti <lb/>manifestissime absolvit. </s>

<s>Nam quae haec consequentia esset: quo tempore <lb/>Galilaeus Florentiae futuras Veneris apparentias praedixit, eodem Marius <lb/>illas eodem ordine observare coepit, ergo Marius ex Galilaei monitis habuit? </s>

<s><lb/>Numquid enim Alpes intersunt et longum iter et viginti dierum mora priu&shy;<lb/>squam literae Florentia digressae Pragam appellant, quando nondum ta&shy;<lb/>men in Franconiam comunicatae sunt Praga a nobis? </s>

<s>&rdquo; (Epistolae mutuae, <lb/>Lipsiae 1718, pag. </s>

<s>551). </s></p><p type="main">

<s>Queste parole collazionate con le ultime scritte nella Prefazione alla <lb/>Diottrica, dove a proposito della controversia insorta fra un Alemanno e un <lb/>Italiano, un Alemanno, di tale e tanta autorit&agrave; qual'&egrave; il Keplero, decide a <lb/>favore del Nostro, bastano a provar che la gloria delle prime scoperte ce&shy;<lb/>lesti, fra le quali &egrave; massima quella de'Satelliti di Giove, &egrave; meritamente do&shy;<lb/>vuta all'Italia. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>E all'Italia &egrave; pure dovuto il merito di aver fatti i primi validi sforzi <lb/>per investigar l'ordine di que'moti, che governano il piccolo Mondo gio&shy;<lb/>viale, in cui par che, come in immagine viva, si specchi il Mondo universo. </s>

<s><lb/>Il Castelli come concorse a prevenire, a promuovere e a perfezionare ognuna <lb/>delle scoperte celesti fatte dal suo Maestro, cos&igrave; dette insiem con lui opera <lb/>assidua ad osservare il moto de'Satelliti intorno a Giove. </s>

<s>Chi raccogliesse <pb xlink:href="020/01/981.jpg" pagenum="424"/>tra queste osservazioni quelle sole, ch'ei comunicava a Galileo nelle sue let&shy;<lb/>tere, per la pi&ugrave; parte rimaste inedite, ne comporrebbe una copiosa Effeme&shy;<lb/>ride. </s>

<s>Se poi fosse una tale Effemeride scritta ordinatamente dal suo Autore <lb/>e disposta in Tavole, da servire a'comodi usi dell'Astronomia &egrave; incerto, ma <lb/>&egrave; certissimo ch'egli compose con gran diligenza una Tavola delle Epoche <lb/>dei moti medii, o come allora si chiamavano delle <emph type="italics"/>Radici,<emph.end type="italics"/> per la massima <lb/>parte da s&egrave; stabilite, ma alcune delle quali, ricevute da Galileo, le inser&igrave; fra <lb/>le sue. </s>

<s>Questa Tavola andava attorno manoscritta fra gli scolari dello stesso <lb/>p. </s>

<s>d. </s>

<s>Benedetto, e una copia vedremo a quale occasione e per che mezzo <lb/>fosse dal Borelli trasmessa al Cassini. </s></p><p type="main">

<s>Per diligenti per&ograve; che fossero le osservazioni del Castelli non potevano <lb/>andar salve da alcuni errori inevitabili a un'arte, allora del tutto nuova, e <lb/>nella quale perci&ograve; s'aggiungeva all'imperizia dell'osservare l'imperfezione <lb/>de'primi fabbricati strumenti. </s>

<s>Nel corso intanto di una trentina d'anni si <lb/>erano quelli strumenti ridotti a tale eccellenza, che non si sarebbe aspet&shy;<lb/>tata mai dalla febbrile arte vetraria, ed essendosi d'ogni parte moltiplicati <lb/>i curiosi delle novit&agrave; celesti, l'assiduo esercizio aveva resi pi&ugrave; esperti gli <lb/>osservatori. </s>

<s>Si segnal&ograve; fra questi Vincenzio Renieri che, nel 1639 pubblicava <lb/>le sue <emph type="italics"/>Tavole medicee<emph.end type="italics"/> dei Secondi mobili &ldquo; qui comprennent, scriveva il <lb/>Cassini, les Tables les plus c&eacute;l&eacute;bres faites depuis 400 ans r&eacute;duites &agrave; une <lb/>mesme forme &rdquo; (Hypotheses des Satell. </s>

<s>de Iuppiter, Amsterdam 1736, <lb/>pag. </s>

<s>368). </s></p><p type="main">

<s>Abbandonate nel 1619 da Galileo le osservazioni, atterrito dalle diffi&shy;<lb/>colt&agrave;, riprese nel 1620 animo quando le propose per uso delle longitudini <lb/>terrestri; proposta che parve essere dagli Olandesi accolta con pi&ugrave; favore <lb/>nel 1636, quando il proponente si sentiva inabile all'opera per la cecit&agrave; so&shy;<lb/>pravvenutagli e per la vecchiezza. </s>

<s>Rivoltosi perci&ograve; al valoroso calcolatore <lb/>delle Tavole medicee lo trov&ograve; in un giovanile ardore di darsi tutto a un'im&shy;<lb/>presa, che prometteva tanta utilit&agrave; e tanta gloria. </s></p><p type="main">

<s>A lui consegn&ograve; Galileo i suoi lunghi calcoli laboriosi, a lui finalmente <lb/>apr&igrave; il segreto de'suoi metodi, a lui insegn&ograve; l'uso di misurar le distanze <lb/>con lo Strumento, sperando che sarebbe riuscito utile, applicato a Telesco&shy;<lb/>pii di tanto maggiore ingrandimento de'suoi. </s>

<s>Sulla fine dell'anno 1637 gli <lb/>scriveva a Genova una lettera, dove gli raccomandava attendesse al concorso <lb/>de'raggi visuali dietro l'occhio, per avere nelle operazioni micrometriche le <lb/>misure angolari pi&ugrave; giuste. </s>

<s>A che rispondeva il Renieri, verso la fin di Gen&shy;<lb/>naio, proponendo di ricevere i raggi attraverso un foro invariabile aperto in <lb/>una carta o in una lamina, piuttosto che aftraverso al foro della pupilla, <lb/>tacitamente insinuando la inutilit&agrave; e anzi la fallacia di una tale operazione <lb/>astronomica, perch&egrave; se gli angoli e le immagini non crescono n&egrave; diminui&shy;<lb/>scono a proporzion del foro nella Camera oscura, non par che dovessero o <lb/>crescere o diminuire nell'occhio, a proporzion del diametro della pupilla. </s>

<s><lb/>Terminava con queste parole il Renieri la sua risposta: &ldquo; Non mancherei <lb/>di tirar avanti le osservazioni delle Medicee, ma per non avere il suo Nun-<pb xlink:href="020/01/982.jpg" pagenum="425"/>zio Sidereo non mi ricordo del modo di misurare le distanze loro: di gra&shy;<lb/>zia V. S. me ne avvisi la forma &rdquo; (Alb. </s>

<s>X, 262). </s></p><p type="main">

<s>Galileo allora, non solo dichiar&ograve; meglio al Renieri il modo di applicar <lb/>le Brattee perforate ad uso micrometrico, e gi&agrave; descritte nel Messaggero, <lb/>ma soggiunse una particolar descrizione dello strumento da misurar le di&shy;<lb/>stanze, osservando con un occhio libero e con l'altro applicato al Telesco&shy;<lb/>pio. </s>

<s>Sempre nella speranza di mandare in breve alla luce &ldquo; tutto il resto <lb/>delle considerazioni fatte intorno alle altre celesti novit&agrave; &rdquo; (Alb. </s>

<s>III, 506) <lb/>dopo quelle descritte nel Nunzio Sidereo, Galileo aveva tenuto occulto quello <lb/>strumento a tutti, infino a'pi&ugrave; intimi amici, fra'quali il Cavalieri, che avendo <lb/>letto nel Discorso delle Galleggianti il modo di assicurarsi &ldquo; a discrizione <lb/>della distanza de'Pianeti medicei fra loro e Giove &rdquo; (Campori, Carteggio <lb/>gal., Modena 1881, pag. </s>

<s>186) era entrato in gran desiderio d'intenderlo. </s></p><p type="main">

<s>Fallite oramai le speranze di scrivere il libro delle <emph type="italics"/>Novit&agrave; celesti,<emph.end type="italics"/> Ga&shy;<lb/>lileo dunque descriveva quello strumento da misurar la distanza fra'Medi&shy;<lb/>cei, a quel modo presso a poco che leggemmo di sopra nel Borelli. </s>

<s>Il Re&shy;<lb/>nieri, dato una scorsa a quella descrizione in furia, non aveva bene inteso <lb/>il modo di contrapporre agli occhi, il Rastrello, o la Righetta, com'ei la <lb/>chiama, e perci&ograve; tornava a scriver cos&igrave; al medesimo Galileo, pregandolo di <lb/>volersi dichiarar meglio e di avvisarlo. </s>

<s>&ldquo; Dalla prima vista della sua lettera <lb/>non ho ben compreso il modo di misurar le distanze coll'Occhiale, ma forse, <lb/>col porre in opera lo Strumento, lo intender&ograve; meglio. </s>

<s>Frattanto mi avvisi <lb/>se la Righetta v&agrave; contro l'occhio libero, perch&egrave; contro all'occhio del Tele&shy;<lb/>scopio non mi par che si possa accomodare &rdquo; (Alb. </s>

<s>X, 285). </s></p><p type="main">

<s>Galileo, bench&egrave; non ne siam certi, avr&agrave; fatte le necessarie dichiarazioni, <lb/>a avr&agrave; tolto via tutti i dubbii riguardo all'uso dello strumento, come gli <lb/>aveva tolti, o piuttosto preveduti, riguardo alla pratica delle osservazioni, <lb/>facendo notar gli errori trascorsi nelle prime Effemeridi descritte nel Mes&shy;<lb/>saggero celeste. </s>

<s>Son queste annotazioni di una certa importanza, e il Re&shy;<lb/>nieri le trascrisse quali le ebbe di mano di Galileo, e come si leggono <lb/>da carte 26-29 del T. VI, P. III de'Manoscritti galileiani, sotto il titolo: <lb/>&ldquo; Observationes Galilaei adnotatae, prout ipse propria manu descripsit. </s>

<s>&rdquo; </s></p><p type="main">

<s>Come saggio di queste galileiane osservazioni sugli errori da notarsi <lb/>nelle prime descritte costituzioni gioviali; errori che dovevano fare accorto <lb/>a cansarli il Renieri, e che dovevano invitarlo ad emendarli col potente <lb/>aiuto de'suoi Telescopii, trascriviamo dal Manoscritto questi due esempii: <lb/>&ldquo; Anno 1610 die 20 Januarii Paduae, in observatione horae 6 duae tantum <lb/>Stellae observatae sunt, ex quo intelligendum IV et III fuisse coniunctas. </s>

<s><lb/>Et licet latitudo inter ipsas magna fuerit, IV tamen ob exilitatem et pro&shy;<lb/>prinquitatem III, et inexperientia observandi non fuit adnotata ........ <lb/>Die 12 Februarii apparuit in observatione quae habetur in Nuncio Sidereo <lb/>fuisse allucinationem. </s>

<s>In observationibus vero omnibus, quae in eo Libro <lb/>notantur, colligimus, ob inexperientiam et Instrumenti insufficientiam, Stel&shy;<lb/>las mediceas conspectas non esse nisi dum essent remotae a centro Jovis <pb xlink:href="020/01/983.jpg" pagenum="426"/>sem. </s>

<s>3 ita notati ad diem 8 Februarii &rdquo; richiamandosi a quel risultato dei <lb/>moti medii calcolati sopra pi&ugrave; corrette Radici, che pubblic&ograve; a pag. </s>

<s>287 del <lb/>suo Tomo V l'Alb&egrave;ri. </s></p><p type="main">

<s>L'eccellenza de'Canocchiali, e la perizia acquistata dal Renieri ne'cal&shy;<lb/>coli e nelle osservazioni, facevano sperare a Galileo, il quale era stato cos&igrave; <lb/>prodigo delle sue fatiche e de'suoi ammaestramenti, che sarebbero final&shy;<lb/>mente uscite perfette le Tavole de'moti gioviali. </s>

<s>Il Renieri stesso incor&ograve; <lb/>questa speranza, e la significava all'amico Lettore delle sue prime Tavole <lb/>medicee pubblicate nel 1639. Il Cassini, avvertendo che nella seconda edi&shy;<lb/>zione di quelle Tavole ampliate e corrette tace affatto l'Autore intorno al&shy;<lb/>l'Effemeridi gioviali, che aveva gi&agrave; cos&igrave; solennemente promesse &ldquo; ce qui, <lb/>soggiunge, donne lieu de juger qu'il y avoit trouv&eacute; plus de difficult&eacute;, qu'il <lb/>n'avoit suppos&eacute; d'abord &rdquo; (Hupoth. </s>

<s>cit., pag. </s>

<s>368). E par che voglia attri&shy;<lb/>buire a questa difficolt&agrave;, piuttosto che a uno smarrimento o ai casi di una <lb/>morte immatura, l'essere stata defraudata la scienza di quelle Effemeridi <lb/>aspettate con tanti desiderii. </s></p><p type="main">

<s>Era dall'altra parte impossibile, chi ben rifiette, che non si trovasse il <lb/>Renieri implicato in gravissime difficolt&agrave;, le quali non gli erano punto, per <lb/>vero dire, appianate da Galileo, suggerendogli i suoi metodi empirici, con&shy;<lb/>sigliandogli la pratica di operazioni astronomiche false e perci&ograve; disutili, po&shy;<lb/>nendogli in mano strumenti impraticabili, e insinuandogli i suoi pregiudizii. </s></p><p type="main">

<s>Uno di cos&igrave; fatti pregiudizii galileiani de'pi&ugrave; dannosi era quello di man&shy;<lb/>tenere, a dispetto del Keplero, le orbite circolari, non volendo in nulla rifor&shy;<lb/>mare l'architettura copernicana degli Eccentrici e degli Epicicli. </s>

<s>Conseguiva <lb/>da ci&ograve;, che essendo ne'circoli il moto uniforme, per la pi&ugrave; precisa misura <lb/>de'tempi, non si teneva altro conto che della cos&igrave; detta <emph type="italics"/>Equazione de'giorni <lb/>naturali,<emph.end type="italics"/> la quale consisteva nel ridurre i moti per l'Ecclittica ai moti fatti <lb/>per l'Equatore. </s>

<s>Il Renieri per&ograve;, prevenendo di un secolo i progressi del&shy;<lb/>l'Astronomia, sentiva vivo il bisogno di aggiungere un'altra <emph type="italics"/>equazione<emph.end type="italics"/> di&shy;<lb/>pendente dal moto realmente variabile della Terra, nella sua orbita ellittica, <lb/>e sottoponeva cos&igrave; questo suo luminoso pensiero al giudizio di Galileo: </s></p><p type="main">

<s>&ldquo; Vedo l'avvertimento che ella mi d&agrave; circa al crescer la Prostaferesi <lb/>dell'Orbe pi&ugrave; sensibilmente, ne'tempi che Giove si trova opposto al Sole, <lb/>di quello che faccia ne'punti delle massime digressioni nell'Epiciclo, e ben&shy;<lb/>ch&egrave; io conosca che io non avea fatto sovra di ci&ograve; la debita considerazione, <lb/>per ogni modo non mi par dalle osservazioni passate poter in tutto levarmi <lb/>qualche scrupolo di questa anomalia del moto del Primo mobile, e pur vado <lb/>dubitando che in questi tempi, ne'quali la Terra &egrave; pi&ugrave; discosta dal Sole, il <lb/>moto diurno venga ad esser pi&ugrave; tardo, che non &egrave; ne'tempi del Perigeo so&shy;<lb/>lare, e che, oltre la solita Equazione de'giorni naturali, ve ne sia bisogno <lb/>di un'altra cagionata dal mancar la velocit&agrave; del moto diurno nello allonta&shy;<lb/>narsi la Terra dal Sole apogeo, in cui risiede la virt&ugrave; motrice &rdquo; (Alb. </s>

<s>X, 339) </s></p><p type="main">

<s>Soggiungeva il Renieri a Galileo che ci pensasse un poco, e poi glie ne <lb/>dicesse il suo parere, il quale a null'altro giov&ograve; che a rintuzzare una pra-<pb xlink:href="020/01/984.jpg" pagenum="427"/>tica astronomica riconosciuta utilissima, e anzi necessaria dagli stranieri, che <lb/>perci&ograve; se ne attribuiron la gloria. </s>

<s>Un altro merito ha nonostante il Disce&shy;<lb/>polo, sopra il Maestro che aveva trattata l'Astronomia gioviale con metodi <lb/>puramente meccanici, ed &egrave; quella di avervi introdotta la Matematica. </s>

<s>Da <lb/>carte 41-59 del sopra citato Tomo dei Manoscritti galileiani si leggono au&shy;<lb/>tografi del Renieri risoluti i principali problemi concernenti l'Ecclissi de'quat&shy;<lb/>tro Satelliti gioviali. </s>

<s>E pe&rgrave;ch&egrave; ad essi problemi pare a noi che sian prin&shy;<lb/>cipalmente raccomandati i meriti dell'Astronomo genovese, &egrave; ben qui darne <lb/>qualche saggio alla luce, anche per mostrar che non tutto delle cose di lui <lb/>ne involarono i casi cos&igrave; variamente narrati, o la deplorata morte invidiosa: </s></p><p type="main">

<s>&ldquo; Rursum hic examinantur umbrae quantitates in transitu quatuor <lb/>Planetarum. </s>

<s>Ex observatione magis accurata anni 1641, die 23 Octobris, <lb/>&there4; observatus est Pisis ingredi umbram hora 8, 17&prime; p. </s>

<s>m., exire autem <lb/>h. </s>

<s>11, 28&prime;, unde, cum in Ecclipsi consumpserit horas 3, 11&prime;, patet in dimi&shy;<lb/>dia mora h. </s>

<s>1, 35&prime;, 30&Prime; consumptam fuisse, quo tempore ex semidiametro <lb/>Jovis &there4; metitur partes 49&prime;, 38&Prime;. </s>

<s>Datur autem eo termpore locus Jovis cen&shy;<lb/>tricus in 11&deg;, 17&prime;, 30&Prime;, Nodi in 3&deg;, 5&prime;, 28&Prime;, unde distantia a Nodo 8&deg;, 12&prime;, 2&Prime;, <lb/>et propterea inclinatio orbitae gr. </s>

<s>1, 15&prime;. </s>

<s>Distat ergo umbrae centrum a plano <lb/><figure id="id.020.01.984.1.jpg" xlink:href="020/01/984/1.jpg"/></s></p><p type="caption">

<s>Figura 83.<lb/>quod ducitur per centrum Jovis Ecclipticae pa&shy;<lb/>rallelum, partibus semid. </s>

<s>Jovis 17&prime;, 45&Prime;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sit igitur via &there4; in plano Ecclipticae pa&shy;<lb/>rallelo AB (fig. </s>

<s>83) cuius dimidium AC, sitque <lb/>DC distantia centri umbrae D ab hoc plano. </s>

<s><lb/>Cum AC inventa sit partium 49&prime;, 38&Prime;; DC, 18&prime;, <lb/>15&Prime; quarum semid. </s>

<s>Jovis est 60; ita AD umbrae <lb/>semidiametrum investigabimus. </s>

<s>&rdquo; E risoluto il <lb/>triangolo ACD, trova AD=52&prime;, 53&Prime;. </s></p><p type="main">

<s>&ldquo; Jam vero his ita repertis, quantitatem <lb/>axis coni umbrae Jovis et semidiametrum eius&shy;<lb/>dem in transitu trium reliquorum ita venabimur. </s>

<s>Sit AB (fig. </s>

<s>84) semidia&shy;<lb/>metrorum Jovis 14, prout pluribus observationibus compertum est &there4; ab Jove <lb/><figure id="id.020.01.984.2.jpg" xlink:href="020/01/984/2.jpg"/></s></p><p type="caption">

<s>Figura 84.<lb/>distare. </s>

<s>Erit ergo DF semidia&shy;<lb/>metros umbrae Jovis in loco <lb/>transitus &there4;, quae superius in&shy;<lb/>venta est continere partes se&shy;<lb/>midiametri Jovis 52&prime;, 53&Prime;. </s>

<s>Au&shy;<lb/>feratur DF aequalis AE et du&shy;<lb/>catur EF. </s>

<s>Erit ergo EB partes 7&prime;, 7&Prime;. </s>

<s>Cum ergo sit ut BE (7&prime;, 7&Prime;) ad EF, <lb/>hoc est AD (14); ita AB (60) ad AC; propterea, in Regula trium, nota erit <lb/>AC semid. </s>

<s>Jovis 118, 2&prime;. </s>

<s>Hinc denique, cognito axe AC 118, 2&prime;, nota erit <lb/>umbrae semidiametros in loco transitus &#x2237;, .. et ., ut si AC (118, 2&prime;) ad <lb/>AB (60), ita DA semidiametrorum 26, distantia &#x2237;, ad EB, scrup. </s>

<s>13&prime;, <lb/>12&Prime;. </s>

<s>Et propterea AE, seu DF erit scr. </s>

<s>46&prime; 48&Prime;, sicut in . DF erit scr. </s>

<s>57&prime;, <lb/>3&Prime;, in .. 55&prime;, 3&Prime;, &rdquo; (ibi, c. </s>

<s>42). </s></p><pb xlink:href="020/01/985.jpg" pagenum="428"/><p type="main">

<s>Corse voce che non solamente le carte, alle quali furono consegnate <lb/>queste Teorie astronomiche, ma che ancora tutte le altre dov'erano scritte <lb/>le Tavole de'Medicei compiute, e alle quali le stesse Teorie astronomiche <lb/>gi&agrave; preparate dovevano esser premesse, erano andate irreparabilmente per&shy;<lb/>dute. </s>

<s>La voce fu avvalorata dall'autorit&agrave; del Riccioli, che nel primo Tomo <lb/>dell'Almagesto nuovo, raccontati i pi&ugrave; minuti particolari di quello smarri&shy;<lb/>mento, terminava la sua storia con le parole: <emph type="italics"/>dblenda profecto iactura.<emph.end type="italics"/></s></p><p type="main">

<s>Leggendo quivi Giovan Battista Hodierna pens&ograve; egli di riparare a cos&igrave; <lb/>dolorosa iattura, pubblicando nel 1656, in Palermo, un libro intitolato &ldquo; Me&shy;<lb/>nologiae Jovis compendium, seu Ephemerides Mediceorum &rdquo; libro che fu dal <lb/>suo Autore diviso in tre parti. </s>

<s>Nella prima tratta del numero, dellla serie, <lb/>delle digressioni, de'congressi e de'Periodi de'Medicei; nella seconda, delle <lb/>variabilit&agrave; delle Latitudini, e nella terza d&agrave; le Tavole astronomiche e i ca&shy;<lb/>noni da calcolarle. </s></p><p type="main">

<s>Dal Nunzio Sidereo in fuori non aveva il nostro Palermitano altri pre&shy;<lb/>decessori che il Mario e lo Schirleo, ad ambedue i quali per&ograve; non prestava <lb/>gran fede, e specialmente allo Schirleo, il quale fra'molti altri suoi sogni <lb/>ed errori aveva detto che i Satelliti gioviali scintillavano di luce propria <lb/>come le Stelle. </s>

<s>&ldquo; Haec mihi non placuerunt, dice l'Hodierna, nam si lucem <lb/>sibi innatam satellites Jovis habent, praesertim Primus et Penextimus, quo&shy;<lb/>modo seipsos ad invecem eclypsare indubitatum esse dicit? </s>

<s>&rdquo; (ibi, pag. </s>

<s>70). </s></p><p type="main">

<s>Un tale errore lo aveva sostenuto pure il Liceti, concludendolo dal prin&shy;<lb/>cipio metafisico delle intelligenze governatrici, mentre lo Schirleo lo aveva <lb/>invece concluso dal fatto fisico del vedere i Satelliti risplendere intorno a <lb/>Giove non men vivamente di quel che si facciano in cielo le Stelle fisse. </s>

<s><lb/>Galileo aveva pensato a confutar quell'errore con argomenti che dovevano <lb/>inserirsi nella <emph type="italics"/>Lettera sul candore lunare,<emph.end type="italics"/> ma che poi rimasero, a quel che <lb/>sembra, fra le carte scritte a dettatura dal Viviani. </s>

<s>Qualcuno di quegli ar&shy;<lb/>gomenti &egrave; ricavato da osservazioni volgari, come sarebbe questo: &ldquo; Se il <lb/>risplendere &egrave; segno di maggior nobilt&agrave; e perfezione, le lucciole e alcuni <lb/>vermi saranno pi&ugrave; perfetti d'infiniti altri animali, che nulla risplendono, e <lb/>quei legni, ch'essendo prima tenebrosi si fanno poi risplendenti, non cam&shy;<lb/>minano come V. S. e comunemente si crede alla corruzione e allo infradi&shy;<lb/>ciarsi, ma al perfezionarsi e nobilitarsi &rdquo; (MSS. Gal., P. III, T. VII, c. </s>

<s>135). </s></p><p type="main">

<s>Alcuni altri argomenti poi sa ben Galileo trarli da pi&ugrave; alte e pi&ugrave; sot&shy;<lb/>tili considerazioni, che noi vogliamo in parte far qui note ai Lettori. </s>

<s>&ldquo; Ve&shy;<lb/>ramente il pensier di V. S. (cos&igrave; aveva fatto intenzione di dire al Liceti) <lb/>dello stimare i tre Pianeti superiori essere per s&egrave; stessi lucidi, come quelli <lb/>che da pi&ugrave; nobili e perfette intelligenze sono generati, mi &egrave; parso mirabile <lb/>e degno di essere abbracciato e ritenuto, tuttavolta per&ograve; che mi venissero <lb/>rimossi alcuni scrupoli, e risolute certe difficolt&agrave;, delle quali per mia debo&shy;<lb/>lezza non so ridurre la soluzione alle Intelligenze, ed essendo che, conforme <lb/>al pronunziato sicurissimo di Aristotile, <emph type="italics"/>qui dat esse dat consequentia ad <lb/>esse,<emph.end type="italics"/> dando l'Intelligenza lo splendore per esempio a Giove, deve in con-<pb xlink:href="020/01/986.jpg" pagenum="429"/>seguenza contenere le cagioni delle variet&agrave;, che nello splendore di Giove si <lb/>scorgono, delle quali ben pare a me di ritrovare apertamente e indubitabil&shy;<lb/>mente le cagioni, mentre che io costituisco Giove per s&egrave; naturalmente te&shy;<lb/>nebroso, e solo lucido per l'illuminazione del Sole. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si rivolgono in cerchi differenti e diseguali, concentrici per&ograve; al cen&shy;<lb/>tro di Giove, quattro minori Stelle, le quali in statuti e preveduti tempi <lb/>restano in tutto prive di lume, e come ecclissate. </s>

<s>Tale accidente non pati&shy;<lb/>scono esse se non vicine a Giove, e costituite nella parte superiore de'cer&shy;<lb/>chi loro, ma nella parte inferiore vengono a congiungersi e a separarsi dal&shy;<lb/>l'istesso Giove, senza patire ecclisse alcuna. </s>

<s>Inoltre si nascondono nelle <lb/>tenebre, alcune volte, avanti che arrivino al contatto di Giove, ed altre volte, <lb/>dopo l'essersi con esso corporalmente congiunte, non tornano a dimostrarsi <lb/>risplendenti, se non in distanze notabili dal disco di Giove, e queste distanze <lb/>si fanno in alcuni tempi maggiori, e in altri minori, e di tutta questa di&shy;<lb/>versit&agrave; puntualissima rispondenza se n'ha dalla diversa costituzione e aspetto <lb/>di Giove col Sole. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di pi&ugrave;, tal perdita di'lume, e con tali regole accadente, a me pare <lb/>che ci assicuri che sola la met&agrave; del disco di Giove che risguarda verso il <lb/>Sole sia luminosa, restando l'altro suo emisfero privo di luce. </s>

<s>Che quando <lb/>egli risplendesse, gli suoi Satelliti, essendogli tanto vicini, riterrebber lume <lb/>bastante a farli cospicui, n&egrave; potrebbe il cono dell'ombra di Giove dal tuttto <lb/>denigrarli. </s>

<s>Oltre che accade talvolta che uno di essi, che in grandezza su&shy;<lb/>pera gli altri, offusca col piccol cono della sua ombra uno che gli &egrave; supe&shy;<lb/>riore. </s>

<s>Come poi tali diverse apparenze possino trarre origine dalla Intelli&shy;<lb/>genza, la quale in genere infonde lo splendore nel corpo di Giove, veramente <lb/>non so io capire, senza porre variet&agrave; e mutazioni nella stessa Intelligenza, <lb/>e per&ograve; volentieri sentirei come tali corde potessero accordarsi col tenore <lb/>della corda principale &rdquo; (ivi, c. </s>

<s>135, 36). </s></p><p type="main">

<s>Ma, per tornare all'Hodierna, egli pens&ograve; a imporre a ciascun Satellite <lb/>un nome proprio. </s>

<s>Galileo gli voleva nominare a principio tutti insieme <emph type="italics"/>Pla&shy;<lb/>netae cosmici,<emph.end type="italics"/> come infatti si legge in una bozza autografa delle ultime pa&shy;<lb/>role scritte nell'Avviso Sidereo (MSS. Gal., P. III, T. III, c. </s>

<s>26). Poi consi&shy;<lb/>gliato dal Vinta, per far partecipe della nuova apoteosi non il solo granduca <lb/>Cosimo, ma tutta insieme la famiglia, gli denomin&ograve; <emph type="italics"/>Planetae Medicaei<emph.end type="italics"/> (Vo&shy;<lb/>linski, Lett. </s>

<s>inedite di Galileo, Firenze 1874, pag. </s>

<s>19). In particolare poi gli <lb/>designava con numeri di ordine, cominciando a contar dal pi&ugrave; intimo, o con <lb/>punti disposti in linea retta, come si vede per esempio a c. </s>

<s>43 del T. V, <lb/>P. III de'Manoscritti. </s>

<s>Il Renieri, come si vide dianzi nel passo trascritto, gli <lb/>distingueva con punti configurati. </s></p><p type="main">

<s>Un nome proprio pareva pi&ugrave; comodo per la trattazione e l'Hodierna, <lb/>giacch&egrave; l'uso, che si voleva far de'Medicei per la ricerca delle Longitudini, <lb/>veniva a costituirli in cielo quasi altrettante luci di <emph type="italics"/>Fari,<emph.end type="italics"/> a'radicali delle <lb/>prime quattro lettere dell'alfabeto greco dava una medesima desinenza tolta <lb/>dal nome <emph type="italics"/>faro,<emph.end type="italics"/> componendone cos&igrave; i nomi di Alfifaro, Bitifaro, Cappifaro e <pb xlink:href="020/01/987.jpg" pagenum="430"/>Deltifaro. </s>

<s>Brutti nomi, n&egrave; per aver convertite le lettere greche nelle per&shy;<lb/>sone del granduca Ferdinando, del padre di lui, della moglie e del principe <lb/>ereditario, i nuovi nomi trasformati in Ferndifaro, Cosmifaro, Vittrifaro e <lb/>Princifaro, riuscirono per verit&agrave; punto pi&ugrave; belli. </s></p><p type="main">

<s>Potrebbe esser questa una prova dell'amoroso studio posto intorno a <lb/>ci&ograve; dall'Hodierna, del quale studio avremmo a dir vero potuto fare un giu&shy;<lb/>dizio pi&ugrave; sicuro, se ci avesse piuttosto descritti gli strumenti, e il partico&shy;<lb/>lar modo di usarli nelle sue osservazioni. </s>

<s>Egli per esempio asserisce &ldquo; nun&shy;<lb/>quam Jovis diametrum excedere secunda 45 &rdquo; (Menologia cit., pag. </s>

<s>11) ma <lb/>non dice in che modo abbia tolta quella scrupolosa misura. </s></p><p type="main">

<s>A pagine 27 e 28, 29 e 30 della Terza parte della sua Menologia si <lb/>vede, per ciascun Satellite in particolare e co'moduli proprii alle loro mas&shy;<lb/>sime digressioni, impressa &ldquo; Orbitae circumscriptio et Orbis dimensiones, <lb/>per singulas circumferentiae partes, ad auspicandas a centro Jovis digres&shy;<lb/>siones, quae mira facilitate promptissime explicantur. </s>

<s>&rdquo; Chi vi getta sopra <lb/>lo sguardo si sovvien facilmente di quelli <emph type="italics"/>Schematismi de'seni,<emph.end type="italics"/> che usava <lb/>Galileo per misurare a occhio le distanze de'Pianetini dal centro di Giove, <lb/>se non che son dall'Hodierna quelli stessi Schematismi ordinati a risolvere <lb/>graficamente, oltre a quello delle distanze, alcuni altri problemi di Astrono&shy;<lb/>mia gioviale. </s></p><p type="main">

<s>N&egrave; qui possiamo lasciar di notare che improprio sembra a noi il nome <lb/>di <emph type="italics"/>Giovilabio<emph.end type="italics"/> dato a questi <emph type="italics"/>Schematismi,<emph.end type="italics"/> quasi fossero strumenti meccanici <lb/>ingegnosamente composti di organi materiali, e di una nuova invenzione di <lb/>Galileo. </s>

<s>Ma lasciando il questionar del nome, a noi par che l'Alb&egrave;ri, e chi <lb/>senza discrezione lo segue, propriamente ne frantendano l'uso. </s></p><p type="main">

<s>Del resto, un autorevolissimo giudizio dell'Opera astronomica dell'Ho&shy;<lb/>dierna fu dato cos&igrave; dal Cassini, nelle sue Effemeridi bolognesi: &ldquo; Non de&shy;<lb/>fuit Joanni Baptistae Hodiernae siculo studium ad Tabularum Mediceorum <lb/>Syderum constructionem, sed cum observationibus annorum tantummodo <lb/>quinque eas fundarit, quam citissime, magnum a Ccelo dissidium exhibuere. </s>

<s><lb/>Praesertim vero latitudinis Canones, prioribus suis observationibus correspon&shy;<lb/>dentes ceu perpetuos edidit, quos panlo post agnovit a succedentibus valde <lb/>et manifeste dissentire, nec tamen eorum reformationem aggressus est, cum <lb/>latitudinis mutationem observationibus deprehenderet, eius vero modum ra&shy;<lb/>tionemque minime perciperet &rdquo; (Bononiae 1668, pag. </s>

<s>5). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Aveva dunque l'Hodierna fatto un passo importante ad occuparsi delle <lb/>variazioni delle Latitudini, di che n&egrave; Galileo, n&egrave; il Castelli, n&egrave; lo stesso Re&shy;<lb/>nieri ebbero alcun sospetto. </s>

<s>E poniamo che ci&ograve; fosse non piccolo merito, il <lb/>Cassini pretendeva di pi&ugrave; di voler sapere il modo e la ragione di cos&igrave; fatte <pb xlink:href="020/01/988.jpg" pagenum="431"/>variazioni Qui stava l'importanza della nuova scoperta astonomica, e qui <lb/>consistevano le principali difficolt&agrave;, a superar le quali s'attendeva nell'Ac&shy;<lb/>cademia del Cimento, tre anni prima che fossero pubblicate le Effemeridi <lb/>bolognesi. </s></p><p type="main">

<s>Giuseppe Campani aveva lavorato per il Granduca un eccellentissimo <lb/>Canocchiale, con cui, nell'estate del 1665, il Borelli incominci&ograve; a osservare <lb/>Saturno e poi Giove. </s>

<s>Sovvenendosi allora di aver fra le mani quella Tavola <lb/>delle Radici, che andava sotto il nome di Galileo, bench&egrave; vi avesse avuto <lb/>gran parte il Castelli, da cui n'ebbe copia quando forse da giovane fre&shy;<lb/>quentava la sua scuola; si sent&igrave; con s&igrave; propizia occasione eccitato a riscon&shy;<lb/>trare i dati di quella Tavola co'nuovi calcoli istituiti. </s>

<s>Gli era allieviata la <lb/>fatica delle osservazioni e dei calcoli dai dotti colloqui che intratteneva, sulle <lb/>ore vespertine, col principe Leopoldo, e con altri Accademici convenuti nelle <lb/>sale de'Pitti, dove frattanto &ldquo; quamplurima de motibus, positionibusque Me&shy;<lb/>diceorum disserebantur &rdquo; (Theoricae Medic. </s>

<s>cit., pag. </s>

<s>VI). </s></p><p type="main">

<s>La notizia, che nell'Accademia fiorentina s'attendeva a studiar le Teo&shy;<lb/>riche de'Medicei, si diffuse per tutta l'Italia, e giunse alle orecchie di Ge&shy;<lb/>miniano Montanari, da cui, come dall'inventor del Micrometro, si poteva <lb/>con ogni buona ragione aspettar la scienza, se non forse teorie sublimi, esat&shy;<lb/>tissime osservazioni. </s>

<s>Tale infatti, di risponder cio&egrave; all'aspettativa, era l'in&shy;<lb/>tenzione dello stesso Montanari, il quale cos&igrave; scriveva da Bologna, il d&igrave; <lb/>25 Agosto 1665, ad Annibale Ranuzzi: </s></p><p type="main">

<s>&ldquo; Ecco a V. S. Ill.ma un poco d'abbozzo dell'Istrumento che, sino vi&shy;<lb/>vente il signor marchese Cornelio Malvasia, felice memoria, avevo pensato <lb/>e cominciato di fabbricare, per rappresentare all'occhio il sito de'Pianeti <lb/>medicei e con facilit&agrave; trovarne a qualsivoglia tempo le configurazioni con <lb/>Giove, data la loro ipotesi giusta, intorno alla quale avevo istituito qualche <lb/>studio. </s>

<s>Avendo perci&ograve; qualche numero d'operazioni fatte vivente detto Si&shy;<lb/>gnore e dopo morto lui ancora, ma distratto da tant'altre cose, non l'ho <lb/>proseguito, ed ora godo sentire da V. S. Ill.ma che il serenissimo signor <lb/>principe Leopoldo vi faccia studiare, e sia in prossimo d'avere da que'grandi <lb/>ingegni tutta la teoria de'Medicei, al che pi&ugrave; facile sar&agrave; loro d'arrivare che <lb/>a me, la debolezza del cui talento non &egrave; da porre con essi a paragone. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Certo che l'Hodierna con tutto che forse, circa que'tempi ch'egli <lb/>stamp&ograve;, le sue Tavole corrispondessero a un bel circa a'tempi odierni, &egrave; <lb/>molto lontano, e le ipotesi sue hanno poco di quella sottigliezza, che a moti <lb/>cos&igrave; veloci e da noi lontani si richiede; oltre qualche non leggero suo in&shy;<lb/>ciampo. </s>

<s>Se fosse per restar servito il serenissimo signor principe Leopoldo <lb/>mio signore d'una scelta di quelle osservazioni, delle quali io faccio pi&ugrave; ca&shy;<lb/>pitale, fatte per lo pi&ugrave; per&ograve; col mio Canocchiale di 18 palmi colla Reticola, <lb/>mediante la quale misuravo assai esattamente le loro distanze ridotte per&ograve; <lb/>sempre a diametri di Giove; io mi pregerei sommamente dell'onore di ser&shy;<lb/>virnelo. </s>

<s>Frattanto sto preparandomi a lavorare una lente di grandezza suf&shy;<lb/>ficiente a veder molto meglio, e forse, se avr&ograve; luogo ove adoperarla, mi <pb xlink:href="020/01/989.jpg" pagenum="432"/>cimenterei a 40 o 50 palmi, e le osservazioni che potr&ograve; poi andar facendo <lb/>le parteciper&ograve; a V. S. Ill.ma, alla quale fo umilissima riverenza &rdquo; (MSS. Cim., <lb/>T. XXIV, c. </s>

<s>185). </s></p><p type="main">

<s>Chi sa quanto fosse il Montanari valoroso in ogni parte della Fisica <lb/>sperimentale, e specialmente nelle osservazioni astronomiche, essendo un <lb/>fatto che il Ramuzzi ademp&igrave; l'ufficio, domanda, desideroso, dopo questa let&shy;<lb/>tura, se Leopoldo de'Medici fece la consueta aspettata accoglienza alle Effe&shy;<lb/>meridi de'Medicei calcolate dal Discepolo del Malvasia. </s>

<s>Noi, per rispondere <lb/>alla domanda, non abbiamo documenti certi, ma se dovessimo andar per <lb/>congetture diremmo che il Principe dell'Accademia fiorentina trascur&ograve; la <lb/>proposta, e ci&ograve; non per altro che per suggestione del Borelli, il quale pre&shy;<lb/>gustava in cuore quelle amarezze contro il Montanari, che poi sprem&egrave;, <lb/>quando questi pubblic&ograve; l'osservazione delle attrazioni per capillarit&agrave; de'cor&shy;<lb/>puscoli galleggianti, che il Borelli pretendeva fosse una sua scoperta fatta <lb/>dodici anni prima. </s>

<s>&ldquo; E perch&egrave; nel medesimo tempo, scriveva da Messina al <lb/>principe Leopoldo, dimorava a Firenze il detto Montanari, e praticava con <lb/>i signori Buoni, e da loro s'informava di tutte le cose, non pu&ograve; allegare <lb/>ignoranza.... Ho ricordato questo a V. A. vedendo la troppa avidit&agrave; di glo&shy;<lb/>ria che ha questo giovane, e la poca gratitudine con i suoi maestri &rdquo; (MSS. <lb/>Cim., T. XIX, c. </s>

<s>96). </s></p><p type="main">

<s>Ma che veramente, vedendosi il Montanari cos&igrave; non curato, non solo <lb/>non proseguisse le sue osservazioni e i suoi calcoli intorno ai Medicei, ma <lb/>lasciasse andare a perdersi la miglior parte dei gi&agrave; fatti, &egrave;, ripetiamo, una <lb/>nostra congettura. </s>

<s>Del resto chi, cercando con pi&ugrave; diligente pazienza e con <lb/>pi&ugrave; comodit&agrave; di quel che non abbiam potuto e saputo far noi, ritrovasse <lb/>quest'altre Effemeridi bolognesi, avrebbe il merito di aggiungere un nuovo <lb/>splendido raggio di gloria alla gi&agrave; per s&egrave; gloriosa scienza gioviale italiana. </s></p><p type="main">

<s>Dicemmo essere un fatto che il Ranuzzi ademp&igrave; fedelmente l'ufficio <lb/>commessogli, e ci&ograve; si argomenta dal veder ch'egli esib&igrave;, e consegn&ograve; nelle <lb/>mani del principe Leopoldo la lettera del Montanari, la quale fu raccolta fra <lb/>le altre carte appartenenti all'Accademia, insiem colla descrizione dello Stru&shy;<lb/>mento, di che si parla in principio della lettera stessa. </s>

<s>Di quella descrizione <lb/>frattanto non vogliamo defraudare il corredo dei documenti riccamente am&shy;<lb/>manniti a questo capitolo della nostra Storia. </s></p><p type="main">

<s>&ldquo; A, A (fig. </s>

<s>85) cinque palline dorate rappresentanti Giove con li quat&shy;<lb/>tro Medicei, delle quali la maggiore sta fitta in uno stile piantato in mezzo <lb/>allo strumento, e l'altre sono sostenute da fili di ottone incurvati, e poste <lb/>in tanta distanza dalla maggiore, quanta &egrave; la maggior digressione di ciascun <lb/>Mediceo da Giove, e sono imperniate nello stilo di mezzo, mediante una lin&shy;<lb/>guetta, che ha dall'altro capo una punta, che mostra li gradi descritti nelle <lb/>rotelle a cui soprastano. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; B, B, quattro rotelle fitte stabili nel medesimo stilo di mezzo, intorno <lb/>le quali &egrave; la divisione del cerchio in 360 gradi, e ciascuna porta il suo Me&shy;<lb/>diceo, come sopra. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/990.jpg" pagenum="433"/><p type="main">

<s>&ldquo; C, C, linguette, per le quali stanno imperniati li Pianetini, la punta <lb/>delle quali segna i gradi nel cerchio delle rotelle. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; D, luogo determinato per vedere con l'occhio la configurazione dei <lb/><figure id="id.020.01.990.1.jpg" xlink:href="020/01/990/1.jpg"/></s></p><p type="caption">

<s>Figura 85.<lb/>Pianeti medicei <lb/>con Giove, e que&shy;<lb/>sto luogo si deve <lb/>far pi&ugrave; basso e <lb/>pi&ugrave; alto del pia&shy;<lb/>no, nel quale si <lb/>muovono li Pia&shy;<lb/>netini, oppure <lb/>stare in esso, con&shy;<lb/>forme la di loro <lb/>latitudine richie&shy;<lb/>de. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E, asse po&shy;<lb/>sta perpendico&shy;<lb/>larmente avanti <lb/>l'Istrumento per&shy;<lb/>ch&egrave; non si veg&shy;<lb/>gano che le pal&shy;<lb/>line, che potran&shy;<lb/>no farsi apparire <lb/>avanti un panno azzurro, o nero come si vuole, per meglio imitare la ve&shy;<lb/>duta del naturale. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La divisione de'cerchi nelle Rotelle deve cominciare in tutte al pari <lb/>una sotto l'altra, e guardare precisamente il luogo d'onde in cielo suppon&shy;<lb/>ghiamo principiare il loro moto, ossia nell'asse del cono dell'ombra di Giove, <lb/>ossia nell'asse della nostra vista, a piacere di chi fabbrica l'ipotesi, e data <lb/>l'ora per fare l'osservazione, devesi calcolare ciascun Pianeta, in quel grado, <lb/>dove trovasi il suo circolo a quell'ora ed ivi nello Strumento collocarlo, il <lb/>che fatto, dal luogo prefisso all'occhio vedrassi la loro configurazione, quale <lb/>in tale ora dovr&agrave; vedersi in cielo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Potrebbonsi ancora disegnare nel muro o panno opposto alcune linee <lb/>parallele fra loro e perpendicolari all'orizzonte, in distanza una dall'altra <lb/>un diametro apparente della Pallina maggiore, e che una di esse corrispon&shy;<lb/>desse all'occhio, per lo centro di essa Palla maggiore, ad effetto di nume&shy;<lb/>rare in un istante le distanze de'Medicei da Giove in diametri di esso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esponendosi in debito luogo un lume, a stanza serrata, si vedrebbe <lb/>qual de'Pianeti e quando restasse ecclissato nell'ombra della Palla mag&shy;<lb/>giore, ossia corpo di Giove. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pensai ultimamente al modo, che non &egrave; difficile, di rappresentare le <lb/>medesime apparenze in un Orologio da pendolo, al moto del quale ciascuna <lb/>delle Palline facesse il proprio moto nel suo cerchio, e da un luogo prefisso <pb xlink:href="020/01/991.jpg" pagenum="434"/>se ne vedesse la configurazione, ma quando non vi sia ipotesi certissima del <lb/>loro moto, ogni anno per lo meno avrebbe bisogno di qualche correzione. </s>

<s><lb/>Per altro sarebbe molto pi&ugrave; comodo lo Strumento se, aggiustato una volta, <lb/>camminasse lungo tempo da s&egrave;, per fuggire il tedio de'calcoli. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; &Egrave; per&ograve; vero che stimavo necessario supporre ellittico il moto de'Me&shy;<lb/>dicei, cos&igrave; indotto da certe mie considerazioni sopra l'osservazione di questi <lb/>tempi ed antichi, e per&ograve; avevo pensato a farli camminare in una Ellisse <lb/>nello Strumento, facendo passare con le linguette C, C medesime un dente <lb/>che avessero sotto, per un canaletto ovato nella Rotella, o in altro de'modi, <lb/>che pu&ograve; suggerire il Torno da ovati. </s>

<s>E finalmente in pratica molte altre <lb/>cose ponno aggiungersi per trarne comodo ed utilit&agrave; maggiore, conforme <lb/>l'occasion suggerisce &rdquo; (MSS. Cim., T. XXIV, c. </s>

<s>186). </s></p><p type="main">

<s>Ma intanto, mentre che il Montanari si sentiva cos&igrave; eccitato a ritornare <lb/>sopra i suoi studii gioviali, da que'colloqui vespertini tenuti nell'Accade&shy;<lb/>mia de'Pitti, e che furono occasione di quelli eccitamenti, ne nacque, dice <lb/>il Borelli, &ldquo; ut hoc Opusculum e manibus exciderit, quod, cum ostendissem <lb/>serenissimo sapientissimoque principi Leopoldo, eiusque acerrimo iudicio <lb/>submisissem, censuit ipse, pariterque alii amici, ut quam primum edere&shy;<lb/>tur &rdquo; (Theoricae cit., pag. </s>

<s>VI, VII). </s></p><p type="main">

<s>Quell'opuscolo conteneva le celeberrime <emph type="italics"/>Theoricae Mediceorum Pla&shy;<lb/>netarum ex causis physicis deductae,<emph.end type="italics"/> divise in due libri, a proposito dei <lb/>quali scriveva l'Autore, il d&igrave; 22 Gennaio 1665: &ldquo; Ho finito di tutto punto <lb/>il II libro delle dette mie teoriche delle Medicee &rdquo; (MSS. Cim., T. XVIII), <lb/>c. </s>

<s>90). Nonostante non fu il Manoscritto in ordine di esser mandato alla <lb/>stampa, che nel seguente mese di Ottobre. </s>

<s>Le vane paure dell'Inquisitore <lb/>fecero indugiare all'anno dopo la pubblicazione, che si doveva fare a Bo&shy;<lb/>logna, affidandola alle cure del Montanari, le amarezze verso il quale si te&shy;<lb/>nevano dal Borelli tuttavia segrete, ond'&egrave; che avendo il motivo e l'occa&shy;<lb/>sione di rimproverarlo, &ldquo; non mi arrischio, diceva, di scrivergli nulla, perch&egrave; <lb/>ho provato in altre occasioni quanto mal volentieri egli riceva gli amiche&shy;<lb/>voli avvertimenti, ed ora tanto pi&ugrave; non vorrei alienarmelo, quando che avrei <lb/>bisogno dell'opera sua per assistere alla correzione della stampa del mio <lb/>Libro &rdquo; (ivi, c. </s>

<s>93). </s></p><p type="main">

<s>Poi la stampa si fece in Firenze, per la fretta, della quale e della data <lb/>del Libro anticipata di un anno furon causa i Dialoghi fisici del Fabry &ldquo; il <lb/>quale mi ha reso attonito, scriveva lo stesso Borelli nel Febbraio del 1666 <lb/>al principe Leopoldo, per quel poco che ho veduto, perch&egrave; veggo che a quel <lb/>cervellaccio gli son sovvenuti concetti assai simili a'miei, con i quali spiego <lb/>le cagioni fisiche de'moti de'Pianeti..... Ho stimato necessario stampar <lb/>furiosamente questa mia Opera cost&igrave; a Firenze, non pi&ugrave; a Bologna, .... per&shy;<lb/>ch&egrave; esca fuori presto sotto la data dell'anno passato, quand'io veramente <lb/>la presentai al serenissimo Granduca e gliela dedicai l'Ottobre passato &rdquo; <lb/>(ivi, c. </s>

<s>111). </s></p><p type="main">

<s>De'due Libri, in che, come dicemmo, &egrave; divisa l'Opera del Borelli, nel <pb xlink:href="020/01/992.jpg" pagenum="435"/>primo s'investigano le cause fisiche e meccaniche de'moti; nel secondo si <lb/>danno le regole per le osservazioni. </s>

<s>Una delle principali cose che occorre <lb/>a notare &egrave; la conferma e dimostrazione fisica matematica delle Orbite ellit&shy;<lb/>tiche, dal Montanari ammessa per induzione, e dalla prima Scuola galileiana <lb/>affatto negata, ed &egrave; altres&igrave; pi&ugrave; notabile che le variazioni e le irregolarit&agrave; os&shy;<lb/>servate nei moti le attribuisca l'Autore ai vari modi degl'impulsi radiosi <lb/>del Sole, o a qualche cosa equivalente insomma all'attrazion neutoniana, <lb/>ch'egli rende ostensibile con ingegnose esperienze fondate sopra le propriet&agrave; <lb/>del Magnete. </s></p><p type="main">

<s>Rispetto alle osservazioni, quanto fossero arguti gli avvedimenti del Bo&shy;<lb/>relli basterebbe a provarlo il cap. </s>

<s>III del Libro II, dove, in trattar delle va&shy;<lb/>riet&agrave; dell'Ecclissi, dimostra sperimentalmente, con Canocchiali via via di <lb/>maggiore ingrandimento, come nemmen co'pi&ugrave; grandi e pi&ugrave; squisiti Stru&shy;<lb/>menti si arriva a togliere affatto l'irradiazione, cosa che pur sarebbe cos&igrave; <lb/>necessaria ad avvisar nell'Ecclissi il tempo de'precisi contatti. </s></p><p type="main">

<s>Altre dottrine di quest'Opera insigne occorrer&agrave; di notarle fra poco, e <lb/>intanto &egrave; da saper che a'colloqui vespertini, che si tenevano in Firenze alla <lb/>presenza del principe Leopoldo, uno de'primi e principali convenutivi era <lb/>il Viviani. </s>

<s>A dissertar di Giove e de'Medicei era per lui come un rinfre&shy;<lb/>scare i pi&ugrave; verdi e pi&ugrave; gloriosi allori del suo adorato Maestro, nel quale ef&shy;<lb/>fetto un acuto stimolo di rivalit&agrave;, oltre al nobile amor della scienza, non gli <lb/>permetteva, a confronto del Borelli, di mostrarsi inoperoso. </s></p><p type="main">

<s>Ei non sa per&ograve; dilungarsi da'metodi praticati da Galileo, e perci&ograve;, co&shy;<lb/>noscendo bene quanto importasse, nelle operazioni micrometriche del suo <lb/>Maestro, il sapere l'ingrandimento del Canocchiale, ne immagin&ograve;, per mi&shy;<lb/>surarlo pi&ugrave; facilmente, questi tre modi: &ldquo; Io. </s>

<s>Sia AB (fig. </s>

<s>86) una tavoletta <lb/>tinta di nero, in mezzo di cui sia una striscia bianca uniforme di larghezza, <lb/>e in mezzo di questa un sottile ago fermato a piombo, sul quale si possano <lb/><figure id="id.020.01.992.1.jpg" xlink:href="020/01/992/1.jpg"/></s></p><p type="caption">

<s>Figura 86.<lb/>infilare dei cerchi di cartone tinti <lb/>neri, i diametri de'quali abbiano <lb/>nota proporzione con la larghezza <lb/>della striscia. </s>

<s>E quivi, infilato or <lb/>un ed ora un altro de'cerchi, si <lb/>osservi con l'Occhiale posto a di&shy;<lb/>rimpetto all'asse qual di loro ap&shy;<lb/>parir&agrave; all'occhio accomodato all'Oc&shy;<lb/>chiale uguale alla larghezza della <lb/>fascia vista con l'altro occhio li&shy;<lb/>bero; che di qui si aver&agrave; la proporzione dell'ingrandimento. II

o. </s>

<s>Ovvero, <lb/>prese le distanze de'fochi dell'obiettivo e della lente oculare, quanto quella <lb/>si trover&agrave; maggiore di questa, di tanto l'Occhiale accrescer&agrave; ogni larghezza <lb/>o altezza di oggetto. </s>

<s>IIIo. </s>

<s>Ovvero, fatti due cerchi uguali e neri, ed uno os&shy;<lb/>servato con l'Occhiale nella distanza che si vuole, in campo bianco, l'altro <lb/>accostisi e discostisi finch&egrave; l'occhio libero lo giudichi, nel medesimo campo, <pb xlink:href="020/01/993.jpg" pagenum="436"/>grande quanto l'altro veduto coll'Occhiale, e misurato quanto &egrave; dall'occhio <lb/>al cerchio visto coll'occhio libero, tante volte quanto questa distanza entra in <lb/>quell'altra, tanto aggrandisce l'Occhiale &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXIV, c. </s>

<s>3). </s></p><p type="main">

<s>Cos&igrave; praticando il Viviani i metodi, che Galileo insegna nel Nunzio Si&shy;<lb/>dereo per misurare le piccole distanze, e quegli altri che avr&agrave; suggerito a <lb/>voce al suo discepolo diletto, e assai poco difformi dagli esposti da noi di <lb/>sopra nel paragrafo I; ritrov&ograve; quegli elementi, che scrisse di sua propria mano <lb/>in una Tavola de'moti de'Satelliti di Giove. </s>

<s>&ldquo; Fere omnes Quatuor in eo&shy;<lb/>dem plano circuitus suos absolvunt, declinante a Jovis orbita gradibus 2, 54&prime;, <lb/>moventurque ab ortu in occasum in parte Jovis a nobis obversa. </s>

<s>Primus <lb/>omnium intimus distat a centro Jovis per semid. </s>

<s>Jovis 5 2/3, periodum suam <lb/>perficit spatio dierum 1, 18h, 22&prime;. </s>

<s>Secundus a Jove distat per semid. </s>

<s>9 et <lb/>revolvitur 3d, 13h, 14. Tertius a Jovis centro distat per semid. </s>

<s>Jovis 14 et <lb/>paulo amplius, et periodum perficit d. </s>

<s>7, h. </s>

<s>3, 42&prime;. </s>

<s>Quartus omnium exti&shy;<lb/>mus distat a centro Jovis per semid. </s>

<s>25 1/3, et revolvitur per d. </s>

<s>16, h. </s>

<s>3, 2&prime; &rdquo; <lb/>(ivi, T. CXXXIX, c. </s>

<s>17). </s></p><p type="main">

<s>Qualunque per&ograve; si fosse l'esattezza di questi calcoli, ne'quali &egrave; nota&shy;<lb/>bile l'inclinazione del piano delle orbite de'Satelliti col piano dell'orbita di <lb/>Giove, il Viviani vi torn&ograve; poi sopra altre volte, ora ricorrendo ai moti me&shy;<lb/>dii, ora a nuove osservazioni dirette. </s>

<s>Ne ebbe qualche variet&agrave; di resultati, <lb/>come pu&ograve; vedersi dalla traduzione delle <emph type="italics"/>Osservazioni intorno al mondo<emph.end type="italics"/> del <lb/>Gadroy, dove il Viviani stesso, ch'&egrave; il traduttore, destramente inserisce i <lb/>suoi nuovi numeri. </s>

<s>&ldquo; Egli (Galileo) si accorse che la Prima delle gioviali, <lb/>cio&egrave; la pi&ugrave; prossima al corpo di Giove &egrave; lontana dal di lui centro cinque <lb/>semidiametri e 50 minuti, e gli gira intorno in tempo di un giorno, ore 18, <lb/>28&prime;, 35&Prime;, 33&tprime;, 14&qprime;. </s>

<s>La seconda distante otto semidiametri e 50 minuti, e <lb/>compisce il suo corso in tre giorni e ore tredici 18&prime;, 21&Prime;, 32&tprime;, 20&qprime;. </s>

<s>La Terza, <lb/>che in apparenza &egrave; la massima delle quattro, &egrave; lontana dal centro di Giove <lb/>tredici semid. </s>

<s>e 52 minuti, e termina il suo giro in sette giorni e due ore <lb/>27&prime;, 25&Prime;, 57&tprime;, 9&qprime;. </s>

<s>E finalmente la Quarta, cio&egrave; la remotissima e che appa&shy;<lb/>risce in grandezza la minima, ne &egrave; distante 24 semid. </s>

<s>e 35&prime;, e fa il suo in&shy;<lb/>tero periodo in sedici giorni e ore diciotto, minuti 7&prime;, 12&Prime;, 21&tprime;, 9&qprime; &rdquo; (ivi, <lb/>T. CXLI, c. </s>

<s>202). </s></p><p type="main">

<s>Nel <emph type="italics"/>Discorso intorno al mondo<emph.end type="italics"/> lo stesso Viviani torna a trattar de'Quat&shy;<lb/>tro pianeti medicei, e riporta gli elementi stessi delle Tavole da noi di sopra <lb/>riferiti: &ldquo; Grande in vero ed utilissimo a noi abitatori della Terra si &egrave; il <lb/>nuovo scoprimento de'quattro Pianeti fatto dalla pi&ugrave; che lincea accortezza <lb/>del nostro Galileo, quali, in onore dell'eroica prosapia della casa reale di <lb/>Toscana, volle che si appellassero Stelle medicee, affinch&egrave; la memoria e la <lb/>fama di Essa godesse della vita e della sorte degli stessi Pianeti. </s>

<s>Tre di <lb/>queste furono la prima volta osservate dal predetto Galileo il d&igrave; 7 Gen&shy;<lb/>naio 1610, nella prima ora della notte, e il quarto nel 14 dell'istesso mese, <lb/>e per molte osservazioni ch'ei vi fece, si accorse che giravano intorno al <lb/>detto Pianeta. </s>

<s>Il pi&ugrave; prossimo di tutti &egrave; lontano dal centro di Giove 5 2/3 <pb xlink:href="020/01/994.jpg" pagenum="437"/>semid. </s>

<s>del medesimo Giove, ed il suo periodo lo termina in un giorno e <lb/>ore 18, 22&prime;. </s>

<s>Il secondo &egrave; lontano per 9 semidiametri, e compisce il suo pe&shy;<lb/>riodo in giorni 3, ore 13, 14&prime;. </s>

<s>Il terzo &egrave; lontano per pi&ugrave; di 14 semid. </s>

<s>ed <lb/>il suo periodo lo termina in giorni 7, h. </s>

<s>3, 42&prime;. </s>

<s>Il quarto pi&ugrave; discosto di <lb/>tutti &egrave; lontano di pi&ugrave; di 25 semid. </s>

<s>e compisce il suo periodo in giorni 16, <lb/>h. </s>

<s>3, 2&prime; &rdquo; (ivi, c. </s>

<s>277). </s></p><p type="main">

<s>In questo mentre che il Viviani attendeva cos&igrave; alle osservazioni e ai <lb/>calcoli de'Medicei, il Cassini, eccitato anch'egli dalla notizia di ci&ograve; che si <lb/>studiava nell'Accademia fiorentina, mand&ograve; a lui manoscritte le Tavole dei <lb/>suoi <emph type="italics"/>Elementi.<emph.end type="italics"/> Aveva parecchi anni avanti, e prima che nascessero fra loro <lb/>le fiere e ostinate inimicizie, il Viviani stesso avuto copia dal Borelli di <lb/>quella Tavola delle Radici, di che abbiamo parlato pi&ugrave; sopra, e intendendo <lb/>di promuovere la gloria di Galileo e di avvantaggiare la scienza, la mandava <lb/>il di 22 Dicembre 1665 al grande Astronomo di Bologna, accompagnata da <lb/>una sua Lettera dove diceva: &ldquo; L'inclusa Tavola del Galileo &egrave; copiata da <lb/>una che anni sono m'invi&ograve; di Messina il signor Borelli, e la quale io tra&shy;<lb/>smetto a V. S. in ordine all'intenzione che mi sovviene di averle data, che <lb/>sarebbe gratissimo che questa potesse in qualche parte conferire alla cor&shy;<lb/>rezione delle osservazioni sue intorno alle Medicee, bench&egrave; io credo che in <lb/>oggi, mediante la maggior perfezione degli Occhiali, ed esquisitezza degli <lb/>Orologi, ed esattezza de'modi ritrovati dopo per misurar le distanze di quelle <lb/>da Giove, si sia arrivati ancora a maggiore approssimazione nelle determi&shy;<lb/>zioni di esse distanze e de'moti medii de'Pianetini, siccome delle loro ec&shy;<lb/>centricit&agrave; &rdquo; (ivi, T. CXLII, c. </s>

<s>107). </s></p><p type="main">

<s>Il Cassini rispondeva il d&igrave; 9 Gennaio seguente essergli stato carissimo <lb/>il Foglio de'moti de'Pianeti gioviali trasmessogli come opera di Galileo, e <lb/>confrontati que'numeri co'suoi, aveva trovato esser queste le pi&ugrave; notabili <lb/>differenze: &ldquo; Ho veduto che i moti del signor Galileo sono presi dalla con&shy;<lb/>giunzion superiore de'Pianetini con Giove, mentre i miei sono presi dal <lb/>principio di Ariete, ma ridotti i miei all'istesso principio trovo essere in ogni <lb/>Pianeta i moti medii pi&ugrave; tardi di quelli del Galileo, almeno quindici secondi <lb/>il giorno, ed almeno un grado e mezzo l'anno, il che dal tempo che si os&shy;<lb/>serva importa almeno 84 gradi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E quanto alle Radici, la mia rappresenta nell'istesso grado le Radici <lb/>del Galileo nel 1636 del III e del IV Pianeta; quella del II nel termine di <lb/>tre, e quella del I nel termine di gradi 20. Ma osservo che il primo era <lb/>allora vicinissimo allo Scorpione, niente opportuno a presentare dalle osser&shy;<lb/>vazioni la sua Radice. </s>

<s>Nel 1616 i miei numeri rappresentano la Radice del <lb/>Galileo del I Pianetino nel termine di 11 gradi, il che dimostra che nel 1636 <lb/>s&igrave; gran differenza non pu&ograve; attribuirsi a difetto de'miei numeri, perch&egrave; molto <lb/>maggiore sarebbe riuscita nel 1616, eppure &egrave; molto minore. </s>

<s>Ma nella Ra&shy;<lb/>dice del II discordiamo 74 gradi, in quella del III 72, in quella del IV so&shy;<lb/>lamente 5 gradi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Nella Radice del 1600 ci allontaniamo tutto il cielo, onde tengo per <pb xlink:href="020/01/995.jpg" pagenum="438"/>fermo che a quelle del Galileo sia stato apposto per errore l'anno 1600, <lb/>invece dell'anno 1610, perch&egrave; i miei numeri quell'anno rappresentano i <lb/>predetti assai da vicino, cio&egrave; la Radice del I nel termine di gradi 8, del <lb/>II di gradi 14, del III di gradi 7, del IV di gradi 5, onde raccolgo che le <lb/>grandi differenze del 1616 nemmeno procedano da'miei numeri, perch&egrave; riu&shy;<lb/>scirebbero maggiori nel 1610. &rdquo; </s></p><p type="main">

<s>&ldquo; Le radici del 1610 e del 1615, non avendo aggiunta l'ora, ho sup&shy;<lb/>posto che siano ridotte al mezzogiorno dell'ultimo dell'anno precedente, n&egrave; <lb/>essendovi aggiunto il luogo non ho tenuto conto della differenza del meri&shy;<lb/>diano, il che non so se fosse per portar maggiore o minor differenza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Le grandezze degli Orbi sono dentro a termini maggiori e minori, e <lb/>che si osservano in diversi tempi maggiori per&ograve; di quelle che osservai l'anno <lb/>passato, ed osservano le regole da me toccate nella Lettera delle ombre, cio&egrave; <lb/>sono quasi in continua proporzione, in modo che la proporzione de'pi&ugrave; este&shy;<lb/>riori agli interiori vicini &egrave; sempre un poco maggiore di quella delli meno <lb/>esteriori agli altri suoi interiori. </s>

<s>Inoltre, paragonati con i loro moti perio&shy;<lb/>dici, risplende quivi ancora prossimamente quella proporzione che, secondo <lb/>la regola de'progetti, avrebbero, se avessero acquistato quell'altezza con es&shy;<lb/>sere stati progetti con tal velocit&agrave; da Giove. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Prego V. S. a confrontare con altri esemplari, se altri ve ne sono, i <lb/>numeri delle prime Radici ed avvisarmi se si trova differenza o no &rdquo; (ivi, <lb/>T. CXLV, c. </s>

<s>1, 2). </s></p><p type="main">

<s>Il Viviani mand&ograve; veramente un'altra Nota delle Radici per confrontare <lb/>con quella prima, accennando al dubbio se fosse quella Nota propriamente <lb/>di Galileo o del Castelli, per cui il Cassini rispondeva ai di 3 Aprile di quel&shy;<lb/>l'anno 1666: &ldquo; Mi &egrave; anche stata carissima la Nota delle Radici delle Medi&shy;<lb/>cee, siano del Galileo o del Castelli, le quali concordano con le prime man&shy;<lb/>date, eccetto che nel 1600 in luogo di 1610 &rdquo; (ivi, c. </s>

<s>8). </s></p><p type="main">

<s>Nel 1668 que'diligentissimi studii, che aveva fatto il Cassini intorno a <lb/>Giove, uscirono in Bologna alla luce sotto il titolo di <emph type="italics"/>Ephemerides bono&shy;<lb/>nienses Mediceorum syderum,<emph.end type="italics"/> n&egrave; vogliamo chiamar altri a giudicarne che <lb/>il proprio Autore, il quale cos&igrave; soggiungeva nell'opuscolo <emph type="italics"/>De l'origine de <lb/>l'Astronomie,<emph.end type="italics"/> dop'aver accennato alla scoperta e alle osservazioni de'Satel&shy;<lb/>liti di Giove: &ldquo; On avoit d&eacute;ja donn&eacute; au public des Tables de leur mouve&shy;<lb/>ment, mais les erreurs imperceptibles, que l'on n'avoit p&ugrave; y &eacute;viter, s'&eacute;toient <lb/>tellement accumul&eacute;es, dans la suite du tems, que ces Tables &eacute;toient deve&shy;<lb/>nu&euml;s inutiles &rdquo; (Divers Ouvr. </s>

<s>d'Astronom., Amsterdam 1736, pag. </s>

<s>44). </s></p><p type="main">

<s>Quegli errori, se il Cassini disse non aver potuto evitarli, doveva anche <lb/>averli presentiti in quelle discrepanze fra'numeri delle massime digressioni, <lb/>che resultavano dalle misure prese in varie osservazioni; discrepanze che il <lb/>Borelli e poi il Newton attribuivano per la massima parte alla mancanza o <lb/>all'imperfezione degli Strumenti micrometrici. </s>

<s>Nell'opuscolo <emph type="italics"/>De mundi Sy&shy;<lb/>stemate,<emph.end type="italics"/> volendo il celebre Inglese riscontrar nel piccolo Mondo gioviale la <lb/>legge delle forze attrattive in ragion reciproca de'quadrati delle distanze <pb xlink:href="020/01/996.jpg" pagenum="439"/>riporta quelle medesime distanze misurate da Galileo, dal Mario, dal Cas&shy;<lb/>sini e dal Borelli, prima dell'invenzione del Micrometro, <emph type="italics"/>et post inventionem <lb/>Micrometri,<emph.end type="italics"/> quelle del Tounley e del Flamsteed. (Lausannae 1744, pag. </s>

<s>9). </s></p><p type="main">

<s>Ma i numeri, per quel che riguarda i nostri Italiani, se si eccettui il <lb/>Cassini che gli pose a pag. </s>

<s>15 delle Effemeridi bolognesi, non son derivati <lb/>da fonti sicure. </s>

<s>Le massime distanze da Giove, ritrovate da Galileo per i <lb/>primi tre Satelliti, il Newton le ricopia dall'Hodierna, ma di dove questi le <lb/>ricavasse non l'abbiamo potuto sapere. </s>

<s>A pag. </s>

<s>11 della citata Menologia fa <lb/>menzione di ci&ograve; che si legge &ldquo; in libro De maculis solaribus &rdquo; dove l'Au&shy;<lb/>tore &rdquo; in schemate Jovis et Satellitum asserit digressiones maximas Quar&shy;<lb/>tae et supremae Stellae, quae tres alias circumambit, non trascendere duo&shy;<lb/>decim apparentes Jovis diametros. </s>

<s>&rdquo; Ma in verit&agrave; non dice altro l'Autore <lb/>delle Macchie solari se non che la IV Stella &ldquo; &egrave; lontana da Giove circa a <lb/>15 minuti, che tanto &egrave; il semidiametro del suo cerchio &rdquo; (Alb. </s>

<s>III, 497, 98). <lb/>Or perch&egrave; Galileo determin&ograve; come vedemmo l'apparente grandezza di Giove <lb/>ora in 39, ora in 41, ora in 50 minuti secondi, la pi&ugrave; piccola delle distanze <lb/>che ne risulterebbe sarebbe 18 diametri di Giove, e non 12 come pone <lb/>l'Hodierna. </s></p><p type="main">

<s>Ma nemmeno le digressioni degli altri tre Satelliti, attribuite a Galileo <lb/>dall'Hodierna e dal Newton, riscontrano con nessuna di quelle, che vera&shy;<lb/>mente Galileo lasci&ograve; ne'suoi scritti, ai tempi de'due detti Astronomi non <lb/>conosciuti. </s>

<s>E perch&egrave; Galileo stesso si prov&ograve; pi&ugrave; volte e per varie vie a de&shy;<lb/>finir pi&ugrave; giustamente che fosse possibile quelle misure, avendone sempre un <lb/>resultato alquanto diverso, noi vogliamo nella Tavoletta seguente riferirle in <lb/>ordine, per maggiore comodit&agrave; di riscontro, aggiungendovi quelle che ri&shy;<lb/>trov&ograve; il Viviani proseguendo i metodi del suo Maestro. </s></p><p type="main">

<s>Noi designeremo i Satelliti co'nomi che impose a loro il Cassini, rac&shy;<lb/>comandandocegli alla memoria col verso <emph type="italics"/>Pallas, Juno, Themisque, Ceres <lb/>tibi Jupiter adstant.<emph.end type="italics"/> Dal n.o I al n.o IV si riferiscono i moduli presi da Ga&shy;<lb/>lileo per i quattro varii Schematism&igrave; de'seni (Alb. </s>

<s>V, 175, 76). Il n.o V ri&shy;<lb/>ferisce le massime digressioni scritte in una Lettera al Castelli (ivi, VI, 319). <lb/>Il n.o VI quelle date come <emph type="italics"/>Rationes pro radiis Orbitarum<emph.end type="italics"/> (ivi, V, 248) e <lb/>il n.o VII quelle che il d&igrave; 14 Gennaio 1617 divis&ograve; di ridurre a nuove mi&shy;<lb/>sure <emph type="italics"/>in gratiam superioris correctionis Tabularum<emph.end type="italics"/> (ibi, pag. </s>

<s>290). Di rin&shy;<lb/>contro al n.o VIII si pongono le massime digressioni poste dal Viviani nella <lb/>Tavola di Giove (MSS. Gal. </s>

<s>Disc., T. CXL, c. </s>

<s>17) e in ultimo il n.o IX ri&shy;<lb/>ferisce le'dette misure inserite dallo stesso Viviani nelle Osservazioni del <lb/>Gadroy (ivi, T. CXLI, c. </s>

<s>202). <pb xlink:href="020/01/997.jpg" pagenum="440"/><figure id="id.020.01.997.1.jpg" xlink:href="020/01/997/1.jpg"/></s></p><p type="caption">

<s><emph type="italics"/>Raggi delle Orbite delle Medicee in semidiametri di Giove.<emph.end type="italics"/></s></p><p type="main">

<s>Chi rivolge lo sguardo su questa Tavola ritrova di fatto quelle discre&shy;<lb/>panze, che misero il Borelli in gran pensiero e in gran sollecitudine di con&shy;<lb/>ciliarle con la pi&ugrave; vera misura, trovata per osservazioni pi&ugrave; diligenti, e con <lb/>Istrumenti pi&ugrave; esatti. </s>

<s>La VII posizione &egrave; quella che il Newton attribuisce <lb/>al Borelli, e ch'ei chiama <emph type="italics"/>magis exacta,<emph.end type="italics"/> ma pi&ugrave; esatta che mai &egrave; la VIII <lb/>del Viviani, la quale, da una piccola differenza in fuori nel III Satellite, ri&shy;<lb/>scontra con quella ritrovata nel 1671 dal Cassini. </s></p><p type="main">

<s>Le massime distanze poste nelle Effemeridi bolognesi furono dall'Au&shy;<lb/>tore misurate in pi&ugrave; modi, ma principalmente col Micrometro a reticolo del <lb/>Montanari, che trov&ograve; descritto nelle Effemer&igrave;di del Malvasia, e per mezzo <lb/>del tempo, che impiega un Satellite, a passare o avanti o dietro il disco di <lb/>Giove, comparato al tempo che Giove stesso impiega a passar per un filo <lb/>teso perpendicolarmente alla direzione del suo moto diurno. </s>

<s>Ma egli avverti <lb/>una causa di errore nella variabilit&agrave; de'tempi de'passaggi per ragion delle <lb/>latitudini de'Satelliti, che perci&ograve; non sempre passano per il centro del Pia&shy;<lb/>neta; causa di errore, ch'egli poi destramente evit&ograve;, nell'occasione presen&shy;<lb/>tatasi l'anno 1671, quando ritornando i Satelliti al loro Nodo boreale, le <lb/>congiunzioni riuscivano senza dubbio centrali. </s></p><p type="main">

<s>Da ci&ograve; che occorse al Cassini si comprende che le notate discrepanze <pb xlink:href="020/01/998.jpg" pagenum="441"/>dipendevano, oltre al difetto e all'imperfezion del Micrometro, da un'altra <lb/>causa, che &egrave; quella delle variabilit&agrave; delle latitudini, intorno alle quali insor&shy;<lb/>sero tali e s&igrave; importanti questioni, che non si vogliono lasciare addietro in <lb/>questa Storia. </s></p><p type="main">

<s>L'Agucchia, nella Lettera altrove citata, dop'aver descritti a Galileo i <lb/>tempi periodici delle Medicee da s&egrave; trovati, soggiunge: &ldquo; Mi &egrave; stato anche <lb/>avviso di comprendere che questa (la Medicea pi&ugrave; lontana) retrogradi al&shy;<lb/>quanto nella dimora o stazione sua occidentale, poich&egrave; due volte in trenta&shy;<lb/>quattro d&igrave; torn&ograve; dai dieci alli otto minuti; onde mi ha fatto cadere nel pen&shy;<lb/>siero che possa avere qualche cerchietto, quasi epiciclo, intorno al quale si <lb/>raggiri, e forse per simile ragione avviene che talora si sieno vedute pie&shy;<lb/>gare all'Ostro, talvolta a Tramontana &rdquo; (Alb. </s>

<s>VIII, 175). </s></p><p type="main">

<s>Galileo, ch'era stato infin da principio nell'opinione che i piani delle <lb/>orbite delle Stelle gioviali fossero paralleli al piano dell'Ecclittica, a queste <lb/>parole cominci&ograve; a pensar meglio al fatto, ma non aveva modo di assicurar&shy;<lb/>sene, infintanto che, inventato lo Strumento micrometrico descritto del Bo&shy;<lb/>relli, sper&ograve; che potesse questo servir bene all'uopo. </s>

<s>&ldquo; Nota quod si in Instru&shy;<lb/>mento, quo distantiae capiuntur, notetur linea, quae illum secet secundum <lb/>angulum, quo ductus Eclypticae secat parallelum Aequatori, in loco Jovis; <lb/>per motum Jovis in hac linea cognoscetur numquid Medicei Planetae feran&shy;<lb/>tur in planis Ecclipticae parallelis &rdquo; Alb. </s>

<s>V, 84). </s></p><p type="main">

<s>Se poi facesse anche quest'uso dello Strumento, e qual resultato ne <lb/>avesse, &egrave; incerto: solamente sappiamo che nella II Lettera solare scriveva <lb/>al Velsero essergli note &ldquo; le cause del quando e perch&egrave; or l'uno or l'altro <lb/>de'Satelliti declina o verso Borea o verso Austro in relazione a Giove &rdquo; <lb/>(Alb. </s>

<s>III, 395). Ma mentre s'aspettava che Galileo dicesse quali fossero que&shy;<lb/>ste cause, che al Velsero non dice, e mentre il Castelli francamente asseriva <lb/>di non essersi &ldquo; ingannato punto in notare le strane declinazioni di queste <lb/>stelle &rdquo; (MSS. Gal., P. III, T. VII, c. </s>

<s>28) Simon Mario pubblicava il suo <lb/><emph type="italics"/>Mundus Jovialis,<emph.end type="italics"/> dove esplicando nella II Parte il Fenomeno VI, cos&igrave; di&shy;<lb/>ceva: &ldquo; Postquam vero mihi etiam de hoc phaenomeno constaret, nimirum <lb/>hos Joviales non semper in linea recta ducta per Jovem Ecclipticae paral&shy;<lb/>lela versari, sed modo in Boream modo in Austrum ab hac deflectere, dif&shy;<lb/>ferentia perceptibili; coepi etiam in hoc phaenomenon diligentius inquirere, <lb/>tandemque deprehendi hos Joviales, in maxima elongatione, semper in prae&shy;<lb/>dicta linea parallela offendi, extra vero hos terminos semper ab hac decli&shy;<lb/>nare, et in superiore quidem parte suae orbitae australes esse, in inferioro <lb/>vero boreales &rdquo; (Norimbergae 1614, pag. </s>

<s>42). </s></p><p type="main">

<s>Galileo indugi&ograve; dopo il Mario nove anni a dir ci&ograve; che pensava di que&shy;<lb/>ste latitudini, e lo fece a principio del <emph type="italics"/>Saggiatore,<emph.end type="italics"/> negando contro lo stesso <lb/>Mario che i quattro cerchi delle Medicee inclinino dal piano dell'Ecclittica, <lb/>e asserendo che &ldquo; anzi sono eglino ad esso sempre equidistanti &rdquo; (Alb. </s>

<s><lb/>IV, 151). Quanto poi al segno della declinazione de'semicerchi superiori, <lb/>ossia di quelli che son pi&ugrave; lontani dalla Terra, rispetto ai semicerchi infe-<pb xlink:href="020/01/999.jpg" pagenum="442"/>riori, che son pi&ugrave; vicini; Galileo stabilisce questa regola per costante e per <lb/>generale: &ldquo; Quando Giove si trover&agrave; fuori del piano dell'Ecclittica, acca&shy;<lb/>der&agrave; che, se la sua latitudine sar&agrave; da esso piano verso Settentrione, restando <lb/>pure i quattro cerchi delle Medicee paralleli all'Ecclittica, si rappresente&shy;<lb/>ranno piegar verso Austro rispetto all'inferiori, che ci si mostreranno pi&ugrave; <lb/>boreali. </s>

<s>Ed all'incontro, quando la latitudine di Giove sar&agrave; australe, le parti <lb/>superiori dei medesimi cerchietti ci mostreranno pi&ugrave; settentrionali dell'in&shy;<lb/>feriori &rdquo; (ivi, pag. </s>

<s>152). </s></p><p type="main">

<s>Trov&ograve; tuttavia pendente la controversia fra l'Astronomo nostro di Fi&shy;<lb/>renze e quello di Brandeburgo l'Hodierna, il quale preso ad esaminarla, <lb/>ebbe a concludere che tutt'e due avevano il torto: Galileo a dire che le <lb/>Medicee non hanno sensibili latitudini, avendole anzi <emph type="italics"/>valde sensibiles,<emph.end type="italics"/> il Mario <lb/>a dire che ne'semicerchi superiori le latitudini sono australi e negl'inferiori <lb/>boreali &ldquo; nam, ex quo Mediceorum latitudines observare cepi, eos perpe&shy;<lb/>tuo boreales in superioribus semicirculis, austrinas vero in inferioribus de&shy;<lb/>prehendo &rdquo; (Menologia cit., pag. </s>

<s>32). </s></p><p type="main">

<s>Rimase a ci&ograve; stupito l'Hodierna, non sapendo da prima persuadersi <lb/>come tanto grossamente si fossero ingannati due cos&igrave; valorosi Osservatori. </s>

<s><lb/>Poi, scoperto che le latitudini erano variabili, allo stupore sottentr&ograve; la ra&shy;<lb/>gione a persuaderlo che, quando osserv&ograve; Galileo, le latitudini dovevano es&shy;<lb/>ser nulle; che quando osserv&ograve; il Mario dovevano esser al modo da lui de&shy;<lb/>scritto, finch&egrave; variando presero la contraria posizione, a quel modo ch'esso <lb/>Hodierna le vide, concludendo essersi ambedue i grandi Astronomi ingan&shy;<lb/>nati nell'asserire il fatto costante. </s></p><p type="main">

<s>Concorda insomma in ci&ograve; con l'Hodierna anche il Cassini, il quale ap&shy;<lb/>parecchiandosi, nel cap. </s>

<s>V delle <emph type="italics"/>Hypotheses des Satellites de Jupiter,<emph.end type="italics"/> a dar <lb/>le regole delle latitudini, nota, a proposito degli Osservatori che lo avevano <lb/>preceduto, &ldquo; comme les uns les ont observ&eacute;es dans un temps, et les autres <lb/>dans un autre, chacun a suppos&eacute; que les r&egrave;gles, qu'il a trouv&eacute;es par les <lb/>observations de son temps, estoient perpetuelles &rdquo; (edit. </s>

<s>cit., pag. </s>

<s>390). N&egrave; <lb/>qui possiamo lasciar di proporre ai Lettori questa considerazione: Che il <lb/>Mario, nel fretteloso circolo delle sue osservazioni, non si accorgesse della <lb/>variabilit&agrave; delle latitudini, s'intende, ma come pu&ograve; intendersi che non se ne <lb/>assicurasse Galileo, il quale dur&ograve; ad osservare i Medicei, con fatica atlantica, <lb/>per ben diciannov'anni? </s>

<s>Intanto che si attende la risposta, la quale vorr&agrave; <lb/>ancora indugiare, noi ci affrettiamo ad aggiunger questo pure agli altri ar&shy;<lb/>gomenti, per provar quanto le Effemeridi pubblicate dall'Alb&egrave;ri fossero poco <lb/>accurate. </s></p><p type="main">

<s>Comunque sia, proseguendo il corso della Storia, prese dopo l'Hodierna <lb/>a trattar la questione delle latitudini il Borelli, nel II Libro delle sue <emph type="italics"/>Theo&shy;<lb/>ricae,<emph.end type="italics"/> e segnatamente ne'quattro ultimi capitoli. </s>

<s>Egli conferm&ograve; il fatto delle <lb/>variabilit&agrave; di esse latitudini, investigando con sottilissima diligenza il periodo <lb/>della retrogradazione della linea de'nodi, ch'egli attribuiva a cause fisiche <lb/>e meccaniche assai somiglianti alle neutoniane. </s></p><pb xlink:href="020/01/1000.jpg" pagenum="443"/><p type="main">

<s>Il Cassini per&ograve;, con riverenza di un <emph type="italics"/>homme si illustre et si consumm&eacute; <lb/>dans le Mathematiques,<emph.end type="italics"/> crede di dover tenere altra via, e che sia perci&ograve; a <lb/>proposito &ldquo; de commencer par la distinction des apparences d'optique, qui <lb/>se sont dans les orbes des Satellites &agrave; cause de la diversit&eacute; des &eacute;levations <lb/>de nostre oeil sur le plan de l'orbite de Jupiter, la quelle diversit&eacute; est une <lb/>des causes principales de la difference, qu'il y a entre les latitudes des Sa&shy;<lb/>tellites v&ucirc;&ecirc;s de la Terre, et celles qui en mesme temps seroient v&ucirc;&ecirc;s du <lb/>Soleil, dont la connaissance est necessaire pour r&eacute;duire les unes aux autres, <lb/>tant dans l'&eacute;tablissement de leur theorie, que dans l'usage, qu'il en faut <lb/>faire &rdquo; (ivi, pag. </s>

<s>392). Ma il Newton, dimostrando poi esser causa princi&shy;<lb/>pale della variet&agrave; delle latitudini l'attrazion reciproca de'Satelliti fra loro e <lb/>con Giove, parve decidere insieme che pi&ugrave; vicina al vero fosse andata a co&shy;<lb/>gliere la Meccanica del Borelli, che non l'Ottica del Cassini. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>L'Ottica piuttosto che l&agrave; dove si tratta di moti, ricorre qua pi&ugrave; oppor&shy;<lb/>tuna, dove si narra come variamente s'appresentasse l'aspetto di Giove ai <lb/>varii osservatori. </s>

<s>E per muover dai primi principii &egrave; da ritornar sopra quelle <lb/>parole, che scriveva il Cigoli a Galileo, e in cui gli diceva che Giove il Pas&shy;<lb/>signano <emph type="italics"/>lo vede montuoso.<emph.end type="italics"/> Ci&ograve; in altre parole significava essere state vedute <lb/>alcune macchie nel disco del Pianeta, le quali si attribuivano all'ombre git&shy;<lb/>tate dai monti insolati, come nella Luna, e forse preluceva alla mente del <lb/><figure id="id.020.01.1000.1.jpg" xlink:href="020/01/1000/1.jpg"/></s></p><p type="caption">

<s>Figura 87.<lb/>nostro Passignano il concetto del Tilorier, che <lb/>credeva esser le fasce oscure lunghi e irsuti <lb/>gioghi di montagne. </s></p><p type="main">

<s>Comunque sia, eccitato Galileo da quelle <lb/>parole si dette pi&ugrave; attentamente ad osservare, <lb/>e con schizzo in penna rappresent&ograve; l'aspetto <lb/>generale di Giove come si vede ritratto qui <lb/>nella 87a figura. </s>

<s>Nel punto A gli appariva una <lb/><figure id="id.020.01.1000.2.jpg" xlink:href="020/01/1000/2.jpg"/></s></p><p type="caption">

<s>Figura 88.<lb/>macchia pi&ugrave; distinta, <lb/>l'apparenza della qua&shy;<lb/>le volle pi&ugrave; particola&shy;<lb/>mente descriver nella <lb/>figura 88, in relazione a un tratto d'ombra, sul&shy;<lb/>l'orlo della quale compariva pi&ugrave; fosca. </s>

<s>Quella mac&shy;<lb/>chia poi solitaria, che rassomiglia a un cratere, e <lb/>quell'altre ombre, che rappresentano qualche dorso <lb/>e qualche vetta di monte, si vedono con diligenza <lb/>disegnate nelle figure 89, 90 e 91. </s></p><p type="main">

<s>Forse la penna, piuttosto che alla distinta visione telescopica, teneva <pb xlink:href="020/01/1001.jpg" pagenum="444"/>dietro alle lucide apprensioni della fantasia, n&egrave; l'esser que'disegni condotti <lb/>nel margine della carta 68 del T. V, P. III de'Manoscritti galileiani, dove <lb/><figure id="id.020.01.1001.1.jpg" xlink:href="020/01/1001/1.jpg"/></s></p><p type="caption">

<s>Figura 89.<lb/><figure id="id.020.01.1001.2.jpg" xlink:href="020/01/1001/2.jpg"/></s></p><p type="caption">

<s>Figura 90.<lb/>son calcoli rela&shy;<lb/>tivi alle Medicee, <lb/>&egrave; argomento cer&shy;<lb/>to che si voglia in <lb/>quel modo raffi&shy;<lb/>gurar l'aspetto <lb/>propriamente di <lb/>Giove, macomun&shy;<lb/>que sia, abbiam <lb/>sopra quelle figure voluto richiamar l'attenzione de'nostri Lettori, se cre&shy;<lb/>dessero di servirsene come argomento da rispondere all'Arago, il quale si <lb/><figure id="id.020.01.1001.3.jpg" xlink:href="020/01/1001/3.jpg"/></s></p><p type="caption">

<s>Figura 91.<lb/>maravigliava che Galileo non abbia fatta men&shy;<lb/>zione mai delle Macchie gioviali, e domandava <lb/>con ghigno maliziosetto se &ldquo; les bandes n'aura&shy;<lb/>ient-elles pas exist&eacute; du temps de cet immortal <lb/>observateur. </s>

<s>&rdquo; </s></p><p type="main">

<s>Di quelle zone la Maest&agrave; di Giove si sar&agrave; <lb/>precinti i fianchi, infin da quando sal&igrave; sul suo <lb/>trono reale, ma per vederle sotto quella distinta <lb/>figura ci bisognavano strumenti un poco pi&ugrave; perfetti di quelli fabbricati da <lb/>Galileo. </s>

<s>Francesco Fontana nel 1630 (Novae Observ., 1646, pag. </s>

<s>110) fu primo <lb/>co'suoi Canocchiali a notare una tal novit&agrave;, ma dubit&ograve; non forse dovesse <lb/>&ldquo; crystalli vitio id accidere &rdquo; (pag. </s>

<s>107). Il Castelli in Roma vide due anni <lb/>dopo la stessa cosa, ma nemmen egli ne aveva certezza. </s>

<s>Intanto per&ograve; l'Ot&shy;<lb/>tico napoletano, per dar credito alla fabbrica, divulg&ograve; la notizia che co'suoi <lb/>nuovi Canocchiali vedevasi Giove &ldquo; fasciolis duabus ambitus &rdquo; (pag. </s>

<s>110). </s></p><p type="main">

<s>Giunse quella voce, circa il 1640, alle orecchie del Granduca in Pisa, <lb/>dove ne tenne discorso col Renieri, a cui sovvenne poco dopo un arguto <lb/>pensiero di servirsi delle mutazioni che avrebbero dovuto far quelle fasce, <lb/>come di nuovo argomento a confermar la verit&agrave; del Sistema copernicano. </s>

<s>Ne <lb/>scrisse in proposito al principe Leopoldo, supposto che fosse stata verificata <lb/>la notizia venuta di Napoli, ma il Principe rispose che, non essendosi po&shy;<lb/>tute vedere in Firenze quelle fascie gioviali, dubitava se l'osservazione degli <lb/>Astronomi napoletani <emph type="italics"/>fosse stata fatta bene<emph.end type="italics"/> (Alb. </s>

<s>V, 368). </s></p><p type="main">

<s>In ogni modo, nel 1642 il Renieri medesimo si assicur&ograve; di ogni dub&shy;<lb/>bio e lasci&ograve; nota a carte 53 de'suoi Manoscritti raccolti nel T. VI della <lb/>P. III insieme co'galileiani, dicendo di aver co'suoi proprii occhi ve&shy;<lb/>duto veramente Giove &ldquo; fasciolis duabus ambitus &rdquo; (Alb. </s>

<s>V, 366) come ave&shy;<lb/>vano dato a intendere le voci venute di Napoli. </s>

<s>L'anno appresso se ne as&shy;<lb/>sicur&ograve; pure anche il Fontana, il quale anzi vide Giove non pi&ugrave; &ldquo; duabus, <lb/>sed tribus fasciolis cinctus &rdquo; (Observ. </s>

<s>cit., pag. </s>

<s>112) e si persuase &ldquo; eas <lb/>vere in ipso Jovis corpore esse &rdquo; (ibi, pag. </s>

<s>107) e non un illusione ottica <pb xlink:href="020/01/1002.jpg" pagenum="445"/>delle lenti. </s>

<s>Pubblicando poi nel 1646 le sue <emph type="italics"/>Novae coelestium terrestrium&shy;<lb/>que Rerum observationes,<emph.end type="italics"/> volle nel cap. </s>

<s>II del Trattato V descriver tuttoci&ograve; <lb/>che da sedici anni aveva osservato in Giove, e dop'aver detto delle fascie <lb/>soggiunge: &ldquo; haec deprehensio nova est &rdquo; (pag. </s>

<s>107). </s></p><p type="main">

<s>Que'primi, che lessero ci&ograve; che cos&igrave; scriveva il povero Occhialaio, do&shy;<lb/>mandavano all'orgoglioso rivale di lui Matematico primario del Granduca: <lb/>&mdash; &Egrave; co'vostri Canocchiali si son vedute simili novit&agrave; in Giove? </s>

<s>&mdash; A che <lb/>rispondeva il Torricelli, dicendo per sua scusa non si poter le fascie gio&shy;<lb/>viali citar come prova della maggior potenza de'Telescopi, essendo anzi state <lb/>vedute da'primi Osservatori con Istrumenti assai mediocri. </s>

<s>&ldquo; Quanto al ve&shy;<lb/>der le fasce in Giove, scriveva il di 10 Febbraio 1646 a Michelangiolo Ricci, <lb/>io non l'ho mai vedute, perch&egrave; non si vedono sempre, e quando io ho avuto <lb/>l'occasione di guardarlo, il che &egrave; stato da quattro o sei volte dopo che son <lb/>tornato in Firenze, non vi si vedevano. </s>

<s>Del resto, D. </s>

<s>Benedetto l'ha vedute <lb/>in Roma in presenza mia, gi&agrave; sono circa 14 anni, con Occhiale mediocre. </s>

<s><lb/>Don Vincenzio Renieri l'ha vedute, gi&agrave; sono sino a sei anni, con Occhiale <lb/>mediocre, ed altri le vedono continuamente con Occhiali, che non sono per&shy;<lb/>fetti &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>93). </s></p><p type="main">

<s>Fatta insomma e assicurata la scoperta delle Fasce gioviali si doman&shy;<lb/>dava da che avessero origine. </s>

<s>Il Fontana dubit&ograve; che fossero profonde fes&shy;<lb/>sure nel corpo di Giove. </s>

<s>&ldquo; Forsitan in Juppiteris corpore circulares rimae <lb/>existunt &rdquo; (Observ. </s>

<s>cit., pag. </s>

<s>107) e questa poteva stare insiem con altre <lb/>opinioni pi&ugrave; strane fondate tutte nel supposto che le fasce dipendessero da <lb/>cause sempre stabilmente operanti. </s>

<s>Ma pi&ugrave; accurate osservazioni vi fecero <lb/>scoprire una tale variabilit&agrave;, che non si conciliava con quelle prime ipotesi. </s>

<s><lb/>L'Huyghens, il quale aveva avvertito a quella instabilit&agrave; di forme che sempre <lb/>presentano in Giove le fasce, descriveva nel suo <emph type="italics"/>Systema Saturnium<emph.end type="italics"/> il fatto <lb/>osservato con queste parole: &ldquo; Porro quae in Jove zonae seu fasciae qui&shy;<lb/>busdam animadversae sunt non semper eadem forma praeditae, has ego et <lb/>qui mecum observarunt perspicue saepe animadvertimus reliquo Jovis cor&shy;<lb/>pore magis lucidas, cum tamen alii obscuriores asserant, quibus forsitan in&shy;<lb/>teriectum spatium inter binas zonas lucidiores pro una obscuriore fuerit. </s>

<s><lb/>Atque anno quidem 1656, multo maiori intervallo, quam sequentibus tri&shy;<lb/>bus, illas a se mutuo distare comperimus &rdquo; (Op. </s>

<s>varia, Lgd. </s>

<s>Batav. </s>

<s>1724, <lb/>pag. </s>

<s>540). </s></p><p type="main">

<s>Il Cassini, per altre sue osservazioni fatte con un eccellente Canoc&shy;<lb/>chiale del Campani, aggiungeva nuove particolarit&agrave; al fatto osservato dal&shy;<lb/>l'Huyghens, che consistevano nell'aver vedute le fasce di Giove anfrattuose <lb/>e variamente asperse d'ombra e di luce, e nell'avere scorto fra que'due <lb/>campi anfrattuosi un sottil filo lucido, e splendente pi&ugrave; delle rimanenti parti <lb/>del disco. (Campani, Ragguaglio ecc., Roma 1664, pag. </s>

<s>39). </s></p><p type="main">

<s>Sopra quelle sue osservazioni stabili dunque l'Huyghens stesso una sua <lb/>ipotesi dell'origine delle fasce gioviali, dedotta da cause meteorologiche si&shy;<lb/>mili a quelle che si vedono operar sulla Terra. </s>

<s>Galileo aveva gi&agrave; in parti-<pb xlink:href="020/01/1003.jpg" pagenum="446"/>colare applicato a Giove l'ipotesi di un'ammosfera vaporosa, che secondo il <lb/>Moestlin involge ogni altro Pianeta. </s>

<s>Con ci&ograve;, sulla fine dell'Avviso Sidereo, <lb/>spiegava in che modo i Satelliti ora appariscano pi&ugrave; grandi ora minori; mi&shy;<lb/>nori quando sono apogei per esser da noi veduti attraverso all'ammosfera <lb/>vaporosa di Giove, minori quando son perigei &ldquo; per eiusdem orbis ablatio&shy;<lb/>nem seu attenuationem &rdquo; (Alb. </s>

<s>III, 99). </s></p><p type="main">

<s>Parve questa ad alcuni una dimostrazione dell'esser lo stesso Giove <lb/>soggetto a vicende meteorologiche somiglianti a quelle della nostra Terra, <lb/>ma venne a infirmar l'argomento il Keplero, spiegando piuttosto il fatto di <lb/>quelle varie apparenze con attribuire ai Satelliti una figura discoide, pre&shy;<lb/>sentandoci la quale in maest&agrave; si mostrassero pi&ugrave; grandi che quando ce la <lb/>presentano per taglio. </s>

<s>&ldquo; Si quatuor hi Planetae disci forma plano ad Jovem <lb/>converso circumeant, ut ad excursus maximos nobis et Soli obiiciantur ut <lb/>lineae, supra et infra irradientur perpendiculariter videnturque magni et <lb/>forte diversicolores sint pro diversitate planitierum &rdquo; (Alb. </s>

<s>V, 436). Ebbe <lb/>anche Simon Mario idee alquanto simili a queste, ma nell'esplicazione del <lb/>VII Fenomeno della Parte seconda v&agrave; anche pi&ugrave; per le sottili, attribuendo <lb/>principalmente la variet&agrave; di grandezza de'Satelliti alla variet&agrave; delle loro fasi, <lb/>come si osserva avvenir della Luna, la quale &egrave; variamente illuminata dal <lb/>Sole e dalla Terra, a quel modo che variamente sono illuminati i Medicei, <lb/>o secondo l'Autore i Brandeburgici, dal Sole stesso e da Giove. </s>

<s>&ldquo; Genuinam <lb/>igitur et veram causam incrementi et decrementi quantitatis apparentis ho&shy;<lb/>rum Siderum hanc esse censeo: videlicet quod illuminentur a Sole, eo <lb/>modo quo Luna.... Judico etiam quatuor sidera Brandeburgica imitari plane <lb/>Lunam, et duplici modo illuminari et a Sole et a vicino Jove &rdquo; (Mundus <lb/>Jov. </s>

<s>cit., pag. </s>

<s>44). </s></p><p type="main">

<s>Erano in ogni modo, a mezzo il secolo XVII, cos&igrave; approvate dagli Astro&shy;<lb/>nomi le idee degli antichi Pitagorici intorno alla fisica costituzion de'Pia&shy;<lb/>neti somigliante a quella della nostra Terra, che l'Huyghens vide nella <lb/>variabilit&agrave; delle fasce un effetto di meteorologia gioviale, da rassomigliarsi a <lb/>quello delle nuvole terrestri. </s>

<s>&ldquo; Qua ex instabilitate non male forsan colli&shy;<lb/>gemus ad instar nubium nostrarum vapores quosdam vicinum Jovi aethe&shy;<lb/>rem insidere, qui nunc his, nunc illis climatis crebri magis consertique exo&shy;<lb/>riantur &rdquo; (Systema Sat., Op. </s>

<s>var. </s>

<s>cit., pag. </s>

<s>539, 40). </s></p><p type="main">

<s>Dicemmo come queste fasce fossero dal Passignano rassomigliate alle <lb/>ombre gittate da lunghi gioghi di monti, e come Galileo descrivesse alcune <lb/>macchie particolari, le quali sembra che s'incominciassero a vedere pi&ugrave; di&shy;<lb/>stintamente verso il 1638. Il Cavalieri infatti il d&igrave; 2 Ottobre di quell'anno <lb/>scriveva una lettera al Castelli, domandandogli s'era vero quel che aveva <lb/>sentito dire, cio&egrave; che coi nuovi Telescopi napoletani &ldquo; si vegga Giove con <lb/>la inegualit&agrave; delle macchie come la Luna &ldquo; (Alb. </s>

<s>X, 319). </s></p><p type="main">

<s>Galileo, come par voglia farci intendere da que'muti disegni che si po&shy;<lb/>nevano dianzi sotto gli occhi de'nostri lettori, attribuiva quelle macchie a <lb/>cavit&agrave; aperte sulla superficie di Giove o a valli insenate fra'monti. </s>

<s>Si ri-<pb xlink:href="020/01/1004.jpg" pagenum="447"/>scontrarono poi in questa opinione alcuni altri Astronomi, infintanto che la <lb/>variabilit&agrave; osservata in esse macchie non consigli&ograve; a riformare, almeno in <lb/>parte, l'ipotesi, a quel modo che s'era dovuto far per le zone. </s>

<s>&ldquo; Licet ergo, <lb/>scriveva il Cassini ammonendo coloro che volessero osservar Giove con le <lb/>sue Effemeridi bolognesi fra le mani, quaedam variationes ex maculis, quae <lb/>saepe advertimus circa medium Jovis discum oriri et revolutionem suam <lb/>cum aliis circa Jovis axem prosequi censeri possint opticae, ut si forte val&shy;<lb/>les aut cavernae essent obliqueae, quae in ea revolutione vario modo nobis <lb/>exponerentur, quod doctissimo p. </s>

<s>Francisco Eschinardo S. J. nobiscum de <lb/>hac re et privatis literis in eruditissimo opere optico disserenti concedimus; <lb/>illae tamen mutationes, quae nullam habent cum huiusmodi revolutione, aut <lb/>cum alio motu connexionem, non possint nobis non censeri physicae &rdquo; (Edi&shy;<lb/>tio cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Intorno alla causa fisica per&ograve; di queste mutazioni fu disputato fra il <lb/>Cassini e l'Huyghens, il quale contemplava in Giove le nuvole piovose ora <lb/>condensate, ora dissipate dai venti. </s>

<s>&ldquo; In Jovis planeta, scriveva nel lib. </s>

<s>I del <lb/>Cosmoteoro, nubium quidem mutabiles tractus cernuntur vapores aquamque <lb/>haud dubie continentes, quam aliunde quoque illic non deesse argumentis <lb/>adstruebamus. </s>

<s>Erunt ergo et imbres et venti, quia attractum a Sole humo&shy;<lb/>rem recidere in terram necesse est, et calore soluti vapores ventorum causa <lb/>sunt, quorum flatus ex illa nubium iovialium mutabili facie cognoscitur &rdquo; <lb/>(Opera cit., pag. </s>

<s>681). </s></p><p type="main">

<s>In queste nubi, che ora velano, ora lasciano allo scoperto la superficie <lb/>di Giove, vedeva altres&igrave; l'Huyghens la causa fisica della variabilit&agrave; delle <lb/>macchie, e considerando come debbono esse nubi riflettere all'occhio nostro <lb/>maggior copia di luce, di quel che non faccia la superficie aspra del Pia&shy;<lb/>neta, a ci&ograve; attribuiva quel candore, dal Cassini attribuito invece alle nevi <lb/>che incanutiscono i monti. </s>

<s>&ldquo; Maculae vero, quae immutabiliter globo eius <lb/>inhaerere conspiciuntur, saepe longo tempore obtectae manent, nubibus vi&shy;<lb/>delicet illis interceptae, e quibus deinde rursus emergunt. </s>

<s>Atque etiam nu&shy;<lb/>bes in medio Jovis disco exoriri quandoque annotatum fuit, et maculas <lb/>quasdam minores existere reliquo corpore magis lucidas, neque eas diu su&shy;<lb/>peresse, quas Cassinus ex nivibus esse coniectabat cacumina montium insi&shy;<lb/>dentibus. </s>

<s>Mihi non improbabile videtur terrae regiones candidiores esse <lb/>superfusis nubibus plerumque occultatas, ac nonnunquam ab iis liberas &rdquo; <lb/>(ibi, pag. </s>

<s>656). </s></p><p type="main">

<s>Il Cassini per&ograve; ebbe sopra l'Huyghens l'abilit&agrave; e la destrezza di far <lb/>servir queste macchie a confermar non solo, ma a stabilir ne'precisi ter&shy;<lb/>mini una importantissima notizia intorno ai moti proprii di Giove. </s>

<s>Il d&igrave; <lb/>6 d'Agosto 1667 scriveva da Parigi una lettera al Viviani, a cui mandando <lb/>in alcuni fogli descritte le configurazioni delle Medicee, per quel corrente <lb/>mese di Agosto e per il Settembre appresso, &ldquo; V. S., gli diceva, osserver&agrave; <lb/>che in questi fogli ho notato una macchia di Giove, ne'giorni che arriver&agrave; <lb/>verso il mezzo del suo disco nel tempo delle osservazioni, che &egrave; quella da <pb xlink:href="020/01/1005.jpg" pagenum="448"/>cui appresi la rivoluzione di Giove attorno al suo asse, la quale, dopo la <lb/>prima discoperta seguita l'anno 1664, &egrave; disparita due volte e ritornata a <lb/>farsi vedere altrettante, dopo essere stata pi&ugrave; anni invisibile &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. CXLVI, c. </s>

<s>157). </s></p><p type="main">

<s>S'ha in queste parole tratteggiata la storia della rotazione di Giove, la <lb/>quale il Cassini chiama una sua scoperta fatta nel 1664. Da cinquantaquat&shy;<lb/>tr'anni per&ograve; gli Astronomi leggevano nella Dissertazion kepleriana sul Nun&shy;<lb/>cio Sidereo queste notabilissime parole: &ldquo; Adeoque et hoc argutissime Wa&shy;<lb/>ckerius iam monuit etiam Jovem circa suum volvi axem, ut nostram Tellurem, <lb/>ut ad illam convolutionem gyratio illa quatuor Lunarum sequatur, uti ad <lb/>nostrae Telluris gyrationem nostrae Lunae conversio in eamdem plagam se&shy;<lb/>quitur, adeoque nunc demum se credere rationibus magneticis, quibus, in <lb/>nupero meo Fhisicae coelestis commentario, volutione Solis circa axem et <lb/>polos corporis causas motuum planetarum expedivi &rdquo; (Alb. </s>

<s>V, 431, 32). </s></p><p type="main">

<s>L'anno dopo, nella Prefazione alla Diottrica, torn&ograve; il Keplero sopra que&shy;<lb/>sto soggetto, e dall'aver trovato il tempo periodico del III Satellite di otto <lb/>giorni, argomentando che al primo e pi&ugrave; vicino due sarebbero bastati, sa&shy;<lb/>gacemente, dietro le sue ragioni magnetiche, divinava &ldquo; etiam ipsum Jovis <lb/>globum convolvi rapidissime et procul dubio celerius quam in unius diei <lb/>nostratis spacio &rdquo; (Augustae Vindelic. </s>

<s>1611, pag. </s>

<s>14). </s></p><p type="main">

<s>Quando poi lo Schirleo Rheita, alle ragioni magnetiche del Keplero so&shy;<lb/>stituendo le proprie fantasie, dette tempo a Giove di rivolgersi in s&egrave; stesso <lb/>284 ore, prima il nostro Torricelli e poi l'Huyghens rammemorarono le <lb/>smarrite dottrine kepleriane, che servirono a loro di sicura guida a cansar <lb/>gli errori e a prevedere il vero. </s>

<s>Nella sopra citata Lettera a Michelangiolo <lb/>Ricci, dop'avere il Torricelli detto della scoperta delle fasce di Giove, sog&shy;<lb/>giunge le seguenti alle gi&agrave; da noi riferite parole: &ldquo; Quanto al girarsi in s&egrave; <lb/>io lo tengo per certo, senza vedervi altro contrassegno. </s>

<s>Ogni corpo lass&ugrave;, <lb/>intorno al quale si girino altri corpi, V. S. dica pure che gira anch'esso, <lb/>ma in tempo pi&ugrave; breve che qualunque altro corpo che gli si muova intorno. </s>

<s><lb/>Per&ograve; io credo che s'inganneranno coloro, che pensano che Giove metta pi&ugrave; <lb/>giorni in fare una rivoluzione sola &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>93). </s></p><p type="main">

<s>L'Huyghens poi par che anche pi&ugrave; fedelmente del Torricelli ripeta, in&shy;<lb/>sieme con le dottrine, le parole scritte nella prefazione alla Diottrica keple&shy;<lb/>riana. </s>

<s>&ldquo; Rursus Tellus haec, egli dice nel Sistema Saturnio, diurno spatio <lb/>gyratur, quam Luna menstruo motu ambit. </s>

<s>Jovis autem Planetam quatuor <lb/>minores, hoc est totidem Lunae circumstant, eadem hac lege ut propiores <lb/>quae sunt celeriore cursu ferantur. </s>

<s>Unde Jupiter quidem breviori forsitan <lb/>tempore quam 24 horarum converti censendus est, cum citissime ei lunula&shy;<lb/>rum minus biduo impendat &rdquo; (Opera cit., pag. </s>

<s>564). </s></p><p type="main">

<s>Cos&igrave; argomentavasi per induzione che dovesse anche Giove rivolgersi <lb/>sul proprio asse, e che in pi&ugrave; breve tempo di un giorno ne dovesse com&shy;<lb/>piere il moto revolutorio, ma non s'aveva ancora una prova fisica n&egrave; del&shy;<lb/>l'un fatto n&egrave; dell'altro. </s>

<s>Quanto alla rivoluzione di Giove in s&egrave; stesso il <pb xlink:href="020/01/1006.jpg" pagenum="449"/>Fontana fu forse il primo ad argomentarla dal variar le fasce d'aspetto e <lb/>di figura. </s>

<s>&ldquo; Jovem etiam circa proprium centrum volvi atque rotari, haec <lb/>fasciarum nova deprehensio indicat, nam non semper omnes, nec eodem <lb/>modo, interdum enim convexae, nonnunquam concavae et aliquando rectae <lb/>apparent, ut supra dictum est, nec in eodem situ semper deprehenduntur.... <lb/>et sic dicerem praedictas fascias mutare figuras, situm atque occultari, quia <lb/>Juppiter circa proprium movetur centrum &rdquo; (Novae observat. </s>

<s>cit., pag. </s>

<s>108). </s></p><p type="main">

<s>Da cos&igrave; fatte apparenze veniva senza dubbio a dimostrarsi che anche <lb/>Giove, come la Terra e il Sole si rivolgeva in s&egrave; stesso, ma era difficile, <lb/>per la figura continuata delle zone, il definire il periodo a quella revolu&shy;<lb/>zione, non potendosi computar giusto, se non che dal ritorno di un qualche <lb/>punto, ben distinto sulla superficie del Pianeta, al medesimo segno della <lb/>mira telescopica d'onde s'era partito. </s>

<s>Il Cassini fiss&ograve; questo punto in una <lb/>delle macchie pi&ugrave; cospicue, e trov&ograve; a questo modo che Giove, bench&egrave; cos&igrave; <lb/>corpulento, non penava pi&ugrave; che 9 ore e 56 minuti a rivolgersi attorno. </s></p><p type="main">

<s>Attendeva il Cassini a queste sue diligenti osservazioni gioviali in Roma, <lb/>nell'estate del 1664, e Giuseppe Campani lo assisteva. </s>

<s>La notte appresso al <lb/>d&igrave; 30 di Luglio, dop'essere stato qualche ora intento e in silenzio contem&shy;<lb/>plativo ad osservar Giove, si leva, e tutto lieto rivolto al Campani &mdash; guar&shy;<lb/>date, gli dice, que'due punti neri, che sono in mezzo alla fascia pi&ugrave; larga. </s>

<s>&mdash; <lb/>Guarda, e a lui maravigliato della novit&agrave;, per non poter esser quelle delle <lb/>solite macchie, il Cassini risponde: &mdash; Que'due punti neri son l'ombre proiet&shy;<lb/>tate da due Satelliti sul disco di Giove, e se osservate attentamente vedrete <lb/>che non si muovono di pari passo con le altre macchie aderenti al Pianeta <lb/>e menate in volta da lui. </s>

<s>&mdash; </s></p><p type="main">

<s>Il Campani subito, in commemorazione della scoperta, fece stampare <lb/>una cartella, della quale fu mandata al principe Leopoldo una copia, che i <lb/>collettori inserirono a carte 48 del Tomo XII del Cimento. </s>

<s>Sotto un qua&shy;<lb/>dretto, in mezzo al quale son finissimamente disegnati Saturno col suo anello, <lb/>e Giove con le sue fasce e con le due ombre de'Pianetin&igrave;, come apparirono <lb/>in quella prima osservazione, si legge: &ldquo; Julii die 30 h. </s>

<s>2 1/2 noctis latio&shy;<lb/>rem Jovis fasciam obscuram perambulabant maculae duae obscuriores quas, <lb/>celeberrimus astronomus Cassinus authori primum indigitavit, easque um&shy;<lb/>bras Satellitum dixit Jovem subeuntium, qui deinde ab eius occiduo mar&shy;<lb/>gine vere emergere visi sunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>Bench&egrave;, della sua scoperta cos&igrave; divulgata, il Cassini fosse sicuro, sen&shy;<lb/>tiva nulladimeno, per dar fondamento ai calcoli, il bisogno di pi&ugrave; diligenti <lb/>osservazioni, ch'ei dovette indugiare fino all'anno seguente. </s>

<s>In questa nota <lb/>che riferiamo s'hanno di tali importantissime osservazioni descritti i pi&ugrave; <lb/>minuti particolari. </s>

<s>&ldquo; A'd&igrave; 9 Luglio 1665 in Roma, con un Occhiale del Cam&shy;<lb/>pani di palmi 16 1/2, si cominci&ograve; ad osservare Giove la notte suddetta a h. </s>

<s>3, <lb/>m. </s>

<s>15 dell'Orologio comune, e si scoperse l'ombra del III Pianetino nel <lb/>centro preciso di quel Pianeta, sopra la terza fascia oscura che da esso ve&shy;<lb/>niva toccata nell'estremit&agrave;. </s>

<s>Il suo moto era verso il margine occidentale vero <pb xlink:href="020/01/1007.jpg" pagenum="450"/>di Giove. </s>

<s>&rdquo; E seguita a notar le osservazioni fatte a ore 4 1/8, a ore 4 1/4, <lb/>a ore 4, m. </s>

<s>52; ecc. (MSS. Cim., T. XII, c. </s>

<s>59). </s></p><p type="main">

<s>Nell'Agosto, distratto dalla visita del Ponte Felice per ordine del Governo <lb/>&ldquo; dispiacemi estremamente, scriveva al Viviani, di non aver tempo di ap&shy;<lb/>plicare ora al pi&ugrave; esatto calcolo dell'ombre de'Pianetini, bench&egrave; a dire il <lb/>vero l'aver essi, da che costituii l'ipotesi, variato evidentemente le digres&shy;<lb/>sioni, senza che io ne abbi fatta esatta misura, non mi lasci speranza di <lb/>conseguire ora molta sottigliezza &rdquo; (ivi, c. </s>

<s>151). </s></p><p type="main">

<s>Aveva nonostante il Cassini divisato l'ordine di que'calcoli, e accen&shy;<lb/>nato all'uso e alle conseguenze importanti in una lettera indirizzata all'abate <lb/>Ottavio Falconieri, dove son notabili quelle leggi delle proporzionalit&agrave; intra&shy;<lb/>vedute fra le velocit&agrave; de'Satelliti e i raggi delle loro orbite, con che illu&shy;<lb/>stravasi un concetto di Galileo, ma non s'iniziava quella nuova Meccanica <lb/>celeste, alla quale attendeva in quel medesimo tempo il Borelli. </s></p><p type="main">

<s>Sottosignata &ldquo; di Roma l&igrave; 7 Ottobre 1665 &rdquo; comparve, quasi nello stesso <lb/>tempo che fu pubblicata la lettera del Cassini al Falconieri, un'altra Let&shy;<lb/>tera di Giuseppe Campani &ldquo; intorno alle ombre delle stelle Medicee nel volto <lb/>di Giove ed altri nuovi fenomeni celesti scoperti co'suoi Occhiali, al signor <lb/>Gio. </s>

<s>Domenico Cassini, primario astronomo dell'Archiginnasio di Bologna, &rdquo; <lb/>lettera stampata in folio in Roma da Fabio De Falco, e che pu&ograve; vedersi in&shy;<lb/>serita da c. </s>

<s>285-93 nel T. XV de'Manoscritti del Cimento. </s></p><p type="main">

<s>Avevano queste due lettere levato un gran rumore, e il Granduca e il <lb/>principe Leopoldo, mentre che il Borelli era tornato a Pisa, e il Viviani forse <lb/>se ne stava in campagna, vollero che si riscontrassero nell'Accademia fio&shy;<lb/>rentina le novit&agrave; venute di Roma. </s>

<s>Risposero gli Accademici che il Cassini <lb/>s'era ingannato, prendendo per ombre de'Satelliti alcune delle solite mac&shy;<lb/>chie inerenti al Pianeta, di che prova certissima era, secondo loro, il veder <lb/>quelle stesse ombre, che si dicevano proiettate, maggiori in diametro appa&shy;<lb/>rente del corpo proietore. </s></p><p type="main">

<s>Il Granduca per&ograve; e il principe Leopoldo, non s'assicurando del parere <lb/>de'loro Accademici, vollero averne sentenza pi&ugrave; definitiva dal Borelli e dal&shy;<lb/>l'Huyghens, a cui nello stesso tempo si rendeva conto anche delle altre os&shy;<lb/>servazioni e scoperte fatte dal Cassini intorno a Giove. </s>

<s>L'Huyghens rispon&shy;<lb/>deva cos&igrave; il d&igrave; 22 Giugno 1666 da Parigi: &ldquo; Quanto alla nuova osservazione <lb/>del Cassini dell'ombre de'Gioviali la m'&egrave; paruta certamente bella e felice, <lb/>n&egrave; ho stimato doversi dubitar della verit&agrave; del fatto, come intendo dubitar&shy;<lb/>sene da altri, e meno ancora, dopo che io stesso ebbi manifestamente os&shy;<lb/>servato, il d&igrave; 26 di Settembre del passato anno 1665, l'ombra del III Com&shy;<lb/>pagno quale aveva predetto il Cassini che doveva apparire. </s>

<s>Ma pi&ugrave; bella <lb/>ancora &egrave; paruta quell'altra sua osservazione del moto di Giove intorno al <lb/>suo asse, perch&egrave; quantunque altri disputino di aver viste le macchie in Giove <lb/>prima di lui, la gloria per&ograve; principale a mio giudizio &egrave; state l'averne, con <lb/>continuate osservazioni e perfetto discorso, cavato il tempo della circumvo&shy;<lb/>luzione &rdquo; (MSS. Cim., T. XVIII, c. </s>

<s>316). </s></p><pb xlink:href="020/01/1008.jpg" pagenum="451"/><p type="main">

<s>Il Borelli poi rispondeva in termini ch'eccitano in chi legge la curio&shy;<lb/>sit&agrave; di saperne qualche cosa pi&ugrave; addentro. </s>

<s>&ldquo; Il serenissimo Granduca, scri&shy;<lb/>veva al Principe Leopoldo, si &egrave; compiaciuto di farmi vedere una lettera del <lb/>Campani diretta al signor Cassini ultimamente stampata. </s>

<s>L'ho letta con <lb/>quella stessa ammirazione, con la quale vidi l'Epistola ultima del signor <lb/>Cassini, e finalmente concludo esser prudenza rimetterci e scapitarci qual&shy;<lb/>che cosa del proprio, piuttosto che toccare o entrare in controversia con <lb/>persone tanto loquaci e fortificatori di s&egrave; medesimi. </s>

<s>Veggo poi in questa <lb/>Epistola far menzione di certi <emph type="italics"/>Dialoghi fisici<emph.end type="italics"/> stampati in Lione dal p. </s>

<s>Fa&shy;<lb/>bry, dei quali ne cita alcuni brani in proposito della Fascia saturnia e del <lb/>sito degli Epicicli delle Medicee &rdquo; (ivi, c. </s>

<s>90). </s></p><p type="main">

<s>L'errore del Fabry in tal proposito fu dimostrato falso dal Borelli in <lb/>una sua scrittura, che si legge da c. </s>

<s>14-16 del T. XIV del Cimento, e la <lb/>dimostrazione assai facile &egrave; dall'Autore conclusa in queste parole: &ldquo; Segue <lb/>dunque che il centro di detti Pianetini precisamente sia il corpo di Giove, <lb/>il che bisognava dimostrare &rdquo; (ivi, c. </s>

<s>16). A c. </s>

<s>17 torna il Borelli sullo stesso <lb/>argomento contro il Fabry, il quale non aveva per verit&agrave; gran bisogno di <lb/>essere confutato perch&egrave; dalle stesse &ldquo; osservazioni antichissime del signor <lb/>Galilei e del Castelli si convince evidentemente che il centro delle revolu&shy;<lb/>zioni delle Medicee sia lo stesso corpo di Giove &rdquo; (ivi, c. </s>

<s>17). </s></p><p type="main">

<s>Ma quel che si diceva eccitar la curiosit&agrave; di chi legge muove dalla prima <lb/>parte della lettera riferita, dove par che il Borelli non voglia concedere al <lb/>Cassini altro merito che di aver prima veduto ci&ograve; che i calcoli avevano a <lb/>lui stesso, al Borelli, mostrato dover essere in quel sito e in quel tempo <lb/>determinato. </s></p><p type="main">

<s>Una tale interpetrazione dall'altra parte sembra esser confermata da <lb/>ci&ograve; che si legge nel cap. </s>

<s>III del II Libro delle <emph type="italics"/>Theoricae Mediceorum,<emph.end type="italics"/> dove, <lb/>dopo di aver confessato che furono le nuove ecclissi per la prima volta os&shy;<lb/>servate in Roma <emph type="italics"/>ab eccellentissimo Cassini,<emph.end type="italics"/> soggiunge avergli fatto gran <lb/>maraviglia l'udir che in Firenze erano state messe in dubbio &ldquo; nam licet <lb/>ego, ob visus debilitatem, videre eas non potuerim, alii docti viri, et acu&shy;<lb/>tissimo visu praediti, in aula serenissimi Magni Ducis, eas conspexerunt, <lb/>iisdem temporibus et locis, quos culculus mihi designaverat &rdquo; (pag. </s>

<s>138), <lb/>anzi, prosegue a dire, fu di pi&ugrave; osservata, da quegli stessi acutissimi osser&shy;<lb/>vatori, la differenza di moto, che &egrave; fra tali ombrelle e le macchie aderenti <lb/>al Pianeta, <emph type="italics"/>differentia sane conspicua et perceptibilis.<emph.end type="italics"/></s></p><p type="main">

<s>Del resto, l'esser l'ombre proiettate maggiori in diametro del corpo opaco <lb/>proiettore, e il non poter sempre, secondo il calcolo, il cono ombroso delle <lb/>Medicee giungere fino a toccar la superficie di Giove, non son tali difficolt&agrave;, <lb/>dice il Borelli, da dover mettere in dubbio le ecclissi cassiniane. </s>

<s>&ldquo; Hoc qui&shy;<lb/>dem apud Opticos certum est, comprobaturque experientia, si parvus glo&shy;<lb/>bulus M (fig. </s>

<s>92), filo tenui suspensus, exponatur radiis solis S atque pa&shy;<lb/>pyrus G in parte eius adversa umbram globuli excipiat, removeaturque <lb/>papyrus a globulo ultra apicem coni umbrosi E ab integro disco solari ge-<pb xlink:href="020/01/1009.jpg" pagenum="452"/>niti. </s>

<s>Tunc quidem conspicitur in papyro G umbra quidem secundaria HI <lb/>circularis non valde obsura sed diluta, cuius diameter HI maior est diame&shy;<lb/><figure id="id.020.01.1009.1.jpg" xlink:href="020/01/1009/1.jpg"/></s></p><p type="caption">

<s>Figura 92.<lb/>tro CD eiusdem globuli M, quia nimirum radii <lb/>penumbram, seu secundariam umbram termi&shy;<lb/>nantes, ut sunt globum M tangentes AD et <lb/>BC decussati se mutuo secant in puncto F <lb/>inter solem S et pilam M positos, quare ab F <lb/>divergentes spatium HI umbrosum gignent <lb/>ampliorem quidem quam CD &rdquo; (pag. </s>

<s>138). </s></p><p type="main">

<s>Cos&igrave; le argomentazioni del Borelli e del&shy;<lb/>l'Huyghens, e i fatti meglio osservati, che ve&shy;<lb/>nivano a confortarle di nuova autorit&agrave;, valsero <lb/>a levar via tutti i dubbii; ond'&egrave; che il Cas&shy;<lb/>sini, trattando in quel suo Discorso <emph type="italics"/>De l'ori&shy;<lb/>gine de l'Astronomie<emph.end type="italics"/> dell'ecclissi de'Satelliti <lb/>di Giove, pot&egrave; francamente, innanzi agli Ac&shy;<lb/>cademici parigini, pronunziare queste parole: <lb/>&ldquo; En faisant ces observations on d&eacute;couvrit une <lb/>nouvelle espece d'&eacute;clipses, qui n'est pas moins <lb/>admirabile, que celles dont on avoit d&eacute;ja con&shy;<lb/>noissance, c'est les &eacute;clipses que ces petite planettes font sur Juppiter en <lb/>passant entre son disque et celui du Soleil: on voit alors leurs petites om&shy;<lb/>bres parcourir le disque de Jupiter d'orient en occident, et l'on peut deter&shy;<lb/>miner la minute, que'elles parviennent au milieu de ce disque. </s>

<s>On s'est <lb/>servy de ces deux sortes d'eclipses dans la correction des Tables &rdquo; (Divers <lb/>ouvr. </s>

<s>d'Astronomie, Amsterdam 1736, pag. </s>

<s>44). </s></p><p type="main">

<s>Queste Tavole cos&igrave; corrette dovevano utilmente servire a sciogliere l'im&shy;<lb/>portantissimo, e da molti anni desiderato, problema delle Longitudini, delle <lb/>quali ci resta ora a parlare, n&egrave; pu&ograve; tanto stringerci la brevit&agrave;, da passare <lb/>in silenzio l'opera, che vi posero attorno, e i solleciti studii che vi dettero <lb/>i molti e illustri predecessori del Cassini. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Il problema delle Longitudini fu in ogni tempo il desiderio de'Geo&shy;<lb/>grafi, desiderio che si accese allora ne'loro animi pi&ugrave; vivo, quando le ar&shy;<lb/>dite navigazioni per lo sconfinato oceano fecero sentire pi&ugrave; urgente il biso&shy;<lb/>gno di risolvere quel difficile problema in qualche modo. </s>

<s>Non &egrave; perci&ograve; <lb/>maraviglia se, dimostratosi questo bisogno al primo grande scopritore del <lb/>Nuovo mondo, gli incorasse una certa fiducia di sodisfarlo per via di quel <lb/>maraviglioso Strumento magnetico, mandato come si diceva a salvar l'uomo <lb/>pericolante in mare direttamente dal Cielo. </s></p><pb xlink:href="020/01/1010.jpg" pagenum="453"/><p type="main">

<s>Cristoforo Colombo fu il primo tra i naviganti ad osservar che la de&shy;<lb/>clinazione magnetica variava al variar del meridiano, ed essendosi facilmente <lb/>persuaso che fosse quella variazione proporzionale al variar delle longitudini, <lb/>pens&ograve; che di queste fosse il Declinatorio la pi&ugrave; giusta misura. </s>

<s>Fa di ci&ograve; te&shy;<lb/>stimonianza Ferdinando, nel cap. </s>

<s>LXIII della Vita che scrisse di suo padre, <lb/>riferendo le parole stesse lasciate scritte da lui nell'Itinerario. </s>

<s>&ldquo; E quan&shy;<lb/>tunque fossero otto o dieci in quelle due caravelle, niun per&ograve; di loro sapeva <lb/>ove fossero, ancorch&egrave; l'Ammiraglio fosse certissimo che si ritrovavano al&shy;<lb/>quanto pi&ugrave; all'occidente delle isole degli Astori, di che rend&egrave; la ragione nel <lb/>suo Itinerario, dicendo: <emph type="italics"/>Questa mattina le aguglie fiamminghe norvesta&shy;<lb/>vano, come sogliono, una quarta, e le genovesi, che solevano conformarsi <lb/>con quelle, non norvestavano se non poco, e per l'avvenire hanno a nor&shy;<lb/>vestare andando il leste, che &egrave; segno che ci ritroviamo cento leghe o al&shy;<lb/>quanto pi&ugrave; all'occidente delle isole degli Astori, perciocch&egrave;, quando fu&shy;<lb/>rono appunto cento, allora era in mare poca cosa di ramoscelli sparsi, e <lb/>le aguglie fiamminghe norvestavano una quarta e le genovesi percotevano <lb/>la tramontana, e quando saremo pi&ugrave; al leste norveste faranno alcuna <lb/>cosa.<emph.end type="italics"/> Il che si verific&ograve; subito la domenica seguente, a'22 di Maggio. </s>

<s>Dal <lb/>quale indizio, e dalla certezza del suo punto, conobbe allora che si ritrovava <lb/>cento leghe lontano dall'isola degli Astori &rdquo; (Traduz. </s>

<s>di A. Ulloa, Lon&shy;<lb/>dra 1867, pag. </s>

<s>216, 17). </s></p><p type="main">

<s>Un altro illustre navigatore italiano, il fiorentino Filippo Sassetti, aveva <lb/>pure a principio conceputa l'ardita speranza di avere a trovar le longitudini <lb/>per via della declinazion della Bussola, scrivendo cos&igrave;, il d&igrave; 8 Giugno 1550, a <lb/>Baccio Valori: &ldquo; Sarebbeci da fare un pieno trattato del reggimento della <lb/>Calamita, della quale son forse note fino a qui le minori virt&ugrave;, dimostrando <lb/>non pure il polo, ma dando modo di trovare le longitudini &rdquo; (Lettere, Mi&shy;<lb/>lano 1874, pag. </s>

<s>133). Due anni dopo per&ograve;, dietro pi&ugrave; attente considerazioni <lb/>e pi&ugrave; precise esperienze, tornava cos&igrave; a scrivere allo stesso Valori de'ser&shy;<lb/>vigi che si potevano avere dalla Calamita: &ldquo; Servonsene i piloti per sa&shy;<lb/>pere se sono presso alla terra o no, sapendo la differenza, ch'ella fa in quel <lb/>luogo, dove e'l'hanno, ma per farne regola per trovare le longitudini, come <lb/>molti si stimano, &egrave; impossibile &rdquo; (ivi, pag. </s>

<s>182). </s></p><p type="main">

<s>Anche il Porta, nella prefazioncella al libro VII della Magia Naturale, <lb/>aveva esaltati i suoi magnetici esperimenti con dire: <emph type="italics"/>Ex his mundi longi&shy;<lb/>tudo investigari potest,<emph.end type="italics"/> ma il Gilberto usc&igrave; incontro cos&igrave; a rintuzzare le <lb/>baldanzose speranze: &ldquo; Gratum hoc opus nautis esset, et Geographiae maxi&shy;<lb/>mum incrementum adferret, sed spe vana et cogitatione illudetur B. Porta, <lb/>cap. </s>

<s>XXXVIII, lib. </s>

<s>VII. </s>

<s>Nam cum existimat quod, secundum motum per <lb/>meridianos, ordinem et proportionem sequeretur magneticum, ut quanto <lb/>proprinquis orienti fuerit, tanto magis versus orientem deviaret, quanto au&shy;<lb/>tem versus occidentem perrexeris, eo ad occidentem ferrea cuspis vergeret, <lb/>quod omnino falsissimum est, putat se longitudinis verum invenisse indi&shy;<lb/>cem, sed fallitur &rdquo; (De Magnete, Londini 1600, pag. </s>

<s>166, 67). </s></p><pb xlink:href="020/01/1011.jpg" pagenum="454"/><p type="main">

<s>Ma s'ingannava anco Odoardo Wright, l'amico del Gilberto, nell'Epi&shy;<lb/>stola premessa e indirizzata all'Autor <emph type="italics"/>De Magnete,<emph.end type="italics"/> sperando di poter risol&shy;<lb/>vere, per mezzo della Bussola, il problema delle Longitudini sul fondamento <lb/>di una proposizione ammessa come vera dal Gilberto, e dietro il modo dal <lb/>Gilberto stesso insegnato di ritrovar la latitudine coll'Inclinatorio. </s>

<s>La pro&shy;<lb/>posizione, che il Wright accetta per fondamento, &egrave; cos&igrave; formulata dall'Au&shy;<lb/>tor <emph type="italics"/>De Magnete: Variatio uniuscuiusque loci constans est<emph.end type="italics"/> (pag. </s>

<s>159). Ora, <lb/>se la declinazione (variatio) per ogni luogo &egrave; costante, argomentava il Wright, <lb/>e s'&egrave; possibile a rinvenirsi, per mezzo dell'Inclinatorio, la latitudine, come <lb/>dal Gilberto stesso s'insegna al cap. </s>

<s>VIII del V libro &ldquo; problemati illi geo&shy;<lb/>graphico de longitudine invenienda, quae tot saeculis doctissimorum Mathe&shy;<lb/>maticorum ingenia exercuit, quodammodo satisfactum fore videatur, quia, <lb/>cognita uniuscuiusque loci maritimi variatione, idem postea ex eadem, quo&shy;<lb/>ties opus fuerit, facillime, non ignota eiusdem loci latitudine, inveniri posset. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il metodo per&ograve; cos&igrave; proposto dal Wright posava sopra due fondamenti, <lb/>che sebben fossero dal Gilberto tenuti per fatti certissimi, erano in realt&agrave; <lb/>due fallacie: quella del creder che le inclinazioni fossero proporzionali alle <lb/>latitudini, cosicch&egrave; le linee, che i moderni chiamano isocliniche, coincides&shy;<lb/>sero sempre co'meridiani, e l'altra del suppor che sempre la declinazione, <lb/>in un medesimo luogo, si mantenga costante. </s></p><p type="main">

<s>Ai tempi del Gilberto e del Wright, per mancanza di osservazioni, ri&shy;<lb/>manevano queste fallacie tuttavia occulte, come pure occulte, per le stesse <lb/>ragioni, rimasero a Galileo, il quale nonostante desiderava che fosse con di&shy;<lb/>ligenza osservato (Alb. </s>

<s>VI, 52) se sia veramente, com'ei supponeva, l'in&shy;<lb/>tensit&agrave; magnetica reciprocamente proporzionale alle latitudini, o se in altre <lb/>parole le linee, cos&igrave; dette isodinamiche, propriamente coincidessero coi pa&shy;<lb/>ralleli terrestri. </s>

<s>Qualche esperienza, che ha una certa relazione con questi <lb/>fatti, fu istituita dagli Accademici del Cimento, i quali per&ograve; confessano di <lb/>non essersi &ldquo; finiti di sodisfare in ordine a molte particolarit&agrave;, che riman&shy;<lb/>gono tuttavia in pendente &rdquo; (Saggi di Natur. </s>

<s>esper., Firenze 1841, pag. </s>

<s>140). </s></p><p type="main">

<s>Come l'altra fallacia del Gilberto, che consisteva nel creder la declina&shy;<lb/>zione in un medesimo luogo mantenersi sempre costante, fosse scoperta e <lb/>dimostrata da pi&ugrave; diligenti osservazioni fatte in diversi tempi e fra s&egrave; com&shy;<lb/>parate, fu da noi detto nel &sect; VI del cap. </s>

<s>VI di questo Tomo. </s>

<s>Qui rimane <lb/>per&ograve; a soggiungere che il Gillibrando, nella sua scoperta, e il Petit, nella <lb/>sua speculazione, erano stati prevenuti dal nostro bolognese Cesare Marsili, <lb/>il quale aveva nel 1631 ritrovato &ldquo; che la Meridiana gi&agrave; scolpita nel pavi&shy;<lb/>mento di San Petronio declina da quella, che di nuovo vi si trova &rdquo; (Alb. </s>

<s><lb/>IX, 229) e aveva spiegato un suo pensiero &ldquo; intorno alla Meridiana, ch'ella <lb/>si muova, cio&egrave; che si muova il Polo del mondo, e perci&ograve; si varii la longi&shy;<lb/>tudine e la latitudine delle citt&agrave; &rdquo; (ivi, pag. </s>

<s>230). Il Cassini stesso, il quale <lb/>vedemmo altrove cos&igrave; ritroso in consentire al Petit, che ripeteva inconsape&shy;<lb/>vole il pensiero del nostro Marsili, ebbe finalmente a concludere, nel suo <lb/><emph type="italics"/>Discorso sul restauramento della Meridiana di San Petronio,<emph.end type="italics"/> esser cosa <pb xlink:href="020/01/1012.jpg" pagenum="455"/>evidentissima &ldquo; che nel medesimo luogo questa direzione della Calamita va&shy;<lb/>ria talmente, che nello spazio di 25 anni l'abbiamo veduta variare a Parigi <lb/>pi&ugrave; di sette'gradi &rdquo; (Bologna 1772, pag. </s>

<s>4). </s></p><p type="main">

<s>Cosi veniva finalmente a dimostrarsi coi fatti essere una vana speranza <lb/>quella del Wright, e di tutti gli altri, che proponevano la soluzione del pro&shy;<lb/>blema delle longitudini, per mezzo della Bussola nautica, ed era questa dal&shy;<lb/>l'altra parte una persuasione ingeritasi molti anni prima nell'animo del <lb/>nostro Sassetti, il quale, diffidato de'metodi magnetici, non vedeva altra riu&shy;<lb/>scibile via che negli astronomici. </s>

<s>Cos&igrave; infatti soggiungeva alle sopra citate <lb/>parole, nella lettera al Valori: &ldquo; Credomi che sia possibile e non molto dif&shy;<lb/>ficile, a chi intende l'uso dell'Astrolabio, trovare la longitudine, di che l'anno <lb/>passato (1581) trattai in Madrid col gentilissimo signor Lorenzo Canigiani, <lb/>figliolo del signor Ambasciatore, e adesso aspetto certa sua difficolt&agrave; per ve&shy;<lb/>derne la risoluzione &rdquo; (Lettere cit., pag. </s>

<s>182). </s></p><p type="main">

<s>Importante sarebbe il conoscere qual fosse questo metodo proposto dal <lb/>Sassetti, ma noi non siamo in grado di darne la desiderata sodisfazione. </s>

<s>Es&shy;<lb/>sendo per&ograve; cosa certa che doveva quello essere un metodo astronomico, non <lb/>&egrave; difficile congetturare che dovesse, nella sostanza, non differir dai metodi <lb/>gi&agrave; proposti dal Werner nel 1514, poi da Appiano nel 1524, dal Fineo <lb/>nel 1529, dal Frisio nel 1530, dal Nunnez nel 1561 e dal Ruscelli final&shy;<lb/>mente nell'anno dopo. </s></p><p type="main">

<s>Questi metodi, in ogni modo, che non in altro consistevano se non in <lb/>argomentar la Longitudine dalla distanza della Luna da una e altra delle <lb/>stelle pi&ugrave; conspicue e pi&ugrave; vicine al Dragone, riconoscevano per primo e prin&shy;<lb/>cipale autore Amerigo Vespucci, come dimostr&ograve; il Canovai, e fu confermato <lb/>da nuovi documenti venuti alla luce. </s>

<s>Il Baldelli, nella sua prefazione al Mi&shy;<lb/>lione di Marco Polo, pubblic&ograve; una lettera, dove Amerigo, dopo aver detto a <lb/>Lorenzo di Pier Francesco Medici com'avesse trovato, per mezzo dell'Astro&shy;<lb/>labio e del Quadrante, la latitudine giusta delle isole Fortunate, intorno alla <lb/>quale eran incorsi in grandi errori Tolomeo e tutti i geografi dopo di lui; cosi <lb/>soggiunge: &ldquo; La longitudine &egrave; cosa pi&ugrave; difficile, che per pochi si pu&ograve; co&shy;<lb/>noscere, salvo per chi molto vegghi&ograve; e guard&ograve; la congiunzione della Luna <lb/>co'Pianeti. </s>

<s>Per causa delle dette longitudini ho perduti molti sonni, e ho <lb/>abbreviato la vita mia di<gap/>i anni, e tutto tengo per bene speso, perch&egrave; spero <lb/>venire in fama lungo secolo, se io torno con salute da questo viaggio. </s>

<s>Iddio <lb/>non me lo reputi a superbia, che ogni mio travaglio raddirizzer&ograve; al suo <lb/>santo servizio &rdquo; (Firenze 1827, pag. </s>

<s>LIV). </s></p><p type="main">

<s>Angelo Maria Bandini pubblicava un'altra lettera di Amerigo allo stesso <lb/>Lorenzo, dove, come un bell'esempio dell'applicazion del suo metodo, di&shy;<lb/>mostrava in che modo, dalla posizion della Luna con Marte, che, secondo <lb/>l'Almanacco del Monteregio, dovevano il d&igrave; 23 Agosto 1499 congiungersi <lb/>insieme a mezzanotte, ritrovasse, osservando e calcolando, ch'egli era in <lb/>luogo distante 82 gradi &ldquo; e tanto mi trovavo di longitudine dal meridiano <lb/>della citt&agrave; di Calis &rdquo; (Vita e lettere di A. Vespucci, Firenze 1745, pag. </s>

<s>72). </s></p><pb xlink:href="020/01/1013.jpg" pagenum="456"/><p type="main">

<s>Questo metodo del Vespucci era senza dubbio il pi&ugrave; sicuro e il pi&ugrave; <lb/>razionale, che si sapesse a que'tempi, bench&egrave; riuscisse imperfetto princi&shy;<lb/>palmente per non conoscersi con precisione i moti della Luna. </s>

<s>N&egrave; pi&ugrave; pre&shy;<lb/>ciso di questo riusciva l'altro metodo allora proposto di servirsi dell'ecclissi <lb/>di luna &ldquo; imperocch&egrave;, quand'ella incomincia a immergersi nel cono dell'om&shy;<lb/>bra terrestre, quell'ombra &egrave; tanto tenue e sfumata, che l'osservatore resta <lb/>perplesso, se la Luna abbia o no cominciato ad intaccarla &rdquo; (Alb. </s>

<s>VI, 241). <lb/>Sciveva cos&igrave; fatte parole Galileo, nella primavera dell'anno 1616, proponendo <lb/>un suo nuovo metodo di trovare le longitudini alla Corte di Spagna, alla <lb/>quale soggiungeva di essere arrivato &ldquo; a scoprire nel cielo cose totalmente <lb/>incognite ai secoli passati, le quali equivalgono a pi&ugrave; di mille ecclissi lunari <lb/>ogni anno, osservabili con minutissime precisioni, e quello che pi&ugrave; importa <lb/>ridotte a tavole giustissime ed esquisite &rdquo; (ivi, pag. </s>

<s>242). </s></p><p type="main">

<s>Fallite le speranze con la corte di Spagna, torn&ograve; Galileo, vent'anni dopo, <lb/>a far la medesima proposta agli Stati generali d'Olanda, designando, nelle <lb/>osservazioni dello scoperto mondo gioviale, tre principali accidenti ben ac&shy;<lb/>comodati ciascuno per l'investigazione delle longitudini. </s>

<s>Primi fra questi acci&shy;<lb/>denti annovera gli ecclissi, de'quali si possono utilmente osservare le im&shy;<lb/>mersioni e le emersioni nel cono dell'ombra di Giove. </s>

<s>&ldquo; Oltre agli ecclissi <lb/>vi sono secondariamente le applicazioni dei loro corpi a quello di Giove,.... <lb/>come anche all'incontro viene osservabile la loro separazione dal medesimo <lb/>disco..... Sono nel terzo luogo osservabili le ingiunzioni e separazioni tra <lb/>di loro dei medesimi Satelliti, li quali, mentre che con movimenti contrarii <lb/>si vanno ad affrontare, scorrendo questi la parte superiore dei loro cerchi, e <lb/>quelli l'inferiore, si conducono all'esatta congiunzione &rdquo; (Alb. </s>

<s>VII, 84). </s></p><p type="main">

<s>Queste pratiche per&ograve; supponevano la cognizione esatta de'moti de'Sa&shy;<lb/>telliti, intorno alla quale, non solo nel 1616, ma in sul primo intraprendere <lb/>l'opera atlantica Galileo si confidava di esser giunto a segno &ldquo; di poter pre&shy;<lb/>dire i siti e le disposizioni, che essi nuovi Pianeti siano per avere in ogni <lb/>tempo futuro, e abbiano anche avuto in ciascun tempo passato &rdquo; (Alb. </s>

<s>VI, 157). <lb/>Quanto vana per&ograve; fosse questa confidenza i fatti narrati posson persuaderlo <lb/>a ciascuno, che saviamente ripensi da quante parti dovesse riuscir difettosa <lb/>l'atlantica fatica di Galileo. </s></p><p type="main">

<s>Per questi difetti e per quella, che se non fosse uscita dalla fantasia di <lb/>un Galileo, si sarebbe tenuta per goffaggine, della sedia nautica del Besson, <lb/>e dell'imperniatura del Cardano applicate al pi&ugrave; comodo uso degli stru&shy;<lb/>menti sulla nave ondeggiante; il nuovo metodo proposto di trovar le Lon&shy;<lb/>gitudini riusciva inutile, ond'&egrave; che parve una provvidenza, per la reputa&shy;<lb/>zione e per la gloria di Galileo, la morte di que'tre Olandesi deputati a <lb/>sperimentar s'era riuscibile ci&ograve; che veniva proposto da Firenze. </s></p><p type="main">

<s>Una tal nuova soluzione del problema delle longitudini, per via de'Sa&shy;<lb/>telliti di Giove, rimase allora solamente nota fra persone private, e non ebbe <lb/>questo concetto di Galileo pubblicit&agrave; che nel 1639, quando nella prefazione <lb/>alle prime Tavole medicee il Renieri scriveva del pi&ugrave; sicuro e pi&ugrave; facile <pb xlink:href="020/01/1014.jpg" pagenum="457"/>modo di emendar le longitudini: &ldquo; exhibent illud quatuor Jovis asseclae <lb/>quatuor Medicei planetae optici Tubi beneficio, per celebrem Virum hunc, <lb/>nostro saeculo reperti, qui quotidianas variant in coelo phases nunc iuncti, <lb/>nunc discedentes, nunc ecclipsim subeuntes, nunc a Jove contacti &rdquo; (Flo&shy;<lb/>rentiae, pag. </s>

<s>IV). </s></p><p type="main">

<s>Sembra nonostante che, massime appresso gli scienziati stranieri, fosse <lb/>poco diffusa la notizia di questo progetto di Galileo. </s>

<s>L'Herigonio, pubbli&shy;<lb/>cando in Parigi nel 1644 il V Tomo del suo <emph type="italics"/>Corso matematico,<emph.end type="italics"/> vi aggiun&shy;<lb/>geva &ldquo; Nova ac facilis methodus inveniendi locorum longitudines &rdquo; la pra&shy;<lb/>tica del qual metodo dall'Autore stesso s'insegnava cos&igrave;: &ldquo; Observetur, ope <lb/>Telescopii, quota hora loci observationis aliquod Jovialium siderum appellat <lb/>ad lineam ab oculo intuentis per centrum Jovis transeuntem. </s>

<s>Deinde, si ope <lb/>Tabularum inquiratur quota hora diei illud sidus iungatur Jovi, differentia <lb/>horarum per observationem et Tabulas inventarum (reducta in gradus et <lb/>minuta graduum, multiplicando singulas horas per 15 gradus) erit quaesita <lb/>differentia longitudinum loci observationis, et loci ad quem constructae sunt <lb/>Tabulae &rdquo; (pag. </s>

<s>857). </s></p><p type="main">

<s>L'Herigonio spacciava questa per una sua invenzione, ma quel Morin, <lb/>autor di un Trattato, nel quale, a giudizio di Galileo, il modo proposto di <lb/>trovare la longitudine, per via del moto della Luna, &egrave; una bella invenzione <lb/>in astratto, ma fallace e impraticabile in concreto (Alb. </s>

<s>VII, 199); quel Mo&shy;<lb/>rin &ldquo; primo dicit Galilaeum esse inventorem methodi inveniendi locorum <lb/>longitudines per Jovialia sidera.... atque in hac civitate Parisiensi ab anno <lb/>iam elapso innotuisse Galilaeum illustrissimis Ordinibus Hollandiae hoc in&shy;<lb/>ventum oblutisse. </s>

<s>&rdquo; Il Gassendo, infatti, nella vita del Peiresc pubblicata a <lb/>Parigi nel 1641, dop'aver narrato come venisse in mente ad esso Peiresc <lb/>di far uso de'Satelliti di Giove, per emendar la Geografia, e per avvantag&shy;<lb/>giar la Nautica, e com'avesse altres&igrave; disposto di dar effetto a questo suo <lb/>pensiero &ldquo; eam curam deposuit, ratus aliunde Galileum Keplerumque in eam <lb/>curam incubituros, et pro sua solertia rem perfectius exsequturos. </s>

<s>Certe <lb/>non parum gavisus est, cum non ita pridem accepit venisse Galileo in men&shy;<lb/>tem ut methodum perficeret, et cum Hollandis communicaret, a quibus ar&shy;<lb/>canum Longitudinum est tantopere expetitum &rdquo; (pag. </s>

<s>133). </s></p><p type="main">

<s>Rispondeva l'Herigonio di non aver nulla saputo di Galileo, <emph type="italics"/>ignotum&shy;<lb/>que esse mihi adhuc an eodem modo, quo ego,<emph.end type="italics"/> proceda nel trattato con <lb/>gli Olandesi, <emph type="italics"/>ad corrigendum tantum errorem Horologii.<emph.end type="italics"/> Pretendeva in&shy;<lb/>somma l'Herigonio che fosse suo almeno il particolar modo di far uso delle <lb/>osservazioni gioviali, per le longitudini. </s>

<s>E Galileo glielo avrebbe facilmente <lb/>concesso, ma gli avrebbe detto nello stesso tempo che non era l'invenzione <lb/>praticabile, in dodici anni, altro che due o quattro o sei volte, perch&egrave; ap&shy;<lb/>punto, a cagion delle loro apparenti latitudini, i Satelliti, con tal rarit&agrave;, in <lb/>tutta una rivoluzione, si congiungono al centro di Giove, se pure &egrave; possi&shy;<lb/>bile, anche in tali rarissime congiunture, il discerner luce da luce. </s></p><p type="main">

<s>Invocava inoltre l'Herigonio, a far testimonianza del vero, uomini degni <pb xlink:href="020/01/1015.jpg" pagenum="458"/>di fede &ldquo; qui asserent me illis communicasse meum inventum, biennio fere <lb/>antequam in lucem ederetur &rdquo; (Cursi mathem. </s>

<s>cit., T. V, pag. </s>

<s>873). Par <lb/>difficile a credere che in Parigi, dove ne parlavano il Beaugrand e il Morin, <lb/>e dove il Gassendo ne aveva scritto in pubblico, non fosse giunta alle orec&shy;<lb/>chie dell'Autor del Corso matematico la notizia del trattato di Galileo con <lb/>gli Olandesi, ma par che non fosse giunta nemmeno in Danzica, quando <lb/>l'Hevelio scriveva la sua celebre Selenografia. </s>

<s>Egli infatti, dissertando ivi <lb/>delle osservazioni di Giove, cred&egrave; essere stato il primo a descriverle in or&shy;<lb/>dinata Effemeride. </s>

<s>La Menologia del nostro Hodierna usciva in Palermo alla <lb/>luce, in quel tempo che la Selenografia era in Danzica sotto i torchi, e il <lb/>Mondo gioviale del Mario, annunziato nel 1611 in quella lettera trascritta in <lb/>fine alla Diottrica kepleriana, dove lo stesso Mario dice de'due estremi Sa&shy;<lb/>telliti <emph type="italics"/>periodos iam indagavi tubulasque construxi;<emph.end type="italics"/> il Mondo gioviale, pub&shy;<lb/>blicato tre anni dopo in fretta, per prevenir Galileo, parve, come poi al Cas&shy;<lb/>sini, troppo povera cosa anche all'Hevelio. </s></p><p type="main">

<s>E non solamente primo si cred&egrave; il celebre Selenografo in dar opera alle <lb/>Effemeridi gioviali, ma par che si credesse primo altres&igrave; in proporle per la <lb/>invenzion delle Longitudini. </s>

<s>&ldquo; Hae observationes, egli dice, quotidie fuerunt <lb/>continuatae, quando per serenitatem coeli licuit, ita ut una nocte quinquies, <lb/>imo etiam sexies, quandoque has animadversiones reiteraverim. </s>

<s>Singulis ctiam <lb/>observationibus suum competens verumque tempus, una cum descriptione <lb/>situs Jovialium, addidi. </s>

<s>Id quod, quantum ego scio, post Galileum a nemine <lb/>adhuc in tali forma est praestitum. </s>

<s>Interim optandum esset serio ut eius&shy;<lb/>modi observationes Jovialium antehac ab Astonomiae cultoribus saepius fuis&shy;<lb/>sent institutae, et quotannis adhuc instituerentur. </s>

<s>Hoc namque pacto inter&shy;<lb/>dum ex coniunctionibus Jovialium, praesertim Jovi viciniorum, quae fiunt <lb/>ex motu contrario, in diversis ac longe dissitis locis, et ex notatione tem&shy;<lb/>poris occultationis alterius ab altera, id quod ex altitudine alicuius fixae <lb/>capta certe cognosci potest; longitudines locorum, ob velocem horum comi&shy;<lb/>tum Jovis incessum, queunt investigari, vel minimum eorum motus exami&shy;<lb/>nari et corrigi &rdquo; (Selenographia, Gedani 1647, pag. </s>

<s>45, 46). </s></p><p type="main">

<s>Il desiderio espresso in queste parole dell'Hevelio fu sodisfatto alquanti <lb/>anni dopo dal Cassini, di cui gi&agrave; narrammo d'onde gli venissero agli studii <lb/>gioviali gl'impulsi. </s>

<s>Nel 1668 uscivano alla luce le Effemeridi bolognosi, nel <lb/>Proemio alle quali termina il cap. </s>

<s>I notando i particolari accidenti osservati <lb/>per uso delle longitudini: accidenti ch'ei riduce agli ecclissi, alle congiun&shy;<lb/>zioni, ai contatti, precisamente com'avea proposto Galileo agli Stati generali. </s></p><p type="main">

<s>Una delle prime copie uscite dalla tipografia de'Manolessi la sped&igrave; il <lb/>Cassini in ossequio al Viviani, il quale fece al libro tanta accoglienza, che <lb/>l'Autore ebbe a rispondergli: &ldquo; &Egrave; un effetto della sua gentilezza aver gra&shy;<lb/>dito il mio libretto delle Medicee, nel quale V.S. riconoscer&agrave; la fretta nello <lb/>stampare, cagionata da un mio particolar domestico interesse, a cui sono stato <lb/>anco troppo tardo a provvedere &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLV, c. </s>

<s>69). </s></p><p type="main">

<s>Si studi&ograve; poi di emendare i trascorsi di quella fretta, tornando sull'ar-<pb xlink:href="020/01/1016.jpg" pagenum="459"/>gomento in quelle ch'egli intitolava &ldquo; Les hypotheses et les Tables des Sa&shy;<lb/>tellites de Jupiter, reform&eacute;es sur de nouvelles observations &rdquo; dove in sul <lb/>principio, a proposito dell'ecclissi per servire ai progressi della Geografia e <lb/>della Idrografia, diceva &ldquo; qui n'avoient jamais est&eacute; auparavant employ&eacute;es &agrave; <lb/>cet usage, quoy-qu'on les eust suppos&eacute;es depuis long-temps tres-propres <lb/>pour servir &agrave; perfectionner la Geographie et la Navigation &rdquo; (Divers ou&shy;<lb/>vres ecc., pag. </s>

<s>366). </s></p><p type="main">

<s>Parve ad alcuni che volesse con queste parole il Cassini attribuirsi le <lb/>prime parti nel propor l'uso dell'ecclissi gioviali nella Geografia e nella <lb/>Nautica, ci&ograve; che per verit&agrave; sembra strano. </s>

<s>Sia pure infatti che non gli fos&shy;<lb/>sero note le lettere di Galileo scritte agli Olandesi; egli aveva senza dubbio <lb/>letto il proemio alle Tavole del Renieri, dove si annoverano que'tre acci&shy;<lb/>denti accomodati, nelle osservazioni de'Satelliti di Giove, a ritrovar con fa&shy;<lb/>cilit&agrave; le longitudini in mare, con parole estratte e compendiate dalle stesse <lb/>lettere galileiane. </s></p><p type="main">

<s>Ma pure, a meglio rimeditarle, s'intende che le parole del Cassini as&shy;<lb/>seriscono nessun altro prima di lui aver dato esecuzione al pensiero di ser&shy;<lb/>virsi delle ecclissi de'Satelliti di Giove, per uso delle longitudini; asserzione <lb/>dall'altra parte verissima, com'&egrave; pure verissimo quello ch'egli soggiunge, <lb/>che cio&egrave; nessuno aveva prima di lui riconosciuta la peculiare utilit&agrave; e il <lb/>vantaggio di quelle ecclissi, sopra gli altri varii accidenti osservati. </s></p><p type="main">

<s>Sulla fine del capitolo infatti par che voglio espressamente il Cassini <lb/>chiarire esser questo proprio il suo concetto, non sovvenutogli a caso, ma <lb/>dietro un gran numero di esperienze. </s>

<s>&ldquo; Ces exp&eacute;riences nous ont fait con&shy;<lb/>noistre qu'il faut pr&eacute;f&eacute;rer &agrave; toutes les autres phases les &eacute;clipses, que ces <lb/>Satellites souffrent en passant par l'ombre de Jupiter, dont on peut obser&shy;<lb/>ver l'entr&eacute;e et la sortie, et quelquefois l'une et l'autre, sans que deux ob&shy;<lb/>servateurs soient in differend entr'eux d'un quart d'une minute d'heure.... <lb/>et que les &eacute;clipses de Premier Satellite, qui est plus viste, que les autres, <lb/>et qui entre plus dir&eacute;ctement dans l'ombre, se peuvent d&eacute;terminer encore <lb/>avec une plus grande precision &rdquo; (ivi, pag. </s>

<s>369). </s></p><p type="main">

<s>Aggiunse per&ograve;, sopra gli annoverati da Galileo, il Cassini altri due ac&shy;<lb/>cidenti, che sono quello delle ombre proiettate da'Satelliti sul disco di Giove, <lb/>e l'altro delle macchie su lui pi&ugrave; visibili e permanenti, le quali, facendo la <lb/>circonvuluzione velocissima, offerirebbero sopra tutti gli altri fenomeni mag&shy;<lb/>gior comodit&agrave; di osservazioni, se il loro passaggio per il centro del Pianeta <lb/>si potesse determinar con la medesima precisione, come si fa delle immer&shy;<lb/>sioni e delle emersioni de'Satelliti dal cono dell'ombra. </s></p><p type="main">

<s>Ma pur tanta esquisitezza era dal Cassini lasciata in un difetto, che ha <lb/>qualche cosa di notabile; difetto che consisteva nell'aver trascurata la cos&igrave; <lb/>detta <emph type="italics"/>Equazion della luce,<emph.end type="italics"/> ponendo in dubbio la scoperta roemeriana, per <lb/>non averla potuta, nella Reale Accademia di Parigi, verificare colla sua pro&shy;<lb/>pria esperienza. </s>

<s>S'era questo per&ograve; osservato, che i tempi di un numero con&shy;<lb/>siderevole d'immersioni d'un medesimo Satellite erano notabilmente pi&ugrave; <pb xlink:href="020/01/1017.jpg" pagenum="460"/>brevi de'tempi di un pari numero d'emersioni &ldquo; ce qui se peut expliquer, <lb/>soggiunge il Cassini, par l'hypothese du mouvement successif de la lumiere: <lb/>mais cela ne lui a pas paru suffisant pour convaincre que le mouvement de <lb/>la lumiere est en effet successif, parceque l'on n'est pas cerain que cette <lb/>inegalit&eacute; de tems ne soit pas produite ou par l'excentricit&eacute; du Satellite, ou <lb/>par l'irregularit&eacute; de son mouvement, ou par quelqu'autre cause jusques ici <lb/>inconnu&euml;, dont on pourra s'&eacute;claireir avec le tems &rdquo; (De l'orig. </s>

<s>de l'Astro&shy;<lb/>nomie cit., pag. </s>

<s>46). </s></p><p type="main">

<s>Fu in ogni modo il Cassini il primo fra gl'Italiani e gli stranieri a <lb/>mettere in atto ci&ograve; che sulla bocca di tanti non era stato altro che un bel <lb/>progetto, e perci&ograve; il Viviani, nel citato suo Discorso intorno al mondo, com&shy;<lb/>pendiando questo tratto di Storia, che concerne l'invenzion delle longitudini, <lb/>non ne riconosce e non ne commemora altri autori che Galileo e il Cassini. </s>

<s>&ldquo; E <lb/>dall'osservare i periodi di questi Pianeti s&igrave; regolari, con la sua &sgrave;olita perspi&shy;<lb/>cuit&agrave;, s'accorse il Galileo che questi potevano esser l'unico mezzo per ri&shy;<lb/>trovare in ogni tempo le longitudini de'luoghi, tanto per terra che per mare, <lb/>invenzione tanto desiderata dagli antichi e da'moderni geografi, ed altret&shy;<lb/>tanto utile alla Navigazione, non avendo per il passato altro modo, che quello <lb/>delle ecclissi del Sole e della Luna, che seguono poche volte l'anno, e non <lb/>possono mai farsi con quell'aggiustatezza, che richiedono tali osservazioni, <lb/>per poter dalla differenza del tempo del principio, mezzo e fine di tali ec&shy;<lb/>clissi osservata in diversi luoghi della Terra, calcolare le longitudini di detti <lb/>luoghi: dove adesso, col mezzo di questi Pianeti, nell'ecclissarsi nell'om&shy;<lb/>bra di Giove, ne possono, non solo farsi una o due, ma talora tre e quat&shy;<lb/>tro osservazioni il giorno, e con tanta facilit&agrave; ed esattezza di tempo, che <lb/>maggiore non pu&ograve; desiderarsi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Egli, nel tempo che fu a Roma nel 1620, per mezzo dell'Ambascia&shy;<lb/>tore di Spagna, la fece proporre alla Maest&agrave; Cattolica. </s>

<s>Di poi, nel 1636, alli <lb/>Stati di Olanda, i quali avevano deputato all'esame di questa nuova inven&shy;<lb/>zione l'illustrissimo signor Lorenzo Realio, capitano generale e consigliere <lb/>di Stato, e i signori Martino Hortensio e il Blaw. </s>

<s>Ma per la morte di que&shy;<lb/>sti, segu&igrave;ta dentro il tempo di anni tre, e di poi del medesimo Galileo, ne <lb/>fu abbandonata per allora l'impresa, la quale poi, essendo stata ben rico&shy;<lb/>nosciuta l'utilit&agrave; di questa dal signor Domenico Cassini, primo astronomo <lb/>di S. M. Cristianissima, l'ha posta in pratica, ed ha con questo mezzo ri&shy;<lb/>trovato molti errori nelle carte geografiche &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLI, <lb/>c. </s>

<s>277). </s></p><p type="main">

<s>L'invenzione del modo di trovar le longitudini ha questo di singolare, <lb/>e di comune a tutte le invenzioni credute pi&ugrave; difficili, che poi uno &egrave; ve&shy;<lb/>nuto a mostrar che invece erano di una facilit&agrave; maravigliosa. </s>

<s>Nell'Agosto <lb/>del 1659 sovvenne in mente al Borelli il modo facilissimo di misurar la dif&shy;<lb/>ferenza de'meridiani, per mezzo delle ore segnate da un Orologio e conver&shy;<lb/>tite in gradi. </s>

<s>Gli parve questa invenzione s&igrave; ovvia, che temendo di non es&shy;<lb/>sere prevenuto, volle deporla nelle mani del principe Leopoldo, a cui scrisse <pb xlink:href="020/01/1018.jpg" pagenum="461"/>il d&igrave; 2 Settembre una lettera pubblicata a pag. </s>

<s>64, 65 del T. II della rac&shy;<lb/>colta di Lettere di uomini illustri, fatta in Firenze dal Fabbroni. </s></p><p type="main">

<s>N&egrave; contento a ci&ograve;, scriveva in quel medesimo giorno un'altra lettera <lb/>al Viviani, dove in proposito gli diceva: &ldquo; Quanto pi&ugrave; ho pensato sopra <lb/>quella mia maniera di misurare le longitudini terrestri, tanto pi&ugrave; ci ho posto <lb/>l'amore, perch&egrave; ho fatto riflessione a tutte le difficolt&agrave;, che occorrono negli <lb/>altri modi finora considerati, e bench&egrave; io, per consiglio di V. S., abbia gi&agrave; <lb/>accennato questo mio concetto a Bologna, tuttavia ho stimato mettermi al <lb/>sicuro in mandare diverse copie attorno di tal lettera, o pur farlo in altra <lb/>maniera, ma prima &egrave; necessario ch'io mi assicuri se l'Evelio o il Riccioli <lb/>ne dicon qualche parola ed in che forma, credendo io fermamente che, se <lb/>ne dicon nulla, saranno parole generali, come quelle delli oracoli: tuttavia <lb/>&egrave; necessario vederli &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLIV, c. </s>

<s>135). </s></p><p type="main">

<s>Nella Salenografia e nella Cometografia dell'Hevelio non avr&agrave; trovato <lb/>nulla in proposito, come nulla non avr&agrave; pure trovato nell'Almagesto nuovo, <lb/>ma nella Geografia riformata, pubblicata nel 1672 in Venezia, a pag. </s>

<s>325 il <lb/>Riccioli cita il Biancani e il Kircher che proposero nella invenzion delle lon&shy;<lb/>gitudini l'uso dell'Orologio. </s>

<s>In qualunque modo pubblicando l'Huyghens <lb/>nel 1658 il suo <emph type="italics"/>Horologium,<emph.end type="italics"/> e dicendo delle grandi utilit&agrave;, che sarebbe per <lb/>recare il nuovo Strumento, concludeva con queste parole: &ldquo; Ut iam de lon&shy;<lb/>gitudinum quam vocant scientia dicere omittam, quae, si nunquam extitura <lb/>est, desideratumque tantopere cursui navigantium praebitura, non aliter quam <lb/>vectis per mare exquisitissimis atque omni errore vacuis Horologiis id obti&shy;<lb/>nere posse multi nobiscum existimant &rdquo; (Op. </s>

<s>varia, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>6). </s></p><p type="main">

<s>Par che dunque il pensiero del Borelli fosse sovvenuto alquanti anni <lb/>prima in mente all'Huyghens e ad altri, i quali per&ograve; si avvidero che il pro&shy;<lb/>getto era bellissimo, ma ch'era difficile d'eseguirlo per gli agitamenti della <lb/>nave che avrebbero arrestato il pendolo all'Orologio. </s>

<s>Fu questa forse la dif&shy;<lb/>ficolt&agrave; che attut&igrave; nel Borelli quel primo ardore della invenzione, la quale, <lb/>non potendosi praticare che in Terra, non s'avvantaggiava di troppo sopra <lb/>quell'altra del Viviani, che aveva proposto di servirsi de'suoni a misurar le <lb/>distanze e le longitudini dei paesi. </s></p><p type="main">

<s>Ma se il Borelli si dette vinto alle difficolt&agrave;, l'Huyghens volle rimaner <lb/>vincitore. </s>

<s>Nel 1664 furono fatte le prime esperienze nautiche con un Orolo&shy;<lb/>gio ugeniano della prima forma, ch'era per&ograve; non a peso ma a molla, e la <lb/>clavicola che frena il pendolo, invece di avere uno sprone solo, ne aveva <lb/>due &ldquo; ne videlicet in gyrum evagari posset penduli motus, unde cessatio&shy;<lb/>nis periculum &rdquo; (ibi, pag. </s>

<s>47). Il successo di questa prova fu felicissimo, ma <lb/>non fu tale per&ograve; in altre, navigazioni, di che dice lo stesso Huyghens &ldquo; ne&shy;<lb/>gligentia eorum, quibus Horologia commissa erant, quam ipsamet Automata <lb/>culpari possunt &rdquo; (ibi, pag. </s>

<s>48). </s></p><p type="main">

<s>Pervenuta la notizia in Italia, Michelangiolo Ricci scriveva il d&igrave; 25 Mag&shy;<lb/>gio 1665 a Firenze al principe Leopoldo: &ldquo; Da Avignone mi viene scritto <lb/>che il signor Hugenio abbia l'invenzione per trovar le longitudini, e che si <pb xlink:href="020/01/1019.jpg" pagenum="462"/>serva di un Oriolo a pendolo. </s>

<s>Il medesimo crede aver trovato, per la dot&shy;<lb/>trina delle Meccaniche, ragione degli effetti pi&ugrave; maravigliosi della Calamita &rdquo; <lb/>(MSS. Cim., T. XVIII, c. </s>

<s>188). A che il Principe, quasi un mese dopo, cos&igrave; <lb/>rispondeva: &ldquo; L'invenzione di trovare la longitudine con il pendolo teorica&shy;<lb/>mente ancora dal signor Galileo fu ritrovata, ma il trovare il modo che il <lb/>pendolo si adopri in mare, senza la perturbazione del moto che dovrebbe <lb/>avere uniforme, a voler conseguire l'intento; questo non &egrave; stato trovato e <lb/>lo tengo per difficile, onde bellissima sar&agrave; l'invenzione, se praticabile l'avr&agrave; <lb/>ritrovata il signor Ugenio &rdquo; (ivi, T. XXII, c. </s>

<s>114). </s></p><p type="main">

<s>Che la bellissima invenzione poi fosse praticabile lo dimostrarono i fatti, <lb/>ond'&egrave; che dopo l'Huyghens s'inger&igrave; in tutti la persuasione che il problema <lb/>delle longitudini si sarebbe finalmente risoluto, non quando si fosse riusciti <lb/>a calcolare esattamente i moti delle Medicee, ma quando si fosse giunti a <lb/>costruire esattissimi e imperturbabili Orologi. </s></p><pb xlink:href="020/01/1020.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO XII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Di Saturno<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle prime osservazioni, e delle prime ipotesi degli Astronomi sul Sistema di Saturno, da Gali&shy;<lb/>leo all'Hevelio. </s>

<s>&mdash; II. </s>

<s>Della grande scoperta ugeniana dell'Anello, e di quel che si pens&ograve; per <lb/>confermarla nell'Accademia del Cimento. </s>

<s>&mdash; III. Dell'origine, della fisica costituzione e del <lb/>moto dell'Anello saturnio, secondo gli Accademici del Cimento. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>La scoperta del nuovo Mondo gioviale dest&ograve;, in tutti quei che n'eb&shy;<lb/>bero l'annunzio, la maraviglia e in alcuni, come sempre suol delle cose <lb/>nuove, la diffidenza, la quale poi ne'pi&ugrave; ragionevoli s'acquiet&ograve; facilmente, <lb/>ripensando come in somma tutto quel che di straordinario s'era scoperto in <lb/>Giove consisteva nel tirarsi dietro, rivolgentisi attorno, quattro Lune invece <lb/>d'una, come si vede fare alla nostra Terra. </s>

<s>Altre novit&agrave; per&ograve; presentava Sa&shy;<lb/>turno, delle quali non s'era per l'innanzi avuto l'esempio, ond'&egrave; che se il <lb/>Sistema gioviale, da qualche ostinato peripatetico in fuori, persuase presto <lb/>e fece riposare nella certezza le menti degli Astronomi, il Sistema saturnio <lb/>invece le tenne, per un mezzo secolo, agitate ne'dubbii pi&ugrave; penosi, infin&shy;<lb/>tanto che non si scoperse il vero di quelle strane apparenze per la perfe&shy;<lb/>zione introdottasi negli strumenti, e per la sagacia, a cui si venivano edu&shy;<lb/>cando gli osservatori. </s></p><p type="main">

<s>Alla fine del Luglio 1610 Galileo da Padova scriveva cos&igrave; a Firenze, in <lb/>una lettera indirizzata a Belisario Vinta: &ldquo; Ho scoperto un'altra stravagan&shy;<lb/>tissima maraviglia, la quale desidero che sia saputa dalle LL. AA. e da V. S. <lb/>tenendola per&ograve; occulta, finch&egrave; nell'Opera che ristamper&ograve; sia da me pubbli-<pb xlink:href="020/01/1021.jpg" pagenum="464"/>cata, ma ne ho voluto dar conto alle LL. AA. Serenissime, acci&ograve;, se altri <lb/>l'incontrasse, sappiano che niuno l'ha osservata avanti di me, sebben tengo <lb/>per fermo che niuno la vedr&agrave;, se non dopo che ne l'avr&ograve; fatto avvertito. </s>

<s><lb/>Questo &egrave; che la stella di Saturno non &egrave; una sola, ma un composto di tre, <lb/>le quali quasi si toccano, n&egrave; mai tra di loro si muovono o mutano e sono <lb/>poste in fila secondo la lunghezza del Zodiaco, essendo quella di mezzo <lb/>circa tre volte maggiore dell'altre due laterali, e stanno situate in questa <lb/>forma <figure id="id.020.01.1021.1.jpg" xlink:href="020/01/1021/1.jpg"/> &rdquo; (Alb. </s>

<s>VI, 114, 15). </s></p><p type="main">

<s>Vedendo cos&igrave; Galileo il suo strumento rivelatore fecondo di nuove sco&shy;<lb/>perte, era incerto se faceva un'altra edizione del Nuncio Sidereo con nuove <lb/>aggiunte, o se scriveva un libro a parte delle <emph type="italics"/>Novit&agrave; celesti.<emph.end type="italics"/> Intanto che <lb/>prendeva seco stesso e con gli amici consiglio intorno al modo pi&ugrave; conve&shy;<lb/>niente di annunziare al pubblico le sue scoperte celesti, con un accortezza <lb/>tante volte ammirata e lodata dal Keplero, diffondeva la notizia di Saturno <lb/>in enimma, che mandato a Praga eccit&ograve; a interpetrarlo la curiosit&agrave; nel&shy;<lb/>l'animo dello stesso Keplero. </s>

<s>&ldquo; Annus iam vertitur (scriveva nel 1611 nella <lb/>prefazione alla Diottrica) ex quo Galilaeus Pragam perscripsit, se novi quid <lb/>in coelo praeter priora deprehendisse. </s>

<s>Et ne existeret qui obtrectationis stu&shy;<lb/>dio priorem se spectatorem ventitaret, spacium dedit propalandi quae quis&shy;<lb/>quis nova vidisset. </s>

<s>Ipse interim suum inventum literis transpositis in hunc <lb/>modum descripsit..... Ex hisce literis ego versum confeci semibarbarum, <lb/>quem Narratiuncula mea inserui, mense septembri superioris anni: <emph type="italics"/>Salve <lb/>umbistineum geminatum Martia proles.<emph.end type="italics"/> Sed longissime a sententia litera&shy;<lb/>rum aberravi: nihil illa de Marte continebat. </s>

<s>Et ne te lector detineam, en <lb/>detectionem Gryphi ipsius Galilaei authoris verbis &rdquo; (Augustae, Vindelic, <lb/>pag. </s>

<s>13). E qu&igrave; prosegue trascrivendo la lettera a don Giuliano de'Medici, <lb/>dove Galileo stesso riduce cos&igrave; la mostruosit&agrave; del Grifo alle forme naturali. <lb/><emph type="italics"/>Altissimum planetarum tergeminum observavi.<emph.end type="italics"/></s></p><p type="main">

<s>Persuaso che tale, cio&egrave; tergemina, fosse la nativa e invariabile faccia <lb/>di Saturno, nella quale infino a tutto l'Aprile 1612 <emph type="italics"/>non s'era scorta mu&shy;<lb/>tazione alcuna<emph.end type="italics"/> (Alb. </s>

<s>III, 396), Galileo, per l'esperienza che aveva di tutti <lb/>gli altri movimenti delle stelle, si rendeva certo che oramai non dovrebbe <lb/>Saturno fare altra mutazione nemmeno per l'avvenire &ldquo; perch&egrave;, ragionava, <lb/>quando in tali stelle fosse movimento alcuno simile ai movimenti delle Me&shy;<lb/>dicee, o di altre stelle, gi&agrave; doveriano essersi separate o totalmente congiunte <lb/>colla principale stella di Saturno, quando anco il movimento loro fosse mille <lb/>volte pi&ugrave; tardo di qualsivoglia altro di altra stella che vada vagando per lo <lb/>cielo &rdquo; (ivi). </s></p><p type="main">

<s>Riposava con pi&ugrave; tranquillit&agrave; che mai Galileo in tal certezza, vedendo <lb/>Saturno seguitar tuttavia a mostrarsi tricorporeo infino all'Estate, dopo la <lb/>quale, intermesse le osservazioni, non torn&ograve; a riprenderle che sulla fin di <lb/>Novembre. </s>

<s>Rimase stupefatto: sparite le due stelle laterali, Saturno era di&shy;<lb/>ventato monosferico come Giove. </s>

<s>Datone avviso a Federigo Cesi, rispose que&shy;<lb/>sti da Roma la novit&agrave; di Saturno parergli tanto pi&ugrave; strana &ldquo; quanto che <pb xlink:href="020/01/1022.jpg" pagenum="465"/>V. S. qui mi disse non avere i suoi laterali moto alcuno, e nella prima Let&shy;<lb/>tera solare dice non essersi in essa scorta mutazione alcuna, n&egrave; dovervisi <lb/>vedere &rdquo; (Alb. </s>

<s>VIII, 244). </s></p><p type="main">

<s>Dicevano in simil modo anche tutti gli altri che vedevano smentirsi da <lb/>s&egrave; stesso l'oracolo di Galileo, il quale mutando tenore al responso confes&shy;<lb/>sava cos&igrave; in pubblico che s'era ingannato; e che non aveva tanto ingegno <lb/>da penetrare l'arcano. </s>

<s>&ldquo; Ora che si ha da dire in cos&igrave; strana metamorfosi? </s>

<s><lb/>forse si sono consumate le due minori stelle al modo delle macchie so&shy;<lb/>lari? </s>

<s>forse sono sparite e repentinamente fuggite? </s>

<s>forse Saturno si ha di&shy;<lb/>vorato i propri figli, oppure &egrave; stata illusione e fraude l'apparenza, colla <lb/>quale i cristalli hanno per tanto tempo ingannato me con tanti altri, che <lb/>meco molte volte gli osservarono? </s>

<s>&Egrave; forse ora venuto il tempo di rinver&shy;<lb/>dir la speranza, gi&agrave; prossima al seccarsi, in quelli che retti da pi&ugrave; profonde <lb/>contemplazioni hanno penetrato tutte le nuove osservazioni esser fallacie, <lb/>n&egrave; potere in veruna maniera sussistere? </s>

<s>Io non ho che dire cosa risoluta <lb/>in caso cos&igrave; strano, inopinato e nuovo: la brevit&agrave; del tempo, l'accidente <lb/>senza esempio, la debolezza dell'ingegno e il timore dell'errore mi rendono <lb/>grandemente confuso &rdquo; (Alb. </s>

<s>III, 506, 7). </s></p><p type="main">

<s>Nonostante non si volle dar Galileo per vinto. </s>

<s>Incominci&ograve; a pensare che <lb/>forse i due Satelliti immobili al fianco di Saturno cangiavano aspetto dipen&shy;<lb/>dente dal moto proprio del Pianeta combinato col moto della Terra, cosic&shy;<lb/>ch&egrave; ora si vedono i detti Satelliti in maest&agrave;, e Saturno si mostra tricor&shy;<lb/>poreo; ora si vedono in profilo o in isbieco, in modo che l'anteriore proietti <lb/>il lume e si confonda colla vista del Pianeta, e il posteriore ne rimanga <lb/>dietro occultato, e il Pianeta stesso si mostra allora monosferico e solitario. </s>

<s><lb/>Sopra una tal conclusione, che Galileo confessa non aver nessuna certezza, <lb/>predisse cos&igrave; al Velsero, infine alla III Lettera solare, le fasi che sarebbe, <lb/>dopo il 1612, per mostrar Saturno ai curiosi osservatori: &ldquo; Le due minori <lb/>Stelle saturnie, le quali di presente stanno celate, forse si scopriranno un <lb/>poco per due mesi intorno al solstizio estivo dell'anno prossimo futuro 1613, <lb/>e poi si asconderanno, restando celate sin verso il brumal solstizio del&shy;<lb/>l'anno 1614, circa al qual tempo potrebbe accadere che di nuovo per qual&shy;<lb/>che mese facessero di s&egrave; alcuna mostra, tornando poi di nuovo ad ascon&shy;<lb/>dersi sin presso all'altra seguente bruma, al qual tempo credo bene con <lb/>maggior risolutezza che torneranno a comparire, n&egrave; pi&ugrave; si asconderanno, se <lb/>non che nel seguente solstizio estivo, che sar&agrave; dell'anno 1615, accenne&shy;<lb/>ranno alquanto di volersi occultare, ma non per&ograve; credo che si asconderanno <lb/>interamente, ma ben tornando poco dopo a palesarsi, le vedremo distinta&shy;<lb/>mente e pi&ugrave; che mai lucide e grandi, e quasi risolutamente ardirei di dire <lb/>che le vedremo per molti anni, senza interrompimento veruno &rdquo; (Alb. </s>

<s>III, 507). </s></p><p type="main">

<s>Di queste predizioni di Galileo per&ograve; non se ne vide avverar compiuta&shy;<lb/>mente nessuna; nemmen quella che, essendosi Saturno divorato il pasto n&egrave; <lb/>avendolo per vecchiezza potuto ben masticare, sarebbe appunto per renderlo <lb/>cos&igrave; intero come l'avea trangugiato (Alb. </s>

<s>VIII, 248), imperocch&egrave;, invece dei <pb xlink:href="020/01/1023.jpg" pagenum="466"/>due soliti globetti, vide sulla fin dell'Agosto 1616 (ivi, 390) Galileo stesso <lb/>dare a Saturno fuori come due mitre o orecchioni &ldquo; che rendono tutto il <lb/>composto di figura ovale, simile a un'oliva. </s>

<s>&rdquo; Dopo le quali parole imme&shy;<lb/>diatamente soggiunge: &ldquo; Si distingue per&ograve; tra le due mitre il globo di mezzo <lb/>perfettamente rotondo, e non di figura ovata, e nel mezzo delle attaccature <lb/>delle mitre al globo di mezzo si veggono due macchie oscure assai &rdquo; (ivi, <lb/>VII, 228). In similissimo aspetto, cio&egrave; ovale &ldquo; ac tum duabus maculis ro&shy;<lb/>tundis ad utrumque verticem &rdquo; dice, nel cap. </s>

<s>VII, lib. </s>

<s>XV <emph type="italics"/>De mundi fa&shy;<lb/>brica,<emph.end type="italics"/> di avere osservato Saturno, dalla fin di Ottobre 1616 al Novembre 1619, <lb/>il padre Biancani. (Mutinae 1635, pag. </s>

<s>155). </s></p><p type="main">

<s>Disegn&ograve; di sua propria mano Galileo questa nuova fase saturnia a tergo <lb/>della carta 94 di quel Tomo, ch'&egrave; in ordine numerico il IV della Parte III <lb/>de'Manoscritti galileiani, e il disegno stesso lucidato dall'originale si rap&shy;<lb/>presenta qui nella figura 93 sotto gli occhi de'nostri Lettori. </s>

<s>Tutto il com&shy;<lb/><figure id="id.020.01.1023.1.jpg" xlink:href="020/01/1023/1.jpg"/></s></p><p type="caption">

<s>Figura 93.<lb/>posto mostrasi chiaramente configurato, come diceva Ga&shy;<lb/>lileo, in somiglianza di oliva, e da'due lati del Globo sa&shy;<lb/>turnio perfettamente rotondo escono i due orecchioni o le <lb/>due mitre, ciascuna colle sue macchie assai oscure nel mezzo. </s></p><p type="main">

<s>Si rende cos&igrave; a tutti i riguardanti manifesta la vera intenzione di chi <lb/>tratteggi&ograve; quella figura colla penna, ma quando l'Alb&egrave;ri annunzi&ograve; con tromba <lb/>sonora ai quattro venti la scoperta delle Effemeridi contenute manoscritte <lb/>nel sopra citato Volume, e i curiosi concorsero d'ogni parte a Firenze a <lb/>veder con gli occhi e a toccar con mano il Codice avventuroso, fu ad uno <lb/>di essi trattenuto lo sguardo sulla detta figura, e vedendoci senz'altro Sa&shy;<lb/>turno inanellato, tanti anni prima che dall'Hugenio, esult&ograve; come di una <lb/>scoperta pi&ugrave; maravigliosa di quella, che diceva d'aver fatto lo stesso Alb&egrave;ri. </s></p><p type="main">

<s>Quest'<emph type="italics"/>homme d'un gran savoir<emph.end type="italics"/> diffuse la notizia della sua scoperta a <lb/>Parigi, dove allora stanziava Guglielmo Libri, il quale subito nel Giugno <lb/>del 1844 dette mano a scrivere, nel <emph type="italics"/>Journal des Savants,<emph.end type="italics"/> un articolo, in <lb/>cui, dopo di aver diffidato se quella specie di Giornale messo fuori dall'Al&shy;<lb/>b&egrave;ri, dove interpolate alle osservazioni celesti si notano le spese fatte in cu&shy;<lb/>cina, contenesse veramente l'atlantica fatica di Galileo, cos&igrave; soggiunge: &ldquo; Il <lb/>parait cependant qu'on trouve dans ces notes un fait extremement remar&shy;<lb/>quable, qui a echapp&eacute; a M.r Alb&egrave;ri; savoir, le dessin fait par Galil&eacute;e de Sa&shy;<lb/>turne avec son anneau. </s>

<s>Si ce fait, qui nous est attest&eacute; par des hommes <lb/>d'un gran savoir, se confirme, c'est l&agrave; une veritable d&eacute;couverte qu'on aura <lb/>fait dans les papiers de Galil&eacute;e &rdquo; (Alb. </s>

<s>V, 34). </s></p><p type="main">

<s>Al rimprovero d'essersi cos&igrave; lasciata scappar di mano una scoperta <lb/>tant'ovvia, eppur s&igrave; <emph type="italics"/>extremement remarquable,<emph.end type="italics"/> l'Alb&egrave;ri si risent&igrave;, ma non <lb/>rispose, com'avrebbe potuto, alle parole inconsiderate. </s>

<s>Avrebbe infatti po&shy;<lb/>tuto opporre che il disegno manoscritto lo fece incidere Galileo nella pa&shy;<lb/>gina 217 della prima impressione del <emph type="italics"/>Saggiatore<emph.end type="italics"/> fatta da Giacomo Mascardi <lb/>in Roma nel 1623, cosicch&egrave; stette per trentasei anni l'immagine di Saturno <lb/>con l'anello sotto gli occhi del Viviani e del Borelli, tanto stupidi da non <pb xlink:href="020/01/1024.jpg" pagenum="467"/>s'avveder che il loro Galileo aveva scoperto, molto tempo prima, quel che, <lb/>come cosa nuova, ammiravano nell'Hugenio. </s>

<s>Stette di pi&ugrave; quello stesso di&shy;<lb/>segno per altri cento e ottantacinque anni scolpito nelle molteplici edizioni <lb/>dell'opere galileiane, sotto gli occhi di tutti gli Astronomi di Europa, senza <lb/>che in nessuno si ritrovasse ancora quel <emph type="italics"/>gran savoir<emph.end type="italics"/> necessario a far la <lb/>scoperta annunziata dal Libri. </s></p><p type="main">

<s>Chi non si fa caso di tanta inconsideratezza, in uomini reputati di s&igrave; <lb/>gran sapere, compatir&agrave; al nostro Targioni Tozzetti, il quale accenn&ograve; in una <lb/>nota a pi&egrave; della pag. </s>

<s>385 del T. </s>

<s>I delle sue <emph type="italics"/>Notizie degli aggrandimenti ecc.<emph.end type="italics"/><lb/>che il Beriguardi nel 1643, sedici anni prima della pubblicazione del <emph type="italics"/>Sy&shy;<lb/>stema saturnium,<emph.end type="italics"/> lodava la scoperta ugeniana dell'anello. </s>

<s>L'errore &egrave; tanto <lb/>grosso, che non par credibile in uno storico della scienza, ma che pure ha <lb/>la stessa radice di quell'altro, che si svel&ograve; da noi a pag. </s>

<s>450 del I Tomo, <lb/>in ambedue i quali errori incorse il Targioni per non avere, in cosa di s&igrave; <lb/>facile sospetto, dubitato punto che l'edizione de'<emph type="italics"/>Circoli pisani,<emph.end type="italics"/> fatta nel 1643, <lb/>non fosse in tutto simile all'altra fatta nel 1661, vivente tuttavia l'Autore, <lb/>e quando gi&agrave; le grandi scoperte del Torricelli e dell'Huyghens avevano della <lb/>loro fama riempiuto il mondo. </s></p><p type="main">

<s>Ma passando sopra gli altrui errori con quella indulgente piet&agrave;, con cui <lb/>vorremmo che si passasse sui nostri, rivolgiamo l'attenzione a quella im&shy;<lb/><figure id="id.020.01.1024.1.jpg" xlink:href="020/01/1024/1.jpg"/></s></p><p type="caption">

<s>Figura 94.<lb/>magine saturnia fatta imprimere da Galileo stesso nella <lb/>citata pagina del <emph type="italics"/>Saggiatore.<emph.end type="italics"/> Noi l'abbiamo di l&agrave; lu&shy;<lb/>cidata e la rappresentiamo nella figura 94 sotto gli occhi <lb/>de'nostri Lettori perch&egrave;, riscontrandola colla precedente, <lb/>ne verifichino da s&egrave; stessi la sostanziale somiglianza. </s></p><p type="main">

<s>Attendendo dunque (bench&egrave; mute sieno le due figure, cos&igrave; qui nella <lb/>stampa, come l&agrave; nel manoscritto) si sa d'altre fonti sicure che voleva Ga&shy;<lb/>lileo rappresentare in que'disegni Saturno co'suoi due orecchioni da cia&shy;<lb/>scun lato, e una macchia oscura nel loro mezzo. </s>

<s>A questo punto si tacque <lb/>il primo scopritor dell'altissimo Pianeta tergemino, n&egrave; ebbe ardire o spe&shy;<lb/>ranza d'avvincer nelle sue reti quel Proteo multiforme, che tante volte gli <lb/>era uscito di mano. </s>

<s>Vedremo come il costrutto lasciato a questo punto in&shy;<lb/>terrotto da Galileo fosse poi ripreso dall'Hodierna, che si studi&ograve; di ridurre <lb/>questa fase saturnia ultimamente osservata a sistema. </s>

<s>Ma perch&egrave; quel si&shy;<lb/>stema accenna piuttosto a un regresso, giova proseguire a diritto il filo di <lb/>quella via che avrebbe finalmente condotto alla desiderata scoperta. </s></p><p type="main">

<s>La prima mossa, bench&egrave; cos&igrave; dalla lontana, venne allor che il Gassendi <lb/>e il Peiresc, osservando, con un Canocchiale mandato a loro da Galileo, l'ul&shy;<lb/>tima fase saturnia rappresentata nel <emph type="italics"/>Saggiatore,<emph.end type="italics"/> dubitarono; se la figura fosse <lb/><emph type="italics"/>macchiata,<emph.end type="italics"/> come diceva Galileo, o <emph type="italics"/>forata<emph.end type="italics"/> piuttosto come pareva a loro (Alb. </s>

<s><lb/>X, 193). Nel 1646 il Fontana pubblic&ograve; le nuove osservazioni fatte co'suoi <lb/>Canocchiali. </s>

<s>La fase del 1630, che rappresenta Saturno rotondo con due pic&shy;<lb/>cole stelle rotonde ai lati (Novae Observ., pag. </s>

<s>119) &egrave; quella che poi illuse <lb/>anche l'Hevelio, ma l'altra del 1633 descritta dallo stesso Fontana a pag. </s>

<s>131 <pb xlink:href="020/01/1025.jpg" pagenum="468"/>del suo libro, &egrave; mostruosa. </s>

<s>Pi&ugrave; conformi al vero sono le osservazioni del 1634 <lb/>(pag. </s>

<s>133) e del 1636 (pag. </s>

<s>134), le quali dettero occasione all'Hevelio di <lb/>immaginare il suo sistema, ma poi, nel passare a descrivere le fasi del 1644 <lb/>(pag. </s>

<s>137) e del 1645 (pag. </s>

<s>139 e 141) ritorn&ograve; il Fontana alle mostruosit&agrave;, <lb/>immaginandosi che i due punti estremi e laterali della figura, vivamente ir&shy;<lb/>radianti, fossero quelle stesse stelle della prima osservazione, che si tenes&shy;<lb/>sero congiunte al pianeta come per due redini di luce. </s></p><p type="main">

<s>Ma intanto si veniva con s&igrave; fatte rappresentazioni a decidere i dubbi <lb/>del Gassendo e del Peiresc se quelle, che si vedevano in mezzo a'due orec&shy;<lb/>chioni di Galileo, erano macchie o fori. </s>

<s>Cos&igrave;, il Boulliaud scriveva al prin&shy;<lb/>cipe Leopoldo de'Medici di aver nel Dicembre del 1648 osservato Saturno <lb/>con due lati ben distinti in modo, da non aver pi&ugrave; dubbio che non sieno i <lb/>due laterali di qua e di l&agrave; disgiunti dal globo del Pianeta. </s>

<s>Per mezzo di <lb/>un Canocchiale eccellente donatogli dal Granduca &ldquo; Saturnum conspexi, dice <lb/>il Boulliaud, mense Decembri superiori dum Terrae vicinus erat hac forma <lb/>(fig. </s>

<s>95): ita ut acutiores cernerentur partes AB <lb/><figure id="id.020.01.1025.1.jpg" xlink:href="020/01/1025/1.jpg"/></s></p><p type="caption">

<s>Figura 95.<lb/>quam circuli circumferentia ferre possit, sed <lb/>ad ellipticam figuram propius accedebat: distin&shy;<lb/>ctae apparebant partes O, O, tamquam hiatus <lb/>tenebrosus utrinque globum Saturni a latero&shy;<lb/>nibus disiungens &rdquo; (MSS. Cim., T. XVI, c. </s>

<s>21). </s></p><p type="main">

<s>Quest'apparenza descritta dal Boulliaud, e nella quale si correggeva ci&ograve; <lb/>che v'aveva di fantastico introdotto il Fontana, rappresentatasi pi&ugrave; scolpita <lb/>che mai all'oculatissimo Hevelio, servi a inspirargli quell'animo di comporre <lb/>un Sistema saturnio, che le strane metamorfosi osservate avevano prima fatto <lb/>smarrire a Galileo. </s>

<s>Nel 1656 pubblicava in Danzica una dissertazione col <lb/>titolo &ldquo; De nativa Saturni facie eiusque variis phasibus certa periodo re&shy;<lb/>deuntibus &rdquo;, dove non dissimulando le gravissime difficolt&agrave;, e anzi aperta&shy;<lb/>mente confessando i dubbi che gli tenevano agitata la mente, s'introduce a <lb/>trattar dell'arduo soggetto con queste parole: &ldquo; Ego hucusque, licet indefesse <lb/>in isto negotio, ab anno 1642 continue, multorum perfectissimorum tam <lb/>nostra quam aliorum artificum sedula manu elaboratorum Telescopiorum <lb/>beneficio desudaverim; nullo tamen modo recte phaenomenon hocce assequi <lb/>et perscrutari potuerim, haerens plane utrum Saturnus sit rotundus,. an <lb/>vero ellipticus, utrum simplex corpus an vero tricorporeus &rdquo; (pag. </s>

<s>2). </s></p><p type="main">

<s>Dopo pi&ugrave; mature considerazioni, parvegli nonostante di potere stabi&shy;<lb/>lire le tre cose seguenti; &ldquo; Primo itaque Saturnum cum plerisque Astro&shy;<lb/>philis a Sole illuminari quidem statuo..... Secundo, pro certo habeo Sa&shy;<lb/>turnum non semper esse uniformem .... sed variam faciem nobis ostentare, <lb/>diversasque exhibere phases..... Tertio, Saturnum pono revera esse tricor&shy;<lb/>poreum et omnino talis speciei qualis est num. </s>

<s>1&deg; adumbratus, medium <lb/>nempe corpus non esse rotundum sed ellipticum; duo laterones eius non <lb/>esse globosa ac pecularia circa Saturnum mobilia, sed firmiter circa partes <lb/>superiores et inferiores adhaerentia corpora, instar brachiorum figurae fere <pb xlink:href="020/01/1026.jpg" pagenum="469"/>hyperbolicae, ac certo et immutabili interstitio circa medium a medio cor&shy;<lb/>pore remoto, mobilia tamen una cum corpore intermedio circa unicam axem <lb/>certa periodo &rdquo; (pag. </s>

<s>3, 4). </s></p><p type="main">

<s>Le figure ombreggiate, di che fa cenno l'Autore, sono in numero di <lb/>sei impresse tutte insieme e per ordine numerate in una Tavola a rappre&shy;<lb/>sentar la successione delle principali fasi saturnie, che si distinguono cia&shy;<lb/>scuna col nome proprio di <emph type="italics"/>Saturnus elliptico-ansatus plenus, S. ellipticus <lb/>ansatus diminutus, S. sphaerico-ansatus, S. sphaerico-cuspidatus, S. tri&shy;<lb/>corporeus, S. monosfaericus.<emph.end type="italics"/></s></p><p type="main">

<s>Prototipa &egrave; la prima figura, la quale nell'intenzion dell'Hevelio rap&shy;<lb/>presenta Saturno composto di un globo ellittico nel mezzo, con un'ansa <lb/>attaccata di qua e di l&agrave; dalle due parti. </s>

<s>Supponeva l'Autore che tutto il <lb/>sistema facesse in 30 anni una rotazione intiera intorno al suo asse minore <lb/>perpendicolarmente eretto e stabile sul piano dell'orbita planetaria, e cos&igrave; <lb/>sperava che sarebbero regolarmente apparite le variet&agrave; delle fasi secondo <lb/>l'ordine divisato. </s>

<s>Ma presto si videro i fatti non approvar l'ipotesi, impe&shy;<lb/>rocch&egrave;, secondo la predizion dell'Hevelio, la fase rotonda del 1656 doveva <lb/>mantenersi infino al Settembre dell'anno appresso, e nonostante infin dal <lb/>d&igrave; 13 d'Ottobre di quell'anno 1656 si vide Saturno riapparire coll'anse, <lb/>mantenendosi in quella medesima apparenza anche dopo. </s></p><p type="main">

<s>Fallace il Sistema heveliano si dimostrava altres&igrave; dal riscontro delle fasi <lb/>antecedentemente osservate, fra le quali insigni nella storia del Pianeta erano <lb/>quelle descritte, nella III Lettera velseriana, da Galileo. </s>

<s>Nel solstizio del&shy;<lb/>l'anno 1612, quando Saturno era nei 18&deg; 22&prime; de'Pesci, Galileo l'osserv&ograve; tri&shy;<lb/>corporeo, mentre sarebbe dovuto per le Tavole dell'Hevelio comparire ro&shy;<lb/>tondo; e similmente, nel Dicembre di quell'anno 1612, essendo Saturno in <lb/>11&deg; 27&prime; de'Pesci, Galileo l'osserv&ograve; rotondo, mentre si doveva per l'Hevelio aspettare trisferico. </s></p><p type="main">

<s>Ma se in ogni modo per prototipo delle altre fasi stabilivasi quella de&shy;<lb/>signata col nome di <emph type="italics"/>ellittico ansata piena,<emph.end type="italics"/> non si vedeva come potessero <lb/>da questa sola derivarsi tutte le varie apparenze del Pianeta. </s>

<s>Sia infatti nella <lb/>figura 96 ABCD il globo ellissoideo di Saturno, a cui sieno attaccate le anse <lb/>EF, GH e si volga tutto il sistema attorno all'asse BD. </s>

<s>Non v'ha dubbio <lb/><figure id="id.020.01.1026.1.jpg" xlink:href="020/01/1026/1.jpg"/></s></p><p type="caption">

<s>Figura 96.<lb/>che da chiunque stesse di faccia a riguar&shy;<lb/>dare le apparenti mutazioni di figura pre&shy;<lb/>sentate da questo moto, si vedrebbero le <lb/>anse andar via via sempre pi&ugrave; ad acco&shy;<lb/>starsi al globo centrale, e cos&igrave; potrebbe <lb/>Saturno in questa ipotesi mostrarsi sotto <lb/>l'aspetto di ellittico ansato diminuito, e di <lb/>sferico ansato. </s>

<s>Seguitando poi tutto il si&shy;<lb/>stema a volgersi regolarmente attorno, giunto a presentar l'asse maggiore <lb/>in direzione del raggio visuale, potrebbe altresi pigliar la forma monosferica, <lb/>ma dovendo secondo il supposto dell'Hevelio, le altezze EF, GH mantenersi <pb xlink:href="020/01/1027.jpg" pagenum="470"/>sempre e in qualunque caso invariabili, non potrebbero perci&ograve; mai tanto <lb/>comprimersi da mostrar le due fasi sferico cuspidata e trisferica. </s></p><p type="main">

<s>Mentre che cos&igrave; discutevasi dagli Astronomi intorno alla possibilit&agrave; del <lb/>Sistema heveliano, che per queste ragioni principalmente rimaneva molto <lb/>dubbioso, l'Huyghens dall'Aja pubblicava, in data del d&igrave; 5 Marzo 1656, <lb/>una breve nota contenente la scoperta di una nuova Luna, la quale, come <lb/>le Medicee intorno a Giove, si rivolgeva in sedici giorni intorno a Saturno. </s>

<s><lb/>Accennava ivi inoltre a una cosa ben pi&ugrave; nuova e pi&ugrave; importante, che cio&egrave; <lb/>la scoperta di quella Luna &ldquo; viam aperuit, tandemque causam rescivimus, <lb/>cur interdum inter binas velut ansas Saturnus medius teneatur, alias recta <lb/>quasi brachia protendat, tum nonnunquam, omnibus amissis, rotundus in&shy;<lb/>veniatur &rdquo; (Opera Varia, Vol. </s>

<s>II, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>525). A che si <lb/>riducesse quella causa intorno alla quale, fra tutti gli Astronomi, il solo <lb/>Hevelio aveva allora allora e non troppo felicemente pronunziata la sua sen&shy;<lb/>tenza, l'Huyghens lo accenn&ograve; alla fine di detta nota in enimma o per grifo, <lb/>imitando le previdenti accortezze di Galileo. </s></p><p type="main">

<s>La curiosit&agrave; di scioglier l'enimma frug&ograve; tutti gli Astronomi, ma due <lb/>soli vi si provarono, il Roberval in Francia, e l'Hodierna in Italia. </s>

<s>S'im&shy;<lb/>maginava il primo che dalla zona torrida di Saturno si sollevassero vapori <lb/>condensati dal freddo, i quali vapori, se riempiono tutta intorno e molto <lb/>spessi la zona, danno a noi che gli vediamo irraggiati dal Sole l'apparenza <lb/>ellittica. </s>

<s>Se sono men densi, e non si vedono perci&ograve; che l&agrave;, dove per pro&shy;<lb/>spettiva appariscono cumulati, cio&egrave; dalle due parti, presentano la fase an&shy;<lb/>sata. </s>

<s>Se poi Saturno &egrave; sereno, precipitatasi qualunque esalazion vaporosa sopra <lb/>la superficie del suo Globo, ci apparisce come Giove perfettamente rotondo. </s></p><p type="main">

<s>Questa ipotesi robervalliana era senza dubbio semplicissima, ma non <lb/>essendosi ancora osservati i ritorni matematicamente regolari delle fasi, non <lb/>si poteva ripudiar per il semplice motivo della capricciosa variabilit&agrave; delle <lb/>stagioni. </s>

<s>Se veramente per&ograve; dipende questa variabilit&agrave; da cause meteorolo&shy;<lb/>giche somiglianti a quelle della nostra Terra, la quale &egrave; pi&ugrave; nuvolosa ai poli <lb/>che no all'Equatore, non s'intende, opponevasi al Roberval, come debba in <lb/>Saturno avvenir cos&igrave; tutto al contrario. </s></p><p type="main">

<s>L'Hodierna, fisso nella contemplazione della fase saturnia descritta nel <lb/><emph type="italics"/>Saggiatore,<emph.end type="italics"/> e ch'ei ci volle rappresentar sott'occhio in quella Tavola, dove <lb/>all'esemplare del Sistema gioviale aggiunse le apparenze degli altri fenomeni <lb/>celesti; ritorn&ograve; in dietro a considerare con Galileo e col Biancani Saturno <lb/>ovale tinto delle due macchie nere alla sua superficie. </s>

<s>Segnando nel sistema <lb/>dell'Hevelio questo regresso, approv&ograve; del resto l'ipotesi di lui, sperando di <lb/>aver cos&igrave; colto nel segno in decifrar l'enimma ugeniano. </s>

<s>Ma l'Hugenio stesso <lb/>gli fece poco dopo capire che non includeva l'enimma per nulla o la prugna <lb/>o l'uovo maculato, col quale, se potevansi rappresentar le fasi monosferi&shy;<lb/>che due volte sole in 30 anni, rimaneva per&ograve; tuttavia inesplicato come tante <lb/>altre volte mostrasse quello stesso aspetto il Pianeta, non potendo ci&ograve; fare <lb/>se non che ascondendo, ma non si vedeva dove, quelle due macchie nere. </s></p><pb xlink:href="020/01/1028.jpg" pagenum="471"/><p type="main">

<s>Nel Luglio del 1659 comparve finalmente il <emph type="italics"/>Systema Saturnium<emph.end type="italics"/> dedi&shy;<lb/>cato al principe Leopoldo de'Medici, e fu allora dall'oracolo stesso del&shy;<lb/>l'Huyghens svelato l'arcano, che ridest&ograve; in generale una lieta maraviglia, <lb/>e in alcuni pochi un impotente prurito di contradizione. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Nel <emph type="italics"/>Systema Saturnium<emph.end type="italics"/> narra da s&egrave; stesso l'Autore la storia della sua <lb/>insigne scoperta, la quale si compendia cos&igrave; in queste parole: &ldquo; Quand'ebbi, <lb/>egli dice, ritrovato che il periodo del nuovo Pianeta era di 16 giorni, pen&shy;<lb/>sai che si sarebbe anche Saturno stesso revoluto intorno al suo asse. </s>

<s>Im&shy;<lb/>perocch&egrave; sul suo asse si rivolge la nostra Terra, sul suo asse il Sole e pro&shy;<lb/>babilmente anche Giove in un periodo di tempo che, secondo me, &egrave; pi&ugrave; <lb/>breve di ventiquattr'ore. </s>

<s>Persuaso dunque cos&igrave; per induzione che dovesse <lb/>Saturno rigirarsi in s&egrave; stesso, ne conclusi che avrebbe seco menato in volta <lb/>anche gli altri corpi circostanti, con tanto maggior velocit&agrave; quanto gli an&shy;<lb/>davano pi&ugrave; vicini. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; M'occorse d'osservare il Pianeta nel 1655, quando mostrava le sue <lb/>braccia sporte lungo una linea retta, come se fosse trafitto e trapassato nel <lb/>mezzo da una clava con le sue estremit&agrave; pi&ugrave; grosse e pi&ugrave; chiare da una <lb/>parte e dall'altra. </s>

<s>Quum itaque quotidie eamdem hanc speciem prae se <lb/>ferret, intellexi id alia ratione fieri non posse, siquidem tam brevis esset <lb/>Saturni, eorumque quae illi cohaerent circuitus, nisi ut globus Saturni a <lb/>corpore alio aequaliter undique cinctus poneretur, atque ita ANNULUS qui&shy;<lb/>dam medium eum ambiret &rdquo; (Op. </s>

<s>varia cit., pag. </s>

<s>565). </s></p><p type="main">

<s>&ldquo; Cos&igrave;, col supposto di questo Anello mi veniva bene quella fase spie&shy;<lb/>gata: bisognava per&ograve; spiegare anche le altre, ci&ograve; che m'avvenne presto <lb/>avvertendo che la linea delle braccia saturnie intersecava l'Ecclittica con un <lb/>angolo maggiore di venti gradi, d'onde ne stabilii che tale, sulla stessa Ec&shy;<lb/>clittica, dovess'esser pure l'inclinazion del piano di quello Anello, ch'io <lb/>m'ero immaginato. </s>

<s>Ne seguiva di qui ch'essendo veduto da noi sotto varii <lb/>aspetti dovesse ora apparirci in figura di un'ellissi pi&ugrave; o meno aperta, e <lb/>ora anche in esquisita linea retta. </s>

<s>La fase ansata poi la spiegavo assai facil&shy;<lb/>mente ammettendo che fra il giro interiore dell'Anello e il globo del Pia&shy;<lb/>neta intercedesse qualche spazio vuoto. </s>

<s>&rdquo; </s></p><p type="main">

<s>Le pi&ugrave; minute particolarit&agrave; che illustrano questa storia, con altre di&shy;<lb/>gressioni sopra soggetti nuovi e importantissimi, si leggevano in Firenze <lb/>dagli Accademici del Cimento, al principe de'quali dedicava l'Autore il suo <lb/>libro, non per cortigianesca adulazione, ma perch&egrave; fosse diligentemente esa&shy;<lb/>minato e imparzialmente giudicato da quei, che sopra gli altri reputava au&shy;<lb/>torevoli nella scienza. </s>

<s>In ordine a che non solo ne furono sodisfatti i desi&shy;<lb/>derii, ma ebbe di pi&ugrave; l'Huyghens a professar gratitudine verso i nostri<pb xlink:href="020/01/1029.jpg" pagenum="472"/>fiorentini, i quali rimossero le difficolt&agrave; e confermarono il vero Sistema sa&shy;<lb/>turnio in un modo ingegnosissimo, riducendo sotto i nostri occhi le appa&shy;<lb/>renze di ci&ograve;, che la Natura opera in un mondo cos&igrave; smisuratamente lontano <lb/>da noi. </s></p><p type="main">

<s>Una delle prime e pi&ugrave; forti di quelle difficolt&agrave; si riduceva a dire che <lb/>essendosi a moltissimi osservatori, dopo Galileo, mostrato Saturno con due <lb/>stelle disgiunte e laterali, non si vedeva come si potesse ridur questa fase <lb/>alla figura dell'anello. </s>

<s>Rispose l'Huyghens che questa di Saturno tricorpo&shy;<lb/>reo era una illusione dei troppo deboli strumenti usati da que'suoi prede&shy;<lb/>cessori, ma non seppe dimostrar di fatto come sparissero le illusioni e ap&shy;<lb/>parisse il vero, usando strumenti pi&ugrave; perfetti. </s></p><p type="main">

<s>La dimostrazione sperimentale di ci&ograve;, che pareva impossibile, fu ritrovata <lb/>nell'Accademia fiorentina dall'ingegno del Borelli, il quale fece fabbricare <lb/>una macchinetta a rappresentare il Globo di Saturno col suo Anello, nelle <lb/>puntuali proporzioni stabilite dall'Hugenio. </s></p><p type="main">

<s>&ldquo; Costituita detta Macchina in testa ad una galleria lunga 128 braccia, <lb/>ed illuminata da quattro Torce, collocate in modo che rimanessero nascoste <lb/>all'occhio dell'Osservatore, si not&ograve; che quanto minore era l'angolo de'raggi <lb/>visuali sopra il piano della Fascia, tanto pi&ugrave; andava restringendosi l'appa&shy;<lb/>rente Ellisse, infin tanto che i tratti GF, CD (fig. </s>

<s>97) ad un Occhiale im&shy;<lb/>perfetto si facevano invisibili, e pur tuttavia con esso si seguitavano a sco&shy;<lb/><figure id="id.020.01.1029.1.jpg" xlink:href="020/01/1029/1.jpg"/></s></p><p type="caption">

<s>Figura 97.<lb/>prire i due estremi B, E, che per la <lb/>lontananza e debolezza della luce per&shy;<lb/>fettamente si rotondavano, a tale che <lb/>l'apparenza della Macchina in tal costi&shy;<lb/>tuzione corrispondeva alla prima delle <lb/>Tavole dell'Hugenio, che &egrave; di tre sfer e, <lb/>la di mezzo maggiore e l'altre due mi&shy;<lb/>nori, per breve tratto disgiunte dal disco <lb/>di Saturno. </s>

<s>Variavasi bene quest'ap&shy;<lb/>parenza riguardando l'istessa Macchina, <lb/>non punto alterata dalla sua prima po&shy;<lb/>sizione e lontananza, con un Occhiale <lb/>di un braccio e un terzo ma d'esquisito <lb/>lavoro, mostrandosi allora Saturno non pi&ugrave; in mezzo delle due stelle B, E, <lb/>ma coronato dalla zona lucida BCDEFG, merc&egrave; delle braccia luminose nuo&shy;<lb/>vamente resegli dall'esquisitezza del secondo Occhiale &rdquo; (Targioni, Noti&shy;<lb/>zie ecc., T. I, pag. </s>

<s>741). </s></p><p type="main">

<s>Un'altra non men grave difficolt&agrave;, ad approvare il Sistema ugeniano, <lb/>nasceva dalla fase monosferica, e l'Huyghens stesso l'avea gi&agrave; prevenuta con <lb/>dire che, sebben l'Anello stia anche allora intorno al Pianeta, &egrave; nonostante <lb/>invisibile a noi perch&egrave;, trovandosi il prolungamento del nostro raggio vi&shy;<lb/>suale sul piano di esso Anello, non ci mostra di s&egrave; che l'esteriore super&shy;<lb/>ficie convessa, o come si direbbe l'esergo. </s></p><pb xlink:href="020/01/1030.jpg" pagenum="473"/><p type="main">

<s>Bisognava per&ograve; qui rendere la ragione di una tale invisibilit&agrave;, la quale <lb/>si poteva credere che dipendesse dal ritrovarsi in quella cos&igrave; espansa figura <lb/>annulare troppo assottigliata la materia. </s>

<s>Ma l'Huyghens nega che possa es&shy;<lb/>ser questa la ragione cercata, perch&egrave; l'Anello dee avere una certa mate&shy;<lb/>rial grossezza resa evidente nell'ombra proiettata da lui sul disco del Pia&shy;<lb/>neta, che lo sega attraverso con una linea oscura. </s>

<s>Perci&ograve; conclude che la <lb/>ragione di una tale invisibilit&agrave; dee non in altro consistere che nell'esser <lb/>l'esergo dell'Anello composto di qualche particolar materia inetta, come <lb/>l'acqua, a render pi&ugrave; vivamente la luce ne'moltiplicati riflessi. </s>

<s>&ldquo; Alioquin <lb/>vel illud forsitan dici possit materiam quandam aquae similem aut certe <lb/>laevi et splendida superficie praeditam, extrema Annuli praecingere, quae <lb/>unico tantum veluti puncto Solis radios reflectens nequaquam nobis conspi&shy;<lb/>cua erit &rdquo; (Opera cit., pag. </s>

<s>577). </s></p><p type="main">

<s>Il Borelli, nell'Accademia del Cimento, conferm&ograve; questa fase con l'espe&shy;<lb/>rienza, situando innanzi alla Macchinetta l'occhio nel piano della Fascia <lb/>&ldquo; nel qual caso, perdendosi per la loro sottigliezza i suoi contorni esterni, <lb/>rimaneva l'apparenza di una sfera perfettamente rotonda &rdquo; (Targioni, cit., <lb/>pag. </s>

<s>743). L'esperienza stessa per&ograve; non parve di voler secondar cos&igrave; bene <lb/>la ragione della invisibilit&agrave; resa dall'Huyghens, perch&egrave; non fu potuto dagli <lb/>Accademici veder la linea nera proiettata sul disco del Pianeta, e dando al&shy;<lb/>l'anello artificiale della Macchina una qualche sensibile grossezza non si pot&egrave; <lb/>far mai che non si rendesse in qualche modo cospicuo. </s>

<s>&ldquo; Ci siamo perci&ograve; <lb/>attenuti, lasciarouo quegli stessi Accademici scritto, a formar l'anello di no&shy;<lb/>tabile sottigliezza, parendoci che questa ci sottragga da altre difficolt&agrave; in&shy;<lb/>contrate nel costituirlo altrimenti &rdquo; (ivi, pag. </s>

<s>743). </s></p><p type="main">

<s>Essendo cos&igrave; nell'Accademia richiamata l'attenzione sull'ombre che dal&shy;<lb/>l'Anello irraggiato dal Sole si debbono necessariamente, essendo opaco, <lb/>proiettare sul disco del Pianeta, si riconobbe la necessit&agrave; di un'altra zona <lb/>ombrosa, la quale dee nascere &ldquo; non dall'aspetto della superficie cilindrica <lb/>convessa, ma dallo sbattimento della larghezza dell'istesso Anello, per lo che <lb/>dee variare anch'ella di sito, ed alcune volte interamente perdersi &rdquo; (ivi). </s></p><p type="main">

<s>Dalla considerazione di questi fatti il Borelli fu condotto a trovare la <lb/>pi&ugrave; decisiva conferma del Sistema ugeniano in certe apparenze, che s'ad&shy;<lb/>ducevano da alcuni per una delle pi&ugrave; forti ragioni a doverlo negare. </s>

<s>Fu <lb/>osservata una volta dagli Accademici, fra quelle cos&igrave; mutabili apparenze. </s>

<s><lb/>una delle pi&ugrave; singolari, e affatto nuova nella storia delle metamorfosi fino <lb/>allora narrate dagli Astronomi: Saturno appariva per l'appunto come se <lb/>fosse un cappello candido di tesa larga, volato via per l'aria di capo a qual&shy;<lb/>cuno. </s>

<s>Il Borelli allora dimostr&ograve; come quella fase, nella quale vedevasi pi&ugrave; <lb/>che in altra mai cancellata l'immagine dell'Anello, dipendeva anzi dall'Anello <lb/>stesso e da un gioco non avvertito della sua ombra. </s></p><p type="main">

<s>&ldquo; E prima di finir questa parte, scriveva al principe Leopoldo, non so <lb/>se io mi debba arrischiare a palesare certa mia fantasia, della quale forse <lb/>l'Hugenio ne farebbe qualche stima. </s>

<s>Le sere passate con eccellenti Telescopi <pb xlink:href="020/01/1031.jpg" pagenum="474"/>fu osservato in Palazzo il globo di Saturno collocato no nel mezzo precisa&shy;<lb/>mente della sua Ciambella, ma collocato un poco all'in su, in maniera che <lb/>molti di quei signori l'assomigliavano a un cappello da cardinali. </s>

<s>Io qui non <lb/>dico che l'anterior parte XV (fig. </s>

<s>98) della ciambella di Saturno doverebbe <lb/>apparire pi&ugrave; larga e pi&ugrave; allontanata dal centro del medesimo Saturno, che <lb/><figure id="id.020.01.1031.1.jpg" xlink:href="020/01/1031/1.jpg"/></s></p><p type="caption">

<s>Figura 98.<lb/>la parte posteriore RS, perch&egrave;, con tutto <lb/>che questo sia vero, in tanta lontananza <lb/>non pu&ograve; cadere sotto i nostri sensi, ma <lb/>avverto bene che in questa ipotesi &egrave; ne&shy;<lb/>cessario che la parte anteriore XV della <lb/>Ciambella produca certa ombra nell'infe&shy;<lb/>rior porzione del disco di Saturno. </s>

<s>E per&shy;<lb/>ch&egrave; i raggi della nostra vista sono assai <lb/>inclinati ai raggi del Sole, perch&egrave; ora la <lb/>prostaferesi dell'orbe &egrave; massima, sar&agrave; l'inferior parte del disco di Saturno <lb/>adombrata esposta alla nostra vista, la qual ombra, coprendo quasi tutto <lb/>quell'estremo orlo del disco di Saturno posto sotto la Ciambella XV, non <lb/>ce lo lascia vedere, ma la parte superiore rimane spiccata e rilevata, per <lb/>non essere coperta da ombra veruna, e per&ograve; deve rappresentarsi in forma <lb/>di cappello. </s>

<s>Sicch&egrave;, come vede V. A., quella esperienza, che mostrava per&shy;<lb/>turbare l'ipotesi dell'Hugenio, la favorisce mirabilmente &rdquo; (MSS. Cim., <lb/>T. XII, c. </s>

<s>56). </s></p><p type="main">

<s>Un'altra particolarit&agrave; fu osservata dagli Accademici del Cimento, ed era <lb/>che una delle anse, senza saper perch&egrave;, non s'andava ad attaccare perfet&shy;<lb/>tamente al disco di Saturno. </s>

<s>Allora il Borelli dimostr&ograve; che in quel punto, <lb/>in cui l'ansa stessa pareva rotta, andava a proiettarsi l'ombra oscura del <lb/>Pianeta. </s>

<s>&ldquo; Con gran mia meraviglia intesi l'osservazione di Saturno fatta <lb/>le sere passate da V. A. S. nella quale si vide che uno dei manichi che ab&shy;<lb/>braccian Saturno non si unisce perfettamente al disco luminoso dello stesso <lb/>Saturno, ma vi s'interpone un piccolo interstizio tenebroso. </s>

<s>Cercai subito <lb/>con gran curiosit&agrave; in qual sito cadesse la detta ombra, e fui assicurato, che <lb/>cadeva dalla parte superiore verso oriente. </s>

<s>Ora, perch&egrave; quest'esperienza ma&shy;<lb/>ravigliosamente confermerebbe l'ipotesi d'Ugenio, ho stimato bene inviarne <lb/>la dimostrazione a V. A. S., insieme con il pronostico delle variazioni, che <lb/>dovr&agrave; fare la detta ombra per i mesi seguenti &rdquo; (ivi, c. </s>

<s>57); dimostrazione <lb/>e pronostici che furono inseriti nel <emph type="italics"/>Parere<emph.end type="italics"/> pubblicato dal Targioni, dove si <lb/>leggono nel Tomo sopra citato a pag. </s>

<s>345, 46. </s></p><p type="main">

<s>Intanto che cos&igrave; nell'Accademia fiorentina si confermava e s'illustrava <lb/>tanto sapientemente il Sistema ugeniano, il padre Onorato Fabry in Roma <lb/>meditava le sue lepidezze. </s>

<s>Egli faceva dal suo cervello scaturire intorno a <lb/>Saturno quattro globi, due bianchi e due neri, che messi opportunamente <lb/>in gioco, col loro chiaro e con l'ombra, supplissero a rappresentar le fasi <lb/>stesse che rappresenta l'Anello. </s>

<s>Fu il nuovo Sistema pubblicato dallo stesso <lb/>Fabry sotto il nome di Eustachio Divini, col titolo di <emph type="italics"/>Brevis annotatio in<emph.end type="italics"/><pb xlink:href="020/01/1032.jpg" pagenum="475"/><emph type="italics"/>Systema saturnium Christiani Hugenii,<emph.end type="italics"/> e fu pure questa Annotazione in&shy;<lb/>titolata al principe Leopoldo. </s></p><p type="main">

<s>L'Huyghens che ai fatti, con laboriose vigilie osservati, si vide contrap&shy;<lb/>porre cos&igrave; strane chimere, ne rimase maravigliato e in una breve scrittura, <lb/>che indirizz&ograve; al medesimo principe di Toscana, col titolo di <emph type="italics"/>Brevis assertio <lb/>Systematis saturnii sui,<emph.end type="italics"/> disse che in somma a sentirsi parlar di que'globi, <lb/>che ora appariscon bianchi ora neri, gli pareva di trovarsi presente a un <lb/>gioco di bussolotti. </s>

<s>&ldquo; Videor mihi circolatorium quemdam calculorum lu&shy;<lb/>dum videre, alios ibi albos, alios nigros esse; nunc hos, nunc illos ostendi <lb/>abscondique vicissim &rdquo; (Op. </s>

<s>cit., pag. </s>

<s>633). </s></p><p type="main">

<s>Il principe Leopoldo, innanzi al quale i due dissenzienti avevano por&shy;<lb/>tato a decidere la questione, fece esaminare nell'Accademia il libro del Di&shy;<lb/>vini, che si lesse nell'adunanza del d&igrave; 17 Luglio 1660 (Targioni, Notizie ecc., <lb/>T. I, pag. </s>

<s>132), e il Borelli ne fece un estratto, riducendo a sommi capi i <lb/>luoghi, sopra i quali dovevano gli Accademici particolarmente rivolgere le <lb/>loro attenzioni, per profferirne poi i loro giudizi. </s>

<s>Nel d&igrave; 7 dell'Agosto se&shy;<lb/>guente, adunatasi di nuovo l'Accademia per sentir que'giudizi intorno al <lb/>decider del vero Sistema saturnio, tra quello che proponeva l'Huyghens, e <lb/>l'altro che il Fabry gli veniva contrapponendo, non par che leggessero se <lb/>non che il Borelli e il Dati. </s>

<s>La Scrittura del Borelli, gittata in bozza da <lb/>c. </s>

<s>99-107 del T. XII de'Manoscritti del Cimento, e poi ridotta in assai ni&shy;<lb/>tida copia da c. </s>

<s>15-20 del T. XXX, s'intitolava &ldquo; Annotazioni sopra l'Apo&shy;<lb/>logia di Eustachio Divini contro il Sistema saturnio del signor Cristiano <lb/>Ugenio. </s>

<s>&rdquo; </s></p><p type="main">

<s>Le risposte alle principali difficolt&agrave; promosse dal Fabry contro il Si&shy;<lb/>stema ugeniano son quelle che, prevenute gi&agrave; dall'Huyghens stesso, erano <lb/>state date nel sopra riferito <emph type="italics"/>Parere<emph.end type="italics"/> letto nell'Accademia dal Borelli, il quale <lb/>in queste Annotazioni ci torna sopra confermandole in altra maniera. </s>

<s>Come <lb/>argomento de'pi&ugrave; concludenti per&ograve; v'aggiunge l'esperienza, la quale se <lb/>aveva allora, in quel primo Discorso, mirabilmente approvata l'ipotesi del&shy;<lb/>l'Huyghens, veniva ora a riprovar la opposta del Fabry colla medesima evi&shy;<lb/>denza di fatto. </s></p><p type="main">

<s>&ldquo; Finalmente, conclude le sue parole il Borelli, secondo l'ordine di <lb/>V. A., si fabbric&ograve; una Macchina, che rappresentava il Sistema di Saturno <lb/>secondo le posizioni del p. </s>

<s>Fabri, e disposta in debita lontananza, adoprando <lb/>il lume di quattro torce, con Telescopi di varie grandezze e perfezioni, non <lb/>fu possibile rappresentare al vivo con essa, se non la prima e seconda figura <lb/>della Tavola di Eustachio, e di pi&ugrave; l'apparenza di Saturno solitario &rdquo; (MSS. <lb/>Cim., T. XXX, c. </s>

<s>18). </s></p><p type="main">

<s>L'altro Discorso del Dati fu inserito, da pag. </s>

<s>66-69, nel II Tomo delle <lb/>Lettere d'uomini illustri, dal Fabbroni, che l'attribu&igrave; per errore al Borelli; <lb/>discorso dove, pi&ugrave; dalla naturalezza del senno, che dalla profondit&agrave; della <lb/>scienza, si decide a favor dell'Hugenio. </s>

<s>Non &egrave; noto a noi se in quella adu&shy;<lb/>nanza accademica, dove il Borelli e il Dati lessero i loro discorsi, fosse in-<pb xlink:href="020/01/1033.jpg" pagenum="476"/>tervenuto anche il Viviani, il quale non par che prendesse in queste astro&shy;<lb/>nomiche controversie gran parte, e in ogni modo rimase indietro al Borelli <lb/>nell'attivit&agrave; e nel fervore. </s>

<s>Scriveva nonostante nel Settembre del 1660 al <lb/>principe Leopoldo, a Pisa, che al ritorno di S. A. avrebbe spiegato per mezzo <lb/>di figure un concetto sovvenutogli intorno all'apparir solitario di Saturuo <lb/>&ldquo; non so, diceva, se avvertito dall'Ugenio &rdquo; e concludeva cos&igrave; quella sua <lb/>lettera: &ldquo; Scrivo in fretta, per non essere appresso l'A. V. prevenuto dal <lb/>sig. </s>

<s>Borelli, al quale tengo per certo che sia per sovvenire l'istesso che <lb/>dir&ograve; all'A. V. e forse molto pi&ugrave; &rdquo; (MSS. Cim., T. XVII, c. </s>

<s>69). </s></p><p type="main">

<s>Fra que'concetti, che facevano a gara a proporre al principe i due ri&shy;<lb/>vali, n'era uno che tendeva a rispondere ad una difficolt&agrave; promossa dal Di&shy;<lb/>vini, il quale asseriva che, attraverso al vuoto lasciato tra l'anello e il globo <lb/>di Saturno, si sarebbe dovuto vedere il cielo del suo colore, e di quando in <lb/>quando trasparire le stelle. </s>

<s>Non essendosi queste mai potute vedere, sov&shy;<lb/>venne al Borelli e al Viviani che ci&ograve; dipendesse dall'esser troppo poveri di <lb/>esse stelle que'punti del cielo trasparenti attraverso all'Anello, ci&ograve; che non <lb/>sarebbe avvenuto quanto s'abbattesse Saturno a navigar per Galassia Le <lb/>ardite speranze le significava il principe Leopoldo all'Huyghens, nel ren&shy;<lb/>dergli conto delle osservazioni sul sistema di Saturno e delle scoperte fatte <lb/>ai mesi addietro nella sua Accademia. </s>

<s>&ldquo; E non meno curioso sar&agrave;, diceva, <lb/>l'osservare Saturno, quando si trover&agrave; in alcuno spazio della Via lattea, e <lb/>mi saria sommamente grato l'intendere se V. S. creda che, per quelli spazi <lb/>che appariscono esservi fra l'Anello e il Globo di Saturno, vi abbia a tra&shy;<lb/>sparire al nostro occhio alcuna delle infinite stelle di quella gran Via &rdquo; (Tar&shy;<lb/>gioni, Notizie cit., T. I, pag. </s>

<s>384). </s></p><p type="main">

<s>Qual si fosse la risposta che venne in tal proposito dall'Huyghens non <lb/>sapremmo dire precisamente, n&egrave; potremmo asserir se davvero avvenisse quel <lb/>che sperava Michelangiolo Ricci, che cio&egrave; dai discorsi degli Accademici fio&shy;<lb/>rentini &ldquo; potr&agrave; molto cavare il signor Ugenio per illustrare e difendere la <lb/>sua posizione &rdquo; (MSS. Cim., T. XVII, c. </s>

<s>92). In ogni modo, qualunque si <lb/>fosse l'animo dell'altero Olandese verso i Nostri, &egrave; un fatto che lo stabili&shy;<lb/>mento del Sistema saturnio fu principalmente opera di loro, n&egrave; si sarebbe <lb/>l'Olanda assicurata cos&igrave; presto della sua gloria, se non fosse venuta a fer&shy;<lb/>marle la corona in fronte, con tanto zelo, l'Italia. </s>

<s>Anzi da quella parte che <lb/>il Fabry moveva i suoi assalti, contro i quali n&egrave; l'Huyghens per s&egrave;, n&egrave; i <lb/>nostri Accademici in alleanza con lui non avevano sicura difesa, a confer&shy;<lb/>mare il sistema di Saturno, i nuovi aiuti vennero principalmente essi pure <lb/>d'Italia. </s></p><p type="main">

<s>Quell'attentato del Fabry, che pareva simile a una mina insidiosa atta <lb/>a sovvertire il Sistema ugeniano dalle sue fondamenta, si concludeva nel <lb/>breve giro delle seguenti parole: &ldquo; Turbinatio Saturni, vel illius annuli, <lb/>licet enim Sol hoc vertiginis motu agatur circa suum centrum, ut evinci&shy;<lb/>tur ex illius maculis, aliis tamen planetis nulla huiusmodi, vel alia quae&shy;<lb/>piam probatio suffragatur &rdquo; (In Op. </s>

<s>var. </s>

<s>Hug. </s>

<s>cit., pag. </s>

<s>615). </s></p><pb xlink:href="020/01/1034.jpg" pagenum="477"/><p type="main">

<s>Contro un tale attentato dicemmo non aver n&egrave; l'Huyghens n&egrave; i fau&shy;<lb/>tori di lui nessuna difesa, perch&egrave; la turbinazion di Saturno s'ammetteva <lb/>solo per induzione dietro quel principio formulato dal Torricelli, che cio&egrave;, <lb/>se intorno a un corpo, negli spazii celesti, girano altri corpi, si pu&ograve; tener <lb/>per certo che gira anch'esso. </s>

<s>Or perch&egrave; s'era trovato girare intorno a Sa&shy;<lb/>turno una Luna, si teneva per fermo che dovesse turbinare in s&egrave; stesso anche <lb/>il Pianeta, ma non se ne aveva ancora nessuna prova di fatto. </s>

<s>Anzi non <lb/>s'aveva prova di questo fatto (e in ci&ograve; si faceva forte il Fabry) in nessun <lb/>altro de'Pianeti che circondano il Sole, quando, come dicemmo, venne il <lb/>Cassini a dar la prima e pi&ugrave; evidente dimostrazione di ci&ograve; che dal Fabry <lb/>stesso mettevasi in dubbio, per le macchie apparenti sulla faccia di Giove. </s></p><p type="main">

<s>Confermavasi cos&igrave; mirabilmente dai fatti il teorema astratto del moto <lb/>vertiginoso di un corpo, che mena seco in volta altri corpi: teorema, il quale <lb/>com'aveva un'applicazione certa nel Sole, nella Terra e in Giove, non la&shy;<lb/>sciava nulla a dubitare nemmen rispetto a Saturno. </s>

<s>Ma il Cassini, proce&shy;<lb/>dendo nelle sue scoperte glorioso, dimostr&ograve; di pi&ugrave; che la turbinazion de'pia&shy;<lb/>neti in s&egrave; stessi era una loro propriet&agrave; generale, indipendentemente dal <lb/>principio meccanico professato gi&agrave; dal Keplero e promosso poi dal Torri&shy;<lb/>celli. </s>

<s>Conforme infatti a questo principio pareva che si dovesse negare o che <lb/>si dovesse almeno mettere in gran dubbio, se Marte, Venere e Mercurio, <lb/>intorno ai quali non si vedevano rivolgersi altri corpi, rimanessero in s&egrave; <lb/>stessi non convertibili e immoti. </s></p><p type="main">

<s>Fu per&ograve; quel dubbio, prima, rispetto a Marte, tolto via dal Cassini, il <lb/>quale, se applaudiva alle metafisiche congetture, che avevano cos&igrave; felicemente <lb/>divinato i turbinamenti di Saturno e di Giove, pensava in ogni modo che <lb/>l'Astronomia era scienza di osservazione. </s>

<s>Osservando dunque il moto di al&shy;<lb/>cune macchie sulla faccia di Marte, si assicur&ograve; che anch'egli si rivolgeva, <lb/>come Giove, in s&egrave; stesso, in un periodo di tempo diligentemente prestabilito. </s>

<s><lb/>Dava della scoperta cos&igrave; avviso al Viviani per lettera del d&igrave; 3 Aprile 1666 <lb/>da Bologna: &ldquo; Ho nuovamente ritrovata la rivoluzione di Marte intorno al <lb/>proprio asse, da alcune macchie apparentissime, che seco si raggirano, le <lb/>quali per&ograve;, essendo simili in varie e quasi opposte parti della superficie, e <lb/>difficilissime a distinguersi immediatamente le une dalle altre, poteano ca&shy;<lb/>gionare qualche confusione. </s>

<s>Ciascuna di esse ritorna da un d&igrave; all'altro <lb/>40 minuti pi&ugrave; tardi, e le seconde succedono alle prime otto ore dopo. </s>

<s>Ne <lb/>ho voluto dar questo saggio a V. S. che mi far&agrave; grazia di parteciparlo <lb/>a S. A. S. &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLV, c. </s>

<s>8). Dava poco di poi al pub&shy;<lb/>blico la importante notizia in una scrittura stampata in folio in quel mede&shy;<lb/>simo anno 1666 in Bologna col titolo: <emph type="italics"/>Martis circa proprium axem revo&shy;<lb/>lubilis, observationes bononienses,<emph.end type="italics"/> dove concludevasi che Marte si rivolge in <lb/>s&egrave; stesso in 24 ore e 39 minuti. </s></p><p type="main">

<s>Ricevuta il principe Leopoldo dal Viviani la notizia, e poco di poi dal&shy;<lb/>l'Autore stesso questo foglio, che pubblicamente la confermava, ne scrisse <lb/>in proposito all'Huyghens, il quale rispondeva cos&igrave; il d&igrave; 22 Giugno 1666 da <pb xlink:href="020/01/1035.jpg" pagenum="478"/>Parigi: &ldquo; Ho anche visto poi quel ch'&egrave; stato pubblicato dal Cassini e da <lb/>Eustachio Divini sopra il moto di Marte, ed ho trovato che il moto perio&shy;<lb/>dico stabilito dal Cassini &egrave; prossimamente il medesimo, che io stesso, la fin <lb/>del Settembre 1659, mosso dalle osservazioni, avevo congetturato che fosse <lb/>di quattro giorni, trovando io notato nel mio <emph type="italics"/>Libro de'ricordi<emph.end type="italics"/> che ogni re&shy;<lb/>voluzione del Pianeta si fa, presso a poco, in ore 24. La forma per&ograve; delle <lb/>macchie, delle quali io osservavo il ritorno, non appariva del tutto simile <lb/>alla forma di quelle, che furono osservate in Roma e in Bologna. </s>

<s>E in ve&shy;<lb/>rit&agrave;, perch&egrave; mi avvedevo che quelle forme non mi si rappresentavano ba&shy;<lb/>stantemente distinte, giudicai di non dover per allora pronunziare alcuna <lb/>cosa senza fondamento, ma d'aspettare fintanto che avessi Telescopi migliori. </s>

<s><lb/>E ora, non racconto a V. A. queste cose, perch&egrave; pretenda che mi sia dato <lb/>in questo fatto tantin di lode, ma perch&egrave; colla mia approvazione, qualunque <lb/>ella si sia, venga confermato il periodo determinato dal Cassini &rdquo; (MSS. <lb/>Cim., T. XVIII, c. </s>

<s>317). </s></p><p type="main">

<s>Anche il Divini, commemorato dall'Huyghens in principio di questo <lb/>passo di lettera, osserv&ograve; le macchie in Marte, e, avendone indi argomentato <lb/>alla rotazione, pretendeva o di aver prevenuto o di avere almeno concorso <lb/>col Cassini nella scoperta. </s>

<s>Il merito per&ograve; di Eustachio, che annunzi&ograve; il sem&shy;<lb/>plice fatto, non solo non &egrave; da paragonar col merito del Cassini, che ne de&shy;<lb/>fin&igrave; il periodo, ma, se per l'esattezza delle osservazioni &egrave; alquanto superiore, <lb/>rispetto al tempo &egrave; inferiore al Fontana, il quale gi&agrave;, in fin dal 1638, da <lb/>una <emph type="italics"/>pillola<emph.end type="italics"/> osservata sulla faccia di Marte, era venuto in sospetto della sua <lb/>girazione. </s>

<s>&ldquo; Martis pilula vel niger conus intuebatur distincte ad circuli ipsum <lb/>ambientis deliquium proportionaliter deficere, quod fortasse Martis gyratio&shy;<lb/>nem circa proprium centrum significat &rdquo; (Novae observat. </s>

<s>cit., pag. </s>

<s>106). </s></p><p type="main">

<s>La stessa cosa che in Marte s'immagin&ograve; il Fontana di avere osservato <lb/>in Venere, e perch&egrave; gli pareva che quelle pillole notassero sulla superfice <lb/>di lei, come i pesci nel mare, ne inferiva che non dovesse essa Venere ri&shy;<lb/>manere inchiodata nel cielo, ma che, sospesa nello spazio, si rivolgesse, pur <lb/>come Marte, intorno al suo centro. </s>

<s>&ldquo; Huiusmodi autem Veneris pilulae non <lb/>semper in eodem deprehenduntur situ, sed huc illucque, tanquam in mari <lb/>pisces, transmigrare, ex quo inferri potest eodem modo Venerem ipsam mo&shy;<lb/>veri, et non esse alicui coeli parti alligatam &rdquo; (ibi, pag. </s>

<s>91). </s></p><p type="main">

<s>Venne a questa fantasia, alquanti anni dopo, il Cassini a dar saldezza <lb/>di vero. </s>

<s>Invece che nelle pillole stravaganti ei ferm&ograve; l'attenzione sopra le <lb/>macchie apparenti, ma difficile era l'osservazione in un Pianeta, che cos&igrave; <lb/>breve sull'orizzonte, e cos&igrave; indistinta, per i vivi splendori, faceva la sua <lb/>comparsa. </s>

<s>I tentativi nonostante che fece, per riuscir nell'intento, e i resul&shy;<lb/>tati che n'ebbe, gli descrisse in una lettera al Petit, dove gli rendeva conto <lb/>di varii altri suoi studi. </s>

<s>Fu quella Lettera pubblicata nel <emph type="italics"/>Journal des Sa&shy;<lb/>vans<emph.end type="italics"/> del 1667, e in Amsterdam, nel 1676, se ne pubblic&ograve; in francese un <lb/>estratto concernente la scoperta della rotazione di Venere col titolo: <emph type="italics"/>Extrait <lb/>d'une Lettere de M. Cassini, professeur d'Astronomie dans l'Universit&eacute; de<emph.end type="italics"/><pb xlink:href="020/01/1036.jpg" pagenum="479"/><emph type="italics"/>Boulogne, a M. </s>

<s>Petit .... touchant la decouverte qu'il a faite du mou&shy;<lb/>vement de la Planete Venus &agrave; l'entour de son axe, du Juin 1667.<emph.end type="italics"/> Una <lb/>bella copia a mano della Lettera intera, che ha l'indirizzo <emph type="italics"/>Clarissimo doctis&shy;<lb/>simoque viro Petro Petit, Regis christianissimi Arcibus muniendis Prae&shy;<lb/>fecto, Jo. </s>

<s>Dominicus Cassinus S. P. D.<emph.end type="italics"/> ordin&ograve; che ne fosse fatta il prin&shy;<lb/>cipe Leopoldo, ed &egrave; quella che, inserita da c. </s>

<s>227-29 del T. XIII del Cimento, <lb/>da noi si tiene sott'occhio. </s></p><p type="main">

<s>La pi&ugrave; importante parte di storia che si contiene in questa Lettera cas&shy;<lb/>siniana, s&igrave; quanto alle difficolt&agrave; incontrate nell'osservazione, e s&igrave; quanto ai <lb/>resultati ottenuti da esse, concludesi dall'Autore nelle seguenti parole: <lb/>&ldquo; Tamque altius se attollente a terra Venere multo difficilior erat huiusmodi <lb/>apparentiarum observatio. </s>

<s>De his vero longe timidius iudicium fero, quam <lb/>de maculis Jovis et Martis. </s>

<s>Has quippe totam noctem, circa oppositiones cum <lb/>Sole, attente contemplari licebat, earumque motus aliquot horarum spatio <lb/>inspicere, atque ex regularibus restitutionibus decernere eaedemque ne an <lb/>diversae essent, quae obiicerentur maculae, earumdemque versari periodos. </s>

<s><lb/>At huiusmodi Veneris apparentiae tam brevi temporis spatio conspiciuntur, <lb/>ut minus tute de earumdem restitutione decernere liceat. </s>

<s>Eadem si semper <lb/>fuerit lucida Veneris particula, huius praesertim anni observationibus obvia, <lb/>suam seu revolutionem seu librationem absolvit spatio minore unius diei, <lb/>ita quidem ut, spatio horarum circiter 23, ad eumdem proxime in Venere <lb/>situm circa eamdem horam restitutam, quod tamen non sine aliqua pro&shy;<lb/>cedit irregularitate &rdquo; (c. </s>

<s>29). Conclude esser nonostante rimasto nell'incer&shy;<lb/>tezza, se quello era un moto seguente di circolazione, o se un'andata o un <lb/>ritorno di librazione, e il determinare in ogni modo il periodo di questo, <lb/>qualunque si fosse moto, lo teneva per difficilissimo. </s></p><p type="main">

<s>Il periodo della rotazione di Venere, prefinito cos&igrave; dal Cassini in 23 ore <lb/>in circa, veniva approvato dagli Astronomi, quando mons. </s>

<s>Francesco Bian&shy;<lb/>chini, ch'ebbe, per la munificenza del cardinale di Polignac, strumenti della <lb/>maggior perfezione, a cui fosse giunta l'arte di Giuseppe Campani, pub&shy;<lb/>blic&ograve;, nel 1728 in Roma, un'opera in folio, col titolo: <emph type="italics"/>Hesperi et Phosphori <lb/>phaenomena, sive observationem circa planetam Veneris.<emph.end type="italics"/> Non deve far me&shy;<lb/>raviglia, ivi dice l'Autore, una s&igrave; gran differenza che passa fra questo nuo&shy;<lb/>vamente assegnato e il periodo cassiniano &ldquo; neque enim definire poterat, ex <lb/>ordinata mutatione seu progressu macularum supra discum Veneris, num <lb/>intra horas 23 an potius intra dies 24 integra rotatio absolveretur, nisi obser&shy;<lb/>vandi Planetae copia talis daretur in eiusdem proximo accessu ad Terrae <lb/>globum, ut tribus horis solidis ante ortum, vel post occasum Solis, esset <lb/>supra horizzontem conspicuus. </s>

<s>Ad hoc demonstrandum accedimus in obser&shy;<lb/>vatis anni 1726, quibus deprehendimus, non horis 23, sed totis diebus 24 <lb/>unicam rotationem globi Veneris circa axem proprium compleri &rdquo; (pag. </s>

<s>60). </s></p><p type="main">

<s>Cos&igrave; il Bianchini, come il Cassini stesso, s'erano ingannati intorno al&shy;<lb/>l'apparenza di quelle macchie di Venere, ma pi&ugrave; notabilmente s'era ingan&shy;<lb/>nato il Bianchini, il quale si propose nel Cap. </s>

<s>IV di divisarle e d'imporre <pb xlink:href="020/01/1037.jpg" pagenum="480"/>a ciascuna il suo nome, com'aveva fatto il Riccioli per le macchie della <lb/>Luna. </s>

<s>&ldquo; Exhibetur Celidographia seu descriptio macularum, in globo Vene&shy;<lb/>ris observatarum, et illarum praecipuis partibus aptantur nomina &rdquo; (pag. </s>

<s>38). <lb/>Non fa perci&ograve; maraviglia se il periodo stabilito da lui in 24 giorni aberrasse <lb/>pi&ugrave; dal vero di quello delle 23 ore in circa, stabilito gi&agrave; dal Cassini. </s>

<s>Non <lb/>essendo in fatti in Venere macchie stabili, e distintamente riconoscibili nel <lb/>loro ritorno, conveniva attenersi ad altri segni, i quali si offersero comodi <lb/>in alcuni vertici delle pi&ugrave; alte montagne illuminati in mezzo alle valli om&shy;<lb/>brose, mentre che il Pianeta si mostra a noi falcato come la Luna. </s>

<s>Cos&igrave; ne <lb/>fu precisato il periodo della restituzione, che si trov&ograve; differir di pochi mi&shy;<lb/>nuti da quello del Cassini. </s></p><p type="main">

<s>Non rimaneva dunque al grande Astronomo nostro inesplorato altro che <lb/>Mercurio, in cui le difficolt&agrave; stesse incontrate in Venere si rendevano anche <lb/>maggiori. </s>

<s>Ma non vedendosi oramai ragione perch&egrave; il pianeta pi&ugrave; vicino al <lb/>Sole s'avesse ad appartare da tutti gli altri, se ne stabili senz'altro la re&shy;<lb/>gola generale che i Pianeti, o menino in volta o no altri corpi, si rivolgono <lb/>tutti in s&egrave; stessi, e cos&igrave; l'argomento d'analogia veniva ritorto a dimostrar <lb/>contro il Fabry esser ragionevolissima l'ipotesi ugeniana della rotazion di <lb/>Saturno. </s></p><p type="main">

<s>Vedemmo come i principii a questa ipotesi venissero dalla scoperta di <lb/>un nuovo Satellite intorno al Pianeta. </s>

<s>Or avendo il Cassini scoperto altri <lb/>satelliti, e avendo perci&ograve; ampliato il mondo saturnio, conferiva anche da que&shy;<lb/>sta parte efficacemente a confermarne il Sistema. </s>

<s>Verso la fine del mese di <lb/>Ottobre 1671, rivolto un Canocchiale del Campani di 17 piedi a Saturno, lo <lb/>trov&ograve; circondato da tre piccole stelle non pi&ugrave; vedute. </s>

<s>Le osservazioni, pro&shy;<lb/>seguite dal 25 di Ottobre al primo di Novembre, lo fecero accorto due di <lb/>tali stelle esser fisse e l'altra un Pianeta, com'appariva dal suo moto &ldquo; le <lb/>quel est tres-manifeste &agrave; l'&eacute;gard des etoiles fixes, mais moins sensible &agrave; <lb/>l'&eacute;gard de Saturne &rdquo; (D&eacute;couverte de deux nouv. </s>

<s>plan., Paris 1673, pag. </s>

<s>6) <lb/>Il centro di questo moto era manifestamente Saturno, e il nuovo Satellite <lb/>doveva senza dubbio essere esterno, facendo le sue massime digressioni tri&shy;<lb/>ple di quelle del Satellite ugeniano. </s></p><p type="main">

<s>Interrotte le osservazioni, non pot&egrave; il Cassini riprenderle che sulla fine <lb/>di Dicembre, quando s'incontr&ograve; in una nuova Stella, che veduta il d&igrave; 10 di <lb/>Gennaio 1673 ritornare alla medesima posizione rispetto a Saturno, riconobbe <lb/>facilmente per un pianeta. </s>

<s>Stette alquanto in dubbio se fosse quello il pia&shy;<lb/>neta medesimo dianzi scoperto, ma preso di maraviglia per alcune partico&shy;<lb/>larit&agrave; osservate, ebbe presto a riconoscerlo cos&igrave; per un satellite nuovo. </s></p><p type="main">

<s>&ldquo; Ce qui nous donna de l'admiration, fut d'avoir trouv&eacute; trois fois de <lb/>suite cette petite Etoile entre Saturne et le Satellite ordinaire, to&ugrave;jours en <lb/>distance presque &eacute;gale de l'un et de l'autre. </s>

<s>Mais nostre admiration cessa <lb/>a l&agrave; quatrieme observation, qui fut faite le 15 de Janvier, dans la quelle le <lb/>Satellite ordinaire estoit oriental, et le nouveau estoit occidental, comme il <lb/>avoit est&eacute; dans l'observation precedente, mais un peu plus proche de Sa-<pb xlink:href="020/01/1038.jpg" pagenum="481"/>turne. </s>

<s>Nous e&ugrave;mes ce soir-l&agrave; assez/de temps pour observer attentivement <lb/>cette Planete une heure de suite, pendant laquelle nous apperce&ugrave;mes qu'elle <lb/>s'approchoit de Saturne vers l'occident, et par consequent qu'elle estoit dans <lb/>la partie superieure de son cercle; ce qui nous confirma entierement dans <lb/>la supposition, &agrave; laquelle nous panchions, que c'estoit un Satellite interieur, <lb/>dont la revolution estoit plus vite que celle du Satellite ordinaire &rdquo; (pag. </s>

<s>10). </s></p><p type="main">

<s>Della <emph type="italics"/>D&eacute;couverte de deux nouvelles planetes autour de Saturne,<emph.end type="italics"/> stam&shy;<lb/>pata in folio e dedicata a Luigi di Francia, XIV nel numero de'Re, come <lb/>XIV era il Saturnio ultimamente scoperto nel numero de'Pianeti; ne furono <lb/>inviati alquanti esemplari a Firenze al cardinale Leopoldo accompagnati da <lb/>una lettera scritta dal Cassini stesso il d&igrave; 6 di maggio 1673 da Parigi (MSS. <lb/>Cim., T. XX, c. </s>

<s>117). </s></p><p type="main">

<s>Que'fiorentini, i quali non credevano che potesse aver veduti tanti <lb/>mondi lontani colui, che non valeva a leggere una lettera di carattere di&shy;<lb/>stintissimo senza gli occhiali, squadernando i fogli dispensati a loro dal prin&shy;<lb/>cipe della Sperimentale Accademia, v'ebbero poca fede, la quale non sa&shy;<lb/>premmo dire se si spengesse affatto, o se piuttosto si ravvivasse nel 1684, <lb/>quando il Cassini stesso torn&ograve; ad annunziar la scoperta d'altri due pi&ugrave; in&shy;<lb/>timi Satelliti saturnii. </s></p><p type="main">

<s>In ogni modo, non ne dubit&ograve; mai l'Huyghens, il quale anzi vaticinava <lb/>che si sarebbero scoperte altre Lune saturnie, oltre alla sua e alle quattro <lb/>cassiniane. </s>

<s>&ldquo; Imo praeter harum numerum alias quoque, vel unam vel plu&shy;<lb/>res latere suspicari licet, non deest ratio &rdquo; (Cosmot., Op. </s>

<s>var. </s>

<s>cit., pag. </s>

<s>698); <lb/>vaticinio che poi fu pienamente avverato. </s></p><p type="main">

<s>Non ne dubit&ograve; nemmeno quel sagace uomo e scevro da pregiudizii, che <lb/>fu il Viviani, il quale, in un capitolo del suo <emph type="italics"/>Discorso<emph.end type="italics"/> altre volte citato <emph type="italics"/>in&shy;<lb/>torno al Mondo,<emph.end type="italics"/> trattando delle apparenze di Saturno, dop'avere accennato <lb/>alla storia del Pianeta, infino alla grande scoperta di Cristiano Huyghens, <lb/>soggiunge che fu egli il primo &ldquo; ad osservare intorno a Saturno un Pia&shy;<lb/>neta che compisce il suo periodo in giorni 15, 22h, 40&prime;. </s>

<s>Altri quattro Pianeti <lb/>ne ha osservati il signor Cassini, primo Astronomo di S. M. Cristianissima, <lb/>che uno termina il suo giro in un giorno 21h, 18&prime;; il secondo in giorni 2, <lb/>17h, 3&prime;; il terzo in giorni 4, 13h, 47&prime;; il quarto in giorni 79, 7h, 53&prime; &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXLI, c. </s>

<s>278). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>La figura vera di Saturno e le varie apparenze di lei, felicemente ri&shy;<lb/>velatesi alla perspicacia dell'Hugenio, venivano insomma, per le ingegnose <lb/>esperienze degli Accademici del Cimento, ridotte a una dimostrazione di <lb/>fatto, e il Cassini aveva colle sue scoperte confermato da pi&ugrave; parti il prin&shy;<lb/>cipio, a cui s'informava quella dimostrazione. </s>

<s>Ma pure intorno a cose che <pb xlink:href="020/01/1039.jpg" pagenum="482"/>tanto uscivano fuori dell'ordinario venivano tentati di diffidenza anche gli <lb/>animi pi&ugrave; sinceri, e le menti pi&ugrave; sicure non potevano deliberarsi dai dub&shy;<lb/>bii. </s>

<s>Com'&egrave; possibile, domandavano, che un anello materiale e pesante si <lb/>regga in s&egrave; sempre cos&igrave; regolarmente in equilibrio e, senz'esservi allegato <lb/>da nulla, seguiti fedel compagno il suo pianeta? </s>

<s>L'Huyghens aveva gi&agrave; ri&shy;<lb/>sposto a questa difficolt&agrave; dicendo che si reggerebde pure, per consenso di <lb/>alcuni, una volta, e senza alcun sostegno, quando fosse possibile continuarla <lb/>per tutto l'ambito della Terra. </s>

<s>&ldquo; Plane sicuti quidam contemplati sunt, quod <lb/>si continuum fornicem per totum terrarum ambitum extrui possibile esset, <lb/>is, absque ullo fulcimento semetipsum esset sustentaturus &rdquo; (Syst. </s>

<s>Sat., Op. </s>

<s><lb/>varia cit., pag. </s>

<s>567). </s></p><p type="main">

<s>Pochissimi per&ograve;, quand'erano cos&igrave; ancora rannuvolate le idee della gra&shy;<lb/>vitazione dei corpi sui loro centri attrattivi, potevano comprendere la forza <lb/>di questo argomento, e dall'altra parte occorreva a fare sul Sistema satur&shy;<lb/>nio tante altre questioni, le quali, perch&egrave; forse erano dall'Huyghens stimate <lb/>pi&ugrave; curiose che importanti, ei lasci&ograve; a disputar liberamente agli Astronomi. </s>

<s><lb/>Nella Sperimentale Accademia fiorentina per&ograve;, affinch&egrave; il nuovo misterioso <lb/>mondo di Saturno, com'era stato dottamente illustrato per quel che riguarda <lb/>la parte fisica, cos&igrave; non mancasse della sua Filosofia speculativa, non si vol&shy;<lb/>lero lasciare indietro quelle questioni, e si trattarono anzi in modo, da fare <lb/>alla semplice curiosit&agrave; prender abito d'importanza. </s></p><p type="main">

<s>Fu il difficile argomento svolto in due discorsi diretti al serenissimo <lb/>Principe dell'Accademia, e ne furono autori due, tanto differenti in et&agrave;, <lb/>quanto nell'indole e nell'ingegno, il Magalotti e il Borelli. </s>

<s>Il Discorso del <lb/>primo non &egrave; altro in sostanza che un ingegnoso commento del Sistema ro&shy;<lb/>bervalliano, ma pur &egrave; tanto l'Autore infervorato del suo soggetto, che non <lb/>si ricorda pi&ugrave; delle censure fattegli pubblicamente dall'Hugenio. </s>

<s>Il Maga&shy;<lb/>lotti, che non aveva concetti suoi propri, sa vagamente adornare concetti al&shy;<lb/>trui, tirandoli con destrezza ingegnosa da varie parti al proposito di Saturno. <lb/></s>

<s>&Egrave; notabile fra questi concetti quello riferito da Galileo, che disperso negli <lb/>insegnamenti orali del gran Maestro ebbe salva la vita in questo stesso <lb/>Discorso. </s></p><p type="main">

<s>E qui sia lecito a noi studiosi d'intendere in tutta la sua integrit&agrave;, e <lb/>nel vero esser suo la mente di un uomo, intorno alla quale, quasi come a <lb/>cardine si volge la nostra Storia, fare una breve digressione per dire che <lb/>male si persuadono di provvedere a quella integrit&agrave; coloro, che vanno so&shy;<lb/>lamente a ricercarla ne'Manoscritti galileiani. </s>

<s>Idee, dimostrazioni e inven&shy;<lb/>zioni del loro Maestro rimangono in gran parte commemorate negli scritti <lb/>de'suoi numerosi e zelantissimi Discepoli, e chi le andasse qua e l&agrave; racco&shy;<lb/>gliendo con intelligenza ed amore, potrebbe a giusta ragion vantarsi di averci <lb/>date le opere di Galileo veramente complete. </s></p><p type="main">

<s>Di quelle idee intanto ne offre una delle pi&ugrave; elette il Magalotti nel suo <lb/>Discorso. </s>

<s>Da raccogliersi fra le dimostrazioni sarebbe quella della Cicloide, <lb/>distesa da Galileo in una lettera al Cavalieri; Lettera, che il padre Stefano An-<pb xlink:href="020/01/1040.jpg" pagenum="483"/>geli scrisse al Viviani di aver inutilmente cercata per Roma, ad istanza del <lb/>Dati (MSS. Cim., T. XVII, c. </s>

<s>176), che suppose esser capitata nelle mani <lb/>del Magiotti o del Ricci, il contenuto della quale, se non la dicitura, non <lb/>sarebbe difficile a ricomporre dietro i cenni fattine da coloro, che intesero <lb/>o lessero, intorno a quel soggetto geometrico, il pensiero galileiano. </s></p><p type="main">

<s>Da raccoglier poi fra le invenzioni sarebbe quella, di cui cos&igrave; parla il <lb/>Magiotti in una lettera al Torricelli: &ldquo; Ho caro la congiuntura del sig. </s>

<s>Vin&shy;<lb/>cenzio Viviani, dal quale desidererei il modo del sig. </s>

<s>Galileo di tirare in <lb/>prospettiva le superficie ed i corpi, per via di due corpi che s'interpongono. </s>

<s><lb/>Questa mi mostr&ograve; il sig. </s>

<s>Aggiunti, e so che molti in Firenze l'usano, ma <lb/>io non me ne ricordo, ed ho promesso ad un cavaliere amico mio di far&shy;<lb/>mela venire &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>71). </s></p><p type="main">

<s>Ma perch&egrave; dimostrazioni e invenzioni di questo genere son propriamente <lb/>aliene dal nostro Tema, ci sia permesso d'invitare i nostri lettori a com&shy;<lb/>prendere in uno sguardo di considerazione altre idee, altre dimostrazioni e <lb/>altre invenzioni appartenenti alle scienze sperimentali, da noi gi&agrave; notate, e <lb/>parecchie altre che si noteranno, da aggiunger com'eletta corona alle opere <lb/>stampate e manoscritte di Galileo. </s></p><p type="main">

<s>E per non indugiar di troppo ad aggiungere a quella corona il pro&shy;<lb/>messo fiore, e con ci&ograve; ritornare a Saturno, ecco la miglior parte del Di&shy;<lb/>scorso del Magalotti, trascritto da una copia, che si legge da c. </s>

<s>70-75 del <lb/>T. XXX del Cimento, nitida di carattere, ma scorretta in pi&ugrave; luoghi da noi <lb/>emendati, e con lacune da noi supplite col riscontro dell'autografo, inserito <lb/>da c. </s>

<s>80-84 del T. XII della medesima collezione. </s></p><p type="main">

<s>&ldquo; Serenissimo principe,...... applicandosi il Robervallio a costituirsi <lb/>l'idea di un ipotesi, con la quale salvar si potessero le stravaganti appa&shy;<lb/>renze, che in Saturno s'osservano; si va immaginando sollevarsi dalla zona <lb/>torrida di quel Pianeta in gran copia i vapori, i quali, per la loro grossezza <lb/>ed intensit&agrave;, divengano specchi potentissimi della riflessione solare, e s&igrave; la <lb/>diversit&agrave; degli aspetti derivarsi dalla difformit&agrave; di queste esalazioni, le quali, <lb/>se per ogni intorno vengono egualmente spirate, apparir&agrave; continuata l'el&shy;<lb/>lisse lucida; se solo da alcune parti, l'apparenza delle due Stelle compa&shy;<lb/>gne; e se finalmente manchi la pioggia ascendente di detti vapori, rimarr&agrave; <lb/>sferico e solitario il Pianeta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Era cos&igrave; facile e puro questo concetto, che a gran fatica credetti po&shy;<lb/>tersene trovar altro che l'agguagliasse, camminando anch'io con quella in&shy;<lb/>vecchiata credenza esser proprio alla Natura l'attenersi ai modi piu facili <lb/>nel suo operare. </s>

<s>Considerando nulladimeno quanto si avesse giustamente <lb/>usurpato la fede universale questo concetto, mi venne in mente un pen&shy;<lb/>siero nobilissimo del signor Galileo, pel quale rimasi certo regolarsi altri&shy;<lb/>menti nelle sue Opere la Natura, da quello che noi, col nostro corto vedere, <lb/>la ci figuriamo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; &Egrave; cos&igrave; facile, dice egli, la formazione di una sfera che, se in una pia&shy;<lb/>stra piana di metallo duro si caver&agrave; un vacuo circolare, dentro al quale si <pb xlink:href="020/01/1041.jpg" pagenum="484"/>vada rivolgendo casualmente qualsivoglia solido assai grossamente tondeg&shy;<lb/>giato, per s&egrave; stesso, senz'altro artifizio, si ridur&agrave; in figura sferica pi&ugrave; che <lb/>sia possibile perfetta, purch&egrave; quel tal solido non sia minore della sfera, che <lb/>passasse per quel cerchio. </s>

<s>E quel che v'&egrave; ancora di pi&ugrave; degno di conside&shy;<lb/>razione, &egrave; che dentro a quel medesimo incavo si formeranno sfere di di&shy;<lb/>verse grandezze. </s>

<s>Attendiamo ora a quel che vi voglia, per ridurre alla so&shy;<lb/>miglianza del vero un cavallo o una locusta, e ritroveremo che non v'har&agrave; <lb/>al mondo scultore cos&igrave; industrioso, che sia valevole a farlo. </s>

<s>Perch&egrave;, siccome <lb/>la grandezza, nel formar la sfera, deriva dalla sua assoluta semplicit&agrave; ed <lb/>uniformit&agrave;; cos&igrave; la somma irregolarit&agrave; rende difficilissimo l'introdurre altre <lb/>figure, e perci&ograve; anco la figura d'un sasso, rotto casualmente con un mar&shy;<lb/>tello o spiccato da un masso o arrotato in un letto di un fiume, sar&agrave; delle <lb/>difficili ad introdursi, essendo essa ancora irregolare, forse pi&ugrave; di quella del <lb/>cavallo. </s>

<s>Eppure &egrave; forza dire quella figura ch'egli ha, qualunque ella si sia, <lb/>averla cos&igrave; perfetta, che alcun altra s&igrave; puntualmente non le s'assesti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Infin qui col signor Galileo: ma applicando al mio proposito, se delle <lb/>figure irregolari, e perci&ograve; difficili a conseguirsi, pur se ne trovano infinite <lb/>in natura perfettissimamente ottenute, come in ogni sasso ci si rappresenta, <lb/>e delle perfette sferiche o niuna o radissime fra essi ne troveremo; con qual <lb/>ragione dovremo noi figurarcela cos&igrave; avara e infingarda, che tenga s&igrave; stretto <lb/>conto di risparmio a fatica nella fabbrica delle sue maraviglie pi&ugrave; rare, e <lb/>non dir piuttosto tutte le operazioni, bench&egrave; ammirabili, esserle egualmente <lb/>agevoli, n&egrave; regolarsi ella dalla bassezza di nostra forza, che ci finghiamo <lb/>difficile ad essa o insolita la costruzione di una Macchina, che troppo da'no&shy;<lb/>stri concetti s&igrave; lievi? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Fatto ardito da questa riflessione, mi sovvenne il principio, che at&shy;<lb/>tribuisce Renato Des-Cartes, nel cap. </s>

<s>IX delle sue <emph type="italics"/>Meteore,<emph.end type="italics"/> all'apparenza <lb/>di quegli Aloni, che intorno al Sole ed alle Stelle talvolta si coloriscono. </s>

<s><lb/>Dice egli essere sparse le regioni pi&ugrave; fredde della nostr'aria di alcuni va&shy;<lb/>pori addiacciati, a guisa di stelline minutissime, le quali, abbattendosi in <lb/>gran copia tra alcune Stelle e la nostra vista, di quelle, oltre alla piramide <lb/>diretta che viene a ferir l'occhio, molti eziandio di que'raggi, che per altri <lb/>dove si spargono, con le loro superficie rifrangono, e s&igrave; all'intorno di essa <lb/>dipingono l'apparenza di un Iride. </s>

<s>Checchessia della verit&agrave; di questo di&shy;<lb/>scorso, discorrer&ograve; cos&igrave;: &rdquo; </s></p><p type="main">

<s>&ldquo; Se intorno alla nostra Terra vegghiamo continuamente sollevarsi va&shy;<lb/>pori, e di quelli, arrivati ad una tal distanza, altri rammassarsi in acqua, <lb/>altri ripiovere in rugiade, altri in nevi e gragnole; non &egrave; egli molto pro&shy;<lb/>babile che l'ammosfera di Saturno, tanto pi&ugrave; lontana dal Sole, sia sempre <lb/>gravida di vapori grossissimi, anzi, che per l'eccessivo freddo a fatica sol&shy;<lb/>levati, non passino pe'gradi di rugiade, di piogge e di nevi, ma ben presto <lb/>si gelino in diaccioli minutissimi, quali sarebbero le stille delle nostre ru&shy;<lb/>giade, se s'addiacciassero? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E notisi che, quantunque esalino per ogni intorno del globo di Sa-<pb xlink:href="020/01/1042.jpg" pagenum="485"/>turno i vapori, non perci&ograve;, sollevati che e'sono, gli formeranno all'intorno <lb/>una perfetta sfera vaporosa, conciossiach&egrave;, intorno all'equinoziale ed alla zona <lb/>torrida, saran molto pi&ugrave; tenui che verso i poli, onde ascenderanno ad equi&shy;<lb/>librarsi pi&ugrave; in alto, che in altri paralleli, e si circonderanno il Pianeta, a <lb/>guisa d'uno sferoide prolato, rivolgendosi intorno ai suoi poli, cio&egrave; intorno <lb/>all'asse minore della loro ellisse. </s>

<s>Sar&agrave; dunque assai probabile che, dopo <lb/>inalzati ad una determinata altezza, finalmente, come dicemmo, si gelino, <lb/>ma quei che sono intorno all'equinoziale, come pi&ugrave; tenui, s'addiaccino in <lb/>stelline pi&ugrave; minute, onde agevolmente s'equilibrino, al contrario di quei pi&ugrave; <lb/>densi, addiacciati di qua e di l&agrave; dall'Equatore per notabile spazio verso i Poli, <lb/>i quali per la loro gravezza saranno pi&ugrave; facili a ricadere. </s>

<s>Sicch&egrave;, spiccandosi <lb/>di qua e di l&agrave; all'asse maggiore dello sferoide vaporoso due porzioni di esso, <lb/>rimane, per notabilissimo spazio, intorno all'Equatore, una zona di minu&shy;<lb/>tissime stelle di diaccio. </s>

<s>&rdquo; <lb/>&hellip; </s></p><p type="main">

<s>&ldquo; Proseguendo tuttavia il conceputo entusiasmo, mi sforzer&ograve; di mo&shy;<lb/>strare non esser tanto lontano dal poter congetturarsi, anche in altri Pia&shy;<lb/>neti, effetti somiglianti, bench&egrave; meno osservabili, a proporzione della maggior <lb/>vicinanza col Sole. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Scrive l'Ugenio, a c. </s>

<s>6 del suo libro del Nuovo sistema, aver egli <lb/>bene spesso osservato le fasce di Giove pi&ugrave; lucide del rimanente del suo <lb/>disco. </s>

<s>Asseriva in oltre d'averle vedute alterare nella loro forma, ed in di&shy;<lb/>versi tempi accostarsi e discostarsi fra loro per qualche tratto; ond'egli <lb/>molto probabilmente inferisce, e dalla riflession pi&ugrave; viva e dall'incostanza <lb/>di figura e di sito, esser materia assai simile alle nostre nuvole generate or <lb/>qua or l&agrave; dalla elevazion de'vapori, che or in questo or in quel clima si <lb/>condensino. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Anche di Marte riferisce una simile apparenza d'una fascia ombrosa, <lb/>che lo cinge, ma questa oscurit&agrave; dev'attendersi per esser forse quei vapori, <lb/>come pi&ugrave; vicini al Sole di quei di Saturno e di Giove, pi&ugrave; tenui, e perci&ograve; <lb/>di riflessione pi&ugrave; debole. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Dov'io noto l'aspetto di queste fasce mostrarsi sempre ai dintorni <lb/>dell'equinoziale, n&egrave; mai vagare in vicinanza dei poli. </s>

<s>Non potrebb'egli dun&shy;<lb/>que esser la cagione produttrice di tali maravigliose apparenze somigliante <lb/>a quella istessa, che resa pi&ugrave; valida, a quella proporzione dell'immensa lon&shy;<lb/>tananza dal Sole, le produce in Saturno s&igrave; facilmente osservabili? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ardir&ograve; di pi&ugrave;: chi sa che quel tratto di cielo, che intorno alla no&shy;<lb/>stra Terra, s&igrave; costantemente nuvoloso, cotanto affligge, con le sue vampe, <lb/>gli abitatori del nostro Equinoziale, e quelle nebbie s&igrave; folte, che dagli 85 <lb/>gradi di latitudine rendon s&igrave; fosca e caliginosa l'aria del polo, non ricono&shy;<lb/>scano una somigliante cagione, e si costituiscasi ne'Pianeti una scala, dir&ograve; <lb/>cos&igrave;, della densit&agrave; dei vapori, mostrandosi massima in Saturno, minore, ma <lb/>per&ograve; assai osservabile pi&ugrave; che in ogni altro in Giove, meno in Marte, mi&shy;<lb/>nima nella Terra, non essendo del certo cos&igrave; ferma e stabile quella striscia <pb xlink:href="020/01/1043.jpg" pagenum="486"/>di nuvole intorno all'Equinoziale, che talvolta, almeno per alcuni tratti, non <lb/>isparisca; e finalmente nulla in Venere ed in Mercurio, vagando quelli vi&shy;<lb/>cinissimi al Sole, sotto la pioggia profusissima de'suoi raggi? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Non &egrave; gi&agrave; ragionevole il dirsi che una luce cos&igrave; accesa, quale ci <lb/>manda la fascia di Saturno, e forse pi&ugrave; viva di quella del di lui disco, sia <lb/>una semplice refrazione, quale supponemmo i colori di quell'Iride cingente <lb/>le stelle, le quali, bench&egrave; a noi vicinissime, pur di colori assai slavati e lan&shy;<lb/>guidi si coloriscono. </s>

<s>Sar&agrave; dunque assai probabile illuminarsi la fascia col <lb/>riflettere, non col rifrangere i raggi solari, e se ad alcuno, per un riperco&shy;<lb/>timento s&igrave; vivo, non giudicasse bastevole la sostanza trasparente di quelle <lb/>stelle di diaccio, potrebbe dirsi che, siccome l'acqua per la sua fluidit&agrave; non <lb/>ubbidisce perfettamente al moto della nostra Terra, quando mai si movesse, <lb/>come nei flussi e reflussi &egrave; manifesto; cos&igrave; forse l'aria ambiente Saturno, <lb/>particolarmente intorno al suo equinoziale dove ha il movimento rapidissimo, <lb/>non obbedisce interamente al moto del suo Pianeta, e tanto men se s'ab&shy;<lb/>battessero intorno a quell'Equatore pianure e tratti grandi di mari, dove <lb/>liberamente vagasse, senza venir portata tra'seni di montagne altissime. </s>

<s>Ne <lb/>abbiamo <gap/> li ci&ograve; l'esempio in quel vento costante, che da oriente in occi&shy;<lb/>dente spira nei nostri mari, attribuito divinamente dal signor Galileo a que&shy;<lb/>sta cagione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Non sar&agrave; dunque maraviglia che quelle stelline di diaccio galleggianti <lb/>nell'aria, tanto quanto contumaci alla vertigine del Pianeta, anch'elleno, in <lb/>quei flussi e riflussi aerei, non essendo tenacemente fra loro collegate, per <lb/>essere di superficie tersissime, variamente urtandosi, ed insieme arrotandosi, <lb/>si stritolino, e si divengano atte alla riflessione del lume, come vegghiamo <lb/>accadere al diaccio, al cristallo, al vetro triti e pesti che, di trasparenti, <lb/>bianchissimi divengono, n&egrave; pi&ugrave; s'imbevono, anzi ribattono, con la molti&shy;<lb/>plicit&agrave; delle loro minime superficie, in larghissima copia, per ogni parte, <lb/>la luce. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cos&igrave; sarebbesi generata intorno all'equatore di Saturno una fascia <lb/>obbedientissima al moto circolare in s&egrave; stessa, ch'essendo la di lei super&shy;<lb/>fice interna, per quei stritolamenti, asprissima, avrebbe molti attacchi per <lb/>esser portata in giro dall'aria, che a lei contigua fa vortice intorno all'asse <lb/>della revoluzione dell'istesso Saturno. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il troppo ossequio alle dottrine di Galileo dette occasione a questa ul&shy;<lb/>tima congettura del Magalotti, la quale &egrave; una futilit&agrave; e un regresso nella <lb/>scienza comparata a quel che sapientemente aveva detto l'Huyghens del&shy;<lb/>l'anello gravitante al centro di Saturno, e partecipante al moto rotatorio di <lb/>lui, come ne partecipano, bench&egrave; non materialmente congiunti, i corpi gra&shy;<lb/>vitanti al centro della nostra Terra. </s>

<s>&ldquo; Porro, quum certo satis colligi posse <lb/>videatur, ob similitudinem ac cognationem magnam quae Saturno cum Tel&shy;<lb/>lure nostra intercedit, illum perinde ut haec in medio sui vorticis situm <lb/>esse, centrumque eius versus omnia natura sua tendere, quae illic gravia <lb/>habentur, inde necessario quoque efficitur, annulum istum omnibus sui par-<pb xlink:href="020/01/1044.jpg" pagenum="487"/>tibus aequali vi ad centrum nitentem, hoc ipso ita consistere ut undequa&shy;<lb/>que pari intervallo a centro absit &rdquo; (Syst. </s>

<s>Sat., Op. </s>

<s>cit., pag. </s>

<s>567). </s></p><p type="main">

<s>Ma il Boreili, nel suo Discorso, anche pi&ugrave; chiaramente dell'Huyghens, <lb/>dimostr&ograve; la causa del moto dell'Anello risiedere in una attrazion magnetica <lb/>di Saturno, non dissimile punto da quella, che Giove esercita su i suoi <lb/>quattro Pianeti. </s>

<s>Non cos&igrave; felice per&ograve; fu il Borelli stesso nel risolvere alcune <lb/>altre questioni concernenti la possibilit&agrave; e la persistenza dell'Anello, per di&shy;<lb/>pender cos&igrave; fatte questioni dalla qualit&agrave; della materia componente esso Anello, <lb/>intorno a che si credeva che non si potesse da ingegno umano formar pro&shy;<lb/>babile congettura. </s>

<s>Eppure le naturali osservazioni celesti, comparate con <lb/>quell'altre ingegnosamente propostesi nella Macchina artificiale, pareva che <lb/>avessero dovuto condurre a diritto il Borelli a congetturar la solidit&agrave; del&shy;<lb/>l'Anello, da quegli stessi indizii ch'ebbero dell'aspra superfice montagnosa <lb/>di lui Astronomi pi&ugrave; recenti. </s>

<s>Leggiamo infatti ci&ograve; ch'egli scrisse in quel suo <lb/><emph type="italics"/>Parere<emph.end type="italics"/> sul sistema ugeniano in proposito del rappresentarsi, per mezzo della <lb/>Macchina, Saturno solitario. </s></p><p type="main">

<s>&ldquo; Avvertir&ograve; bene una fallacia, della quale nel suo primo apparire fu <lb/>intesa la cagione e subitamente rimossa, col rastiare dal piano della Fascia <lb/>quelle scabrosit&agrave; di gesso lasciatevi a fine di renderla pi&ugrave; atta a ripercuo&shy;<lb/>tere per ogni banda il lume, poich&egrave;, per minime che esse si fossero, certo <lb/>&egrave; che a quella piccola Macchinetta avevano sempre proporzione s&igrave; fatta, <lb/>quale non hanno alla Terra montagne altissime, e s&igrave;, quantunque l'occhio <lb/>cadesse nel piano dell'Anello, le dette prominenze vi cadevano perpendico&shy;<lb/>lari, ed essendo illuminate rappresentavano fallacemente, con una linea lu&shy;<lb/>cida, la superfice esteriore convessa della Fascia, bench&egrave; sottilissima, illu&shy;<lb/>minata &ldquo; (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>742). </s></p><p type="main">

<s>Or essendo un fatto che nell'osservar Saturno s'erano gli Accademici <lb/>accorti, come dianzi accennava il Magalotti, apparir l'Anello pi&ugrave; vivamente <lb/>splendido dello stesso Globo saturnio da lui precinto; pareva facilissimo, pa&shy;<lb/>ragonando gli effetti dell'arte con quelli della Natura, a sovvenire il pen&shy;<lb/>siero che il pi&ugrave; vivo splendor dell'Anello naturale fosse dovuto a scabrosit&agrave; <lb/>montagnose, rappresentate da que'minuzzoli di gesso rimasti sull'anello ar&shy;<lb/>tificiale. </s>

<s>Ma fu impedimento alla facilit&agrave; di quel pensiero un concetto, che <lb/>il Borelli aveva letto e apprezzato nell'Hugenio, il quale, per ispiegare in <lb/>che modo si mantenesse l'anello oscuro e invisibile, bench&egrave; riguardasse il <lb/>Sole con tale obliquit&agrave;, da poter esserne alquanto illuminato; disse che <lb/>l'anello stesso doveva essere di superficie non aspra ma levigata. </s>

<s>&ldquo; Qua ta&shy;<lb/>men in re illud ante omnia statuere necesse est, superficiem Annuli non <lb/>esse asperam montibusque obsitam, veluti maxima ex parte Lunae nostrae <lb/>est superficies, sed aequalem planamque &rdquo; (Syst. </s>

<s>Sat., Op. </s>

<s>cit., pag. </s>

<s>583). </s></p><p type="main">

<s>Per conformarsi a un tal concetto il Borelli raschi&ograve; le asperit&agrave; del gesso <lb/>dalla sua Macchina, la quale, non rappresentando perci&ograve; pi&ugrave; il vero natu&shy;<lb/>rale, lo tenne in dubbio se la materia dell'anello fosse solida o fluida, sic&shy;<lb/>ch&egrave; stimando ugualmente probabile tanto l'una cosa quanto l'altra, and&ograve; <pb xlink:href="020/01/1045.jpg" pagenum="488"/>accomunando alle due varie ipotesi, con docilit&agrave;, le sue speculazioni. </s>

<s>Non <lb/>mancano certamente queste speculazioni di quell'ingegno, ch'era tutto pro&shy;<lb/>prio del Borelli, ed essendo in ogni modo primizie d'Astronomia fisica non <lb/>dispiacer&agrave; ai Lettori di vedersele presentare innanzi dall'Autore stesso nel <lb/>suo Discorso, che noi trascriviamo da una copia inserita da c. </s>

<s>66-69 del <lb/>T. XXX de'Manoscritti del Cimento; copia che fu riveduta dal Magalotti. </s></p><p type="main">

<s>&ldquo; Serenissimo Principe, cos&igrave; grande e tanto ammirabile &egrave; la ricchezza <lb/>della Natura, che con gran difficolt&agrave; e dubbiezza arriva l'intelletto umano <lb/>a comprenderne il magistero, ed a profferirne le cagioni. </s>

<s>Siccome adunque <lb/>non si dee chiamar temerario chi si mette a speculare sopra le opere di <lb/>essa pi&ugrave; ammirande, e per vie non battute tenta di salvare insolite e nuove <lb/>apparenze del cielo, da noi separate per s&igrave; gran tratto; cos&igrave; ancora non si <lb/>dee ascrivere a vilt&agrave;, n&egrave; a soverchio timore, se altri si protesta, in tanta <lb/>incertezza, di propor solo dubbiosamente il suo parere, senza mai asserire <lb/>cosa veruna. </s>

<s>Richiesto adunque della mia opinione circa la nuova posizione <lb/>di Saturno, prima di pronunziare quanto mi &egrave; passato per l'intelletto, ri&shy;<lb/>cordo alla discretezza di chi legge questa mia breve scrittura che, se ad al&shy;<lb/>cuno paressero troppo arditi e nuovi questi miei pensieri, nuovo e strano <lb/>&egrave; ancora il problema, di cui si tratta; e se ad altri troppo dubbioso e irre&shy;<lb/>soluto il mio parere, troppo alta ed oscura &egrave; similmente la verit&agrave;, che da <lb/>noi si ricerca. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Dico pertanto che l'ipotesi della Fascia o Ciambella sottile, la quale <lb/>circonda Saturno, staccata per&ograve; dalla superficie di quello, sodisfa, se non in <lb/>tutto, alla maggior parte delle apparenze. </s>

<s>Ma resta tuttavia da esaminare la <lb/>fisica possibilit&agrave; di tal posizione, cio&egrave; in primo luogo se l'esistenza e la ge&shy;<lb/>nerazione di detta Ciambella sia possibile o no. </s>

<s>Secondo, se possa durare <lb/>e conservarsi perpetuamente. </s>

<s>Terzo, se possa obedire e secondare il moto <lb/>di Saturno, mentr'egli scorre per l'etere fluido. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto al primo, pu&ograve; essere la sostanza di detta Ciambella, o di ma&shy;<lb/>teria dura e consistente, o fluida. </s>

<s>Se si volesse conceder dura, non vi scorgo <lb/>impossibilit&agrave;, n&egrave;, perch&egrave; questa &egrave; cosa senza esempio, adunque ne segue che <lb/>non si possa dare in natura, perch&egrave; del tesoro inesausto ed infinito della <lb/>Natura la maggior parte rimane a noi ignota, e per&ograve;, scoprendosi di mano <lb/>in mano qualcheduno degli effetti di essa, saranno la prima volta, senza <lb/>esempi, non conosciuti e non intesi i fini, ai quali la Natura gli adopera. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma chi volesse credere esser la sostanza di detta Ciambella fluida, <lb/>non so vedere che vi siano repugnanze in natura, che la rendano impos&shy;<lb/>sibile, perch&egrave; potrebbe ella generarsi da vapori eruttati da voragini, simili <lb/>ai nostri vulcani e mongibelli, i quali fussero collocati lungo l'equinoziale <lb/>di Saturno, n&egrave; &egrave; impossibile che somiglianti vapori, arrivati a quella tale <lb/>altezza dell'aria o etere ambiente Saturno, dove vengono ridotti all'equili&shy;<lb/>brio, si fermino senza passar pi&ugrave; oltre, e posto che attorno a Saturno non <lb/>vi spirino venti, il che anche non &egrave; impossibile, non ci &egrave; ragione perch&egrave; <lb/>debbano uscir dal piano dell'Equinoziale. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/1046.jpg" pagenum="489"/><p type="main">

<s>&ldquo; Di pi&ugrave;, perch&egrave; &egrave; assai probabile, non che possibile, che Saturno si <lb/>rivolga intorno al proprio asse, che &egrave; parallelo all'asse del Mondo e del no&shy;<lb/>stro Equinoziale, e che tal vertigine sia partecipata dai corpi aderenti al <lb/>medesimo sistema, dentro al quale verr&agrave; ad essere inclusa la detta Ciam&shy;<lb/>bella vaporosa; potr&agrave; in ogni modo, come fluida, non effettivamente secon&shy;<lb/>dare la vertigine di Saturno, e cos&igrave; verranno a riempirsi li spazi della sua <lb/>latitudine, onde venga a perfezionarsi ed a contornarsi la superfice piana <lb/>della detta Ciambella. </s>

<s>Oltre a ci&ograve;, perch&egrave; i detti vapori, nella densit&agrave; e gra&shy;<lb/>vit&agrave;, non sono similari, possono i meno gravi equilibrarsi pi&ugrave; di un diame&shy;<lb/>tro lontani da Saturno, ed i pi&ugrave; gravi &egrave; possibile che si equilibrino con <lb/>l'ambiente fluido poco pi&ugrave; di un semidiametro lontani dallo stesso Sa&shy;<lb/>turno. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Con maggior facilit&agrave; potrebbe generarsi la detta Ciambella fluida, <lb/>senz'avere a condurre tutta la materia vaporosa, che compone la detta Ciam&shy;<lb/>bella, dallo stesso corpo di Saturno in tanta lontananza. </s>

<s>Trovansi non pochi <lb/>fluidi, che dalla mistura di poche gocciole d'altro liquore si trasformano, da <lb/>trasparente in opaco, e per il contrario, d'opaco ch'egli era, divien traspa&shy;<lb/>rente, il che frequentemente d'osserva in tutte l'acque forti ripiene di me&shy;<lb/>talli e minerali da esser corrosi, quali poche gocciole d'olio di tartaro o <lb/>d'altra cosa simile tolgono loro la trasparenza, e le fanno divenire opache, <lb/>niente manco di un marmo. </s>

<s>Anzi questo medesimo effetto nell'orina lo fa <lb/>la semplice freddezza, che di trasparente la fa divenire opaca, e per il con&shy;<lb/>trario il calore la rischiara. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Supposto questo, se la regione aerea ambiente Saturno fusse d'una <lb/>tal natura analoga all'acqua stillata in piombo, o alle acque forti incorpo&shy;<lb/>rate d'argento, e se lungo l'Equinoziale saturnino svaporassero pochissimi <lb/>fumi analoghi a quelle poche gocce d'olio di tartaro, facilissimamente si po&shy;<lb/>trebbe intorbidare attorno a Saturno. </s>

<s>E perch&egrave;, come s'&egrave; detto, si pu&ograve; sup&shy;<lb/>porre quella regione non soggetta all'agitazione de'venti, rimane il detto <lb/>Anello nello stesso sito. </s>

<s>Ne &egrave; maraviglia che, lungo l'Equinoziale saturnino, <lb/>si vomitine de'vapori, e non d'altrove, conforme non da tutte le parti del&shy;<lb/>l'animale e della Terra svaporano, ed escono alcuni determinati vapori e <lb/>liquori. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Secondo, circa la perseveranza e durazione di detta Ciambella, quando <lb/>ella si supponga solida e dura, non ha difficolt&agrave; che possa considerarsi come <lb/>gli altri corpi mondani. </s>

<s>Ma se ella non &egrave; dura, potr&agrave; in ogni modo conti&shy;<lb/>nuarsi, quando il pabulo continuamente gli venga somministrato, come la <lb/>regione vaporosa e crepuscolina della nostra Terra dura sempre, perch&egrave; suc&shy;<lb/>cessivamente si rimette quel che si consuma. </s>

<s>Ma chi ne volesse un effetto <lb/>somigliantissimo nella nostra Terra, consideri la zona fredda, compresa dal <lb/>Cerchio artico, l'aria sovrastante nella quale &egrave; quasi sempre ingombrata <lb/>da'vapori acquei, i quali per lungo tratto sono gi&agrave; agghiacciati in forma di <lb/>neve, che per il suo poco peso, con gran lentezza movendosi allo in gi&ugrave;, ma <lb/>la medesima avvicinandosi a terra si dissolve, e di nuovo riducesi in forma <pb xlink:href="020/01/1047.jpg" pagenum="490"/>fluida acquea, ma per tutto lo spazio superiore, nel quale si manteneva in <lb/>forma di neve, era bianchissima, e per&ograve;, efficacemente riflettendo il lume <lb/>ripercosso, dovrebbe, a chi da lontano riguardasse tal regione trasversal&shy;<lb/>mente, rappresentare come un anello opaco e bianchissimo attorno quella <lb/>Terra settentrionale, staccato dalla superficie terrestre. </s>

<s>E perch&egrave; somigliante <lb/>generazione di vapori e di nevi, in quella regione, &egrave; perpetua, per rimet&shy;<lb/>tersi successivamente quello che va perdendosi; adunque non &egrave; impossibile <lb/>che attorno Saturno si mantenga una somigliante generazione, conservata da <lb/>un successivo pabulo, che dal corpo di Saturno le venga somministrato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Non v'&egrave; pericolo che la figura di detta Ciambella possa variamente <lb/>figurarsi, perch&egrave; si suppone tutta la regione fluida attorno a Saturno, per <lb/>grande spazio, aver naturale inclinazione d'accostarsi, gravare e mantenersi <lb/>aderente a Saturno, ed anche si suppone che in tal regione non vi siano <lb/>venti, ma sia sommamente tranquilla. </s>

<s>Adunque, cessando la cagione d'in&shy;<lb/>torbidamento e variazion di figura, e perseverando la gravit&agrave; naturale a man&shy;<lb/>tenere tutta la detta regione unita ed aderente a Saturno, non potr&agrave; in niuna <lb/>maniera la figura di detta Ciambella alterarsi o mutar sito. </s>

<s>Un effetto so&shy;<lb/>migliante osservasi in una boccia di vetro, nella quale l'acqua, il vino ed <lb/>altri liquori si mantengon separati, anzi striscie di varii colori, nella stessa <lb/>acqua, perseverano nello stesso sito, positura e figura, tutta volta che l'acqua <lb/>si mantenga tranquilla, e non punto agitata da onde o da altri interni mo&shy;<lb/>vimenti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Restaci l'ultimo punto da considerare: in che maniera, girando Sa&shy;<lb/>turno per l'etere fluido, la sua Ciambella non resti indietro o si ripieghi <lb/>od acquisti altra figura, come succede alla fiamma di una torcia velocemente <lb/>girata, la quale lascia una coda, come la Cometa, e finalmente si dissipa. </s>

<s>E <lb/>qui &egrave; da considerare che la fiamma della torcia commossa pu&ograve; essere ac&shy;<lb/>compagnata mai sempre da una medesima porzione di aria, ed in questo <lb/>caso non pu&ograve; n&egrave; piegarsi n&egrave; smorzarsi, come si vede in quei lumi, che son <lb/>chiusi dentro una lanterna, ma allora solamente pu&ograve; ripiegarsi e spengersi, <lb/>quando la medesima fiamma incontra ed urta nell'aria immobile. </s>

<s>Ora, se la <lb/>regione che circonda Saturno fosse pi&ugrave; alta della Ciambella, com'&egrave; credi&shy;<lb/>bile, per essere annessa a Saturno, in virt&ugrave; della sua gravit&agrave; o forza ma&shy;<lb/>gnetica o d'altra cagione somigliante, che tenacemente la mantenesse ade&shy;<lb/>rente a Saturno, sicch&egrave; tutto insieme venisse a formarsi un sistema; verrebbe <lb/>la detta Ciambella di Saturno ad esser coperta e difesa dagli urti dell'etere <lb/>immobile, ed in conseguenza non potrebbe n&egrave; piegarsi n&egrave; dissiparsi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma che occorre cercare altre ragioni consimili? </s>

<s>Non bast'egli veder <lb/>sensatamente che la Natura opera nel cielo effetti somigliantissimi, anzi me&shy;<lb/>desimi appunto? </s>

<s>Giove si rivolge pur nell'etere fluido, n&egrave; i suoi quattro <lb/>pianeti Medicei che lo circondano hanno punto di difficolt&agrave; a secondare il <lb/>suo moto, e mai occorre che restino indietro, per gli urti e impedimenti <lb/>dell'etere immobile. </s>

<s>Venere e Mercurio &egrave; pur vero che non mai abbando&shy;<lb/>nano il Sole, n&egrave; la Stella nuovamente scoperta in Saturno rimane addietro. <pb xlink:href="020/01/1048.jpg" pagenum="491"/>Adunque, se noi concederemo una somigliante virt&ugrave;, potr&agrave; con la medesima <lb/>facilit&agrave; girar con Saturno stabilmente la sua Ciambella. </s>

<s>E per&ograve;, se la virt&ugrave; <lb/>che rapisce seco le Medicee risiede in Giove, diremo parimente che la forza, <lb/>che trasporta la Ciambella di Saturno, risieda nel medesimo Pianeta, e chi <lb/>stimasse ch'ella fosse propria de'Pianetini medicei, o cosa analoga a gra&shy;<lb/>vit&agrave; o virt&ugrave; magnetica, lo stesso appunto si pu&ograve; dire della Ciambella satur&shy;<lb/>nina, sicch&egrave; sar&agrave; lecito a lei, non meno che ai Pianeti gioviali, essere tra&shy;<lb/>sportata insieme con Saturno. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Questo basti per ora, in cosa tanto nuova ed incerta, con ferma spe&shy;<lb/>ranza che il tempo e le future osservazioni sieno per somministrarci pi&ugrave; <lb/>evidenti, e pi&ugrave; solidi discorsi. </s>

<s>&rdquo; </s></p><p type="main">

<s>Di tutto ci&ograve; che s'era letto nell'Accademia, a proposito di Saturno, fu <lb/>spedito copia in Olanda all'Huyghens, e non si manc&ograve; di fargli recapitare <lb/>anche questi due Discorsi, i quali pure furono mandati a Roma a Miche&shy;<lb/>langiolo Ricci. </s>

<s>Il Magalotti, nella qualit&agrave; sua di segretario, accompagnava il <lb/>plico con una lettera, nella quale incomincia a ringraziare esso Ricci di aver <lb/>liberato l'Accademia dal fastidio del Fabry, fecondo sempre di nuovi e stra&shy;<lb/>vaganti discorsi per accomodar Saturno al suo sistema. </s>

<s>Poi, entra pi&ugrave; par&shy;<lb/>ticolarmente delle due Scritture sopra la possibilit&agrave; della costituzione fisica <lb/>dell'anello, qualificando le idee ivi espresse, e dandole &ldquo; come voli permessi <lb/>a due intelletti annoiati oramai di rigirarsi, per si lungo tempo, tra gli an&shy;<lb/>gusti limiti di calcoli e di figure. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il primo, immediatamente il Magalotti soggiunge, &egrave; del Borelli. </s>

<s>Quanto <lb/>al secondo sono cos&igrave; interessato nella reputazione dell'Autore, che non do&shy;<lb/>vrei farle, come suol dirsi, il nome. </s>

<s>Ma ella se l'&egrave; gi&agrave; immaginato, e avr&agrave; <lb/>ripresa a quest'ora la mia temerit&agrave;. </s>

<s>Che vuol ch'io le dica? </s>

<s>Questo &egrave;, si&shy;<lb/>gnor Michelangiolo, quel vantaggio deplorabile, che serve a consolarmi bene <lb/>spesso nelle frequenti meditazioni della mia da me ben conosciuta ignoranza; <lb/>l'essermi lecito il profferire ogni mio concetto; libert&agrave; da non usurparsi da <lb/>coloro, i quali dal proprio sapere vengono costituiti debitori a s&egrave; medesimi, <lb/>anzi all'opinione del mondo, della propria fama. </s>

<s>Qual pregiudizio adunque <lb/>dovr&ograve; io temere dal paragone formidabile dei pensieri del signor Borelli, <lb/>se egli, in venticinque anni confirmati in letture pubbliche, con applauso <lb/>universale delle pi&ugrave; celebri Universit&agrave; d'Italia; conta ben tre anni di pro&shy;<lb/>fessione pi&ugrave; di quel che io mi conti di vita? </s>

<s>&rdquo; (Lettere famil., T. II, Fi&shy;<lb/>renze, 1769, pag. </s>

<s>2, 3). </s></p><p type="main">

<s>E nonostante, non par che avrebbe temuto il Magalotti di venire a con&shy;<lb/>fronto col gran Borelli, non solo privatamente ne'giudizii degli Accademici, <lb/>dell'Huyghens e del Ricci, ma pubblicamente nel giudizio universale degli <lb/>scienziati, essendo suo manifesto desiderio &ldquo; di mettere in sicuro tutto quello <lb/>che l'anno 1660 si specul&ograve;, e si oper&ograve; nell'Accademia intorno a Saturno, <lb/>essendoci accorti che insensibilmente, quando uno e quando un altro, va <lb/>facendosi bello della maggior parte delle nostre cose &rdquo; (Targioni, Notizie cit, <lb/>T. I, pag. </s>

<s>385). </s></p><pb xlink:href="020/01/1049.jpg" pagenum="492"/><p type="main">

<s>Fra questi usurpatori intendeva il Magalotti di comprender principal&shy;<lb/>mente Giuseppe Campani, il quale, nel suo <emph type="italics"/>Ragguaglio di due nuove Os&shy;<lb/>servazioni,<emph.end type="italics"/> parl&ograve;, come di sua propria invenzione, di una &ldquo; Macchinuccia <lb/>che a somiglianza del celeste Saturno composi, egli dice, d'un globo bianco <lb/>cinto d'un cerchio piano, della stessa materia, che con l'aiuto d'un fil di <lb/>ferro, che gli fa diametro e passa pel centro del Globo, pu&ograve; abbassarsi ed <lb/>elevarsi, sempre segando il globo per mezzo, perocch&egrave;, locato questo Stru&shy;<lb/>mento in opportuna distanza e abbastanza illuminato, osservandosi con un <lb/>piccol Canocchiale,.... rappresenta mirabilmente l'apparenza del vero Sa&shy;<lb/>turno &rdquo; (Roma 1664, pag. </s>

<s>19, 20). </s></p><p type="main">

<s>Il Borelli simul&ograve; una certa noncuranza dell'usurpazione, contentandosi <lb/>di richiamarsene appresso il principe Leepoldo, a cui Michelangiolo Ricci, <lb/>ch'era stato messo di mezzo in questo negozio, rispondeva da Roma: &ldquo; Fi&shy;<lb/>nalmente, dell'invenzione da mostrare Saturno con quel Cerchio intorno, <lb/>credo di potere indurre il Campani, in altra scrittura, che ne additi il vero <lb/>e primiero Autore &rdquo; (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>748). </s></p><p type="main">

<s>Quella simulazione poi, in un uomo dell'indole del Borelli, veniva con&shy;<lb/>sigliata dal timor che aveva di non trovarsi implicato in una question col <lb/>Cassini, il quale era dello strumento del Campani anima e vita, e spirito <lb/>che parlava per quella lingua. </s>

<s>Rivelasi un tal sentimento da queste parole, <lb/>che il Borelli stesso scriveva al principle della fiorentina Accademia: &ldquo; Rendo <lb/>umilissime grazie a V. A. del foglio delle figure del Campani, nelle quali <lb/>veggo chiaramente che egli vi aggiunge qualche cosa di pi&ugrave; di quello, che <lb/>veramente ha potuto vedere in Saturno, imperocch&egrave; &egrave; impossibile che si <lb/>allarghi tanto quell'ombra, che egli mostra nel disegno quarto delle sue <lb/>figure, il che facilmente si pu&ograve; dimostrare, ma questa sorta di genti, che <lb/>hanno pi&ugrave; caro l'adulazione che i sinceri avvertimenti, &egrave; bene lasciarli stare &rdquo; <lb/>(MSS. Cim., T. XVIII, c. </s>

<s>92). </s></p><p type="main">

<s>Or, ritornando al proposito di mettere al sicuro le scoperte fatte nel&shy;<lb/>l'Accademia, ne fu distolto il Magalotti dallo stesso Borelli, il quale preten&shy;<lb/>deva che tutto ci&ograve;, che fu operato e speculato intorno a Saturno, fosse opera <lb/>sua, e perci&ograve; voleva che andasse fuori particolarmente sotto il suo nome, <lb/>pensando forse fin d'allora di raccogliere anche queste speculazioni astro&shy;<lb/>nomiche fra le cose geometriche e filosofiche, in varii tempi speculate, e <lb/>delle quali intendeva di comporre un nuovo libro (ivi, T. XX, c. </s>

<s>49). Ma <lb/>perch&egrave; il nuovo libro, qualunque poi se ne fosse la ragione, non fu com&shy;<lb/>posto, l'opera saturnia fatta nell'Accademia fu posta al sicuro, come si por&shy;<lb/>rebbe al sicuro un tesoro, nascondendolo sotto terra, che n&egrave; arricchisce i <lb/>rapaci usurpatori, n&egrave; fruttifica ai legittimi eredi. </s></p><pb xlink:href="020/01/1050.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO XIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle Stelle fisse e delle Comete<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Del luogo e del moto, della sostanza e della generaziono delle Stelle nuove nel cie&igrave;o. </s>

<s>&mdash; II. </s>

<s>Delle <lb/>osservazioni telescopiche delle Stelle fisse; della scintillazione, e della loro parallasse. </s>

<s>&mdash; <lb/>III. </s>

<s>Delle varie ipotesi intorno alla natura e all'essere delle Comete. </s>

<s>&mdash; IV. </s>

<s>Della teoria pla&shy;<lb/>netaria delle Comete. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Saturno ingemmato dell'Anello, come sposo ch'esca fuor del suo ta&shy;<lb/>lamo, Giove seduto sulla maest&agrave; del suo trono, con le quattro elette e fedeli <lb/>scorte all'intorno, s'appresentavano a que'primi fortunati osservatori tranquil&shy;<lb/>lamente veleggiar per i sereni eterni, come per le placide acque di un oceano <lb/>immenso, che mandi scintille vive dal suo seno profondo. </s>

<s>Il Canocchiale of&shy;<lb/>friva uno spettacolo nuovo e maraviglioso: que'punti lucidi apparivano assai <lb/>pi&ugrave; spessi che all'occhio nudo, e impiccoliti raggiavan pi&ugrave; fieri, com'acqua <lb/>che per le angustiate vie pi&ugrave; forte e chiara zampilli, o come pupilla, che <lb/>pi&ugrave; ristrinta guardando, pi&ugrave; sorride amorosa. </s>

<s>La gioia ineffabile di cos&igrave; fatto <lb/>spettacolo spira dalle pagine del Messaggero celeste di Galileo, se non che la <lb/>severit&agrave; del Filosofo la tempera alquanto, e l'essere state le stelle ampio e <lb/>fecondo oggetto di contemplazioni alla vista nuda degli Astronomi la mino&shy;<lb/>rava, come a chi assiste all'inaspettato splendor delle seconde scene in una <lb/>festa gi&agrave; cominciata. </s></p><p type="main">

<s>Dir come cominciasse quella, a cui si dette dall'artificioso linguaggio <lb/>degli Astronomi il nome proprio e particolare di Astroscopia, non si saprebbe <lb/>far cos&igrave; in fretta, e non sarebbe dall'altra parte conforme col nostro isti-<pb xlink:href="020/01/1051.jpg" pagenum="494"/>tuto, ma non possiamo noi Italiani, esaltati al canto dell'Alighieri, non tor&shy;<lb/>nare indietro con la memoria a que'tempi, quando il Divino cantor dei tre <lb/>Regni, rappresentandosi alla fantasia nuove inesplorate terre e nuovi mari, <lb/>vedeva nelle loro acque specchiarsi quattro risplendentissime stelle non viste <lb/>mai fuor che alla prima gente. </s></p><p type="main">

<s>Un altro fiorentino, Amerigo Vespucci, fece poi corporalmente quel viag&shy;<lb/>gio, che aveva fatto in spirito l'Alighieri, e osservando da Astronomo le <lb/>fiammelle, di che pareva godere il polo meridionale &ldquo; mi ricordai, cos&igrave; scrive <lb/>in una lettera a Lorenzo di Pier Francesco de'Medici, d'un detto del no&shy;<lb/>stro Dante, del quale fa menzione nel primo Capitolo del <emph type="italics"/>Purgatorio,<emph.end type="italics"/> quando <lb/>finge di salire di questo emisfero e trovarsi nell'altro, che volendo descri&shy;<lb/>vere il Polo antartico dice: <emph type="italics"/>Io mi volsi a man destra e posi mente ecc.<emph.end type="italics"/> che <lb/>secondo me mi pare che il Poeta in questi versi voglia descrivere per le <lb/>quattro stelle il Polo dell'altro firmamento, e non mi diffido fino a qui che <lb/>quello che dice non valga la verit&agrave;, perch&egrave; io notai quattro stelle, figurate <lb/>come una mandorla, che tenevano poco movimento &rdquo; (Bandini, Vita e let&shy;<lb/>tere, Firenze 1745, pag. </s>

<s>70). </s></p><p type="main">

<s>Che se aveva Dante compassionato al nostro emisfero, per esser vedovo <lb/>di cos&igrave; splendide luci, soggiunge il Vespucci che avrebbe il settentrionale da <lb/>invidiar ben altre nuove bellezze al cielo meridionale &ldquo; vaghissimamente <lb/>adorno di alcune stelle che non sono da noi conosciute, delle quali io asse&shy;<lb/>gnatamente ne ho tenuto memoria, e annoveraine forse venti di tanta chia&shy;<lb/>rezza, di quanta sono appresso di noi le stelle di Venere e di Giove. </s>

<s>Con&shy;<lb/>siderai anche il loro circuito, e i varii movimenti, e misurai la lor circon&shy;<lb/>ferenza e diametro assai facilmente, avendo io notizia della Geometria &rdquo; (ivi, <lb/>pag. </s>

<s>113). Trov&ograve;, facendo uso de'suoi strumenti ch'erano il Quadrante e <lb/>l'Astrolabio, non esser tra le nuove scoperte stella &ldquo; che tenessi men che <lb/>dieci gradi di movimento all'intorno del firmamento, di modo che non re&shy;<lb/>stai sodisfatto di me medesimo di nominar nessuna, essendo il polo del Me&shy;<lb/>ridione, a causa del gran circolo che facevano intorno al firmamento &rdquo; (ivi, <lb/>pag. </s>

<s>70). </s></p><p type="main">

<s>Le osservazioni astronomiche sopra le stelle, e sopra le costellazioni del <lb/>cielo meridionale dice Amerigo stesso di averle diligentemente descritte, e <lb/>rappresentate in figure nel suo libro delle <emph type="italics"/>Quattro giornate;<emph.end type="italics"/> libro ch'ei <lb/>commemora nelle sue lettere pi&ugrave; volte e in modo, da accendere in noi vi&shy;<lb/>vissimo desiderio di s&egrave;, bench&egrave; senza speranza oramai che venga sodisfatto. </s></p><p type="main">

<s>Quel nonostante, che raccogliesi dalle sue lettere e da altre sue scrit&shy;<lb/>ture rimaste, basta a noi Italiani perch&egrave; possiamo qualificare il Vespucci <lb/>come l'alba che, sotto il ciel di Firenze, precede al sole di Galileo, il quale <lb/>inizi&ograve; col disputar delle stelle quella scienza, che l'avrebbe poi fatto coro&shy;<lb/>nare di tanta gloria. </s></p><p type="main">

<s>Aveva appresso gli stranieri Galileo senza dubbio precursori pi&ugrave; imme&shy;<lb/>diati di quel che non fosse il Vespucci, e Ticone, a capo di una numerosa <lb/>schiera di astronomi, era tra que'precursori de'pi&ugrave; celebri e de'pi&ugrave; dili-<pb xlink:href="020/01/1052.jpg" pagenum="495"/>gentemente operosi. </s>

<s>Ebbe a mostrar particolarmente la sua operosit&agrave; nelle <lb/>svariate osservazioni fatte all'Uraniburgo, e la sua diligenza all'occasione che <lb/>si vide apparire in cielo, sui principii del Novembre 1572, una stella nuova. </s>

<s><lb/>Determinata la posizione di lei, s&igrave; quanto alla longitudine e alla latitudine, <lb/>come quanto alla declinazione e all'ascensione retta, la trov&ograve; immobile ri&shy;<lb/>spetto alle altre stelle fisse, e senz'alcuna sensibile parallasse. </s>

<s>Confermatosi <lb/>ci&ograve; dagli altri astronomi, pi&ugrave; esercitati ne'calcoli e nelle osservazioni, ve&shy;<lb/>niva a concludersi che la nuova apparita si doveva sublimar su fino alla <lb/>v&ograve;lta stellata, e senza dubbio molto al di l&agrave; della sfera di Saturno. </s></p><p type="main">

<s>Singolar cosa che a una tal conclusione, tanto contraria alla fede in&shy;<lb/>valsa della incorruttibilit&agrave; de'cieli, non si riscntissero i Peripatetici, almeno <lb/>con quell'ardore come fecero, specialmente in Italia, 32 anni dopo, quando <lb/>apparve il di 10 Ottobre del 1604 un'altra stella nuova. </s>

<s>Galileo, professore <lb/>allora nello studio di Padova, fece alla scolaresca, o meglio al pubblico con&shy;<lb/>venutovi numerosissimo, tre Lezioni su quel soggetto, per rinsavire colla <lb/>ragione la popolare frenetica fantasia. </s>

<s>Il principio della prima fra quelle Le&shy;<lb/>zioni, a cui Galileo stesso accenn&ograve; nella <emph type="italics"/>Difesa contro il Capra<emph.end type="italics"/> (Alb. </s>

<s>XI, 363), <lb/>fu pubblicato nella II Parte delle <emph type="italics"/>Memorie ecc.<emph.end type="italics"/> dal Venturi (Modena 1821, <lb/>pag. </s>

<s>331, 32), e si rileva da questo come il Trattato galileiano fosse distinto <lb/>in due parti: nella prima matematica, dove si dimostrava il luogo e il moto <lb/>della Stella nuova, e nell'altra fisica, dove si congetturava l'origine acciden&shy;<lb/>tale di lei, l'essere e la sostanza. </s>

<s>&ldquo; Quod mei muneris praecipuum est af&shy;<lb/>feram quidquid de motu et loco demonstrative constabit; quid autem ad <lb/>substantiae indagationem horum accidentium conferunt praecognitio,.... nostis <lb/>omnes &rdquo; quanto sia difficile di quaggi&ugrave; aver notizia degli avvenimenti celesti. </s></p><p type="main">

<s>Per quel che riguarda la prima parte dimostrativa non fece altro Ga&shy;<lb/>lileo che applicare a questa stella il metodo usato gi&agrave; da Ticone e dal <lb/>Moestlin, per assicurarsi della immobilit&agrave; e deficienza di parallasse della <lb/>stella del 1572; metodo che Galileo stesso rammemora al Capra, il quale lo <lb/>aveva dimenticato, bench&egrave; celebrasse la scrittura moestliniana sopra la detta <lb/>stella &ldquo; il cui sito, immobilit&agrave; e carenzia di parallasse con altro egli non os&shy;<lb/>serv&ograve; che con un filo, trovandola sempre in linea retta con due coppie di <lb/>stelle fisse &rdquo; (Alb. </s>

<s>XI, 368). Ora avend&ograve; anche il nostro professore di Pa&shy;<lb/>dova osservato mantenersi la Nuova apparita sempre in linea retta con la <lb/>prima stella delle tre nella coda dell'Orsa maggiore, e con la Lucida della <lb/>Corona (ivi, pag. </s>

<s>369 e V, 395) ne concluse dover quella apparenza venirci <lb/>da una regione superiore alla elementare. </s></p><p type="main">

<s>Questo del &ldquo; dimostrare il sito della Nuova stella essere e esser som&shy;<lb/>pre stato molto superiore all'orbe lunare &rdquo; fu, dice Galileo, &ldquo; il principale <lb/>scopo delle mie lezioni &ldquo; (Alb. </s>

<s>VI, 26), ond'&egrave; che la parte fisica, concer&shy;<lb/>nente l'origine e la sostanza di quel fatto straordinario, fu toccata appena <lb/>per le difficolt&agrave; e per l'incertezza, innanzi a cui s'arretrava prudentemente <lb/>la scienza. </s>

<s>Gli era a principio venuto in mente che si potessero tali appa&shy;<lb/>rizioni ed occultazioni salvar &ldquo; per via di epicicli o di qualsivogliano movi-<pb xlink:href="020/01/1053.jpg" pagenum="496"/>menti circolari &rdquo; (ivi, II, 301), ma trovato di fatto esser la stella immobile, <lb/>Galileo ebbe a rinunziare a questo primo pensiero, rivolgendosi ad alcun <lb/>altro che non riusci per&ograve; a sodisfarlo. </s></p><p type="main">

<s>Intanto i Peripatetici fedeli al loro domma insorsero, non propriamente <lb/>contro Galileo, ma contro Ticone, contro il Moestlin, contro tutti gli Astro&shy;<lb/>nomi, che avevano colle loro osservazioni e coi calcoli insegnato a Galileo <lb/>stesso la via e il modo di dimostrar che la Stella nuova s'era ingenerata <lb/>negli incorruttibili spazi celesti. </s>

<s>Fu de'primi fra costoro Antonio Lorenzini, <lb/>il quale, facendo quel conto delle matematiche dimostrazioni che delle fisi&shy;<lb/>che ipotesi, volle provar che le osservazioni di Ticone e degli altri Astro&shy;<lb/>nomi erano fallacie, e i loro calcoli sbagli, ma che corretti gli uni e le altre <lb/>com'egli vuole, concludevano evidentemente il luogo della Stella nuova dover <lb/>essere sullunare. </s></p><p type="main">

<s>Altri Peripatetici per&ograve; pi&ugrave; prudenti, mettendo da parte la Matematica, <lb/>la quale non lascia all'ingegno i suoi liberi voli, si riducevano ne'campi <lb/>della Fisica, pi&ugrave; facilmente trattabili per s&egrave; stessi, e gi&agrave; preparati, nel libro <lb/>degli Omocentrici del Fracastoro, a questo nuovo genere di cultura. </s>

<s>Dice <lb/>l'Autore, nel Cap. </s>

<s>VIII della Sezione II, che egli, oltre all'aria e al vapore <lb/>acqueo riconosce un altro mezzo, attraverso a cui passano le apparenze degli <lb/>astri; mezzo che consiste nella maggiore o minor densit&agrave; delle varie parti <lb/>del cielo. </s>

<s>&ldquo; Ergo, ne conclude da questa ipotesi il Fracastoro, quod eiusmodi <lb/>novumque appareant stellae, causa interdum non in aere sed in coeli par&shy;<lb/>tibus quod modo crassiores, modo tenuiores quibusdam stellis subiiciuntur &rdquo; <lb/>(Op. </s>

<s>omnia, Venetiis 1584, c. </s>

<s>13). </s></p><p type="main">

<s>Applicarono questa ipotesi fracastoriana al caso della Nuova apparita <lb/>nel 1604 Lodovico Delle Colombe e Giovanni Heckio, ma Raffaello Gualtie&shy;<lb/>rotti suppose che alcuni vapori esalati dalla Terra si fossero sublimati nelle <lb/>regioni celesti, e che ivi illuminati dal Sole mostrassero per riflesso a noi <lb/>quella luce in somiglianza di stella. </s></p><p type="main">

<s>Or chi il crederebbe? </s>

<s>A Galileo, che non aveva ancora saputo trovare <lb/>ipotesi che lo sodisfacesse, piacque questo pensiero del Gualtierotti, e si pose <lb/>dietro a cercare argomenti che lo rendessero pi&ugrave; probabile e a rispondere <lb/>alle obiezioni. </s>

<s>Di questo solitario lavor&igrave;o di mente s'hanno le vestigia im&shy;<lb/>presse ne'Manoscritti galileiani, i quali raccolti per le carte disperse spec&shy;<lb/>chian pure in qualche modo il pensiero, come pu&ograve; specchiarsi l'immagine <lb/>di una fiammella ne'frantumi accozzati di un cristallo. </s></p><p type="main">

<s>Si trovano cotesti frammenti in parte scritti da c. </s>

<s>10-13 del T. II, P. III, <lb/>in parte da c. </s>

<s>12-15 del T. VI, P. IV. L'Alb&egrave;ri, che ne pubblic&ograve; qualche <lb/>cosa, e coloro che ci vengono ora ripetendo ci&ograve; che fu detto e fatto da lui, <lb/>danno quelle note di Galileo come brani o come appunti presi per servir&shy;<lb/>sene a distendere le tre Lezioni sopra la stella nuova. </s>

<s>Ma &egrave; facile provar <lb/>che debbono essere quelle note posteriori al 1604, accennandovisi a un'os&shy;<lb/>servazione fatta <emph type="italics"/>die 3 Febraurii 1605<emph.end type="italics"/> (MSS. Gal., P. III, T. II, c. </s>

<s>10), e ci&shy;<lb/>tandovisi il trattato <emph type="italics"/>De stella nova<emph.end type="italics"/> del Keplero (ivi, c. </s>

<s>11) stampa'o nel 1606. <pb xlink:href="020/01/1054.jpg" pagenum="497"/>Dall'altra parte, se fossero stati veramente svolti, al modo che suol Galileo, <lb/>i pensieri accennati in quegli appunti, non sarebbe stato pi&ugrave; vero che il <lb/>principale intento delle tre Lezioni fosse stato quello solo di dimostrar dove <lb/>avesse il luogo, o se si movesse la Stella. </s></p><p type="main">

<s>Con queste note insomma non intendeva Galileo di far altro, che di rac&shy;<lb/>cogliere argomenti da provar la probabilit&agrave; dell'ipotesi del Gualtierotti, la <lb/>quale veniva cos&igrave; in certo modo a far sua, e come tale poi l'avrebbe di&shy;<lb/>stesa in un Discorso, di cui questa era la trama: s'incominciava ad esami&shy;<lb/>nare, per rifiutarle, tutte quelle ipotesi, che parevano meno probabili, delle <lb/>quali per&ograve; non si trovano nel Manoscritto notate che queste due: &ldquo; Quod <lb/>Stella nova non sit pars Lactei circuli patet quia non dissolveretur, sicut <lb/>ipse Circulus non dissolvitur, adversus Ticonem &rdquo; (MSS. Gal., P. III, T. II, <lb/>c. </s>

<s>13). &ldquo; Stella nova non fuisse incendium patet ex eo quod quae citissime <lb/>incendunt brevi quoque extinguntur &rdquo; (Alb. </s>

<s>V, 395). Si concludeva questa <lb/>prima parte del Discorso colle parole: &ldquo; Et haec fere sunt quae meo iudi&shy;<lb/>cio non sunt &rdquo; (ivi, pag. </s>

<s>393). </s></p><p type="main">

<s>&ldquo; Restat modo (cos&igrave; doveva cominciarsi la seconda parte) ut quod tan&shy;<lb/>dem de hac admiranda apparitione sentiam in medium afferam &rdquo; (ivi) e dopo <lb/>essersi scusato se, per la difficolt&agrave;, non fossero i lettori rimasti sodisfatti <lb/>della sua opinione, passava ad annunziarla con queste parole: &ldquo; Quod circa <lb/>Terram eleventur vapores qui ascendentes Solis lumen reflectant, saepissime <lb/>apparet &rdquo; (ivi) e ne adduce gli esempi de'crepuscoli e delle Aurore boreali, <lb/>e avrebbe poi voluto aggiungervi l'esempio di quel cerchio che talvolta ap&shy;<lb/>parisce intorno alla Luna e ch'&egrave; dovuto al lume riflesso dai vapori conden&shy;<lb/>sati (ivi, pag. </s>

<s>334). A rifletter poi il lume del Sole e a dar l'apparenza di <lb/>stella, doveva dimostrarsi che bastava qualunque condensazione anche pi&ugrave; <lb/>leggiera, e si potea desumer l'argomento della dimostrazion dalle nuvole <lb/>&ldquo; quae veluti vastissimi montes in aere pendentes a Sole supra Lunam et <lb/>stellas omnes illuminantur, ita ut condensatio longe minor posset supra stel&shy;<lb/>las illuminari &rdquo; (ivi). </s></p><p type="main">

<s>Esposta cos&igrave; l'ipotesi e dimostratane la probabilit&agrave; con questi e con altri <lb/>argomenti, che sarebbero via via sovvenuti, si doveva nella III Parte del <lb/>Discorso rispondere alle obiezioni, e prima di tutto persuader coloro, i quali <lb/>falsamente credevano non poter la luce venir riflessa che da qualche soli&shy;<lb/>dissimo corpo (ivi, pag. </s>

<s>395). </s></p><p type="main">

<s>Agli altri che domandavano come potesse la Terra somministrar tanta <lb/>smisurata mole di esalazioni, quanta ne sarebbe stata necessaria a comporre <lb/>la Stella nuova, doveva rispondersi non aver ci&ograve; nulla dell'impossibile &ldquo; vi&shy;<lb/>demus enim aerem serenissimum, dicto citius expleri nubibus, et ex viridi <lb/>ligno exposito ad ignem, nulla sensibili eius facta diminutione, ingens fieri <lb/>in fumum evaporatio &rdquo; (ivi). </s></p><p type="main">

<s>A chi poi fosse curioso di saper come mai, evaporando sempre la Terra, <lb/>non si sieno nonostante vedute mai apparir le stelle circa e vicino a lei, <lb/>pensava di rispondere in questa maniera: &ldquo; Alcuni fuochi, che da lontano ap-<pb xlink:href="020/01/1055.jpg" pagenum="498"/>pariscono splendentissimi, da vicino non si veggono niente per la loro te&shy;<lb/>nuit&agrave;. </s>

<s>Cos&igrave; la Stella nuova pu&ograve; essere una esalazione illuminata, e chi vi <lb/>fosse vicino non la vedrebbe, e apparirebbe solo come i vapori elevati e illu&shy;<lb/>minati la notte &rdquo; (ivi). </s></p><p type="main">

<s>Il discorso sopra l'origine e l'essere della Stella nuova, che doveva in&shy;<lb/>tessersi da Galileo con questo ordito, fu lasciato da parte e non riman di <lb/>lui altro che queste fila. </s>

<s>Si potrebbe credere che ripensandoci meglio avesse <lb/>riconosciuta la mostruosit&agrave; dell'ipotesi del Gualtierotti, il quale facendo della <lb/>Stella uno strano composto di celeste e di terreno non poteva andare a ge&shy;<lb/>nio n&egrave; ai seguaci di Aristotile, n&egrave; a quelli del Gilberto, meravigliati che il <lb/>professor di Padova non sentisse come prima e principale difficolt&agrave; contro <lb/>l'ipotesi da lui favorita fosse quella dell'essere affatto impossibile che una <lb/>materia terrea estravaghi cos&igrave; dalla sua sfera attrattiva. </s></p><p type="main">

<s>&Egrave; un fatto per&ograve; che Galileo non pens&ograve; mai a queste sfere attrattive, <lb/>nemmen quando l'ipotesi della Stella nuova venne solennemente nel <emph type="italics"/>Sag&shy;<lb/>giatore<emph.end type="italics"/> ad applicarla alla Cometa, e non sentendo perci&ograve; le difficolt&agrave;, che <lb/>gli si movevano contro dalla nuova scienza magnetica, lasci&ograve; di dare alle note <lb/>scritte forma di discorso, perch&egrave; era persuaso di avere incontrato in altra <lb/>diversa opinione &ldquo; che non abbia evidenti contradizioni e che perci&ograve; possa <lb/>esser vera &rdquo; (Alb. </s>

<s>VI, 27). </s></p><p type="main">

<s>La curiosit&agrave; ci fruga e la importanza della cosa c'invita a ricercar qual <lb/>fosse questo sentimento di Galileo circa la sostanza e generazione della Stella <lb/>nuova, per assicurarsi del qual sentimento soggiunge nel luogo sopra citato <lb/>&ldquo; mi &egrave; bisognato aspettare il ritorno di essa Stella in oriente, dopo la se&shy;<lb/>parazione dal Sole, e di nuovo osservare con gran diligenza quali mutazioni <lb/>abbia fatto, s&igrave; nel sito, come nella visibile grandezza e qualit&agrave; del lume. </s>

<s>E <lb/>continuando la speculazione sopra questa maraviglia, sono finalmente venuto <lb/>in credenza di poterne sapere qualche cosa di pi&ugrave; di quello, in che la sem&shy;<lb/>plice coniettura finisce. </s>

<s>E perch&egrave; questa mia fantasia si tira dietro o piut&shy;<lb/>tosto si mette avanti grandissime conseguenze e conclusioni, per&ograve; ho riso&shy;<lb/>luto di mutar le Lezioni in una parte di Discorso, che intorno a questa <lb/>materia vo distendendo &rdquo; (ivi). </s></p><p type="main">

<s>Or qui nasce una nuova curiosit&agrave; di sapere se quel Discorso fu vera&shy;<lb/>mente disteso, e qual sia e dove si trovi. </s>

<s>Noi, che interpetriamo nel signi&shy;<lb/>ficato di <emph type="italics"/>Dialogo<emph.end type="italics"/> quella parola <emph type="italics"/>Discorso,<emph.end type="italics"/> ritroviam questa <emph type="italics"/>parte di Dialogo<emph.end type="italics"/><lb/>autografa da c. </s>

<s>4-13 del T. II, P. IV de'Manoscritti galileiani, e da c. </s>

<s>14-23 <lb/>del T. II, P. III troviam quegli appunti e quelle note, che sempre era so&shy;<lb/>lito di preparar Galileo, prima di dar mano a distendere qualche scrittura. </s>

<s><lb/>Che tali appunti si riferiscano a questo soggetto se ne persuade facilmente <lb/>chiunque legge cos&igrave; a c. </s>

<s>23: &ldquo; Nota delle osservazioni fatte dai 13 Astro&shy;<lb/>nomi, dove sono notate le altezze polari e le altezze della Stella nuova, tanto <lb/>le minime quanto le massime, prese nel meridiano. </s>

<s>&rdquo; E chiunque attende a <lb/>quest'altra nota, non dubita che non sieno scritte per dialogizzarsene il con&shy;<lb/>cetto queste parole, che di Dialogo presentano gi&agrave; scolpitissime le forme: <pb xlink:href="020/01/1056.jpg" pagenum="499"/>&ldquo; Notabili belli: tutte le prove, che rendono le stelle sopra le fisse, sono <lb/>emendabili, non &egrave; vero? </s>

<s>&mdash; S&igrave;. </s>

<s>&mdash; E le emendazioni le hanno a ritirare in <lb/>gi&ugrave;, non &egrave; vero? </s>

<s>&mdash; S&igrave;. </s>

<s>&mdash; Ma nel ritornare in gi&ugrave; prima hanno a passar <lb/>per le fisse e poi per i Pianeti, avanti che vengano agli elementi.... &rdquo; <lb/>(ivi, c. </s>

<s>15 v.). </s></p><p type="main">

<s>Quel Dialogo dunque incomincia cos&igrave; nel Manoscritto sopra citato: <emph type="italics"/>&ldquo; Sa&shy;<lb/>gredo.<emph.end type="italics"/> Ma che ci dice il signor Salviati in proposito delle Stelle nuove, son <lb/>elleno veramente state trasportate di cielo in queste pi&ugrave; basse regioni, in <lb/>virt&ugrave; de'calcoli dell'Autore prodotto dal signor Simplicio? </s>

<s>&rdquo; E termina con <lb/>quest'altre parole poste pure in bocca allo stesso Sagredo: &ldquo; E perch&egrave; mi <lb/>pare che assai chiaramente si sia dimostrata la differenza grande, che &egrave; tra <lb/>i motivi di quelli Astronomi e di questi loro oppugnatori, sar&agrave; bene che la&shy;<lb/>sciata questa parte torniamo alla nostra principal materia. </s>

<s>&rdquo; </s></p><p type="main">

<s>Chiunque getti lo sguardo sopra questa Scrittura, non esita a ricono&shy;<lb/>scerla per una parte de'Dialoghi dei due Massimi Sistemi, dove fu vera&shy;<lb/>mente inserita nella III Giornata, da pag. </s>

<s>302-48 della edizione dell'Alb&egrave;ri. </s>

<s><lb/>N&egrave; il saperne l'origine storica &egrave; da reputar di lieve importanza, prima perch&egrave; <lb/>ci si rende cos&igrave; la ragione come mai del Manoscritto degli stessi Due mas&shy;<lb/>simi sistemi sien rimaste queste sole nove carte in anticipazione e separate <lb/>dal rimanente; poi, perch&egrave; di qui s'argomenta che Galileo aveva infin da <lb/>quel tempo, non solo pensato a scrivere il suo libro sul Sistema del mondo, <lb/>ma che ne avea gi&agrave; scelti i personaggi interlocutori del Dialogo, a cui aveva <lb/>divisata la forma e l'andamento. </s></p><p type="main">

<s>Essendo cos&igrave;, non s'intende come non si sieno dati o non si diano final&shy;<lb/>mente pace coloro, che rimpiangono la iattura delle tre Lezioni, avendo in&shy;<lb/>teso dalla bocca dello stesso Galileo ch'ei volle mutarle in un Discorso, da <lb/>lui poi inserito in un'Opera, che non ha temuto fin qui n&egrave; temer&agrave; pericolo <lb/>di smarrimento o di morte. </s>

<s>Vero &egrave; che in quella parte di Discorso, scritto <lb/>propriamente contro il Lorenzini, e col solo intento di dimostrar che non <lb/>erano sbagliati i calcoli e le osservazioni, per le quali veniva il luogo della <lb/>Stella nuova a costituirsi nelle regioni stellari; non si legge nulla che ri&shy;<lb/>guardi la generazione e la sostanza di essa stella, ma non &egrave; di questa iat&shy;<lb/>tura da sentirne dolore, avendo Galileo provveduto alla sua gloria, prima, col <lb/>lasciare informe nei presi appunti quel Discorso, nel quale egli intendeva di <lb/>sostener la mostruosa ipotesi del Gualtierotti, e poi col non pensar pi&ugrave; a <lb/>riformar quella ipotesi, che non sarebbe forse per questo riuscita punto mi&shy;<lb/>gliore, mutando lo stesso primo Discorso latino in parte dello splendido dia&shy;<lb/>logo italiano. </s></p><p type="main">

<s>Che qualunque altra ipotesi immaginata da Galileo non dovesse riuscir <lb/>punto migliore di quella, da lui gi&agrave; approvata, delle esalazioni terrestri su&shy;<lb/>blimate in cielo e illuminate dal Sole, s'argomenta dall'esaminar le ipotesi <lb/>sovvenute in mente agli altri celebri Astronomi contemporanei, tutte per man&shy;<lb/>canza di esperienza in qualche parte repugnanti alla natura dei fatti, non <lb/>eccettuata quella dello stesso Keplero, che asser&igrave; il nuovo splendore apparito <pb xlink:href="020/01/1057.jpg" pagenum="500"/>in cielo &ldquo; flammam fuisse quia ut flamma consumpta est quasi deficiente <lb/>alimento &rdquo; (De Stella nova, Pragae 1606, pag. </s>

<s>97). </s></p><p type="main">

<s>Bench&egrave; sempre si proceda (e come sarebbe stato possibile altrimenti?) <lb/>per vie congetturali, pure ipotesi alquanto pi&ugrave; ragionevoli di quelle di Ga&shy;<lb/>lileo e del Keplero, per tacere degli altri, incominciarono ad apparire nella <lb/>storia della scienza col Boulliaud, a cui succede, nel difficile magistero, il <lb/>nostro Montanari. </s>

<s>In un suo Discorso astronomico sopra la sparizione di al&shy;<lb/>cune stelle, posto com'appendice all'Astrologia convinta di falso, dop'aver <lb/>rifiutate le opinioni degli antichi, e le pi&ugrave; recenti altres&igrave; del Cartesio e del <lb/>Riccioli, cos&igrave; soggiunge: </s></p><p type="main">

<s>&ldquo; E giacch&egrave; le Stelle fisse, a guisa di tanti Soli, di propria luce sono <lb/>dotate, come oggimai consentono tutti gli Astronomi da irrefragabili argo&shy;<lb/>menti persuasi, io non veggo alcun inconveniente per dire che debbano esse <lb/>ancora soggiacere all'incursione di queste macchie, che talora in molta quan&shy;<lb/>tit&agrave; crescendo loro attorno le oscurino, le impiccoliscano e le rinchiudano <lb/>affatto, ora per lunghissimi tempi, ora per brevi intervalli, ed ora a vicende, <lb/>giusta che la materia di cui si compongono in molta o poca copia si ra&shy;<lb/>guna. </s>

<s>Se dunque d'improvviso s'adunano tali corpi intorno a una stella, <lb/>che per molti secoli esente da tali oscurit&agrave; scintill&ograve; agli occhi nostri, eccola <lb/>impiccolire, eccola eziandio sparire dal cielo. </s>

<s>Se alcuna, che per l'avanti <lb/>n'ebbe sempre attorno di s&egrave; una quantit&agrave; cos&igrave; costante, che per lungo tempo <lb/>fu stimata per esempio di quarta grandezza, d'improvviso se ne sgombra la <lb/>faccia, eccola tutta rilucente prenden luogo fra quelle di seconda e di prima <lb/>maest&agrave;. </s>

<s>Se taluna, condannata per molti secoli ad un'oscura carcere fra que&shy;<lb/>ste macchie, rompe talora i ceppi, sboccando il rinchiuso fuoco, eccola nuova <lb/>e non pi&ugrave; veduta Stella agli occhi nostri palesarsi illustrando d'inusitati <lb/>raggi quella parte del Cielo. </s>

<s>E se di nuovo, aggregandosi tali macchie, alle <lb/>primiere tenebre viene ristretta, eccone perdute le vestigia, eccone annichi&shy;<lb/>lato il fulgore. </s>

<s>Che se da una sola parte del di lei corpo s'apre luogo al&shy;<lb/>l'interno fulgore, ed abbia intorno al proprio centro un moto periodico, la <lb/>vedrete, non men di quella del Bullialdo nella Balena, a determinati tempi <lb/>apparire, fino a tanto che nuove aggregazioni di macchie o nuova aper&shy;<lb/>tura delle medesime alcuna inaspettata variet&agrave; v'introduca &rdquo; (Venezia 1685, <lb/>pag. </s>

<s>21, 22). </s></p><p type="main">

<s>Cos&igrave; alla felice ipotesi inspirata al Boulliaud dal principio kepleriano, <lb/>che ruotino le stelle fisse in s&egrave; stesse, come ruota il Sole, e per la quale <lb/>non si spiegava altro che il loro apparire e disparire in certi periodi di <lb/>tempo; il nostro Montanari ne sostituiva un'altra non men ragionevole ipo&shy;<lb/>tesi, per la quale si spiegano i fatti pi&ugrave; curiosi, che ora in crescere ora in <lb/>diminuir di grandezza, senz'ordine apparente, presentano alcune Stelle agli <lb/>attenti osservatori. </s>

<s>E perch&egrave; a questa ipotesi hanno fatto plauso gli stessi <lb/>Astronomi pl&ugrave; recenti, si pu&ograve; dir che qui rimanesse assoluta questa parte <lb/>di Fisica stellare, oggetto di tanta maraviglia al volgo, e occasione di tante <lb/>strane congetture al Filosofo. </s>

<s>&Egrave; da passar perci&ograve; ora a vedere gli impulsi <pb xlink:href="020/01/1058.jpg" pagenum="501"/>che vennero, e i progressi che fece l'Astronomia in contemplar la celeste <lb/>v&ograve;lta stellata, quando s'apri un nuovo spettacolo alla vista dal portentoso <lb/>artificio del Canocchiale. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Primo a riferire ai mortali questo stupendo spettacolo, contemplato nel <lb/>cielo, fu Galileo, il quale ebbe a notar come cosa inaspettata che le Stelle <lb/>fisse osservate col Telescopio non ricrescevano in grandezza a quella pro&shy;<lb/>porzione che tutti gli altri oggetti sogliono, non eccettuata la Luna. </s>

<s>Intese <lb/>che ci&ograve; dipendeva dall'irradiazione ascitizia, gli effetti della quale in alterar <lb/>l'apparente grandezza delle stelle furono soggetto di diligenti studii agli <lb/>astronomi, quando il progredir delle scienze accese in loro pi&ugrave; che mai vivo <lb/>il desiderio di farsi almeno un'idea di ci&ograve; che siano, rispetto al piccolo no&shy;<lb/>stro, quegli smisurati lucenti mondi lontani. </s></p><p type="main">

<s>Galileo aveva, dall'esperienza fatta del suo debole strumento, concluso: <lb/>&ldquo; fixae vero Stellae periphaeria circulari nequaquam terminatae conspiciun&shy;<lb/>tur sed veluti fulgores quidam radios circumcirca vibrantes &rdquo; (Alb. </s>

<s>III, 74) <lb/>e il vederle terminate in circoli e senza raggi dipendeva da certi artificii, <lb/>che sovvennero poi pi&ugrave; tardi in mente agli Astronomi. </s>

<s>L'Huyghens faceva <lb/>consistere uno di questi semplici artificii nel tinger leggermente l'oculare <lb/>di un color nero o di filiggenne o di brace, in cui veniva cos&igrave; a spengersi <lb/>intorno all'occhio la luce erratica, che le stelle apparivano quasi come punti <lb/>matematici senza sensibile grandezza. </s></p><p type="main">

<s>Ma si debbono allo stesso Huyghens ben altri pi&ugrave; laboriosi artificii, da <lb/>lui inventati, per dar sodisfazione tutt'insieme a chi volesse contemplar le <lb/>Stelle per suo diletto, e a chi volesse osservarle con intendimento di scienza. </s>

<s><lb/>Descrisse quegli artificii in una sua operetta latina, che ha il titolo di <emph type="italics"/>Astro&shy;<lb/>scopia compendiaria Tubi optici molimine liberata,<emph.end type="italics"/> della quale il Viviani, <lb/>da c. </s>

<s>136-47 del Tomo CXXXVIII de'Discepoli di Galileo, lasci&ograve; manoscritta <lb/>una bella traduzione italiana. </s></p><p type="main">

<s>Incomincia l'Autore dell'Astroscopia a dire com'essendosi tutte le spe&shy;<lb/>ranze di coloro, che attendevano al perfezionamento dei Canocchiali, appun&shy;<lb/>tate nel fabbricare oggettivi di gran distanza focale, per la quale bisogna&shy;<lb/>vano lunghissimi tubi, difficilissimi, anche coi macchinamenti inventati in <lb/>Firenze dal Del Buono e dal Campani in Roma, a maneggiarsi; egli avesse <lb/>rimossa ogni difficolt&agrave;, posando la lente oggettiva sopra una lunga antenna, <lb/>e accomodando l'oculare presso all'osservatore, in un tubo collocato a con&shy;<lb/>veniente distanza. </s>

<s>Il modo di volgere e addirizzare a piacere il cristallo, per <lb/>mezzo di carrucole e di fili, che venissero alla mano dello stesso osserva&shy;<lb/>tore, son dall'Huyghens particolarmente descritti, ma quel che pi&ugrave; importa <pb xlink:href="020/01/1059.jpg" pagenum="502"/>&egrave; ci&ograve; che riguarda l'oculare preparato per le osservazioni pi&ugrave; squisite cos&igrave;, <lb/>come riferiscono tradotte dal Viviani le parole seguenti: </s></p><p type="main">

<s>&ldquo; Ma adesso aggiungeremo altro di pi&ugrave;, per cui rendere pi&ugrave; perfetto <lb/>questo nostro modo di osservare, bench&egrave; se si tralasciasse non pregiudiche&shy;<lb/>rebbe punto, ma per&ograve; non deve disprezzarsi dal curioso osservator delle <lb/>stelle. </s>

<s>E pertanto, mentre io cercavo con maggior diligenza i Pianeti cassi&shy;<lb/>niani di Saturno, e che difficilmente io gli trovava, in particolare nelle notti <lb/>non oscurissime, m'accorsi avvenir ci&ograve; da una certa debole luce, che dal&shy;<lb/>l'aria veniva all'occhio, non gi&agrave; quella che viene per la lente maggiore, <lb/>ma quella che scappa fuori dalle bande. </s>

<s>Per escludere questa tale impor&shy;<lb/>tuna luce io sapeva che avrebbe alquanto giovato, se qui ancora intorno <lb/>alla lente maggiore avessi posto quel cerchio di carta, di cui io mi serviva <lb/>nell'osservare la Luna. </s>

<s>Ma stando applicato a ci&ograve;, mi sovvenne un altro pi&ugrave; <lb/>efficace rimedio, da unirsi a quello, cio&egrave; coll'apporvi una lamina bucata, <lb/>acci&ograve; la pupilla dell'occhio venisse a restringersi, quando per altro ella &egrave; <lb/>solita nelle tenebre di dilatarsi molto. </s>

<s>Di che, subito che io feci sperienza, <lb/>veddi chiaramente tutt'e tre le Stelle di Saturno, che poi, levato quel pic&shy;<lb/>col foro, non ne vedevo altro che la mia di mezzo &rdquo; (c. </s>

<s>130). </s></p><p type="main">

<s>Dalla semplice osservazione de'fatti, che mostravano quanto nocesse alla <lb/>visione distinta delle stelle, e quanto ne alterasse l'apparente grandezza l'ir&shy;<lb/>radiazione avventizia, si pass&ograve; ad istituire particolari esperienze per misurar <lb/>quanto, in un Canocchiale di una lunghezza data, ricrescesse l'immagine, <lb/>per effetto della stessa irradiazione. </s>

<s>Il Picart, con un Telescopio di tre piedi, <lb/>osservava, a una distanza di 191,382 di que'piedi, una fiamma di latitudine <lb/>tripedale, e la trov&ograve; sottendere un angolo di 8&Prime;, mentre che non sarebbe <lb/>dovuto quell'angolo riuscir maggiore di 3&Prime;, 14&tprime;. </s>

<s>Fu questa esperienza delle <lb/>prime, che servirono al Newton per confermar la sua teoria, la quale con&shy;<lb/>cludevasi in dire che, per l'ineguale refrangibilit&agrave; della luce, tutti i punti <lb/>luminosi occupano nel foco dell'obiettivo uno spazio circolare di tal lar&shy;<lb/>ghezza, che &egrave; quasi la cinquantesima parte dell'apertura del vetro. </s>

<s>&ldquo; Ita ta&shy;<lb/>men, soggiunge, ut lux in circuitu rarissima vix, aut ne vix quidem sen&shy;<lb/>tiatur, in medio vero, ubi constipatior est, sensumque satis ferit, lucidum <lb/>constituat circellum, cuius latitudo pro splendore puncti lucentis varia sit, <lb/>ac tertiam circiter, quartamve, aut quintam fere partem latitudinis totius, <lb/>ut plurimum, adaequet &rdquo; (De Mundi systemate, Opuscul., T. II, Lausan&shy;<lb/>nae 1744, pag. </s>

<s>15, 16). </s></p><p type="main">

<s>Cos&igrave; veniva in qualche modo a spiegarsi, ne'principii del secolo XVIII, <lb/>come punti quasi matematici si rendessero alla retina del nostro occhio sen&shy;<lb/>sibili, e come sopr'essa retina operando que'punti lucidi con alternati moti, <lb/>che si direbbero di sistole e di diastole, apparissero scintillanti. </s></p><p type="main">

<s>Che sia la scintillazione propria alle Stelle fisse erasi riconosciuto gi&agrave; <lb/>anche dall'occhio nudo, ma Galileo se ne assicur&ograve; meglio col Telescopio, <lb/>che gli mostrava que'raggi vibrarsi tutto intorno dal nucleo della Stella <lb/>&ldquo; atque admodum scintillantes &rdquo; (Alb. </s>

<s>III, 75). N&egrave; qui nel Nunzio sidereo <pb xlink:href="020/01/1060.jpg" pagenum="503"/>per&ograve;, n&egrave; altrove, per le varie opere galileiane stampate, ci sovvien d'aver <lb/>letto nulla in proposito della ragione del fenomeno misterioso. </s>

<s>Solo a c. </s>

<s>11 <lb/>del T. II, P. III, ci siamo abbattuti a leggere questa nota manoscritta: &ldquo; Kep&shy;<lb/>plerus <emph type="italics"/>De stella nova<emph.end type="italics"/> car. </s>

<s>95 de scintillatione ait fieri posse ex rotatione <lb/>fixarum. </s>

<s>Et licet ad ipsas Sol insensibilis omnino sit, ut a nobis eo consti&shy;<lb/>tutis nulla ratione videri possit; tamen non evanescit ipsis, nam et consi&shy;<lb/>derat quod multo citius evanescit illuminatio corporis lucidi, quam conspectus <lb/>eiusdem, et sic a longissima distantia videmus facem ardentem, quae cor&shy;<lb/>pora nobis adiacentia non illustrat. </s>

<s>&rdquo; </s></p><p type="main">

<s>Si potrebbe dubitar se avesse Galileo presa quella nota per confutare <lb/>il detto del Keplero o per approvarlo, ma riscontrando che la considerazione <lb/>ivi fatta, per salvar dalle opposizioni quella ipotesi, non &egrave; propriamente del <lb/>Keplero, si pu&ograve; argomentar che Galileo la commentasse, coll'intenzione di <lb/>professarla. </s>

<s>Giova poi di vedere in che quel commento particolarmente con&shy;<lb/>sista, perch&egrave; di qui ne scende una conclusione importante ed &egrave;, che Gali&shy;<lb/>leo partecipava a quel tempo in tutto colle idee singolari professate dall'Au&shy;<lb/>tor del trattato <emph type="italics"/>De Stella nova,<emph.end type="italics"/> al Cap. </s>

<s>VIII del quale vien perci&ograve; richiamata <lb/>la nostra attenzione. </s></p><p type="main">

<s>Aveva gi&agrave; lo Scaligero esercitato le sottigliezze del suo ingegno anche <lb/>intorno al fenomeno della scintillazione, riducendolo a cinque cause conco&shy;<lb/>mitanti, che son per lui la grandezza, lo splendore e il moto della Stella, <lb/>il mezzo dell'aria, e il moto della luce, che &egrave; in tempo e no in istante. </s>

<s>Parve <lb/>al Keplero di dover tenere altra via pi&ugrave; facile e pi&ugrave; naturale, che gli si <lb/>present&ograve; in un fatto occorsogli ad osservare in que'festoni (<emph type="italics"/>uniones<emph.end type="italics"/>), e in <lb/>que'pendagli di cristallo, di che si sogliono ornar le lumiere. </s>

<s>Stava una sera <lb/>seduto tutto solo nell'anticamera del palazzo imperiale, e attentamente guar&shy;<lb/>dava quel cangiar di colore, e quello scintillare che facevano i prismi cri&shy;<lb/>stallini, velocemente rotando intorno al loro punto di sospensione, per il <lb/>moto impresso, nell'accendersi, alla lumiera. </s>

<s>Ecco disse allora spiegato il fatto: <lb/>le stelle son di una sostanza diafana, cristallina e angolosa, e rotando in s&egrave;, <lb/>illuminate dal Sole, presentano la variet&agrave; di colori e lo scintillamento, come <lb/>i pendagli della stessa lumiera. </s>

<s>&ldquo; Quare non metuo ut perpetua esse non <lb/>possint corpora stellarum, si angulose aut si intus inaequaliter densa sunt, <lb/>ut solent <emph type="italics"/>Uniones<emph.end type="italics"/> partibus aliis aliter pellucidi..... Tum autem ipsa per <lb/>se rotatio fixarum magna probabilitate, magnis exemplis nititur. </s>

<s>Sed exem&shy;<lb/>plum solus Copernicus dederit hanc nostram Tellurem quae, ut undequa&shy;<lb/>que Soli conspectu frui possit, rotatur in dies singulos, seseque quasi assat <lb/>ad hunc ignem. </s>

<s>Credibile est igitur et Planetas et fixas omnes quosque in <lb/>suis rotari spatiis, ne sit aliquid in Mundo quod centri nobilissimi corporis, <lb/>radiis vitalibus et lumine splendidissimo, penitus privetur &rdquo; (Pragae 1606, <lb/>pag. </s>

<s>94, 95). </s></p><p type="main">

<s>V'erano queste grandi difficolt&agrave; per&ograve;, che guastavano la seducente fa&shy;<lb/>cilit&agrave; dell'ipotesi: l'azione del Sole dee per l'immensa lontananza riuscire <lb/>insensibile sopra le Stelle, le quali, essendo dall'altra parte cos&igrave; corpulente, <pb xlink:href="020/01/1061.jpg" pagenum="504"/>non possono convertirsi in s&egrave; stesse tanto veloci, quanto mostra il vederle <lb/>ad ogni istante cangiar colori. </s>

<s>Alla prima delle quali difficolt&agrave; rispondeva il <lb/>Keplero: &ldquo; Non enim evanescit Sol ipsi rerum naturae.... quia forte, et <lb/>omnino quidem nostris oculis illic constitutis evanesceret, nec enim aequum <lb/>est, nostra visus hebetudine, vim aestimare et acumen Naturae &rdquo; (ibi, pag. </s>

<s>95). <lb/>Rispondeva alla seconda: &ldquo; Si multas habent partes eiusmodi, quales dixi&shy;<lb/>mus scintillationibus et coloribus servire.... iam non est necesse ut quo&shy;<lb/>ties una emicat scintillatio, toties una integra sit absoluta rotatio, sed, ut <lb/>rota multos clavos, sic haec corpora multos angulos, multa fulgura, unica <lb/>rotatione exserere videntur &rdquo; (ibi). </s></p><p type="main">

<s>E giacch&egrave; il Keplero non d&agrave; per risposta alle due difficolt&agrave; altro che <lb/>queste due ragioni, &egrave; un commento dunque di Galileo la considerazione, che <lb/>pi&ugrave; presto svanisce al nostr'occhio l'illuminazione degli oggetti circostanti, <lb/>che non l'aspetto lontano del corpo illuminante. </s>

<s>Quanto erano lontani i due <lb/>grandi uomini dal sollevare ancora a quelle alture, a cui sollevarono poi l'ala <lb/>del potentissimo ingegno! Chi crederebbe che gli Autori dell'<emph type="italics"/>Epitome Astro&shy;<lb/>nomiac copernicanae,<emph.end type="italics"/> e de'Dialoghi intorno i due Massimi Sistemi, dentro <lb/>il primo decennio del secolo XVII, professassero idee cos&igrave; basse intorno al&shy;<lb/>l'essere delle Stelle, rassomigliate a cristalli sfaccettati, che rotano intorno <lb/>al Sole, per goder d'ogni parte i benefici raggi della sua luce e del suo ca&shy;<lb/>lore? </s>

<s>Vero &egrave; bene che Galileo, quando si persuase che le stelle avevano luce <lb/>propria, e che non era perci&ograve; pi&ugrave; accettabile l'ipotesi del Keplero, si ridusse a <lb/>dire che le stelle stesse scintillano, perch&egrave; a differenza dei Pianeti &ldquo; fulgorem <lb/>ab intra emittunt &rdquo; (Alb. </s>

<s>XIV, 331 e VI, 154), ma, oltre che non si rendeva <lb/>cos&igrave; la ragione del cangiare ad ogni istante colore, rimaneva a saper come <lb/>mai l'emetter la luce <emph type="italics"/>ab intra<emph.end type="italics"/> producesse quell'irrequieto scintillare s&igrave; vivo. </s>

<s><lb/>Sembra insomma a noi questo secondo passo di Galileo un ritrarsi indietro, <lb/>e anzi quasi un delirare dal vero, la diritta via del quale era segnata gi&agrave; <lb/>dallo Scaligero, e un altro italiano, Maestro insigne di fisica sperimentale, vi <lb/>aveva impresse orme cos&igrave; profonde, che, dietro a quelle procedendo i mo&shy;<lb/>derni, riuscirono finalmente a sapere perch&egrave;, guardate attraverso alla no&shy;<lb/>str'aria vaporosa, si veggano in cielo coruscare le Stelle. </s></p><p type="main">

<s>Giovan Battista Benedetti, nelle sue Disputazioni <emph type="italics"/>De quibusdam placitis <lb/>Aristotelis,<emph.end type="italics"/> cos&igrave;, a Galileo e al Keplero che non vollero ascoltarlo, insegnava <lb/>la ragione dello scintillar delle fisse, non cavata dalle finzioni della mente, <lb/>ma dall'analogia che passa tra il fenomeno celeste, e alcuni fatti naturali at&shy;<lb/>tentamente osservati. </s>

<s>&ldquo; Ubi Aristotiles ait scintillationem stellarum fieri ra&shy;<lb/>tione aspectus nostri, ob maximam distantiam, maximum errorem committit, <lb/>ut etiam facit cum putat visionem fieri extramittendo, contra id quod alio <lb/>loco, immo contra veritatem ipsam, asseruit. </s>

<s>Scintillatio ergo stellarum, ne&shy;<lb/>que aspectus nostri ratione, neque alicuius mutationis earumdem stellarum, <lb/>sed ab inaequalitate motus corporum diaphanorum mediorum nascitur, que&shy;<lb/>madmodum clare cernitur, quod si inter aliquod obiectum et nos alliquis <lb/>fumus, qui ascendat, intercesserit, videbimus obiectum illud quasi tremere. <pb xlink:href="020/01/1062.jpg" pagenum="505"/>Hoc autem tanto magis fiet, quanto magis distabit obiectum ab ipso fumo, <lb/>unde admirationi locus non erit, si stellas fixas magis scintillare quam er&shy;<lb/>rantes cernamus. </s>

<s>Lumen stellae ad oculum nostrum accedens perpetuo per <lb/>diversas diaphaneitates penetrat, medio continuorum motuum corporum me&shy;<lb/>diorum, unde continuo eorum lumen variatur, et hoc in longinquis, magis <lb/>quam in proprinquis stellis, apparet, quemadmodum ab exemplo de fumo <lb/>allato, et etiam ab aliquibus vitris, ex superficie non plana sed irregu&shy;<lb/>lari constantibus, quilibet cognoscere potest &rdquo; (Speculationum Liber, Vene&shy;<lb/>tiis 1599, pag. </s>

<s>186). </s></p><p type="main">

<s>Lasciando considerare ai lettori quanto fossero feconde di verit&agrave; queste <lb/>speculazioni del Fisico veneziano, a dimenticar le quali ebbero gl'Italiani i <lb/>perniciosi esempi da Galileo, &egrave; da tornare a dir di un altro magnifico spet&shy;<lb/>tacolo, che le Stelle osservate col Canocchiale offersero di s&egrave;, e che lo stesso <lb/>Galileo fu per avventura de'primi a riferire agli attoniti mortali: &ldquo; Perspi&shy;<lb/>cilli beneficio, egli dice, maiores et clariores apparent, quam magnitudinis <lb/>secundae Sidera acie naturali visa. </s>

<s>Ut autem de inopinabili fere illarum fre&shy;<lb/>quentia unam alteramve attestationem videas, Asterismos duos subseribere <lb/>placuit, ut ab eorum exemplo de caeteris iudicium feras &rdquo; (Alb. </s>

<s>III, 75). </s></p><p type="main">

<s>Il primo di quegli Asterismi rappresenta la costellazione di Orione, che <lb/>aveva in animo di rappresentare intera &ldquo; verum ab ingenti stellarum copia, <lb/>temporis vero inopia obrutus, aggressionem hanc in aliam occasionem di&shy;<lb/>stuli &rdquo; (ibi). N&egrave; manc&ograve; Galileo al proposito, ripigliando con pi&ugrave; cura a de&shy;<lb/>scrivere quello stesso Asterismo di Orione, specialmente rispetto a quelle <lb/>stelle che sono intorno al Cingolo, e le rappresent&ograve; in una Mappa, inserita <lb/>a c. </s>

<s>12 del T. VI, P. IV, scrittovi in fronte di propria mano &ldquo; Circa cingu&shy;<lb/>lum Orionis. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il secondo degli Asterismi, descritti nel Nunzio Sidereo, &egrave; quello delle <lb/>Pleiadi, e bench&egrave; si contenti il frettoloso Autore di dar questi due soli per <lb/>saggi, parecchi altri se ne trovano qua e l&agrave; dispersi pe'Manoscritti. </s>

<s>Noi ci <lb/>contenteremo di citar quelli, che si veggono disegnati nelle c. </s>

<s>2, 18 e 28 <lb/>del T. VI, P. IV, senz'alcuna indicazione, e l'altro a c. </s>

<s>29 del medesimo <lb/>Tomo, che porta di mano dell'Autore scritto il nome della <emph type="italics"/>Canicula.<emph.end type="italics"/></s></p><p type="main">

<s>A tergo della c. </s>

<s>32, T. III, P. III, &egrave; un altro Asterismo, distinto di punti <lb/>semplici, a rappresentare le stelle minori, e di punti irraggiati a rappresen&shy;<lb/>tar le maggiori, e l'Autore stesso lo not&ograve; colle parole <emph type="italics"/>exquisita descriptio.<emph.end type="italics"/><lb/>Tanto lavoro &egrave; rimasto ora senza frutto per noi, e senza merito per chi lo <lb/>fece, eppure quelle Mappe, collazionate colle moderne, potrebbero tornare <lb/>utilissime alla scienza, e in ogni modo le dovrebbe la Uranografia tenere in <lb/>preg&igrave;o e aver care, come la Geografia tiene in pregio e ha care le relazioni, <lb/>bench&egrave; imperfette, de'primi esploratori. </s>

<s>Galileo s'era forse proposto di rac&shy;<lb/>cogliere quelle Mappe, e il frutto delle sue fatiche, nel libro delle <emph type="italics"/>Novit&agrave; <lb/>celesti,<emph.end type="italics"/> ma perch&egrave; al suo proposito, qualunque se ne fosse la causa, venne <lb/>meno l'Autore, pareva che v'avesse dovuto supplire l'amorosa sollecitudine <lb/>degli editori. </s></p><pb xlink:href="020/01/1063.jpg" pagenum="506"/><p type="main">

<s>Bench&egrave; questi Asterismi, e specie l'ultimo citato, sieno stati tutti esqui&shy;<lb/>sitamente descritti, e degli stessi due primi riferiti nel Nunzio si dica &ldquo; in&shy;<lb/>terstitia, quo exactius licuit, servavimus &rdquo; (Alb. </s>

<s>III, 75) furono nonostante <lb/>quegli interstizi presi a occhio, e anzi a occhio tutte intere ritratte in dise&shy;<lb/>gno le Mappe. </s>

<s>A tergo per&ograve; della c. </s>

<s>31 del Tomo manoscritto ultimamente <lb/>citato, si vede indicata una stella colle parole: &ldquo; canem minorem credo &rdquo; <lb/>e sotto si legge la nota: &ldquo; Stella A absque Specillo non cernitur, attamen <lb/>Specillo inspecta, apparet tantae magnitudinis, ut infra ipsam aliae secun&shy;<lb/>dae, tertiae, et quartae magnitudinis conspiciantur. </s>

<s>&rdquo; Presso a questo Aste&shy;<lb/>rismo, nella medesima carta, si vede disegnato l'altro del Cane maggiore, <lb/>con le precise misure delle distanze delle stelle minori dalla maggiore, e <lb/>colla dichiarazione: &ldquo; Circa Canem, praeter alias, extant stellulae 7, in con&shy;<lb/>simili configuratione (fig. </s>

<s>99) quarum maxima a Cane distantia non supe&shy;<lb/>rat minuta 20. &rdquo; </s></p><p type="main">

<s>Queste misure in minuti di grado furono senza dubbio prese da Gali&shy;<lb/>leo col primo strumento micrometrico, descritto nel <emph type="italics"/>Nunzio,<emph.end type="italics"/> e i tentativi <lb/><figure id="id.020.01.1063.1.jpg" xlink:href="020/01/1063/1.jpg"/></s></p><p type="caption">

<s>Figura 99.<lb/>che bisognava fare, e il tempo che si dovea per&shy;<lb/>dere, per trovar qual fosse quell'apertura di foro <lb/>nella lamina, che rispondesse per l'appunto all'os&shy;<lb/>servazione, ci rispondono perch&egrave; non si trovi de&shy;<lb/>signata, colle misure precise delle distanze, altro <lb/>che questa poca parte dell'Asterismo del Cane. </s>

<s>Ma <lb/>quando ebbe pensato a quell'altro strumento mi&shy;<lb/>crometrico, col quale si potevano misurar gl'inter&shy;<lb/>stizi fra stella e stella, per mezzo del Rastrello o <lb/>del Reticolo, contrapposto alla mira del Canocchiale, e allora Galileo medit&ograve; <lb/>un gran progetto, ed era quello di ridurre in Mappe tutta una estesa re&shy;<lb/>gione del Cielo. </s>

<s>A collaborare all'opera aveva chiamato il Castelli, a cui <lb/>insegn&ograve; l'uso dello Strumento, e a cui riusc&igrave; di por qualche rimedio a uno <lb/>de'maggiori inconvenienti, che presentava esso Strumento, accomodando la <lb/>lanterna da illuminare il Reticolo in modo, che non abbagliasse la vista al&shy;<lb/>l'osservatore, e che si potessero perci&ograve; discerner da lui anco le pi&ugrave; pic&shy;<lb/>cole stelle. </s></p><p type="main">

<s>A questo negozio, di non lieve importanza nella storia della scienza, ac&shy;<lb/>cennava il Castelli stesso cos&igrave; con queste parole, in una lettera indirizzata a <lb/>Galileo, il d&igrave; 7 Gennaio 1617 da Pisa: &ldquo; Per l'osservazione della Canicola <lb/>ho ritrovato un luogo, nel quale si potr&agrave; collocare il lumicino, e di poi al&shy;<lb/>lontanarsi 150 braccia in circa per osservare, e quanto prima il tempo mi <lb/>dia licenza, mi metter&ograve; all'opera. </s>

<s>Venere lavora tuttavia, ma non &egrave; ancora <lb/>ridotta al semicircolo. </s>

<s>Non manco d'andare in busca di Stelle fisse, ma non <lb/>trovo cosa al proposito, fuorch&egrave; la avvisata nella passata. </s>

<s>Desidererei che <lb/>V. S. E., concedendoglielo la sanit&agrave;, una sera desse un'occhiatina a quella <lb/>stella di mezzo, delle tre che sono nella coda dell'Orsa maggiore, perch&egrave; &egrave; <lb/>una delle pi&ugrave; belle cose che sia in cielo, e non credo che per il nostro ser-<pb xlink:href="020/01/1064.jpg" pagenum="507"/>vigio si possa desiderar di meglio in quelle parti &rdquo; (MSS. Gal., P. III, T. VII, <lb/>Sez. </s>

<s>II, c. </s>

<s>62). </s></p><p type="main">

<s>Della raccolta de'frutti, che s&igrave; prometteva ubertosa, non sappiamo dir <lb/>niente. </s>

<s>Solo a tergo della c. </s>

<s>31, T. III, P. III, si trova preparato un Reti&shy;<lb/>colo, esteso da 24 a 34 gradi di latitudine, <lb/>e da 46 a 54 gradi di longitudine, nelle ma&shy;<lb/><figure id="id.020.01.1064.1.jpg" xlink:href="020/01/1064/1.jpg"/></s></p><p type="caption">

<s>Figura 100.<lb/>glie del quale per&ograve; non si trovano situate <lb/>al loro luogo altro che pochissime stelle, <lb/>come nella rappresentazione della fig. </s>

<s>100 <lb/>si vede. </s>

<s>Ma dovevano esser capitate in mano <lb/>al Viviani altre carte galileiane, dove l'Au&shy;<lb/>tore stesso descriveva lo strumento micro&shy;<lb/>metrico, descritto poi dal Borelli, e dove <lb/>altres&igrave; insegnava a far uso di quello stesso <lb/>strumento per misurar gli interstizi fra stella <lb/>e stella, con qualche altro saggio forse di <lb/>cos&igrave; fatta applicazione. </s>

<s>Di quelle carte &egrave; <lb/>veramente a doler la jattura, e non di tante <lb/>altre scritture galileiane, perdute perch&egrave; <lb/>non fatte, o perdute solamente di nome, <lb/>ma delle quali non san darsi pace i ciechi adoratori del Divino filosofo. </s></p><p type="main">

<s>Il Viviani del contenuto in quelle carte galileiane, ch'egli ebbe in mano, <lb/>e che sono ora smarrite, ne conferi una volta col Cassini, a cui rifiorirono <lb/>quelle idee nella memoria e rinverdirono le speranze, quando sent&igrave; vivo il <lb/>bisogno di una diligente descrizion delle stelle, per riscontrarne le miste&shy;<lb/>riose vicende, e investigar la causa del Ioro mutar grandezza, e ora appa&shy;<lb/>rire improvvise in cielo, ora nuovamente sparire. </s></p><p type="main">

<s>&ldquo; Quando eramo insieme a veder Saturno, scriveva il Cassini stesso al <lb/>Viviani da Bologna il di 6 Agosto 1661, notai che non appariva pi&ugrave; in cielo <lb/>la stella risorta nel petto del Cigno. </s>

<s>Ma giunto in Bologna in tempi sere&shy;<lb/>nissimi l'ho veduta ridotta alla piccolezza delle tre stelline prossime nel prin&shy;<lb/>cipio del collo, nello stesso sito, come per due anni l'ho osservata, e dove <lb/>nel tempo della prima apparizione fu descritta dal Keplero e dal Baiero. </s>

<s>Es&shy;<lb/>sendo scemata, dall'anno passato in qua, dalla terza alla quinta grandezza, <lb/>&egrave; probabile che abbi di nuovo a sparire, come gi&agrave; un'altra volta ha fatto <lb/>in questo secolo, onde non sarebbe inutile seguitarla con esquisitissimi oc&shy;<lb/>chiali, per rintracciare al possibile la cagione di questa singolarit&agrave;. </s>

<s>Spero <lb/>che anco dalle stelle fisse abbiamo ad imparare novit&agrave; non pi&ugrave; immaginate. </s>

<s><lb/>E per&ograve; di qui prendo occasione d'animar V. S. alla perfezione del gran di&shy;<lb/>segno, abbozzato da Galileo ne'Manoscritti che mi conferi, intorno l'esatta <lb/>osservazione di esse, giacch&egrave; sotto la protezione de'Serenissimi principi non <lb/>le pu&ograve; mancare tutte le pi&ugrave; desiderabili comodit&agrave; di sodisfarsi a pubblico <lb/>beneficio &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLIV, c. </s>

<s>193). </s></p><p type="main">

<s>Che si potesse, del resto, anche dalle Stelle fisse imparar novit&agrave; non <pb xlink:href="020/01/1065.jpg" pagenum="508"/>pi&ugrave; immaginate lo avevano, assai prima del Cassini, riconosciuto Galileo e <lb/>il Castelli, i quali, sopra a tutto quel che si potesse sperare dall'Astronomia, <lb/>chiamarono quelle stesse Fisse, non men dei Pianeti e del Sole &ldquo; a com&shy;<lb/>parire in giudizio a render testimonianza del moto a favor della Terra &rdquo; <lb/>(Alb. </s>

<s>I, 415). </s></p><p type="main">

<s>A c. </s>

<s>10 del T. VI, P. IV de'Manoscritti galileiani, si trovano autografe <lb/>due notarelle, chi legge le quali riman sorpreso di maraviglia, che Galileo <lb/>si sia trattenuto in cose tanto elementari, come son queste: &ldquo; Polis con&shy;<lb/>versionis diurnae in Terra immutabilibus et fixis existentibus, immutabilis <lb/>permanet Aequinoctialis, et ad eumdem terrestris superficiei punctum neuter <lb/>Aequatoris polorum attollitur aut deprimitur unquam, sed invariabilis sem&shy;<lb/>per remanet eiusdem loci eadem elevatio poli, quae solummodo mutatur dum <lb/>in superficie Terrae ad Aequatorem vel ad Polum accedimus. </s>

<s>&mdash; Extenso <lb/>terrestris Aequatoris plano et axe usque ad fixas, si quae fixa in axe stete&shy;<lb/>rit, et si stellae in plano Aequatoris reperiantur, circulum maximum desi&shy;<lb/>gnare videbuntur, reliquarum vero unaquaeque circulum describere appa&shy;<lb/>rebit, eo minorem quo ab ipso Aequatoris plano remotior fuerit, et quae ad <lb/>aliquem locum verticales fuerint, semper verticales erunt, quamdiu ad pla&shy;<lb/>num Aequatoris elongationem servabunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>Fa maraviglia, ripetiamo, il trovar fra le peregrine speculazioni di Ga&shy;<lb/>lileo queste cose notissime agli stessi fanciulli, ma la maraviglia cesser&agrave; in <lb/>chi intende non esser questo se non che il principio a un discorso, che si <lb/>voleva concludere in questo modo: Se la Terra &egrave; immobile sul suo asse e <lb/>ne'suoi poli, son tali le semplicissime apparenze di moto, che presentan le <lb/>Stelle fisse nella loro sfera. </s>

<s>Ma se, rimanendo io fermo nel medesimo luogo <lb/>della superficie terrestre, la Terra stessa, movendosi in giro, seco mi tra&shy;<lb/>sporta? </s>

<s>&ldquo; Si manente me in eadem terrestris superficiei loco tota Terra <lb/>transponatur?.... &rdquo; (ibi). </s></p><p type="main">

<s>La risposta non fu data, se non da poi che il Castelli venne cos&igrave; a <lb/>mettere sotto altra forma la domanda: &ldquo; Ho osservata la Stella settentrio&shy;<lb/>nale delle tre della fronte dello Scorpione, quale ha una stellina vicinissima, <lb/>pi&ugrave; settentrionale d'essa, nella continuazione dell'arco delle tre della fronte, <lb/>in questa maniera: <figure id="id.020.01.1065.1.jpg" xlink:href="020/01/1065/1.jpg"/> V. S. mi faccia grazia di scrivermi che gioco dover&agrave; <lb/>fare movendosi la Terra, caso che lei sia assai pi&ugrave; lontana dalla Terra del&shy;<lb/>l'altra compagna visibile con la vista naturale &rdquo; (Campori, Carteggio galil., <lb/>Modena 1881, pag. </s>

<s>260). </s></p><p type="main">

<s>Allora Galileo, a cui il di 7 Agosto 1627 venivano dirette queste pa&shy;<lb/>role da Roma, riprese a'suoi pensieri il filo rimasto in quelle due notarelle <lb/>interrotto, e delle speculazioni, provocate e promosse dalle stesse parole <lb/>scritte in quella lettera del Castelli, arricch&igrave; la III Giornata dei Due Mas&shy;<lb/>simi Sistemi. </s>

<s>&ldquo; Io non credo, pone ivi in bocca al Salviati, che le Stelle <lb/>siano sparse in una sferica superficie egualmente tutte distanti da un cen&shy;<lb/>tro, ma stimo che le loro lontananze da noi siano talmente varie, che al&shy;<lb/>cune ve ne possano essere due o tre volte pi&ugrave; remote di alcune altre, talch&egrave;, <pb xlink:href="020/01/1066.jpg" pagenum="509"/>quando si trovasse col Telesco&pgrave;io qualche piccolissima stella vicinissima ad <lb/>alcuna delle maggiori, e che per&ograve; quella fosse altissima, potrebbe accadere <lb/>che qualche sensibile mutazione succedesse tra di loro, rispondente a quella <lb/>de'Pianeti superiori &rdquo; (Alb. </s>

<s>I, 415). E proseguendo a dimostrare qual di&shy;<lb/>versit&agrave; di aspetto o parallasse debban fare a cagion del moto della Terra le <lb/>Stelle fisse, conclude dover essere questa stessa parallasse &ldquo; maggiore o mi&shy;<lb/>nore secondo che le stelle osservate sono pi&ugrave; o meno vicine al polo del&shy;<lb/>l'Ecclittica, sicch&egrave; finalmente delle stelle che sono nell'Ecclittica stessa, tal <lb/>diversit&agrave; si riduce a nulla &rdquo; (ivi, pag. </s>

<s>417). </s></p><p type="main">

<s>Bel pensiero senza dubbio quello del Castelli, belle speculazioni queste <lb/>di Galileo, ma bisognava che venissero confermate dai fatti, senza che le <lb/>Stelle fisse, chiamate in giudizio, sarebbero rimaste muti testimoni a favor <lb/>del moto della Terra, e anzi avrebbero col loro silenzio, come poi fecero al <lb/>Riccioli, fatto a tutti argomentar del contrario. </s></p><p type="main">

<s>Fu de'primi Giovanni Pieroni che, sulla fine del 1640, credesse di avere <lb/>col Canocchiale osservato il moto delle Stelle fisse di alquanti minuti se&shy;<lb/>condi; fatto che, come dimostrativo del moto della Terra, da Francesco Ri&shy;<lb/>nuccini riferito a Galileo (Alb. </s>

<s>VII, 360), questi che pareva ne dovesse esul&shy;<lb/>tare a sentir che le sue ipotesi eran confermate dal vero, pose invece le <lb/>cose nuovamente osservate dal Pieroni in tal dubbio, da equivalere a una <lb/>aperta negazione, concludendo esser vana speranza il voler raccogliere &ldquo; una <lb/>delicatissima e sottilissima osservazione da esperienze grossolanissime, ed anco <lb/>impossibili a farsi &rdquo; (ivi, pag. </s>

<s>363). </s></p><p type="main">

<s>Queste parole &egrave; vero le dettava Galileo al Viviani in mezzo all'accora&shy;<lb/>mento che sentiva, ripensando alle sorti del suo <emph type="italics"/>Dialogo sfortunato,<emph.end type="italics"/> ma pure <lb/>anche a mente serena si sarebbe persuaso che i moti, nella III Giornata pre&shy;<lb/>scritti a fare alle Stelle fisse, in conseguenza del moto della Terra, erano <lb/>matematiche speculazioni difficilissime, se non impossibili, a esemplifiare <lb/>ne'fatti. </s>

<s>I discepoli e i seguaci se ne persuasero poi anche pi&ugrave; fermamente, <lb/>e il Borelli ripensava alla stella di mezzo del cingolo di Andromeda, e come, <lb/>se potesse verificarsi ch'ella si fosse mossa, offrirebbe un bellissimo argo&shy;<lb/>mento a favor del Copernico &ldquo; ma dubito, soggiungeva, che questa spe&shy;<lb/>ranza ci fallir&agrave;, poich&egrave; dopo molte diligenze e speranze vane non riusc&igrave;, nean&shy;<lb/>che coll'aiuto del Telescopio, in altre fisse vicine, al Pieroni, e ad altri amici <lb/>di verificare una cosa simile &rdquo; (Fabbroni, Lettere ecc., T. I, Firenze 1773, <lb/>pag. </s>

<s>123). </s></p><p type="main">

<s>L'espressione del Borelli per&ograve; vuol esser alquanto rettificata: non &egrave; che <lb/>non fosse riuscito al Pieroni di verificare il moto delle stelle: &egrave; che non gli <lb/>riusc&igrave; di riscontrarci alcuna relazione col moto della Terra. </s>

<s>L'osservazione poi <lb/>fatta da altri e la ferma persuasione che, se le stelle si muovono, non potesse <lb/>il loro moto apparente dipendere da altra causa che dalla parallasse annuale, <lb/>tennero lungamente gli Astronomi perplessi e confusi, infintantoch&egrave; il Brad&shy;<lb/>ley non dimostr&ograve; che i moti delle fisse non dipendono dalla parallasse, ma <lb/>dalla <emph type="italics"/>aberrazione.<emph.end type="italics"/> Cos&igrave; venne la grande inaspettata scoperta a confermare <pb xlink:href="020/01/1067.jpg" pagenum="510"/>due delle pi&ugrave; importanti verit&agrave; astronomiche, e delle pi&ugrave; controverse; il moto <lb/>della Terra e il moto della Luce, che si compongono insieme a far dalla <lb/>nostra vista aberrare il luogo proprio delle stelle. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>&Egrave; oramai pi&ugrave; di un secolo e mezzo che s'ammira da tutti il sottilis&shy;<lb/>simo ingegno del Bradley, il quale non solo osserv&ograve; il moto delle stelle fisse, <lb/>creduto da Galileo e da'suoi seguaci impossibile, ma design&ograve; le vie di quel <lb/>moto in alcune stelle esser circoli, in altre ellissi pi&ugrave; o meno allungate, ri&shy;<lb/>ducendo la sua dimostrazione a tanta evidenza, a quanta pu&ograve; ridursi un teo&shy;<lb/>rema di Meccanica, o una proposizione di Geometria. </s>

<s>N&egrave; cessa l'ammira&shy;<lb/>zione verso il grande Astronomo inglese per sapersi che anche prima del <lb/>Newton conoscevano i Matematici, specialmente stranieri, il modo di com&shy;<lb/>porre in un'unica risultante due forze, non solamente ortogonali, ma qua&shy;<lb/>lunque si fosse l'angolo del loro concorso. </s></p><p type="main">

<s>Pi&ugrave; grande ammirazione ridesta in ogni modo il sottilissimo ingegno del <lb/>nostro Borelli, il quale, prima del Newton, si studi&ograve; di ridurre a una dimo&shy;<lb/>strazione meccanica le vie cos&igrave; apparentemente disordinate, che percorrono <lb/>in cielo le Comete. </s>

<s>Tale &egrave; la conclusion&egrave;, a cui tende questa seconda parte <lb/>del nostro capitolo, ma convien prima toccar brevemente delle varie ipotesi <lb/>fantasticate intorno all'origine e all'essere di quelle strane apparenze cele&shy;<lb/>sti, che furono per lungo tempo il terrore del volgo, e la disperazion degli <lb/>Astronomi. </s></p><p type="main">

<s>Come s'ingerisse negli uomini l'opinione che fossero le Comete presa&shy;<lb/>gio di pubbliche sventure non &egrave; del nostro istituto l'investigare, ma come <lb/>dovessero frugar la curiosit&agrave; degli Astronomi, e come riuscisse a loro diffi&shy;<lb/>cile, di apparenze da noi tanto remote, indagar l'origine e la ragione, &egrave; fa&shy;<lb/>cilissimo a comprendere, tanto pi&ugrave; ripensando al vezzo invalso tra Filosofi <lb/>di non fermarsi in quelle, tra cos&igrave; fatte ragioni, che paressero pi&ugrave; semplici <lb/>e pi&ugrave; naturali. </s></p><p type="main">

<s>Semplice e naturale era senza dubbio il concetto, che s'erano delle Co&shy;<lb/>mete formato i Pitagorici, i <emph type="italics"/>Placiti<emph.end type="italics"/> de'quali venivano sapientemente divul&shy;<lb/>gati da Plutarco, e da Seneca ne'loro libri. </s>

<s>&ldquo; Alcuni de'Pitagorici, riferiva <lb/>lo stesso Plutarco nel suo opuscolo, affermano essere la Cometa una stella <lb/>di quelle, che non sempre appariscono, ma dopo certo tempo determinato <lb/>ritornando in giro surgono dall'orizzonte &rdquo; (Traduz. </s>

<s>ital., Milano 1829, T. V, <lb/>pag. </s>

<s>247). Simile riferisce Seneca nelle Questioni naturali essere stata l'opi&shy;<lb/>nione di Artemidoro. </s></p><p type="main">

<s>Di rincontro a questa semplicit&agrave; di concetto sorsero gl'ingegnosi com&shy;<lb/>menti de'Filosofi, il principe de'quali insegnava, nel Libro delle Meteore, <lb/>essere la Cometa un'esalazione terrena, che menata in volta dal concavo lu-<pb xlink:href="020/01/1068.jpg" pagenum="511"/>nare, ivi a cagion del rapido moto si accenda. </s>

<s>Cos&igrave;, in sull'entrar del se&shy;<lb/>colo XVII, erano fra'Pitagorici e gli Aristotelici divise le opinioni, ma la <lb/>grande autorit&agrave; di Ticone prevaleva a favor dei secondi, anche sulla mente <lb/>degli stessi Peripatetici. </s></p><p type="main">

<s>Le tre Comete apparite nell'anno 1618 eccitarono il fermento delle di&shy;<lb/>scussioni. </s>

<s>Si lesse sopra quel soggetto nel Collegio romano una Disputazione <lb/>astronomica, dove si concludeva essere stato il moto della Cometa per un <lb/>circolo massimo della sfera celeste, a somiglianza degli altri Pianeti. </s>

<s>&ldquo; Fuit <lb/>ergo, quod erat probandum, motus Cometae per circulum maximum ac mo&shy;<lb/>tui Planetarum persimilis &rdquo; (Alb. </s>

<s>IV, 13). Quanto alla natura, dice essere <lb/>la Cometa &ldquo; non ex huius Terrae sordibus in aere succensa, sed coelestia <lb/>inter lumina sedem sortita &rdquo; (ibi) e non dubita, quanto al luogo di essa <lb/>Cometa, di assegnarlo probabilmente &ldquo; Solem inter ac Lunam &rdquo; (ibi). </s></p><p type="main">

<s>Cos&igrave; fatte idee pitagoriche, quanto al moto e all'origine delle Comete, <lb/>non furono approvate da Galileo, il quale profess&ograve; altre opinioni, non diret&shy;<lb/>tamente per s&egrave;, ma per mezzo di Mario Guiducci, che recit&ograve; nell'Accademia <lb/>fiorentina, su quel soggetto, una erudita ed eloquente Lezione. </s>

<s>Nega ivi <lb/>prima di tutto alle Comete qualunque somiglianza coi Pianeti &ldquo; imperocch&egrave; <lb/>i Pianeti avvicinandosi a poco a poco si fanno maggiori, sino a che fatti vi&shy;<lb/>cinissimi ci appariscono nella maggior grandezza; quindi pian piano allon&shy;<lb/>tanandosi si diminuiscono, e con quella stessa uniformit&agrave; mantenuta nel&shy;<lb/>l'aggrandirsi si vedono aggiustatamente rappiccolire. </s>

<s>Ma la Cometa &egrave; grande <lb/>nel suo primo apparire, e indi poco o nulla o per brevissimo tempo ricre&shy;<lb/>sce, diminuendosi poi in tutto il resto del tempo, fino a che fatta piccolis&shy;<lb/>sima, per la sua tenuit&agrave;, del tutto si perde &rdquo; (Alb. </s>

<s>IV, 23). Si nega in se&shy;<lb/>condo luogo dal Guiducci alle Comete l'essere sostanza celeste, e si torna <lb/>ad ammetter con Aristotile la loro origine da esalazioni terrene, non accese <lb/>per&ograve; a quel modo che il Filosofo voleva, ma illuminate dal Sole, ai riflessi <lb/>del quale si debbono le apparenze del nucleo e della coda. </s></p><p type="main">

<s>L'Autore della Disputazione astronomica, letta nel Collegio romano, per&shy;<lb/>suaso, com'era veramente, che le parole del Guiducci fossero inspirate da <lb/>Galileo, si rivolse contro questo direttamente a difendere le sue ragioni in <lb/>un libro, a cui pose il titolo di <emph type="italics"/>Libra astronomica.<emph.end type="italics"/> Usc&igrave; fuori questo libro <lb/>sotto il nome di Lotario Sarsi, anagramma di Orazio Grassi, divenuto fa&shy;<lb/>moso per essere state le ragioni astronomiche di lui ponderate da Galileo, <lb/>non con una volgar <emph type="italics"/>Libra,<emph.end type="italics"/> ma con uno squisitissimo <emph type="italics"/>Saggiatore.<emph.end type="italics"/></s></p><p type="main">

<s>Poco prima che uscisse fuori questo <emph type="italics"/>Saggiatore<emph.end type="italics"/> s'era il padre Giuseppe <lb/>Biancani, collega del Grassi, studiato di ricomporre la controversia fra Pita&shy;<lb/>gorici e Aristotelici, ch'egli pi&ugrave; volentieri distingue co'nomi di Fisiologi e <lb/>di Astronomi, e vi s'era studiato in modo, che se non provvedeva ai pro&shy;<lb/>gressi della scienza, ne teneva nonostante aperte le vie, e non ne impediva <lb/>i progressi, come sventuratamente aveva fatto il Guiducci. </s></p><p type="main">

<s>&ldquo; Solent nonnulli Physiologi (scrive, nel Cap. </s>

<s>IV, Lib. </s>

<s>XVI <emph type="italics"/>De mundi <lb/>fabrica,<emph.end type="italics"/> il Biancani) cum Astronomis de Cometarum materia contendere. </s>

<s>Af-<pb xlink:href="020/01/1069.jpg" pagenum="512"/>firmant enim aliqui ex illis Cometas ex elementari materia constare, atque <lb/>etiam in elementari regione versari, quippe quae Cometas tantum de facie <lb/>norunt. </s>

<s>Cum enim eorum circuitus, vias, motus, parallaxes nec queant per&shy;<lb/>severari, de iis tamen secundum vulgarem apparentiam iudicant. </s>

<s>Verentur <lb/>praeterea ne quam novitatis notam coelo inurant. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ex opposito Astronomi, qui praedicta Cometarum accidentia sagaciter <lb/>rimati sunt, eaque omnino rebus tantum coelestibus competere vident, eas non <lb/>elementares sed coelestes esse autumant. </s>

<s>Verum enim vero me ab utrisque <lb/>gratiam initurum confido, si qua ratione iis haec componi possit ostendero. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ratio igitur est si eorum opinionem sequemur, qui putant Cometas <lb/>coelestes esse ac continuo inter aeterna Mundi corpora perseverare, quamvis <lb/>raro conspicua evadant. </s>

<s>In qua sententia fuere olim Pythagorici, et Italo&shy;<lb/>rum secta, sed et recentiores suas hypotheses ita Cometae accomodant, ut <lb/>cum antiquis consentire possint. </s>

<s>Dum enim eos in magno epiciclo revol&shy;<lb/>vunt, omnes salvant apparentias, et praeterea eas in sublime coelum ita at&shy;<lb/>tollunt, ut paulatim ad visum minuantur, ac tandem non pereant, sed non <lb/>apparent. </s>

<s>Hac enim ratione nihil novi in coelo inferunt, quod Physicis sic <lb/>contingat praecipuae curae est, nec eas elementares faciunt, quod Astronomi <lb/>magnopere aversantur. </s>

<s>Haec sit conciliatio &rdquo; (Mutinae 1635, pag. </s>

<s>160). </s></p><p type="main">

<s>Ma Galileo, avverso a ogni conciliazione proposta dal Gesuita collega del <lb/>Sarsi, esce fuori nel <emph type="italics"/>Saggiatore<emph.end type="italics"/> contro lo stesso Sarsi, e rompe i cancelli <lb/>dei Pitagorici, proseguendo a sostener che il moto della Cometa non si fa <lb/>in un'orbita simile a quella de'Pianeti, o in eccentrici ed epicicli, ma in <lb/>linea retta dal centro della Terra, e rompe anche insieme i cancelli de'Pe&shy;<lb/>ripatetici, affermando che l'esalazioni terrestri non son trattenute dal con&shy;<lb/>cavo della Luna, ma penetrano attraverso al cielo liberamente, sublimandosi <lb/>nelle sue pi&ugrave; alte regioni. </s></p><p type="main">

<s>Il <emph type="italics"/>Saggiatore<emph.end type="italics"/> di Galileo, in parecchie esperienze e speculazioni, ricom&shy;<lb/>pensava la Fisica degli sfregi, che veniva facendo all'Astronomia; sfregi, che <lb/>liberamente riconosciuti e confessati dai discepoli, si pens&ograve; da essi sapien&shy;<lb/>temente, per onor della scienza e della scuola italiana, ad emendarli. </s>

<s>Si dee <lb/>un tal pensiero principalmente al Borelli, il quale intanto che meditava di <lb/>ridurre il sistema pitagorico delle Comete, non solo alla maggior probabi&shy;<lb/>lit&agrave; di una opinione, ma alla certezza di una dimostrazione, chiamava da una <lb/>parte a collaborare all'opera, e dall'altra ad apparecchiarsi le vie uno de'suoi <lb/>discepoli pi&ugrave; valorosi, Alessandro Marchetti. </s>

<s>Di ci&ograve;, che questi allora intorno <lb/>a quel soggetto operava, dava il Borelli stesso parte da Pisa al principe Leo&shy;<lb/>poldo per lettera del di 27 Aprile 1665. &ldquo; Intanto d&ograve; parte a V. A. S. come <lb/>il dottor Marchetti sta scrivendo un Trattato filosofico della Cometa, in lin&shy;<lb/>gua toscana, molto elegante ed erudito &rdquo; (MSS. Cim., T. XVIII, c. </s>

<s>171). </s></p><p type="main">

<s>Questo trattato filosofico del Marchetti si legge autografo da c. </s>

<s>53-71 <lb/>del Tomo XIV del Cimento, in un fascicolo, a cui &egrave; premessa una carta <lb/>bianca coll'occhietto: <emph type="italics"/>Dottor Marchetti, Sulle Comete, Scrittura.<emph.end type="italics"/> &Egrave; divisa <lb/>questa scrittura in capitoli, nel I de'quali si tratta &ldquo; Dei varii nomi delle <pb xlink:href="020/01/1070.jpg" pagenum="513"/>Comete, e delle loro derivazioni. </s>

<s>&rdquo; Nel Cap. </s>

<s>II &ldquo; Delle varie opinioni intorno <lb/>alla natura ed essenza loro &rdquo; e vi si cita fra le altre, per confutarla, l'opi&shy;<lb/>nione dei Pitagorici. </s>

<s>Nel Cap. </s>

<s>VI &ldquo; si riferisce l'opinione di Aristotile e dei <lb/>seguaci e diligentemente esaminandola si convince di falsit&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>L'opinione di Aristotile, confutata gi&agrave; con ampia eloquenza nel <emph type="italics"/>Sag&shy;<lb/>giatore,<emph.end type="italics"/> &egrave; dal Marchetti riferita nella forma seguente: &ldquo; Abbiamo finora, s'io <lb/>non m'inganno, sufficientemente provato contro agli antichi che le Comete <lb/>non siano uno ne'pi&ugrave; Pianeti. </s>

<s>Tempo &egrave; dunque che, scendendo dal cielo fra <lb/>gli elementi, esaminiamo il parere di Aristotile e dei seguaci, che le cre&shy;<lb/>dettero abbruciamenti di terrestri esalazioni. </s>

<s>Egli dunque, imitando forse <lb/>Senofane, e per relazione di Seneca e di Epigene alcuni Stoici e Caldei, si <lb/>persuase che la Cometa altro non fosse che una esalazione terrena solle&shy;<lb/>vata, da qualunque se ne sia la cagione, fino alla concava superficie della <lb/>Sfera lunare, che di materia simile &egrave; sempre piena, e da essa rapidissima&shy;<lb/>mente portata in giro, onde tribbiandosi per la velocit&agrave; del moto e, per cos&igrave; <lb/>dire, sminuzzandosi e stritolandosi le sue parti, ne concepisca calore e final&shy;<lb/>mente si accenda, in quella guisa, dice egli, che per la stessa cagione veg&shy;<lb/>ghiamo liquefarsi per aria il piembo di quelle frecce, che da gagliardo ar&shy;<lb/>ciere vengon vibrate &rdquo; (c. </s>

<s>65). </s></p><p type="main">

<s>Riferisce poi nel Cap. </s>

<s>VII l'opinion del Cartesio, che cio&egrave; non sieno le <lb/>Comete altro che Stelle fisse rimosse a viva forza dalle loro sedi, e scagliate <lb/>con violenza in varie parti; opinione da nominarsi piuttosto &ldquo; sogno d'in&shy;<lb/>fermi o fola di romanzi, che filosofica speculazione &rdquo; (c. </s>

<s>67). L'ultimo capi&shy;<lb/>tolo che &egrave; l'VIII &egrave; riserbato a riferire l'opinione propia dell'Autore, e con&shy;<lb/>tiene la parte, che pi&ugrave; importa a noi, s&igrave; per la conclusione a cui tendiamo, <lb/>e s&igrave; per esservi riferite opinioni, che si sollevano al di sopra delle idee co&shy;<lb/>muni a que'tempi. </s></p><p type="main">

<s>&ldquo; Io dunque, scrive il Marchetti, avendo prima bene osservato con gli <lb/>occhi propri tutti i particolari accidenti delle due moderne Comete, ed oltre <lb/>a ci&ograve; attentissimamente, e con somma diligenza, esaminato intorno a cotal <lb/>materia gli scritti altrui, mi sono finalmente stabilito nell'animo questo pa&shy;<lb/>rere: cio&egrave; che, per investigare la loro natura, non sia punto sicuro lo allon&shy;<lb/>tanarsi pur di un iota da quel tanto, che lasci&ograve; scritto, nel suo eruditissimo <lb/>ed elegantissimo Discorso accademico, il signor Mario Guiducci gentiluomo <lb/>fiorentino, e che fu prima speculato, e poi difeso contro al Sarsi nel <emph type="italics"/>Sag&shy;<lb/>giatore,<emph.end type="italics"/> con dottrina ed eloquenza cos&igrave; mirabile, dal nostro gran Galileo. </s>

<s>Il <lb/>perch&egrave; stimo insieme con esso lui che, ritrovandosi unita insieme, in parte <lb/>dove non giunge l'ombra piramidale del nostro Globo, una materia, qua&shy;<lb/>lunque ella si sia, non del tutto trasparente, come il restante dell'etere e <lb/>dell'aria che la circonda, n&egrave; anco affatto opaca, come la Terra, la Luna e <lb/>tutti gli altri Pianeti, ed essendo questa percossa dai luminosi raggi del Sole, <lb/>parte di essi come opaca agli occhi nostri rifletta, onde il corpo si scorga <lb/>della Cometa, e ad altra parte come trasparente conceda libero passo, e gli <lb/>refranga, onde sia formata la coda. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/1071.jpg" pagenum="514"/><p type="main">

<s>&ldquo; &Egrave; il vero che, acciocch&egrave; questa da noi si vegga, non basta che i detti <lb/>raggi che si refrangono si diffondano nell'aer puro, o per l'etere limpidis&shy;<lb/>simo, ma &egrave; necessario che incontrino ancora essi qualche materia, dalla quale <lb/>siano ripercossi. </s>

<s>Per la qual cosa immaginossi il Keplero, gran Filosofo ed <lb/>Astronomo del suo tempo, ed amico cordialissimo dello stesso Galileo, che <lb/>gli stessi raggi solari, penetranti per il corpo della Cometa, ne limino per <lb/>cos&igrave; dire continuamente, e portin seco alcune piccole particelle, dalle quali <lb/>e'sian riflessi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Alcuni altri si sono creduti che la materia stessa, che da principio <lb/>si adun&ograve; insieme, vada da s&egrave; medesima separandosi, sfumandone di mano <lb/>in mano le parti pi&ugrave; sottili per ogni banda, delle quali non pertanto quelle <lb/>solamente ci sian visibili, che si trovano opposte al Sole, per esser tutte <lb/>l'altre disperse, quasi in un subito, e per l'etere dissipate dal suo gran <lb/>lume: e v'ebbe ancora chi, senza ammettere per necessaria alcuna interna <lb/>dissipazione, si pens&ograve; nondimeno di potere agevolmente salvare il tutto, figu&shy;<lb/>randosi in quella vece che, nell'unirsi insieme, mediante la simpatia loro <lb/>scambievole, le sue parti, cospirando a formare un globo e perci&ograve; premen&shy;<lb/>dosi l'una l'altra e pi&ugrave; e pi&ugrave; calcandosi verso il centro, faccian quivi le <lb/>pi&ugrave; vicine un quasi nocciolo molto denso, intorno al quale vadano poi va&shy;<lb/>gando le pi&ugrave; lontane e meno compresse, non altrimenti che far veggiamo <lb/>a'nuovi sciami delle api, il principe delle quali, appena su qualche ramo <lb/>d'albero arresta il volo, che la maggior parte di esse in un subito gli si <lb/>addossano, mentre il restante, qua e l&agrave; svolazzando, d'ogni intorno gli fan <lb/>corona. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di queste opinioni qual sia la migliore io al presente non mi curo <lb/>di esaminare, stimandole ugualmente tutte probabili, tutte belle, tutte de&shy;<lb/>gne veramente di quei grandi uomini che l'inventarono, n&egrave; avendo per av&shy;<lb/>ventura alcuna difficolt&agrave; di ammetterle per vere tutt'e tre insieme. </s>

<s>Ma, co&shy;<lb/>munque si stia la cosa, a me basta che il Lettore resti avvertito ch'io non <lb/>suppongo che la coda della Cometa sia una semplice refrazione, come poco <lb/>avvedutamente fece il Cardano, da noi perci&ograve; ragionevolmente nel Cap. </s>

<s>VI <lb/>confutato, ma congiungo con essa la riflessione, senza la quale al certo non <lb/>si vedrebbe &rdquo; (c. </s>

<s>70, 71). </s></p><p type="main">

<s>Bench&egrave; protesti il Marchetti, in riferir questa sua opinione delle Co&shy;<lb/>mete, di non dilungarsi un iota dal Guiducci, n&egrave; perci&ograve; da Galileo, se ne <lb/>dilunga per&ograve; sostanzialmente, supponendo che la materia atta a riflettere il <lb/>lume del Sole, e a dar cos&igrave; l'apparenza del nucleo e della coda, non sia <lb/>parte delle fumosit&agrave; terrestri, ma dell'etere preesistente nelle alture de'cieli. </s>

<s><lb/>Cos&igrave; veniva ad emendare uno de'pi&ugrave; gravi, e diciamolo francamente de'pi&ugrave; <lb/>vergognosi errori, che contenesse in s&egrave; l'ipotesi galileiana, e bench&egrave; qui <lb/>non faccia nessun cenno l'Autore di questa sua intenzione, non lasci&ograve; poi <lb/>di dichiararla apertamente, quando, ampliatane la materia, fu la prima scrit&shy;<lb/>tura manoscritta ridotta in forma di Lettera a Francesco Redi, e nel 1684, <lb/>in Firenze, stampata. </s></p><pb xlink:href="020/01/1072.jpg" pagenum="515"/><p type="main">

<s>Ivi, verso la fine, dop'aver concluso non poter le Comete esser pro&shy;<lb/>dotte da aliti terrestri, si rivolge a confutar cos&igrave; la contraria opinione di <lb/>Galileo: </s></p><p type="main">

<s>&ldquo; O voi, signor Galileo, contro a quello che voi vi siete lasciato inten&shy;<lb/>dere ne'vostri Dialoghi, giudicate la Terr&agrave; essere immobile, e quasi centro <lb/>dell'universo, o voi la credete mobile intorno all'asse, e intorno al Sole. </s>

<s>Se <lb/>immobile, per tacere che voi a voi medesimo contradite, e come volete voi <lb/>salvare il moto diurno delle Comete, mediante il quale elleno, nel breve spa&shy;<lb/>zio di un giorno solo naturale, si raggirano intorno a essa Terra da oriente <lb/>movendosi verso occidente, e di nuovo tornando nell'oriente? </s>

<s>&rdquo; <lb/>&hellip; </s></p><p type="main">

<s>&ldquo; Egli fa dunque pur di mestieri che voi dichiarate che essa Terra sia <lb/>quella, alla quale compete almeno il diurno rivolgimento. </s>

<s>Ma non vi sov&shy;<lb/>viene egli di averci altrove avvertito, cio&egrave; in quella vostra divina Opera dei <lb/>due Massimi sistemi, che le materie che son parti di qualche globo, che si <lb/>muova circolarmente, non ponno, bench&egrave; staccate dal loro tutto, muoversi <lb/>di altro moto che circolare? </s>

<s>Certo si dee sovvenirvi, conciossiach&egrave; questo &egrave; <lb/>l'unico fondamento, al qual si appoggia la dottrina de'Pitagorici, da voi con <lb/>tanta altezza d'ingegno, con tanta finezza di giudizio, e con tanta profon&shy;<lb/>dit&agrave; e singolarit&agrave; di dottrina, per la pi&ugrave; ragionevole, sostenuta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma se questo &egrave; vero, com'&egrave; verissimo, adunque, ancorch&egrave; possa per <lb/>avventura difendersi come probabile che alcuna Cometa nel mentovato modo <lb/>si producesse, certo che voi ci&ograve; difendere in niun modo non potete, senza <lb/>incorrere in manifeste contradizioni e repugnanze alle pi&ugrave; salde dottrine di <lb/>voi medesimo &rdquo; (pag. </s>

<s>86, 87). </s></p><p type="main">

<s>Noi abbiamo altrove dimostrato coi fatti che le dottrine di Galileo erano <lb/>anzi da questa parte assai vacillanti, non avendo egli penetrato il vero di <lb/>quella Filosofia magnetica, nella quale unicamente ritrovavasi a quelle stesse <lb/>dottrine la saldezza. </s>

<s>Ma non pare in ogni modo credibile che l'Autor del <lb/><emph type="italics"/>Saggiatore<emph.end type="italics"/> non sentisse quelle contradizioni rinfacciategli poi cos&igrave; libera&shy;<lb/>mente dal Marchetti; contradizioni, ch'erano quelle medesime, in che s'era <lb/>vent'anni prima aggirato lo stesso Galileo, nel Discorso che s'apparecchiava <lb/>a distendere sull'origine della Stella nuova. </s></p><p type="main">

<s>S'era fin d'allora, per salvarsi da quelle contradizioni, offerto il partito <lb/>a cui poi, rispetto alle Comete, s'attenne il Marchetti, e infatti Ticone e <lb/>altri insieme con lui avevano ritrovato in Galassia, a somministrar la ma&shy;<lb/>teria a quelle vagabonde apparenze celesti, una ricca miniera. </s>

<s>Dicemmo per <lb/>quali ragioni Galileo rifiutasse questa ipotesi, rifiutata gi&agrave; dal Keplero, il <lb/>quale pensava essere atta a ingenerar nuove Stelle e nuove Comete qualun&shy;<lb/>que parte del cielo. </s>

<s>&ldquo; Itaque potius in eo sum, ut credam coelum unde&shy;<lb/>quaque aptum ad materiam hisce sideribus praebendam &rdquo; (De Stella nova <lb/>cit., pag. </s>

<s>112). </s></p><p type="main">

<s>Aveva il suo fondamento questa ipotesi kepleriana in quelle macchie <lb/>biancheggianti, che qua e l&agrave; si vedevano variamente disperse per gli spazii <pb xlink:href="020/01/1073.jpg" pagenum="516"/>celesti, e alle quali si dava il nome di <emph type="italics"/>Nebulose.<emph.end type="italics"/> Si mostr&ograve; Galileo intorno <lb/>a ci&ograve; ritroso di seguitare il Keplero, perch&egrave; pensava delle Nebulose quel che <lb/>del Circolo latteo gli riferiva Plutarco, che cio&egrave; &ldquo; sia, secondo Democrito, <lb/>un unito splendore di molte minute stelle vicine l'una all'altra, che per la <lb/>spessezza rilucano insieme &rdquo; (Opus. </s>

<s>e Tomo cit., pag. </s>

<s>247); pensiero dal&shy;<lb/>l'altra parte introdotto nella scienza italiana dal divino canto dell'Alighieri <lb/>(Par., C. XIV, t. </s>

<s>33). </s></p><p type="main">

<s>Quando poi il Canocchiale lo rese certo non essere altro veramente Ga&shy;<lb/>lassia &ldquo; quam innumerarum Stellarum coacervatim consitarum congeries &rdquo; <lb/>(Alb. </s>

<s>III, 76), e le Nebulose &ldquo; Stellarum constipatarum coetum &rdquo; (ibi), e <lb/>allora si conferm&ograve; pi&ugrave; saldamente Galileo nella sua opinione non poter cio&egrave; <lb/>quella materia di gi&agrave; informata trasformarsi a comporre o Stelle nuove o <lb/>Comete. </s></p><p type="main">

<s>Si sono alcuni maravigliati che Galileo discorra in tal sentenza delle <lb/>Nebulose da far creder che tutte sieno allo stesso modo risolubili, come il <lb/>Circolo latteo, o il Capo di Orione, o il Presepe, e ne hanno concluso non <lb/>dover avere egli mai osservato le vere Nebulose non risolubili in Stelle. </s>

<s>La <lb/>conclusione per&ograve; &egrave; prepostera, perch&egrave;, essendosi abbattuto Galileo ad osser&shy;<lb/>var tali macchie albescenti nel cielo, piuttosto che crederle materia informe <lb/>pens&ograve; che rimanessero irresolubili, non per s&egrave;, ma per la debolezza del suo <lb/>Canocchiale. </s>

<s>E fu questo il pensiero che lo salv&ograve; dalle illusioni, che si fe&shy;<lb/>cero altri Astronomi dopo di lui. </s></p><p type="main">

<s>L'Huyghens, nel 1656, osserv&ograve; nella spada di Orione risplendere quat&shy;<lb/>tro stelle <emph type="italics"/>velut trans nebulam,<emph.end type="italics"/> la qual nebbia celeste in tre anni non mut&ograve; <lb/>sembianza. </s>

<s>Annunzi&ograve; questo fenomeno <emph type="italics"/>a nemine hucusque, quod sciam, <lb/>animadversum,<emph.end type="italics"/> nel <emph type="italics"/>Systema Saturnium,<emph.end type="italics"/> dove concludeva esser la nuova <lb/>nebulosa di Orione di natura diversa dalle altre nebulose fino allora osser&shy;<lb/>vate. </s>

<s>&ldquo; Nam caeterae Nebulosae olim existimatae, atque ipsa Via lactea, <lb/>perspicillo inspectae, nullas nebulas habere comperiuntur, neque aliud esse <lb/>quam plurium Stellarum congeries et frequentia &rdquo; (In oper. </s>

<s>var. </s>

<s>cit., Vol. </s>

<s>II, <lb/>pag. </s>

<s>541). </s></p><p type="main">

<s>Si tenne dagli Astronomi, questa descritta dall'Huyghens, per la prima <lb/>scoperta fra le Nebulose cos&igrave; dette <emph type="italics"/>diffuse,<emph.end type="italics"/> ma Telescopii pi&ugrave; squisiti mo&shy;<lb/>strarono ch'era anch'essa, almeno in parte, risolubile come le altre, lasciando <lb/>i pi&ugrave; assennati in una grande incertezza se quella, che apparisce in cielo <lb/>materia informe, sia veramente tale, oppure ci apparisca cos&igrave;, per non es&shy;<lb/>sere gli strumenti, anche pi&ugrave; perfetti che si sieno saputi fabbricare, atti a <lb/>rivelarci cose, che son da noi tanto remote. </s></p><p type="main">

<s>Dietro cos&igrave; fatte considerazioni s'intende come fosse prudente consiglio <lb/>quello di Galileo del non volere ammettere, col Keplero, che le Stelle nuove <lb/>e le Comete siano ingenerate di materia celeste, ma non pu&ograve; per&ograve; scusarsi <lb/>degli errori, in che egli cadde speculando di tali soggetti; errori del grave <lb/>danno de'quali, come ora vedremo, fu largamente in Italia ristorata la scienza <lb/>astronomica per opera del Borelli. </s></p><pb xlink:href="020/01/1074.jpg" pagenum="517"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Gli errori detti intorno alle Comete, da noi sopra narrati, dipendevano <lb/>dall'essersi smarrite le tradizioni dell'antica scuola pitagorica italiana, alle <lb/>quali sapientemente tornava il Borelli in un suo Trattatello, incominciato a <lb/>scrivere in Pisa negli ultimi giorni del Gennaio 1665, terminato ivi il d&igrave; 10 <lb/>del Febbraio appresso, e pubblicato in forma di lettera al padre Stefano An&shy;<lb/>geli, sotto il finto nome di Pier Maria Mutoli, col titolo: <emph type="italics"/>Del moto della Co&shy;<lb/>meta apparsa il mese di Dicembre 1664.<emph.end type="italics"/></s></p><p type="main">

<s>Pu&ograve; distinguersi il Trattatello in tre parti: nella prima, nella quale, ac&shy;<lb/>cennandosi alla generazione delle Comete, si rifiutano le opinioni del Gui&shy;<lb/>ducci e di Galileo con tutti gli altri loro seguaci, che dicevano essere quegli <lb/>insoliti splendori esalazioni terrestri illuminate dal Sole, e anche talvolta dai <lb/>circostanti Pianeti. </s>

<s>Nella seconda, nella quale, volendosi rendere la ragione <lb/>de'moti osservati nelle Comete, si prova che non si possono intendere quegli <lb/>stessi moti in altro sistema diverso dal copernicano, dall'Autore chiamato <lb/>col nome di pitagorico. </s>

<s>Nella terza, nella quale si dimostra, per mezzo di <lb/>osservazioni simultanee fatte in luoghi diversi, che mancando la Cometa di <lb/>sensibile parallasse non pu&ograve;, come il Guiducci e Galileo dicevano, costituirsi <lb/>nella region sullunare. </s>

<s>E perch&egrave; l'argomento della parallasse era infirmato <lb/>da'peripatetici e segnatamente dal Chiaramonti e dal Riccioli, i quali dice&shy;<lb/>vano quell'argomento illusorio per essere le Comete vagabonde nel cielo, il <lb/>Borelli propone il metodo delle due osservazioni contemporanee, che non la&shy;<lb/>sciavano a'sani giudizi luogo a dubitare. </s></p><p type="main">

<s>Cos&igrave; veniva il Mutoli a sollevar le Comete, con gli antichi Pitagorici, <lb/>all'essere e alla dignit&agrave; degli altri Pianeti. </s>

<s>Non s'era per&ograve; pronunziato an&shy;<lb/>cora intorno al decider della linea de'loro moti, ci&ograve; che rende forse la ra&shy;<lb/>gione del non essere le rinnovate dottrine riuscite colla piena approvazione <lb/>degli Astronomi. </s>

<s>S'aggiungeva il non essersi avvertito il loro ritorno, ci&ograve; <lb/>che serviva a molti d'argomento per confermarsi nella loro opinione non <lb/>essere le Comete altro che vane e transitorie apparenze, alle quali non si <lb/>potesse prescrivere un'orbita come ai Pianeti. </s>

<s>S'era all'efficacia di un tale <lb/>argomento principalmente piegato Seth Ward, il quale, addetto all'ipotesi <lb/>di Ticone, vedendo non potersi collocar le Comete nel medesimo cerchio, <lb/>per avere alcune i loro moti da levante a ponente, e altre da un polo al&shy;<lb/>l'altro, immagin&ograve; tanti cerchi massimi intorno al Sole, quante sono in nu&shy;<lb/>mero le stesse Comete, e cos&igrave; supponeva farsi nel loro epiciclo una infles&shy;<lb/>sione e variazione de'Nodi, come una loro propriet&agrave; distinta da quella di <lb/>tutti gli altri Pianeti. </s></p><p type="main">

<s>L'ipotesi del Ward fu approvata poi dall'Auzout, e il Cassini la modi&shy;<lb/>fic&ograve; alquanto, per ridurla al suo nuovo sistema. </s>

<s>Il Cassini era pure nel nu-<pb xlink:href="020/01/1075.jpg" pagenum="518"/>mero di coloro che, lontani dal sospettare il ritorno di una Cometa identica <lb/>e permanente nell'esser suo, s'era confermato nell'idea che fossero tutte <lb/>le Comete evanescenti come quelle che pigliavan sostanza dalle esalazioni <lb/>della nostra Terra. </s>

<s>Primo a speculare intorno ai fenomeni della Luce zodia&shy;<lb/>cale, e a dimostrar ch'ell'era dovuta a un anello di materia cosmica, illu&shy;<lb/>minato dal Sole, pens&ograve; il Cassini, accostandosi col Ward, che un simile <lb/>anello di materia terrestre, e flessibile ne'suoi Nodi, circolasse intorno al <lb/>nostro Globo, e presentasse ora il fenomeno di una, ora di altra Cometa, <lb/>secondo ohe un punto o l'altro di esso anello interrotto rifletteva alla nostra <lb/>vista i raggi del Sole. </s></p><p type="main">

<s>Di un tal sistema cometario del Cassini cos&igrave; il Borelli scriveva il suo <lb/>parere al principe Leopoldo: &ldquo; Circa la teoria della Cometa, che egli (il <lb/>Cassini) pretende aver ritrovata, mi pare che sia nna cosa molto faticosa e <lb/>imbrogliata, dalla quale alla fine poco frutto ed utile se ne cava, il che mi <lb/>pare che egli faccia appostatamente, per mostrar che la sua teoria dell'epi&shy;<lb/>ciclo variabile e flessibile non l'abbia tolta da Seto Wardo inglese &rdquo; (Fab&shy;<lb/>broni, Lett. </s>

<s>cit., T. I, pag. </s>

<s>121). Il Borelli stesso ebbe, poco dopo la pub&shy;<lb/>blicazione della Lettera del Mutoli, una polemica alquanto acerba coll'Auzout, <lb/>il quale andava pure professando l'ipotesi ticoniana modificata, o come di&shy;<lb/>cevasi, perfezionata dal Wardo. </s></p><p type="main">

<s>In quella stessa Lettera del Mutoli non erasi ancora il Borelli, come <lb/>dicemmo, pronunziato intorno alla linea del moto della Cometa, ma poi ri&shy;<lb/>pensando ch'era questo uno de'punti pi&ugrave; vitali della nuova teoria cometa&shy;<lb/>ria, si volse a speculare, aiutandosi de'calcoli e delle esperienze, intantoch&egrave;, <lb/>ai primi di Maggio, che vuol dir dopo tre mesi ch'era stata pubblicata la Let&shy;<lb/>tera del finto Mutoli, cos&igrave; scriveva al principe Leopoldo, da Pisa: &ldquo; Parmi <lb/>primieramente che il vero e real movimento della presente Cometa non possa <lb/>essere in niun conto fatto per linea retta, ma per una curva, tanto simile <lb/>a una parabola, che &egrave; cosa da stupire, e questo non solo lo mostra il cal&shy;<lb/>colo, ma ancora un'esperienza meccanica, che far&ograve; vedere a V. A. al mio <lb/>arrivo a Firenze &rdquo; (ivi, pag. </s>

<s>131). </s></p><p type="main">

<s>Un altro libro del Cassini, in proposito della Cometa, e nel quale veni&shy;<lb/>vansi dall'Autore a professare dottrine alquanto diverse dalle prime, bench&egrave; <lb/>sempre fondate sull'ipotesi dell'epiciclo flessibile, sollecitarono la partenza <lb/>del Borelli da Pisa, e una settimana dopo tornava a scrivere al Principe <lb/>nella seguente maniera: &ldquo; Mi giunge il libro del signor Cassini, il quale mi <lb/>tira di nuovo alla speculazione della Cometa, perch&egrave; egli, soverchiamente <lb/>invaghito dell'epiciclo vastissimo, che attribuisce alla Cometa passata, vo&shy;<lb/>lendo che ella si rivolga intorno alla Canicola, si compiace anche di toccare <lb/>qualche cosetta dell'Epistola del Mutoli; cosa che ne poteva far di meno, <lb/>avendo poca ragione. </s>

<s>Per&ograve; dubito che sar&agrave; bisogno entrare di nuovo in questa <lb/>materia, e scriver qualche altra cosa, forse in occasione di spiegar la figura <lb/>della linea del moto reale della Cometa presente, e penso d'indirizzarla al <lb/>signor Bullialdo, spiegando con figure tutte le cose conforme egli desidera. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/1076.jpg" pagenum="519"/><p type="main">

<s>&ldquo; Per questo bisogner&agrave; affrettar la mia partenza da Pisa, qualche giorno <lb/>prima di quello ch'io pensava, per potermi quietamente porre a travagliare, <lb/>e liberarmi presto dai pensieri e disturbi della partenza. </s>

<s>Per&ograve; supplico V. A. <lb/>che si compiaccia concedermi licenza di potermene venir, prima di Pasqua <lb/>(di Pentecoste), giacch&egrave; qui da ora innanzi in ogni modo la mia stanza, per <lb/>servigio dello Studio, &egrave; infruttuosa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di pi&ugrave;, avendo io commesso a diversi amici che mi trovassero qual&shy;<lb/>che villuccia vicino alla citt&agrave;, oppur qualche casa sulla Costa a S. Giorgio, <lb/>non &egrave; stato finora possibile conseguire n&egrave; l'una n&egrave; l'altra. </s>

<s>Questo lo desi&shy;<lb/>deravo io, non solo per liberarmi da quei martelli e strepiti, che si sentono <lb/>dalle stanze di Palazzo Vecchio, nelle quali poco si pu&ograve; dormire e meno stu&shy;<lb/>diare e speculare, ma anche l'avevo caro, per potere scoprire il cielo e poter <lb/>fare qualche osservazione. </s>

<s>Questo bisogno ora si accresce, comparendo la <lb/>Cometa prima del levare del Sole, la quale desidererei, se fosse possibile, <lb/>continuare ad osservare colla Macchina grande, che ultimamente ho fab&shy;<lb/>bricata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Son dunque costretto di ricorrere al favore di V. A. S., e perch&egrave; io <lb/>non so se questo che mi &egrave; stato anteposto, sia impertinenza e temerit&agrave;, per&ograve; <lb/>lo propongo con le debite riserve, cio&egrave;, quando non sia domanda sproposi&shy;<lb/>tata, perch&egrave;, in altra maniera, sia per non detto. </s>

<s>Mi dicono esservi la For&shy;<lb/>tezza di S. Miniato, e quivi vicino il Convento dei padri zoccolanti, dai quali <lb/>luoghi si scopre l'orizzonte orientale, e mi dicono che ambedue sono copiosi <lb/>di stanze vacue, ma nella Fortezza non so se sia lecito, nel Convento mi <lb/>sarebbe scomodo, non potendo avere il servigio della mia serva &rdquo; (MSS. Gal., <lb/>Filze Nelli, A, B, c. </s>

<s>391). </s></p><p type="main">

<s>Il principe Leopoldo dette generosamente al Borelli licenza di andare <lb/>nella Fortezza di S. Miniato, ch'ebbe l'onore di essere trasformata in una <lb/>delle prime Specule, che fossero per le osservazioni celesti state erette in <lb/>Italia. </s>

<s>Il nuovo Astronomo la corred&ograve; d'importanti strumenti, fra'quali la <lb/>gran Macchina, di che l'abbiamo inteso parlare, e che consisteva in un Se&shy;<lb/>stante di cinque braccia di raggio, costruito di regoli di legno, e che si de&shy;<lb/>scrive a tergo della c. </s>

<s>368 nella Filza citata. </s></p><p type="main">

<s>Quel che pi&ugrave; per&ograve; al presente proposito importa, &egrave; che, ad una parete <lb/>di quelle stanze di S. Miniato, fu applicato lo strumento a dimostrare spe&shy;<lb/>rimentalmente il corso parabolico della Cometa, com'&egrave; attestato dallo stesso <lb/>Borelli in queste parole, che il d&igrave; 2 Aprile 1667 indirizzava al principe Leo&shy;<lb/>poldo da Pisa, prima di abbandonar la Toscana, per tornarsene alla sua patria <lb/>Messina. </s>

<s>&ldquo; E perch&egrave; vado disponendo pian piano le cose per la partenza, <lb/>che non potr&agrave; essere prima di mezzo Maggio, ho pensato di offrire a V. A. <lb/>alcuni Strumenti e Macchine astronomiche, che stanno riposte nelle stanze <lb/>della Fortezza di S. Miniato, dove particolarmente vi &egrave; quella, che rappre&shy;<lb/>senta al vivo la via parabolica che fece la prima Cometa di quelle ultime <lb/>che comparirono. </s>

<s>Vero &egrave; che, per essere fermamente accomodata al muro <lb/>d'una delle dette stanze, vi sar&agrave; difficolt&agrave; al trasportarla in altro luogo, per&ograve; <pb xlink:href="020/01/1077.jpg" pagenum="520"/>sar&agrave; bisogno che non la faccia toccare, prima che arrivino i dottori Marchetti <lb/>e Bellini, i quali sono informati del modo come si dovr&agrave; assettare &rdquo; (MSS. <lb/>Cim., T. XIX, c. </s>

<s>18). </s></p><p type="main">

<s>Ora il desiderio nostro e de'nostri lettori sarebbe quello di aver par&shy;<lb/>ticolarmente descritta quella macchina per l'esperienza della Cometa, ma non <lb/>si pu&ograve; averne sodisfazione, perch&egrave; la macchina stessa dee essere andata <lb/>dispersa, e non se ne trova, per quel che si sappia da noi, negli scritti, me&shy;<lb/>moria. </s>

<s>Si sperava che il Marchetti ne dicesse qualche cosa in proposito, o <lb/>nel Discorso manoscritto o nella Lettera stampata, ma non se ne trova per <lb/>verit&agrave; fatto alcun cenno, essendo ci&ograve; dall'altra parte alieno dal suo istituto, <lb/>ch'era quello di confutare il sistema pitagorico. </s></p><p type="main">

<s>Intanto, nella mancanza di dati certi, non ci siamo rimasti di far qual&shy;<lb/>che uso di congetture, per fondamento delle quali abbiamo prese quelle no&shy;<lb/>tizie, che si son potute raccogliere, e fra le quali &egrave; da far primo conto di <lb/>quella, che ci assicura essere stato il Borelli scorto a concludere la sua teo&shy;<lb/>ria cometaria da'calcoli e dalle esperienze. </s>

<s>I calcoli non potevano esser cer&shy;<lb/>tamente condotti se non che sopra i teoremi gi&agrave; conosciuti della Meccenica, <lb/>per cui, se doveva la Cometa descrivere per sua orbita una Parabola, con&shy;<lb/>veniva riguardarla come soggetta all'azione di due forze, una diretta verso <lb/>il centro, e l'altra rifuggente dal centro stesso, in direzion tangenziale. </s></p><p type="main">

<s>Se avesse il Borelli, come udimmo, mantenuto il proposito di tornare <lb/>a trattar della Cometa in un'altra scrittura, ch'ei voleva indirizzare al Bul&shy;<lb/>lialdo, si sarebbe l&igrave; veduta spiegar, per mezzo dell'esperienza, la figura della <lb/>linea del moto, ma sembra che quella scrittura non avesse poi dall'Autore <lb/>il suo effetto. </s>

<s>Il di 27 Aprile 1665 scriveva al principe Leopoldo: &ldquo; Quelle <lb/>parole del signor Bullialdo mi hanno stuzzicato a fare una mano di propo&shy;<lb/>sizioni, per render ragione del movimento della Cometa secondo l'ipotesi <lb/>pitagorica, le quali ho brevemente notato in scritto, per servirmene se far&agrave; <lb/>bisogno &rdquo; (MSS. Cim., T. XVIII, c. </s>

<s>171). Forse il bisogno non si present&ograve;, <lb/>e le proposizioni, che si dovevano dimostrar coi calcoli e con l'esperienze, <lb/>rimasero nella mente del loro Autore, o per meglio dire non presero quella <lb/>forma di scrittura diretta al Boulliaud, com'era stata la prima intenzione. </s></p><p type="main">

<s>Quanto ai calcoli non &egrave; stata difficile la <lb/>congettura: quanto alle esperienze poi noi <lb/>richiamiamo l'attenzione dei nostri lettori <lb/>sopra quella insigne cos&igrave; descritta nel II li&shy;<lb/>bro delle Theoricae Mediceorum. </s>

<s>&ldquo; Sumatur <lb/><figure id="id.020.01.1077.1.jpg" xlink:href="020/01/1077/1.jpg"/></s></p><p type="caption">

<s>Figura 101. circulus ligneus ABC (fig. </s>

<s>101) cui diameter <lb/>aptetur pariter linea AB eius vero centro D <lb/>aptetur axiculus seu virga DE plano circuli <lb/>ABC erecta, ac eidem centro D apponatur <lb/>portio aliqua Magnetis F, cuius polus meri&shy;<lb/>dionalis respiciat punctum A. </s>

<s>Deinde haec <lb/>omnia ita composita innatent in aqua sta-<pb xlink:href="020/01/1078.jpg" pagenum="521"/>gni RS. </s>

<s>In G autem adsit portio aliqua suberis supra quam sit globulus <lb/>aliquis ferreus I. </s>

<s>Possit autem huiusmodi suber simul cum ferreo globulo <lb/>supposito libere natare in ipsa aqua. </s>

<s>Deinde vero suber praedictum G admo&shy;<lb/>veatur magneti F, quousque incidat in sphaeram activitatis eiusdem Magne&shy;<lb/>tis, usque scilicet ad eum situm, ex quo ipse ferreus globulus incipit lente <lb/>approprinquari ipsi Magneti. </s>

<s>Tunc vero manu orizontaliter circumgiretur <lb/>extremum punctum E ipsius virgae &rdquo; (Florentiae 1665, pag. </s>

<s>48). E propone <lb/>che si giri con tale velocit&agrave;, che la forza centrifuga contemperi l'attrazione <lb/>magnetica. </s>

<s>Si vedr&agrave; cos&igrave;, dice l'Autore, girare la palla di ferro intorno al <lb/>Magnete, come intorno al suo centro, bench&egrave; non sia fisicamente congiunta <lb/>con esso. </s></p><p type="main">

<s>Passa in seguito il Borelli a dir come si potrebbe rendere anche pi&ugrave; <lb/>semplice l'esperienza, rimovendo il Magnete, e facendo che la palla di ferro, <lb/>o di qualunque altra materia, sia impedita di scendere per natural gravit&agrave; <lb/>al centro del circolo di legno, e rimanga sospesa nella scanalatura del rag&shy;<lb/>gio, per la forza centrifuga eccitatavi dal rapidissimo moto. </s>

<s>Dietro le quali <lb/>esperienze poi cos&igrave; conclude: &ldquo; Quapropter si eodem modo concipiamus in <lb/>spatio aethereo Planeta in G (fig. </s>

<s>preced.) qui naturalem habeat instinctum <lb/>approprinquandi soli D, simulque in orbem feratur circa idem solare cen&shy;<lb/>trum tali celeritate, quae sufficiat ad removendum Planetam, praecise tan&shy;<lb/>tum, quantum ipse in unoquoque instanti Soli appropinquaret, dubium pro&shy;<lb/>fecto non est quod hisce duobus motibus contrariis sese invicem compen&shy;<lb/>santibus Stella G, neque admovebitur neque removebitur ab ipso Sole D <lb/>maiori spatio quam semidiameter DG, ideoque librata et innatans apparebit, <lb/>aut retenta ab aliquo firmo vinculo, quamvis sita sit in aethere fluidissimo, <lb/>nullique rei innitetur et a nulla substentetur &rdquo; (ibi, pag. </s>

<s>49). </s></p><p type="main">

<s>La somiglianza delle conclusioni rispetto al moto dei Pianeti e al moto <lb/>delle Comete ci apre la via a congetturar della somiglianza della esperienze. </s>

<s><lb/>Essendo, nell'opinion del Borelli, la sostanza della Cometa materia cosmica <lb/>staccatasi da qualche Pianeta, ed errante per gli spazii eterei, la direzione <lb/>presa dal moto di essa materia doveva essere secondo la tangente dell'or&shy;<lb/>bita planetaria, d'ond'erasi distaccata, e sarebbe, per legge d'inerzia, dovuta <lb/>seguitare a correre in quella direzione, se non fosse entrata nella sfera del&shy;<lb/>l'attrazione del Sole. </s>

<s>Ecco dunque le due componenti del moto parabolico. </s>

<s><lb/>L'intensit&agrave; delle due forze, dalla composizion delle quali il detto moto re&shy;<lb/>sulta, o in altro modo il parametro della Parabola, era soggetto a quei cal&shy;<lb/>coli, da cui dice il Borelli stesso che fu condotto alla sua conclusione. </s></p><p type="main">

<s>L'esperienza poi propria, che poteva render visibili i resultati di que&shy;<lb/>sti calcoli meccanici, noi ci diam facilmente a credere che avesse una gran <lb/>somiglianza con quella, con la quale dimostrava l'Autore della Teorica de'Me&shy;<lb/>dicei il perpetuo circolar de'Pianeti, librati nel libero etere intorno al Sole. </s>

<s><lb/>Consisteva insomma, secondo noi, l'esperienza borelliana da dimostrare il <lb/>moto parabolico fatto dalla Cometa in sopreccitare in una palla di ferro la <lb/>forza centrifuga, e poi lasciarla fuggir lungo la tangente dell'orbita, per la <pb xlink:href="020/01/1079.jpg" pagenum="522"/>quale avrebbe proseguito il suo corso, se non fosse stata attratta da un globo <lb/>magnetico opportunamente collocato nello Strumento. </s></p><p type="main">

<s>Quel che specul&ograve; e speriment&ograve; il Borelli in questo importantissimo sog&shy;<lb/>getto era rimasto dimenticato e sepolto nelle carte manoscritte di lui, e nelle <lb/>stanze della Fortezza di S. Miniato, quando, incontratosi ne'medesimi con&shy;<lb/>cetti l'Hevelio, pubblic&ograve; in Danzica, nel 1668, la sua <emph type="italics"/>Cometografia.<emph.end type="italics"/> La ma&shy;<lb/>teria delle Comete &egrave;, secondo l'Autore, tenuissima ed evanescente, come <lb/>quella delle scorie notanti nella fotosfera, e che producono le macchie del <lb/>Sole. </s>

<s>Conclude di qui non poter le Comete moversi e rigirarsi in orbite <lb/>chiuse, essendo queste convenienti solo alla sempiterna sostanza dei Pianeti. <lb/></s>

<s>&ldquo; Cum igitur Cometae, ex tenuissima materia, atque minimis corpusculis <lb/>primum nascantur, ac successive in magnam excrescant molem, dum rursus <lb/>resolvuntur ac denique in subtilissimam aetheriam materiam rediguntur, si&shy;<lb/>cut lib. </s>

<s>VII prolixe deduximus, neutiquam ergo Cometae sunt corpora per&shy;<lb/>petua, sed potius temporanea, quibus autem motum assignare continuum a<gap/><lb/>perpetuum nimis absurdum esse videtur, nec suadet sane ratio corpora vi&shy;<lb/>delicet caduca in circulo vel ellipsi perpetuo moveri, pariter atque Planetae, <lb/>qui corpora sunt aetherea, perfecta, aeterna, motum nunquam non conti&shy;<lb/>nuum ac perpetuum exercentia &rdquo; (pag. </s>

<s>562). Perci&ograve; conclude, dietro queste <lb/>ragioni, non potere alle Comete competere altro moto che retto. </s>

<s>&ldquo; Gaudent <lb/>igitur Cometae, ex nostra sententia, hocce unico motu, fere recto &rdquo; (pag. </s>

<s>568). </s></p><p type="main">

<s>La direzione poi di questo moto &egrave; secondo la tangente dell'orbita del <lb/>Pianeta, da cui si staccano le materie cometarie, ed uscite da quell'ammo&shy;<lb/>sfera, venendo attratte dal Sole, descrivono per la resultante di queste due <lb/>forze, una delle quali intrinseca e naturale, l'altra estrinseca e violenta, <lb/>un'orbita parabolica, a quel modo che la descrive un sasso cadente, dopo <lb/>essere uscito dalla vertigine della fionda. </s>

<s>&ldquo; Simili plane ratione etiam Co&shy;<lb/>metas duos praecipuos motus favent, cuius alter est extrinsecus, et quasi <lb/>violentus, qui a vertigine atmosphaerae proficiscitur, mediante quo impetus <lb/>Cometae imprimitur (dum atmosphaera exit, et eam deserit, atque suae spon&shy;<lb/>tis redditur) visque ei inditur se ulterius movendi, et quidem secundum <lb/>tangentem, seu lineam rectam, nisi alia causa impediens interveniat. </s>

<s>Alter <lb/>autem pariter naturalis et intrinsecus est, non quidem ex eo quod Come&shy;<lb/>tis acque ac terrestribus gravitatem attribuam, sed alia huic non prorsus <lb/>dissimilis appetentia eis competat, ex qua Cometae omnes erga Solem, tan&shy;<lb/>quam centrum Mundi,.... obvertuntur &rdquo; (pag. </s>

<s>666). </s></p><p type="main">

<s>Quest'apparenza poi, che ha la materia cometaria, alla quale l'Hevelio <lb/>assegna la figura uniforme e costante di un disco o di una tavola piana, la <lb/>rassomiglia alle attrazioni de'due poli magnetici. </s>

<s>&ldquo; Haecque appetentia, sive <lb/>hic motus, cuius beneficio Cometae perpetuo altero lato plano ad centrum <lb/>Universi, altero opposito ad orbes Planetarum propendent, propemodum ae&shy;<lb/>mulatur acum magneticam, quae alteram cuspidem indesinenter Aquilonem, <lb/>alteram Austrum versus obvertit, exporrigit, atque dirigit &rdquo; (pag. </s>

<s>667). </s></p><p type="main">

<s>Da questa part&eacute; per&ograve; l'Hevelio rimane molto indietro al Borelli, il quale, <pb xlink:href="020/01/1080.jpg" pagenum="523"/>oltre alla forza attrattiva, rassomigliata alla magnetica, aveva messo in gioco <lb/>la repulsiva delle forze centrifughe, e cos&igrave; approssimavasi di pi&ugrave; alle sco&shy;<lb/>perte del Newton, il quale soggett&ograve; finalmente le Comete all'eterne leggi <lb/>dei moti planetari. </s>

<s>Si possono fare, egli dice in sulla fine del suo opuscolo <lb/><emph type="italics"/>De mundi systemate,<emph.end type="italics"/> intorno alle Comete'tre ipotesi: o elle si generano e <lb/>si disfanno ogni volta, che appariscono e spariscono, o venendo dalle regioni <lb/>delle stelle fisse penetrano nel nostro sistema planetario, o finalmente si ri&shy;<lb/>volgono in orbite molto eccentriche intorno al Sole. </s>

<s>Nel primo caso descri&shy;<lb/>veranno una qualche sezione conica, la forma propria della quale sar&agrave; de&shy;<lb/>terminata dal vario grado della velocit&agrave;. </s>

<s>Nel secondo caso, descriveranno <lb/>un'Iperbola, e nel terzo un'Ellisse, tanto allungata da rassomigliarsi pi&ugrave; <lb/>presto a una Parabola. </s>

<s>&ldquo; Orbes autem, si lex Planetarum servetur, haud <lb/>multum divaricabunt a plano Ecclipticae. </s>

<s>Et quantum hactenus animadver&shy;<lb/>tere potui, casus tertius obtinet &rdquo; (Lausannae 1744, pag. </s>

<s>59, 60). </s></p><p type="main">

<s>Quanto alla fisica costituzione il Newton riguard&ograve; le code come pro&shy;<lb/>dotte da materie esalate dal nucleo delle Comete, e respinte per circumpul&shy;<lb/>sione dal centro del Sole, come sono respinti i fumi o altri corpi pi&ugrave; leggeri <lb/>dell'aria, per circumpulsione, dal centro della nostra Terra. </s>

<s>&ldquo; Ut in aere no&shy;<lb/>stro fumus corporis cuiusvis igniti petit superiora, idque vel perpendicula&shy;<lb/>riter, si corpus quiescat, vel oblique si corpus moveatur in latus; ita in <lb/>coelis, ubi corpora gravitant in Solem, fumi et vapores ascendere debent a <lb/>Sole &rdquo; (ibi, pag. </s>

<s>57). Cos&igrave; vennero finalmente a ridursi nel dominio della <lb/>scienza fisica e matematica quelli spettri paurosi, che s'eran prima creduti <lb/>apparire di quando in quando nel cielo senz'ordine e senza legge. </s></p><pb xlink:href="020/01/1081.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO XIV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>De'moti dell'Universo<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della scoperta delle Orbite ellittiche, e delle leggi del moto dei Piancti. </s>

<s>&mdash; II. </s>

<s>Delle forze centrali, <lb/>e dei decrementi delle loro intensit&agrave;, in ragione delle distanze. </s>

<s>&mdash; III. </s>

<s>Delle leggi delle forze <lb/>centrali; dell'attrazione universale; dell'origine delle Orbite ellittiche. </s>

<s>&mdash; IV. </s>

<s>Delle varie ipo&shy;<lb/>tesi proposte a spiegar la tendenza dei gravi ai loro centri. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Chi ripensa che, dopo tanti secoli e dopo tante aberrazioni, il Newton, <lb/>rispetto all'essere e al moto delle Comete, conferm&ograve; finalmente una verit&agrave;, <lb/>lo splendor della quale, come raggio di stella in mezzo alle nubi, erasi gi&agrave; <lb/>rivelato alle menti degli antichi Pitagorici italiani, riman preso di tal mara&shy;<lb/>viglia, che il pensiero di lui distende lietamente il volo a considerare altri <lb/>placiti di quella prima Filosofia, per concluderne all'ultimo che non &egrave; l'am&shy;<lb/>mirata scienza moderna altro che un grande albero cresciuto, sotto un lun&shy;<lb/>ghissimo inverno, da quell'arbusto. </s>

<s>A persuadersi intanto di ci&ograve;, si dee sentir <lb/>l'animo disposto chiunque ha per lungo tempo sentito, in discorrere del vero <lb/>sistema del mondo, chiamarlo indifferentemente col nome di Pitagorico e <lb/>di Copernicano, e chiunque altro, in legger la prefazione al libro delle Revo&shy;<lb/>luzioni degli orbi celesti, udi il Copernico stesso commemorare con grande <lb/>onore, come suoi predecessori e maestri, Niceta da Siracusa e Filolao. </s></p><p type="main">

<s>Cos&igrave; veniva la lampada del Mondo a collocarsi al suo posto, in mezzo <lb/>al magnifico tempio, e cos&igrave; fiaccavasi il mostruoso orgoglio di quella Filo&shy;<lb/>sofia, che insegnava il cielo essere stato creato in servigio della Terra. </s>

<s>Di <lb/>pi&ugrave; toglievano affatto di mezzo i Pitagorici quella differenza, e anzi quel con-<pb xlink:href="020/01/1082.jpg" pagenum="525"/>trapposto fra Cielo e Terra, da una parte insegnando che la Terra era essa <lb/>pure celeste, e dall'altra che i corpi stessi celesti partecipavano delle qua&shy;<lb/>lit&agrave; terrene. </s>

<s>Udimmo da Plutarco come si credeva che partecipasse di cos&igrave; <lb/>fatte qualit&agrave; terrene la Luna, e i moderni, con l'aiuto de'Canocchiali, con&shy;<lb/>fermarono pienamente i placiti pitagorici e gli estesero alla costituzione fisica <lb/>di tutti gli altri Pianeti, che trovarono montuosi come la Terra, e come la <lb/>Terra involti in una ammosfera variabile di aspetto fra il sereno e le nubi. </s></p><p type="main">

<s>Quando si giunse a intendere fra il Cielo e la Terra una tal cognazione, <lb/>e confermatesi per i fatti osservati le filosofiche speculazioni si ridusse ad <lb/>unit&agrave; quel che prima. </s>

<s>era diviso, si compiacquero gli uomini di aver fatto <lb/>nella scienza del Cosmo un gran progresso. </s>

<s>Sperarono che sarebbe a un tal <lb/>progresso quasi costituito il suo termine, se si fosse riusciti a dimostrare <lb/>che, formando le varie membra un solo corpo fisico, da un unico principio <lb/>si dispensasse a questo corpo la vita: la qual vita, perciocch&egrave; manifestasi <lb/>nel moto, si comprese che sarebbe allora pienamente dimostrata l'unit&agrave; del&shy;<lb/>l'Universo, quando si vedesse tutto esser mosso da un medesimo impulso, <lb/>e tutto seguitare a moversi con una medesima legge. </s></p><p type="main">

<s>Le speranze che potesse la scienza dell'uomo sollevarsi tanto alto, sulla <lb/>fine del secolo XVII, furono sodisfatte, ma colui, a cui tocc&ograve; tanta gloria, <lb/>non s'intende com'avesse cos&igrave; potuto ignorare i placiti dell'antichissima Fi&shy;<lb/>losofia italica, da scrivere queste parole: &ldquo; Quibus vinculis Antiqui plane&shy;<lb/>tas in spatiis liberis retineri, deque cursu rectilineo perpetuo retractos in <lb/>orbem regulariter agi docuere, non constat &rdquo; (Neutoni, Opusc. </s>

<s>De mundi <lb/>system., Lausannae 1744, pag. </s>

<s>6). Consta anzi fia Plutarco che dicevano que&shy;<lb/>gli Antichi per questo ritenersi ne'liberi spazii la Luna, perch&egrave; si muove <lb/>intorno alla Terra, come riman sospeso un sasso, o girato nella fionda o <lb/>scagliato liberamente nell'aria. </s>

<s>Fa poi tanto pi&ugrave; maraviglia l'avere il Newton <lb/>ignorate le tradizioni dell'antica Scuola italiana, vedendolo incominciare a <lb/>spiegare i suoi pensieri coll'esempio stesso del sasso, il quale se si potesse, <lb/>ei dice, gittare con tanta forza da non lasciarlo cadere, s'aggirerebbe an&shy;<lb/>ch'egli perpetuamente in orbe intorno alla Terra, come la Luna. </s></p><p type="main">

<s>Tra la Filosofia antica e questa nuova ci &egrave; senza dubbio una gran dif&shy;<lb/>ferenza, la quale &egrave; il portato degli anni e della cultura. </s>

<s>E perch&egrave; veramente, <lb/>dai primi anni del secolo XVII, incominci&ograve; quella cultura ad essere frut&shy;<lb/>tuosa, dee aver di l&igrave; principio questa parte di storia, nella quale si vuol da <lb/>noi brevemente narrare per quali vie si riuscisse a scoprir quell'unica forza, <lb/>che d&agrave; legge di moto al sasso scagliato per l'aria, e alle stelle erranti per <lb/>l'etere immenso. </s></p><p type="main">

<s>S'erano studiati i Filosofi antichi di ridurre all'unit&agrave; e alla semplicit&agrave; <lb/>questo moto de'corpi celesti, facendoli rigirar perpetuamente intorno a un <lb/>centro, in orbite circolari. </s>

<s>La desiderata semplicit&agrave; per&ograve;, in tali orbite, si <lb/>dov&egrave; confessare che non erasi conseguita, e quanto pi&ugrave; l'Astronomia faceva <lb/>progressi, e pi&ugrave; ritrovava in quel mondano assettamento disordini e irrego&shy;<lb/>larit&agrave; da correggersi. </s>

<s>N&egrave; a una tal correzione si trovarono sufficienti o la <pb xlink:href="020/01/1083.jpg" pagenum="526"/>complicata macchina degli Equanti e dei Deferenti di Tolomeo, o quella stessa <lb/>pi&ugrave; semplice degli Eccentrici e degli Epicicli copernicani. </s></p><p type="main">

<s>Supposto moversi i Pianeti in orbite circolari, le discrepanze notabilis&shy;<lb/>sime, che passavano fra i calcoli e le osservazioni, si fecero principalmente <lb/>sentire a quel Ticone, che in calcolare e in osservare i moti del cielo aveva <lb/>tutta consacrata la vita. </s>

<s>Sentitosi Giovanni Keplero chiamare a quel mede&shy;<lb/>simo ministero in Germania, si doleva che la troppa lontananza dall'Astro&shy;<lb/>nomo danese gl'impediva di frequentar quella Scuola, di che ebbe poi a <lb/>consolarsi, quando Ticone stesso venne in Boemia. </s>

<s>&ldquo; Eo igitur veni, sub <lb/>initium anni MDC, spe Planetarum correctas eccentricitates addiscendi &rdquo; (De <lb/>Stella Martis, Pragae 1909, pag. </s>

<s>53). Avvenne per divina disposizione, pro&shy;<lb/>segue a dire il Keplero, che in quel tempo, che io venni in Boemia, le os&shy;<lb/>servazioni del gran Maestro e de'familiari di lui fossero tutte rivolte alla <lb/>Stella di Marte &ldquo; ex cuius motibus omnino necesse est nos in cognitionem <lb/>Astronomiae arcanorum venire, aut ea perpetuo nescire &rdquo; (ibi). </s></p><p type="main">

<s>Or quale arcana cognizione astronomica erasi rivelata al Keplero dai moti di <lb/>Marte? </s>

<s>Quella, rispondiamo, che le orbite de'Pianeti non sono altrimenti cir&shy;<lb/>colari, come avevano posto tutti gli Astronomi predecessori di lui, ma ellitti&shy;<lb/>che, come veniva dimostrato dai fatti. </s>

<s>La dimostrazione della grande scoperta <lb/>kepleriana si conduce, e si conclude dall'Autore nel suo Commentario <emph type="italics"/>De <lb/>Stella Martis,<emph.end type="italics"/> nella maniera che qui da noi compendiosamente si riferisce. </s></p><p type="main">

<s>Osservato Marte in tre diversi tempi, cio&egrave; ne'di 31 Ottobre e 31 Di&shy;<lb/>cembre dell'anno 1590, e ne'di 25 Ottobre dell'anno 1595, fu trovato a tre <lb/>differenti distanze dal centro del Sole, le quali, ridotte al medesimo mese <lb/>di Qttobre e al medesimo anno 1590, venivano espresse dal numero 147750, <lb/>essendo Marte in 14&deg;, 16&prime;, 52&Prime; del Tauro; dal numero 163100, essendo il <lb/>Pianeta in 5&deg;, 24&prime;, 21&Prime; della Libbra, e dal numero 166255, essendo lo stesso <lb/>Pianeta in 8&deg;, 19&prime;, 4&Prime; della Vergine. </s></p><p type="main">

<s>Ora, per rappresentarci queste varie po&shy;<lb/>sizioni, sia, nella figura 102, A il Sole, e si <lb/><figure id="id.020.01.1083.1.jpg" xlink:href="020/01/1083/1.jpg"/></s></p><p type="caption">

<s>Figura 102.<lb/>conducano dal centro di lui le linee AK, AT, <lb/>in modo che sia l'angolo KAT=114&deg;, 2&prime;, <lb/>12&Prime;, quanta &egrave; nel Zodiaco la distanza dal 14 <lb/>grado del Tauro all'8&deg; della Vergine. </s>

<s>Si con&shy;<lb/>duca in oltre dal medesimo punto la linea AH <lb/>in modo, che l'angolo KAH riesca uguale a <lb/>27&deg;, 5&prime;, 17&Prime;, quanto &egrave; dall'8&deg; del Tauro al 5&deg; <lb/>della Libbra. </s>

<s>Se per i tre punti T, K, H si fa <lb/>passare un circolo, questo dovrebbe secondo <lb/>gli Astronomi segnar la via percorsa da Marte, <lb/>e se ci&ograve; &egrave; vero debbono le distanze AT, AK, <lb/>AH, ritrovate per l'osservazione, corrispon&shy;<lb/>dere a quelle che resultan dal calcolo, data la posizion del Pianeta e l'ec&shy;<lb/>centricit&agrave; dell'Orbita. </s></p><pb xlink:href="020/01/1084.jpg" pagenum="527"/><p type="main">

<s>Per la pi&ugrave; giusta misura di tale eccentricit&agrave;; dice il Keplero, le osser&shy;<lb/>vazioni mi hanno dato modo di stabilire quel che avevo dall'altra parte con&shy;<lb/>cluso a priori, cio&egrave; la linea degli Apsidi &ldquo; non praeter Solem, ut artificibus <lb/>placet, sed per ipsum centrum corporis Solis transire &rdquo; (pag. </s>

<s>37). Sia dun&shy;<lb/>que ED questa linea degli Apsidi, che p&aacute;ssa per il centro del Sole: sar&agrave; in <lb/>E l'afelio, in D il perielio, e AG=14140 (pag. </s>

<s>209) misurer&agrave; l'eccentri&shy;<lb/>cit&agrave; dell'orbita. </s></p><p type="main">

<s>Condotte ora dal punto G le tre linee GT, GK, GH, i tre nuovi trian&shy;<lb/>goli AGT, AGK, AGH che ne resultano, avendo per comun base il lato AG, <lb/>eccentricit&agrave; nota, e di pi&ugrave; noti i tre angoli ai vertici, che sono le equa&shy;<lb/>zioni ottiche, e gli angoli intorno ad A, essendo dati dalle osservate posizioni <lb/>di Marte nel Zodiaco; potranno dunque risolversi, e risoluti danno le di&shy;<lb/>stanze AK=166605, AH=163883, AT=148539, notabilmente differenti <lb/>come si vede dalle osservate. </s></p><p type="main">

<s>Che si dir&agrave; dunque, esce fuori con enfasi il Keplero, che tal differenza <lb/>&egrave; da attribuirsi al difetto delle osservazioni? </s>

<s>Ma a voi mi rivolgo, o periti <lb/>Astronomi &ldquo; qui sophistica effugia, caeteris disciplinis creberrima, in Astro&shy;<lb/>nomia nulli patere scitis, vos appello &rdquo; (pag. </s>

<s>213). Voi vedete tanta essere <lb/>la differenza, che non pu&ograve; in nessun modo attribuirsi n&egrave; all'imperizia n&egrave; <lb/>all'incertezza dell'osservare. </s></p><p type="main">

<s>Si dir&agrave; forse che convien ritirare l'eccentrico, finch&egrave; non aggiunga alla <lb/>necessaria distanza? </s>

<s>Ma quanto si ritira da una parte, altrettanto vien man&shy;<lb/>cando dall'altra. </s>

<s>Che se si vuol tutto veramente aggiustare, supponete che <lb/>il circolo DTEH sia flessibile, e che tenuto fisso in D si debba allungare <lb/>verso E: l'allungamento non sar&agrave; per&ograve; possibile, se non a patto che il cir&shy;<lb/>colo stesso si trasformi in ovale. </s>

<s>&ldquo; Itaque plane hoc est: Orbita Planetae <lb/>non est circulus, sed ingrediens ad latera utraque paulatim, iterumque ad <lb/>circuli amplitudinem in perigaeo exiens, cuiusmodi figuram itineris <emph type="italics"/>Ovalem<emph.end type="italics"/><lb/>appellitant &rdquo; (pag. </s>

<s>312, 14). </s></p><p type="main">

<s>Dimostrato cos&igrave; che l'orbita planetaria &egrave; un Ellisse, il Keplero torn&ograve; a <lb/>considerare i tempi, in relazione alle porzioni del piano ellittico o dell'aree <lb/>descritte dalla linea, che va dal Sole al Pianeta. </s>

<s>Aveva gi&agrave; dimostrato l'Au&shy;<lb/>tore che in qualunque Sistema o tolemaico o copernicano &ldquo; quo longius <lb/>abest Planeta a puncto illo, quod pro centro mundi assumitur, hoc debilius <lb/>illum incitari circa illud punctum &rdquo; (pag. </s>

<s>167) d'onde ne conseguiva, anche <lb/>nell'ipotesi delle orbite circolari &ldquo; partes plani metiri moras, quas Planeta <lb/>in partibus respondentis circumferentiae eccentricae trahat &rdquo; (pag. </s>

<s>214). </s></p><p type="main">

<s>Or perch&egrave; queste more o questi tempi sono egualmente bene misurati <lb/>dal piano dell'orbita ellittica &ldquo; partes igitur plani diminuti aphelio et pe&shy;<lb/>rihelio proximae metientur tempus maius, quia apud illas tenuis est dimi&shy;<lb/>nutio, sed partes in longitudinibus mediis metientur minus tempus quam <lb/>antea, quia in illis accidit potissima totius plani diminutio. </s>

<s>Tam igitur, si <lb/>utamur hoc diminuto plano ad moderandas aequationes, fiet Planeta circa <lb/>aphelium et perihelium tardior, quam in priori vitiosa aequationum forma, <pb xlink:href="020/01/1085.jpg" pagenum="528"/>circa longitudines medias velocior, quia distantiae hic diminuuntur. </s>

<s>Morae <lb/>igitur hinc abstractae in aphelium et perihelium, sursum deorsumque com&shy;<lb/>pensatione facta accumulabuntur, non secus ac si quis botellum ventrico&shy;<lb/>sum in medio comprimat, eaque compressione minutal infarctum, e ventre <lb/>magis in utrasque extremitates infra supraque manum eminentes exprimat <lb/>et elidat &rdquo; (ibi). Ci&ograve; che tradotto in altre parole significa: <emph type="italics"/>Le aree descritte <lb/>dal raggio vcttore sono proporzionali ai tempi impiegati nel descriverle.<emph.end type="italics"/></s></p><p type="main">

<s>Questa era per il Keplero come una nota nuova nell'armonia dell'Uni&shy;<lb/>verso, ma era una nota sola, che non modulavasi in aria di canto. </s>

<s>Non pago <lb/>perci&ograve; volle mettersi a ricercare l'armonia fra due Pianeti, nelle relazioni <lb/>che passano fra gl'intervalli delle orbite e i tempi periodici. </s>

<s>&ldquo; Inventis enim <lb/>veris orbium intervallis, scrive nel libro V <emph type="italics"/>Harmonices mundi,<emph.end type="italics"/> per obser&shy;<lb/>vationes Brahei, plurimi temporis labore continuo, tandem, tandem genuina <lb/>proportio temporum periodicorum ad proportionem orbium <emph type="italics"/>sera quidem <lb/>respexit inertem, respexit tamen, et longo post tempore venit.<emph.end type="italics"/> Eaque, si <lb/>temporis articulos petis, 8 Martii huius anni millesimi sexcentesimi decimi <lb/>octavi animo concepta, sed infeliciter ad calculos vocata, eoque pro falsa <lb/>reiecta; denique, 15 Maii reversa, novo capto impetu expugnavit mentis meae <lb/>tenebras tanta comprobatione et laboris mei septem decennalis in observa&shy;<lb/>tionibus braheanis, et meditationis huius in unum conspirantium, ut somniare <lb/>me et praesumere quaesitum inter principia primo crederem. </s>

<s>Sed res est <lb/>certissima exactissimaque quod <emph type="italics"/>Proportio quae est inter binorum quorum&shy;<lb/>cumque Planetarum tempora periodica sit praecise sesquialtera proportio&shy;<lb/>nis mediarum distantiarum, idest orbium ipsorum &rdquo;<emph.end type="italics"/> (Lincii 1619, pag. </s>

<s>189). <lb/>Questa &egrave; la terza delle mirabili armonie del mondo scoperte dal Keplero, e che <lb/>suole esprimersi cos&igrave; nel linguaggio moderno: <emph type="italics"/>I quadrati dei tempi periodici <lb/>dei diversi Pianeti sono fra loro come i cubi de'grandi assi delle loro orbite.<emph.end type="italics"/></s></p><p type="main">

<s>Le nuove armonie kepleriane suonano dunque molto diverse dalle an&shy;<lb/>tiche contemplate da Pitagora o da Platone, ai quali bast&ograve; supporre un im&shy;<lb/>pulso iniziale dato ai Pianeti, perch&egrave; seguitassero a muoversi in sempiterna <lb/>uniformit&agrave; di moto nelle loro orbite circolari. </s>

<s>Che se osservavansi alcune irre&shy;<lb/>golarit&agrave; di que'moti, si davano facilmente a credere che ci&ograve; solo apparisse <lb/>rispetto a noi, a cui, per gli eccentrici e per gli epicicli, si fanno i Pianeti <lb/>ora pi&ugrave; da presso ora pi&ugrave; lontani. </s></p><p type="main">

<s>La Stella di Marte aveva invece rivelato al Keplero che quegli eccen&shy;<lb/>trici e quegli epicicli non erano altro che immaginazioni, movendosi in realt&agrave; <lb/>il Pianeta ora pi&ugrave; di lungi, ora pi&ugrave; d'appresso al centro de'suoi moti, in <lb/>modo che la maggiore o la minore distanza da questo centro era la regola <lb/>de'tempi, ora pi&ugrave; lunghi ora pi&ugrave; brevi. </s>

<s>Da ci&ograve; ne concluse argutamente il <lb/>Keplero ch'essendo il centro di que'moti il Sole, dovesse in esso e non in <lb/>altro risiedere la virt&ugrave; motrice. </s>

<s>Ci&ograve; potevasi dall'altra parte, ei soggiunge, <lb/>anco argomentare a priori dalla dignit&agrave; e dalla prestanza dello stesso Sole <lb/>&ldquo; qui est fons vitae mundi .... qui est et lucis, quo totius Machinae constat <lb/>ornatus, qui itidem et caloris quo omnia vegetantur &rdquo; (pag. </s>

<s>169). </s></p><pb xlink:href="020/01/1086.jpg" pagenum="529"/><p type="main">

<s>Ma proseguiamo, dice l'Autore del Commentario <emph type="italics"/>De Stella Martis,<emph.end type="italics"/> a <lb/>contemplare questa virt&ugrave; motrice del Sole: ella non pu&ograve; essere la luce, la <lb/>quale non &egrave; forse altro che il veicolo o lo strumento, di che la stessa virt&ugrave; <lb/>motrice si serve. </s>

<s>In qualunque modo, &egrave; una specie immateriata latitante nel <lb/>corpo del Sole, da cui esce e aderisce al Pianeta, come dall'anima del get&shy;<lb/>tatore esce il moto e aderisce alla pietra. </s>

<s>Ma la pietra segue il moto della <lb/>mano, secondo il quale o va in linea retta o va in giro. </s>

<s>Or perch&egrave; i Pia&shy;<lb/>neti si muovono in giro, &egrave; necessario che in giro pure si muova la <expan abbr="v&itilde;rt&ugrave;">virrt&ugrave;</expan> <lb/>motrice, cio&egrave; il Sole, ma no di spazio in spazio, come nel Sistema di To&shy;<lb/>lomeo &ldquo; sed super suo centro, seu axe immobilibus, partibus eius de loco <lb/>in locum, in eodem tamen spacio toto corpore manente, transeuntibus &rdquo; <lb/>(pag. </s>

<s>173). </s></p><p type="main">

<s>Nasce per&ograve; di qui una difficolt&agrave; ed &egrave; questa: se la virt&ugrave; motrice &egrave; una <lb/>specie immateriata, che non pu&ograve; secondo la sua natura debilitarsi per la <lb/>distanza, com'avviene che, ricevendo Saturno dal Sole la medesima impres&shy;<lb/>sione di moto, si volga nonostante in giro tanto pi&ugrave; lentamente di Mercu&shy;<lb/>rio? </s>

<s>A che risponde il Keplero che, sebbene immateriata sia la virt&ugrave; che <lb/>muove, materiati sono i Pianeti, e perci&ograve; inerti a muoversi, e dediti per na&shy;<lb/>tura loro alla quiete. </s>

<s>&ldquo; Quarum rerum contentione cum nascatur pugna, su&shy;<lb/>perat igitur plus ille Planeta qui in virtute imbecilliore consistit, eaque tardius <lb/>movetur, minus ille qui Soli propior. </s>

<s>Docet hinc analogia statuere omnibus <lb/>Planetis, ipsi etiam Mercurio humillimo, inesse vim materialem sese expli&shy;<lb/>candi nonnihil ex orbe virtutis solaris. </s>

<s>Unde evincitur solaris corporis gyra&shy;<lb/>tionem multo antevertere omnium Planetarum periodica tempora, ideoque <lb/>ad minimum, citius quam trimestri spacio, Solem semel in suo spacio gy&shy;<lb/>rari &rdquo; (pag. </s>

<s>174, 75). </s></p><p type="main">

<s>Ma se non &egrave; la luce, che altro insomma &egrave; questa specie immateriata, <lb/>a cui s'attribuisce la virt&ugrave; di muovere, e contro la quale relutta la corpu&shy;<lb/>lenza de'Pianeti, come allo spirito relutta la materia? </s>

<s>Risponde il Keplero <lb/>che chi volesse farsene un'idea guardi l'esempio del Magnete &ldquo; cuius vir&shy;<lb/>tus residet in universo corpore Magnetis, cum eiusdem mole crescit, cum <lb/>comminutione illius dividitur et ipsa. </s>

<s>Ita in Sole virtus movens tanto vide&shy;<lb/>tur fortior, quod verisimile sit corpus eius esse totius mundi densissimum &rdquo; <lb/>(pag. </s>

<s>176). </s></p><p type="main">

<s>Si direbbe qui, di primo impeto, che fosse formulata in queste parole <lb/>la legge neutoniana delle forze proporzionali alle quantit&agrave; di materia, se in <lb/>quel che il Keplero subito soggiunge, negata al Sole ogni virt&ugrave; attrattiva, <lb/>non si vedesse paragonato al Magnete che per la sola virt&ugrave; direttrice. </s>

<s>E <lb/>questo perch&egrave;? </s>

<s>Perch&egrave; altrimenti i Pianeti andrebbero a congiungersi col <lb/>Sole. </s>

<s>&ldquo; Credibile est in Sole non esse ullam vim Planetarum attractoriam, <lb/>ut in Magnete; accederent enim ad Solem tantisper, donec cum ipso coniun&shy;<lb/>gerentur penitus, sed tantum directoriam &rdquo; (ibi). </s></p><p type="main">

<s>In ci&ograve; che abbiamo fin qui esposto insomma consiste l'Astronomia <lb/>kepleriana, la quale, quanto avesse veramente ragione di essere detta <emph type="italics"/>Nuova,<emph.end type="italics"/><pb xlink:href="020/01/1087.jpg" pagenum="530"/>si comprende da tutti coloro, che la confrontano con l'opera, non diciamo <lb/>di Ticone, ma dello stesso Copernico. </s>

<s>La novit&agrave; introdotta nella scienza astro&shy;<lb/>nomica dal Keplero ritorna da due parti: da una che si pu&ograve; dir matema&shy;<lb/>tica, per distinguerla dall'altra, che ha qualit&agrave; pi&ugrave; proprie alla Fisica. </s>

<s>La <lb/>matematica risulta dalla dimostrazione delle orbite ellittiche de'Pianeti e <lb/>delle relazioni che ne conseguitano fra i tempi periodici e l'aree e gli assi <lb/>delle stesse ellissi; la fisica consiste in quella importantissima conclusione <lb/>che il Sole non &egrave; un semplice punto, intorno a cui si circoscrivono i limiti <lb/>alle varie distanze de'Pianeti, ma &egrave; un centro attivo, dall'azion del quale <lb/>i Pianeti stessi ricevono i primi impulsi e la regola de'loro moti. </s></p><p type="main">

<s>Bench&egrave; abbia una tal conclusione il carattere fisico, come s'&egrave; detto, <lb/>scendendo nulladimeno per diritta via dalla natura delle orbite ellittiche, par&shy;<lb/>tecipava pure della evidenza di una dimostrazione matematica, intantoch&egrave; le <lb/>novit&agrave; kepleriane parevano disposte a persuadere gl'intelletti con quella <lb/>virt&ugrave;, che &egrave; propria dell'amabile Geometria. </s>

<s>Tutt'altrimenti per&ograve; da quel <lb/>che si sarebbe creduto, la Storia in questo fatto ci mostra un esempio no&shy;<lb/>tabilissimo della ritrosia degli uomini ad accogliere le novit&agrave; scoperte, anche <lb/>quando agli intelletti risplendano della pi&ugrave; sincera luce del vero. </s>

<s>E affinch&egrave; <lb/>ci persuadiamo essere stato questo sempre un vizio comune, e non un pre&shy;<lb/>giudizio di qualche setta, &egrave; da veder quale accoglienza facesse alla Nuova <lb/>astronomia kepleriana lo stesso Galileo. </s></p><p type="main">

<s>Avendo riscontrato di fatto che il Sole si rivolge intorno al suo asse, <lb/>come il Keplero aveva supposto, sembra che Galileo poco dopo quel tempo, <lb/>cio&egrave; nel 1614, approvasse anche la conseguenza, che derivava da quello stesso <lb/>supposto l'Autor del Commentario della Stella di Marte. </s>

<s>&ldquo; Ho anco dimo&shy;<lb/>strato, per le osservazioni continuate di tali materie tenebrose (scriveva al <lb/>Dini, nella Lettera sul Sistema copernicano) come il corpo solare per neces&shy;<lb/>sit&agrave; si rivolge in s&egrave; stesso, e di pi&ugrave; accennato quanto sia ragionevole il cre&shy;<lb/>dere che da tal rivolgimento dipendino i movimenti de'Pianeti intorno al <lb/>medesimo Sole &rdquo; (Alb. </s>

<s>II, 25). </s></p><p type="main">

<s>Poco pi&ugrave; tardi avendo a difendere il Sistema copernicano contro i Teo&shy;<lb/>logi paripatetici, i quali adducevano il miracolo operato da Giosu&egrave;, per la <lb/>pi&ugrave; certa prova del moto del Sole; Galileo col Keplero interpetrava il testo <lb/>biblico non del moto solare <emph type="italics"/>de spacio in spacium, sed super suo centro,<emph.end type="italics"/><lb/>mostrando come bene conseguisse l'immobilit&agrave; degli altri corpi celesti, ar&shy;<lb/>restato il moto del Sole, che &ldquo; come ministro massimo della Natura, ed in <lb/>certo modo anima e cuore del Mondo, infonde agli altri corpi che lo cir&shy;<lb/>condano, non solo la luce, ma il moto ancora col rigirarsi in s&egrave; medesimo &rdquo; <lb/>(ivi, pag. </s>

<s>61). </s></p><p type="main">

<s>Queste dottrine cos&igrave; espressamente professate da Galileo vedemmo come <lb/>fossero, secondo il Keplero, una legittima conseguenza delle orbite ellittiche, <lb/>ond'&egrave; che ammettendosi per vera questa tal conseguenza, sembrava che per <lb/>vero pure si dovesse accettare il principio da cui derivava. </s>

<s>Forse a que'tempi <lb/>Galileo profess&ograve; questo principio, ma poi, ne'Dialoghi de'Due massimi si-<pb xlink:href="020/01/1088.jpg" pagenum="531"/>stemi, torn&ograve; co'Pitagorici, con Platone e col Copernico alle orbite circolari, <lb/>riguardando il Sole non pi&ugrave; come centro attivo e causa del moto de'Pia&shy;<lb/>neti, ma come un semplice termine di remozione, o punto saldo da cui mi&shy;<lb/>surar le distanze: o in altro modo, come il centro delle oscillazioni di un <lb/>pendolo, le sensate esperienze del quale, dicesi nella Giornata IV, per bocca <lb/>del Salviati, &ldquo; si confermano con le esperienze dei movimenti celesti de'Pia&shy;<lb/>neti, ne'quali si vede mantener l'istessa regola, che quelli che si muovono <lb/>per cerchi maggiori pi&ugrave; tempo consumano in passargli &rdquo; (Alb. </s>

<s>I, 489). </s></p><p type="main">

<s>Se non &egrave; dunque il Sole centro attivo, come aveva dimostrato il Keplero, <lb/>in che risiede la virt&ugrave; che muove i Pianeti? </s>

<s>Galileo suppl&igrave; alla negazione delle <lb/>cause fisiche proposte dallo stesso Keplero, e rispose poi pi&ugrave; tardi nel IV Dialogo <lb/>delle Due nuove scienze, scoprendo in aspetto di verace storia le poetiche sem&shy;<lb/>bianze di un concetto, degno veramente del gran Platone. </s>

<s>&ldquo; E'mi pare assai <lb/>credibile, dicesi per bocca del Sagredo, che avendo noi per le dottrine astro&shy;<lb/>nomiche assai competente notizia delle grandezze degli orbi e dei Pianeti, e <lb/>delle distanze loro dal centro, intorno al quale si raggirano, come ancora <lb/>delle loro velocit&agrave;; possa il nostro Autore, al quale il concetto platonico non <lb/>era ascosto, aver talvolta per sua curiosit&agrave; avuto pensiero di andare investi&shy;<lb/>gando se si potesse assegnare una determinata sublimit&agrave;, dalla quale, par&shy;<lb/>tendosi come da stato di quiete i corpi dei Pianeti, e mossisi per certi spazii <lb/>di moto retto e naturalmente accelerato, convertendo poi la velocit&agrave; acqui&shy;<lb/>stata in moti equabili, si trovassero corrispondere alle grandezze degli orbi <lb/>loro, e ai tempi delle loro revoluzioni &rdquo; (Alb. </s>

<s>XIII, 238). </s></p><p type="main">

<s>Bench&egrave; una tal corrispondenza, qual'&egrave; fra i tempi delle oscillazioni dei <lb/>pendoli e le lunghezze de'loro fili, non fosse veramente ritrovata fra i tempi <lb/>periodici e i raggi delle orbite de'Pianeti, n&egrave; fosse possibile, per esser con&shy;<lb/>traria al vero, di ritrovarla; la platonica dottrina splendidamente rinnovel&shy;<lb/>lata da Galileo, e secondo la quale attribuivasi a una virt&ugrave; insita nel Pia&shy;<lb/>neta l'effetto di quel moto, che il Keplero diceva derivar principalmente dal <lb/>Sole, trov&ograve; buona accoglienza in uno de'pi&ugrave; valorosi astronomi della Fran&shy;<lb/>cia. </s>

<s>Ma perch&egrave;, dall'altra parte, il Boulliaud era per le proprie osservazioni <lb/>convinto che le orbite planetarie s'aggiravano veramente in ellisse, invece <lb/>di ammettere con Galileo che i Pianeti acquistassero l'uniformit&agrave; del moto, <lb/>scendendo dalla quiete per linea retta, immagin&ograve; che facessero invece la loro <lb/>discesa in una spirale, sulla superficie di un cono scaleno disegnato dalla <lb/>fantasia dell'Astronomo &igrave;n mezzo allo spazio. </s></p><p type="main">

<s>&ldquo; Apprime equidem, dice l'Autore dell'Astronomia filolaica pi&ugrave; chia&shy;<lb/>ramente spiegata, Galileus Dialogo I (cos&igrave;, ma &egrave; il Dial. </s>

<s>IV delle Due nuove <lb/>scienze) contemplatur motus coelestes, et mota recte prius lata fuisse illa <lb/>corpora, ut velocitatis gradus determinatos acquirerent, qua per circulares <lb/>et in se redeuntes rovolutiones perpetuo deinceps ferrentur, validissimis ra&shy;<lb/>tionibus adstruit: descensum sive casum a coni vertice etiam adstruimus, <lb/>sed etiam circa axem ipsius gyrationis adfuisse censemus &rdquo; (Parisiis 1657, <lb/>pag. </s>

<s>53). </s></p><pb xlink:href="020/01/1089.jpg" pagenum="532"/><p type="main">

<s>Sia ABC (fig. </s>

<s>103) questo cono, e sia la sua base BC, il suo asse AI. </s>

<s><lb/>Conducasi la linea EK in modo, che sia segata in X nel mezzo da una linea <lb/>VT parallelamente condotta alla base, e sulla stessa linea EK s'immagini <lb/>elevarsi un piano perpendicolare al triangolo ABC, il qual <lb/><figure id="id.020.01.1089.1.jpg" xlink:href="020/01/1089/1.jpg"/></s></p><p type="caption">

<s>Figura 103.<lb/>piano disegner&agrave; colla sua sezione l'ellisse EQK sulla su&shy;<lb/>perficie del cono. </s>

<s>Il punto M sar&agrave; un foco dell'ellisse, e <lb/>presa XH=XM, sar&agrave; H l'altro foco, dove si suppone <lb/>che risegga il Sole. </s></p><p type="main">

<s>Ora, essendo cos&igrave; disposte le cose, immagina il Boul&shy;<lb/>liaud che, cadendo il Pianeta dal vertice A, quand'&egrave; sceso <lb/>in E, abbia acquistati que'precisi gradi di velocit&agrave; pre&shy;<lb/>scritti dal Creatore, e sia perci&ograve; rivolto <lb/>in quel punto ad aggirarsi con moto <lb/>equabile in un cerchio di raggio ES. </s>

<s><lb/>Immagina inoltre l'Autore che il Pianeta <lb/>stesso, per avvicinarsi sempre pi&ugrave; al <lb/>Sole, vada scendendo infino in P, e poi <lb/>risalga su fino in E, con vicenda inces&shy;<lb/>sante, descrivendo innumerevoli circoli, <lb/>i raggi de'quali sien compresi fra quello <lb/>della minima lunghezza ES, e quello <lb/>della massima PR. </s></p><p type="main">

<s>Cos&igrave; s'intende, secondo l'Autore <lb/>dell'Astronomia filolaica, come sia el&shy;<lb/>littica la via del Pianeta, e come nell'afelio E, descrivendo un circolo di <lb/>minimo raggio, abbia la minima velocit&agrave;, e l'abbia massima nel perielio K, <lb/>dove il circolo stesso descritto ha invece il massimo raggio. </s>

<s>&ldquo; A vertice ita&shy;<lb/>que coni intelligibilis creatum Planetae corpus a Creatore impulsum est, et <lb/>aequali circulationis motu, circa ipsius axem contortum, ita ut lineae spira&shy;<lb/>lis circulationem unam vel plures describendo, per infinitos circulos magni&shy;<lb/>tudine inaequales pertransierit, et gradus velocitatis acquisierit a primo illo <lb/>Agente determinatos. </s>

<s>In motum deinde perpetuum, ad quem decreto suo <lb/>alligaverat, Planetae corpus deflexit, viamque tenere fecit, cuius planum per <lb/>centrum Solis transiret. </s>

<s>Ut vero cum principio suo semper cohaereret ille <lb/>motus circa eumdem axem, quem initio impulsionis circumivit, perseverare <lb/>debuit; et quia perpetuus est, aequalibus temporibus aequales angulos ipsum <lb/>describere etiam conveniebat. </s>

<s>Et ut motum descensus quem in initio quo&shy;<lb/>que habuerat, retineret, postquam in motum perpetuum per unum planum <lb/>deflexit, per aliquod spatium a vertice coni descendit, donec Soli, circa quem <lb/>etiam alligatus est, proximus factus esset. </s>

<s>Unde, propter motus perpetuita&shy;<lb/>tem, digreditur, et rursum versus Coni verticcm ascendit. </s>

<s>Sicque ellipsim <lb/>describit Planeta ut observationes docent &rdquo; (ibi). </s></p><p type="main">

<s>Convinto da queste osservazioni il Boulliaud, non pot&egrave; negare i fatti, i <lb/>quali egli accomod&ograve; piuttosto alle sue fantasie, che alle vere cause reali. </s>

<s>Il <pb xlink:href="020/01/1090.jpg" pagenum="533"/>merito di lui perci&ograve;, ne'progressi dell'Astronomia nuova, consiste principal&shy;<lb/>mente nell'aver confermata la verit&agrave; delle orbite ellittiche. </s></p><p type="main">

<s>Mentre in Italia, in ordine a queste teorie planetarie, prevaleva ancora <lb/>l'autorit&agrave; di Galileo, sorse nella stessa Francia, contemporaneo al Boulliaud, <lb/>Francesco Blaise conte di Pagan, pi&ugrave; comunemente conosciuto da'Nostri <lb/>sotto il nome di conte Pagani. </s>

<s>Noi non avremmo creduto di dargli nome <lb/>nella Storia della scienza italiana, se non avessimo trovato che il Viviani lo <lb/>chiam&ograve; a parte di questo merito, col tradurre la <emph type="italics"/>Teoria de'Pianeti, nella <lb/>quale tutti gli orbi celesti sono geometricamente ordinati contro la sen&shy;<lb/>tenza degli Astronomi;<emph.end type="italics"/> libro pubblicato in francese nel 1657 a Parigi. </s></p><p type="main">

<s>Qual si fosse il motivo e l'intento di questa versione italiana, rimasta <lb/>da c. </s>

<s>127-76 del Tomo CXLI de'Discepoli di Galileo manoscritta, non sa&shy;<lb/>premmo dire precisamente, ma forse, come parecchi altri libri di Autori stra&shy;<lb/>nieri il Viviani prese a tradurli, per inserirvi le dottrine del suo Maestro; <lb/>cos&igrave; prese a tradurre questo libro del conte Pagani, per divulgare in Italia, <lb/>contro gl'insegnamenti del suo stesso Maestro, la dottrina delle orbite ellit&shy;<lb/>tiche, da pi&ugrave; di un mezzo secolo di osservazioni dimostrate oramai come <lb/>una verit&agrave; di fatto. </s></p><p type="main">

<s>In qualunque modo, alla nostra curiosit&agrave; di sapere in che consistano <lb/>le novit&agrave; introdotte nella Teoria de'Pianeti dal Conte avignonese, risponde <lb/>cos&igrave; l'Autore stesso nella sua Prefazione: &ldquo; Nella guisa, egli dice, che l'Astro&shy;<lb/>nomia era anticamente compresa nell'Astrologia, cos&igrave; la teorica de'Pianeti &egrave; <lb/>presentemente nell'Astronomia. </s>

<s>Cleomede fu il primo fra i Greci a distin&shy;<lb/>guere la cognizione delle stelle erranti dalle fisse. </s>

<s>Arato ed Ipparco furono <lb/>gl'inventori della teorica de'Pianeti, cio&egrave; delle Stelle erranti.... Guglielmo <lb/>landgravio d'Hassia e Ticone Brahe, signori danesi, gli diedero l'ultima <lb/>mano; io fui il primo a tor via le cause fisiche, e a rendere tutti li moti <lb/>geometrici. </s>

<s>Questi gran personaggi non poterono ritrovare negli Orbi delle <lb/>loro teoriche li veri moti de'Pianeti. </s>

<s>I Deferenti e gli Epicicli non servi&shy;<lb/>rono nulla alle loro intenzioni, e costretti a rilasciarli alle conietture della <lb/>Fisica, confondevano l'Astronomia colla Filosofia. </s>

<s>Reinoldo e Keplero furono <lb/>i pi&ugrave; famosi nello spiegare questo accomodamento, e stabilirono equazioni <lb/>fisiche, per accomodare ad esse l'equazioni geometriche, e senz'accorgersi <lb/>di un s&igrave; notabile inconveniente, ammessero queste falsit&agrave; per principii na&shy;<lb/>turali. </s>

<s>E fino ai nostri tempi nessuno pot&egrave; giammai immaginarsi cadere er&shy;<lb/>rore in s&igrave; grandi uomini. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In quest'Opera noi aviamo schiarito l'oscurit&agrave; delle loro teoriche, <lb/>togliendo via la confusione di tante cause diverse, ordinando tutti i moti <lb/>de'Pianeti, e parimente quei della Luna, in termini di pura Geometria, ac&shy;<lb/>comodando la semplicit&agrave; de'precetti alla sublimit&agrave; della scienza, la facilit&agrave; <lb/>delle supputazioni alle nuove scoperte dell'Astronomia, ed una molto per&shy;<lb/>fetta aggiustatezza ai moti di tutti i Pianeti, per via della cognizione delle <lb/>singolari propriet&agrave; degli ellissi, che felicemente aviamo scoperte &rdquo; (MSS. <lb/>cit., c. </s>

<s>128). </s></p><pb xlink:href="020/01/1091.jpg" pagenum="534"/><p type="main">

<s>Nel Cap. </s>

<s>III dell'Opera si tratta di proposito <emph type="italics"/>Della natura degli ellissi,<emph.end type="italics"/><lb/>accomodati alle orbite de'Pianeti, in un fuoco delle quali orbite ellittiche <lb/>disposto il Sole, s'insegna il modo di determinare le varie anomalie pre&shy;<lb/>sentate dal moto degli stessi Pianeti. </s>

<s>&ldquo; Tutti i Filosofi, dice quivi l'Autore, <lb/>non gli hanno potuti giammai figurare che per cerchi perfetti. </s>

<s>Keplero fu <lb/>il primo, fra tanti savi e grandi personaggi, a ordinarli in ellissi. </s>

<s>Ci&ograve; non <lb/>fece che leggermente, e per l'uso delle Tavole rodolfine, senza dimostra&shy;<lb/>zione geometrica, e perfetta aggiustatezza, per la poca cognizione ch'egli <lb/>teneva delle propriet&agrave; dell'ellisse &rdquo; (ivi, c. </s>

<s>137). </s></p><p type="main">

<s>S'intende insomma come l'opera del conte Pagani era tutta geometrica, <lb/>e non si vede perci&ograve; come potesse sperarne s&igrave; gran progressi l'Astronomia, <lb/>che non &egrave; scienza astratta di linee, ma di corpi materiali. </s>

<s>L'insistere nono&shy;<lb/>stante sulle propriet&agrave; dell'Ellisse fu una geometria, che pot&egrave; allora givare <lb/>alla combattuta fisica del Keplero, e il Viviani forse prese a far quella ver&shy;<lb/>sione dal francese, per recar questo giovamento alla scienza italiana. </s>

<s>Ma la <lb/>scienza italiana, per tornar sulla dirittura di quella via, dalla quale Galileo <lb/>l'aveva detorta, non ebbe punto bisogno di quel debole aiuto straniero. </s>

<s>Sorse <lb/>fra i discepoli dello stesso Galileo un grande ingegno, il quale tanto pro&shy;<lb/>mosse l'Astronomia nuova, istituita dal Keplero, che pot&egrave; rimetterla al New&shy;<lb/>ton in tal condizione, da non aver d'altro bisogno che dell'ultima mano. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Quel discepolo di Galileo &egrave; Gian Alfonso Borelli, il celebre Autore delle <lb/><emph type="italics"/>Theoricae Mediceorum.<emph.end type="italics"/> Egli fu il primo fra gli Astronomi di Europa a sen&shy;<lb/>tir quanto nuovo vigore di vita venisse a infondersi, dal Commentario della <lb/>Stella di Marte, nella Astronomia. </s>

<s>Che se non erasi in pi&ugrave; di un mezzo se&shy;<lb/>colo quel vigore ancora esplicato, riconobbe la principal ragione di ci&ograve; nel&shy;<lb/>l'essere stato depasciuto dalla falce di Galileo, e in non aver nel Boulliaud <lb/>ritrovato il necessario e opportuno fomento. </s>

<s>Alla deficienza di un tale aiuto <lb/>esterno conobbe il Borelli altres&igrave; che s'aggiungevano alcuni impedimenti <lb/>d'intrinseca natura a viziare le nuove idee kepleriane, e a insterilirne perci&ograve; <lb/>il natio rigoglio de'germi. </s></p><p type="main">

<s>Il primo di questi vizi e de'pi&ugrave; nocivi, non in s&egrave;, ma nelle sue con&shy;<lb/>seguenze, fu quello di aver negato, il Keplero, le qualit&agrave; materiali alla luce. </s>

<s><lb/>Cos&igrave;, quella nuova e feconda verit&agrave; scoperta, che cio&egrave; sia il Sole centro at&shy;<lb/>tivo del moto de'Pianeti, rimaneva rintuzzata dentro le menti, le quali non <lb/>si potevano dare a intendere in che modo potesse corporalmente operare <lb/>una virt&ugrave; incorporea, o come dicevasi una specie immateriata. </s></p><p type="main">

<s>Persuaso dunque il Borelli che fosse il moto impartito dal Sole, per <lb/>mezzo de'vortici kepleriani, non dubit&ograve; che gl'impulsi radiosi di lui non <lb/>operassero corporalmente sopra i Pianeti. </s>

<s>Che poi i raggi della luce possano <pb xlink:href="020/01/1092.jpg" pagenum="535"/>veramente produrre effetti meccanici lo prova coll'esempio di alcuni fiori <lb/>pratensi, che s'agitano al tocco della stessa luce commossi, come a una leg&shy;<lb/>gera aura di venti. </s>

<s>&ldquo; Videmus quoque flores plantarum motu locali cieri ab <lb/>iisdem radiis solaribus, ut videre est in floribus pratensibus &rdquo; (Theoricae <lb/>Medic., Florentiae 1665, pag. </s>

<s>61). </s></p><p type="main">

<s>Un tale impulso per&ograve; non &egrave; n&egrave; pu&ograve; essere altro che debolissimo, e se <lb/>pure &egrave; sufficiente a commovere i gracili stami in un'erba, non par possi&shy;<lb/>bile che valga a trasportare di luogo in luogo, e con tanta velocit&agrave; la smi&shy;<lb/>surata mole, per esempio, di Giove o di Saturno. </s>

<s>A cos&igrave; fatta difficolt&agrave; ri&shy;<lb/>sponde il Borelli opportunamente invocando certi principii di Meccanica che, <lb/>per non essere ancora noti, n&egrave; il VI Dialogo delle Nuove Scienze di Gali&shy;<lb/>leo, n&egrave; le Lezioni accademiche del Torricelli, apparivano perci&ograve; nella scienza <lb/>affatto nuovi. </s>

<s>&ldquo; Radii solares, quamtumvis debiles supponantur, impellere <lb/>poterunt corpora Planetarum. </s>

<s>Et licet huiusmodi virtus motiva initio parvum <lb/>et insensibilem motum Planetis imprimere posse videatur, in progressu ta&shy;<lb/>men motus ad insignem celeritatem augeri poterit, et ratio est, quia sup&shy;<lb/>ponitur quod quolibet temporis instanti radii solares revoluti impellunt Pla&shy;<lb/>netas, parum tamen et insensibiliter, et talis velocitatis gradus minimus non <lb/>extinguitur, sed remanet impressus, ut motus natura exigit. </s>

<s>Huic succedit <lb/>secundus impulsus debilissimus eorumdem radiorum solarium, qui impetum <lb/>Planetae duplum reddit: idipsum tertius impulsus facit, idipsum quartus, <lb/>caeterique alii insequentes &rdquo; (ibi). </s></p><p type="main">

<s>Galileo esemplificava questi principi meccanici nel fatto di colui, che <lb/>serra le porte di bronzo di S. </s>

<s>Giovanni (Alb. </s>

<s>XIII, 332), movendo un corpo <lb/>pesantissimo a forza di ripetere semplici e non molto valide spinte. </s>

<s>Ma il <lb/>Borelli trova un altro esempio, che meglio fa al caso suo, ed &egrave; quello di un <lb/>gran naviglio possibile a esser mosso per acqua a furia di ripetute tratte di <lb/>un filo sottilissimo, come potrebb'essere un capello di donna. </s>

<s>Tanto poi, sog&shy;<lb/>giunge, &egrave; pi&ugrave; concludente l'esempio trasportato ai Pianeti, in quanto che, <lb/>notando questi nel liquidissimo etere, non han da vincere la resistenza op&shy;<lb/>posta dalla tenacit&agrave; dell'acqua. </s></p><p type="main">

<s>Veniva cos&igrave; all'assurdo delle specie immateriate del Keplero pi&ugrave; ragio&shy;<lb/>nevolmente il Borelli a sostituire una causa fisica, e operativa nel Sole a <lb/>muovere efficacemente i Pianeti nelle loro orbite, e poniamo che non fosse <lb/>questa di tali moti planetari la causa vera, si faceva nonostante progredire <lb/>la scienza, sgombrando i pregiudizii inveterati che s'avevano intorno alla <lb/>natura della luce, e all'azione di lei su gli altri corpi. </s>

<s>In ogni modo per&ograve; <lb/>&egrave; verissimo che poco, ai progressi della Meccanica celeste, conferirono que&shy;<lb/>sti emendamenti introdotti dal Nostro nell'ipotesi de'vortici kepleriani. </s></p><p type="main">

<s>Altri emendamenti, che equivalevano ad efficacissimi impulsi al progre&shy;<lb/>dire della scienza, furono dal Borelli stesso introdotti nella Nuova astrono&shy;<lb/>mia da quella parte, che tendeva a rassomigliare la virt&ugrave; del Sole alla virt&ugrave; <lb/>del Magnete. </s>

<s>Udimmo come negasse al Sole magnetico il Keplero la virt&ugrave; <lb/>di attrarre, attribuendogli quella sola del dirigere, e ci&ograve; per questa unica <pb xlink:href="020/01/1093.jpg" pagenum="536"/>ragione, perch&egrave; i Pianeti, sempre pi&ugrave; prossimamente attratti, si sarebbero <lb/>andati all'ultimo a congiungere col loro centro. </s></p><p type="main">

<s>Ben comprendeva il Borelli quanto fosse contrario alle pi&ugrave; note pro&shy;<lb/>priet&agrave; del Magnete il negargli la virt&ugrave; di attrarre, e dall'altra parte poniamo <lb/>che, per vederlo da Galileo cos&igrave; disprezzato, non facesse nessuna stima del <lb/>De Dominis, il quale aveva rassomigliato all'attrazione magnetica l'azione <lb/>esercitata sulle acque del mare dal Sole e dalla Luna; le sue proprie os&shy;<lb/>servazioni sui fenomeni capillari, e sulla viscosit&agrave; de'liquidi, lo avevano con&shy;<lb/>sigliato ad ammettere che si attraessero magneticamente insieme cos&igrave; due <lb/>gocciole di rugiada su un filo d'erba, come due stelle negli smisurati spazii <lb/>del Cielo. </s>

<s>Al timore poi che le due stelle attratte non venissero finalmente <lb/>a congiungersi insieme, provvedeva introducendo una forza centraria, che <lb/>rifugga dal centro &ldquo; quemadmodum experimur in rotae, seu fundae gyro &rdquo; <lb/>(Theoricae Medic. </s>

<s>cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Come fossero i contrarii effetti delle due forze messi ingegnosamente <lb/>in gioco, e dimostrati dal Borelli stesso per mezzo della esperienza, fu de&shy;<lb/>scritto nel capitolo precedente, a proposito del moto parabolico delle Co&shy;<lb/>mete, e ora &egrave; da vedere come ne facesse l'applicazione diretta alla sua nuova <lb/>teoria dei moti planetarii. </s></p><p type="main">

<s>&ldquo; Concipiatur itaque, egli dice, Solaris Globus qui convertatur circa <lb/>proprium axim ab occasu in ortum: deinde vero corpus unius Planetae, qui <lb/>naturali instinctu conetur directo motu approprinquari ipsi Soli, quemadmo&shy;<lb/>dum videmus omnia gravia naturalem habere instinctum approprmquandi <lb/>Telluri nostrae, impulsu scilicet a vi gravitatis sibi connatnralis, et quemad&shy;<lb/>modum quoque videmus ferrum directe moveri versus Magnetem &rdquo; (ibi, <lb/>pag. </s>

<s>76). Questo, egli poco appresso soggiunge, &egrave; il primo elemento &rdquo; ex <lb/>quo componi debet revolutio eccentrica Planetarum &rdquo; (ibi), ed &egrave; quello ele&shy;<lb/>mento, a cui venne dato poi il nome di <emph type="italics"/>Forza centripeta.<emph.end type="italics"/> &ldquo; Secundo loco <lb/>supponamus praedictum Planetam a vertigine solarium radiorum in orbem <lb/>ferri circa Solem, per circulorum peripherias ab occasu ad ortum, et quo&shy;<lb/>niam, ut dictum, motus circularis naturaliter quemdam imprimit impetum <lb/>ipsi mobili, quo mediante a centro removetur &rdquo; (ibi); e perci&ograve; questo &egrave; quel <lb/>secondo elemento del moto planetario, a cui fu dato il nome proprio di <lb/><emph type="italics"/>Forza centrifuga.<emph.end type="italics"/></s></p><p type="main">

<s>Dietro ci&ograve; cos&igrave; conclude la sua nuova teorica il Borelli: &ldquo; Ergo ex com&shy;<lb/>positione dictorum motuum efficitur vis quaedam et impetus compositus, ex <lb/>quo pendet periodus celeritatis acquisitae a Planeta, quae a remotissimo ter&shy;<lb/>mino usque ad propinquissimum augetur ea proportione, qua distantiae de&shy;<lb/>crescunt &rdquo; (ibi, pag. </s>

<s>77). </s></p><p type="main">

<s>Riassumendo dunque, i principii che costituiscono questa nuova teoria bo&shy;<lb/>relliana si riducono ai quattro capi seguenti: 1.&deg; I Pianeti gravitano tendendo <lb/>al centro del Sole, come i corpi tendendo al centro della nostra Terra. </s>

<s>2.&deg; La <lb/>forza, con la quale sono i Pianeti attratti verso il Sole. </s>

<s>decresce a proporzione <lb/>che aumentano le distanze. </s>

<s>3.&deg; L'impulso al moto viene ai Pianeti dai vortici <pb xlink:href="020/01/1094.jpg" pagenum="537"/>radiosi della luce del Sole; e 4.&deg;, quel moto stesso risulta dalla composizione <lb/>di due forze opposte, una che tende al centro e l'altra che ne rifugge. </s></p><p type="main">

<s>Le leggi del moto, che governano gli astri, venivano cos&igrave; dal Borelli <lb/>proposte alla scienza sotto forma d'ipotesi, della verit&agrave; o della falsit&agrave; delle <lb/>quali avrebbero poi deciso i calcoli e i fatti. </s>

<s>Ma intanto quelle ipotesi ri&shy;<lb/>chiamavano a s&egrave; gl'ingegni speculativi, i quali si sentirono, dopo gl'impulsi <lb/>venuti dal Keplero, sollevare alla contemplazione delle Armonie celesti, per <lb/>vie tutto affatto nuove e con voli pi&ugrave; sicuri. </s>

<s>Quella sicurezza per&ograve;, per la <lb/>natura del soggetto, e per le condizioni in che veniva proposto, dipendeva <lb/>principalmente dalla Matematica, piuttosto che dalla Fisica; dal calcolo, piut&shy;<lb/>tosto che dalla esperienza. </s>

<s>Fu perci&ograve; che la scuola italiana, tutta dedita alle <lb/>esperienze e pochissimo esercitata ed esperta dell'Analisi matematica, si trov&ograve; <lb/>insufficiente a condur l'Opera, con s&igrave; fausti auguri dal Borelli iniziata. </s>

<s>D'onde <lb/>avvenne che tocc&ograve; all'Inghilterra, patria di valorosi matematici quali erano <lb/>il Wren, l'Hook, l'Halley e il Newton sopra tutti, la gloria e l'utile di rac&shy;<lb/>cogliere il frutto da ci&ograve; che si era seminato in Italia. </s></p><p type="main">

<s>I tre primi ora commemorati furono de'pi&ugrave; solleciti, fra'Matematici in&shy;<lb/>glesi, a rivolgere la loro attenzione sopra que'nuovi principii di Meccanica <lb/>celcste, che veniva a proporre alla scienza il nostro Borelli, e al Newton se&shy;<lb/>guit&ograve;, come fra poco vedremo, un gran benefizio da quelle prime specula&shy;<lb/>zioni de'suoi illustri connazionali: ma era a lui solo riserbata la gloria di <lb/>dimostrar matematicamente in qual pi&ugrave; riposto seno si asconda, e secondo <lb/>quali leggi si dispensi per l'Universo la vita. </s></p><p type="main">

<s>Ripensava una sera di estate, sotto l'aperto cielo sereno, a quel che <lb/>aveva letto nel libro del Fisico italiano di quell'istinto con cui tendono ad <lb/>avvicinarsi <emph type="italics"/>Planetae Soli, Medicea vero sidera Jovi;<emph.end type="italics"/> istinto ivi rassomi&shy;<lb/>gliato a quel medesimo, che hanno naturalmente <emph type="italics"/>omnia gravia approprin&shy;<lb/>quandi Telluri nostrae impulsa scilicet a vi gravitatis sibi conaturalis.<emph.end type="italics"/> In <lb/>questi pensieri, solleva il Newton gli occhi, e fissandogli nella Luna, che <lb/>sul suo capo di pieno lume splendeva. </s>

<s>&mdash; Anche tu dunque, ei dice, pesi <lb/>costass&ugrave; come quaggi&ugrave; pesa una pietra, e anche tu, se nulla ti ritenesse, <lb/>come ogni altro corpo grave cadresti a Terra? </s>

<s>Sublime, stupenda contem&shy;<lb/>plazione! Ma ma io vorrei saper s'ella &egrave; vera. </s>

<s>&mdash; </s></p><p type="main">

<s>Pareva difficilissimo a sodisfare questo desiderio, ma il Newton pens&ograve; <lb/>che tutto si riduceva a calcolar, dal moto nell'orbita, la velocit&agrave;, con la quale <lb/>sarebbe caduta la Luna, e a paragonar quel moto con le oramai note leggi <lb/>del cader della pietra. </s>

<s>Il calcolo cos&igrave; tornava possibilissimo, non richieden&shy;<lb/>dosi altro a condurlo, che la notizia del periodo lunare e della distanza della <lb/>stessa Luna dal centro della Terra. </s>

<s>Istituiti dal Newton i calcoli, e trovatili <lb/>non riscontrare, rest&ograve; incerto se dovesse diffidar della verit&agrave; dell'ipotesi del <lb/>Borelli, o della sua sufficienza in dimostrarla. </s>

<s>Preponder&ograve; saggiamente il giu&shy;<lb/>dizio di qu&agrave;, riconoscendo per prima cosa l'insufficienza da quella poco esatta <lb/>misura, che s'aveva allora del grado del meridiano terrestre; misura ch'era <lb/>il principal fondamento alla nuova supputazione. </s></p><pb xlink:href="020/01/1095.jpg" pagenum="538"/><p type="main">

<s>Ma quella poca esattezza geodetica avrebbe dovuto ridurre i calcoli a <lb/>pi&ugrave; approssimati riscontri, di che il Newton si maravigliava, e anzi, per dir <lb/>pi&ugrave; vero, si accorava, non vedendo come quel solo divario avesse dovuto <lb/>portare a tale disorbitanza. </s>

<s>Era tuttavia cos&igrave; radicato il pregiudizio che la <lb/>virt&ugrave; motiva della luce o del magnete a cui rassomigliavasi il Sole, si de&shy;<lb/>bilitasse a seconda delle semplici distanze, da non entrar nemmeno in so&shy;<lb/>spetto al Newton che le disorbitanze riscontrate ne'suoi calcoli potessero <lb/>dipendere da questo errore. </s>

<s>E ora che troppo ben si comprende quanto do&shy;<lb/>vesse un tale errore tornare ai progressi della scienza dannoso, giova a noi <lb/>qui vederne l'origine, e dir come disnebbiati finalmente ne venissero gl'in&shy;<lb/>telletti. </s></p><p type="main">

<s>L'origine senz'altro venne dal Keplero, il quale, nel suo primo Ottico <lb/>insegnamento, vedemmo al Cap. </s>

<s>I, &sect; V di questo Tomo com'egli ammet&shy;<lb/>tesse nella luce una attenuazione <emph type="italics"/>in latum,<emph.end type="italics"/> o superficiale, e perci&ograve; un de&shy;<lb/>crescere in lei l'intensit&agrave; a proporzione che crescono le semplici distanze. </s>

<s><lb/>Passando poi, nel Commentario <emph type="italics"/>De Stella Martis,<emph.end type="italics"/> a far l'applicazione dei <lb/>principii ottici all'Astronomia, si trov&ograve; aggirato in una penosa incertezza. </s>

<s><lb/>Sentiva bene che la diffusione superficiale era una ipotesi contraria ai fatti. <lb/></s>

<s>&mdash; Poniamo dunque, diceva il Keplero, che quella diffusione sia sferica: eb&shy;<lb/>bene, come decrescer&agrave; l'intensit&agrave; della luce? </s>

<s>come crescono i quadrati delle <lb/>distanze? </s>

<s>anzi, piuttosto come i cubi, a me pare. </s>

<s>&mdash; &ldquo; Nam sphaerica su&shy;<lb/>perficies ab Archimede demonstrata est quadrupla esse ad planum circuli <lb/>maximi, in sphaera scripti. </s>

<s>Omnino itaque corpus duplo distans longius vi&shy;<lb/>detur octuplo obscurius lucere debuisse, non tantummodo duplo &rdquo; (De Stella <lb/>Martis cit., pag. </s>

<s>179). </s></p><p type="main">

<s>Abbandonata perci&ograve;, in tali e tante incertezze, l'Ottica, il Keplero s'af&shy;<lb/>fid&ograve; tutto alla Meccanica, la quale gli dimostrava che le maggiori o minori <lb/>forze d'impulso, che rendono ora pi&ugrave; ora meno veloci i Pianeti, dipende&shy;<lb/>vano dalle minori o dalle maggiori distanze di essi Pianeti dal centro del <lb/>Sole. </s>

<s>&ldquo; Intelligimus enim hinc quod Planetae pene ratione staterae seu vectis <lb/>moveantur. </s>

<s>Nam si Planeta, quo longior a centro, hinc difficilius, utique <lb/>tardius, a centri virtute movetur, equidem perinde est ac si dicerem pon&shy;<lb/>dus, quo longius exeat ab hypomochlio, hoc reddi ponderosius, non seipso, <lb/>sed propter virtutem brachii substentantis in hac distantia. </s>

<s>Utrinque nam&shy;<lb/>que, et hic et in Statera seu vecte, et illic in motu Planetarum, haec debi&shy;<lb/>litas sequitur proportionem distantiarum &rdquo; (ibi, pag. </s>

<s>168). </s></p><p type="main">

<s>Il Boulliaud nel suo Trattato <emph type="italics"/>De natura lucis<emph.end type="italics"/> venne poi a togliere tutte <lb/>quelle incertezze, nelle quali s'erano, insiem col Keplero, aggirati gli Ot&shy;<lb/>tici, e rifiutata la diffusione superficiale, e avendo fatto osservar che la luce <lb/>nella diffusione sferica si muove in superfice e non in corpo, avea senza <lb/>ambagi concluso che l'attenuazione della luce stessa &egrave; proporzionale ai qua&shy;<lb/>drati delle distanze. </s>

<s>Rimase in quel Trattato il Boulliaud dentro i termini <lb/>dell'Ottica, ma nell'<emph type="italics"/>Astronomia philolaica,<emph.end type="italics"/> riguardando la luce come forza <lb/>impulsiva, a modo del Keplero, fece rilevar gli errori, in ch'era incorso l'Au-<pb xlink:href="020/01/1096.jpg" pagenum="539"/>tore del Commentario di Marte, e ne not&ograve; argutamente i paralogismi. </s>

<s>&ldquo; Vir&shy;<lb/>tus autem illa, qua sol prehendit seu harpagat Planetas, corporalis quae ipsi <lb/>pro manibus est, lineis rectis in omnem mundi amplitudinem emissa, quasi <lb/>species Solis cum illius corpore rotatur. </s>

<s>Cum ergo sit corporalis, imminui&shy;<lb/>tur, et extenuatur in maiori spatio et intervallo. </s>

<s>Ratio autem huius immi&shy;<lb/>nutionis eadem est ac luminis, in ratione nempe dupla intervallorum, sed <lb/>eversa. </s>

<s>Hoc non negavit Keplerus, attamen virtutem motricem in simpla tan&shy;<lb/>tum ratione intervallorum contendit imminui &rdquo; (Parisiis 1645, pag. </s>

<s>23). </s></p><p type="main">

<s>Noi vedemmo dianzi da che fosse condotto il Keplero a rifiutar la legge <lb/>de'quadrati, che non neg&ograve; alla luce, come non le neg&ograve; quella de'cubi, ma <lb/>il Boulliaud procede oltre a notare il paralogismo, che si commetteva dallo <lb/>stesso Keplero in concluder che la luce, operando per contatto di superficie, <lb/>debiliti nonostante la sua virt&ugrave; a proporzione che crescono le semplici di&shy;<lb/>stanze. </s>

<s>&ldquo; Illa virtus agit per contactum speciei solaris, quae cum virtute <lb/>motrice a Sole defluit. </s>

<s>Species autem illa tangit corpus Planetae ut super&shy;<lb/>ficies superficiem, ergo et virtus eodem modo tanget, quippe quae eodem <lb/>modo a Sole defluit. </s>

<s>Ipsam igitur in ratione dupla intervallorum, ut speciem, <lb/>imminui necesse est &rdquo; (ibi). </s></p><p type="main">

<s>Si trova nell'Astronomia filolaica un'altra importantissima applicazione <lb/>dell'Ottica, la qual consiste in determinare la quantit&agrave; di luce, che riceve <lb/>ciascun Pianeta, secondo la sua maggiore o minor distanza dal Sole. </s>

<s>Gli <lb/>Astronomi precedenti s'erano contentati di dire cos&igrave; indeterminatamente, <lb/>come dall'altra parte &egrave; suggerito anco al volgo dall'esperienza comune, che <lb/>i Pianeti tanto ricevon meno di luce dal Sole quanto ne son pi&ugrave; lontani. </s>

<s><lb/>Ma il Boulliaud, con immediata applicazione delle leggi della diffusion della <lb/>luce, da s&egrave; gi&agrave; dimostrate, concluse che l'intensit&agrave; dell'illuminazion de'Pia&shy;<lb/>neti &egrave; in ragion reciproca delle loro distanze quadratiche dal Sole. </s></p><p type="main">

<s>&ldquo; Inquisita (dice, al cap. </s>

<s>X del libro I, l'Autore dell'Astronomia filo&shy;<lb/>laica) apparente diametro Solis in distantiis omnium Planetarum ab ipso, <lb/>inquirenda est deinceps proportio, sub qua imminuitur illuminatio illius, in <lb/>unaquaque distantia. </s>

<s>Omnis autem illuminatio, etsi a corpore lucido produ&shy;<lb/>catur, non tamquam a corpore trinam dimensionem possidente producta con&shy;<lb/>siderari debet, sed quatenus a superficie illius perficitur, et quatenus etiam <lb/>in superficiem corporis illustrati incidunt radii. </s>

<s>Cum itaque luminis effluxus <lb/>sphaerici sint, in superficie sphaerae angustioris consertiores sunt radii, quam <lb/>in ampliore. </s>

<s>Quare in minori distantia a lucido plures radii erunt in una <lb/>aliqua superficie, in maiori vero elongatione in eadem pauciores: rarescit <lb/>enim lumen digrediens a lucido. </s>

<s>Quare, cum lux superficie terminetur et <lb/>illuminet, ut se habebit quadratum diametri sphaerae unius, ad quadratum <lb/>sphaerae alterius; ita illuminatio ad illuminationem, seu ut potentia distan&shy;<lb/>tiae Planetae unius a Sole, ad potentiam distantiae alterius, ita illuminatio <lb/>ad illuminationem, analogia inversa. </s>

<s>Sed est etiam eadem ratione alterna, ut <lb/>distantia ad distantiam, ita diameter apparens ad diametrum apparentem. </s>

<s>Ab <lb/>aequali ergo, ut quadratum semidiametri apparentis unius, ad quadratum <pb xlink:href="020/01/1097.jpg" pagenum="540"/>alterius, ita illuminatio ad illuminationem, ratione alterna &rdquo; (Parisiis 1645, <lb/>pag. </s>

<s>17, 18). </s></p><p type="main">

<s>Noi che prestiamo oramai il nostro assenso ai Teoremi del Boulliaud, <lb/>come alle cose che pi&ugrave; certamente sien dimostrate per vere, crederemmo <lb/>che si dovess'essere la medesima persuasione ingerita nelle menti degli <lb/>Astronomi, a cui furono quegli stessi Teoremi, dopo la prima met&agrave; del se&shy;<lb/>colo XVII, cos&igrave; solennemente annunziati. </s>

<s>Eppure, chi il crederebbe? </s>

<s>furon <lb/>tutte le orecchie sorde a quest'annunzio del vero, a persuadere il quale vi <lb/>bisognarono altri fatti, di cui ci rimane ora a narrar brevemente la storia. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Erano gi&agrave; vent'anni, che si leggeva in pubblico l'Astronomia filolaica, <lb/>quando il Borelli meditava la sua teoria de'Pianeti. </s>

<s>Egli che aveva, dopo il <lb/>Boulliaud, riconosciuto l'error del Keplero riguardo alla natura della luce, <lb/>sembrava che avrebbe, altres&igrave; dopo il Boulliaud, dovuto riconoscere l'altro <lb/>errore, detto pur dal Keplero riguardo alla diffusion della stessa luce; ond'&egrave; <lb/>che supponendo l'Autor della Teorica de'Medicei venire impresso il moto <lb/>ai Pianeti dagl'impulsi radiosi del Sole, pareva che ne avesse dovuto con&shy;<lb/>cludere, conforme a ci&ograve; ch'era stato dimostrato, che le forze di tali impulsi <lb/>solari s'indeboliscono via via a proporzione che crescono i quadrati delle <lb/>distanze. </s>

<s>S'accenn&ograve; gi&agrave; com'avesse infelicemente il Borelli eletto piuttosto <lb/>il falso antico, che n&ograve; il vero nuovo, di che egli e tutti gli altri, che aber&shy;<lb/>rarono con lui per altri vent'anni, non trovano forse scusa che in una con&shy;<lb/>siderazione ed &egrave; questa: L'incertezza, ch'ereditarono dal Keplero gli Ottici <lb/>e gli Astronomi, rispetto al decider se, concessa la diffusion della luce in <lb/>sfera, l'intensit&agrave; luminosa sia reciproca ai quadrati o ai cubi de'raggi, ve&shy;<lb/>niva tolta dal Boulliaud coll'asserir semplicemente che la stessa luce si dif&shy;<lb/>fonde non in solido, ma in superficie, senza dar per&ograve; niuna prova della sua <lb/>asserzione. </s></p><p type="main">

<s>La pi&ugrave; bella prova sarebbe stata quella dell'esperienza, la quale non <lb/>si capirebbe com'avesse indugiato ancora parecchi altri anni, se non si ri&shy;<lb/>pensasse che, almeno fra noi, s'erano in questo proposito e a tale impor&shy;<lb/>tantissimo effetto, tentate esperienze di un altr'ordine, e per la loro appa&shy;<lb/>rente facilit&agrave; seduttrici. </s>

<s>Giacch&egrave; la virt&ugrave; del Sole, in dare impulso ai Pianeti, <lb/>si rassomigliava alla virt&ugrave; del Magnete, e s'era questa stessa virt&ugrave; dal Bo&shy;<lb/>relli principalmente riconosciuta nell'attrazione, s'argomentava che l'acce&shy;<lb/>lerazione di un ferro verso il Magnete stesso attraente fosse la ragione, colla <lb/>quale si accelererebbero i Pianeti attratti verso il centro del Sole. </s>

<s>Ora, ben&shy;<lb/>ch&egrave; il Kircker non avesse saputo affermar altro in proposito, se non che <lb/>&ldquo; Aaequalibus spaciis inaequalia fiunt in propagatione Magnetismi decre&shy;<lb/>menta &rdquo; (De Magnete, Romae 1654), e bench&egrave; dalle prime esperienze fatte <pb xlink:href="020/01/1098.jpg" pagenum="541"/>nell'Accademia del Cimento si ricavasse questo solo fatto, che cio&egrave; &ldquo; Un <lb/>ferro posto notante sull'acqua, ovvero su una tavola, alzato da un pezzo di <lb/>Calamita, se gli accosta con moto sempre pi&ugrave; accelerato &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. CXXXIX, c. </s>

<s>28); si volle in altre esperienze accademiche, dirette dallo <lb/>stesso Borelli, ricercar la legge di questo acceleramento, che sarebbe stata <lb/>la legge medesima, con cui cresce la virt&ugrave; motrice, avvicinandosi i Pianeti <lb/>sempre pi&ugrave; al Sole. </s>

<s>Ma rimasero le belle speranze deluse, come attesta un <lb/>Diario, in cui si legge la nota seguente: &ldquo; A'd&igrave; 5 Luglio 1657. Si dur&ograve; per <lb/>lo restante del mese a osservare e provare in varii modi, se si potesse tro&shy;<lb/>vare in che proporzione un ago galleggiante in acqua accelerasse il suo moto, <lb/>per unirsi alla Calamita posta nella massima distanza, nella quale lo tira, <lb/>misurando i tempi co'quali passava spazii uguali con le vibrazioni di un <lb/>pendolo molto esatto, n&egrave; fu mai possibile riconoscervi proporzione alcuna &rdquo; <lb/>(MSS. Cim., T. II, c. </s>

<s>249). </s></p><p type="main">

<s>La difficolt&agrave; si fece poi sentire anche ad altri valorosi sperimentatori, <lb/>per cui il Newton ritrasse da certe sue osservazioni, da lui stesso ricono&shy;<lb/>sciute per grossolane, che la forza magnetica &ldquo; in recessu a Magnete de&shy;<lb/>crescit in ratione distantiae, non duplicata, sed fere triplicata &rdquo; (Principia <lb/>mathem., Lib. </s>

<s>III, Genevae 1742, pag. </s>

<s>41). Solo fu riserbato pi&ugrave; tardi, a <lb/>quello squisitissimo strumento della <emph type="italics"/>Bilancia di torsione,<emph.end type="italics"/> il dimostrar ch'es&shy;<lb/>sendo veramente la ragion delle distanze duplicata, il Newton era in errore. </s></p><p type="main">

<s>Non fa perci&ograve; maraviglia se il Borelli, a cui mancavano gli strumenti <lb/>inventati tanto tempo dopo, lasciate per le difficolt&agrave; incontratevi le fluttuanti <lb/>vie dell'esperienza, cerc&ograve; di ridursi a quel pi&ugrave; sicuro porto della scienza <lb/>Meccanica, che gli era stato additato dallo stesso Keplero. </s>

<s>&ldquo; Nunc superest, <lb/>egli dice nel lib. </s>

<s>I delle <emph type="italics"/>Theoricae Mediceorum,<emph.end type="italics"/> ut ostendamus quomodo et <lb/>qua ratione motiva facultas, quae in Sole, vel in Jove reperitur, cum sit per&shy;<lb/>petuo eiusdem gradus et sibi ipsi uniformis, possit tamen modo maiorem <lb/>modo minorem celeritatem tribuere eidem Planetae, prout ipse magis mi&shy;<lb/>nusve approprinquat vel removetur a Sole vel Jove. </s>

<s>Hoc autem facillimo <lb/>negotio absolvetur ex aliquibus principiis mechanicis &rdquo; (Florentiae 1665, <lb/>pag. </s>

<s>63). </s></p><p type="main">

<s>Questi principii meccanici son quelli della stadera o del vette, i quali <lb/>avendo esposti al Lettore, il Borelli cos&igrave; prosegue: &ldquo; Concipiatur solare vel <lb/>ioviale corpus AS (fig. </s>

<s>104) torqueri circa proprium centrum S, globus vero <lb/><figure id="id.020.01.1098.1.jpg" xlink:href="020/01/1098/1.jpg"/></s></p><p type="caption">

<s>Figura 104.<lb/>eiusdem Planetae modo sit proprinquum <lb/>Soli in B, modo vero remotum in C. </s>

<s><lb/>Quoniam vis qua Sol operatur move&shy;<lb/>turque Planetam, a suorum radiorum <lb/>potentia mensuratur, qui semper iidem <lb/>et eiusdem energiae sunt, et a celeritate <lb/>propriae vertiginis, quae pariter manet <lb/>inalterata ac ex ambobus hisce eius momentum componitur, cum debeat hoc <lb/>momentum aequari duabus resistentiis eiusdem Planetae in B et in C; ne-<pb xlink:href="020/01/1099.jpg" pagenum="542"/>cesse est ut contra minorem Planetae resistentiam in B maiori operetur <lb/>efficacia, ideoque ipsum maiori celeritate convertat ea qua utitur contra <lb/>maiorem resistentiam eiusdem Planetae siti in maiori distantia C, quem <lb/>proinde tardiori motu torquebit ea proportione quam reciproce habent re&shy;<lb/>sistentiae seu distantiae &rdquo; (ibi, pag. </s>

<s>65). </s></p><p type="main">

<s>Tale, cos&igrave; conclusa dalle Meccaniche, era la legge che sopraffece quel&shy;<lb/>l'altra dal Boulliaud dimostrata dietro i principii dell'Ottica, e tale, cio&egrave; <lb/>delle semplici distanze, era la legge professata allora anche dai matematici <lb/>d'Inghilterra, quando l'Hook si sent&igrave; vivamente eccitato dalle nuove teo&shy;<lb/>rie delle forze centrali proposte alle speculazioni degli Astronomi dal nostro <lb/>Borelli. </s></p><p type="main">

<s>Intese l'arguta mente del Filosofo inglese quello essere piuttosto sog&shy;<lb/>getto da Matematica, che no da esperienza, e not&ograve; che l'Italiano autore delle <lb/>nuove teorie, cos&igrave; ritroso ad accettare il principio della composizione del <lb/>moto, confondeva la forza centrifuga con la forza tangenziale. </s>

<s>Intorno alle <lb/>leggi delle forze centrifughe stesse non si conosceva altro a quel tempo, se <lb/>non quel poco, e misto ad errori, che ne'Dialoghi del Sistema del Mondo <lb/>ne aveva scritto il Galileo, quando si pubblicarono, nel 1673, i teoremi del&shy;<lb/>l'Hugenio. </s>

<s>Allora l'Hook, posto il principio che la forza centrifuga &egrave; da una <lb/>parte direttamente proporzionale alla mole e al raggio dell'orbita dal mobile <lb/>descritta, ed &egrave; dall'altra in ragion recipreca del quadrato del tempo perio&shy;<lb/>dico; suppo sto inoltre che l'azione esercitata dal Sole sui Pianeti sia pro&shy;<lb/>porzionale alle loro moli, calcol&ograve; i moti di due degli stessi Pianeti, per pa&shy;<lb/>ragonarli fra loro, e applicata la terza legge kepleriana, che cio&egrave; i quadrati <lb/>de'tempi periodici son proporzionali ai cubi delle distanze, trov&ograve; che il Sole <lb/>esercitava sulle moli mosse una virt&ugrave; reciprocamente proporzionale ai qua&shy;<lb/>drati di quelle stesse distanze. </s></p><p type="main">

<s>Allora torn&ograve; l'Hook indietro col pensiero sulla dimenticata Astronomia <lb/>filolaica, e il teorema fotometrico applicato ai Pianeti, e la legge con cui il <lb/>Sole dispensa a distanza i suoi impulsi radiosi, gli apparvero nella verit&agrave; <lb/>della loro sembianza. </s>

<s>L'Ottica e l'Astronomia proseguirono da quel punto <lb/>affrettatamente il loro corso, come a rimuovere un gran macigno, che abbia <lb/>tutto ingombrato l'alveo alle ringorgate acque di un fiume. </s></p><p type="main">

<s>La gloriosa opera di condurre il corso a coteste acque, in che scen&shy;<lb/>deva con incredibile impeto il fiume della scienza, fu riserbata principal&shy;<lb/>mente al Newton sollecitatovi dall'Hook stesso, dal Wren e dall'Halley. </s>

<s>Nello <lb/>Scolio alla proposizione IV del Lib. </s>

<s>I l'Autor de'Principii matematici di <lb/>Filosofia naturale confessa pubblicamente di essere stato preceduto da que&shy;<lb/>sti tre suoi illustri connazionali (ediz. </s>

<s>cit., pag. </s>

<s>103), i quali avevano intanto <lb/>raccolto un tal preziosissimo frutto dal connubio delle speculazioni del Bo&shy;<lb/>relli coi teoremi ugeniani. </s></p><p type="main">

<s>Non fu il Newton troppo sollecito di tornare alla dimostrazione dell'ipo&shy;<lb/>tesi borelliana, persuaso che alla precision del calcolo della caduta della Luna <lb/>nuocesse principalmente la poco esatta misura assunta di un grado del me-<pb xlink:href="020/01/1100.jpg" pagenum="543"/>ridiano terrestre. </s>

<s>Ma quando nel 1682 il Picard, nell'Accademia francese, <lb/>ebbe ricercata quella misura con tanta diligenza, e l'ebbe trovata tale da <lb/>poterci affidar sopra i calcoli alla sicura, e allora con questo nuovo dato e <lb/>supposto, com'avevano concluso l'Hook, e il Wren e l'Halley d'accordo con <lb/>lui, che la forza con cui la Terra attrae la Luna s'indebolisca a proporzione <lb/>che aumentano i quadrati delle distanze, il Newton riprese le abbandonate <lb/>supputazioni, delle quali, nell'opuscolo <emph type="italics"/>De mundi systemate,<emph.end type="italics"/> e nella pro&shy;<lb/>posizione IV del Lib. </s>

<s>III de'Principii, ne furono lasciati impressi i vestigi. </s></p><p type="main">

<s>Assunta la distanza media della Luna 60 semidiametri terrestri, il pe&shy;<lb/>riodo lunare, rispetto alle stelle fisse, prefinito in 27 giorni, 7 ore e 43 mi&shy;<lb/>nuti, e posto che l'ambito della Terra corrisponda a 123,249,600 piedi pa&shy;<lb/>rigini &ldquo; uti a Gallis mensurantibus definitum est, si Luna motu omni privari <lb/>fingatur ac dimitti, ut urgente vi illa omni, qua in orbe suo retinetur, de&shy;<lb/>scendat in Terram, haec spatio minuti unius primi cadendo describit pedes <lb/>parisienses 15 1/12 &rdquo; (Principia cit., Lib. </s>

<s>III, pag. </s>

<s>26, 27). </s></p><p type="main">

<s>Supposto poi dall'altra parte che la Luna stessa venga attratta fin presso <lb/>alle nostre regioni, con una forza crescente in ragion reciproca de'quadrati <lb/>delle distanze, la rivoluzione di lei intorno alla Terra si compirebbe in un'ora, <lb/>24 minuti primi e 27 secondi, non tenuto conto della resistenza dell'aria, per <lb/>cui &ldquo; sublato motu suo circolari, et urgente eadem vi centripeta ac prius, <lb/>describeret cadendo pedes parisienses 15 1/12, tempore minuti unius secundi <lb/>(De mundi syst. </s>

<s>cit., pag. </s>

<s>12). Or perch&egrave; quello stesso spazio in piedi pa&shy;<lb/>rigini fu sperimentalmente ritrovato dall'Huyghens esser passato da un grave, <lb/>che sulla superficie della Terra cada liberamente in un minuto secondo, e <lb/>perci&ograve; il Newton cos&igrave; conclude la sua dimostrazione: &ldquo; Et propterea vis, qua <lb/>Luna in orbe suo retinetur, si descendatur in superficiem Terrae, aequalis <lb/>evadit vi gravitatis apud nos, ideoque est illa ipsa vis quam nos gravitatem <lb/>dicere solemus &rdquo; (Principia cit., pag. </s>

<s>29). </s></p><p type="main">

<s>L'ipotesi del Borelli veniva dunque cos&igrave; matematicamente dimostrata, <lb/>rispetto al caso particolare della Luna, ma l'Autor delle Teoriche de'Medi&shy;<lb/>cei aveva esteso quell'ardita ipotesi a tutti i sistemi, e avea detto che non <lb/>solo, come una pietra sulla Terra, gravita sulla Terra stessa la Luna, ma <lb/>che gravitano pure allo stesso modo i Pianeti sul Sole, e i Satelliti su Giove, <lb/>e che insomma la gravitazione era legge universale. </s></p><p type="main">

<s>Rimaneva perci&ograve; al Newton a dimostrar la universalit&agrave; dell'ipotesi bo&shy;<lb/>relliana, ci&ograve; che egli fece nelle prime proposizioni del I libro dei Principii, <lb/>trattando delle propriet&agrave; generali di un corpo, che si rivolga intorno ad un <lb/>centro, in conformit&agrave; delle leggi scoperte dal Keplero, e mostrando che quelle <lb/>propriet&agrave; competono cos&igrave; bene al moto della Luna intorno alla Terra, come <lb/>al moto de'Pianeti intorno al Sole, e de'Satelliti intorno a Giove, cosicch&egrave; <lb/>&ldquo; Si tempora periodica sint in ratione sesquiplicata radiorum &rdquo; per qualun&shy;<lb/>que corpo rivolgentesi in quelle condizioni nella sua orbita &ldquo; vires centri&shy;<lb/>petae erunt reciprocae ut quadrata temporum &rdquo; (Principia cit., pag. </s>

<s>98). Dun&shy;<lb/>que, le forze centripete di qualunque corpo girante intorno a un centro di <pb xlink:href="020/01/1101.jpg" pagenum="544"/>attrazione nel Cosmo, operano secondo le leggi della gravit&agrave; terrestre; dun&shy;<lb/>que la gravit&agrave; o l'attrazione, non &egrave; per una particolare e mutua corrispon&shy;<lb/>denza che passi fra la Terra e la Luna, ma &egrave; legge di moto universale. </s>

<s>La <lb/>qual legge universale, universalmente applicata, conferm&ograve; le ragioni date gi&agrave; <lb/>dal De Dominis del flusso marino, dimostr&ograve; la causa della precessione degli <lb/>equinozii, della nutazione de'poli, e svel&ograve; insomma i pi&ugrave; ascosti misteri del&shy;<lb/>l'antica Filosofia. </s>

<s>Questa sola cosa rimaneva ancora a sapere come mai la <lb/>Natura avesse eletto di comporre le sue celesti armonie, non sopra la per&shy;<lb/>fezione de'circoli, come si persuadevano gli antichi, ma sopra le irregolarit&agrave; <lb/>delle ellissi. </s></p><p type="main">

<s>Il problema si proponeva curiosamente a risolvere sotto quest'altra <lb/>forma: come mai i Pianeti non si tengano sempre dal centro de'loro moti <lb/>ugualmente lontani, ma ora se ne dilunghino di pi&ugrave;, ora gli vadano pi&ugrave; <lb/>d'appresso. </s>

<s>Il Keplero immagin&ograve; nel Sole un polo attrattivo e un polo re&shy;<lb/>pulsivo, come nel Magnete, cosicch&egrave; il Pianeta nel perielio fosse attratto, e <lb/>nell'afelio invece venisse respinto. </s>

<s>Ma perch&egrave; sentiva che sarebbe accusato <lb/>di contradizione, per aver negata allo stesso Sole la virt&ugrave; di attrarre, si stu&shy;<lb/>dia di discolparsene nella guisa seguente: &ldquo; Ego vero supra, Cap. </s>

<s>XXXIX, <lb/>de Sole negavi vim Planetarum attractricem: intelligebatur tamen tantum&shy;<lb/>modo mere attractrix, ut ex usurpato argumento patet. </s>

<s>Hic autem ponitur <lb/>simul attractrix, simul alio situ repultrix. </s>

<s>Vel etiam hoc ponatur ut Sol <lb/>instar ferri nondum imbuti, tantummodo petatur, non vicissim petat, cum <lb/>ipsius filamenta supra fuerint circularia, Planetarum vero hic ponantur recta &rdquo; <lb/>(De Stella Martis cit., pag. </s>

<s>275). Non cessa per&ograve; per questo di rimaner l'ipo&shy;<lb/>tesi kepleriana tuttavia involta in una caligine cos&igrave; densa, che attraverso a <lb/>lei il Sole della verit&agrave; rompe ogni raggio. </s></p><p type="main">

<s>Vedemmo come a tale intento principalmente, cio&egrave; a rendere la ragione <lb/>delle orbite ellittiche, fosse architettato dal Boulliaud quel suo cono scaleno. </s>

<s><lb/>Ma oltre che questa sembrava una fedelissima imitazione de'fantastici mac&shy;<lb/>chinamenti di Tolomeo, non s'intendeva come dovessero i Pianeti avvolgersi <lb/>con tant'ordine intorno a una linea retta immaginaria, e tanto irregolar&shy;<lb/>mente riguardare il Sole, che &egrave; centro fisico e reale del moto. </s></p><p type="main">

<s>Il Borelli, a cui non piacque questa Geometria del Boulliaud, sper&ograve; nella <lb/>Fisica di trovare soccorso, ma era ad ogni modo un medesimo lavorare di <lb/>fantasia, bench&egrave; il campo fosse diverso. </s>

<s>Immagin&ograve; che i Pianeti galleggias&shy;<lb/>sero nel liquido etere, come un cilindro di legno galleggia nell'acqua. </s>

<s>E a <lb/>quel modo che, lasciato verticalmente cader quel cilindro, per impulso di <lb/>gravit&agrave; si profonda alquanto al di sotto del livello conveniente alle leggi idro&shy;<lb/>statiche, e risospinto se ne solleva altrettanto, reciprocando le oscillazioni, <lb/>che diverrebbero perpetue, rimosse tutte le resistenze; cos&igrave; il Pianeta reci&shy;<lb/>proca ondeggiando nell'etere simili oscillazioni, d'ond'&egrave; ch'eccedendo ora <lb/>da una parte ora dall'altra del centro, l'orbite non son circolari, ma confi&shy;<lb/>gurate in ellisse. </s>

<s>Con tal meccanismo facilmente si spiega, secondo il Bo&shy;<lb/>relli, l'origine e la natura delle orbite planetarie, perch&egrave; basta supporre che <pb xlink:href="020/01/1102.jpg" pagenum="545"/>il Creatore nell'inizio del moto avesse collocato ciascun Pianeta nel suo pro&shy;<lb/>prio afelio. </s>

<s>&ldquo; Supponamus divinam Sapientiam, ob eius altissimos et inscru&shy;<lb/>tabiles fines, decrevisse motum Planetarum circa Solem eccentricum efficere <lb/>ac figurae non circularis sed ellipticae: tunc nihil aliud necessarium fuisset <lb/>quam summo compendio ab initio creare locareque Planetam in remotissimo <lb/>puncto &rdquo; (Theoricae medic. </s>

<s>cit., pag. </s>

<s>78). </s></p><p type="main">

<s>A noi per dir vero sembran queste ragioni fisiche del gran Borelli un <lb/>romanzo, eppure ei se ne compiacque, e quando vide che simili fantasie <lb/>erano uscite fuori da quel cervellaccio del Fabry, piuttosto che concluderne <lb/>dover essere le sue stesse parto di un cervellaccio, pens&ograve; di preparare fu&shy;<lb/>riosamente la stampa delle Teoriche de'Medicei, per non parere di essersi <lb/>servito delle altrui invenzioni. </s>

<s>&ldquo; Ho ricevuto oggi (scriveva da Pisa il d&igrave; <lb/>18 Febbraio 1665 al principe Leopoldo) alle 22 ore, il libro del p. </s>

<s>Fabri <lb/>(cio&egrave; i Dialoghi fisici) il quale mi ha reso attonito per quel poco che ho ve&shy;<lb/>duto, perch&egrave; veggo che a quel cervellaccio gli son sovvenuti concetti assai <lb/>simili ai miei, con i quali spiego le cagioni fisiche de'moti de'Pianeti, e <lb/>bench&egrave; quest'uomo dia al solito suo in spropositi, tuttavia non vorrei che <lb/>altri potessi sospettare che io mi fossi servito delle sue invenzioni &rdquo; (MSS. <lb/>Cim., T. XVIII, c. </s>

<s>110). </s></p><p type="main">

<s>Del libro delle Teoriche, appena che ne fu eseguita furiosamente la <lb/>stampa in Firenze, ne mand&ograve; in dono lo stesso principe Leopoldo una copia <lb/>al Boulliaud, il quale rispose una lettera al donatore, dicendo avrebbe de&shy;<lb/>siderato che l'Autor di quelle teoriche gli dimostrasse le cause fisiche dei <lb/>Pianeti, perch&egrave; altrimenti le avrebbe tenute per una semplice congettura, <lb/>non punto pi&ugrave; probabile della sua. </s>

<s>Il Borelli rispose allo stesso Principe, <lb/>che gli aveva fatto recapitare la lettera venuta da Parigi: &ldquo; Ho letto l'epi&shy;<lb/>stola del sig. </s>

<s>Bullialdo, e mi son maravigliato prima, che egli richiegga da <lb/>me dimostrazione delle cause fisiche de'moti de'Pianeti da me assegnate, <lb/>quando io espressi in pi&ugrave; luoghi che le propongo per coniettura e proba&shy;<lb/>bilit&agrave;; secondo, che egli stimi tanto probabile le ragioni fisiche da lui im&shy;<lb/>maginate quanto le mie. </s>

<s>Ma pure io ho manifestato l'impossibilit&agrave; della sua <lb/>opinione &rdquo; (ivi, c. </s>

<s>339). </s></p><p type="main">

<s>La dimostrazione richiesta dal Boulliaud, e che doveva cos&igrave; dissipar la <lb/>sua propria ipotesi geometrica, come l'altra fisica del Borelli, era riserbata <lb/>un po'pi&ugrave; tardi al valore matematico del Newton, il quale si volse tutto a <lb/>considerare gl'impulsi iniziali, da cui dovea principalmente dipendere la na&shy;<lb/>tura delle orbite de'Pianeti. </s>

<s>Si persuase per prima cosa che non potevano <lb/>quegl'impulsi iniziali derivare dai vortici kepleriani, rinnovellati dalla fisica <lb/>del Borelli, e ci&ograve; con facile dimostrazione posta poi per Scolio alla propo&shy;<lb/>sizione LIII del II Libro de'<emph type="italics"/>Principii.<emph.end type="italics"/></s></p><p type="main">

<s>Sia in S il Sole (fig. </s>

<s>105) a cui si circoscriva il circolo CF del vortice <lb/>radioso, il qual vortice, perciocch&egrave; si suppone descriver le aree proporzio&shy;<lb/>nali ai tempi, si mover&agrave; dovunque con moto uniforme. </s>

<s>Sieno AD, BE due <lb/>orbite eccentriche e in D, E si costituiscano i perielii, in A, B poi gli afelii. <pb xlink:href="020/01/1103.jpg" pagenum="546"/>Ora, per legge astronomica, negli afelii i Pianeti debbono andare pi&ugrave; lenti, <lb/>e nonostante per legge meccanica hanno pi&ugrave; validi impulsi, perch'essendo <lb/><figure id="id.020.01.1103.1.jpg" xlink:href="020/01/1103/1.jpg"/></s></p><p type="caption">

<s>Figura 105.<lb/>le velocit&agrave; de'fluidi in ragion reci&shy;<lb/>proca delle sezioni, per gli spazii AB, <lb/>BC, pi&ugrave; angusti degli spazii DE, FE, <lb/>la materia vorticosa deve moversi pi&ugrave; <lb/>veloce. </s>

<s>&ldquo; Quae duo repugnant inter <lb/>se &rdquo; (Editio cit., pag. </s>

<s>421). </s></p><p type="main">

<s>Gl'impulsi iniziali secondo l'ipo&shy;<lb/>tesi platonica, rinverdita di nuove <lb/>fronde da Galileo, non si poteva ora&shy;<lb/>mai pi&ugrave; ammettere, essendo stato di&shy;<lb/>mostrato di fatto che i moti de'Pia&shy;<lb/>neti non sono uniformi ne'circoli <lb/>perfetti, e dall'altra parte non aveva <lb/>alcuna specie di probabilit&agrave; l'ipotesi <lb/>immaginata dal Boulliaud de'circoli equanti. </s>

<s>Fu perci&ograve; che il Newton pens&ograve; <lb/>felicemente di tornare alle antiche idee pitagoriche, secondo le quali il moto <lb/>e la traiettoria della Luna si rassomigliava al moto e alla traiettoria della <lb/>pietra gittata. </s>

<s>&ldquo; Lapis proiectus, urgente gravitate sua, deflectitur de cursu <lb/>rectilineo et curvam lineam in aere describendo, tandem cadit in Terram. </s>

<s><lb/>Si motu velociore proiiciatur, pergit longius. </s>

<s>Augendo velocitatem fieri pos&shy;<lb/>set ut arcum describeret milliaris unius, duorum, quinque, decem, centum, <lb/>mille, ac tandem ut pergendo ultra terminos Terrae non amplius in Terram <lb/>caderet &rdquo; (De Mundi syst. </s>

<s>cit., pag. </s>

<s>6, 7). </s></p><p type="main">

<s>Lo splendor del pensiero, che balena condensato dentro queste parole, <lb/>si riflette, come luce di specchio in specchio, da una in altra delle varie <lb/>proposizioni dimostrate nel Lib. </s>

<s>I dei Principii matematici di Filosofia na&shy;<lb/>turale. </s>

<s>Data la forza equabile di proiezione e l'acceleratrice verso il centro, <lb/>in modo per&ograve; che gli additamenti d'impulso sieno costantemente proporzio&shy;<lb/>nali ai tempi, e perci&ograve;, per le brevi distanze prese sulla superficie terrestre, <lb/>dato che le forze attrattive sieno invariabili, il proietto scagliato descrive una <lb/>parabola. </s>

<s>&ldquo; Hoc est theorema Galilaei &rdquo; (Propos. </s>

<s>X, pag. </s>

<s>149). </s></p><p type="main">

<s>Supponiamo ora, seguitava cos&igrave; a ragionare il gran Filosofo, di avere <lb/>una Forza onnipotente, la quale sia capace di gettar la Luna o altro pi&ugrave; <lb/>ponderoso Pianeta per l'immensit&agrave; del Cielo, come la nostra mano getta <lb/>una pietra per l'aria. </s>

<s>Supponiamo inoltre che quello smisurato Globo cos&igrave; <lb/>lanciato, per esser tanto lontano dal centro del proprio moto, vi sia attratto, <lb/>non con forza costante, ma variabile reciprocamente ai quadrati delle di&shy;<lb/>stanze. </s>

<s>Descriver&agrave; egli ancora una parabola, come nel teorema di Galileo, o <lb/>una curva diversa? </s>

<s>E la risposta, conclusa da alcune proposizioni prece&shy;<lb/>dentemente dimostrate, era questa: &rdquo; Movebitur hoc corpus in aliqua sectio&shy;<lb/>num conicarum, umbilicum habente in centro virium &rdquo; (Prop. </s>

<s>XIII, pag. </s>

<s>161). </s></p><p type="main">

<s>Quel corpo dunque, come in una parabola, cos&igrave; potrebbe rivolgersi bene <pb xlink:href="020/01/1104.jpg" pagenum="547"/>in una ellissi o in una iperbola. </s>

<s>Or in quali casi propriamente avverr&agrave; che, <lb/>poste certe condizioni, il proietto descriva o l'una curva o l'altra? </s>

<s>Una cos&igrave; <lb/>fatta domanda si formul&ograve; dall'Autore nella seguente proposizione, che &egrave; la <lb/>XVII del libro sopra citato: &ldquo; Posito quod vis centripeta sit reciproce pro&shy;<lb/>portionalis quadrato distantiae locorum a centro, et quod vis illius quantitas <lb/>absoluta sit cognita, requiritur linea quam corpus describit in loco dato, cum <lb/>data velocitate, secundum datam lineam egrediens &rdquo; pag. </s>

<s>170). </s></p><p type="main">

<s>Il quesito &egrave; nella sua prima parte cos&igrave; risoluto: &ldquo; Figura erit ellipsis &rdquo; <lb/>(pag. </s>

<s>173). Nella quale ellisse, dati i fochi, e da quello di questi due, di&shy;<lb/>verso dal foco di attrazione, e che sia designato con H, condotto un raggio <lb/>alla traiettoria nel punto P del proietto, se tanta sar&agrave; la forza impressa che <lb/>la lunghezza PH riesca infinita &ldquo; figura erit parabola.... Quod si corpus <lb/>maiori adhuc cum velocitate de loco suo P exeat, capienda erit longitudo PH <lb/>ad alteram partem tangentis; ideoque, tangente inter umbilicos pergente, <lb/>erit hyperbola &rdquo; (pag. </s>

<s>173). </s></p><p type="main">

<s>Ecco risoluto cos&igrave; felicemente l'arduo problema delle traiettorie. </s>

<s>In ge&shy;<lb/>nerale sono esse ellittiche, come si osserva in tutti i Pianeti, e ci&ograve;, non per <lb/>una special disposizione del Creatore, a quel modo che s'immaginavano il <lb/>Boulliaud e il Borelli, ma come conseguenza dell'impulso iniziale e delle <lb/>leggi prescritte al moto degli stessi Pianeti. </s>

<s>Le Comete in particolare pos&shy;<lb/>sono descrivere o l'una o l'altra sezione del cono. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Le idee pitagoriche, le quali erano pure balenate alla mente di Galileo <lb/>(Alb. </s>

<s>VII, 61), avevano cos&igrave; nella matematica del Newton ritrovato il pi&ugrave; <lb/>splendido commento, e la scienza esult&ograve; a veder che l'ipotesi del Borelli <lb/>s'era, oltre ogni umana speranza, stabilita nella fermezza del vero. </s>

<s>Parve <lb/>allora all'uomo orgoglioso esser quasi divenuto simile a Dio, quando seppe <lb/>che a Giove e a Saturno, lanciati per gl'immensi spazii del cielo da una <lb/>Mano onnipotente, erano state prescritte le vie con quelle medesime leggi, <lb/>che son prescritte a un sasso gettato per l'aria dalla mano di un fanciullo. </s>

<s><lb/>Ma quell'orgoglio presto si rintuzz&ograve; nel petto, al prurito di sodisfare a un'al&shy;<lb/>tra brama irrequieta. </s>

<s>&Egrave; una gran conquista, dicevasi, della nostra scienza <lb/>quell'unit&agrave; di legge governatrice dell'Universo, e secondo la quale i Pianeti <lb/>intorno al Sole e i Satelliti intorno a Giove, e la Luna intorno alla Terra <lb/>gravitano ai loro centri, come un pomo maturo che penda dal suo ramo, <lb/>ma che cos'&egrave; questa forza, che fa piegare il ramo, e ne stacca il pomo, fa&shy;<lb/>cendolo finalmente cadere sulle zolle del campo? </s>

<s>Tanto rimaneva ancora a <lb/>sapere, perch&egrave; fossero sodisfatti i desiderii dell'uomo, e la nuova scienza <lb/>del Cosmo riuscisse assoluta, e a tanto attesero studiosamente i Filosofi, con <pb xlink:href="020/01/1105.jpg" pagenum="548"/>quale effetto per&ograve; lo mostrer&agrave; quest'ultima pagina della presente parte di <lb/>Storia. </s></p><p type="main">

<s>Fu primo tra que'Filosofi il Gilberto, il quale rassomigli&ograve; la tendenza <lb/>dei corpi gravi al centro della Terra all'appetito, con cui il ferro vien tratto <lb/>al Magnete. </s>

<s>Pi&ugrave; alto poi sublimando le idee, disse che non la Terra sola, <lb/>ma tutti i corpi celesti esercitavano una loro virt&ugrave; magnetica sui corpi cir&shy;<lb/>costanti, cosicch&egrave; intorno alla Luna, al Sole, ai Pianeti circoscrivesi una <lb/>ammosfera di quegli effluvii attrattivi. </s>

<s>&ldquo; Circumfusa effluvia omnia et in <lb/>illis gravia quovis modo vi pulsa, simul cum Tellure generali cohaerentia <lb/>uniformiter procedunt. </s>

<s>Quod etiam fit in omnibus primariis corporibus, Sole, <lb/>Luna, Tellure, partibus ad sua principia et fontes sese conferentibus, qui&shy;<lb/>bus eadem appetentia annectuntur ut terrena Telluri, quae gravia nos no&shy;<lb/>minamus. </s>

<s>Sic lunaria appellunt Lunam, solaria solem intra effluviorum suo&shy;<lb/>rum orbes &rdquo; (De Magnete, Londini 1600, pag. </s>

<s>229). </s></p><p type="main">

<s>La fecondit&agrave; delle speculazioni che deriv&ograve; dalla Filosofia magnetica, e <lb/>l'argomento che si trov&ograve; in lei a sollevare, o a dir pi&ugrave; vero a diradare il <lb/>velo de'pi&ugrave; ascosti misteri della Natura, sono cose notissime oramai, e per <lb/>quel che riguarda la scienza particolare del Cosmo &egrave; noto pure quanta luce <lb/>di pensiero si deriv&ograve; dal libro del Gilberto in quelli di Galileo, del De Do&shy;<lb/>minis e del Borelli, per non accennar che ad alcuni de'pi&ugrave; insigni fra i <lb/>nostri Italiani. </s></p><p type="main">

<s>Le idee del Borelli vedemmo quanto riuscissero efficaci sulle menti degli <lb/>stranieri, per cui nasce la curiosit&agrave; di sapere se riuscissero affatto sterili fra <lb/>noi. </s>

<s>Ma che veramente sterili non riuscissero, potrebbesi dimostrare per varii <lb/>esempii, fra'quali basti a noi in tanta fretta citarne uno solo dal Magalotti; <lb/>notabile esempio, se si ripensi in che modo egli discorra dell'attrazione uni&shy;<lb/>versale e degli effetti di lei, quando ancora, almeno in Italia, non si cono&shy;<lb/>scevano le teorie neutoniane. </s></p><p type="main">

<s>&ldquo; Suppongo, egli scrive nella IV delle Lettere scientifiche, essere il Globo <lb/>terrestre una gran Calamita, la quale spirando per ogni parte la sua virtude, <lb/>egualmente i corpi e gli elementi tutti ne attragga..... Stabilito ci&ograve;, dico <lb/>la virt&ugrave; della Terra non estendersi in infinito, ma solo diffondersi per un <lb/>determinato spazio, e questa tale sfera della sua potenza porre il termine <lb/>all'ammosfera di ciascun Pianeta. </s>

<s>Se poi s'abbatter&agrave; che due Pianeti siano <lb/>fra loro per tanto spazio lontani, che la sfera della potenza magnetica del&shy;<lb/>l'uno non confini colla sfera dell'altro; questo tratto intermedio o sar&agrave; voto, <lb/>o sparso per avventura di fuoco, di luce o d'etere o d'altro mezzo pi&ugrave; te&shy;<lb/>nue, ed un corpo quivi collocato non avr&agrave; inclinazione al moto, ma tratterrassi <lb/>immobile. </s>

<s>Se le sfere magnetiche di due Pianeti saranno confinanti, allora <lb/>io considero fra l'un Pianeta e l'altro una linea immaginaria, la quale io <lb/>chiamer&ograve; comune distanza, e secondo che un corpo sar&agrave; collocato di qua o <lb/>di l&agrave; da cotal linea, entrer&agrave; nella sfera dell'un Pianeta o dell'altro, e s&igrave; ve&shy;<lb/>nendone attratto, in questo o in quello ander&agrave; a cadere. </s>

<s>Se un Pianeta, gi&shy;<lb/>randosi nell'orbe suo, s'incontrer&agrave; ad abbracciare colla sua sfera di potenza <pb xlink:href="020/01/1106.jpg" pagenum="549"/>magnetica un corpo, collocato immobile in uno spazio intermedio fra le sfere <lb/>di due pianeti, seco lo porter&agrave; &rdquo; (Firenze 1721, pag. </s>

<s>27-29). Applica poi <lb/>questi stessi principii al caso degli aereoliti, con gran maraviglia di coloro, <lb/>che trovan qui la soluzione antica a un problema nuovo. </s></p><p type="main">

<s>Gran sodisfazione trov&ograve; senza dubbio la scienza in quelle intravedute <lb/>somiglianze tra l'attrazione magnetica e la terrestre, che &egrave; quella stessa, la <lb/>quale opera nell'universale, ma in che consiste, si domandava, quella virt&ugrave;, <lb/>per cui il ferro viene attratto al Magnete? </s>

<s>E in provarsi a rispondere alla <lb/>domanda, si conobbe che il mistero cosmico nella Filosofia magnetica rima&shy;<lb/>neva tuttavia, e che nelle mani di lei non altro fece in sostanza che mu&shy;<lb/>tar velo. </s></p><p type="main">

<s>Si sent&igrave; perci&ograve; il bisogno di procedere per altra via, e l'Huyghens fu <lb/>il primo, che risal&igrave; col pensiero ad applicare al Cosmo quelli, che si direb&shy;<lb/>bero ludi della Natura. </s>

<s>Un fatto volgarissimo aveva richiamata la sua atten&shy;<lb/>zione, e fu quello de'corpuscoli galleggianti, che si vedono attratti al centro <lb/>di qualche vortice, formatosi qua o l&agrave; nel correre, sulla superficie dell'acqua. </s>

<s><lb/>L'ipotesi di un etere fluidissimo, che di s&egrave; tutto riempia lo spazio, era ora&shy;<lb/>mai divenuta comune, e il Keplero, nella rotazione del Sole partecipata allo <lb/>stesso etere ambiente, aveva ritrovato il principio ai supposti moti vertigi&shy;<lb/>nosi. </s>

<s>Dato ci&ograve;, bastava, secondo l'Huyghens, che un Pianeta si trovasse nel <lb/>vortice, che s'aggira intorno al Sole, perch&egrave; ne dovesse essere attratto. </s></p><p type="main">

<s>Una tale ipotesi intorno alla causa prima, che produce la gravitazione, <lb/>si trova accennata gi&agrave; dall'Huyghens nel <emph type="italics"/>Systema Saturnium,<emph.end type="italics"/> l&agrave; dove in&shy;<lb/>tende a dimostrar come l'Anello, bench&egrave; staccato, segua senza mai rima&shy;<lb/>nere indietro il moto del suo Pianeta, perch&egrave; gravita sulla superficie di lui, <lb/>a quel modo che i corpi gravi sospesi assecondano il moto della nostra Terra. <lb/></s>

<s>&ldquo; Porro quum certo satis colligi posse videatur, ob similitudinem ac cogna&shy;<lb/>tionem magnam quae Saturno cum Tellure nostra intercedit, illum perinde <lb/>ut haec in medio sui vorticis situm esse, centrumque eius versus omnia na&shy;<lb/>tura sua tendere, quae illic gravia habentur, inde necessario quoque effici&shy;<lb/>tur. </s>

<s>Annulum istum omnibus sui partibus aequali vi ad centrum nitentem, <lb/>hoc ipso, ita consistere ut undiquaque pari intervallo a centro absit &rdquo; (Opera <lb/>varia, Vol. </s>

<s>II, Lugduni Batav. </s>

<s>1724, pag. </s>

<s>567). </s></p><p type="main">

<s>Par che insomma l'ipotesi de'vortici fosse stata speculata dall'Huy&shy;<lb/>ghens infino dal 1659, parecchi anni prima che il Borelli e il Newton pub&shy;<lb/>blicassero le loro teorie. </s>

<s>In un'apposita scrittura poi, che intitol&ograve; <emph type="italics"/>Diatriba,<emph.end type="italics"/><lb/>lo stesso Huyghens spieg&ograve; intorno a quella ipotesi i suoi particolari concetti, <lb/>e vi torn&ograve; sopra alla fine del II libro del Cosmoteoro. </s>

<s>Quivi &egrave; l'Autore in <lb/>gran sollecitudine di notar quanto differisca il suo dal sistema cartesiano, <lb/>ch'egli chiama <emph type="italics"/>commentatio levibus rationibus contexta,<emph.end type="italics"/> e soggiunge es&shy;<lb/>sersi spesso maravigliato <emph type="italics"/>tantum operae in talibus concinnandis figmentis <lb/>eum impendere potuisse &rdquo;<emph.end type="italics"/> (Cosmotheoros in Op. </s>

<s>cit., pag. </s>

<s>721). </s></p><p type="main">

<s>Una delle differenze pi&ugrave; notabili fra il sistema ugeniano e il cartesiano <lb/>consiste in ci&ograve;, che il Cartesio suppone moversi la materia del vortice tutta <pb xlink:href="020/01/1107.jpg" pagenum="550"/>insieme, e dalla medesima parte, mentre a volere spiegare i fatti, secondo <lb/>l'Huyghens, bisogna &ldquo; vorticem turbinemve materiae coelestis circa Solem <lb/>converti, non totum in easdem partes, sed ita ut variis motibus, iisque ce&shy;<lb/>lerrimis, in omne latus secundum diversas sui portiones rapiatur, nec tamen <lb/>dilabi possit, propter circumstantem aetherem, qui non tali nec tam celeri <lb/>motu agitetur &rdquo; (ibi, pag. </s>

<s>720). E semplifica il fatto in que'vortici, che si <lb/>formano qua e l&agrave; sulla superficie di un lago, per la forte agitazione del <lb/>remo &ldquo; et sicut horum motus nequaquam ab unis ad alios perveniunt, nec <lb/>proinde sese mutuo impediunt, ita quoque coelestium vorticum motus cir&shy;<lb/>cum astra aut Soles se habere existimo &rdquo; (ibi, pag. </s>

<s>721). </s></p><p type="main">

<s>Tratt&ograve; senza dubbio l'Huyghens de'vortici da geometra, mentre il Car&shy;<lb/>tesio ne avea trattato piuttosto da romanziere o da poeta, ma non cess&ograve; per <lb/>questo di apparire il sistema stesso de'vortici ugeniani un lavoro di fanta&shy;<lb/>sia. </s>

<s>Il Newton, ne'suoi Principii di Filosofia naturale, essendosi severamente <lb/>imposto di non toccar questione, che non si potesse risolvere nella certezza <lb/>di una verit&agrave; matematica, dimostrando l'esistenza e le leggi della gravita&shy;<lb/>zione universale, lasci&ograve; a disputare ai Filosofi delle cause ultime produt&shy;<lb/>trici di quella forza. </s>

<s>Ma l&agrave; dove s'apre un campo a parte per questionare <lb/>di tutto ci&ograve;, che non &egrave; dimostrabile o per matematiche ragioni o per espe&shy;<lb/>rienza, non tacque di dir ci&ograve; ch'egli pensava esser causa della gravitazione <lb/>universale, ricorrendo anch'egli all'etere, considerato per&ograve; in condizioni sta&shy;<lb/>tiche differenti dalle dinamiche dell'Hugenio. </s></p><p type="main">

<s>&ldquo; Annon hoc medium, prosegue a dir dell'etere cosmico nella XXI Que&shy;<lb/>stione, multo rarius est intra corpora densa Solis, Stellarum, Planetarum et <lb/>Cometarum, quam in vacuis spatiis coelestibus interiectis? </s>

<s>Et a corporibus <lb/>istis ad usque ingentia intervalla, annon densius perpetuo densiusque eva&shy;<lb/>dit, eoque pacto efficit ut et magna ista corpora erga se invicem gravia sint, <lb/>et ipsorum partes singulae erga ipsa corpora, omnibus nimirum corporibus, <lb/>qua parte medium densius est, ea ex parte recedere conantibus in partes <lb/>rariores? </s>

<s>Etenim si hoc medium rarius sit intra corpus Solis quam in <lb/>eiusdem superficie, et in ipsa superficie rarius quam interiecto extrinsecus <lb/>centesimae partis unciae unius a corpore Solis intervallo, et hoc postremo <lb/>in loco rarius quam in orbe Saturni; equidem nihil causae video quamo&shy;<lb/>brem increscenti densitati usquam locorum ullus constitutus sit finis, quo&shy;<lb/>minus per omnia intervalla, et a Sole ad Saturnum, et adhuc usque porri&shy;<lb/>gatur. </s>

<s>Quae quidem densitas, quanquam ingentibus interiectis intervallis, <lb/>fortasse lentissimis augeatur accrementis, poterit tamen, si quidem vis ela&shy;<lb/>stica huius medii admodum sit magna, corpora vi ea omni quam gravitatem <lb/>appellamus a densioribus partibus medii ad rariores versus impellere. </s>

<s>Valde <lb/>autem magnam esse medii huiusce vim elasticam ex vibrationum suarum <lb/>celeritate est colligere &rdquo; (Optices, Lib. </s>

<s>III, Patavii 1773, pag. </s>

<s>143). </s></p><p type="main">

<s>Due secoli son passati da che l'Huyghens e il Newton proposero que&shy;<lb/>ste loro ipotesi, e bench&egrave; l'Autore del Cosmoteoro terminasse il suo libro <lb/>con dire ch'egli stimava le ragioni ultime de'moti dell'Universo <emph type="italics"/>nequa-<pb xlink:href="020/01/1108.jpg" pagenum="551"/>quam humano ingenio cxcogitari, aut coniecturis attingi posse,<emph.end type="italics"/> non volle <lb/>nonostante la scienza cos&igrave; progredita lasciar di fare i suoi sforzi. </s>

<s>E perch&egrave; <lb/>nell'elettricit&agrave; principalmente si trov&ograve; aver fatti que'suoi seducenti pro&shy;<lb/>gressi, nell'elettricit&agrave; pose ogni speranza di giungere a rivelarsi gli ascosti <lb/>misteri. </s></p><p type="main">

<s>Bench&egrave; a vero dire siasi in ci&ograve; da'moderni preso altro indirizzo, l'ap&shy;<lb/>plicazione delle virt&ugrave; elettriche alle forze, che danno anima al Cosmo, risale <lb/>infino a Ottone di Guericke. </s>

<s>Accennammo ad altro proposito la fecondit&agrave; <lb/>delle speculazioni, che derivarono al Filosofo di Magdeburgo, da quella sua <lb/><emph type="italics"/>Terrella elettrica,<emph.end type="italics"/> in che vedeva come in un punto solo contratta e rappre&shy;<lb/>sentata al vivo l'immagine della gran Terra, e fu il primo frutto di cos&igrave; <lb/>fatte speculazioni quello di concludere che dovesse, nel gran Globo terrestre <lb/>e naturale, risiedere la virt&ugrave; medesima di attrarre e di respingere, che i <lb/>fatti dimostravano esser propria al piccolo artificiale globo di zolfo. </s></p><p type="main">

<s>Risalendo pi&ugrave; su ad applicare ai corpi celesti i fatti particolari con lo <lb/>stesso Globo sulfureo sperimentati, in quel seguitar che fa dovunque la <lb/>piuma esso Globo, sempre tenendo verso lui rivolta la medesima parte, vide <lb/>Ottone rappresentarsi in immagine la Luna, che segue fedel compagna nel <lb/>suo viaggio annuale la Terra, a cui tien pure sempre rivolta la medesima <lb/>faccia. </s>

<s>&ldquo; Causam constantiae lunaris faciei naturalem esse detegit simul Glo&shy;<lb/>bus ille sulphureus, qui plumulam, a se semel expulsam, una semper facie <lb/>in orbe virtutis retinet, in quamcumque etiam partem circumducatur &rdquo; <lb/>(Experimenta nova magd., Amstelodami 1672, pag. </s>

<s>179). E come la piuma, <lb/>bench&egrave; non rimanga mai indietro al globo, pur seguitandolo, alquanto tituba <lb/>e vacilla; cos&igrave; tituba e vacilla per conseguenza anco la Luna (ivi). </s></p><p type="main">

<s>Poi l'Hawksbee, quando vide i fili elettrometrici di mussolina ora es&shy;<lb/>sere con s&igrave; costante ordine attratti, ora respinti dal centro del globo torna&shy;<lb/>tile di vetro &ldquo; ho scoperto, annunziava esultando al pubblico, alcune pro&shy;<lb/>priet&agrave; di questa materia elettrica, che possono parere maravigliose a quelli <lb/>che minutamente le considereranno, conciossiach&egrave; somministrano una sorta <lb/>di rappresentazione de'grandi fenomeni dell'Universo &rdquo; (Esper. </s>

<s>fisico mecc, <lb/>traduz. </s>

<s>ital., Firenze 1716, pag. </s>

<s>44). </s></p><p type="main">

<s>Le idee del Guericke e dell'Hawksbee erano nuove, ma non si faceva <lb/>altro per esse che rassomigliare alle attrazioni e alle repulsioni elettriche i <lb/>moti cosmici, che il Gilberto e il Keplero avevano gi&agrave; rassomigliato alle <lb/>virt&ugrave; del Magnete. </s>

<s>La rappresentazione dei fenomeni dell'Universo ne'fatti <lb/>elettrici, per la variet&agrave; delle loro forme pi&ugrave; facilmente accomodabili, pareva <lb/>sodisfare alquanto meglio che non la monotonia de'magnetici, ma il mistero, <lb/>bench&egrave; si mostrasse sotto altro aspetto, rimaneva tuttavia coperto da un'im&shy;<lb/>penetrabile velo, a rimuovere il quale, baldanzosi de'progressi fatti dalla <lb/>scienza elettrica, si provarono i fisici moderni. </s>

<s>Da giudici imparziali per&ograve; <lb/>non pu&ograve; darsi altra sentenza delle nuove speculate ipotesi, se non dicendo <lb/>ch'elle sono un elaborato e assai prolisso commento delle antiche, conside&shy;<lb/>randovisi l'etere elettrico, diffuso in tutto il cosmo, in quelle condizioni sta-<pb xlink:href="020/01/1109.jpg" pagenum="552"/>tiche, in che il Newton lo consider&ograve;, secondo la sopra riferita Questione. </s>

<s><lb/>L'etere, dicono insomma i Fisici novelli, che della sua ammosfera circonda <lb/>le molecole dei corpi, variando in densit&agrave; colla distanza, produce nel ridursi <lb/>all'equilibrio una pressione, e dalla pressione ha origine il conato, e pro&shy;<lb/>ducesi il moto. </s></p><p type="main">

<s>Ma perch&egrave; dee variare in densit&agrave; l'etere? </s>

<s>si domanda. </s>

<s>Questa in ogni <lb/>modo o rimane un'ipotesi gratuita, o volendo rispondere, non si pu&ograve; dire <lb/>altro se non che l'etere &egrave; variamente denso, perch&egrave; variamente attratto al <lb/>suo centro, ma si assumerebbe cos&igrave; per principio della spiegazione, e per <lb/>argomento, il fatto stesso che si voleva spiegare. </s></p><p type="main">

<s>Confessando dunque anche noi coll'Huyghens che l'origine de'moti <lb/>cosmici &egrave; inescogitabile, consideriamo il processo, che per tre secoli ha te&shy;<lb/>nuto la scienza nell'investigar l'origine e la natura della forza. </s>

<s>Vedemmo <lb/>che ne furono ricercate e intravedute l'orme o nella luce o nel fluido ma&shy;<lb/>gnetico o nell'elettrico, e in qualche altra cosa insomma di pi&ugrave; sottile, che <lb/>siasi saputa immaginare, e che sia pi&ugrave; aliena dal partecipare delle qualit&agrave; <lb/>pi&ugrave; comuni della crassa materia. </s>

<s>Gli antichi Filosofi dicevano perci&ograve; che <lb/>principio della forza sia lo spirito, ond'&egrave; che non vedendo come si potes&shy;<lb/>sero movere altrimenti i Pianeti, o davano ad essi un'anima o gli commet&shy;<lb/>tevano al governo delle intelligenze celesti. </s>

<s>In tempi pi&ugrave; prossimi a noi, e <lb/>ne'quali la presente scienza fisica ebbe i suoi inizii, il Gilberto pens&ograve; che <lb/>la virt&ugrave; magnetica fosse animata, e il Keplero, nelle varie sue opere, torn&ograve; <lb/>pi&ugrave; volte a parlar dell'anima, e degli organi animali, di ch'&egrave; compaginata <lb/>la Terra. </s></p><p type="main">

<s>Le forze animastiche furono finalmente bandite dalla scienza del Cosmo, <lb/>per opera del Borelli, che sapientemente vi sostitu&igrave; le forze fisiche. </s>

<s>Ma, ben&shy;<lb/>ch&egrave; fosse questo un progresso effettivo, e una reale conquista del vero, da <lb/>nessuno s'&egrave; saputo poi, in tanto tempo, penetrare addentro alla natura fisica <lb/>di quelle forze. </s></p><p type="main">

<s>Si sapr&agrave; forse in avvenire? </s>

<s>A ci&ograve; risponder&agrave; la storia, scritta in qual&shy;<lb/>che capitolo di quest'altro Tomo, dove si narreranno i progressi fatti dalla <lb/>scienza sperimentale nello studio della vita e degli organi dei sensi, misu&shy;<lb/>ratori angusti del nostro acume e dei nostri voli. </s></p><pb xlink:href="020/01/1110.jpg"/><p type="main">

<s><emph type="center"/>INDICI<emph.end type="center"/><pb xlink:href="020/01/1111.jpg"/></s></p><pb xlink:href="020/01/1112.jpg"/><p type="main">

<s><emph type="center"/>INDICE DEI CAPITOLI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>CAPITOLO I.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Della luce diretta e della luce riflessa.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I De'primi e principali cultori dell'&Ograve;ttica <emph type="italics"/>Pag.<emph.end type="italics"/> 7 </s></p><p type="main">

<s>II Della legge fondamentale della luce riflessa. </s>

<s>&rdquo; 12 </s></p><p type="main">

<s>III De'corpi diafani e degli opachi; delle ombre e delle penombre &rdquo; 20 </s></p><p type="main">

<s>IV Di alcune esperienze singolari sulle ombre; del passaggio della luce attraverso a pic&shy;<lb/>coli fori &rdquo; 26 </s></p><p type="main">

<s>V Delle leggi della intensit&agrave; luminosa. </s>

<s>&rdquo; 32 </s></p><p type="main">

<s>VI Della velocit&agrave; della luce &rdquo; 39 </s></p><p type="main">

<s>VII Delle ipotesi delle ondulazioni eteree, e dell'emissione &rdquo; 46 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO II.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Della luce rifratta.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle prime teorie speculate intorno alla natura delle rifrazioni, e de'primi tentativi <lb/>fatti per iscoprirne le leggi <emph type="italics"/>Pag.<emph.end type="italics"/> 53 </s></p><p type="main">

<s>II Del Teorema dello Snellio, e della legge diottrica indi formulatane dal Cartesio &rdquo; 60 </s></p><p type="main">

<s>III Della legge diottrica dimostrata dall'Herigonio; del principio delle cause finali introdotto <lb/>in quella dimostrazione, e come il Newton ritornasse ai principii meccanici &rdquo; 68 </s></p><p type="main">

<s>IV Della scienza delle rifrazioni in Italia &rdquo; 75 </s></p><p type="main">

<s>V Delle rifrazioni astronomiche &rdquo; 86 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO III.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Della luce diffratta e de'colori.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Dell'esperienze, da cui fu condotto il Grimaldi a professar che la luce, come i liquidi, <lb/>si diffrange <emph type="italics"/>Pag.<emph.end type="italics"/> 96 </s></p><p type="main">

<s>II Come il Newton confermasse le verit&agrave; de'fenomeni grimaldiani, e come v'applicasse <lb/>a spiegarli il principio dell'attrazione &rdquo; 103 </s></p><p type="main">

<s>III Delle teorie de'colori &rdquo; 108 </s></p><p type="main">

<s>IV De'colori, e delle varie apparenze dell'Iride celeste &rdquo; 115 </s></p><p type="main">

<s>V Delle Corone e de'Parelii. </s>

<s>&rdquo; 123 </s></p><pb xlink:href="020/01/1113.jpg" pagenum="556"/><p type="main">

<s><emph type="center"/>CAPITOLO IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del calore.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Dell'antica teoria degl'ignicoli rinnovata da Galileo: della questione del freddo posi&shy;<lb/>tivo o privativo <emph type="italics"/>Pag.<emph.end type="italics"/> 132 </s></p><p type="main">

<s>II Di alcune speculazioni, e sperienze meno note, fatte intorno al calore dagli Accademici <lb/>del Cimento &rdquo; 142 </s></p><p type="main">

<s>III Del calore di comunicazione, e del calorico raggi<gap/>ate &rdquo; 151 </s></p><p type="main">

<s>IV Degli effetti del calore negli agghiacciamenti &rdquo; 160 </s></p><p type="main">

<s>V Degli effetti del calore nelle evaporazioni &rdquo; 170 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO V.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del suono.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della diffusione del suono per l'aria <emph type="italics"/>Pag.<emph.end type="italics"/> 177 </s></p><p type="main">

<s>II Delle varie esperienze ordinate a dimostrar la diffusione, e a misurar la velocit&agrave; del <lb/>suono per l'aria &rdquo; 187 </s></p><p type="main">

<s>III Delle prime fisiche ragioni date delle consonanze &rdquo; 198 </s></p><p type="main">

<s>IV Di ci&ograve; che, intorno al risonar delle corde, fu dimostrato da Galileo &rdquo; 203 </s></p><p type="main">

<s>V Di un trattato fisico matematico, che preparava Niccol&ograve; Aggiunti sui tremori armonici <lb/>nelle corde &rdquo; 212 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del Magnete.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle pi&ugrave; antiche osservazioni, e delle prime esperienze fatte intorno al Magnete <emph type="italics"/>Pag.<emph.end type="italics"/> 223 </s></p><p type="main">

<s>II Di ci&ograve; che, a promuovere la Filosofia magnetica, si cooper&ograve; dal Gilberto, dal Sarpi, e <lb/>da Galileo &rdquo; 230 </s></p><p type="main">

<s>III Delle teorie magnetiche, e di ci&ograve; che particolarmente ne pensarono i Filosofi inglesi &rdquo; 238 </s></p><p type="main">

<s>IV Dell'ipotesi de'due fluidi sostanziali, e del loro modo di operar nel Magnete, secondo <lb/>A. Nardi. </s>

<s>e F. M. </s>

<s>Grimaldi &rdquo; 245 </s></p><p type="main">

<s>V Delle variazioni della declinazione magnetica &rdquo; 251 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dell'Elettro.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle prime esperienze elettriche, e delle ipotesi del Gilberto e del Cabeo; delle espe&shy;<lb/>rienze del Guericke, e degli Accademici del Cimento <emph type="italics"/>Pag.<emph.end type="italics"/> 262 </s></p><p type="main">

<s>II De'fuochi elettrici dell'Hawksbee, dell'elettricit&agrave; per comunicazione, dell'elettricit&agrave; vi&shy;<lb/>trea e resinosa, e dell'elettricit&agrave; positiva e negativa &rdquo; 269 </s></p><p type="main">

<s>III Di ci&ograve; che, a promuovere la scienza elettrica, fu cooperato in Italia, principalmente dal <lb/>Beccaria e dal Volta. </s>

<s>&rdquo; 275 </s></p><p type="main">

<s>IV Dell'elettricit&agrave;, e degli effetti di lei nell'ammosfera. </s>

<s>&rdquo; 284 </s></p><pb xlink:href="020/01/1114.jpg" pagenum="557"/><p type="main">

<s><emph type="center"/>CAPITOLO VIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Delle Meteore.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle sublimazioni de'vapori vescicolari, e de'loro condensamenti in pioggia <emph type="italics"/>Pag.<emph.end type="italics"/> 294 </s></p><p type="main">

<s>II Dell'origine de'venti in generale, e in particolare de'venti tropicali &rdquo; 305 </s></p><p type="main">

<s>III Delle variazioni, che subisce il Barometro al vario stato del cielo &rdquo; 316 </s></p><p type="main">

<s>IV Delle Effemeridi meteorologiche del Ramazzini; delle variazioni barometriche prodotte <lb/>dallo spirare de'venti, e dall'appressarsi delle procelle. </s>

<s>&rdquo; 324 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO IX.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del sistema del Mondo.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Del sistema del Mondo immaginato dagli antichi Peripatetici; della Sintassi platonica <lb/>e della Copernicana, e quali fossero i loro primi incontri appresso gli stranieri <emph type="italics"/>Pag.<emph.end type="italics"/> 331 </s></p><p type="main">

<s>II Del Sistema copernicano in Italia, e segnatamente di Galileo Galilei. </s>

<s>&rdquo; 341 </s></p><p type="main">

<s>III Del Dialogo galileiano sopra i due Massimi sistemi del Mondo &rdquo; 351 </s></p><p type="main">

<s>IV Delle avventure del Copernicismo dai tempi di Galileo alla fine del secolo XVII &rdquo; 363 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO X.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del Sole e della Luna.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle prime osservazioni intorno alle macchie solari fatte in Italia, e descritte da Galileo. <emph type="italics"/>Pag.<emph.end type="italics"/> 372 </s></p><p type="main">

<s>II Delle controversie insorte tra lo Scheiner e Galileo: dell'essere e della natura delle <lb/>Macchie solari &rdquo; 381 </s></p><p type="main">

<s>III Delle macchie, e di varie altre apparenze nel cerchio della Luna &rdquo; 389 </s></p><p type="main">

<s>IV Del Candore lunare, e particolarmente della Lettera di Galileo sopra questo argomento. </s>

<s>&rdquo; 398 </s></p><p type="main">

<s>V Del color rosso nelle Ecclissi di Luna &rdquo; 405 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO XI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Di Giove.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della scoperta de'quattro Pianeti medicei; de'metodi usati da Galileo per definirne i <lb/>tempi periodici, e le massime digressioni <emph type="italics"/>Pag.<emph.end type="italics"/> 411 </s></p><p type="main">

<s>II Degli studii intorno al Sistema gioviale proseguiti dal Castelli, dal Renieri e dall'Ho&shy;<lb/>dierna. </s>

<s>&rdquo; 423 </s></p><p type="main">

<s>III Di ci&ograve; che, a perfezionare le osservazioni e a dimostrare le teoriche de'Medicei, coope&shy;<lb/>rarono il Montanari e il Borelli, il Viviani e il Cassini &rdquo; 430 </s></p><p type="main">

<s>IV Dell'aspetto di Giove, e della fisica costituzione di lui. </s>

<s>&rdquo; 443 </s></p><p type="main">

<s>V Del problema delle Longitudini, e della particolar soluzione di lui, per mezzo delle Ef&shy;<lb/>femeridi gioviali &rdquo; 452 </s></p><pb xlink:href="020/01/1115.jpg" pagenum="558"/><p type="main">

<s><emph type="center"/>CAPITOLO XII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Di Saturno.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle prime osservazioni, e delle prime ipotesi degli Astronomi sul sistema di Saturno, <lb/>da Galileo all'Hevelio <emph type="italics"/>Pag.<emph.end type="italics"/> 463 </s></p><p type="main">

<s>II Della grande scoperta ugeniana dell'Anello, e di quel che si pens&ograve;, per confermarla, <lb/>dagli Accademici del Cimento &rdquo; 471 </s></p><p type="main">

<s>III Dell'origine, della fisica costituzione, e del moto dell'Anello saturnio, secondo gli Acca&shy;<lb/>demici del Cimento &rdquo; 481 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO XIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Delle Stelle fisse e delle Comete.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Del luogo e del moto, della sostanza e della generazione delle stelle fisse nel cielo <emph type="italics"/>Pag.<emph.end type="italics"/> 493 </s></p><p type="main">

<s>II Delle osservazioni telescopiche delle stelle fisse; della scintillazione, e della loro pa&shy;<lb/>rallasse &rdquo; 501 </s></p><p type="main">

<s>III Delle varie ipotesi intorno all'essere e alla natura delle Comete. </s>

<s>&rdquo; 510 </s></p><p type="main">

<s>IV Della teoria planetaria delle Comete &rdquo; 517 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO XIV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>De'moti dell'Universo.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della scoperta delle Orbite ellittiche, e delle leggi del moto dei Pianeti <emph type="italics"/>Pag.<emph.end type="italics"/> 524 </s></p><p type="main">

<s>II Delle forze centrali, e dei decrementi delle loro intensit&agrave;, in ragione delle distanze. </s>

<s>&rdquo; 534 </s></p><p type="main">

<s>III Delle leggi delle forze centrali; dell'attrazione universale; dell'origine delle Orbite el&shy;<lb/>littiche &rdquo; 540 </s></p><p type="main">

<s>IV Delle varie ipotesi proposte a spiegar la tendenza dei gravi ai loro centri &rdquo; 547 </s></p><pb xlink:href="020/01/1116.jpg"/><p type="main">

<s><emph type="center"/>INDICE ALFABETICO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>DEGLI AUTORI E DELLE COSE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Co'numeri s'accenna alle pagine.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="bold"/>Accademici del Cimento<emph.end type="bold"/> fanno inutile prova delle attrazioni elettriche nel vuoto 268, sperimentano <lb/>il poter della fiamma sull'ambra 269. </s></p><p type="main">

<s><emph type="bold"/>Accolti Pietro<emph.end type="bold"/> spiega la ragione della penombra 24, come spieghi il circoleggiar dell'immagine del <lb/>Sole passata attraverso a qualunque irregolarit&agrave; di foro 31. </s></p><p type="main">

<s><emph type="bold"/>Aggiunti Niccol&ograve;,<emph.end type="bold"/> proposizioni meccaniche di lui sulla trazion delle corde 215, sue teorie ed espe&shy;<lb/>rienze della diffusione del suono ne'solidi e ne'liquidi 217, sue proposizioni acustiche dimo&shy;<lb/>strate 220, traduce in latino il Discorso di Galileo sul flusso del mare 350. </s></p><p type="main">

<s><emph type="bold"/>Agucchia Giovan Batista<emph.end type="bold"/> ritrova i tempi periodici della circolazion de'Satelliti intorno a Giove 417. </s></p><p type="main">

<s><emph type="bold"/>Aguilonio,<emph.end type="bold"/> come fosse presso a trovare, e come smarrisse la diretta via, nell'investigar la legge del <lb/>decrescere l'intensit&agrave; della luce, a proporzione che crescono le distanze 34. </s></p><p type="main">

<s><emph type="bold"/>Alighieri Dante,<emph.end type="bold"/> come dimostr&ograve; le due leggi fondamentali della Catottrica 13, ammette Venere e <lb/>Mercurio inferiori 336. </s></p><p type="main">

<s><emph type="bold"/>Ancora della Calamita,<emph.end type="bold"/> origine di questo nome e uso 236. </s></p><p type="main">

<s><emph type="bold"/>Anello di ghiaccio<emph.end type="bold"/> immaginato dal Cartesio a spiegare il modo come si dipingono i Parelii 126. </s></p><p type="main">

<s><emph type="bold"/>Anello di Saturno,<emph.end type="bold"/> come sperimentalmente si dimostri essere montagnoso 487, se sia possibile 488, <lb/>come possa esser durabile 489, come seguiti il moto del Pianeta 490. </s></p><p type="main">

<s><emph type="bold"/>Apelle,<emph.end type="bold"/> sue Lettere sulle Macchie solari 375. </s></p><p type="main">

<s><emph type="bold"/>Archibugio a vento,<emph.end type="bold"/> da chi ritrovato 179. </s></p><p type="main">

<s><emph type="bold"/>Aria,<emph.end type="bold"/> come si trovi nell'acqua 162, come nel mercurio dello Strumento torricelliano 164, ricerche <lb/>inutili del Montanari, per veder d'onde ella entri nel mercurio del Barometro 165, &egrave; il veicolo <lb/>ordinario del suono 188. </s></p><p type="main">

<s><emph type="bold"/>Aristotile,<emph.end type="bold"/> per quali ragioni neghi la mobilit&agrave; della Terra 333, sua opinione delle Comete 513. </s></p><p type="main">

<s><emph type="bold"/>Asterismi<emph.end type="bold"/> varii disegnati ne'Manoscritti di Galileo 505. </s></p><p type="main">

<s><emph type="bold"/>Astri,<emph.end type="bold"/> come spieghi Galileo il loro apparire sull'orizzonte pi&ugrave; grandi 90, come spiegato da Leonardo <lb/>da Vinci 91, come dal Fracastoro 91. </s></p><p type="main">

<s><emph type="bold"/>Astroscopia dell'Huyghens<emph.end type="bold"/> tradotta dal Viviani 501. </s></p><p type="main">

<s><emph type="bold"/>Attrazione universale,<emph.end type="bold"/> come dimostrata 543. </s></p><p type="main">

<s><emph type="bold"/>Attrazioni e repulsioni elettriche,<emph.end type="bold"/> come spiegate dal Nollet 279. </s></p><p type="main">

<s><emph type="bold"/>Aurore boreali,<emph.end type="bold"/> loro origine secondo Galileo 290, secondo il Franklin 291, secondo il Beccaria 292, <lb/>secondo il Bondioli, non per&ograve; secondato dal Volta 292. </s></p><p type="main">

<s><emph type="bold"/>Bacone Francesco,<emph.end type="bold"/> sue esperienze sull'origine dei venti 306. </s></p><p type="main">

<s><emph type="bold"/>Baliani Giovan Batista<emph.end type="bold"/> crede falso il problema delle ombre proposto dal Gassendo 408. </s></p><p type="main">

<s><emph type="bold"/>Bardi Pietro<emph.end type="bold"/> propone a risolvere a Galileo un problema termico 134. </s></p><p type="main">

<s><emph type="bold"/>Barometro,<emph.end type="bold"/> se risenta alcuna variazione nel flusso e riflusso 355. </s></p><p type="main">

<s><emph type="bold"/>Bartoli Daniele<emph.end type="bold"/> muove difficolt&agrave; contro la teoria galileiana delle risonanze 206. </s></p><p type="main">

<s><emph type="bold"/>Beccaria Giovan Batista<emph.end type="bold"/> scopre la legge del moto ne'flussi elettrici 277, d&agrave; la teoria delle punte <lb/>elettriche 278, d&agrave; la teoria della Macchina elettrica 279, dimostra sperimentalmente come le at&shy;<lb/>trazioni elettriche avvengano anche nel vuoto 280, primo a sperimentare in Italia l'elettricit&agrave; <lb/>ammosferica ne'pali frankliniani 288. </s></p><pb xlink:href="020/01/1117.jpg" pagenum="560"/><p type="main">

<s><emph type="bold"/>Benedetti Giovan Batista,<emph.end type="bold"/> come dimostri la legge dell'intensit&agrave; calorifica sulle superflcie variamente <lb/>inclinate 157, sue speculazioni intorno alla generazione del suono 182, conosce la vera causa dei <lb/>venti 305, approva il sistema copernicano 343, ragioni che rende del rosso negli ecclissi di <lb/>Luna 405, dello scintillar delle stelle 504. </s></p><p type="main">

<s><emph type="bold"/>Biancani Giuseppe<emph.end type="bold"/> si studia di ricomporre la controversia insorta fra Pitagorici e Aristotelici intorno <lb/>all'origine delle Comete 511. </s></p><p type="main">

<s><emph type="bold"/>Bianchini Francesco<emph.end type="bold"/> definisce il tempo della rotazione di Venere 479. </s></p><p type="main">

<s><emph type="bold"/>Bianconi Lodovico<emph.end type="bold"/> dimostra la variabile velocit&agrave; del suono, nell'estate e nell'inverno 197. </s></p><p type="main">

<s><emph type="bold"/>Borelli Gian Alfonso<emph.end type="bold"/> pensa a un'esperienza, da concluder se la luce si muove con tempo 43, ri&shy;<lb/>prova le dottrine kepleriane, ma non promuove la Diottrica 68, pensa a un'esperienza dimostra&shy;<lb/>tiva delle astronomiche rifrazioni 94, come dimostri gli effetti dell'acqua nell'agghiacciarsi 164, <lb/>diffonde in Toscana la notizia delle proprieta de'suoni nel loro diffondersi per l'aria, scoperte <lb/>dal Mersenno 192, sue esperienze e ragioni del v<gap/>nto ne'cammini accesi 307, narra la scoperta, <lb/>e dice le ragioni delle variazioni barometriche, secondo il vario stato del cielo 320, dietro alle <lb/>proprie osservazioni trova insufficiente la dottrina del Keplero a render la ragione del lume nella <lb/>Luna ecclissata 400, suo metodo per trovare le longitudini, con gli orologi 460, sua teoria de'moti <lb/>planetarii 536. </s></p><p type="main">

<s><emph type="bold"/>Borro Girolamo<emph.end type="bold"/> scrive del flusso e riflusso marino 352, sua ipotesi delle Macchie lunari 391. </s></p><p type="main">

<s><emph type="bold"/>Bottiglia di Leyda,<emph.end type="bold"/> sua teoria data dal Franklin 276. </s></p><p type="main">

<s><emph type="bold"/>Boulliaud Ismaele,<emph.end type="bold"/> suo teorema fotometrico dimostrato 38, sue teorie plauetarie 531, primo a dimo&shy;<lb/>strar che gl'impulsi radiosi del Sole, in movere i Pianeti, si debilitano a proporzione che cre&shy;<lb/>scono i quadrati delle distanze 539, primo ad applicare la legge fotometrica alla illuminazione <lb/>de'Pianeti 539. </s></p><p type="main">

<s><emph type="bold"/>Branca Giovanni,<emph.end type="bold"/> libro <emph type="italics"/>Delle machine<emph.end type="italics"/> 173. </s></p><p type="main">

<s><emph type="bold"/>Cabeo Niccol&ograve;,<emph.end type="bold"/> come spieghi le attrazioni elettriche 266. </s></p><p type="main">

<s><emph type="bold"/>Calamita,<emph.end type="bold"/> come ne fosse da Galileo perfezionata l'armatura 236, come si sperasse per essa di tro&shy;<lb/>vare le longitudini 453. </s></p><p type="main">

<s><emph type="bold"/>Calcolo del Cartesio<emph.end type="bold"/> intoruo ai raggi rifratti osservati gi&agrave; dallo Snellio 62. </s></p><p type="main">

<s><emph type="bold"/>Calore,<emph.end type="bold"/> sua varia conducibilit&agrave; nelle varie nature de'corpi, da chi prima sperimentata 152, se si dif&shy;<lb/>fonda in sfera 155, leggi della intensit&agrave; del riscaldamento 157, come variamente assorbito dalle <lb/>superf&igrave;cie bianche e dalle nere 158. </s></p><p type="main">

<s><emph type="bold"/>Campani Giuseppe<emph.end type="bold"/> si usurpa l'invenzione della Macchinetta, da rappresentare le fasi di Saturno 492. </s></p><p type="main">

<s><emph type="bold"/>Candore lunare,<emph.end type="bold"/> principio delle controversie insorte fra Galileo e il Liceti 399, su questo argomento <lb/>scrive Galileo un principio di Lettera al Liceti 400, torna, nel seguito di quella Lettera, a rivol&shy;<lb/>gere il discorso al principe Leopoldo 401, pensieri importanti di Galileo su questo argomento 402, <lb/>riepilogo del principale argomento contro il Liceti 404. </s></p><p type="main">

<s><emph type="bold"/>Cappello,<emph.end type="bold"/> fase presentata in tal figura da Saturno 474. </s></p><p type="main">

<s><emph type="bold"/>Cartesio Renato,<emph.end type="bold"/> come dimostri geometricamente la legge dell'uguaglianza fra gli angoli dell'inci&shy;<lb/>denza e quelli di riflessione 15, dimostra la relazione costante, che passa fra i seni degli angoli <lb/>dell'incidenza e i seni degli angoli della rifrazione 63, come e quando s'intese che le leggi diot&shy;<lb/>triche spiegate da lui erano state prima dimostrate dallo Snellio 65, ragione perch&egrave; si creda pro&shy;<lb/>babile ch'egli conoscesse il Teorema diottrico dello Snellio 67, questioni da lui proposte intorno <lb/>al Magnete 240. </s></p><p type="main">

<s><emph type="bold"/>Cassini Gian Domenico,<emph.end type="bold"/> quel che risponda al Petit nel negar la variabilit&agrave; della declinazione ma&shy;<lb/>gnetica 257, riscontra le radici de'Medicei calcolate da Galileo 437, sue Effemeridi bolognesi 438, <lb/>determina il periodo della rotazione di Giove 449, scopre le ombre de'Satelliti proiettate sul disco <lb/>di Giove 449, propone le sue Effemeridi gioviali per la soluzione del problema delle Longitu&shy;<lb/>dini 459, sua teoria delle comete 518. </s></p><p type="main">

<s><emph type="bold"/>Castelli Benedetto,<emph.end type="bold"/> suo Teorema di Fotometria dimostrato 37, suo discorso sopra la Calamita 238, <lb/>d&agrave; opera, insieme con Galileo, alle osservazioni gioviali 424, collaboratore a Galileo nell'osser&shy;<lb/>vare le stelle 506. </s></p><p type="main">

<s><emph type="bold"/>Cavalieri Bonaventura<emph.end type="bold"/> medita intorno al problema delle ombre proposto dal Gassendo 26, come <lb/>ignorasse la legge della diffusione del suono 183, sue idee singolari intorno all'origine dei <lb/>venti 311, concorda con Galileo intorno alla ragione del vedersi ancora la Luna nelle ecclissi 408. </s></p><p type="main">

<s><emph type="bold"/>Ceralacca,<emph.end type="bold"/> se si elettrizzi di elettricit&agrave; simile a quella dell'ambra 273. </s></p><p type="main">

<s><emph type="bold"/>Cervo volante,<emph.end type="bold"/> macchina da esplorare l'elettricit&agrave; ammosferica 287. </s></p><p type="main">

<s><emph type="bold"/>Cesalpino Andrea<emph.end type="bold"/> ammette il moto diurno della Terra 342, sua opinione intorno alle macchie della <lb/>Luna 391. </s></p><p type="main">

<s><emph type="bold"/>Cilindretti di vetro<emph.end type="bold"/> immaginati dall'Huyghens, per spiegare come si dipingano le corone e i parelii 128. </s></p><pb xlink:href="020/01/1118.jpg" pagenum="561"/><p type="main">

<s><emph type="bold"/>Colombo Cristoforo,<emph.end type="bold"/> primo a osservare la declinazione dell'ago magnetico 225, primo a proporre il <lb/>modo di trovar la longitudine, per mezzo della Bussola 453. </s></p><p type="main">

<s><emph type="bold"/>Colori,<emph.end type="bold"/> loro natura secondo i Peripatetici 108, secondo il De Dominis 109, loro generazione per ri&shy;<lb/>frazione, secondo il Maurolico 110, secondo il Grimaldi 111, loro teoria, secondo il Cartesio 112, <lb/>loro analogie coll'armonie de'suoni, secondo il Grimaldi 113, dipendono, secondo il Castelli, dalla <lb/>maggiore o minore velocit&agrave; del raggio emesso 113, loro teoria, secondo il Newton 114, loro com&shy;<lb/>posizione nell'occhio, secondo il Montanari 115. </s></p><p type="main">

<s><emph type="bold"/>Comete,<emph.end type="bold"/> loro orbita parabolica dimostrata sperimentalmente 520, loro natura planetaria dimostrata <lb/>dal Newton 523. </s></p><p type="main">

<s><emph type="bold"/>Condensazione dell'acqua<emph.end type="bold"/> dimostrata impossibilc 163. </s></p><p type="main">

<s><emph type="bold"/>Contradizioni<emph.end type="bold"/> alle leggi diottriche del Cartesio 64. </s></p><p type="main">

<s><emph type="bold"/>Copernico Niccol&ograve;,<emph.end type="bold"/> da che venisse inspirato alle contemplazioni de'fenomeni celesti 335, suo si&shy;<lb/>stema 336, pubblicazione de'sei libri <emph type="italics"/>De revolutionibus<emph.end type="italics"/> 337. </s></p><p type="main">

<s><emph type="bold"/>Cornelio Tommaso<emph.end type="bold"/> ritrova falso un principio assunto da Galileo, per risolvere un problema ter&shy;<lb/>mico 135, come si provi a risolvere lo stesso problema 136, avverte, prima del Pecquet, l'ela&shy;<lb/>sticit&agrave; dell'aria 180. </s></p><p type="main">

<s><emph type="bold"/>Corone,<emph.end type="bold"/> come si dipingano intorno al Sole, secondo Ferrante Imperato 124, come, secondo il Car&shy;<lb/>tesio 125. </s></p><p type="main">

<s><emph type="bold"/>Cristalli del ghiaccio,<emph.end type="bold"/> come spiegati dal Keplero 166, come dal Cartesio 167, loro modo di formarsi, <lb/>secondo il Baliani e il Borelli 168, secondo il Rossetti 169. </s></p><p type="main">

<s><emph type="bold"/>Dalibard<emph.end type="bold"/> mette in esecuzione il progetto frankliniano de'parafulmini 287. </s></p><p type="main">

<s><emph type="bold"/>De Dominis,<emph.end type="bold"/> suoi errori intorno al fatto delle rifrazioni 59, risolve le principali questioni intorno al <lb/>flusso del mare 358. </s></p><p type="main">

<s><emph type="bold"/>Declinatorio magnetico<emph.end type="bold"/> sperimentato dal Sagredo 235. </s></p><p type="main">

<s><emph type="bold"/>Decreto<emph.end type="bold"/> nella sacra Congregazione romana contro il Copernico 347. </s></p><p type="main">

<s><emph type="bold"/>Del Buono Paolo<emph.end type="bold"/> esperimenta la generazione dell'aria dall'acqua 163. </s></p><p type="main">

<s><emph type="bold"/>Del Papa Giuseppe,<emph.end type="bold"/> come risolva un problema termico male risoluto da Galileo 137. </s></p><p type="main">

<s><emph type="bold"/>Diafani e opachi,<emph.end type="bold"/> da che dipendano 23. </s></p><p type="main">

<s><emph type="bold"/>Diffrazione della luce<emph.end type="bold"/> scoperta dal Grimaldi 100. </s></p><p type="main">

<s><emph type="bold"/>Digestore<emph.end type="bold"/> papiniano, e sua teoria data dal Newton 173. </s></p><p type="main">

<s><emph type="bold"/>Digressioni<emph.end type="bold"/> de'Satelliti di Giove trovate da Galileo 416. </s></p><p type="main">

<s><emph type="bold"/>Diottrica,<emph.end type="bold"/> trattata dall'Huyghens, e storia della sua pubblicazione 81. </s></p><p type="main">

<s><emph type="bold"/>Disegno<emph.end type="bold"/> dell'anello di Saturno fatto a penna da Galileo 466. </s></p><p type="main">

<s><emph type="bold"/>Du-Hamel<emph.end type="bold"/> nega, contro l'autorit&agrave; del Pascal e del Borelli, che l'aria nuvolosa pesi pi&ugrave; della se&shy;<lb/>rena 322. </s></p><p type="main">

<s><emph type="bold"/>Effemeridi<emph.end type="bold"/> prime di Galileo 412. </s></p><p type="main">

<s><emph type="bold"/>Elasticit&agrave; dell'aria,<emph.end type="bold"/> quando e come fosse conosciuta 179. </s></p><p type="main">

<s><emph type="bold"/>Elba,<emph.end type="bold"/> isola, se abbia alcuna influenza in alterar la direzione dell'ago calamitato 227. </s></p><p type="main">

<s><emph type="bold"/>Elettriche,<emph.end type="bold"/> forze, rassomigliate alle forze cosmiche 551. </s></p><p type="main">

<s><emph type="bold"/>Elettricit&agrave;<emph.end type="bold"/> per comunicazione scoperta dal Gray, e confermata dal Dufay 272, vitrea e resinosa 273, <lb/>Elettricit&agrave; vindice 283, Elettricit&agrave; ammosferica, sua origine secondo il Franklin 285, come di&shy;<lb/>mostrata dal Volta 289, Elettricit&agrave; per eccesso, sua origine nell'aria 290. </s></p><p type="main">

<s><emph type="bold"/>Empoli (da) Giovanni<emph.end type="bold"/> specula sulle propriet&agrave; della Calamita 225. </s></p><p type="main">

<s><emph type="bold"/>Equazion della luce<emph.end type="bold"/> nelle osservazioni de'Satelliti di Giove 459. </s></p><p type="main">

<s><emph type="bold"/>Esalazioni ascendenti,<emph.end type="bold"/> causa secondo Galileo delle evaporazioni 172. </s></p><p type="main">

<s><emph type="bold"/>Esperienza<emph.end type="bold"/> proposta dal Borelli per misurar la velocit&agrave; della luce 43, di Euclide sulle rifrazioni 53, <lb/>esperienza con cui prima il Grimaldi scopri il fenomeno della diffrazione 98, altra esperienza <lb/>per questo effetto 99, esperienza della luce, che aggiunta a luce fa ombra 101, esperienza im&shy;<lb/>maginata dal Borelli, per dimostrar come l'aria carica di vapori faccia sollevar di pi&ugrave; la co&shy;<lb/>lonna barometrica 317. </s></p><p type="main">

<s><emph type="bold"/>Esperienze acustiche<emph.end type="bold"/> di Galileo, che non rispondono alle prove 2<gap/>8, 211, esperienze magnetiche de&shy;<lb/>scritte dal Porta, nel VII libro della Magia naturale 229, esperienze della Calamita nel vuoto 251. </s></p><p type="main">

<s><emph type="bold"/>Euclide,<emph.end type="bold"/> suo trattato di Prospettiva 8, come dimostri che l'angolo dell'incidenza &egrave; uguale all'an&shy;<lb/>golo della riflessione 12. </s></p><p type="main">

<s><emph type="bold"/>Fabry Onorato,<emph.end type="bold"/> suo sistema saturnio 475, sue opposizioni fatte contro quello dell'Huyghens 476. </s></p><p type="main">

<s><emph type="bold"/>Fasce di Glove,<emph.end type="bold"/> da chi prima osservate 445, loro origine 446. </s></p><pb xlink:href="020/01/1119.jpg" pagenum="562"/><p type="main">

<s><emph type="bold"/>Fata morgana,<emph.end type="bold"/> come spiegata co principii ottici neutoniani 19. </s></p><p type="main">

<s><emph type="bold"/>Fermat<emph.end type="bold"/> si oppone alla legge diottrica dimostrata dal Cartesio 64, come, partendo dal principio delle <lb/>c&aacute;use finali, s'incontrasse nella legge diottrica formulata dal Cartesio 71. </s></p><p type="main">

<s><emph type="bold"/>Ferroni Giuseppe,<emph.end type="bold"/> come spieghi che l'aria serena preme pi&ugrave; sul Barometro, che non la nuvolosa 322. </s></p><p type="main">

<s><emph type="bold"/>Fiamma,<emph.end type="bold"/> come scoperta conduttrice dell'Elettricit&agrave; 273. </s></p><p type="main">

<s><emph type="bold"/>Fontana Francesco,<emph.end type="bold"/> sue osservazioni sul pianeta di Saturno 468. </s></p><p type="main">

<s><emph type="bold"/>Foro,<emph.end type="bold"/> per cui passa la luce e si proietta su un diaframma: fenomeni relativi spiegati 30. </s></p><p type="main">

<s><emph type="bold"/>Fracastoro Girolamo,<emph.end type="bold"/> suo sistema degli Omocentrici 341, sua ipotesi intorno all'apparizione delle <lb/>stelle nuove 496. </s></p><p type="main">

<s><emph type="bold"/>Franklin Beniamino,<emph.end type="bold"/> sua teoria dell'Elettricit&agrave; vitrea e resinosa 275. </s></p><p type="main">

<s><emph type="bold"/>Freddo,<emph.end type="bold"/> se sia positivo: questione insorta fra il Dati e il Rucellai 139. </s></p><p type="main">

<s><emph type="bold"/>Fulmini,<emph.end type="bold"/> loro natura, secondo il Montanari 284. </s></p><p type="main">

<s><emph type="bold"/>Fuoco elettrico,<emph.end type="bold"/> sua differenza dal fuoco ordinario 270. </s></p><p type="main">

<s><emph type="bold"/>Galilei Alessandro,<emph.end type="bold"/> sua macchina a vapore 175. </s></p><p type="main">

<s><emph type="bold"/>Galileo Galilei,<emph.end type="bold"/> sue proposizioni di Fotometria 61, suo errore nel misurar l'intensit&agrave; del lume di <lb/>Luna 39, propone l'esperienza, per decider se la luce si muove in istante 41, sua ambiguit&agrave; <lb/>nell'ammettere le rifrazioni, e d'ond'ella dipendesse 93, rinnova le dottrine de'Filosofi antichi <lb/>intorno al calore 133, come errasse nel paragonare la diffusione della luce con quella del ca&shy;<lb/>lore 154, leggi del risonar delle corde da lui scoperte 209, come spieghi le attrazioni elettriche 265, <lb/>osserva col Canocchiale i vapori ascendenti, e pensa alle ragioni della pioggia 295, sua prima <lb/>professione di Copernicismo 344, scrive il Discorso del flusso e riflusso 348, vicende della pub&shy;<lb/>blicazione del suo Dialogo copernicano 349, quale efficacia, sulla marea, attribuisse alla Luna 354, <lb/>se fosse il primo a pensare alle fasi di Venere, per confermare il Sistema copernicano 358, os&shy;<lb/>serva <emph type="italics"/>averso vultu<emph.end type="italics"/> le macchie del Sole 374, &egrave; incoerente a s&egrave; medesimo, nell'assegnar la data <lb/>della scoperta delle Macchie solari 374, sua incoerenza nell'ammettere l'inversione delle imma&shy;<lb/>gini nel Canocchiale, e no nell'occhio 381, ci&ograve; che, riguardo all'osservazione e alla filosofia delle <lb/>macchie solari, attingesse dal Passignani e dal Castelli 381, sua ipotesi intorno alle stelle nuove 496, <lb/>suo Dialogo intorno a questo soggetto 498, quale accoglienza facesse alla Nuova astronomia keple&shy;<lb/>riana 530. </s></p><p type="main">

<s><emph type="bold"/>Gassendi Pietro,<emph.end type="bold"/> suo problema dell'ombre 26, ammette il freddo positivo 138, sue proposizioni in&shy;<lb/>torno alle propriet&agrave; de'suoni, verificate dagli Accademici del Cimento 194, compendia la storia <lb/>del Magnete 239. </s></p><p type="main">

<s><emph type="bold"/>Ghiacclo,<emph.end type="bold"/> causa del ricrescimento della sua mole 161. </s></p><p type="main">

<s><emph type="bold"/>Giamblico,<emph.end type="bold"/> come racconti la stoma pitagorica de'suoni musicali 199. </s></p><p type="main">

<s><emph type="bold"/>Gilberto Guglielmo,<emph.end type="bold"/> racconta come e da chi fosse prima osservata la direzione dell'ago magne&shy;<lb/>tico 224, non fa il Magnetismo e l'Elettricit&agrave; due cose della stessa natura, come pretendono al&shy;<lb/>cuni 282, in che riconosca la causa della variazione della declinazione magnetica 253, accresce <lb/>il numero de'corpi elettrici 263, investiga le ragioni delle attrazioni elettriche 264, le fa consi&shy;<lb/>stere nell'umido copulatore 265, suoi argomenti fisici in favore del moto terrestre 339. </s></p><p type="main">

<s><emph type="bold"/>Giove,<emph.end type="bold"/> misura del diametro apparente del Pianeta 418, sue macchie 443, sue zone, da chi prima os&shy;<lb/>servate 444, sua rotazione, come scoperta 448. </s></p><p type="main">

<s><emph type="bold"/>Grandi Guido<emph.end type="bold"/> applica un teorema ugeniano a dimostrar la legge diottrica cartesiana, col principio <lb/>delle cause finali 72. </s></p><p type="main">

<s><emph type="bold"/>Grandine,<emph.end type="bold"/> origine della sua formazione, secondo il Volta 293. </s></p><p type="main">

<s><emph type="bold"/>Gray<emph.end type="bold"/> scopre l'Elettricit&agrave; per comunicazione 272. </s></p><p type="main">

<s><emph type="bold"/>Gravi<emph.end type="bold"/> tendono al centro della Terra, come il ferro al Magnete 548. </s></p><p type="main">

<s><emph type="bold"/>Gravit&agrave;,<emph.end type="bold"/> che tiene aderente a Saturno il suo anello 486. </s></p><p type="main">

<s><emph type="bold"/>Grimaldi Franc. </s>

<s>Maria,<emph.end type="bold"/> come fisicamente dimostri la legge dell'uguaglianza, che passa fra gli an&shy;<lb/>goli d'incidenza e di riflessione 16, se professasse l'ipotesi delle ondulazioni 50, censura l'ipo&shy;<lb/>tesi assunta dal Cartesio per la sua diottrica dimostrazione 82, come renda la ragione dell'ac&shy;<lb/>costarsi il raggio rifratto, e discostarsi dalla perpendicolare 83, come dimostri la legge diottrica, <lb/>tenendo una via, da quella del Cartesio, diversa 84, sua importante teoria magnetica 248, suoi <lb/>esperimenti magnetici 249. </s></p><p type="main">

<s><emph type="bold"/>Guericke Ottene,<emph.end type="bold"/> sue esperienze elettriche 267, dimostra artificialmente come faccia il cielo a ran&shy;<lb/>nuvolarsi, piovere, e tornar sereno 304. </s></p><p type="main">

<s><emph type="bold"/>Guglielmini,<emph.end type="bold"/> rispetto alla luce professa l'ipotesi delle ondulazioni 51. </s></p><p type="main">

<s><emph type="bold"/>Guiducci Mario<emph.end type="bold"/> espone il sistema magnetico del Gilberto 231. </s></p><p type="main">

<s><emph type="bold"/>Guy Tachart<emph.end type="bold"/> primo a osservare la variazione magnetica diurna 261. </s></p><pb xlink:href="020/01/1120.jpg" pagenum="563"/><p type="main">

<s><emph type="bold"/>Hawkabee Francesco<emph.end type="bold"/> ripete l'esperienza del Lowthorp, per dimostrare la rifrazion della luce, che <lb/>dal vuoto passa nell'aria 95, sue esperienze, per dimostraro da che dipenda il galleggiar dei <lb/>corpi ne'mezzi specificamente pi&ugrave; leggeri 303, conferma coll'esperienza un concetto sovvenuto al <lb/>Viviani 323, dimostra sperimentalmente l'efflcacia de'venti, in alterar lo stato barometrico 320. </s></p><p type="main">

<s><emph type="bold"/>Herigonio Pietro,<emph.end type="bold"/> suo Corso matematico 68, come dimostri la proporzione costante, che passa fra'seni <lb/>degli angoli dell'incidenza, e i seni degli angoli delle rifrazioni 69, propone il modo di trovare <lb/>le longitudini, per via della congiunzione de'Satelliti col centro di Giove 457. </s></p><p type="main">

<s><emph type="bold"/>Hevelio Giovanni<emph.end type="bold"/> propone di risolvere il problema delle longitudini, per via delle Effemeridi de'Sa&shy;<lb/>telliti di Giove 458, suo sistema saturnio 469, sua teoria del moto parabolico delle Comete 522. </s></p><p type="main">

<s><emph type="bold"/>Hodierna Giovan Batista,<emph.end type="bold"/> sua Menologia di Giove 428, impone i nomi ai Satelliti gioviali 429. </s></p><p type="main">

<s><emph type="bold"/>Hook Roberto<emph.end type="bold"/> conferisce col Viviani i suoi studii intorno al Magnete 243, come riuscisse a conclu&shy;<lb/>dere la legge delle forze centrali 512. </s></p><p type="main">

<s><emph type="bold"/>Huyghens Cristiano,<emph.end type="bold"/> notizie intorno alla pubblicazione della sua Diottrica 127, sua applicazione di <lb/>uno strumento inventato dal Lecuwenoeck 370, narra come scoprisse l'anello di Saturno 471. </s></p><p type="main">

<s><emph type="bold"/>Inclinazione dell'ago magnetico,<emph.end type="bold"/> da chi prima osservata 233. </s></p><p type="main">

<s><emph type="bold"/>Innominato Autore<emph.end type="bold"/> dell'Elettricismo, sua teoria de'vortici elettrici 274. </s></p><p type="main">

<s><emph type="bold"/>Iride<emph.end type="bold"/> si fa per refrazione, secondo i placiti de'Filosofi antichi riferiti da Plutarco e da Dante 115, <lb/>come si dipinga nelle nubi, secondo Vitellione 116, Iride primaria e secondaria, come spiegata da <lb/>Ferrante Imperato 117, teorie del Maurolico 118, del De Dominis 119, del Cartesio 121. </s></p><p type="main">

<s><emph type="bold"/>Irradiazlone,<emph.end type="bold"/> effetti di lei nella falce della Luna 395. </s></p><p type="main">

<s><emph type="bold"/>Kepier Giovanni,<emph.end type="bold"/> &egrave; il primo a dar la dimostrazione geometrica dell'uguaglianza, che passa tra gli <lb/>angoli incidenti, formati dai raggi di luce, e i reflessi 14, come spieghi il rotondarsi dello spettro <lb/>del Sole passato attraverso a un foro irregolare 30, sue proposizioni di fotometria 33, ammette <lb/>che l'intensit&agrave; della luce scemi al crescere delle semplici distanze 35, applica alle rifrazioni il <lb/>principio della composizion delle forze 56, come narri la storia della scoperta delle astronomiche <lb/>rifrazioni 86, primo a osservare i cristallini del ghiaccio 166, a qual numero riducesse le conso&shy;<lb/>nanze 200, osserva il Sole e la Luna, <emph type="italics"/>averso vultu<emph.end type="italics"/> 373, quando osservasse le Macchie solari col <lb/>Canocchiale 383, sua opinione intorno alla natura delle Macchie solari 386, leggi planetarie da <lb/>lui scoperte 528, da che fosse condotto ad ammettere che le forze centrali si debilitano secondo <lb/>le semplici distanze 538. </s></p><p type="main">

<s><emph type="bold"/>Hircker Atanasio,<emph.end type="bold"/> ragioni rese da lui della variazione della declinazione magnetica 254. </s></p><p type="main">

<s><emph type="bold"/>Latitudini de'Gioviali,<emph.end type="bold"/> controversia insorta fra il Mario e Galileo 442. </s></p><p type="main">

<s><emph type="bold"/>Leibniz Gotifredo<emph.end type="bold"/> dimostra, col principio delle cause finali, l'uguaglianza che passa fra gli angoli <lb/>d'incidenza e di riflessione 20, dimostra, con lo stesso principio delle cause finali, il teorema <lb/>diottrico cartesiano 73, suo strumento meccanico adattato a rappresentar le variazioni barome&shy;<lb/>triche, variando lo stato del cielo 326. </s></p><p type="main">

<s><emph type="bold"/>Leeuwenhoeck Antonio,<emph.end type="bold"/> sua esperienza per dimostrare il moto della Terra 369. </s></p><p type="main">

<s><emph type="bold"/>Libri Guglielmo<emph.end type="bold"/> e il disegno galileiano dell'anello di Saturno 466. </s></p><p type="main">

<s><emph type="bold"/>Liceti Fortunio,<emph.end type="bold"/> come risolva ii problema delle ombre proposto dal Gassendo 27. </s></p><p type="main">

<s><emph type="bold"/>Longitudine,<emph.end type="bold"/> modo di ritrovarla proposto da Galileo 446. </s></p><p type="main">

<s><emph type="bold"/>Luce,<emph.end type="bold"/> se sia materiale: opinion degli antichi 40, sua velocit&agrave; come misurata dal Roemer 46, luce ag&shy;<lb/>giunta a luce, fa ombra 101, come possa produrre effetti meccanici 535. </s></p><p type="main">

<s><emph type="bold"/>Lucerna di Herone,<emph.end type="bold"/> come operasse 180. </s></p><p type="main">

<s><emph type="bold"/>Luna,<emph.end type="bold"/> rossore di lei negli ecclissi, da che secondo il Vossio dipenda 2<gap/>, da che dipenda, secondo il <lb/>Benedetti 28, s'irraggia anch'essa come le stelle 396, perch&egrave; si mostri maggiore all'orizzonte 397, <lb/>origine del candor di lei nelle congiunzioni 398, paragonata nel candore alla pietra lucifera 406. </s></p><p type="main">

<s><emph type="bold"/>Macchie del Sole<emph.end type="bold"/> osservate direttamente coll'occhio 376, descritte da Galileo 377, Galileo dimostra <lb/>che non sono stelle 378, controversia insorta fra lo Scheiner e Galileo, come si decida 385, opi&shy;<lb/>nioni varie intorno alla loro origine ed essenza 388, Macchie di Giove osservate e descritte da <lb/>Galileo 443, loro origine 447. </s></p><p type="main">

<s><emph type="bold"/>Macchina inventata<emph.end type="bold"/> dal Borelli a rappresentar l'immagine, e le fasi di Saturno 472. </s></p><p type="main">

<s><emph type="bold"/>Magalotti Loren<gap/>o,<emph.end type="bold"/> come rappresenti la struttura de'pori nelle superficie nere, per assorbir meglio <lb/>il calore 159, sue notabili idee intorno all'attrazione universale 548. </s></p><p type="main">

<s><emph type="bold"/>Magnete,<emph.end type="bold"/> esperienze dell'attrazione di lui a varie distanze 541. </s></p><p type="main">

<s><emph type="bold"/>Maraldi Giacomo Filippe,<emph.end type="bold"/> sue esperienze sull'ombre, a fin di spiegare i fenomeni degli ecclissi di <lb/>Luna 29. </s></p><pb xlink:href="020/01/1121.jpg" pagenum="564"/><p type="main">

<s><emph type="bold"/>Marchetti Alessandro,<emph.end type="bold"/> sua scrittura manoscritta sopra le Comete, e sua opinione intorno a queste <lb/>apparenze 513, confuta l'opinione di Galileo 515. </s></p><p type="main">

<s><emph type="bold"/>Mari nella Luna,<emph.end type="bold"/> se pi&ugrave; chiari o scuri debbano apparire de'continenti 393. </s></p><p type="main">

<s><emph type="bold"/>Mario Simone<emph.end type="bold"/> pretende alla priorit&agrave; della scoperta de'Satelliti di Giove 423. </s></p><p type="main">

<s><emph type="bold"/>Marsili Cesare<emph.end type="bold"/> osserva la variazione della declinazione magnetica 454. </s></p><p type="main">

<s><emph type="bold"/>Marte,<emph.end type="bold"/> sue prime fasi osservate dal Castelli 361, periodo della rivoluzione in s&egrave; stesso 477, d&agrave; oc&shy;<lb/>casione al Keplero a instituir l'Astronomia nuova 526. </s></p><p type="main">

<s><emph type="bold"/>Mattonata,<emph.end type="bold"/> scrittura del Castelli relativa al vario grado di assorbimento del calore incidente sopra <lb/>superficie o bianche o nere 158. </s></p><p type="main">

<s><emph type="bold"/>Mattoni<emph.end type="bold"/> troppo cotti, alterano la declinazione magnetica 257. </s></p><p type="main">

<s><emph type="bold"/>Maurolico Francesco,<emph.end type="bold"/> suo Teorema sulla penombra 24, suoi Teoremi fotometrici 32, suoi Teoremi <lb/>sulle rifrazioni 57. </s></p><p type="main">

<s><emph type="bold"/>Mazzoni Jacopo<emph.end type="bold"/> legge in Pisa, insieme con Galileo, il libro delle Speculazioni del Benedetti 343. </s></p><p type="main">

<s><emph type="bold"/>Medici Leopoldo,<emph.end type="bold"/> ci&ograve; che pensasse intorno alla causa delle variazioni meteorologiche del Baro&shy;<lb/>metro 319. </s></p><p type="main">

<s><emph type="bold"/>Mersenno Marino,<emph.end type="bold"/> come dimostri l'ipotesi cartesiana del diffondersi il lume dal corpo luminoso 47, <lb/>fu primo a misurar la velocit&agrave; del suono 190, applica il suono alla misura delle distanze 191. </s></p><p type="main">

<s><emph type="bold"/>Michelotti Pierantonio<emph.end type="bold"/> difende il Leibniz dalle accuse mossegli contro dal Desaguliers 327. </s></p><p type="main">

<s><emph type="bold"/>Montanari Geminiano,<emph.end type="bold"/> legge fotometrica da lui prima sperimentalmente dimostrata 39, come fosse <lb/>condotto a professar, rispetto alla luce, l'ipotesi delle ondulazioni eterce 51, come spieghi il modo <lb/>dell'operar del vento, nel sollecitar l'evaporazione 174, attende alle Tavole de'Satelliti di Giove 431, <lb/>descrive uno strumento, da rappresentare i moti di Giove 432, sua ipotesi dell'apparizione e spa&shy;<lb/>rizione delle stelle 500. </s></p><p type="main">

<s><emph type="bold"/>Monti<emph.end type="bold"/> nella circonferenza della Luna, da chi prima osservati 394. </s></p><p type="main">

<s><emph type="bold"/>Moto e calore,<emph.end type="bold"/> concetti degli antichi e de'moderni 160. </s></p><p type="main">

<s><emph type="bold"/>Muro scabro,<emph.end type="bold"/> perch&egrave; apparisca pi&ugrave; luminoso di uno specchio levigato 21. </s></p><p type="main">

<s><emph type="bold"/>Musschenbrock Pietro<emph.end type="bold"/> accusa di poco accurati i nostri Accademici fiorentini intorno all'esperienza <lb/>del suono 188. </s></p><p type="main">

<s><emph type="bold"/>Mutoli,<emph.end type="bold"/> pseudonomo del Borelli, suo Discorso della Cometa 517. </s></p><p type="main">

<s><emph type="bold"/>Nardi Antonio,<emph.end type="bold"/> sua teoria delle attrazioni magnetiche 245. </s></p><p type="main">

<s><emph type="bold"/>Nebulose,<emph.end type="bold"/> come e da chi prima osservate 516. </s></p><p type="main">

<s><emph type="bold"/>Newton Isacco,<emph.end type="bold"/> come dimostri, per le leggi della Meccanica, l'uguaglianza che intercede, fra gli angoli <lb/>formati dai raggi incidenti della luce, e dai riflessi 18, sue Questioni intorno alla natura e alla <lb/>diffusion della luce 48, suoi principii meccanici applicati a dimostrare il Teorema diottrico del <lb/>Cartesio 75, s'introduce allo studio de'colori 103, esamina il fenomeno grimaldiano della diffra&shy;<lb/>zione 105, come perfezionasse la teoria dell'Iride celeste, esposta dal De Dominis e dal Carte&shy;<lb/>sio 123, suo giudizio sull'ipotesi proposta dall'Huyghens, per spiegare il modo del dipingersi gli <lb/>Aloni e i Parelii 130, come dimostri la speculazione del Benedetti, che cio&egrave; il suono si produce <lb/>dai condensamenti e dalle rarefazioni dell'aria 183, come dimostri il propagarsi del suono attra&shy;<lb/>verso agli ostacoli 184, suo processo matematico, per misurar la velocit&agrave; della diffusione del <lb/>suono 195, ripensa alla possibile caduta della Luna sopra la Terra 537, suo calcolo della velocit&agrave;, <lb/>con cui la Luna sarebbe caduta sulla Terra 543, sua ipotesi intorno alle cause della gravita&shy;<lb/>zione 550. </s></p><p type="main">

<s><emph type="bold"/>Nollet,<emph.end type="bold"/> non fu il primo a far l'esperienza della diffusione de suoni nell'acqua 189. </s></p><p type="main">

<s><emph type="bold"/>Ombre,<emph.end type="bold"/> se fosse stato il Vossio il primo a trattarne 23, ombre proiettate dai Satelliti sul disco di <lb/>Giove negate dagli Accademici fiorentini 450, confermate dalle osservazioni dell'Huyghens e del <lb/>Borelli 451. </s></p><p type="main">

<s><emph type="bold"/>Onde eteree<emph.end type="bold"/> diffusive della luce professate in Italia, prima dal Montanari 51, diffusive del calore, pro&shy;<lb/>fessate dal Montanari stesso e dal Guglielmini 155. </s></p><p type="main">

<s><emph type="bold"/>Opachi e diafani,<emph.end type="bold"/> qual sia la causa che gli produce 23. </s></p><p type="main">

<s><emph type="bold"/>Orbite elettriche,<emph.end type="bold"/> loro causa fisica, secondo il Borelli 544, loro causa matematica, secondo il New&shy;<lb/>ton 546. </s></p><p type="main">

<s><emph type="bold"/>Orologi,<emph.end type="bold"/> per uso delle longitudini 461. </s></p><p type="main">

<s><emph type="bold"/>Ovale,<emph.end type="bold"/> orbita di Marte, dimostrata dal comparare i calcoli con le osservazioui 527. </s></p><p type="main">

<s><emph type="bold"/>Pagani Francesco,<emph.end type="bold"/> sua teoria de'Pianeti 533. </s></p><p type="main">

<s><emph type="bold"/>Parafulmini,<emph.end type="bold"/> loro primo concetto sovvenuto al Franklin 286. </s></p><p type="main">

<s><emph type="bold"/>Parallasse<emph.end type="bold"/> delle stelle fisse 509. </s></p><pb xlink:href="020/01/1122.jpg" pagenum="565"/><p type="main">

<s><emph type="bold"/>Pardies,<emph.end type="bold"/> sue opposizioni alle teorie ottiche neutoniane 104. </s></p><p type="main">

<s><emph type="bold"/>Pascal Biagio,<emph.end type="bold"/> primo a sperimentare le variazioni meteorologiche del Barometro 316. </s></p><p type="main">

<s><emph type="bold"/>Passignani Domenico<emph.end type="bold"/> osserva e specula sulle macchie del Sole 380, sue controversie con Galileo 387. </s></p><p type="main">

<s><emph type="bold"/>Pendolo,<emph.end type="bold"/> suo moto applicato al moto de'Pianeti 531. </s></p><p type="main">

<s><emph type="bold"/>Petit Pietro,<emph.end type="bold"/> sue osservazioni e studii intorno alla variazione della declinazione magnetica 253, a <lb/>qual causa attribuisse un tale effetto 254, sua lettera al Sauval 255. </s></p><p type="main">

<s><emph type="bold"/>Pianeti,<emph.end type="bold"/> leggi de'loro moti scoperte dal Keplero 528. </s></p><p type="main">

<s><emph type="bold"/>Ploggie,<emph.end type="bold"/> loro origine secondo il Borelli 296, secondo il Cartesio 299, secondo il Baliani 300. </s></p><p type="main">

<s><emph type="bold"/>Pitagorici,<emph.end type="bold"/> loro opinione intorno alle Comete 510. </s></p><p type="main">

<s><emph type="bold"/>Piatone,<emph.end type="bold"/> suo sistema del Mondo 333. </s></p><p type="main">

<s><emph type="bold"/>Piutarco,<emph.end type="bold"/> sua teoria della Luna 389, ne attribuisce le macchie alle ombre de'monti, e a'seni ripieni <lb/>di acque nereggianti 390, ammirato e seguito dal Keplero 391. </s></p><p type="main">

<s><emph type="bold"/>Porta Giovan Batista<emph.end type="bold"/> racconta come e da chi fosse osservata la direzione dell'ago magnetico 224, <lb/>sue esperienze magnetiche giudicate dal Gilberto 228. </s></p><p type="main">

<s><emph type="bold"/>Portavoce,<emph.end type="bold"/> come il Newton ne spiegasse gli effetti 184. </s></p><p type="main">

<s><emph type="bold"/>Presagi del tempo<emph.end type="bold"/> dedotti dal Barometro, secondo il Borelli 328, secondo il Guericke 329, secondo <lb/>il Vossio 330. </s></p><p type="main">

<s><emph type="bold"/>Principio<emph.end type="bold"/> delle cause finali riprovato nella Diottrica 74. </s></p><p type="main">

<s><emph type="bold"/>Questioni varie<emph.end type="bold"/> di Ottica risolute dal Newton, dietro l'ipotesi dell'emissione 49. </s></p><p type="main">

<s><emph type="bold"/>Ramazzini Bernardino,<emph.end type="bold"/> sue Effemeridi modanesi 324, sua nuova ipotesi di Meteorologia barometrica, <lb/>in sostituzione di quella del Borelli 325. </s></p><p type="main">

<s><emph type="bold"/>Renieri Vincenzio,<emph.end type="bold"/> sua opinione intorno al color rosso nella Luna ecclissata 407, 409, ammaestrato <lb/>da Galileo intorno al modo di osservare i satelliti di Giove 424, tien conto di alcune annotazioni <lb/>manoscritte di Galileo 425, sente la necessit&agrave; di ammettere le orbite ellittiche 426, suoi problemi <lb/>astronomici intorno agli ecclissi de'Satelliti di Giove 427. </s></p><p type="main">

<s><emph type="bold"/>Rifrazioni,<emph.end type="bold"/> loro leggi fondamentali 54, d'onde avessero i loro principii dimostrativi 58, primi ten&shy;<lb/>tativi sperimentali fatti intorno ad esse 59, secondo Galileo e altri, son riflessioni interne 76, <lb/>come fossero tardi studiate in Italia 77. </s></p><p type="main">

<s><emph type="bold"/>Rinaldini Carlo,<emph.end type="bold"/> pensa a un'esperienza da dimostrare il moto della luce 44, ci&ograve; che pensasse in&shy;<lb/>torno alle rifrazioni 81, sua singolare esperienza, per decider se il freddo del ghiaccio operi po&shy;<lb/>sitivamente 141. </s></p><p type="main">

<s><emph type="bold"/>Risonanze<emph.end type="bold"/> sperimentate dagli Accademici del Cimento 207. </s></p><p type="main">

<s><emph type="bold"/>Roberval,<emph.end type="bold"/> suo Aristarco Samio 364, suo sistema saturnio 470. </s></p><p type="main">

<s><emph type="bold"/>Rosa Ursina<emph.end type="bold"/> dello Scheiner 382. </s></p><p type="main">

<s><emph type="bold"/>Rotazione<emph.end type="bold"/> di Giove 448 </s></p><p type="main">

<s><emph type="bold"/>Rothmann Cristoforo,<emph.end type="bold"/> sue controversie con Ticone intorno aile astronomiche rifrazioni 87, come ri&shy;<lb/>sponde agli argomenti promossi da Ticone contro il moto della Terra 338. </s></p><p type="main">

<s><emph type="bold"/>Rucellai Orazio,<emph.end type="bold"/> suo Discorso contro il freddo positivo 140. </s></p><p type="main">

<s><emph type="bold"/>Sagredo Giovan Francesco<emph.end type="bold"/> fu il primo a far l'esperienza del suono nel vuoto 187. </s></p><p type="main">

<s><emph type="bold"/>Sarpi Paolo<emph.end type="bold"/> conferisce, intorno allo strumento inclinatorio, con Galileo 234. </s></p><p type="main">

<s><emph type="bold"/>Sassetti Filippo<emph.end type="bold"/> specula intorno alle propriet&agrave; dell'ago magnetico 226, propone il modo di trovar la <lb/>longitudine, per mezzo della calamita 453. </s></p><p type="main">

<s><emph type="bold"/>Satelliti<emph.end type="bold"/> di Giove e i Pianeti non hanno luce propria 428, causa della loro apparente grandezza 446. <lb/>Satelliti di Saturno scoperti dal Cassini 480. </s></p><p type="main">

<s><emph type="bold"/>Saturno,<emph.end type="bold"/> prime osservazioni fatte da Galileo su questo Pianeta 464, sue fasi divinate 465, Sistema <lb/>robervalliano illustrato dal Magalotti 483. </s></p><p type="main">

<s><emph type="bold"/>Saussure,<emph.end type="bold"/> sue osservazioni microscopiche sul vapore vescicolare 303. </s></p><p type="main">

<s><emph type="bold"/>Scaleno,<emph.end type="bold"/> cono, immaginato dal Boulliaud, per spiegar l'origine delle orbite ellittiche 532. </s></p><p type="main">

<s><emph type="bold"/>Scaligero Giuseppe<emph.end type="bold"/> dimostra con buone ragioni che il moto della luce non pu&ograve; essere in stante 45. </s></p><p type="main">

<s><emph type="bold"/>Scatola<emph.end type="bold"/> delle rifrazioni, per farne l'esperienza, inventata dal Viviani 79. </s></p><p type="main">

<s><emph type="bold"/>Scheiner Cristoforo<emph.end type="bold"/> osserva il Sole ellittico, e ne riconosce la causa dalle rifrazioni 88, &egrave; il primo a <lb/>proporre il modo come si possano, per rifrazione, dipingere le Corone e i Parelii 125, narra a <lb/>quale occasione si volgesse a osservar le macchie del Sole 384. </s></p><p type="main">

<s><emph type="bold"/>Schelhamer<emph.end type="bold"/> oppositore in Meteorologia barometrica al Ramazzini 325. </s></p><p type="main">

<s><emph type="bold"/>Scintillazione<emph.end type="bold"/> delle stelle fisse 502, loro causa, secondo il Keplero 503, secondo Galileo e il Bene&shy;<lb/>detti 504. </s></p><p type="main">

<s><emph type="bold"/>Scrittura santa,<emph.end type="bold"/> argomenti da lei addotti contro il moto della Terra 346. </s></p><pb xlink:href="020/01/1123.jpg" pagenum="566"/><p type="main">

<s><emph type="bold"/>Seneca,<emph.end type="bold"/> come spieghi il trapassar del suono attraverso alle pareti di un muro 185. </s></p><p type="main">

<s><emph type="bold"/>Sinclaro Giorgio<emph.end type="bold"/> discute intorno alle ragioni del Copernicismo 366. </s></p><p type="main">

<s><emph type="bold"/>Sismoseopio,<emph.end type="bold"/> sua prima invenzione del Grimaldi 186. </s></p><p type="main">

<s><emph type="bold"/>Snellio Willebrod,<emph.end type="bold"/> sua legge delle rifrazioni formulata 61. </s></p><p type="main">

<s><emph type="bold"/>Sole ellittico,<emph.end type="bold"/> come spiegato da Galileo nel <emph type="italics"/>Saggiatore<emph.end type="italics"/> 91, come nelle Operazioni astronomicbe 93. </s></p><p type="main">

<s><emph type="bold"/>Sovero Bartolommeo<emph.end type="bold"/> non &egrave; inventore dell'armatura delle calamite 237. </s></p><p type="main">

<s><emph type="bold"/>Southwell Roberto<emph.end type="bold"/> riferisce al Viviani gli studii e l'esperienze fatte dall'Hook e dall'Halley intorno <lb/>al Magnete 242. </s></p><p type="main">

<s><emph type="bold"/>Specchi levigati,<emph.end type="bold"/> perch&egrave; appariscan pi&ugrave; bui di un muro aspro 21, come abbiano la virt&ugrave; ustoria, con&shy;<lb/>figurati in qualunque genere di parabola 153. </s></p><p type="main">

<s><emph type="bold"/>Speeie immateriata,<emph.end type="bold"/> secondo il Keplero, motrice del Sole 529. </s></p><p type="main">

<s><emph type="bold"/>Spuma dell'acqua,<emph.end type="bold"/> perch&egrave; apparisca bianca 22. </s></p><p type="main">

<s><emph type="bold"/>Stoici<emph.end type="bold"/> rassomigliavano le onde del suono alle onde, che si forman nell'acqua intorno a un corpo <lb/>grave, che sopra vi cada 178. </s></p><p type="main">

<s><emph type="bold"/>Strumento micrometrico<emph.end type="bold"/> di Galileo descritto dal Borelli 420. </s></p><p type="main">

<s><emph type="bold"/>Suono<emph.end type="bold"/> si credeva prodotto dalla collisione de'corpi 181, legge della sua intensit&agrave;, come fosse tardi <lb/>conosciuta 183, facilit&agrave; della sua trasmissione 186. </s></p><p type="main">

<s><emph type="bold"/>Tavola<emph.end type="bold"/> delle orbite de'Medicei in semidiametri di Giove 440. </s></p><p type="main">

<s><emph type="bold"/>Teoriche<emph.end type="bold"/> de'Medicei del Borelli, quando stampate 434. </s></p><p type="main">

<s><emph type="bold"/>Termostatiei<emph.end type="bold"/> o pesatori del caldo inventati dal Borelli e dal Viviani 149. </s></p><p type="main">

<s><emph type="bold"/>Terrella<emph.end type="bold"/> elettrica 267. </s></p><p type="main">

<s><emph type="bold"/>Ticone,<emph.end type="bold"/> sue controversie col Rothmann intorno alle astronomiche rifrazioni 87, suoi argomenti con&shy;<lb/>tro la mobilit&agrave; della Terra 338. </s></p><p type="main">

<s><emph type="bold"/>Torricelli Evangelista,<emph.end type="bold"/> suo giudizio intorno all'Aristarco Samio del Robervallio 364. </s></p><p type="main">

<s><emph type="bold"/>Umidit&agrave;<emph.end type="bold"/> nociva alle esperienze elettriche 271. </s></p><p type="main">

<s><emph type="bold"/>Unisono<emph.end type="bold"/> di due corde, una delle quali vibrata e l'altra quieta, come fosse spiegato dal Keplero 200, <lb/>come dal Fracastoro 201, come da Guidubaldo Del Monte 201, come da Galileo 204, come Galileo <lb/>illustri la teoria fracastoriana 205. </s></p><p type="main">

<s><emph type="bold"/>Vapori<emph.end type="bold"/> condensati nell'aria e sulle fredde superficie de'corpi, come spiegati dal Benedetti 170, non <lb/>si sollevano perch&egrave; attratti dal Sole, ma perch&egrave; divenuti pi&ugrave; leggeri 171. </s></p><p type="main">

<s><emph type="bold"/>Venere,<emph.end type="bold"/> rotazione intorno al suo asse 478, difficolt&agrave; di definirne il periodo 479. </s></p><p type="main">

<s><emph type="bold"/>Venti,<emph.end type="bold"/> loro effetti nelle evaporazioni, come spiegati 174, loro origine secondo il Cartesio 306, secondo <lb/>il Redi e il Del Papa 308, secondo il Montanari 209, secondo il Torricelli 310, venti tropicali come <lb/>spiegati da Galileo 312, come gli facesse il Guericke argomento a dimostrare il moto della <lb/>Terra 315, ioro effetti in alterar lo stato del Barometro 328. </s></p><p type="main">

<s><emph type="bold"/>Vento<emph.end type="bold"/> fatto da'corpi velocemente girati attorno, a che lo attribuisca il Galileo 313. </s></p><p type="main">

<s><emph type="bold"/>Vescicole<emph.end type="bold"/> vaporose dell'acqua, come salgano in mezzo all<gap/>aria, secondo il Baliani 300, come secondo <lb/>il Montanari 301, come secondo il Guglielmini 302, come secondo il Del Papa 302, come secondo il <lb/>Volta 303. </s></p><p type="main">

<s><emph type="bold"/>Vespucci Amerigo,<emph.end type="bold"/> suo metodo astronomico per la ricerca delle Longitudini 455, osserva da astro&shy;<lb/>nomo le Stelle 494. </s></p><p type="main">

<s><emph type="bold"/>Vinei (da) Leonardo,<emph.end type="bold"/> come dimostri il calore diffondersi in modo, che l'intensit&agrave; scemi col crescere <lb/>de'quadrati delle distanze 154. </s></p><p type="main">

<s><emph type="bold"/>Vista,<emph.end type="bold"/> fenomeni presentati da lei nel guardare gli oggetti 9. </s></p><p type="main">

<s><emph type="bold"/>Vitellione,<emph.end type="bold"/> pollacco, riprova il principio platonico dell'emissione de'raggi dagli occhi 9, giudizio sopra <lb/>l'Ottica di lui 10, applica alla rifrazione il principio della composizion delle forze 55. </s></p><p type="main">

<s><emph type="bold"/>Viviani Vincenzio,<emph.end type="bold"/> sue speculazioni e sperienze intorno al moto della luce 42 e 44, come gli venisse <lb/>a mano la Diottrica del Cartesio 78, come ne rimanesse ammirato 79, sue esperienze intorno alle <lb/>rifrazioni 80, sue esperienze per provar che un raggio di luce si refrange, passando dall'aria nel <lb/>vuoto 94, suo giudizio intorno alla Relazione dell'Huyghens sull'alone osservato a Parigi 129, <lb/>spiega in un suo Discorso il concetto di Galileo intorno alla natura del calore 143, illustra un <lb/>passo del I Dialogo delle Nuove Scienze, relativo agli effetti del calore 146, pone i principii alla <lb/>Termometria 150, come rispondesse alle varie domande fattegli dal Granduca intorno ai suoni 192, <lb/>sue corrispondenze scientifiche con la R. </s>

<s>Accademia di Londra 241, come giudichi un problema me&shy;<lb/>teorologico, che non sapeva essere stato risoluto da Galileo 314, esamina le condizioni delle va&shy;<lb/>riazioni barometriche, in ordine allo stato del cielo 318, suo argomento a provare il moto della <pb xlink:href="020/01/1124.jpg" pagenum="567"/>Terra, dedotto dal moto de'pendoli 367, se prevenisse l'esperienza del Foucault 368, suoi metodi <lb/>proposti per misurar l'ingrandimento del Canocchiale 435, suo Tavole de'moti di Giove 436. </s></p><p type="main">

<s><emph type="bold"/>Volta Alessandro<emph.end type="bold"/> spiega le attrazioni elettriche, per mezzo de'principii neutoniani 282. </s></p><p type="main">

<s><emph type="bold"/>Vortici kepleriani,<emph.end type="bold"/> repugnanze che si trovano in questa ipotesi 545, vortici eterei, secondo l'Huy&shy;<lb/>ghens 549. </s></p><p type="main">

<s><emph type="bold"/>Vossio Isacco<emph.end type="bold"/> &egrave; il primo a pubblicare lo notizie dell'Ottica manoscritta dello Snellio 66, propone a <lb/>risolvere una difficolt&agrave; contro l'esistenza de'monti della Luna 395, dimostra esser falsa la ra&shy;<lb/>gione data dal Keplero della visibilit&agrave; della Luna ecclissata 410. </s></p><p type="main">

<s><emph type="bold"/>Wright,<emph.end type="bold"/> propone di risolvere il problema delle Longitudini, per mezzo della Bussola 454. </s></p><pb xlink:href="020/01/1125.jpg"/><p type="main">

<s>Finito di stampare in Bologna presso la <lb/>Libreria Editrice Forni nel Marzo 1970 <pb xlink:href="020/01/1126.jpg"/></s></p><pb xlink:href="020/01/1127.jpg"/></chap><chap><p type="main">

<s>350478 Storia Del Metodo Sperimentale Italia </s></p><p type="main">

<s><emph type="center"/>THE SOURCES OF SCIENCE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Editor-in-Chief: Harry Woolf<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Willis K. </s>

<s>Shepard Professor of the History of <lb/>Science, The Johns Hopkins University<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="020/01/1128.jpg"/><p type="main">

<s><emph type="center"/><emph type="bold"/><emph type="italics"/>Storia del Metodo <lb/>Sperimentale in Italia<emph.end type="italics"/><emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>by RAFFAELLO CAVERNI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>in Six Volumes<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Volume III<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>THE SOURCES OF SCIENCE, NO. 134 <lb/>JOHNSON REPRINT CORPORATION<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>NEW YORK LONDON 1972<emph.end type="center"/></s></p><pb xlink:href="020/01/1129.jpg"/><p type="main">

<s><emph type="center"/>Reproduced here is the Florence edition of 1891-1900.<emph.end type="center"/></s></p><figure id="id.020.01.1129.1.jpg" xlink:href="020/01/1129/1.jpg"/><p type="main">

<s><emph type="center"/>Copyright &copy; 1972 by Johnson Reprint Corporation All rights reserved <lb/>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT CORPORATION<emph.end type="center"/></s></p><p type="main">

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<s><emph type="center"/>JOHNSON REPRINT COMPANY LTD.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Shipton Group House, 24/28 Oval Road, London, NW17DD, England<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Printed in Italy<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="020/01/1130.jpg"/><p type="main">

<s><emph type="center"/>DEL METODO SPERIMENTALE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>APPLICATO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>ALLA STORIA NATURALE<emph.end type="center"/><pb xlink:href="020/01/1131.jpg"/></s></p><pb xlink:href="020/01/1132.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO I.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dell'Anatomia nello studio della vita animale<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle Istituzioni anatomiche di Galeno, e delle prime instaurazioni dell'arte, per opera del Beren&shy;<lb/>gario e del Vesalio. </s>

<s>&mdash; II. Dell'Anatomia descrittiva, istituita dal Falloppio e proseguita dal&shy;<lb/>l'Eustachio, dall'Acquapendente e dal Casserio. </s>

<s>&mdash; III. </s>

<s>Delle vivisezioni praticate da Realdo <lb/>Colombo, e come s'incominciasse ad applicare le leggi della Fisica a spiegar le funzioni della <lb/>vita. </s>

<s>&mdash; IV. Dell'Anatomia nella Scuola iatromeccanica. </s>

<s>&mdash; V. </s>

<s>Della Scuola iatromatematica ita&shy;<lb/>liana, e de'limiti naturalmente imposti ai progressi dell'Anatomia. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>La Fisica, della quale narrammo i pi&ugrave; notabili progressi fatti con gli <lb/>argomenti dell'arte sperimentale, si propone per oggetto lo studio della na&shy;<lb/>tura, e il modo dell'operar de'corpi secondo le loro propriet&agrave; generali; co&shy;<lb/>sicch&egrave; indaga le leggi per esempio della luce, del calore, del suono, e attende <lb/>al manifestarsi dei moti nel Magnete, nell'Elettro, e nella materia univer&shy;<lb/>sale, senza nulla curarsi di quel particolar corpo che luce, che riscalda, che <lb/>suona, che ora attrae, ora respinge altri corpi. </s>

<s>Ma pure anche il saper le <lb/>particolari e individue propriet&agrave;, per cui un corpo si distingue e si ricono&shy;<lb/>sce da tutti gli altri, era oggetto di curiosit&agrave; agli uomini, a'quali furono <lb/>ovvie le prime differenze che passano fra gli animali e le piante e i mine&shy;<lb/>rali. </s>

<s>La scienza della Natura perci&ograve; si pu&ograve; dire che avesse di qui i suoi <lb/>principii, e quando le altre parti di lei non avevano ancora nessun cultore, <lb/>si leggevano con ammirazione e con diletto i libri di Aristotile e di Plinio, <lb/>per tacere di tanti altri minori. </s></p><p type="main">

<s>Questa per&ograve; per vero dire non era scienza: posta la volgar distinzione <lb/>fra ci&ograve; che pareva non aver moto, e fra ci&ograve; che mostrava di nutrirsi e di <pb xlink:href="020/01/1133.jpg" pagenum="8"/>vegetar solamente, o di pi&ugrave; muoversi con ispontaneit&agrave; d'atto e sentire, si <lb/>stavano contenti quegli Autori a descrivere le esteriori apparenze e gli usi <lb/>di un minerale, la figura e le nat&igrave;e abitudini di una pianta, gli organi della <lb/>locomozione e dei sensi di un animale, i costumi e la patria. </s>

<s>S'intende da <lb/>ci&ograve; com'avesse, e come ben rispondesse all'intenzione degli scrittori e agli <lb/>stessi fatti il nome dato a coteste naturali descrizioni di <emph type="italics"/>Storia.<emph.end type="italics"/></s></p><p type="main">

<s>Se, come &egrave; rimasto il nome, fosse cos&igrave; rimasto a un tal genere di let&shy;<lb/>teratura quel primo semplice carattere descrittivo, non si vedrebbe perch&egrave; <lb/>dovessero gli studii di lei entrar nella nostra trattazione, ufficio della quale <lb/>&egrave; di non narrar solamente quel che si not&ograve; osservando l'esterior faccia della <lb/>Natura, ma quel che si scopr&igrave; nel suo pi&ugrave; intimo seno, per via di pi&ugrave; stu&shy;<lb/>diose osservazioni e di pi&ugrave; laboriosi cimenti, di cui non conobbero l'arte <lb/>quei Naturalisti antichi. </s></p><p type="main">

<s>Ne sentirono per&ograve; il bisogno, infin da quando si provarono a divisare <lb/>l'ordine, secondo il quale si sarebbero pi&ugrave; convenientemente collocate le <lb/>innumerevoli variet&agrave; componenti ciascuno dei tre grandi Regni: perch&egrave;, do&shy;<lb/>vendo quel collocamento dipendere dalla dignit&agrave; gerarchica, per cos&igrave; dire, <lb/>conveniva conoscer le ragioni del merito onde una specie e un genere aves&shy;<lb/>sero a soprastare ad un altro genere e a un'altra specie, e non era pos&shy;<lb/>sibile far quella giusta ragione senza conoscere, in un animale o in una <lb/>pianta, la prestanza degli organi e delle funzioni. </s></p><p type="main">

<s>Ma gli organi poco o nulla porgono a conoscer di s&egrave;, nelle loro parti <lb/>esterne e superficiali, non escluso lo stesso tatto universalmente diffuso per <lb/>gli involucri del corpo. </s>

<s>La semplice Anatomia descrittiva perci&ograve; si sent&igrave;, per <lb/>mancanza di esperienze e di strumenti, impotente a penetrare addentro nella <lb/>composizione degli organi, a vederne le relazioni co'principii della sensibi&shy;<lb/>lit&agrave; e della vita, e a intendere gli uffici, a cui i membri che stanno intorno <lb/>agli stessi organi furono dalla Natura variamente ordinati. </s>

<s>Di qui s'intende <lb/>come quella, che ha tuttavia serbato il nome di <emph type="italics"/>Storia naturale,<emph.end type="italics"/> entrasse <lb/>nel suo progredire a far parte di questa scienza, che s'aiuta delle esperienze <lb/>e degli strumenti a ci&ograve; necessarii, e che &egrave; il soggetto proprio del nostro <lb/>storico discorso. </s></p><p type="main">

<s>Il processo del qual discorso perci&ograve;, chi volesse intanto saperlo, si ri&shy;<lb/>duce a narrare per sommi capi, prima, come dall'esercizio dell'arte speri&shy;<lb/>mentale fosse condotta la scienza a conoscer l'intima composizione dei corpi <lb/>e le varie funzioni della vita, poi, come fosse quella stessa arte utilmente <lb/>applicata a investigar ci&ograve; che &egrave; proprio di un animale o di un altro, di <lb/>una o altra pianta o minerale che sia, perch&egrave; nell'ordinare i tre Regni <lb/>della Natura ciascuna famiglia, specie, genere o classe abbia il suo colloca&shy;<lb/>mento, non eletto a caso o per le notate differenze di caratteri superficiali, <lb/>ma quale egli vien portato dall'intrinseca variet&agrave; degli organi e delle fun&shy;<lb/>zioni, delle membra compaginate e delle parti. </s></p><p type="main">

<s>In questo filosofico ordinamento, che s'intendeva fare degli esseri innu&shy;<lb/>merevoli di che &egrave; popolata la Terra, primi a considerare occorsero gli ani-<pb xlink:href="020/01/1134.jpg" pagenum="9"/>mali. </s>

<s>E perch&egrave; le variet&agrave; presentate al di fuori era facile intendere che <lb/>dovessero dipendere da pi&ugrave; intime variet&agrave; della loro costituzione, furono i <lb/>primi passi che si fecero dalla scienza, a conseguire il fine desiderato, quelli <lb/>di dinudar l'animale stesso della sua prima veste, sotto la quale apparvero <lb/>i muscoli, sotto i muscoli le ossa, e dentro l'ossa i visceri e gli organi prin&shy;<lb/>cipali dei sensi. </s>

<s>Cos&igrave; ebbe principio quella, a cui fu dato il nome di Ana&shy;<lb/>tomia, la quale fu coltivata con grande ardore e con gran diligenza infino <lb/>dagli antichi tempi della civilt&agrave; greca, non semplicemente per promovere lo <lb/>studio della Storia naturale, ma per il desideratissimo intento di riconoscere <lb/>l'occulta origine de'morbi, e d'apprestarvi i pi&ugrave; efficaci rimedii. </s></p><p type="main">

<s>Ippocrate, per la gran distanza da cui si guarda, e per esserci perve&shy;<lb/>nute le sue dottrine in gran parte negli insegnamenti tradizionali, s'&egrave; trasfor&shy;<lb/>mato quasi in simbolo a rappresentar l'arte medica, e i nomi di Erofilo, di <lb/>Polibo, di Erasistrato ci vengono riflessi alle orecchie da'libri di coloro, che <lb/>ne raccolsero i placiti, e principalmente da quelli di Galeno, che riconosce <lb/>e venera cotesti antichi per suoi primi autori e maestri. </s>

<s>Maestro per&ograve; alla <lb/>nuova civilt&agrave; rimase co'suoi libri lo stesso Galeno, il quale si acquist&ograve; nelle <lb/>descrizioni anatomiche, e ne'precetti dell'arte medica, tanta autorit&agrave; e tanta <lb/>fama, che fu tenuto come un oracolo, il contradire al quale reputavasi te&shy;<lb/>merit&agrave; e quasi una ribellione contro la verit&agrave; stessa. </s></p><p type="main">

<s>Per formarsi un'idea di ci&ograve;, che il greco Maestro descrisse concernente <lb/>l'anatomica costituzione del corpo umano, converrebbe svolgere i suoi vo&shy;<lb/>lumi e i commenti che ne fecero gli studiosi, i quali forse non ritrarreb&shy;<lb/>bero nella loro profusione cos&igrave; viva l'immagine dello scrittore, come ce la <lb/>rappresenta il seguente passo estratto dal Cap. </s>

<s>XVI del I Libro <emph type="italics"/>De usu par&shy;<lb/>tium,<emph.end type="italics"/> dove, professando l'Autore di trattar dell'utilit&agrave;, a cui servono le varie <lb/>membra animali, accenna ai discorsi fatti altrove intorno alle loro funzioni: <lb/>&ldquo; De actionibus vero venarum et arteriarum et nervorum et musculorum <lb/>et tendonum neque consentitur, neque apparet quidquam, ac propterea ser&shy;<lb/>mone indiget longiori. </s>

<s>Sed non est nunc tempus de actionibus disquirendi. </s>

<s><lb/>Non enim de ipsis, sed de utilitatibus propositum est nobis dicere. </s>

<s>Neces&shy;<lb/>sarium igitur est, ex iis quae alicubi demonstrata sunt, et nunc et per <lb/>omnem futurum nobis sermonem, conclusiones demonstrationum, tamquam <lb/>aliquas suppositiones accipiendo, ita hunc perficere sermonem. </s>

<s>Quod igitur <lb/>principium nervorum omnium cerebrum est et spinalis medulla, et quod <lb/>ipsius rursus spinalis medullae cerebrum: arteriarum vero omnium cor, ve&shy;<lb/>narum autem hepar: et quod nervi quidem a cerebro animalem virtutem, <lb/>arteriae vero a cordis pulsatione: venae autem ab hepate naturalem acci&shy;<lb/>piunt, in libris de Hippocratis et Platonis dogmatibus demonstratum est. </s>

<s><lb/>Erit itaque nervorum utilitas facultatem sensus et motus a principio in par&shy;<lb/>tes deducere. </s>

<s>Arteriarum autem custodire eam natura est caliditatem et nu&shy;<lb/>trire spiritum animalem. </s>

<s>Sanguinis autem generandi simul et in omnes fe&shy;<lb/>rendi gratia venae factae sunt. </s>

<s>At vero et de tendonibus et nervis et liga&shy;<lb/>mentis quomodo differant in libris de musculorum motu dictum est. </s>

<s>Palam <pb xlink:href="020/01/1135.jpg" pagenum="10"/>autem quod et de natura musculorum in illis dictum est, et quod sunt or&shy;<lb/>gana motus voluntarii, et quod eorum aponevrosis, hoc est derivatio, nomi&shy;<lb/>natur &rdquo; (Lugduni Batav. </s>

<s>1550, pag. </s>

<s>36, 37). </s></p><p type="main">

<s>L'anatomia e la fisiologia galenica, condensate e specchiate in queste <lb/>brevi parole, erano universalmente seguite senza nulla aggiungervi e nulla <lb/>levare, come quelle che erano stimate rappresentar vivo e vero il sapientis&shy;<lb/>simo magistero della natura nella mirabile fabbrica del corpo animale. </s>

<s>In <lb/>tanto ferma e indubitata fede non osavasi di far pure a Galeno una domanda <lb/>ingenua, ed era se l'anatomia degli animali, che s'intraprese a principio <lb/>per promovere lo studio della Storia naturale, si poteva cos&igrave; in tutto appro&shy;<lb/>priare all'uomo, da servire a investigar l'occulta origine de'suoi morbi e a <lb/>curarli, come insegnavano a fare quegli antichi Maestri. </s>

<s>Non facevasi la do&shy;<lb/>manda, perch&egrave; si teneva certa la risposta, che cio&egrave; le fonti della vita nel&shy;<lb/>l'uomo fossero con perfettissima somiglianza rappresentate da quelle del cane <lb/>e della scimmia. </s>

<s>Una tal risposta dall'altra parte sodisfaceva, perch&egrave; sem&shy;<lb/>brava dispensare dall'insozzarsi della sanie de'cadaveri umani, e dal provar <lb/>quel ribrezzo, che mette addosso a ciascuno il violar con mano crudelmente <lb/>sacrilega la pace del sepolcro. </s></p><p type="main">

<s>Quando nel secolo XVI, specialmente nella nostra Italia, l'ardente de&shy;<lb/>siderio di sapere vinse quel ribrezzo, e sanamente si ragion&ograve; che un atto <lb/>intrapreso per amor della scienza, e che non offendeva se non ci&ograve; che era <lb/>stato gi&agrave; offeso dalla morte, non poteva imputarsi a sacrilegio; s'intese al&shy;<lb/>lora, sezionando cadaveri umani, come notabilmente e per moltissime parti <lb/>differissero le membra degli uomini da quelle de'bruti, e come non fosse <lb/>stata da'Medici la vera arte anatomica ancora ben conosciuta. </s></p><p type="main">

<s>Primo a fare il gran passo, tentato gi&agrave; dal Mondino, per uscir fuori <lb/>degli alloggiamenti galenici, dove s'eran da secoli ricoverati con sicurt&agrave; tutti <lb/>i Filosofi e i Medici, fu Iacopo Berengario da Carpi, il quale pubblic&ograve; per <lb/>la prima volta in Bologna, nel 1521, le sue nuove descrizioni anatomiche, in <lb/>un libro intitolato <emph type="italics"/>Commentaria cum amplissimis additionibus super Ana&shy;<lb/>tomia Mundini, una cum textu eiusdem in pristinum et verum nitorem <lb/>redacto.<emph.end type="italics"/> &Egrave; dedicato il libro al cardinale di S. </s>

<s>Lorenzo in Damaso, Giulio <lb/>de'Medici, con lettera che comprende le carte II, III, seguenti alla prima <lb/>del frontespizio disegnato in un elegantissimo antiporto, con lo stemma me&shy;<lb/>diceo sull'architrave, e impressovi il nome di Leon X. </s></p><p type="main">

<s>A pag. </s>

<s>IV incomincia l'<emph type="italics"/>Expositio Anatomiae Mundini cum additioni&shy;<lb/>bus Carpi,<emph.end type="italics"/> e l'intenzione, ch'ebbe nello scriverla l'Autore, viene espressa <lb/>nella seguente forma ai lettori: &ldquo; Visis tot et tantis altercationibus inter <lb/>scribentes de Anatomia, placuit mihi, qui longa experientia vidi secando et <lb/>vivorum et mortuorum corpora et qui longa lectione quaesivi, per viam Com&shy;<lb/>menti in unum breviori quodam summario perstringere. </s>

<s>Et dux meus erit <lb/>optimus Mundinus bononiensis, qui inter omnes sapientes Medicinae in bre&shy;<lb/>viori quodam catalogo omnia de cognitione organicorum membrorum perstrin&shy;<lb/>git, cuius merito primus Anatomes habetur. </s>

<s>Cuius librum exponere intendo, <pb xlink:href="020/01/1136.jpg" pagenum="11"/>quamvis etiam ipsius litera quasi clara sit. </s>

<s>In qua expositione aliqua notatu <lb/>digna, iunioribus non inutilia, addam, duce semper sensu et divini Galeni <lb/>auctoritatibus et rationibus quibusdam, et libri titulus erit <emph type="italics"/>Expositio ana&shy;<lb/>lomica Mundini cum additionibus Carpi. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Tanta fu l'accoglienza fatta a quest'Opera dagli studiosi, i quali ascol&shy;<lb/>tavano dopo tanti secoli discorrer d'Anatomia a un uomo vivo, che l'Autore <lb/>pens&ograve; di farne un Isagoge o un compendio, impresso in Venezia nel 1535, <lb/>e dedicato al suo signor naturale Alberto Pio. </s>

<s>A lui rivolgendosi il Beren&shy;<lb/>gario, dop'aver detto come gli fosse felicemente riuscita la sezione di un ani&shy;<lb/>male vivo, soggiunge le seguenti parole: </s></p><p type="main">

<s>&ldquo; Tanta, testor Deos immortales, ex illo tempore Anatomiae dulcedo <lb/>mentem animumque meum tenuit, ut omnem aetatem iis Medicinae elemen&shy;<lb/>tis non minori bonorum professorum utilitatem, quam privata voluptate con&shy;<lb/>tribuerim: libros huiusce disciplinae quam plurimos sed indigestos lectitan&shy;<lb/>dos, quos eorum authores, ad alia transferentes volumina, fabulas potius <lb/>quam Anatomiam tribuere videbantur, quo factum est ut pauci vel nulli <lb/>hac nostra tempestate tam necessariae ac preciosissimae artis finem nove&shy;<lb/>rint. </s>

<s>Accedebat insuper ad eius ignorationem, sic mea fert opinio, foeda ac <lb/>multis stomacosa membrorum sectio creberrimaque illorum attrectatio. </s>

<s>Et <lb/>quum ego quamplurima centena cadaverum secuerim, quam pauci aetatis <lb/>nostrae Medici hanc artem noverint intellexi. </s>

<s>Quare, praesenti ac futuro sae&shy;<lb/>culo prodesse cupiens, non minus pium quam saluberrimum fore putavi <lb/>Commentarii quaedam et digressiones super anatomia Mundini componere, <lb/>quae antiquorum Philosophorum pariter et Medicorum sapienter scripta de <lb/>humani corporis admirabili mole demonstrant, illaque copiose tradita, a quam&shy;<lb/>plurimis Medicinae studiosissimis viris rogatus, in lucem dedi &rdquo; (Isagoge bre&shy;<lb/>ves, Venetiis 1535, ad Albertum Pium). </s></p><p type="main">

<s>In queste parole del Berengario, chi bene addentro penetra al loro senso, <lb/>si scopre un segreto artificio di conciliare il passato col presente, accennando <lb/>da una parte alle cose scritte sapientemente da'Filosofi e da'Medici prede&shy;<lb/>cessori, ch'egli accoglie nel suo libro e commenta, e santenziando dall'altra <lb/>che, dal sezionar cadaveri umani, s'era accorto <emph type="italics"/>quam pauci aetatis nostrae <lb/>Medici hanc artem noverint.<emph.end type="italics"/> Si proponeva cos&igrave; dunque dall'Autore un'arte <lb/>nuova, e tacitamente insinuavasi, colla proposta, che la insegnata da Galeno <lb/>non era l'arte anatomica vera, e fra'medici che s'accusavano d'avere <lb/>ignorato una tal arte era necessariamente incluso anco il Maestro. </s>

<s>Procede <lb/>per&ograve; il Berengario, nel proporre le sue novit&agrave;, con tal riserbo, che nes&shy;<lb/>suno si sente offeso di quella accusa. </s>

<s>Da un altro canto, non consistendo <lb/>quelle novit&agrave; che in descrivere alcune parti, le quali non si leggevano nel <lb/>testo galenico, era pronto il rifugio da salvar la dignit&agrave; del Maestro, con <lb/>dire ch'egli trascur&ograve; quelle cose, perch&egrave; non le credeva importanti, o forse <lb/>egli non le trascur&ograve; veramente, ma le descrisse in altri libri che ora sono <lb/>smarriti. </s></p><p type="main">

<s>L'anatomico di Carpi sar&agrave; stato di parere diverso da questo degli ido-<pb xlink:href="020/01/1137.jpg" pagenum="12"/>latri di Galeno, ma in ogni modo egli che non erasi trattenuto, con tutta <lb/>quella diligenza che bisognava, a comparar, per rilevarne le differenze, l'ana&shy;<lb/>tomia de'bruti con quella dell'uomo; non si sentiva tanto autorevole da sen&shy;<lb/>tenziar che i difetti notati, e gli errori dell'anatomia galenica derivassero <lb/>dall'aver sezionati cadaveri, e dall'aver perci&ograve; descritte per umane le mem&shy;<lb/>bra dei bruti. </s>

<s>Ma iniziati intanto cos&igrave; felicemente i progressi dell'Anatomia, <lb/>l'opera del nostro Carpense fu animosamente proseguita da Andrea Vesalio, <lb/>da cui comincia l'Anatomia comparata. </s></p><p type="main">

<s>Risult&ograve; veramente da quelle comparazioni intraprese con una fiera gio&shy;<lb/>vanile baldanza, che Galeno aveva attribuite all'uomo le membra, come sono <lb/>configurate ne'cani e nelle scimmie. </s>

<s>E giacch&egrave; si trattava di fatti, ch'egli <lb/>sottoponeva, nell'anfiteatro della Scuola padovana, alla testimonianza degli <lb/>occhi della numerosissima scolaresca, e di chiunque altro se ne fosse voluto <lb/>assicurare; l'accusa contro Galeno non aveva oramai pi&ugrave; difesa: il tempio <lb/>era profanato, e si volevano i sacerdoti dispersi. </s></p><p type="main">

<s>Dalla ristretta cerchia dell'insegnamento orale si diffuse nel pubblico <lb/>lo spirito della rivolta, per mezzo della pubblicazione di un libro, che s'in&shy;<lb/>titolava: <emph type="italics"/>Andreae Vesalii bruxellensis Scholae medicorum Patavinae pro&shy;<lb/>fessoris, de humani corporis fabrica, Basileae M.D.XLIII.<emph.end type="italics"/> Incomincia <lb/>nella prefazione dal rimproverare i Medici, per aver sempre tenuto con tanta <lb/>fedelt&agrave; dietro a Galeno, da non dilungarsene <emph type="italics"/>ne latum quidem unguem,<emph.end type="italics"/><lb/>stimando che nulla sia ne'libri di lui da riprendere. </s>

<s>Eppure &egrave; un fatto, sog&shy;<lb/>giunge il Vesalio, che Galeno stesso &ldquo; se frequenter corrigit, suamque ne&shy;<lb/>gligentiam quibusdam libris commissam in aliis postea, exercitatior redditus, <lb/>non semel indicat contrariamque frequenter docet. </s>

<s>&rdquo; Comunque sia, lasciando <lb/>le parole e venendo ai fatti &ldquo; nobis modo, ex renata dissectionis arte dili&shy;<lb/>gentique Galeni librorum praelectione et in plerisque locis eorumdem non <lb/>poenitenda restitutione, constat nunquam ipsum nuper mortuum corpus hu&shy;<lb/>manum resecuisse. </s>

<s>&rdquo; Si lasci&ograve; sedurre, prosegue a dir l'ardente Brussel&shy;<lb/>lese, dalle sue scimmie, n&egrave; si sa perch&egrave;. </s>

<s>Se non sempre pronti a sezionare <lb/>aveva cadaveri freschi, da studiarvi le viscere e le altre parti molli, vi erano <lb/>le aride ossa, le quali poteva Galeno sempre a suo agio esaminare, e avve&shy;<lb/>dersi delle notabilissime differenze che passano fra le stesse ossa umane e <lb/>quelle delle scimmie. </s></p><p type="main">

<s>Svolgendo i sette libri, in che tutta l'Opera &egrave; divisa, si pu&ograve; dir che il <lb/>Vesalio non passa descrizione di membra umane, che non si trattenga a no&shy;<lb/>tar baldanzosamente gli errori, e le impropriet&agrave; della storia di Galeno. </s>

<s>E fu <lb/>giusto questa baldanza che nocque all'Autore, e nocque ai progressi, ai qual i <lb/>il Berengario aveva tranquillamente avviata la scienza. </s>

<s>Nocque all'Autore, <lb/>per le fiere persecuzioni che gli si suscitarono incontro da tutti coloro, che <lb/>tenevano esser ne'libri galenici i precetti dell'arte medica divinamente ri&shy;<lb/>velati: nocque ai progressi della scienza, perch&egrave;, mentre pareva che si vo&shy;<lb/>lessero liberar gl'ingegni dalla servit&ugrave; antica, si tentava destramente di sog&shy;<lb/>giogarli a una servit&ugrave; nuova. </s></p><pb xlink:href="020/01/1138.jpg" pagenum="13"/><p type="main">

<s>Qual decisa intenzione e qual consapevolezza fosse in questi tentativi <lb/>non si potrebbe affermare, ma che si studiasse il Vesalio di ridurre a s&egrave; <lb/>tutto il merito dell'Anatomia nuova, e tutta l'autorit&agrave; di nuovo maestro, <lb/>apparisce chiaro dalla citata prefazione, nella quale egli si vanta che l'arte <lb/>del dissettare sia per la sola opera sua, a'suoi tempi, rinata. </s>

<s>F&agrave; cechi ado&shy;<lb/>ratori e seguaci di Galeno non solamente Oribasio, Teofilo e gli Arabi, ma <lb/>tutti quanti i moderni, i quali trattando di cose anatomiche &ldquo; nihil umquam <lb/>minus aggressi videntur quam humani corporis sectionem. </s>

<s>&rdquo; Il Mondino, e <lb/>il Berengario, che aveva da s&egrave; solo dissecato centinaia di cadaveri umani, <lb/>non erano certamente del numero di coloro, che cos&igrave; venivano accusati, e il <lb/>Vesalio, tacendo de'due instauratori dell'arte anatomica italiana, n&egrave; potendo <lb/>allegare ignoranza, d&agrave; giusto motivo di sospettare che ci&ograve; facesse, per attri&shy;<lb/>buire a s&egrave; tutto il merito di quella restaurazione. </s>

<s>Aristotile prima, e poi <lb/>Galileo e il Cartesio, che vollero apparire al mondo di naturale Filosofia primi <lb/>e soli maestri, danno anch'essi l'esempio di aver rinnegate le tradizioni dei <lb/>loro maggiori, e parve succeder felicemente l'intenzione al Vesalio, com'era <lb/>felicemente riuscita all'antico Maestro e duce di coloro che sanno. </s></p><p type="main">

<s>Ma fra que'giovani studenti, i quali ascoltavano le fervorose declamazioni <lb/>fatte contro Galeno dal Brussellese venuto a insegnare a Padova, n'erano <lb/>due nati sotto il cielo d'Italia, e non molto di lungi dalla patria di Iacopo <lb/>Berengario, i quali sarebbero divenuti in anatomia celeberrimi maestri, e pro&shy;<lb/>fessandosi amici di Galeno e del Vesalio, ma fermi sopra ogni cosa di voler <lb/>essere amici del vero, liberata la scienza dal giogo antico e dal nuovo, avreb&shy;<lb/>bero dimostrato col loro esempio che argomento unico all'Anatomia per pro&shy;<lb/>gredire erano le osservazioni e l'esperienze. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Que'due giovani, che stavano tranquillamente ad ascoltare, mentre l'altra <lb/>scolaresca applaudiva scompostamente al Maestro, erano Gabbriello Falloppio <lb/>e Realdo Colombo. </s>

<s>Se non fosse rimasto altro che quella turba fremente e <lb/>plaudente, l'Anatomia arrestava senza dubbio nel Vesalio i progressi, i quali <lb/>si componevano di tre passi: del primo, che si arrest&ograve; in Galeno, e in cui si <lb/>descrisse l'anatomia de'bruti; del secondo fatto dal Berengario e da cui inco&shy;<lb/>minci&ograve; l'anatomia del corpo umano, e del terzo ultimamente promosso dallo <lb/>stesso Vesalio, che dal felice connubio delle due precedenti anatomie raccolse <lb/>il frutto ubertoso. </s>

<s>Che fosse tutto intero quel frutto, possibile a raccogliersi <lb/>da'nuovi studii, veramente raccolto dal divino Brussellese, lo andavano ripe&shy;<lb/>tendo i suoi adoratori, mentre volevano dall'altra parte i fierissimi nemici <lb/>di lui persuadere ognuno che quella nuovamente aperta era una scuola di <lb/>errori e di bestemmie. </s></p><p type="main">

<s>Tali due impedimenti opposti ai progressi dell'Anatomia furono vinti <pb xlink:href="020/01/1139.jpg" pagenum="14"/>animosamente dal Falloppio, il quale narra nelle sue Osservazioni anatomi&shy;<lb/>che le battaglie ch'ebbe a combattere nella mente, per conseguire la diffi&shy;<lb/>cile vittoria, e come a scoprir cose nuove, rimaste occulte a Galeno stesso <lb/>e al Vesalio, aprisse a s&egrave; e a'suoi seguaci largamente la via. </s></p><p type="main">

<s>&ldquo; Avevo fatto proposito, cos&igrave; scrive rivolgendo il discorso al suo ami&shy;<lb/>cissimo Pietro Manna, di non mai esercitare la penna intorno a cose spet&shy;<lb/>tanti all'Anatomia, e ci&ograve; perch&egrave; parevami che il Vesalio avesse resa l'opera <lb/>quasi compiuta, non vedendosi quel che aggiungere o quel che si potesse <lb/>desiderare di pi&ugrave; delle ammirabili descrizioni ch'egli fa delle parti del corpo <lb/>umano. </s>

<s>Di qui &egrave; ch'io mi dava a credere perpetuo dover durare quel mo&shy;<lb/>numento del divino ingegno, e tali esser le cose dette, da non poterle dire <lb/>di meglio, n&egrave; in altro modo diverso da lui porgerle, senza venir meritamente <lb/>deriso. </s>

<s>Stetti in questa persuasione pi&ugrave; anni, infin tanto che divenuto pi&ugrave; <lb/>esperto negli esercizii dell'arte, e reso dall'esempio stesso del Vesalio pi&ugrave; <lb/>audace, incominciai a pensare e a voler decidere fra me chi de'due o Ga&shy;<lb/>leno o il Vesalio si fosse pi&ugrave; d'appresso avvicinato a conoscere il vero. </s>

<s>In <lb/>hoc itaque studio quamvis non negarim me illud unum observasse, nempe <lb/>quod optimus anatomicus Andreas Vesalius, veluti exercitus victoriae ardore <lb/>ac impetu actus, saepe aliquid tentat quod minus aut ad gloriam propriam <lb/>conducit aut optimis ducibus ac imperatoribus satisfacit, Galenum aliquando <lb/>in verbis, potius quam in sententiis capit, aliquando mutilum quod facere <lb/>debuerat minime excusat, ac saepe indignius, quam anatomicum philoso&shy;<lb/>phum ac medicum tam insignem deceret, carpit et accusat &rdquo; (Observationes <lb/>anat. </s>

<s>in Op. </s>

<s>omn., Francofurti 1584, pag. </s>

<s>398). </s></p><p type="main">

<s>Nonostante, prosegue a dire il Falloppio, tenni pi&ugrave; dalla parte del Ve&shy;<lb/>salio, che non da quella di Galeno, come possono farne testimonianza tutti <lb/>coloro, che m'intesero descriver le parti del corpo umano dalle pubbliche <lb/>cattedre di Pisa e di Padova. </s>

<s>&ldquo; Post autem hoc iudicium, confirmatis adhuc <lb/>magis animi viribus, quaerere coepi an in hac arte in qua Hippocrates pri&shy;<lb/>mum, deinde Aristotiles, praeterea Erasistratus, Marinus ac Hierophilus, et <lb/>tandem Galenus erravit, solus Vesalius reperiatur, qui nihil unquam dormi&shy;<lb/>tando, non solum hos diversos scriptores, sed etiam Homerum ipsum ali&shy;<lb/>quando, ut fertur in adagio, dormitantem superavit, seu potius aliquid sit <lb/>ab ipso praetermissum, vel non satis integre enarratum, seu aliquid distor&shy;<lb/>tum, vel ab historia partium corporis humani discrepans in illius volumine <lb/>anatomico reperiatur. </s>

<s>In hoc multum revera varias ob causas sudavi, pri&shy;<lb/>mum quia tentavi rem per se difficillimam, secundum, quia in verbis ma&shy;<lb/>gistri iuratus, atque illius auctoritati plurimum tribuens, non audebam ex <lb/>iis carceribus quos ipse arti imposuit egredi, tertium, quod et gravissimum <lb/>est, quod publicam notam pertimescebam, momosque etiam ipsos auribus <lb/>meis oggannientes iam tum audire videbar. </s>

<s>Haec tamen omnia satis strenue <lb/>superavi. </s>

<s>Nam rei difficultatem summo studio, labore et vigiliis plurimis vici. </s>

<s><lb/>Magistri reverentiam et timorem ipsius exemplo lenivi. </s>

<s>Quoniam uti Vesa&shy;<lb/>lius, non in scholis quidem vivae vocis auditor, sed in Musaeo factus, non <pb xlink:href="020/01/1140.jpg" pagenum="15"/>ipsius auctoritate deterritus est quin plurima arti adderet, quae a praeceptore <lb/>eius praetermissa erant; ita et ego in illius schola, quia eius scripta dili&shy;<lb/>genter legerim versatus, alacrius in hoc pariter artem curare tentavi &rdquo; (ibi, <lb/>pag. </s>

<s>398, 99). </s></p><p type="main">

<s>I frutti di questi tentativi, cos&igrave; felicemente riusciti, furono dal Fallop&shy;<lb/>pio raccolti nelle sue <emph type="italics"/>Osservazioni,<emph.end type="italics"/> nelle quali, occorrendogli per prima cosa <lb/>a descrivere le mascelle, tocca della controversia insorta fra Galeno, che de&shy;<lb/>scrisse esse mascelle come composte di due pezzi, e il Vesalio, che asseriva <lb/>invece esser salde e composte di un osso solo. </s>

<s>Il Falloppio osserva che, ri&shy;<lb/>dotte in due pezzi attaccati insieme, si trovano veramente le mascelle negli <lb/>infanti e ne'piccoli nati delle scimmie, per cui concludeva, a difesa di Ga&shy;<lb/>leno e a temperar le fiere accuse avventategli dal Vesalio, che l'antico padre <lb/>e Maestro dell'Anatomia avea descritte le mascelle quali si ritrovano ne'te&shy;<lb/>neri fanciulli e n&ograve; negli adulti. </s>

<s>&ldquo; Quamobrem pro Galeno dici posset ipsum <lb/>de tenerrima maxilla locutum fuisse. </s>

<s>Quod si adversarius respondeat non de&shy;<lb/>cere dogmata de imperfectis partibus assumere, sed de perfectis esse tractan&shy;<lb/>dum, addas hac quoque causa errasse omnes anatomicos, qui de appendici&shy;<lb/>bus ita diffuse loquti sunt, cum illae in imperfectis tantum ossibus non <lb/>autem in adultis reperiantur &rdquo; (ibi, pag. </s>

<s>413). </s></p><p type="main">

<s>Pi&ugrave; avanti, descrivendo il Falloppio i vasi arteriosi che ricorrono sulla <lb/>superficie del cervello, e s'insinuano alquanto al di sotto della sostanza cor&shy;<lb/>ticale, facendone vibrar la membrana al ritmo della loro pulsazione &ldquo; doleo, <lb/>egli dice, et mirum in modum doleo quod divinus Vesalius, quem amo atque <lb/>uti praeceptorem colo venerorque, aliquando, dum acrius accusat Galenum <lb/>ac alios anatomicos, ipse erret, quod ipsi accidit in vasis describendis, quae <lb/>ad sinus ipsius membranae durioris cerebri pertingunt. </s>

<s>Nam accusat Gale&shy;<lb/>num ac reliquos anatomicos, qui non viderint sinus dictos pulsantes cum <lb/>illud manifestissime faciant. </s>

<s>Deinde non invenerint arterias una cum venis <lb/>ad eiusdem sinus pertingentes. </s>

<s>Quorum utrumque mihi videtur aliquantisper <lb/>ab historiae veritate recedere &rdquo; (ibi, pag. </s>

<s>449). </s></p><p type="main">

<s>Proseguendo colla solita libert&agrave;, dimostra il Falloppio, nelle sue <emph type="italics"/>Istitu&shy;<lb/>zioni anatomiche,<emph.end type="italics"/> essersi ingannato il Vesalio, attribuendo all'uomo le pro&shy;<lb/>priet&agrave; del muscolo cremastere de'cani (ivi, pag. </s>

<s>490), come pure dimostra <lb/>avere il Vesalio stesso errato nel descriver come convenienti all'uomo i ca&shy;<lb/>nini muscoli intercostali (pag. </s>

<s>495). Perci&ograve; il Falloppio, a proposito de'mu&shy;<lb/>scoli locomotori dell'occhio, per la descrizione de'quali il Vesalio sezion&ograve; la <lb/>scimmia, rimprovera a lui il difetto stesso e gli ritorce incontro lo strale <lb/>acutissimo e avvelenato, ch'egli avvent&ograve; contro Galeno. </s>

<s>&ldquo; Circa hos muscu&shy;<lb/>los quid dixerit Vesalius iudicent studiosi, cum ipsos in diversis partibus <lb/>artos in diversas partes insertos ita collocet, ut cuivis ipsius positionem consi&shy;<lb/>deranti appareat musculos hos, nisi ita se haberent atque ipse ait, profecto <lb/>in eamdem partem ambo oculum traherent nullo interim oculum ad mediam <lb/>regionem retrahente. </s>

<s>Superaddit his omnibus septimum alium musculum <lb/>Vesalius una cum Galeno, <gap/> quem ipse eamdem notam patietur, quam <pb xlink:href="020/01/1141.jpg" pagenum="16"/>saepissime imputat Galeno, dum ipsum suis delusum simiis multa afferre et <lb/>comminisci ait quae, si humana cadavera secuisset, aliter protulisset &rdquo; (ibi, <lb/>pag. </s>

<s>510). </s></p><p type="main">

<s>Cos&igrave; veniva chiaramente dimostrato dai fatti che tanto Galeno quanto <lb/>il Vesalio erano due uomini, come tutti gli altri, soggetti ad errori; onde <lb/>avendosi per cosa certa essere stata l'Anatomia fino a quel tempo coltivata <lb/>da uomini e non da Dei, nell'imperfezione umana, in ch'era rimasta, dava <lb/>certissima speranza a tutti e prometteva il merito debito a chiunque ne fa&shy;<lb/>vorisse i progressi, per cui il Falloppio stesso, ad avvivar la speranza di con&shy;<lb/>seguir pi&ugrave; facilmente un tal merito, dettava a chi si volesse dare agli eser&shy;<lb/>cizii dell'arte i precetti seguenti: </s></p><p type="main">

<s>&ldquo; I. </s>

<s>Quae non connata sunt facile ac leviter dividi. </s>

<s>II. </s>

<s>Quae connata <lb/>sunt difficillime, nisi maxima adhibita diligentia, dividenda esse. </s>

<s>III. </s>

<s>Nihil <lb/>lacerandum. </s>

<s>IV. </s>

<s>Quod summe est necessarium et difficile ut sciamus quae <lb/>sit una pars, quae vero plures: ne plures partes simul iunctas constituamus <lb/>unam esse, nec ex una plures faciamus. </s>

<s>V. </s>

<s>Quis sit ordo in dissectione obser&shy;<lb/>vandus: possumus enim vario modo incipere et mutare ordinem. </s>

<s>Aut enim <lb/>habemus rationem dignitatis, et tunc incipimus a dignioribus ut a corde, a <lb/>cerebro; aut dirigimus ordinem ad duiturnitatem materiae, et incipimus ab <lb/>iis partibus quae citius pereunt et putrescunt, aut respicimus collocationem <lb/>et situm partium, ut quando extimas prius secamus servato ordine usque <lb/>ad intimas, aut spectamus usum toti corpori exhibitum, et tunc a duriori&shy;<lb/>bus incipit ars, utpote ac quae totum corpus fulciunt. </s>

<s>VI. </s>

<s>Ut cognoscamus <lb/>quibus instrumentis nunc haec particula nunc illa sit dividenda, cui adhi&shy;<lb/>bendi opera ministri, cui minime. </s>

<s>VII. </s>

<s>Ut cognoscamus quae particulae sint <lb/>dividendae et inspiciendae in vivis animalibus, quae vero in mortuis et qua <lb/>ratione; quaedam enim partes etiam mortuae omnia integra reservant, quae&shy;<lb/>dam vero vel nihil vel parum admodum retinent illius quod sensu est per&shy;<lb/>cipiendum &ldquo; (Institutiones anatom. </s>

<s>inter Op. </s>

<s>omnia cit., pag. </s>

<s>521). </s></p><p type="main">

<s>Nella duplice opera delle <emph type="italics"/>Osservazioni<emph.end type="italics"/> anatomiche e delle <emph type="italics"/>Istituzioni,<emph.end type="italics"/><lb/>si rendeva dunque per due conti il Falloppio benemerito de'progressi del&shy;<lb/>l'Anatomia: prima, per aver salvato dagli attentati del Vesalio, che voleva <lb/>reciderle, le pi&ugrave; antiche tradizioni galeniche della scienza; poi, per aver mo&shy;<lb/>strato che alla via gloriosamente corsa dallo stesso Vesalio non era posto il <lb/>termine nelle scoperte di lui, ma che restava molto ancora a scoprire a chi <lb/>vi si fosse rivolto con studio amoroso, com'egli ne'suoi due libri anatomici <lb/>insegnava coi fatti e coi precetti. </s></p><p type="main">

<s>Ma i precetti a dir vero accennano all'arte gi&agrave; progredita, la quale si <lb/>studia di giungere alla sua perfezione per quella via gi&agrave; segnata dai primi <lb/>maestri, senza cercare o saper trovar modo da renderla pi&ugrave; diritta e pi&ugrave; <lb/>aperta. </s>

<s>Vedremo di ci&ograve; l'esempio ne'principali Anatomisti, che successero <lb/>al Falloppio, mettendo in pratica i precetti di lui, mentre che Realdo Co&shy;<lb/>lombo, il quale porgeva nuovi argomenti all'Anatomia per progredire, ri&shy;<lb/>maneva incompreso e per lungo tempo dimenticato. </s></p><pb xlink:href="020/01/1142.jpg" pagenum="17"/><p type="main">

<s>Que'nuovi argomenti consistevano nelle esperienze, che aggiungevansi <lb/>alle osservazioni semplici del Vesalio, e delle quali insegnava unicamente a <lb/>far uso il Falloppio. </s>

<s>In quelle brevi parole di avvertimento al lettore, che <lb/>preparava Realdo per premetterle ai suoi XV libri <emph type="italics"/>De re anatomica,<emph.end type="italics"/> inco&shy;<lb/>mincia a dire che il fine, per cui prese a scrivere, fu quello di riferire <emph type="italics"/>quae <lb/>observavi<emph.end type="italics"/> non solo, ma <emph type="italics"/>et cum rei natura consentire experimento didici.<emph.end type="italics"/></s></p><p type="main">

<s>Ecco proposta una nuova autorit&agrave; superiore a quella di Galeno e del <lb/>Vesalio, l'autorit&agrave; dell'esperienza, e le fiere contese fra due uomini, che si <lb/>reputavano ugualmente divini, si portavano a decidere dalla natura, vera&shy;<lb/>mente divina, dei fatti. </s>

<s>&Egrave; perci&ograve; che Realdo non ha paura di offendere n&egrave; <lb/>d'incontrar le inimicizie di nessuno, anteponendo la verit&agrave; alle sentenze <lb/>scritte ne'libri del Vesalio, e bench&egrave; protesti di venerar Galeno <emph type="italics"/>tamquam <lb/>numen,<emph.end type="italics"/> promette nostante a'suoi buoni lettori che dalle esperienze fatte <lb/>sul cuore palpitante di un cane apprenderanno pi&ugrave; in un'ora, e con pi&ugrave; <lb/>gran diletto, che rileggendo per tre mesi interi il trattato <emph type="italics"/>De pulsibus<emph.end type="italics"/> dello <lb/>stesso Galeno. </s></p><p type="main">

<s>E che cosa potevano rispondere a queste parole i Galenisti, i quali si <lb/>erano cos&igrave; furiosamente levati contro le critiche del Vesalio? </s>

<s>Eppure il no&shy;<lb/>stro Anatomico cremonese non &egrave; men rigido censore di quel che si fosse <lb/>l'Anatomico brussellese, a persuadersi di che basta leggere il libro XIV <emph type="italics"/>De <lb/>re anatomica,<emph.end type="italics"/> dove s'incomincia a dire che Galeno, per questo solo si <lb/>astenne dal sezionar cadaveri umani, perch&egrave; per le infami crudelt&agrave; de'suoi <lb/>predecessori fu severamente divietato dalle leggi civili. </s>

<s>&ldquo; Sed, bone Galene, <lb/>soggiunge Realdo, si tibi crudele nimis videbatur vivum hominem secare, <lb/>si animus horrescebat, si reformidabas, vel si tibi neque vel mortuum homi&shy;<lb/>nem secare per Principum edicta aut inveteratam consuetudinem non lice&shy;<lb/>bat; quo pacto licebat tibi simias secanti veteribus contradicere quos humana <lb/>corpora secuisse, tu ipse testis es locupletissimus? ... Multis in locis vete&shy;<lb/>res reprehendis, cum tute maiore his dignus sis reprehensione. </s>

<s>Nam et si&shy;<lb/>mia simile quid habeat homini, simia tamen est, non homo neque eius com&shy;<lb/>pago hominis fabricae omni ex parte respondet, partesque nonnullas in <lb/>homine conspicies, de quibus veteres anatomici loquebantur, quibus simia <lb/>caret &rdquo; (Venetiis 1559, pag. </s>

<s>256). </s></p><p type="main">

<s>Qui non si ricorre alle gentili furberie del Falloppio, ma si riprende <lb/>apertamente Galeno, come faceva il Vesalio, di cui pure non &egrave; parte ne'libri <lb/>di Realdo, dove non si scopran francamente gli errori. </s>

<s>Eppure &egrave; notabilis&shy;<lb/>simo che non ne facessero risentimento ne'Galenisti, ne'Vesaliani. </s>

<s>Si po&shy;<lb/>trebbe ci&ograve; attribuire all'essere uscito il trattato <emph type="italics"/>De re anatomica<emph.end type="italics"/> postumo, <lb/>se non si fossero veduti i Vesaliani, stessi non risparmiarla dopo morto al <lb/>Falloppio. </s></p><p type="main">

<s>Di Spagna, facendo il Vesalio viaggio a Gerusalemme, pass&ograve; per Ve&shy;<lb/>nezia, e alcuni de'principali medici della citt&agrave;, adoratori del nome di lui, <lb/>erano convenuti insieme per salutarlo nella bottega del libraio Francesco <lb/>de'Franceschi, dove sapevano ch'ei recapitava. </s>

<s>Ivi gli domandarono que'me-<pb xlink:href="020/01/1143.jpg" pagenum="18"/>dici che fosse avvenuto delle critiche fatte alle <emph type="italics"/>Osservazioni<emph.end type="italics"/> del Falloppio, <lb/>in quella scrittura che avevan sentito dire essere stata affidata a Paolo Tie&shy;<lb/>polo, ambasciatore veneto a Madrid, perch&egrave; la recasse nel suo ritorno a Pa&shy;<lb/>dova. </s>

<s>Rispose allora il Vesalio che, dovutosi trattenere per le guerre galli&shy;<lb/>che civili il Tiepolo in Catalogna, era trascorsa l'occasion della pubblicazione, <lb/>perch&egrave; il Falloppio in quel tempo era morto. </s>

<s>Saputo ci&ograve; que'medici ricor&shy;<lb/>sero al Tiepolo stesso, e avutone da lui il manoscritto, lo consegnarono al <lb/>detto Franceschi stampatore, che nel 1564 lo die fuori alla luce. </s></p><p type="main">

<s>Il titolo del libro era questo: <emph type="italics"/>Andreae Vesalii Anatomicarum Gabrie&shy;<lb/>lis Falloppii Observationnm Examen,<emph.end type="italics"/> e lo spirito che l'informava era quello <lb/>di dimostrar che il Falloppio non aveva veramente scoperto in anatomia nulla <lb/>di nuovo, e che non fosse gi&agrave; o esplicitamente o in germe contenuto nei <lb/>VII libri della Fabbrica del corpo umano. </s>

<s>Del Colombo non vi si fa men&shy;<lb/>zione altro che per incidenza, e si sfoga indirettamente l'ira contro il Val&shy;<lb/>verda, il quale &egrave; accusato d'inesperienza delle dissezioni e d'ignoranza delle <lb/>mediche discipline. </s>

<s>Del libro ch'egli scrisse in lingua spagnuola, principal&shy;<lb/>mente per divulgare fra'suoi connazionali le scoperte anatomiche del Colombo, <lb/>&egrave; detto che non fece ivi altro l'Autore che assumersi l'ufficio d'interpetre, <lb/><emph type="italics"/>turpis quaestus causa.<emph.end type="italics"/> (Venetiis 1564, pag. </s>

<s>72). </s></p><p type="main">

<s>I Vesaliani trionfarono, dandosi a credere che venisse da questo Esame <lb/>annichilato il Falloppio coi discorsi, e il Colombo coi silenzii, ma &egrave; da dire, <lb/>per onor dell'Italia e della scienza, che sebbene la prematura istituzione <lb/>sperimentale dell'Autor <emph type="italics"/>De re anatomica<emph.end type="italics"/> non trovasse allora seguaci, i pre&shy;<lb/>cetti intorno al modo di sezionare i cadaveri e di osservarne le parti, che <lb/>il Falloppio dettava dalle cattedre di Pisa e di Padova, e poi diffondeva nei <lb/>libri, educarono all'arte valorosissimi ingegni, i quali trovarono ancora ab&shy;<lb/>bondante pascolo da nutrirsi in quell'albero, che si diceva aver per solo il <lb/>Vesalio menato i suoi fiori e i suoi frutti. </s></p><p type="main">

<s>Vien primo per tempo e per eccellenza tra il fiore di quegl'ingegni <lb/>italiani Bartolommeo Eustachio, il quale a descriver le parti del corpo umano <lb/>si serv&igrave; pi&ugrave; volentieri dell'arte del disegno, prestatagli, come si dice, dal <lb/>celebre Tiziano, che di quella della parola. </s>

<s>Ma le Tavole anatomiche del <lb/>gran Maestro rimasero lungamente in Roma nella biblioteca vaticana, senza <lb/>profitto degli studiosi, infintantoch&egrave; sotto il pontificato di Clemente XI non <lb/>furono, col seguente titolo, pubblicate da Giovanni Maria Lancisi: &ldquo; Tabu&shy;<lb/>lae anatomicae clarissimi viri Bartholommaei Eustachii, quas a tenebris tan&shy;<lb/>dem vindicatas et Sanctissimi Domini Clementis XI Pont. </s>

<s>Max. </s>

<s>munificentia <lb/>dono acceptas, praephatione notisque illustravit, ac ipso suae Bibliotechae <lb/>dedicationis die publici iuris fecit Jo. </s>

<s>Maria Lancisius, intimus cubicularius <lb/>et Archiater pontificius. </s>

<s>Romae 1714. &rdquo; </s></p><p type="main">

<s>A saper solo che il libro usciva fuori per cura del Lancisi, e con pre&shy;<lb/>fazione e note scritte da lui, basterebbe per dover forse tenerne in pi&ugrave; gran <lb/>pregio la pubblicazione, che se fosse stata fatta dal suo proprio autore. </s>

<s>Ma <lb/>perch&egrave; sempre i grandi ingegni sono modesti, diffidando il Lancisi di s&egrave; in <pb xlink:href="020/01/1144.jpg" pagenum="19"/>condur la difficile impresa, volle aiuti e consigli da'pi&ugrave; valorosi medici ita&shy;<lb/>liani d'allora, e principalmente dal Pacchioni e dal Morgagni. </s>

<s>&ldquo; Et quoniam, <lb/>egli cos&igrave; scrive nella Prefazione, ne frequens locorum obscuritas me in er&shy;<lb/>rorem duceret saepe maximeque sum veritus, idcirco in laboris honesti so&shy;<lb/>cietatem vocavi D. </s>

<s>Antonium Pacchionum medicum romanum, et in rebus <lb/>potissimum anatomicis apprime versatum, quo, cum singulas Tabulas ite&shy;<lb/>rum ad examen revocare non detrectavi, atque ubi vel minimus scrupulus, <lb/>quod interdum accidit, nobis iniectus est, statim imaginem cum archetypo, <lb/>nempe iconem cum dissecto cadaveris membro contulimus et comparavimus, <lb/>in partem quoque diligentiee curaeque accito Francisco Soldato, iuvene qui&shy;<lb/>dem medicis studiis cadaverumque sectionibus magnopere exercito. </s>

<s>Neque <lb/>vero, cum opportunum censuimus, per epistolas quoque in consilium admit&shy;<lb/>tere praetermisimus eximios viros Joannem Fantonium et Joannem Bapti&shy;<lb/>stam Morgagnum nostrae aetatis in Italia experientissimos anatomicos &rdquo; <lb/>(pag. </s>

<s>XIV). </s></p><p type="main">

<s>Ciascuno iconismo delle numerose Tavole &egrave; dichiarato, nelle sue parti, <lb/>per lettere di richiamo, nella pagina di rincontro, cosicch&egrave; si rendono agli <lb/>occhi degli attenti osservatori que'disegni anatomici quasi parlanti. </s>

<s>Nono&shy;<lb/>stante per&ograve; che s'usassero tante diligenze, e vi si applicasse con tanto amo&shy;<lb/>roso studio di scienza e di arte, l'Albino not&ograve; nell'opera del Lancisi alcune <lb/>imperfezioni, che lo consigliarono a fare una nuova edizione delle Tavole <lb/>eustachiane uscite in luce in Leida nel 1744. Cos&igrave; in ogni modo si diffuse pi&ugrave; <lb/>largamente la notizia di ci&ograve; che, da quasi due secoli, s'era osservato nella <lb/>fabbrica del corpo umano in Italia, e se non si giov&ograve; molto oramai ai pro&shy;<lb/>gressi dell'anatomia, s'offerse uno de'suoi pi&ugrave; solenni documenti alla storia. </s></p><p type="main">

<s>L'Eustachio apparisce in questi documenti come uno de'primi che, non <lb/>abbarbagliato dall'aureola posta da'fanatici in fronte a Galeno e al Vesalio, <lb/>facesse sull'esempio del Falloppio progredire l'anatomia descrittiva, ma non <lb/>fu il solo: a lui si aggiunsero, osservatori diligenti de'precetti falloppiani, <lb/>Girolamo Fabrizi d'Acquapendente, e il piacentino Giulio Casserio. </s></p><p type="main">

<s>Far l'Acquapendente in anatomia discepolo del Falloppio non sembrer&agrave; <lb/>punto alieno dal vero a chi considera ch'egli &egrave; forse l'unico, che in scusare <lb/>gli errori di Galeno, per non provocarsi l'ire de'galenisti, imiti l'arte gen&shy;<lb/>tilissima del maestro. </s>

<s>Si pu&ograve; citar come esempio di ci&ograve; il fatto che, dalle <lb/>somiglianze notate fra le parti componenti le mani e i piedi, Galeno stesso <lb/>ne argomentava la somiglianza dell'uso. </s></p><p type="main">

<s>L'Acquapendente conferma per altri riscontri questa galenica analogia, <lb/>soggiungendo: &ldquo; Nam sicuti pedis duplex est actio, innixus et apprehensio, <lb/>similiter et manu &rdquo; (De motu locali Patavii 1618, pag. </s>

<s>92), colla qual mano <lb/>si pu&ograve; cos&igrave; ben calcare, per mezzo della palma, come per mezzo della pianta <lb/>e del calcagno del piede. </s>

<s>Cos&igrave; dicendo non sembra aver l'autore altra in&shy;<lb/>tenzione che di rimover l'accusa di paradosso, di che altri imputerebbe il <lb/>discorso galenico. </s>

<s>&ldquo; Si igitur omnes apprehensiones ut in manu et in pede <lb/>similiter fiunt, non est ulterius ambigendum neque ullo modo credendum <pb xlink:href="020/01/1145.jpg" pagenum="20"/>Galenum paradoxum protulisse, cum dixit pedem esse instrumentum ap&shy;<lb/>prehensionis &rdquo; (ibi, pag. </s>

<s>93). </s></p><p type="main">

<s>Il Vesalio sarebbe uscito qui, colla solita baldanza, a far notare a Ga&shy;<lb/>leno che somiglianti son le parti, e perci&ograve; anche gli usi, delle mani e dei <lb/>piedi nelle scimmie, non per&ograve; nell'uomo. </s>

<s>Ma l'Acquapendente trova modo <lb/>a scusar l'errore concludendo cos&igrave; il suo ragionamento: &ldquo; Natura igitur in <lb/>pede construendo respexit superficiem corporis et corpora ipsa super quibus <lb/>facere innixum oportebat. </s>

<s>Quae cum varia essent penes figuram aut an&shy;<lb/>gularem aut planam aut rotundam aut curvam, tum per reliquas dissimi&shy;<lb/>laris corporis differentias, ut tutus super omnia iam dicta corpora innixus <lb/>fiat, factum est ut innixus multiplex sit multipliciterque fiat. </s>

<s>Cum vero ge&shy;<lb/>neraliter omnis innixus comprimendo fiat, tamen a calcaneo et planta sim&shy;<lb/>pliciter solaque compressione et comprimendo; a cavo pedis tum compres&shy;<lb/>sione tum incurvatione; a digitis postremo tum compressione tum apprehen&shy;<lb/>sione absolvitur. </s>

<s>Quo fit ut Galenus pedes instrumenta apprehensionis esse <lb/>dixerit, quod nonnisi ratione digitorum contingit, qui, tam comprimendo <lb/>quam apprehendendo, tutum praestant innixum &rdquo; (ibi, pag. </s>

<s>96). </s></p><p type="main">

<s>Abbiamo detto che, in questo modo di procedere verso Galeno, l'Acqua&shy;<lb/>pendente imit&ograve; le arti del Falloppio, e le chiamiamo arti, perch&egrave; crediamo <lb/>che gli sviscerati ossequi de'Galenisti, in que'liberi petti, non fossero sin&shy;<lb/>ceri. </s>

<s>Frutto di questa libert&agrave; nello stesso Acquapendente fu quello di avere <lb/>introdotto nell'Anatomia un metodo nuovo da distinguere e nominare i mu&shy;<lb/>scoli dalle loro azioni. </s>

<s>Prima di lui, cos&igrave; Galeno come il Vesalio, non ave&shy;<lb/>vano trattato la Miologia, se non che cos&igrave; materialmente, descrivendo i mu&shy;<lb/>scoli secondo che l'uno si mostrava succedere all'altro, o era l'uno all'altro <lb/>contiguo o consociato. </s>

<s>Ma il Nostro, non badando all'ordine e alla mate&shy;<lb/>riale disposizion delle fibre, ne considera gli effetti de'moti, e descrive i <lb/>muscoli secondo che agiscono in uno o in altro modo sulle leve degli ossi, <lb/>a cui come potenza vengono applicati. </s>

<s>Di qui nacque nell'Anatomia muscu&shy;<lb/>lare una importante riforma, la quale volle essere cos&igrave; notata dal nostro <lb/>Autore, affinch&egrave; i lettori non ne prendessero maraviglia: </s></p><p type="main">

<s>&ldquo; Miraberis forsitan, lector, quod musculos non describam ut Vesalius <lb/>in toto suo opere, et Galenus in libro De adm. </s>

<s>anat. </s>

<s>fecit, qui ordinem seu <lb/>commodam dissectionem respicientes eos descripsere, quoniam ii tantum&shy;<lb/>modo eorum dissectionem, prout unus alteri succedit et contiguus est asso&shy;<lb/>ciaturque, nobis saltem ob oculos ponere et monstrare voluerunt. </s>

<s>At nos, <lb/>qui scopum habemus docere, per ea quae insunt musculis, earum actiones <lb/>et usus, merito alio ordine concedendum duximus, qui procul dubio nos <lb/>ducit ad notitiam casuum musculorum et articulorum. </s>

<s>Nam si quis simpli&shy;<lb/>cem dissectionem inquirat, et primum, secundum, tertium et sequentes hoc <lb/>modo numeret, potius confusionem quam notitiam, utilitatem musculorum <lb/>consequetur. </s>

<s>At, quando nos eorum quae insunt musculis causas inquirimus, <lb/>tunc usum inquirimus, et musculorum numerum exactius memoriae man&shy;<lb/>damus &rdquo; (ibi, pag. </s>

<s>82). </s></p><pb xlink:href="020/01/1146.jpg" pagenum="21"/><p type="main">

<s>Proseguendo l'Acquapendente con questo nuovo metodo razionale le sue <lb/>ricerche miologiche, narra come fosse, nel 1599, condotto alla scoperta dei <lb/>muscoli gemelli (pag. </s>

<s>83, 84) e a riconoscer la vera natura e gli uffici del <lb/>lungo estensor comune delle dita de'piedi, notando tre capitalissimi errori, <lb/>in ch'era caduto il Vesalio (ivi, pag. </s>

<s>103, 4). </s></p><p type="main">

<s>Discepolo e familiare dell'Acquapendente, il Casserio, parve compren&shy;<lb/>dere in s&egrave; tutte insieme le virt&ugrave; de'suoi illustri predecessori, non eccet&shy;<lb/>tuato il Colombo, il quale egli imita nel dar di Galeno que'liberi giudizi, <lb/>intorno a che l'Acquapendente stesso e il Falloppio tanto timidi s'erano di&shy;<lb/>mostrati, da parer quasi servili. </s>

<s>Basti di quella filosofica libert&agrave; dell'Anato&shy;<lb/>mico piacentino recar questo esempio dal cap. </s>

<s>XI del libro IV <emph type="italics"/>De auris <lb/>auditus organi structura,<emph.end type="italics"/> dove si tratta dei tre ossicini. </s>

<s>Dal non trovarli in <lb/>Galeno descritti s'era incominciato a dire che gli aveva il gran Maestro igno&shy;<lb/>rati: risposero allora solleciti i Galenisti ch'era di ci&ograve; la ragione, o per es&shy;<lb/>sere andati alcuni libri galenici smarriti, o perch&egrave;, nel libro <emph type="italics"/>De ossibus,<emph.end type="italics"/> si <lb/>dichiara l'Autore di aver per brevit&agrave; lasciate indietro alcune delle pi&ugrave; mi&shy;<lb/>nute descrizioni. </s>

<s>Ma il Casserio non trovava punto ragionevoli queste scuse. <lb/></s>

<s>&ldquo; Enimvero, scriveva, prior coniectura levis admodum est et rationi parum <lb/>consona, posterior vero ratio omnino non satisfacit, nam quemadmodum excu&shy;<lb/>satione dignus videri potest, si in compendioso libro, cuiusmodi est qui <emph type="italics"/>De <lb/>ossibus<emph.end type="italics"/> inscribitur, exacte et minute omnia et praesertim difficilia non expli&shy;<lb/>cat; ita iusta reprehensione carere nequit quod in aliis tractationibus longis <lb/>et copiosis nullam de his ossiculis mentionem facit. </s>

<s>Idcirco ego sane mihi <lb/>persuadeo Galenum non in aliis animalibus quam in simia, si forte non sint <lb/>alia quae ossiculis illis carent, auditus organum interius collustrasse. </s>

<s>Nam in <lb/>simia nulla intus in osse petroso ossicula reperiuntur &rdquo; (De quinque sens., <lb/>Venetiis 1609, pag. </s>

<s>205). </s></p><p type="main">

<s>Che poi il discepolo e il familiare dell'Acquapendente ritenga in s&egrave; le <lb/>virt&ugrave; di osservare e di descrivere le parti, colla diligenza insegnata dal Fal&shy;<lb/>loppio, e della quale cos&igrave; splendidi esempi dava l'Eustachio, basta senz'altro <lb/>a provarlo il fatto che fu egli, il Casserio, il primo che osserv&ograve; e deline&ograve; <lb/>l'artificiosissimo magistero de'muscoli cos&igrave; detti da lui <emph type="italics"/>penniformi.<emph.end type="italics"/> Ma oltre <lb/>al comprendere in s&egrave; le virt&ugrave; de'maggiori ha il nostro Piacentino qualche <lb/>cosa, che lo distingue da tutti gli altri, e che sentita nella propria coscienza <lb/>fa s&igrave; ch'egli si dia, fra gli Autori di que'tempi, oltre a quello di medico <lb/>il titolo di filosofo. </s>

<s>Egli infatti non si contenta solo di osservare, come il <lb/>Vesalio e il Falloppio e l'Eustachio, e di descrivere, ma applicando il me&shy;<lb/>todo dell'Acquapendente non a soli i muscoli, s&igrave; a tutti gli organi, filosofa <lb/>intorno ai fini, per cui furono dalla Natura essi organi ordinati, e non <lb/>lascia di descriver parte del corpo umano, che non tratti degli usi. </s>

<s>&Egrave; in ci&ograve; <lb/>forse imitator di Galeno, pi&ugrave; di quel ch'egli stesso non si creda, ma l'aver <lb/>prediletto di trattar de'sensi, e particolarmente di quello dell'udito, lo fa <lb/>sollevare a questioni metafisiche intorno all'origine delle idee; origine ch'egli <lb/>crede esser da quegli stessi sensi, con anatomico stile aperti a svelarne i misteri. </s></p><pb xlink:href="020/01/1147.jpg" pagenum="22"/><p type="main">

<s>&Egrave; sembrato ad alcuni che questo nuovo modo di filosofare segni nella <lb/>scienza un progresso, ma comunque sia, egli &egrave; ancora troppo affrettato, e <lb/>scavalca per cos&igrave; dire a un altro passo, che nel regolare andamento delle <lb/>idee si sarebbe dovuto premettere, e che, sebben si arrestasse nelle sue <lb/>prime mosse, era stato con valido impulso dato gi&agrave; da Realdo Colombo. </s>

<s>Il <lb/>metodo sperimentale, applicato da lui allo studio della fabbrica del corpo <lb/>umano, inizi&ograve; quella che ora propriamente si dice <emph type="italics"/>Fisiologia,<emph.end type="italics"/> e per la quale <lb/>veniva la semplice arte del dissettare i cadaveri a sollevarsi all'essere e alla <lb/>dignit&agrave; di scienza. </s>

<s>Pi&ugrave; conveniente perci&ograve;, e pi&ugrave; conducevole al desiderato <lb/>perfezionamento, sarebbe riuscita l'opera del Casserio, se piuttosto che di <lb/>filosofo fosse stata di fisiologo, ma non era venuta ancora la stagione oppor&shy;<lb/>tuna a indossar quell'abito nuovo, bench&egrave; le aure che si sentivano spirare <lb/>l'annunziassero vicina. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Come spirassero quell'aure sotto il cielo d'Italia, e giungessero a fe&shy;<lb/>condare un ingegno straniero, &egrave; da rimeditar con pensiero degno della Fi&shy;<lb/>losofia della storia. </s>

<s>Realdo Colombo dicemmo che aveva felicemente appli&shy;<lb/>cato il metodo sperimentale alle dissezioni anatomiche, d'ond'ebbe origine <lb/>fra le altre la dimostrata scoperta delle funzioni fisiologiche del cuore nella <lb/>piccola circolazion polmonare. </s>

<s>Istitutor di quel nuovo metodo il Colombo, in <lb/>principio dalla cattedra e poi nel trattato <emph type="italics"/>De re anatomica,<emph.end type="italics"/> ne dettava le <lb/>regole, che si leggono nel XIV libro, a cui si d&agrave; il titolo <emph type="italics"/>De viva sectione.<emph.end type="italics"/><lb/>Prescrive prima di tutto che si scelgano ad immolare sull'altar di Minerva <lb/>i cani, maschi o femmine che siano, ma giovani, principalmente perch&egrave; la&shy;<lb/>trando pi&ugrave; forte danno modo a conoscere qual sia veramente l'organo della <lb/>voce. </s>

<s>&Egrave; anche questa scoperta un frutto del nuovo metodo istituito dal no&shy;<lb/>stro Cremonese, e bench&egrave; sia importante, non &egrave; quella ancora, sopra la quale <lb/>ha da rivolgersi la nostra considerazione. </s></p><p type="main">

<s>Insegnato il modo di legare sopra una tavola il cane vivo, affinch&egrave; non <lb/>si muova e non morda, si vede, aperto il ventre, come i polmoni circondano <lb/>il cuore e come respirando l'animale giochi il Diaframma. </s>

<s>&ldquo; Ad haec pul&shy;<lb/>cherrima visu illud quoque accedit, motus scilicet cordis quemadmodum am&shy;<lb/>plificetur atque arctetur. </s>

<s>Item qualis sit motus arteriarum in viva Anatome, <lb/>si lubuerit, conspicaberis; numquid idem sit vel oppositus motui cordis. </s>

<s><lb/>Comperies enim dum cor dilatatur constringi arterias et rursus in cordis <lb/>constrictione dilatari. </s>

<s>Verum animadvertas, dum cor sursum trahitur et tu&shy;<lb/>mefieri videtur, tunc constringitur: cum vero se exerit, quasi relaxatus deor&shy;<lb/>sum vergit. </s>

<s>Atque eo tempore dicitur cor quiescere, estque tunc cordis <lb/>systole, propterea quod facilius suscipit minoreque labore, at cum transmittit <lb/>maiori opus est robore. </s>

<s>Neque hoc floccifacias, etenim non paucos reperias <pb xlink:href="020/01/1148.jpg" pagenum="23"/>qui eo tempore cor dilatari certo opinantur, quo vere constringitur &rdquo; (Edi&shy;<lb/>tio cit., pag. </s>

<s>257). </s></p><p type="main">

<s>N&egrave; queste sole, soggiunge poco appresso il Colombo, son le cose che <lb/>si possono imparare dalla viva voce della Natura, piuttosto che dalla lettera <lb/>morta di Galeno, ma si intender&agrave; inoltre per quanto lunga via errassero i <lb/>Peripatetici, dietro il loro principe Aristotile, il quale os&ograve; dire tre essere i <lb/>ventricoli del cuore, nel destro de'quali il sangue accolto &egrave; caldissimo, nel <lb/>sinistro &egrave; freddissimo, e nel mezzar&igrave;o mediocre. </s>

<s>&ldquo; Tu vero dextro cordis ven&shy;<lb/>triculo inciso si digitum immiseris, calor tepidus tibi occurret, at in sinistro <lb/>tantus, ut ferre vix possis. </s>

<s>Illud insuper, quod saepe in disquisitionem venit, <lb/>quo pacto vere se habeat experieris an in arteria venali aer et vapor ille, quem <lb/>capinosum quasi fumidum dicunt, vel sanguis contineatur &rdquo; (ibi, pag. </s>

<s>259). </s></p><p type="main">

<s>All'utilit&agrave; che veniva alla scienza dal mostrarsi in che modo si potesse <lb/>toccar con mano il vero, lungamente rimasto ne'libri de'filosofi antichi an&shy;<lb/>nebbiato, aggiungeva l'Autore il diletto, per cui i cruciati infelicissimi di <lb/>que'poveri animali vuol che sieno da dire piuttosto felici, offerendo uno spet&shy;<lb/>tacolo misto di una dolce piet&agrave;, e d'incredibile stupore. </s></p><p type="main">

<s>Era in sul morire la madre di alcuni cagnolini, che allora allora la mano <lb/>dell'esperto anatomico aveva dall'utero estratti, e l'amore dei figli pareva <lb/>superare i dolori e le agonie della morte. </s>

<s>Perch&egrave; se tu provavi a toccare <lb/>uno di que'cagnolini latrava, se tu glielo appressavi alle labbra, metteva <lb/>fuori la lingua e lo lambiva con grandissimo affetto. </s>

<s>Che se invece tu pre&shy;<lb/>sentavi alla paziente, lacerata dal ferro anatomico, qualche altro oggetto di&shy;<lb/>verso, lo mordeva con rabbia disperata. </s>

<s>&ldquo; Quem naturae amore, atque adeo <lb/>parentum in liberos incredibilem charitatem in publicis theatris maxima <lb/>spectatorum admiratione saepius ostendi, Patavii praesertim, cum adesset <lb/>illustrissimus ac reverendissimus Rainutius Farnesius &rdquo; (ibi, pag. </s>

<s>258) e <lb/>dopo aver nominati molti altri signori, che assisterono allo spettacolo in&shy;<lb/>sieme col Farnese, cos&igrave; il Colombo sogiunge: &ldquo; Hi omnes, item alii multi <lb/>summa cum voluptate huic vivae canis sectioni interfuerunt, et illud insi&shy;<lb/>gne exemplum de ingenti amore vel brutorum in filios se nunquam obli&shy;<lb/>turos asseverabant, neque has duntaxat discendi voluptates quas hactenus <lb/>memoravi &rdquo; (ibi, pag. </s>

<s>258, 59). </s></p><p type="main">

<s>Un Autore che, trattando di Anatomia, sa in fare la descrizione delle <lb/>n uove cose scoperte instillar nell'animo di chi lo ascolta la volutt&agrave; dell'im&shy;<lb/>parare, sembrava che dovess'essere secondato e universalmente applaudito, <lb/>come sempre avviene a colui, che sa mescere l'utile al dolce. </s>

<s>Eppure &egrave; un <lb/>fatto che Realdo Colombo, col suo nuovo metodo e con le sue insigni sco&shy;<lb/>perte, non figura nella storia anatomica del secolo XVI, se non come una <lb/>splendida apparizione svanita, senza lasciar di s&egrave; vestigio nell'aria o negli <lb/>occhi di chi con subita ammirazione l'avea riguardata. </s>

<s>La fisiologia del <lb/>cuore, per tacer di tante altre verit&agrave; anatomiche scoperte negli animali vivi <lb/>per via di osservazioni e di esperienze, rimase una istituzione morta nelle <lb/>pagine di un libro, e il Falloppio stesso ne'suoi scritti pubblicati dopo <pb xlink:href="020/01/1149.jpg" pagenum="24"/>il 1559 e l'Eustachio e l'Acquapendente, che vuol dire insomma i pi&ugrave; so&shy;<lb/>lenni maestri di allora, intorno alla piccola circolazion del sangue e alle fun&shy;<lb/>zioni del cuore e dei polmoni, ripeterono gli errori del Vesalio. </s></p><p type="main">

<s>A commemorare que'nomi, ai quali son da aggiungere il Casserio, il <lb/>Vidio, l'Aranzio, insieme con parecchi altri, la scienza italiana si esalta, ve&shy;<lb/>dendo in essi cos&igrave; numerosa e poderosa oste congiurata insieme a cacciar <lb/>dalle nostre contrade il maggiore de'nostri nemici, l'errore, ma si umilia <lb/>dall'altra parte a pensar che quei valorosi, a cui il Colombo avea presen&shy;<lb/>tato un nuovo vessillo, da conquistar con esso in mano nuove inesplorate <lb/>provincie, si mostrassero tanto poco sollecitamente avveduti, da lasciarselo <lb/>rapire, venuto per avventura in mezzo a loro, da un sagace straniero. </s></p><p type="main">

<s>Guglielmo Harvey fu colui che, venuto d'Inghilterra in Italia, non tanto <lb/>impar&ograve; dalla viva voce dell'Acquapendente, quanto dai libri scritti pi&ugrave; di <lb/>un mezzo secolo prima da Realdo Colombo. </s>

<s>Di quelle pagine, le quali erano <lb/>state oramai dagl'Italiani dimenticate, fece il giovane inglese la sua lettura <lb/>prodiletta, e vi apprese la nuova arte, rimasta per tutto quel tempo incolta, <lb/>di studiare i moti del cuore nella vivisezione. </s>

<s>Tornato in patria, ebbe nel&shy;<lb/>l'aula di Giorgio I animali in copia e di varie specie, che si allevavano nei <lb/>ricchi parchi reali, e ch'egli con pi&ugrave; esperta mano sezionava vivi, larga&shy;<lb/>mente applicandovi i metodi del Colombo, da cui tenne per dimostrata la <lb/>piccola circolazion polmonare. </s>

<s>Proseguendo oltre per l'aperto cammino, riu&shy;<lb/>sc&igrave; a indovinare e a segnar le intralciate vie, per cui il sangue va dal cuore <lb/>a irrigare le membra pe'rami delle arterie, e vi torna con perpetuo circolo <lb/>ricondottovi dalle vene. </s>

<s>Nel 1628 pubblic&ograve; la sua scoperta in un libro, a cui <lb/>di&egrave; il titolo di esercitazione anatomica <emph type="italics"/>De motu cordis et sanguinis,<emph.end type="italics"/> libro <lb/>che non si potrebbe meglio qualificare, che con chiamarlo il pi&ugrave; splendido <lb/>commento fatto al Trattato <emph type="italics"/>De re anatomica<emph.end type="italics"/> del nostro Cremonese, da cui, <lb/>come da albero diligentemente coltivato, il fortunato Britanno trasse unico <lb/>le invidiate dovizie del frutto. </s></p><p type="main">

<s>I due trattati perci&ograve; <emph type="italics"/>De re anatomica<emph.end type="italics"/> e <emph type="italics"/>De motu cordis<emph.end type="italics"/> che non vanno <lb/>disgiunti, perch&egrave; quello mancherebbe del suo seguito, e questo del suo prin&shy;<lb/>cipio, segnano nella storia dell'Anatomia un periodo distinto e un notabi&shy;<lb/>lissimo progresso, il quale consiste, come accennammo, nell'aver congiunto <lb/>con le anatomiche osservazioni lo studio degli organi sorpresi in quell'atto <lb/>stesso, ch'esercitano le funzioni della vita. </s>

<s>Ebbe da quegli studi la sua prima <lb/>origine la Fisiologia, la quale sarebbesi per&ograve; rimasta sterile, senza il con&shy;<lb/>nubio con un'altra scienza, solerte indagatrice delle propriet&agrave; generali della <lb/>materia, e fu il Pecquet che dette il primo solenne esempio di quel connu&shy;<lb/>bio nella sua Dissertazione anatomica <emph type="italics"/>De circulatione sanguinis et chyli <lb/>motu.<emph.end type="italics"/> L'Anatomia del Diepeo ha giusto titolo d'esser chiamata nuova, per&shy;<lb/>ch&egrave; non descrive solamente le parti, com'avevan fatto tutti i pi&ugrave; gran mae&shy;<lb/>stri dell'arte, dal Vesalio all'Acquapendente, n&egrave; osserva solamente o descrive <lb/>i moti vitali come avevan fatto il Colombo e l'Harvey, ma applicando le <lb/>leggi della Fisica si studia di rendere la ragion di que'moti. </s></p><pb xlink:href="020/01/1150.jpg" pagenum="25"/><p type="main">

<s>Abbiam detto che fu il Pecquet il primo a dar solenne esempio di que&shy;<lb/>sta applicazione delle leggi fisiche allo studio della vita animale, ma consi&shy;<lb/>derando poi che la Fisica pecqueziana si riduce tutta nell'esperienza del <lb/>Torricelli, il quale pure insiem col Magiotti non aveva lasciato, ne'privati <lb/>esercizi, di tentar felicemente simili applicazioni, abbiam creduto d'essere <lb/>giusti giudici a non attribuire all'Anatomico francese altro merito, da quello <lb/>in fuori d'essere egli stato il primo a render pubblicamente noti i nuovi <lb/>esperimenti. </s></p><p type="main">

<s>Fu il Torricelli, senza dubbio, l'istitutore della moderna fisica speri&shy;<lb/>mentale, ma lo avevano preceduto il Benedetti e Galileo, e le applicazioni <lb/>della Fisica alla scienza della vita, d'ond'ebbe origine quella che propria&shy;<lb/>mente oggid&igrave; si chiama Fisiologia, son pi&ugrave; antiche non di quelle sole isti&shy;<lb/>tuite dal Pecquet, ma dal Torricelli stesso e dal Magiotti, i quali fecero poi <lb/>del Borelli il fondatore di quella scuola, che indifferentemente si chiama o <lb/>Iatromatematica o Italiana. </s>

<s>Giacch&egrave; dunque l'aver promossa a questo grado <lb/>la semplice arte di descriver le parti del corpo umano, e di compararle con <lb/>quelle de'bruti, &egrave; opera principalmente dei nostri Italiani, giova considerarne <lb/>in uno sguardo i principii e i progressi. </s></p><p type="main">

<s>Risalgono que'principii propriamente al Santorio, che facendo uso di <lb/>uno strumento volgarissimo, qual'&egrave; la Stadera, dimostr&ograve; l'insensibile traspi&shy;<lb/>razione del corpo dell'uomo, e ne fece il fondamento a un sistema medico, <lb/>che &egrave; il primo, a cui si possa dar veramente il titolo di razionale. </s>

<s>Egli primo <lb/>invoc&ograve; la Fisica e la Meccanica a inventare Termometri, Pulsilogi, e altri <lb/>nuovi strumenti, tutti applicabili agli usi della Medicina. </s></p><p type="main">

<s>Galileo che fu al Fisico giustinopolitano amico e collega, e che sali pi&ugrave; <lb/>volte, per fare esperienza della traspirazione del suo proprio corpo, sulla Sta&shy;<lb/>dera medica (Alb. </s>

<s>VIII, 368), deriv&ograve; da lui e dall'Acquapendente un certo <lb/>amore per le cose mediche e per l'Anatomia, com'apparisce da'suoi stessi <lb/>Dialoghi, che sembrano da s&igrave; fatte materie esser pi&ugrave; alieni. </s>

<s>Nell'aforismo V <lb/>della II Sezione della Medicina statica accenna il Santorio all'uso dell'Areo&shy;<lb/>metro, per conoscer fra le acque le pi&ugrave; o meno leggere, e sceglier cos&igrave; le <lb/>pi&ugrave; convenienti allo stomaco de'malati. </s>

<s>&ldquo; Quantum sit aquae ponderositas <lb/>facile intelligitur, si grave perpendatur in aqua: illa enim est levior et per <lb/>consequens salubrior, in qua grave magis gravitat: illa vero, in qua minus <lb/>est ponderosior, est insalubrior &rdquo; (Opera Omnia, T. III, De statera medica, <lb/>Venetiis 1660, pag. </s>

<s>8). E Galileo, nel I Dialogo delle due nuove scienze, <lb/>dop'aver descritti i giochi fatti da una palla di cera immersa in acqua di <lb/>varia gravit&agrave; specifica, &ldquo; Non &egrave; cotesta esperienza, soggiunge, priva di uti&shy;<lb/>lit&agrave;, perch&egrave; trattandosi dai Medici in particolare delle diverse qualit&agrave; di acque <lb/>e tra le altre principalmente della leggerezza e gravit&agrave; pi&ugrave; di questa che di <lb/>quella, con una simil palla aggiustata, s&igrave; che resti ambigua per cos&igrave; dire <lb/>tra lo scendere e il salire in un'acqua, per minima che sia la differenza di <lb/>peso tra due acque, se in una tal palla scender&agrave;, nell'altra che sia pi&ugrave; grave, <lb/>salir&agrave; &rdquo; (Alb. </s>

<s>XIII, 72). </s></p><pb xlink:href="020/01/1151.jpg" pagenum="26"/><p type="main">

<s>Quanto all'Anatomia, dice Galileo stesso nella Giornata II de'Due mas&shy;<lb/>simi Sistemi, per bocca del Sagredo, di essersi trovato in Venezia a veder <lb/>le sezioni fatte da un diligente e pratico Notomista, un giorno che s'andava <lb/>ricercando l'origine de'nervi, per decidere l'antica controversia insorta fra <lb/>Galenisti e Peripatetici (Alb. </s>

<s>I, 121), e voleva forse con questa reminiscenza, <lb/>accomodata alla persona del Patrizio veneziano, accennare alle tante altre <lb/>volte che in Padova, in quel celebre anfiteatro eretto nelle stanze attigue a <lb/>quelle dove dettava le sue lezioni, avr&agrave; assistito alle anatomie dell'Acquapen&shy;<lb/>dente. </s>

<s>In ogni modo &egrave; ragionevolissimo il supporre che il trattato <emph type="italics"/>De motu <lb/>locali<emph.end type="italics"/> di costui invogliasse Galileo ad applicar le leggi della meccanica ai <lb/>movimenti animali, per la quale applicazione era indispensabile la notizia <lb/>dell'anatomia de'muscoli e dell'ossa. </s></p><p type="main">

<s>Essendo cosa certa che, infin dal 1628, aveva l'Harvey pubblicata la <lb/>sua Esercitazione anatomica del moto del cuore e del circolo del sangue, <lb/>nasce una viva curiosit&agrave; di sapere in questo proposito qual si fosse l'acco&shy;<lb/>glienza fatta da Galileo a un libro, in cui s'annunziava una novit&agrave; di tanta <lb/>importanza. </s>

<s>Dovremo intorno a ci&ograve; in altro capitolo intrattenere, non cos&igrave; <lb/>come ora in fretta, il discorso, ma, per sodisfare intanto alle prime curio&shy;<lb/>sit&agrave;, basti il dire che la notizia della scoperta arveiana fu recata in Italia <lb/>nel 1637 da un medico tedesco, che faceva in Roma anatomiche dimostra&shy;<lb/>zioni, alle quali interveniva fra gli altri Raffaello Magiotti. </s>

<s>La circolazione, <lb/>che fa il sangue in noi, e che sembrava al Magiotti stesso &ldquo; bastante a ri&shy;<lb/>volgere tutta la medicina, siccome l'invenzione del Telescopio ha rivolta <lb/>tutta l'Astronomia, la Bussola l'economia e l'Artiglieria tutta l'arte mi&shy;<lb/>litare &rdquo; (Alb. </s>

<s>X, 207) ei la descriveva in una lettera del d&igrave; 25 Aprile di <lb/>quell'anno 1637 a Famiano Michelini, perch&egrave; la riferisse a Galileo, il quale, <lb/>per non dire addirittura che poca fede aveva nell'annunziata scoperta, fece <lb/>intendere di averla letta <emph type="italics"/>con qualche gusto<emph.end type="italics"/> (ivi, pag. </s>

<s>209). Lo stesso Mi&shy;<lb/>chelini ne dette parte anche al Baliani, il quale pi&ugrave; francamente di Galileo <lb/>rispose all'amico che, se gli avesse detto i motivi per cui teneva cos&igrave; sicura <lb/>l'opinion dell'Arveo, forse gli avrebbe addotto qualche cosa in contrario &rdquo; <lb/>(Targioni, Notizie degli aggrandimenti ecc., T. I, Firenze 1780, pag. </s>

<s>204). </s></p><p type="main">

<s>Si par chiaro di qui che la grande innovazione degli studi anatomici e <lb/>fisiologici, introdottasi nella scienza dopo la scoperta dell'Harvey, fu pro&shy;<lb/>mossa in Italia principalmente per opera del Magiotti e del Michelini, il <lb/>quale ebbe una grande efficacia sulla mente del Borelli, a cui fu maestro <lb/>ed amico. </s>

<s>Non &egrave; per&ograve; da negare che pi&ugrave; d'alto vennero quegli efficacissimi <lb/>impulsi, da Galileo cio&egrave; e dal Castelli, perch&egrave;, sebbene non sentisse esso Ga&shy;<lb/>lileo quell'alito di verit&agrave;, che spirava dalle pagine arveiane, e che si sarebbe <lb/>cos&igrave; largamente diffuso a fecondare di s&egrave; la scienza, avevano egli e il Ba&shy;<lb/>liani, cos&igrave; esperti de'metodi sperimentali, qualche ragionevole motivo di <lb/>dubitar di un fatto, che si rendeva, per tanti bene ordinati e concludenti <lb/>argomenti probabilissimo, ma che non veniva in verit&agrave; dimostrato certo da <lb/>nessuna sensata esperienza. </s></p><pb xlink:href="020/01/1152.jpg" pagenum="27"/><p type="main">

<s>I primi esempii insomma dell'applicazione delle leggi fisiche a spiegare <lb/>i varii fatti e le varie passioni della vita, cos&igrave; vegetativa come animale; <lb/>esempii ai quali s'inform&ograve; poi la scuola cos&igrave; detta iatromatematica o iatro&shy;<lb/>meccanica, furono dati da Galileo e dal Castelli, veri padri e maestri di ogni <lb/>disciplina, ch'ebbe dai loro valenti e numerosi discepoli cos&igrave; larga e fio&shy;<lb/>rente cultura. </s>

<s>Non vogliamo di quegli esempii addurne altro che uno, ma <lb/>valevole per tutti gli altri, come quello che pi&ugrave; a vivo di tutti gli altri ri&shy;<lb/>trae le qualit&agrave; proprie di quella istituzione, ed &egrave; l'esempio dell'aria, che ora <lb/>restringendosi ora dilatandosi, a seconda che in lei manca o cresce il calore, <lb/>fa salire o scendere il liquido in una caraffella, il lungo e sottil collo della <lb/>quale, con la sua bocca aperta, in quello stesso liquido s'immerga. </s></p><p type="main">

<s>Galileo applic&ograve; il fatto fisico al moto dell'ascesa e della discesa de'suc&shy;<lb/>chi nutritizi negli alberi, per l'avvicendarsi dei giorni calorosi con le frigide <lb/>notti, e cos&igrave; spiegava in che modo granissero le biade e maturassero i frutti <lb/>(Alb. </s>

<s>XIV, 335). Il Castelli poi trov&ograve;, in quello stesso fatto fisico, modo a <lb/>spiegare un fatto patologico ben pi&ugrave; nuovo e pi&ugrave; curioso. </s>

<s>Erano a un po&shy;<lb/>ver'uomo ferito nel ventre usciti dall'apertura gl'intestini, che rigonfiandosi <lb/>gli producevano acerbissimi dolori. </s>

<s>Chiamato a curarlo Giovanni Trullo, <lb/>espertissimo chirurgo, che oper&ograve; anche intorno agli occhi di Galileo, &ldquo; ve&shy;<lb/>duto ch'ebbe il paziente (dice il Castelli stesso in una lettera al Cesarini, <lb/>pubblicata da D. B. Boncompagni) con gran franchezza e risoluzione prese <lb/>un'ago, e pungendo in diverse parti quell'intestina, scappando via quel flato <lb/>rinchiuso, subito sgonfiarono..... Il caso fu bello ed il rimedio facilissimo <lb/>ed intelligibile, ma io rimasi da una difficolt&agrave; sopraggiunto, la quale mi ha <lb/>dato che pensare assai a questo fatto, poich&egrave; alcuni giorni sono, discorrendo <lb/>col medesimo signor Trullo di questa cura, egli mi disse che sempre in si&shy;<lb/>mili ferite, coll'uscita dell'intestina, seguiva l'istesso accidente del rigon&shy;<lb/>fiarsi, e di pi&ugrave; che sempre il ferito veniva da crudelissimi dolori tormentato. </s>

<s><lb/>In questo mi sovvenne un'esperienza fattami vedere, gi&agrave; pi&ugrave; di trentacin&shy;<lb/>que anni sono, dal nostro signor Galileo &rdquo; (Bullettino di Bibl. </s>

<s>e di Stor. </s>

<s><lb/>matem. </s>

<s>ecc., T. XI, Roma 1878, pag. </s>

<s>645). </s></p><p type="main">

<s>L'esperienza &egrave; quella della caraffina gi&agrave; detta, e la ragion de'fatti os&shy;<lb/>servati nel cannellino di vetro intendeva il Castelli di applicarla ai nuovi <lb/>fatti osservati nel tubo dell'intestino. </s>

<s>Se non che vedeva la cosa avvenire <lb/>tutto al contrario, perch&egrave; l'aria, raffreddandosi nell'intestino uscito fuori del <lb/>ventre, avrebbe dovuto produr piuttosto uno sgonfiamento che un tumore. </s>

<s><lb/>Allora il nostro primo Iatromeccanico pens&ograve; cos&igrave; ragionando di conciliar la <lb/>fisica con la fisiologia. </s>

<s>&ldquo; Perch&egrave; tutte le budella dello stesso animale comu&shy;<lb/>nicano senza dubbio una con altra, e con esse gli altri meati di altri vasi <lb/>del vivente, come mostrano chiaramente gli Anatomisti, e questa tale comu&shy;<lb/>nicanza continuando fino alla respirazione dell'animale, per&ograve; venendo l'aria, <lb/>rinchiusa nelle intestina uscite dal ventre, raffreddata, di necessit&agrave; vien con&shy;<lb/>densata. </s>

<s>E perch&egrave; nelle altre intestina e vasi dell'animale si trovano molti <lb/>flati, i quali sono facilissimi ad esser mossi o forse cercano l'esito; per&ograve; <pb xlink:href="020/01/1153.jpg" pagenum="28"/>questi flati entrano nelle uscita intestina e le rigonfiano. </s>

<s>Che se io non du&shy;<lb/>bitassi in queste difficilissime materie di Medicina d'inciampare, non essendo <lb/>mia professione, direi di pi&ugrave; che, stante la ferita, accendendosi nel corpo <lb/>dell'animale il calor febbrile, ancora questo calore pu&ograve; cooperare al rigon&shy;<lb/>fiamento delle budella fuori del ventre, imperocch&egrave;, riscaldandosi di sover&shy;<lb/>chio le parti interne dell'animale, &egrave; necessario che cagionino la dilatazione <lb/>de'flati rinchiusi nel ventre. </s>

<s>Quindi con maggior forza ed impeto trapassano <lb/>nelle parti delle intestina di gi&agrave; uscite e le rigonfiano &rdquo; (ivi, pag. </s>

<s>648). </s></p><p type="main">

<s>Un altro esempio notabilissimo di questa applicazione dei fatti fisici a <lb/>spiegar le pi&ugrave; misteriose funzioni della vita, ad imitazione di ci&ograve; che gli <lb/>aveva insegnato a fare il suo maestro Castelli, ce l'offre il Magiotti, il quale <lb/>appena ebbe scoperta la renitenza certissima dell'acqua alla compressione, <lb/>ed ebbe inventato il vario e graziosissimo modo di que'suoi giochetti idro&shy;<lb/>statici, vide nel pronto operar del dito sui boccioli pieni d'acqua il segreto <lb/>artificio, con cui la volont&agrave; e gl'istinti degli animali operano sui nervi e sui <lb/>muscoli a muovere in una o in altra parte, a piacere, le varie membra. </s>

<s>Il <lb/>Borelli ritrov&ograve; in questo stesso fatto idrostatico uno de'principali fondamenti <lb/>alla sua teoria fisica de'moti muscolari, ma prima di venire a veder pi&ugrave; <lb/>d'appresso e a comprendere tutta in uno sguardo l'opera di chi istitu&igrave; la <lb/>scuola iatromeccanica, giova commemorare altri suoi pi&ugrave; immediati maestri, <lb/>e valutar l'efficacia, ch'ebbero in quella nuova istituzione i loro insegna&shy;<lb/>menti e i loro esempi. </s></p><p type="main">

<s>Primo e principale fra que'maestri, dopo Galileo e il Castelli, sarebbe <lb/>da annoverare il Torricelli, per questa sola ragione, perch&egrave; fu egli che <lb/>instaur&ograve; la Fisica sperimentale. </s>

<s>Ma perch&egrave; egli stesso applic&ograve; direttamente <lb/>le sue esperienze a soggetti varii di storia naturale, e perch&egrave; nelle inven&shy;<lb/>zioni de'suoi strumenti ebbe di mira l'applicazione anche agli usi medici, <lb/>ha perci&ograve; un particolar diritto e un merito speciale d'entrar nel numero <lb/>de'precursori iatromeccanici. </s></p><p type="main">

<s>Che veramente applicasse il Torricelli le sue esperienze del vuoto a <lb/>varii e importantissimi soggetti di Storia naturale ne fanno pubblica testi&shy;<lb/>monianza gli Accademici del Cimento, i quali lasciarono cos&igrave; scritto: &ldquo; Infin <lb/>dal tempo che il Torricelli invent&ograve; la prima esperienza dell'argentovivo, ebbe <lb/>anche pensiero di rinchiudere nello spazio voto diversi animali, per osser&shy;<lb/>vare in essi il moto, il volo, il respiro ed ogni altro eccidente che quivi pa&shy;<lb/>tissero. </s>

<s>Vero &egrave; che, non avendo egli per allora strumenti a proposito per <lb/>questa prova, si content&ograve; di farla com'ei potette &rdquo; (Saggi di natur. </s>

<s>esper., <lb/>Firenze 1841, pag. </s>

<s>67). </s></p><p type="main">

<s>Fu questa notizia senza dubbio suggerita al Segretario dell'Accademia <lb/>dal Borelli, il quale, non potendo attingerla altronde, la raccolse da quelle <lb/>cartucce disperse, che trov&ograve; in Roma uniche e desolate fra la spazzatura <lb/>della casa, dov'era infelicemente morto di peste Raffaello Magiotti. </s>

<s>Attesta <lb/>il Borelli stesso che si contenevano in quelle carte notate quasi tutte l'espe&shy;<lb/>rienze del vuoto fatte poi dagli Accademici del Cimento, ond'&egrave; lecito, dietro <pb xlink:href="020/01/1154.jpg" pagenum="29"/>questi accenni, immaginar come cosa vera una grande operosit&agrave; nel Torri&shy;<lb/>celli, che da Firenze suggeriva l'esperienze, e nel Magiotti, che in Roma <lb/>le eseguiva. </s>

<s>Considerando poi l'inclinazione e il grande amore, con cui il <lb/>Magiotti stesso prediligeva gli studi anatomici e fisiologici, &egrave; lecito altres&igrave; <lb/>pensare che molte pi&ugrave; e di pi&ugrave; vario argomento delle commemorate dagli <lb/>Accademici fiorentini fossero l'esperienze da'due amici tentate in soggetto <lb/>di Storia naturale. </s>

<s>Che se di tanta operosit&agrave; fosse rimasto qualche pubblico <lb/>documento, non aveva forse a gloriarsi il Pecquet d'essere stato il primo <lb/>ad illustrar la scienza anatomica e fisiologica co'suoi nuovi applauditi espe&shy;<lb/>rimenti. </s></p><p type="main">

<s>Che poi il Torricelli, nell'inventare i suoi varii strumenti, non avesse <lb/>solo in mira di compiacere al granduca Ferdinando, ma di provvedere alla <lb/>pubblica utilit&agrave;, per ci&ograve; che pi&ugrave; particolarmente concerne la cura degl'in&shy;<lb/>fermi, lo attesta una scrittura, forse composta dal Viviani, e in ogni modo <lb/>copiata dalla propria mano di lui, e che s'intitola &ldquo; Fabbrica ed uso degli <lb/>strumenti di vetro inventati dal serenissimo granduca Ferdinando II per <lb/>esaminar l'aria, l'acqua, i vini e per altre curiosit&agrave; &rdquo; (MSS. Cim., T. X, <lb/>c. </s>

<s>227). Gli strumenti quivi descritti si riducono alle varie maniere di Pe&shy;<lb/>saliquori e di Termometri, e alcuni di questi s'applicano all'uso di cono&shy;<lb/>scere quando l'uova sono in punto per darsi a bevere a chi &egrave; infermo o di <lb/>stomaco troppo delicato. </s></p><p type="main">

<s>Dop'aver descritti &ldquo; gli strumentini serrati con migliarole di piombo <lb/>dentro, e col collo diviso in gradi 35 ad uso di conoscere le maggiori o mi&shy;<lb/>nori gravit&agrave; in specie de'vini, che vengono dimostrate dal maggiore o minor <lb/>numero di gradi, che sopravanzano al livello di essi vini &rdquo; (ivi) cos&igrave;, nella <lb/>citata Scrittura, si soggiunge: &ldquo; Gli strumentini serrati, col collo diviso in <lb/>gradi 60, servono a questo che, ponendo a cuocere in acqua fredda del&shy;<lb/>l'uova, bench&egrave; senza bucare, con immergervi nell'istesso tempo uno di que&shy;<lb/>sti strumenti, quando il liquore in esso contenuto sar&agrave; salito, per mezzo del <lb/>calor dell'acqua, al minore de'due numeri di gradi segnati di bianco in <lb/>cima a detto strumento, allora l'uova saranno da bere. </s>

<s>E quando ascender&agrave; <lb/>al maggior numero, allora saranno bazzotte, cio&egrave; nello stato mezzano tra le <lb/>lattate e le sode &rdquo; (ivi). </s></p><p type="main">

<s>Di un'altra foggia di Termometro, accomodato ad uso di conoscere l'in&shy;<lb/>tensit&agrave; del calor febbrile, si dice: &ldquo; Gli strumenti fatti a foggia di botticina, <lb/>con sei palline dentro, legati al braccio di un febbricitante, dimostrano, col <lb/>maggiore o minor numero di palline che discendono, il maggiore o minor <lb/>calore del paziente &rdquo; (ivi, c. </s>

<s>229). </s></p><p type="main">

<s>Eccitato dalle parole, che scrivevagli da Roma il Magiotti, e stimolato <lb/>da questi esempii del Torricelli, che apparivano tanto pi&ugrave; luminosi, in quanto <lb/>venivano dati nella stessa aula del Granduca, il Michelini, presi per fonda&shy;<lb/>mento i tre fatti oramai dimostrati dell'insensibile traspirazione, del moto <lb/>del chilo, e del circolo del sangue, institu&igrave; un nuovo sistema di medicina <lb/>e d'igiene. </s>

<s>Fosse per non essere entrato bene addentro nella struttura ana-<pb xlink:href="020/01/1155.jpg" pagenum="30"/>tomica del corpo umano, o per adattarsi alla capacit&agrave; delle intelligenze <lb/>volgari, presentando la Fisiologia sotto forma di apologo, egli usa un lin&shy;<lb/>guaggio figurato. </s>

<s>&ldquo; Io suppongo, egli dice, che il nostro corpo sia uno stru&shy;<lb/>mento composto d'innumerabili canali grandi, piccoli e minimi. </s>

<s>Suppongo <lb/>ancora esservi una cosa, che li muova tutti, e questi io chiamo i lavoranti, <lb/>ed i canali grandi e piccoli le botteghe. </s>

<s>Certi pezzi di carne, come il fegato, <lb/>il cuore, il pancreas chiamo strumentini da lavorare, stritolare e muovere, <lb/>e fare scorrere le robe lavorate d'una in altra bottega &rdquo; (Targioni, Noti&shy;<lb/>zia cit., T. II, P. I, pag. </s>

<s>223). </s></p><p type="main">

<s>Come si potesse ridurre questo sistema, che tanto si rassomiglia a un <lb/>romanzo, alla precisione geometrica, non &egrave; per verit&agrave; cos&igrave; facile intendere, <lb/>ma pure il Michelini seriveva al principe Leopoldo che andava &ldquo; riducendo <lb/>la Filosofia medica, come le cose matematiche o di Euclide, dai primi prin&shy;<lb/>cipii &rdquo; (ivi, T. I, pag. </s>

<s>200). In qualunque modo, piglia lo stesso apologo nel <lb/>Michelini la forma iatromatematica, per quel che di vero e di reale hanno <lb/>i fatti fisiologici della circolazione del sangue e del moto del chilo ivi adom&shy;<lb/>brati, e quando non si volesse attribuire all'Autore altro merito, non si po&shy;<lb/>trebbe negar ch'egli fu de'primi in Italia, ch'ebbe fede nella scoperta ar&shy;<lb/>veiana, e che sent&igrave; la grande efficacia che avrebbe avuto in ridur l'arte <lb/>medica a qualche grado di scienza. </s>

<s>Ripensando ora alla reputazione ch'ebbe <lb/>in matematica don Famiano, e al magistero ch'esercit&ograve; sul Borelli infino <lb/>alla morte, si giudicher&agrave; qual parte di merito gli competa in quella istitu&shy;<lb/>zione iatromeccanica, la quale occorse al discepolo, scendendogli da pi&ugrave; <lb/>parti, come rivi d'acque correnti, che vanno a riversarsi insieme nell'alveo <lb/>d'un gran fiume. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Discepolo affezionatissimo del Castelli, come poi del Michelini, a cui <lb/>venne da Pisa a consolare le agonie della morte, ammiratore dell'ingegno, <lb/>e inquisitor diligente degli studii del Torricelli e del Magiotti, il Borelli trov&ograve; <lb/>ne'loro insegnamenti il principio a quelle dottrine, che avrebbe poi larga&shy;<lb/>mente svolte nella grande Opera Dei moti animali. </s>

<s>Doveva esser questa la <lb/>corona della sua vita e de'suoi studii, e infatti egli mor&igrave; appena preparato <lb/>il manoscritto da servir per la stampa, a cui si legge con mesto pensiero <lb/>premessa la dedica alla Regina di Svezia, sotto signata dal Collegio delle <lb/>Scuole Pie in S. </s>

<s>Pantaleone di Roma, nel Dicembre del 1679. Divisa l'Opera <lb/>in due Parti, gli Scolopi, che ospitaron l'Autore, e poi ne furono eredi, <lb/>pubblicarono nella stessa Roma la prima parte nel 1680, e la seconda nel&shy;<lb/>l'anno appresso. </s></p><p type="main">

<s>Che veramente, come della vita, cos&igrave; fosse il trattato <emph type="italics"/>De motu anima&shy;<lb/>malium<emph.end type="italics"/> la corona degli studii del Borelli, si pu&ograve; asseverar dal sapere che, <pb xlink:href="020/01/1156.jpg" pagenum="31"/>nella stessa intenzione di lui, non furono gli altri libri presi a scrivere per <lb/>altro fine, che per prepararsi a quest'ultimo, a cui da pi&ugrave; che vent'anni <lb/>s'appuntavano tutti i suoi pensieri. </s>

<s>Dall'altra parte i teoremi di Meccanica <lb/>dimostrati nel trattato <emph type="italics"/>De vi percussionis,<emph.end type="italics"/> che &egrave; il primo di que'due libri <lb/>preparatorii, e i principii della Fisica ricercati ed esposti nel trattato <emph type="italics"/>De mo&shy;<lb/>tionibus naturalibus,<emph.end type="italics"/> che &egrave; il secondo di que'libri, dicono abbastanza chiaro <lb/>che il fine dell'Autore era quello di applicare alla nuova scienza della vita <lb/>animale le leggi de'moti gi&agrave; dimostrate, e i fatti gi&agrave; sperimentati nella ma&shy;<lb/>teria bruta. </s></p><p type="main">

<s>Era in ogni modo necessario conoscere la fabbrica del corpo animale, <lb/>a che non tornarono sufficienti le descrizioni, com'erano state fatte dagli <lb/>Anatomici fino a que'tempi, ma ci volevano anatomie particolari, che servis&shy;<lb/>sero di fondamento ai nuovi studii e di conferma alle nuove speculazioni. </s>

<s>E <lb/>perch&egrave; il Borelli non si sentiva per s&egrave; stesso inclinato a trattare i ferri, si <lb/>serv&igrave; della mano di altri, a cui suggeriva i suoi stessi pensieri, e cosi venne <lb/>educando, nella sua propria casa, una scuola, che fece non solamente pro&shy;<lb/>gredire, ma dette abito nuovo all'Anatomia. </s></p><p type="main">

<s>Il bolognese Carlo Fracassati fu uno de'primi e principali, che fioris&shy;<lb/>sero in quella scuola, ed egli stesso confessa nelle sue Dissertazioni l'effi&shy;<lb/>cacia che, a fargli in anatomia scoprir cose nuove, ebbero i pensieri, di che <lb/>sempre era feconda la gran mente del Borelli. </s>

<s>Nella Esercitazione epistolica <lb/><emph type="italics"/>De cerebro,<emph.end type="italics"/> raccolta fra le Opere del Malpighi, descritta ch'egli ivi ha la <lb/>struttura anatomica delle branchie de'pesci, e le parti in esse ordinate a ri&shy;<lb/>cevere i vasellini sanguigni &ldquo; ut pluries, soggiunge, apud excellentissimum <lb/>Borellum Pisis, qui rerum novarum repertor, sectiones anatomicas promovet <lb/>et perdite peperit, sum expertus &rdquo; (Lugduni Batav. </s>

<s>1687, T. II, pag. </s>

<s>143). </s></p><p type="main">

<s>In questa stessa esercitazione <emph type="italics"/>De cerebro,<emph.end type="italics"/> nella quale, senza volere ap&shy;<lb/>parire, il Fracassati aggiunge all'anatomia di quel viscere molte e impor&shy;<lb/>tantissime cose lasciate indietro dal Malpighi, accenna alla invenzione del <lb/>coagulare il sangue nel cuore e nelle vene, da che tanti vantaggi si ripro&shy;<lb/>metteva l'Anatomia, la Fisiologia e la Medicina. </s>

<s>Ei ne attribuisce, con esem&shy;<lb/>pio rarissimo nella storia, il merito principale a Silvestro Bonfiglioli, ch'egli <lb/>chiama il suo Oreste, e non piglia per s&egrave; altra parte a quel merito, che di <lb/>aver messo in esecuzione, nell'anfiteatro pisano, il ritrovato del carissimo <lb/>suo concittadino ed amico (ivi, pag. </s>

<s>158). Il Borelli per&ograve; ci rivela il vero <lb/>Autore dell'invenzione, scrivendo cos&igrave; in una lettera del d&igrave; 6 Marzo 1665, <lb/>diretta da Pisa al principe Leopoldo: &ldquo; Il signor Fracassati ha speculato ed <lb/>esperimentato il modo d'accagliare il sangue nel cuore e nelle vene, e con <lb/>tale artifizio non solo si scoprono i vasi lattei ed altre cose minutissime .... <lb/>ma altri stravaganti effetti &rdquo; (MSS. Cim., T. XVIII, c. </s>

<s>126). </s></p><p type="main">

<s>Si sente per queste relazioni la premura e la compiacenza, che prova&shy;<lb/>vano il Principe e il Maestro in promovere nell'Ateneo toscano gli studii <lb/>anatomici, e il Borelli d&agrave; spesso nelle sue lettere sfogo a quei sentimenti, <lb/>trattenendovisi, a somiglianza degli agricoltori, a riguardar l'ubert&agrave; de'frutti <pb xlink:href="020/01/1157.jpg" pagenum="32"/>maturati sui rami a questo e a quell'altro albero irrorati tutti dalle stille <lb/>del cielo, e dai propri sudori. </s>

<s>Uno di questi alberi pi&ugrave; ubertosi infino dalla <lb/>giovanezza allevato dal Borelli fu il Bellini, di cui cos&igrave; scrive il d&igrave; 17 Mag&shy;<lb/>gio 1662 allo stesso Principe, dopo varie altre notizie: &ldquo; Do poi nuova a <lb/>V. A. come Lorenzo Bellini ha finito di comporre le sue esercitazioni ana&shy;<lb/>tomiche della struttura ed uso de'Reni &rdquo; (ivi, T. XVII, c. </s>

<s>170). </s></p><p type="main">

<s>Diremo a suo luogo quale efficacia avesse esso Borelli sul coltello ana&shy;<lb/>tomico menato dal Bellini intorno alla lingua, per iscoprirvi il vero organo <lb/>del gusto, ma non &egrave; da tacere intanto di un illustre straniero, Claudio Au&shy;<lb/>bery, il quale, bench&egrave; fosse pubblico professore di Anatomia nella scuola <lb/>antica pisana, risent&igrave; nulladimeno i benefici influssi, che venivano sull'arte <lb/>del dissecare dalle speculazioni di chi istituiva fra noi una scuola nuova. </s>

<s>In <lb/>casa di lui, in Pisa, uel 1657, mostr&ograve; l'Aubery la struttura e gli organi se&shy;<lb/>cretori ne'didimi del cinghiale, essendovi presente anche il Malpighi. </s>

<s>&ldquo; Postea <lb/>idem Auberius meo suasu pulcherrimam hanc observationem typis excudit, <lb/>addita eleganti aenea figura Florentiae eodem anno &rdquo; (De Motu anim., Pars II, <lb/>Romae 1681, pag. </s>

<s>342). </s></p><p type="main">

<s>Quel Malpighi per&ograve;, che vien cos&igrave; in ultimo luogo commemorato, &egrave; il <lb/>primo per meriti fra coloro, che s'educarono alle discipline anatomiche nella <lb/>nuova scuola istituita dal Borelli. </s>

<s>Narra il Malpighi stesso nella sua <emph type="italics"/>Auto&shy;<lb/>biografia<emph.end type="italics"/> com'essendo venuto in Pisa coabitasse con Girolamo Barbato, che <lb/>insegnava in quel fiorente studio toscano la medicina pratica. </s>

<s>Egli era, il <lb/>Barbato, attaccatissimo alle dottrine di Galeno e de'pi&ugrave; antichi Maestri, e <lb/>bench&egrave; ne'privati e familiari colloqui s'attentasse di propor talvolta inda&shy;<lb/>gini nuove, pareva nonostante ch'egli facesse ci&ograve; per confutare i placiti al&shy;<lb/>trui, piuttosto che consolidare i suoi proprii. </s>

<s>&ldquo; Interea, prosegue a dire il <lb/>Malpighi, pro exercenda exponendaque. </s>

<s>Anatomia clarissimus D. </s>

<s>Claudius <lb/>Uberius Patavio Pisas evocatur, qui doctissimi D. </s>

<s>Borelli domi frequentes <lb/>habebat animalium sectiones, inter quas celebris est ea qua, me praesente, <lb/>innotuit testium structura intestinalis compaginata, in Apro deprehensa, et <lb/>sub nomine Vavelii Dathirii Bonclari evulgata. </s>

<s>Tunc pariter in Serenissi&shy;<lb/>mis M. D. et principibus ingens excitata est curiositas rerum anatomicarum <lb/>et physicarum, unde quotidianae in Aula ipsa exercitationes Anatomiae in <lb/>variis brutis exercebantur, quibus interpositis graviores politicae curae tem&shy;<lb/>perabantur. </s>

<s>Hinc famosa celebrisque Cimenti Academia excitata est &rdquo; (Opera <lb/>posthuma, Londini 1697, pag. </s>

<s>4). </s></p><p type="main">

<s>Che da tale occasione avesse origine la celebre Accademia &egrave; credibilis&shy;<lb/>simo, e verrebbe solennemente da questo fatto testimoniato il carattere pro&shy;<lb/>prio della istituzione borelliana, nella quale l'Anatomia si disposava colla <lb/>Fisica. </s>

<s>Come poi prevalesse nelle sessioni accademiche l'esercizio delle espe&shy;<lb/>rienze a quello delle dissezioni, non &egrave; difficile intenderlo dietro ci&ograve; che si <lb/>disse nel nostro Discorso preliminare, a cui rimandando i lettori, pensiam <lb/>d&igrave; ritornare al Malpighi promotore validissimo della scienza, intorno alla <lb/>quale ha da trattenersi la nostra Storia. </s></p><pb xlink:href="020/01/1158.jpg" pagenum="33"/><p type="main">

<s>Abbiamo udito dalla sua propria bocca come si sentisse chiamato al&shy;<lb/>l'Anatomia dalle dissezioni vedute fare all'Aubory nelle case del Borelli, a <lb/>cui, tornato a Bologna, dedic&ograve; la prima insigne scoperta delle vescicole e <lb/>delle cellule de'polmoni. </s>

<s>Presto per&ograve; si alienarono gli animi, intorno a che <lb/>lasci&ograve; cos&igrave; scritto il Malpighi nella sopra citata autobiografia. </s>

<s>&ldquo; Miraberis, <lb/>lector, doctissimum Joannem Alphonsum Borellum, quem nuper amice mea&shy;<lb/>rum Epistolarum editionem sollicitantem audivimus, nunc contradicentem <lb/>castigantemqque erumpere. </s>

<s>Huius autem impulsiva causa ea fuit quoniam, <lb/>intermisso a me litterario cum ipso commercio, ita in me meaque indigna&shy;<lb/>bundus exarsit, ut in his quae ultimo senio composuit, qualia sunt De ani&shy;<lb/>malium motu, occasionem arripuerit mea infirmandi &rdquo; (ibi, pag. </s>

<s>5). </s></p><p type="main">

<s>Che fosse questo il solo o il principal motivo, per cui il Borelli alien&ograve; <lb/>e convert&igrave; l'animo iroso contro il Malpighi, non &egrave; da credere in un tal uomo: <lb/>stillavano quelle amarezze da fonti pi&ugrave; segrete, che il nostro Autobiografo <lb/>o non sospett&ograve;, o non si cur&ograve; di ricercare, ma che non &egrave; molto difficile a <lb/>noi di penetrarle. </s>

<s>Le nuove cose, che in Anatomia andava scoprendo il Mal&shy;<lb/>pighi, e le speculazioni, ch'egli ammanniva dietro a quelle scoperte, lo vol&shy;<lb/>gevano per una via diversa, da quella che il Borelli avea prescritta alla sua <lb/>scuola, e sulla quale s'erano sempre tenuti, il Fracassati e il Bellini. </s>

<s>Il Mi&shy;<lb/>croscopio, felicemente applicato ad osservar le parti dissecate ne'cadaveri <lb/>degli animali e ne'tronchi degli alberi, fece penetrare il Malpighi addentro <lb/>alla composizione degli organi, per cui, risalendo di cost&igrave; a filosofare intorno <lb/>alle funzioni della vita, sent&igrave; vivamente il bisogno di un'arte pi&ugrave; sottile di <lb/>quel che non fosse la Fisica borelliana. </s>

<s>Si fece sentir cotesto bisogno in sul <lb/>primo entrare alle microscopiche scoperte fatte intorno alla compagine dei <lb/>polmoni, e la natura delle vescicole, rivelando l'azione immediata dell'aria <lb/>sul sangue, dette luogo a speculare sull'ematosi, intorno a che nacque fra <lb/>il Borelli e il Malpighi una delle principali divergenze. </s></p><p type="main">

<s>&Egrave; giusto da queste divergenze che si rivela come il Malpighi incli&shy;<lb/>nasse a invocare la iatrochimica, la quale derivava dal Cartesio, come la <lb/>iatrofisica professata dal Borelli derivava da Galileo. </s>

<s>Non &egrave; gi&agrave; che il grande <lb/>Anatomico di Bologna, e che aveva in Pisa imbevuti i principii della scienza <lb/>nelle case del Borelli, intendesse di disertare dalla Scuola italiana, ma vo&shy;<lb/>leva, con consiglio che si dee dire sapiente, delibar anche dalla Filosofia del <lb/>Cartesio quel che ci avesse di buono o che facesse al bisogno. </s>

<s>&Egrave; perci&ograve; che <lb/>nella Autobiografia, dop'aver raccontato come Ovidio Montalbani persuadesse <lb/>il Rettore dell'Universit&agrave; di Torino a proporre ai giovani dottorandi in me&shy;<lb/>dicina questa formula di giuramento: &ldquo; iurabis doctrinam eam te servatu&shy;<lb/>rum et defensurum esse quae publice praelegitur in archigymnasio bono&shy;<lb/>niensi, aliisque in studiis famosis, secundum eos Auctores a tot saeculis iam <lb/>approbatos, qui explicandi et declarandi per Gymnasiarchas doctoribus et <lb/>professoribus ipsis proponuntur, Aristotilem nempe, Galenum et Hippocra&shy;<lb/>tem &rdquo; (ibi, pag. </s>

<s>21), il Malpighi brevemente toccando de'progressi, che aveva <lb/>fatto la scienza nel succedersi di tanti secoli, protesta anch'egli di volerla <pb xlink:href="020/01/1159.jpg" pagenum="34"/>coltivare a quel modo, che avevano ultimamente insegnato il Cartesio e il <lb/>Castelli. </s>

<s>&ldquo; Haec itaque a Graecis exculpta, subsequentibus Arabum Barba&shy;<lb/>rorumque dogmatibus inquinata iacuit, donec vigentibus hoc saeculo iterum <lb/>Anatomicis studiis incrementum coepit, et mechanicis firmata fortiori talo <lb/>stare coepit. </s>

<s>Cum igitur Graecorum et antiqua Italorum sapientia apud Si&shy;<lb/>culos olim floruerunt et novis Cartesii Castellique inventis vigere coeperit, <lb/>hanc eamdem excolendam me professurum pollicitus sum &rdquo; (ibi, pag. </s>

<s>25). </s></p><p type="main">

<s>La nuova Fisica insomma e la nuova Meccanica applicate alle scienze <lb/>mediche le riconosceva il Malpighi derivar da due fonti, dal Castelli o da <lb/>Galileo e dal Cartesio, il quale coltivando a preferenza la fisica sottile o mo&shy;<lb/>lecolare, ch'era un'ombra della chimica moderna, secondava molto il genio <lb/>di quello stesso Malpighi investigator cos&igrave; acuto de'sottilissimi stami, di che <lb/>s'intesse la vita. </s>

<s>S'aggiunga di pi&ugrave; che il Cartesio aveva insegnato a filoso&shy;<lb/>fare intorno all'uomo e intorno alle passioni di lui da fisiologo, mentre che <lb/>Galileo si rimase indifferente alle grandi scoperte dell'Asellio e dell'Harveio, <lb/>e il Castelli non ebbe appena messo il piede in quel campo, che lo ritrasse, <lb/>protestando non esser quella la sua professione. </s></p><p type="main">

<s>Il Cartesio rec&ograve; anche nell'Anatomia i suoi vizii filosofici, i quali prin&shy;<lb/>cipalmente consistono nel volere accomodare i fatti alla ragione. </s>

<s>Distingue <lb/>nella fabbrica del corpo umano due parti: una visibile, la quale egli dice si <lb/>pu&ograve; ciascuno far mostrare ai periti dell'arte; un'altra invisibile, di che egli <lb/>solo intende farsi a tutti gli altri maestro. </s>

<s>&ldquo; Non haereo, scriveva nell'in&shy;<lb/>troduzione al trattato <emph type="italics"/>De homine,<emph.end type="italics"/> in describendis ossibus, nervis, musculis, <lb/>venis, arteriis, stomacho, iecore, corde, cerebro et partibus omnibus aliis.... <lb/>quas curare quis potest sibi demonstrari a perito Anatomico..... Et quan&shy;<lb/>tum ad partes, quae ob parvitatem suam visibiles non sunt, eas facilius et <lb/>clarius potero notas facere, tractando de motibus qui pendent inde &rdquo; (Fran&shy;<lb/>cofurti ad M. 1692, pag. </s>

<s>2). </s></p><p type="main">

<s>Passando infatti, nella seconda parte del libro a trattare de'moti mu&shy;<lb/>sculari, egli immagin&ograve; che spiri dal cervello un vento, il quale entrando e <lb/>uscendo per opportune valvole ne'muscoli ora gli fa inturgidire, ora sgon&shy;<lb/>fiare. </s>

<s>I condotti di quel vento e le valvole nessuno Anatomico le aveva po&shy;<lb/>tute vedere, ma ci&ograve; non vuol dir niente, rispondeva il Cartesio, perch&egrave; ho <lb/>detto che sono invisibili, e da un'altra parte come potrebbe meglio operar <lb/>la Natura di quel che la mia Filosofia cos&igrave; sottilmente le insegna? </s>

<s>&mdash; Or, <lb/>queste al Borelli, discepolo de'discepoli di Galileo, sembravan pazzie, n&egrave; po&shy;<lb/>teva perci&ograve; patire che nessuno Italiano disertasse dalle sapienti instituzioni <lb/>della sua propria scuola, per andar dietro alle follie della scuola straniera. </s>

<s><lb/>Tanto meno poteva ci&ograve; sopportare quell'uomo sdegnoso nel Malpighi, a cui <lb/>aveva egli stesso instillati gli schietti principii della Filosofia galileiana. </s></p><p type="main">

<s>I vizii propri al razionalismo cartesiano, che aveva si pu&ograve; dire sedotto <lb/>il mondo filosofico di que'tempi, venivan nonostante palliati agli occhi degli <lb/>Anatomici dal vedere il Cartesio stesso lasciar da parte le finzioni della <lb/>mente, per risolversi a toccar con mano i fatti concernenti i moti del cuore, <pb xlink:href="020/01/1160.jpg" pagenum="35"/>e poi rivolgersi a quella grande autorit&agrave; dell'Harvey, per dirgli che stavano <lb/>in tutt'altro modo da ci&ograve; che gli avea descritti. </s>

<s>Vedremo a suo luogo come, <lb/>anche in questi seducenti modi di argomentare dalle esperienze e dai fatti <lb/>osservati nelle vivisezioni, fossero riconosciuti i soliti vizii filosofici, i quali <lb/>forse potevansi scusare in quel trattato, dove insegnavasi per la prima volta <lb/>a studiar l'uomo, non nelle metafisiche astrattezze, ma nella fisiologia degli <lb/>organi del corpo, e nell'anatomia di quegli strumenti, di che si serve l'anima <lb/>per impossessarsi del mondo, e per esercitare il pensiero. </s>

<s>Molte altre son <lb/>le fisiologiche dottrine che ricorrono nel trattato <emph type="italics"/>De homine,<emph.end type="italics"/> e che sono in&shy;<lb/>fette non solamente di errori, ma di vizii proprii al razionalismo peripate&shy;<lb/>tico cartesiano, e nonostante il vederle assunte dal Filosofo, che le riveste <lb/>dell'affascinante splendore della sua eloquenza, invitava a ricever le inspi&shy;<lb/>razioni da lui e a pigliar l'abito di quel suo filosofare molti, anche di quei <lb/>che attendevano allo studio del corpo umano e delle sue funzioni. </s>

<s>Si distinse <lb/>fra costoro in Italia Tommaso Cornelio, il quale coltiv&ograve; l'Anatomia e la Fi&shy;<lb/>siologia in quell'Accademia di Napoli, dove Luca Anton&igrave;o Porzio instaurava <lb/>con tanto zelo la Fisica del Cartesio. </s>

<s>Notabile che il Cornelio si professi di&shy;<lb/>scepolo di Michelangiolo Ricci, e dedichi una sua scrittura in segno di ami&shy;<lb/>cizia al Borelli, il quale forse non lo avvers&ograve; come avversava il Malpighi, <lb/>perch&egrave; lo sentiva meno potente a infirmare la sua istituzione, lo zelo verso <lb/>la quale veniva sollecitato dall'amor proprio, che gli suggeriva dover egli <lb/>solo costituirsi principe della Scuola iatromeccanica. </s>

<s>Fu perci&ograve; ch'egli ebbe <lb/>a studiarsi di far dimenticare l'opera di alcuni suoi predecessori, e come ci&ograve; <lb/>gli succedesse felicemente, cos&igrave; per i meriti propri, come per gli eventi na&shy;<lb/>turali, &egrave; ci&ograve; che intorno al presente soggetto ora a noi resta a narrare. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Antonio Deusing pubblicava in Croninga, nel 1661, le sue esercitazioni <lb/><emph type="italics"/>De motu animalium,<emph.end type="italics"/> dove tratta particolarmente del moto de'muscoli e <lb/>della respirazione. </s>

<s>Egli per&ograve;, ferventissimo Galenista e ritroso ad ammettere <lb/>qualunque novit&agrave; si volesse introdur nella scienza, non fa, rispetto ai moti <lb/>animali, altro che commentare e svolgere a suo modo i concetti meditati sui <lb/>libri del suo antico Maestro. </s>

<s>Il Muller e lo Charletton, contro i quali prin&shy;<lb/>cipalmente insorge il Deusingio, intendevano di sostituire allo spiritalismo <lb/>galenico la fisica del fluido nerveo, iniziando cos&igrave; le ipotesi, che verrebbero <lb/>sotto tanto varie forme proposte da'Fisiologi successori, ma Niccol&ograve; Stenone <lb/>riconobbe esser quelle ipotesi troppo affrettate, e che bisognava apparec&shy;<lb/>chiarvisi con una pi&ugrave; diligente Anatomia muscolare. </s>

<s>A tale intento pubblic&ograve; <lb/>in Amsterdam, nel 1664, il suo Saggio di osservazioni <emph type="italics"/>De musculis et glan&shy;<lb/>dulis,<emph.end type="italics"/> dove l'arte del sezionare par da quelle descrizioni che sia giunta <pb xlink:href="020/01/1161.jpg" pagenum="36"/>oramai alla sua maggior perfezione. </s>

<s>Venuto in Toscana, per le virt&ugrave; e per <lb/>la scienza si rese in pregio e amabilissimo ai principi Medicei, e ai dotti <lb/>che fiorivano nella loro Accademia e nella Universit&agrave; di Pisa, dove infin d'al&shy;<lb/>lora il Borelli, dietro esperienze instituite sopra ogni genere di animali, <lb/>speculava intorno a quella ch'egli era solito dire sua nuova e maravigliosa <lb/>Filosofia. </s></p><p type="main">

<s>Tra gli Accademici del Cimento, co'quali si leg&ograve; lo Stenone in pi&ugrave; in&shy;<lb/>tima amicizia, fu Vincenzio Viviani, il quale, concorrendo a gara col Borelli <lb/>in ogni altra delle varie parti in che si distingueva la scienza naturale, per <lb/>questa sola si sentiva rimanere indietro, che concerne gli organi degli ani&shy;<lb/>mali, non avendo avuto occasione d'esercitarvisi, n&egrave; comodit&agrave; di servirsi <lb/>della mano de'Notomisti pisani. </s>

<s>Ma quand'ei ritrov&ograve; nello Stenone, intrat&shy;<lb/>tenuto seco ai servigi di corte in Firenze, quel che aveva in Pisa il Borelli <lb/>ritrovato nell'Aubery, nel Fracassati e nel Bellini, e allora fu che, trasfor&shy;<lb/>matesi le prime emulazioni in fierissime inimicizie, pens&ograve; a fare ogni opera <lb/>perch&egrave; si avesse a disdire chi, colle parole, senza ancora mostrare in pub&shy;<lb/>blico i fatti, si diceva primo Autore e maestro di una nuova Filosofia ma&shy;<lb/>tematica applicata agli organi e alle funzioni della vita. </s></p><p type="main">

<s>Discorrevano ne'frequenti colloqui lo Stenone e il Viviani de'loro stu&shy;<lb/>dii, cosicch&egrave; la Geometria dell'uno, riscontrandosi con l'Anatomia dell'altro, <lb/>strinsero, senz'avvedersene, insieme un maraviglioso connubio. </s>

<s>Fermo l'Ana&shy;<lb/>tomico danese nel suo primo proposito, che cio&egrave; fosse necessario descrivere <lb/>i muscoli con pi&ugrave; diligenza di quel che non si fosse fatto per lo passato, si <lb/>studiava di ridurli alle loro proprie forme distinte, sotto gli occhi del Vi&shy;<lb/>viani, che intravedeva in quelle stesse forme il sapiente magistero della geo&shy;<lb/>metrizzante Natura. </s>

<s>Ebbe di qui origine lo <emph type="italics"/>Specimen Myologiae,<emph.end type="italics"/> ossia la <lb/>Descrizione geometrica de'muscoli, e perch&egrave;, venendo pubblicato e dedicato <lb/>il libro al granduca Ferdinando II a nome dello Stenone, non fosse il Vi&shy;<lb/>viani defraudato della sua parte, si conclude dall'Autore stesso con queste <lb/>parole: &ldquo; Ne vero quisquam ingenio, potius quam experientiae, haec attri&shy;<lb/>buat, amicissimum mihi Vincentium Viviani Serenissimi Magni Ducis Mathe&shy;<lb/>maticum testem appello, qni hisce aliisque praesenti libro contentis plusquam <lb/>spectator adfuit &rdquo; (Florentiae 1667, pag. </s>

<s>119). </s></p><p type="main">

<s>Il libro dunque dell'Anatomico di Coppenhagen, informato alla Geome&shy;<lb/>tria del matematico di Firenze, usciva fuori come cosa nuova e nuove suo&shy;<lb/>navano alle orecchie dei pi&ugrave; quelle parole scritte nella dedica al Granduca, <lb/>e nelle quali si diceva ch'essendo il nostro corpo un organo composto di <lb/>mille altri organi chi presumeva di volerne aver qualche cognizione, senza <lb/>l'uso delle Matematiche, faceva conto d'avere a investigare una materia <lb/>senza estensione, o un corpo senza figura. </s>

<s>N&egrave; altra si soggiungeva esser <lb/>l'origine di quegli innumerevoli errori, che insozzano la storia del corpo <lb/>umano &ldquo; quam quod Matheseos leges Anatome hactenus indignata fuerit. </s>

<s>&rdquo; </s></p><p type="main">

<s>Recalcitravano alle novit&agrave; gli Aristotelici e i Galenisti, i quali non sa&shy;<lb/>pevano comprendere come c'entrasse la Matematica nella loro arte, non usa <pb xlink:href="020/01/1162.jpg" pagenum="37"/>a sottostare ad altra disciplina, che all'autorit&agrave; de'suoi primi istitutori, e <lb/>tacitamente si mostrava avverso per gelosia, vedendo esser messa la falce <lb/>nella proda di quel campo, che largamente coltivava, il Borelli co'valorosi <lb/>seguaci della sua scuola: cosicch&egrave; la Miologia geometrica dello Stenone ri&shy;<lb/>mase senza i favori cos&igrave; di chi amava le novit&agrave;, come di chi le aborriva. </s></p><p type="main">

<s>Il Viviani si sentiva pi&ugrave; dello stesso Stenone accorato di questo repu&shy;<lb/>dio, per parte massimamente di coloro che secondavano i progressi della <lb/>scienza, e conoscendo l'animosit&agrave; del Borelli consigliava il principe Leopoldo <lb/>a interpellare il giudizio de'matematici al Borelli stesso non ossequenti, <lb/>fra'quali era uno de'primi il padre Stefano Angeli. </s>

<s>Nel mese dunque di <lb/>Maggio del 1667 il Principe sped&igrave; a lui una copia della Miologia stenoniana <lb/>accompagnata da una lettera, nella quale si lamentava la poco favorevole <lb/>accoglienza, che avevano ritrovato nel pubblico i nuovi studii. </s>

<s>L'Angeli, il <lb/>d&igrave; 4 di Giugno di quel medesimo anno 1667, rispondeva cos&igrave; da Venezia: </s></p><p type="main">

<s>&ldquo; Mi ha consolato indicibilmente il signore Stenone, vedendo con quanta <lb/>sottigliezza dilata li termini della Geometria, facendo egli anche nell'Anato&shy;<lb/>mia conoscere quanto sia impossibile poter senza Geometria filosofare in qual <lb/>si sia cosa. </s>

<s>Lo compatisco per&ograve; in estremo, mentre vedo che il suo Libro, <lb/>quantunque sia di materia professata da tanti de'quali sono propriet&agrave; <emph type="italics"/>hone&shy;<lb/>ste vestiri, gloriose mentiri<emph.end type="italics"/> ecc., nulladimeno &egrave; per incontrare pochissima <lb/>fortuna. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La Geometria, anche ne'suoi principii, &egrave; intesa da pochi, e sprezzata <lb/>per lo pi&ugrave; dai signori medici, ad alcuni de'quali avendo io lodato il libro <lb/>del signore Stenone l'hanno sprezzato come innovatore, e giurato, per la <lb/>loro veneranda e prolissa barba e corti capelli, di non lo voler n&egrave; anco <lb/>vedere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Tale per&ograve; non &egrave; il signor Molinetto nostro anatomico di Padova, che <lb/>da me di ci&ograve; informato mi risponde con una lettera, che sebbene scritta con <lb/>quella familiarit&agrave; che fra noi passa, invio a V. A. S. </s>

<s>Il Molinetto &egrave; uomo di <lb/>pronto ingegno: ha una facondia e prontezza straordinaria. </s>

<s>Nella cattedra, <lb/>per la sua franchezza di dire, chiarezza e galanteria d'esprimere i suoi sensi, <lb/>ha pochi pari. </s>

<s>Non intende per&ograve; Geometria, quantunque abbi talenti atti ad <lb/>ogni cosa. </s>

<s>Fra'molti discorsi, cha ho avuti seco quante alli muscoli, non mi <lb/>pare molto lontano da'pensieri del signore Stenone. </s>

<s>Solo, non avendo co&shy;<lb/>gnizione di Geometria, non crede abbi geometrizzato sopra essi, riducendo <lb/>la parte media a parallelepipedo, e li tendini a prismi tetragonali. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io ho letto il libro del signore Stenone ed inteso quello dice, ma <lb/>non posso accertarmi di quel che dice con li miei occhi, essendo senza al&shy;<lb/>cuna cognizione di Anatomia, impedito sempre dalla mia schifa natura, che <lb/>non permette veder cosa alcuna in questo proposito senza nausea, scon&shy;<lb/>volgimento di stomaco e inappetenza per molti giorni. </s>

<s>&rdquo; (MSS. Cim., T. XIX, <lb/>c. </s>

<s>27). </s></p><p type="main">

<s>L'avversione del Borelli alle novit&agrave; stenoniane, alle quali aveva presa <lb/>cos&igrave; gran parte l'odiato Viviani, accennammo essere stata segreta, e bench&egrave; <pb xlink:href="020/01/1163.jpg" pagenum="38"/>sia certa, considerata l'indole dell'uomo, non abbiamo per&ograve; a provarla, se <lb/>non che argomenti negativi dedotti dal trattato <emph type="italics"/>De motu animalium,<emph.end type="italics"/> dove <lb/>o si tace o si rappresentano i fatti in modo da levare una parte del merito <lb/>all'opera dello Stenone. </s>

<s>Nella proposizione XXXVII della P. II, per esem&shy;<lb/>pio, si tratta dal Borelli della struttura del cuore, ma fra coloro, ch'eser&shy;<lb/>citarono lo stile per quegli intricatissimi laberinti, non si commemora se non <lb/>che il Malpighi, il Lower e il Bellini, mentre fu forse lo Stenone che smarr&igrave; <lb/>meno la via di tutti gli altri. </s></p><p type="main">

<s>Nella proposizione LXXX della I Parte, si propone il Borelli di dimo&shy;<lb/>strare a priori che i muscoli radiosi si debbono necessariamente comporre <lb/>di pi&ugrave; muscoli penniformi, cosa ch'era stata gi&agrave; dimostrata di fatto dallo <lb/>Stenone nella elegantissima fabbrica del Muscolo deltoide, rappresentata in <lb/>scolpitissimo disegno nella III Tavola della Miologia. </s>

<s>Or perch&egrave; questa volta <lb/>l'Anatomico era necessario invocarlo a confermare le speculazioni del Filo&shy;<lb/>sofo, nello scolio alla citata proposizione il Borelli stesso scriveva: &ldquo; Hanc <lb/>musculorum radiosorum structuram, quam mechanicum ratiocinium mihi <lb/>suaserat, experimentis confirmare non licuit, nisi imperfecte in locustis ma&shy;<lb/>rinis et gammaris. </s>

<s>Postea valde gavisus sum cum viderem diligentissimos et <lb/>praeclaros anatomicos Stenonem et Loverium in humano musculo Deltoide <lb/>belle et exacte eamdem structuram observasse et diligentissime delineatam <lb/>edidisse &rdquo; (Editio cit., pag. </s>

<s>161). </s></p><p type="main">

<s>Ma bench&egrave; in ogni modo la Miologia dello Stenone avesse posto come <lb/>dicemmo la falce per le prode del campo, rimaneva al Borelli intatta la pi&ugrave; <lb/>larga e pi&ugrave; fruttuosa cultura di esso, e dall'altra parte non doveva la nuova <lb/>Filosofia borelliana trattenersi solamente a ridurre i muscoli alle forme geo&shy;<lb/>metriche, ma co'principii matematici dimostrarne la legge dei moti. </s>

<s>Poteva <lb/>per queste ragioni il Borelli assicurarsi che l'Opera sua tornava nuova e <lb/>non adombrare per parer che l'avessero prevenuta lo Stenone stesso e il <lb/>Viviani. </s></p><p type="main">

<s>Se c'era stato qualcuno che avesse veramente prevenuta l'opera <emph type="italics"/>De <lb/>motu animalium<emph.end type="italics"/> era costui piuttosto Guglielmo Croone, il quale, essendo <lb/>amico e connazionale dello Stenone, e avendo conferito pi&ugrave; volte con lui <lb/>intorno al difficilissimo soggetto dei moti musculari, deliber&ograve; di dare alla <lb/>luce in Amsterdam il suo trattatello <emph type="italics"/>De ratione motus musculorum,<emph.end type="italics"/> in quel <lb/>tempo che aveva sentito dire essere sotto i torchi la Miologia stenoniana. </s>

<s>&Egrave; <lb/>quel trattatello, secondo noi, notabilissimo nella storia, perch&egrave; vi si d&agrave; il <lb/>primo saggio della vera Meccanica animale, e il difficile problema della po&shy;<lb/>tenza de'muscoli nel braccio dell'uomo, sui dati dell'esperienza, si risolve <lb/>con l'aiuto dell'Analisi matematica. </s></p><p type="main">

<s>Per quanto abbia importanza storica il trattatello del Croone, non de&shy;<lb/>trasse per&ograve; nulla all'opera del Borelli, la quale, in quella sua ampiezza di <lb/>trattazione, informata a un'unit&agrave; di principio, apparve a tutti nuova e ma&shy;<lb/>ravigliosa. </s>

<s>Tale giova credere che apparisse anche al giudizio del Viviani, a <lb/>cui i padri Scolopi di Roma davano, per lettera del d&igrave; 19 Aprile 1681, an-<pb xlink:href="020/01/1164.jpg" pagenum="39"/>nunzio della pubblicazione della I Parte <emph type="italics"/>De motu animalium,<emph.end type="italics"/> e dicevano di <lb/>far ci&ograve;, per secondare la volont&agrave; dell'Autore &ldquo; il quale, nel passare che fece <lb/>all'altra vita in questa nostra casa di S. Pantaleone, caldamente ci racco&shy;<lb/>mand&ograve; che, subito terminata la stampa, quale egli stava in procinto di co&shy;<lb/>minciare, ne facessimo partecipi i professori di tali materie &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. CXLVI, c. </s>

<s>235). </s></p><p type="main">

<s>L'istituzione del Borelli doveva poi, non al Viviani solo ma a tutti, e <lb/>specialmente agli Italiani apparire meravigliosa, anche per questo, perch&egrave; <lb/>non furono avversate le novit&agrave; di lei, come furono avversate le novit&agrave; della <lb/>istituzione cartesiana ne'due pi&ugrave; insigni fautori che avesse fra noi, Tommaso <lb/>Cornelio e Marcello Malpighi. </s></p><p type="main">

<s>Del primo di questi due ne abbiamo il ritratto in una lettera di Gio&shy;<lb/>vanni Fink, anatomico nello studio di Pisa, e mandato da'principi Medicei, <lb/>insiem con Tommaso Baines, a viaggiare pel Napoletano e per i dintorni di <lb/>Roma, perch&egrave; vi facessero diligente raccolta di oggetti di storia naturale, di <lb/>libri di Anatomia e di Medicina, e perch&egrave; prendessero notizia degli scien&shy;<lb/>ziati, che avessero per quelle parti pi&ugrave; rinomanza. </s>

<s>&ldquo; A Napoli, riferiscono <lb/>al principe Leopoldo i due viaggiatori, abbiamo avuto particolarissima no&shy;<lb/>tizia del signor Tommaso Cornelio, matematico e medico di grande grido ed <lb/>amico del signor Michelangiolo Ricci. </s>

<s>Lui ha scritto un libro intitolato <emph type="italics"/>Pro&shy;<lb/>gymnasmata physica:<emph.end type="italics"/> &egrave; stampato a Venezia, ed una parte di esso dedicata <lb/>al signor D. </s>

<s>Alfonso Borelli. </s>

<s>Lui &egrave; cartesiano, e molto difensore delle cose <lb/>nuove, onde viene a Napoli ad essere odiato da quelli, che giurano fedelt&agrave; <lb/>alli loro maestri. </s>

<s>Quel signore dice in suo libro che lui sia stato inventore <lb/>della ipotesi della compressione dell'aria e della forza elastica di quella innanzi <lb/>Pecqueto ed ogni altro. </s>

<s>&Egrave; della nazione calabrese, uomo vivo ed acuto, ma, <lb/>come la maggior parte di quella, molto caldo &rdquo; (MSS. Cim., T. XVII, <lb/>c. </s>

<s>224). </s></p><p type="main">

<s>N&egrave; meno odiato del Cornelio, com'abbiamo udito dal Fink, era il Mal&shy;<lb/>pighi, il quale faceva il Microscopio rivelatore, ne'succhi delle piante e nel <lb/>sangue, de'misteri della chimica cartesiana. </s>

<s>Se la presero perci&ograve; i suoi fu&shy;<lb/>riosi nemici anche col Microscopio, ond'&egrave; ch'egli, il Malpighi, ebbe a di&shy;<lb/>fenderne l'uso e a mostrare i servigi che aveva resi alla scienza, come fa, <lb/>per recare un esempio curioso, quando spiega in che modo l'ortica battuta <lb/>sopra la nostra pelle si faccia urente. </s>

<s>Il Microscopio svela, egli dice, che ci&ograve; <lb/>dipende dalle spine, di che si vedono essere irsute le foglie dell'ortica; spine <lb/>tutte piene di un sugo attivo, che s'inocula nel sangue. </s>

<s>&ldquo; E perch&egrave; &egrave; assai <lb/>verosimile, prosegue a dire, che il sugo che si trova negli utricoli trasver&shy;<lb/>sali e nelle fibre, le quali compongono il caule e le foglie dell'ortica, sia <lb/>dell'istessa natura, di qui ne nasce che il Microscopio pu&ograve; portare qualche <lb/>lume non solo al mal prodotto dalle spine, ma anche al modo d'operare <lb/>che fa il sugo dell'ortica fermentando prima e poi fissando, come fa lo spi&shy;<lb/>rito di vetriolo infuso nelle vene &rdquo; (Opera posth. </s>

<s>cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Si dir&agrave; che i nemici del Cornelio e del Malpighi, ne'quali due soli ab-<pb xlink:href="020/01/1165.jpg" pagenum="40"/>biamo voluto rappresentare tutti coloro, che trattavano le scienze fisiologi&shy;<lb/>che coi principii della Filosofia cartesiana, crano peripatetici, ma questa che <lb/>pareva una opposizione &egrave; invece una conferma al nostro argomento, perch&egrave; <lb/>essendo costoro, per istituto della loro scuola, inclinati ad avversare cos&igrave; il <lb/>Cartesio come il Borelli, se tanto furiosamente si sollevarono contro quello, <lb/>e non contro questo, ripetiamo che, sebbene abbia ci&ograve; la sua ragion natu&shy;<lb/>rale, &egrave; pure un fatto, che ha l'apparenza di maraviglioso. </s>

<s>Quella ragion na&shy;<lb/>turale &egrave; forse a investigarsi pi&ugrave; difficile di quel che a primo aspetto non <lb/>sembrerebbe, e perci&ograve; lasciando il carico di farlo a chi &egrave; pi&ugrave; acuto di noi, <lb/>ci contenteremo di concludere che, non essendo la nuova Filosofia del Bo&shy;<lb/>relli avversata da'Peripatetici, e venendo dall'altra parte con tanto favore <lb/>accolta da chi attendeva con pi&ugrave; sano giudizio agli studii, pot&egrave; solidamente <lb/>instaurarsi a benefizio comune della scienza, e, in mezzo alle rivalit&agrave; carte&shy;<lb/>siane e alle ingerenze straniere, apparir d'origine e mantenersi schiettamente <lb/>italiana. </s></p><p type="main">

<s>Tale, quale si conclude dal nostro discorso, fu il principio, e tali furono <lb/>le avventure della scuola iatromatematica, da non lasciarsi qui da noi senza <lb/>un breve esame, che ne riveli l'indole e ci faccia estimare i meriti della <lb/>nuova istituzione. </s>

<s>Le funzioni della vita si riducono per essa, nelle piante <lb/>e negli animali, alle leggi della Fisica. </s>

<s>Cos&igrave; per esempio l'ascendere della <lb/>linfa su per i vasellini de'tronchi e de'rami s'attribuisce a quella forza <lb/>fisica, che fa risalire il liquido su per i tubi capillari: il corso del sangue <lb/>per le arterie e per le vene si regola, nella velocit&agrave; del suo moto, dietro le <lb/>leggi idrauliche, e la forza de'muscoli nel contrarsi si paragona alla forza <lb/>di trazione che s'esercita, imbevute che sieno d'umidit&agrave;, nelle funi. </s>

<s>L'oc&shy;<lb/>chio si riguarda come uno strumento ottico fabbricato dall'arte, e l'orec&shy;<lb/>chio come uno strumento acustico. </s></p><p type="main">

<s>Chi ben considera, comprender&agrave; quanto dovess'essere seducente questa <lb/>nuova Filosofia, quando a svelare i misteri della vita o non s'avevano ra&shy;<lb/>gioni, o quelle che s'adducevano si conoscevano troppo bene da'savi per <lb/>sogni di romanzi. </s>

<s>Il sostituire le cause fisiche a que'sogni si reput&ograve; come <lb/>uno de'pi&ugrave; grandi progressi, che avesse fatto la scienza, ed ebbero di qui <lb/>origine i vittoriosi trionfi della istituzion borelliana. </s></p><p type="main">

<s>S'incominciarono per&ograve; presto a raffreddare que'primi fervori, quando <lb/>l'Anatomia, giunta alla sua ultima perfezione, tanto riusc&igrave; ad assottigliare <lb/>la punta dello stile e l'acume della vista, da penetrare addentro al pi&ugrave; se&shy;<lb/>greto magistero degli organi de'sensi. </s>

<s>Il Valsalva, il Morgagni, il Cotugno <lb/>e lo Scarpa, per non commemorare fra'nostri che i principali, descrissero <lb/>cos&igrave; la fabbrica dell'orecchio e dell'occhio, e si sollevarono da quelle de&shy;<lb/>scrizioni a filosofare intorno a que'due nobilissimi organi tant'alto, che di <lb/>lass&ugrave; volgendosi indietro videro quanto gli strumenti acustici e la camera <lb/>ottica, tutte cose morte, fossero per s&egrave; miseri a rappresentar, nell'udito e <lb/>nella vista, lo spirito che v'infonde la vita. </s>

<s>Poi, per pi&ugrave; diligenti esperienze <lb/>condotte principalmente dall'Haller e dallo Spallanzani, si trov&ograve; che il moto <pb xlink:href="020/01/1166.jpg" pagenum="41"/>del sangue nelle arterie e nelle vene non segue precisamente le leggi idrau&shy;<lb/>liche, e che il correre della linfa ne'vasellini organici dipende da bene altra <lb/>forza vitale e pi&ugrave; attiva di quella forza fisica che sospinge i liquidi su per <lb/>i tubi capillari. </s>

<s>Quando si giunse a conoscere per esperienze sensate e libere <lb/>dalle prime apprensioni di una frettolosa immaginazione, che i muscoli e il <lb/>cuore nel contrarsi induriscono e scortano, senz'ammettere nella loro so&shy;<lb/>stanza carnosa un liquido straniero, che gli faccia ricrescere di mole, e al&shy;<lb/>lora ben s'intese che non si potevano attribuire le forze delle loro fibre <lb/>traenti all'effervescenze de'liquidi commisti, n&egrave; paragonare alle trazioni delle <lb/>fila di canapa inumidite, e attorte in fune o comunque sia aggomitolate. </s></p><p type="main">

<s>La iatromatematica, ch'era stata accolta da tutti con s&igrave; gran festa, si <lb/>dov&egrave; allora e per tali giuste ragioni abbandonarla, cosicch&egrave; poco durarono <lb/>i suoi trionfi, e lievi con precipitoso giudizio se ne dissero i benefizi. </s>

<s>Licen&shy;<lb/>ziata per&ograve; che fu dai servigi della scienza, non si seppe chi chiamare a so&shy;<lb/>stituirla. </s>

<s>La scoperta di Luigi Galvani, per quel che particolarmente con&shy;<lb/>cerne i moti muscolari, solletic&ograve; le speranze di molti, che si credettero aver <lb/>dalla nuova Fisica elettrica migliori servigi che non dalla Fisica antica. </s>

<s>Ma <lb/>poi presto si conobbe per esperienza che lo stesso spirito elettrico non era <lb/>altro che una lusinghiera immagine dello spirito della vita. </s></p><p type="main">

<s>E ora da quale altra scienza si potrebbe questo spirito rivelare? </s>

<s>Le dis&shy;<lb/>sezioni operate dall'esperto taglio del coltello anatomico aprirono mirabil&shy;<lb/>mente la via agli studii biologici, dal Vesalio al Malpighi. </s>

<s>Il Microscopio, <lb/>applicato dal Malpighi stesso e da'suoi successori, scopr&igrave; un mondo nuovo <lb/>nella testura delle parti solide del corpo organico, e nella composizione dei <lb/>liquidi che ricircolano in esso, intanto che s'ebbe infin d'allora notizia si <lb/>pu&ograve; dir compiuta di ci&ograve; che si pu&ograve; toccare e vedere nel corpo animale. </s>

<s>La <lb/>macchina de'polmoni aveva fatto conoscere, non a soli i Filosofi antichi, ma <lb/>allo stesso volgo che, oltre ai solidi e ai liquidi, entrano anche gli aeriformi <lb/>a farsi ministri della vita, e poi la Chimica fece meglio conoscere la natura <lb/>di que'corpi che, sebbene sfuggevoli alle sottigliezze del coltello anatomico <lb/>e invisibili a qualunque acume di Microscopio, potevano come gli altri corpi <lb/>trattarsi e farsene soggetto di sperimenti. </s>

<s>All'ultimo il Galvani ebbe indizio <lb/>che, oltre ai solidi, ai liquidi e agli aeriformi, entrasse a compor la mac&shy;<lb/>china animale anche l'etere, non arrendevole a qualunque industria del&shy;<lb/>l'arte, e solo rivelantesi a noi negli effetti dell'elettricit&agrave;, sotto le pi&ugrave; mi&shy;<lb/>steriose sembianze. </s>

<s>E perch&egrave; quel sottilissimo etere, meglio della materia <lb/>crassa di che si componpongono i muscoli e le ossa e il sangue, si conosce <lb/>organo acconcio ai pi&ugrave; intimi servigi della vita, l&agrave; dove se ne sentiva pi&ugrave; <lb/>vivamente il bisogno, l'Anatomia ci abbandona, confessandosi, a sodisfare ai <lb/>nostri desiderii, impotente. </s></p><p type="main">

<s>A questo scoglio si frangono davvero i flutti spumosi dell'orgogliosa <lb/>Filosofia. </s>

<s>Il Cartesio, il quale sagacemente indovin&ograve; non essere le parti vi&shy;<lb/>sibili nel corpo animale n&egrave; i soli n&egrave; i principali organi della vita, suppose <lb/>l'esistenza di parti invisibili, per aprirsi il campo a una Anatomia immagi-<pb xlink:href="020/01/1167.jpg" pagenum="42"/>naria, qual'&egrave; quella degli sfiatatoi del vento, che ne'muscoli esala dal cer&shy;<lb/>vello. </s>

<s>Cos&igrave; il Filosofo, che orgogliosamente credeva di superar quello scoglio, <lb/>ne fu vergognosamente ributtato pi&ugrave; indietro, e possono perci&ograve; dall'esem&shy;<lb/>pio di lui i lettori, che ci seguiteranno, conoscere quali sieno i limiti pre&shy;<lb/>scritti al progresso degli studii, di cui siamo per narrare la storia. </s>

<s>Prepa&shy;<lb/>rativa di quegli studii &egrave; l'Anatomia, le cose della quale fin qui dette e <lb/>concluse ce la fanno rassomigliare a una nave, impotente per la sua corpu&shy;<lb/>lenza a condurci infin l&agrave;, dove le sottili acque, spirate da un agilissimo soffio, <lb/>giungono a toccare il lontanissimo lido. </s></p><pb xlink:href="020/01/1168.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO II.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dei moti muscolari<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle prime ipotesi proposte a rendere la ragione dei moti muscolari, e particolarmente dell'ipo&shy;<lb/>tesi del Cartesio. </s>

<s>&mdash; II. </s>

<s>Di altre varie ipotesi, principalmente speculate dai nostri Italiani. </s>

<s>&mdash; <lb/>III. </s>

<s>Dei moti volontarii e dei naturali. </s>

<s>&mdash; IV. </s>

<s>Della meccanica dei moti muscolari. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>L'impotenza dell'Anatomia a scoprirci, co'suoi materiali strumenti, i <lb/>seni, dove s'asconde quello spirito che vivifica le membra, si manifesta ai <lb/>primi passi di chi si studia di porre il piede in quegl'intimi penetrali. </s>

<s>Esce <lb/>da que'penetrali la vita, e si rivela ne'moti, i quali soli sono a noi indizio <lb/>ch'ella veramente risegga negli organi mossi. </s>

<s>Comprendesi perci&ograve; assai fa&shy;<lb/>cilmente come il primo problema che si proponesse a sciogliere la scienza, <lb/>e che nelle prime ovvie manifestazioni presentasse difficolt&agrave; insuperabili, fu <lb/>quello di rendere in qualche modo la ragione di que'moti volontarii e istin&shy;<lb/>tivi, che sono il primo e principale argomento per noi da riconoscere la <lb/>morte e la vita. </s></p><p type="main">

<s>Chiunque sappia essere stata da Aristotile scritta la prima Storia na&shy;<lb/>turale degli animali, che pure &egrave; tenuta anche dai moderni in qualche re&shy;<lb/>putazione, s'immagina che il gran Filosofo non abbia fra gli altri lasciato <lb/>indietro di trattar questo soggetto de'moti muscolari. </s>

<s>Egli ha infatti, fra le <lb/>opere appartenenti a cose naturali, un trattatello che s'intitola <emph type="italics"/>De incessu <lb/>animalium,<emph.end type="italics"/> a cui vollero alcuni dar la medesima importanza, che agli altri <lb/>libri, ne'quali descrive lo Stagirita la Storia universale degli animali. </s></p><p type="main">

<s>Aristotile per&ograve;, volendo esser conseguente a suoi principii di Anatomia <pb xlink:href="020/01/1169.jpg" pagenum="44"/>e di Fisiologia, si trovava nella impossibilit&agrave; di trattar della Meccanica ani&shy;<lb/>male, non potendovi esser macchina senza composizione di organi o conge&shy;<lb/>gno di parti. </s>

<s>Questi organi infatti e questi congegni rimasero per Aristotile <lb/>affatto inconsiderati, insegnando che l'anima muove da s&egrave; immediatamente <lb/>il corpo, per via degli spiriti, che partendosi dal cuore si partecipano ai nervi, <lb/>e di l&igrave; alle flessure degli articoli e agli ossi. </s>

<s>Che se gli avesse domandato <lb/>qualcuno come mai spiriti cos&igrave; tenui valessero a muover moli tanto ponde&shy;<lb/>rose, quali son quelle per esempio degli elefanti, era pronto a rispondere <lb/>che la Natura sa, con piccole forze, l'arte di produrre effetti straordinarii. </s>

<s><lb/>Aristotile insomma non aveva inteso a che fare stessero nel corpo animale <lb/>quelle fibre carnose e quelle durissime funi, che tanto artificiosamente si <lb/>legano agli ossi. </s></p><p type="main">

<s>Primo a conoscere l'importante ufficio, a cui vennero dalla Natura or&shy;<lb/>dinati i muscoli, i tendini e i ligamenti, fu Galeno, il quale ci lasci&ograve; fra le <lb/>sue Opere scritto un trattatello <emph type="italics"/>De motu musculorum,<emph.end type="italics"/> diviso in due libri. </s>

<s><lb/>Il meccanismo della vita stravolto da Aristotile, che poneva nel cuore il prin&shy;<lb/>cipio de'nervi, fu riordinato sapientemente da esso Galeno, che riconobbe <lb/>avere i nervi principio dal cervello e dalla midolla spinale, d'onde vanno a <lb/>insinuarsi e a partecipare la loro maravigliosa virt&ugrave; a tutti i muscoli. </s>

<s>Che <lb/>sia veramente cos&igrave; &ldquo; cognosces, egli dice, ex passionibus, nam incisus, op&shy;<lb/>pressus, contusus, laqueo interceptus, scirrhis affectus et putrefactus nervus <lb/>aufert musculo omnem motum et sensum. </s>

<s>Quin et nervo inflammato non <lb/>pauci spasmo correpti sunt et mente alienati, quorum quidam sic affecti, <lb/>cum sapientiorem medicum nacti essent, nervo inciso statim spasmo et men&shy;<lb/>tis alienatione liberati sunt, sed postea musculum, in quem nervus insertus <lb/>erat, insensilem atque inutilem ad motum habuerunt. </s>

<s>Adeo certe magna <lb/>quaedam vis est in nervis superne a magno principio affluens, non enim ex <lb/>seipsis eam, neque innatam habent. </s>

<s>Cognoscere etiam potes hinc maxime, <lb/>si incideris quemcumque istorum nervorum aut spinalem ipsam medullam. </s>

<s><lb/>Quantum enim superius est incisione, continuum cerebro, id quidem adhuc <lb/>conservabit principii vires: omne autem quod inferius est, neque sensum, <lb/>neque motum ulli praebere poterit. </s>

<s>&rdquo; Dai quali fatti Galeno &egrave; condotto alla <lb/>seguente importantissima conclusione: &ldquo; Nervi tanquam rivorum in morem a <lb/>cerebro, ceu ex quodam fonte, deducunt musculis vires, quos, cum primum <lb/>attigerint, scinduntur multip<gap/>iciter in aliam subinde atque aliam sectionem, <lb/>tandemque, in tenues et membranaceas fibras toti soluti, totum sic musculi <lb/>corpus intertexunt &rdquo; (Galeni librorum I Classis, Venetiis 1597, pag. </s>

<s>309). </s></p><p type="main">

<s>La Meccanica animale aveva fatto cos&igrave;, per Galeno, un gran passo, non <lb/>posando il pi&egrave; sulla mobilit&agrave; delle filosofiche speculazioni, ma fermandolo <lb/>sulla solidit&agrave; delle esperienze, dalle quali veniva dimostrato essere il cer&shy;<lb/>vello e i nervi che conducono la forza nei muscoli. </s>

<s>Ma perch&egrave; la sete di <lb/>sapere, che pare a un tratto spenta, accende nuova sete pi&ugrave; viva, si voleva <lb/>di pi&ugrave; intendere in che mai consista quella virt&ugrave;, e in che modo operino <lb/>il cervello e i nervi per indur ne'muscoli una tal prontezza di moti. </s>

<s>Il Mae-<pb xlink:href="020/01/1170.jpg" pagenum="45"/>stro antico lasci&ograve; il carico di rispondere ai suoi successori, il primo e pi&ugrave; <lb/>savio de'quali, incontratosi in un gran mistero, non ebbe ardire o speranza <lb/>di riuscire a toglierli il velo. </s>

<s>Il Berengario infatti, contento ad ammettere <lb/>con Galeno essere i muscoli gli organi dei moti volontarii, ecco tutto quel <lb/>ch'egli dice della meccanica di que'moti: &ldquo; Voluntas, cum mittit virtutem <lb/>animalem ad nervum versus lacertum suum, volens per illum plicare ali&shy;<lb/>quod membrum, retrahitur ille lacertus circa sui principium, et statim pli&shy;<lb/>catur membrum. </s>

<s>Et similiter, cum voluerit quod membrum extendatur et <lb/>erigatur, extendit voluntas illum lacertum cum lacerto sibi opposito, et ten&shy;<lb/>duntur simul, et cum cessat operatio voluntatis universaliter, nec mittit ad <lb/>lacertum virtutem, omnino remanet lacertus similis caeteris rebus congela&shy;<lb/>tus, et tendit per suam ponderositatem naturalem cum eo cui adhaeret ad <lb/>inferius, tamquam membrum mortuum &rdquo; (Commentaria super Anat. </s>

<s>Mun&shy;<lb/>dini, Bononiae 1521, fol. </s>

<s>LXXVI a tergo). </s></p><p type="main">

<s>Che possano per&ograve; le membra morire e resuscitare, quante volte &egrave; in <lb/>piacere dell'animale, non parve un concetto de'pi&ugrave; felici, fra'tanti sovve&shy;<lb/>nuti alla mente anatomica del Berengario. </s>

<s>Dall'altra parte potevano anche <lb/>coloro, che non approvan l'audacia di certi Filosofi, accusarlo d'essersi troppo <lb/>ritenuto lontano dall'adempire agli uffici di scienziato, riducendo la ragione <lb/>de'moti muscolari, e concludendola in dire che la volont&agrave; manda verso i <lb/>lacerti ai nervi la sua virt&ugrave; motrice. </s>

<s>Questa, ch'&egrave; contro i Peripatetici dot&shy;<lb/>trina di Galeno, si poteva dire nel secolo XVI anche dottrina volgare, e <lb/>perci&ograve; il Vesalio, in quel risorgere che faceva allora per lui la scienza, sent&igrave; <lb/>che i placiti antichi volevano essere dichiarati con nuovi commenti. </s></p><p type="main">

<s>Come la vena, egli dice, serve a nutrire il muscolo, e l'arteria a fo&shy;<lb/>mentarlo; cos&igrave; il nervo lo ricrea degli spiriti animali, di che mai non lo <lb/>lascia digiuno. </s>

<s>Con ci&ograve; il Brussellese, che ammetteva l'influsso nerveo pe&shy;<lb/>renne, emendava l'errore del nostro Carpense, ma va anche pi&ugrave; oltre a dire <lb/>quale egli creda esser causa efficiente dei moti muscolari; causa ch'egli ri&shy;<lb/>conosce tutt'insieme e nella virt&ugrave; dello spirito animale, e nella particolare <lb/>struttura del muscolo. </s>

<s>&ldquo; Deinde spiritus animalis, vi et debitae peculiarisque <lb/>musculi constructionis gratia, musculum contrahi laxarique sentio &rdquo; (De <lb/>humani corp. </s>

<s>fabrica, Basileae 1543, pag. </s>

<s>222). </s></p><p type="main">

<s>Come l'occhio &egrave; l'organo della vista, l'orecchio dell'udito, la lingua <lb/>del gusto, cos&igrave; il Vesalio crede che i muscoli siano gli organi dol moto. </s>

<s>E <lb/>come un solo e medesimo spirito, entrando nell'occhio e trovandolo a quel <lb/>modo disposto, fa vedere, e nell'orecchio udire, e nella lingua gustare; cos&igrave; <lb/>entrando nel muscolo, per essere a quell'effetto costruito dalla Natura, lo <lb/>fa muovere come si vuole. </s>

<s>&ldquo; Non enim alius animalis spiritus oculo, aut <lb/>linguae, aut auditus organo, quam musculis, diffunditur. </s>

<s>Verum suae con&shy;<lb/>structionis ratione, et accedente spiritu, oculus videt, lingua gustat, au&shy;<lb/>ditus organum sonos percipit, et sane musculus ipse voluntariis motibus <lb/>praeest &rdquo; (ibi). </s></p><p type="main">

<s>Ma perch&egrave; l'anatomia rivela che il muscolo si compone di pi&ugrave; fibre <pb xlink:href="020/01/1171.jpg" pagenum="46"/>raccolte, e in un fascio legate insieme, qual'&egrave; in questo membro, cos&igrave; com&shy;<lb/>posto di pi&ugrave; parti, il precipuo organo del moto? </s>

<s>E risponde il Vesalio es&shy;<lb/>sere la carnosit&agrave; delle stesse fibre muscolari. </s>

<s>&ldquo; Atque hanc carnem praeci&shy;<lb/>puum motus organum esse existimo, et nequaquam dumtaxat fibrarum <lb/>thorum et fulcimentum &rdquo; (ibi). Come per&ograve; operi propriamente la carne mu&shy;<lb/>scolare per rendersi organo precipuo del moto, l'Autore qui non lo dice, <lb/>ma nell'Esame delle Osservazioni anatomiche del Falloppio si spieg&ograve; meglio, <lb/>facendo intendere che l'allungare e lo scorciar del muscolo dipende dalla <lb/>carne che s'aggroppa in esso o si snoda. </s>

<s>&ldquo; Hac namque collectione, et ve&shy;<lb/>luti conglobatione, musculum breviorem reddi: itaque movere existimo, et <lb/>quum is illam collectionem brevitatemque relaxat, ipsum motam prius partem <lb/>suo veluti arbitrio, relinquere mihi persuadeo &rdquo; (Venetiis 1564, pag. </s>

<s>118). </s></p><p type="main">

<s>Si direbbe che quel conglobarsi e distendersi della sostanza carnosa <lb/>fosse, secondo la mente del Vesalio, principalmente governato dall'influsso <lb/>dello spirito animale, se non si sapesse ch'egli stesso, <emph type="italics"/>parum in hoc Ana&shy;<lb/>tomicus,<emph.end type="italics"/> come giustamente lo accusa il Colombo, sentenzi&ograve; che v'erano molti <lb/>muscoli, dentro i quali non entravano nervi. </s>

<s>Intendeva con ci&ograve; il rivoltoso <lb/>Spirito brussellese di contradire a Galeno, di cui dianzi si riferivano in pro&shy;<lb/>posito le dottrine, e non si avvedeva, nell'ardore della passione, che preci&shy;<lb/>devasi cosi ogni via ai progressi della scienza, e che si rendeva impossibile <lb/>a investigar la causa de'moti muscolari. </s>

<s>Benemerito perci&ograve; di que'progressi <lb/>&egrave; da dire il Colombo, il quale, avendo confermato il principio galenico, che <lb/>sieno cio&egrave; i muscoli organi del moto volontario, soggiunge contro il Vesa&shy;<lb/>lio, e a restaurar le vere dottrine dell'antichissimo Maestro, che nessun mu&shy;<lb/>scolo manca de'suoi nervi &ldquo; et cum ad musculum nervum ferri dico, non <lb/>ita intelligo prope musculos nervos ferri, aut per illorum medium recta <lb/>praeterire, ed per musculorum substantiam aio nervos disseminari &rdquo; (De re <lb/>anatom., Venetiis 1559, pag. </s>

<s>119). </s></p><p type="main">

<s>Il Falloppio con la sua scuola, tutti dediti all'Anatomia descrittiva, toc&shy;<lb/>carono appena la difficile questione, la quale, nel risorgere della scienza spe&shy;<lb/>rimentale, si rimase a quel punto in cui l'avevano lasciata il Colombo, o <lb/>diciam meglio Galeno. </s>

<s>Il Cartesio, ch'entr&ograve; primo a filosofare di queste cose, <lb/>trov&ograve; dunque essersi prima di lui insegnato che la virt&ugrave; di muovere viene <lb/>ai muscoli dal cervello, il quale manda a loro il suo spirito, per via de'nervi, <lb/>dentro la stessa muscolare sostanza largamente dispersi. </s>

<s>Si sentiva per&ograve; an&shy;<lb/>cora frugata la filosofica curiosit&agrave; di saper queste cose: che sia e d'onde <lb/>abbia origine quello spirito vitale; come operi propriamente sui muscoli a <lb/>produrre i vari moti animali. </s></p><p type="main">

<s>Alla prima domanda non avea sodisfatto il Colombo, proponendo una <lb/>sua ipotesi, che a noi pare indegna di lui, bench'egli se ne compiaccia come <lb/>di una bella invenzione, per cui rispondeva cos&igrave; il Cartesio, fondando sul&shy;<lb/>l'anatomia e sulla fisiologia del cervello il suo discorso: &ldquo; Quantum ad par&shy;<lb/>tes sanguinis, quae usque in cerebrum penetrant, haec ibi non nutriendae <lb/>ac reficiendae tantum illius substantiae inserviunt, sed imprimis quoque <pb xlink:href="020/01/1172.jpg" pagenum="47"/>subtilissimum quemdam halitum, aut potius valde mobilem et puram flam&shy;<lb/>mam producunt, quae animalium spirituum nomine venit. </s>

<s>Sciendum enim <lb/>est arterias, quae hunc sanguinem a corde ad cerebrum deferunt, primo in <lb/>infinitos tenuissimos ramulos dividi et componere parva illa reticula, quae <lb/>tapetorum instar in fundo ventriculorum cerebri expansa sunt, ac denuo <lb/>coire circum exiguam quandam glandulam, quae circiter in media cerebri <lb/>substantia sita est, in ipso ventriculorum introitu, atque ibi valde multos <lb/>exiguos poros habere, per quos subtilissimae sanguinis quem continent par&shy;<lb/>ticulae effluere possint in hanc glandulam, non vero crassiores, eo quod ni&shy;<lb/>mis angusti sint pori isti &rdquo; (De Homine, Francofurti ad M. 1692, pag. </s>

<s>21). </s></p><p type="main">

<s>Ammesso cos&igrave; che lo spirito o la fiammella della vita sia un vapore del <lb/>sangue esalato nel passar che fa, come per un cribro, attraverso ai pori <lb/>della ghiandola pineale, viene il Cartesio a dire come quello spirito deriva <lb/>dal suo principio ne'muscoli per la via diretta de'nervi, ch'egli immagina <lb/>esser fabbricati a guisa di un gran tubo membranoso involgente altri pi&ugrave; <lb/>piccoli tubi tutti pieni di una certa sostanza midollore, che per&ograve; non serve <lb/>a muover le membra, e che &egrave; composta di molti sottilissimi filamenti. </s>

<s>Rap&shy;<lb/>presenta l'Autore questa immaginata anatomia de'nervi in disegno, illu&shy;<lb/>strato da queste parole: &ldquo; Vides igitur hunc nervum A, cuius exterior tu&shy;<lb/>nica, instar magni tubi est, continentis in se plures minores tubulos .... <lb/>ex interiori tunica compositos.... Insuper notandum in his singulis tubulis <lb/>esse quasi medullam quandam compositam ex plurimis tenuissimis filamen&shy;<lb/>tis a propria cerebri substantia deductis &rdquo; (ibi, pag. </s>

<s>25). </s></p><p type="main">

<s>Son questi tubi nervei lo spiracolo della fiamma vitale, che con per&shy;<lb/>petuo circolo va e torna dal cervello ai muscoli, quando questi per&ograve; stanno <lb/>in riposo. </s>

<s>Ma quando hanno a muoversi, vi sono agl'ingressi e agli egressi <lb/>nella sostanza muscolare certe valvole, che impediscono allo spirito il suo <lb/>libero corso, e fanno s&igrave; che un muscolo s'enfi pi&ugrave; del suo antagonista, per <lb/>cui quello vincendola sopra questo lo tira alla sua parte, verso la quale di&shy;<lb/>rigesi la resultante del moto. </s>

<s>Il fantasticato <lb/><figure id="id.020.01.1172.1.jpg" xlink:href="020/01/1172/1.jpg"/></s></p><p type="caption">

<s>Figura 1.<lb/>macchinamento &egrave; tale, che non pu&ograve; descri&shy;<lb/>versi chiaramente senza l'aiuto delle figure, <lb/>come fa il Cartesio stesso, il quale esem&shy;<lb/>plifica cos&igrave; il suo sistema ne'muscoli motori <lb/>dell'occhio: </s></p><p type="main">

<s>&ldquo; Nota inter duos tubos <emph type="italics"/>bf, ef<emph.end type="italics"/> (fig. </s>

<s>1) <lb/>dari pelliculam quandam H <emph type="italics"/>fi,<emph.end type="italics"/> quae duos <lb/>hos tubos <emph type="italics"/>bf<emph.end type="italics"/> et <emph type="italics"/>ef<emph.end type="italics"/> seiungit, iisque inservit <lb/>tanquam porta quae duas habet plicas G <lb/>et <emph type="italics"/>i,<emph.end type="italics"/> tali modo dispositas, ut cum spiritus <lb/>animales, qui a <emph type="italics"/>b<emph.end type="italics"/> ad H descendere conan&shy;<lb/>tur, maiorem vim habent iis qui conantur adscendere ab <emph type="italics"/>c<emph.end type="italics"/> versus <emph type="italics"/>i<emph.end type="italics"/> depri&shy;<lb/>mant et aperiant hanc pelliculam, adeoque occasionem praebeant iis, qui in <lb/>musculo E sunt, una cum ipsis celerrime versus D fluendi. </s>

<s>Ubi vero spi-<pb xlink:href="020/01/1173.jpg" pagenum="48"/>ritus, qui ascendere nituntur ab <emph type="italics"/>e<emph.end type="italics"/> versus <emph type="italics"/>i<emph.end type="italics"/> fortiores sunt, aut saltem aeque <lb/>fortes ac alii, pelliculam H <emph type="italics"/>fi<emph.end type="italics"/> attollunt clauduntque, atque ita semetipsos im&shy;<lb/>pediunt, quominus exeant ex musculo F; cum alias, si utrimque satis vi&shy;<lb/>rium non habeant ad eam pellendam, naturaliter semiaperta maneat. </s>

<s>Et <lb/>denique si spiritus contenti in musculo D egredi aliquando conentur per <lb/><emph type="italics"/>dfe,<emph.end type="italics"/> aut <emph type="italics"/>dfb,<emph.end type="italics"/> plica H distendi et viam ipsis praecludere potest. </s>

<s>Et eodem <lb/>prorsus modo inter duos tubos <emph type="italics"/>eg,<emph.end type="italics"/> et <emph type="italics"/>dg,<emph.end type="italics"/> pellicula seu valvula <emph type="italics"/>g<emph.end type="italics"/> reperitur <lb/>praecedenti similis, quae naturaliter semiaperta manet et claudi potest a <lb/>spiritibus venientibus a tubulo <emph type="italics"/>dg,<emph.end type="italics"/> et ab iis qui veniunt a <emph type="italics"/>cg<emph.end type="italics"/> aperiri &rdquo; (ibi, <lb/>pag. </s>

<s>40). </s></p><p type="main">

<s>Descritti cos&igrave; gli organi principali, ecco come sono, in questa fantastica <lb/>macchina cartesiana, messe in gioco le forze, perch&egrave; possano i muscoli dare <lb/>all'occhio, a cui sono applicati, quella loro cos&igrave; pronta variet&agrave; di moti. </s>

<s>&ldquo; Unde <lb/>haud difficulter intelligi potest quod si spiritus animales, qui in cerebro sunt, <lb/>prorsus nullum aut fere nullum conatum habeant per tubulos <emph type="italics"/>bf, cg<emph.end type="italics"/> affluendi, <lb/>duas pelliculas seu valvulas <emph type="italics"/>f<emph.end type="italics"/> et <emph type="italics"/>g<emph.end type="italics"/> semiapertas manere, atque ita musoules D <lb/>et E flaccidos et actione destitutos fore, quandoquidem contenti in ipsis ani&shy;<lb/>males spiritus libere ab uno in alium transeunt, ab E per <emph type="italics"/>f<emph.end type="italics"/> versus D, et <lb/>reciproce a D per <emph type="italics"/>g<emph.end type="italics"/> versus E. </s>

<s>At si spiritus qui in cerebro sunt, cum vi <lb/>aliqua conentur ingredi tubos <emph type="italics"/>bf, cg,<emph.end type="italics"/> et haec vis ab utraque parte aequalis <lb/>sit, statim claudunt duas valvulas <emph type="italics"/>g<emph.end type="italics"/> et <emph type="italics"/>f,<emph.end type="italics"/> et duos musculos D et E quan&shy;<lb/>tum possunt distendunt. </s>

<s>Uude fit ut sistatur oculus et immotus teneatur in <lb/>eo situ quem tunc habet. </s>

<s>Deinde, ubi spiritus a cerebro venientes, maiori <lb/>vi fluere nituntur per <emph type="italics"/>bf<emph.end type="italics"/> quam per <emph type="italics"/>cg<emph.end type="italics"/> claudunt pelliculam <emph type="italics"/>g,<emph.end type="italics"/> et aperiunt <emph type="italics"/>f,<emph.end type="italics"/><lb/>idque magis aut minus prout lenius vel vehementius agunt. </s>

<s>Qua ratione spi&shy;<lb/>ritus musculo E contenti se conferunt ad musculum D per meatum <emph type="italics"/>ef,<emph.end type="italics"/> idque <lb/>celerius vel tardius, prout valvula <emph type="italics"/>f<emph.end type="italics"/> magis vel minus aperta est. </s>

<s>Adeo ut <lb/>musculus D, ex quo egredi non possunt, in spiritus contrahatur et E exten&shy;<lb/>datur, atque ita oculus versus D conversus est. </s>

<s>Sicut ex adverso, ubi spi&shy;<lb/>ritus, qui in cerebro sunt, maiori vi fluere nituntur per <emph type="italics"/>cg,<emph.end type="italics"/> quam per <emph type="italics"/>bf,<emph.end type="italics"/><lb/>claudunt pelliculam <emph type="italics"/>f<emph.end type="italics"/> et aperiunt <emph type="italics"/>g,<emph.end type="italics"/> adeo ut spiritus musculi D statim re&shy;<lb/>deant per meatum <emph type="italics"/>dg<emph.end type="italics"/> in musculum E, qui hac ratione contrahitur, et ocu&shy;<lb/>&igrave;um iterum ad se trahit &rdquo; (ibi, pag. </s>

<s>41). </s></p><p type="main">

<s>Chi sa quale efficacia avesse sopra le menti di allora la seducente elo&shy;<lb/>quenza di Renato, non si maraviglier&agrave; di veder queste fantasie approvate e <lb/>seguite, non da'soli metafisici o da'filosofi razionali, ma dagli stessi cultori <lb/>delle scienze mediche. </s>

<s>Da un'altra parte la fortunata scoperta dell'Harvey <lb/>aveva cos&igrave; disposti gl'ingegni ad ammetter negli animali, a somiglianza del <lb/>circolo del sangue, il circolo cartesiano degli spiriti vitali, che Enrico Regi&ograve;, <lb/>amico a Tommaso Bartholin, il quale riferisce il fatto nel suo Spicilegio <lb/>de'vasi linfatici, si lusing&ograve; di aver co'suoi proprii occhi veduto questo cir&shy;<lb/>colo andar da&igrave; ventre al capo attraverso alle cellule trasparenti di una Lu&shy;<lb/>maca. </s>

<s>E a proposite degli stessi vasi linfatici il Glisson costitu&igrave; nel corpo <lb/>animale un altro circolo somigliantissimo a quello arveiano, in cui facevano <pb xlink:href="020/01/1174.jpg" pagenum="49"/>que'vasi, a somiglianza delle vene, tornar la linfa alla sua fonte, dalla quale <lb/>i nervi, col Cartesio creduti tubulari, come le arterie il sangue, l'avevano <lb/>attinta, per nutrir di un alimento tutto proprio di lei le varie membra. </s></p><p type="main">

<s>Non tutti per&ograve;, per amor del vero, furono sedotti dalle eloquenti fan&shy;<lb/>tasie del Filosofo: si trattava di cose naturali, in cui le speculazioni, per <lb/>quanto ingegnose, non potevano aver virt&ugrave; di persuadere, se non venivano <lb/>confermate dai fatti, quali si rivelano all'osservazione e son dimostrati dalle <lb/>esperienze. </s>

<s>Il Cartesio, e dietro lui il Glisson, supponevano che i nervi fos&shy;<lb/>sero tubulari, e il Bartholin gli richiama alle osservazioni anatomiche, dalle <lb/>quali, perciocch&egrave; non vedevasi confermato il supposto, cosi con veemenza <lb/>contro ad essi conclude: &ldquo; Non igitur audiendi qui nervos vasorum instar <lb/>cavos nobis obtrudunt. </s>

<s>Monstrent intento digito ut assentiamur, nam manus <lb/>nobis sunt oculatae. </s>

<s>Quotquot nervos accurato oculo inspexere, nullam in&shy;<lb/>venerunt cavitatem &rdquo; (Spicilegium ex vasis lymphat., Amstelodami 1660, <lb/>pag. </s>

<s>21). </s></p><p type="main">

<s>Eransi immaginati i nervi tubulari dal Cartesio, per dar libero passag&shy;<lb/>gio agli spiriti; dal Glisson per servire al circolo della linfa: il Bartholin <lb/>gli richiam&ograve; all'esperienze, le quali dimostrano che per i nervi non iscorre <lb/>nessuna spiritosa o liquida sostanza. </s>

<s>&ldquo; Quidquid sit, nullum motum seu spi&shy;<lb/>ritus seu liquoris possumus in nervis expiscari. </s>

<s>Tentavi duplici ligatura <lb/>iniecta nervumque vidi inter vincula nihil intumescere, nec discissum liquo&shy;<lb/>rem stillare; unde existimavi nihil humoris contineri, quia regredi non po&shy;<lb/>tuit propter superius vinculum, nec elective trahi pellique, propter inferius <lb/>vinculum. </s>

<s>Quorsum evasit succus inter ligaturas contentus? </s>

<s>&rdquo; (ibi, pag. </s>

<s>32). </s></p><p type="main">

<s>Vedremo com'avesse il Malpighi da simili esperienze resultati diversi, <lb/>ma in oghi modo a dover tenere l'ipotesi cartesiana per non pi&ugrave; che per <lb/>una ingegnosa finzione, basti il saper che nessuno Anatomico, nemmen con <lb/>l'aiuto del pi&ugrave; artificioso Microscopio, &egrave; riuscito a veder quelle pieghe mem&shy;<lb/>branose o quelle valvole poste nell'ingresso de'muscoli dalla fantasia del <lb/>Cartesio. </s>

<s>&Egrave; anzi a notare che le immaginate valvole sono incompatibili col <lb/>fatto della diramazione de'nervi nella sostanza di tutti i muscoli, secondo <lb/>aveva il Colombo dimostrato contro il Vesalio, per cui il Cartesio, ammet&shy;<lb/>tendo che il nervo venga reciso in tronco nell'entrare del muscolo, contra&shy;<lb/>dice al fatto anatomico pi&ugrave; manifesto. </s>

<s>Tutti i pi&ugrave; savi perci&ograve;, persuasi non <lb/>potersi fingere il corpo animale a nostro modo, ma doversi tener quale le <lb/>osservazioni e l'esperienze ce lo mostrano fabbricato dalla Natura, ben co&shy;<lb/>nobhero che non si poteva, in ordine al render la ragione de'moti musco&shy;<lb/>lari, seguitar la Filosofia cartesiana, e ch'era necessario in ogni modo te&shy;<lb/>nere altra via. </s>

<s>Furono per avventura fra que'savi i nostri Italiani, de'quali <lb/>&egrave; da narrar le speculazioni e l'esperienze, di che s'aiutarono studiosamente <lb/>per risolvere il difficilissimo problema. </s></p><pb xlink:href="020/01/1175.jpg" pagenum="50"/><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Giovan Batista Baliani che si studi&ograve;, per quanto valessero le sue forze, <lb/>di emular Galileo nella scienza del moto e che, con pi&ugrave; amoroso studio di <lb/>lui, coltiv&ograve; questa stessa scienza nelle applicazioni, che potevan farsene al <lb/>moto degli animali; ha fra le sue opere diverse, raccolte in Genova dal Ca&shy;<lb/>lenzani, una breve scrittura, nella quale proponesi di rendere la ragione <lb/><emph type="italics"/>Quomodo animal moveatur.<emph.end type="italics"/> Il carattere proprio d&igrave; questa scrittura &egrave; piut&shy;<lb/>tosto quello di una nota, scritta forse con intenzione di tornare a disten&shy;<lb/>derla in pi&ugrave; larga forma, per sodisfare ai lettori meglio, che con quell'arida <lb/>e concisa argomentazione, con la quale si affretta a concludere il suo di&shy;<lb/>scorso. </s>

<s>Bench&egrave; pubblicata nel 1666, ella dee essere di parecchi anni ante&shy;<lb/>riore, e perch&egrave; dettata in tempi, ne'quali non si sapeva a qual genere di <lb/>macchina, fra quelle semplici descritte dalla Scienza meccanica, rassomigliar <lb/>quella messa, nell'economia animale, in opera dalla Natura; e perci&ograve; hanno <lb/>da questa parte le dottrine del Baliani, che ora sembrano s&igrave; comuni, qual&shy;<lb/>che cosa in s&egrave; per que'tempi di notabile. </s></p><p type="main">

<s>Ecco dunque come, ammessa l'ipotesi degli spiriti vitali, si rende la <lb/>ragion del muoversi, a ubbidire alla volont&agrave; o a secondare gl'istinti, secondo <lb/>il Baliani, la varie membra. </s>

<s>&ldquo; Animal movetur per animam, anima movet <lb/>spiritum, spiritus nervos, nervus muscolos, musculi tendines, tendines ossa, <lb/>membra, inde etiam totum corpus.... Dices quomodo spiritus potest mo&shy;<lb/>vere corpus grave? </s>

<s>Respondeo spiritus etiam est corpus, quamvis tenue, <lb/>divisum in tot partes, quot sunt nervi subtilissimi, et proinde quilibet ipso&shy;<lb/>rum a suo spiritu interno facile ad libitum ducitur, unde plures partes spi&shy;<lb/>ritus facile ducunt plures nervos in eodem musculo dispositos, ex quo totus <lb/>musculus de facili movetur et suo motu, mediis tendinibus, ossa et inde <lb/>membra movet: hinc spiritus movet totum corpus, quod explicandum fuit &rdquo; <lb/>(pag. </s>

<s>274). </s></p><p type="main">

<s>Ma queste in ogni modo sono asserzioni, le quali, bench&egrave; si possano <lb/>senza difficolt&agrave; tener per vere, mancano nonostante di quelle ragioni e di <lb/>quelle prove, che le rendano dimostrate: n&egrave; col sentenziare assoluto s'adem&shy;<lb/>piono gli uffici della scienza. </s>

<s>Dall'altra parte, se non si potevano quegli uf&shy;<lb/>fici adempire altrimenti da quel che fece il Cartesio, fu prudente consiglio <lb/>del nostro Baliani l'andar pi&ugrave; cauto ne'malagevoli passi. </s></p><p type="main">

<s>Venne per&ograve; tempo in Italia, in cui i progrediti-studii sperimentali e la <lb/>seducente applicazione delle leggi fisiche ai fatti fisiologici incorarono una <lb/>certa baldanzosa speranza di avere a giungere al vero desiderato, pi&ugrave; d'ap&shy;<lb/>presso di quel che non vi fossero giunti i predecessori, in altri tempi e con <lb/>aiuti pi&ugrave; scarsi. </s>

<s>Intanto che le nuove studiate ipotesi maturavano nella mente, <pb xlink:href="020/01/1176.jpg" pagenum="51"/>volle il Borelli, per assicurarsi della loro verit&agrave; o falsit&agrave;, richiamare a sot&shy;<lb/>tile esame quelle ch'erano state proposte prima di lui. </s></p><p type="main">

<s>La pi&ugrave; antica e universalmente ammessa da Galeno al Cartesio era <lb/>quella degli spiriti perennemente scorrenti dalla fonte del cervello, per i ri&shy;<lb/>voli de'nervi. </s>

<s>L'antico Maestro della scienza della vita non par che si spie&shy;<lb/>ghi bene intorno all'essere di quegli spiriti, se gli creda cio&egrave; composti di <lb/>materia simile all'aria, o di pi&ugrave; sottile sostanza impercettibile ai sensi. </s>

<s>Qual&shy;<lb/>che schiarimento alle idee comincia a venirci da Realdo Colombo, il quale <lb/>fa distinzione fra spiriti vitali, cos&igrave; detti secondo lui perch&egrave; sono un alito <lb/>purissimo della vita, e spiriti animali risultanti di una miscela di essi spi&shy;<lb/>riti vitali e d'aria. </s>

<s>Si fa questa miscela, secondo l'Anatomico cremonese, <lb/>ne'ventricoli superiori del cervello, per il moto de'plessi <emph type="italics"/>coriformi,<emph.end type="italics"/> ch'egli <lb/>pi&ugrave; volentieri chiama <emph type="italics"/>reticulari.<emph.end type="italics"/> L'aria entra poi ne'detti ventricoli attrat&shy;<lb/>tavi dal naso, attraverso ai forellini dell'Etmoide. </s>

<s>Una tal confezione dello <lb/>spirito animale vuole il Colombo che sia una sua nuova scoperta, e perci&ograve; <lb/>invita i lettori a seguirlo in questo passo con pi&ugrave; diligenza che mai. </s>

<s>&ldquo; Per <lb/>hos superiores cerebri ventriculos feruntur plexus coriformes, quos reticu&shy;<lb/>lares appellavimus. </s>

<s>Usus autem horum est animalium spirituum generatio. </s>

<s><lb/>Atque hoc quod nunc dicam, quoniam meum inventum est, diligenter at&shy;<lb/>tende. </s>

<s>Horum ventriculorum origo est supra os sphaenoides ethmoides ver&shy;<lb/>sus. </s>

<s>Aer autem per nares attractus in frontis cunealisque cavitate aliquando <lb/>conservatur. </s>

<s>Alteratus deinde ad hos binos ventriculos, quos ego superiores <lb/>appellavi, per foramina ethmoidis ascendit, at in his ventriculis, ob assi&shy;<lb/>duum tum cerebri tum huius reticularis plexus motum, miscetur cum vi&shy;<lb/>talibus spiritibus aer. </s>

<s>Itaque spiritus animales evadunt ex aere, eo quo di&shy;<lb/>ximus modo praeparato, et ex vitalibus dictis spiritibus, quae res a nemine <lb/>ante me observata fuit &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>191). </s></p><p type="main">

<s>Se dunque lo spirito animale si compone in parte di aria comune, e <lb/>se al dir dello stesso Cartesio &egrave; un'aereosa sostanza esalata dal sangue, si <lb/>dovrebbe, quando veramente scorresse dentro i tubi de'nervi, rivelar come <lb/>l'aria stessa ne'suoi effetti pneumatici, e manifestarsi all'occhio nell'appa&shy;<lb/>renza delle solite bolle, aperto il nervo o il muscolo inturgidito sott'acqua. </s>

<s><lb/>Ora il Borelli, fatta diligentemente questa esperienza, vide che nulla galloz&shy;<lb/>zolava per l'acqua stessa, d'ond'ei ne concluse non venire i muscoli dagli <lb/>spiriti animali n&egrave; enfiati n&egrave; mossi. </s>

<s>&ldquo; Sectis enim in longum musculis vi&shy;<lb/>ventis animalis, intra aquam demersis, in qua ob dolorem vehementissime <lb/>agitantur, in tam grandi, copioso et vehementi fervore et ebullitione illius <lb/>aurae spiritosae in musculis excitata erumperent, et ascenderent a cicatrice <lb/>innumerabiles bullae aereae per aquam, ut in aheno ferventi contingit, quod <lb/>prorsus non apparet. </s>

<s>Igitur non a spiritibus corporeis musculi inflantur et <lb/>moventur &rdquo; (De motu anim., P. II, Romae 1681, pag. </s>

<s>36). </s></p><p type="main">

<s>Altri chiarissimi Fisiologi dicevano che i muscoli s'enfiano inturgiditi <lb/>dal sangue stillatovi dalle arterie e non potuto risorbir dalle vene. </s>

<s>Il Borelli <lb/>dimostr&ograve; ch'era anche questa ipotesi falsa e lo fece prima con argomenti <pb xlink:href="020/01/1177.jpg" pagenum="52"/>conclusi da principii anatomici e fisiologici, e poi ricorrendo in ultimo al&shy;<lb/>l'esperienza. </s>

<s>Se &egrave; vero, diceva, che i muscoli mossi inturgidiscono di san&shy;<lb/>gue ivi stagnante, dovrebbero nell'esercizio pesar pi&ugrave; che quando si riman&shy;<lb/>gono in quiete. </s>

<s>Perci&ograve; fatto giacere un'uomo sopra una tavola, in modo che <lb/>l'umbilico, in cui risiede il centro della gravit&agrave;, risponda esattamente sul <lb/>taglio del prisma o coltello da bilance, sopra il quale si suppone che la ta&shy;<lb/>vola stessa sia equilibrata; se comincer&agrave; quell'uomo a mettere in moto le <lb/>gambe, inturgiditi di sangue, secondo l'ipotesi, i muscoli, dovrebbesi veder <lb/>preponderare il corpo da quella parte, <emph type="italics"/>quod tamen,<emph.end type="italics"/> fattane l'esperienza, dice <lb/>il Borelli, <emph type="italics"/>non contigit<emph.end type="italics"/> (ibi, pag. </s>

<s>39). </s></p><p type="main">

<s>Essendo il cuore come il primo mobile del sistema animale, o secondo <lb/>l'espression dell'Harvey, come il Sole nel Microcosmo, pensarono altri che <lb/>anco ai moti muscolari i primi e pi&ugrave; validi impulsi venissero da lui. </s>

<s>Il Bo&shy;<lb/>relli dimostr&ograve; che nemmeno una tale ipotesi potevasi dimostrare, e ci&ograve;, fra <lb/>le altre principalmente per questa ragione, perch&egrave; le arterie coronarie fa&shy;<lb/>cendo con le respettive vene un circolo a parte, ricevono anch'esse, come <lb/>la grande Aorta, l'impulso dal cuore, ed &egrave; perci&ograve; l'iniezione del sangue <lb/>fra'pori de'muscoli cardiaci un effetto prodotto dalle pulsazioni del mede&shy;<lb/>simo cuore. </s>

<s>Ma non potendo l'effetto produr la sua propria causa, sar&agrave; im&shy;<lb/>possibile che per l'iniezione del sangue si commovano i muscoli, di che il <lb/>cuore s'intesse &ldquo; unde deducitur quod neque caeteri musculi animalis in&shy;<lb/>flari possint a sanguine &rdquo; (ibi, pag. </s>

<s>42). </s></p><p type="main">

<s>Ai seguaci della Scuola iatrofisica era facile sovvenisse il pensiero che <lb/>si potesse l'inturgidire e lo scortar de'muscoli, insinuandosi dentro alle loro <lb/>fibre il sangue, dimostrar per l'esempio di ci&ograve; che si vede avvenir nelle <lb/>funi inumidite. </s>

<s>Forse questo stesso pensiero s'appresent&ograve; anche alla mente <lb/>del Borelli, ma ei dovette presto riconoscerne la fallacia, principalmente per&shy;<lb/>ch&egrave;, bene osservando, tutt'altro che somigliarsi insieme le funi e i muscoli <lb/>tengono nell'operare modi fra loro opposti. </s>

<s>La fune infatti rigonfia e scorta, <lb/>quand'&egrave; imbevuta d'umido, e quand'&egrave; arida s'assottiglia ed allunga, men&shy;<lb/>tre il muscolo invece quand'&egrave; inaridito &egrave; pi&ugrave; teso e pi&ugrave; corto. </s>

<s>S'ha di ci&ograve; <lb/>l'esempio nel cuore che contrattosi impallidisce e disteso torna a rosseg&shy;<lb/>giare, e s'ha la dimostrazione nel fatto che, ferito un muscolo mentre &egrave; <lb/>lasso, manda sangue pi&ugrave; in copia che quando &egrave; turgido e duro. </s></p><p type="main">

<s>Non avendo, cos&igrave;, trovato il Borelli da sodisfarsi di nessuna delle varie <lb/>ipotesi proposte a rendere la ragione dei moti muscolari, si volse con ogni <lb/>studio a specularne una sua nuova, che non patisse le difficolt&agrave; notate, e <lb/>che, senza presumere di darla per cosa certa, avesse pure qualche maggior <lb/>probabilit&agrave; di tutte l'altre. </s>

<s>Gli fu suggerito il principio a quella nuova spe&shy;<lb/>culazione da Raffaello Magiotti, il quale avendo trovato per esperienza che, <lb/>premendo con un dito sulla bocca di un vaso cilindrico pieno d'acqua den&shy;<lb/>tro alla quale fossero galleggianti le figurine da lui descritte nel Discorso <lb/>sopra la Renitenza dell'acqua alla compressione, si potevano, a talento dello <lb/>sperimentatore, ora mettere in un istante in moto quelle stesse figurine, e <pb xlink:href="020/01/1178.jpg" pagenum="53"/>ora nuovamente farle posare; pens&ograve; che per qualche modo simile a questo <lb/>potesse l'anima operare sul corpo, e mettere in moto le varie membra. <lb/></s>

<s>&ldquo; Considero, egli dice, in questo cilindro quell'angustissimo e capacissimo <lb/>vaso della Memoria, con acqua per altri limpida e spiritosa, per altri flem&shy;<lb/>matica e torbida. </s>

<s>Considero le figurine or pi&ugrave; grandi or pi&ugrave; piccole, or ab&shy;<lb/>bagliate or distinte, con diverse operazioni, e quand'una figurina pi&ugrave; avanti <lb/>m'impedisce un'altra pi&ugrave; indietro, qual'io vorrei pur vedere, con una lieve <lb/>scossa di Cilindro, cio&egrave; a dire con una grattata di capo, bene spesso conse&shy;<lb/>guir&ograve; l'intento. </s>

<s>Ma fuor di burla .... se il volere e principiar la compres&shy;<lb/>sione pu&ograve; essere nel medesimo istante, e come un atto solo dell'Anima, <lb/>essendo il dito o polpa della mano congiunto con l'acqua, non potr&agrave; abbas&shy;<lb/>sarsi il dito se l'acqua nel medesimo tempo non sale per le Caraffine, e <lb/>quelle non cominciano diversi giochi. </s>

<s>Adunque il volere e principiar la com&shy;<lb/>pressione e salir dell'acqua, e cominciar diversi giochi a talento e gusto <lb/>dell'Anima, sar&agrave; un atto solo di lei, quale aver&agrave; in un certo modo ampliata, <lb/>per quanto &egrave; lungo il Cilindro, la sfera dell'attivit&agrave; sua. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di pi&ugrave;, quella notabil differenza tra liquidi e solidi svanisce nei mu&shy;<lb/>scoli, nervi, tendini, cartilagini, ecc., come in materia n&egrave; liquida, n&egrave; solida, <lb/>della quale si serve l'anima per fare ad un tempo diverse operazioni. </s>

<s>Bene <lb/>&egrave; ragione che, se la virt&ugrave; impressa nell'acqua, corpo molto grave, pu&ograve; nel <lb/>medesimo istante dare il moto ad altre figurine in giu, ad altre in su, ed <lb/>altre fermare in equilibrio; cos&igrave;, e meglio, possa tutta ad un tempo l'Anima, <lb/>che &egrave; incorporea, cominciare a toccare, a vedere, a pensare, e fare altre di&shy;<lb/>verse operazioni. </s>

<s>Cos&igrave; nel medesimo punto pu&ograve; muovere il Musico la bat&shy;<lb/>tuta, la tastata e la voce. </s>

<s>Cos&igrave; pu&ograve; l'Anima, nel medesimo tempo, attuar <lb/>l'istesso umido e chilo nutricando tutte le nostre membra, trasmutandolo in <lb/>diverse sostanze e figure, non alterando con l'umido e suoi minimi la simme&shy;<lb/>tria. </s>

<s>Dove, se ella si servisse dei solidi, tutte le membra senza alcuna pro&shy;<lb/>porzione darebbero nel rotondo e nel simile. </s>

<s>&rdquo; (Targioni, Notizie degli <lb/>aggr. </s>

<s>ecc., T. II, P. I, Firenze 1780, pag. </s>

<s>190, 91). </s></p><p type="main">

<s>Era facile, dietro questi concetti e dietro gli apparecchiamenti fatti dal&shy;<lb/>l'ipotesi cartesiana, sovvenisse il pensiero che, stillando il cervello un li&shy;<lb/>quido, piuttosto ch'esalare un'aura, e riempiendosi i canaletti de'nervi di <lb/>questo liquido, si potesse la pronta comunicazione di moto ai muscoli attri&shy;<lb/>buire alla volont&agrave;, che per mezzo di qualcuno dei tanti organi cerebrali, <lb/>de'quali non conoscesi l'uso, faccia l'effetto stesso del dito sulla bocca del <lb/>cilindro, nelle esperienze idrostatiche del Magiotti. </s>

<s>Rintuzzavano per&ograve; i ri&shy;<lb/>gogliosi germogli a questo pensiero l'esperienze autorevoli di Tommaso Bar&shy;<lb/>tholin, il quale aveva, come dicemmo, o credeva di aver dimostrato, per <lb/>mezzo delle allacciature, che nessuna aereosa o liquida sostanza scorre nel&shy;<lb/>l'interiore cavit&agrave; dei nervi. </s>

<s>Ma poi il Malpighi, facendo pi&ugrave; diligente ana&shy;<lb/>tomia microscopica del cervello, cred&egrave; di averlo trovato composto di ghian&shy;<lb/>dole secernenti un umore, che di lass&ugrave; scoli attraverso alle fibrille nervee, <lb/>e stim&ograve; fosse il fatto messo fuor di ogni dubbio dallo stillicidio, che seguita <pb xlink:href="020/01/1179.jpg" pagenum="54"/>dopo il taglio nelle ultime propaggini. </s>

<s>Alle esperienze del Bartholin, che <lb/>parevano dimostrar tutto il contrario, rispondeva il Malpighi che il non ve&shy;<lb/>dersi inturgidire il nervo, fra le allacciature, non era argomento concludente, <lb/>perch&egrave; il liquido trova nelle numerose diramazioni libero quel passaggio, che <lb/>gli era stato prima impedito nel tronco. </s></p><p type="main">

<s>Narra esso Malpighi, nella Autobiografia pi&ugrave; volte da noi citata, come <lb/>fosse giunto alla scoperta delle novit&agrave; anatomiche nel cervello, e facendo <lb/>distinzione fra ci&ograve; che si poteva dimostrar come certo, e ci&ograve; che potevasi <lb/>mettere in controversia, cos&igrave; a proposito del succo nerveo, ci lasci&ograve; scritto: <lb/>&ldquo; Nervei succi existentia apud plures controvertitur, vel saltem eius natura <lb/>diversimode exponitur, sicut et usus, ita ut nil fere obscurius occurrat apud <lb/>Auctores. </s>

<s>Illud tamen mihi videtur in hac re maximum habere momentum <lb/>quod, sectis extremis nervorum tubuli, ubi in ultimas solvuntur propagines, <lb/>succus erumpat. </s>

<s>In cauda bovis et similium hinc inde nervus excurrit tri&shy;<lb/>bus vel quatuor fistulis coagmentatus: in his itaque, facta extremo digiti <lb/>ungue compressione, humoris motus intra exaratas fistulas contenti deprehen&shy;<lb/>ditur et successiva turgentia, qui tandem per excitatum foramen exit, the&shy;<lb/>rebinthinae instar, fluidus enim est et glutinosus. </s>

<s>In nervis, immediate a <lb/>spinali medulla erumpentibus, cum ob mollitiem compressi lacerantur, non <lb/>ita facile succus occurrit eiusque motus manifestatur, quare solidiores extre&shy;<lb/>mique nervi lustrandi sunt. </s>

<s>Nec obstat nervum ligatura facta non turgere, <lb/>cum lateraliter propagines habeat reticulariter propaginatas, in qua idem suc&shy;<lb/>cus, impedito ulteriori progressu, derivari potest: languidus enim est impe&shy;<lb/>tus, quem a cerebro recipit nerveus succus, unde ex quocumque impedi&shy;<lb/>mento comprimente et vetante, ulteriorem insinuationem retardari, sisti, et <lb/>ad latera derivari potest &rdquo; (Opera posthuma cit., pag. </s>

<s>27). Queste esperienze <lb/>furono poi dopo il Malpighi ripetute dal Bellini, il quale tenne come cosa <lb/>di fatto che &ldquo; il liquido dei nervi scorre sempre incessantemente e tien sem&shy;<lb/>pre pieni di s&egrave; i suoi canali &rdquo; (Discorsi di Anat., Milano 1837, pag. </s>

<s>15), e <lb/>il Lancisi concludeva alla necessit&agrave; di quel succo, per mettere in moto i <lb/>muscoli, osservando &ldquo; quod ligato nervo .... ad musculum aliquem pertin&shy;<lb/>gente, eius motus deficit, tamdemque, flaccescente musculo, penitus cessat &rdquo; <lb/>(De motu cordis, Romae 1728, pag. </s>

<s>9). </s></p><p type="main">

<s>Quel pensiero di applicare alla trasmissione del moto nei muscoli il <lb/>principio idrostatico del Magiotti, dappoich&egrave; il Malpighi ebbe contro il Bar&shy;<lb/>tholin dimostrata l'esistenza di un liquido fluente dal cervello dentro i tu&shy;<lb/>buli de'nervi; quel pensiero diciam dunque, per ridurci col&agrave; d'onde mosse <lb/>il discorso, essere principalmente sovvenuto al Borelli, che lo pose per fonda&shy;<lb/>mento a questa parte della sua Meccanica animale. </s>

<s>Egli suppone infatti che la <lb/>prima causa eccitante il moto ne'muscoli sia il succo nerveo, il quale &egrave; fatto <lb/>dal cervello stillare in essi muscoli, per un moto di compressione delle fibre <lb/>cerebrali; moto che si comunica nell'istante fino alle ultime diramazioni <lb/>nervose, per quella medesima ragione idrostatica, per cui la pression del dito <lb/>nell'esperienze del Magiotti si comunica nell'istante dalla bocca al fondo del <pb xlink:href="020/01/1180.jpg" pagenum="55"/>Cilindro, e da una estremit&agrave; all'altra di un tubo membranoso pien d'acqua, <lb/>come, per esempio, nel lungo tubo di un intestino. </s>

<s>&ldquo; Et sicuti videmus in <lb/>intestino aqua repleto, et utrimque clauso, quod uno eius extremo impulso, <lb/>compresso et leviter percusso, subito commotio et concussio ad oppositum <lb/>terminum intestini turgidi communicatur, quatenus fluidae partes inter se <lb/>contiguae, longo ordine se consequentes una alteram impellendo et concu&shy;<lb/>tiendo motionem diffundunt usque ad extremam intestini partem; sic pari&shy;<lb/>ter a quacumque levi compressione, ictu, aut irritatione facta in principiis <lb/>canaliculatarum fibrarum nervearum in ipso cerebro existentibus, necesse <lb/>est ut ipsae fibrae concussae et agitatae instillent guttas aliquas illius succi, <lb/>quo turgent internae eorum spongiosae substantiae intra musculorum car&shy;<lb/>neam molem &rdquo; (De motu animal. </s>

<s>cit., P. II, pag. </s>

<s>58, 59). </s></p><p type="main">

<s>Ma bench&egrave; la facile e subitanea trasmissione del moto ne'liquidi avesse <lb/>fatto ritrovare al Borelli la probabile ragion fisica della rapida trasmissione <lb/>dei moti volontari, infino all'estreme propaggini dei nervi, questo solo per&ograve; <lb/>non bastava, ma conveniva di pi&ugrave; spiegare in che modo cos&igrave; fatte stille di <lb/>sacco nerveo avessero potuto indurre ne'muscoli quella s&igrave; facile e repen&shy;<lb/>tina contrazione, dalla quale immediatamente dipendono i moti delle mem&shy;<lb/>bra. </s>

<s>Si risovvenne allora dell'effervescenza, in che si commovono a un tratto <lb/>due liquidi mescolati insieme nelle chimiche ampolle, e immagin&ograve; che una <lb/>simile effervescenza venga a mettersi nel sangue e nella linfa de'muscoli, <lb/>quando scende a stillar sopr'essi il liquido spiritoso de'nervi. </s>

<s>Ond'&egrave; che, <lb/>esaminate altre cause e trovatele tutte insufficienti a spiegare il fatto &ldquo; re&shy;<lb/>stat solummodo, egli conclude, ut ex mistione succi nervei cum lympha, vel <lb/>cum sanguine, fermentatio et ebullitio oriatur similis eis, quae passim in <lb/>chimicis elaborationibus observantur &rdquo; (ibi, pag. </s>

<s>63). </s></p><p type="main">

<s>Questa ipotesi dei moti muscolari, bench&egrave; si pubblicasse nel 1681, l'aveva <lb/>nulladimeno speculata il Borelli parecchi anni avanti, e forse prima che Gu&shy;<lb/>glielmo Croone si fosse incontrato in que'medesimi pensieri, ch'ei pubblic&ograve; <lb/>in Amsterdam, nel 1667, in un Trattatello intitolato <emph type="italics"/>De ratione motus mu&shy;<lb/>sculorum.<emph.end type="italics"/> Premessa una diligente anatomia delle fibre e una nuova fisiologia <lb/>de'loro atti vitali in contrarsi e in dilatarsi, vien l'Autore a proporre la sua <lb/>ipotesi, intorno alla quale, sentite le gravissime difficolt&agrave;, confessa di non <lb/>avere, in cosa tanto oscura, ad affermare nulla di certo. </s>

<s>Ma comunque sia, <lb/>egli dice, per quell'impulso, che riceve l'estremit&agrave; del nervo nel cervello, <lb/>si scuote tutta la serie delle fibre, infino alle loro estreme diramazioni per <lb/>entro la sostanza dei muscoli, dove stillano quel loro liquido spiritoso. </s>

<s>&ldquo; Cum <lb/>enim iam satis probatum sit vim quamdam a cerebro per nervos advehi in <lb/>musculum, nec, si oculis fides habenda sit, quicquam in nervis appareat, <lb/>quod huic usui magis convenire queat, quam opulentissimus ac spirituosus <lb/>iste succus, qui constanti circuitu per omnes nervos traducitur; quid obsecro, <lb/>magis verisimile est, quam vim illam cum hoc liquore deferri, aut potius <lb/>esse hunc ipsum liquorem, sive spiritum animalem fibrarum impetu a ner&shy;<lb/>vorum ramulis excussum? </s>

<s>Quod si sit, illud quoque admodum probabile <pb xlink:href="020/01/1181.jpg" pagenum="56"/>erit ex admistione liquoris huiusce, sive spiritus cum spiritibus sanguinis, <lb/>continuo spirituosarum omnium particularum, quae in vitali motus musculi <lb/>succo insunt, magnam agitationem contingere, uti cum spiritus vini spiritui <lb/>sanguinis humani admiscetur. </s>

<s>Namque omnem animantis partem vivifico <lb/>quodam ac spirituoso liquore turgescere, supra quidem monui, ac omnibus <lb/>est in confesso, ac nemo fere tam in Chymia hospes est, qui nesciat quanta <lb/>particularum commotio ac agitatio ex variis inter se permistis liquoribus ac&shy;<lb/>cidere soleat &rdquo; (pag. </s>

<s>23). </s></p><p type="main">

<s>Prese risoluzione il Croone, com'egli stesso dice nella lettera al Com&shy;<lb/>melin, di dare alla luce questa sua nuova ipotesi de'moti muscolari, in quel <lb/>tempo che gli era venuto avviso in Parigi come lo Stenone aveva sotto i <lb/>torchi i suoi Elementi di miologia. </s>

<s>Apparvero veramente quegli Elementi alla <lb/>luce in Firenze, in quel medesimo anno 1667, e l'Autore, dimostrando geo&shy;<lb/>metricamente la proposizione &ldquo; in omni musculo, dum contrahitur, tumorem <lb/>contingere, etiamsi musculus contractus aequalis maneret musculo non con&shy;<lb/>tracto &rdquo; (pag. </s>

<s>16) rovesciava dalle fondamenta, senza saperlo, l'ipotesi messa <lb/>dallo stesso Croone, in quel medesimo tempo, alla luce, e insieme anche <lb/>l'altra simile, che avrebbe pubblicata il Borelli quattordici anni dopo. </s></p><p type="main">

<s>Scendeva come corollario da quella proposizione che nessuna estranea <lb/>materia s'insinua a ingrossare le fibre muscolari, per indurvi le contrazioni, <lb/>intorno a che lo Stenone si dichiara nella lettera al Thevenot, non osando <lb/>per&ograve; di decider nulla di certo, ma facendo osservare che lo stillarsi il succo <lb/>nerveo in mezzo alle fibre muscolari, e il produrre una subita effervescenza <lb/>nella linfa e nel sangue, di che sono esse fibre sempre imbevute, erano ipotesi <lb/>deboli di per s&egrave;, e non confortate da nessuna esperienza: parole insomma e <lb/>non fatti. </s>

<s>&ldquo; Spiritus animales, subtiliorem sanguinis partem, vaporem eius, et <lb/>nervorum succum multi nominant, sed verba haec sunt, nihil exprimentia. </s>

<s><lb/>Qui ulterius pergunt salinas, sulphureasque partes, vel spiritui vini analo&shy;<lb/>gum quid adferunt, quae vera forsan sed nec certa nec satis distincta. </s>

<s>Ab <lb/>assumpto vini spiritu restitui exhaustas vires experientia docet, sed ipsi hoc <lb/>humori, quem spiritum vocamus, an alii materiae adscribendum, quae spi&shy;<lb/>ritum fluidum reddit, aut aliam forte ob causam illi iuncta est, quis deter&shy;<lb/>minaverit? (ibi, pag. </s>

<s>63). </s></p><p type="main">

<s>Il Borelli non manc&ograve; di rispondere a queste difficolt&agrave; promosse dallo <lb/>Stenone, e se l'effervescenza dentro le fibre de'muscoli non si vede, non <lb/>importa diceva, vedendosene cos&igrave; manifesti gli effetti. </s>

<s>Alla proposizione ste&shy;<lb/>noniana, nella quale provavasi che i muscoli, mentre che si contraggono, <lb/>non ricrescon di mole, contrapponeva un'altra proposizione che &egrave; la XV della <lb/>II Parte <emph type="italics"/>De motu animalium,<emph.end type="italics"/> e nella quale il Borelli stesso dimostrava non <lb/>esser possibile che il muscolo inturgidisca, senza che vi si insinui una ma&shy;<lb/>teria estranea, la quale faccia dentro i pori delle fibre l'effetto meccanico <lb/>de'cunei, e perci&ograve; concludeva esser impossibile che il muscolo indurisca e <lb/>non rigonfi. </s>

<s>&ldquo; Talis autem inflatio esset impossibilis, nisi particulae corpo&shy;<lb/>ris advenientis ad instar cuneorum insinuarentur intra porositates earum-<pb xlink:href="020/01/1182.jpg" pagenum="57"/>dem fibrarum, aut illa spatia, vi percussiva expanderent, quae actio pariter <lb/>ad vim et actionem cunei reducitur &rdquo; (Editio cit., pag. </s>

<s>30). </s></p><p type="main">

<s>Giovanni Bernoulli, cercando un soggetto da porre a nuovo cimento la <lb/>gi&agrave; sperimentata virt&ugrave; del Calcolo differenziale, lo trov&ograve; in questi moti mu&shy;<lb/>scolari, intorno ai quali scrisse una Dissertazione, che seguita com'appen&shy;<lb/>dice al trattato <emph type="italics"/>De separatione liquidorum<emph.end type="italics"/> del Michelotti. </s>

<s>Ivi &egrave; il Bernoulli <lb/>fedel seguace dell'ipotesi del Borelli, e quanto al teorema dello Stenone, in <lb/>cui dimostravasi che il muscolo si contrae, non per aggiunta di materia, ma <lb/>per la sola mutazion di figura, trasformandosi da un parallelogrammo obli&shy;<lb/>quangolo in retto, sentenzi&ograve; che quella era opinione &ldquo; prorsus ridicula, et <lb/>pro mero lusu ingenii Authoris habenda &rdquo; (Venetiis 1721, pag. </s>

<s>4). Eppure <lb/>Fisiologi pi&ugrave; recenti, facendo contrarre i muscoli sott'acqua e notando se <lb/>scorgevasi alcuna variazion di livello, bench&egrave; non ne concludessero nulla di <lb/>certo, pur parvero l'esperienze inclinare a favore dello Stenone. </s></p><p type="main">

<s>Erasi in ogni modo il Borelli acquistata tanta autorit&agrave; in cos&igrave; fatte que&shy;<lb/>stioni di Meccanica animale, che resisterono le sue dottrine a tutte le con&shy;<lb/>tradizioni di allora, e istituitasi la Scuola iatromatematica i discepoli si stu&shy;<lb/>diarono di migliorarle, per renderle cos&igrave; nell'universale pi&ugrave; accette. </s>

<s>Il Bellini, <lb/>che fu tra que'discepoli uno de'pi&ugrave; valentemente operosi, commemorando <lb/>nel suo trattato <emph type="italics"/>De motu cordis<emph.end type="italics"/> in che modo avesse dimostrato il Borelli la <lb/>ragione dei moti muscolari, soggiunge con gran compiacenza che la mede&shy;<lb/>sima cosa &ldquo; nos alia via longe diversa et magis naturali demonstramus &rdquo; <lb/>(Op. </s>

<s>omnia, P. II, Venetiis 1708, pag. </s>

<s>161). Consiste questa ipotesi pi&ugrave; na&shy;<lb/>turale nell'ammettere che le fibre muscolari sieno composte di villi natu&shy;<lb/>ralmente contrattili, cosicch&egrave; non ci sia d'altro bisogno a farle effettivamente <lb/>contrarre, che dell'azione degli stimoli esterni. </s>

<s>Egli osserva che la virt&ugrave; di <lb/>contrarsi non &egrave; propria solo ai tessuti organici, ma a tutta la materia, di <lb/>che cerca le prove in moltissimi fatti naturali, e fra questi nel conglobarsi <lb/>delle gocciole liquide, ammirando la potenza di quella forza di contrazione, <lb/>che vince le resistenze opposte dal pesantissimo argento vivo. </s></p><p type="main">

<s>Egli ammette col Malpighi che sia il cervello una glandula secernente <lb/>un umore spiritoso, che stilla in mezzo alle fibre muscolari per il condotto <lb/>dei nervi, e ammette col Borelli che, mescendosi quell'umor nerveo alla <lb/>linfa e al sangue delle stesse fibre, vi produca una subita effervescenza, e <lb/>cos&igrave; le faccia contrarre. </s>

<s>Ma mentre che il Borelli riduceva la causa imme&shy;<lb/>diata di cos&igrave; fatte contrazioni alle bollicelle sollevatesi nell'effervescenza, le <lb/>quali insinuandosi fra le porosit&agrave; della sostanza fibrosa operano meccani&shy;<lb/>camente in dilatarle, come tanti cunei ficcatisi in mezzo per forza; il Bel&shy;<lb/>lini ammetteva ne'villi, di che s'intessono i muscoli, una nativa loro irri&shy;<lb/>tabilit&agrave;, ad eccitar la quale le bollicelle sollevatesi nella effervescenza operino <lb/>come stimoli accidentalmente sopravvenuti di fuori. </s></p><p type="main">

<s>Alla raccolta delle Opere belliniane, da noi sopra citata e alla quale <lb/>sopraintese Giovanni Bohn con tanto amorose e sapientissime cure, &egrave; pre&shy;<lb/>messa una Sinopsi, nella quale i principii, a cui s'informa l'ipotesi dell'Au-<pb xlink:href="020/01/1183.jpg" pagenum="58"/>tore, son ridotti a sommi capi, quasi essenze stillate dalla polpa di squisi&shy;<lb/>tissimi pomi, e infuse dentro a varie piccole ampolle. </s>

<s>Per quel che riguarda <lb/>il moto del liquido dentro i nervi, i principii belliniani si riducono sostan&shy;<lb/>zialmente ai tre capi seguenti: &ldquo; I. </s>

<s>Datur liquidum in nervis igne concre&shy;<lb/>scens. </s>

<s>II. </s>

<s>Eiusmodi liquido nervi semper in statu naturali sunt pleni. </s>

<s>III. </s>

<s>Vis <lb/>praecipua, qua liquidum nervorum a cerebri glandulis exprimitur, et per <lb/>ipsos influxum agitur, est pressio proveniens a dilatatione arteriarum Piam <lb/>matrem intexentium, et etiam intime totum cerebrum intercurrentium. </s>

<s>&rdquo; </s></p><p type="main">

<s>Per quel che poi pi&ugrave; particolarmente concerne i moti de'muscoli, cos&igrave; <lb/>necessarii che volontarii, le dottrine del Bellini si trovano sostanzialmente <lb/>comprese ne'seguenti principii: &ldquo; I. </s>

<s>Licet ad imperium voluntatis aut ap&shy;<lb/>petitus cresceret impetus et copia liquidi per nervos quantum libet, non ta&shy;<lb/>men id esse potest incrementum, quod satis sit subitae ac vehementi con&shy;<lb/>tractioni villi. </s>

<s>II. </s>

<s>Subita ac violenta villi contractio, nisusque in oppositos <lb/>terminos, fit per influxum liquidi subito rarescentis aut quaquaversum se se <lb/>cum impetu in bullas innumeras effundentis. </s>

<s>Oportet autem liquidum in&shy;<lb/>fluens sit tantae molis, ut cum rarescit aut in bullas effunditur, ipsius par&shy;<lb/>tes per universam villi longitudinem amplitudinemque se premant. </s>

<s>III. </s>

<s>Motus <lb/>villi rarescente intra ipsum, aut se in bullas effundente, liquido componitur <lb/>ex contractione per longitudinem et distractione per amplitudinem: cum vil&shy;<lb/>lus in suam longitudinem restituitur, contrahitur per amplitudinem, et causa <lb/>huius contractionis breviter iudicatur. </s>

<s>&rdquo; </s></p><p type="main">

<s>Udimmo dianzi il Bellini compiacersi di questa sua ipotesi e a para&shy;<lb/>gone di quella del Borelli vantarla per pi&ugrave; naturale, cio&egrave; pi&ugrave; conforme alla <lb/>Natura, la quale non opera ne'muscoli con forze morte, come nelle mac&shy;<lb/>chine, ma con le proprie e particolari virt&ugrave; della vita. </s>

<s>Tanto parve ragione&shy;<lb/>vole questo perfezionamento introdotto nell'ipotesi borelliana, che Alberto <lb/>Haller accolse il fondamento delle idee belliniane nel suo trattato di Fisio&shy;<lb/>logia. </s>

<s>Svolgendo infatti il libro XI, alla terza Sezione, vi si trova insegnato <lb/>che la forza contrattile &egrave; insita al muscolo, e che, sebben non sempre ve&shy;<lb/>dasi in atto, pur si pu&ograve; mettere anche artificialmente per via degli stimoli, <lb/>che vi producono una irritazione. </s>

<s>Questa irritazione, nelle parti vive, diffe&shy;<lb/>risce da quella che osservasi nella morte, e non si pu&ograve; confondere con la <lb/>facolt&agrave; del sentire. </s>

<s>&ldquo; Laurentius Bellinius vim contractilem naturalem fuse <lb/>exposuit, quae ab acribus excitata se causa molestiae liberet, musculos mo&shy;<lb/>veat, sanguinis motum acceleret .... mechanice omnia ex hypothesi citra <lb/>experimentum. </s>

<s>Praeterea et ipse Vir clarissimus, et qui eum sunt secuti, <lb/>contractionem vivam a mortua, hanc a nervosa non satis videntur distinxisse &rdquo; <lb/>(Elem. </s>

<s>Physiol., T. IV, Lausannae 1766, pag. </s>

<s>461). </s></p><p type="main">

<s>S'argomenta assai facilmente da queste parole quali fossero i perfezio&shy;<lb/>namenti introdotti dall'Haller nelle dottrine del Bellini, d'onde ne nacque <lb/>quella celebre Scuola halleriana, ch'ebbe cos&igrave; numerosi e valenti seguaci <lb/>nella Svizzera, in Francia e anche fra noi in Italia. </s>

<s>Il Fisiologo di Berna <lb/>accusa il Nostro di avere speculata la sua ipotesi senza il fondamento del-<pb xlink:href="020/01/1184.jpg" pagenum="59"/>l'esperienze, ma le stesse esperienze halleriane servono benissimo a far di&shy;<lb/>stinguere fra le vie da tenersi l'una dall'altra; rischiarano altres&igrave; quella <lb/>ch'&egrave; la pi&ugrave; diretta; fino a un certo punto per&ograve;, oltre il quale si trovano <lb/>immersi nelle tenebre pi&ugrave; profonde i desiderosi di veder il termine del fa&shy;<lb/>ticoso cammino. </s>

<s>Fu perci&ograve; che molti deliberarono di tornarsene indietro, a <lb/>somiglianza di chi, presumendo di avere in ogni modo a trovare la riu&shy;<lb/>scita, si lusinga di avere smarrita la via, a cui cerca altra pi&ugrave; pratica scorta <lb/>e pi&ugrave; fida. </s></p><p type="main">

<s>&Egrave; notabile esempio nel numero di costoro Stefano Hales, il quale in sul <lb/>cominciar del secolo XVIII ritorn&ograve; indietro a cercare fra le ipotesi proposte <lb/>da'Fisiologi che lo avevano preceduto se qualcuna per avventura sodisfaces&shy;<lb/>segli meglio delle pi&ugrave; recenti. </s>

<s>Rivolse pi&ugrave; particolarmente la sua attenzione <lb/>all'ipotesi di coloro, da'quali s'attribuivano i moti muscolari all'impulso, <lb/>che viene al sangue dal cuore, e non arretrato dalla grande autorit&agrave; n&egrave; dalle <lb/>ragioni, con ch'era stata confutata una tale ipotesi dal Borelli, volle sotto&shy;<lb/>porla all'esame di nuovi e pi&ugrave; delicati esperimenti. </s>

<s>&ldquo; Sono gi&agrave; ventisette <lb/>anni, scriveva, che leggendo le congetture poco sodisfacenti degli Autori, che <lb/>trattano del moto muscolare, mi posi a fare sperienze sugli animali viventi, <lb/>per iscoprire se il sangue, col solo suo moto meccanico, avesse una forza <lb/>bastevole a dilatare le fibre muscolose, e a scemare per tal via in loro lun&shy;<lb/>ghezza, e produrre i grandi effetti del moto muscolare. </s>

<s>Questo si fu il mo&shy;<lb/>tivo che m'indusse ad entrare nel vasto campo delle esperienze che ho fatto &rdquo; <lb/>(Statica animale, traduz. </s>

<s>ital., Napoli 1750, pag. </s>

<s>66). Ebbe per&ograve; da cos&igrave; fatte <lb/>laboriose esperienze ragionevolmente a concludere &ldquo; che la forza del sangue <lb/>ch'entra ne'muscoli &egrave; molto piccola in agguaglio di quel che dovrebb'es&shy;<lb/>sere per produrre il moto muscolare &rdquo; (ivi, pag. </s>

<s>65). </s></p><p type="main">

<s>Rimaneva da questa alesiana conclusione sperimentale rovesciata dalle <lb/>sue fondamenta anche un'altra ipotesi macchinata da Giorgio Baglivi, e gi&agrave; <lb/>da s&egrave; stessa vacillante, per la troppo debole struttura. </s>

<s>Incomincia dal con&shy;<lb/>siderare il celebre Archiatro pontificio la grande efficacia del sangue nei moti <lb/>muscolari; efficacia dimostrata da un'esperienza dello Stenone, che allac&shy;<lb/>ciando l'arteria magna vide gli arti posteriori rimanere immobili in un cane; <lb/>confermata dal veder tuttavia seguitare a pulsare il cuore estratto dalle rane, <lb/>e pi&ugrave; concludentemente dagli aneurismi, che inducono il torpore nelle parti <lb/>non pi&ugrave; irrigate. </s>

<s>Ripensando poi in che modo possa esercitare il sangue <lb/>questa sua efficacia, ricorre a quelle particelle solide di zolfo &ldquo; salium varii <lb/>generis, terrae, globulorum rubrorum, striarum nutritiarum et mille aliarum <lb/>particularum &rdquo; che il sangue stesso &ldquo; ab aere, fossilibus, et vegetabilibus <lb/>continuo haurit, et in sinu fovet &rdquo; (Opera omnia, Dissertatio De motu musc., <lb/>Lugduni 1710, pag. </s>

<s>404). </s></p><p type="main">

<s>Queste particelle solide fanno sopra le fibre muscolari l'effetto stesso <lb/>dei <emph type="italics"/>curri<emph.end type="italics"/> applicati a muovere i pesi. </s>

<s>&ldquo; Et quia velociter currunt impresso <lb/>illis a corde pulsante vehementissimo impetu, necesse est ut fibrarum fila <lb/>ad contactum globulorum currentium premantur, et undulando veluti cri-<pb xlink:href="020/01/1185.jpg" pagenum="60"/>spentur, quae crispatura, quoniam maxime sensibilis est in medio musculi, <lb/>ubi sanguis velocius currit, sequitur inde, ut extrema fibrarum singula&shy;<lb/>rum versus medium contrahantur, brev&igrave;ora fiant et apposita sublevent ossa &rdquo; <lb/>(pag. </s>

<s>405). </s></p><p type="main">

<s>A ci&ograve; semplicemente ridurrebbesi l'effetto prodotto dalle particelle so&shy;<lb/>lide contenute nel sangue, quand'elle fossero perfettamente sferiche. </s>

<s>Ma se <lb/>sono irregolari, allungate pi&ugrave; per un verso che per un altro, si produrranno <lb/>nelle fibre de'muscoli moti pi&ugrave; complicati, sinuosi e vermicolari, come quelli <lb/>per esempio degli intestini. </s>

<s>Una tale irregolarit&agrave; poi nelle particelle solide <lb/>del sangue, &egrave;, soggiunge il Baglivi, prodotta dalla virt&ugrave; propria del succo <lb/>nerveo, il quale &ldquo; cum sit summopere tenue, elasticum, et radiis lucis affine, <lb/>incredibili celeritate a phantasia impulsum, cum sanguine musculi iam iam <lb/>movendi miscetur, et quadam elastica irradiatione, cum proportione tamen <lb/>et aequilibrio, minima eius mutat et alterat, mutataque minimorum figura, <lb/>mutantur etiam diametri &rdquo; (pag. </s>

<s>406). Di qui nasce, secondo lo stesso Ba&shy;<lb/>glivi, che se non ci fossero gli antagonisti, i moti muscolari sarebbero con&shy;<lb/>tinui, come veramente continui son quelli del cuore e degli intestini. </s>

<s>Per <lb/>conseguenza, dal mancare un cos&igrave; fatto antagonismo, si risolve ogni difficolt&agrave;, <lb/>e si rende la ragion chiarissima delle differenze, che passano tra i moti na&shy;<lb/>turali e i volontari (ivi, pag. </s>

<s>406, 7). </s></p><p type="main">

<s>Il mancare a cos&igrave; fatta ipotesi ogni buon fondamento di fisica e di mec&shy;<lb/>canica la fece facilmente repudiare ai Fisiologi, sopra i quali tanto pi&ugrave; torn&ograve; <lb/>inefficace l'autorit&agrave; del'grande Archiatro, ripensando alla sopra riferita con&shy;<lb/>clusione alesiana. </s>

<s>L'Hales stesso, veduto che, per le tante vie fino allora <lb/>tentate, non si riusciva a dare quella cos&igrave; lungamente desiderata ragionevole <lb/>soluzione al problema dei moti muscolari, pieg&ograve; anch'egli con molti altri le <lb/>vele a ricevere le aure, che si sentivano spirare da un nuovo oriente. </s>

<s>I primi <lb/>aliti, bench&egrave; insensibili a molti, movevano incerti dal libro delle Questioni <lb/>neutoniane, nella XXIV delle quali si leggevano queste parole: &ldquo; Annon <lb/>motus animalis medii eiusdem actherei efficitur, vibrationibus quae in cere&shy;<lb/>bro potestate voluntatis excitantur, indeque per solida, pellucida et unifor&shy;<lb/>mia nervorum capillamenta in muscolos eorum contrahendorum ac dilatan&shy;<lb/>dorum gratia propagentur? </s>

<s>Nervorum capillamenta singula solida esse pono <lb/>et uniformia, ut motus vibrans medii aetherei per ea uniformiter et non in&shy;<lb/>terrupte ab usque uno extremo ad alterum propagetur &rdquo; (Optices Lib. </s>

<s>III <lb/>Quaestiones, Patavii 1773, pag. </s>

<s>144). </s></p><p type="main">

<s>I pensieri del Newton, ch'erano appariti s&igrave; oscuri, ebbero a un tratto <lb/>uno splendido commento nelle scoperte di Stefano Gray, dalle quali s'ar&shy;<lb/>gomentava che, come l'etere elettrico diffondevasi da un capo all'altro di <lb/>una corda bagnata, cos&igrave; poteva similmente diffondersi dall'una all'altra estre&shy;<lb/>mit&agrave; del nervo. </s>

<s>L'Hales perci&ograve; inclinava a preferire questa nuova ipotesi a <lb/>tutte le altre, che s'erano dal Cartesio in poi sotto varie forme proposte, e <lb/>a renderla anche pi&ugrave; probabile citava fatti fisiologici e patologici, come per <lb/>esempio quello che, grattandosi talvolta le bolle in alcuna parte del corpo, <pb xlink:href="020/01/1186.jpg" pagenum="61"/>si sente in altre parti lontane risvegliarsi punture, che si succedono al metro <lb/>del menare delle unghie. (Statica anim. </s>

<s>cit., pag. </s>

<s>65). </s></p><p type="main">

<s>Cos&igrave;, l'etere neutoniano, riconosciuto simile negli effetti all'elettrico, si <lb/>applic&ograve; alle funzioni della vita animale sotto il nome di <emph type="italics"/>fluido biotico,<emph.end type="italics"/> e le <lb/>antiche teorie meccaniche del Borelli parvero essere allora dalla Fisiologia <lb/>licenziate per sempre. </s>

<s>Ma come talvolta l'aria combattuta da venti contrarii <lb/>si rischiara da una parte, in quel medesimo tempo che si oscura dall'altra, <lb/>e come, dietro una subitanea luce abbagliante, le tenebre si fanno pi&ugrave; fitte; <lb/>cos&igrave; avvenne alla scienza, quando lieta di avere scoperto nell'elettricit&agrave; i mi&shy;<lb/>steriosi spiriti della vita, si domand&ograve; d'onde avesse cotesta vitale elettricit&agrave; <lb/>l'origine, e com'ella operasse a produrre i moti muscolari. </s>

<s>E perch&egrave; s'am&shy;<lb/>metteva con facilit&agrave; da tutti non potere essere altrove quell'origine che nel <lb/>cervello, sentivasi una viva curiosit&agrave; di sapere in qual modo quel viscere, <lb/>in apparenza inerte, potesse rassomigliarsi ai globi tornatili di zolfo o di vetro <lb/>conosciuti allora dell'artificiosa elettricit&agrave; le sole possibili sorgenti. </s>

<s>Inteso ci&ograve;, <lb/>era men difficile intendere l'azione elettrica sui muscoli, ridotta facilmente <lb/>dall'Haller a uno de'pi&ugrave; efficaci stimoli esterni. </s></p><p type="main">

<s>Era a questo punto del suo faticoso cammino giunta la scienza, quando <lb/>occorse la memoranda scoperta di Luigi Galvani. </s>

<s>E perch'&egrave; un fatto sto&shy;<lb/>rico che i germi di novit&agrave; scientifiche pi&ugrave; fecondi sono quasi sempre sboc&shy;<lb/>ciati sotto il cielo d'Italia, e un'occulta cognazione, inconsapevole anche a s&egrave; <lb/>stessi, &egrave; sempre fra i grandi ingegni, specialmente della medesima nazione; <lb/>non vogliamo lasciar di notare in queste pagine di storia un singolare esem&shy;<lb/>pio della detta cognazione che passa inconsapevole fra il Galvani stesso e il <lb/>Borelli. </s>

<s>Chi legge nel trattato <emph type="italics"/>De motu animalium<emph.end type="italics"/> la proposizione CCXIII <lb/>della Parte II riman sorpreso di gran maraviglia, trovando ivi descritta in&shy;<lb/>torno alle rane scorticate quell'esperienza, che conteneva in s&egrave; come in fonte <lb/>nascosto i fiumi delle dottrine galvaniche non solo, ma di quelle stesse del <lb/>Volta. </s>

<s>&ldquo; Videmus autem quod talis irritatio efficitur in nervis cruralibus <lb/>Ranarum exenteratarum quotiescumque acu punguntur, vel succo salino <lb/>tanguntur &rdquo; (Editio cit., pag. </s>

<s>433). </s></p><p type="main">

<s>Mentre insomma che la Scienza fisiologica confessava d'ignorar come <lb/>avesse origine quell'elettricit&agrave; animale, che dietro le speculazioni del Newton <lb/>e l'esperienze del Gray tenevasi pi&ugrave; per certa oramai che per probabile, <lb/>usciva fuori il Galvani a dimostrar che i muscoli e i nervi componevano, a <lb/>somiglianza di quei ritrovati dall'arte, un nuovo apparecchio elettrico della <lb/>vita. </s>

<s>&ldquo; Huius peculiare nec antea cognitum ingenium esse videtur ut a mu&shy;<lb/>sculis ad nervos vel ab his potius ad illos tendat vehementer, subeatque <lb/>illico vel arcum, vel hominum catenam vel quaecumque alia deferentia cor&shy;<lb/>pora, quae a nervis ad musculos breviori et expeditiori ducant itinere, ce&shy;<lb/>lerrimeque per eadem ab illis ad hos excurrat. </s>

<s>Ex hoc autem duo maxime <lb/>profluere videntur, duplicem scilicet in his partibus electricitatem esse, po&shy;<lb/>sitivam aliam, ut credere est, aliam negativam, atque alteram ob altera pe&shy;<lb/>nitus esse natura seiunctam, secus enim, aequilibrio habito, nullus motus, <pb xlink:href="020/01/1187.jpg" pagenum="62"/>excursus electricitatis nullus, nullum muscularis contractionis phaenomenon &rdquo; <lb/>(A. Galvani, De viribus electric., Mutinae 1792, pag. </s>

<s>39). </s></p><p type="main">

<s>Ammesso per&ograve; che la sede dell'elettricit&agrave; sia nel muscolo, e che perci&ograve; <lb/>il cervello non dia ma riceva del fluido elettrico, difficilissima riusciva la <lb/>ragione dei moti volontari. </s>

<s>Cos&igrave; fatta difficolt&agrave; era ben sentita dallo stesso <lb/>Galvani, ma tanta parvegli essere la certezza, che veniva dai fatti sperimen&shy;<lb/>tati, da non doversi dubitar se il circolo sia veramente dal muscolo al nervo. </s>

<s><lb/>Quando poi il Volta, fatte nuove e pi&ugrave; diligenti esperienze, ritrov&ograve; che l'elet&shy;<lb/>tricit&agrave; veramente fluiva, come pareva pi&ugrave; conveniente, dal nervo al muscolo, <lb/>e allora al Galvani non dispiacque di aver errato, e anzi parve che in certo <lb/>modo se ne compiacesse nella risposta ch'ei diresse a Bassiano Carminati, <lb/>il quale lo aveva da Pavia informato delle prime scoperte elettriche fatte <lb/>ivi dal Volta. </s></p><p type="main">

<s>&ldquo; Gli esperimenti di lui, scriveva del Volta il Galvani, chiaro dimostre&shy;<lb/>rebbono potersi avere i moti muscolari, diretto il fluido elettrico, non solo <lb/>dal muscolo al nervo, siccome io supponeva, ma eziandio dal nervo al mu&shy;<lb/>scolo, e potersi avere, non solo per mezzo della scarica, ma ancora per una <lb/>sopraccarica forzata ed impetuosa della supposta boccia muscolare, lo che <lb/>ammesso, chi non vede quanto riesca felice la spiegazione de'moti musco&shy;<lb/>lari volontarii? </s></p><p type="main">

<s>&ldquo; L'anima, per eccitar questi, non deve che dal cervello ov'ella risiede, <lb/>colla maravigliosa sua ed incomprensibil forza ed impero, determinare una <lb/>maggior copia di fluido elettrico animale nel cervello raccolto pel nervo con&shy;<lb/>duttore al muscolo; oppure dar forse un impulso maggiore a quello che na&shy;<lb/>turalmente in esso nervo esiste. </s>

<s>Si avranno allora le contrazioni non altri&shy;<lb/>menti che si ebbero dal celebratissimo signor Volta, allorch&egrave; egli aggiunse <lb/>all'elettricit&agrave; animale del nervo un pochino di artifiziale elettricit&agrave;, e crebbe <lb/>in conseguenza l'impulso e l'azione di quella, che nell'interna superficie <lb/>della fibra muscolare si stava in una specie di inerzia o di ozioso equilibrio. </s>

<s><lb/>Ma allorch&egrave; si aggiunge elettricit&agrave; ad una superficie di una Boccia di Ley&shy;<lb/>den, ne esce dall'opposta, per la legge dell'uguaglianza e dell'equilibrio <lb/>delle due superficie, e tanta ne esce da una quanto se ne aggiunge all'altra; <lb/>dunque avvependo lo stesso nella supposta boccia muscolare, quanto di fluido <lb/>nerveo elettrico accorrer&agrave; dal cervello pel nervo all'interna parte, ossia su&shy;<lb/>perficie del muscolo, tanto ne escir&agrave; dall'opposta superficie, ossia parte <lb/>esterna del medesimo, che &egrave; gi&agrave; sempre irrigata da fluidi conduttori atti a <lb/>disperderla, e a portarla fuori del corpo, e quindi luogo darassi sempre a <lb/>una nuova copia e carica..... &rdquo; </s></p><p type="main">

<s>&ldquo; Ammesso un tale costante ingresso ed egresso del detto fluido ner&shy;<lb/>veo dal muscolo, per leggi note e costanti, chi non vede tosto essere facile <lb/>lo spiegare come costantemente corra il suddetto fluido al muscolo, senza <lb/>che se ne accumuli in esso all'eccesso, e in modo che impedisca l'aggiunta <lb/>di nuovo copia o naturalmente fluente dal cervello al medesimo muscolo o <lb/>dall'anima determinatavi? </s>

<s>Fenomeno che certo in niuno de'sistemi finora <pb xlink:href="020/01/1188.jpg" pagenum="63"/>inventati facilmente intendesi &rdquo; (Appandice al trattato De virib. </s>

<s>electric. </s>

<s>cit., <lb/>pag. </s>

<s>72, 73). </s></p><p type="main">

<s>Ma poco dopo venne il Volta a tentare colle sue valide forze di distrug&shy;<lb/>gere il bello architettato edifizio, dimostrando come quella che si credeva <lb/>essere un'elettricit&agrave; propria e intrinseca all'animale, non era altro che uno <lb/>stimolo esterno, sopravveniente dall'elettricit&agrave; naturale eccitatasi dal contatto <lb/>di due diversi metalli. </s>

<s>Il Galvanismo ebbe al poderoso incorso a cedere il <lb/>campo, il quale si prov&ograve; di riconquistar pi&ugrave; volte con l'aiuto di valorosi Fi&shy;<lb/>siologi, che vennero in sua difesa, ma le vicende di questa lotta e la vit&shy;<lb/>toria non bene ancora decisa stanno ad attestare quanto sia ottuso l'ingegno <lb/>dell'uomo a penetrare addentro ai misteri della vita. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Le studiose esercitazioni fatte da tanti e si valorosi Fisiologi, che si <lb/>trasmisero dall'uno all'altro l'ufficio di render sodisfazione ai curiosi di <lb/>saper la causa dei moti muscolari, tornarono insomma inutili, come conclu&shy;<lb/>desi dalla passata storia, e l'infelice frutto che se ne raccolse fu di accen <lb/>dere, in chi ricorreva a quelle fonti desideroso, una sete pi&ugrave; viva. </s>

<s>Ma l'infe&shy;<lb/>licit&agrave; di questi studii, che parevano per verit&agrave; meritevoli d'altro premio, si <lb/>giudica dal considerar di pi&ugrave; come, anco quando quelli cos&igrave; ingegnosamente <lb/>divisati fossero stati i modi, secondo i quali opera la Natura sui muscoli a <lb/>produrre i moti volontarii, rimanevasi nonostante inesplicato il modo dei moti <lb/>necessarii, che procedono indipendenti affatto o dalla volont&agrave; o dagli istinti <lb/>animali. </s>

<s>Il cuore, per esempio, pulsa ne'suoi moti di sistole e di diastole, <lb/>anche in chi dorme, e l'intestino reciproca le sue peristaltie e l'antiperi&shy;<lb/>staltie o voglia o non voglia l'animale. </s>

<s>Non par per&ograve; che i processi mecca&shy;<lb/>nici, immaginati a spiegare in che modo faccia la volont&agrave; convellere le fibre <lb/>nervee e spremere il loro succo nelle fibre muscolari, perch&egrave; debbano a un <lb/>tratto contrarsi; si possano applicare al moto di que'visceri sempre continuo, <lb/>e ne'naturali suoi ordini non mai perturbato. </s></p><p type="main">

<s>Il Cartesio, descrivendo nel suo trattato <emph type="italics"/>De homine<emph.end type="italics"/> gli organi, per <lb/>mezzo de'quali si muove la macchina animale, non par che si curi se non <lb/>che di rendere la ragione dei moti volontarii. </s>

<s>Il moto d&egrave;l cuore &egrave; secondo <lb/>lui necessario, com'&egrave; necessario il restringersi e il dilatarsi di tutti i corpi, <lb/>ai quali scemino o s'accrescano i gradi del calore. </s>

<s>Questo calore per&ograve; non <lb/>&egrave; nativo del cuore, ma gli vien partecipato dal sangue, il quale entra in una <lb/>subita calorosa effervescenza, mescolandosi quel poco rimasto ne'ventricoli <lb/>con l'altro che sopravviene per l'arteria venosa. </s>

<s>&ldquo; Paulum vero illud rare&shy;<lb/>facti sanguinis, quod in ventriculis eius restabat, se illi, qui recens ingre&shy;<lb/>ditur statim immiscens, est fermenti cuiuspiam loco, sanguinem illum re&shy;<lb/>pente calefacientis et dilatantis, qua opera cor intumescit et durescit, et <pb xlink:href="020/01/1189.jpg" pagenum="64"/>mucro nonnihil accedit ad basin &ldquo; (Editi cit., pag. </s>

<s>163). Ma dappoich&egrave; il <lb/>sangue cos&igrave; rarefatto ha cominciato a correre per le arterie &ldquo; cor continuo <lb/>detumescit mollescitque eiusque mucro recedit a base, quia scilicet non re&shy;<lb/>manet ipsi parum sanguinis in ventriculis eius &rdquo; (ibi). </s></p><p type="main">

<s>Bench&egrave; questa ipotesi cartesiana fosse anch'ella, come le altre imma&shy;<lb/>ginaria, pur non conoscendosi ancora bene le funzioni della respirazione, e <lb/>gli uffici de'polmoni, non avevansi argomenti ragionevoli per confutarla. </s>

<s>Si <lb/>diceva che non erano allora ben conosciute le funzioni della respirazione, <lb/>perch&egrave; il Cartesio ebbe qualche sentore del vero, osservando che l'aria, <lb/>nell'atto che l'animale respira, si mescola in qualche modo col sangue, e <lb/>serve ad accrescergli l'intensit&agrave; del calore (ivi, pag. </s>

<s>80). Ma perch&egrave;, co&shy;<lb/>munque sia, ritenevasi per secondario quello, che era il fatto principale, e <lb/>s'ignorava perci&ograve; la fisiologia polmonare, non si poteva allora o ripudiare <lb/>o confutare l'ipotesi del Cartesio, n&egrave; con la certezza dei fatti, n&egrave; con l'au&shy;<lb/>torit&agrave; delle ragioni. </s></p><p type="main">

<s>Cotesta certezza e cotesta autorit&agrave; nella scienza erano per&ograve; venute ai <lb/>tempi del Borelli, il quale si avvide bene che la sua ipotesi dei moti mu&shy;<lb/>scolari non si poteva applicare ai moti del cuore, o che almeno per appli&shy;<lb/>carvela bisognavano nuovi commenti industriosamente da lui stesso condotti <lb/>ed esposti nel Cap. </s>

<s>VI della II Parte Dei moti animali. </s>

<s>Incomincia prima di <lb/>tutto a distinguere, fra le cause motive del cuore, una immediata e l'altra <lb/>mediata, e mentre vuol nella proposizione LXXVII dimostrar che la prima <lb/>di queste cause non differisce da quella medesima, che muove i muscoli vo&shy;<lb/>lontari, conclude nella proposizione seguente che la differenza non &egrave; altro <lb/>che nella seconda; vale a dire nella causa mediata. </s></p><p type="main">

<s>Essendo che dunque i muscoli volontari si contraggono &ldquo; inflatis vexi&shy;<lb/>culis eorum pororum &rdquo; e dall'altra parte il modo di operare della Natura <lb/>&egrave; nell'ordine e negli strumenti sempre consimile a s&egrave; medesimo, &ldquo; sic quo&shy;<lb/>que immediata causa tensionis cordis erit inflatio vexicularum pororum eius <lb/>facta a fermentativa ebullitione tartarearum partium sanguinis a succo spi&shy;<lb/>rituoso ex orificiis nervorum instillato &rdquo; (Editio cit., pag. </s>

<s>151). </s></p><p type="main">

<s>La causa prima e mediata per&ograve; che muove il cuore, prosegue nelle sue <lb/>dimostrazioni il Borelli, non pu&ograve; essere in nessum modo quella stessa degli <lb/>altri muscoli che muovon le membra, perch&egrave; mentre un braccio o una <lb/>gamba, per esempio, si muove quando, e come e dove io voglio, il cuore <lb/>&ldquo; non obsequitur voluntatis praecepto, sed non secus ac moletrina sem&shy;<lb/>per movetur, sive velimus, sive nolimus, etiam dormientibus nobis &rdquo; (ibi, <lb/>pag. </s>

<s>152). Di pi&ugrave;, non &egrave; lecito al cuore, come ai muscoli che muovono le <lb/>sopra dette membra, perseverare lungamente nel moto o cessare a talento <lb/>&ldquo; sed caeca quadam necessitate efficit vehementissimos ac fere momenta&shy;<lb/>neos ictus alternis vicibus interceptis, pausis et morulis aeque temporaneis, <lb/>nec unquam, donec animal vivit et non aegrotat, talem obstinatam metho&shy;<lb/>dum operandi interrumpit &rdquo; (ibi). </s></p><p type="main">

<s>Essendo cos&igrave;, &egrave; da cercar dunque, seguita il Borelli il suo ragiona-<pb xlink:href="020/01/1190.jpg" pagenum="65"/>mento, qual sia la causa prima e immediata che fa muovere il cuore con <lb/>metro s&igrave; regolato, e indipendentemente da qualunque deliberata volont&agrave; del&shy;<lb/>l'animale. </s>

<s>Che si possa un tal metro rassomigliare a quello del pendolo non <lb/>sembra, perch&egrave; converrebbe immaginare un'organo, come sarebbe una val&shy;<lb/>vola, che aprendosi e chiudendosi con moto sempre equitemporaneo, ora ri&shy;<lb/>tenga gli spiriti animali dentro il cervello, e ora gli anmetta. </s>

<s>Ma oltre che <lb/>non si vedono queste valvole, e nessuno ne ha potuto osservare mai il gioco, <lb/>resterebbe s sapere qual sia la causa, che le apre e le chiude sempre in <lb/>tempo cos&igrave; ben regolato. </s>

<s>&ldquo; Alia igitur organica structura inquiri debet, quae <lb/>nedum possibilis et facilis sit, sed praeterea passim in naturalibus operatio&shy;<lb/>nibus observetur, et sufficiens sit ad superius phaenomena pulsationum cor&shy;<lb/>dis salvanda &rdquo; (ibi, pag. </s>

<s>155). </s></p><p type="main">

<s>Di cos&igrave; fatta struttura organica parve al Borelli di aver trovato l'esem&shy;<lb/>pio in quei filtri, o in quelle sottilissime fistole di vetro, le quali, bench&egrave; <lb/>sieno di liquido tutte piene, lo fanno nonostante cadere a gocciole, che si <lb/>succedono l'una all'altra con pause quasi uguali. </s>

<s>Immagina perci&ograve; che i <lb/>nervi sieno simili a quelle fistole, sempre pieni di un umor viscido, che <lb/>ha nel cervello la fonte. </s>

<s>L'ordine regolare, secondo il quale si succedono <lb/>quelle gocciole insinuandosi tra le fibre del cuore, &egrave; secondo il Borelli, una <lb/>conseguenza delle leggi idrauliche. </s>

<s>Perch&egrave; mantenendosi sempre a un ugual <lb/>livello il liquido nella cavit&agrave; cerebrale, e permanendo i nervi sempre nello <lb/>stesso calibro, la quantit&agrave; e la velocit&agrave; del flusso proseguono sempre con <lb/>una medesima legge tanto inalterabile, che si pu&ograve; col moto dei flussi liquidi, <lb/>poste quelle condizioni che pur si verificano nell'organo cerebro nervoso, <lb/>dar regola di moto agli stessi orologi. </s></p><p type="main">

<s>&Egrave; questa, secondo il Borelli, la speculata ragione delle pulsazioni del cuore: <lb/>che se non si vedono cos&igrave; ugualmente pulsare i muscoli, ne'quali s'aprono <lb/>in modo simile gli orifici dei nervi, dipende egli dice da ci&ograve; che quegli orifici, <lb/>quando gli spiriti hanno a servire al moto dei muscoli, non si possono aprire, <lb/>se non che dall'atto imperioso della volont&agrave;, che ne scuote le fibre. </s>

<s>Ma quando <lb/>hanno a servire ai meti del cuore, trovano il passaggio facile e aperto, senza <lb/>che quelle stesse fibre sentano altrimenti il bisogno di essere vellicate. </s></p><p type="main">

<s>Immaginata cos&igrave; e descritta la struttura organica, creduta sufficiente a <lb/>salvare il fenomeno delle pulsazioni del cuore, ritornandovi sopra col pen&shy;<lb/>siero, parve all'Autore stesso quella essere una speculazione non troppo fe&shy;<lb/>lice, e perci&ograve; ne soggiunge un'altra, che commove i lettori colla novit&agrave;, <lb/>forse perch&egrave; si presenta nelle sembianze di un paradosso. </s>

<s>&ldquo; Non erit su&shy;<lb/>pervacaneum videre an adsint rationes dubitandi utrum cordis motus fieri <lb/>possit, non a mera naturali mechanica necessitate, sed ab eadem animae <lb/>facultate, a qua omnes alii musculi moventur &rdquo; (ibi, pag. </s>

<s>458). Il dubbio si <lb/>risolve nell'appresso proposizione LXXX, nella quale il Borelli intende di <lb/>dimostrare esser possibile che il moto de&igrave; cuore si faccia dalla medesima <lb/>facolt&agrave; animale conoscitiva, ma senza alcuna avvertenza, per la consuetudine <lb/>e per l'abito inveterato. </s></p><pb xlink:href="020/01/1191.jpg" pagenum="66"/><p type="main">

<s>Nel trattato <emph type="italics"/>De motu animalium<emph.end type="italics"/> avevano avuto questi concetti relativi <lb/>alle pulsazioni del cuore una preparazione dalle proposizioni antecedente&shy;<lb/>mente dimostrate, e specie dalla XXV di questa stessa Parte II, dove l'abi&shy;<lb/>tuale perizia, con cui gli spiriti animali si ammettono dalla volont&agrave; a com&shy;<lb/>movere certi determinati nervi invece di altri, s'attribuisce, non alla Natura <lb/>ma all'esercizio e all'esperienza acquistata infino dall'infanzia, la quale sto&shy;<lb/>lida, smemorata e studiosa pi&ugrave; dell'utile che del sapere &ldquo; fit ut nobis insciis <lb/>retineamus postea altius impressam artem et habitum, quo spiritus in cere&shy;<lb/>bro moveri debent, ut certas artium motiones exequi valeant &rdquo; (ibi, pag. </s>

<s>62). </s></p><p type="main">

<s>Da una simile esperienza crede il Borelli che sieno da principio gover&shy;<lb/>nati i moti del cuore, i quali in seguito divengono abituali, e anzi necessarii <lb/>di modo che non ci pu&ograve; poi pi&ugrave; la volont&agrave; col suo imperio. </s>

<s>Ne reca di ci&ograve; <lb/>varii esempii, qual sarebbe quello de'muscoli delle palpebre, i quali bench&egrave; <lb/>sieno volontarii pur giungono a coprire e ad aprire gli occhi, per un'abi&shy;<lb/>tudine contratta infin dalla infanzia, intanto che talvolta, non avendosi al&shy;<lb/>cun timore di offesa, pur chiudiam le palpebre, come facciamo quando ve&shy;<lb/>diam per esempio moversi al nostro viso un'amica mano, che ci accarezza. <lb/></s>

<s>&ldquo; Non est igitur impossibile ut dici possit actio voluntaria illa quae habit&ugrave; <lb/>fit, et nos non advertimus eam v&ograve;luisse, imo putamus eam nolle. </s>

<s>Quia nempe <lb/>talis habitus non acquiritur nisi praecedant plurimi et frequentes actus a <lb/>voluntate imperati, a quibus tandem, ob exercitium spiritus, peritiam quan&shy;<lb/>dam acquirunt et instrumenta organica quasi laevigantur, et promptiores <lb/>redduntur ad operandum, et in hoc consistere videtur vis et potentia con&shy;<lb/>suetudinis &rdquo; (ibi, pag. </s>

<s>160). </s></p><p type="main">

<s>S'opporr&agrave; in contrario, cos&igrave; prevede il Borelli, che il cuore estratto da <lb/>una testuggine seguita per pi&ugrave; ore a pulsare, ma seguitano, si risponde, a <lb/>contrarsi, dop'essere stati recisi da un serpente, anche i muscoli del suo <lb/>dorso, i quali servonc senza dubbio ai moti volontarii. </s>

<s>Ci&ograve; avviene perch&egrave; <lb/>rimangono ivi gli organi e le cause efficienti del moto volontario, anche <lb/>dopo la scissione, ond'&egrave; da dire del cuore, tuttavia palpitante bench'estratto <lb/>vivo dal petto, quel che si dice della coda recisa in un serpente (ivi, pag. </s>

<s>161). </s></p><p type="main">

<s>Tali essendo le ipotesi proposte dal Borelli a sciogliere il tanto difficile <lb/>e controverso problema dei moti muscolari, o governati dalla necessit&agrave; o <lb/>dall'arbitrio, il giudizio che se ne pu&ograve; dare dagl'imparziali &egrave; che le sopra <lb/>riferite proposizioni si concludono sull'esempio di fatti fisici, che mal si con&shy;<lb/>vengono colle funzioni della vita animale. </s>

<s>Quell'entrare che fa l'Autore in <lb/>tanti e tanto minuti particolari distrae pi&ugrave; presto che condurre alla persua&shy;<lb/>sione, perch&egrave; nessuno che si sia formato un giusto concetto della dignit&agrave; <lb/>degli organi ordinati agli esercizi della vita, pu&ograve;, per esempio, patir di udirsi <lb/>rassomigliare il cervello alto sgocciolare di una Clessidra. </s>

<s>I seguaci perci&ograve; <lb/>della stessa Scuola borelliana evitarono di entrare in cos&igrave; fatte minutaglie, <lb/>che parevano un volere spendere la propria ignoranza in moneta spicciola, <lb/>e sentita la terribilit&agrave; del mistero, che si parava ai loro occhi, stettero mo&shy;<lb/>desti a supporre che un fluido stilli dal cervello nei muscoli per la via di-<pb xlink:href="020/01/1192.jpg" pagenum="67"/>retta dei nervi. </s>

<s>Colla modesta semplicit&agrave; del principio si resero anche pi&ugrave; <lb/>chiare e pi&ugrave; accettabili le conclusioni, di che ne porge un'esempio notabi&shy;<lb/>lissimo fra tutti gli altri il Lancisi. </s></p><p type="main">

<s>Egli chiama tonici in generale tutti quei moti che si dicevano neces&shy;<lb/>sarii o naturali, e suppone che questi si producano da un continuo e pe&shy;<lb/>renne influsso del liquido cerebrale, per esempio, ne'muscoli del cuore o <lb/>nelle fibre della tunica membranosa degl'intestini. </s>

<s>Quel perenne influsso lo <lb/>ricevono altresi i muscoli motori delle membra, ma essi non si muovono, <lb/>se non per aggiunta di liquido, che alla loro nativa inerzia dia nuovo ecci&shy;<lb/>tamento; aggiunta, che pu&ograve; farsi o non farsi ad arbitrio, e per la quale si <lb/>determina nelle varie membra o la quiete o il moto. </s></p><p type="main">

<s>Questa semplicissima ipotesi la proponeva il Lancisi nella sua Disser&shy;<lb/>tazione <emph type="italics"/>De structura et usu Gangliorum,<emph.end type="italics"/> la quale, perciocch&egrave; ha il discorso <lb/>rivolto al Morgagni, fu com'appendice inserita nell'<emph type="italics"/>Adversaria anatomica <lb/>Quinta<emph.end type="italics"/> di lui. </s>

<s>&ldquo; In hoc enim, scrive l'Autore di quella Dissertazione, mo&shy;<lb/>tus tonicos a superadditis differre arbitramur, quod illi a continuo perenni&shy;<lb/>que influxu liquidorum musculares lacertos villosque tendentium oriantur; <lb/>hi secus a temporaria immissione, vel saltem ab aucto nuper influxu eorum&shy;<lb/>dem liquidorum excitantur, ac tandiu perdurant, donec idem recens addi&shy;<lb/>tus influxus perseveraverit. </s>

<s>Hoc sane in singulis artefactis machinis, quae <lb/>per decursum, impetumque aquarum, statis temporibus moventur, usuve&shy;<lb/>nire comperimus: in cartariis enim aliisque hydraulicis certum quoddam <lb/>sufflamen praesto est, cuius contrariis motibus laticum illapsus artificis ar&shy;<lb/>bitrio, prout res postulat, promoveri vel prohiberi solet &rdquo; (Patavii 1719, <lb/>pag. </s>

<s>113). </s></p><p type="main">

<s>Scorto da un s&igrave; felice pensiero, si dette il Lancisi con ogni sollecitu&shy;<lb/>dine a cercare se nulla fosse nei nervi che si potesse credere far l'ufficio <lb/>di quei moderatori del flusso, che si sogliono applicare agli edifizii idraulici. </s>

<s><lb/>Per trovar ci&ograve; conveniva rivolgersi alle osservazioni anatomiche, alle quali <lb/>il diligentissimo Falloppio aveva da un secolo e mezzo dati gl'inizii. </s>

<s>Descri&shy;<lb/>vendo il sesto paio, &ldquo; Verum unum notetur, egli scrive nelle <emph type="italics"/>Osservazioni,<emph.end type="italics"/><lb/>quod maximi momenti est, in hoc sexto pari, quod tunica vel membrana <lb/>illa qua vestitur, dum per forameu elabitur, aliquando manifeste adsorbens <lb/>aliquot fibrillas istius nervi, aliquando etiam immanifeste, cum extra calva&shy;<lb/>riam est producit quoddam <emph type="italics"/>corpus oblongum olivaris figurae,<emph.end type="italics"/> aliquando <lb/>simplex, aliquando geminum in utroque latere, quod colore carneum vide&shy;<lb/>tur, ac substantia nerveum durumque admodum est. </s>

<s>Hoc corpus olivare in <lb/>quamdam desinit fibram nerveam, quae per cervicem declinans propagini&shy;<lb/>bus quibusdam nervorum, qua cervice oriuntur, a primo scilicet et secundo <lb/>pari et quarto et quinto et sexto, vel a primo, secundo, quinto sexto et <lb/>septimo copulata est, veluti reticulum aut complicationem quamdam effor&shy;<lb/>mat, quae per totam cervicem in unoquoque latere anteriori descendit, atque <lb/>in ista complicatione nova alia corpora olivaria aliquando concrescunt, in&shy;<lb/>certo tamen numero, quae nulla alia substantia quam nervea, et quasi in <pb xlink:href="020/01/1193.jpg" pagenum="68"/>callum concrescente, constant. </s>

<s>Cum ego primus talem nervorum copulam <lb/>observarim, primum quoque nomine imposito <emph type="italics"/>plexum sexti paris<emph.end type="italics"/> appellabo &rdquo; <lb/>(Francofurti 1584, pag. </s>

<s>456). </s></p><p type="main">

<s>Descrive cos&igrave; il Falloppio, il quale ne fu veramente il primo osserva&shy;<lb/>tore, com'egli dice, quel nervo che si presenta come un lungo cordone di&shy;<lb/>steso dalla base del cranio al coccige, e che &egrave; oggid&igrave; fra gli Anatomici co&shy;<lb/>nosciuto sotto il nome di <emph type="italics"/>Gran simpatico<emph.end type="italics"/> o d'<emph type="italics"/>Intercostale.<emph.end type="italics"/> Rigonfia quel <lb/>nervo di qnando in quando nel suo decorso in alcuni nodi rassomigliati dal <lb/>Falloppio nella loro forma alle olive, e perci&ograve; detti da lui <emph type="italics"/>corpi olivari,<emph.end type="italics"/> e <lb/>ricevendo radicelle nervose da ogni punto dell'asse cerebro spinale e som&shy;<lb/>ministrandole alla sua volta, d&agrave; luogo a formarsi quei <emph type="italics"/>plessi,<emph.end type="italics"/> i filamenti dei <lb/>quali attraversano pel loro mezzo qua e l&agrave; nuovi corpi olivari, dal Fallop&shy;<lb/>pio stesso ivi diligentemente descritti. </s></p><p type="main">

<s>A que'corpi olivari fu dato poi il nome proprio di <emph type="italics"/>Gangli,<emph.end type="italics"/> e bench&egrave; al <lb/>grande Anatomico modenese non isfuggisse nulla che concernesse la loro <lb/>intima costituzione, non sa per&ograve; o non dice almeno quale, nell'intenzione <lb/>della Natura, ne potesse esser l'uso. </s>

<s>Il Vesalio che, per detrarre qualche <lb/>parte del merito al suo rivale, riduceva le olive falloppiane al numero di <lb/>quelle ghiandolette descritte gi&agrave; da Galeno, rassomigliandole ai nodi delle <lb/>canne, disse ch'erano ordinate alla robustezza del nervo, come pure al fine <lb/>di tener bene in posto esso nervo cred&egrave; che fossero dalla Natura ordinati <lb/>que'cos&igrave; artificiosi intrigamenti dei plessi. </s>

<s>&ldquo; Ut ligamentosam substantiam <lb/>musculis quibusdam nunc ad opportunum exortum, nunc ad innexum inser&shy;<lb/>tionemve, nunc roboris occasione imprimis accedere mihi habeo persuasis&shy;<lb/>simum; sic membraneam substantiam propriae nervorum qui procul sunt <lb/>ducendi substantiae ad robur conferre una est docendum. </s>

<s>Uti ad substan&shy;<lb/>tiae illius augmentum et robur illae etiam conducunt Glandulae, quas a Ga&shy;<lb/>leno in ultimo De partium usu libro pertractatas esse mox subiiciam &rdquo; (Gabr. </s>

<s><lb/>Falloppii Observ. </s>

<s>Examen, Venetiis 1564, pag. </s>

<s>100). </s></p><p type="main">

<s>Dell'uso de'Gangli non furono, in un secolo e mezzo decorso dalla loro <lb/>scoperta, dette da nessuno cose importanti infino al Lancisi, il quale sotto&shy;<lb/>postili a nuova e pi&ugrave; diligente anatomia cred&egrave; di aver ritrovato in essi quel&shy;<lb/>l'organo moderatore del flusso nerveo, preveduto s&igrave; necessario a intendere <lb/>il vario governo de'moti naturali e dei volontarii. </s>

<s>&ldquo; Perspicis, Morgagni <lb/>praeclarissime, Gangliorum usum, tametsi alii quoque inferioris notae con&shy;<lb/>siderari possint, praecipuum esse ut eadem nervis admota atque intertexta, <lb/>sint veluti moderatores, rectoresve eorum animalium motuum, qui vel ar&shy;<lb/>bitrio obsecundant vel ipso arbitrio celerius moveri aut retardari debent &rdquo; <lb/>(Dissertatio in loco cit., pag. </s>

<s>113). </s></p><p type="main">

<s>Si confermava il Lancisi in questa supposizione dal veder che i nervi, <lb/>i quali servono ai sensi, procedono oltre liberi senz'essere interrotti da gan&shy;<lb/>gli moderatori, perch&egrave; debbono essere come porte sempre aperte a ricevere <lb/>le impressioni, che a loro vengono d'ogni parte dagli oggetti, per i sottili <lb/>mezzi interposti. </s>

<s>&ldquo; Nervos qui sensibus ancillantur, ut olfactorios, opticos etc. <pb xlink:href="020/01/1194.jpg" pagenum="69"/>nullis gangliis munitos esse reperio. </s>

<s>Id vero tu, Vir praeclarissime, haud <lb/>frustra Naturam molitam esse intelligis, siquidem cum organa sensuum exci&shy;<lb/>piendis externis pulsibus aeque semper exposita esse debeant, ut non tam <lb/>ad agendum quam ad patiendum sint comparata, par erat ut spiritus anima&shy;<lb/>les, et quidquid cum iisdem fluitat, per apertos obviorum nervorum ductus <lb/>aequabili tenore influerent. </s>

<s>Sunt enimvero sensus in corpore quasi quaedam <lb/>viae, ut Tullius ait, ad oculos, ad aures a sede animi perforatae. </s>

<s>Nulla idcirco <lb/>in iis aut repagula aut incitamenta addenda vel interponenda erant &rdquo; (ibi, <lb/>pag. </s>

<s>112). </s></p><p type="main">

<s>In conclusione hanno per il Lancisi i Gangli un uso importantissimo e <lb/>nuovo: gli riguarda come altrettanti piccoli cervelli collocati fuori del cra&shy;<lb/>nio, o come tante sentinelle avanzate ad avvisar del subitaneo incorrere dei <lb/>nemici il Re, che se ne sta rinchiuso nella sua Rocca. </s>

<s>&ldquo; Quamobrem per&shy;<lb/>pendenti olim mihi detectam structuram menteque conceptum officium Gan&shy;<lb/>gliorum, subiit animo suspicari an eadem in cerebri subsidium ita sint com&shy;<lb/>parata ut appellari possint exigua quaedam ac peculiaria cerebella, voluntariis <lb/>tamen ac superadditis dumtaxat motibus excitandis hic, illic, extra calvariam, <lb/>per corpus dispersa ac distributa, veluti militares quaedam stationes ad su&shy;<lb/>bitos hostium incursus collocatae &rdquo; (ibi, pag. </s>

<s>114). </s></p><p type="main">

<s>L'ipotesi del Lancisi intorno all'uso de'Gangli fu accolta con gran fa&shy;<lb/>vore da Fisiologi e da Notomisti e perciocch&egrave; le ben concepite idee son fe&shy;<lb/>conde di altre idee che, sebben sempre non raggiungano il vero, pur vi <lb/>tendono con sospiri di desiderio; s'assegn&ograve; agli stessi Gangli un altr'uso <lb/>tutto loro particolare, qual'&egrave; quello di presiedere alla vita organica e vege&shy;<lb/>tativa, ond'&egrave; che lo Chaussier chiam&ograve; il Grande simpatico <emph type="italics"/>Sistema nervoso <lb/>della vita organica,<emph.end type="italics"/> e il Bichat <emph type="italics"/>Sistema nervoso vegetativo.<emph.end type="italics"/> Cos&igrave; veniva a <lb/>intendersi come non solo i moti ritmici del cuore e i vermicolari degl'in&shy;<lb/>testini fossero indipendenti dalla volont&agrave;, ma e le funzioni stesse che in vario <lb/>modo s'esercitano dall'organismo animale. </s></p><p type="main">

<s>Faceva a principio qualche difficolt&agrave; contro l'ipotesi lancisiana il veder <lb/>che da Gangli son pure interrotti i nervi, che presiedono ai moti volontarii, <lb/>come i nervi cervicali e gli spinali, ma poi una pi&ugrave; diligente anatomia, mo&shy;<lb/>strando la differenza che passa fra questi e quelli nella loro intima strut&shy;<lb/>tura, lasci&ograve; libert&agrave; di supporre che non tutti essi Gangli moderassero gl'im&shy;<lb/>peti della volont&agrave; a un modo, ma variamente, secondo che pi&ugrave; o men <lb/>contengono e son rimpolpati di materia grigia, o secondo che son le fibre <lb/>sensorie in maggiore o minor copia conteste con le fibre motrici. </s></p><p type="main">

<s>Comunque sia, avevano gli Halleriani trovato cos&igrave; facile e semplice il <lb/>modo di sciogliere il problema de'moti necessarii e de'volontarii nelle dot&shy;<lb/>trine del loro Maestro, che non si vollero dipartire da esse, per seguir l'ipo&shy;<lb/>tesi del Lancisi, nella quale non pareva a loro possibile spiegare come mai <lb/>impedissero i Gangli il corso al fluido nerveo diretto dalla volont&agrave;, e non <lb/>impedissero il passaggio alla corrente elettrica capace di eccitar nell'animale <lb/>dolorosissime sensazioni. </s></p><pb xlink:href="020/01/1195.jpg" pagenum="70"/><p type="main">

<s>L'Haller dunque, posto il principio che i muscoli si muovono per irri&shy;<lb/>tazione, sempre che sopravvengono a loro gli stimoli proporzionati, diceva <lb/>non far nessuna maraviglia che il cuore, il ventricolo, gl'intestini si muo&shy;<lb/>vano di continuo e spontaneo moto, non mancando mai a loro il sangue, <lb/>l'aria, il cibo stimolatori. </s>

<s>I muscoli poi delle membra ora si muovono, ora <lb/>si rimangono in quiete, perch&egrave; la volont&agrave; ora manda a loro e ora gli tien <lb/>digiuni del necessario liquido stimolante. </s>

<s>&ldquo; Omnes musculi a stimulo ad <lb/>motum cientur, sed viribus v&igrave;talibus et involuntariis ut agant, stimulos na&shy;<lb/>tura adplicat: cordi sanguinem et arteriis; aerem, cibum ventriculo, inte&shy;<lb/>stinis; urinam vesicae urinariae. </s>

<s>Nunc si stimulantur ii musculi, necesse est <lb/>agere, nam et voluntarii si forent, stimulo sibi admoto operarentur. </s>

<s>Procte&shy;<lb/>rea haec organa, certe cor et eius potissimum auriculae et intestinum, sti&shy;<lb/>muli esse impatientissima, diutissime in motu perseverare, et musculos in&shy;<lb/>voluntarios ea in praerogativa superare per experimenta ostendimus. </s>

<s>Etsi <lb/>etiam aliquoties musculi voluntarii contrahi visi sunt, quando cor et inte&shy;<lb/>stina quieverant, rarum id tamen est.... Si ergo vehementer irritabilia sunt <lb/>haec organa, et si perpetuo irritantur, nihil omnino miri est si moventur <lb/>perpetuo &rdquo; (Elem. </s>

<s>Physiol., T. IV, Lausannae 1766, pag. </s>

<s>534). </s></p><p type="main">

<s>Per quel che poi riguarda i muscoli volontarii, prosegue a dir l'Haller, <lb/>essi essendo meno irritabili, e venendo dalle contrarie forze antagonistiche <lb/>contemperati, non possono uscire in atto di cospicui moti. </s>

<s>&ldquo; Iidem tamen <lb/>stimulo admoto, veneni, radentis chalybis, electrici torrentis, acrimoniae <lb/>cuiuscumque perinde in contractiones involuntarias cientur. </s>

<s>Pro stimulo au&shy;<lb/>tem videntur in voluntatis imperio spirituum nervosorum quamcumque ef&shy;<lb/>ficaciam a natura adhiberi. </s>

<s>Dum stimulus superest, contrahuntur, ac sub&shy;<lb/>ducto quiescunt. </s>

<s>Nihil adeo in discrimine musculorum involuntariorum a <lb/>reliquis arbitrio mentis subiectis musculis nodi est, quod anima vindice <lb/>egeat &rdquo; (ibi, pag. </s>

<s>535), </s></p><p type="main">

<s>Questa ipotesi halleriana veniva con gran semplicit&agrave; e facilit&agrave; conclusa <lb/>dall'ipotesi degli spiriti vitali scorrenti dal cervello ne'muscoli per la via <lb/>de'nervi, ed era ugualmente bene applicabile o si facessero consistere essi <lb/>spiriti nel succo nerveo o nel fluido elettrico, bastando che, qualunque si <lb/>fosse la loro natura, si riconoscesse il loro operare a modo di stimolo esterno. </s>

<s><lb/>L'elettricit&agrave; galvanica modific&ograve; alquanto l'ipotesi halleriana, ma l'efficacia <lb/>della causa stimolante fu anche dal Galvani approvata e seguita, sol ch'egli <lb/>faceva questa causa intima alla compage organica, e compartecipe della vita. </s></p><p type="main">

<s>&ldquo; Haec autem si concedantur, soggiungeva il Galvani dop'aver descritte <lb/>l'esperienze, dalle quali voleva concluder l'esistenza dell'elettricit&agrave; animale, <lb/>aditus forte aperietur aliquis ad explicandos musculares motus, qui in vi&shy;<lb/>vente animali fiunt, quosque considerare nunc aggredimur. </s>

<s>Nam ad volun&shy;<lb/>tarios quod attinet, poterit forte animus, mira sua vi, aut in cerebrum, ut <lb/>proclivius est credere, aut extra idem, in eum quem sibi libuerit nervum, <lb/>impetum quasi quemdam facere, quo fiet ut nerveo-electricum fluidum a <lb/>respondente musculo confestim ad eam nervi partem confluat, ad quam <pb xlink:href="020/01/1196.jpg" pagenum="71"/>fuerit per impulsum revocatum, quo cum perventum erit, cohibenti nerveae <lb/>substantiae parte per auctas tunc vires superata, ab eaque exiens excipie&shy;<lb/>tur, aut ab extrinseca nervi humiditate, aut a membranis, aut a contiguis <lb/>aliis deferentibus partibus, per easque, ceu per arcum, ad musculum a quo <lb/>discessit restituetur, ut nempe, iuxta aequilibrii legem, ad negativae muscu&shy;<lb/>larium fibrarum electricam partem ea copia tandem confluat, qua a positiva <lb/>electrica earumdem parte, per impulsum in nervo, ut opinari placuit, antea <lb/>effluxerit &rdquo; (De viribus electric. </s>

<s>comment. </s>

<s>cit., pag. </s>

<s>52). </s></p><p type="main">

<s>Ammessa questa ipotesi de'fluidi eccitatori governati dalla volont&agrave; a <lb/>produrre interrottamente i moti delle membra, restava al Galvani molto pi&ugrave; <lb/>facile a spiegare i moti naturali, ne'quali le cause stimolanti son continua&shy;<lb/>mente regolate dalle necessarie leggi della Natura. </s>

<s>&ldquo; Non dissimili forte, <lb/>immo minus difficili, si quid iudico, ratione expediri res poterit in invitis <lb/>et praeternaturalibus motibus, acribus scilicet, et stimulantibus principiis <lb/>nervos vel spinalem medullam vel cerebrum irritantibus, nerveumque simul <lb/>fluidum advocantibus, ut a deferentibus partibus exceptum ad musculos tan&shy;<lb/>dem tamquam per arcum restituatur &rdquo; (ibi, pag. </s>

<s>53). </s></p><p type="main">

<s>Il Volta usciva fuori poco tempo dopo con la sua <emph type="italics"/>Prima Memoria sopra <lb/>l'Elettricit&agrave; animale,<emph.end type="italics"/> e nella prima parte di essa, esaminando l'opinione di <lb/>que'Fisiologi, i quali si r&igrave;ducevano a considerare i nervi in certo modo quali <lb/>conduttori degli spiriti animali, come i metalli son conduttori del fluido elet&shy;<lb/>trico; concludeva non esser quelle altro che idee vaghe e indeterminate. </s>

<s><lb/>Comprendeva altres&igrave; in quella sua sentenza anche il Sauvages con i suoi <lb/>numerosi seguaci, i quali confortavano principalmente la loro opinione col <lb/>fatto sperimentato della grande efficacia del fluido elettrico e della sua at&shy;<lb/>tivit&agrave; in far, senza altro stimolo, repentinamente contrarre le fibre musco&shy;<lb/>lari. (Opere, T. II, P. I, Firenze 1816, pag. </s>

<s>25-28). </s></p><p type="main">

<s>Nella seconda parte di quella Memoria procedeva pi&ugrave; oltre il Volta a <lb/>scoprire un errore, in che era incorso il Galvani, il quale, avendo rassomi&shy;<lb/>gliato i muscoli all'armatura e i nervi al conduttore di una Bottiglia di <lb/>Leyda, aveva detto che il circolo si fa dal di dentro di esso muscolo al di <lb/>fuori, mentre &egrave; il vero ch'essendo l'elettricit&agrave; negativa nell'interior super&shy;<lb/>ficie muscolare e positiva nell'esterna, come per l'Elettrometro aveva riscon&shy;<lb/>trato lo stesso Volta, il flusso elettrico si fa con circolo diretto dal di fuori <lb/>al di dentro, se qualche scarica avvenga o spontanea o naturale (ivi, pag. </s>

<s>41). </s></p><p type="main">

<s>Dato avviso di ci&ograve; a Bologna, per mezzo del Carminati, come altrove <lb/>accennammo, il Galvani ridusse le nuove osservazioni del Volta a render pi&ugrave; <lb/>semplice la sua spiegazione dei moti volontarii, ma l'Autor della <emph type="italics"/>Memoria <lb/>seconda sull'Elettricit&agrave; animale,<emph.end type="italics"/> esce a dichiararsi apertamente come quelle <lb/>sue osservazioni, tutt'altro che porgersi ai servigi del Galvanismo, medita&shy;<lb/>vano di condurlo passo passo in rovina. </s>

<s>Si dimostrava infatti nella detta <lb/><emph type="italics"/>Memoria<emph.end type="italics"/> che il fluido elettrico non agisce direttamente sui muscoli che sono <lb/>gli organi del moto, ma termina la sua azione immediata nel nervo, ond'&egrave; <lb/>che venivano cos&igrave; disperse al vento le belle speranze di tutti coloro, che <pb xlink:href="020/01/1197.jpg" pagenum="72"/>nell'elettricit&agrave; stimolante le fibre muscolari si lusingavano di aver finalmente <lb/>scoperta la misteriosa causa dei moti animali (ivi, pag. </s>

<s>81-85). </s></p><p type="main">

<s>N&egrave; quel mistero &egrave; stato ancora svelato dopo un altro secolo di pro&shy;<lb/>gressi, ed &egrave; tale la sua natura, tale l'ottusit&agrave; de'sensi dell'uomo a penetrare <lb/>addentro ne'pi&ugrave; segreti organi componenti la macchina animale, che di so&shy;<lb/>disfare a quei desiderii &egrave; ne'prudenti creduta vana ogni speranza. </s>

<s>Cos&igrave; la <lb/>Fisiologia &egrave; costretta a confessar ora la sua impotenza, come la confessava <lb/>verso la met&agrave; del secolo XVII, quando poche erano tuttavia l'esperienze delle <lb/>difficolt&agrave;, che s'incontravano per conseguire il fine desiderato. </s>

<s>Noi vogliamo <lb/>qui di quella ingenua confessione recare un documento, e tanto ci&ograve; pi&ugrave; vo&shy;<lb/>lentieri facciamo, in quanto che &egrave; da una parte un riepilogo delle cose gi&agrave; <lb/>dette, e dall'altra un avviamento a quelle che ci rimangono a dire. </s></p><p type="main">

<s>&Egrave; il documento accennato una scrittura, della quale il Viviani fra'suoi <lb/>manoscritti ci conserv&ograve; la copia, e porta il titolo di <emph type="italics"/>Pareri diversi circa <lb/>varie materie avute da varie persone letterate.<emph.end type="italics"/> Dop'essersi ivi accennato <lb/>ad altre varie questioni di Fisica, si passa a dire in che modo sciogliesse il <lb/>Borelli alcuni curiosi problemi di Meccanica animale, aiutandosi del fatto <lb/>dell'insensibile traspirazione. </s>

<s>Poi si soggiunge: &ldquo; Ma perch&egrave; nello sciogli&shy;<lb/>mento che si &egrave; di sopra apportato, cio&egrave; che rimanendo nel nostro corpo <lb/>questi avanzi d'escrementi, essendoli impedito il traspirare, s'internino nei <lb/>nostri muscoli, e gl'impediscano il potere esercitare ad arbitrio le forze; <lb/>non sar&agrave; affatto fuor di proposito il dire in qual maniera si generino tanti <lb/>e tanti movimenti nel nostro corpo, altri per un verso, altri per un altro, <lb/>e conforme la volont&agrave; ci detta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per intenderne dunque qualche cosa, oppure, per averne qualche <lb/>lume bench&egrave; oscuro, bisogna immaginarsi o per dir meglio tener per certo <lb/>che, dove i movimenti si fanno, vi sono alcuni mobili attaccamenti, che si <lb/>chiamano giunture, poich&egrave; in uno stinco non si far&agrave; moto nessuno, perch&egrave; <lb/>non vi &egrave; giunture. </s>

<s>Per intelligenza di che descrivasi la linea AB (fig. </s>

<s>2), e <lb/><figure id="id.020.01.1197.1.jpg" xlink:href="020/01/1197/1.jpg"/></s></p><p type="caption">

<s>Figura 2.<lb/>nel punto A attacchisi la linea AC in maniera tale, <lb/>che possa girare e muoversi ora in AE, ora in AF <lb/>o dove pi&ugrave; gli aggrada: certa cosa &egrave; che se io la <lb/>tirer&ograve; verso D, con la linea DC, ella seguir&agrave; la me&shy;<lb/>desima linea DC. </s>

<s>Restar dunque chiari potremo <lb/>i movimenti che si fanno nel nostro corpo tutti farsi per alcune linee o cor&shy;<lb/>dicelle o altro che tirino. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Inteso questo, veniamo all'esperienze, e se io vorr&ograve; muovere una <lb/>mano o un dito, mossa che io l'avr&ograve;, sentir&ograve; che ingrossato mi s'&egrave; ed as&shy;<lb/>sodato un muscolo nel braccio, talch&egrave; per questa esperienza &egrave; necessario <lb/>dire che questo moto non possa seguire senza l'ingrossamento del muscolo, <lb/>perch&egrave; tanto quanto resti piegata la mano, tanto durer&agrave; a star sodo il mu&shy;<lb/>scolo, ed abbiamo di sopra visto che il moto non dipende da altro, che da <lb/>alcune cordicelle tirate. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora vediamo dunque in che maniera possa questo muscolo assodan-<pb xlink:href="020/01/1198.jpg" pagenum="73"/>dosi far forza a tirare, e non altrimenti dico io ci&ograve; possa fare, che come fa <lb/>il canapo bagnato, il quale, non solo doventa pi&ugrave; grosso e pi&ugrave; sodo, ma <lb/>s'accorcia per non poche braccia. </s>

<s>La ragione di ci&ograve; &egrave; che quelle particelle <lb/>dell'acqua, che penetrano per il canapo, vogliono anch'esse luogo, onde son <lb/>causa che il canapo sia forzato ad alzarsi e fargli luogo, ond'egli viene a <lb/>ritirare i suoi filamenti e per conseguenza ad accorciarsi: e, se esso sar&agrave; <lb/>ancora attaccato, a far non poca forza a ci&ograve; che lo trattiene, come dal Ga&shy;<lb/>lileo chiaramente ed apertamente &egrave; provato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Altra non diremo dunque esser la causa di questo tiramento de'mu&shy;<lb/>scoli, che stanno attaccati passato le giunture, vedendosi uno di quelli in&shy;<lb/>grossarsi, quando segue il movimento, se non che penetri dentro ai medesimi <lb/>muscoli qualche umore o altro che, facendoli ingrossare, faccia che mediante <lb/>loro ne segua il ritiramento. </s>

<s>Ma perch&egrave; si vede che i muscoli sono un ag&shy;<lb/>gregato di fila tutte ad una medesima dirittura condotte, e sto per dire pa&shy;<lb/>rallele, senza punto attorcigliarsi come il canapo, si potrebbe dubitare che <lb/>non ne dovesse seguire il medesimo effetto. </s>

<s>Senza dubbio per&ograve; il medesimo <lb/>effetto ne segue, come in un canapo, poich&egrave;, se piglieremo un budello o <lb/>qualsivoglia altra cosa composta di lineamenti non attorcigliati, gonfiandoli <lb/>e facendoli venir grossi, si vedr&agrave; che raccorceranno. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma &egrave; ora da investigarsi da noi ci&ograve; che sia questo, che ne fa diven&shy;<lb/>tar grosso questo muscolo, e se io, dal signor dottor Borelli persuaso, ne <lb/>dovessi assegnare il mio parere, direi liberamente che non lo so. </s>

<s>Alcuni vo&shy;<lb/>gliono che sia sangue, ma a me si rende difficile l'intendere dove stia que&shy;<lb/>sto sangue, che ha da servire per questo effetto, non ne vedendo vasi, o <lb/>altro dove si ricoveri, quando sta fuora de'muscoli. </s>

<s>Altri vogliono che sia <lb/>uno spirito purissimo, che penetri l&agrave; di dentro. </s>

<s>Basta: ci&ograve; che si sia, l'es&shy;<lb/>sere spirito o sangue non mi capacita. </s>

<s>Siccome ancora in che maniera ad <lb/>un semplice atto della mia volont&agrave; abbia io a muovere tutto il corpo, que&shy;<lb/>sto ancora non l'intendo, e confesso che non &egrave; cosa per me il dirmi che <lb/>&egrave; una potenza dell'anima e non altro. </s>

<s>Neppure mi sodisfa, poich&egrave; io vorrei <lb/>saper come fa, in che maniera; cose tutte difficilissime a spiegarsi. </s>

<s>&rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXXXVI, c. </s>

<s>13, 14). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Si diceva che il documento ora trascritto avrebbeci avviato a quel che, <lb/>in ordine alla Storia scientifica dei moti muscolari, ci rimaneva a narrare in <lb/>questa ultima parte. </s>

<s>Abbiamo ivi letto in principio a che insomma si ridu&shy;<lb/>cesse la macchina produttrice di que'moti, intorno a che, sebben si avessero <lb/>nelle Meccaniche i principii gi&agrave; dimostrati, s'eran pure, infino alla met&agrave; <lb/>del secolo XVII, detti di gravissimi errori. </s>

<s>A diffondere con maggiore am&shy;<lb/>piezza e lucidit&agrave; que'meccanici principii, avevano efficacemente conferito <pb xlink:href="020/01/1199.jpg" pagenum="74"/>gl'insegnamenti di Galileo, il quale fu de'primi a farne l'applicazione al <lb/>muoversi degli animali. </s>

<s>Ma in quel tempo che Galileo stesso, gi&agrave; professore <lb/>nello studio di Padova, scriveva al Vinta d'aver tra mano materiali da com&shy;<lb/>porre un opuscolo <emph type="italics"/>de Animalium motibus<emph.end type="italics"/> (Alb. </s>

<s>VI, 98), Girolamo Fabricio <lb/>d'Acquapendente speculava intorno a quel medesimo soggetto, e otto anni <lb/>dopo, nel 1618, ne pubblicava, pure in Padova, un trattato col titolo <emph type="italics"/>De <lb/>motu locali animalium secundum totum.<emph.end type="italics"/></s></p><p type="main">

<s>Sarebbe senza dubbio curiosa la nostra storia d'investigare quali com&shy;<lb/>merci d'idee passassero fra il Matematico e l'Anatomico, e bench&egrave; non si <lb/>sappia intorno a ci&ograve; dire nulla di certo, pur &egrave; lecito, e anzi ragionevolis&shy;<lb/>simo, l'immaginare che Galileo, frequentando l'Anfiteatro dove sezionava il <lb/>Fabricio, ne ritornasse erudito di quella scienza anatomica, che gli era ne&shy;<lb/>cessaria a confutar gli errori di Aristotile e de'ciechi settatori di lui. </s></p><p type="main">

<s>Ma infin di qui comincia intanto a trasparire una qualche notabile dif&shy;<lb/>ferenza fra le intenzioni de'due celebri Professori padovani, imperocch&egrave;, <lb/>sebbene il Fabricio venisse via via scoprendo in Anatomia cose nuove, era <lb/>per&ograve; sollecito di dimostrare come tali novit&agrave; non si opponevano agl'inse&shy;<lb/>gnamenti aristotelici, n&egrave; importava se, per una tale dimostrazione, si sen&shy;<lb/>tiva costretto a cadere in contradizioni o ad avvolgersi in paralogismi. </s>

<s>Il <lb/>Fabricio insomma, ch'&egrave; pure cos&igrave; benemerito della Storia naturale, non aveva <lb/>avuto il coraggio di disertare dalla scuola dello Stagirita, e perci&ograve;, se po&shy;<lb/>teva essere a Galileo congiunto in amichevoli affetti, doveva esser fra loro <lb/>un divorzio negli scientifici pensieri. </s></p><p type="main">

<s>Comunque sia, apparisce di un tal divorzio un argomento certissimo <lb/>nella presente trattazione de'moti animali, in cui l'Acquapendente, riducen&shy;<lb/>dosi a far l'ufficio di semplice Anatomico descrittivo, non partecipa in nulla <lb/>delle speculazioni meccaniche di Galileo. </s>

<s>Fintantoch&egrave; infatti si tratta di de&shy;<lb/>scrivere un muscolo o l'inserzione tendinosa di lui in un osso, per eserci&shy;<lb/>tarvi ora l'una ora l'altra specie di moto, e fintantoch&egrave; non intendevasi che <lb/>a notar le differenze tra gli organi della locomozione negli uomini e negli <lb/>animali, il Fabricio &egrave; il pi&ugrave; eccellente di quanti l'han preceduto, da Galeno <lb/>in poi. </s>

<s>Ma quando si passa a determinare in qual modo i muscoli eserci&shy;<lb/>tino meccanicamente il moto, il novello Professore null'altro sa ripetere, col <lb/>suo Maestro antico Galeno, se non che il tendine &egrave; quasi un vette. </s>

<s>E pro&shy;<lb/>vandosi di applicare e di dare qualche estensione al pensiero galenico, si <lb/>trova impacciato nell'assegnare il punto di appoggio del vette stesso, e del&shy;<lb/>l'applicazione della potenza, l'effetto meccanico prodotto dalla quale ei non <lb/>sa misurarlo dalla lunghezza del vero vette, ch'&egrave; nell'osso, ma dalla lun&shy;<lb/>ghezza del muscolo e del tendine, per cui conclude che questi organi danno <lb/>moti tanto pi&ugrave; gagliardi, quanto sono pi&ugrave; lunghi. </s></p><p type="main">

<s>&ldquo; Quaeritur, cos&igrave; propriamente dice l'Autore, cur hic musculus est lon&shy;<lb/>gus, cum tamen hi motus omnes breves sint. </s>

<s>Respondetur quod longi mu&shy;<lb/>sculi interdum dant robustos motus nequaquam longos, eomodo quo pondera <lb/>quae manibus movere non possumus, vectibus adhibitis moliri comperimus, <pb xlink:href="020/01/1200.jpg" pagenum="75"/>aut similiter fune adhibita et longius trahente pondus, quod alioquin mani&shy;<lb/>bus trahi non poterat, facile trahitur et movetur. </s>

<s>Aut forte melius dicamus <lb/>carnosam musculorum partem longam et brevem, ut puta quae contrahitur <lb/>et aut breviatur, dare longos aut breves motus: tendineam vero, ut puta <lb/>quae tenditur et obduratur, breves aut longos motus non exhibere, sed ro&shy;<lb/>bustos. </s>

<s>Musculus autem propositus brevem omnino carnosam partem obti&shy;<lb/>net, longam vero tendineam, quae, cum se habeat ut vectis et ut funis <lb/>longius a pondere trahens, ideo hac ratione robustum motum perficit. </s>

<s>Sum&shy;<lb/>matim, ut carnosus brevem, ut tendineus longus robustum dat motum &rdquo; (De <lb/>motu locali, Patavii 1618, pag. </s>

<s>105). </s></p><p type="main">

<s>N&egrave; dopo l'Acquapendente seppero i Filosofi investigar nulla di meglio, <lb/>in ordine al determinare i veri organi della locomozione animale. </s>

<s>Il Gas&shy;<lb/>sendo, persuaso esso pure di ci&ograve; che anticamente aveva affermato Galeno, <lb/>che cio&egrave; quegli organi appartenessero alla natura dei vetti, si dette studio&shy;<lb/>samente a ricercar nel corpo animale la materia e la forma propria di que&shy;<lb/>gli strumenti, ma non gli parve di trovarci altro che funi nelle fibre mu&shy;<lb/>scolari e ne tendini, o troclee nelle estremit&agrave; arrotondate degli ossi. </s>

<s>Egli <lb/>ridusse perci&ograve; ogni maniera di macchinamento animale al modo di operar <lb/>delle taglie o dei polispasti, ne'quali s'accresce l'effetto della forza col mol&shy;<lb/>teplice ritessersi delle fila traenti. </s>

<s>Cos&igrave; lusingavasi di avere in qualche modo <lb/>a intendere la ragione e l'uso di quella grande matassa di fibre, in che si <lb/>avvolgono e di che si compongono i muscoli. </s></p><p type="main">

<s>Altri asserirono lo stesso, ma con diversa ragione, e dissero che le fibre <lb/>muscolari e i tendini agiscono a modo di una macchina, perch&egrave; con la pic&shy;<lb/>cola virt&ugrave; degli spiriti vitali valgono pure a sollevare di grandissimi pesi. </s>

<s><lb/>Sembra che rimanessero costoro infetti di quell'errore, cos&igrave; acutamente sco&shy;<lb/>perto da Galileo, relativo all'utilit&agrave; delle macchine, la quale si faceva con&shy;<lb/>sistere in poter mover gran pesi con pochissima forza. </s>

<s>E tanto fu contagioso <lb/>quell'error meccanico, che ne rimasero infetti Fisiologi valentissimi, fra'quali <lb/>basti a noi citare quel Croone che, inconsapevole di ci&ograve; che speculavasi in <lb/>Toscana, prevenne le ipotesi e le teorie del Borelli. </s></p><p type="main">

<s>Egli, prima dello stesso Borelli, misur&ograve; la forza di alcuni muscoli in <lb/>sostener varii gradi di peso, e perch'erano le sue misure dirette a provar <lb/>che la forza principalmente risiede ne'tendini, di che i muscoli non man&shy;<lb/>cano mai, fece particolar soggetto alle sue esperienze quel muscolo, che serve <lb/>a tirare indietro la coscia e a piegar la gamba, detto, per mancar di carne <lb/>e per esser in gran parte tendinoso, <emph type="italics"/>Gracile<emph.end type="italics"/> dagli antichi e dal Soemme&shy;<lb/>ring, ma conosciuto pi&ugrave; comunemente oggid&igrave; sotto il nome di <emph type="italics"/>Retto interno.<emph.end type="italics"/><lb/>&ldquo; De fibris autem tendinosis, dice il Croone, tria summopere notanda sunt: <lb/>Primo, ex iis potissimum musculos constare, quod ex eo liquet quod octo&shy;<lb/>ginta librarum pondo alligatum istius musculi tendini, quam <emph type="italics"/>Gracilem in&shy;<lb/>ternum<emph.end type="italics"/> in homine vocant, ab humo sublatum facile sustinuerim, altera mu&shy;<lb/>sculi extremitate manu apprehensa &rdquo; (De ratione motus muscul. </s>

<s>cit., pag. </s>

<s>14). </s></p><p type="main">

<s>Ma quando passa il Croone a considerar quella forza muscolare, in <pb xlink:href="020/01/1201.jpg" pagenum="76"/>quanto ella opera a produrre i moti nelle membra dell'animale, fonda an&shy;<lb/>ch'egli la sua dimostrazione sul principio che la Natura, con pochissima <lb/>forza vitale, non solo muova le membra, ma altri gravi pesi che sieno a loro <lb/>attaccati. </s>

<s>&ldquo; Accedo iam ad demonstrandum huiusmodi intumescentia mu&shy;<lb/>sculi, quantum exigua fingatur, non tantum satis valere ad quodlibet cor&shy;<lb/>poris membrum attollendum, sed etiam ad aliud quodcumque pondus ten&shy;<lb/>dini appensum &rdquo; (ibi, pag. </s>

<s>14). </s></p><p type="main">

<s>Primo a riconoscer l'errore cos&igrave; comunemente invalso, e a dimostrar <lb/>che la cosa era tutt'al contrario di quel che prima di lui s'era creduto, fu <lb/>il Borelli, il quale non si fa punto maraviglia che fosse rispetto a ci&ograve; da <lb/>tutti seguito il falso, avendo la verit&agrave; ch'egli prende a dimostrare le appa&shy;<lb/>renti sembianze di un assurdo. </s>

<s>&ldquo; Etsi hoc absurdum iure censetur, qui fieri <lb/>poterit ut Natura sapientissima, quae ubique compendia, simplicitatem et <lb/>facilitatem quaerit, tanta industria machinas in organis animalis elaborave&shy;<lb/>rit, non ut parva virtute magna pondera, sed e contra immenso propemo&shy;<lb/>dum robore parva pondera moveat; hoc quidem, licet videatur monstrum <lb/>et contra communem sententiam, non diffiteor me posse evidentissime de&shy;<lb/>monstrare, et petita prius venia ostendere contrariae sententiae assertores <lb/>hallucinatos fuisse &rdquo; (De motu anim., P. I, Romae 1780, pag. </s>

<s>18). </s></p><p type="main">

<s>L'evidenza delle dimostrazioni, dal Borelli promessa in queste parole, <lb/>risulta necessariamente dai processi matematici da lui seguiti, ma Giovanni <lb/>Bernoulli trov&ograve; un difetto nella ipotesi, su cui si fondano i calcoli borel&shy;<lb/>liani, difetto ch'egli attribuisce, non all'uomo, ma ai tempi, quando ancora <lb/>del Calcolo differenziale non conoscevasi bene n&egrave; la natura n&egrave; l'uso. </s>

<s>Il Bo&shy;<lb/>relli, per esempio, d&agrave; agli elementi, di che si compongono le fibre musco&shy;<lb/>lari, la figura di rombi, ma essendo molti e d'ogni parte ugualmente com&shy;<lb/>pressi, dimostra il nuovo Calcolo non poter configurarsi quegli elementi o <lb/>quelle macchinette, come al Borelli stesso piaceva chiamarle, in altra forma <lb/>diversa dalla circolare. </s>

<s>Nel preloquio dell'Autore alla sopra citata Disserta&shy;<lb/>zione <emph type="italics"/>De motu musculorum,<emph.end type="italics"/> il Bernoulli infatti scriveva: &ldquo; Jo: Alphonsi <lb/>Borelli vestigiis insistemus, amplectendo eius hypothesim, quam tamen ni&shy;<lb/>mis oscitanter applicuisse ostendemus, quando suis machinulis vel vesiculis <lb/>fibrarum muscularium figuram rhomboidalem attribuit, ubi simul apparebit <lb/>hance figuram rectilineam prae aliis ipsis assignasse, tum facilitatis ergo, <lb/>nimirum ut commodiori calculo relationes virium dilatantium ad resistentias <lb/>supputaret, tum etiam quia iustam et debitam figuram, quam circularem <lb/>esse ex natura pressionis liquidorum demonstrabimus, et quae exinde emer&shy;<lb/>gunt vires distendentes, non potuit non ignorare sine novo nostro calculo <lb/><emph type="italics"/>Integralium<emph.end type="italics"/> verbo appellato, qui tum profundissima caligine adhuc tectus <lb/>latitabat, cuiusque prima stamina magno Geometrae G. G. </s>

<s>Leibnitio de&shy;<lb/>bemus. </s>

<s>&rdquo; </s></p><p type="main">

<s>Per via del calcolo degl'Integrali, soggiunge il Bernoulli di aver tro&shy;<lb/>vato che le forze traenti i muscoli non operano, secondo il supposto borel&shy;<lb/>liano, a modo di cunei, ma come tante infinite particelle elastiche, che tutte <pb xlink:href="020/01/1202.jpg" pagenum="77"/>con egual forza agendo contro le vescicole muscolari faranno ad esse pi&shy;<lb/>gliar, non la figura de'rombi &ldquo; sed aliam curvilineam conciliabunt, quam <lb/>nunc indagabimus &rdquo; (ibi, pag. </s>

<s>11) e ch'egli dice resultar similissima alla <lb/><emph type="italics"/>Velaria.<emph.end type="italics"/></s></p><p type="main">

<s>Un altro grave difetto, non notato qui dal Bernoulli nella Meccanica <lb/>borelliana, e di cui non si pu&ograve; addurre nessuna scusa, consiste nell'aver ri&shy;<lb/>pudiato come falso il principio herigoniano della composizione delle forze. </s>

<s><lb/>Ma perch&egrave; dovremo intorno a ci&ograve; trattenersi di proposito altrove, passeremo <lb/>senz'altro a delibar qualche cosa de'tanti e insigni teoremi dal Borelli di&shy;<lb/>mostrati, e relativi alla meccanica dei moti muscolari. </s></p><p type="main">

<s>&Egrave; il primo di que'Teoremi cos&igrave; formulato: &ldquo; Motus articulorum flexi&shy;<lb/>vus sphaericus est, vel circularis, aut in superficie conica, circa centrum <lb/>imaginarium factus &rdquo; (De motu anim. </s>

<s>Pars I cit., pag. </s>

<s>18). Questo stesso <lb/>Teorema, che &egrave; il fondamento a tutto il nuovo edifizio della Meccanica mu&shy;<lb/>scolare, era stato gi&agrave; dimostrato da Galileo nella seconda Giornata de'Due <lb/>massimi sistemi. </s>

<s>Ivi infatti il Salviati, volendo rispondere alle strane obie&shy;<lb/>zioni di un certo Filosofo peripatetico contro il moto annuale della Terra, <lb/>cos&igrave; gli dice: &ldquo; Voi primieramente ammettete per vero che la Natura abbia <lb/>fatto gli articoli, le flessure e snodature degli animali, acciocch&egrave; si possano <lb/>muovere di molti e diversi movimenti, e io vi nego questa proposizione, e <lb/>dico che le flessioni son fatte, acciocch&egrave; l'animale possa muovere una o pi&ugrave; <lb/>delle sue parti, restando immobile il resto, e dico che, quanto alle spezie e <lb/>differenze dei movimenti, quelli sono di una sola, cio&egrave; tutti circolari, e per <lb/>questo voi vedete tutti i capi degli ossi mobili esser colmi o cavi, e di que&shy;<lb/>sti altri sono sferici, che son quelli che hanno a muoversi per tutti i versi, <lb/>come fa nella snodatura della spalla il braccio dell'alfiere nel maneggiar <lb/>l'insegna, e dello strozziere nel richiamar col logoro il falcone, e tale &egrave; la <lb/>flessura del gomito, sopra la quale si gira la mano nel forar col succhiello. </s>

<s><lb/>Altri son circolari per un sol verso, e quasi cilindrici, che servono per le <lb/>membra, che si piegano in un sol modo, come le parti delle dita l'una sopra <lb/>l'altra. </s>

<s>Ma senza pi&ugrave; particolari incontri un solo general discorso ne pu&ograve; <lb/>far conoscere questa verit&agrave;: e questo &egrave; che di un corpo solido che si muova, <lb/>restando uno de'suoi estremi senza mutar luogo, il moto non pu&ograve; esser se <lb/>non circolare, e perch&egrave; nel muover l'animale uno delle sue membra non <lb/>lo separa dall'altro suo conterminale, adunque tal moto &egrave; circolare di ne&shy;<lb/>cessit&agrave; &rdquo; (Alb, I, 282). </s></p><p type="main">

<s>Premesso dunque quel Teorema fondamentale, cos&igrave; da Galileo premo&shy;<lb/>strato, passa il Borelli alla dimostrazione di altri Teoremi di Meccanica <lb/>astratta &ldquo; quasi lemmata utilia ad robur, seu momentum musculorum de&shy;<lb/>monstrandum &rdquo; (Loco cit., pag. </s>

<s>26). Il volere entrare addentro a queste sot&shy;<lb/>tili speculazioni, per farne la storia, ci condurrebbe troppo al di l&agrave; degii an&shy;<lb/>gusti limiti, che ci sono prescritti, e perci&ograve;, lasciando indietro l'esame di <lb/>questi importantissimi Lemmi, e di quegli altri pure, co'quali incomincia il <lb/>cap. </s>

<s>XVI, ci contenteremo di dire come la conclusione, a cui tendono tutte <pb xlink:href="020/01/1203.jpg" pagenum="78"/>le hellissime proposizioni, &egrave; quella in principio da lui promessa, che cio&egrave;, <lb/>calcolate le potenze de'muscoli e le resistenze degli ossi, quelle si trovano <lb/>sempre a queste di molto superiori. </s></p><p type="main">

<s>Infino a tutto il cap. </s>

<s>XVII della prima parte del suo Trattato, posti <lb/>que'teoremi fondamentali gi&agrave; da noi detti, e applicando i Lemmi meccanici <lb/>via via dimostrati, il Borelli tratta della Dinamica dei moti animali. </s>

<s>Nel <lb/>cap. </s>

<s>XVIII, con cui si termina la soluzione dei problemi pi&ugrave; generali, si <lb/>tratta poi dall'Autore della Statica animale, e intorno ad essa pure si sco&shy;<lb/>prono molte nuove verit&agrave; e si correggono antichi errori. </s>

<s>Basti all'intento <lb/>nostro recar come saggio di queste nuove dottrine statiche la soluzione di <lb/>quel problema enunciato nella proposizione CXLIII, e formulato con que&shy;<lb/>ste parole: &ldquo; Quare stando alternis pedibus, perpendiculariter innixis, mi&shy;<lb/>nus fatigamur. </s>

<s>quam quando a duobus simul operantibus fulcimur &rdquo; (ibi, <lb/>pag. </s>

<s>233). </s></p><p type="main">

<s>Erasi il problema stesso assai prima proposto dall'Acquapendente a scio&shy;<lb/>gliere sotto quest'altra forma: &ldquo; Cur ambobus cruribus stando, magis la&shy;<lb/>boramus, quam uno tantum crure stante et altero ocioso et nihil agente, <lb/>cum contrarium potius evenire deberet, quod uni cruri stanti totum corpo&shy;<lb/>ris pondus commissum sit, post dicemus &rdquo; (De motu loc. </s>

<s>cit., pag. </s>

<s>13). Poco <lb/>pi&ugrave; sotto infatti, applicandosi a sciogliere il promesso problema, cos&igrave; l'Acqua&shy;<lb/>pendente stesso scriveva: &ldquo; Videamus primo quomodo se habent ambo crura <lb/>in statione. </s>

<s>Quando ambo crura stant, etsi nullus ad oculum apparet in eis <lb/>musculorum motus, revera omnes musculi moventur et agunt. </s>

<s>Qui sane <lb/>motus ad sensum latens <emph type="italics"/>tonicus,<emph.end type="italics"/> idest quasi extensus appellatur. </s>

<s>Est enim <lb/>tonicus motus ille, in quo brachium, aut crus, aut aliud membrum exten&shy;<lb/>sum detinetur, propter musculos omnes, tum flectentes quam extendentes, <lb/>in eo operantes, videlicet tensos redditos, quem Galenus, <emph type="italics"/>De motu musc. </s>

<s><lb/>cap. </s>

<s>VIII,<emph.end type="italics"/> declarans dicit: Concipias aliquem aliquod pondus, ut puta lapi&shy;<lb/>dem aut lignum, chorda trahentem: si alius alia chorda ponderi appensa ad <lb/>contrariam partem trahat, sed minori robore, dubio procul pondus versus <lb/>priorem tractum movebitur, sed difficilius et minus quam si non adesset se&shy;<lb/>cundus trahens. </s>

<s>At si primus et secundus trahens aequalis sint roboris, non <lb/>movebitur pondus, utcumque uterque totis viribus trahat. </s>

<s>Sic est in motu <lb/>tonico: utrique musculi, tam flectentes quam extendentes, ita trahunt ut <lb/>neuter alterum superet. </s>

<s>In quo casu membrum extensum et immobile ad <lb/>sensum apparet, quamvis omnes musculi tensi et contracti ad extremum <lb/>sint. </s>

<s>Ubi igitur amborum crurum statio se se offert, tunc crura motu tonico <lb/>moventur et agunt, licet motus sensu non percipiatur, neque homo locum <lb/>mutet. </s>

<s>Quia vero in hoc tonico motu omnes musculi agunt, et agunt non <lb/>moderate sed validissimo et extremo motu; ideo multum laborant, impen&shy;<lb/>seque defatigantur quam in alio quovis motu &rdquo; (ibi, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Ma il Borelli, dop'aver riferita questa dottrina dell'Acquapendente, senza <lb/>per&ograve; nominarlo, e confondendolo con altri, i quali andavano ripetendo il detto <lb/>gi&agrave; da Galeno e da lui, argutamente cos&igrave; osserva, prima di dar del problema <pb xlink:href="020/01/1204.jpg" pagenum="79"/>la vera risoluzione sicura: &ldquo; At non animadvertunt hi praeclari Viri falsi&shy;<lb/>tatem assumpti eorum. </s>

<s>Verum est minori labore, nempe sub duplo, ab una <lb/>manu dextra pondus decem librarum sustineri, quam si aliae decem librae <lb/>a sinistra quoque suspenderentur, nam tunc duae manus duplum pondus <lb/>20 libr. </s>

<s>elevarent, quam una manus sola. </s>

<s>At falsum est quod idem pon&shy;<lb/>dus 20 libr. </s>

<s>facilius ab unica manu sustineatur, quam si subdiviso onere <lb/>10 librae a singulis manibus suspenderentur. </s>

<s>Eodem modo fatigari magis <lb/>deberent musculi unius pedis, duplum pondus totius hominis sustinendo, <lb/>quam subdiviso onere super duobus pedibus, ita ut medietas ab unoquoque <lb/>fulciri deberet &rdquo; (De motu anim. </s>

<s>P. cit., pag. </s>

<s>233, 34). </s></p><p type="main">

<s>Cos&igrave; &egrave; di fatti, conforme a ci&ograve; che detta la ragion naturale, che cio&egrave; <lb/>un piede solo, sopportando il peso di tutto il corpo, deve pi&ugrave; affaticarsi che <lb/>ripartendolo con quell'altro. </s>

<s>Ma come dunque va che tante volte facciam <lb/>questo gioco di appoggiarsi su un piede solo, parendo che s'allievi a quel <lb/>modo in noi la stanchezza? </s>

<s>A che il Borelli risponde, invocando in propo&shy;<lb/>sito la dottrina galileiana della vera causa, che induce in noi stessi e negli <lb/>altri animali il senso della stanchezza. </s>

<s>&ldquo; Lo stancarsi il corpo dell'animale, <lb/>dice Galileo, deriva per mio credere dall'impiegare una parte sola per muo&shy;<lb/>vere s&egrave; stessa e tutto il resto del corpo, come v. </s>

<s>g. </s>

<s>per camminare s'im&shy;<lb/>piegano le cosce e le gambe solamente per portar loro stesse e tutto il ri&shy;<lb/>manente &rdquo; (Alb. </s>

<s>I, 295). Tale essendo la ragione della stanchezza, il Borelli <lb/>soggiunge, e cos&igrave; conclude la sua dimostrazione: &ldquo; Cum e contra actione <lb/>interrupta, pausis interpositis minus molesta pondera graviora sustineamus, <lb/>sicuti stando maiorem lassitudinem patimur quam leniter deambulando; quare <lb/>patet quod alterna positura et innixio modo super unum, modo super alium <lb/>pedem est quaedam commutatio similis deambulationi &rdquo; (De motu anim. </s>

<s><lb/>Pars cit., pag. </s>

<s>234). </s></p><p type="main">

<s>Perch&egrave;, stando per qualche tempo in piedi sentiamo maggiore stanchezza <lb/>che passeggiando per tutto quel tempo, &egrave; un altro curioso problema di Mec&shy;<lb/>canica animale, che il Borelli cita nelle sopra riferite parole, com'esempio, <lb/>senza curarsi di darne la soluzione. </s>

<s>Chi fosse per&ograve; desideroso di saperla pu&ograve; <lb/>sodisfarsene leggendola in quei <emph type="italics"/>Pensieri diversi circa varie materie,<emph.end type="italics"/> cho noi <lb/>citammo pi&ugrave; sopra, dove troverebbe altres&igrave; risolute altre questioni in simile <lb/>soggetto. </s>

<s>E perch&egrave; il discorso non &egrave; poi tanto lungo, e pu&ograve; da un'altra <lb/>parte servir di complemento alle dottrine borelliane, bench&egrave; non sieno gli <lb/>argomenti per verit&agrave; rigorosamente desunti da principii meccanici; pen&shy;<lb/>siamo di trascriver qui le relative parole, per sodisfare al desiderio dei no&shy;<lb/>stri Lettori: </s></p><p type="main">

<s>&ldquo; Nel ritrovarsi un giorno, mentre si celebravano gli uffici della Set&shy;<lb/>timana santa, nella Chiesa del Duomo di Pisa, nel rizzarsi che fece uno dal <lb/>luogo dove stava a sedere, disse: io son pi&ugrave; stracco, che se tutt'oggi io <lb/>avessi camminato. </s>

<s>A questo proposito furono proposti dall'Ecc.mo Sig. </s>

<s>Bo&shy;<lb/>relli due graziosissimi teoremi: l'uno &egrave; perch&egrave;, stando v. </s>

<s>g. </s>

<s>ritto senza muo&shy;<lb/>vermi una mezz'ora, mi stracco assai pi&ugrave; che se per mezz'ora io passeggiassi. <pb xlink:href="020/01/1205.jpg" pagenum="80"/>Certa cosa &egrave; che passeggiando io duro la medesima fatica, che richiedesi per <lb/>stare in piedi, ed oltre a questo duro la fatica nel muovermi e nel portare <lb/>il corpo. </s>

<s>Dovrebbesi dunque dire che, durandosi in uno degli atti assai mag&shy;<lb/>gior fatica che nell'altro, pi&ugrave; si dovesse stancare in quello che nell'altro: <lb/>eppure il contrario apertamente se ne vede seguire. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Con l'occasione d'esaminarsi questo, un altro pi&ugrave; curioso ne pro&shy;<lb/>pose, e fu: due v. </s>

<s>g. </s>

<s>d'ugual valore concordano di trovarsi a duello tra <lb/>quattro giorni. </s>

<s>Uno di essi, volendo risparmiare le forze per la giornata <lb/>prefissa, tutt'e quattro i giorni consuma in dormire o nel letto: l'altro in <lb/>quei quattro giorni, non curante di riposo, tutto il giorno in varie cose si <lb/>esercita. </s>

<s>Si domanda chi di loro dovrebbe essere pi&ugrave; valoroso o chi ripos&ograve; <lb/>o chi si affatic&ograve;? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pareva ridicolo il dire che quello che s'affatic&ograve; fosse stato pi&ugrave; pode&shy;<lb/>roso, per l'esempio di quello, che avendo a fare una cena sontuosa, in cam&shy;<lb/>bio di avanzarsi in danari, gettasse via e piatti e tavole e danari, e tuttoci&ograve; <lb/>che poteva servire per la cena. </s>

<s>Cos&igrave; questo che doveva fare il duello, in&shy;<lb/>vece di avanzarsi in forze, e non le spendere nei quattro giorni antecedenti, <lb/>le getta, si strapazza e si affatica, sicch&egrave; parrebbe doversi dire che quello <lb/>che stette in ozio dovesse essere il pi&ugrave; valoroso: eppure, per l'esperienza, <lb/>tutto segue il contrario. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per intelligenza di che due bellissimi esempi possono addursi: l'uno <lb/>&egrave; che se v. </s>

<s>g. </s>

<s>da un pozzo, ancorch&egrave; d'acqua perfettissima, si star&agrave; lungo <lb/>tempo senza trarne acqua, il pozzo resta guasto e l'acqua putrida. </s>

<s>Il me&shy;<lb/>desimo ancora si vede seguire in uno scalpello, ancorch&egrave; di tempra ottimo, <lb/>che se lascerassi stare per molto tempo, senza punto adoperarsi, tutto ir&shy;<lb/>rugginito andr&agrave; a male, n&egrave; potr&agrave; di quello alcuno servirsi, se prima, o con <lb/>la ruota o con altro consumandolo, non lo ridurr&agrave; netto e pulito. </s>

<s>Dubbio <lb/>veruno non vi &egrave; che, se il medesimo scalpello fosse stato adoprato, consu&shy;<lb/>mato non si fosse, ma nello stesso consumarsi veniva a restar pulito e netto <lb/>da quella ruggine, che l'ha reso inabile al fendere, e del tutto inutile per <lb/>quello che fu fatto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cos&igrave; ancora dir si potr&agrave; di quello, che stette ritto senza punto muo&shy;<lb/>versi, e dur&ograve; meno fatica di quello, che cammin&ograve;, ed era pi&ugrave; stracco. </s>

<s>Im&shy;<lb/>perocch&egrave; non vi &egrave; dubbio alcuno che quello che cammina fa pi&ugrave; forza di <lb/>quello, che resta semplicemente ritto, ma &egrave; ben vero anche che quello che <lb/>cammina dura assai meno fatica in far pi&ugrave; forza, che dura quello che sta <lb/>ritto in far meno forza, poich&egrave; quel primo, nella forza che fa, si vien anco <lb/>a mondare da quella ruggine, che impedisce al secondo adoperare a suo pia&shy;<lb/>cere la forza. </s>

<s>Imperocch&egrave; nel moto che fa, aprendosi i meati della carne, <lb/>traspira facilmente certa materia, la quale imprigionata dentro, entrando per <lb/>i muscoli, cagiona non poco impedimento per esercitar le forze. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sicch&egrave; verissimo stimo io che quello posando nel letto getti via meno <lb/>forza di quello, che tutto il giorno si esercita, ma &egrave; anco vero ch'ei, con lo <lb/>stare ozioso, non d&agrave; luogo alla traspirazione, onde ne seguita che il giorno <pb xlink:href="020/01/1206.jpg" pagenum="81"/>prefisso al duello egli resti di forze svantaggiato. </s>

<s>N&egrave; paia cosa ci&ograve; fuori di <lb/>proposito, cio&egrave; che le semplici traspirazioni per i meati possano essere giu&shy;<lb/>sta e adeguata ragione per lo scioglimento delle predette difficolt&agrave;. </s>

<s>Poich&egrave;, <lb/>se noi prenderemo tuttoci&ograve; che si mangia ed esattissimamente lo peseremo, <lb/>messo poi insieme tutti gli escrementi mandati fuora o per orina o per se&shy;<lb/>cesso o per sputo, pesandoli, troveremo questi essere molto minori di peso <lb/>di quello, che sopra si ponder&ograve; mangiato. </s>

<s>Avvertasi per&ograve; che la detta espe&shy;<lb/>rienza non si deve fare n&egrave; in un giorno n&egrave; in due o poco pi&ugrave;, ma per mesi <lb/>continui, per torre molte difficolt&agrave;, che potrebbero alterare l'esattezza del&shy;<lb/>l'esperienza fatta tanto bene dal Santorio e dal Michelini. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se dunque si trover&agrave; tanto svantaggio o diminuimento di forze del <lb/>peso secondo, dove potr&agrave; essere andato il peso che non si trova? </s>

<s>N&egrave; si pu&ograve; <lb/>dire che vada tutto per accrescimento del corpo, poich&egrave; in breve tempo re&shy;<lb/>steremmo cos&igrave; grassi e corpulenti, dovendoci avanzare e crescere di raggua&shy;<lb/>gliato quasi una libbra al giorno, che appena ci potremmo muovere, oppure <lb/>di statura cos&igrave; dell'ordinaria superiore, che in quarant'anni e pi&ugrave; che cor&shy;<lb/>rono di vita, da che l'uomo finisce di crescere, avanzeremmo i Morganti e <lb/>i Rodomonti, che dettero materia di favoleggiare a pi&ugrave; di uno. </s>

<s>Sicch&egrave;, per <lb/>concludere, altro non resta a dire, se non che l'avanzo del peso &egrave; traspi&shy;<lb/>rato per i meati ed i pori della nostra carne, ed in questa maniera, con&shy;<lb/>frontandosi con l'esperienza, si salveranno tutte le altre apparenze ed ef&shy;<lb/>fetti. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXVI, c. </s>

<s>10-12). </s></p><p type="main">

<s>Essendo queste cose dette dal Borellli in una conversazione di amiei, <lb/>i quali non tutti erano matematici, s'intende come, per adattarsi all'intelli&shy;<lb/>genza di ognuno, ricorresse a cercare le prove del suo discorso negli esempi <lb/>volgari e nel fatto allora notissimo dell'insensibile traspirazione, trascurando <lb/>que'principii meccanici di Galileo, ch'egli sapientemente deriva nel trattato <lb/><emph type="italics"/>De motu animalium<emph.end type="italics"/> alle sue intenzioni, e dell'applicazion de'quali giova, <lb/>a'riferiti di sopra, aggiungere qualche altro esempio. </s></p><p type="main">

<s>Nel secondo Dialogo delle Due nuove scienze, dopo la dimostrazione del <lb/>Teorema VIII della resistenza de'solidi allo spezzarsi, Galileo, cos&igrave; por modo <lb/>di corollario o di scolio, compendiava una scienza nuova dell'equilibrio delle <lb/>macchine animali: &ldquo; Or vedano come dalle cose sin qui dimostrate aperta&shy;<lb/>mente si raccoglie l'impossibilit&agrave; del poter, non solamente l'arte, ma la Na&shy;<lb/>tura stessa crescer le sue macchine a vastit&agrave; immensa.... Disegnai gi&agrave; la <lb/>figura di un osso allungato solamente tre volte, ed ingrossato con tal pro&shy;<lb/>porzione, che potesse nel suo animale grande far l'ufficio proporzionato a <lb/>quel dell'osso minore dell'animal pi&ugrave; piccolo, e le figure son queste .... <lb/>dove vedete sproporzionata figura che diviene quella dell'osso ingrandito. </s>

<s><lb/>Dal che &egrave; manifesto che chi volesse mantenere in un vastissimo gigante le <lb/>proporzioni, che hanno le membra in un uomo ordinario, bisognerebbe o <lb/>trovar materia molto pi&ugrave; dura e resistente per formare le ossa, ovvero am&shy;<lb/>mettere che la robustezza sua fosse a proporzione assai pi&ugrave; fiacca, che negli <lb/>uomini di statura mediocre: altrimente, crescendoli a smisurata altezza, si ve-<pb xlink:href="020/01/1207.jpg" pagenum="82"/>drebbono dal proprio peso opprimere e cadere. </s>

<s>Dovecch&egrave; all'incontro si vede, <lb/>nel diminuire i corpi, non si diminuire con la medesima proporzione le <lb/>forze, anzi nei minori crescer la gagliardia con proporzion maggiore &rdquo; <lb/>(Alb. </s>

<s>XIII, 128, 29). </s></p><p type="main">

<s>Il Borelli applica destramente queste dottrine galileiane alla meccanica <lb/>del salto, concludendo che per la ponderosit&agrave; del corpo i grandi son assai <lb/>meno agili de'piccoli animali. </s>

<s>&ldquo; Demonstravit eximius Galileus, <emph type="italics"/>De motu <lb/>locali,<emph.end type="italics"/> quod in corporibus animalium proportionaliter decrescentium minui&shy;<lb/>tur pondus in maiori proportione, nempe duplicata resistentiae et roboris <lb/>eorum, et ideo ossa maiorum animalium crassiora fieri debebant, ut suo ro&shy;<lb/>bore incrementum ponderis sustentare valerent. </s>

<s>Et hinc fit ut animalia vasta, <lb/>quae corpus valde ponderosum habent, minus vivacia et minus agilia sint <lb/>quam exigua animalia. </s>

<s>Quare verum est quod minus ponderosa animalia <lb/>maiores saltus respectu sui corporis efficiunt &rdquo; (De motu anim. </s>

<s>Pars cit., <lb/>pag. </s>

<s>282). </s></p><p type="main">

<s>Di questa curiosit&agrave; di meccanica muscolare, vogliam dire del salto, erasi <lb/>pure occupato Galileo, come apparisce da quella Selva di Problemi varii, <lb/>che raccolse il Viviani. </s>

<s>&ldquo; Assai manco si salterebbe, ivi si legge, a pi&egrave; giunti, <lb/>se minor fosse la lunghezza del piede, e forse il salto sarebbe nullo, se si <lb/>posasse sopra la punta di due coni &rdquo; (Alb. </s>

<s>XIV, 322). Ma il Borelli dette <lb/>di queste particolarit&agrave; di moto ne'varii animali la teoria assoluta, che poi <lb/>osarono d'infirmare due stranieri, il Barthez e il Dumas. </s>

<s>Dicevano costoro <lb/>che non pu&ograve;, come fa il nostro Italiano, paragonarsi il salto dell'uomo al <lb/>rimbalzar di una molla, perch&egrave; le ossa e tutte le altre parti componenti la <lb/>macchina umana non hanno quell'elasticit&agrave;, che fa risalire le molle. </s>

<s>Vin&shy;<lb/>cenzio Brunacci per&ograve; prese a difendere valorosamente, in un suo Discorso <lb/>accademico, le dottrine borelliane, dimostrando che i due suddetti Fisiologi <lb/>stranieri le posero in dubbio, per non averle troppo bene comprese, essen&shy;<lb/>doch&egrave; &ldquo; il Borelli al fenomeno del balzo prodotto dalla elasticit&agrave; de'corpi <lb/>riferisce la spiegazione del salto, non perch&egrave; la macchina rimbalzi in virt&ugrave; <lb/>di una elasticit&agrave; a lei propria,... ma perch&egrave;, come accade nel risalto dei <lb/>corpi, il centro di gravit&agrave; della macchina, obbligato a prendere un moto di <lb/>direzione verticale, fa distaccare la macchina umana dal suolo &rdquo; (Discorsi <lb/>accadamici, Milano 1827, pag. </s>

<s>178, 79). </s></p><p type="main">

<s>Ritornando ora alle dottrine meccaniche di Galileo, intorno alle condi&shy;<lb/>zioni di naturale equilibrio fra le parti componenti le moli animali, contro <lb/>i principii esposti nel Dialogo del Salviati, e da noi gi&agrave; riferiti, promuove <lb/>Simplicio una difficolt&agrave;, sovvenutagli dal pensare alle smisurate moli de'ce&shy;<lb/>tacei. </s>

<s>Quella difficolt&agrave;, risponde ivi lo stesso Salviati, lo fa accorto di una <lb/>condizione lasciata addietro nel primo discorso; condizione potente a far s&igrave; <lb/>&ldquo; che i giganti ed altri animali vastissimi potessero consistere e agitarsi, <lb/>non meno che i minori, e ci&ograve; seguirebbe, quando non solo si aggiugnesse <lb/>gagliardia all'ossa ed all'altre parti, ufficio delle quali &egrave; il sostenere il pro&shy;<lb/>prio e sopravveniente peso, ma lasciata la struttura delle ossa con le me-<pb xlink:href="020/01/1208.jpg" pagenum="83"/>desime proporzioni, pur nell'istesso modo, anzi pi&ugrave; agevolmente consiste&shy;<lb/>rebbono le medesime fabbriche, quando con certa proporzione si diminuisse <lb/>la gravit&agrave; della materia delle medesime ossa, e quella della carne o di altro <lb/>che sopra l'ossa si abbia ad appoggiare, e di questo secondo artifizio si &egrave; <lb/>prevalsa la Natura nella fabbrica dei pesci, facendogli le ossa e la polpa non <lb/>solamente assai leggere, ma senza veruna gravit&agrave; &rdquo; (Alb. </s>

<s>XIII, 130). </s></p><p type="main">

<s>Dottrine galileiane son queste, che il Borelli ebbe a ripetere con lo <lb/>stesso costrutto di discorso, se non colle medesime parole: &ldquo; Et idoo pisces, <lb/>egli dice nella citata Parte prima della Meccanica animale, non indigent pe&shy;<lb/>dibus, sicut terrestria et volatilia. </s>

<s>Secundo, non fatigantur, neque ullam las&shy;<lb/>situdinem percipiunt stando, quia membra aequilibrata, non gravitant, neque <lb/>comprimunt partes subiectas. </s>

<s>Tertio, vastiora esse possunt corpora piscium <lb/>quam terrestrium animalium, ut docuit Galileus, quia pisces non coguntur <lb/>sustinere proprium pondus, quod nullam vim compressivam exercent, ob <lb/>aequilibrium cum aqua &rdquo; (pag. </s>

<s>332). </s></p><p type="main">

<s>Altre bellissime speculazioni di Meccanica applica Galileo a interpetrare <lb/>il sapiente magistero della Natura in fabbricare il corpo, e particolarmente <lb/>le ossa a varie qualit&agrave; di animali; speculazioni largamente illustrate dal Bo&shy;<lb/>relli, e sulle quali ritorneremo in altro capitolo di questa terza parte della <lb/>nostra Storia. </s>

<s>Ma non vogliamo intanto lasciarci sfuggir l'occasione di far <lb/>notare un singolar merito, che dee giustamente attribuirsi a Galileo, bench&egrave; <lb/>gli stessi cechi adoratori di lui non ne facciano il debito conto, ed &egrave; che fu <lb/>egli veramente il primo ad applicare le leggi dell'equilibrio e del moto dei <lb/>solidi alle leggi dell'equilibrio e del moto de'corpi animali. </s></p><p type="main">

<s>Qual efficacia avesse in avviare questa nuova parte di Filosofia natu&shy;<lb/>rale l'Acquapendente, lo abbiamo qua e l&agrave; accennato pi&ugrave; volte, e qui in <lb/>ultimo, per compendio, s'aggiunge che la massima parte de'problemi gali&shy;<lb/>leiani, accennati nella <emph type="italics"/>Selva<emph.end type="italics"/> e risoluti ne'Dialoghi del mondo e in quegli <lb/>altri del moto, furono proposti dallo stesso Acquapendente, ma perch'egli <lb/>ci and&ograve; con gli errati principii di Meccanica aristotelica, Galileo fu che ne <lb/>dette per il primo la vera soluzione. </s></p><p type="main">

<s>Il soggetto accomodatissimo a ricreare gl'ingegni, di che quell'uomo <lb/>di natura conversevole e gioviale si compiaceva, ebbe maggior cultura di <lb/>quel che non possa apparire dalle due massime Opere di lui, e la detta <lb/><emph type="italics"/>Selva<emph.end type="italics"/> messa insieme dal Viviani lo attesta, e lo attestano con pi&ugrave; efficacia <lb/>i pensieri galileiani fatti rivivere dal Borelli, non solo nella grande Opera <lb/>sua, ma in altre scritture pochissimo conosciute, alcune delle quali s'indi&shy;<lb/>cheranno presentandocisi l'occasione. </s></p><pb xlink:href="020/01/1209.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO III.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dei moti del cuore<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della struttura muscolare del cuore; de moti di sistele e di diastole. </s>

<s>&mdash; II. </s>

<s>Delle forze motive del <lb/>cuore, e della loro misura; del moto del sangue per le arterie e per le vene. </s>

<s>&mdash; III. </s>

<s>Delle leggi <lb/>idrauliche applicate al moto del sangue. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Se la vita &egrave; moto, i muscoli, che son le potenze applicate a muovere <lb/>la macchina animale, si dovevan rappresentare alla mente de'Fisiologi an&shy;<lb/>tichi come primi e principali organi di quella stessa vita, che per tutte le <lb/>esperienze e con universale consenso si concepiva avere il suo principio, e <lb/>quasi la sua fonte, nel cuore. </s>

<s>Non fa perci&ograve; maraviglia se colui, ch'&egrave; tra'Fi&shy;<lb/>siologi conosciuto per il pi&ugrave; antico, scorto dalla luce naturale di questo con&shy;<lb/>cetto, sentenzi&ograve; senza timor di dubbio che il cuore &egrave; un muscolo molto forte. </s>

<s><lb/>Non dubitava Ippocrate della verit&agrave; di questa sua sentenza, vedendo essere <lb/>il cuore stesso quasi un lago, da cui muovono con impeto i fiumi del san&shy;<lb/>gue a irrigare le membra, riseccato il quale, irreparabilmente l'uomo sen <lb/>muore. </s>

<s>&ldquo; Cor musculus est valde fortis, non nervo, sed densitate ac con&shy;<lb/>strictione carnis, et duos ventriculos habet discretos in uno amiculo, ab utra&shy;<lb/>que parte unum.... Hi fontes sunt humanae naturae, et hic flumina sunt, <lb/>quibus totum corpus irrigatur, atque hi etiam vitam homini conferunt, et, <lb/>ubi resiccati fuerint, homo moritur &rdquo; (Opera, Lib. </s>

<s>De corde, Venetiis 1619, <lb/>fol. </s>

<s>25). </s></p><p type="main">

<s>Il concetto sbocciato cos&igrave; nella mente d'Ippocrate, come un vergine <lb/>fiore in balza solitaria, fu nella sua natia bellezza e nella soavit&agrave; della fra-<pb xlink:href="020/01/1210.jpg" pagenum="85"/>granza guasto e corrotto, quando Galeno lo traspose ne'suoi orti accademici, <lb/>per esercitarvi attorno un'artificiosa cultura. </s>

<s>&Egrave; uno de'pi&ugrave; fiorenti fra que&shy;<lb/>sti orti galenici quello che &egrave; inscritto <emph type="italics"/>De anatomicis demonstrationibus,<emph.end type="italics"/><lb/>nel VII libro del quale il capitolo VIII &egrave; intitolato: <emph type="italics"/>De substantia et motu <lb/>cordis adversus antiquos.<emph.end type="italics"/> Il cuore non pu&ograve;, ragiona ivi l'Autore, essere un <lb/>muscolo, perch&egrave; ne differisce sostanzialmente nelle funzioni: il muscolo in&shy;<lb/>fatti si muove ad arbitrio, ed il cuore non cessa mai. </s>

<s>&ldquo; Etenim cordis mo&shy;<lb/>tus non arbitrarius esse, nec cessare, quoad animal ita fruitur, potest: mu&shy;<lb/>sculorum autem functio subinde quiescit, ac rursus excitatur, animantis <lb/>arbitrio subserviens &rdquo; (Venetiis 1597, fol. </s>

<s>95). N&egrave; dee far maraviglia, sog&shy;<lb/>giunge Galeno, che il cuore e i muscoli differiscano nelle funzioni, essendo <lb/>cos&igrave; notabilmente differenti nella sostanza. </s>

<s>&ldquo; Quapropter neque musculi eam&shy;<lb/>dem cum corde functionem habent, quoniam neque substantiam. </s>

<s>Certe, si <lb/>quis cor et musculum quemlibet pariter coctum utrumque gustare voluerit, <lb/>hand mediocrem ipsorum gustu differentiam deprehendet;.... cor quovis <lb/>musculo durius est, et fibrarum varietate sic colore palam discrepat &rdquo; (ibi). </s></p><p type="main">

<s>Per poi meglio persuadere della diversit&agrave;, che passa tra le funzioni del <lb/>cuore e dei muscoli, Galeno richiama l'attenzione al principio dei moti vitali <lb/>rivelatoci chiaramente dall'esperienza. </s>

<s>Quel principio risiede nei nervi, recisi <lb/>i quali, dovrebbe cos&igrave; rimanersi inerte il muscolo come il cuore: ma si vede <lb/>a questo anche dopo l'incisione durare il polso &ldquo; quare superest vim pul&shy;<lb/>satilem ex ipsius cordis corpore oriri: non autem oriretur, si viscus eam&shy;<lb/>dem cum totius corporis musculis naturam obtineret &rdquo; (ibi, fol. </s>

<s>96). Ond'&egrave; <lb/>che, dietro questo e dietro gli altri sopra addotti argomenti, Galeno cos&igrave; con&shy;<lb/>clude: &ldquo; Horum igitur ignari nobis videntur qui cor musculum esse exi&shy;<lb/>stimant, non intelligentes actionis ipsius excellentiam ex sua visceri substan&shy;<lb/>tia necessario in&egrave;sse, quapropter maxime errant qui cor musculum esse <lb/>censent &rdquo; (ibi). </s></p><p type="main">

<s>Ecco, fra'tanti, un altro esempio storico de'tristi effetti della Filosofia, <lb/>la quale bene spesso, piuttosto ch'educare il Vero, nato spontaneo nelle <lb/>menti, lo sradica per imporvi in quella vece le sue finzioni. </s>

<s>Il buon senso <lb/>dell'uomo, se il Filosofo non glielo avesse suggerito, non avrebbe pensato <lb/>mai che la Natura tanto aristocratica procedesse nelle sue leggi, da non per&shy;<lb/>metter che il nobilissimo cuore s'avesse a scambiare, anco nell'apparenza, <lb/>con gli altri muscoli plebei. </s>

<s>Ma era facilissimo rispondere a Galeno che male <lb/>avrebbe provveduto la Natura a far nella fabbrica de'muscoli e del cuore <lb/>una cos&igrave; onorevole distinzione, se poi voleva condannar tanto questo che <lb/>quelli alla medesima servilit&agrave; degli uffici. </s>

<s>Questo, a cui poi riducesi nella sua <lb/>nativa semplicit&agrave; il concetto ippocratico, fu scorta ai Fisiologi per non smar&shy;<lb/>rir del tutto la via, facilmente persuadendosi che se sono i muscoli gli or&shy;<lb/>gani del moto, non pu&ograve; il cuore, che &egrave; il primo mobile, non essere anch'egli <lb/>un muscolo schietto. </s>

<s>Da questo ragionamento scorto anche il Berengario, <lb/>bench&egrave; non qualifichi addirittura il cuore per un muscolo, pur, come ve&shy;<lb/>dremo tra poco, insinua la cosa indirettamente, dando al viscere, nelle no-<pb xlink:href="020/01/1211.jpg" pagenum="86"/>tabili differenze di struttura che passano tra lui stesso e gli altri muscoli, <lb/>un'attribuzione de'medesimi uffici. </s></p><p type="main">

<s>Venuto il tempo della nuova instaurazione dell'Anatomia, il Vesalio esce <lb/>con pi&ugrave; libert&agrave; fuori de'cancelli preclusi a lei da Galeno, e bench&egrave; senta <lb/>con l'antico Maestro quanto abbia d'importanza, in costituirsi la differenza <lb/>tra il cuore e i muscoli, il veder che quello si muove per necessit&agrave; e que&shy;<lb/>sti ad arbitrio; pure egli &egrave; il primo a notar che essi hanno, que'due or&shy;<lb/>gani dei moti animali, una somiglianza notabilissima nella struttura delle <lb/>fibre carnee, di che son contessuti. </s>

<s>&ldquo; Ut enim in musculis fibrae, ne rum&shy;<lb/>perentur, carnem undique habent circumpositam; sic et cordis fibrae pecu&shy;<lb/>liari ipsis carne continentur uniunturque..... Dein, quemadmodum cordis <lb/>fibrae cum musculorum fibris nonnulla consequntur communia, sic etiam ut <lb/>et illae motui famulantur, sed prorsus diversa: musculorum enim motus ar&shy;<lb/>bitrarius est, cordis vero naturalis &rdquo; (De humani corp. </s>

<s>fabrica, Basileae 1543, <lb/>pag. </s>

<s>587). Si sentirebbe da queste considerazioni sospinto il Vesalio a tor&shy;<lb/>nare indietro a consentir con Ippocrate, ma egli non s'attenta di dichia&shy;<lb/>rarsene aperto, e gli emuli successori poi rintuzzarono ogni conato di lui <lb/>confermandosi piuttosto, come in solido fondamento, ne'placiti di Galeno. </s>

<s>Il <lb/>Colombo, per esempio, sentenzi&ograve;, come se fosse sicuro di pronunziare un <lb/>oracolo: &ldquo; nullo pacto potest cor inter musculos connumerari, quamvis di&shy;<lb/>vinus Hippocrates in Libro <emph type="italics"/>De corde<emph.end type="italics"/> ipsum musculum esse dicere non eru&shy;<lb/>buerit &ldquo; (De re anat., Venetiis 1559, pag. </s>

<s>176, 77). </s></p><p type="main">

<s>L'importanza, che sempre e da tutti fu riconosciuto avere il cuore nelle <lb/>funzioni della vita, facevano vivamente sentire il bisogno di decider della <lb/>natura di un organo s&igrave; principale, e la decisione dipendeva, com'&egrave; facile <lb/>comprendere, da una pi&ugrave; diligente anatomia del cuore stesso e de'muscoli; <lb/>anatomia, che per le difficolt&agrave; naturali incontrate, sopraggiunta l'imperizia <lb/>dell'arte e l'imperfezione degli strumenti, indugi&ograve; fino ai tempi dello Ste&shy;<lb/>none. </s>

<s>Egli pubblic&ograve; in Amsterdam nel 1664 un trattato col titolo <emph type="italics"/>De mu&shy;<lb/>sculis et glandulis,<emph.end type="italics"/> dove incomincia a narrare come, nella primavera del <lb/>precedente anno 1663, si fosse dato con ogni industria, per compiacere al <lb/>suo proprio genio e agli amici, a fare anatomia del cuore, e come gli venis&shy;<lb/>sero da una tal prima dissezione rivelati questi tre fatti importanti: I, non <lb/>esser nel cuore altro paranchima diverso dalle fibre; II, non andar nessuna <lb/>fibra a diritto, ma tutte intorte; III, non esser l'andamento delle stesse <lb/>fibre, n&egrave; retto n&egrave; circolare, ma incurvato alquanto nel mezzo. </s>

<s>Soggiunge <lb/>poco appresso l'Autore come, proseguendo a esercitare intorno a s&igrave; difficile <lb/>soggetto lo stile, vedesse sopra quella stessa luce apparitagli d'oriente, sten&shy;<lb/>dersi nuove tenebre inaspettate &ldquo; ad quas discutiendas nullum, nisi ab mu&shy;<lb/>sculorum cognitione remedium &rdquo; (pag. </s>

<s>3). </s></p><p type="main">

<s>Datosi dunque a esaminare i muscoli ordinati al moto di varii organi, <lb/>per conoscerne le differenze, lo Stenone cos&igrave; conclude: &ldquo; Quae hic de mu&shy;<lb/>sculis proposita, si cordi applicentur, sufficiunt propositae initio demonstran&shy;<lb/>dae propositioni: <emph type="italics"/>Cor vere musculum esse &rdquo;<emph.end type="italics"/> (pag. </s>

<s>24). Promette di tornare <pb xlink:href="020/01/1212.jpg" pagenum="87"/>in altro libro a dimostrare pi&ugrave; profusamente la verit&agrave; di questa annunziata <lb/>proposizione, ma intanto qui riduce a tre i principali argomenti formulati <lb/>nell'ordine e nel modo che segue: &ldquo; I. </s>

<s>In universa cordis substantia nihil <lb/>occurrit sequentia praeter arterias, venas, nervos, fibras, membranas. </s>

<s>Sed nec <lb/>in musculo praeter dicta occurrunt alia (pag. </s>

<s>24). II. </s>

<s>Inter cordis fibras nulla <lb/>scrutanti mihi obvenit, quae non medio carnosa, extremis utrinque tendi&shy;<lb/>nosa: id quod et omnibus musculorum fibris commune. </s>

<s>In corde, non mi&shy;<lb/>nus ac in alio musculo, villorum uniformis est ductus (pag. </s>

<s>25). III. </s>

<s>Mem&shy;<lb/>brana cordi propria, transverso fibrarum ductu, cordis secat fibras, eodemque <lb/>inter illas se insinuat ritu, nec aliud in musculi occurrit membrana &rdquo; (pag. </s>

<s>29) <lb/>Essendo cos&igrave; dimostrato, conclude all'ultimo lo Stenone che, tutti gli attri&shy;<lb/>buti de'muscoli competendo con egual ragione anche al cuore, <emph type="italics"/>vere cor mu&shy;<lb/>sculi nomine salutandum,<emph.end type="italics"/> ed &egrave; perci&ograve; verissima e confermata dai fatti os&shy;<lb/>servati la sentenza dell'antichissimo Ippocrate. </s></p><p type="main">

<s>Cos&igrave; parve finalmente decisa la questione, che insorta fra i due pi&ugrave; an&shy;<lb/>tichi greci Maestri dell'Anatomia si rinnovell&ograve; ai tempi del Vesalio in Italia. </s>

<s><lb/>Ma bench&egrave; lo Stenone fosse espertissimo in esercitare lo stilo, e oculatissim<gap/><lb/>in osservare quel che dalla punta di lui gli veniva scoperto, tante erano nul&shy;<lb/>ladimeno le difficolt&agrave;, che presentava il cuore nel districare l'implicata tes&shy;<lb/>situra delle sue fibre, che &agrave;lcuni lo trovarono oscuro in descriverle, altr<gap/><lb/>difettoso in esaminarle. </s>

<s>Di qui &egrave; che, verso la met&agrave; del secolo XVII, dura&shy;<lb/>vano tuttavia nelle menti i dubbi, in che, infino dai restauramenti dell'arte, <lb/>s'erano incontrati i primi Anatomisti. </s></p><p type="main">

<s>Il Berengario confess&ograve; ch'essendo il cuore cos&igrave; sodo non potevano com&shy;<lb/>prendersi dal senso le variet&agrave; delle fibre, di ch'&egrave; intessuto, ma dalle opera&shy;<lb/>zioni di lui, che consistono principalmente in dilatarsi per attrarre, e ind<gap/><lb/>ritenere ed espellere il sangue, congetturava che di tre ordini dovesser es&shy;<lb/>sere quelle stesse fibre: lunghe cio&egrave;, disposte nell'interno del viscere, per <lb/>servire all'attrazione; trasverse, collocate nel mezzo, per meglio ritenere l<gap/><lb/>stesso sangue; larghe, ricorrenti sull'esterior superficie, per esser pi&ugrave; vali<gap/><lb/>a spremerlo fuori e ad irrigarne tutte le membra. </s>

<s>&ldquo; Non sunt tales inu<gap/><lb/>in corde, sicut in musculis, in situ neque in substantia, quia situs istorun, <lb/>villorum in corde .... sunt absque ordine, et non sunt sic in musculis. </s>

<s>Prima <lb/>namque operatio cordis, teste Galeno <emph type="italics"/>V. </s>

<s>De iuvamentis membrorum,<emph.end type="italics"/> e<gap/><lb/>dilatare, et sic attrahit, et attractioni deserviunt villi, et in unoquoque men<gap/><lb/>bro villi longi deserviunt attractioni, et consiti sunt in interiori parte; <gap/><lb/>retentioni deserviunt transversi, qui necessario sunt siti in medio, scilic<gap/><lb/>supra istos; et expulsioni deserviunt lati, qui necessario sunt exteriores. </s>

<s>In <lb/>corde tamen, propter suam soliditatem, talis diversitas non potest ad sensum <lb/>comprehendi, et fuerunt in corde praedictae speties villorum, quia in eo ne&shy;<lb/>cessario sunt diversi motus &rdquo; (Commentaria super Anat. </s>

<s>Mundini, Bono&shy;<lb/>niae 1521, fol. </s>

<s>CCCXXXIX). </s></p><p type="main">

<s>Il Vesalio non sembra aver fatto altro in questo proposito che comme<gap/><lb/>tare i detti del Notomist<gap/> di Carpi. </s>

<s>Se tu prendi, egli dice, a esaminare u<gap/><pb xlink:href="020/01/1213.jpg" pagenum="88"/>muscolo, e o cotto o crudo, tu lo discerpi col coltello o coll'unghie, ti si <lb/>rivela senza difficolt&agrave; la struttura delle sue fibre. </s>

<s>&ldquo; At cordis quidem caro <lb/>fibris compactissimis et inter se plurimum differentibus oppleta videtur. </s>

<s>Quae <lb/>vero earumdem situs differentiarumque sit ratio, coniectura potius quam <lb/>sectione assequimur &rdquo; (De hum. </s>

<s>corporis fabrica cit., pag. </s>

<s>586). </s></p><p type="main">

<s>La congettura si riduce, ad esempio del nostro Berengario, ad ammet&shy;<lb/>tere un triplice ordine di fibre, le pi&ugrave; intime delle quali facciano l'ufficio <lb/>di attrarre, le mezzane di ritenere e l'esterne di espellere il sangue. </s>

<s>Per&ograve; <lb/>soggiunge che non si pu&ograve; propriamente assegnare a quelle stesse fibre un <lb/>ordine certo o una collocazione determinata, mescolandosi insieme dovunque <lb/>le rette con le oblique e con le transverse. </s>

<s>&ldquo; Sectio ipsa triplex hoc fibra&shy;<lb/>rum genus invicem commisceri ostendit, et nunc rectas, nunc obliquas, nunc <lb/>transversas, et rursus rectas et obliquas et transversas quodammodo com&shy;<lb/>mostrat, quasi tres priores differentiae singulis ventriculis peculiares essent, <lb/>posteriores vero toti cordi ambobusque ventriculis dedicarentur. </s>

<s>Appello au&shy;<lb/>tem in corde rectas fibras quas in eo, per quam elixato, ex ipsius basi ad <lb/>mucronis usque ipsius centrum deduci, tam per cordis ventriculorum septum, <lb/>quam reliquam sedem, conspicimus; transversas autem, quae orbiculatim cor <lb/>ventriculosque ambiunt; obliquas vero, quae quidem orbiculatim cor ven&shy;<lb/>triculosque ambiunt, at oblique, secundum cordis longitudinem, procedunt &rdquo; <lb/>(ibi, pag. </s>

<s>587). </s></p><p type="main">

<s>Quelle fibre rette ammesse dal Vesalio e nelle sue descrizioni accolte <lb/>dal Colombo (De re anat. </s>

<s>pag. </s>

<s>176), bench&egrave; si possano salvare nell'anato&shy;<lb/>mia di alcuni bruti, son per&ograve; cosa affatto immaginaria, se si tratti del cuore <lb/>dell'uomo. </s>

<s>Pure, anche il Lower poi ripet&egrave; lo stesso, e il Morgagni, per ta&shy;<lb/>cere di altri, confess&ograve; che avendo diligentemente tenuto dietro alla rettitu&shy;<lb/>dine di quelle fibre &ldquo; numquam videre potuisse, ob eamque causam facile <lb/>crediderim a diligentissimo anatomico Vieussenio in fibrarum cordis descrip&shy;<lb/>tione esse praetermissas &rdquo; (Adversaria anat. </s>

<s>V, Patavii 1719, pag. </s>

<s>21). </s></p><p type="main">

<s>Ma, ripigliando il filo della nostra storia, quando lo Stenone pubblicava <lb/>nel suo trattato <emph type="italics"/>De musculis et glandulis<emph.end type="italics"/> di aver trovato il dutto delle fibre <lb/>del cuore non esser n&egrave; retto n&egrave; circolare, &ldquo; sed tantum circa medium sui <lb/>nonnihil incurvatum &rdquo; (pag. </s>

<s>2), il Borelli in Pisa aveva tredici anni prima <lb/>con pari diligenza osservato di esse fibre cardiache la configurazione e la <lb/>struttura, e non essere dirette n&egrave; parallele, ma curve e spirali; non intes&shy;<lb/>sute come i giunchi nelle cestelle, secondo che parve al Vesalio, ma dispo&shy;<lb/>ste con artificio assai pi&ugrave; maraviglioso. </s>

<s>&ldquo; Immediate enim sub externa cor&shy;<lb/>dis membrana a basi cordis et ab orificiis circularibus tendinosis, in quibus <lb/>desinunt venae cavae et pulmonaris auriculae, nec non a principiis arteria&shy;<lb/>rum Aortae et Pulmonaris, propagatur stratum fibrarum carnosarum, quae <lb/>fere aequidistantes sunt inter se et directe a basi versus cordis mucronem <lb/>tendentes, ubi varie inflexae et contextae reflectuntur versus internas cavi&shy;<lb/>tates ventriculorum. </s>

<s>Huic strato succedunt alia fibrarum strata oblique et <lb/>spiraliter descendentia, quorum fibrae semper magis ac magis inclinatae, pa-<pb xlink:href="020/01/1214.jpg" pagenum="89"/>riter versus mucronem tendentes, antequam apicem attingant, decussantur, <lb/>et texuntur inter se, et cum aliis ordinibus fibrarum, et inde interius reflec&shy;<lb/>tuntur, et partim spiris obliquis et transversis, veluti fasciis, ad basim cordis <lb/>reflectuntur; partim internas columnas componere videntur, quibus funiculi <lb/>valvularum tricuspidum et mitralium alligantur; partim transverse contextae, <lb/>sinum ventriculi dextri efformant &rdquo; (De motu anim. </s>

<s>cit., P. II, pag. </s>

<s>89). </s></p><p type="main">

<s>Dopo di avere il Borelli descritta questa cos&igrave; mirabile struttura, occor&shy;<lb/>sagli a vedere nel 1657 in Pisa, soggiunge di aver sentito dire che poi altri <lb/>avevano osservato lo stesso, e voleva senza dubbio alludere allo Stenone, il <lb/>quale pubblic&ograve; i suoi trattati anatomici parecchi anni prima che uscisse alla <lb/>luce la grande opera intorno ai Moti animali. </s>

<s>Noi, che non abbiamo ragioni <lb/>da smentirla, crediamo perci&ograve; sincera la confessione che il Borelli stesso fa <lb/>colle seguenti parole: &ldquo; Hanc mirabilem structuram primum mihi videri <lb/>contigit Pisis, adstante clarissimo Malpighio, anno 1657. Postea novi alios <lb/>eadem adnotasse: tandem clariss. </s>

<s>Lower et Laurentius Bellinus exactam cor&shy;<lb/>dis contexturam indagarunt, dissolvendo fibrarum perplexam colligationem <lb/>ad instar glomi &rdquo; (ibi, pag. </s>

<s>90). </s></p><p type="main">

<s>Al Malpighi per&ograve; non parve troppo esatta, n&egrave; conforme alla verit&agrave; delle <lb/>cose la storia della scoperta delle fibre spirali del cuore, cos&igrave; esposta. </s>

<s>E per&shy;<lb/>ci&ograve;, sul principio della sua <emph type="italics"/>Antobiografia,<emph.end type="italics"/> narra com'essendo stato, nel 1656, <lb/>eletto dal Granduca professore di Medicina teorica nella Universit&agrave; di Pisa, <lb/>vi conobbe ed ebbe familiarit&agrave; con uomini dottissimi, fra'quali il Borelli, con <lb/>cui teneva frequentemente colloqui intorno a cose di Anatomia. </s>

<s>&ldquo; Ut autem, <lb/>mutuis officiis eximiae tanti Viri curiositati satisfacerem, eius domi frequen&shy;<lb/>ter anatomicas moliebar sectiones, inter quas, dum incocto maceratoque corde <lb/>fibrarum inclinationem indagabam, spiralis ipsarum tractus occurrit, quem <lb/>ipsi primo ostendi, licet, in suo posthumo libro <emph type="italics"/>De motu anim.,<emph.end type="italics"/> me exara&shy;<lb/>tae observationis testem tantum enunciet &rdquo; (Opera postuma cit., pag. </s>

<s>2). </s></p><p type="main">

<s>Dopo la pubblicazione dell'Opera del Borelli altri valorosi anatomici <lb/>esercitarono lo stilo intorno al cuore, e son fra questi a commemorare, per <lb/>diligenza fra'primi, Raimondo Vieussens e il nostro Lancisi. </s>

<s>Questi, nel suo <lb/>trattato postumo <emph type="italics"/>De motu cordis,<emph.end type="italics"/> intitolava cos&igrave; la XXVIII proposizione: <lb/>&ldquo; Ostenditur cor esse musculum quadricavum suis tendinibus instructum &rdquo; <lb/>(Romae 1728, pag. </s>

<s>46). </s></p><p type="main">

<s>Fu il Lancisi de'primi a far particolare attenzione ai muscoli cavi, e ad <lb/>interpetrarne il sapiente magistero della Natura, applicandovi le dottrine mec&shy;<lb/>caniche di Galileo. </s>

<s>Nel primo dialogo delle Due nuove scienze proponesi dal <lb/>Salviati a sciogliere questo problema: &ldquo; Come possano i filamenti di una <lb/>corda, lunga cento braccia, s&igrave; saldamente connettersi insieme, non essendo <lb/>ciascheduno di essi lungo pi&ugrave; di due o tre, che gran violenza ci voglia a <lb/>dissepararli &rdquo; (Alb. </s>

<s>XIII, 12). E si risolve con dire ch'essendo, per la tor&shy;<lb/>tura, i fili della canapa tenuti stretti in tutta la loro lunghezza, converrebbe <lb/>sbarbarli, facendoli strisciar l'uno sopra l'altro, ci&ograve; che sarebbe pi&ugrave; diffi&shy;<lb/>cile assai che romperli. </s></p><pb xlink:href="020/01/1215.jpg" pagenum="90"/><p type="main">

<s>Il Lancisi dunque, osservando che i muscoli cavi son tessuti a una certa <lb/>similitudine delle funi, congettura che la Natura abbia voluto provvedere in <lb/>quel modo alla solidit&agrave;, contorcendone le fibre e rendendole cos&igrave; pi&ugrave; diffi&shy;<lb/>cili a rompersi, con l'artificio che si rendono, secondo Galileo, difficili a <lb/>rompersi le stesse funi. </s>

<s>&ldquo; Quadricavus cordis musculus, egli scrive, non ex <lb/>una, eaque simplici carnearum ac tendinearum fibrarum advolutione, sed <lb/>ex mirabili complexione, tum glomi, tum viminei contextus, assurgit et so&shy;<lb/>lidascit. </s>

<s>Inter multiplices modos cohaerentium partium in animalibus ille, <lb/>meo quidem iudicio, magis est inspiciendus, quo Natura, in coagmentandis <lb/>cavis musculis, utitur. </s>

<s>Hi enim compinguntur ex varia, circum determinatas <lb/>capacitates villorum fibrarumque, contorsione, ac prius minus spirali prae&shy;<lb/>sertim advolutione, cuius quanta sit facultas et vis prius docuit Gali&igrave;eus, u<gap/><lb/>conficiendae funis artificium expendit &rdquo; (De motu cordis cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Si pu&ograve; dir che nel Lancisi in sostanza si compiessero le notizie, ch'era <lb/>possibile avere dell'anatomia del cuore, intorno alla quale per questo s'&egrave; <lb/>intrattenuta la nostra storia, perch&egrave; dipende principalmente da quelle noti&shy;<lb/>zie la pi&ugrave; esatta cognizione delle pulsazioni di lui. </s>

<s>La necessit&agrave; di premettere <lb/>l'Anatomia a rischiarare tante difficolt&agrave;, in che si trov&ograve; avvolta la scienza <lb/>di questi moti, fu sentita gi&agrave; dal Berengario, il quale si compiacque d'es&shy;<lb/>sersi, per via dello studio che fece sulla testura de'villi nel cuore, chiarito <lb/>di un fatto, da pochissimi medici allora conosciuto. </s>

<s>&ldquo; Ex praedicto textu in&shy;<lb/>telligitur qualiter per villos aperiatur cor et qualiter claudatur, et qualiter <lb/>inter istos motus est quies.... Istam quietem in pulsu rari sunt Medict <lb/>qui eam cognoscant: tamen, ni fal&igrave;or, ego comprehendo per intellectum <lb/>minimum temporis esse inter dyastolem et systolem &rdquo; (Commentaria cit., <lb/>fol. </s>

<s>CCCXL). </s></p><p type="main">

<s>Un esempio a questo contrario, e per cui si dimostra come gli erro<gap/><lb/>nell'anatomia del cuore condussero ad errare altres&igrave; intorno ai moti di lu<gap/><lb/>ce lo porge il Vesalio, il quale, come dicemmo, descrisse le fibre rette, ch<gap/><lb/>dalla base ricorrono all'apice, e che il Morgagni ed altri, perch&egrave; veramen<gap/><lb/>non ci sono, attestarono di non aver mai vedute. </s>

<s>S'immagin&ograve; dunque esse <lb/>Vesalio, sul fondamento di quelle immaginate fibre rette, che fosse il cuore <lb/>contessuto dalla parte di fuori a guisa di un canestro, in cui, essendo dalla <lb/>parte del taglio legati i giunchi intorno intorno a un cerchio, fossero da<gap/><lb/>l'altra parte delle punte raccolti e legati insieme, da far prendere al cane&shy;<lb/>stro stesso la figura di un cono, o come dicevasi allora di una piramide <lb/>Cos&igrave; essendo, suppongasi che sia attaccata al vertice di questa piramide una <lb/>cordicella, e che si tiri, facendola attraversare il centro del cerchio: il c<gap/><lb/>nestro si schiaccer&agrave; divenendo pi&ugrave; capace. </s>

<s>E cos&igrave; il cuore, a cui si ass<gap/><lb/>miglia nella forma e nella testura, quando la sua punta si avvicina all<gap/><lb/>base, si dilata e divien cos&igrave; pi&ugrave; capace ad attrarre in quell'atto il sangu<gap/><lb/>&ldquo; Porro cordis dilatationem, qua mucronis ipsius ad basis centrum est a<gap/><lb/>tractio et omnium latorum cordis distentio, rectae efficiunt fibrae, mucronen <lb/>versus bas&igrave;m contrahentes. </s>

<s>Quod sane ita perficitur, ac si vimineo circu<gap/><pb xlink:href="020/01/1216.jpg" pagenum="91"/>orbiculatim eademque serie complurimas iuncorum scirporumve radices con&shy;<lb/>necteres, et capitibus illorum simul collectis velut pyramidem quamdam <lb/>efformares, ac demum funiculum ex mucronis medio per circuli centrum <lb/>dimitteres: quo, deorsum tracto, pyramis brevior intusque multo capacior <lb/>redderetur &rdquo; (De hum. </s>

<s>corp. </s>

<s>fabrica cit., pag. </s>

<s>587). </s></p><p type="main">

<s>Quando insomma la punta si avvicina alla base, il cuore, secondo il <lb/>Vesalio, si dilata: riceve allora in s&egrave; il sangue, e si ritrova in quella fase <lb/>del suo moto, che si disse <emph type="italics"/>Diastole.<emph.end type="italics"/> Queste cose per&ograve;, e il Vesalio stesso lo <lb/>confessa, sono congetturate e non dedotte da quella osservazione de'fatti, <lb/>che fu riserbata poco pi&ugrave; tardi a Realdo Colombo. </s>

<s>Egli, proseguendo quel <lb/>sicuro metodo della vivisezione da s&egrave; istituito, trov&ograve; che gli stessi fatti erano <lb/>tutt'al contrario di quel che il divino Brussellese aveva congetturato. </s></p><p type="main">

<s>Ritorniamo al trattato <emph type="italics"/>De re anatomica,<emph.end type="italics"/> e leggiamo nel libro XIV. Ivi, <lb/>dop'avere insegnato il modo di preparare il cane, per disseccarlo vivo, sog&shy;<lb/>giunge l'Autore ci&ograve; che pu&ograve; vedersi, aperto il ventre, in quelle viscere pal&shy;<lb/>pitanti, e fra le altre cose bellissime, ei dice &ldquo; illud quoque accedit motus <lb/>scilicet cordis quemadmodum amplificetur atque arctetur: item qualis sit <lb/>motus arteriarum in viva Anatome, si lubuerit, conspicaberis: numquid idem <lb/>sit vel oppositus motui cordis. </s>

<s>Comperies enim, dum cor dilatatur, constringi <lb/>arterias, et rursus, in cordis constrictione, dilatari. </s>

<s>Verum animadvertas, dum <lb/>cor sursum trahitur et tumefieri videtur, tunc constringitur: cum vero se <lb/>exerit, quasi relaxatus deorsum vergit, atque eo tempore dicitur cor quie&shy;<lb/>scere: estque tunc cordis <emph type="italics"/>Systole,<emph.end type="italics"/> propterea quod facilius suscipit minore <lb/>labore. </s>

<s>At cum transmittit, maiori opus est robore &rdquo; (Editio cit., pag. </s>

<s>257). </s></p><p type="main">

<s>L'osservazione dei fatti nell'animale vivo insegna dunque che, avvici&shy;<lb/>nandosi la punta alla base, il cuore non si dilata, come diceva il Vesalio, ma <lb/>si contrae, e non &egrave; allora in diastole ma in sistole. </s>

<s>Avviene il contrario <lb/>quando la punta si abbassa, nel qual tempo il cuore si posa ed &egrave; in dia&shy;<lb/>stole, bench&egrave; nel testo si legga <emph type="italics"/>sistole,<emph.end type="italics"/> forse per inavvertenza di chi cur&ograve; <lb/>questa edizione postuma. </s>

<s>Il Colombo descrive i fatti senza per&ograve; accennare <lb/>che fanno contro al Vesalio, e perch&egrave; prevedeva che la grande autorit&agrave; di <lb/>quell'uomo reputato divino avrebbe fatto prevalere il falso congetturato al <lb/>nuovo vero scoperto, si raccomanda ai Lettori che quel ch'egli dice dei moti <lb/>del cuore non lo ritengan per cosa di lieve importanza. </s>

<s>&ldquo; Neque hoc flocci&shy;<lb/>facias: etenim non paucos reperias, qui, eo tempore cor dilatari certo opi&shy;<lb/>nantur, quo vere constringitur &rdquo; (ibi). </s></p><p type="main">

<s>Le parole sopra citate dal XIV libro <emph type="italics"/>De re anatomica<emph.end type="italics"/> a noi parrebbe <lb/>che potrebbero inscriversi per testo alla prima parte del celebre trattato del&shy;<lb/>l'Harvey, che &egrave; di quelle stesse parole del Colombo il pi&ugrave; splendido e il pi&ugrave; <lb/>glorioso commento. </s>

<s>Anche l'Inglese, proseguendo le vie segnategli dall'ita&shy;<lb/>liano Maestro, incomincia a descrivere i moti del cuore quali gli si rappre&shy;<lb/>sentarono agli occhi nelle sezioni de'vivi, ond'&egrave; ch'egli si propone perci&ograve; <lb/>di dimostrare nel cap. </s>

<s>II <emph type="italics"/>De motu cordis.<emph.end type="italics"/> &ldquo; Ex vivorum dissectione qualis <lb/>sit cordis motus &rdquo; (Lugduni Batav. </s>

<s>1737, pag. </s>

<s>24). </s></p><pb xlink:href="020/01/1217.jpg" pagenum="92"/><p type="main">

<s>Nelle viscere palpitanti aperte, no nel ventre de'soli cani o di altri ani&shy;<lb/>mali a sangue caldo, ma e de'pesci, delle rane e di altri cos&igrave; fatti animali <lb/>freddi, osservando dunque l'Harvey i moti del cuore, si assicur&ograve; esser vero <lb/>quel che aveva detto il Colombo, e lo conferm&ograve; con l'esperienza e con la <lb/>ragione. </s>

<s>Prese per fondamento del suo argomentare gli altri muscoli, e <lb/>com'egli vedeva mettersi questi in moto, accorciandosi nelle estremit&agrave; e in&shy;<lb/>turgidendo nel mezzo; cos&igrave; diceva avvenir nel cuore che, accorciandosi dal&shy;<lb/>l'apice verso la base, intumidisce ne'ventricoli, i quali perci&ograve; divengono pi&ugrave; <lb/>angusti e premono il sangue. </s>

<s>Di qui coglieva occasione di notare in che avesse <lb/>preso errore il Vesalio, il quale non ebbe un'idea chiara della fabbrica del <lb/>cuore, n&egrave; seppe applicare ad essa la meccanica muscolare. </s></p><p type="main">

<s>Uno de'pi&ugrave; notabili tra questi fatti meccanici &egrave; che, quando il muscolo <lb/>&egrave; in forze, indurisce, stringendosi pi&ugrave; fortemente le une addosso all'altre <lb/>le fibre; ond'&egrave; che, come una fune bagnata e attorta indurisce essa pure <lb/>e spreme fuori l'umore, cos&igrave; il muscolo spreme il sangue e ne d&agrave; segno <lb/>con l'impallidire. </s>

<s>Quando poi succede la quiete, torna, per il sangue che ri&shy;<lb/>sorbe di nuovo, a porporeggiare, cosicch&egrave;, se anche il cuore &egrave; un muscolo <lb/>come gli altri, si potr&agrave; facilmente conoscere quand'egli &egrave; in quiete o in <lb/>moto dal suo stesso colore. </s>

<s>Questo continuo cangiar di colore &egrave; visibilissimo <lb/>negli animali a sangue freddo, nel cuor de'quali pu&ograve; confermarsi il fatto col <lb/>ferire il ventricolo, dopo che si vede che, mentre il cuore biancheggia, il <lb/>sangue non esce, ma spiccia con viva forza quando torna a porporeggiare. </s></p><p type="main">

<s>&ldquo; Ex quibus observatis, conclude l'Harvey, rationi consentaneum est, <lb/>Cor eo quo movetur tempore et undique constringitur, et secundum parie&shy;<lb/>tes incrassescit: secundum ventriculos coarctari et contentum sanguinem <lb/>protrudere, quod ex quarta observatione satis patet, cum in ipsa tensione <lb/>sua, propterea quod sanguinem in se prius contentum expresserit, albescit, <lb/>et denuo, in laxatione et quiete, subingrediente de novo sanguine in ven&shy;<lb/>triculum, redit color purpureus et sanguineus cordi. </s>

<s>Verum nemo amplius <lb/>dubitare poterit, cum, usque in ventriculi cavitatem inflicto vulnere, singu&shy;<lb/>lis motibus, sive pulsationibus cordis, in ipsa tensione, prosilire cum impetu <lb/>foras contentum sanguinem viderit &rdquo; (ibi, pag. </s>

<s>26). </s></p><p type="main">

<s>Si veniva da tutti questi fatti osservati a dimostrare la falsit&agrave; dell'opi&shy;<lb/>nione comune, concludendosi non essere il moto proprio del cuore la dia&shy;<lb/>stole, come si credeva, ma la sistole, nel qual tempo la punta si avvicina <lb/>alla base, i muscoli si mettono in forza intorno ai ventricoli, che perci&ograve; spre&shy;<lb/>mono fuori il sangue. </s>

<s>Il Cartesio insorse allora contro le innovazioni arve&shy;<lb/>iane, e mentre diceva da una parte lo Scopritore del circolo del sangue <emph type="italics"/>pro <lb/>tam utili inventu numquam satis laudandum,<emph.end type="italics"/> notava dall'altra che non solo <lb/>era contrario alla comune opinione dei Medici, ma ripugnante all'ordinario <lb/>giudizio degli occhi l'affermar che nella Sistole consiste il moto del cuore. </s>

<s><lb/>Degli argomenti del Medico inglese il Filosofo bretone non fa nessun conto, <lb/>anzi glie ne suggerisce uno in apparenza pi&ugrave; concludente di tutti gli altri. <lb/></s>

<s>&ldquo; Et hoc quidem poterat, soggiunge il Cartesio, dop'aver commemorati gli <pb xlink:href="020/01/1218.jpg" pagenum="93"/>argomenti dell'Harvey, adhuc valde specioso experimento confirmari, nempe <lb/>si canis vivi mucro cordis abscindatur et per incisionem inferatur digitus in <lb/>alterutrum ventriculorum eius, quoties mucro cordis accedet ad basim, ma&shy;<lb/>nifeste sentietur digitum comprimi, desinetque pressio quoties recedet &rdquo; (De <lb/>homine cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Il Lower e il Bellini si servirono poi di questa bellissima esperienza <lb/>per confermare i fatti osservati dal Colombo e dall'Harvey, che cio&egrave; strin&shy;<lb/>gendosi il cuore dall'apice verso la base, il ventricolo si fa pi&ugrave; angusto, ed <lb/>&egrave; allora in sistole, e spreme il sangue. </s>

<s>Ma il Cartesio gli perveniva dicendo <lb/>che ci&ograve; null'altro prova &ldquo; nisi quod ipsa experimenta nobis saepe halluci&shy;<lb/>nandi occasionem offerunt, si quidem illorum causas omnes possibiles non <lb/>satis expendamus &rdquo; (ibi, pag. </s>

<s>168). </s></p><p type="main">

<s>Coloro che, dopo tanti esempi fin qui offerti dalla nostra Storia, dubi&shy;<lb/>tano tuttavia se il Cartesio procedesse ne'metodi sperimentali e quel modo, <lb/>che da noi si disse nel nostro primo <emph type="italics"/>Discorso,<emph.end type="italics"/> rimeditino le citate parole, <lb/>che ritraggono in immagine viva l'indole della Filosofia cartesiana. </s>

<s>Si diceva <lb/>essere una tale indole quella di accomodare, come facevano i Peripatetici, <lb/>alle speculazioni filosofiche i fatti naturali: e in verit&agrave;, nell'esempio che ab&shy;<lb/>biamo fra mano, il Cartesio professa che a nulla valgono gli sperimenti, <lb/>quando non si sappia trovar delle cose le cause possibili. </s>

<s>Che vuol egli dire <lb/>il potersi toccar con mano che i ventricoli del cuore, quando la punta si <lb/>avvicina alla base si restringono, se la Filosofia investigatrice delle cause <lb/>possibili ci conclude invece che si debbono dilatare? </s></p><p type="main">

<s>I filosofici argomenti, che il Cartesio contrapponeva ai fatti sperimen&shy;<lb/>tali dell'Harvey, si fondano sull'osservazione che il sangue esce dal cuore <lb/>molto pi&ugrave; caldo che non &egrave; quando c'entra. </s>

<s>Ma s'&egrave; natura del calore il di&shy;<lb/>latare, dunque, quando il cuore manda fuori di s&egrave; il sangue, si dilata ne&shy;<lb/>cessariamente e non si ristringe. </s>

<s>Che se il calore stesso indurisce le fibre, <lb/>e nell'indurirle anche le distende &ldquo; fieri potest ut digitum in ventriculis <lb/>positum comprimatur, quamvis inde ventriculi nihilo magis coartentur, sed <lb/>potius dilatentur &rdquo; (ibi, pag. </s>

<s>169). </s></p><p type="main">

<s>Tanto poi si compiacque il Cartesio di aver cos&igrave; trovato nel calore la <lb/>causa motrice del cuore, della quale l'Harvey, con tutta la sua scienza spe&shy;<lb/>rimentale, non aveva fatta alcuna menzione, che si maraviglia della gran po&shy;<lb/>tenza della sua propria Filosofia, dalla quale fu scorto a una tale e cos&igrave; <lb/>nuova scoperta. </s>

<s>&ldquo; Quapropter valde miror quod, quamvis ab omni aevo no&shy;<lb/>tum fuerit plus esse caloris in corde quam in cactero corpore, sanguinem&shy;<lb/>que posse calore rarefieri; nemo tamen hactenus repertus sit, qui cordis <lb/>motum ab hac sola rarefactione proficisci animadverterit. </s>

<s>Nam quamquam vi&shy;<lb/>detur Aristotiles de hoc cogitasse, cum libri <emph type="italics"/>De respiratione,<emph.end type="italics"/> cap. </s>

<s>XX, dicit <lb/><emph type="italics"/>motum hunc esse similem actioni liquoris vi caloris bullientis,<emph.end type="italics"/> atque etiam <lb/>causam pulsus <emph type="italics"/>esse quod succus ciborum quos manducavimus, in cor per&shy;<lb/>petuo ingrediens, ultimam eius membranam elevet;<emph.end type="italics"/> tamen, quia nullam <lb/>ibi sanguinis mentionem facit, aut structurae cordis, liquet illum casu tan-<pb xlink:href="020/01/1219.jpg" pagenum="94"/>tum in aliquid a vero non alienum et sine ulla cogitatione certa incidisse. </s>

<s><lb/>Et certe haec eius sententia sectatores nullos invenit &rdquo; (ibi, pag. </s>

<s>169). </s></p><p type="main">

<s>Ma questa &egrave; una lusinga, che si faceva il Cartesio, a cui sarebbero sa&shy;<lb/>liti nel viso i rossori della vergogna e i livori del dispetto, se gli avesse al&shy;<lb/>cuno aperto sotto gli occhi le <emph type="italics"/>Questioni peripatetiche<emph.end type="italics"/> del Cesalpino, l&agrave; dove, <lb/>commentando la sentenza aristotelica, si dice che il cuore, sorgente del calor <lb/>vitale, &egrave; simile a una pignatta che bolle, intorno alla quale, perch&egrave; il san&shy;<lb/>gue contenutovi andando in spuma non trabocchi, son posti i flabelli dei <lb/>polmoni. </s>

<s>&ldquo; Ut igitur sufficiens maneret vasorum tensio, ignis autem interim <lb/>non suffocaretur, remedium molita est Natura modica ferventis sanguinis re&shy;<lb/>frigeratione iuxta principium, quemadmodum ii faciunt qui ollae ferventis <lb/>tumorem cohibent insufflando: modica enim hac refrigeratione non impedi&shy;<lb/>tur coctio, sed solum intumescentis humoris nimius fastus &rdquo; (Venetiis 1571, <lb/>fol. </s>

<s>111). </s></p><p type="main">

<s>Ma l'effervescenza e il calore, dice il Cesalpino, producono moto, ed <lb/>hanno di qui principio i moti del cuore. </s>

<s>Movendosi cos&igrave; per la turgenza il <lb/>cuore si muovono tutt'insieme anche l'arterie. </s>

<s>&ldquo; Cum enim pulsatio cor&shy;<lb/>dis et arteriarum sit accidens quoddam quod ex necessitate insequitur hu&shy;<lb/>moris in corde effervescentiam, qua sanguinis generatio perficitur, ut in cae&shy;<lb/>teris quae igne elixantur accidit, intumescente corde necesse est simul omnes <lb/>arterias dilatari, in quas derivatur fervor &rdquo; (ibi, fol. </s>

<s>109). </s></p><p type="main">

<s>Forse nessuno avr&agrave; rammemorato al Filosofo, che tutta la scienza fa&shy;<lb/>ceva scaturire dal suo proprio cervello, questo passo del nostro Peripatetico <lb/>italiano, ma l'Harvey stesso, verso la fine della seconda esercitazione ana&shy;<lb/>tomica <emph type="italics"/>De circulatione sanguinis,<emph.end type="italics"/> mentre da una parte ringrazia come di <lb/>una gran degnazione il Cartesio <emph type="italics"/>ob mentionem sui nominis honorificam,<emph.end type="italics"/><lb/>conclude liberamente dall'altra che quell'acutissimo ingegno e tutti gli altri <lb/>con lui, i quali quando il cuore &ldquo; erigitur, attollitur et vigoratur, ampliari, <lb/>aperiri, ventriculosque suos exinde capaciores esse autumant, haud recte me&shy;<lb/>cum observant &rdquo; (ibi, pag. </s>

<s>164). </s></p><p type="main">

<s>Il Cartesio nonostante, com'era da aspettarsi da quella sua indole, ri&shy;<lb/>mase, contro la verit&agrave; dimostrata dai fatti, ostinato nella sua filosofica sen&shy;<lb/>tenza, di che presero poi maraviglia i Cartesiani stessi anco pi&ugrave; infervorati. </s>

<s><lb/>Tommaso Cornelio, nel suo Proginnasma VII <emph type="italics"/>De vita,<emph.end type="italics"/> dopo aver riferita <lb/>l'opinion del Filosofo, secondo la quale il sangue entrato ne'ventricoli gli <lb/>dilata col suo calore, ch'&egrave; perci&ograve; la causa efficiente del moto &ldquo; sed nescio, <lb/>soggiunge, quomodo Vir clarissimus contra autopsiam obstinatione quadam <lb/>sententiae pugnaverit. </s>

<s>Enimvero, seu vena cava ligetur ut nullus omnino <lb/>sanguis permanare possit in cor, sive cor ipsum ita vulneretur, ut influens <lb/>in eiusdem ventriculos sanguis totus pene effluat, videbimus quidem etiam <lb/>tum cor ut ante mobiliter palpitare, alterneque astringi, atque laxari &ldquo; (Nea&shy;<lb/>poli 1688, pag. </s>

<s>271). </s></p><p type="main">

<s>Tanto erano questi e altri simili fatti offerti dall'autopsia evidenti, che, <lb/>nonostante la seducente eloquenza del Filosofo, trionf&ograve; il vero osservato prima <pb xlink:href="020/01/1220.jpg" pagenum="95"/>dal Colombo e dimostrato poi dall'Harveio. </s>

<s>Proseguendo questi con la solita <lb/>diligenza le sue osservazioni intorno ai moti del cuore, ebbe a notar gli er&shy;<lb/>rori in ch'erano incorsi due uomini reputati dottissimi e peritissimi del&shy;<lb/>l'arte, Gaspero Bauhino e Giovanni Riolano, i quali ammettevano quattro <lb/>essere que'moti distinti di tempo e di luogo. </s>

<s>Osservava l'Harvey che una <lb/>tal distinzione potevasi bene far quanto al luogo, non per&ograve; quanto al tempo <lb/>&ldquo; simul enim ambae auriculae movent et simul ambo ventriculi, ut quatuor <lb/>loco motus distincti sunt, duobus tantum temporibus, atque hoc se habet <lb/>modo: Duo sunt quasi eodem tempore motus, unus auricularum, alter ipso&shy;<lb/>rum ventriculorum; nec enim simul omnino fiunt, sed praecedit motus au&shy;<lb/>ricularum &rdquo; (De motu cordis cit., pag. </s>

<s>31). </s></p><p type="main">

<s>Questi due moti per&ograve; si seguono l'uno all'altro con ritmo s&igrave; misurato, <lb/>che appariscono all'occhio essere un moto solo, d'ond'ebbero occasione gli <lb/>inganni di parecchi osservatori. </s>

<s>Ma che in ogni modo il moto delle orrec&shy;<lb/>chiette preceda quello dei ventricoli, il Borelli, nella proposizione LV della <lb/>II Parte <emph type="italics"/>De motu animalium,<emph.end type="italics"/> lo dimostra come una necessaria conseguenza <lb/>della particolare struttura della macchina del cuore, nella quale, quando il <lb/>moto del ventricolo precedesse o coincidesse con quello della orecchietta, le <lb/>valvole tricuspidali o sarebbero inutili o produrrebbero effetti contarii a quelli <lb/>intesi dalla Natura (pag. </s>

<s>113, 14). </s></p><p type="main">

<s>Di quegl&igrave; inganni, che si diceva conseguitar dalle difficolt&agrave; dell'osser&shy;<lb/>vazione, ne offerse un esempio notabilissimo il Lancisi, il quale formulava <lb/>cos&igrave; la XL sua proposizione <emph type="italics"/>De motu cordis.<emph.end type="italics"/> &ldquo; Ex vivorum sectionibus <lb/>ostenditur contractionem auricularum non esse vere alternam cum ventri&shy;<lb/>culis, sed nonnihil antevertere, citiusque desinere ac propterea magna ex <lb/>parte synchronam esse &rdquo; (Editio cit., pag. </s>

<s>88). Ammetteva il Lancisi certe <lb/>diciamo cos&igrave; consonanze nel ritmo cardiaco, che i Fisiologi dissero non esi&shy;<lb/>stere in natura, ond'&egrave; che l'Haller riserb&ograve; il &sect; XXII, Sezione IV del IV libro <lb/>del suo grande trattato di Fisiologia, per confutare l'opinion lancisiana (T. I, <lb/>Lausannae 1757, pag. </s>

<s>418-20). </s></p><p type="main">

<s>Cos&igrave;, per amor del vero e per l'autorit&agrave; dell'Haller, si torn&ograve; a profes&shy;<lb/>sare l'alterna contrazione de'ventricoli e delle orecchiette, specialmente in <lb/>Italia, dove il Bellini aveva dato un'ingegnosissima spiegazione di quel per&shy;<lb/>petuo alternarsi di moti. </s>

<s>Egli, come gi&agrave; sappiamo, riteneva che i nervi ec&shy;<lb/>citino il moto ne'muscoli e nello stesso cuore, stillandovi il loro succo, di <lb/>che sempre hanno pieni i canali, cosicch&egrave;, nella contrazione de'ventricoli, <lb/>le orecchiette si rilasciano perch&egrave;, restando compressi i nervi, non ricevono <lb/>da loro il succo necessario par mettersi in moto. </s>

<s>Quando poi i nervi son <lb/>compressi dal contrarsi delle orecchiette, i ventricoli si rilasciano, perch&egrave; non <lb/>stilla pi&ugrave; fra le loro fibre il succo eccitatore. </s>

<s>A questa ipotesi dava il Bel&shy;<lb/>lini stesso forma di proposizione, ch'&egrave; la prima del suo trattato <emph type="italics"/>De motu <lb/>cordis<emph.end type="italics"/> ed &egrave; cos&igrave; formulata: &ldquo; Si liquidum nervorum est illud, quod prae&shy;<lb/>cipue facit ad contractionem musculorum, datur de facto tempus quo eius&shy;<lb/>modi liquidum ita cessat ab influxu in musculis auricularum et ventriculo-<pb xlink:href="020/01/1221.jpg" pagenum="96"/>rum cordis, ut, quo tempore influit in musculum auricularum, iam influxus <lb/>erit in musculum ventriculorum; et, quo tempore influit in musculum <lb/>ventriculorum, iam influxerit in musculum auricularum &rdquo; (Venetiis 1732, <lb/>pag. </s>

<s>106). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>La macchina del cuore, che agisce con alterno moto a quel modo, e per <lb/>quelle ragioni immaginatesi dal Bellini, fu rassomigliata a uno de'com<gap/><lb/>strumenti idraulici, i quali da una parte aspirano il liquido, e dall'altra lo <lb/>premono e lo sollevano in alto. </s>

<s>Nello stringersi e nel dilatarsi de'ventricoli <lb/>vedevano l'immagine dello stantuffo, che scorre su e gi&ugrave; per il corpo di <lb/>tromba, e nelle vene e nelle arterie i canali da attingere e da sospingere il <lb/>sangue. </s>

<s>Questa analogia per&ograve;, nella quale bene applicata, contenevasi la sco&shy;<lb/>perta della circolazione, fu intraveduta assai tardi, ma in ogni modo che, <lb/>specialmente le arterie, fossero vasi comunicanti col cuore e dipendenti da <lb/>lui, fu con assai facilit&agrave; conosciuto anche dagli antichi. </s>

<s>Fu riconosciuto al&shy;<lb/>tres&igrave; per facile esperienza che dai moti di sistole e di diastole dipendono i <lb/>polsi, ma si errava comunemente nell'assegnare l'ordine di queste dipen&shy;<lb/>denze, credendosi che l'arteria pulsi, quando pulsa il ventricolo sinistro. </s>

<s>Non <lb/>vedendosi chiara ancora la somiglianza che passa fra gli strumenti idraulici <lb/>dell'arte e quello della Natura, non si comprendeva l'impossibilit&agrave; che fosse <lb/>nello stesso tempo pieno di liquido il corpo di tromba, e il canale irrigatore. </s></p><p type="main">

<s>La via perci&ograve; da conoscere il vero, che pareva chiusa d'ogni parte alle <lb/>filosofiche speculazioni, fu aperta alle osservazioni anatomiche, quando Realdo <lb/>Colombo raccomand&ograve;, come fecondissimo organo di scoperte, e insegn&ograve; le <lb/>regole della vivisezione. </s>

<s>Come caparra di tali promesse l'Autor <emph type="italics"/>De re ana&shy;<lb/>tomica<emph.end type="italics"/> citava quel ch'egli stesso, proseguendo il metodo propostosi, era riu&shy;<lb/>scito a scoprire, e fra le altre nuove e mirabili cose, che invita a vedere <lb/>nelle viscere palpitanti di un cane, questa &egrave; fra le principali, perch&egrave; scopre <lb/>agli occhi di qualunque persona volgare l'inganno che s'eran fatto i Filo&shy;<lb/>sofi speculando con la mente sublime: <emph type="italics"/>comperies enim, dum cor dilatatur, <lb/>constringi arterias, et rursus in cordis constrictione dilatari.<emph.end type="italics"/></s></p><p type="main">

<s>Tanto poi sentiva il Colombo essere l'importanza di questa verit&agrave; sco&shy;<lb/>perta contro l'errore cos&igrave; universalmente invalso, che non contento di quella <lb/>prima preparazione anatomica vuol, per meglio persuadere i Filosofi in libris, <lb/>e chi giura sulla veneranda autorit&agrave; de'loro fogli, immolare un'altro cane, <lb/>e apertogli egli prima il torace, invita i desiderosi d'imparare il vero dalla <lb/>Natura, a proseguire la vivisezione. </s>

<s>&ldquo; Thorace igitur huius secundi canis <lb/>primum aperto per rectam lineam in cartilaginem: sed illum confestim aperi <lb/>atque una pericardion. </s>

<s>Deinde, abdomine quoque aperto, magnae arteriae <lb/>manum admoveto: diligenterque, quoad eius fieri poterit, considera an illa <pb xlink:href="020/01/1222.jpg" pagenum="97"/>dilatetur dum constringitur cor, vel opposito modo se res habeat, ibique <lb/>differentias omnes pulsium sub oculos intueberis in rem praesentem de&shy;<lb/>ductos, magnos, longos, latos, veloces, latos celeres, frequentes, parvos. </s>

<s>Ne&shy;<lb/>que hos modo, sed veloces quidem tardosve, aut frequentes sed interpola&shy;<lb/>tos, item frequentissimos, minimos, tardissimos, undosos et formiculares &rdquo; <lb/>(De re anat. </s>

<s>cit., pag. </s>

<s>261). </s></p><p type="main">

<s>Non insegna dunque l'Harvey, nel suo cap. </s>

<s>III <emph type="italics"/>De motu cordis,<emph.end type="italics"/> nulla <lb/>di nuovo, e nel dimostrare il vero <emph type="italics"/>contra communia dogmata<emph.end type="italics"/> non fu giu&shy;<lb/>sto il tacere che quella stessa dimostrazione l'aveva data, ottant'anni prima, <lb/>Realdo Colombo. </s>

<s>Cos&igrave; sembra che null'altro merito competasi, rispetto a ci&ograve;, <lb/>al Fisiologo inglese, da quello in fuori di aver con nuove esperienze con&shy;<lb/>fermati i fatti osservati dal Nostro. </s>

<s>L'esperienza arveiana, in proposito di <lb/>dimostrar che, quando il cuore &egrave; in sistole, le arterie invece vanno in dia&shy;<lb/>stole; son semplicissime, e nello stesso tempo concludentissime, come vedesi <lb/>per l'esempio della prima, che consiste nell'incidere un'arteria, e nell'os&shy;<lb/>servar che, quando il ventricolo sinistro si ristringe, ella gitta allora il san&shy;<lb/>gue con maggior forza. </s>

<s>Altre esperienze a conferma di ci&ograve; furono dall'Har&shy;<lb/>vey fatte sul cuore dei pesci, e in ultimo richiama l'attenzione sui varii <lb/>casi, che, nel far risalire il sangue ora pi&ugrave; ora meno lontano, presenta l'ar&shy;<lb/>teriotomia. </s>

<s>&ldquo; Ex his videtur manifestum, poi ne conclude, contra communia <lb/>dogmata, quod arteriarum diastole fit eo tempore, quo cordis systole, et ar&shy;<lb/>terias repleri et distendi propter sanguinis a constrictione ventriculorum cor&shy;<lb/>dis immissionem et intrusionem; quin etiam distendi arterias, quia replentur <lb/>ut utres aut vesica, non repleri, quia distenduntur ut folles &rdquo; (De motu cor&shy;<lb/>dis cit., pag. </s>

<s>29). </s></p><p type="main">

<s>Con queste ultime parole s'accenna a una questione importantissima, <lb/>della quale aveva avanti l'Harvey trattato nel Proemio al suo libro. </s>

<s>Era una <lb/>tal questione con Galeno, il quale scrisse appositamente un libro, per rispon&shy;<lb/>dere a Erasistrato, e a chi con lui dubitava <emph type="italics"/>An sanguis in arteriis natura <lb/>contineatur.<emph.end type="italics"/> E dopo avere in sette capitoli dimostrato che veramente le ar&shy;<lb/>terie son tutte piene di sangue, nel cap. </s>

<s>VIII intitola la seguente proposi&shy;<lb/>zione: &ldquo; Motrix facultas a corde in tunicas arteriarum venit qua se pandunt <lb/>omnes simul et spiritum attrahunt &rdquo; (Opera I Classis, Venetiis 1597, fol. </s>

<s>62 <lb/>ad terg.). Incomincia Galeno a dire com'essendosi, nelle proposizioni prece&shy;<lb/>denti, dimostrato che nelle arterie contienesi il sangue, potrebbe sembrare <lb/>alquanto difficile a intendere come mai gli spiriti sieno dispensati per tutto <lb/>il corpo dal cuore. </s>

<s>&ldquo; Quocirca, cum ambigunt quo modo spiritus in totum <lb/>corpus a corde feratur, si plenae sanguinis arteriae sint, difficile non est <lb/>eiusmodi dubitationem solvere, et dicere, non ferri, sed trahi spiritum in <lb/>arteriis nec a corde solo sed undequaque..... Vim tamen, quae arterias <lb/>extendit a corde, ceu fonte quodam manare, a nobis est in aliis libris expli&shy;<lb/>catum &rdquo; (ibi). </s></p><p type="main">

<s>Qui, prosegue a dire Galeno per dimostrar che le arterie son veramente <lb/>mosse dalla forza del cuore, che le distende come un mantice, e apre cos&igrave; <pb xlink:href="020/01/1223.jpg" pagenum="98"/>libera la via al sangue; addurr&ograve; una esperienza, ed &egrave; tale: &ldquo; Arteriam unam, <lb/>e magnis et conspicuis quempiam, si voles, nudabis, primoque pelle remota <lb/>ipsam ab adiacenti suppositoque corpore tamdiu separare non graveris, quoad <lb/>filum circum immittere valeas. </s>

<s>Deinde, secundum longitudinem, arteriam in&shy;<lb/>cide, calamumque, et concavum et pervium, in foramen intrude, vel aeneam <lb/>aliquam fistulam, qua et vulnus obturetur, et sanguis exilire non possit. </s>

<s><lb/>Quoadusque sic se arteriam habere conspicies, ipsam totam pulsare videbis: <lb/>cum primum vero obductum filum in laqueum contrahens arteriae tunicas <lb/>calamo obstrinxeris, non amplius arteriam ultra laqueum pulsare videbis, <lb/>etiamsi spiritus et sanguis ad arteriam quae est ultra filum, sicuti prius <lb/>faciebat, per concavitatem calami feratur. </s>

<s>Quod si propterea pulsabant arte&shy;<lb/>riae, pulsarent et nunc partes quae sunt ultra laqueum, sed non pulsant, <lb/>igitur perspicuum est quoniam moveri posse desinunt, non per spiritum, in <lb/>concavitatibus discurrentem, sed ob virtutem in tunicam transmissam arte&shy;<lb/>rias a corde moveri &rdquo; (ibi). </s></p><p type="main">

<s>Altre esperienze avevano, come vedemmo, dimostrato all'Harvey essere <lb/>il sangue, che sospinto con impeto nella sistole del cuore, distende e fa pul&shy;<lb/>sare le arterie, le quali perci&ograve; s'empiono come un otre: e non &egrave; il sangue <lb/>che v'entra per l'aperta via, trovandole distese dal cuore stesso con la sua <lb/>forza, come un mantice. </s>

<s>Conveniva in ogni modo per&ograve; conciliar queste con <lb/>la esperienza galenica, a far che l'Harvey medesimo si trov&ograve; in grande im&shy;<lb/>paccio, per uscir dal quale disse che quella esperienza ei non l'aveva fatta, <lb/>reputandola impossibile a farsi nell'animale vivo, per la impetuosa incur&shy;<lb/>sione del sangue, e per esser difficile, senza le legature, a turar la ferita; <lb/>dall'altra parte, soggiungeva, &egrave; tanto concludente dimostrazione quella tolta <lb/>dall'arteriotomia, che lo stesso sperimento di Galeno, quando fosse pratica&shy;<lb/>bile, non potrebbe far altro che confermarla. </s>

<s>&ldquo; Nec ego feci experimentum <lb/>Galeni, nec recte posse fieri, vivo corpore, ob impetuosi sanguinis ex arte&shy;<lb/>riis eruptionem, puto, nec obturabit sine ligatura vulnus fistula: et per fistu&shy;<lb/>lae cavitatem ulterius prosilire sanguinem non dubito. </s>

<s>Tamen hoc experi&shy;<lb/>mento et probare videtur Galenus facultatem pulsificam per tunicas arteriarum <lb/>a corde manare, et quod arteriae, dum distenduntur ab &igrave;lla facultate pul&shy;<lb/>sifica, repleantur, quia distenduntur ut folles, non distendantur, quia replen&shy;<lb/>tur ut utres. </s>

<s>Sed et in arteriotomia et vulneribus contrarium manifestum <lb/>est &rdquo; (De motu cordis cit., Proemium, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Nella seconda Esercitazione anatomica per&ograve;, <emph type="italics"/>ad Riolanum,<emph.end type="italics"/> torna l'Har&shy;<lb/>vey a trattare di questo soggetto, e dice che, a fine d'investigare il vero, <lb/>consigli&ograve; Galeno agli studiosi quel suo sperimento, e lo prescrisse poi pure <lb/>a loro anche il Vesalio &ldquo; sed neque Vesalius neque Galenus dicit experi&shy;<lb/>mentum hoc fuisse ab illis, sicut a me, probatum &rdquo; (ibi, pag. </s>

<s>129). La prova <lb/>per&ograve;, impossibile all'arte, venne preparata all'Harvey dalla Natura, nella <lb/>ossificazione delll'arteria crurale di un suo malato, nella quale la fistola ossea <lb/>della ciste faceva le veci del calamo, nello sperimento galenico. </s>

<s>In questo <lb/>caso dunque, a conferma del vero e a confutazione dell'error di Galeno, <pb xlink:href="020/01/1224.jpg" pagenum="99"/>dice esso Harvey: &ldquo; Inferiores arterias, trans hoc tale aneurisma, pulsare <lb/>valde exiliter senties, quando superius, et praesertim in aneurismate ipso, <lb/>pulsus magni et vehementer apparent &rdquo; (ibi, pag. </s>

<s>130). </s></p><p type="main">

<s>Quando poi i Fisiologi e i Chirurgi acquistarono maggior pratica nel&shy;<lb/>l'operare, e si trovarono forniti di pi&ugrave; squisiti strumenti, si persuasero che <lb/>non dovess'essere lo sperimento galenico d'impossibile riuscita, e il Flou&shy;<lb/>rens, nelle sue Ricerche sperimentali sulle propriet&agrave; e le funzioni del si&shy;<lb/>stema nervoso, si compiacque di averlo messo in pratica nell'arteria magna <lb/>di un montone (Paris 1842, pag. </s>

<s>368). </s></p><p type="main">

<s>Il Fisiologo francese per&ograve; era stato preceduto, di ben cento ottant'anni, <lb/>da un nostro Italiano, il quale fu, contro l'opinion dell'Harvey, persuaso <lb/>che lo sperimento della fistola inserita nell'arteria incisa fosse possibile, e <lb/>che Galeno non lo avesse solamente proposto agli studiosi, ma che lo avesse <lb/>altres&igrave; praticato, bench&egrave;, per le gravi difficolt&agrave;, prendesse abbaglio nell'os&shy;<lb/>servare. </s>

<s>Cos&igrave; infatti scriveva, nel 1661, Tommaso Cornelio, in quel suo <lb/>VII Proginnasma, che s'intitola <emph type="italics"/>De vita:<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Harveius autem, quum multis et gravibus argumentis docuisset ar&shy;<lb/>terias ab impulsu sanguinis distendi, ausus est Galeni experimentum in du&shy;<lb/>bium vocare. </s>

<s>Scripsit enim nec a se eius rei periculum factum esse, nec <lb/>recte in vivis animantibus fieri posse, ob vim sanguinis ex maioribus arte&shy;<lb/>riis magno impetu erumpentis, sibi verisimile videri ut vulnus calamo obduci <lb/>sine ligamine possit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Atqui ego non omnem Galeno fidem in hacre derogandam velim, <lb/>quippe mihi haec aliquando licuit experiri. </s>

<s>Ligata utrinque hinc et illinc <lb/>arteria, spatioque inter vincula diffiso, fistulam per vulnus in arteriam inse&shy;<lb/>rui, ac discissam arteriae partem praetenui filo fistulae alligavi. </s>

<s>Tum, disru&shy;<lb/>ptis confestim prioribus vinculis, sanguis per fistulam permanabat in ulte&shy;<lb/>riorem arteriae partem. </s>

<s>At interea videre erat arteriam ultra vinculum, sed <lb/>paulo obscurius, pulsantem. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quod autem eiusmodi motum Galenus non animadverterit, causam <lb/>fuisse suspicor calami crassitudinem qui, quoniam exiguo pertusus erat fo&shy;<lb/>ramine, traiectioni sanguinis officere potuit. </s>

<s>Ad haec accedit quod sanguis <lb/>intra fistulam facile coit atque densatur, quapropter tale experimentum no&shy;<lb/>vum industriumque postulat observatorem &rdquo; (Neapoli 1688, pag. </s>

<s>274-76). </s></p><p type="main">

<s>Conclude il Cornelio a favor dell'Harvey la descrizione di questo suo <lb/>esperimento, dicendo: &ldquo; Arterias igitur ab impulsu sanguinis moveri, atque <lb/>micare, palam fit ab ipso Galeni experimento &rdquo; (ibi, pag. </s>

<s>276). Veniva cos&igrave; <lb/>d'ogni parte confermato quel che l'Harvey stesso intendeva di dimostrare, <lb/>che cio&egrave; le arterie vanno in diastole e danno il polso, per solo impulso del <lb/>sangue e non per una qualche innata virt&ugrave; pulsifica o partecipata a loro <lb/>dal cuore. </s>

<s>La pulsante onda del sangue poi nelle arterie l'assomigliava al&shy;<lb/>l'acqua sollevata, a ogni colpo di sifone, nelle fistole plumbee. </s>

<s>&ldquo; Quemad&shy;<lb/>modum cum aqua, vi et impulsu syphonis, per fistulas plumbeas in altum <lb/>cogitur, singulas compressiones instrumenti, per multa licet stadia distent, <pb xlink:href="020/01/1225.jpg" pagenum="100"/>in ipso aquae exeuntis fluxu, singulorum ictuum ordinem, principium, in&shy;<lb/>crementum, finem, vehementiam, observare et distinguere possumus; ita ex <lb/>abscissae arteriae orificio &rdquo; (Exercitatio anat. </s>

<s>II app. </s>

<s>De motu cordis cit., <lb/>pag. </s>

<s>158, 59). </s></p><p type="main">

<s>S'attribuiva allora ai sifoni una duplice azione, quella di premere e l'al&shy;<lb/>tra di attrarre, e una tale duplice azione &egrave; dall'Harvey attribuita pure anche <lb/>al cuore. </s>

<s>Nell'ultimo capitolo del suo trattato, dove anatomicamente descrive <lb/>gli organi del moto del cuore, e il modo com'essi esercitano le loro forze <lb/>sul sangue; conclude dall'Embriologia comparata un'avvertenza importante, <lb/>ed &egrave; che l'orecchietta destra &egrave; la prima a pulsare, <emph type="italics"/>primum vivens, ulti&shy;<lb/>mum moriens,<emph.end type="italics"/> e vien perci&ograve; da lei il primo impulso al moto del sangue <lb/>stesso, il quale &egrave; trasfuso nel ventricolo sottoposto. </s>

<s>&ldquo; Qui ventriculus, poi <lb/>soggiunge, continuo seipsum contrahendo, iam ante in motu existentem san&shy;<lb/>guinem commodius elidat, et violentius propellat, ut cum ludas pila a re&shy;<lb/>verberatione, fortius et longius percutiendo quam simpliciter proiiciendo, <lb/>impellere poteris. </s>

<s>Quin etiam contra vulgarem opinionem, quia neque cor <lb/>neque aliud quidpiam seipsum distendere sic potest, ut in seipsum attrahere <lb/>sua diastole quicquam possit, nisi ut spongia, vi prius compressa, dum redit <lb/>ad constitutionem suam &rdquo; (pag. </s>

<s>97). </s></p><p type="main">

<s>Dopo la grande esperienza dimostrativa del peso dell'aria, come il Ba&shy;<lb/>liani e il Torricelli avevano rimossa la forza attrattiva del vacuo dalla Fi&shy;<lb/>sica, cos&igrave; fu il Pecquet de'primi a rimoverla dalla Fisiologia. </s>

<s>Nel cap. </s>

<s>VII <lb/>della sua Dissertazione anatomica <emph type="italics"/>De circulatione sanguinis,<emph.end type="italics"/> s'introduce ad <lb/>esaminar le due forze, alle quali principalmente s'attribuiva prima di lui il <lb/>moto del sangue; l'intrinseco impulso cio&egrave; della sistole, e l'attrazione della <lb/>diastole. </s>

<s>E riferiti que'celebri esperimenti del vuoto, ne conclude con dire <lb/>che l'azione attribuita ai corpi di attrarre niente altro era in verit&agrave; che una <lb/>pressione sopravveniente in essi dal peso dell'aria. </s>

<s>E perch'egli credeva non <lb/>potersi ridurre la forza d'impulsione, se non che nella naturale gravit&agrave; del <lb/>sangue, e perch&egrave;, scoperta essere una fallacia l'attrazione, vedeva andare <lb/>svanita quella forza, a cui commettevasi la diastole; &ldquo; superest, dice il <lb/>Pecquet, ut vasorum constrictionem et eorumdam a vicinarum partium agi&shy;<lb/>tatione, vel etiam pondere, compressionem expendamus &rdquo; (Parisiis 1654, <lb/>pag, 73). E dop'aver ponderato il momento di queste forze di contrazione <lb/>e di compressione de'vasi, cos&igrave; conclude: &ldquo; Ergo triplici pronuntio sangui&shy;<lb/>nem incitabulo circumrolvi: systoles videlicet impulsione, vasorum seu spon&shy;<lb/>tanea seu violenta contractione, atque, ab adiacentium connixu partium, va&shy;<lb/>sorum eorumdem compressione: tribus invicem ita dispositis, ut aliqua semper <lb/>aliarum defectus, etsi lentiuscule, quidem officii perseverantia compenset &rdquo; <lb/>(ibi, pag. </s>

<s>75, 76). </s></p><p type="main">

<s>La compressione per&ograve;, se da una parte pu&ograve; promuovere il corso del <lb/>sangue, gli serve dall'altra d'impedimento, e anzi il Borelli not&ograve; che que&shy;<lb/>sto impedimento era insigne. </s>

<s>&ldquo; Et noto quod resistentia contra impulsum <lb/>sanguinis, quae exercetur, ut viae aperiantur inter carnes et intra viscera, <pb xlink:href="020/01/1226.jpg" pagenum="101"/>est insignis, quia sanguis terebrare debet porositates partium corporis ani&shy;<lb/>malis solidarum, grandi impetu &rdquo; (De motu anim. </s>

<s>cit., P. II, pag. </s>

<s>149). Fu <lb/>perci&ograve; che il Borelli stesso, de'tre incitamenti che a promuovere il corso <lb/>del sangue annoverava il Pecquet, non ne ritenne altro che due: la forza <lb/>del cuore e la contrazion delle arterie, rassomigliate al moto peristaltico <lb/>degl'intestini (ivi, pag. </s>

<s>147). Ma alle fibre muscolari del cuore attribuiva il <lb/>massimo effetto, e fu egli il primo che si prov&ograve; di ridurlo a misura. </s></p><p type="main">

<s>Ammesso che la potenza di un muscolo sia proporzionale al peso, per&shy;<lb/>ciocch&egrave; la mole carnosa del cuore uguaglia quella di uno de'muscoli tem&shy;<lb/>porali e di un messetere, la potenza di questi due sar&agrave; dunque uguale alla <lb/>potenza dello stesso cuore. </s>

<s>E perch&egrave; si trova per l'esperienze che le fibre <lb/>tutte insieme riunite dei due muscoli sopraddetti possono sostenere un peso <lb/>maggiore delle tremila libbre &ldquo; igitur elicere possumus quod vis quam exer&shy;<lb/>cent omnes minimae fibrae cordis, simul sumptae, si impellerent radium <lb/>externum librae, bifariam in centro sectae, superare potest pondus 3000 li&shy;<lb/>brarum &rdquo; (ivi, pag. </s>

<s>134). </s></p><p type="main">

<s>Messa questa potenza muscolare in azione nella macchina idraulica del <lb/>cuore, dimostra il Borelii che la forza motiva di lui, a tutta la forza con la <lb/>quale il sangue nelle arterie resiste all'espulsione, sta come uno a sessanta. </s>

<s><lb/>Di qui, e dai dati precedenti, si deduce con facilit&agrave; la cercata misura. </s>

<s>&ldquo; Quia <lb/>vis absoluta, quam exercet musculus cordis inflando vexiculas omnes po&shy;<lb/>rosas eius, tam grandis est, ut immediate et absque machina superare pos&shy;<lb/>set pondus maius quam 3000 librarum: at eadem vis motiva ad eiusdem <lb/>momentum, seu ad vim, qua sanguinis motus in arteriis impeditur, eamdem <lb/>proportionem habet quam 1 ad 60; ergo vis absoluta, a qua sanguinis mo&shy;<lb/>tus in arteriis impeditur, et quam cordis potentia superat, maior est vi pon&shy;<lb/>deris 180,000 librarum &rdquo; (ibi, pag. </s>

<s>143). </s></p><p type="main">

<s>Questa non &egrave; altro per&ograve; che la forza, la quale dee superarsi dal cuore, <lb/>per empir le arterie fino alla turgenza. </s>

<s>Ma perch&egrave; possa fuori di loro uscire <lb/>il sangue, il quale ha da aprirsi la via tra la porosit&agrave; de'muscoli e il pa&shy;<lb/>renchima de'visceri, vi bisogna una nuova forza, che il Borelli giudica non <lb/>potere esser minore delle 135 mila libbre. </s>

<s>Di qui &egrave; che, per empir le ar&shy;<lb/>terie e per sopraggiunger nuov'impulso al sangue che n'esca, conviene al <lb/>cuore, secondo questi calcoli, superar tutto insieme una resistenza, ch'equi&shy;<lb/>vale al peso di 315 mila libbre. </s>

<s>&ldquo; Stupenda profecto, esclama qui il Borelli, <lb/>est tam vasta vis et incredibilis omnino esset, nisi adesset energia percus&shy;<lb/>sionis, quae ex sui natura superare potest quamcumque finitam resistentiam <lb/>quiescentem &rdquo; (ibi, pag. </s>

<s>150). </s></p><p type="main">

<s>La infinita forza della percossa, invocata qui dal Borelli in questi cal&shy;<lb/>coli di meccanica animale, ci fa sovvenir dell'esempio della palla, che per&shy;<lb/>cossa, dop'essersi riflessa, si manda pi&ugrave; di lungi che a semplicemente get&shy;<lb/>tarla: esempio recato al medesimo proposito dall'Harvey, ma in ogni modo <lb/>i resultamenti di que'calcoli borelliani parvero esagerati. </s></p><p type="main">

<s>L'esagerazione dall'altra parte rendevasi manifesta a comparar la po-<pb xlink:href="020/01/1227.jpg" pagenum="102"/>tenza meccanica messa in esercizio, con l'effetto utile da lei prodotto, il <lb/>quale effetto si pu&ograve; per l'arteriotomia riconoscer tutto negli zampilli verti&shy;<lb/>cali, e ne'getti parabolici del sangue. </s>

<s>Quegli zampilli e que'getti si vedono <lb/>similmente prodursi ne'vasi pieni d'acqua, forati nel fondo, con impeti <lb/>uguati e forse maggiori di quel che non avvenga nel sangue: eppure, la <lb/>potenza che gli produce, tutt'altro ch'essere infinita, riducesi alla semplice <lb/>pressione, che fa il liquido soprincombente al centro del foro. </s></p><p type="main">

<s>Questi pensieri passavano per la mente a Jacopo Keill, a cui parve anzi <lb/>che la questione, promossa dal Borelli intorno alla misura delle forze del <lb/>cuore, si potesse facilmente risolvere coi principii noti dell'Idrometria. </s>

<s>&Egrave; <lb/>anche il cuore, secondo lui, un vaso che contiene un liquido, e bench&egrave; ne <lb/>esca fuori con forza violenta, pur si pu&ograve; ridurre a una forza naturale. </s>

<s>&Egrave; anzi <lb/>questo l'intendimento, che principalmente si propone il Keill nel III de'suoi <lb/><emph type="italics"/>Tentamina medico-hpysica,<emph.end type="italics"/> dove, comparata la velocit&agrave; del sangue nell'aorta <lb/>alla velocit&agrave; del flusso in un vaso pieno d'acqua, applica la misura della <lb/>forza, che produce un tal flusso, alla misura della forza del cuore stesso. <lb/><figure id="id.020.01.1227.1.jpg" xlink:href="020/01/1227/1.jpg"/></s></p><p type="caption">

<s>Figura 3.</s></p><p type="main">

<s>Un gran maestro di scienza idrometrica al mon&shy;<lb/>do era, specialmente in Inghilterra, patria del Keill, <lb/>riconosciuto il Newton, il quale, dop'aver definito, <lb/>nella proposizione XXXVI del II libro dei Principii <lb/>matematici di Filosofia naturale, il moto dell'acqua <lb/>fluente dal foro EF (fig. </s>

<s>3) aperto in fondo a un <lb/>vaso cilindrico, in cui sia GI la distanza che passa <lb/>dal centro del foro stesso alla superficie AB di li&shy;<lb/>vello; soggiunge il seguente corollario II: &ldquo; Et vis, <lb/>qua totus aquae exilientis motus generari potest, <lb/>aequalis est ponderi cylindricae columnae aquae, cu&shy;<lb/>ius basis est foramen EF, et attitudo 2 GI &rdquo; (Ge&shy;<lb/>nevae 1711, pag. </s>

<s>291). </s></p><p type="main">

<s>Applicando perci&ograve; il Keill questo Teorema, e rappresentandosi nel vaso <lb/>AF il ventricolo sinistro del cuore, nel foro EF l'apertura dell'aorta, e in <lb/>GI l'altezza, a cui dovrebbe livellarsi il sangue, per produr naturalmente <lb/>nell'aorta stessa quella velocit&agrave; violentemente prodotta dalla sistole, e che <lb/>con i dati sperimentali si suppone essere stata gi&agrave; misurata; la forza pro&shy;<lb/>duttrice di una tal velocit&agrave;, ch'&egrave; la forza impulsiva del cuore, conclude es&shy;<lb/>sere uguale alla pressione di una colonna di sangue, alta quant'&egrave; il doppio <lb/>di GI, e larga quant'&egrave; EF nella sua base. </s>

<s>Il peso premente di una tal co&shy;<lb/>lonna sanguigna, ch'&egrave;, come si disse, la misura della pressione del cuore, <lb/>trov&ograve; il Keill stesso non esser pi&ugrave; che cinq'once. </s>

<s>&ldquo; Haec altitudo, bis sum&shy;<lb/>pta, dat 1,48, sive digitos 17,76, et haec est altitudo cylindri sanguinis pleni, <lb/>cuius basis aequalis est Aortae orificio, quod 0,4187 aequale esse posuimus. </s>

<s><lb/>Solidum itaque contentum est 7,436112, cuius pondus vi cordis absolutae <lb/>est aequale. </s>

<s>Hoc pondus est pondus quinque unciarum. </s>

<s>Cordis itaque vis <lb/>quinque unciarum ponderi est aequalis &rdquo; (Lucae 1756, pag. </s>

<s>57). </s></p><pb xlink:href="020/01/1228.jpg" pagenum="103"/><p type="main">

<s>La nuova via idrometrica aperta, e che prometteva del problema delle <lb/>forze del cuore dare una pi&ugrave; facile e pi&ugrave; certa soluzione di quella, che per <lb/>via meccanica avea data il Borelli; fu proseguita da quel solertissimo spe&shy;<lb/>rimentatore, che fu Stefano Hales, il quale, fatto accorto dal Michelotti che <lb/>si potevano scansare alcune delle pi&ugrave; gravi opposizioni, che incontr&ograve; il cal&shy;<lb/>colo del Keill, vide che si poteva dallo zampillo verticale dedur la quantit&agrave; <lb/>del sangue premente sulle pareti del ventricolo sinistro del cuore, applican&shy;<lb/>dovi direttamente il teorema idrostatico del Torricelli. </s>

<s>Incisa l'arteria cru&shy;<lb/>rale a un cane, trov&ograve; che lo zampillo verticale risaliva a sei piedi e otto <lb/>pollici, e che risaliva pure a una tale altezza il sangue dall'incisa arteria <lb/>carotide sinistra. </s>

<s>Fattavi dentro l'iniezione di cera, trov&ograve; che la superficie <lb/>interna del ventricolo sinistro era di undici pollici quadrati, ond'&egrave; che mol&shy;<lb/>tiplicando questo numero per la trovata altezza verticale dello zampillo, con&shy;<lb/>cludeva che il prodotto dei 180 pollici che ne resulta esprimeva i pollici <lb/>cubi del sangue &ldquo; i quali premono sopratutto le interne pareti di quello <lb/>stesso ventricolo, quand'&egrave; contratto giusto quanto debb'esserlo, per soste&shy;<lb/>nere ed eguagliare la forza del sangue nell'aorta &rdquo; (Statica degli anim., <lb/>trad. </s>

<s>ital., T. I, Napoli 1750, pag. </s>

<s>39). </s></p><p type="main">

<s>Passando poi ad applicare lo stesso metodo sperimentale a misurar la <lb/>forza della resistenza, che supera ne'suoi moti di sistole il cuore dell'uomo, <lb/>&ldquo; supponiamo, dice l'Hales, com'&egrave; verisimile, che il sangue di una carotide <lb/>umana, in un cannello ad essa verticalmente applicato, s'inalzerebbe all'al&shy;<lb/>tezza di piedi 7,5 e che la superficie interna del ventricolo sinistro del cuore <lb/>sia di 15 pollici quadrati. </s>

<s>Moltiplicando questi per quell'altezza, avremo il pro&shy;<lb/>dotto di 1350 pollici cubi di sangue, che premono questo ventricolo, quando <lb/>comincia a stringersi, ed uguagliano il peso di libbre 51,5 &rdquo; (ivi, pag. </s>

<s>42). </s></p><p type="main">

<s>La differenza che passa fra questi calcoli dell'Hales e quelli del Keill, <lb/>e le disorbitanze che si notano, fra'numeri dati da questi due sperimenta&shy;<lb/>tori e quelli prima conclusi dal Borelli, posero alcuni in gran diffidenza degli <lb/>usi e delle applicazioni, che s'intendeva far delle leggi della Meccanica e <lb/>della Idrostatica allo studio della Fisiologia. </s>

<s>Altri, pi&ugrave; zelanti del metodo <lb/>iatromatematico e pi&ugrave; savi, facevano notare che i vizii non erano da attri&shy;<lb/>buirsi a esso metodo, ma a chi partiva da principii non certi, e da suppo&shy;<lb/>sti reputati falsi, e trascurava la massima parte di quei coefficienti neces&shy;<lb/>sarii per ridurre i calcoli, e per averli pi&ugrave; giusti. </s></p><p type="main">

<s>L'Haller, per esempio, osserva che si pu&ograve; molto dubitare dell'ipotesi <lb/>assunta dal Borelli, che cio&egrave; le potenze de'muscoli sieno proporzionali ai <lb/>pesi, potendovi essere in diversi muscoli fibre di diverse virt&ugrave;, come si pu&ograve; <lb/>congetturar facilmente dal veder che alcune son pi&ugrave; irritabili alla luce che <lb/>all'aria, altre pi&ugrave; all'aria che all'acqua. (Elem. </s>

<s>Fhysiologiae cit., T. I, <lb/>pag. </s>

<s>448). Francesco de Sauvages pose in dubbio l'assunto dall'Hales, che <lb/>cio&egrave; il tempo della sistole sia un terzo di quello della diastole, parendo pi&ugrave; <lb/>ragionevole che dovesser essere que'due tempi uguali, ma contro i calcoli <lb/>del Keill uno de'pi&ugrave; fervorosi a insorgere fu il Michelotti. </s></p><pb xlink:href="020/01/1229.jpg" pagenum="104"/><p type="main">

<s>Nota in que'calcoli dell'Inglese il Nostro che non si fa differenza fra la <lb/>tenacit&agrave; dell'acqua e quella del sangue, n&egrave; si tien conto degli attriti, che su&shy;<lb/>bisce il sangue stesso, in rasentar le pareti, e in passar per le volte e le <lb/>rivolte dei vasi. </s>

<s>Gli errori per&ograve;, che seguitano nel calcolo dal trascurar que&shy;<lb/>ste cose, sono un nulla, soggiunge il Michelotti, rispetto a quelli che deri&shy;<lb/>vano dall'ammetter per vera quella proposizion neutoniana della legge dei <lb/>flussi, sopra la quale il calcolo stesso ha il suo principal fondamento. </s>

<s>&ldquo; Hanc <lb/>vero propositionem absolute falsam esse eo liquet quod velocitas aquae, ex <lb/>foramine vasis effluentis, ea omnino sit quam grave libere cadendo ex alti&shy;<lb/>tudine aquae supra foramen acquireret. </s>

<s>Nam, quum infra videbimus, eius&shy;<lb/>modi velocitatem aquae ex vase effluentis acceptam referre totam debeamus <lb/>pressioni aquae foramini incumbentis, nimirum ponderi columnae aquae, <lb/>cuius basis est foramen et altitudo aequalis altitudini supremae superficiei <lb/>aquae supra foramen; evidens est vim illam, per quam fluidum ex orificio <lb/>alicuius canalis effluens certam velocitatem acquirit, eam nempe quam grave <lb/>acquireret ex altitudine AB delapsum, esse aequalem ponderi cylindri eius&shy;<lb/>dem fluidi, cuius basis aequalis est orificio, per quod fluidum egreditur, al&shy;<lb/>titudo vero aequalis ipsi simplae AB, non autem huius duplae, quemadmo&shy;<lb/>dum existimat clariss. </s>

<s>Keillius, fidenter eminentem geometram Js. </s>

<s>Neuto&shy;<lb/>num in hac re secutus &rdquo; (De separat. </s>

<s>fluid. </s>

<s>Venetiis 1721, pag. </s>

<s>112). </s></p><p type="main">

<s>Il dir le ragioni, per le quali il Michelotti credeva che la proposizione, <lb/>in cui dal Newton si dimostrava il moto de'flussi liquidi da un foro aperto <lb/>in un vaso, era falsa, vien riserbato ad altra parte di questa storia, e perci&ograve; <lb/>confessandosi, per la variet&agrave; de'resultati numerici, le difficolt&agrave; incontrate, <lb/>qualunque metodo si tenesse in definir la pi&ugrave; giusta misura della forza del <lb/>cuore; tutti i Fisiologi erano concordi in ammetter che, o piccola o grande <lb/>si tenesse quella forza, non era in ogni modo per s&egrave; sola sufficiente a so&shy;<lb/>spingere il sangue infino alle ultime e pi&ugrave; lontane diramazioni delle arterie, <lb/>non composte di pareti rigide, ma cedevoli e molli. </s></p><p type="main">

<s>Questo elaterio delle tuniche arteriose era stato posto in evidenza da <lb/>quelle belle esperienze, con le quali l'Harvey dimostrava contro Galeno che <lb/>l'arterie stesse pulsano perch&egrave; violentemente dilatate dall'onda del sangue, <lb/>passata la quale, ritornano al loro primo stato. </s>

<s>L'efficacia poi di quell'ela&shy;<lb/>terio in promuovere il circolo sanguigno fu sperimentalmente dimostrata dal <lb/>Pecquet, legando un'arteria e osservando che al di l&agrave; del vincolo rimaneva <lb/>esausta, senza dubbio, perch&egrave; la molla delle sue fibre spremeva il liquido <lb/>contenuto (Dissertatio anat. </s>

<s>De circul. </s>

<s>sang. </s>

<s>cap. </s>

<s>VII, edit. </s>

<s>cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Ma il moto del sangue per l'arterie, e i particolari accidenti di lui, e <lb/>l'inturgidirsi e il restituirsi delle tuniche arteriose, che sono in parte causa <lb/>e in parte effetto di quello stesso moto, furono pi&ugrave; che da altri mai diligen&shy;<lb/>temente studiati da Domenico Guglielmini, nella mente del quale preluce&shy;<lb/>vano le dimostrate ragioni del moto delle acque correnti dentro i canali. </s></p><p type="main">

<s>Consideriamo, incomincia egli cos&igrave; il suo ragionamento, il sangue nel&shy;<lb/>l'atto che, per la contrazione del sinistro ventricolo, &egrave; spremuto dentro <pb xlink:href="020/01/1230.jpg" pagenum="105"/>l'Aorta dal cuore. </s>

<s>Egli avr&agrave; una determinata velocit&agrave; iniziale, che dipende <lb/>in parte dal tempo pi&ugrave; o meno breve intercedente fra una diastole e il fine <lb/>di una sistole, e in parte dalla capacit&agrave; dell'Aorta. </s>

<s>Imperocch&egrave;, rimanendo <lb/>in questa sempre la sezione costante, se pi&ugrave; veloci saranno i moti del cuore <lb/>pi&ugrave; veloci saranno altres&igrave; i moti del sangue. </s>

<s>Ma se rimanendo invariabile il <lb/>tempo, in cui il cuore passa da una diastole all'altra, l'Aorta varia la sua <lb/>sezione, e divien per esempio minore, anche per ci&ograve; il sangue si mover&agrave; <lb/>pi&ugrave; veloce. </s>

<s>Questi fatti si succedono cos&igrave; indubitatamente, supposto che in <lb/>qualunque sistole sia uguale la quantit&agrave; emessa del sangue, ma se questa <lb/>&egrave; diversa, la velocit&agrave; sar&agrave; pure alterata, anche per questa terza cagione. </s></p><p type="main">

<s>&ldquo; Itaque, prosegue a ragionare il Guglielmini, exit a corde in arteriam <lb/>aortam sanguis determinata velocitate, quam quidem, si retineret in toto suo <lb/>usque ad extrema arteriarum excursu, nulla fieret earumdem arteriarum <lb/>extrusio. </s>

<s>Verum hoc impossibile est; aflrictus enim, quem habet sanguis ad <lb/>latera arteriarum, necessario aliquid velocitatis subtrahit sanguini pertran&shy;<lb/>seunti, in quo duo subsequi necesse est: primum, quod sanguis fluens per <lb/>arterias non uniformi feratur velocitate, sed minori quidem qui versus cir&shy;<lb/>cumferentiam est, maiori vero, qui per medium tubuli arteriosi, et veluti <lb/>per eius axem, fluit; alterum, quod cum velocitas retardetur, ob supra dic&shy;<lb/>tam rationem, non potest totus sanguis, a corde expulsus, per eiusdem <lb/>multo minus per minoris diametri arterias pertransire. </s>

<s>Ideo eius pars qui&shy;<lb/>dem per longum arteriosi tubuli iter suum prosequitur, altera vero in eius&shy;<lb/>dem arteriae capacitate subsistit, locum sibi quaerens ad extra, ex quo oritur <lb/>arteriae ad latera extrusio, idest dilatatio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cumque, quo maior est recessus sanguinis a corde versus partes, sem&shy;<lb/>per plures offendantur resistentiae, non modo affrictus, de quo supra, verum <lb/>etiam divisionis, curvitatis et obliquitatis vasorum, sequitur quod, quo maior <lb/>est via sanguinis a corde, eo maior fiat velocitatis amissio, et consequenter <lb/>quod minori impetu afficiatur sanguis praecedens, maiori vero succedens. </s>

<s><lb/>Igitur sanguis, subsequenti systole a corde extrusus, duplicem invenit, vel <lb/>ipso sui motus initio, in arterias resistentiam: alteram affrictus vasorum, al&shy;<lb/>teram antecedentis sanguinis. </s>

<s>Ideoque, sui velocitate ab affrictu reliqua, par&shy;<lb/>tim urgebit antecedentem sanguinem, partim contra arteriarum membranas <lb/>nitetur, quas idcirco dilatabit in ampliorem diametrum, absque eo quod ta&shy;<lb/>men, quod observabile, cesset in toto sanguine fluxus per arteriarum longi&shy;<lb/>tudinem &rdquo; (De sanguinis natura, Venetiis 1701, pag. </s>

<s>7-9). </s></p><p type="main">

<s>Assai pi&ugrave; gravi difficolt&agrave; presentava a intendersi il moto del sangue <lb/>nelle vene, non pi&ugrave; aiutato, come dianzi per le arterie, dalla macchina im&shy;<lb/>pellente del cuore, ond'&egrave; che, non vedendoci nulla di violento, furono i Fi&shy;<lb/>siologi costretti ad affidare tutta quella forza d'impulso alla gravit&agrave; naturale. </s>

<s><lb/>Dicevano che le vene con le arterie, come per esempio la Cava discendente <lb/>con l'Aorta ascendente, componevano un sifone, e che perci&ograve; il sangue, per <lb/>legge d'equilibrio idrostatico, tanto discendeva in quella, quanto in questa <lb/>ascendeva. </s>

<s>Il Pecquet riserb&ograve; il cap. </s>

<s>VI della citata Dissertazione anatomica <pb xlink:href="020/01/1231.jpg" pagenum="106"/><emph type="italics"/>De circulatione sanguinis<emph.end type="italics"/> a confutare una cos&igrave; fatta opinione, dimostran&shy;<lb/>done da pi&ugrave; parti la falsit&agrave; con le ragioni e con l'esperienze. </s></p><p type="main">

<s>La prima di quelle ragioni &egrave; che, dovendo i liquidi ne'rami di un sifone <lb/>ascendere e discendere nel medesimo tempo, perch&egrave; se non operassero con&shy;<lb/>temporaneamente le due forze non potrebbero comporsi in equilibrio, conver&shy;<lb/>rebbe, applicato quello strumento idrostatico al sangue, che si facessero nello <lb/>stesso tempo dal medesimo mobile due moti contrarii, che son nel caso <lb/>nostro la sistole e la diastole del cuore. </s>

<s>&ldquo; Patebit tum quam sit incongrua <lb/>Siphonis cum sanguineo motu iugis fluendi successio, nam eodem instanti <lb/>et in cor influeret sanguis et ex corde deflueret &rdquo; (pag. </s>

<s>45). </s></p><p type="main">

<s>La falsit&agrave; dell'ipotesi del Sifone, prosegue a dire il Pecquet, &egrave; confer&shy;<lb/>mata dall'osservazione sui cadaveri, e dall'esperienza su gli animali vivi. </s>

<s><lb/>Imperocch&egrave;, se per mantener l'equilibrio idrostatico debbono mantenersi i <lb/>due rami sempre di liquido ugualmente pieni &ldquo; qui fiat ut in cadavere mors <lb/>turgidis venis arterias prorsus exhauriat? </s>

<s>&rdquo; (ibi). La vena guigulare rap&shy;<lb/>presenta un sifone con la curvatura superiore. </s>

<s>&ldquo; Hanc, dice il Pecquet, cum <lb/>in collo ligavi, nihilominus per ascendentes arterias sursum immissus est <lb/>sanguis &rdquo; (ibi). Altre esperienze, che seguita l'Autore a descrivere, confer&shy;<lb/>mavano l'insufficienza del sifone, ond'&egrave; che ridusse tutta la macchina del <lb/>moto sanguineo dentro le vene alla nativa contrattilit&agrave; delle loro fibre. </s></p><p type="main">

<s>Il Borelli poi conobbe che bisognava con pi&ugrave; diligenza studiare questo <lb/>meccanismo, e ne consider&ograve; distintamente l'opera in tre tempi diversi: nel&shy;<lb/>l'atto, in cui il sangue arterioso entra per le bocche aperte delle vene ca&shy;<lb/>pillari; quando entratovi segue un primo tratto della sua via lungo questi <lb/>stessi capillari; e in ultimo, quando avvicinandosi pi&ugrave; al cuore vi scende <lb/>per canali venosi sempre pi&ugrave; larghi. </s></p><p type="main">

<s>Il primo atto, che &egrave; dell'ingresso del sangue arterioso nelle estremit&agrave; <lb/>capillari delle vene, presentava la massima difficolt&agrave; sopra gli altri, perch&egrave;, <lb/>sebbene ai tempi in che fu pubblicata o forse anche scritta dal Borelli que&shy;<lb/>sta Parte dei moti animali, avesse il Malpighi veduto co'suoi eccellenti mi&shy;<lb/>croscopi continuarsi le estremit&agrave; arteriose con le venose in alcuni organi <lb/>secretori delle rane, rimasero tuttavia, anche lungo tempo dopo, in dubbio <lb/>i Fisiologi di queste anastomosi, parendo forse a loro, come parve al Pe&shy;<lb/>cquet, pi&ugrave; naturale ammettere un'estravasamento del sangue, con che ren&shy;<lb/>devasi assai pi&ugrave; facile a intendere la nutrizione. </s></p><p type="main">

<s>Comunque sia, il Borelli stesso, nella XXXII proposizione della II Parte <lb/><emph type="italics"/>De motu anim.,<emph.end type="italics"/> confess&ograve; che la ragion meccanica del moto del sangue nelle <lb/>vene non &egrave; cos&igrave; chiara, principalmente per ci&ograve; che concerne il modo come <lb/>si sugge il sangue arterioso dalle ultime venuzze capillari. </s>

<s>&ldquo; Nam venae ca&shy;<lb/>pillares, egli dice, non uniuntur cum extremis arteriolis per anastomosin, et <lb/>ideo sanguis immitti non potest immediate ab arteriis ad venas, cum haec <lb/>vasa sint separata ad invicem. </s>

<s>Et licet opinemur adesse communicationem <lb/>quandam inter extrema orificia arteriarum et venarum capillarium, per in&shy;<lb/>termediam spongiosam substantiam carnium, viscerum, aut per cribrosam <pb xlink:href="020/01/1232.jpg" pagenum="107"/>substantiam ossium, tamquam per pumicis porositates; attamen non perci&shy;<lb/>pimus a qua vi motiva insinuari sanguis possit intra capillares venas. </s>

<s>Primo, <lb/>quia vis impulsiva, qua systole cordis sanguinem intra arterias immittit, con&shy;<lb/>sentaneum est ut sensim debilitetur, et tandem langueat in angustiis illis <lb/>extremorum vasorum et porositatum intermediarum. </s>

<s>Secundo, quia orificia <lb/>venularum non possunt semper dilatata et aperta permanere, cum earum <lb/>consistentia non sit dura ut ossea, sed membranosa, mollis et lubrica, et <lb/>ideo facile elaudantur et ingressum novi sanguinis impedire possint. </s>

<s>Tertio, <lb/>neque ad compressionem viscerum et carnium recurrere possumus, a qua <lb/>per expressionem sanguis ibidem insinuatur &rdquo; (Editio cit., pag. </s>

<s>79, 80). </s></p><p type="main">

<s>Questa terza ragione &egrave; manifestamente contro l'ipotesi del Pecquet, la <lb/>quale dice il Borelli &egrave; insufficiente a spiegar la causa del sofficcarsi cos&igrave; il <lb/>sangue arterioso nelle bocchuzze delle vene, vedendosi avvenir ci&ograve; non solo <lb/>quando i muscoli enfiandosi esercitano la loro compressione, ma quando al&shy;<lb/>tres&igrave; riposano e rimangono affatto relassati. </s></p><p type="main">

<s>Quella ipotesi del Pecquet, soggiunge il Borelli, &egrave; di pi&ugrave; insufficiente <lb/>a spiegare in che modo, imboccato il sangue, proceda con impeto per tutto <lb/>il tratto delle venuzze capillari, vedendolo procedere con quel medesimo <lb/>impeto anche attraverso alla stessa dura sostanza, non punto compressibile, <lb/>degli ossi. </s>

<s>E qui il nostro Italiano introduce com'efficiente di quel moto <lb/>una causa, rimasta incognita agli stranieri, infin dopo la prima met&agrave; del se&shy;<lb/>colo XVII, bench&egrave; Andrea Cesalpino avesse attribuita ad essa l'ascendere della <lb/>linfa nelle piante. </s>

<s>Niccol&ograve; Aggiunti, morto come sappiamo nel 1635, riduce <lb/>a una occulta virt&ugrave;, che poi fu detta di capillarit&agrave;, il moto de'liquidi per <lb/>gli angusti meati de'corpi, e specialmente per le venuzze degli animali, men&shy;<lb/>tre, nel 1651, il Pecquet non sapeva attribuire ad altra causa che alle com&shy;<lb/>pressioni e agli agitamenti del torace e de'muscoli intercostali, nell'atto <lb/>della respirazione, il moto cos&igrave; veloce del chilo per i vasi aselliani. </s></p><p type="main">

<s>I fenomeni capillari furono, come narreremo a suo tempo, uno de'primi <lb/>soggetti intorno ai quali s'intrattennero l'esperienze de'nostri Accademici <lb/>del Cimento, e il Borelli ne fa qui una insigne applicazione alla Meccanica <lb/>animale, rassomigliando i primi moti del sangue, che s'insinua nelle aperte <lb/>boccuzze delle vene, all'insinuarsi dell'acqua ne'pori aperti delle spugne, <lb/>de'filtri, delle funi, o nell'interno di sottilissimi cannellini, per intrinseco <lb/>impulso, non punto diverso da quello della gravit&agrave; universale. </s>

<s>&ldquo; Sic vis mo&shy;<lb/>tiva gravitatis, qua sanguis carere non potest, ad instar aquae, cum offendit <lb/>canaliculos patulos capillarium venarum, eo quod nunquam a conniventia <lb/>membranosa tam stricta et tenaci clausura constringi possunt, ut aditus aliqui <lb/>non remaneant, ut in funium porulis patet; necesse est ut, energia motiva <lb/>qua pollent, inertem angustiarum resistentiam superet, et proinde actione <lb/>simili filtrationi sanguis intra capillares venulas insinuetur &rdquo; (ibi, pag. </s>

<s>80). <lb/>Insinuatosi cos&igrave;, per l'impulso iniziale, procede nel suo moto oltre sospinto <lb/>dal sangue che sussegue &ldquo; ut videmus aquam a filtro exuctam a suprema <lb/>finbria reclinata et pendula percolari &rdquo; (ibi, pag. </s>

<s>81). </s></p><pb xlink:href="020/01/1233.jpg" pagenum="108"/><p type="main">

<s>All'ultimo, proseguendo il sangue nelle vene il suo corso, dagli angu&shy;<lb/>sti seni de'capillari trapassa nelle pi&ugrave; aperte vie de'tronchi venosi; ond'&egrave; <lb/>che, accresciutasi ivi la sezione, la velocit&agrave; naturalmente diminuisce. </s>

<s>&ldquo; Ideo <lb/>deinceps auxiliaribus manibus indiget ut promoveri ulterius possit &rdquo; (ibi). <lb/>Consistono principalmente questi ausiliari, soggiunge tosto il Borelli, nel <lb/>moto vermicolare o peristaltico delle vene, a cui s'aggiungono la compres&shy;<lb/>sione dell'aria ambiente, e l'elasticit&agrave; dell'interna, nonch&egrave; il moto de'mu&shy;<lb/>scoli, de'visceri e de'fluidi nel corpo animale continuamente scorrenti. </s></p><p type="main">

<s>Non occorre entrar nella questione dell'aria contenuta nel sangue, ma <lb/>&egrave; da notar come il Borelli, annoverando fra i coefficienti del moto la pres&shy;<lb/>sion dell'aria ambiente le vene, emendava uno de'pi&ugrave; gravi difetti della <lb/>meccanica pecqueziana, la quale, contenta a escludere il nome vano dell'at&shy;<lb/><figure id="id.020.01.1233.1.jpg" xlink:href="020/01/1233/1.jpg"/></s></p><p type="caption">

<s>Figura 4.<lb/>trazione del vacuo, non attribu&igrave; nessuna efficacia in sol&shy;<lb/>lecitare il moto del sangue a quel grave peso dell'am&shy;<lb/>mosfera, sotto il torchio del quale gemono, o in quiete o <lb/>in moto che sieno, tutti i corpi terrestri. </s></p><p type="main">

<s>Mentre dunque cos&igrave; il Borelli da una parte emen&shy;<lb/>dava la meccanica animale del Pecquet, la compieva dal&shy;<lb/>l'altra, attribuendo al gioco delle valvole principalmente <lb/>l'impulso a proseguire oltre verso il cuore, il sangue, <lb/>nelle vene pi&ugrave; grosse. </s>

<s>Rappresenti il cilindro KLHI <lb/>(fig. </s>

<s>4) un grosso tronco di vena, e nelle interne pareti <lb/>di lui sieno apposte le due valvole membranose AONMP, <lb/>BONQR. </s>

<s>Ecco in che modo il Borelli descrive il mecca&shy;<lb/>nismo delle valvole, in protrudere innanzi il sangue verso <lb/>il ventricolo destro del cuore: </s></p><p type="main">

<s>&ldquo; Intelligatur eadem portio HMQL sanguine repleta, <lb/>et quia a fibris circularibus eius, et ab ambientibus mu&shy;<lb/>sculis et visceribus stringitur una pars post aliam, oportet <lb/>ut eius laterales parietes S, T ad sese propius accedant <lb/>versus V, et tunc vena restricta cylindricam formam amit&shy;<lb/>tet, transformabiturque in duo infundibula HVL, MVQ, <lb/>quae minus capacia sunt ipso cylindro, et proinde san&shy;<lb/>guis, qui continebatur in spatiis VHS et VLT expelletur <lb/>extra orificium HL: reliqua vero moles sanguinis contenta in spatiis VSM, <lb/>VQT eiicietur extra orificium MQ versus IK. &rdquo; </s></p><p type="main">

<s>&ldquo; Patet igitur quod ex praedicta compressione parietum venae expri&shy;<lb/>mitur sanguis, pelliturque aequali copia ad partes oppositas, et hoc contin&shy;<lb/>geret, si valvulae non adessent. </s>

<s>At quia, in internis parietibus MP, QR ve&shy;<lb/>nae, appositae sunt valvulae, seu sacculi membranosi superius expositi, <lb/>necesse est ut sanguis impulsus a compressione facta in ST insinuetur per <lb/>rimam NO, quia fluidum cedens in sacculis contentum, ab adveniente san&shy;<lb/>guine contusum, constringitur, evacuaturque, et ideo latera valvularum NO <lb/>ab invicem recedendo patulam viam relinquunt, per quam sanguineus fluor <pb xlink:href="020/01/1234.jpg" pagenum="109"/>ab MSTQ adveniens insinuari potest, et pertransire ultra AB. Porro, post&shy;<lb/>quam sanguis confinia valvularum PO, RO transgressus est, necessario subse&shy;<lb/>quitur spontanea restrictio et clausura rimulae NO, nam ipse sanguis, mole <lb/>sua gravi et propensione fluida, replere debet sacculos valvularum, et ideo <lb/>latera mollia eorum dilatata, quousque se mutuo exacte tangant, rimulam NO <lb/>arcte claudere debent &rdquo; (ibi, pag. </s>

<s>82, 83). </s></p><p type="main">

<s>Quando ancora non s'&egrave; restituita nel suo primo stato la parte venosa <lb/>T, S, incomincia, proseguendo il moto peristaltico, a contrarsi la porzion <lb/>superiore F, E, e il sangue contenuto nell'infondibolo GBA, trovando di sotto <lb/>le valvole chiuse, non retrocede per&ograve;, ma vien oltre sospinto verso DC &ldquo; non <lb/>secus ac pila lusoria parieti illisa &rdquo; (ibi). Nello stesso tempo &egrave; spinto pure <lb/>per la medesima via il sangue contenuto negli spazii EDG, FCG, cosicch&egrave;, <lb/>dello stesso sangue sospinto in quella medesima compressione, doppia viene <lb/>ad esser la mole. </s>

<s>E perch&egrave; doppia mole produce doppia velocit&agrave;, &egrave; questo, <lb/>conclude il Borelli, un altro singolar benefizio delle valvole delle vene (ivi). </s></p><p type="main">

<s>La difficolt&agrave; d'investigar la causa e la ragion meccanica del moto del <lb/>sangue nelle vene pareva in questo modo assai ingegnosamente superata, e <lb/>poniamo che rimanga tuttavia occulto quel che ad esaltare i moti puramente <lb/>meccanici vi conferisce lo spirito della vita, non si potevano i Fisiologi aspet&shy;<lb/>tar nulla di pi&ugrave; sottile di queste borelliane speculazioni. </s>

<s>In ogni modo, per&shy;<lb/>ciocch&egrave; la forza che si cercava (la quale essendo vitale dev'esser semplicis&shy;<lb/>sima) si lusingavano gli Iatromatematici che dovesse resultare di compo&shy;<lb/>nenti non tutte computabili dalle deboli forze del nostro ingegno, credettero <lb/>che, per far concorrere in pi&ugrave; gran numero possibile le stesse componenti <lb/>pi&ugrave; conosciute, si potesse riuscire ad avere almeno per approssimazione il <lb/>valore della forza resultante. </s></p><p type="main">

<s>Una tal tendenza della scienza fisiologica, specialmente in Italia, dove <lb/>la scuola iatromatematica avendo avuto la sua prima istituzione, ebbe anche <lb/>maggior cultura; vien rappresentata dalla dottrina del Guglielmini, il quale, <lb/>dopo aver divisate come vedemmo le ragioni meccaniche del moto del san&shy;<lb/>gue nelle arterie, passa a considerar le cause efficienti di quello stesso moto <lb/>nelle estremit&agrave; capillari delle vene, e ne'loro tronchi. </s></p><p type="main">

<s>Che un moto, simile a quello discorrente per le arterie, lo abbia altres&igrave; <lb/>il sangue per le vene, pu&ograve; dimostrarsi, egli dice, da ci&ograve; &ldquo; quod non aliunde <lb/>sanguis venis subministretur quam ab arteriarum osculis, vel, quod proba&shy;<lb/>bilius, a porosis carnium meatibus, in quos sanguis arteriosus, tum nutri&shy;<lb/>tionis, tum motionis musculorum, tum aliorum usuum causa effunditur. </s>

<s>In <lb/>hos enim hiantia tum arteriarum tum venarum ora illa vehunt, haec, quod <lb/>superest revehunt. </s>

<s>Ideoque, qua ratione exit ab arteriis sanguis, eadem et <lb/>carnium interstitia perluere et venas subingredi cogitur &rdquo; (De sanguinis na&shy;<lb/>tura cit, pag. </s>

<s>13). </s></p><p type="main">

<s>Se dunque, ne conclude il Guglielmini, vien rapito dal cuore per le ar&shy;<lb/>terie un fiume non interrotto di sangue; un fiume non interrotto di sangue <lb/>&egrave; pur necessario che sia rimenato al cuore dalle vene. </s>

<s>Favoriscono questo <pb xlink:href="020/01/1235.jpg" pagenum="110"/>ricorso, ei soggiunge, pi&ugrave; cause coefficienti e son quelle considerate gi&agrave; dal <lb/>Borelli e da altri Fisiologi nostrali e stranieri. </s>

<s>Ma prima di veder il nostro <lb/>Autore ridurre in ordine e annoverare le ragioni altrui, non vogliamo la&shy;<lb/>sciare inavvertito che in quelle parole: <emph type="italics"/>si igitur per arterias, non inter&shy;<lb/>rupto flumine, vehitur, id etiam per venas contingere necesse est,<emph.end type="italics"/> conclu&shy;<lb/>desi la principal causa del moto del sangue per le vene, qui dal Guglielmini <lb/>accennata, ma che, nella II delle sue <emph type="italics"/>Lettere idrostatiche,<emph.end type="italics"/> ha il pi&ugrave; chiaro <lb/>e pi&ugrave; pieno commento. </s>

<s>Ivi dimostra le vere leggi del moto dell'acqua den&shy;<lb/>tro i sifoni, e osserva che una parte del fluido si tira necessariamente die&shy;<lb/>tro, con la stessa velocit&agrave;, l'altra parte che addietro la segue, per non poter <lb/>rimanervisi spazii vuoti interposti. </s>

<s>D'onde segue che il moto dello stesso <lb/>fluido non &egrave; naturale ma violento, come quello che necessariamente sog&shy;<lb/>giace alla prepotente pressione di tutta l'ammosfera. </s>

<s>La continuit&agrave; del cir&shy;<lb/>colo mette il sangue in queste medesime condizioni idrostatiche, ond'&egrave; im&shy;<lb/>possibile che il sangue stesso sgorghi dalla vena Cava, ch'&egrave; l'estremit&agrave; del <lb/>sifone, dentro il ventricolo destro, senza che quel che gli &egrave; dietro tutto in&shy;<lb/>sieme lo segua, con la velocit&agrave; conveniente alle sezioni. </s></p><p type="main">

<s>Accennata questa, che &egrave; la causa principale del ricorso del sangue nelle <lb/>vene &ldquo; Huic autem recursui, soggiunge il Guglielmini, opem ferunt, tum <lb/>impetus sanguini a corde et arteriis communicatus a parte post partem ab <lb/>arterioso sanguine in venosum transiens; tum ratio aequilibrii in ascenden&shy;<lb/>tibus venis. </s>

<s>Sicuti enim in recurvis syphonibus fluida ad eamdem altitudi&shy;<lb/>nem aequilibrantur, et per unum syphonis crus tantum ascendunt, quantum <lb/>per alterum descenderunt, etiam precisa quacumque vi externa; ita consi&shy;<lb/>milis aequilibrii ratione irruens per Aortam descendentem eiusque propagi&shy;<lb/>nes, sanguis, qui uti in viventi animali fluidus est, ita et reliquorum flui&shy;<lb/>dorum naturam sequitur, per minores ramulos a Cava descendente prognatos <lb/>primo, mox in eius truncum adscendere cogitur usque ad cor, etiam si huius <lb/>vis subtraheretur. </s>

<s>Quanto ergo magis si legibus aequilibrii copuletur altera <lb/>vis extrinseca, scilicet cordis et arteriarum constrictiva facultas! &rdquo; </s></p><p type="main">

<s>&ldquo; Aliquando etiam regressui sanguinis in cor suffragatur eiusdem gra&shy;<lb/>vitas, ut in venis descendentibus. </s>

<s>Protrusus enim per Aortam ascendentem <lb/>in caput sanguis, ubi minima lustraverit cerebri vascula et in venulas com&shy;<lb/>mearit, quae in cavam ascendentem hiant, huius declivitas et perpendicularis <lb/>situs efficit ut nullo externo indigeat sanguis auxilio ut ad priora reverta&shy;<lb/>tur contubernia. </s>

<s>Addunt alii peristalticum venarum motum et valvularum, <lb/>quae in iis sunt adiumentum: ille enim motum sanguinis promovet, hoc <lb/>versus certam partem determinat, ut obstendit praeclarissimus Borellus &rdquo; <lb/>(ibi, pag. </s>

<s>14, 15). </s></p><pb xlink:href="020/01/1236.jpg" pagenum="111"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Chi bene attende all'indole delle esposte dottrine del Guglielmini, ci <lb/>vede profondamente impresse le vestigia di quella scienza idraulica, nella <lb/>quale egli fu cos&igrave; insigne Maestro. </s>

<s>Potremo fra poco, da quello stesso trat&shy;<lb/>tato <emph type="italics"/>De sanguinis natura,<emph.end type="italics"/> desumere di ci&ograve; altri pi&ugrave; chiari esempi, ma in&shy;<lb/>tanto &egrave; da considerare ch'essendo quell'indole tutta propria alla istituzione <lb/>iatromatematica, il Guglielmini stesso doveva avere appreso di l&agrave; i nuovi <lb/>modi, seguendo l'orme dell'applauditissimo Istitutore. </s></p><p type="main">

<s>Anche prima di averne la riprova dei fatti, si prevede facilmente da <lb/>ognuno che il Borelli, discepolo dell'Autore <emph type="italics"/>Della misura delle acque cor&shy;<lb/>renti,<emph.end type="italics"/> doveva prevalersi delle leggi idrauliche a investigar le cause e le ra&shy;<lb/>gioni del moto del sangue: e fu di fatto cos&igrave;, com'accennava gi&agrave; la storia <lb/>passata, e come si dimostrer&agrave; meglio dalla presente. </s>

<s>S'asserisce anzi di pi&ugrave; <lb/>che il Borelli stesso fu il primo a far, tra l'Idraulica e la Fisiologia, quel <lb/>connubio, che parve ai successori cos&igrave; fecondo, e se una tale fecondit&agrave; ha <lb/>nessuna ragion di merito, il merito di ci&ograve; principalmente, e forse tutto, &egrave; <lb/>da attribuirsi alla scuola italiana. </s></p><p type="main">

<s>&Egrave; vero che l'Harvey rassomigli&ograve; il cuore a quella macchina artificiale <lb/>da attrar l'acqua dalle cisterne e da sollevarla, da lui chiamata <emph type="italics"/>Sifone,<emph.end type="italics"/> ma <lb/>egli che professava allora, insiem coi filosofi de'suoi tempi, il principio del&shy;<lb/>l'attrazion del vuoto, era troppo di lungi dall'intendere la ragione di ci&ograve; <lb/>ch'esemplificava, non intendendo la ragion dell'esempio. </s>

<s>Il Pecquet stesso, <lb/>che fu il primo a cacciare dalla meccanica del cuore il falso principio di <lb/>quell'attrazione, non seppe progredire pi&ugrave; oltre, e anzi, sotto le macerie del <lb/>vecchio edifizio da lui distrutto, rimase sepolto e dimenticato anche l'esem&shy;<lb/>pio del Sifone recato dall'Harveio. </s></p><p type="main">

<s>Ch'ei non progredisse veramente pi&ugrave; oltre, il Pecquet, e che non gli <lb/>sovvenisse di applicare alla scienza delle cause e delle ragioni del moto <lb/>de'fluidi nel corpo animale la scienza delle cause e delle ragioni del moto <lb/>dell'acqua ne'tubi, scienza fuori allora non coltivata come in Italia, si di&shy;<lb/>chiara per alcuni fatti occorsi al Pecquet stesso, nella storia della celebre <lb/>scoperta del Canale toracico. </s>

<s>Gli dinegava il Riolano la verit&agrave; di quella sco&shy;<lb/>perta, perch'essendo, ei diceva, sproporzionata la capacit&agrave; del ricettacolo ai <lb/>due condotti, che sboccano nelle vene succlavie, non poteva il chilo essere <lb/>ne'due vasi ugualmente veloce, n&egrave; perci&ograve; continuarvi il suo moto. </s></p><p type="main">

<s>Avrebbe il Pecquet, ricorrendo all'Idraulica, potuto fare avvertire al <lb/>Riolano che la stessa quantit&agrave; d'acqua passa in un ruscello per i pi&ugrave; lar&shy;<lb/>ghi seni, e fra i pi&ugrave; avvicinati margini delle sue sponde, proseguendo a di&shy;<lb/>ritto e non interrotto il suo corso, eppure, soggiogato per una parte dalle <lb/>difficolt&agrave;, e per l'altra assicurato dal fatto, non sa come meglio rispondere <pb xlink:href="020/01/1237.jpg" pagenum="112"/>che col dire che la medesima sproporzione, notata fra il Ricettacolo e i ca&shy;<lb/>naletti chiliferi, si trovava fra le vene del mesenterio e i pori epatici, per i <lb/>quali, secondo lo stesso Riolano, il chilo trasformato in sangue &egrave; portato alla <lb/>vena Cava dalla vena Porta diramatasi nel fegato attraverso al suo paren&shy;<lb/>chima. (Epistolae, Parisiis 1654, pag. </s>

<s>213). </s></p><p type="main">

<s>Come dunque, trattando del moto del chilo, non seppe vedervi il Pecquet <lb/>la causa, che fa scorrere i liquidi ne'tubi capillari; cos&igrave;, abbattendosi a dover <lb/>notare alcune accidentali anomalie di quel moto, non seppe vedervi la con&shy;<lb/>formit&agrave; con le leggi delle acque correnti. </s>

<s>Queste leggi dimostrate per i primi <lb/>dagl'Italiani trapassarono dal campo delle Matematiche in quello della Fisio&shy;<lb/>logia per opera del Borelli, il quale, ripigliando il dimenticato concetto ar&shy;<lb/>veiano, dimostr&ograve; come il cuore si conformasse veramente nell'operare alle <lb/>leggi idrauliche del Sifone. </s></p><p type="main">

<s>Il capitolo V della II Parte <emph type="italics"/>De motu animalium<emph.end type="italics"/> &egrave; tutto riserbato dal&shy;<lb/>l'Autore a esporre in varie proposizioni questa nuova dimostrazione, ed &egrave; <lb/>reputato uno de'luoghi pi&ugrave; insigni dell'Opera borelliana. </s>

<s>Dopo avere sneb&shy;<lb/>biate le menti dei dannosi errori vesaliani, e dop'aver fatto notare che le <lb/>cavit&agrave; del cuore si restringono, non perch&egrave; s'accorcino le lunghezze dei ven&shy;<lb/>tricoli, ma perch&egrave; c'accostano l'una all'altra le pareti laterali (prop. </s>

<s>I, edit. </s>

<s><lb/>cit., pag. </s>

<s>103) passa a dimostrar che l'azione propria dei muscoli, di ch'&egrave; <lb/>contessuto lo stesso cuore &ldquo; est constrictio ventriculorum eius et compressio <lb/>et expressio sanguinis in eis contenti, ad instar praeli facta &rdquo; (ibi, pag. </s>

<s>105). </s></p><p type="main">

<s>Per dimostrare l'azion meccanica di questo torchio sul sangue s'appa&shy;<lb/>recchia il Borelli la via, configurando uno strumento idraulico a somiglianza <lb/>del cuore, e dimostrando le relazioni che passano tra la potenza e la resi&shy;<lb/>stenza, supposto che lo strumento stesso venga applicato a spingere e a sol&shy;<lb/>levar l'acqua dentro una fistola, per la quale intende poi di rappresentare <lb/>l'Aorta. </s>

<s>La dimostrazione &egrave; sotto questa forma annunziata: &ldquo; Vis utrem <lb/>aqua plenum stringens, ad resistentiam aquae per fistulam ei annexam expul&shy;<lb/><figure id="id.020.01.1237.1.jpg" xlink:href="020/01/1237/1.jpg"/></s></p><p type="caption">

<s>Figura 5.<lb/>sae, eamdem proportionem habet quam <lb/>amplitudo utris ad amplitudinem fistu&shy;<lb/>lae &rdquo; (ibi, pag. </s>

<s>121). </s></p><p type="main">

<s>Suppongasi, per comodit&agrave; della di&shy;<lb/>mostrazione, che cos&igrave; la fistola come <lb/>l'otre siano ridotti alla perfetta geome&shy;<lb/>trica figura dei cilindri, e sia rappresen&shy;<lb/>tato con ABCD l'otre (fig. </s>

<s>5) e con IGH <lb/>la fistola annessa, dentro alla quale &egrave; <lb/>sospinto il liquido dall'embolo LM. </s>

<s>A <lb/>chi volesse sapere qual relazione passa <lb/>in questo meccanico esercizio, fra la potenza P dell'embolo, e la forza R, <lb/>con cui resiste la mole liquida alla pressione, risponde il Borelli dicendo <lb/>&ldquo; potentiam P ad R se habere ut amplitudo circuli AD ad amplitudinem <lb/>circuli IG &rdquo; (ibi). </s></p><pb xlink:href="020/01/1238.jpg" pagenum="113"/><p type="main">

<s>Il teorema, dimostrato da Galileo nel Discorso intorno alle galleggianti <lb/>col principio delle velocit&agrave; virtuali, &egrave; dal Borelli concluso da un altro prin&shy;<lb/>cipio, che per conformarsi al linguaggio degli scienziati moderni si pu&ograve; enun&shy;<lb/>ciar sotto questa forma: &ldquo; Alloch&egrave; due pesi o due altre potenze son dispo&shy;<lb/>ste in maniera, che l'una non possa muoversi, senza far muover l'altra, se <lb/>lo spazio che deve percorrere uno de'pesi, secondo la sua direzione propria <lb/>e naturale, stia allo spazio che deve percorrer l'altro nel medesimo tempo, <lb/>secondo la sua direzione propria e naturale, reciprocamente come quest'ul&shy;<lb/>timo peso sta al primo; questi due pesi staranno in equilibrio. </s>

<s>&rdquo; </s></p><p type="main">

<s>Analiticamente il Teorema, nel caso particolare contemplato qui dal <lb/>Borelli, viene espresso dalle seguenti equazioni: AB:HG=......... <lb/>HGXIG:ABXAD; P:R=ABXAD:GHXIG, onde avremo, nel caso <lb/>e nella supposizione dell'equilibrio, P:R=HG:AB=AD:IG. &ldquo; Igitur <lb/>potentia P ad resistentiam R se habet ut GH velocitas ipsius R ad AB ve&shy;<lb/>locitatem ipsius P, seu ut amplitudo circularis AD ad amplitudinem cir&shy;<lb/>culi IG &rdquo; (ibi). </s></p><p type="main">

<s>Dal medesimo principio &egrave; pure conclusa la seguente proposizione LIX, <lb/>che d&agrave; le leggi meccaniche tra la potenza e la resistenza nelle utilissime ap&shy;<lb/>plicazioni del Torchio idraulico, a cui rassomigliasi dal Borelli il cuore nella <lb/>sua potenza e nella resistenza oppostagli dal sangue: &ldquo; Si intra fistulam <lb/>aquam continentem, a maiori tubo, nova aqua embolo impellatur, vis embo&shy;<lb/>lum impellens ad resistentiam aqueae molis praeesistentis et de novo im&shy;<lb/>pulsae intra fistulam, eamdem proportionem habebit quam amplitudo orificii <lb/>tubi ad amplitudinem orificii fistulae &rdquo; (ibi, pag. </s>

<s>122). </s></p><p type="main">

<s>Come fu il primo e il pi&ugrave; studioso il Borelli d'applicare in queste, e <lb/>in altre simili proposizioni, le leggi idrauliche ai moti del cuore, cos&igrave; fu <lb/>primo ad applicarle ai moti del sangue, parendogli che, dovendo anch'esso <lb/>partecipare della natura di tutti i fluidi, non potesse sottrarsi dalle leggi ge&shy;<lb/>nerali dimostrate gi&agrave; dal Castelli. </s></p><p type="main">

<s>&Egrave; la fondamentale di queste leggi che le quantit&agrave; son proporzionali alla <lb/>velocit&agrave; moltiplicata per la sezione, d'onde ne segue che, duplicandosi la <lb/>quantit&agrave; e rimanendo la sezione costante, la velocit&agrave; &egrave; pure anch'essa ne&shy;<lb/>cessariamente duplicata. </s>

<s>Applica questa legge idraulica il Borelli al moto del <lb/>sangue nelle vene, per le valvole apposte alle quali sospingendosi innanzi, <lb/>nella medesima compressione e nel medesimo tempo, una doppia quantit&agrave; <lb/>dello stesso sangue, convien che si cacci in corso doppiamente veloce. </s>

<s>&ldquo; Cum&shy;<lb/>que ab eadem compressione sanguis qui continebatur in spatiis EDG, FCG <lb/>(fig. </s>

<s>4 preced.) propellatur ultra DC, igitur dupla moles sanguinis, eodem <lb/>tempore quo fit compressio, expellitur per idipsum ostium DC. </s>

<s>Sed quando <lb/>dupla fluidi moles, eodem tempore, per idem orificium emittitur, excurrere <lb/>debet velocitate dupla, igitur, per machinam valvularum, compressiones ve&shy;<lb/>narum duplo velociori motu sanguinem versus cor protrudunt, non fluxu <lb/>continuo, sed interpositis morulis et velocitatibus inaequalibus &rdquo; (ibi, pag. </s>

<s>83). </s></p><p type="main">

<s>Se le quantit&agrave; stanno in ragion composta della velocit&agrave; e della sezione, <pb xlink:href="020/01/1239.jpg" pagenum="114"/>conforme alla sopra detta legge fondamentale, ne segue che rimanendo le <lb/>sezioni uguali le quantit&agrave; stanno in semplice ragione delle velocit&agrave;, e ci&ograve; <lb/>vuol dire che da un vaso sgorga, in un medesimo tempo, tanto maggior <lb/>quantit&agrave; di liquido quant'&egrave; pi&ugrave; veloce. </s>

<s>Or proponendosi il Borelli di enar&shy;<lb/>rare i preclari effetti che si producono dalla velocit&agrave; del circolo sanguigno <lb/>per far comprendere la gran quantit&agrave; del sangue, con cui la Natura prov&shy;<lb/>vede alla nutrizione dell'animale, applica il corollario di quella legge delle <lb/>acque correnti. </s>

<s>&ldquo; In unaquaque cordis pulsatione grandis copia sanguinis a <lb/>subtilissimis arteriosis canaliculis effunditur et eiaculatur, quia eo maior <lb/>copia fluoris ab eisdem canalibus effluit, quanto velociori motu per eos mo&shy;<lb/>vetur, ut B. </s>

<s>Castellus demonstravit, et proinde sanguis, ad instar pleni et <lb/>rapidissimi torrentis, intra spongiosas carnium et viscerum porositates im&shy;<lb/>mittitur &rdquo; (ibi, pag. </s>

<s>85). </s></p><p type="main">

<s>Consegue altres&igrave; da quella sopra citata legge fondamentale delle quan&shy;<lb/>tit&agrave; in relazione colle velocit&agrave; e colle sezioni, ch'essendo le velocit&agrave; o i tempi <lb/>uguali, le quantit&agrave; tornano proporzionali alle semplici sezioni. </s>

<s>Trov&ograve; anche <lb/>questo corollario un'applicazione ai moti animali, avendolo il Borelli pre&shy;<lb/>messo come lemma alla proposizione CXCVII, nella quale vuol dimostrare <lb/>come la quantit&agrave; del sangue, ch'esce dalla vena splenica, &egrave; presso a poco <lb/>la quarta parte del fluido, che nel tempo di una intera circolazione viene <lb/>espulso dalla vena mesenterica. </s></p><p type="main">

<s>Il lemma dunque, che si premette dal Borelli in servigio di dimostrar <lb/>la citata proposizione, &egrave; cos&igrave; formulato: Da due fistole molli inegualmente <lb/><figure id="id.020.01.1239.1.jpg" xlink:href="020/01/1239/1.jpg"/></s></p><p type="caption">

<s>Figura 6.<lb/>ampie, ugualmente turgide, e dalla stessa potenza compresse, <lb/>fluiscono nello stesso tempo due moli ineguali, che hanno <lb/>fra loro la proporzione stessa degli orifizi. </s>

<s>E ci&ograve; appunto per <lb/>questa ragione: &ldquo; quia duae fistulae humore plenae ab eadem <lb/>potentia, scilicet ab eadem vi impulsiva, eodemque tempore <lb/>comprimuntur, ergo eodem impetu et eadem velocitate ex&shy;<lb/>primuntur, et exiliunt fluores ex orificiis AC, DF (fig. </s>

<s>6). <lb/>Sed moles fluidae, effusae eadem velocitate eodemque tem&shy;<lb/>pore, eamdem proportionem habent quam orificia,.... ergo <lb/>moles fluidi egressa ex fistula AB, ad eam quae profluit ex <lb/>DE, se habet ut orificium AC ad DF &rdquo; (ibi, pag. </s>

<s>405). </s></p><p type="main">

<s>La nuova via aperta cos&igrave; dal celebratissimo Maestro in&shy;<lb/>vitava a proseguirla alacremente i discepoli, uno de'pi&ugrave; stu&shy;<lb/>diosi fra i quali fu, come sappiamo, il Bellini. </s>

<s>Gli esercizi <lb/>dell'arte medica, fra'quali era d'uso frequente la flebotomia, facevangli fa&shy;<lb/>cilmente risovvenir, fra gli zampilli del sangue, degli zampilli delle acque <lb/>da'fori aperti ne'vasi, e le emissioni sanguigne diligentemente raccolte e <lb/>ridotte a giusta misura, secondo l'abito degli infermi e le condizioni della <lb/>malattia, potevano in questi casi direttamente condurre un Iatromatematico <lb/>dell'indole del Nostro a fare, intorno al sangue raccolto ne'salassi, l'ufficio <lb/>sperimentale dell'Idrometra. </s></p><pb xlink:href="020/01/1240.jpg" pagenum="115"/><p type="main">

<s>La quantit&agrave; del sangue emesso, ripensava il Bellini tutto piena la mente <lb/>di quelle applicazioni delle leggi idrauliche alla Fisiologia, che aveva appresa <lb/>dalla viva voce del Borelli; dipende dalla velocit&agrave; moltiplicata per la sezione. </s>

<s>E <lb/>perch&egrave; questa, aperta che sia la vena, riman nel tempo del flusso sempre la <lb/>stessa, &egrave; dunque la velocit&agrave; unica regolatrice della quantit&agrave; di quel flusso. </s>

<s>Or <lb/>egli considerava come non era possibile che tutto il sangue uscito in un dato <lb/>tempo dalla ferita, fosse uguale a quello, che sarebbe passato in quel mede&shy;<lb/>simo tempo per la vena chiusa, procedendo a diritto per la sua via: la quan&shy;<lb/>tit&agrave; gli pareva dover esser maggiore, e ci&ograve; necessariamente importava una <lb/>maggior velocit&agrave; nel sangue stesso, che d'ogni parte affluisce al varco aperto. </s></p><p type="main">

<s>Forse il rassomigliar che faceva il Borelli il circolo sanguigno a un <lb/>pieno e rapidissimo torrente dette occasione al Bellini di considerar ci&ograve; che <lb/>segue, rompendosi l'argine ai fiumi, e di rassomigliarne a quelli della rotta <lb/>vena gli effetti. </s>

<s>In qualunque modo il Guglielmini, annoverando per primo <lb/>tra quegli effetti <emph type="italics"/>Lo scemarsi repentino della piena nelle parti superiori <lb/>del fiume,<emph.end type="italics"/> dop'aver detto esser la ragion di ci&ograve; che le ripe, facendo resi&shy;<lb/>stenza, indugiano il corso dell'acqua, la quale perci&ograve; tolti quegl'impedimenti <lb/>si rende anche nelle parti superiori necessariamente pi&ugrave; veloce, cos&igrave; sog&shy;<lb/>giunge: &ldquo; Effetto simile &egrave; stato dimostrato dal signor Lorenzo Bellini, in&shy;<lb/>signe medico e matematico fiorentino e famosissimo per le sue opere rice&shy;<lb/>vute dal mondo con tanto applauso, dovere succedere nella cavata del san&shy;<lb/>gue dalle vene e dalle arterie degli animali, avendo una grande analogia il <lb/>corso del sangue per li proprii vasi a quello dell'acque per gli alvei dei <lb/>fiumi, ed equivalendo l'apertura della vena alla rottura di un argine, siccome <lb/>con questo simbolizzano le tuniche de'vasi predetti &rdquo; (Della natura de'fiumi, <lb/>Vol. </s>

<s>II, Milano 1821, pag. </s>

<s>172). </s></p><p type="main">

<s>Fra le opere del Bellini, ricevute dal mondo con tanto applauso, prin&shy;<lb/>cipale si &egrave; quella che intitol&ograve; <emph type="italics"/>De sanguinis missione,<emph.end type="italics"/> distinta in proposi&shy;<lb/>zioni, per conformarsi anche nelle parti accessorie ai metodi dimostrativi del <lb/>Borelli. </s>

<s>&Egrave; nella prima di quelle proposizioni, che si dimostra il velocitarsi <lb/>del circolo per l'aperta vena, concludendo la dimostrazione dal principio che <lb/>la quantit&agrave; del sangue fluente dalla ferita &egrave; maggiore di quella che passe&shy;<lb/>rebbe in egual tempo addiritto per la vena illesa, e per l'arteria contigua. <lb/></s>

<s>&ldquo; A quacumque vena mittatur sanguis, per totum spatium temporis quo <lb/>mittitur, quantitates eius singulis contractionibus cordis influens in truncum <lb/>arteriae, cuius aliquis ramus continuus sit venae a qua mittitur sanguis; <lb/>maiorem proportionem habet ad quantitatem eodem tempore influentem in <lb/>truncum alterum, quam quantitates eodem tempore in eosdem truncos homo&shy;<lb/>loge influentes, quando nihil sanguinis mittitur, sed totus fluit per canales <lb/>suos &rdquo; (Opera omnia, Pars I, Venetiis 1708, pag. </s>

<s>64). </s></p><p type="main">

<s>La maggior quantit&agrave; del sangue emesso, rispetto a quello che proce&shy;<lb/>derebbe per i suoi canali addiritto, non poteva, secondo la legge del Ca&shy;<lb/>stelli, dipendere da altro che da un incremento della velocit&agrave;, e perci&ograve; bi&shy;<lb/>sognava ritrovar la causa di questo incremento, perch&egrave; venisse dimostrata <pb xlink:href="020/01/1241.jpg" pagenum="116"/>la verit&agrave; della proposizione. </s>

<s>Considerava a tale effetto il Bellini che le tu&shy;<lb/>niche venose fanno resistenza al sangue, no nei soli punti adiacenti, ma in <lb/>quelli altres&igrave; che li precedono: e no nelle vene sole, ma e nelle diramazioni <lb/>delle arterie influenti, nelle quali il sangue fa uno sforzo continuo sul san&shy;<lb/>gue che precede; sforzo ch'esce poi in azione di libero moto, quando aperta <lb/>la vena le resistenze opposte sono in parte diminuite. </s></p><p type="main">

<s>&ldquo; Quoniam sanguis fluens per arterias mittitur in sanguinem fluentem <lb/>per venas, et sanguis per venas praecedens impedimento est sanguini per <lb/>easdem succedenti; amoto igitur impedimento succedenti per venas sanguini, <lb/>idem sanguis continue per venas succedens fluet velocius, adeoque sanguis <lb/>per arterias in ipsum nitens, quoties impedimentum illud remotum erit, mi&shy;<lb/>norem resistentiam a sanguine venarum patietur. </s>

<s>Sed facto emissario in qua&shy;<lb/>libet vena, ita ut sanguis possit effluere et reipsa effluat, fit, ut sanguini <lb/>per venas succedenti nihil obsistat sanguis per easdem praecedens, cum liber <lb/>illi pateat effluxus in nihil repugnantem aera; facto igitur in qualibet vena <lb/>emissario, sanguis per arterias in venis continuas fluens et in earumdem <lb/>sanguinem nitens, minori resistentiae occurret. </s>

<s>Est autem sanguis per omnes <lb/>arterias sibi ipsi continuus, et succedens per ipsas nititur in praecedentem. </s>

<s><lb/>Igitur nisus sanguinis fluentis per arterias omnes continuus est in sangui&shy;<lb/>nem fluentem per venas quaslibet, adeoque, facto emissario in vena quali&shy;<lb/>bet, ita ut sanguis effluat, minuetur resistentia, non solum sanguini per <lb/>summas arterias venae illi continuas, sed per earumdem ramos maiusculos, <lb/>maiores, ac demum truncum ad usque cor &rdquo; (ibi, pag. </s>

<s>65). </s></p><p type="main">

<s>Ritrovarono queste applicazioni iatromatematiche del Bellini tanto ap&shy;<lb/>plauso, segnatamente appresso i medici, che altri valorosi si sentirono ani&shy;<lb/>mati a proseguire per que'sentieri, per i quali il Borelli aveva con tanta <lb/>gloria avviata la sua nuova scuola. </s>

<s>Il Guglielmini, infin da quando pubbli&shy;<lb/>cava la sua prima opera idraulica <emph type="italics"/>Aquarum fluentium mensura,<emph.end type="italics"/> promet&shy;<lb/>teva ai lettori che avrebbe trasportate quelle sue considerazioni &ldquo; al moto <lb/>s&igrave; naturale come violento de'fluidi tutti, oltre i confini delle Matematiche, <lb/>sino cio&egrave; alli studi pi&ugrave; ascosi dell'arte medica &rdquo; (Prefazione al Trattato nella <lb/>raccolta degli Idraulici, T. I, Firenze 1765, pag. </s>

<s>317). E nel trattato <emph type="italics"/>Della <lb/>natura de'fiumi,<emph.end type="italics"/> dopo aver commemorate le somiglianze che riscontr&ograve; il <lb/>Bellini tra l'accelerarsi della piena, rotto l'argine, e l'accelerarsi del san&shy;<lb/>gue aperta la vena &rdquo; il che ho voluto, soggiunge, in questo luogo motivare, <lb/>acci&ograve; paia non essere cos&igrave; disparate le dottrine idrostatiche dalle mediche, <lb/>anco pratiche, come altri per avventura si crede, anzi essere affatto neces&shy;<lb/>sarie le prime a chi vuol bene intendere in molte parti le seconde, come <lb/>spero di far vedere a suo tempo, applicando molte notizie desunte da que&shy;<lb/>sto Trattato alla Fisiologia medica ed alla dottrina de'mali particolari &rdquo; <lb/>(Tomo cit., pag. </s>

<s>172, 73). Nel 1701 infatti, mantenendo le sue promesse, <lb/>pubblicava il trattato <emph type="italics"/>De sanguinis natura,<emph.end type="italics"/> dove alcune delle leggi princi&shy;<lb/>pali che governano il moto delle acque sono applicate, come rilevasi dagli <lb/>stessi luoghi da noi dianzi riferiti, al moto del sangue. </s></p><pb xlink:href="020/01/1242.jpg" pagenum="117"/><p type="main">

<s>Della splendida triade iatromatematica composta del Borelli, del Bellini <lb/>e del Guglielmini, si gloriava compiacente la scienza italiana, quando la cri&shy;<lb/>tica inesorabile venne a turbare la tranquillit&agrave; di quella compiacenza. </s>

<s>Pie&shy;<lb/>ranton Michelotti, che fu di tanta autorit&agrave; in quella stessa Scuola, ammirava <lb/>gli egregi studi di que'tre, ch'ei chiama <emph type="italics"/>Italorum medicorum principes,<emph.end type="italics"/><lb/>ma poi soggiunge: &ldquo; Verum plura ab ipsis praetermissa, quaedam non ani&shy;<lb/>madversa, quaedam imperfecte tractata, et nonnulla non rite fuisse deter&shy;<lb/>minata quilibet experiri poterit, cui fuerit in animo motiones fluidorum <lb/>omnium per canales animantium haudquaquam aequabiles, sed mille modis <lb/>variantes, geometrico mechanica methodo pervestigare &rdquo; (De separat. </s>

<s>liquid. </s>

<s><lb/>cit., pag. </s>

<s>82). E concludeva che, a voler trattare e per arte di computo <lb/>svolgere il difficile tema &ldquo; desunt experimenta, sive sufficientia data &rdquo; (ibi, <lb/>pag. </s>

<s>82). </s></p><p type="main">

<s>La critica del Michelotti non riguardava dunque altro che la scienza in <lb/>s&egrave; stessa, o nel metodo geometrico meccanico delle sue speculazioni. </s>

<s>Ma per&shy;<lb/>ch&egrave; quelle speculazioni erano applicabili, e da alcuni applicate di fatto agli <lb/>usi medici, al dubbio degli errori innocenti della mente s'aggiungeva il pe&shy;<lb/>ricolo dei danni alla salute e alla vita degli uomini. </s>

<s>Nel Filosofo insomma <lb/>era zelo del vero, mentre nel Medico era un coscienzioso dovere di esami&shy;<lb/>nare le novelle dottrine, e specialmente quelle che proponeva il Bellini. </s></p><p type="main">

<s>Se infatti &egrave; vero che si acceleri nel salasso il corso del sangue, anche <lb/>per le arterie corrispondenti alla vena incisa, posto che le malattie infiamma&shy;<lb/>torie, alle quali riducevansi la frenesia e la pleurisia, sien malattie delle ar&shy;<lb/>terie, avrebbe avuto buon fondamento la speranza del Boerhaave e de'se&shy;<lb/>guaci di lui, che aprendosi una vena si provocasse il corso del sangue <lb/>ristagnante nella parte infiammata, e cos&igrave; disostruendosi le estremit&agrave; arte&shy;<lb/>riose restituire al sangue stesso la sua fluidit&agrave; primitiva. </s>

<s>Ma se il teorema <lb/>belliniano &egrave; falso, la cura del Boerhaave si comprendeva con facilit&agrave; che sa&shy;<lb/>rebbe per riuscir disutile, e anzi sempre pi&ugrave; o meno dannosa. </s></p><p type="main">

<s>L'occasione d'esaminar di proposito quanto fosse di vero nelle applau&shy;<lb/>ditissime dottrine del Bellini venne quando il Silva, in Parigi, sul fonda&shy;<lb/>mento di quelle stesse dottrine, pubblicava il suo trattato <emph type="italics"/>De la saign&eacute;e.<emph.end type="italics"/> Il <lb/>Quesnay, e una pi&ugrave; grande autorit&agrave; fisiologica e medica, il Senac, negarono <lb/>assolutamente che il sangue dalla vena incisa fluisca pi&ugrave; veloce, d'onde av&shy;<lb/>venne un gran dissidio fra i pratici della Facolt&agrave; medica parigina. </s></p><p type="main">

<s>In questo tempo l'Haller attendeva nella stessa Parigi agli esercizi del&shy;<lb/>l'Anatomia, e di tanta importanza gli parve, che si dette studiosamente a <lb/>cercare il modo di decidere la questione. </s>

<s>Conveniva bene col Michelotti che <lb/>non si sarebbe potuti giungere a quella cos&igrave; desiderata decisione finale, altro <lb/>che per via delle esperienze, ma come penetrare addentro a misurare il <lb/>moto del sangue, per le vie gelosamente chiuse dell'animale vivo? </s>

<s>Si ri&shy;<lb/>sovvenne allora che il Malpighi e il Lecuwenhoeck avevano pur veduto il <lb/>circolo del sangue attraverso ai vasi trasparenti delle rane e dei pesci, e <lb/>incor&ograve; di l&igrave; una viva speranza che i globuli del sangue, in cos&igrave; fatti ani-<pb xlink:href="020/01/1243.jpg" pagenum="118"/>mali, avrebbero potuto far l'ufficio e prestare i servigi dell'Idrometro a <lb/>galleggiante. </s></p><p type="main">

<s>Di qui ebbero occasione le due Memorie <emph type="italics"/>Sur le mouvement du sang,<emph.end type="italics"/><lb/>che risvegliarono nello Spallanzani il desiderio di nuove osservazioni, e fe&shy;<lb/>cero s&igrave; che si arricchisse di nuove e importantissime scoperte la scienza ita&shy;<lb/>liana. </s>

<s>L'Haller dunque sui vasi sanguiferi delle rane, e lo Spallanzani sui <lb/>vasi delle salamandre, verificarono con maraviglia universale in che il moto <lb/>del sangue sia conforme, in che difforme dalle leggi idrauliche, d'onde si <lb/>venne per l'uno a pronunziare e per l'altro a confermare questa sentenza, <lb/>che serv&igrave; di canone utilissimo alla nuova Fisiologia: &ldquo; Non ideo repudian&shy;<lb/>das leges crediderim, quibus extra corpus animale vires motrices regun&shy;<lb/>tur: id volo nunquam transferendas ad nostras animati corporis machinas, <lb/>nisi experimentum consenserit &rdquo; (Haller, Elem. </s>

<s>Physiol. </s>

<s>Praefatio, Lausan&shy;<lb/>nae 1757, pag. </s>

<s>VI). </s></p><p type="main">

<s>Procedendo dunque per questa sicura via sperimentale, dopo aver l'Hal&shy;<lb/>ler riferiti i nomi illustri di quei Francesi, che negarono fede al teorema <lb/>belliniano, &ldquo; Pour moi j'ai v&ucirc; tr&egrave;s souvent, et aussi souvent que je l'ai <lb/>voulu voir, puisque le resultat a toujours &ecirc;t&ecirc; le m&ecirc;me, j'ai v&ucirc;, disje, que <lb/>quelle que fut la directions du sang dans la veine que j'ouvrois, soit qu'il <lb/>allat naturellement du cot&eacute; du coeur, soit que par un mouvement retro&shy;<lb/>grade il fut port&eacute; vers les intestins, soit qu'il se balan&ccedil;at, ou qu'il fut en <lb/>repos, soit enfin qu'on eut arrach&eacute; le coeur, ou li&egrave;, ou coup&eacute; les aortes, le <lb/>sang dans tous ces cas sortoit de la veine coup&eacute;e, avec une vitesse beau&shy;<lb/>coup plus grande que celle qu'il a dans aucune veine entiere, et m&ecirc;me plus <lb/>vite qu'il ne par court les arteres &rdquo; (Lausanne 1756, pag. </s>

<s>99, 100). </s></p><p type="main">

<s>Questa verificazione per&ograve;, che l'Haller dice in nota essere stata fatta <lb/>pure dall'Heide, riguardava pi&ugrave; la scienza astratta che la pratica medica, <lb/>per la quale sarebbe stato assai pi&ugrave; importante il sapere se, come affermava <lb/>il Bellini, l'aumento della velocit&agrave; del sangue fluente dalla vena provocasse <lb/>una corrispondente velocit&agrave; nelle arterie. </s>

<s>Ma questa seconda verificazione, <lb/>dice lo stesso Haller, &egrave; pi&ugrave; difficile della prima a farsi per via dell'espe&shy;<lb/>rienze. </s>

<s>&ldquo; Leur resultat n'a pas toujours &eacute;t&eacute; le m&ecirc;me, et celle que j'ai faits <lb/>sur moi m&ecirc;me, ne repondit point &agrave; mon attente &rdquo; (ivi, pag. </s>

<s>106). </s></p><p type="main">

<s>Pi&ugrave; felice dell'Haller fu il nostro Spallanzani, il quale, sperimentando <lb/>sopra le salamandre piuttosto che sopra le rane, verific&ograve; del Teorema bel&shy;<lb/>liniano no quella parte sola che riguardava la scienza astratta, ma quella al&shy;<lb/>tres&igrave;, che pi&ugrave; importava alla pratica medica. </s>

<s>Nella Dissertazione quarta in&shy;<lb/>fatti <emph type="italics"/>Sui fenomeni della circolazione,<emph.end type="italics"/> esponendo i resultati dell'esperienze <lb/>fatte e descritte nella Dissertazion precedente, dice che vien per essi con&shy;<lb/>fermata una delle pi&ugrave; importanti verit&agrave; mediche, ed &egrave; questa: &ldquo; Aperta una <lb/>vena, il sangue di lei, quello delle vene vicine e quello dell'arteria che loro <lb/>somministra il sangue, acquista un novello grado di velocit&agrave;, e si precipita <lb/>alla ferita. </s>

<s>Cotal verit&agrave;, che dopo di essere stata scoperta dal celebre Bellini, <lb/>ha avuto tanti oppositori, &egrave; stata infine comprovata dal fatto, merc&egrave; le spe-<pb xlink:href="020/01/1244.jpg" pagenum="119"/>rienze del De Heide, ma assai pi&ugrave; dall'Haller nel mesenterio delle rane. </s>

<s><lb/>Imperocch&egrave; ferita una delle sue vene, la trasparenza delle membrane gli ha <lb/>conceduto di vedere quali cangiamenti nascono allora nella circolazione, ed <lb/>ha trovato essere que'dessi, ch'erano stati asseriti dal prelodato Bellini. </s>

<s><lb/>Quanto dunque ha scoperto l'Haller nel mesenterio delle rane ho avuto il <lb/>piacere di vederlo confermato ne'vasi delle salamandre, e quel che &egrave; pi&ugrave; <lb/>ne'vasi degli animali caldi, cio&egrave; del pulcino &rdquo; (Opere, Vol. </s>

<s>IV, Milano 1826, <lb/>pag. </s>

<s>418). </s></p><p type="main">

<s>Da queste osservazioni sopra gli animali caldi risulta principalmente <lb/>l'eccellenza del Nostro sopra il fisiologo di Berna, la quale eccellenza in tal <lb/>proposito si misura non solamente dall'aver veduto lo Spallanzani veloci&shy;<lb/>tarsi il sangue anche nell'arteria contigua alla vena incisa, ci&ograve; che l'Haller <lb/>confess&ograve; di non aver potuto sperimentare, ma dall'aver ne'varii casi parti&shy;<lb/>colari verificato se alle leggi idrauliche si conformava il moto del sangue, <lb/>secondo le speculazioni de'nostri Italiani. </s></p><p type="main">

<s>Il Borelli tenne, come vedemmo, per cosa certa che il sangue, restrin&shy;<lb/>gendosi la vena e riducendo alla met&agrave; la sua sezione, vi corresse doppiamente <lb/>veloce, a somiglianza di quel che vedesi fare all'acqua corrente ne'canali. </s>

<s><lb/>Lo Spallanzani, nella sua Dissertazione <emph type="italics"/>Dell'azione del cuore ne'vasi san&shy;<lb/>guigni,<emph.end type="italics"/> verific&ograve; il fatto in questo modo. </s>

<s>&ldquo; Avendo, egli stesso dice, un giorno <lb/>sott'occhio una vena del mesenterio formata di due rami, trovai esser que&shy;<lb/>sta, non so per qual vizio, ristretta talmente in un sito, che quantunque <lb/>prima e dopo il cilindro del sangue fosse assai grosso, pure ivi non ne potea <lb/>passare che un filetto alla volta. </s>

<s>In siffatta angustia il suo acceleramento si <lb/>facea tale, che appena l'occhio vi potea tener dietro. </s>

<s>All'opposito, passato <lb/>lo stretto, il sangue riacquistava il primiero movimento &rdquo; (ivi, pag. </s>

<s>127). </s></p><p type="main">

<s>Questo principio idraulico delle velocit&agrave; reciprocamente proporzionali <lb/>alle sezioni ebbe un'altra applicazione ai moti e alle funzioni del sangue, di <lb/>non lieve importanza nella storia della Fisiologia. </s>

<s>Guglielmo Cole, ripen&shy;<lb/>sando alle funzioni della nutrizione, la quale non &egrave; altro secondo lui &ldquo; nisi <lb/>congruae cuiusdam substantiae partibus in deperditae locum appositio &rdquo; in&shy;<lb/>cominci&ograve; a dubitare di quel che si credeva comunemente, che cio&egrave; la stessa <lb/>quantit&agrave; di sangue si contenesse ne'grossi tronchi e nelle ultime dirama&shy;<lb/>zioni arteriose, parendogli che non dovesse esser questa sufficiente a nutrir <lb/>le parti, e non avere il sangue stesso il tempo necessario per trattenersi a <lb/>dispensare a ciascuna il suo vitale alimento. </s></p><p type="main">

<s>Bench&egrave; fosse il Cole un inglese, egli ebbe pure molta familiarit&agrave; con <lb/>la scienza italiana, e trov&ograve; modo a risolvere i dubbi nelle dottrine apprese <lb/>dal trattato <emph type="italics"/>Della misura delle acque correnti.<emph.end type="italics"/> Ivi, al corollario XI, scopre <lb/>il Castelli l'errore, in che era incorso Giovanni Fontana, il quale, avendo <lb/>fatto misurar tutti i fossi e i fiumi che mettevano al Tevere, e avendo tro&shy;<lb/>vato che la somma delle loro sezioni era doppia di quella del Tevere stesso <lb/>al ponte Quattrocapi, ne aveva concluso che si dovesse render doppiamente <lb/>largo l'alveo del fiume, perch&egrave; potesse in ogni caso ricever la piena. </s>

<s>Il Ca-<pb xlink:href="020/01/1245.jpg" pagenum="120"/>stelli notava che l'errore dell'Architetto romano consisteva nel credere che <lb/>le misure dell'acque, prese negli alvei de'fossi e de'fiumi, dovessero man&shy;<lb/>tenersi le medesime nel Tevere, mentre &egrave; il vero che &ldquo; se l'aeque ridotte <lb/>nel Tevere crescono di velocit&agrave;, scemano di misura &rdquo; (Bologna 1660, pag. </s>

<s>16). </s></p><p type="main">

<s>Ora il Cole, applicando queste dottrine al moto del sangue nelle arte&shy;<lb/>rie, ne concludeva che la somma delle sezioni de'rami dovess'esser mag&shy;<lb/>giore della sezione del tronco principale. </s>

<s>Congetturava inoltre che avesse <lb/>provveduto, con s&igrave; fatto artificio, la sapiente Natura ad aumentar la misura <lb/>del sangue ne'vasi capillari, e a rattemperare i primi impeti ricevuti dal <lb/>cuore, per modo da poter con pace dispensare alle parti il necessario ali&shy;<lb/>mento. </s>

<s>&ldquo; Isthaec vero vitari possunt incommoda supposito quod vasorum <lb/>istorum capillaria, proportione ad truncum aucta, fabricavit Natura: satis <lb/>enim placide sic movebitur sanguis ut adhibita singulis partibus esca sup&shy;<lb/>peditetur &rdquo; (De secretione anim., Oxon. </s>

<s>1674, pag. </s>

<s>101). </s></p><p type="main">

<s>Il supposto del Cole era dunque fondato sopra ci&ograve; che sapeva essere <lb/>stato osservato sui fiumi, e il Guglielmini, che aveva ridotte quelle osserva&shy;<lb/>zioni a regola generale, sentenziando che &ldquo; se si misureranno le larghezze <lb/>di tutti i fiumi, che unendosi formano un fiume maggiore, si trover&agrave; infal&shy;<lb/>libilmente che esse insieme unite supereranno quella del fiume maggiore &rdquo; <lb/>(Della natura de'fiumi cit., Vol. </s>

<s>II, pag. </s>

<s>120) non dubit&ograve;, trasportando la <lb/>legge idraulca al moto del sangue, di approvare per vere le dottrine del Fi&shy;<lb/>siologo inglese. </s>

<s>&Egrave; anzi da notare, a questo proposito, come sembrasse allo <lb/>stesso Guglielmini tanto pi&ugrave; certo il fatto del diminuirsi la velocit&agrave;, come <lb/>pi&ugrave; il sangue si dilunga dal cuore, che da ci&ograve; conclude dover essere la se&shy;<lb/>zion dell'Aorta minore delle sezioni dei rami arteriosi tutte sommate in&shy;<lb/>sieme. </s>

<s>&ldquo; Cum eaeteri violenti motus, quo magis a movente elongantur, eo <lb/>semper languidiores fiant,.... sequitur velocitatem sanguinis semper debi&shy;<lb/>liorem evadere, quo sanguis longius a corde spatium emensus est, unde in <lb/>arteriarum finibus languidissimus erit sanguinis circulantis motus. </s>

<s>Cumque, <lb/>ex Hydrometricis, fluentium liquorum sectiones debeant velocitatibus esse <lb/>reciprocae, oritur, ut quam rationem habet velocitas versus cor ad veloci&shy;<lb/>tatem in extremis arteriarum, eamdem habere debeant omnia oscula extre&shy;<lb/>marum arteriarum, simul sumpta, ad sectionem Aortae prope cor. </s>

<s>Ideoque <lb/>si, ut ostensum est, velocitas sanguinis in finibus arteriarum longe minor <lb/>est velocitate eiusdem in Aorta prope cor, necessar&igrave;o omnia oscula arteria&shy;<lb/>rum simul sumpta multo ampliora erunt orificio, aut sectione Aortae prope <lb/>cor, ut optime ex aliis rationibus colligit Guglielmus Cole, in libro <emph type="italics"/>De se&shy;<lb/>cretione animali &rdquo;<emph.end type="italics"/> (De sang. </s>

<s>nat. </s>

<s>cit., pag. </s>

<s>19). </s></p><p type="main">

<s>Questo processo dimostrativo del Guglielmini rende ragione dell'ordine, <lb/>che presero gli studi sperimentali de'Fisiologi posteriori, i quali, tenendosi <lb/>certi che il sangue si velociti come tutti gli altri fluidi in ragion reciproca <lb/>delle sezioni, si rivolsero tutti a ricercar s'era vero, e in qual precisa pro&shy;<lb/>porzione aumentassero le luci de'rami arteriosi, rispetto a quella della grande <lb/>Aorta. </s>

<s>Il Keill, prendendo a fondamento delle sue esperienze e de'suoi cal-<pb xlink:href="020/01/1246.jpg" pagenum="121"/>coli i vasi dello scheletro, da Guglielmo Cowper ripieni di cera, trov&ograve;, come <lb/>lasci&ograve; scritto nel IV de'suoi <emph type="italics"/>Tentamina<emph.end type="italics"/> &ldquo; arteriae cuiusvis ramos simul <lb/>sumptos ipsa arteria maiores esse &rdquo; (Lucae 1756, pag. </s>

<s>90). Quanto alle pro&shy;<lb/>porzioni di questa maggioranza &ldquo; Aortae ratio, egli scrive, ad ramos trunco <lb/>suo immediate propagatos, est ut 100,000 ad 120,740, et quasi Naturae pro&shy;<lb/>posito in bilis secretione haud sufficeret haec ratio, arteriam mesentericam <lb/>multo magis superant sui rami. </s>

<s>Huius arteriae medium Mesenterium tran&shy;<lb/>seuntis, et unum et viginti ramos emittentis talis est forma, interque trun&shy;<lb/>cum et ramos sequentes rationes obtinere deprehendi &rdquo; (ibi). E dopo aver <lb/>qui ordinata una tavoletta numerica &ldquo; Ex his rationibus palet, egli sog&shy;<lb/>giunge, ramorum summam arteriae mesentericae truncum plus duplo axce&shy;<lb/>dere, adeoque in his suae velocitatis dimidium amittit sanguis &rdquo; (ibi, pag. </s>

<s>100). </s></p><p type="main">

<s>Che se questa &egrave; la maggior diminuzione trovata, par che s'ingannas&shy;<lb/>sero il Cole e il Guglielmini a credere che il sangue nelle estremit&agrave; arte&shy;<lb/>riose <emph type="italics"/>languidissimus erit.<emph.end type="italics"/> L'Hales poi tenne altra via, e iniettando nelle <lb/>arterie di un cadavere l'acqua, la quale si vedeva nelle diramazioni perdere <lb/>una notabile parte della sua prima velocit&agrave;, ne congetturava che maggiore <lb/>dovess'essere quella perdita subita dal sangue. </s>

<s>&ldquo; Quindi vediamo, cos&igrave; con&shy;<lb/>clude dalle sue esperienze intorno alle arterie de'muscoli, quanto la velo&shy;<lb/>cit&agrave; dell'acqua si scema, quando questa dal tronco di un'arteria grande passa <lb/>a scorrere nelle sue ramificazioni di diverso ordine, nonostante che la somma <lb/>delle sezioni di questi rami sia molto maggiore delle sezioni del loro tronco. </s>

<s><lb/>La velocit&agrave; del sangue dee dunque in tal passaggio maggiormente scemarsi, <lb/>perch&egrave; questo fluido &egrave; molto pi&ugrave; dell'acqua grosso e viscoso, ma dee sopra <lb/>tutto la velocit&agrave; del sangue scemarsi, per cagione delle divisioni rettango&shy;<lb/>lari delle arteriuzze, il cui diametro giunge ad essere di una sola mille se&shy;<lb/>cen ventesima parte di pollice, di maniera che i globetti del sangue non pos&shy;<lb/>sono passarvi pi&ugrave; che uno per volta &rdquo; (Statica anim. </s>

<s>cit., pag. </s>

<s>62). </s></p><p type="main">

<s>Erano anche questi per&ograve; sentieri tentati al buio, che si riconobbero <lb/>tortuosi, quando venne a sicura guida del passo la chiara luce degli occhi. </s>

<s><lb/>Nella dissertazion I De'fenomeni della circolazione, lo Spallanzani scriveva <lb/>cos&igrave; sotto l'esperienza XXI: &ldquo; In pi&ugrave; salamandre sonomi singolarmente pre&shy;<lb/>fisso di osservare se il sangue, in passando dai tronchi polmonari ai rami, <lb/>scema di velocit&agrave;, ed ho trovato che no, qualunque siasi l'angolo del ramo <lb/>col tronco &rdquo; (Opere cit., T. IV, pag. </s>

<s>175). E perch&egrave; lo Spallanzani stesso <lb/>ci faceva di sopra veder con gli occhi che anche il sangue, passando attra&shy;<lb/>verso alle angustie di un vaso, velocit&agrave; come l'acqua il suo moto, si do&shy;<lb/>vrebbe egli forse dubitare della verit&agrave; del teorema del Cole, o della esattezza <lb/>dell'esperienze e dei calcoli del Keill? </s>

<s>Ma &egrave; pure lo Spallanzani che di quella <lb/>verit&agrave; e di quella esattezza ci assicura, nell'appresso esperienza XXXIII, di&shy;<lb/>cendo che anche nelle arterie mesenteriche delle salamandre osservate &ldquo; la <lb/>somma de'lumi ne'rami &egrave; sempre maggiore del lume del loro tronco &rdquo; (ivi, <lb/>pag. </s>

<s>184). </s></p><p type="main">

<s>L&agrave; dunque il sangue si conforma alle leggi idrauliche, e qui rompe <pb xlink:href="020/01/1247.jpg" pagenum="122"/>l'ordine di quelle leggi. </s>

<s>Ma vi sono di ci&ograve; altri notabili esempii. </s>

<s>Il Gugliel&shy;<lb/>mini fu primo a congetturare che il sangue, verso il centro della sezion di <lb/>un suo vaso, dovess'essere pi&ugrave; veloce che presso alla circonferenza, per <lb/>l'esempio di ci&ograve; che si vede fare all'acque correnti ne tubi, le pareti dei <lb/>quali indugiano al liquido il moto, per via degli attriti. </s>

<s>Or venne a confer&shy;<lb/>mare una tal congettura l'oculata osservazione dei fatti. </s>

<s>&ldquo; L'ampiezza dei <lb/>vasi medii venosi del Mesenterio, scriveva lo Spallanzani nella citata disser&shy;<lb/>tazione Dell'azion del cuore ne'vasi sanguigni, rivolgendo all'Heller il suo <lb/>discorso; mi diede agio di esaminare un problema, che ha esercitata la vo&shy;<lb/>stra industria. </s>

<s>Ei concerne il sapere se pi&ugrave; rapido sia il movimento del san&shy;<lb/>gue lungo l'asse dei vasi, che ai lati, come trovato avete da alcune vostre <lb/>esperienze. </s>

<s>La colonna sanguigna, siccome assai ampia, poteva essere oppor&shy;<lb/>tunissima al caso, ma qui pure &egrave; mestiere prendere il destro, in cui la Na&shy;<lb/>tura parla all'osservatore. </s>

<s>Essendo il circolo del sangue vigorosissimo, la <lb/>rapidit&agrave; dei globetti &egrave; tale, che l'occhio quantunque attentissimo non pu&ograve; <lb/>notare se siavi tal differenza. </s>

<s>Bisogna dunque aspettare che si calmi un poco <lb/>il suo impeto. </s>

<s>Allora veramente comincia a scoprirsi che il sangue dell'asse <lb/>gode di un movimento un po'poco maggiore che quello dei lati. </s>

<s>Ma per <lb/>averne il netto, con pi&ugrave; sicurezza, fa d'uopo aspettare che la sua cor&shy;<lb/>rente divenga lentissima. </s>

<s>Allora non pu&ograve; cader dubbio su tal verit&agrave; &rdquo; (ivi, <lb/>pag. </s>

<s>125, 26). </s></p><p type="main">

<s>Non essendovi dunque dubbio che l'attrito del sangue contro le pareti <lb/>dei vasi ne indugia il moto, chi non giurerebbe che un uguale attrito, e <lb/>perci&ograve; un simile indugio, non dovess'esser prodotto da quel cos&igrave; spesso e <lb/>repentino mutar via di quegli stessi vasi? </s>

<s>Raccogliendo la quantit&agrave; di <lb/>acqua fluita da due uguali lunghezze e luci di tubi, ma l'uno diritto e <lb/>l'altro ritorto, si trova che in ugual tempo il l&igrave;quido erogato da questo &egrave; <lb/>minore dell'altro, segno evidentissimo dell'accresciuta resistenza, per l'at&shy;<lb/>trito maggiore incontrato in quelle sinuosit&agrave;, per cui indugiasi maggior&shy;<lb/>mente il moto. </s>

<s>Chi dunque s'aspettava per cosa certa che cos&igrave; pure dovesse <lb/>avvenire, per la resistenza incontrata dal sangue nelle curvature de'vasi, <lb/>sarebbe tolto d'inganno da questa e da altre esperienze dello Spallanzani: <lb/>&ldquo; Un'arteriuzza, egli dice delle salamandre osservate, veniva gi&ugrave; per il me&shy;<lb/>senterio, facendo da undici in dodici curvature, ed un suo delicatissimo ramo <lb/>si stendeva alla regione degli intestini, su cui si diramava in altri pi&ugrave; esili, <lb/>non conducenti ciascuno che una serie di globetti. </s>

<s>Questi ultimi ramicelli, <lb/>col ripiegar verso il mesenterio, generavano una vena, la quale diveniva un <lb/>ramo di una maggiore, che varcato il mesenterio, riconduceva il sangue al <lb/>cuore: le curvature nulla toglievano di velocit&agrave; al sangue &rdquo; (ivi, pag. </s>

<s>193). <lb/>E pi&ugrave; sotto dice risultare da un'altra esperienza &ldquo; che ad onta di venticin&shy;<lb/>que rivolgimenti, che fa una venina posta su di un budello, il sangue non <lb/>rallenta punto il moto &rdquo; (ivi, pag. </s>

<s>199). </s></p><p type="main">

<s>Parecchie altre bellissime osservazioni in proposito si potrebbero rac&shy;<lb/>cogliere da quelle CLXVI, di che l'insigne professor di Pavia arricch&igrave; la <pb xlink:href="020/01/1248.jpg" pagenum="123"/>sua prima dissertazione <emph type="italics"/>De'fenomeni della circolazione osservata nel giro <lb/>universale dei vasi,<emph.end type="italics"/> ma giova piuttosto trattenersi a meditar sulla conclu&shy;<lb/>sione ultima, ch'egli trae sapientemente dai numerosi fatti sperimentali. </s></p><p type="main">

<s>&ldquo; Il resultato, egli dice, di questi e degli antecedenti fatti mette dun&shy;<lb/>que in buon lume la teoria concernente il genuino andamento del sangue <lb/>dal principio delle arterie, fino alle loro estremit&agrave;, la qual teoria, siccome <lb/>per l'addietro mancante delle necessarie osservazioni, non &egrave; maraviglia se <lb/>&egrave; stata fino al presente poco pi&ugrave; che congetturale, e conseguentemente sot&shy;<lb/>toposta all'incomodo delle dispute. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Da questi fatti ridonda pure un altro vantaggio, cio&egrave; la conferma di <lb/>quanto saviamente stabilisce l'Haller intorno al diffidare dell'applicazione <lb/>de'principii idraulici al corpo animale, mancandovi l'appoggio dell'espe&shy;<lb/>rienza confermatrice. </s>

<s>E di vero se questi principii qui avessero dominato, <lb/>come non dovevano le menzionate cagioni ritardare considerabilissimamente <lb/>la corrente sanguigna, a quel modo che considerabilissimamente ritardano i <lb/>fluidi scorrenti per entro i canali? </s>

<s>Non &egrave; gi&agrave; che tali cagioni, anche nel <lb/>corpo animale, non producano, quanto &egrave; ad essa, ritardamento nel sangue, <lb/>ma dir bisogna che questo ritardamento venga sminuito da contrarie cagioni <lb/>residenti ne'vasi animali, e concorrenti ad accrescere il moto del sangue, <lb/>qualunque poi esse sieno, le quali cagioni non hanno luogo ne'canali idrau&shy;<lb/>lici &rdquo; (ivi, pag. </s>

<s>288, 89). </s></p><p type="main">

<s>In queste ultime parole si compendia il pi&ugrave; sapiente giudizio, che sia <lb/>stato mai dato dalla Scuola iatromatematica, la quale non si avvide che la <lb/>vita sublima, diciam cos&igrave;, nelle sue alture i fatti fisici da trasformarne bene <lb/>spesso la prima loro natura. </s>

<s>Giova inoltre considerare, nel nostro particolar <lb/>proposito, che il moto dell'acqua ne'tubi &egrave; naturale, ossia non soggetto che <lb/>alle sole leggi di gravit&agrave;, mentre il moto del sangue &egrave; violento, governato <lb/>dalle forze vitali di quella macchina maravigliosa, che appellasi Cuore. </s>

<s>E <lb/>un'ultima considerazione da farsi, e pi&ugrave; importante di tutte, &egrave; questa: che <lb/>ne'fatti fisici il soggetto dell'esperienza &egrave; sempre una materia definita, o <lb/>acqua o aria, o insomma qualche altra trattabile sostanza, mentre ne'fatti <lb/>fisiologici tante sottilissime essenze, da noi, per non saperne altro, chiamate <lb/>eteree, e dalle quali efficientemente dipendono le funzioni animali, sono sco&shy;<lb/>nosciute, perch&egrave; affatto sfuggevoli ai nostri sensi, d'onde hanno origine i <lb/>misteri della vita, e d'onde &egrave; derivata la sentenza, che umilia l'orgoglio <lb/>de'Filosofi, ed &egrave; che que'misteri all'uomo non saranno mai rivelati. </s></p><pb xlink:href="020/01/1249.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Del circolo del sangue<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Del circolo polmonare. </s>

<s>&mdash; II. </s>

<s>Del circolo universale. </s>

<s>&mdash; III. </s>

<s>Delle esperienze e delle osservazioni, <lb/>che dimostrano la verit&agrave; del circolo universale. </s>

<s>&mdash; IV. </s>

<s>Del sistema arveiano in Italia, e della <lb/>trasfusione del sangue. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Chi torna addietro sul capitolo precedente, e la variet&agrave; delle cose ivi <lb/>discorse comprende in uno sguardo solo, ritrova che s'incominciava la sto&shy;<lb/>ria de'moti del cuore con Ippocrate, il quale rassomigliava il viscere a una <lb/>fonte perenne, da cui scaturiscono i fiumi del sangue a irrigare tutto il <lb/>corpo dell'animale, e si terminava pure col rassomigliare lo stesso sangue <lb/>ai fiumi, che scorrono dentro i loro alvei ristretti, ora con qualche variet&agrave;, <lb/>e ora con perfetta uniformit&agrave; di leggi. </s>

<s>Aristotile, anzi altri Scrittori pi&ugrave; an&shy;<lb/>tichi, e per i divini inspirati concetti ben assai pi&ugrave; autorevoli, vedevano in <lb/>quel perpetuo correre de'fiumi un perpetuo ricircolare di moti, essendo che <lb/>vanno le loro acque a scender nel mare, dove non hanno pace, ma solle&shy;<lb/>vate in vapori per l'aria, di lass&ugrave; cadono, per andare a correre nuovamente <lb/>ne'fiumi. </s></p><p type="main">

<s>Il simbolico pensier degli antichi venne a incarnarsi, tanti secoli dopo, <lb/>nella mente di Guglielmo Harvey, quando rappresentandosi per l'acqua cor&shy;<lb/>rente ne'fiumi il sangue, che corre dentro le vene, e pel mare rappresen&shy;<lb/>tandosi il cuore, da cui, al calor della vita, si solleva lo stesso sangue, per <lb/>tornar, come l'acqua sollevata dal calor del sole, alla sua origine prima; <lb/>esult&ograve; d'aver ritrovato che la Natura, nel gran mondo delle Meteore e nel <lb/>piccolo mondo animale, somigliava nell'operare a s&egrave; stessa, e quel mede-<pb xlink:href="020/01/1250.jpg" pagenum="125"/>simo nome di <emph type="italics"/>circolo<emph.end type="italics"/> dagli antichi imposto al perpetuo moto dell'acqua che <lb/>irriga la Terra, lo applic&ograve; al perpetuo moto del sangue, che irriga agli ani&shy;<lb/>mali le membra. </s>

<s>&ldquo; Quem motum <emph type="italics"/>circularem<emph.end type="italics"/> eo pacto nominare liceat, quo <lb/>Aristoteles aerem et pluviam circularem superiorum motum aemulatus est. </s>

<s><lb/>Terra enim madida a Sole calefacta evaporat: vapores sursum elati conden&shy;<lb/>sant: condensati in pluvias rursum descendunt, terram madefaciunt, et hoc <lb/>pacto sunt hic generationes et similiter tempestatum et metereorum ortus, <lb/>a Solis circulari motu accessu et recessu &rdquo; (De motu cordis cit., pag. </s>

<s>56). <lb/>E che altro &egrave; in fatti il Cuore, prosegue a dire l'Harvey, se non che <emph type="italics"/>Sol <lb/>Microcosmi,<emph.end type="italics"/> per virt&ugrave; del quale il sangue si muove, si perfeziona, e si pre&shy;<lb/>serva dalla corruzione? </s>

<s>Ei dispensa i suoi benefizi a tutto il corpo, &ldquo; Lar <lb/>iste familiaris, fundamentum vitae, author omnium &rdquo; (ibi, pag. </s>

<s>57). </s></p><p type="main">

<s>Questa sublime comparazione arveiana, tra il cuore nel Microcosmo, e <lb/>il Sole nell'immenso Mondo creato, dette occasione ad alcuni di rassomi&shy;<lb/>gliar piuttosto il circolo del sangue al circolo de'Pianeti, e di attribuire al&shy;<lb/>l'Harvey stesso in promuovere la scienza un merito non punto inferiore a <lb/>quello, che s'attribuiva al Copernico. </s>

<s>&Egrave; infatti cosa degna della considera&shy;<lb/>zion del Filosofo la mirabile analogia, che passa tra l'ordine de'moti car&shy;<lb/>diaci, e l'ordine dei moti celesti, non che tra i processi della mente del&shy;<lb/>l'uomo in investigar le ragioni degli uni e degli altri. </s>

<s>Tre sono i circoli <lb/>del sistema solare: quello de'due pianeti inferiori, quello di tutto insieme <lb/>l'ordine planetario, quello del Sole in s&egrave; stesso, ai quali tre circoli corri&shy;<lb/>spondono nel sistema della vita animale il circolo polmonare, il circolo nel <lb/>giro universale dei vasi, e finalmente il circolo coronario. </s>

<s>Come della circo&shy;<lb/>lazione de'due Pianeti inferiori s'ebbero dagli orti e dagli occasi i primi <lb/>indizii, cos&igrave; del circolo polmonare, dall'andar della vena arteriosa e dal tor&shy;<lb/>nar al cuore dell'arteria venosa, s'ebbero le prime persuasioni. </s>

<s>Gli Astro&shy;<lb/>nomi egiziani, col loro sistema introdotto in Italia da Marziano Capella e <lb/>divulgato dall'Alighieri, mossero i primi passi per quella via, per la quale <lb/>il Copernico avrebbe fatto si gran progresso, come Galeno e il Colombo e <lb/>il Cesalpino iniziarono la scoperta, alla quale avrebbe dato glorioso compi&shy;<lb/>mento l'Arveio. </s>

<s>Ultimo a rivelarsi, dopo il circolo universale de'Pianeti, fu <lb/>il circolo del Sole in s&egrave; stesso, come, dopo il circolo del sangue nel giro <lb/>universale dei vasi, ultimo a dimostrarsi fu il circolo coronario. </s>

<s>I passaggi <lb/>dalla luce all'ombra servirono a quello, come l'alternarsi il pallor della si&shy;<lb/>stole al purpureo della diastole servi a questo, e fu il Canocchiale a Galileo <lb/>ministro della scoperta, com'allo Spallanzani fu il Microscopio. </s></p><p type="main">

<s>Ma come l'Harvey, dop'avere eloquentemente accennato alle ragioni, <lb/>per cui il cuore pu&ograve; dirsi il Sole nel Micromosmo, a quel modo che il Sole <lb/>stesso pu&ograve; dirsi il cuore del Mondo, soggiunge tosto: &ldquo; sed de his conve&shy;<lb/>nientius, cum de huiusmodi motus causa finali speculabimur &rdquo; (ibi); cos&igrave; <lb/>noi soggiungiamo che pi&ugrave; convenientemente s'intenderanno le divisate ana&shy;<lb/>logie nell'ordine particolare de'fatti, de'quali entriamo senz'altro a narrare <lb/>la storia. </s></p><pb xlink:href="020/01/1251.jpg" pagenum="126"/><p type="main">

<s>E giacch&egrave; l'Harvey, come vedemmo, commemorava Aristotile, nell'atto <lb/>d'imporre il nome alla sua grande scoperta, al lungo ordine delle idee, che <lb/>si svolgerebbero nel decorrere di tanti secoli, conviene in Aristotile stesso <lb/>appiccare le prime fila. </s>

<s>Il gran Maestro della scienza universale non lasci&ograve; <lb/>indietro la descrizione delle membra degli animali, e ne compose quel Trat&shy;<lb/>tato diviso in quattro libri col titolo <emph type="italics"/>De partibus animalium,<emph.end type="italics"/> da cui prin&shy;<lb/>cipalmente imparassero i discepoli il sapiente magistero della Natura nella <lb/>fabbrica del corpo dell'uomo. </s>

<s>Ma in realt&agrave; la Natura, qui come in altre <lb/>parti di scienza naturale, conforma que'suoi magisteri alle speculazioni del <lb/>Filosofo, di che il cap. </s>

<s>IV del III libro ne porge fra'tanti altri un notabile <lb/>esempio. </s>

<s>Ivi si conclude che il cuore &egrave; il principio delle vene. </s>

<s>&ldquo; Cor autem <lb/>venarum principium est, ex hoc enim venae et per hoc esse videntur &rdquo; (Ope&shy;<lb/>rum Tomus sextus, Venetiis 1560, fol. </s>

<s>231). Infatti, ei soggiunge, tutti gli <lb/>altri visceri son corsi dalle vene, fuor che il cuore, il quale &egrave; cavo, per <lb/>contenere il sangue da s&egrave; generato, e per dispensarlo al corpo per la via <lb/>delle vene: &egrave; spesso &ldquo; ut principium caloris servare possit &rdquo; (ibi). &mdash; Ma an&shy;<lb/>che il Fegato &egrave; tutto pieno di sangue: or perch&egrave; non potrebb'egli esserne <lb/>il generatore, e il principio delle vene invece del cuore? </s>

<s>&mdash; Risponde Aristo&shy;<lb/>tile, non dietro le osservazioni anatomiche o l'esperienze, ma dietro i sug&shy;<lb/>gerimenti della sua propria ragione, ch'egli vuole imporre alla Natura per <lb/>legge, e dice che tanta eccellenza si conviene al cuore, perch'egli &egrave; collo&shy;<lb/>cato nel mezzo: &ldquo; in medio enim positum est. </s>

<s>&rdquo; Al Fegato non potrebbe <lb/>convenirsi una tale eccellenza, n&egrave; perci&ograve; dirsi il principio o di tutto il corpo <lb/>o del sangue, perch'ei non &egrave; collocato nel luogo principale. </s>

<s>&ldquo; Jecur etiam <lb/>omnibus sanguine praeditis inest, sed nemo id censuerit esse principium <lb/>vel corporis totius, vel sanguinis, situs enim nequaquam obtinet principa&shy;<lb/>lem &rdquo; (ibi). </s></p><p type="main">

<s>Quando, cinque secoli dopo, i fatti anatomici osservati parvero persua&shy;<lb/>dere a molti che la Natura esercita un magistero tutto suo proprio, e molto <lb/>differente da quello impostole dalla ragion di Aristotile, Galeno tolse dalla <lb/>sedia principale il Cuore, per porvi il Fegato, e fatta distinzione fra arterie <lb/>e vene disse che queste avevano dal Fegato stesso gl'inizii, come quelle <lb/>lo avevano invece dal Cuore. </s>

<s>&ldquo; Nam quemadmodum venae ab Hepate, ita <lb/>Arteriae a Corde ducunt initium &rdquo; (De usu partum, Lugduni 1550, pag. </s>

<s>335). <lb/>L'innovazione galenica segnava senza dubbio un regresso dal termine, a <lb/>cui doveva giunger la scienza, per scoprire il circolo del sangue, ma ci&ograve; <lb/>dipendeva piuttosto dalla naturale imperfezione dell'uomo, che dal metodo <lb/>sperimentale o di osservazione sostituito dall'Anatomico al metodo raziona&shy;<lb/>listico del Filosofo. </s>

<s>Che ci&ograve; sia il vero vien dimostrato dal veder che quel <lb/>metodo di osservazione condusse direttamente Galeno stesso a scoprire il cir&shy;<lb/>colo polmonare. </s>

<s>Le vene, secondo il Medico di Coo, vanno dal Fegato a in&shy;<lb/>figgersi nelle cavit&agrave; destre del cuore, e le arterie muovono dalle cavit&agrave; si&shy;<lb/>nistre come da loro principio. </s>

<s>Quel vaso dunque, che va dalla parte destra <lb/>del cuore al polmone, &egrave; una vena, ma perch&egrave; ha costituzione di arteria vuol <pb xlink:href="020/01/1252.jpg" pagenum="127"/>perci&ograve; appellarsi <emph type="italics"/>Vena arteriosa.<emph.end type="italics"/> L'altro vaso, che va al Polmone stesso <lb/>dalla parte sinistra del Cuore, &egrave; una arteria, ma perch&egrave; ha costituzione di <lb/>vena dovr&agrave; dunque dirsi <emph type="italics"/>Arteria venosa.<emph.end type="italics"/> Fu appunto per la diligente os&shy;<lb/>servazione di questi due vasi singolari, che Galeno si condusse alla sua <lb/>scoperta. </s></p><p type="main">

<s>Nel VI libro <emph type="italics"/>De usu partium<emph.end type="italics"/> il cap. </s>

<s>X s'intitola, secondo l'interpe&shy;<lb/>trazione del medico calabrese Niccol&ograve; Regio, &ldquo; Vena ad pulmonem per&shy;<lb/>veniens arterialis est et arteria &egrave; converso &rdquo; (ibi, pag. </s>

<s>323). Incomincia ivi <lb/>a dire l'Autore che per gli scambievoli beneficii fra que'due visceri, organi <lb/>principalissimi della vita animale, il polmone &egrave; nutrito direttamente dal <lb/>Cuore, e non essendo conveniente che gli fosse mandato il sangue nutri&shy;<lb/>tizio per la vena Cava, la sapiente Natura ordin&ograve; a quell'effetto un'apposita <lb/>vena, a cui dette, per renderla singolare, costituzione propria di arteria. <lb/></s>

<s>&ldquo; Nam ut aliud nihil in omnibus animantibus, ita in ipso Pulmone, utique <lb/>sapiens Natura temere nihil neque sine causa quidquam fecit. </s>

<s>Commutavit <lb/>autem vasorum tunicas, venam quidem faciens arteriosam, arteriam vero <lb/>venosam. </s>

<s>In aliis vero omnium partibus, cum arteria sit aequabilis tunica&shy;<lb/>rum, tamen crassitudo non est eadem, sed tantum utique differt, quantum <lb/>Herophilus recte collegisse videtur, qui arteriam venae crassitudine sexcu&shy;<lb/>plam esse definierit &rdquo; (ibi). </s></p><p type="main">

<s>Fatta l'osservazione di questo notabile scambio fra arterie e vene, trat&shy;<lb/>trandosi che il cuore doveva direttamente e per s&egrave; nutrire il polmone, Ga&shy;<lb/>leno passa a investigare e ad esporre <emph type="italics"/>quamobrem Natura,<emph.end type="italics"/> in cos&igrave; fatto <lb/>modo, <emph type="italics"/>machinata est,<emph.end type="italics"/> spendendo tutto quanto il capitolo in cos&igrave; fatta inve&shy;<lb/>stigazione, per apparecchiarsi alla quale dice esser conveniente premettere <lb/>quest'altra ricerca: perch&egrave; cio&egrave; la Natura abbia contessute le arterie di fibre <lb/>pi&ugrave; robuste delle vene. </s>

<s>Ci&ograve; egli dice <emph type="italics"/>longa egere oratione non arbitror,<emph.end type="italics"/><lb/>essendo che le vene, ordinate a condurre un sangue crasso, grave e pigro, <lb/>bastava che fossero rivestite di una semplice tunica, ma era conveniente il <lb/>raddoppiarla per contener, come fanno le arterie, un sangue ch'&egrave; tutto spi&shy;<lb/>ritoso, tutto mobile e diffusivo. </s>

<s>Ora, perch&egrave; il polmone composto di sostanza <lb/>spiritosa voleva esser nutrito di un sangue raffinato e pur anch'esso spiri&shy;<lb/>toso, ecco che la sapiente Natura glielo manda per una vena, la quale ha <lb/>la costituzione e la compagine propria di un'arteria. </s></p><p type="main">

<s>Il cap. </s>

<s>XI del citato libro galenico &egrave; cos&igrave; intitolato: &ldquo; Arteriosum vas <lb/>aut eius generis membranas ex vena cava produci non potuisse docet osten&shy;<lb/>diturque utilitatem dextri ventriculi cordis &rdquo; (ibi, pag. </s>

<s>332). La dimostra&shy;<lb/>zione si conclude all'ultimo colle parole seguenti: &ldquo; Ex quibus intelligi po&shy;<lb/>test multo melius fuisse pulmonem a corde nutriri. </s>

<s>Porro cum vas alterum <lb/>quod tunica simplici constat in cor infigatur, alterum vero quod duplici ex <lb/>ipso producatur, communem utrique locum, quasi lacunam quamdam, pa&shy;<lb/>rari necesse fuit. </s>

<s>Ad quam pertinentibus utrisque, per alterum quidem tra&shy;<lb/>datur sanguis, per reliquum vero immittatur. </s>

<s>Atque hic dexter cordis ven&shy;<lb/>triculus est pulmonis causa, quemadmodum demonstravimus, comparatus. <pb xlink:href="020/01/1253.jpg" pagenum="128"/>Quocirca quae animalia pulmonem non habent, eadem neque in corde duos <lb/>habent ventriculos, sed illis solis is inest, qui motus arteriis omnibus dux <lb/>est &rdquo; (ibi, pag. </s>

<s>335). </s></p><p type="main">

<s>Si raccoglie da cos&igrave; fatti documenti essere stata intenzione principalis&shy;<lb/>sima di Galeno quella di dimostrar che il Polmone veniva direttamente nu&shy;<lb/>trito dal Cuore, e in qual modo venisse quello a ricever da questo il vitale <lb/>suo nutrimento. </s>

<s>Includeva in s&egrave; un tal processo dimostrativo la descrizione <lb/>de'vasi particolari ordinati a quel nutrimento, e delle comuni relazioni, che <lb/>hanno quegli stessi vasi fra loro e col cuore, in che consiste insomma la <lb/>scoperta galenica del circolo polmonare. </s></p><p type="main">

<s>Era come vedemmo dottrina insegnata dall'antico Maestro che le vene <lb/>avessero tutte la loro origine dal Fegato, e che le non portassero altro che <lb/>sangue crasso, per nutrir le membra di tutto il corpo animale, dal Polmone <lb/>in fuori, il quale veniva direttamente irrigato dal destro ventricolo di pu&shy;<lb/>rissimo sangue spiritoso. </s>

<s>E perch&egrave; giusto appunto doveva esser quel sangue <lb/>di sostanza spiritosa, ordin&ograve; la Natura che la vena irrigatrice avesse consi&shy;<lb/>stenza di arteria. </s>

<s>Non potendosi per&ograve; tutto il sangue portato da questa vena <lb/>esaurire in alimentare il polmone, il superfluo fu fatto ritornare al cuore, <lb/>non per la medesima via indietreggando, perch&egrave; ne sarebbe potuto seguire <lb/>un tumultuoso flusso e riflusso, ma per la via della vena arteriosa lasciata <lb/>aperta nelle bene apposte anastomosi. </s></p><p type="main">

<s>Per meglio conseguire un tale effetto, la stessa sapientissima Natura <lb/>apparecchi&ograve; le opportune valvole, tanto nel principio della vena arteriosa, <lb/>perch'entrato il sangue non ne dovesse uscire, quanto pure allo sbocco del&shy;<lb/>l'arteria venosa, perch&egrave; uscito non dovesse rientrare. </s>

<s>Per il gioco dunque <lb/>delle valvole il sangue dalla vena &egrave; costretto a passar nell'arteria, e la forza <lb/>d'impulso nasce dai moti del torace, che ampliandosi dilata i vasi, i quali <lb/>perci&ograve; attraggono pi&ugrave; facilmente, restringendosi gli comprime, e sforza cos&igrave; <lb/>il sangue a passare attraverso alle troppo anguste anastomosi. </s>

<s>&ldquo; Fieri nun&shy;<lb/>quam potuisset ut per invisibilia, atque exigua ossilla, sanguis in arterias <lb/>transumetur..... Cum autem thorax contrahitur pulsae atque intro com&shy;<lb/>pressae undique, quae in pulmone sunt venosae arteriae, exprimunt quidem <lb/>quam celerrime qui in seipsis est spiritus. </s>

<s>Transumunt autem per subtilia <lb/>illa ossilla sanguinis portionem aliquam, quod numquam accidisset profecto, <lb/>si sanguis per maximum os retro remeare potuisset &rdquo; (ibi, pag. </s>

<s>336). </s></p><p type="main">

<s>Bench&egrave; insomma Galeno non avesse compresa la vera intenzione della <lb/>Natura nel condurre il sangue al Polmone, e nel ridurlo poi al Cuore, ei <lb/>descrisse pure il circolo polmonare con tanta precisione, da servir come ve&shy;<lb/>dremo di esempio alla grande scoperta dell'Harveio. </s>

<s>Sarebbe forse, prose&shy;<lb/>guendo per l'aperta via, riuscito pi&ugrave; d'appresso a conoscere il circolo uni&shy;<lb/>versale del sangue quell'antico Maestro, se il negare al Cuore il principato <lb/>aristotelico non glielo avesse impedito. </s>

<s>Illuso dal sistema della vena Porta <lb/>e dal parenchima sanguinolento del Fegato, attribu&igrave; a questo viscere le fun&shy;<lb/>zioni generative del sangue, e riconobbe da lui solo l'origine di tutte le <pb xlink:href="020/01/1254.jpg" pagenum="129"/>vene. </s>

<s>Cos&igrave;, il circolo, che la Natura aveva fatto continuo, si veniva dal Fi&shy;<lb/>losofo a rendere spezzato, dando al sangue venoso altro principio diverso <lb/>dal sangue arterioso; altre qualit&agrave;, altre funzioni. </s>

<s>Le numerose vene eran <lb/>secondo Galeno disperse per tutte le membra a recarvi il necessario ali&shy;<lb/>mento, e la Cava scendeva nell'orecchietta destra per colar di l&igrave; nel sotto&shy;<lb/>posto ventricolo il sangue, che dovevasi dispensare in due parti: l'una <lb/>andando ad alimentare il Polmone, e l'altra attraverso al setto medio pene&shy;<lb/>trando nel ventricolo sinistro, dove acquistava qualit&agrave; spiritose, e i conce&shy;<lb/>puti spiriti, entrando per l'Arteria magna ed esalando per le numerose <lb/>anastomosi, facevano pulsar le membra e infondevano in esse i balsami <lb/>della vita. </s></p><p type="main">

<s>Come onde, bench&egrave; interrotte qua e l&agrave; da qualche ostacolo, si propa&shy;<lb/>garono per un lungo ordine di secoli queste dottrine, infin tanto che non <lb/>arrivarono al Berengario da Carpi. </s>

<s>O illuso dalla propria esperienza o sog&shy;<lb/>giogato dall'autorit&agrave; di coloro, che asserivano di aver veduto ne'cadaveri <lb/>l'arteria venosa vuota di sangue, dubit&ograve; da questo lato della verit&agrave; delle dot&shy;<lb/>trine galeniche, e ripensando a quale altro fine fosse ivi tra il Polmone e <lb/>il Cuore disposto quel vaso, immagin&ograve; che rassomigliasse alla gola di un <lb/>cammino, attraverso alla quale passassero i fumi filigginosi sollevatisi dal <lb/>ventricolo sinistro nella concozione del sangue. </s>

<s>&ldquo; In isto etiam ventre sini&shy;<lb/>stro est aliud orificium in basi cordis, in quo incipit arteria venalis, dicta <lb/>arteria quia vaporem portat, vel, ut inquit Galenus VII <emph type="italics"/>De iuvamentis,<emph.end type="italics"/><lb/>quia pulsat. </s>

<s>Et dicitur venalis quia tantum unam habet tunicam, per quam <lb/>transit extra corpus fumus capnosus &rdquo; (Comment. </s>

<s>in Anat. </s>

<s>Mundini cit., <lb/>fol. </s>

<s>CCCL). </s></p><p type="main">

<s>Del resto, negata la verit&agrave; del circolo polmonare, il Berengario segue <lb/>fedelmente Galeno. </s>

<s>Diligentissimo nel descrivere il setto medio, dice che le <lb/>cavit&agrave; aperte in esso, dalla parte che guarda il ventricolo destro, si vanno <lb/>sempre pi&ugrave; restringendo, infino a ridursi in sottilissimi pori, che vanno a <lb/>sboccare nel ventricolo sinistro. </s>

<s>Questo ei lo crede un artificio della Natura <lb/>perch&egrave; attraverso allo stesso setto medio il sangue quasi si cribra e si as&shy;<lb/>sottiglia, disponendosi intanto a pigliar quella spirituosit&agrave;, che gli sar&agrave; im&shy;<lb/>partita dalle forze proprie del Cuore, prima di esser dispensato alle memhra <lb/>per la via dell'Aorta. </s>

<s>&ldquo; Visis ventriculis lateralibus cordis, scilicet dextro et <lb/>sinistro, ad ventriculum medium cordis me converto. </s>

<s>Et dico in pariete, qui <lb/>est communis ventriculo dextro et sinistro, qui est in medio cordis....esse <lb/>certas concavitates, seu foramina, quae ut supra dixi notabiles sunt in cor&shy;<lb/>dibus magnorum bouum,.... quae foramina dicuntur a Medicis Venter me&shy;<lb/>dius cordis, et ipsa foramina pertranseunt parietem praedictum, a dextro <lb/>ventriculo incipiendo usque ad concavitatem ventriculi sinistri, et talia fora&shy;<lb/>mina sunt latiora et ampliora versus ventriculum dextrum quam sunt ver&shy;<lb/>sus ventrem sinistrum. </s>

<s>Et haec foramina reperiuntur semper ad magis <lb/>strictum procedere, usquequo transeant totum praedictum parietem,.... et <lb/>ita per talia foramina transit sanguis a ventre dextro ad sinistrum, qui con-<pb xlink:href="020/01/1255.jpg" pagenum="130"/>tinue in transitu subtiliatur et sie praeparatur ad spirituositatem &rdquo; (ibi, <lb/>fol. </s>

<s>CCCLI). </s></p><p type="main">

<s>Cos&igrave;, diligentemente illustrata quella parte che conteneva il falso, im&shy;<lb/>provvidamente negata quell'altra che dimostrava il vero, tramandavasi ai <lb/>posteri dal Berengario la dottrina, che intorno al circolo del sangue avea <lb/>insegnata Galeno. </s>

<s>Al modesto Anatomico di Carpi successe, non molti anni <lb/>dopo, il vanitoso Anatomico brussellese, il quale essendo riuscito a far cre&shy;<lb/>dere ch'egli era proceduto senza maestro, com'uomo apparito al mondo <lb/>senza padre e senza madre, s'acquist&ograve; il titolo di divino. </s>

<s>Maravigliosa &egrave; da <lb/>dir senza dubbio quella virt&ugrave;, che valse a indurre nelle menti una tal per&shy;<lb/>suasione, per cui sempre e in ogni modo appariranno uomini maravigliosi <lb/>Aristotile, e Galileo e il Cartesio, ma pure hanno i pi&ugrave; savii sempre pensato <lb/>che com'&egrave; impossibile non riconoscere un padre nella generazione animale, <lb/>cos&igrave; &egrave; impossibile nella generazione intellettuale non riconoscere un maestro. </s>

<s><lb/>Il Vesalio ebbe a suoi principali maestri Galeno e il Berengario, bench&egrave;, per <lb/>non apparire discepolo di nessuno, questo copra sotto l'ombra de'silenzii, e <lb/>quello sotto la mora degl'insulti. </s></p><p type="main">

<s>Non ingrato allo studioso, n&egrave; disutile alla storia riuscirebbe il percor&shy;<lb/>rere i VII libri <emph type="italics"/>De humani corporis fabrica,<emph.end type="italics"/> per notar come e quanto ivi <lb/>ritragga l'Autore dai libri di Galeno, e dai Commentarii del Berengario, di <lb/>che quello che ci occorrer&agrave; ora a notare, in proposito della fisiologia del <lb/>sangue, pu&ograve; valer per esempio. </s>

<s>Si pongano di grazia sotto gli occhi i let&shy;<lb/>tori il cap. </s>

<s>X del VI libro <emph type="italics"/>De usu partium,<emph.end type="italics"/> che incomincia <emph type="italics"/>Mutuam enim <lb/>cor pulmoni gratiam referre.....<emph.end type="italics"/> e lo vengano insiem con noi riscon&shy;<lb/>trando col cap. </s>

<s>XI del libro VI dell'Anatomia del Vesalio, se vogliono ve&shy;<lb/>dere com'essendo in ambedue quegli Autori ugualmente difettosa la Fisio&shy;<lb/>logia, la Rettorica dell'uno sia inferiore a quella dell'altro, quant'esser pu&ograve; <lb/>inferiore la studiata maniera di un Barbaro alla nativa eleganza di un Greco. </s></p><p type="main">

<s>&ldquo; Pulmo enim, cos&igrave; scrive il Vesalio, qui instar promptuarii cordi cir&shy;<lb/>cumponitur ut id ab illo aerem perpetuo allicere queat, rarus, fungosus, <lb/>levis, ac ad thoracis motus sequacissimus fieri debuit. </s>

<s>Neque eiusmodi pro&shy;<lb/>fecto suis functionibus idoneo nutrimento ali potuit, nisi privatim illi san&shy;<lb/>guis ex eo quem Cava continet, levis, aereus, spumosus, expurgatus, nihilque <lb/>minus quam foeculentus, ab alio organo praepararetur, atque ita ipsi pul&shy;<lb/>moni ad opportunam nutritionem deduceretur. </s>

<s>At nullum organum corde <lb/>ipso calidissimo et pulmoni proximo viscere ad id munus erat aptum. </s>

<s>Neque <lb/>etiam aliud omnino iustius pulmoni hac in re famulari poterat, quandoqui&shy;<lb/>dem nimis quam ingratum Cor habendum foret, si Pulmoni tam amice ae&shy;<lb/>rem, quo nisi ilico concidere emorique velit, perpetuo indiget, ipsius nomine <lb/>attrahenti ac obsequentissimi famuli ritu praeparanti, et illius potissimum <lb/>gratia fabricanti, nullas vices referendas putaret, ac non modis omnibus cor, <lb/>ut gratiam reponeret pulmoni, opportunum alimentum, cum id citra incom&shy;<lb/>modum possit, conficere praeparareque studeret &rdquo; (De hum. </s>

<s>corp. </s>

<s>fabrica, <lb/>Basileae 1543, pag. </s>

<s>596). </s></p><pb xlink:href="020/01/1256.jpg" pagenum="131"/><p type="main">

<s>Tale &egrave; il tratto di Rettorica uscito dalla penna anatomica del Vesalio <lb/>per dimostrare, a imitazion di Galeno, che il polmone vuol essere diretta&shy;<lb/>mente alimentato dal cuore. </s>

<s>Ma perch&egrave; Galeno stesso non lasci&ograve; le froude <lb/>dell'eloquenza vuote affatto de'frutti della Filosofia, argutamente deducendo <lb/>che le due destre cavit&agrave; cardiache erano poste in servigio de'polmoni, per&shy;<lb/>ch&egrave; gli animali privi della respirazion polmonare hanno il cuore mancante <lb/>di quelle parti: anche il Vesalio non trascura di mandar all'ultimo la sua <lb/>dimostrazione condita di questo galenico sale. </s>

<s>&ldquo; Pulmonis igitur occasione <lb/>dexter cordis ventriculus creatus est, quod etiam liquidissimo animalia con&shy;<lb/>firmant pulmone carentia, ac ob id dextro cordis ventriculo destituta &rdquo; (ibi) </s></p><p type="main">

<s>Dall'osservazione di questi fatti per&ograve; Galeno fu condotto a scoprire il <lb/>circolo polmonare, ma il Vesalio abbandona a questo punto l'antica guida, <lb/>per seguir piuttosto quella del Berengario. </s>

<s>Da lui ritrae l'anatomia del setto <lb/>medio poroso e la fisiologia del ventricolo destro, esprimendosi con queste <lb/>parole: &ldquo; Hic namque ventriculus, in animalibus quae illo donantur, a vena <lb/>Cava, quoties Cor dilatatur ac distenditur, magnam sanguinis vim attrahit, <lb/>quem adiuvantibus ad hoc ventriculi foveis excoquit, ac suo calore atte&shy;<lb/>nuans levioremque et qui aptius impetu postmodum per arterias ferri pos&shy;<lb/>sit reddens, maxima portione per ventriculorum cordis septi poros in sini&shy;<lb/>strum ventriculum desudare sinit. </s>

<s>Reliquam autem eius sanguinis partem, <lb/>dum cor contrahitur, arctaturque, per venam arterialem in pulmonem de&shy;<lb/>rivat &rdquo; (ibi). </s></p><p type="main">

<s>Dal Berengario deriv&ograve; pure il Vesalio la dottrina delle funzioni del <lb/>sinistro ventricolo e dell'arteria venosa, la quale ei non cred&egrave; che fosse or&shy;<lb/>dinata a portare il sangue avanzato alla nutrizion del polmone, com'aveva <lb/>detto l'antico Maestro di Coo, ma a condur fumi e aria, com'aveva pensato <lb/>il Maestro nuovo da Carpi. </s>

<s>&ldquo; Quemadmodum enim dexter ex Cava sangui&shy;<lb/>nem trahit, ita quoque sinister, aerem ex pulmone in arteriam venalem at&shy;<lb/>tractum ad se dilatato, corde allicit, illoque ad caloris innati refrigerationem <lb/>et substantiae ipsius enutritionem spiritumque vitalem utitur, hunc aerem <lb/>excoquens et praeparans, ut is una cum sanguine, qui ex dextro ventriculo <lb/>in sinistrum, per ventriculorum septum copiosius resudavit, in magnam Ar&shy;<lb/>teriam totumque adeo corpus delegari possit &rdquo; (ibi, pag. </s>

<s>598). </s></p><p type="main">

<s>La grande autorit&agrave; del Vesalio aveva rese approvatissime nel giudizio <lb/>de'pi&ugrave; queste dottrine galeniche riformate dal Berengario, quando Realdo <lb/>Colombo si propose di volere investigare il vero nella Natura e no ne'libri. </s>

<s><lb/>Dando dunque effetto a questo savio proposito, per le dissezioni de'cada&shy;<lb/>veri e degli animali vivi, si assicur&ograve; che l'arteria venosa conteneva vera&shy;<lb/>mente sangue, com'aveva detto Galeno, e non fumi e aria com'avevano in&shy;<lb/>segnato poi il Berengario e il Vesalio. </s>

<s>Nel riferire al pubblico la verit&agrave; <lb/>dimostrata dai fatti anatomici, contro gli errori vesaliani, il Colombo &egrave; ar&shy;<lb/>gutissimo perch&egrave;, senza nominar nessuno, scopre non solo quegli errori, ma <lb/>ci&ograve; che pi&ugrave; doveva cuocere al superbo Brussellese, l'origine di quegli er&shy;<lb/>rori, ripetizioni inconsiderate dei detti altrui. </s>

<s>Egli perc&igrave;&ograve; insiste sopra quei <pb xlink:href="020/01/1257.jpg" pagenum="132"/>fumi fuligginosi usciti dalla penna del buon Berengario, e si ride di quegli <lb/>anatomici, a cui tanto piacque questa finzione &ldquo; quippe qui certo existimant <lb/>in corde ea fieri, quae in caminis assolent, quasi in corde viridia ligna exi&shy;<lb/>stant, quae, dum cremantur, fumum edant &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>178). </s></p><p type="main">

<s>Ma &egrave; il vero, soggiunge tosto il Colombo, che l'arteria venale &egrave; fatta <lb/>&ldquo; ut sanguinem cum aere a pulmonibus mixtum afferant ad sinistrum cor&shy;<lb/>dis ventriculum. </s>

<s>Quod tam verum est, quam quod verissimum, nam non <lb/>modo si cadavera inspicis, sed si viva etiam animalia hanc arteriam in omni&shy;<lb/>bus refertam invenies, quod nullo pacto eveniret, si ob aerem duntaxat et <lb/>vapores constructa foret &rdquo; (ibi). Ma perch&egrave; il fatto dimostrato nella vena <lb/>dell'animale, mentre respira e mentre che la vita d&agrave; moto al sangue, do&shy;<lb/>veva riuscire pi&ugrave; concludente, il Colombo stesso, l&agrave; dove tratta delle fun&shy;<lb/>zioni del polmone, invita i suoi lettori e gli scongiura che ricorrano alle vi&shy;<lb/>visezioni, e che tocchino da s&egrave; stessi con mano se quello ch'egli asserisce <lb/>&egrave; vero; se &egrave; vero cio&egrave; che l'arteria venosa &egrave; anch'essa piena di sangue, <lb/>come tutte le altre vene, &ldquo; quemadmodum peroptume maximus Galenus <lb/>probat eo libello <emph type="italics"/>An sanguis in arteriis contineatur,<emph.end type="italics"/> contra Erasistratum &rdquo; <lb/>(ibi, pag. </s>

<s>224). </s></p><p type="main">

<s>Ma d'onde atting'ella il sangue quest'arteria venosa? </s>

<s>Da quello, ri&shy;<lb/>sponde il Colombo, riversato nel Polmone dalla vena arteriosa, e sopravan&shy;<lb/>zato al nutrimento del viscere, il qual sangue rimescolandosi ivi con l'aria <lb/>diventa spiritoso e cos&igrave; confezionato entra per le diramazioni dell'arteria ve&shy;<lb/>nosa, dalla quale &egrave; portato al ventricolo sinistro. </s>

<s>&ldquo; Vena enim haec arte&shy;<lb/>rialis, praeterquam quod sanguinem pro sui alimento defert, adeo ampla est, <lb/>ut alius usus gratia deferre possit. </s>

<s>Sanguis huiusmodi, ob assiduum pulmo&shy;<lb/>num motum, agitatur, tenuis redditur, et una cum aere miscetur, qui et <lb/>ipsa in hac collisione refractioneque praeparatur, ut simul mixti sanguis et <lb/>aer per arteriae venalis ramos suscipiantur, tamdemque per ipsius truncum <lb/>ad sinistrum cordis ventriculum deferantur &rdquo; (ibi, pag. </s>

<s>223). </s></p><p type="main">

<s>&Egrave; dunque il Colombo cos&igrave; condotto dagli esercizii della vivisezione a <lb/>descrivere quel circolo polmonare del sangue, che il Berengario aveva ne&shy;<lb/>gato a Galeno, sostituendovi ipotesi dannosamente diffuse dall'autorit&agrave; del <lb/>Vesalio. </s>

<s>Tanto poi diritte furon le vie, che condussero l'Anatomico cremo&shy;<lb/>nese alla sua conclusione, e tanto si fiss&ograve; la mente di lui in cacciare i fumi <lb/>fuligginosi del Berengario, piaciuti al Vesalio, che non, pensando a Galeno, <lb/>a cui giov&ograve; come une de'pi&ugrave; validi strumenti il principio delle cause finali, <lb/>si compiacque di avere scoperto il vero con gli schietti metodi e co'legit&shy;<lb/>timi strumenti sperimentali. </s></p><p type="main">

<s>Ma il Vesalio, che aveva bene inteso come quel rimprovero agli Ana&shy;<lb/>tomici, a'quali piacque tanto la comparazione del Berengario tra il sangue <lb/>nel cuore e le legna verdi gittate ad ardere ne'cammini, era scritto per lui, <lb/>se ne risent&igrave; fieramente, e nell'<emph type="italics"/>Esame del Falloppio<emph.end type="italics"/> accus&ograve; il Colombo e <lb/>il Valverda, scolare di lui, di non aver mai letto Galeno, di che fanno prova, <lb/>egli dice, que'luoghi nel trattato <emph type="italics"/>De re anatomica<emph.end type="italics"/> &ldquo; quibus subinde glo-<pb xlink:href="020/01/1258.jpg" pagenum="133"/>riatur a se compertum esse venalem arteriam sanguinem continere, cum <lb/>scilicet id tam diffuse vereque a Galeno, multisque insuper aliis fuerit per&shy;<lb/>tractatum &rdquo; (Venetiis 1564, pag. </s>

<s>93). </s></p><p type="main">

<s>Parrebbe di qui che, confessandosi per vera la sentenza galenica del&shy;<lb/>l'arteria venale piena di sangue e non d'aria fumosa, il Vesalio avesse poi <lb/>riformata la sua dottrina intorno al circolo polmonare, ma sventuratamente, <lb/>pi&ugrave; che gli emendati insegnamenti, ebbe grande efficacia in diffondere i <lb/>falsi, intantoch&egrave; la piccola circolazione del sangue, anche nel primo venten&shy;<lb/>nio del secolo appresso, come fra poco vedremo, o era dimenticata, o ve&shy;<lb/>niva messa in dubbio, dimenticate oramai le speculazioni anatomiche del lon&shy;<lb/>tano Galeno, e le vivisezioni del pi&ugrave; vicino Colombo. </s></p><p type="main">

<s>Ci&ograve; che poi fa pi&ugrave; maravigliare di questa dimenticanza, specialmente <lb/>in Italia, si &egrave; che il Cesalpino aveva confermata la scoperta anatomica del <lb/>Colombo, e fu anzi egli il primo che impose al giro del sangue il nome di <lb/><emph type="italics"/>Circolo,<emph.end type="italics"/> e che tolse di mezzo quel bisticcio di Arteria venosa e di Vena ar&shy;<lb/>teriosa, dicendo che il vaso, da cui &egrave; portato il sangue al polmone, &egrave; un'ar&shy;<lb/>teria addirittura, perch&egrave; pulsa, e l'altro vaso, da cui il sangue &egrave; riportato <lb/>al cuore, &egrave; una vera vena, facendo ella gli ufficii, ed essendo fabbricata al <lb/>modo consueto delle altre vene. </s>

<s>I Medici, egli dice nella III delle Questioni <lb/>peripatetiche, usi a chiamar vene i vasi che sboccano nella parte destra, e <lb/>arterie quelli che sboccano nella parte sinistra del cuore, escogitarono molte <lb/>finzioni e molte assurdit&agrave; per intenderne l'uso. </s>

<s>&ldquo; Pulsat igitur in pulmone <lb/>vas dextri ventriculi, hoc enim a corde accipit ut Arteria magna, et simi&shy;<lb/>liter fabricatum est eius corpus. </s>

<s>Vas autem sinistri ventriculi non pulsat, <lb/>quia introducit tantum, et eius corpus simile est reliquis venis &rdquo; (Vene&shy;<lb/>tiis 1571, fol. </s>

<s>111 a tergo). </s></p><p type="main">

<s>Le nuove idee, ch'esalano fragranti dalla novit&agrave; del linguaggio, traspor&shy;<lb/>tano in un mondo intellettuale, in cui il cielo &egrave; pi&ugrave; limpido e pi&ugrave; aperto, <lb/>perch&egrave; il Cesalpino aveva felicemente sgombrata quella nuvola, che faceva <lb/>ombra alla vista del vero. </s>

<s>Come fosse quella nuvola sgombrata dal nostro <lb/>Peripatetico lo vedremo in quest'altro capitolo, e intanto ascoltiamo come <lb/>per lui si metta il circolo polmonare in tal nuova luce, da veder chiari in <lb/>essa gli albori del nascente Sole arveiano. </s>

<s>&ldquo; Idcirco Pulmo, per venam ar&shy;<lb/>teriis similem, ex dextro cordis ventriculo fervidum hauriens sanguinem, <lb/>eumque per anastomosim arteriae venali reddens qua in sinistrum cordis <lb/>ventriculum tendit, transmisso interim aere frigido per asperae arteriae ca&shy;<lb/>nales qui iuxta arteriam venalem protenduntur, non tamen osculis commu&shy;<lb/>nicantes, ut putavit Galenus, solo tactu temperat. </s>

<s>Huic sanguinis <emph type="italics"/>circulationi<emph.end type="italics"/><lb/>ex dextro cordis ventriculo per pulmones in sinistrum eiusdem ventriculum <lb/>optime respondent ea quae in dissectione apparent. </s>

<s>Nam duo sunt vasa in <lb/>dextrum ventriculum desinentia, duo etiam in sinistrum Duorum autem <lb/>unum intromittit tantum, alterum educit, membranis eo ingenio constitutis. </s>

<s><lb/>Vas igitur intromittens vena est magna, quidem in dextro, quae Cava ap&shy;<lb/>pellatur: parva autem in sinistro ex pulmone intraducens, cuius unica est <pb xlink:href="020/01/1259.jpg" pagenum="134"/>tunica ul caeterarum venarum. </s>

<s>Vas autem educens arteria est magna, qui&shy;<lb/>dem in sinistro, quae Aorta appellatur: parva autem in dextro ad pulmo&shy;<lb/>nes derivans, cuius similiter duae sunt tunicae ut in caeteris arteriis &rdquo; (ibi). </s></p><p type="main">

<s>Cos&igrave;, nella storia della risorta Anatomia, lasciato in dimenticanza l'an&shy;<lb/>tico Galeno, si poteva dire e si diceva veramente da alcuni essere stato il <lb/>Colombo che prima del Cesalpino o di qualunque altro o italiano o stra&shy;<lb/>niero avesse descritto il circolo polmonare, quando il Morgagni, per citare <lb/>uno storico de'pi&ugrave; autorevoli, insorse contro una tale asserzione scrivendo <lb/>&ldquo; non Columbum, sed .... hispanum medicum Michaelem Servetum, sex et <lb/>viginti annis ante Columbum, minorem illum circuitum sanguinis diserte <lb/>tradidisse &rdquo; (Epistolae anat. </s>

<s>Lugduni Batav. </s>

<s>1728, pag. </s>

<s>95). </s></p><p type="main">

<s>Cita il Morgagni, in questa Epistola anatomica prima, il Sievert, che <lb/>nella sua dissertazione <emph type="italics"/>De morbis<emph.end type="italics"/> trascrisse il luogo da quell'esemplare del <lb/>libro <emph type="italics"/>De Christianismi restitutione,<emph.end type="italics"/> che si dice esser unico rimasto salvo <lb/>dalle fiamme di quel rogo, in mezzo alle quali fu l'Autore stesso bruciato <lb/>vivo. </s>

<s>Altri citano il Wotton, che fece la trascrizione da quel medesimo esem&shy;<lb/>plare, bench'ei lo dica edito, no nel 1533, ma venti anni dopo, cosicch&egrave; lo <lb/>Spagnolo avrebbe preceduto, non di 26 anni come il Morgagni sulla fede <lb/>del Sievert dice, ma di soli 6 il nostro Italiano. </s>

<s>Anche Lodovico Dutens, nel <lb/>II Tomo <emph type="italics"/>Dell'origine delle scoperte,<emph.end type="italics"/> tradotto in italiano e stampato prima <lb/>in Napoli, e poi in Venezia nel 1789, rifer&igrave; in nota al &sect; 191 il passo del <lb/>Sievert relativo alla circolazione del sangue, dicendo di averlo fedelmente tra&shy;<lb/>scritto dalle <emph type="italics"/>Riflessioni<emph.end type="italics"/> del Wotton <emph type="italics"/>sopra gli Antichi e i Moderni.<emph.end type="italics"/> Ma verso <lb/>la met&agrave; del secolo presente un illustre Fisiologo francese venne ad assicu&shy;<lb/>rarci di ogni impostura e di ogni inganno col dire: &ldquo; J'ai vu, j'ai touch&eacute; <lb/>le livre de Servet &rdquo; (Flourens, Histoire da la decouverte de la circulation <lb/>du sang, Paris 1854, pag. </s>

<s>138). </s></p><p type="main">

<s>Racconta ivi il Flourens come l'esemplare del libro, da lui veduto e <lb/>toccato, fu quello medesimo, ch'ebbe sotto gli occhi il Colladon per esami&shy;<lb/>narlo, e per dar la crudele sentenza provocata dalla invidiosa empiet&agrave; di <lb/>Calvino. </s>

<s>Venuto il libro alle mani di Riccardo Mead, il Mead lo don&ograve; al <lb/>Boze, e dagli eredi di lui lo compr&ograve; la Biblioteca reale di Parigi, dove tut&shy;<lb/>tavia si conserva. </s>

<s>Egli &egrave;, soggiunge il Flourens, questo <emph type="italics"/>malheureux exem&shy;<lb/>plaire,<emph.end type="italics"/> di una autenticit&agrave; <emph type="italics"/>irrecusable.<emph.end type="italics"/> &ldquo; Plusieurs pages sont en partie rous&shy;<lb/>sies et consum&eacute;es par le feu. </s>

<s>Il ne fut sauv&eacute; du bucher o&ugrave; l'on brulait &agrave; <lb/>la fois le livre et l'auteur, que lorsque l'incendie avait dej&agrave; commenc&eacute; &rdquo; <lb/>(ivi, pag. </s>

<s>138, 39). </s></p><p type="main">

<s>In appendice a questa <emph type="italics"/>Histoire<emph.end type="italics"/> trascrive l'Autore da pag. </s>

<s>202-14 il <lb/>passo estratto dal libro <emph type="italics"/>Christianismi Restitutio, Viennae Allobrogorum, <lb/>MDLIII,<emph.end type="italics"/> n&egrave; la trascrizione di quel passo si limita solamente a ci&ograve; che con&shy;<lb/>cerne la circolazione del sangue, ma altre parti importanti di Fisiologia. </s></p><p type="main">

<s>Tolta dunque da cos&igrave; autorevoli testimonianze ogni ragion di sospetto <lb/>intorno all'autenticit&agrave; del documento, e alla fedelt&agrave; della trascrizione, non <lb/>abbiamo potuto escludere dalla nostra Storia il Servet, e anzi, esaminando <pb xlink:href="020/01/1260.jpg" pagenum="135"/>quel ch'egli specul&ograve; della circolazione del sangue, siamo stati costretti di <lb/>confessare, con grande nostra sorpresa, aver lui gi&agrave; scoperte tutte quelle <lb/>novit&agrave;, che si lessero poi scoperte dal Colombo. </s>

<s>Egli avverte prima di tutto, <lb/>il Medico spagnolo, che sar&agrave; per intendere facilmente le cose solamente colui, <lb/><emph type="italics"/>qui in Anatome fuerit exercitatus.<emph.end type="italics"/> Poi passa a distinguere la trinit&agrave; degli <lb/>spiriti: il naturale nel fegato e nelle vene, il vitale nel cuore e nelle arte&shy;<lb/>rie, l'animale nel cervello e nei nervi. </s>

<s>Lo spirito vitale si genera propria&shy;<lb/>mente nel ventricolo sinistro del cuore, ma perch&egrave; vi son misti insieme <lb/>aria, acqua e fuoco, concorrono molto a quella generazione i polmoni, che <lb/>somministrano l'aria al sangue. </s>

<s>&ldquo; Generatur ex facta in pulmonibus mix&shy;<lb/>tione inspirati aeris cum elaborato subtili sanguine, quem dexter ventricu&shy;<lb/>lus cordis sinistro communicat. </s>

<s>Fit autem communicatio haec, non per pa&shy;<lb/>rietem cordis medium, ut vulgo creditur, sed magno artificio a dextro cordis <lb/>ventriculo longo per pulmones ductu agitatur sanguis subtilis. </s>

<s>A pulmoni&shy;<lb/>bus praeparatur, flavus efficitur, et a vena arteriosa in arteriam venosam <lb/>transfunditur &rdquo; (Flourens, Histoire cit., pag. </s>

<s>203, 4). </s></p><p type="main">

<s>Quel che soggiunge il Servet a rendere questa sua descrizione del cir&shy;<lb/>colo cardiaco polmonare originale, sopra quella datane da Galeno, lo vedremo <lb/>tra poco, ma intanto &egrave; da concludere che la scoperta, e nelle morte pagine <lb/>dell'eterodosso Spagnuolo e nelle vive del Colombo e del Cesalpino, era stata <lb/>fatta e diffusa tra gli studiosi della scienza. </s>

<s>Si giudicherebbe perci&ograve; che sopra <lb/>l'errore del Berengario, protetto dall'autorit&agrave; del Vesalio, la vera dottrina <lb/>galenica suffragata dall'autorit&agrave; del Colombo e del Cesalpino dovesse avere <lb/>compiuta vittoria, almeno in Italia, ma &egrave; pure un fatto degno di nota quel <lb/>che s'accennava di sopra, che cio&egrave; rimase fra la verit&agrave; e l'errore una lotta, <lb/>nella quale parve questo sventuratamente prevalere su quella. </s></p><p type="main">

<s>Il Falloppio, tutto intento alle descrizioni anatomiche, e tutto in cerca <lb/>di quelle squisitezze sfuggite all'occhio e all'acutissimo stilo del Vesalio, <lb/>poco dice delle funzioni del cuore o del moto del sangue, e in quel poco <lb/>non si dilunga insomma dalla fisiologia del Berengario. </s>

<s>L'Acquapendente <lb/>pure, come se il Colombo e il Cesalpino non avessero insegnato dalle mag&shy;<lb/>giori cattedre d'Italia, e come se avessero le loro dottrine segnate sull'arena, <lb/>e non impresse sopra la carta, nel discorrere, come fa per esempio nel <lb/>cap. </s>

<s>VIII. <emph type="italics"/>De formato foetu,<emph.end type="italics"/> delle funzioni del cuore e del polmone, non <lb/>aggiunge nulla di nuovo a ci&ograve; che tutti apprendevano dall'Oracolo brus&shy;<lb/>sellese. </s></p><p type="main">

<s>Bench&egrave; cos&igrave; fervorosamente, come vedemmo, raccomandasse il Colombo <lb/>le vivisezioni a chi volesse assicurarsi di fatto se l'arteria venosa contenesse <lb/>dentro s&egrave; sangue o aria, il Vidio scriveva nel cap. </s>

<s>IV del VI libro <emph type="italics"/>De ana&shy;<lb/>tome corporis humani:<emph.end type="italics"/> &ldquo; Sed utrum cum aere sanguis, per hanc arteriam <lb/>feratur, dubium est. </s>

<s>Veteres solum aerem per ipsam ferri dixerunt.... re&shy;<lb/>centiores asserunt sanguinem in ea secundum naturam contineri &rdquo; (Vene&shy;<lb/>tiis 1611, pag. </s>

<s>298). Vero &egrave; bene che nel capitolo appresso, persuaso oramai <lb/>che &ldquo; nullum foramen conspicitur in septo medio inter dextrum et sinistrum <pb xlink:href="020/01/1261.jpg" pagenum="136"/>ventriculum cordis &rdquo; non vede altra via aperta al sangue che per l'arteria <lb/>venale &ldquo; quae cum aere affert aliquid sanguinis ad sinistrum ventriculum <lb/>cordis, quem sanguinem arteria venalis in pulmone accipit a vena arteriali &rdquo; <lb/>(ibi, pag. </s>

<s>302) ma anche sopra la verit&agrave; qui riconosciuta soffia il vento freddo <lb/>dei dubbii dalle pagine precedenti. </s></p><p type="main">

<s>Inutile potrebbe sembrare oramai recare altre testimonianze, ma noi vo&shy;<lb/>gliamo condurre i nostri lettori proprio infin sulle soglie della scoperta ar&shy;<lb/>veiana, dove vedremo l'Autore di un'altra insigne scoperta cos&igrave; parlare del <lb/>circolo del sangue, come se avendo la storia da Galeno, anzi da Aristotile <lb/>al Vidio e all'Aranzio, fatto naufragio, si guardasse attraverso al cupo fondo <lb/>delle acque, o si studiasse di tirarne a galla qualche frammento, con gli <lb/>ami della memoria. </s></p><p type="main">

<s>Gaspero Asellio, tutto in filosofica contemplazione de'maravigliosi arti&shy;<lb/>ficii, con cui la Natura d&agrave; alla macchina animale continuo moto di vita, ri&shy;<lb/>pensa al sangue, e com'egli possa trapassare dall'una all'altra parte del <lb/>cuore. </s>

<s>&ldquo; Quid igitur prohibet, poi dice, riscossosi da quella contemplazione, <lb/>talis quoque e dextro cordis sinu in sinistrum per septum eius, cum Ga&shy;<lb/>leno, ob eas quas adducit rationes, statuere? </s>

<s>Accedit quod istae viae, etsi in <lb/>mortuis ut aliae plurimae cernuntur, quod in his, ut Galenus ibidem ait, <lb/>omnia sunt perfrigerata et densata, in vivis tamen quis praestabit aut nul&shy;<lb/>las eas esse aut non manifestas et patentes? </s>

<s>&rdquo; (De lactibus ecc., Medio&shy;<lb/>lani 1627, pag. </s>

<s>16). </s></p><p type="main">

<s>Ma sia pure, prosegue a dire l'Asellio, che non si trovino nel setto <lb/>medio que'fori intraveduti da Galeno, &ldquo; neque sic tamen deerit fortassis <lb/>alia et commodior via sanguini venoso a dextro in sinistrum ventriculum <lb/>traducendo. </s>

<s>Mihi sane nequaquam absurdum videtur eum sanguinem, qui <lb/>per venam arteriosam in pulmones e dextro cordis sinu effunditur, ibi assi&shy;<lb/>duo eorum verbere extenuatum cum aere, altera vitalis spiritus materia, in <lb/>ventriculum sinistrum relabi, quam viam forte nec Galenus ignoravit &rdquo; (ibi). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>L'anno dopo che uno de'pi&ugrave; insigni investigatori de'segreti della vita <lb/>animale divulg&ograve; queste parole in Italia, dove s'erano dimenticate le antiche <lb/>e le pi&ugrave; recenti tradizioni della scienza, Guglielmo Harvey pubblicava in <lb/>Francfort la sua esercitazione anatomica <emph type="italics"/>De motu cordis.<emph.end type="italics"/> L'occasione e il <lb/>diritto al merito della grande scoperta, e tutt'insieme le ragioni, per cui <lb/>gl'Italiani se la lasciarono carpire a uno straniero, sono eloquentemente <lb/>espresse nel cap. </s>

<s>VII della detta Esercitazione, dove scrive l'Autore di es&shy;<lb/>sersi sentito fecondare l'ingegno dal rimeditar sopra quella cos&igrave; chiara de&shy;<lb/>scrizione del circolo polmonare, della quale udimmo dianzi l'Asellio parlar <lb/>con tanta oscitanza. </s>

<s>&ldquo; Quod argumentum Galenus pro transitu sanguinis per <pb xlink:href="020/01/1262.jpg" pagenum="137"/>dextrum ventriculum de vena Cava in pulmones adducit, eodem nobis rec&shy;<lb/>tius pro transitu sanguinis de venis per cor in arterias, mutatis tantum ter&shy;<lb/>minis, liceat &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1737, pag. </s>

<s>53). </s></p><p type="main">

<s>Confessa insomma l'Harvey che la via, dalla quale fu condotto ad ar&shy;<lb/>gomentar la verit&agrave; del circolo universale, fu quella, da cui fu condotto Galeno <lb/>ad argomentar l'esistenza del circolo polmonare. </s>

<s>Ripensava l'arguto Inglese <lb/>che, per la gran copia, e per la grande velocit&agrave; del sangue, non sarebbe <lb/>stato possibile che le arterie non si rompessero o che non rimanessero le <lb/>vene esinanite, se a queste il fluido sanguigno non ritornasse da quelle, e <lb/>ripensando al modo come ci&ograve; potesse avvenire, &ldquo; coepi egomet mecum co&shy;<lb/>gitare, egli dice, an motionem quamdam, quasi in circulo haberet, quam <lb/>postea veram esse reperi, et sanguinem a corde per arterias in habitum <lb/>corporis et omnes partes protrudi et impelli a sinistri cordis ventriculi pulsu, <lb/>quemadmodum in pulmones, per venam arteriosam a dextris; et rursus, per <lb/>venas, in venam Cavam et usque ad auriculam dextram remeari, quemad&shy;<lb/>modum ex pulmonibus, per arteriam dictam venosam, ad sinistrum ventri&shy;<lb/>culum &rdquo; (ibi, pag. </s>

<s>56). </s></p><p type="main">

<s>Sopra lo storico dei pensamenti altrui grandissima efficacia dovrebbe <lb/>aver senza dubbio la fede, che ne fa di s&egrave; stesso l'Autore. </s>

<s>Ma perch&egrave; pu&ograve; <lb/>esser benissimo che manchi della necessaria sincerit&agrave; e interezza quella con&shy;<lb/>fessione, abbiamo perci&ograve; il dovere di esaminarla. </s>

<s>Attesta dunque l'Harvey <lb/>che il Circolo galenico gli fece ripensare al Circolo da s&egrave; poi felicemente <lb/>scoperto. </s>

<s>Chi ben riflette per&ograve; trova che questo &egrave; troppo gran salto, e non <lb/>par credibile, secondo le leggi degli svolgimenti dell'umano pensiero, che <lb/>la lontana scintilla del Fisiologo greco, senz'altra esca mediata, abbia nella <lb/>mente del Fisiologo inglese suscitato quel grandissimo incendio. </s></p><p type="main">

<s>Per potere infatti legittimamente indurre il Circolo universale dal Cir&shy;<lb/>colo polmonare, la copia e la velocit&agrave; del sangue ne'vasi non sarebbe stato <lb/>argomento efficace, senz'esser certi che il setto medio &egrave; imperforato, che <lb/>non hanno le vene la loro origine dal Fegato, e che il circolo fra la vena <lb/>arteriosa e l'arteria venosa non &egrave; ordinato a nutrire il polmone. </s>

<s>La descri&shy;<lb/>zione galenica era come vedemmo viziata da tutti questi errori, e perch&egrave; <lb/>non dice l'Harvey di essere stato egli il primo a scoprirli, e tacitamente <lb/>insinua essere stato fatto ci&ograve; per opera di altri, la sua scoperta dunque dovette <lb/>aver, per questi altri, una mediata preparazione pi&ugrave; prossima di quella di <lb/>Galeno. </s></p><p type="main">

<s>Nel cap. </s>

<s>VII <emph type="italics"/>De motu cordis<emph.end type="italics"/> s'accenna &egrave; vero al Colombo <emph type="italics"/>peritissimo <lb/>doctissimoque Anatomico<emph.end type="italics"/> (pag. </s>

<s>50), ma poi, sul principio del capitolo ap&shy;<lb/>presso, si d&agrave;, rispetto alla descrizione del circolo polmonare, per un sem&shy;<lb/>plice ripetitore dei detti dell'antico Maestro, e se nel Proemio non si de&shy;<lb/>frauda di aver notato che il sangue della vena arteriosa &egrave; alla nutrizion del <lb/>polmone soverchio, si fa in un'asciutta parentesi e sotto voce. </s>

<s>Eppure noi <lb/>ripetiamo qui quel che dicemmo altrove, ed &egrave; che l'Harvey apprese dalle <lb/>vivisezioni del Colombo ad osservare nella Natura i moti del cuore e del <pb xlink:href="020/01/1263.jpg" pagenum="138"/>sangue, e la ragione, che indusse il Discepolo a tacere com'avesse il Mae&shy;<lb/>stro per il primo osservato che alla sistole dell'arteria corrisponde la dia&shy;<lb/>stole del cuore, fu forse la ragion medesima, che lo indusse a tacer in che <lb/>modo facesse l'Autor <emph type="italics"/>De re anatomica<emph.end type="italics"/> progredire cos&igrave; le dottrine galeniche <lb/>intorno al giro del sangue, da renderle pi&ugrave; prossime e pi&ugrave; efficaci inspira&shy;<lb/>trici della grande scoperta. </s>

<s>Se dunque &egrave; trasmesso a noi il dovere ed &egrave; af&shy;<lb/>fidato l'ufficio di parlare, diremmo che tra Galeno e l'Harvey tramezzano le <lb/>speculazioni e le scoperte del Colombo e del Cesalpino, che sono i due no&shy;<lb/>stri Italiani, da'quali, come da sotterranea radice, scoppiarono al fortunato <lb/>Inglese i verdi allori. </s></p><p type="main">

<s>Dalle remote rive di Coo, quale onda malefica rinforzata dal Berengario <lb/>e dal Vesalio, s'era come vedemmo diffuso l'errore che il sangue trovasse <lb/>aperto un passaggio dal destro al sinistro ventricolo del cuore, attraverso al <lb/>setto medio, quando ad arrestare quell'onda, che pur seppe vincere e tra&shy;<lb/>passare l'ostacolo, sorse il Colombo, tutto compiacente d'essere stato egli <lb/>il primo ad annunziare al mondo una verit&agrave; rimasta occulta per tanto tempo. <lb/></s>

<s>&ldquo; Inter hos ventriculos, egli dice, septum adest, per quod fere omnes exi&shy;<lb/>stimant sanguini a dextro ventriculo ad sinistrum aditum patefieri, id ut fiat <lb/>facilius in transitu, ob vitalium spirituum generationem, tenuem reddi, sed <lb/>longa errant via, nam sanguis per arteriosam venam ad pulmonem fertur, <lb/>ibique attenuatur. </s>

<s>Deinde cum acre una, per arteriam venalem, ad sini&shy;<lb/>strum cordis ventriculum defertur, quod nemo hactenus aut animadvertit, <lb/>aut scriptum reliquit, licet maxime sit ab omnibus animadvertendum &rdquo; (De <lb/>re anat. </s>

<s>cit., pag. </s>

<s>177). </s></p><p type="main">

<s>Sarebbe per&ograve; il Colombo dovuto rimaner sorpreso di gran maraviglia, <lb/>se gli avesse il Flourens aperto sotto gli occhi il libro del Servet, additan&shy;<lb/>dogli questo passo: &ldquo; Fit autem communicatio haec, non per parietem cor&shy;<lb/>dis medium, ut vulgo creditur, sed magno artificio a dextro cordis ventri&shy;<lb/>culo.... (Histoire cit., pag. </s>

<s>203), seguitando a descrivere il circolo polmonare <lb/>con parole molto simili a quelle ora trascritte dal VII libro <emph type="italics"/>De re ana&shy;<lb/>tomica.<emph.end type="italics"/></s></p><p type="main">

<s>Il fatto, bench&egrave; sia notabile, pur si potrebbe attribuire a qualche for&shy;<lb/>tuito riscontro d'idee, se si fossero i due Autori riscontrati in quel punto <lb/>solo, ma perch&egrave; son que'punti tutti quelli, ne'quali si tratta del circolo del <lb/>sangue, nasce un gran sospetto che l'uno abbia ripetuto quel che aveva <lb/>letto o udito dire dall'altro. </s>

<s>E perch&egrave; meglio si senta la ragione di questo <lb/>sospetto, confrontiamo le idee e le speculazioni del Nostro con le idee e con <lb/>le speculazioni dello Spagnolo. </s></p><p type="main">

<s>Una dalle pi&ugrave; importanti osservazioni fatte dal Colombo, l'utilit&agrave; della <lb/>quale, in promovere le dottrine galeniche verso la scoperta del circolo uni&shy;<lb/>versale del sangue, nemmen l'Harvey pot&egrave; negare, fu quella che la vena <lb/>arteriosa era troppo grande, per dover solamente dispensare il necessario <lb/>alimento al polmone, d'onde argutamente ne concludeva che dovess'esser <lb/>lo stesso circolo polmonare ordinato, non in servigio di quel viscere solo, <pb xlink:href="020/01/1264.jpg" pagenum="139"/>ma di tutte le membra. </s>

<s>&ldquo; Vena arteriosa haec, quam diximus, magna est <lb/>satis, immo vero multo maior quam necesse fuerit, si sanguis ad pulmones <lb/>supra cor exiguo intervallo deferendus duntaxat erat &rdquo; (De re anat. </s>

<s>cit., <lb/>pag. </s>

<s>178). Alle quali parole fanno esatto riscontro quest'altre del Servet: <lb/>&ldquo; Confirmat hoc magnitudo insignis venae arteriosae, quae nec talis, nec tanta <lb/>facta esset, nec tantam a corde ipso vim purissimi sanguinis in polmones <lb/>emitteret, ob solum suum nutrimentum &rdquo; (Flourens, Histoire cit., pag. </s>

<s>204). </s></p><p type="main">

<s>Dop'avere il Colombo, per le dette ragioni, argomentato che il circolo <lb/>polmonare doveva servire agli usi di tutto il corpo, determina particolar&shy;<lb/>mente questi usi, e dice che consistono in preparare gli spiriti, da dispen&shy;<lb/>sarsi poi, per mezzo del cuore e delle arterie, a tutte le membra. </s>

<s>&ldquo; Est <lb/>autem praeparatio et pene generatio vitalium spirituum, qui postmodum in <lb/>corde magis perficiuntur. </s>

<s>Aerem namque per nares et os inspiratum su&shy;<lb/>scipit, nam asperae arteriae vehiculo per universum pulmonem fertur. </s>

<s>Pulmo <lb/>vero aerem illum una cum eo sanguine miscet, qui a dextro cordis ven&shy;<lb/>triculo profectus per arterialem venam deducitur. </s>

<s>Vena enim haec arterialis, <lb/>praeter quam quod sanguinem pro sui alimento defert, adeo ampla est ut <lb/>alius usus gratia deferre possit. </s>

<s>Sanguis huiusmodi, ob assiduum pulmonum <lb/>motum, agitatur et una cum aere miscetur, qui et ipse in hac collisione <lb/>refractioneque praeparatur, ut simul mixti sanguis et aer per arteriae ve&shy;<lb/>nalis ramos suscipiantur, tamdemque per ipsius truncum ad sinistrum cor&shy;<lb/>dis ventriculum deferantur. </s>

<s>Deferuntur vero tam belle mixti atque atte&shy;<lb/>nuati ut cordi exiguus praeterea labor supersit. </s>

<s>Post quam exiguam elabo&shy;<lb/>rationem, quasi extrema imposita manu, vitalibus hisce spiritibus reliquum <lb/>est ut illos, ope arteriae ahorti, per omnes corporis partes distribuat &rdquo; (De <lb/>re anat. </s>

<s>cit., pag. </s>

<s>223) </s></p><p type="main">

<s>Bench&egrave; dica con gran fidanza il Colombo esser questo nuovo uso dei <lb/>polmoni tale, <emph type="italics"/>quem nemo Anatomicorum hactenus somniavit,<emph.end type="italics"/> pure &egrave; un <lb/>fatto che nel Servet si trovano, con mirabile fedelt&agrave;, espresse tutte le pi&ugrave; <lb/>minute particolarit&agrave; di quei concetti. </s>

<s>&ldquo; Est prius intelligenda substantialis <lb/>generatio ipsius vitalis spiritus, qui ex aere inspirato et subtilissimo san&shy;<lb/>guine componitur et nutritur. </s>

<s>Vitalis spiritus in sinistro cordis ventriculo <lb/>suam originem habet, iuvantibus maxime pulmonibus ad ipsius generatio&shy;<lb/>nem.... Generatur ex facta in pulmonibus mixtione inspirati aeris cum ela&shy;<lb/>borato subtili sanguine, quem dexter ventriculus cordis sinistro communi&shy;<lb/>cat. </s>

<s>&rdquo; E dopo aver detto che la comunicazione si fa per via del circolo <lb/>polmonare, soggiunge: &ldquo; Deinde in ipsa arteria venosa inspirato aeri mi&shy;<lb/>scetur.... atque ita tandem a sinistro cordis ventriculo totum mixtum <lb/>attrahitur, apta supellex ut fiat spiritus vitalis &rdquo; (Flourens, Histoire cit., <lb/>pag. </s>

<s>203, 4). </s></p><p type="main">

<s>Il Colombo, come ad altro proposito avvertimmo, dice che questi spi&shy;<lb/>riti vitali si strasformano in animali ne'plessi coroidei, da lui pi&ugrave; volentieri <lb/>chiamati <emph type="italics"/>retiformi,<emph.end type="italics"/> per il moto de'quali &ldquo; miscetur cum vitalibus spiritibus <lb/>aer. </s>

<s>Itaque spiritus animales evadunt ex aere eo quo diximus modo prae-<pb xlink:href="020/01/1265.jpg" pagenum="140"/>parato, et ex vitalibus dictis spiritibus &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>191). Ora, <lb/>bench&egrave; immediatamente soggiunga queste parole: <emph type="italics"/>quae res a nemine ante <lb/>me observata fuit,<emph.end type="italics"/> il Servet, fedelmente riscontrandosi col Colombo anche <lb/>nel chiamar retiforme il plesso coroideo, cos&igrave; scrive: &ldquo; Hic itaque spiritus <lb/>vitalis a sinistro cordis ventriculo in arteriis totius corporis deinde tran&shy;<lb/>sfunditur, ita ut qui tenuior superiora petat, ubi magis adhuc elaboratur, <lb/>praecipue in <emph type="italics"/>plexu retiformi,<emph.end type="italics"/> sub basi cerebri sito, in quo ex vitali fieri <lb/>incipit animalis &rdquo; (Flourens, Histoire cit., pag. </s>

<s>205). </s></p><p type="main">

<s>Queste somiglianze, cos&igrave; ripetutamente notate fra le idee e le stesse <lb/>espressioni, son tali, che anche i nostri lettori saranno oramai persuasi non <lb/>si potere attribuire al caso, ond'&egrave; necessit&agrave; concludere o che il Servet ap&shy;<lb/>prese quelle dottrine in Italia dalla viva voce del Colombo, mentre pubbli&shy;<lb/>camente insegnava dalle cattedre di Padova, di Pisa e di Roma, o che il <lb/>Colombo stesso ebbe fra le mani e impar&ograve; l'Anatomia dal libro teologico <lb/>del Serveto. </s>

<s>Cosicch&egrave; ogni volta che nel Trattato <emph type="italics"/>De re anatomica<emph.end type="italics"/> si legge <lb/><emph type="italics"/>questa cosa prima di me nessuno l'aveva detta,<emph.end type="italics"/> oppure: <emph type="italics"/>nessun altro ana&shy;<lb/>tomico l'aveva nemmen sognata,<emph.end type="italics"/> non faccia altro l'Autore se non che ri&shy;<lb/>petere una gran menzogna. </s></p><p type="main">

<s>Chi si forma un giusto giudizio de'due uomini, ripensando principal&shy;<lb/>mente che tutti gli Spagnuoli, a'quali era per legge ecclesiastica e civile <lb/>proibito di sezionar cadaveri umani, si trovavan costretti o ad imparare <lb/>l'Anatomia sui libri o a venire a scuola in Italia; e chi pone a confronto <lb/>il Teologo fanatico col Padre dell'Anatomia sperimentale, non esita a dar di <lb/>ci&ograve; sentenza definitiva. </s>

<s>Questa sentenza poi &egrave; nuova e importante per la <lb/>Storia della Fisiologia in Italia, rivendicandosi per essa, con giuste ragioni, <lb/>al Colombo il merito di aver egli anatomicamente e fisiologicamente descritto <lb/>per il primo il circolo polmonare, e dimostrato quanto si fossero ingannati <lb/>gli Anatomici prima di lui a creder nel cuore aperti al sangue que'fori, che <lb/>ne attraversano il setto medio. </s></p><p type="main">

<s>Le illustrate galeniche dottrine e i rimossi errori preparavano cos&igrave; le <lb/>vie alla gloria dell'Harvey, ma rimaneva ancora un grande ostacolo al li&shy;<lb/>bero progredire per quelle vie, ostacolo che il Colombo non valse a sgom&shy;<lb/>brare. </s>

<s>Malaugurato seguace de'falli di Galeno assever&ograve; che il Fegato doveva <lb/>annoverarsi &ldquo; inter principes nostri corporis partes &rdquo; (De re anat., pag. </s>

<s>163. <lb/>Egli &egrave;, soggiunge, il viscere dedicato alla sanguificazione, e in verit&agrave; non <lb/>altrove che in lui e da lui e non dal cuore, come Aristotile scrisse, si ge&shy;<lb/>nera il sangue. </s>

<s>&ldquo; Est igitur Jecur omnium venarum caput, fons, origo et <lb/>radix &rdquo; (ibi, pag. </s>

<s>164). </s></p><p type="main">

<s>Il Fegato e il Cuore son nel microcosmo il Sole e la Terra dell'uni&shy;<lb/>verso: s'aspettava perci&ograve; che sorgesse anche alla Fisiologia il suo Coper&shy;<lb/>nico, il quale riordinasse i moti, e riponesse il cuore nella sua sede. </s>

<s>&Egrave; sin&shy;<lb/>golare che nella storia della Fisiologia e dell'Astronomia, scambiate le parti, <lb/>un Aristotelico esca fuori a far gli uffici del Copernico, e Aristotile stesso <lb/>scambi l'abito con Niceta di Siracusa o con Aristarco. </s></p><pb xlink:href="020/01/1266.jpg" pagenum="141"/><p type="main">

<s>Quell'Aristotelico, che venne a restaurare il principato del cuore, come <lb/>il Copernico avea restaurato il principato del Sole, &egrave; Andrea Cesalpino. </s>

<s>Egli <lb/>&egrave; il primo, nella risorta Anatomia, il quale osa di contrapporre all'oracolo <lb/>di Galeno la sentenza che il cuore e non il Fegato &egrave; il principio del san&shy;<lb/>gue. </s>

<s>&ldquo; Quod si cor principium est sanguinis, venarum quoque et arteria&shy;<lb/>rum principium esse debet; vasa enim haec sanguini sunt destinata &rdquo; (Quae&shy;<lb/>stiones perip., Venetiis 1571, fol. </s>

<s>102 ad terg.). </s></p><p type="main">

<s>Sar&agrave; dunque il cuore invece del Fegato l'organo della sanguificazione? </s>

<s><lb/>No, risponde il Cesalpino: quest'organo risulta da tutto insieme il sistema <lb/>venoso, che egli appella col nome di <emph type="italics"/>Viscere,<emph.end type="italics"/> e al quale attribuisce le fun&shy;<lb/>zioni dagli anatomici precursori attribuite al Fegato stesso. </s></p><p type="main">

<s>Il sangue insomma cos&igrave; raccolto e continuamente restaurato dalle vene <lb/>mesenteriche, che assorbono il chilo, ha, secondo il Cesalpino, due moti <lb/>opposti <emph type="italics"/>ad instar Euripi,<emph.end type="italics"/> uno nello venuzze capillari diretto alle parti per <lb/>nutrirle, e l'altro ne'pi&ugrave; grossi tronchi venosi diretto al cuore. </s>

<s>Questa se&shy;<lb/>conda direzione, che va al cuore opposta all'altra del sangue che va alle <lb/>parti, la dimostra il Nostro per via delle allacciature. </s>

<s>&ldquo; Sed illud specula&shy;<lb/>tione dignum videtur propter quid ex vinculo intumescunt venae ultra locum <lb/>apprehensum, non citra, quod experimentum sciunt qui venam secant, vin&shy;<lb/>culum enim adhibent citra locum sectionis, non ultra, quia tument venae <lb/>ultra vinculum, non citra. </s>

<s>Debuisset autem opposito modo contingere, si mo&shy;<lb/>tus sanguinis et spiritus a <emph type="italics"/>Visceribus,<emph.end type="italics"/> fit in totum corpus &rdquo; (Quaestionem <lb/>medicarum, Venetiis 1593, pag. </s>

<s>234). </s></p><p type="main">

<s>Il fine poi, per cui il sangue scende nel cuore, &egrave; quello di concocersi <lb/>nel ventricolo destro, ch'&egrave; la fucina del calore. </s>

<s>Cos&igrave; concetto e purificato <lb/>passa attraverso al setto medio nel ventricolo sinistro, ma perch&egrave; sarebbe <lb/>troppo fervente, una parte, invece di attraversare il setto, va a refrigerarsi <lb/>per la vena arteriosa nel polmone, d'onde cos&igrave; refrigerato torna, per l'ar&shy;<lb/>teria venosa, nel ventricolo sinistro a mescolarsi con l'altro sangue, dive&shy;<lb/>nuto pi&ugrave; sincero e tutto spiritoso. </s>

<s>&ldquo; Cum enim fervere oporteret in corde <lb/>sanguinem ut fieret alimenti perfectio, primo quidem in dextro ventriculo, <lb/>in quo crassior adhuc continetur sanguis, deinde autem in sinistro, ubi sin&shy;<lb/>cerior iam sanguis est, partim per medium septum, partim per medios pul&shy;<lb/>mones, refrigerationis gratia, ex dextro in sinistrum transmittitur &rdquo; (Quae&shy;<lb/>stiones perip. </s>

<s>cit., fol. </s>

<s>112). </s></p><p type="main">

<s>Il sangue nel ventricolo sinistro, divenuto cos&igrave; spiritoso, &egrave;, per la ela&shy;<lb/>sticit&agrave; degli stessi spiriti, diffusivo. </s>

<s>Si diffonde di fatti attraverso all'Aorta <lb/>per l'estreme diramazioni arteriose, dove giunto lo spirito esala, lasciando <lb/>come per sedimento la materia del sangue, che serve a nutrire ogni parte <lb/>del corpo in cui rimane. </s>

<s>&ldquo; Motus igitur continuus a corde in omnes cor&shy;<lb/>poris partes agitur, quia continua est spiritus generatio, qui sua amplifica&shy;<lb/>tione diffundi celerrime in omnes partes aptus est. </s>

<s>Simul autem alimentum <lb/>nutritivum fert, et auctivum ex venis elicit, per osculorum communionem, <lb/>quem Graeci <emph type="italics"/>anastomosim<emph.end type="italics"/> vocant. </s>

<s>Tandem vero, spiritu in aerem ambien-<pb xlink:href="020/01/1267.jpg" pagenum="142"/>tem difflante, alimenti corpulentia remanet partim frigore, partim calore <lb/>coagulata &rdquo; (ibi, fol. </s>

<s>109). </s></p><p type="main">

<s>Chi bene attende a questi chiarissimi sensi facilmente si persuade es&shy;<lb/>sere stata vana l'opera, e inutilmente avere spese tante parole tutti coloro, <lb/>i quali vollero al Cesalpino rivendicare la scoperta del circolo universale. </s>

<s><lb/>Perch&egrave;, lasciamo stare ch'egli, non dando fede al Colombo, ripet&egrave; l'antico <lb/>errore galenico del passaggio del sangue attraverso al setto medio, disse, <lb/>com'apparisce chiaro dall'ultimo luogo citato, che il sangue arterioso non <lb/>ritorna alle vene, ma che si esaurisce tutto nelle estremit&agrave; capillari, parte <lb/>dissipandosi in esalazioni, e parte rimanendo a nutrire le parti. </s>

<s>Anzi, tut&shy;<lb/>t'altro che ricevere le vene dalle arterie, il sistema arterioso <emph type="italics"/>elicit alimen&shy;<lb/>tum auctivum ex venis per osculorum communionem,<emph.end type="italics"/> ossia per i contatti, <lb/>che le due diverse specie di vasi hanno qua e l&agrave; lungo i loro decorsi. </s></p><p type="main">

<s>Il Cesalpino insomma non conobbe formalmente il circolo universale, <lb/>bench&egrave;, tolto di mezzo il Fegato, avesse materialmente descritta la continua&shy;<lb/>zione di tutto il sistema de'vasi sanguiferi, e la loro riunione nel cuore, <lb/>dando cos&igrave; (n&egrave; piccolo ne dovrebhe essere perci&ograve; il merito) la pi&ugrave; prossima <lb/>e immediata preparazione alla grande scoperta arveiana. </s>

<s>Che altro in vero <lb/>rimaneva a fare all'Harvey, dopo il Colombo e il Cesalpino, se non che ri&shy;<lb/>conoscere la vanit&agrave; degli spiriti nella sostanza del sangue, il quale perci&ograve; <lb/>uon esala dagli estremi vasi arteriosi, ma ritorna tutto alle vene? </s></p><p type="main">

<s>Quella vanit&agrave; degli spiriti poi non era difficile lo scoprirla, imparando <lb/>l'arte da chi per esperienza l'aveva confermata. </s>

<s>Il Colombo infatti, in trat&shy;<lb/>tar della vivisezione di un cane aveva scritto: &ldquo; Si arteriam asperam, inter <lb/>annulum et annulum, secueris, et arundinem immiseris, si eam ori admo&shy;<lb/>veris et buccis infles, pulmones illico attolluntur et cor ipsum amplexabun&shy;<lb/>tur, et paulo post pulsus immutabitur seipso maior factus &rdquo; (De re anat., <lb/>pag. </s>

<s>261) attribuendo questa frequenza di polso alla maggior copia d'aria <lb/>passata dal polmone nell'arteria venosa e nel cuore. </s>

<s>L'Harvey, dopo aver os&shy;<lb/>servato che all'ingresso e all'egresso dell'aria si sarebbero dovute opporre <lb/>le valvole tricuspidali e semilunari, ripet&egrave; l'esperienza, ch'ei d&agrave; com'ese&shy;<lb/>cuzion di un progetto di Galeno, e non come un fatto del Colombo, con&shy;<lb/>cludendone contro lo stesso Colombo che dal polmone insufflato non passa <lb/>punto d'aria nella vena polmonare, n&egrave; nel ventricolo sinistro. </s>

<s>&ldquo; Si quis <lb/>experimentum Galeni faceret et cani adhuc viventi tracheam incideret, et <lb/>follibus pulmones aere impleret per vim et distentos ligaret fortiter, idem <lb/>mox dissecto pectore multam aeris copiam in pulmonibus usque ad extre&shy;<lb/>mam illorum tunicam invenerit, sed neque in arteria venosa, neque in si&shy;<lb/>nistro ventriculo cordis quidquam &rdquo; (De motu cordis cit., pag. </s>

<s>18). </s></p><p type="main">

<s>Or essendo i fatti cos&igrave;, come da noi sono stati narrati, domandiamo ai <lb/>nostri Lettori se credono sincera la confessione fattaci dall'Harvey, che cio&egrave; <lb/>unico inspiratore alla sua scoperta sia stato il circolo polmonare descritto <lb/>da Galeno. </s>

<s>Chi sa che Galeno ritenne essere il setto medio perforato, e aver <lb/>le vene la loro origine dal Fegato, domander&agrave; ancora, prima di rispondere, <pb xlink:href="020/01/1268.jpg" pagenum="143"/>se fu egli il primo l'Harvey che emend&ograve; que'galenici errori, e fatto certo che <lb/>non fu cos&igrave;, dovr&agrave; concluderne essere per lo meno sospetta la confessione ar <lb/>veiana, parendo assai pi&ugrave; naturale il riuscir felicemente al termine col fare <lb/>un passo solo, che col dare un gran salto smisurato. </s>

<s>E veramente dal Ce&shy;<lb/>salpino &egrave; un passo, e da Galeno all'Harvey &egrave; un salto tale, che si direbbe <lb/>impossibile alle pi&ugrave; snelle gambe di un uomo. </s></p><p type="main">

<s>Comunque sia, che troppo in lungo ci porterebbe il discorso, uno stra&shy;<lb/>niero, e sia pur se cos&igrave; vuolsi che ne fosse inconsapevole, sent&igrave; viva nella <lb/>mente quell'efficacia delle tradizioni scientifiche italiane, alla quale gl'Ita&shy;<lb/>liani stessi rimasero ottusi, e a lui tocc&ograve; il merito di dar l'ultima perfezione <lb/>alle idee del Cesalpino, sentenziando il sangue arterioso non restar nelle <lb/>estremit&agrave; capillari, n&egrave; esser le vene dello stesso sangue riproduttrici e re&shy;<lb/>stauratrici, ma &ldquo; ab unoquoque membro ipsas venas hunc sanguinem per&shy;<lb/>petuo retroducere ad cordis locum &rdquo; (De motu cordis cit., pag. </s>

<s>58). La ve&shy;<lb/>rit&agrave; della qual sentenza &egrave; provata nel suo libro dall'Harvey con argomenti <lb/>di vario genere, nell'ammannire i quali e nel convalidarli ebbero, come ve&shy;<lb/>dremo nella seguente storia, grandissima parte i nostri Italiani. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Che il sangue abbia nelle vene il suo corso diretto verso il cuore si <lb/>prova dall'Harvey prima di tutto per via delle allacciature, nel modo stesso <lb/>indicato dal Cesalpino, ed &egrave; questo anzi l'argomento, di che si fanno prin&shy;<lb/>cipalmente forti gl'inconsiderati zelanti, che vorrebbero sopra l'Inglese al <lb/>Nostro rivendicare la gloriosa scoperta. </s>

<s>L'altra prova sperimentale &egrave; dal&shy;<lb/>l'Autore <emph type="italics"/>De motu cordis<emph.end type="italics"/> dedotta dalle valvole, la scoperta delle quali &egrave; ivi <lb/>attribuita o al Fabricio d'Acquapendente o a Giacomo Sylvio, come vuole <lb/>il Riolano. </s>

<s>Ma perch&egrave; veramente il Sylvio non ha gran parte in quella sco&shy;<lb/>perta, e il Fabricio, bench&egrave; ve n'abbia grandissima, non pu&ograve; pretendersi i <lb/>primi onori, convien che, in cosa di tanto momento, la nostra storia risalga <lb/>a investigar del fatto i primi principii. </s></p><p type="main">

<s>Ritrovandosi in Ratisbona don Francesco d'Este gravemente infermo, <lb/>fu da Ferrara mandato a curarlo Giovan Batista Canani, archiatro ducale. </s>

<s><lb/>O fosse chiamato a consulto o si trovasse ivi per caso, visitava col Canani <lb/>l'infermo anche il Vesalio, e i due Medici, trovandosi nella medesima ca&shy;<lb/>mera insieme, vi si trattenevano a colloquio di cose anatomiche. </s>

<s>Era sui primi <lb/>anni della pubblicazione della grande opera <emph type="italics"/>De corporis humani fabrica,<emph.end type="italics"/><lb/>e il nostro Ferrarese, lieto di poter significare la sua ammirazione alla pre&shy;<lb/>senza del celebre Autore, rivolse un giorno il discorso sopra ci&ograve; che, in <lb/>principio del cap. </s>

<s>IV del III libro, aveva letto della fabbrica delle vene e <lb/>delle arterie, riassumendo il senso di queste parole, stampate a pag. </s>

<s>261 <lb/>della prima edizione dell'Opera vesaliana fatta nel 1543 in Basilea. </s>

<s>&ldquo; Sicut <pb xlink:href="020/01/1269.jpg" pagenum="144"/>Natura venae et arteriae, praeter proprias ipsarum tunicas, aliam subinde <lb/>membranam circumdedit, cuius beneficio opportune conterminis partibus <lb/>alligatur, tuteque prorepat; sic quoque, cum minime ignoraret unumquod&shy;<lb/>que vas inibi noxiis opportunius expositum esse, ubi in ramos discinditur, <lb/>tutae fixionis gratia, praeter eiusmodi membranas, substantiam quamdam <lb/>mediocriter mollem modiceque cedentem condidit, qua nodorum in arbori&shy;<lb/>bus ritu vasorum divaricationes sic passim replent. </s>

<s>&rdquo; </s></p><p type="main">

<s>Soggiungeva il Canani di avere altre singolarit&agrave; scoperto nelle vene, e <lb/>specialmente nel principio della vena azygos o <emph type="italics"/>senza pari,<emph.end type="italics"/> nelle vene renali, <lb/>e in quelle adiacenti alla parte pi&ugrave; elevata dell'osso sacro, ed erano quelle <lb/>nuove cose scoperte alcune membrane similissime nella struttura e nella <lb/>disposizione a quelle, che si osservano ne'principii della vena arteriale e <lb/>della grande arteria, l'ufficio proprio delle quali membrane credeva il Ca&shy;<lb/>nani che fosse quello d'impedire il reflusso del sangue. </s>

<s>Udito ci&ograve; e tornan&shy;<lb/>dogli cosa nuova, si sent&igrave; il Vesalio frugato da una viva curiosit&agrave; di veri&shy;<lb/>ficarla, tanto pi&ugrave;, quando nel 1547 Amato Lusitano divulg&ograve; la scoperta dello <lb/>stesso Canani, aggiungendovi di suo per confermarla un'esperienza, la quale <lb/>essendo manifestamente falsa, anzi mendace, tinse della sua pece il vero, <lb/>che fu perci&ograve; dagli Anatomici, per tutto il rimanente secolo XVI, con fiera <lb/>ostinazione perseguitato. </s></p><p type="main">

<s>L'esperienza del Lusitano consisteva nel soffiar nella Vena senza pari, <lb/>e nell'asseverare che il fiato, nonch&egrave; il sangue, per l'impedimento oppo&shy;<lb/>stogli dalle valvole non andava a riuscire nella vena Cava. </s>

<s>Il Vesalio dun&shy;<lb/>que, datosi a far pi&ugrave; diligente anatomia, e non trovando segni evidenti della <lb/>figura di quelle valvole, e dall'altra parte facilmente scoperta la menzogna <lb/>del Lusitano, ne concluse che tutti coloro, i quali dopo il Canani dicevano <lb/>di avere osservate le dette valvole in tutte le vene del corpo, e particolar&shy;<lb/>mente delle braccia e delle gambe, dovevano essere stati allucinati da quelle <lb/>membrane, che la Natura appose qua e l&agrave; ne vasi sanguiferi per loro rin&shy;<lb/>forzo. </s>

<s>Nella seconda edizione perci&ograve; della sua Opera anatomica, al capitolo <lb/>sopra citato aggiunse queste parole: &ldquo; Venarum haec crassior substantia, <lb/>quum venae sanguine inanitae intus conspiciuntur, flaccidaeque secundum <lb/>ipsarum ductum dissectae propendent; ita versus venarum amplitudinem <lb/>connivet, ut inter secandum astantium nonnulli eam instar membranei cor&shy;<lb/>poris procreatam aliquando contenderint, quod urinam in meatibus hanc a <lb/>renibus in vesicam deferentes refluere, retrudive prohibet. </s>

<s>Ubi etiam nonnun&shy;<lb/>quam eminentem illam venarum corporis substantiam membranis compa&shy;<lb/>rare studuerunt, quae magnae arteriae et venae arterialis, ubi haec e corde <lb/>prodeunt spectantur orificiis, perinde sane ac si, e vena sine pari et e venis <lb/>brachia caput, renes et crura adeuntibus, eiusmodique compluribus venis <lb/>sanguinem in Cavae caudicem, vel in sanguinis missione et variis animi mo&shy;<lb/>tibus, eiusmodique occasionibus, remeare refluereve, secus multo quam ego <lb/>existimo, foret impossibile, qui crassiorem eam venae corporis, in ipsa ra&shy;<lb/>morum dissectione occurrentem substantiam, roboris cuiusdam gratia e Na-<pb xlink:href="020/01/1270.jpg" pagenum="145"/>tura procreatam esse in scholis contendere soleo, pravi quorundam iudicio <lb/>haud ignarus, qui, integris venis, ne flatum quidem, e vena pari carente in <lb/>Cavae caudicem, duci posse turpiter confingunt &rdquo; (Basileae 1555, pag. </s>

<s>278). </s></p><p type="main">

<s>A cos&igrave; fiero risentimento, espresso in queste ultime parole contro il <lb/>Lusitano, fece eco il Falloppio, il quale anzi rincrudeli l'accusa dicendo <lb/>quello essere non un pravo giudizio, n&egrave; una turpitudine, ma un vero de&shy;<lb/>litto. </s>

<s>Nelle Osservazioni anatomiche infatti, dop'aver riferito ci&ograve; che lo stesso <lb/>Lusitano dice delle valvole nella vena azygos, e in altre, soggiunge che co&shy;<lb/>stui, presente alle dissezioni del Canani, non dovette aver n&egrave; bene veduto <lb/>i fatti, n&egrave; bene intese le parole di quel dottissimo e venerabile uomo, l'at&shy;<lb/>tribuire al quale i proprii errori era un rendersi colpevole del delitto della <lb/>calunnia. </s>

<s>&ldquo; Quare ego in Amatum, virum alioquin doctum, potius culpam <lb/>huius criminis reiicerem, quoniam non ita recte omnia, quae ad Anatomen <lb/>pertinent, aut viderit aut intellexerit, ut recte sunt a Canano explicata &rdquo; <lb/>(Opera omnia, Francofurti 1584, pag. </s>

<s>443). </s></p><p type="main">

<s>Fu da queste parole che, passando il Vesalio ad esame ogni detto del <lb/>Falloppio, prese occasione di compendiar la storia da noi narrata in princi&shy;<lb/>pio del presente discorso. </s>

<s>&ldquo; Ratisbonae, quum dom. </s>

<s>Franciscum Estensem <lb/>aegrum cum ipso Canano viserem, is mihi retulit se in Venae coniuge ca&shy;<lb/>rentis initio, et idem in venarum renes adeuntium, et in sectionum venae, <lb/>iuxta elatiorem sacri ossis sedem occurrentium orificiis, membranas eiusmodi <lb/>observare, quales in Venae arterialis et Magnae arteriae occurrunt princi&shy;<lb/>piis, hasque sanguinis refluxui obstare asseruit. </s>

<s>Unde aliam hinc occasio <lb/>afferebatur ut rem num ita se haberet mox sectione expedirem. </s>

<s>Cumque <lb/>Amatum insuper in Canani comperirem esse sententia, illumque ex huius <lb/>iudicio pendere legerem, fini capitis illius, quo qui natura venarum robori <lb/>in distributione prospexit, prosequor, satis dilucide addidi quidnam de eius&shy;<lb/>modi membranis veniat statuendum: has nemque non reperi &rdquo; (Anatomi&shy;<lb/>carum Gabr. </s>

<s>Falloppii Observat. </s>

<s>Examen, Venetiis 1564, pag. </s>

<s>83). </s></p><p type="main">

<s>Il Colombo pure, tacendone, sembra che non le trovasse ne'tronchi e <lb/>ne'rami delle altre vene, fuor che nelle meseraiche, l&agrave; dove s'aprono a sug&shy;<lb/>gere dagli intestini il chilo, dicendo essere state con grand'arte dalla Natura <lb/>ivi apposte &ldquo; ut chylum facile suscipere possent, ne autem egrediatur mem&shy;<lb/>branulae illae prohibent &ldquo; (De re anat. </s>

<s>cit., pag. </s>

<s>165). Sulla fine del se&shy;<lb/>colo XVI Giovan Batista Carcano e Andrea Laurent, per citar due de'pi&ugrave; <lb/>celebri anatomici fra gl'Italiani e gli stranieri di que'tempi, negarono essi <lb/>pure l'esistenza delle valvole, intorno a che il Laurent stesso ha queste <lb/>espresse parole: &ldquo; Quas autem in azygos ramis somniavit membranulas, <lb/>velut hostiola sanguinis refluxum impedientia, Amatus Lusitanus, nobis nec <lb/>cuiquam adhuc vidisse contigit &rdquo; (Historia anat. </s>

<s>corporis hum., Parisiis 1599, <lb/>pag. </s>

<s>92). </s></p><p type="main">

<s>Come se la storia de'fatti fin qui narrati fosse stata cancellata dai libri, <lb/>il Fabricio d'Acquapendente un giorno del 1574 preme a caso col dito una <lb/>vena, e vede formarsi in essa un rigonfiamento, senza dubbio per un ri-<pb xlink:href="020/01/1271.jpg" pagenum="146"/>stagno di sangue: frega in gi&ugrave; col dito sulla stessa vena, e vede farsi lo <lb/>stesso. </s>

<s>Non sapendo in sull'istante qual si fosse la causa di ci&ograve;, gli occorse <lb/>poi sezionando di trovar le vene attraversate qua e l&agrave; dalle valvole, alle quali <lb/>non ebbe dubbio di attribuire quell'osservato ristagno. </s>

<s>Che tal si fosse ve&shy;<lb/>ramente l'origine della scoperta lo dice da s&egrave; l'Autore, con queste parole: <lb/>&ldquo; Si enim premere, aut deorsum fricando adigere sanguinem tentes, cursum <lb/>ipsius ab ipsis ostiolis intercipi remorarique aperte videbis, neque enim ali&shy;<lb/>ter ego in huiusmodi nolitiam sum deductus &rdquo; (De vunarum ostiolis, Pa&shy;<lb/>duae 1603, pag. </s>

<s>2). </s></p><p type="main">

<s>Contento per allora il Fabricio a diffonder con la viva voce negli sco&shy;<lb/>lari la sua scoperta, Salomone Alberto, tedesco, ne scrisse il primo, nel 1579, <lb/>per le stampe, divulgandola fra'suoi nazionali, col darne la debita gloria allo <lb/>scopritore, ci&ograve; che fece risolverlo finalmente a pubblicare in Padova quel&shy;<lb/>l'opuscolo <emph type="italics"/>De venarum ostiolis,<emph.end type="italics"/> dedicato all'inclita nazione germanica, e <lb/>dove pi&ugrave; efficacemente delle brevi parole parlano le bellissime otto grandi <lb/>tavole aggiunte. </s>

<s>Chi ha letto la storia sopra narrata non pu&ograve; certamente <lb/>capacitarsi come nel 1603 il Fabricio potesse cos&igrave; scrivere, nell'introdursi a <lb/>trattare di quell'argomento. </s>

<s>&ldquo; De his itaque in praesentia locuturi, subit <lb/>primum mirari quomodo ostiola haec, ad hanc usque aetatem, tam priscos <lb/>quam recentiores Anatomicos adeo latuerint, ut non solum nulla prorsus <lb/>mentio de ipsis facta sit, sed neque aliquis prius haec viderit, quam anno <lb/>Domini septuagesimo quarto supra millesimum et quingentesimum, quo a <lb/>me summa cum laetitia inter dissecandum observata fuere &rdquo; (pag. </s>

<s>1). </s></p><p type="main">

<s>Un altro fatto riman pure incompreso in questa storia, ed &egrave; che, osti&shy;<lb/>natamente negata la scoperta delle valvole al Canano, fosse poi creduta al&shy;<lb/>l'Acquapendente da tutti senza contradizione. </s>

<s>Si potrebbe forse attribuire <lb/>la cosa al progresso, fatto dal pensiero scientifico in pi&ugrave; di un mezzo secolo <lb/>di tempo, ma v'ebbe forse gran parte l'antipatia al Lusitano, ebreo, e la <lb/>simpatia per l'Acquapendente, venerabile vecchio. </s></p><p type="main">

<s>Da questo, che giusto &egrave; detto <emph type="italics"/>venerabilis senex,<emph.end type="italics"/> confessa di aver avuto <lb/>la scoperta l'Harvey, n&egrave; gli giova chiamare in parte del merito il Sylvio, <lb/>posteriore al Canano, e complice di quel crimine, di che facevasi terribile <lb/>accusatore il Falloppio. </s>

<s>Poco pi&ugrave; tardi s'incominci&ograve; a dare all'Acquapen&shy;<lb/>dente un altro competitore in Paolo Sarpi, alla qual voce dovette aver ag&shy;<lb/>giunto non poco credito il Peiresc, che a proposito della scoperta arveiana, <lb/>discorrendo delle valvole, si ricordava, secondo che riferisce il Gassendi nella <lb/>Vita di lui, esserne stato <emph type="italics"/>inventorem primum Sarpium servitam<emph.end type="italics"/> (Pari&shy;<lb/>siis 1641, pag. </s>

<s>222). Ma perch&egrave; i fanatici non seppero poi confermar la sen&shy;<lb/>tenza coi documenti, non rimane ai savii a ragionare in altro modo da quel <lb/>che insegnava il Morgagni, a cui non pareva possibile che un fraticello no&shy;<lb/>vizio di 22 anni si facesse dimostratore a un vecchio e peritissimo anato&shy;<lb/>tomico. </s>

<s>N&egrave; val che l'Acquapendente ricordi il Sarpi nell'osservazione della <lb/>pupilla, che si dilata e si restringe secondo che la luce &egrave; debole o viva, <lb/>&ldquo; haec autem, bene avverte lo stesso Morgagni, non quae ad corporis struc-<pb xlink:href="020/01/1272.jpg" pagenum="147"/>turam, sed quae ad actiones attinebant; non quae ad scalpellum require&shy;<lb/>bant, sed quae per se ante oculos posita erant; non quae Sarpius primum, <lb/>sed quae alii antea animadverterant &rdquo; (Epistolae anat., T. II, Venetiis 1740, <lb/>pag. </s>

<s>155). </s></p><p type="main">

<s>Comunque sia, n&egrave; l'Acquapendente n&egrave; il Sarpi conobbero l'uso delle <lb/>membrane applicate alle interiori pareti delle vene, e quelli stessi primi, che <lb/>riconobbero un tal uso nel proibire il reflusso del sangue, credendone di&shy;<lb/>retto il moto dal cuore alle parti, interpetrarono al contrario del vero le in&shy;<lb/>tenzioni della Natura. </s>

<s>Che il vero ufficio delle valvole consistesse nel pro&shy;<lb/>durre un effetto, contrario a quello creduto dal Canani e dai seguaci di lui; <lb/>che consistesse insomma nel facilitare l'ingresso, e no nell'impedire il re&shy;<lb/>gresso del sangue nel cuore, fu primo a intenderlo l'Harvey, il quale anzi <lb/>lo rese visibile per via dello spicillo, che intromesso dalle radici ai rami non <lb/>passa impedito dalle valvole, mentre passa con facilit&agrave; intromesso dai rami <lb/>alle radici. </s>

<s>&ldquo; Ego illud saepissime in dissectione venarum expertus sum, si <lb/>a radice venarum initio facto versus exiles venarum ramos spicillum mitte&shy;<lb/>rem, quanto potuerim artificio, ob impedimentum valvularum longius im&shy;<lb/>pellere non potuisse: contra vero forinsecus, a ramulis radicem versus, fa&shy;<lb/>cillime &rdquo; (De motu cordis cit., pag. </s>

<s>78). </s></p><p type="main">

<s>Cos&igrave;, con questo nuovo efficace argomento confermandosi la verit&agrave; <lb/>insegnata dal Cesalpino, che cio&egrave; il sangue nelle vene non va dal cuore <lb/>alle parti, ma dalle parti, attinto alle arterie, ritorna nel cuore; si rendeva <lb/>probabilissimo il fatto del circolo universale del sangue, che nel 1628 ve&shy;<lb/>niva in pubblico a proporre ai Fisiologi Guglielmo Harvey. </s>

<s>Abbiamo detto <lb/>che si rendeva probabilissimo quel fatto, non per&ograve; ancora con certezza di&shy;<lb/>mostrato, rimanendo per avere una tal certezza a verificarsi due supposti <lb/>dell'Harvey, il primo de'quali era che il sangue della Vena porta mettesse <lb/>nella Cava, e il secondo che il sangue entrato nelle estremit&agrave; venose fosse <lb/>veramente quello uscito dalle arteriose. </s></p><p type="main">

<s>Il primo supposto deriv&ograve;, come vedemmo, nell'Harvey dal Cesalpino, <lb/>il quale ne dette una dimostrazione a suo modo, per cui sarebbe allo stesso <lb/>Harvey bisognato ridurre gli argomenti peripatetici a prove sperimentali. </s>

<s>Ma <lb/>perch'ei non volle o non seppe farlo, si trov&ograve; senza difesa assalito dalle <lb/>armi del Riolano, che propugnando gli antichi errori non negava il circolo <lb/>universale, ma lo rompeva in due, uno che avesse per centro il Fegato e <lb/>l'altro il Cuore. </s>

<s>Tenne quel poderoso assalto vacillante la dottrina arveiana, <lb/>infin tanto che il Pecquet non venne coll'esperienza a riconfermarla. </s>

<s>Es&shy;<lb/>sendo egli ben persuaso che quel profluvio di sangue della Vena porta si <lb/>affretta di scendere alla Cava, se ne assicur&ograve; soffocando con un laccio il <lb/>ramo della stessa Cava, ch'entra sotto alla gibbosit&agrave; del Fegato, &ldquo; ac tum <lb/>ad vinculum sanguis proruens, ingurgitato supramodum a Jecore ramo, do&shy;<lb/>cuit Portae cum Cava manifestum commercium, quamque apposite doctis&shy;<lb/>simus inter anglos medicos Io. (sic) Harveius universi motum sanguinis <lb/>dixerit circularem &rdquo; (Dissertatio de circul. </s>

<s>sang., Parisiis 1654, pag. </s>

<s>33). </s></p><pb xlink:href="020/01/1273.jpg" pagenum="148"/><p type="main">

<s>L'altro supposto arveiano, che cio&egrave; il sangue estravasato dalle arterie <lb/>ritornasse tutto alle vene, era anche di pi&ugrave; difficile dimostrazione. </s>

<s>Galeno <lb/>aveva insegnato che ne'polmoni le estremit&agrave; capillari dell'arteria venosa <lb/>avevano comunicazione diretta, per via delle anastomosi, colle estremit&agrave; della <lb/>vena arteriosa &ldquo; sed nec ipse Galenus, dice lo stesso Harvey, neque ulla <lb/>experientia unquam sensibiles anastomoses conspexerunt aut ad sensum <lb/>ostendere potuerunt &rdquo; (Exercitatio Ia De circulat. </s>

<s>sanguinis, in appendice <lb/>all'Exercit. </s>

<s>De motu cordis cit., pag. </s>

<s>124). N&egrave; ci&ograve; asserisce per le relazioni <lb/>altrui, ma per la testimonianza degli occhi suoi proprii, perch&egrave;, avendo con <lb/>laboriosa diligenza esplorate quelle galeniche anastomosi, non gli era mai <lb/>riuscito di rinvenirle. </s>

<s>&ldquo; Ego qua potui diligentia perquisivi, et non parum <lb/>olei et operae perdidi in anastomosi exploranda, nusquam autem invenire <lb/>potui vasa invicem, arterias scilicet cum venis per orificia copulari &rdquo; (ibi). <lb/>Non per questo, con quella modesta saviezza ch'&egrave; propria de'grandi inge&shy;<lb/>gni, cred&egrave; di dovere assoluta<gap/>ente negare il fatto, ma tenendo per cosa certa <lb/>che il sangue in ogni modo dalle arterie tornava alle vene, lasci&ograve; indeciso <lb/>se ci&ograve; avvenisse &ldquo; per anastomosin immediate, vel mediate per carnis po&shy;<lb/>rositates &rdquo; (De motu cordis cit., pag. </s>

<s>66). </s></p><p type="main">

<s>Il Pecquet, non potutosi poi nemmen egli assicurare, per esperienza sua <lb/>propria, di quella immediata comunicazione tra'vasi, teneva che fosse molto <lb/>pi&ugrave; probabile un estravasamento del sangue arterioso, e con ci&ograve;, forse senza <lb/>saperlo, emendava le idee del Cesalpino, e le riduceva al senso arveiano, <lb/>asserendo col nostro Peripatetico che una parte di quello stesso sangue ar&shy;<lb/>terioso estravasato rimaneva per nutrimento delle parti, e che l'altra non <lb/>esalava, ma, rimescolata colla fluidit&agrave; del siero, tornava alle vene. </s>

<s>&ldquo; Imo po&shy;<lb/>tius autumarem, per anastomoseis extra arteriarum claustra, transcolandam <lb/>in carnes exuberare sanguinis partem, ut inde, quod exactiori coctione dispo&shy;<lb/>situm est, in similarium sidet nutrimentum; quidquid vero minus digestum, <lb/>cum fluidiori sero in venas, a foris in interiora circumquaque pervias, re&shy;<lb/>fugiat. </s>

<s>Nam si perpetuus intra vasa fluor nullnm extra sanguinem effundat, <lb/>unde corporeae molis augmentum? </s>

<s>et si sit in iugi motu corporearum par&shy;<lb/>tium substantia, unde tabidam fatiscentium maciem instaurari? </s>

<s>&rdquo; (Disser&shy;<lb/>tatio anat. </s>

<s>de circ. </s>

<s>sang. </s>

<s>cit., pag. </s>

<s>39). </s></p><p type="main">

<s>Erano dunque XXIII anni passati, da che aveva l'Harvey pubblicate le <lb/>sue esercitazioni anatomiche <emph type="italics"/>De circulatione sanguinis,<emph.end type="italics"/> e il gran fatto fisio&shy;<lb/>logico, bench&egrave; si tenesse da'pi&ugrave; savii per certo, non era per&ograve; d'ogni sua <lb/>parte tanto ben dimostrato, da levare ai dubbiosi ogni motivo, e ai contra&shy;<lb/>dittori ogni pretesto. </s>

<s>Nel 1661 esercitava il Malpighi la sua perizia anatomica <lb/>intorno ai polmoni, e tra l'esame del paranchima, che gli frutt&ograve; tante nuove <lb/>e gloriose scoperte, non volle lasciare inesplorate quelle anastomosi, che <lb/>aveva a Galeno <emph type="italics"/>nimis forsan audacter<emph.end type="italics"/> negato lo stesso Harvey. </s>

<s>Dando il <lb/>primo esempio ai Fisiologi futuri, fu esso Malpighi che si serv&igrave; per quella <lb/>esplorazione delle iniezioni, scegliendo a principio il mercurio, che vedeva <lb/>trasparire in un bell'albero di argento, e poi dell'acqua tinta di nero. </s>

<s>Ma <pb xlink:href="020/01/1274.jpg" pagenum="149"/>i trasudamenti attraverso ai pori de'vasellini rendevano difficile a discer&shy;<lb/>nere, fra tante intricate vie, qual fosse la pi&ugrave; immediata e diretta, cosicch&egrave; <lb/>nulla venivasi da tali delicatissime esperienze a decider di certo intorno alle <lb/>anastomosi desiderate. </s>

<s>&ldquo; An haec vasa in sinibus vel alibi mutuam habeant <lb/>anastomosim, ita ut sanguis a vena resorbeatur continuato tramite, an vero <lb/>hient omnes in pulmonum substantiam, dubium quod adhuc mentem meam <lb/>torquet, pro quo enodando incassum licet plura et plura molitus sum aere <lb/>et liquidis varie tinctis. </s>

<s>Saepius enim immissam aquam nigram syphone per <lb/>arteriam pulmonarem, a pluribus erumpentem vidi partibus, nam facta levi <lb/>compressione solet exsudare a membrana investiente, partim etiam coacer&shy;<lb/>vari in interstitiis, maior vero copia cum immixto sanguine erumpit per ve&shy;<lb/>nam pulmonarem, et quod mirabilius est per tracheam diluta et minus co&shy;<lb/>lore tincta cum levi spuma &rdquo; (Opera omnia, Londini 1687, pag. </s>

<s>136). </s></p><p type="main">

<s>Anche dopo queste prime esperienze, che promettevano di riuscire cos&igrave; <lb/>concludenti, il sistema arveiano dunque si trovava in quelle medesime con&shy;<lb/>dizioni, che ritrovavasi il sistema copernicano, quando ancora nessuno, in <lb/>Venere falcata o in Marte scantonato, se n'era assicurato con gli occhi. </s>

<s>Il <lb/>Copernico rilasciava questa gloria a Galileo, e una gloria simile al Malpighi <lb/>la rilasciava l'Harveio. </s></p><p type="main">

<s>Nella Lettera seconda al Borelli sull'anatomia de'polmoni incomincia <lb/>a dir l'Autore di aver nella prima lasciata indietro la soluzione di due im&shy;<lb/>portantissimi problemi: &ldquo; Primum erat quodnam sit rete illud descriptum, <lb/>quo singulae vesicae et sinus quodammodo vinciuntur in pulmonibus: al&shy;<lb/>terum erat an pulmonum vasa mutua anastomosi iunganlur an vero hient <lb/>in communem pulmonum substantiam et sinus: problemata quae soluta <lb/>maioribus sibi viam agent, et ob oculos Naturae operationes clarius sunt po&shy;<lb/>situra, pro quibus enodandis fere totum ranarum genus perdidi, quod non <lb/>contingit in effera illa Homeri Batrachomyomachia. </s>

<s>In ranarum enim ana&shy;<lb/>tome, quam favente excellentissimo D. </s>

<s>Carolo Fracassato collega meo insti&shy;<lb/>tueram, ut certior fierem circa membraneam pulmonum substantiam, talia <lb/>mihi videre contingit ut non immerito illud Homeri usurpari possim ad rem <lb/>praesentem melius: <emph type="italics"/>Magnum certum opus oculis video.<emph.end type="italics"/> Nam in hac, propter <lb/>structurae simplicitatem vasorumque et fere totius diaphanitatem quae ocu&shy;<lb/>los in penitiora admittit, evidentius res ita demonstrantur, ut caeteris obscu&shy;<lb/>rioribus lucem sint tandem allaturae &rdquo; (ibi, pag. </s>

<s>140, 41). </s></p><p type="main">

<s>Ecco dunque lo spettacolo, meglio di quello divinamente descritto da <lb/>Omero, degno di poema eroico e di storia: ecco il sistema del Microcosmo, <lb/>rivelato gi&agrave; al Copernico inglese, fatto finalmente veder con gli occhi dal <lb/>nuovo Galileo di Bologna: &ldquo; Aperto igitur ranarum abdomine, et retracto <lb/>mesenterio, appensisque intestinis, motum sanguinis in ramis Venae portae <lb/>et sociae arteriae reliquorumque infimi ventris vasis contemplatus, haec fre&shy;<lb/>quentius succedere observavi. </s>

<s>Sanguis itaque in venis movetur a peripheria <lb/>corporis ex ramis minimis in minores, et successive in truncos et postremo <lb/>in cor &rdquo; (M. Malpighi, Opera postuma cit., pag. </s>

<s>91). </s></p><pb xlink:href="020/01/1275.jpg" pagenum="150"/><p type="main">

<s>A diffondere per&ograve; la scoperta, invitando i Naturalisti ad assicurarsi della <lb/>verit&agrave; lungamente desiderata, e i curiosi a ricrearsi del giocondo spettacolo <lb/>maraviglioso, efficacemente concorsero i discepoli del Malpighi, fra'quali <lb/>Giorgio Baglivi, che nel 1696, pubblicando i suoi Esperimenti anatomici, in&shy;<lb/>titolava l'XI di essi <emph type="italics"/>De circulatione sanguinis in Rana.<emph.end type="italics"/> Dava quivi l'Au&shy;<lb/>tore alcune importanti notizie taciute dal suo Maestro, relative alle qualit&agrave; <lb/>de'Microscopii da usarsi, avvertendo che non voglion essere composti di due <lb/>lenti, come quelli fabbricati dal Divini, ma di una lente sola, tenuta colla <lb/>mano destra per osservare al sole la Rana presa con le dita della sinistra. <lb/></s>

<s>&ldquo; Ad haec experimenta peragenda utendum est Mycroscopio unius lentis, <lb/>quod dextra manu tenendum: e contra Rana sinistrae manus digitis ac&shy;<lb/>curate prehensa, lumini Solis obiiciatur &rdquo; (Opera omnia, Lugduni 1710, <lb/>pag. </s>

<s>680). </s></p><p type="main">

<s>La notizia delle nuove cose osservate in Italia si diffuse ben presto al&shy;<lb/>l'intorno, e il Leuwenhoeck, in quel medesimo anno 1696 che il Baglivi <lb/>pubblicava il suo sperimento anatomico sopra la Rana, scriveva di aver fatte <lb/>le medesime osservazioni sopra la coda di alcune piccole anguille. </s>

<s>&ldquo; Hisce <lb/>anguillis, Mycroscopio appositis oculisque demissis in pinnam caudalem,.... <lb/>cum voluptate vidi sanguinis periodum &rdquo; (Arcanorum Naturae continuatio, <lb/>Lugduni Batav. </s>

<s>1722, pag. </s>

<s>131) e lo fece poi vedere all'amico suo Cristiano <lb/>Huyghens, il quale cos&igrave; solennemente commemor&ograve; nella sua <emph type="italics"/>Dioptrica<emph.end type="italics"/> il filo&shy;<lb/>sofico piacere provato in quella naturale contemplazione: &ldquo; In his (cio&egrave; nei <lb/>Microscopi semplici da lui detti <emph type="italics"/>batavici,<emph.end type="italics"/> e dai nostri Fiorentini <emph type="italics"/>della per&shy;<lb/>lina<emph.end type="italics"/>) est observatio manifesta circularis motus sanguinis, quem, monstrante <lb/>A. </s>

<s>Lewenoechio nostro diligentissimo horum investigatore, in angnillae cauda <lb/>summa cum voluptate conspeximus. </s>

<s>Est enim perlucida ac sanguis, globulis <lb/>subrubentibus constans, celeri motu per canaliculos arteriarum, qui venis <lb/>continuantur, discurrit. </s>

<s>Quod haud dubio in caeteris quoque animalibus ani&shy;<lb/>madverteretur, sed non facile partes luci perviae in his reperiuntur. </s>

<s>Anguil&shy;<lb/>lulam vivam in tubum vitreum demiserat, aqua semiplenum, cui extrinse&shy;<lb/>cus Mycroscopium applicabat, ea parte, qua cauda extrema vitrum tangebat &rdquo; <lb/>(Lugduni Batav. </s>

<s>1703, pag. </s>

<s>226, 27). </s></p><p type="main">

<s>L'argomento dall'analogia, di che fa uso qui l'Huyghens, era senza <lb/>dubbio ragionevole: era ragionevole cio&egrave; che le cose osservate in Italia sopra <lb/>le rane e in Olanda sopra le anguille, <emph type="italics"/>in caeteris quoque animalibus ani&shy;<lb/>madverterentur,<emph.end type="italics"/> ma pur v'era anche ragionevole motivo di dubitarne, po&shy;<lb/>tendo il sangue caldo, pi&ugrave; denso e pi&ugrave; coagulabile, non passar cos&igrave; facil&shy;<lb/>mente per i minimi vasi, come vi si vedeva passare il sangue freddo. </s>

<s>Fu <lb/>questa forse la ragione per cui, nonostante le osservazioni del Malpighi sopra <lb/>le rane, il Borelli e il Guglielmini, come si par dai passi altrove recati, ri&shy;<lb/>masero tuttavia in dubbio delle anastomosi negli animali a sangue caldo, e <lb/>inclinarono ad ammettere col Pecquet un estravasamento del sangue arte&shy;<lb/>rioso nelle porosit&agrave; della carne, d'onde attingessero le vene ci&ograve; che v'era <lb/>d'avanzo per la nutrizione. </s></p><pb xlink:href="020/01/1276.jpg" pagenum="151"/><p type="main">

<s>A voler che dunque la dimostrazione del circolo arveiano risultasse da <lb/>ogni parte completa, conveniva anch'estenderla agli animali a sangue caldo. </s>

<s><lb/>Ma l'opacit&agrave; delle tuniche de'vasi, e il sangue che cos&igrave; facilmente si rap&shy;<lb/>piglia nell'aperto ventre dell'animale, sotto le impressioni dell'aria, avevano, <lb/>infino a qualche anno dopo la prima met&agrave; del secolo XVIII, resa inutile <lb/>ogni pi&ugrave; sollecita industria. </s>

<s>Perci&ograve; l'Haller scriveva nel I Tomo della sua <lb/>grande Fisiologia: &ldquo; Primus Guilielmus Cowper in fele iuniori, in mesen&shy;<lb/>terio canino et in omento felis rete arteriolarum et venularum sibi lnoscu&shy;<lb/>latarum delineavit, raro certe felicitatis exemplo. </s>

<s>Mihi enim in calidi san&shy;<lb/>guinis animalibus hactenus ne motum quidem sanguinis, et multo minus <lb/>circuitum, conspicuum videre datum est &rdquo; (Lausannae 1757, pag. </s>

<s>238). </s></p><p type="main">

<s>Ma le osservazioni del Cowper intorno agli animali caldi, essendo ri&shy;<lb/>strette all'accennare il semplice moto de'globetti sanguigni ne'vasi pi&ugrave; sot&shy;<lb/>tili, parvero al caso troppo piccola cosa allo Spallanzani, il quale si sentiva <lb/>ardere di quella nuova sete di scienza, n&egrave; aveva ancora potuto spengerla, <lb/>quando inaspettatamente dalla sua buona ventura si trov&ograve; condotto sul verde <lb/>margine di una fonte nascosta. </s></p><p type="main">

<s>&ldquo; Un giovane medico (cos&igrave; egli stesso nell'introduzione al libro <emph type="italics"/>De'fe&shy;<lb/>nomeni della circolazione<emph.end type="italics"/> ci narra questa importantissima storia) valente in <lb/>Anatomia, il signor dottor Rezia comasco, ripetendo per utile suo svaga&shy;<lb/>mento le sensate osservazioni dell'Haller <emph type="italics"/>Sulla formazione del pulcino,<emph.end type="italics"/> volle <lb/>farmene partecipe col mostrarmi giornalmente i progressi di quell'uccello <lb/>racchiuso ancora nell'uovo. </s>

<s>Un giorno portommi uno di quest'uova covate, <lb/>rotto ed aperto nella parte ottusa del guscio, il qual uovo era pi&ugrave; rimarca&shy;<lb/>bile delle altre per mostrare in maniera pi&ugrave; distinta e pi&ugrave; risentita il cuo&shy;<lb/>ricino, che spessamente batteva, l'orditura dell'embrione e la membrana <lb/>ombelicale tutta intrecciata di bellissimi vasi sanguigni. </s>

<s>Siccome da molto <lb/>tempo io ardeva dal desiderio di scoprir pure negli animali caldi la circo&shy;<lb/>lazione, e di scoprirla con quell'ampiezza di giro, con cui l'aveva scoperta <lb/>negli animali di freddo temperamento; cos&igrave; que'vasi, per appartenere ad <lb/>animale di simil fatta, pi&ugrave; d'ogni altro a s&egrave; rapirono i miei sguardi, e m'in&shy;<lb/>vitarono a contemplarli. </s>

<s>La camera ov'io mi trovava, non avendo luce che <lb/>bastasse, e volendo pure in qualche maniera render paga la mia curiosit&agrave;, <lb/>mi appigliai al partito di esaminar l'uovo all'aperto ed immediato lume del <lb/>sole. </s>

<s>Apprestatolo adunque alla macchinetta del Lyonet, di subito l'impun&shy;<lb/>tai con la lente, e nonostante la gran luce ond'era attorniato, potei, purch&egrave; <lb/>aguzzassi ben gli occhi, nettamente veder correre il sangue per l'intiero cir&shy;<lb/>cuito de'vasi ombelicali, arteriosi e venosi. </s>

<s>Preso allora da gioia inaspettatta, <lb/>credetti quell'una volta di poter dire anch'io <emph type="italics"/>evreca, evreca.<emph.end type="italics"/> La scoperta <lb/>la feci nel maggio 1771, e nell'estive vacanze di quell'anno m'ingegnai di <lb/>svolgerla come conveniva &rdquo; (Opere, T. IV, Milano 1826, pag. </s>

<s>155). </s></p><p type="main">

<s>Questa singolarissima osservazione microscopica nel sistema del cuore <lb/>s'assomiglia all'osservazione telescopica di Mercurio nel sistema del Sole, e <lb/>come si rendeva per questa d'ogni parte assoluta la dimostrasione dell'or-<pb xlink:href="020/01/1277.jpg" pagenum="152"/>dine de'moti nell'Universo, cos&igrave; per quella si rendeva per ogni parte asso&shy;<lb/>luta la dimostrazione dell'ordine dei moti nel Microcosmo. </s>

<s>Ma era allo stesso <lb/>Spallanzani riserbata un'altra gloria, ch'&egrave; quella d'esser egli stato il primo <lb/>ad osservare il circolo coronario. </s>

<s>La difficolt&agrave; di una tale osservazione con&shy;<lb/>sisteva nel color sanguigno del cuore, che non facendo discernere il color <lb/>sanguigno de'vasi non dava perci&ograve; speranza di vedervi correre il sangue, <lb/>altro che nel pallor della sistole. </s>

<s>In questa fase del cuore di una salaman&shy;<lb/>dra vide esso Spallanzani certe piegoline rosse, che facevano credere di esser <lb/>vasi, dentro i quali corresse il sangue. </s>

<s>&ldquo; Un giorno, egli scrive nella dis&shy;<lb/>sertazione <emph type="italics"/>Dell'azione del cuore ne'vasi sanguigni,<emph.end type="italics"/> considerando il cuore <lb/>d'una grossa salamandra, ebbi il piacer di conoscere che giusti erano i miei <lb/>sospetti. </s>

<s>Le rosse piegoline si convertirono in altrettanti vasetti. </s>

<s>Nell'atto <lb/>che restringevasi il cuore, per questi scorreva il sangue rapidamente, ma <lb/>dilatandosi egli di nuovo, sminuivasi a vista la velocit&agrave; del sangue &rdquo; (Opere <lb/>e Tomo cit., pag. </s>

<s>120, 21). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Giunti al termine di un viaggio fatto attraverso a tanti secoli, quanti <lb/>sono da Aristotile allo Spallanzani, &egrave; bene tutto in uno sguardo conside&shy;<lb/>rarne l'andamento, come fa colui che le smisurate distanze da un punto <lb/>all'altro della terra si rappresenta in brevi tratti disegnate sopra una mappa. </s>

<s><lb/>Ci rivela facilmente un tale sguardo, comprensivo di tutta la storia fin qui <lb/>narrata, come la scoperta della circolazione del sangue ebbe in Italia la sua <lb/>pi&ugrave; prossima preparazione, e in Italia l'ultima mano. </s>

<s>Resta per&ograve; ancora <lb/>una curiosit&agrave; da sodisfare, ed &egrave; in che modo gl'Italiani, che non seppero <lb/>concludere il vero dalle dottrine premesse dagli avi, accettassero poi quella <lb/>conclusione, quando venne ad annunziarla al mondo l'Harvey. </s>

<s>Ma perch&egrave; <lb/>ci&ograve; accenna necessariamente a un risveglio, giova, a meglio intenderne le <lb/>circostanze e gli atti, investigare l'origine di quel sonno. </s></p><p type="main">

<s>A noi par che una tale origine sia da Girolamo Fabricio d'Acquapen&shy;<lb/>dente, il quale tenendosi affatto fuori da quelle battaglie insorte fra il Ve&shy;<lb/>salio e il Colombo e il Falloppio, come se tante valide forze si fossero so&shy;<lb/>lamente impiegate a distruggere, ridusse tutto il progredir della scienza ai <lb/>commenti da s&egrave; fatti agli insegnamenti galenici, i quali perci&ograve; sulla fine del <lb/>secolo XVI si diffusero, sotto questa nuova forma, a dominare per le Scuole <lb/>d'Italia. </s>

<s>Se dunque nel 1574 esso Fabricio, ch'era per farsi maestro e prin&shy;<lb/>cipe di questa Scuola, si maraviglia che nessuno abbia fatto mai menzione <lb/>delle valvole delle vene, non &egrave; una menzogna detta per farsene credere egli <lb/>primo discopritore, ma &egrave; perch&egrave; non si cur&ograve; di leggere, almeno con atten&shy;<lb/>zione e tutti interi, que'libri dove il Falloppio e il Vesalio tanto passiona&shy;<lb/>tamente avevano scritto del Canani e del Lusitano. </s></p><pb xlink:href="020/01/1278.jpg" pagenum="153"/><p type="main">

<s>Reciso cos&igrave; il filo delle tradizioni scientifiche, principalmente per ci&ograve; che <lb/>riguardava il Colombo, e rimasto involto nella forfora peripatetica il Cesal&shy;<lb/>pino, la scienza italiana, in proposito della fisiologia del cuore e del moto <lb/>del sangue, come ramo reciso dal suo tronco, cadde in un languore di vita <lb/>e in un torpore di sonno, in mezzo a cui la realt&agrave;, ch'era presso a sboc&shy;<lb/>ciare, si sciupava in larve stranamente mostruose. </s>

<s>Come la circolazion pol&shy;<lb/>monare, cos&igrave; esattamente descritta dal Colombo e dal Cesalpino, si trasformi <lb/>in quelle mostruosit&agrave; nella mente di Girolamo Fabricio, pu&ograve; vedersi dal <lb/>cap. </s>

<s>VIII della II Parte <emph type="italics"/>De formato faetu,<emph.end type="italics"/> dove si trova spenta anche quella <lb/>scintilla di vero, che attraverso al fondo buio de'secoli traspariva lieta <lb/>dalle pagine di Galeno. </s>

<s>Tre sono i vasi, ivi si legge, cbe si diramano <lb/>nel polmone: l'aspera arteria, che v'introduce l'aria, la vena arteriosa, <lb/>che per nutrimento del viscere vi spinge il purissimo sangue, e l'arteria <lb/>venosa, che mena la stessa aria inspirata nel ventricolo sinistro, dove si <lb/>trasforma in spirito, e tutto insieme refrigera il cuore. </s>

<s>&ldquo; Pulmones, cum <lb/>publicum usum corpori praebent, tria illa vasorum genera in sui substan&shy;<lb/>tiam disseminatam, scilicet asperam arteriam, venam arterialem, et arteriam <lb/>venalem hoc modo administrant: Per asperam arteriam aerem respiratione <lb/>attractum primo rapiunt, et recipiunt qui postea a cordis pulsu per arteriam <lb/>venalem in sinistrum cordis sinum defertur conquoquendum, et in spiritum <lb/>vitalem commutandum, refrigeriumque cordi praestandum. </s>

<s>Per tertium vero <lb/>vas quod vena arterialis dicitur pulmones purissimo tenuissimoque sanguine <lb/>enutriuntur. </s>

<s>Itaque hoc tempore pulmo nutritur vase quod arteriae corpus <lb/>obtinet, tum vero spiritum suscipit per vias quod venae substantiam obti&shy;<lb/>net &rdquo; (Venetiis 1600, pag. </s>

<s>138). </s></p><p type="main">

<s>Seguace delle dottrine di quella Scuola, e disposto per acume d'inge&shy;<lb/>gno a specularne altre da s&egrave;, e per indole a rimanersi nella libert&agrave; del pro&shy;<lb/>prio pensiero, era Paolo Sarpi, che avendo saputo l'arte di tacere, lasci&ograve; che <lb/>tanto ne parlassero gli altri. </s>

<s>E ora non son molti anni, che il Bianchi Gio&shy;<lb/>vini gli fa rompere dalla tomba que'lunghi silenzii, si vuol che non faccia <lb/>scomparire gli encomiatori, in ogni modo approvando i loro detti, bench&egrave; <lb/>nient'altro in realt&agrave; si provi da quel frammento di lettera pubblicato da <lb/>esso Giovini, se non che egli, e tutti coloro che vorrebbero a fra Paolo sal&shy;<lb/>vare il merito della scoperta del circolo sanguigno e delle valvole, si sono <lb/>ingannati, come que'fanciulli, che credono le nebbie esser monti scesi mi&shy;<lb/>racolosamente a colmare le valli. </s></p><p type="main">

<s>Noi leggiamo quel frammento di lettera sarpiana, in francese, nella <lb/>Storia altre volte citata del Flourens, dove il Sarpi, ringraziato un amico <lb/>che gli aveva donato l'opera anatomica dell'illustre Vesalio, cos&igrave; prosegue: <lb/>&ldquo; Il y a r&eacute;ellement une grande analogie entre les choses d&eacute;ja remarqu&eacute;es <lb/>et not&eacute;es par moi, &agrave; l'&eacute;gard du mouvement du sang dans le corps animal, <lb/>et de la structure ainsi que de l'usage des valvules &rdquo; (Histoire de la circulat. </s>

<s><lb/>du sang cit., pag. </s>

<s>124). Se un tal documento &egrave; autentico, la questione &egrave; <lb/>dunque decisa: il Sarpi credeva come il Vesalio che il sangue passasse at-<pb xlink:href="020/01/1279.jpg" pagenum="154"/>traverso ai pori del setto medio dal vetricolo destro nel sinistro, e che fosse <lb/>l'arteria venosa, come la gola di un cammino, per dar esito ai fumi filig&shy;<lb/>ginosi. </s>

<s>E perch&egrave; passa una analogia fra queste e le mostruosit&agrave; dell'Acqua&shy;<lb/>pendente, &egrave; da concluder che il Sarpi avesse della circolazion polmonare <lb/>idee simili a quelle che scrisse il suo amico, e che noi trascrivemmo di <lb/>sopra dal libro <emph type="italics"/>De formato foetu.<emph.end type="italics"/></s></p><p type="main">

<s>Che se lo stesso Sarpi teneva anche delle valvole opinioni analoghe a <lb/>quelle del Vesalio, e il Vesalio le credeva membrane apposte alle tuniche <lb/>delle vene, per invigorirne la natural debolezza, &egrave; pur anche da questa parte <lb/>decisa la questione, ond'&egrave; che se, prima del Giovini, si credeva che fra Paolo <lb/>l'avesse dimostrate all'Acquapendente, ora &egrave; da dire invece ch'ei le neg&ograve; <lb/>allo stesso Acquapendente, che le aveva scoperte, come il Vesalio le aveva <lb/>gi&agrave; negate al Canani. </s>

<s>Da questa controversia forse prese l'Autore <emph type="italics"/>De vena&shy;<lb/>rum ostiolis<emph.end type="italics"/> occasione di osservare con pi&ugrave; diligenza, e di render pubbli&shy;<lb/>camente noto ci&ograve; che per l'avanti o non aveva pensato, o non s'era atten&shy;<lb/>tato di fare; unico merito rivendicato al Sarpi dal documento pubblicato <lb/>nel 1838 sulla <emph type="italics"/>Revue de Londres<emph.end type="italics"/> dal Bianchi Giovini. </s></p><p type="main">

<s>Giorgio Ent, nelle sue <emph type="italics"/>Metamorfosi di Apolline ed Esculapio,<emph.end type="italics"/> vuol che <lb/>il Sarpi sia stato il primo in Italia ad aver notizia della scoperta arveiana, <lb/>prima della sua pubblicazione, e ci&ograve; per mezzo del Legato veneto, che di <lb/>Londra nel 1619 tornava in patria. </s>

<s>&Egrave; certo che in quell'anno faceva l'Har&shy;<lb/>vey la circolazione universale del sangue soggetto alle sue pubbliche lezioni, <lb/>e che nel 1622, un'anno prima della morte del Sarpi, aveva presentato il <lb/>manoscritto a Gaspero Hofmann, che tanto freddamente lo accolse, da di&shy;<lb/>sanimar l'Autore e da indugiarne per altri sei anni la pubblicazione. </s>

<s>Per <lb/>cui, ripensando che il detto Frate italiano teneva dietro a tutte le novit&agrave; <lb/>straniere, l'opinione dell'Ent ha del probabile. </s>

<s>Ma noi siam persuasi che <lb/>anche al Sarpi, imbevuto delle idee dell'Acquapendente e di analoghe a <lb/>quelle del Vesalio, le cose dette dall'Harvey saranno sembrate cos&igrave; nuove <lb/>e inaudite &ldquo; ut non solum ex invidia quorumdam metuam malum mihi, sed <lb/>verear ne habeam inimicos omnes homines: tantum consuetudo aut semel <lb/>inibibita doctrina altisque defixa radicibus, quasi altera natura apud omnes <lb/>valet! &rdquo; (De motu cordis cit., pag. </s>

<s>55). </s></p><p type="main">

<s>I presentiti giusti timori, fondati sull'esperienza degli uomini, si sa&shy;<lb/>ranno dissipati dall'animo dell'Harvey, quando vide il Cartesio fare alle <lb/>nuove idee cos&igrave; lieta e inaspettata accoglienza. </s>

<s>Che se lo stesso favorevole <lb/>incontro avessero avuto in Galileo, per l'autorit&agrave; dei due Principii della <lb/>scienza, era spettatore esso Harvey in vita de'suoi pi&ugrave; pieni e pi&ugrave; gloriosi <lb/>trionfi. </s>

<s>Ma Galileo alieno da quegli studii, e da tutto ci&ograve; che non promet&shy;<lb/>teva di renderlo il primo ed il solo, si mostr&ograve; verso il Copernico inglese <lb/>tanto freddo, quanto s'era mostrato fervente verso il vero Copernico prus&shy;<lb/>siano, cosicch&egrave; n&egrave; a lu&igrave; n&egrave; al Sarpi &egrave; da attribuire alcun merito in restau&shy;<lb/>rare i perturbati ordini naturali ne'moti del Microcosmo. </s>

<s>Que'meriti si <lb/>debbon tutti a due nostri Toscani, i quali, bench&egrave; sieno nella Repubblica <pb xlink:href="020/01/1280.jpg" pagenum="155"/>scientifica pochissimo conosciuti, pur furono essi veramente i primi, che ap&shy;<lb/>plicassero allo studio della vita animale i metodi galileiani, rendendo dei <lb/>nuovi frutti negletti dall'Istitutore ubertoso l'albero della scienza italiana. </s></p><p type="main">

<s>Il d&igrave; 31 Marzo 1637 Raffaello Magiotti scriveva a Galileo da Roma in <lb/>una lettera queste parole: &ldquo; Qu&agrave; si trova un Medico tedesco, anatomista <lb/>raro, quale mostra in fatto assaissimi errori <emph type="italics"/>De natura anim.<emph.end type="italics"/> e quand'io <lb/>li contai del cavallo del Gattamelata, che sta sopra due gambe dalla mede&shy;<lb/>sima banda, contro il detto di Aristotile, rise veramente di tutto cuore, ed <lb/>ogni giorno porta qualche luogo per farci sempre pi&ugrave; ridere &rdquo; (MSS. Gal., <lb/>P. VI, T. XIII, c. </s>

<s>14). </s></p><p type="main">

<s>Quel Medico tedesco, chiunque egli sia, dimostrava in Roma, in mezzo <lb/>alle sue anatomie, il circolo universale del sangue, cosicch&egrave; fu egli il primo <lb/>a diffondere in Italia le dottrine arveiane gi&agrave; diffuse nelle libere citt&agrave; ger&shy;<lb/>maniche, in una delle quali, piuttosto che nella patria dell'Hofmann e del <lb/>Riolano, fece l'Autore stampare il suo libro <emph type="italics"/>De motu cordis.<emph.end type="italics"/> Erano a quelle <lb/>anatomie del Tedesco spettatori assidui Raffaello Magiotti e Antonio Nardi, <lb/>i duumviri della Scienza sperimentale, secondo Galileo, rimasti in Roma dopo <lb/>la partenza del Torricelli. </s>

<s>Il Nardi, nella veduta Ia della Scena VIII, dava <lb/>cos&igrave; la prima pietosa mano a rivestir del nuovo abito inglese le nudit&agrave;, e <lb/>anzi lo squallore a ch'era stata ridotta la Fisiologia italiana dai discepoli <lb/>dell'Acquapendente: </s></p><p type="main">

<s>&ldquo; Ora, seguendo, dico come le orecchie del cuore sono una natura di <lb/>mezzo ed un certo legame tra il cuore ed i vasi venali ed arteriali: anche <lb/>sono le prime e l'ultime a vivere e muoversi tra le parti solide dell'ani&shy;<lb/>male. </s>

<s>Battono, non in virt&ugrave; propria, ma del sangue spiritoso, il quale come <lb/>fuoco artifiziosissimo ha movimento ed atto perpetuo, insino che resta san&shy;<lb/>gue. </s>

<s>Al battere delle orecchie segue il restringersi o allargarsi del cuore, <lb/>poich&egrave; riempito di sangue il ventricolo destro dalla Vena cava, e dalla de&shy;<lb/>stra orecchia, restringesi per il soverchio caldo, e discaccia il sangue per i <lb/>vasi, e di nuovo ritornando al primiero e naturale stato torna a riempirsi <lb/>alternamente, e cos&igrave; un certo moto circolare e perpetuo formasi del sangue, <lb/>mentre dal destro ventricello se ne passa per i condotti al polmone, e quindi <lb/>se ne ritorna al sinistro, a che ancora il moto del polmone serve. </s>

<s>Ed osser&shy;<lb/>visi che il cuore non solo ha il movimento suddetto di restringersi ed al&shy;<lb/>largarsi, ma anche l'arterie, massime maggiori, ed anche la Vena cava presso <lb/>il cuore, e questo seconda per consenso quello del cuore. </s>

<s>Quindi ancora il <lb/>sangue per le vene passa dalle parti al cuore, e per le arterie dal cuore <lb/>passa alle parti, e l'uno spinge l'altro. </s>

<s>E'non &egrave; dubbio che questa moderna <lb/>osservazione del moto circolare del sangue non sia una delle belle cose, che <lb/>si sia mai trovata nell'arte, onde moltissime considerazioni farsi potrebbono, <lb/>di che vedasi l'Harveio &rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>1097). </s></p><p type="main">

<s>Il Magiotti, per lettera del 25 Aprile 1637, rendeva cos&igrave; noto a don Fa&shy;<lb/>miano Michelini il grandissimo gusto, che aveva delle anatomie del Tedesco, <lb/>e cos&igrave; gli descriveva la circolazione che fa il sangue in noi, scoperta a <pb xlink:href="020/01/1281.jpg" pagenum="156"/>que'tempi e bastante, com'ei si esprimeva, a rivolgere tutta la medicina, <lb/>siccome l'invenzione del Telescopio ha rivolta tutta l'Astronomia, la Bus&shy;<lb/>sola l'economia, e l'Artiglieria tutta l'arte militare: </s></p><p type="main">

<s>&ldquo; Sono molti anni che un Medico milanese osserv&ograve; negli animali, pa&shy;<lb/>sciuti di fresco e poi ammazzati, massime nei cani, che nel mesenterio sono <lb/>molte vene lattee, quali da tutti gl'intestini tirano succo, ovvero chilo, alla <lb/>volta del panereas e per quello al fegato ed alla Vena cava, per la quale <lb/>finalmente s'annida, si riscalda e concuoce dentro al destro ventricolo del <lb/>cuore. </s>

<s>Di quivi, dalla vena arteriosa, passa a refrigerarsi nel polmone per <lb/>meglio concuocersi, e dal polmone, per l'arteria venosa torna nel sinistro <lb/>ventricolo del cuore, dove si fa l'ultima concozione. </s>

<s>Di l&agrave;, per l'arteria ma&shy;<lb/>gna, e da lei per tutte l'arterie, si sparge il sangue spiritoso per tutto il <lb/>corpo, e cos&igrave; si diffondono gli spiriti e il calore, e cos&igrave; il moto del pulsare <lb/>a tutte le membra. </s>

<s>Dalle membra tutte succhiano le vene capillari il san&shy;<lb/>gue, quale era stato portato dalle arterie per nutrire le parti, come se fos&shy;<lb/>sero tante radiche e barbe, e riconducono il sangue cos&igrave; con pochissimi spi&shy;<lb/>riti al cuore per la Vena porta, acci&ograve; l&agrave; di nuovo con qualche porzione di <lb/>nuovo chilo, per opera delle vene lattee, si riscaldi e concuocia.... &rdquo; (Opere <lb/>di Gal., Alb. </s>

<s>X, 207). </s></p><p type="main">

<s>Il Michelini tanto conforto sent&igrave; all'ingegno di questa nuova rivelazione, <lb/>che avendo avuto ordine dal Magiotti di rivelarla al signor Galileo, non <lb/>manc&ograve; di adempire all'ufficio. </s>

<s>E non si potendo persuadere come colui, <lb/>ch'era con tanto ardire concorso a infrangere l'idolo aristotelico, si mo&shy;<lb/>strasse ora cos&igrave; irresoluto contro il galenico, ch'era ai progressi delle scienze <lb/>sperimentali e dell'arte medica tanto pi&ugrave; dannoso, rivolsesi a cercar nuovi <lb/>conforti al suo giudizio nel giudizio di Giovan Batista Baliani, tenuto per la <lb/>seconda autorit&agrave;, che dopo lo stesso Galileo si conoscesse allora in cos&igrave; fatto <lb/>scientifico magistero. </s>

<s>Ma, contro ogni espettativa del Michelini, il Baliani da <lb/>Genova cos&igrave; gli rispondeva: &ldquo; Rispetto alla circolazione del sangue, se mi <lb/>dicesse i motivi che le hanno fatta stimare sicura l'opinione dell'Arveo, <lb/>forse che le addurrei qualche cosa in contrario &rdquo; (Targioni, Notizie degli <lb/>aggrandimenti ecc., T. I, Firenze 1780, pag. </s>

<s>204). </s></p><p type="main">

<s>Quali fossero veramente quelle ragioni in contrario noi non sappiamo, <lb/>ma dovettero esser tali da persuaderlo a preferire alle verit&agrave; arveiane le <lb/>mostruosit&agrave; invalse nell'universale, per l'autorit&agrave; del Vesalio, e in Italia in <lb/>particolare per quella non punto minore dell'Acquapendente; persuasione <lb/>che il Baliani stesso rivela in quel trattato che scrisse <emph type="italics"/>Della pestilenza.<emph.end type="italics"/> Ivi <lb/>incomincia con ragioni fisiche, per que'tempi del tutto nuove, a dimostrar <lb/>che i miasmi contagiosi si producono nell'aria, e dipoi passa a indagar le <lb/>vie segrete, per le quali s'inoculano cos&igrave; fatti miasmi nel sangue ricirco&shy;<lb/>lante nel corpo a nutrire e a vivificare le parti al modo che segue: </s></p><p type="main">

<s>&ldquo; Presuppongo io primieramente, egli scrive, insieme con molti, an&shy;<lb/>corch&egrave; altri che sono gi&agrave; in credito sentano in contrario, che qualora, per <lb/>essersi fatta la diastole, il cuore si sia gonfiato e i suoi vani, seni o ventri-<pb xlink:href="020/01/1282.jpg" pagenum="157"/>coli che gli chiamino, aggranditi e ripieni, esso per naturale istinto con la <lb/>sistole si restringa, e che allora il sangue del seno diritto, perci&ograve; fortemente <lb/>compresso, non solo sia spinto per la vena arteriale nel polmone, ma che <lb/>una porzione pi&ugrave; sottile ne sia cacciata per li meati del tramezzo, forse in&shy;<lb/>sensibili sol nel cadavere, nel seno manco. </s>

<s>Il che essendo vero, parmi con&shy;<lb/>seguentemente di veder chiaramente che tal porzione di sangue, per passare <lb/>a forza per quei pori sottilissimi, ritrovando il vano, anzi per cos&igrave; dire spruz&shy;<lb/>zatovi, si sparga in minutissimi zampilli, che per restar privi per la loro <lb/>piccolezza di attivit&agrave; e di vigor bastante a resistere all'azione del calore che <lb/>vi ritruovano e che gli penetra, si riducano subitamente in vapore e bolli&shy;<lb/>cini, che gonfiandosi e con gran celerit&agrave; dilatandosi sforzino e spingano le <lb/>pareti del ventricolo, e con nuova diastole l'aggrandiscano. </s>

<s>Parmi inoltre <lb/>a ci&ograve;, non potendo esse bolle sanguigne per la forma loro sferica termi&shy;<lb/>narsi co'termini altrui, acciocch&egrave; spazio vuoto non ci rimanga, che con ra&shy;<lb/>gione vi supplisca la Natura con preparare una materia arrendevole, pronta <lb/>a sottentrarvi, e acconcia a riempire i vani che tra'detti bollicini si ritro&shy;<lb/>vano, cio&egrave; a dir l'aria portatavi dall'arteria venale, di quella che inspirata <lb/>risiede nel polmone, non ad altro uso per avventura stato da essa Natura <lb/>formato, e tal composto di bolle sanguigne e d'aria &egrave; al creder mio quella <lb/>sostanza che spirito vitale si domanda &rdquo; (Savona 1647, pag. </s>

<s>61-63). </s></p><p type="main">

<s>Ma il Michelini sent&igrave; la verit&agrave; pi&ugrave; potente degli autorevoli pregiudizi <lb/>di Galileo e del Baliani, e tra il 1645 e il 47 compose, sulle scoperte del&shy;<lb/>l'Asellio e dell'Harvey, quel nuovo sistema di medicina razionale, che la&shy;<lb/>sci&ograve; abbozzato in alcune lettere pubblicate pi&ugrave; di un secolo dopo dal Tar&shy;<lb/>gioni (Notizie cit., T. II, P. I, pag. </s>

<s>221-25). Scoperto il canal toracico, fece <lb/>anche questa terza notizia entrare in quel sistema d'Igiene, che, rimasto di&shy;<lb/>menticato infino al 1780, fu dato alla prima luce dallo stesso Targioni (T. III, <lb/>pag. </s>

<s>329-45). </s></p><p type="main">

<s>Chi legge ora quelle cose le giudica una meschinit&agrave;, non ripensando <lb/>che da queste aride stille fu rinfrescata a novella vita la Medicina in Italia, <lb/>che per opera del Michelini prese abito e complessione di scienza, e fu per <lb/>lui solo introdotta nella scuola galileiana. </s>

<s>Basti il dire che fu inspirato a <lb/>quelle meschinit&agrave; il gran Borelli, che vi ritrov&ograve;, come ne'cotiledoni del <lb/>germe, quel vital nutrimento da cui crebbe a tanto maravigliosa grandezza, <lb/>e in s&igrave; breve tempo, la nuova Fisiologia. </s>

<s>Quando nel 1661 il Malpighi, che <lb/>discende esso pure direttamente dal Michelini per la linea dello stesso Bo&shy;<lb/>relli, rese il circolo del sangue visibile agli occhi di tutti, e allora gl'Ita&shy;<lb/>liani si riscossero dal loro sonno, e per rifarsi di un tesoro perduto anda&shy;<lb/>rono, con la speranza di metterle in corso, a ricercar le arrugginite monete <lb/>rimaste chiuse nelle arche degli avi. </s></p><p type="main">

<s>Il Fracassati, per citar qualche esempio, nella sua dissertazione <emph type="italics"/>De ce&shy;<lb/>rebro,<emph.end type="italics"/> accolta fra le opere del Malpighi, a provar che il mondo &egrave; tante volte <lb/>ingiusto dispensator del merito, &ldquo; sanguinis circulatio, scrive, Galaxia in mi&shy;<lb/>crocosmo humano, scilicet via chyli ad cor, nonne Caesalpinum agnoscit <pb xlink:href="020/01/1283.jpg" pagenum="158"/>auctorem, ac Eustachium <emph type="italics"/>De vena sine pari?<emph.end type="italics"/> et tamen solos in scholis <lb/>auctores crepant anglos Harveos, ac diepenses Pecquetos &rdquo; (Operum, T. II, <lb/>Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>138). Tommaso Cornelio, acceso dal medesimo zelo, <lb/>venne a rammemorare a'suoi che il moto del sangue descritto dall'Harvey <lb/>era stato gi&agrave; conosciuto da Paolo Sarpi, e anzi molto tempo prima dal Ce&shy;<lb/>salpino. </s>

<s>&ldquo; Motum sanguinis ab Harveio descriptum iampridem agnoverat et <lb/>amicis indicaverat Paulus Sarpi venetus, quin etiam illum multo ante de&shy;<lb/>signaverat Andreas Caesalpinus &rdquo; (Progymnasmata physica, Neapoli 1688, <lb/>pag. </s>

<s>296). </s></p><p type="main">

<s>Di qui ebbero principio e vennero gli esempii a que'profluvii di scrit&shy;<lb/>ture insulse, che si rassomigliano ai pugni dati in aria, e agli urli di chi, <lb/>ridestatosi a un tratto dal lungo sonno, si mette a gridare al ladro al vi&shy;<lb/>cino, che ha operosamente vegliato, bench&egrave; il Borelli avesse dato agl'Ita&shy;<lb/>liani altri esempi di pi&ugrave; assennati giudizi. </s>

<s>&ldquo; Inveatum profecto admirabile, <lb/>egli dice della circolazione del sangue, partim a Cesalpino, sed postea exac&shy;<lb/>tissime ab Harveio nuper mortalibus tanta evidentia demonstratum, ut nemo <lb/>supersit qui de eius veritate adhuc dubitet &rdquo; (De motu anim., P. II, Ro&shy;<lb/>mae 1681, pag. </s>

<s>77). </s></p><p type="main">

<s>La vana loquacit&agrave; dei tanti scrittori, che si dettero a seguir gli esempi <lb/>del Fracassati e del Cornelio, piuttosto che del Borelli, si manifesta anche <lb/>dal fatto che, mentre vogliono glorificare i loro connazionali di finti meriti, <lb/>non si curano poi di ricercarne i meriti veri. </s>

<s>Benemeriti della Fisiologia ar&shy;<lb/>veiana sono tutti coloro, che la confermarono con vario genere di argomenti, <lb/>fra'quali &egrave; anche da annoverare la trasfusione del sangue, splendido pen&shy;<lb/>siero, bench&egrave; malaugurato negli effetti. </s>

<s>Prima dell'Harvey ebbero quel pen&shy;<lb/>siero Pico della Mirandola, Girolamo Cardano, e Giovanni Colle fra'nostri, <lb/>e in mezzo a loro Andrea Libavio, lusingato di poter per via di tubi tra&shy;<lb/>sfondere il sangue e trasformare un vecchio in un giovane, come s'era lu&shy;<lb/>singato d'aver, per via de'processi alchimici, a trasformare il peltro in <lb/>purissimo oro. </s>

<s>Nel cap. </s>

<s>XVI <emph type="italics"/>De motu cordis,<emph.end type="italics"/> dove il circolo del sangue dal <lb/>cuore alle parti e dalle parti al cuore si mostra dai veleni e dai morsi ve&shy;<lb/>lenosi, che inducono rapidamente il malore per tutte le membra, si conte&shy;<lb/>neva in germe la possibile trasfusione del sangue, ma Francesco Folli sog&shy;<lb/>giunge che concorse in quell'inspirazione la viva voce della Natura. </s>

<s>Egli &egrave; <lb/>storico diligentissimo di s&egrave; stesso, e perci&ograve; a lui ci convien cedere la parola. </s></p><p type="main">

<s>&ldquo; Nell'anno 1652 lessi il libretto di Guglielmo Arveo, inglese, che tratta <lb/>del moto del cuore e del sangue, la qual lettura, con qualche notizia che <lb/>aveva dell'innestar le piante, produsse nella mia fantasia questo terzo pro&shy;<lb/>blema, che data la circolazione del sangue fosse possibile la trasfusione, con <lb/>la quale si potesse non solo curare alcuni mali, ma ringiovanire e ingigan&shy;<lb/>tire ancora, come l'accennai nel mio libretto <emph type="italics"/>Della cultura della vite,<emph.end type="italics"/> che <lb/>non pubblicai per altro, che per far palese a tutti che la trasfusione del <lb/>sangue era da me stata inventata, e fin dall'anno 1654 manifestata al Se&shy;<lb/>renissimo Ferdinando II, granduca..... &rdquo; </s></p><pb xlink:href="020/01/1284.jpg" pagenum="159"/><p type="main">

<s>&ldquo; Scorsero undici anni, n&egrave; mai intesi novella alcuna di questo problema, <lb/>n&egrave; per allora io abitava in Fiorenza, come fo adesso, ma timido quanto cu&shy;<lb/>rioso non sapeva qual mezzo termine prendere per averne notizia. </s>

<s>Determi&shy;<lb/>nai scrivere la mia <emph type="italics"/>Recreatio physica,<emph.end type="italics"/> la quale, e dal geroglifico del fron&shy;<lb/>tespizio e dalla materia che vi tratto, potr&agrave; ciascuno leggendola riconoscere <lb/>che in grazia della trasfusione fu scritta, e anco dedicata al medesimo gran&shy;<lb/>duca Ferdinando, acciocch&egrave; presentandogliela, come feci nel 1665, mi pale&shy;<lb/>sasse qualche cosa di essa. </s>

<s>Ma esso tacendo supposi o che non ne avesse <lb/>fatta fare esperienza alcuna, oppure avendone fatte non volesse che fossero <lb/>note, e restando nella medesima ingnoranza di prima non ardiva di sco&shy;<lb/>prirmi con alcuno. </s>

<s>Ma quando meno vi pensava, mi fu detto da ser Ippo&shy;<lb/>lito Tei da Bibbiena, mio amico e che allora dimorava in casa dell'illustris&shy;<lb/>simo signor marchese Filippo Niccolini, come in Inghilterra avevano trovato <lb/>una bellissima invenzione di ringiovanire, col trasfondere del sangue di gio&shy;<lb/>vanetti nelle vene de'vecchi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quale io restassi a tale avviso, lo lascio considerare a chi ha aspet&shy;<lb/>tato un tempo, e poi conseguito all'improvviso una buonissima nuova, ac&shy;<lb/>coppiata con un dolore altrettanto grande, quanto fusse l'allegrezza, per <lb/>perdere nell'istesso momento l'onore, che sperava e credeva acquistato. </s>

<s>Poi&shy;<lb/>ch&egrave; non sapeva se era accaduto ad altri nell'istesso secolo il medesimo pen&shy;<lb/>siero, oppure di Toscana avesse navigato in Londra. </s>

<s>Mi lusingava per&ograve; che, <lb/>per essere stati qui alla corte di Firenze alcuni virtuosi Inglesi, e presenti <lb/>ancora a molte esperienze, come l'attesta il signor Redi, fra'quali era il <lb/>signor Finchio, che al presente si ritrova ambasciator residente alla Porta <lb/>ottomana per la corona d'Inghilterra, potessero averla in questa corte in&shy;<lb/>tesa, e trasportata poi alla patria. </s>

<s>S'aggiunga a questo verisimile che di <lb/>tutte le altre belle invenzioni, che di l&agrave; sieno venute, si &egrave; anco inteso il <lb/>nome dell'autore, eccetto che di questa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma impaziente non volli star pi&ugrave; celato, e pigliando scusa di scri&shy;<lb/>vere della cultura della vita, mi scopersi per inventore di essa, chiaman&shy;<lb/>done in testimonio il prefato serenissimo Ferdinando II, che in quel tempo <lb/>viveva, n&egrave; mai ho saputo che altri si sia detta invenzione arrogata. </s>

<s>Con <lb/>ragione adunque posso chiamarla mia. </s>

<s>&rdquo; (Stadera medica, Firenze 1680, <lb/>pag. </s>

<s>35-38). </s></p><p type="main">

<s>Non erano questi per&ograve; del Folli altro che progetti: egli stesso confessa <lb/>nel suo <emph type="italics"/>Dialogo intorno alla cultura della vite<emph.end type="italics"/> di non averne mai fatta <lb/>esperienza (Firenze 1670, pag. </s>

<s>44). Le prime prove della trasfusione del <lb/>sangue furono, secondo l'Haller, fatte in Inghilterra da Timoteo Klarke <lb/>nel 1657 (Elementa physiol. </s>

<s>cit., T. I, pag. </s>

<s>233), tre anni dopo la proposta <lb/>fatta dallo stesso Folli al Granduca, e il Senac dice che l'anno dopo furono <lb/>anche dall'Hansbau cos&igrave; fatte nuove esperienze tentate in Francia (Della <lb/>struttura del cuore, traduz. </s>

<s>ital., T. III, Brescia 1783, pag. </s>

<s>58). Ma perch&egrave; <lb/>non sono cos&igrave; fatte testimonianze di questi celebri scrittori confortate di do&shy;<lb/>cumenti, che a volerli sottoporre ad esame non basterebbo forse un intero <pb xlink:href="020/01/1285.jpg" pagenum="160"/>volume, noi sceglieremo, fra tutte le altre, per vera la pi&ugrave; diritta e pi&ugrave; spe&shy;<lb/>dita via, che a nostro giudizio ci si presenta. </s></p><p type="main">

<s>Ne'principii dell'anno 1665 Carlo Fracassati in Pisa proponeva la sua <lb/>nuova <emph type="italics"/>Medicina infusoria.<emph.end type="italics"/> Consisteva questo nuovo metodo nell'iniettare <lb/>per le incise vene alcune sostanze, che restituissero le perdute sue buone <lb/>qualit&agrave; al sangue. </s>

<s>In mezzo a questi pensieri sovvenne all'inventore un altro <lb/>pensiero assai pi&ugrave; seducente, che gli ragionava come parendo probabile di&shy;<lb/>pendere la causa dell'apoplessia da un improvviso coagulo sopravvenuto nel <lb/>sangue, si potessero i colpiti da cos&igrave; fatto accidente, coll'iniezione di alcuni <lb/>solventi, ridonare felicemente alla vita. </s>

<s>Il granduca Ferdinando, a cui il Fra&shy;<lb/>cassati aperse questo pensiero, lo incoraggi&ograve;, e lo consigli&ograve; a diffonderne la <lb/>notizia, ci&ograve; che fece subito l'Autore in quella sua Epistola <emph type="italics"/>De cerebro<emph.end type="italics"/> di&shy;<lb/>retta al Malpighi, e stampata, dentro quello stesso anno 1665, in Bologna. <lb/></s>

<s>&ldquo; Cum Pisis, ivi egli scrisse, in theatrum anatomicum curassem inventum <lb/>conglaciationis sanguinis,.... subiit mentem posse hoc experimentum multa <lb/>docere: videbatur enim pari passu sanguinis solutionem nos fuisse deprehen&shy;<lb/>suros, dum concretionem tenebamus, quae infusa per iugularem ac simul <lb/>etiam cruralem venam aqua forti communi succedebat. </s>

<s>Quare sanguinis re&shy;<lb/>putans congelationes, quod in apoplecticis aperit autopsia, credidi non male <lb/>nos esse consulturos laborantibus si, secta statim vena, dissolvens aliquod <lb/>iniceretur. </s>

<s>Propterea cogitationes meas novit Ser. </s>

<s>M. D., cui inventum pa&shy;<lb/>tefeceram, et fassus est posse inde multa innotescere &rdquo; (Inter Opera M. Mal&shy;<lb/>pighi, T. II, Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>158, 59). </s></p><p type="main">

<s>La notizia da Pisa e da Bologna giunse presto a Londra e ad Oxford, <lb/>e Riccardo Lower fu de'primi ad accoglierla e ad eseguire il progetto, prima <lb/>che sugli uomini, sopra vario genere di animali. </s>

<s>Anzi egli applic&ograve; il metodo <lb/>del Fracassati non a infonder solo liquori medicinali, ma varie sorta di suc&shy;<lb/>chi nutritizi, d'onde ei confessa essergli spontaneamente sovvenuto il pen&shy;<lb/>siero di iniettare lo stesso sangue. </s>

<s>&ldquo; Complures anni sunt (cos&igrave; scrive nel <lb/>cap. </s>

<s>II del trattato <emph type="italics"/>De corde<emph.end type="italics"/> pubblicato per la prima volta in Londra <lb/>nel 1669) cum alios Oxonii viderim, et ipse, experiendi causa, varios liquo&shy;<lb/>res opiatos emeticos, in vivorum animalium venas iniecerim.... Cum vero <lb/>insuper plures alimentares succos simili modo infuderim, atque cum variis <lb/>vini tum cerevisiae iniectionibus sanguinem diversorum animalium satis apte <lb/>et amice congruere vidissem; animum mox subiit experiri an non multo <lb/>magis sanguis diversorum animalium inter se conveniret, et sine periculo <lb/>aut lucta commisceretur.... Quare spem hinc animo concipiens, ad expe&shy;<lb/>rimentum eius tentandum animum et manus adhibui &rdquo; (In Mangct&igrave; Biblio&shy;<lb/>theca anat., T. II, Genevae 1685, pag. </s>

<s>108). </s></p><p type="main">

<s>Preparate fistole, e tutt'altro che occorreva per l'esperienza, &ldquo; quo&shy;<lb/>circa, prosegue il Lower a dire, cum ex voto omnia expectationi respon&shy;<lb/>derent, tandem Oxonii, sub finem Februarii anni 1665, praesentibus doctis&shy;<lb/>simis viris doct. </s>

<s>Johanne Wallis, dom. </s>

<s>Thoma Millington, aliisque medicis, <lb/>experimentum hoc novum, iucundo sane spectaculo atque optimis auspiciis, <pb xlink:href="020/01/1286.jpg" pagenum="161"/>exhibui &rdquo; (ibid.) e prosegue a descrivere la trasfusione del sangue da un <lb/>cane in un altro. </s>

<s>Poi all'ultimo cos&igrave; conclude: &ldquo; Horum fama, cum mox <lb/>Londinum pervolaret, aecepta epistola a clariss. </s>

<s>Boyleo, impense rogatus sum <lb/>ut totius experimenti methodum Societati regiae impertirem, quod non ita <lb/>multo post a me praestitum in philosoficis eiusdem Societatis Transactio&shy;<lb/>nibus, Decembri insequente anno 1666, publici iuris factum est. </s>

<s>Et tum ru&shy;<lb/>mor eius ad exteras gentes et Galliam pervagatus est, ubi mox, rei novi&shy;<lb/>tate allecti, diligentius illam prosequi et aliis subinde experimentis augere, <lb/>illustrare; quodque ego solum in brutis perfeceram, ad hominis usum ac&shy;<lb/>commodare coeperunt, uti in scriptis illorum, sequenti martio anni 1667 <lb/>tunc primum editis, apparet &rdquo; (ibid.). </s></p><p type="main">

<s>Il rumore di questi francesi esperimenti, giunto presto in Italia, riscosse <lb/>gli animi dei concittadini del Folli. </s>

<s>Il cardinale Leopoldo de'Medici, non po&shy;<lb/>tendo fare eseguir l'esperienza nella sede dell'Accademia, per essere gli <lb/>accademici dispersi, ne mostr&ograve; desiderio al Montanari, che si dette all'opera <lb/>in Bologna insieme col Cassini. </s>

<s>Le prove riuscirono con non poco provento, <lb/>ond'&egrave; che il Cassini stesso, in quella celebre lettera al Petit del d&igrave; 18 Giu&shy;<lb/>gno 1667, dop'aver riferite le osservazioni fatte intorno a Venere, per defi&shy;<lb/>nirne il periodo della rotazione, passando a dire degli altri suoi studi, cos&igrave; <lb/>soggiunge: &ldquo; Experimenta multa de transfusione sanguinis ab uno in aliud <lb/>animal, exemplo eorum quae apud vos habita sunt, deque ipsius sanguinis <lb/>motu saepius fecimus, non parum proventu &rdquo; (MSS. Cim., T. XIII, c. </s>

<s>228). </s></p><p type="main">

<s>L'anno dopo, avendo il Montanari dovuto abbandonare Bologna e an&shy;<lb/>dare in Udine per suoi negozii, non lasci&ograve; le intraprese esperienze, una delle <lb/>quali, che consisteva nella trasfusione del sangue da un agnello in un cane <lb/>decrepito, gli riusc&igrave; tanto lusinghiera, che ne scrisse una breve relazione <lb/>indirizzata al Cassini. </s>

<s>La relazione per&ograve;, qualunque se ne fosse la forma, <lb/>apparteneva all'Accademia del Cimento, al Principe della quale ne fu man&shy;<lb/>data dall'Autore una copia, accompagnata da una lettera sottoscritta in Bo&shy;<lb/>logna il d&igrave; 13 di Giugno 1668 (MSS. Cim., XIX, c. </s>

<s>184), e l'accluso foglio, <lb/>acciocch&egrave; lo sappiano anche i nostri lettori, cos&igrave; diceva: </s></p><p type="main">

<s>&ldquo; La trasfusione del sangue d'un animale nelle vene d'un altro, l'espe&shy;<lb/>rienze di cui in tante parti del mondo gi&agrave; fatte sono oramai rese famose, &egrave; <lb/>materia, e per s&egrave; stessa e per le conseguenze che seco porta, cos&igrave; degna del&shy;<lb/>l'attenzione de'Filosofi, che non potr&agrave; cred'io riuscire discara a V. S. Ecc.ma<lb/>una succinta narrativa, che le far&ograve; con la presente, d'una prova che ulti&shy;<lb/>mamente ne fu fatta in Udine del Friuli, quando m'ero col&agrave; recato per varii <lb/>affari, ma principalmente per riverire e godere i favori dell'illustrissimo <lb/>signor conte Girolamo Savorgnano del Monte, cavaliere principalissimo di <lb/>quelle parti e mio stimatissimo signore. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ci trovassimo dunque, il dopo pranzo del giorno di Pentecoste, 20 di <lb/>Maggio 1668, il predetto illustrissimo sig. </s>

<s>conte Girolamo, l'Ecc.mo sig. </s>

<s>dot&shy;<lb/>tore Giov Batista Coris nostro bolognese ed io, in casa gli Ecc.mi signori <lb/>dottori Antonio e Giuseppe Griffoni, gentiluomini di quella citt&agrave;, presenti i <pb xlink:href="020/01/1287.jpg" pagenum="162"/>quali e con l'assistenza ancora del sig. </s>

<s>Andrea Ceraffini, eccellente cerusico <lb/>che ne favor&igrave; non solo de'suoi ferri ma in gran parte dell'opera diligentis&shy;<lb/>sima delle sue mani, preparammo in primo luogo un agnello, di cui sco&shy;<lb/>perta l'arteria crurale e fattevi le debite legature, delle quali quella che ri&shy;<lb/>guardava la parte verso il cuore era a laccio scorrente, v'adattammo dentro <lb/>con ogni possibile diligenza il cannellino, che avevamo preparato rivolto con <lb/>l'orificio verso il cuore, e sopra di quello legammo assai bene l'arteria me&shy;<lb/>desima. </s>

<s>Dopo di che scopersimo la vena iugulare d'un cane bracco, di cui <lb/>fra poco racconter&ograve; le condizioni, e legatala a laccio scorrente in due luo&shy;<lb/>ghi, nello spazio di mezzo, aperto con lancetta, inserimmo un altro cannello <lb/>rivolto pure con l'orificio verso il cuore, ed attorno di lui legammo suffi&shy;<lb/>cientemente la vena. </s>

<s>Poscia adattando in sito proporzionato l'agnello, inne&shy;<lb/>stassimo insieme i cannellini, il che fatto sciogliemmo in primo luogo la <lb/>legatura della vena del cane, che riguardava verso il cuore, ed osservammo <lb/>che non ne venne perci&ograve;, nel cannellino ch'era di vetro, porzione alcuna <lb/>di sangue, ma sciolta la legatura dell'arteria dell'agnello, dalla parte pur <lb/>verso il di lui cuore, scorse d'improvviso il sangue per lo cannellino sino <lb/>nella vena del cane, ed in quella trasfondendosi, slegassimo subito anche la <lb/>legatura della vena del cane, che riguardava il capo, dalla quale lasciammo <lb/>uscire il sangue di lui, sebbene non cos&igrave; continuo come per lo cannellino <lb/>entrava, poich&egrave; considerato essere quella vena assai pi&ugrave; grossa dell'arteria <lb/>dell'agnello, ad effetto che non uscisse molto maggiore copia di quello che <lb/>v'entrava, si comprimeva talvolta col dito. </s>

<s>E finalmente, quando ci parve <lb/>che poco pi&ugrave; ne restasse nell'agnello venuto meno, rilegassimo l'una e <lb/>l'altra legatura della vena del cane, e ne estraessimo i cannellini. </s>

<s>Dopo di <lb/>che ricucimmo in parte la piaga, lasciando un poco d'apertura, perch&egrave; po&shy;<lb/>tesse purgandosi guarire, e dall'agnello estraessimo quanto di sangue po&shy;<lb/>temmo di vantaggio, che non emp&igrave; un guscio d'uovo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; &Egrave; per&ograve; da avvertire che qualche poco del sangue dell'agnello nel&shy;<lb/>l'operazione estravasava dai cannellini, a cagione che questi non s'erano <lb/>potuti cos&igrave; bene innestare insieme, come si desiderava, perch&egrave; in difetto di <lb/>pi&ugrave; adattati avevamo scelto un pezzo di cannello, staccato da uno di que'stru&shy;<lb/>menti di vetro, che usano le donne lattanti per votarsi le poppe, sebbene <lb/>andammo cos&igrave; riparando col dito, che non giudicammo esserne uscito un'on&shy;<lb/>cia per questa via, onde il rimanente di tutto l'agnello si trasfuse nel cane. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Era questo cane bracco barbone, allevato in casa di que'signori Grif&shy;<lb/>foni, non molto grande fra gli altri di quella specie, vecchio di tredici anni <lb/>e pi&ugrave;, sordo affatto, gi&agrave; pi&ugrave; di tre anni, sicch&egrave; per rumore, fischio o chia&shy;<lb/>mata ad alta voce non dava cenno, pur con gli occhi, di udire. </s>

<s>Pochissimo <lb/>camminava, e non potendo per la debolezza alzare i piedi, gli strascicava in <lb/>modo, che ne faceva sentire il rumore per le stanze con lo strascino delle, <lb/>unghie sul suolo. </s>

<s>Poco e di poca voglia mangiava, e gi&agrave; da molto tempo <lb/>aveva tralasciato il costume di far carezze, neppure col moto della coda, ai <lb/>padroni. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/1288.jpg" pagenum="163"/><p type="main">

<s>&ldquo; Dopo la trasfusione, sciolto dalla croce di legno ove s'era legato, rest&ograve; <lb/>per un'ora in circa sulla medesima tavola, dove s'era fatta l'operazione, <lb/>nel qual tempo, essendo noi discesi in altre stanze, comparve egli final&shy;<lb/>mente, avendo da s&egrave; discesa la tavola e la scala, ma non volle cibo, che <lb/>quindi ad un'altr'ora. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Li due giorni seguenti, ne'quali andai per diporto a vedere la for&shy;<lb/>tezza d'Osopo ed altre terre di giurisdizione di quell'Illustriss. </s>

<s>sig. </s>

<s>conte <lb/>Girolamo, mi riferirono que'signori Griffoni che aveva incominciato a stare <lb/>pi&ugrave; sollevato d'assai, anzi, che il marted&igrave; egli era uscito di casa, e contro <lb/>suo solito postosi a correre con altri cani per la piazza, non pi&ugrave; strasci&shy;<lb/>cando i piedi come prima soleva, ma fatto manifestamente pi&ugrave; robusto. </s>

<s>Tor&shy;<lb/>nato a casa, fece insolite carezze ai padroni, e quel che pi&ugrave; ci parve consi&shy;<lb/>derabile, oltre il mangiare pi&ugrave; e con pi&ugrave; avidit&agrave; di prima, incominci&ograve; a dar <lb/>segni manifesti di recuperar l'udito, perch&egrave; infatti molte volte al fischio e <lb/>alla voce de'padroni si voltava, sebbene il sesto e settimo giorno, comin&shy;<lb/>ciando a suppurare gagliardamente la ferita, egli paresse reso di nuovo pi&ugrave; <lb/>malinconico e debole, il che s'attribuiva ai sintomi che dalla ferita mede&shy;<lb/>sima le provenissero. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Partii poscia da quelle parti, ed ora mi trovo in Bologna, aspettando <lb/>giornalmente da quegli Eccellentiss. </s>

<s>signori Griffoni altre relazioni di ci&ograve; <lb/>che sar&agrave; seguito..... Bologna, 8 Giugno 1668. &rdquo; (MSS. Cim., T. XIX, <lb/>c. </s>

<s>180, 81). </s></p><p type="main">

<s>Di quest'altre relazioni non abbiamo trovato il documento, dal quale <lb/>forse si concluderebbe che la giovent&ugrave; renduta al cane dei signori Griffoni <lb/>di Udine non era che un'illusione. </s>

<s>Illusioni simili apparvero nelle trasfu&shy;<lb/>sioni del sangue negli uomini, che perci&ograve; furono severamente proibite dalle <lb/>leggi civili, ma l'invenzione del Folli e le esperienze del Montanari, bench&egrave; <lb/>disonorate da certi medici cerretani, rimasero pure una delle pi&ugrave; belle di&shy;<lb/>mostrazioni del circolo del sangue, rendendosi evidente non andar egli alle <lb/>parti, se non che per la via del cuore. </s></p><pb xlink:href="020/01/1289.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO V.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Della respirazione<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle cause motive, degli organi e dei modi della respirazione. </s>

<s>&mdash; II. Dell'azione dell'aria inspi&shy;<lb/>rata sul sangue dei polmoni. </s>

<s>&mdash; III. </s>

<s>Della respirazione dei neonati: del problema arveiano. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Il cuore posto in grembo ai polmoni, i quali anzi, quasi incubandolo, <lb/>par che lo tengano sotto le loro ali, dava facile indizio di quegl'intimi com&shy;<lb/>merci, che passano tra lui e il viscere che lo circonda nell'economia della <lb/>vita animale. </s>

<s>Risoneranno forse ancora nelle orecchie dei nostri lettori gli <lb/>idillii, ne'quali Galeno e il Vesalio cantarono del cuore, che nutrisce e mi&shy;<lb/>nistra da s&egrave; stesso ai polmoni, e de'polmoni che per contraccambio sono in <lb/>assiduo moto per refrigerare gli ardori del cuore; tant'oltre procedendo in <lb/>questa amorosa corrispondenza, da non isguagliarsi i polsi dai moti del to&shy;<lb/>race: Comunque siasi, &egrave; pur vero che sono i due visceri tra loro tanto stretti <lb/>consorti, che l'aver parlato dell'uno porta necessariamente che si parli anche <lb/>dell'altro, e insaparabili nelle pi&ugrave; alte funzioni della vita non vogliono andar <lb/>disgiunti ne'fasti della Storia. </s></p><p type="main">

<s>I fatti per&ograve; che passiamo a narrare hanno vicende alquanto diverse <lb/>dalle narrate, perch&egrave; prima di tutto, per ci&ograve; che concerne il tempo, si pu&ograve; <lb/>dire che, quando la scienza del cuore era gi&agrave; compiuta, quella de'polmoni <lb/>invece era appena cominciata. </s>

<s>La ragione di ci&ograve; non &egrave; difficile investigarla, <lb/>essendo che, a bene intendere i moti del sangue, non era necessario pre&shy;<lb/>cedesse altra scienza, mentre, a bene intendere i moti dell'aria nella respira&shy;<lb/>zione e gli effetti di lei sullo stesso sangue, conveniva precorressero la Mec-<pb xlink:href="020/01/1290.jpg" pagenum="165"/>canica e la Chimica de'corpi aeriformi; due nuove scienze, la prima delle <lb/>quali, incominciata sull'entrar del secolo XVII, verso la met&agrave; di lui fu quasi <lb/>assoluta, e la seconda non comparve che verso il terminar del secolo XVIII. </s></p><p type="main">

<s>&Egrave; perci&ograve; che, non dovendo pretergredire i limiti posti alla nostra Sto&shy;<lb/>ria, non resta a dir altro a noi se non che de'presentimenti, che s'ebbero <lb/>dell'azione chimica dell'aria sul sangue, ond'&egrave; insomma che il frutto noi <lb/>dobbiam presentarlo ai lettori sotto le forme dell'ovario chiuso intorno in&shy;<lb/>torno e adombrato dalle foglie del fiore. </s>

<s>Ma tutta dentro il nostro campo <lb/>rinchiusa riman la meccanica dei moti respiratorii, progredita col progredire <lb/>della Pneumatica, nella quale si possono segnare questi tre passi: Il primo, <lb/>che termina col secolo XVI, quando s'aveva della natura dell'aria e delle <lb/>propriet&agrave; fisiche di lei un'idea vaga e indistinta, fra ci&ograve; che si concepisce <lb/>come spirito, e ci&ograve; che si concepisce come materia; il secondo, che da'primi <lb/>anni del secolo giunge fino al 1644, quando, per opera del Porta, del Keplero <lb/>e di Galileo, si dimostr&ograve; che l'aria essendo pesante era materia, non diffe&shy;<lb/>rente da tutta l'altra, fuor che nell'apparenza; il terzo finalmente, che <lb/>dal 1644 passa oltre alla met&agrave; del secolo, quando per via del celebre Stru&shy;<lb/>mento del Torricelli e delle Macchine del Gueriche e del Boyle, si fece espe&shy;<lb/>rienza che, oltre all'esser l'aria pesante, &egrave; elastica e perci&ograve; operativa di <lb/>tutti quegl'innumerevoli effetti naturali, che parvero agli antichi altrettanti <lb/>misteri. </s></p><p type="main">

<s>Se sempre la Fisiologia fosse stata sollecita di giovarsi delle scoperte <lb/>della Fisica, a que'tre passi, segnati ne'progressi della Pneumatica, corri&shy;<lb/>sponderebbero esattamente i progressi fatti dalla scienza de'moti respiratorii. </s>

<s><lb/>Ma perch&egrave; le solite ritrosie ad accettare le novit&agrave;, e una certa natural pi&shy;<lb/>grizia del pensiero, in distendere e sollevare le ali, ora indugiarono que'con&shy;<lb/>nubii, e ora consigliarono a seguitar di fornicare con gli antichi errori; quei <lb/>tre passi non procedono, nella Pneumatisa e nella Fisiologia, sincroni, ma <lb/>perturbati, come vibrazioni di pendoli, che pur soggiacendo alle leggi gene&shy;<lb/>rali della Meccanica si risentono de'primi impulsi pi&ugrave; o meno gagliardi, e <lb/>del pi&ugrave; o men temperato influsso delle stagioni. </s>

<s>Che se il veder gl'intrecci <lb/>di pi&ugrave; pendoli, e il precedere e il susseguire de'moti diletta i curiosi, e <lb/>porge soggetto di utili considerazioni ai Filosofi; di non minor utilit&agrave; e di&shy;<lb/>letto sar&agrave; per riuscire questa parte di storia a chi, nelle diversioni e nelle <lb/>stesse retrogressioni del pensiero, sa riconoscer la legge provvidamente im&shy;<lb/>posta a'suoi progressi. </s></p><p type="main">

<s>Incominciando dunque dal primo passo sopra segnato, l'aria in s&egrave; stessa <lb/>riguardavasi come qualche cosa di spiritoso o di etereo, se non che la coin&shy;<lb/>quinano necessariamente materie terree e fuligginose. </s>

<s>S'attribuivano a cos&igrave; <lb/>fatte materie gli effetti sensibili dell'aria stessa, come i moti ventosi e la <lb/>varia temperatura, e la facolt&agrave; di alimentare o di estinguer la fiamma. </s>

<s>Que&shy;<lb/>sta idea della composizione dell'aria applicata alle funzioni respiratorie, tra&shy;<lb/>sparisce distinta nel Vesalio sotto una tal forma: &ldquo; Ex faucibus enim aerem, <lb/>per nares aut os attractum, recta in pulmonem ducit (aspera arteria), hunc <pb xlink:href="020/01/1291.jpg" pagenum="166"/>per universum pulmonis corpus ita numerosa ipsius serie distribuens, ut <lb/>pulmonis substantia hunc prompte alteret, atque cordis muneribus aptum <lb/>reddat. </s>

<s>Caeterum quod pulmonis proprium sit munus, suo dicemus loco, <lb/>nunc etiam sat est asperam arteriam, ita efformatam, innuere quod aptis&shy;<lb/>sime aerem dum respiramus pulmoni deferat, ac rursus omnem, qui cordi <lb/>inutilis est, una cum fuliginosis ipsius excrementis inter expirandum reddat. </s>

<s><lb/>Neque arteriae venalis usus nulli incognitus est, cum is praecipuus sit ut <lb/>aerem cordi aptum, ac a pulmonis substantia in asperae arteriae ramis con&shy;<lb/>fectum, in se pelliciat ipsiusque interventu cor eumdem in sinistrum ven&shy;<lb/>triculum attrahat &rdquo; (De corporis hum. </s>

<s>fabrica, Basileae 1543, pag. </s>

<s>577 e 583). </s></p><p type="main">

<s>Di qui ebbero origine le varie ipotesi degli ufficii dell'aria nella respi&shy;<lb/>razione. </s>

<s>Coloro, che la riguardarono in s&egrave; stessa o nella sua purit&agrave; eterea, <lb/>la fecero genitrice degli spiriti animali; quegli altri, che la considerarono <lb/>come necessariamente commista con parti terree, le attribuirono l'ufficio di <lb/>rinfrescare il cuore, ventilatagli intorno dalle ali del Polmone. </s></p><p type="main">

<s>L'ipotesi della generazion degli spiriti dall'aria entrata per la trachea <lb/>ne'polmoni, ipotesi professata gi&agrave; dagli antichi, il Colombo si lusing&ograve; come <lb/>vedemmo di averla ridotta alla certezza dei fatti, per via dell'esperienza, la <lb/>quale fu primo il Cesalpino a riconoscer per falsa, e a dir perci&ograve; che l'aria, <lb/>artificialmente insufflata per l'aspera arteria, non passa nella sostanza de'pol&shy;<lb/>moni, e tanto meno nel ventricolo sinistro del cuore. </s>

<s>L'ipotesi degli spiriti <lb/>veniva cos&igrave; ragionevolmente repudiata, ond'&egrave; che il Cesalpino stesso non <lb/>seppe vedere a quale altro uso dovesse entrar l'aria nel petto, se non che <lb/>a temperare il soverchio calor del sangue. </s>

<s>&ldquo; Transmisso interim aere fri&shy;<lb/>gido per asperae arteriae canales, qui iuxta arteriam venalem protenduntur, <lb/>non tamen osculis communicantes, ut putavit Galenus, solo tactu temperat &rdquo; <lb/>(Quaestiones perip., Venetiis 1571, fol. </s>

<s>111 ad terg.). </s></p><p type="main">

<s>Se l'aria dunque non attraversa i polmoni, come possono questi refri&shy;<lb/>gerare il cuore? </s>

<s>Mosso da tal ragione, &egrave; sollecito il Cesalpino di emendar <lb/>quell'errore invalso nell'insegnamento di alcuni, e di mostrar come il re&shy;<lb/>frigerio non va direttamente al cuore stesso, che non ne ha il bisogno, ma <lb/>al sangue, uscito cos&igrave; fervente dal ventricolo destro attraverso alla vena ar&shy;<lb/>teriale. </s>

<s>Ecco perci&ograve; qual'&egrave; l'ufficio proprio dal nostro Autore assegnato ai <lb/>polmoni: &ldquo; Maximo igitur ingenio Natura fabricata est pulmones in pede&shy;<lb/>stribus, et branchias in aquatibus, ut sanguinis fervorem moderaretur, illaeso <lb/>corde. </s>

<s>Nam cordi ad tutelam pericardium membranam circumduxit, tam&shy;<lb/>quam eius capsulam: ferventem autem in eo sanguinem ad pulmones aut <lb/>branchias derivaus, iterumque cordi restituens. </s>

<s>Interim in transitu, ex aeris <lb/>frigidi aut aquae contactu, refrigerationem molita est &rdquo; (ibi). </s></p><p type="main">

<s>Noi non possiamo con certezza asserire che fosse proprio il Cesalpino <lb/>inspirator dell'Arveo, ma pure &egrave; un fatto che, negatosi dal Nostro il passag&shy;<lb/>gio dell'aria attraverso alla sostanza del polmone, il Fisiologo inglese vol&shy;<lb/>sesi a ripetere l'esperienza del Colombo, e provato che, soffiandosi col man&shy;<lb/>tice nella trachea, non si trova dell'aria <emph type="italics"/>neque in arteria venosa, neque in<emph.end type="italics"/><pb xlink:href="020/01/1292.jpg" pagenum="167"/><emph type="italics"/>sinistro ventriculo cordis quidquam,<emph.end type="italics"/> fu dalle ragioni medesime del Cesal&shy;<lb/>pino condotto a negar che la respirazione fosse propriamente ordinata alla <lb/>generazione degli spiriti animali. </s>

<s>Ond'&egrave; che, trovandosi costretto a ricono&shy;<lb/>scere in altro quell'uso, venne, o fosse caso o fosse tacito e consapevole <lb/>consenso di idee, nella sentenza dello stesso Cesalpino. </s>

<s>&ldquo; Unde quoque pro&shy;<lb/>babile foret pulmonum expirationem esse qua his efflatis eventaretur et de&shy;<lb/>puraretur sanguis: atque inspirationem esse ut sanguis, pertranseundo inter <lb/>ventriculos duos cordis, contemperetur ambientis frigore, ne excandescens et <lb/>intumescens quadamque fermentatione inflatus, sicuti effervescens mel et lac, <lb/>adeo distenderet pulmonem, ut suffocaretur animal &rdquo; (Exercitatio I. </s>

<s>De circul. </s>

<s><lb/>sang. </s>

<s>post tractatum <emph type="italics"/>De motu cordis<emph.end type="italics"/> cit., pag. </s>

<s>139). </s></p><p type="main">

<s>Anche il Cartesio, il quale dopo il Cesalpino rinnov&ograve; l'errore aristote&shy;<lb/>lico del maggior calore, che &egrave; dentro il cuore, rispetto a quello delle altre <lb/>membra, e per cui il sangue esce dal ventricolo destro cos&igrave; bollente, da dis&shy;<lb/>siparsi facilmente in vapore; anche il Cartesio, come l'Harvey, nell'asse&shy;<lb/>gnare l'ufficio proprio del polmone, revoc&ograve; a s&egrave; l'ipotesi dello stesso Ce&shy;<lb/>salpino. </s>

<s>&ldquo; Et praecipuus quidem pulmonis usus (scrive nella Descrizione del <lb/>corpo umano, posta per appendice al trattato <emph type="italics"/>De homine<emph.end type="italics"/>) in hoc solum <lb/>consistit, quod aeris quem spiramus ope, sanguinem ex dextro cordis ven&shy;<lb/>triculo affluentem condenset et temperet, antequam in sinistrum ingredia&shy;<lb/>tur &rdquo; (Francofurti ad M. 1692, pag. </s>

<s>165). </s></p><p type="main">

<s>L'ipotesi degli spiriti animali, direttamente generati dalla parte eterea <lb/>dell'aria, introdotta nel sangue per opera immediata della respirazione, ve&shy;<lb/>niva cos&igrave; bandita dalla Fisiologia, e dopo i primi esempi dati dal Cesalpino <lb/>si conferm&ograve; il bando, allorch&egrave;, dimostratosi per l'esperienza esser l'aria in s&egrave; <lb/>stessa ponderosa, si riguard&ograve; come uno degli altri corpi, atta perci&ograve; a produrre <lb/>effetti naturali. </s>

<s>Fu allora che resuscit&ograve; tra'Fisiologi una questione rimasta <lb/>alquanto sopita: se cio&egrave; i moti respiratorii dipendano dal polmone enfiato <lb/>per la corpulenza dell'aria, o dall'alterno sollevarsi e abbassarsi del torace. </s></p><p type="main">

<s>Le origini della controversia risalgono al Berengario, ne'primi impulsi <lb/>che vennero da lui al risorgere della scienza. </s>

<s>Egli entra a discutere se i <lb/>moti de'polmoni sieno necessarii o volontarii, e dopo aver riferite le altrui <lb/>opinioni. </s>

<s>&ldquo; Ego tamen credo, soggiunge, quod pulmo interdum habeat so&shy;<lb/>lum motum naturalem per proprios villos, qui sunt in suis venis et arteriis, <lb/>qui tamen motus dependet a motu cordis, et sic motus pulmonis est acci&shy;<lb/>dentalis; nam in corde, de consensu omnium, conceditur motus naturalis, <lb/>a quo motu fit aeris attractio, et etiam sanguinis, at ita etiam a motu na&shy;<lb/>turali fit aeris, capnosorum fumorum et sanguinis et spirituum expulsio. </s>

<s>Cum <lb/>autem iste aer attractus a corde prius ingrediatur pulmonem, et ipsum in&shy;<lb/>flet, necessario movet eum.... Huic motui naturali necessario obediunt mu&shy;<lb/>sculi qui sunt inter costas et etiam diafragma, et moventur, quia pectus <lb/>necessario debet dilatari ad ampliationem et inflationem pulmonis propter in&shy;<lb/>gressum aeris in ipso &rdquo; (Commentarium super Anat. </s>

<s>Mundini, Bononiae 1521, <lb/>fol. </s>

<s>CCCXXVIII ad terg.). </s></p><pb xlink:href="020/01/1293.jpg" pagenum="168"/><p type="main">

<s>Quando la sperimentata ponderosit&agrave; dell'aria dette quasi si direbbe corpo <lb/>a queste dottrine, i fautori si studiarono di confermarle sul fondamento di <lb/>una esperienza, che fu primo a farla il Vesalio; ripetuta poi da tanti quando <lb/>si pens&ograve; di applicarla a soccorrere gli annegati, e attribuita comunemente <lb/>all'Hook. </s>

<s>Consisteva quella maravigliosa vesaliana esperienza nell'insnfflare <lb/>i polmoni di un animale rimasto morto, e nel restituirgli nuovamente la <lb/>vita &ldquo; Ut vero vita animali quodammodo restituatur, foramen in asperae <lb/>arteriae caudice tentandum est, cui canalis ex calamo aut arundine indetur, <lb/>isque inflabitur ut pulmo assurgat, ac ipsum animal quodammodo aerem <lb/>ducat. </s>

<s>Levi enim inflatu in vivo hoc animali pulmo tantum quanta thoracis <lb/>erat cavitas intumet, corque vires denuo assumit et motus differentia pul&shy;<lb/>chre variat &rdquo; (De corp. </s>

<s>hum. </s>

<s>fabrica cit., pag. </s>

<s>658). &Egrave; dunque ne'polmoni <lb/>e no nel torace il principio ai moti della respirazione. </s></p><p type="main">

<s>I fautori per&ograve; dell'altra sentenza, che poi era la vera, non potevano <lb/>persuadersi come i polmoni, privi affatto di organi motori, valessero a dare <lb/>impulso al torace fornito di tanti muscoli, e credettero meglio che, al dila&shy;<lb/>tarsi e al restringersi del torace stesso, l'aria entrasse ed uscisse dal petto, <lb/>com'entra ed esce nel mantice al distendersi e al ripiegarsi delle sue pelli. </s>

<s><lb/>Ebbe, nell'instaurare questa pi&ugrave; sana dottrina, grande efficacia il Cartesio, <lb/>il quale, dop'aver nel trattato <emph type="italics"/>De homine<emph.end type="italics"/> descritto il gioco de'muscoli pet&shy;<lb/>torali, conclude col dire che essi operano in modo &ldquo; ut spatium quo pul&shy;<lb/>mones continentur reddatur amplius, quo fit ut aer in eos ingrediatur, eo <lb/>prorsus modo quo in follem ingreditur, quando illum aperimus. </s>

<s>Ubi vero <lb/>horum musculorum antagonistae inflantur, spatium illud fit angustius, atque <lb/>ideo aer iterum egreditur &rdquo; (Editio cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Il Van Horne, in quel suo libretto intitolato il <emph type="italics"/>Microcosmo,<emph.end type="italics"/> e nel quale <lb/>si rendevano in facile ed elegante modo popolari l'Anatomia e la Fisiologia <lb/>di que'tempi, diffuse fra gli Olandesi la dottrina, che la respirazione &ldquo; non <lb/>contingit a pulmonis propria virtute, sed a thoracis distentione et coarcta&shy;<lb/>tione, ope potissimum diafragmatis &rdquo; (Lugduni Batav. </s>

<s>1665, pag. </s>

<s>78). E il <lb/>Deusingio fra'Tedeschi commemor&ograve;, invece delle cartesiane moderne, le pi&ugrave; <lb/>antiche tradizioni aristoteliche, insegnando che il torace si distende per virt&ugrave; <lb/>sua propria &ldquo; ac dum distenditur, et quia distenditur, ingreditur aer. </s>

<s>Sicque <lb/>verissimum est quod dicit Aristotelis, <emph type="italics"/>De respiratione c. </s>

<s>XXI,<emph.end type="italics"/> cum attollitur <lb/>pectus eodem, perinde ut in folles, aerem externum influere necesse est &rdquo; <lb/>(Exercitationes de Respir., Croningae 1661, pag. </s>

<s>99). </s></p><p type="main">

<s>Tra gl'Inglesi Natanaele Ighmor, amicissimo del Boyle, si dette, con <lb/>pi&ugrave; sollecito e amoroso studio de'predecessori e de'contemporanei, a trattar <lb/>la questione dei moti respiratorii, consacrando a ci&ograve; il Cap. </s>

<s>III della P. III <lb/>Lib. </s>

<s>II della sua <emph type="italics"/>Disquisizione anatomica del corpo dell'uomo.<emph.end type="italics"/> Incomincia <lb/>ivi dal sottoporre a un diligente esame le ipotesi di coloro, che attribuivano <lb/>ai polmoni una virt&ugrave; propria di respirare, e dimostratane con argomenti di <lb/>fatto e di ragione la falsit&agrave;, cos&igrave; all'ultimo conclude: &ldquo; A motu itaque tho&shy;<lb/>racis motum pulmonum dependere statuendum est. </s>

<s>Quando scilicet thorax <pb xlink:href="020/01/1294.jpg" pagenum="169"/>dilatatur, pulmones ad implendam eius cavitatem, ob vacui fugam, attollun&shy;<lb/>tur, et internae eius superficiei undique se applicantes illorum porosas ca&shy;<lb/>vitates etiam distendunt, in quas, ne daretur vacuum, per bronchias aer ir&shy;<lb/>ruit. </s>

<s>Laxatis vero thoracis fibris, et cavitate hoc modo constricta, proprio <lb/>gravati pondere, pulmones sponte decidunt, aeremque, spongiosos illorum <lb/>poros comprimendo, expirant &rdquo; (Hagae comitis, 1651, pag. </s>

<s>186). </s></p><p type="main">

<s>Fin qui per&ograve; l'Igmoro niente altro fa che le parti di sapiente Filosofo, <lb/>ma perch&egrave; sentiva che sarebbero l'esperienze riuscite molto pi&ugrave; concludenti <lb/>delle ragioni, spogliato il pallio filosofale e impugnato il coltello anatomico, <lb/>tanto vi si esercit&ograve;, da credere di aver dispersa in quegli atti tutta intera <lb/>la razza dei cani, &ldquo; quibus, egli dice, in vivorum dissectionibus semper usi <lb/>sumus. </s>

<s>&rdquo; </s></p><p type="main">

<s>Ferito dunque il torace, i polmoni presentavano all'attento osservatore <lb/>fatti diversi. </s>

<s>Se la ferita facevasi nel mezzo, si venivano bene spesso a vio&shy;<lb/>lare le membrane del Mediastino, cosicch&egrave; l'aria, liberamente entrando dalle <lb/>due parti nel petto &ldquo; vacui metum tollat, ideoque cum thoracis cavitas di&shy;<lb/>stendatur non assurgunt pulmones, dempta necessitate illos ad motum co&shy;<lb/>gente &rdquo; (ibi, pag. </s>

<s>188). Lo stesso avviene quando, aperti ambedue i lati con <lb/>larghe e profonde ferite, l'aria a furia d'ogni parte v'irrompe. </s>

<s>Se per&ograve; <lb/>feriscasi un lato solo, rimanendosi l'altro inviolato, qui osservammo, egli <lb/>dice, che il polmone seguita a muoversi, mentre l&agrave; rimane affatto inerte. </s>

<s><lb/>La ragione &egrave; &ldquo; quia Mediastinum exacte cavitatem illaesi lateris claudit, adeo <lb/>ut aer externus necessitatem illam movendi in pulmonibus demere nequeat, <lb/>quia omnino excluditur &rdquo; (ibi). </s></p><p type="main">

<s>Stava tutto ci&ograve; a dimostrar chiaramente all'Igmoro che il moto dei pol&shy;<lb/>moni dipende dal torace, quando venne una difficolt&agrave; a dare improvviso as&shy;<lb/>salto alla sua persuasione. </s>

<s>Ferito leggermente il cane in petto, in modo che <lb/>l'aria non irrompa a furia, ma vi trapeli appena, &ldquo; aliquando motus illorum <lb/>loborum continuatur, imo saepe tam violento agitantur motu, ut etiam extra <lb/>vulnus evolare saepe cernantur &rdquo; (ibi). Ci&ograve; pareva confermar l'ipotesi di co&shy;<lb/>loro, che attribuivano al polmone un moto proprio, ma <emph type="italics"/>post longam con&shy;<lb/>templationem frequentesque observationes,<emph.end type="italics"/> l'Igmoro stesso scopri l'inganno, <lb/>e intese da che veramente dipendeva quel fatto: &ldquo; quod scilicet lobi pulmo&shy;<lb/>num lateris illaesi et integri, ob vacui fugam, moventes, ut supra dictum <lb/>est, aerem externum confertim arripiant, quam violentam attractionem plus <lb/>aeris sequitur quam in illis contineri queat. </s>

<s>Ideoque, cum ad lobos utriusque <lb/>lateris per eumdem canalem aer feratur, et lobi lateris integri repleti sint, <lb/>adeo ut totum illud aeris commoti quod insequitur recipere non possint; <lb/>ille vero incitatus non statim a motu desistit, sed qua patet via ruit, se&shy;<lb/>quensque priorem urget, et cum in parte attrahente spatium non invenit, <lb/>in bronchias patentes loborum iam fatiscentium, qui a thorace non moven&shy;<lb/>tur, irruit, eosque, ob levitatem eximiam, paululum attollit et motum quen&shy;<lb/>dam languidum aliquandiu efficit &rdquo; (ibi, pag. </s>

<s>189). </s></p><p type="main">

<s>Chi legge oggidi queste parole, scritte dopo sette anni da ch'era stata <pb xlink:href="020/01/1295.jpg" pagenum="170"/>fatta l'esperienza del Torricelli, si maraviglia che, a intendere il fatto sopra <lb/>descritto, bisognassero all'Igmoro lunghe contemplazioni, e si maraviglia <lb/>anche di pi&ugrave; ehe frutto di osservazioni frequenti fosse la sopra riferita con&shy;<lb/>clusione. </s>

<s>Consegue per&ograve; da una tal maraviglia una notizia importante, ed &egrave; <lb/>che l'arguto Anatomico inglese aveva della respirazione risoluto il problema <lb/>meccanico, ma no il pneumatico, lasciando ancora a spiegare in che modo, <lb/>dilatandosi e restringendosi il torace, l'aria entri ed esca dal petto. </s></p><p type="main">

<s>La notizia delle scoperte italiane non era ancora penetrata in quelle <lb/>estranee regioni, nelle quali dominava piuttosto la Filosofia cartesiana, in <lb/>conformit&agrave; de'placiti della quale s'ammetteva che il petto attraesse l'aria a <lb/>s&egrave; prossima, la quale fosse spinta dalla contigua, e questa dalla precedente <lb/>via via per una serie continuata di moti, rimasta nota nella storia sotto il <lb/>nome di <emph type="italics"/>circolo cartesiano.<emph.end type="italics"/> L'Igmoro applic&ograve; questo circolo alla pi&ugrave; com&shy;<lb/>piuta soluzion del problema de'moti del polmone dalla parte del petto leg&shy;<lb/>germente ferito, e rimasto nell'altra parte inviolato. </s>

<s>&ldquo; Sic cum pulmonum <lb/>lobi in latere illaeso et integro moveantur, ac in aere motum quemdam ra&shy;<lb/>pidum excitent, particulae aeris quae primo attrahuntur a subsequentibus <lb/>etiam impelluntur, hae ab aliis, illae a subsequentibus, illas aliae promovent, <lb/>adeo ut lobos elatos copiose infarcientes ad flaccidam etiam et immotam pul&shy;<lb/>monum partem aer commotus, per eamdem canalem, irruat, illamque paulo <lb/>attollat ac distendat, perinde ac vesica quae per tubulum inflatur &rdquo; (ibi, <lb/>pag. </s>

<s>189). N&egrave; &egrave; a passare in tal prop&ograve;sito senza nota che l'Autore, quat&shy;<lb/>tordici anni dopo la pubblicazione de'Dialoghi galileiani delle Due nuove <lb/>scienze, ammetta in quel circolo d'aria inspirata un velocitarsi di moto dalla <lb/>bocca infino al polmone, somigliante a quello che produce, secondo il Pe&shy;<lb/>reirio, il velocitarsi de'corpi gravi cadenti. </s>

<s>&ldquo; Huius motus exemplum in <lb/>motu lapidis ab excelso descendentis habemus, cuius progressus in aere, in <lb/>fine velocior est quam in principio, ob aerem scilicet illum subsequentem <lb/>et promoventem, referente Pereirio, cap. <emph type="italics"/>De motu.<emph.end type="italics"/> Delabente enim lapide <lb/>partes aeris proxime inferiores, plus a lapide pulsae ac divulsae, ut locum <lb/>ab illo relictum occupent, magno impetu et celaritate ad terga lapidis con&shy;<lb/>currunt, ipsumque impellunt ac ulterius promovent, et quo plures fuerint <lb/>aeris particulae, maiorique nixu impulsae ac maiori vi confluentes, lapidem <lb/>a tergo vehementius urgent et protrudunt, ac lapis velocius descendit &rdquo; (ibi, <lb/>pag. </s>

<s>188). </s></p><p type="main">

<s>Ebbe l'Igmoro in quella ipotesi del circolo cartesiano molti consorti, <lb/>fra'quali &egrave; da citar lo Charletton, di cui le dottrine trovarono nelle contro&shy;<lb/>versie col Deusingio un commento. </s>

<s>Essendo un fatto oramai certo che l'aria <lb/>entra, come nel mantice, nella cavit&agrave; del torace, si disputava se ci&ograve; avve&shy;<lb/>nisse per attrazione o per impulsione, a che rispondeva il Deusingio che <lb/>poteva essere e nell'un modo e nell'altro. </s>

<s>&ldquo; Nempe, dum dilatatur thorax, <lb/>pellitur aer circumstans ab ipso thorace se distendente: is vero aerem vi&shy;<lb/>cinum propellit. </s>

<s>Cumque nullibi vacuum detur in rerum natura.... neces&shy;<lb/>sum omnino est aerem sic pulsum, quasi circulatione quadam facta, thora-<pb xlink:href="020/01/1296.jpg" pagenum="171"/>cem subire.... Sed et vicissim dum dilatatur thorax, amplior redditur interior <lb/>eius cavitas in quam necessitate quadam, cum vacuum dari nequeat, subin&shy;<lb/>trat aer, ipsumque spatium replet, sicque aer videtur attractione in cavum <lb/>thoracis subire &rdquo; (Exercitatio de respir. </s>

<s>cit., pag. </s>

<s>99, 100). </s></p><p type="main">

<s>Che di alquanti anni varcata la met&agrave; del secolo XVII si durasse cos&igrave; fra <lb/>gli stranieri a commentare il circolo cartesiano, e a pronunziare quelle insi&shy;<lb/>gnificanti parole di <emph type="italics"/>fuga del vacuo,<emph.end type="italics"/> fa senza dubbio gran maraviglia, ma <lb/>pi&ugrave; gran maraviglia fa Giovanni Swammerdam, che pretese di dimostrare <lb/>la propulsione dell'aria ne'polmoni per mezzo dell'esperienza. </s></p><p type="main">

<s>Nel 1667, diciannove anni dopo le pubbliche esperienze torricelliane fatte <lb/>dal Pascal a Roano e a Parigi, e tredici anni dopo che il Pecquet avea pub&shy;<lb/>blicato quegli stessi esperimenti, fatti pure in Parigi, intorno alle propriet&agrave; <lb/>elastiche dell'aria; il celebre Medico olandese, che frequentava la Francia, <lb/>instaurava la sua fisiologia della respirazione sopra la dottrina &ldquo; de rare&shy;<lb/>factione et condensatione iuxta nobilissimi et subtilissimi Cartesii fundamenta <lb/>firmissima et inconcussae veritatis &rdquo; (De respiratiene usuque pulmonum, <lb/>Lugduni Batav. </s>

<s>1667, pag. </s>

<s>119). Gli esperimenti poi, che secondo lo Swam&shy;<lb/>merdam rendono quelle cartesiane verit&agrave; fermissime ed inconcusse, son varii, <lb/>ma notabile fra gli altri &egrave; quello delle due ampolle disegnate a pag. </s>

<s>55 della <lb/>citata edizione, e riprodotte da noi <lb/>nella fig. </s>

<s>7, che per i nostri lettori <lb/>non ha bisogno d'altra dichiarazione. </s>

<s><lb/>I moti dello stantuffo GH, che aspi&shy;<lb/>rando o premendo l'aria nella storta <lb/>A fanno zampillare il liquido ora dal <lb/>beccuccio D, ora dall'altro C, rap&shy;<lb/>presentano i moti del petto, e gli ef&shy;<lb/>fetti dell'espulsione e dell'impulsione <lb/><figure id="id.020.01.1296.1.jpg" xlink:href="020/01/1296/1.jpg"/></s></p><p type="caption">

<s>Figura 7.<lb/>dell'aria ne'polmoni; effetti che si vedono, dice l'Autore, seguire allo stesso <lb/>modo, se al collo della storta, invece d'applicarvi uno stantuffo &rdquo; iungantur <lb/>totidem tubuli aenei oblongi, qui in asperam alicuius canis arteriam succes&shy;<lb/>sive immittantur, arcteque huic alligentur &rdquo; (ibi, pag. </s>

<s>58). </s></p><p type="main">

<s>La nuova scienza pneumatica, istituita dal Torricelli, fu primo il Pecquet <lb/>ad applicarla sapientemente alla Fisiologia, mettendo in piena evidenza quella <lb/>singolar propriet&agrave; che ha l'aria di dilatarsi spontaneamente; propriet&agrave; ri&shy;<lb/>masta, prima dello sperimento torricelliano, inconsiderata. </s>

<s>Ma il Pecquet, ben&shy;<lb/>ch&egrave; avesse aperti gli occhi dei Fisiologi intorno all'errore della suzione e <lb/>dell'attrazione, e avesse nelle sue Dissertazioni anatomiche sentenziato che <lb/>&ldquo; folles aerem non attrahunt exuguntve, sed intrusum externa vi coguntur <lb/>excipere &rdquo; (Parisiis 1654, pag. </s>

<s>66); non si cur&ograve; di applicare questa teoria <lb/>pneumatica dai mantici ai polmoni, lasciandone tutto il merito al Boyle, che <lb/>sperimentando la vita degli animali nel vuoto della sua Macchina, prese di <lb/>li occasione a dimostrar come l'aria, spontaneamente e senz'altro esteriore <lb/>impulso, entra a riempire l'aperta cavit&agrave; del torace. </s></p><pb xlink:href="020/01/1297.jpg" pagenum="172"/><p type="main">

<s>Dal XLI de'suoi Nuovi esperimenti fisico-meccanici fa una digressione, <lb/><emph type="italics"/>in qaa dubitationes nonnullae de respiratione continentur,<emph.end type="italics"/> e dopo avere <lb/>accennato all'ipotesi del circolo cartesiano, e alle esperienze immaginate per <lb/>confermarlo, e alle ragioni da alcuni addotte in centrario; &ldquo; huic autem diffi&shy;<lb/>cultati, soggiunge il Boyle, Machina nostra facilem nobis suppeditat solutio&shy;<lb/>nem, cum ex multis superioribus pateat experimentis quod in re de qua <lb/>agitur nulla omnino sit necessaria, quamvis verum sit in usitata respiratione <lb/>aliquam istiusmodi fieri solitam, ex thoracis vel abdominis dilatatione, aeris <lb/>in pulmones propulsio: quod quidem a sola thoracis dilatatione, interni istius <lb/>aeris seu halituosae substantiae spira, quae cavitatem possidere solet, quo&shy;<lb/>usque a pulmonibus non adimpletur, plurimum debilitata, externus et con&shy;<lb/>tiguus aer necessario per apertam arteriam asperam in pulmones irrumpit, <lb/>quoniam illic minorem quam alibi reperit oppositam sibi contranitentiam &rdquo; <lb/>(Opera omnia, T. I, Venetiis 1697, pag. </s>

<s>103). </s></p><p type="main">

<s>Cos&igrave;, nel 1659, entrava animosamente il Boyle in mezzo a quel grande <lb/>scompiglio d'idee provocato dal vizioso fermento della Filosofia cartesiana, <lb/>e le riduceva sapientemente negli ordini del vero. </s>

<s>Il sale depurativo, per <lb/>cos&igrave; dire, delle false dottrine accolte nella sua patria e altrove le aveva il <lb/>grande Fisico inglese attinte dallo sperimento torricelliano, intanto che non <lb/>poca parte del merito &egrave; per i giusti giudici da attribuirsi all'Italia. </s>

<s>N&egrave; qui <lb/>&egrave; a tacere che, a confronto dell'attivit&agrave; degli stranieri, i Nostri appariscono <lb/>inerti, di che non &egrave; difficile intraveder le ragioni, la prima e principal delle <lb/>quali &egrave; da riconoscersi in quella severit&agrave; degl'istituti galileiani, che non per&shy;<lb/>mettevano di coltivare altra scienza, da quella in fuori che ha il fondamento <lb/>nelle matematiche, e nell'osservazione dei fatti naturali. </s>

<s>&Egrave; degno nonostante <lb/>di considerazione che fu il Malpighi, che dette al Bartholin occasione di di&shy;<lb/>mostrare, nel Cap. </s>

<s>V <emph type="italics"/>De pulmonibus,<emph.end type="italics"/> &ldquo; Aerem a thorace non pelli in pulmo&shy;<lb/>nes contra Cartesium &rdquo; (Inter Malpighii Opera, T. II, Lugd. </s>

<s>Batav. </s>

<s>1687, <lb/>pag. </s>

<s>372-79). </s></p><p type="main">

<s>Col trattato <emph type="italics"/>De homine<emph.end type="italics"/> applicava il Cartesio la sua Filosofia allo stu&shy;<lb/>dio del corpo umano, per cui egli ebbe grande efficacia e dette valido im&shy;<lb/>pulso a promovere la Fisiologia; impulso che manc&ograve; agli Italiani, i quali, <lb/>riguardando il cartesianismo come un contagio, rimasero da questa parte <lb/>lungamente indietro agli stranieri. </s>

<s>La maravigliosa fecondit&agrave; della scoperta <lb/>torricelliana, applicabile a ogni ordine di scienza, veniva debolmente colti&shy;<lb/>vata fra noi dal Michelini e dal Magiotti, non anatomici per verit&agrave; n&egrave; fisio&shy;<lb/>logi, i quali non porsero ai loro connazionali, come al Boyle l'Igmoro, il <lb/>Bartholin, il Willis e tanti altri, un subietto preesistente da instaurarvi, sulle <lb/>ipotesi immaginate, i nuovi fatti scoperti. </s></p><p type="main">

<s>Narrammo in altra parte della nostra Storia come quella, che si pu&ograve; <lb/>chiamare Filosofia nuova torricelliana, rimanesse per alquanti anni in Italia <lb/>inculta e quasi dimenticata, &egrave; com'ella solamente risorgesse nell'Accademia <lb/>del Cimento, quando gi&agrave; il Pascal, il Guericke e il Boyle l'avevano con tanto <lb/>splendore diffusa tra le pi&ugrave; studiose nazioni di Europa. </s>

<s>I nostri accademici <pb xlink:href="020/01/1298.jpg" pagenum="173"/>fiorentini dunque ripeterono gli esperimenti degli animali nel vuoto, sopra <lb/>i quali il Borelli fond&ograve; poi la sua teoria della respirazione divisa in due <lb/>parti, nella prima delle quali tratta <emph type="italics"/>De motu respirationis,<emph.end type="italics"/> e nell'altra <emph type="italics"/>De <lb/>usu respirationis primario.<emph.end type="italics"/> Delle dottrine borelliane, che concernono questa <lb/>seconda parte, diremo nel paragrafo appresso, per trattenerci qui solamente <lb/>a riferir ci&ograve; che concerne la pneumatica e la meccanica de'moti respiratorii. </s></p><p type="main">

<s>&Egrave; questa de'moti respiratorii, incomincia a dire il Borelli, una cogni&shy;<lb/>zione assai perplessa ed oscura, non essendo noi certi quali sieno le vere <lb/>cause motive, quali gli strumenti, e quali i modi veri della respirazione. </s>

<s>No&shy;<lb/>nostante egli &egrave; certamente dimostrato nella propos. </s>

<s>LXXXII della P. II <emph type="italics"/>De <lb/>motu anim.<emph.end type="italics"/> che n&egrave; l'aria, n&egrave; i polmoni sono cause effettive della respira&shy;<lb/>zione, ma che solo passivamente concorrono a produrre quegli atti. </s>

<s>Il pro&shy;<lb/>cesso dimostrativo &egrave; semplice e spedito, imperocch&egrave;, non avendo l'aria altra <lb/>forza motiva che nella sua gravit&agrave; e nel suo elaterio, non pu&ograve; perci&ograve; pro&shy;<lb/>durre nessuna azione, mentre che il fluido si rimane in mezzo all'atmosfera <lb/>in equilibrio, perch&egrave; ugualmente d'ogni parte compresso. </s>

<s>&ldquo; Quare est im&shy;<lb/>possibile, dum in quiete persistit, ut tanta violentia dilatet pulmones, eos&shy;<lb/>que repleat, et postea motu contrario eosdem constringat ut aufugiat &rdquo; (Ro&shy;<lb/>mae 1681, pag. </s>

<s>155). Che non sieno poi causa effettiva della respirazione i <lb/>polmoni &egrave; chiaro, non essendo essi composti di fibre muscolari, per cui non <lb/>si possono muovere da s&egrave; stessi (ivi). </s></p><p type="main">

<s>Cause efficienti della respirazione, soggiunge nella proposizione appresso <lb/>il Borelli, son le forze de'muscoli, che allargano il torace, e il peso con&shy;<lb/>giunto alla forza elastica dell'aria. </s>

<s>Rispetto al designare i muscoli, ai quali <lb/>sono stati propriamente dalla Natura commessi quegli uffici, gli Anatomici, <lb/>anco ai tempi del Borelli, non si trovavano pienamente concordi, ma pure <lb/>il Vidio fra'Nostri, ne aveva scritto con assai precisione. </s>

<s>Dopo aver detto <lb/>che s'inspira, quando il torace si dilata, e si espira, quand'egli si contrae, <lb/>&ldquo; quamobrem, soggiunge, quicumque musculi thoracem dilatant ad inspira&shy;<lb/>tionem pertinent, quicumque contrahuut, ad expirationem. </s>

<s>Sed cum utra&shy;<lb/>que et naturaliter fiat et cum quadam vi, plures musculi concurrunt ad eam <lb/>quae fit cum vi, quam ad eam quae naturaliter. </s>

<s>In naturali respiratione di&shy;<lb/>latando thoraci sufficit septum transversum duntaxat. </s>

<s>Sed in ea quae fit <lb/>cum vi, thorax necesse est dilatetur, non tantum a septo transverso, sed <lb/>etiam a primo ex musculis,.... qui inter costas sibi fibras habent superne <lb/>deorsum tendentes: hi autem sunt externi in omnibus spaciis inter costas. </s>

<s><lb/>Expirationem naturalem satis praestat per se gravitas thoracis qui, relaxato <lb/>septo transverso, descendit et ita contrahitur, sed ubi cum vi expiramus con&shy;<lb/>currunt ad eum contrahendum musculi, qui siti inter costas fibras habent <lb/>ab inferiori parte sursum ascendentes &rdquo; (De anat. </s>

<s>corp. </s>

<s>hum., Venetiis 1611, <lb/>pag. </s>

<s>201, 2). Il Borelli pure, approvando in sostanza queste dottrine del Vidio, <lb/>concludeva la sua LXXXIV proposizione col dire che i moti respiratori, cos&igrave; <lb/>placidi e naturali come violenti, si compiono dai soli muscoli intercostali e <lb/>dal diaframma insieme operanti (De motu anim. </s>

<s>Pars cit., pag. </s>

<s>171). </s></p><pb xlink:href="020/01/1299.jpg" pagenum="174"/><p type="main">

<s>L'altra causa efficiente della respirazione, aggiunge il Borelli, consiste <lb/>nel peso e nella elasticit&agrave; dell'aria, ci&ograve; che, senza ricorrere alle artificiali <lb/>esperienze del Boyle, semplicemente dimostra per l'esempio del mantice, <emph type="italics"/>qui <lb/>utrem inclusum habeat,<emph.end type="italics"/> nel quale otre si rappresenta il polmone contenuto <lb/>nella cavit&agrave; del torace (ivi, pag. </s>

<s>167). </s></p><p type="main">

<s>Venivano cos&igrave; dimostrate le vere cause motive e gli strumenti della re&shy;<lb/>spirazione: rimaneva a dire dei modi, ci&ograve; che il Borelli fa nella proposi&shy;<lb/>zione XC, premesse altre cinque per lemmi, in cui le costole si rappresen&shy;<lb/>tano per archi semiellittici, con le loro estremit&agrave; imperniate in una colonna <lb/>fissa, che rende immagine della colonna vertebrale. </s>

<s>Sollevandosi quegli archi, <lb/>la capacit&agrave; compresa fra essi e la colonna aumenta, e abbassandosi diminui&shy;<lb/>sce, d'onde all'ultimo il nostro Autore ne conclude, facendone l'applicazione <lb/>ai moti respiratorii del petto: &ldquo; contractis musculis intercostalibus, una cum <lb/>diaphragmate, necessario pectoris cavitas ampliari et aer inspirari debet <lb/>&ldquo; (ibi, pag. </s>

<s>176). </s></p><p type="main">

<s>Bench'entrasse il Borelli in questa trattazione, com'udimmo, con passo <lb/>incerto, pur ne usc&igrave; fuori fiancheggiato dal vero, che i Fisiologi insomma <lb/>hanno poi confermato. </s>

<s>La teoria meccanica della respirazione, iniziata dal <lb/>Boyle fra gli stranieri, ebbe cos&igrave; l'ultima mano in Italia, dove si sarebbe <lb/>creduto che dovess'essere universalmente accolta, s&igrave; per la grande autorit&agrave; <lb/>del Maestro che l'insegnava, e s&igrave; per le patrie scientifiche tradizioni, che, <lb/>dopo aver lungamente esulato, un Italiano riduceva quasi trionfali nella sua <lb/>patria. </s>

<s>Eppure il Baglivi, tanto autorevole a que'tempi, mostruosamente ac&shy;<lb/>coppiando il vero dimostrato col falso gi&agrave; confutato, scriveva in una delle <lb/>sue Dissertazioni ch'entrando l'aria nel petto, col proprio peso e con la pro&shy;<lb/>pria elasticit&agrave; d&agrave; moto ai polmoni, a cui necessariamente conseguitano i moti <lb/>del torace. </s>

<s>&ldquo; Et videtur probabile motum thoracis ab inflatis aere pulmoni&shy;<lb/>bus pendere, thoracemque dilatari ut locum det pulmonibus aere se expan&shy;<lb/>dentibus; nam primo succedit aeris ingressus, deinde dilatatio thoracis. </s>

<s>&rdquo; <lb/>(Opera omnia, Lugduni 1710, pag. </s>

<s>455). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Male per&ograve; giudicherebbe de'progressi, dalla Fisiologia fatti in Italia <lb/>sulla fine del secolo XVII, per impulso principalmente della grande opera <lb/>del Borelli, colui che volesse pigliar l'esempio da Giorgio Baglivi. </s>

<s>A lui, <lb/>divenuto celebre nella prassi medica, troppo gran difetto facevano i prin&shy;<lb/>cipii della Fisica e della Matematica, n&egrave; reca maraviglia che ripetesse in&shy;<lb/>torno agli organi della respirazione gli errori confutati un mezzo secolo prima <lb/>dall'Igmoro egli, che preferiva in astronomia Tolomeo a Galileo, e in chi&shy;<lb/>mica al Boyle l'Helmontio. </s></p><p type="main">

<s>Nella prima parte insomma del suo trattato della respirazione si pu&ograve; <pb xlink:href="020/01/1300.jpg" pagenum="175"/>dir che il Borelli ne dava la teoria, per ogni sua parte assoluta, e univer&shy;<lb/>salmente approvata dagli stranieri e dai nostri, che secondavano i progressi <lb/>della scienza. </s>

<s>Ma quanto era certo che l'aria entra spontaneamente ne'pol&shy;<lb/>moni, per la propria elasticit&agrave; e pel proprio peso, altrettanto era dubbio qual <lb/>ne fosse nell'economia della vita l'uso primario. </s>

<s>&ldquo; Nec tandem, si sentiva <lb/>costretto di confessar lo stesso Borelli, usus eius primarius exacte perceptus <lb/>est &rdquo; (De motu anim., P. II cit., pag. </s>

<s>162). </s></p><p type="main">

<s>Quel <emph type="italics"/>tandem<emph.end type="italics"/> accenna a un qualche laborioso esercizio della mente dei <lb/>Fisiologi precursori, in investigare un tal uso, che dal Nostro si riduce al <lb/>refrigerio del calor del cuore, alla ventilazione della fiamma vitale, e all'espul&shy;<lb/>sione delle materie filigginose; usi tutti che il Borelli, con assai facili ra&shy;<lb/>gioni rifiuta, ma per&ograve; tace di altre ipotesi pi&ugrave; sottili, nelle quali ei non senti <lb/>sventuratamente la fragranza di quel fior del vero, che sarebbe in terra stra&shy;<lb/>niera, e dopo lunga stagione, allegato nel frutto. </s>

<s>Noi dobbiamo dunque in&shy;<lb/>trattenerci alquanto sopra s&igrave; fatte ipotesi, tanto pi&ugrave; che possiamo da un Ita&shy;<lb/>liano pigliare i principii alla nostra storia. </s></p><p type="main">

<s>Potrebbe essere quell'Italiano l'Acquapendente, il quale, nel cap. </s>

<s>IV, <lb/>libro I <emph type="italics"/>De respiratione,<emph.end type="italics"/> prendeva sapientemente la Fisica per sicura scorta <lb/>alla Fisiologia, e diceva l'aria generare e conservare gli spiriti animali a <lb/>quel modo, che genera e conserva la fiamma; ond'&egrave; che, a voler conoscere <lb/>fra le varie opinioni quale sia la vera, &ldquo; quomodo tum generetur tum con&shy;<lb/>servetur omnis flamma indagandum est &rdquo; (Opera omnia, Lugd. </s>

<s>Batav 1738, <lb/>pag. </s>

<s>163). Ma seguendo in cos&igrave; fatte indagini, l'Autore, piuttosto l'autorit&agrave; <lb/>di Galeno che l'esperienza, ne lasciava perci&ograve; il primo merito, un mezzo <lb/>secolo dopo, a un altro Medico italiano. </s></p><p type="main">

<s>Nel 1661 Tommaso Cornelio meditava seriamente sopra i pi&ugrave; difficili <lb/>problemi della vita. </s>

<s>Fautor del Cartesio, da lui creduto professare una Filo&shy;<lb/>sofia, &ldquo; quae a rebus incertis assensionem cohibendo, ea tantum admittat, <lb/>quae cognita plane fuerint penitusque perspecta &rdquo; (Progymnasmata, 1688, <lb/>pag. </s>

<s>279), ebbe a riconoscere di quando in quando di essersi ingannato, e <lb/>specialmente udendo il suo Autore farsi seguace di Aristotile e dire che il <lb/>cuore &egrave; negli animali tanto fervente, da non potersegli tener sopra la mano, <lb/>per cui entratovi dentro il sangue si leva subito in gran bollore. </s>

<s>&mdash; Ma come <lb/>poteva persuadersi di ci&ograve; il gran Filosofo, pensa il Cornelio, se a toccare il <lb/>cuore e a intingervi, come tante volte ho fatt'io, il dito, non si sente punto <lb/>pi&ugrave; caldo delle altre viscere? </s>

<s>&mdash; </s></p><p type="main">

<s>Veduta perci&ograve; di qui la necessit&agrave; di abbandonare il Maestro, fu per&shy;<lb/>suaso esso Cornelio che il calore sia n&ograve; nel cuore ma nel sangue, a cui si <lb/>comunichi e in cui si conservi in virt&ugrave; del continuo moto, a produrre il <lb/>quale occorsegli per prima cosa al pensiero che fosse principalmente ordi&shy;<lb/>nata la respirazione. </s>

<s>&ldquo; Quippe sanguis ille, qui e dextero cordis ventriculo <lb/>in pulmones, per venam ut vocant, arteriosam, propellitur, nequit in sini&shy;<lb/>strum ventriculum permanare, nisi aer spiritu ductus arteriae asperae sur&shy;<lb/>culos inflet atque distendat. </s>

<s>Hinc enim fit ut venae arteriosae ramuli com-<pb xlink:href="020/01/1301.jpg" pagenum="176"/>primantur atque adeo conclusus in his sanguis protrudatur in surculos <lb/>arteriae venosae &rdquo; (ibi, pag. </s>

<s>283). </s></p><p type="main">

<s>Qui, proseguendo il Cornelio le sue meditazioni, sentiva sollevarsi nella <lb/>mente un dubbio, che cos&igrave; gli ragionava: &mdash; Se la respirazione a questo <lb/>principale effetto di promuovere il circolo del sangue &egrave; comparata, come <lb/>mai un uomo non pu&ograve; lungamente vivere chiuso per esempio in un orcio, <lb/>che non abbia da nessuna parte il traspiro? </s>

<s>O perch&egrave; ci dovrebb'egli al&shy;<lb/>lora esser bisogno che l'aria da respirarsi tratto tratto sia rinnovata? </s>

<s>Anzi <lb/>n&egrave; ogni sorta di aria, atta per il suo peso e per la sua elasticit&agrave; a dare im&shy;<lb/>pulso di moto al sangue, &egrave; buona alla respirazione, come si vede per l'esem&shy;<lb/>pio di quella, che traspira dalle cave del carbon fossile o ch'esala dai cre&shy;<lb/>pacci di alcune caverne. </s></p><p type="main">

<s>&mdash; Io ho avuto a questo proposito, seguita a dire il Cornelio, a far <lb/>osservazione di un fatto singolare, ed &egrave; che quell'aria, la quale soffoca gli <lb/>uomini, &egrave; quella stessa ch'estingue la fiamma. </s>

<s>So ben che l'Hobbes im&shy;<lb/>magin&ograve; un terzo genere di corpi, che non siano n&egrave; aria n&egrave; umore, ma qual&shy;<lb/>che cosa di mezzana natura, e che sebben sieno come l'aria stessa cos&igrave; <lb/>trasparenti, riescon pure in ogni modo nocivi al petto degli animali. </s>

<s>Ma che <lb/>ci &egrave; egli bisogno d'immaginar cose nuove e straordinarie, quando possiamo <lb/>ricorrere alle comuni? </s>

<s>&mdash; (ivi, pag. </s>

<s>287-89). </s></p><p type="main">

<s>Di qui passa il Cornelio a dire che molte cose egli aveva pensate delle <lb/>qualit&agrave; dell'aria, e degli usi di lei nella respirazione, ma che essendosi pro&shy;<lb/>posto di trattarne particolarmente in un suo libro, qu&igrave; nel Proginnasma che <lb/>abbiam sott'occhio <emph type="italics"/>De vita,<emph.end type="italics"/> si contenta solo di farne un breve cenno. </s>

<s>Que&shy;<lb/>sto cenno crediamo che sia il solo rimasto delle speculazioni del Medico co&shy;<lb/>sentino, le quali se fossero veramente venute alla luce esposte in un volume, <lb/>davano nell'Autore anche agli Italiani per tempo il loro Pascal, il loro Boyle <lb/>e il loro Guericke: n&egrave; d'essere il seme della sua scorperta con men solle&shy;<lb/>cito amore coltivato fra'suoi che fra gli stranieri, si sarebbe potuto giusta&shy;<lb/>mente dolere lo spirito superstite del Torricelli. </s></p><p type="main">

<s>Il Nostro, il Filosofo inglese e l'altro di Magdeburgo mirabilmente si <lb/>riscontrano, quasi allo stesso tempo, insieme in assegnare il vero uso del&shy;<lb/>l'aria nella respirazione, argomentandolo dal fatto sperimentale del morir <lb/>gli animali al mancare dell'aria stessa, e dell'estinguersi, in ugual modo e <lb/>per somiglianti cagioni, la fiamma. </s>

<s>&ldquo; Mihi itaque persuasum in primis est, <lb/>scrive il Cornelio, parem esse aeris necessitatem, quum ad animalium vitam, <lb/>tum ad ignem conservandum: ad utrumque vero utilis esse videtur aer ille, <lb/>qui nec valde rarus sit nec valde densus, item neque praeter modum com&shy;<lb/>pressus neque distractus. </s>

<s>Quare si ignis in laterna conclusus ardeat, at e <lb/>foramine, quod in ipsius laternae fundo est, spiritus exugatur, statim flamma <lb/>contrahi ac languescere incipiet, et brevi tandem extinguetur. </s>

<s>Idem prorsus <lb/>continget, si per illud ipsum foramen in laternam aer copiosius inspiretur &rdquo; <lb/>(ibi, pag. </s>

<s>289, 90). </s></p><p type="main">

<s>L'esperienza fatta naturalmente coll'aspirar delle guance, e senz'al-<pb xlink:href="020/01/1302.jpg" pagenum="177"/>tr'uso di Macchina pneumatica, non &egrave; molto precisa, e non son perci&ograve; troppo <lb/>precise nemmen le idee derivate da quella. </s>

<s>Ottone di Guericke, estraendo <lb/>con la pompa da s&egrave; nuovamente macchinata l'aria da un pallone di vetro, <lb/>dentro il quale era accesa una candela, vedeva la fiamma a poco a poco <lb/>impiccolire, infintanto che, ridottasi a una hollicina di color ceruleo a fior <lb/>del lucignolo, non si spengeva. </s>

<s>Di qui ne conclude non poter rendersi altra <lb/>ragione del fatto &ldquo; nisi quod cogitarem ignem ex aere aliquid alimenti ac&shy;<lb/>cipere, ac proinde aerem consumere, et sic propter defectum ulterius vivere <lb/>non posse &rdquo; (Experimenta nova magdeb., Amstelodami 1672, pag. </s>

<s>90). Tolta <lb/>la candela e posto in quella vece nel pallone di vetro un passero, simil&shy;<lb/>mente concluse dai nuovi fatti osservati che, per difetto d'aria, s'estingueva <lb/>intorno al cuore la vita, <emph type="italics"/>veluti spiritus vini flamma.<emph.end type="italics"/></s></p><p type="main">

<s>Veniva cos&igrave; il Guericke a rispondere a un importante quesito, che pro&shy;<lb/>posto dal Cornelio era nonostante da lui lasciato irresoluto: onde avvenga <lb/>cio&egrave; che l'animale non possa lungamente vivere in un vaso chiuso, se l'aria <lb/>di quando in quando non si rinnova. </s>

<s>Esso Guericke dunque aveva sagace&shy;<lb/>mente riconosciuto che la candela, mentre arde, e l'animale, mentre respira, <lb/>prendono qualche cosa dall'aria circostante, che serve ad alimentare la luce <lb/>e la vita, ma rimaneva tuttavia nella incertezza rispetto a un punto della <lb/>questione, il quale era se l'estinguersi e il morire dipendesse perch&egrave; l'aria <lb/>stessa si fosse consumata, o trasformatasi piuttosto in qualche altra crassa <lb/>o terrea sostanza, inabile a fare gli ufficii di prima. </s>

<s>&ldquo; Posterius, poi con&shy;<lb/>clude, credo verum esse, quanquam sit adeo exile, ut nullo modo percipien&shy;<lb/>dum &rdquo; (ibi, pag. </s>

<s>91). </s></p><p type="main">

<s>La medesima questione si par&ograve; pure per prima cosa alla mente del <lb/>Boyle, quando nel digredire dal suo XLI esperimento si dette ad applicare <lb/>i fatti fisici pneumatici osservati alla respirazione degli animali. </s>

<s>Tanto par&shy;<lb/>vegli quel soggetto importante, da trovar qualche cosa di serio nelle stesse <lb/>stramberie del Paracelso, il quale diceva, secondo riferisce lo stesso Boyle, <lb/>&ldquo; quod, uti ventriculus alimenta conquoquit, partemque in usum corporis <lb/>convertit, aliamque partem reiicit; ita pulmo partem aeris consumit, aliam&shy;<lb/>que proscribit. </s>

<s>Adeo ut, iuxta hermeticum hunc philosophum, sic enim secta <lb/>illius eum compellari voluit, supponamus licet aliquid in aere esse vitalis <lb/>eiusdem elixiris, sit verbo venia, quod refrigerandis restaurandisque vita&shy;<lb/>libus nostris spiritibus inserviat, cui usui, cum crassior et ultra compara&shy;<lb/>tionem maior aeris pars incommoda sit, mirum videri non debet &rdquo; (Opera <lb/>omnia, T. I, Venetiis 1697, pag. </s>

<s>109). </s></p><p type="main">

<s>Cos&igrave; intendesi, per questa ermetica dottrina, soggiunge il Boyle, come <lb/>l'animale abbia bisogno che gli sia continuamente rinnovata l'aria, della <lb/>quale ei solamente consuma la parte vitale, rimanendo l'altra quasi come <lb/>feccia o come sedimento. </s></p><p type="main">

<s>Insieme con le dottrine, che secondo i Filosofi reputati di senno ave&shy;<lb/>vano dello strano, si tirava dentro alla questione un fatto, che teneva del <lb/>portentoso, e l'Autore de'Nuovi esperimenti fisici-meccanici lo veniva, in <pb xlink:href="020/01/1303.jpg" pagenum="178"/>mezzo alle alte speculazioni della scienza, a raccontare al visconte di Dun&shy;<lb/>garvan suo nipote, tale quale lo aveva avuto da persona non punto volgare, <lb/>sperando che sarebbe a Sua Signoria riuscito caro saperlo &ldquo; potissimum cum <lb/>idem ab alio scriptore commemoratum haud repererim &rdquo; (ibi, pag. </s>

<s>110). </s></p><p type="main">

<s>Il fatto dunque divulgato per la prima volta dal Boyle, in proposito <lb/>della necessit&agrave; dell'aria e degli usi di lei nella respirazione, &egrave; questo: Cor&shy;<lb/>nelio Drebbellio, divenuto per le invenzioni meccaniche e per le scoperte <lb/>chimiche a'suoi tempi famoso, si diceva che fra le tante sue opere ammi&shy;<lb/>rande avesse costruita una nave sottomarina, della quale fece, presente lo <lb/>stesso re Giacomo, esperienza nel Tamigi con successo stupendo. </s>

<s>Il naviglio <lb/>era fatto vogare dalle robuste braccia di dodici remiganti, da uno de'quali, <lb/>rimasto infino a queste presente anno 1659 unico superstite, riseppe il fatto <lb/>un Matematico di gran nome, <emph type="italics"/>a quo,<emph.end type="italics"/> attesta il Boyle, <emph type="italics"/>ego ipse accepi<emph.end type="italics"/> (ibi, <lb/>pag. </s>

<s>110). </s></p><p type="main">

<s>Chi fosse quel gran Matematico l'Autore non dice, ma il Cavalieri, da <lb/>Bologna, in una sua lettera del primo Agosto 1645, dop'aver dato al Tor&shy;<lb/>ricelli notizia di varie curiosit&agrave; scientifiche, soggiunge: &ldquo; In altro proposito <lb/>dir&ograve; del nostro buon padre Mersenno. </s>

<s>Mi bisogn&ograve; sentire una farraggine di <lb/>cose.... Tra le altre mi maravigliai molto di quel suo navigar sott'acqua, <lb/>del quale ha riempito ogni luogo dov'&egrave; passato &rdquo; (MSS. Gal., T. XLI, c. </s>

<s>224). <lb/>Potrebb'esser perci&ograve; che quel Matematico di gran nome, di cui fa menzione <lb/>il Boyle, fosse lo stesso Mersenno, il quale sentendosi costretto ad essere <lb/>con gl'Inglesi pi&ugrave; sincero, che con i nostri Italiani, avesse anche l&agrave; susci&shy;<lb/>tata la memoria di un ritrovato non suo, ma abbellito dalla sua viva imma&shy;<lb/>ginazione, e commentato dal suo poco giudizio. </s></p><p type="main">

<s>Comunque sia, rimase il Boyle in udir ci&ograve; stupefatto, ed entr&ograve; allora <lb/>in gran curiosit&agrave; di sapere come mai potessero gli uomini star cos&igrave; lunga&shy;<lb/>mente sott'acqua, senza rimanervi affogati. </s>

<s>E perch&egrave; sembra che quel gran <lb/>Matematico non gli avesse intorno a ci&ograve; data la richiesta sodisfazione, si mise <lb/>dietro a interrogare i parenti dello stesso Drebbellio, e specialmente un me&shy;<lb/>dico ingegnoso, che aveva sposata una figliola di lui, dal qual medico gli <lb/>fu risposto &ldquo; putasse Drebbellium non totum aeris corpus at certam illius <lb/>partem efficere ut respirationi inserviat, qua consumpta, crassius quod reli&shy;<lb/>quum est corpus, sive cadaver, sit verbo veniam, aeris vitalem flammam in <lb/>corde residentem fovere non valet &rdquo; (ibi). </s></p><p type="main">

<s>Cos&igrave;, per quanto mi fu possibile intendere, prosegue il Boyle la sua <lb/>narrazione, oltre all'avere inventato il macchinamento del naviglio, trov&ograve; il <lb/>Drebbellio il modo di confezionare un qualche chimico liquore, nell'uso del <lb/>quale principalmente consistesse il segreto di quella sottomarina navigazione. <lb/></s>

<s>&ldquo; Quotiescumque enim puriorem aeris partem consumptam vel nimium re&shy;<lb/>spiratione depravatam, et eorum effluviis qui navigarunt saturatam animad&shy;<lb/>vertit, recluso vase illo liquore completo, derepente turbato aeri talem vi&shy;<lb/>talium partium proportionem restituit, qualis efficere potuit ut respirationi <lb/>aliquamdiu subserviret &rdquo; (ibi). </s></p><pb xlink:href="020/01/1304.jpg" pagenum="179"/><p type="main">

<s>Questa notizia per&ograve; m'accese, soggiunge lo stesso Boyle, nuova ardente <lb/>sete di saperne un'altra, qual cio&egrave; si fosse quel cos&igrave; stupendo liquore, che <lb/>avesse virt&ugrave; di purgare dalle infezioni e di render nuovamenre respirabile <lb/>l'aria corrotta. </s>

<s>Mi fu risposto esser questo un segreto, che il Drebbellio non <lb/>aveva voluto mai rivelare a nessuno: anzi ei non fece vedere. </s>

<s>e ci&ograve; solo <lb/>materialmente, altro che ad uno, quella sostanza ristoratrice, e fu quell'uno <lb/>colui &ldquo; qui me de ipsa rei veritate fecit certiorem &rdquo; (ibi). </s></p><p type="main">

<s>Ma il Digby, comunque poi se ne fosse assicurato, afferm&ograve; che qnella <lb/>misteriosa sostanza, ristoratrice dell'aria gi&agrave; viziata dai respiranti sott'acqua <lb/>nel naviglio drebbelliano, consisteva nel sal nitro, ch'ei rassomiglia nel suo <lb/>trattato <emph type="italics"/>De plantarum vegetatione<emph.end type="italics"/> al magnete, perch&egrave; ha virt&ugrave; di attrarre un <lb/>altro sale simile, <emph type="italics"/>quo aer redditur foecundus<emph.end type="italics"/> (Amstelodami, 1669, pag. </s>

<s>54). <lb/>Questo stesso sale, poi soggiunge l'Autore, &egrave; l'alimento dei polmoni e il <lb/>nutrimento degli spiriti vitali. </s>

<s>&ldquo; Cornelius Drebbellius, contracta magna <lb/>huiusce salis quantitate in angustum quoddam spatium, suos animo defi&shy;<lb/>cientes hospites, in sua angusta domo sub aqua, postquam omne balsamum <lb/>in secluso aere, in quo et ipsi seclusi erant consumpserant; aperiendo quam&shy;<lb/>dam phialam, quae per istum vetustum, depravatum et exhaustum aerem <lb/>novos infundebat spiritus, recreare et rofocillare potuit &rdquo; (ibi, pag. </s>

<s>54, 55). </s></p><p type="main">

<s>Questa per&ograve; del Digby dee in ogni modo essere stata una congettura, <lb/>fondata sulle nozioni che della Chimica si potevano avere a que'tempi, n&egrave; <lb/>il Boyle era uomo da rimanere indietro agli altri. </s>

<s>Ma perch&egrave; sentiva a quelle <lb/>stesse congetture de'commentatori del Drebbellio, e alle opinioni del Para&shy;<lb/>celso, mancare ogni buon fondamento di scienza, ei si protesta di averle <lb/>semplicemente commemorate, senza approvarle, inclinando piuttosto a con&shy;<lb/>sentir con coloro, che dicevano, come dall'altra parte sembrava lo sconfer&shy;<lb/>massero l'esperienze, che l'aria &egrave; necessaria a ventilare e a fomentar nel <lb/>cuore la fiamma vitale. </s>

<s>&ldquo; Quapropter aliquando iis consentire propensus fui, <lb/>quibus visus est aer necessarius ventilandae fovendaeque vitali flammae, <lb/>quam in corde sine intermissione ardentem suspicantur. </s>

<s>Videre est enim <lb/>quod in Machina nostra flamma lampadis, post aeris exuctionem, haud mul&shy;<lb/>tum diutius quam vita animalis perdurabit &rdquo; (Opera et T. cit., pag. </s>

<s>110). </s></p><p type="main">

<s>Cos&igrave; gli assennati consigli rintuzzavano all'ingegno quelli che parevano <lb/>arditi, ed eran pure liberi voli, n&egrave; si avvedeva il Boyle che pi&ugrave; del balsamo <lb/>e dell'elixir della vita, contenuto nell'aria, era strana cosa rassomigliare il <lb/>cuore a una lampada accesa. </s>

<s>Tommaso Willis e Giovanni Mayow, in ci&ograve; pi&ugrave; <lb/>sagaci, riconobbero nelle idee del Paracelso un simbolo del vero, che nella <lb/>storia del Drebbellio prende forma di poemetto. </s>

<s>E bench&egrave; non riuscissero <lb/>a sostituire alle immaginate le cose reali, sanno pur sollevarsi al di sopra <lb/>degli altri, e sono i primi fra gli estranei all'Italia, in cui si veda la chi&shy;<lb/>mica della respirazione balenare da'loro pensieri, come luce che rivela im&shy;<lb/>provviso un nuovo mondo, e poi subito lo nasconde. </s>

<s>Il precipuo fine per <lb/>cui, secondo il Willis, l'aria si accoglie ne'polmoni &ldquo; est ut sanguis veno&shy;<lb/>sus a circuitu redux, chymo recenti dilutus, proindeque crudus et veluti <pb xlink:href="020/01/1305.jpg" pagenum="180"/>semiextinctus, tum perfectius misceatur, et velut subigatur, tum potissimum, <lb/>ut secundum omnes suas partes, ab aere nitroso de novo accendatur &rdquo; (Phar&shy;<lb/>maceutices ration. </s>

<s>P. II, Opera omnia, T. II, Lugduni 1681, pag. </s>

<s>22). E il <lb/>Mayow, ricercando nel suo trattato <emph type="italics"/>De respiratione<emph.end type="italics"/> qual sia quell'elemento <lb/>aereo, che &egrave; cos&igrave; necessario a noi per condurre la vita, &ldquo; verisimile est, egli <lb/>dice, particulas quasdam indolis nitrosalinae easque valde subtiles, agiles, <lb/>summeque fermentativas, ab aere, pulmonum ministerio, secerni, inque cruo&shy;<lb/>ris massam transmitti &rdquo; (In Mangeti Bibliotheca anat., T. I, Genevae 1699, <lb/>pag. </s>

<s>1063). </s></p><p type="main">

<s>Dicemmo il Willis e il Mayow essere stati i primi fra gli stranieri a <lb/>sentir che l'aria dovea avere un'azione chimica sul sangue dei polmoni, <lb/>perch&egrave; in quello stesso tempo in Italia si speculava sottilmente intorno a <lb/>quel medesimo soggetto da due de'pi&ugrave; insigni cultori della scienza, e le loro <lb/>comuni speculazioni son, ne'docili consensi e ne'liberi dissensi, argomento <lb/>importantissimo di storia. </s></p><p type="main">

<s>Verso il 1660 il Borelli, per farsi via dalla vita vegetativa a introdursi <lb/>ne'pi&ugrave; astrusi misteri della vita animale, meditava intorno al modo, che <lb/>tengono nel nutrirsi le piante, e domandava per qual miracolo le materie <lb/>terree, introdotte dall'acqua nelle radici, potessero trasformarsi in tanta lus&shy;<lb/>suria di foglie, in tanta eleganza di fiori, e in tanta dolcezza di frutti. </s>

<s>Il mi&shy;<lb/>racolo offerto dalla Natura, pensava, non &egrave; molto differente da quello cos&igrave; <lb/>spesso provocato dall'arte, quando s'inocula una verbena domestica sul <lb/>tronco di qualche albero agreste; ci&ograve; che non pu&ograve; spiegarsi altrimenti se <lb/>non con dire che i succhi agresti, entrando per i vasi dell'albero domestico, <lb/>prendono ivi altra configurazione e abito nuovo. </s>

<s>Questa trasformazione il <lb/>Borelli l'attribuiva tutta alla virt&ugrave; de'vasi, i quali danno a'succhi la loro <lb/>impronta, ed essi la ricevono in s&egrave;, come cedevole materia che docilmente <lb/>s'adatti alla nuova forma. </s></p><p type="main">

<s>Simili speculazioni erano dal nostro Autore applicate al modo del nu&shy;<lb/>trirsi le piante, per mezzo delle radici, il qual modo ei dice di aver dopo <lb/>lunga meditazione riconosciuto non poter consistere in altro, se non in quelle <lb/>configurazioni, che acquistano le particole nutritizie in passar per gli acco&shy;<lb/>modati orifizii delle radici, &ldquo; unde fluores illi percolati et transpositi in planta <lb/>inducunt configurationem et indolem illius plantae propriam &rdquo; (De motu <lb/>anim. </s>

<s>P. II cit., pag. </s>

<s>253). Riguardava insomma il Borelli le boccuzze aperte <lb/>nelle innumerevoli fibrille radicellari come i fori di un cribro, per i quaii <lb/>passano diverse e determinate particelle fluide; o in altre parole, passano in <lb/>ciascuna radicella quelle parti del succo, che trovano meglio adattato l'ori&shy;<lb/>ficio al loro ingresso (ivi, pag. </s>

<s>371). </s></p><p type="main">

<s>Non vedeva per&ograve; ancora il nostro Fisiologo come si potessero queste <lb/>speculazioni applicare alla nutrizione degli animali, quando il Malpighi gli <lb/>venne a dare avviso della sua nuova scoperta intorno alla testura de'pol&shy;<lb/>moni, la quale tanto parve al Borelli importante, che sollecit&ograve; l'Autore a <lb/>pubblicarla, e per lettera del di 18 Gennaio 1661 tornava di nuovo ad in-<pb xlink:href="020/01/1306.jpg" pagenum="181"/>culcargli si risolvesse di farlo, e di farlo presto &ldquo; perch&egrave; altrimenti l'ander&agrave; <lb/>a bordello, oppure altri se ne accorger&agrave; e la dar&agrave; fuori, perch&egrave; la cosa &egrave; di <lb/>tanta importanza, che merita comparire in pubblico, ancorch&egrave; fosse un mezzo <lb/>foglio &rdquo; (Malpighi, Opera postuma, Londini 1677, pag. </s>

<s>6). Il Malpighi dun&shy;<lb/>que, cos&igrave; calorosamente eccitato, dette mano a scrivere e a pubblicare la <lb/>sua Prima epistola <emph type="italics"/>De pulmonibus,<emph.end type="italics"/> indirizzata allo stesso Borelli. </s></p><p type="main">

<s>Ivi non si sta contento l'Autore a far la semplice parte di Anatomico, <lb/>descrivendo quelle <emph type="italics"/>vescicole,<emph.end type="italics"/> che per unanime consenso furon poi dette <emph type="italics"/>mal&shy;<lb/>pighiane,<emph.end type="italics"/> ma trapassa a far da Fisiologo, speculando sull'uso del Polmoni, <lb/>i quali egli dice essere a questo principalmente fabrefatti dalla Natura, cio&egrave; <lb/><emph type="italics"/>ad sanguinariae molis miscelam<emph.end type="italics"/> (Londini 1687, pag. </s>

<s>136). Per sangue poi, <lb/>soggiunge, io non intendo quell'aggregato di quattro elementi volgarmente <lb/>riconosciuti, &ldquo; sed totam illam corporaturam, quae per venas et arterias con&shy;<lb/>tinuo fluit, quae licet pene infinitis constet particulis, omnes tamen sub du&shy;<lb/>plici parte comprehendi posse videntur ad rudem nostrum sensum quodam&shy;<lb/>modo similari; sub alba scilicet, quae vulgo dicitur serum, et sub rubra &rdquo; <lb/>(ibi, pag. </s>

<s>137). </s></p><p type="main">

<s>I polmoni insomma son per il Malpighi fatti a mantenere, fra il siero <lb/>e la parte rossa del sangue, una conveniente miscela, ci&ograve; ch'essi, com'adat&shy;<lb/>tato strumento, eseguiscono per i moti d'inspirazione e d'espirazione, nei <lb/>quali, empiendosi e votandosi d'aria le vescicole, in quel continuo andare <lb/>e venire contundono il sangue, e avvien qualche cosa di simile a ci&ograve; che <lb/>tutti i giorni si vede, &ldquo; dum farina in massam impingitur; ut enim eam <lb/>exacte misceamus, crebra tundimus manu &rdquo; (ibi, pag. </s>

<s>138). E come mesco&shy;<lb/>landosi la farina, per l'intruso fermento, nello stesso tempo anche si ri&shy;<lb/>scalda; cos&igrave; avviene del sangue, e di qui ha l'origine il suo calore. </s>

<s>&ldquo; Eodem <lb/>tempore ex deducta materia, intercedente fermentatione, sanguineae massae <lb/>instauratio contingit, calor emergit, et maior et maior inducitur particula&shy;<lb/>rum libertas &rdquo; (ibi). Concorre, soggiunge il Malpighi, efficacemente a pro&shy;<lb/>durre una tal fermentazione l'aria, ma non tutta: s&igrave; bene una parte di lei, <lb/>che vien secreta dalle vescicole, e attraverso a'loro pori continuamente ri&shy;<lb/>versata nel sangue. </s></p><p type="main">

<s>Queste idee malpighiane intorno alle funzioni fisiologiche del polmone <lb/>erano state tacitamente approvate dal Borelli, infino dalla prima lettura del <lb/>manoscritto, e bench&egrave; sentisse che non consonavano in tutto con le sue, ri&shy;<lb/>manendo queste tuttavia involte quasi negli inviluppi dell'embrione, non <lb/>aveva nulla di pronto da contrapporre. </s>

<s>Ma la stessa Epistola del Malpighi, <lb/>rimeditata, venne presto a fare gli ufficii di ostetricante. </s>

<s>In quella compli&shy;<lb/>catissima rete di vasi capillari, che ricorrono per il parenchima polmonare, <lb/>vide il Borelli una grandissima somiglianza con le fibrille delle radici degli <lb/>alberi, ed esult&ograve; per gran compiacenza vedendosi allora inaspettatamente <lb/>aperta la via di applicare al sangue quelle sue prime speculazioni intorno <lb/>al succo delle piante; cosa, che lungamente desiderata, non era ancora riu&shy;<lb/>scito a conseguire. </s></p><pb xlink:href="020/01/1307.jpg" pagenum="182"/><p type="main">

<s>Le particelle del sangue venoso, deformate e perturbate dalla miscela <lb/>col chilo e colla linfa, vanno, secondo questa teoria borelliana, a riordinarsi <lb/>e a conformarsi nuovamente coi loro prototipi nelle sottilissime fibrille della <lb/>vena polmonare che si ramificano &ldquo; ad instar extremitatum radieum ar&shy;<lb/>borum. </s>

<s>Ab hisce villosis fistulis suscipiuntur determinati liquores, nempe in <lb/>unaquaque illi qui figurae orificii vasculi aptari et ingredi possunt &rdquo; (De <lb/>motu anim. </s>

<s>P. II cit., pag. </s>

<s>256). Cos&igrave; riordinata ciascuna particola sangui&shy;<lb/>gna, e tutte vivificate dagli spiriti, son riversate nel ventricolo sinistro del <lb/>cuore, d'onde si dispensano a nutrir le varie parti del corpo animale. </s></p><p type="main">

<s>Questi pensieri sovvenuti ingegnosamente al Borelli che, tutto iatromec&shy;<lb/>canico, aborriva dalla chimica della fermentazione; pensieri che poi furono <lb/>espressi e pubblicati nella proposizione CXXIX <emph type="italics"/>De motu anim.,<emph.end type="italics"/> vennero <lb/>proposti in sostituzione de'suoi al Malpighi, il quale rimase maravigliato di <lb/>quel cambiamento. </s>

<s>Si direbbe anzi che ne rimase di pi&ugrave; mortificato, come <lb/>trasparisce da un luogo della sua Autobiografia, in cui, dopo aver detto <lb/>come fosse la Prima epistola <emph type="italics"/>De Pulmonibus<emph.end type="italics"/> in tutto e per tutto approvata <lb/>dal Borelli, &ldquo; qui, soggiunge, mutato consilio, instetit ut, castigatis quibus&shy;<lb/>dam, novum pulmonum usum ab eodem propositum, exponerem, quod al&shy;<lb/>tera Epistola, ut plenissime eidem satisfacerem, libens executus sum &rdquo; (Opera <lb/>posth. </s>

<s>cit., pag. </s>

<s>6). </s></p><p type="main">

<s>Nella seconda Epistola infatti, che il Malpighi diresse al Borelli, <emph type="italics"/>De pul&shy;<lb/>monibus,<emph.end type="italics"/> dop'aver descritto il circolo del sangue, dal Microscopio rivelato <lb/>all'occhio che l'osserva con dolcissima maraviglia attraverso ai vasi traspa&shy;<lb/>renti delle rane, passa a investigare a che fine sia quel perpetuo circolo <lb/>disposto dalla Natura, e non volendo, per fare ossequio al Maestro, contra&shy;<lb/>dire a s&egrave; stesso, approva che un tal uso, oltre a quello della miscela del <lb/>sangue accennato nell'Epistola precedente, possa essere anche l'altro sug&shy;<lb/>geritogli dallo stesso Borelli, a cui rivolge cos&igrave; il discorso: &ldquo; In quem vero <lb/>finem haec omnia fiant ultra ea quae superiori Epistola tetigi de pulmo&shy;<lb/>naria miscela, tu ipse visus es apprime deprehendisse, nec celeberrimo tuo <lb/>hoc inventu mens est fraudanda, quod humanitate tua ad me exaratis lite&shy;<lb/>ris commisisti, quibus subtiliter philosopharis mira in vegetabilibus portenta <lb/>Naturae observando, dum miramur poma ex trunco non suo pendere.... <lb/>Miri huius effectus tua philosophandi methodo secretum aperis: existimare <lb/>enim debemus eatenus massilici mali acidum succum in meri naturam dul&shy;<lb/>cescere, quatenus particulae illius succi, licet feliciter excurrant per exiles <lb/>meatus proprii trunci, non eodem tamen modo possunt continuatos vitis tu&shy;<lb/>bulos subire, hinc suo percitae motu et subsequentium impulsu extra suum <lb/>ordinem divulsae et fractae, necesse est ut ad superinductam meatus figu&shy;<lb/>ram se componant, et novam induant naturam, qua et vitis et iesminum <lb/>producitur. </s>

<s>Similem operationis modum in pulmonibus Natura perficit: redit <lb/>enim ab ambitu corporis viduatus alibilibus particulis turbatus sanguis, cui <lb/>novus e vena subclavia humor additur alteriori naturae actione perficiendus. </s>

<s><lb/>Hic igitur ut in particularum carnis, ossis, nervis etc., disponatur et prae-<pb xlink:href="020/01/1308.jpg" pagenum="183"/>paretur, dum subit pulmonarium vasculorum myriades, velut in diversa mi&shy;<lb/>nima stamina ducitur, et ita sanguineis particulis conciliatur nova figura, <lb/>situs et motus, quibus carnes, ossa et spiritus possint efformari. </s>

<s>Cumulatur <lb/>tui dicti fides a consimili seminalium vasorum structura, ac si animantis <lb/>nutritio quaedam esset eiusdem regeneratio &rdquo; (Opera omnia cit., pag. </s>

<s>143). </s></p><p type="main">

<s>Di queste ossequiosissime approvazioni per&ograve;, e di questo splendido com&shy;<lb/>mento fatto alle sue dottrine, il Borelli non rimase punto sodisfatto. </s>

<s>Voleva <lb/>che il Malpighi si disdicesse di tutto ci&ograve;, che aveva scritto intorno alla mi&shy;<lb/>scela del sangue, e alle fermentazioni indotte in lui dall'aria, secreta dalle <lb/>vescicole polmonari. </s>

<s>Pretendeva insomma che, rinnegasse ogni idea chimica, <lb/>per professare quella schietta teoria meccanica della respirazione, ch'egli in&shy;<lb/>segnava. </s>

<s>Ma perch&egrave; il Malpighi sentiva che a lasciarsi imporre prepotente&shy;<lb/>mente il giogo a quel modo era una vilt&agrave;, che digradava troppo un Filosofo, <lb/>prosegu&igrave; con dignitosa libert&agrave; per la sua via, lungo la quale il Borelli, fie&shy;<lb/>ramente sdegnato, gli si mise dietro le spalle a perseguitarlo. </s></p><p type="main">

<s>Tutto il capitolo VIII della II Parte <emph type="italics"/>De motu anim.<emph.end type="italics"/> &egrave; contro i chimisti <lb/>seguaci specialmente del Willis e del Mayow, i quali &ldquo; proferre non ve&shy;<lb/>rentnr aerem habere nitrosam naturam, quae a caliditate agitata sanguinis <lb/>motum promovet &rdquo; (Editio cit., pag. </s>

<s>221). Ma &egrave; particolarmente rivolto quello <lb/>stesso capitolo a confutar le dottrine accennate nella I Epistola <emph type="italics"/>De Pulmo&shy;<lb/>nibus,<emph.end type="italics"/> a sovvertir le quali s'apparecchian dal Borelli le mine in quelle dieci <lb/>proposizioni precedenti alla CVIII, la quale finalmente esplode in questa sen&shy;<lb/>tenza: &ldquo; Est impossibile ut in pulmonibus partes sanguinis etherogeneae, <lb/>quamtumvis contusae, misceantur exacte inter se &rdquo; (ibi, pag. </s>

<s>207). </s></p><p type="main">

<s>Confutate dunque le dottrine dell'azione chimica dell'aria nitrosa e fer&shy;<lb/>mentativa sul sangue, vuole il Borelli instaurare le sua teoria meccanica <lb/>della respirazione, richiamando prima di tutto l'attenzion de'Fisiologi sopra <lb/>i fatti sperimentati dal Boyle, o meglio dagli Accademici del Cimento, che <lb/>sono ben pi&ugrave; decisivi, dimostrandosi per essi che, al mancare a un tratto <lb/>l'aria nel recipiente del vuoto torricelliano, l'animale ivi dentro rinchiuso <lb/>si vede a un tratto cader moribondo. </s>

<s>Si comprende di qui come l'aria &egrave; la <lb/>causa potissima della vita, per cui ella dee necessariamente penetrare nel <lb/>sangue, ma com'ella ci&ograve; faccia &egrave; dubbio, essendo dimostrato da antiche espe&shy;<lb/>rienze che, insufflata per l'aspera arteria, non penetra nel polmone. </s>

<s>Io so, <lb/>prosegue a dire il Borelli, tacendo al solito il nome del Malpighi, che al&shy;<lb/>cuni hanno detto essere, nelle tuniche de'vasi polmonari e delle vescicole, <lb/>pori simili a quelli della cute, per i quali possa traspirar l'aria insensibil&shy;<lb/>mente, ma &egrave; ci&ograve; contrario all'esperienza, vedendosi ben entrare ed uscire <lb/>attraverso ai pori di una membrana i liquidi, ma no l'aria stessa. </s>

<s>&ldquo; Sicuti <lb/>ergo aer per praedictas membranas porosas non penetrat, sic per poros ve&shy;<lb/>narum non transibit &rdquo; (ibi, pag. </s>

<s>217). </s></p><p type="main">

<s>Ma perch&egrave; in ogni modo &egrave; necessario che l'aria inspirata si mescoli <lb/>col sangue ne'polmoni, il Borelli in proposito ripensa che sempre son le ve&shy;<lb/>scicole malpighiane ripiene di qualche succo acqueo o sieroso, ivi dentro stil-<pb xlink:href="020/01/1309.jpg" pagenum="184"/>lato, il quale si fa menstruo all'aria, e penetrando attraverso ai pori mem&shy;<lb/>branosi, com'&egrave; propriet&agrave; dimostrata de'liquidi, traduce seco l'aria stessa nel <lb/>sangue. </s>

<s>&ldquo; Atque talis aquea serositas conquassata a vento aeris inspirati in <lb/>spumas proculdubio facesset, et hinc aqua illa impraegnatur a particulis <lb/>aeris. </s>

<s>Cumque eadem aqua per poros venarum facile exudare et penetrare <lb/>valeat, fieri non potest quin secum deferat ei inclusas aeris particulas easque <lb/>sanguini immisceat &rdquo; (ibi, pag. </s>

<s>219). </s></p><p type="main">

<s>Come si concilino queste dottrine con quell'altre professate nella pro&shy;<lb/>posizione CXXIX, nella quale, per confutar pi&ugrave; direttamente la teoria chi&shy;<lb/>mica dei fermenti sostenuta dal Malpighi, si dice che nei polmoni &ldquo; nulli <lb/>succi fermentitii repositi sunt, cum vesiculae malpighianae solo aere replean&shy;<lb/>tur &rdquo; lo lasciamo al giudizio di chi sa che il passionato amor de'sistemi fa <lb/>travedere anche i pi&ugrave; grandi ingegni, trapassando piuttosto a dire a quale <lb/>uso credesse il Borelli che fosse l'aria trasportata in circolo per le arterie. </s></p><p type="main">

<s>Quell'uso, come oramai ci aspettiamo di udire dal Nostro, &egrave; puramente <lb/>meccanico, consistente negli effetti delle minime particelle aeree &ldquo; quae sunt <lb/>machinae spirales, quae comprimi a vi externa possunt, et deinceps sponte <lb/>resilire, ad instar arcus &rdquo; (ibi, pag. </s>

<s>225). Introdotte queste macchinette nel <lb/>sangue, e spiegando per le angustie de'vasi il loro elaterio, concepiscono un <lb/>moto oscillatorio &ldquo; ad instar penduli &rdquo; (ibi, pag 228) e cos&igrave; inducono una <lb/>tremola commozione vitale in tutto il corpo. </s>

<s>&ldquo; Hinc forsan spirituum, seu <lb/>succi nervei et musculorum agitatio, saltem ex parte, dependet &rdquo; (ibi). </s></p><p type="main">

<s>Questo era per verit&agrave; un ritornare pi&ugrave; di un secolo indietro a rinnovar <lb/>la dottrina della generazione degli spiriti, insegnata da Realdo Colombo. </s>

<s>Il <lb/>Malpighi, nella tranquillit&agrave; del suo senno, ben comprese le aberrazioni, melle <lb/>quali l'ira e l'amor proprio avevano sospinta quella gran mente, e l'acco&shy;<lb/>ramento che ne prov&ograve; lo espresse in alcune belle pagine della sua Autobio&shy;<lb/>grafia. </s>

<s>Ivi egli prende ad esaminare le dottrine, con tanta animosit&agrave; dal Bo&shy;<lb/>relli contrapposte alle sue, e con esempio, in casi simili raro, dimenticando <lb/>le offese e compatendo alle umane debolezze, con sereno giudizio ne fa no&shy;<lb/>tare i difetti gravissimi, e gl'incredibili errori. </s>

<s>All'ultimo, confermatosi sem&shy;<lb/>pre meglio nel suo pensiero, che cio&egrave; l'aria abbia sul sangue un'azione <lb/>paragonabile a quella che produce i fermenti, cos&igrave; conclude con memora&shy;<lb/>bili parole la maggior probabilit&agrave;, ch'egli crede avere la sua ipotesi chimica <lb/>della respirazione sopra quella meccanica del Borelli: &ldquo; Externum vero et <lb/>turbativum principium ab aere perpetuo separatur, media membranea pul&shy;<lb/>monum substantia, et pertranseunti sanguini ubique miscetur et affunditur. </s>

<s><lb/>Et licet doctissimus Vir admittat minimas particulas spirales aeris sanguinem <lb/>ingredi, probabilius tamen est quid latitans in aere et aquae etiam, summe <lb/>mobile et activum separari, quod fortasse luminis naturam sapit &rdquo; (Opera <lb/>posthuma cit, pag. </s>

<s>16). </s></p><p type="main">

<s>A questa misteriosa sostanza sommamente mobile ed attiva e che il <lb/>sangue separa continuamente dall'aria, il Paracelso dava il nome metafo&shy;<lb/>rico di <emph type="italics"/>elixir della vita.<emph.end type="italics"/> Il Willis e il Mayow, nel linguaggio chimico di <pb xlink:href="020/01/1310.jpg" pagenum="185"/>que'tempi, l'appellarono <emph type="italics"/>aria nitrosa,<emph.end type="italics"/> balbuziendo cos&igrave; una parola, che un <lb/>secolo e mezzo dopo la bene snodata lingua del Lavoisier pronunzi&ograve; colla <lb/>voce di <emph type="italics"/>ossigeno.<emph.end type="italics"/> Allora finalmente fu dimostrata la vera analogia, che passa <lb/>fra la candela che arde e l'animal che respira, e com'avesse ragione il Mal&shy;<lb/>pighi di rassomigliare quel non so che sommamente attivo e vivificatore del <lb/>sangue alla natura medesima della luce. </s>

<s>Ma perch&egrave; ebbe quella dimostra&shy;<lb/>zione a patir cos&igrave; lungo indugio, &egrave; da accennar brevemente quali fossero <lb/>le dottrine seguite specialmente in Italia, dopo il Borelli e il Malpighi e <lb/>prima del Lavoisier, intorno alla respirazione. </s></p><p type="main">

<s>Le divise opinioni de'due insigni Maestri ebbero, com'&egrave; facile a pre&shy;<lb/>vedere, una grande influenza sui discepoli, alcuni de'quali si studiarono in&shy;<lb/>gegnosamente di tirarsi fuori d'ogni controversia, mentre altri o professa&shy;<lb/>rono le schiette teorie meccaniche, o le accoppiarono alle chimiche, quasi <lb/>credessero che da due cause concomitanti ne dovesse riuscire pi&ugrave; pieno e <lb/>pi&ugrave; approvato l'effetto. </s>

<s>Il primo di questi esempii ci &egrave; offerto da Lorenzo <lb/>Bellini, il quale studiando la respirazione dell'uovo, e osservando gli effetti <lb/>dell'aria sopra gli svolgiment&igrave; embrionali del pulcino, applic&ograve; fuori di ogni <lb/>controversia i nuovi fatti osservati alla respirazione polmonare. </s>

<s>Egli non di&shy;<lb/>scute se, intorno al modo d'introdursi l'aria nel sangue, abbia ragione il <lb/>Borelli o il Malpighi, ma &ldquo; quemadmodum certum est aerem folliculi obtu&shy;<lb/>sum ovi verticem occupantis, aut aliquid ab eodem aere separatum derivari, <lb/>ex eodem folliculo, in cavitatem amnii et liquidum eius; ita certum erit, ex <lb/>modo praemissis, aerem e pulmonibus in cavitatem canalium pulmonarium <lb/>et eorum sanguinem derivari &rdquo; (A propos. </s>

<s>VIII <emph type="italics"/>De motu cordis,<emph.end type="italics"/> Digressio <lb/><emph type="italics"/>De ovo,<emph.end type="italics"/> etc., Operum Pars II, Vanetiis 1703, pag. </s>

<s>142). </s></p><p type="main">

<s>N&egrave; degli usi dell'aria occorre pure di questionare; ella fa, dice il Bel&shy;<lb/>lini, sopra i liquidi rimescolati col sangue dei polmoni quel ch'ella fa sopra <lb/>i liquidi stessi, che riempiono l'uovo. </s>

<s>&ldquo; Sed ille illa mutat in liquida pri&shy;<lb/>mae et succedentibus fermentationibus apta, igitur aer pulmonis mutabit <lb/>memorata liquida in illa liquida quae sunt apta continuae fermentationi ani&shy;<lb/>malis, hoc est conservationi eiusdem. </s>

<s>Sed hoc dicitur producere sangui&shy;<lb/>nem, igitur sanguis in pulmonibus per admistionem aeris producitur &rdquo; (ibi, <lb/>pag. </s>

<s>143). </s></p><p type="main">

<s>Esempio di chi si dette fra noi a seguitar le dottrine schiettamente <lb/>meccaniche ce lo porge il Baglivi, il quale pens&ograve; che fosse la respirazione <lb/>a questo principale effetto ordinata &ldquo; ut huius magni follis motibus tota <lb/>fluidorum moles solidorumque compages in vivida veluti vibratione perma&shy;<lb/>neat &rdquo; (Opera omnia, Dissertatio IV <emph type="italics"/>De experimentis circa sanguinem,<emph.end type="italics"/><lb/>Lugduni 1710, pag. </s>

<s>458). Che se in ordine a ci&ograve; sembra il nostro Autore <lb/>inspirarsi al Borelli, in assegnar poi altri usi all'aria inspirata approva opi&shy;<lb/>nioni dal Borelli stesso dimostrate per false. </s>

<s>Dice infatti il Baglivi che un <lb/>altro degli effetti della respirazione &egrave; quello di promovere ne'polmoni e nel <lb/>cuore il corso del sangue, divenuto oramai troppo crasso e torpido per la <lb/>subita miscela colla linfa e col chilo. </s>

<s>&ldquo; Quare ut per ingentem pulmonum <pb xlink:href="020/01/1311.jpg" pagenum="186"/>molem pertransire possit, et ad sinistrum thalamum pervenire, valido forti&shy;<lb/>que impellente, et nunquam cessaturo, indigebat, quod nonnisi aer, vi ela&shy;<lb/>stica gravitateque sua, poterat absolvere &rdquo; (ibi, pag. </s>

<s>457). </s></p><p type="main">

<s>Domenico Guglielmini, nel suo trattato <emph type="italics"/>De sanguinis natura et consti&shy;<lb/>tutione,<emph.end type="italics"/> distendendo le idee pi&ugrave; al largo forse di tutti i Fisiologi suoi con&shy;<lb/>temporanei, invoca l'aiuto delle dottrine meccaniche e delle chimiche a <lb/>rivelargli i segreti misteri della vita, che per lui consistono principalmente <lb/>nel sangue. </s>

<s>&Egrave; una follia, egli dice, la fiamma vitale suggerita all'immagi&shy;<lb/>nazione di molti da certi fatti di fosforescenza, che si osservano talvolta nelle <lb/>carni putrescenti de'pesci, nelle uova delle lucertole, nelle nottiluche, ecc. </s>

<s><lb/>Sorgente unica di calore nel corpo animale &egrave; il sangue, che si riscalda pel <lb/>continuo moto e per le particelle sulfuree, che in s&egrave; contiene. </s>

<s>Di qui facil&shy;<lb/>mente s'intende come sia tanto pi&ugrave; caldo intorno al cuore e ai polmoni <lb/>&ldquo; ubi magis a respiratione et attractis aeris particulis agitatur; ubi celeriore <lb/>a corde recepto motu urgetur &rdquo; (Venetiis 1701, pag. </s>

<s>93). Che maraviglia fa <lb/>dunque che sia sempre il cuore cos&igrave; fervente? </s>

<s>&ldquo; id quod fefellit vitalis flam&shy;<lb/>mae propugnatores qui ab excedenti caliditate in corde necessitatem arden&shy;<lb/>tis in eo fomitis deduxere &rdquo; (ibi, pag. </s>

<s>94). Ma il vero &egrave;, conclude il Gu&shy;<lb/>glielmini, che null'altro fomite &egrave; veramente nel cuore &ldquo; praeter sanguinem <lb/>transeuntem &rdquo; (ibi). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Chi ripensa a quello splendore d'idee, che simile a raggio di sole attra&shy;<lb/>verso a una squarciata nube trasparisce dalle parole del Willis e del Mayow, <lb/>del Malpighi e del Guglielmini, ammmira la sagacia di quegli ingegni, che <lb/>videro cos&igrave; viva la immagine del vero in ci&ograve; che si rappresentava agli occhi <lb/>di tutti gli altri sotto forma di larva mostruosa, e considerando poi quanto <lb/>fosse ancora lontana la scienza dal dare una dimostrazione certa di quelle <lb/>argutissime congetture, ben comprende come quel sottil filo di luce dovesse <lb/>andar facilmente disperso in mezzo alle comuni tenebre dell'errore. </s>

<s>A que&shy;<lb/>sta natural condizione s'aggiungevano, per rintuzzar con pi&ugrave; forza i pro&shy;<lb/>gressi delle idee, gli efficacissimi influssi della Filosofia cartesiana, la quale, <lb/>per non ismentir mai l'indole propria, sostituendo ai fatti naturali le ar&shy;<lb/>guzie dell'ingegno, come nella immaginata effervescenza del sangue rico&shy;<lb/>nobbe la ragione de'moti del cuore, cos&igrave; vi ritrov&ograve; pure i fini e gli usi <lb/>refrigeranti della respirazione. </s></p><p type="main">

<s>Questa cartesiana dottrina dall'altra parte veniva confermata dalla grande <lb/>autorit&agrave; dell'Harvey, il quale, come vedemmo, nelle sue prime Esercitazioni <lb/>intorno alla circolazione, approv&ograve; l'ipotesi del Cesalpino, che disse esser <lb/>l'uso precipuo de'polmoni quello di ventilare e di depurare il sangue. </s>

<s>Poi, <lb/>negli ultimi tempi della sua vita, ai quali si riferiscono quelle esercitazioni <pb xlink:href="020/01/1312.jpg" pagenum="187"/><emph type="italics"/>De partu,<emph.end type="italics"/> che Giorgio Ent pubblic&ograve; in appendice alle altre esercitazioni <emph type="italics"/>De <lb/>generatione animalium,<emph.end type="italics"/> tornato esso Harvey a meditar pi&ugrave; di proposito <lb/>sopra i misteriosi ufficii dell'aria inspirata, parve dubitare di quella sua <lb/>prima opinione. </s>

<s>&ldquo; Verum num refrigerii gratia respiratio instituta sit, an in <lb/>alium finem, alibi plenius ex observationibus nostris disputabimus &rdquo; (Lugduni <lb/>Batav. </s>

<s>1737, pag. </s>

<s>353). </s></p><p type="main">

<s>Quelle osservazioni e quelle disputazioni arveiane <emph type="italics"/>De respiratione<emph.end type="italics"/> an&shy;<lb/>darono sventuratamente disperse, ma intanto qui soggiunge l'Autore un fatto <lb/>singolariss&igrave;mo, ch'ei confessa di non sapere spiegare, e che gli fu prima e <lb/>principale occasione di dubitar se l'aria sia propriamente inspirata per re&shy;<lb/>frigerare gli ardori del cuore. </s>

<s>Il fatto &egrave; cos&igrave; proposto, sotto forma di pro&shy;<lb/>blema, per chiederne ai Fisiologi la soluzione: &ldquo; Qui fit ut foetus in lucem <lb/>editus, ac membranis integris opertus, et etiamnum in aqua sua manens, <lb/>per aliquot horas, citra suffocationis periculum, superstes sit; idem tamen <lb/><emph type="italics"/>secundis<emph.end type="italics"/> exutus, si semel aerem intra pulmones attraxerit, postea ne mo&shy;<lb/>mentum quidem temporis absque eo durare possit sed confestim moria&shy;<lb/>tur? </s>

<s>&rdquo; (ibi). Intanto ch'egli attende la desiderata risposta, l'Harvey si serve <lb/>del fatto stesso per concluder che se l'aria, una volta inspirata, &egrave; cos&igrave; dal <lb/>neonato avidamente richiesta &ldquo; fervor in eo ab aere accenderetur, potius <lb/>quam restingueretur &rdquo; (ibi). </s></p><p type="main">

<s>Lasciata dunque da parte la question dell'uso dell'aria ne'polmoni, pro&shy;<lb/>mossa poi pi&ugrave; utilmente dall'esperienze del Guericke e del Boyle, e dalle <lb/>speculazioni del Borelli e del Malpighi, meglio che dalle esercitazioni del&shy;<lb/>l'Harvey; &egrave; da veder come i Fisiologi si studiassero di risolvere il proposto <lb/>problema. </s>

<s>Ci vien di qua aperto l'adito a una trattazione storica di non <lb/>lieve importanza, perch&egrave; avendo noi fin ora riferito le dottrine, che concer&shy;<lb/>nono gli organi, i modi e gli usi della respirazion negli adulti, ci conduce <lb/>a narrare i progressi della scienza nello studio di quelle funzioni, che in <lb/>particolar maniera s'esercitano nei neonati. </s>

<s>La stretta cognazione inoltre, <lb/>ch'&egrave; fra il cuore e i polmoni, d&agrave; estensione, e aggiunge nuova importanza <lb/>a questa parte di storia, per quel che riguarda i modi della circolazione del <lb/>sangue nel feto, a cui furono deputati dalla Natura organi speciali, che nel&shy;<lb/>l'adulto, divenuti inutili, non lasciano di s&egrave; vestigi. </s>

<s>Alla storia fisiologica <lb/>perci&ograve; delle funzioni precede la storia anatomica delle parti, che ci fa risa&shy;<lb/>lire a Galeno, e ce lo fa salutare, con giusta compiacenza de'galenisti, per <lb/>il primo e pi&ugrave; sagace maestro di anatomia fetale. </s></p><p type="main">

<s>Lasciati da parte altri luoghi parecchi delle varie opere galeniche, dove <lb/>si tratta di questo soggetto, basta per noi trattenerci sul cap. </s>

<s>VI del XV libro <lb/><emph type="italics"/>De usu partium,<emph.end type="italics"/> che s'intitola <emph type="italics"/>De ordine generationis in foetu.<emph.end type="italics"/> Ivi &egrave; tutto <lb/>intento l'Autore in contemplare il magistero ammirabile esercitato dalla Na&shy;<lb/>tura intorno a quel corpicciolo, che vive una vita non sua in grembo all <lb/>madre, e principalmente ammira in tal natural magistero i modi e le vie, <lb/>per le quali il sangue va a somministrar materia conveniente a formarsi il <lb/>polmone. </s>

<s>Il quale, essendo organo cos&igrave; importante alla vita e cos&igrave; delicato, <pb xlink:href="020/01/1313.jpg" pagenum="188"/>riceve non di quel sangue comune, che vien dalla Vena cava, ma di un <lb/>sangue purificato, e perci&ograve; trasmessogli da un'arteria, che ha natura venosa. </s>

<s><lb/>Cos&igrave; essendo a questo stesso vaso commesso un ufficio, che &egrave; proprio delle <lb/>vene, fu necessario rimanesse a fare all'altro l'ufficio delle arterie, ond'ei <lb/>venne messo in diretta comunicazione con l'Arteria magna. </s>

<s>&ldquo; Cum autem <lb/>id was venae officium huic visceri praestaret, necesse fuit alterum vas in <lb/>arteriae usum transmutari, quocirca Natura id quoque in magnam Arteriam <lb/>pertudit. </s>

<s>Verum, cum hic vasa inter se aliquantum distarent, aliud <emph type="italics"/>tertium <lb/>vas esiguum,<emph.end type="italics"/> quod utrumque coniungeret, effecit. </s>

<s>In reliquis vero duobus, <lb/>cum haec quoque mutuo sese coniungerent, velut <emph type="italics"/>foramen quoddam<emph.end type="italics"/> utri&shy;<lb/>que commune fecit. </s>

<s>Tum membranam quamdam in eo, instar operculi <gap/><lb/>machinata, quae ad pulmonis vas facile resupinaretur, quo sanguini a Vena <lb/>cava impetu affluenti cederet quidem, prohiberet autem ne sanguis rursum <lb/>in venam cavam reverteretur &rdquo; (Opera, T. I, Venetiis 1597, fol. </s>

<s>212). </s></p><p type="main">

<s>Venivan cos&igrave; con mirabile chiarezza descritte le particolar&igrave; disposizioni <lb/>de'vasi, e i vasi stessi aggiunti per servire al proprio modo della circolazion <lb/>del sangue nel feto, in cui la vena cava comunica con la vena polmonare, <lb/>per mezzo di un foro, e l'arteria polmonare &egrave; congiunta all'Aorta per mezzo <lb/>di un <emph type="italics"/>piccolo condotto.<emph.end type="italics"/> Nel rinnovamento della scienza anatomica al Beren&shy;<lb/>gario sfuggirono queste galeniche osservazioni fetali, e furono perci&ograve; dimen&shy;<lb/>ticate dal divino Vesalio, a cui il Berengario stesso, che in molte cose gli <lb/>serviva di guida, non le aveva rammemorate. </s>

<s>Sfuggirono altres&igrave;, forse per <lb/>simili ragioni, all'oculatissimo Colombo, che se ne passa in quel trattar che <lb/>egli fa, nel XII libro della sua Anatomia, <emph type="italics"/>De formatione foetus.<emph.end type="italics"/></s></p><p type="main">

<s>Primo a resuscitare, bench&egrave; solamente in parte, quelle antiche spente <lb/>memorie, fu nelle sue Anatomiche osservazioni il Falloppio, il quale mara&shy;<lb/>vigliato, in ritesser ch'egli fa la storia delle arterie, raccogliendo le tante <lb/>fila lasciate indietro, domanda: &ldquo; Qua ratione factum sit quod Anatomici <lb/>fere omnes tam negligenter observaverint partem illam canalis vel arteriae, <lb/>qua iungitur vena arterialis circa basim cordis ipsi Aortae, cum in foetu <lb/>tam aperte pateat, tantusque sit aditus ab Aorta ad venam arterialem &rdquo; <lb/>(Opera omnia, Francofurti 1584, pag. </s>

<s>447). La maraviglia, poi soggiunge il <lb/>Falloppio stesso, tanto pi&ugrave; mi cresce, e tanto pi&ugrave; cresce insieme la ragione <lb/>di rimproverar la negligenza degli anatomici miei predecessori, in quanto <lb/>che quel canale arterioso &ldquo; qua iungitur vena arterialis circa basim cordis <lb/>ipsi Aortae &rdquo; bench&egrave; <emph type="italics"/>paucissimis verbis,<emph.end type="italics"/> pur fu chiaramente descritto da <lb/>Galeno nel cap. </s>

<s>VI del XV libro <emph type="italics"/>De usu partium.<emph.end type="italics"/></s></p><p type="main">

<s>Sent&igrave; il Vesalio che que'rimproveri di negligenza venivano direttamente <lb/>a lui, e per iscolparsene, in quell'Esame ch'egli prese a fare delle Osser&shy;<lb/>vazioni falloppiane, raccont&ograve; come desiderando Francesco Rota di veder, nella <lb/>grande Opera <emph type="italics"/>De humani corporis fabrica,<emph.end type="italics"/> l'anatomia comparata tra il feto <lb/>e l'adulto, di che ivi affatto si tace, per compiacere ai desiderii dell'amico <lb/>e di tutti gli studiosi, si volgesse con gran diligenza a rimeditar sui passi <lb/>di Galeno, per illustrarli. </s>

<s>&ldquo; Adinvento itaque connexu, prosegue a dire il <pb xlink:href="020/01/1314.jpg" pagenum="189"/>Vesalio, mox in foetu venae cavae caudicem, ubi connatam habet dextram <lb/>cordis auriculam, et qua illi transversim subiicitur ea venalis arteriae por&shy;<lb/>tio, quae dextram pulmonis sedem petit, longa sectione secundum rectitu&shy;<lb/>dinem operui. </s>

<s>Hic sese tum nihil manifestius mihi obtulit quam maximum <lb/>venae cavae in venalem arteriam pertinens <emph type="italics"/>foramen,<emph.end type="italics"/> vasorumque elegans <lb/>unio, ex quo specillum in omnem venalis arteriae seriem protrudere erat <lb/>promptissimum. </s>

<s>Ut vero membranea mihi illa observaretur substantia, quam <lb/>instar materiae, qua foramen nunc dictum et <emph type="italics"/>ovata praeditum effigie<emph.end type="italics"/> in <lb/>foetu iam in lucem edito promptius et ocyus obsignaretur; hic subsistere <lb/>prius monui &rdquo; (Venetiis 1664, pag. </s>

<s>91, 92). </s></p><p type="main">

<s>Questo lo fa il Vesalio per dire ch'egli aveva osservato qualche cosa <lb/>di pi&ugrave; del Falloppio, e per ritorcere contro lui stesso l'accusa di negligenza. </s>

<s><lb/>Ma poi soggiunge di aver anch'egli ritrovato il canale arterioso descritto da <lb/>Galeno, e di averlo esaminato come il forame ovale, e con pari artificio. <lb/></s>

<s>&ldquo; Pari artificio venae arterialis caudicem, qua is anteriori magnae Arteriae <lb/>sedi adnascitur, et secundum posteriorem huius sedem dextra parte sua ad <lb/>dextram pulmonis regionem contorquetur, longa etiam sectione patefeci, cau&shy;<lb/>dicisque illius cum magna Arteria unionem et mutuum foramen observavi &rdquo; <lb/>(ibi, pag. </s>

<s>92). </s></p><p type="main">

<s>Quel Francesco Rota, persona dall'altra parte di non gran nominanza, <lb/>si pu&ograve; facilmente sospettar che fosse introdotto dal Vesalio nel suo racconto, <lb/>per non avere a coefessare che, a fargli rivolgere l'attenziono sul testo ga&shy;<lb/>lenico, fosse stata necessaria quella frugata di gomito, che gli veniva a dare <lb/>il Falloppio. </s>

<s>Ma comunque sia, egli fu il primo fra'nuovi anatomici che, fa&shy;<lb/>cendo emenda della sua propria e della negligenza dello stesso Falloppio, <lb/>descrisse e impose il nome di <emph type="italics"/>forame ovale<emph.end type="italics"/> a quella apertura, che mette <lb/>nel cuor del feto in comunicazione la vena cava con la vena polmonare. </s>

<s><lb/>Queste osservazioni fetali occorsero al Vesalio poco dopo la pubblicazione <lb/>delle Osservazioni anatomiche del Falloppio, ma per le vicende altrove da <lb/>noi narrate non comparvero alla luce prima del 1564. </s></p><p type="main">

<s>Frattanto Giulio Cesare Aranzio, medico bolognese, chiamato spesso <lb/>dalle partorienti, &ldquo; et quandoque in huiusmodi occasiones casu incidens, <lb/>perbelle, sensu ipso observare et examinare potui quomodo scilicet quae <lb/>scribimus sese habeant, quod aliis peritissimis in Anatome viris, ut admi&shy;<lb/>rabili Andreae Vesalio, aliisque recentioribus raro contigit &rdquo; (pag. </s>

<s>46), e di <lb/>qui ebbe origine quel trattatello <emph type="italics"/>De humano foetu,<emph.end type="italics"/> da cui si son trascritte <lb/>queste parole, e che vide la prima luce in Bologna in quel medesimo <lb/>anno 1564, in cui il Franceschi in Venezia pubblicava il manoscritto del&shy;<lb/>l'Esame fatto dal Vesalio alle Osservazioni anatomiche del Falloppio. </s></p><p type="main">

<s>Bench&egrave; l'Aranzio si proponga di scriver le cose conforme ai fatti os&shy;<lb/>servati, ei si protesta nonostante difensore acerrimo di Galeno (ivi, pag. </s>

<s>7) <lb/>e perci&ograve;, trattando nell'ultimo capitolo della congiunzione de'vasi del cuore, <lb/>dice di non far altro intorno a ci&ograve; che spiegare, e dar pubblica dimostra&shy;<lb/>zione di quel che si legge nel XV libro <emph type="italics"/>De usu partium,<emph.end type="italics"/> maravigliandosi <pb xlink:href="020/01/1315.jpg" pagenum="190"/>molto che il Falloppio citi questo stesso testo galenico in quel luogo &ldquo; in <lb/>quo de utraque coniunctione pertractat, duo tamen maxima observatione <lb/>digna, ibidem exposita interim praetermittat: iam dictam scilicet Cavae cum <lb/>venali arteria coniunctionem, et enarrata ostiola. </s>

<s>Sed quandoque bonus dor&shy;<lb/>mitat Homerus &rdquo; (ibi, pag. </s>

<s>75). </s></p><p type="main">

<s>L'Aranzio insomma, nell'illustrare il canale arterioso e il forame ovale, <lb/>si riscontra con ci&ograve; che, nello stesso tempo o non molto prima, aveva fatto <lb/>il Vesalio, di cui, s'&egrave; men minuto, &egrave; forse per&ograve; pi&ugrave; preciso. </s>

<s>Ma il Nostro <lb/>sul Brussellese ha il vantaggio di aver notate alcune imperfezioni, in che <lb/>descrivendo incorse Galeno, il quale scrisse, come udimmo, che l'arteria <lb/>polmonare, perch&egrave; molto distante dall'Aorta, voleva essergli congiunta per <lb/>mezzo di un canale, mentr'essendo la Vena cava alla vena polmonare con&shy;<lb/>tigua, potevan facilmente comunicarsi insieme per via di un semplice foro. </s>

<s><lb/>Ma l'Aranzio osserva che le cose stanno tutte al contrario. </s>

<s>&ldquo; Cava enim <lb/>multum abest ab Arteria venali, et sub corde latenter ad eam reptat ca&shy;<lb/>nalis coniungens, et propterea dissecanti minus conspicua quam coniunctio <lb/>altera, quae in superficie est sita. </s>

<s>Aorta vero venae arteriali ita vicina po&shy;<lb/>sita fuit, ut brevissimo ductu ad coniunctionem et continuationem sit opus &rdquo; <lb/>(ibi, pag. </s>

<s>77, 78). </s></p><p type="main">

<s>Si venivano cos&igrave; tutto insieme a correggere dall'Aranzio le imperfette <lb/>osservazioni del Vesalio, a cui parve che l'arteria polmonare e l'Aorta fos&shy;<lb/>sero quasi contigue, per cui si maraviglia molto che Galeno le abbia vedute <lb/>distare per qualche notabile intervallo, a ricongiungere il quale sia stato bi&shy;<lb/>sogno alla Natura di apporvi un terzo vaso distinto. </s>

<s>Per ci&ograve;, dopo aver detto <lb/>che per esaminar meglio le cose avea aperta la vena arteriale <emph type="italics"/>longa sectione,<emph.end type="italics"/><lb/>cos&igrave; il Vesalio stesso soggiunge: &ldquo; Quod cum facerem, videremque in hac <lb/>unione connexioneve nullum insigne medium esse intervallum, quo vasa illa <lb/>ab invicem dehiscunt, miratus fui quamobrem Galenus hic tam dilucide vasis <lb/>privatim meminit, quo vena arterialis in magnam arteriam pertinet, cum <lb/>scilicet nisi mutua quaedam hic consurgat citra manifestum, aut saltem ali&shy;<lb/>quousque eductum vasis canalisve progressum, vasorum arteriae corpore con&shy;<lb/>stantium apertio &rdquo; (Examen cit., pag. </s>

<s>92). L'Aranzio dunque defin&igrave; in que&shy;<lb/>sto proposito che l'arteria polmonare e l'Aorta non si toccano, come parve <lb/>al Vesalio, n&egrave; si ricongiungono per un notabile tratto, come diceva Ga&shy;<lb/>leno, ma per un <emph type="italics"/>brevissimo dutto.<emph.end type="italics"/></s></p><p type="main">

<s>Mentre che dai nuovi Embriologi si pubblicavano queste descrizioni in <lb/>Venezia e in Bologna, un nostro piemontese, Leonardo Botallo, passato in <lb/>Francia ad esercitarvi la medicina pratica, attendeva per suo diletto a qual&shy;<lb/>che cosa di Anatomia. </s>

<s>Prediligeva tra'nuovi Maestri il Colombo, di cui forse <lb/>fu discepolo, e la circolazion polmonare da lui mirabilmente descritta sen&shy;<lb/>tiva esser contrariata da molti Galenisti, i quali asserivano avere il sangue <lb/>passaggio dal destro al sinistro ventricolo del cuore, attraverso ai pori del <lb/>setto medio. </s>

<s>Rimasto cos&igrave; il Botallo in tal penosa incertezza, gli occorse un <lb/>giorno di avere un cuore da sezionare, in cui tenendo dietro al corso della <pb xlink:href="020/01/1316.jpg" pagenum="191"/>vena polmonare, l&agrave; dove ella si insinua addentro nel viscere, osserv&ograve; una <lb/>assai cospicua apertura, che metteva in comunicazione l'orecchietta destra <lb/>con la sinistra. </s>

<s>Ecco, disse allora esultando, trovata finalmente la via vera <lb/>del sangue molto diversa da quella designata da Galeno e dal Colombo: <lb/>ecco a tuttte le arterie scoperta l'origine prima e la radice. </s>

<s>Raccolse que&shy;<lb/>sta, insieme con altre poche osservazioni anatomiche, in un libretto pubbli&shy;<lb/>cato in sedicesimo, dopo i &ldquo; Commentarioli duo, alter de medici, alter de <lb/>aegroti munere &rdquo; stampati in Lione nel 1565. </s></p><p type="main">

<s>Il Van Horne, pubblicando poi in Leyda, nel 1660, tutte le opere del <lb/>Medico astigiano, vi raccolse anche le Osservazioni anatomiche, nella terza <lb/>e ultima delle quali, intitolata <emph type="italics"/>Vena arteriarum nutrix a nullo antea no&shy;<lb/>tata,<emph.end type="italics"/> si legge cos&igrave; la scoperta del passaggio del sangue dalla destra alla si&shy;<lb/>nistra parte del cuore: &ldquo; Diebus iis proximis peractis, cum Galenum atque <lb/>Columbum dissentire viderem de via qua in Cor sanguis qui per arterias <lb/>vagatur, fertur, asserente Galeno hunc in Cor transfundi per parva forami&shy;<lb/>nula cordis, septo insita, Columbo vero per alia ad arteriam venosam quae, <lb/>etsi frustra olim perquisiverim, nuper tamen denuo eidem inquisitioni me <lb/>tradens, cor dividere occepi, ubi paulo supra coronalem, quam stephanoidem <lb/>appellant Graeci, satis conspicatum reperi ductum iuxta auriculam dextram, <lb/>qui statim in sinistram aurem recto tramite fertur, qui ductus vel vena iure <lb/>arteriarum vitaliumque spirituum nutrix dici potest, ob id quod per hanc <lb/>feratur sanguis arterialis in cordis sinistrum ventriculum, et consequenter <lb/>in omnes arterias, non autem per septum vel venosam arteriam, ut Gale&shy;<lb/>nus vel Columbus putaverunt &rdquo; (Leonardi Botalli, Opera omnia, Lugduni <lb/>Batav. </s>

<s>1660, pag. </s>

<s>66-69). </s></p><p type="main">

<s>Il foro osservato dal Botallo &egrave; senza dubbio il forame ovale del feto, <lb/>rimasto per qualche caso singolare aperto nel cuor dell'adulto, ma pur, non <lb/>si trattando qui d'Anatomia fetale, &egrave; notahilissimo che i Francesi, fra'quali <lb/>ebbe grandissima fama il Nostro, incominciassero allora, e durino tuttavia a <lb/>chiamare <emph type="italics"/>Trou de Botal<emph.end type="italics"/> quello stesso forame ovale, commettendo due impro&shy;<lb/>priet&agrave; di linguaggio: una fisiologica, perch&egrave; il Botallo non tratta del feto ma <lb/>dell'adulto, e una storica, perch&egrave; la scoperta del forame ovale era stata fatta <lb/>mille quattrocento anni prima, e l'anno avanti che il Botallo stesso pubbli&shy;<lb/>casse in Lione i suoi <emph type="italics"/>Commentarioli,<emph.end type="italics"/> erano usciti alla pubblica luce in Ve&shy;<lb/>nezia e in Bologna i commenti fatti all'Embriologia galenica dal Vesalio e <lb/>dall'Aranzio. </s></p><p type="main">

<s>Ma come sempre suole avvenire, l'impropriet&agrave; del linguaggio port&ograve; un <lb/>disordine nelle idee, di cui s'ha l'esempio nello stesso Van Horne, il quale <lb/>in una nota al testo rimprovera al Botallo quel che doveva rimproverar piut&shy;<lb/>tosto ai francesi, e a s&egrave;, che l'avevan franteso. </s>

<s>Con pace d'uomo s&igrave; egre&shy;<lb/>gio, leggesi in quella nota, &ldquo; dixerim caecutiisse, dum pro nova observatione <lb/>et peculiaris nobis obtrudit, quam Galenus, abhine plusquam mille quin&shy;<lb/>gentis annis, praedicit &rdquo; (ibi, pag. </s>

<s>67). </s></p><p type="main">

<s>N&egrave; che cecuzzisse il Botallo fa dall'altra parte gran maraviglia, con-<pb xlink:href="020/01/1317.jpg" pagenum="192"/>fessando di avere insieme con lui, e per le medesime ragioni, cecuzzito pa&shy;<lb/>recchi anni dopo il grandissimo Arveo, il quale, dop'aver detto nel cap. </s>

<s>VI <lb/><emph type="italics"/>De motu cordis<emph.end type="italics"/> che il forame ovale riman talvolta per qualche mese aperto <lb/>dopo la nascita, anzi per qualche anno, e per tutto il tempo della vita, in <lb/>alcun caso pi&ugrave; straordinario, &ldquo; quae res imposuit, soggiunge, forsan Botallo <lb/>se novum transitum sanguini de vena cava in sinistrum ventriculum cordis <lb/>invenisse, et fateor me quoque, cum in mure maiori iam adulto hoc reperi, <lb/>tale quid statim existimasse &rdquo; (Editio cit., pag. </s>

<s>46). </s></p><p type="main">

<s>Un altro anche pi&ugrave; notabile esempio del disordine, che portarono nel <lb/>giudizio filosofico i pregiudizi popolari, ce l'offre il Flourens, il quale ingan&shy;<lb/>nato forse dal vederne tutte insieme raccolte e pubblicate le opere nel 1660, <lb/>fa apparire la scoperta del Botallo parecchi anni dopo il Vesalio e l'Aranzio <lb/>non solo, ma e dopo Giovan Batista Carcano, e, congegnate le molle alle <lb/>parti del suo discorso, ne fa con francese arguzia scattare il ridicolo, scri&shy;<lb/>vendo che dopo essere divulgate le nuove osservazioni fetali e i commenti <lb/>fatti all'antico testo galenico da que'tre valentissimi e celebratissimi Ana&shy;<lb/>tomici, &ldquo; Botal s'imagina qu'il venait de faire la plus grande d&eacute;couverte qui <lb/>p&ucirc; &ecirc;tre faite &rdquo; (Histoire de la circul. </s>

<s>du sang, Paris 1854, pag. </s>

<s>49). </s></p><p type="main">

<s>Ma che accecati veramente e illusi fossero, invece del Nostro, i due stra&shy;<lb/>nieri che presero a giudicarlo, senza esaminarne il processo, apparir&agrave; chiaro <lb/>a chi pensa ch'essendo la osservazion del Botallo pubblicata nel 1565 dovea <lb/>necessariamente essere stata fatta qualche tempo avanti, quando non era pos&shy;<lb/>sibile che fossero ancora capitati in Francia l'Esame del Vesalio al Fallop&shy;<lb/>pio o il trattatello embriologico dell'Aranzio, e tanto meno il <emph type="italics"/>De cordis <lb/>vasorum in foetu unione<emph.end type="italics"/> di Giovan Batista Carcano, pubblicato in Pavia <lb/>nel 1574. </s></p><p type="main">

<s>Cosicch&egrave;, quando il Botallo osserv&ograve; nel cuore quel foro che mette in <lb/>comunicazione le due orecchiette, per riscontrar se qualcuno de'pi&ugrave; recenti <lb/>Maestri ne aveva parlato, non c'era da consultar altri che il Berengario, il <lb/>Vesalio nella grande opera anatomica, il Colombo e il Falloppio, i quali tutti <lb/>trovatili tacere intorno a quel punto, aveva dunque diritto il nostro Asti&shy;<lb/>giano di scrivere in fronte alla sua anatomica osservazione: <emph type="italics"/>a nullo antea <lb/>notata.<emph.end type="italics"/> E tanto pi&ugrave; ne aveva diritto in quanto che dallo stesso Galeno non <lb/>era stato notato quel foro altro che nel feto, e senza intenzione di ridurlo <lb/>a dimostrar le vie del sangue nell'adulto, intanto che il Botallo &egrave; il terzo <lb/>degl'Italiani, dopo il Colombo e l'Acquapendente, introdotto in quel dramma <lb/>arveiano, che ebbe per sua finale risoluzione la grande scoperta. </s>

<s>N&egrave; Colui, <lb/>che si merit&ograve; dall'Harvey un tanto onore, &egrave; quel presuntuoso che ci &egrave; di&shy;<lb/>pinto dal Flourens, il quale se ne sarebhe facilmente persuaso se avesse <lb/>lette queste parole con cui si termina dall'Autore l'osservazione anatomica, <lb/>che poteva a que'tempi parere una vera scoperta, della vena nutrice delle <lb/>arterie: &ldquo; Haec obiter dicta sint monitionis gratia, non ut Galenum vel Ve&shy;<lb/>salium, Columbumve vel alios si qui sint, qui probe de rebus anatomicis <lb/>scripserunt, redarguere putemus, nam iis sane nos et tota posteritas pluri-<pb xlink:href="020/01/1318.jpg" pagenum="193"/>mum debemus. </s>

<s>Verum incidit interdum ut qnicquam in quavis arte a mi&shy;<lb/>nus exercitato retegatur, quod ab exercitatissimis non fuerit antea cogni&shy;<lb/>tum &rdquo; (Opera cit., pag. </s>

<s>70). </s></p><p type="main">

<s>Ma perch&egrave; l'origine prima e la radice de'falsi giudizii del Flourens <lb/>intorno al Botallo &egrave; dall'avere ignorato il tempo, in cui il Botallo stesso <lb/>pubblic&ograve; le sue anatomiche Osservazioni, e ci&ograve; forse per essere i <emph type="italics"/>Commen&shy;<lb/>tarioli duo<emph.end type="italics"/> citati, divenuti assai rari, eccone il preciso titolo com'apparve <lb/>la prima volta alla luce: &ldquo; Leonardi Botalli astensis, medici regii, Commen&shy;<lb/>tarioli duo, alter de medici, alter de aegroti munere. </s>

<s>Huic accedit admonitio <lb/>fungi strangulatorii. </s>

<s>Lugduni apud Antonium Gryphium 1565. &rdquo; Nel tergo <lb/>di questa carta &egrave; impressa la nota de'saguenti opuscoli aggiunti &ldquo; eiusdem <lb/>Auctoris et ab eodem recogniti: De chatarro, in cuius fine addita est figura <lb/>monstruosorum renum in cadavere repertorum. </s>

<s>Ostenditur etiam locus, per <lb/>quem fertur sanguis in sinistrum cordis ventriculum, nondum antea cogni&shy;<lb/>tus (che comprende le pag. </s>

<s>180-82). De lue venerea, De vulneribus sclo&shy;<lb/>petorum. </s>

<s>&rdquo; </s></p><p type="main">

<s>Lasciando ora il Botallo, che in virt&ugrave; di un motto pronunziato con ele&shy;<lb/>ganza francese si trov&ograve; intruso, senza merito e senza colpa, nella storia della <lb/>Embriologia, diciamo che a mezzo il secolo XVI, quanto erasi resa dimo&shy;<lb/>strativa l'anatomia galenica del feto, altrettanto misteriosa ne rimaneva la <lb/>fisiologia. </s>

<s>A qual fine, si domandava, fu lasciato aperto quel foro o aggiun&shy;<lb/>tovi quel condotto? </s>

<s>Galeno lasci&ograve; scritto per risposta che, avendo bisogno il <lb/>polmone nel feto solamente di crescere, la Natura gli somministr&ograve; un pu&shy;<lb/>rissimo sangue; &ldquo; cum vero ad motum fuit translatum, carnem levem instar <lb/>alae cuiusdam fecit, ut facile a thorace dilataretur ac comprimeretur. </s>

<s>Ob eam <lb/>igitur causam in foetibus vena cava in arteriam venosam est pertusa. </s>

<s>Cum <lb/>autem id vas venae officium huic visceri praestaret, necesse fuit alterum <lb/>vas in arteriae usum transmutari, quocirca Natura id quoque in magnam <lb/>arteriam protrudit &rdquo; (Opera cit., fol. </s>

<s>212). Questo era quel solo che poteva <lb/>dirne il Maestro: a chi ne avesse voluto saper di pi&ugrave;, rispondeva che, a <lb/>intendere a qual fine sieno state fatte quelle cose, <emph type="italics"/>humani ingenii captum <lb/>superat<emph.end type="italics"/> (ibi). </s></p><p type="main">

<s>L'Aranzio vollesi provare a spiegare un po'meglio i concetti di Galeno, <lb/>ma gl'intric&ograve; pi&ugrave; che mai, com'era da aspettarsi da chi credeva che am&shy;<lb/>bedue i vasi polmonari recassero sangue, l'uno per somministrar le materie <lb/>necessarie a formarsi la carne dei polmoni, l'altro &ldquo; ut eorum caro, ex spi&shy;<lb/>rituum rarefacientium multitudine, exinde magis rara reddatur, et eius san&shy;<lb/>guinis calore vivat, hocque beneficium ei libenti animo Cor per aortam <lb/>affert, eam forte ob causam, quia postea parem gratiam, inspirando et refri&shy;<lb/>gerando, cum infans esset in lucem editus, erant relaturi pulmones &rdquo; (De <lb/>hum. </s>

<s>foetu cit., pag. </s>

<s>76). </s></p><p type="main">

<s>La circolazione del sangue nel feto era per episodio riserbata alla grande <lb/>epopea arveiana, nel cap. </s>

<s>VI della quale si trova descritta. </s>

<s>La vena e l'ar&shy;<lb/>teria polmonare, secondo le nuove rivelazioni, rimangono nel loro proprio <pb xlink:href="020/01/1319.jpg" pagenum="194"/>essere di vena e di arteria anche nell'adulto, n&egrave; si scambiano ufficio, come <lb/>insegnava Galeno, il quale distingueva le due specie di vasi, non principal&shy;<lb/>mente dalla direzione del moto, ma dalla qualit&agrave; del sangue in essi conte&shy;<lb/>nuto. </s>

<s>La vena polmonare induce e l'arteria educe ugualmente nel feto e <lb/>nell'adulto: ci &egrave; la sola differenza che, in questo, i due vasi appartengono <lb/>a un circolo sanguigno proprio e distinto, mentre in quello rientrano nel <lb/>sistema generale della Vena cava, con cui la vena polmonare comunica at&shy;<lb/>traverso al forame ovale, e rientrano nel sistema generale dell'Aorta, a cui <lb/>l'arteria polmonare, per via del canale arterioso, &egrave; ricongiunta. </s>

<s>Il passag&shy;<lb/>gio insomma dal destro nel sinistro ventricolo del cuore, senza l'intermezzo <lb/>de'polmoni, si fa, secondo l'Harvey, in questo modo: &ldquo; Dexter, sanguinem <lb/>ab auricula recipiens, inde per venam arteriosam et progaginem suam, ca&shy;<lb/>nalem arteriosam dictam, in magnam Arteriam propellit. </s>

<s>Similiter sinister, <lb/>eodem tempore, mediante auriculae motu, recipit sanguinem, in illlam si&shy;<lb/>nistram auriculam diductum scilicet per foramen ovale e Vena cava, et ten&shy;<lb/>sione sua et constrictione, per radicem Aortae, in magnam itidem Arteriam <lb/>simul impellit &rdquo; (De motu cordis cit., pag. </s>

<s>46). Nel cuor dell'embrione <lb/>perci&ograve;, come nel cuore degli animali che non hanno polmoni, non giocano <lb/>che un'orecchietta e un ventricolo solo. </s>

<s>Quando poi il feto &egrave; venuto alla <lb/>luce, e comincia a respirare, il forame ovale che si richiude, e il canale ar&shy;<lb/>terioso, che si oblitera, riducono i ricettacoli del sangue a quattro: due inser&shy;<lb/>vienti alla circolazion polmonare, e i due altri al circolo nel giro universale <lb/>dei vasi. </s></p><p type="main">

<s>Era stata fatta da alquanti anni alla scienza fisiologica questa nuova <lb/>rivelazione, quando fu proposto a risolvere il problema arveiano. </s>

<s>Primo a <lb/>entrar nello stadio fu il Boyle, il quale, digredendo da'suoi fisici meccanici <lb/>esperimenti, scrisse che sebbene &ldquo; tam difficili problemati solvendo nos im&shy;<lb/>pares esse fatemur, hoc autem de eo experimentum fecimus &rdquo; (Opera omnia, <lb/>T. I, Venetiis 1697, pag. </s>

<s>111). A una cagna, ch'era per partorire, aperse <lb/>il ventre e n'estrasse quattro cagnolini. </s>

<s>Ne scelse uno che, appena liberato <lb/>dalle membrane involgenti, lo vide aprire la bocca all'aria, muover la lin&shy;<lb/>gua, respirare insomma. </s>

<s>Poco dopo, apertogli il petto e dissecatogli il dia&shy;<lb/>framma, lo vide nonostante seguitare a tentare il respiro, e a dimenare in <lb/>modo maraviglioso la lingua. </s>

<s>Poi svolse gli altri tre cagnolini rimasti &ldquo; in <lb/>quibus dissectis, tantum spiritus vitalis non invenimus, et qui ulli in corde <lb/>eorum motui perceptibili producendo sufficeret, cum tamen alterius catuli <lb/>cor, qui respirationem semel exercuisset, tam diu pulsum continuavit ut <lb/>nos ipsi auriculam pulsare quinque vel sex horas postea observaverimus. </s>

<s>&rdquo; <lb/>E conclude con dire: &ldquo; super hac observatione cum doctoris Harvei pro&shy;<lb/>blemate collata, cogitationes suas exercere aliis relinquo &rdquo; (ibi). </s></p><p type="main">

<s>In ogni modo s'intende che il Boyle riduceva tutta la soluzione del <lb/>problema arveiano ai moti del cuore, ch'eccitato una volta dagli spiriti, ossia <lb/>dall'aria inspirata, prosegue spontaneo a muoversi, n&egrave; riprende il suo primo <lb/>esercizio se per caso gli sia stato interrotto. </s>

<s>La falsit&agrave; di questa soluzione <pb xlink:href="020/01/1320.jpg" pagenum="195"/>per&ograve; veniva, lasciamo stare le tante altre ragioni, dimostrata dai fatti citati <lb/>dallo stesso Harvey contro coloro, i quali dicevano, come par che credesse <lb/>il Boyle, il cuor nell'embrione non muoversi punto, ma rimanersi in per&shy;<lb/>fetto riposo, &ldquo; cum in ovo, cui gallina incubuit, et in embryonibus recenter <lb/>ex utero crectis, autopsia patet cor movere, sicut in adultis &rdquo; (De motu cor&shy;<lb/>dis cit., pag. </s>

<s>45). </s></p><p type="main">

<s>Non fa perci&ograve; maraviglia se lo Swammerdam ripose anche questa del <lb/>Boyle fra le altre nenie. </s>

<s>Incomincia il Fisiologo olandese il suo trattato <emph type="italics"/>De <lb/>respiratione<emph.end type="italics"/> coll'accusar la negligenza di coloro, che non considerarono il <lb/>primo moto de'polmoni nel feto, &ldquo; hoc enim percepto, de ipso qui in adul&shy;<lb/>tis fit motu iudicare erit facillimum. </s>

<s>Sed quis circa foetus respirationem <lb/>praeter naenias nobis obtrusit? </s>

<s>&rdquo; (Lugduni Batav. </s>

<s>1667, pag. </s>

<s>2, 3). E sog&shy;<lb/>giunge che solo l'Arveo propose intorno a ci&ograve; un problema, ch'ei lasci&ograve; <lb/>irresoluto, promettendo di farlo in un trattato da pubblicarsi intorno alla <lb/>respirazione, il qual trattato, perch&egrave; ancora non s'&egrave; veduto, dice lo Swam&shy;<lb/>merdam, ho pensato bene di supplirvi io stesso con questo mio. </s>

<s>Cos&igrave; leg&shy;<lb/>gesi nella prefazione, e nella conclusione dell'opera, tornando l'Autore in&shy;<lb/>dietro sopra ci&ograve; che aveva dimostrato intorno al maraviglioso modo come <lb/>incomincia la respirazione nel feto, &ldquo; in qua explicanda, tutto compiacente <lb/>egli scrive, nos primi glaciem fregimus, cum Autores praeter chimeras nihil <lb/>nobis obtruserint &rdquo; (ibi, pag. </s>

<s>119). </s></p><p type="main">

<s>I giudici imparziali per&ograve; non trovano troppo giuste ragioni a quella <lb/>compiacenza, non avendo fatto altro ivi lo Swammerdam che dimostrare <lb/>come la cavit&agrave; del petto nel feto &egrave; tutta piena di umori, e l'aria che prima <lb/>v'entra, con l'acrimonia de'suoi sali, rimescolatisi col sangue, irrita i nervi <lb/>e i muscoli, che perci&ograve; incominciano a mettere in moto il diaframma e il <lb/>torace. </s>

<s>&ldquo; Hisce bene consideratis, evidenter patebit quomodo motus pectoris <lb/>primo incipiat, atque postmodum, ob musculorum respirationi inserventium <lb/>alternatam continuatamque contractionem, necessario continuetur &rdquo; (ibi, <lb/>pag. </s>

<s>76). Di qui concludesi, secondo il Fisiologo d'Amsterdam, la soluzione <lb/>del problema arveiano, che non differisce da quella data dal Boyle, se non <lb/>che pi&ugrave; ragionevolmente si considera l'aria come prima eccitatrice de'mu&shy;<lb/>scoli del torace, piuttosto che delle fibre del cuore. </s></p><p type="main">

<s>Un altro degli atleti, sceso a esercitare le forze in questo agone, fu il <lb/>nostro Borelli, il quale avendo ammesso per vero che l'aria &ldquo; quae vitae sal <lb/>nuncupari potest &rdquo; sia cos&igrave; necessaria che l'animale &ldquo; ne momentum quidem <lb/>vivere potest absque respiratione &rdquo; (De motu anim., Pars II cit., pag. </s>

<s>232); <lb/>disse che nel feto &egrave; supplito il bisogno dalla respirazion della madre. </s>

<s>Contro <lb/>una tal soluzione per&ograve; veniva un fatto gi&agrave; notato, nel proporre il problema, <lb/>dallo stesso Harvey, il qual fatto &egrave; che &ldquo; in sectione caesarea foetus horis <lb/>complusculis post matris obitum eximitur, vitalis tamen reperitur, et intra <lb/>secundas sepultus, aeris nihil indigus, superest &rdquo; (De partu cit., pag. </s>

<s>353), <lb/>nel qual caso il feto non riman certamente superstite, per essergli stata <lb/>mantenuta la vita, come il Borelli diceva, dalla respirazione materna. </s></p><pb xlink:href="020/01/1321.jpg" pagenum="196"/><p type="main">

<s>A pensar che un Harvey, un Boyle, uno Swammerdam, un Borelli o <lb/>non vi si vollero nemmen provare, atterriti dalle difficolt&agrave;, o provativisi non <lb/>riuscirono a risolvere il problema, convien dire ch'ei fosse davvero d'im&shy;<lb/>possibile risoluzione. </s>

<s>Ma l'impossibilit&agrave;, che non era nella cognizione dei <lb/>fatti, veniva messa agl'ingegni dallo stesso Harvey, il quale insomma pro&shy;<lb/>poneva a dimostrare una cosa falsa. </s>

<s>E il non avvedersi di ci&ograve; l'Harvey stesso, <lb/>e il non avvedersene que'grandi ingegni, &egrave; uno de'pi&ugrave; notabili fatti di que&shy;<lb/>sta Storia. </s></p><p type="main">

<s>Era fra'supposti del problema arveiano che, ammessa la prima aria nel <lb/>petto del neonato, non ne potesse poi far senza, nemmeno un momento, <emph type="italics"/>sed <lb/>confestim moriatur, illico suffocetur.<emph.end type="italics"/> Suppor ci&ograve; era un supporre insieme <lb/>che il forame ovale <emph type="italics"/>confestim<emph.end type="italics"/> si chiuda, ed <emph type="italics"/>illico<emph.end type="italics"/> si obliteri il canale arte&shy;<lb/>rioso. </s>

<s>Ora era questo un supposto contrario alla ragione, all'autorit&agrave; de'mag&shy;<lb/>giori, e all'esperienza, com'&egrave; per persuadercene facilmente il discorso. </s></p><p type="main">

<s>Che fosse contrario alla ragione &egrave; approvato da ognuno, che sa come <lb/>nulla dalla Natura s'operi nell'istante. </s>

<s>Che fosse quel supposto contrario <lb/>all'autorit&agrave; de'maggiori, &egrave; chiaramente dimostrato dai documenti, per primo <lb/>dei quali occorre anche questa volta a citar quello lasciatoci dall'antico Ga&shy;<lb/>leno. </s>

<s>Nel passo da noi sopra citato dal lib. </s>

<s>XV <emph type="italics"/>De usu partium,<emph.end type="italics"/> dop'aver <lb/>descritta la valvola del forame ovale, &ldquo; haec quidem omnia, esclama il con&shy;<lb/>templativo Antore, Naturae opera sunt admiranda. </s>

<s>Superat vero omnem admi&shy;<lb/>rationem praedicti foraminis haud ita multo post conglutinatio. </s>

<s>Etenim, cum <lb/>primum animans in lucem est editum, aut ante unum vel duos dies, in qui&shy;<lb/>busdam vero ante quatuor aut quinque vel plures, membranam quae est ad <lb/>foramen coalescentem reperias nondum tum coaluisse. </s>

<s>Cum autem animal <lb/>perfectum fuerit, aetateque iam floruerit, si locum hunc ad unguem densa&shy;<lb/>tum inspexeris, negabis fuisse aliquod tempus, in quo fuerit pertusus, multo <lb/>autem magis in iis, quae adhuc utero geruntur, aut in nupero genitis mem&shy;<lb/>branam conspicatus ad solam quidem radicem firmatam, reliquum vero to&shy;<lb/>tum corpus in vasorum cavitate pendulum; existimabis fieri non posse ut <lb/>ipsa unquam perfecte coalescat.... Pari modo id vas quod magnam arteriam <lb/>venae, quae fertur ad pulmonem connectit, cum aliae omnes animalis par&shy;<lb/>ticulae augeantur, non modo non augetur, verum etiam tenuius semper ef&shy;<lb/>fici conspicitur, adeo ut, tempore procedente, penitus tabescat atque exice&shy;<lb/>tur &rdquo; (Opera cit., fol. </s>

<s>212). </s></p><p type="main">

<s>Galeno dunque stimava che il forame ovale si richiudesse dopo due o <lb/>tre giorni o pi&ugrave; dalla nascita, e il canale arterioso si obliterasse <emph type="italics"/>tempore <lb/>procedente.<emph.end type="italics"/> Ma il Vesalio, bench&egrave; non assegni nessun tempo determinato, <lb/>par nonostante che ammetta una maggiore prontezza. </s>

<s>Quella membrana, che <lb/>dallo stesso Galeno era stata descritta come una valvola applicata al forame <lb/>ovale, perch&egrave; il sangue sospinto nella vena polmonare non dovesse refluir <lb/>nella Cava; il Vesalio, che rifiutava nelle vene ogni artificio di valvole, la <lb/>credeva materia preparata dalla Natura, per otturar prontamente nel cuore <lb/>del neonato l'apposto forame. </s>

<s>&ldquo; Observatio in nascendis proxime foetibus <pb xlink:href="020/01/1322.jpg" pagenum="197"/>est promptissimam huic operationi orbiculatim adnatam esse illam tenuis&shy;<lb/>simae membranae substantiam, quae superius <emph type="italics"/>promptae<emph.end type="italics"/> post nativitatem <lb/>occlusioni foraminis accommoda censebatur &rdquo; (Examen Falloppii cit., pag. </s>

<s>92). </s></p><p type="main">

<s>Queste osservazioni intorno al tempo impiegato dalla Natura, per tra&shy;<lb/>sformare gli organi della circolazion fetale negli organi della circolazion pol&shy;<lb/>monare, trascurate dall'Harvey, posero il Boyle, lo Swammerdam e il Bo&shy;<lb/>relli nell'impossibilit&agrave; di risolvere il proposto problema. </s>

<s>Ma il Cartesio, in <lb/>raccomandare alla sua scuola queste dottrine, s'espresse con una chiarezza <lb/>e con una precisione maravigliosa. </s>

<s>&ldquo; Experientia enim comportum est, egli <lb/>scrive, infantes, qui dum in utero matris sunt, nequeant respirare, duas <lb/>habere in corde aperturas, quae in adultioribus non reperiuntur. </s>

<s>Et quidem, <lb/>per unam ex his aperturis, sanguinem Venae cavae, una cum arteriae ve&shy;<lb/>nosae sanguine, in sinistrum cordis ventriculum fluere, per alterum vero, <lb/>quae ad instar exigui tubi facta est, partem sanguinis ex dextro ventriculo <lb/>defluentis transire ex vena arteriosa in magnam arteriam, neque pulmonem <lb/>usquam ingredi. </s>

<s>Compertum est etiam hasce duas aperturas in natis infan&shy;<lb/>tibus <emph type="italics"/>ultro paulatim occludi, postquam respirationis usum adepti sunt &rdquo;<emph.end type="italics"/><lb/>(De homine cit., pag. </s>

<s>166). </s></p><p type="main">

<s>Tommaso Cornelio, imbevuto a queste cartesiane dottrine, dal saper che <lb/>il foro ovale si chiude a poco a poco, ne congetturava che dunque, infin&shy;<lb/>tantoch&egrave; non siasi esso foro richiuso affatto, l'infante, bench&egrave; privato d'aria <lb/>non dee morire, circolando nel cuore di lui liberamente il sangue, anche <lb/>senza passare attraverso al polmone. </s>

<s>Una tal congettura s'opponeva diret&shy;<lb/>tamente al supposto dell'Harvey, e scoprendone la falsit&agrave;, spiegava final&shy;<lb/>mente in che modo il problema embriologico, che proponeva ai Fisiologi, <lb/>fosse trovato di cos&igrave; difficile, anzi impossibile risoluzione. </s>

<s>Era perci&ograve; impor&shy;<lb/>tantissima cosa il verificare quella congettura, per mezzo dell'esperienza, e <lb/>il Cornelio la verific&ograve; negli infanti, e l'espresse cos&igrave;, nel 1661, nel suo Pro&shy;<lb/>ginnasma <emph type="italics"/>De vita.<emph.end type="italics"/> &ldquo; Videmus recens natos pueros posse aliquandiu, sine <lb/>vitae valetudinisque incommodo, respiratione privari, quia scilicet in eisdem <lb/>patent viae ductusque, per quos, praecluso pulmonum transitu, sanguis per&shy;<lb/>labitur &rdquo; (Neapoli 1668, pag. </s>

<s>287). </s></p><p type="main">

<s>Di qui, ripensando il nostro Fisiologo calabrese a quel <emph type="italics"/>Cola,<emph.end type="italics"/> famoso <lb/>palombaro, che, dallo star lungamente sott'acqua senza riceverne offesa, ebbe <lb/>il soprannome di <emph type="italics"/>Pesce,<emph.end type="italics"/> spieg&ograve; il portento col dire che doveva il cuor di <lb/>quell'uomo, come di quell'altro sezionato gi&agrave; dal Botallo, aver serbato il <lb/>forame ovale tuttavia aperto. </s>

<s>Pass&ograve; poi da questa considerazione a imma&shy;<lb/>ginare arditamente che si potessero i fanciulli educare alla vita amfibia; <lb/>inconsiderata proposta, che torn&ograve; un mezzo secolo dopo l'Ettmuller a ri&shy;<lb/>mettere in campo, nel suo trattatello <emph type="italics"/>De circulatione sanguinis in foetu.<emph.end type="italics"/></s></p><p type="main">

<s>L'esperienze per&ograve; fatte dal Cornelio sopra gl'infanti, essendo perico&shy;<lb/>lose, si pens&ograve; di farle poi con pi&ugrave; sicurt&agrave; sopra gli animali. </s>

<s>Il Mery speri&shy;<lb/>ment&ograve; che i neonati possono senza offesa rimanere lungamente nel vuoto, e <lb/>il Bohn vide un feto, che aveva aperta la bocca ai primi respiri, rimaner <pb xlink:href="020/01/1323.jpg" pagenum="198"/>per alquante ore sotterrato, senza morire, e senza morire vide pure alcuni <lb/>animali nati di fresco star per ventiquattr'ore intere co'bronchi intasati. </s>

<s><lb/>L'Haller fece una gentile esperienza: prese un cagnolino, che aveva comin&shy;<lb/>ciato a respirare, e osserv&ograve; che visse sommerso per mezz'ora in un'acqua <lb/>tiepida. </s>

<s>&ldquo; Vidi catellum, qui semel respiraverat, et cuius pulmo in aqua na&shy;<lb/>tavit, tamen per dimidiam horam in tepida vixisse. </s>

<s>Vidit Bohonius, et bis <lb/>vidit, fetum, qui respiraverat et vivebat, aliquot horis sub ipsa terra, absque <lb/>aere, vixisse. </s>

<s>Sed etiam, bronchio intercepto, nuper nata animalia vivunt, et <lb/>totis 24 horis supersunt &rdquo; (Elem. </s>

<s>physiol., T. III, Lausannae 1766, pag. </s>

<s>314). </s></p><p type="main">

<s>Ma non solo il forame ovale si ottura negli animali cos&igrave; assoggettati <lb/>alle esperienze, e il canale arterioso si oblitera a poco a poco: lo stesso Haller <lb/>speriment&ograve; che non tutti a un tratto si spiegano nemmeno i polmoni, quasi <lb/>ali, che si addestrino a poco a poco ai liberi voli della vita. </s>

<s>Preso il pol&shy;<lb/>mone di un uccello, che aveva fatte alcune respirazioni, trov&ograve; che non gal&shy;<lb/>leggiava nell'acqua, segno che non tutte ancora si erano ripiene d'aria le <lb/>sue vescichette. </s>

<s>&ldquo; In avibus ostendimus etiam, post plusculas respirationes, <lb/>pulmonem ne natare quidem, non adeo continuo mutari &rdquo; (ibi). </s></p><p type="main">

<s>Ecco dimostrato cos&igrave; dalle esperienze esser falso che il feto, attratta <lb/>l'aria nel primo respiro, <emph type="italics"/>ne momentum quidem temporis absque eo durare <lb/>possit,<emph.end type="italics"/> ed ecco insomma scoperta l'impossibilit&agrave; del problema arveiano, non <lb/>avvertita n&egrave; da chi lo propose, n&egrave; riconosciuta poi da que'grandi ingegni, <lb/>che tanto s'affaticarono per trovarne la soluzione. </s>

<s>Pi&ugrave; fidando nell'autorit&agrave; <lb/>di un uomo, che nell'esperienza dei fatti naturali, non pensarono che la <lb/>vita non si accende improvvisa, n&egrave; improvvisa si estingue, ma come fiac&shy;<lb/>cola, che sorge su su lambendo infino al sommo gli stami, e crepitando <lb/>scintilla, prima di sparire. </s></p><pb xlink:href="020/01/1324.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Della nutrizione<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle varie dottrine professate dai Fisiologi intorno alla digestione, e delle esperienze in proposito <lb/>di Lazzero Spallanzani. </s>

<s>&mdash; II. </s>

<s>Della scoperta delle vie del chilo, per le vene lattee del Mesen&shy;<lb/>terio. </s>

<s>&mdash; III. </s>

<s>Della scoperta del Ricettacolo del chilo, e del Canale toracico. </s>

<s>&mdash; IV. </s>

<s>Della sco&shy;<lb/>perta de'vasi linfatici; dell'esequie al Fegate defunto. </s>

<s>&mdash; V. Dell'opera data particolarmente <lb/>dai nostri Italiani allo studio dei vasi bianchi. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>La storia delle cose passate, intorno all'importantissimo soggetto della <lb/>respirazione, ci dimostra come, dopo lunghi e penosi errori, finalmente i Fi&shy;<lb/>siologi riconoscessero che l'aria inspirata dai polmoni agisce direttamente <lb/>sul sangue. </s>

<s>Si discuteva se fosse quell'azione puramente meccanica o chi&shy;<lb/>mica; non si sapeva decidere se tutta l'aria concorresse insieme a produr <lb/>l'effetto, o una sola parte di lei, nella quale consistesse quella mirabile effi&shy;<lb/>cacia attribuita poi pi&ugrave; tardi all'ossigeno; ma in ogni modo, sul finir del <lb/>secolo XVIII, apparvero agl'ingegni speculativi, sotto le amabili sembianze <lb/>del vero, i pensieri del Willis, del Mayow e del Malpighi, che rivelarono <lb/>com'ha propriamente l'aria un'azione chimica e vitale sul sangue. </s></p><p type="main">

<s>Cos&igrave; fatte dottrine per&ograve; erano il portato di altre dottrine, frutto di lun&shy;<lb/>ghe e laboriose esperienze, per le quali tanto strabocchevolmente s'arricch&igrave;, <lb/>in un secolo, il tesoro delle <expan abbr="scie&ntilde;ze">sciennze</expan> cos&igrave; scarso ereditato dagli <lb/>avi. </s>

<s>Quando <lb/>si credeva che le vene compartissero l'alimento alle membra come le arte&shy;<lb/>rie, e il sangue di queste non si sapeva per altro che per esterne qualit&agrave; <lb/>distinguere dal sangue di quelle, non era possibile riconoscer nello stesso <lb/>sangue il bisogno che aveva di ristorarsi, fuor che per la quantit&agrave;, delle per-<pb xlink:href="020/01/1325.jpg" pagenum="200"/>dite subite in nutrire le parti, ci&ograve; che si diceva effettuarsi dalle vene del <lb/>mesenterio, che suggono avidamente il chilo dagli intestini. </s>

<s>E poich&egrave; la con&shy;<lb/>versione d'esso chilo in sangue si affidava tutta al Fegato, non era possi&shy;<lb/>bile pensare all'aria introdottasi ne'polmoni, alla quale perci&ograve;, come sap&shy;<lb/>piamo, s'attribuivano gli ufficii pi&ugrave; inverosimili e strani. </s></p><p type="main">

<s>La grande, e veramente innovatrice scoperta arveiana, dimostr&ograve; che il <lb/>sangue si dispensa per le arterie alle membra, di dove, assorbito dalle estreme <lb/>diramazioni venose, va a confluire in un vaso solo, che sbocca nel cuore. </s>

<s><lb/>Allora fu facile pensar che il sangue arterioso avesse perduto qualche cosa <lb/>di s&egrave;, piuttosto nella qualit&agrave; che nella quantit&agrave;, per cui a ristorarsene s'af&shy;<lb/>frettasse cos&igrave; di ritornar per le vene. </s>

<s>S'aggiungeva a confermare questo pen&shy;<lb/>siero il perduto ufficio sanguificatore del Fegato, che nonostante si seguit&ograve; <lb/>a fare il ricettacolo del chilo. </s>

<s>Ma quando scopertesi le vene lattee, e dimo&shy;<lb/>stratosi il canale toracico, s'intese che il chilo si riversa immediatamente <lb/>nella Vena cava, per andare a diritto col sangue di lei nel cuore, e allora <lb/>quel pensiero, che ragionava ai Fisiologi aver necessit&agrave; il sangue venoso di <lb/>ristorarsi, per divenir nuovamente atto alla nutrizione, prese forme anche <lb/>pi&ugrave; scolpite. </s>

<s>Il luogo e il modo di quel ristoro non fu poi molto difficile a <lb/>indovinarlo, vedendo che il sangue venoso mescolato col chilo era mandato <lb/>al polmone. </s>

<s>Il luogo dunque, dove il sangue ripiglia vita e si rif&agrave; delle per&shy;<lb/>dite col chilo che ha raccolto per via, &egrave; senza dubbio lo stesso polmone. </s>

<s>&mdash; E <lb/>il modo? </s>

<s>&mdash; Che altro modo pu&ograve; avere il polmone d'operar sul sangue, fuor <lb/>che per via dell'aria, da lui messa in moto con s&igrave; assidua faccenda? </s></p><p type="main">

<s>La teoria della respirazione insomma si vede ben di qui essere una <lb/>conseguenza della scoperta del circolo del sangue, e degli organi ordinati <lb/>alla nutrizione. </s>

<s>Per rendere perci&ograve; compiuta, almeno nelle cose pi&ugrave; sostan&shy;<lb/>ziali, questa prima parte della nostra storia, ci rimane a narrare da chi e <lb/>come furono scoperti e dimostrati quegli organi, e ci&ograve; che, dietro la sicura <lb/>scorta dell'esperienza, giunsero a intendere i Fisiologi di una funzione, che <lb/>&egrave; il primo e principal fondamento posto dalla Natura all'economia animale. </s></p><p type="main">

<s>Principio alla nutrizione, e non ci voleva troppa scienza ad accorger&shy;<lb/>sene, &egrave; il cibo, che per la bocca introdotto nello stomaco si riduce in chimo, <lb/>da cui com'essenza distillasi il chilo. </s>

<s>Questa funzione dello stomaco, nel lin&shy;<lb/>guaggio degli scienziati e dal popolo, s'appella col nome di <emph type="italics"/>digestione,<emph.end type="italics"/> in&shy;<lb/>torno alla quale i filosofi e i medici antichi non trovarono molte difficolt&agrave;, <lb/>rassomigliandola alle cozioni artificiali de'cibi, per far lo stomaco da reci&shy;<lb/>piente, il calore innato da fuoco, e i liquidi animali da acqua di elissazione. </s>

<s><lb/>Cos&igrave; avevano insegnato Ippocrate e Aristotile ne'loro libri, ma Erasistrato <lb/>v'aggiunse l'azion meccanica dell'attrito, che subiscono fra le angustie del <lb/>ventricolo i cibi, ivi dentro continuamente agitati dai muscoli, e quasi pesti. </s></p><p type="main">

<s>Nel rinnovamento della scienza uno de'primi e de'pi&ugrave; autorevoli Mae&shy;<lb/>stri, che si studi&ograve; d'insegnar cose nuove intorno alle funzioni digestive, sol&shy;<lb/>levandole coll'ingegno da quelle bassezze, in cui le avean lasciate gli anti&shy;<lb/>chi, fu il Cartesio, il quale rassomigli&ograve; il decomporsi de'cibi nello stomaco, <pb xlink:href="020/01/1326.jpg" pagenum="201"/>in cui &egrave; sempre qualche umore, al disfarsi della calce viva a contatto del&shy;<lb/>l'acqua, e not&ograve; di pi&ugrave; che alcune delle sostanze alimentari hanno la pro&shy;<lb/>priet&agrave; di decomporsi spontaneamente, e di riscaldarsi, come si vede avvenir <lb/>del fieno, se talvolta &egrave; riposto nelle capanne o &egrave; ammontato nelle biche non <lb/>secco. </s>

<s>A queste cause chimiche aggiunta l'azion meccanica degl'intestini e <lb/>delle loro fibre, che tengono i cibi ingesti continuamente agitati e compressi, <lb/>ben s'intender&agrave;, dice il Cartesio, come si possano i cibi stessi concocere e <lb/>spremersene i necessari succhi nutritizi. </s></p><p type="main">

<s>&ldquo; In primis, in machinae huius stomacho, cibi digeruntur vi liquorum <lb/>quorumdam, qui cum interfluunt ciborum partes separant, agitant et cale&shy;<lb/>faciunt eas, ut communis aqua in calce viva, et aqua fortis in metallis fa&shy;<lb/>cit. </s>

<s>Cui adde quod hi liquores quam celerrime a corde per arterias advecti <lb/>non possint non valde calidi esse. </s>

<s>Imo ipsi cibi eius plerumque naturae sunt, <lb/>ut etiam soli et per se corrumpi et incalescere possint, quemadmodum foe&shy;<lb/>num recens in horreo facit, quando satis siccum non est. </s>

<s>Et quod notan&shy;<lb/>dum, agitatio quam incalescendo accipiunt hae ciborum particulae, iuncta <lb/>cum motu stomachi et iutestinorum quibus continentur, ac cum dispositione <lb/>omnium filamentorum, ex quibus intestina componuntur, in causa est ut, <lb/>quamprimum facta fuerit concoctio, aliqua paulatim descendant versus duc&shy;<lb/>tum illum, quo partes crassiores excerni debent &rdquo; (De homine cit., pag. </s>

<s>4). </s></p><p type="main">

<s>Vedremo quale efficacia avessero cos&igrave; fatte dottrine sulla mente di quei <lb/>Fisiologi, che professarono la Filosofia cartesiana, ma intanto il celebratis&shy;<lb/>simo Harvey richiamava l'attenzione degli studiosi sopra un singolar modo, <lb/>che nel digerire i cibi tengon gli uccelli. </s>

<s>Essi hanno un doppio ventricolo: <lb/>l'<emph type="italics"/>ingluvie,<emph.end type="italics"/> nella quale ritengono i grani interi or ora divorati, gli ammolli&shy;<lb/>scono, gli macerano e gli fanno di li passar nel <emph type="italics"/>ventriglio<emph.end type="italics"/> propriamente detto, <lb/>dove come sotto una macina si riducono in minutissimi frantumi. </s>

<s>&Egrave; per aiu&shy;<lb/>tar l'opera di questo trituramento, prosegue a dire l'Harvey, che quasi tutti <lb/>i pennati ingollano pietruzze aspre e dure, che poi vengono fortemente agi&shy;<lb/>tate e sconvolte da que'due robustissimi muscoli di che il ventriglio stesso <lb/>&egrave; composto. </s>

<s>Che se tali pietruzze s&igrave; riducano per il lunge attrito ad es&shy;<lb/>sere levigate, e tornino perci&ograve; inabili a triturare, que'sagaci animali le vo&shy;<lb/>mitano, per ingollarne altre, che scelgono tentandone prima colla lingua la <lb/>scabrosit&agrave; e la durezza. </s>

<s>Eleggono talvolta a quest'uso anche il ferro, e l'ar&shy;<lb/>gento, ch'io, dice, ho trovato nel ventriglio di alcuni struzzi, d'onde fu cre&shy;<lb/>duto dal volgo, vedendoli cos&igrave; consumati dal forte attrito, che valessero quei <lb/>voraci animali a digerire gli stessi metalli. </s>

<s>&ldquo; Hoc pacto alimenta conficiunt <lb/>et chylificant, posteaque compressione facta, quemadmodum ex herbis aut <lb/>fructibus contusis succum vel pulticulum exprimere solemus, pars mollior <lb/>et liquidior sursum attollitur, eamque in principium intestinorum, quod in <lb/>illis iuxta ingressum gulae, in ventriculi parte superiore collocatur, transfe&shy;<lb/>runt &rdquo; (De generatione anim., Lugduni Batav. </s>

<s>1737, pag. </s>

<s>27). </s></p><p type="main">

<s>Si diceva dianzi che sopra queste curiosit&agrave; naturali fu richiamata l'at&shy;<lb/>tenzione degli studiosi, e a chi ripensa alla grande autorit&agrave;, che s'era oramai <pb xlink:href="020/01/1327.jpg" pagenum="202"/>nella scienza acquistato l'Harvey, non far&agrave; punto maraviglia che, per i non <lb/>curanti e i disprezzatori della Filosofia cartesiana, s'incominciassero da quelle <lb/>arveiane osservazioni gli esercizii sperimentali intorno alla digestione. </s>

<s>Furono <lb/>que'primi esercizii fra noi intrapresi, nel secondo periodo della fiorentina <lb/>Accademia, in Pisa dal Borelli, il quale, dopo aver nella propos. </s>

<s>CLXXXIX <lb/>della II P. <emph type="italics"/>De motu anim.,<emph.end type="italics"/> ripetuto con l'Autore inglese esser l'ufficio dei <lb/>sassolini nel ventriglio degli uccelli quello di contundere i cibi, cos&igrave; prov&shy;<lb/>vidamente supplendo al natural difetto dei denti; &ldquo; Hoc verissimum esse, <lb/>soggiunge, expertus sum Pisis, iussu Sereniss. </s>

<s>M. D. </s>

<s>Ferdinandi secundi: <lb/>globulos enim vitreos, seu vesiculas vacuas, et tubulos plumbeos pariter exca&shy;<lb/>vatos et ligneas pyramidulas, et alia plurima intra gallorum indicorum in&shy;<lb/>gluviem per os immisi, et die sequenti plumbeas massas contusas et ero&shy;<lb/>sas, vitra pulverizata, et sic reliqua ingesta reperi &rdquo; (Editio cit., pag. </s>

<s>395). </s></p><p type="main">

<s>Nel terzo splendido periodo dell'illustre Accademia furono, sotto la di&shy;<lb/>rezione dello stesso Borelli, ripetute simili esperienze sopra le galline e le <lb/>anatre, e si lasci&ograve; fatto di esse questo breve cenno in fine al libro dei <emph type="italics"/>Saggi:<emph.end type="italics"/><lb/>&ldquo; Mirabile &egrave; la forza, con la qual s'opera la digestione delle galline e delle <lb/>anatre, le quali imbeccate con palline di cristallo massicce (il Redi not&ograve; che <lb/>dovea dirsi <emph type="italics"/>vuote,<emph.end type="italics"/> come leggesi a pag. </s>

<s>49 del T. II delle Opere di lui, stam&shy;<lb/>pate a Napoli nel 1741) sparate da noi in capo di'parecchie ore, ed aperti i <lb/>loro ventrigli al sole, parevano foderati d'una tunica rilucente, la qual ve&shy;<lb/>duta col microscopio si conobbe non esser altro che un polverizzamento finis&shy;<lb/>simo ed impalpabile di cristallo. </s>

<s>In alcune, imbeccate parimente con palle <lb/>di cristallo ma vote e forate sottilmente, ci siamo abbattuti a veder delle <lb/>suddette palle altre gi&agrave; peste e macinate, ed altre solamente incominciate a <lb/>fendersi, e ripiene di certa materia bianca, simile al latte rappreso, entra&shy;<lb/>tavi per quel piccolissimo foro, ed abbiamo sottosopra osservato che quelle <lb/>macinano meglio dell'altre, che hanno ne'loro ventrigli maggior copia di <lb/>sassolini inghiottiti. </s>

<s>Quindi con minor maraviglia stritolano e pestano .... <lb/>i noccioli delle olive, i pinocchi durissimi ed i pistacchi fatti loro ingollar <lb/>con la buccia. </s>

<s>Le palle di pistola, in capo di ventiquattr'ore, le abbiamo <lb/>trovate schiacciate notabilmente, e di alcuni quadrelli di stagno voti parte <lb/>ne trovammo graffiati e storti, e parte sfondati da parte a parte &rdquo; (Saggi <lb/>di natur. </s>

<s>esper., Firenze 1841, pag. </s>

<s>174, 75). </s></p><p type="main">

<s>Questi mirabili effetti meccanici al Borelli, che si studiava di ridurre a <lb/>soli effetti meccanici tutte le funzioni della vita animale, arrisero in modo, <lb/>da fargli stabilire quella sua teoria meccanica della digestione, che invalse <lb/>a principio nelle scuole italiane. </s>

<s>Studiata, per impulso avutone dall'Harvey, <lb/>sugli uccelli, egli intendeva applicarla a tutti gli animali a ventricolo mem&shy;<lb/>branoso, ne'quali l'effetto della triturazione, in che principalmente consi&shy;<lb/>stono per lui le funzioni digestive, producesi dalla mola dei denti. </s>

<s>Ne'pesci <lb/>soli, che non han denti n&egrave; ventricolo musculoso, il Borelli s'indusse ad am&shy;<lb/>mettere l'opera di un fermento, eccitato sui cibi ingesti da un succo cor&shy;<lb/>rosivo, secreto da certe ghiandole sparse per le membrane ventricolari. </s>

<s>Di <pb xlink:href="020/01/1328.jpg" pagenum="203"/>questo succo per&ograve;, in cui fu poi dimostrato risiedere principalmente l'effi&shy;<lb/>cacia della digestione, il Borelli stesso non fece nessun conto negli altri ani&shy;<lb/>mali, come pure ei non fece nessun conto di quella materia bianca, simile <lb/>al latte, entrata per i fori delle palline e dei tubi fatti ingollare alle anatre, <lb/>e ai galli indiani; osservazioni importantissime, che rimasero per le carte <lb/>del <emph type="italics"/>Cimento<emph.end type="italics"/> come lucerna spenta, infintanto che, riaccesa dalla mano indu&shy;<lb/>stre dello Spallanzani, non gli serv&igrave; di luminosa guida in quelle sue mara&shy;<lb/>vigliose esperienze, che si riguardarono da tutti come altrettante scoperte. </s></p><p type="main">

<s>Quando il celebre professor di Pavia intraprese le sue esperienze in&shy;<lb/>torno alla digestione, incominciando dal ripetere quelle del Borelli, era nella <lb/>scienza fisiologica sorto primo Maestro Ermanno Boerhaave, di cui quasi <lb/>universalmente si seguivano le dottrine. </s>

<s>Ma quelle dottrine del celebratis&shy;<lb/>simo Medico straniero, intorno alle funzioni digestive, erano prettamente <lb/>italiane, e Tommaso Cornelio, inspiratosi alla filosofia cartesiana, le aveva <lb/>insegnate infino dal 1661 fra noi, dev'ebbe seguaci anche coloro, che per <lb/>amor del vero sentirono nella coscienza il dovere di disertar dalla scuola <lb/>dello stesso Borelli. </s></p><p type="main">

<s>Il Proginnasma VI del nostro Fisiologo calabrese &egrave; tutto dedicato a trat&shy;<lb/>tare di questo importantissimo soggetto, e s'intitola perci&ograve; <emph type="italics"/>De nutricatione.<emph.end type="italics"/><lb/>Incomincia dal dimostrare l'impossibilit&agrave; che sieno i cibi concotti nello sto&shy;<lb/>maco dal calore animale, secondo l'opinion degli antichi, osservando che i <lb/>pennati digeriscono corpi tanto duri, che non si potrebbero disfare a un <lb/>debol fuoco, n&egrave; infusi nell'acqua stessa pi&ugrave; fervente. </s>

<s>Il ricorrere alle qua&shy;<lb/>lit&agrave; occulte, prosegue il Cornelio, &egrave; un non far altro insomma che un con&shy;<lb/>fessare la propria ignoranza. </s>

<s>&ldquo; Quapropter ad similitudinem veri propius ac&shy;<lb/>cedere videtur illorum sententia, qui censent ciborum concoctionem fieri a <lb/>succis quibusdam mordacibus, in animalium ventriculos distillantibus, qui <lb/>instar menstrui, ita chymici eiusmodi liquores appellant, escam comminuant, <lb/>dissolvantque, ut inde particulae ad alendum idoneae extrahi, secernique <lb/>possint &rdquo; (Progynnasmata physica, Neapoli 1688, pag. </s>

<s>211). </s></p><p type="main">

<s>Se non che, cos&igrave; procede l'Autore nel suo discorso, avendo i menstrui <lb/>virt&ugrave; diverse, converrebbe ammettere nel ventricolo la secrezione di tanti <lb/>succhi distinti, quante sono le innumerevoli variet&agrave; dei cibi, ci&ograve; che non c'in&shy;<lb/>duciamo facilmente a pensare, per essere contrario alla semplicit&agrave; degli or&shy;<lb/>dini naturali, ond'&egrave; che, ad esplicare il modo della digestione de'cibi, con&shy;<lb/>viene speculare altre ragioni. </s>

<s>&ldquo; Ego vero, ut quid ipse sentiam exponam, <lb/>arbitror in unam ciborum confectionem plures convenire causas, nempe et <lb/>ipsam escam fermentari debere, et calidorum spirituum, halitumque expira&shy;<lb/>tione foveri, et rursus ventriculi motu pressuque misceri, cogi atque con&shy;<lb/>fundi, ac demum apto humore irrorari atque dilui, ut hac ratione confecta <lb/>per peculiares ductus distribuatur &rdquo; (ibi, pag. </s>

<s>213). </s></p><p type="main">

<s>Passa quindi il Cornelio a spiegare particolarmente ciascuna di queste <lb/>cause concorrenti a produrre la digestione, ma prima si trattiene a descri&shy;<lb/>vere la struttura del ventricolo, notandovi certe cose che da nessuno, egli <pb xlink:href="020/01/1329.jpg" pagenum="204"/>dice, &ldquo; quod sciam, animadversa hactenus fuere. </s>

<s>&rdquo; Queste anatomiche os&shy;<lb/>servazioni concernono la tunica interiore trapunta, come da un ago, da innu&shy;<lb/>merevoli forellini, intorno ai maggiori de'quali stanno alcune ghiandolette <lb/>lenticolari che, leggermente compresse, stillano nel ventricolo un certo umor <lb/>biancheggiante. </s>

<s>A queste osservazioni anatomiche soggiunge poi la descri&shy;<lb/>zione del moto vermicolare degl'intestini, dopo di che ritorna a dire della <lb/>confezione de'cibi. </s></p><p type="main">

<s>La prima funzione del ventricolo &egrave; quella di concuocere l'esca, la quale <lb/>perci&ograve; incomincia a fermentare, essendovi disposta per sua natura. </s>

<s>Concorre <lb/>all'opera il calore animale, co'suoi aliti, l'efficacia de'quali in ammollire i <lb/>cibi si pu&ograve; facilmente argomentare da quelle essenze distillate dai Chimici, <lb/>e che rinchiuse dentro le ampolle rodono il sughero de'loro otturamenti. </s>

<s><lb/>Aperto molte volte lo stomaco agli animali vivi, mentre che i cibi ingesti <lb/>son presi dai fermenti, abbiam sentito, egli dice, sempre esalarne certi va&shy;<lb/>pori tanto acri, da fare zuffa col naso e con gli occhi. </s>

<s>Gustate allora quelle <lb/>sostanze, si trovano di sapore ingrato, come le materie che incominciano a <lb/>putrefarsi, ond'&egrave; che non a torto Empedocle e Plistonico annoverarono la <lb/>stessa putrefazione fra le cause, che concorrono alla confezione de'cibi. </s></p><p type="main">

<s>Si trasformano essi cibi, cos&igrave; conclude il Cornelio le sue dottrine in&shy;<lb/>torno alla digestione, specialmente negli uomini, in una sostanza di color <lb/>bianco, a produrre il qual colore efficacemente concorre quel succo &ldquo; quem <lb/>e vasis a nobis primum notatis intra ventriculum influere praemonuimus &rdquo; <lb/>(ibi, pag. </s>

<s>221). &Egrave; poi la principale utilit&agrave; di un tal succo quella di diluire <lb/>gli alimenti, e di ridurli in parti cos&igrave; minute, che possano facilmente entrare <lb/>per le boccuzze aperte dei vasi. </s></p><p type="main">

<s>Il Fisiologo cosentino avviava cos&igrave;, per altri sentieri diversi da quelli <lb/>designati dalla Scuola fiorentina, le dottrine della digestione, per la qual <lb/>funzione animale diceva non esser sufficiente la meccanica triturazione, ma <lb/>bisognarvi di pi&ugrave; qualche altra cosa, che assottigli i cibi gi&agrave; macinati, e gli <lb/>converta in chilo. </s>

<s>Erano dall'altra parte quelle dottrine dell'Autore de'Pro&shy;<lb/>ginnasmi cos&igrave; confortate di ragioni e di esperimenti, che le predicate ve&shy;<lb/>rit&agrave; del Cornelio prevalsero anche fra noi sulla grande autorit&agrave; del Borelli, <lb/>e degli Accademici del Cimento. </s></p><p type="main">

<s>Primo a darne il coraggioso esempio fu Francesco Redi, il quale avendo <lb/>occasione, in mezzo alle sue <emph type="italics"/>Esperienze intorno a cose naturali,<emph.end type="italics"/> di toccare <lb/>anche delle funzioni digestive, intanto che raccomandava come degno e uti&shy;<lb/>lissimo da leggersi in questo proposito il dottissimo Proginnasma <emph type="italics"/>De nutri&shy;<lb/>catione<emph.end type="italics"/> scritto da Tommaso Cornelio, cos&igrave;, dop'aver riferite l'esperienze dei <lb/>suoi Fiorentini, e aver fatto particolare attenzione a quella materia di color <lb/>bianco entrata nelle palline ingollate dai polli, ne esponeva compendiosa&shy;<lb/>mente, accettandole per verosimili, le dottrine: &ldquo; D'onde possa scaturire que&shy;<lb/>sto cos&igrave; fatto liquor bianco io per me crederei che fosse spremuto da quelle <lb/>infinite papille, le quali son situate in quella parte interna dell'esofago di <lb/>tutti gli uccelli, la quale &egrave; attaccata alla bocca superiore del ventricolo, e <pb xlink:href="020/01/1330.jpg" pagenum="205"/>tanto pi&ugrave; lo crederei, quanto che in altre simili esperienze ho posto mente <lb/>che le palline piene solamente di tal liquore, senz'altra mistura di cibo, le <lb/>ho trovate sempre nella bocca superiore del ventriglio. </s>

<s>Le altre ch'eran piene <lb/>e di cibo e di liquor bianco l'ho trovate nell'interna cavit&agrave; di esso ventri&shy;<lb/>glio. </s>

<s>Se poi a questo liquor bianco se ne mescoli qualcun altro, che gli co&shy;<lb/>munichi l'amarezza, &egrave; facile il congetturarlo, siccome &egrave; facile il rinvenire <lb/>qual sia il suo ufficio. </s>

<s>Io tengo che la digestione ne'ventrigli degli uccelli <lb/>non sia fatta e perfezionata totalmente dalla triturazione, come alcuni hanno <lb/>voluto, ma che dopo di essa ci voglia ancora un mestruo per fermentare, <lb/>dissolvere, assottigliare e convertire il cibo di gi&agrave; macinato in chi&igrave;o &rdquo; (Opere, <lb/>T. II, Napoli 1741, pag. </s>

<s>50, 51). </s></p><p type="main">

<s>I seguaci di quella fiorente Scuola toscana fondata dal Redi, rifiutata ad <lb/>imitazion del Maestro la teoria meccanica degli Accademici del Cimento, si <lb/>volsero a professare intorno alla digestione dottrine pi&ugrave; confacenti a quelle <lb/>introdotte dal Cornelio in Italia, di che pu&ograve; per tutti gli altri servire d'esem&shy;<lb/>pio il Vallisnieri, che nel descrivere l'anatomia dello struzzo, volendo deci&shy;<lb/>dere se sia conforme alla verit&agrave; la comune opinione, ch'ei digerisca il ferro, <lb/>&ldquo; se io ho da parlare colla solita ingenuit&agrave;, ne conclude, io giudico che ve&shy;<lb/>ramente vengano assaliti (i metalli ingesti) dallo stomacale fermento, come <lb/>da un'acqua forte, prodigiosa,.... e vengano cos&igrave; corrosi e ridotti in mi&shy;<lb/>nutissimi e impalpabili tritoli &rdquo; (Opere, T. I, Venezia 1733, pag. </s>

<s>242). </s></p><p type="main">

<s>La persona per&ograve; di Tommaso Cornelio, che fu primo a introdurre cos&igrave; <lb/>fatte nuove dottrine nella scienza della digestione, disparve anche agli occhi <lb/>degli stessi Italiani, quando quel medesimo abito del nostro Cosentino s'ac&shy;<lb/>comod&ograve; al dosso di uno straniero, che abbagliava collo splendore del volto, <lb/>innanzi a cui il mondo chinava riverente le ciglia, come alla presenza di un <lb/>Nume adorato. </s>

<s>Vedemmo come esso Cornelio ammettesse a produr la dige&shy;<lb/>stione pi&ugrave; cause concomitanti, le quali si riducono per lui alla fermentazion <lb/>naturale, e alla spontanea putrefazione de'cibi, che si diluiscono nel chilo <lb/>agitati dal moto vermicolare dei vasi digerenti. </s>

<s>Ermanno Boerhaave propose, <lb/>dopo un mezzo secolo, nelle sue celebri Istituzioni mediche, dove a princi&shy;<lb/>pio tratta <emph type="italics"/>De oeconomia animalis,<emph.end type="italics"/> quelle medesime dottrine italiane, sotto <lb/>queste forme: &ldquo; Cibi et potus deglutiti ventriculo clauso, humido, calidoque <lb/>excepti, diluti, aere commisti, sponte in hoc loco pro diversitate materiae <lb/>fermentescere inciperent vel putrescere: utroque vero modo mire mutari vel <lb/>in acescentem vel in alcalescentem, vel in rancidam, aut in glutinosam de&shy;<lb/>nique massam...... Si consideres ad cibos hos eo loci salivam magna copia <lb/>assidue fluere ex ore et oesophago, ventriculum eos transudante humore di&shy;<lb/>luere perpetuo, reliquias prioris alimenti iis permistas eos agitare, aerem iis <lb/>subactum eos intime movere calorem loci cuncta haec excitare, videbis ef&shy;<lb/>fectus hic praestitos esse: macerare, diluere, in tumorem attollere, attenuare, <lb/>fermentationem inchoare, dissolvere, meatibus et humoribus corporis nostri <lb/>adaptare ingesta &rdquo; (Opera omnia medica, Venetiis 1722, pag. </s>

<s>11). </s></p><p type="main">

<s>Cos&igrave; spiega il Boerhaave il modo come si digeriscono i cibi pi&ugrave; molli <pb xlink:href="020/01/1331.jpg" pagenum="206"/>e pi&ugrave; facili a disfarsi: per la digestion de'pi&ugrave; solidi invoca, com'ausiliare <lb/>delle sopra dette cause, l'azion meccanica de'muscoli adiacenti al ventri&shy;<lb/>colo, non che de'vasi arteriosi ivi con ripetuto continuo moto pulsanti. </s>

<s>&ldquo; Ne&shy;<lb/>que tamen hinc videris quomodo solidiores cibi non admodum mansi, feli&shy;<lb/>citer digerantur in ventriculo..... Ut vero causa haec quaesita inveniatur, <lb/>speculeris fabricam muscularem ventriculi, expendesque quaenam inde actio <lb/>pendeat &rdquo; (ibi, pag. </s>

<s>11, 12). </s></p><p type="main">

<s>Queste del Cornelio assunte nella gloria del Boerhaave erano le dot&shy;<lb/>trine, che universalmente si seguivano intorno alla digestione, quando Laz&shy;<lb/>zero Spallanzani, lasciate addietro le ipotesi e non soggiogato dall'autorit&agrave; <lb/>di un uomo, pose mano alle esperienze, risalendo alle prime dimenticate tra&shy;<lb/>dizioni della scienza italiana. </s>

<s>&ldquo; Nell'anno 1777, egli stesso scrive, io ripeteva <lb/>a'miei uditori le famose sperienze dell'Accademia del Cimento, riguardanti <lb/>la mirabile forza, con la quale le galline e l'anitre macinano in poche ore <lb/>e polverizzano ne'loro ventrigli le palline vote di cristallo. </s>

<s>Trovato avendo <lb/>veracissime tali esperienze, m'invogliai di estenderle ad alcuni altri di que&shy;<lb/>gli uccelli, che a guisa delle galline e dell'anatre diconsi di ventricolo mu&shy;<lb/>scoloso. </s>

<s>Queste furono le prime linee d'un lavoro, al quale allora non avrei <lb/>mai pensato, e che poi &egrave; andato crescendo a proporzione che cresceva in <lb/>me la curiosit&agrave; in un argomento s&igrave; bello e s&igrave; utile, come si &egrave; quello che <lb/>riguarda la grand'opera della digestione &rdquo; (Dissertazioni di Fisica anim., T. I, <lb/>Modena 1780, pag. </s>

<s>1). </s></p><p type="main">

<s>Furono i frutti di un tal lavoro tutti insieme raccolti e in bell'ordine <lb/>esposti al pubblico in sei eloquentissime Dissertazioni. </s>

<s>Nella prima s'illu&shy;<lb/>strano le esperienze degli Accademici fiorentini intorno alla potenza del ven&shy;<lb/>tricolo dei gallinacei, per dimostrare i quali portentosi effetti lo Spallanzani <lb/>operava nel modo che segue: &ldquo; Dentro a tubetti di latta, della lunghezza <lb/>ciascheduno di otto linee e del calibro di quattro, io cacciava varie qualit&agrave; <lb/>di semenze, conficcandone in ciascuna un dato numero proporzionale alla <lb/>maggiore o minore grandezza di esse. </s>

<s>Le due estremit&agrave; de'tubi le lasciava <lb/>aperte, a riserva di essere attraversate da pi&ugrave; filetti di ferro, che taglian&shy;<lb/>dosi in croce venivano a formare una specie d'ingraticolamento, che non im&shy;<lb/>pediva a<gap/> succhi del ventriglio di entrare ne'tubi, e che vietava alle sostanze <lb/>rinchiuse in essi di uscire..... Per dar poi maggiore adito a codesti liquidi, <lb/>oltre al continuare a lasciare aperte le estremit&agrave;, feci fare una moltitudine <lb/>di fori alle pareti de'suddetti tubi, cosicch&egrave; i succhi gastrici vi potessero <lb/>piover dentro da tutte le parti &rdquo; (ivi, pag. </s>

<s>4, 5). </s></p><p type="main">

<s>Fatti ingollare cotesti tubi alle galline nostrali, alle anatre, ai galli d'India <lb/>e a simili altri, ed estrattili dopo parecchie ore, non si pot&egrave; mai accorgere <lb/>che le semenze ivi dentro rinchiuse, bench&egrave; ammorbidite, avessero incomin&shy;<lb/>ciato a disciogliersi. </s>

<s>D'ond'ei ne raccolse per cosa gi&agrave; dimostrata che il tri&shy;<lb/>turamento negli uccelli granivori &ldquo; non pu&ograve; essere che un effetto della ga&shy;<lb/>gliarda pressione e di ripetuti violenti urti delle interne pareti del ventriglio, <lb/>mediante i robustissimi muscoli ond'&egrave; corredato &rdquo; (ivi, pag. </s>

<s>6). </s></p><pb xlink:href="020/01/1332.jpg" pagenum="207"/><p type="main">

<s>Essendo cos&igrave;, penseremo noi, prosegue a dire lo Spallanzani &ldquo; che da <lb/>questa azione dipenda anche la digestione dei cibi dentro al ventricolo, di <lb/>maniera che, in grazia della triturazione, arrivino essi in fine a convertirsi <lb/>in quella pultacea sostanza, che chiamasi <emph type="italics"/>chimo?<emph.end type="italics"/> O pi&ugrave; veramente che que&shy;<lb/>sta sostanza si generi mediante i succhi preparati o raccolti nel ventriglio, <lb/>e che la triturazione aiuti bens&igrave; con lo spezzamento de'cibi, ma non pro&shy;<lb/>duca la digestione? </s>

<s>&rdquo; (ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>Per rispondere efficacemento a cos&igrave; fatta importantissima domanda pens&ograve; <lb/>lo Spallanzani di metter dentro i tubi gi&agrave; descritti alcune sostanze alimen&shy;<lb/>tari, come sarebbe mollica di pane, la quale trov&ograve; che veramente era stata <lb/>consunta, per aver soggiaciuto all'azione del succo gastrico nel ventriglio di <lb/>una gallina. </s>

<s>Ma perch&egrave; con sostanze non solubili l'esperienze sarebbero riu&shy;<lb/>scite pi&ugrave; concludenti, riempi&egrave; i medesimi tubetti con carne di vitella smi&shy;<lb/>nuzzata, ed estrattala dai ventrigli osserv&ograve; che quella carne, dov'era venuta <lb/>a contatto col succo gastrico, avea cangiato di colore, e acquistati tutti i segni <lb/>caratteristici di una vera digestione. </s></p><p type="main">

<s>Cos&igrave; fatte esperienze erano senza dubbio per s&egrave; concludenti, ma perch&egrave; <lb/>riuscissero anche pi&ugrave; decisive venne in mente allo Spallanzani di sperimen&shy;<lb/>tare se il succo gastrico mantenesse quella sua vitale virt&ugrave; di sciogliere i <lb/>cibi, anche fuor de'ventrigli. </s>

<s>L'abbondanza di liquido, che vedeva secer&shy;<lb/>nersi dagli organi digerenti delle galline d'India e dell'oche, gl'incor&ograve; buona <lb/>speranza d'avere a riuscir nell'intento, e perci&ograve; ne riempi&egrave; due piccoli tubi <lb/>di vetro serrati ermeticamente da una parte, e con ceralacca dall'altra, dopo <lb/>aver posto in uno de'pezzettini di carne di castrato, e in quell'altro varii <lb/>grani spezzati di frumento. </s>

<s>Si la carne poi che i grani aveva lasciato ma&shy;<lb/>cerar prima nel gozzo di un gallo d'India, perch&egrave; avessero dalla Natura <lb/>quelle disposizioni, che in cos&igrave; fatti animali precedono sempre alla digestione. <lb/></s>

<s>&ldquo; E siccome il calore del ventriglio, cos&igrave; propriamente scrive lo stesso Spal&shy;<lb/>lanzani, era probabilmente una condizione richiesta allo scioglimento de'cibi, <lb/>cos&igrave; pensai di supplirvi col far provare ai tubi un grado di caldo presso a <lb/>poco consimile, mettendomeli tutti e due sotto le ascelle. </s>

<s>Li lasciai interpo&shy;<lb/>latamente in tal sito tre giorni, indi apertili e visitato prima il tubetto dei <lb/>grani di frumento, la maggior parte di questi non aveva pi&ugrave; che la nuda <lb/>scorza, essendone gi&agrave; uscita la polpa farinosa, che nel fondo del tubetto for&shy;<lb/>mato aveva un sedimento grigio bianchiccio e densetto. </s>

<s>La carne poi del&shy;<lb/>l'altro tubo, senza dare il minimo odor di putredine, era in massima parte <lb/>sciolta ed incorporatasi al succo gastrico, fattosi quindi pi&ugrave; torbido e denso. </s>

<s><lb/>I pochi avanzi di lei perduto avevano il rosso naturale, e si eran fatti tene&shy;<lb/>rissimi. </s>

<s>Rimessi quegli avanzi nel proprio tubetto, che empiuto avea di no&shy;<lb/>vello succo gastrico, e ripetuta la prova sotto l'ascella, dopo un altro giorno, <lb/>quel resto di carne sciolto erasi interamente &rdquo; (ivi, pag. </s>

<s>41). </s></p><p type="main">

<s>Confermatasi cos&igrave; per le digestioni artificiali l'efficacia del succo gastrico <lb/>nelle digestioni naturali de'gallinacei e degli uccelli, che tutti hanno il ven&shy;<lb/>tricolo muscoloso, passa lo Spallanzani a dimostrar che lo stesso avviene <pb xlink:href="020/01/1333.jpg" pagenum="208"/>nelle digestioni degli animali a ventricolo membranoso, come sono le rane, <lb/>le salamandre, le bisce terrestri e le acquatiche, le vipere, i pesci, le pecore, <lb/>i buoi e i cavalli. </s>

<s>Rimaneva ancora a sperimentare sull'uomo. </s>

<s>Vero &egrave; bene <lb/>che avendo anch'egli ventricolo membranoso si potevano dedurre dai fatti <lb/>sperimentati sopra gli altri animali argomenti probabilissimi di analogia: in <lb/>ogni modo per&ograve;, non se ne conseguiva l'assoluta certezza. </s>

<s>Ma fare ingollare <lb/>a un uomo, com'ai galli, tubetti di latta o palline di vetro pareva pericoloso, <lb/>e dall'altra parte si paravano innanzi alla fantasia dell'Autore esempi di corpi <lb/>non digeribili, che inavvedutamente ingollati dai fanciulli avevano in essi ec&shy;<lb/>citato molesti urti di stomaco, e altri funestissimi effetti. </s>

<s>Altri fatti in con&shy;<lb/>trario per&ograve;, quali erano il veder che i noccioli durissimi delle ciriegie, delle <lb/>susine, ecc., ingoiati pure cos&igrave; spesso dagl'ingordi fanciulli erano innocua&shy;<lb/>mente renduti per secesso, gl'infusero coraggio, e vinta ogni repugnanza de&shy;<lb/>liber&ograve; di fare esperienza su s&egrave; medesimo, cos&igrave; almeno per saggio. </s></p><p type="main">

<s>&ldquo; Consisteva questo saggio, scrive esso Spallanzani, nel prender per <lb/>bocca una borsetta di tela, entrovi una porzione di pane masticato, del peso <lb/>di cinquantadue grani. </s>

<s>La prova fu da me fatta di mattino dopo l'esser le&shy;<lb/>vato, trovandomi a stomaco digiuno, e queste furono le circostanze, che ac&shy;<lb/>compagnarono sempre l'altre susseguenti esperienze. </s>

<s>La borsetta stette den&shy;<lb/>tro di me ventitre ore, senza ch'io ne provassi il pi&ugrave; piccolo male, e rimandata <lb/>che fu, trovossi spogliata interamente di pane. </s>

<s>Il refe, che strettamente cu&shy;<lb/>civa insieme i due lembi della borsetta, non si era n&egrave; rotto n&egrave; guasto, e lo <lb/>stesso era di quello, che ne serrava la gola perch&egrave; il pane non uscisse. </s>

<s>Non <lb/>si vide tampoco sdrucitura di sorta nella tela stessa, e per&ograve; era patente che <lb/>tanto nel mio ventricolo quanto negli intestini la piccola borsa non era stata <lb/>niente pregiudicata. </s>

<s>Io non posso esprimere al Lettore la confidenza, in che <lb/>mi pose il buon esito di questa esperienza, per intraprenderne altre. </s>

<s>Non <lb/>indugiai pertanto a ripeterla con due altre borsette della medesima tela con&shy;<lb/>tenenti ciascuna l'istessa dose di pane masticato, variata soltanto la circo&shy;<lb/>stanza che una delle borsette era formata di due invogli di tela, e l'altra di <lb/>tre. </s>

<s>Per le cose dette altrove egli &egrave; facile l'indovinare il motivo di tal va&shy;<lb/>riazione, ch'era quello di vedere se, a norma del crescente numero degl'in&shy;<lb/>vogli, rendevasi pi&ugrave; difficile la digestione del pane. </s>

<s>E questo effettivamente <lb/>successe. </s>

<s>Imperocch&egrave;, uscite essendo dal mio corpo le due piccole borse, <lb/>dopo ore ventisette non ben compiute, il pane, quantunque fosse stato di&shy;<lb/>gerito del tutto nella borsetta dai due invogli, ne rimaneva per&ograve; una pie&shy;<lb/>cola quantit&agrave; in quella dai tre. </s>

<s>Tal quantit&agrave;, quantunque in parte perduto <lb/>avesse del proprio sugo, riteneva per&ograve; la natura di pane &rdquo; (ivi, pag. </s>

<s>194, 95). </s></p><p type="main">

<s>Restava cos&igrave; d'ogni parte ben dimostrato che la digestion&egrave; &egrave; opera uni&shy;<lb/>camente del succo gastrico. </s>

<s>Ma perch&egrave; riuscisse la dimostrazione anco pi&ugrave; <lb/>compiuta, conveniva persuadere i seguaci del Boerhaave non essere in quel <lb/>fatto fisiologico nulla che si possa attribuire ai fermenti o alla putredine. </s>

<s><lb/>Quanto ai fermenti, prima di venire alla prova delle esperienze, osserva lo <lb/>Spallanzani che i cibi ingesti non hanno il tempo sufficiente per passare <pb xlink:href="020/01/1334.jpg" pagenum="209"/>via via da uno in altro di quegli stati necessarii, perch&egrave; possa la materia <lb/>subire le sue complete trasformazioni. </s>

<s>Quanto poi alla putredine dimostr&ograve; <lb/>lo stesso Spallanzani che anzi il succo gastrico &egrave; antisettico, concludendo ci&ograve; <lb/>dall'osservazione di questi fatti: &ldquo; Due piccoli vasi di vetro pieni di succo <lb/>gastrico, l'uno corvino l'altro canino, entrovi carne di vitella e di pecora, <lb/>restarono in tempo d'inverno in una stanza per l'intervallo di trentasette <lb/>giorni, senza che si avesse mai soluzione n&egrave; infracidamento, nonostante che <lb/>dette carni, tenute con acqua in altri due simili vasi, verso il settimo giorno <lb/>cominciassero a puzzare, e nel vigesimo fossero gi&agrave; degenerate in una feten&shy;<lb/>tissima corruttela &rdquo; (ivi, pag. </s>

<s>263). </s></p><p type="main">

<s>Quando vennero queste sei Dissertazioni dell'illustre professor di Pavia <lb/>alla luce, i Fisiologi ne rimasero ammirati, e ci&ograve; che pi&ugrave; importa persuasi <lb/>di quel che ivi si dimostrava coi fatti. </s>

<s>Insorsero &egrave; vero contradittori, e fra <lb/>questi alcuni, come l'Hunter, valorosissimi, ma non fecero altro le discus&shy;<lb/>sioni che confermare le verit&agrave; nuovamente rivelate da quelle, che tutti, ma <lb/>specialmente gli stranieri, predicavano per maravigliose esperienze di Fisica <lb/>animale del nostro Spallanzani. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Verso la fine del secolo XVIII era dunque la Scienza fisiologica, dopo <lb/>tante aberrazioni, giunta a intendere in che modo si facesse la digestione, <lb/>e come il cibo nello stomaco si riducesse in chimo, da cui poi gl'intestini <lb/>ricevessero il chilo. </s>

<s>Che tutto quel sostanzial nutrimento rimanesse in ser&shy;<lb/>vigio de'soli visceri, dentro i quali erasi generato, fu antica opinione di al&shy;<lb/>cuni di grossolano ingegno, ma i pi&ugrave; seguivano gl'insegnamenti di Galeno, <lb/>il quale aveva nel IV libro <emph type="italics"/>De usu partium<emph.end type="italics"/> lasciato scritto: &ldquo; Prius elabo&shy;<lb/>ratum in ventricolo alimentum venae ipsae deferunt ad aliquem concoctio&shy;<lb/>nis locum communem totius animalis, quem Hepar nominamus &rdquo; (Opera, <lb/>T. I, Venetiis 1597, fol. </s>

<s>135). </s></p><p type="main">

<s>Quelle vene son secondo Galeno le meseraiche, le quali come radici d'al&shy;<lb/>bero si partono dagl'intestini, e vanno a riunirsi in un tronco solo, che &egrave; <lb/>quello della <emph type="italics"/>Vena,<emph.end type="italics"/> la quale entra per la <emph type="italics"/>porta<emph.end type="italics"/> del Fegato, a cui fuor che <lb/>per essa non giunge nulla, <emph type="italics"/>quemadmodum in urbes nihil, nisi per portas, <lb/>invehi potest.<emph.end type="italics"/> &ldquo; Colligens vero Natura, ut in arboribus, exiguas illas radi&shy;<lb/>ces in crassiores, ita in animalibus vasa minora in maiora, et ea rursus in <lb/>alia maiora, idque semper agens usque ad Hepar in unam omnia venam <lb/>coegit, quae ad portas sita est &rdquo; (ibi, fol. </s>

<s>141). </s></p><p type="main">

<s>Tali erano le vie da Galeno prescritte al chilo, per giungere al Fegato, <lb/>dove fomentato dal calor naturale del viscere si trasforma in sangue &ldquo; ve&shy;<lb/>luti vinum ipsum in doleo mustum &rdquo; (ibi, fol. </s>

<s>136), e tali, in conformit&agrave; di <lb/>quelle del Maestro, furono le opinioni cecamente seguite in tal proposito dai <pb xlink:href="020/01/1335.jpg" pagenum="210"/>Medici, infintantoch&egrave;, nel risvegliarsi che fece la scienza per opera del Be&shy;<lb/>rengario, revocatesi quelle galeniche dottrine ad esame, non incominciarono <lb/>i dubbii a sottentrare alla fede. </s>

<s>Com'&egrave; possibile, si domandava, che le vene <lb/>meseraiche portino il chilo, se si vedono sempre rosseggiare di sangue, o <lb/>come si pu&ograve; credere che lo succhino dagl'intestini, se non si vedono entrare <lb/>nel loro interno con le bocche aperte? </s></p><p type="main">

<s>Il dubbio era ragionevole; nessuno per&ograve; lo sapeva risolvere, intanto che <lb/>Giovanni Fernelio trovatosi, come si dice, alle strette, usc&igrave; a dire che in ogni <lb/>modo al senso doveva in questo caso prevaler la ragione. </s>

<s>Il cap. </s>

<s>II del <lb/>VI libro della sua Fisiologia, pubblicata la prima volta in Parigi nel 1538, <lb/>s'intitola cos&igrave;: &ldquo; Ut e ventriculo per intestina et venas meseraicas in iecur <lb/>fiat alimenti distributio. </s>

<s>&rdquo; Ricerca ivi il Fernelio quali possano essere i vasi <lb/>proprii deputati dalla Natura a suggere il chilo, e pensa per prima cosa non <lb/>poter essere le arterie, che vanno, e s'inseriscono negl'intestini, le quali, se <lb/>pur possono suggere qualche poco di umore, &ldquo; id omnino perexiguum esse <lb/>debet, quod crassior illic succus existat, sintque arteriae spiritui halitiuque <lb/>trahendo accommodatae &rdquo; (Johannis Fernelii Universa medicina, Lugduni 1602, <lb/>pag. </s>

<s>155, 56). </s></p><p type="main">

<s>Non possono esser dunque i vasi chiliferi, cos&igrave;, prosegue il Fernelio <lb/>stesso a ragionare, altro che le vene del mesenterio: e bench&egrave; elle non sem&shy;<lb/>brino far quest'ufficio a giudizio del senso, nonostante la ragione ci persuade <lb/>non poter aversi dagl'intestini al Fegato altra via diversa, n&egrave; che sia meglio <lb/>accomodata di quella. </s>

<s>&ldquo; Qui unum sensum aestimatorem iudicemque adhi&shy;<lb/>buerit, mesenterii venas ventriculi et intestinorum nutricationi, non autem <lb/>succorum distributioni, destinatas esse contendet, quod omnes semper rubro, <lb/>nunquam albo succo, confertae videntur, quodque in ventriculi et intestino&shy;<lb/>rum substantiam se figant, neque ad interiorem capacitatem apertae sint. </s>

<s><lb/>Verumtamen, quoniam aliae nusquam viae ex intestinis in iecur directae <lb/>feruntur, per quas alimentum influat; ratio, magis quam sensus, convincit <lb/>eas etiam ad distributionem accommodari &rdquo; (ibi, pag. </s>

<s>156). </s></p><p type="main">

<s>Intanto che il senso durava ancora, ne'seguaci del Fernelio, a conten&shy;<lb/>dere coll'intelletto, il Colombo usciva fuori ad annunziare in questo propo&shy;<lb/>sito una sua nuova scoperta; non &egrave; vero che le vene meseraiche, negligen&shy;<lb/>temente fin qui osservate, non penetrino nella cavit&agrave; intestinale; elle anzi <lb/>vanno ad aprirvi dentro le loro bocche, alle quali l'industriosa Natura ap&shy;<lb/>pose alcune ingegnose valvole, perch&egrave; assorbito il chilo non dovesse ritor&shy;<lb/>narsene indietro. </s>

<s>Nel VI libro <emph type="italics"/>De re anatomica,<emph.end type="italics"/> dop'aver descritto il quinto, <lb/>il sesto e il settimo ramo della Vena porta, cos&igrave; il Colombo stesso prosegue: <lb/>&ldquo; Ex quibus tres illi, quos ad intestina ferri diximus, cum in mesenterium <lb/>pervenere, in meseraicas dictas venas innumeras, ac pene infinitas, scindun&shy;<lb/>tur, quae intestina, non modo amplectuntur, sed etiam ad internam usque <lb/>cavitatem perforant, quo loco Natura sagax extremae unicuique harum mem&shy;<lb/>branam apposuit, qualem in vesicae cavitate extremis ureteris apposuit, quae <lb/>lotio ad vesicam descendenti aditum praebent, prohibentque ne ad superiora <pb xlink:href="020/01/1336.jpg" pagenum="211"/>amplius revertatur. </s>

<s>Idem in extremitate harum mesaraicarum, quas innume&shy;<lb/>ras diximus, effecit Natura: quod a nemine, quod sciam, adhuc animadver&shy;<lb/>sum est. </s>

<s>Licet omnes uno ore dicant factas fuisse meseraicas ut chylum ab <lb/>intestinis exugerent, in eo tamen parum diligentes fuere quod finem earum <lb/>persequi neglexerint, ut magnam Naturae industriam facile perspicerent, <lb/>quanta scilicet arte effecerit ut hae venae chylum facile suscipere possent, <lb/>ne autem egrediatur, membranulae illae prohibent &rdquo; (Venetiis 1559, pag. </s>

<s>165). </s></p><p type="main">

<s>N&egrave; il Colombo per&ograve; n&egrave; i suoi contemporanei riconobbero la maggiore <lb/>importanza di quella scoperta, anzi non par che la riconoscesse nemmeno <lb/>lo stesso Asellio, il quale intese, o volle intendere, che Realdo avesse de&shy;<lb/>scritte le meseraiche volgate, per argomento di che adduceva la disposizion <lb/>delle valvole, diversa nelle meseraiche stesse comunemente conosciute, e nelle <lb/>lattee, da s&egrave; nuovamente scoperte. </s>

<s>Diceva insomma l'Asellio che le valvole <lb/>del Colombo s'aprono dal di fuori al di dentro, in che son dissomiglianti <lb/>dalle nuove scoperte, le quali si aprono invece dal di dentro al di fuori. <lb/></s>

<s>&ldquo; Hac tamen inter utrasque constituta dissimilitudine et differentia, ut illae <lb/>Columbi foris intro ferantur, nostrae contra intus foris spectent &rdquo; (De lacti&shy;<lb/>bus, Mediolani 1627, pag. </s>

<s>39). </s></p><p type="main">

<s>Ma s'&egrave; veramente tale la disposizion delle valvole, secondo il Colombo, <lb/>com'avrebbero potuto servire a far entrar dentro ai vasi deferenti il chilo, <lb/>e a proibire a lui <emph type="italics"/>ne egrediatur?<emph.end type="italics"/> L'Asellio dunque frantese, e fu causa del <lb/>suo inganno l'aver sentito rassomigliare le valvole, apposte alle estremit&agrave; <lb/>delle meseraiche, alla valvola applicata all'estremit&agrave; dell'uretere, la quale <lb/>veramente s'apre dal di fuori al di dentro, affinch&egrave; non ringorghi il liquido, <lb/>che ha da scendere nella vescica. </s></p><p type="main">

<s>Il desiderio forse, che aveva esso Asellio di non esser costretto a rico&shy;<lb/>noscere nessun prossimo premostratore della sua scoperta, non gli lasci&ograve; li&shy;<lb/>bert&agrave; di pensare che il Colombo rassomigliava i due organi nell'ufficio, ma <lb/>no nel proprio e particolar modo di esercitarlo. </s>

<s>Se poi si ripensi che il si&shy;<lb/>stema della Vena porta &egrave; privo di valvole, e che le valvole descritte nel <lb/>VI libro. <emph type="italics"/>De re anatomica<emph.end type="italics"/> hanno la medesima disposizione delle aselliane, <lb/>non si avr&agrave; nessuna difficolt&agrave; ad ammettere che il Colombo osservasse le <lb/>vere lattee, e non le meseraiche <emph type="italics"/>alterius et vulgati generis,<emph.end type="italics"/> come l'Asellio <lb/>stesso facilmente si lusingava (ivi). Ma il trovarle cos&igrave; esili, e incerte quanto <lb/>al liquido contenuto, precise la via della scoperta, fatta poi gloriosamente <lb/>dal pi&ugrave; giovane suo concittadino, al vecchio Anatomico di Cremona, il quale, <lb/>mentre pareva esser giunto cos&igrave; dappresso a toccare la riva, si rituff&ograve; nel <lb/>pi&ugrave; profondo gorgo de'comunali errori, cos&igrave; scrivendo nel cap. </s>

<s>IV del sopra <lb/>citato libro, presso a finir di descrivere l'anatomia del ventricolo: &ldquo; Venae <lb/>vero, tum illi nutrimentum deferunt, tum chylo suscepto illum ad iecur de&shy;<lb/>ferunt &rdquo; (227). </s></p><p type="main">

<s>Tanto per&ograve; sembrava impossibile darsi in natura un canale, in cui due <lb/>liquidi diversi avessero moto contrario, che alcuni si ridussero ad ammettere <lb/>nelle meseraiche due ordini distinti: uno che portasse il sangue, e l'altro <pb xlink:href="020/01/1337.jpg" pagenum="212"/>che asportasse il chilo, e forse era questa l'intenzion del Colombo. </s>

<s>Ma il <lb/>non essersi bene spiegato gli tolse il merito di aver preparate le vie alla <lb/>scoperta aselliana, meglio di Erofilo, di Galeno, di Polluce, di Rhasis e di <lb/>quanti altri fra gli antichi si commemorano dalla Storia. </s></p><p type="main">

<s>Contro tutti costoro per&ograve;, che volendo essere pi&ugrave; ragionevoli ammette&shy;<lb/>vano nel Mesenterio i due sopra detti ordini di vasi, insorse il lodigiano Gio&shy;<lb/>vanni Cost&egrave;o, il quale pubblic&ograve; in Venezia, nel 1565, un libretto cos&igrave; inti&shy;<lb/>tolato: &ldquo; De venarum mesaraicarum veteris opinionis confirmatione adversus <lb/>eos, qui chyli in iecur distributionem fieri negant per mesaraicas venas. </s>

<s>&rdquo; <lb/>Ma perch&egrave; il Cost&egrave;o non dimostrava il suo assunto coll'esperienze, ma col&shy;<lb/>l'autorit&agrave; e co'ragionamenti, non fu perci&ograve; ascoltato dai savii, dalla mente <lb/>de'quali non si pot&egrave; rimovere l'assurdo che nasceva dal far le meseraiche <lb/>tutt'insieme conduttrici del sangue che va, e del chilo che viene. </s></p><p type="main">

<s>Andrea Cesalpino, quand'ebbe riconosciuta la vera direzione del san&shy;<lb/>gue venoso, venne a togliersi una delle maggiori difficolt&agrave;, che si paravano <lb/>innanzi agli altri, e dall'avere scoperto che il sangue stesso e il chilo vanno <lb/>nelle meseraiche pel medesimo verso, fu condotto a dare una nuova solu&shy;<lb/>zione al difficilissimo problema. </s>

<s>Quel che va, disse, per le vene del mesen&shy;<lb/>terio non &egrave; sangue, ma &egrave; chilo, e, se mostra di color rosso, &egrave; perch&egrave; le <lb/>arterie, che si anastomizzano con le vene stesse meseraiche, v'infondono il <lb/>loro sangue, ond'&egrave; che il chilo si tinge di quel colore, come fa l'acqua alla <lb/>quale si mescola il vino. </s>

<s>&ldquo; Cum enim necesse sit omnes partes nutriri san&shy;<lb/>guine, venae meseraicae non possunt illis sanguinem tribuere, quia datae <lb/>sunt ut sugant chylum et ferant ad hepar. </s>

<s>Simul autem per easdem ferri <lb/>sursum chylum et sanguinem deorsum absurdum est, neque diversis tem&shy;<lb/>poribus, nunquam enim venae meseraicae repertae sunt chylo plenae, sed <lb/>semper sanguine. </s>

<s>Quomodo igitur sugunt chylum ut omnes fatentur?.... <lb/>Quod autem sanguis semper reperiatur in vasis istis, nunquam autem ma&shy;<lb/>teria alba, causa est quia arteriae cum venis delatae, per anastomosin san&shy;<lb/>guinem in venas transfundunt, unde chyli fit conversio in sanguinem ut vi&shy;<lb/>num facit aquae mixtum &rdquo; (Artis medicae, Lib. </s>

<s>VII, Romae 1603, pag. </s>

<s>9). </s></p><p type="main">

<s>L'ingegnosa ipotesi del Cesalpino per&ograve; non ebbe accoglienza nel pub&shy;<lb/>blico, cos&igrave; alieno allora dal professare le innovatrici dottrine di lui intorno <lb/>alla natura e alla direzione del sangue nelle vene, ond'&egrave; che Gaspero Asel&shy;<lb/>lio si conferm&ograve; sempre pi&ugrave; nella sua opinione che avesse la Natura ordi&shy;<lb/>nati a condurre il chilo vasi appropriati, e che la risoluzione del gran pro&shy;<lb/>blema consistesse tutta in trovarli. </s>

<s>Datosi perci&ograve; alle autopsie, anco per <lb/>seguire il consiglio di Galeno che raccomandava di creder solo <emph type="italics"/>propriis ocu&shy;<lb/>lis. </s>

<s>non libris<emph.end type="italics"/> (Praefatio in dissert. </s>

<s>De lact. </s>

<s>cit.), non era ancora riuscito a <lb/>trovar nulla, quando quello, che gli era stato cos&igrave; ostinatamente negato dallo <lb/>studio, gli fu spontaneamente offerto dalla fortuna. </s>

<s>&ldquo; Casu magis, ut verum <lb/>fatear, quam consilio aut data in id peculiari opera &rdquo; (De lactibus cit., pag. </s>

<s>18). </s></p><p type="main">

<s>Adducono alcuni questa ingenua confessione come un esempio di sin&shy;<lb/>golare modestia, ma &egrave; la sincera espressione della verit&agrave;, che vuole avere <pb xlink:href="020/01/1338.jpg" pagenum="213"/>un commento dalla storia. </s>

<s>Questo commento poi si conclude tutto nella ri&shy;<lb/>sposta a una tale domanda: come mai tanti valorosi Anatomisti, con tanti <lb/>solleciti studi, non riuscirono a vedere quel che, premostrante poi l'Asellio, <lb/>tutti videro senza difficolt&agrave; nel mesenterio degli animali o vivi o morti? </s>

<s>Par&shy;<lb/>rebbe si potesse rispondere esser facile avvertire la presenza di un oggetto <lb/>in un luogo, dop'averci qualcuno assicurato che guardandoci noi ve lo tro&shy;<lb/>veremo di certo, ma non farebbe questa risposta per l'Asellio, nella mente <lb/>di cui e nell'animo si vuol penetrare, e non s'intenderebbe come, fuor <lb/>d'ogni modestia, egli avesse attribuita la sua scoperta al caso. </s></p><p type="main">

<s>A intender ci&ograve; giova osservare che, da poi che il Colombo, dettando le <lb/>regole per le vivisezioni, consigli&ograve; di praticarle sui cani, i cani furono, prima <lb/>e dopo l'Asellio, quasi i soli immolati, e gli esempi del Pecquet e dell'Igmoro <lb/>possono valere per tutti gli altri. </s>

<s>Ma la fame dei cani &egrave; proverbiale, a che <lb/>s'aggiungeva che i dissettori gli tenevano ad arte digiuni pi&ugrave; che mai, perch&egrave; <lb/>i poveri animali, lasciandosi andar, fra gli spasimi, a deporre il superfluo <lb/>del ventre, non dovessero gli assistenti allo spettacolo rimanere offesi dalla <lb/>schifezza, e ammorbati dal fetore. </s></p><p type="main">

<s>Aveva dunque anche l'Asellio sempre praticato cos&igrave;, e una volta che <lb/>ebbe a incidere un cane, non secondo il solito digiuno, ma anzi benissimo <lb/>pasciuto, ebbe ragione di attribuire il fatto a un benefizio singolare della <lb/>fortuna. </s>

<s>Che tali fossero davvero i sentimenti dell'avventuroso primo dimo&shy;<lb/>stratore delle vene lattee, &egrave; confessato nella storia, da lui stesso descrittaci <lb/>con mirabile grazia e naturalezza, e nella quale s'incomincia cos&igrave; a raccon&shy;<lb/>tare a quale occasione, e in che modo gli occorresse di fare l'inaspettata <lb/>scoperta. </s></p><p type="main">

<s>&ldquo; Canem, ad diem Julii 23 eiusdem anni (1622) bene habitum, beneque <lb/>pastum incidendum vivum sumpseram, amicorum quorumdam rogatu, qui&shy;<lb/>bus recurrentes nervos videre forte placuerat. </s>

<s>Ea nervorum demonstratione <lb/>perfunctus cum essem, visum est eodem in cane, eadem opera, diaphragma&shy;<lb/>tis quoque motum observare. </s>

<s>Hoc dum conor, et eam in rem abdomen ape&shy;<lb/>rio, intestinaque cum ventriculo, collecta in unum deorsum manu, impello, <lb/>plurimos repente, eosque tenuissimos candidissimosque ceu funiculos, per <lb/>omne mesenterium et per intestina, infinitis propemodum propaginibus di&shy;<lb/>spersos, conspicor. </s>

<s>Eos primo aspectu nervos esse ratus, non magnopere mi&shy;<lb/>ratus sum, sed mox falsum me cognovi, dum nervos, qui ad intestina per&shy;<lb/>tinent, distinctos a funiculis illis et longe diversos esse, ac seorsim praeterea <lb/>ferri, animadverti. </s>

<s>Quare, rei novitate perculsus, haesi aliquamdiu tacitus, <lb/>cum menti varia occurrerent, quae inter Anatomicos versantur de venis me&shy;<lb/>seraicis et eorum officio, plenae non litium minus quam verborum contro&shy;<lb/>versiae. </s>

<s>Et forte fortuna congruerat ut, paucis ante diebus, quendam de hoc <lb/>argumento proprie scriptum a Joanne Costaeo libellnm evolverem. </s>

<s>Ut me <lb/>collegi experiundi causa, adacto acutissimo scalpello, unum ex illis, et ma&shy;<lb/>iorem funiculum pertundo. </s>

<s>Vix bene ferieram, et confestim liquorem album, <lb/>lactis aut cremoris instar, prosilire video. </s>

<s>Quo viso, cum tenere laetitiam non <pb xlink:href="020/01/1339.jpg" pagenum="214"/>possem, conversus ad eos qui aderant, ad Alexandrum Tadinum, et Sena&shy;<lb/>torem Septalium .... <emph type="italics"/>evreca,<emph.end type="italics"/> inquam cum Archimede, et simul ad rei tam <lb/>insolitae, tam iucundum spectaculum invito eius novitate ipsos quoque com&shy;<lb/>motos &rdquo; (De lactibus cit., Cap. </s>

<s>IX, pag. </s>

<s>19, 20). </s></p><p type="main">

<s>I beneficii per&ograve; della fortuna, con tanto affetto poi commemorati, non <lb/>furono dall'Asellio riconosciuti, se non da poi ch'esalati il cane gli ultimi <lb/>spiriti vide dall'aperto abdome sparire l'incantevole scena di quei sottilis&shy;<lb/>simi cordoncini lattei. </s>

<s>Per tornar dunque a godere le volutt&agrave; dello spetta&shy;<lb/>colo, si volse a por le mani sopra un altro cane, il quale eletto di qualit&agrave; <lb/>conformi al desiderio dei male accorti dissettatori, era magro e digiuno. </s>

<s>Ma <lb/>aperto con tanta avidit&agrave; il ventre, e messa la rete del mesenterio allo sco&shy;<lb/>perto, rimase! &ldquo; Nullum prorsus, vel minimum album vasculum, quanta&shy;<lb/>cumque etiam diligentia perquirenti, in conspectu sese dabat. </s>

<s>Et iam abiici <lb/>animo coeperam, ac cogitare ne quae in cane illo primo se obtulissent mihi, <lb/>ex illis assent quae raro spectari in anatome solebat Galenus dicere &rdquo; (ibi, <lb/>pag. </s>

<s>20). Riprese poi presto animo, quando pens&ograve; al digiuno, e procuratosi <lb/>ad arte un terzo cane, come quello primo che gli era stato offerto dal caso, <lb/>benissimo pasciuto, fu nuovamente consolato dello spettacolo, e riconobbe <lb/>allora quanta parte del merito avesse avuto la Fortuna in quella scoperta, <lb/>e ne fece commemorazione solenne nel capitolo VIII, che serve di proemio <lb/>a questa storia. </s></p><p type="main">

<s>Fatto cos&igrave; certo l'Asellio della scoperta, e ripensando che i quadrupedi <lb/>son dalla Natura formati sopra lo stesso stampo, sper&ograve; di ritrovar le vene <lb/>lattee in tutti essi ugualmente come ne'cani. </s>

<s>Le trov&ograve; di fatto, diligente&shy;<lb/>mente cercandole, nei gatti, negli agnellini di latte, e ne'pi&ugrave; adulti, nelle vac&shy;<lb/>che, nei porci e in un cavallo comperato a questo unico intento, e sventrato <lb/>vivo. </s>

<s>Quanto poi all'uomo, sebbene Erasistrato ed Erofilo non temessero d'in&shy;<lb/>ciderlo, &ldquo; non incidi, fateor, nec incidam qui nefas et piandum morte, cum <lb/>Celso, existimo praesidem salutis humanae artem pestem alicui, eamque atro&shy;<lb/>cissimam, inferre. </s>

<s>Ita nihilominus, idque pro certo statuo, quae in tot bru&shy;<lb/>tis visa mihi sunt, iis fieri nullo modo posse unus et solus homo ut defi&shy;<lb/>ciatur &rdquo; (ibi, pag 20). </s></p><p type="main">

<s>Chiunque in ogni modo loda l'Asellio, per essersi astenuto dall'incidere <lb/>un uomo vivo, si maraviglia ch'ei non tentasse di farlo sui cadaveri, ai quali <lb/>sempre erano ricorsi gli Anatomici, per esplorare e descriverne fedelmente <lb/>le altre parti. </s>

<s>Cessa ogni maraviglia per&ograve; in chi ripensa che l'Asellio stesso, <lb/>al veder le vene lattee sparire a un tratto fuggitive insiem colla vita, si per&shy;<lb/>suase che non fossero visibili ne'cadaveri, dove il chilo non va a riempirle <lb/>di s&egrave;, sospinto innanzi dall'impulso de'moti vitali. </s></p><p type="main">

<s>Ma l'Igmoro poi riconobbe, per ripetute esperienze, che non sempre il <lb/>suceo latteo fugge dalle vene del cane, al fuggir della vita. </s>

<s>&ldquo; At vero cum <lb/>anima lacteus ile succus a vasis non semper fugit, sed saepissime post inspec&shy;<lb/>tionem motuum pulmonum et cordis, imo diu postquam animam efflavit <lb/>canis, illas venas lacteas inveni &rdquo; (Corporis hum. </s>

<s>disquisitio anat. </s>

<s>cit., pag. </s>

<s>38). <pb xlink:href="020/01/1340.jpg" pagenum="215"/>Dal veder le lattee esser dopo morte rimaste impresse nel mesenterio dei <lb/>bruti, incor&ograve; l'Igmoro una buona speranza di averle a ritrovare altres&igrave; ne'ca&shy;<lb/>daveri umani, e nel 1639 scrisse di avervele ritrovate di fatto. </s>

<s>Anzi aggiunge <lb/>che un medico suo amico gli aveva dato avviso di essersi due anni prima <lb/>incontrato ad osservare la medesima cosa in un uomo, la notte e gran parte <lb/>del giorno dopo ch'era spirato. </s>

<s>&ldquo; Mihi amicissimus Medicus oxoniensis idem <lb/>haec scripturo enunciavit quod, in dissectione corporis humani, anno 1637, <lb/>apparuerunt lacteae, postquam expirasset animam per spatium totius noctis <lb/>et partis maioris diei. </s>

<s>Idem et ipse, in dissectione humani corporis, anno 1639, <lb/>perlustravi, licet perfectam illarum disquisitionem copia pinguedinis obnu&shy;<lb/>bilavit: illarum tamen plurimas chylo refertas adstantibus demonstravi. </s>

<s>Non <lb/>itaque statim post mortem semper evanescunt &rdquo; (ibid). </s></p><p type="main">

<s>Di queste anatomiche ispezioni, fatte in Inghilterra sui cadaveri umani, <lb/>non s'ebbe per&ograve; pubblica notizia prima del 1651, quando comparve alla luce <lb/>all'Aja l'opera dell'Igmoro. </s>

<s>Ma dodici anni prima un nostro Anatomico ve&shy;<lb/>neziano, Cecilio Folli, aveva nella sua citt&agrave; nativa pubblicato un libretto <lb/>in 4&deg; col titolo: &ldquo; Sanguinis a dextro in sinistrum cordis ventriculum de&shy;<lb/>fluentis facilis reperta via, cui non vulgaris in lacteas nuper patefactas ve&shy;<lb/>nas animadversio proponitur, Venetiis 1639. &rdquo; Ivi dice l'Autore di avere <lb/>osservate e di avere altres&igrave; in pubblico dimostrate le vene lattee ne'cada&shy;<lb/>veri umani, in quel frattempo che asserirono poi di avervele scoperte i due <lb/>anatomici stranieri. </s></p><p type="main">

<s>Ha il Folli, in quel suo libretto, considerazioni intorno alle lattee di <lb/>qualche pregio, come sarebbe per esempio quella che i vasi chiliferi vanno <lb/>tutti a confluire in un tronco, di che &egrave; da alcuni attribuito al Nostro il me&shy;<lb/>rito di aver additato, bench&egrave; dalla lontana, il Ricettacolo pecqueziano. </s>

<s>Ma <lb/>nocque alla pubblica stima di lui l'aver, dopo l'Harvey, creduto essere le <lb/>vie vere del sangue attraverso alla cavit&agrave; del cuore quelle, che tanti anni <lb/>prima avevano sedotto il Botallo. </s>

<s>Per questa ragione, fra le altre, quando <lb/>nel 1641 comparve la Vita di Niccol&ograve; Fabrizi di Peiresc, s'ebbe fede e si <lb/>accett&ograve; per pi&ugrave; autentico documento di storia la testimonianza, che ne fece <lb/>il celebre biografo di lui Pietro Gassendo, il quale narra com'esso Peiresc, <lb/>desideroso di osservare le vene lattee nell'uomo, e disperato di averle a tro&shy;<lb/>var ne'cadaveri, dietro ci&ograve; che aveva scritto l'Asellio, tentasse in ogni modo, <lb/>nel 1634, la prova sul cadavere di un uomo condannato alle forche. </s>

<s>&ldquo; Quamo&shy;<lb/>brem damnatum suspendio procuravit primum, antequam iudicium capitale <lb/>pronunciaretur, secure et egregie pasci, ut nempe esset unde chylus lacte&shy;<lb/>sceret, quo tempore requireretur, ac inde, non nisi hora cum semisse post <lb/>suspendium expectata, cadaver devehi curavit in anatomicum theatrum. </s>

<s>Prae&shy;<lb/>stitum est vero ea diligentia ut aperto abdomine venae albescentes apparue&shy;<lb/>rint, utque ex nonnullis resectis colligi potuerit liquor lacteus, quod profecto <lb/>visum est mirum &rdquo; (Petri Gassendi, Fabricii De Peiresc Vita, Parisiis 1641, <lb/>pag. </s>

<s>283). </s></p><p type="main">

<s>Narra ivi lo stesso Gassendo come, avuta il Peiresc la notizia della sco-<pb xlink:href="020/01/1341.jpg" pagenum="216"/>perta dell'Asellio, si procurasse varii esemplari del libro &ldquo; quae in medicos <lb/>amicos distribuit &ldquo; (pag. </s>

<s>222) e cos&igrave;, infin dal 1628, alquanti mesi dopo la <lb/>pubblicazione, si diffuse in Francia la novella scoperta italiana, dal Peiresc <lb/>stesso, e da'suoi molti e valorosi amici in ogni genere di animali, e nel&shy;<lb/>l'uomo stesso, come vedemmo, non molti anni dipoi, verificata. </s></p><p type="main">

<s>Non par per&ograve; che fosse fra quegli amici il Cartesio, il quale insegnando <lb/>nel suo trattato <emph type="italics"/>De homine<emph.end type="italics"/> in che modo il ventricolo digerisca il cibo, dice <lb/>che le particelle di lui pi&ugrave; sottili attraversano i minutissimi pori intestinali <lb/>&ldquo; per quos fluunt in ramos magnae cuiusdam venae quae ad hepar eas de&shy;<lb/>fert, nec non in alias venas, quae eas alio deferunt &rdquo; (Editio cit., pag. </s>

<s>4). </s></p><p type="main">

<s>Avverte il De-la-Forge in nota (pag. </s>

<s>6) che il non aver qui il Cartesio <lb/>fatto menzione delle vene lattee &egrave; sicuro argomento dell'essere il trattato <lb/><emph type="italics"/>De homine<emph.end type="italics"/> pi&ugrave; antico della dissertazione <emph type="italics"/>De lactibus,<emph.end type="italics"/> ci&ograve; che per verit&agrave; a <lb/>noi non sembra, dando manifesta prova dell'essere quel trattato cartesiano <lb/>stato scritto dopo il 1628 la circolazione del sangue, ivi professata a modo <lb/>dell'Harvey, e sapendo che in quel medesimo anno il Peiresc si fece ban&shy;<lb/>ditore solenne in Francia della scoperta aselliana. </s>

<s>Noi crediamo piuttosto es&shy;<lb/>sere quel silenzio in conformit&agrave; del genio di Renato, che presumeva essere, <lb/>appetto alle sue, tutte quelle degli altri scoperte da nulla, bastando dall'al&shy;<lb/>tra parte alle sue funzioni la macchina umana, com'ei l'aveva filosoficamente <lb/>congegnata. </s>

<s>Che se fa grazia all'Harvey &egrave; un miracolo, e l'Harvey stesso <lb/>glie ne professa riconoscenza: e il medesimo crediamo avrebbe fatto, se ne <lb/>fosse stato in tempo, il Gilberto. </s></p><p type="main">

<s>Che se il repudio della tanto aspettata scoperta fa maraviglia in un filo&shy;<lb/>sofo, quale era creduto il Cartesio, pi&ugrave; gran maraviglia fa in un Fisiologo <lb/>qual'era di fatto l'Harvey. </s>

<s>Egli ha per aperto e dimostrato il chilo, in tutti <lb/>gli animali che si nutriscono &ldquo; ex intestinis per venas mesaraicas deferri, <lb/>nec opus esse ut novum iter, venas lacteas scilicet, inquiramus &rdquo; (De gene&shy;<lb/>ratione anim. </s>

<s>cit., pag. </s>

<s>221). Cos&igrave; il sospiro di tanti anatomici, succedutisi <lb/>senza interruzione, dal Fernelio in poi, non era stato per l'Harvey che un <lb/>vano inutile desiderio. </s></p><p type="main">

<s>Molti commenti hanno fatto gli storici intorno alla strana sentenza del <lb/>celeberrimo uomo. </s>

<s>Vollero dire alcuni che fu disprezzo delle cose italiane: <lb/>altri che fu gelosia e dispetto del non esser stato egli il primo eletto ad ac&shy;<lb/>cogliere le divine aure, che incominciavano a commoversi allora, inspiratrici <lb/>di un nuovo stupendo genere di scoperte. </s>

<s>La dissertazione <emph type="italics"/>De lactibus<emph.end type="italics"/> in&shy;<lb/>fatti comparve in pubblico un anno prima della Esercitazione anatomica <emph type="italics"/>De <lb/>motu cordis,<emph.end type="italics"/> e le valvole, che promuovono e dirigono il chilo, troppo gran <lb/>somiglianza hanno colle valvole, che promovono e dirigono il sangue, da ama&shy;<lb/>reggiare alquanto la compiacenza in chi aveva scritto che lo scopritor delle <lb/>valvole nelle vene non ne conobbe l'uso &ldquo; nec alii addiderunt &rdquo; (De motu <lb/>cordis cit., pag. </s>

<s>77). </s></p><p type="main">

<s>Usi a vedere su questa terra tanto pi&ugrave; in basso umiliarsi le valli, quanto <lb/>in alto pi&ugrave; si erigono i monti, non fa a noi maraviglia il veder quel sublime <pb xlink:href="020/01/1342.jpg" pagenum="217"/>ingegno dell'Harvey, ch'era pure un uomo di questa terra, scendere cos&igrave; <lb/>in basso fra le passioni volgari e gli errori. </s>

<s>Nonostante diremmo che l'aver <lb/>egli negata la necessit&agrave; delle vene lattee, cos&igrave; vivamente sentita da tutti nel&shy;<lb/>l'economia animale, fosse una legittima conseguenza di ci&ograve; che gli era oc&shy;<lb/>corso a osservare nell'uovo incubato, e di alcune ipotesi da lui stesso fon&shy;<lb/>date sopra l'ordine di quegli ammirati svolgimenti embrionali. </s>

<s>All'albume, <lb/>che nutrisce il pulcino chiuso dentro nell'uovo, vide sostituito il chilo, che <lb/>lo nutrisce escluso. </s>

<s>E siccome quell'albume &egrave; portato dalle vene meseraiche <lb/>al Fegato, che lo riduce in sostanza meglio atta e pi&ugrave; disposta a nutrire; <lb/>cos&igrave; pens&ograve; che i medesimi vasi diramati pel mesenterio, non potendo rima&shy;<lb/>nere ivi inutili e come fuor di servigio, esaurito l'albume dell'uovo, e il <lb/>pulcino escluso, di li in poi servissero invece a trasportare il chilo. </s>

<s>&ldquo; Porro <lb/>cum dicta vasa in ovo in albumen parit&egrave;r ac vitellum spargantur, non ali&shy;<lb/>ter quam plantae radices in terram solent; constat utrumque hunc liquorem <lb/>pro nutrimento foetui esse, eundemque per vasa illa ad hunc deferri..... <lb/>Absumitur equidem primo albumen et vitellus sero tandem pro cibo est, <lb/>lactisque vicem in iam natis animalibus supplet..... Manifestum igitur est <lb/>pullum iam exclusum, dum adhuc tenellus est, vitello nutriri. </s>

<s>Et quemad&shy;<lb/>modum is intra ovum, partim ab albumine, partim ex vitello alitur, prae&shy;<lb/>cipue vero ab albuminibus, quae et maiore copia adsunt, et citius absu&shy;<lb/>muntur; ita similiter, iam exclusus, cui omne adveniens alimentum iecur <lb/>pertransit, et ibidem ulterius praeparatur, partim vitello partim chylo ex in&shy;<lb/>testinis hausto nutritur, praesertim autem chylo, quem plures venarum me&shy;<lb/>saraicarum ramuli ad se rapiunt &rdquo; (ibi, pag. </s>

<s>219, 20). </s></p><p type="main">

<s>Lasciamo andare che l'albume e il chilo non si rassomigliano in altro <lb/>che nell'ufficio di nutrire e nel colore, ma che pensiamo rispondesse l'Har&shy;<lb/>vey a quell'antica difficolt&agrave;, mossa contro coloro che, come lui, dicevano le <lb/>meseraiche essere conduttrici del chilo, mentre si vedon sempre rosseggiare <lb/>di sangue? </s>

<s>Forse chi sa che non avesse pronta la risposta del Cesalpino. </s>

<s><lb/>Sarebbe allora anche questo da annoverar fra'molti silenziosi incontri di <lb/>que'due uomini, dall'altra parte cos&igrave; diversi, non solo per et&agrave; e per patria, <lb/>ma per educazione d'ingegno; incontri, che darebbero, a chi non avesse <lb/>fretta come noi, soggetto importantissimo a un altro nuovo capitolo di storia. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Ma perch&egrave; siam consigliati di proseguire addiritto il nostro cammino, <lb/>riprendiamo le mosse da quell'Harveio, che abbiamo ora lasciato. </s>

<s>Il celebre <lb/>e valoroso Fisiologo ripeteva, nella prima met&agrave; del secolo XVII, intorno al&shy;<lb/>l'economia della nutrizione, le dottrine stesse insegnate dall'antico Galeno: <lb/>le vene meseraiche, come le radici degli alberi dalla terra, suggono il chilo <lb/>dagl'intestini, e confluendo tutte insieme alla Porta, lo riversan nel Fegato, <lb/>che lo rende colla sua virt&ugrave; perfetto alimento. </s></p><pb xlink:href="020/01/1343.jpg" pagenum="218"/><p type="main">

<s>Tanto aveva il Fegato, con la sua mole superiore a quella di molti <lb/>altri visceri, con la sua sede che &egrave; fra le pi&ugrave; cospicue nell'interno del bene <lb/>architettato edifizio, col suo colore e col suo tessuto, a cui par che il san&shy;<lb/>gue stesso abbia prestato le fila, sedotta la fantasia degli anatomici, per di <lb/>pi&ugrave; commossa dalle epopee galeniche, ricantate da tanti; che l'Asellio stesso, <lb/>come se ce le avesse vedute entrare, tenne per cosa certa che le lattee, dopo <lb/>aver confluito insieme nella Ghiandola pancreatica, s'inserissero nel Fegato, <lb/>per riversare in lui il chilo, come frumento nel prontuario di una citt&agrave; ben <lb/>munita. </s></p><p type="main">

<s>N&egrave; dopo parecchi anni ancora di esercitazioni e di studii, aveva il Fe&shy;<lb/>gato lasciato sugli anatomici o rimesso punto della sua affascinatrice potenza. </s>

<s><lb/>Fra'molti, basti a noi citare due esempii, che possono valere per tutti gli <lb/>altri, e sia primo quello di Giovanni Veslingio, nel <emph type="italics"/>Sintagma anatomico<emph.end type="italics"/><lb/>pubblicato la prima volta in Padova nel 1641, e poi in Amsterdam nel 1666 <lb/>coi commenti di Gerardo Blasio. </s>

<s>Trattando l'Autore nel citato <emph type="italics"/>Syntagma<emph.end type="italics"/><lb/>particolarmente del Pancreas e del suo ufficio, &ldquo; suscipit, egli dice, chilum, <lb/>susceptumque iecori subministrat, non per venas ullas a Porta descendentes <lb/>aut arterias, sed per singulares ductus, quos ob similitudinem aliquam, tum <lb/>conformationis, tum distributionis, venas Asellius nuncupavit, easque lac&shy;<lb/>teas.... Longa autem sunt et tereta vascula.... a Pancreate sursum circa <lb/>descendentis Venae portae truncum ad iecur, deorsum vero ad intestina mi&shy;<lb/>nutissimis propaginibus dispersa.... Colligere easdem in communem aliquem <lb/>truncum, ob latitudinem Pancreatis insignem, divino Conditori non placuit &rdquo; <lb/>(Amstelodami 1666, pag. </s>

<s>56). </s></p><p type="main">

<s>L'altro esempio di coloro che, ingannati dalle nuove rivelazioni del Pan&shy;<lb/>creas, e sedotti dall'ossequio antico al principato del Fegato, ripeterono e <lb/>confermarono le dottrine dell'Asellio, ci &egrave; porto dal famoso Riolano salu&shy;<lb/>tato principe degli Anatomici, a que'tempi, in Francia, e per tutto il mondo. </s>

<s><lb/>Nel suo <emph type="italics"/>Enchiridio,<emph.end type="italics"/> dove tutti apprendevano in compendio la scienza ana&shy;<lb/>tomica dettata per gli studiosi dal nuovo Galeno, trattando, al cap. </s>

<s>XVIII <lb/>del II libro, <emph type="italics"/>De mesenterio,<emph.end type="italics"/> cos&igrave; profferiva l'Autore la sua sentenza: &ldquo; Quar&shy;<lb/>tum genus vasorum, quae Venae lacteae dicuntur ab Asellio inventore, adiec&shy;<lb/>tum fuit, de quo non est amplius dubitandum, cum sit iam vulgatum et ac&shy;<lb/>ceptum. </s>

<s>Hoc unum multos anxios tenet distributionis diversitas. </s>

<s>Nam in <lb/>animali vivente, saturo et aperto, notantur quidem istae venae lacteae spar&shy;<lb/>sae per mesenterium, sed aliae ad Pancreas progrediuntur, aliae ad Hepar, <lb/>aliae ad truncum. </s>

<s>Cavae derivantur, nullae ad lienem. </s>

<s>Nec, more venarum, <lb/>Portae in unum caudicem coeunt: videntur potius radicem et fundamentum <lb/>habere in Pancreate, et inde hinc et illinc dispergi &rdquo; (Lugduni Batavo&shy;<lb/>rum 1649, pag. </s>

<s>109). </s></p><p type="main">

<s>Aveva di poco l'Oracolo parigino profferita questa sentenza, quand'esce <lb/>fuori un giovane sconosciuto, venuto di Dieppe a Parigi, a sentenziare au&shy;<lb/>dacemente contro il Maestro: &ldquo; non ad Hepar, non ad venas Portae, non <lb/>ad cavam prope emulgentes derivari chylum, sed ab intestinis ad <emph type="italics"/>Recepta-<emph.end type="italics"/><pb xlink:href="020/01/1344.jpg" pagenum="219"/><emph type="italics"/>culum<emph.end type="italics"/> quoddam &rdquo; e soggiungeva con giuramento che chiunque, sezionando <lb/>con arte, si mettesse diligentemente a cercare, troverebbe che cos&igrave; era, come <lb/>egli asseverava di fatto. </s></p><p type="main">

<s>Rimase il Riolano di tanta giovanile baldanza, e brontolando andava ag&shy;<lb/>girandosi per l'aula magna dell'Accademia, e diceva non esser quelle sco&shy;<lb/>perte da giovani, e che in ogni modo conveniva, com'avea fatto del suo ca&shy;<lb/>nale il Virsungo, interrogare i seniori della scuola parigina, e un principiante <lb/>inesperto, com'era quel Giovanni Pecqueto, docilmente accettarne l'infalli&shy;<lb/>bile responso. </s>

<s>&ldquo; Non ita Pecquetus, nec anatomicorum Principi persolvit <lb/>tributum: haec belli causa, haec ratio in lacteas thoracicas Riolanum arma&shy;<lb/>vit &rdquo; (Brevis destructio responsionis Riolani, inter Opera Pecqueti, Pari&shy;<lb/>siis 1654, pag. </s>

<s>197). </s></p><p type="main">

<s>Ma la navicella del pellegrino ingegno ha oramai spiegate le vele, e le <lb/>celesti aure la sospingono innanzi cos&igrave; fortemente veloce, che la remora del <lb/>Riolano &egrave; non men ridicolmente impotente di quella del favoloso pesciolino <lb/>di mare. </s>

<s>Il felice corso di quella nave nel profondo pelago della vita, e le <lb/>lunghe durate fatiche e il conquistato premio della scoperta son raccontati <lb/>cos&igrave; dallo stesso Nauclero, appena ritornato trionfale dal suo viaggio: </s></p><p type="main">

<s>&ldquo; Post acquisitam ante annos aliquot, ex cadaverum sectione, mutam <lb/>alioqui frigidamque sapientiam, placuit et ex vigenti vivarum animantium <lb/>harmonia veram sapientiam exprimere. </s>

<s>Et quia hae ab illis solo propemo&shy;<lb/>dum differunt motu, cuius in corde praecipua sedes, consilium fuit eundem, <lb/>expedito involucris, avulsoque corde, manifestius contemplari. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ergo diffissa viventis, quae media est, alvo molossi, inchoo extispi&shy;<lb/>cium. </s>

<s>Nec mora: cor, rescissis quibus reliquo adhaeret corpori, vasculorum <lb/>retinaculis, avello. </s>

<s>Tum exhausta, quae statim restagnaverat, spectantisque <lb/>confuderat oblutus, copia cruoris, albicantem subinde lactei liquoris, nec <lb/>certe parum fluidi scaturiginem intra Venae cavae fistulam, circa dextri se&shy;<lb/>dem ventriculi, miror effluere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; ..... Venam cavam a Diaphragmate ad iugulum aperio: apparuit <lb/>illico nivei humoris, omni tum cruoris expurgatum mixtura, fluentulum. </s>

<s>A <lb/>ramis usque subclaviis ad pericardium, intra Venam, subsidebat candidus <lb/>apprime liquor, et effuso per Mesenterium chylo simillimus, sicut inter utrum&shy;<lb/>que collatos invicem et nitor et odor et sapor et consistentia nullum inesse <lb/>discrimen ostenderint. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Extinctus animalis exenterati motus, stiterat fluorem, nec, qua lac&shy;<lb/>teus erupisset, aut quo scaturiisset ab ubere latex, sinebat quies interno&shy;<lb/>scere. </s>

<s>Tamen, gliscente reconditioris doctrinae desiderio, thymum comprimo, <lb/>collum stringo, ipsos etiam anteriorum partium artus, si qua forte albicantis <lb/>substantiae residuum ex vasculosis stillaret anfractibus, sollicito. </s>

<s>Sed inde <lb/>sanguinis tantum effluxerunt aliquot guttulae, nihil lacteum in Cavam ir&shy;<lb/>rupit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ergo, quod unicum industriae meae superfuit, Mesenterii lacteas, quid <lb/>hanc sibi iuris in rem obtinerent, pondere digiti gravitantis, adigo com-<pb xlink:href="020/01/1345.jpg" pagenum="220"/>monstrare. </s>

<s>Parent urgenti, nam e ramis subclaviis tanta succi, quem obser&shy;<lb/>vabam, copia profunditur, ut per eiusdem esse lacteas originem agnoverim, <lb/>et a chylo diversum putare duxerim insanissimum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ne tamen quid inexploratum relinqueretur, cum e superioribus ra&shy;<lb/>morum eiusmodi partibus praeceps rueret, has in longum, una cum caeta&shy;<lb/>ris colli et artuum anteriorum venis, diffindo, compressaque mox inferioris <lb/>alvi capacitate, et exerto in apertos iuxta claviculas alveos obtutu, ecce com&shy;<lb/>pletorio mei voti exitu, indubitato iam tum in superiores ramorum subcla&shy;<lb/>viorum partes utrinque chylus redundavit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; <foreign lang="greek">*exbol<gap/>s</foreign> noto pronas oculis et spectantibus manifestas scaturigines, <lb/>foraminula scilicet, paulo infra iugulares venas et axillarum cataractas, nu&shy;<lb/>merosis ostiolis hiscentla. </s>

<s>Sed et iugularium illic valvulas observo ruituro <lb/>in cordis gurgitem chylo faciles ascensu penitus interdicere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Verum, qua tandem via, quibus meatibus eo chylus devolveretur, non <lb/>licuit, ob exhaustum animalis iamdudum mactati mesenterium, evanescen&shy;<lb/>tibus plane lacteis cum expressi liquoris effluxu deprehendere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; ..... Suffecissem illico, in demortui locum, quem mihi tum ex im&shy;<lb/>proviso fors canem obtulerat..... Ergo illaqueatum canem .... subigo, et <lb/>cum ieiunii moras largissima dape compensassem, demum, hora circiter a <lb/>saturitate quarta, extorum accingimur examini. </s>

<s>Summa consilii fuit.... toto <lb/>studio in thoracem incumbere.... Observo surculos Cavae: omnes livebant. </s>

<s><lb/>Nullus ascendentium arteriarum ramus ad lactea foramina, quae recens in&shy;<lb/>veneram, emicabat. </s>

<s>Sexti paris sequor propagines, quarum hae diaphragmatis <lb/>obice sistebantur, illas imus venter absorbebat. </s>

<s>Tandem exerto in suprema <lb/>vertebrarum dorsi latera contuitu, nescio quid albedinis, instar chylosi cana&shy;<lb/>liculi, oculos meos moratur. </s>

<s>Sinuoso aliquantisper et ad spinam impacto ser&shy;<lb/>pebat volumine. </s>

<s>Dubium an, ex similitudine, nervus, an foret vasculum, <lb/>quale sollicitus vestigabam. </s>

<s>Ergo subducto paulo infra claviculas vinculo, cum <lb/>a ligatura sursum flaccesceret, superstite deorsum turgentis alveoli tumore, <lb/>dubium meum penitus enervavit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; ..... Num chyli ductus quispiam aut ad caput exiliret, aut ad artus <lb/>derivaretur anteriores, eorumdem incumbit scrutandum hortamine. </s>

<s>Sed cum <lb/>amputatum caput, truncatosque artus nihil lactis, ne compressu quidem in&shy;<lb/>ferioris alvi sequeretur, ex illa quae se receperat intra Cavam chylosae sub&shy;<lb/>stantiae copia, argumentor neque ad caput, neque ad anteriores artus diver&shy;<lb/>tere chylum, sed totum in ramos subclavios confluere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; ..... Redeo ad vincula..... Quarta vertebra coeuntes sustentabat, <lb/>reliquum ad decimam spatium bifidos anfractibus disiunxerat, fluvialium <lb/>more, tortuosis. </s>

<s>Pari tumore diffluebant transversis non raro incilibus, ve&shy;<lb/>lut ad opem mutuam, oblique colligati. </s>

<s>Confuso demum vado, rursusque <lb/>distracto flumine, in ampullatos alveos sensim excrescentes, ad diaphragmatis <lb/>centrum intumuerant, non leve vicinorum, unde per thoracem in subclavias <lb/>venas immittitur chylus, fontium argumentum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ergo, cum et ipsum diaphragma, ut extremo quod sperabam desine-<pb xlink:href="020/01/1346.jpg" pagenum="221"/>ret obesse scrutinio, satagerem a lacteis vasis seiungere, lacerata forte sini&shy;<lb/>strorsum, ad duodecimam circiter dorsi vertebram, ampulla, cuius est apprime <lb/>tenuis membranula, restagnantem demiratus lactis effusi copiam, suspicor <lb/>non exiguum illic eiusdem liquoris occuli <emph type="italics"/>Receptaculum.<emph.end type="italics"/> Sed manus im&shy;<lb/>prudentia stitit laborem et reliquum ad resegmina cadaver amandavit .... &rdquo; </s></p><p type="main">

<s>&ldquo; Commodum ad cibum canis, quem pransum opipare, post horas ali&shy;<lb/>quot, in anatomicum edo Theatrum..... Lacteos mesenterii rivulos quaqua&shy;<lb/>versum exploravi, nullus ad iecur porrigi inventus est. </s>

<s>Portam diffidi, sple&shy;<lb/>nicum aperui meatum, nec ipsi mesenterio peperci .... et omni ex parte <lb/>cruor effusus est, nulla chyli scaturigo male creditam viam dealbavit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; ..... Tantis testimoniis enucleata veritate, <emph type="italics"/>non ad hepar videlicet <lb/>chylum, non ad venas Portae, non ad Cavam prope emulgentes derivari,<emph.end type="italics"/><lb/>lustrata viscera quarendus alibi chylus .... praecepit. </s>

<s>Tum frustatim ad cau&shy;<lb/>telam revulso diaphragmate, licuit residuum, qui sub eius apophysibus de&shy;<lb/>litescebat, Aortae truncum et nostras in propatulo lacteas contueri. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Hac sinistrorsum pariter sub Aorta .... ampullescentem alveum expli&shy;<lb/>cabant.... Illic, res mira! gravitanti digito facile stratum seipsum ultro com&shy;<lb/>planabat, arguente subsultim mollitie delitescentem sub mesenterico centro, <lb/>non exiguae capacitatis chyli vesicam. </s>

<s>Demum celantia, parcente scalpello, <lb/>dissipo involucra.... Sic tandem patuit optatissimum reconditi chyli penus, <lb/>et tantis laboribus quaesitum <emph type="italics"/>Receptaculum. </s>

<s>&rdquo;<emph.end type="italics"/><lb/>&hellip; </s></p><p type="main">

<s>&ldquo; Ita, mi lector, habes exactam Lactearum venarum historiam. </s>

<s>Intra <lb/>triplicis dissectionis spatium assiduum semel trium annorum (dal 1648 <lb/>al 1651, anno, sui principii del quale fu per la prima volta pubblicata in <lb/>Parigi questa stessa storia) laborem coarctavi, quia tantilli temporis dispen&shy;<lb/>dio potes ab erroribus desciscere. </s>

<s>Trinum tibi ut expono canicidium dabit, <lb/>quod mihi centena plusquam vivarum animantium exenteratione, vix tandem <lb/>concessum est. </s>

<s>&rdquo; (Experimenta nova anat., Parisiis 1654, pag. </s>

<s>4-17). </s></p><p type="main">

<s>L'anno dopo ch'era stata in Parigi divulgata la nuova storia, comparve <lb/>in Leyda, dalla tipografia di Francesco Hack, un libretto di 36 pagine in 4&deg;, <lb/>intitolato <emph type="italics"/>Novus ductus chyliferus, nunc primum delineatus.<emph.end type="italics"/> L'Autore era <lb/>Giovanni Van-Horne che, rivolgendosi ai Provveditori della leidese Accade&shy;<lb/>mia, diceva di aver, per quella sua scoperta, tratto dagli stessi penetrali della <lb/>natura <emph type="italics"/>novam et inauditam doctrinam.<emph.end type="italics"/></s></p><p type="main">

<s>&Egrave; il trattatello, dopo una breve prefazione, diviso in due parti: nella <lb/>prima, storica e anatomica, e nella seconda, dottrinale e fisiologica. </s>

<s>Narra, <lb/>quanto alla storia, come ne'primi mesi dell'anno 1652 gli occorresse a caso <lb/>di sezionare un cane, e come, sollevando verso il rene sinistro, sopra le ap&shy;<lb/>pendici del diaframma, la duplicatura del peritoneo, che separa i reni, la <lb/>vena cava e l'aorta dalle altre viscere dell'addome; gli venissero veduti al&shy;<lb/>cuni tenuissimi vasi membranosi, dai quali rotti fluiva il chilo. </s>

<s>&ldquo; Haec prima <lb/>fuit novi inventi occasio &rdquo; imperocch&egrave; nessuno aveva trovato cos&igrave; fatti vasi <lb/>bianchi altro che nel mesenterio. </s>

<s>&mdash; Ma che sieno davvero vene lattee? </s>

<s>&mdash; <pb xlink:href="020/01/1347.jpg" pagenum="222"/>cominci&ograve; a dubitare il Van-Horne, e se ne assicur&ograve; dal veder che comuni&shy;<lb/>cavano direttamente col Pancreas leggermente premuto. </s>

<s>Gli venne allora de&shy;<lb/>siderio d'investigar le segrete vie di quella comunicazione, e da principio <lb/>non gli riusciva trovarle. </s>

<s>&ldquo; Tandem audacior factus, ipsum quoque dia&shy;<lb/>phragma discindere aggressus sum, sopra quod, intra thoracis cavitatem, <lb/>apparuit <emph type="italics"/>vas aliquod lacte turgidum &rdquo;<emph.end type="italics"/> (pag. </s>

<s>14). </s></p><p type="main">

<s>Strinto questo vaso per via di un filo, permise l'intumescenza di po&shy;<lb/>terne pi&ugrave; facilmente seguitar, ne'canali inferiori, il decorso, e trov&ograve; che <lb/>questo terminava negli intestini. </s>

<s>Ci&ograve; valse a confermarlo meglio nella prima <lb/>opinione che appartenessero veramente que'vasi alle vene lattee falsamente <lb/>credute dall'Asellio convenire nel Pancreas, e di li, senza progredire pi&ugrave; <lb/>oltre, andare al Fegato, da cui invece escono, per diramarsi in varii mod&igrave;. </s>

<s><lb/>Di alcuni di questi rami seguendo diligentemente il progresso, trov&ograve; che <lb/>dopo molti giri andavano a riunirsi in un tronco, della grandezza di una <lb/>penna da scrivere, il quale, trapassato sopra le vertebre lombari il diaframma, <lb/>penetra nella cavit&agrave; del torace, e l&igrave;, nello spazio che resta di mezzo fra la <lb/>colonna vertebrale e l'Aorta, incomincia a salire. </s>

<s>&ldquo; Ascendit itaque ductus <lb/>hic, uti dictum est, per thoracis longitudinem, sensim tenuior evadens, atque <lb/>ubi cor superavit, quo loco alius observatus fuit ramus versus cor tendens, <lb/>non amplius aortae accumbit, sed oesophago incumbens, ad axillares usque <lb/>ramos pertingit, quantum primo intuitu licet cognoscere. </s>

<s>Sed vero diligen&shy;<lb/>tius inquirenti manifestum evadet ad iugularem internam sinistri lateris de&shy;<lb/>ferri, praecipuo suo ramo inseri sub thymo glandula, in illam Venae cavae <lb/>partem, quae claviculis subiaciens, in homine ab illis subclavia denomina&shy;<lb/>tur &rdquo; (pag. </s>

<s>16, 17). </s></p><p type="main">

<s>Nella seconda parte del trattatello, intitolata <emph type="italics"/>Ductus officium,<emph.end type="italics"/> dimostra <lb/>essere un tale ufficio quello di condurre il chilo a riversarsi nel sangue. </s>

<s>Di <lb/>qui, presa occasione di notar l'errore, in ch'erano caduti gli antichi, ne con&shy;<lb/>clude non solo non andare al Fegato nessuna porzione dell'alimento, ma <lb/>esser questo affatto impossibile, per trovar d'ogni parte d'andare al Fegato, <lb/>il chilo chiuse le vie. </s></p><p type="main">

<s>Era questa la nuova, e inaudita dottrina <emph type="italics"/>ex ipsis Naturae penetrali&shy;<lb/>bus eruta,<emph.end type="italics"/> che veniva dal Van-Horne a'suoi Accademici, solennemente, per <lb/>la prima volta, annunziata, e si credeva che dovesse come a loro cos&igrave; a tutto <lb/>il mondo veramente apparir cosa nuova e inaudita, quando giunse a Enrico <lb/>Born, professore di Leyda, una lettera da Parigi, nella quale si diceva ma&shy;<lb/>ravigliarsi che il Van-Horne avesse data per nuova la scoperta del dutto <lb/>chilifero, che da due anni in Francia si sapeva da tutti: si consigliava <lb/>l'Horne stesso a fare la sua pubblica ritrattazione, se non voleva essere in&shy;<lb/>criminato di plagio, e si concludeva al Born stesso raccomandandogli &ldquo; ut <lb/>virum doctissimum caute officii sui admoneret &rdquo; (In Pecqueti Experim. </s>

<s><lb/>anat. </s>

<s>cit., pag. </s>

<s>180). </s></p><p type="main">

<s>L'Horne, uomo retto, non volle entrare in questioni, e dall'altra parte <lb/>davan vinta al Pecquet la causa del primato i numer&igrave;, colla irresistibile <pb xlink:href="020/01/1348.jpg" pagenum="223"/>forza della loro fredda eloquenza. </s>

<s>Nel &sect; 37 del <emph type="italics"/>Microcosmo<emph.end type="italics"/> infatti, senza <lb/>fare il minimo accenno agli inventori e alle loro controversie, dice esser uf&shy;<lb/>ficio delle vene lattee &ldquo; ut chyli laudabilior portio per illas quidem defera&shy;<lb/>tur, porro in <emph type="italics"/>Receptaculum,<emph.end type="italics"/> et hinc ascendendo, per ductum chyliferum &rdquo; <lb/>(Lugd. </s>

<s>Batav. </s>

<s>1655, pag. </s>

<s>54). </s></p><p type="main">

<s>Gli Olandesi per&ograve; stettero fermi in riconoscer per loro premostratore <lb/>del Canale toracico il Professore leidese, e fu tra quelli uno de'pi&ugrave; zelanti <lb/>quel Gerardo Blasio, che facendo notare nel commentario al Veslingio come <lb/>il chilo non va al pancreas, n&egrave; al fegato, secondo diceva il suo Autore con <lb/>l'Asellio, ma a un certo ricettacolo nuovamente scoperto; &ldquo; Hac de re, sog&shy;<lb/>giunge, consule primum eius, hisce in oris, inventorem in canibus, Johannem <lb/>Van-Horne, anatomicum leidensem exercitatissimum &rdquo; (Editio cit., pag. </s>

<s>53). </s></p><p type="main">

<s>Fra gli estranei varii furono del caso singolare i giudizii, ma richiama <lb/>a s&egrave; particolarmente la nostra attenzione ci&ograve; che scrive in proposito, nel suo <lb/>primo libro <emph type="italics"/>De homine,<emph.end type="italics"/> il padre Onorato Fabry. </s>

<s>&ldquo; Forte alter, egli dice del <lb/>Pecquet e del Van-Horns, ab altero accepit, forte uterque legitimus inven&shy;<lb/>tor, sed hanc litem non definio. </s>

<s>Utut sit, modica locorum distantia, cursores <lb/>publici, qui singulis hebdomadis ultro citroque commeant, librariorum com&shy;<lb/>mercium, novi inventi publica fama, aemula eiusdem artis professorum cu&shy;<lb/>riositas, et alias huiusmodi aliquam plagii suspicionem movere possent, sed <lb/>neminem iudico &rdquo; (Parisiis 1666, pag. </s>

<s>216). </s></p><p type="main">

<s>Par che sia in queste parole espressa una conoscenza delle cose del <lb/>mondo, che si direbbe troppo maliziosa, ma chi penetrasse in quel cervel&shy;<lb/>laccio, anche pi&ugrave; addentro, vi troverebbe ascosto un senso di dispetto, per <lb/>aver trovato un altro, ch'era entrato col Pecquet a roder quell'osso. </s>

<s>Altri&shy;<lb/>menti il padre Onorato si sarebbe aperto, coi denti e colla lingua, un varco <lb/>da entrar l&agrave;, dove s'era il Van-Horne fatto largo, esercitandovi la mano ana&shy;<lb/>tomica e il ferro. </s>

<s>Danno saldo fondamento a sospettar cos&igrave; alcuni altri fatti, <lb/>fra'quali, per non uscir dal presente soggetto, ch'&egrave; intorno a cose anato&shy;<lb/>miche e fisiologiche, basti addur questi due. </s></p><p type="main">

<s>Nella proposizione II del citato libro <emph type="italics"/>De homine,<emph.end type="italics"/> dove spiega la circo&shy;<lb/>lazion del sangue, dop'aver commemorato l'Harvey e il Cartesio e il Pecquet, <lb/>che ne illustrarono la scoperta, &ldquo; Ego verissimam esse, prosegue, semper <lb/>putavi, eamque, antequam libellus Harvei prodiret, publice docui, iam ab <lb/>anno 1638, qui certe longo post tempore in meas manus venit, quod ad <lb/>ostentationem non dico &rdquo; (ibid., pag. </s>

<s>204). Ma, con buona pace, &egrave; questa <lb/>una vera ostentazione o di gran malizia o di grande ignoranza, essendoch&egrave; <lb/>nel 1638 il libro dell'Harvey era, da ben dieci anni, per le mani di tutti. </s></p><p type="main">

<s>Nella proposizione XVII spiega la secrezione del sangue ne'reni, e dopo <lb/>aver ripetute, intorno alla struttura e alle funzioni di quelle glandule, le <lb/>nuove cose scoperte, e infin dal 1662 divulgate nella esercitazione anato&shy;<lb/>mica <emph type="italics"/>De structura et usu renium<emph.end type="italics"/> da Lorenzo Bellini, &ldquo; Haec iam, dice il <lb/>Fabry, a multis annis scripseram, cum forte incidi in elegantissum opuscu&shy;<lb/>lum a Laurentio Bellino florentino in publicam lucem datum, dignum sane <pb xlink:href="020/01/1349.jpg" pagenum="224"/>quod a Philosophis et Medicis legatur, in quo eadem fere quae supra repe&shy;<lb/>ries &rdquo; (ibid., pag. </s>

<s>237). </s></p><p type="main">

<s>E giacch&egrave; questo Gesuita francese, dimorante a Roma, &egrave; quasi fatto da <lb/>alcuni Accademico del Cimento, e in ogni modo &egrave; come attore entrato nella <lb/>altre parti della nostra Storia, diremo qui tutto insieme quel poco, che anche <lb/>per questa parte lo riguarda, imitando colui, che fa tutt'in una volta i conti <lb/>di saldo con certi creditori, o troppo importuni, o troppo esigenti. </s></p><p type="main">

<s>Il trattato <emph type="italics"/>De homine,<emph.end type="italics"/> che abbiamo dianzi citato, &egrave; il secondo dopo un <lb/>altro, che ha per soggetto le piante e la generazione degli animali. </s>

<s>I nostri <lb/>Lettori hanno oramai, per questi e per gli altri esempi da noi recati ne'pre&shy;<lb/>cedenti due Tomi, riconosciuta l'indole del Gesuita straniero corrispondente <lb/>coi nostri Accademici fiorentini, la quale era di sfiorare ogni loro scoperta, <lb/>per adornarsene, e apparire in pubblico il primo. </s>

<s>Aveva da Michelangiolo <lb/>Ricci inteso come il Borelli attendeva in Pisa a instituire la sua nuova Fi&shy;<lb/>losofia degli animali e delle piante, e come il principe Leopoldo ve lo ecci&shy;<lb/>tava con grande ardore, ben conoscendo quanto, da un tant'uomo e in s&igrave; <lb/>importante e nuovo soggetto, sarebbe per venir gloria agli studii toscani, e <lb/>benefizio universale alla scienza. </s></p><p type="main">

<s>Il Fabry dunque, per prevenir l'opera, colla facilit&agrave; di chi, a volere sve&shy;<lb/>lare i pi&ugrave; reconditi misteri della Natura, non ha a far altro che consultare <lb/>il proprio cervello, dette mano a scrivere i due trattati, e a farli da Fran&shy;<lb/>cesco Muguet frettolosamente imprimere in Parigi. </s>

<s>Il Ricci dava a Firenze <lb/>notizie della stampa, e come uno de'libri del II trattato avesse per soggetto <lb/>particolare il moto degli animali. </s>

<s>Si pu&ograve; immaginar quanto ci&ograve; dovesse fru&shy;<lb/>gare la curiosit&agrave; del Borelli, per soddisfare alla quale il principe Leopoldo, <lb/>anch'egli divenuto di ci&ograve; curioso, scrisse al Bigot a Parigi, il d&igrave; 18 Giu&shy;<lb/>gno 1666, che desiderando di averlo, gli mandasse il libro, col&agrave; stampato, <lb/>del p. </s>

<s>Fabry (MSS. Cim., T. XXIII, c. </s>

<s>133). Ma poco dopo venne a offrir&shy;<lb/>glielo in dono lo stesso Autore, di che il Principe lo ringrazi&ograve;, per lettera <lb/>del d&igrave; 19 Ottobre di quel medesimo anno (ivi, c. </s>

<s>141), e data una scorsa, <lb/>sped&igrave; al Borelli a Pisa la copia. </s>

<s>Il Borelli, il d&igrave; 19 Dicembre, cos&igrave; rispon&shy;<lb/>deva: &ldquo; Subito che ricevetti l'onore fattomi da V. A. del libro del p. </s>

<s>Fabri, <lb/>mi posi con grandissima avidit&agrave; a leggerlo, e primieramente vidi tutto quello, <lb/>che egli scrive intorno ai movimenti degli animali, dove non vi trovai altre <lb/>cose che le comuni e dozzinali, tolto che alcune sue osservazioni sopra lo <lb/>starnuto e la tosse &rdquo; (ivi, T. XVIII, c. </s>

<s>368). Avremo dato dunque al Fabry, <lb/>in questo saldo finale, quella parte del merito che gli compete, salutandolo <lb/>Fisiologo dello starnuto e della tosse, di che, non richiedendovisi tanta ana&shy;<lb/>tomia, si fece pi&ugrave; facilmente credere autore, che non del Canale toracico, da <lb/>lui perci&ograve; lasciato alle libere contenzioni fra il Pecquet e il Van-Horne. </s></p><p type="main">

<s>Come i fatti decidevano dunque a favore del Pecquet, primo a intra&shy;<lb/>prendere le esercitazioni anatomiche, e primo a pubblicare la scoperta indi <lb/>seguitane; cos&igrave;, a favore del Pecquet, ha deciso oramai il giudizio dei po&shy;<lb/>steri. </s>

<s>Ma sarebbe una calunnia l'accusare il. </s>

<s>Van-Horne di plagio, come fu <pb xlink:href="020/01/1350.jpg" pagenum="225"/>una tirannia quella del Pecquet, che lo voleva costringere a una ritratta&shy;<lb/>zione. </s>

<s>Chi legge la scoperta del Nuovo dutto chilifero, e la confronta con <lb/>quella descritta negli Esperimenti nuovi anatomici, sente che ambedue le <lb/>storie sono ugualmente originali, e i loro incontri inconsapevoli, e no studiati. </s></p><p type="main">

<s>Che poi l'uno Anatomico non si sia vestito dell'abito dell'altro, si con&shy;<lb/>clude dal veder che ognuno porta quello, ch'&egrave; tagliato bene al suo dosso. </s>

<s><lb/>Il Pecquet &egrave; pi&ugrave; giovane e pi&ugrave; poeta; il Van-Horne &egrave; pi&ugrave; positivo. </s>

<s>Chi <lb/>getta lo sguardo, ora sull'una ora sull'altra delle due tavole, dove ciascuno <lb/>Autore esibisce in disegno le cose vedute por l'aperte viscere dell'animale, <lb/>non ha, a persuadersene, bisogno d'altre parole. </s>

<s>Nel Pecquet, per esempio, <lb/>il Canal toracico &egrave; doppio, e i due rami comunicano, lungo il loro decorso, <lb/>per frequenti anastomosi, finch&egrave; uno non va a terminare nella giugulare de&shy;<lb/>stra, e l'altro nella sinistra. </s>

<s>Nel Van-Horne il dutto chilifero &egrave; semplice e <lb/>schietto, e sbocca nella giugulare sinistra. </s></p><p type="main">

<s>I fautori del Pecquet dissero che sezionando s'era incontrato a caso a <lb/>veder nel cane quell'anomalia, e ci&ograve; si potrebbe credere se si trattasse di <lb/>un esempio solo. </s>

<s>Ma perch&egrave; il Pecquet ebbe a trucidare un gran numero <lb/>di cani, &egrave; egli credibile ostentassero tutti quel fatto anomalo, che il Masca&shy;<lb/>gni quasi si doleva non essergli mai toccato a vedere in tanti cadaveri se&shy;<lb/>zionati di uomini e di bruti? </s></p><p type="main">

<s>Pi&ugrave; ragionevole perci&ograve; &egrave; il dire che, dove sfugge al Pecquet la vista, <lb/>soccorre pronta a supplirvi la fantasia, ond'il Van-Horne, che seppe aste&shy;<lb/>nersi da quel vizio, riesce tanto pi&ugrave; preciso e pi&ugrave; vero. </s>

<s>Si direbbe che giov&ograve; <lb/>a una tal precisione l'essere prevenuto, se non si riconoscesse piuttosto come <lb/>il portato dell'esercizio, e se non ci persuadesse l'Anatomico olandese, col <lb/>suo discorso, che cos&igrave; a lui come al Pecquet sufficiente preparazione era la <lb/>scoperta dell'Asellio. </s></p><p type="main">

<s>Ebbe di qui origine quel sentimento di riconoscenza e di ammirazione, <lb/>che spira verso il nostro Italiano dalle pagine de'due celebri Notomisti stra&shy;<lb/>nieri, i quali se lo proposero per imitabile esempio di scienza non solo, ma <lb/>di morale. </s>

<s>Il Pecquet, dop'avere annoverate le varie specie di animali, nei <lb/>quali tutti ritrov&ograve; il ricettacolo del chilo, &ldquo; homines non dixi, soggiunge <lb/>tosto, quia thoanteos ritus execror, mitioribus sacris innutritus.... Fugienda <lb/>est medicina, quam docet crudelitas, et abominanda sapientia, quam parit <lb/>homicidium &rdquo; (Experimenta nova anat. </s>

<s>cit., pag. </s>

<s>18). Si contenta perci&ograve; di <lb/>creder per analogia l'esistenza del Canale toracico nell'uomo, imitando anche <lb/>in questi particolari il modo di argomentar dell'Asellio, bench&egrave; citi l'autopsia <lb/>del Peiresc, e dalla notizia che soggiunge paresse esser consigliato ad imi&shy;<lb/>tarla: &ldquo; Huic et interfuit Gassendus spectaculo, quod ipse pridem mihi, dum <lb/>Parisiis degeret, viva voce confirmavit &rdquo; (ibi). </s></p><p type="main">

<s>Il Van-Horne poi &egrave; dell'Asellio imitatore anche pi&ugrave; espresso. </s>

<s>&ldquo; At hic <lb/>non levis exoritur de homine dubitatio, num similiter in illo existat &rdquo; dice <lb/>dopo aver descritto il dutto chilifero di un cane. </s>

<s>&rdquo; Equidem hac in parte <lb/>idem fatum experietur Ductus hic cum lacteis Asellii, quas cum in homine <pb xlink:href="020/01/1351.jpg" pagenum="226"/>non viderit idem, quia nefas existimavit vivum hominem incidere, necessa&shy;<lb/>ria tamen sequela intulit fieri vix posse ut unus et solus homo iis desti&shy;<lb/>tuatur, quae in tot brutis, ob similem necessitatem, reperiuntur &rdquo; (Novus <lb/>ductus delineatus cit, pag. </s>

<s>17, 18). Bench&egrave;, prosegue a dire l'Autore, dan&shy;<lb/>dosi l'opportunit&agrave; di avere a sezionare il cadavere di un uomo, morto di <lb/>morte subitanea nel levarsi da mensa, sarebbe men difficile osservar questo <lb/>Dutto, che le vene aselliane. </s>

<s>&ldquo; Et siquidem ullo unquam tempore eiusmodi <lb/>contigerit subiectum, quo omnis hac de re lis terminetur, nostrae non deeri&shy;<lb/>mus diligentiae &rdquo; (ibi). </s></p><p type="main">

<s>Ma fu prevenuto dalla sollecitudine di Tommaso Bartholin, il quale, <lb/>avendo avuto da suo fratello Erasmo notizia della scoperta pecqueziana, e <lb/>datosi con Michele Lyser suo amicissimo a verificarla, s'avvide che le con&shy;<lb/>trazioni spasmodiche dell'animale inciso vivo erano quelle, che facevano spa&shy;<lb/>rire i vasi chiliferi pi&ugrave; presto. </s>

<s>Pensava perci&ograve; che pi&ugrave; opportuni all'estispicio <lb/>dovessero essere gli animali strangolati, fra'quali anche l'uomo. </s>

<s>&ldquo; Meditato <lb/>consilio, scrisse nel trattato <emph type="italics"/>De lacteis thoracicis,<emph.end type="italics"/> pubblicato la prima volta <lb/>nel 1652, optatus eventus adspiravit, plurimisque in canibus factis experi&shy;<lb/>mentis, humano tandem cadavere ex voto publico, serenissimo rege Fride&shy;<lb/>rico III annuente, rotae alioquin et perpetuae cruci adiudicato, beneque pasto, <lb/>nacti in singula accuratius tam in publico theatro anatomico solemni de&shy;<lb/>monstratione, quam privata opera, tanto maiori studio inquisivimus, quod <lb/>primi haec in homine tentaverimus &rdquo; (In Mangeti Bibliotheca anat. </s>

<s>cit., T. II, <lb/>pag. </s>

<s>660). Soggiunge che fu fatta l'autopsia in due cadaveri, il primo di un <lb/>infanticida scorbutico e macilento, l'altro di un ladro obeso, ben fatto e di <lb/>perfetta salute. </s></p><p type="main">

<s>Fu tratto il primo, narra pi&ugrave; particolarmente lo stesso Bartholin nella <lb/>storia LIII della I Centuria, nel Teatro anatomico il d&igrave; 19 Febbraio del&shy;<lb/>l'anno 1652, dove essendosi prima diligentemente esaminate le altre viscere, <lb/>quanto al ricettacolo del chilo cos&igrave; dice: &ldquo; Reclinatis ad latus intestinis, vidi <lb/>novum receptaculum lacteum in suo situ, ipsis vertebris lumbaribus instra&shy;<lb/>tum, inter Cavam descendentem et Aortam, in angulo fere, quem emulgens <lb/>dexter cum Cava efformat. </s>

<s>Candidum illud exque eo rami lactei ad mesen&shy;<lb/>terium et pancreas eius derivari. </s>

<s>Ablatis prorsus intestinis, et Cava ad su&shy;<lb/>periora reclinata, et Aorta quoque ad latus nonnihil diducta, apparuit re&shy;<lb/>ceptaculum non unum, nec una cavitate praeditum, sicut in brutis, sed ex <lb/>glandulis duabus longioribus, invicem superpositis, variisque lacteis surculis <lb/>commeantibus ultro citroque &rdquo; (Historiarum anat. </s>

<s>rariorum Cent. </s>

<s>I, Amste&shy;<lb/>lodami 1654, pag. </s>

<s>80). </s></p><p type="main">

<s>Fu dell'altro cadavere fatta nel Teatro anatomico l'autopsia il d&igrave; 24 Marzo <lb/>di quel medesimo anno, e aperta l'ascellare, narra il Bartholin nell'appresso <lb/>storia LIV, &ldquo; vidimus osculum eius unicum sub internae iugularis ingres&shy;<lb/>sum, et valvulam circularem tenerrimam osculo praefixam, quae, pro vario <lb/>flatus impulsu, modo elevabatur, modo concidebat. </s>

<s>Reliqua, quae de lacteis <lb/>thoracicis primi in homine observavimus, operosius in <emph type="italics"/>Historia<emph.end type="italics"/> nostra <emph type="italics"/>ana-<emph.end type="italics"/><pb xlink:href="020/01/1352.jpg" pagenum="227"/><emph type="italics"/>tomica De lacteis thoracicis,<emph.end type="italics"/> publice diducta, lector curiosus inveniet &rdquo; (ibid., <lb/>pag. </s>

<s>85). </s></p><p type="main">

<s>Era tale il progresso fatto fino al 1652 nella scoperta de'vasi chiliferi <lb/>dopo l'Asellio, quando l'anno appresso comparve in Vuesterat (Arosiae) un <lb/>libretto in 4&deg; di Olao Rudbeck, intitolato <emph type="italics"/>Nova exercitatio anatomica, exhi&shy;<lb/>bens ductus hepaticos aquosos.<emph.end type="italics"/> Nel cap. </s>

<s>III, dopo avere osservato che il <lb/>Veslingio e l'Igmoro, persuasi della verit&agrave; degli antichi insegnamenti gale&shy;<lb/>nici intorno alle funzioni epaietiche, s'erano ingannati descrivendo per vasi <lb/>chiliferi diretti al Fegato quelli che forse non erano altro che nervi; &ldquo; anxie&shy;<lb/>tas haec, soggiunge l'Autore, quae iamdiu multos tenuerat, discussa est anno <lb/>millesimo sexcentesimo quinquagesimo dum, nescio quo casu, vituli macta&shy;<lb/>tionem inspicere contingebat.... ut aperto thorace motum cordis, post eva&shy;<lb/>cuatum sanguinem, pernoscerem &rdquo; (In Mangeti Bibliotheca anat., cit., pag. </s>

<s>702). </s></p><p type="main">

<s>Vede fluire dalla vena giugulare un succo simile al siero del latte!... <lb/>Gli entra allora una gran curiosit&agrave; di sapere d'onde avesse origine, e com&shy;<lb/>prato dal beccaio il vitello, e fattoselo portare a casa, trov&ograve; il canale che <lb/>conduceva quel siero, ma per essere lacerate l'interiora, non ne pot&egrave; rin&shy;<lb/>tracciar la radice. </s></p><p type="main">

<s>Per quell'anno, distratto da altre cure, non pot&egrave; attendere a fare ana&shy;<lb/>tomie. </s>

<s>L'anno seguente preso un gatto, dopo cinque ore ch'era stato pa&shy;<lb/>sciuto, gli apr&igrave; il ventre, e perch&egrave; il chilo non si dissipasse cos&igrave; tosto, allacci&ograve; <lb/>le vene lattee in due luoghi: sopra il pancreas, e l&agrave; dove il mesenterio si <lb/>collega col dorso. </s>

<s>Sezionato poi il torace, e tolto lo sterno, rivide quel me&shy;<lb/>desimo canale, l'anno avanti scoperto nel vitello, e lo allacci&ograve; in quel punto, <lb/>che risponde sotto il cuore. </s>

<s>Sciolti poi i due detti legami intorno alle lat&shy;<lb/>tee, &ldquo; tunc chylus aliquibus ramulis, sive venulis contentus, Vesiculam quan&shy;<lb/>dam inter diaphragma et renes, sub vena cava et arteria aorta sitam, patuit <lb/>unde tumescebat &rdquo; (ibid., pag. </s>

<s>703). </s></p><p type="main">

<s>Quella Vessica &egrave; il ricettacolo del Pecquet, da Olao cos&igrave; felicemente <lb/>scoperto. </s>

<s>Rimaneva a verificare se da quella stessa vessica e dal canale an&shy;<lb/>nesso, che ricevono il chilo dal mesenterio, derivasse quell'umor latteo ve&shy;<lb/>duto la prima volta fluire dalle giugulari del macellato vitello. </s>

<s>Lega a tale <lb/>intento le vene ascellari insieme e le giugulari, e aperto il destro ventricolo <lb/>del cuore spreme col dito da que'vasi sotto la legatura il sangue. </s>

<s>Rimasti <lb/>cos&igrave; esausti, scioglie il filo, con che il canale chilifero era stato allacciato, <lb/>&ldquo; et chylus citissime axillarem ad coniunctionem eius cum iugulari ingre&shy;<lb/>diebatur &rdquo; (ibid.). Non rimaneva all'ultimo da verificare se non se il chilo, <lb/>dalla giugulare, scendesse per la Cava add&igrave;ritto nel cuore, ci&ograve; che fu dimo&shy;<lb/>strato in quel medesimo istante, imperocch&egrave; vedevasi, attraverso all'apertura, <lb/>il sinistro ventricolo rimaner sotto quel profluvio di chilo tutto imbiancato. <lb/></s>

<s>&ldquo; Tandem per Cavam superius resistentibus valvulis descendens, dextrum <lb/>cordis ventriculum dealbavit &rdquo; (ibid.). </s></p><p type="main">

<s>La vessicola chilosa fu dallo Svedese inventore dimostrata in pubblico <lb/>nell'Aprile del medesimo anno 1652, alla presenza della Maest&agrave; di quella <pb xlink:href="020/01/1353.jpg" pagenum="228"/>vergine Cristina, a cui dedicava il nostro Borelli, poco prima di morire, la <lb/>grande opera dei Moti animali. </s>

<s>Ma cost&igrave;, mentre Olao faceva le sue pubbli&shy;<lb/>che dimostrazioni, i regii medici gli sussurrano nelle crecchie esser venuto <lb/>il Pecquet stesso a Stockolm a divulgare le sue esperienze, e il Tonson li&shy;<lb/>braio aver venali, nella sua bottega, il libretto del Nuovo dutto chilifero del <lb/>Van-Horne, e il trattato Delle lattee del Torace, dove Tommaso Bartholin <lb/>attesta di aver veduta la vescicola del chilo anche nell'uomo. </s>

<s>Ma Olao, che <lb/>pi&ugrave; della sua gloria amava la scoperta del Vero, vuol dir dunque, rispose <lb/>tranquillamente a que'medici, che dalla concorde testimonianza di tanti scrit&shy;<lb/>tori verr&agrave; meglio confermata questa importantissima verit&agrave;: &ldquo; Hepar non <lb/>esse primarium sanguificationis organum &rdquo; (ibid.). </s></p><p type="main">

<s>Quel fortuito incontro de'tre inventori separati fra loro qua da monti <lb/>e l&agrave; da mari, ha senza dubbio qualche cosa di maraviglioso, e poniamo che <lb/>ricevessero tutt'e tre uguale impulso dalla scoperta del nostro Asellio, ri&shy;<lb/>man tuttavia a maravigliare come mai si trovassero tutt'e tre ispirati nel <lb/>medesimo tempo. </s>

<s>Nonostante, per la perizia dell'arte e per l'amore agli <lb/>studii, furono di quella inspirazione tutti ugualmente degni, e la Sapienza, <lb/>nell'eleggerli a sedere al suo convito, non seppe usar quella preferenza, di <lb/>che, scrivendo le loro storie, si resero colpevoli i giudizi degli uomini appar&shy;<lb/>tenenti alle tre varie nazioni. </s></p><p type="main">

<s>Ma se que'tre furono chiamati al convito, non mancarono altri, che vi <lb/>s'intromisero di furto, e sotto vesti mentite, o non proprie d'uomo sapiente. </s>

<s><lb/>Basti di ci&ograve; addurre due esempi, e sia primo quello di Lodovico Bils. </s>

<s>Ba&shy;<lb/>rone di Koppensdam, ebbe il prurito di fare il Notomista, e per non insoz&shy;<lb/>zare il decoro della tunica baronale, avea trovato un balsamo emostatico, <lb/>intantoch&egrave; riuscivano le sue dissezioni incruente. </s>

<s>Fin qui avrebbe potuto <lb/>utilmente giovare, se non in altro, ai comodi dell'arte, ma si fu il male che <lb/>volle riformare a suo modo la scienza. </s>

<s>Il chilo, che da tutti si credeva esser <lb/>per le vene lattee del mesenterio e del torace riversato nel ricettacolo pecque&shy;<lb/>ziano, ei lo chiama <emph type="italics"/>rugiada,<emph.end type="italics"/> e vuol che, attinto questo rugiadoso umore agli <lb/>intestini, confluisca nel <emph type="italics"/>Dutto rorifero,<emph.end type="italics"/> che per lui si divide in due rami, <lb/>uno de'quali va alla glandula affissa alla Vena porta, l'altro al ricettacolo <lb/>glanduloso del mesenterio. </s>

<s>Insorsero contro una tale scempiataggine il Van&shy;<lb/>Horne e Paolo Barbette, ai quali il Bils rispose, o per meglio dire, essendo <lb/>illitterato, fece rispondere una scrittura pubblicata in Rotterdam nel 1661. </s></p><p type="main">

<s>Par che tutto il nervo delle sue ragioni e tutta l'arte della difesa la <lb/>faccia consistere nel notar la differenza, che passa fra il suo Dutto rorifero <lb/>e il chilifero del Van-Horne, per concluderne poi, da un tal confronto, quanto <lb/>egli fosse pi&ugrave; veridico interpetre della Natura. </s>

<s>A una tavola perci&ograve;, che esi&shy;<lb/>bisce il disegno del dutto bilsiano, fa seguirne un'altra, ch'esibisce il dise&shy;<lb/>gno del dutto horniano, &ldquo; unde videre licet magnam differentiam, quae in&shy;<lb/>tercedit inter huius chyliferum et roriferum nobilissimi D. D. </s>

<s>Ludovici de <lb/>Bils &rdquo; (Responsio ad admonitiones J. ab Horne etc., Roterodami 1661, pag. </s>

<s>11). </s></p><p type="main">

<s>L'altro esempio, che si diceva, &egrave; quello di Giovanni Finck, venuto d'In-<pb xlink:href="020/01/1354.jpg" pagenum="229"/>ghilterra a insegnare anatomia nello studio di Pisa, il quale inglese dimo&shy;<lb/>str&ograve; alla presenza del Granduca, facendola credere una sua nuova scoperta, <lb/>come il chilo va per le vene lattee a riversarsi in un dutto; e di l&igrave;, per le <lb/>giugulari e per la Vena cava, nel cuore. </s>

<s>&Egrave; Claudio Beriguardo, come si ve&shy;<lb/>dr&agrave; meglio nell'ultima parte di questo capitolo, che in uno de'suoi Circoli <lb/>pisani ci d&agrave; una tale inaspettata notizia. </s>

<s>Il Targioni che, a pag. </s>

<s>272 del <lb/>I Tomo de'suoi Aggrandimenti delle scienze fisiche in Toscana, cita dal libro <lb/>del Beriguardo il passo, letto senza dubbio nella seconda edizione fatta in <lb/>Padova nel 1661, senza niente sospettar che fosse un'aggiunta alla prima <lb/>edizione del 1643; ne conclude un'altra notizia, che giunge anche pi&ugrave; ina&shy;<lb/>spettata, ed &egrave; che il Finck avesse scoperto il Canale toracico prima di quel&shy;<lb/>l'anno 1643, che vuol dir quando ancora il Pecquet era in Mompellieri sco&shy;<lb/>lare. </s>

<s>La semplicit&agrave; del Targioni &egrave; maggiore di quella di un fanciullo, ed <lb/>essendo la terza volta, che da quella semplicit&agrave; o difetto di critica &egrave; con&shy;<lb/>dotto in errore, intorno a questioni storiche di cos&igrave; facile risoluzione, e di <lb/>tanto grave importanza; non crediamo di esser troppo rigidi a giudicarlo <lb/>immeritevole di ogni scusa. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Dappoich&egrave; Giovanni Pecquet ebbe scoperto che le vene lattee del me&shy;<lb/>senterio non conducono il chilo al Fegato, ma al Ricettacolo e al Canale <lb/>toracico, per riversarlo, mediante la Vena cava, nel ventricolo destro del <lb/>cuore; gli Anatomici incominciarono a dubitare intorno all'essere e all'uso <lb/>di certi vasi, che apparivano della natura stessa de'lattei, e che senza dub&shy;<lb/>bio penetravano addentro al Fegato, e si diramavano nel suo parenchima. </s>

<s><lb/>Il Veslingio aveva trovato cos&igrave; fatti vasi nel feto, e l'Igmoro gli avea dili&shy;<lb/>gentemente descritti. </s>

<s>Olao Rudbeck, che fu de'primi a rivolgere la sagacia <lb/>del proprio ingegno sopra quelle anatomiche descrizioni, perciocch&egrave; non <lb/>erano i nuovi vasi, da que'Notomisti pur cos&igrave; valorosi, esplorati n&egrave; collo <lb/>stilo, n&egrave; per via delle legature o delle insufflazioni, e non davano dall'altra <lb/>parte indizio che vi scorresse dentro alcun umore, pens&ograve; non fossero altro <lb/>che nervi. </s>

<s>&ldquo; Quae autem Veslingius, scrisse nel cap. </s>

<s>III della sua Nuova eser&shy;<lb/>citazione anatomica, in figura foetus dissecti apposuit, et Nathanael Hygmo&shy;<lb/>rus elegantissimis delineamentis illustravit, nervulos fuisse existimo, quippe <lb/>cum illa, nec stylo, nec inflatione, nec ligatura, nec denique motu humoris <lb/>probaverint &rdquo; (In Mangeti Bibliotheca cit., pag. </s>

<s>702). </s></p><p type="main">

<s>Ma frugava pi&ugrave; vivamente che mai la curiosit&agrave; del Rudbeck la seconda <lb/>Tavola dell'Asellio, nella quale son designati colle lettere N. N. due vasi assai <lb/>cospicui, con questa dichiarazione in margine: &ldquo; Progressus Lactearum ex <lb/>pancreate ad Hepar. </s>

<s>&rdquo; Se non son que'due vasi, pensava, immaginari, la <lb/>sentenza del Pecquet non si pu&ograve; tenere assolutamente per vera. </s></p><pb xlink:href="020/01/1355.jpg" pagenum="230"/><p type="main">

<s>A decidere una questione di tanta importanza, un giorno allaccia in&shy;<lb/>sieme la Vena porta e il canal coledoco, e osserva un fatto singolare: i cre&shy;<lb/>duti vasi aselliani si vedevano, tra il Fegato e la legatura, inturgidire, e vo&shy;<lb/>tarsi al di sotto. </s>

<s>Era da ci&ograve; manifesto che non portavano, ma estraevano <lb/>anzi umore dal viscere, e tra per questa ragione, e per trovarli pieni di un <lb/>liquido, non pi&ugrave; bianco e denso come il latte, ma liquido e sciolto come <lb/>l'acqua, si persuase esser quelli vasi di un nuovo genere, differenti da'lat&shy;<lb/>tei dell'Asellio per la strutura e per l'uso. </s>

<s>La scoperta occorse, come narra <lb/>lo stesso Autore, fra il 1650 e il 1651, in mezzo a quelle dissezioni del vi&shy;<lb/>tello e del gatto da noi sopra narrate, e per cui si rivelarono all'Anatomico <lb/>svedese, nel tempo stesso che al Diepeo, il Canal toracico e la vescicola del <lb/>chilo. </s>

<s>&ldquo; Dum anno 1650 et 1651 in venarum lactearum originem et inser&shy;<lb/>tionem inquirendam versabar, iniectaque supra venam Portae cum ductibus <lb/>cholidocis ligatura, non semel apparuere ductus manifeste ab Hepate ad liga&shy;<lb/>turam intumescentes, infra evanescentes, quos venas esse lacteas minime <lb/>sum arbitratus &rdquo; (ibid., pag. </s>

<s>701). Essendo vasi nuovamente scoperti, ci vo&shy;<lb/>leva anche un nome nuovo per designarli, e fu dal Rudbeck scelto quello <lb/>di <emph type="italics"/>Dutti epatico acquosi.<emph.end type="italics"/> &ldquo; Et quidem <emph type="italics"/>Ductuum<emph.end type="italics"/> hepaticorum quum et hu&shy;<lb/>morem ferant ac ducant, et quod illum ab Hepate accipiant, indeque suam <lb/>originem depromant; deinde <emph type="italics"/>aquosorum,<emph.end type="italics"/> quod tali humore ipsorum cavitas <lb/>infarta sit &rdquo; (ibid.). </s></p><p type="main">

<s>Proseguendo attentamente il Rudbeck il decorso di questi dutti epatico <lb/>acquosi, da s&egrave; cos&igrave; felicemente scoperti, trov&ograve; che i pi&ugrave;, e anzi quasi tutti, <lb/>&ldquo; glandulam quandam ingrediuntur, ramulis dispersis, atque deinde, cum <lb/>reliquis eandem praetervectis, in Vesiculam chyli, sitam inter renes sub Vena <lb/>cava et arteria aorta, sese insinuant &rdquo; (ibid.). </s></p><p type="main">

<s>D&agrave; l'Autore a queste ghiandole, esse pure nuovamente scoperte almeno <lb/>per quel che riguarda le loro relazioni co'dutti epatico acquosi, il nome di <lb/><emph type="italics"/>Vasi ghiandolari sierosi,<emph.end type="italics"/> perch&egrave; gli parve che contenessero un liquido pi&ugrave; <lb/>denso, e in certo modo simile al chilo. </s>

<s>Il qual siero pens&ograve; che venisse tra&shy;<lb/>sudato dagl'intestini e dagli altri visceri, tanto pi&ugrave; dopo ch'egli ebbe a <lb/>notar questo fatto, &ldquo; quod mihi ter, egli dice, videre contigit: manifestam <lb/>anastomosin hosce inter ductus epaticos et duas vel tres lactearum venas <lb/>dari &rdquo; (ibid.). D'onde gli fu facile congetturare che l'uso di tali ghiandole <lb/>sierose fosse quello di confezionar meglio il chilo, e di rimandarlo cos&igrave; ela&shy;<lb/>borato al comun Ricettacolo. </s></p><p type="main">

<s>Cos&igrave;, tra il 1650 e il 1651, era stata fatta la scoperta di que'nuovi or&shy;<lb/>gani della vita animale, conosciuti poi sotto il nome di <emph type="italics"/>Vasi<emph.end type="italics"/> e di <emph type="italics"/>ghiandole <lb/>linfatiche,<emph.end type="italics"/> ma l'Autore non si cur&ograve; di pubblicare la sua scoperta, gi&agrave; mo&shy;<lb/>strata nel 1652 sotto gli occhi della Regina, quando a proposito della Ve&shy;<lb/>scicola del chilo <emph type="italics"/>hos quoque ductus in medium adduxit;<emph.end type="italics"/> se non che nel&shy;<lb/>l'anno appresso, in un libretto in 4&deg;, a cui dette il titolo: &ldquo; Nova exercitatio <lb/>anatomica exhibens ductus hepaticos aquosos, et Vasa glandularum serosa &rdquo; <lb/>e stampato in Vuesterat (Arosiae) piccola citt&agrave; della Svezia. </s></p><pb xlink:href="020/01/1356.jpg" pagenum="231"/><p type="main">

<s>In quel medesimo anno 1652, in cui il Rudbeck fece alla regina Cri&shy;<lb/>stina e ai regii medici la sua solenne dimostrazione, Tommaso Bartholin pub&shy;<lb/>blicava in Coppenaghen (Hafniae) la sua Storia anatomica <emph type="italics"/>De lacteis thora&shy;<lb/>cicis.<emph.end type="italics"/> Venne all'Autore l'impulso ai nuovi studii da quella parte stessa, che <lb/>era venuta al Rudbeck, imperocch&egrave;, avendogli la scoperta del Pecquet, tante <lb/>volte verificata, dimostrato che il chilo non v&agrave; al Fegato, ma al Ricettacolo <lb/>e di li al cuore, stava pensando che cosa potess'essere, nella Tavola III del&shy;<lb/>l'Asellio, quella vena designata colla lettera N e qualificata per una lattea <lb/>&ldquo; iuxta Cavam ascendens ad Hepar, et ad Venam Portae propagatam eamque <lb/>coronans. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il primo consiglio, che gli fu suggerito dalla sua propria saviezza e dal <lb/>buon metodo sperimentale, fu quello di verificar se i vasi descritti dall'Asel&shy;<lb/>lio intorno alla Vena porta erano una realt&agrave; o una immaginazion dell'Au&shy;<lb/>tore, o altro simile inganno. </s>

<s>Preso perci&ograve; un cane, alla presenza di varii <lb/>Medici amici, cos&igrave; il Bartolino stesso racconta nella storia XLVIII della <lb/>II centuria, &ldquo; quarta hora a pastu aperui, die 25 Decembris 1651. Viso re&shy;<lb/>ceptaculo chyli pecquetiano, aliisque huc spectantibus, ad Hepar oculorum <lb/>cultrique aciem convertimur. </s>

<s>Ecce multi comparebant ductus pinguedini im&shy;<lb/>mersi prope Hepar portam amplexantes, non candidi, lacteorum more, sed <lb/>splendentes colore hydatidum..... Nihil de novis vasis cogitans, quanquam <lb/>lacteas Asellii esse venas humor contentus dissuadebat, pro lacteis tamen <lb/>habui .... chylumque evanidum seri speciem induisse suspicabar. </s>

<s>9 Jan. </s>

<s>se&shy;<lb/>quentis anni 1652, in cane adhuc maiore, esperimentum feci..... Insciis <lb/>oculis iidem ductus aquosi ultro se obtulerunt, annuli in morem, Portam <lb/>cingentes, limpida aqua tumentes, qua et Receptaculum et vasa thoracica, <lb/>alias lactea, scatebant &rdquo; (Histor. </s>

<s>anatom. </s>

<s>rariorum Cent. </s>

<s>II cit., pag. </s>

<s>225, 26). </s></p><p type="main">

<s>Nel d&igrave; 28 Febbraio di quel medesimo anno 1652 fece, aiutato dal suo <lb/>fedele amico Michele Lyser, altre dissezioni, per le quali venne sempre me&shy;<lb/>glio confermato che i vasi descritti intorno alla Porta dall'Asellio eran reali, <lb/>e non punto, come si sospettava, immaginarii. </s>

<s>Ebbe di qui a concludere il <lb/>Bartolino che la sentenza del Pecquet non era assolutamente vera, e fu da <lb/>questo fatto osservato condotto a intitolare il cap. </s>

<s>XV <emph type="italics"/>De lacteis:<emph.end type="italics"/> &ldquo; Non <lb/>omnem chylum per thoracicas lacteas ad cor ferri, sed aliquem ad hepar <lb/>per lacteas mesenterii. </s>

<s>&ldquo; (In Mangeti Bibl. </s>

<s>cit., pag. </s>

<s>667). Vuol l'Autore, <lb/>fra gli antichi e i recenti Anatomisti, entrare mediatore di pace &ldquo; ne hepati <lb/>tot saeculis opere sanguificationis gloriose defuncto plane eamus exsequias. </s>

<s>&rdquo; <lb/>Se ho da pronunziar dunque una sentenza che concilii le due parti e fac&shy;<lb/>cia andare pecqueziani e galenisti ugualmente contenti, &ldquo; existimo, dice il <lb/>Bartholin, operas inter se partiri hepar et cor, ut vel promiscuos humores <lb/>alimentarios admittat uterque, vel diviso munere hoc tenuem, illud cras&shy;<lb/>sum &rdquo; (ibid.). </s></p><p type="main">

<s>Dop'aver cos&igrave; solennemente pronunziato questo giudizio, senza dir n&egrave; <lb/>come n&egrave; quando gli occorresse di dover riformarlo, prende in fretta la <lb/>penna, <emph type="italics"/>celerrimo calamo<emph.end type="italics"/> com'egli stesso si esprime, per scrivere una Sto-<pb xlink:href="020/01/1357.jpg" pagenum="232"/>ria nuova <emph type="italics"/>Vasorum lymphaticorum,<emph.end type="italics"/> pubblicata in Coppenaghen in quello <lb/>stesso anno 1653, in cui il Rudbeck avea divulgata fra'suoi, fatta gi&agrave; da due <lb/>anni, la sua propria scoperta. </s>

<s>Il Bartholin, che avea fin allora tenuti per lattei <lb/>que'vasi aselliani coronanti la Vena porta, ha scoperto che son vasi di nuovo <lb/>genere, e che, invece di portare, estraggono dal fegato quel loro umore sie&shy;<lb/>roso. </s>

<s>&ldquo; Vidimus quippe vasa illa prope hepar sui esse generis .... ex hepate <lb/>ad Receptaculum aquam inferre, ligataque intumescere prope hepar &rdquo; (ibid, <lb/>pag. </s>

<s>699). </s></p><p type="main">

<s>E qui &ldquo; dans un petit acc&egrave;s de gaiet&eacute; savante &rdquo; diremo anche noi col <lb/>Flourens (Histoire de la circul. </s>

<s>du sang, Paris 1854, pag. </s>

<s>94), si spoglia la <lb/>prima toga di avvocato, per indossar l'abito pontificale, e cantare al Fegato <lb/>l'esequie solenni. </s>

<s>Mi duole, egli dice, d'aver dovuto cos&igrave; cambiar veste, ma <lb/>son le solite vicende del mondo; &egrave; questa la sorte propria dei grandi Eroi; <lb/>ora nella polvere, ora sopra gli altari. </s>

<s>&ldquo; Ego interim, antiquae venerationis <lb/>memor, ne sine publico monumento tot saeculorum abdominis nostri Rector <lb/>ignotus iam busto inseratur, in perpetuam bene feliciterque, per bis octo <lb/>saecula administrati ac cruenti imperii memoriam, donec panegyris conda&shy;<lb/>tur, hanc ultimae devotionis inscriptionem tumulo illius conservavi: SISTE <lb/>VIATOR.CLAUDITUR HOC TUMULO QUI.TUMULAVIT.PLURIMOS.PRINCEPS COR&shy;<lb/>PORIS TUI COCUS.ET ARBITER.HEPAR NOTUM SAECULIS.SED.IGNOTUM NA&shy;<lb/>TURAE.QUOD NOMINIS MAIESTATEM ET.DIGNITATIS.FAMA FIRMAVIT.OPINIONE <lb/>CONSERVAVIT.TAMDIU COXIT.DONEC.CUM CRUENTO IMPERIO.SEIPSUM.DE&shy;<lb/>COXERIT.ABI SINE IECORE VIATOR.BILEMQUE HEPATI CONCEDE.UT SINE BILE <lb/>BENE.TIBI COQUAS ILLI PRECERIS &rdquo; (ibid.). </s></p><p type="main">

<s>Furono queste cose, come nella storia XLVIII citata il Bartolino stesso <lb/>ci attesta, pubblicate in Coppenaghen nelle calende di Maggio del 1653, <lb/>&ldquo; partim ne Naturae faventis sprevisse viderer indulgentiam, partim ne in&shy;<lb/>ventum nostrum fama hinc inde divulgatum .... scioli alii suffurarentur &rdquo; <lb/>(pag. </s>

<s>231). Ma giunse in quel punto da Vuesterat la Nuova esercitazione <lb/>anatomica, per la quale si scopriva, e anzi si dimostrava coi fatti, essere il <lb/>ladr&ograve; il Bartolino stesso che temeva dei ladri. </s></p><p type="main">

<s>Si dimostrava coi fatti, dicendovisi che il Rudbeck nel 1651 aveva sco&shy;<lb/>perto, e nel 1652 dimostrato in pubblico ai regii medici e alla stessa Regina, <lb/>i nuovi dutti, che trasportano il loro umor sieroso dal Fegato, di che il Bar&shy;<lb/>tholin, per confessione sua propria, non s'accorse che l'anno dopo. </s>

<s>Ma come <lb/>se n'accorse? </s>

<s>Ei non lo dice, per tenere il furto nascosto, ma noi abbiamo <lb/>tutte le buone ragioni di sospettare che la notizia delle pubbliche dimostra&shy;<lb/>zioni, fatte nella reggia di Svezia, con sollecitudine si diffondesse nella vi&shy;<lb/>cina Danimarca. </s>

<s>In che altro modo infatti si spiegherebbe quella trasforma&shy;<lb/>zione del Bartholin che di avvocato del Fegato diventa a un tratto sacer&shy;<lb/>dote delle sue esequie? </s>

<s>Ma come spesso avviene de'rei, patrocinatori della <lb/>causa propia, ei si tradisce da s&egrave; medesimo. </s>

<s>Nel II capitolo infatti della <emph type="italics"/>Histo&shy;<lb/>ria nova,<emph.end type="italics"/> ripensendo ai nomi pi&ugrave; convenienti ai dutti nuovamente scoperti, <lb/>&ldquo; fuere, egli dice, qui <emph type="italics"/>serosa vasa<emph.end type="italics"/> indiderint quod serum contineant &rdquo; (In <pb xlink:href="020/01/1358.jpg" pagenum="233"/>Mangeti Bibliotheca cit., pag. </s>

<s>694). Se prima dunque avevano avuto un nome, <lb/>dovevano essere stati anche prima scoperti, e il Rudbeck fu giusto quello, <lb/>che aveva imposto alle ghiandole linfatiche il nome di vasi sierosi. </s></p><p type="main">

<s>Diffusasi pi&ugrave; largamente in pubblico la notizia della scoperta dei dutti <lb/>epatico acquosi, e delle ghiandole sierose, venuta di Svezia, il Bartholin, che <lb/>voleva in ogni modo far sua legittima propriet&agrave; quella, che all'acuto giu&shy;<lb/>dizio altrui non appariva che un furto, sper&ograve; che avesse l'oratoria a far di&shy;<lb/>menticare la storia. </s>

<s>Scrisse perci&ograve; con grand'enfasi ed eloquenza, nella Cen&shy;<lb/>turia II, i pi&ugrave; minuti particolari della scoperta dei vasi linfatici &ldquo; propter <lb/>quod inventum, omni saeculo invisum, hecatomben promisimus &rdquo; (pag. </s>

<s>228). <lb/>Soggiungeva non essere ostentazione il magnificar ch'egli fa la propria sco&shy;<lb/>perta, ma un render lode a Dio creatore, <emph type="italics"/>et patriae nostrae celebritatem<emph.end type="italics"/><lb/>(pag. </s>

<s>231). </s></p><p type="main">

<s>Ma perch&egrave; sentiva minaccioso dalla lontana mormorarsi il nome di Olao <lb/>Rudbeck, vuole il Bartholin aver parlato della nuova scoperta &ldquo; paucis ver&shy;<lb/>bis cap. </s>

<s>VI, et XII et XV <emph type="italics"/>De lacteis thoracicis,<emph.end type="italics"/> Hafniae, 5 Maii 1652, edi&shy;<lb/>tis &rdquo; (pag. </s>

<s>231). Troppo debole provvedimento per&ograve; era questo alla difesa, <lb/>perch&egrave;, se nell'avere osservati vasi bianchi intorno al fegato e in altre parti <lb/>consistesse la scoperta de'vasi linfatici, ne sarebbero da dire piuttosto Au&shy;<lb/>tori il Veslingio, il Van-Horne, l'Igmoro, anzi il Falloppio, anzi Galeno stesso, <lb/>o qualcun altro de'pi&ugrave; antichi anatomici greci. </s></p><p type="main">

<s>Pi&ugrave; tardi usc&igrave; in mezzo fra il Rudbeck e il Bartholin un altro compe&shy;<lb/>titore, e ne fu dagli Inglesi a Francesco Glisson affidata la gelosa tutela. </s>

<s><lb/>Nel cap. </s>

<s>XXXI <emph type="italics"/>De anatomia hepatis,<emph.end type="italics"/> accennando esso Glisson ai vasi acquosi <lb/>nuovamente scoperti, &ldquo; incidi primum in eorum notitiam, egli ivi dice, in&shy;<lb/>ditio D. Jolivii, idque anno 1652, sub initium Junii, quo tempore ille, docto&shy;<lb/>ratus gradum adepturus, me Cantabrigiae in eum finem convenerat &rdquo; (Amste&shy;<lb/>lodami 1659, pag. </s>

<s>319). Ma perch&egrave; il Giolivio non aveva nulla lasciato scritto, <lb/>rimaneva franco il Rudbeck, e il Bartolino difeso. </s>

<s>Al qual Bartolino, bench&egrave; <lb/>avesse due altri casi valorosi competitori, riusc&igrave; nulladimeno di conseguire <lb/>il trionfo. </s></p><p type="main">

<s>Di questo, ch'&egrave; dei pi&ugrave; notabili fra'tanti altri ingiusti giudizii degli uo&shy;<lb/>mini, chi volesse ricercar le ragioni, le troverebbe facilmente nell'essere stato <lb/>il Bartholin pi&ugrave; eloquente, e pi&ugrave; procacciante del Rudbeck, e nell'aver tro&shy;<lb/>vato, tanta &egrave; la potenza delle parole, ne'<emph type="italics"/>Vasi linfatici<emph.end type="italics"/> un nome pi&ugrave; facile <lb/>a pronunziarsi di quello di <emph type="italics"/>Dutti epatico acquosi.<emph.end type="italics"/> Ma forse pi&ugrave; di ogni altra <lb/>cosa giovarono a fermargli in fronte la corona i risentimenti fieri de'Gale&shy;<lb/>nisti, che in quella parodia del Fegato si vedevano amaramente derisi. </s>

<s>Il <lb/>gran Riolano, che non s'era anoora riavuto delle fatiche durate, prima con&shy;<lb/>tro l'Harvey, poi contro il Pecquet, per mantener saldo il combattuto regno <lb/>galenico, si trova di fronte il Bartholin, che aggiunge alla punta acuta del&shy;<lb/>l'armi il ridicolo pi&ugrave; pungente degli insulti. </s>

<s>Fa i suoi risentimenti col bi&shy;<lb/>sbetico brontolio e con l'ira impotente dei vecchi, ma non lascia intanto di <lb/>meditar ragioni, o affinare arguzie, per salvare al Fegato il suo primo e no-<pb xlink:href="020/01/1359.jpg" pagenum="234"/>bilissimo ufficio. </s>

<s>Danno mano alla pietosa opera, come animosi soldati in&shy;<lb/>torno al capitano, Iacopo De Back, Isacco Cattier, Carlo Le Noble, Claudio <lb/>Tardy, a uno a uno redarguiti dal Bartolino stesso, nel suo Spicilegio secondo. </s></p><p type="main">

<s>Ma in tutti i sopra commemorati era l'ardor passionato d'una setta, <lb/>piuttosto che il sereno amor della scienza, il quale, per onor degli uomini <lb/>e del vero, non manc&ograve; d'inspirare alcuni animi eletti. </s>

<s>&Egrave; de'principali fra <lb/>questi da annoverare il Van-Horne, il quale, amicissimo del Bartholin, non <lb/>si lasci&ograve; tanto dalla passione o dall'affetto annuvolare il giudizio, da non co&shy;<lb/>noscer che quel piccolo accesso di gaiet&agrave;, da cui fu condotto a cantar l'ese&shy;<lb/>quie al Fegato, non era stato sapiente. </s>

<s>Fece l'Autore della Storia nuova <lb/>de'vasi linfatici il viscere defunto da'suoi primi ufficii, perch&egrave; i vasi, invece <lb/>di portarvelo, n'estraevano quell'umore, che si diceva dover essere trasfor&shy;<lb/>mato in sangue. </s>

<s>Ma il rifondere un liquido, ragionava giustamente il Van&shy;<lb/>Horne, &egrave; anzi argomento certissimo che vi sia nel vaso stato prima infuso, <lb/>ond'&egrave; che, se dal Fegato esce un umor nutritizio, &egrave; di necessit&agrave; che in qual&shy;<lb/>che modo siavi entrato. </s>

<s>N&egrave; fa difficolt&agrave; il veder l'umore che esce aver ap&shy;<lb/>parenza o natura diversa da quello che entra, imperocch&egrave; il viscere ha virt&ugrave; <lb/>di concuocere il chilo, per mandarlo cos&igrave; confezionato, attraverso ai vasi lin&shy;<lb/>fatici, al Canal toracico, e al cuore. </s>

<s>Queste insomma erano le funzioni asse&shy;<lb/>gnate dal Rudbeck alle ghiandole sierose, e il Van-Horne le estese al Fe&shy;<lb/>gato, quasi esso fosse una grande ghiandola sierosa, e le stesse ghiandole <lb/>seriose non fossero altro che tanti piccoli fegati. </s></p><p type="main">

<s>Non era dunque, secondo queste idee, il Rettore e il principe delle vi&shy;<lb/>scere animali affatto defunto: se gli era tolto il dignitoso ufficio di fattore <lb/>del sangue, gli&egrave; ne rimaneva un altro, non punto meno importante, qual era <lb/>quello di elaborare un umor nutritizio atto a ristorare il sangue. </s>

<s>Cos&igrave; il <lb/>Van-Horne, non per amor di Galeno, ma per amor del vero tanto pi&ugrave; an&shy;<lb/>tico, attendeva a rivendicare il Fegato dagli insulti del Bartholin, e il Rud&shy;<lb/>beck dalle usurpazioni. </s></p><p type="main">

<s>La fisiologia epatica nuova, insiem coi liberi giudizii intorno al primo <lb/>inventore dei vasi linfatici, vengon lucidamente esposti nel <emph type="italics"/>Microcosmo,<emph.end type="italics"/> e <lb/>son parte, in questo presente articolo di storia, di non lieve importanza. </s>

<s><lb/>Parve all'Autore la struttura del viscere, tanto avvilito dal Bartholin, ma&shy;<lb/>ravigliosa, ond'ebbe a concluderne &ldquo; usum eius haud vulgarem esse &rdquo; <lb/>(Lugduni Batav., pag. </s>

<s>56). Quest'uso poi ei lo riconobbe nella elaborazione <lb/>di quella parte di chilo pi&ugrave; crasso, che non va per i vasi aselliani al Ca&shy;<lb/>nale toracico. </s></p><p type="main">

<s>La rete del mesenterio &egrave;, secondo il Van-Horne, intessuta di un du&shy;<lb/>plice ordine di vene: lattee, e rosse, &ldquo; quod in hunc finem factum arbitror, <lb/>ut chyli laudabilior portio per illas quidem deferatur, porro in Receptacu&shy;<lb/>lum, et hinc, ascendendo per Ductum chyliferum, infundatur venae axil&shy;<lb/>lari aut iugulari; per has vero una cum sanguine ab intestinis remeante <lb/>devehatur ad Portae truncum, e sima parte hepatis erumpentem &rdquo; (ibid., <lb/>pag. </s>

<s>54, 55). </s></p><pb xlink:href="020/01/1360.jpg" pagenum="235"/><p type="main">

<s>Entrato il chilo insieme col sangue nel Fegato, attraverso alla Vena <lb/>porta, si distribuisce per le numerose propaggini di lei, che lo riversano <lb/>dentro le porosit&agrave; del viscere, d'onde viene assorbito dai rami della Vena <lb/>cava ivi dispersi, per i quali &egrave; direttamente condotto al cuore. </s>

<s>&ldquo; Atque in <lb/>hac chyli et sanguinis traductione unum Jecoris officium consistit &rdquo; (ibid., <lb/>pag. </s>

<s>59). Dell'altro ufficio, che &egrave; quello di secerner la bile, promette il Van&shy;<lb/>Horne di parlarne in seguito, per trattenersi a descriver le vie di quell'al&shy;<lb/>tra porzione di chilo schietto, ch'e per le vene lattee riversato &ldquo; in Vesi&shy;<lb/>culam chylo aquoso, hoc est lympha, permixto repletam &rdquo; (ibid., pag. </s>

<s>61). <lb/>E qui, a proposito de'nuovi dutti acquosi, sentenzia da giusto giudice, e <lb/>sicuro di pronunziare il vero, che elegantemente gli deline&ograve; &ldquo; et erudito <lb/>orbi communicavit Olaus Rudbeck in tractatu suo De ductibus hepaticis <lb/>aquosis &rdquo; (ibid.) e riprendendo pi&ugrave; sotto il Bartholin, che avesse nell'uomo <lb/>sostituito alla Vescicola del chilo e al Canal pecqueziano le ghiandole lom&shy;<lb/>bari, &ldquo; sed ego, soggiunge, cum doctissimo Rudbeckio, horum naturae ar&shy;<lb/>canorum scrutatori maximo, in homine vesiculam inveni &rdquo; (ibid., pag. </s>

<s>63). </s></p><p type="main">

<s>Nonostante, ebbe il Bartholin assai maggiore efficacia del Rudbeck in <lb/>diffondere con gli stessi scritti apologetici la notizia, e in promuovere lo <lb/>studio di questi nuovi dutti scoperti, il quale studio versava principalmente <lb/>intorno alla ragione del moto dell'umore in essi dutti contenuto, e dell'uso, <lb/>a cui furono dalla Natura i nuovi organi preparati. </s>

<s>Quanto alla direzion di <lb/>quel moto, furono sempre sicura scorta le valvole, a fare attenzione alle <lb/>quali fu primo, con sua dolce maraviglia, l'Asellio. </s>

<s>&ldquo; In his, dice nella ci&shy;<lb/>tata dissertazione <emph type="italics"/>De venis lacteis,<emph.end type="italics"/> illud admiratione dignum, quod pluribus <lb/>valvulis, sive ostiolis, interstinctae sunt sive intercisae, quas ego valvulas, <lb/>saepius vanescente iam chylo,.... animadverti &rdquo; (pag. </s>

<s>38, 39). </s></p><p type="main">

<s>Aperta cos&igrave; dal Nostro la via, per la quale gloriosamente s'introdusse <lb/>l'Harvey, che fece delle valvole argomento a dimostrare il corso del sangue <lb/>per le vene; il Pecquet, sulle orme dell'anatomico Italiano e dell'Inglese, <lb/>fece le stesse valvole argomento a dimostrar che il chilo ha il suo moto <lb/>diretto per le vene lattee al Ricettacolo comune. </s>

<s>Consisteva la dimostrazione <lb/>in allacciare una delle dette vene, e in osservar che, premuta col dito fra <lb/>l'allacciatura e il Ricettacolo stesso, il chilo non ritorna indietro verso l'in&shy;<lb/>testino, ci&ograve; che manifestamente prova, cos&igrave; esprimesi il Pecquet, &ldquo; esse intra <lb/>Receptaculi cavitatem valvularum obiectacula in mesentericarum ostiis, ad <lb/>excubias seu regressus interdictum, constituta &rdquo; (Opera anat., Parisiis 1654, <lb/>pag. </s>

<s>121). E perch&egrave; nessun dubitasse esser forse questa una conclusione <lb/>troppo affrettata, &ldquo; certe mihi, soggiunge lo stesso Pecquet, non sunt explo&shy;<lb/>ratae minus eiusmodi valvulae, quam quas in venis descripsit Fabricius ab <lb/>Aquapendente &rdquo; (ibid). </s></p><p type="main">

<s>Quando il Rudbeck, dal veder quelle manifeste anastomosi fra i dutti <lb/>epatici e due o tre delle vene lattee, ebbe indizio che, comunicandosi in&shy;<lb/>sieme i vasi, anche gli umori passerebbero dagli uni negli altri, fu a lui <lb/>altres&igrave; facilissimo a congetturare che, essendo fornite di valvole le vene lat-<pb xlink:href="020/01/1361.jpg" pagenum="236"/>tee, i dutti acquosi non ne andrebbero esenti. </s>

<s>Davano fondamento alle con&shy;<lb/>getture quelle nodosit&agrave;, di che i dutti stessi gli si mostravano involti, e ne <lb/>ebbe all'ultimo certezza di dimostrazione dallo stile introdotto nelle cavit&agrave;, <lb/>e dalle insufflazioni. </s>

<s>Descrivendo perci&ograve;, nella sua citata Nuova esercitazione <lb/>anatomica, i nuovi vasi scoperti, &ldquo; figuram, egli dice, ipsis rotundam, fistu&shy;<lb/>losam, ac mirabiliter nodosam, ob contentas valvulas concessit Natura &rdquo; <lb/>(pag. </s>

<s>702). </s></p><p type="main">

<s>Tanto poi parvero al Rudbeck queste valvole certe, nella loro esistenza <lb/>e nell'ufficio, che non si cur&ograve; di far del suo metodo delle insufflazioni altro <lb/>che un lieve accenno. </s>

<s>Ma perch&egrave; alcuni, fra'quali quel Bils, non si sa se <lb/>pi&ugrave; famoso per le sue invenzioni o per le sue pazzie, non mancarono di ne&shy;<lb/>gare assolutamente ci&ograve; ch'era meno aperto agli occhi che all'intelletto, si <lb/>trovarono i Fisiologi costretti a far delle stesse valvole de'linfatici pi&ugrave; evi&shy;<lb/>dente dimostrazione. </s></p><p type="main">

<s>Attese a questo studio con singolare zelo lo Swammerdam, il quale, <lb/>soffiando entro esilissimi tubettini metallici a quest'uso proprio fabbricati, <lb/>pose le valvole e la direzione del moto da esse indicata sotto gli occhi dei <lb/>curiosi osservatori. </s>

<s>&ldquo; Asserimus, egli dice, quod iam, anno 1664, 19 Junii, <lb/>Salmurii in Gallia, praesentibus variis Medicinae doctoribus celeberrimis, tu&shy;<lb/>bulorum aeneorum ac tenuissimorum ope,.... valvulas in vasis lymphati&shy;<lb/>cis, motum iam adsignatum lymphae ad oculum quoque confirmantes, obser&shy;<lb/>vaverimus, figuris illustraverimus, atque amicorum nostrorum curiosioribus, <lb/>tum alibi, tum praesertim Amstelodami degentibus, communicaverimus. </s>

<s>Quas <lb/>figuras delineatas, una cum praeparandi modo, postquam a nobis accepisset <lb/>clariss. </s>

<s>D. Blasius,.... easdem adiunxit Commentariis suis in Veslingii syn&shy;<lb/>tagma &rdquo; (De respiratione, Lugd. </s>

<s>Batav. </s>

<s>1667, pag. </s>

<s>90). </s></p><p type="main">

<s>Ma perch&egrave; il Bils seguitava nonostante a strepitare e a dire che avrebbe <lb/>voluto veder le valvole dentro i vasi con gli occhi, e che nessuno ancora <lb/>gliele aveva sapute mostrare, Federigo Ruysch usc&igrave; fuori, nel 1665, con un <lb/>libretto in 12&deg;, appositamente intitolato <emph type="italics"/>Dilucidatio valvularum in vasis <lb/>lymphaticis et lacteis,<emph.end type="italics"/> dove esprimeva cos&igrave; nel proemio la speranza di aver <lb/>finalmente vinta, colle sue lucide dimostrazioni, la ritrosia del nobilissimo e <lb/>lungamente ostinato oppositore: &ldquo; Bilsius, per multos annos, obstrepere non <lb/>cessavit neminem sibi posse ostendere in vasis lymphat&igrave;cis valvulas has in <lb/>rerum natura extare neganti. </s>

<s>Ego e contra, eas, non solum in rerum na&shy;<lb/>tura extare assero, ast illi quoque luculenter demonstravi &rdquo; (In Mangeti Bi&shy;<lb/>bliotheca anat. </s>

<s>cit., pag. </s>

<s>712). </s></p><p type="main">

<s>La dimostrazione dall'altra parte non era troppo difficile, trattandosi di <lb/>fatti. </s>

<s>Ma ben pi&ugrave; difficile riusciva a intendere a che fine servisse un umore, <lb/>a dispensare il quale equabilmente e con moto non interrotto, aveva la Na&shy;<lb/>tura macchinata quell'artifiziosa struttura di valvole, che si vedono ne'dutti <lb/>acquosi ricorrere cos&igrave; frequenti. </s>

<s>Il Bartholin, nella Storia nuova dei vasi <lb/>linfatici, riserb&ograve; il cap. </s>

<s>VII a trattare appositamente de'loro usi, che furono <lb/>da lui ridotti a questi due principali: &ldquo; I ut nutriendas partes onere inu-<pb xlink:href="020/01/1362.jpg" pagenum="237"/>tilis sibi aquae levent; II ut aquam aliis partibus certos in fines apportent, <lb/>in primis cordi, sive ad sanguinem alioquin crassiorem nonnihil diluendum, <lb/>sive calidiorem temperandum, sive ad sanguinis concoctionem promovendam &rdquo; <lb/>(In Mangeti Bibliotheca cit., pag. </s>

<s>697). </s></p><p type="main">

<s>Il Pecquet, che fu de'pi&ugrave; fervorosi ad applaudire alla scoperta, perch&egrave; <lb/>essendo il suo Ricettacolo sempre in faccenda di ricever la linfa aveva che <lb/>rispondere a coloro, i quali opponevano ch'esso Ricettacolo negli animali <lb/>digiuni si rimaneva inutile e ozioso; immagin&ograve; che l'umore acqueo fosse <lb/>dalla Natura ordinato nell'economia animale per rilavare i vasi, e tenerli <lb/>liberi dalle ostruzioni. </s>

<s>&ldquo; Adde, poi soggiunge, virtuti lotivae, ex aciduloso <lb/>succo sanguinis ipsius aut chyli fermentativam. </s>

<s>In intestinis diffunditur ut <lb/>bilis mordacem reprimat impetum &rdquo; (Opera cit., pag. </s>

<s>117). </s></p><p type="main">

<s>Il Glisson approv&ograve; alcuni di questi usi dell'umore acquoso, e ne esco&shy;<lb/>git&ograve; altri de'nuovi: &ldquo; Nimirum sanguinis coagulationem probibet, et cum <lb/>maxima illius pars iam antea ad volatilitatem, sive exhalationem perducta <lb/>sit, spiritibus vitalibus socium sibi adiungit, sanguinisque micationem pro&shy;<lb/>movet &rdquo; (Anatomie hepatis cit., pag. </s>

<s>552). Era opinione per&ograve; dell'illustre <lb/>Anatomico di Cambridge che male s'indovinerebbero gli usi della linfa, senza <lb/>prima determinarne bene l'origine e la natura. </s>

<s>Il Pecquet, nel luogo ulti&shy;<lb/>mamente citato, aveva espressa una sua opinione, che cio&egrave; l'umore acqueo <lb/>portato dai nuovi vasi bartoliniani fosse un escremento del sangue. </s>

<s>&ldquo; Et licet <lb/>excrementum sanguinis aqueum eiusmod&igrave; liquorem existimem, non eum ta&shy;<lb/>men susp&igrave;cer inutilem usquequaque. </s>

<s>&rdquo; Ma il Glisson neg&ograve; alla linfa la na&shy;<lb/>tura di escremento, perch&egrave; saviamente ragionava, se fosse tale, si sarebbe <lb/>dovuta espellere come tutti gli altri escrementi del corpo, e non farla tor&shy;<lb/>nar di nuovo a rimescolarsi col sangue. </s>

<s>&ldquo; Non est sanguinis excrementum, <lb/>quoniam denuo in venas regreditur, et cum sanguine remiscetur &rdquo; (ibid., <lb/>pag. </s>

<s>483, 84). </s></p><p type="main">

<s>Hanno una gran somiglianza, argutamente pensava il Glisson stesso, il <lb/>sangue arterioso e la linfa: ambedue reflui dalle varie parti del corpo, per <lb/>appositi canali forniti di valvole, e ambedue influenti nel ventricolo destro <lb/>del cuore. </s>

<s>Che se si assomigliano cos&igrave;, i due generi di vasi e gli umori in <lb/>essi contenuti, nel termine, debbono altres&igrave; rassomigliarsi ne'principii. </s>

<s>I pr&igrave;n&shy;<lb/>cipii delle vene son dalle estremit&agrave; arteriose, alle quali esse vene attingono <lb/>il sangue, che ha servito alla nutrizione. </s>

<s>&Egrave; probabile perci&ograve; che anche i lin&shy;<lb/>fatici attingano il loro umore avanzato ad altri vasi, che hanno portato alle <lb/>membra qualche altra sorta di nutrimento differente dal sangue arterioso. </s></p><p type="main">

<s>Or il Glisson si mise tutto in sollecitudine di cercar quali fossero que&shy;<lb/>sti vasi, che sarebbero come le arterie dei dutti acquosi, e gli parve di tro&shy;<lb/>varli ne'nervi, che perci&ograve; furono da lui costituiti, nella economia animale, <lb/>a far gli ufficii di un quinto e nuovo genere di condotti. </s>

<s>&ldquo; Sunt etiam co&shy;<lb/>niecturae probabiles quae suadeant haud esse uspiam quinti generis vasa <lb/>communia, hactenus ignota, quae liquorem succulentum in partes illas omnes <lb/>immittant &rdquo; (ibid., pag. </s>

<s>486). </s></p><pb xlink:href="020/01/1363.jpg" pagenum="238"/><p type="main">

<s>Le congetture poi che persuadevan l'Autore dover essere quel quinto <lb/>genere di vasi i nervi, avevano il loro fondamento sull'osservazione di quei <lb/>tanti rami nervosi, mandati alle viscere e alle numerose ghiandole conte&shy;<lb/>nute nell'abdome. </s>

<s>Qual'&egrave; dunque l'ufficio proprio di cotesti nervi, che non <lb/>&egrave; certo quello di presiedere alla sensazione o al moto? </s>

<s>E prendeva il Glis&shy;<lb/>son per particolare esempio la milza, i nervi della quale, perciocch&egrave; non <lb/>servono alla glandola per sentire o per muoversi, &ldquo; nulli insigni usui, ne <lb/>conclude, destinari videntur, nisi quidpiam, vel ad lienem adferant, vel ab <lb/>eodem auferant. </s>

<s>Non autem existimandum est quicquam eorum adminiculo <lb/>ad lienem apportari, quoniam neque id huic ex usu fuerit, nec vas excre&shy;<lb/>torium ullum adest, per quod ingestus humor egeratur foras. </s>

<s>Ideoque opor&shy;<lb/>tet aliquid e liene educant, quod deinde in superiorem abdominis plexum <lb/>transferant, unde postea data occasione, vel immediate per nervos sexto pari <lb/>connexos, vel mediantihus cerebro et medulla spinali, in omnes totius cor&shy;<lb/>poris nervos distribuatur &rdquo; (ibid., pag. </s>

<s>520, 21). Applica il medesimo ragio&shy;<lb/>namento alle altre ghiandole, e specialmente a quelle del mesenterio, le quali <lb/>&ldquo; prae caeteris, egli dice, ad propositum nostrum maxime spectant &rdquo; (ibid., <lb/>pag. </s>

<s>530). </s></p><p type="main">

<s>Il nuovo inaudito ufficio, commesso dal Glisson ai nervi, lev&ograve; gran ro&shy;<lb/>more fra i Fisiologi, e il Bartholin fu primo a insorgere contro l'Anatomico <lb/>inglese, che aveva introdotto nella scoperta de'vasi linfatici, in persona del <lb/>Giolivio, un terzo odioso competitore. </s>

<s>Altri per&ograve; non dubitarono di segui&shy;<lb/>tar le ipotesi glissoniane o schiette, com'avevale proposte l'Autore, o mo&shy;<lb/>dificate, secondo un notabile esempio, che tra poco vedremo, offertoci dal <lb/>Borelli. </s></p><p type="main">

<s>E qui il sentire, dopo lungo silenzio, risonarci alle orecchie il nome di <lb/>un Italiano, rallegra, e dall'altra parte accora, per vederlo comparire all'ul&shy;<lb/>timo, e come personaggio, se non estraneo, certamente secondario in que&shy;<lb/>st'amplissima scena, che apertasi pure in Italia pass&ograve; in Francia, e and&ograve; a <lb/>chiudersi in Svezia e in Danimarca. </s>

<s>Il Pecquet, il Rudbeck e il Bartholin, <lb/>inspirati dall'Asellio, ne compierono la gloriosa scoperta, verso la quale gli <lb/>Italiani si mostrarono inoperosi, come inoperosi s'erano mostrati nelle sco&shy;<lb/>perte del Colombo e del Cesalpino, compiute poi non meno gloriosamente <lb/>dall'Harveo. </s>

<s>Intorno a che lasciamo per un poco meditabondi i nostri let&shy;<lb/>tori Italiani, per poi ripigliar con essi il cammino, che dopo lunga peregri&shy;<lb/>nazione ci riconduce in patria. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Siamo nelle sale anatomiche del liceo di Pisa, dove Giovanni Finck eser&shy;<lb/>cita il suo coltello per dimostrare, ai curiosi ivi convenuti e allo stesso <lb/>Granduca, una cosa nuova: il Canale cio&egrave; che prende il chilo dalle vene <pb xlink:href="020/01/1364.jpg" pagenum="239"/>mesenteriche, e per la giugulare destra lo riversa nella Vena cava, d'onde <lb/>egli scende a diritto nel cuore. </s>

<s>&Egrave; Claudio Beriguardo che, nel VII della <lb/>III Parte de'suoi Circoli pisani, ci attesta il fatto con queste espresse pa&shy;<lb/>role, dop'avere accennato alla scoperta delle vene lattee: &ldquo; Illae ab intesti&shy;<lb/>nis, per mesenterium dispersae, quamplurimae immittunt ramos ad pancreas, <lb/>iugularem dextram, et inde ad cor per ductus, quos praeclare ostendit <lb/>Jo. </s>

<s>Finchius, nobilis anglus, in Lyceo pisano anatomicus ordinarius, ut et <lb/>multa alia scitu dignissima coram serenissimo Magno Duce &rdquo; (Patavii 1661, <lb/>pag. </s>

<s>617). Che poi riuscisse l'Anatomico inglese a far credere quella una <lb/>sua nuova scoperta, s'argomenta pure dalle espressioni dello stesso Beri&shy;<lb/>guardo, che soggiunge aversi perci&ograve; il Finchio meritata non minor lode e <lb/>gloria &ldquo; quam Guilielmus Harveius, decus inclitae suae nationis, cuius et <lb/>ille spes altera dici potest &rdquo; (ibid.). </s></p><p type="main">

<s>Si prova da questo documento pi&ugrave; cose degne di considerazione, e prin&shy;<lb/>cipalmente che, in uno de'pi&ugrave; fiorenti Studii italiani, s'ignorava cos&igrave; la sco&shy;<lb/>perta pecqueziana, che uno straniero pot&egrave; dimostrarla in pubblico per sua. </s>

<s><lb/>N&egrave;, in secondo luogo, &egrave; da lasciare inconsiderato che, non il Finchio solo, <lb/>ma molti degli Anatomici pisani di que'tempi erano stranieri, e particolar&shy;<lb/>mente inglesi: l'Aubery, il Tilmann, il Fava, il Baines e altri. </s>

<s>&Egrave; ci&ograve; un <lb/>argomento certo della penuria, che s'aveva allora in Italia, dove il campo <lb/>anatomico era rimasto isterilito dalle viete discipline galeniche instaurate dal&shy;<lb/>l'Acquapendente, il quale s'interpose fra il Cesalpino, che preparava le vie <lb/>alla scoperta del circolo del sangue, e l'Asellio, che iniziava le scoperte del <lb/>Canal toracico e de'vasi linfatici, come argine attraversato al fiume della <lb/>scienza italiana, che fece impaludar l'alveo di sopra, e rimaner vuoto l'alveo <lb/>di sotto. </s></p><p type="main">

<s>A riempir dunque cotesto vuoto si chiamarono in Italia, e segnatamente <lb/>in Pisa, stranieri, infintantoch&egrave; non fu istituita la nuova scuola anatomica <lb/>del Borelli, la quale cresceva su rigogliosa, a pigliare il suo posto, e a ri&shy;<lb/>vendicar la patria del patito servaggio e dell'onta. </s></p><p type="main">

<s>Una delle pi&ugrave; notabili fra queste rivendicazioni, e che pi&ugrave; strettamente <lb/>s'attiene al presente argomento storico, &egrave; quella relativa alla scoperta del <lb/>canale toracico. </s>

<s>L'opuscolo, pubblicato dal Pecquet in Parigi nel 1651, non <lb/>s'introdusse cos&igrave; facilmente in Toscana, dove piuttosto che l'anatomia si <lb/>coltivava la fisica, diciamo cos&igrave;, torricelliana. </s>

<s>Ma quando il solitario opuscolo <lb/>disperso s'aggiunse alle altre Dissertazioni pecqueziane, dove quella stessa <lb/>Fisica trovava cos&igrave; nuova e s&igrave; importante cultura, non pot&egrave; non essere pre&shy;<lb/>murosamente ricercato dai professori Pisani, chiamati intanto in Firenze dal <lb/>principe Leopoldo ai nuovi accademici consessi. </s></p><p type="main">

<s>Quelle pecqueziane Dissertazioni, alle quali precedevano gli Sperimenti <lb/>nuovi anatomici, furono pubblicate nel 1654 in Parigi, e bench&egrave; non sia fa&shy;<lb/>cile determinare il tempo, in che ne giunse in Firenze e in Pisa la notizia, <lb/>&egrave; certo nulladimeno che, nel Luglio del 1657, erano state esaminate nell'Ac&shy;<lb/>cademia del Cimento, in un Diario della quale, sotto il di 13 di quel mese, <pb xlink:href="020/01/1365.jpg" pagenum="240"/>di mano del Rinaldini, si legge: &ldquo; Si fece l'esperienza del Roberval<gap/>e della <lb/>vescica di pesce, che si gonfia nel vacuo, proposta dal signor Borelli &rdquo; (MSS. <lb/>Cim., T. II, P. I, c. </s>

<s>49). </s></p><p type="main">

<s>Al comparire del documento, che faceva autentica testimonianza del <lb/>primo inventore del Canale toracico, ebbe a rimanere svergognato il Fin&shy;<lb/>chio, e quell'uggia segreta, sentita dalla vecchia scuola inglese verso la nuova <lb/>italiana, fu allora che proruppe in aperti dissidii. </s>

<s>In mezzo a cos&igrave; fatti dis&shy;<lb/>sidii s'ebbe quel singolare esempio di rivendicazione, che si diceva di sopra, <lb/>e il quale consisteva nel pretendere e nel dimostrar, che facevano i Nostri, <lb/>come il primo a scoprire il Canal toracico non era stato n&egrave; il Finchio e n&egrave; <lb/>il Pecquet stesso, ma un Anatomico italiano del secolo XVI, Bartolommeo <lb/>Eustachio. </s>

<s>A qual occasione, e qual parte avessero i dissenzienti stranieri in <lb/>resuscitare le sepolte tradizioni della scienza italiana, &egrave; notizia che non pu&ograve; <lb/>non essere desiderata dai curiosi d'intendere questa storia. </s></p><p type="main">

<s>In Pisa, e poi anche in Messina, sotto la disciplina del Borelli, s'edu&shy;<lb/>cavano il Malpighi specialmente e il Fracassati a sezionar la pi&ugrave; eletta parte <lb/>di quella pesca, che si faceva nel vicino mare, e ch'era dalla munificenza <lb/>de'Principi medicei offerta al Borelli stesso, perch&egrave; vi potesse studiare gli <lb/>organi e gli artificii del nuoto. </s>

<s>Quegli esperti e curiosi anatomici per&ograve; non <lb/>lasciavano a quella occasione di esaminare anche le altre parti, fra le quali <lb/>il nervo ottico, che ne'pesci spada, ne'Tonni e in simili pesci pi&ugrave; grossi, <lb/>apertamente mostr&ograve;, contro la comune opinione, d'esser composto di una <lb/>larghissima membrana nervosa, gentilmente ristretta con pieghe simili a <lb/>quelle, che s'usano nei fazzoletti. </s></p><p type="main">

<s>Fece la dimostrazione il Fracassati in Pisa, alla presenza del Granduca <lb/>e degli Anatomici inglesi, i quali a principio non mostrarono, racconta il <lb/>Borelli, che tal notizia giungesse loro nuova. </s>

<s>&ldquo; Poi si mutarono d'opinione, <lb/>e di pi&ugrave; dissero che, per esser tal nervo tenero e di sostanza midollare, fa&shy;<lb/>cilmente poteva col coltello essere spianato in quella forma di membrana, e <lb/>con franchezza dissero quella esser tale, senza per&ograve; averla voluta vedere ed <lb/>osservare diligentemente, il che se avessero fatto, non l'avrebbero detto. </s>

<s>Dopo <lb/>tre giorni, quei medesimi signori Inglesi mostrarono al serenissimo Gran&shy;<lb/>duca un libro (Opuscula anatomica) di Bartolommeo Eustachio, anatomico <lb/>italiano del secolo passato, il qual dice queste parole, nel trattato <emph type="italics"/>De ossi&shy;<lb/>bus,<emph.end type="italics"/> pag. </s>

<s>227 (Venetiis 1564): <emph type="italics"/>Tam cito admiratio illa evanuit quam ner&shy;<lb/>vum visorium, in eo animali, quod cognitum nunc habes, tibi ac pluri&shy;<lb/>mis aliis movisse praedicabas, qui nervus, veluti tenuissimum matronarum <lb/>linteum, in innumeras rugas aequales, et pari serie distributas complica&shy;<lb/>tus, tuniculasque illas ambiente coactus, hanc eadem incisa evolvi sese <lb/>permittebat, et in amplam membranam totum explicari atque estendi. </s>

<s>&rdquo;<emph.end type="italics"/><lb/>(Inter M. Malpighi, Opera posthuma, Londini 1697, P. II, pag. </s>

<s>1, 2). </s></p><p type="main">

<s>Cos&igrave; gl'Inglesi, svergognati alla presenza del Granduca per l'accusa di <lb/>plagio del Canale toracico, s'erano vendicati degl'Italiani, accusandoli in&shy;<lb/>nanzi allo stesso Granduca di manifesto plagio della struttura del nervo ot-<pb xlink:href="020/01/1366.jpg" pagenum="241"/>tico. </s>

<s>Ma i Nostri non erano in verit&agrave; d'altro colpevoli, che di aver troppo <lb/>trascurate le tradizioni della scienza italiana, e di aver mostrato di non co&shy;<lb/>noscere, altro che forse di nome, Bartolommeo Eustachio. </s>

<s>Si pu&ograve; credere <lb/>allora se la curiosit&agrave; gli spinse a ricercare il libro dell'Anatomico italiano, <lb/>e attentamente leggendolo, s'abbatterono a notar, nell'opuscolo <emph type="italics"/>De vena <lb/>sine pari,<emph.end type="italics"/> l&agrave; nell'antigramma XIII, queste parole, che seguono alla descri&shy;<lb/>zione del tronco giugulare sinistro, osservato dall'Autore stesso nell'anato&shy;<lb/>mia di un cavallo: &ldquo; Itaque, in illis animantibus, ab hoc ipso insigni trunco <lb/>sinistro iuguli, qua posterior sedes radicis venae internae iugularis spectat, <lb/>magna quaedam propago germinat, quae, praeter quam quod in eius origine <lb/>hostiolum semicirculare habet, est etiam alba, et aquei humoris plena, nec <lb/>longe ab ortu in duas partes scinditur, paulo post coeuntes in unam, quae <lb/>nullos ramos diffundens, iuxta sinistrum vertebrarum latus, penetrato septo <lb/>transverso, deorsum ad medium usque lumborum fertur. </s>

<s>Quo loco latior <lb/>effecta, magnamque arteriam circumplex, obscurissimum finem, mihique <lb/>adhuc non bene perceptum, obtinet &rdquo; (Opuscula anat. </s>

<s>cit., pag. </s>

<s>301). </s></p><p type="main">

<s>Non vi &egrave; dubbio che quella vena bianca, piena di un umore acquoso, <lb/>la quale, penetrato il diaframma presso i lombi, si allarga, non sia il Canal <lb/>pecqueziano col suo Ricettacolo, ma l'Eustachio non la riconosce punto per <lb/>tale, n&egrave; nel principio n&egrave; nel termine o nell'uso, e tutt'altro che stimarla <lb/>uno degli organi primarii nell'economia animale, crede che sia una prov&shy;<lb/>videnza della natura tutta propria al cavallo. </s></p><p type="main">

<s>Nonostante, gli Anatomici pisani, a capo de'quali era il Fracassati, esul&shy;<lb/>tarono della scoperta, e inconsideratamente uscirono fuori a vantarsi che, <lb/>quasi un secolo prima del Pecquet, il Canal toracico e il Ricettacolo del chilo <lb/>erano stati scoperti, e pubblicamente descritti da un Italiano. </s>

<s>Anzi, in quel <lb/>fervore, e in quel risvegliarsi che faceva la scienza anatomica fra'Nostri, <lb/>quasi dolce lusinga escusatrice de'lunghi sonni, e riparatrice di perduti <lb/>acquisti, a quel modo che si volevano i meriti del Pecquet rivendicare al&shy;<lb/>l'Eustachio, si pretese di attribuire al Cesalpino gli onori conquistati dal&shy;<lb/>l'Harveo. </s></p><p type="main">

<s>Sedussero queste lusinghe cos&igrave; l'animo degli Italiani, che il Borelli e <lb/>il Malpighi ebbero a dar mano alla penna per consigliare ai loro stessi amici, <lb/>discepoli e connazionali, pi&ugrave; giusti e pi&ugrave; assennati giudizi. </s>

<s>Fu a quest'unico <lb/>intendimento composta dal Borelli, nel 1664, una scrittura, la quale il Mal&shy;<lb/>pighi inseri a principio della II parte delle sue Opere postume, da noi sopra <lb/>citate. </s>

<s>Egli ivi invita i troppo fervorosi zelanti del nome italiano a conside&shy;<lb/>rare pi&ugrave; cose: &ldquo; Prima, che se questo fosse lecito, per una sola parola in&shy;<lb/>cidentemente detta a modo di enimma, privar tutti gli inventori delle cose <lb/>nuove di quella gloria che loro si deve; darebbero troppo vantaggio questi <lb/>signori a coloro, che hanno voluto privar l'Harveio della gloria della in&shy;<lb/>venzione della circolazione del sangue. </s>

<s>La qual cosa, non parendomi giusta <lb/>n&egrave; ragionevole, mi sforza a distendermi qualche poco sopra questo parti&shy;<lb/>colare. </s>

<s>&rdquo; <pb xlink:href="020/01/1367.jpg" pagenum="242"/>&hellip; </s></p><p type="main">

<s>&ldquo; Egli &egrave; bene applicar questo discorso al proposito nostro: Scrisse il Cesal&shy;<lb/>pino espressamente che il sangue girava dal destro ventricolo del cuore per li <lb/>polmoni, passando dalla vena arteriosa nell'arteria venosa, conducendosi al si&shy;<lb/>nistro ventricolo del cuore, e quivi finisce, n&egrave; ebbe tanta accortezza di cono&shy;<lb/>scere che gran tesoro gli era venuto alle mani, ma trapassa questa cosa come <lb/>se niente importasse. </s>

<s>Successe poi l'Harveio, e con maravigliosa accortezza e <lb/>profondo giudizio conobbe non solo la circolazione per i polmoni, ma l'ampli&ograve; <lb/>a tutto il resto del corpo, e la dimostr&ograve; evidentemente con l'esperienza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Similmente Bartolommeo Eustachio racconta di aver ne'cavalli osser&shy;<lb/>vato certo canale pieno di una materia bianca aderente alla schiena, ch'egli <lb/>stesso non sa se sia sangue o acqua o altra materia, n&egrave; intese il principio, <lb/>n&egrave; il fine di detto condotto, n&egrave; che fosse il Canale del chilo, che si condu&shy;<lb/>cesse dagl'intestini direttamente al cuore, n&egrave; niun altro di quegli usi ma&shy;<lb/>ravigliosi, che da tale invenzione si sono cavati. </s>

<s>Venne poi quel fortunato <lb/>giovane Pecqueto, il quale, da un semplice indizio di vedere uscir dal cuore <lb/>un liquor bianco, si mosse a cercar l'origine del detto vaso, e mostr&ograve; evi&shy;<lb/>dentemente tutto il suo progresso ed uso, e non solo riconobbe una cosa <lb/>tanto preziosa, ma ancora la sparse, e comunic&ograve; a noi tutti questa recondita <lb/>e preziosissima verit&agrave;. </s>

<s>Or chi non vede che l'invenzione d'Eustachio di questo <lb/>dutto fu casuale, dubbiosa, incerta, non conosciuta n&egrave; apprezzata da lui stesso, <lb/>n&egrave; da niuno de'posteri in maniera, che si assomiglia piuttosto agli enimmi <lb/>degli antichi, li quali s'intendono solamente dop'esser seguito l'effetto, e <lb/>piuttosto si attribuisce a loro credulamente quel significato che non avevano, <lb/>n&egrave; gli autori di essi se l'avevano immaginato n&egrave; sognato? </s>

<s>&rdquo; (pag. </s>

<s>2, 3). </s></p><p type="main">

<s>Il Malpighi, in pi&ugrave; concise parole, ripeteva gli stessi concetti. </s>

<s>Posto il <lb/>principio che &ldquo; in artibus et scientiis inventor is dicendus est, qui Naturae <lb/>arcanum per suas causas patefecit, rationum et experimentorum cumulatis <lb/>argumentis firmavit, et usum Naturae congruum dilucide exposuit, &rdquo; ne <lb/>faceva scendere per legittima conclusione esser l'Harvey &ldquo; sanguinis circu&shy;<lb/>lationis inventor, et Pecquetus Thoracici ductus auctor &rdquo; (ibid, pag. </s>

<s>7). </s></p><p type="main">

<s>I giudizii del Borelli e del Malpighi eran giusti, ma non era la sola se&shy;<lb/>renit&agrave; della mente che gli guidava. </s>

<s>Dall'aver dimostrato che la scoperta del <lb/>Canal toracico fu all'Eustachio casuale, intendevano di concluderne che fosse <lb/>pure casuale, incerta e non intesa, la scoperta del nervo ottico, e cos&igrave; di&shy;<lb/>fendersi, appresso al Finchio e agli altri inglesi, dell'accusa di plagio La <lb/>difesa per verit&agrave; non era legittima, perch&egrave; l'argomento da sostenerla era <lb/>quello di confessar liberamente che s'erano dimenticate in Italia le patrie <lb/>tradizioni della scienza, e che perci&ograve; gli opuscoli eustachiani erano rimasti <lb/>per loro un tesoro nascosto. </s>

<s>N&egrave; il Borelli per&ograve;, n&egrave; il Malpighi, n&egrave; il Fra&shy;<lb/>cassati vollero mai fare questa confessione. </s>

<s>Eppure in essa sola &egrave; dato in&shy;<lb/>tendere le ragioni storiche, per cui le due massime scoperte della circola&shy;<lb/>zione del sangue e delle vie del chilo, cominciate in Italia, andarono a <lb/>compiersi in terra straniera. </s></p><pb xlink:href="020/01/1368.jpg" pagenum="243"/><p type="main">

<s>Ma perch&egrave; sempre gli uomini preferiscono le deboli scuse alle ingenue <lb/>confessioni, furono presto dimenticati in Italia i giudizii del Borelli e del <lb/>Malpighi, e sui principii del secolo XVIII risorsero i fanatici a tor via le <lb/>corone dai simulacri dell'Harvey e del Pecquet, per riporle in fronte al Ce&shy;<lb/>salpino e all'Eustachio. </s>

<s>Rispetto al Sanseveritano, fu la nuova sommossa, <lb/>rivendicatrice de'meriti di lui, capitanata dal Lancisi, quando pubblic&ograve; in <lb/>Roma, nel 1714, le Tavole eustachiane, e nella prefazione al libro fece il <lb/>panegirico dell'Autore. </s>

<s>Ivi, dop'aver dall'Antigramma XIII <emph type="italics"/>De vena sine <lb/>pari<emph.end type="italics"/> trascritte le parole stesse da noi sopra citate, &ldquo; quid clarius, conclude <lb/>il Lancisi, de canali toracico Pecquelus? </s>

<s>&rdquo; (pag. </s>

<s>XI). </s></p><p type="main">

<s>I savii Italiani nonostante seguitarono a riconoscere, col Borelli e col <lb/>Malpighi, nel Pecquet il vero autore della scoperta, n&egrave; si ostinarono a ri&shy;<lb/>vendicarla alla loro patria, costretti in ogni modo a confessare che, per ci&ograve; <lb/>che rende quella stessa scoperta compiuta, va la scienza anatomica debitrice <lb/>alla sola opera degli stranieri. </s></p><p type="main">

<s>Come non s&igrave; sollecito ai Nostri giunse l'opuscolo pecqueziano di Parigi, <lb/>cos&igrave; indugiarono anche di pi&ugrave; a giungere, da Vuesterat e da Copenaghen, <lb/>gli opuscoli del Rudbeck e del Bartholin. </s>

<s>Da un'altra parte la vecchia scuola <lb/>inglese era in decadenza, e la nuova non coltivava l'Anatomia pe s&egrave;, ma in <lb/>servigio della fisica e della meccanica animale. </s>

<s>Da ci&ograve; s'intende come gli <lb/>Anatomici borelliani non si mostrassero cos&igrave; solleciti di tener dietro alla <lb/>nuova scoperta dei vasi linfatici, che insieme con gli altri vasi bianchi s'in&shy;<lb/>cominciarono a studiare verso il 1664, come par che si provi da queste pa&shy;<lb/>role, scritte il d&igrave; 26 dicembre di quell'anno, in una lettera del Bellini al <lb/>Borelli. </s>

<s>&ldquo; Delle cose, gli dice, ch'ella desidera di sapere, non ce n'&egrave; che <lb/>meriti gran racconto ed osservazione. </s>

<s>Solo pochi giorni sono si ammazz&ograve; <lb/>una cerva viva, idest si tagli&ograve; viva. </s>

<s>Vi si veddero le vene lattee, il canal to&shy;<lb/>racico del Pecqueto, e i vasi linfatici grossissimi &ldquo; (Targioni, Notizie cit., <lb/>T. I, pag. </s>

<s>287). </s></p><p type="main">

<s>Si diceva dianzi che tardi giunse ai Nostri la notizia delle nuove cose <lb/>scoperte in Svezia e in Danimarca, e ora soggiungiamo che quella prima <lb/>notizia giunse indirettamente col libro <emph type="italics"/>Anatomia Hepatis<emph.end type="italics"/> di Francesco Glis&shy;<lb/>son. </s>

<s>Capitato in Pisa alle mani del principe Leopoldo, lo dette ad esaminare <lb/>al Borelli, a cui parvero le cose ivi scritte una nuova rivelazione, o come si <lb/>diceva in schietta frase toscana, uno scoprir paese, specialmente per ci&ograve; che <lb/>vi si diceva delle ghiandole, intorno alle quali vi si commemorava con gran <lb/>lode l'opera anatomica del Warthon. </s></p><p type="main">

<s>Ma ci&ograve; che pi&ugrave; sedusse il Borelli fu quel qu&igrave;nto ordine di vasi, per cui <lb/>si venivano i nervi a costituire arterie del chilo, delle quali i linfatici fos&shy;<lb/>sero le vene. </s>

<s>Il cap. </s>

<s>XI del II Tomo <emph type="italics"/>De motu animalium<emph.end type="italics"/> &egrave; in gran parte <lb/>inspirato a cotesta ipotesi glissoniana, la quale, se parve nell'Inglese ardita, <lb/>il Nostro vi gioc&ograve; intorno forse pi&ugrave; arditamente col proprio ingegno. </s>

<s>Dal ve&shy;<lb/>der quell'immensa copia di rami nervosi andare all'addome, ai visceri, alle <lb/>ghiandole, anche il Borelli, che non pensava aver la vita vegetativa essa <pb xlink:href="020/01/1369.jpg" pagenum="244"/>pure bisogno d'innervazione, si persuase facilmente che l'uso di que'nervi <lb/>fosse quello di concorrere, col loro succo instillato, a comporre il chilo, a <lb/>confezionarlo, &ldquo; et per consequens ad nutritionem partium &rdquo; (Romae 1681, <lb/>pag. </s>

<s>318). E perch&egrave; quel succo vien dal cervello alle parti, e dalle parti <lb/>ritorna al cervello, l'Autor De'moti animali, che aveva esclusa l'opera dei <lb/>vasi linfatici, non dubit&ograve; di dimostrar come cosa possibile &ldquo; Spiritus per <lb/>eosdem canales nerveos contrariis motibus agitari &rdquo; (ibid., pag. </s>

<s>319). </s></p><p type="main">

<s>Chiamato dunque dal Principe a render relazione del libro del Glisson, <lb/>il Borelli ne parl&ograve; con tanta lode, che il Principe stesso lo commend&ograve; a'suoi <lb/>Accademici di Firenze, ai quali, scrivendo da Pisa come un Notomista in&shy;<lb/>glese aveva osservato che i linfatici pigliano il ritorno di quell'umor nutri&shy;<lb/>tivo, che i nervi suggono dalle ghiandole del ventre, per dispensarlo alle <lb/>parti; lasciava, come se venisse a proporre a loro la soluzione di un nuovo <lb/>importante problema, che ne indovinassero il resto. </s></p><p type="main">

<s>Ardente di giovent&ugrave; e desideroso di gloria era fra quegli accademici il <lb/>Magalotti, che lusingandosi di poter colla fantasia e con l'ingegno supplire <lb/>al difetto della scienza anatomica, si fec&egrave; innanzi a distendere su quel tema <lb/>un discorso. </s>

<s>Non avendo un'idea chiara degli ufficii e degli usi de'vasi lat&shy;<lb/>tei e de'linfatici, al sentir che riducevano il loro umore nel cuore, pens&ograve; <lb/>che, no nell'interno di lui ci&ograve; facessero, rimescolandosi col sangue, ma nel&shy;<lb/>l'esterno, cosicch&egrave; fosse il ricettacolo della linfa no il ventricolo, ma il pe&shy;<lb/>ricardio. </s>

<s>Non pare ch'egli avesse nemmeno uso del linguaggio anatomico, <lb/>designando le parti destra e sinistra del cuore, non secondo la positura che <lb/>hanno nell'interno dell'animale, relativamente alle altre membra, ma secondo <lb/>che corrispondono alla mano di chi le osserva al di fuori. </s></p><p type="main">

<s>Il discorso del Magalotti insomma, anatomicamente considerato, &egrave; da dire <lb/>addirittura uno scorbio, e l'Autore stesso lo riconosce e lo confessa. </s>

<s>Ma certe <lb/>notizie, come sarebbe quella della nuova foggia di Barometro elegantissimo <lb/>inventato dal Viviani, ce lo rendono importante, e pi&ugrave; importante che mai <lb/>si rende per s&egrave; medesimo come documento che attesti qual si fosse, verso <lb/>il 1661, la cognizione, che avevasi dell'anatomia e delle funzioni dei vasi <lb/>bianchi, dalla pi&ugrave; eletta parte dei cultori delle scienze sperimentali in Italia. </s>

<s><lb/>Speriamo perci&ograve; che non dispiacer&agrave; ai nostri Lettori d'intendere quel Di&shy;<lb/>scorso, da noi fedelmente trascritto da una copia ritoccata qua e l&agrave; dalla <lb/>stessa penna del Magalotti: </s></p><p type="main">

<s>&ldquo; Fui avvisato dal serenissimo principe Leopoldo che si era veduto in <lb/>Pisa un libro di certo Notomista inglese, il quale scriveva di avere osser&shy;<lb/>vato come i vasi linfatici pigliano il ritorno di quell'umore, che circolando <lb/>per i nervi fa nel corpo umano un corso a noi novello d'acqua, come per <lb/>le arterie e le vene lo fa il sangue, onde in un certo modo vengono ad es&shy;<lb/>sere i nervi come arterie dei suddetti vasi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Altro non mi fu comunicato dall'A. S., come apparisce dalle seguenti <lb/>parole, che sono l'istesse della sua lettera: <emph type="italics"/>&Egrave; ben vero che un Inglese ana&shy;<lb/>tomista ha stampato un librettino, che scopre paese, e tratta quello di os-<emph.end type="italics"/><pb xlink:href="020/01/1370.jpg" pagenum="245"/><emph type="italics"/>servare le ghiandole, che sono nel corpo umano, e fra le altre cose mostra <lb/>che le vene linfatiche servono a riportar l'umido, che viene da quello, <lb/>che circola per i nervi, e cos&igrave; scopre una nuova circolazione, facendo le <lb/>vene linfatiche una parte simile a quella, che fanno le vene; e li nervi, <lb/>simile a quella che fanno le arterie. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Questa per&ograve; &egrave; troppo scarsa notizia per poter sensatamente discor&shy;<lb/>rere sopra questa novit&agrave;, onde vi vorrebbero molte e molte esperienze e <lb/>tagli replicati, e s&igrave; chiarirsi di alcune particolarit&agrave; essenzialissime, per fon&shy;<lb/>dare un mio debole discorso, il quale voglio nondimeno qui brevemente ac&shy;<lb/>cennare, per quei rispetti che ho gi&agrave; comunicati al serenissimo Principe. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Crederei che tutta l'acqua dei vasi linfatici metta nel pericardio, come <lb/>fa il sangue nel cuore. </s>

<s>Ma come poi dal pericardio sia succhiata dai nervi <lb/>(se pure &egrave; vero ci&ograve; che mi si suppone che per quelli si trovi circolare) <lb/>questo stimo io difficilissimo a rinvenirsi, s&igrave; per non sapersi se bea quivi <lb/>alcun ramoscello di essi, s&igrave; per la difficolt&agrave; che avrebbe quell'acqua a im&shy;<lb/>penetrare per le cavit&agrave; sue, conciossiach&egrave; si dubiti ancora se gli spiriti, che <lb/>per essi meano, o per angustissimi fori come per canale scorrendo, o a <lb/>grande stento cacciandosi tra filo e filo della fibrosa sostanza loro, vi cor&shy;<lb/>rano come per le ritorte di una corda umore. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma siasi di ci&ograve; quel che vuole, bisogna qui assicurarsi se veramente <lb/>arrivi al pericardio alcun tronco o ramo di nervi, e come il tronco della <lb/>grande arteria nel destro ventricolo si ribee il sangue; cos&igrave; questo risorbi&shy;<lb/>sce l'acqua versata dai vasi linfatici, della quale vi si fa conserva. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma quando questo vi si ritrovi, si cerca il modo col quale possa que&shy;<lb/>st'acqua penetrarvi, poich&egrave;, se il sangue passa nell'Arteria, ci&ograve; accade per&shy;<lb/>ch&egrave;, stringendosi il destro ventricolo nel moto costrittivo del cuore, e quello <lb/>trovandosi pieno di sangue, lo caccia a forza dentro all'Arteria, dalla quale <lb/>non pu&ograve; ricadere nella cavit&agrave; del ventricolo, bench&egrave; questo sotto se gli apra, <lb/>perocch&egrave; riman chiuso dalle valvole, che sono in essa. </s>

<s>Ma il pericardio, non <lb/>avendo tal moto di sistole e di diastole, come potr&agrave; schizzare ne'nervi quel&shy;<lb/>l'acqua, che in s&egrave; contiene? </s>

<s>N&egrave; mi si dica non esservi a forza cacciata <lb/>l'acqua, ma naturalmente sollevarvisi, come fa pe'cannelli sottilissimi di cri&shy;<lb/>stallo, perch&egrave; ci&ograve; si rende impossibile, per la grande strettezza della cavit&agrave; <lb/>interna de'nervi, se pur son forati, e direi piuttosto che non vi salga l'acqua, <lb/>ma che s'attragga da'filamenti, che la nervosa sostanza compongono, come <lb/>da un lucignolo, da un capo tuffato nell'acqua, succhiarlasi veggiamo e dal&shy;<lb/>l'altra gemerla. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma supponiamo pure esser forati i nervi, il che ha molto del vero&shy;<lb/>simile, e mi ricordo aver sentito raccontare dal p. </s>

<s>Fabri una cotale espe&shy;<lb/>rienza: Prese egli un grosso nervo, tagliato da un castrato allora aperto e <lb/>fumante, e messolo sur una padella di ferro d'un braciere, dov'era per&ograve; <lb/>dianzi stato il fuoco, rigonfi&ograve; s&igrave; pel calore, che adoprandovi il Microscopio <lb/>vi scorse nel mezzo il foro, e se ben mi rammento, tent&ograve; di ritrovare il suo <lb/>seno con un sottilissimo fil di vetro, e pot&egrave; farlo. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/1371.jpg" pagenum="246"/><p type="main">

<s>&ldquo; Questo foro per&ograve; &egrave; cos&igrave; piccolo e stretto, che forse l'acqua non vi <lb/>pu&ograve; penetrare, se non vi &egrave; cacciata con gran violenza. </s>

<s>Io gliela dava uguale <lb/>a quella, con cui viene scagliato il sangue nell'arteria, anzi l'istessa appunto, <lb/>e ricordandomi di certa esperienza veduta gi&agrave; del signor Vincenzio Viviani, <lb/>adattandola al mio proposito, discorreva cos&igrave;: &rdquo; </s></p><p type="main">

<s>&ldquo; Se al fondo della boccia A (fig. </s>

<s>8) sar&agrave; attaccata ad un fil di seta <lb/>la vescica B, non interamente gonfia d'aria, ma tutta quella che v'&egrave; sia <lb/><figure id="id.020.01.1371.1.jpg" xlink:href="020/01/1371/1.jpg"/></s></p><p type="caption">

<s>Figura 8.<lb/>presa al fondo di qual&shy;<lb/>che torre, ed essa ve&shy;<lb/>scica nuoti nell'acqua <lb/>arzente, la quale non <lb/>solo riempia tutta la <lb/>boccia A, ma si sollevi <lb/>in C, C, C, nei sotti&shy;<lb/>lissimi cannellini di <lb/>cristallo, i quali per <lb/>di sopra sieno tutti <lb/>aperti; certissima co&shy;<lb/>sa &egrave; che, se tal boc&shy;<lb/>cia si porter&agrave; in alto, <lb/>pi&ugrave; e pi&ugrave; s'andr&agrave; sol&shy;<lb/>levando l'acqua nei <lb/>cannellini, e ci&ograve;, non <lb/>perch&egrave; si sollevi l'a&shy;<lb/>cqua per s&egrave; medesi&shy;<lb/>ma, ma perch&egrave;, di <lb/>mano in mano che <lb/>pi&ugrave; si va in alto, sce&shy;<lb/>ma la pressione dell'aria ne'cannellini, onde quella che si conserva nella <lb/>vescica, senza alterarsi dallo stato di sua natural pressione, tanto acquista <lb/>quanto quella perde, e respirando, in mezzo a quell'acqua che la circonda, <lb/>&egrave; forza che se la discacci d'intorno, e discacciandola la sollevi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si metta ora, in cambio della vescica, in mezzo della boccia il cuore, <lb/>sospeso nel mezzo del pericardio pien d'acqua, la qual tocchino e vi si ba&shy;<lb/>gnino le bocche de'ramicelli nervosi figurati da'medesimi cannellini, e si <lb/>consideri che quel medesimo schizzar d'acqua, che si fa in essi dalla vescica <lb/>per il suo dilatarsi, quell'istesso si fa dal cuore, nel dilatarsi che anch'egli <lb/>fa, per lo continuo moto che l'agita, detto da'greci sistole e diastole, e quindi <lb/>avviene che, nella diastole del cuore, viene discacciata l'acqua ne'nervi, con <lb/>quella stessa forza, che poi nella sistole si scaglia nell'arteria il sangue, e <lb/>in questo tempo che si restringe il cuore, gemono per avventura i vasi lin&shy;<lb/>fatici per altre docce nel pericardio la loro acqua, in quella stessa guisa che, <lb/>stringendosi il destro ventricolo, il sinistro s'apre, e riceve il sangue, che <lb/>vi trasmette la Vena cava &rdquo; </s></p><pb xlink:href="020/01/1372.jpg" pagenum="247"/><p type="main">

<s>&ldquo; Molte altre bellissime conietture possono dedursi da quest'acqua di&shy;<lb/>scorrente pe'nervi, ne'quali, se pure &egrave; vero che stiano gli spiriti, questo <lb/>adacquarli che fa la Natura dimostra che debbono essere un vino molto po&shy;<lb/>tente, e quell'acqua che lo tempera non avrebbe ad essere un'acqua pazza, <lb/>come suol dirsi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Altre speculazioni possono farsi sopra quest'acqua, la quale mi per&shy;<lb/>suado che di qui avanti dovr&agrave; essere molto risguardata ne'mali, e nella pa&shy;<lb/>ralisia e idropisia particolarmente. </s>

<s>Rimane per ultimo che io mi protesti di <lb/>aver disteso questo mio concetto, con quella pura semplicit&agrave; ch'ei nacque, <lb/>ond'&egrave; che, riconoscendolo sottoposto ad infiniti errori, mi dichiaro non me&shy;<lb/>ritare che se ne faccia alcun conto, infinch&egrave; le diligenti osservazioni e le <lb/>replicate esperienze non istabiliscano il fondamento a pi&ugrave; saldi discorsi. </s>

<s>&rdquo; <lb/>(MSS. Cim., T. IX, c. </s>

<s>59-62). </s></p><p type="main">

<s>Chi volesse da questo Discorso del Magalotti pigliare argomento da giu&shy;<lb/>dicare della cultura, che intorno a cose anatomiche e fisiologiche avevasi <lb/>dagli Accademici fiorentini, verrebbe ad una conclusione troppo sfavorevole <lb/>ad essi ed ingiusta. </s>

<s>Ma &egrave; pure un fatto, per ci&ograve; che particolarmente concerne <lb/>i vasi bianchi, che poco si promosse quella cultura dalla scuola del Borelli, <lb/>il quale, senza fare nemmeno un cenno degli organi nuovamente scoperti <lb/>dagli stranieri, se ne passa in quelle sue meccaniche speculazioni intorno <lb/>alla nutrizione, esposte nella II parte dei Moti animali. </s></p><p type="main">

<s>La nuova Fisiologia perci&ograve;, cos&igrave; splendidamente iniziata dall'Asellio, si <lb/>pu&ograve; dir che incominciasse a coltivarsi in Italia alquanti anni dopo la prima <lb/>met&agrave; del secolo XVII, per opera di due insigni Naturalisti, il primo de'quali, <lb/>ch'&egrave; Tommaso Cornelio, erasi ridotto in disparte dagli altri suoi connazio&shy;<lb/>nali, per professar solitario la Filosofia cartesiana, e l'altro, ch'&egrave; Marcello <lb/>Malpighi, e che, per riconquistarsi la filosofica libert&agrave;, era quasi disertato <lb/>dalla scuola del Borelli. </s></p><p type="main">

<s>Il Cornelio trattando, nel citato proginnasma VI, <emph type="italics"/>De nutricatione,<emph.end type="italics"/> tut&shy;<lb/>t'altro che astenersene, com'avea fatto il Borelli, entra animosamente in <lb/>mezzo alle questioni suscitate nella scienza dalle nuove scoperte, ed &egrave; an&shy;<lb/>ch'egli uno degli insorti a difendere la causa del Fegato, che il Bartholin <lb/>voleva, <emph type="italics"/>iocosis monimentis,<emph.end type="italics"/> defunto. </s>

<s>&ldquo; Compertum quidem est nobis, egli <lb/>asserisce con gran confidenza, vel omne alimentum, vel certe maximam <lb/>eiusdem partem, per vulgares ventriculi, et mesenterii venas ad iecur con&shy;<lb/>fluere &rdquo; (Progymnasmata cit., pag. </s>

<s>232). </s></p><p type="main">

<s>Le ragioni, che mossero il Cornelio ad asserir cos&igrave; contro l'opinion <lb/>pecqueziana, son presso a poco quelle del Van-Horne, se non che, mentre <lb/>l'Olandese credeva che l'umor nutritizio passasse dal Fegato nel Canal chi&shy;<lb/>lifero, il Nostro, compiacendosene come di una sua propria scoperta, lo fa&shy;<lb/>ceva ritornare agl'intestini, e di li nuovamente al Fegato, <emph type="italics"/>iterato saepe cir&shy;<lb/>cuitu,<emph.end type="italics"/> infin tanto che tutta la sostanza nutritizia non si fosse, cos&igrave; tessendo <lb/>e ritessendo le medesime vie, consumata. </s>

<s>&ldquo; Nemo tamen hactenus animadver&shy;<lb/>tit liquorem hunc ab intestinis et alvo, una cum succo alibili, ad iecur aliasve <pb xlink:href="020/01/1373.jpg" pagenum="248"/>partes lapsum, magnam partem ad intestina relabi, easdemque vias saepius <lb/>iterare, donec alimentum omne fuerit transumptum &rdquo; (ibid., pag. </s>

<s>245). </s></p><p type="main">

<s>Rivendicata cos&igrave; la dignit&agrave; del Fegato, con attribuirgli l'importantissimo <lb/>ufficio di confezionare il chilo, e di stillar la bile, tanto necessaria per la <lb/>buona distribuzione dell'alimento; passa il Cornelio a investigar le origini <lb/>della linfa, &ldquo; cui, secondo egli crede, praecipua liquandi diluendique chyli <lb/>vis inest &rdquo; (ibid., pag. </s>

<s>245). Ei riconosce quella origine non d'altronde es&shy;<lb/>sere che dal cibo e dalla bevanda, e i vasi, ordinati dalla Natura a condurre <lb/>quell'alimento, partono dal Fegato, come fu primo ad osservarli il Fallop&shy;<lb/>pio, e poi a descriverli Natanaele Igmoro. </s>

<s>&ldquo; Tandem vero Thomas Bartho&shy;<lb/>linus, cum haec ipsa vasa diligentius contemplaretur, observavit in illis con&shy;<lb/>tineri aqueum liquorem &rdquo; (ibid., pag. </s>

<s>246). Di questo liquore, <emph type="italics"/>ab alimento <lb/>secretus,<emph.end type="italics"/> &egrave; il destino, conclude cos&igrave; il Cornelio la sua linfatica fisiologia, che, <lb/>com'&egrave; partito dagl'intestini, &ldquo; ad intestina relabatur &rdquo; (ibid., pag. </s>

<s>248). </s></p><p type="main">

<s>Se questo, insiem con gli altri Proginnasmi del nostro Fisiologo cosen&shy;<lb/>tino, che portan la data di Napoli 1661, ma che furono pubblicati tutti in&shy;<lb/>sieme in Venezia nel 1663; giungessero alla notizia del Bartholin, non si <lb/>saprebbe da noi dimostrare, ma, quando pure gli fossero pervenuti, non <lb/>avrebbero forse sodisfatta l'ambizione di chi voleva esser creduto primo <lb/>inventore de'vasi linfatici, punto meglio di quel che l'avesse sodisfatta il <lb/>Van-Horne, il quale liberamente attribuiva al Rudbeck quell'ambita in&shy;<lb/>venzione. </s></p><p type="main">

<s>In ogni modo non &egrave; credibile che quell'uomo, il quale, con l'opera <lb/>propria e con quella degli amici, s'era dato tanta faccenda di diffondere <lb/>negli scienziati, e di persuaderli che la scoperta de'linfatici era sua; non <lb/>sentisse dispiacere degl'Italiani, che l'avessero cos&igrave; negletta, e che non fosse <lb/>ancora sorto fra loro a parlarne altro che il Cornelio, in maniera non troppo <lb/>degna di s&egrave;, n&egrave; della scienza. </s></p><p type="main">

<s>Per la mediazione di Erasmo Bartholin, suo fratello, che teneva amici&shy;<lb/>zia e corrispondenza epistolare col Viviani, entr&ograve; in relazione con gli Acca&shy;<lb/>demici del Cimento, e Carlo Dati, per offerire all'illustre straniero un sag&shy;<lb/>gio di ci&ograve;, che intorno a cose anatomiche s'era scoperto in Italia, gli mand&ograve; <lb/>l'Epistole malpighiane <emph type="italics"/>De pulmonibus.<emph.end type="italics"/> L'Anatomico danese, tutto dedito <lb/>allora allo studio de'vasi lattei, rimase maravigliato, e tanta riconobbe es&shy;<lb/>sere la novit&agrave;, tanta la bellezza del soggetto e l'importanza, che dette mano <lb/>a scrivere quella eruditissima dissertazione <emph type="italics"/>De pulmonum substantia et <lb/>motu,<emph.end type="italics"/> la quale fu, nel II Tomo delle opere raccolte in Leyda nel 1687, in&shy;<lb/>serita dopo le Epistole dello stesso Malpighi. </s>

<s>La principale intenzione per&ograve;, <lb/>ch'ebbe l'Autore in distendere quella scrittura, fu &ldquo; ut illam gratiam labo&shy;<lb/>ribus aliorum et feliciter inventis exhiberet &rdquo; ch'egli sperava avrebbero gli <lb/>Italiani retribuita a'suoi Linfatici, a che far disponeva gli animi loro con <lb/>questi encomii: &ldquo; Debemus plurimum Italorum ingeniis et humanitati, nec <lb/>unquam patiar ut tantae gentis gloria apud nostros taceatur. </s>

<s>Mater studio&shy;<lb/>rum Bononia has <emph type="italics"/>De pulmonibus<emph.end type="italics"/> observationes per Malpighium peperit, <pb xlink:href="020/01/1374.jpg" pagenum="249"/>florentissima Pisa, per Borellum, suscepit, Florentia cultissima pluribus vo&shy;<lb/>luit, per Datum, esse communes &ldquo; (pag. </s>

<s>336). </s></p><p type="main">

<s>Le intenzioni del Bartholin non andarono a vuoto, imperocch&egrave; il Mal&shy;<lb/>pighi ben conoscendo come la parte del sistema linfatico, che pi&ugrave; aveva bi&shy;<lb/>sogno di essere illustrata, era quella delle glandole, si rivolse con gran di&shy;<lb/>ligenza a quello studio, e nel 1668 pubblic&ograve; la sua Epistola <emph type="italics"/>De structura <lb/>glandularum conglobatarum.<emph.end type="italics"/> Riconobbe quella struttura essere di vasi san&shy;<lb/>guigni e di nervi, ai quali s'implica un nuovo genere di vasi escretori, che <lb/>sono i linfatici, e bench&egrave; trovasse molto difficile, per l'esilit&agrave; delle parti e <lb/>per la friabilit&agrave; della sostanza, l'usarvi attorno il coltello; cred&egrave; nulladimeno <lb/>di poter asserire: &ldquo; quamlibet conglobatam glandulam lymphaticis ditari &rdquo; <lb/>(Lugduni Batav. </s>

<s>1668, pag. </s>

<s>7). A conferma di che vide per mezzo delle <lb/>iniezioni, che il liquido passava da una ghiandola all'altra, attraverso ai vasi <lb/>sierosi, per andare indi a riversarsi nel Ricettacolo pecqueziano. </s></p><p type="main">

<s>Altri importantissimi problemi erasi proposto di risolvere in s&igrave; difficile <lb/>soggetto il Malpighi, e fra questi, che da'Fisiologi erano pi&ugrave; desiderati, i tre <lb/>seguenti: I. </s>

<s>Se le prime origini de'vasi linfatici sieno dalle ghiandole mi&shy;<lb/>nori, come da fonti. </s>

<s>II. </s>

<s>Qual sia l'origine de'linfatici, che ricorrono intorno <lb/>agl'intestini, e particolarmente nel fegato e nella milza. </s>

<s>III. </s>

<s>Se sia qualche <lb/>organo applicato alle estreme diramazioni de'vasi, mediante il quale sia se&shy;<lb/>greta la linfa. </s>

<s>Ma trov&ograve; la cosa tanto difficile, ch'ebbe, dopo lunghi e dili&shy;<lb/>gentissimi studii, e confessare: &ldquo; nec adhuc quid certi enunciare mihi <lb/>licet &rdquo; (ibid.). </s></p><p type="main">

<s>I problemi, lasciati cos&igrave; nella loro prima incertezza dal Malpighi, furono <lb/>non infelicemente risoluti dagli anatomici e da'fisiologi posteriori, ma ne ri&shy;<lb/>manevano altri ancora a risolversi, e ch'esercitarono l'ingegno dei nostri <lb/>Italiani. </s>

<s>Venuti tardi a sedersi al convito ripararono i Nostri alla negligenza <lb/>col mandarvi que'due validissimi commensali, che furono il Morgagni e il <lb/>Mascagni, e che soli basterebbero per tutti gli altri. </s>

<s>L'opera loro, di che <lb/>troppo lungo sarebbe a parlare, basti a noi qui accennarla con qualche <lb/>esempio. </s></p><p type="main">

<s>Fra'pi&ugrave; curiosi problemi intorno ai linfatici era quello degli usi, a cui <lb/>furono le numerose ghiandole riserbate, e con tanta frequenza disposte lungo <lb/>il decorso dei vasi. </s>

<s>Il Morgagni sagacemente not&ograve; che quella frequenza era, <lb/>dagli arti inferiori verso il centro del Dutto toracico, maggiore negli uomini <lb/>che ne'bruti. </s>

<s>Ripensando sopra le ragioni di ci&ograve;, gli parve di ritrovarla nel&shy;<lb/>l'aver l'uomo positura eretta, e i bruti inclinata, per cui si condusse facil&shy;<lb/>mente a congetturare, dietro questa comparazione, che l'uso delle ghiandole <lb/>fosse quello di promuovere il corso della linfa, e di sostenerla di grado in <lb/>grado contro la tendenza della gravit&agrave; naturale. </s>

<s>&ldquo; Porro ex eiusdem obser&shy;<lb/>vatione quod vasa lymphatica, ab artubus inferioribus versus thoracici ductus <lb/>initium pergentia, plures in homine quam in brutis conglobatas glandulas <lb/>subeant; ego illum istarum usum confirmari posse animadverto, quod vide&shy;<lb/>licet lymphae motum iuvent, qui quoniam in nobis, ob erectum corporis <pb xlink:href="020/01/1375.jpg" pagenum="250"/>positum, multo est per ea vasa difficilior, quam in brutis; ideo plures glan&shy;<lb/>dulas et brevioribus intervallis distributas videtur requisivisse &rdquo; (Adversaria <lb/>anat. </s>

<s>omnia, Patavii 1719, pag. </s>

<s>88). </s></p><p type="main">

<s>Un altro de'pi&ugrave; curiosi e de'pi&ugrave; importanti problemi da risolversi in&shy;<lb/>torno ai linfatici, e che gli stessi Fisiologi moderni confessano non essere <lb/>stato ancora ben risoluto, &egrave; quello della causa meccanica, che s&igrave; agevolmente <lb/>sospinge la linfa ne'vasi. </s>

<s>Dopo il Pecquet, che riconobbe quella causa prin&shy;<lb/>cipalmente nella compression del torace e nelle pulsazioni arteriose, l'Haller <lb/>v'applic&ograve; la sua ipotesi degli stimoli e delle azioni irritanti. </s>

<s>Ma il Mascagni <lb/>dubit&ograve; di questa ipotesi, vedendo gli stessi vasi spontaneamente espellere le <lb/>materie iniettate, anche ne'cadaveri, e alla irritabilit&agrave; alleriana sostitui la <lb/>naturale elasticit&agrave; delle fibre. </s>

<s>&ldquo; Cum aquam calentem, seu imbutam colore <lb/>seu destitutam, in vasa sanguinea iniecissem &rdquo; trovai, egli scrive, che anche <lb/>i linfatici apparivano inturgiditi, e passato oltre il liquido, sparivano di nuovo. <lb/></s>

<s>&ldquo; Itaque vis huiusmodi, dietro ci&ograve; ne conclude, qua lymphaticorum humor <lb/>propellitur, non solum in cadaveribus post multos a morte horas, iamque <lb/>frigefactis, perdurat, sed et per annos servatur, quae tanta activitatis diutur&shy;<lb/>nitas, num cum irritabilitate conveniat, Hallerus diudicet..... Porro vim ita <lb/>agentem in elasticitate tunicarum esse reponendam ex eo patet, quod vis eius&shy;<lb/>modi in hoc prorsus consistit quod partes compressae, flexae ac distractae, in <lb/>statum a quo recesserant redire conentur, statimque redeant ubi vis distra&shy;<lb/>hens removeatur &rdquo; (Vasorum lymphatic. </s>

<s>Historia, Senis 1787, pag. </s>

<s>27, 28). </s></p><p type="main">

<s>Il magnifico volume, ora citato, &egrave; degno della grandezza regia di quel <lb/>Pietro Leopoldo, granduca di Toscana, a cui volle il Mascagni che fosse de&shy;<lb/>dicato, nelle numerose Tavole aggiunte al quale chi guarda, non sa se pi&ugrave; <lb/>debba ammirare il magistero della Natura in condur quelle sottilissime e <lb/>intricatissime reti di vasi, per ogni membro del corpo umano, o la perizia <lb/>di chi seppe far di loro cos&igrave; splendida apparizione, col quasi magico soffio <lb/>della sua bocca. </s></p><pb xlink:href="020/01/1376.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dei sensi<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Del tatt<gap/> del gusto e dell'odorato: &mdash; II. Dell'organo dell'udito: dell'o<gap/>cchio medio. </s>

<s>ossia della <lb/>Cassa del timpano. </s>

<s>&mdash; III. Dell'orecchio interno, ossia del Labirinto. </s>

<s>&mdash; IV. </s>

<s>Del senso dell'udito. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Chi nello studio degli svolgimenti embrionali attende a que'sottilissimi <lb/>innumerevoli vasi, che s'insinuano nell'albume e nel vitello dell'uovo, o <lb/>nella placenta aderente all'utero, per dispensare il necessario alimento al <lb/>pulcino e al feto, non esita punto in ammettere come verissime le somi&shy;<lb/>glianze, tante volte notate dagli Embriologi, tra gli animali e le piante, nelle <lb/>quali le innumerevoli radicelle suggono gli alimenti dalla terra, come le in&shy;<lb/>numerevoli venuzze suggon gli umori alibili dall'uovo stesso o dall'utero <lb/>della madre. </s></p><p type="main">

<s>Ma la pianta si riman perpetuamente in quella sua prima e natia con&shy;<lb/>dizione, mentre per l'animale non &egrave; che precaria. </s>

<s>Schiuso l'uovo e aperto <lb/>l'utero, riceve il nuovo nato in altri modi, e per altre vie l'alimento: si <lb/>suggellano le fonti de'vasi umbilicali, e s'apre al sacco dello stomaco e degli <lb/>intestini la bocca. </s>

<s>L'albume e il latte simulano da principio i modi della <lb/>prima nutrizione fetale, ma poi vien tempo che quel nutrito di latte si rende <lb/>indipendente anche dalle mammelle, divenuto atto d'andar per s&egrave; medesimo <lb/>in cerca del cibo. </s>

<s>Gli organi, che lo pongono in cos&igrave; fatte nuove condizioni, <lb/>sono princ&igrave;palmente quelli del moto, per i quali si pone in volontaria e spon&shy;<lb/>tanea relazione coi corpi circostanti, per ridurli a sodisfare ai bisogni, e alle <lb/>comodit&agrave; della vita. </s></p><pb xlink:href="020/01/1377.jpg" pagenum="252"/><p type="main">

<s>La locomozione spontanea per&ograve;, alla quale servono i muscoli degli arti <lb/>e le ossa, aveva bisogno di qualche guida, dall'animale ritrovata fedelissima <lb/>nei sensi, e principalmente in quello del tatto, che perci&ograve; &egrave; s&igrave; squisito nelle <lb/>mani e ne'piedi, e, per tutto l'integumento esposto a ricevere le prime <lb/>esterne impressioni del moto, largamente diffuso. </s></p><p type="main">

<s>La superficialit&agrave; del tatto era dunque cos&igrave; benissimo accomodata a ser&shy;<lb/>vire all'animale di guida, in quel libero aggirarsi che fa per lo spazio pieno <lb/>di tanti altri corpi, de'quali era necessario conoscere le relazioni di posi&shy;<lb/>zione, per cercarli con amore o per rifuggire da essi con odio. </s>

<s>Primo e prin&shy;<lb/>cipale oggetto di questo amore e di quest'odio erano que'corpi buoni a ser&shy;<lb/>vire di cibo, de'quali era necessario avesse l'animale stesso conoscenza pi&ugrave; <lb/>che superficiale, e fu a questo scopo dalla provvidente Natura ordinato l'or&shy;<lb/>gano del gusto. </s></p><p type="main">

<s>Si pu&ograve; dire che sia il gusto un finissimo tatto di ci&ograve; che hanno i corpi <lb/>alibili, no nella loro esterior superficie, ma nell'intima loro sostanza, che ha <lb/>da trasformarsi nella sostanza stessa dell'animale, e perci&ograve; si sciolgono quei <lb/>corpi sopra la lingua, come in mestruo nella saliva, per rendersi cos&igrave; a pi&ugrave; <lb/>intimo contatto colle papille nervee, pi&ugrave; squisitamente elaborate di quelle <lb/>disperse sopra la cute. </s></p><p type="main">

<s>I due detti sensi perci&ograve; sono il fondamento della vita di relazione, per <lb/>conferma di che si osserva che ne partecipano in qualche modo anche le <lb/>piante. </s>

<s>Del tatto danno indizio alcune foglie che si risentono, o toccate da <lb/>qualche corpo solido, o ripercosse dagli stessi raggi di luce, ma questa pro&shy;<lb/>priet&agrave; non &egrave; visibile che in alcuni casi particolari. </s>

<s>S'ha pi&ugrave; manifesto indi&shy;<lb/>zio e universale esempio di ci&ograve; nelle radicelle, le quali si vedono andar sotto <lb/>terra a cercare, e, come avessero gusto, a scegliere gli alimenti, preferendo, <lb/>se libera, la pi&ugrave; facile via e pi&ugrave; spedita, o divertendo il passo, se qualche <lb/>ostacolo s'interponga o dall'arte o dalla Natura. </s></p><p type="main">

<s>L'animale per&ograve;, che appartiene ad un ordine superiore, &egrave; fornito di altri <lb/>sensi, di che mancano affatto le piante, e patiscono difetto gli stessi animali <lb/>inferiori. </s>

<s>L'eccellenza de'nuovi sensi sopra il tatto ed il gusto si rivela prin&shy;<lb/>cipalmente da ci&ograve;, che mentre in questi non si produce la sensazione, se <lb/>non sia l'oggetto immediatamente applicato al sensorio, in quelli agisce l'og&shy;<lb/>getto stesso anche a distanza, o per una diffusione di s&egrave; o per un qualche <lb/>mezzo interposto. </s></p><p type="main">

<s>Sono i corpi, individualmente e nella mondana composizione, in vario <lb/>modo di s&egrave; diffusivi, cosicch&egrave; un'aura circonda ogni oggetto particolare sopra <lb/>la terra; un'aura circonda tutta insieme la terra stessa in s&egrave; conglobata; <lb/>un'aura circonda l'universo. </s>

<s>Ogni corpo terreno perci&ograve; si trova continua&shy;<lb/>mente immerso in tre distinte ammosfere, le quali, oltre ad avere un'azione <lb/>fisica sulle cose circondate, hanno un'azione specifica sopra gli organi del&shy;<lb/>l'animale. </s>

<s>L'esalazione di alcuni corpi particolari agisce sull'odorato; l'esa&shy;<lb/>lazione della terra, ossia l'aria, agisce specificamente sull'udito, e l'esalazione <lb/>dell'Universo, ossia l'etere, agisce sopra la vista. </s></p><pb xlink:href="020/01/1378.jpg" pagenum="253"/><p type="main">

<s>Nell'annoverare i sensi, l'odorato ricorre per ordine nel mezzo, e ve&shy;<lb/>ramente partecipa della qualit&agrave; e della natura de'due antecedenti, e de'due <lb/>conseguenti. </s>

<s>Ne differisce per&ograve; da questi notabilmente perch&egrave;, mentre l'aura <lb/>odorosa &egrave; sostanziale dell'oggetto, l'aria e l'etere nell'orecchio e nell'oc&shy;<lb/>chio non hanno altra ragion che di segno, i caratteri del quale sono i tre&shy;<lb/>mori armonici, la luce, l'ombra, i colori. </s></p><p type="main">

<s>Passar dal segno al significato &egrave; opera tutta propria dell'intelligenza, <lb/>la quale par che abbia ne'due nobilissimi sensi i principali strumenti del <lb/>suo esercizio, e che ritrovi in essi le necessarie condizioni al suo magistero. <lb/></s>

<s>&Egrave; perci&ograve; che i due organi sono elaborati con arte maravigliosa, dalla quale, <lb/>piuttosto che dal cervello, si pu&ograve; trarre argomento de'gradi dell'intensit&agrave; <lb/>di luce intellettuale, che si accendono ne'diversi individui, e nei diversi or&shy;<lb/>dini animali. </s></p><p type="main">

<s>Quella luce dall'altra parte, ch'&egrave; splendore di vita, &egrave; per noi chiusa in <lb/>tenebre profonde: per noi, che non abbiamo della vita stessa altro argo&shy;<lb/>mento, che dai moti delle membra e dalle impressioni, che fanno in noi i <lb/>corpi, o applicati immediatamente alla cute, alla lingua, alla pituitaria, o <lb/>trasmessi all'orecchio, e resi parventi all'occhio attraverso al mezzo dell'aria <lb/>che circonda la terra, o dell'etere che circonda l'universo. </s>

<s>Che se i tremori <lb/>armonici e le ondulazioni eteree si trovarono involte nel mistero, quando si <lb/>considerarono sotto il semplice aspetto fisico, pensiamo che dovr&agrave; essere, <lb/>quando si vengano a riguardare sotto l'aspetto fisiologico; quando si pre&shy;<lb/>tende cio&egrave; di avere scienza del modo, come un increspamento d'aria diventi <lb/>udito, o un ondeggiare di etere vista. </s></p><p type="main">

<s>Si dovrebbe da queste considerazioni concludere che lo studio della fisio&shy;<lb/>logia dei sensi non &egrave; soggetto d'esperienza, e che perci&ograve; non entra nella <lb/>nostra Storia, se non fosse vero dall'altra parte che son di ogni senso esterno <lb/>strumenti fisiologici un organo proprio e un sensorio, e che oggetto di ogni <lb/>percezion sensitiva &egrave; un corpo, il quale fisicamente agisce, bench&egrave; l'azione <lb/>fisica si trasformi, esaltata in azion fisiologica, in un certo modo per noi mi&shy;<lb/>sterioso. </s>

<s>Ma l'organo e il sensorio son soggetti di anatomiche osservazioni, <lb/>e la Fisiologia pu&ograve; illustrarsi con fisiche esperienze, come fa per esempio <lb/>l'Acustica, rispetto all'udito, e l'Ottica rispetto alla vista. </s></p><p type="main">

<s>Non &egrave; dunque il metodo sperimentale inutile in questo studio, e anzi <lb/>a lui solo si deve se nulla s'&egrave; inteso, specialmente intorno al modo come <lb/>si rappresentano le immagini nell'occhio per apprenderne la vista; come i <lb/>tremori armonici risveglino l'udito; quali siano gli organi proprii dell'odo&shy;<lb/>rato, del gusto e del tatto. </s>

<s>Ampio soggetto &egrave; questo di narrazioni, bench&egrave; <lb/>la brevit&agrave; ci consigli di restringer le molte cose da dire nelle poche pagine, <lb/>in che si svolge questo insiem col seguente capitolo di Storia. </s></p><p type="main">

<s>Incominciando dal tatto, che a giudizio dei pi&ugrave; &egrave; il senso fondamentale, <lb/>chi avesse domandato agli antichi qual ne fosse di lui lo strumento, si sa&shy;<lb/>rebbe sentito rispondere: &ldquo; Tactus instrumentum esse quiddam intus in cor&shy;<lb/>pore abditum, quod potestate tale est, quale actu est tangibile. </s>

<s>&rdquo; L'enim-<pb xlink:href="020/01/1379.jpg" pagenum="254"/>matico responso &egrave; in qualche modo interpetrato dal Cesalpino nella V delle <lb/>sue Peripatetiche questioni, cos&igrave; esplicando le teorie aristoteliche: &ldquo; Ob haec <lb/>igitur solum instrumentum tactus internum est, reconditum; caeterorum sen&shy;<lb/>suum sensoria exteriora sunt et quodammodo media: unum enim est pri&shy;<lb/>mum omnium sensorium sanguinem. </s>

<s>Sanguineam quoque esse oportet eorum <lb/>naturam, non enim receptio sine materia fit, sine spiritu, qui in sanguine <lb/>est &rdquo; (Venetiis 1571, pag. </s>

<s>115). </s></p><p type="main">

<s>Quando poi Galeno dimostr&ograve; che la sensibilit&agrave; non appartiene al sangue <lb/>ma ai nervi, i quali hanno la loro origine, no dal cuore ma dal cervello, e <lb/>allora s'incominci&ograve; a dire pi&ugrave; saviamente che lo strumento del tatto era la <lb/>cute, ma non se ne seppe, infin a mezzo il secolo XVII, riconoscere l'or&shy;<lb/>gano speciale. </s>

<s>Fu primo il Malpighi a fare quella scoperta, la quale &egrave;, se <lb/>altra mai, per s&egrave; e per le sue conseguenze, degna di storia. </s></p><p type="main">

<s>Attendeva l'insigne Fisiologo bolognese a studiare la composizione ana&shy;<lb/>tomica della lingua, e diligentemente osservando col microscopio quella dei <lb/>bovi, delle capre, delle pecore e dell'uomo stesso, ne ritrov&ograve; la superfice <lb/>sparsa di piccole eminenze coniche, o di papille, differenti cos&igrave; tra loro, nella <lb/>struttura e nella grandezza, da poterle con facilit&agrave; distinguere in tre classi. <lb/></s>

<s>&ldquo; Observantur enim aliquae grandiores, quae ad latera praecipue apicis lin&shy;<lb/>guae situantur inter infra exarandas. </s>

<s>In area etiam superiori linguae qua&shy;<lb/>drato ordine disponuntur: circa mediam regionem, ubi albescit lingua, rarae <lb/>observantur: in basis autem lateribus aliquae et insigniores. </s>

<s>Haec, substantia <lb/>et figura, videntur aemulari cornua emissilia et conductilia, quae in limacibus <lb/>conspiciuntur; ... exordium habent a nervoso et papillari corpore.... Succe&shy;<lb/>dunt alterius ordinis papillae copiosiores exaratis: quot enim cornua exterius <lb/>linguam tegunt, tot etiam huius generis nerveae papillae intus reperiuntur. </s>

<s><lb/>Hae, exortae a communi papillari corpore, in mediocrem altitudinem elevan&shy;<lb/>tur, et ab extremo capite nerveas propagines ulterius emittunt, quae subin&shy;<lb/>trant iam exaratos sinus, et eorum radiclbus occorrunt.... Circa basim lin&shy;<lb/>guae, in cornuum situ, papillae nerveae enarratae foras eminentes mutant <lb/>figuram, et obtusiores, mox subrotundae et depressiores fiunt, et harum insi&shy;<lb/>gniores non valde absimiles sunt iis, quae ad radices dentium in buccis obser&shy;<lb/>vantur &rdquo; (Opera Omnia, De lingua, Londini 1687, pag. </s>

<s>15, 16). </s></p><p type="main">

<s>A quale uso possono mai servire queste papille, che debbon essere senza <lb/>dubbio una espansione dei nervi? </s>

<s>incominci&ograve; a domandare a s&egrave; medesimo <lb/>il Malpighi. </s>

<s>Sarebb'egli vero, che qui risegga l'organo del gusto? </s>

<s>L'idea. </s>

<s><lb/>che tale dovess'essere veramente il fine, per cui furono dalla Natura impo&shy;<lb/>sti sopra la lingua que'corpi papillari ora nuovamente scoperti; si rappre&shy;<lb/>sentava al discopritore sotto il pi&ugrave; lusinghiero aspetto della verit&agrave;, ripen&shy;<lb/>sando a ci&ograve; che, intorno allo speciale strumento del gusto, era stato detto <lb/>da'suoi predecessori. </s>

<s>Il Bartholin e il Veslingio, forse per l'opinione che <lb/>avevano non trovarsi in tutto il corpo carne che si somigli con quella della <lb/>lingua, credettero che il senso del gusto non avesse altr'organo che la so&shy;<lb/>stanza di lei carnosa. </s>

<s>Il Warthon, avendo trovato alcune glandole alla radice <pb xlink:href="020/01/1380.jpg" pagenum="255"/>della lingua, sospett&ograve; che fosse in esse la sede propria del senso, ma poi lo <lb/>Stenone dimostr&ograve; che appartenevano al genere delle glandole salivali, e che <lb/>erano perci&ograve; ordinate a secernere e no a sentire. </s>

<s>N&egrave; punto pi&ugrave; ragionevole <lb/>di queste sembrava al Malpighi l'opinion di coloro, che attribuivano la fa&shy;<lb/>colt&agrave; di gustare alla membrana, da cui superficialmente &egrave; rivestita la lingua, <lb/>perch&egrave; &ldquo; si exteriores membranae gustandi munus haberent, Natura forte <lb/>sinuosas non abdidisset vias in binis exterioribus involucris exculptas, qui&shy;<lb/>bus videtur ulteriorem aditum permittere sapidis corporibus &rdquo; (ibid., pag. </s>

<s>18). </s></p><p type="main">

<s>Di qui ne trae il Malpighi una conclusione, che riesce nuova nella storia <lb/>della Fisiologia, ed &egrave; che il senso del gusto consista in quel vellicar che <lb/>fanno, le particelle sapide, le papille nervee disperse sopra la lingua, a quel <lb/>modo che, dal vellicar che fanno l'aria e la luce, co'loro tremori, il tim&shy;<lb/>pano e la retina, si produce la sensazion dell'udito e della vista. </s>

<s>&ldquo; Quare, <lb/>cum dictis meatibus insignibus occurrant papillaria corpora, probabilius est <lb/>in his ultimo, ex subintranti sapido humore, titillationem et mordicationem <lb/>quamdam fieri, quae gustum efficiat. </s>

<s>Fusa enim salia et consimilia, salivae <lb/>vel alteri humori commixta, proprio pondere, vel prementis aeris ope, sinus <lb/>mox expositos, substantia, nerveas papillas diversimode feriunt, vel blando <lb/>quodam motu ipsas demulcent, ita ut, ex diversa figura ingredientis salini <lb/>corporis, eiusque vario motu et insinuatione, diversae corporum species na&shy;<lb/>turae cognatae vel eidem aversae emergant &rdquo; (ibid., pag. </s>

<s>18). Hanno di qui <lb/>origine le varie impressioni del gusto, le quali possono talvolta ridursi a do&shy;<lb/>lorose, come racconta il Cardano di quell'Augusto Corbetta, che sentiva do&shy;<lb/>iore a toccar la lingua col pepe, &ldquo; nam ex pipere quidem subintrante lace&shy;<lb/>rabantur nerveae papillae, unde dolor. </s>

<s>Non aderat autem saporis sensus, quia <lb/>prima radix nervosi corporis ad gustum destinati non consentiebat, vel non <lb/>commovebatur blanda illa motione et affectione qua gustum edit, sicut in au&shy;<lb/>ditu et visu contingit, organum plus iusto concutiente vel vellicante obiecto &rdquo; <lb/>(ibid., pag. </s>

<s>19, 20). </s></p><p type="main">

<s>Come nella scoperta dell'organo del gusto, e nelle ipotesi speculate per <lb/>rendere la ragione della variet&agrave; de'sapori, s'incontrassero quasi nel mede&shy;<lb/>simo tempo il Bellini e il Fracassati, lo diremo tra poco, per non interrom&shy;<lb/>pere il filo della storia, dalla quale ha da mostrarsi in che modo la scoperta <lb/>delle papille nervee sopra la lingua, ad uso del gusto, conducesse il Malpi&shy;<lb/>ghi stesso alla scoperta delle papille nervee sopra la cute, ad uso generale <lb/>del tatto. </s>

<s>Quella storia poi &egrave; cos&igrave; narrata dall'Autore medesimo in questa <lb/>forma a Giacomo Ruffo, visconte di Francavilla: </s></p><p type="main">

<s>&ldquo; Mens de ambiguo usu, pyramidalibus in lingua descriptis papillis assi&shy;<lb/>gnato, anxia torquebatur. </s>

<s>Mens igitur aciem microscopio munitam veluti auxi&shy;<lb/>liares convocat copias, et quia brutorum non aderant illico perquirenda mem&shy;<lb/>bra, extremum digiti lustro apicem, et dum attentive inaequales illas rugas <lb/>quasi in gyrum vel in spiras ductas contemplor, eo e quibusdam alveolis et <lb/>finibus subrotunda, ac veluti diaphana emergunt corpora, miro ordine per <lb/>interiorem totius digiti faciem copiose dispersa. </s>

<s>Exultavit animus rei novi-<pb xlink:href="020/01/1381.jpg" pagenum="256"/>tate laetabundus, et praecipiti subitoque quodam iudicio in eum venit sen&shy;<lb/>sum exigua haec corpora eandem naturam et usum cum pyramidalibus lin&shy;<lb/>guae papillis sortiri, latumque philosophandi campum mihi videbar aperuisse. </s>

<s><lb/>Sed breve conceptae hoc felicitatis momentum ocyus effluxit, dum enim lon&shy;<lb/>giori iterum indagine perquiro papillas, deterso digiti apice, frustra eas quaero <lb/>mox sensim erumpentes compresso digito auctiores, et diaphanas reddo, et <lb/>tandem mutata figura effluere, non sine animi moerore, ut verum tibi fa&shy;<lb/>tear, intueor, atque iterum absterso digito humoris instar eas abire conspexi. </s>

<s><lb/>His tamen nequaquam fractus animus ex concepto in utrisque papillis usu, <lb/>quo sibi maxime complacuerat, aliena iubet rimari ex inaequalitate cutis <lb/>quae in nobis etiam observatur, latens aliquod papillae consimile se reper&shy;<lb/>turum confidens &rdquo; (Ibid., De externo tactus organo, pag. </s>

<s>22). E in fatti se&shy;<lb/>zionando i piedi a varii animali, e diligentemente osservando, ritrov&ograve; quello <lb/>che gli era prima apparito e poi scomparso nel suo proprio dito, intorno al <lb/>quale non si poteva con troppa confidenza esercitare il ferro anatomico. </s></p><p type="main">

<s>And&ograve; il sagace investigatore a posare a dirittura la sua attenzione sui <lb/>piedi, parendogli esser quelli gli organi, che meglio corrispondessero nei <lb/>bruti alle mani degli uomini, ma poi ripensando che dev'essere ne'palpi <lb/>delle labbra pi&ugrave; che altrove squisitissimo il tatto, si volse ad esaminar quelle <lb/>parti con grandissima diligenza, e vi trov&ograve; in gran numero papille simili a <lb/>quelle scoperte gi&agrave; sulla lingua. </s>

<s>&ldquo; Sed quia brutorum aliqua, praecipue qua&shy;<lb/>drupedia, superiori labro et externis naricibus, veluti manibus, terram et <lb/>obiecta alimenta explorare solent, necessarium duxi inquirere an in huius&shy;<lb/>modi consimilem structuram molita fuerit Natura. </s>

<s>Bovis igitur labrum ad <lb/>trutinam revoco, et in superiori praecipue parte, elatae quaedam areae, di&shy;<lb/>versae tamen figurae in cuticula sese offerunt; nigriores tamen papillas in <lb/>singulis areis copiose dispersas reperio, inter quae latiora quaedam hiant <lb/>foramina, quae salivam sive sudorem, compressa narium mole, pleno ore <lb/>eructant. </s>

<s>Dum interim externum involucrum evellitur, ecce papillarum pe&shy;<lb/>dunculos abripi disrumpique video. </s>

<s>Hi autem erumpunt, ut mos est, a re&shy;<lb/>ticulari et mucoso corpore, et tandem altas habent radices in subiecta cute, <lb/>sub qua copiosissimae locantur glandulae proprio vase excretorio ditatae, ad <lb/>exposita orificia desinente. </s>

<s>In sue etiam eandem fere structuram adinveni &rdquo; <lb/>(Ibid., pag. </s>

<s>25). </s></p><p type="main">

<s>Passa con pi&ugrave; diligenza che mai ad esaminare la mano, e ne trova <lb/>l'epidermide composta di una membrana muccosa e di una reticolare, nelle <lb/>fitte areole della quale s'annidano le papille nervee, insiem con altre di pi&ugrave; <lb/>fosco aspetto (dalle quali ei crede dipendere la nigrizia degli Etiopi) e le <lb/>ghiandole sudorifere. </s>

<s>In quelle papille-nervee disperse tutto intorno per la <lb/>cute, ma pi&ugrave; condensatamente in alcune parti di lei, riconobbe il Malpighi <lb/>il precipuo organo del tatto, il quale opera secondo lui a produrre la sen&shy;<lb/>sazione in un modo simile a quello delle papille nervee ricorrenti sopra la <lb/>lingua. </s>

<s>&ldquo; Haec repetitis sectionibus deprehendi, ex quibus non improbabi&shy;<lb/>liter deducam, sicuti ex grandioribus et elatioribus papillis, alias a me in <pb xlink:href="020/01/1382.jpg" pagenum="257"/>lingua observatis, gustus organum elicitur ex peculiari situ et nervorum pro&shy;<lb/>tractu; ita, ex copiosa harum papillarum congerie et copiosiori grandiorique <lb/>earum proventu in organis, ubi maxime animalia tactus motione afficiuntur, <lb/>ex earundem etiam propagine in reliquo ambitu, ubi tactus vires etiam exe&shy;<lb/>rit, adaequatum tactus organum sufficienter haberi &rdquo; (Ibid., pag. </s>

<s>23). </s></p><p type="main">

<s>Cos&igrave; la scoperta delle papille nervee sopra la lingua condusse il Malpi&shy;<lb/>ghi all'altra simile scoperta delle papille nervee sopra la cute, e l'organo <lb/>del tatto gli si rivel&ograve;, in questo modo per analogia, dall'organo del gusto, <lb/>dove le dette papille nervee, essendo in pi&ugrave; ristretta superficie raccolte e <lb/>perci&ograve; pi&ugrave; notabili, davano anche pi&ugrave; facile indizio de'loro ufficii. </s>

<s>Ci&ograve; rende <lb/>forse la ragione di un fatto singolarissimo nella storia, ed &egrave; che concorsero <lb/>col Malpighi nella scoperta dell'organo del gusto il Bellini, che la divulg&ograve; <lb/>nel suo trattato <emph type="italics"/>Gustus Organum,<emph.end type="italics"/> e il Fracassati, che dottamente la com&shy;<lb/>ment&ograve; nella sua esercitazione epistolica <emph type="italics"/>De lingua<emph.end type="italics"/> indirizzata allo stesso <lb/>Malpighi. </s></p><p type="main">

<s>Il Bellini, ch'ebbe primo a notare la singolarit&agrave;, alla quale abbiamo ac&shy;<lb/>cennato, qualific&ograve; il fatto per una vittoria riportata cogli amici in comune, <lb/>della quale sarebbe indegna cosa sentire invidia. </s>

<s>Dove altri ne avrebbe pro&shy;<lb/>vato dispiacere, egli anzi ne godeva. </s>

<s>&ldquo; Gaudeo tamen, tum quia alienam mihi <lb/>sapientiam obfuturam non iudico, tum quia observationi non easdem forte <lb/>meditationes aptamus, sed quisque suas pro genio; tum quia, cum res inter <lb/>amicos peracta sit, communia quoque dicenda, potius quam propria, hac <lb/>in re videntur; tum denique quod, si de hoc communi invento dolerem, aut <lb/>invidus aut arrogans audirem, quorum utrumque cane peius et angue sem&shy;<lb/>per odi, utpote quae et a societatibus expellunt, et humanitate spoliant, et <lb/>nos ridiculos faciunt, quibus quid homini accidere iniucundius potest, quid <lb/>miserabilius? </s>

<s>&rdquo; (Gustus org. </s>

<s>Bononiae 1665, pag. </s>

<s>243, 44). </s></p><p type="main">

<s>Nonostante, non possono non sentirsi i lettori frugare a una viva cu&shy;<lb/>riosit&agrave; di sapere in che modo occorresse al Bellini di fare la scoperta del&shy;<lb/>l'organo del gusto, entrando quasi dentro i reconditi pensieri, che s'agita&shy;<lb/>vano per la mente al Malpighi. </s>

<s>E giacch&egrave; il Bellini stesso si esibisce spontaneo <lb/>a sodisfare a quella curiosit&agrave;, ascoltiamone le parole da noi cos&igrave; liberamente <lb/>tradotte dal citato trattatello latino: </s></p><p type="main">

<s>&ldquo; M'incontrai un giorno in Firenze in Gian Alfonso Borelli, mio aman&shy;<lb/>tissimo Maestro, e dopo averlo salutato gli domandai: &mdash; Che cosa ci &egrave; di <lb/>nuovo? </s>

<s>&mdash; Oh! ci ho una bellissima nuova da darti, ei mi rispose allora, <lb/>non per&ograve; da parte mia, ma da parte del nostro signor Marcello. </s>

<s>Leggi ci&ograve; <lb/>che il nostro accuratissimo osservatore ha ultimamente scoperto sopra la lin&shy;<lb/>gua elissata: &mdash; e ponendomi in mano la lettera seguitava a dire: &mdash; Medita <lb/>attentamente quel che ci &egrave; scritto, e ci troverai una novit&agrave; elegantissima. <lb/></s>

<s>&mdash; Allora io, bench&egrave; non conoscessi di persona il Malpighi, ma solo per i suoi <lb/>scritti, mosso dalla grande stima che avevo di quell'uomo, mi detti avida&shy;<lb/>mente a leggere tutto quel trattato, nel quale, ritrovando cos&igrave; particolarmente <lb/>descritta la muccosa della lingua, a cui nessuno prima di lui aveva pensato; <pb xlink:href="020/01/1383.jpg" pagenum="258"/>&mdash; e noi, dissi fra me, ci staremo cosi oziosi ad ascoltare le belle cose sco&shy;<lb/>perte dagli altri? </s>

<s>Perch&egrave; non diam mano all'opera, e sulle orme segnateci <lb/>da Marcello non ci mettiamo a consultar la Natura, per comprovar con l'ora&shy;<lb/>colo di lei quel ch'egli ha asserito? </s>

<s>&mdash; S'aggiungevano intanto gli stimoli <lb/>che mi venivano dal Borelli, cosicch&egrave; datomi alacremente allo studio anato&shy;<lb/>mico della lingua in varii animali, ritrovai finalmente tutto quello, e anzi <lb/>qualche cosa di pi&ugrave;, in quell'organo del gusto, non scoperta dallo stesso <lb/>Malpighi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Mentre che cos&igrave; fatte cose seguivano in Firenze, anche al signor Carlo <lb/>Fracassati, mio amicissimo, &egrave; partecipata dal Borelli la medesima notizia, solo <lb/>per&ograve; accennandogli cos&igrave; in generale che il Malpighi aveva ritrovata qualche <lb/>importante novit&agrave; sopra la lingua. </s>

<s>Quell'uomo perspicacissimo allora, non <lb/>sospettando qual fosse propriamente la nuova scoperta malpighiana, datosi <lb/>alacremente allo studio di quel membro, mi scrive pochi giorni dopo da Bo&shy;<lb/>logna in tali termini, che io mi avvidi essersi egli abbattuto a fare la mia <lb/>medesima scoperta. </s>

<s>Ci rallegrammo a vicenda, compiacendoci che, simili es&shy;<lb/>sendo nel genio, riuscissimo compagni nella fortuna. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Stavano le cose in questi precisi termini, quand'ecco venir di Mes&shy;<lb/>sina nuove lettere del Malpighi, le quali annunziavano la scoperta stessa <lb/>delle papille nervee disseminate sulla muccosa linguale, ch'era occorsa a <lb/>fare a me in Firenze e al Fracassati in Bologna, E perch&egrave; l'epistola mal&shy;<lb/>pighiana era stata di Messina mandata apposta perch&egrave; dovessesi pubblicare, <lb/>aveva fatto proposito di bruciare le mie scritture come inutili oramai e anzi <lb/>come dispregevoli, imperocch&egrave; chi poteva mettersi a correre il palio con quel <lb/>genio di Marcello Malpighi, senza farsi o deridere dal volgo o compassionare <lb/>dai dotti? </s>

<s>&rdquo; (Gustus Organum cit., pag. </s>

<s>177-80). </s></p><p type="main">

<s>Nonostante, forse ai conforti dello stesso Malpighi, deliber&ograve; di dare alla <lb/>luce in Bologna il suo trattatello, dove s'illustravano le teorie della sensa&shy;<lb/>zione, affermandosi che le varie affezioni sensitive dipendono dalle varie forme <lb/>cristalline de'corpi &ldquo; et nihil aliud esse saporem quam ipsum sal determina&shy;<lb/>tis linguae partibus applicatum, in quibus et ratione figurarum ipsius, et <lb/>ratione conformationis partium linguae, illa passio excitetur, ex qua dolor <lb/>aut delectatio determinata proveniens dicatur iucunda vel iniucunda gustatio, <lb/>suavis aut insuavis, talis ac talis sapor &rdquo; (ibid., pag. </s>

<s>44). </s></p><p type="main">

<s>L'anno dopo la pubblicazione del trattato del Bellini usciva fuori, pure <lb/>in Bologna, l'esercitazione epistolica <emph type="italics"/>De lingua<emph.end type="italics"/> del Fracassati, in principio <lb/>della quale narra l'Autore come esaminando la lingua elissata di un vitello <lb/>rimanesse preso di maraviglia dal trovar che sotto quelle piccole eminenze <lb/>coniche, che la rendono tutta scabrosa, si ascondevano le estremit&agrave; papillari&shy;<lb/>di tanti funicoli nervosi, che scaturivano di sotto dalla sostanza carnosa della <lb/>stessa lingua. </s>

<s>Mentre pensava tutto fra s&egrave; a che cosa potessero mai servire <lb/>quelle cos&igrave; cospicue e numerose papille nervee, gli giunge la lettera nella <lb/>quale il Borelli, come al Bellini, dava anche a lui la notizia della nuova sco&shy;<lb/>perta del Malpighi. </s>

<s>Conobbe allora il Fracassati di essersi egli pure incon-<pb xlink:href="020/01/1384.jpg" pagenum="259"/>trato in quella medesima scoperta, ond'&egrave; che scriveva nella citata Esercita&shy;<lb/>zione epistolica allo stesso Borelli, come mosso da quell'avviso, &ldquo; ad primam <lb/>meam redeo perfunctoriam observationem &rdquo; dalla quale si vide allora spa&shy;<lb/>rire ogni dubbio. </s>

<s>&ldquo; Credo enim, poi immediatamente soggiunge, posse non <lb/>valde ab amici invento nostrum, qualecumque sit, abludere, adeo ut ambo&shy;<lb/>rum circa rem eamdem, licet impari successu, idem forte sit futurus cona&shy;<lb/>tus &rdquo; (Inter Malpighi Opera, T. II, Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>176). E prose&shy;<lb/>gue a illustrare l'anatomia dell'organo e le speculazioni del Malpighi e del <lb/>Bellini intorno alle forme cristalline de'sali, che variamente impressionando <lb/>la lingua son causa del sentirsi in essa le variet&agrave; de'sapori. </s></p><p type="main">

<s>La scoperta dei tre nostri insigni anatomici riusc&igrave; molto proficua ai pro&shy;<lb/>gressi della Fisiologia dei sensi, perch&egrave; dimostrava, anche per il tatto e per <lb/>il gusto, esser organo primario, non la cute o la sostanza carnosa della lin&shy;<lb/>gua, ma il nervo, che fu perci&ograve; riconosciuto per il sensorio comune. </s>

<s>Nono&shy;<lb/>stante per&ograve; che fossero queste cose dimostrate per certe, nei principii del <lb/>secolo XVIII disputavasi tuttavia qual fosse il nervo che presiedesse all'ol&shy;<lb/>fatto, alcuni attribuendo quel particolare ufficio alle diramazioni del primo, <lb/>altri a quelle del quinto paio. </s></p><p type="main">

<s>Ma ben pi&ugrave; antichi erano i dubbii agitati intorno all'organo, distrigan&shy;<lb/>dosene tutti facilmente col dire che quell'organo era il naso, il quale attra&shy;<lb/>verso ai cribri dell'osso etmoide mette in comunicazione con l'aria esterna <lb/>il cervello. </s>

<s>Fu anzi questa ipotesi, la quale fece credere a Galeno e agli <lb/>stessi suoi predecessori che gli effluvii odorosi agissero immediatamente sui <lb/>processi mamillari. </s></p><p type="main">

<s>I grandi nostri Italiani restauratori della scienza anatomica ripeterono <lb/>queste medesime dottrine. </s>

<s>Realdo Colombo descrivendo, sulla fine del cap. </s>

<s>V <lb/>del I libro <emph type="italics"/>De re anatomica,<emph.end type="italics"/> l'osso etmoide, cos&igrave; detto dai Greci <emph type="italics"/>quod ima&shy;<lb/>ginem cribri referat,<emph.end type="italics"/> &ldquo; per quae foramina, soggiunge, patere solet ascensus <lb/>odoribus cerebrum petentibus, cuius rei argumentum inde sumimus, quod <lb/>coriza, vel gravi destillatione laborantes odorandi facultatem interim amit&shy;<lb/>tunt, opplentur enim foraminula haec pituita spirituum gravitate detenta, <lb/>atque olfactiva organa ita impediuntur, ut ne ullum quidem odorem sentire <lb/>queant, aut sensili virtuti suggerere &rdquo; (Venetiis 1559, pag. </s>

<s>25). E nel cap. </s>

<s>II <lb/>del libro VIII, proponendosi di descrivere gli organi e i nervi dell'odorato, <lb/>incomincia a dire che nella parte anteriore del cervello, verso la sua base, <lb/>occorrono ad osservarsi due corpi bislunghi detti processi mamillari, ai quali <lb/>due organi &ldquo; odores per nares attracti ascendunt: itaque distinguimus quae <lb/>bene, quae male oleant, propterea odoratus instrumenta merito appellari pos&shy;<lb/>sunt &rdquo; (ibid., pag. </s>

<s>194). </s></p><p type="main">

<s>Un mezzo secolo dopo non aveva ancora la scienza progredito di un <lb/>passo, nemmen per opera di Colui, che si applic&ograve; con speciale amore allo <lb/>studio dei cinque sensi, e ne riport&ograve; la gloria di varie scoperte. </s>

<s>Intendiamo <lb/>dire del piacentino Giulio Casserio, il quale, dal considerar che gli odori na&shy;<lb/>turalmente salgono in alto, argomentando che le parti del cerebro meglio <pb xlink:href="020/01/1385.jpg" pagenum="260"/>esposte a riceverne le impressioni <emph type="italics"/>ad os cribrosum locatae esse debuerunt, <lb/>ut tamquam fidelissimi exploratores quidquid aeris ingreditur examinent;<emph.end type="italics"/><lb/>si persuase facilmente con Galeno e con Aristotile esser organo dell'olfatto <lb/>i processi mamillari. </s>

<s>A cos&igrave; fatta opinione poi soggiunge &ldquo; unusquisque <lb/>acquiescet facilius, si ubi ossa colatoria obstructa sunt olfactum impediri <lb/>meminerit, signum profecto id quod statim post haec ossa occurrit verum <lb/>olfactus organum censeri debere &rdquo; (De quinque sensibus, Venetiis 1609, <lb/>pag. </s>

<s>137). </s></p><p type="main">

<s>Ma non avevano le questioni per solo argomento il sensorio e l'organo: <lb/>si disputava altres&igrave; intorno all'oggetto, perch&egrave;, sebben tutti facilmente ap&shy;<lb/>prendiamo gli odori pel senso, non a tutti &egrave; facile definire in che consista <lb/>la loro natura. </s>

<s>I Fisiologi per lo pi&ugrave;, o per crederlo difficile o per crederlo <lb/>inutile, si passano sopra questo argomento, e non sar&agrave; perci&ograve; discaro agli <lb/>studiosi che si riferiscano in tal proposito i pensieri di uno scrittore pochis&shy;<lb/>simo noto; pensieri che dall'altra parte ci rivelano in poche parole la fe&shy;<lb/>condit&agrave; e, se non l'importanza, la curiosit&agrave; almeno di questo soggetto. </s>

<s>An&shy;<lb/>tonio Nardi, nella veduta XXX della scena I, &egrave; colui che verso il 1640 ci <lb/>lasciava manoscritti cos&igrave;, intorno all'odorato e agli odori, quelli che si di&shy;<lb/>ceva suoi filosofici pensieri: </s></p><p type="main">

<s>&ldquo; Risolvonsi tutte le composte sostanze a poco a poco in minime par&shy;<lb/>ticelle, mediante gli universali o particolari movimenti e momenti, e cos&igrave; ve&shy;<lb/>diamo dentro delle camere volare infiniti corpicelli, per il raggio del sole, <lb/>quali dal pavimento, dalle vesti, dai libri e da ogni quasi cosa esalano. </s>

<s>Molto <lb/>pi&ugrave; facilmente esala dall'acqua il vapore, massime se rotta ella sia o assot&shy;<lb/>tigliata, mentre s'imbeve dalla terra, e cos&igrave; l'umido, il freddo e il ventoso <lb/>di lei sentiamo. </s>

<s>Dal vino ancora e dalle vivande apprendiamo gli odori simili <lb/>ai sapori, ma pi&ugrave; sottili, come quelli che per l'aria vanno vagando. </s>

<s>Di nuovo <lb/>pi&ugrave; di questi sottili sono gli altri odori, i quali non convengono coi sapori, <lb/>se non per analogia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Diciamo pertanto che l'aria principalmente &egrave; il mezzo rimoto, per cui <lb/>gli animali sentono gli odori, ma i pi&ugrave; grossi odori anco nell'acqua s'ap&shy;<lb/>prendono dai pesci in grazia del cibo, e cos&igrave; molti pesci odorano senza naso, <lb/>quasi che le branchie, ove talora terminano i condotti proporzionali a quelli <lb/>del naso, siano a loro per attrar gli odori bastevoli. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il prossimo strumento dell'odorato sono i processi mamillari, ma i <lb/>canaletti che a quelli conducono, e l'aria che in essi sta, servono di con&shy;<lb/>dotto e di mezzo all'odore, il quale per essi tirato pi&ugrave; valentemente penetra <lb/>il senso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io m'immagino che, siccome il sapore, cos&igrave; anche l'odore sia in uni&shy;<lb/>versale dall'uomo squisitamente appreso, per esser questo temperatissimo e <lb/>perfettissimo animale, di maniera che molte pi&ugrave; differenze di sapori e di <lb/>odori conosce che gli altri. </s>

<s>&Egrave; ben vero che qualcuno di questi animali pi&ugrave; <lb/>esattamente e pi&ugrave; di lontano conosce qualche odore, conforme alla tempe&shy;<lb/>ratura sua, a che giova molto l'attenzione, la consuetudine, il portare il naso <pb xlink:href="020/01/1386.jpg" pagenum="261"/>per terra, e la lunghezza dei canali. </s>

<s>Ma l'uomo, poich&egrave; molti pi&ugrave; sono gli <lb/>odori che offendono che quei che giovano, viene a liberarsi dalle molestie <lb/>col portar da terra alto il viso. </s>

<s>Ora, che gli animali molte meno differenze <lb/>di odori conoscano che l'uomo, scorgesi chiaramente, poich&egrave; per lo solo nu&shy;<lb/>drirsi e moltiplicarsi osserviamo odorar gli animali. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; &Egrave; poi l'odore diffusione nell'ambiente fatta dalla cosa odorifera e sue <lb/>particelle esalanti. </s>

<s>Il fiore dunque pi&ugrave; odorar si sente, mentre le sue sotti&shy;<lb/>lissime particelle diffonde d'ogni intorno. </s>

<s>Ora, in quanto alla natura di essi <lb/>odori, non &egrave; dubbio che hanno questi molta somiglianza con le focose na&shy;<lb/>ture, e cos&igrave; dall'aria premuti vengono d'ogni intorno. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. XX, pag. </s>

<s>149, 50). </s></p><p type="main">

<s>Bench&egrave; il Nardi segua, rispetto all'organo dell'odorato, l'opinione del <lb/>Colombo e del Casserio, accenna nulladimeno a certe squisitezze nell'organo <lb/>stesso trascurate da quegli insigni Anatomici, che l'avevano preceduto. </s>

<s>Par <lb/>ch'egli senta la Natura, stata cos&igrave; semplice negli organi del tatto e del gu&shy;<lb/>sto, incominciare ora nel naso a dare un saggio di quello squisitissimo la&shy;<lb/>voro, con cui sarebbe poi per condurre l'orecchio e l'occhio. </s>

<s>Quell'elabo&shy;<lb/>rato apparecchio strumentale, di che d&agrave; nel naso la Natura il primo esempio, <lb/>lo riconosceva il Nardi in que'canaletti dell'osso cribroso, per i quali, tirato <lb/>pi&ugrave; valentemente l'odore, penetra il senso. </s></p><p type="main">

<s>Lo spiegar per&ograve; come mai le fistole ossee servano ad attrar pi&ugrave; valen&shy;<lb/>temente gli odori era riserbato a un valoroso anatomico e fisiologo pado&shy;<lb/>vano, Antonio Molinetti, il quale rassomigliava lo strumento dell'olfatto a <lb/>quello dell'udito e della vista, e diceva che, siccome i suoni passano per la <lb/>finestra ovale, e i colori per la finestra dell'uvea; cos&igrave; passavano gli odori <lb/>per la finestra aperta fra le pinne delle narici. </s>

<s>E a quel modo che i cana&shy;<lb/>letti spirali del laberinto moltiplicano il suono, e la lente cristallina accre&shy;<lb/>sce intensit&agrave; alla luce; cos&igrave; le fistole, che serpeggiano dentro l'osso cribroso, <lb/>servono a condensare gli odori, che perci&ograve; pi&ugrave; fortemente s'imprimono sul <lb/>nervo. </s>

<s>&ldquo; Pinnas narium fistulae statim excipiunt ex squamis tenuissimis, in <lb/>ossea structura narium et faciei, compositae circinato quodam modo, aut po&shy;<lb/>tius spirali se mutuo pervadentes, ita dispositae, ut labyrintheum iter pan&shy;<lb/>dant corpusculis odorum delatoribus, non secus ac sonum excipiunt, et acuunt <lb/>Labyrinthi aurium spirales canaliculi, et lumen unit ac compingit in conum <lb/>lens illa oculi crystallina. </s>

<s>Foras enim hiantes fistulae ad instar tubarum an&shy;<lb/>gustantur interius, magis magisque, quo propius accesserint ad nervum. </s>

<s>Hinc <lb/>sequitur quod pyramis odora illico incipiat acui et inspissari ac cogi com&shy;<lb/>pingenda iterum in fistulis superioribus, ut spissior vel crebrior appulsus <lb/>evadat corpusculorum odor abilium in nervum, organum scilicet odoratus <lb/>formale &rdquo; (Dissertationes anat., Patavii 1669, pag. </s>

<s>59). </s></p><p type="main">

<s>All'ultimo, in quel modo che l'affezion della luce non termina nella re&shy;<lb/>tina, n&egrave; le vibrazioni dell'aria nel nervo acustico, ma per la continuit&agrave; degli <lb/>spiriti si propagano infino al Sensorio comune, che ha la sua sede nella mi&shy;<lb/>dolla allungata, designata dall'Autore col nome proprio di <emph type="italics"/>Ponte;<emph.end type="italics"/> &ldquo; ita affec-<pb xlink:href="020/01/1387.jpg" pagenum="262"/>tus, seu contactus odorabilium in mamillari non desinit, verum per spiritus, <lb/>qui in nervo, primum in ventriculos cerebri, postea in ipsius medullam se <lb/>insinuat, eo quidem vehementius, quod corpuscula producta ulterius impe&shy;<lb/>tum semper maiorem concipiant, agitentque validius spiritus illos, qui in <lb/>fonte suo haerent &rdquo; (ibid., pag. </s>

<s>61). </s></p><p type="main">

<s>Le opinioni de'Fisiologi intorno all'organo dell'olfatto e alle vie, per le <lb/>quali giungono gli odori al sensorio, erano fondate sull'ipotesi che i forellini <lb/>dell'osso cribroso fossero vuoti. </s>

<s>Ma il Berengario, e dietro lui il Vesalio, ave&shy;<lb/>vano da gran tempo dimostrato che invece erano pieni, e perci&ograve; coloro che <lb/>facevano quegli stessi forellini gli scolatoi del mucco, di che si ripurga il <lb/>cervello, pensarono di trovare altre vie perch&egrave; potessero cos&igrave; fatti umori giun&shy;<lb/>gere al naso. </s>

<s>Il Molinetti stesso asseriva che vi giungevano &ldquo; per forami&shy;<lb/>nula in angulis internis oculorum patentia primum in nares &rdquo; (ibid.) ma <lb/>non perci&ograve; crede di dover riformare la sua opinione intorno al sensorio, se&shy;<lb/>guitando a riconoscerlo ne'processi mamillari, ai quali giungono gli odori <lb/>attraverso all'umido, di che appunto la Natura riemp&igrave; l'ossa nasali &ldquo; ut acu&shy;<lb/>men plerumque nimium odorabilium, motusque spirituum, ex appulsu eorum&shy;<lb/>dem nimis concitatos, humore interiecto compesceret ac moderaretur &rdquo; (ibid.). </s></p><p type="main">

<s>Ma bench&egrave; fossero queste speculazioni del Molinetti ingegnose, il vero <lb/>strumento dell'olfatto era stato scoperto gi&agrave; da Currado Vittorio Schneider <lb/>nella seconda sezione del III libro <emph type="italics"/>De catarrhis,<emph.end type="italics"/> pubblicato in Wittemberg <lb/>nel 1661, e dove si descrive cos&igrave; dall'Autore la membrana pituitaria, che <lb/>glien'&egrave; attribuito il merito della scoperta. </s>

<s>N&egrave; si vuol da noi qui contender&shy;<lb/>gliela, permettendoci solo di far osservare ch'esaminando il Falloppio le fosse <lb/>nasali, e con molta diligenza descrivendo i seni frontali e gli sfenoidali, n&egrave; <lb/>lasciando indietro i mascellari, che poi furono detti <emph type="italics"/>Antri dell'Igmoro,<emph.end type="italics"/> dice <lb/>che son tutti questi seni rivestiti, &ldquo; tenuissima quadam membrana aut pel&shy;<lb/>licola &rdquo; (Observat. </s>

<s>anat. </s>

<s>inter Opera omnia cit., pag. </s>

<s>410), nella quale hanno <lb/>voluto alcuni riconoscere la pituitaria. </s></p><p type="main">

<s>In qualunque modo si dissiparono dopo lo Schneider tutti gli antichi <lb/>errori, e in quel che egli insegn&ograve; si continua tuttavia a riconoscere da'Fi&shy;<lb/>siologi le rivelate sembianze del vero. </s>

<s>Ma gli odori seguitarono ancora a ri&shy;<lb/>maner misteriosi pi&ugrave; della luce e de'suoni, e parendo dall'altra parte cosa <lb/>tutta soggettiva, pochissimi si curarono di studiarla nel proprio oggetto. </s>

<s>Non <lb/>possono perci&ograve; in tanta penuria, a noi che teniamo particolarmente d'occhio <lb/>la Scuola toscana, sfuggire dimenticate quelle due <emph type="italics"/>Lettere scientifiche<emph.end type="italics"/> dal <lb/>Magalotti scritte intorno agli odori. </s></p><p type="main">

<s>Le idee &egrave; vero son vaporose, e il discorso &egrave; risonante di molte parole, <lb/>nel fluir delle quali son pur da raccogliere non poche perle. </s>

<s>Pare a noi una <lb/>delle pi&ugrave; pregevoli tra queste l'osservazione che, mentre il tatto &egrave; il pi&ugrave; in&shy;<lb/>fallibile de'sensi, l'odorato &egrave; il pi&ugrave; dubbioso di tutti. </s>

<s>Dell'infallibilit&agrave; del <lb/>tatto basta dire, osserva il Magalotti, ch'ella si piglia per traslato dell'evi&shy;<lb/>denza, essendo che, per assicurar altri della verit&agrave; di una cosa, si suol dire <lb/>ch'ella si tocca con mano. </s>

<s>Conferma l'osservazione coll'esempio dei ciechi, <pb xlink:href="020/01/1388.jpg" pagenum="263"/>i quali suppliscono col tatto al difetto della vista, e commemora in propo&shy;<lb/>sito il famoso Cieco di Gambassi, che a forza di brancicare faceva somiglian&shy;<lb/>tissimi i ritratti nella creta, e quell'altro non men famoso Cieco che, pure <lb/>a toccarli, co'polpastrelli delle dita, sapeva dire alla granduchessa Vittoria <lb/>di Toscana di che colore fossero i nastri, i veli, le vesti e altri oggetti mes&shy;<lb/>sigli innanzi. </s></p><p type="main">

<s>&ldquo; A proposito di quel modo di dire <emph type="italics"/>questa &egrave; una verit&agrave; che si tocca <lb/>con mano,<emph.end type="italics"/> osservate, soggiunge il Magalotti, che da tutti i cinque senti&shy;<lb/>menti cavandosi varie graduazioni d'espressioni di maggiore o minore evi&shy;<lb/>denza d'una verit&agrave;, l'infima e la pi&ugrave; meschina di tutte &egrave; quella che si de&shy;<lb/>duce dal testimonio del naso, tanto &egrave; generalmente riconosciuto il poco accerto <lb/>de'suoi giudizi. </s>

<s>Di grazia osservate. <emph type="italics"/>Questa cosa si tocca con mano:<emph.end type="italics"/> ecco <lb/>il sommo dell'indubitabilit&agrave;. <emph type="italics"/>Questa cosa si vede con gli occhi:<emph.end type="italics"/> comincia a <lb/>poterci essere della fallacia. <emph type="italics"/>Questa cosa si sente bisbigliare:<emph.end type="italics"/> ci &egrave; il caso di <lb/>frantendere. <emph type="italics"/>Questa cosa si comincia a assaporare:<emph.end type="italics"/> siamo indietro assai. <lb/><emph type="italics"/>Questa cosa si subodora:<emph.end type="italics"/> non se ne pu&ograve; saper manco &rdquo; (Firenze 1721, <lb/>pag. </s>

<s>82). </s></p><p type="main">

<s>Un'altra notabile osservazione del Magalotti, per tacere delle altre, &egrave; <lb/>che il senso dell'odorato si raffina anche indipendentemente dall'organo, <lb/>ossia dalla maggiore o minor perfezione di &ldquo; quelle due laminette cartilagi&shy;<lb/>nose, che abbiamo fitte per punta di qua e di l&agrave; nel naso, alle radici del&shy;<lb/>l'osso cribroso, nella tunica che investe le quali pare che resti convinto for&shy;<lb/>marsi il senso dell'odorato &rdquo; (ivi). Di qui s'argomenta essersi largamente <lb/>diffusa in Italia la scoperta sneideriana emendatrice di quegli errori antichi, <lb/>per liberarsi dai quali faceva come si vide gli ultimi conati fra noi Antonio <lb/>Molinetti. </s></p><p type="main">

<s>Ma se il Molinetti e la maggior parte dei successori studiarono l'organo <lb/>secondario, e specularono intorno al pi&ugrave; squisito modo come possa l'aura <lb/>odorosa agir sopra lui, si passarono con qualche negligenza sull'organo pri&shy;<lb/>mario o sulla distribuzione delle filamenta nervose ordinate a ricevere il <lb/>senso. </s>

<s>Fu questo importantissimo studio lasciato alle indagini di Antonio <lb/>Scarpa, delle quali rendeva conto al pubblico in un suo libro intitolato <emph type="italics"/>De <lb/>organo olfactus praecipuo, deque nervis nasalibus interioribus e pari quinto <lb/>nervorum cerebri.<emph.end type="italics"/> Avendo osservato l'Autore che pochi sono i filamenti ner&shy;<lb/>vosi dispersi ne'turbinati, &ldquo; quam ob rem, ei soggiunge, non temere pro&shy;<lb/>nunciare posse videor organum olfactus praecipuum septo narium late su&shy;<lb/>perinductum esse, quandoquidem et confertae admodum fere undique supra <lb/>septum nervi olfactorii fibrillae sunt, et quibusdam in sedibus ad imam <lb/>usque septi basim exporrectae &rdquo; (Ticini Regii 1785, pag. </s>

<s>51). </s></p><p type="main">

<s>Che se altri credesse invece di dover circoscrivere la sede del senso nei <lb/>seni pituitarii, si contrapporrebbero all'opinione di lui i fatti, che i fanciulli <lb/>tutti hanno l'odorato squisito, e l'hanno anche alcuni adulti, ne'quali pure <lb/>o mancano questi seni, o non vi sono altro che rudimentari. </s>

<s>&ldquo; Et quoniam, <lb/>all'ultimo conclude, suadente Anatome, spongiosum os inferius nihil conferre <pb xlink:href="020/01/1389.jpg" pagenum="264"/>videtur ad distributionem nervi olfactorii; ideo haud spernendam esse cen&shy;<lb/>seo illorum sententiam, qui docuerunt spongiosa ossa non una atque unica <lb/>de causa, nempe pro distributione nervi olfactilis esse creata, sed illud quo&shy;<lb/>que utilitatis et commodi narium cavitatem apte angustando praestare, ut <lb/>respirationi et quae ab hac pendent functionibus famulentur, utque timenda <lb/>pulmonibus e magna narium amplitudine, magneque inde irruentis aeris <lb/>flumine, pericula avertant &rdquo; (ibid., pag. </s>

<s>52). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Dicemmo che nell'olfatto dava la Natura il primo esempio di un organo <lb/>elaborato, ma la fabbrica insomma era assai semplice, come quella che non <lb/>aveva altro fine, da quello in fuori di far percepire al senso la variet&agrave; delle <lb/>aure odorose. </s>

<s>Ben assai per&ograve; pi&ugrave; sottili e pi&ugrave; difficili ad approdare al sen&shy;<lb/>sorio erano le onde sonore e l'eteree, per cui bisognava elaborare un organo <lb/>pi&ugrave; gentile e squisito, tanto pi&ugrave; che l'oggetto, secondo che osservammo, <lb/>non si riduceva, come ne'tre primi sensi, alle sole particelle materiali o so&shy;<lb/>lide o vaporose, ma pigliava, per dirla coi Filosofi, forma intelligibile di <lb/>segno. </s>

<s>Se un finissimo magistero perci&ograve; conveniva s'esercitasse dalla Natura <lb/>nel fabbricar l'orecchio e l'occhio de'bruti, doveva quello stesso natural ma&shy;<lb/>gistero giungere alla sua massima eccellenza nell'uomo. </s>

<s>Per quali lunghe e <lb/>penose vie giungessero gli Anatomici a riconoscere questa eccellenza &egrave; ci&ograve; <lb/>che ci proponiam di narrare nella seguente parte di storia, la quale, per pro&shy;<lb/>cedere con l'ordine oramai preso, prima che dell'occhio tratta dell'anatomia <lb/>e delle funzioni dell'orecchio. </s></p><p type="main">

<s>Galeno, cosa notabilissima, non descrisse propriamente nessun organo <lb/>auditivo, cosicch&egrave; la vecchia Anatomia manc&ograve; affatto di questa parte di scienza <lb/>nuovamente instituita dal Mondino e dal Berengario. </s>

<s>Il XXXVII Testo mun&shy;<lb/>diniano infatti, citato e commentato dal Berengario stesso, dop'avere accen&shy;<lb/>nato al foro esterno e alle cavernosit&agrave; che s'aprono nella parte interiore del&shy;<lb/>l'orecchio, soggiunge: &ldquo; eius foramen vel cavernositates cooperit panniculus <lb/>subtilis contextus ex villis nervorum auditus &rdquo; (Carpi, Commentaria super <lb/>Anat. </s>

<s>Mundini, Bononiae 1521, fol. </s>

<s>CCCCLXXVI). </s></p><p type="main">

<s>Questo <emph type="italics"/>pannicolo sottile<emph.end type="italics"/> &egrave; dunque il primo organo auditivo descritto <lb/>nella risorta Anatomia, la quale progred&igrave; presto in altre pi&ugrave; nuove e pi&ugrave; <lb/>insigni scoperte, innanzi di venire alle quali giova intrattenersi su questa <lb/>prima mundiniana. </s>

<s>Ella di fatto accusava Galeno di negligenza, e perci&ograve;, <lb/>mentre da una parte infervorava i novatori, metteva dall'altra in gran sol&shy;<lb/>lecitudine i conservatori degli ordini antichi, i quali disperati di trovare un <lb/>testo galenico che parlasse chiaro, accennavano a que'barlumi, che vedevano <lb/>i loro cupidi occhi trasparire dal cap. </s>

<s>VI dell'VIII libro, e dal XII del li&shy;<lb/>bro XI <emph type="italics"/>De usu partium.<emph.end type="italics"/> Fu in questo sollecito studio de'primi l'Acquapen-<pb xlink:href="020/01/1390.jpg" pagenum="265"/>dente, il quale ardendo di gran desiderio, com'egli stesso si esprimeva, di <lb/>dimostrar &ldquo; Galeno et Aristotili nihil occultum extitisse &rdquo; (De Aure, Opera <lb/>omnia, Lugd. </s>

<s>Batav. </s>

<s>1738, pag. </s>

<s>250), non potendo salvar Galeno, si com&shy;<lb/>piaceva che Aristotile e anzi Ippocrate prima di lui avessero conosciuto gi&agrave; <lb/>quel che si credeva essere stato primo a insegnare il Mondino. </s>

<s>Dal libello <lb/>ippocratico infatti <emph type="italics"/>De carnibus<emph.end type="italics"/> traduceva cos&igrave;: &ldquo; Pellicula in aure iuxta os <lb/>durum tenuis est, veluti aranearum tela et omnium pellicularum siccis&shy;<lb/>sima &ldquo; (ibid.). </s></p><p type="main">

<s>Pi&ugrave; importante, per l'efficacia ch'ebbero sopra molti le teorie, &egrave; il <lb/>testo 83, che l'Acquapendente cita dal II libro aristotelico <emph type="italics"/>De anima.<emph.end type="italics"/> Ivi <lb/>dice il Filosofo che l'aria per s&egrave; medesima &egrave; insonora, essendo naturalmente <lb/>dissipabile, e non si fa altrimenti il suono che quando ne sia proibita cos&igrave; <lb/>fatta dissipazione. </s>

<s>Ci&ograve; avviene appunto, dice Aristotile, nell'orecchio, &ldquo; hic <lb/>autem aer inaedificatus est, ad hoc ut immobilis sit, quatenus certe sentiat <lb/>omnes differentias motus &rdquo; (Operum, T. VII, Venetiis 1560, fol. </s>

<s>66). Che <lb/>poi il suono non sia prodotto nell'aria dissipabile esterna, ma in quella che <lb/>&egrave; nell'interno immobilmente implantata, lo prova lo Stagirita dal fatto che <lb/>si ode bene anche sott'acqua, e si diventa sordi quando &ldquo; membrana labo&shy;<lb/>ret, sicut cum quae super pupillam est pellis laborat &rdquo; (ibid.) perch&egrave; allora <lb/>l'aria immobile divien dissipabile attraverso alla stessa membrana lesa. </s></p><p type="main">

<s>Non &egrave; dubbio dunque che la pellicola di Empedocle, e la membrana di <lb/>Aristotile rassomigliata alla cornea, non siano la medesima cosa che il pan&shy;<lb/>nicolo sottile del Mondino. </s>

<s>Ma chi ripensa che, dimenticato il vecchio Ippo&shy;<lb/>crate, e non curato, anzi dai pi&ugrave; disprezzato Aristotile, non riconoscevano <lb/>gli Anatomici altro Maestro che Galeno, si persuader&agrave; facilmente che la prima <lb/>notizia della membrana tesa come sipario tra il meato esterno e l'interna <lb/>cavit&agrave; dell'orecchio fu nell'Anatomia intradotta dal nostro Bolognese, ed ha <lb/>perci&ograve; il merito di una vera scoperta. </s></p><p type="main">

<s>Divulgatasi quella scoperta da'Commentari e dalle Isagogi del Beren&shy;<lb/>gario, il Vesalio esamin&ograve; la membranula mundiniana con maggior diligenza <lb/>e la trov&ograve; <emph type="italics"/>prorsus pellucida,<emph.end type="italics"/> per cui, adombrando un poco tra quella che <lb/>fu poi detta Corda del timpano e il manico del martello, disse che questo <lb/>&ldquo; intus transversum insternitur, quemadmodum in <emph type="italics"/>tympanis<emph.end type="italics"/> fidem unam <lb/>atque alteram crassiorem membranae obtendi conspicimus &rdquo; (De hum. </s>

<s>corp. </s>

<s><lb/>fabrica, Basileae 1543, pag. </s>

<s>35). Questa espressione sugger&igrave; l'altra al Co&shy;<lb/>lombo, intendendo della parte pi&ugrave; grossa del Martello: &ldquo; illam ipsam <emph type="italics"/>Mem&shy;<lb/>branam tympani<emph.end type="italics"/> modo quatit &rdquo; (De re anat. </s>

<s>cit., pag 26) e di l&igrave; in poi <lb/>quella, che Ippocrate chiamava <emph type="italics"/>pellicola,<emph.end type="italics"/> Aristotile <emph type="italics"/>membrana<emph.end type="italics"/> e il Mondino <lb/><emph type="italics"/>pannicolo,<emph.end type="italics"/> ebbe il nome proprio e sacro oramai nella scienza di <emph type="italics"/>Membrana <lb/>del timpano.<emph.end type="italics"/></s></p><p type="main">

<s>Il Falloppio, a cui parvero le cose relative all'organo dell'udito &ldquo; ab <lb/>aliquot Anatomicis satis imperfecte, ab aliquot vero false descriptae &rdquo; da&shy;<lb/>tosi con incredibile ardore al nuovo studio, incominci&ograve; dalla membrana del <lb/>timpano, ch'ei ritrov&ograve; tesa a un apposito anello osseo, non perpendicolar-<pb xlink:href="020/01/1391.jpg" pagenum="266"/>mente, ma un po'inclinata: &ldquo; Extenditur autem ipsa, non per transversum <lb/>sed oblique &rdquo; (Observat. </s>

<s>anat. </s>

<s>inter, Op. </s>

<s>omn. </s>

<s>cit., pag. </s>

<s>409). E ci&ograve; per ri&shy;<lb/>cever minore offesa dai colpi dell'aria, &ldquo; Ictus enim obliquus minus loedit <lb/>quam qui recta fertur &rdquo; (ibid.). </s></p><p type="main">

<s>Nelle figure 12 e 13, impresse nella Tavola apposta al suo trattato <emph type="italics"/>De <lb/>aure auditus organo,<emph.end type="italics"/> l'Acquapendente disegn&ograve; con molta diligenza l'anello <lb/>osseo descritto dal Falloppio, e not&ograve; inoltre che il setto membranoso tesovi <lb/>intorno non era perfettamente piano, &ldquo; sed in medio centroque quodam&shy;<lb/>modo interius incurvatum et gibbum, extra cavum, ita ut concinne herbam <lb/>cymbalitidem, seu umbilicum veneris, prae se ferat &rdquo; (Op. </s>

<s>omn. </s>

<s>cit., pag. </s>

<s>250). </s></p><p type="main">

<s>Un'altra osservazione importantissima ha, in proposito della membrana <lb/>del timpano, l'Acquapendente, ed &egrave; che talvolta, bench&egrave; di rado, suole in&shy;<lb/>nanzi a quella stessa membrana, dalla parte esterna, &ldquo; tunica quaedam cras&shy;<lb/>sior praeter naturam adnasci opponique, quam ego in pueris bis deprehendi &rdquo; <lb/>(ibid.). Quel che fu per&ograve; dall'Autore creduto preternaturale venne poi ri&shy;<lb/>conosciuto per cosa ordinaria, e il Molinetti perci&ograve; descriveva cos&igrave; la mem&shy;<lb/>brana del timpano composta di due pagine soprapposte: &ldquo; Una quidem per <lb/>se est, cui tamen altera supertenditur, tractu temporis tendo futura musculi <lb/>externi, quam et in nuper natis semper reperimus; quare seminalem utram&shy;<lb/>que esse non dubito. </s>

<s>Atque interiorem quidem tenuiorem altera, et magis <lb/>transparentem videmus; crassiorem secundam, quae marginibus externi cir&shy;<lb/>culi ossei circumtensa, dum succrescunt ossa, vel extenduntur ad construen&shy;<lb/>dum meatum auditorium, cum iisdem obtenditur ut ea intrinsecus vestiat; <lb/>mox, acceptis filamentis aliquot carneis ab iisdem ossibus, speciem musculi <lb/>induit, non sine motu et actione aliqua musculorum propria, siquidem dum <lb/>corripitur, contractis more reliquarum filamentis illis carneis, pars ultima <lb/>superstrata Tympano nonnihil contrahitur, simulque cum illa subiecta Tym&shy;<lb/>pani membrana tenditur &rdquo; (Dissertationes anat. </s>

<s>cit, pag. </s>

<s>48). </s></p><p type="main">

<s>Nonostante che tali fossero la tradizioni della scienza, le quali anzi ri&shy;<lb/>salgono al Vidio, che sebben senz'altra dichiarazione asser&igrave; <emph type="italics"/>duplice<emph.end type="italics"/> essere <lb/>la membrana del timpano (De anat. </s>

<s>corp. </s>

<s>hum., Venetiis 1611, pag. </s>

<s>322); <lb/>il Valsalva, sul principio del cap. </s>

<s>II del suo celebre trattato <emph type="italics"/>De aure hu&shy;<lb/>mana,<emph.end type="italics"/> dop'aver descritta come cosa nuova la membrana stessa doppiamente <lb/>compaginata, &ldquo; a qua, conclude, usque adhuc ignota compositione, ex Durae <lb/>matris scilicet et cutis membraneis expansionibus, considerabilis membranae <lb/>tympani firmitas et robur dependet &rdquo; (Venetiis 1740, pag. </s>

<s>18). </s></p><p type="main">

<s>Questa nuova anatomia e questa sentenza dettero occasione al Morga&shy;<lb/>gni, in principio della sua Epistola anatomica V, di esaminare pi&ugrave; diligen&shy;<lb/>temente la cosa, comparando le osservazioni sue proprie con quelle gi&agrave; de&shy;<lb/>scritte dal Ruysch, dal Kerckring, dal Du-Verney e da altri Anatomici illustri. </s>

<s><lb/>E giacch&egrave; aveva detto il Valsalva essere la composizione della membrana del <lb/>timpano nel feto umano patente, su quel soggetto il Morgagni stesso eser&shy;<lb/>citando l'industria, scopr&igrave; essere essa membrana composta di tre pagine di&shy;<lb/>stinte, procedendo nell'amministrazione anatomica nel modo che segue: </s></p><pb xlink:href="020/01/1392.jpg" pagenum="267"/><p type="main">

<s>&ldquo; Aggressus igitur a cavo tympani, cum aliquo huius pariete investien&shy;<lb/>tem membranam sensim attollendo, ad proximam usque tympani membranam <lb/>deduxissem, eadem porro ratione pergens, praeclare vidi continuari illam ac <lb/>produci in laminam per huius posteriora se se extendentem. </s>

<s>Qua detracta, <lb/>continuo ad alteram sive exteriorem faciem oculos manumque transtuli. </s>

<s>Cum&shy;<lb/>que in ultimo auditorii meatus recessu quidquid erat integumentorum dili&shy;<lb/>genter attollere coepissem, sensimque ad tympani membranam reducerem, <lb/>et avellere per hanc pergerem, alteram ab hac quoque facie, et facilius qui&shy;<lb/>dem et aequalius, laminam dempsi, et duabus lamellis constantem, quarum <lb/>exterior nihil erat aliud nisi materia sebacea, interior autem reapse erat <lb/>membranea, in quam se integumenta auditorii meatus evidentissime pro&shy;<lb/>ducebant. </s>

<s>Hac quoque altera ablata lamina, etiam tum in sua sede restabat <lb/>tertia, quae inter utramque media fuerat, ut, nulla adhibita maceratione, <lb/>mihi esset manifestum tribus laminis compactam tympani membranam ap&shy;<lb/>parere &rdquo; (Epist. </s>

<s>anat. </s>

<s>XXII, Venetiis 1740, pag. </s>

<s>89, 90). </s></p><p type="main">

<s>Colla macerazione per&ograve; fu trovata quella compagine di quattro lamine <lb/>distinte provenienti dall'epidermide, dalla cute del meato auditivo, dal pe&shy;<lb/>riostio dello stesso meato, e dal periostio del timpano. </s>

<s>&ldquo; Inter secundam et <lb/>tertiam, prosegue a dir l'Haller, conspicua cellulosa tela est, cum vasculis <lb/>illis elegantibus, arbusculum referentihus: alia similis inter tertiam et quar&shy;<lb/>tam.... Qui duas tantum laminas numerarunt, aut tres, ii vel cutem omi&shy;<lb/>serunt ex eo numero, vel epidermidem &rdquo; (Elementa Physiol, T. V, Lausan&shy;<lb/>nae 1769, pag. </s>

<s>201) </s></p><p type="main">

<s>Tale infino alla met&agrave; del secolo XVIII &egrave; la storia compendiosa della <lb/>scoperta fatta dal Mondino, &ldquo; sed ultra ea quae dicuntur a Mundino de au&shy;<lb/>ribus, soggiunge il Berengario, aliquid a nobis est dicendum. </s>

<s>&rdquo; La princi&shy;<lb/>pale di queste cose da dire &egrave; che al panniculo mundiniano &ldquo; adiacent duo <lb/>ossicula parva, quae moventur ab aere moto, et se invicem percutiunt, et <lb/>secundum aliquos sunt illa quae, propter suum motum, causant sonum in <lb/>aure, et ista est res in rei veritate notatu digna a paucis visa &rdquo; (Comment. </s>

<s><lb/>cit., fol. </s>

<s>CCCCLXXVI ad t.). </s></p><p type="main">

<s>Ecco scoperti altri due organi che si credettero allora gli efficienti del&shy;<lb/>l'udito, bench&egrave; non ne fossero poi riconosciuti che per sole elegantissime ed <lb/>essenzialissime parti. </s>

<s>Ma il Vesalio, secondando il suo genio d'apparire in <lb/>ogni cosa il primo e il solo, s'appropri&ograve; quelle scoperte, illustrandole con la <lb/>sua arte e diffondendole colla sua autorit&agrave;, tanto superiore a quella del no&shy;<lb/>stro Carpense. </s>

<s>Il cap. </s>

<s>VIII del I libro <emph type="italics"/>De humani corporis fabrica<emph.end type="italics"/> &egrave; con&shy;<lb/>sacrato a descrivere le interne cavit&agrave; dell'orecchio, una delle quali, egli dice, <lb/>&egrave; orbicolare e piana &ldquo; et osseo circulo parumper extuberante septa. </s>

<s>Ad huius <lb/>circuli quinti paris nervo obducti exteriorem atque auri proximam sedem <lb/>ossiculum observatur, quod duobus tenuibus acutisque processibus tanquam <lb/>cruribus huic osseo circulo adstabilitur, superius, ubi crura ipsius coeunt, <lb/>spissus crassiusque, incudis instar effectum.... Caeterum si hoc ossiculum, <lb/>quia tantum binis donatur cruribus, incudi assimilare minus placuerit, nihil <pb xlink:href="020/01/1393.jpg" pagenum="268"/>profecto obstiterit molari denti duabus tantum radicibus ornato id conferre. </s>

<s><lb/>Alterum ossiculum auditus organi fabricam ingrediens a iam commemorato <lb/>plurimum variat, et alteri membranae innascitur &rdquo; (Basileae 1543, pag. </s>

<s>34, 35). <lb/>Alla qual membrana, che &egrave; quella del timpano, fu quell'ossicino saldamente <lb/>fermato per via di un lungo e sottile processo. </s>

<s>&ldquo; Hunc processum liceret <lb/>femoris ossis parti comparari, quae ab ipsius processibus, quae rotatores vo&shy;<lb/>camus, ad inferiora usque femoris capita pertinet ... A membrana intror&shy;<lb/>sum abscedit in rotundum caput desinens, quod laeve minimeque asperum <lb/>est, et superiori parti alterius ossiculi, quod molari denti aut incudi assi&shy;<lb/>milavimus, ita tenuissimarum membranarum interventu committitur, ac si <lb/>malleus incudi laxe alligaretur, non secus quam si ossiculum postremo enar&shy;<lb/>ratum malleoli praestaret munus, alterum vero incudis vicem gereret &rdquo; (ibid., <lb/>pag. </s>

<s>35). </s></p><p type="main">

<s>Di qui vennero imposti i nomi di <emph type="italics"/>Martello<emph.end type="italics"/> e d'<emph type="italics"/>Incudine<emph.end type="italics"/> ai due ossi&shy;<lb/>cini innominati del Berengario, che rimase in questa vesaliana descrizione <lb/>affatto dimenticato. </s>

<s>L'orgoglioso Conquistatore straniero si vide per&ograve; presto <lb/>insorgere incontro uno stuolo di prodi a rivendicare l'onore degli avviliti <lb/>fratelli. </s>

<s>Si componeva quello stuolo del Colombo e del Falloppio, che usa&shy;<lb/>rono verso il Vesalio una certa gentilezza di modi, e del Massa e dell'Eu&shy;<lb/>stachio pi&ugrave; sdegnosi e pi&ugrave; fieri. </s>

<s>Io vorrei volentieri, dice il Colombo, rico&shy;<lb/>noscere per primo inventore di questi ossicini il Vesalio, &ldquo; nisi Carpus de <lb/>his ante illum suis scriptis meminisset &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>26). E il <lb/>Falloppio solennemente rammemora che primo a dare di quegli ossicini no&shy;<lb/>tizia &ldquo; fuit Jacobus Carpensis, primus quoque, procul dubio anatomicae artis, <lb/>quam Vesalius postea perfecit, restaurator &rdquo; (Observ. </s>

<s>anat. </s>

<s>Op. </s>

<s>omnia cit., <lb/>pag. </s>

<s>409). </s></p><p type="main">

<s>Niccol&ograve; Massa, non osando pronunziare quel nome tremendo, &mdash; que&shy;<lb/>sta gente, badava a dire in una sua Epistola che noi non abbiamo potuto <lb/>consultare nelle sue fonti, come si &egrave; arrogata la mia, cos&igrave; arrogandosi le <lb/>scoperte degli altri, si crede d'essere stata la prima a ritrovare e a descri&shy;<lb/>vere i due ossicini dell'udito, ma &egrave; certo che erano stati gi&agrave; ritrovati dagli <lb/>Anatomici infin dai tempi di Alessandro Achillini, e di Jacopo da Carpi. </s>

<s>&mdash; <lb/>&ldquo; Haec ossicula Anatomici, tempore Alexandri Achillini viri in omni scien&shy;<lb/>tiarum genere eminentissimi, ut ex eius scriptis clarissime videre est, inve&shy;<lb/>nerunt. </s>

<s>Quare non ab istis sunt primo inventa, nec ostensa, cum etiam Ja&shy;<lb/>cobus Carpensis loca istorum ossiculorum invenire doceat. </s>

<s>Mitto quae a me <lb/>inventa sibi arrogant &rdquo; (Morgagni, Epist. </s>

<s>VI cit., pag. </s>

<s>114). </s></p><p type="main">

<s>Ben assai pi&ugrave; del Massa &egrave; l'Eustachio fieramente sdegnoso contro Colui <lb/>che, sebbene abbia detto tanti e s&igrave; grossi errori, <emph type="italics"/>anatomicae hodie artis <lb/>inventor et quasi architectus ab omnibus pene creditur;<emph.end type="italics"/> contro Colui, che <lb/>ingratissimo, dop'avere espilato il Carpense, non si vergogn&ograve; di avvilirlo <lb/>chiamandolo la feccia de'Notomisti. </s>

<s>&ldquo; Caeterum, quantum ipse scio, haec <lb/>duo oss&igrave;cula primi indicarunt Alexander Achillinus hononiensis, philosophus <lb/>insignis, et Jacobus Carpensis, chirurgus et anatomicus non ita contemnen-<pb xlink:href="020/01/1394.jpg" pagenum="269"/>dus, quanquam eum ingratissimi qu&igrave;dam, postquam expilarunt, ut ab omni&shy;<lb/>bus parvifieret, anatomicorum faeciem nominare non erubuerunt: neuter ta&shy;<lb/>men eorum sibi tantum sumpsit, ut inventionis sibi palmam vindicaret &rdquo; <lb/>(Opusc. </s>

<s>anat. </s>

<s>Venetiis 1564, De auditus org., pag. </s>

<s>153). </s></p><p type="main">

<s>Trovatosi il Vesalio cos&igrave; colto in fallo circondato da tante e s&igrave; valorose <lb/>armi vendicative, cercava di uscirne per la via pi&ugrave; spedita, &mdash; e io, diceva, <lb/>non so nulla io n&egrave; de'vostri Achillini, n&egrave; de'vostri Carpensi: questo solo <lb/>so che, rimondando un giorno un cranio, vidi a caso uno degli ossicini cader <lb/>dall'orecchio, aperto il quale vi trovai dentro anche quell'altro, e come gli <lb/>trovai gli descrissi. </s>

<s>&ldquo; Quum enim mihi inter mundandum ad sceleti appa&shy;<lb/>ratum calvariam casu ossiculum quoddam ex aure procidisset, auditus orga&shy;<lb/>num in cruda calvaria aperui, et cum illo ossiculo secundum insuper quod&shy;<lb/>dam reperi, remque ut tum mihi occurrit descripsi &rdquo; (Falloppi Examen, <lb/>Venetiis 1564, pag. </s>

<s>24). </s></p><p type="main">

<s>Come si rende per questi documenti chiaro essere stati i due primi os&shy;<lb/>sicini dell'udito ritrovati e resi noti, molti anni prima che venisse il Vesalio, <lb/>altrettanto incerto rimane il nome proprio dell'inventore. </s>

<s>L'Achillini e il <lb/>Carpense, commemorati dal Massa e dall'Eustachio, fecero andare il Valsalva <lb/>a pronunziare questo giudizio: &ldquo; Malleus et Incus primum Anatomicis inno&shy;<lb/>tuere, inventore Carpo, aut potius Achillino &rdquo; (De aure hum. </s>

<s>cit., pag. </s>

<s>21). <lb/>Ma perch&egrave; il Massa dice che la scoperta fu fatta non dall'Achillini, ma ai <lb/>tempi dell'Achillini, e l'Eustachio soggiunge che n&egrave; esso Achillini n&egrave; il Be&shy;<lb/>rengario ardirono d'attribuirsene il merito dell'invenzione, l'Haller, migliore <lb/>interpetre dei due citati scrittori, si limit&ograve; a pronunziare cos&igrave; fatta sentenza: <lb/>&ldquo; Circa ultimam partem saeculi XV innotuit, dice del Martello, non quidem <lb/>inventore Jacobo Berengario, sed teste &rdquo; (Elem. </s>

<s>Phys., T. V, cit., pag. </s>

<s>208). </s></p><p type="main">

<s>Il giudiziosissimo uomo esclude a ragione l'Achillini, il quale, tutt'altro <lb/>che Anatomista, era un peripatetico sottilissimo commentator di Aristotile, <lb/>e perci&ograve; avverso o non curante di Galeno. </s>

<s>Amico, concittadino e collega del <lb/>Berengario, &egrave; probabile che avesse avuto da lui la notizia della scoperta, e <lb/>ch'ei la divulgasse col suo autorevole magistero a viva voce nella sua scuola. </s>

<s><lb/>Diciamo a viva voce perch&egrave;, cominciando dal Massa e dall'Eustachio, tutti <lb/>coloro che predicano il Filosofo bolognese o inventore o primo relatore degli <lb/>ossicini non citano n&egrave; le parole n&egrave; il luogo degli scritti di lui. </s>

<s>Noi per cu&shy;<lb/>riosit&agrave;, consultando la raccolta delle Opere ristampate nel 1568 in Venezia da <lb/>Girolamo Scoto, al leggere fra gli altri impressi nel frontespizio anche il titolo <lb/><emph type="italics"/>De physico auditu,<emph.end type="italics"/> siamo andati desiderosi a squadernare al luogo accen&shy;<lb/>nato il volume in folio, e abbiamo trovato che di tutt'altro vi si tratta che <lb/><emph type="italics"/>De physico auditu.<emph.end type="italics"/> Chi avesse il coraggio di mettersi a frugare per tutti i <lb/>seni di quell'immenso mare peripatetico, e s'abbattesse per fortuna a ritro&shy;<lb/>varvi la perla preziosa, si persuaderebbe forse averla in ogni modo il Filosofo <lb/>dovuta ripescar con l'amo di qualche Notomista. </s></p><p type="main">

<s>Potrebb'essere questo Notomista facilmente il Berengario, e non cono&shy;<lb/>scendosi a que'tempi nessun altro pi&ugrave; valoroso di lui, noi daremmo la cosa <pb xlink:href="020/01/1395.jpg" pagenum="270"/>come certa, se non avessimo in contrario, per non curarsi di tutti gli altri, <lb/>i giudizii autorevolissimi dell'Haller e del Morgagni. </s>

<s>Ripensando poi che <lb/>non hanno que'giudizii altro fondamento che sopra le parole dell'Eustachio, <lb/>si vorrebbe sapere quali fossero le ragioni, per le quali s'indusse l'Anato&shy;<lb/>mico sanseveritano a sentenziare che Jacopo da Carpi, divulgando la noti&shy;<lb/>zia degli ossicini dell'udito, non se ne rivendic&ograve; per questo la palma del&shy;<lb/>l'invenzione. </s></p><p type="main">

<s>Non possono quelle ragioni avere altro argomento che nel modo di <lb/>esprimersi dello stesso Carpense, il quale disse i due piccoli ossicini esser <lb/>cosa <emph type="italics"/>a paucis visa.<emph.end type="italics"/> Ma chi seguita a leggere, al sentirsi citare le opinioni <lb/>varie di tanti intorno all'uso di quegli ossicini, direbbe che que'<emph type="italics"/>pochi<emph.end type="italics"/> si <lb/>riducono a <emph type="italics"/>molti,<emph.end type="italics"/> e par che la cosa nuova abbia dato luogo a tante dispute <lb/>quanto una verit&agrave; da lungo tempo gi&agrave; conosciuta. </s>

<s>Nelle espressioni del Be&shy;<lb/>rengario insomma, per que'<emph type="italics"/>pauci<emph.end type="italics"/> s'intende <emph type="italics"/>nessuno,<emph.end type="italics"/> e le parole <emph type="italics"/>aliqui vo&shy;<lb/>lunt, aliqui dicunt<emph.end type="italics"/> si traducono in quell'altre: <emph type="italics"/>si potrebbe credere da alcuni, <lb/>si potrebbe dire da altri ....<emph.end type="italics"/> Chi ha pratica del linguaggio usato dall'Autore <lb/>in tutto il suo libro se ne persuade assai facilmente, e l'Eustachio s'ingann&ograve; <lb/>forse, per aver pi&ugrave; badato alla sostanza che alla forma dell'espressione. </s></p><p type="main">

<s>Il Colombo ebbe per&ograve; tempo d'avvedersi dell'inganno e di confessarlo, <lb/>e perciocch&egrave; il modo pi&ugrave; conveniente di far quella confessione gli fu divie&shy;<lb/>tato dalla morte, ingiustamente il Morgagni lo accus&ograve; di essere stato <emph type="italics"/>sibi <lb/>parum constans<emph.end type="italics"/> (Epist. </s>

<s>VI cit., pag. </s>

<s>115). Nel I libro infatti <emph type="italics"/>De re anat.,<emph.end type="italics"/><lb/>parlando degli ossicini, &ldquo; quis tamen inventor fuerit, dice, me plane latet &rdquo; <lb/>(pag. </s>

<s>26) perch&egrave; ci&ograve; non appariva chiaro dalle parole del Berengario. </s>

<s>Poi, <lb/>ripensandoci meglio e interpetrando nel loro vero significato le espressioni <lb/>dell'Autore de'commentarii sopra Mondino, scrivendo alcuni anni dopo il <lb/>libro VIII pubblicato insieme con gli altri postumo, non dubit&ograve; di asserire <lb/>che i due ossicini <emph type="italics"/>Carpus primum invenit<emph.end type="italics"/> (ibid., pag. </s>

<s>196). E perch&egrave; in&shy;<lb/>somma a questa sentenza si riducono, e in ogni modo non contradicono <lb/>l'espressioni del Massa e del Falloppio, crediamo anche noi con questi grandi <lb/>uomini aver primo di tutti scoperto il Martello e l'Incudine nella cavit&agrave; del&shy;<lb/>l'orecchio Jacopo Berengario. </s></p><p type="main">

<s>Aperta dai due nostri Bolognesi alle gloriose scoperte dell'organo del&shy;<lb/>l'udito la via, rimasta sempre chiusa infin da Galeno, si trov&ograve; che que'due <lb/>primi ossicini componevano nella mediana cavit&agrave; dell'orecchio una catena <lb/>continua, a cui s'aggiungevano altri due anelli, intorno alla invenzione dei <lb/>quali ha da esercitarsi non poco la nostra Storia. </s></p><p type="main">

<s>Lodovico Collado pubblicava nel 1555 un suo libro col titolo: <emph type="italics"/>In Ga&shy;<lb/>leni lib. </s>

<s>De ossibus ad tirones enarrationes,<emph.end type="italics"/> dove, dopo di aver nel cap. </s>

<s>I <lb/>trattato de'due primi ossicini conosciuti da qualche tempo in Italia, &ldquo; ego, <lb/>soggiunge, una cum Cosmo Medina, in inclyta Academia salmanticensi nunc <lb/>publico Anatomes professore longe doctissimo, discipulo meo mihi carissimo, <lb/>aliud os reperi, cui, quod simile esset equitandi instrumento quo pades fir&shy;<lb/>mantur, <emph type="italics"/>stapedae<emph.end type="italics"/> nomen imposui &rdquo; (Valentiae, pag. </s>

<s>12). </s></p><pb xlink:href="020/01/1396.jpg" pagenum="271"/><p type="main">

<s>Quattro anni dopo vedeva la luce, molto tempo prima meditata e scritt<gap/><lb/>l'opera del Colombo, nel I libro della quale al cap. </s>

<s>VII, dopo aver l'Au <lb/>tore descritti gli ossicini del Martello e dell'Incudine, &ldquo; his tertium accedi <lb/>soggiunge, nemini quod sciam ante nos cognitum. </s>

<s>Jacet hoc vel latitat po <lb/>tius in cavernula quadam ferme rotunda intra sinum auditorium exculpta <lb/>quo fit, ut ad organi auditus fabricam non pertinere non possit. </s>

<s>Cavum es <lb/>et perforatum, egregie ferrei instrumenti naturam imitatur, quod <emph type="italics"/>Staphan<emph.end type="italics"/><lb/>novo vocabulo nuncupamus, in quo equorum sellis insidentes pedes sistunt <lb/>(De re anat. </s>

<s>cit., pag. </s>

<s>27). </s></p><p type="main">

<s>Ma quando, due anni dopo da che erano state divulgate queste notizi<gap/><lb/>comparvero le Osservazioni anatomiche del Falloppio, vi si lesse dentro un <lb/>storia, dalla quale appariva essere stato il Colombo, nello scrivere a que <lb/>modo, o menzognero od illuso. </s>

<s>Quella storia, per la quale dimostravasi in <lb/>vece essere stato il primo a scoprire la Staffa il siciliano Filippo Ingrassia <lb/>&egrave; cos&igrave; particolarmente narrata dall'Autore a Pietro Manna: </s></p><p type="main">

<s>&ldquo; Anno Domini millesimo quingentesimo quadragesimo octavo, quo eg <lb/>primum Pisis profiteri coepi, cum neque a Vesalio qui multo antea, nequ <lb/>a Columbo cive tuo, qui anno proxime superiori Anatomen Pisis tractave <lb/>rat, nulla fuisset facta mentio istius ossis, dum eam ego celebrarem, ad m <lb/>venit quidam auditor meus iuvenis doctissimus, qui si recte memini docto <lb/>ratus ornamento iam insignis erat, Ingrassiaeque affinitate coniunctus, nome<gap/><lb/>nunc memoria haud retineo, hicque me monuit Joannem Philippum tertium <lb/>ossiculum in tympano invenisse, quod <emph type="italics"/>Stapedis<emph.end type="italics"/> nomine et figura appellarit <lb/>Ego hac re commotus, adhibito maiori studio, ossiculum laetus inveni, sta <lb/>timque publice protuli, omnibus admirantibus. </s>

<s>Atque praeterea Bartholom <lb/>maeo Madio, sanctissimae memoriae, medico doctissimo ac celeberrimo pe <lb/>epistolam communicavi. </s>

<s>Scripsi etiam de hac re quibusdam amicis qui Ro <lb/>mae erant de quo, et rescripsere, a Columbo qui paulo ante Anatome<gap/><lb/>tractarat, nihil audiverant, neque ab ullo alio, cum in Italia tunc temporis <lb/>uno excepto Johanne Baptista Canano medico et Anatomico celeberrimo <lb/>nullus alius praeter dictos reperiatur, qui docte Anatomen publicam docer<gap/><lb/>potuisset &rdquo; (Op. </s>

<s>omnia cit., pag. </s>

<s>409). </s></p><p type="main">

<s>Ferirono queste parole come saetta acuta la coscienza a Bartolomme<gap/><lb/>Eustachio, che insegnava pure allora in Roma, e che si sentiva tante supe&shy;<lb/>riore a Bartolommeo Maggi e a Giovan Batista Canani. </s>

<s>Risolutosi perci&ograve; d <lb/>render conto al pubblico di ci&ograve; che aveva scoperto intorno all'organo del&shy;<lb/>l'udito, dette mano a scrivere quella sua Epistola a Francesco Alciato, sot&shy;<lb/>toscritta negl'idi di Ottobre del 1562, nella quale accennando all'invenzione <lb/>della Staffa e alla Storia del Falloppio, &ldquo; sed referat eam quisque, conclude<gap/><lb/>cui mavult acceptam. </s>

<s>Ego quidem scio me neque edoctum, neque monitum <lb/>ab aliquo, multo antequam ipsi scribant, id ossiculum novisse, Romaequ<gap/><lb/>non paucis ostendisse, atque in aes incidendum curasse &rdquo; (Opusc. </s>

<s>anat. </s>

<s>cit., <lb/>pag. </s>

<s>154). </s></p><p type="main">

<s>Il Falloppio, il quale aveva enfaticamente conclusa la storia della Staffa <pb xlink:href="020/01/1397.jpg" pagenum="272"/>con le parole: &ldquo; Deus tamen gloriosus scit Ingrassiae fuisse inventum &rdquo; fa <lb/>quella invenzione anteriore al 1548, e l'Eustachio afferma di averla fatta <lb/><emph type="italics"/>multo antequam ipsi scribant.<emph.end type="italics"/> Il tempo per&ograve; che non fu scritto da costoro <lb/>preciso, non si seppe prima del 1604 quando in Palermo comparve postumo <lb/>il libro dell'Ingrassia <emph type="italics"/>De ossibus commentaria in Galenum,<emph.end type="italics"/> dove dice l'Au&shy;<lb/>tore di avere scoperta la Staffa nel 1546. Ma perch&egrave; fu questo libro mani&shy;<lb/>festamente scritto dopo la pubblicazione degli Opuscoli dell'Eustachio, e dopo <lb/>la morte dell'Autore, avvenuta nel 1580, da un nipote di lui fu pubblicato; <lb/>non rimane altro documento ad attestar della scoperta del Medico siciliano <lb/>che le parole, e la fede avuta alle parole altrui dal Falloppio. </s></p><p type="main">

<s>Se devesi dunque la storia appoggiare sopra la fede, primi a scoprire <lb/>la Staffa furono l'Eustachio e l'Ingrassia; se si deve appoggiare ai pubblici <lb/>documenti, furon primi invece il Collado e il Colombo. </s>

<s>Cos&igrave; le storie pri&shy;<lb/>vate per&ograve; che le pubbliche a nulla conducono senza la critica, che pu&ograve; sola <lb/>decidere del vero o espresso nelle parole o impresso sopra le carte. </s>

<s>Un ca&shy;<lb/>none di critica giustissima ce lo suggerisce molto a proposito l'Eustachio, <lb/>il quale, dop'avere asserito che fu il terzo ossicino da lui scoperto in Roma, <lb/><emph type="italics"/>neque edoctum neque monitum ab aliquo,<emph.end type="italics"/> soggiunge che della verit&agrave; della <lb/>sua asserzione faranno testimonianza le cose, che sar&agrave; per dire, dalle quali <lb/>decideranno i lettori, &ldquo; num propria ego industria auditus organa investi&shy;<lb/>garim et invenerim, an potius aliorum opera usus &rdquo; (De auditus org. </s>

<s>cit., <lb/>pag. </s>

<s>154). </s></p><p type="main">

<s>Seguendo questo criterio, si dovrebbe escludere dal merito dell'inven&shy;<lb/>zione il Collado, spagnolo, e riporre nel primo luogo il Colombo, il quale &egrave; <lb/>probabilissimo che avesse scoperta, e, nonostante le relazioni avute in con&shy;<lb/>trario dal Falloppio, dimostrata nelle sue scuole la Staffa molti anni prima <lb/>che fosse pubblicato il suo libro. </s>

<s>Chi ripensa all'egual valore di quegli Ana&shy;<lb/>tomici, e che, scoperto il Martello e l'Incudine, era naturalissimo il ritrovar <lb/>la catena degli ossicini continuata nella Staffa, non avr&agrave; nessuna difficolt&agrave; <lb/>a credere che il Colombo, l'Eustachio e l'Ingrassia, cos&igrave; studiosi dell'organo <lb/>dell'udito, s'incontrassero tutti e tre insieme e inconsapevoli nella scoperta <lb/>di quel terzo ossicino. </s>

<s>Tanta poi era manifesta agli occhi di tutti la somi&shy;<lb/>glianza fra l'esemplare e l'esemplato, che non fa maraviglia se tutti e tre, <lb/>senza nulla saper l'uno dell'altro, convennero nell'imporre a quello stesso <lb/>ossicino il nome di <emph type="italics"/>Staffa.<emph.end type="italics"/></s></p><p type="main">

<s>I tre ossicini cos&igrave;, innanzi alla prima met&agrave; del secolo XVI, scoperti for&shy;<lb/>marono l'ammirazione degli Anatomici seguenti, i quali si dettero con amo&shy;<lb/>roso studio a contemplarli in s&egrave; stessi Desiderosi di descriverli nelle loro <lb/>vere sembianze, aguzzarono gli occhi nelle loro minuzie pi&ugrave; sfuggevoli, tra <lb/>le quali ne notarono una in quella parte, che il processo dell'Incudine si <lb/>articola colla Staffa. </s>

<s>Dissero che cotesta articolazione si faceva per l'inter&shy;<lb/>medio di un osso distinto, che perci&ograve; sarebbe in ordine il quarto, e che va&shy;<lb/>riamente presentandosi all'occhio dell'osservatore ebbe vario nome, secondo <lb/>l'apparente variet&agrave; delle sue forme. </s>

<s>Anche questo, ch'&egrave; il pi&ugrave; piccolo degli <pb xlink:href="020/01/1398.jpg" pagenum="273"/>ossicini dell'udito, ha una storia sua propria, che non vuol essere nel pre&shy;<lb/>sente argomento taciuta. </s></p><p type="main">

<s>Aveva gi&agrave; il Vesalio da lungo tempo osservato che l'estrema gamba <lb/>dell'Incudine andava a terminare &ldquo; quasi in unculum &rdquo; (De corp. </s>

<s>hum. </s>

<s>fa&shy;<lb/>brica cit., pag. </s>

<s>35) ci&ograve; che l'avrebbe potuto mettere in sospetto dell'esi&shy;<lb/>stenza di un terzo ossicino, a cui quell'uncinetto servirebbe di attacco. </s>

<s>Ma <lb/>al Colombo, nella serie completa degli ossicini da lui osservata, si present&ograve; <lb/>quel punto di attacco sotto la forma di un capolino di spillo collocato nella <lb/>staffa ossea al posto dell'anello in cui, nelle staffe da cavalcare, s'infila la <lb/>correggia pendente dalla sella. </s>

<s>&ldquo; Una re tamen a stepede differt quod caret <lb/>eo foramine in quod lora immittuntur ad stapedem sellae utrinque alligan&shy;<lb/>dam. </s>

<s>At huius loco capitulum quoddam extat rotundum, quo ad incudis <lb/>processum accedit &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>27). Fu questo capolino descritto <lb/>poi anche dall'Aranzio, come fece notare il Morgagni a pag. </s>

<s>122 dell'Epi&shy;<lb/>stola anatomica VI da noi pi&ugrave; volte citata, e nostante, sulla fine della prima <lb/>met&agrave; del secolo XVII, form&ograve; per alcuni Anatomici, com'apparir&agrave; dal rac&shy;<lb/>conto che segue, il vanto di una nuova scoperta. </s></p><p type="main">

<s>Visitando Tommaso Bartholin l'Italia e i pi&ugrave; eccellenti professori del&shy;<lb/>l'arte, ch'ei coltivava con tanta fama, giunto in Venezia, s'introdusse in <lb/>casa di Cecilio Folli, che volle onorar l'ospite col mostrargli certe sue pre&shy;<lb/>parazioni degli ossicini auditivi, fra'quali glie ne additava uno, compiacen&shy;<lb/>dosi di averlo egli il primo da poco tempo scoperto. </s>

<s>&mdash; Ma cotesto, disse <lb/>allora il Bartholin, &egrave; il quarto ossicino scoperto, gi&agrave; sono alcuni anni, dal <lb/>mio amico Francesco Sylvio, e ch'io stesso, dietro la notizia avutane da lui, <lb/>pure scopersi e descrissi in una mia dissertazioncella anatomica, della quale, <lb/>se vi piace, posso mandarvi una copia. </s>

<s>&mdash; Rest&ograve; il Folli a queste parole <lb/>senza fiato, n&egrave; lo riebbe, se non che dalla speranza espressa al Bartholino <lb/>che quell'osso sylviano potess'essere qualche cosa di differente dal suo. </s></p><p type="main">

<s>In questo, l'Ospite che vedeva non esser quello n&egrave; il luogo n&egrave; il tempo <lb/>di entrare in dispute, si conged&ograve; per andare a Padova, di dove mand&ograve; a <lb/>Venezia la promessa Dissertazione, accompagnata da una lettera sottoscitta <lb/>il d&igrave; 25 di Ottobre 1644, nella quale, a proposito degli ossicini dell'udito, <lb/>cos&igrave; al Folli diceva: &ldquo; Auditus ossicula nitida erant quae nobis ostendebas. </s>

<s><lb/>Quod vero quartum Os sylvianum diversum a tuo diceres, mirum mihi vi&shy;<lb/>debatur. </s>

<s>Quaeso per otium auditus instrumenta, tuo more separata, et si <lb/>quid circa illa dignum memoria notasti, nobis communica &rdquo; (T. Barthol., <lb/>Epistolarum medic. </s>

<s>Centuria I, Hagae Comitum 1740, pag. </s>

<s>249, 50). </s></p><p type="main">

<s>Il Folli infatti rispose il d&igrave; 19 di Novembre appresso poche parole, con <lb/>le quali accompagnava al Bartholin sei figure rappresentative de'varii stru&shy;<lb/>menti dell'organo dell'udito, semplicemente dichiarate con lettere di ri&shy;<lb/>chiamo. </s>

<s>Nella figura II, quella parte disegnata colla lettera <emph type="italics"/>l<emph.end type="italics"/> si dichiara cos&igrave;: <lb/>&ldquo; Stapedis osseus quidam globulus Thomae Bartholino in Anatomia Paren&shy;<lb/>tis descriptus &rdquo; (ibid., pag. </s>

<s>258). Par di qui che il Folli rinunziasse al me&shy;<lb/>rito della scoperta, ma nella seguente figura III, bench&egrave; il piccolo strumento <pb xlink:href="020/01/1399.jpg" pagenum="274"/>indicato colla lettera <emph type="italics"/>g<emph.end type="italics"/> si dichiari nuovamente: &ldquo; Stapedis osseus globulus &rdquo; <lb/>(ibid., pag. </s>

<s>259) in disegno apparisce diverso dalla forma globulare, e rap&shy;<lb/>presenta piuttosto quella <emph type="italics"/>squamula oblonga,<emph.end type="italics"/> a cui ben lo rassomigliava il <lb/>Molinetti nel cap. </s>

<s>IX delle sue <emph type="italics"/>Dissertazioni<emph.end type="italics"/> (ediz. </s>

<s>cit., pag. </s>

<s>52). Questa era <lb/>forse la diversit&agrave; che il Folli diceva passare fra il suo e l'Osso sylviano, ma <lb/>poi sembra si persuadesse non esser la forma di lui squamosa ma globu&shy;<lb/>lare, non avvedendosi n&egrave; egli n&egrave; il Bartholin che il Sylvio era stato di quasi <lb/>un secolo prevenuto dal Colombo e dall'Aranzio. </s>

<s>Gli Anatomici poi, asse&shy;<lb/>gnando al quarto ossicino la figura lenticolare, dichiarano che il Folli avrebbe <lb/>fatto meglio a non si lasciar persuadere al Bartholino, e a dichiarare, come <lb/>aveva rappresentato in disegno, il piccolissimo strumento, intorno al quale <lb/>nonostante si disputa se sia un osso distinto o un apofisi del pi&ugrave; lungo pro&shy;<lb/>cesso dell'Incudine, e la lite &egrave; sotto il giudice ancora. </s></p><p type="main">

<s>In quella III figura, dove il Folli disegn&ograve; gli ossicini, il Martello &egrave; rap&shy;<lb/>presentato con tre processi, il maggiore e il minore gi&agrave; da lungo tempo co&shy;<lb/>nosciuti e descritti, e un altro pi&ugrave; minuto, ch'esso Folli dichiara <emph type="italics"/>a nemine <lb/>antea observatus<emph.end type="italics"/> (ibid., pag. </s>

<s>259). Ma a che fine usar la Natura tant'arte in <lb/>cos&igrave; sfuggevoli minuzie? </s>

<s>Era questa una domanda che, tutto in contempla&shy;<lb/>zione di quelle maraviglie, si faceva un giorno l'Eustachio. </s>

<s>Sospett&ograve; che <lb/>dovessero que'processi servire di attacco a qualche muscolo, e dall'altra <lb/>parte, se gli ossicini si muovono, come da tutti s'ammette per certo, qual'&egrave; <lb/>il principio e lo strumento del moto? </s></p><p type="main">

<s>Dietro la scorta di queste idee, incidendo il peritissimo Anatomico l'osso <lb/>&ldquo; quod petram refert, eo loco, quo linea minime alte penetrante exculptum <lb/>est et versus tenuiorem ossis temporis sedem in anteriorem partem magis <lb/>eminet, eiusque squammam accurate detrahens &rdquo; gli venne trovato un mu&shy;<lb/>scolo &ldquo; qui etsi omnium minimus sit, elegantia tamen et constructionis ar&shy;<lb/>tificio nulli cedit. </s>

<s>Oritur a substantia ligamentis simili qua parte os, quod <lb/>cuneum imitatur cum temporis osse committitur, indeque carneus evadens <lb/>redditur sensim ad medium usque aliquanto latior, deinde vero angustior <lb/>effectus tendinem gracillimum producit qui, in maiorem apophysim ossiculi <lb/>malleo comparati, fere e regione minoris apophysis eiusdem inseritur &rdquo; (De <lb/>auditus org. </s>

<s>cit., pag. </s>

<s>158). </s></p><p type="main">

<s>Poco per&ograve; al moto parve un muscolo solo, l'inserzion del quale lasciava <lb/>inutili gli altri processi. </s>

<s>L'Eustachio forse intravide la necessit&agrave; di altri pic&shy;<lb/>coli muscoli, che servissero a quell'armonica corrispondenza di moti, in che <lb/>si dovevano mettere gli ossicini, ma oltre quel primo non pot&egrave; nell'interno <lb/>dell'orecchio ritrovarvene altri. </s>

<s>Il d&igrave; 7 di Marzo del 1593 la ventura tocc&ograve; <lb/>poi al Casserio, che fece in quel tempo incidere il nuovo muscolo felice&shy;<lb/>mente scoperto a perpetua memoria, aspettando l'occasione propizia d'an&shy;<lb/>nunziarlo pubblicamente in iscritto. </s>

<s>Stava intanto in gran trepidazione che <lb/>qualcuno non lo prevenisse, e avendo saputo che Andrea Laurent attendeva <lb/>in Parigi alla stampa della sua <emph type="italics"/>Anatomia,<emph.end type="italics"/> volle per mezzo degli amici del&shy;<lb/>l'Autore spiare se nulla vi dicesse di questo secondo muscolo interno del-<pb xlink:href="020/01/1400.jpg" pagenum="275"/>l'orecchio, e n'ebbe per risposta che il Laurent accennava solo essere or&shy;<lb/>gani delle pulsazioni auditive i tre ossicini e alcuni muscoli, senza designarli <lb/>per&ograve; n&egrave; nel numero n&egrave; nella specie. </s></p><p type="main">

<s>Il Relatore, chiunque egli fosse, come sbagli&ograve; nell'indicare il titolo del&shy;<lb/>l'Opera, cos&igrave; sbagli&ograve; nell'indicare il libro e il capitolo, dove l'Anatomico <lb/>parigino trattava dell'udito, ond'&egrave; che il Casserio cos&igrave; citava, dietro le poco <lb/>esatte informazioni, il volume tuttavia inedito, come se fosse gi&agrave; venuto alla <lb/>luce. </s>

<s>&ldquo; Andreas Laurentius philos. </s>

<s>e med. </s>

<s>celeberrimus, suorum operum <lb/>anat., lib. </s>

<s>IV, cap. </s>

<s>XVIII, scribit pulsationi, quam concussis invicem audi&shy;<lb/>tus organi ossiculis quidam pro efficienda auditione fieri opinantur, exiles <lb/>dicatos esse musculos. </s>

<s>An autem duo tantum sint an plures, et ubi consi&shy;<lb/>stant, unde orti, quomodo progrediantur, ubi inseruntur non docet.... Cae&shy;<lb/>terum musculum hunc consistentem in auditorio meatu ego anno millesimo <lb/>quingentesimo nonagesimo tertio, mense martio die septima, in praesentia <lb/>excellentissimi Domini Christofori Malvicini .... et plurium studiosorum, ... <lb/>observavi, et statim ab honorabili viro Josepho Mureto germano pictore, tunc <lb/>temporis mihi, pro pingendis figuris anatomicis cohabitanti, delineari in per&shy;<lb/>petuam memoriam curavi &rdquo; (De auris auditus organii historia, Ferrariae 1600, <lb/>pag. </s>

<s>79). </s></p><p type="main">

<s>In quell'anno, che appariva in Ferrara questo trattato del Casserio alla <lb/>luce, il Laurent pubblicava in Parigi la sua <emph type="italics"/>Historia anatomica humani <lb/>corporis,<emph.end type="italics"/> nell'XI libro della quale, al cap. </s>

<s>XIII, si leggevano queste parole: <lb/>&ldquo; Stapes enim superiorem fenestram claudens ab Incude movetur. </s>

<s>Incus a <lb/>Malleo, Malleus a membrana aeris externi appulsu percussa. </s>

<s>Haec igitur pul&shy;<lb/>sationis sunt organa: ossicula tria, chorda et musculi &rdquo; (pag. </s>

<s>428). </s></p><p type="main">

<s>Ma in quel medesimo anno 1600 comparve alla luce in Venezia anche <lb/>il trattato <emph type="italics"/>De aure auditus organo<emph.end type="italics"/> dell'Acquapendente, nella Prima parte <lb/>del quale, al cap. </s>

<s>VI, dop'aver descritto il muscolo eustachiano, si soggiunge: <lb/>&ldquo; Praeterea hoc anno 1599 musculum invenire visus sum in meatu audito&shy;<lb/>rio, qui extra membranam est, exiguus, carneus, non expers tendinis &rdquo; <lb/>(Opera omnia cit., pag. </s>

<s>251). &Egrave; questa come ognuno vede la descrizione del <lb/>muscolo che il Casserio, discepolo dell'Acquapendente, diceva di avere sco&shy;<lb/>perto sei anni prima, e che l'Albino stesso liberamente confessava essere <lb/>stato pi&ugrave; diligentemente descritto dal discepolo che dal maestro (Ibid., Al&shy;<lb/>bini praefatio De Hier. </s>

<s>Fabricio). </s></p><p type="main">

<s>Quella diligenza per&ograve; verr&agrave; anche meglio apprezzata, considerando le <lb/>difficolt&agrave; dell'invenzione, per le quali, appresso a molti Anatomici posteriori, <lb/>and&ograve; affatto dimenticato quel nuovo muscolo casseriano, che si sta tutto invi&shy;<lb/>sibilmente nascosto sotto il corpo dell'Incudine e il Meato auditorio. </s>

<s>Fu <lb/>perci&ograve; che il Valsalva cred&egrave; necessario d'insegnare il pi&ugrave; facile modo di <lb/>farne l'indagine &ldquo; cum multi ex Recentioribus eumdem musculum omni&shy;<lb/>fariam sileant, quasi nunquam hunc docuisset Casserius, .... immo quasi <lb/>nunquam hic musculus in aure extitisset &rdquo; (De aure hum. </s>

<s>cit., pag. </s>

<s>22). </s></p><p type="main">

<s>Da questo zelo trasportato aument&ograve; lo stesso Valsalva il numero di que-<pb xlink:href="020/01/1401.jpg" pagenum="276"/>sti muscoli interni, assegnandone uno a ciascun de'processi da lui distinti <lb/>col nome di <emph type="italics"/>processo maggiore<emph.end type="italics"/> e di <emph type="italics"/>processo minore<emph.end type="italics"/> dato ai due primi an&shy;<lb/>ticamente conosciuti, e col nome di <emph type="italics"/>processo minimo<emph.end type="italics"/> dato a quello scoperto <lb/>dal Folli. </s>

<s>&ldquo; Musculus processus minimi, a pariete Tympani faciem spectante <lb/>incipiens et per hunc progrediens, inflectitur, deinde, et Tympani chordam <lb/>subtermeans, in Mallei partem praecedentis musculi insertioni quasi oppo&shy;<lb/>sitam, nempe in processum minimum, insertum se venit, et sic Malleus ex <lb/>utraque parte, ope huius et praecedentis musculi, firmatus consistit, non sic <lb/>tamen ut immobilis sit, verum ut in ipsorum insertis extremitatibus hypo&shy;<lb/>mochlium in propriis motibus habeat &rdquo; (ibid.). Ma gli Anatomici posteriori, <lb/>fra'quali lo stesso Morgagni, messero in dubbio questo terzo muscolo appli&shy;<lb/>cato dal Valsalva a fermare e a servire d'ipomoclio al Martello. </s></p><p type="main">

<s>Essendo questo primo ossicino, conforme alla pi&ugrave; comune opinione di <lb/>quei tempi, il principio del moto, si poteva facilmente credere che non aves&shy;<lb/>sero gli altri nessun bisogno di muscoli motori, ma il Casserio ne ritrov&ograve; <lb/>uno applicato alla staffa nell'orecchio di un cavallo, e fra le figure della Ta&shy;<lb/>vola IX lo disegn&ograve; nella XXIV colla lettera C cos&igrave; dichiarata: &ldquo; Musculus <lb/>internus alter, a nemine hactenus inventus et observatus, suo tendine te&shy;<lb/>nuissimo Stapedi adiunctus &rdquo; (De auris historia cit., pag. </s>

<s>56). </s></p><p type="main">

<s>Il Riolano, a cui non riusc&igrave; di ritrovare il muscolo equino descritto e <lb/>disegnato nelle sue Tavole dal Casserio, sentenzi&ograve; con gran confidenza che <lb/>egli era fittizio: molti lo negarono affatto nell'uomo. </s>

<s>Lo Schelhammer ha <lb/>nel suo trattato <emph type="italics"/>De auditu<emph.end type="italics"/> queste espresse parole: &ldquo; Huie etiam ossiculo <lb/>(alla staffa) musculum destinatum esse Dn. </s>

<s>Lamy asserit, in quo fortassis <lb/>fallitur &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1684, pag. </s>

<s>47). Ma pure que'grandi Anatomici ita&shy;<lb/>liani del secolo XVI non erano cos&igrave; facili ad ingannarsi, e il Vidio accen&shy;<lb/>nava a un filo <emph type="italics"/>seu chorda tenuissima,<emph.end type="italics"/> che passa attraverso alla Finestra ro&shy;<lb/>tonda &ldquo; pertinetque ad commissuram incudis cum stapede &rdquo; (De Anatome <lb/>corp. </s>

<s>hum., Venetiis 1611, pag. </s>

<s>322). Il Varolio poi riconobbe (De resolu&shy;<lb/>tione corp. </s>

<s>hum., Francofurti 1591, pag. </s>

<s>28) essere quella corda tenuissima <lb/>il tendine di un muscolo, che il Valsalva liber&ograve; da tutte le contradizioni di&shy;<lb/>mostrando avere il suo corpo carnoso annidato &ldquo; in curvo canali osseo late&shy;<lb/>raliter, circa mediam falloppiani Aquaeductus partem, insculpto &rdquo; (De aure <lb/>hum. </s>

<s>cit., pag. </s>

<s>25). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>La storia descrittiva di quelle corde, sopra le quali cantano i loro idillii <lb/>le divine Sirene mollemente sedute sopra gli orli della Conca auditiva, &egrave; <lb/>ormai giunta al suo termine, e non resta altro a noi che di scendere nel <lb/>profondo di quella Conca, per i riposti anfratti, per i seni tortuosi e per gli <lb/>intricati labirinti a narrare ci&ograve; che di nuovo e di maraviglioso v'ha scoperto <lb/>l'industria dell'uomo. </s></p><pb xlink:href="020/01/1402.jpg" pagenum="277"/><p type="main">

<s>Gli Anatomici antichi impaurirono timorosi di smarrire la via, e i primi <lb/>restauratori dell'arte s'affacciarono appena alla bocca dell'antro misterioso, <lb/>sollevando la prima lapide che la chiudeva. </s>

<s>Realdo Colombo dice del pi&egrave; della <lb/>staffa, in cui ci si rappresenta l'immagine di quella lapide: &ldquo; Jacet, vel la&shy;<lb/>titat potius, in cavernula quadam, ferme rotunda, intra sinum auditorium <lb/>exculpta &ldquo; (De re anat. </s>

<s>cit., pag. </s>

<s>27), e quel seno auditorio &egrave; dall'Autore <lb/>vagamente descritto come vacuo &ldquo; ac diversis veluti speluncis excavatum &rdquo; <lb/>(ibid., pag. </s>

<s>23). &Egrave; da notare, altrove soggiunge, fra quelle spelonche un pro&shy;<lb/>cesso &ldquo; ad cerebri basim, qui in iugi modum extenditur in acutum desi&shy;<lb/>nens, cavernamque intus habet instar labyrinthi &rdquo; (ibid., pag. </s>

<s>26), penetrar <lb/>nel quale non era a nessuno permesso, che non avesse avuto il filo d'Arianna. </s></p><p type="main">

<s>Aveva perci&ograve; ragione il Falloppio a dire delle cavit&agrave; scolpite nell'osso <lb/>temporale per uso dell'udito, &ldquo; hae ab aliquot Anatomicis satis imperfecte, <lb/>ab aliquot vero falso descriptae sunt. </s>

<s>Igitur, soggiunge tosto a Pietro Manna, <lb/>quales sint audi &rdquo; (Observat. </s>

<s>anat. </s>

<s>in loco cit., pag. </s>

<s>409). E dop'essersi di&shy;<lb/>ligentemente ed eruditamente trattenuto intorno alla membrana e agli ossi&shy;<lb/>cini, entra addentro a esplorare la cavit&agrave; da lui detta il Timpano &ldquo; ob eam <lb/>quam habet cum militari tympano similitudinem &rdquo; e la trova insigne per <lb/>due cavit&agrave;, e per un canale, a cui piacegli d'imporre il nome di <emph type="italics"/>Acquedotto.<emph.end type="italics"/><lb/>Le due cavit&agrave; pure non vuol lasciarle senza un nome distinto, ch'&egrave; quello <lb/>di <emph type="italics"/>Finestre<emph.end type="italics"/> e cos&igrave; le descrive: &ldquo; Altera elatior, et quasi in media concame&shy;<lb/>ratione Tympani collocata, quam Stapedis basis claudit. </s>

<s>Figura istius ovalis <lb/>penitus est, quae aperta desinit in secundam cavitatem, quam <emph type="italics"/>Labyrinthum<emph.end type="italics"/><lb/>nominabo. </s>

<s>Altera vero humilior est rotundaque et ad posteriora cavitatis <lb/>declinans, quae per os penetrans in geminum canalem aut viam fenditur, <lb/>quarum viarum unam in dictum labyrinthum, alteram in tertiam cavitatem <lb/>cochlearem vel <emph type="italics"/>Cochleam<emph.end type="italics"/> a me dictam tendit. </s>

<s>Haec secunda fenestella nullo <lb/>osse clauditur, cum tamen prior Stapedis basi semper clausa maneat &rdquo; (ibid.). </s></p><p type="main">

<s>Aperti cos&igrave; una volta gli occhi a contemplare ci&ograve; ch'era prima sfuggito <lb/>all'attenzione di tutti, gli Anatomici posteriori al Falloppio esaminarono con <lb/>pi&ugrave; diligenza quelle due finestre, e trovarono che v'era qualche cosa da cor&shy;<lb/>reggere nella figura e nelle parti annesse. </s>

<s>Il Vidio, il Plater e il Casserio <lb/>disegnarono, nelle loro Tavole, rotonda quella pi&ugrave; alta finestra, com'era stata <lb/>veduta dallo stesso Falloppio, ma l'Acquapendente, nella figura XIX illustra&shy;<lb/>tiva del suo trattato <emph type="italics"/>De aure,<emph.end type="italics"/> la dipinse in forma pi&ugrave; tendente al triangolo <lb/>che al cerchio, e tale, in pi&ugrave; casi, ebbe veramente a ritrovarla il Morgagni. <lb/></s>

<s>&ldquo; Nam quod ego in pluribus, ne dicam in plerisque auribus, continenter <lb/>inspectis animadverteram, rotundam Fenestram ad trianguli magis, cuius <lb/>vertex sit ad superiora conversus, quam ad circuli figuram accedere, id olim <lb/>a Fabricio nostro expressum video &rdquo; (Epist. </s>

<s>anat. </s>

<s>XXII cit., pag. </s>

<s>175). </s></p><p type="main">

<s>La lode per&ograve;, come giustamente osserva lo Scarpa, &egrave; immeritata, perch&egrave; <lb/>l'Acquapendente dipinse a caso quella figura &ldquo; cui tamen nullam explica&shy;<lb/>tionem adiecit, quia, sicuti ex eius verbis colligitur, rem non adhuc sibi <lb/>satis cognitam delincabat &rdquo; (De structura Fenestrae rotundae, Mutinae 1772, <pb xlink:href="020/01/1403.jpg" pagenum="278"/>pag. </s>

<s>26). Le parole, a cui qui accenna lo Scarpa, sono principalmente quelle <lb/>scritte nel cap. </s>

<s>VII della I Parte <emph type="italics"/>De aure auditus organo,<emph.end type="italics"/> dalle quali ve&shy;<lb/>ramente si conclude che il celebre Autore non descrisse dell'orecchio, sul&shy;<lb/>l'esempio degli Anatomici antichi, altro che la parte esterna. </s>

<s>Quanto all'in&shy;<lb/>terna cavit&agrave;, egli dice, &egrave; piena di cos&igrave; innumerevoli seni &ldquo; ut assequi ac <lb/>denumerare possibile non sit &rdquo; (Opera omnia cit., pag. </s>

<s>252). E bench&egrave; citi <lb/>il Falloppio &ldquo; cui in rebus abstrusis maximam fidem adhibeo, utque prae&shy;<lb/>ceptorem colo &rdquo; nonostante dice che i canali semicircolari, in cui si raggira <lb/>il labirinto, son tali e tanti, che si possono bene ammirare &ldquo; dinumerare <lb/>autem seu ad ordinem quemdam redigere aut dirigere non est ut quisquam <lb/>tentet &rdquo; (ibid.) dimentic&ograve;, a quel che pare, che il Falloppio stesso avea ri&shy;<lb/>dotti quegli innumerevoli canali a tre, e come gli avea distintamente veduti, <lb/>cos&igrave; gli avea in pubblico diligentemente descritti. </s></p><p type="main">

<s>Queste osservazioni, alle quali ha dato occasione il giudizio autorevolis&shy;<lb/>simo di Antonio Scarpa, servano a difendere noi contro i ciechi ammiratori <lb/>di Girolamo Fabricio, ai quali sar&agrave; forse dispiaciuto che si sia in varie pa&shy;<lb/>gine di questa storia fatto apparire il celebre uomo come un ostacolo al li&shy;<lb/>bero progredire della scienza in Italia. </s></p><p type="main">

<s>Ritornando ora alla cos&igrave; detta <emph type="italics"/>Finestra rotonda,<emph.end type="italics"/> trov&ograve; il Cotunnio da <lb/>correggere anche la figura stessa descritta dal Morgagni, e disse che quel <lb/>forame &ldquo; lumine gaudet non plane circulari, sed potius parabolico, et poste&shy;<lb/>riora versus integre patente &rdquo; (De Aquaeductibus etc., Neapoli 1775, pag. </s>

<s>20). <lb/>Questa correzione in ogni modo fatta dagli Anatomici posteriori alla prima <lb/>descrizion del Falloppio &egrave; una squisitezza anatomica, ma vi erano in quelle <lb/>stesse descrizioni altre cose da correggere, che dovevano avere per la teoria <lb/>della percezione de'suoni una non lieve importanza. </s></p><p type="main">

<s>Nel passo, da noi sopra citato dalle <emph type="italics"/>Osservazioni<emph.end type="italics"/> falloppiane, si conclu&shy;<lb/>deva dall'Autore la descrizione delle due Finestre, cos&igrave; dicendo in partico&shy;<lb/>lare della Rotonda: &ldquo; Haec secunda fenestella nullo osse clauditur, cum <lb/>tamen prior Stapedis basi semper clausa maneat. </s>

<s>&rdquo; Ma perch&egrave; non par che <lb/>il Falloppio avesse posto mente alle membrane che rivestono le interne ca&shy;<lb/>vit&agrave; dell'orecchio, dicendo della Finestra rotonda <emph type="italics"/>nullo osse clauditur,<emph.end type="italics"/> in&shy;<lb/>tendeva ch'ella fosse del tutto aperta. </s>

<s>Il Vidio per&ograve;, nel suo Manoscritto <lb/>edito molto tardi, dava cos&igrave; de'seni interni auriculari, il primo dopo il Fal&shy;<lb/>lopio, una descrizione assai pi&ugrave; precisa: &ldquo; At basis Stapedis foramen unum <lb/>claudit ex duobus sitis in primo sinu, ad quem iam aggredimur. </s>

<s>Unum ova&shy;<lb/>tam figuram habens situm est ad superiorem ac mediam partem sinus, te&shy;<lb/>nuissimaque membrana clauditur ambiente universum sinum: clauditur au&shy;<lb/>tem a basi Stapedis. </s>

<s>Alterum versus pesteriorem atque inferiorem partem <lb/>est rotundum, atque eadem membrana obductum &rdquo; (De Anatome, Vene&shy;<lb/>tiis 1611, pag. </s>

<s>322). </s></p><p type="main">

<s>La Finestra rotonda non &egrave; dunque aperta, ma &egrave; per il Vidio chiusa da <lb/>una membrana, che &egrave; la continuazione del periostio del Timpano. </s>

<s>Il Casse&shy;<lb/>rio pure riconobbe questo opercolo, ma lo descrisse come proveniente in-<pb xlink:href="020/01/1404.jpg" pagenum="279"/>vece dalla parte membranacea della lamina spirale, ossia dal periostio del <lb/>Laberinto. </s>

<s>Dop'aver detto infatti che l'elice consta di due lamine, una ossea <lb/>e l'altra membranacea, &ldquo; quam ea format, soggiunge, membrana quae du&shy;<lb/>plex hoc antrum vestiens utramque obserat fenestram &rdquo; (De auris historia <lb/>cit., pag. </s>

<s>59). Questa apparente contradizione poi tra il Vidio e il Casserio <lb/>fu riconciliata dallo Scarpa, il quale dimostr&ograve; che la membrana, dalla quale <lb/>&egrave; chiusa la Finestra rotonda, &ldquo; ex tenui periostio Tympani et tenuissimo La&shy;<lb/>byrinthi componitur &rdquo; (De fenestra rotunda cit., pag. </s>

<s>56). </s></p><p type="main">

<s>Cos&igrave; insomma la diligenza, dagli Anatomici usata intorno all'esame della <lb/>struttura delle due finestre, aveva supplito al difetto delle prime descrizioni <lb/>del Falloppio, il quale, oltre ai due detti forami, ritrov&ograve; nella cavit&agrave; del Tim&shy;<lb/>pano un terzo organo insigne, a cui piacquegli, come dicemmo, d'imporre <lb/>il nome di <emph type="italics"/>Acquedotto.<emph.end type="italics"/> &ldquo; Tertium, quod ego observatione dignum existimo, <lb/>cos&igrave; scrive nelle sopra citate <emph type="italics"/>Osservazioni,<emph.end type="italics"/> canalis quidam osseus est, qui <lb/>tecto huius cavitatis quasi subtenditur, exitque extra calvariam post radicem <lb/>calcaris inter illam ac mamillarem processum: principium autem ipsius est <lb/>intra calvariam. </s>

<s>Nam si recte inspicias videbis quintum par nervorum a re&shy;<lb/>liquis Anatomicis ita vocatum extendi ad medium ferme processuum ossis <lb/>temporum, quem internum atque petrosum appellamus. </s>

<s>Illuc tensum hoc <lb/>par ingreditur in canalem quemdam insculptum in quo latens in duas fin&shy;<lb/>ditur partes, alteram quidem magnam, alteram vero parvam et gracilem <lb/>valde duroriemque. </s>

<s>Haec posterior, perforato osse occulto quodam canali, <lb/>versus anteriora capitis serpit, deinde reflexa Tympanumque ingressa pro&shy;<lb/>prio hoc canali osseo deorsum et posteriora versus ad pinnae ipsius auri&shy;<lb/>culae radicem erumpit et disseminatur. </s>

<s>Via igitur istius nervi canalis hic est <lb/>de quo loquor, et <emph type="italics"/>Aquaeductum<emph.end type="italics"/> a similitudine appello &rdquo; (pag. </s>

<s>410). </s></p><p type="main">

<s>La similitudine per&ograve;, com'ebbe a fare osservare il Cotunnio (loco cit., <lb/>pag. </s>

<s>14), non era tolta dall'opinione che il nervo menasse seco un umore <lb/>acquoso, ma dall'essere quell'osso scavato a somiglianza de'canali aperti <lb/>ne'sotterranei, o sostenuti dagli archi nelle citt&agrave;, e che gli antichi Architetti <lb/>romani chiamavano giusto col nome di Acquedotti. </s>

<s>Ma, oltre a questo ca&shy;<lb/>nale, l'Eustachio, che attendeva a studiar l'interno dell'orecchio in quel <lb/>medesimo tempo e con ugual diligenza del Falloppio, ne scopr&igrave; un altro che <lb/>metteva in aperta comunicazione l'aria esterna attinta dalle fauci con quella <lb/>implantata nelle cavernosit&agrave; dell'osso petroso. </s>

<s>&ldquo; A caverna ossis lapidei in <lb/>quam meatus auditorius conchion appellatus finitur, via in narium cavitatem <lb/>perforata est. </s>

<s>Ab illa enim meatus alter oritur, rotundo canaliculo similis, <lb/>et instar tenuioris calami amplius, qui oblique ad anterius interiusque basis <lb/>capitis latus procedens, in medio quatuor foraminum totum istud os pene&shy;<lb/>trat atque perfodit.... Caeterum hunc meatum, de quo sermo est, arbitra&shy;<lb/>bitur fortasse quispiam eo loco desinere: res autem non ita se habet, sed <lb/>alterius generis substantia auctum, inter duos faucium seu gulae musculos, <lb/>a paucis hucusque bene cognitos, secundum paulo ante memoratae fissurae <lb/>ductum ulterius procedit, et iuxta radicem internae partis apophysis ossis <pb xlink:href="020/01/1405.jpg" pagenum="280"/>alis vespertilionum similis in alteram narium cavitatem terminatur &rdquo; (De <lb/>auditus org. </s>

<s>cit., pag. </s>

<s>161, 62). </s></p><p type="main">

<s>Anche a questo canaliculo, che il suo Inventore lasci&ograve; senza un nome <lb/>proprio, gli Anatomici posteriori, come l'Acquapendente, dettero sull'esem&shy;<lb/>pio del Falloppio il nome di acquedotto: &ldquo; meatusque est, quem veluti aquae&shy;<lb/>ductum dixeris &rdquo; (De aure cit., pag. </s>

<s>252). La somiglianza de'nomi dette in&shy;<lb/>tanto occasione a certi Anatomici, in ci&ograve; pochissimo diligenti, di confonder <lb/>le cose, scambiando il primo Acquedotto descritto dal Falloppio con questo <lb/>secondo scoperto dall'Eustachio, che si rimase per molti ignorato. </s>

<s>Ci&ograve; fu che <lb/>accese fieramente lo zelo dello Schelhammer, il quale deplorava che a'suoi <lb/>tempi le anatomiche dimostrazioni fosser fatte &ldquo; ad pompam potius, quam <lb/>usum &rdquo; (De auditu cit., pag. </s>

<s>57). E al veder che quell'errore da lui detto <lb/>sozzissimo, s'era introdotto nell'Anatomia riformata, per l'autorit&agrave; di un <lb/>Bartholin, padre, e di un Riolano, disperava di poterlo oramai sradicare dalle <lb/>giovani menti: &ldquo; adeoque hic error nostrae iuventuti nec evitari quidem <lb/>potest &rdquo; (ibid.). </s></p><p type="main">

<s>Il Valsalva per&ograve; prese la cosa con pace, e lasciate le declamazioni si <lb/>volse a trovare e ad applicare efficacemente i rimedii. </s>

<s>Riconosciuto che l'er&shy;<lb/>rore aveva avuto origine dal mancare il canaliculo scoperto dall'Eustachio <lb/>di un nome proprio, incominci&ograve; a chiamarlo <emph type="italics"/>Tuba eustachiana.<emph.end type="italics"/> &ldquo; Tubam <lb/>eustachianam appellabo &rdquo; (De aure hum. </s>

<s>cit., pag. </s>

<s>30) e gli Anatomici una&shy;<lb/>nimi ne seguirono l'esempio. </s>

<s>E perch&egrave; il mancar quell'organo di un nome <lb/>proprio e l'averlo avuto comune con quell'altro scoperto dal Falloppio dette <lb/>origine a quella confusione, cos&igrave; deplorata dallo Schelhammer, il Valsalva scolp&igrave; <lb/>nella Tavola VII la figura V a questo fine principalmente &ldquo; ut cuicumque <lb/>constare possit aliud esse aquaeductum Falloppii, aliud Tubam eustachianam, <lb/>cum alioqui a multis, saltem nomine, haec duo confundantur &rdquo; (ibid., pag. </s>

<s>103). </s></p><p type="main">

<s>Fu per questi motivi che il Morgagni disse il Valsalva della scoperta <lb/>eustachiana &ldquo; plusquam instauratorem existimandum esse &rdquo; (Epist. </s>

<s>anat. </s>

<s>XXII <lb/>cit., pag. </s>

<s>187) ma una pi&ugrave; vera ragione del merito &egrave; da riconoscersi nell'aver <lb/>lo stesso Valsalva con pi&ugrave; diligenza di nessun altro esaminata la figura, la <lb/>composizione e i muscoli della Tuba instaurata. </s>

<s>Ei l'assomigli&ograve; a due coni <lb/>d'ineguale altezza, che si tocchino per gli apici troncati. </s>

<s>&ldquo; Eius cavitatis <lb/>figura assimilari potest duobus contrapositis inaequalis altitudinis conis, com&shy;<lb/>pressiorem ellypsim pro basi habentibus, et antequam in apices desinant <lb/>coeuntibus &rdquo; (De aure hum. </s>

<s>cit., pag. </s>

<s>30); disse esser composta &ldquo; ex parte <lb/>ossea, membranacea cartilaginea atque carnea &rdquo; (ibid., pag. </s>

<s>31), e la trov&ograve; <lb/>fornita di un nuovo muscolo, &ldquo; a quo, ubi opus sit, eadem potest dilatari. </s>

<s><lb/>Quod assertum sicut in anatomicis scholis novum est, ita mihi, quem diutina <lb/>conquisitio et improbus labor id docuere, inter ea, de quibus certiores su&shy;<lb/>mus, videtur reponendum &rdquo; (ibid., pag. </s>

<s>32). </s></p><p type="main">

<s>Le scuole anatomiche ritennero infatti cos&igrave; questa come le altre novit&agrave; <lb/>ritrovate dal Valsalva intorno alla Tuba per cosa certissima, e accoppiando <lb/>l'erudizione alla scienza si misero dietro a investigare del restaurato organo <pb xlink:href="020/01/1406.jpg" pagenum="281"/>la prima storia. </s>

<s>Lo Schelhammer, da cui ebbe quella restaurazione l'im&shy;<lb/>pulso, aveva scritto: &ldquo; Fuit autem Aristoteli hic ductus non ignotus &rdquo; (De <lb/>auditu cit., pag. </s>

<s>54); espressione ripetuta poi dal Valsalva (De haure hum. </s>

<s><lb/>cit., pag. </s>

<s>30) e dal Morgagni, incerto se l'invenzione si dovesse dir propria <lb/>dell'Eustachio &ldquo; vel potius Aristotelis. </s>

<s>&rdquo; Cos&igrave; scrisse nella VII delle XXII <lb/>Epistole anatomiche a pag. </s>

<s>185, ma nella prima delle <emph type="italics"/>Epistolae anatomi&shy;<lb/>cae duae<emph.end type="italics"/> rifer&igrave;, dal cap. </s>

<s>XI del I libro dell'<emph type="italics"/>Historia animalium,<emph.end type="italics"/> le parole <lb/>proprie di Aristotile stesso, le quali suonano cos&igrave;: &ldquo; in oris palatum usque <lb/>semita pertendit &rdquo; movendo dalla parte pi&ugrave; interna dell'orecchio (Lugd. </s>

<s><lb/>Batav. </s>

<s>1728, pag. </s>

<s>109). </s></p><p type="main">

<s>La sentenza aristotelica dall'altra parte era vera, perch&egrave; fondata sopra <lb/>un esperimento, che pu&ograve; secondo il Vesalio facilmente ripetersi da ciascuno <lb/>di noi &ldquo; si attracto in os aere, illum quasi per aures propellere conemur &rdquo; <lb/>(De humani corp. </s>

<s>fabrica cit., pag. </s>

<s>40). Eppure n&egrave; il Vesalio n&egrave; il volgo <lb/>hanno preteso mai d'appropriarsi la scoperta eustachiana, come s'intende di <lb/>appropriarla ad Aristotile, che non and&ograve; punto pi&ugrave; l&agrave; del Vesalio e del volgo. </s></p><p type="main">

<s>Forse lo Schelhammer, e dopo lui il Valsalva e il Morgagni, messero <lb/>lo Stagirita a parte dell'invenzione eccitati dall'esempio dello stesso Eusta&shy;<lb/>chio, a cui piacque piuttosto di citare Alcmeone, e non par si accorgessero <lb/>que'valentuomini della finissima satira, con la quale l'Anatomico sanseveri&shy;<lb/>tano derideva le sciocche pretensioni di coloro che tutte le cose nuove &ldquo; a <lb/>maioribus nostris inventa atque instituta esse semper praedicant &rdquo; (De au&shy;<lb/>ditus organis cit., pag. </s>

<s>156). Dal non aver penetrato addentro a cotesti sensi <lb/>satirici ebbe origine l'inganno di quegli altri, i quali attribuirono a mode&shy;<lb/>stia l'aver esso Eustachio riconosciuto Empedocle inventor della Chiocciola, <lb/>com'avea riconosciuto Alcmeone primo inventor della Tuba, egli che dall'al&shy;<lb/>tra parte, ammirando il naturale artificio, senza tanta modestia, lo disse <emph type="italics"/>a <lb/>me inventum<emph.end type="italics"/> (ibid., pag. </s>

<s>162). Nel particolare esempio della Chiocciola per&ograve; <lb/>il sale era mescolato col fiele, di cui volle l'Autor <emph type="italics"/>De auditus organis<emph.end type="italics"/> asper&shy;<lb/>gere il Falloppio suo odiato rivale. </s></p><p type="main">

<s>Nelle Osservazioni anatomiche dunque, alle quali dobbiam ora tornare, <lb/>dop'aver l'Autore diligentemente descritto il Timpano, passa all'altra cavit&agrave; <lb/>contigua assai minore, la quale avvolgendosi per tante intricate sinuosit&agrave;, <lb/>&ldquo; merito Labyrinthus dicetur, in quam prospicit Fenestra ovalis clausa a Sta&shy;<lb/>pede, et altera orbicularis, quae etiam in caecam cavitatem tendit, de qua <lb/>iam loquar. </s>

<s>Est itaque tertia dicta cavitas insculpta in eodem processu pe&shy;<lb/>troso, in latere ipsius anteriori, interque hanc et canalem illum, in quem <lb/>primum quinti paris nervi gemini, durus scilicet et mollis, integri ingrediun&shy;<lb/>tur, tenuissimum quoddam interstitium continetur. </s>

<s>Nam in eodem situ pa&shy;<lb/>res sunt, verum canalis in medio processu cavitas in anteriori ipsius latere <lb/>est collocata, quae duobus aut tribus gyris in morem cochleae constat, ne&shy;<lb/>que exitum habet. </s>

<s>Unde <emph type="italics"/>Cochlea,<emph.end type="italics"/> vel cochlearis cavitas, vel caeca etiam est <lb/>dicenda. </s>

<s>Haec in intima superficie, velut etiam secunda cavitas, ut cuniculi <lb/>eiusdem, et omnes etiam dentium naturales cavitates, membranula quadam <pb xlink:href="020/01/1407.jpg" pagenum="282"/>mollissima ac tenuissima vestiuntur, quae an sit nervus expansus an aliud <lb/>non refert &rdquo; (Opera omnia cit., pag. </s>

<s>410). </s></p><p type="main">

<s>L'Eustachio, a leggere queste cose scritte come diceva da gente che si <lb/>inspira al divino Vesalio, e che nonostante si vanta di rendere inutili le fa&shy;<lb/>tiche di tutti coloro, &ldquo; qui operam dederint ut inventis suis addant aliquid &rdquo; <lb/>(De auditus org., pag. </s>

<s>156), pens&ograve; di avvilire l'iattanza col mettere il Fal&shy;<lb/>loppio a pari di Empedocle &ldquo; qui auditum impulsione spiritus fieri docuit, <lb/>qui cochleae simile intra aurem, tintinnabuli instar suspensum, percutit atque&shy;<lb/>pulsat, cui etiam Aristotiles assentire videtur &rdquo; (ibid., pag. </s>

<s>161). </s></p><p type="main">

<s>La satira &egrave; sanguinosa, e fa gran maraviglia che il Morgagni non l'ab&shy;<lb/>bia intesa. </s>

<s>Nella prima infatti delle <emph type="italics"/>Epistolae anatomicae duae<emph.end type="italics"/> si mette <lb/>dietro sul serio a riceroare i passi di Empedocle e di Aristotile, ai quali ne <lb/>aggiunge un'altro di Celso, e dal leggere in quegli Autori descritta l'orec&shy;<lb/>chia <emph type="italics"/>in modum cochleae obvolutam,<emph.end type="italics"/> e dal sentir dire a esso Celso che il <lb/>meato uditorio, dop'essersi flessuosamente prolungato &ldquo; iuxta cerebrum in <lb/>multa et tenuia foramina diducitur, per quae facultas audiendi est &rdquo; (De re <lb/>medica, Parisiis 1529, fol. </s>

<s>116 ad t.); ne argomenta essere stata la chioc&shy;<lb/>ciola del laberinto nota agli antichi, anche prima che venisse a descriverla <lb/>il Falloppio (Lugd. </s>

<s>Batav. </s>

<s>1728, pag. </s>

<s>108). </s></p><p type="main">

<s>Non pens&ograve; il Valentuomo che le due cose non si riscontrano veramente <lb/>altro che nel nome, rassomigliando Empedocle e Aristotile e Celso alla forma <lb/>del ben noto mollusco, non quell'organo ch'&egrave; riposto nella pi&ugrave; interna ca&shy;<lb/>vit&agrave; dell'orecchio, ma il pi&ugrave; patente di lui meato esterno. </s>

<s>In conferma di <lb/>che pu&ograve; addursi la testimonianza del Berengario, che pi&ugrave; saviamente del <lb/>Morgagni e di tanti scrittori moderni interpetr&ograve; il testo aristotelico. </s>

<s>&ldquo; Fi&shy;<lb/>gura aurium, egli dice nel citato Commentario al Mundino, omnibus nota <lb/>est: suum foramen est anfractuosum ut conchilia testa, sensu et teste Arist., <lb/>primo <emph type="italics"/>De Historia &rdquo;<emph.end type="italics"/> (fol. </s>

<s>CCCCLXXVII ad t.). </s></p><p type="main">

<s>La Chiocciola del Laberinto insomma, sconosciuta agli Antichi, fu primo <lb/>a descriverla il Falloppio, ma egli, dice l'Eustachio, la descrisse cos&igrave; super&shy;<lb/>ficialmente, come descrisse Empedocle il suo campanello, che dallo spirar <lb/>dell'aria &egrave; fatto sonare. </s>

<s>Quell'elegantissimo organo, poi soggiunge, non &egrave; <lb/>cos&igrave; semplice n&egrave; cos&igrave; volgare, che debba vergognarsi di venire rassomigliato <lb/>alle palustri lumache, dovendosi saper che l'osso, rappresentante nella Rocca <lb/>petrosa una tal figura, si compone di un doppio genere di spire, &ldquo; quorum <lb/>alterum ab ossea substantia admodum tenui, sicca et quae facile teritur, <lb/>creatur: alterum vero, omnibus Anatomicis adhuc ignotum, ex materia qua&shy;<lb/>dam fit molli et mucosa, firma tamen, et quae nescio quid arenosi per&shy;<lb/>mixtum habet, oriturque ex medio spacio priorum spirarum tamquam ex <lb/>ampliore basi, sensimque extenuatum in aciem desinit. </s>

<s>Comparari potest <lb/>appositissime eius forma testae cochlearum, exteriore prius ex ea superficie <lb/>rotunda detracta, et parte interiore quae in spiras contorquetur reservata. </s>

<s><lb/>Qua autem substantia posteriores hae spirae efficiantur fateor me ignorare &rdquo; <lb/>(De aud. </s>

<s>org. </s>

<s>cit., pag. </s>

<s>160). </s></p><pb xlink:href="020/01/1408.jpg" pagenum="283"/><p type="main">

<s>Conoscere queste sottigliezze, ignorate dall'Eustachio, era riserbato ai <lb/>progressi, che sarebbe per fare l'Anatomia pi&ugrave; di un secolo dopo, ma in <lb/>sostanza la composizione della cavit&agrave; cocleare scolpita nel Laberinto &egrave; vera&shy;<lb/>mente quella cos&igrave; descritta dal nostro Sanseveritano. </s>

<s>Di quell'altra cavit&agrave;, <lb/>di che il Labirinto stesso si rende insigne, e che risulta dei cos&igrave; detti <emph type="italics"/>Ca&shy;<lb/>nali semicircolari,<emph.end type="italics"/> l'Eustachio se ne passa con assai brevit&agrave;, quasi suo mal&shy;<lb/>grado confessando che nulla era da aggiungere alla descrizione, datane in <lb/>questi precisi termini dal Falloppio: &ldquo; Ab hac cavitate tres cuniculi oriun&shy;<lb/>tur, et in eamdem redeunt, circulares penitus, a quibus nomen accepit ipsa <lb/>cavitas. </s>

<s>Quorum unus est inferior, qui ab anteriori parte cavitatis divertens <lb/>versus exteriora, ac deinde reflexus in eamdem cavitatem, per posteriorem <lb/>angulum recurrit. </s>

<s>Alter cuniculus oritur ab eodem anterioris cavitatis an&shy;<lb/>gulo, sursumque elatus quasi ad hortogonion facto semicirculo, iterum in <lb/>cavitatem, per angulum posteriorem, regreditur. </s>

<s>Tertius oritur et occidit, aut <lb/>sinit in posteriori angulo cavitatis; nam inde ortus, perforatoque osse cir&shy;<lb/>culari quodam canali, exteriora versus illuc item revertitur &rdquo; (Observat. </s>

<s><lb/>anat. </s>

<s>inter. </s>

<s>Op. </s>

<s>omnia cit., pag. </s>

<s>410). </s></p><p type="main">

<s>A questa falloppiana descrizione dei Canali semicircolari il diligente <lb/>Vidio, e il diligentissimo Casserio non trovarono da aggiunger nulla di nuovo <lb/>n&egrave; di pi&ugrave; preciso, sia quanto alle parole, sia quanto ai disegni, i quali anzi <lb/>rimasero trascurati o non condotti con le debite cure infino al 1644, quando <lb/>venne primo ad esibirli al Bartholin, nella sopra citata Epistola anatomica, <lb/>Cecilio Folli. </s>

<s>La Figura prima &ldquo; quae ostendit Cochleam, Labyrinthum, fo&shy;<lb/>ramina ovale et rotundum, nec non Aquaeductum Falopii &rdquo; (Thomae Bartho&shy;<lb/>lini Epist. </s>

<s>medic. </s>

<s>Centuria I cit., pag. </s>

<s>256), e la Figura quarta &ldquo; quae habet <lb/>Cochleam inversam ut videatur cavitas cum propriis foraminibus et loco ner&shy;<lb/>vorum &rdquo; (ibid., pag. </s>

<s>260), son reputate sufficientemente precise, e in ogni <lb/>modo hanno il pregio di esser delle prime a comparire nella storia dell'Ana&shy;<lb/>tomia. </s></p><p type="main">

<s>Quel Laberinto in conclusione, intorno a cui s'erano gli Anatomici an&shy;<lb/>tichi smarriti, col filo ammannito gi&agrave; dal Falloppio, era stato, verso la pr&igrave;ma <lb/>met&agrave; del secolo XVII, specialmente da'Nostri cos&igrave; diligentemente esplorato, <lb/>che poco pi&ugrave; rimaneva a saper di lui quanto alla figura o agli andamenti <lb/>delle vie scolpite nell'Osso petroso. </s>

<s>Una cos&igrave; fatta esplorazione per&ograve; non era <lb/>completa, sfuggendo anche ai pi&ugrave; attenti osservatori certe parti essenzialis&shy;<lb/>sime dell'organo auditivo, le quali o per esser molli s'erano staccate dagli <lb/>ossi duri, o per esser liquide erano col tempo esalate, o le avevano avida&shy;<lb/>mente imbevute, nel riseccarsi, le spugnose pareti. </s>

<s>Un esempio notabilissimo <lb/>di ci&ograve; ce l'offire il muscolo della Staffa, il quale fu soggetto di tante contra&shy;<lb/>dizioni, perch&egrave; chi lo negava non aveva ancora osservata la struttura del&shy;<lb/>l'orecchio ne'cadaveri freschi. </s></p><p type="main">

<s>Primi a confermar l'esistenza di quel muscolo nell'uomo furono il Val&shy;<lb/>salva e il Cotunnio, i quali furono anche i primi a notomizzare l'organo <lb/>nelle orecchie recenti, da che venne a loro porta l'occasione di scoprir que-<pb xlink:href="020/01/1409.jpg" pagenum="284"/>gli umori, che trasudano dalle interne membrane, e che poi vanno a riem&shy;<lb/>pir di s&egrave; ogni pi&ugrave; riposto seno del Laberinto. </s>

<s>&ldquo; Porro huius cavitatis coro&shy;<lb/>nide, cos&igrave; termina il Valsalva la prima parte del suo trattato, scire iuvat <lb/>Labyrinthum humore quodam aqueo, et hoc copioso, intus madefactum re&shy;<lb/>periri, unde contentae membranae humescunt, de quo nulli fecere mentio&shy;<lb/>nem. </s>

<s>Humor hoc in recenti aure observatur &rdquo; (De aure hum. </s>

<s>cit., pag. </s>

<s>51). </s></p><p type="main">

<s>Passa poi il Valsalva a proporre alcune questioni intorno all'origine, e <lb/>intorno alla natura di quell'umore; questioni ch'ei lascia irresolute, perch&egrave; <lb/>dice mancargli la necessaria preparazione delle osservazioni e degli esperi&shy;<lb/>menti. </s>

<s>Furono le parole di un tant'uomo eccitamento al Cotunnio, il quale <lb/>intanto, ripensando che la scoperta era stata fatta sui cadaveri freschi, fu <lb/>sollecito di sezionare subito dopo la morte. </s>

<s>Rimuove leggermente la Staffa <lb/>dalla Finestra ovale; &ldquo; totum Vestibulum aqua plenissimum observatur &rdquo; <lb/>(De aquaeduc. </s>

<s>cit., pag. </s>

<s>38). Prende uno de'Canali semicircolari, lo rompe <lb/>di un colpo; &ldquo; lumen aqua plenissimum ostendit, quod in Cochlea discissa <lb/>manifestissimum est &rdquo; (ibid.). Maravigliato che nessun'altro avesse notato <lb/>questa cosa, intese poi che tutto dipendeva dallo stato del cadavere: fre&shy;<lb/>schissimo ha il Laberinto tutto pieno di umore, come a lui stesso era per <lb/>la prima volta occorso di osservarlo. </s>

<s>Poi, a poco a poco quell'umore esa&shy;<lb/>lando, lascia per&ograve; ancora impregnate di s&egrave; le membrane, e in tale stato sco&shy;<lb/>pr&igrave; l'orecchio il Valsalva. </s>

<s>Resta all'ultimo tutto asciutto e secco, cosicch&egrave; <lb/>all'umidit&agrave; sottentra l'aria, e in tale stato, cio&egrave; d'una cavit&agrave; tutta piena <lb/>d'aria secca, fu sempre osservato il Labirinto da tutti gli Anatomici ante&shy;<lb/>riori allo stesso Valsalva. </s></p><p type="main">

<s>Il Cotunnio perci&ograve;, nell'atto di pubblicare la sua scoperta, trepidava, <lb/>ripensando che aveva a persuadere una gente per tanti secoli rimasta ingan&shy;<lb/>nata, e nell'opinion della quale era ingerito che mezzo naturale della trasmis&shy;<lb/>sione dei suoni fosse l'aria e non l'acqua. </s>

<s>&ldquo; Hoc est primum paradoxon, <lb/>quod in medium afferre videbor, in tanta quidem Anatomicorum omnium, <lb/>quod sciam, consensione existimantium madescere quidem, non ad amussim <lb/>impleri hoc umore Labyrinthum, et aerem a Tympano venientem simul <lb/>continere &rdquo; (ibid., pag. </s>

<s>37). </s></p><p type="main">

<s>La scoperta del Valsalva, alla quale in queste parole s'accenna, aveva <lb/>predisposte le menti ad accogliere con docilit&agrave; la scoperta del Cotunnio, e <lb/>perch&egrave; i fatti, cos&igrave; nell'uomo come negli animali, erano in ogni modo pa&shy;<lb/>tenti, s'acconsent&igrave; che il nervo acustico ricevesse le impressioni, mediante <lb/>il liquido in cui trovasi immerso. </s></p><p type="main">

<s>A compiere poi le gloriose scoperte degli Italiani venne il Breschet colla <lb/>sua <emph type="italics"/>otoconia,<emph.end type="italics"/> ma chi ripensa a quel <emph type="italics"/>quid avenosi,<emph.end type="italics"/> di che disse l'Eustachio <lb/>essere permista la sostanza molle e muccosa, che s'aggira in lamina spirale <lb/>intorno alla Chiocciola, s'avvedr&agrave; avere avuti i suoi principii in Italia anco <lb/>quest'ultima scoperta straniera. </s></p><pb xlink:href="020/01/1410.jpg" pagenum="285"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>La descrizione dell'organo dell'udito ci ha mostra<gap/>o fin qui, nella sua <lb/>storia, le grandi difficolt&agrave; incontrate dagli Anatomici: eppure non dipende&shy;<lb/>vano da altro quelle difficolt&agrave;, che dall'artificiosa struttura delle parti, a bene <lb/>esaminar le quali, e a descriverle, facevano spesso difetto l'acume degli os&shy;<lb/>servatori, e l'imperfezione degli strumenti. </s>

<s>Di qui &egrave; che, col tempo e con <lb/>l'esercizio, si fecero i sopra narrati progressi dal Berengario al Cotunnio. </s>

<s><lb/>Quando poi dalla semplice e material descrizione si volle passare a inten&shy;<lb/>dere del complicatissimo organo le funzioni, e allora le difficolt&agrave; si fecero <lb/>sentir tanto maggiori, da non sperar di vincerle col tempo e con lo studio. </s>

<s><lb/>Si sapeva esser quello, cos&igrave; sottilmente notomizzato, l'organo dell'udito, ma <lb/>dove abbia la sua propria sede l'udito, e come un oggetto materiale che <lb/>agisce sopra uno strumento materiale si sublimi negli atti del senso e della <lb/>vita, questo si voleva sapere, ma ne torn&ograve; l'acuta fame dell'uomo sempre <lb/>digiuna. </s>

<s>Alla Fisiologia perci&ograve;, trovatasi cos&igrave; involta nella nuvola del mi&shy;<lb/>stero, non rimaneva altra via di progredire che quella apertale innanzi dal&shy;<lb/>l'Anatomia, ond'&egrave; che, secondo le venivano pi&ugrave; precise notizie intorno alla <lb/>composizione dell'organo, pi&ugrave; probabili, intorno alle funzioni di lui, e meno <lb/>estranee dal vero si rendevano via via le congetture. </s>

<s>Ci&ograve; &egrave; appunto dimo&shy;<lb/>strato dai fatti, che siam per narrare nel presente paragrafo di storia. </s></p><p type="main">

<s>Empedocle, che credeva tutto l'organo consistere nell'orecchio esterno, <lb/>dalla figura, nella quale materialmente gli si rappresentava la conca, disse <lb/>ch'ell'era un campanello sospeso di qua e di l&agrave; dagli ossi delle tempia. </s>

<s>Ai <lb/>tempi di Aristotile, entrati pi&ugrave; addentro, s'era osservata la membrana del <lb/>Timpano, e il Timpano stesso tutto pieno di aria, la quale perci&ograve; si fece <lb/>principale e immediato strumento della sensazione. </s>

<s>Ma quando il Berenga&shy;<lb/>rio scopr&igrave; in quella cavit&agrave; i due primi ossicini, i quali non dovevano certa&shy;<lb/>mente esser fatti per altro che per servire all'udito, incominci&ograve;, in quel primo <lb/>risorgere della scienza, il desiderio d'intender quegli usi, per i quali si ve&shy;<lb/>nivano o a correggere o ad illustrare i concetti de'Filosofi antichi. </s>

<s>&ldquo; Sunt <lb/>aliqui, scrisse lo stesso Berengario, qui volunt quod illa ossicula moveant <lb/>aerem intra stantem et pelliculam praedictam, sicut pene vel digiti movent <lb/>cordas citarae, et aerem complantatum in citara. </s>

<s>Sunt tamen aliqui alii, qui <lb/>volunt quod cordae in citara sint loco illorum ossiculorum, et quod pene <lb/>vel digiti sint loco aeris exterioris meventis ossicula, et quod isto modo cum <lb/>aere implantato fiat sonus. </s>

<s>Et dicunt aliqui alii quod pellicula praedicta non <lb/>moveatur, sed quod est ibi ut teneat cavernam ante dictam clausam, in qua <lb/>est aer implantatus &rdquo; (Commentaria cit., fol. </s>

<s>CCCCLXXVII ad t.). Cos&igrave; si&shy;<lb/>gnificava il Berengario le varie ipotesi, che avrebbero potuto fare i Filosofi, <pb xlink:href="020/01/1411.jpg" pagenum="286"/>speculando sopra la sua invenzione, e, non decidendosi n&egrave; per l'una n&egrave; per <lb/>l'altra, le proponeva come questioni a risolversi da'suoi successori. </s></p><p type="main">

<s>Se i lunghi processi per&ograve; e la continuata catena degli ossicini avevano <lb/>suggerito al Carpense l'immagine delle corde di una cetra, le loro estre&shy;<lb/>mit&agrave; e le loro congiunzioni, rappresentando pi&ugrave; scolpitamente al Vesalio gli <lb/>esempi del martello e dell'incudine, gli fecero balenare al pensiero che fosse <lb/>il suono udito prodotto piuttosto dalla percussione interna dei due stru&shy;<lb/>menti. </s>

<s>Ma la difficolt&agrave; d'intendere il modo e la ragion dell'udire, e il ri&shy;<lb/>pensar che troppo poco conoscevasi ancora della costruzione dell'organo, gli <lb/>fecero prudentemente sospendere il giudizio. </s>

<s>&ldquo; Num autem ossicula Incudis <lb/>et Malleoli officia ita fungantur, quemadmodum sane formam referunt, .... <lb/>a me haudquaquam assertum velim, quandoquidem auditus rationem non <lb/>satis ex sententia percipiam. </s>

<s>Non quod mihi animo exciderit commune illud <lb/>Medicorum ad partium temporum asylum, et aeris gyri, quos ex huius per&shy;<lb/>cussu in aurem ferri et quandam membranam ferire, vulgo nobis e lapil&shy;<lb/>lorum in aquam iactu persuademus; interim organi huius constructionis <lb/>ignari &rdquo; (De hum. </s>

<s>corp. </s>

<s>fabrica cit., pag. </s>

<s>35). </s></p><p type="main">

<s>Ma perch&egrave;, lette queste cose, incominci&ograve; il Colombo a pensare, non dee <lb/>il suono interno prodursi dal percotere del Martello sopra l'Incudine? </s>

<s>A che <lb/>altro fine avrebbe allora la Natura dato agli ossicini quella tal forma, o per&shy;<lb/>ch&egrave; gli avrebbe cos&igrave; ben disposti l'un sotto l'altro a dare e a ricevere i <lb/>colpi? </s>

<s>&ldquo; Nam cum ex aeris motu auditio fiat, ictus aeris in meatum ad haec <lb/>ossicula defertur, fitque ibi quaedam repercussio ad eum ciendum sonitum <lb/>qui sentitur. </s>

<s>Haec igitur ossicula cedente membrana moveri, atque invicem <lb/>confricari necesse est, ut cum primum os aeris ictu percussum in alterum <lb/>impingat, illudque feriat, merito malleoli, secundum vero incudis, officio pa&shy;<lb/>riter et vocabulo donatum est &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>27). </s></p><p type="main">

<s>Cos&igrave; decidevansi con troppa fretta i dubbi del Vesalio, il quale sagace&shy;<lb/>mente era entrato in sospetto contenersi dentro a quel misterioso Laberinto <lb/>organi dell'udito pi&ugrave; importanti de'due ossicini, e de'quali, ignorando l'es&shy;<lb/>sere e la natura, era impossibile che si conoscessero gli usi. </s>

<s>Il Colombo <lb/>per&ograve;, con minor considerazione e con pi&ugrave; baldanza, a che altro diceva pos&shy;<lb/>sono servire quelle molteplici aggirate cavit&agrave; che a riflettere i colpi dell'aria, <lb/>e a rendere cos&igrave; pi&ugrave; sensibile il suono? </s>

<s>&ldquo; Adest quidem processus alius <lb/>iuxta hunc ipsum in longum protuberans interiore calvariae parte, in quo <lb/>effingitur Labyrinthus, reflectendis aeris ictibus quam appositissimus &rdquo; (ibid., <lb/>pag. </s>

<s>23). </s></p><p type="main">

<s>Quando quelle cieche tenebrose cavit&agrave; entr&ograve; colla sua face il Falloppio <lb/>a illuminarle, si sarebbe creduto che l'ardito esploratore avesse pi&ugrave; da presso <lb/>assistito a que'misteri che si celebravano dalla Natura ne'gelosi penetrali, <lb/>ma par ch'egli non intendesse nulla di meglio di quel che, stando di fuori, <lb/>s'era immaginato il Colombo. </s>

<s>Vero &egrave; bene ch'egli si confidava di dire la <lb/>sua sentenza intorno al suono, e di chiaramente spiegare &ldquo; quis sit usus <lb/>istorum ossium, et fortasse verum &rdquo; (Observat. </s>

<s>anat. </s>

<s>in loco cit., pag. </s>

<s>411), <pb xlink:href="020/01/1412.jpg" pagenum="287"/>ma perch&egrave;, n&egrave; qui n&egrave; altrove mantiene le sue promesse, l'Eustachio disse <lb/>esser quelle delle solite vanitose parole del suo orgoglioso rivale, impotente, <lb/>per i suoi errori detti specialmente intorno alla costruzion della Coclea, a <lb/>penetrare i segreti della Natura. </s>

<s>E giacch&egrave; nessuno aveva ancora proposto <lb/>un ragionevole modo a spiegare l'udito, egli crede di potere insegnarlo an&shy;<lb/>che a coloro &ldquo; in quos hodie oculi coniecti sunt omnium anatomicae facul&shy;<lb/>tatis studiosorum &rdquo; (De aud. </s>

<s>org. </s>

<s>cit., pag. </s>

<s>156). </s></p><p type="main">

<s>La freccia &egrave; principalmente appuntata al Falloppio, ma viene indiretta&shy;<lb/>mente a ferire anche il Colombo, col quale tutti convenivano allora nel dire <lb/>&ldquo; aerem, qui dum sonus editur, tanquam unda fluctuat, membranam audi&shy;<lb/>torio meatu obductam pulsare; ab illa deinceps consecutione quadam illa <lb/>ossicula moveri. </s>

<s>At quid obsecro, argomenta contro le comuni dottrine l'Eu&shy;<lb/>stachio, oportebat ad hunc rudem motum obeundum sapientissimum ani&shy;<lb/>mantium Opificem tantum studium adhibere, et de horum ossiculorum figura, <lb/>articulatione ac positione esse tam sollicitum, quando aere irruente mem&shy;<lb/>brana quae tympano similis est, sine tali organorum apparatu, percuti aut <lb/>ossiculo aut aliquo solidiori corpore, nulla arte elaborato, poterat? </s>

<s>&rdquo; (ibid., <lb/>pag. </s>

<s>157). </s></p><p type="main">

<s>Non &egrave; dunque, ragionevolmente concludeva contro il Colombo e contro <lb/>i seguaci di lui esso Eustachio, prodotto il suono dal percotere del martello <lb/>sulla membrana del Timpano o sull'incudine, e non sono i tre ossicini gli <lb/>organi principali dell'udito, come parve di credere il Falloppio, il quale, se <lb/>avesse pi&ugrave; diligentemente esaminato il Laberinto, e se, specialmente della <lb/>Coclea, avesse inteso il sapientissimo magistero, non avrebbe egli col Co&shy;<lb/>lombo assegnato a quelle cavit&agrave; l'ignobile ufficio di riflettere e di moltipli&shy;<lb/>care i colpi dell'aria. </s>

<s>Non &egrave; propriamente la Coclea un canale a fondo cieco, <lb/>n&egrave; le spire, in ch'ella si avvolge, mancano, come nelle lumache terrestri, <lb/>del loro forame, &ldquo; Sed in medio, ea nimirum parte cui spirae innituntur, <lb/>a principio ad extremum usque, angusto et recto meatu est pervium, et ab <lb/>eo foramine, cui triangulum ossiculum praeest, via aperta est, quae in maio&shy;<lb/>rem huius ossis spiram desinit. </s>

<s>Etenim, si cavitas caeca esset, percussus aer <lb/>nervo occurrere nullo modo posset. </s>

<s>Sed quia, ita ut dixi res, se habet, ar&shy;<lb/>bitror ipse aerem a Tympano et ab ossiculis agitatum, eo quo exposui iti&shy;<lb/>nere, ad maiorem ossis spiram pervenire, indeque ad minorem reflecti, mox <lb/>per medium foramen rectum ad nervum ascendere &rdquo; (ibid., pag. </s>

<s>160). </s></p><p type="main">

<s>Accennando cos&igrave; l'Eustachio al pi&ugrave; intimo organo dell'udito, avente la <lb/>sede sua principale nel Laberinto, dentro il quale i tremori dell'aria entrano <lb/>a impressionare il nervo, attraverso a quella finestra, innanzi a cui sta pa&shy;<lb/>rato l'osso triangolare, ossia la Staffa; apriva il primo le vie ai progressi <lb/>della scienza. </s>

<s>Si misero per quelle vie poco dopo il Vidio e l'Ingrassia, ma <lb/>perch&egrave; i loro libri postumi videro la luce quasi un mezzo secolo da poi che <lb/>furono scritti, la buona sementa, sparsa con frettolosa mano nella Epistola <lb/>eustachiana a Francesco Alciato, rimase soffocata da que'voraci prunai ari&shy;<lb/>stotelici trapiantati nel campo della nuova scienza dal malefico magistero <pb xlink:href="020/01/1413.jpg" pagenum="288"/>dell'Acquapendente. </s>

<s>Fermo in quella sua strana opinione che sia la scienza <lb/>rimasta stagnante ne'libri di Aristotile e di Galeno, e che perci&ograve; non faccia <lb/>e non abbia bisogno di far progressi, perciocch&egrave; il Filosofo insegnava esser <lb/>l'aria materia del suono, che si diffonde ed &egrave; portato da essa &ldquo; sensorium <lb/>audiendi aeris esse fatemur &rdquo; ci&ograve; che dall'altra parte conferma Galeno in&shy;<lb/>segnando &ldquo; aereum constituendum esse auditus sensorium, quia sonos qui <lb/>vehuntur aere, ipsiusque aeris sunt affectiones, ipsum suscipere oportebat &rdquo; <lb/>(De aure auditus org. </s>

<s>cit., pag. </s>

<s>256). </s></p><p type="main">

<s>A che dunque giovarono alla scienza le scoperte del Berengario, del <lb/>Falloppio e dell'Eustachio? </s>

<s>A null'altro, risponde l'Acquapendente, che ad <lb/>illustrare le dottrine di Aristotile e di Galeno. </s>

<s>Gli ossicini essendo duri, densi <lb/>e politi sono attissimi <emph type="italics"/>ad soni receptionem et delationem,<emph.end type="italics"/> ci&ograve; che egli prova <lb/>per l'esperienza di una lunghissima trave, all'una estremit&agrave; della quale, egli <lb/>dice, se tu farai stare qualcuno, mettendoti tu dall'altra, &ldquo; tum percutias <lb/>digito partem tuam ita leniter, ut ictus vix a te percipiatur, alter vero ex <lb/>altero fine trabis collocatus; si aurem propius ei admoverit, quamvis longis&shy;<lb/>sime a te dissitus, exquisitius tamen ictus percipiet atque tu, qui aurem non <lb/>admoveris, utcumque ictui propior fueris &rdquo; (ibid., pag. </s>

<s>262). </s></p><p type="main">

<s>O di quel Laberinto, cos&igrave; dal Falloppio artificiosamente descritto, qual <lb/>si fu l'intenzione della Natura? </s>

<s>E risponde l'Acquapendente che, ne'colpi <lb/>forti e terribili, il suono troppo grand'impeto farebbe nella Miringe (cos&igrave; <lb/>egli chiama la membrana del timpano) da lacerarla, se non entrasse per <lb/>quelle cavit&agrave; a scaricarsi, e a sfogar la sua possa. </s>

<s>&ldquo; Nunc vero in haec fo&shy;<lb/>ramina, in prima cavitate exculpta, sonus suapte natura sese insinuat et in&shy;<lb/>greditur, et ita anaclasis soni, sive reverberatio aut repercussus repulsusque <lb/>et echo prohibetur &rdquo; (ibid., pag. </s>

<s>265). </s></p><p type="main">

<s>Se poi tu mi domandi, prosegue l'Acquapendente, la ragione dell'am&shy;<lb/>piezza e della lunghezza di que'laberintici canali, io ti rispondo che son per <lb/>ammettere le differenze de'suoni. </s>

<s>&ldquo; Nam amplum gravem, angustum acu&shy;<lb/>tum sonum admittit. </s>

<s>Ratio ex Arist. </s>

<s>desumitur in Problem. </s>

<s>Copiosus igitur <lb/>aer et gravis sonus amplum foramen exposcit ut ingrediatur: contra acu&shy;<lb/>tus..... Longitudo ad eam soni differentiam sese accommodat, quae per <lb/>magnum et parvum variat..... Itaque maior sonus longiores, minor brevio&shy;<lb/>res cavernulas exposcit &rdquo; (ibid.). </s></p><p type="main">

<s>L'ingegno, ch'era pur grande, di Girolamo Fabricio si perde tutto, come <lb/>si vede, nell'adattar le vecchie masserizie a un edificio nuovo, la qual no&shy;<lb/>vit&agrave; per&ograve; per lui non consiste nella sostanza, ma negli accessorii. </s>

<s>Egli &egrave; <lb/>convinto che i canali semicircolari, la Coclea e tutto il laberinto sieno le ca&shy;<lb/>vit&agrave; dell'orecchie <emph type="italics"/>antiquis cognitae<emph.end type="italics"/> (ibid.). Che fosse pur cognita a loro la <lb/>Tuba eustachiana l'Acquapendente, sull'autorit&agrave; di Aristotile e di Galeno, <lb/>non ne dubita, ma &egrave; qui, nell'assegnare gli usi di lei, dove il prurito di far <lb/>tutta la scienza tanto ringorgare indietro da confondersi col mare aristote&shy;<lb/>lico, che lo mette in impaccio. </s>

<s>Come pu&ograve; infatti conciliarsi la dottrina del&shy;<lb/>l'aria ingenita e immobile con questo, che &egrave; uno degli ufficii che l'Autore <pb xlink:href="020/01/1414.jpg" pagenum="289"/>assegna al meato <emph type="italics"/>a concha in palatum pertuso?<emph.end type="italics"/> &ldquo; Itaque praedictus mea&shy;<lb/>tus ventilationem respirationemque simul et refectionem aeri complantato <lb/>adhibet &rdquo; (ibid., pag. </s>

<s>267). Far complice Aristotile di una tal contradizione <lb/>&egrave;, a volere esser giusti, una calunnia, perch&egrave; egli veramente non seppe nulla <lb/>di quel meato. </s>

<s>Ma pur parve un s&igrave; fatto organo, dopo la scoperta dell'Eu&shy;<lb/>stachio, di tanta importanza, da far grande onore all'Idolo venerato, per cui <lb/>libero l'Acquapendente prosegul per la nuova via aperta, ostinandosi a cre&shy;<lb/>dere di camminar per la vecchia. </s></p><p type="main">

<s>Era oramai divulgata esperienza che alcuni difettosi dell'udito sentis&shy;<lb/>sero con facilit&agrave; i corpi sonori, mettendoli in comunicazione colla bocca per <lb/>mezzo di una verga rigida stretta fra'denti. </s>

<s>Il Porta raccolse anche questa <lb/>fra le maraviglie scritte nella sua Magia naturale in quattro libri, e termina <lb/>pazzamente l'articolo inserito nel cap. </s>

<s>XXV del II libro con dire, che da <lb/>quel fatto si dimostrava non sentirsi per l'udito ma per il gusto: &ldquo; dicique <lb/>poterit non auditus sensu sed gustu percipere &rdquo; (Neapoli 1558, pag. </s>

<s>99). </s></p><p type="main">

<s>Anche l'Ingrassia, ne'suoi Commentarii al trattato <emph type="italics"/>De ossibus<emph.end type="italics"/> di Ga&shy;<lb/>leno, cap. </s>

<s>I, Testo VIII, raccontava di un suo amico, bravo sonatore di ce&shy;<lb/>tra, il quale divenuto sordo si consolava di poter tornare ad udire il dolce <lb/>suono, mordendo, mentr'ei ne toccava le corde, il lungo manico dello stru&shy;<lb/>mento. </s>

<s>Ma l'Acquapendente fu il primo che, invocando gli usi della Tuba <lb/>eustachiana, spieg&ograve; questo non solo, ma anche altri fatti pi&ugrave; curiosi, come <lb/>per esempio perch&egrave;, quando un discorso ci diletta stiamo ad ascoltarlo, se&shy;<lb/>condo che proverbialmente si dice, a bocca aperta. </s>

<s>&ldquo; Quarta et ultima prae&shy;<lb/>dicti meatus utilitas est ut si forte fortuna membrana laedatur, unde audi&shy;<lb/>tus difficilior obtusiorque reddatur, per hanc viam sonus per os ingressus <lb/>ad aurium intima pertingat, atque hac ratione surdastris subveniatur. </s>

<s>Nam <lb/>et illi, ut exquisitius audiant, hiante ore, voces et sonos excipere consueve&shy;<lb/>runt. </s>

<s>Neque modo surdastri sed alii quoque, cum quidpiam obscure audiunt, <lb/>ore adaperto melius percipere videntur. </s>

<s>Idem quoque testantur musica in&shy;<lb/>strumenta, quae, si utraque aure diligenter obturata, baculo quem dentibus <lb/>apprehenderis contingas, exquisitius pulsari audies. </s>

<s>Sic et qui in via, noctu <lb/>potissimum, alicuius procul advenientis strepitum captant, si baculi aut ensis <lb/>alterum extremum terrae affigant, alterum vero dentibus apprehendant, e <lb/>longinquo magis audiunt, idque potissimum contingit, quando via duris saxis <lb/>operta est &rdquo; (ibid., pag. </s>

<s>267). </s></p><p type="main">

<s>I Fisiologi approvarono poi tutti unanimi questi usi della Tuba eusta&shy;<lb/>chiana, non avvertiti dal suo proprio inventore, il quale riconobbe il nuovo <lb/>organo utile solamente &ldquo; ad rectum medicamentorum usum &rdquo; (De aud. </s>

<s>org. </s>

<s><lb/>cit., pag. </s>

<s>163). Lo spirito dell'Eustachio forse avrebbe, del benefizio, sen&shy;<lb/>tito riconoscenza verso l'Acquapendente, se ne fosse stato da lui riconosciuto <lb/>per inventore. </s>

<s>Ma non fu questo il legame che ricongiunse i due ingegni, <lb/>cos&igrave; opposti nelle opinioni: fu il trovarsi consorti nella scoperta de'musco&shy;<lb/>lini auditivi interni. </s>

<s>L'Autore dell'epistola all'Alciato si condusse da una <lb/>tale scoperta ad emettere una sua idea, che nella novit&agrave; aveva qualche cosa <pb xlink:href="020/01/1415.jpg" pagenum="290"/>dello strano. </s>

<s>&ldquo; Cum instituisset Natura, egli scrive, auditus organa arbitrio <lb/>voluntatis moveri, articulationem quoque ac musculum, sine quibus fieri is <lb/>motus nequit, tribuere illis voluit &rdquo; (ibid., pag. </s>

<s>157, 58). N&egrave; si spiega pi&ugrave; <lb/>da vantaggio, ma l'Acquapendente, ripigliando il costrutto eustachiano ri&shy;<lb/>masto interrotto, lo concludeva in questo argomento: &ldquo; Quod s&igrave; motus est <lb/>a musculo et per dearticulationem factus, dubio procul voluntarius est &rdquo; (De <lb/>aure cit., pag. </s>

<s>251). </s></p><p type="main">

<s>A togliere la maraviglia dalla mente di coloro, che reluttassero ad am&shy;<lb/>mettere una sentenza tanto nuova, l'Acquapendente ricorre a certi esempii, <lb/>ch'egli stesso confessa esser di difficile persuasione, perch&egrave; si tratta di fe&shy;<lb/>nomeni subiettivi. </s>

<s>Pur fatta in s&egrave; medesimo esperienza di poter a volont&agrave; <lb/>suscitar nell'orecchio uno strepito, e fermo in credere e in insegnare che <lb/>l'udito &egrave; arbitrario. </s>

<s>&ldquo; Hic igitur motus ille est arbitrarius quem in auribus <lb/>meis percipio, et alteri ostendere aut docere aliter non possum, quia intus <lb/>in auribus fit et exiguus, sed tamen evidens est motus, et sicuti in constrin&shy;<lb/>genda manu decipi non possum, sic neque in hoc decipior. </s>

<s>Hoc dico prop&shy;<lb/>terea quod aliqui sunt, qui cum observare in seipsis non possint praedictum <lb/>motum, illum negare audent, sed tamen multos semper in publicis theatris <lb/>reperi, qui illum exploraverint et confessi sunt &rdquo; (ibid.). </s></p><p type="main">

<s>Bench&egrave; il trattato dell'Acquapendente, in cui si professano cos&igrave; fatte <lb/>dottrine, vedesse la luce nel medesimo anno di quello del Casserio, &egrave; certo <lb/>nulladimeno che all'uno autore debbono essere state note le idee dell'altro, <lb/>o le avesse attinte nella scuola o ne'familiari colloqui, o gli fosse dato di <lb/>leggerle nel manoscritto. </s>

<s>&Egrave; in ogni modo un fatto che il Piacentino confuta <lb/>alcune teorie fisiologiche esposte nel libro <emph type="italics"/>De aure<emph.end type="italics"/> del suo Maestro, di cui, <lb/>perch&egrave; non profferisce il nome, crediamo che ci&ograve; si faccia da lui per rive&shy;<lb/>renza, vedendolo spesso passare dalle confutazioni ai commenti. </s></p><p type="main">

<s>Confuta l'idea che il sensorio consista nell'aria ingenita, perch&egrave;, do&shy;<lb/>vend'essere organo della sensazione un corpo vivente, &ldquo; vivere ipsum aerem <lb/>dici non potest &rdquo; (De auris aud. </s>

<s>org. </s>

<s>Historia anat. </s>

<s>cit., pag. </s>

<s>82), ma poi <lb/>egli ammette, con Aristotile e con l'Acquapendente, l'aere ingenito, e con&shy;<lb/>sente ch'egli sia libero e quieto, come quello che &ldquo; ad soni extrinsecus in&shy;<lb/>trantis receptionem aptissimum est, at e contra inquietum a motu aliquo <lb/>agitatum ineptissimum ratio dictitat, et quotidiana experientia comprobat &rdquo; <lb/>(ibid., pag. </s>

<s>121). L'ufficio per&ograve; di un tal aere ingenito interno &egrave;, secondo <lb/>il Casserio, quello di rispondere all'unisono coll'esterno, che fa vibrare la <lb/>membrana del Timpano &ldquo; atque consimilem soni speciem in actum indu&shy;<lb/>cit &rdquo; (ibid., pag. </s>

<s>85). </s></p><p type="main">

<s>Contradice inoltre esso Casserio al Maestro intorno all'uso degli ossicini, <lb/>pensando che non sieno ordinati a condurre i suoni, ma &ldquo; ad stabiliendum <lb/>et defendendum Tympanum, ne, dum aer internus aut externus vehemen&shy;<lb/>tius in illud irruat, divellatur &rdquo; (ibid., pag. </s>

<s>118), per&ograve; consente nell'ammet&shy;<lb/>tere che i muscolini governino a volont&agrave; del senziente i moti del Martello. <lb/></s>

<s>&ldquo; Porro fuit illud munus cohibendi motum Mallei musculis et voluntariis <pb xlink:href="020/01/1416.jpg" pagenum="291"/>instrumentis commissum, ut sicuti variae sunt aeris ad membranas impul&shy;<lb/>siones, sic cohibitio ac distantia motus Mallei varia fieret. </s>

<s>Ad hanc sane <lb/>functionem non ligamenta, eodem semper tenore agentia, sed musculi vo&shy;<lb/>luntarii motus organa et qui cum quadam analogia et mensura operantur, <lb/>et plus minusve, prout opus est, contrahendo sese et laxando, aeris variis <lb/>impulsionibus, quarum quidem varietas in maioris minorisve ratione con&shy;<lb/>sistit, vario motu resistere poterant &rdquo; (ibid., pag. </s>

<s>120). </s></p><p type="main">

<s>S'&egrave; d unque al Casserio, come all'Acquapendente, appiccato in far l'udito <lb/>arbitrario il contagio dell'Eustachio, con cui, ambedue insieme rivaleggiando, <lb/>si compiacciono d'essere stati, nell'invenzione de'muscoli auditivi interni, <lb/>fortunati consorti. </s>

<s>Ma da questo contatto in poi, i due Anatomici pi&ugrave; recenti <lb/>si dilungano troppo dal Sanseveritano, nelle idee del quale contenevansi <lb/>come avvertimmo principii pi&ugrave; sani e pi&ugrave; fecondi. </s></p><p type="main">

<s>Nal 1604 comparvero i Commentarii a Galeno dell'Ingrassia. </s>

<s>Egli &egrave; ve&shy;<lb/>ramente il primo che, sebben non sia amico all'Eustachio, sente quanto le <lb/>dottrine di lui sieno pi&ugrave; conformi al vero delle puerilit&agrave; del Colombo. </s>

<s>Ma <lb/>l'Autore <emph type="italics"/>De auditus organis,<emph.end type="italics"/> insegnando che i tremori armonici entrano <lb/>nel Labirinto per la Finestra ovale, non diceva a che fine fosse aperta nella <lb/>volta del vestibolo la Finestra rotonda. </s>

<s>Or perch&egrave; non &egrave; credibile che la Na&shy;<lb/>tura la lasciasse ivi oziosa, si dette l'Ingrassia a specularne gli usi, da che <lb/>fu condotto a immaginare che l'aria compressa dal pi&egrave; della Staffa, dopo <lb/>aver risonato in quelle cavit&agrave; senza fondo, echeggi sulle soglie della stessa <lb/>Finestra rotonda, dalla quale ritorni nella cassa del Timpano, d'ond'era par&shy;<lb/>tita. </s>

<s>&ldquo; Stapha sic deorsum compressa, sua quidem basi sub se contentum a <lb/>naturaque insitum in Labyrintho aerem alium comprimit, percutitque, qui <lb/>sic denique commotus verberatusque, per cavernulas, anfractus ac gyros <lb/>secundae et tertiae cavitatis decurrens, ad quos auditorius quinti paris ner&shy;<lb/>vus terminatur, in membranulas quasdam dissolutus extenuatusque illos <lb/>obliniens, ibique tintinnans, quamdam veluti echo facit per aliam fenestram, <lb/>in eamdem primam cavitatem resiliens &rdquo; (De ossibus, commentaria in Ga&shy;<lb/>lenum, Panormi 1604, pag. </s>

<s>45). </s></p><p type="main">

<s>Quest'uso, prosegue a dire l'Ingrassia, assegnato alla seconda Finestra, <lb/>ossia alla Rotonda, &egrave; importante, perch&egrave;, se l'aria condensata non potesse <lb/>tornare indietro, non diverrebbe atta a risonare, &ldquo; membranulasque illas <lb/>intercipientes cavernulisque illitas frangeret &rdquo; (ibid.). La teorica per&ograve; era <lb/>fondata sull'ipotesi che la Finestra rotonda, come l'avea descritta il Fallop&shy;<lb/>pio, rimanesse aperta: ma il Vidio che trov&ograve; sopra lei teso il periostio del <lb/>Timpano, ebbe a svolgere in altri termini i concetti dell'Eustachio. </s>

<s>Disse <lb/>che i tremori del suono si propagano dal Timpano nel Labirinto attraverso <lb/>alle membrane che chiudono le due finestre, come la comune esperienza ci <lb/>dimostra che si propagano attraverso alle chiuse pareti da una stanza all'al&shy;<lb/>tra. </s>

<s>Sebben egli confessi esser difficilissimo a noi l'intendere il meccanismo <lb/>dell'udito, &ldquo; illud tamen in aperto est quod, ubi agitatur Membrana, agita&shy;<lb/>tur etiam Malleus, per manubriolum Membranae illigatum, et propterea In-<pb xlink:href="020/01/1417.jpg" pagenum="292"/>cus et Stapes, et ita aperitur ovatum foramen, adeo ut sonus, per hoc et <lb/>per alterum rotundum, penetrare ad alios sinus possit obductos membranula <lb/>ex nervulo quinti paris dilatato, ubi domicilium est facultatis audiendi ce&shy;<lb/>rebro transmissae &rdquo; (De anatome corp. </s>

<s>humani, Venetiis 1611, pag. </s>

<s>323). </s></p><p type="main">

<s>Scritte queste cose, certamente prima del 1567, anno in cui il Vidio <lb/>mor&igrave;, quando comparvero in Venezia alla luce, le dottrine dell'Acquapen&shy;<lb/>dente da undici anni tenevano soggiogati alla loro autorit&agrave; la maggior parte <lb/>dei dotti, resi oramai indocili ad attemperare l'ingegno a pi&ugrave; razionali prin&shy;<lb/>cipii. </s>

<s>I magisteri del Casserio dall'altra parte si rimanevano inefficaci, s&igrave; <lb/>perch&egrave; le sue confutazioni si notavano d'ingratitudine verso il venerabile <lb/>Maestro e l'insigne benefattore; s&igrave; perch&egrave; non seppe mettere in evidenza <lb/>l'azion dell'aria risonante sul nervo, ignorati e negletti gli ufficii principa&shy;<lb/>lissimi del Laberinto. </s>

<s>L'Ingrassia e il Vidio poi, quasi dopo un mezzo secolo, <lb/>tornavano a parlar dalla tomba a gente, che non era ad essi legata n&egrave; coi <lb/>vincoli dell'affetto, n&egrave; con quelli della memoria, per cui non fa maraviglia <lb/>se i pi&ugrave; celebri Anatomici fioriti nella prima met&agrave; del secolo XVII costituis&shy;<lb/>sero sensorio dell'udito l'aria ingenita, con fanciullesco inganno inghiot&shy;<lb/>tendo l'errore aristotelico confettato dall'esperte mani dell'Acquapendente. </s></p><p type="main">

<s>Altri &egrave; vero professarono, come per esempio il Deusing, che proprio <lb/>organo dell'udito &ldquo; non est Tympanum, nec aer insitus, nec ossiculorum <lb/>aliqua compages, sed ipse nervus auditorius &rdquo; (Exercitatio De sensuum func&shy;<lb/>tionibus, Croningae 1661, pag. </s>

<s>273), ma non ci voleva altro che l'autorit&agrave; <lb/>del Cartesio, alla scuola del quale furono addetti tutti costoro, a preva&shy;<lb/>lere, bench&egrave; per piccoli momenti, sopra quella di Girolamo Fabricio. </s>

<s>Nella <lb/>IV Parte dei <emph type="italics"/>Principia Philosophiae,<emph.end type="italics"/> l&agrave; dove l'Autore tratta dei sensi e dei <lb/>nervi deputati alle loro particolari funzioni, &ldquo; Duo alii nervi, egli dice, in <lb/>intimis aurium cavernis reconditi excipiunt tremulos et vibratos totius aeris <lb/>circumiacentis motus. </s>

<s>Aer enim membranulam Tympani concutiens sub&shy;<lb/>iunctam trium ossiculorum catenulam, cui isti nervi adhaerent, simul quatit, <lb/>atque ab horum motuum diversitate diversorum sonorum sensus oriuntur &rdquo; <lb/>(Amstelodami 1650, pag. </s>

<s>293). </s></p><p type="main">

<s>La Scuola cartesiana fu dunque da questa parte benemerita della Fisio&shy;<lb/>logia, ma se pot&egrave; ridursi ne'retti sentieri, per que'vizii ingeniti a lei, che <lb/>hanno la loro radice nell'orgoglioso ripudio delle tradizioni, rimase debole <lb/>in dare alla scienza per progredire gl'impulsi. </s>

<s>Primo, dopo la met&agrave; del se&shy;<lb/>colo XVII, a risalire alle tradizioni eustachiane, fu Antonio Molinetti, il quale <lb/>riconosceva nell'orecchio quell'eccellenza di squisito natural magistero, che <lb/>tutti ammiravano nell'occhio. </s>

<s>Rassomigliava perci&ograve; la finestra ovale alla pu&shy;<lb/>pilla, il cristallino, dove la luce si refrange, ai Canali semicircolari, dove il <lb/>suono si riflette, e il nervo espanso sul fondo della Coclea alla Retina espansa <lb/>sul fondo del globo oculare. </s>

<s>&ldquo; Cochlea primum suscipit perque cochleares, <lb/>idest spirales suos ambitus multum diffundi cogit, non sine roboris incre&shy;<lb/>mento atque impulsus, demum in tunicam perducit simillimam Retinae, pro&shy;<lb/>ductam ab expansa substantia molli nervi auditorii, osseos parietes ipsius <pb xlink:href="020/01/1418.jpg" pagenum="293"/>obliniente, non aliter ac Retina extimam Vitrei superficiem. </s>

<s>Quis autem du&shy;<lb/>bitet quin durities illa plusquam ossea parietum et canaliculorum Cochleae <lb/>mirum in modum conducat ad determinandum sonum, non secus atque ni&shy;<lb/>ger choroidis color ad sistendum progressum luminis illudque terminandum <lb/>in Retina? </s>

<s>Ea igitur percussa soni sensus excitatur qui antea non erat, nec <lb/>quicquam omnino, praeter aerem agitatum ab externo movente. </s>

<s>Fit autem <lb/>hoc communicatis vibrationibus, quibus substantia nervi afficitur, et cum <lb/>illa spiritus per ipsam diffusus cerebro spiritibusque successive continuis, <lb/>usque in principium nervi &rdquo; (Dissert. </s>

<s>anat. </s>

<s>cit., pag. </s>

<s>44). </s></p><p type="main">

<s>E perch&egrave;, rinnovellando cos&igrave; di nuove fronde il gentile arbusto pian&shy;<lb/>tato nel campo della scienza dall'Eustachio, fosse meglio difeso dal soffiar <lb/>di quel vento, che lo poteva inaridire, il Molinetti risolve la questione del&shy;<lb/>l'udito arbitrario, liberando anche da questa parte la scienza dagl'impacci <lb/>frapposti ai liberi passi di lei dall'Acquapendente. </s>

<s>&ldquo; Neque hic oportet im&shy;<lb/>peria voluntatis quaerere, cuius instrumenta musculi esse perhibentur, eadem <lb/>enim necessitas, quae ciliaria dicta ligamenta in oculo producit ut corripian&shy;<lb/>tur vel laxentur, quo luminis exuberantiae excludantur, aut eiusdem de&shy;<lb/>fectui occurratur; eadem musculum auris suscitat, ad motus varios obeun&shy;<lb/>dos, pro appulsibus soni diversis ad membranam Tympani &rdquo; (ibid., pag. </s>

<s>50). </s></p><p type="main">

<s>Le grandi scoperte delle vene lattee, del circolo del sangue, del Canale <lb/>toracico e de'vasi linfatici troppo avevano agitata e commossa la scienza, da <lb/>farla superare quegli argini, dentro i quali la voleva ritenere stagnante Colui, <lb/>che insignito di una duplice autorit&agrave;, scientifica e morale, era dal grande <lb/>Harvey salutato col nome di <emph type="italics"/>Venerabile vecchio.<emph.end type="italics"/> Ma bench&egrave; fosse il magi&shy;<lb/>stero del Molinetti secondato dall'influsso dei tempi, egli ha pure il merito <lb/>di aver ritirata la fisiologia dell'udito ai suoi veri principii. </s></p><p type="main">

<s>Ai quali principii ritornando Guntero Cristoforo Schelhammer badava a <lb/>ripensare fra s&egrave; in che maniera l'Eustachio, non facendo nessun conto della <lb/>Finestra rotonda, ch'ei certamente dovea col Falloppio credere affatto aperta, <lb/>dicesse che i tremori armonici passano nel Labirinto attraverso alla Fine&shy;<lb/>stra ovale &ldquo; cui triangulum ossiculum praeest. </s>

<s>&rdquo; Potrebbe quella parola <lb/><emph type="italics"/>praeest<emph.end type="italics"/> dar luogo a interpetrare che il pi&egrave; della Staffa stia innanzi al suo <lb/>forame, senza chiuderlo esattamente, ma forse non fu questa l'intenzione <lb/>dell'Autore. </s>

<s>Nelle <emph type="italics"/>Osservazioni<emph.end type="italics"/> falloppiane (in loco cit., pag. </s>

<s>410) erasi gi&agrave; <lb/>divulgata l'esperienza che, traforando la membrana del Timpano colla punta <lb/>di un ago, e toccando il capolino del Martello, il moto si propagava alla <lb/>Staffa, cosicch&egrave;, facendo vibrare la mano armata di quella punta, si sentiva <lb/>a quel tenore vibrare essa Staffa. </s>

<s>Di qui era facilissimo immaginare che, <lb/>operando simili effetti le onde sonore, facessero aprire e chiudere la Fine&shy;<lb/>stra ovale con tal moto oscillatorio, molto opportuno a diffonder non solo, <lb/>ma a produrre le risonanze. </s></p><p type="main">

<s>Questa dall'altra parte era l'interpetrazione, che de'sensi eustachiani <lb/>avea data il Vidio, le teorie e le scoperte del quale, o ignorate o ripudiate <lb/>dallo Schelhammer, lo fecero andare in quella falsa opinione che la Fine-<pb xlink:href="020/01/1419.jpg" pagenum="294"/>stra ovale rimanesse chiusa sempre dalla Staffa, e la Rotonda invece sem&shy;<lb/>pre aperta, n&egrave; perci&ograve; velata da nessuna membrana. </s>

<s>Di qui ne scendeva che <lb/>la via dei suoni per entrare nel Labirinto fosse necessariamente questa, e <lb/>non quella. </s>

<s>Nel venir per&ograve; a una tal conclusione ebbe facilmente a com&shy;<lb/>prendere che l'Eustachio non fece per l'ammissione del suono nessun conto <lb/>della Finestra rotonda, perch'ella si rimane in disparte dalla membrana del <lb/>Timpano, d'onde giungono i tremori esterni, mentre la Finestra ovale torna <lb/>a quella stessa membrana in diritto. </s>

<s>Ma pur, sempre fermo in quella sua <lb/>opinione della struttura delle due Finestre, pens&ograve; lo Schelhammer a togliere <lb/>le difficolt&agrave; ricorrendo alle riflessini de'suoni. </s></p><p type="main">

<s>Gli Assiomi <emph type="italics"/>De sono,<emph.end type="italics"/> posti nel II cap. </s>

<s>della I Parte <emph type="italics"/>De auditu,<emph.end type="italics"/> non <lb/>son tutti ammissibili come certi, e i Teoremi perci&ograve; non rimangono con <lb/>certezza dimostrati, tanto pi&ugrave; che bene spesso alla scienza si sostituisce l'au&shy;<lb/>torit&agrave; del Kircher o di altri cos&igrave; fatti. </s>

<s>Ma pure egli &egrave; benemerito, lo Schel&shy;<lb/>hammer, per aver primo tentate queste nuove vie di fisica matematica, ap&shy;<lb/>plicando l'Acustica alla Fisiologia dell'udito. </s>

<s>Volendo aver di queste appli&shy;<lb/>cazioni qualche esempio, nel Teorema ultimo che &egrave; il XXIII si propone <lb/>l'Autore di dimostrare: &ldquo; Sonus in cochleis maximas vires obtinet &rdquo; (editio <lb/>cit., pag. </s>

<s>157), e nel cap. </s>

<s>V della Parte II ne fa, cos&igrave; dicendo, l'applica&shy;<lb/>zione al moltiplicarsi per naturale artificio il suono nella Chiocciola dell'orec&shy;<lb/>chio: &ldquo; Hic igitur incomparabile prorsus et stupendum Naturae artificium <lb/>depraedicandum venit. </s>

<s>Comprehendit enim in parvo spatio quicquid ad so&shy;<lb/>num et multiplicandum in immensum et sistendum unquam poterat exco&shy;<lb/>gitari. </s>

<s>Quantum enim valeat ad sonum in infinitum multiplicandum tubus <lb/>cochleatus disci potest ex ultimo theorematum, quod ex Athanasio Kirchero <lb/>excripsimus &rdquo; (ibid., pag. </s>

<s>237). </s></p><p type="main">

<s>Cos&igrave; fatti moltiplicati riflessi si fanno, secondo lo Schelhammer, nella <lb/>Coclea dai raggi sonori, similmente riflessi dalla cassa del Timpano nella Fi&shy;<lb/>nestra rotonda, a quest'uso principalmente creduta dallo stesso Schelham&shy;<lb/>mer aperta. </s>

<s>Debbono senza dubbio avere avuto qualche efficacia, sopra que&shy;<lb/>sta opinione del Fisiologo tedesco, le parole, nelle quali il nostro Molinetti <lb/>diceva comunicar liberamente l'aria del labirinto colla timpanica &ldquo; per fo&shy;<lb/>ramen rotundum, hoc nomine puto praecipue apertum &rdquo; (Dissert. </s>

<s>anat. </s>

<s>cit., <lb/>pag. </s>

<s>53). Ma perch&egrave; il Vidio e il Casserio avevano oramai da lungo tempo <lb/>dimostrato che quel forame &egrave; chiuso dal periostio, che riveste le due pi&ugrave; <lb/>intime cavit&agrave; auricolari, cadevano le teorie infrante dalla forza dei fatti, e <lb/>dall'altra parte escludere dall'ufficio d'intromettere i suoni la Finestra ovale, <lb/>come intendeva lo Schelhammer, pareva men ragionevole ch'escludere la <lb/>Finestra rotonda, com'avea fatto l'Eustachio, perch&egrave; altrimenti a qual fine <lb/>congegnar cos&igrave; sapientemente la Natura la catena dei tre ossicini? </s></p><p type="main">

<s>Persuasi perci&ograve; i Fisiologi che dovessero i due forami essere ugual&shy;<lb/>mente utili, si volsero a speculare di quella utilit&agrave; le ragioni. </s>

<s>Nel 1683 com&shy;<lb/>pariva in Parigi un libretto in 12&deg; di Giuseppe Duverney intitolato <emph type="italics"/>Trait&eacute; <lb/>de l'organe de l'oui&edot;,<emph.end type="italics"/> e perch&egrave; vi si trattava di cose non comuni, il Man-<pb xlink:href="020/01/1420.jpg" pagenum="295"/>get lo raccolse, tradotto in latino, nella sua Biblioteca anatomica da cui noi <lb/>lo citiamo. </s></p><p type="main">

<s>Che le speculazioni del Francese, come quelle del Tedesco sopra com&shy;<lb/>memorato, avessero impulso da quelle del nostro Anatomico veneziano a noi <lb/>par credibile, imperocch&egrave;, dop'aver detto il Molinetti che i suoni si molti&shy;<lb/>plicano nel Labirinto, soggiunge che nella Coclea &ldquo; quo magis aer in spiris <lb/>minoribus coarctatur, in nervum mollem impingitur oblinientem ultimam <lb/>partem Cochleae, quem vibrationibus similibus etiam movet &rdquo; (ibid., pag. </s>

<s>54). </s></p><p type="main">

<s>Anche il Duverney dunque ammette che la sede dell'udito sia nel La&shy;<lb/>birinto, e segnatamente nel nervo espanso, dentro la Coclea stessa, in quella <lb/>che, scoperta gi&agrave; dall'Eustachio, si chiam&ograve; <emph type="italics"/>Lamina spirale.<emph.end type="italics"/> Rimaneva per&ograve; <lb/>ancora a decidere per quali porte s'intromettessero i suoni, e perch&egrave; la ra&shy;<lb/>gion suggeriva che ci&ograve; si dovesse fare in amichevole societ&agrave; dai due forami, <lb/>il Duverney fu il primo a specularne i modi. </s>

<s>La lamina spirale divide tutto <lb/>il dulto cocleare in due scale, che si appoggiano allo stesso modiolo, di modo <lb/>che la superiore non comunica colla inferiore. </s>

<s>La finestra rotonda si apre <lb/>in questa, e l'Ovale in quella, e i tremori armonici passano ugualmente bene <lb/>comunicati alle membrane chiudenti l'una e l'altra di quelle stesse Fine&shy;<lb/>stre, &ldquo; atque ita spiralis laminae, cum ipsa utrinque verberetur, tremuli mo&shy;<lb/>tus vividiores et fortiores esse debent &rdquo; (In Biblioth. </s>

<s>anat. </s>

<s>cit., T. II, Ge&shy;<lb/>nevae 1685, pag. </s>

<s>436). </s></p><p type="main">

<s>Cos&igrave; il Fisiologo parigino, dop'avere svolte le idee del Molinetti, esplicava <lb/>i sensi del Vidio, e proseguendo nelle sue speculazioni passava ad illustrar <lb/>l'ipotesi dell'Acquapendente intorno all'uso de'canali pi&ugrave; o meno lunghi, e <lb/>pi&ugrave; o meno larghi in modulare i tuoni, rassomigliando anch'egli l'organo <lb/>dell'udito a quelle trombe, co'loro tubi avvolti in spira fra'musicali stru&shy;<lb/>menti. </s>

<s>Anzi, perch&egrave; quella variet&agrave; di armonie dev'essere immediatamente <lb/>sentita dal sensorio primario, ei crede che la stessa Lamina spirale, vibrando <lb/>ora nella parte pi&ugrave; stretta ora nella pi&ugrave; larga, sia a questo principale effetto <lb/>disposta di rappresentare i tuoni gravi e gli acuti. </s>

<s>&ldquo; Lamina haec aeris mo&shy;<lb/>tus tremulos recipere non tantum apta est, sed ipsius structura eam omni&shy;<lb/>bus eorumdem motuum differentibus caracteribus respondere posse argu&shy;<lb/>mento esse debet. </s>

<s>Cum enim in primae suae revolutionis principio quam in <lb/>ultimae extremo, ubi veluti in cuspidem desinit, latior est, cum aliae itidem <lb/>ipsius partes quoad latitudinem proportionaliter minuantur; dicere possumus <lb/>partes latiores, quandoquidem immotis reliquis, commoveri possunt tremulis <lb/>motibus, seu vibrationibus lentioribus, quae sonis proinde gravibus respon&shy;<lb/>deant aptas duntaxat esse, et e contra, ubi angustiores ipsius partes verbe&shy;<lb/>rantur, earum vibrationes celeriores esse, et sonis acutis ideo respondere &rdquo; <lb/>(ibid., pag. </s>

<s>437). </s></p><p type="main">

<s>Le dottrine del Duverney raccolte dai varii Autori italiani, via via nel <lb/>nostro discorso commemorati, e in bell'ordine esposte, apparvero e furono <lb/>ricevute come nuove, plaudendo i dotti all'Autore. </s>

<s>Anche il Valsalva si vide <lb/>a quella luce cos&igrave; condensata e riflessa rischiarare le vie, ma desideroso di <pb xlink:href="020/01/1421.jpg" pagenum="296"/>andar da s&egrave; in cerca della perfezione, costitu&igrave; primario sensorio, insiem colla <lb/>Lamina spirale, le zone contenute ne'Canali semicircolari &ldquo; unde, cum ipsae <lb/>quidem nil aliud sint quam mollis auditorii nervi expansiones, sensatio exci&shy;<lb/>tatur &rdquo; (De aure hum. </s>

<s>cit., pag, 79). </s></p><p type="main">

<s>Ma perch&egrave; la Natura, sentiva domandarsi, commise l'ufficio a tre, piut&shy;<lb/>tosto che a una zona sola? </s>

<s>Per rispondere alla qual domanda l'Autore in&shy;<lb/>voca il fatto notissimo del mettersi spontanea a risonare una corda non <lb/>tocca, e tesa all'unisono di un altro strumento. </s>

<s>&ldquo; Haec cum ita sint, poi <lb/>soggiunge, iam aliquem suspicari posse: cum tam varii soni a nobis audiri <lb/>et distincte percipi debuerint, per impressiones quidem ab illis in membra&shy;<lb/>nulam demum factas, ut eorum perceptio vividior esset curasse Naturam ut <lb/>singuli non utcumque membranulam attingerent, sed quam possent maio&shy;<lb/>rem impressionem in eamdem facerent. </s>

<s>At sicuti varii toni non possunt <lb/>omnes facere maiorem impressionem in unam aut unius conditionis chor&shy;<lb/>dam, sed singuli variae conditionis chordas exposcunt; ita neque varios so&shy;<lb/>norum tonos in unam simplicemve membranulam potuisse requisitam maio&shy;<lb/>rem impressionem facere. </s>

<s>Ideo non unum canalem unamque membranulam <lb/>sive zonam, sed plures canales, et plures zonas Naturam posuisse, et istas <lb/>quidem variae conditionis, saltem quo ad longitudinem attinet, nam maior <lb/>una, minor altera, tertia vero minima est &rdquo; (ibid., pag. </s>

<s>79, 80). </s></p><p type="main">

<s>Si pu&ograve; anche questo tenere per un bello e ingegnoso commento alle <lb/>dottrine di Girolamo Fabricio, ma il desiderio di tentar cose nuove condusse <lb/>il Valsalva a un esito non troppo felice quando, dal Duverney che avea, ri&shy;<lb/>spetto agli usi delle due Finestre seguito il Vidio, si dilung&ograve; per rinnovel&shy;<lb/>lare l'opinion dell'Eustachio. </s></p><p type="main">

<s>I suoni dunque secondo l'Autore, non si comunicano dal meato udito&shy;<lb/>rio esterno al Labirinto, acusticamente ne'tremori attraverso alla cavit&agrave; del <lb/>Timpano, ma giunti ivi alle soglie operano meccanicamente sopra la mem&shy;<lb/>brana, e il moto meccanico si propaga attraverso alla catena degli ossicini <lb/>infino alla Staffa, la quale, comprimendo l'aria contenuta nel Labirinto, la <lb/>mette in moto di risonanza. </s>

<s>S'indusse il Valsalva, contro le pi&ugrave; comuni opi&shy;<lb/>nioni, a creder cos&igrave;, per gl'impedimenti che troverebbero le onde sonore in <lb/>propagarsi per la cavit&agrave; del Timpano imperturbate; &ldquo; scilicet, non solum <lb/>membrana ipsius Tympani, sed hinc stapes ovalem fenestram obturans, illinc <lb/>membrana Fenestram rotundam claudens, nec non situs eiusdem Fenestrae, <lb/>advenientibus sonoris motibus, non adversae, sed lateralis &rdquo; (ibid., pag. </s>

<s>60). </s></p><p type="main">

<s>Persuaso cos&igrave; che i moti aerei apportatori dei suoni operino meccani&shy;<lb/>camente sopra la Staffa, il Valsalva, che par non conoscesse le propriet&agrave; <lb/>elastiche dei fluidi aeriformi, disse non potere alla stessa Staffa ceder l'aria <lb/>il suo luogo, se non a patto o di trovar da ricoverarsi altrove, o di aver <lb/>qualche sfogo. </s>

<s>Questo secondo caso per&ograve; non &egrave; possibile, perch&egrave; ammette <lb/>col Duverney anche il Nostro, che la Scala inferiore, ossia del Timpano, non <lb/>abbia alcuna comunicazione colla Scala superiore, ossia del Vestibolo; ond'&egrave; <lb/>che l'aria contenuta in questa dee necessariamente trovare altro luogo, n&egrave; <pb xlink:href="020/01/1422.jpg" pagenum="297"/>s'intende come potesse trovarlo altrove che nella cuna della Lamina spirale, <lb/>o della Zona incurvata per la pressione. </s>

<s>Ne &egrave; da temer che oppongasi a <lb/>questa incurvatura, soggiunge l'Autore, la resistenza dell'aria, di che &egrave; piena <lb/>quell'altra Scala, la quale aria trova da rifarsi dello spazio perduto, pre&shy;<lb/>mendo e facendo cos&igrave; rigonfiare verso la cavit&agrave; del Timpano la sottile e fles&shy;<lb/>sibile membrana, che chiude la Finestra rotonda. </s>

<s>&ldquo; Aer enim Scalae Vesti&shy;<lb/>buli propulso non obstat, cum ipse propellere illum possit, qui in Tympani <lb/>Scala continetur, non quidem per poros aut certam aliquam communicatio&shy;<lb/>nem, ut quidam suspicari visus est, sed per ipsius tenuis Zonae, qua utra&shy;<lb/>que Scala distinguitur, compressionem. </s>

<s>Nam rursus aer iste, qui in Tympani <lb/>Scala continetur, compressae Zonae facile cedit, non dico in Tympanum per <lb/>Fenestram rotundam prorumpendo, ut idem Auctor, hanc membrana claudi <lb/>non advertens, credidit, sed istam eandem membranam, quoad opus est (exi&shy;<lb/>guo autem spatio opus est) versus Tympanum urgendo atque curvando &rdquo; <lb/>(ibid., pag. </s>

<s>81). </s></p><p type="main">

<s>Tale &egrave;, secondo il Valsalva, l'uso della Finestra rotonda, non avendo <lb/>propriamente la Natura assegnato per l'ammissione del suono altro che la <lb/>Finestra ovale. </s>

<s>Che se cos&igrave; rinnovellava l'Autore l'opinion dell'Eustachio, <lb/>dall'altra parte la peggiorava, attribuendo agli ossicini un ufficio non acu&shy;<lb/>stico, ma meccanico, come, rinnovellando altres&igrave; l'opinione del Molinetti, in <lb/>conformit&agrave; della quale l'aria sonora agisce sul nervo, premendolo, volgeva <lb/>in peggio le idee proposte dal Duverney per illustrarla. </s></p><p type="main">

<s>Mentre che cos&igrave; fatte considerazioni tenevano fra la grande stima che <lb/>si faceva dell'uomo, e le irragionevolezze e gli errori, in questo particolar <lb/>proposito della teoria dell'udito, il pubblico dei dotti perplesso, fu instanta&shy;<lb/>neamente decisa la questione da un colpo dato dal Cotunnio a uno de'ca&shy;<lb/>naletti semicircolari, a vedere il quale pieno d'acqua e non d'aria. </s>

<s>&ldquo; Quid <lb/>zonae sonorae, esclama, a Valsalva propositae? </s>

<s>Aliquid in quo bonus dor&shy;<lb/>mitavit Homerus. </s>

<s>Quid aer ille, ingenitus Aristoteli dictus, et toti prope an&shy;<lb/>tiquitati acceptus, cui tantum Anatomici et Physici videntur tribuisse? </s>

<s>&rdquo; <lb/><emph type="italics"/>Patet,<emph.end type="italics"/> risponde a s&egrave; medesimo, da questo umore che cola (De aquaeducti&shy;<lb/>bus auris. </s>

<s>hum. </s>

<s>cit., pag. </s>

<s>39). </s></p><p type="main">

<s>E giacch&egrave;, dopo tanti secoli, era toccato a lui il primo finalmente a <lb/>scoprire il mistero, intese perch&egrave; l'aria non all'aria ma a un liquido comu&shy;<lb/>nichi i suoi tremori. </s>

<s>Le ossa dure, dentro alle quali s'accoglie il pi&ugrave; intimo <lb/>organo dell'udito, sono, ei pensa, attissime a ricevere e a conservare i tre&shy;<lb/>mori, &ldquo; oportuit tamen nervos humore inundari, ne si ab ipso immediato <lb/>ossium contactu deberent sibi tremorem comparare, nimium pro teneritudine <lb/>sua lacessirentur. </s>

<s>Humor etenim intermedius leniter inundans, ob acceptum <lb/>ab ossibus impulsum, concutit nervos, sed molli nec aspero contactu &rdquo; (ibid., <lb/>pag. </s>

<s>40). </s></p><p type="main">

<s>Quanto al meccanismo della funzione non ha il Cotunnio difficolt&agrave; di <lb/>seguire il Valsalva, sull'esempio del quale, dall'altra parte, procede sicuro <lb/>di non contradire alle leggi della Fisica, essendo propriamente i liquidi ane-<pb xlink:href="020/01/1423.jpg" pagenum="298"/>lastici e incompressibili. </s>

<s>Ma egli ebbe in quel meccanismo a ritrovare gli <lb/>usi di due canaletti da s&egrave; nuovamente scoperti, uno de'quali, facendosi via <lb/>attraverso all'osso petroso, deriva dal Vestibolo in tempi prestabiliti l'umore <lb/>nel prossimo seno laterale della dura madre, e l'altro che dalla Chiocciola <lb/>deriva un simile umore nelle cavit&agrave; del cranio. </s>

<s>D&agrave; al primo il nome di <lb/><emph type="italics"/>Acquedotto del Vestibolo,<emph.end type="italics"/> e al secondo quello di <emph type="italics"/>Acquedotto della Chioc&shy;<lb/>ciola,<emph.end type="italics"/> e da questi due organi, ai quali principalmente accomoda la sua nuova <lb/>teoria dell'udito, intitola il Cotunnio il suo classico libro. </s></p><p type="main">

<s>La Staffa dunque, secondo l'Autore, messa meccanicamente in moto <lb/>dalle onde sonore pulsanti la membrana del Timpano, comprime l'umore <lb/>del Labirinto, che dalla cavit&agrave; anteriore del Vestibolo, per via del canale <lb/>esterno, passa alla cavit&agrave; posteriore, e indi, per il canal comune, ritorna alla <lb/>medesima cavit&agrave; anteriore, quasi compiendo un circolo (ivi, pag. </s>

<s>57). A que&shy;<lb/>sto moto circolare, a cui s'opporrebbe l'incompressibilit&agrave; naturale del liquido, <lb/>e l'impenetrabilit&agrave; del corpo, favorisce la membrana della Finestra rotonda, <lb/>che d&agrave;, cedendo, luogo a ricoverarsi dentro la sua cavit&agrave; l'umore spostato, <lb/>e favoriscono altres&igrave; gli Acquedotti, che danno a quello stesso umore un <lb/>esito, ristorato poi dalle arterie esalanti, delle quali &egrave; s&igrave; ricca la cavit&agrave; del <lb/>Labirinto (ivi, pag. </s>

<s>105). </s></p><p type="main">

<s>Tale insomma &egrave;, secondo il Cotunnio, il meccanismo dell'umore, che <lb/>dee partecipare i tremori armonici ai nervi. </s>

<s>&ldquo; Integra igitur perceptio soni <lb/>in singulorum tremorum a sonante corpore editorum perceptione consistit, <lb/>atque anima tum integrum aliquem sonum percipit, cum plenum eius tre&shy;<lb/>morum numerum agnoscit. </s>

<s>Ita similes dicimus sonos quoties eumdem in <lb/>utroque tremorum numerum percipimus. </s>

<s>Sunt igitur nervi acustici quasi <lb/>chordae in singulo tremore sonori corporis semel oscillantes, totque, cum <lb/>audimus, impressiones cerebro numeratim impertientes, quot numero sunt <lb/>sonori corporis vibrationes &rdquo; (ibid., pag. </s>

<s>103). </s></p><p type="main">

<s>L'organo generale della percezione del suono &egrave; il setto membranoso, <lb/>che divide il Vestibolo. </s>

<s>&ldquo; Hoc enim Septum amplam firmamque chordam, <lb/>sive seriem tot chordarum paralellorum, quot nervosa fila complectitur, re&shy;<lb/>praesentat, quae moto a Stapede humori, undique opponuntur eiusque vim <lb/>integram accipiunt &rdquo; (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>I Canali semicircolari, le zone contenute ne'quali son, come sopra nar&shy;<lb/>rammo, fatte dal Valsalva strumenti principali dell'audizione, non hanno per <lb/>il Cotunnio altro che un ufficio secondario, ed &egrave; quello di dirigere cos&igrave; il <lb/>corso all'umore, che non debba il Setto rimanersene in secco. </s></p><p type="main">

<s>Ma s'&egrave; questo Setto l'organo della percezion generale, qual'&egrave; lo stru&shy;<lb/>mento della particolar percezione de'suoni? </s>

<s>E risponde il Cotunnio essere <lb/>la Chiocciola &ldquo; in qua series chordarum paralellarum tensarumque cymbalo <lb/>similis absconditur, cuius in zona Cochleae sedes est, quae fila nervosa a spi&shy;<lb/>rali lamina accepta et parallela continet longitudinis variae. </s>

<s>Harum ego chor&shy;<lb/>darum minimam in zonae origine pono, prope orificium Scalae Tympani, <lb/>ubi arctissima zona est, maximam vero versus zonae hamulum. </s>

<s>Quemadmo-<pb xlink:href="020/01/1424.jpg" pagenum="299"/>dum ergo, edito sono aliquo etiam vocis humanae, observatur ex tot cym&shy;<lb/>bali chordis unam tremere, quae in eodem unisono cum sono dato est; ita <lb/>in quovis dato sono, intra Cochleam, quae cymbalum nostrum est, propria <lb/>unisone respondens chorda datur, quae unisone contremiscens eius soni ani&shy;<lb/>mae distinctionem exhibet &rdquo; (ibid., pag. </s>

<s>105). E conclude questa fisiologia <lb/>dell'udito, che &egrave; la pi&ugrave; filosoficamente bella che sia stata pensata: &ldquo; Septo <lb/>igitur sonum percipimus, Cochlea tonos discernimus &rdquo; (ibid.). </s></p><p type="main">

<s>La teoria del Cotunnio fondata sopra la sua scoperta dell'umore, di <lb/>ch'&egrave; tutto ripieno il Labirinto, fu accolta universalmente, e si fece plauso <lb/>ai nuovi usi assegnati al Setto del Vestibolo, ai Canali semicircolari e alla <lb/>Chiocciola. </s>

<s>Quanto alla Finestra rotonda, dell'utilit&agrave; della quale i Fisiologi, <lb/>dai tempi dell'Eustachio in poi, erano rimasti s&igrave; incerti, volle esso Cotun&shy;<lb/>nio insignirla di un duplice ufficio, di quello acustico cio&egrave; attribuitole dal <lb/>Duverney, e di quell'altro meccanico del Valsalva. </s>

<s>&ldquo; Duplex mihi videtur <lb/>ratio esse. </s>

<s>Prima, ut eo tempore quo Tympani membranam sonora unda <lb/>impellit, aer Tympani percussus tremorem acceptum membranae communi&shy;<lb/>caret Fenestrae rotundae, quae oscillatione sua proximum humorem Scalae <lb/>Tympani agitaret, et per orificium Cochleae aquaeductus eodem tempore <lb/>expelleret, quo Vestibuli humor a Stapede movetur.... Alteram, ut qui Fe&shy;<lb/>nestram rotundam premit humor, tempore quo nova quantitas ex vestibulo <lb/>advehitur, non in superpositam Cochleae zonam, etsi breviorem hic robu&shy;<lb/>stioremque, totus ageret, sed in cedentem hanc Rotundae Fenestrae mem&shy;<lb/>branam impulsus partem perderet &rdquo; (ibid., pag. </s>

<s>83). </s></p><p type="main">

<s>Parvero questi usi della Finestra rotonda ad Antonio Scarpa poco pro&shy;<lb/>babili, e in un suo trattatello si studi&ograve; di dimostrar che quell'organo era <lb/>un sussidiario del Timpano, per cui ei lo design&ograve; col nome di <emph type="italics"/>Timpano <lb/>secondario.<emph.end type="italics"/> Il modo proprio di operare di lui si rassomiglia dallo stesso <lb/>Scarpa al Corno acustico &ldquo; quo instrumento, egli dice, nihil similius est <lb/>provido artificio, quod in Secundarii Tympani commodum Natura elabora&shy;<lb/>vit. </s>

<s>Id enim boni quod oscillans membrana ad basim instrumenti posita prae&shy;<lb/>stat membranae Tympani in aure, illud idem membrana isthaec primarii <lb/>Tympani membranae Secundarii conciliat &rdquo; (De structura Fenestrae rotun&shy;<lb/>dae auris, et de Tympano secundario, Mutinae 1772, pag. </s>

<s>79). </s></p><p type="main">

<s>Assegnando lo Scarpa questo nuovo uso alla membrana della Finestra <lb/>rotonda, e alla cavit&agrave; del Timpano annessa, intendeva di perfezionare il si&shy;<lb/>stema del Cotunnio, ch'ei del resto approva, come lo approvarono i Fisio&shy;<lb/>logi pi&ugrave; insigni del secolo XVIII, fa'quali l'Haller, che sciolse le difficolt&agrave; <lb/>di alcuni ritrosi ad ammettere la somiglianza fra le fila nervose e le corde <lb/>dei musici strumenti (Elem. </s>

<s>Phys. </s>

<s>T. </s>

<s>V cit., pag. </s>

<s>294), e dette al nostro <lb/>Napoletano il titolo di <emph type="italics"/>Sommo.<emph.end type="italics"/></s></p><pb xlink:href="020/01/1425.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Anc&ograve;ra Dei sensi.<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>I. Dell'organo della vista; delle membrane dell'occhio. </s>

<s>&mdash; II. </s>

<s>Degli umori di refrangenza nell'occhio.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>III. </s>

<s>Del senso della vista<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Le analogie fra il modo come funziona l'Orecchio, e il modo come fun&shy;<lb/>ziona l'Occhio, sagacemente riscontrate dal Molinetti, e le pi&ugrave; strette rela&shy;<lb/>zioni, che si riconobbe con general maraviglia passare fra i due organi, <lb/>quando primo il Cotunnio dimostr&ograve; ch'erano ambedue ripieni di umori, <lb/>aprono le vie a intendere un fatto, che ci occorre a notare, nel dar princi&shy;<lb/>pio a questa nuova parte di storia. </s>

<s>Il fatto notabile &egrave; questo: che maggiori <lb/>difficolt&agrave; trovarono gli Anatomici nell'investigar la struttura dell'organo del&shy;<lb/>l'udito, che non di quello della vista; ond'&egrave; che, mentre gli Antichi in quello <lb/>non andaron pi&ugrave; l&agrave; della superficial descrizione del meato uditorio esterno, <lb/>di questo si pu&ograve; dir che abbiamo la storia compiuta ne'libri di Galeno. </s>

<s>Ma <lb/>quanto la cosa &egrave; per s&egrave; certa, altrettanto perplesse ne rimangono le ragioni, <lb/>perch&egrave;, se da una parte si direbbe che l'udito &egrave; pi&ugrave; eccellente della vista, <lb/>essendo quello quasi l'ostetrico e il maestro dell'intelligenza, per cui l'uomo <lb/>sordo si ridurrebbe in istato inferiore a quello del bruto; dall'altra, essendo <lb/>l'aria, ch'&egrave; il veicolo del suono, pi&ugrave; materiale dell'etere, ch'&egrave; il veicolo <lb/>della luce, pareva che dovesse servire a quello un organo pi&ugrave; grossolano e <lb/>pi&ugrave; trattabile dagli argomenti dell'arte. </s></p><p type="main">

<s>Ma &egrave; giusto nelle diverse propriet&agrave; de'due elementi, che si trova la ra&shy;<lb/>gione della varia struttura degli organi, e delle maggiori o minori difficolt&agrave;, <pb xlink:href="020/01/1426.jpg" pagenum="301"/>ch'ebbe l'arte a trovare in divisar dell'uno e dell'altro le parti. </s>

<s>Perch&egrave;, <lb/>dovendo l'aria comunicare i suoi tremori ai nervi, conveniva fosse servita <lb/>da corpi atti a risentirsi con facilit&agrave; a quegli stessi tremori, e perci&ograve; ebbe <lb/>la Natura a rinchiudere il setto, la lamina spirale e le zone dentro i duris&shy;<lb/>simi ossi del Vestibolo, della Chiocciola e dei Canali semicircolari. </s>

<s>La luce <lb/>invece, avendo l'aria non per veicolo ma per semplice mezzo, richiedeva che <lb/>gli umori della sua refrangenza si trovassero a contatto con quello stesso <lb/>mezzo, e che perci&ograve; l'organo fosse esterno. </s>

<s>Di qui &egrave; che, mentre per l'udito <lb/>si scav&ograve; dentro la Rocca petrosa quell'inestricabile Labirinto, che fece di&shy;<lb/>sperare i primi Anatomici di poter entrarvi addentro a esplorarlo, per la <lb/>vista s'apr&igrave; sotto l'osso frontale quelle due semplici orbite, dentro alle quali, <lb/>come tutto intero fu posto l'occhio dalla Natura per servire al senso, cos&igrave; <lb/>tutto intero e raccolto pot&egrave; estrarlo l'arte, per istudiarne il maraviglioso <lb/>magistero. </s></p><p type="main">

<s>Que'primi Anatomici, che o sui bruti o sull'uomo si dettero a un tale <lb/>studio, ebbero a trovar facilmente che tutta la fabbrica del preziosissimo or&shy;<lb/>gano si riduceva a membrane involgenti alcuni trasparentissimi umori; n&egrave; <lb/>men difficile era a loro avvedersi che quelle stesse membrane dipendevano <lb/>dal nervo ottico, il quale uscito dal suo foro s'apre innanzi e si espande. </s>

<s><lb/>Distinguere e annoverare queste soprapposte espansioni, riconoscere la na&shy;<lb/>tura diversa degli umori, la grandezza, la figura, l'ordine che tengon fra <lb/>loro e le relazioni, erano agli Anatomici soggetto di studii, che non presen&shy;<lb/>tarono grandi difficolt&agrave;, infin tanto che la scienza si content&ograve; di aver del&shy;<lb/>l'Occhio una descrizione sommaria, ma quando volle investigarne quelle pi&ugrave; <lb/>minute particolarit&agrave;, che si comprendeva non dover essere a caso, e allora <lb/>s'incontrarono dubbii, e incominciarono le dispute a dar soggetto alla storia. </s></p><p type="main">

<s>Quelle dispute poi e que'dissensi, per ci&ograve; che specialmente concerne <lb/>l'origine, il numero e la natura delle membrane, ebbero occasione dal con&shy;<lb/>siderar le cose sotto aspetti diversi, e dal riguardar uno tutto insieme con&shy;<lb/>giunto quel che un altro invece voleva separato e distinto. </s>

<s>&ldquo; Numerus tuni&shy;<lb/>carum oculi, osserva a questo proposito l'Acquapendente, non est apud omnes <lb/>certus et definitus, sed variat, non quidem re, ut dicit Galenus, sed potius <lb/>quia alii quasdam partes tunicis annumerant, alii seiungunt. </s>

<s>Propterea septem, <lb/>sex, quinque, quatuor, tres, duae denique oculorum tunicae a quibusdam re&shy;<lb/>censentur &rdquo; (De oculo visus organo, Opera omnia cit., pag. </s>

<s>188). </s></p><p type="main">

<s>Celso infatti, dietro Herofilo e gli altri Anatomici greci, due dice essere <lb/>le tuniche degli occhi; la Cheratoide cio&egrave; e la Ragoide, in latino Uvea, alle <lb/>quali aggiunge l'Aracnoide, per la quale intende forse la Retina, e una mem&shy;<lb/>brana propria involgente il Vitreo, e poi detta Gialloidea, bench&egrave; l'Autore la <lb/>lasci innominata. </s>

<s>&ldquo; Oculus summas habet duas tunicas, ex quibus superior <lb/>a Graecis <emph type="italics"/>Cheratoides<emph.end type="italics"/> vocatur. </s>

<s>Ea, qua parte alba est satis crassa, pupillae <lb/>loco extenuatur. </s>

<s>Huic inferior adiuncta est, media parte qua pupilla est, mo&shy;<lb/>dico foramine concava, circa tenuis, ulterioribus partibus ipsa quoque pla&shy;<lb/>nior, quae Ragoides a Graecis nominatur..... Deinde infra rursus tenuis-<pb xlink:href="020/01/1427.jpg" pagenum="302"/>sima tunica, quam Herophilus Aracnoides nominavit. </s>

<s>&rdquo; E dopo aver descritto <lb/>l'umor vitreo, &ldquo; id autem, soggiunge, superveniens ab interiore parte mem&shy;<lb/>branula includit &rdquo; (De re medica, Parisiis 1529, fol. </s>

<s>100 ad t.). </s></p><p type="main">

<s>Galeno, che pi&ugrave; diligentemente de'suoi predecessori anatomizz&ograve; l'occhio <lb/>nelle altre sue parti, per quel che concerne le membrane ne vide, fra la <lb/>Cheratoide e la Ragoide, un'altra distinta col nome proprio di Coroide, e <lb/>cos&igrave; ridusse a quattro quegli involucri, specificando l'Aracnoide di Herofilo <lb/>col nome di Corpo retiforme. </s></p><p type="main">

<s>Gli Arabi poi, per natura propria e per gl'istituti aristotelici, usi a smi&shy;<lb/>nuzzare la scienza, applicando i loro metodi all'esame anatomico dell'occhio, <lb/>fecero delle tre pi&ugrave; intime membrane distinzione, fra quella parte che riman <lb/>di dietro, e l'altra che si protende in avanti, e cos&igrave; colla Congiuntiva, che <lb/>sola riguardarono andantemente circondar tutto il globo, ridussero quelle <lb/>stesse membrane a sette, cos&igrave;, seguendo gli Arabi, dal nostro Berengario <lb/>annoverate per ordine e descrite: &ldquo; Prima harum..... <emph type="italics"/>Coniunctiva.<emph.end type="italics"/> Se&shy;<lb/>cunda, diaphana et lucida ut cornu, et ideo dicitur communiter <emph type="italics"/>Cornea.....<emph.end type="italics"/><lb/>Post Corneam,.... versus latera et versus retro, correspondit una tunica <lb/>ipsi Corneae alligata et continua, quae vocatur <emph type="italics"/>Schlerotica.....<emph.end type="italics"/> Cornea et <lb/>schlerotica oriuntur a dura Matre..... Post istas tunicas ante est una alia <lb/>tunica, quae vocatur <emph type="italics"/>Uvea,<emph.end type="italics"/> quae occupat ante medictatem oculi tendendo <lb/>retro versus, et aliam medietatem occupat una tunica, quae correspondet <lb/>huic versus retro quae vocatur <emph type="italics"/>Secundina<emph.end type="italics"/> (la Coroide di Galeno), et istae <lb/>duae tunicae sunt simul continuae, et oriuntur ambae duae a pia Matre..... <lb/>Post istas tunicas, ante versus, est una alia tunica, quae vocatur <emph type="italics"/>Aranea,<emph.end type="italics"/><lb/>quia est subtilissima, cui retro correspondet una alia tunica posterior dicta <lb/><emph type="italics"/>Rhetina &rdquo;<emph.end type="italics"/> (Commentaria cit., fol CCCCLXVIII). </s></p><p type="main">

<s>Tale era la descrizione delle parti involgenti gli umori dell'occhio, che <lb/>il Berengario tramandava al Vesalio, &ldquo; quem, esclamano ancora i lettori col <lb/>Colombo, mirum est in membri adeo nobilis descriptione tantopere lapsum <lb/>esse &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>220). Vedremo di questi lassi nella nostra breve <lb/>storia gli esempii, ma perch&egrave; il Colombo stesso, nel principio del suo lib. </s>

<s>X <lb/><emph type="italics"/>De oculis,<emph.end type="italics"/> accusa di pi&ugrave; il Vesalio anche di negligenza, si pu&ograve; in questo rie&shy;<lb/>pilogo veder le non ingiuste ragioni di quella accusa. </s>

<s>&ldquo; Fuit itaque haec <lb/>Oculi partium series: humor chrystallinus; tunicula cepis pelliculae tenuis&shy;<lb/>simae modo pellucida, anteriorique Chrystallini humoris sedi adnata, humor <lb/>vitreus in posteriori oculi sede tantum positus; tunica, in quam visorii nervi <lb/>substantia resolvitur, ac posteriorem humoris vitrei sedem tantum amplecti&shy;<lb/>tur; tunica Uvea a tenui Cerebri membrana principium ducens; tunica, seu <lb/>Orbis araneae telae modo tenuis et nigricans, et interstitium vitrei humoris <lb/>ab aqueo; tunica dura, quae in anteriori oculi sede, cornu modo pellucida, <lb/>redditur; aqueus humor; septem Oculum moventes musculi; tunica adhae&shy;<lb/>rens, se alba, anteriori tantum Oculi sede obnata; palpebrae, et demum ve&shy;<lb/>nae et arteriae &rdquo; (De hum. </s>

<s>corporis fabrica cit., pag. </s>

<s>649). </s></p><p type="main">

<s>Pi&ugrave; per&ograve; che questa negligenza, la quale apparisce manifesta nella stessa <pb xlink:href="020/01/1428.jpg" pagenum="303"/>disordinata enumerazion delle parti, &egrave; disposto il Colombo a scusar l'errore, <lb/>ch'egli attribuisce all'aver piuttosto il Vesalio sezionato l'occhio del bruto, <lb/>che non quello dell'uomo, la vera descrizion del quale, forse dimentico del <lb/>Berengario, si vanta d'essere stato a darla egli il primo. </s>

<s>&ldquo; Scito praeterea <lb/>neminem ante me hominis oculum descripsisse, sed omnes belluinum ocu&shy;<lb/>lum describere, magno et turpi errore &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>215). </s></p><p type="main">

<s>Proponendosi dunque di dar la prima e nuova descrizione dell'occhio <lb/>umano, distingue il Colombo sei membrane, ch'egli cos&igrave; annovera e de&shy;<lb/>scrive: &ldquo; Prima exterior est, pluribus nominibus insignita, nam Adnata, <lb/>Alba, Adhaerens et Coniunctiva appellatur..... Secunda oculi membrana <lb/>nomine caret, neque id mirum est cum hactenus incognita fuerit..... Mem&shy;<lb/>brana tertia Ceratois, idest Cornea, duraque dicitur..... Arabes autem Ana&shy;<lb/>tomici, unica fidelia duos parietes dealbantes, partem anteriorem Corneam, <lb/>quod instar cornu pelluceat, posteriorem Sclerotica, a duritie, appellarunt. </s>

<s><lb/>Sed una duntaxat est, non duae..... Quarta oculi membrana Uvea dici&shy;<lb/>tur..... Uveae nomen sortita est, eo quod uvae granum videatur esse..... <lb/>Quinta oculi membrana Amphiblistroides, hoc est Retina dicta..... Sexta <lb/>membrana, Arachnois graece, latine Aranea dicitur, nam aranei telam prae se <lb/>ferre videtur &rdquo; (ibid., pag. </s>

<s>217, 18). </s></p><p type="main">

<s>Il Falloppio non si dilung&ograve; molto da questa enumerazione, e cos&igrave; il Pla&shy;<lb/>ter, ch'esplicando la figura dell'occhio disegnata nella Tavola XLIX, distinse <lb/>le due tuniche proprie involgenti il Vitreo e il Cristallino; la Hialoides e <lb/>la Chrystalloides (De corporis hum. </s>

<s>structura, Basileae 1603): e cos&igrave; il Vidio, <lb/>che aggiunse alle sei del Colombo una <emph type="italics"/>Tunica ciliare,<emph.end type="italics"/> per cui si riducono a <lb/>sette, cos&igrave; annoverate: &ldquo; Arachnoides, Retiformis, Ciliaris, Uvea, Cornea, Al&shy;<lb/>bum oculi, et ea quae oritur a chordis musculorum &rdquo; (De anat. </s>

<s>cit., pag. </s>

<s>321). <lb/>Ma l'Acquapendente ritorn&ograve; alla prima semplicit&agrave;, riducendo le membrane <lb/>a tre: alla Sclerotica, alla quale &egrave; congiunta la Cornea, alla Coroide, dalla <lb/>quale dipende l'Iride, e alla Retina, che si trasforma, intorno al Cristallino, <lb/>nella tunica Aranea. </s></p><p type="main">

<s>Non fu per&ograve; questa sapiente semplicit&agrave; seguita da tutti: il Molinetti per <lb/>esempio ritorn&ograve; presso a poco alla enumerazion del Colombo, e vi torn&ograve; il <lb/>Ruysch, che oltre alla Vitrea e alla Cristallina, entrate gi&agrave; nella enumerazion <lb/>del Platero, aggiungendovene un'altra nuova da s&egrave; scoperta, ridusse in tutte <lb/>quelle tuniche a otto: &ldquo; I. Adnata, seu Coniunctiva, II. Tendinea, III. Schle&shy;<lb/>rotica, IV. Choroidea, V. Ruyschiana, VI. Retina, VII Vitrea, VIII. </s>

<s>Chrystal&shy;<lb/>lina &rdquo; (De Oculorum tunicis, Epistola ad Christ. </s>

<s>Wedelium, Amstelodami 1720, <lb/>pag. </s>

<s>10). </s></p><p type="main">

<s>Verso la met&agrave; del secolo XVIII Giovanni Gotifredo Zinn, che arricch&igrave; <lb/>la scienza della pi&ugrave; compiuta descrizione anatomica dell'Occhio umano, ve&shy;<lb/>duta la confusione, la quale nasceva forse pi&ugrave; dalla capricciosa variet&agrave; dei <lb/>nomi che dalla reale distinzion delle parti, ritorn&ograve; con sapiente consiglio alla <lb/>semplicit&agrave; proposta dall'Acquapendente, riconoscendo anch'egli nell'occhio <lb/>tre principali membrane, delle quali quelle, da altri descritte come distinte, <pb xlink:href="020/01/1429.jpg" pagenum="304"/>non sieno pi&ugrave; che parti integranti. </s>

<s>E perch&egrave; l'esempio del Zinn &egrave; oramai <lb/>imitato da tutti coloro, che nella semplicit&agrave; ritrovano la chiarezza, noi segui&shy;<lb/>remo quello stesso ordine tenuto da lui nell'espor brevemente, delle tre tu&shy;<lb/>niche e delle loro parti componenti, la storia. </s></p><p type="main">

<s>Fu il Colombo il primo a dare autorit&agrave; a una certa opinione, che cio&egrave; <lb/>fossero sopra la Sclerotica distese due altre membrane, una detta Congiun&shy;<lb/>tiva, e l'altra rimasta Innominata, &ldquo; cum hactenus, dice esso Colombo, inco&shy;<lb/>gnita fuerit &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>217), e generata, secondo ch'egli tien <lb/>per certo, &ldquo; a nerveis musculorum Oculi tenuitatibus &rdquo; (ibid.). I principali <lb/>Anatomici, succeduti nel secolo XVI a Realdo, senza disputar se la cosa fosse <lb/>veramente nuova, ammisero l'esistenza di quella Tunica tendinosa, e il Vidio <lb/>fra gli altri cos&igrave; la descriveva: &ldquo; Vestit praedictam tunicam alia, quam effi&shy;<lb/>ciunt chordae musculorum Oculum moventium, non tamen totam vestit, sed <lb/>usque ad nigrum oculi duntaxat, qua Schlerotica dicitur &rdquo; (De anat. </s>

<s>corp. </s>

<s><lb/>humani cit., pag. </s>

<s>320). Ma il Casserio e il Riolano, sui principii del se&shy;<lb/>colo XVII, dop'avere osservato che Galeno, nel cap. </s>

<s>II del libro X <emph type="italics"/>De usu <lb/>partium,<emph.end type="italics"/> lasci&ograve; scritto i tendini dei quattro muscoli retti &ldquo; ad anteriora Oculi <lb/>in unum circulum lati tendinis convenire, et propriam ibi membranam con&shy;<lb/>stituere &rdquo; (Op. </s>

<s>cit., T. I, fol. </s>

<s>177), e che Carlo Stefano avea sulla Sclerotica <lb/>riconosciuta una tunica, nata dalle aponeurosi muscolari; negarono assolu&shy;<lb/>tamente di quella stessa Tunica l'esistenza. </s>

<s>Nonostante, per tutto il se&shy;<lb/>colo XVII, prevalse a quella del Casserio e del Riolano la pi&ugrave; antica auto&shy;<lb/>rit&agrave; del Colombo. </s>

<s>Il Molinetti fra'Nostri descriveva come sottoposta imme&shy;<lb/>diatamente alla Congiuntiva l'Innominata &ldquo; quam expansio musculorum <lb/>tendinosa, protensa usque ad terminos Iridis, componit &rdquo; (Dissert. </s>

<s>anat. </s>

<s>cit., <lb/>pag. </s>

<s>24), e lo Spigelio e il Veslingio, fra gli stranieri, la illustrarono con <lb/>figure, e il Winslow le impose il nome di <emph type="italics"/>Albuginea<emph.end type="italics"/> accettato da molti, spe&shy;<lb/>cialmente francesi. </s>

<s>Sui principii per&ograve; del secolo XVIII il Senac e il Leiu&shy;<lb/>taud incominciarono a dubitare, e il Zinn ebbe per cosa certa i tendini <lb/>&ldquo; nunquam in unum iungi, aut propriam tunicam continuam constituere <lb/>posse &rdquo; (Descriptio anat. </s>

<s>cit., pag. </s>

<s>15). In Italia il Valsalva, che dietro le <lb/>sue proprie osservazioni anatomiche sentenziava: &ldquo; Tunicam innominatam <lb/>nullam esse &rdquo; (Dissertatio anat. </s>

<s>II, Venetiis 1740, pag. </s>

<s>142) avrebbe rassi&shy;<lb/>curato le menti, se non fosse poco dopo venuto il Morgagni a mettere scru&shy;<lb/>poli con dire che se i tendini, presso alla Cornea, non si avvicinano cos&igrave; da <lb/>comporre una membrana continua, &ldquo; multo tamen propius quam putemus &rdquo; <lb/>(Epistola anat. </s>

<s>XVI cit., pag. </s>

<s>195). Nonostante gli Anatomici poi si assicu&shy;<lb/>rarono non esser da mettere in dubbio le sentenze del Valsalva e del Zinn, <lb/>ma, se negarono la membrana tendinea, riconobbero collo Stenone la Scle&shy;<lb/>rotica &ldquo; magna ex parte ex fibrarum motricium tendinibus esse compo&shy;<lb/>sitam, quandoquidem, non modo durae tunicae vere tendineae sit conti&shy;<lb/>nua, sed etiam tendines vere excipiat &rdquo; (Elem. </s>

<s>Myologiae, Florentiae 1667, <lb/>pag. </s>

<s>103). </s></p><p type="main">

<s>E perch&egrave; la notizia della composizion della Sclerotica dipende in mas-<pb xlink:href="020/01/1430.jpg" pagenum="305"/>sima parte dalla notizia dell'origine di lei, &egrave; da saper che furono fra gli <lb/>Anatomici, intorno a questo punto, di gran dissensioni. </s>

<s>Tutti per lungo <lb/>tempo ritennero consenzienti con Galeno che la Sclerotica derivasse dalla <lb/>dura madre. </s>

<s>I dissensi propriamente cominciarono dai Francesi, in sui prin&shy;<lb/>cipii del secolo XVIII, quando il Winslow e il Senac, avendo trovato colla <lb/>macerazione ch'eran diverse le fila, di che s'intesse la Sclerotica, da quelle <lb/>con le quali la dura Madre si compila; dissero che essa Sclerotica era una <lb/>membrana propria e peculiare dell'Occhio, strettamente congiunta coll'invo&shy;<lb/>lucro che, derivato dalla dura madre stessa, accompagna e invagina il nervo. </s></p><p type="main">

<s>Il Valsalva usc&igrave; fuori in mezzo a quei dissensi con una nuova propo&shy;<lb/>sta, dicendo che dal concorso di tutte le fibre de'muscoli motori dell'Occhio <lb/>si componeva un anello tendineo carnoso, da cui il nervo, nel suo primo <lb/>ingresso nell'orbita, e la Pia madre, che all'esterno l'investe, sono con <lb/>stretto vincolo legati insieme. </s>

<s>Di qui ne deduce tre conseguenze &ldquo; iis omnino <lb/>contraria, quae ab Anatomicis fere passim in scholis traduntur &rdquo; la seconda <lb/>delle quali &egrave; &ldquo; Scleroticam non a dura matre, sed a tendinibus musculorum <lb/>oculi, et a pia Meninge ortum ducere &rdquo; (Dissertatio II cit., pag. </s>

<s>142). </s></p><p type="main">

<s>Ripensando il Zinn a queste novit&agrave; introdotte nell'Anatomia dell'occhio <lb/>dal nostro insigne Italiano, ebbe, dietro alle sue diligentissime osservazioni, <lb/>a confessare non essere i limiti tra la vagina del nervo ottico e l'origine <lb/>della Sclerotica cos&igrave; insensibili e oscuri, da lasciar luogo ai dubbi. </s>

<s>&ldquo; Scle&shy;<lb/>rotica enim in fundo crassior, non ex mutata et sensim incrassata dura <lb/>matre nascitur, sed leniter prominulo, rotundo, nervum versus convexo, ad <lb/>minimum octies crassiori involucro nervi, circa eius insertionem oritur, nervo, <lb/>quem uti annulus digitum, arcte complectitur &rdquo; (Descriptio oculi hum. </s>

<s>cit., <lb/>pag. </s>

<s>10, 11). Per quel poi riguarda l'origine dalla pia Meninge, si studia <lb/>il Zinn di interpetrare le idee del Valsalva, come divinatrici della tunica sco&shy;<lb/>perta da Niccol&ograve; Le Cat, il quale affermava che la pia madre, dopo la con&shy;<lb/>trazione del nervo ottico, si divide in due lamine, una delle quali va alla <lb/>Coroide e l'altra si applica alla solida interna faccia della Sclerotica e la <lb/>tappezza. </s>

<s>&ldquo; Num Valsalva, son le parole proprie dell'Anatomico di Gottinga, <lb/>forte iam simile quid vidit, ubi Scleroticam, non ex dura matre, sed ex pia <lb/>meninge tendinibusque musculorum oriri scripsit? </s>

<s>&rdquo; (ibid., pag. </s>

<s>13). </s></p><p type="main">

<s>Galeno, nel cap. </s>

<s>III del X libro <emph type="italics"/>De usu partium,<emph.end type="italics"/> in ci&ograve; consenziente <lb/>con gli Anatomici suoi predecessori, aveva detto che la Sclerotica, giunta a <lb/>mezzo l'occhio, dalla parte anteriore s'assottiglia, e divien pi&ugrave; spessa e pel&shy;<lb/>lucida come un corno. </s>

<s>&ldquo; Cum enim crassa quidem esset admodum haec tu&shy;<lb/>nica, sed densa minus quam usus flagitabat, tenuiorem simul ac densiorem <lb/>coepit producere. </s>

<s>Post autem paulatim promovens, partem eius maxime me&shy;<lb/>diam longe tenuissimam ac densissimam efficit. </s>

<s>Apte diceres eam cornibus <lb/>admodum extenuatis similem, unde ei nomen &rdquo; (Op. </s>

<s>omnia cit., f. </s>

<s>178). </s></p><p type="main">

<s>Questa connessione e questa origine della Cornea dalla Sclerotica era <lb/>tenuta certa dalla maggior parte degli Anatomici, quando venne il Falloppio <lb/>a metterla in dubbio, dicendo non si poter persuadere &ldquo; Corneam esse tu-<pb xlink:href="020/01/1431.jpg" pagenum="306"/>nicae durioris partem, quae a dura cerebri meninge erigitur, cum non so&shy;<lb/>lum substantia, sed et crassitie et figura differat &rdquo; (Observat. </s>

<s>an., Op. </s>

<s>omnia <lb/>cit., pag. </s>

<s>478). L'autorit&agrave; del grande Anatomico tenne per lungo tempo in&shy;<lb/>certa la scienza, infin tanto che gli Accademici parigini, sui principii del <lb/>secolo XVIII, non dimostrarono chiaramente congiungersi la Cornea colla <lb/>Sclerotica negli occhi di un lupo cerviero. </s>

<s>Non si erano ancora diffusi gli <lb/>atti dell'Accademia, n&egrave; s'era ancora divulgato il trattato del Brisseau in <lb/>Italia, quand'occorse al Morgagni di far negli occhi de'bovi, e poi anche <lb/>degli uomini, quella stessa scoperta. </s>

<s>&ldquo; Haud scio an res adhuc satis de&shy;<lb/>scripta fuerit, sed ego certe, priusquam de ipsa aliquid ex Commentariis <lb/>Regiae scientiarum Academiae parisiensis intellexissem, nam cl. </s>

<s>Brissaei vi&shy;<lb/>dere tractatum nondum potui, in boum oculis, communibus scleroticae et <lb/>corneae perlustratis finibus, sic inveneram opacam ibi illius substantiam <lb/>huius pellucidae substantiae impositam, utramque autem sensim, quo magis <lb/>progreditur, eo magis extenuatam, sic inter se committi, ut quantum exte&shy;<lb/>rius Sclerotica excrescit ad corneam ellypticis oris contegendam, tantum in&shy;<lb/>terius producatur Cornea ad Scleroticam circulari ambitu occupandam &rdquo; (Epi&shy;<lb/>stola anat. </s>

<s>XVII, pag. </s>

<s>251, 52). </s></p><p type="main">

<s>Queste osservazioni, confermate poi da tanti altri, rendevano certi della <lb/>identit&agrave; di natura che passa fra la Sclerotica e la Cornea, ma restava di <lb/>sodisfare alla curiosit&agrave; di chi avrebbe voluto sapere in che modo, dall'opa&shy;<lb/>cit&agrave; dell'una si passasse alla perfetta trasparenza dell'altra. </s>

<s>Il fatto noto di <lb/>alcuni corpi che imbevuti di acqua divengon diafani, avrebbe potuto pre&shy;<lb/>parar la risposta, ma intanto non se ne vide l'analogia, n&egrave; si pens&ograve; di farne <lb/>l'applicazione all'occhio, se non che verso la met&agrave; del secolo XVIII, dopo <lb/>essersi fatta della cornea una pi&ugrave; sottile anatomia. </s>

<s>La struttura lamellare di <lb/>lei fu riconosciuta infino dagli antichissimi tempi, cosicch&egrave; l'Acquapendente, <lb/>nel darne l'appresso descrizione, citava Ruffo Efesino. </s>

<s>&ldquo; Et quamvis, egli <lb/>dice giusto della Cornea, tenuis sit tunica, ut diaphana sit, non tamen sim&shy;<lb/>plex censenda est, sed triplex, quadruplexque conspicitur, quasi ex pluribus <lb/>corticibus constare videatur, cum laminae, quarum una alteri superposita est <lb/>valdeque adhaeret, multae sint &rdquo; (De oculo cit., pag. </s>

<s>189). </s></p><p type="main">

<s>La prima e importante novit&agrave; scoperta in tal proposito dagli Anatomici <lb/>pi&ugrave; recenti &egrave; dovuta allo Stenone, il quale dice nel suo trattato <emph type="italics"/>De muscu&shy;<lb/>lis et glandulis:<emph.end type="italics"/> &ldquo; Semel iterumque in Cornea observavi, non sine admi&shy;<lb/>ratione, poros quandam aquei humoris transmittentes partem &rdquo; (Amstelo&shy;<lb/>dami 1664, pag. </s>

<s>49). Il Leuwenoeck poi conferm&ograve; la scoperta stenoniana, <lb/>dimostrando che la cornea compressa trasuda un umor rugiadoso che l'ap&shy;<lb/>panna. </s>

<s>N&egrave; egli per&ograve;, n&egrave; lo stesso Stenone seppero decider se fosse un tale <lb/>umore espresso dalla sostanza della Cornea, o vi trapelasse dall'interno del&shy;<lb/>l'occhio. </s>

<s>&ldquo; Vidi quidem per poros exeuntem humorem, sed ipsine tunicae <lb/>adscribendus substantiae, an ab inclusa aqua deducendus, non facile ante <lb/>ulterius examen determinavero &rdquo; (ibid.). </s></p><p type="main">

<s>Se questo ulteriore esame fosse poi fatto non sappiamo, ma &egrave; certo in <pb xlink:href="020/01/1432.jpg" pagenum="307"/>ogni modo che rimase dubbia la scienza intorno all'origine di quell'acqua <lb/>trasudata dalla Cornea compressa, infino a che il Morgagni, esaminando certe <lb/>schedule lasciate dal Valsalva, non vi trov&ograve; scritto: &ldquo; Corneam ex diversa <lb/>duplici constare substantia, tenuibus membranis duabus eiusdem naturae, et <lb/>substantia his interiecta, quae videtur spongiosa &rdquo; (Epistola anat. </s>

<s>XVI cit., <lb/>pag. </s>

<s>200). In questa cos&igrave; fatta sostanza spugnosa pens&ograve; allora lo stesso Mor&shy;<lb/>gagni che risedesse l'umor veduto stillare dallo Stenone, e pi&ugrave; copiosamente <lb/>espresso dal Leuwenoeck, di cui volle ripetere l'esperienze: &ldquo; Quod si forte <lb/>quaeras de hoc humore quid ipse adnotaverim, respondere possum in plu&shy;<lb/>ribus humanis oculis expertum esse an comprimendo exprimerem, ex illis&shy;<lb/>que omnibus expressisse: ad singulas enim compressiones madore quodam, <lb/>quas&igrave; opaco velo, corneae facies obducebatur, qui mox abstersus, continuo <lb/>ad novam compressionem redibat &rdquo; (ibid., pag. </s>

<s>201). </s></p><p type="main">

<s>A qual fine per&ograve; introdusse la natura, fra le lamelle cornee, quella so&shy;<lb/>stanza cellulare o spugnosa atta a imbevere e a ritenere in s&egrave; l'acqua, fu <lb/>primo a investigarlo il Zinn, il quale riusc&igrave; per questa via a sciogliere il pro&shy;<lb/>blema della trasparenza della Cornea. </s>

<s>&ldquo; A qua ipsa cellulosa, aqua ebria, <lb/>egli dice, pelluciditatem corneae unice pendere fere crediderim &rdquo; (Descriptio <lb/>Oculi cit., pag. </s>

<s>20). </s></p><p type="main">

<s>La cornea &egrave; per la sua trasparenza, diciamo cos&igrave;, quasi la porta mae&shy;<lb/>stra che introduce nell'interno dell'occhio, dove son la Coroide e la Retina <lb/>deputati principali ministri a celebrare i naturali misteri. </s>

<s>I pi&ugrave; antichi Ana&shy;<lb/>tomici greci, confondendo questa seconda membrana coll'Aracnoide, distin&shy;<lb/>sero la prima col nome di Ragoide, che insieme colla Sclerotica, alla quale <lb/>immediatamente soggiace, forma per essi il principale involucro dell'occhio. </s>

<s><lb/>Anche Celso, seguendo queste dottrine, dop'aver descritta la Cheratoide, <lb/>soggiunge: &ldquo; Huic inferior adiuncta est, media parte qua pupilla est, medio <lb/>foramine concava, circa tenuis, ulterioribus ipsa quoque plenior, quae Ra&shy;<lb/>goides a graecis nominatur &rdquo; (De re med. </s>

<s>cit., fol. </s>

<s>100 ad t.). </s></p><p type="main">

<s>Il nome proprio di Coroide par che fosse primo a introdurlo nel lin&shy;<lb/>guaggio scientifico Galeno, il quale designava con esso tutta la parte poste&shy;<lb/>riore della tunica, riserbando il nome di Ragoide a sola quella parte anteriore, <lb/>che Ruffo appell&ograve; <emph type="italics"/>Iride,<emph.end type="italics"/> ed egli <emph type="italics"/>Tunica cerulea.<emph.end type="italics"/> &ldquo; Ibi nam Tunicam cae&shy;<lb/>ruleam, Ragoide dico, hoc est viniformem seu vineam pertudit. </s>

<s>Appellant <lb/>autem ipsam ita, acino uvae levitatem eius externam et asperitatem inter&shy;<lb/>nam opinor comparantes &rdquo; (De usu partium, Op. </s>

<s>omnia cit., fol. </s>

<s>179). La <lb/>comparazione per&ograve; tra la buccia, o il fiocino dell'uva, proprissima nelle de&shy;<lb/>scrizioni di Herofilo e di Celso, nelle descrizioni galeniche diventa impropria, <lb/>e da questa impropriet&agrave; nacquero alcune confusioni, che dai semplici nomi <lb/>passarono nelle cose. </s>

<s>Coloro infatti, che prendevano a rigore la compara&shy;<lb/>zione tra l'Uvea e la Coroide, intendevano che l'Iride fosse una continua&shy;<lb/>zione della Coroide stessa, mentre quegli altri, che pur seguitarono a chia&shy;<lb/>mar uvea la sola parte anteriore, la quale veramente, presentandosi sotto <lb/>l'aspetto di un cerchio, non rende altra immagine del fiocino dell'uva, se <pb xlink:href="020/01/1433.jpg" pagenum="308"/>non forse nel colore; passarono facilmente a riguardarla come una mem&shy;<lb/>brana distinta. </s></p><p type="main">

<s>Le novit&agrave; che introdusse il Mariotte nell'organo della visione, resero, <lb/>verso la met&agrave; del secolo XVII, di grande importanza la sentenza data da <lb/>tutti gli Anatomici concordi intorno alla origine della Coroide dalla pia madre <lb/>del nervo. </s>

<s>E perch&egrave;, quando fosse stata quella sentenza falsa, tutto il si&shy;<lb/>stema del Mariotte cadeva, si dettero i fautori ogni pi&ugrave; sollecito studio di <lb/>confermarla. </s>

<s>Porse uno de'principali argomenti a cotesta conferma Federico <lb/>Ruyschio, il quale, iniettando un giorno le arterie coroidee, sent&igrave; colla mano <lb/>la tela de'vasi staccarsi da un'altra tela. </s>

<s>&ldquo; Hoc a me viso, scrive nella ci&shy;<lb/>tata Epistola XIII a Cristiano Wedelio, suspicari coepi annon Tunica cho&shy;<lb/>roidea esset gemina, et artificio quodam in duas lamellas separabilis. </s>

<s>Hoc <lb/>ex voto bis successit, et portionem satis magnam a Choroidea separabam, <lb/>per quam, aeque bene ac per Choroidem, observabam arterias peculiares di&shy;<lb/>verso reptatu repantes esse dispersas &rdquo; (pag. </s>

<s>13). Facendo poi di ci&ograve; pub&shy;<lb/>blica dimostrazione, sent&igrave; il bisogno che aveva la nuova tunica scoperta di <lb/>un nome. </s>

<s>&ldquo; Itaque filius meus Henricus proponebat nomen <emph type="italics"/>Tunicae ruy&shy;<lb/>schianae,<emph.end type="italics"/> cui calculum apponebam &rdquo; (ibid.). </s></p><p type="main">

<s>A una tale scoperta dunque esultarono i seguaci del Mariotte, perch&egrave; <lb/>l&agrave; dove prima nell'assegnar le origini della Coroide pareva che rimanesse <lb/>l'Aracnoide inutile, ora s'intendeva come, derivando da questa la sola pa&shy;<lb/>gina esterna, ossia la Coroide propria, dalla pia madre schietta si produ&shy;<lb/>cesse la Ruischiana. </s>

<s>Come al Mariotte per&ograve; cos&igrave; al Ruyschio non mancarono <lb/>contradittori, fra'quali uno de'pi&ugrave; fieri fu il Rau, ma perch&egrave; in cosa di non <lb/>lieve importanza parevano le contese riuscir troppo dannose ai progressi <lb/>della scienza, si levarono alcuni autorevoli giudici, fra'quali il nostro Mor&shy;<lb/>gagni. </s>

<s>Egli, accennando a Francesco Sylvio e al Casserio, ch'ebbero della <lb/>Ruischiana qualche presentimento, rammemorava che il Guenellon, infino <lb/>dal 1686, aveva trovata duplice la membrana coroidea ne'pesci, e narrando <lb/>le esperienze sue proprie fatte sui bovi, e sopra simili altri animali, &ldquo; non <lb/>difficulter, ei dice, eae laminae sunt divulsae. </s>

<s>Et divulsarum facies, quam&shy;<lb/>vis non omnino, sic satis tamen fuerunt aequales, ut proclive esset intelli&shy;<lb/>gere eam separationem, si peculiare aliquod accederet anatomicum artifi&shy;<lb/>cium, longe melius esse successuram. </s>

<s>Quo facilius adducor ut credam, excel&shy;<lb/>lenti in eiusmodi administrationibus Ruyschio, aliisque eius viam rationemque <lb/>callentibus, rem hanc felicissime provenire &rdquo; (Epist. </s>

<s>anat. </s>

<s>XVII cit., pag. </s>

<s>243). <lb/>Queste parole per&ograve;, se persuasero tutti potersi la Coroide sdoppiare nei bruti, <lb/>lasciavano riguardo all'uomo alcuni ragionevoli dubbii, ond'&egrave; che il Zinn fra <lb/>gli altri confess&ograve; non potersi ancora persuadere &ldquo; in oculo humano Choroi&shy;<lb/>dem ex duabus lamellis aut pluribus esse compositam &rdquo; (Descriptio oculi <lb/>cit., pag. </s>

<s>53), e di qui incominci&ograve; la Ruischiana ad andare in dimenticanza. </s></p><p type="main">

<s>La dubbiosa scoperta del Ruysch ebbe, per coloro che la tennero certa, <lb/>una grande efficacia rispetto al determinar le origini dell'Iride, e dei Corpi <lb/>ciliari, dicendo esser quella una propaggine della pagina coroidea esterna, e <pb xlink:href="020/01/1434.jpg" pagenum="309"/>questi una continuazione della pagina interna. </s>

<s>Ma quelle due appendici della <lb/>Coroide, i corpi ciliari vogliam dire e l'iride, hanno tanta importanza come <lb/>organi della vista, che non pu&ograve; tacersi da noi la loro particolare storia. </s></p><p type="main">

<s>Scrisse Galeno, come cosa avuta da'suoi predecessori, che dalla Coroide <lb/>si partono <emph type="italics"/>tenues quaedam productiones, et araneae similes,<emph.end type="italics"/> le quali giun&shy;<lb/>gono a toccare il cristallino, a cui fanno da ligamento. </s>

<s>Tu diresti, ei sog&shy;<lb/>giunge, che fossero que'sottilissimi processi altrettanti vasellini da recare <lb/>allo stesso cristallino il necessario alimento, se non si vedessero ritornare <lb/>indietro alla loro prima inserzione. </s>

<s>&ldquo; Revertitur nam immensam vasorum <lb/>tenuium sibi ipsis proprinquorum copiam quandam afferens, cum quibus <lb/>omnibus sursum in superiorem productionem inseritur, ut eorum insertio <lb/>palpebrarum pilis persimilis esse videatur. </s>

<s>Sic enim comparant, idque meo <lb/>iudicio non absurde, qui Naturae opera studiosius perscrutantur.... Cum <lb/>enim praedicta insertio in medium crystallinum, quod rotundum est, undi&shy;<lb/>que facta sit, circulus necessarius est factus, qui certe maximus est in chry&shy;<lb/>stallino, ipsumque in duo dividit &rdquo; (De usu partium, Op. </s>

<s>omnia, T. </s>

<s>I cit., <lb/>fol. </s>

<s>178). </s></p><p type="main">

<s>Nella risorta Anatomia, tacendosi dal Berengario di questo anello ci&shy;<lb/>liare, che tutto intorno circonda il cristallino, fu primo a rinnovellarne la <lb/>memoria il Vesalio. </s>

<s>Raffigurando mostruosamente l'Occhio in un circolo, <lb/>alla circonferenza del quale &egrave;, quasi per due anse, ricongiunto un altro cer&shy;<lb/>chio concentrico, assai minore, e per cui viene inteso il cristallino; son quelle <lb/>due anse, colla lettera di richiamo K, cos&igrave; dichiarate: &ldquo; Tunica ab Uvea <lb/>initium ducens, et ciliis seu palpebrarum pilis imagine correspondens, ac <lb/>interstitium pariter vitrei humoris ab aqueo &rdquo; (De hum. </s>

<s>corp. </s>

<s>fabrica cit., <lb/>pag. </s>

<s>643). </s></p><p type="main">

<s>Al sentir cos&igrave; i processi ciliari qualificarsi per una tunica, che fa da <lb/>tramezzo all'umor vitreo e all'acqueo, il Colombo disse che il Vesalio aveva <lb/>sognato, non essendo quelli presi per cigli altro che rughe impresse nel&shy;<lb/>l'Aracnoide, da quella parte che involge il cristallino. </s>

<s>&ldquo; Atque hae solae <lb/>sunt verae oculi membranae; quare ne expectetis dum ego de illa loquar <lb/>membrana instar ciliorum, quam Vesalius somniavit, nam lineae illae, quae <lb/>humorem cristallinum circumstant, in hac, quam paulo ante descripsimus <lb/>Aranea, collocantur &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>218). </s></p><p type="main">

<s>Ma il Falloppio esamin&ograve; la cosa con pi&ugrave; diligenza, e bench&egrave; convenisse <lb/>col Colombo non esser quella descritta dal Vesalio una tunica vera, la ri&shy;<lb/>conobbe nonostante per un corpo reale intessuto di fila, da rassomigliarsi <lb/>benissimo ai cigli impiantati sulle palpebre, che servissero a tener legate <lb/>insieme l'uvea e la membrana estrema del cristallino. </s>

<s>&ldquo; In ciliari corpore <lb/>illo, quod inter uveam et humorem crystallinum ac vitreum intercedit, a di&shy;<lb/>vino Vesalio discrepo. </s>

<s>Quia tunica minime est, sed potius nexus aut liga&shy;<lb/>mentum, quo Uvea iungitur extremae membranae crystallini. </s>

<s>Ideo non est <lb/>dicendum tunica, neque pro tunica numerandum, sed potius pro ligamento <lb/>quod nos <emph type="italics"/>Ciliare<emph.end type="italics"/> vocabimus &rdquo; (Observat. </s>

<s>anat, Op. </s>

<s>omnia cit., pag. </s>

<s>479). </s></p><pb xlink:href="020/01/1435.jpg" pagenum="310"/><p type="main">

<s>Anche l'Eustachio, nelle figure 8 e 9 della Tavola XL, disegn&ograve;, per cor&shy;<lb/>reggere l'errore del Vesalio, i corpi ciliari, a quel modo che gli aveva de&shy;<lb/>scritti il Falloppio, ma l'Acquapendente, non approvando cos&igrave; fatte novit&agrave;, <lb/>torn&ograve; col Colombo a dire che quegli immaginati corpi ciliari non son altro <lb/>che le vestigia delle fibre nere dell'uvea lasciate impresse sulla tunica re&shy;<lb/>tina, meglio che sul cristallino. </s>

<s>&ldquo; Comminiscuntur nescio quam ciliarem tu&shy;<lb/>nicam Anatomici circa crystallinum, quae circulus et copula tunicarum est, <lb/>quae nulla alia sunt quam nigra uveae tunicae fibrarum vestigia in crystal&shy;<lb/>linum, aut potius in retinam tunicam impressa &rdquo; (De oculo, Op. </s>

<s>omnia cit., <lb/>pag. </s>

<s>190). </s></p><p type="main">

<s>Parve il Casserio a parole consentire coll'Acquapendente, ma poi nelle <lb/>figure 7 e 9 della Tavola V dipinse, in ci&ograve; molto superiore all'Eustachio, <lb/>con mirabile verit&agrave;, e il primo fra gli Anatomici, i corpuscoli oblonghi, dai <lb/>quali, disposti a modo di raggi, s'intesse il corpo ciliare, e che pi&ugrave; tenui <lb/>dalla parte convessa del giro, e dalla parte concava pi&ugrave; crassi, danno allo <lb/>stesso corpo ciliare quasi la composizion di due anelli. </s>

<s>Non essendo per&ograve; <lb/>gl'Iconismi dichiarati da nessuna parola, e quelle espresse nel testo facendo <lb/>l'Autore consenziente col Colombo e col Fabrizio, si rimase la cosa inespli&shy;<lb/>cata, infintantoch&egrave; non l'avvert&igrave; il Morgagni, riscontrando quegli stessi cas&shy;<lb/>seriani iconismi nell'autopsia. </s>

<s>&ldquo; Quarum rerum omnium, cum Auctor nul&shy;<lb/>lam, non modo descripsisset, verum ne indicasset quidem, non ante illas <lb/>animadverti quam in bovillis oeulis ipse adnotassem &rdquo; (Epist. </s>

<s>anat. </s>

<s>XVII <lb/>cit., pag. </s>

<s>253, 54). </s></p><p type="main">

<s>Ma forse avea prima del Morgagni avvertite queste stesse cose Giovan <lb/>Batista Verle, che venuto da Venezia ai servigi della Corte medicea, nel ve&shy;<lb/>der lo Stenone sezionare alla presenza del granduca Ferdinando II l'occhio <lb/>di un coniglio, s'invogli&ograve; dello studio di quel mirabile organo, intorno al <lb/>quale scrisse un opuscolo di poche pagine, pubblicato nel 1679 in Firenze <lb/>col titolo <emph type="italics"/>Anatomia artifiziale dell'occhio umano.<emph.end type="italics"/> Fu la novit&agrave; ricevuta con <lb/>tanto applauso, che per diffonderla anche fra gli stranieri si pens&ograve; di tra&shy;<lb/>durre il detto opuscolo in latino, e il Mangeto lo reput&ograve; meritevole d'essere, <lb/>sotto questa forma, inserito nella sua scelta Biblioteca. </s></p><p type="main">

<s>Anche il Verle dunque disegn&ograve; e descrisse con molta verit&agrave; i corpi ci&shy;<lb/>liari, anzi and&ograve; tanto per le minute da contarne a una a una le fibre e le <lb/>semifibre, riducendole al preciso numero di ottanta (Anatomia artif. </s>

<s>cit., <lb/>pag. </s>

<s>33 e 35). </s></p><p type="main">

<s>Il Morgagni per&ograve;, poco curandosi di cos&igrave; fatte minuzie, ne'&sect;&sect; XI-XVI <lb/>dell'Epistola anatomica XVII, insegn&ograve; molte cose nuove e utilissime intorno <lb/>al vero sito, alla connessione, all'origine de'corpi ciliari e alla loro strut&shy;<lb/>tura, descrivendoli particolarmente nell'uomo come circondanti il Cristallino <lb/>a guisa di una elegantissima corona, da non potersi rassomigliar meglio che <lb/>al disco di un fiore raggiato, in cui sieno tutti i petali della stessa lunghezza. <lb/></s>

<s>&ldquo; Quin etiam interdum accidit, idque in homine, ut depositum cum vitreo <lb/>humorem crystallinum elegantissima corona, quasi radiati floris discum, ae-<pb xlink:href="020/01/1436.jpg" pagenum="311"/>qualibus omnibus et consimillimis oblongis petalis circumcirca ornatum, <lb/>conspexerim &rdquo; (Epist. </s>

<s>cit, pag. </s>

<s>255). </s></p><p type="main">

<s>Rivendicata cos&igrave; dunque alla scienza la verit&agrave; di quella corona di cigli, <lb/>che avevano intorno al cristallino descritta gli Anatomici antichi, si doman&shy;<lb/>dava qual fosse di que'cigli la propria e particolare struttura. </s>

<s>Vedemmo come <lb/>Galeno gli qualificasse per vasi, ma l'ufficio e la denominazione di lega&shy;<lb/>mento, dato a loro poi dal Falloppio, gli fece facilmente credere di natura <lb/>muscolosa a coloro che, per la teorica della visione, introdussero nel cristal&shy;<lb/>lino una certa mutabilit&agrave; di sito e di figura. </s>

<s>Le autorit&agrave; del Keplero e del <lb/>Cartesio erano s&igrave; grandi, e le loro teorie ottiche apparivano cos&igrave; seducenti, <lb/>che si tennero i corpi ciliari per un composto di fibre muscolose inserite <lb/>nel cristallino, senza troppo controversie, infino ai tempi del Bocrhaave, il <lb/>quale afferm&ograve; di aver pi&ugrave; volte vedute e riconosciute nell'occhio quelle stesse <lb/>fibre (Institutiones med., Venetiis 1722, pag. </s>

<s>65). Il Winslow incominci&ograve; a <lb/>dubitarne, e l'Hoow, non punto timoroso di tornare all'antico Galeno, disse <lb/>esser que'cigli intorno al cristallino, non fibre muscolari, ma vasi. </s>

<s>L'Haller <lb/>second&ograve; in principio la dottrina del venerato Maestro, poi parve esitare, e <lb/>all'ultimo, trattando nel Tomo V degli Elementi di Fisiologia del corpo ci&shy;<lb/>liare, sentenzi&ograve;: &ldquo; Musculosi nihil quidquam habet &rdquo; (Editio cit., pag. </s>

<s>382). </s></p><p type="main">

<s>Cos&igrave; i Ruischiani, che facevano i ciliari e l'iride derivare dalla Coroide, <lb/>come tutti coloro, che vedevano, in ogni modo fra'due organi una grande <lb/>somiglianza di struttura, pigliarono argomento di negar l'esistenza delle fibre <lb/>muscolose in essi corpi ciliari, perch&egrave; vedevano mancarne l'Iride stessa. </s>

<s>Que&shy;<lb/>sta, ne'misteriosi silenzi eloquente rivelatrice de'pi&ugrave; intimi affetti, prima di <lb/>lasciarsi lacerare al ferro invit&ograve; sempre gli Anatomici a contemplarne le di&shy;<lb/>vine bellezze. </s>

<s>Dalla pi&ugrave; rimota antichit&agrave;, che risale oltre a Ruffo, ebbe il <lb/>nome di Iride &ldquo; a coelestis Iridis, dice il Colombo, similitudine translatum &rdquo; <lb/>(De re anat. </s>

<s>cit., pag. </s>

<s>217), e Galeno, che fu de'pi&ugrave; infervorati in quelle <lb/>estetiche contemplazioni, fu de'primi altres&igrave; a filosofarvi attorno, esponendo <lb/>un certo suo singolare concetto, che trov&ograve; poi nel Vidio il pi&ugrave; fedele com&shy;<lb/>mento. </s>

<s>&ldquo; Scire autem licet circulum illum, qui in priore parte Oculi, inter <lb/>album et nigrum, deprehenditur, a coloris varietate Iridem appellari. </s>

<s>Effi&shy;<lb/>ciunt hanc varietatem septem substantiae, quae ibi inter se committuntur: <lb/>prima, ut ab externa parte incipias, est album oculi, secunda est tunica orta <lb/>a chordis musculorum, tertia cornea, quarta uvea, quinta retiformis, sexta <lb/>humor crystallinus, septima humor vitreus &rdquo; (De anat. </s>

<s>corp. </s>

<s>hum. </s>

<s>cit., <lb/>pag. </s>

<s>321) </s></p><p type="main">

<s>Ma il primo a dare delle colorate apparenze dell'Iride una spiegazione <lb/>originale crediamo sia stato il Molinetti, il quale attribuisce quella diversit&agrave; <lb/>di colori alle varie riflessioni subite dalla luce nell'incontrarsi in quelle mol&shy;<lb/>teplici superficie presentate dai ligamenti ciliari. </s>

<s>&ldquo; Decernendum est discri&shy;<lb/>mina huiusmodi oriri.... ex diversa proportione superficierum, in quas lu&shy;<lb/>men incidit, aut etiam quas traiiciit, non alia certe ratione quam columbarum <lb/>collo refulgentes observamus varios colores &rdquo; (Dissertationes anat. </s>

<s>cit., pag. </s>

<s>23). </s></p><pb xlink:href="020/01/1437.jpg" pagenum="312"/><p type="main">

<s>Il Valsalva, secondo riferisce il Morgagni, tutto intento alla contempla&shy;<lb/>zione di quella mirabile rete di vasi, che ricorrono per tutta la sostanza della <lb/>Coroide, credeva &ldquo; non exiguam Iridis portionem et coloris varietatem haud <lb/>aliunde quam a varia sanguiferorum vasculorum divisione ac complicatione <lb/>esse repetendam &rdquo; (Epist. </s>

<s>anat. </s>

<s>XVII cit., pag. </s>

<s>244). Ma l'Haller, dop'aver <lb/>descritti que'fiocchi, che si vedono vivamente fiammeggiare sulla lamina este&shy;<lb/>riore dell'Iride, e che dice essere di una sorprendente bellezza, &ldquo; ab his <lb/>flocculis ostendimus, ne conclude, colores Iridis pendere &rdquo; (Elem. </s>

<s>Phys. </s>

<s>T. </s>

<s>V <lb/>cit., pag. </s>

<s>369). </s></p><p type="main">

<s>Prende parte a variare il tuono di cotesti colori il pigmento disteso sulla <lb/>lamina interiore dell'Iride, e che &egrave; comune ai corpi ciliari e a tutta la Co&shy;<lb/>roidea. </s>

<s>Tal pigmento, osserv&ograve; l'Acquapendente, non solo tinge e macchia <lb/>del suo color nero, &ldquo; sed etiam, si abluatur, nigrities fere omnis abolitur, <lb/>et membrana cui inhaeret alba evadit, ut proinde non alium quam adsciti&shy;<lb/>tium huiusmodi nigrum colorem, si velis, nominare possis. </s>

<s>Cui quidem illud <lb/>rarius accidit quod hic color niger adscititius ubique non est. </s>

<s>Nam qua parte <lb/>Uvea et Choroides crystallinum, aqueum, corneam et omnino diaphana pu&shy;<lb/>raque oculorum corpora respiciunt, nigrities apparet, potius innata quam <lb/>apposita.... Unde tota Choroides hac parte tantum tingit qua Sclerotica con&shy;<lb/>tigua est. </s>

<s>Uvea vero neutrobique, cum interna facie aqueum humorem, <lb/>externa vero corneam respiciat contingatque &rdquo; (De oculo, Op. </s>

<s>omnia cit., <lb/>pag. </s>

<s>226). </s></p><p type="main">

<s>Il Morgagni, che avrebbe desiderato fosse veramente cos&igrave;, perch&egrave; allora <lb/>s'intenderebbe come, in tanto rimescolarsi dell'umor acqueo per le sue ca&shy;<lb/>mere, non rimanesse tinto di nero, trov&ograve; per esperienza che anche sull'Iride <lb/>il pigmento era ascitizio, per cui cred&egrave; bene d'accostarsi con coloro che di&shy;<lb/>cevano &ldquo; nigram materiam non extrinsecus insidere Choroidi, sed laminae <lb/>exteriori subiectam, per hanc translucere &rdquo; (Epist. </s>

<s>cit., pag. </s>

<s>254, 55). </s></p><p type="main">

<s>Stim&ograve; l'Acquapendente che fosse l'atramento coroideo escreto come fec&shy;<lb/>cia dal sangue, e non ritrovandosi nell'occhio manifesti organi secretori, ri&shy;<lb/>mase lungamente quella origine incerta, infintantoch&egrave; il Zinn non la rico&shy;<lb/>nobbe in quei filamenti fioccosi, ch'ei vide scaturire dalla faccia interna della <lb/>Membrana. </s>

<s>&ldquo; Quae cum ita sint, coniectura non parum inde confirmare vi&shy;<lb/>detur ex iisdem flocculis secerni pigmentum nigrum Choroidi obductum &rdquo; <lb/>(Descriptio oculi cit., pag. </s>

<s>48). </s></p><p type="main">

<s>Questo &egrave; ci&ograve; che riconobbero i Filosofi contemplativi intorno alla ele&shy;<lb/>gante variet&agrave; dei colori, che dipingono all'occhio il sottoposto ovario e gli <lb/>aperti petali del suo fiore. </s>

<s>Ma quando s'accorsero che quel fiore ora apriva, <lb/>ora chiudeva la sua corolla, per consolar gl'interiori spiriti sensitivi d'una <lb/>pi&ugrave; soave temperanza d&igrave; luce, e allora non perdonarono alla punta del ferro <lb/>anatomico, che ne ricerc&ograve; la pi&ugrave; intima testura delle fibre. </s>

<s>Perch&egrave; dunque <lb/>fu questa anatomia dell'Iride principalmente provocata dal singolar fatto <lb/>osservato della mobilit&agrave; della pupilla, sotto le varie impressioni della luce, <lb/>giova toccar qui di quel fatto brevemente la storia. </s></p><pb xlink:href="020/01/1438.jpg" pagenum="313"/><p type="main">

<s>Nel capitolo V del X libro <emph type="italics"/>De usu partium<emph.end type="italics"/> dice Galeno di avere osser&shy;<lb/>vato che, chiudendo un occhio e tenendo l'altro aperto, questo ha la pupilla <lb/>pi&ugrave; dilatata di quello. </s>

<s>Bench&egrave; sieno in s&egrave; le parole assai chiare, parve no&shy;<lb/>nostante il testo galenico a tutti oscuro, e ci&ograve; perch&egrave; la naturale osserva&shy;<lb/>zione non si descriveva secondo la verit&agrave;, come quella che veniva male in&shy;<lb/>formata dalla filosofica teoria. </s>

<s>Portava infatti questa teoria, che Galeno si <lb/>studi&ograve; di convalidare coll'esperienza, insufflando l'occhio estratto dall'orbita <lb/>dalla parte di dietro, e avvertendo che all'impeto del fiato l'Iride si con&shy;<lb/>traeva; portava, diciamo, che a moderar l'apertura del foro pupillare concor&shy;<lb/>resse esclusivamente la quantit&agrave; degli spiriti animali. </s>

<s>Or perch&egrave; all'occhio <lb/>aperto dovevano questi spiriti affluire in maggior copia che al chiuso, e perci&ograve; <lb/>se ne concludeva, contro l'esperienza dei fatti, ch'era la pupilla pi&ugrave; ristretta <lb/>in questo caso che in quello. </s></p><p type="main">

<s>Ma Colui, che fu tra gli antichi il pi&ugrave; valido promotore del metodo spe&shy;<lb/>rimentale, riguardando l'Occhio, non come subietto anatomico ma come or&shy;<lb/>gano delle osservazioni celesti, ebbe occasione di riconoscere, secondo il vero <lb/>esser loro, i moti pupillari, quando insegn&ograve; nell'Arenario il modo di misu&shy;<lb/>rar con la pi&ugrave; scrupolosa esattezza l'apparente diametro del Sole. </s>

<s>Bench&egrave; <lb/>per&ograve; le parole &ldquo; porro quoniam visus non respicit ab uno puncto, sed ab <lb/>aliqua quantitate &rdquo; e la prescrizione, che tosto si soggiunge, di adattare a <lb/>questa maggiore o minor quantit&agrave; &ldquo; aliqua magnitudo teres non minor visu &rdquo; <lb/>(Archimedis Opera, Parisiis 1615, pag. </s>

<s>453), insinuino e presuppongano la <lb/>mobilit&agrave; della pupilla, rimase in quella universale decadenza degli studii la <lb/>gentile osservazione obliata, infintantoch&egrave; gli ecclissati splendori archimedei <lb/>non tornarono a illuminare le riaperte vie ai progressi delle scienze speri&shy;<lb/>mentali, rivelandosi all'ingegno di Paolo Sarpi. </s>

<s>Egli, rimeditando sui libri <lb/>del Matematico di Siracusa, e com'era suo uso riducendo le speculazioni <lb/>all'esperienza, trov&ograve;, nell'adattare i diametri de'cilindri torniti all'apertura <lb/>della pupillla, che questa da un momento all'altro variava nella grandezza. </s>

<s><lb/>Della quale maravigliosa variabilit&agrave; ricercando la causa, non seppe altro ve&shy;<lb/>dere se non ch'ella dipendeva dalla varia intensita della luce. </s></p><p type="main">

<s>Giovan Batista Porta, in quel tempo, come s'ha dalla prefazioncella al <lb/>VII libro della Magia naturale &ldquo; Venetiis eodem studio invigilans, cognovit <lb/>R. M. </s>

<s>Paulum Venetum, a quo aliqua didicisse fatetur &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1651, <lb/>pag. </s>

<s>287). Un giorno dunque fra Paolo, sedendo coll'amico fra le chiuse <lb/>pareti della sua cella, presso a por fine al dotto colloquio tenuto con lui, lo <lb/>invita per curiosit&agrave; a guardargli la pupilla degli occhi, e a stimarne la gran&shy;<lb/>dezza dell'apertura. </s>

<s>Poi si leva movendosi verso la finestra e, stato alquanto <lb/>a riguardare l'aperto cielo-vivamente irraggiato dal Sole, invita nuovamente <lb/>il Porta a guardar quel medesimo occhio, in cui la pupilla, che appariva <lb/>dianzi grande quanto una lente, ora agguagliava appena il capo di uno spillo. </s>

<s><lb/>Sorpreso dalla novit&agrave;, il Fisico napoletano pubblic&ograve; nel suo ottico trattato <lb/><emph type="italics"/>De refractione<emph.end type="italics"/> il fatto in tal forma, da lasciarvi impresse visibilmente le <lb/>vestigie della secreta storia ora svelata. </s>

<s>&ldquo; Si amici oculos, egli dice, aper-<pb xlink:href="020/01/1439.jpg" pagenum="314"/>tos intentosque vehementius solis lumini obiectos contemplaberis, adeo pu&shy;<lb/>pillam coarctari videbis, ut per angustissimum foramen vix tenuis acus aciem <lb/>admitteret. </s>

<s>Eosdem, si in obscuro cubiculo convertat, parvo temporis curri&shy;<lb/>culo foramen adeo dilatari conspicies, ut fere lentem capiat.... Huins rei <lb/>instrumento certius fies compos quod Archimedes in dignoscenda solis quan&shy;<lb/>titate usus est &rdquo; (Neapoli 1593, pag. </s>

<s>74). </s></p><p type="main">

<s>Poco dopo avvenute queste cose, occorse all'Acquapendente, che non <lb/>ne sapeva ancora nulla, di maravigliarsi della variabilit&agrave; della pupilla osser&shy;<lb/>vata ne'gatti. </s>

<s>E vedendola passare in quelle alterne vicende di maggiore e <lb/>di minor grandezza, in cos&igrave; brevi intervalli di tempo, pens&ograve; a principio che <lb/>fossero que'moti volontarii. </s>

<s>Non vedendoci per&ograve; muscoli atti a far ci&ograve;, ri&shy;<lb/>mase in dubbio. </s>

<s>Comunicata intanto l'osservazione al suo amico Paolo Sarpi, <lb/>gli fu da lui risposto che egli aveva osservato avvenir ci&ograve; nella pupilla degli <lb/>uomini stessi, com'aveva gi&agrave; detto e fatto vedere al Porta. </s>

<s>Ma l'osserva&shy;<lb/>zione dell'Acquapendente invogli&ograve; fra Paolo a fare altre numerose espe&shy;<lb/>rienze, dalle quali finalmente concluse che il restringersi la pupilla a una <lb/>luce pi&ugrave; intensa, e il dilatarsi a una luce pi&ugrave; rimessa, era una propriet&agrave; <lb/>dell'occhio in tutti gli animali. </s>

<s>&ldquo; Res igitur, cos&igrave; l'Acquapendente stesso <lb/>racconta, cum amico quodam nostro communicata, ille tandem forte id obser&shy;<lb/>vavit, scilicet non modo in cato, sed in homine et quocumque animali, fo&shy;<lb/>ramen Uveae in maiori luce contrahi, in minori dilatari. </s>

<s>Quod arcanum <lb/>observatum est, et mihi significatum a Rev. </s>

<s>patre magistro Paulo Veneto.... <lb/>mathematicarum disciplinarum, praecipueque Optices, maxime studioso &rdquo; (De <lb/>oculo, Opera omnia cit., pag. </s>

<s>229). </s></p><p type="main">

<s>Fecero osservare alcuni per&ograve; che a quell'arcano erasi Galeno stesso stu&shy;<lb/>diato di togliere la pi&ugrave; densa parte del velo, e che l'osservazione del dila&shy;<lb/>tarsi e del restringersi la pupilla ne'gatti l'avea il Cardano accennata nei <lb/>suoi libri <emph type="italics"/>De subtilitate<emph.end type="italics"/> parecchi anni prima dell'Acquapendente. </s>

<s>Giovan <lb/>Batista Ruschi, anatomico pisano, cos&igrave; infatti scriveva in un suo trattato <emph type="italics"/>De <lb/>visus organo<emph.end type="italics"/> pubblicato in Pisa nel 1631: &ldquo; Pupillae motum, nec mille lin&shy;<lb/>guis exprimendus, quam obscure Galenus agnovit?... Catos existimat Hye&shy;<lb/>ronimus Cardanus, in libris <emph type="italics"/>De subtilitate,<emph.end type="italics"/> oculos voluntarie contrahere ac <lb/>laxare &rdquo; (pag. </s>

<s>42). </s></p><p type="main">

<s>Quando nonostante, nel 1632, Galileo pubblic&ograve; i Dialoghi dei due mas&shy;<lb/>simi Sistemi, volle far credere l'osservazione dei moti della pupilla, e l'ap&shy;<lb/>plicazione di lei a ritrovar l'angolo del concorso de'raggi secondo il metodo <lb/>archimedeo sapientemente illustrato dal Sarpi, per cosa del tutto nuova. </s>

<s>In <lb/>colorir tali novit&agrave;, noi svelammo a varie occasioni la scaltrissima arte del&shy;<lb/>l'Autore, ma perch&egrave; l'Acquapendente non seppe entrare per la nuova via <lb/>de'progressi, e l'opera del Porta fu repressa e avvilita dalla prepotente vit&shy;<lb/>toria del suo rivale, si pu&ograve; creder vero quel che il Salviati dice, che cio&egrave; <lb/>&ldquo; tra mille, che hanno osservato ne'gatti stringersi e allargarsi assaissimo <lb/>la pupilla dell'occhio, non ve ne sono due n&egrave; forse uno che abbia osser&shy;<lb/>vato un simile effetto farsi nelle pupille degli uomini &rdquo; (Alb. </s>

<s>I, 394); come <pb xlink:href="020/01/1440.jpg" pagenum="315"/>dall'altra parte &egrave; verissimo che si diffusero da que'Dialoghi, insiem con <lb/>questa ch'&egrave; il soggetto del presente discorso, moltissime altre notizie, le <lb/>quali apparvero e furono credute per nuove, perch&egrave; rimaste immote nelle <lb/>neglette pagine di pochi dotti. </s></p><p type="main">

<s>Ripensando poi a questa larga diffusion della scienza, per opera de'Dia&shy;<lb/>loghi galileiani; considerando che aveva il Sarpi lasciate vive ancora in Ve&shy;<lb/>nezia le tradizioni de'suoi ritrovati; che il trattato dell'Acquapendente fu <lb/>pubblicato in Padova e quel del Ruschi in Pisa; fa certo maraviglia che il <lb/>Verle veneziano scrivesse in Firenze di avere osservato i moti della pupilla <lb/>farsi solo nei bambini, e ne'fanciulli dai quattro ai quindici anni, che hanno <lb/>l'iride di color celestino, concludendo: &ldquo; Nelle pupille poi, d'altro colore <lb/>che de'suddetti, non ho fatta fin qui considerazione se ci&ograve; succeda o altri&shy;<lb/>menti &rdquo; (Anat. </s>

<s>artifiz. </s>

<s>cit., pag. </s>

<s>38). </s></p><p type="main">

<s>Diminuisce per&ograve; quella maraviglia ripensando che il Verle era uomo <lb/>pratico, e che la storia dell'Anatomia non aveva avuto ancora i suoi eruditi <lb/>e diligenti cultori, i quali, quando in sul cominciar del secolo XVIII si det&shy;<lb/>tero a quello studio, ritrovarono compiacenti che l'osservazione, la quale <lb/>Galileo scommetteva non essere stata fatta a'suoi tempi che forse da uno <lb/>solo, si leggeva in numerosi e antichissimi autori. </s></p><p type="main">

<s>Il Morgagni, nell'<emph type="italics"/>Adversaria anatomica I,<emph.end type="italics"/> annunziava di aver trovato <lb/>rivelato l'arcano nelle Annotazioni anatomiche dell'Achillini, dalle quali tra&shy;<lb/>scrive in calce queste parole: &ldquo; Uvea, cuius foramen est pupilla, aperitur <lb/>in mediocri lumine, excessivo constringitur in suo foramine &rdquo; (Patavii 1719, <lb/>pag. </s>

<s>54). Noi non abbiamo potuto consultare queste <emph type="italics"/>Annotationes<emph.end type="italics"/> del Filo&shy;<lb/>sofo bolognese, le quali del resto non si trovano inserite nell'<emph type="italics"/>Opera omnia <lb/>in unum collecta<emph.end type="italics"/> da Panfilio Monti, e per la seconda volta nel 1568 pub&shy;<lb/>blicate in Venezia; ci&ograve; che ingerisce in noi qualche dubbio, reso anche pi&ugrave; <lb/>forte dall'essere esse Annotazioni postume. </s>

<s>Il saper dall'altra parte che <lb/>l'Achillini, tutto involto nel lezzo peripatetico, non era anatomico, ci fa so&shy;<lb/>spettar che avesse avuto la notizia dalla viva voce di Leonardo da Vinci, il <lb/>quale, nel dipinger dal vero gli occhi, badando ad ogni minuzia, disse di <lb/>essersi accorto che l'apertura della pupilla, secondo le varie luci, strana&shy;<lb/>mente variava di grandezza. </s></p><p type="main">

<s>Nell'Epistola anatomica XVII poi soggiunse lo stesso Morgagni ch'era <lb/>tra gli osservatori del fatto da annoverar non solo l'Achillini, &ldquo; sed ipsum <lb/>Rhazen longe antiquiorem, et locupletiorem testem &rdquo; da cui trascrive le se&shy;<lb/>guenti parole: &ldquo; Constring&igrave;tur enim cum lumen est multum, et dilatatur <lb/>cum est in obscuro. </s>

<s>Hoc autem foramen est pupilla &rdquo; (Editio cit, pag. </s>

<s>248). <lb/>L'Haller (Elem. </s>

<s>Phys. </s>

<s>T. </s>

<s>V sit., pag. </s>

<s>374) aggiunse a Rhazen e ad Avi&shy;<lb/>cenna anche Areteo: altri eruditi potrebbero con facilit&agrave; arricchir la storia <lb/>di altri nomi forse pi&ugrave; antichi, ma no certo pi&ugrave; illustri di quello di Archi&shy;<lb/>mede, dall'Arenario del quale zampillarono le tradizioni com'acqua viva, che <lb/>viene da lontane sorgenti a riversarsi nel fiume della scienza. </s></p><p type="main">

<s>Se il Sarpi, che fu il primo ad accogliere queste tradizioni, oltre all'os-<pb xlink:href="020/01/1441.jpg" pagenum="316"/>servare il fatto attendesse a specularne le cause, per verit&agrave; non sappiamo, <lb/>ond'&egrave; che riman solo per noi l'Acquapendente, il quale persuaso dal difetto <lb/>di muscoli non dover essere i moti della pupilla volontarii, e dall'altra parte <lb/>considerando non poter quegli stessi moti esser causati, come Galeno inse&shy;<lb/>gnava, dagli spiriti affluenti, che produrrebbero effetti necessariamente con&shy;<lb/>trarii: rassomigli&ograve; il restringersi e il dilatarsi dell'iride alla sistole e alla <lb/>diastole del cuore, o meglio alla flaccidit&agrave; e alla turgenza de'corpi caver&shy;<lb/>nosi. </s>

<s>&ldquo; Quocirca dicere satius est motus huius efficientem causam proficisci <lb/>a propria Uveae tunicae facultate, quae hunc motum efficiendi vim a Na&shy;<lb/>tura habeat, perinde ac cor dilatandi se et contrahendi potentiam obtinet. </s>

<s><lb/>Melius autem forte fuerit virilis pudendi motui uveae foraminis motum assi&shy;<lb/>milare &rdquo; (De oculo, Op. </s>

<s>omnia cit., pag. </s>

<s>230). </s></p><p type="main">

<s>Poco dopo, il Cesalpino attribu&igrave; i moti della pupilla a certe speculate <lb/>ragioni, che rimaste soffocate ne'libri di lui dalla lussuria d'immaginati si&shy;<lb/>stemi, quando questi dovettero inaridire, quelle tornarono nuovamente alla <lb/>luce. </s>

<s>&ldquo; Causa dilatationis, egli dice nel cap. </s>

<s>XLVI del V libro <emph type="italics"/>Artis me&shy;<lb/>dicae,<emph.end type="italics"/> est Uveae repletio aut a spiritu, aut ab humoribus collectis intra <lb/>Uveam..... Constrictionis causa est inanitio &rdquo; (Romae 1603, pag. </s>

<s>284). </s></p><p type="main">

<s>Gl'immaginati sistemi che si diceva son quelli del Cartesio. </s>

<s>Che vuole <lb/>egli dire se l'Acquapendente non ha trovato nulla nell'iride di muscolare, <lb/>n&egrave; perci&ograve; di volontario? </s>

<s>Il Filosofo ha arbitrio di prescrivere alla Natura <lb/>quel che gli fa bisogno per la sua teoria. </s>

<s>Dunque il forame della pupilla <lb/>&ldquo; speciem exigui musculi habet, qui diducitur aut contrahlitur, prout obiecta <lb/>quae contuemur vel propius vel longius absunt, vel magis aut minus illu&shy;<lb/>minantur, vel prout magis aut minus curiose illa contemplari animus est &rdquo; <lb/>(Dioptrices, cap. </s>

<s>III, Francofurti ad M. 1692, pag. </s>

<s>54). Dunque lo sfintere, <lb/>che ha da fare al Filosofo cos&igrave; fatti servigi, bisogna che sia necessariamente <lb/>un muscolo volontario &ldquo; licet ut plurimum nobis ignorantibus peragatur, <lb/>quemadmodum labiorum et linguae motus, pronuntiationi inserviens, volun&shy;<lb/>tarius dicitur, quoniam loquendi voluntatem sequitur, licet saepissime igno&shy;<lb/>remus qualem singulae literae requirant &rdquo; (Ibid., pag. </s>

<s>54, 55). </s></p><p type="main">

<s>Quando Ernesto Sthal introdusse nelle questioni fisiologiche il fermento <lb/>della Filosofia cartesiana, soggiogata la scienza da due cos&igrave; prepotenti auto&shy;<lb/>rit&agrave;, per seguir le speculate teorie non si curarono le osservazioni dei fatti. </s>

<s><lb/>Anche i pi&ugrave; liberi ingegni, e quelli stessi che facevano scuola da s&egrave;, nel <lb/>particolar proposito dei moti della pupilla, convennero che doveva al difetto <lb/>delle sensate esperienze supplir l'acume filosofico della mente. </s>

<s>Il Ruyschio <lb/>parl&ograve; chiaro, e disse le fibre orbicolari, necessarie per la reale esistenza <lb/>dello sfintere cartesiano, &ldquo; non tam luculenter conspici posse, quin oculi <lb/>mentis in auxilium sint vocandi &rdquo; (Epist. </s>

<s>ad Wedelium cit., pag. </s>

<s>10). E il <lb/>Boerhaave, immaginandosi che le fibre della Coroide, entrate nell'Uvea, di&shy;<lb/>ventino muscolari, movendo dalla circonferenza esterna e intessendosi a <lb/>compor lo stesso sfintere cartesiano intorno al lembo orbicolare, che circo&shy;<lb/>scrive il foro della pupilla; &ldquo; Unde patet, ne conclude, orbiculares constrin-<pb xlink:href="020/01/1442.jpg" pagenum="317"/>gere, longitudinales dilatare foramen pupillae &rdquo; (Institutiones med. </s>

<s>cit., <lb/>pag. </s>

<s>65). </s></p><p type="main">

<s>In Italia, in grazia degli istituti e dell'opera de'discepoli di Galileo, ri&shy;<lb/>maste pi&ugrave; che altrove salve le menti dal contagio cartesiano, indipendente&shy;<lb/>mente da ogni autorit&agrave;, si vollero esaminare i fatti. </s>

<s>Fu de'primi il Valsalva, <lb/>il quale, al riferir del Morgagni, distesa l'iride sopra un vetro, bench&egrave; vi <lb/>vedesse apparir le fibre da lui credute muscolari andar dalla circonferenza <lb/>esterna alla orbicolare della pupilla, &ldquo; nullas autem in annuli modum cir&shy;<lb/>cumductas adnotavit &rdquo; (Epist. </s>

<s>anat. </s>

<s>XVII cit., pag. </s>

<s>244). Il Morgagni stesso <lb/>poi con le osservazioni sue proprie conferm&ograve; quelle del suo Maestro, asse&shy;<lb/>verando che tra le fibre dell'iride, diligentemente osservate attraverso a una <lb/>lamina di vetro, non ne aveva potuto avvertir nessuna, che si rigirasse in&shy;<lb/>torno alla pupilla a guisa di anello. </s>

<s>&ldquo; Cum has, sive fibrillas sive vascula, <lb/>non in eo tantum sed et in compari oculo ad eumdem modum conspexissem, <lb/>nulla usquam annularia filamenta potui animadvertere &rdquo; (ibid., pag. </s>

<s>250). </s></p><p type="main">

<s>A confermare anche meglio ci&ograve; che, intorno alle musculose fibre orbi&shy;<lb/>colari della pupilla, avevano affermato i due insigni nostri Italiani, concor&shy;<lb/>sero poco dopo il Duvernoi e il Weitbrecht: poi il Zinn appose a quelle affer&shy;<lb/>mazioni l'autorevole suo suggello, dicendo: &ldquo; Neque ipse certe crediderim <lb/>fibras musculares unquam ullo microscopio demonstrari posse &rdquo; (Descriptio <lb/>oculi cit., pag. </s>

<s>91). Ond'&egrave; che pot&egrave; coll'Haller la scienza de'fatti contro le <lb/>immaginazioni del Cartesio finalmente sentenziare: &ldquo; Circulus in Uvea con&shy;<lb/>strictor nullus est &rdquo; (Elem. </s>

<s>Physiol. </s>

<s>T. </s>

<s>V cit., pag. </s>

<s>378). </s></p><p type="main">

<s>Ma pure il Cartesio stesso aveva preteso che le sue filosofiche dottrine <lb/>fossero non immaginazioni ma fatti, richiamando i dubbiosi alle esperienze. <lb/></s>

<s>&ldquo; Et fidem huic rei pueri oculus cuivis dubitanti astruere poterit. </s>

<s>Nam s&igrave; <lb/>iusseris ut vicinum aliquod obiectum attente respiciat, videbis aliquanto <lb/>arctius pupillam eius contrahi, quam si aliud multo remotius.... Et obser&shy;<lb/>vandum hunc motum voluntarium esse dicendum &rdquo; (Dioptrices cap. </s>

<s>cit., <lb/>pag. </s>

<s>54). I Cartesiani poi, specialmente seguaci dello Stahl, aggiunsero fra <lb/>le molte altre cose essere in arbitrio del fanciullo il restringere la pupilla <lb/>e il dilatarla, bench&egrave; poi gli adulti dimentichino questo gioco. </s>

<s>Ai quali final&shy;<lb/>mente rispose la vera scienza sperimentale, per bocca del medesimo Haller: <lb/>&ldquo; Verum haec omnia nimia sunt et facillime experimentis refutantur. </s>

<s>Im&shy;<lb/>peret sibi ipsi homo ut vel constringat pupillam vel relaxet: nihil efficiet, <lb/>dum idem erit luminis vigor &rdquo; (Elem. </s>

<s>Phys. </s>

<s>cit., pag. </s>

<s>378). </s></p><p type="main">

<s>Francata cos&igrave; dunque la scienza dal giogo degli immaginati sistemi, si <lb/>apparecchi&ograve; a investigare il mistero dei moti pupillari, esaminando con gran <lb/>diligenza l'Iride nella sua vera struttura. </s>

<s>L'esame cominci&ograve; dal Valsalva, il <lb/>quale, al riferir del Morgagni, osservando l'iride elegantissima di una lepre, <lb/>not&ograve; che tutta era intessuta di fibre &ldquo; quae ab ambitu centrum versus fe&shy;<lb/>runtur &rdquo; (Epist. </s>

<s>anat. </s>

<s>XVII cit., pag. </s>

<s>244). Il Morgagni stesso poi descrisse <lb/>quell'intrecciamento di fibrille fosche &ldquo; ad convexum zonulae ambitum, quam <lb/>minorem illum esse Ruyschii circulum non dubitavi &rdquo; (ibid., pag. </s>

<s>250). </s></p><pb xlink:href="020/01/1443.jpg" pagenum="318"/><p type="main">

<s>Ma della fabbrica striata dell'Iride non fu il bellissimo spettacolo da <lb/>nessun altro meglio descritto che dal Zinn, contemplandolo col microscopio in <lb/>un occhio recente. </s>

<s>&ldquo; In annulo enim maiori apparent fibrae innumerae ma&shy;<lb/>gis minusve albidae et gryseae, aliae maiores, quae plerumque magis can&shy;<lb/>didae, aliae minores et tenuiores minusque diluti coloris, omnes parallelae <lb/>et densissimo ordine sibi appositae ut plures recipere non posse videatur. </s>

<s><lb/>Ab ipso ergo ambitu exteriori Iridis versus annulum minorem convergunt, <lb/>serpentino flexu incedentes, eo maioribus flexionibus quo iris angustior et <lb/>pupilla amplior fuerit..... Ubi autem ad zonulam, quae pupillam proxime <lb/>ambit, sive ad annulum minorem ventum est, fibrae maiores saepe in duos <lb/>ramos abire videntur, qui ad angulum satis obtusum discedunt.... Ex mu&shy;<lb/>tua ergo coniunctione trunculorum inter se ad angulos acutos coeuntium, <lb/>et per arcus sibi unitorum formari videtur circulus serratus et flexuosus.... <lb/>Ex ora illa serrata, quae circuli instar maiorem annulum terminat, et inpri&shy;<lb/>mis ex convexitate arcuum, ex duobus trunculis inter se unitis factorum, <lb/>oriuntur plurimae fibrae tenuissimae, parallelae fere, rectae in radiorum mo&shy;<lb/>dum versus centrum pupillae convergentes, rariores et saepe intervallo quo&shy;<lb/>dam inter se disiunctae, subtilissima cellulositate inter se connexae, quae <lb/>annulum interiorem foramine circulari pertusum constituunt &rdquo; (Descriptio <lb/>cit., pag. </s>

<s>86-88). </s></p><p type="main">

<s>Tali essendo gli organi inservienti al moto dell'Iride, si domandavano <lb/>le ragioni di que'moti. </s>

<s>E giacch&egrave; l'Acquapendente gli aveva rassomigliati <lb/>a&igrave;la sistole e alla diastole del cuore si domandava a qual fase dell'Iride cor&shy;<lb/>rispondesse la diastole, ossia lo stato naturale, e rispondevasi comunemente <lb/>che al restringimento di lei, ossia alla dilatazione della pupilla. </s>

<s>Pareva con&shy;<lb/>fermassero questa opinione i fatti osservati in caso di sincope o di morte, <lb/>ma il Zinn trov&ograve; che ci&ograve; avveniva infintantoch&egrave; l'occhio si lasci nel suo sito <lb/>naturale, ma estratto dal cadavere, &ldquo; iteratis experimentis edoctus fui, egli <lb/>dice, pupillam post mortem sensim angustiorem factam fuisse.... Cum an&shy;<lb/>tem ad explicandum hoc phaenomenon neque vires contractiles fibrarum <lb/>orbicularium, neque vis irruens humorum in animale diu ante mortuo in <lb/>auxilium vocari possint, parum abest quin ad credendum adducar dilatatio&shy;<lb/>nem multum omnino pendere ab elasticitate fibrarum Iridis longitudinalium, <lb/>contractionem autem fere esse naturalem et sponte sequi, si fibrae longitu&shy;<lb/>dinales plane relaxatae, et a puncto fixo cui adnectuntur divisae fuerint &rdquo; <lb/>(ibid., pag. </s>

<s>102). </s></p><p type="main">

<s>Cos&igrave; tornavasi a ripetere la sentenza antica del Cesalpino: <emph type="italics"/>Constrictio&shy;<lb/>nis causa est inanitio.<emph.end type="italics"/> Se non che non pareva credibile che la vivacissima <lb/>attivit&agrave; della luce si dovesse all'ultimo ridurre ad una semplice inanizione. </s>

<s><lb/>Non fa perci&ograve; maraviglia se i Fisiologi non convennero col Zinn, reputando <lb/>pi&ugrave; ragionevole interpetrare a dovere un concetto sovvenuto all'Acquapen&shy;<lb/>dente, il quale, risaputo dal Sarpi il fatto che la pupilla si restringeva al&shy;<lb/>l'aperta luce e si dilatava nell'ombra, disse che avrebbe creduto dovere avve&shy;<lb/>nire tutto al contrario, &ldquo; quod lucis natura potius sit disgregare, dilatareque, <pb xlink:href="020/01/1444.jpg" pagenum="319"/>tenebrarum vero constringere, densare et comprimere &rdquo; (De oculo, Op. </s>

<s>omnia <lb/>cit., pag. </s>

<s>229). </s></p><p type="main">

<s>Ma i Fisiologi trovarono la verit&agrave; in quel che aveva dato occasione di <lb/>dubitare all'Acquapendente, il quale non pens&ograve; che il dilatamento della pu&shy;<lb/>pilla era una conseguenza necessaria della restrizione dell'Iride. </s>

<s>Ammesso <lb/>perci&ograve; come vero che la luce, colla sua propria attivit&agrave;, spieghi le pliche <lb/>serpentinose delle fibre, e distenda le cellule delle strie, confermarono con&shy;<lb/>tro il Zinn la pi&ugrave; comune opinione, che cio&egrave; sia la pupilla dilatata e non <lb/>ristretta nello stato suo naturale. </s>

<s>&ldquo; Videtur, scrisse l'Haller, potius causa <lb/>esse in irritante luce, quae, excitatis viribus, iridem introrsum pellat, evo&shy;<lb/>lutis plicis serpentinis vasorum et striarum cellulosarum, ut in rectitudinem <lb/>conversae iridem dilatent.... Naturalis ergo status Iridis foret angustia et <lb/>pupillae latitudo &rdquo; (Elem. </s>

<s>Phys. </s>

<s>T. cit., pag. </s>

<s>378). </s></p><p type="main">

<s>Cos&igrave;, essendo naturalmente aperte, chiude da s&egrave; la luce le gelose cor&shy;<lb/>tine nell'entrare addentro al riposto talamo, sopra cui ella trova mollemente <lb/>distesa quella tela, in filar la quale e in lavorarla la Natura us&ograve; la sua mas&shy;<lb/>sima industria. </s>

<s>Che fosse la sottilissima orditura veramente filata dalle pi&ugrave; <lb/>intime viscere del cervello, lo dissero gli Anatomici pi&ugrave; antichi, e furono i <lb/>loro detti solennemente confermati da Galeno, il quale anzi dubit&ograve; se con&shy;<lb/>venisse a quel nobilissimo e principale organo della vista il nome di mem&shy;<lb/>brana &ldquo; cum, si exemptam ipsam seposueris, in unum acervum coniiciens, <lb/>tibi plane videbere videre cerebri portionem quamdam exemptam &rdquo; (De usu <lb/>partium, Opera omnia cit., T. I, fol. </s>

<s>177); espressione fra'tanti altri ripe&shy;<lb/>tuta da Realdo Colombo (De re anat. </s>

<s>cit., pag. </s>

<s>218). </s></p><p type="main">

<s>La rassomigliarono a principio alle tele di ragno per la testura, e perci&ograve; <lb/>la chiamarono Aracnoidea: poi, rispetto principalmente alla figura dell'am&shy;<lb/>bito e del fondo, la paragonarono o a un uovo dimezzato o a una rete da <lb/>pescatori. </s>

<s>&ldquo; Est enim hoc involucrum, dice il Vesalio, forma dimidiato tan&shy;<lb/>tum ovo comparandum, aut minori piscatorum reti, quod uni accomodatur <lb/>baculo, et ex ampla basi dimidiati globi modo in obtusum mucronem fer&shy;<lb/>tur. </s>

<s>Ab huiusmodi enim retis imagine arbitror praesens involucrum Graecis <lb/><emph type="italics"/>amphiblistroides<emph.end type="italics"/> muncupatum fuisse &rdquo; (De hum. </s>

<s>corp. </s>

<s>fabrica cit., pag 647). </s></p><p type="main">

<s>Questo nome di Amfiblistroide, derivato <emph type="italics"/>a circumiiciendo,<emph.end type="italics"/> indica che il <lb/>paragone toccava semplicemente la figura della Retina distesa e applicata <lb/>sull'umor vitreo, ma Herofilo, come not&ograve; l'Acquapendente (De oculo cit., <lb/>pag. </s>

<s>191), aveva inteso di rassomigliarla alle stesse reti anche nella testura <lb/>delle maglie. </s>

<s>Notabile che sotto questa forma reticolare fosse la membrana <lb/>descritta da tutti gli Anatomici per tanti secoli, infino al Valsalva, il quale <lb/>usc&igrave; inaspettatamente a dire: &ldquo; Sciatis hanc non in retis formam construc&shy;<lb/>tam esse, ut communiter docent Anatomes magistri. </s>

<s>Verum res ita se habet: <lb/>Nervus opticus interna sui substantia oculi cameram ingreditur, dimissa prius <lb/>pia meninge pro tunica sclerotica, arachnoide vero pro coroide. </s>

<s>Statim au&shy;<lb/>tem ac ingressus est, radiatim expanditur in quamplurima filamenta, quae <lb/>versus peripheriam excurrunt usque ad unionem lentis crystallinae cum vi-<pb xlink:href="020/01/1445.jpg" pagenum="320"/>treo humore, quibus duobus, una cum ciliari processu, firmiter adhaeret &rdquo; <lb/>(Dissertationes anat. </s>

<s>cit., pag. </s>

<s>142). </s></p><p type="main">

<s>La testura dell'Amfibilistroide in ogni modo, o reticolare come la dice&shy;<lb/>vano gli Anatomici, o raggiata come la descrisse il Valsalva, dipendeva dalla <lb/>struttura del nervo ottico, dalla sostanza midollare del quale convenivano <lb/>tutti che si espanda. </s>

<s>Una lunga questione ebbero per&ograve; gli Anatomici del se&shy;<lb/>colo XVI e XVII intorno alla struttura di quel nervo, ordinato a riferire le <lb/>impressioni degli oggetti illuminati al cervello. </s>

<s>Herofilo disse di avere osser&shy;<lb/>vato in ciascun nervo ottico reciso due pori, che Cicerone, nel III libro <emph type="italics"/>De <lb/>natura Deorum,<emph.end type="italics"/> chiam&ograve; le vie, per le quali gli spiriti visivi giungono dalle <lb/>pi&ugrave; intime sedi dell'anima agli occhi. </s>

<s>Confermata l'osservazione di Herofilo <lb/>da Galeno, il Berengario disse che, sebbene i nervi ottici, &ldquo; secundum ali&shy;<lb/>quos sint notabiliter perforati, hoc tamen negat sensus in mortuo animali &rdquo; <lb/>(Isagogae breves, Venetiis 1535, fol. </s>

<s>52). E il Vesalio neg&ograve; assolutamente il <lb/>fatto ne'vivi e nei morti. </s></p><p type="main">

<s>Consentirono in ci&ograve; col Vesalio il Colombo, il Valverde e il Falloppio, <lb/>ma l'Eustachio insorse a rivendicare Galeno in quell'<emph type="italics"/>Examen Ossium et <lb/>de motu capitis,<emph.end type="italics"/> che dette tanta occasione di mormorar contro l'Autore <lb/>agl'infervorati seguaci del divino Brussellese. </s>

<s>Dicevano ch'egli sviava la fa&shy;<lb/>cile giovent&ugrave; dal secondare i progressi della scienza, e che s'era messo a <lb/>difender Galeno, non punto per amor del vero, ma per una odiosa rivalit&agrave; <lb/>col Vesalio. </s>

<s>Dalle quali accuse si difendeva l'Eustachio innanzi al suo ca&shy;<lb/>rissimo Fabio Amicio, citandogli, fra'varii esempii non di parole ma di fatti, <lb/>che stavano a confermar contro le moderne le dottrine pi&ugrave; antiche, anche <lb/>quello de'nervi ottici, i quali, in alcuni grandi pesci, mostrano evidente&shy;<lb/>mente d'essere perforati. </s>

<s>&ldquo; Nonne, soluto prius oculo in singulas sui mem&shy;<lb/>branas, quod vix animus capere potest, foramen nervi visorii tibi et aliis, <lb/>vel multis reclamantibus, ante oculos sexcenties exposui? </s>

<s>Iam cito admira&shy;<lb/>tio illa evanuit quam nervum visorium, in eo animali quod cognitum nunc <lb/>habes, tibi ac plurimis aliis movisse praedicabas, qui nervus, veluti tenuis&shy;<lb/>simum matronarum linteum, in innumeras rugas aequales et pari serie di&shy;<lb/>stributas complicatus, tuniculaque illas ambiente coactus, hac eadem incisa, <lb/>evolvi sese permittebat, et in amplam membranam totum explicari atque <lb/>extendi &rdquo; (Examen ossium, inter Opuscula anat. </s>

<s>cit., pag. </s>

<s>227). </s></p><p type="main">

<s>La questione pareva che dovess'essere cos&igrave; finalmente decisa, ma alle <lb/>dispute fervorose sottentrati i placidi esami, nel secolo XVII si seguit&ograve; col <lb/>Vesalio a negar l'esistenza dei pori erofiliani. </s>

<s>Allora, come se l'opuscolo <lb/>eustachiano non fosse mai stato scritto, il Malpighi torn&ograve; a dimostrar la par&shy;<lb/>ticolare struttura del nervo ottico nelle Xifie e in altri simili pesci, conclu&shy;<lb/>dendone anch'egli come cosa nuova: &ldquo; Ex his omnibus aliquid colligere <lb/>poteris ad solvendum illud, quod antiquos et neotericos diu vexavit, num <lb/>scilicet optici perforati sint &rdquo; (De Cerebro, Operum, T. II, Lugd. </s>

<s>Batav. </s>

<s>1687, <lb/>pag. </s>

<s>121). </s></p><p type="main">

<s>Ma il nuovo, e nella esperienza in s&egrave; stessa e nelle applicazioni di lei, <pb xlink:href="020/01/1446.jpg" pagenum="321"/>a decider le controversie riscontra cos&igrave; coll'antico, che fu da alcuni il Mal&shy;<lb/>pighi accusato di plagio. </s>

<s>&ldquo; Verum, risponderemo anche noi coll'Haller, Mal&shy;<lb/>pighius alienis non egebat divitiis &rdquo; (Elem. </s>

<s>Phys. </s>

<s>T. </s>

<s>V cit., pag. </s>

<s>353), ma <lb/>il fatto in ogni modo &egrave; notabile, e fa gran maraviglia come potesse la scuola <lb/>anatomica del Borelli cos&igrave; aver dimenticata la pi&ugrave; eletta parte delle patrie <lb/>tradizioni. </s></p><p type="main">

<s>Comunque sia per&ograve;, n&egrave; l'Eustachio n&egrave; il Malpighi, insinuando che i <lb/>fori ottici son prodotti dalle pieghe del nervo linteolare, tolsero affatto i <lb/>dubbi, imperocch&egrave;, se potevano da coteste pieghe pigliare apparenza i pori <lb/>pi&ugrave; minuti, rimaneva tuttavia incerta l'origine di quel forame pi&ugrave; grande, <lb/>che, reciso presso l'occhio il nervo per traverso, veniva oramai a rivelarsi <lb/>come cosa fuor d'ogni dubbio alle pi&ugrave; diligenti inspezioni dei moderni. </s></p><p type="main">

<s>Il Zinn dimostr&ograve; che cotesto foro niente altro era che la luce aperta <lb/>dell'arteria centrale, e perch&egrave;, sopra l'inserzione di essa arteria il nervo &egrave; <lb/>solido e non presenta alcun vestigio di pori, si studia di conciliar Galeno <lb/>col Vesalio, dicendo che il primo dovette aver reciso il nervo dopo, e il se&shy;<lb/>condo prima della detta inserzione. </s>

<s>&ldquo; Pori autem vacui in medio nervo nul&shy;<lb/>lum reperitur vestigium supra insertionem ipsius arteriae centralis, ubi ner&shy;<lb/>vus solidus plane apparet, ut inde facile diversae opiniones Galeni, qui nervum <lb/>foramine pertundi asserit, et Vesalii, qui foramen illud negat, conciliari posse <lb/>videantur &rdquo; (Descriptio oculi cit., pag. </s>

<s>194). </s></p><p type="main">

<s>Se, cos&igrave;, il Morgagni, dal veder que'misteriosi meati impediti sempre <lb/>&ldquo; membranea quadam structura, quasi cellulosa &rdquo; (Epist. </s>

<s>anat. </s>

<s>XVII cit., <lb/>pag. </s>

<s>301), ne aveva concluso contrariar questo solo fatto l'ipotesi degli An&shy;<lb/>tichi delle vie di diretta comunicazione fra il cervello e gli occhi; il Zinn, <lb/>rivelando il mistero, confin&ograve; quella ipotesi per sempre nella reggia de'sogni, <lb/>con avvantaggio di quella pi&ugrave; ragionevole Filosofia della visione, che former&agrave; <lb/>il soggetto della nostra storia, dopo questa dell'organo, a completar la quale <lb/>ci rimane ancora a dir degli umori. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Gli Anatomici anteriori a Galeno non conobbero che l'umor vitreo e il <lb/>Cristallino. </s>

<s>Celso infatti, nel &sect; 13 del VII libro <emph type="italics"/>De re medica,<emph.end type="italics"/> dop'aver de&shy;<lb/>scritta la Retina, ch'ei con Herofilo chiama Aracnoidea, &ldquo; ea media, sog&shy;<lb/>giunge, subsidit, eaque cavo continet quiddam quod, a vitri similitudine, <lb/>Jaloides graeci vocant.... Sub his gutta humoris est, ovi albo similis: Chry&shy;<lb/>stalloides a graecis nominatur &rdquo; (Editio cit., fol. </s>

<s>100). Ma sotto la cornea <lb/>&ldquo; qua parte pupilla est, locus vacuus est &rdquo; (ibid.). </s></p><p type="main">

<s>Si direbbe, pensava l'Haller, che gli Antichi non avessero inciso altro <lb/>che l'occhio de'pesci, ne'quali l'umor acqueo &egrave; scarsissimo, &ldquo; cum planis&shy;<lb/>sima cornea iridi incumbat &rdquo; (Elem. </s>

<s>Phys. </s>

<s>T. </s>

<s>V cit., pag. </s>

<s>409), ma forse, <pb xlink:href="020/01/1447.jpg" pagenum="322"/>non avendo diligenza di scegliere per le dissezioni occhi freschi, quello stesso <lb/>umore o era stato assorbito o esalato. </s>

<s>In qualunque modo, Galeno, nel cap. </s>

<s>IV <lb/>del libro X <emph type="italics"/>De usu partium,<emph.end type="italics"/> pens&ograve; che la previdente Natura, affinch&egrave; non <lb/>dovesse il Cristallino moversi e patire attrito, facesse protuberare la cornea, <lb/>non lasciando lo spazio interposto vuoto, ma riempiendolo di un certo umor <lb/>viscido, somigliante all'albume dell'uovo. </s>

<s>&ldquo; Simul autem providit humorem <lb/>quendam tenuem ac sincerum, cuiusmodi in ovis reperitur, crystallino cir&shy;<lb/>cumfundens, ac tertio praeter haec spiritu aereo ac splendido omnem pu&shy;<lb/>pillae locum opplens &rdquo; (Op. </s>

<s>omnia cit., T. I, fol. </s>

<s>179). </s></p><p type="main">

<s>Da queste ultime parole si comprende che dovette Galeno aver trovato <lb/>quell'umore albugineo cos&igrave; scarso, da non rimanerne totalmente piena la <lb/>camera dell'occhio, nel vuoto della quale, secondo lui, vivamente splendeva <lb/>lo spirito aerio. </s>

<s>Cos&igrave; veniva a partecipar con l'inganno de'suoi predeces&shy;<lb/>sori, occasionato senza dubbio dal non aver avuto, come quelli non ebbero, <lb/>l'accortezza di sezionar occhi freschi. </s></p><p type="main">

<s>Non manc&ograve; poi, nel risorgere degli studii anatomici, questa accortezza <lb/>a Jacopo Berengario, il quale dice di aver tante volte esaminata e riesami&shy;<lb/>nata la composizione dell'organo, &ldquo; modo in oculo humano, modo in oculis <lb/>brutorum, modo dequoquendo oculos, modo capiendos ipsos crudos &rdquo; (Com&shy;<lb/>mentaria super Mund. </s>

<s>cit., fol. </s>

<s>CCCCLXIX), e di aver trovato, dietro un tale <lb/>diligentissimo esame, che fra la cornea e il cristallino lo spazio &egrave; tutto pieno <lb/>di umore, concedendo nonostante che si possa, alla parte di questo stesso <lb/>umore che sta innanzi alla pupilla, per esser pi&ugrave; che altrove splendente, <lb/>dare il nome di <emph type="italics"/>etereo.<emph.end type="italics"/> &ldquo; Post tunicas dicendum est de humoribus, qui sunt <lb/>communiter tres: Primus quorum est albugineus, qui est inter corneam et <lb/>uveam tunicam,.... qui quidem humor albugineus, in directo pupillae ten&shy;<lb/>dendo ab humore crystallino seu ab aranea tunica usque ad corneam, vo&shy;<lb/>catur ab aliquibus etereus, quia est clarus et lucidus sicut eter..... Est <lb/>unus alter humor in oculo vitreus dictus, qui est in quantitate maior aliis <lb/>duobus,.... et in medio eius, non in centro sed circa medium eius, in parte <lb/>anteriori, est situs ille alter humor, qui dicitur crystallinus, quia lucet ad <lb/>instar crystalli &rdquo; (ibid., fol. </s>

<s>CCCCLXVIII). </s></p><p type="main">

<s>Cos&igrave; veniva, per opera del Berengario, alla sua sommaria integrit&agrave;, e alle <lb/>sue pi&ugrave; ragionevoli proporzioni ridotta la descrizione dell'occhio. </s>

<s>Ma il Vesalio <lb/>non seppe giovarsi degli studii, per via de'quali riusc&igrave; il nostro Carpense ad <lb/>emendare gli errori antichi, e, come Galeno, condotto anch'egli dalla scarsezza <lb/>dell'umor acqueo ad ammettere l'esistenza di uno spirito aereo repletivo <lb/>della camera anteriore dell'occhio, ne esager&ograve; cos&igrave; l'ampiezza, da farla uguale <lb/>allo spazio occupato in dietro dall'umor vitreo. </s>

<s>Fu l'errore messo in pi&ugrave; ver&shy;<lb/>gognosa mostra, che dalle parole, da quel malaugurato iconismo impresso al <lb/>cap. </s>

<s>XIV del VII libro <emph type="italics"/>De humani corporis fabrica,<emph.end type="italics"/> alla pagina altrove citata. </s></p><p type="main">

<s>Diciamo quell'iconismo malaugurato, perch&egrave; gli offesi dalle soverchianze <lb/>orgogliose dell'Autore si gittarono a quella vista sopra lui, come cani in <lb/>caccia sulla preda ferita. </s>

<s>Chi non sente spirare la volutt&agrave; della vendetta da <pb xlink:href="020/01/1448.jpg" pagenum="323"/>queste parole, colle quali il Colombo termina il suo X libro? </s>

<s>&ldquo; Errores Ve&shy;<lb/>salii deprehendes, qui tota errat via, existimans cristallinum humorem in <lb/>centro oculi exquisite situm esse, item tantum humoris aquei quantum vi&shy;<lb/>trei reperiri &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>220). </s></p><p type="main">

<s>Giovanni Valverde spagnolo che nel 1559 ridusse in compendio l'ana&shy;<lb/>tomia del Colombo, e che con quella traduzione italiana del suo libro, fatta <lb/>per lui l'anno dopo da Antonio Tabo, confer&igrave; a diffondere le nozioni pi&ugrave; <lb/>elementari della scienza in chi non la professava, scrivendo nel V libro <emph type="italics"/>Degli <lb/>occhi,<emph.end type="italics"/> dop'aver detto della cornea e dell'iride, cos&igrave; soggiungeva: &ldquo; Lo spa&shy;<lb/>zio tra queste due tele &egrave; pieno di un umore chiamato Hialoydes, che vuol <lb/>dire acquoso, per esser simile all'acqua. </s>

<s>Altri il chiamarono albugineo, per <lb/>esser simile al chiaro dell'uovo, il quale non &egrave; tanta quantit&agrave; quanta si <lb/>pens&ograve; il Vesalio, perch&egrave; aprendo l'occhio, ancor che sia finito di morir <lb/>l'uomo, non escono pi&ugrave; di sei o sette gocciole d'acqua &rdquo; (Anatomia del <lb/>corpo umano, Roma 1560, pag. </s>

<s>113). </s></p><p type="main">

<s>Il Falloppio, sempre pi&ugrave; gentile ne'modi, anche pi&ugrave; efficacemente cor&shy;<lb/>resse gli errori del Vesalio, descrivendo con la maggior diligenza il vero, e <lb/>lasciando che altri ne facessero a loro piacere il confronto o ne rilevassero <lb/>il contrapposto. </s>

<s>Perci&ograve; nell'<emph type="italics"/>Examen observationum<emph.end type="italics"/> il Brussellese risponde, <lb/>piuttosto che al Falloppio, al Colombo e al Valverde, e rispondendo, esem&shy;<lb/>pio raro, confessa il suo errore, di cui par che voglia addur per sua scusa <lb/>l'esempio dello stesso Galeno, che per simili cause, come sopra osservammo, <lb/>s'era pure ingannato. </s>

<s>&ldquo; Quum enim oculum, cos&igrave; leggesi nel citato <emph type="italics"/>Exa&shy;<lb/>men,<emph.end type="italics"/> frequentius mea vulgari illa, quam in meis libris descripsi, admini&shy;<lb/>stratione, solebam secare, omnes tres simul humores in volam ex oculo pro&shy;<lb/>cidebant, et quando tum duae aut tres tantum aquei humoris se offerebant <lb/>guttulae, universum illud spatium, quod illi humori in oculo adscribimus, <lb/>etiam spiritu oppleri existimabamus. </s>

<s>Et quamvis impar omnino aquei hu&shy;<lb/>moris cum vitreo videbatur tum proportio, spirituum tamen illorum et oculi <lb/>mox a morte anteriore in sede collapsus, ac curationis denique, quam in <lb/>suffusionum depressionibus acu molimur, occasionem, cristallinum humorem, <lb/>magis quam oportuit, in posteriora retrusi, quemadmodum etiam iusta vi&shy;<lb/>trei humoris moles a me non est explicata &rdquo; (Venetiis 1564, pag. </s>

<s>162). </s></p><p type="main">

<s>Cosicch&egrave;, se l'errore del Vesalio si disse da una parte malaugurato, si <lb/>pu&ograve; chiamar dall'altra felice, avendo non solamente fruttato il merito di que&shy;<lb/>sta confessione, ma dato impulso a quel pi&ugrave; diligente esame anatomico, e <lb/>a quella pi&ugrave; acconcia amministrazione dell'occhio, della quale il Berenga&shy;<lb/>rio avea dato l'esempio. </s>

<s>Il Colombo e il Falloppio insegnarono con gli scritti: <lb/>l'Eustachio, di quelle dissoluzioni delle parti componenti l'organo della vi&shy;<lb/>sta, da s&egrave; fatte con tant'arte, <emph type="italics"/>quod vix animus capere potest;<emph.end type="italics"/> lasci&ograve; che <lb/>ne parlassero gl'iconismi. </s>

<s>Da questi tre insigni Autori, insieme col Beren&shy;<lb/>gario, ebbe propriamente principio lo studio anatomico dell'occhio dell'uomo, <lb/>come lo dimostrava dianzi la storia delle membrane, e come lo confermer&agrave; <lb/>ora quella, che siam per dar brevemente, dei tre umori in particolare. </s></p><pb xlink:href="020/01/1449.jpg" pagenum="324"/><p type="main">

<s>Gli antichi non si espressero chiaramente intorno al definir la quantit&agrave; <lb/>dell'umor vitreo, rispetto agli altri due: il Berengario si limit&ograve; a dire che <lb/>&egrave; &ldquo; in quantitate maior aliis duobus &rdquo; (Comment. </s>

<s>cit., fol. </s>

<s>CCCCLXIX), e, <lb/>nell'Isagoge, che &ldquo; est longe maior cristallino &rdquo; (editio cit., fol. </s>

<s>52), ci&ograve; che <lb/>dette occasione al Vesalio di dir nelle sue ritrattazioni: &ldquo; Nulla nemque vi&shy;<lb/>trei cum aqueo est proportio, isque magis quam ad mediam oculi sedem <lb/>antrorsum ducitur &rdquo; (Examen cit., pag. </s>

<s>162). </s></p><p type="main">

<s>Primo a definire quelle proporzioni fu il Colombo, il quale scrisse che <lb/>l'ialoide &egrave; di tal mole &ldquo; ut ex quatuor oculi partibus tres occupet &rdquo; (De re <lb/>anat., cit., pag. </s>

<s>219). L'Acquapendente lo disse &ldquo; fere quadruplo crystal&shy;<lb/>loidem exsuperantem &rdquo; (De oculo cit., pag. </s>

<s>193) e il Casserio quadruplo <lb/>del cristallino, e quasi doppio dell'acqueo. </s>

<s>&ldquo; Maximus omnium est humor <lb/>vitreus et crystallinum quadruplo, albugineum duplo fere superans &rdquo; (Pen&shy;<lb/>taestheseion, Venetiis 1609, pag. </s>

<s>289). Ma per la diffluente mollizie essendo <lb/>difficile a determinarsi quelle precise misure, anche all'arte peritissima dei <lb/>moderni, si contentarono questi d'affermar cos&igrave; in generale col Zinn: &ldquo; hu&shy;<lb/>more vitreo longe maximam cavitatis oculi partem occupari &rdquo; (Descriptio <lb/>oculi cit., pag. </s>

<s>118). </s></p><p type="main">

<s>La fisica costituzion dell'umore, che lo fece infino dagli antichissimi <lb/>tempi rassomigliare al vetro fuso, rivel&ograve; con facilit&agrave; l'esistenza di quella, al&shy;<lb/>trimenti sfuggevole, membrana che gli serve da recipiente. </s>

<s>&ldquo; Id, scrisse <lb/>Celso dell'ialoide, neque liquidum neque aridum est, sed quasi concretus <lb/>humor..... Id autem, superveniens ab interiore parte, membranula inclu&shy;<lb/>dit &rdquo; (De re medica cit., fol. </s>

<s>100). Pretermessa negligentemente questa mem&shy;<lb/>branula nelle sue descrizioni dal Vesalio, fu il Falloppio il primo a rinfre&shy;<lb/>scarne la perduta memoria, annoverandola fra le altre tuniche dell'occhio. <lb/></s>

<s>&ldquo; Verum enim vero tunica, quae vitreum humorem ambit, et in illa cavi&shy;<lb/>tate crystallo dicata, et in reliqua totius humoris superficie a Vesalio prae&shy;<lb/>termissa, procul omni dubio addi debet &rdquo; (Observat. </s>

<s>anat., Op. </s>

<s>omnia cit., <lb/>pag. </s>

<s>479). Nonostante il Vesalio stesso disse, nel poco fa citato <emph type="italics"/>Esame,<emph.end type="italics"/> di <lb/>non aver avuto ancora tanti occhi, &ldquo; ut peculiarem quandam tunicam, a me <lb/>non descriptam, vitreo humori tribuere valeam &rdquo; (pag. </s>

<s>163). Il Plater per&ograve; non <lb/>ebbe alcun dubbio di designar, nella Tavola XLIX illustrativa del suo trat&shy;<lb/>tato <emph type="italics"/>De corporis humani structura,<emph.end type="italics"/> fra le tuniche anche l'<emph type="italics"/>ialoides,<emph.end type="italics"/> ma il <lb/>Vidio assegn&ograve; propriamente alla Retina l'ufficio d'involgere l'umor vitreo <lb/>&ldquo; a posteriori parte et a priori &rdquo; (De anatome cit., pag. </s>

<s>320), e tale si fu <lb/>pure l'opinione dell'Acquapendente che, designando le tre membrane del&shy;<lb/>l'occhio, la scleroide, la coroide e la Retina, dice che si espandono in emi&shy;<lb/>sferio, &ldquo; humorem vitreum intus posteriusque complexae &rdquo; (De oculo cit., <lb/>pag. </s>

<s>187). </s></p><p type="main">

<s>Giovan Batista Ruschi, bench&egrave; affermasse essere stata la ialoide cono&shy;<lb/>sciuta da suo padre, che per&ograve; la confuse coll'aracnoide, nel passare a farne, <lb/>nel cap. </s>

<s>XI del II libro del suo <emph type="italics"/>Visus organo,<emph.end type="italics"/> una particolar descrizione, <lb/>la riguard&ograve; come cosa di poco momento, per non essere altro in sostanza <pb xlink:href="020/01/1450.jpg" pagenum="325"/>che la superficie dello stesso umor vitreo. </s>

<s>&ldquo; Videtur autem fere ipsa vitrei <lb/>substantia: corpora enim omnia in superficie quasi pellicula vel crustula <lb/>obducuntur, etsi, hac etiam dissecta tunica, si tunica meretur nominari, vi&shy;<lb/>treum nihilominus consistat &rdquo; (editio cit., pag. </s>

<s>46). </s></p><p type="main">

<s>Questa opinione del Ruschi fu, per tacere di tanti altri, seguita dal <lb/>Briggs, nel cap. </s>

<s>III della sua Ottalmografia, tra gli stranieri, e fra'nostri <lb/>dal Molinetti, il quale disse avere la ialoidea origine dallo stesso umore &ldquo; su&shy;<lb/>perficie scilicet ipsius crassescente in tunicam, prout plerisque probabile vi&shy;<lb/>sum est &rdquo; (Dissert. </s>

<s>anat. </s>

<s>cit., pag. </s>

<s>22). </s></p><p type="main">

<s>Ma perch&egrave; le probabilit&agrave; e i pareri altrui non fanno scienza, si volle <lb/>ricorrere alle esperienze. </s>

<s>Il Morgagni, estratto l'umor vitreo dagli occhi di <lb/>varii animali, e per sessant'ore tenutolo esposto all'aria, non vide perci&ograve; <lb/>&ldquo; crassiorem pelliculam ostendisse &rdquo; (Epist. </s>

<s>XVII cit., pag. </s>

<s>274). Altre espe&shy;<lb/>rienze fatte dal Desmours dimostrarono, contro l'asserzione del Ruschi, che <lb/>ferita la membrana si vede uscir l'umore per la rottura, e anzi trasudare <lb/>spontaneamente attraverso ai pori naturali, lasciata all'aria essa membrana <lb/>illesa. </s>

<s>Del resto il vederla, iniettandovi il fiato, rigonfiare e staccarsi dal&shy;<lb/>l'umor sottoposto, fu tale conclusiva esperienza, da togliere anche l'ombra <lb/>del dubbio. </s></p><p type="main">

<s>Fra il vitreo e il cristallino era naturalissimo veder che passava una <lb/>strettissima relazione, e bench&egrave; distinti di forma e di natura si trovavano, <lb/>a qualunque pi&ugrave; ovvio esame, sempre fra loro amichevolmente congiunti in&shy;<lb/>sieme. </s>

<s>Il Berengario disse che il legame di cos&igrave; fatta congiunzione consi&shy;<lb/>steva nella retina, che dalla parte anteriore si trasforma nell'aranea. </s>

<s>&ldquo; Et <lb/>hic cristallinus humor, absque aliquo medio, ante habet tunicam araneam, <lb/>et sic tunica aranea, rethina et cristallinus humor cum vitreo sunt ligati &rdquo; <lb/>(Commentaria cit., fol. </s>

<s>CCCCLXIX). </s></p><p type="main">

<s>Il Colombo fece poi dell'aranea una membrana distinta, sottilissima e <lb/>trasparente come i veli delle cipolle, l'ufficio della quale fosse &ldquo; ut humo&shy;<lb/>res vitreum et cristallinum complecteretur &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>218). &Egrave; <lb/>tutta andantemente, soggiunge, una membrana sola &ldquo; licet ea parte, quae <lb/>ante cristallinum locatur, paulo crassior sit quam in reliquis partibus &rdquo; (ibid.). </s></p><p type="main">

<s>Nonostante il Ruschi, tornando indietro al Berengario, disse che, giunta <lb/>la retina alla circonferenza del cristallino, in quel punto che questo emerge <lb/>dal vitreo, &ldquo; in duplicem abit tenuissimam tunicam, quae a dicto circulo <lb/>orta tenuiori sui parte inferius dimidietatem crystallini vitreo mersam inve&shy;<lb/>stit, altera nonnihil crassiori emergentem dimidietatem obvolvit, ita ut undi&shy;<lb/>quaque hac eadem membrana crystallinus investiatur, quae, cum tenuissima <lb/>sit, araneae nomen sortita est &rdquo; (De visus org. </s>

<s>cit., pag. </s>

<s>3). </s></p><p type="main">

<s>Queste dimenticate osservazioni del nostro Anatomico pisano, sui prin&shy;<lb/>cipii del secolo XVIII, quando l'esperienze avevano oramai dimostrata l'esi&shy;<lb/>stenza della gialloidea, rifiorirono in Francia, dove il Petit, riconoscendo in <lb/>essa gialloidea quella divisione in due lamine, che aveva il Ruschi descritta <lb/>nella Retina o nell'Aranea, scopr&igrave; che, nel punto della loro separazione, la-<pb xlink:href="020/01/1451.jpg" pagenum="326"/>sciavano uno spazio vuoto, da cui veniva a formarsi un certo canale distinto <lb/>col nome di <emph type="italics"/>Canal godronn&edot;<emph.end type="italics"/> dall'inventore, ma che pi&ugrave; volentieri gli Ana&shy;<lb/>tomici designarono poi col nome di <emph type="italics"/>Canal del Petit.<emph.end type="italics"/></s></p><p type="main">

<s>La curiosa scoperta richiam&ograve; a s&egrave; l'attenzione degli Anatomici, uno <lb/>de'pi&ugrave; studiosi fra'quali fu il Zinn, a cui occorse di scoprire o di mettere <lb/>in maggiore evidenza, in tale occasione, una parte distinta di quell'organo, <lb/>che lega insieme il vitreo col cristallino. </s>

<s>&ldquo; Dum enim, cos&igrave; egli stesso rac&shy;<lb/>conta, in oculis et humanis et bubulis in fabricam Canalis petitiani inquiro, <lb/>iteratis experimentis, demum edoctus fui in eodem plano, ubi corpus ciliare <lb/>ex choroide producitur, ex tunica vitrea oriri membranulam aut zonulam &rdquo; <lb/>(Descriptio oculi cit., pag. </s>

<s>122). </s></p><p type="main">

<s>Si risovvenne allora che questa zonula era quella medesima, che il Mor&shy;<lb/>gagni trov&ograve; fra le schedule del Valsalva descritta come veduta separarsi dal <lb/>cristallino &ldquo; ad formam plani circularis, quae solam tegat partem ipsius an&shy;<lb/>teriorem &rdquo; (Epist. </s>

<s>XVII cit., pag. </s>

<s>272), e impose a quello stesso piano, che <lb/>a guisa di collare circonda la lente, il nome di <emph type="italics"/>Corona ciliare:<emph.end type="italics"/> &ldquo; nomine <lb/>Coronae ciliaris mihi dicta &rdquo; bench&egrave; gli Anatomici oggid&igrave; comunemente la <lb/>chiamino <emph type="italics"/>Zona del Zinn.<emph.end type="italics"/></s></p><p type="main">

<s>La membrana dunque, che involge il <emph type="italics"/>Canal godronn&edot;,<emph.end type="italics"/> non &egrave; una con&shy;<lb/>tinuazione della gialloidea, come si dette a credere il Petit, ma &egrave; quella <lb/>Zona, che porse al Zinn nello scoprirla occasion di descrivere il canal pe&shy;<lb/>titiano pi&ugrave; diligentemente del suo stesso inventore. </s>

<s>Uscita dalla gialloidea, <lb/>dice esso Zinn, e rimasta da lei libera, bench&egrave; contigua, la <emph type="italics"/>Corona,<emph.end type="italics"/> da quella <lb/>parte che s'insinua tra il corpo vitreo e il corpo ciliare, &ldquo; sensim, quo pro&shy;<lb/>pius ad lentem accedit, eo magis a corpore vitreo dimovetur, et in conve&shy;<lb/>xitate demum anteriori lentis ultra circulum maximum capsulae illius inse&shy;<lb/>ritur, ut adeo spatium nascatur naturale exiguum triangulare curvilineum <lb/>inter humorem vitreum et hanc modo dictam membranulam, cuius trianguli <lb/>basin sistit illa portio convexitatis anterioris lentis, inter circulum maximum <lb/>et insertionem eius membranulae intermedia. </s>

<s>Illa autem zonula, a prima <lb/>origine ex tunica vitrea ad insertionem in lentem usque, percurritur fibris <lb/>fortioribus transversis, et ipsa membrana multo brevioribus, quae illam per <lb/>intervalla sic stringunt et contrahunt, ut per vulnusculum membranulae illi <lb/>inflictum, flatu in spatium illud triangulare immisso, canalis se sistat con&shy;<lb/>tinuus, et lentem undique ambiens, spatiis alternis immisso flatu turgenti&shy;<lb/>bus et contractis, qui, si comparationem instituere liceat, figuram fere expri&shy;<lb/>mere videtur intestini coli flatu repleti, a ligamentis longitudinalibus intestino <lb/>brevioribus in rugas contracti &rdquo; (ibid., pag. </s>

<s>123). </s></p><p type="main">

<s>La facile esperienza poi, per la quale si dimostrava che, insuffiato l'in&shy;<lb/>volucro della lente, il fiato non passava dentro il Canale, mentre veniva a <lb/>confermare il fatto non potere, come dicevasi, un tale involucro nascere <lb/>dalla duplicatura della gialloidea, dimostrava nel tempo stesso quel ch'era <lb/>stato cos&igrave; lungamente controverso, che cio&egrave; essa lente cristallina era involta <lb/>da una capsula sua propria. </s>

<s>La ragione di cos&igrave; fatte controversie, che du-<pb xlink:href="020/01/1452.jpg" pagenum="327"/>rarono fino ai primi anni del secolo XVIII, non &egrave; difficile trovarla nella te&shy;<lb/>nuit&agrave; e trasparenza di quel velo, che, sfuggevole a ogni vista pi&ugrave; acuta, si <lb/>rivel&ograve; solo allora che si vide mobile al fiato. </s></p><p type="main">

<s>Fu questa stessa trasparenza anche causa del non poter gli Anatomici <lb/>cos&igrave; per tempo riconoscere la particolare struttura dell'umor cristallino. </s>

<s>Lo <lb/>Stenone, sezionando l'occhio delle Carcarie e di molti altri pesci, fu il <lb/>primo che trovasse in essi la lente affaldata nel mezzo di lamelle, come le <lb/>tuniche nelle cipolle, circondate da una materia glutinosa, sopra la quale <lb/>galleggiava un liquido affatto simile all'acqua. </s>

<s>&ldquo; Crystallini humoris substan&shy;<lb/>tia triplex erat: media dura, et ex lamellis composita; huic undique adhae <lb/>rens alia multum glutinosa; tertia, tunicae proxima, omnino aquea &rdquo; (Ele&shy;<lb/>mentorum myol. </s>

<s>specimen cit., pag. </s>

<s>80). </s></p><p type="main">

<s>Il difficile esame anatomico dello Stenone rimase per parecchi anni senza <lb/>riscontro, infino al Morgagni, il quale trov&ograve; che la struttura lamellare del <lb/>nucleo era propria al cristallino di tutti gli animali. </s>

<s>Trov&ograve; di pi&ugrave; che le la&shy;<lb/>mine si fanno dall'interno all'esterno sempre pi&ugrave; molli, infino a ridursi in <lb/>quella sostanza glutinosa gi&agrave; descritta dallo stesso Stenone. </s>

<s>&ldquo; Illud tamen <lb/>constantius observare consuevi, non modo in piscibus, verum etiam in cae&shy;<lb/>teris animalibus, crystallini corpus, quo magis ab interiore medio nucleo re&shy;<lb/>cedit, eo magis magisque mollescere, quod et in resiccato lamellae ostendunt <lb/>eo magis friabiles quo exteriores, et in recenti substantia exterior, gelatinam <lb/>quasi quandam et interdum vitraei humoris consistentiam aemulans, quod <lb/>neque intermediae et multo minus intimae substantiae convenit, plane con&shy;<lb/>firmat &rdquo; (Adversaria anat., Patavii 1719, pag. </s>

<s>90). </s></p><p type="main">

<s>Del terzo strato acqueo, descritto dallo Stenone, il Morgagni pure am&shy;<lb/>mise l'esistenza, affermando &ldquo; tunica incisa, humorem quendam aqueum <lb/>prodire &rdquo; (ibid.). Mossi da una tale affermazione gli Anatomici dettero a quel <lb/>liquido acqueo il nome di <emph type="italics"/>Umor del Morgagni,<emph.end type="italics"/> ma l'Haller fu, se non <lb/>de'primi, de'pi&ugrave; autorevoli senza dubbio in negarne l'esistenza. </s>

<s>&ldquo; Nullam, <lb/>egli dice nel citato Tomo degli Elementi di Fisiologia, in crystallina lente <lb/>aqulam reperi &rdquo; (pag. </s>

<s>405) e quella trovatavi dal Morgagni la crede un'esa&shy;<lb/>lazion vaporosa, condensatasi nel cadavere, provvidamente ordinata dalla Na&shy;<lb/>tura a impedir l'adesione della capsula con la lente. </s>

<s>&ldquo; Nam ea aquula, <lb/>emissa lens crystallina, collabitur, sicca fit et opaca, et suae capsulae adhae&shy;<lb/>ret &rdquo; (ibid., pag. </s>

<s>406). </s></p><p type="main">

<s>Pi&ugrave; facile che la struttura pareva a definire della lente cristallina la <lb/>forma, eppure quanto furono intorno a ci&ograve; varii i giudizii degli Anatomici, <lb/>da'pi&ugrave; antichi infino ai moderni! Anzi Galeno stesso, nelle varie sue opere, <lb/>d&agrave; di quella stessa forma giudizii diversi, imperocch&egrave;, mentre nel cap. </s>

<s>II del <lb/>libro X <emph type="italics"/>De usu partium,<emph.end type="italics"/> al fol. </s>

<s>178 del I Tomo delle Opere pi&ugrave; volte ci&shy;<lb/>tato, dice del cristallino <emph type="italics"/>quod rotundum est,<emph.end type="italics"/> e ch'egli nuota nel vitreo <lb/>&ldquo; quasi semisecta quaepiam sphaera in aqua, &rdquo; nel cap. </s>

<s>VIII del VII libro <lb/><emph type="italics"/>De'placiti d'Ippocrate e di Ptatone<emph.end type="italics"/> lo rappresenta invece a somiglianza di <lb/>un globo compresso. </s>

<s>Gli Arabi si accostarono con Ruffo Efesio e con Teofilo, <pb xlink:href="020/01/1453.jpg" pagenum="328"/>che fecero il cristallino dalla parte anteriore men convesso e quasi piano; <lb/>ci&ograve; che fu poi confermato dalle osservazioni del Berengario. </s>

<s>&ldquo; Sua figura, <lb/>egli scrive, non est totaliter sphaerica: sphaerica tamen est versus anterius <lb/>cum aliquali planitie.... et ideo Hali vocat suam partem anteriorem sub&shy;<lb/>planam &rdquo; (Comment. </s>

<s>cit., fol. </s>

<s>CCCCLXXIV). </s></p><p type="main">

<s>Nella instaurazione della nuova Anatomia il Vesalio ripet&egrave; ci&ograve; che, nei <lb/>Placiti sopra citati, avea detto Galeno, rappresentando il cristallino non come <lb/>esattamente rotondo, &ldquo; sed et anteriori et posteriori parte leviter non secus <lb/>compressum, quam si lignei globi medio, secundum lineas aequidistantes, <lb/>orbem crassiusculum serra exemisses, et dein duas globi partes denuo con&shy;<lb/>glutinasses.... ad lentis similitudinem &rdquo; (De hum. </s>

<s>corp. </s>

<s>fabrica cit., pag. </s>

<s>646). <lb/>Ma il Colombo convenne piuttosto col Berengario, dicendo esser l'umor cri&shy;<lb/>stallino conglobato s&igrave; in sfera, per&ograve; compressa, dalla parte che guarda l'umor <lb/>acqueo, in modo, &ldquo; ut lentis formam referat &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>219). <lb/>La quale affermazione confortata dall'altra del Falloppio, che scrisse essere <lb/>il cristallino sferico dalla parte posteriore, &ldquo; in anteriori vero depressus <lb/>ita, ut haec facies parum a plana distet &rdquo; (Observat. </s>

<s>anat., Op. </s>

<s>omnia cit., <lb/>pag. </s>

<s>479), valse a far dimenticare la descrizione, che ne aveva fatta il Ve&shy;<lb/>salio &ldquo; a Galeno assumens &rdquo; (ibid.). </s></p><p type="main">

<s>L'Acquapendente fu il primo a comparar la figura dell'umore ne'varii <lb/>generi di animali, e ne'pesci la trov&ograve; esattamente rotonda, ma negli uo&shy;<lb/>mini, ne'bovi e in altri simili &ldquo; non usquequaque et ad unguem perfecta <lb/>rotunditas apparet, sed quidem, qua vitreum contingit in eumque mergitur, <lb/>perfectam habet rotunditatem, Galeno ignotam. </s>

<s>Anterius autem ad aqueum <lb/>humorem depressus est, et lenticulae extuberantiam refert, unde haec pars <lb/>lenticularis a Ruffo est appellata &rdquo; (De oculo, Op. </s>

<s>omnia cit., pag. </s>

<s>192). </s></p><p type="main">

<s>Pi&ugrave; minute osservazioni in proposito furono poi fatte, al riferir del Gas&shy;<lb/>sendo, dal Peirese, il quale &egrave; il primo che abbia tentato di misurare se&shy;<lb/>condo qual ragione stieno, ne'varii animali, i raggi di curvatura delle due <lb/>faccie della lente, bench&egrave; confessi di non aver potuto da cos&igrave; fatte misure <lb/>concluder nulla, in ordine al determinar la vera figura geometrica della <lb/>stessa lente, &ldquo; praesertim quia mortuo animali humor flaccescit collabitur&shy;<lb/>que, et seu a digitis tractetur, seu suspensus teneatur, seu supra papyrum <lb/>resideat, vix potest non deflectere a nativa sua figura &rdquo; (Vitae, lib. </s>

<s>V, Pa&shy;<lb/>risiis 1641, pag. </s>

<s>279). </s></p><p type="main">

<s>Nascevano cos&igrave; fatte difficolt&agrave; naturalmente dall'esame anatomico dei <lb/>fatti, ma i Diottrici si lusingarono di poterle superare, prescrivendo alla <lb/>stessa Natura quelle leggi, che avevano con l'aiuto della geometria presta&shy;<lb/>bilite nelle loro astratte speculazioni. </s>

<s>Il Keplero, nel &sect; I del cap. </s>

<s>V de'Pa&shy;<lb/>ralepomeni a Vitellione, assegn&ograve; al cristallino, da quella parte che riguarda <lb/>l'acqueo, la figura di un conoide ellissoideo, e da quell'altra, che riguarda <lb/>il vitreo, la figura di un conoide iperbolico. </s>

<s>&ldquo; Chrystallinus, ea facie quae <lb/>aqueo immergitur, figuram accepit aut sphaericam aut sphaeroidis lenticu&shy;<lb/>laris portionem circumducta ellipsi per axem divisa;.... a posteriore parte, <pb xlink:href="020/01/1454.jpg" pagenum="329"/>quae vitreo immergitur, figura ipsi est conoides hyperbolica &rdquo; (Franco&shy;<lb/>furti 1604, pag. </s>

<s>167). Nella Diottrica accenn&ograve; poi che cos&igrave; fatta figura <emph type="italics"/>con&shy;<lb/>stat experientia Anatomicorum,<emph.end type="italics"/> ma ch'ella fosse dedotta piuttosto dalle <lb/>teorie, lo tradisce il processo stesso delle dimostrazioni. </s>

<s>Dop'avere infatti <lb/>nella propos. </s>

<s>LIX dimostrato: &ldquo; Superficies densi, quae parallelos per cor&shy;<lb/>pus venientes, post corpus refractione facta, perfecte concurrere facit, est <lb/>hyperbolicae adfinis &rdquo; (Augustae Vindel. </s>

<s>1611, pag. </s>

<s>2); passa immediata&shy;<lb/>mente a farne l'applicazione all'umor cristallino dell'occhio, scrivendo: <lb/>&ldquo; Chrystallinus humor oculi est lens convexa forma hyperbolae &rdquo; (ibid.). </s></p><p type="main">

<s>Era una tal maniera di argomentare dalle teorie ai fatti conformissima <lb/>al genio del Cartesio, il quale avendo nella Diottrica dimostrato che la linea <lb/>del perfetto concorso non &egrave; n&egrave; l'iperbola n&egrave; la parabola, ma l'ellisse, ne <lb/>concluse che dovesse avere la lente cristallina, dalle due facce, una figura <lb/>ellissoidea. </s>

<s>Vedesi questa figura esquisitamente rappresentata negli iconismi <lb/>impressi nel cap. </s>

<s>III della Diottrica, e nel trattato <emph type="italics"/>De homine,<emph.end type="italics"/> dov'essen&shy;<lb/>dosi designata la lente per la lettera L vien nel testo dichiarata con queste <lb/>parole: &ldquo; Figura humoris L, qui <emph type="italics"/>crystallinus<emph.end type="italics"/> dicitur, similis est illi figurae <lb/>vitrorum, quam in tractatu de Dioptrica descripsi, quorum interventu omnes <lb/>radii, ab uno quodam puncto venientes, coeunt in puncto quodam alio &rdquo; <lb/>(Francofurti ad M. 1692, pag. </s>

<s>62). </s></p><p type="main">

<s>Mentre gli Anatomici rimanevano tuttavia incerti de'loro esami, non <lb/>mancarono nel secolo XVII alcuni, che si confidarono meglio delle specu&shy;<lb/>late teorie de'Diottrici, e il Philippeau, riferente lo Stenone &ldquo; crystallini <lb/>figuram ex duabus hyperbolis in homine compositam credit &rdquo; (Elem. </s>

<s>Myol. </s>

<s><lb/>specimen cit., pag. </s>

<s>82), e il Molinetti vide colla mente &ldquo; crystallinum bina <lb/>superficie praeditum, utraque ad ellipsim vergente &rdquo; (Dissertat. </s>

<s>anat. </s>

<s>cit., <lb/>pag. </s>

<s>18), dietro i dimostrati teoremi cartesiani. </s></p><p type="main">

<s>Svaporati nel secolo XVIII i fumi di quella inebriatrice Filosofia car&shy;<lb/>tesiana, e pi&ugrave; sanamente radicatasi l'opinione non si dare altra scienza in <lb/>natura, da quella infuori che resulta dall'osservazione dei fatti e dalla espe&shy;<lb/>rienza; si pot&egrave; nel presente proposito concluderne questo solo, che cio&egrave; la <lb/>convessit&agrave;, nella parte anteriore della lente, &egrave; sempre maggior che nella po&shy;<lb/>steriore. </s>

<s>&ldquo; Omnes certe meae observationes in eo consentiunt, scrisse il <lb/>Zinn, lentis convexitatis anterioris sectionem ad maioris circuli ambitum, <lb/>quam posterioris attinere,.... semperque mihi contigit videre utramque fa&shy;<lb/>ciem, habita ratione ad diametrum transversalem, eo esse convexiorem quo <lb/>propior homo est origini, ut in fetu aut infante recens nato ad figuram fere <lb/>sphaericam accedere, et diameter ab anterioribus ad posteriora parum a dia&shy;<lb/>metro transversali abludere videatur, quae lens in utraque facie eo planior <lb/>deprehenditur, quo homo adultior fuerit: post annum tamen tricesimum <lb/>figura lentis parum amplius mutari &rdquo; (Descriptio oculi cit., pag. </s>

<s>128, 29). </s></p><p type="main">

<s>Venivano da queste osservazioni a conciliarsi le varie sentenze degli <lb/>Anatomici, specialmente pi&ugrave; antichi, essendo facile che le varie figure da <lb/>essi notate nel cristallino dipendessero in gran parte dalle varie et&agrave; degli <pb xlink:href="020/01/1455.jpg" pagenum="330"/>individui, gli occhi de'quali si sottoponevano all'anatomico esame, ma per <lb/>nulla rendevasi da tuttoci&ograve; probabile che la Natura usi in lavorar la lente <lb/>dell'occhio l'arte usata dagli uomini in fabbricare e configurare i vetri da <lb/>servire ai loro diottrici strumenti. </s>

<s>Comunque siasi per&ograve;, non pot&egrave; per gli <lb/>usi della vista naturale negarsi, n&egrave; agli antichi n&egrave; ai moderni, l'eccellenza <lb/>del cristallino sopra gli altri due umori, e specialmente sopra l'acqueo, la <lb/>storia del quale si riduce per noi a pochi e semplici fatti. </s></p><p type="main">

<s>Dopo Galeno, i primi studii a noi noti incominciano col Berengario, il <lb/>quale descrivendo quell'umore, che si rassomigliava all'albume dell'uovo, <lb/>e dicendolo invece &ldquo; fluxibilis ut aqua &rdquo; (Comment. </s>

<s>cit., fol. </s>

<s>CCCCLXX), <lb/>confer&igrave; a fargli, nel linguaggio degli Anatomici posteriori, scambiar l'antico <lb/>e improprio nome di albugineo in quello di <emph type="italics"/>acqueo.<emph.end type="italics"/> Il Colombo, che fu dei <lb/>primi ad usare quella nuova denominazione, la quale poi si rese comune, <lb/>raccomanda alla memoria de'suoi lettori un fatto singolare, che fu in tal <lb/>proposito da lui stesso osservato: &ldquo; Hoc quod dicam, obsecro lector, ne exci&shy;<lb/>dat me certa coniectura deprehendisse humorem hunc instar excrementi <lb/>esse: nam ego bis hisce oculis vidi totum prorsus effusum esse ob vulnera, <lb/>tamen spatio temporis renatum, ita ut eodem oculo cernere deinceps potu&shy;<lb/>erit &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>219). Dello stesso fatto, che reputavasi allora <lb/>maraviglioso, torn&ograve; un mezzo secolo dopo a pigliar nuova esperienza il padre <lb/>di Giovan Batista Ruschi, cos&igrave; commemorato nel cap. </s>

<s>II del III libro <emph type="italics"/>De <lb/>visus organo:<emph.end type="italics"/> &ldquo; Egregiam habeo ac iuxta vulgi opinionem admirabilem pa&shy;<lb/>tris mei observationem, qui cuidam ex vulnere aqueum humorem viderat <lb/>excidisse, ac ita visionem interceptam, eodem regenerato, non multo tem&shy;<lb/>pore restitutam &rdquo; (editio cit., pag. </s>

<s>49). </s></p><p type="main">

<s>Andate queste tradizioni della scienza in dimenticanza, un altro mezzo <lb/>secolo dopo il Redi, che tante favolose storie degli antichi ridusse alla ve&shy;<lb/>rit&agrave; dei fatti naturali, avendo letto in Dioscoride e in Plinio che l'erba ce&shy;<lb/>lidonia fu ritrovata dalle Rondini, per usarla come medicina intorno agli <lb/>occhi lacerati de'loro pulcini, si assicur&ograve; per ripetute esperienze esser ca&shy;<lb/>gionata quella guarigione dalla sola Natura, senz'altro medicamento, &ldquo; come <lb/>potr&agrave; esser manifesto ad ognuno che voglia aver curiosit&agrave; di forar gentil&shy;<lb/>mente, o con ago o con lancetta da cavar sangue, gli occhi alle rondini o <lb/>a qualsivoglia altro uccello. </s>

<s>Io n'ho fatta la prova ne'colombi, nelle galline, <lb/>nell'oche, nelle anatre e ne'galli d'India, e gli ho veduti spontaneamente <lb/>guarire in meno di ventiquattr'ore &rdquo; (Esper. </s>

<s>intorno a cose nat., Opere, <lb/>T. II, Napoli 1741, pag. </s>

<s>10). </s></p><p type="main">

<s>Capitato questo Discorso del Redi alle mani del Naturalista empolese <lb/>Ippolito Neri, volle provare se per fortuna avvenisse la stessa guarigione <lb/>negli occhi de'quadrupedi. </s>

<s>&ldquo; E di fatto, scrive Giuseppe Zambeccari in una <lb/>sua elegantissima descrizione d'<emph type="italics"/>Esperienze intorno a diverse viscere ta&shy;<lb/>gliate,<emph.end type="italics"/> e intitolata allo stesso Redi, avendogli V. S. illustrissima sommini&shy;<lb/>strate tutte le cose necessarie, sdruc&igrave; gentilmente tutt'e due gli occhi, con <lb/>una lancetta da cavar sangue, ad un cane, e ne fece uscire tutto quanto <pb xlink:href="020/01/1456.jpg" pagenum="331"/>l'umido acquoso a segno tale, che gli occhi rimasero come due borselli voti <lb/>e grinzi. </s>

<s>Lasciato poscia il cane a benefizio di natura, si conobbe eviden&shy;<lb/>tissimamente, sei ore dopo e forse in pi&ugrave; breve tempo, che gli occhi si erano <lb/>ripieni e tornati nel loro stato naturale col segno solamente della cicatrice, <lb/>ed il cane era festoso ed allegro, come se non gli fosse fatto male veruno, <lb/>e quel che pi&ugrave; importa non era rimasto cieco, ma ci vedeva benissimo.... <lb/>Si ritent&ograve; di nuovo la stessa esperienza in diversi altri cani, e ne'conigli <lb/>ancora, e ne'porcellini d'India, ed in un agnello, e sempre con grandissima <lb/>felicit&agrave; guarirono tutti in poche ore, senza che veruno di essi rimanesse mai <lb/>cieco. </s>

<s>Galeno, nel cap. </s>

<s>II del I libro <emph type="italics"/>Delle cagioni de'sintomi,<emph.end type="italics"/> ancorch&egrave; <lb/>affermasse che era difficilissimo, anzi quasi impossibile, il non perder la <lb/>vista dopo che per ferita era uscito l'umor acqueo fuori dell'occhio, nondi&shy;<lb/>meno pur al fine confessa che una volta un fanciullo non ne rimase cieco.... <lb/>Se ne potranno vedere altri esempi in diversi animali, se si legger&agrave; il cap. </s>

<s>VI <lb/>del XXIX libro di Plinio, ancorch&egrave; non se ne dichiari, ma attribuisca forse <lb/>quelle sanazioni ad alcune ridicolose cerimonie e superstizioni in quel ca&shy;<lb/>pitolo descritte. </s>

<s>Or siccome bella opera della sola Natura si &egrave; la rigenera&shy;<lb/>zione dell'umor acqueo negli occhi degli animali, cos&igrave; ancora della stessa <lb/>Natura &egrave; opera la rigenerazione dell'umor vitreo e del cristallino &rdquo; (Fi&shy;<lb/>renze 1680, pag. </s>

<s>26-28). </s></p><p type="main">

<s>Della rigenerazione di questi due umori promette il Zambeccari di trat&shy;<lb/>tarne ad altra occasione. </s>

<s>Se avesse mantenuta la sua promessa, bench&egrave; noi <lb/>non sappiamo dirlo, avrebbe fatto cosa di grande importanza per la noso&shy;<lb/>logia e per la operazione della cateratta, da che fecesi poco dopo vivamente <lb/>sentire il bisogno di definire la relativa grandezza delle cos&igrave; dette <emph type="italics"/>Camere <lb/>dell'occhio.<emph.end type="italics"/></s></p><p type="main">

<s>Galeno dicendo, nel cap. </s>

<s>IV del citato libro X <emph type="italics"/>De usu partium,<emph.end type="italics"/> che <lb/>affinch&egrave; il cristallino non patisse attrito contro la cornea, la quale potrebbe <lb/>giungere facilmente a toccarlo attraverso al foro della pupilla, la previdente <lb/>Natura gli avea circumfuso &ldquo; humorem quendam tenuem ac sincerum cuius&shy;<lb/>modi in ovis reperitur &rdquo; (fol. </s>

<s>179); mostr&ograve; chiaramente di aver riconosciute <lb/>le due Camere distinte e separate fra loro per l'intermezzo dell'Iride. </s>

<s>Il <lb/>Berengario poi ne avea data una descrizione assai pi&ugrave; chiara e pi&ugrave; minuta, <lb/>dicendo che l'albugineo riempie non quello spazio solo, ch'&egrave; fra la cornea <lb/>e l'uvea, ma quell'altro eziandio, ch'&egrave; pi&ugrave; indietro, non occupato dall'ara&shy;<lb/>nea tela e dalla retina. </s>

<s>&ldquo; Primus est albugineus, qui est inter corneam et <lb/>uveam tunicam, et est etiam hic humor intra uveam versus araneam et re&shy;<lb/>thinam tunicam, et tota illa pars quae est ante, quae non est occupata ab <lb/>aranea tela nec a rethina, est plena isto humore albugineo &rdquo; (Comment. </s>

<s>cit., <lb/>fol. </s>

<s>CCCCLXVIII). </s></p><p type="main">

<s>Vedemmo com'avesse il Vesalio esagerata cos&igrave; la grandezza della ca&shy;<lb/>mera posteriore, da ridurla a mezza la cavit&agrave; dell'occhio, ma il Colombo, <lb/>dal trovar l'umor acqueo cos&igrave; scarso, andato nell'errore contrario, non par <lb/>che riconosca altro che la camera anteriore compresa in quell'angusto spa-<pb xlink:href="020/01/1457.jpg" pagenum="332"/>zio, ch'&egrave; tra l'Uvea e la Cornea. </s>

<s>&ldquo; Aqueum Natura anteriore in parte lo&shy;<lb/>cavit inter membranam uveam corneamque: qui humor paucus admodum <lb/>est &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>219). </s></p><p type="main">

<s>Gli Anatomici posteriori al Colombo e al Valverde riconobbero in ge&shy;<lb/>nerale che l'umor acqueo era d'assai maggior quantit&agrave;, che di poche stille, <lb/>e che perci&ograve; rimaneva da lui inondato l'occhio anche a tergo dell'Iride. </s>

<s>Ma <lb/>dissentivano grandemente intorno al definir la capacit&agrave; delle parti inondate, <lb/>dipendendo i dissensi dal vario modo di disegnar la cornea, e l'iride, e i <lb/>processi ciliari, d'onde venivano a variarsi notabilmente gli spazii interpo&shy;<lb/>sti e circoscritti. </s>

<s>Quei per esempio, che facevano la cornea di raggio uguale <lb/>e concentrica con la sclerotica, diminuivano notabilmente la capacit&agrave; della <lb/>camera anteriore, e quegli altri, i quali facevano l'Iride concava e piani i <lb/>corpi ciliari, accrescevano la capacit&agrave; della Camera posteriore. </s></p><p type="main">

<s>Questo punto di storia, con pi&ugrave; concisa chiarezza che dalle parole, ci <lb/>viene enodato dagli Iconismi, e specialmente da quegli impressi ne'varii <lb/>trattati di Ottica, perch&egrave; dovendosi gli Autori rivolgere agli Anatomici, e <lb/>trovando fra loro tanti dissensi, ebbero a studiarsi d'attenersi al meglio o <lb/>a ci&ograve; che aveva maggiori suffragi. </s></p><p type="main">

<s>Quando nel 1554 il Vesalio esercitava sopra la scienza il suo pacifico <lb/>dominio, il Maurolico, che scriveva in quel tempo i suoi <emph type="italics"/>Photismi,<emph.end type="italics"/> rappre&shy;<lb/>sent&ograve; a pag. </s>

<s>72 la figura dell'occhio col cristallino nel centro, e coi corpi <lb/>ciliari, che separano le due uguali capacit&agrave; riempite dall'acqueo e dal vi&shy;<lb/>treo, secondo le descrizioni da lui lette nel VII libro <emph type="italics"/>De humani corporis <lb/>fabrica.<emph.end type="italics"/> &ldquo; Haec, egli dice dopo la dichiarazione della detta figura, ex Ana&shy;<lb/>tomia Andreae Vesalii bruxellensis, viri actate nostra perspicacissimi, excer&shy;<lb/>psimus &rdquo; (Photismi De lumine, Neapoli 1611, pag. </s>

<s>72), non accettando per&ograve; <lb/>la forma vesaliana della lente, che anch'egli disegna compressa s&igrave;, &ldquo; sed a <lb/>parte anteriori compressior &rdquo; (ibid., pag. </s>

<s>69). </s></p><p type="main">

<s>L'Aguilonio, disegnando l'occhio a pag. </s>

<s>3 del suo grande trattato in <lb/>folio (Antuerpiae 1613), si giov&ograve; degl'iconismi del Plater e del Vidio, con&shy;<lb/>dotti sopra le descrizioni del Colombo e del Falloppio, ma la verit&agrave; natu&shy;<lb/>rale parve non essere stata da nessun altro meglio rappresentata che dal <lb/>Cartesio, a pag. </s>

<s>54 della Diottrica, e a pag. </s>

<s>62 del trattato <emph type="italics"/>De homine,<emph.end type="italics"/><lb/>nelle edizion&igrave; da noi citate. </s>

<s>Il Molinetti anatomico non trov&ograve; nulla da cor&shy;<lb/>reggere nel Filosofo, di cui con gran fedelt&agrave;, a pag. </s>

<s>21 delle sue <emph type="italics"/>Disserta&shy;<lb/>tiones,<emph.end type="italics"/> ricopia la figura, nella quale il Briggs ammir&ograve; tanta esattezza, da <lb/>creder che il Cartesio l'avesse ritratta dallo stesso esemplare dell'occhio <lb/>consolidato dal ghiaccio (Ophtalmographia, in Mangeti Biblioth. </s>

<s>anat. </s>

<s>cit, <lb/>T. II, pag. </s>

<s>363). </s></p><p type="main">

<s>Rimaste poi, specialmente in Italia, pi&ugrave; libere le menti, e osservando <lb/>che il Cartesio stesso non pretendeva di farla da anatomico, rimandando <lb/>anzi per le pi&ugrave; particolari descrizioni dell'occhio i suoi lettori ai trattati di <lb/>Anatomia, ne'quali &ldquo; plura circa hanc materiam notari solent &rdquo; (Dioptriees, <lb/>cap. </s>

<s>III cit., pag. </s>

<s>55); si giudic&ograve; che il modo di congelar l'occhio, secondo <pb xlink:href="020/01/1458.jpg" pagenum="333"/>il Briggs consueto al Cartesio, <emph type="italics"/>in votis potius quam in more fuisse.<emph.end type="italics"/> Que&shy;<lb/>sto giudizio &egrave; del Morgagni (Epist. </s>

<s>XVII cit., pag. </s>

<s>261), che trov&ograve; nel tea&shy;<lb/>tro anatomico padovano l'uso di congelar l'occhio s&igrave; antico, da creder che <lb/>risalisse ai tempi dell'Acquapendente. </s>

<s>Come altrimenti avrebb'egli infatti, <lb/>argomenta lo stesso Morgagni, potuto rappresentar nelle loro vere sedi i tre <lb/>umori, secondo che vedesi in quell'Iconismo impresso al cap. </s>

<s>VIII del III li&shy;<lb/>bro <emph type="italics"/>De oculo,<emph.end type="italics"/> con intenzione di giovare agli Ottici &ldquo; ut accurate observare <lb/>possint progressum varium radiorum, dum ab uno in alium humorem tran&shy;<lb/>seunt, atque angulos refractionis dimetiri? </s>

<s>&rdquo; (Op. </s>

<s>omnia cit., pag. </s>

<s>235). </s></p><p type="main">

<s>Parve quell'Iconismo all'Autore delle Epistole anatomiche cos&igrave; rappre&shy;<lb/>sentativo del vero, da non trovarsi di meglio, ei dice, se non forse nei tempi <lb/>moderni. </s>

<s>&ldquo; Attamen, poi soggiunge, si quaedam paulo diligentius essent re&shy;<lb/>praesentata, quaedam, Irisque praesertim, paulo amplius expressa, nihil aliis, <lb/>nihil mihi ipsi laboris relictum erat &rdquo; (Epist. </s>

<s>cit., pag. </s>

<s>461). Ond'&egrave; ch'ei <lb/>crede di aver ragione di maravigliarsi e di deplorare una cos&igrave; bell'opera <lb/>del Fabricio <emph type="italics"/>a posteris fere neglectam.<emph.end type="italics"/></s></p><p type="main">

<s>Voleva dire insomma il Morgagni che se non fosse stata dimenticata <lb/>la figura dell'occhio delineata e impressa dal Fabricio, si dovevano a que&shy;<lb/>sta tributare le prime lodi, per esser ritratta conforme alla verit&agrave; naturale, <lb/>meglio di quella del Cartesio. </s>

<s>Ma con riverenza di un tant'uomo ei s'in&shy;<lb/>gannava, bastando mettere a riscontro i due iconismi, per dover persuadersi <lb/>che il Cartesiano &egrave; di quel del Fabricio assai pi&ugrave; perfetto, non solo nel rap&shy;<lb/>presentar l'iride, e le altre parti dal Morgagni desiderate, ma, ci&ograve; che pi&ugrave; <lb/>importa, nel dipingere l'inserzione del nervo fuori dell'asse ottico. </s></p><p type="main">

<s>Da questa parte dunque aveva ragione il Briggs, ma s'ingannava an&shy;<lb/>ch'egli nel credere che cos&igrave; fatti perfezionamenti fossero stati nell'icono&shy;<lb/>grafia ottica introdotti dal Cartesio E perch'era facile avvedersi che il Filo&shy;<lb/>sofo speculava sul fondamento dei fatti da qualche Anatomico prima osservati, <lb/>sarebbe stato bisogno ricercar chi fosse quell'Anatomico, il quale perfezion&ograve; <lb/>l'opera dell'Acquapendente. </s>

<s>La ricerca non fu fatta dal Briggs, persuaso che <lb/>quell'anatomico fosse lo stesso Cartesio, e non fu fatta dal Morgagni, fissa <lb/>la mente nelle pagine del Fabricio, delle quale non fu, secondo lui, dipinto <lb/>mai meglio. </s>

<s>Che se avessero que'due valentuomini aperto per caso il libro <lb/>dello Scheiner intitolato <emph type="italics"/>Oculus,<emph.end type="italics"/> e gettato lo sguardo sopra quell'iconismo <lb/>impresso a pag. </s>

<s>17 (Oeniponti 1619), non bisognava altro per riconoscerlo <lb/>similissimo a quello del Cartesio. </s>

<s>In ogni modo &egrave; da questo Autore, negletto <lb/>dal Briggs e dal Morgagni, che vien rischiarato questo tratto di storia, avendo <lb/>lo Scheiner, reputato non pi&ugrave; che un semplice Ottico, avuto gran parte ai <lb/>progressi dell'iconografia anatomica dell'occhio. </s>

<s>Fu per servire alla maggior <lb/>precisione di questa iconografia che si dette a misurar la quantit&agrave; dell'umor <lb/>acqueo, rispetto al cristallino, e trov&ograve; che quella stava a questa in propor&shy;<lb/>zion sesquialtera, ossia come uno e mezzo sta ad uno, o come nove sta a <lb/>sei. </s>

<s>&ldquo; Ego oculum taurinum adhuc calentem caute aperui, aqueumque hu&shy;<lb/>morem provide in sphaerulam vitream excepi, quam semel totam deinde <pb xlink:href="020/01/1459.jpg" pagenum="334"/>dimidiam ex eo implevi: tum intrusi humorem cristallinum ex eodem oculo, <lb/>et spharulam praecise totam occupavit. </s>

<s>Itaque aqueus humor esset ad cri&shy;<lb/>stallinum in proportione sexquialtera &rdquo; (Oculus cit., pag. </s>

<s>16). </s></p><p type="main">

<s>Cos&igrave; riusc&igrave; a definir la grandezza delle Camere, e lo spazio occupato <lb/>dal cristallino, lasciando tutto il rimanente al vitreo. </s>

<s>Ma l'iconografia schei&shy;<lb/>neriana &egrave; come accennammo superiore a quelle de'predecessori, non eccet&shy;<lb/>tuato il Fabricio, specialmente per ci&ograve; che riguarda il punto dell'inserzione <lb/>del nervo &ldquo; qui non iacet in axe optico, sed sinistrorsum vergit in oculo <lb/>dextro, dextrorsus in sinistro. </s>

<s>Docet hoc experientia in oculo bovino, ovili, <lb/>caprino, suili et similium brutorum, cuius ego rei periculum coram aliis <lb/>frequentissimum feci.... Neque dicas ex eo quod nullus Anatomicorum hoc <lb/>asseruerit, probabile non videri id in hominis oculo verum esse, nam etiam <lb/>nullus id vel observavit vel affirmavit de oculo bestiae &rdquo; (ibid., pag. </s>

<s>18). </s></p><p type="main">

<s>Descritti gli umori, le tuniche e l'inserzione del nervo, vuol lo Scheiner <lb/>sodisfare ai curiosi di sapere in che modo, per ritrarlo pi&ugrave; esattamente, si <lb/>fosse preparato l'esemplare in natura, e dice che prendeva un bulbo fresco <lb/>e che lo lasciava essiccare all'aria, tenuto per lo stesso nervo sospeso a un <lb/>filo. </s>

<s>&ldquo; Et sic ideam oculi talem dedi qualem natura fabricante didici, qua&shy;<lb/>lem etiam Hyeronymus Fabricius ab Aquapendente, anno 1600, quem post <lb/>meam inquisitionem gratulabundus sum nactus, inventam posteritati com&shy;<lb/>mendavit &rdquo; (Ibid., pag. </s>

<s>20). </s></p><p type="main">

<s>Non aveva dunque ragione di lamentarsi della negligenza dei posteri il <lb/>Morgagni, se rivisse l'Acquapendente nello Scheiner, l'iconismo del quale, <lb/>delineato dalla stessa penna del Viviani (MSS. Cim., T. X, c. </s>

<s>34), tennero <lb/>sotto gli occhi gli Accademici fiorentini. </s>

<s>I Cartesiani credettero quella opera <lb/>del loro Maestro e bench&egrave; s'ingannassero conferirono efficacemente in dif&shy;<lb/>fondere la invenzione pubblicata nel 1600 da un nostro Italiano, e da un <lb/>successore di lui nella cattedra padovana, dopo pi&ugrave; di un secolo perfezio&shy;<lb/>nata, &ldquo; cum, petente anatomico praestantissimo Heistero, dice il Morgagni, <lb/>humanum iterum oculum delineandum curavi &rdquo; (Epist. </s>

<s>cit., pag. </s>

<s>261). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>L'organo &egrave; dunque, in tutte le sue parti pi&ugrave; minute, delineato dalla <lb/>pi&ugrave; esperta mano che si possa desiderare, ci&ograve; che accende in noi il desi&shy;<lb/>derio, e incora la speranza di sapere com'ei funziona. </s>

<s>Ma la via &egrave; lunga e <lb/>penosa, e le fatiche, dalla mente durate in percorrerla, non sono all'ultimo <lb/>consolate dal dolce riposo. </s>

<s>Ci rimane in ogni modo a dire, con la solita bre&shy;<lb/>vit&agrave;, quali frutti si raccogliessero dalle esperienze dei Fisici, e dalle specu&shy;<lb/>lazioni dei Filosofi, in riconoscer l'organo primario, e in penetrare le mi&shy;<lb/>steriose funzioni della vista. </s></p><p type="main">

<s>Galeno aveva, nel cap. </s>

<s>I del libro X <emph type="italics"/>De usu partium,<emph.end type="italics"/> lasciato scritto <pb xlink:href="020/01/1460.jpg" pagenum="335"/>essere il cristallino <emph type="italics"/>primum videndi instrumentum<emph.end type="italics"/> (Op. </s>

<s>omnia cit., T. I, <lb/>fol. </s>

<s>177), e fra'seguaci dell'antico Maestro alcuni interpetrarono quella sen&shy;<lb/>tenza come assoluta, altri pi&ugrave; savii dissero che voleva essere commentata <lb/>con altre dottrine, espresse nel medesimo testo, e per le quali si rendeva <lb/>la mente dell'Autore compiuta. </s></p><p type="main">

<s>Que'primi dunque attribuirono allo stesso cristallino la virt&ugrave; di sentire, <lb/>come si par dal nostro Berengario, che ne'citati Commentarii sopra Mundino <lb/>riferisce una tale opinione, invalsa gi&agrave; fra gli Arabi, ed egli pure la segue. <lb/></s>

<s>&ldquo; Hali vocat partem anteriorem cristallini subplanam, ut occurrat plurimae <lb/>quantitati eorum quae sentit. </s>

<s>Si enim esset haec pars rotunda perfecte, non <lb/>sentiret parva corpora, et non sentiret pariter, neque stabiliter, quia rotunda <lb/>figura non recipit in se, nisi vix aliqua fixa, cuius oppositum facit planities &rdquo; <lb/>(fol. </s>

<s>CCCCLXXIV). </s></p><p type="main">

<s>Quegli altri per&ograve; che, pi&ugrave; da savii, erano ben persuasi non poter la <lb/>virt&ugrave; di sentire riseder che solo nei nervi, ritrovarono questa verace dot&shy;<lb/>trina chiaramente espressa dallo stesso Galeno, l&agrave; dove nel cap. </s>

<s>II del ci&shy;<lb/>tato libro, discorrendo della retina, disse: &ldquo; Porro utilitas ipsius, prima qui&shy;<lb/>dem ac maxima, propter quam superne fuit demissa, est ut, cum crystallinus <lb/>alteratur, id sentiat &rdquo; (De usu partium, in loco cit., fol. </s>

<s>177). Non &egrave; dun&shy;<lb/>que, secondo Galeno, il cristallino che sente, ma le alterazioni prodotte in <lb/>lui dalle specie impresse, son tradotte al cervello per via della retina, che <lb/>perci&ograve; <emph type="italics"/>superne fuit demissa.<emph.end type="italics"/></s></p><p type="main">

<s>Molti furono gl'interpetri di Galeno, che professarono cos&igrave; fatte dot&shy;<lb/>trine, in mezzo ai quali s'annovera uno de'primi, fra gli Arabi stessi, Alha&shy;<lb/>zen, anche in ci&ograve; fedelmente seguito da Vitellione, che per la concavit&agrave;, in <lb/>cui spandesi il nervo ottico, intendendo la retina, scrisse come le immagini <lb/>degli oggetti, attraverso all'umor vitreo, giungessero infino a lei. </s>

<s>&ldquo; Quoniam <lb/>formae rerum visibilium, quando perveniunt in corpus humoris vitrei, exten&shy;<lb/>ditur sensus ab illo in corpus sentiens extensum in concavo nervi, conti&shy;<lb/>nuati inter visum et anterius cerebri &rdquo; (Optices libri, Norimbergae 1535, <lb/>pag. </s>

<s>60). </s></p><p type="main">

<s>Cos&igrave;, nella prima met&agrave; del secolo XVI, rimaneva il campo della scienza <lb/>diviso fra gli stessi seguaci di Galeno, alcuni de'quali professavano col Be&shy;<lb/>rengario bastare alla visione il cristallino, altri con Vitellione dicevano che <lb/>esso cristallino riceve solo le immagini degli oggetti, delle quali poi rimette <lb/>l'impressione alla retina, che sola &egrave; atta a sentire. </s>

<s>Fra gli Autori delle nuove <lb/>instaurazioni il Vesalio dubit&ograve; se fosse veramente il cristallino organo pri&shy;<lb/>mario, liberamente confessando &ldquo; hac in parte quod sanum undique sit a <lb/>me non adferri posse &rdquo; (De humani corporis fabrica cit., pag. </s>

<s>649). Ma per&shy;<lb/>ch&egrave; il dubbio e le difficolt&agrave; incontrate in risolverlo supponevano l'opinione <lb/>di quei Galenisti, che davano al cristallino la virt&ugrave; tutto insieme di ricevere <lb/>e di sentire; il Maurolico se ne deliber&ograve;, da una parte ammettendo che <lb/>l'umor glaciale sia quello &ldquo; in quo visiva virtus tanquam in sede consistit &rdquo; <lb/>(Photismi cit., pag. </s>

<s>69), e dicendo dall'altra che, ricevute le specie, esso <pb xlink:href="020/01/1461.jpg" pagenum="336"/>umor glaciale &ldquo; per opticum nervum ad communis sensus indicium defert &rdquo; <lb/>(ibid., pag. </s>

<s>70). </s></p><p type="main">

<s>Questa era come vedemmo dottrina comunemente professata dai migliori <lb/>interpetri di Galeno. </s>

<s>Non essendo per&ograve; il Maurolico notomista, e rimaste per <lb/>lungo tempo le sue speculazioni ottiche sconosciute, il Colombo ripet&egrave; con <lb/>gli Arabi e col Berengario essere il cristallino &ldquo; praecipuum ac pene princeps <lb/>videndi instrumentum &rdquo; (De re anat. </s>

<s>cit., pag. </s>

<s>219), n&egrave; in sentenza punto <lb/>diversa and&ograve; il Falloppio, che, per essere esso cristallino diafano, &ldquo; facil&shy;<lb/>lime, disse, colorum species suscipit &rdquo; (Instit. </s>

<s>anat., Op. </s>

<s>omnia cit., pag. </s>

<s>511). </s></p><p type="main">

<s>Ma cos&igrave; gli uni come gli altri seguaci di Galeno, che rimasero nelle <lb/>opinioni, come s'&egrave; veduto, infino ai tempi del Falloppio, divisi, lasciavano <lb/>a desiderar molte cose, e intorno al modo come il cristallino sente, e intorno <lb/>a quella parte, o a quella trasformazione del nervo ottico, che ha da rice&shy;<lb/>vere la sensazione. </s>

<s>L'Acquapendente fu tra'Galenisti il primo, che pretese <lb/>di dimostrare com'essendo la retina opaca, e perci&ograve; inalterabile alla luce, <lb/>era in tanto solo atta a ricevere le impressioni visive, in quanto ella si tra&shy;<lb/>sforma nell'aranea lucida, che riveste il cristallino dalla sua parte anteriore. <lb/></s>

<s>&ldquo; Natura tunicam retinam opacam et corpulentam fecit, nequaquam diapha&shy;<lb/>nam, quo fit ut a luce affici immutarique minime possit.... Quod si non <lb/>afficitur, neque etiam sentire potest.... Igitur retina quatenus a nervi me&shy;<lb/>dulla et cerebri substantia exorta, eatenus sentientem secum defert faculta&shy;<lb/>tem, quatenus insuper ad crystallinum progressa, eatenus ad araneae gene&shy;<lb/>rationem sese offert &rdquo; (De oculo, Op. </s>

<s>omnia cit., pag. </s>

<s>235). </s></p><p type="main">

<s>In questa e in altre dottrine di Fisiologia ottica, esposte nel trattato <lb/>dell'Acquapendente, ritrovava la scienza galenica il suo massimo svolgimento. </s>

<s><lb/>Ma rimaneva il modo come si fa la vista tuttavia oscuro, non appagando la <lb/>mente quel che si diceva delle specie impresse nel cristallino diafano, e nel&shy;<lb/>l'aranea lucida, che ne trasmette le impressioni al sensorio comune. </s>

<s>Dal&shy;<lb/>l'altra parte si disputava tra'Filosofi, seguaci di Aristotile e di Platone, se <lb/>quelle specie venivano dagli oggetti all'occhio, o s'era l'occhio stesso che <lb/>le mandava agli oggetti. </s></p><p type="main">

<s>A dare a intendere il modo come si fa la vista, e a decidere fra gli <lb/>aristotelici e i platonici la lunga questione, soccorse opportunissima un'espe&shy;<lb/>rienza, che risale al secolo XV, trovandosene ne'manoscritti di Leonardo da <lb/>Vinci, per quanto se ne sappia, la pi&ugrave; antica memoria. </s>

<s>&ldquo; La sperienzia (cos&igrave; <lb/>leggesi in una di quelle note vinciane pubblicate da Guglielmo Libri) che <lb/>mostra come li obietti mandino le loro spezie, ovvero similitudini, interse&shy;<lb/>gate dentro all'occhio nello umore albugineo, si dimostra quando, per al&shy;<lb/>cuno piccolo spiracolo rotondo, penetreranno le spezie delli obietti allumi&shy;<lb/>nati in abitazione forte oscura. </s>

<s>Allora tu riceverai tale spezie in una carta <lb/>bianca, posta dentro a tale abitazione alquanto vicina a esso spiracolo, e ve&shy;<lb/>drai tutti li predetti obbietti in essa carta colle lor proprie figure e colori, <lb/>ma saran minori, e fieno sottosopra, per causa della detta intersegazione &rdquo; <lb/>(Histoire des sciences mathem., T. IV, Paris 1841, pag. </s>

<s>305, 6). </s></p><pb xlink:href="020/01/1462.jpg" pagenum="337"/><p type="main">

<s>Se si potesse penetrare addentro alle tenebre di quei tempi, si vedreb&shy;<lb/>bero i dimenticati Fisiologi contemporanei di Leonardo disputare fra loro <lb/>intorno all'analogia, che si diceva passar fra la camera oscura e l'occhio, <lb/>e alcuni pi&ugrave; ritrosi negarla, per cagion delle immagini, che si rappresente&shy;<lb/>rebbero a rovescio. </s>

<s>Gli amatori delle cose nuove, dall'altra parte, si dovet&shy;<lb/>tero studiar di vincere una tal ritrosia, e vi riuscirono, accomodando nello <lb/>strumento uno specchio concavo, che addirizzasse le immagini, e dicendo <lb/>che nell'occhio era quello specchio rappresentato dalla retina, alla quale fa <lb/>da amalgama il pigmento coroideo. </s></p><p type="main">

<s>Di questo segreto lavor&igrave;o della scienza, dissipato nelle parole de'dispu&shy;<lb/>tanti, o consegnato a carte manoscritte, in parte dimenticate e in parte di&shy;<lb/>sperse, n'&egrave; rimasto qualche memoria nella prima Magia naturale scritta in <lb/>quattro libri dal Porta. </s>

<s>Nel II capitolo del III libro, dop'aver l'Autore de&shy;<lb/>scritta la camera oscura, e il modo d'accomodarvi lo specchio per dirizzar <lb/>le immagini, &ldquo; Hinc philosophis, soggiunge, et medicis patet quo fiat in ocu&shy;<lb/>lis visus loco, ac intromittendi dirimitur quaestio sic agitata, nec alio prae&shy;<lb/>stantius utrunque artificio demonstrari poterat. </s>

<s>Intromittitur enim idolum <lb/>per pupillam fenestrae instar, vicemque obtinet speculi parva magnae sphae&shy;<lb/>rae portio ultimo locata oculi &rdquo; (Neapoli 1588, pag. </s>

<s>143, 44). Che poi per <lb/>questa piccola porzione della sfera grande si debba intendere il fondo del&shy;<lb/>l'occhio, ossia il concavo del nervo ottico espanso, come gli specchi artifi&shy;<lb/>ciali anch'egli impiombato dal pigmento coroideo, s'argomenta da quelle <lb/>parole, che si leggono nel cap. </s>

<s>XVIII del IV libro, dove, dop'avere inse&shy;<lb/>gnato il modo come si pone agli specchi di vetro la piastra, soggiunge: <lb/>&ldquo; Hinc Natura, rerum omnino parens, oculum speculi instar composuit, <lb/>quippe a tergo pellucentibus partibus nigriorem quemdam apposuit, quo <lb/>sublato, et tolleretur videndi facultas &rdquo; (ibid., pag. </s>

<s>155). </s></p><p type="main">

<s>In questa teoria della visione per&ograve; gli umori non fanno altro ufficio, che di <lb/>ricevere le immagini venute dal foro della pupilla, come le riceve il diaframma <lb/>posto di rincontro al foro della camera oscura. </s>

<s>Anzi non &egrave; propriamente <lb/>quell'ufficio assegnato che all'albugineo, secondo Leonardo, o al cristallino <lb/>secondo il Porta: dell'uso particolare di ciascuno degli altri umori i nuovi <lb/>dimostratori della recezion delle immagini non ne intendono ancora nulla. </s></p><p type="main">

<s>Galeno aveva insegnato che l'uso naturale dell'umor vitreo era quello <lb/>di alimentare il cristallino. </s>

<s>&ldquo; Humori autem crystallino nutrimentum ei obti&shy;<lb/>git, comparatumque ei a Natura fuit accomodatum humor vitreus &rdquo; (De usu <lb/>partium, Op. </s>

<s>omnia cit., T. I, fol. </s>

<s>177). L'umor acqueo, secondo lo stesso <lb/>Galeno, non &egrave; nella parte anteriore dell'occhio ad altro ufficio disposto, che <lb/>a impedire gli attriti, che potrebbe il cristallino patir dalla durezza della <lb/>cornea, attraverso al foro aperto della pupilla. </s>

<s>&ldquo; Ut igitur nec per hoc fo&shy;<lb/>ramen tunica cornea aliquando crystallinum humorem tangeret, Opifex no&shy;<lb/>stri providit, simul quidem portionem hanc corneae foras longius abducens, <lb/>simul autem humorem quendam tenuem ac sincerum, cuiusmodi in ovis <lb/>reperitur, crystallino circumfundens &rdquo; (ibid., fol. </s>

<s>179). </s></p><pb xlink:href="020/01/1463.jpg" pagenum="338"/><p type="main">

<s>Alhazen e Vitellione avevano fatto qualche cenno alle rifrazioni, che su&shy;<lb/>bisce la luce attraverso agli umori dell'occhio, prima di andar direttamente <lb/>a ferire il concavo del nervo. </s>

<s>Ma rimasero i germi delle loro idee sterili nel <lb/>campo de'Galenisti, i quali facevano recettore delle specie e primario organo <lb/>della vista il cristallino. </s></p><p type="main">

<s>Nonostante, l'Acquapendente, fra quegli stessi seguaci di Galeno, fu il <lb/>primo a riformare e a ridurre a miglior senso gli oramai invalsi placiti del&shy;<lb/>l'antico Maestro. </s>

<s>Egli assegn&ograve; il poter rifrangente alla cornea e all'umor <lb/>acqueo, i quali fanno come una pila di vetro convergere e appuntare nel <lb/>cristallino i raggi visivi, che altrimenti andrebbero dispersi. </s>

<s>&ldquo; Cui rei aquei <lb/>humoris copi&agrave; valde astipulatur, quae tanta est, quanta est necessaria ut <lb/>lux, unita et fortissima reddita, ad crystallinum pertingat, priusquam disper&shy;<lb/>datur; ita ut punctum illud, in quo radiorum fit concursus, crystallinus sit &rdquo; <lb/>(De oculo cit., pag. </s>

<s>224). N&egrave; il vitreo &egrave;, soggiunge l'Acquapendente, ordi&shy;<lb/>nato a nutrire il cristallino, come insegnava Galeno, ma gli fu posto dietro <lb/>questo diafano, affinch&egrave; i raggi non avessero a riflettersi sopra lo stesso umor <lb/>cristallino, incontrandosi in un corpo opaco, e tingendosi de'colori di lui. <lb/></s>

<s>&ldquo; Propter hoc Natura diaphanum corpus, nimirum vitreum, post crystalloi&shy;<lb/>dem locavit, ne lux crystallinum transverta statim, ab opacis coloratisque <lb/>corporibus foedata, ad crystallinum revertatur &rdquo; (ibid., pag. </s>

<s>236). </s></p><p type="main">

<s>In ogni modo, bench&egrave; cos&igrave; riformata la teoria galenica della visione, non <lb/>sodisfaceva i migliori ingegni speculativi, ai quali arridevano piuttosto le <lb/>analogie ricavate dall'esperienza. </s>

<s>Pochi anni dopo che l'Acquapendente scri&shy;<lb/>veva, furono quelle analogie messe dal Keplero nella pi&ugrave; chiara luce, ma <lb/>alla storia dell'Ottico alemanno ne precede un'altra schiettamente italiana, <lb/>della quale dobbiamo ora far qualche cenno, riappiccando il filo del nostro <lb/>discorso col&agrave;, dove in Leonardo e nel Porta lo lasciammo interrotto. </s></p><p type="main">

<s>Que'Filosofi che accolsero le speculazioni, delle quali l'Artista da Vinci <lb/>e il Fisico di Napoli ci porgevano dianzi i documenti, dovettero ripensare a <lb/>qual uso fossero cos&igrave; ben disposti gli umori, i quali non potevano starvi <lb/>inutili, come pareva insinuarsi dalle esperienze della prima Camera oscura, <lb/>e non potevano dall'altra parte essere, come si diceva, recettori delle imma&shy;<lb/>gini, per esser queste in ogni diafano dissipabili. </s></p><p type="main">

<s>Or occorse, in mezzo a questi pensieri che, per rendere anche pi&ugrave; <lb/>stretta la somiglianza fra l'organo naturale e lo strumento artificioso, si <lb/>adattasse al foro di questo una lente biconvessa, che faceva le veci del cri&shy;<lb/>stallino. </s>

<s>Le immagini, che apparivano sul diaframma pi&ugrave; distinte, fecero gli <lb/>osservatori accorti del poter rifrangente che dovevano avere, in rendere la <lb/>vista pi&ugrave; distinta, gli umori, e l'analogia fra il modo del rappresentarsi le <lb/>immagini nella Camera oscura, e nell'occhio, riusc&igrave; per ogni parte mirabil&shy;<lb/>mente compiuta. </s></p><p type="main">

<s>Chi primo avesse cos&igrave; ingegnosamente, ne'giochi dell'arte, scoperti i <lb/>segreti della Natura, non si potrebbe additar da noi con certezza. </s>

<s>Ma perch&egrave; <lb/>nel Libro delle speculazioni di Giovan Batista Benedetti, nel 1580, se ne <pb xlink:href="020/01/1464.jpg" pagenum="339"/>trova fatta di ci&ograve; la prima menzione, non dubitiamo di riconoscerne il Ma&shy;<lb/>tematico veneziano per primo Autore. </s>

<s>&ldquo; Ratio unde fiat ut videamus di&shy;<lb/>stincte omnes colores, egli dice, cum in qualibet aeris parte, quo lumina <lb/>reflexa possunt pervenire, mixta sint et non distincta, oritur a parvitate <lb/>ipsius pupillae oculorum, et a magna expansione virtutis visivae in super&shy;<lb/>ficie concava orbis continentis humores diaphanos oculorum, per ramuscu&shy;<lb/>los nervi optici remote ab ipsa pupilla. </s>

<s>Et quamvis radii luminosi frangan&shy;<lb/>tur ab unoquoque humore diversimode, hoc nihilominus maxime iuvat ad <lb/>distinctionem radiorum, sed et si directe procederent idem fere eveniret, non <lb/>tamen suis locis. </s>

<s>Cogita ex. </s>

<s>gr. </s>

<s>lineam AUE (fig. </s>

<s>9) ut communis sectio <lb/><figure id="id.020.01.1464.1.jpg" xlink:href="020/01/1464/1.jpg"/></s></p><p type="caption">

<s>Figura 9.<lb/>cuiusdam plani secantis sphaeram <lb/>oculi, per centrum ipsius et pupillae, <lb/>et O punctum sit proximum centro <lb/>ipsius pupillae, sed interius aliquan&shy;<lb/>tulum: extra autem oculum sint varii <lb/>colores, ut C, N, T in dicto diaphano. </s>

<s><lb/>Iam nulli dubium est quod lumina, <lb/>quae producuntur ab C, N, T ad O, in <lb/>ipso O mixta et non distincta. </s>

<s>Procedendo igitur ulterius ipsi radii citra O, <lb/>tunc disgregantur et separantur ad invicem, et cum parveniunt ad lineam <lb/>AUE, sentiuntur distincti alii ab aliis &rdquo; (Speculationum Liber, Venetiis 1599, <lb/>pag. </s>

<s>296, 97). </s></p><p type="main">

<s>In queste speculazioni per&ograve; si sollevava cos&igrave; l'Autore sopra la scienza <lb/>de'suoi tempi, che non fa maraviglia se rimase incompreso. </s>

<s>Avendo letto <lb/>il Plater in Realdo Colombo che, estratto il cristallino dall'occhio, e avvi&shy;<lb/>cinatolo ai caratteri scritti, questi apparivano pi&ugrave; grandi e pi&ugrave; distinti, e che <lb/>perci&ograve; credeva di qui &ldquo; specillorum inventionem originem duxisse &rdquo; (De re <lb/>anat. </s>

<s>cit., pag. </s>

<s>219); immagin&ograve; che lo stesso cristallino, in ingrandir gli og&shy;<lb/>getti alla retina, facesse da occhiale, e lo scrisse nel III libro <emph type="italics"/>De corporis <lb/>humani structura,<emph.end type="italics"/> pubblicato la prima volta nel 1583 in Basilea, con que&shy;<lb/>ste parole, che noi per&ograve; trascriviamo dalla seconda edizione: &ldquo; Cristallinus <lb/>humor, qui perspicillum est nervi visorii, atque ante ipsum et pupillae fo&shy;<lb/>ramen collocatus species oculo illabentes veluti radios colligit, et in ambi&shy;<lb/>tum totius retiformis nervi diffundens, res maiores illi, ut commodius eas <lb/>perciperet, perspicilli penitus modo, repraesentat &rdquo; (Basileae 1603, pag. </s>

<s>187). </s></p><p type="main">

<s>N&egrave; punto meglio del Plater seppe interpetrare il Libro delle Specula&shy;<lb/>zioni il Porta, il quale, nel riformar che fece nel 1585 e ridurre in XX libri <lb/>la Magia naturale, descritta la Camera oscura, co'perfezionamenti introdot&shy;<lb/>tivi dal Benedetti, passa a farne l'applicazione alla vista, e l&agrave; dove prima <lb/>aveva detto far le veci dello specchio il fondo dell'occhio, ora si corregge <lb/>scrivendo tener luogo del diaframma recettor delle immagini il cristallino. <lb/></s>

<s>&ldquo; Vicemque obtinet tabulae crystallinae sphaerae portio in medio ocnli lo&shy;<lb/>cata &rdquo; (Magiae natur., libri XX, Lugd. </s>

<s>Batav. </s>

<s>1651, pag. </s>

<s>590). </s></p><p type="main">

<s>Volle la mala ventura che capitassero al Keplero, invece delle Specula-<pb xlink:href="020/01/1465.jpg" pagenum="340"/>zioni del Benedetti, i commenti che, senza intenderle, ne avevano fatti il <lb/>Plater e il Porta. </s>

<s>E quanto al primo parve all'Autore de'Paralipomeni a <lb/>Vitellione che l'ufficio di amplificare le immagini, attribuito al cristallino, <lb/>fosse cosa tutta aliena dal proposto negozio, imperocch&egrave; &ldquo; haec amplificatio <lb/>literarum per crystallinum, vel ei analogon quippiam, in oculo, non infor&shy;<lb/>mat visionem &rdquo; (Francofurti 1604, pag. </s>

<s>208). </s></p><p type="main">

<s>Quanto al Porta, che chiama eccellente investigatore de'misteri della <lb/>Natura, al sentirgli spiegare il modo della visione per mezzo della Camera <lb/>ottica, dirimendo cos&igrave; le antiche liti fra i seguaci di Aristotile e quelli di <lb/>Platone, <emph type="italics"/>equidem beasti nos,<emph.end type="italics"/> esclama il Keplero. </s>

<s>&ldquo; Caeterum de modo vi&shy;<lb/>sionis, poi prosegue, paulo accuratius verba tua, Porta, consideranda sunt. <lb/><emph type="italics"/>Hinc,<emph.end type="italics"/> inquis, <emph type="italics"/>patet quonam fiat visus loco.<emph.end type="italics"/> Et postea explicans, <emph type="italics"/>transmit&shy;<lb/>titur,<emph.end type="italics"/> inquis, <emph type="italics"/>idolum per pupillam fenestrae foraminis instar, vicemque <lb/>obtinet tabulae crystallinae sphaerae portio.<emph.end type="italics"/> Ergo, si te bene capio, tu si <lb/>interrogeris quo loco visio fiat respondebis in superficie crystallini ceu in <lb/>tabula..... Sane si hic scopum fixum habes, si non ultra crystallinum de&shy;<lb/>scendis, errasti sententia..... Itaque, ut concludam, si hoc unum, Porta so&shy;<lb/>lertissime, tuae sententiae addideris: picturam in crystallino adhuc confusam <lb/>esse admodum, praesertim dilatato foramine uveae, nec fieri visionem per <lb/>coniunctionem lucis cum crystallino, sed descendere in retinam, descensu&shy;<lb/>que eo et magis separari diversorum et coniungi eiusdem puncti radiatio&shy;<lb/>nes, inque ipsa retina locum esse collectionis ad punctum, quae evidentiam <lb/>picturae praestat, fierique et per illam intersectionem ut imago fiat eversa, <lb/>et per hanc collectionem ut distinctissima sit et evidentissima; hoc, in&shy;<lb/>quam, si addideris, tuae sententiae plane absolveris visionis modum &rdquo; (ibid., <lb/>pag. </s>

<s>210, 11). </s></p><p type="main">

<s>Se avesse il Keplero letto il libro del Benedetti, <emph type="italics"/>equidem beasti nos<emph.end type="italics"/><lb/>avrebbe detto a lui con pi&ugrave; ragione, per essere stato lui veramente che, <lb/>dietro le analogie colla camera ottica, insegn&ograve; che la visione si faceva sulla <lb/>retina per modo di pittura. </s>

<s>Ma rimasto fra gli stessi Italiani dimentico il <lb/>Matematico di Venezia, l'onore dell'invenzione and&ograve; tutto intero all'Astro&shy;<lb/>nomo di Praga. </s></p><p type="main">

<s>Ad eccitar pi&ugrave; che mai viva la curiosit&agrave; de'Filosofi intorno a cotesta <lb/>invenzione concorse efficacemente la scoperta del Telescopio, il modo del&shy;<lb/>l'operar del quale reputandosi affatto simile a quello dell'occhio, faceva spe&shy;<lb/>rare che insiem con l'uno si rivelerebbe anche l'altro mistero. </s>

<s>Fu tra co&shy;<lb/>loro, che ingerirono una s&igrave; lusinghiera speranza, Gian Francesco Sagredo, <lb/>gentiluomo veneziano, che il d&igrave; 2 Giugno 1612 cos&igrave; scriveva in una sua let&shy;<lb/>tera a Galileo: &ldquo; Versa ora la mia speculazione sopra il modo come si faccia <lb/>la vista, e come gli occhiali, cos&igrave; gli ordinarii come questi della nuova in&shy;<lb/>venzione, siano di aiuto per accrescerla. </s>

<s>E perch&egrave;, come V. S. E. sa, io sono <lb/>matematico di nome e niente di essenza e verit&agrave;, perci&ograve;, non avendo ve&shy;<lb/>duto n&egrave; Vitellione n&egrave; altri Autori che trattano della Prospettiva, io non ho <lb/>in testa altra dottrina che quella che mi ha dettata il mio proprio discorso &rdquo; <pb xlink:href="020/01/1466.jpg" pagenum="341"/>(Alb. </s>

<s>VIII, 204). Nella verit&agrave; del qual discorso riposerebbe tranquillo, se <lb/>non gli fosse contrariato da Agostino Mula e da Paolo Sarpi, i quali si fa&shy;<lb/>cevano forti dell'autorit&agrave; degli scrittori. </s>

<s>&ldquo; E perch&egrave;, prosegue a dire il Sa&shy;<lb/>gredo a Galileo, io stimo pi&ugrave; lei e il suo giudizio che quello degli scrittori, <lb/>in particolare la prego scrivermi sommariamente la sua opinione &rdquo; (ivi). </s></p><p type="main">

<s>Galileo ricus&ograve; di compiacere all'amico, il quale torn&ograve; cos&igrave; a fare istanza, <lb/>come un povero affamato, che chieda la carit&agrave; di un po'di pan secco a qual&shy;<lb/>che ricco avaro: &ldquo; Giacch&egrave; ella non vuol significarmi la sua opinione, in&shy;<lb/>torno al modo che si fa la vista, almeno la prego a scriver la volgata per <lb/>modo storico, senza dimostrazioni &rdquo; (ivi, pag. </s>

<s>213). </s></p><p type="main">

<s>La lettera, in cui si scrivevano queste parole, fu data da Venezia quat&shy;<lb/>tordici giorni dopo la precedente, nel qual tempo sembra che fosse per la <lb/>prima volta capitato alle mani del Sagredo il trattato <emph type="italics"/>De radiis visus et lucis<emph.end type="italics"/><lb/>di Marc'Antonio De Dominis, del quale il Sagredo stesso ne parlava in que&shy;<lb/>sti termini a Galileo: &ldquo; Io non so se ella abbia veduto un trattato dell'Ar&shy;<lb/>civescovo di Spalatro circa l'Occhiale. </s>

<s>Se cost&igrave; non si trova, mi avvisi che <lb/>glielo mander&ograve; subito, perch&egrave; mi sarebbe caro intendere il giudizio di V. S. <lb/>sopra esso trattato &rdquo; (ivi). </s></p><p type="main">

<s>Ma verso la fine del mese, bench&egrave; Galileo ch'era allora tutto dietro a <lb/>far sua quella ch'ei chiamava <emph type="italics"/>istituzione circa la vista,<emph.end type="italics"/> promettesse d'in&shy;<lb/>segnare il modo di misurare il concorso degli angoli visuali, avuto riguardo <lb/>alla maggiore o minore apertura della pupilla, che il mondo tutto da tanti <lb/>anni aveva imparato da Archimede; quanto al dar giudizio del trattato del <lb/>De Dominis era ancora rimasto in silenzio, per cui il Sagredo cos&igrave; tornava <lb/>a sollecitarlo: &ldquo; Io sto con gran desiderio attendendo la sua istituzione circa <lb/>la vista, e mi sar&agrave; caro che ella non si scordi di scrivermi il suo parere <lb/>sopra il libro intitolato <emph type="italics"/>De radiis visus et lucis<emph.end type="italics"/> dell'Arcivescovo di Spala&shy;<lb/>tro, il quale a carte 15 confuta con assai familiarit&agrave; la mia opinione, che <lb/>cio&egrave; la vista si faccia dentro l'occhio, per le rifrazioni che fanno le spezie, <lb/>passando per l'umore cristallino &rdquo; (ivi, pag. </s>

<s>217). </s></p><p type="main">

<s>Sanno i nostri Lettori oramai quanto fosse alieno dal professar cos&igrave; fatti <lb/>sani principii di Fisiologia ottica quel Galileo, che credeva co'Platonici nel&shy;<lb/>l'emission delle specie; che faceva concorrere i raggi visuali dietro l'occhio <lb/>irrefratti e non decussati; che teneva co'Galenisti essere il cristallino sensi&shy;<lb/>tivo, e recettore delle immagini. </s>

<s>Vinto dall'importunit&agrave;, scrisse finalmente <lb/>intorno alla vista una tal sua opinione, ch'era l'impasto di tutti questi er&shy;<lb/>rori, e alla quale il Sagredo francamente si oppose: &ldquo; Quanto a quello, che <lb/>ella mi scrive dei raggi visivi e delle spezie, io non so trattare della diffe&shy;<lb/>renza tra loro, poich&egrave; io non credo che vi sieno raggi visivi, n&egrave; per ancora <lb/>comprendo come questi sieno necessarii per vedere. </s>

<s>Ma siccome il suono <lb/>nelle nostre orecchie si fa, per la percussione causata dall'aere nel timpano, <lb/>senza che da esso timpano parta cosa alcuna; cos&igrave; credo che succeda al&shy;<lb/>l'occhio. </s>

<s>E circa a quello che mi scrive della inversione delle macchie del <lb/>sole, che si vedono nella carta, io non metto dubbio che l'istesso non oc-<pb xlink:href="020/01/1467.jpg" pagenum="342"/>corra nell'occhio, il quale, per essere avvezzo ad apprendere tutte le spezie <lb/>rovescie, le giudica dirette &rdquo; (Alb. </s>

<s>XVI, 59). </s></p><p type="main">

<s>In queste idee del gentiluomo, che non faceva professione di scienza, <lb/>concorse in quel medesimo tempo un Artista, amico anch'egli e familiare <lb/>di Galileo. </s>

<s>Lodovico Cigoli, dop'aver descritta nella sua Prospettiva pratica <lb/>la camera oscura, sul diaframma della quale si dipingono le immagini degli <lb/>oggetti a rovescio. </s>

<s>&ldquo; Nel medesimo modo, egli dice, le immagini esterne <lb/>vengono riportate, e non sopra la sfera dell'occhio, perch&egrave;, quando si fa <lb/>qualche concorso di materia fra il cristallino e la cornea, ci par di vedere <lb/>per l'aria, alquanto lontano, qualche cosa di simile alle tele del ragno, e <lb/>cos&igrave; di colore oscuro, perch'essendo tal materia illuminata dalla parte este&shy;<lb/>riore, e veduta dalla parte interiore ch'&egrave; l'ombrosa, perci&ograve; ci apparisce <lb/>oscura. </s>

<s>Il che ci fa manifesto che la sensazione &egrave; pi&ugrave; interna dell'umore <lb/>acqueo, e non pare possa essere nel centro del cristallino, perch&egrave; come cen&shy;<lb/>tro non &egrave; capace delle diverse quantit&agrave;. </s>

<s>Ma piuttosto, passando i raggi per <lb/>il centro di esso, come per lo esempio della stanza e formando un angolo <lb/>alla cima, si dir&agrave; che faccino la base nella superficie del nervo ottico, dove <lb/>s'imprimono le specie ad esempio della stanza, e di tanto maggiore squisi&shy;<lb/>tezza, quanto le requ&igrave;site condizioni si trovano in pi&ugrave; squisito grado &rdquo; (MSS. <lb/>Gal. </s>

<s>Contemporanei, T. VIII, c. </s>

<s>25). </s></p><p type="main">

<s>Il Cigoli e il Sagredo che ritrovano cos&igrave; la scienza della visione non <lb/>ne'libri ma nel loro proprio discorso, mentre Galileo veniva ostinatamente <lb/>ripetendo i pi&ugrave; vieti errori letti ne'libri di Platone e di Galeno, dimostrano <lb/>che le dottrine del Benedetti, divulgate dal Keplero, si presentavano sotto <lb/>l'aspetto di verit&agrave; naturali, rintuzzate dall'aculeo dei sofismi, e adombrate <lb/>dalle caligini dei pregiudizii. </s>

<s>Dicevasi che la retina, essendo opaca, non era <lb/>atta a specchiare in s&egrave; le immagini degli oggetti. </s>

<s>Ma rispondeva a questa <lb/>difficolt&agrave; il Santorio nella questione CXXIII de'suoi Commentarii sopr'Avi&shy;<lb/>cenna, facendo notare che, appunto per ritenere le immagini, deve essa re&shy;<lb/>tina essere opaca, perch&egrave; altrimenti, come tutti i diafani sogliono, diffonde&shy;<lb/>rebbe la luce e ne disperderebbe i raggi in altri mezzi. </s>

<s>&ldquo; In illa parte debet <lb/>fieri visio, in qua obiecta non transferuntur in aliena loca, sed hic est quod <lb/>refractiones, quae fiunt in aqueo, crystallino et vitreo, reducant visibile in <lb/>aliena loca, ergo in ipsis non fiet visio. </s>

<s>Retina vero cogit omnes radios re&shy;<lb/>fractos, impeditque ne ulterius penetrare possint, itaque firmantur &rdquo; (Opera <lb/>omnia, T. III, Venetiis 1660, pag. </s>

<s>1065). </s></p><p type="main">

<s>Faceva inoltre difficolt&agrave; la manifesta inversione delle immagini sul dia&shy;<lb/>framma della Camera oscura, mentre l'occhio vede gli oggetti diretti. </s>

<s>&ldquo; Omnia <lb/>cernuntur inversa, scriveva il De Dominis, quia radii sese in illo angusto <lb/>foramine intersecant, quod in oculo neque contingit neque contingere po&shy;<lb/>test: visio enim fit valde prope foramen uveae, antequam sese radii possent <lb/>intersecare, et quia visio debet fieri in unico puncto, qui sit vertex coni <lb/>visivi, illa vero simulacra occupant magnum spatium &rdquo; (De radiis visus et <lb/>lucis, Venetiis 1611, pag. </s>

<s>15). </s></p><pb xlink:href="020/01/1468.jpg" pagenum="343"/><p type="main">

<s>Il Cigoli aveva invece dimostrato che la visione dee farsi molto pi&ugrave; in&shy;<lb/>dietro dell'Uvea, e il Sagredo aveva detto che l'occhio giudica esser tutti <lb/>gli oggetti diritti, per essere avvezzo ad apprenderne le specie tutte a ro&shy;<lb/>vescio. </s>

<s>A questa spiegazione del fatto singolare, che parve anche ai moderni <lb/>la pi&ugrave; filosofica di tutte, si riduce quell'altra dello Scheiner, il quale dice <lb/>che perci&ograve; le immagini dipinte sulla retina a rovescio si vedon diritte &ldquo; quod <lb/>nimirum visus rem eo loco esse apprehendat, quo radius formaliter visorius, <lb/>si produceretur, exiret &rdquo; (Oculus cit., pag. </s>

<s>192). </s></p><p type="main">

<s>Il Baliani pi&ugrave; tardi, in quel suo trattatello <emph type="italics"/>De visione,<emph.end type="italics"/> raccolto fra le <lb/>Opere diverse pubblicate in Genova dal Calenzani, nel 1666, era, a spiegare <lb/>il fatto, ricorso ai varii poteri rifrangenti del vitreo e del cristallino da lui <lb/>stesso sperimentati sui cadaveri (pag. </s>

<s>321), ma il Santorio non aveva ve&shy;<lb/>duto miglior partito di togliersi d'ogni impaccio che col negar la supposta <lb/>inversione delle immagini, dicendo che queste venivano raddirizzate sopra <lb/>la retina dalle seconde rifrangenze del vitreo. </s>

<s>&ldquo; Sicuti uno vitro convexo, <lb/>scrive nella sopra citata Questione, species visibilis in charta non erigitur, <lb/>sed duobus vitris erigitur.... quia crystallinus est unum vitrum convexum, <lb/>vitreus vero humor est aliud, sic in retina figurae eriguntur &rdquo; (Op. </s>

<s>omnia <lb/>cit., pag. </s>

<s>1065). </s></p><p type="main">

<s>L'errore del Santorio si veniva a scoprir facilmente dalle sopra accen&shy;<lb/>nate esperienze del Baliani, ma perch&egrave; queste erano difficili troppo, e su&shy;<lb/>periori alla perizia, che in tal genere d'arte sperimentale poteva aversi a <lb/>que'tempi, non c'era migliore argomento dimostrativo che quello dei fatti. </s>

<s><lb/>Lo Scheiner aveva opportunamente citato l'esempio di quell'uomo, a cui es&shy;<lb/>sendo rimasta la pupilla annuvolata, fuor che per un breve tratto da rasso&shy;<lb/>migliarsi a una sottil falce di luna, non vedeva gli oggetti se non che quando <lb/>i loro raggi v'entravano obliqui (Oculus cit., pag. </s>

<s>36). </s></p><p type="main">

<s>Chi fosse propriamente il primo ad osservare sul fondo dell'occhio, come <lb/>sul diaframma di una Camera ottica preparata dalle stesse mani della Na&shy;<lb/>tura, le immagini rovesciate, crediamo non si poter con fiducia asserirlo. </s>

<s><lb/>Uno fra costoro in ogni modo, se ha da credersi al Gassendo, sarebbe stato <lb/>il Peiresc, il quale, persuaso che la retina amalgamata a tergo dalla coroide <lb/>faccia nell'occhio l'ufficio degli specchi, che raddirizzan le immagini, rin&shy;<lb/>novell&ograve; nel 1634 l'ipotesi invalsa a mezzo il secolo XVI, e riferita, come <lb/>vedemmo dal Porta in uno di quei quattro libri, di che compose la sua <lb/>prima Magia Naturale. </s>

<s>Per dar dunque il Peiresc fondamento alla sua ipo&shy;<lb/>tesi, volle osservare quel che realmente avviene nell'occhio, in cui gli ap&shy;<lb/>par&igrave; &ldquo; posticam illam interioremque circumductionem oculi speculum esse <lb/>concavum, propter inversam, tam candelae quam aliorum quorumlibet obiecto&shy;<lb/>rum, refiexionem &rdquo; (Vita cit., pag. </s>

<s>275). </s></p><p type="main">

<s>Chi ripensa a quello zelante fervore del Peiresc in diffondere cos&igrave; le <lb/>proprie come le altrui scoperte, pi&ugrave; efficacemente forse che per mezzo degli <lb/>scritti, per via de'familiari colloqui co'pi&ugrave; dotti amici, convenuti dalla non <lb/>lontana Parigi nelle sue case, e intrattenuti in privati accademici consessi; <pb xlink:href="020/01/1469.jpg" pagenum="344"/>intender&agrave; che anche di questa esperienza delle immagini, che si vedono di&shy;<lb/>pinte a rovescio sul fondo dell'occhio, si dovesse facilmente divulgar la no&shy;<lb/>tizia, e dalle tradizioni orali passare ne'libri. </s>

<s>Comunque sia, il Cartesio, nel <lb/>cap. </s>

<s>V della Diottrica, sugger&igrave; pubblicamente di servirsi dell'occhio stesso per <lb/>osservar in lui di fatto quel che gli era prima stato attribuito per conget&shy;<lb/>ture fondate sopra semplici argomenti di analogia. </s>

<s>&ldquo; Omnia tamen, sog&shy;<lb/>giunge dop'avere accennato alla Camera oscura, magis explorata et certa <lb/>erunt, si evulsum recens defuncti hominis, aut, si illius copia non sit, bovis <lb/>vel alterius magni alicuius animalis oculum, ita secemus, ut ablata ea parte <lb/>trium eius membranarum, quae cerebro obversa est, satis magna pars hu&shy;<lb/>moris vitrei appareat nuda, nec tamen iste humor effundatur, sed continea&shy;<lb/>tur charta, vel ovi putamine vel alia quavis materia alba et tam tenui, ut, <lb/>quamvis non sit pellucida, omnem tamen luminis transitnm non excludat &rdquo; <lb/>(editio cit., pag. </s>

<s>59). </s></p><p type="main">

<s>Il Briggs consigli&ograve; poi di servirsi degli occhi delle civette, &ldquo; quod expe&shy;<lb/>rimentum, egli dice, luculentius, ut mihi videtur, quam illud Cartesii mo&shy;<lb/>dum visionis explicat, cum partes hoc more &igrave;n situ naturali et integrae <lb/>conspiciantur &rdquo; (Ophtalmographia in loco cit., pag. </s>

<s>363). E infatti si dif&shy;<lb/>fuse cos&igrave; quel piacevole esperimento, che il Malpighi lo commemorava come <lb/>il pi&ugrave; bello e il pi&ugrave; facile modo di persuadere ognuno della pittura delle <lb/>immagini rovesciate sopra la retina. </s>

<s>&ldquo; La propagazione delle specie alla Re&shy;<lb/>tina inversa, tanto controversa, con l'occhio della civetta usato come un ca&shy;<lb/>nocchiale, per essere la parte posteriore della cornea diafana, si stabilisce &rdquo; <lb/>(Opera posthuma cit., P. II, pag. </s>

<s>151). </s></p><p type="main">

<s>Questa stessa diafaneit&agrave; poi delle membrane negli occhi delle civette <lb/>sugger&igrave; al Morgagni uno de'pi&ugrave; efficaci argomenti, per confutare una no&shy;<lb/>vit&agrave;, che avendo, poco dopo passato mezzo il secolo XVII, levato cos&igrave; gran <lb/>romori nel campo dell'Ottica fisiologica, non pu&ograve; da noi passarsi senza qual&shy;<lb/>che cenno da inserirsi in questo tratto di storia. </s></p><p type="main">

<s>Dopo lo Scheiner par che fosse Edmondo Mariotte il primo ad atten&shy;<lb/>dere con diligenza alla inserzione eccentrica del nervo nell'occhio, per cui <lb/>le immagini, che si dipingono simmetriche intorno all'asse ottico, vanno a <lb/>dipingersi necessariamente fuor di quella inserzione. </s>

<s>Ripensando sopra ci&ograve; <lb/>il Mariotte, fu preso da una curiosit&agrave; di sapere qual effetto facessero i raggi <lb/>della luce, quando ad arte si facessero cadere sul punto proprio del nervo, <lb/>e nel 1668 istitui le opportune esperienze, delle quali, in una <emph type="italics"/>Lettre a mon&shy;<lb/>sieur Pecquet,<emph.end type="italics"/> cos&igrave; descriveva i modi particolari, e dava conto all'amico e <lb/>al collega dei resultati: &ldquo; J'avois souvent observ&eacute;, par l'Anatomie tant des <lb/>hommes que des animaux, que iamais le nerf-optique ne repond iustement <lb/>au milieu du fond de l'oeil, c'est a-dire, &agrave; l'endroit ou se fait la peinture <lb/>des objets, qu'on regard directement; et que dans l'homme il est un peu <lb/>plus haut, et a cot&eacute; tirant vers le nez. </s>

<s>Pour faire donc tomber les rayons <lb/>d'un objet sur le nerf-optique de mon oeil, et &eacute;prouver ce qui en arrive&shy;<lb/>rait, j'attachai sur un fond obscur, environ &agrave; la hauteur de mes yeux, un <pb xlink:href="020/01/1470.jpg" pagenum="345"/>petit rond de papier blanc, pour me servir de point de v&ucirc;&euml; fixe; et cepen&shy;<lb/>dant j'en fis tenir un autre &agrave; cot&eacute; vers ma droite, &agrave; la distance d'environ <lb/>deux pieds, mais un peu plus bas que le premier, afin qu'il p&ucirc;t donner sur <lb/>le nerf-optique de mon oeil droit, pendant que je tiendrois le gauche ferm&eacute;. </s>

<s><lb/>Je me pla&ccedil;ai vis-&agrave;-vis du premier papier, et m'en eloignai peu &agrave; peu, te&shy;<lb/>nant toujours mon oeil droit arrit&eacute; dessus; et lorsque je fus &agrave; la distance <lb/>d'environ neuf pieds, le second papier, qui &eacute;toit grand de pr&egrave;s de quatre <lb/>pouces, me disparut entierement &rdquo; (Nouvelle decouverte touchante la v&ucirc;e, <lb/>Ouvres, T. II, A la Haye 1740, pag. </s>

<s>496). </s></p><p type="main">

<s>Il fatto inaspettato si verific&ograve; privatamente da alcuni amici, e poi l'Au&shy;<lb/>tore stesso lo dimostr&ograve; in pubblico consesso in Parigi nella Biblioteca del <lb/>Re, dove deposit&ograve; una scrittura, che conteneva la spiegazione. </s>

<s>Si diceva che <lb/>organo essenziale della visione non doveva esser la Retina, come da tutti <lb/>s'era creduto e si credeva, ma la Coroide, la quale perch&egrave; &ldquo; part des bords <lb/>de nerf-optique, et n'en couvre point le mileu &rdquo; (ivi, pag. </s>

<s>497) rende la ra&shy;<lb/>gion chiarissima del perch&egrave; il punto dello stesso nervo sia cieco. </s></p><p type="main">

<s>Gli argomenti con cui il Mariotte si studiava, nella citata scrittura, di <lb/>dimostrare una cosa tanto nuova, che cio&egrave; organo primario della vista fosse <lb/>la Coroidea, erano diversi, ma questi due s'annoverano fra'principali: <emph type="italics"/>I, que <lb/>la retine ne pen&eacute;tr&eacute; point dans le cerveau, comme fait la Choroide, qui <lb/>enveloppe le nerf-optique au-del&agrave; de l'oeil, et l'accompagne jusqu'un mi&shy;<lb/>lieu du cerveau; II, que la Choroide, &eacute;tant fort d&eacute;li&eacute;e et opaque, elle <lb/>peut recevoir en un point les rayons d'un m&eacute;me point lumineaux<emph.end type="italics"/> (ivi, <lb/>pag. </s>

<s>500, 503). </s></p><p type="main">

<s>Il Pecquet, a cui aveva il Mariotte indirizzata la sua prima lettera de&shy;<lb/>scrittiva dell'esperienza chiedendone l'autorevole giudizio di lui intorno al <lb/>modo tenuto nello spiegarla, neg&ograve; che fosse la Coroide <emph type="italics"/>le principal organe <lb/>de la vision,<emph.end type="italics"/> n&egrave; le ragioni addotte dallo stesso Mariotte gli parevano con&shy;<lb/>cludenti. </s>

<s>Quanto alla prima di quelle ragioni, diceva che la pia madre, di <lb/>ch'&egrave; composta la Coroide, pu&ograve; bene impartire un senso di dolore a questa, <lb/>come a tutte le altre membrane, &ldquo; mais non pas celui de la v&ucirc;e, qui de&shy;<lb/>mande une autre impression que celle qui fait la douleur &rdquo; (ivi, pag. </s>

<s>501). <lb/>Quanto alla seconda poi delle sopra riferite ragioni conveniva che la Coroide <lb/>opaca avrebbe potuto ritenere in s&egrave; l'impressione dei raggi luminosi, quando <lb/>per&ograve; la Retina non fosse ella pure sufficientemente opaca da impedire il <lb/>passo libero a quegli stessi raggi (ivi, pag. </s>

<s>503). </s></p><p type="main">

<s>Un altro, non men valido n&egrave; meno autorevole oppositore contro l'opi&shy;<lb/>nione del Mariotte, sorse in seno alla stessa Accademia parigina nella per&shy;<lb/>sona di Claudio Perrault, il quale avendo stabilito che &ldquo; la polissure et <lb/>l'exacte &eacute;galit&eacute; de la surface de la membrane, qui doit etre reput&eacute;e l'organe <lb/>de la vision, est une condition, sans la quelle on ne peut concevoir que la <lb/>vision se puisse faire &rdquo; (ivi, pag. </s>

<s>518); n'ebbe a concluder che il difetto <lb/>di una tal requisita uguaglianza di superficie nella stessa Coroide &egrave; ci&ograve; che <lb/>&ldquo; la rend mal-propre a recevoir l'impression des esp&egrave;ces &rdquo; (ivi, pag. </s>

<s>519). </s></p><pb xlink:href="020/01/1471.jpg" pagenum="346"/><p type="main">

<s>N&egrave; fuori dell'Accademia parigina mancarono al Mariotte oppositori, <lb/>fra'quali non &egrave; da trascurare il Briggs, che propostisi ad esaminare quei <lb/>principali da noi sopra riferiti argomenti rispondeva a loro cos&igrave; in contra&shy;<lb/>rio con queste ragioni: &ldquo; Ad prius argumentum respondeo quod, licet hi <lb/>colores per fibrarum interstitia transluceant, ipsas tamen fibras non adeo <lb/>permeant, praesertim versus nervi optici exitum, ubi densius agglomerantur, <lb/>quin hae, fere instar chartae purissimae et diaphanae, ad sistendas species <lb/>sufficiant. </s>

<s>Obiectio secunda facile refellitur ex eo quod tunica retiformis <lb/>eiusdem substantiae cum cerebro existat, quod tamen ad omnes obiectorum <lb/>impressiones, tam retinendas quam alio deferendas, idoneum esse reperi&shy;<lb/>tur &rdquo; (Ophtalmog. </s>

<s>cit., pag. </s>

<s>358). </s></p><p type="main">

<s>In Italia la risoluzione della questione si trovava preparata gi&agrave; dal San&shy;<lb/>torio, il quale aveva dimostrato, come vedemmo, che la Retina ha la pellu&shy;<lb/>cidit&agrave; necessaria, per ritenere le immagini, simile a quella della carta bianca <lb/>o della pelle d'uovo, sopra cui poi il Cartesio, detratte le naturali membrane, <lb/>riceveva le pitture degli oggetti venute attraverso agli umori dell'occhio. </s>

<s><lb/>Galileo avrebbe, cos&igrave; di questa come di ogni altra parte d'Ottica fisiologica, <lb/>lasciata digiuna la sua scuola, se non ci avessero provveduto il Castelli col <lb/>suo <emph type="italics"/>Discorso sopra la vista,<emph.end type="italics"/> e il Baliani col suo trattatello <emph type="italics"/>De visione,<emph.end type="italics"/> com&shy;<lb/>mentando le teorie del Keplero, ch'erano insomma schiettamente italiane, <lb/>per aver avuto, come si dimostr&ograve;, i principii non dalle giocose fantasie del <lb/>Porta, ma dalle matematiche speculazioni del Benedetti. </s></p><p type="main">

<s>&Egrave; notabile che in tanta penuria di scienza ottica, in ch'era lasciata la <lb/>Scuola galileiana, il sopra citato <emph type="italics"/>Discorso<emph.end type="italics"/> rimanesse lungamente inedito, ed <lb/>&egrave; pi&ugrave; notabile che si risolvesse il cardinale Leopoldo de'Medici di farlo pub&shy;<lb/>blicare, insiem con gli altri Opuscoli filosofici del Castelli, nel quarto pe&shy;<lb/>riodo dell'Accademia del Cimento. </s>

<s>Essendo questa risoluzione avvenuta nel&shy;<lb/>l'anno 1669 &egrave; facile congetturare che fosse provocata dai rumori sollevati <lb/>dal Mariotte in Francia. </s>

<s>In ogni modo per&ograve; &egrave; cosa certa che il principe del&shy;<lb/>l'Accademia fiorentina fece in Parigi diligente ricerca delle famose Lettere <lb/>sopra la <emph type="italics"/>Nouvelle decouverte touchant la v&ucirc;e,<emph.end type="italics"/> n&egrave; fu sua colpa, se venne <lb/>mal servito dal gesuita Bertet, il quale gli scriveva da Lione, il d&igrave; 3 d'Ot&shy;<lb/>tobre di quell'anno 1669, in tali termini, da far chiara mostra di non avere <lb/>inteso nulla di quel che si trattava, scambiando fra le altre la sclerotica colla <lb/>coroidea. </s>

<s>&ldquo; Lasciai partendo da Parigi a uno de'nostri padri la nuova sco&shy;<lb/>perta del sig. </s>

<s>Mariotte intorno all'organo del viso, ch'egli prova essere la <lb/>sclerotide..... &rdquo; (MSS. Cim., T. XIX, c. </s>

<s>274). </s></p><p type="main">

<s>Che dunque il Principe e gli Accademici del Cimento rivolgessero i loro <lb/>studii intorno all'organo della visione, proponendosi per loro testo gli Opu&shy;<lb/>scoli del Castelli, &egrave; cosa dimostrata dai documenti, ma noi non sappiamo i <lb/>particolari di quegli studii, cosicch&egrave; a insorgere contro le innovazioni del <lb/>Mariotte, alquanti anni dopo, apparisce primo fra noi il Morgagni. </s>

<s>L'Epi&shy;<lb/>stola anatomica XVII, dal &sect; 35 alla fine, s'intrattien tutta in dimostrare che <lb/>non pu&ograve; la Coroide essere organo primario della vista, confutando le ra-<pb xlink:href="020/01/1472.jpg" pagenum="347"/>gioni del Mariotte con argomenti, che hanno le radici nella scienza pi&ugrave; adden&shy;<lb/>tro di quelli addetti dal Pecquet, dal Perrault e da altri stranieri. </s>

<s>Sent&igrave; bene <lb/>il Morgagni che tutto il forte di quelle ragioni stava nella composizion della <lb/>retina, e risalendo alle tradizioni della scienza italiana commemor&ograve; il Cas&shy;<lb/>serio, che ripensando da una parte alla gran sensibilit&agrave; di essa retina, e <lb/>dall'altra alla stupidit&agrave; della polpa cerebrale, congettur&ograve; che dovess'essere <lb/>la membrana, organo precipuo della visione, intessuta di filamenti derivati <lb/>dalla pia madre. </s>

<s>Or si propose il Morgagni di ridurre le congetture ai fatti, <lb/>dai quali soli si poteva sperare che sarebbero bandite per sempre dalla <lb/>scienza le irragionevoli innovazioni francesi. </s>

<s>Ma la cosa era tanto difficile <lb/>che, non osando ripromettersi dimostrazioni, si contentava d'indizi. </s>

<s>&ldquo; Idcirco <lb/>videndum est nobis possitne res demonstrari, aut, si non possit, ullane sal&shy;<lb/>tem ex anatome indicia existant, quae, si quis in re difficillima sequatur, is <lb/>minus a veri similitudine, quam qui non sequantur, discedat &rdquo; (editio cit., <lb/>pag. </s>

<s>288). E gl'indizii dell'esser veramente la Retina intessuta di filamenti <lb/>derivati dalla pia madre furono tali, da aver in s&egrave; quella verosimiglianza <lb/>che si poteva desiderare. </s></p><p type="main">

<s>Quanto alla seconda delle sopra riferite ragioni, che il Mariotte addu&shy;<lb/>ceva per conferma della sua opinione, il Morgagni invocava il fatto speri&shy;<lb/>mentato dal Briggs negli occhi della civetta, ne'quali, perciocch&egrave; le imma&shy;<lb/>gini si vedevano cos&igrave; bene dipingersi sopra tutte le membrane soprapposte, <lb/>ne concludeva che l'attitudine di ritener le pitture degli oggetti, dallo stesso <lb/>Mariotte attribuita alla sola Coroide, era propria, non che alla retina che si <lb/>diceva mancare della necessaria pellucidit&agrave;, alla stessa scleroide (ivi, pag. </s>

<s>286). </s></p><p type="main">

<s>La gloria della <emph type="italics"/>Nouvelle decouverte,<emph.end type="italics"/> combattuta dagli stessi Francesi <lb/>nel suo primo fiore, fu per opera del Morgagni finalmente divelta dalle sue <lb/>radici, cosicch&egrave; tutti ritennero come vero che si facesse la vista per la pit&shy;<lb/>tura degli oggetti sopra la Retina, secondo avevano insegnato il Benedetti <lb/>e il Keplero. </s>

<s>Questa dottrina per&ograve; sembrava implicare in s&egrave; il supposto che <lb/>sien quasi nel cervello due occhi intenti a contemplare le immagini, ci&ograve; che, <lb/>giudicandosi inconveniente dal Cartesio, lo fece andare ad ammetter l'ipo&shy;<lb/>tesi che ciascun punto delle immagini muova diversamente i filamenti ner&shy;<lb/>vosi espansi sopra la retina, dai quali si traducono le impressioni al cer&shy;<lb/>vello. </s>

<s>&ldquo; Licet autem haec pictura sic transmissa in cerebrum semper aliquid <lb/>similitudinis ex obiectis a quibus venit, retineat, non tamen ob id creden&shy;<lb/>dum est hanc similitudinem esse, quae facit ut illa sentiamus, quasi denuo <lb/>alii quidam oculi in cerebro nostro forent, quibus illam contemplari posse&shy;<lb/>mus. </s>

<s>Sed potius motus esse, a quibus haec pictura componitur, qui imme&shy;<lb/>diate in animam nostram agentes, quatenus illa corpori unita est, a natura <lb/>instituti sunt ad sensus tales in ea excitandos &rdquo; (Dioptrices, cap. </s>

<s>VI, edit. </s>

<s><lb/>cit., pag. </s>

<s>66). </s></p><p type="main">

<s>L'ingegnosa ipotesi cartesiana per&ograve; ebbe a cadere, quando l'Anatomia <lb/>dimostr&ograve; non essere il nervo ottico composto di filamenti distinti, e quando <lb/>l'osservazione del ristringimento dello stesso nervo persuase il Malpighi che, <pb xlink:href="020/01/1473.jpg" pagenum="348"/>se fosse vero quel che insegna il Cartesio, non si potrebbe veder altro che <lb/>poca e determinata parte dell'oggetto. </s>

<s>&ldquo; Antequam retinae fiat expansio <lb/>tam arcte constringitur extrema optici latitudo, ut necessario intestinulorum <lb/>et fibrarum, si quae sint, intima fiat connexio et nodus..... Si autem sin&shy;<lb/>gula illa intestinula unici filamenti vicem gererent, paucas et numero deter&shy;<lb/>minatas tantum obiecti partes intueremur &rdquo; (Malpighi, Operum, T. II, Lugd. </s>

<s><lb/>Batav. </s>

<s>1687, pag. </s>

<s>123). </s></p><p type="main">

<s>Quell'Anatomia per&ograve;, che aveva col coltello del Malpighi uccisa l'ipo&shy;<lb/>tesi cartesiana, non seppe sostituirvene un'altra, che avesse del vero miglior <lb/>sembianza, infintantoch&egrave; non venne a fare intorno a ci&ograve; nuove prove del <lb/>suo ingegno il Valsalva. </s>

<s>Scoperta ch'egli ebbe la testura raggiata della re&shy;<lb/>tina, immagin&ograve; che gli spiriti visivi, tendendo pi&ugrave; o meno cotesti raggi, pro&shy;<lb/>ducessero pi&ugrave; o meno viva nel sensorio l'impression degli oggetti. </s>

<s>Confor&shy;<lb/>tava questa sua ipotesi con una esperienza, ch'ei diceva di avere appresa <lb/>da un suo Collega, e che consisteva nel ricever le immagini venute attra&shy;<lb/>verso al foro di una Camera oscura sopra una pelle bagnata, sulla quale <lb/>si osserva che le pitture di esse immagini appariscono sempre pi&ugrave; distinte, <lb/>secondo che, rasciugandosi via via la pelle, viene tutto insieme ad essere <lb/>anco pi&ugrave; tesa. </s>

<s>&ldquo; Quod autem, iuxta diversam retinae dispositionem, obiecto&shy;<lb/>rum impressiones variari possint, experimento evincitur, quod a doctissimo <lb/>Sodali accepi: nimirum si in Camera optica, ad terminandas obiectorum vi&shy;<lb/>sibilium impressiones, adhibeatur pellis illa, qua in ducendis bracteis utun&shy;<lb/>tur auri malleatores, obiecta ipsa satis vivida et satis distincta apparebunt, <lb/>modo ea pellis arida sit; quod si aqua fuerit madefacta, languida fiet obiec&shy;<lb/>torum pictura &rdquo; (Dissertatio anat. </s>

<s>II cit., pag. </s>

<s>143). Ma perch&egrave; questa ipo&shy;<lb/>tesi si divulg&ograve; quando la scienza, tutta intenta alle prime scoperte elettri&shy;<lb/>che, incominciava a negar fede all'antica esistenza degli spiriti vitali, non <lb/>trov&ograve; ne'Fisiologi accoglienza, ond'&egrave; che le intravedute analogie fra la Ca&shy;<lb/>mera ottica e l'occhio, apparite da principio cos&igrave; lusinghiere, si conobbe poi <lb/>che non toglievano in tutto il velo al mistero. </s></p><p type="main">

<s>I dubbi erano incominciati gi&agrave; infin da quando, sapendosi che per la <lb/>pi&ugrave; precisa pittura nello strumento artificiale vuol l'oggetto avere una po&shy;<lb/>situra determinata rispetto alla lente, si pens&ograve; che nell'organo naturale in&shy;<lb/>vece s'accomoda cos&igrave; bene la vista alle pi&ugrave; avariate distanze. </s>

<s>Aveva gi&agrave; il <lb/>Keplero presentita questa difficolt&agrave; alle sue teorie, ed ebbe a fare perci&ograve; <lb/>ricorso all'azione de'processi ciliari, sopra la quale non molto dopo lo Schei&shy;<lb/>ner torn&ograve; con pi&ugrave; spiegati concetti. </s>

<s>&ldquo; Hinc Natura, egli scrisse, motricem <lb/>facultatem, tam tunicae uveae, quam processibus ciliaribus attribuit, ut suo <lb/>astrictu, et specierum nimium affluxum castigarent, et humorem crystalli&shy;<lb/>num aut conglobarent circumcirca comprimendo, aut attenuarent attractione: <lb/>vel in anteriora protruderent, seu denique introrsus regererent, quibus re&shy;<lb/>bus, non tantum refractio maior aut minor evaderet, pro varia crystallini <lb/>effigiatione, verum etiam retina eidem vicinior longiorque constitueretur, et <lb/>sic, quantum fieri posset, basin communem semper arriperet &rdquo; (Oculus cit., <pb xlink:href="020/01/1474.jpg" pagenum="349"/>pag. </s>

<s>162, 63). E confermava questa sua congettura sul fatto che, nell'aguz&shy;<lb/>zar la vista e nella prolungata attenzione, s'affaticano tanto i muscoli ciliari <lb/>da produrre un senso di dolore. </s></p><p type="main">

<s>Il Cartesio pure, nel trattato <emph type="italics"/>De homine,<emph.end type="italics"/> descrivendo i processi ciliari, <lb/>gli qualificava per tendini esigui &ldquo; quorum ope crystallini humoris figura <lb/>mutari potest, et paulo magis plana vel magis convexa reddi, prout usus <lb/>exigit &rdquo; (editio cit., pag. </s>

<s>62). Ma in cos&igrave; belle speculazioni si supponeva la <lb/>virt&ugrave; motrice ne'corpi ciliari e la elasticit&agrave; nel cristallino, senza per&ograve; esser <lb/>certi se ai supposti rispondessero i fatti. </s>

<s>La struttura di esso umor cristal&shy;<lb/>lino, come descrivevasi allora, e la sperimentata incompressibilit&agrave; dei liquidi <lb/>rendevano il secondo supposto pi&ugrave; inverosimile del primo, e perci&ograve; il Mo&shy;<lb/>linetti pens&ograve; di attribuire il gioco della trasformazion di figura sotto l'azion <lb/>de'muscoli a tutto il bulbo dell'occhio, piuttosto che alla semplice lente. </s>

<s>Il <lb/>modo come ci&ograve; avviene, secondo l'Autore, &egrave; questo: &ldquo; Ubi sese ciliarium <lb/>processuum filamenta corripiunt, bulbus oculi, qui sphaericus pene est, con&shy;<lb/>tractus ad latera, in longum procurrit. </s>

<s>Ita fundus oculi et retina cum illo <lb/>deducitur a crystallino. </s>

<s>Contrarium vero accidit contrahentibus se musculis <lb/>exterius, quippe bulbus tractus ad latera undique dilatatur, et cum multo <lb/>maius tunc temporis spatium illud sit, quod est a latere ad latus, illo, quod <lb/>est a pupilla ad fundum; necessum est ut crystallinus et retina propiora <lb/>fiant, sive crystallinus ad illam accedat, sive haec ad illum &rdquo; (Dissert. </s>

<s>anat. </s>

<s><lb/>cit., pag. </s>

<s>19). </s></p><p type="main">

<s>In quel mentre che il Molinetti si disponeva a scrivere queste cose, lo <lb/>Stenone pubblicava le sue anatomiche descrizioni della struttura del cristal&shy;<lb/>lino ne'pesci, e dal trovarlo composto di un nucleo solido, circondato da una <lb/>materia cedevole e molle, prese occasione di confermar l'ipotesi, ch'egli at&shy;<lb/>tribuisce al Philippeau, secondo la quale, cedendo per la sua esteriore mol&shy;<lb/>lezza il cristallino alla pressione de'muscoli ciliari, si trasforma anche nel&shy;<lb/>l'uomo cos&igrave; di figura, da accomodarsi a vedere gli oggetti a varia distanza. <lb/></s>

<s>&ldquo; Haec in crystallino substantiae diversitas ingeniosissimi Philippeau opinio&shy;<lb/>nem confirmare videtur, qui et ipse, cum sine dubio in piscibus idem con&shy;<lb/>firmasse, persuasit sibi processus ciliares crystallino humori undique anne&shy;<lb/>xos, dum breviores fiunt, crystallini convexitatem tanto facilius deprimere, <lb/>quanto minus actioni illorum contenti fluidi mobilitas resistere poterit, eaque <lb/>ratione crystallini figuram, quam ille ex duabus hyperbolis in homine com&shy;<lb/>positam credit, pro obiecti varia distantia varie mutari &ldquo; (Elementorum myol. </s>

<s><lb/>specimen cit., pag. </s>

<s>82). </s></p><p type="main">

<s>I Cartesiani esultarono, vedendo quel che pareva il pi&ugrave; inverosimile <lb/>fra'supposti del loro Maestro confermato dall'autorit&agrave; anatomica dello Ste&shy;<lb/>none, alla quale pi&ugrave; tardi s'aggiunse quell'altra del Morgagni. </s>

<s>Nell'<emph type="italics"/>Adver&shy;<lb/>saria anatomica VI,<emph.end type="italics"/> dop'aver detto che la struttura stenoniana del cristal&shy;<lb/>lino ne'pesci era quella medesima, ch'egli avea ritrovata negli uomini. <lb/></s>

<s>&ldquo; Mihi tamen, ne conclude nell'Animadversione LXXI, in praesentia cum <lb/>illis facere satis est, qui ante me docuere istam crystallini exteriorem mol-<pb xlink:href="020/01/1475.jpg" pagenum="350"/>litudinem eius figurae mutationem multo faciliorem reddere. </s>

<s>Igitur proxi&shy;<lb/>mae tunicae crystalloidi, nunc a ciliari ligamento contractae, nunc vicissim <lb/>sua vi elastica et interiorum lamellarum restituenti, cum sive iste crystal&shy;<lb/>lini aqueus humor, sive ista aquos&igrave;or molliorque substantia non promptis&shy;<lb/>sime obsequi, et sese veluti opus est non conformare non possit; haud video <lb/>sane qui plicae illae et corrugationes in crystallini superficie tunc adeo fa&shy;<lb/>cile produci queant &rdquo; (Adversaria anat. </s>

<s>omnia, Patavii 1719, pag. </s>

<s>91). </s></p><p type="main">

<s>Ebbero questi argomenti, co'quali confortava il Morgagni la sua opi&shy;<lb/>nione, tanta efficacia sopra gl'ingegni, che s'ammetteva oramai da tutti <lb/>l'ipotesi attribuita al Philippeau, lusingando dall'altra parte cos&igrave; l'apparente <lb/>struttura fibrosa de'corpi ciliari, da farli facilmente credere muscolosi. </s>

<s>Ma <lb/>intanto, in mezzo ai lunghi dissensi che avevano avuto sempre quasi uguali <lb/>momenti, incominciava, poco dopo il Morgagni, a prevaler l'opinione dalla <lb/>parte di coloro, che negavano a quelli stessi corpi ciliari la natura e l'uffi&shy;<lb/>cio di muscoli, infin tanto che, di pochi anni oltrepassata la prima met&agrave; del <lb/>secolo XVII, non usc&igrave; l'Anatomia a pronunziare per bocca dell'Haller quella <lb/>sua assoluta sentenza, che intorno al cristallino <emph type="italics"/>musculosi nil quidquam <lb/>habet.<emph.end type="italics"/> S'ebbe allora a confessare che i morti strumenti fabbricati dall'arte <lb/>erano ombre, le quali sparivano nell'atto stesso che intendevasi dare a loro <lb/>un corpo rappresentativo de'vivi organi della Natura. </s>

<s>S'era la scienza umana, <lb/>dopo tanti secoli di studii faticosi, compiaciuta d'aver finalmente ritrovate <lb/>le corde della lira nell'orecchio, e il pennello del pittore nell'occhio, ma al <lb/>domandar che poi si fece con quali organi s'ascoltano tali suoni, o si con&shy;<lb/>templano tali spettacoli, s'ebbe a riconoscere nella risposta che quegli im&shy;<lb/>maginati orecchi, e quegli occhi, che s'attribuivano all'anima, eran giusto <lb/>l'organo dell'udito e della vista, che si cercava. </s>

<s>La iatromatematica del Bo&shy;<lb/>relli ebbe di qui l'ultimo crollo, per cedere il suo luogo alle speculazioni <lb/>psichiche dello Stahl, le quali intanto ebbero seguaci, in quanto che lo stesso <lb/>enimmatico linguaggio pareva meglio conformarsi ai naturali misteri. </s></p><pb xlink:href="020/01/1476.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO IX.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Degli ordinamenti naturali<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>I. Dell'ordinamento degli animali. </s>

<s>&mdash; II. Dell'ordinamento delle piante. </s>

<s><lb/>III. Dell'ordinamento dei minerali.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Gli organi e le funzioni, intorno allo studio delle quali s'&egrave; fin qui trat&shy;<lb/>tenuta la nostra Storia, appartengono agli animali degli ordini superiori e <lb/>principalmente all'uomo, che fu per questo appellato <emph type="italics"/>Microcosmo<emph.end type="italics"/> perch&egrave; in <lb/>lui tutta si compendia e sublimasi la Natura. </s>

<s>Perch&egrave; si sia la scienza ri&shy;<lb/>volta con tanto ardore a meditare sulla gran Sintassi, non finendo il Ve&shy;<lb/>salio di rimproverar Galeno, per avere inciso a preferenza i bruti, e il Co&shy;<lb/>lombo e il Falloppio ritorcendo contro il Vesalio stesso le accuse, che al <lb/>Colombo e al Falloppio non manc&ograve; poi di raffacciare l'Eustachio; non sa&shy;<lb/>rebbe a dir n&egrave; s&igrave; facile n&egrave; s&igrave; spedito: ma fu in ogni modo provvido istinto <lb/>della stessa Scienza, la quale, avendo nell'alta mente riposto di dare ordine <lb/>alle numerosissime e disperse variet&agrave; degli esseri naturali, sent&igrave; quanto fosse <lb/>per riuscir proficuo al suo intento il considerar que'vari esseri nell'uomo <lb/>solo tutti insieme riassunti. </s></p><p type="main">

<s>La necessit&agrave; per&ograve; di que'naturali ordinamenti non fu cos&igrave; subito rico&shy;<lb/>nosciuta, parendo che i tre grandi regni degli animali, delle piante e dei <lb/>minerali fossero dalla Natura stessa stabilmente definiti, e, quanto agli ani&shy;<lb/>mali in particolare, vedendoli assai naturalmente ordinati e distinti in qua&shy;<lb/>drupedi, in uccelli, in pesci e in insetti. </s>

<s>Le piante, per aver da una parte <lb/>troppe variet&agrave; fra loro, e dall'altra troppe somiglianze, si trov&ograve; pi&ugrave; difficile <pb xlink:href="020/01/1477.jpg" pagenum="352"/>a distribuirle, cosicch&egrave; gli antichissimi Naturalisti non s'attentarono nemmen <lb/>di venire al cimento: difficile poi non solo, ma impossibile, si reput&ograve; il dar <lb/>convenevole ordine ai minerali. </s></p><p type="main">

<s>I primi conati dunque, che si fecero dalla scienza, furono intorno agli <lb/>animali, e incominciarono da Aristotile, a cui si fece anche per il primo <lb/>sentir la necessit&agrave; di ordinare il pi&ugrave; alto e supremo regno della Natura, <lb/>quando, dalle famiglie che popolavano l'angusta Grecia, si pass&ograve; a cono&shy;<lb/>scerne tante altre disperse per le regioni dell'aria, per i mari e per le terre, <lb/>di che si componevano gli smisurati imperi di Filippo e di Alessandro. </s></p><p type="main">

<s>Dallo Stagirita insomma incominciano i metodi, cos&igrave; dall'altra parte con&shy;<lb/>formi al genio particolare di quella Filosofia. </s>

<s>&ldquo; Animalium vero differentias <lb/>(scriveva nelll'introdursi a trattar <emph type="italics"/>De historia animalium<emph.end type="italics"/>) aut per vitas, <lb/>aut per actiones, aut per mores, aut per partes constitui dignum est &rdquo; (To&shy;<lb/>mus VI Operum, Venetiis 1560, fol. </s>

<s>84). Le fonti annoverate in ultimo luogo <lb/>erano le legittime, ma perch&egrave; troppo tornava difficile il desumere le diffe&shy;<lb/>renze dagli organi, non troppo bene ancora conosciuti, tenendo pochissimo <lb/>conto de'caratteri essenziali e intrinseci, s'intrattien lungamente Aristotile <lb/>a notar quelle sole differenze fondate sopra caratteri accidentali ed esterni. </s></p><p type="main">

<s>La principal distinzione, che consegue da questo metodo, &egrave; in animali <lb/>acquatici e in terrestri. </s>

<s>La prima poi di tali due grandi classi si divide in <lb/>due ordini: &ldquo; alia enim in fluido degunt victumque petunt ex humore, quem <lb/>etiam humorem per vices recipiunt et reddunt, nec vivere possunt nisi ver&shy;<lb/>sentur in humore, quod plurimae piscium parti evenire apertum est. </s>

<s>Alia <lb/>degunt quidem in fluido victumque inde emoliuntur, sed aerem non humo&shy;<lb/>rem recipiunt, et foris patere solent. </s>

<s>Complura huius generis sunt partim <lb/>gressilia, ut lutris, latax, crocodilus; partim volucres, ut mergi, ut natrix &rdquo; <lb/>(ibid.). Si suddividono poi gli stessi acquatici, rispetto alle varie qualit&agrave; degli <lb/>ambienti, in marini, in fluviatili e in lacustri. </s></p><p type="main">

<s>I terrestri pure son da Aristotile divisi in due grandi classi: in quelli <lb/>che respirano &ldquo; ut homo et quaecumque habent pulmonem &rdquo; (ibid., fol. </s>

<s>85); <lb/>e in quelli che non respirano &ldquo; ut vespae, apes et reliqua insecta, quo no&shy;<lb/>mine ea appello, quorum corpus incisuris praecingitur &rdquo; (ibid.). Le due <lb/>grandi classi si dividono poi in ordini, e si suddividono in generi, desu&shy;<lb/>mendo le loro distinzioni da differenze non punto meno accidentali, d'ond'&egrave; <lb/>condotto, volendo ridurre in un ordine quegli animali che convivono in so&shy;<lb/>ciet&agrave;, a ricongiungere insieme l'uomo, l'ape, la vespa, la formica e la grue. </s>

<s><lb/>Quando poi passa Aristotile a divisar le differenze, che nascono dalle parti, <lb/>non entra punto addentro alla composizione organica, ma nota di quelle <lb/>stesse parti le pi&ugrave; esterne sole e pi&ugrave; apparenti, dando cos&igrave; il primo esem&shy;<lb/>pio ai futuri Naturalisti di quelli, che poi si chiamarono <emph type="italics"/>Metodi artificiali.<emph.end type="italics"/></s></p><p type="main">

<s>Da cos&igrave; fatti metodi informata procede, ne'suoi dieci libri l'<emph type="italics"/>Historia <lb/>animalium,<emph.end type="italics"/> che si ammir&ograve; e si studi&ograve; con amore dai dotti, infin tanto che <lb/>non sent&igrave; Plinio il bisogno di ampliarla, e di ridurla a quella universalit&agrave; <lb/>di cose, a cui tendeva l'indole e l'ingegno di un Console dell'imperio ro-<pb xlink:href="020/01/1478.jpg" pagenum="353"/>mano. </s>

<s>Degli ordinamenti naturali per&ograve; l'Autore della nuova Storia non si <lb/>prende troppo gran cura, e in quattro distinti libri, che son l'VIII, il IX, <lb/>il X e l'XI, trattando de'quadrupedi, degli acquatici, degli uccelli e degli <lb/>insetti, non par che senta il dovere di rispondere a'suoi lettori perch&egrave; dal <lb/>descrivere alcuni generi o alcune specie si passi a descriverne altre, che si <lb/>trovano bene spesso associate insieme, piuttosto nelle pagine del libro, che <lb/>nel regno della Natura. </s></p><p type="main">

<s>La variet&agrave; delle cose, e la semplice eleganza delle descrizioni, ne ren&shy;<lb/>devano cos&igrave; piacevole la lettura, che le Storie naturali di Plinio divennero <lb/>la delizia degli eruditi. </s>

<s>Ma quando si scopr&igrave; il nuovo mondo, si trovaron <lb/>mancare di quella universalit&agrave;, dall'Autore stesso con s&igrave; grande studio cer&shy;<lb/>cata, intantoch&egrave; scriveva Amerigo Vespucci, in una sua lettera a Lorenzo di <lb/>Pier Francesco de'Medici, che le cose descritte dallo stesso Plinio, bench&egrave; <lb/>fossero tante, pur non giungevano alla millesima parte di quelle, che gli era <lb/>occorso a vedere ne'suoi Viaggi, o a scoprire ne'nuovi paesi da s&egrave; sco&shy;<lb/>perti. </s>

<s>&ldquo; Hanno molte perle, egli dice, e pietre preziose, com'abbiamo ricor&shy;<lb/>dato di sopra, le quali tutte cose, quand'io volessi raccontar particolarmente, <lb/>per la gran moltitudine di esse e per la lor diversa natura, questa storia <lb/>diventerebbe troppo grande opera, perciocch&egrave; Plinio, uomo perfettamente <lb/>dotto, il quale compose istoria di tante cose, non giunse alla millesima parte <lb/>di questa, e se di ciascuna di loro egli avesse trattato averia, in quanto alla <lb/>grandezza, fatto opera molto maggiore, ma del vero perfettissima, e sopra <lb/>tutto porgono maraviglia non piccola le molte sorte di pappagalli di varii e <lb/>diversi colori. </s>

<s>Gli arbori tutti rendono odore tanto soave, che non si puote <lb/>immaginare, e per tutto mandano fuori gemme e liquori e sughi &rdquo; (Ban&shy;<lb/>dini, Vita e Lettere di A. V., Firenze 1745, pag. </s>

<s>112, 13). </s></p><p type="main">

<s>Fra il secolo XIV e il XV dunque, mentre da una parte il regno della <lb/>Natura smisuratamente si ampliava, per le scoperte e per le descrizioni dei <lb/>Viaggiatori, specialmente Italiani, dall'altra, a rappresentar meglio abiti e <lb/>forme nuove o non troppo domestiche, soccorreva opportuna alla Storia na&shy;<lb/>turale l'arte della pittura. </s>

<s>Di ci&ograve;, in Leonardo da Vinci che prest&ograve; l'opera <lb/>sua ad Antonio Torriani, e nel Tiziano, che rappresentava in disegno ci&ograve; <lb/>che gli diceva di avere scoperto, nelle sue sottili anatomie, l'Eustachio, ab&shy;<lb/>biamo tali insigni esempii, che ci dispensano dal noverar que'tanti altri, <lb/>per i quali si vedono con arte squisitissima disegnate dal vero piante e ani&shy;<lb/>mali, da imprimersi ne'libri per illustrare le descrizioni, che ne davano &igrave; <lb/>Naturalisti. </s></p><p type="main">

<s>L'arte in ogni modo poteva servire alla facilit&agrave; delle descrizioni, ma <lb/>il cresciuto numero delle specie, oltre al dare maggior faccenda agli scrit&shy;<lb/>tori, aumentava, ci&ograve; che pi&ugrave; rileva, le difficolt&agrave; di bene ordinarle. </s>

<s>Succes&shy;<lb/>sero, nella seconda met&agrave; del secolo XVI, all'antico Plinio tre Autori, che <lb/>si ripartirono l'opera laboriosa, bench&egrave; non si stendesse molto al di l&agrave; del <lb/>sommo regno animale. </s>

<s>Guglielmo Rondelet tratt&ograve; de'pesci, Ulisse Aldovrandi <lb/>degli uccelli, e Currado Gesner de'quadrupedi. </s></p><pb xlink:href="020/01/1479.jpg" pagenum="354"/><p type="main">

<s>Al primo entrare alla lettura del Rondelezio si sente sollecito l'Autore <lb/>d'andare in cerca di quelle note, per cui si differenziano tutte le cose ge&shy;<lb/>nerate sopra la terra, e senza le quali &ldquo; notitia nulla haberi potest &rdquo; (De <lb/>piscibus marinis, Lugduni 1554, pag. </s>

<s>1). Quelle massime differenze per&ograve; <lb/>confessa esser difficilissime a ritrovarsi, e dall'altra parte non vede nessun <lb/>filosofo, di cui possa seguire gli esempii, da Aristotile in fuori, che perci&ograve; <lb/>prende a guida sicura per ordinare i suoi pesci. </s>

<s>&ldquo; Piscium igitur, ut cae&shy;<lb/>terorum animalium, differentiae a vita vivendique consuetudine, a partibus, <lb/>ab actionibus, a moribus omnino sumuntur, et his, tanquam illustribus no&shy;<lb/>tis, omnium quae in aqua vivunt animalium discrimina distinguemus. </s>

<s>Hanc <lb/>viam nobis indicavit Aristotiles, et ea animalium naturam est persequutus. </s>

<s><lb/>Eadem, in plantarum historia describenda, progressus est Theophrastus, ei&shy;<lb/>dem et nos, in ea quae mare continet, penetrabimus &rdquo; (ibid., pag. </s>

<s>3). </s></p><p type="main">

<s>Il Rondelezio per&ograve; &egrave; molto pi&ugrave; diligente di Aristotile in ricercar le note <lb/>differenziali, che si desumono dall'esame delle parti, e anzi &egrave; questo che lo <lb/>rende superiore a tutti i Naturalisti de'suoi tempi, non eccettuato lo stesso <lb/>Aldovrandi. </s>

<s>L'<emph type="italics"/>Ornithologia<emph.end type="italics"/> di lui, ch'&egrave; l'unica opera venuta in luce vivente <lb/>l'Autore, &egrave; distribuita in venti libri compresi in tre grandi Tomi in folio, <lb/>il primo de'quali fu pubblicato in Bologna nel 1599, ma noi non abbiamo <lb/>potuto avere sott'occhio che l'edizione fatta in Francfort nel 1610. </s></p><p type="main">

<s>Al primo de'XII libri raccolti insieme in questo Tomo precedono i <emph type="italics"/>Pro&shy;<lb/>legomeni,<emph.end type="italics"/> ne'quali l'Autore tratta fra le altre cose <emph type="italics"/>De ordine,<emph.end type="italics"/> nello sce&shy;<lb/>gliere il quale, troppo indulgendo all'indole cavalleresca dei tempi, s'attiene <lb/>alle dignit&agrave;, che nascono dall'uso della forza o dal valore nelle armi, per <lb/>cui viene a costituirsi il primo ordine degli uccelli rapaci. </s>

<s>&ldquo; Cum itaque <lb/>particularem omnium avium, tam ab antiquis et recentioribus descriptarum, <lb/>quam nostris diuturnis observationibus conquisitarum, historiam contexen&shy;<lb/>dam susceperim; in huius enarratione seriem dignitatis servare duxi, pri&shy;<lb/>mumque rapacibus, tanquam nobilitate reliquis longe praeferendis, inter <lb/>omnes aves dare locum statui &rdquo; (Ornithol., Francof. </s>

<s>1610, pag. </s>

<s>4). E perch&egrave;, <lb/>fra gli stessi uccelli rapaci, di pi&ugrave; nobile e generoso animo son quelli, che <lb/>vanno in aperta caccia di giorno, che non gli altri, i quali meditano nel&shy;<lb/>l'oscurit&agrave; della notte insidie e tendono agguati; ne fa la prima e principal <lb/>divisione in diurni e notturni. </s>

<s>&ldquo; Carnivora autem isthaec, cum quaedam <lb/>diurna, quaedam nocturna habeantur; ego primum de diurnis, quod praedam <lb/>interdiu rapientia sensu et viribus aliis praepolleant, tractabo &rdquo; (ibid.). Nel <lb/>II Tomo, che comprende i libri XIII-XVIII, divide gli altri uccelli non ra&shy;<lb/>paci in granivori, in baccivori e in vermivori, facendo questa volta giudici <lb/>delle dignit&agrave; i cuochi ed i ghiotti, che gli mettono primi innanzi i pavoni, <lb/>le pavoncelle e i fagiani. </s>

<s>Ne'libri XIX e XX del III Tomo, dedicato al car&shy;<lb/>dinal di Montalto, e che noi leggiamo nell'edizione fatta in Francfort nel 1613, <lb/>tratta degli uccelli acquatici, ai quali assegna l'ultimo luogo, per essere pi&ugrave; <lb/>ignobili e pi&ugrave; insipidi di tutti gli altri. </s></p><p type="main">

<s>Si vede bene di qui che, in ordine alla ricerca delle note differenziali, <pb xlink:href="020/01/1480.jpg" pagenum="355"/>l'Ornitologia dell'Aldovrandi segna un regresso da Aristotile e dal Ronde&shy;<lb/>lezio, i quali presero di mira il vario modo di vita, i costumi e le parti. </s>

<s>Ma <lb/>ben pi&ugrave; manifesto e notabile &egrave; quel regresso nel Gesnero, che per levarsi <lb/>d'impaccio, scambiando l'abito di Naturalista in quello di Filologo, si mette <lb/>ad ordinare i suoi Quadrupedi vivipari secondo le lettere dell'alfabeto, co&shy;<lb/>sicch&egrave; in queste storie gesneriane (come del resto in tante altre storie, che <lb/>non hanno il titolo di naturali) toccano all'Asino, e poi subito al Bue, le <lb/>prime dignit&agrave; e i primi seggi. </s></p><p type="main">

<s>In quel medesimo tempo che l'Aldovrandi e il Gesner, associando l'opera <lb/>loro a quella del Rondelezio, rendevano quasi compiuta la Storia particolare <lb/>degli animali, Ferrante Imperato pensava a dare all'Italia una storia pi&ugrave; <lb/>compendiosa, ma comprensiva di tutte quelle parti, che si leggevano nel&shy;<lb/>l'Opera di Plinio, dalla quale toglie alle sue nuove trattazioni gli esempi. </s>

<s><lb/>Se non che poco si trattiene intorno agli animali e alle piante, per riser&shy;<lb/>bare la maggior parte dei libri e dei capitoli alla descrizione dei minerali, <lb/>e alla risoluzione di problemi, fra'quali alcuni importantissimi di Meteoro&shy;<lb/>logia e di Geologia, cosicch&egrave;, piuttosto che <emph type="italics"/>Historia naturale,<emph.end type="italics"/> s'intitolerebbe <lb/>il suo libro <emph type="italics"/>Fisica generale<emph.end type="italics"/> in preparazione alla scienza dei moderni. </s>

<s>&ldquo; Messi <lb/>mano, egli dice, a questa messe con restringermi nelle cose, o per l'anti&shy;<lb/>chit&agrave; de'scrittori e mutazioni di voci gi&agrave; sconosciute, oppur da quelli tra&shy;<lb/>lasciate, ovvero imperfettamente e oscuramente trattate. </s>

<s>Questo fa che pi&ugrave; <lb/>negli minerali, che nelle materie degli animali, e men di tutto nelle piante <lb/>mi sia disteso &rdquo; (Hist. </s>

<s>natur., Venezia 1672, pag. </s>

<s>1). Di qui &egrave; che Ferrante, <lb/>come Plinio, non si prende alcuna cura di ordinamenti, e dall'altra parte <lb/>venivano a dispensarlo dal difficile assunto le scarsit&agrave; delle specie descritte, <lb/>proponendosi di trattar solamente di quelle &ldquo; l'istoria delle quali &egrave; stata <lb/>dagli altri meno osservata &rdquo; (ivi, pag. </s>

<s>654). </s></p><p type="main">

<s>Stando le cose in questi termini, aveva giusti motivi Francesco Bacone <lb/>di scrivere, nel cap. </s>

<s>III del II libro <emph type="italics"/>De augmentis scientiarum,<emph.end type="italics"/> che la sto&shy;<lb/>ria Naturale &ldquo; tam inquisitione sua, quam congerie, nullo modo in ordine, <lb/>ad eum quem diximus finem, aptata est &rdquo; (Lugani, P. I, 1763, pag. </s>

<s>115). <lb/>Vedeva il Verulamio essa Storia com'era stata dagli Autori trattata infino <lb/>a'suoi tempi, perdersi piuttosto nelle superfluit&agrave; degli iconismi, che fondarsi <lb/>in solide e diligenti osservazioni &ldquo; quare, ne concludeva, Historiam inducti&shy;<lb/>vam desiderari pronunciamus &rdquo; (ibid.). </s></p><p type="main">

<s>Il generoso desiderio per&ograve; non poteva essere cos&igrave; presto adempiuto, ri&shy;<lb/>chiedendosi per quella induzione l'esame di fatti particolari, smisurati di <lb/>numero, per esser tanti quante sono le specie dei vegetabili e degli animali; <lb/>difficilissimi ad essere riconosciuti nella loro propria natura e qualit&agrave; di as&shy;<lb/>sidui e fedeli ministri del senso e della vita. </s>

<s>L'opera della mente dunque <lb/>trovava, in ordinar la Natura, tutt'insieme difficolt&agrave; nelle variet&agrave; degli or&shy;<lb/>gani, e nelle qualit&agrave; delle funzioni. </s></p><p type="main">

<s>Per assegnare la dignit&agrave; degli organi pareva giusto criterio quello della <lb/>cos&igrave; detta division del lavoro, di che, ne'civili consorzii e nelle stesse umane <pb xlink:href="020/01/1481.jpg" pagenum="356"/>famiglie, si ha opportunissimo esempio. </s>

<s>A un piccolo proprietario bastano <lb/>pochi lavoratori delle sue terre: se la possessione cresce, e crescono i la&shy;<lb/>voratori, ci vuol chi sopraintenda ad essi, ed abbia cura delle cantine e dei <lb/>granai. </s>

<s>Se cresce la possessione anche di pi&ugrave;, quel fattore solo non basta: <lb/>ci vuol chi particolarmente abbia cura di confezionare e di conservare i vini, <lb/>chi di dispensare i grani, e chi attenda a tanti altri varii ufficii, che vo&shy;<lb/>gliono esser via via ripartiti in pi&ugrave; gran numero di persone, secondo che <lb/>al signore crescono le possessioni. </s></p><p type="main">

<s>Similmente, ad alcuni animali basta un gomitolino di fibre muscolari, <lb/>che faccia da cuore, ma in altri s'intessono quelle fibre con assai maggiore <lb/>artificio, e dividono in due la interiore cavit&agrave; del gomitolo. </s>

<s>Altri ne vogliono <lb/>tre, e risalendo ai pi&ugrave; alti gradi, all'ultimo, quelle interne cavit&agrave; si molti&shy;<lb/>plicano in quattro seni. </s>

<s>La varia struttura del cuore pareva dunque porgere <lb/>sufficiente argomento a costituire i varii seggi di dignit&agrave;, dai crostacei, ai <lb/>mammiferi e agli uccelli; distinzione che risultava dall'altra parte assai ma&shy;<lb/>nifesta da quelle estrinseche note, sulle quali fermarono l'attenzione Aristo&shy;<lb/>tile e i suoi seguaci. </s></p><p type="main">

<s>Se l'attendere ai soli organi bastasse, questo accennato sarebbe forse <lb/>il solo sufficiente, o almeno il principale de'criterii da seguirsi nell'ordinare <lb/>le variet&agrave; degli animali. </s>

<s>Ma convien di pi&ugrave; al Naturalista tener conto delle <lb/>funzioni, le quali si mettono in atto da un organismo, che non cade sotto <lb/>i sensi, e che non &egrave; trattabile dal coltello anatomico. </s>

<s>Cotesto invisibile or&shy;<lb/>ganismo si compone di elementi eterei, i quali non siamo certi se corri&shy;<lb/>spondano proporzionalmente in numero, in qualit&agrave; e in composizione agli <lb/>elementi materiali. </s>

<s>Danno buon fondamento al dubbio gl'istinti, vedendosi <lb/>alcuni insetti, che son costituiti negl'infimi gradi, esser rispetto a ci&ograve; tanto <lb/>superiori a molti mammiferi, com'alle pecore, per esempio, le formiche e <lb/>le api. </s></p><p type="main">

<s>In ogni modo, essendo la proporzione tra l'organismo etereo e il ma&shy;<lb/>teriale un'ipotesi impossibile a verificarsi, la scienza umana l'ammette, e <lb/>ammette insieme per essenzial nota distintiva le parti, sicura che, quanto pi&ugrave; <lb/>son queste elaborate, altrettanto ne resultino le funzioni pi&ugrave; perfette. </s>

<s>Es&shy;<lb/>sendo questa l'unica via, che si parava innanzi alla mente per riuscire a <lb/>mettere in caratteri distinti e leggibili il volume immenso della Natura, s'in&shy;<lb/>tender&agrave; come primi ad additar non solo, ma ad aprir quella stessa via fos&shy;<lb/>sero coloro, che dettero opera alle dissezioni degli animali. </s>

<s>Furono cos&igrave; fatte <lb/>dissezioni, ai tempi di Galeno, principalmente rivolte all'uso della medicina, e <lb/>si riducevan perci&ograve; tutte all'Anatomia umana, la quale, risorgendo nel se&shy;<lb/>colo XVI, si fece uno scrupoloso dovere di non dissecare che i soli cada&shy;<lb/>veri dell'uomo. </s>

<s>L'istituto era senza dubbio ragionevole, trattandosi di voler <lb/>descrivere le sole parti del corpo umano, e di evitar di confonderle con <lb/>quelle delle belve, ma riusciva altres&igrave; proficuo ai progressi della storia Na&shy;<lb/>turale, perch&egrave;, come s'accennava sui principii di questo discorso, tutti gli <lb/>organismi inferiori si trovavano compresi insomma nella grande Sintassi. </s></p><pb xlink:href="020/01/1482.jpg" pagenum="357"/><p type="main">

<s>Perch&egrave; per&ograve; riuscissero cos&igrave; fatti studii veramente proficui era neces&shy;<lb/>sario far, nella sintesi, l'analisi delle parti, e notar con gran diligenza le <lb/>differenze, che presenta un organo nell'uomo e negli altri animali. </s>

<s>L'Ana&shy;<lb/>tomia comparata ebbe dal Vesalio, dal Colombo, dal Falloppio e dagli altri <lb/>insigni anatomici di quel tempo niuna o pochissima cultura, la quale pro&shy;<lb/>priamente comincia con Girolamo Fabricio. </s>

<s>Questo nuovo instituto, che tra&shy;<lb/>sparisce qua e l&agrave; dalle varie opere dell'Anatomico d'Acquapendente, si ri&shy;<lb/>vela pi&ugrave; che mai esplicito in quel trattatello, ch'egli intitol&ograve; <emph type="italics"/>De ventriculo, <lb/>intestinis et gula,<emph.end type="italics"/> dove si paragonano dall'Autore questi organi della dige&shy;<lb/>stione nelle varie classi degli animali, e se ne fanno rilevare le differenze. </s>

<s><lb/>Quanto ai ventricoli, per esempio, paragona quelli dei Ruminanti, che son <lb/>quattro, con quelli dei Pennati che son tre, e con quelli de'pesci che si ri&shy;<lb/>ducono in uno solo, e argutamente nota le differenze che presentano i sot&shy;<lb/>toposti intestini. </s>

<s>&ldquo; Diversitas autem potissimum apparet in caeco intestino, <lb/>quod in homine tenuis oblongaque appendicula: in brutis quadrupedibus <lb/>oblongum, unicum et crassissimum: in piscibus nullum apparet caecum in&shy;<lb/>testinum &rdquo; (Opera omnia cit., pag. </s>

<s>99). E da cos&igrave; fatte osservazioni, ini&shy;<lb/>ziando l'Acquapendente quell'altra nuova scienza, che si disse Zoonomia, <lb/>passa a dire che da queste variazioni dell'intestino ceco dipendono neces&shy;<lb/>sariamente le variet&agrave;, che presenta il colon a lui prossimo. </s>

<s>&ldquo; Nam cui cae&shy;<lb/>cum intestinum, ceu manca et exigua appendicula traditum est, ut homini, <lb/>huic per colon ei proximum et continuum, quod extuberans et amplissimum <lb/>in sui initio est, compensatum fuit. </s>

<s>Cui vero caecum amplissimum factum <lb/>est, ut quadrupedi, eidem coli in sui principio proposita amplitudo defecit. </s>

<s><lb/>Rursus, cui duo fuere comparata caeca intestina, ut pennato, eidem colon <lb/>universum denegatum est. </s>

<s>Denique piscium genus, quod caeco ex toto ca&shy;<lb/>ruit, colo quoque caruisse patet &rdquo; (ibid.). </s></p><p type="main">

<s>Fu il nuovo istituto proseguito dal pi&ugrave; insigne dei discepoli dell'Acqua&shy;<lb/>pendente, Giulio Casserio, il quale, nel descrivere gli organi dei sensi, pa&shy;<lb/>ragona quelli dell'uomo con gli altri dei varii bruti, e le differenze notate <lb/>parvero alla Scienza una nuova rivelazione. </s>

<s>Marc'Aurelio Severino si mise <lb/>poi per quella nuova via aperta con tanto ardore che forse, come giudica&shy;<lb/>rono a&igrave;cuni, esager&ograve; nel designarne la riuscita, e nell'esaltare sopra l'Ana&shy;<lb/>tomia umana la nuova Anatomia comparata, ma per lui intanto quella Zoo&shy;<lb/>nomia, di che l'Acquapendente e il Casserio avevano dati i primi esempii, <lb/>prese abito proprio e distinto di scienza; abito a cui la <emph type="italics"/>Zootomia,<emph.end type="italics"/> nella <lb/>quale ei fece e descrisse tante e s&igrave; notabili scoperte, porgeva solida se non <lb/>elegante corporatura. </s></p><p type="main">

<s>Confer&igrave; a dare eleganza a cotesta nuova scienza zootomica Francesco <lb/>Redi, il quale, dopo la prima met&agrave; del secolo XVII, in mezzo a tanti Ana&shy;<lb/>tomici non in altro esercitanti il coltello che ne'cadaveri umani, osservava <lb/>la differente struttura delle viscere ne'varii animali. </s>

<s>Fa di ci&ograve; testimonianza <lb/>lo stesso Redi in una lettera da s&egrave; scritta a Jacopo del Lapo, a nome di <lb/>Alessandro Fregosi. </s>

<s>&ldquo; Fa di mestiere che io le dica che, nell'essere am-<pb xlink:href="020/01/1483.jpg" pagenum="358"/>messo dal signor Redi, mi &egrave; paruto di entrare in un mondo nuovo, con&shy;<lb/>ciossiach&egrave; nelle cose naturali ed anatomiche io non mi era esercitato mai, <lb/>se non in una diligente ricerca fatta ne'cadaveri umani, ... e il signor Redi <lb/>solamente osserva per ora la differente struttura delle viscere degli uccelli e <lb/>de'quadrupedi, e ne ha messo insieme grandissimi fasci di scritture &rdquo; (Opere, <lb/>T. IV, Napoli 1741, pag. </s>

<s>80). </s></p><p type="main">

<s>Comprendesi con facilit&agrave; quai vantaggi fosse per recare, nel pi&ugrave; sa&shy;<lb/>piente ordinamento degli animali, il conoscere le differenze che passano <lb/>fra'loro organi, per cui l'Acquapendente, il Casserio, il Severino e il Redi <lb/>ci si presentano fra'pi&ugrave; benemeriti Autori della Storia naturale. </s>

<s>Ma troppo <lb/>erano ancora scarsi al profitto i soggetti comparati, nel pi&ugrave; esteso studio <lb/>de'quali aveva solo speranza la stessa Storia di ritrovar pi&ugrave; efficace impulso <lb/>ai desiderati progressi. </s></p><p type="main">

<s>L'Harvey, ripigliando la trattazione sopra la generazion degli animali <lb/>rimasta in Aristotile e nell'Acquapendente interrotta, porgeva in sintesi quello <lb/>studio, intorno al quale poi si ripartiron l'opera tanti e s&igrave; valorosi ingegni. </s>

<s><lb/>Fra'Nostri, principe di una Scuola fecondissima di scoperte naturali ci si <lb/>presenta il Borelli, che primo ridusse alle leggi della Meccanica il passo <lb/>de'quadrupedi, il volo degli uccelli, il nuoto de'pesci, e a cui succede il <lb/>Malpighi, dal quale propriamente comincia la Fisiologia degl'insetti. </s>

<s>E giac&shy;<lb/>ch&egrave; si pu&ograve; anche lo Stenone annoverare fra'Nostri, a lui dobbiamo la de&shy;<lb/>scrizione della struttura muscolare de'pesci, e del loro organo della vista, <lb/>che tanto valse a illustrare il medesimo preziosissimo organo nell'uomo. </s></p><p type="main">

<s>L'efficacia della Scuola del Borelli in promovere la Storia naturale si <lb/>fece anche sentire nell'Accademia del Cimento, dove si speriment&ograve; nel vuoto <lb/>torricelliano la vita di varii animali pi&ugrave; efficacemente di quel che non avesse <lb/>fatto, nel vuoto della sua macchina pneumatica, il Boyle. </s>

<s>L'esperienze sulla <lb/>fosforescenza delle lucciole, che si fecero nel quarto periodo di essa Acca&shy;<lb/>demia dietro gl'impulsi avutine dallo stesso Boyle, conferirono alla soluzione <lb/>di uno de'pi&ugrave; curiosi problemi concernenti la fosforescenza degli animali. </s></p><p type="main">

<s>Il Segretario Lorenzo Magalotti, quando cominci&ograve; a dilettarsi dei viaggi, <lb/>imitando l'esempio de'pi&ugrave; antichi Viaggiatori italiani, non trascur&ograve;, per ser&shy;<lb/>vire alla Storia, le osservazioni delle cose naturali, ch'ei descriveva elegan&shy;<lb/>temente in varie lettere indirizzate a'suoi amici di Firenze. </s>

<s>In una, data da <lb/>Amsterdam li 2 Dicembre 1667, terminava quelle sue descrizioni con que&shy;<lb/>ste parole: &ldquo; Ho veduto uccelli dell'India maravigliosi, e uno non pi&ugrave; ca&shy;<lb/>pitato in queste parti. </s>

<s>&Egrave; venuto con un vascello, che vien d'America, il <lb/>quale, trovandosi vicino alle Barbade, vedde venir questa bestia per l'aria, <lb/>e tutta affannata posarsi sulla gabbia, onde, fatto forza di prenderla, si lev&ograve;, <lb/>e non potendo reggersi casc&ograve; in mare, dove fu subito presa con le <emph type="italics"/>chaluppe.<emph.end type="italics"/><lb/>Il nome suo, come potete credere, non si sa, perch&egrave; non l'ha saputo dire' <lb/>non parlando ancora il fiammingo. </s>

<s>Si crede per&ograve; che anche al suo paese <lb/>sia in stima, raffigurandosi per un uccello che si vede sulle pitture pi&ugrave; <lb/>nobili, che vengono di quelle parti. </s>

<s>Non ve lo descrivo, perch&egrave; lo fo ri-<pb xlink:href="020/01/1484.jpg" pagenum="359"/>trarre in un quadro con diversi altri uccellacci inauditi &rdquo; (MSS. Cim., <lb/>T. XXXIII, c. </s>

<s>86). </s></p><p type="main">

<s>Apparteneva a quella stessa Accademia Francesco Redi, a cui va di <lb/>tante cose debitrice la storia naturale, e specialmente dell'essersi liberata <lb/>dall'errore delle generazioni equivoche, che per l'esperienze di Antonio Valli&shy;<lb/>snieri ebbe l'ultima e pi&ugrave; compiuta disfatta. </s>

<s>Il Redi, da cui non vogliono <lb/>separarsi Giuseppe Zambeccari, Giovan Batista Caldesi e Diacinto Cestoni, <lb/>insieme col Vallisnieri, pellegrinando per l'immenso campo delle cose na&shy;<lb/>turali, si soffermarono qua e l&agrave;, dove il terreno o era sodo o era guasto, e <lb/>lo bonificarono e lo ridussero alla pi&ugrave; nuova e pi&ugrave; fiorente cultura. </s></p><p type="main">

<s>Quel Francesco Fontana, ch'ebbe tanta parte nell'invenzione del Mi&shy;<lb/>croscopio, fu altres&igrave; de'primi ad applicarlo alle osservazioni naturali, ma <lb/>Roberto Hook ne fece uso pi&ugrave; esteso e rivel&ograve; nella sua <emph type="italics"/>Micrografia<emph.end type="italics"/> nuovi <lb/>popoli di viventi. </s>

<s>Antonio Leeuwenhoeck ridusse le osservazioni microsco&shy;<lb/>piche ad arte, e cos&igrave; semplice artista com'era, penetrando coll'acume del&shy;<lb/>l'occhio armato per i pi&ugrave; riposti seni della Natura, merit&ograve; d'esser chiamato <lb/>a sedere in luogo distinto al convito della Scienza. </s></p><p type="main">

<s>Riducendoci ora tutta in uno sguardo l'opera di tanti che, comparando <lb/>gli organi di una medesima funzione tra varii animali, descrivendo le parti, <lb/>gli abiti e i costumi proprii di tante varie specie, e ne'viaggi pel grande e <lb/>per il piccolo mondo scoprendone delle nuove, facilitarono alla mente il modo <lb/>di porre ordine negli animali, non pi&ugrave; secondo l'arbitrio, ma secondo le <lb/>leggi della loro creazione; si direbbe che nel secolo XVIII si fosse la scienza <lb/>ridotta in grado di adempire i voti e di sodisfare ai filosofici desiderii del <lb/>toparca di Verulamio. </s></p><p type="main">

<s>In quel secolo infatti si diffuse il sistema proposto dal Linneo, il quale <lb/>ordinava tutti gli animali in sei classi, quadrupedi, uccelli, amfibii, pesci, <lb/>insetti e vermi. </s>

<s>Il Buffon giudic&ograve; questo ordinamento affatto arbitrario, e lo <lb/>riconobbe difettoso, per non trovarvi luogo molti animali: i serpenti per <lb/>esempio, le conchiglie e i crostacei. </s>

<s>Difettosa pure e arbitraria not&ograve; che riu&shy;<lb/>sciva la division linneiana de'quadrupedi, mettendovisi in societ&agrave; con l'uomo <lb/>e con la scimmia la lucertola squammosa. </s></p><p type="main">

<s>Questo strano accozzamento di esseri cos&igrave; disparati avrebbe dovuto far <lb/>sovvenire alla mente del Buffon Aristotile, che associava all'uomo le gru e <lb/>le formiche, e lo avrebbe dovuto far accorto che il sistema dello Stagirita <lb/>non era punto meno arbitrario di quello immaginato dal Naturalista svedese. </s>

<s><lb/>Eppure il valentuomo non se ne avvede, e Aristotile e Teofrasto e Plinio <lb/>sembrano a lui <emph type="italics"/>i primi e massimi Naturalisti,<emph.end type="italics"/> de'quali perci&ograve;, sicuro di <lb/>non errare, segue gli esempii. </s>

<s>Tutto imbevuto del razionalismo aristotelico <lb/>vuol che s'ordini la Natura secondo le relazioni, ch'ella ha con l'uomo, <lb/>da che segue, egli dice, nel suo primo <emph type="italics"/>Discorso intorno alla storia natu&shy;<lb/>rale,<emph.end type="italics"/> che troveranno il primo luogo quegli oggetti, i quali s'appresentano <lb/>all'uomo stesso come pi&ugrave; dilettevoli, o come pi&ugrave; necessarii. </s>

<s>&ldquo; Per esempio <lb/>egli dar&agrave; nell'ordine degli animali la preferenza al cavallo, al cane, al bue, ecc. <pb xlink:href="020/01/1485.jpg" pagenum="360"/>e sar&agrave; sempre migliore conoscitore di quelli, che gli saranno pi&ugrave; familiari. </s>

<s><lb/>In appresso si volger&agrave; a quelli che, sebbene non sieno familiari, non la&shy;<lb/>sciano per&ograve; di abitare gli stessi luoghi, gli stessi climi, come i cervi, i lepri <lb/>e gli animali tutti selvatici e solo, dopo di avere acquistate tutte queste co&shy;<lb/>gnizioni, sar&agrave; spinto dalla curiosit&agrave; a ricercare che cosa siano essi gli ani&shy;<lb/>mali de'climi stranieri, come gli elefanti, i dromedarii, ecc Il simile sar&agrave; <lb/>de'pesci, degli uccelli, degl'insetti, delle conchiglie, delle piante, de'mine&shy;<lb/>rali e di tutte le altre produzioni della Natura. </s>

<s>Le studier&agrave; a proporzione <lb/>dell'utile che sperer&agrave; di ricavarne, le osserver&agrave; a misura che gli si faranno <lb/>pi&ugrave; familiari, e le ordiner&agrave; nella sua mente secondo l'ordine delle sue co&shy;<lb/>gnizioni, poich&egrave; tale si &egrave; appunto l'ordine, secondo cui le ha acquistate, e <lb/>secondo cui gl'importa di osservarle. </s>

<s>Un ordine siffatto, che &egrave; fra tutti il <lb/>pi&ugrave; naturale, &egrave; quello che noi creduto abbiamo di dover seguire &rdquo; (Opere, <lb/>Vol. </s>

<s>I, Venezia 1820, pag. </s>

<s>114). </s></p><p type="main">

<s>Che sembrasse questo metodo naturale a chi faceva con Aristotile l'uomo <lb/>centro, e la ragione di lui legislatrice della Natura, non fa maraviglia. </s>

<s>Ma <lb/>chi tutt'altrimenti credeva che la Natura stessa si governi con leggi pro&shy;<lb/>prie, ebbe facilmente a persuadersi che gli ordinamenti di lei si dovevano <lb/>trovare in quelle stesse leggi, indipendenti dall'arbitrio degli uomini. </s>

<s>Di li <lb/>solo poteva aversi speranza che que'tanto desiderati ordinamenti riuscissero <lb/>veramente naturali, e fu Giorgio Cuvi&egrave;r il primo che, escluse le note estrin&shy;<lb/>seche e gli arbitrii, si studi&ograve; di costituire le varie dignit&agrave; secondo gli organi <lb/>e le funzioni. </s>

<s>Cos&igrave; parvero i voti di Francesco Bacone adempiuti, e che la <lb/>Storia naturale avesse trovato il suo pi&ugrave; convenevole assetto, quando usci&shy;<lb/>rono gli evoluzionisti a dire essere inutile cercar distinzioni, non volute <lb/>dalla Natura. </s>

<s>Quel che credevasi la stabile gradinata di un edifizio &egrave; invece <lb/>l'increspamento di un'onda, che va, e che, andando, sempre pi&ugrave; ingrossa. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Chi ripensa che le difficolt&agrave;, incontrate dai Naturalisti in ordinare gli <lb/>animali, dipendevano principalmente dalla difficolt&agrave; di conoscere e di com&shy;<lb/>parare gli organi e le funzioni, intender&agrave; quanto si dovessero quelle diffi&shy;<lb/>colt&agrave; presentar maggiori in bene ordinare le piante, l'anatomia e la fisio&shy;<lb/>logia delle quali fu coltivata tanto pi&ugrave; tardi. </s>

<s>Dall'altra parte il vitto, le <lb/>medicine e le delizie stesse, che si ricavano dagli alberi e dall'erbe, acce&shy;<lb/>sero sempre negli uomini il desiderio di riconoscere i vegetabili, non men <lb/>vivamente di quel che avessero fatto gli animali, e per riconoscerli, in tanta <lb/>variet&agrave; e in tanta profusione, si fece molto per tempo sentire ai Botanici il <lb/>bisogno di un sistema, che, secondo l'arguta espression del Linneo, &egrave; il <lb/>filo di Arianna &ldquo; sine quo chaos est res herbaria &rdquo; (Philosophia botanica, <lb/>Viennae Austriae 1763, pag. </s>

<s>102). </s></p><pb xlink:href="020/01/1486.jpg" pagenum="361"/><p type="main">

<s>Non fa perci&ograve; maraviglia se, a studiarsi di sodisfare in qualche modo <lb/>a questo bisogno, fosse primo quell'antico Autore, di cui i libri due <emph type="italics"/>De <lb/>vegetabilibus<emph.end type="italics"/> si divulgarono sotto il nome, e si raccolsero perci&ograve; fra le altre <lb/>opere di Aristotile. </s>

<s>Il capitolo III del I libro &egrave; riserbato espressamente a <lb/>trattare <emph type="italics"/>De plantarum differentiis.<emph.end type="italics"/> Si possono queste differenze, secondo <lb/>l'Autore, ricavare da moltissime parti, nell'enumerar minutamente le quali <lb/>&egrave; notabile che comprendesse tutti quei sistemi scelti e proposti poi dai Bo&shy;<lb/>tanici infino al Linneo, e che si qualificarono col nome di <emph type="italics"/>artificiali.<emph.end type="italics"/></s></p><p type="main">

<s>Le prime e pi&ugrave; ovvie differenze ci fanno distinguere le piante in al&shy;<lb/>beri, in frutici, in suffrutici e in erbe. </s>

<s>&ldquo; Plantarum aliae arbores sunt, aliae <lb/>inter arbores et herbas mediae, et frutices dicuntur, aliae herbae sunt, aliae <lb/>olera &rdquo; (Tomus VI operum Arist., Venetiis 1560, fol. </s>

<s>76). I varii generi, <lb/>appartenenti a queste tre grandi classi, si possono distinguere dalle foglie, <lb/>le quali per esempio, rispetto agli alberi, &ldquo; quarundam aspera sunt, qua&shy;<lb/>rumdam levia. </s>

<s>Et aliorum folia sunt parva, aliorum scissa, ut vitis et ficuum. </s>

<s><lb/>Aliarum multas scissuras habent, ut pinus folia &rdquo; (ibid., fol. </s>

<s>77). Si possono <lb/>altres&igrave; distinguere dai frutti. </s>

<s>&ldquo; Succorum quoque, qui in fructibus sunt, alii <lb/>potabiles sunt, velut uvarum succus .... et aliorum unctuosi sunt, ut oli&shy;<lb/>vae succus.... Aliorum item dulces, ut dactylorum,.... alii amari ut absin&shy;<lb/>thii. </s>

<s>Quidam fructuum compositi ex carne sunt et osse, ut pruna, alii e <lb/>carne et grano ut cucumeros, quidam ex humore et granis, ut melagranata. </s>

<s><lb/>Et alii corticem foris habent, carnem intus, ut poma, pyra; quidam carnem <lb/>foris, os intus. </s>

<s>Sunt quoque alii, quibus statim semen fit cum tegumento <lb/>quo operiuntur, ut dactyli et amygdala; quidam non tales sunt..... Item <lb/>fructuum alii in siliquis sunt, velut fabae grana, alii in tegumentis et veluti <lb/>telis, ut triticum visitur, et caeteri; alii in carne, ut dactylorum fructus; <lb/>quidam velut in casis multis et tela ac testis, ut sunt nuces &rdquo; (ibid.). </s></p><p type="main">

<s>Le molte altre note distintive son prolissamente enumerate, e bench&egrave; <lb/>tutte sieno accidentali, &egrave; nonostante cosa meritevole di osservazione che per <lb/>certe piante, per le palme per esempio e per i fichi, assegni come nota da <lb/>distinguerle dalle altre i sessi. </s>

<s>&ldquo; In palmis quoque si folia vel foliorum pul&shy;<lb/>vis, vel palmae masculinae cortex foliis foemellae palmae apponantur, ut <lb/>cohaerescant, cito maturescent eius fructus, casusque eorum prohibebitur.... <lb/>Alicubi vero ex aliquo horum, vel ex omnibus istud contingit. </s>

<s>Quod si forte <lb/>ex odore masculi abduxerit quippiam ventus ad foemellam, sic quoque ma&shy;<lb/>turescent ipsius fructus, quemadmodum cum folia masculi ex illa fuerit <lb/>aspersa. </s>

<s>Ficus quoque sylvestres, per terram expansae, ficubus hortensibus <lb/>conferunt. </s>

<s>Eodem modo balaustia oleis conducunt, quando una plantan&shy;<lb/>tur &rdquo; (ibid.). </s></p><p type="main">

<s>Si diceva che in questa prolissa enumerazione delle note da differen&shy;<lb/>ziare le piante si comprendevano i varii sistemi, i quali dovevano in somma <lb/>consistere nella scelta di quelle, fra tali innumerevoli note, che fossero ri&shy;<lb/>conosciute per pi&ugrave; essenziali. </s>

<s>Ma qui stava la difficolt&agrave;, non alleviata punto <lb/>dall'Autore aristotelico, il quale anzi faceva come chi, per saziar la sete a <pb xlink:href="020/01/1487.jpg" pagenum="362"/>uno, lo affogasse nell'acqua. </s>

<s>Di che sentito il pericolo, i pi&ugrave; si ritennero <lb/>sulla riva, contentandosi di quella massima e principal distinzione delle piante <lb/>in alberi, in frutici e in erbe, che appariva pi&ugrave; manifesta. </s>

<s>Dioscoride ordin&ograve; <lb/>i generi appartenenti a queste grandi classi, secondo le loro virt&ugrave; medici&shy;<lb/>nali, e Teofrasto gli denomin&ograve; dai loro luoghi nativi. </s></p><p type="main">

<s>Le difficolt&agrave; insomma di cogliere quelle note, che riducessero le piante <lb/>alle loro pi&ugrave; vere somiglianze, e alle loro pi&ugrave; sostanziali differenze, e dall'al&shy;<lb/>tra parte il non sentirne cos&igrave; grande il bisogno, per lo scarso numero delle <lb/>stesse piante, ch'erano a que'tempi meglio conosciute; fecero s&igrave; che gli <lb/>Antichi non s'attentassero di proporre o di seguitare in Botanica nessun si&shy;<lb/>stema, di cui i primi tentativi si videro far nel secolo XVI per Currado <lb/>Gesner. </s>

<s>Sembr&ograve; a lui, attentamente osservando e comparando, che le note <lb/>desiderate, e con tanta sollecitudine ricercate invano dagli studiosi di Ari&shy;<lb/>stotile, non consistessero nelle foglie o in altro, ma ne'fiori e ne'frutti. </s>

<s><lb/>Preso questo per il filo di Arianna, riusc&igrave; a scoprire che alcune piante cre&shy;<lb/>dute differenti, come per esempio le Stafisagrie e gli Aconiti, appartenevano <lb/>alla medesima famiglia, mentre altre invece, come la Melissa e l'Ortica, che <lb/>sembrano s&igrave; vicine, esaminato bene il seme, si trova non aver fra loro nes&shy;<lb/>suna parentela. </s>

<s>Nell'Epistola a Teodoro Zuingger, dop'avere stabilito per <lb/>fondamento alla distinzion delle piante il fiore e il frutto, &ldquo; ex his enim, <lb/>soggiunge, potius quam foliis, stirpium naturae et cognationes apparent. </s>

<s>His <lb/>notis Staphisagriam et Consolidam regalem, vulgo dictam Aconito, <foreign lang="greek">sumfulous <lb/>einxi bota\nas</foreign> facile deprehendi &rdquo; (Epistolae, Basileae 159, pag. </s>

<s>113). E ad <lb/>Adolfo Occone, medico di Augusta, scriveva in un'altra Epistola: &ldquo; Melissa <lb/>costantinopolitana ad Lamium vel Urticam mortuam quodammodo videtur <lb/>accedere, seminis tamen, <emph type="italics"/>unde ego cognationes stirpium iudicare soleo,<emph.end type="italics"/><lb/>figura differt &rdquo; (ibid., pag. </s>

<s>65). </s></p><p type="main">

<s>Il fondamento a queste note per&ograve; lo trovava il Gesner nella semplice <lb/>osservazione, ma il Cesalpino and&ograve; a ricercarlo pi&ugrave; addentro nella fisiologia <lb/>delle piante, per cui, piuttosto che al Naturalista di Zurigo, si dee al Nostro <lb/>il merito di avere speculato, nel suo trattato <emph type="italics"/>De plantis,<emph.end type="italics"/> il primo sistema <lb/>botanico razionale. </s>

<s>&ldquo; Cum igitur omnis substantiae ratio, egli scrive, a fine <lb/>petatur (propter illum enim substantiae quoque sunt quae illius gratia haben&shy;<lb/>tur) videndum est in plantis quae similitudo et dissimilitudo in iis fuerit, <lb/>quae primi animae operis gratia data sunt, deinde quae secundi, et si quae <lb/>alia sequantur deinceps &rdquo; (De plantis, Florentiae 1583, pag. </s>

<s>27). </s></p><p type="main">

<s>Dalle varie operazioni dunque, o manifestazioni dell'anima vegetativa, <lb/>intende il Cesalpino di desumere le note essenziali, da servirgli per ordi&shy;<lb/>nare le piante. </s>

<s>Di queste manifestazioni, soggiunge, alcune sono primarie, <lb/>altre secondarie. </s>

<s>Primarie sarebbero quelle, che appartengono alle funzioni <lb/>della nutrizione, secondarie le altre, che appartengono alle funzioni della ri&shy;<lb/>produzione. </s>

<s>Le primarie perci&ograve; daranno la prima e pi&ugrave; grande distribuzione <lb/>delle piante in alberi, in frutici, in suffrutici e in erbe; e le secondarie ser&shy;<lb/>viranno per distinguere i varii generi in quelle stesse prime classi compresi. </s></p><pb xlink:href="020/01/1488.jpg" pagenum="363"/><p type="main">

<s>E perch&egrave; &egrave; questa la distinzion pi&ugrave; importante, dai frutti, dice il Ce&shy;<lb/>salpino, si desumeranno le note. </s>

<s>&ldquo; Secundum autem vegetativi opus est <lb/>generare sibi simile, quod et perfectione prius est, cuius gratia dati sunt <lb/>fructus et partes ad fructificationem facientes. </s>

<s>Cum igitur id non omnibus <lb/>insit, sed perfectioribus, pro fructificationis similitudine et dissimilitudine, <lb/>posteriora genera, tum in genere arboreo, tum in humiliori materia, consti&shy;<lb/>tuenda erunt..... Et merito ex modo fructificandi multa emersunt planta&shy;<lb/>rum genera. </s>

<s>In nullis enim aliis partibus tantam organorum multitudinem <lb/>et distinctionem Natura molita est, quanta in fructibus condendis spectatis &rdquo; <lb/>(ibid., pag. </s>

<s>27, 28). </s></p><p type="main">

<s>Al Cesalpino successe, in sul finir del secolo XVI, un altro insigne <lb/>cultore della Botanica in Fabio Colonna. </s>

<s>Giovane di XXV anni, pubblic&ograve; <lb/>nel 1592 il suo primo libro, che intitolava <foreign lang="greek">*f*u*t*o*b*a*s*a*n*o*s</foreign>, perch&egrave; vi si met&shy;<lb/>tevano le varie piante a tortura di rivelare il vero esser loro. </s>

<s>Gli fu il fine <lb/>pr&igrave;ncipale dell'opera suggerito dal bisogno di dichiarare il testo di Diosco&shy;<lb/>ride, dalla lettura del quale nascevano tante oscurit&agrave; e tante incertezze, per <lb/>esser dall'Autore una medesima pianta chiamata con pi&ugrave; nomi, che pote&shy;<lb/>vano ridursi a diversi significati. </s>

<s>Il principal merito perci&ograve; del <emph type="italics"/>Fitobasano<emph.end type="italics"/><lb/>consiste nell'avere introdotta nella scienza botanica la propriet&agrave; del linguag&shy;<lb/>gio; merito che si apprezzer&agrave; da coloro, i quali sanno quanto in una nu&shy;<lb/>merosa societ&agrave; d'individui sia necessario, per riconoscerli, evitare le incer&shy;<lb/>tezze e le confusioni dei nomi. </s></p><p type="main">

<s>Del resto, non par che il giovane Botanico avesse ancora pensato a <lb/>comporre un sistema suo proprio, o a seguire gli esempii del Gesnero e del <lb/>Cesalpino, perch&egrave;, occorrendogli di assegnare il luogo proprio a una pianta <lb/>di quelle da s&egrave; nuovamente scoperte, la riduce fra le variet&agrave; delle Trache&shy;<lb/>lie, non guardando alla forma del fiore, ma alla polpa delle foglie e al sa&shy;<lb/>pore. </s>

<s>&ldquo; Non e florum forma, natali loco, annique tantum tempore quo floret, <lb/>sed et a lactis copia, substantia foliorum, et sapore totius plantae, Trache&shy;<lb/>liorum varietati (sic a recentioribus, quia tracheae locisque vicinis medea&shy;<lb/>tur, appellatarum) reddenda est haec nova planta, in D. M. </s>

<s>Virginis Monte, <lb/>sic vulgo dicto, exoriens &rdquo; (<foreign lang="greek">*futob<gap/>sanos</foreign>, cui accessit adnotat. </s>

<s>auctore Iano <lb/>Planco, Florentiae 1744, pag. </s>

<s>118). </s></p><p type="main">

<s>Pubblicato il Fitobasano, e fatto Fabio da Marzio Colonna vice-principe <lb/>di Zagarola, si dette a perlustrare i monti della Puglia, dove fece diligente <lb/>raccolta di molte piante o meno note o affatto sconosciute, ch'egli poi de&shy;<lb/>scrisse in un libro stampato col seguente titolo, in Roma, nel 1606, da Gu&shy;<lb/>glielmo Facciotti. </s>

<s>&ldquo; Fabii Columnae Lyncei minus cognitarum rariorumque <lb/>nostro coelo orientium stirpium <foreign lang="greek">*e*k*f*p*a*s*i<gap/></foreign>, qua non paucae ab antiquiori&shy;<lb/>bus Theophrasto, Dioscoride, Plinio, Galeno aliisque descriptae, praeter illas <lb/>etiam in <foreign lang="greek">*f*u*t*o*b*a*s*a*n*w</foreign> editas, disquiruntur ac declarantur. </s>

<s>&rdquo; Ma nemmen <lb/>qui il Colonna segue una ragion certa, in ordinar le piante antiche e le <lb/>nuove ch'egli descrive. </s></p><p type="main">

<s>Proseguendo per&ograve; con pi&ugrave; ardore che mai nell'intrapreso studio, aveva <pb xlink:href="020/01/1489.jpg" pagenum="364"/>nel 1616 aggiunta un'altra parte all'Ecfrasi, la quale fu, insiem colla prima, <lb/>pubblicata in quel medesimo anno in Roma coi tipi di Giacomo Mascardi. <lb/></s>

<s>&Egrave; giusto in questo libro, che s'intitola: &ldquo; Fabii Columnae Lyncei, minus <lb/>cognitarum stirpium <emph type="italics"/>Pars altera,<emph.end type="italics"/> in qua non tam novae plures plantae <lb/>eaeque rariores a nemine hactenus aut animadversae aut descriptae nunc <lb/>primum proponuntur, quam nonnullae aliae apud antiquos dubiae atque <lb/>obscurae dilucidantur; &rdquo; &egrave; in questo libro diciamo che l'Autore stabilisce, <lb/>in conferire i generi, per note specifiche, non quelle desunte dalle foglie, <lb/>ma dal seme e dai fiori. </s>

<s>&ldquo; Foliorum effigiem in conferendis generibus parvi <lb/>fecimus. </s>

<s>Non enim ex foliis, sed ex flore seminisque conceptaculo, et ipso <lb/>potius semine plantarum, affinitatem diudicamus, respondente praesertim <lb/>sapore in reliqua plantae parte &rdquo; (pag. </s>

<s>62). </s></p><p type="main">

<s>Fors'ebbero in questa deliberazione di lasciar le foglie, per seguir le <lb/>note differenziali offerte dai fiori e dai semi, non poca efficacia sul Colonna <lb/>gli esempii del Gesner e del Cesalpino, ma perch&egrave; sempre i fatti hanno pi&ugrave; <lb/>virt&ugrave; delle parole, crediamo che la diversit&agrave; delle idee, espresse nel Fito&shy;<lb/>basano e nell'Ecfrasi seconda, dipendesse dall'uso, che incominci&ograve; l'Autor <lb/>di questa a fare allora del Microscopio. </s>

<s>Egli, s&igrave; amante de'nomi greci, fu <lb/>che sugger&igrave; un tal nome a Federigo Cesi, principe di que'Lincei, fra'quali <lb/>ebbe il nuovo strumento la prima e pi&ugrave; feconda applicazione alle scienze <lb/>naturali. </s>

<s>Il Colonna dunque, mettendosi ad osservar diligentemente col Mi&shy;<lb/>croscopio la composizione de'fiori e de'semi, ebbe a persuadersi esser vero <lb/>il detto del Cesalpino, che cio&egrave; non potrebbe, per conferire i generi, ritro&shy;<lb/>varsi in altre parti della pianta tanta moltitudine di organi e tante di&shy;<lb/>stinzioni. </s></p><p type="main">

<s>Fu un tal princip&igrave;o sistematico applicato dall'Autore, non solo in or&shy;<lb/>dinar le piante descritte nell'Ecfrasi II, ma in quelle erudite illustrazioni <lb/>altres&igrave;, ch'egli fece alla Storia di Francesco Hernandez, a cui aveva il re <lb/>di Spagna ordinato che descrivesse tutto ci&ograve;, che di applicabile alla fisica e <lb/>alla medicina si trovasse nel Regno messicano. </s>

<s>La morte imped&igrave; all'Her&shy;<lb/>nandez di dar forma ai numerosi e pregevolissimi materiali raccolti, di che <lb/>fu la cura dallo stesso Re commessa a Nard'Antonio Recchi, il quale di&shy;<lb/>stese le storie messicane in X libri. </s>

<s>Morto il Recchi, il manoscritto venne <lb/>alle mani di un nipote di lui da parte di sorella, Marc'Antonio Petilio, da <lb/>cui l'ebbe il principe Cesi. </s>

<s>Esaminata l'Opera, la trov&ograve; degna che v'eser&shy;<lb/>citassero l'ingegno attorno i suoi Lincei, fra'quali scelse Giovanni Terrenzio <lb/>di Cosenza, e Giovanni Faber bambergese e medico del Papa, perch&egrave; illu&shy;<lb/>strassero particolarmente la Zoologia, e dette a Fabio Colonna ordine che <lb/>illustrasse la Botanica, ci&ograve; ch'egli fece in quelle Note, nelle quali il sistema <lb/>d'ordinar le piante, secondo la distinzion del fiore e del frutto, trova larga <lb/>e sapiente applicazione. </s></p><p type="main">

<s>Ma queste Note, gi&agrave; finite di scrivere nel 1628, videro la prima luce <lb/>insiem col testo nell'anno 1648, e nel 1651 con aggiunte, per opera di Cas&shy;<lb/>siano del Pozzo e di Francesco Stelluti, i due soli Lincei rimasti in quel <pb xlink:href="020/01/1490.jpg" pagenum="365"/>tempo superstiti, e dall'altra parte l'Ecfrasi e gli altri libri furono, vivente <lb/>l'Autore, cos&igrave; poco diffusi, che non fa maraviglia se, tra per l'una e per <lb/>l'altra ragione, non avendo avuto, nella prima met&agrave; del secolo XVI, il Co&shy;<lb/>lonna lettori, non ebbe delle sue dottrine perci&ograve; n&egrave; seguaci. </s></p><p type="main">

<s>Cos&igrave; essendo, non rimaneva ai Botanici, amatori dei progressi della <lb/>scienza, altro che la scuola del Cesalpino, alla quale si ascrissero molti, e <lb/>fra questi Paolo Hermann, che ordin&ograve; la sua <emph type="italics"/>Flora batavica<emph.end type="italics"/> sull'esame dei <lb/>soli frutti, e Giovanni Ray, che nel cap. </s>

<s>XX del I libro <emph type="italics"/>De historia plan&shy;<lb/>tarum,<emph.end type="italics"/> trattando delle loro specifiche differenze, scriveva queste parole: &ldquo; Ut <lb/>plantarum numerus iniri possit, et earumdem divisio recte instititui, oportet <lb/>ut notas aliquas, seu indicia specificae distintionis, investigemus. </s>

<s>Nobis au&shy;<lb/>tem diu multumque indagantibus nulla certior occurrit, quam distincta pro&shy;<lb/>pagatio ex semine..... Quae plantae ex alterius semine non proveniunt, nec <lb/>unquam semine satae transmutantur in se invicem, eae demum specie di&shy;<lb/>stinctae sunt &rdquo; (Londini 1686, pag. </s>

<s>40). </s></p><p type="main">

<s>Ma queste note di specifica distinzione, che il Ray teneva per cos&igrave; certe, <lb/>parvero a Pietro Magnol per lo meno insufficienti, n&egrave; che valesse a com&shy;<lb/>pierle l'aggiungere all'esame de'semi quello de'fiori. </s>

<s>Gli si veniva a di&shy;<lb/>mostrare una tale insufficienza dai fatti, osservando, per esempio, che, fra <lb/>trifogli congeneri, altri erano monopetali, e altri invece polipetali, e che tra <lb/>le stesse vere e proprie Linarie n'erano alcune col seme piano, altre col <lb/>seme rotondo. </s>

<s>Perci&ograve; pensava il Magnol che le note specifiche non si do&shy;<lb/>vessero ridurre a una sola o a due, ma a pi&ugrave;, raccolte da varie parti e da <lb/>qualit&agrave; anche accidentali, purch&egrave; accennino a quelle somiglianze fra le varie <lb/>piante, che hanno fra s&egrave; i membri di una stessa famiglia. </s></p><p type="main">

<s>Esprimeva queste idee nella Prefazione al Catalogo delle piante del&shy;<lb/>l'Orto regio di Mompellieri, nella qual prefazione, dop'aver detto che dal Ca&shy;<lb/>talogo stesso, ch'&egrave; per dare alla luce, resulter&agrave; la smisurata variet&agrave; delle <lb/>piante raccolte insieme e disposte nel giardino reale; cos&igrave; soggiunge: &ldquo; At <lb/>vero quandoquidem, dum tractatur de plantis, cavendum est ne infinito pene <lb/>earum numero memoria obruatur, et suboriantur errores ex nominum di&shy;<lb/>versitate et mutatione, id unum mihi cordi fuit, non modo ut ad certas <lb/>quasi familias et classes revocarentur, sed etiam ut ad pauciora, quantum <lb/>fieri potest, genera reducerentur. </s>

<s>Quantum inquam fieri potest, nec enim <lb/>puto certos omnino dari posse plantarum caracteres, quibus varia earum <lb/>genera perfecte, certo et semper, a se invicem distinguerentur &rdquo; (Hortus <lb/>regius monspelliensis, Monspelii 1697, pag. </s>

<s>VII). </s></p><p type="main">

<s>Questo &egrave; ci&ograve; che fu pi&ugrave; volte tentato da peritissimi Botanici, ma an&shy;<lb/>cora, prosegue a dire il Magnol, non par che si sia da-nessuno conseguito <lb/>l'intento. </s>

<s>&ldquo; Nec mirum, nam desumi non potest huiusmodi caracter, nisi <lb/>ex floribus, vel ex capsulis, vel ex seminibus. </s>

<s>Atqui ex iis desumi semper <lb/>non posse et experientia certo constat, et uno aut altero exemplo sic de&shy;<lb/>monstro: Quippe, si trifoliorum aut limoniorum flores spectes, habent alii <lb/>monopetalon alii polypetalon: congeneres tamen esse species quis neget? <pb xlink:href="020/01/1491.jpg" pagenum="366"/>Inter veras et genuinas Linarias recensere necesse est tum eas quae semen <lb/>planum, tum eas quae rotundum habent, et, sive lotus habeat siliquas cel&shy;<lb/>lulis distinctas, sive non habeat, germanae sunt loti species. </s>

<s>Ex quibus luce <lb/>clarius conficitur neque ex floribus, neque ex seminibus, neque ex capsulis <lb/>semper argui posse generum diversitatem &rdquo; (ibid., pag. </s>

<s>VIII). </s></p><p type="main">

<s>A coloro per&ograve; i quali, per essere alcuni tentativi riusciti infelici, non <lb/>avevano perduta la speranza di cogliere le vere note specifiche delle piante, <lb/>parve questa conclusione del Magnol dedotta da principii non veri, o almeno <lb/>non troppo precisi, imperocch&egrave;, se il Cesalpino e il Colonna avevano pro&shy;<lb/>posto l'esame de'semi, non intendevano che si dovesse il Botanico fermare <lb/>sulla loro apparente figura, o sopra le varie accidentalit&agrave; de'loro inviluppi, <lb/>ma sopra l'intima composizione degli organi. </s></p><p type="main">

<s>Giuseppe Pitton di Tournefort fu il pi&ugrave; valoroso fra gli oppositori usciti <lb/>contro il Magnol, e rimeditando sopra la ragione di ordinare le piante, espo&shy;<lb/>sta dal Cesalpino, disse ch'era la sola &ldquo; inter Herbarios philosopho dignam &rdquo; <lb/>(Institutiones rei herbariae, Parisiis 1719, pag. </s>

<s>66). Confermava la verit&agrave; <lb/>di una tal sua sentenza mostrando che la Filosofia delle piante propriamente <lb/>comincia col nostro Aretino, il quale paragon&ograve; i semi agli ovi, e afferm&ograve; <lb/>che simili erano negli uni e negli altri le virt&ugrave; e i modi dei loro svolgi&shy;<lb/>menti. </s>

<s>&ldquo; Fuit insuper Caesalpinus in rebus physicis, ut ferebant illa tem&shy;<lb/>pora, multum versatus, seminaque plantarum cum animantium ovis et vim, <lb/>qua ovi partes explicantur, cum fermentatione conferre non dubitavit &rdquo; (ibid.). </s></p><p type="main">

<s>Dice che fu dotto in Fisica il Cesalpino secondo i suoi tempi, perch&egrave; <lb/>intanto era venuto il Malpighi, filosofo prestantissimo e sottile indagatore <lb/>delle opere della Natura, &ldquo; qui veram Plantarum anatomen instituit, et opus <lb/>admirationis plenum exegit &ldquo; (ibid., pag. </s>

<s>54). Egli, soggiunge, fu primo a <lb/>dimostrar che le piante si compongono di cellule e che son fornite di un <lb/>doppio ordine di vasi, gli uni per servire al nutrimento, e gli altri alla re&shy;<lb/>spirazione. </s></p><p type="main">

<s>La fiducia dunque che aveva il Tournefort di poter riuscire a quel che <lb/>il Magnol disperava, era fondata sulla nuova scienza anatomica e fisiologica <lb/>istituita dal Malpighi, e della quale aveva nel Cesalpino sagacemente intra&shy;<lb/>veduti i principii. </s>

<s>Scorto da queste nuove scienze, esamina diligentemente <lb/>le piante, per desumer dalla loro intima struttura le note specifiche, e ne <lb/>conclude che i semi soli son per s&egrave; insufficienti, se non si congiungono ai <lb/>fiori. </s>

<s>Riconosciuto perci&ograve; difettoso il sistema del Cesalpino, la ragione ana&shy;<lb/>litica lo conduce ad approvar piuttosto l'opinione del Gesner e del Colonna. <lb/></s>

<s>&ldquo; Analiticam rationem adhibui, quae mox patebit, coegit me ad Gesneri et <lb/>Columnae sententiam amplectendam. </s>

<s>Quod ingenii bonitate tanti viri conse&shy;<lb/>cuti sunt, arte explorandi acquisivi &rdquo; (ibid.). </s></p><p type="main">

<s>Seguendo dunque quest'arte sperimentale, nella quale il Tournefort ri&shy;<lb/>conosce per maestro il Malpighi, si condusse a ricercare i particolari organi <lb/>e le funzioni, e ne concluse dalla dimostrazione dei fatti, meglio che dall'au&shy;<lb/>torit&agrave; dei detti, non si potere i generi delle piante stabilire altrimenti, che <pb xlink:href="020/01/1492.jpg" pagenum="367"/>esaminando insieme i fiori e i frutti. </s>

<s>&ldquo; Haec cum ita sint, genera planta&shy;<lb/>rum statui non posse liquet nisi flores simul et fructus adhibeantur. </s>

<s>Eamque <lb/>methodum vim fere demonstrationis habere existimo &rdquo; (ibid., pag. </s>

<s>57). </s></p><p type="main">

<s>Le regole poi di questo dimostrato metodo, dalle quali si professa di <lb/>non declinare se non per cause gravi, le riduce il Tournefort a sei, ma le <lb/>principali fra le altre son le quattro seguenti: &ldquo; I. </s>

<s>Plantae quae floribus et <lb/>fructibus, vel alterutro carent, in genera redigi debent ratione rerum magis <lb/>insignium, perinde ac illae, quarum flores et fructus solo microscopio pate&shy;<lb/>fiunt. </s>

<s>II. </s>

<s>Floris simul et fructus structurae ratio semper habenda est ad <lb/>constituenda genera plantarum, quae floribus et fructibus donantur. </s>

<s>III. </s>

<s>Flo&shy;<lb/>ribus simul et fructibus standum est, cum abunde sufficiunt ad genera di&shy;<lb/>stinguenda. </s>

<s>IV. </s>

<s>Non solum caeterae omnes plantarum partes, sed earum <lb/>affectiones, crescendi modus, habitus et facies exterior in auxilium vocari <lb/>debent, cum flos simul et fructus non sufficiant ad genera recte distin&shy;<lb/>guenda &rdquo; (ibid., pag. </s>

<s>61). </s></p><p type="main">

<s>Secondo queste regole ordina il Tournefort le sue XXII classi, incomin&shy;<lb/>ciando dalla prima, nella quale son riposte l'erbe e i suffrutici a fiori mo&shy;<lb/>nopetali campaniformi, infino all'ultima, che comprende gli alberi e i fru&shy;<lb/>tici a fiori papiglionacei. </s>

<s>Il nuovo ordinamento, fatto con tanto studio d'arte <lb/>e di scienza sperimentale, fu accolto con plauso, e ne fu approvato il me&shy;<lb/>todo, che veramente, come sperava di aver fatto l'Autore, <emph type="italics"/>caeteras omnes <lb/>antecellit,<emph.end type="italics"/> infintantoch&egrave; non venne a commovere la scienza una scoperta <lb/>inaudita. </s>

<s>Andrea Cesalpino aveva detto che le piante nascono come gli ani&shy;<lb/>mali, e dopo un secolo e mezzo Carlo Linneo soggiungeva che si fecondano <lb/>altres&igrave;, con distinzione di sessi, come gli stessi animali. </s>

<s>La sentenza com&shy;<lb/>mosse, perch&egrave; riusciva inaspettata. </s>

<s>E infatti quel Tournefort, che tanto aveva <lb/>richiamata l'attenzione degli studiosi sopra le forme de'fiori, e che unico <lb/>fra Sistematici era dietro il Malpighi entrato cos&igrave; addentro a penetrarne le <lb/>funzioni; ripeteva quel che aveva imparato dagli altri, che cio&egrave; son gli uf&shy;<lb/>ficii del fiore quelli di preparare l'alimento al formarsi e allo svolgersi dei <lb/>semi. </s>

<s>&ldquo; Flores autem sunt veluti viscera quaedam, in quibus alimentum <lb/>multiplici circuitu ad primam ovi formationem vel amplificationem aptius <lb/>evadit &rdquo; (ibid., pag. </s>

<s>68). </s></p><p type="main">

<s>Il Linneo invece dimostr&ograve; che ufficio proprio de'fiori era quello, non <lb/>di servire al nutrimento, ma alla fecondazione, organi femminei della quale <lb/>sono i pistilli, e organi maschili gli stami. </s>

<s>Secondando meno la profondit&agrave; <lb/>del Tournefort, che la superficialit&agrave; de'Sistematici suoi predecessori, il Lin&shy;<lb/>neo pens&ograve; d'istituire, sopra quella distinzione d'organi sessuali da s&egrave; sco&shy;<lb/>perta, un metodo nuovo, che fece a molti dimenticare quell'altro dal Tour&shy;<lb/>nefort stesso, quarant'anni prima, con tanto studio e con tanta scienza <lb/>elaborato. </s></p><p type="main">

<s>La <emph type="italics"/>Philosophia botanica<emph.end type="italics"/> &egrave; una mirabile sintesi della mente linneana <lb/>non solo, ma della scienza. </s>

<s>Pubblicati gi&agrave; i libri <emph type="italics"/>Classes plantarum,<emph.end type="italics"/> e <emph type="italics"/>Spon&shy;<lb/>salia plantarum,<emph.end type="italics"/> &ldquo; reliquas sectiones fundamentorum, dice l'Autore rivol-<pb xlink:href="020/01/1493.jpg" pagenum="368"/>gendo <emph type="italics"/>Lectori botanico<emph.end type="italics"/> il suo discorso, coniunctim cum prioribus in unum <lb/>opus compingere, et auctas novis exemplis, observationibus, demonstratio&shy;<lb/>nibus, sub <emph type="italics"/>Philosophiae botanicae<emph.end type="italics"/> titulo edere diu animo volvi &rdquo; (editio <lb/>cit., pag. </s>

<s>3). </s></p><p type="main">

<s>Alla parte scientifica dell'Opera fa erudito corredo la parte storica, nella <lb/>quale, dop'aver contratti in poche parole e in pochi numeri i sistemi del <lb/>Cesalpino, del Morison, dell'Hermann, del Ray, del Tournefort e del Ma&shy;<lb/>gnol, per tacere degli altri meno importanti, ma che pur non sono in que&shy;<lb/>sto Specchio dimenticati; &ldquo; Ego, ne conclude, sexuale Systema secundum nu&shy;<lb/>merum, proportionem et situm staminum cum pistillis, elaboravi &rdquo; (pag. </s>

<s>28). <lb/>E dalle Monandrie alle Poliandrie, dalle Didinamie alle Tetradinamie, dalle <lb/>Monadelfie alle Poliadelfie, dalle Singenesie alle Ginandrie, dalle Monoecie <lb/>alle Diecie, dalle Poligame alle Crittogame, ne annovera ordinatamente le <lb/>classi (ibid., pag. </s>

<s>28, 29). </s></p><p type="main">

<s>Questo nuovo sistema per&ograve;, per quanto seducesse i Botanici, non fu <lb/>trovato esente da gravi difetti. </s>

<s>Il numero degli stami, per esempio, e cos&igrave; <lb/>variabile nelle diverse specie d'uno stesso genere, che spesso spesso &egrave; a <lb/>certe piante assegnato dal Linneo il loculo, che meno a loro appartiene. </s>

<s><lb/>Senza che, difficilissimo &egrave; riconoscere i sessi, e perci&ograve; il modo della fecon&shy;<lb/>dazione, di certi fiori, come per esempio, di quelli delle Singenesie. </s></p><p type="main">

<s>Dietro queste considerazioni si giudic&ograve; il sistema linneano non meno <lb/><emph type="italics"/>artificiale<emph.end type="italics"/> di quelli prima elaborati, e l'Autore stesso sent&igrave; nella sua pro&shy;<lb/>pria coscienza la verit&agrave; di quei giudizii, ai quali sembra che volesse ritro&shy;<lb/>vare una scusa col dire, che le classi artificiali eran necessarie nelle pre&shy;<lb/>senti condizioni della Scienza, come succedanee alle naturali. </s>

<s>Che se aveva <lb/>segu&igrave;to piuttosto l'arte che la Natura, aveva ci&ograve; fatto per non perdere, come <lb/>gli pareva fosse avvenuto al Morison e al Ray, il filo di Arianna. </s>

<s>&ldquo; Artifi&shy;<lb/>ciales classes succedaneae sunt naturalium, usquedum omnes naturales sint <lb/>detectae, quas plura genera nondum detecta revelabunt, et tum limites <lb/>classium difficillimi evadant. </s>

<s>Cavendum ne imitando Naturam filum ariad&shy;<lb/>neum amittamus uti Morisonus, et Rajus &rdquo; (ibid., pag. </s>

<s>104, 5). </s></p><p type="main">

<s>Riconosce nulladimeno il Linneo e confessa che il carattere naturale &egrave; <lb/>veramente quello, che pu&ograve; porgere stabile fondamento alle classificazioni <lb/>delle piante &ldquo; quo destitutus, nullus de genere rite iudicabit, adeoque abso&shy;<lb/>lutum fundamentum cognitionis plantarum est, et erit &rdquo; (ibid., pag. </s>

<s>135). <lb/>Questi eran per&ograve; precetti, piuttosto che fatti, intorno ai quali lasci&ograve; l'Au&shy;<lb/>tore della Filosofia botanica che si travagliassero i suoi successori. </s>

<s>Vennero <lb/>essi non molto dopo, e furono Bernardo e Lorenzo di Jussieu e Michele <lb/>Adanson, riconosciuti da tutti per i pi&ugrave; laboriosi e fortunati architettori di <lb/>Metodi naturali. </s></p><pb xlink:href="020/01/1494.jpg" pagenum="369"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Le piante, nelle quali trov&ograve; a principio l'uomo da sodisfare alle prime <lb/>necessit&agrave; della vita, educarono l'arte dell'agricoltura, che ha il suo princi&shy;<lb/>pal fondamento nella cognizione delle varie qualit&agrave; dei terreni, meglio atti <lb/>a ricevere, e a far lietamente prosperare i surculi e i semi. </s>

<s>Ma non si po&shy;<lb/>teva l'industre opera condurre senza l'uso di opportuni strumenti, i quali <lb/>furono ritrovati a principio in quelle pietre sparse qua e l&agrave;, consistenti in <lb/>s&egrave; stesse, e ritrose a lasciar l'apparente irregolarit&agrave; delle loro forme. </s></p><p type="main">

<s>S'intende facile di qui come la prima e pi&ugrave; natural distinzione, che <lb/>occorresse a fare delle sostanze dette ora da noi minerali, fosse quella di <lb/>Terre e di Pietre, le varie specie delle quali si desumevano, come da note <lb/>caratteristiche, dalle varie attitudini alla cultura, e dalla durezza. </s>

<s>In seguito <lb/>si scopr&igrave; il ferro che, sostituito alla pietra in que'primi rozzi strumenti, <lb/>dette insieme con la perfezionata agricoltura mirabile incremento a tutte le <lb/>arti fabbrili. </s>

<s>Furono poi dopo il ferro conosciute altre sostanze, che gli so&shy;<lb/>migliavano nella durezza e nello splendore, e alle Terre e alle Pietre quegli <lb/>antichissimi mineralogisti, che descrivevano la Natura secondo le prime ap&shy;<lb/>prensioni dei sensi, aggiunsero anche i Metalli. </s></p><p type="main">

<s>Vennero dopo lungo tempo ad esercitar l'intelletto intorno a quelle <lb/>prime sensate apprensioni i Filosofi, il principe de'quali, nel seno della gran <lb/>madre Terra investigando le origini, insegn&ograve; a distinguere i minerali se&shy;<lb/>condo la variet&agrave; dei loro nascimenti. </s>

<s>Il terzo Libro meteorologico si conclude <lb/>da Aristotile in trattar di quelle cose, che si generano dentro la Terra, e <lb/>dice ch'essendo due le esalazioni, come antecedentemente crede di aver ben <lb/>dimostrato, dalla fumosa hanno origine i Fossili, e dalla vaporosa i Metalli. <lb/></s>

<s>&ldquo; Sicca igitur exhalatio igniens facit fossibilia omnia ut lapidum genera inae&shy;<lb/>liquabilia, et Sandaracam et Ochram et Minium et Sulfur et alia talia. </s>

<s>Plu&shy;<lb/>rima autem fossibilium sunt, haec quidem pulvis coloratus, illa autem lapis, <lb/>ex tali consistentia factus, velut Cinnabari. </s>

<s>Exhalationis autem vaporosae <lb/>quaecumque metallica sunt, et sunt aut fusibilia aut ductilia ut ferrum, au&shy;<lb/>rum, aes. </s>

<s>Facit autem haec omnia exhalatio vaporosa cum includitur, et <lb/>maxime in lapidibus, propter siccitatem, in unum coarctatur et concrescit, <lb/>velut ros aut pruina &rdquo; (Tomus VI, Operum cit., fol. </s>

<s>57). </s></p><p type="main">

<s>Termina Aristotile cos&igrave; il riassunto del suo discorso: &rdquo; Communiter <lb/>igitur dictum est de omnibus his, sigillatim autem considerandum intenden&shy;<lb/>tibus circa unumquodque genus &rdquo; (ibid, fol. </s>

<s>58). Ma chi attendeva all'agri&shy;<lb/>coltura, come per esempio Columella, consider&ograve; particolarmente i generi delle <lb/>terre coltivabili; chi attendeva alla medicina, come Galeno, consider&ograve; quei <lb/>generi di minerali, che servono per medicamenti, e Plinio nell'ampiezza del <lb/>suo soggetto vi comprese altres&igrave; que'varii generi di minerali, che porgono <pb xlink:href="020/01/1495.jpg" pagenum="370"/>materia alla costruzione degli edifizii, o che si ricercano per l'esercizio <lb/>delle arti. </s></p><p type="main">

<s>Una considerazione perci&ograve; bene ordinata intorno alle varie specie di <lb/>minerali, ch'era il desiderio della Scienza, non si vide apparir che sulla fine <lb/>del secolo XVI, per opera di Andrea Cesalpino. </s>

<s>S'aggiungeva in quel tempo, <lb/>ad accendere pi&ugrave; che mai vivo un tal desiderio, la curiosit&agrave; di trovar la so&shy;<lb/>luzione a un problema, che s'era incominciato allora a propor con pi&ugrave; <lb/>instanza intorno all'origine delle lapidefatte reliquie marine, che si trovano <lb/>sparse per le alte cime dei monti. </s>

<s>Attribuivano i pi&ugrave; cotesta origine al Di&shy;<lb/>luvio universale, ma perch&egrave; in Aristotile non si trovavano, intorno a una <lb/>tale universale inondazion della Terra, i testi chiari, molti Peripatetici in&shy;<lb/>vocavano i superni influssi celesti, e anzi alcuni affermavano con gran fidu&shy;<lb/>cia che le reliquie fossili dei monti, tutt'altro ch'essere ivi deposte dal mare, <lb/>v'erano addirittura piovute dal cielo. </s>

<s>Uno di costoro scrisse in tal proposito <lb/>un libro nel quale, perciocch&egrave; davasi maggiore autorit&agrave; ad Aristotile che alla <lb/>Bibbia, fu condannato dalla Chiesa Romana. </s></p><p type="main">

<s>Bench&egrave; sembrasse un tal libro al Cesalpino scritto <emph type="italics"/>diligentissime atque <lb/>eleganter,<emph.end type="italics"/> non pot&egrave; nonostante patir l'offesa, che veniva a riceverne ingiu&shy;<lb/>stamente la Filosofia peripatetica, attribuendo a menzogna o ad ignoranza il <lb/>dire che Aristotile non ammetteva che un diluvio parziale. </s>

<s>A riparar dun&shy;<lb/>que a una tale offesa, deliber&ograve; il Cesalpino di darsi allo studio dei minerali, <lb/>e di pubblicare un suo trattato, nel quale interpetrerebbe Aristotile in vero <lb/>senso ortodosso, e si ridurrebbe la questione degli avanzi fossili ritrovati sui <lb/>monti all'ordine dei fatti naturali. </s>

<s>Nel dedicar quel trattato, col titolo <emph type="italics"/>De <lb/>metallicis,<emph.end type="italics"/> a papa Clemente VIII, esprimeva in questa forma lo stesso Au&shy;<lb/>tore le sue prese deliberazioni, e i suoi intendimenti: &ldquo; Materia metallica, <lb/>beatissime Pater, philosophiae studiosis valde expetita, nec non medicis ap&shy;<lb/>prime necessaria, quamvis nuper diligentissime atque eleganter fuerit tra&shy;<lb/>dita, duo tamen impulerunt me ut opus idem aggrederer: Primum, quod <lb/>multa in ea traditione reperiantur principiis philosophiae minus congruam, <lb/>et peripateticam doctrinam evertentia; alterum quod Auctor, utpote a sancta <lb/>romana Ecclesia expulsus, haberi nequaquam concedatur. </s>

<s>Cum. </s>

<s>igitur plan&shy;<lb/>tarum historiam edidissem, visum fuit opere praecium, eadem methodo, cor&shy;<lb/>porum metallicorum explicationem adiungere. </s>

<s>&rdquo; </s></p><p type="main">

<s>E come nel dar la storia delle piante, ritenuta la comune e naturale <lb/>distinzione d'alberi, di frutici, di suffrutici e d'erbe, aveva nel diligente <lb/>esame dei frutti ritrovato il modo di ordinarle in generi e in specie; cos&igrave; <lb/>nel dar la storia dei minerali, ritenuta la natural distinzione di terre, di pie&shy;<lb/>tre e di metalli, a ciascuna delle quali differenze consacra un libro del suo <lb/>tripartito discorso; ora dalle generazioni per via di soluzione o di sublima&shy;<lb/>zione, e ora da qualit&agrave; e propriet&agrave; fisicamente specifiche desume le note <lb/>opportune per ridur la molteplice e infino allora confusa variet&agrave; di sostanze <lb/>ai loro pi&ugrave; convenevoli ordinamenti. </s></p><p type="main">

<s>Le prime differenze delle Terre si desumono dalla variet&agrave; dei loro sol-<pb xlink:href="020/01/1496.jpg" pagenum="371"/>venti, che sono acqua o olio. </s>

<s>Solubili nell'acqua sono le terre propriamente <lb/>dette, i sali, gli allumi e altri corpi a questi assa&igrave; somiglianti. </s>

<s>&ldquo; Terra igi&shy;<lb/>tur, ut a simplicioribus ordiamur, ea proprie appellatur, quae sicca cum sit <lb/>sine humore non cohaeret, sed pulveris modo diffluit: humore autem ma&shy;<lb/>defacta glutinatur in lutum..... Multae autem sunt terrarum differentiae <lb/>pro ariditate, aut pinguedine, densitate, raritate, asperitate, levitate, tenaci&shy;<lb/>tate, fragilitate et aliis huiusmodi: item coloribus et saporibus..... Quoniam <lb/>autem ad diversos usus petuntur ab artificibus, secundum hos, diversa no&shy;<lb/>mina imposita sunt speciebus. </s>

<s>Agricolae enim suas terras quaerunt, alias <lb/>figuli et plastici, alias fullones, alias pictores, alias medici &rdquo; (De metallicis, <lb/>Romae 1596, pag. </s>

<s>25). </s></p><p type="main">

<s>Dei sali ne riconosce con Dioscoride tre generi: fossile, marino e la&shy;<lb/>custre. </s>

<s>&ldquo; Ad salem reducuntur spuma salis, muria, et flos salis &rdquo; (ibid., <lb/>pag. </s>

<s>43). Gli allumi son, per la veemenza del sapore astringente, dai Greci <lb/>chiamati <emph type="italics"/>stipterii,<emph.end type="italics"/> e gli antichi ne annoverarono varie specie, riguardandoli <lb/>o come efflorescenze della Terra o come concrezioni di varia figura. </s>

<s>&ldquo; Multa <lb/>alia hodie recensent inter alumina, ut alumen plumae, quod amiantum esse <lb/>diximus, alumen scaliolum, qui Lapis est specularis inter genera gypsi, alu&shy;<lb/>men Catinum quod vulgo sodam vocant inter nitra factitia, alumen faecis, <lb/>quae faex vini est combusta inter nitra factitia, alumen zuccharinum..... <lb/>Alumen iamenum Arabes intelligunt scissile Dioscoridis &rdquo; (ibid., pag. </s>

<s>55). </s></p><p type="main">

<s>Le sostanze terrose, che si sciolgon nell'olio, son per il Cesalpino il <lb/>solfo, i bitumi &ldquo; et congenera his &rdquo; (pag. </s>

<s>62) quali sarebbero l'Arsenico, <lb/>la Sandracca, l'Asfaltide, la Canfora e l'Ambra, i quali due ultimi corpi gli <lb/>riguarda &ldquo; ut genera Bituminis odorata &rdquo; (pag. </s>

<s>71). E con la descrizione <lb/>delle propriet&agrave; naturali relative a ciascuna di queste recensite sostanze, e <lb/>de'loro usi o nella pratica medicina o nell'esercizio delle arti, termina il <lb/>nostro Autore il suo primo libro <emph type="italics"/>De metallicis.<emph.end type="italics"/></s></p><p type="main">

<s>Il secondo, come si disse, &egrave; consacrato a trattar delle sostanze lapidee, <lb/>che il Cesalpino, seguendo l'uso volgare, distingue in marmi, in sassi, in <lb/>gemme preziose e in pietre propriamente dette. </s>

<s>&ldquo; Quatuor autem genera <lb/>summa lapidum traduntur vulgo nota: marmora, saxa, gemmae, lapides &rdquo; <lb/>(pag. </s>

<s>81). I generi de'marmi, soggiunge, non &egrave; facile, in tanta moltitudine <lb/>e in tanta variet&agrave; di colori, annoverarli, non essendovi luogo che non abbia i <lb/>suoi proprii. </s>

<s>&ldquo; Nos tamen breviter ex numero colorum colligemus &rdquo; (pag. </s>

<s>89). <lb/>E passa a descrivere il Marmo pario, il Numidico, le Ofiti, le Serpentine, <lb/>le Porfiriti, le Terebintine. </s></p><p type="main">

<s>In due sommi generi ripartisce i sassi, in Tufi e in Silici: queste du&shy;<lb/>rissime, e quelli molli. </s>

<s>La silice, che fu tra le pietre, egli osserva, ritrovata <lb/>la prima per servir cos&igrave; bene ad uso di macina, quando sia cotta al fuoco <lb/>perde la sua prima durezza, e si trasforma in calce o in gesso; ond'&egrave; che <lb/>quelle specie d'essa silice, che si scelgono a quest'usi particolari, si distin&shy;<lb/>guono con nomi proprii. </s>

<s>&ldquo; Saxum, unde calx excoquitur, calcariam dici po&shy;<lb/>test.... Cognata res calci Gypsum est &rdquo; (pag. </s>

<s>85). </s></p><pb xlink:href="020/01/1497.jpg" pagenum="372"/><p type="main">

<s>Gemme si dicono quelle pietre insignemente dure, che dilettano per la <lb/>loro chiarezza e per il loro splendore, e s'usano ad ornamento degli anelli <lb/>e dei monili. </s>

<s>Si distinguono in chiare, in colorite e in opache. </s>

<s>&ldquo; Perspicuae <lb/>aliae sola claritate oblectant, ut Crystallus, Adamas: aliae colorum quoque <lb/>pulchritudine ut Smaragdus, Carbunculus; opacae solo splendere et colorum <lb/>pulchritudine &rdquo; (pag. </s>

<s>96). </s></p><p type="main">

<s>Le pietre all'ultimo propriamente dette si dividono in Coti e in Arene. </s>

<s><lb/>Delle Coti alcune sono Aquarie, perch&egrave; non hanno per aguzzare altro biso&shy;<lb/>gno che d'esser bagnate con acqua, come le Naxie e le Armenie; altre <lb/>sono oleari, come le Cretiche e le Laconiche. </s>

<s>&ldquo; Quaedam aqua et oleo in&shy;<lb/>digent ut Ciliciae, quaedam hominis saliva, sed mollissimae, ut Flammini&shy;<lb/>tanae ex Hispania citeriore &rdquo; (pag. </s>

<s>87). Delle arene, che son sassi stritolati <lb/>e ridotti in minutissime parti, ne assegna il Cesalpino, sull'esempio di Pli&shy;<lb/>nio, tre generi: le fossili, le fluviatili e le marine (ivi). </s></p><p type="main">

<s>Il terzo libro &egrave; dall'Autore riserbato ai metalli, fra'quali, repudiata <lb/>com'arbitraria la comun distinzione in sette specie annoverate secondo l'or&shy;<lb/>dine e denominate dai sette Pianeti, riconosce due primi e massimi generi, <lb/>di fusibili e di duttili. </s>

<s>Dai metalli poi distingue quelle parti ch'escono dagli <lb/>stessi metalli, alcune delle quali, egli dice, hanno origine nelle fornaci, come <lb/>le scorie, altre fuori, come la ruggine. </s>

<s>Alle stesse scorie in ultimo riduce <lb/>anche il vetro &ldquo; substantia enim similis est scoriis metallorum &rdquo; (pag. </s>

<s>212). </s></p><p type="main">

<s>Il libro, in cui venivano dal Cesalpino in questo modo ordinate, e se&shy;<lb/>condo le loro propriet&agrave; fisiche descritte le varie sostanze metalliche, &egrave; il <lb/>primo documento, che avesse, in quella nuova instaurazione delle scienze <lb/>sperimentali in Italia, la Mineralogia. </s>

<s>Ma un valoroso discepolo dell'Autore <lb/>dava in quel medesimo tempo in Roma opera a quegli stessi studii, di che <lb/>il Maestro non punto di ci&ograve; geloso, ma anzi tutto compiacente faceva, nella <lb/>citata dedica a Clemente VIII, questa commemorazione solenne: &ldquo; Sed ecce, <lb/>quamprimum Romam petii ut medicinam publice profiterer, comperi ean&shy;<lb/>dem provinciam a reverendissimo ac perillustri Michaele Mercato viro doctis&shy;<lb/>simo susceptam eamque, cum is mihi communicasset tanquam praeceptori <lb/>suo, quo usus est dum Pisis Simplicia profiterer, incredibili laetitia affectus <lb/>sum, quod discipulum praeclarissimum ex schola mea tanquam ex proprio <lb/>ventre prodeuntem adeo profecisse viderem ut toto orbe admirabilis redde&shy;<lb/>retur. </s>

<s>Inter caeteras enim lucubrationes <emph type="italics"/>Metallothecam vaticanam<emph.end type="italics"/> miro or&shy;<lb/>dine construxit, loculis propriis singula corpora distribuens, ut ingens eorum <lb/>turba, absque ulla turbatione, intuentibus praesto esset. </s>

<s>Eorumdem imagi&shy;<lb/>nes aeneis typis imprimendas curavit, adiuncta enarratione facundissima ex <lb/>omnibus auctoribus tam priscis quam posterioribus collecta, ut desiderari <lb/>quid amplius nequiret. </s>

<s>&rdquo; </s></p><p type="main">

<s>Pareva per queste ragioni, prosegue a dire il Cesalpino, che dovesse <lb/>riuscir superflua l'opera nostra, ma sventuratamente il Mercati aveva appena <lb/>disteso il primo Tomo, dove tratta delle Terre, de'Sali, degli Allumi, de'Solfi <lb/>e di altri simili, quando la morte sopravvenutagli gl'imped&igrave; di proseguire il <pb xlink:href="020/01/1498.jpg" pagenum="373"/>bene incamminato lavoro, lasciandolo cos&igrave;, con grave danno della scienza, <lb/>imperfetto. </s>

<s>&ldquo; Deest enim de Marmoribus tractatio et de gemmis et metallis, <lb/>quorum sylvam esse quidem apud se in fragmentis quibusdam asserebat, <lb/>sed minus elaboratam. </s>

<s>&rdquo; </s></p><p type="main">

<s>Questo elogio dell'Autore e dell'Opera fatto da un tal giudice, qual'&egrave; <lb/>il Cesalpino, invoglia di saperne pi&ugrave; avanti i nostri lettori, per sodisfare ai <lb/>quali diciamo che negli ultimi giorni di Settembre dell'anno 1666 fu veduto <lb/>da certi pescatori alla Gorgona presso Livorno un gran pesce andar placi&shy;<lb/>damente leccando la spalmatura di una tartana, ond'&egrave; che gli si pot&egrave; facil&shy;<lb/>mente avventare un laccio intorno al capo e trarlo, bench&egrave; dopo grandis&shy;<lb/>sima resistenza, dentro la barca. </s>

<s>Il capo di questo pesce, conosciuto dai <lb/>Naturalisti di allora sotto il nome di <emph type="italics"/>Lamia,<emph.end type="italics"/> fu fatto dal Granduca venire <lb/>a Firenze per consegnarlo a Niccol&ograve; Stenone, che ne facesse diligente ana&shy;<lb/>tomia. </s></p><p type="main">

<s>I Fiorentini accorsero curiosi a vedere questa nuova maraviglia: ai lon&shy;<lb/>tani trov&ograve; modo di sodisfar Carlo Dati, mandando quella stessa testa dise&shy;<lb/>gnata con finissimo intaglio. </s>

<s>Chi vide cotesta immagine andare attorno, pochi <lb/>giorni dopo che fu chiappato il pesce, prese a far forse maggiori maraviglie <lb/>di quegli altri, ch'ebber agio di saziar la vista nell'oggetto reale, non in&shy;<lb/>tendendo come potess'essere che in s&igrave; breve tempo fosse stato condotto in <lb/>Firenze sul rame un s&igrave; squisito lavoro. </s></p><p type="main">

<s>Fra i maravigliati di ci&ograve; era in Roma Ottavio Falconieri, a cui il Dati <lb/>stesso, che gli aveva mandato pochi giorni innanzi il disegno, rispondeva <lb/>cos&igrave; rivelandogli il mistero. </s>

<s>&ldquo; Agli anni passati io comprai la <emph type="italics"/>Metalloteca <lb/>vaticana<emph.end type="italics"/> manoscritta con tutti i suoi rami intagliati mirabilmente, descritta <lb/>da mons. </s>

<s>Michele Mercati, con pensiero di farla una volta stampare, perch&egrave; <lb/>veramente &egrave; opera insigne. </s>

<s>Il detto Autore, con occasione di trattare delle <lb/>glossopetre, dice che elle sono tanto simili ai denti del pesce Lamia, che da <lb/>alcuni sono spesse volte scambiate, e dop'averne assegnate le differenze pone <lb/>il disegno del capo di questo pesce. </s>

<s>Mi sovvenne di ci&ograve;, e trovando il rame, <lb/>ne ho fatti tirare dodici soli, per non offendere l'intaglio che &egrave; gentilis&shy;<lb/>simo, risparmiandolo per la stampa dell'opera &rdquo; (Lettere di C. Dati, Fi&shy;<lb/>renze 1825, pag. </s>

<s>56, 57). </s></p><p type="main">

<s>&ldquo; Di mons. </s>

<s>Michele Mercati, dice il Dati stesso in un'altra sua lettera <lb/>al medesimo Falconieri, non perdo tempo a darle notizia, perch&egrave; il valore <lb/>di esso e l'opera <emph type="italics"/>Degli obelischi<emph.end type="italics"/> l'ha reso celebre e particolarmente in co&shy;<lb/>testa citt&agrave; di Roma. </s>

<s>Anzi io spero da lei a suo tempo qualche aiuto per <lb/>fare di questo Letterato un breve elogetto storico. </s>

<s>Fra gli altri studii di que&shy;<lb/>sto. </s>

<s>Prelato fu quello delle cose naturali, e specialmente delle metalliche, <lb/>onde, mentr'era al servizio di Sisto V P. M., form&ograve; nel Vaticano una co&shy;<lb/>copiosissima Metalloteca, la quale poi descrisse in lingua latina secondo l'or&shy;<lb/>dine col quale era disposta, trattando le principali materie con eguale cu&shy;<lb/>riosit&agrave;, erudizione ed eleganza, e adornolla di figure intagliate in rame con <lb/>estrema finezza, senza guardare a spesa o diligenza veruna. </s>

<s>Prevenuto dalla <pb xlink:href="020/01/1499.jpg" pagenum="374"/>morte, non potette pubblicar detta opera, che gi&agrave; era riveduta e passata <lb/>da'Superiori e resa famosa dal testimonio dell'Eminentissimo card. </s>

<s>Baronio <lb/>nel primo tomo degli <emph type="italics"/>Annali ecclesiastici.<emph.end type="italics"/> Restarono adunque presso agli <lb/>eredi il manoscritto e i rami con grandissimo pericolo d'andar male, e fu&shy;<lb/>rono pi&ugrave; volte in cimento d'andar portati oltre i monti. </s>

<s>Agli anni passati, <lb/>avendone io qualche precedente cognizione, procurai di veder l'uno e gli <lb/>altri, e talmente me ne invogliai, che avanti di restituirgli negoziai e con&shy;<lb/>clusi la compra con qualche mio scomodo per la somma di settanta dop&shy;<lb/>pie..... Mi mossi a far questa spesa, a me veramente sproporzionata, per <lb/>desiderio che quest'Opera si pubblicasse, ma essendo per me, com'&egrave; noto <lb/>ad ognuno, corsi molti anni disastrosi, non &egrave; possibile che io faccia s&igrave; grande <lb/>sborso quanto sarebbe necessario a volerla stampar nobilmente..... Tal&shy;<lb/>mente che senza qualche buono aiuto mi son perduto d'animo, e in Olanda, <lb/>dove avrei occasione di mandarla, non voglio, per non mettere a risico <lb/>i rami. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per essere questa Galleria stata eretta in Vaticano, e perci&ograve; <emph type="italics"/>Vaticana<emph.end type="italics"/><lb/>intitolata, a diletto e spese d'un Sommo Pontefice, il mio concetto era pub&shy;<lb/>blicandola consacrarla al nome glorioso del regnante Pontefice Ottimo Mas&shy;<lb/>simo, e riempire i voti dell'armi pontificie con l'insegne trionfali di casa <lb/>Ghigi. </s>

<s>Le lettere dedicatorie, prefazione, vita dell'Autore, indici, assistenza, <lb/>correzione, ecc., tutto son pronto a fare. </s>

<s>E siccome fui pronto al primo <lb/>sborso, cos&igrave; farei al restante, se i miei negozii non fossero andati in ma&shy;<lb/>lora. </s>

<s>Ma nello stato presente non mi resta se non un buon desiderio e un <lb/>godimento d'avere assicurata quest'opera degnissima, perch&egrave; altri, quando <lb/>che sia, abbia miglior fortuna di pubblicarla &rdquo; (ivi, pag. </s>

<s>62-66). </s></p><p type="main">

<s>Da queste espressioni, fatte in una lettera del d&igrave; 6 Novembre 1666, <lb/>collazionate con quelle che si leggono nella precedente del d&igrave; 17 Settem&shy;<lb/>bre, e nella quale il Dati pregava il Falconieri che si volesse far mediatore <lb/>appresso Alessandro VII per la stampa dell'opera del Mercati, si raccoglie <lb/>che non doveva avere avuto lo stesso Dati troppo buone speranze di riu&shy;<lb/>scire per quella via all'intento. </s>

<s>E infatti ei mor&igrave;, lasciando il manoscritto <lb/>e i rami in eredit&agrave; a'suoi figli, i quali gli presentarono in dono a Cle&shy;<lb/>mente XI, per secondare i desiderii del padre. </s></p><p type="main">

<s>Di ci&ograve; che prometteva di fare il Dati stesso intorno alla edizione, per&shy;<lb/>ch&egrave; riuscisse corredata di tutte le sue parti, e corretta, dette cura Clemente <lb/>al suo Archiatro Giovan Maria Lancisi, il quale pubblic&ograve; l'Opera in Roma <lb/>nel 1717 col titolo seguente: &ldquo; Michaelis Mercati Metallotheca Opus postu&shy;<lb/>mum, Auctoritate et munificentia Clementis XI e tenebris in lucem eductum, <lb/>Opera autem et studio Joannis Mariae Lancisii illustratum. </s>

<s>&rdquo; Due anni dopo <lb/>a un certo numero di copie si reimpresse, pure in Roma dallo stesso Lan&shy;<lb/>cisi, il titolo dell'Opera &ldquo; cui accessit appendix cum XIX recens inventis <lb/>iconibus. </s>

<s>&rdquo; </s></p><p type="main">

<s>Apparisce dai fatti fin qui narrati che le notizie tramandate intorno alla <lb/>Metalloteca vaticana dal Cesalpino non sono molto precise, imperocch&egrave; le <pb xlink:href="020/01/1500.jpg" pagenum="375"/>immagini de'loculi e delle figure dei metalli non rimanevano <emph type="italics"/>aeneis typis <lb/>imprimendae,<emph.end type="italics"/> ma erano gi&agrave; state impresse, e il Dati scrive che &ldquo; fatta di&shy;<lb/>ligente rassegna de'rami finiti, abbozzati e rifatti, in tutto sono cento trenta &rdquo; <lb/>(ivi, pag. </s>

<s>64). </s></p><p type="main">

<s>Se poi fosse vero quel che dianzi udimmo dire dallo stesso Dati, che <lb/>cio&egrave; il manoscritto della Metalloteca era stato riveduto e passato dai Supe&shy;<lb/>riori, parrebbe si dovesse dubitare anche del Cesalpino l&agrave; dove dice essere <lb/>stata l'Opera lasciata dal suo Autore imperfetta. </s>

<s>In ogni modo &egrave; vero che <lb/>manca, nella pubblicazion del Lancisi, il trattato delle gemme e dei metalli, <lb/>e quel de'marmi &egrave; manifestamente interrotto ne'suoi principii. </s>

<s>Ma suppli&shy;<lb/>sce il Mercati al difetto coll'introdurre nella sua trattazione tre nuovi sog&shy;<lb/>getti, de'quali il Cesalpino non tocca, e per cui l'opera del discepolo vien <lb/>principalmente a pigliare importanza sopra quella dello stesso Maestro. </s></p><p type="main">

<s>&Egrave; tutta insieme la Metalloteca dunque magnificamente ordinata in <emph type="italics"/>Ar&shy;<lb/>madi,<emph.end type="italics"/> eretti intorno intorno alle pareti di una delle grandi sale del Vati&shy;<lb/>cano. </s>

<s>Primo e principal pensiero dell'Autore &egrave; quello di far s&igrave; che i varii <lb/>oggetti trovino da collocarsi in un medesimo Armadio, coi loro congeneri, <lb/>specificati ciascuno ne'loculi convenienti. </s>

<s>Prende l'Autore a guida de'suoi <lb/>pensieri Aristotile, il dilungarsi dal quale egli stima pericoloso, per l'esem&shy;<lb/>pio di un Autore, che l'aveva di poco preceduto, e di cui dice che &ldquo; peri&shy;<lb/>patetica luce orbatus, nil mirum si in graves incidit errores &rdquo; (pag. </s>

<s>5). E <lb/>perch'&egrave; per lui di grande autorit&agrave; Teofrasto, fedel discepolo di Aristotile, si <lb/>studia di conciliarlo col Maestro, ripudiando senza esitare Galeno, che pro&shy;<lb/>poneva di ordinar le varie sostanze minerali in pietre, in corpi metallici e <lb/>in terre coltivabili, e insiem con lui Avicenna, che le stesse sostanze distri&shy;<lb/>buiva tutte in pietre, in metalli, in solfori e in sali. </s>

<s>&ldquo; Sed ne videamur inu&shy;<lb/>tilia persequi, poi tosto soggiunge dop'aver dimostrato essere difettoso ogni <lb/>altro ordinamento, che si dilunghi dagl'insegnamenti aristotelici, ad nostrum <lb/>institutum revertamur ab iis incipientes, quae a sicca exhalatione fiunt, quo&shy;<lb/>rum alia humore solubilia sunt, ut terrae proprie vocatae quae in lutum <lb/>transeunt, sales qui in aquam, sulphur quod in oleum. </s>

<s>Alia insolubilia, ut la&shy;<lb/>pides illiquabiles. </s>

<s>Postremo explicabuntur quae humida exhalatione constant: <lb/>haec autem igne liquabilia sunt aut ductilia &rdquo; (ibid.). </s></p><p type="main">

<s>Qui l'Editore avverte esser nel manoscritto una lacuna, lasciatavi se&shy;<lb/>condo noi dal trovarsi incerto e pensoso l'Autore, per vedersi innanzi smar&shy;<lb/>rite a un tratto l'orme del suo fedele Aristotile, negli ordinamenti del quale <lb/>non pareva che trovassero luogo proprio le sostanze lapidee innate negli ani&shy;<lb/>mali, o che presentano figure simili a quelle di corpi o di membra animali. </s>

<s><lb/>Ebbe perci&ograve; all'ultimo a deliberarsi di assegnare a questi corpi di natura <lb/>e di forme singolari due Armadi distinti, da collocarsi fra le sostanze lapi&shy;<lb/>deo terrose e i marmi. </s>

<s>Il discorso dell'Autore intorno a questi ultimi si ri&shy;<lb/>duce a tre soli capitoli, nel primo de'quali tratta delle definizioni, e nel <lb/>secondo delle differenze, ch'egli desume da pi&ugrave; numerose note di quelle, <lb/>alle quali sole avevano atteso i suoi primi Maestri. </s>

<s>&ldquo; Differentiae marmo-<pb xlink:href="020/01/1501.jpg" pagenum="376"/>rum aliae oriuntur a substantiae temperamento, aliae a compositione par&shy;<lb/>tium, nonnullae a magnitudine corporis a qua gignuntur, quaedam a duri&shy;<lb/>tia, quaedam a nitore, sed plures a colore et specie macularum et locis <lb/>natalibus &rdquo; (pag. </s>

<s>353). </s></p><p type="main">

<s>Di qui preparavasi ampia la trattazione de'marmi, la quale invece si <lb/>assolve tutta ne'principii del cap. </s>

<s>III, in cui, proponendosi il Mercati di trat&shy;<lb/>tare del Marmo pario, si divaga in descrivere le statue antiche del Laocoonte, <lb/>dell'Apollo e dell'Antinoo, collocate per ornamento de'giardini vaticani, e <lb/>scolpite in quella stessa elettissima qualit&agrave; di marmo bianco. </s>

<s>Dovevasi qui <lb/>insieme co'marmi trattare anche delle gemme, nelle quali e ne'metalli pro&shy;<lb/>priamente detti si lasci&ograve; veramente, come il Cesalpino diceva, la Metalloteca <lb/>vaticana imperfetta. </s></p><p type="main">

<s>Secondo che dunque pot&egrave; raccogliersi dal manoscritto, la Metalloteca <lb/>stessa si lasci&ograve; cos&igrave; dal Mercati ordinata in X distinti Armadi. </s>

<s>Nel I si ri&shy;<lb/>ponevano le Terre, nel II i sali e i Nitri, nel III gli Allumi, nel IV i Suc&shy;<lb/>chi acri (crisocolla, ruggine, arsenico, sandracca), nel V i Succhi pingui <lb/>(solfo, bitumi, succino), nel VI le sostanze d'origine marina (coralli, spugne, <lb/>pomici), nel VII <emph type="italics"/>Lapides terrae similes<emph.end type="italics"/> (calamina, manganese, tufo, mica, <lb/>magnetide, pietra speculare, amianto, ematite), nell'VIII <emph type="italics"/>Lapides animali&shy;<lb/>bus innati<emph.end type="italics"/> (bezoar, bufoniti, chelonie, perle, ecc.). </s></p><p type="main">

<s>Fra la ricca raccolta delle varie produzioni naturali se ne trovava il <lb/>Mercati a mano di quelle, alle quali, neanche fermandosi sulle note fisiche, <lb/>si sarebbe saputo trovare il luogo conveniente, simulando l'origine vera la <lb/>loro apparente figura ora per esempio di ova o di lingue, ora di rami d'al&shy;<lb/>beri o di code di serpenti. </s>

<s>Disputavasi se avessero veramente codesti og&shy;<lb/>getti nascimento dagli animali, o se fossero, come le altre pietre, prodotti <lb/>dalla terra. </s>

<s>Ond'&egrave; che risolutosi il Mercati di seguire questa seconda opi&shy;<lb/>nione, riserb&ograve; un Armadio distinto, ch'&egrave; in ordine il IX, a que'particolari <lb/>oggetti da lui stesso insigniti del nome d'<emph type="italics"/>Idiomorfi<emph.end type="italics"/> &ldquo; idest peculiari forma <lb/>praediti &rdquo; (pag. </s>

<s>215). Trovarono in cotesto Armadio dove riporsi le ooliti, <lb/>le ammoniti, le ofiti, i lepidoti, le dendriti, le glossopietre e simili, che hanno <lb/>dato appresso al volgo origine a tante favole francamente derise dal nostro <lb/>Autore. </s>

<s>L'ultimo Armadio, ch'&egrave; il X, era stato appena aperto per riporvi <lb/>i marmi, ma l'inesorabile morte fece s&igrave; che, dal primo loculo in fuori si <lb/>rimanesse del resto vuoto. </s></p><p type="main">

<s>Chi ripensa a questi ordinamenti dei minerali, proposti sulla fine del <lb/>secolo XVI, contemporaneamente dal Cesalpino e dal Mercati, non pu&ograve; non <lb/>apprezzarne il sollecito studio e l'ammirabile industria. </s>

<s>L'averli anzi ten&shy;<lb/>tati, quando la smisurata variet&agrave; sbigottiva gl'ingegni, e le difficolt&agrave; d'in&shy;<lb/>vestigar le prime origini, e di penetrare addentro alla pi&ugrave; intima natura <lb/>de'corpi, non eran vinte ancora dalla scienza o dall'arte; forma tutt'insieme <lb/>la ragion del merito e la scusa dei difetti, che si trovan nell'opera de'due <lb/>nostri Autori. </s>

<s>Se la Mineralogia infatti ha potuto oggid&igrave; proporre ordina&shy;<lb/>menti pi&ugrave; razionali non v'&egrave; per altro riuscita, che per esser venute in va-<pb xlink:href="020/01/1502.jpg" pagenum="377"/>lido soccorso di lei la Geologia, la Cristallografia e la Chimica; tre scienze <lb/>che, ai tempi del Cesalpino e del Mercati, o non erano nate o si trovavano <lb/>nella loro prima infanzia. </s></p><p type="main">

<s>La Geologia ponendo mente ai varii strati sedimentarii, in che il ter&shy;<lb/>restre globo s'affalda, pot&egrave; con certezza di fatto dimostrar l'opera e l'effi&shy;<lb/>cacia di quelle inondazioni, che si appellarono col nome di diluvii, e presa <lb/>per sua ancella la Paleontologia dare un giusto criterio da distinguer le pie&shy;<lb/>tre fossili dalle reliquie animali. </s>

<s>Cos&igrave; veniva a espurgarsi delle Glossopetre, <lb/>e di tanti altri Idiomorfi, il IX Armadio mineralogico del Mercati. </s></p><p type="main">

<s>La Cristallografia dimostrando che non alla sola figura sessangola, ma <lb/>a varii tipi pi&ugrave; semplici si riducono le forme primigenie de'cristalli, apriva <lb/>largo campo a raccogliere nuove note specifiche del pi&ugrave; gran numero di <lb/>minerali, mentre nel tempo stesso soccorreva opportuna la Chimica a sve&shy;<lb/>lar l'inganno, in ch'erano inevitabilmente caduti tutti gli Antichi, mostrando <lb/>che bene spesso, sotto un simile abito esterno, s'ascondon corpi tanto fra <lb/>s&egrave; diversi d'origine e di sostanza. </s></p><p type="main">

<s>Cos&igrave; essendo la Chimica, a conoscere la testura de'corpi bruti, stru&shy;<lb/>mento meglio proporzionato di quel che non fosse, a investigar la trama <lb/>organica, l'Istologia, si pu&ograve; dire che gli ordinamenti de'Minerali, a princi&shy;<lb/>pio appariti tanto difficili, e perci&ograve; venuti pi&ugrave; tardi, si trovarono fondati sopra <lb/>pi&ugrave; stabili principii, che non gli ordinamenti degli altri due regni superiori. </s></p><p type="main">

<s>In ogni modo furon tali, quali si son potuti accennare in questo capi&shy;<lb/>tolo, i laboriosi studii fatti dalla Scienza, per ridurre in convenevole ordine <lb/>i tre grandi eserciti, che militano su questa Terra. </s>

<s>Ond'ora non rimane a <lb/>noi che a delibare il frutto delle sensate osservazioni e delle artificiose espe&shy;<lb/>rienze nello studio degli organi e delle funzioni proprie ai varii generi di <lb/>animali; della struttura delle piante, e della vita vegetativa; dell'origine, <lb/>delle forme e delle propriet&agrave;, che distinguono le varie sostanze minerali. </s></p><pb xlink:href="020/01/1503.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO X.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>De'Mammiferi e degli Uccelli<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della generazione dagli svolgimenti embrionali dell'uovo. </s>

<s>&mdash; II. De'moti locali: del passo e del <lb/>volo. </s>

<s>&mdash; III. </s>

<s>Di alcune questioni concernenti le funzioni digestive ne'quadrupedi ruminanti e <lb/>negli uccelli gallinacei: delle vescicole pneumat&igrave;che negli uccelli. </s>

<s>&mdash; IV. </s>

<s>Di certe pi&ugrave; notabili <lb/>differenze negli organi dei sensi: degli strumenti della voce e del canto. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Gli organi e le funzioni di quelli animali, che appartengono agli ordini <lb/>superiori, e che o s'appellano <emph type="italics"/>Mammiferi<emph.end type="italics"/> dal modo del loro allevamento, o <lb/><emph type="italics"/>Quadrupedi<emph.end type="italics"/> dagli strumenti della locomozione, non differiscono sostanzial&shy;<lb/>mente dagli organi e dalle funzioni animali dell'uomo. </s>

<s>Essendosi perci&ograve;, <lb/>nella serie de'capitoli precedenti intrattenuta la nostra Storia in narrar ci&ograve; <lb/>che, per via dell'arte sperimentale, riusc&igrave; la scienza a intendere della strut&shy;<lb/>tura del corpo umano e della vita di lui, viene a restringersi il soggetto <lb/>della narrazione che resta in que'pi&ugrave; notabili particolari, per cui i bruti <lb/>hanno una storia naturale a loro propria. </s>

<s>Che se nel Microcosmo, come ci <lb/>occorse di osservare altra volta, si trova la Natura tutta insieme raccolta e <lb/>sublimata, riducesi dunque ogni officio, che incombe al nuovo studio, in <lb/>comparare l'anatomia e la fisiologia dell'uomo coll'anatomia, e colla fisio&shy;<lb/>logia de'varii sottoposti ordini animali, e in osservare e sperimentare che <lb/>sia ci&ograve; che gli differenzia, e che gli costituisce ne'gradi, dalla Natura stessa <lb/>a ciascun di loro assegnati. </s></p><p type="main">

<s>Intorno al resultato insomma di quelle comparazioni, ch'ebbero a scorta <lb/>l'osservazione e l'esperienza, ha da trattenersi il nostro Discorso, alle prime <pb xlink:href="020/01/1504.jpg" pagenum="379"/>mosse del quale si fanno incontro gli Anatomici del secolo XVI fieramente <lb/>disputanti fra loro. </s>

<s>E perch&egrave; dalla risoluzione di quelle dispute viene a de&shy;<lb/>cidersi se i primi documenti della comparata Anatomia si trovino per i libri <lb/>galenici, e se l'antico Maestro descrivesse la struttura del corpo umano o <lb/>del belluino, ci consiglia il soggetto che prendiamo a trattare di soffermarci <lb/>brevemente su questo punto. </s></p><p type="main">

<s>Che il Vesalio, per le numerose pagine della sua Anatomia descrittiva <lb/>della fabbrica del corpo umano, non s'abbattesse a descriver parte, d'onde <lb/>non pigliasse avida occasione di coglier Galeno in fallo, s'&egrave; detto e ripe&shy;<lb/>tuto pi&ugrave; volte anche da noi. </s>

<s>Il Colombo pure, bench&egrave; fosse nelle accuse pi&ugrave; <lb/>mite, ebbe a riconoscere che molte delle galeniche descrizioni, volutesi da <lb/>lui appropriare all'uomo, ritraevan piuttosto la particolare struttura degli <lb/>organi dei cani e delle scimmie; ond'&egrave; che insorsero fieramente i Vesaliani <lb/>ad accusare i Galenisti d'avere spacciata per l'anatomia dell'uomo quella, <lb/>ch'&egrave; piuttosto propria del bruto. </s></p><p type="main">

<s>Erasi il campo della contesa particolarmente restrinto nell'esame degli <lb/>ossi, intorno a che s'esercitarono il Falloppio e l'Ingrassia, scrivendone par&shy;<lb/>ticolari trattati che, divulgatissimi per le pi&ugrave; celebri scuole d'Italia, furono <lb/>ambedue pubblicati postumi. </s>

<s>Quel del Falloppio, dato in luce nel 1570 da <lb/>Francesco Michino, &egrave; il pi&ugrave; importante, e com'ebbe maggiore autorit&agrave; del&shy;<lb/>l'altro in compor gli animi de'disposti alla pace, cos&igrave; dette nuovo motivo <lb/>ai dissidenti di sostener, con pi&ugrave; ardore che mai, le loro gi&agrave; pregiudicate <lb/>opinioni. </s></p><p type="main">

<s>Il trattato falloppiano, che porta il titolo di <emph type="italics"/>Observationes in librum <lb/>Galeni de ossibus,<emph.end type="italics"/> &egrave; un'introduzione allo studio dell'Anatomia, della quale <lb/>l'Autore d&agrave; la definizione, e investiga l'origine, riconoscendola co'Platonici <lb/>nella naturale curiosit&agrave; di sapere. </s>

<s>Nota poi che la nuova scienza ebbe in&shy;<lb/>cremento per opera d'Ippocrate e di Democrito mosso, da coloro che lo de&shy;<lb/>ridevano, a cercar ne'dutti biliari le riposte sorgenti della pazzia. </s></p><p type="main">

<s>Come introduzione perci&ograve; incomincia il Falloppio dagli ossi, e descrive <lb/>lo scheletro, comparando via via le osservazioni sue proprie con le descri&shy;<lb/>zioni, che si leggono ne'libri di Galeno. </s>

<s>Nel cap. </s>

<s>XXII per esempio tratta <lb/>dell'osso sacro, e relativamente alla figura delle parti che lo compongono <lb/>scrive: &ldquo; Observandum est quod spina in osse sacro est similis spinae alia&shy;<lb/>rum vertebrarum secundum Galenum, quod quidem verum est in canibus <lb/>et simiis, sed in hominibus est exilis et fere non conspicua. </s>

<s>&rdquo; (Venetiis, apud <lb/>Karera, 1570, fol. </s>

<s>54). Rispetto al numero poi di quelle parti, dop'aver letto <lb/>nel testo galenico che son tre, soggiunge: &ldquo; Quot sint partes ossis sacri <lb/>nunc docet Galenus, sed haec descriptio multum differt ab ossibus humanis. </s>

<s><lb/>Ascribit nam illi tres partes, cum tamen sint sex. </s>

<s>Quibus tribus partibus, <lb/>tanquam propriis vertebris, adiungit %o%%<foreign lang="greek">uga</foreign> &rdquo; (ibid., fol. </s>

<s>55). </s></p><p type="main">

<s>Cos&igrave; proseguendo il Falloppio il suo diligente esame, per tutte le altre <lb/>parti, veniva a concludersene che Galeno avesse piuttosto descritto lo sche&shy;<lb/>letro delle scimmie. </s>

<s>Sorse Bartolommeo Eustachio a confutare una tal con-<pb xlink:href="020/01/1505.jpg" pagenum="380"/>clusione, dimostrando anzi che l'antico Maestro non poteva aver avuto sot&shy;<lb/>t'occhio altro che la struttura delle ossa dell'uomo. </s>

<s>Quanto al sacro, osservava <lb/>che nell'Autor greco la confusione nasce tutta dai nomi, perch'egli del re&shy;<lb/>sto, dando al coccige tre parti, viene insomma a dire che, tutto insieme, esso <lb/>osso sacro si compone di sei. </s>

<s>&ldquo; Quantum ego penetrare ad sensum opinio&shy;<lb/>nemque Galeni possum, rudi linea ipse nobis abumbravit, quando in libro <lb/><emph type="italics"/>De ossibus,<emph.end type="italics"/> et in illis, quos <emph type="italics"/>De administratione anatomica<emph.end type="italics"/> inscripsit, os <lb/>sacrum in tres portiones et totidem os coccygis partiri docuit &rdquo; (Opusc. </s>

<s><lb/>anat., Venetiis 1564, Ossium examen, pag. </s>

<s>220, 21). Argomenta dall'altra <lb/>parte l'Eustachio che dee aver veramente Galeno descritte le parti dell'osso <lb/>sacro nell'uomo, perch&egrave; se le avesse osservate nelle scimmie &ldquo; dubio procul <lb/>eas nominare vertebras, sicut profecto sunt, non praetermisisset &rdquo; (ibid., <lb/>pag. </s>

<s>221). </s></p><p type="main">

<s>Nel secolo XVIII uno de'pi&ugrave; valorosi Naturalisti della Francia, atten&shy;<lb/>dendo con particolare studio all'anatomia <emph type="italics"/>De l'Orang-outang et de quel&shy;<lb/>ques autres especes de singes,<emph.end type="italics"/> ben comprese quanto fosse importante il de&shy;<lb/>cider l'antica questione, insorta fra gli Anatomici del secolo XVI, le contrarie <lb/>parti de'quali venivano rappresentate dalle due grandi autorit&agrave; del Fallop&shy;<lb/>pio e dell'Eustachio. </s>

<s>E dal riscontro delle osservazioni sue proprie con le <lb/>descrizioni galeniche ebbe, con imparziale giudizio, a dar sentenza finale: <lb/>&ldquo; Que jamais Galien n'a diss&eacute;qu&edot; de cadavres humains, ou que du moins <lb/>il ne s'en est pas servi pour composer ses ouvrages &rdquo; (Oeuvres de Pierre <lb/>Camper, T. I, Paris 1803, pag. </s>

<s>43). </s></p><p type="main">

<s>Si vien ora da cos&igrave; fatta decisiva sentenza del Camper a concludere che <lb/>trovasi da'Galenisti antichi gi&agrave; descritta l'anatomia di quegli animali di <lb/>ordine superiore, il trattar de'quali &egrave; parte del presente capitolo di storia. </s>

<s><lb/>Non vuol tacersi per&ograve; che gli argomenti del Naturalista francese, bench&egrave; <lb/>fondati sopra un maggior numero di osservazioni, sono in sostanza quegli <lb/>stessi, di che s'era due secoli prima servito il Falloppio, il quale inoltre, <lb/>comparando l'anatomia dell'uomo e delle scimmie ne'feti, e facendone no&shy;<lb/>tare la somiglianza, si studi&ograve; di compor la lite col dire che Galeno s'in&shy;<lb/>gann&ograve; talvolta, per aver creduto che gli organi embrionali si mantenessero <lb/>invariabili in ogni pi&ugrave; minuta particolarit&agrave; delle loro forme, anche negli <lb/>adulti. </s></p><p type="main">

<s>Poi pi&ugrave; tardi, svolgendosi nel progredir della scienza il fecondo concetto <lb/>falloppiano, si riconobbe che quelle somiglianze intravedute ne'feti s'allar&shy;<lb/>gano mirabilmenle considerate negli ovi, da che s'ebbe a concluderne che <lb/>i Mammiferi hanno origine da un principio simile a quello degli Uccelli. </s>

<s>Ma <lb/>vien qui a rappresentarcisi un soggetto nuovo di tale importanza, che non <lb/>pu&ograve; non concederglisi convenevole luogo fra le stesse angustie, a cui ci ri&shy;<lb/>duce il vicin termine prescritto a questa terza Parte della nostra Storia. </s></p><p type="main">

<s>Aristotile, nel secondo capitolo del VI libro <emph type="italics"/>De historia animalium,<emph.end type="italics"/><lb/>iniziava l'Embriologia, descrivendo le trasformazioni osservate nelle uova <lb/>delle galline rese feconde, e incominciando dal loro primo concepimento, <pb xlink:href="020/01/1506.jpg" pagenum="381"/>&ldquo; concipit, egli dice, foemina quae coierit ovum superius ad septum tran&shy;<lb/>sversum, quod ovum primo minutum et candidum cernitur, mox rubrum <lb/>cruentumque, deinde increscens luteum et flavum efficitur totum &rdquo; (T. VI, <lb/>operum, Venetiis 1560, fol. </s>

<s>138). </s></p><p type="main">

<s>Stettero lungamente queste dottrine aristoteliche per infallibile docu&shy;<lb/>mento di scienza, infin tanto che Ulisse Aldovrandi non pens&ograve; di riscon&shy;<lb/>trarle colle naturali esperienze, dalle quali torn&ograve; maravigliato che avesse il <lb/>Filosofo trascurata la descrizion di quell'organo, dentro cui l'uova stesse <lb/>hanno la loro ultima perfezione. </s>

<s>&ldquo; Atque isthaec est doctrina Aristotilis, sed <lb/>mirum quod uteri non meminerit, in quo tamen ovum perficitur, etsi extra <lb/>eum primo propriae substantiae habeat rudimenta, sed formam absolutissi&shy;<lb/>mam in eo recipit. </s>

<s>Locus itaque inchoationis, quae ab Aristotilis Interpetre <lb/><emph type="italics"/>conceptio<emph.end type="italics"/> dicitur, est ventris inferioris superior ac media pars ad septum <lb/>transversum. </s>

<s>Dixit enim: <emph type="italics"/>faeminae concipiunt ova ad septum transversum.<emph.end type="italics"/><lb/>Hoc addimus nos, ex anatomica inspectione, esse supra ipsam spinam ad <lb/>divaricationem vasorum, quae in crura descendunt. </s>

<s>Locus vero perfectionis <lb/>est ipse uterus, cuius forma plurimum differt ab utero viviparorum &rdquo; (Or&shy;<lb/>nithologiae, lib. </s>

<s>XIV, Francofurti 1610, pag. </s>

<s>99). </s></p><p type="main">

<s>Ma perch&egrave; il maraviglioso naturale artificio nella concezione degli ovi <lb/>non si pu&ograve; intendere, se non da chi con gli occhi suoi proprii lo contem&shy;<lb/>pla, io, prosegue a dir l'Aldovrandi, per provvedere alla comune utilit&agrave; degli <lb/>studiosi, mi rivolsi a quell'eccellentissimo auatomico ch'&egrave; Antonio Ulmo, <lb/>perch&egrave; mi facesse la dissezione di alquante galline. </s>

<s>Ei disegn&ograve; diligentemente <lb/>le cose come le vide stare in natura, e io vi rappresento, o lettori, sott'oc&shy;<lb/>chio quegli stessi disegni nelle cinque figure, che troverete impresse nella <lb/>mia Tavola quarta. </s>

<s>&ldquo; Prior icon, quae Tab. </s>

<s>IV num. </s>

<s>9 extat, ovorum sub <lb/>septo conceptorum magnitudinem et locum per quem in uterum descendunt, <lb/>item in quo luteum ab albumine ambitur, nec non etiam ubi testae duri&shy;<lb/>tiem acquirunt, aliosque demonstrat locos generationi destinatos.... Alterae <lb/>tres subsequentes eiusdem Tabulae, nn. </s>

<s>10, 11 et 12, isthaec fere omnia <lb/>sed dilucidius ostendunt; nempe qua magnitudine ova a septo in matricem <lb/>descendant, nec non et uteri protensionem. </s>

<s>Ultima num. </s>

<s>13 dictae Tabulae <lb/>solius uteri figura est, demonstratque utrunque eius orificium, per quod <lb/>scilicet ova sub septo contenta recipiat, item per quod ea postremo exclu&shy;<lb/>dat &rdquo; (ibid.). </s></p><p type="main">

<s>Quest'ultima figura, secondando le generose intenzioni dell'Aldovrandi, <lb/>com'apparir&agrave; dal processo della presente storia, giov&ograve; davvero moltissimo <lb/>agli studiosi, specialmente da poi che Girolamo Fabricio venne colle sue elo&shy;<lb/>quenti parole ad illustrarla. </s>

<s>Nel principio del suo trattato <emph type="italics"/>De formatione ovi <lb/>et pulli<emph.end type="italics"/> l'Anatomico d'Acquapendente, per supplire anche meglio al difetto <lb/>aristotelico, d&agrave; il nome di utero, non a quell'organo solo in cui l'uova si <lb/>perfezionano, ma a quell'altro aziandio in cui si concepiscono, e ch'ei de&shy;<lb/>scrive com'un acervo di ovicini attaccati per un pedunculo al ramo, come <lb/>i grani dell'uva. </s>

<s>A quest'organo, ossia all'Ovaia, d&agrave; l'Autore il nome di <pb xlink:href="020/01/1507.jpg" pagenum="382"/><emph type="italics"/>utero primo<emph.end type="italics"/> e <emph type="italics"/>superiore,<emph.end type="italics"/> a cui soggiace l'altr'utero rappresentato nella <lb/>quinta figura dell'Aldovrandi, e che l'Acquapendente rassomiglia a una <lb/>tromba col suo padiglione, o infundibolo com'ei lo chiama. </s>

<s>&ldquo; Hoc enim fo&shy;<lb/>ramen tubae et infundibulo est simile, quam ob causam <emph type="italics"/>infundibulum<emph.end type="italics"/> ap&shy;<lb/>pello &rdquo; (Op. </s>

<s>omnia cit., pag. </s>

<s>2). </s></p><p type="main">

<s>Questo Trattato del nostro Italiano, venuto postumo alla luce nel 1621, <lb/>richiam&ograve; a s&egrave; l'attenzione di Guglielmo Harvey, che si sent&igrave; da quegli esempii <lb/>eccitato a studiare gli svolgimenti embrionali nell'uova delle galline, seguendo <lb/>l'orme di Aristotile fra gli antichi, e del Fabricio d'Acquapendente fra're&shy;<lb/>centi, da lui tenuti &ldquo; illum tanquam <emph type="italics"/>Deum,<emph.end type="italics"/> hunc ut <emph type="italics"/>Praemonstratorem. </s>

<s>&rdquo;<emph.end type="italics"/><lb/>Cos&igrave; fatte espressioni, che si leggono in sul finir della prefazione alle Eser&shy;<lb/>citazioni anatomiche <emph type="italics"/>De generatione animalium,<emph.end type="italics"/> rivelano l'occulta radice <lb/>de'difetti pi&ugrave; notabili in quest'Opera arveiana, la quale tanto ritrae dalla <lb/>viziata mente di Aristotile nelle filosofiche speculazioni, e de'fallaci instituti <lb/>del Fabricio nelle naturali esperienze, che, se fosse soppresso il nome del&shy;<lb/>l'Autore nel titolo del libro, difficilmente si crederebbe questo fratello al&shy;<lb/>l'altro <emph type="italics"/>De motu cordis.<emph.end type="italics"/> S'aggiungono ai vizii della materia i difetti della <lb/>forma, i quali per&ograve; trovano una ragionevole scusa ne'tumulti delle guerre <lb/><emph type="italics"/>plusquam civilia,<emph.end type="italics"/> nelle quali si trov&ograve; involto l'Harveio, com'ei deplora in <lb/>fine alla sua LXVIII Esercitazione, e nell'essere stato il manoscritto rimesso <lb/>insieme da Giorgio Ent e dato in luce da lui in Londra nel 1651, senza che <lb/>se ne volesse prendere alcuna cura l'Autore, gi&agrave; vecchio, e disgustato ora&shy;<lb/>mai de'tempi, degli uomini e di s&egrave; stesso. </s></p><p type="main">

<s>Rimangono in ogni modo queste nuove esercitazioni arveiane monu&shy;<lb/>mento solenne della scienza, perch&egrave;, lasciato il suo <emph type="italics"/>Dio<emph.end type="italics"/> sul lido, e spiegate <lb/>le vele innanzi al suo <emph type="italics"/>Premostratore,<emph.end type="italics"/> si mette tutto solo a correre un nuovo <lb/>mare. </s>

<s>Lo studio dell'uovo gallinaceo non termina per l'Harveio, come per <lb/>Aristotile e per l'Aldovrandi, in s&egrave; stesso, ma viene a questo principale in&shy;<lb/>tento prescelto, perch&egrave;, nella generazione degli animali d'ordine superiore, <lb/>possa servire come di pi&ugrave; facile e trattabile chiave ad aprire il mistero. </s>

<s>&ldquo; Cur <lb/>ab ovo gallinaceo documentum sumerem, iampridem dictum est: nempe quod <lb/>illud parvo veniret, et ubique obviam esset.... In viviparorum autem ge&shy;<lb/>neratione cognoscenda eadem facilitas non occurrit. </s>

<s>Ab humani enim uteri <lb/>dissectione fere omnino excludimur: in equis vero, bobus, capris caeteris&shy;<lb/>que pecoribus, aliquid ad hanc rem experiri, citra ingentem laborem et im&shy;<lb/>pendium haud exiguum, non licet &rdquo; (De generat. </s>

<s>anim. </s>

<s>Lugd. </s>

<s>Batav. </s>

<s>1737, <lb/>pag. </s>

<s>287, 88). Ma la munificenza del re Carlo, giovane amante della caccia <lb/>specialmente de'cervi, liber&ograve; l'Harveio da ogni spesa, e da ogni sollecitu&shy;<lb/>dine di cercare animali vivipari, permettendogli di sezionar le damme ridotte <lb/>dalle selve de'monti inglesi ne'rinchiusi cancelli del suo parco reale. </s>

<s>Par <lb/>che il frutto di cos&igrave; fatte esperienze l'abbia l'Herveio stesso voluto tutto <lb/>concludere in seno a queste parole: &ldquo; Fabricius ab Aquapendente, tanquam <lb/>omnis viviparorum conceptus ovum quoddam esset, ab hoc tractatum auspi&shy;<lb/>catur.... Nos vero, in observationum harum vestibulo, cuncta animalia quo-<pb xlink:href="020/01/1508.jpg" pagenum="383"/>dammodo ex ovo nasci affirmavimus &rdquo; (ibid., 288). Chi credesse che in que&shy;<lb/>ste osservazioni si contenga una scoperta, s'ingannerebbe, perch'elle in verit&agrave; <lb/>non son altro che una fallacia, per scoprir la quale non debbonsi le sen&shy;<lb/>tenze dell'Acquapendente e dell'Harveio riguardare a parte, ma nel com&shy;<lb/>plesso della Storia, che vuol perci&ograve; risalire a'suoi primi principii. </s></p><p type="main">

<s>Ippocrate dava autorit&agrave; alla comune opinione invalsa, che cio&egrave; si gene&shy;<lb/>rassero gli uomini e gli altri animali affini dal seme virile commisto al <lb/>femineo, il quale operasse dentro l'utero come il caglio sul latte. </s>

<s>Aristotile, <lb/>a cui parve questa teoria troppo semplice, la sublim&ograve; colle arguzie del suo <lb/>ingegno su per le regioni metafisiche, dicendo che il sangue menstruo som&shy;<lb/>ministra al feto la materia, che poi riceve dal virile atto la forma. </s>

<s>Ma a qual <lb/>uso, si domandava, stanno allora i <emph type="italics"/>testes<emph.end type="italics"/> in seno alle femmine? </s>

<s>Dall'altra <lb/>parte quel profluvio di umore, che vien dall'utero alla vagina, nell'atto stesso <lb/>del concepire, era tale esperienza in favor d'Ippocrate, da poter sugl'inge&shy;<lb/>gni pi&ugrave; efficacemente delle aristoteliche teorie. </s>

<s>Come, dall'altra parte, si co&shy;<lb/>nosceva da cotesti creduti testicoli femminei l'origine di quell'umore, che <lb/>vien per l'utero alla vagina; cos&igrave; immaginavasi che i ligamenti uterini cre&shy;<lb/>duti vuoti, servissero a quello stesso umore da'canicoli conduttori. </s>

<s>Di cos&igrave; <lb/>fatte immaginate ipotesi informavasi l'anatomia descrittiva degli organi mu&shy;<lb/>liebri, che la nuova scienza risorta, non reluttando i Peripatetici stessi, ac&shy;<lb/>colse docilmente dalle lezioni del nostro Jacopo da Carpi. </s></p><p type="main">

<s>Ei descrive l'utero, o il ricettacolo come lo chiama, di forma quadran&shy;<lb/>golare, <emph type="italics"/>cum aliquali rotunditate,<emph.end type="italics"/> che ha verso la cervice, di qua e di l&agrave;, <lb/>attaccati due freni o ligamenti simili alle corna delle lumache. </s>

<s>Intorno a <lb/>queste, che perci&ograve; si chiamano corna dell'utero, sta un testicolo da una parte <lb/>e dall'altra <emph type="italics"/>durior et minor quam in mare,<emph.end type="italics"/> non perfettamente rotondo, ma <lb/>compresso a guisa di mandorla, e in cui <emph type="italics"/>generatur sperma.<emph.end type="italics"/> &ldquo; Istis testibus <lb/>implantantur vasa seminaria, quae a chili et ab Aorta et ab emulgentibus <lb/>descendunt, dicta <emph type="italics"/>praeparantia.<emph.end type="italics"/> Inde alia vasa <emph type="italics"/>deportantia<emph.end type="italics"/> nominata, con&shy;<lb/>tinue se dilatando, usque ad receptaculum tendunt, et intra matrices con&shy;<lb/>cavitatem sperma ducunt &rdquo; (Isagogae, Venetiis 1535, fol. </s>

<s>20 ad t.). </s></p><p type="main">

<s>Il Vesalio e il Colombo non lasciarono ne'loro libri descrizioni punto <lb/>pi&ugrave; felici, poco dopo apparite nel Falloppio, il quale ebbe a notare ne'suoi <lb/>predecessori una gran confusione, principalmente rispetto ai vasi, che vanno <lb/>alla matrice. </s>

<s>Quell'organo, che il Berengario rassomigliava alle corna delle <lb/>lumache, disse il Falloppio aver piuttosto le sembianze di una <emph type="italics"/>tromba,<emph.end type="italics"/> la <lb/>quale, movendo dalle cos&igrave; dette corna dell'utero, &ldquo; cum parum recesserit <lb/>ab eo, latior sensim redditur, et capreoli modo crispat se, donec veniat prope <lb/>finem. </s>

<s>Tunc, demissis capreolaribus rugis, atque valde latus redditus, finit <lb/>in extremum quoddam quod membranosum, carneumque ob colorem ru&shy;<lb/>brum videtur, extremumque lacerum valde et attritum est, veluti sunt pan&shy;<lb/>norum attritorum fimbriae, et foramen amplum habet, quod semper clausum <lb/>iacet, concidentibus fimbriis extremis, quae tamen, si diligenter aperiantur <lb/>ac dilatentur, <emph type="italics"/>tubae<emph.end type="italics"/> cuiusdam aeneae extremum orificium exprimunt. </s>

<s>&rdquo; Da <pb xlink:href="020/01/1509.jpg" pagenum="384"/>che &egrave; condotto a dar a quel <emph type="italics"/>classico organo<emph.end type="italics"/> il nome di <emph type="italics"/>Tuba.<emph.end type="italics"/> &ldquo; Ideo a me <lb/>uteri <emph type="italics"/>Tuba<emph.end type="italics"/> vocatus est &rdquo; (Op. </s>

<s>omnia, Observ. </s>

<s>anat., Francof. </s>

<s>1584, pag. </s>

<s>472). </s></p><p type="main">

<s>Ma perch&egrave; alcuni Anatomici davano a cos&igrave; fatta Tuba dell'utere, rico&shy;<lb/>nosciuta dal Berengario per un ligamento, l'ufficio di canal deferente il se&shy;<lb/>minale umore femmineo, questa &egrave; cosa, disse il Falloppio, <emph type="italics"/>quod minime <lb/>placet,<emph.end type="italics"/> e ci&ograve; per pi&ugrave; ragioni. </s>

<s>Prima di tutto perch&egrave;, ne'supposti testicoli <lb/>femminei, non ho trovato mai indizio di sperma. </s>

<s>&ldquo; Vidi quidem in ipsis <lb/>quasdam veluti vesicas, aqua vel humore aquaeo, alias luteo, alias vero lim&shy;<lb/>pido turgentes, sed nunquam semen vidi, nisi in vasis ipsis spermaticis, vel <lb/>delatoriis vocatis &rdquo; (ibid.). </s></p><p type="main">

<s>In secondo luogo, quando pure si fossero cos&igrave; fatte vesciche ritrovate <lb/>piene di umor seminale, sarebbe impossibile che stillassero quel loro umore <lb/>nell'utero per la via delle tube, come per appositi meati seminarii &ldquo; quo&shy;<lb/>niam nunquam observare potui meatus istos seminarios coninnctos cum te&shy;<lb/>stibus.... Si igitur non connascuntur, vide an verum illud sit quod dixerim, <lb/>dogmata aliquot, quae ad generationem seminis pertinent, valdene titubent, <lb/>laborare &rdquo; (ibid.). </s></p><p type="main">

<s>Veniva da queste ragioni e da questi fatti veramente l'ipotesi ippocra&shy;<lb/>tica a ricevere un colpo tale, che troppo grande sforzo sarebbevi bisognato, <lb/>per reggersi in piedi in quel gran titubare. </s>

<s>Ma se il Falloppio dava da una <lb/>parte il crollo all'edifizio antico, confessava dall'altra di non sapervene so&shy;<lb/>stituire un altro nuovo, a cui primo a por mano fu senza dubbio l'Harveio. </s>

<s><lb/>Sezionando le damme allevate nel parco reale, al ritrovarne i testicoli dopo <lb/>il coito non punto inturgiditi, e anzi di nulla alterati dalla loro solita co&shy;<lb/>stituzione, volle argomentarne, confermando i sospetti del Falloppio, che <lb/>quegli organi non servono a generare, e ch'&egrave; loro ufficio proprio quello di <lb/>&ldquo; stabilire venarum divaricationes, et humorem lubricandis partibus conser&shy;<lb/>vare &rdquo; (Exercit. </s>

<s>De generat. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>299). </s></p><p type="main">

<s>Un'altra nuova osservazione gli occorse a fare in proposito confermata <lb/>dalle esperienze e fu che l'utero delle damme, com'anche delle pecore, <lb/>delle vacche e delle capre, &egrave; cos&igrave; chiuso, da dar bene esito ai menstrui, ma <lb/>da non ammettere nulla dal di fuori, non eccettuata l'aria stessa. </s>

<s>&ldquo; Debuit <lb/>namque statui sanguini menstruo, aliisque humoribus excernendis, via pa&shy;<lb/>tefacere, verum autem externarum, etiam minimarum, aeris puta aut semi&shy;<lb/>nis ingressui, omnino praecludi &rdquo; (ibid., pag. </s>

<s>295). E infatti non trov&ograve; nel&shy;<lb/>l'utero delle damme, aperto a tale intento, nessuna traccia di questo seme, <lb/>ci&ograve; che avendo fatto osservare e credere al Re, i custodi del parco e i cac&shy;<lb/>ciatori andavano dicendo che quello era un inganno, e che il fatto dipen&shy;<lb/>deva solo dal fresco delle piogge, per cui s'era indugiato il tempo degli <lb/>amori. </s>

<s>&ldquo; Postea vero, cum coeundi tempus praeteriisse cernerent, egoque <lb/>idem usque assererem, constanter affirmabant et me deceptum esse et a me <lb/>Regem ipsum, debereque necessario aliquid conceptus in utero reperiri, do&shy;<lb/>nec propriis oculis, rem ut erat perscrutati, summa cum admiratione de lite <lb/>desisterent &rdquo; (ibid., pag. </s>

<s>306). </s></p><pb xlink:href="020/01/1510.jpg" pagenum="385"/><p type="main">

<s>Ritenute queste cose per vere, l'ipotesi di Ippocrate non solo, ma quella <lb/>altres&igrave; di Aristotile venivano ambedue ugualmente dimostrate per false, non <lb/>potendosi l'umor virile, che non &egrave; ammesso altrimenti nell'utero, n&egrave; com&shy;<lb/>mescersi col seme femmineo, n&egrave; col sangue menstruo. </s>

<s>&ldquo; Adeo ut explora&shy;<lb/>tum habeam non ex spermate maris aut foeminae, nec ex ambobus simul <lb/>mistis, neque ex sanguine menstruo, conceptus aliquid necessario constitui &rdquo; <lb/>(ibid., pag. </s>

<s>307). </s></p><p type="main">

<s>Come si costituisce dunque al concepimento il principio? </s>

<s>E rispondono <lb/>all'Harveio le proprie osservazioni fatte nello stesso utero delle damme, den&shy;<lb/>tro cui ebbe a vedere &ldquo; mucosa quaedam filamenta, quae simul iuncta mem&shy;<lb/>branosam seu mucilaginosam tunicam, sive <emph type="italics"/>manticam<emph.end type="italics"/> vacuam referunt &rdquo; <lb/>(ibid, 308). Questo sacchetto vide poi empirsi di un umore albuminoso, non <lb/>dissimile da quello dell'uovo, da che fu condotto a sentenziare aver tutti <lb/>gli animali anche vivipari origine dall'uovo: sentenza che, in s&egrave; stessa &egrave; <lb/>vera, ma che nella mente dell'Harveio, come s'accennava dianzi, contiene <lb/>una gran fallacia. </s>

<s>Domandandogli infatti da che ha origine quell'uovo, ei <lb/>risponde dall'utero. </s>

<s>&ldquo; Nos autem brevitati studentes, ut facile concedimus <lb/>uteri officium et usum procreandis ovis destinatum esse, ita efficiens adae&shy;<lb/>quatum et immediatum in ovo ipso contineri asseveramus, ovumque non ab <lb/>utero, sed ab interno principio naturali sibique proprio, tum generari tum <lb/>augeri censemus &rdquo; (ibid., pag. </s>

<s>34). Viene quella virt&ugrave; di procrear l'uovo a <lb/>riceverla l'utero dall'umore prolifico, il quale &ldquo; citra tactum agit &rdquo; (ibid., <lb/>pag. </s>

<s>5), e opera perci&ograve; &ldquo; per spiritualem substantiam et irradiationem &rdquo; <lb/>(pag. </s>

<s>179). </s></p><p type="main">

<s>Avevano cos&igrave; fatte dottrine la natura schietta di paradosso, facilmente <lb/>riconoscibile dagli scienziati di Londra, se era stata gi&agrave; riconosciuta dagli <lb/>stessi custodi del parco reale. </s>

<s>Pure, era tanta l'autorit&agrave; dell'Harveio, che <lb/>non fa maraviglia se ne rimasero vinti tutt'insieme la scienza e il senso co&shy;<lb/>mune. </s>

<s>Dall'altra parte &egrave; da ripensare che, dopo la distruzione avvenuta per <lb/>opera del Falloppio, era questa arveiana la prima restaurata teoria della ge&shy;<lb/>nerazione. </s>

<s>Il Cartesio, in appendice al suo trattato <emph type="italics"/>De homine,<emph.end type="italics"/> s'era pro&shy;<lb/>vato a render la ragione <emph type="italics"/>De formatione animalis;<emph.end type="italics"/> ragione ch'egli riduce <lb/>ai due sessuali umori commisti, i quali si fanno da fermento a vicenda, co&shy;<lb/>sicch&egrave; dal calore che ne consegue &ldquo; nonnullae eorum particulae dilatentur <lb/>premantque alias, hacque ratione illas paulatim eo disponant modo, qui ad <lb/>membra formanda requiritur &rdquo; (Francof. </s>

<s>ad M. 1692, pag. </s>

<s>173). Ma l'antica <lb/>teoria ippocratica cos&igrave; rinnovellata, succisa gi&agrave; dal coltello anatomico del Fal&shy;<lb/>loppio, veniva affatto diradicata dalle esperienze dell'Harveio, nelle quali forse <lb/>riducesi l'unico benefizio da lui recato all'Ovologia. </s>

<s>Egli francamente asse&shy;<lb/>riva che l'umor vaginale non ha natura di seme, e che perci&ograve; non &egrave; ne&shy;<lb/>cessario alla generazione. </s>

<s>&ldquo; Novi enim plurimas quae, citra talem eiectio&shy;<lb/>nem, foecundae satis essent &rdquo; (Exercit. </s>

<s>de gener. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>127). </s></p><p type="main">

<s>Avvenne, per tutte queste ragioni, che seguaci de'paradossi dell'Harveio <lb/>si facessero anche alcuni Cartesiani, fra'quali &egrave; notabile per noi Tommaso <pb xlink:href="020/01/1511.jpg" pagenum="386"/>Cornelio. </s>

<s>Il proginnasma V s'intitola per lui <emph type="italics"/>De generatione hominis,<emph.end type="italics"/> e in <lb/>mezzo a s&igrave; felte tenebre, non trovata altra guida, s'atiene all'Harveio, con&shy;<lb/>forme alle dottrine del quale, da un suo ragionamento pi&ugrave; abbondante di <lb/>parole che ricco d'idee, cos&igrave; ne conclude: &ldquo; Quare superest ut dicamus ge&shy;<lb/>niturae vim omnem positam esse in substantia quadam prorsus <emph type="italics"/>insensili,<emph.end type="italics"/><lb/>quae materiam a foemina collatam subigens, generationis sit efficiens &rdquo; (Pro&shy;<lb/>gymnasm. </s>

<s>phys., Neapoli 1688, pag. </s>

<s>177, 78). Dall'esser l'atto virile sulla <lb/>genitura <emph type="italics"/>insensile<emph.end type="italics"/> ne veniva per conseguenza che si potesse anche senza gli <lb/>organi materiali esercitare; altro paradosso che pareva dovesse risvegliar la <lb/>mente a riconoscer quel primo. </s>

<s>Eppure il Cornelio con tutta confidenza <lb/>scrive: &ldquo; Mihi vero experientia compertum est canem, cui testes fueront <lb/>abscissi, filios generasse &rdquo; (ibid., pag. </s>

<s>165). </s></p><p type="main">

<s>Ma queste son sentenze pronunziate in un momento di sonnolenza o di <lb/>ebbrezza, dalle quali passioni riavutasi felicemente la scienza, riconobbe che, <lb/>nella dottrina della generazione animale, s'era l'Harveio dimostrato inferiore <lb/>a s&egrave; stesso e al portato del tempo. </s>

<s>Le strane dottrine conseguivano da os&shy;<lb/>servazioni poco diligenti, e dal vizio aristotelico di voler fare alle precon&shy;<lb/>cette teorie servire le naturali esperienze. </s>

<s>Egli ingann&ograve; veramente con s&egrave; <lb/>stesso il re Carlo, affermando che non si trovava nell'utero traccia di sperma, <lb/>mentre il Falloppio lo avea gi&agrave; ritrovato infin dentro alle Tube. </s>

<s>&ldquo; Testes <lb/>enim mihi adfuere plurimi fide digni spectatores quod saepius in his mea&shy;<lb/>tibus semen exquisitissimum repererim &rdquo; (Observ. </s>

<s>anat. </s>

<s>inter. </s>

<s>Op. </s>

<s>omnia <lb/>cit, pag. </s>

<s>472). </s></p><p type="main">

<s>Quella borsettina ripiena di un umore albuminoso la vide l'Harveio nel&shy;<lb/>l'utero, dopo quindici giorni e pi&ugrave; dall'atto fecondativo, e senza ricercar se <lb/>potesse esservi venuta d'altrove, pensa che sia ivi prodotta nell'utero come <lb/>le galle, e i vermi contenutivi dentro, son prodotti dall'anima vegetativa <lb/>delle piante. </s>

<s>Ma l'esser la manteca fetale, nella cavit&agrave; uterina, erratica <lb/>avrebbe dovuto far sospettare al grand'uomo che non poteva essere indi na&shy;<lb/>tiva, e se avesse pensato di servirsi per quelle osservazioni delicatissime del <lb/>Microscopio, come se ne serv&igrave; per osservare gl'insetti (De motu cordis, <lb/>cap. </s>

<s>XVII), avrebbe potuto riconoscer meglio l'essere e la natura di quel <lb/>primo concetto, a cui dava a caso, e fuor del suo proprio significato, il nome <lb/>di uovo. </s></p><p type="main">

<s>Eran tali quelle giuste considerazioni e quelle libere censure che, ol&shy;<lb/>trepassata la prima met&agrave; del secolo XVII, si facevano all'opera dell'Har&shy;<lb/>veio dagli Embriologi, avviando l'Ovologia per pi&ugrave; diritti sentieri. </s>

<s>Lo Ste&shy;<lb/>none, per meglio confermare e illustrare le osservazioni fatte dagli amici <lb/>intorno all'origine degli animali dall'uovo, si dette a sezionar varie specie <lb/>di vivipari, e in render conto, innanzi all'Accademia medica di Koppena&shy;<lb/>ghen, dell'esito de'suoi studii, fu primo a chiamare i testicoli femminili <lb/><emph type="italics"/>ovari<emph.end type="italics"/> e le tube falloppiane <emph type="italics"/>ovidutti.<emph.end type="italics"/> &ldquo; Ovi autem nomine intelligo, non <lb/>modo rotundas vesiculas humore plenas, testiculorum magnam partem consti&shy;<lb/>tuentes, sed et chorion cum omnibus suis contentis. </s>

<s>Utor plerumque ter-<pb xlink:href="020/01/1512.jpg" pagenum="387"/>minis solitis, per testiculos faemellarum ovaria, per tubas cornuaque et ute&shy;<lb/>ros oviductus intelligo &rdquo; (Observationes anat. </s>

<s>in Mangeti biblioth., T. I, <lb/>Genevae 1685, pag. </s>

<s>483). Si convengono, soggiunge l'Autore, a quegli or&shy;<lb/>gani nomi simili, perch&egrave; si rassomigliano perfettamente nelle funzioni. </s>

<s>&ldquo; Ova&shy;<lb/>ria, scilicet testiculi, dant ovis principium, oviductus autem seu uteri vel <lb/>cornua cum tubis dant quidquid requiritur ad perfectum incrementum foe&shy;<lb/>tus &rdquo; (ibid.). </s></p><p type="main">

<s>La poca diffusione ch'ebbero queste idee, rimaste per alquanto tempo <lb/>chiuse nelle sale di un'Accademia, fece s&igrave; che altri, forse inconsapevoli di <lb/>quel che s'era detto in Danimarca, le annunziassero al pubblico, al cospetto <lb/>del quale Giovanni Van-Horne si present&ograve; il primo di tutti. </s>

<s>Pigliando dal&shy;<lb/>l'Harveio l'occasione e l'impulso ai suoi nuovi studi, esamin&ograve; diligentemente <lb/>col microscopio quel che l'Autore <emph type="italics"/>De generatione animalium<emph.end type="italics"/> avea descritto <lb/>come una piccola borsa chiusa gettata a caso dentro la cavit&agrave; dell'utero, e <lb/>non esit&ograve; a riconoscere cotesto corpicciolo per un uovo propriamente detto, <lb/>ritrovandolo simile a una vescichetta rivestita di una pellicola, dalla quale <lb/>scaturiva un certo liquido albuminoso. </s>

<s>E giacch&egrave; tutto lo persuadeva non <lb/>poter essere quell'uovo all'utero nativo, pensava fra s&egrave; d'onde mai potes&shy;<lb/>s'essere venuto. </s></p><p type="main">

<s>Le vescicole, di che diceva il Falloppio esser composti i <emph type="italics"/>testes foemi&shy;<lb/>nei,<emph.end type="italics"/> avendo a s&egrave; richiamata l'attenzione del Van-Horne, gli fecero nascere <lb/>il sospetto che si fosse staccato di l&igrave; il misterioso ovicino embrionale, ma <lb/>non vedeva come potess'esser passato alla matrice. </s>

<s>Nelle tube non era al&shy;<lb/>cuna speranza di trovar quel veicolo, per queste ragioni: perch&egrave; l'infondi&shy;<lb/>bulo si credeva chiuso, e i <emph type="italics"/>testes<emph.end type="italics"/> segregati da esso. </s>

<s>Una tal chiusura per&ograve; <lb/>si teneva sulla autorit&agrave; del Falloppio, il quale, potendosi essere ingannato, <lb/>lasciava il fatto a decidersi dalle esperienze. </s>

<s>Il Van-Horne dunque, ammet&shy;<lb/>tendo il fiato e iniettando un liquido, trov&ograve; che la Tuba era aperta, con che <lb/>veniva a togliere alla sua ipotesi la prima e principale delle due difficolt&agrave; <lb/>sopra dette. </s></p><p type="main">

<s>Rimaneva l'altra, la quale pure o posava o rallentava l'arco, contrappo&shy;<lb/>nendole alla mira il confronto fra le Tube, descritte dal Falloppio ne'vivipari, <lb/>e le Tube disegnate da Antonio Ulmo nelle tavole dell'Aldovrandi, con questo <lb/>stesso nome di <emph type="italics"/>Tube<emph.end type="italics"/> appellate dall'Acquapendente, nel trattar della generazione <lb/>ovipara degli Uccelli. </s>

<s>Avendo avuto que'due organi, pensava il Van-Horne, <lb/>ne'due varii ordini di animali, nomi uguali dall'arte e figura simile dalla <lb/>Natura, perch&egrave; non potrebbero dalla stessa Natura essere stati deputati al <lb/>medesimo ufficio? </s>

<s>Perch&egrave; facendo la Tuba ulmiana da ovidutto non potrebbe <lb/>da ovidotto fare ugualmente bene anche la Falloppiana? </s>

<s>Se dall'altra parte <lb/>gli organi, che stanno intorno al padiglione de'due varii generi di Tube, <lb/>hanno strettissima somiglianza fra loro nella situazione e nella figura, perch&egrave; <lb/>non converranno insieme nell'essere e nella denominazione di ovaie e di ova? </s>

<s><lb/>E se queste cascano, staccate da quelle, dentro l'infondibulo delle tube negli <lb/>uccelli, perch&egrave; non farebbero il simile nel ventre degli animali superiori? </s></p><pb xlink:href="020/01/1513.jpg" pagenum="388"/><p type="main">

<s>Il ragionamento era bello e la conclusione gloriosamente lusinghiera, n&egrave; <lb/>mancava altro che confortarla di nuove esperienze, e metterla in forma di <lb/>trattato. </s>

<s>Mentre a far ci&ograve; alacremente attendeva il Van-Horne, giunge in <lb/>Leida una lettera stampata, nella quale Regnero De Graaf dava, il d&igrave; 20 di <lb/>Febbraio del 1668, notizia a Francesco de la Boe Sylvio <emph type="italics"/>De nonnullis circa <lb/>partes genitales inventis novis.<emph.end type="italics"/> Il Van-Horne stesso allora, perch&egrave; diceva <lb/>meglio prevenire ch'esser prevenuti, pubblic&ograve; una lettera indirizzata a Guer&shy;<lb/>nero Rolfinck, la quale era come il Prodromo al trattato sulla struttura degli <lb/>organi ne'due sessi, e sul sistema della generazione, che da lungo tempo <lb/>fra s&egrave; meditava. </s>

<s>Fra le varie cose in quel Prodromo annunziate la pi&ugrave; ru&shy;<lb/>morosamente nuova era quella delle ovaie muliebri sostituite agli antichi <lb/>testicoli, i quali non sono inutili organi, come l'Hoffman seguendo l'Harveio, <lb/>nel cap. </s>

<s>XLIV del II libro delle Istituzioni insegna, &ldquo; imo ab ipsis totum <lb/>generationis opus materiale dependet: quod enim est ovarium in oviparis, <lb/>sunt testes muliebres, utpote qui perfecta ova intra se contineant &rdquo; (Inter <lb/>opera omnia Regneri de Graaf, Lugd. </s>

<s>Batav. </s>

<s>1677, pag. </s>

<s>439). E soggiunge <lb/>che son quest'uova ne'loro ovarii fecondate dall'umor virile, il quale giunge <lb/>dalla matrice infin l&agrave; attraverso alle Tube falloppiane. </s></p><p type="main">

<s>Lette queste cose il Graaf, divulg&ograve; in quel medesimo anno 1668 per <lb/>le stampe, e dispens&ograve; fra gli amici il suo trattato <emph type="italics"/>De virorum organis ge&shy;<lb/>nerationi inservientibus,<emph.end type="italics"/> nella prefazione al quale confutava la descrizione <lb/>horniana dell'arteria spermatica, dicendo ch'ella procede a diritto, e non si <lb/>contorce in s&egrave; stessa a formare il Corpo piramidale. </s>

<s>&ldquo; Quibus clariss. </s>

<s>Van&shy;<lb/>Horne, racconta il Graaf stesso, per annum quo supervixit et dimidium, licet <lb/>ab aliis professoribus atque medicis aliquoties rogatus, nihil omnino respon&shy;<lb/>dit. </s>

<s>Interea temporis, quantum per otium mihi licuit, mulierum organa ge&shy;<lb/>nerationi inserventia, maiori quam ante diligentia, examini subieci, nec non <lb/>figuras aliquas delineare coepi, quarum primarias anno 1670 Swammerdamio <lb/>me invisenti amice demonstravi, cui figurae illae ita placuerunt, ut anno 1671 <lb/>me ad divulgandas adhortaretur &rdquo; (Partium genit. </s>

<s>Defensio, Op. </s>

<s>omnia cit, <lb/>pag. </s>

<s>441, 42). </s></p><p type="main">

<s>Premessa infatti un'Epistola a Luca Schacht, sottoscritta il d&igrave; 30 Mag&shy;<lb/>gio 1671, usciva alla luce in Leida l'anno dopo il trattato nuovo <emph type="italics"/>De mu&shy;<lb/>lierum organis generationi inservientibus,<emph.end type="italics"/> nel quale a dir vero, rispetto alla <lb/>generazione dell'uomo dall'uovo, niente altro fa il Graaf ch'esplicare e con&shy;<lb/>fermare i concetti del Van-Horne. </s>

<s>Dal Prodromo di lui confessa di volere <lb/>accettare le denominazioni di uova date agli organi muliebri (Op. </s>

<s>omnia cit., <lb/>pag. </s>

<s>298), e cos&igrave; conclude, in sentenza dello stesso Van-Horne: &ldquo; Commu&shy;<lb/>nis itaque foemellarum testiculorum usus est generare, fovere et ad matu&shy;<lb/>ritatem promovere, sic ut in mulieribus eodem quo volucrum ovario mu&shy;<lb/>nere fungantur &rdquo; (ibid., pag. </s>

<s>302). </s></p><p type="main">

<s>Quell'argomento d'analogia, che aveva condotto il Van-Horne ad am&shy;<lb/>mettere la possibilit&agrave; non solo, ma la natural facilit&agrave; nell'uova muliebri di <lb/>cader nelle tube falloppiane, a quel modo che l'uova delle galline cadono <pb xlink:href="020/01/1514.jpg" pagenum="389"/>nelle tube ulmiane; &egrave; quello stesso argomento che alle asserzioni del Graaf <lb/>d&agrave; valore. </s>

<s>&ldquo; Quod tanto liberius asserimus, cum in variis quadrupedibus <lb/>extremam tubarum expansionem eiuscemodi, ut oviductus infundibulum, <lb/>quod in avibus vitellos excipit, efformatam offenderimus &rdquo; (ibid., pag. </s>

<s>351). </s></p><p type="main">

<s>Il Prodromo horniano prometteva che nella trattazione distesa si sa&shy;<lb/>rebbe non solo spiegato <emph type="italics"/>quomodo haec ova intra uterum suscipiantur,<emph.end type="italics"/> ma <lb/>come altres&igrave; vengano attuate <emph type="italics"/>a semine virili<emph.end type="italics"/> (ibid., pag. </s>

<s>439). Ma perch&egrave; <lb/>per la sua crassizie non pareva ad alcuni possibile che, almeno in ogni caso, <lb/>il viril seme risalisse su per le tube, s'argoment&ograve; il Graaf di togliere la <lb/>difficolt&agrave; col dire che non era punto necessario &ldquo; quod semen ipsum ad <lb/>uterum aut tubas ascendat, sed sufficere quod seminalis aura, illa loca per&shy;<lb/>transeundo, ad testiculorum ova pertingat &rdquo; (ibid., pag. </s>

<s>346). </s></p><p type="main">

<s>Bench&egrave; sia questo il tradizional magistero delle dottrine antropogeni&shy;<lb/>che esposte dal Graaf, ei si studi&ograve; nonostante di dare a loro tal forma, da <lb/>farle apparir per la massima parte originali. </s>

<s>Ma lo Swammerdam d'amico <lb/>per rivalit&agrave; e per invidia divenuto nemico, pubblicando pochi mesi dopo il <lb/>suo <emph type="italics"/>Miraculum naturae, seu uteri muliebris fabrica,<emph.end type="italics"/> dimostrava che nel <lb/>trattato del Graaf non era parte, che non avesse tolta a s&egrave;, al Van-Horne, <lb/>e prima che a loro due allo Stenone. </s>

<s>Di che il pover uomo, o si credesse <lb/>scoperto in fallo o calunniato, nonostante la difesa fatta innanzi alla grande <lb/>Societ&agrave; regia anglicana, prov&ograve; tanto accoramento, che dicono ne morisse. </s></p><p type="main">

<s>Comunque sia le speculate teorie e le istituite esperienze intorno al&shy;<lb/>l'oviparismo dell'uomo e degli animali affini pervennero d'oltremonti in <lb/>Italia, per mezzo del <emph type="italics"/>Trattato nuovo<emph.end type="italics"/> del Graaf dedicato al granduca Co&shy;<lb/>simo III di Toscana. </s>

<s>I Nostri, che riconobbero nelle dottrine straniere lo <lb/>svolgimento di que'germi posti nella scienza embriologica dagli avi, non re&shy;<lb/>luttarono alle novit&agrave;, ma le vollero sottoporre a un pi&ugrave; diligente esame. </s>

<s>Il <lb/>Malpighi scelse per soggetto di quell'esame gli organi delle vacche, e non <lb/>dubit&ograve; di qualificare per vere ovaie quelle &ldquo; quae, come dice nella sua Dis&shy;<lb/>sertazione epistolica di vario argomento a Giacomo Spon, antiquitus testes <lb/>censebantur &rdquo; (Operum, T. II, Lugd. </s>

<s>Batav. </s>

<s>1787, pag. </s>

<s>202). &ldquo; In vaccis, <lb/>soggiunge, in quibus ampla et manifesta extant, obducta membrana fibris <lb/>carneis firmata, ambiuntur. </s>

<s>Qua ratione ovum ab ovario emergat et in Tu&shy;<lb/>bas transducatur, solicita multaque eget indagine. </s>

<s>Quae tamen ex fortuitis <lb/>ovarii in vaccis lustrationibus colligere potui tibi brevibus aperiam &rdquo; (ibid.). <lb/>E l'esposizione che segue &egrave; una delle pi&ugrave; sapienti illustrazioni, e delle pi&ugrave; <lb/>autorevoli conferme del sistema degli Ovaristi. </s>

<s>Il Redi pure concorreva nel <lb/>medesimo effetto, sperimentando che poste a bollire nell'acqua si conden&shy;<lb/>sano e si rappigliano quell'uova, che si trovano ne'testicoli femminili o <lb/>ovaie de'quadrupedi &ldquo; conforme, egli scrive nel trattato <emph type="italics"/>Degli animali vi&shy;<lb/>venti negli animali viventi,<emph.end type="italics"/> ho osservato nelle uova delle leonesse, dell'orse, <lb/>delle vacche, delle bufale, dell'asine, delle daine, delle cerve e di altri ani&shy;<lb/>mali quadrupedi &rdquo; (Opere, T. I, Napoli 1741, pag. </s>

<s>74). </s></p><p type="main">

<s>Del resto esso Redi, bench&egrave; non componesse in tal soggetto un trattato <pb xlink:href="020/01/1515.jpg" pagenum="390"/>disteso, ne tocc&ograve; qua e l&agrave; ne'suoi scritti in modo, da illustrare con argo&shy;<lb/>menti, e da confermare, con esperienze nuove allo stesso Graaf, i concetti <lb/>horniani. </s>

<s>Teodoro Kerkring nella sua <emph type="italics"/>Antropogenia iconografica,<emph.end type="italics"/> pubblicata <lb/>in Amsterdam nel 1671, approvava e difendeva la generazione umana dal&shy;<lb/>l'uovo, ma sosteneva che fanno da ovidutti i vasi deferenti degli antichi, e <lb/>no le tube del Falloppio. </s>

<s>&ldquo; Non son uomo, entra qui a dire il Redi, da po&shy;<lb/>ter dar sentenze, ma se a me toccasse di far la parte di giudice, sentenzie&shy;<lb/>rei a favore delle Tube falloppiane. </s>

<s>E per dar fuora di ci&ograve; i motivi, dico che <lb/>nel fondo della cavit&agrave; interna dell'utero non sono se non due soli forami <lb/>aperti, per i quali si possa introdurre uno stile o una tenta, e questi forami <lb/>riescono nelle Tube falloppiane, sicch&egrave;, introdotto per essi forami lo stile, <lb/>ei passa nelle Tube, e pel contrario, introdotto lo stile nelle Tube, penetra <lb/>per essi forami nella cavit&agrave; dell'utero. </s>

<s>Inoltre, gonfiato l'utero con uno <lb/>schizzatoio a vento, si gonfiano ancora le Tube falloppiane, e si vede uscir <lb/>l'aria per l'apertura che &egrave; in quella parte, che confina co'testicoli femmi&shy;<lb/>nili, ovvero ovaie &rdquo; (Lettere nel T. IV dell'Opere cit., pag. </s>

<s>63, 64). </s></p><p type="main">

<s>Alla gran difficolt&agrave; promossa dal Falloppio, e che nasceva dal non aver <lb/>mai potuto veder le Tube <emph type="italics"/>coniunctas cum testibus,<emph.end type="italics"/> rispondeva il Graaf che <lb/>simile si osserva negli uccelli, ma il Redi notava di pi&ugrave; che quella congiun&shy;<lb/>zione si fa ne'quadrupedi mediante una certa espansione membranosa del&shy;<lb/>l'infondibulo della stessa Tuba; espansione che nella donna &egrave; sostituita &ldquo; da <lb/>certe fimbrie intagliate a guisa di foglie, onde l'uovo maturo e fecondo, <lb/>mentre &egrave; cascato fuor dell'ovaia tra le pieghe di queste fimbrie, va ad en&shy;<lb/>trare nell'ovidutto &rdquo; (Istorie mediche, nel T. VI dell'Op. </s>

<s>cit., pag. </s>

<s>142). </s></p><p type="main">

<s>L'ovarismo poi tutto intero nel suo sistema veniva dallo stesso elegan&shy;<lb/>tissimo Redi esposto agl'Italiani in questa forma: &ldquo; Le uova della donna <lb/>non si formano nell'utero, ma si formano e si conservano nelle proprie e <lb/>determinate ovaie, le quali dagli antichi Notomisti fu creduto che fossero i <lb/>testicoli femminili. </s>

<s>Congiungendosi insieme, passa il seme del maschio ad <lb/>imbrattare le pareti uterine, e da questo imbrattamento si solleva un'aura <lb/>seminale, o uno spirito fecondatore, il quale, penetrando per li canali delle <lb/>Tube falloppiane, trapassa all'ovaia, e quivi feconda e galla un uovo e tal&shy;<lb/>volta pi&ugrave; d'uno. </s>

<s>L'uovo fecondato e gallato si stacca dall'ovaia, ed entrando <lb/>poscia per quel forame, che &egrave; nell'estremit&agrave; pi&ugrave; larga delle Tube fallop&shy;<lb/>piane, spinto dal moto peristaltico di esse Tube, se ne cala gi&ugrave; pel loro ca&shy;<lb/>nale, ed entra nelle cavit&agrave; dall'utero, e quivi s'inzuppa di quel liquore. </s>

<s>Da <lb/>tale inzuppamento, crescendo l'uovo, si comincia nell'interna sua cavit&agrave; a <lb/>formare il fanciullo &rdquo; (Consulti medici, T. VI cit., pag. </s>

<s>80, 81). </s></p><p type="main">

<s>Nonostante, non mancarono molti, pi&ugrave; forse fra gli stranieri che fra'no&shy;<lb/>stri, i quali, adombrando ad ogni novit&agrave;, ripetevano, per mantenere gli or&shy;<lb/>dini antichi, che le femmine secernono di fatto il loro umor seminale, nel&shy;<lb/>l'atto stesso che concorrono all'opera della generazione. </s>

<s>Non curando punto <lb/>costoro n&egrave; le osservazioni anatomiche del Falloppio, n&egrave; le sensate esperienze <lb/>dell'Harveio, si facevano forti dell'autorit&agrave; d&igrave; Galeno, confermata da tanti <pb xlink:href="020/01/1516.jpg" pagenum="391"/>insigni anatomici pi&ugrave; recenti, quali erano il Fernelio, il Varolio, il Laurent <lb/>e sopra tutto il gran Riolano. </s>

<s>Ma il Redi, che leggeva il libro della Natura <lb/>piuttosto che quelli degli uomini, sgombrava de'loro ostinati errori alla <lb/>scienza, cos&igrave; scrivendo, i sentieri: &ldquo; Quanto poi a'vasi deferent&igrave; degli An&shy;<lb/>tichi, pe'quali essi credevano che il seme femminile scendesse nell'utero, <lb/>io me ne rimetto all'esperienza se sieno <emph type="italics"/>in rerum natura<emph.end type="italics"/> o se non sieno; <lb/>se sieno aperti e scanalati, oppure se sieno solidi. </s>

<s>Io so bene che Galeno <lb/>fu il primo che fece menzione di questi vasi deferenti, e scrisse che ave&shy;<lb/>vano un ramo solo, il quale metteva capo nel fondo dell'utero. </s>

<s>Dopo di Ga&shy;<lb/>leno il Fernelio e il Laurenzio, l'Higmoro, il Plagzonio e il Varolio dissero <lb/>che non un sol ramo ma due ve ne avea, uno de'quali andava, come disse <lb/>Galeno, a scaricarsi nel fondo dell'utero, e l'altro nel collo o nella imboc&shy;<lb/>catura di esso utero. </s>

<s>Per quel ramo, che metteva capo nel fondo dell'utero, <lb/>crederono ch'entrasse nell'utero il seme delle donne non gravide, per quel <lb/>ramo, che imboccava nel collo dell'utero, crederono ch'entrasse e si spar&shy;<lb/>gesse il seme delle donne gravide. </s>

<s>Or vengane per terzo Rodomonte, e que&shy;<lb/>sto Rodomonte sia il famoso dottissimo Riolano, il quale, oltre i due sud&shy;<lb/>detti rami de'vasi deferenti, ne volle inventare ancora un altro, che fosse <lb/>il terzo, ma io per&ograve; non ho mai saputo vedere queste ramificazioni, e se <lb/>pure per disgrazia vi fossero, dico che non sono vasi deferenti, n&egrave; possono <lb/>introdurre cosa solida dentro la cavit&agrave; dell'utero, perch'essi non vi pene&shy;<lb/>trano e non v'imboccano, e questa cosa consta di fatto &rdquo; (Lettere, T. IV <lb/>dell'Op. </s>

<s>cit., pag. </s>

<s>64). </s></p><p type="main">

<s>Ma perch&egrave; pur costava di fatto la secrezione di quell'umor femmineo, <lb/>si domandava dunque da che avesse origine, se non scendeva dagli organi <lb/>seminali. </s>

<s>Il Van-Horne aveva detto nel suo Prodromo che scaturiva cotesto <lb/>umore &ldquo; ex ipsa glandulosa osculi uteri interni substantia, per multos mi&shy;<lb/>nutosque meatus &rdquo; (loco cit., pag. </s>

<s>439); meati pi&ugrave; diligentemente descritti <lb/>dal Graaf, in fine al cap. </s>

<s>XIII <emph type="italics"/>De mulierum organis.<emph.end type="italics"/> Il Diemerbroeck no&shy;<lb/>nostante non ne restava capace, e a Gasparo Bartholin, figlio di Tommaso, <lb/>dimostratore zelante dell'uova muliebri in Coppenaghen, in Leida, in Parigi, <lb/>in Firenze e in Roma, proponeva i suoi dubbi. </s>

<s>Il Bartholin gli riconobbe <lb/>non irragionevoli, perch&egrave; veramente i dutti cechi descritti dal Graaf al com&shy;<lb/>messo ufficio non parevano sufficienti. </s>

<s>Datosi dunque a un pi&ugrave; diligente <lb/>esame anatomico sopra le vacche, ritrov&ograve; che &ldquo; ad latera vaginae, non pro&shy;<lb/>cul ab urethrae exitu, utrinque glandula insignis canalem emittit, qui conspi&shy;<lb/>cuo et in papilla, quando premitur glandula, protuberante ostio intra vul&shy;<lb/>vam, aperitur &rdquo; (De ovariis mulierum, Florentiae 1700, pag. </s>

<s>18). &Egrave; da questa <lb/>ghiandola compressa da certe fibre carnose, che si costringono <emph type="italics"/>in actu ve&shy;<lb/>nereo,<emph.end type="italics"/> dimostr&ograve; che scaturisce l'umor vaginale. </s></p><p type="main">

<s>Pareva cos&igrave; l'Ovarismo rimasto de'suoi nemici nella scienza embriolo&shy;<lb/>gica vittorioso, quando una strana inaspettata scoperta venne a dargli nuovo <lb/>e valido assalto. </s>

<s>Antonio Leuwenoeck, appuntando un giorno un suo squi&shy;<lb/>sitissimo microscopio sopra il seme maschile, ebbe a restar maravigliato di <pb xlink:href="020/01/1517.jpg" pagenum="392"/>vedervi dentro guizzar vivacissime innumerevoli anguillette &ldquo; cuius delinea&shy;<lb/>tionem, scrisse in una di quelle lettere, di che compilasi la <emph type="italics"/>Continuatio ar&shy;<lb/>canorum Naturae,<emph.end type="italics"/> ego anno 1677 ad regiam Societatem londinensem misi, <lb/>quamque celeberrimi eius Collegii socii aeri incidi fecerunt, ac, cum aliquot <lb/>ex litevis meis excerptis, latino idiomata, inter Acta philosophica no 141, <lb/>pag. </s>

<s>1049 orbi erudito communicarunt, atque illic fig. </s>

<s>II et III exhibue&shy;<lb/>runt &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1722, pag. </s>

<s>22). </s></p><p type="main">

<s>Prima per&ograve; di darne formale notizia alla Societ&agrave; di Londra, aveva pri&shy;<lb/>vatamente fatto vedere il Leuwenoeck gli animalucci spermatici a Cristiano <lb/>Huyghens, il quale, da quel gran filosofo ch'egli era, pens&ograve; che dovessero <lb/>avere un ufficio importantissimo nell'opera della generazione. </s>

<s>Esprimeva <lb/>cos&igrave; i suoi pensieri, nel riferir la nuova scoperta olandese ai colleghi suoi <lb/>Accademici parigini: &ldquo; Quae in animalium semine deteguntur, translucida <lb/>omnia sunt, celerrime moventur, et ranis, antequam horum pedes formen&shy;<lb/>tur, similia sunt. </s>

<s>Haec animalcula in Hollandia primum fuere observata, et <lb/>horum inventio admodum mihi utilis videtur, et quae opus suppeditabit <lb/>illis, qui in animalium genesim inquirunt &rdquo; (Opera varia, Lugd. </s>

<s>Batav., <lb/>T. IV, 1724, pag. </s>

<s>765). </s></p><p type="main">

<s>Ripensando poi l'Huyghens in che consistesse quella particolare utilit&agrave;, <lb/>non dubit&ograve; di credere che gli spermatozoi entrassero nell'uova delle fem&shy;<lb/>mine, per costituire al nascituro gl'inizi. </s>

<s>Esponeva questa sua ipotesi, che <lb/>gli arrideva in aria di certezza, nella Diottrica, l&agrave; dove, trattando del Mi&shy;<lb/>croscopio e delle applicazioni di lui, cos&igrave; dice accennando alla scoperta delle <lb/>anguillette seminali: &ldquo; quae animalcula intrare ova faeminarum, atque esse <lb/>ipsorum animalium inde excludendorum initia, vix mihi dubitandum vide&shy;<lb/>tur &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1703, pag. </s>

<s>228). </s></p><p type="main">

<s>L'ipotesi erasi divulgata dalla viva voce, prima che per le stampe; e <lb/>perch&egrave; la persona dell'Huyghens non appariva, s'attribu&igrave; al Leuwenoeck e <lb/>si disse che voleva sostituirla all'Ovarismo. </s>

<s>Le idee, che venivano a dare <lb/>tanta importanza alla scoperta, furono accolte non solo, ma applaudite dal&shy;<lb/>l'Autore di essa scoperta, il quale non le aveva per&ograve; ancora professate in <lb/>pubblico, come pareva volesse far credere uno scrittore. </s>

<s>&ldquo; Est liber, son pa&shy;<lb/>role dello stesso Leuwenoeck, in quo notor quasi eo tempore (nell'anno 1677) <lb/>iam statuissem ex animalculo seminis virilis oriri hominem, cum tamen e <lb/>contrario meam circa eam rem sententiam nunquam aperuerim &rdquo; (Arcana <lb/>Naturae detecta, Lugd. </s>

<s>Batav. </s>

<s>1722, pag. </s>

<s>27). </s></p><p type="main">

<s>Perch&egrave; potesse la nuova ipotesi prevalere sull'ovarismo, sentiva l'Au&shy;<lb/>tore degli scoperti arcani della Natura il bisogno di dimostrare che anche <lb/>gli spermazoi, come l'uova, costituiscono gl'inizii alla generazione d'ogni <lb/>sorta d'animali. </s>

<s>A un'altra curiosit&agrave; si voleva che sodisfacesse la scienza, <lb/>ed era quella d'assegnar l'origine de'due sessi. </s>

<s>Il Falloppio, dimostrando <lb/>che tutte le membra del maschio si contengono nella femmina, non eccet&shy;<lb/>tuati i muscoli sospensori del pene, e che tutte le parti della femmina si con&shy;<lb/>tengon nel maschio, non eccettuate le mammelle, porgeva il pi&ugrave; ragionevole <pb xlink:href="020/01/1518.jpg" pagenum="393"/>modo di sodisfare alla curiosit&agrave;, ammettendo per verosimile che si dispon&shy;<lb/>gano le parti nell'embrione secondo un certo dimorfismo, cosicch&egrave; la fem&shy;<lb/>mina venga quasi ad essere un'allotropia del maschio. </s>

<s>Ma perch&egrave; molti ri&shy;<lb/>ducevano le osservazioni del Falloppio a quelle del Berengario, il quale <lb/>anch'egli diceva esser le membra a'due sessi comuni &ldquo; sed membra viro&shy;<lb/>rum sunt completa extra.... foeminarum vero sunt diminuta intra &rdquo; (Isa&shy;<lb/>gogae cit., fol. </s>

<s>20 ad t.), d'onde venivasi a confermar l'esistenza de'testi&shy;<lb/>coli femminili; gli Ovaristi, scansando il pericoloso incontro, si contentaron <lb/>di dire altre essere uova di femmine, altre di maschi. </s>

<s>Il Leuwenoeck voleva <lb/>poter dir questo stesso delle anguillette, e perch&egrave; le due ipotesi non solo <lb/>concorressero insieme, ma l'una potesse prevalere sull'altra, sentiva il bi&shy;<lb/>sogno di mostrar in quelle stesse anguillette qualche manifesto indizio delle <lb/>variet&agrave; sessuali. </s>

<s>Avendo perci&ograve; ritrovato veramente il medes&igrave;mo brulicare <lb/>anguifero in tutti i semi, e lusingandosi d'aver notati in un medesimo seme <lb/>due generi d'animali diversi, cred&egrave; il Leuwenoeck che fosse venuto il tempo <lb/>di potere apertamente professare quella ipotesi ugeniana, che veniva a pro&shy;<lb/>movere tant'alto la sua scoperta. </s>

<s>&ldquo; Sed iam, ubi etiam in seminibus mascu&shy;<lb/>linis animalium quadrupedum, avium, piscium, imo etiam insectorum repe&shy;<lb/>rio animalcula, multo certius statuo quam antea hominem, non ex ovo sed <lb/>ex animalculo in semine virili contento oriri, ac praesertim cum reminiscor <lb/>me in semine masculino hominis, et etiam canis, vidisse duorum generum <lb/>animalcula. </s>

<s>Hoc videns, mihi imaginabar alterum genus mares, alterum foe&shy;<lb/>minas esse &rdquo; (Arcana Naturae cit., pag. </s>

<s>27, 28). </s></p><p type="main">

<s>E perch&egrave; non sembrasse esser dall'amor proprio, piuttosto che dal&shy;<lb/>l'amore del vero, condotto a far nell'Embriologia questa innovazione, diceva <lb/>il Leuwenoeck non si poter persuadere che sia l'uovo attratto e tradotto <lb/>per le Tube falloppiane s&igrave; anguste. </s>

<s>&ldquo; Credere non possum Tubam fallop&shy;<lb/>pianam ovum ab ovario posse exsugere sive trahere, ac illud traducere per <lb/>meatum adeo angustum &rdquo; (ibid., pag. </s>

<s>26, 27). Che se alcuno gli avesse do&shy;<lb/>mandato a che fine dunque ha la Natura nelle galline e in altri simili ani&shy;<lb/>mali disposto l'uovo, rispondeva che a somministrar l'alimento e la materia <lb/>necessaria alla formazion del pulcino. </s>

<s>&ldquo; Omnem enim illam materiam, quae <lb/>in ovis gallinarum aliorumve animalium continetur,.... nulli alii fini in&shy;<lb/>servire censeo, quam alendo intra ovum galli gallinacei semini eique in pul&shy;<lb/>lum formando &ldquo; (ibid., pag. </s>

<s>66). </s></p><p type="main">

<s>Gli Ovaristi non videro migliore argomento per rifiutare la nuova ipo&shy;<lb/>tesi che negar l'esistenza de'vermicelli spermatici, ma il Leuwenoeck rispose <lb/>francamente ad essi che tutto dipendeva dal non averli saputi vedere, non <lb/>conoscendo n&egrave; la fabbrica n&egrave; l'uso de'Microscopii, e un nostro illustre Na&shy;<lb/>turalista ebbe a confessare che il Micrografo olandese cos&igrave; dicendo aveva ra&shy;<lb/>gione. </s>

<s>&ldquo; Anch'io candidamente confesso, scriveva il Vallisnieri a proposito <lb/>degli spermatozoi, sono stato lungo tempo ostinato nel non volergli conce&shy;<lb/>dere.... ma quando ebbi la sorte d'avere ordigni, a tali fini fabbricati da <lb/>peritissime mani maestre, i quali con evidenza veder me gli fecero, non <pb xlink:href="020/01/1519.jpg" pagenum="394"/>ebbi vergogna n&egrave; ribrezzo alcuno di mutare consiglio &rdquo; (Istoria della gene&shy;<lb/>razione dell'uomo e degli animali, Venezia 1721, pag. </s>

<s>48). </s></p><p type="main">

<s>Bench&egrave; per&ograve; il Vallisnieri vedesse cos&igrave; distintamente que'vermi, da non <lb/>poter negarne in verit&agrave; l'esistenza, non approvava che fossero gl'inizi fetali <lb/>del nascituro. </s>

<s>Gli pareva che l'Ovarismo fosse bene oramai dimostrato dalle <lb/>osservazioni dell'Aldovrandi, dell'Acquapendente e dell'Harvey, le quali ve&shy;<lb/>nivano ad aver la pi&ugrave; solenne e autorevole conferma dalla sentenza del Mal&shy;<lb/>pighi: &ldquo; pulli stamina in ovo praeesistere &rdquo; (De formatione pulli in ovo, <lb/>Operum T. II, Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>54). Il fatto per&ograve; non riguardava che <lb/>sole le ova fecondate, ma il Malpighi stesso volle anche di pi&ugrave; esam&igrave;nar le <lb/>parti, che si offerissero a notar nelle suvventanee, e trov&ograve; che, non molto <lb/>lungi dal centro, &ldquo; glob&ograve;sum candidumque corpus, seu cinereum, quasi mola <lb/>locabatur, quod laceratum nullum peculiare exhibebat corpus a se diversum. </s>

<s><lb/>Appendices reticulares habebat, quarum spatia diversas referebant figuras, <lb/>non raro ovales, diaphanoque replebantur colliquamento; denique tota haec <lb/>moles, iridis instar, plurimis circumdabatur circulis &rdquo; (ibid.). D'onde ragio&shy;<lb/>nevolmente argomentava cos&igrave; il Vallisnieri: &ldquo; Se il verme spermatico deve <lb/>entrare nella cicatrice, e non far altro se non crescere e manifestarsi, a qual <lb/>fine ci &egrave; quel <emph type="italics"/>corpo globoso e candido o cinereo, quasi mola,<emph.end type="italics"/> con tutto <lb/>quell'altro grande apparato d'intorno che vien descritto? </s>

<s>Bastava un sem&shy;<lb/>plice e puro sacchetto con un poco di liquore, dove avesse potuto spogliarsi <lb/>e nuotare. </s>

<s>Ma quel <emph type="italics"/>quasi mola,<emph.end type="italics"/> con tutti gli altri ordigni circondatori, mo&shy;<lb/>stra che in quella fosse il feto, di fibre ancor diafane e dilicatissime com&shy;<lb/>posto, che aspettasse il moto e l'ultimo sviluppo dallo spirito del maschil <lb/>seme &rdquo; (Istoria della generaz. </s>

<s>cit., pag. </s>

<s>81). </s></p><p type="main">

<s>In queste parole del Vallisnieri si conclude la verit&agrave; scoperta per l'espe&shy;<lb/>rienza, ma prudentemente lasciata tuttavia sotto un velo di naturale mistero. </s>

<s><lb/>Filosofi pi&ugrave; audaci pretesero di spiegare in che modo il maschil seme opera <lb/>sull'uovo, e non riuscendovi ricorsero a una virt&ugrave; attiva insita nella Na&shy;<lb/>tura, per la quale si plasmano gl'inizii fetali, che nell'utero della madre ri&shy;<lb/>cevono poi gl'incrementi. </s>

<s>Fondavano la loro ipotesi sopra l'esperienze de&shy;<lb/>gl'infusorii, ma lo Spallanzani, nel suo <emph type="italics"/>Saggio di osservazioni microscopiche <lb/>concernenti il sistema della generazione dei signori di Needham e Buffon,<emph.end type="italics"/><lb/>dimostr&ograve; che quelli animalucci non hanno origine dalla virt&ugrave; vegetatrice <lb/>della Natura, ma da'germi, che altri simili animalucci avevano prima de&shy;<lb/>posti nelle varie materie assoggettate alle infusioni. </s>

<s>Cos&igrave; rimase nel suo pi&ugrave; <lb/>sincero splendore, a scorta dell'Embriologia, la sentenza del Malpighi, che <lb/>cio&egrave; gli stami del pulcino e di ogni altro animale preesistan nell'uovo, da <lb/>cui si svolgono in virt&ugrave; dell'atto fecondatore a noi misterioso. </s></p><pb xlink:href="020/01/1520.jpg" pagenum="395"/><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>L'ipotesi del Needham ora commemorata si posava sul fondamento che <lb/>gl'infusorii, e con essi anche i vermi spermatici, fossero veri e proprii ani&shy;<lb/>mali. </s>

<s>Lo Spallanzani perci&ograve;, nell'istituire le sue microscopiche esperienze <lb/>col fine di confutar quella ipotesi, ebbe prima a decidere della supposta ani&shy;<lb/>malit&agrave;, ch'egli pure si persuase esser manifesta da certi atti, in apparenza <lb/>instintivi, e da certi moti che mostravano d'essere spontanei. </s>

<s>&ldquo; Quel pren&shy;<lb/>der di mira, egli dice, e dolcemente ferire co'loro beccucci le briciole dei <lb/>vegetabili disperse nelle infusioni; quel raccogliersi mancando il fluido e <lb/>unirsi in calca, dove questo pi&ugrave; tardi finisce; quel passar dalla quiete a un <lb/>movimento veloce, senza apparenza di corpi, che ne li sospingano e caccino; <lb/>quell'andar tante volte al contrario della corrente; quel saper cos&igrave; bene schi&shy;<lb/>far s&egrave; stessi, non meno nell'affacciarsi, che gli ostanti imbarazzi che incon&shy;<lb/>tran per via; quel finalmente variar d'improvviso di direzione e determi&shy;<lb/>narsi ad opposito movimento, sono tutti segnali manifestissimi ed innegabili <lb/>di un tal principio animale &rdquo; (Dissertaz. </s>

<s>varie, T. II, Milano 1826, pag. </s>

<s>275). </s></p><p type="main">

<s>Forse lo Spallanzani s'ingannava, non sospettando che la luce e l'elet&shy;<lb/>tricit&agrave;, per tacere di altri pi&ugrave; materiali e incomputabili agenti, possono con <lb/>minimo momento turbar cos&igrave; l'equilibrio di quell'esigue particelle solide <lb/>sospese in mezzo al liquido, da farle facilmente credere animate, ma in ogni <lb/>modo &egrave; il moto per noi il pi&ugrave; sicuro argomento della vita. </s>

<s>Le questioni <lb/>sarebbero state fra'Micrografi senza dubbio decise, quando fossesi potuto di&shy;<lb/>mostrare che le lunghe code degli infusorii son, come ne'pesci, organi della <lb/>locomozione, ma rimarrebbe anche cos&igrave; tuttavia incerto se dipenda il vivace <lb/>guizzar d'esse code da intrinseca attivit&agrave;, o piuttosto da esterno impulso. </s>

<s><lb/>Per la final decisione in ogni modo sarebbe convenuto dimostrar la ragione <lb/>di un tal moto, coniugando la Fisiologia alla Meccanica, come si fa del re&shy;<lb/>sto rispetto agli animali degli ordini superiori, che in grazia del moto locale <lb/>hanno apposite e distinte membra. </s>

<s>Ma pure nell'esercizio di queste rimase <lb/>quella ragion meccanica per lungo tempo oscura e involta nell'errore, come <lb/>apparir&agrave; dalla seguente storia, la quale, limitandosi per ora al passo de'qua&shy;<lb/>drupedi e al volo degli uccelli, dispone intanto gl'ingegni a riconoscere nelle <lb/>inaspettate difficolt&agrave; quelli, che in esseri semoventi e d'invisibili membra, <lb/>alla lusingata scienza dell'uomo torneranno misteri. </s></p><p type="main">

<s>Della meccanica del passo nessuno fr&agrave; gli Antichi aveva fatto il soggetto <lb/>a filosofiche speculazioni prima di Aristotile, il quale ci lasci&ograve; fra le Opere <lb/>un trattatello intitolato <emph type="italics"/>De animalium incessu.<emph.end type="italics"/> Proponendosi nel cap. </s>

<s>XII <lb/>d'insegnare in che modo si faccia l'incesso de'quadrupedi, non dubit&ograve; di <lb/>affermare che i piedi s'incrociano cos&igrave;, che al destro posteriore corrisponde <lb/>sempre, e nella quiete e nel moto, il sinistro anteriore, e un tale alternato <pb xlink:href="020/01/1521.jpg" pagenum="396"/>metro osservano gli altri due. </s>

<s>&ldquo; Moventur autem posteriora ad priora per <lb/>diametrum: post enim dextrum prius, sinistrum movet posterius. </s>

<s>Ita sini&shy;<lb/>strum prius, post illud autem dextrum posterius &rdquo; (Tomus VI, Oper., Ve&shy;<lb/>netiis 1560, fol. </s>

<s>277). </s></p><p type="main">

<s>Se questo gioco veramente riscontri coll'esperienza &egrave; inutile fatica al <lb/>Filosofo l'investigarlo, non potendo essere altrimenti da quel che la ragione <lb/>prescrive alla Natura. </s>

<s>Imperocch&egrave;, se non per la diagonale, dice Aristotile, <lb/>si facesse l'incesso del quadrupede, ma per i lati del quadrangolo, manche&shy;<lb/>rebbe al centro di gravit&agrave; il suo sostegno, e il moto dell'animale evidente&shy;<lb/>mente sarebbe ruinoso. </s>

<s>Il medesimo inconveniente ne seguirebbe, ei sog&shy;<lb/>giunge, se movesse insieme i pi&egrave; d'avanti e poi quelli di dietro. </s>

<s>&ldquo; Causa <lb/>autem est quoniam, si priora simul et prius, distraheretur sane aut prae&shy;<lb/>cidua esset ambulatio.... Si autem utrisque dextris primis, extra sane ful&shy;<lb/>crorum fierent sustentacula &rdquo; (ibid.). </s></p><p type="main">

<s>Dopo gl'istauramenti della scienza primo a rivolgere le sue speculazioni <lb/>sopra questo argomento fu Girolamo Fabricio, il quale, nel suo libro <emph type="italics"/>De <lb/>motu locali animalium secundum totum,<emph.end type="italics"/> riserb&ograve; a trattar <emph type="italics"/>De gressu qua&shy;<lb/>drupedum<emph.end type="italics"/> in particolare poche parole, che ripetevano ai nuovi risvegliati <lb/>dal lungo sonno le sentenze dell'antico Aristotile. </s>

<s>&ldquo; Fit itaque ambulatio <lb/>altero crure ad terram firmato, altero autem translato.... Ex quatuor cru&shy;<lb/>ribus bina anteriora dum incedunt ita quidem constitui et moveri ut alte&shy;<lb/>rum transferatur, alterum innitatur. </s>

<s>Quo tempore duo posterius posita, et <lb/>ipsa quoque idem praestantia, alterum eorum transferatur, alterum innita&shy;<lb/>tur, ita tamen ut ei quod transfertur anterius non respondeat ex eodem la&shy;<lb/>tere quod posterius est in translatione,.... ita ut ipsius quadranguli dia&shy;<lb/>metri sint similes, hoc est crus anterius et posterius nequaquam sibi invi&shy;<lb/>cem per latus respondentia, sed tantum inter se vicissim, per diametrum <lb/>opposita, similem habeant constitutionem &rdquo; (Opera omnia, Lug. </s>

<s>Batav. </s>

<s>1738, <lb/>pag. </s>

<s>371). L'Acquapendente per&ograve;, quasi volesse mostrare di aver anch'egli <lb/>risentiti i tepori della nuova stagione, si lusingava di confermar cos&igrave; fatte <lb/>dottrine con l'esperienze, le quali, sebbene egli dice esser difficili a farsi, <lb/>per la loro celerit&agrave;, ne'cani e ne'cavalli, &ldquo; in testudine id non difficulter <lb/>observatur &rdquo; (ibid.). </s></p><p type="main">

<s>L'aristotelismo rinnovellato dall'Acquapendente seduceva cos&igrave; gl'inge&shy;<lb/>gni, non solamente disposti a mantenere gli ordini antichi, ma liberi nel&shy;<lb/>l'accogliere le novit&agrave;, che s'aggiunge anche questo fra'tanti altri esempii <lb/>di quella seduzione, dimostratici dalla storia. </s>

<s>Pier Gassendo rest&ograve; dalle ra&shy;<lb/>gioni di Aristotile, e dall'esperienze dello stesso Acquapendente, cos&igrave; ben <lb/>persuaso moversi i pi&egrave; dei quadrupedi, per usar le sue proprie parole, <emph type="italics"/>com&shy;<lb/>mutatione in crucem facta,<emph.end type="italics"/> che stando un giorno in Parigi nella chiesa di <lb/>S. </s>

<s>Martino a vedere il cavallo, su cui siede il celeste Guerriero, co'due pi&egrave; <lb/>sinistri posati e co'due destri sollevati da terra, ebbe a dare al pittore il <lb/>titolo di sciocco. </s>

<s>&ldquo; Et quo proinde intelliges quam fuerit Pictor ille ineptus, <lb/>qui Parisiis, in alteram alam organorum S. Martini, ita equum pinxit, ut <pb xlink:href="020/01/1522.jpg" pagenum="397"/>terrae insistens duobus sinistris pedibus, duos dextros elatos in aerem ha&shy;<lb/>beat &rdquo; (Syntagma philosophicus, Operum, T. II, Florentiae 1727, pag. </s>

<s>469). </s></p><p type="main">

<s>Forse in quel medesimo tempo, che nella chiesa di S. </s>

<s>Martino a Pa&shy;<lb/>rigi, si rappresentava una scena molto diversa in una sala anatomica di <lb/>Roma. </s>

<s>Quel Medico tedesco, che dicemmo altrove essere stato il primo a <lb/>dimostrare in Italia il circolo del sangue, si studiava argutamente, sezionando <lb/>cadaveri, di scoprire alla presenza de'discepoli e degli amici ivi convenuti <lb/>gli errori astotelici, in ci&ograve; tanto dando nel genio a Raffaello Magiotti. </s>

<s>Que&shy;<lb/>sti, caduto un giorno il discorso sull'incesso degli animali, rammemorava <lb/>allo stesso tedesco Maestro il cavalllo del Gattamelata, che era sulla piazza <lb/>di Padova con due gambe dalla medesima parte, contro il precetto del Fi&shy;<lb/>losofo, il quale perci&ograve; ambedue insieme tanto deridevano, lodando l'arte <lb/>dello Scultore italiano, quanto il Gassendo lo venerava, rimproverando l'igno&shy;<lb/>ranza del Pittor parigino. </s></p><p type="main">

<s>E qui s'offrirebbe largo e fecondo campo di osservazioni intorno alla <lb/>storia dell'arte in relazione colla storia naturale, dalle quali verrebbe a con&shy;<lb/>fermarsi quel che altrove dicemmo di Leonardo da Vinci, dai dipinti del <lb/>quale si raccoglierebbe un trattato <emph type="italics"/>De animalium incessu<emph.end type="italics"/> dimostrativo del <lb/>vero naturale meglio di quelli stessi scritti dai Filosofi ne'loro libri. </s>

<s>Ma, per <lb/>non interrompere il filo alla nostra storia, diciamo che le confutazioni del ra&shy;<lb/>zionalismo aristotelico, ritrovate da quell'Anatomice tedesco nell'osservazione <lb/>dei fatti naturali, fecero al Magiotti risovvenire che Galileo, anche in quel <lb/>particolar soggetto <emph type="italics"/>De natura animalium,<emph.end type="italics"/> aveva con grande zelo intrapreso <lb/>il medesimo istituto, per cui non pot&egrave; in quel filosofico fervore tenersi di <lb/>prendere la penna in mano, per eccitare il suo valoroso Maestro a prose&shy;<lb/>guirlo. </s>

<s>&ldquo; Godo in estremo, gli scriveva da Roma il d&igrave; 31 Marzo 1637, che <lb/>Ella si occupi intorno al moto de'proietti, e tanto pi&ugrave; quanto meno mi d&agrave; <lb/>sodisfazione Aristotile. </s>

<s>Per fine la prego quanto so e posso a non lasciare <lb/>indietro le speculazioni <emph type="italics"/>De incessu animali,<emph.end type="italics"/> acci&ograve; con questo tutta ancora <lb/>si sbarbi quella opinionaccia, che questo Autore sia in tutto e per tutto un <lb/>oracolo.... Mi &egrave; sovvenuto questo, perch&egrave; qua si trova un Medico tedesco, <lb/>anatomista raro, quale mostra in fatto assaissimi errori <emph type="italics"/>De natura anima&shy;<lb/>lium,<emph.end type="italics"/> e quand'io li contai del cavallo del Gattamelata, che sta sopra due <lb/>gambe dalla medesima banda, contro il detto di Aristotile, rise veramente <lb/>di tutto cuore, ed ogni giorno porta qualche luogo per farci sempre pi&ugrave; ri&shy;<lb/>dere &rdquo; (MSS. Gal., P. VI, T. XIII, c. </s>

<s>14). </s></p><p type="main">

<s>Il trattato <emph type="italics"/>De motu locali animalium,<emph.end type="italics"/> pubblicato dall'Acquapendente <lb/>in Padova nel 1618, aveva eccitato Galileo a rivolgere la mente anche su <lb/>questa curiosa parte della Meccanica, e nella <emph type="italics"/>Selva di problemi varii<emph.end type="italics"/> (Alb. </s>

<s><lb/>XIV, 319) si trovano appunti relativi a questo tema, non preso ancora a <lb/>svolgere dall'Autore nel 1637. L'esortazioni del Magiotti par che avessero <lb/>avuto efficacia, perch&egrave; non molto tempo dopo lo stesso Galileo si deliber&ograve; <lb/>di dettare a Francesco Renuccini, se non la forma, la sostanza a un discorso <lb/><emph type="italics"/>Intorno il camminare del cavallo,<emph.end type="italics"/> di cui il Venturi e poi l'Alberi pubbli-<pb xlink:href="020/01/1523.jpg" pagenum="398"/>carono l'introduzione. </s>

<s>Si confuta ivi Aristotile, dicendo che la Natura non <lb/>ha cos&igrave; limitato l'adoperare i piedi al cavallo, che debbano necessariamente <lb/>venire come ad incrociarsi, ma chi si piglier&agrave; la briga d'andare a qualun&shy;<lb/>que cavallerizza potr&agrave; da s&egrave; stesso &ldquo; osservare in quanti modi mova, ad un <lb/>fischio di bacchetta, il cavallo i piedi obbedienti &rdquo; (ivi, pag. </s>

<s>310). </s></p><p type="main">

<s>I concetti galileiani, rimasti in quel saggio del Rinuccini per lungo <lb/>tempo dimenticati, avevano avuto pi&ugrave; dotta esplicazione e pi&ugrave; solenne pub&shy;<lb/>blicit&agrave; per opera del Borelli, il quale riserb&ograve; il cap. </s>

<s>XX della I Parte <emph type="italics"/>De motu <lb/>animalium<emph.end type="italics"/> a trattare dell'incesso de'quadrupedi. </s>

<s>La proposizione CLXV si <lb/>legge cos&igrave; formulata: &ldquo; Gressum quadrupedum non fieri motis alternatim <lb/>duobus pedibus diagonaliter oppositis, reliquis duobus quiescentibus &rdquo; (Ro&shy;<lb/>mae 1680, pag. </s>

<s>263). Della qual proposizione sembrano all'Autore le prove <lb/>cos&igrave; evidenti, che si fa maraviglia come Aristotile e i suoi seguaci non si <lb/>sieno avveduti dell'assurdit&agrave; della contraria. </s>

<s>Imperocch&egrave; se negano moversi <lb/>il cavallo co'pi&egrave; commutati secondo il lato del quadrangolo, perch&egrave; cadendo <lb/>il centro di gravit&agrave; sopra una linea l'equilibrio riuscirebbe instabile, non <lb/>s'intende come possano persuadersi d'accomodar le partite, ricorrendo alla <lb/>commutazione de'pi&egrave; per diametro, il quale pure essendo una linea rende&shy;<lb/>rebbe l'equilibrio instabile per la stessa, stessissima ragione. </s>

<s>&ldquo; Sed quid <lb/>quaerimus rationes, conclude il Borelli, quando experientiae reclamant? </s>

<s><lb/>Observa equum lento motu gradientem: nunquam videbis duos pedes dia&shy;<lb/>gonaliter oppositos simul tempore mov&egrave;ri, sed semper unicus pes a terra <lb/>elevatur, tribus reliquis firmis manentibus. </s>

<s>Idipsum postea, diligenti inspec&shy;<lb/>tione, etiam observabis in gressu celeriori in omnibus quadrupedum specie&shy;<lb/>bus &rdquo; (ibid., pag. </s>

<s>265). </s></p><p type="main">

<s>Nella seguente proposizione CLXVI passa l'Autore a esporre il modo <lb/>come si fa l'incesso de'quadrupedi, e preconcetta gi&agrave; l'opinione che tutta <lb/>la sicurt&agrave; di quell'esercizio dipenda dal trovarsi il centro della gravit&agrave; com&shy;<lb/>preso dentro il perimetro di una superficie, dimostra essere quella super&shy;<lb/>ficie o un triangolo o un parallelogrammo o un rombo o un trapezio, se&shy;<lb/>condo che tre, nelle loro pose naturali, o quattro variamente spostate son <lb/>le colonne delle gambe insistenti sul suolo, per promuovere sempre pi&ugrave; in&shy;<lb/>nanzi la macchina animale. </s></p><p type="main">

<s>Abbiamo detto essere quella del Borelli un'opinione preconcetta, se&shy;<lb/>condo la quale si reputava impossibile che procedessero i cavalli co'due pi&egrave; <lb/>mossi dalla medesima parte. </s>

<s>Eppur la pittura e la statua equestre del S. </s>

<s>Mar&shy;<lb/>tino e del Gattamelata son l'immagine rappresentativa di una cosa natural&shy;<lb/>mente vera, vedendosi propriamente ai cavalli movere sempre le gambe a <lb/>quel modo, quando vanno di trotto. </s>

<s>Fu questa verit&agrave; di fatto conosciuta <lb/>bene da Galileo, affermando esser falso &ldquo; che i quadrupedi non possano <lb/>levar da terra nel medesimo tempo i due piedi dalla medesima banda &rdquo; <lb/>(Alb. </s>

<s>XIV, 319), e secondo che riferisce il Rinuccini rende altres&igrave; la ragione <lb/>del perch&egrave;, insistendo la gran macchina pure a quel modo sopra una linea, <lb/>non tema perci&ograve; il pericolo di cadere. </s>

<s>&ldquo; &Egrave; forse vero che il cavallo cade-<pb xlink:href="020/01/1524.jpg" pagenum="399"/>rebbe, se movesse tutt'a due i piedi dalla medesima banda, e nell'istesso <lb/>tempo con intenzione di star fermo, ma si vede che cos&igrave; facendo piega a <lb/>quella parte, e con lui fa piegar chi ci &egrave; sopra, e se l'aiuto degli altri due <lb/>indugiasse male ne avverrebbe &rdquo; (ivi, pag. </s>

<s>309). </s></p><p type="main">

<s>Si raccoglie da queste espressioni che Galileo, del non cadere il cavallo <lb/>mentre corre bench&egrave; posi sopra due piedi dalla medesima parte, rendeva una <lb/>duplice ragione: la prima ch'egli piega s&egrave; e il cavaliere verso il lato ove <lb/>sono i pi&egrave; fermi, e la seconda che per un attimo solo rimane in tale stato <lb/>cos&igrave; vacillante. </s>

<s>Quella prima ragione per&ograve; vien contradetta dall'esperienza, <lb/>andando il cavallo nel trotto cos&igrave; pari, che il cavaliere non sente il minimo <lb/>ondeggiamento, e quanto alla seconda converrebbe dire che fosse stata poco <lb/>provvida la Natura, se avesse messo in pericolo l'animale anche per un mo&shy;<lb/>mento solo. </s>

<s>Forse ebbe Galileo a sentir la forza dell'argomento, e in quel <lb/>ch'egli osserva <emph type="italics"/>che il cavallo cadrebbe se movesse tutt'a due i piedi dalla <lb/>medesima banda e nell'istesso tempo, con intenzione di star fermo,<emph.end type="italics"/> avr&agrave; <lb/>non difficilmente potuto ritrovar del fatto altra pi&ugrave; verosimile spiegazione. </s>

<s><lb/>Sia pure che il cavallo in corsa possa reggersi per un brevissimo tempo <lb/>anche su due soli piedi, ma perch&egrave; non pu&ograve; tenersi a quel modo quand'egli <lb/>&egrave; fermo nemmeno un istante? </s></p><p type="main">

<s>Il problema, che veniva cos&igrave; a proporsi, era similissimo a quell'altro <lb/>meccanico problema, dallo stesso Galileo cos&igrave; formulato: &ldquo; Qual sia la ra&shy;<lb/>gione che le trottole e le ruzzole girate si mantengono ritte, e ferme no ma <lb/>traboccano? </s>

<s>&rdquo; (Alb. </s>

<s>XIV, 321). N&egrave; la risoluzione era punto bisogno di ri&shy;<lb/>cercarla, essendo gi&agrave; stata data dal Benedetti nel suo libro Delle specula&shy;<lb/>zioni. </s>

<s>Egli ivi osserva, in un'Epistola a Paolo Capra, che ne'corpi mossi <lb/>velocemente attorno si ridesta una potente inclinazione di andare per linea <lb/>retta, che distrae i corpi stessi dalla naturale direzione dei gravi. </s>

<s>&ldquo; Ab eius&shy;<lb/>modi inclinatione, poi soggiunge, rectitudinis motus partium alicuius corpo&shy;<lb/>ris rotundi fit ut per aliquod temporis spacium trochus, cum magna vio&shy;<lb/>lentia seipsum circumagens, omnino rectus quiescat super illam cuspidem <lb/>ferri quam habet, non inclinans se versus mundi centrum magis ad unam <lb/>partem quam ad aliam, cum quaelibet suarum partium in huiusmodi motu <lb/>non inclinet omnino versus mundi centrum, sed multo magis per transver&shy;<lb/>sum ad angulos rectos cum linea directionis aut verticali aut orizontis axe, <lb/>ita ut necessario huiusmodi corpus rectum stare debeat &rdquo; (Venetiis 1599, <lb/>pag. </s>

<s>286). </s></p><p type="main">

<s>Che il corpo nella sua vertigine non inclini veramente al centro del <lb/>mondo argomentasi, prosegue il Benedetti, dal veder ch'ei diventa pi&ugrave; leg&shy;<lb/>gero. </s>

<s>La palla infatti tanto pi&ugrave; resiste per l'aria al peso che la tira, secon&shy;<lb/>dando la direzione della tangente, quant'ella viene gittata con pi&ugrave; gran forza. </s>

<s><lb/>Avrebbe agli esempi meccanici potuto l'Autore soggiungere tante altre fisi&shy;<lb/>che esperienze, per le quali si dimostra di fatto che i corpi in moto tanto <lb/>son pi&ugrave; leggeri quanto vanno pi&ugrave; veloci, ma in quel ridur le molte ragioni <lb/>alla sola meccanica de'proietti intravediam l'occasione, venuta di l&agrave; a Ga-<pb xlink:href="020/01/1525.jpg" pagenum="400"/>lileo, d'applicare il problema delle trottole e delle ruzzole al moto del ca&shy;<lb/>vallo, sapendosi che il Magiotti lo richiamava su quel soggetto giusto in quel <lb/>tempo, ch'egli attendeva a instituire la scienza nuova de'proietti. </s>

<s>Comun&shy;<lb/>que sia, la ragion meccanica per cui i moderni <emph type="italics"/>velocipedi,<emph.end type="italics"/> per esempio, ca&shy;<lb/>dono quando stan fermi e si tengono cos&igrave; ben ritti quando sono in moto, <lb/>&egrave; quella stessa per cui il cavallo, che stando fermo cadrebbe, si regge anche <lb/>su due soli piedi dalla medesima parte, quando va di trotto. </s>

<s>Farebbe per&shy;<lb/>ci&ograve; gran maraviglia se n&egrave; a Galileo n&egrave; a nessuno di que'suoi tanti disce&shy;<lb/>poli studiosi della meccanica non fosse sovvenuto di emendare gli errori ari&shy;<lb/>stotelici, applicando all'incesso de'quadrupedi le nuove bellissime teorie del <lb/>Benedetti. </s></p><p type="main">

<s>N&egrave; i settatori dunque di Aristotile n&egrave; i discepoli di Galileo, a quel che <lb/>par dalla storia, si sarebbero mai creduti che la Natura avesse cos&igrave; com&shy;<lb/>plicato il passo de'quadrupedi nelle pi&ugrave; astruse leggi della Meccanica, da <lb/>renderne tanto difficile e faticoso lo studio de'Filosofi; difficolt&agrave; e fatica, <lb/>che non s'ebbe dall'altra parte a incontrar punto minore, quando si volle <lb/>allo stesso modo filosofare intorno al volo degli uccelli. </s>

<s>Aristotile, nel cap. </s>

<s>X <lb/><emph type="italics"/>De animalium incessu,<emph.end type="italics"/> ne tratt&ograve; con molta oscurit&agrave; dipendente in parte <lb/>dalla concision del discorso, e in parte dalla difficolt&agrave; della cosa, che non lo <lb/>rendeva sicuro del vero naturale. </s>

<s>S'intese nonostante ch'ei volesse appro&shy;<lb/>vare, e quasi colla sua autorit&agrave; suggellar la comune opinione, che cio&egrave; fa&shy;<lb/>cessero l'ali l'ufficio e producessero l'effetto stesso dei remi. </s>

<s>Volendo in&shy;<lb/>fatti rendere la ragione del perch&egrave; alcuni insetti abbiano un volo cos&igrave; tardo <lb/>e imbecille, dice che ci&ograve; da null'altro dipende che dall'aver l'ali non pen&shy;<lb/>nute ma membranose, o sproporzionate alla corpulenza del resto, cosicch&egrave; <lb/>avvien di esse quel che avviene de'deboli remi, i quali abbiano da sospin&shy;<lb/>gere innanzi una nave ponderosa. </s>

<s>&ldquo; Quemadmodum igitur si quis oneratam <lb/>navim remis tentet propellere, simili isthaec modo volatu utuntur, et ala&shy;<lb/>rum naturae imbecillitas ad id non nihil facere videtur &rdquo; (T. VI, Operum <lb/>cit., fol. </s>

<s>275 ad t.). Ma gli uccelii, prosegue a ragionare il Filosofo, hanno <lb/>in generale un volo velocissimo, cosicch&egrave; le ali fanno in essi l'ufficio dei <lb/>remi applicati a un'agilissima nave. </s>

<s>Quell'analogia insomma, che vedevasi <lb/>passare tra le ali e i remi, supponeva per cosa certa e gi&agrave; dimostrata che <lb/>fosse l'uccello specificamente pi&ugrave; leggero dell'aria, come la nave &egrave; specifi&shy;<lb/>camente pi&ugrave; leggera dell'acqua. </s></p><p type="main">

<s>Girolamo Fabricio, che nel suo trattato <emph type="italics"/>De motu locali animalium<emph.end type="italics"/> non <lb/>lasci&ograve; indietro il volo, dice cho questo si fa per via dell'instancabile agitarsi <lb/>delle penne, le quali sospingono indietro l'aria. </s>

<s>&ldquo; Ex quo motu, poi sog&shy;<lb/>giunge, et aeris impulsu, contingit Volatile anterius locum mutare, non dis&shy;<lb/>simili ratione ac, remigantibus aquam retro impellendo, navim antrorsum <lb/>moveri accidit &rdquo; (Opera omnia cit., pag. </s>

<s>375). Ma non poteva l'Acquapen&shy;<lb/>dente ammettere questa similitudine, senz'ammettere insieme che l'uccello <lb/>mentre vola galleggi sull'aria soggiacente, come la nave stessa galleggia sul&shy;<lb/>l'acqua, cosicch&egrave; non incomba alle ali altro ufficio che di promovere il corpo <pb xlink:href="020/01/1526.jpg" pagenum="401"/>dell'animale, senz'avere il car&verbar;co di sostenerlo. </s>

<s>Tale infatti &egrave; l'espressa opi&shy;<lb/>nion dell'Autore, che dice constar gli uccelli di duplice elemento, dell'aereo <lb/>cio&egrave; e del terreo, essendo cos&igrave; disposti dalla Natura, da potere starsene ora <lb/>in aria, ora per terra. </s>

<s>&ldquo; Verumtamen, cum non perpetuo in aere esse sed <lb/>saepenumero ad terram dimitti esset commodum, idcirco Natura per pen&shy;<lb/>nas leve quidem sed non ipso aere levius animal reddidit. </s>

<s>Ad id praestan&shy;<lb/>dum leviusque aere ipsum reddendum, alarum potissimum caudaeque adiu&shy;<lb/>tricis motus et expansio comparata est, ita ut, dum evolat levius redditum, <lb/>non impediatur volatus ab elementi terrei propensione &rdquo; (ibid., pag. </s>

<s>374). </s></p><p type="main">

<s>Se insomma galleggia secondo l'Acquapendente l'uccello sull'aria, ci&ograve; <lb/>non &egrave; per altro che per l'espansion delle penne delle ali e della coda. </s>

<s>Ma una <lb/>similitudine ch'egli porta, per dar meglio a intendere come avvenga la cosa, <lb/>produce sulla mente di chi legge un effetto contrario. </s>

<s>La similitudine &egrave; tolta <lb/>dal lenzuolo, che ripiegato precipita dall'alto, e disteso cade con lentissimo <lb/>moto. </s>

<s>Ma pur in ogni modo egli cade, e se ci&ograve; si avverasse dell'uccello, colle <lb/>penne espanse, non sarebbe dunque pi&ugrave; vero ch'egli &egrave; assolutamente pi&ugrave; <lb/>leggero dell'aria, e che l'ali non han da far altro che servire al volo. </s>

<s>Senti <lb/>perci&ograve; bene il Fabricio, per salvar l'ipotesi aristotelica, il bisogno di ricor&shy;<lb/>rere a qualche altro espediente, che fu quello della condensazione dell'aria <lb/>fatta dentro il suo corpo dal volante, nell'atto specialmente di sollevarsi da <lb/>terra. </s>

<s>&ldquo; Causa autem ob quam spiritus cohibitio ad suspendendum susti&shy;<lb/>nendumque in aere volatile conferat, ea certe est quod spiritus cohibitio <lb/>aeris copiam intro in corpus coercet, constringit et continet, quae volatile <lb/>levius reddit &rdquo; (ibid., pag. </s>

<s>373). </s></p><p type="main">

<s>Diremo pi&ugrave; qua come trovasse questa ipotesi, che ha in apparenza <lb/>qualche cosa di singolare, il suo fondamento nella particolare struttura degli <lb/>organi della respirazion degli uccelli, ma l'Acquapendente non par che l'ap&shy;<lb/>poggi sopra questo principio fondamentale, ma su quell'altro degli spiriti, <lb/>che muovono dal cervello come da fonte, e che per la via de'nervi, come <lb/>per appositi canali, corrono e ricorrono a insufflare, e cos&igrave; a dar moto ai <lb/>muscoli. </s>

<s>Questa infatti &egrave; la dottrina galenica professata dal nostro Autore, <lb/>il quale, nella Parte seconda del suo trattato <emph type="italics"/>De musculis,<emph.end type="italics"/> cos&igrave; spiegava <lb/>l'origine de'loro moti. </s>

<s>&ldquo; Etenim a cerebro, seu spinali midulla, ceu prin&shy;<lb/>cipio et fonte, et per nervos, ceu per canales et rivos, vim motoriam diffundi <lb/>in muscolos apparet &rdquo; (ibid., pag. </s>

<s>399). </s></p><p type="main">

<s>Narrammo a suo luogo come dimostrasse il Borelli per mezzo dell'espe&shy;<lb/>rienza che l'ipotesi di quegli spiriti aerei non era altro che una immagina&shy;<lb/>zione, ond'essendo persuaso dalla scienza idrostatica e dai fatti che l'uccello, <lb/>nemmeno per accidentalit&agrave;, divien pi&ugrave; leggero dell'aria, n'ebbe saviamente <lb/>a concludere che l'antica teoria del volo, rinnovellata dall'Acquapendente, <lb/>non si poteva oramai pi&ugrave; salvare. </s>

<s>Se dunque le ali non operano a modo di <lb/>remi, e se l'uccello ha bisogno d'esser non solamente promosso ma soste&shy;<lb/>nuto, qual pu&ograve; essere la nuova meccanica del volo? </s></p><p type="main">

<s>Il Borelli la riconosce principalmente nell'elasticit&agrave; dell'aria, la quale <pb xlink:href="020/01/1527.jpg" pagenum="402"/>prima nell'abbassarsi l'ala, compressa, poi nel sollevarsi di lei si dilata, e <lb/>fa di sotto in su tale una corrente ventosa, da sostener con facilit&agrave; la leg&shy;<lb/>gera macchina volante. </s>

<s>Ma nello stesso tempo anche la promove, e a spie&shy;<lb/>gar come ci&ograve; avvenga ricorre il nostro Autore <emph type="italics"/>De motu animalium<emph.end type="italics"/> all'azion <lb/>meccanica del cuneo, in figura del quale dispone il volante stesso le ali sol&shy;<lb/>levate sul dorso. </s>

<s>Consideriamo, egli dice, questo cuneo, che ha diretto il <lb/>taglio verso la coda, e la base rivolta alla parte del capo. </s>

<s>L'aria prima com&shy;<lb/>pressa, nello spiegar poi la sua elasticit&agrave;, fa forza su'due lati del cuneo <lb/>stesso, in che si sono disposte gi&agrave; l'ali, e le caccia innanzi, presso a poco <lb/>come il nocciolo di ciliegia compresso dalle dita. </s>

<s>Il medesimo effetto mecca&shy;<lb/>nico si produce quando le ali si abbassano, e ora il cuneo s'appunta sotto, <lb/>come s'appuntava dianzi sopra la coda. </s>

<s>&ldquo; Coacta igitur fuit Natura mirabili <lb/>solertia adhibere motum, qui eadem actione avem suspenderet, et eam hori&shy;<lb/>zontaliter impelleret. </s>

<s>Hae quidem praestitit percutiendo aerem subiectum <lb/>perpendiculariter ad horizontem, sed obliquis ictibus, quod sola pennarum <lb/>flexibilitate consequitur. </s>

<s>Nam flabella alarum in actu percussionis formam <lb/>cunei acquirunt, a cuius expressione necessario avis anterius promoveri de&shy;<lb/>bet &rdquo; (De motu anim., P. </s>

<s>I cit., pag. </s>

<s>311). </s></p><p type="main">

<s>In quel medesimo anno 1680, in cui in Roma appariva postuma alla <lb/>luce la prima Parte <emph type="italics"/>De motu animalium,<emph.end type="italics"/> il Coignard in Parigi pubblicava <lb/>i tre primi Tomi de'Saggi di Fisica di Claudio Perrault, nel terzo de'quali <lb/>&egrave; la <emph type="italics"/>Mechanique des animaux.<emph.end type="italics"/> Trattando ivi del volo dice l'Autore che il <lb/>meccanismo n'&egrave; maraviglioso, segnatamente per tre precauzioni prese in&shy;<lb/>torno ad esso dalla Natura, e che sono: &ldquo; de rendre les instrumens du vol <lb/>tout-ensemble et legers et fermes; de leur donner une puissances suffisante <lb/>de se remuer fort vite; et de les disposer de sorte que ce mouvement soit <lb/>capable d'elever l'animal en l'air &rdquo; (Oeuvres diverses de C. et P. Perrault, <lb/>a Leide 1721, pag. </s>

<s>377). </s></p><p type="main">

<s>Il primo effetto vien conseguito per via della particolare struttura delle <lb/>penne, che il Perrault minutamente descrive, e in ogni minima parte delle <lb/>quali s'ammira la gran sapienza della Natura per renderle, pi&ugrave; che sia pos&shy;<lb/>sibile, leggere. </s>

<s>&Egrave; pure il secondo effetto sapientemente conseguito con adat&shy;<lb/>tar le penne delle ali alle braccia dell'uccello messe in moto dai pi&ugrave; robu&shy;<lb/>sti muscoli di tutto il corpo. </s>

<s>L'ultimo intento &egrave; dalla stessa sapientissima <lb/>Natura facilmente ottenuto col far che le ali, nell'abbassarsi e nel solle&shy;<lb/>varsi, prendano una disposizione diversa. </s>

<s>&ldquo; Cette differente disposition, cos&igrave; <lb/>esprimesi lo stesso Perrault, consiste en deux choses: la premi&egrave;re est que <lb/>les plumes qui sont plates, lorsque l'aile s'abaisse, sont tourn&ecirc;es verticale&shy;<lb/>ment lorsqu'elles se levent, ce qui fait que l'air qu'elles coupent leur resiste <lb/>moins.... La seconde disposition, qui est to&ugrave;jours iointe &agrave; la premi&egrave;re, est <lb/>que les grandes plumes, qui sont au bout des ailes etant couch&eacute;es les unes <lb/>sur les autres, elles se d&eacute;plient et s'elargissent, lorsque l'oiseau frappe de <lb/>son aile, et se replient et se retrecissent, lorsqu'il la leve &rdquo; (ivi, pag. </s>

<s>380, 81). </s></p><p type="main">

<s>In queste osservazioni, nelle quali si compendia dall'Autore francese <pb xlink:href="020/01/1528.jpg" pagenum="403"/>tutta la meccanica del volo, possono i lettori trovare il criterio pi&ugrave; giusto <lb/>per giudicar della differenza che passa fra la <emph type="italics"/>Mechanique des animaux<emph.end type="italics"/> e <lb/>il trattato <emph type="italics"/>De motu animalium,<emph.end type="italics"/> in cui le leggerezze della Fisica son corro&shy;<lb/>borate dalla solidit&agrave; della Geometria. </s>

<s>&Egrave; il Borelli altres&igrave; superiore al Per&shy;<lb/>rault per non aver come lui neglette le tradizioni della scienza antica, e per <lb/>aver anzi mostrato come da esse derivi la nuova, ci&ograve; che dall'altra parte <lb/>molto conferisce a rendere la sua trattazione pi&ugrave; autorevole di quella del <lb/>Francese e tutto insieme pi&ugrave; piena. </s>

<s>Le prove di questa asserzione s'hanno <lb/>dal seguito della storia, dalla quale intanto apparisce come il Borelli nella <lb/>scienza sua propria e in quella de'suoi maestri ritrovasse, oltre alla gene&shy;<lb/>rale ragion meccanica del volo, le speciali ragioni di certe accidentalit&agrave;, in&shy;<lb/>torno a che avevano errato gli antichi. </s></p><p type="main">

<s>Aristotile, nel cap. </s>

<s>VIII <emph type="italics"/>De animalium incessu,<emph.end type="italics"/> aveva detto che la coda <lb/>negli uccelli serve a dirigere il volo, come il timone delle navi, e perci&ograve;, in <lb/>quelle specie in cui la coda non cos&igrave; facile s'inflette, come ne'pavoni per <lb/>esempio e ne'gallinacei, si vede il volo essere per lo pi&ugrave; debole e affaticato. <lb/></s>

<s>&ldquo; Uropygium autem volatili inest generi ad dirigendos volatus, ut navigiis <lb/>gubernacula, quod necesse est etiam in ipsa inflecti adhaesione. </s>

<s>Quamobrem <lb/>et illa, quae discretas alas habent, verum uropygium ad ei&ugrave;smodi usum est <lb/>ineptum, ut pavones existunt et gallinacei &rdquo; (Operum, T. VI cit., fol. </s>

<s>275). </s></p><p type="main">

<s>Accolte per lungo tempo queste sentenze come vere da chi in venerar <lb/>l'oracolo teneva gli occhi bassi, fu primo arditamente a sollevarli Ulisse <lb/>Aldovrandi, il quale non si poteva persuadere che dipendesse dalla coda il <lb/>debole volar de'pavoni, vedendo ch'essi, non solo l'inflettono con facilit&agrave;, <lb/>ma la riducono in forma di rota, ci&ograve; che non sanno fare gli uccelli stessi <lb/>anche pi&ugrave; veloci. </s>

<s>&ldquo; Pavones et gallinas inter aves enumerat quae parum <lb/>volatu valent, et causam illius rei assignat quod uropygium ineptum, hoc <lb/>est, non actum flecti obtinent. </s>

<s>Uropygium enim ad dirigendos volatus a Na&shy;<lb/>tura datum esse ait quemadmodum temones navigiis. </s>

<s>Verum cum Pavo cau&shy;<lb/>dam non tantum flectat, ut reliquae volucres, verum etiam in rotae modum <lb/>erigat, itaque Aristotiles veram nobis rationem brevitatis huiusce volatus <lb/>nondum omnino expresserat &rdquo; (Ornithologiae, T. II cit., pag. </s>

<s>9, 10). </s></p><p type="main">

<s>Osserva inoltre l'Aldovrandi non esser troppo conforme all'esperienza <lb/>de'fatti la dottrina che la coda serva a dirigere il corso agli uccelli, come <lb/>il timone alle navi, vedendosi le Ardee per esempio e le Cicogne scodate <lb/>andar velocissime per diritto senza mai balenare. </s>

<s>&ldquo; Quod vero uropygium <lb/>volatus ut temon navem dirigat, ut ille ait, id quoque in omni avium ge&shy;<lb/>nere locum non habet. </s>

<s>Siquidem multae, quales sunt Ardeae et Ciconiae, <lb/>cauda omnino destitutae, velocissimum tamen volatum exercent &rdquo; (ibid., <lb/>pag. </s>

<s>10). </s></p><p type="main">

<s>Ebbe la forza di questi argomenti a farsi sentire anche all'intelletto <lb/>dell'Acquapendente, il quale riconobbe la precipua causa delle varie dire&shy;<lb/>zioni del volo nel vario moto delle ali. </s>

<s>Battute ambedue insieme e soave&shy;<lb/>mente, quella direzione riesce orizzontale: concitate di pi&ugrave;, la macchina vo-<pb xlink:href="020/01/1529.jpg" pagenum="404"/>lante si solleva, e rilassate un poco si abbassa: volgesi a destra o a sinistra, <lb/>secondo che l'una delle stesse ali &egrave; battuta pi&ugrave; forte o pi&ugrave; veloce dell'altra. <lb/></s>

<s>&ldquo; In quibus sane figuris et positionibus, soggiunge per&ograve; l'Acquapendente, <lb/>caudam quoque operari non est inficiandum, quam verisimile est navis gu&shy;<lb/>bernaculum, ut dicit Aristotiles <emph type="italics"/>De anim. </s>

<s>incessu<emph.end type="italics"/> cap. </s>

<s>VIII, imitari &rdquo; (De <lb/>volatu, Op. </s>

<s>omnia cit., pag. </s>

<s>375). </s></p><p type="main">

<s>S'intende bene che questa aggiunta alla precipua causa direttrice del <lb/>volo fu dall'Acquapendente fatta solo in ossequio di Aristotile, ma Galileo <lb/>ne'suoi liberi pensieri conobbe che la coda e le ali hanno ufficii tutt'affatto <lb/>diversi, e che se queste, come diceva benissimo lo stesso Acquapendente, <lb/>servono a dirigere il volo da destra a sinistra, quella non pu&ograve; far altro che <lb/>volgerlo o in alto o in basso. </s>

<s>Di tali speculazioni di meccanica animale si <lb/>trova fra le opere galileiane la proposta, nella citata <emph type="italics"/>Selva di problemi varii,<emph.end type="italics"/><lb/>sotto questa forma: &ldquo; Del volar degli uccelli e qual sia l'uso delle penne <lb/>della coda in questa operazione, e com'essa coda non serva loro per timone, <lb/>e qual parte del corpo faccia l'ufficio di timone &rdquo; (Alb. </s>

<s>XIV, 319). </s></p><p type="main">

<s>Il Discorso, disteso o dettato da Galileo per dimostrar l'enunciato di <lb/>queste proposizioni, non si trova fra le opere di lui o stampate o mano&shy;<lb/>scritte, ma il Borelli ne raccolse il concetto, e ne tramand&ograve;, bench&egrave; sotto <lb/>altra forma, ai posteri la memoria nella I Parte <emph type="italics"/>De motu animalium.<emph.end type="italics"/> La <lb/>proposizione CLXXXXVIII si legge dall'Autore cos&igrave; formulata: &ldquo; Usus cau&shy;<lb/>dae avium est flectere cursus volantium sursum et deorsum, non vero ad <lb/>dexterum et sinistrum latus &rdquo; (editio cit., pag. </s>

<s>311). Del quale asserto son <lb/>principalmente le prove dedotte dall'esperienza, osservandosi che i colombi <lb/>per esempio o le rondini, quando vogliono piegare il volo o a destra o a <lb/>sinistra, non danno il minimo segno di mover la coda. </s></p><p type="main">

<s>Qual'&egrave; dunque lo strumento che fa da timone al volante? </s>

<s>E il Borelli <lb/>stesso risponde cos&igrave;, dimostrando la proposizione che Galileo, nelle sopra <lb/>riferite parole, in secondo luogo enunciava: &ldquo; Ablato temone navis, si remi <lb/>dextri lateris flectantur, aquam impellendo versus puppim, sive navis quie&shy;<lb/>scat sive directe moveatur, semper velocissime prora revolvetur versus si&shy;<lb/>nistrum latum. </s>

<s>Idipsum continget si remi dextri lateris celerius quam sini&shy;<lb/>stri retrorsum impellant.... Ergo eodem modo, dum avis in medio fluido <lb/>aeris innatat, volando aequilibrata in centro gravitatis eius, si sola dextra <lb/>ala deorsum sed oblique flectatur, aerem subiectum impellendo versus cau&shy;<lb/>dam, necessario ad instar navis mox memoratae promovebitur latus eius <lb/>dextrum, quiescente aut tardius moto sinistro latere. </s>

<s>Ex quo fit ut avis pars <lb/>anterior, circa centrum gravitatis eius revoluta, flectatur versus sinistrum <lb/>latus &rdquo; (ibid., pag. </s>

<s>314). </s></p><p type="main">

<s>Si disse esser queste borelliane proposizioni un'esplicazione dei concetti <lb/>di Galileo, di che, sebbene l'Autore non faccia ivi alcun cenno, abbiamo non <lb/>probabili congetture ma certissimo documento. </s>

<s>Nel trattato <emph type="italics"/>De vi percussio&shy;<lb/>nis<emph.end type="italics"/> aveva il Borell&igrave; stesso dimostrate alcune sue proposizioni relative agli <lb/>effetti, che produce il moto del timone sul moto della nave, pigliando in-<pb xlink:href="020/01/1530.jpg" pagenum="405"/>torno a ci&ograve; facile occasione di confutar le teorie meccaniche di Aristotile, il <lb/>quale riduceva il modo di operar del timone stesso al modo proprio d'ope&shy;<lb/>rare del vette. </s>

<s>I Peripatetici, al solito gelosi della dignit&agrave; del Maestro, si ri&shy;<lb/>sentirono, e il Borelli prese in una apposita scrittura a fare le sue difese. <lb/></s>

<s>&ldquo; Vengo finalmente, dice nell'ultima parte di quella, a mostrare in qual <lb/>maniera e per qual cagione pu&ograve; esser vero in qualche caso che il timone <lb/>acquisti impeto di urtare e di spingere attraverso la poppa della barca. </s>

<s>Que&shy;<lb/>sto dipende da una sottile sperienza del mio riverito Galileo, in proposito <lb/>di uno delli due timoni, che soglino adoperare i volatili, mentre scorrono <lb/>per l'aria, e per brevit&agrave; applicher&ograve; il suo discorso al caso nostro del timone <lb/>della nave. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Intendasi alla barca CB (fig. </s>

<s>10) essere applicato un vasto timone CD, <lb/><figure id="id.020.01.1530.1.jpg" xlink:href="020/01/1530/1.jpg"/></s></p><p type="caption">

<s>Figura 10.<lb/>situato nella stessa direzione DCB <lb/>dell'asse della barca CB, ed allora <lb/>sia tirata la barca dalla potenza M <lb/>(o sia spinta dal vento o dalla forza <lb/>de'remi) per la stessa direzione da <lb/>C verso B, tirandosi dietro il timo&shy;<lb/>ne CD. </s>

<s>Non ha dubbio che la barca <lb/>ed il timone, in virt&ugrave; di detta spinta, <lb/>averanno acquistato un determinato grado d'impeto, il quale a similitudine <lb/>de'proietti seguiter&agrave; a spingerli da C verso B, anco dopo essere abbando&shy;<lb/>nati dalla forza esterna, mentre dura e vige il detto moto impresso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Girisi il timone CD nel sito CE: &egrave; manifesto che il timone ripiegato <lb/>riterr&agrave; tuttavia l'impeto di muoversi da C verso E, col quale &egrave; necessario. </s>

<s><lb/>Questa spinta, aggiunta alla forza dell'urto dell'acqua stagnante sopra il ti&shy;<lb/>mone obliquo CE, far&agrave; che la poppa C della barca giri intorno al centro M, <lb/>verso la sinistra, con forza maggiore di quest'ultima sola, e tale eccesso sar&agrave; <lb/>molto sensibile in questo caso che il timone &egrave; di notabile ed eccessiva gran&shy;<lb/>dezza &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXII, c. </s>

<s>86, 87). </s></p><p type="main">

<s>Da questa applicazione, fatta dal Borelli al timone delle navi, s'intende <lb/>facilmente qual doves'essere il discorso di Galileo intorno all'ufficio della <lb/>coda in dirigere il volo degli uccelli, imperocch&egrave;, supposto che CB nella pre&shy;<lb/>cedente figura rappresenti l'asse del corpo dell'animale, e che per CD debba <lb/>intendersi la coda, si vede che, sollevata in CE, la resistenza dell'aria fa <lb/>nell'urto verticale piegare in basso l'animale stesso, come il timone faceva <lb/>dianzi, nell'urto orizzontale, piegar la nave da lato. </s>

<s>Cosicch&egrave; l'esperienza, <lb/>descritta dal Borelli nella proposizione CLXXXXVIII (ibid., pag. </s>

<s>313), &egrave; <lb/>sotto altre forme quella stessa che, ad esplicare il concetto galileiano, leg&shy;<lb/>gesi nel passo da noi sopra trascritto. </s></p><p type="main">

<s>Il trattato borelliano per&ograve; <emph type="italics"/>De volatu<emph.end type="italics"/> non si sta contento a discutere <lb/>quelle semplici questioni, che avea proposte Aristotile, e che dettero soggetto <lb/>agli studii dell'Acquapendente e di Galileo, n&egrave; si rimane in quelle astratte <lb/>generalit&agrave; di osservazioni, che fanno il merito principale della Meccanica del <pb xlink:href="020/01/1531.jpg" pagenum="406"/>Perrault, ma la statica e la dinamica vi son trattate in tutte le loro parti, <lb/>e con rigoroso ordine geometrico concluse dai loro principii. </s>

<s>Cosicch&egrave; in&shy;<lb/>torno all'azion de'muscoli nella stazione, e ne'tanti e svariati moti degli uc&shy;<lb/>c&egrave;lli, si dimostrano teoremi, che trovan facile applicazione a risolvere pro&shy;<lb/>blemi i pi&ugrave; nuovi e pi&ugrave; curiosi. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Le cose fin qui storicamente da noi discorse mostrano come i quadru&shy;<lb/>pedi differiscano dagli uccelli negli organi e negli atti della locomozione. </s>

<s>Ma <lb/>perch&egrave; sempre ogni abito esterno ha la sua ragione in qualche intimo prin&shy;<lb/>cipio, la differenza ch'&egrave; fra i piedi e le ali accenna a una pi&ugrave; intrinseca dif&shy;<lb/>ferenza nell'organismo e nelle sue principali funzioni. </s>

<s>Son, rispetto alla vita <lb/>vegetativa, quelle principali funzioni le appartenenti alla nutrizione e alla <lb/>respirazione, e rispetto alla vita di relazione con quelle, che concernono i <lb/>sensi, e dalle quali massimamente dipende la superiorit&agrave; del grado degli <lb/>animali. </s></p><p type="main">

<s>Nel fabbricare i varii organi, che dovevano servire a cos&igrave; fatte funzioni, <lb/>la Natura oper&ograve; con mano alquanto diversa ne'quadrupedi e negli uccelli, <lb/>presentando largo e fecondo campo a nuovi studii sperimentali, che non vo&shy;<lb/>gliono esser passati senza un qualche cenno, bench&egrave; brevissimo, in questa <lb/>Storia. </s></p><p type="main">

<s>Lo stomaco &egrave; il principale organo della digestione, e gli Anatomici e i <lb/>Fisiologi pi&ugrave; antichi ne intrapresero lo studio sugli uomini, sulle scimmie, <lb/>sui cani, e sopr'altri cos&igrave; fatti, ne'quali tutti si compone e funziona presso <lb/>a poco in simili modi. </s>

<s>Ma s'ebbero in certi altri animali a notar differenze <lb/>di tal momento, che la struttura dell'organo e la propria ragione degli usi <lb/>di lui dettero gran faccenda allo studio de'Naturalisti. </s>

<s>Si distinse questo <lb/>particolar genere di animali col nome di <emph type="italics"/>ruminanti,<emph.end type="italics"/> e Aristotile, nel cap. </s>

<s>XIV <lb/>del III libro <emph type="italics"/>De partibus animalium,<emph.end type="italics"/> not&ograve; che son generalmente tutti cor&shy;<lb/>nuti, e che mancano dei denti superiori. </s>

<s>Nonostante anche il Cammello, sog&shy;<lb/>giunge il Filosofo, rumina, bench&egrave; non sia fornito di corna, avendo, ci&ograve; che <lb/>pi&ugrave; importa, il ventre composto alla stessa maniera degli altri ruminanti. <lb/></s>

<s>&ldquo; Ruminat etiam Camelus more cornigerorum, quoniam ventres similes cor&shy;<lb/>nigeris habeat. </s>

<s>Habent haec singula plures ventres, ut ovis, capra, cervus et <lb/>similia, ut cum officium oris non satis in molendo cibo adhibetur propter <lb/>inopiam dentium, munus ventrium expleat dum alius ab alio cibum reci&shy;<lb/>pit, scilicet primus infectum, secundus aliquantulum confectum, tertius ple&shy;<lb/>nius, quartus perquam plene confectum. </s>

<s>Ita fit ut genus hoc animalium <lb/>receptacula cibi habeat plura, quibus nomina haec, aut indita sunt, aut in&shy;<lb/>dere licet: venter, arsineum, sive reticulum, omasum, abomasum &rdquo; (Ope&shy;<lb/>rum, T. VI cit., fol. </s>

<s>245). </s></p><pb xlink:href="020/01/1532.jpg" pagenum="407"/><p type="main">

<s>I nomi imposti da Aristotile son generalmente usati anc'oggid&igrave; dalla <lb/>scienza, la quale per verit&agrave; impar&ograve; poco pi&ugrave; oltre dal Maestro di coloro che <lb/>sanno, non avendo egli ivi nulla soggiunto n&egrave; del particolar modo, n&egrave; degli <lb/>organi pi&ugrave; speciali della ruminazione. </s>

<s>Anche Galeno, nel III cap. </s>

<s>del VI li&shy;<lb/>bro <emph type="italics"/>De anatomica administratione,<emph.end type="italics"/> lasciava digiuna di pi&ugrave; saperne la sua <lb/>scuola, infin presso al terminar del secolo XVI, quando Girolamo Mercuriale <lb/>usc&igrave; a tentar qualche cosa di nuovo. </s>

<s>Egli fece una osservazione, la quale, <lb/>sebbene a noi possa sembrare ovvia, ha nonostante tutta l'importanza e il <lb/>merito di una scoperta, e fu che il cibo ruminato non ritorna al gran ven&shy;<lb/>tre, come parevano insinuare i testi aristotelici e i galenici, ma nel reticolo, <lb/>per una via tutta sua propria e differente dall'altra. </s>

<s>&ldquo; Et ne quis dubitet <lb/>quomodo secunda vice in reticulum, non autem prima, labatur, sciendum est <lb/>foramen in gula esse satis angustum, quod pertingit in reticulum, et per <lb/>quod cibus prima vice, cum sit crassior et solidior, adhuc minime transire <lb/>potest; transit vero secunda vice, quando liquidus et mollis ita factus est, ut <lb/>iam transire queat &rdquo; (Variarum lectionum libri sex, Venetiis 1598, fol. </s>

<s>111). <lb/>Sarebbero da questo primo passo venuti facilmente aperti i sentieri a nuove <lb/>scoperte, se non fosse il Mercuriale stato per disavventura contradetto da <lb/>coloro, i quali si professavano amici di Aristotile e di Galeno pi&ugrave; che del vero. </s>

<s><lb/>Non ebbe da quello stuolo peripatetico coraggio di disertare questa volta <lb/>nemmeno Ulisse Aldovrandi, che, ne'Prolegomeni ai libri <emph type="italics"/>De quadrupedi&shy;<lb/>bus bisulcis,<emph.end type="italics"/> trattando de'ruminanti, cos&igrave; argomentava contro lo stesso Mer&shy;<lb/>curiale: &ldquo; Vel Aristotiles foramen, quod ait Mercurialis pertingere in reti&shy;<lb/>culum, non advertit, vel falsum est viam ab ore ad reticulum dari, quae non <lb/>prius ad primum ventrem pertingat. </s>

<s>Mihi eam viam minime necessariam <lb/>esse videtur &rdquo; (Bononiae 1621, editio secunda, pag. </s>

<s>2). </s></p><p type="main">

<s>La ragione di ci&ograve;, che ad esso Aldovrandi sembra probabilissima, &egrave; che <lb/>essendo il primo ventre irsuto, si trova perci&ograve; in bonissima condizione di <lb/>ritenere il cibo grossolano, ma ruminato ch'e'sia divien atto meglio a ri&shy;<lb/>ceverlo il reticolo levigato, ond'ei non &egrave; maraviglia se il bolo chimoso di&shy;<lb/>rettamente scende in questo, piuttosto che in quello. </s>

<s>&ldquo; Utcunque tamen sit, <lb/>poi ne conclude, diligens anatomici inspectio controversiam dirimet &rdquo; (ibid.). </s></p><p type="main">

<s>Venivano cos&igrave; fatte parole a dar sollecito impulso all'Acquapendente, <lb/>il quale per vero dire non seppe rispondere all'invito, n&egrave; secondo i desi&shy;<lb/>derii della scienza, n&egrave; secondo il bisogno. </s>

<s>Quell'Anatomia, dalla quale si <lb/>doveva dirimere la lite, fu lasciata da lui qualche passo pi&ugrave; indietro che non <lb/>dal Mercuriale, e la Fisiologia della ruminazione, che si legge nel suo nuovo <lb/>trattato, &egrave; un prolisso commentario ai concetti dell'Aldovrandi. </s>

<s>Chi vuol per&shy;<lb/>suadersene legga quella parte, che trovasi scritta sotto il titolo <emph type="italics"/>De varietate <lb/>ventriculorum,<emph.end type="italics"/> dove dall'Autore s'espongono tre ragioni del perch&egrave; il latte, <lb/>non solo si rinvenga di fatto, ma debba necessariamente rinvenirsi nell'abo&shy;<lb/>maso e no nell'omaso, come diceva Aristotile. </s>

<s>Chi volesse poi risparmiarsi <lb/>la fatica, e vedere in poche parole conclusa la sostanza del lungo discorso, <lb/>ecco in proposito come si esprime l'Autore stesso: &ldquo; Cum igitur cibus ru-<pb xlink:href="020/01/1533.jpg" pagenum="408"/>minatus vel mansus, beneficio oris, suam asperitatem et duritiam aliquo <lb/>modo deposuerit, secundus quoque ventriculus in ruminantibus minus asper <lb/>sit quam primus, utique probabile est credere cibum mansum et rumina&shy;<lb/>tum potius in secundum quam in primum, propter suam similitudinem et <lb/>convenientiam descendere et ingredi, quemadmodum in lactantibus lac, non <lb/>in primo nec in secundo nec tertio, sed in quarto trahi et recipi videmus &rdquo; <lb/>(Opera omnia cit., pag. </s>

<s>137). </s></p><p type="main">

<s>Pochi anni dopo la pubblicazione di questo trattato dell'Acquapendente, <lb/>fatta in Padova nel 1618, Giovanni Faber, venuto di Norimberga a farsi in <lb/>Roma d'abito e di spiriti Italiano, si dette con pi&ugrave; diligente amore allo stu&shy;<lb/>dio della ruminazione, parendogli soggetto non indegno n&egrave; di medico n&egrave; di <lb/>filosofo. </s>

<s>Secondando l'istituto di que'Lincei, fra'quali era stato chiamato dal <lb/>principe della nuova Accademia, Federigo Cesi, e sentendo che a dirimer le <lb/>liti insorte fra'suoi predecessori l'Aldovrandi invocava l'autorit&agrave; degli Ana&shy;<lb/>tomici, attese ad apparecchiarsi le vie coll'esperienze e colle anatomiche <lb/>dissezioni. </s>

<s>Che si raccolga il latte non altrove che nell'abomaso lo riconobbe <lb/>come un fatto s&igrave; ovvio che, tutt'altro che aver bisogno d'esser provato co'tre <lb/>argomenti speculativi dell'Acquapendente, si maraviglia come fosse da Ari&shy;<lb/>stotile ignorato quel che sapevasi benissimo &ldquo; a quovis e trivio pastore, vel <lb/>a quavis anicula caseorum fabra &rdquo; (Aliorum novae Hispaniae animalium <lb/>Nardi Antonii Recchi imagines et nomina, Johannis Fabri Lyncei exposi&shy;<lb/>tione, Romae 1651, pag. </s>

<s>623). Scopr&igrave; inoltre che il cibo ruminato non va al <lb/>secondo ventricolo, come dietro il Mercuriale avevano creduto l'Aldovrandi <lb/>e l'Acquapendente, ma s&igrave; al terzo, di dove all'ultimo scende nel quarto. </s></p><p type="main">

<s>L'esperienze poi, congiunte colle anatomiche dissezioni, insegnarono al <lb/>Faber una cosa nuova, dalla quale fu poi condotto a scoprir le segrete vie, <lb/>per cui il chilo, scansando i due primi, va direttamente a infondersi ne'due <lb/>ultimi ventricoli. </s>

<s>&ldquo; Didici enim, ex frequenti ventrium sive stomachorum <lb/>dissectione, tam vitulos quam haedos aliquando solo lacte frui ab uberibus <lb/>maternis facto, aliquando etiam, si foeni et herbarum copia detur, et haec <lb/>non illibenter carpere, atque ita, partim cibo tenerrimo, lacte scilicet quod <lb/>non ruminant, partim etiam duriore alimento, quod remandunt, vesci, et hoc <lb/>quidem in primum saeculum, illud in quartum ablegare, nullo itineris im&shy;<lb/>pedimento facto &rdquo; (ibid., pag. </s>

<s>625). </s></p><p type="main">

<s>Di qui sent&igrave; il Faber frugarsi a una pi&ugrave; viva curiosit&agrave; di sapere in che <lb/>modo passando, come si credeva, per una medesima via le due diverse qua&shy;<lb/>lit&agrave; di cibo, riuscissero pure <emph type="italics"/>nullo itineris impedimento facto,<emph.end type="italics"/> a un termine <lb/>tanto diverso. </s>

<s>Quella specie di simpatia, ammessa dall'Aldovrandi e dal&shy;<lb/>l'Acquapendente, fra l'asprezza del gran ventricolo e la rigidezza del primo <lb/>cibo ingollato, come fra il secondo ventricolo di levigate interne pareti e il <lb/>pi&ugrave; morbido cibo gi&agrave; ruminato; al Linceo, severo nell'osservanza de'canoni <lb/>sperimentali, non andava punto a genio. </s>

<s>Sentiva che gli si preparava pros&shy;<lb/>sima una scoperta, e aiutato dal Microscopio torn&ograve; all'autopsia. </s>

<s>Ecco final&shy;<lb/>mente svelato il mistero. </s>

<s>Quell'unica via dell'esofago ora mette a un ter-<pb xlink:href="020/01/1534.jpg" pagenum="409"/>mine ora a un altro, perch&egrave; ora si trova pi&ugrave; corta e ora invece diventa pi&ugrave; <lb/>lunga; succedendo ci&ograve; per una maravigliosa semplicit&agrave; di artificio, varia&shy;<lb/>mente governato o dalla crassizie o dalla mollezza del cibo. </s>

<s>Sarebbe forse la <lb/>gentile invenzione, fra gli atti de'Lincei rimasta dimenticata, se nell'esporre <lb/>le immagini e i nomi di altri animali della Nuova Spagna, non scoperti dal&shy;<lb/>l'Hernandez e non descritti dal Recchi, non si fosse al Faber porta solenne <lb/>occasione di trattarne, a proposito di quel terribile ruminante appellato da <lb/>lui stesso col nome di <emph type="italics"/>Toro messicano.<emph.end type="italics"/></s></p><p type="main">

<s>Ivi, dop'avere diligentemente esaminate le dottrine de'suoi predeces&shy;<lb/>sori, e dimostrato in che modo e perch&egrave; riuscissero difettose, passa cos&igrave; a <lb/>descrivere, il nostro acuto Linceo, quel nuovamente scoperto artificio indu&shy;<lb/>strioso della Natura. </s>

<s>&ldquo; In fine oesophagi, quem Itali <emph type="italics"/>il grumale<emph.end type="italics"/> vocant, hoc <lb/>est in superiore stomachi orificio, duo oblonga, et teretia veluti labia, mea&shy;<lb/>tum illum obserant clauduntque, ut si cibus crassus densusque foenum, sar&shy;<lb/>menta ac paleae aut similia semicommansa descendunt, haec labia carnosa <lb/>nimirum et membranosa facile cedant, et aditum graviori ac ponderosiori <lb/>cibo in saccum maiorem, primum nempe ventrem, permittant. </s>

<s>Ubi vero lac <lb/>ipsum liquidum delabitur, conniventia reperit haec oblonga corpora, quare <lb/>super hisce, tanquam super canali quodam declivi, currens, ad tertium im&shy;<lb/>mediate ventrem labitur, et ex hoc ad quantum &rdquo; (ibid., pag. </s>

<s>622, 23). </s></p><p type="main">

<s>Scritte queste cose verso il 1625, e circa venticinqu'anni dopo pubblicate, <lb/>si crederebbe che i Naturalisti avessero dovuto plaudire al Faber, e di una <lb/>insegnata verit&agrave;, per tanti secoli rimasta a tutti occulta, riconoscerlo autore. </s>

<s><lb/>Eppure, presso al finir di quel secolo, Giovan Currado Peyer trattava degli <lb/>organi e delle funzioni della ruminazione come se fosse venuto a instituire <lb/>una scienza nuova, alla quale dava lo specioso titolo di <emph type="italics"/>Merycologia.<emph.end type="italics"/> Com&shy;<lb/>memorando nel primo capitolo dell'Opera tutti coloro, che lo avevano pre&shy;<lb/>ceduto in quello studio, non lascia indietro i nomi del Mercuriale, dell'Al&shy;<lb/>dovrandi e dell'Acquapendente, ma si tace affatto del Faber, e come se la <lb/>scoperta della duplice via esofogea, e specialmente di quella, dallo stesso ar&shy;<lb/>guto inventore detta <emph type="italics"/>via lattea,<emph.end type="italics"/> fossero cose di nessuna novit&agrave; e importanza, <lb/>Gian Giacomo Wepfer non riconosceva altri Naturalisti precursori del Peyer <lb/>che il Gesner e l'Aldovrandi. </s>

<s>&ldquo; Quis enim horum, egli dice, accuratam ven&shy;<lb/>triculorum descriptionem nobis tradidit, aut modum ruminationis explicuit? </s>

<s>&rdquo; <lb/>(Merycologia, Basileae 1685, Appendix, pag. </s>

<s>273). E avrebbe avuto senza <lb/>dubbio ragione il Wepfer, quando a'due scrittori da lui citati non fosse suc&shy;<lb/>ceduto il Faber, di cui si tace anche qui il nome. </s>

<s>E perch&egrave; in uomini cos&igrave; <lb/>eruditi della storia scientifica non sembra che si possa ammettere ignoranza <lb/>della celebre opera dell'Hernandez, e de'famosi Lincei che la illustrarono, <lb/>la curiosit&agrave; ci spinge a indagare il motivo, per cui la scienza che largamente <lb/>s'attinge dalla descrizione del Toro messicano sia stata dai nuovi cultori <lb/>della Mericologia tenuta in s&igrave; poco pregio. </s></p><p type="main">

<s>Il Peyer lo dice chiaro: &ldquo; Neque Faber ipse rem exhausit, confessus <lb/>se quae ad Anatomen attinent, potius quam illa quae philosophica obscu-<pb xlink:href="020/01/1535.jpg" pagenum="410"/>raque ratione erui possent, indagaturum &rdquo; (ibid., pag. </s>

<s>200). Ma insomma <lb/>si riconosce in questo giudizio il merito anatomico del nostro Linceo, ond'&egrave; <lb/>che non s'intende come non fosse creduto degno d'essere annoverato nem&shy;<lb/>meno fra gli scrittori d'infimo pregio, che trattarono della ruminazione. </s></p><p type="main">

<s>&ldquo; Ego denique, si soggiunge alle parole sopra citate, argumentum utro&shy;<lb/>que modo pertractare allaboro &rdquo; cio&egrave; coll'anatomia e colla fisiologia: cosic&shy;<lb/>ch&egrave; il Peyer tacitamente confessa di non aver fatto altro che compier l'opera <lb/>e perfezionare la scoperta del Faber, il quale, dall'altra parte, non trascur&ograve; <lb/>del tutto la fisiologia, come si potr&agrave; giudicar dalle cose di lui sopra nar&shy;<lb/>rate, messe a riscontro con questi brevi cenni, che siam per dare dell'opera <lb/>peieriana. </s></p><p type="main">

<s>Ne'capitoli II, III, IV e V si descrivono i ventricoli, incominciando dal <lb/>primo infino al quarto, e una buona e diligente anatomia sornuota felice&shy;<lb/>mente a un pelago di parole erudite. </s>

<s>Passando a trattar nel seguente capi&shy;<lb/>tolo VII dell'esofago nota che quel canale, chiamato dal Faber via lattea, &egrave; <lb/>improprio riguardarlo come una continuazione dello stesso esofago &ldquo; cum <lb/>reapse oriatur ex ipsa reticuli substantia, attollentibus se fibris et membra&shy;<lb/>nis utrinque replicantibus, labrorum similitudine &rdquo; (ibid., pag. </s>

<s>168). </s></p><p type="main">

<s>Questi si pu&ograve; dire che sieno i tratti principali, per cui l'anatomia del <lb/>Peyer s'avvantaggia sopra quella del Faber. </s>

<s>Quanto alla Fisiologia ella si <lb/>riduce tutta nello spieg&agrave;re in che modo sia preso il cibo dal gran ventre e <lb/>dal reticolo, e come sia fatto risalire su in fino alla bocca, per esservi ru&shy;<lb/>minato. </s>

<s>Il Faber &egrave; vero si content&ograve; di ammettere il fatto senza nemmen <lb/>provarsi di renderne qualche ragione: &ldquo; quocumque id demum modo fiat, <lb/>haud disputo &rdquo; ci&ograve; che porse al Peyer il principale argomento per asserire <lb/>che l'opera faberiana mancava di Filosofia, la quale dall'altra parte, par <lb/>ch'egli dica, era assai naturale. </s>

<s>Imperocch&egrave; la difficolt&agrave;, che trovasi nello <lb/>spiegare in che modo il cibo risalga dal ventre alla bocca nella ruminazione, <lb/>&egrave; quella medesima che trovasi nello spiegare in che modo il cibo stesso <lb/>salga dalla bocca al ventre, quando l'animale pasce l'erbe per terra col cello <lb/>inclinato. </s>

<s>Ci&ograve; non significa altro, dice l'Autore della Filosofia mericologica, <lb/>se non che il moto del bolo lungo il canale esofageo &egrave; indipendente dalla <lb/>naturale propensione de'gravi, intantoch&egrave; si rassomiglierebbe piuttosto a <lb/>qualche moto violento, a cui &egrave; studio del Fisiologo il ricercare d'onde venga <lb/>l'impulso. </s>

<s>Il Peyer lo riconobbe nelle fibre muscolari, di che l'esofago stesso <lb/>&egrave; cos&igrave; artificiosamente intessuto, le quali fibre contraendosi diversamente ser&shy;<lb/>vono a produrre due moti, &ldquo; quorum altero pabulum ad ventrem impelli&shy;<lb/>tur, altero in os repellitur, singulari ruminationis privilegio &rdquo; (ibid., pag. </s>

<s>164). </s></p><p type="main">

<s>A che altro uso infatti, argomenta l'Autore, potrebbero essere state di&shy;<lb/>sposte in quel modo le fibre? </s>

<s>Se dovesse l'esofago servir da semplice canale <lb/>sarebbero state sufficienti le membrane, dalle quali egli &egrave; involto, ma dee <lb/>di pi&ugrave; spingere e risospingere il bolo, e a ci&ograve; appunto servono i muscoli. <lb/></s>

<s>&ldquo; Meatum itaque dant membranae, potior autem pars musculosa motioni <lb/>subservit. </s>

<s>Quamprimum enim aliquid ex ore aut ventre in gulam immitti-<pb xlink:href="020/01/1536.jpg" pagenum="411"/>tur, fibrae, a re ingrediente dilatatae, allectis spiritibus animalibus, per or&shy;<lb/>dinem naturae se protinus constringunt fortiter, pastumque promovent ocys&shy;<lb/>sime, et sursum quidem, si motus infra a ventre incipiat, quod ruminatione <lb/>contingit et vomitu; deorsum vero, si supra ab ore ducatur exordium &rdquo; (ibid., <lb/>pag. </s>

<s>166). </s></p><p type="main">

<s>Questo moto insomma, prodotto dalle fibre muscolari nel canale esofa&shy;<lb/>geo, sarebbe simile a quello vermicolare degl'intestini o alle contrazioni pe&shy;<lb/>ristaltiche delle Tube falloppiane, per cui possono, bench'elle sieno si an&shy;<lb/>guste, facilmente tradurre i germi dagli ovarii nella matrice. </s>

<s>Ma come gli <lb/>avversi all'Ovarismo non concedevano punto volentieri allo Stenone, al Van&shy;<lb/>Horne e al Graaf queste peristaltie negli ovidutti; cos&igrave; gli avversi alla nuova <lb/>Mericologia non le consentivano all'Autore nella gola dei ruminanti, e ri&shy;<lb/>correvano piuttosto a invocar l'aiuto di quel semicanale, chiamato dal Faber, <lb/>come sopra udimmo, <emph type="italics"/>via lattea,<emph.end type="italics"/> perch&egrave; ordinato a condurre il latte: e per&shy;<lb/>ch'&egrave; altres&igrave; disposto a infondere ne'ventricoli le bevande, appellato dal Peyer <lb/>col nome di <emph type="italics"/>acquedotto.<emph.end type="italics"/> Dicevano costoro, appropriandosi un pensiero ch'era <lb/>allora allora venuto a suggerire ai Naturalisti un anonimo Autore della Fi&shy;<lb/>losofia vecchia e nuova, &ldquo; tubum illum utroque margine, instar manus <lb/>cuiusdam, concessum videri a Natura, quo occluso, bolos stringi et sursum <lb/>deferri. </s>

<s>&rdquo; </s></p><p type="main">

<s>Ma rispondeva esso Peyer, dop'avere a pag. </s>

<s>167 trascritte queste pa&shy;<lb/>role, contenervisi idee pi&ugrave; speciose che meritevoli di fede, perch&egrave; la via lat&shy;<lb/>tea o l'acquidutto non &egrave; riposto nel primo ventre, ma nel secondo, in cui <lb/>l'esperienza c'insegna non ritrovarsi mai il cibo cos&igrave; male confezionato, da <lb/>aver bisogno d'una nuova masticazione. </s>

<s>Soggiunge poi a questa altre cos&igrave; <lb/>fatte ragioni: &ldquo; Canalis porro angustiae proportione non respondent ascen&shy;<lb/>dentium bolorum magnitudini, neque labra eius adeo sunt ductilia, ut re&shy;<lb/>pente admodum expandi et captare cibum possint &rdquo; (ibid., pag. </s>

<s>167). </s></p><p type="main">

<s>Eppure i moderni, ritornando a fare in proposito esperienze pi&ugrave; dili&shy;<lb/>genti, hanno approvato il pensiero dell'anonimo Autore della Filosofia, e <lb/>hanno insegnato che il pasto dentro il reticolo vien veramente preso dai <lb/>margini contrattili dell'acquidotto, i quali palpano con moti simili a quelli <lb/>delle labbra nella stessa bocca, e dagli avvolgimenti di esse labbra, quasi <lb/>aggomitolato, per quel moto peristaltico peierrano, si riconduce il bolo su <lb/>dal ventre alla gola. </s>

<s>Notabile che alcuni francesi autori di Zoologia attri&shy;<lb/>buiscano a un loro illustre Fisiologo del secolo XVIII questa teorica della <lb/>ruminazione, lusingandosi di aver dati gli sperimenti di lui per nuovi e da <lb/>nessuno prima tentati, mentre discendono, com'abbiamo veduto, dalle lon&shy;<lb/>tane tradizioni della scienza, specialmente italiana. </s></p><p type="main">

<s>Gli organi e le funzioni della digestione dei quadrupedi, che non appar&shy;<lb/>tengono all'ordine dei ruminanti, non porgono altro particolar soggetto di <lb/>discorso ai limitati intenti della nostra Storia, e perci&ograve;, passando ai pennuti, <lb/>rammemoriamo ai nostri lettori come incominciassero da essi gli studii dei <lb/>Fisiologi, fra'quali l'Acquapendente ci si presenta de'primi. </s>

<s>Nel trattatello <pb xlink:href="020/01/1537.jpg" pagenum="412"/>di lui altre volte citato <emph type="italics"/>De varietate ventriculorum,<emph.end type="italics"/> dop'aver detto dell'in&shy;<lb/>gluvie, ch'&egrave; secondo Aristotile il prontuario dell'alimento, passa a descri&shy;<lb/>vere il secondo ventricolo &ldquo; exiguus, carnosus ac mollis, minumeque pon&shy;<lb/>derosus &rdquo; e l'ufficio proprio del quale &egrave; &ldquo; ad mollia potius concoquenda <lb/>cibaria &rdquo; (Op. </s>

<s>omnia cit., pag. </s>

<s>131). Gli soggiace immediatamente il ventri&shy;<lb/>colo terzo, molto maggiore degli altri due, carnoso all'esterno e rubicondo <lb/>come laveggio, che per meglio concocere il cibo sia tutto intorno circondato <lb/>dal fuoco. </s>

<s>Il qual fuoco &egrave; a lui tanto pi&ugrave; necessario, in quanto che nella <lb/>sua interna concavit&agrave; &egrave; freddo e duro &ldquo; et quadatenus aspera membrana <lb/>obducitur, ad consimiles cibos excipiendos accommodata. </s>

<s>Nam et lapilli non <lb/>pauci in hoc quoque ventre comperiuntur, quos conficere et chylum eva&shy;<lb/>dere, ut in struthio camelo ferrum, consentaneum est &rdquo; (ibid.). </s></p><p type="main">

<s>Ebbe di qui principio fra'Naturalisti una questione che, durata due se&shy;<lb/>coli, fu risoluta finalmente, come siam per narrare, dall'esperienze dello <lb/>Spallanzani. </s>

<s>Si credeva assai probabile dall'Acquapendente che le pietruzze <lb/>ingollate dagli uccelli si trasformassero in chilo, perch&egrave; le riconosceva come <lb/>durabilissimo viatico alle lunghe pellegrinazioni intraprese da alcuni di essi, <lb/>come per esempio dalle Gru e dalle Cicogne, ma l'Harvey nel suo senno <lb/>pens&ograve; che quello era un certo pane pi&ugrave; che biscotto. </s>

<s>Non potendo dall'altra <lb/>parte negar l'esistenza di cotesti calcoli, ne'ventrigli anserini, disse esser <lb/>loro ufficio proprio di servir come da macine per triturare il cibo, supplendo <lb/>opportunamente al naturale difetto dei denti. </s>

<s>&ldquo; Ut hoc modo, ceu duobus <lb/>lapidibus molaribus, binis invicem cardinibus colligatis, molere cibaria et <lb/>pinsere possint, vicemque dentium molarium, quibus carent, calculi sup&shy;<lb/>pleant &rdquo; (De generat. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>27). </s></p><p type="main">

<s>La nuova ingegnosa ipotesi tanto parve pi&ugrave; ragionevole della prima, <lb/>che i migliori ingegni plaudirono all'Harvey, anche fra gli stessi nostri Ita&shy;<lb/>liani, e Tommaso Cornelio dimostrava la potenza meccanica del ventricolo <lb/>de'pennuti con questa bella esperienza. </s>

<s>Prendeva delle monete o di rame <lb/>o di argento, le accartocciava, e poi le faceva ingollare a un gallo d'India. </s>

<s><lb/>Estratte dopo una diecina di giorni, &ldquo; erat exterior, seu convexa illorum <lb/>superficies, insigniter attrita, at interior tamen seu concava omnimo integra <lb/>permanserat. </s>

<s>Unde palam est istiusmodi corpora in alitum ventriculis non <lb/>liquescere aut dissolvi, sed collisa potius exteri atque comminui &rdquo; (Pro&shy;<lb/>gymnasmata, Neapoli 1688, De nutricatione, pag. </s>

<s>208). </s></p><p type="main">

<s>Anche gli Accademici del Cimento sperimentando intorno alla dige&shy;<lb/>stione delle anatre, e dicendo di avere osservato che sottosopra &ldquo; quelle <lb/>macinano meglio delle altre, che hanno ne'loro ventrigli maggior copia di <lb/>sassolini inghiottiti &rdquo; (Saggi di natur. </s>

<s>esp., Firenze 1841, pag. </s>

<s>175); mo&shy;<lb/>strarono di approvar l'ipotesi arveiana, e anzi ci&ograve; s'asserisce come cosa certa <lb/>dal Redi, autorevole interpetre dei loro sensi. </s>

<s>Essendoglisi nelle <emph type="italics"/>Esperienze <lb/>intorno a cose naturali<emph.end type="italics"/> presentata l'occasione di commentare un passo di <lb/>Eliano, forse aveva, egli dice, conosciuto il greco Scrittore &ldquo; che gli uccelli <lb/>mangiano le pietruzze, perch'elle servon loro per far ben digerire il cibo, <pb xlink:href="020/01/1538.jpg" pagenum="413"/>il che poi &egrave; stato detto pi&ugrave; chiaramente da'moderni, e spezialmente da'no&shy;<lb/>stri Accademici del Cimento, da Guglielmo Arveo, e da Tommaso Cornelio, <lb/>i quali tengono che la digestione nello stomaco degli uccelli si faccia in gran <lb/>parte ovvero si aiuti per mezzo della triturazione, e che quelle pietruzze <lb/>sieno come tante macinette raggirate da quei due forti e robusti muscoli, <lb/>de'quali &egrave; composto il ventriglio &rdquo; (Opere, T. II, Napoli 1741, pag. </s>

<s>47). </s></p><p type="main">

<s>Dieci anni da poi che il Redi aveva cos&igrave; storicamente riferite queste <lb/>opinioni altrui, intorno all'uso delle pietruzze ne'ventricoli de'pennuti, senza <lb/>per&ograve; pronunziare ancora in proposito nessun suo giudizio; usc&igrave; alla luce la <lb/>seconda parte <emph type="italics"/>De motu animalium,<emph.end type="italics"/> dove nel cap. </s>

<s>XIV si tratta giusto della <lb/>nutrizione. </s>

<s>Parve anche il Borelli secondare in principio il parer dell'Har&shy;<lb/>vey, confortato da lui colle teorie meccaniche, come l'aveva il Cornelio con&shy;<lb/>fermato prima colle semplici esperienze. </s>

<s>Perciocch&egrave;, egli dice nella CXCI pro&shy;<lb/>posizione, l'azione del ventricolo carnoso &egrave; simile a quella dei denti, &ldquo; igitur <lb/>coniiciere possumus vires motivas eorum aequales esse. </s>

<s>Verum ostensa fuit <lb/>vis musculorum humanam mandibulam stringentium maior potentia ponde&shy;<lb/>ris librarum 1350. Igitur vis ventriculi galli indici non est minor potentia <lb/>librarum 1350 &rdquo; (Romae 1681, pag. </s>

<s>398). </s></p><p type="main">

<s>Riflettendo poi il Borelli che una tal misurata potenza era per s&egrave; me&shy;<lb/>desima sufficiente a stritolare anche le pietre pi&ugrave; dure, e osservando inoltre <lb/>che alcuni testacei marini, i quali vivono continuamente sotto l'arena, non <lb/>possono d'altronde ricavare il necessario nutrimento che pur da essa, in&shy;<lb/>cominci&ograve; a persuadersi che l'opinione dell'Acquapendente non dovess'es&shy;<lb/>ser poi cos&igrave; strana, come a principio pareva. </s>

<s>Intitolava perci&ograve; la proposi&shy;<lb/>zione CXCIV: &ldquo; Suspicari licet animalia pennata in sui nutrimentum assu&shy;<lb/>mere lapillos quos tam avide vorant &rdquo; (ibid., pag. </s>

<s>401). </s></p><p type="main">

<s>Si fondava quel sospetto sopra l'osservazione dei cigni trovati sempre <lb/>nell'aperto ventre ripieni di copiosissima arena, senz'alcun vestigio di so&shy;<lb/>stanze o animali o vegetali, da qualche sottilissimo filo di erba in fuori, e <lb/>si fondava altres&igrave; sopra buone ragioni, imperocch&egrave; se si vuole, argomentava <lb/>il Borelli, che i sassolini non servano di cibo, ma di strumenti da macinare <lb/>il cibo, perch&egrave; gl'ingollano cos&igrave; avidamente le galline domestiche e i co&shy;<lb/>lombi nutriti sempre di morbido pane e di farina? </s>

<s>&ldquo; laborarent frustra, <lb/>contra naturae indigentiam, fere toto die ore prono lapillos colligendo, sicuti <lb/>nos non utimur dentibus quando pultam comedimus &rdquo; (ibid., pag. </s>

<s>403). Ne <lb/>conclude perci&ograve; che i gallinacei sciolgono nel ventricolo le pietruzze, per <lb/>servirsi del loro succo ad alimentar certe parti del corpo, che tengono del <lb/>lapideo e del lamellare, come sarebbero le ossa e le penne. </s></p><p type="main">

<s>La curiosit&agrave; del soggetto e la grande autorit&agrave; del Maestro fecero si che <lb/>il Redi si risolvesse di lasciare i libri e gli Autori, nelle sue prime <emph type="italics"/>Espe&shy;<lb/>rienze intorno a cose naturali<emph.end type="italics"/> citati, per consultar piuttosto la Natura, dalla <lb/>quale fu accertato che quelle pietruzzole inghiottite dagli uccelli non confe&shy;<lb/>riscono niente alla nutrizione. </s>

<s>&ldquo; Imperocch&egrave;, egli scrive nel trattato <emph type="italics"/>Degli <lb/>animali viventi negli animali viventi,<emph.end type="italics"/> in tempo di verno rinchiusi in una <pb xlink:href="020/01/1539.jpg" pagenum="414"/>gabbia un cappone, senza dargli mai n&egrave; da mangiare n&egrave; da bere, e passati <lb/>che furono cinque giorni interi si mor&igrave;, siccome altri capponi, tenuti pur <lb/>senza mangiare e senza bere, non vissero pi&ugrave; che sette, otto e nove giorni. </s>

<s><lb/>Eppure, aperti i loro ventrigli, vi trovai in tutti una considerabile quantit&agrave; <lb/>di pietruzzole, che avevano inghiottite prima che fossero rinchiusi, ed in <lb/>tempo di cos&igrave; gran bisogno non si erano consumate n&egrave; passate in nutri&shy;<lb/>mento &rdquo; (Opere, T. I, P. II, Napoli 1741, pag. </s>

<s>51). </s></p><p type="main">

<s>Queste e altre simili esperienze, che prosegue il Redi a descrivere nel <lb/>luogo citato, erano decisive contro la proposizion del Borelli, la quale poteva <lb/>per&ograve; salvarsi con dire che non aveva inteso l'Autore di dimostrare essere <lb/>il succo lapideo ristoratore di ogni parte del corpo, ma di sole le ossa e le <lb/>penne. </s>

<s>Non fa perci&ograve; meraviglia che in dubbio si rimanessero tuttavia molti, <lb/>e fra questi anche il Vallisnieri, il quale, giudicando che il ferro e altri corpi <lb/>pi&ugrave; duri nello stomaco degli struzzi non siano meccanicamente consumati, <lb/>ma che quasi da un'acqua forte prodigiosa vengano assaliti, &ldquo; se poi, dice, <lb/>cavino nutrimento da quelli &egrave; difficile da determinarsi, bench&egrave; il chiarissimo <lb/>G. </s>

<s>Alfonso Borelli affermi alcuni animali potersi forse nutrire di sola terra <lb/>arenosa, lo che certamente &egrave; verissimo de'lombrichi terrestri. </s>

<s>Ma se ci&ograve; si <lb/>possa dire ancor degli uccelli, io non ardirei di francamente asserirlo, tanto <lb/>pi&ugrave; che, per esperienze fatte dal Redi, morirono di fame alcuni capponi posti <lb/>in gabbia con acqua sola e pietruzze &rdquo; (Anatomia dello Struzzo, nel T. </s>

<s>I <lb/>delle Opere, Venezia 1733, pag. </s>

<s>243). </s></p><p type="main">

<s>Nonostante, sempre meglio chiarendosi le idee de Fisiologi intorno alla <lb/>nutrizione, la quale viene ad ogni parte dal sangue, continuamente risto&shy;<lb/>rato dal chilo, furono l'esperienze del Redi riconosciute come dimostrative <lb/>delle false opinioni del Borelli e dell'Acquapendente. </s>

<s>Non potendosi dall'al&shy;<lb/>tra parte intendere a qual naturale uso si trovassero le pietruzze ingeste nei <lb/>ventrigli anserini, si torn&ograve; ad ammettere coll'Harvey che facessero ivi l'uf&shy;<lb/>ficio di mole, opportunamente supplendo al difetto dei denti. </s></p><p type="main">

<s>Erano in tale stato le cose, quando lo Spallanzani si assicur&ograve; per espe&shy;<lb/>rienza non esser vera nemmeno l'ipotesi arveiana, unica, dopo tante vicende, <lb/>rimasta vittoriosa. </s>

<s>&ldquo; Alcuni piccioni terragnoli allora usciti dall'uovo, cos&igrave; <lb/>scrive nelle sue <emph type="italics"/>Dissertazioni di fisica animale,<emph.end type="italics"/> non avevan come doveva <lb/>succedere pietruzze di sorta, e parecchi di essi mi presi io la pena di cu&shy;<lb/>stodirli, tenendoli in sito caldo per tutto il tempo che erano ancora svestiti <lb/>di penne, e alimentandoli finch&egrave; atti fossero a mangiare da s&egrave;. </s>

<s>In seguito <lb/>li racchiusi in gabbia, apprestando loro il cibo seguente. </s>

<s>Da principio fu vec&shy;<lb/>cia macerata nell'acqua, indi veccia asciutta e dura che fu poi l'alimento, <lb/>che proseguii sempre a somministrare ad essi. </s>

<s>Solamente, trascorso un mese <lb/>da che mangiavan da s&egrave;, io cominciai a framischiare al cibo di tanto in tanto <lb/>de'corpi duri, come alcuni rari tubetti di latta, qualche vuota sferetta di <lb/>vetro, varie piccole schegge di vetro altres&igrave;, e a taluno de'colombi non feci <lb/>prendere che uno di questi corpi. </s>

<s>Dopo due giorni furono tratti a morte. </s>

<s><lb/>Nessuno de'colombi aveva nel ventriglio la minima pietruzza, eppure i tu-<pb xlink:href="020/01/1540.jpg" pagenum="415"/>betti di latta erano schiacciati, le sferette e le schegge di vetro rotte e smus&shy;<lb/>sate..... Ecco dunque decisa una volta la famosa questione delle pietruzze <lb/>annidate ne'ventrigli di varii uccelli, per s&igrave; lungo tempo dagli Autori agi&shy;<lb/>tata, voglio dire che allo spezzamento de'cibi pi&ugrave; duri e de'corpi stranieri <lb/>durissimi non sono esse punto necessarie, contro quello che &egrave; stato cre&shy;<lb/>duto da tanti Naturalisti e Fisiologi s&igrave; moderni che antichi &rdquo; (Modena 1780, <lb/>pag. </s>

<s>18, 19). </s></p><p type="main">

<s>Ecco dunque l'ipotesi dell'Harvey e del Cornelio dimostrata falsa dal&shy;<lb/>l'esperienze dello Spallanzani, come l'ipotesi dell'Acquapendente e del Bo&shy;<lb/>relli era stata dimostrata falsa dalle esperienze del Redi; ond'&egrave; che, doman&shy;<lb/>dando con gran curiosit&agrave;, sulla fine del secolo XVIII, Naturalisti e Fisiologi <lb/>a che fine insomma si credesse che i gallinacei beccassero i sassolini, ri&shy;<lb/>spondeva cos&igrave;, dop'essersi consigliato con la sua propria scienza, lo stesso <lb/>Spallanzani: &ldquo; Io adunque sarei di parere che la ricchezza delle pietruzze, <lb/>che d'ordinario s'incontra ne'ventrigli degli uccelli gallinacei, nascesse, non <lb/>gi&agrave; dall'andarne essi in cerca e dal farne volontariamente raccolta, com'&egrave; <lb/>sentimento di molti, ma piuttosto dal trovarsi non di rado questi estranei <lb/>corpiccioli mescolati a'cibi che prendono &rdquo; (ivi, pag. </s>

<s>21). E cos&igrave; potrebbesi <lb/>saviamente rispondere rispetto all'arida arena e al crasso limo, di che tro&shy;<lb/>vasi ripieno il ventre ai testacei marini, e ai lombrichi terrestri. </s></p><p type="main">

<s>Da quello stesso Acquapendente, da cui mossero, sui principii del se&shy;<lb/>colo XVII, le questioni relative alle funzioni digestive de'ruminanti e dei <lb/>gallinacei, muove ora un'altra non meno importante questione storica con&shy;<lb/>cernente gli organi della respirazion negli uccelli. </s>

<s>Aristotile aveva detto, nel <lb/>cap. </s>

<s>X del III libro <emph type="italics"/>De partibus animalium,<emph.end type="italics"/> che son precinti del setto tra&shy;<lb/>sverso o del diaframma tutti quegli stessi animali che son forniti di sangue <lb/>rosso, e che ci&ograve; era stato fatto dalla Natura per separar le pi&ugrave; nobili parti <lb/>del corpo dalle pi&ugrave; vili. </s>

<s>&ldquo; Habent hoc omnia quae sanguinem obtinent aeque <lb/>ut cor et iecur, cuius rei causa est quod ideo habetur, ut sedem cordis a <lb/>ventre dirimat, videlicet ut animae sentientis origo inoffensa servetur, nec <lb/>facile occupetur exhalatione cibi, et caloris adventitii copia. </s>

<s>Hac enim causa <lb/>Natura intercepit praecordiorum quasi parietis sepisque interventu, distin&shy;<lb/>xitque partem nobiliorem ab ignobiliori &rdquo; (Operum, T. VI cit., fol. </s>

<s>243). </s></p><p type="main">

<s>Ma l'Acquapendente osserv&ograve; che gli uccelli, in cos&igrave; grande abbondanza <lb/>forniti di sangue rosso, non hanno questa siepe, la quale, perciocch'egli cre&shy;<lb/>deva non fosse data dalla Natura per dirimere il cuore dal ventre, ma per <lb/>servire alla respirazione, pensava che venisse negli stessi uccelli supplita dai <lb/>pi&ugrave; validi moti delle coste. </s>

<s>Voleva questo primo pensiero per&ograve; essere con&shy;<lb/>fermato da pi&ugrave; diligenti osservazioni, e un giorno entrato tutto in fervore <lb/>di ci&ograve;, mentre solitario meditava nel suo domestico studio, non avendo da <lb/>sezionare altri animali, mette le mani addosso al suo pappagallo, che pure <lb/>aveva carissimo, e coraggiosamente l'immola al culto della scienza. </s>

<s>&ldquo; Quae <lb/>omnia, ac ea potissimum quae ad thoracis motum, dum obscure ita explico, <lb/>ac mihi ipsi vix satisfacio, ecce domi forte psittacus obiit, qui, etsi gratis-<pb xlink:href="020/01/1541.jpg" pagenum="416"/>simus erat, multo tamen gratius fuit per eum in exactam motus thoracis <lb/>notitiam, ni fallor, pervenisse &rdquo; (De respiratione, Op. </s>

<s>omnia cit., pag. </s>

<s>178). </s></p><p type="main">

<s>Sodisfatto cos&igrave; di s&egrave; medesimo, consigliava il Fabricio i Fisiologi che, <lb/>se volevano studiare i moti del torace, ricorressero agli uccelli, ne'quali, <lb/>per la mancanza del diaframma, sono evidentissimi, &ldquo; cum in hominibus, <lb/>propter obscurum et exiguum motum, difficile admodum, et non nisi a <lb/>valde in re anatomica exercitatis et peritis, probe intelligi valeat &rdquo; ibid.). <lb/>Fu quel consiglio seguito in seno all'Accademia parigina da Giovanni Mery, <lb/>il quale, confermando le osservazioni fatte prima dal Nostro sopra gli uc&shy;<lb/>celli, confer&igrave; a chiarir molto le idee intorno all'avvicendarsi de'moti delle <lb/>coste nella respirazione, in quel tempo che pi&ugrave; fervevano nella scienza le <lb/>controversie. </s>

<s>Nella storia accademica infatti del 1689 si trova cos&igrave; riferito <lb/>delle osservazioni del Mery <emph type="italics"/>sur la respiration.<emph.end type="italics"/> &ldquo; Pour rendre ce mouve&shy;<lb/>ment plus sensible, on ferma, pendant quelque tems, le bec et les narines <lb/>et les ayant ensuite ouvertes, on vit manifestement que le ventre se com&shy;<lb/>prime beaucoup, en dedans, que le sternum s'&eacute;leva plus qu'auparavant, et <lb/>que les c&ograve;tes s'eloign&egrave;rent davantage les unes des autres en s'elevant. </s>

<s>On <lb/>observa au contraire, dans l'expiration, que le sternum se rapprochoit des <lb/>vertebres, les c&ograve;tes les unes des autres, et que le ventre s'elevoit &rdquo; (Col&shy;<lb/>lection de pi&egrave;ces acad., T. I, a Dijon 1754, pag. </s>

<s>146). </s></p><p type="main">

<s>Ma tornando all'Acquapendente, nell'introdursi ch'ei fa a trattare <emph type="italics"/>De <lb/>formatione ovi,<emph.end type="italics"/> s'imbatte al solito in Aristotile, che dice incominciarsi a <lb/>far l'uovo nella gallina presso il setto trasverso. </s>

<s>&ldquo; Nos autem in Respira&shy;<lb/>tionis tractatu negavimus pennata septum obtinere. </s>

<s>Solvitur dubium pennata <lb/>septo prorsus non destitui, quia membranam habent tenuem loco septi po&shy;<lb/>sitam, quam Aristotiles cinctum et septum appellavit, sed non habent septum <lb/>quod musculus sit, et ad respirationem conferat, ut alia animalia. </s>

<s>Aristoti&shy;<lb/>les autem musculum non agnovit &rdquo; (Op. </s>

<s>omnia cit., pag. </s>

<s>1, 2). </s></p><p type="main">

<s>Quando l'Harvey s'esercitava intorno a cos&igrave; fatte questioni di embrio&shy;<lb/>logia, tenendo intorno a s&egrave; a man destra i libri di Aristotile, e dall'altra <lb/>quelli dell'Acquapendente, volle esaminar meglio quella tenue membrana, <lb/>che si diceva essere negli uccelli posta in luogo del diaframma, e trov&ograve; che <lb/>erano invece pi&ugrave; membrane tese l'une a distanza dall'altre, fra gl'inter&shy;<lb/>stizi delle quali rimanevano certe cavit&agrave; cellulari, senza dubbio ripiene d'aria. </s>

<s><lb/>Incerto se quest'aria era innata, o se veniva di fuori, si risovvenne di que&shy;<lb/>ste parole, che aveva lette nel trattato <emph type="italics"/>De respiratione<emph.end type="italics"/> del suo Fabricio: <lb/>&ldquo; In pennatis igitur diaphragma non fuit appositum, ut non modo thorax, <lb/>sed etiam abdomen, per respirationem facile distendatur, attollaturque, tum <lb/>vero aere impleatur, atque hac ratione totus corporis truncus, qui sua na&shy;<lb/>tura gravis et minus idoneus ad volandum erat futurus, levis omnino red&shy;<lb/>datur &rdquo; (ibid., pag. </s>

<s>178). </s></p><p type="main">

<s>L'aria nel ventre, a cui qui s'accenna, pensava l'Harvey, non pu&ograve; es&shy;<lb/>sere altro che quella compresa fra'sepimenti delle membrane, e se il Fa&shy;<lb/>bricio dice che v'entra <emph type="italics"/>per respirationem<emph.end type="italics"/> dee necessariamente venire dalla <pb xlink:href="020/01/1542.jpg" pagenum="417"/>trachea per i bronchi, attraverso ai polmoni. </s>

<s>Or perch&egrave; la decisione era ri&shy;<lb/>serbata all'esperienza, apre il becco a un uccello, vi soffia con un soffietto, <lb/>e ode il fremere del fiato che trapassa nel ventre. </s>

<s>Non contento, infila nella <lb/>trachea uno stilo, che trova dai polmoni nell'abdome, con grandissima fa&shy;<lb/>cilit&agrave;, il passo aperto. </s>

<s>Volendo anche di pi&ugrave; dar sodisfazione agli occhi, ne&shy;<lb/>gletto il Microscopio, cerca uno degli uccelli pi&ugrave; grossi, e trova nello Struzzo <lb/>i fori polmonari s&igrave; larghi, da ricever facilmente le punte delle dita. </s>

<s>Esult&ograve; <lb/>della scoperta, e nella III esercitazione <emph type="italics"/>De generatione animalium<emph.end type="italics"/> la ren&shy;<lb/>deva nota al pubblico in questa forma: &ldquo; Perforatio pulmonum a me in&shy;<lb/>venta haud obscura et caeca est, sed in pennatis praesertim patula admo&shy;<lb/>dum adeo ut in struthiocamelo meatus plurimos repererim, qui digitorum <lb/>meorum apices facile exciperent. </s>

<s>In gallo indico et gallinaceo ipso, omni&shy;<lb/>busque fere pennatis, immisso in tracheam stylo, transitus e pulmonibus in <lb/>cavitate abdominis apertos et patentes invenias. </s>

<s>Aer in eorum pulmones, <lb/>follium opera inspiratus, non sine impetu ad inferiora pertransit &rdquo; (Lugd. </s>

<s><lb/>Batav. </s>

<s>1737, pag. </s>

<s>6). </s></p><p type="main">

<s>Trent'anni dopo la pubblicazione di questa scoperta Claudio Perrault, <lb/>perfezionata, la illustrava nel cap. </s>

<s>V della III Parte della sua <emph type="italics"/>Mechanique <lb/>des animaux,<emph.end type="italics"/> esibendo nella fig. </s>

<s>I della Tavola XVIII la disposizione delle <lb/>vescicole pneumatiche, situate quattro di qua e quattro di l&agrave; nel petto dello <lb/>Struzzo, e due altre, una per parte, nel basso ventre. </s>

<s>&ldquo; Les quatre vessies <lb/>d'en-haut ont quatre trous, qui re&ccedil;oivent le vent du poumon. </s>

<s>La seconde <lb/>en a deux. </s>

<s>Celui d'en-haut re&ccedil;oit l'air du poumon, celui d'en-bas l'envoye <lb/>&agrave; la vessie, qui est enferm&eacute;e dans le bas ventre &rdquo; (ediz. </s>

<s>cit., pag. </s>

<s>464). </s></p><p type="main">

<s>In Italia, quasi nello stesso tempo, confermava queste osservazioni Fran&shy;<lb/>cesco Redi, facendo cos&igrave; dire a Pietro Alessandro Fregosi, nel II Tomo del <lb/>supplemento al <emph type="italics"/>Giornale dei letterati:<emph.end type="italics"/> &ldquo; Ieri appunto (5 Dicembre 1682) <lb/>il signor Redi riscontrava le sue osservazioni intorno a'polmoni degli uc&shy;<lb/>celli, e con mia grandissima sodisfazione vidi che questi polmoni de'volanti <lb/>non istanno liberi e sciolti, come quegli de'quadrupedi e degli uomini, ma <lb/>sono fortemente attaccati alle costole e al groppone, e che di pi&ugrave; son forati <lb/>da alcuni determinati e regolati forami, i quali forami sboccano in certe <lb/>particolari vesciche membranose che, moltiplicate fino in cinque, arrivano <lb/>l'una dopo l'altra infino a tutto il ventre inferiore &rdquo; (Opere, T. IV, Na&shy;<lb/>poli 1741, pag. </s>

<s>81). </s></p><p type="main">

<s>Dall'Anatomia, trapassando alla Fisiologia, si domandava qual potesse <lb/>essere l'uso proprio di queste vescicole membranose. </s>

<s>Udimmo dalle sopra <lb/>riferite parole che l'Acquapendente credeva conferissero alla leggerezza del <lb/>corpo, in grazia del pi&ugrave; facile volo, ma l'Harvey, considerando che il pol&shy;<lb/>mone, dando transito all'aria, non poteva perci&ograve; dirsi organo della respira&shy;<lb/>zione adeguato, riguard&ograve; piuttosto quelle stesse vescicole membranose come <lb/>un polmone secondario. </s>

<s>&ldquo; Ita in pennatis pulmones potius transitus et via <lb/>ad respirationem videntur, quam huius adaequatum organum &rdquo; (De generat. </s>

<s><lb/>animal. </s>

<s>cit., pag. </s>

<s>5). </s></p><pb xlink:href="020/01/1543.jpg" pagenum="418"/><p type="main">

<s>Il Perrault illustr&ograve; benissimo questo concetto arveiano, dicendo che il <lb/>polmone degli uccelli si compone di due parti: una carnosa, come negli ani&shy;<lb/>mali terrestri, e una membranosa. </s>

<s>Riconobbe in queste membrane l'uso dei <lb/>muscoli nel basso ventre de'quapredi; uso che non era sfuggito alla mente <lb/>dell'Harvey: ma anche un altro volle aggiungervene, il Perrault, e fu quello <lb/>di comprimere gl'intestini per la pi&ugrave; equabile e non interrotta distribuzione <lb/>degli alimenti. </s>

<s>&ldquo; L'usage de cette partie membraneuse est de suppleer au <lb/>d&eacute;faut des muscles du bas ventre, qui sont tres petits dans le oiseaux, &agrave; <lb/>cause de la grandeur de l'os de la poitrine, dont presque tout le ventre est <lb/>couvert, car ces muscles du bas ventre etant tres petits, et leur action pres&shy;<lb/>que nulle, la compression importante, qu'ils font sur les entrailles aux au&shy;<lb/>tres animaux pour la coction et pour la distribution de la noutriture, auroit <lb/>manque aux oiseaux, si la partie membraneuse de leur poumon n'y avoit <lb/>suppl&eacute;e &ldquo; (Mechanique cit., pag. </s>

<s>462). </s></p><p type="main">

<s>Il Redi poi, educato alla scuola galileiana, ripensando che dai principii <lb/>meccanici aveva Galileo (Alb. </s>

<s>XIII, 145) conclusa la ragione dell'essere state <lb/>fatte le ossa degli uccelli fistolose, perch&egrave; riuscissero tutto insieme leggere <lb/>e resistenti, non cred&egrave; doversi rigettare quello proposto dall'Acquapendente <lb/>fra gli usi, alle vescicole pneumatiche nuovamente assegnati. </s>

<s>Perci&ograve; faceva <lb/>dire al medesimo Fregosi &ldquo; che l'aria che entra per l'aspera arteria non <lb/>si ferma ne'polmoni, ma per quei forami de'medesimi polmoni passa nelle <lb/>vesciche membranose e le gonfia, e gonfiandole fa crescere e dilatare le ca&shy;<lb/>vit&agrave; del ventre, onde l'animale ne divien pi&ugrave; tronfio e per cos&igrave; dire pi&ugrave; <lb/>leggiero, e di pi&ugrave; in questa dilatazione, venendo le viscere naturali ad es&shy;<lb/>sere premute, elle possono, per via di questa alternata compressione, met&shy;<lb/>tere in opera quegli ufizii, ai quali dalla natura sono state destinate &rdquo; <lb/>(Opere, Tomo cit., pag. </s>

<s>81). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Se, negli organi e nelle funzioni della digestione e della respirazione, <lb/>la feconda variet&agrave; del natural magistero apr&igrave; cos&igrave; largo campo d'osserva&shy;<lb/>zioni e d'esperienze ai Naturalisti, non lo ridusse certo in termini punto <lb/>pi&ugrave; circoscritti, per quel che concerne gli organi dei sensi. </s>

<s>Anzi quel sottil <lb/>lavor&igrave;o presenta tante e tali variet&agrave; nella trama e nell'ordito, che sfuggono <lb/>alle pi&ugrave; attente osservazioni, e dall'altro lato l'impossibilit&agrave; di comprendere <lb/>i reconditi usi rende anche pi&ugrave; difficile ogni diligenza in ricercar quelle mi&shy;<lb/>nime differenze, che passano fra le parti. </s></p><p type="main">

<s>Questo, che pu&ograve; dirsi di tutti gli strumenti dei sensi, applicasi con pi&ugrave; <lb/>ragione che mai alla vista e all'udito, negli organi delle quali due princi&shy;<lb/>palissime funzioni il cristallino per esempio e gli ossicini uditivi, sebben si&shy;<lb/>mili nella sostanziale struttura in un medesimo genere, presentano pure va&shy;<lb/>riet&agrave; notabili in ciascuna specie. </s>

<s>Essendo nonostante gli animali terrestri e <pb xlink:href="020/01/1544.jpg" pagenum="419"/>i volanti cos&igrave; fra loro diversi, non solo nella vita organica ma in quella di <lb/>relazione, non possono non intercedere fra gli organi de'loro sensi differenze, <lb/>che debbano sfuggire, o comecchessia venir trascurate nella loro storia, e <lb/>intorno ad alcune di queste, o per meglio dire intorno ai validi aiuti, che <lb/>in riconoscerle ebbe la scienza della Natura dall'arte sperimentale, si vuole <lb/>intrattener la presente limitata parte del nostro discorso. </s></p><p type="main">

<s>Rispetto agli occhi una delle pi&ugrave; notabili differenze, che passano fra i <lb/>quadrupedi e gli uccelli, consiste in quel particolare organo, a cui fu dato <lb/>il nome di <emph type="italics"/>pettine.<emph.end type="italics"/> Fu primo ad esaminarlo il Petit, nelle memorie dell'Ac&shy;<lb/>cademia parigina del 1735, e poi l'Haller ne fece una descrizione assai pi&ugrave; <lb/>accurata, s&igrave; quanto alla sua origine dal nervo ottico, s&igrave; quanto alla sua forma <lb/>e alla sua struttura. </s>

<s>&ldquo; Parallelogramma fere membrana est, utriculosa, va&shy;<lb/>sculosa, fusca et pene nigra, tenera, ad morem flabelli super seipsam pli&shy;<lb/>cata, non similis bursae neque cavum aliquod continens, et quam maceratam <lb/>imperfectam planitiem explices &rdquo; (Elementa physiol., T. V, Lausannae 1769, <lb/>pag. </s>

<s>391). Il Petit pens&ograve; che il pettine servisse ad assorbire i raggi avven&shy;<lb/>tizi, e a liberar l'occhio dalle riflessioni irregolari, come il naturale pigmento <lb/>coroideo o quella tinta nera, che si d&agrave; intorno alle lenti degli strumenti no&shy;<lb/>stri artificiali, ma l'Haller &ldquo; mihi videtur, disse, similis arteriae albinianae <lb/>et bursulae piscium, advehere sanguinem lenti crystallinae &rdquo; (ibid.). </s></p><p type="main">

<s>L'anatomia comparata e la fisiologia dell'organo dell'udito, se ci fosse <lb/>permesso pi&ugrave; lungo discorso, porgerebbero alla nostra storia altro nuovo ar&shy;<lb/>gomento, ma non &egrave; da far altro per noi che a delibare, anche da questo <lb/>pelago, qualche stilla di umore. </s>

<s>Non isfugg&igrave; nemmeno agli Antichi l'osser&shy;<lb/>vazione che l'orecchia esterna &egrave; variamente configurata negli animali timidi <lb/>e nei feroci, e ch'&egrave; altres&igrave; variamente disposta in quegli, che aspettano la <lb/>venuta del suono o di sotto o di sopra, o dalla parte d'avanti del loro in&shy;<lb/>corso, o da quella di dietro. </s>

<s>Il Porta, avendo a proporre, nel cap. </s>

<s>V del <lb/>XX libro della Magia naturale, uno strumento da udir di pi&ugrave; lontano, si <lb/>inspirava sapientemente agli esempi della Natura. </s>

<s>&ldquo; Sancitum est enim in <lb/>Magiae naturalis praeceptis, quum aliqua nova investiganda sunt, Naturam <lb/>perscrutandam et imitandam censeamus. </s>

<s>Ut igitur animalia consideremus, <lb/>quae optimi auditus sunt, timida quaeramus oportet. </s>

<s>Natura enim eorum <lb/>saluti cavit ut quae minus viribus valerent saltem auditus praestantia fuga <lb/>saluti consulerent, ut cuniculus, lepus, cervus, asinus, bos et similia. </s>

<s>Haec <lb/>animalia aurita sunt, et aures apertas habent versus frontem, et hiatus di&shy;<lb/>rigunt ex quo soni veniunt..... Quum erexere aures, acerrimi auditus, <lb/>quum remisere, timidi. </s>

<s>Et, ne per caetera animalia vagemur, quae aures am&shy;<lb/>plas arrectas et apertas habent dicimus perfectissimum auditum habere. </s>

<s>Vi&shy;<lb/>debimus nunc, contraria causa, quae parvas habent aures et obscuras obtu&shy;<lb/>sioris esse auditus. </s>

<s>Magna piscium pars auribus caret, et qui solos meatus <lb/>habent et sine auriculis sensu hoc audiendi hebetiori esse necesse est. </s>

<s>Sunt <lb/>enim auriculae a Natura constructae ut veluti per eas in aures infundantur <lb/>soni &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1651, pag. </s>

<s>654, 55). </s></p><pb xlink:href="020/01/1545.jpg" pagenum="420"/><p type="main">

<s>Or perch&egrave; anche gli uccelli hanno i soli meati esterni, senza le auri&shy;<lb/>cole, parrebbe che dovess'essere in essi il senso non troppo squisito, ci&ograve; <lb/>che da un'altra parte argomentavasi con pi&ugrave; ragione da coloro, che vede&shy;<lb/>vano mancare a quegli animali gli ossicini attaccati alla membrana, e altre <lb/>parti, che si reputavano di grand'uso, nella cassa del timpano e nel labi&shy;<lb/>rinto. </s>

<s>Non ebbe quella falsa opinione per&ograve; altra origine che dall'ignoranza <lb/>dell'anatomia di questi organi, l'esatta e compiuta descrizione de'quali fu <lb/>a darla primo lo Scarpa. </s>

<s>Quand'egli ebbe con tanti dotti argomenti dimo&shy;<lb/>strato che l'ufficio della finestra rotonda era quello di far da timpano se&shy;<lb/>condario, passando alcuni a professare un'opinione contraria a quella dianzi <lb/>accennata, e dicendo che l'udito &egrave; anzi negli uccelli finissimo, bench&egrave; non <lb/>sia il suono rinforzato dalla finestra rotonda, negavano perci&ograve; che, quale ve&shy;<lb/>niva a quest'organo assegnato, tale veramente ne fosse l'uso. </s>

<s>Lo Scarpa al&shy;<lb/>lora si dette con gran diligenza a studiar l'orecchio degli uccelli, e non solo <lb/>vi ritrov&ograve; la finestra rotonda, con tutto quell'apparecchio acustico moltipli&shy;<lb/>catore del suono, ma tante altre cose vi scopr&igrave; non pi&ugrave; vedute, che il cap. </s>

<s>V <lb/>posto per appendice al trattato, e che s'intitola <emph type="italics"/>Historia organi auditus <lb/>avium,<emph.end type="italics"/> apparve, presso a trent'anni prima che terminasse il secolo XVIII, <lb/>come una nuova rivelazione alla scienza. </s></p><p type="main">

<s>Passa ivi l'Autore ordinatamente dall'esame dell'orecchio esterno a quello <lb/>della Cassa del timpano e del Labirinto, ed esposta una sua ipotesi del per&shy;<lb/>ch&egrave; negli uccelli manchin le auricole, descrive in loro luogo nelle tempie <lb/>de'Galli d'India un organo che, sebbene egli dica essere ovvio &ldquo; nemo <lb/>hactenus animadvertit &rdquo; (De structura fen. </s>

<s>rotundae, Mutinae 1772, pag. </s>

<s>103). <lb/>Consiste quell'organo in certi muscoli ordinat&igrave; a muovere una corona di <lb/>piume, di ch'&egrave; interiormente orlato il margine del meato uditorio, e che <lb/>hanno co'cigli delle palpebre una grandissima somiglianza nella disposizione, <lb/>ne'movimenti e nell'uso. </s></p><p type="main">

<s>Di pi&ugrave; grande importanza era l'esame della Cassa del timpano, nella <lb/>quale lo Scarpa osserv&ograve; diligentissimamente quell'unico ossicino, in cui par <lb/>si compendino i quattro proprii agli animali terrestri. </s>

<s>Lo Schelhammer, <lb/>dalla similitudine, l'avea chiamato <emph type="italics"/>columna,<emph.end type="italics"/> e il Perrault, che nel suo trat&shy;<lb/>tato <emph type="italics"/>Du bruit<emph.end type="italics"/> s'era asciuttamente contentato di dire, che nell'orecchia media <lb/>degli uccelli &ldquo; les osselets son reduits a un seul &rdquo; (Oeuvres, T. </s>

<s>I cit., <lb/>pag. </s>

<s>247), rappresentava poi nella figura II della Tavola VIII quest'unico <lb/>ossicino come un sottile cilindro, che da una parte &ldquo; bouche le trou ova&shy;<lb/>laire &rdquo; ed ha l'altra, informemente rappresentata, &ldquo; attach&eacute;e &agrave; la peau du <lb/>tambour &rdquo; (ivi, pag. </s>

<s>248). Ma il nostro Scarpa descrisse e fece nella sua ta&shy;<lb/>vola II disegnare quell'ossicino nella sua pi&ugrave; vera e natural figura, ch'&egrave; <lb/>a somiglianza del gambo e del cappello di un fungo. </s>

<s>&ldquo; Figura stilus fun&shy;<lb/>giformis videtur: desinit enim in planam latamque ac fere triangularem su&shy;<lb/>perficiem, quae ovalem fenestram, sicuti stapes in aure humana, penitus <lb/>claudit &rdquo; (De structura f. </s>

<s>rot. </s>

<s>cit., pag. </s>

<s>112). </s></p><p type="main">

<s>Per quel che poi pi&ugrave; particolarmente riguarda il Labirinto, i tre canali <pb xlink:href="020/01/1546.jpg" pagenum="421"/>semicircolari erano a tutti patenti, ma &ldquo; au lieau du conduit spiral, diceva <lb/>il Perrault, il y a seulement un conduit court et droit en maniere d'un pe&shy;<lb/>tit sac &rdquo; (loc. </s>

<s>cit., pag. </s>

<s>247). Nonostante lo Scarpa pi&ugrave; veramente rassomi&shy;<lb/>gliava questo sacchetto all'appendice vermiforme degl'intestini. </s>

<s>&ldquo; Canales <lb/>semicirculares e directo prospicit Cocblea inferius producta, quae non ut in <lb/>homine et quadrupedibus convolvitur in spiram, sed canalem efficit non&shy;<lb/>nihil recurvum et vermiformem intestinorum appendiculum simulantem &rdquo; <lb/>(De structura f. </s>

<s>r. </s>

<s>cit., pag. </s>

<s>124). </s></p><p type="main">

<s>La finestra rotonda, che dette occasione e frutt&ograve; alla scienza questo te&shy;<lb/>soro di anatomia comparata, non riconosciuta ancora da nessuno de'prede&shy;<lb/>cessori, viene, insiem con la ovale, dallo Scarpa cos&igrave; descritta: &ldquo; Fenestra <lb/>ovalis, triangularem ferme figuram referens, superiorem partem occupat, et <lb/>a mobili capitulo ossiculi, tanquam a stapede, penitus obturatur. </s>

<s>Altera fe&shy;<lb/>nestra, nempe rotunda, figura oblonga et inferius altera collocata, duplo <lb/>semper priore latior est, et in quibusdam avibus amplior. </s>

<s>Membrana ostium <lb/>fenestrae rotundae obtegit non intro convexa, ut in brutis ed homine, sed <lb/>plana distentaque admodum ut in tympano bellico et ad tremores aptis&shy;<lb/>sima &rdquo; e a far perci&ograve; benissimo anche negli uccelli l'ufficio di timpano se&shy;<lb/>condario (ivi, pag. </s>

<s>121). </s></p><p type="main">

<s>&Egrave; tale in compendio e nella sua pi&ugrave; ridotta sostanza la storia ornito&shy;<lb/>logica dell'organo dell'udito, per ci&ograve; che spetta gli strumenti ossei musco&shy;<lb/>lari e membranosi. </s>

<s>&ldquo; Superest nunc, prosegue a dire lo stesso Scarpa, ad <lb/>eorum auditus historiam absolvendam, ut ea quoque addamus quae su&shy;<lb/>sceptos soni tremores sensorio communi traducunt, nervum nempe acusti&shy;<lb/>cum &rdquo; (ibid., pag. </s>

<s>125). Il Casserio, che fu primo a scoprire l'ingresso di <lb/>un certo allungamento del cervelletto attraverso a un foro aperto fra la la&shy;<lb/>mina ossea e interiore del cranio (Venetiis 1609, pag. </s>

<s>165), pens&ograve; che te&shy;<lb/>nesse questo stesso processo cerebellare il luogo del nervo acustico. </s>

<s>N&egrave; fu <lb/>molto differente da questo il parere dello Schelhammer, ma in verit&agrave;, sog&shy;<lb/>giunge lo Scarpa, non si vede mandare il cervelletto da quella sua sostanza <lb/>allungata nessun filamento che penetri nell'interna parte del labirinto, e <lb/>non &egrave; perci&ograve; possibile che faccia le funzioni acustiche nel nervo. </s>

<s>&ldquo; Deest <lb/>ergo nervus acusticus? </s>

<s>Non sinunt observationes nostrae in hac sententia <lb/>morari. </s>

<s>Nervus enim acusticus, non tam in volucribus maioribus, sed in <lb/>aviculis etiam, perpetuus est et facile demonstrabilis. </s>

<s>Oritur enim ex oblon&shy;<lb/>gata medulla, deinde statim in pluribus ramulis distinctus, nullo interposito <lb/>auditorio canale, extremam osseam labyrinthi laminam attingit, foraminibus <lb/>pertusam, per quae ad internam labyrinthi superficiem descendunt &rdquo; (ibid., <lb/>pag. </s>

<s>127). Ivi dentro penetrati cos&igrave; fatti ramuscoli nervei si trasformano in <lb/>quella sostanza polposa, che investe l'uno e l'altro vestibolo, i canali semi&shy;<lb/>circolari e la chiocciola. </s></p><p type="main">

<s>Cos&igrave; intendesi come debba l'orecchio degli uccelli riuscire organo per&shy;<lb/>fettissimo dell'udito. </s>

<s>&ldquo; Quare aves liquide audire necessario debent.... Fa&shy;<lb/>tendum tamen est aliquod intercedere discrimen inter stridulas aves atque <pb xlink:href="020/01/1547.jpg" pagenum="422"/>canoras. </s>

<s>In istis enim quae exquisito auditu donantur, tria potissimum exhi&shy;<lb/>bet auditus organum observatione dignissima: fenestram nempe rotundam <lb/>ovali triplo maiorem quam in stridulis volatilibus, vestibulum praesertim <lb/><emph type="italics"/>Tympani secundarii<emph.end type="italics"/> latius, ac denique cochleam longiorem magisque re&shy;<lb/>curvam &rdquo; (ibid., pag. </s>

<s>130). D'onde si conclude che l'arte del canto &egrave; negli <lb/>uccelli educata dall'orecchio; fatto del resto che si avvera in ogni genere <lb/>di animali, e in pi&ugrave; eccellente modo nell'uomo. </s>

<s>La stretta relazione perci&ograve;, <lb/>che passa fra'due organi, ci consiglia a non trascurare un breve cenno sto&shy;<lb/>rico dello strumento della voce, a complemento di quel che qui, e pi&ugrave; lun&shy;<lb/>gamente altrove, s'&egrave; detto dell'udito. </s></p><p type="main">

<s>In mezzo a tanti Vesaliani, dispregiatori dell'antico Galeno, sorgeva Giu&shy;<lb/>lio Casserio ad ammirare l'intrepido petto di Colui &ldquo; qui contra Zenonem, <lb/>Stoicos, Diogenem, Babilonium et Chrysippum, pro ea vocis formatione de&shy;<lb/>fendenda magnanimiter pugnavit. </s>

<s>Eorum autem alii a corde, ut Zeno, alii <lb/>a gutture vocem oriri putabant &rdquo; (De laringis hist. </s>

<s>anat., Ferrariae 1600, <lb/>pag. </s>

<s>148). Galeno invece sosteneva, per amor del vero, che aveva origine <lb/>la voce da uno strumento tanto simile al flauto, che dee il suo primo in&shy;<lb/>ventore aver preso l'esempio dalla stessa Natura. </s>

<s>&ldquo; Simile quidem est lin&shy;<lb/>guae alicuius fistulae, potissimum si infernam ac supernam eius partem <lb/>spectes: infernam autem dico, ubi arteria et larinx inter sese connectun&shy;<lb/>tur; supernam vero ad orificium quod fit a finibus, qui ibi sunt, arytenoi&shy;<lb/>deos cartilaginis et scutiformis &rdquo; (De usu partium, lib. </s>

<s>VII, cap. </s>

<s>XIII, Lug&shy;<lb/>duni 1550, pag. </s>

<s>406). Come per&ograve; nel flauto organo precipuo del suono &egrave; la <lb/>linguetta, cos&igrave; nella laringe organo precipuo della voce &egrave; la glottide. </s>

<s>&ldquo; Ut <lb/>autem vocem edat animal indiget omnino etiam ea spiritus motione, quae <lb/>ab infernis repente simul erumpat. </s>

<s>Indiget autem nihil minus hac transitu <lb/>etiam angustiore, qui in larynge est. </s>

<s>Neque simpliciter angustiore, sed qui <lb/>paulatim quidem ex amplo ad strictius tendat, paulatim rursus ex strictiore <lb/>amplificetur. </s>

<s>Id quod penitus efficit corpus id, de quo nunc agimus, quod <lb/>lingulam et linguam laryngis nomino &rdquo; (ibid., pag. </s>

<s>407). </s></p><p type="main">

<s>Introdotte queste naturali verit&agrave; nella nuova scienza risorta, per opera <lb/>d'Iacopo Berengario, il quale aveva lasciato scritto esser la glottide &ldquo; prin&shy;<lb/>cipalissimum vocis organum &rdquo; (Isag., Venetiis 1535, fol. </s>

<s>44); non per que&shy;<lb/>sto crederono i Peripatetici di dover negar fede al loro Aristotile. </s>

<s>Dicevano <lb/>anzi che ci&ograve; ch'egli insegnava della voce generata dal cuore veniva confer&shy;<lb/>mato dall'esperienze, vedendosi diventar fioco, e talvolta anche affatto muto, <lb/>allacciate le arterie carotidi, un animale. </s>

<s>Ma Realdo Colombo rispondeva <lb/>a costoro ci&ograve; dipendere dal venire offesa la laringe e no il cuore, perch'&egrave; <lb/>troppo facile ad esser preso, insierne con la carotide, anche quel sottil nervo, <lb/>che d&agrave; spirito alla stessa laringe: nervo scoperto gi&agrave; da Galeno, e dagli Ana&shy;<lb/>tomici poi detto <emph type="italics"/>ricorrente<emph.end type="italics"/> o <emph type="italics"/>reversivo,<emph.end type="italics"/> perch&egrave; &ldquo; per camdem revertitur <lb/>viam qua prius descenderat, ceu cursum reciprocans &rdquo; (De usu partium cit., <lb/>pag. </s>

<s>418). </s></p><p type="main">

<s>Per dimostrar di fatto che l'afonia dipende dal nervo offeso, e non dal <pb xlink:href="020/01/1548.jpg" pagenum="423"/>cuore o da qualunque altro membro, esso Realdo ricorreva alla vivisezione. </s>

<s><lb/>Erano presenti, fra tanti altri filosofi e anatomici illustri, Girolamo Pontano, <lb/>Paolo Manilio e Giovanni Valverde, mentre il misero cane, legato sulla ta&shy;<lb/>vola e colle viscere aperte, metteva lunghi urli acuti in mezzo a quegli spa&shy;<lb/>simi atroci. </s>

<s>L'espertissimo vivisettore mostra agli astanti un sottilissimo filo <lb/>bianco decorrere lungo l'aspera arteria, e dice: questa &egrave; una propaggine <lb/>del nervo riversivo. </s>

<s>Tocca leggermente col dito quel nervo, e l'urlo dalla <lb/>gola della vittima infelice esce fioco; lo preme di pi&ugrave;, e'cessa affatto. </s>

<s>Sa&shy;<lb/>rebbe oggid&igrave; sembrato di assistere all'esperienze della soneria elettrica, sul <lb/>filo conduttor della quale il dito facesse quel medesimo gioco. </s>

<s>&Egrave; da creder <lb/>perci&ograve; se, vinta la piet&agrave; del dolore dalla curiosit&agrave; del sapere, rimanessero <lb/>quegli astanti maravigliati dallo spettacolo, e l'Autore stesso non pot&egrave; te&shy;<lb/>nersi di esclamare, dop'averlo descritto: &ldquo; Profecto pulchrum est spectatu <lb/>consideratuque pulcherrimum quo pacto duo nervuli adeo parvuli tam bel&shy;<lb/>lam edant actionem, qualis est vocis ipsius efformatio &rdquo; (De re anat. </s>

<s>cit., <lb/>pag. </s>

<s>259). L'esperimento poi ripetuto da tanti, e con particolare eloquenza <lb/>descritto dal Casserio (De laryngis hist. </s>

<s>cit., pag. </s>

<s>67), fece s&igrave; che a quei <lb/>nervi si desse indifferentemente il nome di ricorrenti e di <emph type="italics"/>vocali.<emph.end type="italics"/></s></p><p type="main">

<s>Pareva cos&igrave; fatto argomento sperimentale sufficiente a disingannare i <lb/>Peripatetici, ma perch&egrave;, se non dovevano credere ad Aristotile, preferi&shy;<lb/>vano le dottrine degli altri filosofi a quelle di Galeno, e perci&ograve; dicevano <lb/>che, se la voce non nasce dal cuore, pu&ograve; venir benissimo dalla gola e dai <lb/>polmoni. </s>

<s>In questo, apparve un Aristotelico autorevolissimo in Girolamo Fa&shy;<lb/>bricio, il quale si trov&ograve; costretto a confessar dai fatti osservati che non si <lb/>potevano in nessun modo salvare le opinioni de'filosofi antichi. </s>

<s>Prima, per&shy;<lb/>ch'essendovi bisogno a produr la voce dell'elisione dell'aria non hanno mu&shy;<lb/>scoli per comprimerla n&egrave; i polmoni n&egrave; i bronchi; poi perch&egrave; si vede che, <lb/>incisa la trachea, passa bene il respiro, ma la voce cessa, e ritorna subito <lb/>allora che viene a richiudersi la ferita. </s>

<s>Da ci&ograve; conclude esso Fabricio esser <lb/>veramente organo della voce la laringe, o la glottide in lei che, vociferando <lb/>l'animale, restringe la sua fessura. </s>

<s>Di che, egli soggiunge, ne'polli, i quali <lb/>hanno quella stessa laringe cos&igrave; semplice, e collocata a sommo la trachea, <lb/>pu&ograve; aversi dimostrazione oculata. </s>

<s>&ldquo; Quod si etiam oculata fide id experiri <lb/>placet, gallinaceus pullus aut pennatum sumatur animal, et aperto ore vo&shy;<lb/>ciferari cogatur: manifesto apparebit rem ita se habere, nam quando vocem <lb/>emittunt rimulam angustant, ubi vero abstinent, ipsam latiorem reddunt &rdquo; <lb/>(De larynge, Opera omnia cit., pag. </s>

<s>280). </s></p><p type="main">

<s>Dopo queste dimostrazioni, confermate da quell'accuratissimo trattato, <lb/>che ne distendeva della laringe in quel medesimo tempo il Casserio; rimase <lb/>a pochi oramai pi&ugrave; dubbio intorno alle verit&agrave; galeniche, ma pur si voleva <lb/>sapere, per meglio acquietare la mente, come da cos&igrave; semplice disposizion <lb/>della glottide venisse a modularsi tanta variet&agrave; di note e di tuoni. </s>

<s>Lo stesso <lb/>Acquapendente, in quel suo curioso trattatello <emph type="italics"/>De brutorum loquela,<emph.end type="italics"/> ne <lb/>avea tanto pi&ugrave; ardente acceso il desiderio, in quanto v'avea scritto che il <pb xlink:href="020/01/1549.jpg" pagenum="424"/>passar la voce dal grave all'acuto &ldquo; videtur ad animi affectus nuntiandos <lb/>non mediocriter conferre &rdquo; (ibid., pag. </s>

<s>323), no negli uomini soli, ma nei <lb/>bruti; anzi nelle stesse cose inanimate, come si vede per esempio nelle corde <lb/>tese all'unisono, che si risentono quasi vive al suono di un altro strumento. </s></p><p type="main">

<s>L'intraveduta somiglianza fra l'organo musicale e quello animale por&shy;<lb/>geva non difficile risoluzione al nuovo proposto problema, e infatti l'Acqua&shy;<lb/>pendente fu primo a insegnar che la voce si modula nella gola, a quel modo <lb/>che nel flauto stesso si modula il suono. </s>

<s>E come in tale strumento s'ottien <lb/>dall'arte il grave e l'acuto, allargando e stringendo l'apertura della lin&shy;<lb/>guetta, e rendendo il tubo ora pi&ugrave; ora meno largo, ora pi&ugrave; ora meno lungo; <lb/>cos&igrave; opera la Natura nell'organo animale per produrre il medesimo effetto. <lb/></s>

<s>&ldquo; Itaque tribus modis vox gravis acutaque perficitur, aut ex angustia, rimu&shy;<lb/>lae maiore vel minore, aut ex longitudine et brevitate canalis, aut demum <lb/>ex eiusdem canalis latitudine maiore minoreque. </s>

<s>Nam ex minore rimulae <lb/>angustia, et canalis tum longitudine tum latitudine, maiore gravior, contra <lb/>vero acutior vox efficitur &rdquo; (De larynge cit., pag. </s>

<s>301). </s></p><p type="main">

<s>Il Casserio si diffonde prolissamente in descrivere le somiglianze, che <lb/>passano fra la laringe e i varii strumenti musicali a fiato, cos&igrave; in produr <lb/>la voce, come in modulare i varii tuoni, e per un secolo intero si ripete&shy;<lb/>rono le dottrine di lui e dell'Acquapendente, senza muover dubbio se fos&shy;<lb/>sero vere. </s>

<s>Si venne per&ograve; col tempo a riconoscere in quelle prime cos&igrave; se&shy;<lb/>ducenti analogie qualche fallacia, perch&egrave; ogni strumento musicale a fiato si <lb/>compone di tre parti: di quella che manda l'aria, di quella che produce il <lb/>suono, e della terza infine che produce la risonanza. </s>

<s>Ora nella teorica del&shy;<lb/>l'Acquapendente e del Casserio si davano alla trachea due ufficii fra s&egrave; <lb/>incompatibili, quali erano tutto insieme di mandare il fiato e di risonare. </s></p><p type="main">

<s>Denis Dodart nel 1700 fu primo a rivelare innanzi all'Accademia pa&shy;<lb/>rigina questa fallacia, e ritenuto essere la trachea semplice strumento pneu&shy;<lb/>matico, esser la glottide precipuo organo acustico, si dette a ricercar quel&shy;<lb/>l'altro, che facesse nell'animale da corpo di risonanza. </s>

<s>Riguardando dunque <lb/>prima di tutto la trachea come il tubo pneumatico della laringe, il Gassendo, <lb/>in trattar <emph type="italics"/>De voce animalium,<emph.end type="italics"/> avea posto il fondamento alle relative teorie <lb/>acustiche, con dir che l'aria dee uscire dall'aspera arteria con tanta velo&shy;<lb/>cit&agrave;, con quanta si vede esser necessario che si metta a vibrare una corda <lb/>sonora. </s>

<s>&ldquo; Et quanta quidem pernicitate aerem ex arteria prosilire necesse <lb/>sit, ut vox simpliciter creetur, intelligitur abunde ex iis, quae suo loco de <lb/>natura soni disserentes deduximus, cum esse eam non minorem oporteat <lb/>quam ituum et redituum fidis, quippe esse illos debere incredibiliter celeres <lb/>et crebros declaravimus &rdquo; (Syntagmatis philos., P. II, S. III, Operum T. II, <lb/>Florentiae 1727, pag. </s>

<s>457). </s></p><p type="main">

<s>Ripensando ora il Dedart a questa incredibile celerit&agrave;, necessaria a pro&shy;<lb/>dur la voce, ebbe a riconoscere, applicando all'aria che passa per la tra&shy;<lb/>chea la legge delle velocit&agrave; de'liquidi ne'canali in ragion reciproca delle <lb/>sezioni, che dee l'aria stessa risalir da'bronchi alla laringe sempre pi&ugrave; <pb xlink:href="020/01/1550.jpg" pagenum="425"/>lenta. </s>

<s>Anche Galeno, facilmente persuaso della necessaria celerit&agrave; dell'aria <lb/>in uscir dalla glottide, pare presentisse quella medesima difficolt&agrave;, che venne <lb/>tanti secoli dopo ad affacciarsi alla mente dell'Accademico parigino, e sco&shy;<lb/>perti dall'antico padre dell'Anatomia i ventricoli, rimasti ignoti a tutti i <lb/>suoi predecessori, pens&ograve; che in essi, chiusa la glottide, si comprimesse l'aria, <lb/>la quale poi sfogandosi, quand'essa glottide apre le labbra, entri in quella <lb/>celerit&agrave; richiesta a produrre il suono. </s>

<s>&ldquo; Natura ventriculum apposuit non <lb/>parvum, ad quem, quum aer vias nactus amplas in animal ingreditur, rur&shy;<lb/>susque exit, nihil in ventrem prosilire. </s>

<s>Porro, si transitus fuerit obstructus, <lb/>ibi tum arctatus aer pellitur violenter in obliquum lingulae, quae aperit <lb/>orificium, quod labiis applicatis clausum hactenus erat &rdquo; (De usu partium <lb/>cit., pag. </s>

<s>408). </s></p><p type="main">

<s>Anche l'Acquapendente e il Casserio ripeterono esser questo assegnato <lb/>da Galeno il principale ufficio de'ventricoli della laringe, ma il Dodart, in&shy;<lb/>vocando la legge idraulica sopra accennata, dalla quale si conclude che la <lb/>celerit&agrave; di ogni fluido che corre dentro un canale da null'altro dipende che <lb/>dalla sezione, facilmente riconobbe che poteva la glottide cos&igrave; restringere la <lb/>sua apertura, e ridurla tanto minore rispetto a quella della trachea, da ba&shy;<lb/>star questo solo a metter l'aria in moto di risonanza. </s></p><p type="main">

<s>Emendati cos&igrave; questi errori colla scienza del moto de'fluidi, ignota a <lb/>tutti coloro che avevano preceduto Benedetto Castelli, ci&ograve; che pi&ugrave; impor&shy;<lb/>tava al Dodart era quello di ritrovare il corpo della risonanza. </s>

<s>E giacch&egrave; <lb/>questo corpo, stando l'organo sonoro nel mezzo, riesce ne'musicali stru&shy;<lb/>menti dalla parte opposta a quella che manda il fiato, dove in altro luogo <lb/>pi&ugrave; acconcio, ragionava esso Dodart, pu&ograve; farsi la risonanza che nella cavit&agrave; <lb/>del naso e della bocca? </s>

<s>&ldquo; On ne peut, selon cette analogie, attribuer le ton <lb/>qu'&agrave; la bouche et aux narines, qui font le r&eacute;sonnement, ou &agrave; la glotte qui <lb/>fait le son; et comme tous les differens tons sont produits dans l'homme <lb/>par le m&ecirc;me instrument, il faut que la partie qui les produit soit capable <lb/>de changemens qui puissent y avoir rapport. </s>

<s>Pour un ton bas il faut plus <lb/>d'air que pour un ton haut. </s>

<s>La trach&eacute;e pour laisser passer cette plus grande <lb/>quantit&eacute; d'air se dilate, s'accourcit, et en s'accourcissant tire le canal de la <lb/>bouche et l'allonge. </s>

<s>Au contraire pour un ton haut elle se resserre, s'al&shy;<lb/>longe et permet au canal de la bouche de s'accourcir. </s>

<s>On pourroit donc <lb/>croire que le canal de la bouche plus long pour les tons graves, et plus <lb/>court pour les aigus, est iustement ce qu'il faut pour la production des <lb/>tons &rdquo; (Collection acad&eacute;mique, T. </s>

<s>I cit., pag. </s>

<s>497). </s></p><p type="main">

<s>Queste dottrine, in cui al flauto della voce animale si ritrovavan le pi&ugrave; <lb/>giuste parti, dandosi a loro nello stesso tempo la disposizione pi&ugrave; conve&shy;<lb/>niente ai flauti musicali; furono accolte con gran plauso e approvate dai <lb/>pi&ugrave; eletti ingegni del secolo XVIII, fra'quali basti per noi poter citare il <lb/>Morgagni. </s>

<s>Se non che il grande Anatomico, pi&ugrave; diligentemente esaminando <lb/>i ventricoli, ebbe a maravigliarsi che il Dodart, nella sua nuova instituzione, <lb/>non ne facesse alcun conto, di che riconobbe la causa nelle negligenti de-<pb xlink:href="020/01/1551.jpg" pagenum="426"/>scrizioni dell'Acquapendente e del Casserio, i quali, in tanto assiduo studio <lb/>posto intorno alla laringe dell'uomo, non si comprende come non fermas&shy;<lb/>sero mai la loro attenzione in que'seni ventricolari, per delinearne almeno <lb/>gli orificii. </s>

<s>Lo stesso Acquapendente, dop'aver detto &ldquo; ventricolos obtinere <lb/>equum et porcum, ex iis quae novi &rdquo; (De larynge cit., pag. </s>

<s>292), si con&shy;<lb/>tenta di soggiunger semplicemente: &ldquo; homines autem habent quidem, sed <lb/>non ita profundos &rdquo; (ibid.), e il Casserio, limitandosi all'esame della laringe <lb/>porcina, &ldquo; opera horum ventriculorum, egli dice, porcos vocem illam, quam <lb/>grunnitum dicimus, absolvere verisimile est &rdquo; (De laryngis hist. </s>

<s>cit., pag. </s>

<s>183). </s></p><p type="main">

<s>Il Morgagni dunque, avendo riconosciuto che il poco diligente esame <lb/>dell'organo era stato causa che ne fosse da'suoi predecessori cos&igrave; poco ve&shy;<lb/>rosimile designato l'uso, cominci&ograve; a meditar di proposito intorno a ci&ograve;, e a <lb/>sospettar che i ventricoli servissero principalmente a modulare i suoni. </s>

<s>Dava <lb/>fondamento al suo sospetto l'Acquapendente, il quale si ricordava aver os&shy;<lb/>servato che fra le rane gracidano in tuono pi&ugrave; grave di tutte l'altre quelle <lb/>&ldquo; quae prope aures ex utraque parte foramen obtinent, membrana quadam <lb/>tenui ac laxissima obductum, per quod in expiratione aer egrediens, mem&shy;<lb/>branam exterius impulsam utrinque inflat ampullam, veluti faciens ut ex <lb/>maiori facta cavitate gravior vox subsequatur &rdquo; (De larynge cit., pag. </s>

<s>304). </s></p><p type="main">

<s>Or pensava il Morgagni che i ventricoli della laringe, come si possono <lb/>facilmente restringere, cos&igrave; anche facilmente si possono dilatare: o perch&egrave; <lb/>dunque si negherebbe che quegli stessi ventricoli servano all'uomo e agli <lb/>animali, come le vescicole alle rane, per far d'uno in altro tuono passare <lb/>a talento la voce? </s>

<s>&ldquo; Sunt enim ventriculi, ut ante demonstrabam, statim <lb/>intra paris thyroarytaenoidaei atque adeo etiam intra thyroidis circumferen&shy;<lb/>tiam constitutis, sic ut, his contractis aut relaxatis, illi quoque compriman&shy;<lb/>tur vel amplientur. </s>

<s>Illud autem musculorum par, sicuti in acutis tonis, <lb/>constringendae glottidis gratia, contrahitur, un&agrave;qu&egrave;, ob eandem causam, thy&shy;<lb/>roides ab staphylo pharingaeis, atque a thyro pharingaeis coarctatur; ita <lb/>apposita de causa illud idem thyroarytaenoidaeum par, eademque cartilago <lb/>in tonis gravibus remittuntur &rdquo; (Adversaria anat. </s>

<s>omnia, Patavii 1719, pag. </s>

<s>18). </s></p><p type="main">

<s>La tranquilla meditazione intorno alla verosimiglianza di questa ipotesi, <lb/>che il Morgagni proponeva agli studiosi, venne a un tratto turbata dai ru&shy;<lb/>mori sollevati da Antonio Ferrein in mezzo alla stessa Accademia di Parigi, <lb/>dove, leggendo nel 1741 una sua dissertazione <emph type="italics"/>De la formation de la voix <lb/>de l'homme,<emph.end type="italics"/> sosteneva, contro il Dodart e contro tutti i Galenisti, che la <lb/>laringe non &egrave; uno strumento a fiato ma a corda; non &egrave; simile al flauto, ma <lb/>alla lira. </s>

<s>La cosa per verit&agrave; non era nuova: l'aveva accennata gi&agrave; nel <lb/>IV libro <emph type="italics"/>De resolutione corporis humani<emph.end type="italics"/> il Varolio, e pi&ugrave; recentemente il <lb/>Perrault aveva, nel suo trattato <emph type="italics"/>De bruit,<emph.end type="italics"/> cos&igrave; lasciato scritto: &ldquo; Pour ce <lb/>qui regarde le ton de la voix, il est bas et grave quand la glotte fait une <lb/>sente bien longue: car alors la longueur de l'une et de l'autre membrane <lb/>qui composent la glotte rendant chaque membrane l&agrave;che et peu rendue, <lb/>leurs ondoyemens sont rares et lents, d'ou il s'ensuit que les parties em&ugrave;es <pb xlink:href="020/01/1552.jpg" pagenum="427"/>ne froissent les particules que loin &agrave; loin, ce qui fait le ton grave; le ton <lb/>aigu se fait par des causes oppos&eacute;es &rdquo; (Oeuvres cit., pag. </s>

<s>220). Nonostante <lb/>seppe cos&igrave; bene il Ferrein con esperienze nuove e con nuovi argomenti so&shy;<lb/>stener l'ipotesi antica, che molti, abbandonata quella del Dodart, si volsero <lb/>a professarla. </s>

<s>Ma l'Accademia, esaminando le parti per decider se la laringe <lb/>operi come uno strumento a fiato o come uno strumento a corda, pronun&shy;<lb/>zi&ograve; in giudizio, tuttavia approvato dai savii &ldquo; qu'aucun instrument de mu&shy;<lb/>sique artificial ne rassemble a la glotte &rdquo; (Collection acad&eacute;mique, T. II, a <lb/>Diion 1754, pag. </s>

<s>426). </s></p><p type="main">

<s>Cos&igrave;, verso la met&agrave; del secolo XVIII, concludevasi, rispetto all'organo <lb/>della voce nell'uomo e ne'quadrupedi, la sua storia cominciata gi&agrave; da Ga&shy;<lb/>leno. </s>

<s>Per ci&ograve; poi che riguarda gli uccelli son le tradizioni assai meno lon&shy;<lb/>tane, perch&egrave; propriamente muovono dall'Aldovrandi. </s>

<s>Ripensava egli un giorno <lb/>a quella voce cos&igrave; forte e acuta, che mettono le anatre anche sott'acqua, e <lb/>perch'egli era di parere che si generasse essa voce dai polmoni, e che i <lb/>bronchi e la trachea facessero da corpi di risonanza, pens&ograve; di dover ritro&shy;<lb/>vare, anatomizzando, in quegli organi qualche cosa, da cui si venisse a ren&shy;<lb/>dere la ragione di un fatto, che gli recava stupore. </s>

<s>&ldquo; Vocem Anas cur tam <lb/>acutam atque magnam edat, tamquam sub aquam caput teneat, cum apud <lb/>meipsum mirarer, eam dissecui, causam eius scrutaturus haud dubio ex ar&shy;<lb/>teriae asperae figura, quam sane diversam esse ab aliis reperi. </s>

<s>Quae igitur <lb/>bifariam divaricatur in pulmones vesicam quandam habet duram, cartilagi&shy;<lb/>neam, concavam ubi maior apparet dextrorsum vergentem, eiusque bene&shy;<lb/>ficio quae hactenus in ea stupebam obire iudicavi &rdquo; (Ornithologiae, T. III, <lb/>lib. </s>

<s>XIX, Francof. </s>

<s>1613, pag. </s>

<s>83). </s></p><p type="main">

<s>S'inger&igrave; da questa scoperta nella mente dell'Aldovrandi l'opinione, che <lb/>tutti quegli uccelli, i quali hanno voce pi&ugrave; sonora o canto pi&ugrave; dolce, sieno <lb/>anche serviti da qualche organo aggiunto alla semplice laringe superiore. </s>

<s><lb/>Trov&ograve; fra poeti e filosofi antichi una famosa controversia, dicendo questi che <lb/>il Cigno non canta, e quelli asserendo che anzi modula dolcissime armonie, <lb/>piene d'una ineffabile mestizia, quando sentesi presso alla morte. </s>

<s>Riducen&shy;<lb/>dosi perci&ograve; la cosa a una questione ornitologica, il nostro Autore nel cap. </s>

<s>I <lb/>del sopra citato libro ne tratta, prima eruditamente, e poi, inclinando a fa&shy;<lb/>vorire i poeti, si rivolge all'anatomia, la quale, gli rivelava ne'Cigni organi <lb/>simili a quelli gi&agrave; scoperti nell'Anatre, ma tanto pi&ugrave; squisiti, da non si du&shy;<lb/>bitar che servissero al canto. </s>

<s>&ldquo; Non modicam fidem faciet praeclara illa et <lb/>suspicienda arteriae asperae structura, ante hac a nullo alio, quod equidem <lb/>sciam, observata. </s>

<s>Ea enim, cum duplici reflexione tubae bellicae figuram <lb/>exactissime repraesentet, qua quamlibet tam acutorum quam gravium so&shy;<lb/>norum varietatem modulantes tibicines effingere solent; Natura nihil frustra <lb/>facere neque etiam actionem illam sine idoneis functionique accomodatis <lb/>instrumentis obire soleat, minime vulgaris organi argumento; facile inducor <lb/>ut verisimiliorem eorum esse credam sententiam, qui dulce melos, praeser&shy;<lb/>tim morte vicinos, Cycnos cantare dicunt &rdquo; (ibid., pag. </s>

<s>9). </s></p><pb xlink:href="020/01/1553.jpg" pagenum="428"/><p type="main">

<s>In quel medesimo tempo, che si pubblicava questa Ornitologia, il Cas&shy;<lb/>serio e l'Acquapendente attendevano ai loro particolari trattati intorno alla <lb/>laringe, ne'quali, poco tempo dopo venuti alla luce, non facevasi nessun <lb/>cenno de'nuovi organi scoperti dall'Aldovrandi. </s>

<s>Cosicch&egrave;, dietro l'autore&shy;<lb/>volissimo magistero de'due insigni Autori commemorati, si tenne general&shy;<lb/>mente, e per quasi tutto il secolo XVII, esser organo del canto negli uc&shy;<lb/>celli quella laringe, che lo stesso Acquapendente diceva esser s&igrave; facilmente <lb/>visibile nelle aperte fauci di tutti gli animali pennuti, e di cos&igrave; semplice <lb/>struttura, &ldquo; siquidem asperam arteriam in rimulam desinere in iis apparet &rdquo; <lb/>(De larynge cit., pag. </s>

<s>284) </s></p><p type="main">

<s>Se non che, ripensandoci in seguito meglio, pareva impossibile che in <lb/>certi uccelli un organo cos&igrave; semplice si prestasse a tanta mobile variet&agrave;, e <lb/>a tanta squisita arte di canto. </s>

<s>Fu perci&ograve; il Perrau&igrave;t uno de'pi&ugrave; studiosi in&shy;<lb/>torno ai dimenticati organi scoperti dall'Aldovrandi, e giovandosi della pro&shy;<lb/>pria esperienza e del portato dei tempi fu assai pi&ugrave; felice in riconoscerne <lb/>gli usi. </s>

<s>Ripudiatasi dal Nostro la scienza galenica, e credendo, come sopra <lb/>dicemmo, che la voce movesse dai polmoni, errava nel dire che quel du&shy;<lb/>plice flesso, osservato nella trachea de'Cigni, a ci&ograve; solo servisse &ldquo; ut ne <lb/>vox in tam longo arteriae spacio evanesceret, neve prolixo adeo itinere fa&shy;<lb/>tisceret, sed in ipso revolutae arteriae angulo repercussa maiori cum clan&shy;<lb/>gore erumperet, ac veluti morulae exiguae in eo anfractu quiete recreata <lb/>vires acquirat eundo &rdquo; (Ornithol., T. cit., pag. </s>

<s>9) </s></p><p type="main">

<s>Lette queste cose il Perrault non dubit&ograve; di credere che organo cos&igrave; <lb/>artificioso, piuttosto che a rinforzarla, servisse a produrre la voce, e che fosse <lb/>insomma una vera e propria laringe. </s>

<s>Era in ogni modo per&ograve; necessario che <lb/>un'idea tanto nuova fosse confermata dall'esperienza. </s>

<s>Ripensando al modo <lb/>migliore di eseguirla, si sovvenne di aver letto nel trattato <emph type="italics"/>De larynge<emph.end type="italics"/> che, <lb/>mentre un giorno l'Acquapendente esponeva in pubblico anfiteatro gli usi <lb/>di quell'organo della voce, si lev&ograve; un uditore a dire: &mdash; Maestro, a un uc&shy;<lb/>cello morto soffiando per l'aspera arteria, ho trevato che mandava la stessa <lb/>voce come se fosse vivo. </s>

<s>&mdash; Non apprezzando il Fabricio quanto si meri&shy;<lb/>tava quella esperienza, si content&ograve; di rispondere che si poteva da quel fatto <lb/>concluderne &ldquo; adesse cuique animali proprium organum, idest suam laryn&shy;<lb/>gis constitutionem &rdquo; (De larynge cit., pag. </s>

<s>305). </s></p><p type="main">

<s>Ma il Perrault pens&ograve; che si poteva l'esperienza dello scolare di Padova <lb/>bellamente e utilmente applicare al suo intento, ch'era quello di mostrar <lb/>come l'organo, posto al punto in cui la trachea si biforca negli uccelli, &egrave; <lb/>una vera laringe. </s>

<s>Se ucciso infatti l'animale, col tagliargli la testa e col por&shy;<lb/>targli via perci&ograve; la laringe superiore, in soffiare al modo che diceva colui <lb/>nell'anfiteatro anatomico padovano, o in premere le vescicole pneumatiche <lb/>del ventre, la voce tuttavia si produce, qual pi&ugrave; manifesta prova potrebbesi <lb/>desiderare dell'aver veramente gli uccelli una laringe inferiore? </s></p><p type="main">

<s>Si fu tale il ragionamento, che condusse il Perrault a quella sua bella <lb/>e cos&igrave; ben dimostrativa esperienza, della quale cos&igrave; dice nella seconda parte <pb xlink:href="020/01/1554.jpg" pagenum="429"/>della sua <emph type="italics"/>Mechanique dex animaux,<emph.end type="italics"/> dop'aver confermata la struttura della <lb/>trachea nell'anatre, scoperta quasi un secolo prima dall'Aldovrandi: &ldquo; L'effet <lb/>de cette structure se peut aisement conno&icirc;tre, si ayant coup&eacute; la t&egrave;te a ces <lb/>animaux, et le larynx leur etant &ocirc;t&eacute;, on leur presse le ventre: car alors ils <lb/>ne laisseront pas de produire la m&ecirc;me voix que lorsqu'ils &eacute;toient vivans, <lb/>et qu'ils avoient un larynx &rdquo; (Oeuvres, T. </s>

<s>I cit., pag. </s>

<s>394). </s></p><p type="main">

<s>L'Haller trov&ograve; poi la laringe inferiore anche nei passeri e ne'galli <lb/>(Elem. </s>

<s>physiol., T. III cit., pag. </s>

<s>435), ed avendo altri Naturalisti osservato <lb/>ch'&egrave; con pi&ugrave; sottil magistero elaborata negli uccelli canori, nessun dubit&ograve; <lb/>ch'ella non sia veramente precipuo organo, in cui si forma la voce, e per <lb/>cui si modula il canto. </s></p><pb xlink:href="020/01/1555.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO XI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dei pesci<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>I. </s>

<s>Degli ergani e degli esercizi del nuoto. </s>

<s>&mdash; II. </s>

<s>Della respirazione branchiale e del circolo del sangne.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>III. </s>

<s>Degli organi dei sensi.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>L'ordine oramai preso in questa nostra storica trattazione porterebbe <lb/>che, dopo aver detto di ci&ograve; che i metodi sperimentali conferirono a far pro&shy;<lb/>gredire la Storia naturale de'Quadrupedi e degli Uccelli nella pi&ugrave; esatta no&shy;<lb/>tizia de'loro precipui organi e delle loro funzioni, si passasse a far lo stesso <lb/>coi <emph type="italics"/>Rettili,<emph.end type="italics"/> che immediatamente succedono in grado e in dignit&agrave; zoologica <lb/>agli stessi uccelli. </s>

<s>Ma perch&egrave; quei cos&igrave; fatti animali a sangue freddo in non <lb/>poche n&egrave; lievi cose s'assomigliano ai pesci, nella storia di questi si vedr&agrave; <lb/>specchiata qualche immagine anche di quelli. </s>

<s>E dall'altra parte non &egrave; pos&shy;<lb/>sibile a noi, in questa general comprensione delle scienze sperimentali, come <lb/>campo immenso dato a mietere a una falce sola, cogliere che le poche spi&shy;<lb/>ghe pi&ugrave; mature, e perci&ograve; pi&ugrave; eminenti. </s></p><p type="main">

<s>In conformit&agrave; dei precedenti discorsi ci occorre per prima cosa a trat&shy;<lb/>tar dei moti locali, trattazione che, in questo particolar soggetto, si riduce <lb/>alla storia degli organi e degli esercizi del nuoto. </s>

<s>Lusingavano cos&igrave; le pinne <lb/>e le ali, per le loro apparenti somiglianze con la struttura e con gli usi <lb/>de'remi, che nessun dubitava non fossero le pinne stesse organo ai pesci di <lb/>qualunque loro movimento locale. </s>

<s>Come cosa ovvia perci&ograve; i Filosofi e i Na&shy;<lb/>turalisti antichi non fecero nemmeno un cenno del meccanismo animale del <lb/>nuoto ne'loro libri, e Plinio, che si trov&ograve; costretto a rendere la ragione per-<pb xlink:href="020/01/1556.jpg" pagenum="431"/>ch&egrave; alcuni di essi pesci nuotino anche senza le pinne, come si vede far per <lb/>esempio alle pastinache e ai rombi, se ne sped&igrave; con dire che <emph type="italics"/>ipsa latitu&shy;<lb/>dine natant.<emph.end type="italics"/></s></p><p type="main">

<s>Nell'et&agrave; del risorgimento, tacendosene il Rondelezio, fu primo l'Acqua&shy;<lb/>pendente che spendesse intorno al nuoto poche parole, proponendosi di ri&shy;<lb/>solvere i tre seguenti problemi: &ldquo; I. </s>

<s>Quomodo pisces et pleraque alia anima&shy;<lb/>lia, vel ponderosissima et maxime terrestria, in aqua innatando sustentantur. </s>

<s><lb/>II. </s>

<s>Quomodo natatus in aqua fiat. </s>

<s>III. </s>

<s>Qua ratione aquatile animal ad omnes <lb/>loci positiones permutatur &rdquo; (De natatu, Op. </s>

<s>omnia cit., pag. </s>

<s>377). E perch&egrave; <lb/>veramente tutta la meccanica del nuoto concludesi dentro questi tre pro&shy;<lb/>blemi, si riduce l'intento nostro a narrar brevemente come quando e da chi <lb/>venissero risoluti. </s></p><p type="main">

<s>Quanto al primo non &egrave; difficile, dice lo stesso Acquapendente, inten&shy;<lb/>dere in che modo galleggino i pesci nell'acqua, vedendovisi galleggiare gli <lb/>uomini stessi e i quadrupedi pi&ugrave; ponderosi. </s>

<s>Di che, poi soggiunge, tanto pi&ugrave; <lb/>facilmente ci persuaderemo pensando che hanno gli stessi pesci poche ossa, <lb/>carne floscia alleviata anche di pi&ugrave; da quella vescica &ldquo; oblonga, ex tunica <lb/>tenuissima, et densissima aereque sola plena &rdquo; (ibid.). </s></p><p type="main">

<s>Poco dopo venne Galileo a illustrare co'nuovi principii meccanici e idro&shy;<lb/>statici questi concetti, cominciando dal dimostrare in che modo si possan <lb/>facilmente sostenere nell'acqua moli di animali pi&ugrave; smisurate di quelle <lb/>stesse, che si sostengono in aria. </s>

<s>La dimostrazione galileiana &egrave; conclusa dal <lb/>principio, che equilibrandosi i pesci dentro l'acqua, per essere in loro il <lb/>peso dell'ossa compensato dalla leggerezza della polpa, non sentono perci&ograve; <lb/>la propria gravezza. </s>

<s>&ldquo; Talch&egrave; negli acquatici avverr&agrave; l'opposto di quel che <lb/>accade negli animali terrestri, cio&egrave; che in questi tocchi all'ossa a sostenere <lb/>il peso proprio e quel della carne, e in quelli la carne regge la gravezza <lb/>propria, e quella dell'ossa. </s>

<s>E per&ograve; deve cessar la maraviglia come nell'acqua <lb/>possano essere animali vastissimi, ma non sopra la terra, cio&egrave; nell'aria &rdquo; <lb/>(Alb. </s>

<s>XIII, 131). </s></p><p type="main">

<s>Per ci&ograve; poi che riguarda l'equilibrio idrostatico aveva l'Acquapendente <lb/>osservato che, ne'notanti per l'acqua dolce, come nelle tinche, nei lucci, e <lb/>forse in altri, &egrave; affissa alla spina del dorso una vescica, perch'essendo essa <lb/>acqua dolce pi&ugrave; tenue della marina &egrave; anche perci&ograve; men valida a sostenere. </s>

<s><lb/>Il Rondelezio per&ograve; aveva molto tempo prima pensato all'uso di questa ve&shy;<lb/>scica, e aveva detto servire a rendere pi&ugrave; leggero il pesce e a facilitargli il <lb/>modo di risalire in alto. </s>

<s>&ldquo; Aspera igitur arteria, in iis piscibus qui pulmo&shy;<lb/>nibus spirant, ducendi spiritus et respirandi gratia est constructa, eiusque <lb/>aliquando retinendi cohibendique, ut sursum facilius ferantur: aer enim re&shy;<lb/>tentus velut suspendit in aqua, demergique prohibet. </s>

<s>Cuius utilitatis causa <lb/>vesicam aere plenam quibusdam branchias habentibus dedit Natura &rdquo; (De <lb/>piscibus marinis, Lugduni 1554, pag. </s>

<s>61). </s></p><p type="main">

<s>Quel ch'era dunque per l'Acquapendente uno strumento inerte, e quasi <lb/>diremo vanitoso, riusciva pel Rondelezio un organo attivo, facendone po&igrave; <pb xlink:href="020/01/1557.jpg" pagenum="432"/>Galileo rilevar meglio l'attivit&agrave; coll'attribuirgli l'ufficio di mantenere il pe&shy;<lb/>sce sempre equilibrato in mezzo a un liquido continuamente soggetto a va&shy;<lb/>riar la sua propria gravit&agrave; in specie. </s>

<s>&ldquo; I pesci, egli dice, ad arbitrio loro si <lb/>equilibrano, non solo con un'acqua, ma con differenti notabilmente o per <lb/>propria natura o per una sopravvenente torbida o per salsedine, che fa dif&shy;<lb/>ferenza assai grande; si equilibrano dico tanto esattamente che, senza punto <lb/>moversi, restano in quiete in ogni luogo, e ci&ograve; per mio credere fanno eglino, <lb/>servendosi dello strumento datogli dalla natura a cotal fine, cio&egrave; di quella <lb/>vescichetta che hanno in corpo, la quale per uno assai angusto meato ri&shy;<lb/>sponde alla lor bocca, e per quello a posta loro o mandano fuori parte del&shy;<lb/>l'aria, che in dette vesciche si contiene, o, venendo col nuoto a galla, altra <lb/>ne attraggono, rendendosi con tale arte or pi&ugrave; or meno gravi dell'acqua, ed <lb/>a lor beneplacito equilibrandosegli &rdquo; (Alb. </s>

<s>XIII, 71, 72). </s></p><p type="main">

<s>Se quell'angusto meato, che mette la vescica in comunicazion colla <lb/>bocca, non fosse stato da Galileo semplicemente supposto, la sua ingegnosa <lb/>ipotesi veniva del resto a verificarsi nell'esempio di quei pesciolini artifi&shy;<lb/>ciali, inventati e costruiti in Roma da Raffaello Magiotti, per dimostrar la <lb/>renitenza certissima dell'acqua alla compressione, e tutt'insieme a spetta&shy;<lb/>colo dei curiosi. </s>

<s>Dop'aver descritti i galleggianti i quali, alterandosi la den&shy;<lb/>sit&agrave; dell'aria in essi inclusa col variarne la temperatura o la pressione, si <lb/>posson rendere a piacere pi&ugrave; o men leggeri, e cos&igrave; farli imitatori de'na&shy;<lb/>turali moti di ascesa e di discesa de'pesci dentro i vivai; &ldquo; sebbene &egrave; forza, <lb/>soggiunge esso Magiotti, con tutti i nostri artifizi, che questi pesci finti ce&shy;<lb/>dano all'esattezza dei veri, quali, ritenendo in certe vescichette pi&ugrave; o meno <lb/>aria, sanno in ogni sorte d'acqua ragguagliarsi e contrappesarsi a maravi&shy;<lb/>glia &rdquo; (Targioni, Notizie degli aggrandimenti ecc., T. II, P. II, Firenze 1780, <lb/>pag. </s>

<s>187). </s></p><p type="main">

<s>Rimase perci&ograve; ai seguaci della scuola galileiana l'ufficio di dimostrare <lb/>la reale esistenza del supposto canale di comunicazione tra la vescica de'pe&shy;<lb/>sci e la bocca, e intanto che s'aspettava qualche esperto Anatomico per aver <lb/>da lui una decisione di fatto, gli Accademici del Cimento gli preparavano la <lb/>via con lo sperimentar se l'aria trova propriamente il passo aperto, e collo <lb/>scoprir da qual parte ella esce dalle interiori viscere dell'animale all'esterno. </s>

<s><lb/>S'accendeva ne'nostri Accademici fiorentini tanto pi&ugrave; vivo il desiderio di <lb/>questa ricerca, in quanto che Tommaso Cornelio aveva, in una sua Epistola, <lb/>gi&agrave; diffusa nel manoscritto prima che per le pubbliche stampe, dimostrato <lb/>per esperienze che l'acqua si trasforma in aria dentro il corpo de'pesci, co&shy;<lb/>sicch&egrave; essendo essa aria in loro innata non hanno bisogno, come Galileo <lb/>diceva, d'andare a cercarla a somma l'acqua, ed &egrave; vano perci&ograve; supporre o <lb/>dar travaglio all'Anatomia di scoprir nessun occulto meato, per cui qualche <lb/>cosa esca o venga di fuori. </s>

<s>&ldquo; Hinc patet, cos&igrave; concludeva il Cornelio quella <lb/>citata Epistola a Marc'Aurelio Severino, non omnino opus esse piscibus <lb/>aliisque aquatilibus ad summam aquae superficicm eniti, ut inde hauriant <lb/>aerem qui passim invenitur in eorundem utriculis. </s>

<s>Potest enim aer ille in <pb xlink:href="020/01/1558.jpg" pagenum="433"/>ipsis piscium corporibus gigni, et exinde in praefatas vesiculas, tanquam in <lb/>propria conceptacula, deferri, siquidem facillime humor, uti iam dictum est, <lb/>vertitur in aerem &rdquo; (De cognatione aeris et aquae inter Progymnasm. </s>

<s>cit., <lb/>pag. </s>

<s>399). </s></p><p type="main">

<s>Per decider dunque se l'aria negli utricoli de'pesci era innata, o co&shy;<lb/>municava coll'esterno, posero i nostri Accademici un Barbio nel vuoto, e <lb/>trovarono poi esso utricolo nelle aperte viscere raggrinzato ed esausto. </s>

<s>As&shy;<lb/>sicuratisi cos&igrave; che quell'aria inclusa era uscita, non vedendo manifeste rot&shy;<lb/>ture nella membrana artificialmente distesa col fiato, e dall'altra parte si&shy;<lb/>curi che dovesse aver l'aria nell'uscire in ogni modo trovato qualche varco; <lb/>sospettarono che ci&ograve; fosse nella pi&ugrave; aguzza parte della vescica. </s>

<s>&ldquo; Quindi fu <lb/>pensato a far s&igrave; che l'acqua medesima ce lo discoprisse. </s>

<s>Per lo che, fatta <lb/>cavare un'altra vescica da un pesce vivo e sano, s'involse in un brandello <lb/>di rete, e quella aggravata di conveniente peso si messe al solito in acqua, <lb/>sotto alla quale essendo rimasta, fatto il vuoto, si veddero uscire per la <lb/>parte aguzza molte gallozzole d'aria, onde parve di poter verisimilmente cre&shy;<lb/>dere esser quivi il meato naturale che la trasmette &rdquo; (Saggi di natur. </s>

<s>esper., <lb/>Firenze 1841, pag. </s>

<s>74). </s></p><p type="main">

<s>Restava, per pi&ugrave; piena conferma del supposto galileiano, a dimostrar <lb/>che essa aria veniva veramente trasmessa alla bocca, e i nostri Accademici <lb/>non mancarono di farlo per via della seguente esperienza: &ldquo; Si rinvolse una <lb/>Lasca nella stessa rete, acciocch&egrave;, trattenuta in fondo dal peso attaccatole, <lb/>avesse per necessit&agrave; a rimaner sott'acqua. </s>

<s>Fattosi dunque il voto, se le <lb/>vedde fare grandissima copia d'aria per bocca, la qual veniva in grossis&shy;<lb/>sime bolle, nello stesso modo che s'era veduta uscire dalla vescica som&shy;<lb/>mersa &rdquo; (ivi). </s></p><p type="main">

<s>Messo cos&igrave; in piena evidenza il passaggio dell'aria dalla vescica alla <lb/>bocca, Carlo Fracassati venne finalmente a rendere, colla sua sottile arte <lb/>anatomica, visibile agli occhi di ognuno quel canale di comunicazione indo&shy;<lb/>vinato gi&agrave; da Galileo, gl'insegnamenti del quale tornavano intanto d'ogni <lb/>parte vittoriosi sopra quelli di Tommaso Cornelio. </s>

<s>&ldquo; Ipse quidem, scrive il <lb/>Fracassati nell'Epistola <emph type="italics"/>De cerebro<emph.end type="italics"/> a Marcello Malpighi, ipse quidem de&shy;<lb/>prehendi meatum ad folliculum aeris quo pisces perpetuo nataturi gaudent, <lb/>ex quo patet non ingenitum esse in utricolo natatorio aerem, sed ades se <lb/>quaedam commercia extrinseci, vel in aqua deliquescentis aeris cum illo &rdquo; <lb/>(M. Malpighi, Operum, T. II cit., pag. </s>

<s>144). </s></p><p type="main">

<s>Cos&igrave; venivano pienamente dimostrati gli usi, rimasti prima s&igrave; incerti, <lb/>della vescica dei pesci, la quale nessuno poi dubit&ograve; di chiamarla <emph type="italics"/>natatoria,<emph.end type="italics"/><lb/>dietro il primo esempio datone dal Fracassati. </s>

<s>L'incertezza nasceva special&shy;<lb/>mente dal parer che ella servisse piuttosto alla respirazione e al pi&ugrave; al pi&ugrave; <lb/>s'ammetteva che potesse aver quell'organo qualche ufficio secondario nel <lb/>nuoto. </s>

<s>L'Harvey infatti rassomigliava la vescicola pneumatica de'pesci alle <lb/>vescicole pneumatiche degli uccelli, nelle quali egli dice che si compie la <lb/>respirazione incominciatasi ne'polmoni. </s>

<s>&ldquo; Quin etiam (quod tamen a nemine <pb xlink:href="020/01/1559.jpg" pagenum="434"/>hactenus observatum memini) earum bronchia, sive asperae arteriae fines <lb/>in abdomen perforantur, aeremque inspiratum intra cavitates illarum mem&shy;<lb/>branarum recondunt, quemadmodum pisces et serpentes intra amplas vesi&shy;<lb/>cas in abdomine positas eumdem attrahunt, et reservant, eoque facilius na&shy;<lb/>tare existimantur &rdquo; (De generat. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>5). </s></p><p type="main">

<s>Nel Mersenno, per citar l'esempio di un'altra grande autorit&agrave; nella <lb/>scienza a que'tempi, l'incertezza se la vescica serva da polmone o da gal&shy;<lb/>leggiante &egrave; anche pi&ugrave; chiaramente espressa l&agrave; dove, nel terzo Tomo delle <lb/>Nuove osservazioni, dice a proposito della respirazione esser dubbio se da <lb/>essa propriamente dipende la vita, vedendosi i pesci vivere senza respirare <lb/>&ldquo; nisi forte, poi per&ograve; soggiunge, vim aliquam seu facultatem habeant qua <lb/>separent aerem ab aqua, eoque nobis nescientibus utantur. </s>

<s>Quod ex illorum <lb/>videtur confirmari follibus seu vesiculis aere inflatis, quales reperiuntur in <lb/>carpionibus et aliis piscibus, licet plerique censeant huiusmodi vesiculas illis <lb/>solum datas ut natare possint &rdquo; (Parisiis 1647, pag. </s>

<s>106). </s></p><p type="main">

<s>L'esperienze dunque de'nostri Accademici, alle quali s'aggiungevano <lb/>quelle del Boyle, venivano a dissipare i dubbi del Mersenno e dell'Harvey, <lb/>dimostrandosi per esse evidentemente che, votatasi ai pesci d'ogni aria la <lb/>vescica, non era a loro pi&ugrave; possibile sollevarsi, come prima facevano, a galla, <lb/>ma si vedevano dentro i vivai &ldquo; sempre andarsene terra terra notando con <lb/>la pancia rasente il fondo &rdquo; (Saggi cit., pag. </s>

<s>72). Dal vedere altres&igrave; in quelle <lb/>esperienze i pesci colla vescica esausta rivoltarsi supini, senza mai per qua&shy;<lb/>lunque sforzo potersi riavere, veniva a dimostrarsi un altr'uso importantis&shy;<lb/>simo della stessa vescica, qual'&egrave; quello di stabilire il centro della gravit&agrave; nel <lb/>punto pi&ugrave; conveniente alla natural posizione dell'animale. </s></p><p type="main">

<s>Chi ripensa ora, dopo le cose narrate, che la massima parte dell'espe&shy;<lb/>rienze si facevano nell'Accademia fiorentina sotto la direzione del Borelli, <lb/>in casa del quale in Pisa il Fracassati stesso, nella sopra citata Epistola <emph type="italics"/>De <lb/>cerebro<emph.end type="italics"/> (pag. </s>

<s>143), confessa d'essersi esercitato intorno alle sue prime ana&shy;<lb/>tomie dei pesci; anche prima di svolgere le pagine del libro s'aspetta di <lb/>vedere stillato il succo di quelle dottrine e, come in suo proprio vaso, rac&shy;<lb/>colto nell'Opera dei moti animali. </s></p><p type="main">

<s>Nella proposizione CCXI infatti della Parte I, attendendo l'Autore a ri&shy;<lb/>cercar l'organo per cui i pesci s'equilibran nell'acqua, lo ritrova facilmente <lb/>nella vescica, l'aria della quale pensa che si potrebbe ora condensare e ora <lb/>dilatare per l'azion delle fibre muscolari, di ch'&egrave; intessuta la stessa mem&shy;<lb/>brana, operanti a quel modo che nello sfintere dell'ano o nella vescica uri&shy;<lb/>naria. </s>

<s>Questo pensiero, che apparisce nuovo e tutto proprio al Borelli, ve&shy;<lb/>niva confermato da quella esperienza degli Accademici del Cimento, per la <lb/>quale mostravasi che in un Barbio, stato prima nel vuoto, avevano le deli&shy;<lb/>cate fibre della vescica nel violento sforzo cos&igrave; sofferto, da non essere ora&shy;<lb/>mai pi&ugrave; atte al loro ufficio. </s>

<s>Ond'&egrave; che, sebbene al paziente si trovasse dopo <lb/>morto la vescica stessa &ldquo; gonfia come suol esser naturalmente &rdquo; l'esser <lb/>per&ograve; &ldquo; men dura a comprimersi che non son quelle degli altri pesci &rdquo; era <pb xlink:href="020/01/1560.jpg" pagenum="435"/>a quel Barbio causa che movendosi non potesse far altro che rasentar, senza <lb/>mai sollevarsene, il fondo del vivaio (Saggi cit., pag. </s>

<s>72). </s></p><p type="main">

<s>Nonostante riconobbe il Borelli esser questa operazione dello sfintere <lb/>della vescica d'assai poco momento, e perci&ograve;, a spiegar in che modo i pesci <lb/>contemperino cos&igrave; destramente la loro propria gravit&agrave; in specie a quella cos&igrave; <lb/>mutabile dell'acqua, invoc&ograve; come pi&ugrave; efficaci delle sue nuove le dottrine <lb/>antiche di Galileo. </s>

<s>&ldquo; Haec autem vesicae aereae piscium dilatatio exigua esse <lb/>videtur, et ideo non sufficiet ad aequilibrium transmutandum in locis, in <lb/>quibus aqua dulcis est et parum gravis, et tunc puto quod pisces vi remi&shy;<lb/>gatiouis sustinentur, et ad summitatem aquae perducuntur, ut novum aerem <lb/>deglutiendo minus graves in specie reddantur. </s>

<s>Qui postea, si superfluus fue&shy;<lb/>rit in locis aquae profundioribus et gravioribus, evomitur per os, et solum <lb/>modo retinetur portio adaequata, ut absque laboriosa compressione aequili&shy;<lb/>brata in fundo permanere et quiescere possint. </s>

<s>Quod postea aer praedictae <lb/>vesicae piscium multiplicari, novum aerem sorbendo, et minui, evomendo <lb/>superfluum, per os possit, prout necessitas aequilibrii eorum exigit, suade&shy;<lb/>tur ex canali manifesto, licet subtili et stricto, praedictae vesicae, qui in <lb/>fundo stomachi desinit, et frustra factus esse non potest. </s>

<s>Imo per eum in <lb/>vacuo torricelliano talis vesica aere exinanitur, quando piscis per os mul&shy;<lb/>tiplices spumosas ampullas eructat &rdquo; (De motu anim., P. I, Romae 1680, <lb/>pag. </s>

<s>338, 39). </s></p><p type="main">

<s>Il manifesto, bench&egrave; sottile e stretto canale, di che qui parla il Borelli, <lb/>&egrave; senza dubbio quello scoperto dal Fracassati, il quale dee essersi senza <lb/>altro abbattuto a sezionare una Cheppia, quando per la prima volta mo&shy;<lb/>str&ograve; in Pisa quell'organo tanto desiderato da'Galileiani alla presenza dei <lb/>cortigiani medicei e degli amici convenuti insieme nelle case dello stesso Bo&shy;<lb/>relli. </s>

<s>Nelle Cheppie infatti quel cannellino della vescica mette capo in fondo <lb/>allo stomaco e vien dal Fracassati, nell'Epistola <emph type="italics"/>De Cerebro,<emph.end type="italics"/> cos&igrave; descritto: <lb/>&ldquo; In Clupea, postquam a ventriculi inferiori parte innumera pene intestinula <lb/>coeca prodierint, videtur totus ventriculus in hunc meatum abire, qui ad <lb/>bifidam aeream vesicam eadem prorsus implantatione progredetur &rdquo; (loco <lb/>cit., pag. </s>

<s>145). Or il Borelli cred&egrave; che il termine del canaliculo nelle Chep&shy;<lb/>pie fosse il medesimo che in tutti i pesci, e perci&ograve; sentenzi&ograve; in generale <lb/>che <emph type="italics"/>in fundo stomachi desinit.<emph.end type="italics"/> Ma aveva gi&agrave; il Fracassati diligentemente <lb/>notato che <emph type="italics"/>variat meatus huius in aliis piscibus origo,<emph.end type="italics"/> e nella Tinca per <lb/>esempio non &egrave; dal fondo dello stomaco, ma dal principio. </s>

<s>&ldquo; In Tinca mea&shy;<lb/>tus hic (quem antea ignotum fuisse credo) oritur ab initio stomachi ubi <lb/>dilatatur, et cavitatem infundibulo similem aemulatur. </s>

<s>Mox attenuatur, ac ad <lb/>medium utriculi illius ducitur, qui in medio se cogens, veluti duorum tur&shy;<lb/>binum coalitu, clepsydram pulverariam refert, ibique implantatur &rdquo; (ibid., <lb/>pag. </s>

<s>144). </s></p><p type="main">

<s>Il Redi poi osserv&ograve; che tale, quale il Fracassati la descrisse nella Tinca, <lb/>&egrave; la disposizione del canaliculo nella vescica della massima parte dei pesci, <lb/>e non pot&egrave; con tutta la riverenza tenersi dallo svelare ai Naturalisti l'er-<pb xlink:href="020/01/1561.jpg" pagenum="436"/>rore, che s'ascondeva nelle sentenziose parole del Borelli. </s>

<s>&ldquo; Il famoso e ve&shy;<lb/>ramente grandissimo Geometra Giovanni Alfonso Borelli (cos&igrave; egli scrive nel <lb/>trattato <emph type="italics"/>Degli animali viventi negli animali viventi<emph.end type="italics"/>) afferm&ograve; che questo <lb/>suddetto canale, per cui pu&ograve; uscire ed entrare l'aria nel notatoio o vescica, <lb/>partendosi da essa vescica, va ad insinuarsi e a metter capo nel fondo dello <lb/>stomaco de'pesci: ma non in tutti i pesci mette capo quel canale nel fondo <lb/>dello stomaco, conforme per avventura parve a questo grand'uomo, anzi per <lb/>dire il vero in una sola spezie di pesci ho trovato che nel fondo dello sto&shy;<lb/>maco egli termina e s'impianta, e questa &egrave; la spezie delle Lacce o Chep&shy;<lb/>pie. </s>

<s>Nelle altre generazioni di pesci mette foce o nella gola o nel principio <lb/>dello stomaco, o nel mezzo della lunghezza dello stomaco medesimo. </s>

<s>N&egrave; in <lb/>tutte queste generazioni &egrave; ugualmente manifesto questo canale, imperoc&shy;<lb/>ch&egrave;, se ne'pesci di acqua dolce per lo pi&ugrave; si vede e si trova a prima vista <lb/>e senza difficolt&agrave; veruna, pel contrario in molti pesci di mare non cos&igrave; su&shy;<lb/>bito si trova e si ravvisa, e ci vuole una particolar premurosa diligenza e <lb/>pazienza per rinvenirlo, a segno tale che in alcuni, ancorch&egrave; sia probabi&shy;<lb/>lissimo e certissimo ch'e'vi sia, io molte volte non ho saputo rinvenirlo, <lb/>ma da me medesimo ne incolpo la mia poca diligenza e destrezza con&shy;<lb/>giunte forse con qualche mia insolita impazienza &rdquo; (Opere cit., T. I, P. II, <lb/>pag. </s>

<s>99, 100). </s></p><p type="main">

<s>Questa stessa difficolt&agrave;, cos&igrave; trovata dal Redi in ravvisare il canaliculo <lb/>di comunicazione fra l'aria interna e l'esterna in alcune generazioni di pe&shy;<lb/>sci, fece forse sentenziare al Fracassati: &ldquo; in grandioribus piscibus haec ve&shy;<lb/>sica deest &rdquo; (De cerebro, loco cit, pag. </s>

<s>145). Ma il Redi osserv&ograve; che, seb&shy;<lb/>ben di quell'organo si trovino alcune specie di pesci veramente mancanti, <lb/>non &egrave; per&ograve; questione n&egrave; di piccoli n&egrave; di grandi, come diceva il Fracassati, <lb/>n&egrave; di fluviatili o di marini com'avevano infin dal 1658 pensato gli speri&shy;<lb/>mentatori Accademici di Firenze (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>679). <lb/>Nel luogo sopra citato dal libro <emph type="italics"/>Degli animali viventi negli animali vi&shy;<lb/>venti,<emph.end type="italics"/> annovera l'Autore un lungo ordine di pesci, distinguendo quelli che <lb/>hanno il notatoio da tanti altri che non l'hanno, d'onde presero alcuni oc&shy;<lb/>casione di dubitare se sia veramente la vescica il precipuo organo che serve <lb/>ad equilibrare il pesce nell'acqua. </s>

<s>Il Fracassati per&ograve; aveva gi&agrave; pensato a <lb/>risolvere il dubbio dicendo che ne'pesci a cui manca la vescica supplisce <lb/>per notatoio l'aria inclusa nelle cavit&agrave; dell'addome, e particolarmente quella, <lb/>ch'&egrave; compresa fra le pagine di certe loro singolari membrane. </s>

<s>&ldquo; Putaverim <lb/>tamen totum abdomen sui cavitate illius munera implere (quando patere <lb/>possit aeris illuc aditus, quod nondum percipere potui) nam clausum est <lb/>suo diaphragmate. </s>

<s>In his tamen piscibus, qua in anterioribus dorsum sinua&shy;<lb/>tus, videtur aer latitare, etenim, membrana a spina divulsa, latibulum ali&shy;<lb/>quod aeris accusat &rdquo; (De cerebro cit. </s>

<s>p. </s>

<s>145). </s></p><p type="main">

<s>Il Redi poi trov&ograve; che, almeno in certe specie di pesci, si compone di <lb/>quella stessa membrana divulsa dalla spina la tunica alla vera e propria ve&shy;<lb/>scica, ma la disposizione di lei in ogni modo era tale che, anche quando vi <pb xlink:href="020/01/1562.jpg" pagenum="437"/>fosse il canaliculo di comunicazion coll'esterno, non potutosi sempre vedere <lb/>dal medesimo oculatissimo Redi, si rendeva nulladimeno assai difficile a in&shy;<lb/>tendere come mai il pesce valga a deglutir l'aria soprapposta all'acqua in <lb/>tanta copia, da produr l'effetto idrostatico voluto da Galileo. </s></p><p type="main">

<s>Fu la nuova difficolt&agrave; risoluta pure dal Fracassati, ammettendo che <lb/>l'aria si trovi delitescente anche in mezzo all'acqua, e che il pesce s'equi&shy;<lb/>libri non sempre coll'aumentare o col diminuire il suo peso, ma talvolta <lb/>altres&igrave; coll'espandere e col restringere la sua mole. </s>

<s>&ldquo; Pisces nataturi his <lb/>aecoliis utriculis utuntur: enatant enim ad superiora, si corpus laxaverint; <lb/>inferius subsistunt, si contracti corpore constringatur aer et ita gravius cor&shy;<lb/>pus reddatur &rdquo; (ibid.). </s></p><p type="main">

<s>Fu cos&igrave; finalmente risoluto il primo dei tre problemi meccanici propo&shy;<lb/>sti dall'Acquapendente intorno al nuoto dei pesci. </s>

<s>Quanto agli altri due, <lb/><emph type="italics"/>quomodo natatus fiat, e qua ratione aquatile animal ad omnes loci po&shy;<lb/>sitiones permutatur,<emph.end type="italics"/> dicemmo come l'Autore seguisse la corrente opinione, <lb/>che riconosceva qual principale strumento del notare le pinne. </s>

<s>Un'attenta <lb/>osservazione fece per&ograve; indovinare all'Acquapendente altri usi delle stesse <lb/>pinne, vedendo i lucci stare quasi a fior d'acqua tenendole aperte e ferme, <lb/>per cui congettur&ograve; che servissero tutto insieme e a sostener la macchina <lb/>animale, e a fermarla in quel cos&igrave; lubrico posare sull'acqua. </s>

<s>&ldquo; Propterea <lb/>lucios saepenumero prope aquae superficiem videbis ex toto corpore et pin&shy;<lb/>nis, quasi alis immobilibus et latis extensisque, consistentes, ut propterea <lb/>hoc loco asseverandum sit extentas pinnas et ad oculum immobiles, non <lb/>modo ad sustinendos, sed imprimis ad firmandos in aqua pisces usum prae&shy;<lb/>bere &rdquo; (De natatu, Op. </s>

<s>omnia cit., pag. </s>

<s>378). </s></p><p type="main">

<s>La direzione poi del nuoto, ch'era il terzo problema, l'Acquapendente <lb/>l'affidava ai moti della coda rassomigliata al timone delle navi, concorren&shy;<lb/>dovi la direzione pi&ugrave; o meno obliqua delle pinne. </s>

<s>&ldquo; Oblique igitur ad ali&shy;<lb/>quam loci differentiam volvi, revolvi, inclinare, permutarique, partim pinnae, <lb/>partim caudae munus esse constat, sed cauda privatim navis gubernaculum <lb/>exacte imitatur &rdquo; (ibid.). </s></p><p type="main">

<s>Se non fosse stato l'Acquapendente soggiogato da quella sua ostinata <lb/>opinione che cio&egrave; si trovi tutta insieme la scienza raccolta ne'libri dei Fi&shy;<lb/>losofi e de'Fisici antichi, veniva dalle sue proprie osservazioni intorno alla <lb/>meccanica animale del nuoto condotto a riconoscer quel vero, che poi cos&igrave; <lb/>facilmente si rivel&ograve; al pi&ugrave; libero ingegno di Galileo. </s>

<s>Era infatti cos&igrave; ovvio <lb/>osservare, per le acque de'fiumi e dei domestici vivai, non farsi da'pesci <lb/>nessun pi&ugrave; piccolo moto, senza che gli preceda il guizzo della coda; e dal&shy;<lb/>l'altra parte apparivano cos&igrave; sproporzionate le pinne ai remi delle navi nella <lb/>struttura e negli usi, ch'esso Galileo non dubit&ograve; d'affermare esser falso <lb/>che, per l'effetto del nuoto, <emph type="italics"/>si servono i pesci delle ali che hanno sotto la <lb/>pancia.<emph.end type="italics"/></s></p><p type="main">

<s>A queste semplici parole, che si leggono scritte sotto forma di fretto&shy;<lb/>losa nota nella <emph type="italics"/>Selva di problemi varii<emph.end type="italics"/> (Alb. </s>

<s>XIV, pag. </s>

<s>319), si riduce tutto <pb xlink:href="020/01/1563.jpg" pagenum="438"/>ci&ograve; ch'&egrave; nelle pubbliche opere galileiane rimasto intorno a un tal soggetto <lb/>di meccanica animale. </s>

<s>Supplivano per&ograve; alla mancanza delle scritture le tra&shy;<lb/>dizioni, amorosamente secondo il solito raccolte, e ingegnosamente illustrate <lb/>dal Borelli. </s>

<s>Si diceva dunque in quelle orali tradizioni dell'insegnamento <lb/>galileiano, mantenuto vivo con tanto zelo nella scuola fioritissima del Ca&shy;<lb/>stelli, che la verit&agrave; naturale era molto diversa da ci&ograve; che ne avea scritto <lb/>l'Acquapendente, perch&egrave; tutt'altro ch'esser la coda organo secondario del <lb/>nuoto, e organo principale le pinne, sono anzi le pinne secondarie al prin&shy;<lb/>cipale strumento del nuoto ch'&egrave; la coda. </s>

<s>Di tutto ci&ograve; venne in mente al <lb/>Borelli di dar sodisfazione ai dubbiosi, per via di elegantissime esperienze, <lb/>fatte a'di 25 Agosto 1662 innanzi al principe, e ai Colleghi dell'Accademia <lb/>del Cimento, nelle carte della quale ne fu lasciata la seguente memoria: <lb/>&ldquo; Tagliate l'ali ad un pesce, giva non pertanto notando per l'acqua, ma <lb/>con gran fatica andava barcollando. </s>

<s>Tagliata ad un altro pesce la coda, per <lb/>moversi gli bisognavano forze grandissime, il che appariva dai continui e <lb/>violenti divincolamenti, onde andava sbattendosi &rdquo; (Targioni, Notizie e T. cit., <lb/>pag. </s>

<s>679). </s></p><p type="main">

<s>Queste prime esperienze, cos&igrave; felicemente riuscite sui piccoli pesci <lb/>d'Arno, invogliarono il Borelli a proseguir lo studio della meccanica del <lb/>nuoto sopra pesci pi&ugrave; grandi, e pi&ugrave; svariatamente configurati, del mare, <lb/>ond'&egrave; ch'essendo nel Marzo 1663 obbligato a rimanere in Pisa, per atten&shy;<lb/>dere alle lezioni, pregava don Famiano Michelini a sentire il principe Leo&shy;<lb/>poldo &ldquo; se si compiace che la seguente settimana io venga a Livorno per <lb/>far quelle poche esperienze de'pesci vivi, che io li accennai, e che averei <lb/>bisogno per capire perfettamente come si muovono e nuotano i pesci &rdquo; <lb/>(MSS. Cim., T. XVII, c. </s>

<s>188). </s></p><p type="main">

<s>Del resultato poi di cos&igrave; fatte esperienze rendeva il Borelli pubblico e <lb/>solenne conto in varie proposizioni, scritte nel cap. </s>

<s>XXII della I Parte <emph type="italics"/>De <lb/>motu animalium.<emph.end type="italics"/> La CCXII &egrave; volta a mostrar l'errore di coloro, che face&shy;<lb/>vano le pinne organo principale del nuoto, non considerando che, applicati <lb/>a una nave remi a proporzione cos&igrave; piccoli e flessibili come sono le pinne <lb/>stesse dei pesci, o non si moverebbe affatto o con tardissimo moto. </s>

<s>Sog&shy;<lb/>giunge esser ci&ograve; benissimo confermato da quella esperienza, fatta gi&agrave; pri&shy;<lb/>vatamente nella sperimentale Accademia fiorentina, e ora cos&igrave; resa in pub&shy;<lb/>blica forma: &ldquo; Tandem hac experientia idipsum evidenter evincitur: forfi&shy;<lb/>cibus resecui pinnas alarum piscium viventium usque ad earum radices, et <lb/>sic tonsos in piscina reposui, et vidi quod, etiam pinnis alarum carentes, <lb/>veloci cursu per aquam ferebantur sursum, deorsum et lateraliter. </s>

<s>Ergo non <lb/>a remigio pinnarum, sed ab alia causa pisces natando per aquam promo&shy;<lb/>ventur &rdquo; (Editio cit., pag. </s>

<s>340). </s></p><p type="main">

<s>Non passa immediatamente il Borelli a dir qual'&egrave; questa precipua causa <lb/>del nuoto, per trattenersi a contemplare e a descrivere il curioso spettacolo <lb/>offertogli da uno di que'pesciolini, cos&igrave; tosato delle pinne del ventre, il <lb/>quale, quasi avesse a un tratto dimenticato l'uso del nuoto, ora andava a <pb xlink:href="020/01/1564.jpg" pagenum="439"/>destra ora a sinistra &ldquo; sicut ebrii casuri et vacillantes inde incedere solent &rdquo; <lb/>(ibid.), da che venivano a confermarsi sperimentalmente i detti dall'Acqua&shy;<lb/>pendente, che cio&egrave; le ali servono talvolta, come i piedi, alla posa del pesce <lb/>e alla stazione. </s></p><p type="main">

<s>Dopo ci&ograve; vien l'Autore a dimostrar, nella proposizione CCXIV, che lo <lb/>strumento con cui notano i pesci &egrave; propriamente la loro coda. </s>

<s>Desume la <lb/>prova di ci&ograve; dall'esperienza delle navi, alla poppa delle quali se facciasi vi&shy;<lb/>brare, come la coda dei pesci, un unico remo, si vedono pure velocemente <lb/>progredire per l'acqua, come se fossero spinte dall'azione concorde di pi&ugrave; <lb/>remi laterali. </s>

<s>Il modo poi, soggiunge, di questa operazione, &egrave; tale: quel&shy;<lb/>l'unico remo, mentre si volge obliquamente intorno alla poppa, trovando <lb/>l'acqua che gli fa resistenza, spinge necessariamente innanzi la navicella, <lb/>bench&egrave; il moto per verit&agrave; sia per riuscirne balenante e tortuoso. </s>

<s>&ldquo; Verum, <lb/>quia talis declinatio subito corrigitur vel a motu contrario, vel a firma remi <lb/>retentione in situ obliquo, officium temonis exercendo, fit ut non advertan&shy;<lb/>tur illae momentaneae declinationes, et sic solummodo directus motus con&shy;<lb/>spicuus remanet &rdquo; (ibid., pag. </s>

<s>342). Parve al Borelli questa dimostrazione <lb/>cos&igrave; concludente, che trascur&ograve; di confermarla con quell'altra esperienza, <lb/>fatta gi&agrave; nell'Accademia del Cimento, e per la quale vedevansi come udimmo <lb/>i pesci colla coda tagliata far a s&egrave; stessi per moversi grandissima violenza. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Al <gap/>ilo storico della meccanica del nuoto, che, proceduto lungamente <lb/>uguale da Plinio all'Acquapendente, va a risolversi senza tante vicende e a <lb/>confermarsi nella scuola di Galileo, succede una tela, sulla quale una mano <lb/>disfa il primo bene avviato lavoro, e poi vengono nuove mani, che tirano <lb/>innanzi alcune fila, e altre ne rivolgono indietro, studiandosi d'intrecciarle <lb/>con assidua affannosa faccenda, durata lunghi secoli, prima che la sciolta <lb/>estrema orditura trovi nel vivagno la sua fermezza. </s>

<s>Intendiamo dire della <lb/>respirazione dei pesci, la scienza della quale, oltre a quella massima diffi&shy;<lb/>colt&agrave;, ch'ebbe comune colla respirazion de'quadrupedi, e che dipendeva dal&shy;<lb/>l'ignorare gli antichi la chimica de'nostri giorni, incontr&ograve; nuovi ostacoli <lb/>a'suoi progressi dal non aver saputo veder bene addentro alla struttura ana&shy;<lb/>tomica delle branchie, e dal non intender come possa l'aria cos&igrave; facilmente <lb/>entrare per i chiusi penetrali dell'acqua. </s>

<s>Ma la verit&agrave; di questo secondo <lb/>fatto, che si nascose tante volte innanzi agli affaccendamenti dell'arte e della <lb/>scienza moderna, s'era felicemente rivelata ad alcuni antichissimi Filosofi, <lb/>quasi a quel modo che una cattura, non riuscita agli esperti, vien talvolta <lb/>alle mani di semplici fanciulli. </s>

<s>E chi non direbbe che fanciulleggiassero dav&shy;<lb/>vero que'buoni antichi, i quali, confondendo nella medesima voce <emph type="italics"/>pneuma<emph.end type="italics"/><lb/>l'anima e l'aria, intendevano che il respirar di questa fosse un continuo <pb xlink:href="020/01/1565.jpg" pagenum="440"/>infondere, e ristorare nell'animale gli spiriti della vita? </s>

<s>Mirabile fanciullag&shy;<lb/>gine, la balbuzie della quale noi cos&igrave; vecchi non abbiamo saputo dimenti&shy;<lb/>care, e come chi, in mezzo all'acquistata scienza, ammira le prime sponta&shy;<lb/>nee rivelazioni della sua infanzia, anche noi ripensiamo con maraviglia a <lb/>Ippocrate e a Galeno, che indovinarono il respirar della cute, e a Demo&shy;<lb/>crito abderita, che, dall'avere spiriti animali, ne concludeva respirar neces&shy;<lb/>sariamente non i pesci soli, ma anche gl'insetti. </s>

<s>Conseguiva da questa <lb/>un'altra necessit&agrave;, ed era che lo pneuma, a vivificare gli stessi pesci, si do&shy;<lb/>vesse, anticipatamente a qualunque fisica esperienza, trovare sciolto in mezzo <lb/>all'acqua. </s>

<s>Anassagora diceva che, passando l'acqua dalla bocca alle bran&shy;<lb/>chie, vi sottentra a riempire il vuoto tant'aria, che basta alla respirazione, <lb/>e Diogene, esplicando meglio il concetto, soggiungeva che per forza del va&shy;<lb/>cuo s'estrae l'aria inesistente nell'acqua. </s></p><p type="main">

<s>Ma questi teneri e rigogliosi germi di scienza venne presto a conco&shy;<lb/>cerli il freddo fiato pestilenziale della Filosofia aristotelica, la quale senten&shy;<lb/>zi&ograve; che le cose dette da Anassagora e da Diogene intorno alla respirazione <lb/>di pesci erano affatto impossibili. </s>

<s>&ldquo; Ait Anaxagoras quidem, cum emittunt <lb/>aquam per branchias, eum qui in ore sit aerem trahentes respirare pisces, <lb/>non enim esse vacuum ullum. </s>

<s>Diogenes autem, cum emittunt aquam per <lb/>branchias, ex circumstante circa os aqua trahere vacuo quod in ore aerem, <lb/>tanquam inexistento in aqua aere: haec autem sunt impossibilia &rdquo; (Arist., <lb/>Op. </s>

<s>T. VII, De respiratione, Venetiis 1560, fol. </s>

<s>270). </s></p><p type="main">

<s>Prosegue quivi Aristotile a dir le ragioni perch'egli creda impossibile <lb/>che respirino i pesci, e poi, proponendo altrove dottrine ch'egli giudica esser <lb/>le vere, dice che gli animali a sangue caldo non per altro hanno bisogno <lb/>dell'aria che per refrigerio del calore innato, al quale effetto, ne'pesci ba&shy;<lb/>stando l'acqua, son apposte le branchie invece dei polmoni. </s>

<s>&ldquo; Extrinsecus <lb/>autem vel aere vel aqua refrigerari necesse est, quamobrem piscium nullus <lb/>habet pulmonem, sed pro ea branchias obtinent: aqua enim refrigerantur ut <lb/>aere quae spirant &rdquo; (Arist., Op. </s>

<s>T. VI, De partibus anim., Venetiis 1560, fol. </s>

<s>238). </s></p><p type="main">

<s>A restaurare quel che Aristotile aveva distrutto venne provvidamente <lb/>Galeno, il quale, perch&egrave; il Filosofo aveva sostituito le branchie ai polmoni <lb/>per caso, da anatomico insegn&ograve; che i due diversi organi ne'quadrupedi e <lb/>ne'pesci servono veramente alle medesime funzioni. </s>

<s>Persuaso dalla scienza <lb/>de'suoi predecessori che debbono necessariamente i pesci trovar da risto&shy;<lb/>rare i loro spiriti anche in mezzo all'acqua, vide in questa necessit&agrave;, con <lb/>gli occhi della mente se non con quelli del corpo, esser le branchie fornite <lb/>di certi piccoli fori atti ad ammetter l'aria, e ad escluder l'acqua, come ad <lb/>ammetter l'aria tenue e ad escluder la crassa hanno opportuni canaliculi i <lb/>polmoni. </s>

<s>&ldquo; Sed carum, quas <emph type="italics"/>branchias<emph.end type="italics"/> nuncupamus, constructio ipsis vice <lb/>pulmonis est. </s>

<s>Cum enim crebris ac tenuibus foraminibus sint branchiae hae <lb/>interceptae, aeri quidem et vapori perviis subtilioribus tamen quam pro mole <lb/>aquae, hanc quidem extra repellunt, illa autem prompte intromittunt &rdquo; (De <lb/>usu partium, Lugd. </s>

<s>1550, pag. </s>

<s>312). </s></p><pb xlink:href="020/01/1566.jpg" pagenum="441"/><p type="main">

<s>Qui e altrove avea promesso Galeno di trattenersi pi&ugrave; di proposito in&shy;<lb/>torno alla respirazione dei pesci, ma perch&egrave; non si videro, nelle opere di <lb/>lui rimaste salve dai naufragi del tempo, mantenute le promesse, supposto <lb/>che si fosse fatto ci&ograve; dall'Autore in qualche libro smarrito, uno zelante di&shy;<lb/>scepolo pens&ograve; di riparare alla iattura col libro <emph type="italics"/>De utilitate respirationis,<emph.end type="italics"/><lb/>studiandosi d'indovinar nello scriverlo la mente del Maestro. </s>

<s>Si dubita dai <lb/>pi&ugrave;, egli ivi dice, se i pesci respirino in mezzo all'acqua, bench&egrave; sia que&shy;<lb/>sta certissima cosa rispetto ai maggiori, i quali hanno manifestamente i pol&shy;<lb/>moni. </s>

<s>&ldquo; Minores vero pisces, qui loco pulmonis branchias habent, spirant <lb/>intra aquam, spirantque aerem, qui modicus est intra aquam, per poros <lb/>branchiarum, qui sunt proportionales fistulis pulmonis. </s>

<s>Quemadmodum enim <lb/>fistulae pulmonis, ita similiter et pori branchiarum usque adeo angustantur <lb/>in ea parte, quae terminatur ad cor, ut non capiant aquam sed aerem so&shy;<lb/>lum, qui per poros excolatur ab aqua, transiens ad cor &rdquo; (Spurii Galeno <lb/>ascripti libri, Venetiis 1609, fol. </s>

<s>64). </s></p><p type="main">

<s>Il pi&ugrave; recente Autore galenico non ammette l'aria ospitante nell'acqua <lb/>in conseguenza di quell'astratto principio psicologico, che informava la fisio&shy;<lb/>logia di Anassagora e di Diogene, ma dietro ci&ograve; che si osserva nel fatto na&shy;<lb/>turale del ghiaccio, in cui l'aria che vi si occultava, restringendosi la mole, <lb/>si vede manifestamente separarsi dall'acqua. </s>

<s>&ldquo; Quod autem aer sit intra <lb/>aquam probatur ex eo quod, cum congelatur aqua, fit minor, propter aeris <lb/>expressionem &rdquo; (ibid.). Notabili parole, che presentavano sotto il suo vero <lb/>aspetto la questione del gelo se sia acqua dilatata o condensata, per cui tanto <lb/>si contese ai tempi di Galileo. </s></p><p type="main">

<s>Sentendosi forte di una scienza sperimentale innanzi alle dominatrici <lb/>vanit&agrave; filosofiche, l'Autore di quello spurio libro galenico insorge ardita&shy;<lb/>mente contro Aristotile, che vuol dar l'acqua a refrigerare le branchie, <lb/>com'aveva data l'aria a refrigerare i polmoni, non avvedendosi che l'aria <lb/>stessa, tutt'altro che a refrigerio, &egrave; data a nutrimento del calore del san&shy;<lb/>gue. </s>

<s>&ldquo; Aristotili visum est quod pisces, qui branchias habent loco pulmo&shy;<lb/>nis, non attrahant aerem, sed aquam, ad refrigerandum calorem cordis. </s>

<s>Nam <lb/>et similiter de habentibus pulmonem dicit Aristotiles quod attrahunt aerem, <lb/>ad refrigerandum calorem cordis, cum ostensum sit aerem inspiratum prae&shy;<lb/>stare nutrimentum calori cordis &rdquo; (ibid.). </s></p><p type="main">

<s>Ma per qualunque opposizione gli si facesse rimasto l'Aristotelismo vin&shy;<lb/>citore, aveva infino a mezzo il secolo XVI condotte le sue vittorie, quando <lb/>apparve sulla cattedra di Mompellieri Guglielmo Rondelezio. </s>

<s>Ei professa <lb/>questo principio, e lo raccomanda a'suoi scolari, a cui dice: &ldquo; ut nunquam <lb/>temere a magnorum et vetustorum authorum sententiis discedendum esse; <lb/>sic eorum dicta omnia tanquam ex oraculo Apollinis pythii edita non esse <lb/>semper accipienda, sed omnia circumspicienda, diligenter observanda, expe&shy;<lb/>rientia, quando licet, comprobanda &rdquo; (De piscibus mar. </s>

<s>cit., pag. </s>

<s>64). </s></p><p type="main">

<s>Seguendo questo sapientissimo canone di filosofia sperimentale, in tempi <lb/>ne'quali i detti di Aristotile da una parte e di Galeno dall'altra si tenevano <pb xlink:href="020/01/1567.jpg" pagenum="442"/>da tutti propriamente com'oracoli pitii, trov&ograve; falso il Rondelezio che potes&shy;<lb/>sero i pesci vivere anche senz'aria, e che nelle branchie si trovin cribri, <lb/>per secernerla pi&ugrave; facilmente dall'acqua. </s>

<s>Dop'aver nel cap. </s>

<s>IX del IV libro <lb/>risposto a uno a uno a tutti gli argomenti, co'quali intendeva Aristotile di <lb/>dimostrare che le cose dette da Anassagora e da Diogene della respirazione <lb/>de'pesci eran tutte impossibili; e dop'avere invocato, per concludere la ne&shy;<lb/>cessit&agrave; di cos&igrave; fatta respirazione, il vitale spirito pitagorico, che infuso per <lb/>le membra tutta agita la gran mole, e perci&ograve; anco il piccolo corpo del pe&shy;<lb/>sce; &ldquo; quoniam autem, all'ultimo ei dice, iis quae sensibus evidentia et <lb/>perspicua sunt refragrari nemo potest, inde sumptam rationem unam aut <lb/>alteram superioribus adiungemus. </s>

<s>Si in vase angusti oris et aquae pleno <lb/>concludantur pisces, illic vivunt et natant, non dies aut menses, sed annos <lb/>aliquot. </s>

<s>Si vel manu, vel aliquo operculo, ita os vasis obtures, ut omnis aeri <lb/>aditus intercludatur, subito suffocantur: cuius rei ipse saepius periculum <lb/>feci &rdquo; (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>Qual pi&ugrave; evidente sensata dimostrazione di questa si potrebbe avere, <lb/>dice il Rondelezio, della falsa dottrina aristotelica? </s>

<s>Se bastasse infatti la sola <lb/>acqua per refrigerio del sangue, perch&egrave; rimarrebbero soffocati i pesci pri&shy;<lb/>vati d'aria? </s>

<s>Che poi dall'altra parte, soggiunge esso Rondelezio, sia a quei <lb/>muti animali necessaria l'aria per respirare, lo dimostra in essi stessi quella <lb/>contenziosa avidit&agrave;, con la quale, se talvolta ne hanno difetto, si vedono an&shy;<lb/>dare a cercarla. </s>

<s>&ldquo; Porro si in eodem vase, ad summum os non oppleto <lb/>neque obtecto, ut maior aeri locus sit, contineantur, illic natantes et luden&shy;<lb/>tes pisciculos cum voluptate cernas. </s>

<s>Si manum ori vasis admoveas, tum <lb/>certatim alius alio superior in aqua esse contendit, ut modici aeris usura <lb/>fruantur &rdquo; (ibid.). </s></p><p type="main">

<s>Conclude perci&ograve; legittimamente l'Autore da queste esperienze: <emph type="italics"/>quare <lb/>piscium genus omne respirat.<emph.end type="italics"/> Ma qual'&egrave; l'organo che serve a questa fun&shy;<lb/>zione? </s>

<s>Galeno, e il galenico Autore del libro <emph type="italics"/>De utilitate respirationis,<emph.end type="italics"/> ave&shy;<lb/>vano detto essere nelle branchie cribri da secernere l'aria dall'acqua: io <lb/>per&ograve;, dice il Rondelezio, non ho saputo trovar n&egrave; fori n&egrave; canalicoli, che si <lb/>possa credere essere ivi disposti a quell'uso. </s>

<s>&ldquo; In branchiis animadverti fo&shy;<lb/>ramina nulla esse aut cavitates per se attrahendo aeri vel aquae, aut istis <lb/>attractis ad cor transmittendis accommodatas &rdquo; (ibid., pag. </s>

<s>64). Perci&ograve; presi <lb/>di qui occasione a dubitare, ei soggiunge, non sieno organi della respira&shy;<lb/>zione gli opercoli ossei, piuttosto che le branchie. </s>

<s>&ldquo; Quae faciunt ut dubi&shy;<lb/>tem num hiatus illius operculi ossei, dilatatione aperti et eiusdem compres&shy;<lb/>sione occlusi, potius quam branchiarum beneficio, fiat respiratio &rdquo; (ibid.). </s></p><p type="main">

<s>Qual'&egrave; dunque l'uso delle branchie ne'pesci? </s>

<s>Quello, risponde il Ron&shy;<lb/>delezio, di far da sipario, e come da rete interposta fra l'apertura della <lb/>bocca e quella dei cos&igrave; detti <emph type="italics"/>orecchi,<emph.end type="italics"/> affinch&egrave; il cibo imboccato non sfugga, <lb/>&ldquo; sed recta ad ventriculum delaberetur, et aqua, simul cum cibo hausta, <lb/>reiiceretur &rdquo; (ibid.). </s></p><p type="main">

<s>Perch&egrave; questo nuovo uso assegnato alle branchie (non vedendosi per <pb xlink:href="020/01/1568.jpg" pagenum="443"/>quali organi s'insinui l'aria direttamente nel sangue) rendeva inesplicabili <lb/>quelle stesse esperienze, che parevano cos&igrave; evidentemente dimostrare la ne&shy;<lb/>cessit&agrave; dell'elemento aereo per la vita dei pesci; s'intende come gli argo&shy;<lb/>menti del Rondelezio, a convincere di falsit&agrave; le peripatetiche dottrine, riu&shy;<lb/>scissero inefficaci. </s>

<s>Quasi un secolo dopo si negava dunque la respirazione <lb/>branchiale, non solo dagli Aristotelici, ma dagli stessi addetti alla scuola di <lb/>Galileo, da cui avevano appreso non inesister l'aria nell'acqua, e non essere <lb/>quelle bollicelle gallezzolanti su dal liquido riscaldato altro che visibili atomi <lb/>di fuoco. </s></p><p type="main">

<s>In mezzo per&ograve; a quell'ardore di rivolta contro Aristotile, capitanato <lb/>dallo stesso Galileo, sorse Marc'Aurelio Severino con animo d'espugnar la <lb/>rocca anco da quella parte, dalla quale i Galileiani l'avevano lasciata illesa. </s>

<s><lb/>Esaminando un giorno un pesce, dove la carena si rende molto concava, <lb/>vide il Severino ascondervisi dentro qualche cosa, che gli parve aver grande <lb/>analogia con le vescicole pneumatiche degli uccelli, le quali ei conobbe <lb/>che servivano alla respirazione, prima che venisse a insegnarlo al mondo <lb/>l'Harvey. </s>

<s>Ecco, disse allora, i polmoni dei pesci: e que'forellini aperti nelle <lb/>branchie, e annunziati gi&agrave; da Galeno, che altro mai possono esser fuorch&egrave; <lb/>le boccuzze di tanti sifoncini, alcuni de'quali sien disposti ad assorbir l'aria, <lb/>altri a rigettar l'acqua? </s>

<s>Ed ecco cos&igrave;, ai polmoni de'pesci, trovate anche le <lb/>trachee; due potentissime mine da far saltare all'aria come una paglia l'edi&shy;<lb/>fizio aristotelico, e per accender le quali dette mano il Severino a scrivere <lb/>la sua <emph type="italics"/>Antiperipatias.<emph.end type="italics"/></s></p><p type="main">

<s>In mezzo a tanta esultanza per&ograve; si sentiva l'Autore rimproverare dai <lb/>suoi lettori, che non avesse sufficientemente dimostrato come potessero l'aria <lb/>e l'acqua fare insieme connubio, quando dall'amicissimo suo Tommaso Cor&shy;<lb/>nelio giunsegli il manoscritto dell'epistola <emph type="italics"/>De cognatione aeris et aquae,<emph.end type="italics"/><lb/>nella quale, per varie esperienze, e particolarmente per quella dello schioppo <lb/>pneumatico, si dimostrava non essere altro l'aria che una trasformazione <lb/>subita, per effetto del calore, dall'acqua. </s>

<s>Il Severino allora, ch'era per dare <lb/>alle stampe la gi&agrave; compiuta <emph type="italics"/>Antiperipatias,<emph.end type="italics"/> approvando, anzi accogliendo <lb/>con gioia la fisica del Cornelio, aveva seco medesimo deliberato d'applicarla <lb/>a dimostrar pi&ugrave; pienamente la respirazione de'pesci in un supplemento al <lb/>libro, ma il fiero morbo pestilenziale del 1654 lo tolse alla scienza, e la <lb/>stessa <emph type="italics"/>Antiperipatias<emph.end type="italics"/> non vide la luce in Napoli se non cinque anni dopo. </s></p><p type="main">

<s>Al sentire i pesci inaspettatamente ridotti all'ordine dei polmonati l'Ittio&shy;<lb/>logia ne rimase commossa, aspettando il giudizio che ne darebbero anato&shy;<lb/>mici o pi&ugrave; esperti del Severino, o colla mente pi&ugrave; libera da pregiudizii. </s>

<s>In&shy;<lb/>tanto, l'esperienze fisiche del barometro ad acqua e gli esercizi della macchina <lb/>pneumatica avevano reso agli stessi occhi evidente sollevarsi di mezzo al&shy;<lb/>l'acqua bollicelle, da credersi facilmente ripiene d'aria. </s>

<s>&ldquo; Dum tamen, disse <lb/>il Boyle nel XXII de'suoi Esperimenti nuovi fisico-meccanici, suppetat no&shy;<lb/>bis occasio plura de natura aeris faciendi experimenta, non isthoc fidenter <lb/>definiemus an aer corpus primigenium sit, eiusmodi scilicet ut nequeat vel <pb xlink:href="020/01/1569.jpg" pagenum="444"/>generari vel in aquam aliudve corpus transmutari &rdquo; (Op. </s>

<s>omnia, T. I, Ve&shy;<lb/>netiis 1697, pag. </s>

<s>48). </s></p><p type="main">

<s>Qualunque sia per&ograve; la natura e l'origine dell'aria nell'acqua, crede il <lb/>Boyle che serva alla respirazione dei pesci, e all'esperienze del Rondelezio, <lb/>e a quella cos&igrave; volgare del vedere morire i notanti ne'vivai, quando l'acqua <lb/>l'inverno ghiaccia alla superficie, aggiunge l'altra del vederli morire egual&shy;<lb/>mente posti sotto la campana del vuoto. </s>

<s>&ldquo; Cepimus magnam anguillam (quia <lb/>nullum alium vivum piscem assequi tum potuimus) et ex vase, in quo ad <lb/>nos educta est, exemptam, magno recipienti immisimus, aeremque exhauriri <lb/>curavimus, observavimusque anguillam, post aliquam ultro citroque motio&shy;<lb/>nem in vitro, aliquo modo affici videri. </s>

<s>Cumque aerem, obstinato et inde&shy;<lb/>fesso conatu, exsussisemus, resupino se convertit ventre, quomodo mori&shy;<lb/>bundi pisces solent, et ex eo tempore mortuae similis immota iacuit &rdquo; <lb/>(ibid., pag. </s>

<s>112). </s></p><p type="main">

<s>Anzi, a ridur pi&ugrave; dappresso questa nuova Fisica pneumatica a servire <lb/>alla Fisiologia della respirazione, il Boyle stesso altrove si propone di scio&shy;<lb/>gliere questo problema: &ldquo; Queritur quousque mereatur a nobis considerari <lb/>num ne in aqua communi tantum aeris lateat, qui usui frigidorum eiusmodi <lb/>animalium ut sunt pisces sufficiat, atque num separabilis ille sit ab aqua, <lb/>quae per branchias ipsorum percolatur &rdquo; (Nova experim. </s>

<s>pneum. </s>

<s>respira&shy;<lb/>tionem spectanctia, in T. cit., pag. </s>

<s>433). Immagina, per riuscire al difficile <lb/>intento, varii strumenti, il pi&ugrave; semplice e il meglio accomodato dei quali &egrave; <lb/>notabile che tanto si rassomigli a quelle caraffelle di lunghissimo collo gra&shy;<lb/>duato, colle quali il nostro Paolo del Buono misurava la quantit&agrave; dell'aria, <lb/>generata da varie acque, o da una medesima acqua posta in diverse condi&shy;<lb/>zioni di temperatura. (Targioni, Notizie cit., T. II, P. I, pag. </s>

<s>311-13). </s></p><p type="main">

<s>Bench&egrave; ritrovasse il Boyle questa misura dell'aria risolutasi dall'acqua <lb/>assai scarsa, la cred&egrave; nulladimeno bastante, se non alla respirazione propria&shy;<lb/>mente detta come ne'quadrupedi e negli uccelli, a quella almeno che si fa <lb/>per via delle branchie, le quali &ldquo; non absurdum est dicere quamdam habere, <lb/>quoad usum saltem, cum pulmonibus analogiam &rdquo; (Experim. </s>

<s>physico-mecha&shy;<lb/>nica in loco cit., pag. </s>

<s>112). Cos&igrave;, col non farne alcun conto, confer&igrave; pi&ugrave; effi&shy;<lb/>cacemente a bandire dalla Ittiologia le novit&agrave; introdotte dal Severino, ma <lb/>non arrogandosi nessuna autorit&agrave; di anatomico lasciava ad altri decidere se <lb/>siano veramente i pesci instrutti de'polmoni, e se ricorrano per le branchie <lb/>canalicoli aerei, da rassomigliarsi negli usi a quelli de'bronchi. </s></p><p type="main">

<s>Quando in Pisa il Borelli, per apparecchiarsi alla grande opera dei moti <lb/>animali, pens&ograve; d'invocare l'esperta mano anatomica dei discepoli suoi pi&ugrave; <lb/>eletti, Carlo Fracassati attendeva ad esaminare con grandissima diligenza <lb/>quelle branchie, nelle quali, da Galeno al Severino, si ripeteva da tanti tro&shy;<lb/>varvisi forellini da vagliar l'aria, e sifunculi ordinati a recarla al cuore e <lb/>ai polmoni. </s>

<s>Ei tutt'altrimenti le trov&ograve; composte di molteplici absidi ossei, <lb/>che hanno nella loro parte convessa infisse innumerevoli pinne radiate, e <lb/>scannellate in modo, che possano ricevere in s&egrave; e sostentare quei, che col&agrave; <pb xlink:href="020/01/1570.jpg" pagenum="445"/>mettono, numerosissimi vasellini sanguigni. </s>

<s>&ldquo; Branchiae sunt absides osseae <lb/>multiplices, scilicet in utroque latere octonarium numerum constituentes in <lb/>parte convexa, contra ac consuescat in rotis, pinnae quaedam radiorum instar <lb/>figuntur, quae ab implantatione assurgentes tenuantur in cuspides, et in <lb/>utroque latere striis quibusdam minimis exarantur, quae vascula sanguinea <lb/>admittunt, ut pluries apud excellentiss. </s>

<s>Borellum Pisis, qui rerum novarum <lb/>repertor, sectiones anatomicas promovet, sum espertus &rdquo; (De cerebro, Mal&shy;<lb/>pighi, Operum T. II cit., pag. </s>

<s>143). </s></p><p type="main">

<s>Trovato cos&igrave; che il Severino avea da questa parte giocato d'immagi&shy;<lb/>nazione, si volse il Fracassati pi&ugrave; curiosamente che mai ad esaminare que&shy;<lb/>gli organi, ch'esso Severino avea veduti addentro nella carena de'pesci, <lb/>riguardandoli come i loro polmoni, e s'accorse pur troppo che anche que&shy;<lb/>sta visione era all'Anatomico napoletano apparita in sogno. </s>

<s>Di ci&ograve; infatti che <lb/>potesse servire alla respirazione ivi non trovavasi indizio, e a tutti i segni <lb/>pareva piuttosto quella mole sanguigna, presa per parenchima polmonare, <lb/>una glandula conglobata, co'suoi canaliculi escretori, che il Fracassati opin&ograve; <lb/>facesse l'ufficio de'reni. </s>

<s>&ldquo; Porro si spectemus substantias illas ad dorsum, <lb/>quas ipse pulmones autumat, quae literam T graphice affingunt, non quid <lb/>a veritate alienum protulit: si tamen illas continuo pulmones appellare non <lb/>libeat, has et ipse in thymno offendi, et sanguinem concretum statim dixis&shy;<lb/>sem, ni vasorum plurium sobole substantiae illae affluerent. </s>

<s>Has potius re&shy;<lb/>nem, aut emunctorium, sum arbitratus .... maxime cum videatnr recensi&shy;<lb/>tus meatus aliquid recrementosum ab illis extra ventrem derivare &rdquo; (ibid., <lb/>pag. </s>

<s>144). </s></p><p type="main">

<s>Venivano dunque per queste anatomiche osservazioni degradati i pesci <lb/>da quella dignit&agrave;, di che il Severino gli avea insigniti, ond'essendo vero che <lb/>non &egrave; in essi vestigio d'organi pneumatici si domandava al Fracassati che <lb/>cosa si dovesse pensare intorno alla gran questione della respirazione dei <lb/>pesci. </s>

<s>E il Fracassati rispondeva con argomenti che riducevan la causa, cos&igrave; <lb/>lungamente promossa e cos&igrave; fervidamente agitata, all'antica sentenza ari&shy;<lb/>stotelica. </s>

<s>Ei non negava l'esistenza dell'aria nell'acqua: anzi si professava <lb/>seguace della fisica del Cornelio, che il Boyle stesso confess&ograve; non aver ra&shy;<lb/>gioni di riprovarla. </s>

<s>Per&ograve; essendo cos&igrave;, diceva il Fracassati, per separar l'aria <lb/>dall'acqua ci bisognano o le forze dissolutrici del calore o delle valide brac&shy;<lb/>cia agitatrici della macchina pneumatica. </s>

<s>Ma dov'&egrave; questo calore ne'pesci, <lb/>o questa cos&igrave; gran forza nelle branchie? </s>

<s>&ldquo; Tanta egemus vi ut excludatur <lb/>ab aqua inditus aer, ut boyleano experimento validorum lacertorum robora <lb/>exigantur &rdquo; (ibid., pag. </s>

<s>143). &Egrave; impossibile perci&ograve;, ne concludeva, che le <lb/>branchie abbian virt&ugrave; d'estrar l'aria dall'acqua, per servire alla respira&shy;<lb/>zione. </s>

<s>Qual'&egrave; dunque il loro uso? </s>

<s>e il Fracassati risponde esser quello di <lb/>far da sostegno ai vasellini sanguigni, i quali, premuti dall'acqua, nel rin&shy;<lb/>chiudersi che fanno gli opercoli, pi&ugrave; facilmente promovono il sangue. </s>

<s>&ldquo; Sunt <lb/>igitur branchiae vasorum fulcra, quae dum moventur ac aqua interlabitur, <lb/>accedente operculi ossei pressione, motum sanguinis iuvant &rdquo; (ibid., pag. </s>

<s>144). <pb xlink:href="020/01/1571.jpg" pagenum="446"/>Cos&igrave; veniva a negarsi la respirazione de'pesci, e le funzioni delle branchie <lb/>si riducevano tutte a quella semplice azion meccanica propria alle cartila&shy;<lb/>gini e agli ossi. </s></p><p type="main">

<s>Non molto diversa da questa del Fracassati &egrave; facile congetturare che <lb/>fosse l'opinione in proposito del Borelli. </s>

<s>Egli infatti, pi&ugrave; savio del Cornelio <lb/>e men dubbioso del Boyle, supponeva, per spiegar la maravigliosa dilata&shy;<lb/>zione dell'acqua ghiacciata, che vi preesistessero molti atometti aerei &ldquo; o vi <lb/>siano stati cacciati i detti atometti aerei dentro l'acqua dall'agitazione e <lb/>vari movimenti dell'aria contigua all'acqua, o perch&egrave; continuamente dalle <lb/>parti inferiori terrestri traspirano molte parti aeree &rdquo; (Fabbroni, Lett. </s>

<s>ined., <lb/>Firenze 1773, T. I, pag. </s>

<s>103, 4). Non perci&ograve; credeva servissero queste parti <lb/>aeree nell'acqua alla respirazione de'pesci, i quali solennemente sentenzi&ograve; <lb/>esser tali &ldquo; qui non respirant &rdquo; (De motu anim., P. II cit., pag. </s>

<s>215). </s></p><p type="main">

<s>Or essendo cos&igrave;, non pu&ograve; non venire, in chi legge queste storie, la cu&shy;<lb/>riosit&agrave; di saper come mai il Fracassati e il Borelli si volgessero a professar <lb/>dottrine tanto contrarie all'esperienze fatte dal Rondelezio, e pi&ugrave; recente&shy;<lb/>mente, e in forma assai pi&ugrave; dimostrativa, dal Boyle. </s>

<s>A che intendere senza <lb/>difficolt&agrave; basta osservare che il Fracassati, approvando l'ipotes&igrave; della tra&shy;<lb/>sformazione dell'acqua in aria, diceva non provar punto l'esperienze ronde&shy;<lb/>leziane che, otturandosi il vaso, i pesci moiono per non succedere altr'aria <lb/>alla gi&agrave; inspirata, ma perch&egrave; ne vengono impediti gli aerei effluvii dall'acqua: <lb/>&ldquo; Hoc non probat omnino aeris succedentis defectu pisces interire, cum <lb/>cohibitum potius effluvium ipsos perimat &rdquo; (De cerebro cit., pag. </s>

<s>142). Cos&igrave; <lb/>fatti effluvii poi non servono alla respirazione, ma a riempir la vescicola na&shy;<lb/>tatoria, ed &egrave; questo uno de'precipui usi, per cui rendesi l'aria tanto neces&shy;<lb/>saria ai pesci. </s>

<s>&ldquo; Vel piscibus necessarius aer, qui medias incolunt aquas, <lb/>scilicet ut saltem natatorii repleantur utriculi &rdquo; (ibid., pag. </s>

<s>146). </s></p><p type="main">

<s>Di questa necessit&agrave; poi era tanto ben persuaso il Borelli che, nella pro&shy;<lb/>posizione CXII della II parte <emph type="italics"/>De motu anim.,<emph.end type="italics"/> dice esser cosa veramente <lb/>maravigliosa tanta avidit&agrave; ne'pesci d'andare in cerca dell'aria. </s>

<s>Non dubita, <lb/>come altri facevano, che sia quell'avidit&agrave; per riempir la vescica natatoria, <lb/>e cos&igrave; pi&ugrave; facilmente equilibrarsi nell'acqua, perch&egrave; ne'morti sotto il ghiac&shy;<lb/>cio ritrov&ograve; quella stessa vescica cos&igrave; sempre enfiata e piena, come ne'vivi. </s>

<s><lb/>Ci dee esser dunque in quegli avidi animali qualche altra insigne necessit&agrave; <lb/>&ldquo; quae alia non videtur esse posse, dice il Borelli, quam desiderium con&shy;<lb/>servationis vitae &rdquo; (Editio cit., pag. </s>

<s>215). </s></p><p type="main">

<s>Ora, ai non pregiudicati intelletti, questo <emph type="italics"/>desiderio della conservazion <lb/>della vita<emph.end type="italics"/> parve un sofistico rifugio, per non confessar che i pesci respi&shy;<lb/>rano, e il refugio stesso tanto apparve pi&ugrave; manifesto, in quanto che quella <lb/>sopra citata borelliana proposizione si formulava: &ldquo; Aer, per respirationem <lb/>receptus, est causa pot&igrave;ssima vitae animalium &rdquo; (ibid., pag. </s>

<s>213). </s></p><p type="main">

<s>Comunque sia, i paralogismi del Fracassati e del Borelli, in proposito <lb/>della respirazione dei pesci, rimanevano impressi di tali note, ch'ebbero fa&shy;<lb/>cilmente a riconoscerli anche gli ammiratori di que'due valorosi ingegni, <pb xlink:href="020/01/1572.jpg" pagenum="447"/>ond'&egrave; che la stessa Scuola toscana si consigli&ograve; saviamente di disertare in&shy;<lb/>torno a ci&ograve; dall'insegnamento de'suoi maggiori. </s>

<s>Il Redi cos&igrave;, sotto il nome <lb/>di Pier Alessandro Fregosi, diffondeva notizie, che parvero a molti dotti <lb/>nuove, e al volgo straordinarie: &ldquo; Oh questa non l'avrei mai n&egrave; immagi&shy;<lb/>nata n&egrave; creduta che i pesci avessero i polmoni negli orecchi, eppure il si&shy;<lb/>gnor Redi me l'ha fatto vedere manifestamente, e mi ha fatto, sto per dire, <lb/>toccar con mano che quel gran lavoro del giro e rigiro o circolazion del <lb/>sangue, che negli animali ragionevoli e quadrupedi si fa dal cuore a'pol&shy;<lb/>moni, e da'polmoni al cuore, ne'pesci si fa in quelle parti, che il popolo <lb/>le chiama <emph type="italics"/>orecchie,<emph.end type="italics"/> e dagli Scrittori della Storia naturale son chiamate lati&shy;<lb/>namente <emph type="italics"/>branchiae &rdquo;<emph.end type="italics"/> (Opere, T. IV cit., pag. </s>

<s>83). </s></p><p type="main">

<s>Sarebbe stato desiderabilissimo che il Redi, lasciando l'abito popolare, <lb/>e rivestendo quello scientifico, avesse particolarmente descritta, e non cos&igrave; <lb/>semplicemente accennata la circolazione branchiale, tanto pi&ugrave; che si rimane <lb/>in dubbio se si tratta di osservazioni proprie e di scoperte originali, o non <lb/>si fa altro dal Nostro che ripetere e illustrare quel che aveva pubblicamente <lb/>detto il Perrault due anni avanti. </s>

<s>In qualunque modo, prima di passare a <lb/>vedere i progressi fatti dalla Scuola parigina, giova trattenersi sopra quelli <lb/>fatti, in tempi un poco anteriori, dalla Scuola nostra fiorentina, nella quale <lb/>sedeva allora sapientissimo maestro di queste cose, insiem col Redi, Niccol&ograve; <lb/>Stenone. </s>

<s>Questi aveva, infino dal 1664, pubblicato in Amsterdam, per ap&shy;<lb/>pendice al trattatello <emph type="italics"/>De musculis et glandulis,<emph.end type="italics"/> un'Epistola al medico Gu&shy;<lb/>glielmo Pisone intorno all'anatomia della <emph type="italics"/>Razza,<emph.end type="italics"/> dove si toccano le questioni <lb/>cos&igrave; vivamente agitate allora intorno alla respirazione de'pesci. </s>

<s>De'polmoni, <lb/>egli dice, non &egrave;, qui nella razza, n&egrave; pi&ugrave; chiaro n&egrave; pi&ugrave; oscuro che negli altri <lb/>pesci il vestigio, ma &egrave; veramente maravigliosa quella finissima tessitura di <lb/>vasi, di che vanno superbe le branchie. </s>

<s>Ora a quale altro fine potrebbe esser <lb/>ivi disposto un tale ordine di vasi, fuor che a fare al sangue subire una <lb/>mutazione &ldquo; sive id contingat de suo aliquid emittendo, sive recipiendo <lb/>externa, sive una et eadem opera utrunque praestando? </s>

<s>&rdquo; (De raiae ana&shy;<lb/>tome, Amstelodami 1664, pag. </s>

<s>70). </s></p><p type="main">

<s>Fra le tante cose a quei tempi pensate intorno alle misteriose funzioni <lb/>della respirazione, e intorno all'azion dell'aria sul sangue, che il Fracassati <lb/>dianzi diceva consister tutta nella virt&ugrave; elastica di lei, &ldquo; qua circularis san&shy;<lb/>guinis motus foveatur &rdquo; (pag. </s>

<s>141); questa dello Stenone &egrave; la sola, che mi&shy;<lb/>rabilmente adombri il vero, un secolo e mezzo dopo messo dalla Chimica <lb/>della combustione allo scoperto. </s>

<s>S'&egrave; infatti da questa nuova scienza ricono&shy;<lb/>sciuto esser verissimo quel che lo Stenone diceva, che cio&egrave;, respirando l'ani&shy;<lb/>male, il sangue subisce una mutazione, rimettendoci del suo e tutto insieme <lb/>ricevendo qualche cosa dall'esterno. </s></p><p type="main">

<s>Certo insomma di questo princip&igrave;o filosofico, lo Stenone era dubbio in&shy;<lb/>torno ai particolari, ond'&egrave; che applicandolo alla respirazione dei pesci di&shy;<lb/>ceva: &ldquo; quis scit anne idem illis praestet aqua quod nobis aer, subtiliora <lb/>suis amplexibus contenta corpora, quae quorundam sunt spiritus, illis lar-<pb xlink:href="020/01/1573.jpg" pagenum="448"/>giendo, si alias largiuntur quicquam, nam si tantum recipiunt egesta, res <lb/>facilis et nulli controversiae obnoxia est &rdquo; (De Raiae anat. </s>

<s>cit., pag. </s>

<s>71). </s></p><p type="main">

<s>Questa proposta facilit&agrave; lusing&ograve; Stefano Lorenzini, che onorava in Fi&shy;<lb/>renze la scuola anatomica dello Stenone e del Redi, dando mano a sezio&shy;<lb/>nare le Torpedini, intorno alle quali scrisse quello, che l'Haller, nel I Tomo <lb/>della sua Bibliografia anatomica, chiamava <emph type="italics"/>eximium opusculum<emph.end type="italics"/> (Tiguri 1774, <lb/>pag. </s>

<s>656). Il Lorenzini dunque, fra i varii partiti messigli innanzi dall'insi&shy;<lb/>gne Maestro, s'attenne e quello, per cui si faceva consistere l'azione del&shy;<lb/>l'ambiente esterno sul sangue in <emph type="italics"/>recipere egesta,<emph.end type="italics"/> ci&ograve; che da un'altra parte <lb/>parevagli mirabilmente convenire con quella disposizione inversa, che lo Ste&shy;<lb/>none argutamente notava aver le branchie convesse, rispetto ai polmoni con&shy;<lb/>cavi, e per la quale inversa disposizione esse branchie, diceva l'Autore <emph type="italics"/>De <lb/>Raiae anatome,<emph.end type="italics"/> &ldquo; ab ambiente possunt affici &rdquo; (pag. </s>

<s>73). </s></p><p type="main">

<s>Per adattar le branchie, che sono in luogo de'polmoni, e l'acqua che <lb/>&egrave; in luogo dell'aria a quell'uso di esportazione ne'due diversi ordini di <lb/>animali, il Lorenz&igrave;ni premette per fondamento al suo discorso alcuni prin&shy;<lb/>cipii fisiologici, che hanno qualche cosa di notabile. </s>

<s>Per lui tutta la cute <lb/>respira, come i polmoni, vedendosi e comprendendosi troppo bene &ldquo; che le <lb/>angustie del ricettacolo sanguigno, che sono e nella cute e nei polmoni, sono <lb/>dell'istesso genere, e che quelle che sono ne'polmoni sono state radunate <lb/>in quel luogo, non per altro, che per supplire ed aiutare la separazione di <lb/>quell'escremento, che si doveva separare per tutto l'abito del corpo, cio&egrave; <lb/>per la cute, giacch&egrave; questa per s&egrave; stessa non era bastante a quest'uso &rdquo; <lb/>(Osservazioni intorno alle Torpedini, Firenze 1678, pag. </s>

<s>94). E perch&egrave; il <lb/>massimo e principal benefizio della respirazione consiste nell'ambiente, che <lb/>rilava e porta via gli escrementi del sangue, &egrave; quello stesso ambiente di varia <lb/>qualit&agrave; e natura secondo i varii individui, ai quali deve servire. </s>

<s>&ldquo; Impe&shy;<lb/>rocch&egrave;, siccome altri degl'individui sono aerei ed altri acquatici, cos&igrave; anco <lb/>il fluido esterno, che serve per levar via l'escremento da'polmoni di questi <lb/>individui, altro &egrave; acqueo, altro &egrave; aereo, e di questi l'aereo serve agli aerei, <lb/>cio&egrave; a quegli che vivono nell'aria, e l'acqueo agli acquei, cio&egrave; a quegli che <lb/>vivono nell'acqua, servendo ambedue per un istesso fine, ma per&ograve; in modo <lb/>diverso, imperocch&egrave; il fluido esterno aereo, per la medesima via che egli &egrave; <lb/>stato ammesso a toccare la superficie esterna de'polmoni, per la medesima <lb/>egli &egrave; mandato fuori, cio&egrave; reciprocato, dove l'acqueo &egrave; mandato fuori per <lb/>via diversa da quella, che egli &egrave; stato ammesso a toccare e radere la su&shy;<lb/>perfice esterna de'polmoni. </s>

<s>La ragione perch&egrave; questi due fluidi operano con <lb/>modo diverso si &egrave; perch&egrave; il fluido, che vien separato ne'polmoni in diversi <lb/>animali, &egrave; diverso, imperocch&egrave; in quel luogo, dal quale &egrave; mandato fuora un <lb/>fluido tenace e viscoso, come ne'polmoni de'pesci, si ricerca che vi trapassi <lb/>con veemenza un fluido, che rada e lavi la superfice, e che per conseguenza <lb/>la superfice, ch'egli ha da radere, sia convessa, altrimenti, se la superfice <lb/>che il fluido ha da radere e lavare fosse concava, ne seguirebbe che il fluido <lb/>non potrebbe trapassare con veemenza per fare l'uffizio suo..... E di qui <pb xlink:href="020/01/1574.jpg" pagenum="449"/>si cava un argomento evidentissimo della sapienza e provvidenza del sommo <lb/>Artefice, conciossiach&egrave; egli ha disposto in ciascheduno animale gl'istrumenti <lb/>del moto e a figura de'vasi secondo la natura de'fluidi de'medesimi ani&shy;<lb/>mali, imperocch&egrave; a quegli animali, che hanno l'escremento pi&ugrave; crasso, a <lb/>questi stessi egli ha dato la superfice esterna de'polmoni, che &egrave; contigua al <lb/>fluido esterno, convessa, e vi ha aggiustato e adattato gl'istrumenti in tal <lb/>forma, che essi strumenti potessero spingere, anzi spingessero continuamente <lb/>a quella superfice una nuova porzione di fluido esterno, dal qual fluido <lb/>esterno, sempre rinnovato, fosse essa superfice esterna de'polmoni, come da <lb/>un fiume che sempre scorre, lavata .... ma agli altri animali, che hanno <lb/>l'escremento de'polmoni pi&ugrave; rado e pi&ugrave; dilatato, esso Divino Artefice fece <lb/>la superfice de'polmoni, ch'&egrave; contigua al fluido esterno, concava, e diede <lb/>loro istrumenti atti a reciprocare il moto del fluido esterno &rdquo; (ivi, pag. </s>

<s>95-98). </s></p><p type="main">

<s>Secondo il Lorenzini dunque il sangue ne'polmoni de'pesci, ossia nelle <lb/>branchie, non subisce altra mutazione che ripurgandosi, e dando del suo, <lb/>per ristoro di che, dice esso Lorenzini, bastare il chilo. </s>

<s>Ma lo Stenone aveva <lb/>pi&ugrave; saviamente sospettato non venisse piuttosto quel ristoro, vivificatore dello <lb/>stesso chilo sanguificato, elargito dagli spiriti latenti nell'acqua; concetto che <lb/>fu destramente preso dal Perrault e svolto nella Parte III della sua <emph type="italics"/>Mecha&shy;<lb/>nique des animaux,<emph.end type="italics"/> l&agrave; dove, nel cap. </s>

<s>V, tratta de'polmoni e de'vasi di di&shy;<lb/>stribuzione del sangue. </s>

<s>&ldquo; L'usage des branchies des poissons, egli ivi dice, <lb/>n'est guere different de celui des poumons des animaux terrestres, puis&shy;<lb/>qu'elles sont faites pour la circulation du sang au travers des branchies .... <lb/>ou vrai-semblablement il re&ccedil;oit une alteration pareille a celle qu'il trouve <lb/>dans les poumons, y ayant app&agrave;rence qu'il y a de l'air m&egrave;l&egrave; parmi l'eau, <lb/>qui peut agir au travers des branchies sur le sang que leurs vaisseaux con&shy;<lb/>tiennent &rdquo; (Edizione cit., pag. </s>

<s>466). </s></p><p type="main">

<s>Il Perrault &egrave; de'primi che, riguardate le branchie in relazione col cuore, <lb/>si sia studiato di descrivere in qualche modo la circolazione del sangue. </s>

<s>Lo <lb/>Stenone innanzi a lui, dop'avere accennato alla somiglianza che passa tra <lb/>il circolo branchiale e il polmonare, sente disposti alcuni a negarla, per avere <lb/>il cuore un ventricolo solo. <emph type="italics"/>Nec haec tanti nobis erit,<emph.end type="italics"/> risponde, perch&egrave;, sia <lb/>pure che non tutto il sangue passi per le branchie: hanno osservato gli Ana&shy;<lb/>tomici che anche in certi uomini adulti, essendo la via aperta dalla destra <lb/>alla sinistra orecchietta, non tutto il sangue perci&ograve; vien trasmesso dal cuore <lb/>ai polmoni. </s>

<s>&ldquo; Sed ne ab insolitis ad solita procedere videar, consideretur <lb/>quaeso illa sanguinis quantitas, quae per branchias transfertur, et patebit <lb/>sufficere illam ut cum reliquo inde sanguine in auricula concurrens ad con&shy;<lb/>venientem omnia proportionem facile reducat &rdquo; (De Raiae anat. </s>

<s>cit., pag. </s>

<s>72). </s></p><p type="main">

<s>Or il Perrault attese a dimostrare questa conveniente proporzione che <lb/>passa tra la quantit&agrave; del sangue trasportato alle branchie, e quell'altro ri&shy;<lb/>versato per l'orecchietta nel ventricolo del cuore. </s>

<s>Ei rassomigliava esse bran&shy;<lb/>chie a tante sottilissime fogliette cartilaginee, soprapposte le une alle altre, <lb/>tagliuzzate cos&igrave;, da mettere esilissimi filamenti, come le barbe delle penne. <pb xlink:href="020/01/1575.jpg" pagenum="450"/>Un osso, a cui sono queste barboline attaccate, serve a quelle stesse fo&shy;<lb/>gliette di base, e ciascun filamento sostiene un'arteriuzza capillare. </s>

<s>&ldquo; Le <lb/>coeur des poissons, qui n'a qu'un ventricule, a comme deux aortes, ou du <lb/>moins l'aorte a deux troncs: car le premier s'&eacute;tant divise en plusieurs ra&shy;<lb/>meaux, ces rameaux se rejoignent et produisent un second tronc, qui jette <lb/>d'autres rameaux qui se distribuent dans tout le corps. </s>

<s>Or le premier tronc <lb/>de l'aorte, qui sort du ventricule du coeur par son oreille superieure, jette <lb/>quatre rameaux de chaque c&ograve;t&eacute;, qui passent chacun dans la base d'un des <lb/>fevillets des branchies. </s>

<s>Ces rameaux apres avoir jett&egrave; les petites arteres ca&shy;<lb/>pillaires, qui se coulent dans les pointes de chacune des petites barbes, s'as&shy;<lb/>semblent deux &agrave; deux, et vont se joindre au second tronc de l'aorte, qui <lb/>descend le long de l'&egrave;pine, et se divise en plusieurs rameaux, qui portent <lb/>le sang par tout le corps. </s>

<s>Pour ce qui est des veines, il y en a aussi de <lb/>capillaires, qui accompagnent les petites arteres et qui rapportant le sang, <lb/>qu'elles ont re&ccedil;u, aboutissent &agrave; un rameau, qui accompagne aussi le rameau <lb/>de l'artere, qui se coule dans la base du fevillet: ces quatre rameaux s'as&shy;<lb/>semblent aussi deux &agrave; deux, et forment un tronc qui rapporte le sang dans <lb/>le ventricule, s'inserant &agrave; son oreille inferieure, dans la quelle deux autres <lb/>rameaux, qui rapportent le sang des parties inferieures, s'inserent aussi. </s>

<s>&rdquo; <lb/>E la descrizione &egrave; illustrata da due figure, che rappresentano il circolo san&shy;<lb/>guigno per le arterie e per le vene branchiali di una Carpa. (Meccanica degli <lb/>anim. </s>

<s>cit., pag. </s>

<s>466, 67). </s></p><p type="main">

<s>Riguardando per&ograve; attentamente i disegni, e considerando le parole, che <lb/>servono a dichiararli, si trova che tra il sangue arterioso e il venoso non <lb/>passa differenza per la sostanza, ma per i vasi, a cui s'impongono nomi di&shy;<lb/>versi: perch&egrave;, passando attraverso alle branchie il sangue del ventricolo, <lb/>ch'&egrave; un sangue venoso, e ritornando per vasi, che dovrebbero avere ugual <lb/>nome de'primi, essendo una continuazione di loro; quel che si dispensa ad <lb/>alimentare le membra non si pu&ograve; dir che sia vero e schietto sangue arte&shy;<lb/>rioso. </s>

<s>Questo sarebbe un circolo, da meritarsi propriamente il titolo di vi&shy;<lb/>zioso, non essendo forse utile ad altro, che a tenere in moto il liquido, per&shy;<lb/>ch&egrave; oziando non si corrompa. </s>

<s>Lo Stenone aveva sapientemente detto che <lb/>nella respirazione questo per prima cosa si richiede: &ldquo; ut ambiens, sive id <lb/>aqua fuerit, sive aer, semper novum ad vasorum feratur extrema &rdquo; (De <lb/>Raiae anat., pag. </s>

<s>71) perch&egrave; altrimenti non potrebbe il sangue subire al&shy;<lb/>cuna trasformazione. </s>

<s>E affinch&egrave; pienamente l'effetto si conseguisca, &egrave; ne&shy;<lb/>cessario che il sangue stesso cos&igrave; trasformato passi in altri vasi distinti, e <lb/>non, come il Perrault disegna, prosegua addirittura per i medesimi. </s></p><p type="main">

<s>Quella dunque, che l'Autore della Meccanica degli animali chiama aorta <lb/>ascendente, non &egrave;, per volerla ragguagliare con l'organo dei polmonati, che <lb/>l'arteria polmonare, la quale dai suoi capillari branchiali riversa il sangue <lb/>vivificato dall'aria ne'capillari di altri vasi distinti, e confluenti in un tronco <lb/>solo, che il Perrault chiama aorta discendente, ma ch'&egrave; piuttosto analogo <lb/>alla vena polmonare. </s></p><pb xlink:href="020/01/1576.jpg" pagenum="451"/><p type="main">

<s>Qui s'incontra una novit&agrave; notabilissima, che fece adombrare l'Ittiologo <lb/>francese: la vena polmonare, senza toccare il cuore, prosegue a diritto, e <lb/>si moltiplica in rami per andar, vera e propria aorta discendente, a vivifi&shy;<lb/>care le membra inferiori del pesce. </s>

<s>Una semplice considerazione per&ograve; ba&shy;<lb/>stava a rimovere ogni ombra: Perch&egrave; infatti, si pu&ograve; domandare, la vena negli <lb/>animali aerei dal polmone ritorna al cuore? </s>

<s>Non mica perch&egrave; il sangue <lb/>acquisti qualche cosa nella sostanza, ma s&igrave; nella velocit&agrave; del suo moto. </s>

<s>Or <lb/>dunque se si ammetta che quello stesso sangue esca dalle branchie con tale <lb/>velocit&agrave;, da non aver bisogno, per giungere a'suoi vasi estremi, che gli so&shy;<lb/>praggiunga altro estrinseco impulso, s'intender&agrave; perch&egrave; al pesce non sia <lb/>altrimenti bisogno d'avere al cuore n&egrave; l'orecchietta n&egrave; il ventricolo sinistro. </s></p><p type="main">

<s>Ritornando ora con lo sguardo sulla pagina, e sopra gl'iconismi del <lb/>Perrault, si vede che impropriamente &egrave; dato da lui alla radice dell'arteria <lb/>branchiale il nome di <emph type="italics"/>orecchietta superiore.<emph.end type="italics"/> L'orecchietta propriamente &egrave; <lb/>una sola, e in essa la vena cava superiore infonde il sangue raccolto per <lb/>ogni parte del capo, e la inferiore quello attratto da tutte le capillari arte&shy;<lb/>riose, diramate per le membra inferiori del pesce. </s></p><p type="main">

<s>Queste considerazioni non era forse facile farle con lucidezza, prima che <lb/>fosse dimostrata la chimica azione dell'aria sul sangue, e quando Giuseppe <lb/>Du-Verney nel 1699 n'ebbe qualche rivelazione, i colleghi suoi Accademici <lb/>parigini stettero ad ascoltare le nuove cose proposte con qualche diffidenza. </s>

<s><lb/>Anche il Du-Verney dunque prese per soggetto de'suoi studi le branchie <lb/>delle Carpe, ch'ei trov&ograve; disposte in modo da ridur quasi l'acqua a'suoi mi&shy;<lb/>nimi atomi. </s>

<s>Quel moto poi alternativo di dilatazione e di compressione l'as&shy;<lb/>somigli&ograve; negli effetti alle trombe idrauliche, le quali, perciocch&egrave; anch'esse <lb/>ricevon l'acqua quando si dilatano, e la rigettano allora che si comprimono; <lb/>&ldquo; il y a plus d'apparence que c'est dans l'instant du reserrement qu'elles <lb/>obligent l'air exprim&eacute; de l'eau &agrave; p&eacute;n&eacute;trer les pores des petits vaisseaux san&shy;<lb/>guins &rdquo; (Collection academique, T. </s>

<s>I cit., pag. </s>

<s>653). </s></p><p type="main">

<s>Cos&igrave; veniva il Du-Verney a ritrovar nelle branchie quella forza di aspi&shy;<lb/>razione, non creduta possibile dal Fracassati, e s'avviava a conoscere, pi&ugrave; <lb/>distintamente di quel che non avesse fatto il Perrault, dai loro propri usi <lb/>la struttura dei vasi. </s>

<s>Se il cuore, domandava a s&egrave; stesso, non ha che un <lb/>ventricolo solo, e che una sola arteria, la quale si ramifica nelle branchie, <lb/>&ldquo; quels canaux arroseront le reste du corps, et porteront le sang vivifi&eacute; par <lb/>le m&ecirc;lange de l'air? </s>

<s>&rdquo; E rispondeva proponendo a considerar il fatto che, <lb/>come la vena polmonare uscendo dal cuore prende costituzione di arteria, <lb/>cos&igrave; la prende similmente la vena branchiale, nell'uscir dalle stesse bran&shy;<lb/>chie. </s>

<s>&ldquo; Apres que le sang des arterioles des ou&iuml;es s'est charg&eacute; d'air, il passe <lb/>par la loi de la circolation dans toutes le petites veines qui leur r&eacute;pondent. </s>

<s><lb/>Mais ce qui est fort singulier, c'est que les veines des ou&iuml;es en &eacute;tant une <lb/>fois sorties, devennient aussi-tot art&eacute;res, et vont se r&eacute;pandre dans toutes <lb/>les parties du corps, d'ou d'autres veines veritables rapportent le sang au <lb/>coeur &rdquo; (ivi). </s></p><pb xlink:href="020/01/1577.jpg" pagenum="452"/><p type="main">

<s>La diffidenza ingerita a principio da queste nuove dottrine, che avevano <lb/>apparentemente dello strano, si convert&igrave; presto in una piena fiducia, quando <lb/>la fisiologia chimica della respirazione dette l'ultima conferma alla mecca&shy;<lb/>nica della circolazione del sangue, e cos&igrave; per il Du-Verney incominciava, sul <lb/>terminar del secolo XVII, a decidersi conforme alla verit&agrave; naturale, passata <lb/>per cos&igrave; lunghe vicende, la questione della respirazione dei pesci, che &egrave; forse <lb/>la pi&ugrave; notabile nella loro storia, dopo quella degli organi de'sensi, alla quale <lb/>riserbiamo quest'altra parte del nostro discorso. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Che, essendo il tatto senso fondamentale, non ne mancassero i pesci, <lb/>nessun poteva dubitarne, ma quanto all'organo si limitarono gli antichi a <lb/>dir cos&igrave; vagamente ch'era la cute o qualunque se ne fosse l'integumento <lb/>esteriore. </s>

<s>A ci&ograve; dall'altra parte si riduceva tutto quel che sapevasi da quegli <lb/>stessi Filosofi antichi intorno all'organo del tatto, negli animali d'ordine su&shy;<lb/>periore, non che nell'uomo. </s>

<s>Lo studio anatomico della cute di questi co&shy;<lb/>minci&ograve; dallo Stenone, il quale scopr&igrave; le ghiandole miliari coi loro nervi, e <lb/>i condotti sudoriferi coi loro vasi sanguigni. </s>

<s>Quando poi il Malpighi ebbe <lb/>nelle papille cutanee scoperto l'organo essenziale del tatto, pens&ograve; che quelle <lb/>miliari ghiandolette stenoniane fossero ordinate a secernere il loro umore <lb/>&ldquo; ut madidae forte papillae nerveae reddantur ne arescant, et ne callo quo&shy;<lb/>dam ex assiduo usu tententur &rdquo; (De externo tactus organo, Operum, T. II <lb/>cit., pag. </s>

<s>209) per cui argutamente not&ograve; che nelle parti, in cui il tatto &egrave; <lb/>pi&ugrave; squisito, come nella pianta de'piedi, per esempio, e sotto le ascelle, son <lb/>le ghiandolette miliari altres&igrave; pi&ugrave; numerose, e il sudore perci&ograve; in pi&ugrave; gran <lb/>copia vi si secerne. </s></p><p type="main">

<s>Esplorata ch'ebbe lo Stenone la cute dell'uomo e de'quadrupedi, si <lb/>volse con pari diligenza a esplorare anche quella de'pesci, per la quale, <lb/>nelle razze segnatamente, trov&ograve; dispersi certi piccoli fori &rdquo; unde viscidi hu&shy;<lb/>moris prodeunt guttae &rdquo; (De musc. </s>

<s>et gland. </s>

<s>cit., pag. </s>

<s>39). Ritrovati poi <lb/>simili forellini in altri pesci, come in uno che prese a sezionare del genere <lb/>dei Cani, pens&ograve; che l'untuoso umore, per cui si rendono cos&igrave; lubrici i pesci <lb/>tutti, non ad altro fine venisse in loro stillato, che per renderne, come la <lb/>spalmatura delle navi, pi&ugrave; agevole il noto. </s>

<s>&ldquo; Patet inde Naturae solertis in&shy;<lb/>dustria, quae superficiem piscium unxit, quo facilius obstantes aquas finde&shy;<lb/>rent &rdquo; (Myologiae specimen, Florentiae 1667, pag. </s>

<s>112). </s></p><p type="main">

<s>Il Lorenzini, proseguendo sui pesci questi studii iniziati dall'illustre <lb/>Maestro, trov&ograve; per la cute delle Torpedini altri pi&ugrave; minuti forellini coi loro <lb/>respettivi canali, per i quali distillavasi il solito viscido umore. </s>

<s>Mettendosi <lb/>poi a ricercar l'origine di un tale umore, non dubit&ograve; d'attribuirla a certe <lb/>ghiandole, che si rassomiglierebbero alle miliari, dallo stesso Stenone sco-<pb xlink:href="020/01/1578.jpg" pagenum="453"/>perte in tutti i quadrupedi, e pi&ugrave; abbondantemente nelle mani dell'uomo. <lb/></s>

<s>&ldquo; Nelle torpedini dunque, scrive esso Lorenzini, ed in tutti gli altri pesci, <lb/>che hanno canali simili o rispondenti a questi, una buona quantit&agrave; di quel&shy;<lb/>l'umore, che si separa dalle glandule miliari, si raduna in essi canali, e tutto <lb/>insieme al bisogno vien portato fuori per quei forami manifesti &rdquo; (Osser&shy;<lb/>vazioni intorno alle Torp. </s>

<s>cit., pag. </s>

<s>30). </s></p><p type="main">

<s>Or la somiglianza della struttura portando ad argomentare somiglianza <lb/>uguale negli usi, fu lecito agl'Ittiologi dire, sull'esempio del Malpighi, che <lb/>l'umor viscido de'pesci rappresentante l'umor sudorifico degli animali ter&shy;<lb/>restri, sia, oltre al render lubrico il nuoto, destinato a mantener morbide <lb/>ne'pesci le papille del tatto; ond'&egrave; che, avendoci la Natura provveduto con <lb/>tal sollecitudine e con tanta solerzia, s'ebbe ragionevolmente a concluderne <lb/>non potere in que'taciturni animali il senso non essere in qualunque modo <lb/>esquisito. </s></p><p type="main">

<s>Fra'sensi particolari il pi&ugrave; distinto organo ne'pesci, e che and&ograve; esente <lb/>da ogni controversia, &egrave; quello della vista, in cui si porse allo Stenone un <lb/>soggetto insigne da studiarvi la struttura lamellare del cristallino, propria <lb/>agli occhi di tutti gli altri animali. </s>

<s>Notarono anche gli Antichi che vi manca <lb/>l'umor acqueo, e che la stessa lente cristallina &egrave; sferica in questi notanti <lb/>per l'acqua, a differenza degli animali, che vivono in mezzo all'aria. </s>

<s>Gli <lb/>Ittiologi riconobbero non difficile a intendere la ragione di cos&igrave; fatta parti&shy;<lb/>colare struttura, e la significarono cos&igrave; per mezzo del Perrault: &ldquo; La figure <lb/>du crystallin est toujours sph&eacute;rique aux poissons et lenticulare aux autres <lb/>animaux. </s>

<s>Cette difference vient de la differente nature du milieu de leur <lb/>v&ugrave;e: car &agrave; l'&eacute;gard des poissons tout ce qni sert de milieu &agrave; leur v&ugrave;e de&shy;<lb/>puis l'obiet jusqu'au crystallin est aqueux, s&ccedil;avoir, l'eau dans laquelle ils <lb/>sont, et l'humeur aqueuse de l'oeuil qui est au devant du crystallin. </s>

<s>Mais <lb/>dans les autres animaux ce milieu est compose de l'air et de l'eau de leur <lb/>oeuil, laquelle commence la refraction, que le crystallin acheve avec l'hu&shy;<lb/>meur vitr&eacute;e c'est pourquoi il a fallu que le crystallin des poissons f&ugrave;t sphe&shy;<lb/>rique, ayant besoin d'une refraction plus forte, puisqu'il doit suppleer eelle <lb/>qui se fait aux autres animaux dans l'humeur aqueuse, qui n'est pas capa&shy;<lb/>ble de faire de refraction dans les poissons, parce qu'elle est de m&egrave;me na&shy;<lb/>ture que le reste du milieu &rdquo; (Mecanique des animaux cit., pag. </s>

<s>358). </s></p><p type="main">

<s>Negli occhi dunque dei pesci fu facilmente riconosciuta la struttura delle <lb/>parti, e dietro i noti principii d'Ottica se ne intesero le differenze e gli usi. </s>

<s><lb/>Ma gli altri organi dei sensi presentarono tali e tante difficolt&agrave; da lasciar <lb/>dubbiose le menti, cosicch&egrave; i dubbi dettero tra'Filosofi luogo a questioni, <lb/>della storia delle quali dobbiamo far argomento il presente nostro discorso. </s>

<s><lb/>Incominceremo dal senso del gusto, l'organo del quale almeno, sebben non <lb/>col&agrave; dove si credeva da tutti, fu ritrovato nello stesso tempo e colla stessa <lb/>certezza, che furono anche per l'integumento dei pesci scoperte le papille <lb/>nervee del tatto. </s></p><p type="main">

<s>Che sia veramente ne'pesci il senso del gusto &egrave; dimostrato dalle pi&ugrave; <pb xlink:href="020/01/1579.jpg" pagenum="454"/>volgari quotidiane esperienze, vedendoli fare scelta de'cibi pi&ugrave; saporiti, e <lb/>trarre con grande avidit&agrave; all'esca insidiosamente a loro offerta dagli ami. </s>

<s><lb/>Scorto perci&ograve; Aristotile dalla certa notizia di questi fatti, argoment&ograve; ragio&shy;<lb/>nevolmente dall'esistenza della funzione all'esistenza dell'organo corrispon&shy;<lb/>dente, e perch&egrave; si credeva allora consistere un tal organo nella sostanza <lb/>carnosa della lingua, si mise con gran diligenza a ricercare essa lingua per <lb/>la bocca de'pesci. </s>

<s>&Egrave; facile che, preformato cos&igrave; il giudizio, si lusingasse di <lb/>avervela ritrovata, e infatti la descrisse come tale nella <emph type="italics"/>Storia degli ani&shy;<lb/>mali,<emph.end type="italics"/> bench&egrave; dura e quasi irta di acute punte: anzi avvert&igrave; i Naturalisti <lb/>che ci era, sebben, rimasta talvolta aderente al palato, potesse facilmente <lb/>sfuggire alla loro vista. </s>

<s>&ldquo; Linguam autem ipsam duram, et pene spineam <lb/>habent, et adhaerentem, ut interdum carere lingua videantur &rdquo; (Operum, <lb/>T. VI cit., fol. </s>

<s>99). In un altro libro di questa stessa Storia degli animali <lb/>confess&ograve; che la lingua negli acquatici, sebben sia certo che vi sia, &egrave; nulla&shy;<lb/>dimeno imperfetta, e soggiunge che in alcuni, ne'quali ella par che affatto <lb/>vi manchi, come per esempio ne'Ciprini, vi supplisce opportunamente il pa&shy;<lb/>lato carnoso. </s>

<s>&ldquo; Aquatilium tamen generi, quos pisces vocamus, data quidem <lb/>est lingua, sed imperfecta incertaque: ossea enim nec absoluta. </s>

<s>Sed pa&shy;<lb/>latum nonnullis carnosum pro lingua est, velut inter fluviales cyprino, ita <lb/>ut, nisi diligenter inspexeris, lingua id esse videatur &rdquo; (ibid., fol. </s>

<s>120). </s></p><p type="main">

<s>Il Rondelezio poi accolse queste dottrine aristoteliche, svolgendole e illu&shy;<lb/>strandole nel III libro de'suoi Pesci marini, l&agrave; dove, nel cap. </s>

<s>IX, si riserba <lb/>a trattar di proposito della lingua e del palato. </s>

<s>Ammesso dunque con Ari&shy;<lb/>stotile, e come gli pareva lo confermasse la sua propria osservazione, che <lb/>sia nella bocca de'pesci la lingua, domanda il Rondelezio a quale uso possa <lb/>esser data a loro dalla Natura. </s>

<s>No certo per servire alla voce, essendo afoni, <lb/>n&egrave; per rivoltare i cibi e rimandarli in qua e in l&agrave; sotto la mola de'denti, <lb/>non masticando quegli animali, n&egrave; facendo altro essi denti colle punte ri&shy;<lb/>volte verso lo stomaco, che ingerir pi&ugrave; facilmente la preda, e proibir ch'ella <lb/>scappi a loro di bocca. </s>

<s>&ldquo; Quare, ne conclude, alimentorum sapores ut di&shy;<lb/>scernant linguam eis datam dicere necesse est &rdquo; (Editio cit., pag. </s>

<s>58). Man&shy;<lb/>cano infatti, soggiunge l'Autore, della lingua que'pesci, che non hanno sa&shy;<lb/>pori da scegliere, nutrendosi di sola acqua pura, come i testacei, o d'acqua <lb/>limacciosa, come le carpe e le tinche, nelle quali nulladimeno, secondo os&shy;<lb/>serv&ograve; Aristotile, supplisce al difetto della stessa lingua il palato carnoso. </s></p><p type="main">

<s>Nessuno ancora degl'Ittiologi aveva saputo metter dubbi negl'insegna&shy;<lb/>menti aristotelici, cos&igrave; dal Rondelezio autorevolmente confermati, quando, <lb/>per opera del Malpighi e del Bellini, scopertosi l'organo del gusto in ogni <lb/>sorta di animali terrestri, venne al Fracassati curiosit&agrave; di ricercarlo anche <lb/>nella bocca dei pesci. </s>

<s>Rivolgendo perci&ograve; l'attenzione sopra la lingua, per <lb/>esplorare essa la prima, non sapeva risolversi a qual membro propriamente <lb/>attribuir questo nome. </s>

<s>Ma pur anch'egli chiamando lingua quella parte, che <lb/>Aristotile e il Rondelezio avevano gi&agrave; designata per tale, non vi trov&ograve; vesti&shy;<lb/>gio delle papille nervee, riconosciute oramai per essenziale organo del gusto <pb xlink:href="020/01/1580.jpg" pagenum="455"/>in tutti gli altri animali. </s>

<s>&ldquo; Quantumvis itaque lingua sit quod dubitavi pro <lb/>lingua habere, nullas tamen illa, saltem evidentes, exhibuit papillas &rdquo; (De <lb/>lingua in loco cit., pag. </s>

<s>178). </s></p><p type="main">

<s>Non perdutosi per questo d'animo, il Fracassati pens&ograve; che, trapassando <lb/>il cibo celeremente per bocca, non fosse questa del gusto sede opportuna, <lb/>ma che si dovesse trovar riposta pi&ugrave; addentro, l&agrave; dove lo stesso cibo si trat&shy;<lb/>tiene pi&ugrave; a lungo ad eccitar nell'ingordo animale le cupe volutt&agrave; del senso. </s>

<s><lb/>Dietro dunque la scorta di questi pensieri cercando, &ldquo; invenio membranam <lb/>expansam, quae initium oesophagi est. </s>

<s>Hanc papillulis refertam linguae vi&shy;<lb/>cariam credidi, cum differat a continuato stomacho. </s>

<s>Palati etiam fornix ali&shy;<lb/>quibus papillulis distinguebatur, et videbatur ad idem munus vocatus, al&shy;<lb/>bescens tamen piscium caro minus conspicuas has nerveas notas reddebat &rdquo; <lb/>(ibid.). Esult&ograve; il Fracassati della scoperta, non solamente per s&egrave; ma perch&egrave; <lb/>veniva mirabilmente a confermare la scoperta del Malpighi e del Bellini, <lb/>vedendosi le papille nervee presiedere all'organo del gusto anche nei pesci. <lb/></s>

<s>&ldquo; Quare, poi ne concludeva, cum fere omnia animantia haec papillaria ca&shy;<lb/>pitula, in lingua vel in adiacentibus, promant, quid mirum si constans haec <lb/>structura, non tantum oculos, verum et mentem certiorem fecerit, in hac <lb/>scilicet circa gustum animantium linguae operationem, quae hactenus ana&shy;<lb/>tomicis non innotuerat, sese manifestare? </s>

<s>&rdquo; (ibid., pag. </s>

<s>179). </s></p><p type="main">

<s>Pochi infatti dubitarono della scoperta, alla quale erano insieme con&shy;<lb/>corsi i tre illustri anatomici nostri italiani, ma le ultime osservazioni del <lb/>Fracassati dettero luogo a una curiosa questione fra gl'Ittiologi, se cio&egrave; possa <lb/>dirsi che i pesci hanno la lingua. </s>

<s>Il Lorenzini non avendola trovata nelle <lb/>torpedini, la neg&ograve; anche in tutti gli altri pesci, per la ragione che, non ser&shy;<lb/>vendo n&egrave; alla voce n&egrave; alla masticazione de'cibi, sarebbe stata inutile ingom&shy;<lb/>bro nella bocca di cos&igrave; fatti animali. </s>

<s>E a chi gli opponeva col Rondelezio <lb/>essere utile la lingua a discernere i sapori, rispondeva ritorcendo cos&igrave; l'ar&shy;<lb/>gomento, e dicendo &ldquo; che quelle lingue, le quali non avranno cos&igrave; fatte pa&shy;<lb/>pille, non saranno abili a discernere i sapori, e tali appunto sono quei corpi <lb/>dentro le bocche dei pesci, ai quali comunemente si vuol dare il nome di <lb/>lingua. </s>

<s>E che questi tali corpi non abbiano papille si rende chiarissimo e <lb/>dalla quotidiana esperienza, che se ne pu&ograve; fare, e dalle oculatissime osser&shy;<lb/>vazioni del signor Fracassati, il quale non vide mai queste papille nella sup&shy;<lb/>posta lingua de'pesci, ma le vide bene e nel palato e nel principio dell'eso&shy;<lb/>fago, e nelle branchie. </s>

<s>Adunque quel corpo, che comunemente si chiama <lb/>lingua ne'pesci, non essendo dotato di quelle papille, che sono l'istrumento <lb/>della sensazione, non pu&ograve; gustare, e per conseguenza, non potendo gustare, <lb/>non si pu&ograve; chiamar lingua &rdquo; (Osservazioni intorno alle Torped. </s>

<s>cit., pag. </s>

<s>41). <lb/>Ma passiamo a questioni di ben altra importanza. </s></p><p type="main">

<s>Che i pesci odano, scrisse Aristotile nel IV libro della Storia degli ani&shy;<lb/>mali, in quel cap. </s>

<s>VIII citato dianzi a proposito del gusto; &egrave; cosa a tutti <lb/>palese, imperocch&egrave; si vedono furiosamente fuggire a un rumore insolito, <lb/>com'&egrave; per esempio quello dei remi agitati. </s>

<s>Di ci&ograve; dall'altra parte soglion <pb xlink:href="020/01/1581.jpg" pagenum="456"/>prendere quotidiana esperienza i pescatori, che ora strepitando gli riducono <lb/>nella rete, e ora silenziosi gli van cogliendo ne'loro nidi. </s>

<s>N&egrave; men certo &egrave;, <lb/>soggiunge il Filosofo, che i pesci odorino, perch&egrave; non sono attratti a ogni <lb/>genere di esca, e i pescatori ora gli allettano, e ora gli deviano purch&egrave; in <lb/>ogni modo diano negli agguati, spargendo per l'acqua sostanze, alcune delle <lb/>quali siano al senso de'pesci odorose, altre fetenti. </s>

<s>Bench&egrave; per&ograve; sian cos&igrave; <lb/>certi i fatti rispetto alle funzioni, &ldquo; auditus vero, dice Aristotile nel capi&shy;<lb/>tolo sopra citato, olfactusve nullum continent membrum manifestum. </s>

<s>Quod <lb/>enim tale videri potest per loca narium id non ad cerebrum usque trans&shy;<lb/>meat, sed partim obseptum et caecum mox desinit, partim ad branchias <lb/>fertur &rdquo; (fol. </s>

<s>120). </s></p><p type="main">

<s>Il Rondelezio in parte trov&ograve; queste aristoteliche dottrine vere, e in <lb/>parte, usandovi pi&ugrave; diligente anatomia, le trov&ograve; false e le corresse, special&shy;<lb/>mente per ci&ograve; che concerne le orecchie, intorno alle quali ha nel III libro <lb/><emph type="italics"/>De piscibus<emph.end type="italics"/> un capitolo insigne. </s>

<s>Son le orecchie, ivi egli dice, disposte nel&shy;<lb/>l'uomo a ricevere i suoni, e per esse a imbeversi delle erudite discipline, <lb/>e son date ne'pesci a tutela e a conservazion della vita. </s>

<s>Atterriti infatti con <lb/>minaccioso strepito sen fuggono, e chiamati con dolce suono rispondono <lb/>&ldquo; ut nos frequenter in delphinis, luciis, aliisque huiusmodi experti sumus &rdquo; <lb/>(pag. </s>

<s>49). </s></p><p type="main">

<s>Si fa in questi pesci l'udito, prosegue a dire l'Autore, senza alcuna <lb/>esterna inspirazione, bench&egrave; siavi interiormente riposto l'organo, il quale si <lb/>compone di alcune parti cartilaginose e di altre cutanee e secche, affinch&egrave; <lb/>possano pi&ugrave; facilmente riflettere e fare echeggiare il suono per le pi&ugrave; in&shy;<lb/>terne parti turbinate e anfrattuose. </s>

<s>&ldquo; In osse lithoide foramen est insigne, <lb/>in quo veluti tympanum est: obtenditur enim membrana tenuissima et sim&shy;<lb/>plicissima, cui ossicula duo alligantur, quorum unum incudis vicem gerit, <lb/>dentisque molaris figura est, et perforatum acus modo in terrestribus, in <lb/>piscibus sinuosum, quo foramine nervum ut acus filum recipit, eoque nervo <lb/>suspenditur simul et membranae interius alligatur. </s>

<s>Alterum malleoli offi&shy;<lb/>cio fungitur, ex quorum percussu sonus ad cerebrum per nervum defer&shy;<lb/>tur &rdquo; (ibid.). </s></p><p type="main">

<s>Ma perch&egrave; Aristotile aveva detto, nel cap. </s>

<s>XI del I libro <emph type="italics"/>De historia <lb/>animalium,<emph.end type="italics"/> che il Vitello marino ha manifesto il meato uditorio esterno, <lb/>di cui manca il Delfino, bench&egrave; anche in lui l'udire sia certo, il Rondele&shy;<lb/>zio pensava che senza comunicar col di fuori avrebbe inutilmente la Natura <lb/>scolpito l'organo nell'osso petroso. </s>

<s>&ldquo; Qua ratione impulsus, cum Delphini <lb/>cranium diligentissime contemplatus essem, manifestissimum audiendi mea&shy;<lb/>tum, qui ad cerebrum usque patet, inveni e regione in vivi Delphini capite <lb/>foramen tam exiguum, ut fere oculorum aciem fugiat statim post oculum, <lb/>qui situs in causa est cur difficilius reperiatur: sunt enim oculi et foramina <lb/>illa in eadem fere linea cum oris scissura &rdquo; (ibid., pag. </s>

<s>465). </s></p><p type="main">

<s>Questo &egrave; ci&ograve;, conclude all'ultimo il Rondelezio, che si &egrave; saputo di certo <lb/>dagli antichi e da me intorno alla funzione e all'organo dell'udito ne'Ce-<pb xlink:href="020/01/1582.jpg" pagenum="457"/>tacei. </s>

<s>Quanto agli altri pesci poi &ldquo; vix constat qua parte audiant: nescias <lb/>enim an foramina ante oculos posita ad audiendum, an ad odorandum data <lb/>sint &rdquo; (ibid., pag. </s>

<s>49), perch&egrave;, com'&egrave; certo che i pesci odorano, cos&igrave; &egrave; cer&shy;<lb/>tissimo che, essendo ciechi que'fori posti innanzi ai loro occhi, non pos&shy;<lb/>sano perci&ograve; servire a trarre gli odori; intorno a che l'Autore De'pesci ma&shy;<lb/>rini ripete le cose stesse, e quasi le stesse parole dell'antico Autore della <lb/>Storia degli animali. </s></p><p type="main">

<s>Per le parole del Rondelezio trasmesso l'eco delle dottrine aristoteliche <lb/>a quei grandi anatomici, che fiorirono sulla fine del secolo XVI, il Casserio, <lb/>dop'avere atteso con si assiduo e diligente studio all'anatomia degli organi <lb/>de'sensi nell'uomo, e nella maggior parte degli animali terrestri, &ldquo; omni <lb/>animi contentione, cos&igrave; narra di s&egrave; medesimo, ac insigni patientia, in plu&shy;<lb/>ribus eius generis piscium, de quibus hucusque dubitatum est utrum per <lb/>foramina ante eorum oculos posita audirent av vero odorarent, exploravi per <lb/>quosnam meatus a foris sonus eiusque species intus deferreretur, ad quid&shy;<lb/>nam recipiendi et diudicandi gratia intus fabricatum esset &rdquo; (De auditus <lb/>hist. </s>

<s>anat., Ferrariae 1600, pag. </s>

<s>95). Per la quale esplorazione, soggiunge, <lb/>mi si rivelarono agli occhi tali cose, da non lasciarmi alcun dubbio intorno <lb/>all'uso di que'forami, e da venirmi anzi di l&igrave; di tutte insieme le parti del&shy;<lb/>l'organo una notizia completa. </s></p><p type="main">

<s>Questa &egrave; come un'avvertenza, dall'Autore premessa all'esplicazione <lb/>della terza figura con assai bel disegno impressa nel testo, e per la quale <lb/>si esibiscono le vescicole piene d'acqua dentro il cranio del Luccio, e si rap&shy;<lb/>presenta la posizione de'nervi acustici, insieme con altri nervi propagati <lb/>dalla midolla spinale. </s>

<s>Per la lettera A si designa particolarmente una ve&shy;<lb/>scicola &ldquo; ovalem figuram praeseferens, aqua plena, cui insunt duo corpu&shy;<lb/>scula ossea discontinua, divisa, ac ob omni vinculo libera, super quam ve&shy;<lb/>siculam duae nervorum propagines B, B, a spinali medulla ortae, instar <lb/>filamentorum tenuissimorum, progrediuntur, quibus quidem obiectorum so&shy;<lb/>norum inditium concreditum est &rdquo; (ibid.). </s></p><p type="main">

<s>Ma la figura IV seguente sta per rappresentare agli occhi de'lettori le <lb/>parti pi&ugrave; distinte di quel medesimo organo, che ha da servir nel pesce a <lb/>due si diverse funzioni. </s>

<s>Le cavit&agrave; de'due forami, che son sotto gli occhi, <lb/>sono esternamente rivestite di una membrana rotonda, &ldquo; variis ac pene innu&shy;<lb/>meris filamentis, quasi a circumferentia ad centrum, roboris gratia, ductis, <lb/>tympano auris aliorum animalium respondens, nec non auditui et olfactui <lb/>celebrando maxime deserviens &rdquo; (ibid.). Di cost&igrave; partono due canali &ldquo; per <lb/>quos aer sonorus ad praecipuum audiendi organum comportatur; &rdquo; canali <lb/>che, dopo un breve tratto, confluiscono in un altro pi&ugrave; largo, il quale va a <lb/>morire nella pia madre. </s></p><p type="main">

<s>Sopra queste e sopra le altre pi&ugrave; minute nuove cose scoperte, racco&shy;<lb/>gliendo il Casserio l'animo e la mente, prende occasione di ammirare la <lb/>somma Arte e Provvidenza di Dio nella Natura, e ne fa argomento per con&shy;<lb/>futar l'errore di coloro, che tutto dicono nel mondo essere stato fatto dal <pb xlink:href="020/01/1583.jpg" pagenum="458"/>caso. </s>

<s>Chi, dopo queste anatomie, oserebbe dire esser fatto a caso l'organo <lb/>dell'udito nel Luccio? </s>

<s>&ldquo; Hic enim etiam tympanum, quamvis sepe, loco et <lb/>structura ab aliorum animalium tympano longe diversum, reperis; hic duc&shy;<lb/>tum etiam admodum longum, mea sententia, olfactui et auditui communem <lb/>offendis; hic quoque mirabilis quorundam vinculorum aquam continentium, <lb/>capreolorumque ritu constructorum, plexus, nec non circumvolutiones con&shy;<lb/>tueris; hic nonnulla corpora, aqua plena, figuram aut fructus olivae aut zi&shy;<lb/>ziphi eleganter exprimentia, vides; hic demum ossicula magnitudine, figura, <lb/>positione dissimilia invenis &rdquo; (ibid.). </s></p><p type="main">

<s>L'avere il Casserio piuttosto accennate che descritte tutte queste gran <lb/>cose, che dice di aver vedute nell'organo auditorio del Luccio, e l'aver la&shy;<lb/>sciate le parti, trasportato dagli ardori dell'eloquenza, senza determinarne <lb/>gli usi, conferirono, insieme con altre cause che si scopriranno nel processo <lb/>di questa storia, a far s&igrave; che venissero le novit&agrave; di lui accolte da pochi, e <lb/>pi&ugrave; ragionevolmente ripudiate da molti. </s>

<s>Marc'Aurelio Severino e Pietro Gas&shy;<lb/>sendo son di tanta celebrit&agrave;, che possono servire a rappresentar, fino a mezzo <lb/>il secolo XVII, le contrariet&agrave; delle due parti. </s></p><p type="main">

<s>Il nostro Napoletano dunque non dubita di ammettere, persuaso dal&shy;<lb/>l'esperienze di Aristotile, del Rondelezio, e dalle sue proprie, che i pesci <lb/>odano, bench&egrave;, con que'due Autori convenendo, anch'egli ripeta: &ldquo; Nulla <lb/>tamen pars est manifesta, quae sensus ministrat audiendi &rdquo; (Antiperipatias, <lb/>Neapoli 1659, pag. </s>

<s>32). </s></p><p type="main">

<s>Il non esser per&ograve; una cosa manifesta, ragionava il Severino, non vuol <lb/>dire che non ci sia, e da un'altra parte &egrave; cos&igrave; chiaramente visibile l'organo <lb/>interno, da far necessariamente argomentare all'esistenza di un qualche invi&shy;<lb/>sibile meato esterno. </s>

<s>Ma a un s&igrave; fatto modo di ragionare conseguiva il na&shy;<lb/>tural desiderio di sapere qual, fra le tante parti di che si compone l'organo <lb/>auditorio de'pesci, fosse la principale, ci&ograve; che il Casserio aveva ai soli buoni <lb/>interpetri lasciato intendere, scrivendone tanto in confuso. </s>

<s>E perch&egrave; preva&shy;<lb/>leva tuttavia la teoria meccanica, che insegnava risvegliarsi l'udito nel tim&shy;<lb/>pano dal risonar dell'incudine percossa dal martello, vide il Severino ne'cas&shy;<lb/>seriani iconismi accennato a questi strumenti, in que'due corpuscoli ossei <lb/>fra s&egrave; divisi, e chiusi in una vescicola, alla quale giungono le propaggini di <lb/>que'nervi, <emph type="italics"/>quibus quidem obiectorum sonorum inditium concreditum est.<emph.end type="italics"/><lb/>Ecco infatti quali sono l'espressioni proprie dell'Autore dell'<emph type="italics"/>Antiperipatias,<emph.end type="italics"/><lb/>l&agrave; dove argomenta esser ne'pesci la facolt&agrave; di udire, dal vederli dotati degli <lb/>organi principali, che servono a questa funzione: &ldquo; Facultatis auditoriae pi&shy;<lb/>sces non sunt expertes, sed quantum horum natura capit participes, con&shy;<lb/>stantibus auscultatorii organis internis apprime nobilibus, quorum unus, cum <lb/>sit lapillus malleo respondens sensus percussorio, hic, capite gestus, suam <lb/>facit audiendi promptitudinem &rdquo; (ibid, pag. </s>

<s>95). </s></p><p type="main">

<s>Il Gassendo, non anatomico n&egrave; zootomo come il Severino, ma fisico e <lb/>filosofo, ripudiava addirittura le novit&agrave; introdotte dal Casserio negli organi <lb/>delle sensazioni dei pesci, perch&egrave; ripugnanti <emph type="italics"/>cum analogia aliorum omnium<emph.end type="italics"/><pb xlink:href="020/01/1584.jpg" pagenum="459"/><emph type="italics"/>animalium.<emph.end type="italics"/> Studiosissimo della fisica de'suoni, argomentava che i pesci non <lb/>possono udire, perch&egrave; i tremori armonici non si profondan nell'acqua. </s>

<s>Che <lb/>se pur odono i Cetacei, com'&egrave; certo, avendo gli organi dell'udito patenti, <lb/>ci&ograve; fanno solo, egli dice, quando sollevano il capo, e tengono le orecchie in <lb/>mezzo all'aria. </s>

<s>&ldquo; Ad haec, scrive cos&igrave; trattando dei sensi in particolare nella <lb/>sezione III del suo <emph type="italics"/>Sintamma filosofico,<emph.end type="italics"/> utcumque perhibeant sonum pene&shy;<lb/>trare per ipsam aquam, id tamen aut nihil, aut perexiguum est, et ad ipsam <lb/>quidem aquae superficiem duntaxat. </s>

<s>Nam primum quidem sonum aliquem <lb/>ex loco intra aquam advenire constat, cum corpora dura ac metallica prae&shy;<lb/>sertim intra aquam collidimus, aut unum in alium demittimus, sed nimi&shy;<lb/>rum id prope superficem..... At si moles aquae sit tanta, ut aut tremori <lb/>corporum obstet, aut ipsa non tremat, vel tremorem ita in orbem diffundat, <lb/>ut ad superficiem perveniens nullus pene sit, neque aerem movere sensi&shy;<lb/>biliter posset; tunc nullus plane exauditur sonus &rdquo; (Operum, T. II, Flo&shy;<lb/>rentiae 1727, pag. </s>

<s>319). </s></p><p type="main">

<s>Si opponevano a queste teoriche conclusioni l'esperienze antiche, rife&shy;<lb/>rite da Aristotile, e confermate dai quotidiani esercizi dei pescatori. </s>

<s>A che <lb/>trov&ograve; da rispondere ingegnosamente il Gassendo, cogliendo un concetto dal <lb/>libro del Rondelezio, il quale, dop'aver detto che le ostriche, mancando degli <lb/>occhi, mancano senza dubbio anche degli orecchi, soggiunge che &ldquo; etsi sese <lb/>contrahunt, cum ferreis hamis appetuntur, agitatione aquae, potius quam <lb/>auditione admonita, id faciunt &rdquo; (De piscibus cit., pag. </s>

<s>49). Ai seguaci di <lb/>Aristotile dunque che, per provar l'udito ne'pesci, adducevano il fatto del <lb/>vederli fuggire allo strepito dei remi, rispondeva il Gassendo stesso, gene&shy;<lb/>ralizzando quel concetto rondeleziano, e dicendo esser non i tremori sonori <lb/>dell'aria eccitanti l'udito, ma i moti ondosi dell'acqua eccitanti il tatto, <lb/>quelli per cui si rendon cauti gli acquatici animali d'evitare il pericolo. </s>

<s>Una <lb/>bella esperienza egli cos&igrave; racconta, per confermare il suo asserto: &ldquo; Tran&shy;<lb/>siens alias prope piscinam cum quatuor aut quinque familiaribus, deprehen&shy;<lb/>dimus Lucium in summa aqua soporatum: ille vero nullo aut pedum aut <lb/>sermonum nostrorum strepitu excitatus fuit, imo neque levioribus leviterque <lb/>aquam commoventibus festucis iniectis, sed solum, cum, paullo maiore con&shy;<lb/>citatione, commovimus aquam: prorsus ut surdus, non strepitu, sed motu <lb/>solum excitatur &rdquo; (ibid., pag. </s>

<s>320). </s></p><p type="main">

<s>In ogni modo, tanto il Gassendo contradittore, quanto il Severino illu&shy;<lb/>strator del Casserio avevano lasciata negli studiosi una viva curiosit&agrave; di sa&shy;<lb/>pere se quella membrana rotonda, designata con le lettere B, B nel sopra <lb/>citato IV iconismo casseriano, era veramente la membrana del timpano, e se <lb/>quei due canali C, C, confluenti nell'unico canale D, servivano propriamente <lb/>a condurre al cervello i suoni e gli odori. </s>

<s>Si vide quella curiosit&agrave;, che <lb/>aspettava qualche esperta mano anatomica, con grande maraviglia sodisfatta <lb/>nel 1667, quando lo Stenone, in appendice al suo libro <emph type="italics"/>Myologiae speci&shy;<lb/>men,<emph.end type="italics"/> descrisse la storia anatomica di un pesce del genere dei Cani. </s>

<s>Dicemmo <lb/><emph type="italics"/>con gran maraviglia,<emph.end type="italics"/> perch&egrave; la membrana, che il Casserio rassomigliava al <pb xlink:href="020/01/1585.jpg" pagenum="460"/>timpano, compariva piuttosto analoga alla pituitaria; quei filamenti, creduti <lb/>posti ivi a rinforzar esso timpano, si descrivevano come tante lamelle, da <lb/>moltiplicar la superfice di contatto, ad esempio delle ossa turbinate; e i sup&shy;<lb/>posti canali auditivi e olfattivi si vedevano, quasi per incanto, trasformati <lb/>ne'processi mamillari. </s></p><p type="main">

<s>Venne poco dopo il Lorenzini a confermare queste nuove cose rivelate <lb/>agli Ittiologi dal Maestro, quando attese a descrivere pi&ugrave; minutamente il cer&shy;<lb/>vello delle Torpedini, tutta la mole del quale nuota, egli dice, in un certo <lb/>umore viscoso, che si racchiude per entro alla cavit&agrave; della dura Madre (Os&shy;<lb/>servazioni cit., pag. </s>

<s>99, 100). Non dubita che le membrane, delle quali son <lb/>rivestiti i forami posti sotto gli occhi, non servano veramente, anche nelle <lb/>Torpedini, al senso dell'odorato, ricevendo esse i nervi olfattivi, che si ritro&shy;<lb/>vano negli altri animali (ivi, pag. </s>

<s>12), i quali nervi si vedono, uno di qua <lb/>e uno di l&agrave;, attaccati nella base di quel tubercolo grande, posto nella parte <lb/>anteriore del cervello (pag. </s>

<s>101). Per aggiunger nuove prove a dimostrare <lb/>che la moltiplicazione di superficie sia cagione dell'acutezza dell'odorato, <lb/>descrive minutamente le ossa turbinate nel naso di un orso, e riconoscendo <lb/>anch'egli con lo Stenone quest'ossa analoghe alle lamelle commesse sulla <lb/>membrana delle cos&igrave; dette narici dei pesci, ne conclude ch'essendo cos&igrave; fatte <lb/>lamelle nelle Torpedini scarse, dee essere in loro l'odorato assai ottuso <lb/>(pag. </s>

<s>12). </s></p><p type="main">

<s>Cos&igrave; essendo, non venne dunque il Perrault a dire in Ittiologia nulla <lb/>di nuovo, quando, facendo pi&ugrave; finamente dello Stenone incidere, nella fig. </s>

<s>III <lb/>della tavola IX della sua Meccanica degli animali, il cervello e gli organi <lb/>dell'odorato di un pesce, gli dichiarava alla mente de'suoi lettori colle se&shy;<lb/>guenti parole: &ldquo; La plus grande partie du cerveau des poissons est em&shy;<lb/>ploy&eacute;e aux organes de l'odorat. </s>

<s>Tout le cerveau, qui est rec&ograve;uvert d'une <lb/>pie-mere couch&eacute;e immediatement sur la substance de cerveau est conferm&eacute; <lb/>danse la dure-mere, qui est une espece de sac, rempli d'une substance olea&shy;<lb/>gineuse, dans laquelle le cerveau nage. </s>

<s>Les organes de l'odorat, comme aux <lb/>animaux terrestres, eonsistent en un grand nombre de membranes, posant <lb/>les unes sur les autres, et composant deux masses de la figure d'un oeuf. </s>

<s><lb/>Les productions du cerveau auxquelles ces masses sont attach&eacute;es, qui sont <lb/>les apophyses mammillaires, sont creuses, et sont comme deux grands ven&shy;<lb/>tricules &rdquo; (Oeuvres cit., T. I, pag. </s>

<s>409). </s></p><p type="main">

<s>Non aveva nulla ancora letto il Morgagni di queste nuove cose, sco&shy;<lb/>perte ne'pesci e pubblicamente descritte in Francia e in Italia dopo il Cas&shy;<lb/>serio, col quale nonostante non conveniva, perch&egrave; avea conosciuto non poter <lb/>esser nervi acustici quelli, da lui delineati per tali, e perch&egrave;, scambiati i <lb/>processi mammillari in canali, non aveva nemmeno indicato all'esistenza dei <lb/>nervi olfaltorii. </s>

<s>Desideroso dunque di ricercare i veri organi dell'odorato nei <lb/>pesci, si dette il Morgagni a sezionarne alcuni di quei cos&igrave; detti Acipenseri, <lb/>e volgarmente chiamati <emph type="italics"/>porcelletti,<emph.end type="italics"/> ne'quali riscontr&ograve; i forami, la cavit&agrave; sot&shy;<lb/>toposta e la membrana che la riveste. </s>

<s>&ldquo; Verum, soggiunge, neque hanc Cas-<pb xlink:href="020/01/1586.jpg" pagenum="461"/>serii auditoriis nervis subservire, neque caveam, ut Rondeletius aiebat, ad <lb/>branchias ferri, sed ad cerebrum, quod ille negabat, permeare, in acipen&shy;<lb/>serum quidem utroque genere manifestum fuit &rdquo; (Epistol. </s>

<s>anat., T. II, Ve&shy;<lb/>netiis 1740, pag. </s>

<s>294). </s></p><p type="main">

<s>Che la cavea fosse cieca e che mettesse alle branchie, piuttosto che al <lb/>cervello, l'avea detto Aristotile, com'apparisce dai passi di lui sopra alle&shy;<lb/>gati, prima del Rondelezio, ma lo Stenone stesso, bench&egrave; dubitasse se l'as&shy;<lb/>serito da que'due Autori era vero, confess&ograve; nonostante di non essersene po&shy;<lb/>tuto assicurare. </s>

<s>&ldquo; An ex hoc foramine, egli cos&igrave; si esprime, in cavitatem <lb/>anfractuosam, cranio insculptam, via sit meatui auditorio analoga, necdum <lb/>observare mihi licuit &rdquo; (Myologiae specimen cit., pag. </s>

<s>112). </s></p><p type="main">

<s>Fatto dunque dal Morgagni questo primo passo nella desiderata ricerca <lb/>dell'organo dell'odorato, con l'assicurarsi essere dai forami, che son per <lb/>naso dei pesci, veramente aperta la via nelle cavit&agrave; anfrattuose scolpite nel <lb/>cranio; quel che maggiormente gl'importava era di seguitare il corso del <lb/>nervo olfaltorio, e di osservarne il termine nell'espandersi sulla membrana <lb/>rotonda. </s>

<s>Rivolgendo perci&ograve; l'attenzione sopra quei sottilissimi filamenti, che <lb/>negli Acipenseri apparivano di un certo colore oscuro, si trovava penosa&shy;<lb/>mente combattuto dal dubbio se fossero nervi o vasellini sanguigni, quando <lb/>gli capit&ograve; alle mani la Storia anatomica del pesce Cane sezionato dallo Ste&shy;<lb/>none. </s>

<s>Al veder nella figura illustrativa que'fili, che decorrono dal centro alla <lb/>circonferenza a modo di raggi, dichiarati cos&igrave; sotto la lettera di richiamo F: <lb/>&ldquo; nervea filamenta in tunicam narium a processibus mamillaribus diffusa &rdquo; <lb/>(ibid., pag. </s>

<s>114); il Morgagni, dietro l'autorit&agrave; di un tant'uomo, o diciam <lb/>meglio dietro cos&igrave; chiara dimostrazione anatomica del vero, si trov&ograve; libero <lb/>d'ogni dubbio, e si rese sempre pi&ugrave; certo che nelle parti del suo Acipen&shy;<lb/>sero, corrispondenti alle descritte dallo Stenone in quel suo pesce Cane, ri&shy;<lb/>siede veramente l'organo dell'odorato. </s></p><p type="main">

<s>Vennero poi altre osservazioni a confermare l'Anatomico padovano in <lb/>questa certezza, e furono la secrezione di un mucco, simile a quello del naso, <lb/>nella cos&igrave; detta <emph type="italics"/>Canicula,<emph.end type="italics"/> e la manifesta e unica inserzione dei nervi del <lb/>primo paio nella membrana rotonda di questo pesce: d'onde trasse ragio&shy;<lb/>nevole motivo a congetturare che, anche nel naso dell'uomo, sebbene s'in&shy;<lb/>seriscano parecchi altri nervi, i preposti nulladimeno all'odorato sieno pro&shy;<lb/>priamente quelli del primo paio. </s>

<s>Dopo le quali cose, ritornando il Morgagni <lb/>al Casserio, d'ond'era mosso il discorso intorno all'organo olfaltorio de'pe&shy;<lb/>sci, cos&igrave; riassume e conclude il &sect; 41 della citata Epistola anatomica, dopo <lb/>aver confermata l'analogia stenoniana fra le lamelle membranose, e le ossa <lb/>turbinate: &ldquo; Id quoque, et is de quo dicebam mucus, et potissimum Pri&shy;<lb/>mum nervorum par, valde crassum, ad hanc pariter in Canicula caveam <lb/>perductum, ut nihil cum auditus, plurimum cum olfactus instrumento con&shy;<lb/>veniunt; ita Casserii opinioni, utrumque hic organum coniungentis, inter <lb/>alia quae sciens praetereo, non obscure adversantur &rdquo; (pag. </s>

<s>295). </s></p><p type="main">

<s>Dimostratosi cos&igrave; con tanta evidenza dallo Stenone, e confermatosi dal <pb xlink:href="020/01/1587.jpg" pagenum="462"/>Lorenzini, dal Perrault, e pi&ugrave; autorevolmente che mai dal Morgagni, non <lb/>convenire gli organi casseriani de'pesci altro che all'odorato, rimaneva negli <lb/>Ittiologi una viva curiosit&agrave; di sapere qual si fosse dunque l'organo dell'udito <lb/>in quegli acquatici animali. </s>

<s>Vedemmo come il Morgagni stesso diffidasse ul&shy;<lb/>timamente di riconoscer per nervo acustico quello, che nel capo del Luccio <lb/>avea fatto rappresentare in disegno l'Anatomico piacentino, ma da un'altra <lb/>grande autorit&agrave; nella scienza era stato pronunziato, assai tempo prima, che <lb/>il nervo auditorio ne'pesci, a'suoi pi&ugrave; diligenti esami, tuttavia rimaneva un <lb/>desiderio. </s>

<s>Tommaso Willis riserb&ograve; il cap. </s>

<s>V del suo trattato <emph type="italics"/>De cerebri ana&shy;<lb/>tome<emph.end type="italics"/> a descrivere il cervello degli uccelli e de'pesci, dove osserva che, seb&shy;<lb/>bene il capo sia a proporzione delle altre membra maggiore ne'pesci che <lb/>negli altri animali, il cervello &egrave; nulladimeno a loro il minimo di tutti. </s>

<s>&ldquo; Nam <lb/>duae moleculae anterius positae totum cerebri, ita proprie dicti, locum sub&shy;<lb/>stinent. </s>

<s>Ex his duo nervi olfactorii insignes procedunt, qui longo et recto <lb/>itinere ad foramina, ex utroque oris latere excavata, quaeque instar narium <lb/>sunt, feruntur, atque piscibus singulare est.... Nervi auditorii hic deside&shy;<lb/>rantur, licet Casserius placentinus hoc munus nervis olfactoriis attribuat &rdquo; <lb/>(In Mangeti, Bibliotheca anat., T. II, Genevae 1685, pag. </s>

<s>255 et 258). </s></p><p type="main">

<s>Quanto agli organi esterni, e a quegli altri pi&ugrave; internamente scolpiti <lb/>nella cavit&agrave; anfrattuosa del cranio, udimmo dianzi il Casserio eloquentemente <lb/>descrivere la membrana del timpano, e il meato uditorio, e i maravigliosi <lb/>plessi capreolari, e i lapilli olivari, e, varii di grandezza, di forma e di po&shy;<lb/>situra, gli ossicini. </s>

<s>Al Perrault nonostante, guarda e riguarda, non riusci <lb/>mai di veder nulla di tutto ci&ograve; nella rocca petrosa de'pesci, fuor che qual&shy;<lb/>che cosa, da potersi senza dubbio rassomigliare ai canaliculi semicircolari. <lb/></s>

<s>&ldquo; Dans le poissons, egli dice nel trattato <emph type="italics"/>Du bruit,<emph.end type="italics"/> nous n'avons point en&shy;<lb/>core p&ugrave; trouver ni de tambour, ni d'osselets, ni de couduit dans le laby&shy;<lb/>rinthe qui ait aucune analogie avec le lima&ccedil;on: il y en a m&ecirc;me beaucoup <lb/>o&ugrave; il ne se trouve point d'ouverture au dehors qui soit visible. </s>

<s>Tout ce <lb/>qu'on y void distinctement sont les conduits principalement du labyrinthe, <lb/>qui se trouvent en quelques poissons au nombre de trois comme aux oi&shy;<lb/>seaux: il y en a o&ugrave; il ne s'en trouve que deux &rdquo; (Oeuvres, T. </s>

<s>I cit., <lb/>pag. </s>

<s>247). </s></p><p type="main">

<s>Come potessero per&ograve; questi canali semicircolari, senza nervo acustico, <lb/>senza nessuna apparente comunicazion coll'esterno, rappresentare essi soli <lb/>l'organo dell'udito, riusciva difficile intenderlo ai pi&ugrave;, i quali facilmente si <lb/>persuasero ch'essendo muti i pesci fossero perci&ograve; da credere anche sordi. </s>

<s><lb/>Ma inaspettatamente, poco prima che il secolo XVIII giungesse a mezzo il <lb/>suo corso, si videro uscire in Danzica due volumi, con numerose bellissime <lb/>tavole ittiologiche, nel primo de'quali Iacopo Teodoro Klein, che n'era l'Au&shy;<lb/>tore, premetteva alla Storia de'pesci un discorso intitolato <emph type="italics"/>De piscium au&shy;<lb/>ditu.<emph.end type="italics"/> In quel tempo che l'anatomia dell'organo e la teoria della funzione <lb/>avevano gi&agrave; avuto tanti insigni cultori nello Schelhammer, nel Duverney, <lb/>nel Perrault, nel Valsalva, per tacer di tanti altri, nessun sarebbesi aspet-<pb xlink:href="020/01/1588.jpg" pagenum="463"/>tato fosse venuto un Naturalista a dire che il suono si produce nell'orec&shy;<lb/>chio dall'incudine percossa dal martello. </s>

<s>Eppure il Klein si gloria principal&shy;<lb/>mente di avere illustrate, co'suoi nuovi studii, le oramai viete e meritamente <lb/>ripudiate teorie del Casserio, a cui egli attribuisce la prima palma nella sco&shy;<lb/>perta de'lapilli de'pesci, l'uso dei quali ei non dubita esser quello attri&shy;<lb/>buito a loro dal Severino. </s>

<s>&ldquo; Casserius placentinus omnibus palmam prae&shy;<lb/>ripuit, utpote qui primus tria paria lapillorum in cerebro Lucii detexit, et <lb/>si non adulari nullum involvit periculum audeamus dicere neminem Casse&shy;<lb/>rio simul propius ad organa auditus piscium accessisse, via licet, quam pro <lb/>meatu auditorio elegit, plane regia non fuerit &rdquo; (Historiae piscium, P. I, <lb/>Gedani 1741, pag. </s>

<s>12). </s></p><p type="main">

<s>Cercando dunque il Klein questa nuova via regia, si compiacque di aver <lb/>fatto una scoperta, perch&egrave;, mentre il Casserio non avea veduto nel suo Luc&shy;<lb/>cio altro che due soli forami, egli ebbe a ritrovarvene venti. </s>

<s>&ldquo; Ulterius Cas&shy;<lb/>serii experimenta examinare cupidi, sumpsimus aliud Lucii maioris cranium, <lb/>cuius in superficiem mox offendimus decem paria foraminum, sive foramina <lb/>externa viginti: Casserius non nisi nares exhibet &rdquo; (ibid., pag. </s>

<s>13). Ma, se <lb/>non il Casserio, lo Stenone aveva descritto il rostro del suo Pesce cane &ldquo; mul&shy;<lb/>tis undique foraminibus pertusum &rdquo; (Historia in Myol. </s>

<s>spec. </s>

<s>cit., pag. </s>

<s>112) <lb/>e il Lorenzini, a proposito delle Torpedini, avea cos&igrave; pubblicamente scritto, <lb/>illustrando e compiendo le osservazioni anatomiche de'suoi due illustri mae&shy;<lb/>stri: &ldquo; Tutta la pelle, che &egrave; sopra il dorso, &egrave; piena d'infiniti forami, de'quali <lb/>alcuni sono pi&ugrave; grandi, altri pi&ugrave; piccoli, e tanto i grandi quanto i piccoli <lb/>sono pi&ugrave; numerosi in vicinanza del capo..... Questi stessi forami sono stati <lb/>osservati e descritti dal signore Stenone nel pesce chiamato Razza, con que&shy;<lb/>sta differenza per&ograve; che egli ha osservato una sola sorta di forami grandi, ed <lb/>io ho osservato i maggiori e i minori. </s>

<s>Il signor Francesco Redi, nel suo trat&shy;<lb/>tato <emph type="italics"/>Delle anguille<emph.end type="italics"/> non ancora stampato, osserv&ograve; ancor egli questa differenza <lb/>di forami maggiori e minori, e gli ha descritti diligentemente, e di pi&ugrave; ha <lb/>osservato che, messa la setola per un forame e camminando lunghesso il <lb/>canale sottoposto, va la setola a uscire fuora del canale per la bocca del fo&shy;<lb/>rame pi&ugrave; vicino. </s>

<s>Inoltre egli ha osservato che, non solamente i pesci carti&shy;<lb/>laginei e senza squame sono dotati di questi cos&igrave; fatti forami e canali, ma <lb/>ancora i pesci squamosi, come i Lucci, le Tinche, le Reine, le Trote &rdquo; (Os&shy;<lb/>servazioni intorno alle Torp. </s>

<s>cit., pag. </s>

<s>7, 8). </s></p><p type="main">

<s>Non nuovo era dunque al Klein nemmen l'artificio d'esplorare le ri&shy;<lb/>poste vie, e le loro riuscite, per mezzo delle setole porcine infilate in quegli <lb/>aperti forami, ma novissimo sarebbe riuscito al Redi e allo Stenone e al Lo&shy;<lb/>renzini quel che lo stesso Klein diceva di avere scoperto, che cio&egrave; alcune di <lb/>quelle vie mettono al cervello, e che servono perci&ograve; al pesce in qualit&agrave; di <lb/>meato uditorio esterno. </s>

<s>Cos&igrave;, mentre il Perrault non aveva saputo veder nel&shy;<lb/>l'osso litoide de'pesci altro che i canali semicircolari, egli, il Klein, ci vide <lb/>tutto ci&ograve; che v'avea veduto il Casserio, e ci vide anzi di pi&ugrave;, oltre il mar&shy;<lb/>tello e l'incudine, la staffa e lo stesso osso lenticolare. </s>

<s>&ldquo; Quaenam vero di-<pb xlink:href="020/01/1589.jpg" pagenum="464"/>verticula sint, quae seta reflexa perrepserit, et utrum e fig. </s>

<s>III ossis petrosi <lb/>aut alius nescio, cuius vices subeat, peritiores, qui se anatomicos profiten&shy;<lb/>tur, iudicent. </s>

<s>Similiter quid obstare possit quo minus maior lapillus pro <lb/>incude, proximus illi minor et longiusculus pro malleo, sive percussorio, <lb/>proximior vero et minimus orbicularis ac crenatus pro esse lenticulari Cas&shy;<lb/>serii sive orbicolari, vel loco stapedis, foramina demum B, B figurae I pro <lb/>meatibus auditus externis, et vesicula ovalis figurae, diaphana, pro tympano <lb/>habenda? </s>

<s>&rdquo; (Historiae piscium, P. </s>

<s>I cit., pag. </s>

<s>14). </s></p><p type="main">

<s>Questi in ogni modo furono giudicati sogni dagl'Ittiologi del secolo XVIII, <lb/>i quali, essendo oramai ben persuasi che gli ossicini hanno un ufficio se&shy;<lb/>condario, anche nell'orecchio de'quadrupedi e degli uccelli, non riconobbero <lb/>col Perrault ne'pesci altr'organo dell'udito che i canali semicircolari. </s>

<s>L'Hal&shy;<lb/>ler diceva nel Tomo V della sua Fisiologia (pag. </s>

<s>292) che se si potesse aver <lb/>di ci&ograve; qualche certezza, si verrebbe a dar gran valore alla sentenza di co&shy;<lb/>loro, che riponevano in quegli stessi canali la sede principale dell'udito, ma <lb/>le nuove scoperte del Cotunnio avviavano la mente per ben altri sentieri. </s></p><p type="main">

<s>Se l'orecchio infatti &egrave; tutto internamente pieno di umore, e se il nervo <lb/>riceve da questo, e non immediatamente dall'aria, i tremori, i pesci, che vi&shy;<lb/>vono in mezzo all'acqua, non han dunque bisogno del risonar della dura <lb/>rocca petrosa, e perci&ograve; anche i canali semicircolari del Perrault si dubitava <lb/>che fossero da ripor nel numero de'sogni casseriani. </s>

<s>Pensarono perci&ograve; sa&shy;<lb/>viamente costoro tornasse piuttosto vera la sentenza del Gassendo, che cio&egrave; <lb/>al senso speciale dell'udito ne'pesci, come a quello della vista ne'pipristelli <lb/>accecati dallo Spallanzani, supplisse il senso fondamentale del tatto, il quale <lb/>ha le sue papille continuamente immerse nell'acqua, come sono continua&shy;<lb/>mente immerse le filamenta nervose nell'umor del Cotunnio. </s>

<s>Che dall'altra <lb/>parte sia l'acqua sensibilissimo e prontissimo mezzo di trasmissione di qua&shy;<lb/>lunque minimo moto, lo dimostrano l'esperienze del Magiotti, e i telegrafi <lb/>idraulici, fondati sul principio idrostatico dell'uguaglianza delle pressioni. </s></p><p type="main">

<s>Un tal modo di ricevere i segni conviene oltres&igrave; col modo particolare <lb/>di emetterli, non sapendosi persuadere coloro, che accoglievano questi nuovi <lb/>pensieri, come si pretendesse che avessero i pesci organi da inspirar la voce, <lb/>non avendo strumenti da espirarla. </s>

<s>Come dunque i segni vengono a loro, <lb/>non dai moti acustici ma idrostatici dell'acqua; cos&igrave; gli trasmettono per <lb/>questi stessi moti, e in tal maniera s'intendono insieme, e vivono in comu&shy;<lb/>nanza, e si partecipano a vicenda ora i minacciosi odii, ora i placidi amori. </s></p><pb xlink:href="020/01/1590.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO XII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Degl'insetti<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della generazione spontanea e delle varie esperienze istituite per dimostrarla falsa. </s>

<s>&mdash; II. </s>

<s>Della <lb/>Micrografia e delle particolari applicazioni di lei alla scoperta degli organi della respirazione, <lb/>&mdash; III. </s>

<s>Degli organi dei sensi e particolarmente degli occhi. </s>

<s>&mdash; IV. De'fenomeni di fosfore&shy;<lb/>scenza, segnatamente nelle lucciole marine e nelle terrestri. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>A quella Filosofia che, secondo l'animo proprio e la propria mente, fa&shy;<lb/>ceva operatrice la Natura, parve quasi essere dalla sua dignit&agrave; degradata, <lb/>quando, da contemplare i quadrupedi, gli uccelli e i pesci, la pi&ugrave; parte dei <lb/>quali dominati dall'uomo si porgevano docili e vinti a sodisfare alle neces&shy;<lb/>sit&agrave; della vita di lui e ai piaceri; abbass&ograve; lo sguardo su quell'indiscipli&shy;<lb/>nato indomabile esercito d'innumerevoli animalucci, spesso nocivi, sempre <lb/>molesti, e ne'quali, degradatasi la Natura stessa, non si riconosceva altra <lb/>immagine che della vilt&agrave; e della abbiettezza. </s>

<s>Aristotile, gran Maestro di cos&igrave; <lb/>fatta Filosofia, nell'introdursi a scrivere la Storia degli Animali, disse di <lb/>essere stato il primo a imporre a cotesti abietti esseri viventi il nome di <lb/><foreign lang="greek">e/ntoma zw_a</foreign>, che i Latini tradussero in <emph type="italics"/>Insecta animalia,<emph.end type="italics"/> e le lingue volgari <lb/>in <emph type="italics"/>Insetti.<emph.end type="italics"/> A pochi di costoro concesse il Filosofo l'onore di riconoscere per <lb/>loro primo parente una gocciola d'umor viscido e albuminoso, che avesse <lb/>qualche somiglianza con l'uovo: i pi&ugrave; disse essere ingenerati dalla pu&shy;<lb/>tredine e dal fango: &ldquo; Procreantur porro insecta aut ex animalibus gene&shy;<lb/>ris eiusdem, ut phalangia et aranei, ex phalangiis et araneis, ut bruci, lo&shy;<lb/>custae, cicadae, aut non ex animalibus sed sponte, alia ex rore, qui frondibus <pb xlink:href="020/01/1591.jpg" pagenum="466"/>insudat, item alia ex coeno aut fimo putrescente &rdquo; (De historia anim, Ope&shy;<lb/>rum, T. VI cit., fol. </s>

<s>132). </s></p><p type="main">

<s>I Filosofi posteriori si studiarono di nobilitare coteste generazioni, ri&shy;<lb/>correndo alla indeficiente fecondit&agrave; della madre Terra, sotto i benigni influssi <lb/>celesti, e Guglielmo Rondelezio, nel risorgere degli studi sperimentali, in&shy;<lb/>troduceva i principii della Filosofia stoica nella Storia naturale, quando volle <lb/>ridurre a scienza lo spontaneo nascere di alcuni pesci. </s>

<s>A quel modo, egli <lb/>dice, che la Terra, in stabiliti tempi, senza seme e senz'altr'opera d'uomo, <lb/>produce per sua propria virt&ugrave; tant'erbe e tanti animali; cos&igrave; medesima&shy;<lb/>mente fa il Mare partecipe tutto insieme delle virt&ugrave; dell'umido, dell'aereo <lb/>e del terreo, e perci&ograve; dispostissimo per s&egrave; a procreare. </s>

<s>&ldquo; Generantur ergo <lb/>in terra et in humore animantes et plantae, propterea quod in terra qui&shy;<lb/>dem inest humidum, in humore spiritus, in universo autem calor animale, <lb/>ut quodammodo omnia anima plena sint &rdquo; (De piscibus cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Pi&ugrave; immediato promotore della Storia naturale, che non il Rondelezio, <lb/>Girolamo Fabricio d'Acquapendente non seppe far altro, per meglio confor&shy;<lb/>marsi alle dottrine del Maestro, che ripetere verbo a verbo i detti sopra ri&shy;<lb/>feriti di Aristotile, ai quali solo aggiunse, come per commento, di suo, dopo <lb/>avere annoverati i varii insetti che hanno varia generazion casuale, queste <lb/>parole: &ldquo; quorum nullum ex ovo, quod non preest, suam generationem <lb/>adipiscitur &rdquo; (De formatione ovi, Op. </s>

<s>omnia cit., pag. </s>

<s>25). E nell'introdursi <lb/>a trattare della generazione, si proponeva di distinguere cos&igrave; in tre diversi <lb/>ordini le varie feture animali. </s>

<s>&ldquo; Animalium autem foetus alius ex ovo, alius <lb/>ex semine, alius ex putri gignitur, unde alia ovipara, alia vivipara, alia ex <lb/>putri, seu sponte naturae nascentia <foreign lang="greek">auto/mata</foreign> graece dicuntur &rdquo; (ibid., pag. </s>

<s>1). </s></p><p type="main">

<s>Guglielmo Harvey, quando si dette con tanto ardore a proseguir l'opera <lb/>dell'Acquapendente, che avea cos&igrave; a soli alcuni animali assegnata la gene&shy;<lb/>razione dall'uovo, &ldquo; nos autem asserimus, gloriosamente scriveva, omnia <lb/>omnino animalia, etiam vivipara atque hominem adeo ipsum, ex ovo pro&shy;<lb/>gigni &rdquo; (De generat. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>2). E per accennare a un altr'amo, a <lb/>cui rimasero presi alcuni, che delibarono qua e l&agrave; qualche cosa del libro <lb/>dell'Harvey, trattando in altra esercitazione, l'Autore, de'primordii oviformi <lb/>dai quali hanno origine le piante stesse, cos&igrave; interrompe il cominciato di&shy;<lb/>scorso: &ldquo; Sed de his quoque generatim plura dicemus, cum multa anima&shy;<lb/>lia, praesertim insecta, ab inconspicuis prae exiguitate principiis et seminibus, <lb/>quasi atomis in aere volitantibus, a ventis huc illuc sparsis ac disseminatis, <lb/>oriri ac progigni docebimus, quae tamen sponte, sive ex putredine orta, iu&shy;<lb/>dicantur, quia eorum semina nusquam comparent &rdquo; (ibid., pag. </s>

<s>149). </s></p><p type="main">

<s>Per gli ami, de'quali abbiam citato questi due esempii, vogliamo in&shy;<lb/>tender l'inganno di coloro, che crederono essere stato l'Harvey il primo e <lb/>solenne maestro venuto fuori a insegnare la generazione di ogni animale <lb/>dall'uovo, e che si dovesse perci&ograve; a lui principalmente il merito di aver <lb/>dimostrata la falsit&agrave; della generazione spontanea. </s>

<s>I nostri lettori del passato <lb/>capitolo X, che sono stati oramai disingannati rispetto al primo punto, si <pb xlink:href="020/01/1592.jpg" pagenum="467"/>disinganneranno altres&igrave; con facilit&agrave; rispetto al secondo, attendendo con noi, <lb/>per via di diligenti collazioni, al significato proprio, che dava l'Harvey a <lb/>que'semi, quasi atomi vaganti per l'aria, e da'quali s'ingenerano que'vi&shy;<lb/>venti, che il volgo crede aver origine dalle materie putrefatte. </s>

<s>Non son mica <lb/>cotesti germi univoci, per usare il linguaggio proprio di que'tempi, ma equi&shy;<lb/>voci; ossia non vengono essi deposti dall'utero di altri animali della mede&shy;<lb/>sima specie, ma sono un fortuito accozzamento di atomi materiali, a cui si <lb/>d&agrave; promiscuamente il nome di <emph type="italics"/>uova<emph.end type="italics"/> e di <emph type="italics"/>primordii vegetali.<emph.end type="italics"/> &ldquo; Liceat hoc <lb/>nobis <emph type="italics"/>primordium vegetale<emph.end type="italics"/> nominare, nempe substantiam quandam corpo&shy;<lb/>ream vitam habentem potentia, vel quoddam per se existens, quod aptum <lb/>sit in vegetativam formam, ab interno principio operante, mutari. </s>

<s>Quale <lb/>nempe primordium ovum est et plantarum semen, tale etiam viviparorum <lb/>conceptus et insectorum vermis; diversa scilicet diversorum viventium pri&shy;<lb/>mordia. </s>

<s>Pro quorum vario discrimine alii atque alii sunt generationis ani&shy;<lb/>malium modi, qui tamen omnes in hoc uno conveniunt, quod a primordio <lb/>vegetali, tamquam e materia efficientis virtute dotata, oriantur. </s>

<s>Differunt <lb/>autem quod primordium hoc vel sponte et casu erumpit, vel ab alio preesi&shy;<lb/>stente tanquam fructus erumpat, unde illa sponte nascentia, haec e paren&shy;<lb/>tibus genita dicuntur &rdquo; (ibid., pag. </s>

<s>283). </s></p><p type="main">

<s>Parecchi altri sarebbero i passi, che si potrebbero collazionare, e nei <lb/>quali tutti si professa apertamente la generazione equivoca degli animali, con <lb/>questa sola differenza dalle idee degli Aristotelici che, invece di far di essi <lb/>animali immediata genitrice la putredine, si fanno i primordii vegetali o gli <lb/>archei. </s>

<s>Il Redi, dop'aver citato alcuno di questi passi, accusava l'Autore <lb/>piuttosto di oscurit&agrave; che di errore, accagionandone i tumulti delle guerre <lb/>civili, ma lo Swammerdam, senza tanti riguardi, citato il testo, soggiunge: <lb/><emph type="italics"/>Hucusque Harveus: verum quot verba tot fere errores haec ipsius Disser&shy;<lb/>tatio continet.<emph.end type="italics"/></s></p><p type="main">

<s>E in verit&agrave; rendevasi l'errore manifesto considerandone la causa, che <lb/>vi conduceva necessariamente; causa, che riducevasi all'aver l'Hrvey, in <lb/>questo trattato <emph type="italics"/>De generatione animalium,<emph.end type="italics"/> abbandonate quelle sicure e di&shy;<lb/>rette vie sperimentali, cos&igrave; felicemente proseguite nel trattato <emph type="italics"/>De motu cor&shy;<lb/>dis,<emph.end type="italics"/> per tener dietro alle astrazioni della metafisica aristotelica corroborata <lb/>dello stoicismo e, a modo degli Scolastici, inoculata ne'principii della Filo&shy;<lb/>sofia cristiana. </s>

<s>Nella esercitazione XLV appoggia la ragione del generarsi <lb/>spontaneamente gli animali al principio, professato nel VII dei <emph type="italics"/>Matafisici<emph.end type="italics"/> di <lb/>Aristotile, che cio&egrave; <emph type="italics"/>materia potest a seipsa moveri,<emph.end type="italics"/> e nella esercitazione LVII <lb/>invoca que'medesimi principii aristotelici, dai quali consegue poter avvenir <lb/>nella natura quel che nell'arte, che cio&egrave; producasi fortuitamente talvolta <lb/>quel che &egrave; consueto d'operarsi dall'arte stessa, per applicar cos&igrave; tali meta&shy;<lb/>fisici principii alle generazioni animali: &ldquo; Similiter se habet generatio quo&shy;<lb/>rumlibet animalium, sive semen eorum casu adsit, sive ab agente univoco, <lb/>eiusdemque generis, proveniat. </s>

<s>Quippe etiam in semine fortuito inest prin&shy;<lb/>cipium generationis motivum, quod ex se et per seipsum procreet idemque <pb xlink:href="020/01/1593.jpg" pagenum="468"/>quod in animalium congenerum semine reperitur, potens scilicet anima effor&shy;<lb/>mare &rdquo; (ibid., pag. </s>

<s>253, 54). </s></p><p type="main">

<s>Il seme per&ograve; fortuitamente composto non ha potenza di formar l'ani&shy;<lb/>male per virt&ugrave;, che sia inerente alla materia, ma per una pi&ugrave; alta virt&ugrave; <lb/>partecipata a lei da quella Mente e da quello Spirito, che agita la gran mole <lb/>(ivi, pag. </s>

<s>115); Mente e Spirito, che altrove cristianeggiando l'Harvey chiama <lb/>Dio creatore, Sommo e Onnipotente, e che &egrave; la Mente Divina di Aristotile, <lb/>l'Anima del mondo di Platone, la Natura naturante, o il Saturno o il Giove <lb/>de'pagani, &ldquo; vel potius, ut nos decet, Creatorem ac Patrem omnium quae <lb/>in coelis et terris, a quo animalia eorumque origines dependent, cuiusque <lb/>nutu, sive effato, fiunt et generantur omnia &rdquo; (ibid., gag. </s>

<s>228). </s></p><p type="main">

<s>Ma perch&egrave; riconoscevasi che questi nobili e sublimi concetti erano fuor <lb/>di luogo, trattandosi di una questione, che voleva essere risoluta per via di <lb/>diligenti osservazioni microscopiche, e di esatte esperienze, cos&igrave; dall'Harvey <lb/>dannosamente neglette; ne'primi congressi della prima Accademia speri&shy;<lb/>mentale istituita in Europa si volle mettere a cimento quel che, filosofi e <lb/>volgo, credevano intorno al generarsi spontaneo di alcuni animali dal fango <lb/>e dall'umido della terra. </s>

<s>In un registro infatti delle cose naturali, osservate <lb/>nell'Accademia fiorentina sotto la presidenza del principe Leopoldo, si legge <lb/>questa nota colla data del d&igrave; 6 Settembre 1657. &ldquo; Non &egrave; vero che le botte <lb/>si generino dalla pioggia, ma allora si disascondono, come anco si &egrave; osser&shy;<lb/>vato diligentemente in que'luoghi, che in quel tempo ne paiono pi&ugrave; abbon&shy;<lb/>danti, la mattina escono fuori al fresco dell'aurora, con tutto che per la <lb/>notte nessuna ne apparisca &rdquo; (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>680). </s></p><p type="main">

<s>Fra que'filosofi peripatetici, cos&igrave; colti in fallo dagli Accademici fioren&shy;<lb/>tini, erano i Gesuiti, che gelosi di mantenersi il principato della scienza te&shy;<lb/>nevano gli occhi aperti sopra Firenze, per espiarne i segreti. </s>

<s>Forse erasi di <lb/>gi&agrave; divulgato il modo insegnato dal padre Atanasio Kircher, per ottenere una <lb/>nuova generazione di rane, con aspergere d'acqua piovana la melma delle <lb/>paludi, e i nostri Accademici ne risero pi&ugrave; facetamente di quel che, nelle <lb/>sue <emph type="italics"/>Esperienze intorno agl'insetti,<emph.end type="italics"/> non facesse poi il Redi (Opera, T. I. cit., <lb/>pag. </s>

<s>91). In ogni modo i Gesuiti intesero che s'ordinava nelle sale medicee <lb/>un valoroso esercito a combattere contro il loro peripatetico magistero, ond'&egrave; <lb/>che minacciosi s'armarono alle difese. </s>

<s>Di coteste minacce ebbe Carlo Ri&shy;<lb/>naldini qualche sentore, e ne dava cos&igrave; avviso al principe Leopoldo, rivol&shy;<lb/>gendosi direttamente al Viviani: &ldquo; Mi vien detto per cosa certissima che i <lb/>padri Gesuiti fanno strepito avanti il tempo, conciossiach&egrave; dicono che, se <lb/>nel <emph type="italics"/>Libro delle osservazioni naturali<emph.end type="italics"/> fatte cost&igrave;, ci sar&agrave; cosa che possi toc&shy;<lb/>care qualcheduno di loro, che averanno uomini, ai quali d&agrave; l'animo di ri&shy;<lb/>spondere, e che frattanto tutto che possono sapere delle cose fatte procu&shy;<lb/>rano di sperimentare, e ne fanno un libro. </s>

<s>Deridono oltre a ci&ograve; molte cose <lb/>fatte da noi, come l'esperienza delle botticine, dicendo di averla fatta con <lb/>porre dell'arena nel lastricato, e vedute nascere al cader della pioggia. </s>

<s>E <lb/>molte altre cose, che per brevit&agrave; tralascio..... Mi &egrave; parso bene di avvisare <pb xlink:href="020/01/1594.jpg" pagenum="469"/>il tutto a V. S. perch&egrave;, se stima bene, lo confidi al serenissimo Leopoldo, il <lb/>quale forse potrebbe creder ben fatto le cose che occorrono alla giornata non <lb/>doversi palesare, e restringere il negozio in pochi..... Pisa, 9 Marzo 1658 &rdquo; <lb/>(MSS. Cim., T. XXIV, c. </s>

<s>45). </s></p><p type="main">

<s>Lasciando considerare ai lettori l'importanza di questo documento per <lb/>la storia dell'illustre Accademia, e proseguendo addiritto il nostro ragiona&shy;<lb/>mento, diciamo che, mentre gli Accademici insieme adunati si compiacciono <lb/>di aver cos&igrave; felicemente scoperto l'inganno di coloro, che si davano a cre&shy;<lb/>dere nascere spontaneamente le botticine dalla terra inumidita, vedono en&shy;<lb/>trar nella sala un paggio, che recava a nome del Granduca alcune foglie di <lb/>olmo, perch&egrave; fosse esaminato col microscopio il contenuto dentro certe na&shy;<lb/>scenze, che apparivano sopra le foglie stesse in guisa di boccioli o di ve&shy;<lb/>scichette. </s>

<s>Del resultato di tali osservazioni si legge presa nota cos&igrave; nel so&shy;<lb/>pra citato registro: &ldquo; Fra le foglie dei rami d'olmo si trovano alcuni boc&shy;<lb/>cioli, nei quali aprendosi si trova una quantit&agrave; di vermi bianchissimi, i quali <lb/>col microscpio si veggono come trasparenti di cristallo, con alie simili alle <lb/>mosche, ed in mezzo ad essi si trova bene spesso una vescichetta bianca <lb/>piena d'umore. </s>

<s>Col microscopio medesimo si ritrov&ograve; nascere dall'uova, ve&shy;<lb/>dendone alcuni non interamente usciti di esse &rdquo; (Targioni, Notizie, T. cit., <lb/>pag. </s>

<s>680, 81). </s></p><p type="main">

<s>Della natura e dell'origine di cotest'uova non si sa quel che propria&shy;<lb/>mente ne pensassero gli Accademici, ma &egrave; probabile che avessero fin d'al&shy;<lb/>lora principio quelle controversie, tornate sett'anni dopo, nel 1664, ad agi&shy;<lb/>tarsi con pi&ugrave; vivo ardore che mai, all'occasione che ora diremo. </s>

<s>Quando il <lb/>Pontefice e il Granduca, a ricompor le controversie nate fra'due stati per <lb/>causa delle Chiane, mandarono in visita l'uno il Viviani e l'altro Gian Do&shy;<lb/>menico Cassini, questi trov&ograve; da consolare la solitudine della campagna atten&shy;<lb/>tamente osservando la nascita e il progresso delle galle sopra la querce, e <lb/>de'vermi che sempre, con sua gran maraviglia, vi trov&ograve; dentro nascosti. </s>

<s>Si <lb/>lusing&ograve; a principio che fosse l'osservazione sua nuova, ma poco dopo s'ab&shy;<lb/>batt&egrave; a leggere nel Mattioli, l&agrave; dove, commentando il primo libro di Diosco&shy;<lb/>ride, tratta nel capitolo CXXIV delle Galle, cos&igrave; fatte parole: &ldquo; Hanno le <lb/>galle in s&egrave; questa loro particolar virt&ugrave;, che predicono ogni anno, con il <lb/>parto loro, la bont&agrave; o malizia dell'anno futuro. </s>

<s>Perciocch&egrave; se, rompendosi <lb/>quelle che si ricolgono secche e non pertugiate, vi si ritrovano dentro mo&shy;<lb/>sche, significa guerra; se ragni, peste, e se vermini, carestia. </s>

<s>N&egrave; si mara&shy;<lb/>vigli alcuno che delle galle nascano questi animali, perciocch&egrave; n'ho veduto <lb/>io spessissime volte la esperienza, e poche o niuna se ne ritrova, che per&shy;<lb/>tugiata non sia, e che di gi&agrave; non se ne sia uscito l'animale che vi nasce, <lb/>che non si trovi pregna d'uno di questi tre vermi. </s>

<s>Laonde si pu&ograve; dire che <lb/>la querce produce frutto e animale &rdquo; (Venezia 1555, pag. </s>

<s>131, 32). </s></p><p type="main">

<s>Ma perch&egrave; qui non si fa cenno della trasformazione del verme in in&shy;<lb/>setto alato, rimase nel Cassini almeno la speranza di avere egli il primo os&shy;<lb/>servata la metamorfosi, che subiscono gli animalucci nati dentro le galle, e <pb xlink:href="020/01/1595.jpg" pagenum="470"/>si compiacque di ci&ograve; col Viviani, discorrendone un giorno insieme. </s>

<s>Gli avrebbe <lb/>il Viviani potuto rispondere che di quel primato rimaneva la gloria tutta in&shy;<lb/>tiera all'Harvey, il quale aveva, tredici anni prima, lasciato cos&igrave; pubblica&shy;<lb/>mente scritto nella esercitazione XVIII <emph type="italics"/>De generatione animalium:<emph.end type="italics"/> &ldquo; Appa&shy;<lb/>ret nempe forma vermiculi sive galbae, sicut in frondibus arborum, corticum <lb/>pustulis, fructibus, floribus alibique vermium et erucarum primordia conspi&shy;<lb/>cimus, praesertim vero in gallis quercinis, quarum in centro, intra crustu&shy;<lb/>lam rotundam, seu nucleum, liquor limpidus continetur, qui sensim crasse&shy;<lb/>scens et coagulatus subtilissimis lineamentis distinguitur, galbaeque formam <lb/>induit. </s>

<s>Manet autem aliquantisper immobilis, posteaque, motu et sensu prae&shy;<lb/>ditus, fit animal, tandemque musca avolat &rdquo; (editio cit., pag. </s>

<s>80, 81). </s></p><p type="main">

<s>Ma il Viviani, o che non si sovvenisse di questo passo arveiano, o che <lb/>lo movesse pi&ugrave; potentemente il desiderio di glorificare il Granduca e gli <lb/>Accademici suoi, disse al Cassini che di tutte quelle cose, da lui credute <lb/>nuove, era stata fatta sette anni prima in Firenze diligentissima osservazione <lb/>da Sua Altezza. </s>

<s>Nonostante, informatosi meglio esso Cassini e ritrovato, ci&ograve; <lb/>che dall'altra parte facilmente dubitava, nelle risposte del Viviani molta <lb/>cortigianeria (non essendo state fatte veramente in Firenze altre osserva&shy;<lb/>zioni che sulle vescicole delle foglie degli olmi) ne dette avviso a Ovidio <lb/>Montalbani, che promise di pubblicar le osservazioni fatte sulle querce delle <lb/>Chiane nella <emph type="italics"/>Dendrologia,<emph.end type="italics"/> la quale laboriosamente allora preparava per la <lb/>stampa sul manoscritto di Ulisse Aldovrandi. </s>

<s>Il Cassini infatti descrisse le <lb/>galle quercine e i vermi e le loro metamorfosi in una lettera latina, che il <lb/>Montalbani inser&igrave;, da pag. </s>

<s>220-21, nella detta Dendrologia pubblicata nel 1668 <lb/>in Bologna. </s></p><p type="main">

<s>Il Viviani intanto di ci&ograve; che aveva osservato e che pretendeva il Cas&shy;<lb/>s&igrave;ni dette subito avviso a Firenze, dipingendo la cosa come gliel'avr&agrave; sug&shy;<lb/>gerita quella inevitabile rivalit&agrave; di due, che si trovavano a dover far le parti <lb/>d'ingegneri periti fra due litiganti loro padroni. </s>

<s>Gli Accademici, gi&agrave; per s&egrave; <lb/>medesimi mal disposti verso il Cassini, ritornarono allora sull'argomento dei <lb/>vermi nati sopra le piante, e vi si dedicarono in modo, che si venissero di <lb/>l&igrave; a colorire le ragioni di quel primato, che a rigor di giustizia era una <lb/>ingiusta pretesa. </s>

<s>E perch&egrave; ben comprendevano che sempre la Filosofia pri&shy;<lb/>meggia sopra la Fisica, di ci&ograve; che prima avevano semplicemente osservato <lb/>si volsero a speculare le misteriose ragioni. </s>

<s>Il Cassini delle cause, che pro&shy;<lb/>ducono i vermi, non aveva voluto dir nulla, discorrendone col Viviani, e <lb/>anche nella pubblica lettera, inserita nella Dendrologia dell'Aldovrandi, se <lb/>ne scusa e se ne sbriga con dire che quelle cose derivano dalle pi&ugrave; alte <lb/>fonti della Filosofia. </s>

<s>&ldquo; Harum productionum causas, quas meditatus sum, <lb/>hic non refero: eae enim sunt ut altius ex non vulgaris philosophiae prin&shy;<lb/>cipiis sint petenda &rdquo; (Aldovrandi, Dendrol., pag. </s>

<s>221). </s></p><p type="main">

<s>Le ipotesi professate dai Filosofi precursori de'nostri Accademici fio&shy;<lb/>rentini, lasciando da parte l'Harvey, che da'suoi principii ne concludeva i <lb/>vermi ne'frutti e nelle galle &ldquo; propria anima gubernari &rdquo; (De generat. <pb xlink:href="020/01/1596.jpg" pagenum="471"/>anim. </s>

<s>cit., pag. </s>

<s>112), si pu&ograve; dir che si riducevano a quelle derivate da Ari&shy;<lb/>stotile, e a una affatto nuova derivata da Pietro Gassendo. </s>

<s>Gli Aristotelici, <lb/>fra'quali va a rassegnarsi il sopra citato Mattioli, dicevano esser genitrice <lb/>dell'animale la pianta, com'&egrave; del frutto, concludendo una tal dottrina dal <lb/>testo del Filosofo, l&agrave; dove, nel cap. </s>

<s>XIX del V libro <emph type="italics"/>De historia anima&shy;<lb/>lium,<emph.end type="italics"/> descrivendo la vita delle farfalle, dice che &ldquo; nascuntur ex erucis, eru&shy;<lb/>cae ex virentibus foliis &rdquo; (Operum, T. VI cit., fol. </s>

<s>132). Il Gassendo poi <lb/>il quale diceva nascere i vermi dentro i frutti dalle uova, che le madri pre&shy;<lb/>gnanti avevan prima deposte ne'fiori; rendeva applicabile ragionevolmete una <lb/>simile origine a questi vermi dentro le galle. </s></p><p type="main">

<s>Forse qualcuno degli Accademici propose qualche ipotesi sua propria, <lb/>ma dai documenti, che ci son rimasti, apparisce che furono nell'Accademia <lb/>grandi contese fra chi faceva co'Gassendisti genitori de'vermi quercini un <lb/>altro simile verme, e chi non riconosceva con gli Aristotelici altra genitrice <lb/>di loro che la madre pianta. </s>

<s>Nel numero de'primi era Antonio Uliva, e <lb/>fra'secondi, calorosissimo peripatetico, il Magalotti, che scriveva cos&igrave; da Fi&shy;<lb/>renze il d&igrave; 16 Settembre 1664 in una sua lettera familiare a Ottavio Fal&shy;<lb/>conieri: &ldquo; Vedete, signor Ottavio, io rido di quelli che dicono che questi <lb/>bachi o mosche non sono cos&igrave; veri e legittimi parti della quercia, come le <lb/>ghiande e le medesime coccole, ma nati dal seme di simili animali cammi&shy;<lb/>nati su'fiori, onde nasce la coccola, o introdotti con qualche loro aculeo o <lb/>in altro modo nella medesima coccola dopo nata. </s>

<s>Mi dicano un po'costoro, <lb/>se questo fosse, perch&egrave; avrebbono a esser tutti senza fallo della medesima <lb/>spezie, e sempre situati nel centro? </s>

<s>Niente meno mi rido dell'opinion del&shy;<lb/>l'Uliva, il quale si d&agrave; ad intendere che di questa cosa se n'abbia a fare un <lb/>grande scalpore fra'peripatetici. </s>

<s>Fate conto, i'sto per dire, ch'e'darebbe <lb/>l'animo a me di salvare Aristotile, col quale, non essendo egli tenuto a te&shy;<lb/>nere per soprannaturale l'infusione della nostr'anima, si potrebbe dire che <lb/>assai pi&ugrave; maraviglioso passaggio &egrave; quello che si vede tuttod&igrave; dell'umane ge&shy;<lb/>nerazioni, dove la materia trapassa dal sensibile all'intellettivo, che non &egrave; <lb/>questa, dove il passaggio solamente si fa dal vegetativo al sensibile &rdquo; (Let&shy;<lb/>tere famil. </s>

<s>di L. Magalotti, Vol. </s>

<s>I, Firenze 1769, pag. </s>

<s>94, 95). </s></p><p type="main">

<s>Cos&igrave; fatta opinione peripatetica del Magalotti fu quella che prevalse nel&shy;<lb/>l'Accademia, e Angelo Fabbroni, editore delle Lettere familiari alle quali <lb/>appartiene anche questa ora citata, avverte in nota a pag. </s>

<s>92 del medesimo <lb/>Tomo I: &ldquo; L'Uliva approv&ograve; poi l'opinione del Magalotti, com'ho veduto in <lb/>una sua lettera. </s>

<s>&rdquo; </s></p><p type="main">

<s>Non ammesso ancora a far parte dell'Accademia, Francesco Redi si <lb/>sentiva frugato da una viva curiosit&agrave; di sapere quel che si faceva nelle se&shy;<lb/>grete sale sperimentali di corte, e n'era facilmente sodisfatto da que'dotti <lb/>amici suoi cortigiani colleghi. </s>

<s>La questione de'vermi delle galle secondava <lb/>pi&ugrave; che altra mai quella sua potente inclinazione agli studii della Storia na&shy;<lb/>turale, e considerata la grande importanza, ch'ella aveva nella scienza, si <lb/>sent&igrave; nascere il desiderio d'entrare egli in mezzo a deciderla. </s>

<s>Datosi perci&ograve; <pb xlink:href="020/01/1597.jpg" pagenum="472"/>a ricercar diligentemente gli Autori, le varie ipotesi de'quali erano state <lb/>nell'Accademia discusse, meditava attentamente quel che, nel <emph type="italics"/>Sintamma <lb/>filosofico,<emph.end type="italics"/> trattando il Gassendo della generazione degli animali, scrive nel <lb/>cap. </s>

<s>I di essi <emph type="italics"/>sponte nascentibus.<emph.end type="italics"/> La causa di cos&igrave; fatta spontanea genera&shy;<lb/>zione, dice il Filosofo francese, &egrave; il seme stesso o la piccola anima ivi den&shy;<lb/>tro infusa a far questo ufficio. </s>

<s>Ma perch&egrave; di tanto minima piccolezza risulti <lb/>una mole pi&ugrave; grandicella e sensibile, &egrave; necessario che molte di quelle pic&shy;<lb/>cole anime vivificanti gli atomi della materia si congiungano insieme. </s>

<s>An&shy;<lb/>che negli animali di generazione equivoca la causa interna precipua e pros&shy;<lb/>sima &egrave; nel detto principio seminale, come negli univoci, ci&ograve; che si prova, <lb/>dice il Gassendo, con molti argomenti, fra'quali, dall'esser varie le gene&shy;<lb/>razioni secondo i climi e secondo gl'incunabili, come si vede per esempio <lb/>che da varie sorta di legumi escono varie specie di insetti. </s>

<s>&ldquo; Neque obstare <lb/>debet quod propterea homo animalve aliud constet ex variorum animalium <lb/>seminibus, siquidem ut silex, quatenus est silex, constat ex ignis semini&shy;<lb/>bus, quae atterendo se explicent; ita animal, quatenus animal, hoc est cor&shy;<lb/>pus heterogeneum diversis, similibusque rebus connutritum, constitui potest <lb/>ex diversis animalium seminibus, quae putrescendo explicentur, ut per aesta&shy;<lb/>tem, dum muscae depascuntur carnes, in iis vermes generant, videlicet eden&shy;<lb/>tos ova, quae statim, prae caloris vehementia, excludantur in vermes, ex <lb/>quibus deinde grandiores muscae procreari, ut ex erucis per varias transmu&shy;<lb/>tationes papiliones, possint: Ut vermes gignuntur intra pulpas fructuum, <lb/>quod muscae aut apes etc. </s>

<s>floribus insidentes reliquerint ova, quae fructi&shy;<lb/>bus conclusa, accedente maturationis calore, excludantur: Ut muscae possint <lb/>impressisse herbarum et arborum foliis, quae a vaccis, capris, ovibus de&shy;<lb/>pasta et lacte contenta caseoque conclusa, succescente et ab antiperistasi <lb/>incalescente substantia, in vermes formentur &rdquo; (Petri Gassendi, Operum, <lb/>T. II, Florentiae 1727, pag. </s>

<s>229). </s></p><p type="main">

<s>Sent&igrave;, a rimeditar queste cose, il Redi fecondarsi la mente, la quale gli <lb/>mostrava quanto fosse di vero in quelle nuove dottrine del Gassendo, nelle <lb/>quali insegnavasi che gl'insetti, piuttosto che dalle sostanze imputridite, na&shy;<lb/>scono dalle uova ivi dentro deposte da altri simili insetti. </s>

<s>Quel che dunque <lb/>il Filosofo francese avea concluso colla ragione, il nostro Naturalista attese <lb/>a dimostrarlo coll'esperienze, particolarmente poi descritte in quel celebro <lb/>trattato <emph type="italics"/>Intorno agl'insetti,<emph.end type="italics"/> indirizzato in forma di epistola a Carlo Dati. </s>

<s><lb/>Consistevano queste esperienze in lasciare imputridire varie materie, special&shy;<lb/>mente carnami, e in osservar che non inverminavano mai, quando, dentro <lb/>vasi chiusi o sotto fitti veli, era proibito alle mosche gettarvisi sopra a pa&shy;<lb/>scere e a deporvi, come in ben disposto nido, le loro uova. </s>

<s>Tanto parvero <lb/>anzi al Redi gli sperimentati fatti dimostrativi, che a questa immediata de&shy;<lb/>posizione di uova attribu&igrave; l'origine de'vermi del cacio, senza que'passaggi <lb/>accennati dal Gassendo. </s>

<s>&ldquo; Il sapientissimo Pietro Gassendo, egli dice, ac&shy;<lb/>cenna che forse le mosche ed altri animali volanti, avendo impresse e disse&shy;<lb/>minate le loro semenze sopra le foglie dell'erbe e degli alberi, e quelle pa-<pb xlink:href="020/01/1598.jpg" pagenum="473"/>sciute poi dalle vacche, dalle capre e dalle pecore, possano introdurre nel <lb/>latte e nel formaggio quei semi abili in progresso di tempo a produrre i <lb/>vermi. </s>

<s>E certo tale opinione a molti non dispiace, n&egrave; io vo'negare ora cos&igrave; <lb/>poter essere, ma tuttavia non so, colla dovuta riverenza che a questo gran&shy;<lb/>dissimo e ammirabile filosofo io porto, non so, dico, in qual maniera quei <lb/>semi tritati dai denti degli animali, e nel loro stomaco cotti, abbiano potuto <lb/>conservar sana e salva la loro virtute. </s>

<s>Per lo che sarei forse di parere che <lb/>l'inverminamento del latte, del formaggio e della ricotta abbia quella stessa <lb/>cagione da me soprammentovata nelle carni e ne'pesci, cio&egrave; a dire che le <lb/>mosche ed i moscherini vi partoriscano sopra le loro uova, dalle quali na&shy;<lb/>scano i vermi &rdquo; (Opere, T. </s>

<s>I cit., pag. </s>

<s>83, 84). </s></p><p type="main">

<s>Imbevuta la mente delle idee, ch'eran prevalse fra gli Accademici del <lb/>Cimento, relative all'origine de'vermi nelle galle e dentro i frutti nasco&shy;<lb/>sti, era il Redi da questi suoi esperimenti tentato a ripudiarle, per seguire <lb/>invece le idee del Gassendo, quando nuove difficolt&agrave;, nate da certe consi&shy;<lb/>derazioni sue particolari, aggiungendo forza a quelle degli Accademici me&shy;<lb/>desimi, lo fecero andar con essi a credere &ldquo; che quell'anima o quella virt&ugrave;, <lb/>la quale genera i fiori e i frutti nelle piante viventi, sia quella stessa che <lb/>generi ancora i bachi di esse piante &rdquo; (ivi, pag. </s>

<s>100), alle quali, per ridurre <lb/>alle ultime conseguenze i principii premessi gi&agrave; infino dal Mattioli, e pro&shy;<lb/>fessati dai Fisici fiorentini, esso Redi, oltre alla vita vegetativa, attribu&igrave; an&shy;<lb/>cora la sensibile, perch&egrave; &ldquo; le condizionasse e le facesse abili alla generazione <lb/>degli animali &rdquo; (ivi, pag. </s>

<s>104). </s></p><p type="main">

<s>A provar poi che dare il senso alle piante non era <emph type="italics"/>un gran peccato in <lb/>Filosofia,<emph.end type="italics"/> l'Autore delle <emph type="italics"/>Esperienze intorno agl'insetti<emph.end type="italics"/> profonde a larga <lb/>mano autorit&agrave; di scrittori antichi e di Poeti &ldquo; pensando, dice a proposito il <lb/>Vallisnieri, che Virgilio, Dante e gli altri toscani Poeti, con quelle lor fa&shy;<lb/>vole, volessero insegnarci che le piante non sono affatto prive di senso &rdquo; <lb/>(Esperienze ed osservazioni spettanti alla Storia Nat., Padova 1713, pag. </s>

<s>33). <lb/>Lo stesso peripatetico Filippo Bonanni scrisse nel suo libro <emph type="italics"/>Delle chiocciole<emph.end type="italics"/><lb/>che il citar le sentenze di Pitagora e di Empedocle, i quali credettero dav&shy;<lb/>vero le piante aver senso, era &ldquo; piuttosto un rammentar i favolosi giardini <lb/>di Alcina e le boscaglie incantate del Berni &rdquo; (Roma 1681, pag. </s>

<s>55, 56), e <lb/>il Reaumur confessava essere una grande umiliazione al filosofico orgoglio <lb/>&ldquo; voir qu'un si bel esprit ait pu adopter un sentiment si peu vraisemblabe, <lb/>ou pour trancher le mot si pitoyable &rdquo; (Memoires pour servir a l'hist. </s>

<s>des <lb/>insectes, T. III, P. II, a Amsterdam 1738, pag. </s>

<s>269). </s></p><p type="main">

<s>Il Malpighi per&ograve;, che comprendeva qual potenza dovesse avere sul gio&shy;<lb/>vane ingegno del Redi l'autorit&agrave; degli Accademici fiorentini, sentitosi libero <lb/>da un tal giogo, prosegu&igrave; a dirittura per quella via di esperienze, nella quale <lb/>erasi arretrato esso Redi, e dimostr&ograve; nel suo trattato <emph type="italics"/>De gallis<emph.end type="italics"/> che, com'era <lb/>vero quel che avea detto il Gassendo dell'uova deposte dalle mosche sulle <lb/>carni infradiciate, cos&igrave; era vero dell'uova da simili mosche deposte nelle in&shy;<lb/>cise cortecce degli alberi, e in seno agli aperti fiori, d'onde hanno origine <pb xlink:href="020/01/1599.jpg" pagenum="474"/>i vermi, che si trovan chiusi dentro le galle quercine, e in mezzo ai pomi <lb/>maturi. </s>

<s>&ldquo; Ex hucusque instituta indagine, dice ivi dop'aver descritte le par&shy;<lb/>ticolarit&agrave; delle galle nate sopra varie specie di alberi, patet exaratos qua&shy;<lb/>rundam plantarum tumores reliquasque syderatas partes muscas et diversa <lb/>insectorum genera fovere et alere, donec emancipata viam sibi faciant. </s>

<s>Plura <lb/>enim insecta sua edunt ova omni fere auctivo succo destituta, quorum ali&shy;<lb/>qua cortice privantur, ita ut mollis primaeva partium compages occurrat <lb/>sub specie quasi vermis. </s>

<s>Ut igitur inclusum animal debitam acquirat par&shy;<lb/>tium manifestationem et soliditatem, uterum vel saltem ipsius vicariam opem <lb/>exigit, quam in plantis sagax insectorum natura perquirit &rdquo; (Op. </s>

<s>omnia, T. I, <lb/>Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>130). </s></p><p type="main">

<s>Di qui vedeva il Malpighi scendere spedita la soluzione a quelle diffi&shy;<lb/>colt&agrave; che, promosse nell'Accademia del Cimento dal Magalotti, duravano tut&shy;<lb/>tavia a tenere i Peripatetici ritrosi contro il Gassendi. </s>

<s>Se la pianta infatti <lb/>serve come d'utero all'uova, porgendo a loro quell'alimento, di che per s&egrave; <lb/>stesse hanno difetto, e se quell'alimento &egrave; variamente richiesto, secondo la <lb/>varia natura di esse uova, si comprende come, scegliendo le sagaci madri <lb/>la cuna pi&ugrave; convenevole alla maturazione de'loro parti, abbiano in galle non <lb/>solo ma in parti uguali delle piante a ritrovarsi vermi sempre della mede&shy;<lb/>sima specie. </s>

<s>&rdquo; Quare, ex diversa ovorum contentorumque animalium indi&shy;<lb/>gentia, a parentibus muscis varie diversis plantarum partibus ova commit&shy;<lb/>tuntur vel deponuntur &rdquo; (ibid.). </s></p><p type="main">

<s>Cos&igrave; dal campo della Filosofia gassendistica veniva trapiantata in quello <lb/>della Storia naturale la vera generazione univoca de'vermi delle piante, e <lb/>il Redi stesso nella sua ingenuit&agrave; abiur&ograve; il proprio errore per professar la <lb/>sentenza del Malpighi. </s>

<s>&ldquo; Dominus Redius, ingenuitate sua, attenta propo&shy;<lb/>sita a me observationum serie, in meam postea ivit sententiam &rdquo; (Opera <lb/>posthuma, Londini 1697, pag. </s>

<s>77). Scriveva queste cose esso Malpighi per <lb/>consolarsi degli assalti, che gli avea dato il Bonanni co'suoi raggiri, degli <lb/>insulti vomitatigli contro dallo Sbaraglia, e delle petulanze del Trionfetti, che <lb/>si faceva forte del nome, pi&ugrave; che della Filosofia, dell'Harvey. </s>

<s>&ldquo; Resto ol&shy;<lb/>tremodo scandalizzato e dolente, scriveva acceso di zelo il Vallisnieri, quando <lb/>nel leggere trovo Italiani contro Italiani in materie particolarmente di fatto, <lb/>attaccandosi piuttosto ad opinioni fantastiche d'Autori stranieri, stimandole <lb/>come merci pellegrine pi&ugrave; preziose e pi&ugrave; care &rdquo; (Esper. </s>

<s>ed osservaz. </s>

<s>cit., <lb/>pag. </s>

<s>38). E intanto il Malpighi stesso, parlando dalla tomba di s&egrave; e delle <lb/>cose sue, rammentava agli oppositori suoi connazionali e colleghi un illu&shy;<lb/>stre straniero venuto a confermar ci&ograve; che egli aveva osservato e scritto in&shy;<lb/>torno alle galle. </s>

<s>&ldquo; Has autem morbosos tumores esse ortos ex intrusis a <lb/>parente musca ovis et tanquam in utero conclusis habui, quam positionem <lb/>plures exinde confirmarunt, et praecipue clarissimus Leewenoeck &rdquo; (Opera <lb/>posthuma cit., pag. </s>

<s>77). </s></p><p type="main">

<s>In una delle epistole infatti, di che si compagina il libro <emph type="italics"/>Arcana Na&shy;<lb/>turae detecta<emph.end type="italics"/> il celebre Micrografo olandese tratta di proposito delle galle, <pb xlink:href="020/01/1600.jpg" pagenum="475"/>dimostrando anch'egli, come il Malpighi, che irragionevolmente s'eran cre&shy;<lb/>dute un frutto della querce, essendo che pigliano incremento da certe spe&shy;<lb/>cie di vermi originati da mosche, e in mosche nuovamente tornanti, i quali <lb/>rodendo le foglie sono col loro morso causa del formarsi cos&igrave; fatte morbose <lb/>escrescenze. </s>

<s>&ldquo; Ex observationibus hisce statui animalia haecce ita produci: <lb/>videlicet praedictum genus animalculorum sive muscarum ova sua in foliis <lb/>quercinis deponere, quibus in vasis folii depositis, vaseque folii ita a verme <lb/>ex ovulo exeunte perfosso ut liquor ex eodem effluat, succus ille coagula&shy;<lb/>tur in globulos, simulque circulariter se se in vase dispergit, et ita produ&shy;<lb/>citur galla exiensque hic in globulos coagulatus succus vermem excipit et <lb/>in medio collocat &rdquo; (Lugd. </s>

<s>Batav. </s>

<s>1722, pag. </s>

<s>213). </s></p><p type="main">

<s>Non men valoroso del Leeuwenoeck sorse poco dopo il Vallisnieri, il <lb/>quale, per dimostrarsi pi&ugrave; innamorato del vero che affezionato al suo ca&shy;<lb/>rissimo Maestro, mentre ne illustrava da una parte le dottrine, con rive&shy;<lb/>renza dall'altra ne faceva notare gli errori. </s>

<s>Egli il primo osserv&ograve; che il ta&shy;<lb/>glio, fatto dalle mosche sulle foglie e sulle cortecce degli alberi, era spalmato <lb/>di un succo lucido e viscosetto colato dietro le uova, per impedire che le <lb/>aperte labbra non ritornassero ad unirsi e rammarginarsi, e dalle variet&agrave; di <lb/>questi succhi crede abbiano origine, nella forma e nella struttura, quelle <lb/>cos&igrave; moltiplici variet&agrave; d'escrescenze. </s>

<s>Egli fu altres&igrave; il primo ad osservare e <lb/>a descrivere lo strumento in forma di artificiosissima sega, con cui le mo&shy;<lb/>sche incidono a'rosai la buccia, per apprestare ai loro nascituri pi&ugrave; comoda <lb/>cuna. </s>

<s>Studiando poi i costumi de'cos&igrave; detti <emph type="italics"/>Convolvoli<emph.end type="italics"/> trov&ograve; che s'era in&shy;<lb/>gannato il Malpighi a credere che le foglie per esempio de'pioppi e delle <lb/>viti rimangano accartocciate in virt&ugrave; degli effluvii delle uova ivi dentro de&shy;<lb/>poste &ldquo; essendo quello, dice il Vallisnieri, un industre lavorio della madre &rdquo; <lb/>(Esper. </s>

<s>ed osserv. </s>

<s>cit., pag. </s>

<s>55). </s></p><p type="main">

<s>S'aggiunse non molti anni dopo a questa del Vallisnieri l'opera del <lb/>Reaumur, il quale, nella sua IX Memoria per servire alla storia degl'In&shy;<lb/>setti, tratt&ograve; dell'escrescenze nate sulle foglie degli alberi, e la X riserb&ograve; <lb/>particolarmente alle galle. </s>

<s>Egli &egrave; senza dubbio uno de'pi&ugrave; valorosi promo&shy;<lb/>tori delle dottrine insegnate dal Malpighi, di cui cos&igrave; scrive: &ldquo; M. </s>

<s>Malpi&shy;<lb/>ghi nous a donn&eacute; un curieux Trait&eacute; de ces esp&egrave;ces de galles; mais je ne <lb/>fache point qu'on ait encore fait attention, par rapport aux productions de <lb/>cette nature, &agrave; un fait qui en meritoit beaucoup; savoir qu'il y a un genre <lb/>d'insectes, qui comprend plusieurs especes, dont chaque m&ecirc;re fait naitre sur <lb/>un arbre une galle, dans laquelle elle se laisse enfermer elle-m&ecirc;me, et sem&shy;<lb/>ble chercher &agrave; se faire renfermer de toutes parts pour y produire une nom&shy;<lb/>breuse famille &rdquo; (A Amsterdam 1738, T. III, P. II, pag. </s>

<s>30). E prosegue <lb/>il Reaumur a notare altre parti delle dottrine malpighiane o men proprie o <lb/>difettose, ch'egli sapientemente perfeziona colle sue proprie osservazioni, ed <lb/>emenda colla sua sagacia. </s></p><p type="main">

<s>Le osservazioni descritte nel trattato <emph type="italics"/>De gallis,<emph.end type="italics"/> con s&igrave; autorevole ma&shy;<lb/>gistero confermate dal Vallisnieri e dal Reaumur, che valgono per tanti altri, <pb xlink:href="020/01/1601.jpg" pagenum="476"/>avevano efficacemente conferito a persuadere la sentenza del Redi, la quale <lb/>sarebbe altrimenti rimasta per una parte dubbiosa, cio&egrave; che la Terra, dalle <lb/>prime piante e dai primi animali, non abbia poi mai pi&ugrave; spontaneamente <lb/>prodotto nessun vivente. </s>

<s>Ma pure parevano ancora pochi i fatti osservati e <lb/>descritti dai due grandi Naturalisti italiani, per indur di l&igrave; quell'<emph type="italics"/>omne ani&shy;<lb/>mal ab ovo,<emph.end type="italics"/> ch'era la general conclusione, alla quale intendeva di perve&shy;<lb/>nire la scienza. </s>

<s>Eravi una sorta di animali, che si riducevano allora nella <lb/>classe degl'insetti, ma che si reputavano tanto pi&ugrave; nobili di quelli generati <lb/>dalla putredine o dalle piante, e intorno alla generazione de'quali non ave&shy;<lb/>vano ancora insegnato nulla di certo n&egrave; il Redi n&egrave; il Malpighi. </s>

<s>Questi in&shy;<lb/>setti, che sono i molluschi, specialmente testacei, ai quali appartengono le <lb/>preziose conchiglie margaritifere, si credevano dai Peripatetici esser gene&shy;<lb/>rati dal limo della terra, cos&igrave; avendo insegnato a loro il Maestro nel cap. </s>

<s>XV <lb/>del V libro della Storia degli animali. </s>

<s>&ldquo; Universim omnia testacea sponte <lb/>Naturae in limo, diversa pro differentia limi, oriuntur, nam in caenoso Ostreae <lb/>in arenoso conchae &rdquo; (Operum, T. VI cit., fol. </s>

<s>130). N&egrave; in quel primo ri&shy;<lb/>svegliarsi della scienza dai sogni peripatetici seppe nulla insegnare di nuovo <lb/>il Rondelezio, il quale credeva che nascessero le conchiglie per una virt&ugrave; <lb/>insita nell'umore marino. </s>

<s>&ldquo; Quod si testis intecta diligentius consideres, ea <lb/>marini humoris vi, sine semine, sine mare et faemina procreari perspicue <lb/>cernes &rdquo; (De piscibus cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Corse voce ne'principii del secolo XVII di alcune esperienze fatte in <lb/>Germania intorno alla generazione delle conchiglie margaritifere, che sem&shy;<lb/>brava potess'essere dalle semenze deposte, per opera delle madri, nella terra <lb/>o ne'fiumi. </s>

<s>Giovanni Faber stim&ograve; ragionevolissime cos&igrave; fatte congetture, e <lb/>anzi sper&ograve; che si potessero col benefizio del Microscopio facilmente ricono&shy;<lb/>scere le uova, sfuggevoli a qualunque attenzione dell'occhio nudo. </s>

<s>&ldquo; Ego <lb/>prorsus nihil dubito si quis Microscopio ..... favaginem hanc examinare <lb/>posset, quin in hac ova testaceorum manifestissima reperturus esset..... <lb/>Accedit hae maximum probabilitatis indicium ostrea et conchas genitalia se&shy;<lb/>mina terris committere et fluminibus, ex quibus nova soboles, sublatis ma&shy;<lb/>tribus, paulatim renascantur. </s>

<s>Experti sunt id Germani nostri in conchis mar&shy;<lb/>garitiferis &rdquo; (Revum medicarum Novae Hispaniae Thesaurus cit., pag. </s>

<s>757). </s></p><p type="main">

<s>Il Lister poi e il Willis ammisero le uova delle conchiglie come cosa <lb/>certa, e lo Stenone pi&ugrave; sentenziosamente scriveva nel suo prodromo <emph type="italics"/>De so&shy;<lb/>lido:<emph.end type="italics"/> &ldquo; Experientia constat ostrea et alia testacea ex ovis, non ex putredine <lb/>nasci &rdquo; (Florentiae 1669, pag. </s>

<s>58). Quali sieno per&ograve; queste esperienze l'Au&shy;<lb/>tore non dice, cosicch&egrave; al peripatetico Bonanni rimaneva salva l'autorit&agrave; del <lb/>suo Aristotile, la quale ei contrapponeva come prevalente per tanti antichi <lb/>diritti sull'autorit&agrave; nuova dello Stenone. </s>

<s>Dietro il particolare esempio dei <lb/>cos&igrave; detti <emph type="italics"/>Ballani<emph.end type="italics"/> ammetteva esso Bonanni che la virt&ugrave; di generar le con&shy;<lb/>chiglie risiedesse non in solo l'umore, come diceva il Rondelezio, ma negli <lb/>spiriti saligni altres&igrave;, e nella potenza prolifica del mare. </s>

<s>&ldquo; Converr&agrave; dunque <lb/>dire, scrive nel citato libro <emph type="italics"/>Delle chiocciole,<emph.end type="italics"/> che trovandosi nella terra al-<pb xlink:href="020/01/1602.jpg" pagenum="477"/>cune particelle primigenie atte alla formazione del Ballano, questo potr&agrave; sem&shy;<lb/>pre nascere, quando non manchino altre concause e disposizioni necessarie <lb/>di un umido mescolato con spiriti saligni e prolifici del mare, e cos&igrave; pos&shy;<lb/>sano fermentarsi, finch&egrave; giungano ad esser capaci della vita &rdquo; (pag. </s>

<s>57). </s></p><p type="main">

<s>A leggere queste cose Anton Felice Marsili, ch'era per le osservazioni <lb/>sperimentali del Redi e del Malpighi rimasto persuaso della generazione dei <lb/>vermi dall'uovo, si sent&igrave; assalire da un dubbio, che lo tenne per qualche <lb/>tempo in pene, infin tanto che non gli occorse di fare la scoperta, ch'egli <lb/>stesso cos&igrave; racconta: &ldquo; Effodebantur bulbuli florum in hortulo nunc usui <lb/>simplicium a me destinato. </s>

<s>Dum terra removebatur, saepius accidit ut ali&shy;<lb/>quot ovorum acervi reperirentur, quae primo non cognoscebam, nam licet <lb/>multa paterent, quod nondum perfectionem essent adepta, albumen merum <lb/>emittebant, nec poteram in illis reperire principium aliquod animalculi. </s>

<s>Tan&shy;<lb/>dem vero factum est ut prope lapides cuiusdam horrei sese eorundem ovo&shy;<lb/>rum tantus cumulus proderet, ut impleta manu facile mihi fuerit observare <lb/>quaedam eorum fractioni proxima, alia ad dimidiam sui partem, alia omni <lb/>ex parte iam fracta atque ex illis cochleolas exeuntes &rdquo; (De ovis cochl. </s>

<s><lb/>Malpighi, Operum, T. II cit., pag. </s>

<s>95, 96). Mostr&ograve; queste uova agli amici, <lb/>che si confermarono, insieme coll'inventore, nella verit&agrave;, con s&igrave; nuovo effi&shy;<lb/>cace argomento dimostrata, della generazione univoca di tutti gl'Insetti. </s></p><p type="main">

<s>Faceva eco ai Nostri fra gli stranieri Antonio Leewenoeck, che avendo <lb/>ripetute e confermate l'esperienze del Redi e del Malpighi, sicuro di pro&shy;<lb/>nunziare il vero cos&igrave; in una delle sue Epistole scriveva: &ldquo; Est apud me <lb/>ratum ac firmum nulla viventia animalia, sive demum vermem, sive mu&shy;<lb/>scam, pulicem, pediculum, imo ne blatam quidem ex succo vel foliis ullius <lb/>arboris vel plantae, aut etiam putredine vel sudore produci posse &rdquo; (Arcana <lb/>Naturae, T. </s>

<s>I cit., pag. </s>

<s>215, 16). E cos&igrave; come scriveva in pubblico andava <lb/>fra gli amici ne'familiari colloqui ripetendo, quando un giorno un Signore <lb/>assai dotto gli confessa aver certissima esperienza del generarsi da non altro <lb/>che dal sudore certi molesti ospiti, i quali avevano invaso il suo letto, sopra <lb/>cui una volta la settimana, e talora anche pi&ugrave; spesso, si stendevano le len&shy;<lb/>zuola di bucato. </s>

<s>Il Leewenoeck rispondeva poter ci&ograve; dipendere dalla gente <lb/>che rif&agrave; le camere, da che entrato quel signore in sospetto &ldquo; postea intel&shy;<lb/>ligebam, cos&igrave; il Leewenoeck stesso termina il curioso racconto, quod ancil&shy;<lb/>lam suam dimississet, quoniam pediculis undique scatebat &rdquo; (ibid., pag. </s>

<s>216). </s></p><p type="main">

<s>Queste del Naturalista olandese per&ograve; sembra che fossero induzioni ra&shy;<lb/>gionevoli, non conclusioni di fatti, osservati poi da altri Naturalisti, fra'quali <lb/>&egrave; a commemorare il nostro Vallisnieri, storico di un altro insetto che, seb&shy;<lb/>bene sia un po'meno schifoso di quello ora detto, &egrave; in ogni modo ospite <lb/>all'uomo e ai pelosi quadrupedi non punto meno molesto. </s>

<s>Aristotile aveva <lb/>intorno a ci&ograve; lasciata in gran confusione la sua scuola, insegnando nel cap. </s>

<s>I <lb/>del V libro della Storia degli animali che anche i due insetti, de'quali pre&shy;<lb/>ghiamo i lettori a sopportar un momento per amor della scienza le punture <lb/>e il prurito, hanno sessi distinti, e generano qualche cosa per s&egrave; ingenera-<pb xlink:href="020/01/1603.jpg" pagenum="478"/>bile, essendo la loro generazione dalla putredine: &ldquo; verbi gratia coitu pedi&shy;<lb/>culorum lendes dictae procreantur, pulicum genus vermiculorum ovi spe&shy;<lb/>ciem referens, ex quibus nec ea quae generant proveniunt &rdquo; (Op., T. VI cit., <lb/>fol. </s>

<s>124). Ma nel cap. </s>

<s>XXXI di questo medesimo libro poi dice &ldquo; pediculi <lb/>et pulices generant ea quae lendes vocantur &rdquo; (ibid., fol. </s>

<s>136), cosicch&egrave; gli <lb/>studiosi del Filosofo non sapevano raccapezzarsi se le pulci generano uova <lb/>(lendes) o vermiccioli molto simili all'uova. </s>

<s>Parve l'incertezza esser tolta <lb/>dalle osservazioni microscopiche di Francesco Fontana, il quale avendo fo&shy;<lb/>rato colla punta di un ago il ventre a uno di quegli insetti, &ldquo; ex eius vul&shy;<lb/>nere ova prosiluere et e vitiatis ovis pulli semiformes in lucem editi sunt &rdquo; <lb/>(Novae observationes, Neapoli 1646, pag. </s>

<s>149). </s></p><p type="main">

<s>I sagaci Naturalisti per&ograve; riconobbero facilmente esser questa dell'Oc&shy;<lb/>chialaio napoletano una illusione, ond'&egrave; che sui principii del secolo XVIII <lb/>s'ignorava ancora la generazione de'fastidiosi insetti, che perci&ograve; persiste&shy;<lb/>vasi da molti a credere generati dal sudiciume, quando apparve alla luce la <lb/>Lettera del Vallisnieri, <emph type="italics"/>nella quale si d&agrave; notizia della nuova scoperta del&shy;<lb/>l'origine delle pulci dall'uovo, contro i difensori de'nascimenti sponta&shy;<lb/>nei.<emph.end type="italics"/> Dalle accurate osservazioni dell'insigne Naturalista result&ograve; che i noti <lb/>insetti generano l'uova, d'onde schiudonsi i vermi, che stimolati si raggo&shy;<lb/>mitolano cos&igrave;, da rendersi interpetri dell'espressione aristotelica: <emph type="italics"/>genus ver&shy;<lb/>miculorum ovi speciem referens.<emph.end type="italics"/> Giunti a maturit&agrave;, cos&igrave; fatti vermi si fab&shy;<lb/>bricano attorno un bozzoletto bianco, come quelli da seta. </s>

<s>&ldquo; La pulce, finat&shy;<lb/>tantoch&egrave; sta rinchiusa nel bozzolo, resta bianca lattata, ancorch&egrave; munita <lb/>delle sue gambe, ma due giorni avanti che deve uscire diventa colorata, si <lb/>indura e piglia forza, di modo che subito uscita salta addirittura &rdquo; (Esper. </s>

<s><lb/>ed osservaz. </s>

<s>cit., pag. </s>

<s>85). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Esaminando sottilmente il Vallisnieri in questo proposito i processi del <lb/>pensiero aristotelico, dice che il Filosofo s'ingann&ograve; nel veder nascere dalle <lb/>mosche i vermi, credendo che sempre si rimanessero in tale stato, senza <lb/>ritornar mosche, e che perci&ograve; fosse quella loro una generazione imperfetta. <lb/></s>

<s>&ldquo; Sospettava inoltre, prosegue a dire l'Autore della lettera all'Andriani, che <lb/>si abbagliasse cos&igrave; al digrosso, perch&egrave;, fidandosi troppo dell'ingegno suo, <lb/>sdegn&ograve; d'abbassarsi tanto e pazientare fino al fine delle osservazioni mi&shy;<lb/>nute, contentandosi di dare rozzamente una semplice e superficiale occhiata <lb/>alle prime cose, e supponendo vedere il restante colla propria acutissima <lb/>perspicacit&agrave;, giudic&ograve; del non veduto egualmente che del veduto, e pens&ograve; non <lb/>poter succedere in altro modo una tale faccenda di quello s'immaginava &rdquo; <lb/>(Esper. </s>

<s>ed osserv. </s>

<s>cit., pag, 87). </s></p><p type="main">

<s>Questo giudizio del Vallisnieri intorno al Filosofo &egrave; giusto, ma giova <pb xlink:href="020/01/1604.jpg" pagenum="479"/>aggiungere una considerazione, ed &egrave; che in quel caso l'abuso dell'ingegno <lb/>veniva in certo modo scusato dal difetto delle osservazioni, che, fatte cos&igrave; <lb/>com'erano ad occhio nudo, non rappresentavano i piccoli insetti sotto altro <lb/>aspetto che d'informi automi. </s>

<s>Il Microscopio perci&ograve;, rivelando anche in que&shy;<lb/>gli spregevoli esseri gli organi e le funzioni proprie alla vita animale, giov&ograve; <lb/>molto a smentire il falso giudizio, che bastasse a ingenerarli il limo della <lb/>terra o altra cosa pi&ugrave; vile. </s>

<s>Perciocch&egrave; dunque si fu tale il benefizio della <lb/>Micrografia, crediam bene di dover premettere un breve cenno di lei a ci&ograve; <lb/>che saremo per dire degli organi scoperti e delle funzioni, rivelate dal diot&shy;<lb/>trico strumento nella Storia naturale degl'Insetti. </s></p><p type="main">

<s>I primi inventori e tutti coloro, ai quali capit&ograve; in mano la prima volta <lb/>un Microscopio, non lasciarono di contemplar le maraviglie della Natura <lb/>nella fabbrica degl'Insetti, ma era per una semplice curiosit&agrave;, che frutt&ograve; <lb/>solo alla scienza qualche notizia delle pi&ugrave; esterne apparenze di quegli ani&shy;<lb/>mali. </s>

<s>Anche Galileo, bench&egrave; aprisse l'adito alla meccanica animale, sco&shy;<lb/>prendo l'organo per cui possono le mosche cos&igrave; facilmente camminare at&shy;<lb/>taccate agli specchi, si tratteneva a riguardare con gran compiacenza cos&igrave; <lb/>le bellissime zanzare e le tignole, come le orribilissime pulci (Alb. </s>

<s>Vl, 298). </s></p><p type="main">

<s>Delle applicazioni del Microscopio alla scienza entomologica ricorre il <lb/>primo e solenne documento nel trattato <emph type="italics"/>De motu cordis<emph.end type="italics"/> dell'Harvey, l&agrave; dove <lb/>nel cap. </s>

<s>XVII dice di aver osservato <emph type="italics"/>ope perspicilli multiplicantis<emph.end type="italics"/> (ediz. </s>

<s>cit., <lb/>pag. </s>

<s>91) un che pulsante nell'interno delle api, delle mosche e de'calabroni, <lb/>da potersi ragionevolmente credere sia quell'organo il loro cuore. </s>

<s>Che se dee <lb/>darsi fede a ci&ograve; che si dice essere quelle Esercitazioni anatomiche, pubbli&shy;<lb/>cate nel 1628, le Prelezioni recitate dodici anni prima dallo stesso Harvey <lb/>alla scolaresca di Londra; par che dunque le microscopiche osservazioni in&shy;<lb/>torno al cuore pulsante degl'insetti siano di qualche poco anteriori al 1616. <lb/>Notabile che il grand'uomo non sentisse gli stupendi benefizii del nuovo <lb/>strumento, da abbandonarlo cos&igrave; presto anche col&agrave;, dove trattando <emph type="italics"/>De ge&shy;<lb/>neratione animalium<emph.end type="italics"/> gli sarebbe servito di sicura scorta a evitar certi er&shy;<lb/>rori, sopra i quali la storia getta uno sguardo di compassione. </s>

<s>Cosicch&egrave; se <lb/>l'Harvey nella Micrografia entomologica primeggia per tempo, per l'estesa <lb/>e intensa cultura rimane di gran lunga inferiore ai nostri Lincei. </s></p><p type="main">

<s>Tanto si rese familiare negli studii naturali de'nostri Accademici il diot&shy;<lb/>trico strumento, che abbisognando d'esser chiamato con qualche nome Fa&shy;<lb/>bio Colonna ellenista propose quello di <emph type="italics"/>Microscopio;<emph.end type="italics"/> nome approvato dal&shy;<lb/>l'Accademia, e di cui il Faber nelle sue pubbliche scritture fu primo a far <lb/>uso. </s>

<s>Esso Faber, nelle annotazioni al Recchi altre volte citate, commemora <lb/>l'anatomia degli organi esterni delle api, fatta da Francesco Stelluti Linceo, <lb/>con l'aiuto di un Microscopio &ldquo; quo res minutissimas triginta mille vicibus <lb/>et amplus grandiores quam in se sunt apparere solent &rdquo; (editio cit., pag. </s>

<s>757). <lb/>E altrove in queste stesse Annotazioni, a proposito del dito pollice de'cani, <lb/>dice di aver trovato con suo grande stupore quell'organo della prensione <lb/>anche negl'insetti, e ci&ograve; per via di un eccellentissimo Microscopio, lavorato <pb xlink:href="020/01/1605.jpg" pagenum="480"/>e donatogli da due suoi Tedeschi. </s>

<s>&ldquo; In pediculo, foedo quodam animalculo, <lb/>hominis tamen non raro socio, non os modo oculosque, barbam et pretensa <lb/>duo in fronte cornicula, sed pedes insuper ex utroque latere ternos prae&shy;<lb/>longos et articulatos, qui omnes ungues habebant recurvos duos, longum <lb/>unum, brevem alterum, et pollicis apprime locum supplentem, quibus et <lb/>cutem apprehendit, et serpendo gradum figit. </s>

<s>Tantum huic pollici aut cui&shy;<lb/>piam particulae simili huius loco industria et nunquam deficiens Natura, in <lb/>minimis etiam et abiectissimis animalculis, studere voluit! &rdquo; (ibid., pag. </s>

<s>473). </s></p><p type="main">

<s>E qui il Faber, dop'essersi compiaciuto di aver egli il primo mandato <lb/>in pubblico il Microscopio insignito di un nome proprio, accenna alla inven&shy;<lb/>zione di lui nata gemella con quell'altra del Telescopio, della teoria del <lb/>quale riconosce autore il Porta, e dell'esecuzione alcuni occhialai tedeschi <lb/>ovvero olandesi. </s>

<s>Da giusto giudice al linceo collega suo Galileo non attri&shy;<lb/>buisce altro merito che di aver il primo in Italia lavorate lenti diottriche, <lb/>non cos&igrave; per&ograve; che ne sia defraudato il principe Cesi, il quale in quel me&shy;<lb/>desimo tempo in Roma avea fatto, sull'esempio degli Ottici stranieri, co&shy;<lb/>struire Telescopi e Microscopi, col&agrave; diffusi qualche tempo prima che s'avesse <lb/>notizia degli strumenti galileiani. </s>

<s>Per quel che poi riguarda la fabbrica del <lb/>Microscopio in particolare, loda il Faber l'esperta mano di Galileo, che si <lb/>riman per&ograve; molto inferiore a quella degli artefici tedeschi &ldquo; qui sedulam <lb/>in hoc nobis operam praestitere, nec pauca huiusmodi Microscopia, quae <lb/>Urbem totam in admirationem pertraxerunt, elaborata nobis exhibuerunt &rdquo; <lb/>(ibid., pag. </s>

<s>474). </s></p><p type="main">

<s>Prima per&ograve; che fossero pubblicate queste Annotazioni del Faber alle <lb/>Storie naturali del Messico, Giovan Batista Hodierna s'era co'suoi <emph type="italics"/>Opuscoli<emph.end type="italics"/><lb/>acquistato uno de'precipui meriti nella Micrografia entomologica, descrivendo <lb/>la mirabile struttura dell'occhio delle mosche. </s>

<s>&ldquo; Or quanto, egli scrive, fin <lb/>qui ho detto intorno a questa nuova anatomia, l'ho io scoverto, non con la <lb/>nuda vista dell'occhio, ma col mezzo di un Occhialino, lavorato a vetri con&shy;<lb/>vessi di figura semirotonda, pi&ugrave; piena della lenticolare, simili a quelli dico <lb/>che oggi il volgo se ne serve per ammirare l'ingrandimento apparente di <lb/>qualche bestiola, come d'un pulce racchiuso, ma con doppio cristallo e con <lb/>artificio assai divario di quello, mentre per il mezzo di quei cristalli mi vien <lb/>rappresentato qualsivoglia piccolissimo granello d'arena pi&ugrave; di millecuplata <lb/>grandezza &rdquo; (Palermo 1644, pag. </s>

<s>16). </s></p><p type="main">

<s>Due anni per&ograve; innanzi che fosse fatta la prima edizione delle Storie na&shy;<lb/>turali del Recchi, e che perci&ograve; il Faber consacrasse in pubblico il nome di <lb/>Microscopio, seguitato a chiamar dall'Hodierna, come udimmo, <emph type="italics"/>occhialino,<emph.end type="italics"/><lb/>Francesco Fontana, sull'esempio del Gassendo nella Vita del Peiresc (Pa&shy;<lb/>risiis 1641, pag. </s>

<s>186), denominava lo strumento diottrico da s&egrave; inventato <lb/>anch'egli, o consapevole o no, conformandosi ai Lincei, <emph type="italics"/>Microscopio,<emph.end type="italics"/> ponendo <lb/>in appendice al suo nuovo trattato alcune osservazioni, fatte con quel va&shy;<lb/>lido aiuto, intorno agli organi esterni e ai visceri di varii insetti. </s>

<s>Ma per&shy;<lb/>ch'egli non aveva avuta altra scuola che la bottega, e i Gesuisti napoletani, <pb xlink:href="020/01/1606.jpg" pagenum="481"/>che gli suggerivano la scienza, erano ostinatissimi peripatetici, non fa per&shy;<lb/>ci&ograve; meraviglia se non vedessero sempre chiaro gli occhi del corpo attraverso <lb/>alle caligini della mente. </s></p><p type="main">

<s>Altro Artefice, che seppe per&ograve; da s&egrave; medesimo educarsi l'ingegno, e <lb/>sulle proprie ali sollevarsi alle pi&ugrave; ardue cime della scienza, fu l'inglese <lb/>Roberto Hook, autore di una Micrografia, dove, in mezzo alla molteplice va&shy;<lb/>riet&agrave; delle cose, non isfuggono all'osservazione gl'insetti. </s>

<s>La prima edizione <lb/>fu fatta in Londra nel 1665, e nel primo Schematismo si rappresenta lo <lb/>strumento in tal modo, che al primo sguardo apparisce il sollecito studio <lb/>di moltiplicar, quanto fosse possibile, l'effetto della vista, condensando sugli <lb/>oggetti per rifrazione il vivo lume di una candela. </s></p><p type="main">

<s>Eustachio Divini, altro semplice artefice, si studi&ograve; di conseguire per altre <lb/>vie questa tanto desiderata incontentabile moltiplicazione, lavorando con pi&ugrave; <lb/>squisita arte le lenti, ch'ebbero la fortuna di venire applicate ai veggentis&shy;<lb/>simi occhi del Malpighi e del Redi. </s>

<s>Ma il Leewenoeck, per i particolari usi <lb/>delle osservazioni entomologiche, trov&ograve; molto opportuna un'unica lente, la <lb/>quale, perciocch&egrave; faceva migliore effetto delle lenti composte, fu volentieri <lb/>adoperata dai Micrografi, che grati del servigio la insignirono, bench&egrave; cos&igrave; <lb/>nudo occhiale, del nome di <emph type="italics"/>Microscopio leuvenecchiano.<emph.end type="italics"/> Era insomma que&shy;<lb/>sto il microscopio detto <emph type="italics"/>della perlina<emph.end type="italics"/> dai nostri Fiorentini, e <emph type="italics"/>batavo<emph.end type="italics"/> dagli <lb/>stranieri, adattato poi dal Lyonet, per l'anatomia degli insetti, a quella sem&shy;<lb/>plice macchinetta descritta dallo Spallanzani, e della quale si serv&igrave; a mara&shy;<lb/>viglia l'insigne nostro Naturalista, per osservare la circolazione del sangue <lb/>nel giro universale dei vasi. (Dissertazione, T. I, Milano 1726, pag. </s>

<s>140, 41). </s></p><p type="main">

<s>Gli artificiosi strumenti e l'acume delle osservazioni de'Micrografi sopra <lb/>commemorati, ai quali sarebbero da aggiunger tanti altri, come per esem&shy;<lb/>pio il Lister e lo Swammerdam, fanno presentire i maravigliosi progressi <lb/>dell'Entomologia, dall'Harvey allo Spallanzani, e quanto sarebbe soprabbon&shy;<lb/>dante la messe da raccogliersi in questa storia. </s>

<s>Venendo per&ograve; a noi pre&shy;<lb/>scritti limiti s&igrave; angusti, ci contenteremo d'accennare a ci&ograve; che il Microsco&shy;<lb/>pio rivel&ograve; degli organi inservienti ad alcune delle principali funzioni della <lb/>vita animale degl'insetti, e della loro vita di relazione. </s></p><p type="main">

<s>La principale fra quelle funzioni animali &egrave; senza dubbio il respiro, che <lb/>secondo i Filosofi antichi &egrave; il divino alito, da cui agile si ridesta nella ma&shy;<lb/>teria, e perenne vi si mantiene la vita. </s>

<s>Aristotile nonostante, per confutar <lb/>Diogene, che sentenziava aver tutti gli animali necessit&agrave; di respirare, addu&shy;<lb/>ceva l'esempio degl'insetti, i quali che non respirino &egrave; provato, dice il Fi&shy;<lb/>losofo, dal fatto che durano tuttavia a vivere, bench&egrave; tagliati in due o pi&ugrave; <lb/>parti, come si vede nelle scolopendre: per cui domanda a Diogene stesso <lb/>in quali di queste parti, e in che modo occorra all'insetto di trarre il re&shy;<lb/>spiro: &ldquo; quae, qualiter aut in quonam contingit respirare? </s>

<s>&rdquo; (De respir., <lb/>Operum, T. VII cit., fol. </s>

<s>270). </s></p><p type="main">

<s>Rimase a tale domanda muta la posterit&agrave; infintanto che il Rondelezio <lb/>non isciolse la lingua, per dir liberamente ch'ei si maravigliava come mai <pb xlink:href="020/01/1607.jpg" pagenum="482"/>quell'Aristotile, il quale aveva scritto refrigerarsi tutti gli animali a sangue <lb/>freddo dall'aria ambiente, facesse poi per gl'insetti un'eccezione particolare. </s>

<s><lb/>Ond'&egrave; che posto il principio esser ogni corpo animato <foreign lang="greek">e)ipnoun</foreign> et <foreign lang="greek">e<gap/>pnoun</foreign>, cio&egrave; <lb/>inspiratore ed espiratore, cos&igrave; contro il Filosofo il Rondelezio stesso con&shy;<lb/>clude: &ldquo; Cum igitur scolopendrae et aliorum insectorum partes dissectae <lb/>moventur et vivunt, tenuioris aeris aliquid undique inspirant et expirant &rdquo; <lb/>(De piscibus cit., pag. </s>

<s>101). </s></p><p type="main">

<s>Era venuto per&ograve; il tempo che si voleva nelle cose naturali argomentar <lb/>dai fatti, e no dalle astratte speculazioni, e perci&ograve; l'Acquapendente si trov&ograve; <lb/>costretto anch'egli col Rondelezio d'abbandonare il suo Aristotile, persuaso <lb/>che gl'insetti respirano dagli anelli del ventre, per aver pi&ugrave; volte osservato <lb/>che di li mandan vento. </s>

<s>&ldquo; Quo circa iis membrana tenuissima sub septo <lb/>transverso dimota, qua etiam murmur efficiunt et aerem paulum movent, <lb/>ad refrigerationem fit opportuna &rdquo; (Op. </s>

<s>omnia cit., pag. </s>

<s>165). </s></p><p type="main">

<s>Queste troppo frettolose osservazioni del Maestro viziate dai grossolani <lb/>errori aristotelici intorno alla respirazione, furon riprese a far con pi&ugrave; dili&shy;<lb/>genza che mai dall'Harveio, il quale dall'attendere a quel continuo allun&shy;<lb/>garsi e contrarsi degli anelli del ventre, che ha tanta analogia coll'anelar <lb/>delle coste del torace, venne a confermarsi nell'opinione che gl'insetti re&shy;<lb/>spirino per la coda. </s>

<s>&ldquo; Crabrones et apes et alia insecta, non solum pulsum <lb/>habere sed et respirationem, in illa parte quam caudam nominant, experi&shy;<lb/>mentis quibusdam me posse demonstrare arbitror, unde ipsam elongare e <lb/>contrahere contingit modo frequentius, modo rarius, prout anhelosi magis <lb/>videntur, et aere magis indigere &rdquo; (De motu cordis cit., pag. </s>

<s>96). I primi <lb/>esperimenti, di che qui si fa cenno, consistevano nel rendersi visibili gli <lb/>effetti di quel vento, che l'Acquapendente avea detto spirar dagli anelli del&shy;<lb/>l'insetto, ma l'Harvey se ne assicur&ograve; poi anche in un altro pi&ugrave; evidente <lb/>modo, affogando gl'insetti stessi o nell'acqua o nell'olio, e osservando che, <lb/>cos&igrave; sommersi, mandavano bolle d'aria fuor dalla coda. </s>

<s>&ldquo; Hoc enim modo, <lb/>crabrones, vespas et huiusmodi insecta, in oleo demersa et suffocata, ultimo <lb/>aeris bullulas e cauda, dum emoriuntur, emittunt, unde ita respirare vivos <lb/>non est improbabile &rdquo; (ibid., pag. </s>

<s>141). </s></p><p type="main">

<s>Intanto eran venuti postumi alla luce in Bologna i sette libri <emph type="italics"/>De ani&shy;<lb/>malibus insectis<emph.end type="italics"/> dell'Aldovrandi, ne'prolegomeni ai quali, trattando l'Au&shy;<lb/>tore degl'insetti in genere, propone per question principale <emph type="italics"/>an respirent.<emph.end type="italics"/><lb/>Riferisce ivi eruditamente le varie opinioni scritte dagli antecessori in pro&shy;<lb/>posito, e trattenutosi particolarmente a infirmare gli argomenti del Ronde&shy;<lb/>lezio, si volge a professar la dottrina di Aristotile, perch&egrave; il ragionamento <lb/>di lui lo persuade. </s>

<s>Singolar cosa a notare &egrave; che fra gli scrittori neganti il <lb/>respirar degl'insetti annovera l'Aldovrandi Basilio Magno, da un Omelia del <lb/>quale sopra l'Esaemerone trascrive queste parole: &ldquo; Cum volatilium ea con&shy;<lb/>spexeris, quae insecta vocantur, ut apes et vespas, veniat tibi in mentem ea <lb/>praedita respiratione non esse, pulmoneque carere, sed totis omnia sui cor&shy;<lb/>poris partibus nutriri aere. </s>

<s>Quapropter si oleo fuerint madefacta, occlusis <pb xlink:href="020/01/1608.jpg" pagenum="483"/>meatibus pereunt, sin aceto protinus asperseris, ea reclusis foraminibus re&shy;<lb/>viviscunt &rdquo; (De anim. </s>

<s>insectis, Bononiae 1638, pag. </s>

<s>14). </s></p><p type="main">

<s>La bella esperienza, cos&igrave; commemorata, del Santo Padre della Chiesa <lb/>greca, fu letta in queste pagine dell'Aldovrandi da Antonio Nardi, il quale, <lb/>in quella universal comprensione delle scienze naturali, attendendo alla sto&shy;<lb/>ria degl'insetti, s'era, per le osservazioni dell'Acquapendente e per l'espe&shy;<lb/>rienze dell'Harvey, persuaso che quegli animali respirano, com'ei si esprime, <lb/>dalle fasce del ventre. </s>

<s>Rivelava questa sua persuasione nella veduta I della <lb/>Scena VIII l&agrave; dove, accennando alla circolazione del sangue, dop'avere ap&shy;<lb/>provata l'opinione dello stesso Harveio, cos&igrave; soggiunge: &ldquo; &Egrave; ben vero che <lb/>molto paradossa parr&agrave; l'opinione di questo dottissimo uomo, mentre che nel&shy;<lb/>l'inferior ventre pensasi che le vespe ed altri somiglianti animali abbiano <lb/>il cuore, perch&egrave;, se dal battere una sua parte ci&ograve; si potesse argomentare, <lb/>seguiriane che gli animali pi&ugrave; perfetti l'avessino in capo, vedendosi il cer&shy;<lb/>vello battere. </s>

<s>Alcuno piuttosto penser&agrave; che la parte battente nell'inferior <lb/>ventre delle vespe siano i vasi seminali. </s>

<s>Nulla nondimeno affermo in mate&shy;<lb/>ria cos&igrave; dubbia, perch&egrave; sperienza fatto non ne ho: nemmeno rifiuto il pa&shy;<lb/>rere di tale Autore, quale concorda col mio, cio&egrave; che gl'insetti spirino per <lb/>le fasce &rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>1098). </s></p><p type="main">

<s>Or avendo duuque il Nardi letto nelle parole trascritte dall'Aldovrandi <lb/>che Basilio Magno diceva respirare gl'insetti, non da sole le fasce, ma da <lb/>tutto il corpo, pens&ograve; di applicare l'esperienza dell'olio a decidere il dub&shy;<lb/>bio. </s>

<s>Unti perci&ograve; gli anelli caudali a varie specie d'insetti, lasciando le ri&shy;<lb/>manenti parti del loro corpo scoperte, trov&ograve; che morivano. </s>

<s>E perch'egli era <lb/>persuaso che ci&ograve; avvenisse per la tenacit&agrave; dell'untuosa materia, che intasa <lb/>le vie del respiro, ne concluse che sien dunque queste vie aperte, non in <lb/>tutta la superficie del corpo animale, ma fra le sole incisure del ventre. <lb/></s>

<s>&ldquo; Gli animali volatili insieme e intagliati, scrive nella veduta VII della <lb/>Scena IX, quali caldissimi sono e focosi, hanno pi&ugrave; di tutti di respirare bi&shy;<lb/>sogno, e cos&igrave; respirano, non solo dalla bocca, ma forse anco, quasi per tante <lb/>branchie, dalle commessure del ventre; il che si raccoglie dalla distanza, e <lb/>quasi separazione del petto dal ventre, quali parti talvolta non comunicano <lb/>se non per un lungo e sottilissimo canaletto, come negli Icneumoni, per cui <lb/>appena il cibo pare che trasmetter si possa. </s>

<s>Anco il suono che volando, e <lb/>talora anco fermi stando, fuori mandano gl'insetti, argomenta, come nei <lb/>quaglieri avviene, frangasi per il moto l'aria nei pori per d'onde esce, poi&shy;<lb/>ch&egrave; il pensare che dal moto delle ali tal suono cagionisi, non parmi verisi&shy;<lb/>mile. </s>

<s>Parimente il manifesto allargarsi e stringersi delle fasce, che loro cin&shy;<lb/>gono il petto, tal mio parere conferma, quali ancora se d'olio o d'altra <lb/>grassezza vengano unti, muore l'animale. </s>

<s>Il che forse non da altro nasce <lb/>che dall'impedirsi alla respirazione il passaggio, e ci&ograve; non solo le vespe e <lb/>le api e gli altri insetti fanno, ma anco le mosche e tutti i sibilanti nel <lb/>suolo &rdquo; (ivi, pag. </s>

<s>1259, 60). </s></p><p type="main">

<s>Rimasti i concetti di Basilio Magno affogati nel mare peripatetico del-<pb xlink:href="020/01/1609.jpg" pagenum="484"/>l'Aldovrandi, e l'esperienza del Nardi sepolta ne'manoscritti, a mezzo il <lb/>secolo XVII, da chi avea badato all'espressioni, uscite per incidenza dalla <lb/>penna dell'Harvey, si teneva la respirazion degl'insetti per una probabile <lb/>congettura, senza ricercare pi&ugrave; avanti. </s>

<s>Il Boyle, nel suo XL esperimento, <lb/>aveva osservate le mosche, le api e altri simili volanti in mezzo al vuoto <lb/>della sua macchina pneumatica; gli Accademici nostri fiorentini avevano in <lb/>mezzo al vuoto torricelliano sperimentato il fatto de'grilli, delle mosche e <lb/>delle farfalle: e bench&egrave; resultasse da tutte queste esperienze avere anche <lb/>gl'insetti per vivere bisogno dell'aria, non si scorge negli sperimentatori <lb/>nessun intenzione d'investigare in che modo soccorra l'aria stessa a man&shy;<lb/>tenere in questi animali la vita. </s></p><p type="main">

<s>Lo stesso Redi, tutto inteso allo studio degl'insetti, non si prende altra <lb/>cura che di mettere a cimento del vero i detti di Galeno, di Luciano, di <lb/>Alessandro afrodisco, di Ulisse Aldovrando e di Giovanni Sperlingio affer&shy;<lb/>manti che le mosche, se gustano dell'olio o se con quello sono unte, si <lb/>moiono. </s>

<s>&ldquo; Ed in vero, egli scrive, che fattane da me l'esperienza, ogni qual&shy;<lb/>volta che io faceva che da una sola gocciola di olio fosse tocca ed inzup&shy;<lb/>pata una mosca, in quello stesso momento ella cadeva fuor d'ogni credere <lb/>morta &rdquo; (Esper. </s>

<s>intorno agl'insetti, Op., T. </s>

<s>I cit., pag. </s>

<s>75). Ma non si fa <lb/>nemmeno un cenno che ci&ograve; accada per venir dall'olio intasate le vie del <lb/>respiro. </s></p><p type="main">

<s>Mentre il Redi proseguiva questo genere di esperienze, non con altro <lb/>intendimento che di riscontrar coi fatti quel che si credeva dal volgo e dai <lb/>Filosofi intorno alla morte e alla resurrezione degl'insetti, annegati in varie <lb/>sorte di liquidi; Marcello Malpighi dava assidua e diligente opera a noto&shy;<lb/>mizzare i vermi da seta. </s>

<s>Nota sulla loro superficie alcune incisure, quasi <lb/><emph type="italics"/>stimmate<emph.end type="italics"/> impresse, dalle quali si propagano a modo di arterie alcuni vasi <lb/>che, quanto pi&ugrave; si dilungano dal tronco, tanto si fanno pi&ugrave; gracili e pi&ugrave; <lb/>frequenti, intrecciandosi insieme a comporre una rete maravigliosa, da ras&shy;<lb/>somigliarsi in qualche modo a quella formata dalle foglie degli alberi. </s>

<s>Una <lb/>tale diramazione, che avea fatto sovvenire al Malpighi quella osservata gi&agrave; <lb/>nella trachea e ne'bronchi degli animali perfetti, fin&igrave; di confermarlo nella <lb/>persuasione che i due organi, analoghi nella struttura, servissero ai mede&shy;<lb/>simi usi, quando vide in quasi tutti i bruchi, e specialmente nei Cervi vo&shy;<lb/>lanti, rigonfiarsi le estremit&agrave; di que'vasi in vescicole similissime alle polmo&shy;<lb/>nari. </s>

<s>&ldquo; Unde, ex his et inferius dicendis, coniectatus sum tracheas esse, <lb/>quae suis productionibus pulmones efforment &rdquo; (De Bombycibus, Operum, <lb/>T. II cit., pag. </s>

<s>17). </s></p><p type="main">

<s>Essendo le stimmate bocche di cos&igrave; fatte trachee, dovrebbero essere <lb/>esse che ammettono l'aria dentro i polmoni: per certificarsi di che il Mal&shy;<lb/>pighi ricorse all'antica esperienza dell'olio, o di altre materie grasse, come <lb/>sarebbero il sevo ed il burro. </s>

<s>Intasate alcune delle superficiali incisure con <lb/>qualche stilla di queste appiccaticce sostanze, trov&ograve; che si rendevano para&shy;<lb/>litiche le sole membra corrispondenti, ma che moriva immediatamente l'ani-<pb xlink:href="020/01/1610.jpg" pagenum="485"/>male, quando l'intasatura si faceva sopra tutte le stimme ugualmente. </s>

<s>Inno&shy;<lb/>cue poi speriment&ograve; che riuscivano sempre le unzioni, quando, salve esse <lb/>stimme, si facevano sul ventre, sul capo, intorno alla bocca o sul dorso. <lb/></s>

<s>&ldquo; Quare interitum ex oleo, eatenus contingere conieci, quatenus, occlusis <lb/>tracheae orificiis, suffocatio vel quid simile succedit &rdquo; (ibid., pag. </s>

<s>19). </s></p><p type="main">

<s>La verit&agrave;, traveduta in ombra infin dai tempi di Basilio Magno, e del <lb/>suo pi&ugrave; superficial velo scoperta da Antonio Nardi, aveva avuto nelle os&shy;<lb/>servazioni anatomiche e nelle esperienze del Malpighi cos&igrave; piena dimostra&shy;<lb/>zione, che per pi&ugrave; di un mezzo secolo nessuno ebbe dubbio di ammettere <lb/>quel ch'esso Malpighi avea concluso: &ldquo; aerem in haec bombycis vasa conti&shy;<lb/>nuatim subingredi et egredi, ut in caeteris quibus insunt pulmones &rdquo; (ibid.). </s></p><p type="main">

<s>Parve per&ograve; al Reaumur pi&ugrave; conforme agli ordini naturali che si facesse <lb/>la respirazione dei bruchi, non a modo degli animali perfetti, ma piuttosto <lb/>a modo dei pesci, i quali inspirano l'aria da una parte, e la espirano dal&shy;<lb/>l'altra. </s>

<s>&ldquo; Nous sommes donc conduits par les experiences (dice nella III <lb/>delle Memorie per servire alla storia degl'insetti, compresa nella prima parte <lb/>del Tomo primo) &agrave; reconnoitre que la respiration complette, je veux dire <lb/>l'inspiration et l'expiration, se fait dans les Chenilles, et par consequent <lb/>dans un grand nombre d'insectes, d'une mani&egrave;re singuliere et tout-&agrave;-fait <lb/>differente de celle dont elle se fait dans les grands animaux &rdquo; (Amster&shy;<lb/>dam 1737, pag. </s>

<s>172). </s></p><p type="main">

<s>Le diciotto stimmate scoperte e diligentemente annoverate nel bombice <lb/>dal Malpighi son, prosegue a dire il Reaumur, diciotto bocche &ldquo; qui don&shy;<lb/>nent entr&eacute;e &agrave; l'air dans les principaux canaux, dans les plus gros troncs <lb/>des trach&eacute;es, d'ou il est conduit dans leurs differentes ramifications; il en&shy;<lb/>file des canaux de plus &eacute;troits en plus &ecirc;troits, et c'est par les derni&egrave;res <lb/>extremit&eacute;s de ces canaux qu'il s'&eacute;chappe; elles ont des ouvertures qui lui <lb/>permettent la sortie &rdquo; (ivi). </s></p><p type="main">

<s>L'esperienze rivelatrici al Reaumur della verit&agrave; di questi fatti son varie, <lb/>ma la prima e principale consiste nell'avere immerso il bruco nell'acqua, <lb/>e nell'avere osservato che l'aria esce in bollicelle dalla superficie dell'ani&shy;<lb/>male, fuor che dalle stimme, dalle quali anzi si sarebbe aspettato che do&shy;<lb/>vesse vedersi uscire l'aria stessa in forma di getto, se fosse stata vera l'ipo&shy;<lb/>tesi del Malpighi. </s>

<s>L'anatomia sovveniva pure a conferma del medesimo fatto, <lb/>rivelando all'occhio armato del Microscopio ch'&egrave; la pelle del bruco tutta <lb/>trapunta da spessi e minutissimi pori. </s></p><p type="main">

<s>Questo modo di respirar degl'insetti, ricevendo l'aria per le stimmate <lb/>e rigettandola per gl'innumerevoli pori aperti sopra la superficie del corpo, <lb/>rende la ragione, dice il Reaumur, di certi fatti, che si osservano avvenire <lb/>in questi animali in un modo assai diverso dagli animali degli ordini supe&shy;<lb/>riori assoggettati all'azione del vuoto pneumatico. </s>

<s>Le vesciche dei pesci, i <lb/>ventricoli delle rane, i polmoni degli uccelli inturgidiscono sempre pi&ugrave; al <lb/>rarefarsi dell'aria, intantoch&egrave; si vede notabil<gap/> ricrescere sotto il reci&shy;<lb/>piente tutta insieme la mole animale. </s>

<s>&ldquo; Il ne arrive tout autrement a nos <pb xlink:href="020/01/1611.jpg" pagenum="486"/>chenilles; on a eu beau epuiser d'air le petit recipient ou elles &eacute;toient, leur <lb/>volume n'a pas augment&eacute; sensiblement, sans doute parce que l'air de leur <lb/>corps trouve par-tout des passages pour s'echapper &rdquo; (ivi, pag. </s>

<s>177). </s></p><p type="main">

<s>Un altro fatto singolare, e proprio a soli gl'insetti, s'osserva in questo <lb/>genere di esperienze, ed &egrave; che, sebbene estratta l'aria s'abbandonino come <lb/>morti, al riammetterla, anche dopo qualche giorno, riprendono la primiera <lb/>vivacit&agrave;, e ci&ograve; non per altro avviene, dice il Reaumur, se non perch&egrave; l'aria <lb/>facilmente uscendo da tutti i pori del corpo &ldquo; emp&ecirc;che qu'il n'y produise <lb/>des derangemens lorsqu'il se rar&eacute;fie &rdquo; (ivi). </s></p><p type="main">

<s>All'assunto del Malpighi, ch'era quello di dimostrare essere gli organi <lb/>da s&egrave; scoperti ne'vermi da seta inservienti alla respirazione, i nuovi fatti, <lb/>dal Reaumur colla macchina pneumatica sperimentati, erano di una grande <lb/>importanza. </s>

<s>In fin dai tempi dell'Accademia del Cimento dovea senza dub&shy;<lb/>bio recar non poca maraviglia il veder che nel vuoto torricelliano morivano <lb/>immediatamente gli uccelletti, mentre i grilli vi si mantenevano &ldquo; per lo <lb/>spazio di un quarto d'ora vivacissimi, movendosi sempre ma non saltando &rdquo; <lb/>(Saggi di natur. </s>

<s>esper. </s>

<s>cit., pag. </s>

<s>88); ci&ograve; che dovette avere grande effica&shy;<lb/>cia sulla mente di coloro, che negavano agl'insetti il respiro. </s>

<s>Il Malpighi <lb/>stesso non par che sentisse questa difficolt&agrave;, fidandosi delle esperienze degli <lb/>Accademici di Londra, i quali, avendo posti de'bruchi sotto il recipiente <lb/>della macchina pneumatica, dalle troppo frettolose osservazioni conclusero <lb/>che &ldquo; orbata aere, interiere &rdquo; (De bombyc. </s>

<s>cit., pag. </s>

<s>19). Che il Reaumur <lb/>dall'altra parte non avesse tolte le difficolt&agrave; dubitavasi ragionevolmente da <lb/>coloro, i quali comprendavano che poteva l'aria trovar cos&igrave; facile esito per <lb/>le stimmate, come per i pori cutanei, n&egrave; si persuadevano come mai i mor&shy;<lb/>tiferi effetti della privazione dell'aria si riducessero a un <emph type="italics"/>derangemens<emph.end type="italics"/> degli <lb/>organi. </s></p><p type="main">

<s>Queste prime considerazioni invitarono ad entrar pi&ugrave; addentro all'esame <lb/>della questione Carlo Bonnet, il quale diligentemente bagnando il bruco, <lb/>prima di sommergerlo nell'acqua, trov&ograve; che l'aria non usciva altrimenti dai <lb/>pori cutanei, come pretendeva il Reaumur, ma dalle stimate, com'avea detto <lb/>il Malpighi. </s>

<s>&ldquo; Queste esperienze, scrive lo Spallanzani in una nota alla sua <lb/>traduzione della <emph type="italics"/>Contemplazione della Natura,<emph.end type="italics"/> non mai pubblicate dal no&shy;<lb/>stro Autore, che sono in buon numero e ingegnosamente variate, si con&shy;<lb/>servano presso di me riserbandomi a darle fuori allora quando uscir&agrave; la mia <lb/>Opera sulle <emph type="italics"/>Riproduzioni animali &rdquo;<emph.end type="italics"/> (Tomo I, Modena 1759, pag. </s>

<s>279). </s></p><p type="main">

<s>Restava cos&igrave; dimostrato per queste bonnettiane esperienze che l'aria <lb/>entra ed esce per le stimme dei vermi, come per la bocca degli animali <lb/>perfetti, ma non &egrave; da aspettarsi che in tempi, ne'quali ignoravansi gli usi <lb/>dell'aria nella respirazione, si potessero sciogliere cos&igrave; fatte proposte que&shy;<lb/>stioni, le quali furono perci&ograve; dal Malpighi e dal Reaumur, come dallo stesso <lb/>Bonnet, lasciate alla progredita scienza dei Naturalisti del secolo seguente. </s></p><pb xlink:href="020/01/1612.jpg" pagenum="487"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Bench&egrave; la ignorata azione chimica dell'aria sul sangue impedisse agli <lb/>Entomologi del secolo XVII e del XVIII di ridur compiuta la fisiologia della <lb/>respirazione, avevano nonostante avuto dal Microscopio cos&igrave; valido aiuto, da <lb/>scoprire gli organi inservienti a quella, che &egrave; la precipua funzione della vita <lb/>animale. </s>

<s>Si sarebbe sperato che il benefico diottrico strumento fosse venuto <lb/>a rivelare all'occhio desideroso qualche apparenza almeno degli organi dei <lb/>sensi, invisibili per la piccolezza, non riconoscibili per la particolare strut&shy;<lb/>tura. </s>

<s>Era per le pi&ugrave; volgari esperienze noto che le api per esempio disperse <lb/>facilmente si convocano al risonar di un metallo percosso, e che le mosche <lb/>traggono d'ogni parte nelle cucine all'odore delle vivande, bench&egrave; nulla <lb/>apparisse in quegli insetti, che avesse qualche somiglianza con gli orecchi <lb/>e col naso nostro o degl&igrave; altri animali. </s>

<s>Tanto la cos&igrave; certa esistenza della <lb/>funzione provocava l'intelletto ad argomentare all'esistenza dell'organo, che <lb/>del non averlo saputo ancora scoprire s'accusava la debolezza della vista, <lb/>per cui venivano di qui ad incorarsi pi&ugrave; vive le speranze riposte nel Mi&shy;<lb/>croscopio. </s>

<s>N&egrave; i primi imperfetti strumenti diottrici per&ograve;, n&egrave; i pi&ugrave; perfetta&shy;<lb/>mente elaborati dipoi scoprirono negl'insetti vestigio di organi, che si po&shy;<lb/>tesse credere esser disposti dalla Natura per ricevere le impressioni de'suoni <lb/>e degli odori. </s>

<s>Al Lyonet, che indicava le barboline intorno alla bocca per <lb/>organo dell'olfatto, nessuno o pochissimi fra'Naturalisti dettero fede, non <lb/>avendo una tal congettura miglior fondamento dell'altra, che volesse rico&shy;<lb/>noscer piuttosto l'organo olfattorio ne'peli del dorso, della testa o del ven&shy;<lb/>tre. </s>

<s>Che se quelle barboline son palpi, non par che possano servire se non <lb/>al senso generale del tatto. </s></p><p type="main">

<s>Anche il Bonnet sospett&ograve; che servissero all'odorato degl'insetti le <emph type="italics"/>an&shy;<lb/>tenne,<emph.end type="italics"/> per avverar la qual congettura lo Spallanzani proponeva ingegnosa&shy;<lb/>mente di far questa esperienza: &ldquo; Sappiamo, egli dice, per l'una parte che <lb/>la privazione delle antenne non toglie all'insetto l'esercitare le sue funzioni <lb/>corporee, e per l'altra, che ci sono certi insetti, massime nel numero dei <lb/>volanti, i quali dalla sola forza dell'odore sembrano avidamente essere por&shy;<lb/>tati l&agrave; dove giacciano materie acconce a fomentare, e a far nascere le uova, <lb/>che chiudono in seno, e delle quali hanno allora bisogno di sgravarsi. </s>

<s>Si <lb/>potrebbe dunque stare a osservare se tali insetti si determinano eziandio a <lb/>quella volta, mutilati essendo nelle antenne. </s>

<s>Se s&igrave;, bisogna dire che l'or&shy;<lb/>gano dell'odorato non risegga nelle antenne; se no, abbiam motivo di cre&shy;<lb/>dere il contrario &rdquo; (Traduz. </s>

<s>della Contemplazion della Natura, T. I, Mo&shy;<lb/>dena 1769, in nota a pag. </s>

<s>85). Ma eseguitasi o no la proposta esperienza <lb/>rimasero gli Entomologi nella prima incertezza rispetto a ci&ograve; che, dell'or&shy;<lb/>gano olfattorio negli insetti, erasi dal Bonnet congetturato. </s></p><pb xlink:href="020/01/1613.jpg" pagenum="488"/><p type="main">

<s>Nessuno poi, nemmeno per congettura, os&ograve; d'indicare un qualche or&shy;<lb/>gano dell'udito, bench&egrave; le sopra accennate esperienze ne facessero conclu&shy;<lb/>der certa l'esistenza nelle api, e la facolt&agrave; di emettere i suoni in tanti insetti <lb/>facesse necessariamente arguire a un sensorio da percepirli. </s>

<s>Il Casserio di&shy;<lb/>ligentemente descrisse gli organi e il meccanismo di quel suono, che pro&shy;<lb/>ducono, fregate insieme o percosse, le ali delle locuste e de'grilli, e perch&egrave; <lb/>non si pu&ograve; credere che la Natura usasse un cos&igrave; sottil magistero per dare <lb/>all'animale un'inutile sollazzo, convien dire che abbia con pi&ugrave; alto inten&shy;<lb/>dimento cos&igrave; disposte le parti, per servire alla vita di relazione. </s></p><p type="main">

<s>&ldquo; Sonum locustarum genus alis edit, scrive il Piacentino nel suo trat&shy;<lb/>tato <emph type="italics"/>De vocis organi historia anatomica,<emph.end type="italics"/> ita ut sibi invicem impositae mo&shy;<lb/>veantur alae, quarum superior parte intima corpus habet subnigrum, durum, <lb/>per transversum locatum. </s>

<s>Inferior eiusdem substantiae corpusculum in extre&shy;<lb/>mitate orae superioris, parte externa, cui adiacet perbellum tympanum. </s>

<s>Ho&shy;<lb/>rum mutuo attritu stridor ille, imo et mortuis styli tactu excitatur, at multo <lb/>maior in vivente animali, ubi copiosior intercipitur aer et, natura monente, <lb/>validius alae colliduntur, non inutile membranae, quae admodum tensa cer&shy;<lb/>nitur, opera &rdquo; (Ferrariae 1600, pag. </s>

<s>116). </s></p><p type="main">

<s>Pi&ugrave; complicato di questo &egrave; l'artificio, con cui la Natura condusse lo <lb/>stridulo organo delle Cicale, e il Casserio medesimo non trascur&ograve;, in quel <lb/>nuovo campo aperto all'Entomologia, d'esercitarvi l'acume dello stilo ana&shy;<lb/>tomico e dell'occhio. </s>

<s>Chi, sodisfatta la curiosit&agrave; nella lettura delle pagine <lb/>casseriane, passa a svolgere le <emph type="italics"/>Memorie<emph.end type="italics"/> del Reaumur, comprese nella prima <lb/>Parte del Tomo quinto, resta maravigliato in trovarvi scritto che il Ponte&shy;<lb/>dera, a proposito del detto organe risonante &ldquo; assure avec raison qu'il sem&shy;<lb/>ble qu'ils ont et&eacute; mal vus. </s>

<s>Il est certain au moins qu'ils ont et&eacute; mal d&eacute;&shy;<lb/>crits, et qu'il y en a quelques-uns qui sont difficiles &agrave; decouvrir. </s>

<s>Quand on <lb/>observa du c&ocirc;te du ventre un m&acirc;le des Cigales on y remarque bient&ograve;t deux <lb/>assez grandez plaques &eacute;cailleuses, qu'on ne trouve point aux femelles &rdquo; <lb/>(Amsterdam 1741, pag. </s>

<s>199). E prosegue la descrizione, che i nostri Let&shy;<lb/>tori possono confrontare con questa fatta dal nostro Anatomico piacentino <lb/>quasi un secolo e mezzo prima. </s>

<s>&ldquo; In cicada vero, plane mirabile sagacis Natu&shy;<lb/>rae artificium, tympanum duplex sub thorace duplici obtegitur velut squama. </s>

<s><lb/>Thorax et abdomen magno excavata sunt antro, cuius superior pars, mem&shy;<lb/>brana lutea tanquam fornice cincta, sonum excipit. </s>

<s>Hic a concusso aere, <lb/>resilit in amplam illam cameram. </s>

<s>Aerem autem quatiunt praedurae quaedam <lb/>membranulae, a lateribus sitae, quarum substantiam non obscure conferas <lb/>cum bracteris illis ex auricalcho, quae agitatae consimilem fere sonum fa&shy;<lb/>ciunt. </s>

<s>Muniuntur hae suo cortice, ita tamen, ut omnino conclusae non sint, <lb/>sed liber aeri pateat aditus. </s>

<s>Voluntarie moventur duobus musculis, ab osse, <lb/>quod supremum ventrem cingit, ortis, validis ob motum respectu animalis <lb/>haud invalidum &rdquo; (De vocis hist. </s>

<s>cit, pag. </s>

<s>116). </s></p><p type="main">

<s>Ma insomma, bench&egrave; sia il canto ne'maschi delle Cicale ordinato ad <lb/>allettare le femmine, non &egrave; stato possibile di riconoscere in queste nessun <pb xlink:href="020/01/1614.jpg" pagenum="489"/>vestigio d'organo, da stare in silenzio ad ascoltar l'amorosa canzone: co&shy;<lb/>sicch&egrave; de'sensorii, e non in tutti gl'insetti, non s'ebbe indizio altro che <lb/>degli occhi. </s>

<s>Gli antichi fondarono questi indizi sulla esterior lucentezza cri&shy;<lb/>stallina, e sulla posizione, che hanno i due creduti globuli occellari rispetto <lb/>alla bocca, e rispetto alle altre parti analoghe a quelle degli animali supe&shy;<lb/>riori, ma coll'aiuto del Microscopio quegli stessi indizi, che avevano avuto <lb/>cos&igrave; debole fondamento, per la pi&ugrave; intima somiglianza scoperta con gli oc&shy;<lb/>chi veri vennero a farsi pi&ugrave; probabili, e dopo lunghe discussioni, delle quali <lb/>accenneremo alla storia, si pu&ograve; dire anche certi. </s></p><p type="main">

<s>Incominciano i naturali avvenimenti storici anche questa volta in Italia, <lb/>dove Giovan Batista Hodierna, poco dopo il 1640, attendeva il primo ad os&shy;<lb/>servare il maraviglioso spettacolo offertogli dall'occhio delle mosche e degli <lb/>altri insetti. </s>

<s>&ldquo; Vedesi dunque, egli dice, per cominciare la descrizione di <lb/>questa singolare anatomia, da niuno prima, quant'io sappia, che da me ten&shy;<lb/>tata e scoverta, nell'estrinseco dell'occhio nella Mosca, e in qualsivoglia in&shy;<lb/>dividuo delle specie annoverate sotto il genere degl'insetti, o sia quello vo&shy;<lb/>latile come la Mosca o pedestre come la formica, o aquatile come il gran&shy;<lb/>chio; nella superfice convessa dell'occhio, in quella dico che dalli periti <lb/>Anatomisti vien detta cornea tunica, dalla durezza che tiene e dall'esser <lb/>trasparente come una laminetta di corno; dico nell'estrinseca superfice della <lb/>cornea ambiente tutta la sostanza dell'occhio, un grandissimo numero d'or&shy;<lb/>dinatissime sezioni designate e tirate per linee curve e circolari, che tra di <lb/>s&egrave; sono equidistanti e parallele, sicch&egrave;, attraversandosi gli uni con l'altre ad <lb/>angoli retti, rendono tutta la convessit&agrave; distinta in numero cos&igrave; grande, che <lb/>eccede il tremillesimo, rappresentando l'ambito dell'occhio un emisfero di&shy;<lb/>stinto in tre mila piazzette quadre, che rassembra una vaghissima struttura <lb/>di mosaico &rdquo; (Opuscoli, Palermo 1644, pag. </s>

<s>9). </s></p><p type="main">

<s>Dalle semplici osservazioni risalendo l'Hodierna col pensiero a scrutar <lb/>le intenzioni della provvida Natura, che contenta di dar due soli occhi agli <lb/>animali superiori ne fornisse poi gl'insetti di tanto numero, da sembrare <lb/>alle menti volgari eccessivo; &ldquo; io intendo, prosegue a dire, che la Natura <lb/>nella fabbrica mirabile dell'occhio dell'insettile si sia servita, non a caso di <lb/>s&igrave; fatta struttura cotanto diversa dagli altri, ma acci&ograve; supplisca al bisogno, <lb/>che tengono questi animaletti nel vedere, qual bisogno parmi che avendo <lb/>tutti gli altri animali il capo mobile e volubile, mediante il collo che lo so&shy;<lb/>stiene, eccettuandone il genere degl'insetti, il quale, mancando di collo, tiene <lb/>il capo fisso e costante, senza poterlo piegare, e conseguentemente non pu&ograve; <lb/>menar l'occhio per adattarlo agli obietti; la providente Natura dunque, per <lb/>supplire a tanto bisogno, l'ha dotato d'un occhio prominente, con attitudine <lb/>di poter discernerne tutti gli obietti circostanti, senza menare il capo, e senza <lb/>muovere l'occhio &rdquo; (ivi, pag. </s>

<s>15). E di qui crede il nostro Entomologo di <lb/>poter formular la seguente legge zoonomica: che cio&egrave; tutti gli animali man&shy;<lb/>canti di collo hanno occhi poliedrici, e al contrario, tutti quelli che si ve&shy;<lb/>dono avere occhi poliedrici son mancanti di collo. </s></p><pb xlink:href="020/01/1615.jpg" pagenum="490"/><p type="main">

<s>Dopo l'Hodierna, Francesco Fontana, nella sua VI Osservazione micro&shy;<lb/>scopica, descriveva i ragni, che gli apparvero ferocemente armati di denti <lb/>come i cinghiali, e di unghie laceratrici, come quelle degli orsi. </s>

<s>&ldquo; Oculos <lb/>indicibili ordine distinctos habent, quatuor enim in fronte et binos in capi&shy;<lb/>tis vertice, alterum a laeva, a dextera parte alterum, totam corporis imagi&shy;<lb/>nem mirifice illustrantes, atqne horrendum reddentes lumen pellucide, ve&shy;<lb/>lut ex nigricanti vitro, hispidis et longis setis septos &rdquo; (Novae observat. </s>

<s>cit., <lb/>pag. </s>

<s>150). Nel 1665 poi l'Hooke, pubblicando in Londra la sua <emph type="italics"/>Microgra&shy;<lb/>phia,<emph.end type="italics"/> tornava con pi&ugrave; diligenza sulla scoperta pubblicata ventun'anno prima <lb/>dal nostro Hodierna, e con migliore strumento osservando gli occhi delle <lb/>Mosche ne rappresentava, nel XXIV iconismo, i quattordicimila occhi, dei <lb/>quali, da pag. </s>

<s>175-80 della citata edizione, divisava i pi&ugrave; minuti particolari, <lb/>in tal maraviglioso spettacolo della Natura, da s&egrave; contemplati. </s></p><p type="main">

<s>Bench&egrave; l'Hodierna e l'Hooke, se non il Fontana, fossero Micrografi e <lb/>uomini di tale ingegno, da creder che non si fossero cos&igrave; facilmente illusi, <lb/>riguardando i globuli lenticolari scoperti nella fronte degl'insetti come oc&shy;<lb/>chi; a confermar nonostante quella loro opinione s'aggiunsero poco dopo <lb/>due delle pi&ugrave; grandi autorit&agrave; in Entomologia, il Malpighi e lo Swammer&shy;<lb/>dam. </s>

<s>Il Nostro, nel rappresentare il Bombice nella fig. </s>

<s>XI della Tavola I, <lb/>dichiara que'sei puntolini nereggianti, segnati colla lettera H, per gli ocelli <lb/>del bruco. </s>

<s>&ldquo; In anteriori parte, ad latera tamen, globuli H quidam, numero <lb/>sex, diaphani protuberant, qui oculi censentur &rdquo; (Tomus Operum cit., pag. </s>

<s>13). <lb/>E nella fig. </s>

<s>I della Tavola VII que'due globuli diafani, segnati colla lettera B, <lb/>nella fronte dello stesso bruco, giudica che sieno propriamente gli occhi di <lb/>lui. </s>

<s>&ldquo; Diaphanos quosdam globulos B pro oculis habendos esse reor &rdquo; (ibid., <lb/>pag. </s>

<s>27) Nel descriver poi il capo della Farfalla rappresentato nella fig. </s>

<s>II <lb/>della Tavola IX, &ldquo; caput habet A, dice, exiguum tamen, in quo bini locan&shy;<lb/>tur oculi B, ut in consimilibus observatur, qui semisphaeram multis segmen&shy;<lb/>tis distinctam exhibent, unde innumeri, quasi intercepti assurgunt oculi &rdquo; <lb/>(ibid., pag. </s>

<s>34). </s></p><p type="main">

<s>Lo Swammerdam nel 1669 pubblicava in Utrecht nella patria lingua <lb/>un libro, che sedici anni dopo Enrico Cristiano Henning traduceva col titolo <lb/>d'<emph type="italics"/>Historia generalis Insectorum.<emph.end type="italics"/> L'Autore ivi non si contenta di riguar&shy;<lb/>dare i trasparenti globuli malpighiani com'occhi, ma, esercitando pi&ugrave; adden&shy;<lb/>tro la perita arte anatomica, trov&ograve; nelle vespe partirsi dal cervello a cia&shy;<lb/>scuna cornea filamenti nervosi, da potersi riguardar come nervi ottici, e negli <lb/>emerobii, come gi&agrave; l'Hooke nelle libellule, osserv&ograve; che si espandeva cos&igrave; <lb/>esso nervo ottico, da emular la struttura e l'ufficio della retina. </s>

<s>Si dee pure <lb/>allo Swammerdam la graziosa esperienza delle mosche che, bendati gli oc&shy;<lb/>chi, non si risolvon di muoversi, e costrette si vedono andare con volo in&shy;<lb/>certo, e come propriamente cieche urtar negl'incontri. </s></p><p type="main">

<s>Mentre per&ograve; si credeva che fosse l'organo della vista negl'insetti dimo&shy;<lb/>strato, per le citate autorit&agrave; e per le narrate esperienze, come cosa di fatto, <lb/>prevalsero cos&igrave; nella scienza le negazioni di alcuni rispetto all'uso assegnato <pb xlink:href="020/01/1616.jpg" pagenum="491"/>ai due diafani globi maggiori, che Filippo De la Hire, appuntando un giorno <lb/>la lente microscopica sulla testa di una mosca, la pos&ograve; esultando per andare <lb/>a riferire agli Accademici parigini colleghi suoi che avea in quegl'insetti <lb/>scoperto il vero organo della vista. </s>

<s>E que'Parigini, i quali s'erano, come il <lb/>De la Hire, dimenticati che gli <emph type="italics"/>ocelli<emph.end type="italics"/> erano stati con gran solennit&agrave; figurati <lb/>e descritti nel Bombice del Malpighi, in questa forma accademica furono <lb/>solleciti di divulgare la nazionale scoperta: &ldquo; Plusieurs personnes ont cr&ucirc; <lb/>que les mouches et la plupart des autres insectes volans n'avoient point <lb/>d'yeux. </s>

<s>La raison sur laquelle ils fondoient ce sentiment, est qu'ils ne pou&shy;<lb/>voient pas se persuader que les pelotons divises par quarr&eacute;s ou exagones <lb/>qu'ils ont au c&ograve;t&eacute; de la t&ecirc;te en fussent effectivement, n'ayant autre rapport <lb/>&agrave; ceux des autres animaux que la situation. </s>

<s>M. de la Hire a trouv&eacute; que les <lb/>insectes en ont trois qui sont places entre les deux pelotons, sur la partie <lb/>la plus &eacute;lev&eacute;e de la t&ecirc;te, et sur une petite &eacute;minence, deux desquels regar&shy;<lb/>dent en haut et un peu vers le c&ocirc;t&eacute;s, et l'autre regarde un peu de front. </s>

<s><lb/>Ils sont dispos&eacute;s en triangle. </s>

<s>Ces yeux ont des paupi&egrave;res que l'on voit fort <lb/>bien..... Ces yeux sont ronds et fort polis, representant fort nettement les <lb/>obiets qui leur sont pr&eacute;sent&eacute;s, et leur partie oppos&eacute;e &agrave; la lumiere paroit <lb/>d'un jaune dor&eacute;, ce qui fait voir qu'ils sont remplis d'une humeur traspa&shy;<lb/>rente, laquelle se s&eacute;che ais&eacute;ment. </s>

<s>Ces remarques sont assez suffisantes, comme <lb/>il dit, pour nous persuader que ce sont des yeux &rdquo; (Collection acad., T. </s>

<s>I <lb/>cit., pag. </s>

<s>397). </s></p><p type="main">

<s>Non tutti per&ograve;, nemmen nella stessa Accademia parigina, ingerirono <lb/>questa persuasione. </s>

<s>Uno anzi de'pi&ugrave; valorosi fra loro neg&ograve; ogni probabilit&agrave; <lb/>che i cristallini globi grandi e piccoli, o i cos&igrave; detti <emph type="italics"/>occhi<emph.end type="italics"/> e gli <emph type="italics"/>ocelli<emph.end type="italics"/> fos&shy;<lb/>sero negl'insetti occhi veri. </s>

<s>Claudio Perrault infatti terminava con queste <lb/>parole il cap. </s>

<s>I della I parte della Meccanica animale, proponendosi di di&shy;<lb/>mostrar che gl'insetti non hanno che un senso solo: &ldquo; Pour ce qui est des <lb/>parties qu'on d&eacute;couvre dans les insectes avec le microscope, qui paroissent <lb/>&ecirc;tre des yeux, et dont on en void trois sur la t&ecirc;te des mouches, et plus de <lb/>cent sur celle des Scorpions, on n'est point convaincu qu'elles soient des <lb/>yeux veritables &rdquo; (Oeuvres, T. </s>

<s>I cit., pag. </s>

<s>338). </s></p><p type="main">

<s>Il senso unico di che dice il Perrault esser dotati gl'insetti &egrave; quello <lb/>del tatto, il quale &egrave; per&ograve; in essi tanto squisito, che supera ogni nostra im&shy;<lb/>maginazione. </s>

<s>Quando le mosche per esempio entrano in una cucina o in <lb/>una camera aperta non &egrave; la luce che serve a loro di scorta, ma il tiepor <lb/>dell'ambiente; e cos&igrave; non &egrave; punto lo splendore, che attrae le farfalle, ma <lb/>il calor della fiamma. </s>

<s>Le stesse percezioni, prosegue a dire il Perrault, che <lb/>da noi si ricevono per il senso dell'odorato, gl'insetti lo ricevono per via <lb/>del tatto, come per esempio le mosche, che par sien tratte da gran distanza <lb/>all'odore de'putrescenti carcami, o le formiche, a cui par che in fin gi&ugrave; <lb/>ne'riposti nidi giunga il lontano odore del grano. </s>

<s>&ldquo; Or quoique toutes ces <lb/>especes d'animaux ne paroissent pas seulement avoir l'usage de l'odorat, mais <lb/>qu'il semble aussi qu'ils voyent et qu'ils entendent, il est n&eacute;anmoins, ce me <pb xlink:href="020/01/1617.jpg" pagenum="492"/>semble, plus aise de comprendre que la delicatesse de leur toucher peut <lb/>suffire &agrave; toutes ces connoissances; car tous les obiets des sens differens ne <lb/>se pouvant faire connoitre que par un certain mouvement particulier qui <lb/>les rend sensibles, il me semble qu'il n'est pas difficile de concevoir que les <lb/>insectes, qui sont tres petits, et qui par consequent ont les particules dont <lb/>l'organe de leur sens est compos&eacute; plus petites, et formant une substance, <lb/>s'il faut ainsi dire, beaucoup plus fine que dans les grands animaux, ce sens <lb/>est plus ais&eacute;ment &eacute;m&ugrave; par le mouvement des obiects quelque delicat qu'il <lb/>puisse &ecirc;tre, et tout d'une autre maniere que dans les grands animaux, ou <lb/>le toucher ne peut &ecirc;tre &eacute;branl&egrave; que par des mouvemens d'une grandeur <lb/>considerable: et que de m&egrave;me qu'un mouvement, qui ne fait qu'emouvoir <lb/>legerement le toucher d'un grand animal, est capable d'&eacute;craser un insecte, <lb/>il est croyable que ce qui &eacute;meut sensiblement un insecte ne cause aucun <lb/>sentiment &agrave; un grand animal &rdquo; (ivi, pag. </s>

<s>337, 38). </s></p><p type="main">

<s>L'elegante novit&agrave; di queste dottrine ebbe grande efficacia sulle menti <lb/>degli Entomologi, non solo in Francia, ma anche fra noi, dove il Vallisnieri, <lb/>disertando per un momento dalla scuola del Malpighi, inclinava col Perrault <lb/>a credere che negli insetti al senso particolar della vista soccorresse quello <lb/>universale del tatto. </s>

<s>&ldquo; Il vedere delle lumache, scriveva, e di molti vermi e <lb/>insetti &egrave; diverso dal nostro, e non consiste che nell'allungamento delle loro <lb/>pieghevoli corna, o in altri di certe antenne, che fan l'uffizio di spiare e <lb/>sentire col tatto la qualit&agrave; degli oggetti che incontrano &rdquo; (Esperienze ed <lb/>osservaz. </s>

<s>cit., pag. </s>

<s>107). </s></p><p type="main">

<s>Chi conosce l'indole del Vallisnieri, e il riverente amore che portava <lb/>al suo celebre Maestro, facilmente comprende che se non convenne con lui <lb/>essere i globuli trasparenti maggiori e minori nel bruco e nella farfalla del <lb/>Bombice occhi veri, ci&ograve; dovett'essere per alcune forti ragioni. </s>

<s>Di dire in&shy;<lb/>fatti queste ragioni non manc&ograve; esso Vallisnieri ne'suoi <emph type="italics"/>Dialoghi,<emph.end type="italics"/> nelle sue <lb/><emph type="italics"/>Osservazioni intorno alla generazione dei vermi,<emph.end type="italics"/> e pi&ugrave; di proposito nella <lb/><emph type="italics"/>Storia della nascita del verme nel naso delle pecore,<emph.end type="italics"/> dentro gli occhi del <lb/>qual verme &ldquo; osservai, scrive nella lettera a Giacinto Gemma sopra questo <lb/>argomento, con mio stupore una selva regolatissima di peli, che spuntava <lb/>fra l'uno e l'altro interstizio dalle graticole, il che pure notai negli occhi <lb/>di molti altri insetti, strabiliando come la sagacissima Natura offuschi di peli <lb/>un organo s&igrave; delicato e gentile, quando proviamo che un solo bruscolo cos&igrave; <lb/>stranamente l'intorbida. </s>

<s>N&egrave; &egrave; sola questa mosca, cui si veggano i peli negli <lb/>occhi suoi, mentre molti moscioni, certe api, alcune farfalle ed altri insetti gli <lb/>hanno manifestamente carichi de'medesimi. </s>

<s>Quindi fu che allora sospettai <lb/>se veramente fossero occhi &rdquo; (ivi, pag. </s>

<s>106). Un'altra ragione veniva a con&shy;<lb/>fermare il sospetto del Vallisnieri, ed era che di que'globi, onorati col titolo <lb/>di occhi, son forniti anche alcuni insetti, i quali, standosene continuamente <lb/>immobili e al buio, non par perci&ograve; che abbiano bisogno di vedere (pag. </s>

<s>108). </s></p><p type="main">

<s>In questo medesimo tempo che il Vallisnieri in Italia attendeva a de&shy;<lb/>molire l'edifizio fondato dall'Hodierna, il Leeuwenoeck in Olanda lo rimet-<pb xlink:href="020/01/1618.jpg" pagenum="493"/>teva in onore, istituendo nuove regole, con l'aiuto di dotti geometri amici <lb/>suoi, per computar pi&ugrave; giusto il numero delle cornee oculari ridotte nella <lb/><emph type="italics"/>Mordella<emph.end type="italics"/> a 25,088. &ldquo; Sequitur Mordellam oculis 25,088 instructam esse. </s>

<s>Qui <lb/>numerus expectationem meam longe exsuperat, nam de muscarum oculis <lb/>disserens singulis illarum tunicis oculos inesse quater mille, atque adeo sin&shy;<lb/>gulas muscas octo oculorum millibus praeditas esse statuebam &rdquo; (Epist. </s>

<s>phy&shy;<lb/>siologicae, Delphis 1719, pag. </s>

<s>343). </s></p><p type="main">

<s>In questi calcoli supponeva il Leeuwenoeck che il maraviglioso organo <lb/>contemplato servisse alla vista, indottovi dall'analogia e dalle prime tradi&shy;<lb/>zioni della scienza, diffuse al di la dei monti dall'Hooke, con pi&ugrave; gagliardo <lb/>impulso che dall'Hodierna. </s>

<s>Ma poi vennero a dimostrargli il supposto certe <lb/>osservazioni, dalle quali appariva essere una pi&ugrave; intima somiglianza anche <lb/>nelle parti fra l'occhio degl'insetti e quello degli animali superiori. </s>

<s>&ldquo; Post <lb/>haec oculos Mordellae attentius quam ante visu examinavi, et singulis ocu&shy;<lb/>lis exiguam maculam eamque translucidam, imo reliquis oculi partibus longe <lb/>lucidiorem inesse, animadverti..... Quod si istam oculorum fabricam cum <lb/>hominis et reliquorum animalium oculis conferamus, et corneas horum ocu&shy;<lb/>lorum tunicas a partibus inferioribus separatas intueamur, nonne locum il&shy;<lb/>lum rotundum, sive pupillam in humano oculo, quae radium opticum tran&shy;<lb/>smittit, lucidiori quam dixi maculae respondere fatebimur? </s>

<s>Brevi, quidquid <lb/>artificii atque perfectionis oculis inest maiorum animalium, etiam inest <lb/>oculis minorum, licet in his, ob partium exiguitatem, visui nostro inconspi&shy;<lb/>cuum &rdquo; (ibid., pag. </s>

<s>345). </s></p><p type="main">

<s>E in verit&agrave; scopertasi dal Leeuwenoeck la pupilla, come s'erano dallo <lb/>Swammerdam scoperti il nervo ottico e la retina, sembrava ragionevolissimo <lb/>l'inferirne che s'avessero a riscontrar negli occhi degli insetti anche le altre <lb/>parti corrispondenti a quelle degli animali maggiori, bench&egrave; riuscissero per <lb/>la loro esiguit&agrave; invisibili a qualunque potenza di microscopi. </s>

<s>Il Vallisnieri <lb/>stesso, se non rimase da questi argomenti persuaso, rallent&ograve; nulladimeno <lb/>l'arco al suo dubbio, com'apparisce dalle seguenti espressioni uscitegli dalla <lb/>penna nel 1721, nel descriver la <emph type="italics"/>Storia della generazione dell'uomo.<emph.end type="italics"/> &ldquo; E <lb/>se &egrave; vero che questi insetti abbiano un'infinit&agrave; di occhi, come ne induce <lb/>la figura e il sito di quelle membrane lucide e graticolate, e che a guisa <lb/>di tante finestrelle pare che ricevano il lume da tutte le parti; qual picco&shy;<lb/>lezza averanno le immagini in questi innumerabili specchi a faccette? </s>

<s>&rdquo; <lb/>(Opere, T. II, Venezia 1733, pag. </s>

<s>206). </s></p><p type="main">

<s>Il Reaumur poi, quel veramente <emph type="italics"/>princeps insectorum historicus,<emph.end type="italics"/> come <lb/>all'Haller amico suo piacque di salutarlo (Bibliotheca an., T. II, Tiguri 1777, <lb/>pag. </s>

<s>61), colle ragioni e colla eloquenza fin&igrave; cos&igrave; di dissipare le ombre, che <lb/>parve chiara agli occhi di tutti la luce, quando la videro come da specchio <lb/>riflessa dalla Memoria IV del citato Tomo I per servire alla storia degl'in&shy;<lb/>setti. </s>

<s>Ivi richiamasi dall'Autore l'attenzione de'suoi lettori sulla spattacolosa <lb/>esperienza del Catelan ripetuta dal Leeuwenoeck e dal Puget, i quali, avendo <lb/>prima estratta e poi ben ben rinettata la cornea di un insetto, &ldquo; ont mis <pb xlink:href="020/01/1619.jpg" pagenum="494"/>et tenu cette corn&eacute;e au foyer d'un microscope, qu'ils ont dirig&eacute; ensuite vers <lb/>quelque obiet, de maniere que les rayons qu'il envoyoit a leurs yeux, pas&shy;<lb/>soient par cette corn&eacute;e, et par la lentille du microscope. </s>

<s>Il faut lire dans <lb/>M. </s>

<s>Puget m&ecirc;me la description du spectacle qu'il se donnoit, et qu'il don&shy;<lb/>noit &agrave; tous ceux qui vouloient avec lui admirer la Nature. </s>

<s>La corn&eacute;e poin&shy;<lb/>t&eacute;e vis-a-vis un seul soldat faisoit voir une arm&eacute;e de pigm&eacute;es: point&eacute;e vers <lb/>le arches d'un pont, elle montroit une quantit&eacute; de rangs d'arches les unes <lb/>au-dessus des autres, qui surpassoit de beaucoup tout ce qui a jamais &eacute;t&eacute; <lb/>entrepris de plus grand pour la conduite des eaux. </s>

<s>La lumiere d'une bou&shy;<lb/>gie se multiplioit prodigieusement. </s>

<s>Jamais on n'avra de verres &agrave; faccettes qui <lb/>multiplient autant les obiets, que ces corn&eacute;es les moltiplient &rdquo; (pag. </s>

<s>265, 66). </s></p><p type="main">

<s>Proseguendo il Reaumur a descrivere eloquentemente la maravigliosa <lb/>struttura di queste cornee, all'ultimo poi esclama: a che usar la Natura <lb/>tanto sottil magistero se non a lavorare un qualche organo del senso? </s>

<s>&ldquo; Et <lb/>&agrave; quelle sensation, dont nous ayons quelque id&eacute;e, sont n&eacute;cessaires des len&shy;<lb/>tilles transparentes, des crystallins, qu'a celle de la vue? </s>

<s>&rdquo; (ivi, pag. </s>

<s>268). <lb/>Si fanno contro questo argomento alcune difficolt&agrave;, e quella cos&igrave; poderosa&shy;<lb/>mente messa in campo dal Vallisnieri, quand'ebbe scoperto esser gli occhi <lb/>degl'insetti tutti ispidi e ingombri di peli, &egrave;, dice il Reaumur, <emph type="italics"/>une obiection <lb/>assez forte.<emph.end type="italics"/> &Egrave; vero per&ograve;, poi soggiunge, che quella selva di peli ingombre&shy;<lb/>rebbe la vista, quando fosse un occhio solo, ma essendo pi&ugrave; occhi distinti <lb/>quegli stessi peli, che s'interpongono fra gli uni e gli altri, forse fanno l'uf&shy;<lb/>ficio di tante piccole palpebre. </s>

<s>In ogni modo &egrave; certo che &ldquo; ces poils qui <lb/>s'elevent perpendicolairement sur le globe n'emp&eacute;chent pas des rayons d'ar&shy;<lb/>river &agrave; chaque petit oeil, &agrave; chaque crystallin &rdquo; (ivi, pag. </s>

<s>272). </s></p><p type="main">

<s>Passando poi da queste generalit&agrave;, nel Tomo IV delle dette Memorie e <lb/>altrove, il Reaumur a descrivere particolarmente gli occhi di alcuni insetti, <lb/>fu primo a introdurre, in grazia del pi&ugrave; chiaro e pi&ugrave; spedito linguaggio, le <lb/>denominazioni di occhi <emph type="italics"/>a rezeau<emph.end type="italics"/> e di occhi <emph type="italics"/>lisci,<emph.end type="italics"/> date ai globi cristallini mag&shy;<lb/>giori e minori. </s>

<s>Il Bonnet adott&ograve; nella <emph type="italics"/>Contemplazione della Natura<emph.end type="italics"/> questo <lb/>stesso linguaggio, che fu dallo Spallanzani tradotto in <emph type="italics"/>occhi a zigrino<emph.end type="italics"/> (T. </s>

<s>I <lb/>cit., pag. </s>

<s>81). E in nota, a pi&egrave; della pagina ora citata e delle due seguenti, <lb/>si trattien brevemente il Traduttore intorno alla questione se quegli sieno <lb/>occhi veri, dove, dop'avere accennato all'esperienza della benda fatta dallo <lb/>Swammerdam sopra le mosche, e dal Reaumur ripetuta sopra le pecchie, <lb/>conclude all'ultimo cos&igrave; il suo discorso: &ldquo; Siccome poi non solo i segmenti <lb/>emisferici, ma anche i piccoli corpi lisci sono in tutto soggetti a pari vi&shy;<lb/>cende, quindi si ha solido fondamento di concludere che, non meno gli uni <lb/>che gli altri sieno negl'insetti il verace organo della vista &rdquo; (pag. </s>

<s>83). </s></p><p type="main">

<s>Furono poi, dopo tante passate vicende, coronate le scoperte dell'Ho&shy;<lb/>dierna e del Malpighi del pacifico alloro della vittoria, quando l'Haller in&shy;<lb/>segn&ograve; dall'alto della sua cattedra constare per esperienza i due grandi re&shy;<lb/>ticolati e i tre pi&ugrave; piccoli globi posti in fronte alle mosche &ldquo; veros esse et <lb/>ad videndum aptos oculos &rdquo; (Elem. </s>

<s>Physiol., T. </s>

<s>V cit., pag. </s>

<s>308), e quando, <pb xlink:href="020/01/1620.jpg" pagenum="495"/>colla medesima autorit&agrave; di magistero, descrisse cos&igrave; l'organo della vista nel&shy;<lb/>l'ape maggiore, da mostrar che nulla a lui manca in sostanza per doverlo <lb/>rassomigliare all'occhio stesso di un animale perfetto (ivi, pag. </s>

<s>390). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Questi sopra narrati progressi fatti col potente aiuto del microscopio, <lb/>nella storia naturale degl'insetti, furono, chi ben ripensa, i pi&ugrave; efficaci ar&shy;<lb/>gomenti da persuadere in tutto coloro, ne'quali fosse ancora rimasto qual&shy;<lb/>che piccolo dubbio intorno alla generazione di quegl'infimi animali. </s>

<s>Impe&shy;<lb/>rocch&egrave;, rivelando le microscopiche osservazioni all'occhio maravigliato dei <lb/>Naturalisti organi inservienti alla vita vegetativa e a quella di relazione, non <lb/>punto meno elaborati negli spregiati automi, che negli animali stimati pi&ugrave; <lb/>perfetti; dalla riconosciuta nobilt&agrave; della vita veniva giusta ragion di credere <lb/>alla nobilt&agrave; dell'origine. </s></p><p type="main">

<s>Essendosi nonostante scoperta, col benefizio del medesimo diottrico stru&shy;<lb/>mento, un'altra popolazion di animali, l&agrave; dove non si sarebbe aspettato nes&shy;<lb/>suno che fosse segno di vita, ritornarono le peripatetiche ipotesi, con tante <lb/>e s&igrave; valorose armi cacciate via dal campo entomologico, ad applicarsi a spie&shy;<lb/>gar la misteriosa generazione di questi nuovi viventi. </s>

<s>L'irrequieto insorgere <lb/>di costoro, che non s'erano ancora saputi terger l'ingegno dall'appiccatic&shy;<lb/>cia pece aristotelica, fu ben presentito dall'acutissimo Huyghens, quando, <lb/>alla descrizione degl'infusorii del pepe fatta in una lettera indirizzata all'Au&shy;<lb/>tore del Diario parigino, soggiunse: &ldquo; Quis forte defendet animalcula haec <lb/>corruptione aut fermentatione generari &rdquo; (Opera varia, T. IV, Lugd. </s>

<s>Ba&shy;<lb/>tav. </s>

<s>1724, pag. </s>

<s>764). </s></p><p type="main">

<s>S'incominciarono infatti poco dopo a elaborare que'filosofici sistemi, <lb/>ne'quali rimettevansi in onore gli <emph type="italics"/>archei<emph.end type="italics"/> dell'Helmont, o i <emph type="italics"/>primordii<emph.end type="italics"/> del&shy;<lb/>l'Harvey sotto il nuovo nome di <emph type="italics"/>forze plastiche<emph.end type="italics"/> o di <emph type="italics"/>forze attive,<emph.end type="italics"/> in virt&ugrave; <lb/>delle quali in ogni modo asserivano il Nehedam e il Buffon che si generas&shy;<lb/>sero gli animalucci delle infusioni. </s>

<s>Lo Spallanzani fece rispetto a questi quel <lb/>che avea fatto il Redi gi&agrave; rispetto agl'insetti, e poniamo che fosse nell'arte <lb/>sperimentale il valore dei due Naturalisti pari, parve nulladimeno il Profes&shy;<lb/>sor di Pavia rimanere indietro al Medico aretino, per aver forse troppo con&shy;<lb/>fidentemente creduto che il meccanico agitarsi dalle particelle, scioltesi dalle <lb/>materie infuse, fosse un moto vivace. </s></p><p type="main">

<s>Ma perch&egrave; non &egrave; lo scopo nostro quello di entrare in questioni, non <lb/>bene ancora definite o forse non definibili mai dalla scienza, faremo sog&shy;<lb/>getto alla nostra storia un genere di animali, ch'&egrave; per tale oggid&igrave; ben ri&shy;<lb/>conosciuto, e che sta quasi di mezzo fra gl'insetti propriamente detti e gli <pb xlink:href="020/01/1621.jpg" pagenum="496"/>infusorii; genere di animali ministro di quel lampeggiare di luce sull'agi&shy;<lb/>tata acqua marina, che fu un giorno il tormento della Filosofia antica, ed &egrave; <lb/>ora una gloria della moderna. </s>

<s>L'esser poi questa gloria italiana ci ha con&shy;<lb/>sigliato a scegliere, fra'tanti altri che ci si presentavano innanzi, e tutti me&shy;<lb/>ritevoli di storica trattazione, questo argomento, e a farlo risalire in fin l&agrave;, <lb/>dove incomincia a ingrossare la sua sorgente. </s></p><p type="main">

<s>Volendo il Cartesio porre i principii della Filosofia a tutte le cose, an&shy;<lb/>che pi&ugrave; difficili a intendersi nella loro natura, com'&egrave; la luce, non lascia <lb/>d'adoprar la magica chiave del suo sistema ad aprire il mistero della fosfo&shy;<lb/>rescenza marina. </s>

<s>Egli si confida di riuscirvi con gran facilit&agrave;, dicendo che <lb/>le particelle rigide componenti l'acqua, escono agili, commosse dalla tempe&shy;<lb/>sta, a cacciare i globuli del secondo elemento, e cos&igrave; senz'altro producono <lb/>quell'apparenza di luce. </s>

<s>&ldquo; At in guttis aquae marinae, cuius naturam supra <lb/>explicuimus, facile est videre quo pacto lux excitatur. </s>

<s>Nempe dum illae <lb/>earum particulae, quae sunt flexiles, sibi mntuo manent implexae, aliae, quae <lb/>sunt rigidae ac laeves, vi tempestatis alteriusve cuiuslibet motus, ex gutta <lb/>excutiuntur et, spiculorum instar vibratae, facile ex eius vicinia globulos <lb/>secundi elementi expellunt, sicque lucem producunt &rdquo; (Principia Philos. </s>

<s><lb/>Amstelodami 1650, pag. </s>

<s>237). </s></p><p type="main">

<s>I Cartesiani avevano con gran docilit&agrave; imbevuta, insieme con le altre <lb/>dottrine del Maestro, anche questa, ma i ritrosi di professar quella perico&shy;<lb/>losa Filosofia confessavano piuttosto ingenuamente di non sapere intendere <lb/>come si potessero congiungere insieme due cos&igrave; contrari elementi, quali son <lb/>l'acqua e il fuoco. </s>

<s>Quel languido e fuggitivo splendore per&ograve; aveva, pi&ugrave; che <lb/>di fuoco vero e di vera luce, sembianza di luce riflessa, ond'&egrave; che il Bo&shy;<lb/>relli, ricercando alle specchiate immagini l'oggetto reale, riconobbe non si <lb/>potere in altro ritrovar che nelle stelle. </s>

<s>Troppo scarso nonostante parendo, <lb/>specie sotto ciel tempestoso, quel lume celeste, ricav&ograve; da certe sue sottilis&shy;<lb/>sime osservazioni sul vapore vescicolare, che parvero nuove ad alcuni mo&shy;<lb/>derni fisici stranieri, e da certe teorie ottiche apprese dagli scritti di Galileo <lb/>e dalla viva voce di Benedetto Castelli, la causa fisica della richiesta molti&shy;<lb/>plicazione di quel fosforo marino, che, viaggiando una notte da Messina a <lb/>Catania, ed essendoglisi reso pi&ugrave; che altre volte spettacoloso, lo indusse a <lb/>scriverne in questa forma a un amico: </s></p><p type="main">

<s>&ldquo; Del viaggio di Catania dovrei dir piuttosto i miei patimenti che l'os&shy;<lb/>servazioni fatte in quello, poich&egrave; io mi credevo sicuro di riportarne una in&shy;<lb/>fermit&agrave; pericolosissima, ma grazie a Dio me la sono passata con leggerissima <lb/>indisposizione. </s>

<s>Circa le osservazioni fatte nel navigare credo che mi sia suc&shy;<lb/>cesso l'avere intesa la cagione di un problema assai agitato, che &egrave;: onde <lb/>avvenga che nella notte pi&ugrave; oscura, percotendosi il mare con li remi, ci si <lb/>vede un fulgore assai notabile. </s>

<s>Egli &egrave; indubitatamente riflessione del lume <lb/>delle stelle, mentre nel battere i remi nell'acqua si conduce quantit&agrave; d'aria <lb/>nella profondit&agrave; d'essa acqua, la quale poi si risolve in minute particole, le <lb/>quali, circondate ognuna d'acqua, pigliano figura sferica, e vanno lentamente <pb xlink:href="020/01/1622.jpg" pagenum="497"/>ascendendo verso la superfice dell'aria. </s>

<s>E perch&egrave; da ognuna di queste sfe&shy;<lb/>rette si suol riflettere all'occhio il lume quasi di tutte le stelle, che ingom&shy;<lb/>brano il nostro emisfero, ne avviene che la riflessione di tutta questa mol&shy;<lb/>titudine di globetti, conducendosi all'occhio, fa apparenza notabile. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E ci &egrave; anco un altro particolare che, nello sbattere che si fa l'acqua, <lb/>risaltano in aria moltitudine grande di stille d'acqua, alcune delle quali, <lb/>com'ho io diligentemente osservato, non solo mentre volano per la profon&shy;<lb/>dit&agrave; dell'aria ritengono la figura sferica, ma anche arrivate che sono alla <lb/>superfice dell'acqua ritengono per qualche tempo la medesima figura, prima <lb/>che confondersi col rimanente dell'acqua, e ci&ograve; esser vero mi mostra il ve&shy;<lb/>dere sdrucciolare questi medesimi globetti d'acqua per qualche poco sopra <lb/>la superfice dell'altr'acqua. </s>

<s>Ora in questi, ne'quali non so se ci sia inclusa <lb/>parte d'aria, la riflessione si fa pi&ugrave; che in altro vivacissima in modo, che <lb/>appariscono talvolta tanti carboncini accesi. </s>

<s>Intorno a che credo che ancora <lb/>lavori l'accrescimento e moltiplicazione di lumi in essi globelti merc&egrave; della <lb/>rifrazione che si fa nel nostro occhio, come accade di tutti gli altri lumi <lb/>minuti, secondo la dottrina del Maestro. </s>

<s>Io non so se mi sono affrontato col <lb/>vero: lei parlando col padre don Benedetto se ne potr&agrave; assicurare ed avver&shy;<lb/>tirmene della fallacia &rdquo; (MSS. Cim., T. XXV, c. </s>

<s>151). </s></p><p type="main">

<s>A scoprir la fallace applicazione delle bellissime e importantissime os&shy;<lb/>servazioni fisiche qui descritte non c'era per verit&agrave; bisogno dell'acume di <lb/>un Benedetto Castelli, essendo sufficiente notar che il mare non solo fosfo&shy;<lb/>reggia, ma che fosforeggia anzi pi&ugrave; vivamente, quando il cielo &egrave; privato di <lb/>stelle. </s>

<s>Cosicch&egrave;, anche quando si fosse divulgata questa ipotesi del Borelli, <lb/>non avrebbe facilmente riportata l'approvazione dei Fisici, i quali si rima&shy;<lb/>sero perci&ograve; intorno al curioso problema incerti, infin tanto che le recenti <lb/>scoperte elettriche non vennero colla loro solita baldanza a proporre una <lb/>nuova soluzione. </s></p><p type="main">

<s>Era un fatto, oramai da lunghe e non dubbie osservazioni confermato, <lb/>che il fosforeggiare &egrave; proprio di sole le ondose acque del mare, le quali, <lb/>perciocch&egrave; non si differenziano dalle dolci se non per i bitumi e per i sali, <lb/>che tengono in s&egrave; disciolti; fu perci&ograve; facile a pensare nient'altro essere il <lb/>fosforo marino che una luce elettrica eccitata dal confricarsi insieme le par&shy;<lb/>ticelle solide coll'acqua stessa. </s>

<s>Fu primo a divulgare questo pensiero l'Inno&shy;<lb/>minato autore <emph type="italics"/>Dell'elettricismo,<emph.end type="italics"/> il quale, avendo di pi&ugrave; osservato che ri&shy;<lb/>splendono allora l'acque pi&ugrave; vivamente, quando l'aria soprastante &egrave; umida <lb/>e fredda, trov&ograve; in ci&ograve; una buona ragione da confermar la sua ipotesi col <lb/>dire ch'essa aria umida si trova meglio disposta ad elettrizzarsi per comu&shy;<lb/>nicazione, &ldquo; cio&egrave; pi&ugrave; pronta a ricevere in s&egrave; la materia elettrica, che scappa <lb/>fuori &rdquo; (Napoli 1747, pag. </s>

<s>227). </s></p><p type="main">

<s>Riuscirono ai Fisici di que'tempi queste dottrine cos&igrave; seducenti, che il <lb/>Franklin pens&ograve; di avvalorarle coll'esperienze. </s>

<s>Prese una bottiglia d'acqua, <lb/>v'infuse sal marino, e si dette ad agitare fortemente il miscuglio. </s>

<s>Non vide <lb/>per&ograve; farsi alcuna apparenza di luce, n&egrave; darsi altri segni di elettricismo, per <pb xlink:href="020/01/1623.jpg" pagenum="498"/>cui, ripetute l'esperienze stesse pi&ugrave; volte, e sempre trovandosi defraudato <lb/>della sua aspettazione, ebbe a concluderne che &ldquo; cette lumiere dans l'eau <lb/>de la mer devoit &ecirc;tre attribu&eacute;e &agrave; quelques autres principes &rdquo; (Oeuvres, T. I, <lb/>Paris 1773, pag. </s>

<s>116). </s></p><p type="main">

<s>In quel tempo, che si pronunziava in faccia alla giovanile umiliata bal&shy;<lb/>danza degli Elettricisti questa decisiva autorevole sentenza, Giuseppe Via&shy;<lb/>nelli, medico di Chioggia e diligente osservatore dei fatti naturali, che gli <lb/>presentava a studiare la patria laguna, aveva gi&agrave; scoperto quel principio di <lb/>natura tutt'affatto diversa dall'elettrica, e in cui diceva il Franklin doversi <lb/>ricercar la causa della fosforescenza marina. </s>

<s>&ldquo; In una notte della state <lb/>del 1746, cos&igrave; racconta il Vianelli stesso la storia della sua scoperta, rac&shy;<lb/>colsi con appropriato vaso buona quantit&agrave; d'acqua marina, ed in mia casa <lb/>avendola all'oscuro riposta, osservai che, dibattuta e colle mie mani sovente <lb/>agitata, di questa brillantissima luce andava ricolma. </s>

<s>Poich&egrave; per&ograve; la passai <lb/>per un panno lino ben tessuto, per quanto l'andassi scotendo ed insieme <lb/>agitando, nientissimo affatto di cotal luce mandava fuori. </s>

<s>Tutta bens&igrave; la pri&shy;<lb/>miera luce mi si rappresentava in minutissime particelle separata e divisa, <lb/>ed allo stesso panno lino attaccata. </s>

<s>Per la qual cosa ben francamente e fuor <lb/>d'ogni dubbio potrei persuadermi che i luminosi corpiccioli erano qualche <lb/>cosa totalmente distinta dall'acqua stessa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Mi rincrebbe allora altamente nell'animo di non trovarmi in pronto <lb/>un de'migliori vetri, che i piccoli oggetti vagliono ad ingrandire, per poter <lb/>subito farne paga la curiosit&agrave; mia, rilevando che cosa mai questi <emph type="italics"/>fisici enti<emph.end type="italics"/><lb/>si fossero. </s>

<s>Cosa certamente che a cagione della loro piccolezza non mi riu&shy;<lb/>sc&igrave; con occhio disarmato di potere ottenere giammai, quantunque ben a <lb/>lungo aguzzassi le ciglia <emph type="italics"/>come vecchio sartor fa nella cruna. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Frattanto, avendo posto mente che i risplendenti corpicelli erano pi&ugrave; <lb/>numerosi e vivaci sopra le foglie dell'alga marina, un'altra notte strappai <lb/>dal fondo dell'acque una pianta dell'alga stessa, la quale mi si di&egrave; subito <lb/>a divedere piena zeppa di questi brillantissimi lumicini. </s>

<s>Non ingrandisco <lb/>certo la cosa essendo che sopra una sola foglia di alga poteano contarsene <lb/>pi&ugrave; di trenta. </s>

<s>Scuoter poi volli la foglia stessa, lusingandomi di poter al&shy;<lb/>meno raccorne uno su d'una bianca carta, che per quest'uso avea apparec&shy;<lb/>chiata. </s>

<s>Essendo che mi stava molto a cuore di farlo vedere agli amici miei <lb/>pi&ugrave; cari, i quali dalle solite osservazioni mie mi stavano ansiosamente aspet&shy;<lb/>tando. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; N&egrave; dal divisato buon esito and&ograve; punto diversa la cosa. </s>

<s>Imperocch&egrave; <lb/>il luminoso corpicciolo sulla stessa carta raccolto, e fra le pieghe di quella <lb/>a bello studio nascosto, anche cos&igrave; rinserrato com'erasi diede agli astanti <lb/>tutti a conoscere per la sua vaga luce, che da'pori della carta mandava <lb/>fuori. </s>

<s>Del che poi ne potrebbe far certa testimonianza il signor Francesco <lb/>Cestari stimatissimo amico mio, e con esso lui moltissimi altri, che al gra&shy;<lb/>zioso spettacolo furon presenti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Dispiegata poi la carta medesima, e diligentemente il lucidissimo cor-<pb xlink:href="020/01/1624.jpg" pagenum="499"/>picciolo riguardando, venni a scoprire che nella sua mole eguagliava appena <lb/>la met&agrave; d'un sol pelo delle palpebre, che nel colore ad un croceo fosco <lb/>tendeva, e ch'era d'una assai tenera e fragil sostanza formato. </s>

<s>Buona sorte <lb/>per&ograve; che allor mi trovava provveduto di un ottimo Microscopio, che per <lb/>quest'uso a bella posta s'era compiaciuto d'inviarmi da Bologna l'erudi&shy;<lb/>tissimo signor dottore Pio Fantoni, dolcissimo amico mio, per mezzo del <lb/>quale potei rilevare che l'esaminato brillantissimo lumicino si era un ele&shy;<lb/>gante animaletto vivente. <emph type="italics"/>Io non potea da tal vista levarme,<emph.end type="italics"/> tanto egli mi <lb/>sembrava in tutte le sue parti e curioso e bizzarro. </s>

<s>E perciocch&egrave; sopra tutto <lb/>mi feriva la bella luce che tramandava fuori piacquemi di dargli il nome <lb/>di <emph type="italics"/>Cicindela<emph.end type="italics"/> o <emph type="italics"/>Luccioletta dell'acqua marina &rdquo;<emph.end type="italics"/> (Nuove scoperte ecc., Ve&shy;<lb/>nezia 1749, pag. </s>

<s>XVI-XX). </s></p><p type="main">

<s>Qui prosegue il Vianelli a descrivere la sua <emph type="italics"/>Luccioletta,<emph.end type="italics"/> ed &egrave; la de&shy;<lb/>scrizione illustrata da due figure, impresse a tergo della pag. </s>

<s>XI della citata <lb/>Dissertazione. </s>

<s>Il Grisellini poi, tessendo una storia particolare dell'insetto, <lb/>lo ridusse al genere delle Scolopendre, e gl'impose il nome di <emph type="italics"/>Scolopendra <lb/>marina lucens<emph.end type="italics"/> (Observat. </s>

<s>sur le Scolopendre marine luisante. </s>

<s>Vened. </s>

<s>1751). <lb/>Torn&ograve; meglio provata da questa storia naturale l'esistenza e la natura del <lb/>lucente insetto marino, cos&igrave; felicemente scoperto, ma perch&egrave; si potesse ra&shy;<lb/>gionevolmente attribuire a lui, come a causa unica ed efficiente, la fosfore&shy;<lb/>scenza della Laguna, rimaneva a sodisfare ancora a queste due domande: <lb/>prima perch&egrave; non fosforeggino altro che le acque del mare, e poi perch&egrave; <lb/>per lo pi&ugrave; non fosforeggino quell'acque stesse, se non che quando, o ad <lb/>arte come nel menare dei remi, o naturalmente, come nelle burrasche, ven&shy;<lb/>gano agitate e sconvolte. </s></p><p type="main">

<s>Il Vianelli, studiando la storia naturale degl'insetti scoperti, trov&ograve; modo <lb/>a rispondere adeguatamente ai due proposti quesiti, dimostrando che quei <lb/>marini animalucci non possono affatto vivere nell'acque dolci, e che non <lb/>mandan luce al di fuori de'loro corpiccioli, se non che quando o da in&shy;<lb/>terne passioni o da esterni stimoli vengano in qualche modo irritati, cosic&shy;<lb/>ch&egrave; cessano di rappresentare il grazioso spettacolo, quando son morti. </s>

<s>Una <lb/>delle pi&ugrave; concludenti fra le dimostrazioni sperimentali di questi fatti vien <lb/>cos&igrave; dall'Autore stesso descritta in una sua lettera indirizzata da Chioggia, <lb/>ai d&igrave; 10 Settembre 1751, al conte Lodovico Barbieri: &ldquo; Ella avr&agrave; rilevato <lb/>di gi&agrave; dalla mia <emph type="italics"/>Dissertazione<emph.end type="italics"/> che questi piccoli viventi sono luminosi per <lb/>una certa agitazione o dibattimento delle parti de'corpiccioli loro, e che <lb/>qualora si stanno quieti non mandano splendore di sorte. </s>

<s>Io adunque strap&shy;<lb/>pai dal fondo della laguna buona quantit&agrave; d'alga pienissima di questi bril&shy;<lb/>lantissimi insetti, e parte ne immersi subito in un vaso d'acqua di fiume, <lb/>e parte in un altro d'acqua marina. </s>

<s>Quella del primo vaso, appena che fu <lb/>attuffata nell'acqua dolce, si fece luminosissima e costantemente per cinque <lb/>minuti conserv&ograve; sempre la luce. </s>

<s>Se non che la luce medesima s'andava <lb/>illanguidendo a poco a poco; e per modo che in cinque minuti s'estinse <lb/>affatto. </s>

<s>Cosa che non mi successe di gi&agrave; nell'altr'alga posta nel secondo vaso <pb xlink:href="020/01/1625.jpg" pagenum="500"/>d'acqua di mare, la quale si facea luminosa sol quando o io agitava l'acqua, <lb/>o gli animaletti da se s'agitavano, il che io ho potuto notare persino il giorno <lb/>dappoi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che pare a Lei, illustrissimo signor mio, di questo grazioso feno&shy;<lb/>meno? </s>

<s>Non si vede forse chiaramente che, dalla luce che mandano inces&shy;<lb/>santemente le Lucciolette nell'acqua dolce, sono in una continua molestis&shy;<lb/>sima agitazione? </s>

<s>Che a misura che questo molesto ed improprio soggiorno <lb/>nell'acqua dolce va togliendo loro la vita, vanno elleno svenendo e perdendo <lb/>co'vitali moti la luce? </s>

<s>Non si vede forse, replico, fuor d'ogni dubbio che <lb/>quelle povere bestiole nello spazio di cinque minuti si rimangono estinte <lb/>nell'acqua dolce? </s>

<s>Io per me ne sono certo e persuaso del tutto. </s>

<s>E tanto pi&ugrave; <lb/>perciocch&egrave; se, estinta che sia nell'acqua dolce la luce dell'alga, si voglia <lb/>tornare ad immergere l'alga stessa nell'acqua salsa, ella non acquista pi&ugrave; <lb/>i primieri lumicini; segno evidentissimo che gli animaletti che cagionavano <lb/>la luce sono di gi&agrave; morti &rdquo; (Calogera, Raccolta di opuscoli, T. XLVII, Ve&shy;<lb/>nezia 1752, pag. </s>

<s>336-38). </s></p><p type="main">

<s>Nell'estate del 1749, quando avea gi&agrave; il Vianelli fatta da tre anni nelle <lb/>acque della Laguna la sua scoperta, soggiornava in Venezia il Nollet, il <lb/>quale, poco dopo ritornato a Parigi, raccont&ograve; a'suoi che, maravigliato di <lb/>veder la notte lampeggiar l'onde nel frangersi che facevano contro le mura <lb/>de'palazzi veneti, e datosi a investigar di ci&ograve; la ragione, scoprisse che di&shy;<lb/>pendeva da certi minutissimi insetti, de'quali trov&ograve; gremite le foglie del&shy;<lb/>l'alga. </s>

<s>E perch&egrave; s'era anche prima compiaciuto di una tale scoperta, nella <lb/>stessa Venezia, in casa il cardinale Quirini, e il Vianelli lo riseppe, nel pub&shy;<lb/>blicar quella sua Dissertazione intitolata <emph type="italics"/>Nuova scoperta intorno le luci not&shy;<lb/>turne delle acque marine, Venezia 1749,<emph.end type="italics"/> si lasci&ograve; nella prefazione uscir <lb/>dalla penna certe parole che venivano ad accusare il Nollet stesso di usur&shy;<lb/>patore. </s>

<s>Dop'avere ivi scritto esso Vianelli che non s'era in tre anni riso&shy;<lb/>luto ancora di stampar nulla, in proposito degli scoperti insetti fosforici, <lb/>impaurito dalle difficolt&agrave; che s'incontrano da tutti coloro, i quali espongono <lb/>al pubblico giudizio i loro scritti; &ldquo; se non che, soggiunge, attrovandosi ai <lb/>passati mesi in Venezia il celebre signor abate Nollet, chiaro ornamento dei <lb/>Letterati francesi, e portando la congiuntura che seco lui tra'virtuosi col&shy;<lb/>loqui s'intertenesse il nobil'uomo signor Girolamo Giustiniani, al quale in <lb/>tempo del sempre glorioso suo reggimento di Chioggia essa scoperta mia <lb/>avea appalesata; egli non si rec&ograve; a vile di umanamente ad esso signor Nol&shy;<lb/>let significarla, invitandomi poscia con un molto cortese foglio perch&egrave; io vo&shy;<lb/>lessi delle osservazioni mie qualche memoria recarne. </s>

<s>Posto adunque ogni <lb/>riguardo da parte, mi sono indotto, qualunque egli sia, esso scoprimento <lb/>mio a pubblicare &rdquo; (Nuove scoperte cit., pag. </s>

<s>X). </s></p><p type="main">

<s>Ma il Nollet, che pretendeva d'essersi incontrato nella scoperta mede&shy;<lb/>sima del Vianelli, senz'averne avuto precedente avviso, nella XV delle <emph type="italics"/>Le&shy;<lb/>zioni di Fisica<emph.end type="italics"/> che &egrave; <emph type="italics"/>Della luce,<emph.end type="italics"/> accennando l'Autore ad alcuni insetti, che <lb/>consolan di lei infin le cupe acque del mare, &ldquo; una gran quantit&agrave; se ne <pb xlink:href="020/01/1626.jpg" pagenum="501"/>vede, egli ivi scrive, sopratutto nelle lagune di Venezia, dovunque vi ha del <lb/>muschio o di quell'erba, che <emph type="italics"/>alga marina<emph.end type="italics"/> vien detta. </s>

<s>Quivi ne feci la sco&shy;<lb/>perta nel 1749, dopo di avere con grandissima sollecitudine ed assiduit&agrave; ri&shy;<lb/>cercato qual esser potesse la cagione di tanti fuochi, ch'io vedeva brillar la <lb/>sera sotto a'colpi de'remi, all'incontro delle gondole, e lungo le mura per&shy;<lb/>cosse da'flutti. </s>

<s>Io era gi&agrave; stato prevenuto, come il seppi dappoi, dal signor <lb/>Vianelli, dottore di medicina in Chioggia. </s>

<s>Si pu&ograve; vedere in un libretto, da <lb/>lui fatto stampare in Venezia alcuni mesi dopo la mia partenza, ed invia&shy;<lb/>tomi dopo il mio ritorno in Francia. </s>

<s>In leggendo la prefazione di quest'ope&shy;<lb/>retta a pag. </s>

<s>10, potrebbe creder taluno che, in seguito alla relazione fattami <lb/>della scoperta del signor Vianelli, io avessi riconosciuto che la luce notturna <lb/>dell'acqua di Venezia veniva cagionata dagl'insetti. </s>

<s>Ma la verit&agrave; si &egrave; che la <lb/>detta relazione non mi fu fatta se non dopo la mia osservazione, in casa <lb/>dell'emin. </s>

<s>cardinal Quirini, ed alla presenza di otto o dieci persone, che me <lb/>ne renderebbono all'occorrenza bonissima testimonianza. </s>

<s>Io son certo che <lb/>il signor Vianelli m'avrebbe risparmiate queste parole, s'egli avesse saputo <lb/>in qual modo eran passate le cose. </s>

<s>Anzi l'avrei taciute io medesimo, quando <lb/>non avessi altro interesse che quello di conservarmi la parte, che posso avere <lb/>in questa scoperta. </s>

<s>Ma mi preme assaissimo che non si creda ch'io me l'ab&shy;<lb/>bia voluta appropriare, come ragion si avrebbe di pensare, se fosse vero <lb/>ch'io ne fossi stato istruito prima di osservare gl'insetti luminosi, e se, <lb/>quando feci menzione della mia scoperta, nelle Memorie dell'Accademia delle <lb/>scienze, 1759, pag. </s>

<s>50, non avessi resa sopra di ci&ograve; quella giustizia, che al <lb/>signor Vianelli si deve &rdquo; (Nollet, Lez. </s>

<s>di Fisica sperim., traduz. </s>

<s>ital., T. V, <lb/>Venezia 1762, pag. </s>

<s>20, 21). </s></p><p type="main">

<s>Dietro queste pubbliche e solenni dichiarazioni, che senza prove in con&shy;<lb/>trario nessuno ha ragionevole diritto di credere menzognere, le accuse date <lb/>da alcuni scrittori italiani al Nollet sembrano a noi simili al prurito nella <lb/>gola di certi avvocati, che si fanno merito collo strepitoso declamare nella <lb/>causa dalle stesse parti gi&agrave; risoluta. </s>

<s>Che fosse poi la ragion del primato fra <lb/>gli stessi inventori gi&agrave; risoluta, non le parole sole nei riferiti documenti lo <lb/>attestano, ma lo attestano altres&igrave;, ci&ograve; che pi&ugrave; importa, i fatti, non essendovi <lb/>nessuno, nemmeno fra gli stranieri, che dubitasse di riconoscere nella sco&shy;<lb/>perta de'fosforici insetti marini il primato del Vianelli. </s>

<s>Basti fra'pi&ugrave; cele&shy;<lb/>bri di questi stranieri citare Carlo Linneo, il quale, in un suo opuscolo in&shy;<lb/>titolato <emph type="italics"/>Noctiluca marina,<emph.end type="italics"/> incomincia a raccontare che, navigando per il <lb/>vasto e procelloso Mare chinese, si trovasse una notte co'compagni in mezzo <lb/>alle acque cos&igrave; scintillanti, <emph type="italics"/>ut si in undis et flammis igneis navigaverimus.<emph.end type="italics"/><lb/>Poi soggiunge che n&egrave; a lui n&egrave; a nessun altro era ancora riuscito di sco&shy;<lb/>prir la causa del portentoso spettacolo &ldquo; usque ad dominum Vianelli, qui <lb/>lumen hocce ex infinita minimorum vermium multitudine causari demon&shy;<lb/>stravit &rdquo; (Upsaliao 1752, pag. </s>

<s>4). E di qui coglie il grand'uomo occasione <lb/>a celebrare i Naturalisti italiani de'suoi tempi, non degeneri dalle virt&ugrave; dei <lb/>loro maggiori. </s></p><pb xlink:href="020/01/1627.jpg" pagenum="502"/><p type="main">

<s>Nacquero i dubbi piuttosto intorno alle applicazioni, che s'intendeva <lb/>fare della scoperta, dicendo alcuni che delle frequenti e vive luci dell'Oceano <lb/>non par che possano essere sufficiente causa que'piccoli insetti, i quali ba&shy;<lb/>stano ad accender l'acqua fra gli angusti lidi e i bassi fondi della veneta <lb/>laguna. </s>

<s>Uno de'primi fra noi ad accogliere questi dubbi fu il Beccaria, il <lb/>quale non rimase cos&igrave; vinto dall'esperienze francliniane, che disperasse di <lb/>potere attribuire all'elettricismo, fra le tante, anche questa nuova ingerenza <lb/>di render luminose le acque del mare, specialmente dell'India, di cui il <lb/>Bourgez aveva descritti di poco gl'insoliti splendori. </s>

<s>&ldquo; So bene (cos&igrave; scrive <lb/>in nota al cap. </s>

<s>VII della II parte dell'<emph type="italics"/>Elettricismo naturale<emph.end type="italics"/>) simile luce <lb/>comparire altrove ancora. </s>

<s>Cos&igrave; nel 1707, navigando io da Savona a Livorno, <lb/>avvenne che una corda, con che la nostra barca era raccomandata e veleg&shy;<lb/>giava d'accordo con un'altra barca, ogni volta che batteva l'acqua secondo <lb/>tutta la lunghezza splendeva, e dava una luce veramente elettrica. </s>

<s>So inol&shy;<lb/>tre che il diligente Vianelli da Chioggia ne ha esso il primo fatti divisare <lb/>gl'insetti, che nella laguna di Venezia eccitano di notte una simile luce, ma <lb/>dalla relazione del p. </s>

<s>Bourgez pare ne risulti che nell'Oceano tale luce sia <lb/>oltremodo frequente e viva, e che non debbasi altrimenti attribuire a simili <lb/>insetti &rdquo; (Torino 1753, pag. </s>

<s>217). </s></p><p type="main">

<s>Lo Spallanzani per&ograve;, prima di terminare il cap. </s>

<s>XXVII de'suoi <emph type="italics"/>Viaggi <lb/>alle due Sicilie,<emph.end type="italics"/> dove descrive le meduse fosforiche dello Stretto di Mes&shy;<lb/>sina, dal ragionar della luce, che manda fuori un marino animale, prende <lb/>occasione di commemorare le lucciole scoperte nella laguna veneta dal Via&shy;<lb/>nelli, e dice d'aver di esse lucciole scoperto altre cinque specie nel medi&shy;<lb/>terraneo, presso alla riviera di Genova. </s>

<s>Riferite poi le osservazioni proprie, <lb/>fatte intorno a queste nuove specie d'insetti, cos&igrave;, terminando il capitolo, <lb/>soggiunge: &ldquo; Intanto dalle riferite osservazioni concludo non essere la sola <lb/>laguna di Venezia albergatrice di questi minutissimi viventi fosforici, ma s&igrave; <lb/>ancora il Mare ligustico e quello della Sicilia, e per dirlo innanzi tratto <lb/>eziandio l'Arcipelago, il mare di Marmara, lo stretto di Costantinopoli <lb/>e il mar Nero, come apparir&agrave; dal mio <emph type="italics"/>Viaggio &rdquo;<emph.end type="italics"/> (Tomo III, Milano 1826, <lb/>pag. </s>

<s>38). </s></p><p type="main">

<s>Le scoperte dello Spallanzani insomma conferirono alla completa riso&shy;<lb/>luzione di quel problema avviato dal Vianelli, e per cui fu rivelato alla <lb/>scienza il mistero della fosforescenza dei mari. </s>

<s>Ma l'accresciuta famiglia degli <lb/>insetti splendenti accrebbe anche il desiderio di saper la causa e l'origine <lb/>di cotesti vivi splendori, ond'&egrave; che l'istituto della nostra storia ci consiglia <lb/>a trattenerci brevemente, per dire quali fossero le prime esperienze e le <lb/>prime notizie indi raccolte intorno a que'notissimi insetti che, svolazzando <lb/>nelle serate estive sui nostri campi, furono da qualche arguto ingegno ras&shy;<lb/>somigliati alle stelle di questo basso cielo. </s></p><p type="main">

<s>Abbiamo certissimi documenti che quelle prime esperienze sopra le luc&shy;<lb/>ciole terrestri furono istituite nell'Accademia del Cimento, in quell'ultimo <lb/>periodo, che non fu punto meno operoso degli altri, come basterebbero a <pb xlink:href="020/01/1628.jpg" pagenum="503"/>provarlo le cose che siam per dire, quando pure mancassero quegli argo&shy;<lb/>menti da noi altrove accennati. </s>

<s>L'occasione di sperimentare le lucciole nel <lb/>vuoto venne al cardinale Leopoldo dei Medici dalla notizia di una esperienza <lb/>del Boyle, diffusa in Italia dalla <emph type="italics"/>Gazzetta letteraria di Roma;<emph.end type="italics"/> la quale boie&shy;<lb/>liana esperienza consisteva nel sottoporre le carni fosforescenti di alcuni pe&shy;<lb/>sci alla campana della macchina pneumatica, e nel mostrar ch'estratta l'aria <lb/>si perde da esse carni ogni luminosa apparenza. </s>

<s>I nostri Accademici dun&shy;<lb/>que riscontrarono il fatto nel vuoto torricelliano, di che sodisfattissimo il <lb/>Principe dava la lieta nuova al Borelli, in una lettera scritta sulla fine del <lb/>Giugno 1669 e indirizzata a Messina. </s>

<s>Il Borelli rispondeva il seguente 2 Lu&shy;<lb/>glio: &ldquo; Rallegromi sommamente dell'esperienza del Boyle, che V. A. ha <lb/>fatto confrontare, la quale veramente &egrave; mirabile e di gran conseguenza &rdquo; <lb/>(MSS. Cim., T. XIX, c. </s>

<s>263). Ma perch&egrave;, non recapitata questa responsiva <lb/>a Firenze, il Principe dubit&ograve; fosse andata smarrita la sua missiva, torn&ograve; a <lb/>scrivere il d&igrave; 25 Luglio &ldquo; per ogni caso che fosse andata male una lettera <lb/>che le scrissi per saper nuova di sua salute e di quello che sta operando. </s>

<s><lb/>Scrivo parte delle stesse cose .... che sono il desiderio d'aver qualche par&shy;<lb/>ticolare informazione delli accidenti del fuoco di Catania. </s>

<s>In oltre le diedi <lb/>conto di una esperienza fatta in Inghilterra e rifatta qui da me, la quale &egrave; <lb/>che mettendosi un pezzetto di pesce o interiora di quelle ch'essendo vicine <lb/>a infradiciarsi fanno lume da s&egrave; stesse, dato il solito strumento del vacuo <lb/>e facendosi la consueta operazione di quello che comunemente si dice il <lb/>vacuo, il lume del pesce si perde, e facendo appresso un piccolo foro per <lb/>introdurvi l'aria, all'ingresso di quella, di nuovo ritorna a splendere il pez&shy;<lb/>zetto di pesce. </s>

<s>Ed io ho gi&agrave; fatto l'esperienza con un pezzetto di pesce <lb/>spada. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Mi venne poi in mente di fare l'esperienza stessa con le lucciole, le <lb/>quali ancora nel vuoto persero il lume. </s>

<s>&Egrave; ben vero che all'istante dell'in&shy;<lb/>trodursi dell'aria si allumin&ograve; per brevissimo tempo tutto il vaso, ed io du&shy;<lb/>bitando che questo splendore potesse procedere che, nel ricevere le lucciole <lb/>la consolazione del ritorno dell'aria, facessero moto nel quale scoprissero la <lb/>parte luminosa, rifeci l'esperienza, mettendo dentro nel vaso tutte le luc&shy;<lb/>ciole morte, e nondimeno successe l'istessa istantanea illuminazione del vaso <lb/>nell'atto dell'introdurre l'aria per il solito piccolo foro formato da uno spillo. </s>

<s><lb/>Or &egrave; da sapersi di pi&ugrave; che, dopo questa illuminazione, il lume che hanno <lb/>le lucciole &egrave; rimasto, sempre che si &egrave; fatta l'operazione, meno vivace, ma <lb/>con tale differenza che non si &egrave; potuto mettere in dubbio che non sia cos&igrave;. </s>

<s><lb/>Questa &egrave; una esperienza facile e galante, ma tale che io credo che meriti <lb/>che vi si faccia riflessione &rdquo; (MSS. Cim., T. XXIII, c. </s>

<s>171, 72). </s></p><p type="main">

<s>Che avesse il Boyle notizia di queste fiorentine esperienze non ci sono <lb/>n&egrave; prove n&egrave; congetture, ma &egrave; certo in ogni modo che l'esperienze inglesi <lb/>sopra le lucciole nel vuoto son di qualche anno posteriori alle nostre. </s>

<s>Si <lb/>trovano infatti non descritte prima che negli Esperimenti nuovi <emph type="italics"/>circa re&shy;<lb/>lationem inter aerem et flammam vitalem animalium,<emph.end type="italics"/> a fine di confutar <pb xlink:href="020/01/1629.jpg" pagenum="504"/>l'errore di coloro che, fautori di essa fiamma vitale, l'additavano nel ven&shy;<lb/>tre delle lucciole agli occhi degl'increduli viva e vera. </s></p><p type="main">

<s>L'istituto boileiano era importantissimo per s&egrave; medesimo, perch&egrave; ten&shy;<lb/>deva a illustrare la teorica della respirazione, ma tornava altres&igrave; accidental&shy;<lb/>mente importante, per il modo di fare il vuoto, diverso da quello tenuto <lb/>dagli Accademici fiorentini, d'onde venivano a ricevere notabili variet&agrave; le <lb/>stesse osservazioni. </s>

<s>Nel vuoto torricelliano infatti la sparizione e la riappa&shy;<lb/>rizione della luce erano istantanee, mentre nel vuoto boileiano si vedeva a <lb/>ogni colpo di stantuffo mirabilmente spengersi un grado di quel primiero <lb/>splendore. </s>

<s>&ldquo; Ad ipsam primam exsuctionem fieri coepit admodum manifesta <lb/>lucis diminutio, quae gradatim caliginosior evasit prout aer magis educeba&shy;<lb/>tur, donec eadem tandem prorsus evanuit &rdquo; (Operum, T. III, P. II, Vene&shy;<lb/>tiis 1697, pag. </s>

<s>170). E in altro esperimento: &ldquo; Per gradus aerem intromi&shy;<lb/>simus et cum uno alterove intervallo ad observandum, ut et a nobis factum, <lb/>quod sicut diminutio lucis continuo maior erat, prout aer magis ac magis <lb/>exsugebatur; sic etiam rediens splendor gradatim intensior fiebat, quando <lb/>nobis libebat aerem magis ac magis in vermes immittere &rdquo; (ibid.). </s></p><p type="main">

<s>E qui vorremmo trattenerci pi&ugrave; a lungo in una considerazione impor&shy;<lb/>tante. </s>

<s>I Nostri fecero quasi sempre uso dello strumento torricelliano, piut&shy;<lb/>tosto che della macchina boileiana, per mostrare di non aver bisogno di <lb/>ricorrere agli stranieri. </s>

<s>E poniamo che non fosse questo uno de'pi&ugrave; vir&shy;<lb/>tuosi propositi albergati nell'animo degli Accademici fiorentini, giov&ograve; nono&shy;<lb/>stante alla scienza, trattandosi specie di sperimentare la vita degli animali, <lb/>la qual vita dipendere dall'aria pi&ugrave; ne'polmonati che negli insetti veniva <lb/>efficacemente dimostrato da quel rimanere a un tratto e non a poco a poco <lb/>il recipiente esausto. </s>

<s>Il Boyle stesso provocato a rispondere al quesito se <lb/>giovasse meglio servirsi dello strumento torricelliano o del suo, confess&ograve;, nel <lb/>proemio agli Esperimenti nuovi <emph type="italics"/>circa relationem inter flammam et aerem,<emph.end type="italics"/><lb/>che trattandosi di piccoli corpi, operando a modo degl'Italiani, &ldquo; exhaustio <lb/>expediri potest maiori cum celeritate et consequenter efficere ut effectus sit <lb/>magis conspicuus, quam usitata nostra experiendi via &rdquo; (Opsrum, T. III cit., <lb/>pag. </s>

<s>145). Ma trattandosi di corpi di non piccola mole, affermava il Boyle <lb/>esser molto pi&ugrave; comodo servirsi della sua Macchina, nella quale dall'altra <lb/>parte si pu&ograve; render quanto si vuole spedita l'esaustione col diminuire la <lb/>capacit&agrave; del recipiente. </s>

<s>Or perch&egrave; il Borelli non poteva negare che, ne'casi <lb/>contemplati dal Boyle, la Macchina di lui s'avvantaggiava sullo strumento <lb/>torricelliano, si dette, per non rimanere indietro, a immaginar quello ch'ei <lb/>chiama <emph type="italics"/>Strumento del gran vacuo,<emph.end type="italics"/> e ch'ei particolarmente descrive al prin&shy;<lb/>cipe Leopoldo in una lettera da Messina, responsiva a quella, nella quale il <lb/>Principe stesso gli riferiva l'esito dell'esperienze fatte in Firenze sopra le <lb/>carni fosforescenti, e sopra il lume delle lucciole. </s>

<s>&ldquo; Io ebbi l'onore della <lb/>lettera di V. A. delli 11 Giugno (1669), alla quale risposi la settimana se&shy;<lb/>guente prolissamente intorno agli accidenti dell'incendio di Catania, e di pi&ugrave; <lb/>vi accompagnai una pianta a disegno delle montagne di detta citt&agrave;..... <pb xlink:href="020/01/1630.jpg" pagenum="505"/>Avevo io letto nella <emph type="italics"/>Gazzetta letteraria di Roma<emph.end type="italics"/> l'esperienza del signor <lb/>Boyle, e mi pareva veramente mirabile, e per&ograve; desideravo sommamente di <lb/>confrontarla, sicch&egrave; pu&ograve; giudicare quanta consolazione io abbia avuto, sen&shy;<lb/>tendo che l'A. V. l'abbi sperimentata nella sua eruditissima Accademia, e <lb/>poi con tante belle circostanze di pi&ugrave; di quelle che aveva osservato il Boyle: <lb/>per&ograve; vorrei di nuovo supplicarla che ne facesse un'altra con la pietra lu&shy;<lb/>cifera di Bologna..... Ma perch&egrave; il modo antico di fare il vuoto, in vasi <lb/>grandi, &egrave; difficile e richiede lungo tempo, potrebbe l'A. V. comandare che <lb/>si adoprasse lo strumento inventato da me &rdquo; e che il Borelli passa imme&shy;<lb/>diatamente a descrivere. (MSS. Cim., T. XIX, c. </s>

<s>267). </s></p><p type="main">

<s>Forse anche queste esperienze furono eseguite dai Fiorentini nella loro <lb/>Accademia, ma per non dilungarci di pi&ugrave; dal nostro argomento, ritorniamo <lb/>sopra quelle parole, colle quali il cardinale Leopoldo terminava di descri&shy;<lb/>vere le sue esperienze sopra le lucciole, dicendo ch'elle si meritavano <emph type="italics"/>vi si <lb/>facesse sopra reflessione.<emph.end type="italics"/> Il Borelli stesso riconobbe ch'era cosa di <emph type="italics"/>gran <lb/>conseguenza,<emph.end type="italics"/> e ci&ograve; non per altro se non perch&egrave; veniva di li luce a scoprir <lb/>la natura del misterioso fosforo animale, vedendosi avere anche questo come <lb/>la fiamma bisogno dell'alimento dell'aria. </s>

<s>Ma la ignorata chimica della com&shy;<lb/>bustione tronc&ograve; il volo alle filosofiche riflessioni del cardinale Leopoldo, e <lb/>arrest&ograve; il corso a quelle scientifiche conseguenze, dalle quali sentivasi tra&shy;<lb/>sportata la mente del sagace Borelli. </s></p><p type="main">

<s>Bench&egrave; sentisse pur troppo queste difficolt&agrave; anche il Malpighi, ei si con&shy;<lb/>fid&ograve; nonostante che il suo microscopio e la perita arte, che oramai trovavasi <lb/>in mano, di sezionare gl'insetti, gli avrebbero almeno in parte rivelato il <lb/>mistero. </s>

<s>Trov&ograve; che la sede del lume era nelle lucciole limitata alle due <lb/>estreme incisure del ventre, attraverso alle quali, con ritmo simile a quello <lb/>del cuore, si vedono frequentemente apparire e sparire i fulgori. </s>

<s>Talvolta, <lb/>bench&egrave; sia l'animale integro e vivo, &egrave; pure spento d'ogni suo lume, ma <lb/>emergono da un recondito succo certe bollicelle rotonde e lucide, le quali <lb/>ora si dissipano, e ora moltiplicandosi all'improvviso fanno corruscare tutt'a <lb/>un tratto la loro congerie, presso a poco come vampa, che si sollevi da un <lb/>mucchio di granelli di polvere pirica incendiata. </s>

<s>&ldquo; Vigente splendore, tre&shy;<lb/>pidatio quaedam minimarum particularum evidenter observatur. </s>

<s>Extructus <lb/>huiusmodi succus ab animali adhuc lucet, absque tamen periodica corusca&shy;<lb/>tione et si comprimatur ita ut lacteus ichor loco moveatur, lumen extendi&shy;<lb/>tur et intenditur, et tamdiu durat lux quamdiu exaratus succus fluidus per&shy;<lb/>manet, unde exsiccatus lumine orbatur. </s>

<s>Succus hic immersus aqua, aceto <lb/>et spiritu vini lumen conservat, sed diutius et intensius in aere lucet. </s>

<s>Splen&shy;<lb/>dor in expositis animalculis succedit Maii mense et Junii medietate, qua <lb/>transacta, sensim deficit &rdquo; (Opera posthuma, Londini 1697, pag. </s>

<s>85). </s></p><p type="main">

<s>Descritti cos&igrave; gli organi della fosforescenza nelle lucciole, soggiunge to&shy;<lb/>sto il Malpighi d'aver con sua grande maraviglia scoperta una simile strut&shy;<lb/>tura, e forse anco pi&ugrave; evidente, nelle Farfalle. </s>

<s>&ldquo; Analogam structuram, et <lb/>forte evidentiorem, in consimilibus animalculis, pyraustis scilicet, vulgo <emph type="italics"/>Far-<emph.end type="italics"/><pb xlink:href="020/01/1631.jpg" pagenum="506"/><emph type="italics"/>falle<emph.end type="italics"/> dictis, admiratus sum &rdquo; (ibid.). E da ci&ograve; forse, pi&ugrave; efficacemente che <lb/>dalle osservazioni della marchesa Sessi, fu indotto lo Spallanzani a studiare <lb/>la fosforescenza negli occhi delle stessse Farfalle. </s>

<s>I caratteri di questo fo&shy;<lb/>sforo nuovamente scoperto son dal Traduttore della <emph type="italics"/>Contemplazione della <lb/>Natura<emph.end type="italics"/> ridotti a quattro, e cos&igrave; esposti in una nota illustrativa del testo: <lb/>&ldquo; I. </s>

<s>Il fosforo si manifesta tanto per la luce del giorno, quanto per quella <lb/>della candela, e ci&ograve; qualor la farfalla &egrave; vigorosa, perch&egrave; in caso diverso si <lb/>scopre il fosforo con la seconda luce, e non con la prima. </s>

<s>Anzi qualche <lb/>volta fa d'uopo, essendo la farfalla languida, coprir con la mano il chiaro <lb/>della candela, se vuol vedersi detto fosforo. </s>

<s>E qui avvertasi come questo ca&shy;<lb/>rattere distingua il fosforo presente dagli altri scoperti dal celebre Beccari, <lb/>la maggior parte de'quali ha bisogno per risplendere dell'immediato lume <lb/>del sole, e talor questo non basta. </s>

<s>Di pi&ugrave; il fosforo delle farfalle &egrave; visibile <lb/>anche in mezzo alla luce, laddove i fosfori beccariani, per fare impressione <lb/>nell'occhio, sogliono esigere interissima oscurit&agrave;. </s>

<s>II. </s>

<s>La luce del fosforo &egrave; <lb/>accesa e tira al color di bragia pallida. </s>

<s>III. </s>

<s>Il fosforo non apparisce che negli <lb/>occhi delle farfalle vive. </s>

<s>Almeno di tante esaminate, dop'essere state morte, <lb/>una sola ha dato qualche indizio di luce, lo che d&agrave; a temere che forse morta <lb/>non fosse interamente. </s>

<s>IV. </s>

<s>Gli occhi di tutte le farfalle non sono fosforici, <lb/>per quanto sinora si &egrave; rilevato, ma solamente quelli, che a proporzione della <lb/>grandezza degli occhi sono grossi, protuberanti e d'un sol colore che tende <lb/>al nero. </s>

<s>&rdquo; (Tomo I cit., pag. </s>

<s>83, 84). </s></p><p type="main">

<s>Ma se allo Spallanzani, quando scriveva queste note al Bonnet, per non <lb/>dire al Malpighi, che notomizzava gl'insetti un secolo prima, fosse stato do&shy;<lb/>mandato qual'&egrave; la natura di cos&igrave; fatta luce animale, avrebbero questo solo <lb/>potuto rispondere: che &egrave;, a somiglianza delle luci artificiali, alimentata dal&shy;<lb/>l'aria, per cui nel vuoto, come fu primo a sperimentare il cardinale Leo&shy;<lb/>poldo de'Medici, anch'essa si spenge. </s>

<s>Perch&egrave; per&ograve; non sapevasi a que'tempi <lb/>quali intime relazioni passassero fra l'aria stessa e la fiamma, la combu&shy;<lb/>stione diventava anche pi&ugrave; misteriosa, trovandosi complicata colle pi&ugrave; re&shy;<lb/>condite funzioni della vita. </s></p><p type="main">

<s>Dall'altra parte il principio della fiamma vitale, dall'esperienze del Boyle, <lb/>e da pi&ugrave; ragionevoli ipotesi proposte intorno all'azion dell'aria sul sangue, <lb/>era stato oramai relegato nel mondo delle follie, cosicch&egrave; non fa meravi&shy;<lb/>glia se in tanta incertezza si rivolgessero gli occhi desiderosi a quell'elet&shy;<lb/>tricismo, che il Beccaria destramente ripose nel vuoto, rimasto fra le dot&shy;<lb/>trine de'Filosofi antichi. </s>

<s>Come questi infatti vedevano con gli occhi proprii <lb/>ardere attraverso alle trasparenti membrane delle lucciole la fiamma in&shy;<lb/>teriore della vita; cos&igrave; il Beccaria vedeva con gli occhi proprii, nello splen&shy;<lb/>dor di que'medesimi insetti, il vapore elettrico, in cui s'accende a ogni es&shy;<lb/>sere animato la vita. </s>

<s>&ldquo; Quella luce di fosforo, che brilla in certe parti di <lb/>alcuni insetti, e che in alcuni non si fa vedere che alternativamente in certo <lb/>alternativo movimento del loro corpicciolo, non ne mostrerebbe in essi e <lb/>l'esistenza e generalmente alcuna azione del vapore suddetto? </s>

<s>E questo va-<pb xlink:href="020/01/1632.jpg" pagenum="507"/>pore, che probabilmente esiste ed opera in tutti gli animali, non rendereb&shy;<lb/>besi solo visibile in quelli, che avesssero alcune parti diafane, e in che si <lb/>potesse esso scorgere mentre si vibra attraverso ad esse parti meno elettri&shy;<lb/>che per comunicazione, come scorgesi a lucere similmente il rado vapore <lb/>che attraversa un sottile strato di acqua? </s>

<s>&rdquo; (Dell'elettricismo cit., pag. </s>

<s>217). </s></p><p type="main">

<s>Tanto &egrave; ardente nell'uomo la sete de<gap/> sapere che, se non trova acqua <lb/>da estinguerla, s'acquieta in appressar le labbra anche a un arido sasso, <lb/>che specchi in s&egrave; gli oggetti come una fonte! </s></p><pb xlink:href="020/01/1633.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO XIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle piante<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle principali funzioni nutritive: delle forze concorrenti a produr l'ascesa dei succhi; dell'azione <lb/>e delle propriet&agrave; delle foglie. </s>

<s>&mdash; II. </s>

<s>Del circolo della linfa, e della respirazione. </s>

<s>&mdash; III. Dell'uf&shy;<lb/>ficio de'fiori, della distinzione dei sessi, e della fecondazione dei semi. </s>

<s>&mdash; IV. </s>

<s>Della germina&shy;<lb/>zione: dell'uso dei lobi e delle foglie seminali: dell'azione dell'aria e de'semi posti a ger&shy;<lb/>mogliare nel vuoto. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Chi la passata storia commemorando ripensa a quell'opinione dei Fi&shy;<lb/>losofi antichi, ripullulata nel Redi, e secondo la quale si credeva possibile <lb/>che partecipasse la polpa vegetabile ai vermi il sentimento e la vita, gi&agrave; <lb/>conclude fra s&egrave; che dovessero quegli stessi Antichi far precellere, nelle na&shy;<lb/>turali dignit&agrave;, le piante agli insetti. </s>

<s>La maestosa sublimit&agrave; degli alberi, il <lb/>decoro delle fronde, la gentilezza dei fiori, la soavit&agrave; dei frutti erano dal&shy;<lb/>l'altra parte una continua attestazione all'uomo, e quasi un documento, <lb/>messogli tutti i giorni a leggere sotto gli occhi, di quella nobilt&agrave;, di che <lb/>avea voluto, a preferenza degli abietti vermiccioli schifosi, insignir le piante <lb/>la munificente Natura. </s></p><p type="main">

<s>Non potevano nonostante que'Filosofi negare a s&egrave; medesimi che il giu&shy;<lb/>dizio, dato dell'eccellenza di esseri immobili sopra i semoventi, non fosse, <lb/>meglio considerato, per apparire illusorio, e se ne sarebbero forse non dif&shy;<lb/>ficilmente ricreduti, quando non avessero nelle piante stesse intraveduta una <lb/>viva immagine di quegli organi della vita animale, che non discernevano, <lb/>n&egrave; credevan possibili a riscontrarsi nella informe e compendiosa struttura <pb xlink:href="020/01/1634.jpg" pagenum="509"/>degl'insetti. </s>

<s>Mentre questi infatti rappresentavansi ai loro occhi come una <lb/>particella di materia, che si muove da s&egrave; senza esser mossa, riconoscevano <lb/>nella terra l'utero, nelle radici le vene, nel bulbo radicellare il cervello e <lb/>il cuore, nel midollo del tronco l'asse cerebro spinale, e perfino i muscoli <lb/>stessi nelle fibre legnose. </s>

<s>Vedere la radicella andare in cerca dell'alimento <lb/>industriosa, i rami sporgere verso la luce del sole desiderosi le braccia, e le <lb/>foglie mostrarsi spesso ritrose che altri le tocchi, parevano indizi certi di <lb/>una volont&agrave; elettiva, di un moto di desiderio nella ricerca del bene, di un'at&shy;<lb/>tenta e sollecita fuga dalle molestie. </s></p><p type="main">

<s>Il grazioso apologo s'applica mirabilmente al nostro intelletto, il quale <lb/>anch'egli, come gli alberi, non allega in frutto, se non &egrave; preceduto dal fiore. </s>

<s><lb/>E giacch&egrave; per frutto s'intende le idee, e per fiore l'immaginazione, la sto&shy;<lb/>ria che siamo per accennare nel presente capitolo nient'altro fa che dimo&shy;<lb/>strar col fatto come, nelle immaginate analogie fra gli organi della vita ani&shy;<lb/>male e quelli della vita vegetativa, allegasse via via il frutto della Fisiologia <lb/>delle piante. </s></p><p type="main">

<s>Incominciano per noi le istituzioni della nuova scienza da Andrea Ce&shy;<lb/>salpino, il quale, sul declinar del secolo XVI, pubblicando i suoi XVI libri <lb/><emph type="italics"/>De plantis,<emph.end type="italics"/> trattava delle funzioni della loro vita, comparandole a quelle <lb/>degli animali. </s>

<s>&ldquo; Natura venarum, son fra le prime parole ch'egli scrive, <lb/>quae alimentum ex ventre hauriunt, ut illud in universum corpus distri&shy;<lb/>buant, aliqua in parte respondere videtur cum plantarum radicibus; nam <lb/>similiter hae ex terra, tamquam ex ventre cui implantantur, trahunt alimen&shy;<lb/>tum &rdquo; (Florentiae 1583, pag. </s>

<s>1). Ma perch&egrave; le radici portano le raccolte so&shy;<lb/>stanze nutritizie a concocersi nei ventricoli del cuore, non son di cuore perci&ograve; <lb/>sfornite nemmeno le piante, le quali lo hanno anzi opportunamente collo&shy;<lb/>cato fra la radice e il tronco, come fra le membra superiori e le inferiori <lb/>lo hanno gli animali, in mezzo al loro corpo, convenientemente disposto. </s>

<s>E <lb/>perciocch&egrave; in questi il sangue &egrave; dal cuore stesso dispensato alle membra, <lb/>per via delle arterie; cos&igrave; a dispensar la linfa ricorrono per il tronco e per <lb/>i rami degli alberi vasi simili agli arteriosi. </s>

<s>Il Cesalpino, che non aveva an&shy;<lb/>cora strumenti da poterli osservare con gli occhi, argomenta alla necessaria <lb/>esistenza di questi vasi, indifferentemente chiamati col nome di vene, dal <lb/>fatto delle viti tagliate o delle recise piante lattigginose. </s>

<s>&ldquo; Venas quoque <lb/>datas esse plantis, licet exiguas, argumento sunt illae quae lacte manant, <lb/>ut tithymalorum genus, et ficus .... quod et in vite maxime contingit, sed <lb/>propter meatuum exiguitatem cospici nequaquam possunt &rdquo; (ibid., pag. </s>

<s>4). </s></p><p type="main">

<s>Se non che rimaneva in queste analogie una cosa importantissima a <lb/>dimostrare: qual si fosse cio&egrave; la forza impulsiva della linfa, che sostituisce <lb/>la forza impulsiva del sangue. </s>

<s>A tale effetto richiamavasi il Cesalpino ai suoi <lb/>principii di fisiologia animale, secondo i quali non vien tanto al sangue l'im&shy;<lb/>pulso dai moti di sistole del cuore, quanto dall'effervescenza del calore in&shy;<lb/>nato. </s>

<s>Or di questo stesso calore innato non vuol che ne sia defraudato il cuore <lb/>della pianta, perch&egrave; il non rendersi a noi sensibile non &egrave;, egli dice, buona <pb xlink:href="020/01/1635.jpg" pagenum="510"/>ragione a negarlo. </s>

<s>&ldquo; Quamvis autem sensui immanifestus sit calor, non ob <lb/>id negandum est: quae enim minus calida sunt, quam tactus noster, frigida <lb/>iudicantur &rdquo; (ibid.). </s></p><p type="main">

<s>Ammessa dunque nella ceppaia dell'albero l'esistenza di un calore in&shy;<lb/>nato, e osservando che non sono i canaliculi radicellari liberi e andanti come <lb/>le vene, ma tutti ingombri di villosit&agrave; nel loro interno calibro, cosicch&egrave; il <lb/>liquido non sale in essi a modo che ne'tubetti di vetro, ma a somiglianza <lb/>di quel che vede farsi ai canapi attorti; rassomiglia il Cesalpino l'attra&shy;<lb/>zione, che fan del succo nutritizio le radici dall'utero della madre terra, <lb/>all'attrazion dell'olio fatta dal lucignolo di una lampada accesa. </s>

<s>&ldquo; Idcirco <lb/>eae non, ad venarum similitudinem, meatu quodam continuo perviae sunt, <lb/>sed potius instar nervorum ex villosa constant substantia. </s>

<s>Sic enim bibula <lb/>earum natura continue humorem ad principium caloris innati ducit, ut in <lb/>lucernarum luminibus videmus, funiculo enim quodam utuntur, quo oleum <lb/>continue ad flammam ducatur &rdquo; (ibid.). </s></p><p type="main">

<s>Concotti i succulenti umori nelle ceppaie, come il chilo nel cuore, deb&shy;<lb/>bono per i vasi del tronco risalire su ai rami e alle foglie. </s>

<s>E qui invocasi <lb/>dal Cesalpino per questo moto di ascesa una forza simile alla precedente, se <lb/>non che il centro del calore attrattivo &egrave; su in alto, ne'germi che si svol&shy;<lb/>gono, e nei frutti che maturano, aggiuntovi il calore esterno del sole. </s>

<s>Cos&igrave;, <lb/>poi soggiunge, si spiega perch&egrave; comincino le piante ad andare in succhio, <lb/>quando germogliano di primavera, e continuino tutta l'estate, infintanto che <lb/>non abbiano i loro frutti maturi. </s>

<s>&ldquo; Adiuvat autem hunc motum caliditas <lb/>innata humorem affluentem absumens in germina et fructus: necesse est <lb/>enim alium subinde consequi, absumpto priori, ob easdem causas, ut hi fa&shy;<lb/>ciunt, qui penicillo in humore imposito ut altera eius pars extra vas pro&shy;<lb/>pendeat, humorem a feculentia secernunt..... Ob id plantae pleraeque vere <lb/>et estate germinant magis et fructus edunt, quia a calore externo augetur <lb/>humoris attractio &rdquo; (ibid., pag. </s>

<s>4, 5). </s></p><p type="main">

<s>Nell'allegar delle idee, ci si permetta anche questa volta l'immagine, <lb/>che consuona dall'altra parte col soggetto del discorso, avvien quello stesso <lb/>che nell'allegare de'fiori: le pi&ugrave; esterne foglie e pi&ugrave; appariscenti cadono e <lb/>vanno disperse, mentre le pi&ugrave; riposte rimangono per trasformarsi nell'ova&shy;<lb/>rio e nel frutto. </s>

<s>Vedremo in seguito di queste cesalpiniane dottrine qual <lb/>fosse quella loro parte, che felicemente alleg&ograve; nella scienza: ora &egrave; da notar <lb/>la sorte di que'petali lussuriosi, che si dissiparono dal vento contrario alla <lb/>Filosofia peripatetica. </s>

<s>Il calore innato nel cuor della pianta fu quello appunto, <lb/>ch'ebbe primo a subir questa sorte, tolto il qual calore all'ipotesi del Ce&shy;<lb/>salpino, veniva tutto insieme anche tolta la causa efficente dell'ascesa del <lb/>succo dalle radici al tronco e alle fronde, come cessa il fluir dell'olio at&shy;<lb/>traverso al lucignolo, spenta che sia la fiamma della lucerna. </s></p><p type="main">

<s>Vero &egrave; bene che, avendo forse presentito il Cesalpino l'insorgere di co&shy;<lb/>loro, i quali gli sarebbero venuti a negare il calore nelle piante innato, per&shy;<lb/>ch&egrave; non si rende come negli animali sensibile al tatto; invocava sussidiario, <pb xlink:href="020/01/1636.jpg" pagenum="511"/>a spiegare il continuo moto di ascesa del succo, il fatto del vaso che si vuota <lb/>attraverso alle fila di un <emph type="italics"/>penicillo,<emph.end type="italics"/> come attraverso a un sifone, che travasi <lb/>il liquido con flusso non interrotto. </s>

<s>Ma a rispondere che questo era, a con&shy;<lb/>ferma della proposta ipotesi, troppo debole aiuto, bastava semplicemente os&shy;<lb/>servare, come poi fece il Borelli che, troncato il ramo a un albero, il succo <lb/>tuttavia stilla dalla cicatrice anche supina, mentre il penicillo non travasa <lb/>se, risalito all'orlo del vaso, non ripiega in basso gli stillanti suoi stami. </s></p><p type="main">

<s>Sgombrate dunque le idee peripatetiche, non rimaneva a riconoscersi <lb/>dai seguaci del Cesalpino altra vera causa naturale dell'ascesa del succo <lb/>nelle piante che il calore del sole. </s>

<s>Ma quale si fosse il modo dell'operare di <lb/>questa causa non fu prima insegnato che nella privata scuola di Galileo. </s>

<s><lb/>Raccontano i biografi di lui ch'e'si tratteneva a coltivare di sua propria <lb/>mano l'orticello attiguo alla sua casa di Arcetri, e di varii fatti, osservati <lb/>nella vita e nelle passioni delle piante, si studiava di ritrovare le fisiche ra&shy;<lb/>gioni. </s>

<s>Uno di questi fatti per esempio sarebbe quello che &ldquo; alcune volte, <lb/>dopo una nebbia, scoprendosi il sole, le foglie di vite ed altre frondi diven&shy;<lb/>gono aride e si seccano &rdquo; di che nel problema VII (Alb. </s>

<s>XIV, 328) d&agrave; Ga&shy;<lb/>lileo una tale spiegazione, che fu nel secolo XVIII applicata da alcuni a ren&shy;<lb/>dere la ragione de'perniciosi effetti, che producono sui teneri polloni le <lb/>sferette del ghiaccio, quando appena son ferite dai raggi del sole. (Spallan&shy;<lb/>zani, Pref. </s>

<s>alla traduzione della <emph type="italics"/>Contemplazion della Natura,<emph.end type="italics"/> T. </s>

<s>I cit., <lb/>pag. </s>

<s>29, 30). Concetto galileiano, inspiratogli dall'Alighieri (Purg. </s>

<s>XXV, <lb/>v. </s>

<s>77), prolissamente illustrato dal Magalotti, e ripetuto con ammirazione da <lb/>tanti, perch&egrave; par che trovi nella moderna Chimica il suo commento, &egrave; che <lb/>&ldquo; il vino &egrave; un composto di umore e di luce &rdquo; (Magalotti, Lett. </s>

<s>scientif., Fi&shy;<lb/>renze 1721, pag. </s>

<s>36-57). Ma pi&ugrave; originalit&agrave; e pi&ugrave; sicurezza di scienza &egrave; in <lb/>quei dimostrati principii meccanici intorno alla resistenza dei solidi allo spez&shy;<lb/>zarsi, ne'quali trov&ograve; Galileo stesso la ragione del perch&egrave; un filo di paglia <lb/>sostenga una spiga pi&ugrave; grave di tutto il gambo (Alb. </s>

<s>XIII, 145). </s></p><p type="main">

<s>Quel che per&ograve;, in queste galileiane applicazioni delle forze fisiche alla <lb/>storia delle piante, si riferisce pi&ugrave; strettamente all'argomento, e di che dianzi <lb/>facevasi cenno, &egrave; la spiegazione del modo come operi il calor del sole sui <lb/>succhi nutritivi circolanti nel tronco e ne'rami. </s>

<s>Chi si rammemora l'espe&shy;<lb/>rienza della caraffella, il lungo e sottilissimo collo della quale riceve pi&ugrave; o <lb/>men di quell'acqua in che tiene immersa la bocca, intende quanto fosse fa&shy;<lb/>cile a sovvenire al pensiero di Galileo che il calor del sole produca nella <lb/>linfa delle piante un effetto molto analogo a quello, che produce nel Ter&shy;<lb/>mometro ad aria. </s>

<s>Le ragioni particolari poi di cos&igrave; fatta analogia furono me&shy;<lb/>glio spiegate e largamente diffuse ne'suoi insegnamenti orali da Benedetto <lb/>Castelli, primo ad aprire in Roma una scuola di vera Fisica sperimentale, <lb/>nella quale il Borelli attesta, come fra poco vedremo, di avere attinti i prin&shy;<lb/>cipii alla ragion meccanica del nutrirsi le piante e del germogliare. </s></p><p type="main">

<s>Di questa nuova scienza dei vegetabili, ch'ebbe gl'inizii da'familiari <lb/>colloqui di Galileo gi&agrave; vecchio col Castelli, non &egrave; rimasto altro documento <pb xlink:href="020/01/1637.jpg" pagenum="512"/>che quello raccolto fra'<emph type="italics"/>Pensieri<emph.end type="italics"/> galileiani, e in cui, per analogia dello <emph type="italics"/>Stru&shy;<lb/>mento,<emph.end type="italics"/> e supposto esser le piante e i loro prodotti composti di vescicole o <lb/>di otricelli, come fu poi dimostrato vero dall'anatomia del Malpighi, si rende <lb/>la ragion del crescere e del maturare le uve, i fichi, i pomi granati. </s>

<s>&ldquo; L'uva <lb/>&egrave; composta di grani, o vogliamo dire vesciche, e questo si vede apparente&shy;<lb/>mente nell'uva, dove ogni grano &egrave; una vescica. </s>

<s>Il simile ne'pomi granati, <lb/>fichi, cocomeri ed altri; onde tali vesciche, essendo piene di umore, venendo <lb/>il caldo del sole, le spreme e sgonfia, e mandano fuori parte di quell'umore, <lb/>onde la sera son passe. </s>

<s>Ma nel sopraggiunger la notte e raffreddarsi l'aria, <lb/>tali vesciche si vengono a riempire di nuovo umore, e maggior di quello <lb/>che il giorno avanti avevano mandato fuori, onde esse vesciche vengono a <lb/>molto pi&ugrave; farsi capaci, e'per questa alterazione si maturano, facendo l'istesso <lb/>effetto che fa lo <emph type="italics"/>Strumento &rdquo;<emph.end type="italics"/> (Alb. </s>

<s>XIV, 335). </s></p><p type="main">

<s>Secondo questa ipotesi la circolazione del succo nelle piante non sa&shy;<lb/>rebbe dunque continua, ma si farebbe per accessi e per recessi, all'alter&shy;<lb/>narsi dei gioni e delle notti, com'ora accede ora recede per cause simili il <lb/>liquido nello Strumento, ossia nel Termometro ad aria. </s>

<s>L'ipotesi del Cesal&shy;<lb/>pino corrispondeva meglio al fatto naturale, ma vedemmo da quali ragioni <lb/>Galileo e il Castelli, avversi alla Filosofia peripatetica, fossero indotti a ri&shy;<lb/>fiutarla. </s>

<s>L'avea per quelle stesse ragioni rifiutata pure un collega del Ca&shy;<lb/>stelli, troppo presto rapito dalla morte agl'incrementi delle scienze sperimen&shy;<lb/>tali, Niccol&ograve; Aggiunti, il quale nonostante molto bene conobbe che il succo <lb/>vegetativo aveva impulso pi&ugrave; simile a quello che fa ascendere l'olio nel lu&shy;<lb/>cignolo, che non all'altro per cui l'acqua va e viene nello Strumento. </s>

<s>Una <lb/>cosa sola per&ograve; lo riteneva dal professar liberamente l'ipotesi cesalpiniana, <lb/>ed era il credere con tutti gli altri che fosse il liquido nella lucerna attratto <lb/>in virt&ugrave; del calor della fiamma. </s>

<s>Ma quando esso Aggiunti scopr&igrave; la vera <lb/>causa fisica universale di cotesti fenomeni di capillarit&agrave; nel <emph type="italics"/>moto occulto<emph.end type="italics"/> del&shy;<lb/>l'acqua, non dubit&ograve; di applicarla alla vegetazion delle piante, lieto di poter <lb/>sostituire all'immaginario calore innato la realt&agrave; di una causa fisica, e per <lb/>la quale veniva ad aversi del fatto una spiegazione pi&ugrave; verosimile di quella <lb/>stessa insegnata dal Castelli o da Galileo. </s></p><p type="main">

<s>Ammessa insomma l'esistenza de'vasi capillari nel tronco delle piante, <lb/>il succo nutritizio, secondo l'Aggiunti, vi ascende, non attratto dal calore <lb/>innato o dal calore del sole, ma per un moto occulto nell'acqua e da cui <lb/>dipende altres&igrave; la ragione del &ldquo; perch&egrave; bisogni applicare nei nesti i surculi <lb/>e gemme, che corrispondano co'lor meati a quelli del ramo innestato, e <lb/>l'umore subentra in essi. </s>

<s>Ond'ei non &egrave; maraviglia se, colla medesima di&shy;<lb/>ligenza fatti, alcuni nesti si attaccano ed altri no, perch&egrave;, secondo che pochi <lb/>o molti meati, per i quali ha da passare il nutrimento, corrisponderanno con <lb/>quelli della pianta innestata, dalla quale vien somministrato il succo nutri&shy;<lb/>tivo; succeder&agrave; il fatto &rdquo; (Nelli, saggio di storia letter., Lucca 1759, pag. </s>

<s>95). </s></p><p type="main">

<s>Questa prima scoperta di fisica molecolare sub&igrave; l'infelice sorte del suo <lb/>Autore, rimanendo anch'essa morta e seppellita co'manoscritti di lui. </s>

<s>Quando <pb xlink:href="020/01/1638.jpg" pagenum="513"/>poi torn&ograve; a rivivere nell'Accademia del Cimento, vedremo come l'escludesse <lb/>il Borelli da ogni ingerenza nella fisiologia delle piante. </s>

<s>Intanto, oltrepas&shy;<lb/>sata di poco la prima met&agrave; del secolo XVII, i germi di quella nuova scienza <lb/>fisiologica, posti da Galileo, dal Castelli e dall'Agguinti, si videro a un tratto <lb/>in Italia e fuori giungere a maraviglioso incremento, quasi come all'improv&shy;<lb/>viso cader di una pioggia estiva sopra le inaridite zolle di un campo gi&agrave; <lb/>seminato. </s></p><p type="main">

<s>Furono cotesti maravigliosi effetti operati nel campo della nuova scienza <lb/>dalla Micrografia, quando l'Ottica seppe fabbricare strumenti pi&ugrave; squisiti, e <lb/>i laboriosi esercizi educaron l'arte di bene usarli. </s>

<s>In Italia avevano dato i <lb/>Lincei i primi esempi, e in Italia, dove Eustachio Divini e Giuseppe Cam&shy;<lb/>pani erano artefici peritissimi, ebbe la Fitologia microscopica la sua prima <lb/>e pi&ugrave; sapiente cultura. </s>

<s>Federigo Cesi e Fabio Colonna si erano trattenuti <lb/>ad esaminar l'esterna superfice de'petali e delle foglie, per dedur di l&igrave; pi&ugrave; <lb/>sicure note caratteristiche a distinguere la variet&agrave; delle piante: Marcello <lb/>Malpighi volle penetrare pi&ugrave; addentro ad esaminar di tutte le parti, dalla <lb/>radice al tronco, dall'arido seme al germoglio gi&agrave; sviluppato, l'intima tes&shy;<lb/>situra, per passar dalla notizia degli organi a investigare i misteri della vita <lb/>vegetativa. </s></p><p type="main">

<s>Ebbero principio questi suoi studi mentr'era professore a Messina, e <lb/>gli venne l'occasione d'applicarvisi, trattenendosi spesso in campagna a vil&shy;<lb/>leggiar col visconte Giacomo Ruffo. </s>

<s>&ldquo; Ruri interdum, racconta nell'Auto&shy;<lb/>biografia, non longe ab urbe, in villa illustrissimi vicecomitis d. </s>

<s>d. </s>

<s>Jacobi <lb/>Ruffi morans, plantarum structuram rimabar, et ibidem, in frustulo ligni <lb/>castaneae, ampli occurrere ductus aeris, seu <emph type="italics"/>tracheae,<emph.end type="italics"/> quas in aliis etiam <lb/>vegetabilibus adesse comperi. </s>

<s>Quare tantae rei clarissimum Borellum monui, <lb/>qui die XXVII aprilis 1663 haec mihi rescripsit: <emph type="italics"/>La ringrazio della repli&shy;<lb/>cata sperienza delle fistole dell'aria nelle piante. </s>

<s>L'ho anch'io fatta, ma <lb/>per&ograve; la vista non mi aiuta. </s>

<s>Io per&ograve; credo che siano l'istesse fistole che <lb/>portano l'umore e l'aria e non differenti, fintantoch&egrave; l'esperienza non <lb/>mi dimostri altrimenti &rdquo;<emph.end type="italics"/> (Opera posthuma, P. I, Londini 1697, pag. </s>

<s>25). </s></p><p type="main">

<s>Lieto della scoperta delle trachee, occorsagli felicemente, com'abbiamo <lb/>udito, nella primavera del 1663, si dette il Malpighi ad esaminare col mi&shy;<lb/>croscopio degli alberi e dell'erbe ogni parte, cosicch&egrave; nel 1671 avea tutta <lb/>esplorata la composizione anatomica delle piante, di cui dette in poche pa&shy;<lb/>gine un'<emph type="italics"/>Idea<emph.end type="italics"/> alla R. </s>

<s>Societ&agrave; di Londra. </s>

<s>Il segretario Enrico Holdenburg, <lb/>ricevute da Bologna le carte sottosignate il d&igrave; primo di Novembre di quel&shy;<lb/>l'anno 1671, rispondeva al Malpighi sotto il d&igrave; 14 Dicembre appresso, lo&shy;<lb/>dandogli altamente, a nome del&igrave;'Accademia, l'opera, ed esortandolo a pro&shy;<lb/>seguirla. </s>

<s>&ldquo; Hoc interim celare te nolim, vir praestantissime, poi soggiunge <lb/>lo stesso Segretario, quendam e societate regia Virum medicum nostratem, <lb/>idem illud argumentum tractandum suscepisse, quinimo ea qua hora, quod <lb/>forte miraberis, qua scriptum tuum a me proferebatur, libellum suum an&shy;<lb/>glice iam editum laudatae Societati exhibuisse, in quo <emph type="italics"/>Plantarum anato-<emph.end type="italics"/><pb xlink:href="020/01/1639.jpg" pagenum="514"/><emph type="italics"/>men<emph.end type="italics"/> tum ab ipso arcessit semine, tum, singulis earum partibus earumque <lb/>vegetandi ratione consideratis, cum semine claudit &rdquo; (Epist. </s>

<s>circa tractatus <lb/>De Anat. </s>

<s>plant., Malpighi, Op. </s>

<s>omnia, T. I, Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>164). </s></p><p type="main">

<s>Quel Medico inglese, a cui qui si accenna, era Neemia Grew, il quale <lb/>presentava stampato alla Societ&agrave; anglicana il suo libro <emph type="italics"/>The anathomy of <lb/>vegetlabes begun<emph.end type="italics"/> in quel medesimo giorno che il Malpighi presentava il ma&shy;<lb/>noscritto della sua <emph type="italics"/>Anatomes plantarum idea.<emph.end type="italics"/> L'opera inglese, divisa in <lb/>sette capitoli, ne'quali, come abbiamo udito dire all'Oldenburg, dal seme <lb/>che germoglia si giunge al frutto che allega, percorrendo tutto il ciclo della <lb/>vita vegetativa; fu poco dopo tradotta in latino col titolo di <emph type="italics"/>Anatomiae ve&shy;<lb/>getabilium primordia,<emph.end type="italics"/> e inserita nelle Effemeridi de'<emph type="italics"/>Curiosi della Natura<emph.end type="italics"/><lb/>in Germania, in appendice all'anno VIII della I Decuria. </s></p><p type="main">

<s>Del fortuito incontro ce ne maravigliamo ora noi, ma pi&ugrave; ebbero a far&shy;<lb/>sene maraviglia gli Autori. </s>

<s>Il Malpighi, curiosissimo di vedere il libro del <lb/>suo concorrente, l'ebbe nell'originale inglese dopo il Marzo del 1672, e nei <lb/>primi giorni di Ottobre rispondeva d'esserselo fatto da un suo amico tra&shy;<lb/>durre in latino, e di averne inteso quanto faceva bisogno. </s>

<s>&ldquo; Gaudeo inte&shy;<lb/>rim, poi soggiungeva, me cum accuratissimo Viro in quamplurimis obser&shy;<lb/>vationibus et placitis convenire: reliqua autem, in quibus intercedere aliquid <lb/>diversitatis videtur, ulteriori instituta indagine, solertius examinabo, ne, quae <lb/>tanti Viri aciem effugere, illusione quadam languidae meae imponant fanta&shy;<lb/>siae &rdquo; (ibid., pag. </s>

<s>166). </s></p><p type="main">

<s>Forse avrebbe il Grew con la pubblicazione del suo primo libro tenuta <lb/>l'opera dell'Anatomia delle piante per assoluta, e si sarebbe dolcemente <lb/>riposato sotto l'ombra de'conquistati allori, se il Malpighi, che operosamente <lb/>attendeva a colorire la sua proposta <emph type="italics"/>Idea,<emph.end type="italics"/> non fosse, con gli acuti stimoli <lb/>dell'emulazione, venuto a turbargli i riposi. </s>

<s>Riguardando perci&ograve; anch'egli, <lb/>il Grew, il suo libro come un'<emph type="italics"/>Idea,<emph.end type="italics"/> o come i <emph type="italics"/>Primordii<emph.end type="italics"/> di ci&ograve;, che sarebbe <lb/>poi da fare nel larghissimo campo aperto; si propose, per non rimanere in&shy;<lb/>dietro al Malpighi, di tornare all'esame anatomico delle singole parti com&shy;<lb/>ponenti le piante, e delle radici, del tronco, delle foglie, de'fiori, de'frutti e <lb/>de'semi scrivere via via, di ciascuno, distintamente un trattato. </s></p><p type="main">

<s>Nel 1673 pubblic&ograve; in Londra il discorso fitologico delle radici col ti&shy;<lb/>tolo <emph type="italics"/>An idea of a phytological hystory of roots,<emph.end type="italics"/> che i <emph type="italics"/>Curiosi della Na&shy;<lb/>tura<emph.end type="italics"/> tradussero in latino col titolo <emph type="italics"/>Idea historiae phytologicae cum conti&shy;<lb/>nuatione anatomiae vegetabilium, speciatim in radicibus,<emph.end type="italics"/> e che poi inse&shy;<lb/>rirono in appendice agli anni IX e X della prima Decuria. </s>

<s>Nella prefazione <lb/>il Grew tocca cose riguardanti il Malpighi, delle quali, perch&egrave; sono impor&shy;<lb/>tantissimo documento di storia, non bibliografica solo, ma che pi&ugrave; importa <lb/>scientifica, trascriveremo nella sua integrit&agrave; il discorso, come ce lo tradus&shy;<lb/>sero gli Accademici leopoldini. </s></p><p type="main">

<s>&ldquo; Immediate ab harum publicatione (delle sette parti cio&egrave; in ch'era <lb/>stato distinto il libro dei <emph type="italics"/>Primordii<emph.end type="italics"/>) discursus a doctissimo Malpighio, cu&shy;<lb/>ius ingeniosissimae et accuratae industriae mundus obstrictissimus tenetur, <pb xlink:href="020/01/1640.jpg" pagenum="515"/>oblatus est regiae Societati de eodem subiecto 7 Dec. </s>

<s>1671, scriptus Bono&shy;<lb/>niae 1&deg; Nov. </s>

<s>1671. Cuius suffragio laetabar me videre veritatem observatio&shy;<lb/>num mearum in universum omnium confirmatam, dum eius parum admo&shy;<lb/>dum a meis differunt, licet ipse nbique usus fuerit Microscopio. </s>

<s>Exempli <lb/>gratia quod vasa aerea, quae illi dicuntur fistulae spirales, licet diu abhinc <lb/>eorum habuerim notitiam, utpote quae cum reliquis longe ampliora sint, fa&shy;<lb/>cilius deteguntur, modum tamen spiralis eorum conformationis, nonnisi per <lb/>Microscopium observabilis, primo ab ipso didici, qui elegantissimam eorum <lb/>descriptionem dedit. </s>

<s>Quasdam suas <emph type="italics"/>De usu partium oeconomico<emph.end type="italics"/> cogitatio&shy;<lb/>nes non comunicat. </s>

<s>Et nonnulla observatione digna de partibus floris, fructus <lb/>et seminis, ibi non reperiunda, ipsum inter alia secum reservasse possibile <lb/>est. </s>

<s>Optarem animitus edidisset suum Discursum, sed quoniam non vult an&shy;<lb/>tequam ornatus sit figuris, ea de ratione aequum mihi visum est haec de <lb/>illo admonere &rdquo; (Acta Curios, Naturae Dec. </s>

<s>I, Ann. </s>

<s>IX et X, app. </s>

<s>Norim&shy;<lb/>bergae 1674, pag. </s>

<s>104, 5). </s></p><p type="main">

<s>Quel che in questa storia concerne la scoperta delle trachee &egrave; veris&shy;<lb/>simo, e vedremo in altra occasione il Grew addurre i documenti necessari <lb/>per dimostrarlo. </s>

<s>Ma in paragonare il rimanente dell'opera sua con quella <lb/>del poderoso rivale gli molce l'animo una dolce lusinga, incoratagli dalla <lb/>manifesta ragion del primato. </s>

<s>Quando infatti, ambedue seguitando d'eserci&shy;<lb/>tarsi nella medesima gloriosa palestra, si trov&ograve; il Grew stesso dal Malpighi <lb/>precorso, e allora quella prima compiacenza della concordia fra le idee si <lb/>trasform&ograve; nella sollecitudine di fare apparir tra loro un'aperta discordia. </s></p><p type="main">

<s>Mentre intanto l'Anatomico inglese presentava alla reale Societ&agrave; ma&shy;<lb/>noscritto il suo III libro <emph type="italics"/>The anatomy of tuncks,<emph.end type="italics"/> dava il nostro Italiano, <lb/>il d&igrave; 20 Agosto 1674, una lettera all'Oldenburg, con la quale della sua <emph type="italics"/>Ana&shy;<lb/>tome plantarum<emph.end type="italics"/> accompagnavagli manoscritta la maggior parte trattante <lb/><emph type="italics"/>De cortice, De partibus caulem vel caudicem componentibus, De caudicis <lb/>augmento et nodis, De gemmis, De foliis, De floribus, De seminum gene&shy;<lb/>ratione, De uterorum augmento et ipsorum succedente forma,<emph.end type="italics"/> e finalmente <lb/><emph type="italics"/>De secundinis et contento plantarum foetu.<emph.end type="italics"/> Non avendo per&ograve; avuto ancora <lb/>della fatta spedizione il riscontro, tornava a scrivere il d&igrave; 27 Settembre ap&shy;<lb/>presso: &ldquo; Mensis iam elapsus est, ex quo Anatomiam plantarum cum ico&shy;<lb/>nismis capsula conclusam ad Ill.um Dom.um Ablegatum, Venetiis morantem, <lb/>transmisi, ut tibi tuta et opportuna occasione reddatur. </s>

<s>Tuis epistolis adeo <lb/>me sollicitatum vidi ut imperfectum, necdum absolutum, opus transmittere, <lb/>decreverim. </s>

<s>Plura enim <emph type="italics"/>De seminum vegetatione, Gallis, Radicibus et Spi&shy;<lb/>nis<emph.end type="italics"/> delineanda mihi supersunt &rdquo; (Malp. </s>

<s>et Oldenb. </s>

<s>epistolae variae, Operum <lb/>T. </s>

<s>I cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Non molti mesi dopo, dato ordine anche a questi trattati, furono per la <lb/>medesima via spediti da Bologna a Londra. </s>

<s>Veniva cos&igrave;, per le due distinte <lb/>spedizioni, l'opera malpighiana divisa in due parti, ma si comprende bene <lb/>come non era quella una divisione logica, avendo l'Autore, sollecitato dalle <lb/>promesse e dagli stimoli dell'emulazione, mandati prima quei quaderni, il <pb xlink:href="020/01/1641.jpg" pagenum="516"/>soggetto de'quali non avea bisogno d'ulteriore studio per parte dell'Autore, <lb/>e per parte dell'Artista era gi&agrave; terminato d'illustrare dai relativi iconismi. </s></p><p type="main">

<s>Esaminati dall'Accademia cotesti quaderni manoscritti, si consegnarono <lb/>al tipografo, il quale, tenuta la divisione delle due parti, com'era venuta <lb/>fatta dalle due diverse consegne del procaccia veneto, gli compose secondo <lb/>gli venivano a mano, e gli dette in Londra alla luce nel 1675, senza che <lb/>fosse l'opera manuale diretta da nessuna amorosa intelligenza. </s>

<s>Ebbe di qui <lb/>origine quel disordine, che si lamenta da tutti, e di che si pu&ograve; giustamente <lb/>rimproverar l'Oldenburg e i suoi colleghi. </s></p><p type="main">

<s>Il leydese editore di tutte le Opere del Malpighi, raccogliendo nel primo <lb/>Tomo l'Anatomia delle piante, si volle provare a dar miglior ordine ai di&shy;<lb/>versi trattati, ma avendo anch'egli mantenuta la prima duplice accidental <lb/>partizione, non s'avvide come veniva in ogni modo l'opera con tal disegno, <lb/>che avea, non solo dell'informe, ma del mostruoso. </s>

<s>Si chiude infatti col <lb/>trattato <emph type="italics"/>De radicibus,<emph.end type="italics"/> rappresentando un albero capovolto in selva scompi&shy;<lb/>gliata dalla tempesta. </s></p><p type="main">

<s>Se avesse l'Oldenburg, prima di consegnare al tipografo il manoscritto, <lb/>consultato l'Autore, forse avrebbe il Malpighi prescritto un tal ordine ai suoi <lb/>trattati. </s>

<s>Nel primo, <emph type="italics"/>Anatomes plantarum Idea,<emph.end type="italics"/> e <emph type="italics"/>De seminum vegetatione,<emph.end type="italics"/><lb/>che l'assomiglierebbero al primo libro del Grew; nel secondo, <emph type="italics"/>De radici&shy;<lb/>bus,<emph.end type="italics"/> che farebbe esatto riscontro col II libro dell'Anatomia inglese; nel <lb/>terzo, <emph type="italics"/>De cortice, De partibus caulem, vel caudicem componentibus, De <lb/>caudicis augmento et nodis,<emph.end type="italics"/> soggetti di trattazioni, che rientrano nel III li&shy;<lb/>bro <emph type="italics"/>Of trunks;<emph.end type="italics"/> nel quarto <emph type="italics"/>De gemmis, De foliis, De floribus, De seminum <lb/>generatione,<emph.end type="italics"/> distintamente delineati nel IV libro greviano. </s></p><p type="main">

<s>L'Embriologia malpighiana descritta nelle dissertazioni <emph type="italics"/>De uterorum <lb/>augmento, et ipsorum succedente forma, De secundinis et contento plan&shy;<lb/>tarum foetu;<emph.end type="italics"/> la Patologia, di che s'ha un saggio insigne ne'discorsi <emph type="italics"/>De <lb/>gallis, De variis plantarum tumoribus et excrescentiis;<emph.end type="italics"/> l'Anatomia degli <lb/>organi accessorii e trasformati <emph type="italics"/>De pilis et spinis, De capreolis et consimi&shy;<lb/>libus vinculis,<emph.end type="italics"/> e all'ultimo quella pi&ugrave; importante parte e pi&ugrave; nuova <emph type="italics"/>De <lb/>plantis quae in aliis vegetant,<emph.end type="italics"/> non trovano ne'trattati del Grew confronto, <lb/>per cui verrebbe, infin dell'indice, quando specialmente fossero le materie <lb/>bene ordinate, a rivelarsi la maggiore estensione, che sopra quella dell'ln&shy;<lb/>glese ha l'opera anatomica del Nostro. </s></p><p type="main">

<s>Alla pubblicazione di questa successe pochi mesi dopo la pubblicazione <lb/>della III parte di quella, col titolo <emph type="italics"/>The anatomy of trunks,<emph.end type="italics"/> tradotta dai <emph type="italics"/>Cu&shy;<lb/>riosi della Natura,<emph.end type="italics"/> col titolo <emph type="italics"/>Comparativa anatomia truncorum.<emph.end type="italics"/> Dedicando <lb/>l'Autore al presidente Brouncker il suo libro, torna per la seconda volta a <lb/>parlare in pubblico del Malpighi, la compiuta opera del quale si studiava <lb/>di comparare alla sua non ancora perfetta. </s>

<s>Rivendicava a s&egrave; la scoperta <lb/>delle trachee, delle quali nel cap. </s>

<s>II dei Primordii avea data la descrizione, <lb/>se non che, riserbando a un secondo conato le osservazioni microscopiche, <lb/>confessava di non avere scorto in quegli organi la struttura spirale. </s>

<s>&ldquo; Si-<pb xlink:href="020/01/1642.jpg" pagenum="517"/>mili ratione, poi soggiunge, eiusmodi observationes, quales D. </s>

<s>Malpighius <lb/>non inseruit libro suo primo, inventa sunt in primo meorum, ex. </s>

<s>gr. </s>

<s>de&shy;<lb/>scriptio comae floridae in omnibus Corymbiferis et aliis floribus similari&shy;<lb/>bus; de acetario in centro pyrorum omnis generis; de nucleo in prunis <lb/>omnis generis; de tertio quodam et interno integumento reperto in omni&shy;<lb/>bus fere seminibus cuiuscumque generis analogo saepe secundinae; intume&shy;<lb/>scentia prodigiosa involucrorum, in specie in fructibus cum nucleo, in gene&shy;<lb/>ratione seminis, et post eorum contractio iuxta rationem uteri in quibusdam <lb/>animalibus, cum variis aliis, quorum quaedam non rcperiuntur in secundo <lb/>D. </s>

<s>Malpighi libro, et quaedam adhuc desiderantur..... Id imponam mode&shy;<lb/>stiae notandae me a D. </s>

<s>Malpighio <emph type="italics"/>variare in omnibus,<emph.end type="italics"/> ut mihi videtur, exhi&shy;<lb/>bitis exemplis &rdquo; (Appendix anni IX et X, Norimbergae 1676, pag. </s>

<s>228, 29). </s></p><p type="main">

<s>Da quali sentimenti fossero inspirate queste parole &egrave; troppo facile in&shy;<lb/>tendere, ma convien dire che fosse ardentissimo il desiderio del Grew d'ap&shy;<lb/>parir superiore in certe cose al suo rivale, e in certe altre da'pensieri di <lb/>lui indipendente, se s'indusse a istituire il confronto fra un'opera gi&agrave; com&shy;<lb/>piuta e la sua propria lasciata a mezzo. </s>

<s>Gli rimaneva infatti a rivestire il <lb/>tronco di <emph type="italics"/>Fronde<emph.end type="italics"/> e di <emph type="italics"/>Fiori;<emph.end type="italics"/> di fiori, che allegano in <emph type="italics"/>Frutti,<emph.end type="italics"/> di frutti che <lb/>concepiscono <emph type="italics"/>Semi.<emph.end type="italics"/> Le quattro trattazioni erano nel 1676 compiute, ma ne <lb/>fu indugiata dall'Autore le stampa perch&egrave;, componendosi di esse il IV libro <lb/>dell'Anatomia delle piante, voleva esser questo riunito agli altri tre libri, <lb/>che lo avevano di alcuni anni preceduto, per esibire al pubblico in un vo&shy;<lb/>lume l'opera tutta intiera. </s>

<s>Quel volume in folio apparve in fatti in Londra <lb/>nel 1682 col titolo: <emph type="italics"/>The anatomy of plants, with an idea of a philoso&shy;<lb/>phical history of plants.<emph.end type="italics"/> Cosicch&egrave; quel che primo avea preso le mosse fu <lb/>l'ultimo a toccare la meta. </s>

<s>Ma il Malpighi non se ne vant&ograve;, che si sappia, <lb/>e pi&ugrave; prudente del Grew lasci&ograve; libero il giudizio ai posteri, l'opinion dei <lb/>quali oramai &egrave; che ambedue gli Autori concorressero a instituire la Fitolo&shy;<lb/>gia col fortuito riscontro delle idee, e pi&ugrave; forse con le divergenze, d'onde <lb/>venne occasione a ricercare il vero, per via di nuove osservazioni e di pi&ugrave; <lb/>accurati esperimenti. </s>

<s>Non parve in ogni modo agl'imparziali n&egrave; ingiusta n&egrave; <lb/>lusinghiera la sentenza di chi concluse esser l'opera dell'Italiano pi&ugrave; estesa <lb/>e pi&ugrave; profonda. </s></p><p type="main">

<s>In quel medesimo tempo in Francia due Fisici illustri, inconsapevoli <lb/>essi pure l'uno dell'altro, attendevano alla Fisiologia delle piante. </s>

<s>E perch&egrave; <lb/>il soggetto de'loro studii era circoscritto a sole alcune particolari funzioni <lb/>dell'Economia vegetabile, in dar pubblicit&agrave; alle loro idee, per mezzo delle <lb/>accademiche relazioni, prevennero di qualche anno il Grew e il Malpighi. </s>

<s>Il <lb/>primo de'commemorati Autori, che fra'suoi <emph type="italics"/>Essais de Physique<emph.end type="italics"/> ha il primo <lb/>intitolato <emph type="italics"/>De la vegetation des plants,<emph.end type="italics"/> &egrave; il Mariotte, e il secondo &egrave; il Per&shy;<lb/>rault, il quale cos&igrave; scrive in un avvertimento premesso al suo trattato <emph type="italics"/>De <lb/>la circulation de la seve des plantes:<emph.end type="italics"/> &ldquo; Celles d'entre les experiences qui <lb/>sont novelles, ont &eacute;t&eacute; faites sur les Memoires que M. </s>

<s>Mariotte et moi avons <lb/>donnez: car cette pens&eacute;e de la circulation de la seve des plantes nous &egrave;toit <pb xlink:href="020/01/1643.jpg" pagenum="518"/>venue &agrave; tous deux sans nous l'&ecirc;tre communiqu&eacute;e. </s>

<s>La premi&egrave;re fois qu'on <lb/>en parla dans la Compagnie ce fut &agrave; l'Assemblee du 15 Janvier 1667 ou <lb/>dans le Plan que je faifois d'une Historie generale des plantes, au chapitre <lb/><emph type="italics"/>Des causes des plantes<emph.end type="italics"/> entre autres choses j'expliquai les coniectures sur <lb/>lesquelles je fondois le nouveau paradoxe, et dont je ne croyois point que <lb/>personne e&ucirc;t jamais eu la pens&eacute; &rdquo; (Oeuvres, T. </s>

<s>I cit., pag. </s>

<s>69, 70). </s></p><p type="main">

<s>Il bisogno di provar l'assunto, per via di esperienze, porse al Mariotte <lb/>e al Perrault occasione di applicar le leggi della fisica, non a sola la circo&shy;<lb/>lazion del succo, ma a parecchie altre funzioni della vita vegetativa o male <lb/>intese o non ancora scoperte; cosicch&egrave;, aggiunta l'opera de'due citati Fran&shy;<lb/>cesi a quella del Malpighi e del Grew, si pu&ograve; dir che toccasse in pochi anni <lb/>la storia delle piante quella perfezione, per raggiunger la quale avea tanti <lb/>secoli penato la storia degli animali. </s>

<s>Se avessimo alla storia della Botanica <lb/>potuto consacrare un libro, sarebbe stato ivi il luogo a descrivere le ragioni e <lb/>il modo di cos&igrave; mirabili progressi, ma essendo assegnata al soggetto la sola <lb/>prima angusta parte di questo capitolo, non &egrave; possibile che di qualche stilla, <lb/>attinta a quell'ampio mare, soccorrere alla sete dei nostri Lettori. </s>

<s>E giac&shy;<lb/>ch&egrave; la causa dell'ascesa della linfa ci si present&ograve; nella storia come una delle <lb/>prime e principali investigazioni, a cui si volse la scienza, giova riappiccar <lb/>l&agrave; dove fu lasciato interrotto il filo del nostro discorso, per accennare a <lb/>que'progressi, che fece una s&igrave; astrusa e desiderata notizia in tempi, che la <lb/>Fisiologia delle piante ebbe, dall'opera contemporanea degli Autori sopra <lb/>commemorati, cos&igrave; validi impulsi. </s></p><p type="main">

<s>Il Malpighi, scoperte le trachee delle piante, ch'ei reput&ograve; servire come <lb/>negl'insetti alla respirazione, applic&ograve; ad esse trachee legnose l'ufficio se&shy;<lb/>condario di promovere il succo, a quel modo che promovono il chilo e il <lb/>sangue ne'vasi degli animali i moti alternativi del torace. </s>

<s>&ldquo; Et sicut in no&shy;<lb/>bis, reliquisque sanguineis analogis respirationis motus, interpolatis impul&shy;<lb/>sibus, promovet chyli et aliorum succorum motum, per lactea et consimilia <lb/>vasa; ita ex trachearum dilatatione, intus urgente aere, necessario urgentur <lb/>interceptae ligneac fibrae et horizontales utriculorum appendices, et ita pro&shy;<lb/>babiliter fit contenti succi expressio in contiguas partes. </s>

<s>Remittente vero <lb/>tumore, laxiores redditi utriculi et fistulae ligneae, facilius novum admit&shy;<lb/>tunt humorem &rdquo; (De cortice Op. </s>

<s>omnia, T. </s>

<s>I cit., pag. </s>

<s>34). </s></p><p type="main">

<s>Il Borelli per&ograve; che, come udimmo, non consentiva col Malpighi intorno <lb/>all'uso primario delle trachee, non consentiva nemmeno intorno a questo <lb/>particolare uso secondario, e in altre cause meccaniche ricerc&ograve; nelle piante <lb/>la virt&ugrave; impulsiva del succo. </s>

<s>Gli si presentavano alla mente in questa ri&shy;<lb/>cerca le ipotesi dell'Aggiunti e del Castelli, mantenute vive ne'tradizionali <lb/>insegnamenti di que'due primi e valorosi discepoli di Galileo, e suoi stima&shy;<lb/>tissimi Maestri; ma perch&egrave; gli sembrava che alcuni fatti non favorissero <lb/>l'ipotesi dell'ascesa della linfa per cause capillari, si volse ad applicare a <lb/>quell'effetto la meccanica del Termometro santoriano. </s>

<s>Signific&ograve; questi suoi <lb/>pensieri al Malpighi, il quale, per non irritarsi l'animo di quell'uomo sde-<pb xlink:href="020/01/1644.jpg" pagenum="519"/>gnoso, dop'aver fatto qualche segno di secondarli, pens&ograve; bene di togliersi <lb/>d'ogni impaccio col dire che lasciava la dimostrazione di quelle cose ai sa&shy;<lb/>gaci Meccanici. </s>

<s>&ldquo; Subintrans itaque humor sursum ascendit et quasi suspen&shy;<lb/>ditur. </s>

<s>Singula namque portio quae invicem fibrarum frustula unit cum pa&shy;<lb/>rum interius emineat valvulae vices supplet, et ita minima quaelibet guttula <lb/>veluti per funem, seu per gradus ad ingens deducitur fastigium. </s>

<s>Hunc au&shy;<lb/>tem ascensum non tantum fistularum interior asperitas iuvat, sed et succes&shy;<lb/>siva aeris temperies, calida scilicet et frigida ex diei noctisque variis crasibus, <lb/>eiusque elasticus motus qui exteriora corticis involucra urgens contentorum <lb/>liquorum motum superiora versus promovere et iuvare potest: quae singula <lb/>sagacioribus Mechanicis demonstranda relinquo &rdquo; (ibid., pag. </s>

<s>22, 23). </s></p><p type="main">

<s>Queste ultime parole accennano senza dubbio al Borelli, il quale rispose <lb/>all'invito nel capitolo XIII della II parte <emph type="italics"/>De motu animalium,<emph.end type="italics"/> dove, intro&shy;<lb/>ducendosi a trattar della generazione e vegetazion delle piante, dop'avere <lb/>accennato al Malpighi che, coll'aiuto del microscopio, dette della struttura <lb/>di esse piante esattissima cognizione, &ldquo; ego tantum proferam theoricam, poi <lb/>soggiunge, quam ex B. </s>

<s>Castello praeceptore didici, et quae deinceps medi&shy;<lb/>tatus sum &rdquo; (Editio cit., pag. </s>

<s>358). </s></p><p type="main">

<s>Descritto nella proposizione CLXXV quello, da Galileo chiamato <emph type="italics"/>Stru&shy;<lb/>mento<emph.end type="italics"/> e da lui, discepolo del Castelli, <emph type="italics"/>Termometro santoriano,<emph.end type="italics"/> passa a farne <lb/>l'applicazione, dicendo che il cannello di vetro rappresenta le fistole spu&shy;<lb/>gnose delle piante, su per le quali, facendo esse spugnosit&agrave; da valvole, il <lb/>succo ascende per gradi, succedendo al calore rarefacente del giorno la con&shy;<lb/>densatrice frigidit&agrave; della notte. </s>

<s>&ldquo; Ergo inflando vesciculas porosas molles <lb/>tota moles augebitur. </s>

<s>Postea, superveniente refrigeratione nocturna, aut a <lb/>vento facta, aer in spongioso spatio contentus denuo condensabitur, et proinde <lb/>aqua ulterius promovebitur, et sic novis vicissitudinibus priori similibus &rdquo; <lb/>(ibid., pag. </s>

<s>359). </s></p><p type="main">

<s>Il Borelli escluse come accennammo l'attrazion capillare perch&egrave;, reciso <lb/>un ramo, seguita a stillar l'umore sul tronco eretto dalla cicatrice supina <lb/>(ibid., pag. </s>

<s>372), ma il Mariotte non invocava altre forze attrattive che quelle <lb/>stesse capillari, ritornando a vita, e dando autorit&agrave; all'abbandonata ipotesi <lb/>dell'Aggiunti. </s>

<s>&ldquo; Cette premi&egrave;re entr&eacute;e de l'eau dans les racines, scrive nel <lb/>Saggio fisico <emph type="italics"/>De la vegetation des plantes,<emph.end type="italics"/> se fait par una loi de la nature, <lb/>car par-tout ou il y a des tuyaux tres-&eacute;troits, qui touchent l'eau, elle y <lb/>entre, et m&ecirc;me elle y monte contre sa pente naturelle de descendre &rdquo; (Oeu&shy;<lb/>vres, T. </s>

<s>I cit., pag. </s>

<s>130). E prosegue a descrivere la notissima esperienza <lb/>dell'acqua, che ascende su per i sottilissimi tubi di vetro, applicandola non <lb/>a sole le radici ma ai vasi del tronco. </s></p><p type="main">

<s>Il Perrault dall'altra parte elabor&ograve; cos&igrave; l'ipotesi del Castelli, da darle <lb/>quasi una impronta di originalit&agrave;, assegnando a spiegare il fatto del passare <lb/>il succo dalle radici ai rami le due cause seguenti: &ldquo; l'un est l'impulsion, <lb/>l'autre est l'ouverture des conduits, qui doivent recevoir et donner passage <lb/>&agrave; ce qui est pouff&eacute;. </s>

<s>L'un et l'autre se fait par la rarefaction, qui est capa-<pb xlink:href="020/01/1645.jpg" pagenum="520"/>ble non seulement de dilater les conduits et les pores des racines, mais aussi <lb/>de faire gonfler le suc contenu dans la terre, lorsque par la chaleur du <lb/>dehors, iointe &agrave; celle qui est dans la terre, et par celle de la fermentation <lb/>qu'il con&ccedil;oit &agrave; l'attouchement des racines, qui en contiennent le principe, il <lb/>souffre une dilatation qui lui fait avoir besoin d'un lieu plus spacieux pour <lb/>s'&eacute;tendre: car cette dilatation le force &agrave; s'insinuer dans les conduits qu'il <lb/>rencentre ouverts, soit dans la racine, soit dans le tronc et dans les branches, <lb/>jusqu'&agrave; l'extr&eacute;mit&eacute; de la plante &rdquo; (De la circol. </s>

<s>de la seve, Ouvres cit., pag. </s>

<s>77). </s></p><p type="main">

<s>In tutte queste ipotesi per&ograve; fin qui recensite non si rendeva chiaro a <lb/>intendere quel cos&igrave; continuo e regolare afflusso del succo dalla radice alle <lb/>foglie, che il Cesalpino vedeva tanto bene rappresentato dall'immagine della <lb/>fiamma, alla quale regolarmente affluisce l'olio della lucerna. </s>

<s>Le splendide <lb/>analogie cesalpiniane si dovettero come inutili e anzi nocive ripudiare dalla <lb/>Fisica nuova, infintanto che non venne a sostituirsi una causa reale all'im&shy;<lb/>maginario calore innato de'germogli che si svolgono, e dei frutti che ma&shy;<lb/>turano, come una causa reale era stata dall'Aggiunti sostuita all'immaginato <lb/>calor del cuore vegetativo, che attira il succo dalle radici. </s>

<s>E perch&egrave; questa <lb/>reale causa fisica risiedeva propriamente col&agrave; dove il Cesalpino l'aveva un <lb/>po'in confuso indicata, cio&egrave; nelle foglie, a compier l'opera dell'Aggiunti <lb/>conveniva aver quella esatta notizia della fisiologia delle stesse foglie, che <lb/>s'ebbe solo un secolo dopo che l'anatomia del Malpighi dette instituto e <lb/>impulso di progredire al&igrave;a nuova scienza. </s>

<s>Apparvero notabilissimi questi pro&shy;<lb/>gressi nel secolo XVIII, quando Stefano Hales, Enrico Lodovico Du-Hamel <lb/>e Carlo Bonnet raccolsero ne'loro libri i frutti di tante varie e ingegnose <lb/>esperienze. </s>

<s>Hanno molte di quelle esperienze per soggetto le foglie, e giac&shy;<lb/>ch&egrave; elle sono un organo principalissimo, a cui fra le altre funzioni della vita <lb/>vegetativa &egrave; attribuita anche quella di promovere efficacemente l'ascesa del <lb/>succo nutritizio; per le relazioni coll'argomento che trattiamo, e per l'im&shy;<lb/>portanza che ha in s&egrave; medesimo, sopra le foglie intratterremo il discorso. </s></p><p type="main">

<s>S'acquistarono dagli antichi le foglie il titolo di lussuriose, e tutto al <lb/>pi&ugrave; si ammetteva che fossero in s&igrave; bell'ordine disposte sui rami, per ripa&shy;<lb/>rare dai soverchi ardori del sole la delicata giovanezza dei frutti. </s>

<s>Ma quando <lb/>il Malpighi notomizzandole trov&ograve; in esse tutti insieme raccolti i varii organi, <lb/>da rappresentarglisi come in compendio tutta intera la pianta, s'avvide che <lb/>dovevano quelle fronde calunniosamente credute una lussuria esser precipue <lb/>e insigni parti integranti degli alberi e dell'erbe. </s>

<s>Ripensava a quale impor&shy;<lb/>tante ufficio fossero dunque ordinate, e vedendo che ne'germoglianti semi <lb/>quell'ufficio &egrave; di nutrire, ebbe a congetturarne perci&ograve; che, serbando le fo&shy;<lb/>glie adulte la medesima natura delle seminali, dovessero proseguire altres&igrave; <lb/>i medesimi ministeri. </s>

<s>&ldquo; Taliter excitata folia videntur a Natura fabrefacta <lb/>ut coctioni alimenti, quae praecipua est, inserviant..... Probabilem nutri&shy;<lb/>titii succi in foliis coctionem indicare videtur seminalis ptantulae structura: <lb/>hanc constare geminis foliis evidens est, quae propriis vasculis et utriculis <lb/>succo turgidis ditantur &rdquo; (De foliis, Op. </s>

<s>omnia cit., pag. </s>

<s>54). </s></p><pb xlink:href="020/01/1646.jpg" pagenum="521"/><p type="main">

<s>In quel medesimo tempo che l'Anatomia al Malpighi, l'esperienze fisi&shy;<lb/>che rivelavano al Mariotte e al Perrault l'importanza grandissima delle fo&shy;<lb/>glie nell'economia vegetabile. </s>

<s>S'era il secondo di questi Autori trattenuto <lb/>pi&ugrave; volte innanzi a que'grandi alberi, che sorgono dal lastricato delle piazze <lb/>cittadine, per domandar come mai, non andando una stilla di pioggia alle <lb/>loro radici, potessero pur cos&igrave; lietamente vivere e prosperare. </s>

<s>Si credette <lb/>averne per risposta che mantenevansi in quella loro giovanile freschezza <lb/>&ldquo; par le moyen des humiditez qu'ils re&ccedil;oivent de l'air des pluyes et des ro&shy;<lb/>sees &rdquo; (De la circ. </s>

<s>cit., pag. </s>

<s>92). Anche il Malpighi, accennando, nella <emph type="italics"/>Ve&shy;<lb/>getazione dei semi,<emph.end type="italics"/> ai cotiledoni, che ora sono <emph type="italics"/>ipogei,<emph.end type="italics"/> come oggidi si dice, <lb/>ora sono <emph type="italics"/>apogei,<emph.end type="italics"/> sospett&ograve; che giusto rimanessero questi sopra terra per at&shy;<lb/>trar l'umore dell'aria ambiente, e somministrarlo alla tenera pianticella. <lb/></s>

<s>&ldquo; Longe a terra locantur et post primos incubationis dies humor a terreno <lb/>utero per caulem communicatur, ni velimus suspicari ab ambiente aere iis <lb/>subministrari &rdquo; (Oper., T. </s>

<s>I cit., pag. </s>

<s>111). Ma il Mariotte se ne assicur&ograve; <lb/>per una bella esperienza, ch'egli, nel sopra citato <emph type="italics"/>Saggio della vegetazion <lb/>delle piante,<emph.end type="italics"/> cos&igrave; descrive: &ldquo; Si l'on coupe une petite branche d'arbre ou <lb/>de quelque herbe, comme du persil, cerfevil, etc., ou il y ait quelque bran&shy;<lb/>chette &agrave; c&ocirc;t&eacute;, et qu'on trempe l'extr&eacute;mit&eacute; des fevilles dans de l'eau, lais&shy;<lb/>sant la tige avec la branchette sur le bord du vaisseau ou sera l'eau, cette <lb/>branchette se conservera verte trois ou quatre jours..... Au lieu que si on <lb/>met d'autres herbes ou petites branches d'arbre semblables sur le bord du <lb/>vaisseau, sans toucher &agrave; l'eau, elles se fletriront et secheront en peu de <lb/>tems. </s>

<s>&rdquo; D'onde con certezza di fatto ne conclude che: &ldquo; le primier suc qui <lb/>vient de dehors, n'entre pas seulement par la racine dans les plantes, mais <lb/>aussi par les fevilles et par les branches, et elles le re&ccedil;oivent de la ros&eacute;e <lb/>ou de la pluie, ou des vapeurs dont l'air est toujours rempli &rdquo; (Oeuvres <lb/>cit., pag. </s>

<s>133). </s></p><p type="main">

<s>Il nuovo fatto cos&igrave;, verso il 1667, scoperto in Francia e dimostrato, fu <lb/>quasi il primo talento trasmesso a que'valorosissimi Fisici botanici del se&shy;<lb/>colo XVIII che, coltivandolo n'ebbero a ricavare un s&igrave; largo frutto. </s>

<s>L'Hales <lb/>lo conferm&ograve; per via di una diligentissima esperienza, descritta nel cap. </s>

<s>IV <lb/>della sua Statica de'vegetabili, tagliando un grosso ramo di melo, e tenen&shy;<lb/>dolo capovolto colla punta immersa nell'acqua di una caraffella di vetro. </s>

<s>&ldquo; In <lb/>tre giorni e due notti, egli dice, attrasse in questa maniera e traspir&ograve; quat&shy;<lb/>tro libbre e due once e mezzo di acqua, e le fronde si conservarono verdi, <lb/>mentre quelle d'un altro ramo, nell'istesso tempo separato dall'istesso al&shy;<lb/>bero, senza metterlo nell'acqua, invizzirono quarant'ore prima &rdquo; (Traduz. </s>

<s><lb/>ital., Napoli 1756, pag. </s>

<s>107). </s></p><p type="main">

<s>La dimostrata importanza delle foglie, nella nutrizione degli alberi e <lb/>dell'erbe, invogli&ograve; a mezzo il secolo XVIII Carlo Bonnet a far quegli or&shy;<lb/>gani soggetto di uno studio particolare. </s>

<s>Avendo notata la differenza grande <lb/>che passa negli alberi, fra la superficie inferiore di esse foglie e la supe&shy;<lb/>riore, la prima cosa che gli occorse al pensiero fu quella d'investigare il <pb xlink:href="020/01/1647.jpg" pagenum="522"/>fine, ch'ebbe di far cos&igrave; la sapiente Natura. </s>

<s>Avvertendo perci&ograve; che le ru&shy;<lb/>giade salgono da terra incominci&ograve; a dubitare se i peli e altre scabrosit&agrave; fos&shy;<lb/>sero date alla pagina fogliacea inferiore, per ritener pi&ugrave; facilmente l'umi&shy;<lb/>dit&agrave;, che incontro a lei sale. </s>

<s>&ldquo; L'experience d&eacute;montre que la ros&eacute;e s'&eacute;leve <lb/>de la terre. </s>

<s>La surface inferieure des fevilles auroit-elle &eacute;t&eacute; principalement <lb/>destin&eacute;e &agrave; pomper cette vapeur, et &agrave; la transmettre dans l'interieur de la <lb/>plante? </s>

<s>La position des fevilles relativement &agrave; la terre et le tissu de leur <lb/>surface inferieure semblent l'indiquer &rdquo; (Recherches sur l'usage des fevil&shy;<lb/>les a Neuchatel 1779, pag. </s>

<s>19, 20). Furono poi i dubbi confermati dall'espe&shy;<lb/>rienze, osservando che molto pi&ugrave; s'imbeve una foglia posata sull'acqua colla <lb/>superfice inferiore, in che trovava altres&igrave; il Bonnet la ragione perch&egrave; le umili <lb/>erbe immerse nella rugiada abbiano le due pagine delle loro foglie disposte <lb/>a sorbir l'umido ugualmente. </s>

<s>Il vento e le mani dell'agricultore fanno so&shy;<lb/>vente cangiar direzione alle foglie, cosicch&egrave; si trovano com'animale supino <lb/>fuori della loro posizion naturale. </s>

<s>Ma elle, tanto importa alla loro prospera <lb/>vita, &ldquo; savent la rependre d'elles-m&egrave;mes, par un mouvement qui leur est <lb/>propre, et qui paroit presque aussi spontane que ceux que se donnent di&shy;<lb/>vers animaux pour des fins analogues &rdquo; (ivi, pag. </s>

<s>11). </s></p><p type="main">

<s>Le foglie assorbiscono dunque come la cute: e perch&egrave; da un secolo e <lb/>mezzo d'esperienze veniva dimostrato ch'essa cute, mentre da una parte <lb/>riceve dal di fuori, dall'altra lo rimanda, si volle saper se le piante abbiano <lb/>con gli animali comune anche la virt&ugrave; di traspirare. </s>

<s>Il Malpighi dal trovar <lb/>nelle foglie vasi sudoriferi, simili ai cutanei, aveva gi&agrave; congetturato in esse <lb/>l'esistenza di questa funzione. </s>

<s>&ldquo; In folia, compendio quodam singula vasa <lb/>tracheae scilicet, fistulae ligneae et peculiaria vascula desinunt extremis fini&shy;<lb/>bus, nec desinunt sudoris vascula et transpiratus, quare credidi cutis seu <lb/>corii munia subire &rdquo; (De foliis in loco cit., pag. </s>

<s>54). </s></p><p type="main">

<s>Primo a dimostrare sperimentalmente il supposto sembra fosse il Mu&shy;<lb/>schenbroeck, operando in un modo simile a quello descritto nella XVII fra <lb/>le statistiche esperienze halesiane. </s>

<s>&ldquo; Avendo dalle precedenti esperienze co&shy;<lb/>nosciuto evidentemente che le piante gran copia attraggono e respirano <lb/>d'umido, volli tentar di raccogliere la materia della loro traspirazione, e <lb/>per venirne a capo presi diverse storte di vetro, delle quali feci entrare in <lb/>ciascuna un ramo per sorte di diversi alberi colle sue frondi sopra, chiu&shy;<lb/>dendo l'apertura con vescica ben legata intorno al collo della storta. </s>

<s>Ed in <lb/>questa maniera molt'once raccolsi della respirazione della vite, del fico, del <lb/>melo, ecc. </s>

<s>&rdquo; (Traduz. </s>

<s>cit., pag. </s>

<s>45). </s></p><p type="main">

<s>Bench&egrave; non fosse l'Hales il primo a far l'esperienza fu per&ograve; il primo <lb/>ad applicarla alla causa dell'ascesa del succo, dimostrando che la traspira&shy;<lb/>zione fa l'effetto appunto della fiamma sull'olio della lucerna. </s>

<s>&ldquo; Dall'an&shy;<lb/>zidette osservazioni e sperienze vien dimostrato, egli dice, che le foglie danno <lb/>un grandissimo aiuto alla vegetazion delle piante, poich&egrave; servono per dir <lb/>cos&igrave; come tante trombe per sollevar le particelle nutritive e per farle giun&shy;<lb/>gere fino alla sfera d'attrazione del frutto &rdquo; (ivi, pag. </s>

<s>255). Sopra queste <pb xlink:href="020/01/1648.jpg" pagenum="523"/>halesiane dottrine sperimentalmente dimostrate il Du-Hamel, nel <emph type="italics"/>Trait&eacute; des <lb/>arbres fruitiers,<emph.end type="italics"/> formul&ograve; la sua VII proposizione: &ldquo; Les fevilles influent tal&shy;<lb/>lement sur la quantit&eacute; et le mouvement de la seve, qu'elle augmente ou <lb/>diminue a proportion de leur nombre et de leur &ecirc;tat &rdquo; (Paris 1782, pag. </s>

<s>122). <lb/>Cos&igrave; un fatto fisico veniva un'altra volta a sostituirsi all'immaginario calore <lb/>innato del Cesalpino, e se non l'unico era senza dubbio ritrovato all'ascesa <lb/>del succo nutritizio il pi&ugrave; valido impulso. </s>

<s>Il Bonnet poi chiam&ograve; tutte insieme <lb/>a concorso le varie forze, proposte a produr quell'ascesa dai varii Autori <lb/>che lo avevano preceduto; ci&ograve; che in cosa di tanta difficolt&agrave;, e soggetta a <lb/>tanti differenti giudizii, trov&ograve; lode ne'successori e imitazion dell'esempio. <lb/></s>

<s>&ldquo; L'estrema finezza dei condotti del succo, leggesi nella <emph type="italics"/>Contemplazione <lb/>della Natura,<emph.end type="italics"/> che li fa essere in certo modo capillari, l'azione dell'aria <lb/>sulla lama elastica delle trachee, e l'impressione di queste sulle fibre legnose <lb/>che abbracciano, o da cui sono abbracciate, il calore che raref&agrave; il succo, <lb/>quel calore massimamente che agendo sulla superfice delle foglie vi attrae <lb/>il superfluo del succo nutritivo, e vi produce lo svaporamento; sembrano <lb/>essere le cagioni principali dell'ascendere di questo fluido dentro le piante &rdquo; <lb/>(Traduz. </s>

<s>cit., T. I, pag. </s>

<s>188). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Le singolarissime esperienze fisiche, per via delle quali s'incominci&ograve; a <lb/>riconoscere la grande importanza fisiologica delle foglie, furono intraprese <lb/>dal Mariotte e dal Perrault per servir d'argomento a dimostrare una loro <lb/>opinione, secondo la quale si pretendeva che circolasse la linfa nelle piante, <lb/>come circola il sangue negli animali. </s>

<s>Vedeva di questa circolazione il Per&shy;<lb/>rault ricorrergli all'immaginoso pensiero due esempi: quello dell'acqua, che <lb/>si solleva in aria, dove sciolti i sali infin lass&ugrave; sollevati ritorna con essi in <lb/>pioggia a deporli sopra la terra; e quello dell'aratura, l'effetto della quale <lb/>&egrave; di rivoltare continuamente le zolle in modo, che la parte di sopra, fecon&shy;<lb/>data dal sole, dall'aria e dalle piogge torni di sotto a partecipar la sua fe&shy;<lb/>condit&agrave; alle radici degli alberi, e alle barboline dei semi. </s></p><p type="main">

<s>&ldquo; Il semble donc que ces circulations dans les &ecirc;tres non-vivans ont <lb/>quelque rapport avec celle que l'on estime se devoir faire dans les plantes, <lb/>quoiqu'elles se fassent d'une maniere oppos&eacute;e a celle des plantes et des ani&shy;<lb/>maux: car de m&ecirc;me que les eaux de la pluye descendent sur la terre pour <lb/>y laisser ce qu'elles ont contract&eacute; de gras et de propre a nourrir dans ces <lb/>regions superieures, et qu'elles en ressortent maigres et steriles lorsqu'elles <lb/>en sont &eacute;lev&eacute;es, c'est &agrave;-peu-pres de la m&ecirc;me maniere que l'humidit&eacute;, dont <lb/>les plantes sont nourries, sortant de la racine monte dans la tige, dans les <lb/>branches, et dans les fevilles, avec des qualitez convenables &agrave; chacune de <lb/>ces parties, et apres y avoir laiss&eacute; ce qu'elle a de propre pour leur nour-<pb xlink:href="020/01/1649.jpg" pagenum="524"/>riture et pour leur accroissement, le reste qui est inutile descend dans la <lb/>racine, pour y &egrave;tre cuit et pr&eacute;par&eacute; de nouveau, et la &eacute;tant iointe &agrave; l'autre <lb/>suc que la racine re&ccedil;oit de la terre, ce suc remonte dans les parties supe&shy;<lb/>rieures de la plante, et l'on suppos&eacute; que cela se fait de la m&egrave;me fa&ccedil;on que <lb/>dans les animaux, ou le sang arteriel sortant du coeur, qui est &agrave; leur &eacute;gard <lb/>ce que la partie la plus noble de la racine est dans les plantes, se distribue <lb/>dans tout le corps, qui ayant retenu ce que ce sang a de propre pour l'en&shy;<lb/>tretenir, renvoye le reste au coeur, afin qu'&eacute;tant joint au suc que les veines <lb/>lact&eacute;es ont re&ccedil;u des intestins, qui sont aux animaux ce que la terre est aux <lb/>plantes, il retourne dans toutes les parties du corps, pour entretenir une <lb/>circulation continuelle &rdquo; (Oeuvres, T. </s>

<s>I cit., pag. </s>

<s>73). </s></p><p type="main">

<s>L'Autore, a cui sovvennero questi concetti, se ne compiacque nel pub&shy;<lb/>blicarli come di una scoperta, in parte della quale sent&igrave; con suo grande <lb/>rammarico che fosse venuto il Mariotte. </s>

<s>Diremo fra poco i giudizi che ne <lb/>dettero i pi&ugrave; savi di que'tempi e del secolo appresso, ma perch&egrave; molti fra <lb/>i concorsi nell'opinione di un continuo circolo del succo dalle radici ai rami <lb/>e dai rami alle radici ammettono terzo dopo i due Francesi il nostro Mal&shy;<lb/>pighi, giova esaminare quali idee avesse in proposito il sapiente Maestro <lb/>dell'anatomia delle piante. </s></p><p type="main">

<s>Il rumore che se ne fece in Francia, per la cosa in s&egrave; stessa e per le <lb/>contese fra'due celebri rivali &egrave; facilissimo che giungesse a Bologna. </s>

<s>Ma a <lb/>richiamar l'attenzion del Malpighi sull'argomento bastava il pensare alla <lb/>gloriosa scoperta dell'Harvey, rammemoratagli dalle intravedute analogie fra <lb/>la vita delle piante e degli animali: analogie intorno alle quali si trovava <lb/>egli stesso, insieme co'due Francesi, prevenuto da Daniele Major, medico di <lb/>Hambourg, che aveva infino dal 1665 pubblicato il suo libro <emph type="italics"/>De planta <lb/>monstrosa gottorpiensi, et circulatione succi nutrititii.<emph.end type="italics"/></s></p><p type="main">

<s>Comunque sia, nel chiudere quelle s&igrave; dotte pagine descrittive dell'ana&shy;<lb/>tomia delle piante s'appresent&ograve; al giudizio del Malpighi quel circolo della <lb/>linfa <emph type="italics"/>sursum et deorsum,<emph.end type="italics"/> di che s'era trattato in Hambourg e in Parigi, e <lb/>tutt'altrimenti da quel che si dice sentenzi&ograve; sembrargli molto dubbioso. <lb/></s>

<s>&ldquo; Quaenam sit alimenti semita et an ab extremis plantarum apicibus re&shy;<lb/>fluat succus ad imas partes, et iuxta indigentiam in omnem peripheriam <lb/>sursum et deorsum protrudatur, dubium est &rdquo; (De radicibus, Op. </s>

<s>omn. </s>

<s>cit., <lb/>pag. </s>

<s>159). Le ragioni di questo dubbio le ritrova il Nostro nell'osservazione <lb/>dei fatti, dai quali si dimostra che non ha il succo un moto regolare e an&shy;<lb/>dante, ma fa talvolta anche viaggio ritroso, come per esempio, quando pian&shy;<lb/>tato un ramo d'albero mette sotto terra le sue radici. </s>

<s>Dall'altra parte non <lb/>si vedono aver le fistole delle piante, a dare un corso determinato alla linfa, <lb/>valvole, com'hanno le vene a dirigere il moto del sangue. </s>

<s>&ldquo; Radices ab <lb/>extremis ramorum apicibus erumpentes, contento succo inversum iter, no&shy;<lb/>vumque motum praescribunt: nullae enim interseruntur valvulae, determi&shy;<lb/>natum inducentes motum (ibid.). </s></p><p type="main">

<s>I principali argomenti, addotti poi contro il circolo del Perrault, si ri-<pb xlink:href="020/01/1650.jpg" pagenum="525"/>ducono a questi: tanto &egrave; falso che fosse il Malpighi fautore delle dottrine <lb/>francesi! Ma pure egli, il nostro Bolognese, volle investigare qual sia il vero <lb/>viaggio, che fa nelle viscere della pianta la linfa, alla quale investigazione, <lb/>egli dice, &ldquo; aliquid lucis praebent ea quae in diversis arboribus tentavi. </s>

<s>&rdquo; <lb/>L'esperienze notabilissime son dall'Autore cos&igrave; appresso descritte: &ldquo; In va&shy;<lb/>riis itaque surculis et ramis, horizontalem sectionem in cortice feci, ablata <lb/>eiusdem et libri annulari portione, ita ut subiectum lignum denudatum pa&shy;<lb/>teret. </s>

<s>In opii ramis, prunorum, mali Cydoniae, quercus, salicis, populi, avel&shy;<lb/>lanae, etc., excitata huiusmodi circulari sectione pars superior surculi, seu <lb/>caudicis supra sectionem brevi vegetans ita excrescit ut longe turgida red&shy;<lb/>datur: cortex enim, in quercu praecipue, in prunis et cydonia malo hori&shy;<lb/>zontales utriculorum ordines ita elongat, ut frequenter appendices proman&shy;<lb/>tur, quibus denudata ligni portio cooperitur, et facta denuo mutua anastomosi <lb/>cum inferiori secti corticis labio continuus redditur cortex. </s>

<s>Rami quoque <lb/>portio ultra sectionem ligneo superexcrescente circulo, et involucro impense <lb/>crassa protuberat. </s>

<s>Denudata vero lignea portio adhuc subsistit nullo vigente <lb/>incremento, quod reliquo quoque surculi infra sectionem contingit. </s>

<s>Idem <lb/>mihi saepius accidit facta spirali sectione in pomis et prunis &rdquo; (ibid.). </s></p><p type="main">

<s>Da ci&ograve; parve al Malpighi fosse evidentemente dimostrato che il succo <lb/>alimentare scende veramente dai rami fra il legno e la corteccia. </s>

<s>Se non <lb/>che venne a turbargli la pace della mente un dubbio che cos&igrave; gli ragionava: <lb/>non potrebb'esser che il succo ascendente, costretto a passar fra gli angu&shy;<lb/>sti vasi del legno snudato, poi trovato da respirare pi&ugrave; al largo, si espan&shy;<lb/>desse tutto intorno a produrre quell'escrescenza sopravvenuta alla legatura? </s>

<s><lb/>Per assicurarsi di ci&ograve; incise in giro la buccia a un querciolo in modo, che <lb/>rimanesse al di sopra dell'incisione poca parte del ramo, e trov&ograve; che non <lb/>si produceva il solito tumore. </s>

<s>A uno poi di quegli alberi adulti, che avea <lb/>veduto protuberare, fece l'incisione annulare in modo che la buccia di sopra <lb/>continuasse con quella di sotto, per via di una listerella sottile quanto un'un&shy;<lb/>ghia, e trov&ograve; che l'ipertrofia avveniva nella listerella lasciata e nell'orlo su&shy;<lb/>periore della corteccia incisa. </s>

<s>&ldquo; Quare ex his probabilius conieci nutrititii <lb/>succi motum a superioribus etiam ad inferiora promoveri &rdquo; (ibid., pag. </s>

<s>160). </s></p><p type="main">

<s>La descrizione dunque del viaggio che fa la linfa, secondo il Malpighi, <lb/>&egrave; questa: ascende per la parte legnosa del tronco infino alle foglie, dentro <lb/>alle quali si concuoce e si elabora: torna poi cos&igrave; elaborata a scendere fra <lb/>lo stesso legno e la buccia, e ivi tutta si consuma a produrre quegli an&shy;<lb/>nuali strati incrementizi, resi cos&igrave; ben visibili dalla sega menata perpendi&shy;<lb/>colarmente all'asse di atterrati alberi antichi, e ne'quali strati concentrici <lb/>annoverati si pu&ograve; legger l'et&agrave; della pianta, scrittavi dallo stesso infallibile <lb/>dito della Natura. </s></p><p type="main">

<s>Si comprende bene come questo malpighiano non &egrave; propriamente un <lb/>circolo, ma se pur vuolsi in qualche modo rassomigliare al circolo del san&shy;<lb/>gue, diremmo ch'egli &egrave; il circolo harveiano, il circolo grande. </s>

<s>Vi son poi <lb/>tanti altri piccoli circoli quante sono le parti della pianta, le quali, se vege-<pb xlink:href="020/01/1651.jpg" pagenum="526"/>tano tutte insieme e in comune nel composto, posson anche separate avere <lb/>una vita, e una individualit&agrave; loro propria. </s>

<s>Questo fatto notissimo ai pratici <lb/>agricultori, che di quasi ogni frustolo di legno traggon gli <emph type="italics"/>ovoli,<emph.end type="italics"/> da cui nasce <lb/>un albero novello, era per scienza notissimo al Malpighi, il quale avea ri&shy;<lb/>trovati ripetuti in ogni parte gli organi, che servono alla vita di tutta la <lb/>pianta. </s></p><p type="main">

<s>Ma mentre il valent'uomo poneva alla fisiologia de'vegetabili per fon&shy;<lb/>damento le anatomiche dissezioni, e instituiva una scienza, il Perrault a imi&shy;<lb/>tazion del Cartesio accomodava la Natura al suo ingegno, e fabbricava si&shy;<lb/>stemi. </s>

<s>Chi credesse essere questo giudizio da noi dato dell'illustre Accade&shy;<lb/>mico parigino troppo severo legga l&agrave; in fine alla seconda parte del trattato <lb/><emph type="italics"/>De la circulation de la seve,<emph.end type="italics"/> dove l'Autore descrive l'esperienza delle due <lb/>spugne, una imbevuta d'olio essenziale, e l'altra d'acqua pura, e ambedue <lb/>poste nell'alambicco &ldquo; pour donner une idee par analogie de quelle maniere <lb/>les differens sucs montent dans les plantes, et comment les utiles sont re&shy;<lb/>tenus, lorsque les inutiles retournent &agrave; la racine &rdquo; (Oeuvres cit., pag. </s>

<s>104). </s></p><p type="main">

<s>Ma &egrave; superfluo e pericoloso l'ingerire il nostro e il giudizio de'nostri <lb/>lettori in una questione, che il pubblico scienziato ha oramai da lungo tempo <lb/>decisa. </s>

<s>L'esperienze descritte dal Malpighi in fine all'ultimo suo trattato <emph type="italics"/>De <lb/>radicibus plantarum,<emph.end type="italics"/> rimangono tuttavia il filo arianneo, a cui s'attengono <lb/>anche i moderni per non andare smarriti nell'intricatissimo laberinto, men&shy;<lb/>tre l'esperienze del Perrault, che trovarono ragionevoli oppositori infino dal <lb/>loro nascere, per le poderose argomentazioni del Magnol, dell'Hales e del <lb/>Bonnet rimasero inconcludenti. </s>

<s>Basti fra l'esperienze halesiane citare la LXV, <lb/>la quale &egrave; forse nella sua semplicit&agrave; pi&ugrave; efficacemente dimostrativa, perch&egrave; <lb/>se nel ramoscello pi&ugrave; alto, al di sopra dell'incisione annulare della cortec&shy;<lb/>cia, circolasse veramente la linfa che ritorna alla radice, poniamo pure che <lb/>fosse come vuol lo stesso Perrault inutile a nutrire, dovrebbe almeno essere <lb/>utile a tener fresche le foglie, ci&ograve; che in farne esperienza dice l'Hales &ldquo; non <lb/>avvenne, anzi nemmeno nel punto dell'incisione vi fu segno alcuno di umi&shy;<lb/>dit&agrave; &rdquo; (Traduz. </s>

<s>cit., pag. </s>

<s>117). </s></p><p type="main">

<s>Il Bonnet, nella quinta delle sue <emph type="italics"/>Recherches sur l'usage des fevilles,<emph.end type="italics"/><lb/>facendo alcune osservazioni contro l'opinione della circolazion del succo, in&shy;<lb/>fonde novelli spiriti di vita nelle sapienti dottrine del Malpighi. </s>

<s>&ldquo; Les plan&shy;<lb/>tes n'ont point de parties qui repondent, par leur structure ou par leur jeu, <lb/>a celles qui op&egrave;rent la circulation du sang dans les grands animaux. </s>

<s>Elles <lb/>n'ont ni coeur, ni arteres, ni veines. </s>

<s>Leur structure est tres-simple et tres&shy;<lb/>uniforme. </s>

<s>Les fibres lignenses, les utricules, les vases propres, les trachees <lb/>composent le systeme entier de leurs visceres; et ces visceres sont r&eacute;pan&shy;<lb/>dus universellement dans tout le corps de la plante: on les retrouve jus&shy;<lb/>ques dans les moindres partiee. </s>

<s>Les vaisseaux s&eacute;veux n'ont point de valvu&shy;<lb/>les destin&eacute;es &agrave; favoriser l'ascension de la seve et &agrave; en empecher la retro&shy;<lb/>gradation. </s>

<s>Quand ces valvules &eacute;chapperoient au microscope, l'experience en <lb/>d&eacute;montrevoit la fausset&eacute;, puisque les plantes que l'on plonge dans l'eau, ou <pb xlink:href="020/01/1652.jpg" pagenum="527"/>que l'on met en terre par leur extr&eacute;mit&eacute; superieure ne laissent pas de ve&shy;<lb/>g&eacute;t&eacute;r &rdquo; (pag. </s>

<s>369). </s></p><p type="main">

<s>Questo fatto del vedersi un ramo vegetare anche messo in terra per <lb/>l'estremit&agrave; sua superiore, come quell'altro citato gi&agrave; dal Malpighi dei rami <lb/>che piantati mettono tutto attorno radici, dimostrano, prosegue a dire il Bon&shy;<lb/>net, che il succo sale e scende indifferentemente per i medesimi vasi. </s>

<s>Anzi <lb/>&egrave; ci&ograve; tanto vero che, se alla bella stagione s'introdurr&agrave; un ramoscello vivo <lb/>in un tubo di vetro pieno di mercurio, si vedr&agrave; questo sollevarsi di giorno <lb/>e abbassarsi di notte con tanto maggior variet&agrave; di livello, quanto saranno <lb/>maggiori gli avvicendamenti del caldo e del freddo. </s>

<s>&ldquo; La marche de la seve <lb/>dans la belle saison, rassemble donc assez &agrave; celle de la liqueur d'un Ther&shy;<lb/>mometre: l'une et l'autre dependent &eacute;galement des alternatives du chaud <lb/>e du frais &rdquo; (ivi, pag. </s>

<s>370). </s></p><p type="main">

<s>Cos&igrave;, a mezzo il secolo XVIII, tornavasi a ripetere in sostanza quel che <lb/>era stato detto da Galileo, e ci&ograve; insegna al Filosofo orgoglioso essere ineffi&shy;<lb/>caci a penetrar negli arcani della vita i lunghi e ripetuti conati del nostro <lb/>ingegno. </s>

<s>Ma pur v'ha un'altra fra le funzioni della vita vegetativa, che ha <lb/>strettissime relazioni col circolo della linfa, e che, sebbene infino a tutto il <lb/>secolo XVIII fosse riuscita misteriosa, ebbe nonostante rimosso il velo dalla <lb/>Chimica pi&ugrave; moderna. </s>

<s>Noi intendiamo dire della respirazione, la quale si <lb/>porta o si potrebbe portare per argomento contro coloro, che di poco animo <lb/>e vile disperano de'progressi della scienza dell'uomo. </s>

<s>Intorno a che per&ograve; <lb/>&egrave; a considerare che la scienza progredisce infin l&agrave; dove posson sospingerla <lb/>le forze sue naturali, dipendenti dai sensi che ammanniscono all'intelletto. </s>

<s><lb/>Or perch&egrave; &egrave; limitata l'apprensione de'sensi, limitate son perci&ograve; le notizie, <lb/>che approdan per essi. </s>

<s>Quante cose ci saranno, che non si toccano, non si <lb/>gustano, non si odorano, non si odono e non si veggono, e che pur possono <lb/>essere organi essenziali della vita vegetativa e dell'animale? </s>

<s>Chi riconosce <lb/>ci&ograve;, riconosce nello studio della vita il mistero, chi non lo riconosce, &egrave; irra&shy;<lb/>gionevole, negando l'esistenza a quel che non &egrave; disposto a cadergli sotto le <lb/>passioni del senso. </s></p><p type="main">

<s>Per tornar dunque alla respirazione, la scienza moderna ha progredito <lb/>perch&egrave; l'ossigeno &egrave; cosa trattabile e visibile ne'suoi effetti, ma s'inganne&shy;<lb/>rebbe chi credesse che nella chimica dei corpi aerei fossero rivelate le fun&shy;<lb/>zioni della vita. </s>

<s>La storia della scienza moderna raccontando le baldanze <lb/>precedute ai dubbi, e i dubbi nuovamente insorti ad attutir le baldanze, po&shy;<lb/>trebbe assai bene coi fatti dimostrar quell'inganno, ma a noi non resta a <lb/>dir altro, se non quel che della respirazion delle piante si seppe dagli scien&shy;<lb/>ziati anteriori alla prima met&agrave; del secolo XVIII. </s></p><p type="main">

<s>Il Malpighi, appena ebbe scoperta quella delicatissima testura dei vasi <lb/>spirali, non dubit&ograve; di qualificarli per polmoni delle piante, e gl'insign&igrave; per&shy;<lb/>ci&ograve; di quel medesimo nome di <emph type="italics"/>trachee,<emph.end type="italics"/> che avevano avuto negli animali, <lb/>come quelli che secondo lui erano deputati ai medesimi uffici. </s>

<s>La respira&shy;<lb/>zione dall'altra parte gli sembrava una delle principali funzioni della vita, <pb xlink:href="020/01/1653.jpg" pagenum="528"/>e nel divisarne gli organi, nella variet&agrave; dei viventi, riconosce una provvi&shy;<lb/>dentissima legge della Natura. </s>

<s>&Egrave; questa legge &ldquo; ut quae perfectiora nobis <lb/>censentur, ea minori pulmonum apparatu gaudeant &rdquo; (De cortice, Op. </s>

<s>omn. </s>

<s><lb/>cit., pag. </s>

<s>32). Negli animali superiori infatti, come nell'uomo e ne'quadru&shy;<lb/>pedi, i polmoni son due soli, ma negli uccelli vi si aggiungono le vescicole <lb/>dell'aria, che sono un'appendice agli organi polmonari. </s>

<s>Ne'pesci i polmoni <lb/>son tanti quante son le fogliette delle branchie, ma negl'insetti se ne con&shy;<lb/>tano otto e talvolta dieci, che si moltiplicano per tutte le membra in innu&shy;<lb/>merevoli diramazioni. </s>

<s>&ldquo; In plantis vero, quae infimum animalium attingunt <lb/>ordinem, tantam trachearum copiam et productionem extare par est, ut his <lb/>minimae vegetantium partes, praeter corticem, irrigentur &rdquo; (ibid.). </s></p><p type="main">

<s>Bench&egrave; sia per&ograve; tanta la necessit&agrave; della respirazione, e la Natura vi <lb/>provveda con s&igrave; laborioso apparato di organi, l'uso di lei, prosegue a dire <lb/>il Malpighi, &ldquo; adeo tamen obscurus, mihique adhuc ignotus est, ut post <lb/>multas meditationes ea tantum mihi repetere liceat, quae alias subindicavi &rdquo; <lb/>(ibid., pag. </s>

<s>33). Dicemmo altrove quali fossero queste malpighiane medita&shy;<lb/>zioni, e qui ripetiam coll'Autore che forse l'uso principale dell'aria, intro&shy;<lb/>dottasi nelle parti delle piante e degli animali, &egrave; quello di provocar la fer&shy;<lb/>mentazione, e di mantener la fluidit&agrave; nella linfa e nel sangue. </s>

<s>L'aria poi <lb/>produce que'benefici effetti per via de'sali, specialmente nitrosi, volitanti <lb/>continuamente in mezzo a lei, e questa &egrave; forse, soggiunge, la ragione per&shy;<lb/>ch&egrave; &ldquo; in arborum plantatione altae excitantur per longum ante tempus fo&shy;<lb/>veae &rdquo; (ibid.). </s></p><p type="main">

<s>Le irose divergenze fra il Malpighi e il Borelli, a proposito della respi&shy;<lb/>razione animale, ritornarono pertinaci anche nell'applicar la teorica di quella <lb/>funzione alle piante; ond'&egrave; che, escludendo il Borelli stesso ogni azione chi&shy;<lb/>mica, e tutto riducendo alla meccanica, disse non esser l'aria per altro ne&shy;<lb/>cessaria alla vita dei vegetanti, che per allieviare la natia gravezza, e cos&igrave; <lb/>pi&ugrave; facile in alto promovere il succo. </s>

<s>&ldquo; Quod postea plantae nutriri et cre&shy;<lb/>scere non possent, si omnino aere carerent, probatur quia succi aquei, ob <lb/>nativam gravitatem, per se sursum ascendere non possunt e radicibus ver&shy;<lb/>sus truncum et ramos &rdquo; (De motu anim., P. II cit., pag. </s>

<s>372). </s></p><p type="main">

<s>Queste e altre teorie meccaniche del Borelli furono facilmente dimen&shy;<lb/>ticate dagli stessi suoi pi&ugrave; immediati successori, ma scopertasi la sensibile <lb/>e insensibile traspirazion delle foglie ebbero a subire una modificazione an&shy;<lb/>che le sapienti dottrine del Malpighi. </s>

<s>Quel notabilissimo fatto del traspirare <lb/>sembrava tanto simile al respirare, e in animali imperfettissimi (che come <lb/>tali si riguardavan le piante) ne simulava cos&igrave; bene le veci, che s'inclin&ograve; <lb/>molto a credere facessero le foglie stesse, piuttosto che le trachee, l'ufficio <lb/>di polmoni. </s>

<s>L'Hales anzi si cred&egrave; d'aver colle sue statiche esperienze tolto <lb/>ogni dubbio, e cos&igrave; sentenziosamente ne concluse: &ldquo; Or possiam dunque <lb/>con ragione persuadersi di quello, che per tanto tempo si &egrave; dubitato, cio&egrave; <lb/>che le foglie fanno l'ufficio ne'vegetabili, che i polmoni negli animali &rdquo; <lb/>(Traduz. </s>

<s>cit., pag. </s>

<s>256). </s></p><pb xlink:href="020/01/1654.jpg" pagenum="529"/><p type="main">

<s>La sentenziosa conclusione halesiana per&ograve; era di tanta novit&agrave; e di tanta <lb/>importanza, che non peteva sfuggire all'esame del Bonnet in quella diligen&shy;<lb/>tissima fisiologia, ch'egli istituiva dell'uso delle foglie. </s>

<s>Avranno gi&agrave; i nostri <lb/>lettori notata nel celebre Naturalista ginevrino una tale inclinazione alle dot&shy;<lb/>trine non solo, ma alle ipotesi malpighiane, ch'egli non fa bene spesso altro <lb/>che lumeggiarle di nuove idee, e confermarle meglio coll'esperienze. </s>

<s>Il Mal&shy;<lb/>pighi aveva, come vedemmo, rassomigliate le foglie alla cute, e il Bonnet, <lb/>dop'avere osservato che il giorno il succo nutritizio esala per le aperture <lb/>della pagina fogliacea inferiore, e che la notte, chiudendosi quelle aperture <lb/>e costringendosi le trachee, fanno rifluire il succo verso la radice; &ldquo; on <lb/>voit, soggiunge, par cette l&eacute;gere esquisse de la theorie du mouvement de <lb/>la seve, que les fevilles ont beaucoup de rapport dans leurs usages avec la <lb/>peu du corps humain &rdquo; (Recherches cit., pag. </s>

<s>92). </s></p><p type="main">

<s>La persuasione anzi di questa analogia s'era tanto pi&ugrave; fermamente sta&shy;<lb/>bilita nel Bonnet, che nello stesso Malpighi, in quanto che l'uno avea con&shy;<lb/>fessato che ansiosamente cercando &ldquo; an in foliis et cortice orificia pro aere <lb/>paterent, nec ea unquam deprehendere potui &rdquo; (De cortice cit., pag. </s>

<s>32, 33), <lb/>e l'altro avea scoperto gli <emph type="italics"/>stomi,<emph.end type="italics"/> ed era di pi&ugrave; intervenuto a certe anato&shy;<lb/>mie di Gian Lodovico Calandrini, che dimostravano nelle stesse foglie &ldquo; une <lb/>membrane r&eacute;ticulaire analogue &agrave; celle du corps humain &rdquo; (Recherches cit., <lb/>pag. </s>

<s>93); ossia analoga al <emph type="italics"/>Reticolo malpighiano.<emph.end type="italics"/></s></p><p type="main">

<s>Confermatosi dunque il Bonnet per questi nuovi, aggiunti agli argo&shy;<lb/>menti antichi, che le foglie fanno le veci della cute, e che perci&ograve; l'ufficio <lb/>di polmoni rimane alle trachee, senti, in questa persuasione, che si faceva, <lb/>e non senza ragionevoli motivi, gran conto della sentenza pronunziata dal&shy;<lb/>l'Hales. </s>

<s>Perci&ograve; volle istituire alcune nuove esperienze, ch'egli poi descrisse <lb/>nella prima delle sue <emph type="italics"/>Recherches,<emph.end type="italics"/> per iscoprir se veramente le foglie siano, <lb/>come si diceva, i polmoni delle piante. </s></p><p type="main">

<s>La prima cosa, che in tal proposito gli occorse al pensiero, fu quella <lb/>di osservar ci&ograve; che accade immergendo i rami con tutte le foglie nell'acqua. </s>

<s><lb/>Fece la prima esperienza nell'estate del 1747 sopra un tralcio di vite, ed <lb/>ebbe a notarvi questo fatto singolarissimo: &ldquo; D&egrave;s que la soleil commen&ccedil;a <lb/>&agrave; &eacute;chauffer l'eau des vases, je vis paroitre sur les fevilles des rameaux beau&shy;<lb/>coup de bulles semblabes &agrave; de petites perles..... Toutes disparurent apr&egrave;s <lb/>le coucher du soleil. </s>

<s>Elles reparurent le lendemain matin, lorsque cet astre <lb/>vint a darder ses rayons sur les poudriers &rdquo; (ivi, pag. </s>

<s>46, 47). Vedeva gal&shy;<lb/>lozzolar quell'aria pi&ugrave; numerosa e pi&ugrave; grossa, via via che, sollevandosi il <lb/>sole, dava nel vaso d'acqua pi&ugrave; ardente, cosicch&egrave; aderendo le bollicelle per <lb/>un certo visco lor proprio, pi&ugrave; che ad altro, alla superficie inferiore, resi <lb/>perci&ograve; i pampani assai pi&ugrave; leggeri venivano a sollevarsi con tutto il tralcio <lb/>a galla. </s></p><p type="main">

<s>Forse fu l'esperienza suggerita al Bonnet da quell'altra simile espe&shy;<lb/>rienza instituita, come narrammo nel precedente capitolo, dal Reaumur per <lb/>assicurarsi del modo come respirano i bruchi. </s>

<s>Ma comunque sia, il Bonnet <pb xlink:href="020/01/1655.jpg" pagenum="530"/>stesso confessa ch'ebbero le remurriane dottrine sulla respirazion degl'in&shy;<lb/>setti molta efficacia in farlo andare a credere che anche sulle foglie, come <lb/>sopra la cute animale, fossero quelle bollicelle d'aria effetto della respira&shy;<lb/>zione. </s>

<s>&ldquo; L'apparition de ces bulles &agrave; la pr&egrave;sence du soleil, leur disparition <lb/>&agrave; l'entr&eacute;e de la nuit me firent d'abord penser qu'elles &ecirc;troient produites par <lb/>une sorts de respiration de la plante, par une respiration dont les alterna&shy;<lb/>tives d&eacute;pendoient des alternatives du chaud et du frais; du chaud, pour <lb/>l'expiration; du frais pour l'inspiration &rdquo; (ivi, pag. </s>

<s>47, 48). </s></p><p type="main">

<s>Ma poi osservando che la superficie inferiore era sempre molto pi&ugrave; bol&shy;<lb/>licosa dell'altra, e risovvenutosi delle antecedenti esperienze, le quali gli <lb/>avevano dimostrato esser quella stessa inferior superfice molto meglio di&shy;<lb/>sposta ad assorbire l'umidit&agrave;, ebbe a mutarsi d'idea, e a dire che quella <lb/>non era aria respirata dalle foglie, ma che queste piuttosto, come fanno le <lb/>branchie de'pesci, hanno virt&ugrave; di discriminarla dall'acqua. </s>

<s>Impaziente di ve&shy;<lb/>rificare il fatto, ripurgata l'acqua stessa d'ogni aria col tenerla per tre quarti <lb/>d'ora a bollire, e nel solito vaso ripieno di essa, messo un ramicello ver&shy;<lb/>deggiante agli ardori del sole, &ldquo; je ne vis pourtant paroitre aucune bulle &rdquo; <lb/>(pag. </s>

<s>49). Volle anche fare l'esperienza opposta, insufflando nell'acqua nuova <lb/>quantit&agrave; d'aria, e vide allora ricoprirsi le foglie di bollicelle pi&ugrave; numerose, <lb/>e pi&ugrave; grosse di quelle prima osservate, ci&ograve; che pareva confermar la conce&shy;<lb/>puta opinione esser l'aria, rimasta cos&igrave; presa in quelle bollicelle, uscita fuori <lb/>dal liquido ambiente e non dal verde. </s></p><p type="main">

<s>Questo fluttuare della mente era al Bonnet penoso, e presagio certo che, <lb/>non spirando le aure uguali, non avrebbero cos&igrave; facilmente sospinta la na&shy;<lb/>vicella del suo ingegno a toccare il porto desiderato. </s>

<s>Ma ecco a un tratto <lb/>vede balenare una luce, che gli scopre il suo errore: quelle esperienze riu&shy;<lb/>scivano cos&igrave; equivoche, perch&egrave; avea trascurata una precauzione importante, <lb/>qual era quella di liberar dall'aria, che naturalmente vi aderisce, le foglie, <lb/>prima di sommergerle, come faceva, nell'acqua. </s>

<s>Fu questa stessa negligenza <lb/>che lo condusse ad ammettere, col Reaumur e contro il Malpighi, essere <lb/>espirate dalle trachee quelle bollicelle d'aria, che si vedevano apparir sot&shy;<lb/>t'acqua sopra tutta la cute dei bruchi, ma &ldquo; lorsque j'ai plong&eacute; ces insectes <lb/>dans l'eau, apres avoir eu soin de chasser l'air de leur ext&ecirc;rieur, en le frot&shy;<lb/>tant &agrave; diverses reprises avec un pinceau movill&eacute;, je n'ai point vu s'&eacute;lever <lb/>de bulles sur la peau, mais j'en ai vu sortir un grand nombre des stigma&shy;<lb/>tes. </s>

<s>On peut voir dans les <emph type="italics"/>Transactions philosophiques<emph.end type="italics"/> n.o 487, le pr&eacute;cis <lb/>de ces recherches sur la respiration des chenilles &rdquo; (pag. </s>

<s>52). Son quivi de&shy;<lb/>scritte in gran parte quelle esperienze, che lo Spallanzani prometteva di <lb/>pubblicare nel suo <emph type="italics"/>Prodromo,<emph.end type="italics"/> e dalle quali venivasi a confermare contro il <lb/>Reaumur quel che del Bombice avea scritto il Malpighi, che cio&egrave; per le <lb/>stimmate veramente entra ed esce l'aria in quel respirare che fanno i pol&shy;<lb/>moni degli insetti. </s></p><p type="main">

<s>Applicatesi dunque dal Bonnet quelle stesse cure in rinettar dall'aria <lb/>le foglie, trov&ograve; molto maggiori difficolt&agrave; che intorno agl'insetti, perh&egrave; es-<pb xlink:href="020/01/1656.jpg" pagenum="531"/>sendo le foglie naturalmente intonacate di quella loro vernice, l'umidit&agrave; del <lb/>pennello vi s'attacca difficilmente, e mentre si passa a inumidir la parte vi&shy;<lb/>cina, quella inumidita gi&agrave; &egrave; bell'e rasciutta. </s>

<s>Questo per lo pi&ugrave; avviene alle <lb/>foglie degli alberi sempre verdi: alcune altre per&ograve; si riesce a tenerle umide, <lb/>e perci&ograve; libere da ogni aria aderente, infintantoch&egrave; non sia il punto d'im&shy;<lb/>mergerle nell'acqua. </s>

<s>Or &ldquo; toutes les fevilles qui ont pu &ecirc;tre humect&eacute;es a <lb/>fond avant que d'&ecirc;tre plong&eacute;es dans l'eau, n'ont donn&eacute; que peu ou point <lb/>de bulles, lorsqu'elles y ont &eacute;t&eacute; plong&eacute;es. </s>

<s>Il en a paru un assez grand nom&shy;<lb/>bre sur les fevilles dont je n'ai pu parvenir &agrave; chasser &eacute;nti&eacute;rement l'air, mais <lb/>ces bulles ont toujours &eacute;t&eacute; en moindre quantit&eacute; que celles qui se sont &eacute;le&shy;<lb/>v&eacute;es sur de semblabes fevilles que je n'avois point humect&eacute;es avant que de <lb/>les plonger dans l'eau &rdquo; (pag. </s>

<s>54). </s></p><p type="main">

<s>Ecco a qual conclusione andarono finalmante a riuscire le cos&igrave; bene av&shy;<lb/>viate esperienze del Bonnet: a negar cio&egrave; ogni atto di respirazione alle fo&shy;<lb/>glie, perch&egrave; quella, che da principio credeva essere aria esalata dall'interno, <lb/>trov&ograve; invece che aderiva alla esterior superfice, com'aderisce a tutti i corpi <lb/>secchi, non eccettuate le stesse foglie inaridite, le quali, tolte da un albero <lb/>gi&agrave; tagliato da un anno, trov&ograve; che facevano sott'acqua il medesimo effetto <lb/>delle verdi. </s>

<s>Ebbe perci&ograve; a venire alla final conclusione: &ldquo; que les bulles qui <lb/>s'&eacute;levent sur les fevilles vertes, et qui v&eacute;getent encore, ne sont pas l'effet de <lb/>quelque mouvement vital &rdquo; (pag. </s>

<s>56). </s></p><p type="main">

<s>Poniamo che si fosse avventurosamente abbattuto il Bonnet a veder <lb/>fatte le sue proprie esperienze dalla Natura nell'acqua di una vasca, dal <lb/>fondo della quale ferito da'vivi raggi del sole si vedono sollevarsi le fila di <lb/>cert'erbe, che ci vivono dentro, e sulla sera tornare a ricoricarsi nel loro <lb/>letto. </s>

<s>L'effetto idrostatico, diligentemente osservando, l'avrebbe senza dubbio <lb/>attribuito a quell'aeree bollicelle, che appariscono e spariscono insieme col <lb/>sole, e l'origine delle quali, non rimanendo mai le pianticelle in secco, era <lb/>forza attribuirla all'esalar che fanno esse pianticelle per una specie di re&shy;<lb/>spirazione. </s>

<s>N&egrave; sarebbe stato molto difficile accorgersi che negli sperimen&shy;<lb/>tati effetti l'azione era propria della luce e no del calore, vedendosi rima&shy;<lb/>nere a giacer le fila erbose in fondo alla vasca, sempre che, essendo l'aria <lb/>intorno caldissima, non giunge a penetrarvi dentro raggio vivo di sole. </s>

<s>Cos&igrave; <lb/>sarebbe stato direttamente condotto il Bonnet a scoprir che la luce ha una <lb/>particolare efficacia sulla respirazion delle piante; scoperta che rimase ai <lb/>botanici del secolo appresso, osservando con gli occhi illuminati dalla Chi&shy;<lb/>mica i fatti delle stesse esperienze bonnettiane. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Chi ripensa al gagliardo impulso, che dovette venire alla scienza della <lb/>vita vegetativa per fare, in s&igrave; breve tempo, i progressi fin qui narrati, lo <lb/>riconosce facilmente nella felicissima idea che s'ebbe di riscontrare essa vita <pb xlink:href="020/01/1657.jpg" pagenum="532"/>vegetativa con gli organi, e con le funzioni della vita animale. </s>

<s>L'esempio <lb/>del Cesalpino, da cui quella scienza ha gl'inizi, fu con fedelt&agrave; seguito dal <lb/>Malpighi, che la ridusse ai pi&ugrave; alti fastigi, e che non dubit&ograve;, come poco fa <lb/>udimmo, di riguardar le piante quali animalit&agrave; degl'infimi gradi. </s>

<s>Una cosa <lb/>per&ograve; in queste considerazioni assai notabile &egrave; che, concedendosi al Cesalpino <lb/>stesso senza tante difficolt&agrave;, anzi con quasi universale approvazione, la so&shy;<lb/>miglianza fra i semi e le uova, si combattesse poi tanto, e tanto s'aberrasse <lb/>in riconoscer ch'essendo, negli animali e nelle piante, le due geniture si&shy;<lb/>mili, simili ne dovevan esser pure gli organi e le funzioni. </s>

<s>Deve anzi il fatto <lb/>sembrare anche pi&ugrave; notabile a coloro, i quali ripensano che i nomi di <emph type="italics"/>ma&shy;<lb/>schi<emph.end type="italics"/> e di <emph type="italics"/>femmine<emph.end type="italics"/> furono introdotti, e divennero d'uso comune fra gli an&shy;<lb/>tichissimi cultori dei fichi e delle palme. </s>

<s>Dal popolo accettarono quel lin&shy;<lb/>guaggio gli scrittori, e dagli scrittori pass&ograve;, per l'aristotelico magistero, fra <lb/>gli studiosi della Storia naturale. </s>

<s>Nel primo libro infatti <emph type="italics"/>De plantis,<emph.end type="italics"/> com&shy;<lb/>preso fra quelli di Aristotile, cos&igrave; nel cap. </s>

<s>III si legge: &ldquo; In palmis quoque, <lb/>si folia vel foliorum pulvis vel palmae masculinae cortex foliis foemellae pal&shy;<lb/>mae apponantur, ut cohaereant, cito maturescent eius fructus, casusque co&shy;<lb/>rum prohibebitur. </s>

<s>Discerniturque masculus a foemella, quia prius pullulant <lb/>eius folia, suntque minora quam illius: itidem e fragrantia discernnntur. </s>

<s><lb/>Quod si forte ex odore masculi abduxerit quippiam ventus ad foemellam, <lb/>sic quoque maturescent ipsius fructus, quemadmodum cum folia masculi ex <lb/>illa fuerit suspensa. </s>

<s>Ficus quoque sylvestres per terram expansae ficubus <lb/>hortensibus conferunt &rdquo; (Arist., Operum T. VI cit., fol. </s>

<s>77). </s></p><p type="main">

<s>Chi per&ograve;, fra quelli poco sopra notati, avesse dalla lettura di questo testo <lb/>presa occasione di maravigliarsi come mai, avendo avuto la sessualit&agrave; delle <lb/>piante cos&igrave; favorevoli auspici, e cos&igrave; antichi e autorevoli principii, s'indu&shy;<lb/>giasse nonostante tanti secoli a professarla come una delle pi&ugrave; faticose con&shy;<lb/>quiste della scienza moderna; si sentirebbe cessare ogni maraviglia in saper <lb/>che quei nomi di maschi e di femmine, dati alle palme, non son sulla lin&shy;<lb/>gua dell'Autore aristotelico altro che per una metafora, o per secondare i <lb/>predominanti usi del volgo, dalle idee del quale per&ograve; fa il Filosofo sdegno&shy;<lb/>samente divorzio. </s></p><p type="main">

<s>Il primo e dichiarato atto di questo divorzio apparisce in uno de'pi&ugrave; <lb/>illustri discepoli di Aristotile, Teofrasto, il quale nel cap. </s>

<s>XXIII del III libro <lb/><emph type="italics"/>De causis plantarum,<emph.end type="italics"/> si rivolge con filosofico sopracciglio contro coloro, che <lb/>dichiaravano le palme femmine insufficienti per s&egrave; medesime a condurre il <lb/>loro parto, perch&egrave; dicevano che avean bisogno d'essere asperse delle pol&shy;<lb/>veri del maschio. </s>

<s>Che se fosse veramente cos&igrave;, argomenta il Filosofo, do&shy;<lb/>vrebb'essere per una legge universale della Natura, a stabilir la quale non <lb/>basta un semplice fatto osservato in una sola specie di piante. </s>

<s>Vero &egrave; che <lb/>soggiungono costoro avvenir qualche cosa di simile nel fico, ma del capri&shy;<lb/>ficio io comprendo, presegue a dir Teofrasto, la ragione, perch&egrave; il frutto do&shy;<lb/>mestico non giungerebbe a maturit&agrave;, se gl'insetti, usciti fuor dal silvestre, <lb/>non gli aprissero, entrando a pascervisi, la coroncina, d'onde s'apre l'adito <pb xlink:href="020/01/1658.jpg" pagenum="533"/>a ricevere i benefici influssi dell'aria e del sole: della necessit&agrave; per&ograve; delle <lb/>polveri maschili, ad avvalorare le deboli virt&ugrave; delle femminee palme, non <lb/>si sa che alcuno n'abbia resa qualche ragione. </s>

<s>&ldquo; Fructum autem perdurare <lb/>in palma foemina nunquam posse, nisi florem maris cum pulvere super eam <lb/>concusserint, ita enim quidam confirmant, peculiare profecto est, sed simile <lb/>caprificationi ficorum qua fructus perficitur. </s>

<s>Ergo foeminam minus ad per&shy;<lb/>ficiendum sibi sufficere aliquis potissimo dicet. </s>

<s>Sed hoc non in uno genere <lb/>aut duobus, sed vel in omnibus, vel in pluribus constare deberet: naturam <lb/>etenim generis ita diiudicamus. </s>

<s>Et in his tamen ipsis paucis generibus mi&shy;<lb/>rum quod palmae nulla ratio dari possit cum caprificationis causa conspi&shy;<lb/>cua esse putetur &rdquo; (Theodoro Gaza interpetre, Luteciae 1529, pag. </s>

<s>167, 68). <lb/>In conformit&agrave; di queste opinioni, per le quali veniva a ripudiarsi la distin&shy;<lb/>zion di maschi e di femmine, nel vero e proprio significato che hanno que&shy;<lb/>sti nomi applicati agli animali, Teofrasto, ammesso che molte fra quelle <lb/>piante sieno per loro propria natura sterili, attribuisce, nel cap. </s>

<s>VIII del <lb/>II libro <emph type="italics"/>De historia plantarum,<emph.end type="italics"/> la fecondit&agrave; indifferentemente ad ambedue <lb/>i sessi. </s></p><p type="main">

<s>Nel risorgimento delle lettere, e in quel primo risveglio che n'ebbero <lb/>a risentire anche le scienze, Pier Andrea Mattioli &egrave; dopo tanti secoli il primo, <lb/>che per industria propria, con le modeste intenzioni di tradurre e di com&shy;<lb/>mentar Dioscoride, coltivi la storia delle piante. </s>

<s>Trattando, nel cap. </s>

<s>CXXVII <lb/>del I libro, <emph type="italics"/>Della corteccia dei frutti della palma,<emph.end type="italics"/> riferisce il detto di Pli&shy;<lb/>nio, che cio&egrave; non fruttifica la femmina, se non ha il maschio da presso. </s>

<s>Ma <lb/>quasi sollecito di spiegarsi in che modo s'abbia a intendere lo strano lin&shy;<lb/>guaggio, soggiunge tosto, sull'autorit&agrave; di Teofrasto, che tanto i maschi quanto <lb/>le femmine portano i loro frutti allo stesso modo. </s>

<s>&ldquo; E secondo che si legge <lb/>al IV del XIII di Plinio, le palme femmine non producono il frutto loro, se <lb/>non hanno il maschio appresso, il quale, se per sorte lor vien tagliato o si <lb/>secca, non fanno pi&ugrave; frutto. </s>

<s>Ma non &egrave; per&ograve; da credere che i maschi non <lb/>portino ancora loro il frutto, imperocch&egrave;, scrive Teofrasto, che tra le frut&shy;<lb/>tifere, perciocch&egrave; assai son le sterili, tanto portano i frutti i maschi quanto <lb/>le femmine &rdquo; (Venezia 1555, pag. </s>

<s>134). </s></p><p type="main">

<s>Per l'autorevole magistero del Mattioli trovavan dunque le scienze spe&shy;<lb/>rimentali, nel loro istituirsi e ne'loro primi progressi, ingerita gi&agrave; l'opinione <lb/>ch'essendo le femmine delle palme e i maschi ugualmente fruttiferi non <lb/>fossero i loro amori altro che un poetico idillio gentile. </s>

<s>Francesco Redi per&ograve;, <lb/>che sapeva esser bene spesso la poesia il fiore della sapienza, in mezzo a <lb/>que'giovanili ardori che lo trasportavano a coltivar la storia della Natura, <lb/>per ci&ograve; che specialmente concerne la generazione degli animali, rivolgeva di <lb/>quando in quando il pensiero anche sopra le piante. </s>

<s>Che queste, alle quali <lb/>attribuiva una vita sensitiva, non si generassero a caso, ma con certa legge <lb/>di organi e di funzioni, analoghe a quelle ch'ei ritrov&ograve; proprie infino dei <lb/>vilissimi insetti, gli pareva tanto probabile, quanto per&ograve; difficile a dimostrare. </s>

<s><lb/>Non aveva a rimeditare sopr'altro esempio che sopra le Palme, intorno alle <pb xlink:href="020/01/1659.jpg" pagenum="534"/>quali, non essendogli possibile d'istituire esperienze, conveniva starsene alle <lb/>relazioni degli scrittori, che o antichi o recenti sagacemente riconosceva te&shy;<lb/>ner rimescolato insieme il vero col falso. </s>

<s>Volle la sua buona ventura che <lb/>capitasse in Firenze uno schiavo affricano, redento dal Granduca, di nome <lb/>Abulgaith Ben Farag, che cominci&ograve; a interrogarlo con gran curiosit&agrave;, spe&shy;<lb/>rando di raccoglier qualche cosa di pi&ugrave; certo da lui, ch'era nato in mezzo <lb/>ai palmeti. </s>

<s>Quell'uomo, educato nelle scuole di Fessa, e poi statovi per quin&shy;<lb/>dici anni maestro di legge, era, per maomettano, assai dotto, ond'&egrave; che, per <lb/>le avutene relazioni, pot&egrave; il senno del Redi sceverare dal vero quel che di <lb/>immaginario o di superstizioso aveva letto nei libri. </s>

<s>Egli si certific&ograve; cos&igrave; di <lb/>un fatto importantissimo, il quale, se fosse stato com'avevalo riferito il Mat&shy;<lb/>tioli sull'autorit&agrave; di Teofrasto, bastava a dichiarare addirittura per una fol&shy;<lb/>lia l'assunto di concluder, dall'esempio delle palme, la sessualit&agrave; di tutte le <lb/>piante. </s>

<s>Si certific&ograve; dunque il Redi che solamente le femmine, fra quegli al&shy;<lb/>beri, menano frutti. </s>

<s>Si certific&ograve; inoltre che, per fecondare esse femmine, ba&shy;<lb/>stava aspergerle delle polveri del maschio, nelle quali polveri conoscendo una <lb/>virt&ugrave; analoga a quella dell'umor seminale, e argomentando, contrariamente <lb/>alla logica di Teofrasto che, per esser la Natura in tutto e sempre simile <lb/>a s&egrave; medesima, un esempio solo poteva farsi rivelatore di una legge uni&shy;<lb/>versale; stabil&igrave; seco medesimo che, s'&egrave; vera, la sessuale generazion delle <lb/>palme, <emph type="italics"/>l'erbe tutte e gli alberi hanno il maschio e la femmina.<emph.end type="italics"/> Nel venir <lb/>per&ograve; a significare, in una Lettera che ha la data del primo Maggio 1666, <lb/>questi pensieri suoi propri, per non inimicarsi i ritrosi d'ogni novit&agrave;, gli <lb/>attribuisce a'suoi antecessori, che avevane scritto delle virt&ugrave; delle piante. </s>

<s>E <lb/>perch&egrave; nell'eleganza dei modi raccolgon le parole del Redi quell'erudizione <lb/>storica, lasciata indietro da noi, crediamo di supplire con larga usura al di&shy;<lb/>fetto trascrivendole ai nostri lettori. </s></p><p type="main">

<s>&ldquo; Ma siccome, secondo che scrivono coloro, i quali le virt&ugrave; delle piante, <lb/>ovvero la lor natura investigarono, l'erbe tutte e gli alberi hanno il maschio <lb/>e la femmina; cos&igrave; in nessuna pianta &egrave; pi&ugrave; manifesto che nella Palma, im&shy;<lb/>perocch&egrave; vanno raccontando che la femmina senza maschio non genera e <lb/>non mena i frutti, e che all'intorno del maschio molte femmine distendono <lb/>i loro rami, e pare che lo allettino e lo lusinghino, ed egli, ruvido ed aspro, <lb/>col fiato, col vedere, colla polvere la ingravida. </s>

<s>E se il maschio, o si secca <lb/>o venga tagliato, le femmine che gli verdeggiano intorno, fatte per cos&igrave; dir <lb/>vedove, diventano sterili. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Achille Tazio, nel primo libro degli Amori di Leucippe e di Clito&shy;<lb/>fonte, descrive teneramente questi amori della Palma, e con non minor ga&shy;<lb/>lanteria ne fanno menzione Teofilatto Simocatta nell'Epistole, Michele Glica <lb/>negli Annali, Ammiano Marcellino e Claudiano, che nelle Nozze di Onorio <lb/>disse: <emph type="italics"/>Vivunt in Venerem frondeis omnisque vicissim felix arbor amat, <lb/>nutant ad mutua Palmae foedera. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Invilupparono per&ograve; tutti costoro la verit&agrave; con mille poetiche fole, con&shy;<lb/>ciossiach&egrave; egli &egrave; menzogna, per quanto Abulgaith mi dice, che sia neces-<pb xlink:href="020/01/1660.jpg" pagenum="535"/>sario che il maschio si pianti vicino alla femmina, e che dalla femmina sia <lb/>veduto o ne sia da lei sentito l'odore, imperocch&egrave; vi sono de'giardini e <lb/>de'palmeti, ne'quali non vi ha maschi, eppure le femmine vi sono feconde, <lb/>e l&agrave; dove sono i maschi, se dal suolo sien recisi, non pertanto quelle desi&shy;<lb/>stono ogni anno dal fruttificare. </s>

<s>Egli &egrave; con tutto ci&ograve; vero che i maschi con&shy;<lb/>tribuiscono un non so che per fecondar le femmine, ed io ne scriver&ograve; qui <lb/>a V. S. quanto ne ho potuto comprendere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ci&ograve; &egrave; che la Palma, dall'et&agrave; sua di tre o di quattro o di cinque anni, <lb/>infino al trentesimo, produce al primo apparir della novella primavera, dalle <lb/>congiunture di molti de'pi&ugrave; bassi rami, un certo verde invoglio, che cresce <lb/>alla grandezza d'un mezzo braccio in circa, il qual poi, nel mese di Aprile, <lb/>quando &egrave; il tempo di fiorire, da s&egrave; medesimo screpola e si apre, e vedesi <lb/>pieno di moltissimi bianchi ramoscelli, su de'quali in abbondanza spuntano <lb/>fiori simili a quelli del gelsomino, bianchi lattati, con un poco di giallo nel <lb/>mezzo. </s>

<s>Questo invoglio e questi fiori tanto son prodotti dal maschio che dalla <lb/>femmina, ma i fiori del maschio hanno un soave odore, e ne cade una certa <lb/>polvere bianca, somigliante alla farina di castagno, dolce al gusto e delicata, <lb/>e se ne vanno tutti in rigoglio, e mai non producono i dattili, ancorch&egrave; di <lb/>diverso parere fosse Teofrasto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pel contrario i fiori della femmina, che non hanno cos&igrave; buono odore, <lb/>e non ispolverano quella farina, fanno i dattili in gran copia, ma bisogna <lb/>usarci alcuna diligenza, imperocch&egrave;, quando incominciano a sbocciar dall'in&shy;<lb/>voglio, o dal mallo che dir lo vogliamo, si taglia tutto intorno tutto l'invo&shy;<lb/>glio, e nudi si lasciano i rami de'fiori, tra'quali s'intessono due o tre ra&shy;<lb/>muscelli, pur di fiori colti dal maschio. </s>

<s>Quindi tutti uniti si legano insieme <lb/>in un mazzo, e cos&igrave; legati si tengono sino a tanto che quegli inseriti ramu&shy;<lb/>scelli del maschio sieno secchi, ed allora si tolgono via i legami, e cos&igrave; ven&shy;<lb/>gono fecondate le femmine con quest'opera, senza la quale non condurreb&shy;<lb/>bono i dattili alla perfezione e alla buona maturezza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se poi questa sia una superstizione, oppure un consueto modo di <lb/>fare, forse ed inutile, io per me non saprei che credermene. </s>

<s>So bene che il <lb/>costume &egrave; antichissimo, e su questo fondamento and&ograve; favoleggiando Achille <lb/>Tazio, quando disse che, se il maschio della Palma sia piantato gran tratto <lb/>lontano dalla sua femmina, tutto appassito infralisce e quasi vien meno, e <lb/>ben tosto diverrebbe arido tronco, se il sagace agricoltore, conosciuto il di <lb/>lui male, non istrappasse una vermena dalla desiderata femmina, e non l'in&shy;<lb/>nestasse nel cuore di esso maschio, cio&egrave; nella pi&ugrave; interna midolla, da alcuni <lb/>chiamata il cuore della Palma. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io non posso per&ograve; tacere che da alcuni altri mi &egrave; stato affermato che <lb/>non &egrave; necessario, per render feconda la femmina, l'inserire que'due o tre <lb/>ramoscelli de'fiori del maschio tra'fiori di essa femmina, ma che basta so&shy;<lb/>lamente spolverizzare sopra un poco di quella bianca farina, che cade da'fiori <lb/>del maschio, e se ci&ograve; fosse il vero, potremmo dar fede a Plinio che, scri&shy;<lb/>vendo delle Palme, ebbe a dire: <emph type="italics"/>Adeoque est Veneris intellectus, ut coitus<emph.end type="italics"/><pb xlink:href="020/01/1661.jpg" pagenum="536"/><emph type="italics"/>etiam excogitatus sit ab homine ex mariti flore ac lanugine, interim vero <lb/>tantum pulvere insperso foeminis &rdquo;<emph.end type="italics"/> (Della nat. </s>

<s>delle Palme, Opere, T. VI, <lb/>Napoli 1740, pag. </s>

<s>154-56). </s></p><p type="main">

<s>L'ipotesi in ogni modo, che la femmina delle palme rimanga fecondata <lb/>dalla polvere maschile, si riduceva per il Redi a una certezza di fatto, die&shy;<lb/>tro le relazioni avute da Abulgaith, che tanto si conformavano co'suoi prin&shy;<lb/>cipii fisiologici intorno alla generazion dei viventi. </s>

<s>Attendeva perci&ograve; con sol&shy;<lb/>lecito studio a investigare gli organi di cos&igrave; fatte generazioni, ch'ei sperava <lb/>di trovar simili in tutti gli alberi e in tutte le erbe, ma le difficolt&agrave; incon&shy;<lb/>trate lo sbigottirono, e gli fecero poi deporre ogni pensiero, quando usci <lb/>fuori il Malpighi a descrivere la struttura e gli uffici de'fiori in modo, che <lb/>coloro, i quali v'avean riconosciuta qualche immagine dei sessi, ci vedes&shy;<lb/>sero specchiato il proprio inganno. </s></p><p type="main">

<s>Nella grande opera malpighiana <emph type="italics"/>De anatome plantarum<emph.end type="italics"/> il trattato <emph type="italics"/>De <lb/>floribus<emph.end type="italics"/> &egrave; uno de'pi&ugrave; insigni, ed &egrave; l'Autore tanto diligente in descriver non <lb/>solo, ma in disegnar le foglie, gli stami e i pistilli, che il Boherave, per no&shy;<lb/>tarne i generi, cit&ograve; spesso gl'iconismi di lui. </s>

<s>Il frutto poi di queste dili&shy;<lb/>genze, ordinate a scoprir le varie propriet&agrave; e la natura de'fiori, si pu&ograve; ve&shy;<lb/>der concluso ne'paragrafi ultimi di questo stesso trattato. </s></p><p type="main">

<s>De'fiori, vi si legge, alcuni sono sterili, altri fecondi. </s>

<s>Son fecondi tutti <lb/>quelli, che son forniti di calice, di foglie, di stami e di stilo, e sono sterili <lb/>tutti i rimanenti che dello stesso stilo son privi. </s>

<s>&Egrave; il fiore come il compen&shy;<lb/>dio di tutta intera la pianta: dalla buccia nasce il calice, e dalla sostanza del <lb/>legno, composta di fistole e di trachee, hanno origine le foglie. </s>

<s>&ldquo; Non longe <lb/>a foliis stamina a lignea portione attolluntur, peculiarem succum in propriis <lb/>loculis (nelle antere) cribrantia et servantia: hunc patenti hiatu, data via, <lb/>sub globulorum forma (cos&igrave; descrive i granellini del polline) effundunt et <lb/>dispergunt. </s>

<s>In horum medio stylus fovetur, cuius concavitate colliquamenti <lb/>vesicula, vel seminis inchoamentum, conditur, et in ipso augetur, unde plan&shy;<lb/>tarum uterum esse automo &rdquo; (Opera omnia, T. </s>

<s>I cit., pag. </s>

<s>69). </s></p><p type="main">

<s>Da quest'utero sorge lo stilo, che l'Autore disse pi&ugrave; avanti esser parte <lb/>del fiore <emph type="italics"/>uterinis tubis analogam<emph.end type="italics"/> (pag. </s>

<s>64), ma perch&egrave; l'analogia de'nomi <lb/>non si lusingasse alcuno che importasse qualche reale somiglianza nelle fun&shy;<lb/>zioni, &egrave; sollecito il Malpighi di dire che coteste trombe uterine non sono <lb/>aperte, come negli animali, a dar libero passaggio al seme maschile, ma s&igrave; <lb/>all'aria esterna, perch&egrave; il germe pi&ugrave; copiosamente ne possa respirare. </s>

<s>N&egrave; <lb/>il viscido umore, segreto da que'peli che sono in cima allo stilo, &egrave;, come <lb/>negli animali, il mucco vaginale, ordinato a deglutir pi&ugrave; facilmente la virt&ugrave; <lb/>fecondatrice, ma &ldquo; ut reliquum alimenti depuretur, et ne insecta intus ir&shy;<lb/>ruant &rdquo; (ibid., pag. </s>

<s>70). </s></p><p type="main">

<s>Dubitai talvolta, prosegue a dire il Malpighi, se sien le foglie del fiore, <lb/>come del resto conclusi rispetto alle altre foglie, ordinate a concuocere nei <lb/>loro utricoli l'alimento, per farlo refluire all'utero tenerello; ma poi pen&shy;<lb/>sai meglio che fosse quello di depurare gli umori il loro natural ministero. <pb xlink:href="020/01/1662.jpg" pagenum="537"/>Servono inoltre a questa depurazione gli stami, attraendo i corrotti umori <lb/>dentro i loro otricelli papillari &ldquo; unde fas est dubitare naturam plurimum <lb/>humoris, huncque diversae substantiae, seminum generationi incongruum, <lb/>per haec quasi emunctoria eliminare &rdquo; (ibid.). </s></p><p type="main">

<s>Ma per non finirla in congetture, soggiunge lo stesso Malpighi, ricor&shy;<lb/>riamo alle esperienze. </s>

<s>Spesso, svelte le foglie prima che aprisse il fiore, aspet&shy;<lb/>tai se lo stilo cos&igrave; denudato crescesse, e trovai a quel suo incremento un <lb/>notabile indugio. </s>

<s>Ma qualche altra volta i semi, senza riceverne offesa, giun&shy;<lb/>sero alla loro perfetta maturit&agrave; e grandezza &ldquo; unde adhuc dubius sum an <lb/>floris folia a solis et externi aeris irruentibns conatibus tenellum uterum <lb/>tutentur, an ulterius etiam depurando praeparent auctivam seminis mate&shy;<lb/>riam &rdquo; (ibid.). </s></p><p type="main">

<s>Tali essendo le dottrine, diffuse dall'autorevolissimo magistero del Mal&shy;<lb/>pighi intorno all'uso de'fiori, &egrave; da veder quali fossero gl'insegnamenti, che <lb/>venivano con autorit&agrave; non molto minore dal Grew intorno a quel medesimo <lb/>soggetto. </s>

<s>Il capitolo V dei <emph type="italics"/>Primordii<emph.end type="italics"/> s'intitola giusto <emph type="italics"/>De flore,<emph.end type="italics"/> e vi s'in&shy;<lb/>comincia a dir ch'&egrave; il fiore a tutela e ad incremento, perch&egrave; le foglie di <lb/>lui promovono il succo. </s>

<s>Le antere, alle quali d&agrave; il nome di <emph type="italics"/>Chioma<emph.end type="italics"/> (attire), <lb/>crederebbe che fossero date a semplice ornamento, se non che non com&shy;<lb/>prende perch&egrave; sien cave, con quella sottilissima polvere dentro, e perch&egrave; <lb/>ell'abbiano a rompersi, infelicemente perdendo la loro prima bellezza. </s>

<s>&ldquo; Usus <lb/>ergo praeterea alius nobis cognoscendus est et observandus, isque est pro <lb/>victu animalium..... Cur enim alias hic adeo frequenter reperiuntur? </s>

<s>Or&shy;<lb/>dine florem a flore considera, a maioribus ad minimos nullum offendes ab <lb/>his hospitibus non obsessum..... Cogitandum haud est Deum Omnipoten&shy;<lb/>tem reliquisse quampiam e tota creaturarum familia cuius necessitatibus non <lb/>providerit, sed velut Maximum Promocondum hinc et inde pro omnibus <lb/>distribuisse cibum, isque pro ingenti turbac huius exiguae copia ut suffice&shy;<lb/>ret penum ipsi extruxisse in <emph type="italics"/>Florum comis,<emph.end type="italics"/> ut ita flos quivis fiat diverso&shy;<lb/>rium et caenaculum, dum in quovis utrumque reperiunt &rdquo; (Acta Curios. </s>

<s><lb/>Naturae, Dec. </s>

<s>I, An. </s>

<s>VIII, appendix; Norimbergae 1672, pag. </s>

<s>359). </s></p><p type="main">

<s>Cinque anni dopo, tornando il Grew a scriver de'fiori uno special trat&shy;<lb/>tato, che doveva col titolo <emph type="italics"/>The anatomy of flowers<emph.end type="italics"/> far parte del IV libro, <lb/>aveva da queste prime sostanzialmente riformate le idee, concorrendo a una <lb/>tal riforma in vario modo la lettura del Malpighi e i familiari colloqui con <lb/>l'amico suo Tommaso Millington, professor Saviliano. </s>

<s>&ldquo; In discourse hereof <lb/>with vur learned Savilian professor, sir Thomas Millington, he told me he <lb/>conceived: that the Attire doth serve as the male, for the generation of the <lb/>seed &rdquo; (The anatomy of Plants, London 1682, pag. </s>

<s>171). </s></p><p type="main">

<s>S'era il Millington, come il nostro Redi, formato questo concetto sul&shy;<lb/>l'esempio delle Palme, ed era felicemente passato a riconoscer le polveri <lb/>maschili di esse simili a quelle, che si diffondono dalle antere, ne'fiori a noi <lb/>pi&ugrave; familiari. </s>

<s>Piacque al Grew molto il pensiero del Saviliano, ma perch&egrave; <lb/>il maschio ha necessaria relazione con l'altro sesso, sottilmente investigava <pb xlink:href="020/01/1663.jpg" pagenum="538"/>qual potess'esser nel fiore il corrispendente organo femmineo. </s>

<s>Non era in <lb/>questa investigazione difficile incontrarsi nell'ovario, e riconoscerlo analogo <lb/>all'utero, ma perch&egrave; non si dava altro che un'importanza secondaria allo <lb/>stilo, e le filamenta staminee, insidenti sull'ovario stesso, si credevan muo&shy;<lb/>vere e far parte di lui, accadde al Grew di confondere con quello degli stami <lb/>l'uso proprio e distinto de'pistilli. </s>

<s>Lo stame dunque &egrave; &ldquo; <foreign lang="greek">arren<gap/>qhlus</foreign>, or male <lb/>and female &rdquo; (ivi). Compie certamente le funzioni di maschio, quando getta <lb/>le polveri, e quelle di femmina?.... Qui si sovvenne il Grew di aver poco <lb/>fa letto nel trattato <emph type="italics"/>De floribus<emph.end type="italics"/> del Malpighi: &ldquo; Huic muneri subserviunt <lb/>stamina, unde fas est dubitare Naturam plurimum humoris, huncque diver&shy;<lb/>sae substantiae seminum generationi incongruum, per haec, quasi emuncto&shy;<lb/>ria, eliminare. </s>

<s>Hinc fortasse non incongrue derivato nomine <emph type="italics"/>menstruae pur&shy;<lb/>gationis,<emph.end type="italics"/> quae, in mulieribus, conceptionis tempora proxime antecedunt, veluti <lb/>florum eruptiones succedunt.... Et quoniam in menstruorum eruptione ma&shy;<lb/>turitas quaedam temporis requiritur ut prorumpant riteque celebrentur, et <lb/>his suppressis generatio tollitur et vitiatur; ita florum pariter productio in <lb/>plantis non illico succedit, sed post determinatum tempus, nec perpetuo foe&shy;<lb/>cunda sunt semina &rdquo; (Operum, T. </s>

<s>I cit., pag. </s>

<s>70). Dunque compie lo stame, <lb/>concluse di qui il Grew, l'ufficio di femmina, quando attrae dall'ovario e <lb/>ripurga il seme dai soverchianti umori, come fa l'utero ne'suoi flussi men&shy;<lb/>sili. </s>

<s>&ldquo; And as the young and early attire before it opens, answers tho the <lb/>menses in the femal; so is it probable theat afterward when it opens or <lb/>cracks, it performs the office of the male &rdquo; (The anat. </s>

<s>of Plants cit. </s>

<s>pag. </s>

<s>172). </s></p><p type="main">

<s>Essendo cos&igrave;, conveniva risolversi intorno al modo come le polveri ma&shy;<lb/>schili esercitano sul soggiacente utero la loro virt&ugrave; fecondatrice. </s>

<s>Non entrano <lb/>materialmente addentro, perch&egrave; il Malpighi, micrografo espertissimo e a cui <lb/>bisognava credere, avea detto che per le tube non pu&ograve; entrare altro che <lb/>l'aria. </s>

<s>Ma facile trov&ograve; a tutto il Grew risoluzione, invocando le dottrine ar&shy;<lb/>veiane, rimaste fra gli Embriologi, anche a que'tempi, in Inghilterra tenaci. </s>

<s><lb/>Come dice l'Harvey, nell'esercitazione XLVIII <emph type="italics"/>De generatione animalium,<emph.end type="italics"/><lb/>&ldquo; semen illud spiritali substantia et irradiatione quadam in ovum usque pe&shy;<lb/>netrare, eiusque chalazas foecundare atque inde pullum effingere &rdquo; (Lugd. </s>

<s><lb/>Batav. </s>

<s>1737, pag. </s>

<s>177); cos&igrave; diceva il Grew, cadendo il polline sull'esterior <lb/>superfice dell'ovario, fecondarne i semi ivi dentro rinchiusi, per una certa <lb/>spiritale irradiazione, senz'alcun materiale contagio. </s>

<s>&ldquo; Which so soon as <lb/>the penis is exerted, or the testicles come to break, falls dawn upon the <lb/>seed-case or womb and so touches it with a prolifick virtuc..... And that <lb/>these particles only by falling ont the uterus, should comunicate to it or to <lb/>the sap therein a prolifick virtue, it may scem the more credible from the <lb/>manner wherein coition is made by some animals &rdquo; e cita, come l'Harvey, <lb/>l'esempio degli uccelli e dei pesci (ivi, pag. </s>

<s>172, 73). </s></p><p type="main">

<s>A ripensar ora che al Malpighi e al Grew, com'a due splendidi soli <lb/>appariti contemperanei sull'orizzonte, si rivolgevano i cupidi occhi di tutti <lb/>coloro, che attendevano allo studio delle piante, si comprender&agrave; come, in-<pb xlink:href="020/01/1664.jpg" pagenum="539"/>formate da principii diversi, anche a diversi termini, rispetto alla feconda&shy;<lb/>zion de'fiori, dovessero per lo pi&ugrave; riuscire le seguenti opinioni. </s>

<s>Gl'inspirati <lb/>alla scuola del Malpighi ripudiarono l'ipotesi dei sessi delle piante, reputan&shy;<lb/>dola un ludibrio indegno della Natura e repugnante all'anatomia; gl'inspi&shy;<lb/>rati alla scuola del Grew ammirarono invece l'uniforme sapienza de'natu&shy;<lb/>rali ordinamenti in propagar cos&igrave; le vite vegetative come le animali. </s>

<s>Quanto <lb/>all'anatomia, ritrovaron che s'erano i due grandi Maestri ingannati intorno <lb/>alla struttura e agli uffici de'pistilli, ne'quali, rimosse le mostruose <emph type="italics"/>arre&shy;<lb/>notelie,<emph.end type="italics"/> scoprirono distintamente gli organi femminei. </s>

<s>Concorsero efficace&shy;<lb/>mente alla scoperta le nuove dottrine embriologiche, diffuse dai libri dello <lb/>Swammerdam e del Graaf, i quali, svelando i paradossi arveiani, col dimo&shy;<lb/>strare l'impossibilit&agrave; delle fecondazioni <emph type="italics"/>spirituali,<emph.end type="italics"/> e la reale azione dello <lb/>sperma sugli ovi; aprirono gli occhi ai Botanici novelli per veder chiara&shy;<lb/>mente, negli stimmi e negli stili, aperte al polline le vie di giungere a toc&shy;<lb/>car fisicamente i semi, e colla sua virt&ugrave; prolifica a fecondarli. </s></p><p type="main">

<s>A tal punto, verso la fine del secolo XVII, erano state promosse le <lb/>deformi idee del Grew intorno al sessualismo de'fiori, ma nessuno s'atten&shy;<lb/>tava ancora di pronunziarle al pubblico, il quale, se inorrid&igrave; a sentir gli <lb/>Anatomici dire che l'uomo nasce come le galline dall'uovo, pensiamo che <lb/>farebbe in tornargli i Botanici sfacciatamente a soggiungere che anche le <lb/>piante hanno come l'uomo intelletto di amore. </s></p><p type="main">

<s>Primo a rompere il ghiaccio fu Rodolf'Iacopo Camerarius, che nel 1694 <lb/>pubblicava in Tubinga una Epistola di quattro pagine in 8&deg;, indirizzata a <lb/>Michel Bernardo Valentin col titolo <emph type="italics"/>De sexu plantarum;<emph.end type="italics"/> Epistola che, pre&shy;<lb/>sentitane gi&agrave; l'importanza, perch&egrave;, affidata com'era a pochi fogli leggeri, <lb/>non fosse ai progressi della scienza dannosamente involata, fu raccolta fra <lb/>l'Effemeridi dei <emph type="italics"/>Curiosi della Natura<emph.end type="italics"/> in appendice all'anno III della III De&shy;<lb/>curia impressa nel 1696 in Norimberga. </s></p><p type="main">

<s>Nell'ardita mossa nonostante, sentita il Camerarius una certa trepida&shy;<lb/>zione, quasi ad esempio del nostro Redi, espone i pensieri non come parto <lb/>della mente sua propria, ma di quella di uno fra botanici nobilissimo Au&shy;<lb/>tore, in mano del quale, dietro ci&ograve; che aveva osservato il Grew, si espoliva <lb/>la storia della generazion delle piante, come, dietro le osservazioni dell'Har&shy;<lb/>veio, dello Stenone e dello Swammerdam, era stata gi&agrave; per altri espolita la <lb/>storia della generazione degli animali. </s>

<s>&ldquo; Hinc et utraque generationis histo&shy;<lb/>ria idem fere fatus experta, et a modernis successive et pedetentim expo&shy;<lb/>lita fuit, cum qnod Harvaeus, Steno, Svammerdamius in animalibus, Grevius <lb/>et alii in plantis simul observarint &rdquo; (Ephem. </s>

<s>Appendix. </s>

<s>Dec. </s>

<s>et anno cit., <lb/>pag. </s>

<s>35). </s></p><p type="main">

<s>Quel nobilissimo Botanico dunque, incomincia a dire nella sua Epistola <lb/>il Camerarius, non giudica punto secondo il volgo le fioriture dallo specioso <lb/>colore de'petali, ma, consideratele come ordinate al frutto, d&agrave; tutta l'impor&shy;<lb/>tanza agli apici, che con la loro minutissima polvere caduta sopra gli stili <lb/>impregnano il seme, e son perci&ograve; essi apici che costituiscono il vero e pro-<pb xlink:href="020/01/1665.jpg" pagenum="540"/>prio fiore. </s>

<s>&ldquo; Apices ergo vere et proprie flores dicendos esse, non tantum <lb/>criticis celebrioribus placere, sed et texturae et naturae illorum convenire <lb/>putat, cum nihil aliud sint quam vascula quaedam et capsulae, petiolis pro&shy;<lb/>priis insidentes, et pulvere quodam minutissimo, tamquam seminio specifico, <lb/>repletae, quo vasculum seminale impregnandum erat &rdquo; (ibid., pag. </s>

<s>33). </s></p><p type="main">

<s>Son questi apici talvolta in un medesimo fiore congiunti agli stili, e son <lb/>tal'altra disgiunti o sull'individuo stesso o in individui diversi, d'onde ven&shy;<lb/>gono, secondo questo rispetto, le piante a distribuirsi dal nobilissimo Autore <lb/>in tre classi: &ldquo; Prima illis distinguitur floribus, in quibus apices seminalis <lb/>vasculi stylum seu appendicem immediate circumstant, ut in Tulipa, Vale&shy;<lb/>riana, etc..... Secunda classis plantas continet apetalas, quae alia in parte <lb/>flores, alia vero semina et fructus, adeoque divulsos a stylis apices habet ut <lb/>in Frumento turcico, Ricino, etc..... Tertia classis illarum est plantarum <lb/>apetalarum, in quibus individua quaedam semen, alia vero florem gerunt, ut <lb/>in Mercuriali, Cannabi, Junipero, etc. (ibid., pag. </s>

<s>33, 34). </s></p><p type="main">

<s>Premesse queste cose, confronta il nobilissimo Botanico la generazione <lb/>degli animali con quella delle piante, e la trova mirabilmente riscontrare in <lb/>tutte le parti che si possono ridurre alle principali otto seguenti: &ldquo; Quod <lb/>enim primo in animalibus sunt testes, semine prolifico gaudentes, hoc in <lb/>plantis apices pulvere suo turgescentes; et quod in foemellis uterus cum <lb/>ovario, hoc in plantis foemininis stylus et vasculum seminale a priore im&shy;<lb/>praegnandum, quae utrobique a petalis, tanquam partibus continentibus <lb/>externis, ab externa quavis iniuria vindicantur &rdquo; (ibid., pag. </s>

<s>34, 35). In se&shy;<lb/>condo luogo, prosegue il Camerarius la sua relazione, come giungono nel <lb/>medesimo tempo alla pubert&agrave; i due sessi negli animali, cos&igrave; giungono anche <lb/>ne'fiori. </s>

<s>In terzo e in quarto luogo, son qua e l&agrave; uguali esempi di erma&shy;<lb/>froditi, e i rudimenti del nascituro appariscono in simil modo nell'uovo fe&shy;<lb/>condato, e nella fecondata pianticella seminale. </s>

<s>S'ha per quinto riscontro il <lb/>polline globuloso, che feconda il fiore come feconda la donna il seme virile; <lb/>e come le uova de'pesci, se non sono irrorate dal maschio, sono inutili alla <lb/>generazione; cos&igrave; pu&ograve; in sesto luogo notarsi che, senz'essere irrorati dalle <lb/>polveri maschili degli apici, non maturano i frutti. </s>

<s>In settimo luogo, come <lb/>si distinguono in gallate e in suvventanee le ova de'polli, cos&igrave; si distinguono, <lb/>secondo la medesima ragione, i semi dei vegetanti; e all'ultimo, ma che &egrave; <lb/>il principale e pi&ugrave; ponderoso argomento di tutti, &ldquo; certum est ad anima&shy;<lb/>lium generationem copulam utriusque sexus exigi, quam in plantis (Author), <lb/>adeo quoque necessariam ostendit, ut si vel maris apices vel faeminarum <lb/>styli, vel utraque deficiunt, nulla proles sequi possit, ut in Frumento tur&shy;<lb/>cico, cui iuba praemature resecatur, et Mercuriali mare a foemina separata <lb/>constat &rdquo; (ibid., pag. </s>

<s>35). </s></p><p type="main">

<s>Crederebbe, dietr&ograve; queste considerazioni e dietro queste esperienze quel&shy;<lb/>l'illustre Botanico di poter concludere la generazion sessuale delle piante <lb/>come cosa certa, se non lo tenessero in dubbio alcuni fatti osservati, come <lb/>per esempio che ci son talvolta maschi senza femmine, e femmine senza <pb xlink:href="020/01/1666.jpg" pagenum="541"/>maschi. </s>

<s>Ma ci&ograve; che gli d&agrave; maggior pena &egrave; il vedere, in alcune della terza <lb/>classe, come per esempio nella Canapa, che senza vicinanza di maschi le <lb/>femmine bene spesso rimangon feconde. </s>

<s>Nonostante, cos&igrave; il Camerarius con&shy;<lb/>clude la breve esposizione del suo sistema fingendo di riferire pensieri al&shy;<lb/>trui, &ldquo; ulterioribus experimentis institutis, Naturam se magis explicaturam <lb/>fore confidat &rdquo; (ibid, pag. </s>

<s>36). </s></p><p type="main">

<s>Il qual costrutto ripreso dal Valentin nella sua <emph type="italics"/>Epistola responsoria,<emph.end type="italics"/><lb/>mentre questi ringraziava l'Autore, <emph type="italics"/>qui glaciem fregit,<emph.end type="italics"/> e gli dava, dopo il <lb/>Malpighi e il Grew, per aver distinti e dimostrati i sessi delle piante, nella <lb/>scienza botanica, i terzi onori; diceva che per poche apparenti difficolt&agrave; non <lb/>era da mettere in dubbio un sistema, che da tante parti consonava col vero. </s>

<s><lb/>Che del resto pu&ograve; il polline seminale invisibilmente ricircolare dentro le fibre <lb/>delle femmine cannabine, le quali non son poi tanto lontane dai loro ma&shy;<lb/>riti &ldquo; quin a proportionatis horum particulis seminalibus, per ventos, apici&shy;<lb/>bus excussis et in aere volitantibus, impraegnari possint, cum te neutiquam <lb/>lateat quanta saepe locorum, imo regionum intercapedine, actiones fiant <lb/>magneticae per effluviorum eiusmodi contactum unice explicandae &rdquo; (ibid., <lb/>pag. </s>

<s>40). </s></p><p type="main">

<s>La fiducia del Camerarius in ogni modo che, nonostante le prime in&shy;<lb/>contrate difficolt&agrave;, sarebbero venuti a confermar le sue ipotesi i futuri espe&shy;<lb/>rimenti, consegu&igrave; non molti anni dopo il suo effetto, per la studiosa opera, <lb/>che vi posero attorno Botanici valorosissimi, fra'quali son da commemorar <lb/>de'primi Sebastiano Vaillant, e Riccardo Bradley. </s>

<s>Il Francese, disertando dalla <lb/>scuola del Tournefurt, lesse nel 1717 innanzi all'Accademia parigina un suo <lb/>Discorso, che fu l'anno dopo, insiem con altre operette botaniche dell'Au&shy;<lb/>tore, pubblicato in Leyda col titolo di <emph type="italics"/>Sermo de structura florum.<emph.end type="italics"/> Pren&shy;<lb/>dendo principalmente le Parietarie per soggetto delle osservazioni, descrive <lb/>l'esplosion del polline che va dagli stami ai pistilli, e ne feconda l'utero, <lb/>non per materiale contagio, ma in virt&ugrave; dello spirito seminale. </s></p><p type="main">

<s>Il Bradley pubblic&ograve; in Londra nel 1724 il suo libro <emph type="italics"/>New experiments <lb/>and observations relative to the generation of plants.<emph.end type="italics"/> I pi&ugrave; conclusivi espe&shy;<lb/>rimenti del Botanico inglese consistono nell'avere estesa a un gran numero <lb/>di piante quella mutilazione operata dal Camerarius sopra il Granturco, e <lb/>nell'avere in tutti i casi trovato ch'evirati de'loro apici gli stami sempre <lb/>gli ovarii sotto i pistilli rimanevano sterili de'loro frutti. </s>

<s>Le bradleiane os&shy;<lb/>servazioni si riducevano principalmente a notar che quasi sempre lo stimma <lb/>soggiace all'antera, e che ne'fiori penduli va lo stilo pi&ugrave; lungo delle stami&shy;<lb/>gne, per rimaner cos&igrave; pi&ugrave; facilmente asperso della seminale polvere cadente. </s></p><p type="main">

<s>Prima insomma di Carlo Linneo, bench&egrave; rimanessero tuttavia alcune di <lb/>quelle difficolt&agrave;, che avean fatto andar cos&igrave; timido il Camerarius, il sistema <lb/>sessuale delle piante si teneva per cosa gi&agrave; sperimentalmente dimostrata, e <lb/>assai confacevole al consueto modo tenuto nell'operare dalla Natura; intanto <lb/>che Efraimo Chambers lo ripose qual moneta legittima nel tesoro univer&shy;<lb/>sale della scienza, come pu&ograve; vedersi sotto le denominazioni di <emph type="italics"/>Stami<emph.end type="italics"/> e di <pb xlink:href="020/01/1667.jpg" pagenum="542"/><emph type="italics"/>Pistilli<emph.end type="italics"/> nel suo <emph type="italics"/>Dizionario,<emph.end type="italics"/> e particolarmente sotto quello di <emph type="italics"/>Piante,<emph.end type="italics"/> dove <lb/>tratta della loro generazione. </s></p><p type="main">

<s>Abbiamo fin qui veduto a qual punto fosse stata promossa la scienza <lb/>della generazion delle piante, nel primo trentennio del secolo XVIII, per gli <lb/>impulsi avuti dal Grew: or &egrave; da riconoscere la penosa immobilit&agrave;, in cui <lb/>quella medesima scienza rimase specialmente in Italia, dove bene a ragione <lb/>qual solenne maestro di lei si venerava il Malpighi. </s></p><p type="main">

<s>Francese di origine e di magistero il Tournefort, s'era per suoi prin&shy;<lb/>cipali Autori eletto tre italiani: il Cesalpino, il Colonna e il Malpighi stesso, <lb/>da cui confessava aver la Botanica avuto i massimi incrementi. </s>

<s>In trattar <lb/>dei fiori ei si volle, anche nelle minime cose (se pur fra le minime cose &egrave; <lb/>da riporre la scientifica, propriet&agrave; delle parole), mostrar fedele ai maestri, <lb/>chiamando sempre <emph type="italics"/>petali,<emph.end type="italics"/> sull'esempio del Colonna, le foglie colorite intorno <lb/>al calice fiorale, per distinguerle dalle foglie propriamente dette verdeggianti <lb/>sui rami: &ldquo; Partes florum dicuntur petala, calyx, stamina, apices, pistillum. </s>

<s><lb/>Fabius Columna, vir praeclari ingenii, primus, omnium, quod sciam, <emph type="italics"/>petali<emph.end type="italics"/><lb/>vocem proprie usurpavit, ut folia florum a foliis proprie dictis distingueret &rdquo; <lb/>(Instit. </s>

<s>herbariae, Parisiis 1719, pag. </s>

<s>70). </s></p><p type="main">

<s>Dalle parole passando alle idee, non crede punto il Tournefort quel <lb/>ch'era arditamente venuto a proporre il Camerarius, che cio&egrave; sien quegli <lb/>splendidi petali le seriche cortine, sotto le quali, gelosamente tirate all'in&shy;<lb/>torno, celebrano i fiori pudibondi le nozze; ma fedele al suo Malpighi crede <lb/>che servano ad apprestar, come le mammelle il latte al bambino, al tenero <lb/>seme appropriato alimento, il superfluo del quale sia deposto negli apici &ldquo; ve&shy;<lb/>lut in cloacas. </s>

<s>Floris igitur proprium munus est nutriendi tenerum fructum, <lb/>ipsaque nutricatio paucarum horarum vel dierum est. </s>

<s>Lactis enim, ut <lb/>ita dicam fructus tantum indiget in prima partium explicatione &rdquo; (ibid., <lb/>pag. </s>

<s>68). </s></p><p type="main">

<s>S'aggiunse a questa del Tournefort contro i Sessualisti un'altra grande <lb/>botanica potenza in Giulio Pontedera, il quale consacr&ograve; a trattar de'fiori un <lb/>libro, che perci&ograve; intitolava <emph type="italics"/>Anthologia.<emph.end type="italics"/> Il Malpighi, com'udimmo, non si di&shy;<lb/>chiar&ograve; intorno all'uso proprio degli stami, lasciando in dubbio i lettori se <lb/>fossero, come i petali, da dir organi nutritizii, o piuttosto escrementizi. </s>

<s>Il <lb/>Tournefort, com'abbiamo ora letto, attribu&igrave; a loro questo secondo uso, ma <lb/>il Pontedera disse &ldquo; nulla ratione efficere possumus ut haec Auctoris opi&shy;<lb/>nio cum ratione congruere censeamus &rdquo; (Anthol., Patavii 1720, pag. </s>

<s>111), <lb/>e parendagli pi&ugrave; ragionevole attenersi all'altra malpighiana sentenza, con&shy;<lb/>cluse che le antere secernono un succo, il quale poi &ldquo; per filamenta ad re&shy;<lb/>ceptaculum transmittunt, a quo embryoni subministratur &rdquo; (ibid.). Quanto <lb/>ai pistilli segue con fedelt&agrave; le dottrine espressamente insegnate dallo stesso <lb/>Malpighi, concludendo, nel cap. </s>

<s>XXV del I libro della citata Antologia, dal <lb/>non aver mai veduto senza tuba allegar frutto essere essa tuba la prima e <lb/>principal parte del fiore. </s>

<s>Ricercando poi nel capitolo appresso di quel par&shy;<lb/>ticolare organo gli usi, dice esser quelli di tradur l'aria esterna nell'interno <pb xlink:href="020/01/1668.jpg" pagenum="543"/>del seme &ldquo; quod nihil aliud nisi aer in fructus cavitatem per tubas potest <lb/>admitti &rdquo; (ibid., pag. </s>

<s>62). </s></p><p type="main">

<s>Stabiliti cos&igrave; fatti principii dottrinali, passa nel suo II libro il Ponte&shy;<lb/>dera a esaminare la gran questione dei sessi, e alle prime incontrate diffi&shy;<lb/>colt&agrave; naturali sa l'arguto ingegno trovarne altre nuove, ch'ebbero gran <lb/>momento nel giudizio degli studiosi. </s>

<s>Uno de'primi argomenti a cos&igrave; fatte <lb/>difficolt&agrave; lo desume il Botanico padovano dall'esame de'fiori petaloidi, nella <lb/>maggior parte dei quali egli dice &ldquo; apices et tubas ita disponi, ut apicum <lb/>corpora ad tubarum oscula aut fistulas posse transferri perdifficile videtur &rdquo; <lb/>(ibid., pag. </s>

<s>118). Altro simile argomento glielo porge la popolosa famiglia <lb/>delle Umbellate, sul calice delle quali, quando son gli stami gi&agrave; adulti, le <lb/>tube, che han per lui le prime parti nel fiore, non son ancora cresciute. </s></p><p type="main">

<s>Ma son due fruttescenze in particolare sopra le quali il Pontedera s'in&shy;<lb/>trattiene a lungo, per concluderne nel cap. </s>

<s>XVII del citato II libro &ldquo; nul&shy;<lb/>lam dari in plantis foecundationem &rdquo; (pag. </s>

<s>140). Son le fruttescenze, di che <lb/>si tratta, quella delle Palme e dei Fichi, a cui pur s'associano, a dar valore <lb/>all'argomento contro i sessi, la Canapa, il Luppolo e altre simili piante com&shy;<lb/>prese dal Camerarius in quella terza classe, che oggid&igrave; si denomina delle <lb/><emph type="italics"/>Diecie.<emph.end type="italics"/> Domandava l'Autore dell'Antologia come mai, avendo queste piante <lb/>i talami cos&igrave; disgiunti, potessero nonostante celebrare insieme i coniugi. </s>

<s>E <lb/>perch&egrave; Prospero Alpino, e il Valentin fra'pi&ugrave; recenti, avevano invocato in <lb/>proposito l'azione del vento, gli sembrava impossibile che il fiato del Lup&shy;<lb/>polo maschio potesse, attraverso a monti e a mari, giungere a fecondar le <lb/>femmine negli orti di Parigi. </s>

<s>&ldquo; Deinde, cum adhuc in eo quaestionis statu <lb/>res versaretur, ut scilicet qua ratione et quibus viis quae non haberent a <lb/>cognatis acciperent esset explanandum, cum nulla alia ratio suppeteret, ad <lb/>ventorum providentiam conversi sunt, iisque mirificum faecunditatis opus <lb/>attribuerunt. </s>

<s>Quare faecundari tradunt ex. </s>

<s>gr. </s>

<s>Lupulum marem in Horto <lb/>regio parisiensi a Lupolo faemina, quae in insulis Sequanae et Matronae <lb/>longe distantibus nascitur, ventorum vi, qui apicum corpuscula ad tubas <lb/>usque ferunt &rdquo; (ibid., pag. </s>

<s>131). </s></p><p type="main">

<s>Ma il Fico presentava, nella storia sua naturale, tali note, da bastare <lb/>esse sole per il pi&ugrave; dimostrativo argomento contro l'esistenza dei sessi. </s>

<s><lb/>Unico fra gli alberi fruttiferi appariva senza fiore, eppur, cos&igrave; senza fiore, <lb/>vedevasi maturare i suoi frutti, o a questo effetto concorrere tutt'altre cause <lb/>dalle florali, conosciute sotto il nome di <emph type="italics"/>caprificazione<emph.end type="italics"/> infino dai tempi pi&ugrave; <lb/>antichi. </s>

<s>Era <emph type="italics"/>caprifico<emph.end type="italics"/> chiamata la pianta silvestre, la quale, sebben non ma&shy;<lb/>turi i suoi frutti, d&agrave; nonostante la virt&ugrave; che non ha alla pianta domestica, <lb/>generando in s&egrave; e dalla sua corruzione il maraviglioso e provvido istinto di <lb/>alcuni insetti. </s>

<s>&ldquo; Ficos, disse Teofrasto de'cultori di queste piante, caprifi&shy;<lb/>cant, quod ea de causa faciunt ut culices parvi, qui ex caprificubus appen&shy;<lb/>sis nascuntur, poma fici aperiant &rdquo; (De causis plant. </s>

<s>cit., pag. </s>

<s>90). Aperto <lb/>il fico, v'entran dentro l'aria e il calor del sole, che concocendo la natural <lb/>crudezza lo fanno maturare. </s></p><pb xlink:href="020/01/1669.jpg" pagenum="544"/><p type="main">

<s>Non si poteva per&ograve; la causa della maturazion de'fichi tanto attribuir <lb/>dagli Antichi all'opera degl'insetti, che non vi riconoscessero altres&igrave; il con&shy;<lb/>corso delle polveri, l'effetto delle quali volevano che consistesse nel risec&shy;<lb/>care i soverchi umori, e cos&igrave; impedire al frutto la corruzione. </s>

<s>Era in quelle <lb/>polveri, che si confondevano facilmente con le sollevate per le vie maestre, <lb/>qualche presentimento del vero, e Teofrasto stesso osservando che, anche le <lb/>palme, in qualche modo si caprificano, attribu&igrave; alle asperse polveri maschili <lb/>i medesimi effetti essiccativi. </s>

<s>Ma da un'altra parte gli era balenato alla <lb/>mente il luminoso pensiero di rassomigliar la negata fecondazion sessuale <lb/>delle Palme alla reale fecondazion sessuale delle uova dei pesci. </s>

<s>&ldquo; Quapro&shy;<lb/>pter caprificari Palmas quoque fari consuevere. </s>

<s>Flore enim a masculo, et <lb/>pulvere et lanugine cum fructus insperguntur, siccitatem ex caliditate ac re&shy;<lb/>liqua potestate concipiunt, atque spirantiores redduntur, quibus causis vis <lb/>perdurandi acquiritur. </s>

<s>Huic quodammodo simile in piscium quoque genere <lb/>evenit, cum mas, editis ovis, vitale suum virus aspergit &rdquo; (ibid., pag. </s>

<s>95). </s></p><p type="main">

<s>Plinio, nel cap. </s>

<s>XIX del XV libro della Storia naturale, descrisse e in&shy;<lb/>terpetr&ograve; la caprificazione allo stesso modo che abbiamo inteso da Teofrasto, <lb/>e anzi, a mezzo il secolo XVII, furono nel Tomo I dell'<emph type="italics"/>Historia plantarum <lb/>universalis<emph.end type="italics"/> ripetute da Giovanni Bahuin, rispetto al modo dell'operar sulla <lb/>pianta domestica il caprifico, le tradizionali storie de'Naturalisti antichi (Ebro&shy;<lb/>duni 1650, pag. </s>

<s>135). Pochi anni insomma prima del Malpighi e del Grew, <lb/>porgeva il Fico, contro chi avesse pensato alla sessualit&agrave; delle piante, due <lb/>validissimi argementi: l'uno col maturar senza fiore, l'altro col mostrare <lb/>o di ritrovare in s&egrave; la sua propria fecondit&agrave;, o di riceverla da individui di <lb/>natura tanto diversa, da parer follia il vederci pur l'immagine di un connubio. </s></p><p type="main">

<s>La forza di quel primo argomento per&ograve; rimase affievolita, quando il Mal&shy;<lb/>pighi mostr&ograve; ai Botanici anche nel Fico il fiore desiderato. </s>

<s>&ldquo; In ficu, cuius <lb/>flos apud Botanicos desideratur, inversa et opposita via videtur procedere <lb/>Natura, nam, sicut in exaratis floribus pericarpii moles ita assurgit et attol&shy;<lb/>litur, ut conicum vel piricale fiat corpus, quod postea flosculis seu stylis te&shy;<lb/>gitur et cooperitur; ita in ficu, etevato exteriori ungue, fit concameratio sty&shy;<lb/>los et flosculos continens. </s>

<s>Floris vero foliola parum-rubescentia, quae in <lb/>Heliotropio et reliquis extremam floralis areae oram ambiunt, in Ficu, in <lb/>angustum compressa circulum, exiguum ornant hiatum, et anteriora versus <lb/>expansa videntur inversum producere florem &rdquo; (De floribus, Op. </s>

<s>omnia, <lb/>T. </s>

<s>I cit., pag. </s>

<s>60). </s></p><p type="main">

<s>Verissima &egrave; la nuova struttura e la nuova inflorescenza cos&igrave; descritta <lb/>nel Fico, il quale, perciocch&egrave; ha nel suo ricettacolo per flosculi i soli stili, <lb/>sarebbe dunque seconde i Sessualisti un individuo femmineo. </s>

<s>Eppure ben&shy;<lb/>ch&egrave; vergine solitaria concepisce secondo il Malpighi, ed espone il suo parto. <lb/></s>

<s>&ldquo; Ab interiori concavitate pericarpii styli seu flosculi minimi erumpunt cum <lb/>seminum loculis: hi sensim augentur, donec crescente pericarpio tota re&shy;<lb/>pleatur concameratio &rdquo; (ibid.). Questa era quella <emph type="italics"/>partenogenesi<emph.end type="italics"/> delle piante, <lb/>che il Pontedera opponeva ai seguaci del Camerarius, i quali, notabile cosa, <pb xlink:href="020/01/1670.jpg" pagenum="545"/>non dubitarono di tenere, infino a questi ultimi giorni, per bene accetta <lb/>l'eterodossa opinione, rispetto alla generazion delle Api. </s></p><p type="main">

<s>In chi, sull'autorit&agrave; del Malpighi, credeva essere il vero pericarpio il <lb/>frutto maturato de'Fichi, e aver le tube la parte principale ne'fiori, gli ar&shy;<lb/>gomenti, che dagli stessi Fichi e dalle Umbellate il Pontedera adduceva con&shy;<lb/>tro i Sessualisti, erano di tal valore, da non ammetter dubbi. </s>

<s>La feconda&shy;<lb/>zione a distanza, nelle Palme e nelle altre Diecie, conferiva dall'altra parte <lb/>a rendere sempre pi&ugrave; ritrose le menti, presentando difficolt&agrave; meglio intese, <lb/>e pi&ugrave; sentite da tutti, cosicch&egrave; non &egrave; maraviglia se in Italia, sotto la disci&shy;<lb/>plina di tali e tanti maestri, quali erano il Malpighi, il Tournefort e il Pon&shy;<lb/>tedera, si lasciassero agli immaginosi oltramontani le romantiche storie sulle <lb/>nozze dei fiori. </s>

<s>Tanto anzi, soggiogati dall'autorit&agrave; e per un certo nat&igrave;o pu&shy;<lb/>dore del senno, erano gl'Italiani, nel primo quarto del secolo XVII, alieni <lb/>da cos&igrave; fatti pensieri, che gli annotatori del Redi rintuzzarono con gli acu&shy;<lb/>lei del Pontedera i lieti germogli spuntati dalla <emph type="italics"/>Lettera intorno alle Palme,<emph.end type="italics"/><lb/>ridendosi de'Pistacchi belli e freschi, ma vani per esser rimasti vedovi del <lb/>compagno, come diceva il bal&igrave; Girolami nel presentarli all'ab. </s>

<s>Salvini (T. VI <lb/>dell'Op. </s>

<s>cit., nota a pag. </s>

<s>156), e a Pieranton Micheli, che cos&igrave; attentamente <lb/>osserv&ograve; e per il primo descrisse le passioni della Vallisniera palustre (Nova <lb/>plantarum genera, Florentiae 1729, pag. </s>

<s>12, 13), non pass&ograve; nemmen per la <lb/>mente che la vicina Vallisnieroide le fosse amorevolmente congiunta co'pi&ugrave; <lb/>stretti vincoli maritali. </s></p><p type="main">

<s>Si direbbe che avesse risentiti questi influssi in parte anche l'Hales, il <lb/>quale, tirandosi fuori dalla questione dei sessi, stette contento a speculare <lb/>intorno al modo com'agisse il polline, entrato per il pistillo, in dar vita alla <lb/>pianta seminale. </s>

<s>Le fragranze del fiore s'attribuivano principalmente alle <lb/>esalazioni sulfuree &ldquo; nam sulphur, scrisse il Dygby, est magnus ille uni&shy;<lb/>versalis pictor et odorum excitator huius mundi &rdquo; (De veget. </s>

<s>plant., Amste&shy;<lb/>lodami 1669, pag. </s>

<s>31). Secondando la comune opinione anche il Grew, che <lb/>avea notato esser sempre le antere o bianche o gialle, disse che il color di <lb/>queste dipendeva dal predominarvi lo zolfo. </s>

<s>&ldquo; Hence also it is that the co&shy;<lb/>lour of the parts of the attire is usually withe or yellow, never red: the <lb/>former depending upon a greater participation of aer, the latter of sulphur &rdquo; <lb/>(The anatomy of plants cit., pag. </s>

<s>172). </s></p><p type="main">

<s>Non ebbe dietro ci&ograve; difficolt&agrave; l'Hales di tener che fossero le particelle <lb/>del polline addirittura altrettanti granellini di zolfo. </s>

<s>Era venuto il tempo che <lb/>il Newton, dop'Ottone di Guerike, avea richiamata l'attenzione dei dotti e dei <lb/>curiosi sopra le virt&ugrave; elettriche di questo elemento, attraente e se i solidi <lb/>corpiccioli non solo, ma l'aria e la fiamma. </s>

<s>Di qui &egrave; che l'Autore della Sta&shy;<lb/>tica dei vegetabili vedeva in quei granellini pollinici penetranti gli ovari una <lb/>miscela attivissima di zolfo, d'aria e di luce, dal tocco della qual miscela <lb/>credeva che venisse a infondersi nel seme il principio della vita. </s>

<s>&ldquo; E se noi, <lb/>fondati sulle esperienze del signor Newton, il quale ha ritrovato che il zolfo <lb/>attrae il lume, supponiamo che a queste particelle di zolfo e di aria mi-<pb xlink:href="020/01/1671.jpg" pagenum="546"/>schiate ed unite insieme si aggiungano alcune particelle di lume, non pos&shy;<lb/>siamo dire che il resultato di questi tre principii, i pi&ugrave; attivi della Natura, <lb/>formi quello che chiamano <emph type="italics"/>punctum saliens,<emph.end type="italics"/> ossia il principio di vita, che <lb/>dee comunicarla a tutta la pianta seminale? </s>

<s>&rdquo; (Traduz. </s>

<s>cit., pag. </s>

<s>278, 79). </s></p><p type="main">

<s>Mentre che l'Hales cos&igrave; penosamente tergiversava, e assottigliava l'in&shy;<lb/>gegno, Carlo Linneo era, dalle osservazioni e dagli esperimenti de'suoi tanti <lb/>e valorosi predecessori, cos&igrave; ben persuaso essere alla generazion delle piante <lb/>e degli animali prescritta dalla Natura una somiglianza di leggi, da non bi&shy;<lb/>sognarvi altro che la potenza logica del ragionamento a persuadere i ritrosi. </s>

<s><lb/>Nel 1735 perci&ograve; pubblicava in Amsterdam un libro col titolo di <emph type="italics"/>Philosophia <lb/>botanica,<emph.end type="italics"/> dove si esplicavano i <emph type="italics"/>Fondamenti<emph.end type="italics"/> della scienza per via di osser&shy;<lb/>vazioni, di dimostrazioni sperimentali e di esempi. </s>

<s>L'aridit&agrave; della forma afo&shy;<lb/>ristica &egrave; largamente compensata dal lucido ordine, e da una sintesi maravi&shy;<lb/>gliosa, cosicch&egrave; tanta scienza in poche pagine condensata produsse l'effetto <lb/>desiderato, simile a quel che suol fare un cibo essenzialmente nutritivo in&shy;<lb/>gesto in uno stomaco flatulento. </s></p><p type="main">

<s>Il capitolo V s'intitola <emph type="italics"/>Sexus,<emph.end type="italics"/> e il filosofico ragionamento cos&igrave;, da prin&shy;<lb/>cipii o ammessi per certi o dimostrati, procede con rigoroso ordine alla sua <lb/>conclusione: Se &egrave; vero l'assioma <emph type="italics"/>omne vivum ex ovo,<emph.end type="italics"/> dunque ci&ograve; vale an&shy;<lb/>che per i vegetabili, i semi de'quali esser uova, oltre alla ragione, ci &egrave; di&shy;<lb/>mostrato dall'esperienza, per l'analogia che ha l'<emph type="italics"/>hilo<emph.end type="italics"/> col vitello, e i cotile&shy;<lb/>doni colla placenta degli animali. </s>

<s>E come in questi la prole non deriva <lb/>dall'ovo solo o dalla sola genitura, ma d'ambedue insieme; cos&igrave; &egrave; ragio&shy;<lb/>nevole che avvenga delle piante, nelle quali la genitura &egrave; il polline eiacu&shy;<lb/>lato dalle antere sopra gli stimmi, che sono i veri e proprii genitali femmi&shy;<lb/>nei. </s>

<s>Ambedue questi organi infatti giungono nel medesimo tempo alla pu&shy;<lb/>bert&agrave;, e l'uno evirato l'altro si rimane irreparabilmente sterile come negli <lb/>stessi animali. </s>

<s>&ldquo; Calyx ergo, conclude il Linneo, est thalamus, corolla au&shy;<lb/>leum, filamenta vasa spermatica, antherae testes, pollen genitura, stigma <lb/>vulva, stylus vagina, germen ovarium, pericarpium ovarium foecundum, se&shy;<lb/>men ovum &rdquo; (Philos. </s>

<s>bot. </s>

<s>editio altera, Viennae 1753, pag. </s>

<s>96). </s></p><p type="main">

<s>Ogni orazione per&ograve; non solo dimostra la tesi, ma scioglie le difficolt&agrave;, <lb/>intorno a che lasci&ograve; il Linneo s'esercitassero i suoi discepoli. </s>

<s>Era uno dei <lb/>primi fra costoro Giovan Gustavo Wahlbom, il quale, a'di 11 Giugno 1746, <lb/>lesse nell'Accademia di Upsalia, innanzi allo stesso Linneo preside, una dis&shy;<lb/>sertazione intitolata <emph type="italics"/>Sponsalia plantarum,<emph.end type="italics"/> che fu poi raccolta fra le Acca&shy;<lb/>demiche amenit&agrave; upsaliensi. </s>

<s>Gli articoli del cap. </s>

<s>V della Filosofia linneiana <lb/>son qui dall'Autore in altrettanti articoli, con facile e spiegato discorso, com&shy;<lb/>mentati, ora per gli esempi stessi addotti nel testo, ora per altri nuovi, e le <lb/>obiezioni contro il sistema sessuale, cos&igrave; strenuamente propugnato, trovano <lb/>qua e l&agrave; all'occasione le pi&ugrave; appropriate risposte. </s></p><p type="main">

<s>L'obiezione prima del Pontedera, che cio&egrave; son gli apici cos&igrave; disposti, <lb/>da giunger difficilmente il polline a toccare gli stimmi, se non per tutti i <lb/>Petaloidi, come l'obiciente voleva, aveva certo un gran valore rispetto a certi <pb xlink:href="020/01/1672.jpg" pagenum="547"/>fiori, come quelli per esempio delle Passiflore e delle Nigelle, ne'quali i pi&shy;<lb/>stilli sopravanzano di gran lunga gli stami. </s>

<s>Rispondeva il Wahlbom da <lb/>null'altro dipendere la difficolt&agrave;, che da difetto di osservazione, la quale, di&shy;<lb/>ligentemente instituita, riesce anzi uno de'tratti pi&ugrave; eloquenti nella storia <lb/>amorosa de'fiori. </s>

<s>Imperocch&egrave; nella Nigella arvense &ldquo; cum flos primum expan&shy;<lb/>ditur, quinque pistilla erecta staminibus longiora sunt. </s>

<s>Flore autem bene <lb/>explicato, retorquentur styli ut circumpositos pistillis maritos attingant. </s>

<s>Ac&shy;<lb/>cepto vero polline, iterum elevantur, semperque manent erecti. </s>

<s>In Tama&shy;<lb/>rindo, Passiflora et Cassiis eodem fere modo reflectuntur styli versus anthe&shy;<lb/>ras &rdquo; (Amoenitates acad. </s>

<s>upsal., Holmiae 1749, pag. </s>

<s>360). </s></p><p type="main">

<s>Quanto alle Umbellate, l'argomento del Pontedera, osserva il Vahlbom, <lb/>si fonda sopra una fallacia, che consiste nell'aver col Malpighi creduto che <lb/>sien le tube o i pistilli organi essenziali del fiore, mentre in verit&agrave; non son <lb/>che gli stimmi. </s>

<s>&ldquo; Ast stigma est pars illa generationi inserviens, minime <lb/>vero stylus. </s>

<s>Hic enim in multis abesse potest, quippe essentiam floris non <lb/>constituit. </s>

<s>Sufficiat itaque quod stigmata in Umbellatis eodem cum antheris <lb/>tempore vigeant, stylus vero Umbellatarum post conceptionem elongetur, <lb/>quemadmodum et in Acere cernitur &rdquo; (ibid., pag. </s>

<s>359). </s></p><p type="main">

<s>La fecondazione delle Diecie presentava difficolt&agrave; di pi&ugrave; grave momento, <lb/>e furon quelle massimamente, che fecero arretrare il Camerarius. </s>

<s>Notava <lb/>nulladimeno il Wahlbom avvenir talvolta che la Canapa seminifera porti an&shy;<lb/>che insieme qualche fiore stamineo &ldquo; quo nonnullae feminae impraegnari <lb/>possint, quod Rudolphum Camerarium lusit &rdquo; (ibid., pag. </s>

<s>369). Rimaneva <lb/>per&ograve; ancora in tutto il suo pieno vigore la difficolt&agrave; delle fecondazioni in <lb/>distanza, non crollatasi n&egrave; per gli effluvi magnetici del Valentin, n&egrave; per le <lb/>correnti ventose dell'Alpino. </s>

<s>Non pretendeva il Wahlbom di avere in tutto <lb/>rivelato il mistero, ma osserv&ograve; che concorrevano in gran parte a celebrarlo, <lb/>attratti dalla dolcezza del nettare, gl'insetti, e specialmente le Api, le quali <lb/>&ldquo; sub indefessis laboribus pollinem spargunt ut pistillum attingat, quippe <lb/>nondum constat quid humor hic nectareus in physiologia floris certo prae&shy;<lb/>stet &rdquo; (ibid., pag. </s>

<s>372). </s></p><p type="main">

<s>Di rispondere all'altra, che sembrava non punto pi&ugrave; lieve difficolt&agrave;, ri&shy;<lb/>cavata dalla fruttescenza del Fico, non si cur&ograve; il Wahlbom, avendolo gi&agrave; <lb/>fatto il collega suo Cornelio Hegardt, il quale, nella medesima sopra com&shy;<lb/>memorata upsaliense Accademia, innanzi al Preside illustre, lesse, il di 15 di <lb/>Settembre dell'anno 1744, una dissertazione intitolata <emph type="italics"/>Ficus,<emph.end type="italics"/> ch'entr&ograve; pure <lb/>a far parte delle <emph type="italics"/>Amenit&agrave;<emph.end type="italics"/> dianzi citate. </s>

<s>L'enimma della caprificazione vi si <lb/>trova finalmente, nella promulgata legge matrimoniale, spiegato: il Caprifico <lb/>&egrave; il maschio, e la pianta domestica la femmina, i fiori della quale, rimanen&shy;<lb/>dosi dentro il ricettacolo rinchiusi e stipati, sarebbe stato impossibile che <lb/>venissero dalla polvere fecondatrice aspersi, se la previdente Natura non <lb/>avesse all'opera chiamate ministre le Tentredini. </s>

<s>Questi insetti, che udimmo <lb/>poco fa dal traduttore di Teofrasto chiamar col nome di <emph type="italics"/>Culici,<emph.end type="italics"/> nascono <lb/>dalle uova gi&agrave; deposte nel Caprifico dalle madri pregnanti, e al tempo, che <pb xlink:href="020/01/1673.jpg" pagenum="548"/>la Natura ha stabilito alle sue provvide intenzioni opportuno, di bruchi, come <lb/>tutti gli altri, diventano alati. </s>

<s>&ldquo; Tenthredinibus iam mutatis, alisque instruc&shy;<lb/>tis, tempus adest quo Caprificus, seu Ficus mas, florescit, hoc est farinam <lb/>edit antherarum. </s>

<s>Tunc Tenthredines e Caprifici cavitatibus farina, molitoris <lb/>instar e mola sua prodeuntis, obducti, evolant et coniugibus acquisitis de <lb/>ovis pariendis solliciti sunt. </s>

<s>Hinc, ad singulos grossos transvolantes, cavita&shy;<lb/>tes Ficus feminae, dolii instar clavis ferreis vel spiculis seu pistillis ab omni&shy;<lb/>bus lateribus intus completas, intrando, non possunt non farinam illam, qua <lb/>contecti sunt, excutere. </s>

<s>Patet igitur hoc modo Ficum hanc feminam facil&shy;<lb/>lime impraegnari &rdquo; (ibid., pag. </s>

<s>42). </s></p><p type="main">

<s>Sia pure, instavano ancora i seguaci del Pontedera, ma ne'nostri do&shy;<lb/>mestici orti, anche senz'artificio di caprificazione, ci maturano i Fichi, e ci&ograve; <lb/>vuol dire che riescono le femmine feconde, anche senza gli amplessi virili. </s>

<s><lb/>Per rispondere a questa difficolt&agrave;, l'Hegardt soggiunge che possono i Fichi <lb/>domestici maturare, bench&egrave; non sieno stati prima fecondati, perch&egrave; il loro <lb/>frutto non &egrave; propriamente il pericarpio, ma il ricettacolo o il clinanto, come <lb/>nelle Fravole e nelle More, che pur maturano allo stesso modo. </s>

<s>Rimase dun&shy;<lb/>que il Pontedera ingannato dal Malpighi, il quale qualific&ograve; per ovario quello <lb/>che in verit&agrave; niente altro era che il calice del Fico. </s>

<s>&ldquo; Botanici quidam, qui&shy;<lb/>bus hoc non satis fuit perspectum, arbores hasce sine praevia fecundatione <lb/>edere fructus videntes, argumentum contra generationem plantarum satis <lb/>validum se hinc invenisse crediderunt, at fructus Ficuum non pericarpium <lb/>sed receptaculum commune esse minime perpenderunt &rdquo; (ibid., pag. </s>

<s>42). </s></p><p type="main">

<s>Cos&igrave;, per opera del Linneo e de'Linneidi suoi upsaliensi, veniva stabi&shy;<lb/>lito e difeso dai contradittori il sistema sessuale delle piante, che s'applic&ograve; <lb/>largamente come nota specifica in quella classificazione, i fondamenti alla <lb/>quale erano stati gi&agrave; posti dal Camerarius. </s>

<s>Dopo un mezzo secolo di com&shy;<lb/>battimenti, capitanati da una parte dal Malpighi e dall'altra dal Grew, i se&shy;<lb/>guaci di questo ebbero stabile vittoria, a proclamar la quale fra i ritrosi ita&shy;<lb/>liani fu uno de'primi e pi&ugrave; faccendieri Filippo Arena. </s>

<s>Nel 1768 egli pub&shy;<lb/>blic&ograve; in Palermo, a nome di suo nipote Ignazio, un trattato diviso in due <lb/>parti, col titolo <emph type="italics"/>Della natura e cultura de'fiori;<emph.end type="italics"/> trattato che fu impresso <lb/>la seconda volta nel 1771 col nome proprio dell'Autore, ma colla data di <lb/><emph type="italics"/>Cosmopoli.<emph.end type="italics"/></s></p><p type="main">

<s>Descrive con vivacit&agrave; l'Autore le Passiflore colte in fallo negli amorosi <lb/>congressi, e ne fa argomento da rispondere alle obiezioni del Pontedera, ma <lb/>par non sappia o non si ricordi che quelle osservazioni erano state fatte, e <lb/>che quelle risposte erano state pubblicamente date dal Wahlbom ventidue <lb/>anni avanti: come pur non sospetta che al capitolo suo XXXII, dove spiega <lb/>la ragione del caprificio, sia stata da ventiquattr'anni preletta, nell'upsa&shy;<lb/>liense accademia, la dissertazion dell'Hegardt sullo stesso argomento. </s></p><p type="main">

<s>Nulla di nuovo &egrave; pure nell'Arena rispetto al ministero degl'insetti nelle <lb/>fecondazioni a distanza, ma una certa diligenza nelle descrizioni, e un co&shy;<lb/>lorirle in modo, che vengan le cose a ricever maggiore importanza, lo ren-<pb xlink:href="020/01/1674.jpg" pagenum="549"/>don da questa parte superiore al Wahlbom, e agli altri commentatori della <lb/>Filosofia linneana. </s>

<s>Ei non crede per nulla all'azione del vento. </s>

<s>&ldquo; Chi vede <lb/>e osserva, scrive nel cap. </s>

<s>XXVIII, conosce chiaro che il vento non &egrave; mica <lb/>un mezzo abile ad altro, che a disperder le polveri. </s>

<s>Posso io attestare che, <lb/>in tant'anni di cultura di fiori, non mi son potuto accorgere mai che il <lb/>vento abbia trasferite polveri da un fiore all'altro, ancorch&egrave; sopra l'istessa <lb/>pianta, fuorch&egrave; quando sono stati fra s&egrave; contig<gap/>i o si vicini, che agitati dal <lb/>vento insieme fregando con gli apici si loccassero. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Queste e simili difficolt&agrave;, che io incontrava insuperabili nella comune <lb/>opinione, m'impegnarono alla ricerca del vero modo come posson le polveri <lb/>di una pianta passare all'altra. </s>

<s>L'ho io detto allegoricamente che il vero <lb/>proprio ed universal mezzo sieno certe artifiziosissime macchinette, dalla <lb/>provvida Natura preparate e tenute pronte in ogni luogo, per lo trasporto <lb/>delle polveri. </s>

<s>Ma ora &egrave; tempo di svelarle apertamente, sebbene voi gi&agrave; ve <lb/>ne sarete accorti quali sieno, per quel tanto che se n'&egrave; parlato. </s>

<s>Son mac&shy;<lb/>chine, alle quali la Natura diede occhi perspicaci per vedere, ancor di lon&shy;<lb/>tano, onde pigliare e dove lasciar le polveri; diede piedi per moversi, op&shy;<lb/>pur diede lor le ali per facilitarne fino a molta distanza il trasporto. </s>

<s>Gi&agrave; vi <lb/>accorgete che son gl'insetti di ogni genere, massimamente volatili, e che <lb/>sien dessi che portan le polveri lo ander&ograve; mostrando in tutto il seguente <lb/>capo, sebbene, per accertarsene ad evidenza, la miglior prova sar&agrave; che cia&shy;<lb/>scun da s&egrave;, per sua maggior sicurezza, in un prato o giardino fiorito vada ci&ograve; <lb/>osservando co'proprii occhi, e cos&igrave; spero che molto meglio ne rester&agrave; indu&shy;<lb/>bitabilmente convinto &rdquo; (Della natura de'fiori, Cosmopoli 1771, pag. </s>

<s>256, 57). </s></p><p type="main">

<s>Forse nel diffondere anche in Italia le nuove dottrine il libro dell'Arena <lb/>non ebbe grande efficacia, ma egli &egrave; in ogni modo primo fra gl'Italiani a <lb/>dar colore di verit&agrave; alle lontane previsioni del Redi. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Comunque siasi, al sol meridiano ripurgato d'ogni macchia, e scoperto <lb/>di ogni nube all'intorno, chi aveva occhi in fronte non poteva oramai pi&ugrave; <lb/>negare la luce del vero, e s'ammir&ograve; da tutti la sapiente Natura, che a man&shy;<lb/>tener le specie facesse anche alle insensibili piante gustare il gaudio del&shy;<lb/>l'amore. </s>

<s>Ma sarebbe quel gaudio rimasto una infeconda lascivia, se a dif&shy;<lb/>fondere i lieti conceputi germi non si fossero aperti gli uteri materni. </s></p><p type="main">

<s>Gl'insetti, divenuti ne'maritali amplessi fecondi, perch&egrave; non si trovan, <lb/>come gli animali perfetti, mammelle da allattare i loro teneri parti, e per&shy;<lb/>ch&egrave; non hanno il natural calore sul petto e sotto le ali da incubar le loro <lb/>uova, come gli uccelli; costretti a mendicare una cuna l'eleggono sagace&shy;<lb/>mente ora in mezzo a un calice fiorito, ora dentro l'incisa scorza di un al-<pb xlink:href="020/01/1675.jpg" pagenum="550"/>bero, ora anche nel limo, purch&egrave; il materno amor ne assicuri che non sar&agrave; <lb/>ai dolci pegni deposti tradita la fedelt&agrave; dell'ospizio, o crudelmente negata <lb/>la carit&agrave; del nutrimento. </s></p><p type="main">

<s>Le piante non han bisogno di tante sollecitudini in eleggere quel pi&ugrave; <lb/>appropriato ospizio o quel pi&ugrave; convenevole nutrimento: dovunque si trovi <lb/>terra all'intorno, che sia scoperta alle pioggie e alle rugiade, all'aria e al <lb/>sole, ivi trovan le disperse uova chi le fomenti nella loro tenera infanzia, e <lb/>le nutrisca. </s>

<s>Giacch&egrave; dunque il fine de'patiti amori &egrave; unicamente conseguito <lb/>per via della dispersione, mirabile &egrave; l'industria, che pongono intorno a ci&ograve; <lb/>gli alberi e l'erbe. </s>

<s>Per lo pi&ugrave; involgono le loro uova, come in morbide fa&shy;<lb/>sce, nella polpa del pericarpo, il quale serve mirabilmente all'intento. </s>

<s>Ro&shy;<lb/>tondo, ruzzola pi&ugrave; facilmente per il declivio, e son pi&ugrave; pronte le acque a <lb/>travolgerlo nelle loro rapine: gustoso, lo divoran le fiere, e vanno qua e l&agrave; <lb/>ad affidare i riposti semi alla terra, con le deposizioni del ventre: corrotto, <lb/>il passeggero nauseato lo gitta con la mano, e lo disperde colla punta in&shy;<lb/>sultatrice del piede. </s>

<s>Le ruinose cadute, le corse precipitose, i divoramenti <lb/>laceratori, le dispettose iatture, tutto che insomma han di pi&ugrave; pericoloso a <lb/>temere per la vita de'loro parti le madri, sono altrettanti benefizii, di che <lb/>lieta la madre pianta ringrazia. </s></p><p type="main">

<s>Vi sono arboscelli, che provvedono alla dispersione delle loro uova in <lb/>modo assai pi&ugrave; diretto. </s>

<s>Ora le forniscono di ami, con che attaccandosi ai <lb/>peli degli animali viaggiano insieme con essi: ora le muniscono di pinne, <lb/>perch&egrave; volino velocissime trasportate sulle ali de'venti. </s>

<s>Non infrequente &egrave; <lb/>poi il caso che, facendo per elaterio di molla scattar dalle silique i granel&shy;<lb/>lini risecchi, imiti la stessa pianta l'industre opera, che fa la mano dei se&shy;<lb/>minatori. </s>

<s>&ldquo; Mirabile quoddam elateris genus, scriveva nel 1682 Tommaso <lb/>Cornelio in quel suo Proginnasma postumo <emph type="italics"/>De sensibus,<emph.end type="italics"/> percipimus in fructi&shy;<lb/>bus cucumeris sylvestris, qui maturescentes vix ita leniter contrectari pos&shy;<lb/>sunt, quin statim dissiliant, succumque et semina magno impetu eiaculen&shy;<lb/>tur. </s>

<s>Nec dissimilis, licet aliquanto obscurior, vis est in fructibus Momordicae, <lb/>seu Balsaminae, aliisque compluribus, qui ad maturitatem perducti sponte <lb/>dissiliunt, mirisque motibus agitantur &rdquo; (Thomae Cornelii, Op. </s>

<s>posth., Nea&shy;<lb/>poli 1688, pag. </s>

<s>14). </s></p><p type="main">

<s>Ma degno di maggior considerazione &egrave;, prosegue a dire il Cornelio, quel <lb/>che in un certo genere di Trifoglio ebbi pi&ugrave; volte, con mia grandissima com&shy;<lb/>piacenza, a notare. </s>

<s>&Egrave; un'erba volgarissima che ha il nome di <emph type="italics"/>Trifolium <lb/>acetosum<emph.end type="italics"/> nel linguaggio degli scienziati, e di <emph type="italics"/>Alleluia<emph.end type="italics"/> in quello del popolo, <lb/>e bench&egrave; il Mattioli descriva e rappresenti anche in disegno la pianticella, <lb/>non fa per&ograve; motto della meravigliosa propriet&agrave;, ch'io v'ho scoperto. </s>

<s>&ldquo; Fol&shy;<lb/>liculos profert in metae formam quodammodo figuratos. </s>

<s>In his semina in&shy;<lb/>cluduntur, quae maturescentia minimarum lentium, striato cortice, speciem <lb/>exhibere videntur. </s>

<s>Unumquodque autem seminis granulum, dum infra fol&shy;<lb/>liculum adhuc latet, alba tenuique tunica circumtegitur, at maturo iam se&shy;<lb/>mine alba illa membranula, sponte, magnaque vi exilit, pericarpii corticem <pb xlink:href="020/01/1676.jpg" pagenum="551"/>disrumpit, et adnexum seminis granulum ad trium vel quatuor pedum lon&shy;<lb/>gitudinem mirabili celeritate provehit. </s>

<s>Atque interea alba illa tunica a se&shy;<lb/>mine secreta et in maiorem molem expansa, vermiculi instar cieri contor&shy;<lb/>querique videtur. </s>

<s>Quod si semina ad maturitatem proxima nondum sponte <lb/>sua exsilierint, tunc ad minimam pericarpii contrectationem statim impetu <lb/>facto prosiliunt. </s>

<s>Id autem, quod de Trifolio recitavimus, posse aliis quibus&shy;<lb/>dam plantis contingere non diffitemur &rdquo; (ibid., pag. </s>

<s>14, 15). </s></p><p type="main">

<s>Disseminati per questi, e per i tanti altri provvidi modi, gli ovoli delle <lb/>piante, trovan dentro all'utero della terra quell'umido tiepore, necessario a <lb/>potere svolgersi dai loro involucri, e venire a poco a poco a rappresentar <lb/>le sembianze, e a rinnovellar la vita stessa della madre. </s>

<s>A investigar quali <lb/>sieno di questa novella vita i principii e le fasi, attesero, com'a principa&shy;<lb/>lissima parte della loro scienza, i Botanici, e a noi resta ora a narrar l'or&shy;<lb/>dine e il frutto che raccolsero dai loro studi. </s></p><p type="main">

<s>Pass&ograve; per la mente di Empedecle, filosofo antico, la felice idea di ras&shy;<lb/>somigliare i semi alle uova e fu dopo tanti secoli quella stessa idea nuova&shy;<lb/>mente espressa dal Cesalpino, che scrisse nel suo trattato <emph type="italics"/>De plantis:<emph.end type="italics"/> &ldquo; Se&shy;<lb/>men enim tanquam ovum est, in quo est principium vitale &rdquo; (Florentiae 1583, <lb/>pag. </s>

<s>11). Se non che, mentre l'antico Autore non vedeva tra i semi delle <lb/>piante e le uova degli animali altro punto di somiglianza, che nel poter dagli <lb/>uni e dagli altri ugualmente svolgersi due vite simili a quelle dei generanti; <lb/>il Cesalpino, scrutando addentro l'intima composizione, trov&ograve; da farne il pi&ugrave; <lb/>esatto riscontro fra le parti. </s>

<s>Come nell'interno dell'uovo, egli dice, &egrave; delineato <lb/>tutto il futuro animale, e l'albume che lo circonda serve alla nutrizione del <lb/>feto; cos&igrave; nell'interno dei semi si contien la radichetta e la gemma, in che <lb/>compendiasi tutta intera la pianticella, al crescer della quale la rimanente <lb/>materia che la circonda somministra il necessario alimento. </s>

<s>&ldquo; Quemadmo&shy;<lb/>dum enim in ovo quaedam particula continetur, in qua est animalis futuri <lb/>veluti delineatio, reliquum autem corpulentiae pro alimento est; sic in plan&shy;<lb/>tarum seminibus pars illa principatum continet unde radix erumpit et ger&shy;<lb/>men; est enim quasi corculum quoddam, reliqua parte seminis alimentum <lb/>illi primum subministrante &rdquo; (ibid., pag. </s>

<s>12). </s></p><p type="main">

<s>Una condizione essenzialissima perch&egrave; il seme inducasi a germogliare <lb/>&egrave;, prosegue a dire il Cesalpino, l'umidit&agrave;, la quale mette in calorosa fer&shy;<lb/>mentazione la corpulenta materia dell'uovo stesso, a quel modo che fa l'acqua <lb/>versata sopra la calce viva. </s>

<s>Cos&igrave;, preparato il domestico nutrimento, crescono <lb/>le gracili membra alla rinchiusa pianticella, la quale, mettendo la radichetta <lb/>al di sotto e la gemmula al di sopra, esce finalmente da'suoi involucri, come <lb/>il pulcino esce dal guscio. </s>

<s>&ldquo; Deinde excitato ignis principio in ipsis latente, <lb/>ut calei contingit, in humoris occursu, idem humor cum lactea seminis sub&shy;<lb/>stantia permixtus et concoctus, tanquam familiare alimentum auget con&shy;<lb/>ceptum ante incoatum. </s>

<s>Tunc autem radix primo emergit peciolo quodam ex <lb/>corde seminis prodeunte, qua corticem dehiscere et egressum semini con&shy;<lb/>cedere necesse est. </s>

<s>Postquam autem radicem in terram egerit, reliqua se-<pb xlink:href="020/01/1677.jpg" pagenum="552"/>minis corpulentia in plurimis ex suo cortice, tamquam ex ovo, in lucem <lb/>prodit &rdquo; (ibid., pag. </s>

<s>12, 13). </s></p><p type="main">

<s>Sebben sia l'albume dell'uovo in alcuni semi rappresentato da una so&shy;<lb/>stanza, che circonda l'imbrional pianticella, non facendo per&ograve; parte inte&shy;<lb/>grale di lei, osserva il Cesalpino che, nella maggior parte di quegli stessi <lb/>semi, l'alimento &egrave; somministrato da due organi, tanto simili alle altre fo&shy;<lb/>glie nella struttura e nella inserzione, quanto differenti negli usi, non es&shy;<lb/>sendo queste foglie stesse sui rami fatte per altro che per difender dalle <lb/>intemperie i frutti. </s>

<s>&ldquo; Quae enim heec duo folia exortum ducunt cor est, <lb/>quippe radicis caput et germinis principium. </s>

<s>Sunt autem haec alterius ge&shy;<lb/>neris folia, quam quae in germinatione exoriuntur: illa enim tantum ad tu&shy;<lb/>telam data sunt, tenuia, ex solo cortice orta; haec partes sunt seminis ad <lb/>alimentum primum cordi ministrandum, ideo crassa sunt &rdquo; (ibid., pag. </s>

<s>13). </s></p><p type="main">

<s>Tali essendo intorno alla generazion delle piante dal seme i documenti <lb/>del Cesalpino, convien dire che troppo presto fossero nella stessa nostra Ita&shy;<lb/>lia dimenticati, se Giuseppe degli Aromatari venendo, quasi un mezzo se&shy;<lb/>colo dopo, a ripetere quelle medesime cose, scriveva in una lettera a Barto&shy;<lb/>lommeo Nati essere andato con lento passo a profferirle, perch&egrave; potrebbero <lb/><emph type="italics"/>nimium prorsus nova videri multis, et ab humano conceptu aliena.<emph.end type="italics"/></s></p><p type="main">

<s>La novit&agrave; de'peregrini concetti fu grandemente ammirata dagli stra&shy;<lb/>nieri, e quella Lettera al Nanti, che l'Autore premetteva al suo trattato me&shy;<lb/>dico <emph type="italics"/>De rabie contagiosa,<emph.end type="italics"/> pubblicato nel 1625 in Venezia, fu nuovamente <lb/>impressa <emph type="italics"/>ob dignitatem materiae<emph.end type="italics"/> in Francfort l'anno dopo, e poi, come pre&shy;<lb/>ziosa gemma, raccolta nelle Filosoficali transazioni di Londra. </s>

<s>All'ultimo Gio&shy;<lb/>vacchino Joung la trascrisse in appendice a'suoi <emph type="italics"/>Opuscoli botanico fisici<emph.end type="italics"/><lb/>stampati nel 1747 in Coburgo, celebrando nella prefazione l'Autore con an&shy;<lb/>noverarlo fra'primi &ldquo; qui observarunt et docuerunt maximam inter semina <lb/>vegetabilium et ova animalium intercedere analogiam. </s>

<s>&rdquo; </s></p><p type="main">

<s>Un'altra ragion del merito &egrave; riconosciuta dall'Joung nelle dottrine del&shy;<lb/>l'Aromatari, per aver questi scritto in fine alla sua lettera che, rispetto alle <lb/>uova delle galline &ldquo; existimamus equidem pullum in ovo delineatum esse, <lb/>antequam foveatur &rdquo; (Joung, in opusc. </s>

<s>cit., Appendix, pag. </s>

<s>183), non ripen&shy;<lb/>sando esser questa una ripetizione, non del concetto solo, ma delle parole <lb/>stesse del Cesalpino, le quali suonano, come poco fa udimmo, rappresentarsi <lb/>la pianticella nel seme <emph type="italics"/>quemadmodum in ovo quaedam particula contine&shy;<lb/>tur, in qua est animalis futuri veluti delincatio.<emph.end type="italics"/> Ond'&egrave; che precursore e <lb/>inspiratore all'Harvey, anche intorno a ci&ograve;, &egrave; probabilissimo fosse il Cesal&shy;<lb/>pino, piuttosto che, come parve ad alcuni, l'Aromatari, il quale lasci&ograve; il li&shy;<lb/>bero studio a'suoi ammiratori di riscontrar con le nuove cose da altrui <lb/>scoperte &ldquo; quae in libro <emph type="italics"/>De generatione animalium,<emph.end type="italics"/> Deo dante, enarrabi&shy;<lb/>mus &rdquo; (ibid.). </s></p><p type="main">

<s>Forse &egrave; vero che l'autore della lettera al Nanti fu pi&ugrave; preciso del&shy;<lb/>l'autor <emph type="italics"/>De plantis<emph.end type="italics"/> in osservare le varie forme, e gli svolgimenti vari delle <lb/>foglie seminali, ma ci esprimiamo cos&igrave; in forma di dubbio, perch&egrave; gli afo-<pb xlink:href="020/01/1678.jpg" pagenum="553"/>rismi IV-VII non ci sembrano molto chiari. </s>

<s>Certo &egrave; in ogni modo non es&shy;<lb/>sere sfuggito all'attenzione dell'Aromatari quel fascetto di fibre, che tiene <lb/>il fusticino congiunto alle stesse foglie seminali, e ch'egli acutamente ras&shy;<lb/>somigli&ograve; al cordone umbilicale. </s>

<s>&ldquo; Plurimae harum plantarum, dice nell'afo&shy;<lb/>rismo IX, quousque extant in vocatis seminibus latentes, nutriuntur per <lb/>adnatas quasdam, ut ita dicam, umbilicales vias &rdquo; (ibid., pag. </s>

<s>182). E della <lb/>pianticella, che ha messe gi&agrave; le radici, nell'aforismo XVII e ultimo, sog&shy;<lb/>giunge: &ldquo; Nec amplius per adnatas vias nisi ut diximus parum, sed per ra&shy;<lb/>dicem sugit, non aliter ac animal quod primo per umbilicales venas creditur <lb/>nutrimentum capere, exortum vero per os assumit &rdquo; (ibid., pag. </s>

<s>183). </s></p><p type="main">

<s>Secondo l'Aromatari dunque la pianticella gi&agrave; nata attinge la massima <lb/>parte del nutrimento dalla terra, per via delle radici, non cos&igrave; per&ograve; che sia <lb/>cessato affatto l'ufficio delle foglie seminali, da cui dura tuttavia la pianti&shy;<lb/>cella stessa ad attrarre qualche poco di umore. </s>

<s>Bench&egrave; avessero per&ograve; que&shy;<lb/>ste aforistiche asserzioni molta probabilit&agrave;, sentivasi nonostante il bisogno di <lb/>metterle al cimento dell'esperienza, di che dette i primi esempi il Malpi&shy;<lb/>ghi, diligentemente osservando che effetto facessero i germogli, tagliate ai <lb/>semi le foglie o i cotiledoni, com'egli fu primo a chiamarle. </s>

<s>L'effetto dun&shy;<lb/>que fu questo: &ldquo; Pluries seminales Fabarum plantulas, detractis omnino <lb/>cotyledonibus, plantavi, quorum nullae penitus vegetarunt. </s>

<s>Idem expertus <lb/>sum in plantulis Cucurbitae, Peponum, Lupinorum et Phaseolorum, qui in&shy;<lb/>signi pollent trunco et gemma &rdquo; (De seminum veget., Op. </s>

<s>omnia, T. </s>

<s>I cit., <lb/>pag. </s>

<s>199). </s></p><p type="main">

<s>Di qui &egrave; lecito congetturare, prosegue a dire lo stesso Malpighi, che <lb/>all'uova delle piante manchi qualche cosa di pi&ugrave; che all'uova degli animali, <lb/>e che sia la madre Terra colei, che largamente supplisce: &ldquo; Plantulae enim <lb/>seminali haerent quidem gemina, ut plurimum, crassa folia, quae albumini <lb/>ovi analoga, uterinae placentae vel cotyledonum vices explent. </s>

<s>Haec humo&shy;<lb/>rem exposcunt a terreno utero emanantem quo soluti fermentativi et sper&shy;<lb/>matici succi, per propria umbilicalia vascula, plantulae quotidianam suppe&shy;<lb/>ditant alimoniam, et auctivam materiam. </s>

<s>Unde plantulae foetus ex fermen&shy;<lb/>tatis, et in motum actis particulis in placentis, scilicet in seminalibus foliis, <lb/>iam concretis, non solum laxatis meatulis augetur, sed ad vegetandum exci&shy;<lb/>tatur &rdquo; (ibid., pag. </s>

<s>110). </s></p><p type="main">

<s>Parve al Borelli per&ograve; che troppo scarsa fosse la materia contenuta nei <lb/>cotiledoni per servire a nutrire la pianticella, alla quale sosteneva contro il <lb/>Malpighi esser sufficientissima l'acqua, per cui l'umidit&agrave; di lei &egrave; condizione <lb/>essenziale al risvegliarsi ne'semi gli spiriti latenti della vita. </s>

<s>Che l'incre&shy;<lb/>mento poi, il quale diceva incominciare ad apparir nella radichetta, provenga <lb/>dall'intrusione di materie esterne, piuttosto che dall'interior sostanza de'co&shy;<lb/>tiledoni, credeva di poter dimostrarlo coll'esperienza delle bacche del lauro <lb/>poste in luogo umido a germogliare. </s>

<s>&ldquo; Hae quidem exporrigebant per ter&shy;<lb/>ram praelongas radices nigricantes et fere ligneas similes funiculis, quarum <lb/>aliquae semipedis longitudinem aequabant, et tunc baccarum cortices inte-<pb xlink:href="020/01/1679.jpg" pagenum="554"/>gri et aridi erant, atque interna substantia seminis adhuc candida, dura, <lb/>eiusdem saporis eiusdemque figurae et magnitudinis erat, quam reliquae <lb/>baccae radice carentes habebant &rdquo; (De motu anim., P. II cit., pag. </s>

<s>364). </s></p><p type="main">

<s>Conseguiva da ci&ograve; che l'uso de'cotiledoni non poteva esser quello as&shy;<lb/>segnato dal Malpighi, e perci&ograve; il Borelli ne pens&ograve; un altro, che gli sembr&ograve; <lb/>non affatto improbabile, e che dice di aver ritrovato nella scienza fisica &ldquo; fa&shy;<lb/>cie praeferente eximio Benedicto Castello praeceptore &rdquo; (ibid., pag. </s>

<s>362). <lb/>Sulla germogliazion de'semi deve esso Castelli aver fatte quelle osservazioni <lb/>e quelle esperienze, dalle quali concluse le savie regole economiche inse&shy;<lb/>gnate nel discorso <emph type="italics"/>Del modo di conservare i grani<emph.end type="italics"/> (Opusculi filos., Bolo&shy;<lb/>gna 1669, pag. </s>

<s>40-45). Di tali esperienze, non pubblicate e forse nemmeno <lb/>scritte, il Borelli ebbe notizia nella scuola dalla viva voce del Maestro, e poi <lb/>le ridusse ingegnosamente al suo proposito nella proposizione CLXXVII della <lb/>II parte <emph type="italics"/>Dei moti animali.<emph.end type="italics"/> Ivi disse che i cotiledoni facevano le veci di due <lb/>Termometri santoriani, attraendo la notte gli umori acquosi, e al sopravve&shy;<lb/>nire del calor diurno respingendoli in ogni parte della tenera pianticella, che <lb/>riceve cos&igrave; al vegetare l'impulso e l'incremento. </s>

<s>&ldquo; Postquam vero plantula <lb/>adoleverit, ut per se officium folliculorum supplere possit, tunc auxiliarii illi <lb/>Thermometri, ut inutiles, sensim arescunt &rdquo; (ibid.). </s></p><p type="main">

<s>Bench&egrave; dicesse il Borelli di professar queste dottrine come tradizionali <lb/>nella scuola italiana, il Malpighi nonostante sospett&ograve; fosse per il mal'animo <lb/>che lo eccitava a contradirgli, e di ci&ograve; sfogavasene nell'Autobiografia l&agrave; dove <lb/>racconta l'origine e la causa delle fiere inimicizie. </s>

<s>Ivi dice che, preso a ri&shy;<lb/>scontrar l'esperienze delle bacche del lauro, trov&ograve; che mirabilmente confer&shy;<lb/>mavano le sue dottrine, d'avversar le quali non ancora contento, &ldquo; prosequi&shy;<lb/>tur doctissimus Borellus impugnare usum foliarium seminalium, ut successive <lb/>concludat aqueum succum in planta non transformari a virtute fermenta&shy;<lb/>tiva &rdquo; (Opera posth. </s>

<s>cit., Pars II, pag. </s>

<s>75). </s></p><p type="main">

<s>Le contradizioni per&ograve; del Borelli circa l'uso delle foglie seminali, po&shy;<lb/>niamo pure che ci fosse il mal'animo di mezzo, venivano avvalorate da un <lb/>fatto, che tenne lungamente in pena i Botanici. </s>

<s>&Egrave; quel fatto che la polpa <lb/>carnosa dei cotiledoni o il perisperma non son solubili nell'acqua, ci&ograve; che <lb/>pareva sufficiente a concludere control il Malpighi esser l'acqua stessa per <lb/>s&egrave; sola, e non intorbidata dalla sostanza farinosa del seme, che si dispensa <lb/>ad alimentare la tenera pianticella. </s>

<s>Oltre alle esperienze del Van-Helmont <lb/>&ldquo; qui vidit virgam salicis librarum quinque adeo excrevisse in quinque <lb/>annis, ut 169 librarum penderet et tale incrementum superaddidit sola aqua <lb/>irrigata &rdquo; (De motu anim., P. cit., pag. </s>

<s>364), s'aggiungevano a confermar <lb/>l'ipotesi del Borelli i nuovi fatti sperimentati dal Du-Hamel, il quale pre&shy;<lb/>sent&ograve; nel 1748, innanzi agli Accademici parigini, pianticelle nate sopra le <lb/>spugne e sui muschi, non imbevuti d'altro che d'acqua. </s>

<s>Parve perci&ograve; che <lb/>anche l'Hales concorresse in quella ipotesi borelliana, quando, dalla sua <lb/>CXXIV statica esperienza, concluse esser probabilissimo &ldquo; che quelle fronde <lb/>seminali rendano al germe gli stessi uffici, che le fronde, che sono intorno <pb xlink:href="020/01/1680.jpg" pagenum="555"/>ai pomi, ai cotogni ed altri frutti rendono a questi frutti medesimi, cio&egrave; di <lb/>sollevare l'umor nutritivo e di condurlo fin dentro alla loro sfera di attra&shy;<lb/>zione &rdquo; (Traduz. </s>

<s>cit., pag. </s>

<s>274). </s></p><p type="main">

<s>Da un'altra parte che l'acqua per una certa virt&ugrave; fermentativa sciolga <lb/>i cotiledoni in nutrimento era dimostrato chiaro al Malpighi per l'esperienze <lb/>sue p<gap/>oprie sopra tante variet&agrave; di semi, non eccettuate le bacche del lauro, <lb/>e per l'esperienze del volgo sui bulbi delle cipolle o de'vari pomi riposti <lb/>nelle domestiche dispense, i quali, quando per l'umidit&agrave; dell'aria e per i <lb/>tiepori della stagione cominciano a mettere, si sentono tanto alterati di sa&shy;<lb/>pore. </s>

<s>S'aggiungevano alle volgari esperienze le autorit&agrave; degli scienziati, e <lb/>massimamente dell'Harvey, il quale giudicando impossibile che l'acqua sola, <lb/>o venga dall'aria o dalla terra, si trasformi in tanta variet&agrave; di organi, disse <lb/>che per i fermenti alteravasi, dentro la sostanza del seme, in diversi modi, <lb/>e cos&igrave; veniva a far le veci de'liquori negli ovi. </s>

<s>&ldquo; Nam ut plantae omnes <lb/>ex eodem communi nutrimento, sive rore seu terrae humore, diversimode <lb/>alterato coctoque oriuntur, nutriuntur atque augentur; ita pariter ex iisdem <lb/>ovi liquoribus, albuminibus nempe et vitello, totus pullus, singulaeque eius <lb/>partes procreantur et crescunt &rdquo; (De generat. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>165). </s></p><p type="main">

<s>Ma le verit&agrave; professate dal Malpighi, e che s'additavano gi&agrave; prefulgere <lb/>in queste citate parole dell'Harvey, rimasero vittoriose sopra gl'ingegnosi <lb/>commenti del Borelli, quando pi&ugrave; attentamente si studi&ograve; la natura delle fo&shy;<lb/>glie seminali. </s>

<s>Risult&ograve; da tale studio ch'esse foglie non erano strumenti ac&shy;<lb/>cessori, come due fistule di termometri santoriani apposte per la nutrizione <lb/>dei germi, ma che erano anzi parti del seme tanto essenziali, che il Bohe&shy;<lb/>rave le costitu&igrave; per note da distinguere ne'due grandi ordini delle Dicotile&shy;<lb/>doni e delle Monocotiledoni l'immenso e svariato popolo delle piante. </s>

<s>Il Linneo <lb/>poi e i Linneidi revocarono alla mente e posero in maggiore evidenza le dot&shy;<lb/>trine dell'Harvey trasfuse nelle malpighiane, quando con tant'assidua dili&shy;<lb/>genza riscontrarono la generazion delle piante con quella degli animali. </s>

<s>&ldquo; Haec <lb/>folia seminalia antea totum constituerunt semen, excepto hilo, atque alimen&shy;<lb/>tum tenerrimae plantae praeparant, donec firmiores in terra egerit radices, <lb/>non secus ac vitellus in ovo, placenta uterina factus, nutrimentum per fu&shy;<lb/>niculum umbilicalem porrigit pullo &rdquo; (Sponsalia plant. </s>

<s>cit., pag. </s>

<s>345). </s></p><p type="main">

<s>Per tali autorit&agrave;, e per tante ragioni, si decideva a mezzo il secolo XVIII <lb/>la controversia fra il Malpighi e il Borelli, i quali essendo pienamente con&shy;<lb/>cordi in riconoscer le foglie seminali necessarie alla vegetazione e all'incre&shy;<lb/>mento del germe, discordavano solo intorno al modo del porgersi quegli or&shy;<lb/>gani a due tali prestantissimi uffici. </s>

<s>Nonostante, il Bonnet si cred&egrave; lecito di <lb/>scriver cos&igrave; in capo alla sua LXXXIX ricerca sull'uso delle foglie: &ldquo; L'usage <lb/>des lobes et des fevilles seminales n'est pas encore bien connu. </s>

<s>On sait en <lb/>g&eacute;n&eacute;ral qu'ils fournisent &agrave; la jeune plante une noutriture appropri&eacute;e &agrave; son <lb/>&eacute;tat: mais on ne sait pas assez combien ils sont utiles a son accroisse&shy;<lb/>ment. </s>

<s>Une exp&eacute;rience que je vais rapporter le fera connoitre &rdquo; (Ediz. </s>

<s>cit., <lb/>pag. </s>

<s>310, 11). </s></p><pb xlink:href="020/01/1681.jpg" pagenum="556"/><p type="main">

<s>L'esperienze che l'Autore passa immediatamente a descrivere, fatte <lb/>nello stesso modo, ebbero il medesimo resultato di quelle del Malpighi, se <lb/>non che, mentre questi s'esercit&ograve; solo intorno alle Dicotiledoni, il Bonnet <lb/>non lasci&ograve; indietro, per farne il confronto, le Monocotiledoni. </s>

<s>Scelse perci&ograve; <lb/>i semi de'Fagioli da una parte, e quelli della Saggina dall'altra, e ai primi <lb/>tagliati i lobi, ai secondi la foglia seminale, trov&ograve; che &ldquo; le retranc<gap/>ement <lb/>des fevilles seminales a eu de beaucoup plus grandes suites dans le Sar&shy;<lb/>rasin que n'en a eu celui des lobes dans le Haricot. </s>

<s>Presque toutes les plan&shy;<lb/>tes de Sarrasin, qui ont subi cette op&eacute;ration, ont p&eacute;ri. </s>

<s>Celles qui l'ont sou&shy;<lb/>tenue sont demeur&eacute;es si ch&eacute;tives, qu'elles ont toujours &eacute;t&eacute; &agrave; l'&eacute;gard des <lb/>autres ee qu'est la plus petit nain a l'egard du plus grand g&eacute;ant &rdquo; (ivi, <lb/>pag. </s>

<s>312). </s></p><p type="main">

<s>Dietro queste esperienze, che parevano dimostrare esser pi&ugrave; dell'altre <lb/>gelose di ricevere offesa le piante a un cotiledone solo, quasi come son pi&ugrave; <lb/>gelosi della vista i monoculi di quelli che hanno in fronte due occhi, venne <lb/>desiderio al Bonnet d'instituirne altre, per determinare anche meglio l'im&shy;<lb/>portanza e l'uso delle foglie seminali. </s></p><p type="main">

<s>Il Malpighi aveva lasciato scritto in proposito: &ldquo; Primo itaque vere Fa&shy;<lb/>barum plurimas plantulas sevi, detractis prius cotyledonibus seu farinaceo <lb/>pericarpio: ex his binae tantum plantulae, reliquis corruptis, parum vege&shy;<lb/>tarunt &rdquo; (De sem. </s>

<s>veget. </s>

<s>cit., pag. </s>

<s>100). E pi&ugrave; sotto: &ldquo; Mense quoque Maii <lb/>alias seminales plantulas Fabarum et Phaseolorum, ablatis pariter binis se&shy;<lb/>minalibus foliis, seu cotyledonibus, incubandas posui, e quibus unica Fabae <lb/>plantula vegetavit &rdquo; (ibid.). Parevano i resultati di queste esperienze un <lb/>po'incerti, e l'incertezza poteva forse dipendere da ci&ograve;, che nel detrarre i <lb/>cotiledoni venisse a riceverne finalmente offesa anche l'ilo. </s></p><p type="main">

<s>S'accorse in ogni modo il Bonnet che, fatta l'operazione colla punta di <lb/>uno scarpello, riusciva sui semi secchi assai pericolosa, ma poi trov&ograve; facile <lb/>e sicura la riuscita tenendo per qualche giorno gli stessi semi in una spu&shy;<lb/>gna imbevuta d'acqua. </s>

<s>L'umidit&agrave; gli fa rigonfiare &ldquo; et il est alors plus fa&shy;<lb/>cile de diviser les lobes, et d'en separer le germe sans l'offenser &rdquo; (Recher&shy;<lb/>ches cit., pag. </s>

<s>314). Ottenuti con tal arte ili nudi e interi di alquanti fagioli, <lb/>gli semin&ograve;, e gli vide tutti nascere contro la sua aspettazione. </s>

<s>Ma sarebbe <lb/>stato molto difficile il riconoscerli nel vero esser loro, tanto erano rimpic&shy;<lb/>coliti: &ldquo; un botaniste los auroit pris pour une nouvelle espece de <emph type="italics"/>Harricot <lb/>nain &rdquo;<emph.end type="italics"/> pag. </s>

<s>315). Seminati il di 10 d'Agosto, il di 19 d'Ottobre incomin&shy;<lb/>ciarono a fiorire, ma i fiori furono scarsi, e piccoli a proporzione. </s>

<s>Lasciati <lb/>allo scoperto, caddero ai primi freddi, e caddero con essi insieme le spe&shy;<lb/>ranze di vederli probabilmente allegare ne'piccoli frutti. </s>

<s>Da ci&ograve; se ne con&shy;<lb/>cluse, lasciando addietro le curiosit&agrave;, che le foglie seminali son, pi&ugrave; che alla <lb/>vegetazion delle piante, necessarie al loro incremento. </s></p><p type="main">

<s>Nella Contemplazione della Natura il Bonnet stesso formul&ograve; questa con&shy;<lb/>clusione, dicendo che le foglie seminali <emph type="italics"/>servono principalmente a purificare <lb/>il succo nutritizio,<emph.end type="italics"/> e lo Spallanzani, in tradur dal francese queste parole, <pb xlink:href="020/01/1682.jpg" pagenum="557"/>dop'aver riferite in nota le narrate bonnettiane esperienze, soggiunge che <lb/>&ldquo; sarebbe bene il promoverle coll'applicare il taglio a tante altre piante, ora <lb/>levando interamente le due foglie seminali e i due lobi, ora levandone una <lb/>sola o un solo &rdquo; (T. </s>

<s>I cit., pag. </s>

<s>198, 99). Ci&ograve; confermerebbe il dubbio che <lb/>s'affacciava alla mente di chi legge il principio della citata Ricerca LXXXIX <lb/>sull'uso delle foglie, che cio&egrave;, tanto l'autor della Contemplazione della Na&shy;<lb/>tura, quanto l'illustre italiano traduttore, avessero dimenticate le numerose <lb/>e, per esser le prime, diligentissime esperienze del Malpighi, il quale non <lb/>trascur&ograve; nemmeno di far quella qui desiderata e proposta dallo Spallanzani. </s>

<s><lb/>Chi svolge infatti il trattato <emph type="italics"/>De seminum vegetatione<emph.end type="italics"/> vi legge fra le altre <lb/>anco queste parole: &ldquo; Plantulis vero a primordiis vegetantibus, unico de&shy;<lb/>tracto folio, altero autem superstite, germinatio producebatur, non tanta ta&shy;<lb/>men felicitate qualis in non mutilatis observabatur &rdquo; (pag. </s>

<s>109). E poniamo <lb/>pure che anche queste malpighiane esperienze avessero bisogno d'esser pro&shy;<lb/>mosse, era dovere di un Italiano in ogni modo il commemorarle, all'occa&shy;<lb/>sione specie che uno straniero veniva quasi un secolo dopo a proporle in <lb/>forma, che paressero sue primizie. </s></p><p type="main">

<s>Comunque sia, dobbiamo esser grati al Bonnet che promosse, e allo Spal&shy;<lb/>lanzani che intese di promuovere l'esperienze del Malpighi, dalle quali in&shy;<lb/>somma veniva a intendersi perch&egrave; fosse necessaria l'umidit&agrave; alla germoglia&shy;<lb/>zione. </s>

<s>Se poi questa necessit&agrave; sia l'unica, o se vi si richieda anche insieme <lb/>il concorso dell'aria, bench&egrave; le volgari esperienze de'semi rimasti nelle chiuse <lb/>profondit&agrave; sepolti ne paressero una prova certa, non eran per&ograve; ancora le <lb/>menti disposte a bene intenderla. </s>

<s>Secondavano molto queste disposizioni, da <lb/>poi che si fece notare la somiglianza che passa fra i semi delle piante e gli <lb/>ovi degli animali, le dottrine insegnate dall'Harvey, il quale, escludendo dal&shy;<lb/>l'utero nell'atto ch'&egrave; reso fecondo ogni minima cosa che venga di fuori, <lb/><emph type="italics"/>aeris puta aut seminis,<emph.end type="italics"/> dava argomento a concluderne che, non essendo <lb/>l'aria necessaria per concepire, non fosse perci&ograve; necessaria nemmeno per <lb/>germinare. </s></p><p type="main">

<s>Parve questa logica conclusione esser confortata dalle esperienze, quando <lb/>il Boyle tent&ograve; di produrre creature viventi nel vuoto. </s>

<s>Essendosi l'illustre Fi&shy;<lb/>sico proposto di confutar l'ipotesi della fiamma vitale sentiva che sarebbe <lb/>un grande argomento in favore di lei &ldquo; si comperiatur quod vitae princi&shy;<lb/>pium in seminalibus rudimentis indigeat, non secus ac caeterae flammae, <lb/>aeris concursum ut in actum revocetur &rdquo; (Op. </s>

<s>omnia cit., T. III, P. II, <lb/>pag. </s>

<s>173). Prov&ograve; a quest'intento di far nascere sotto la campana della mac&shy;<lb/>china pneumatica alcune uova di bombici e di altri insetti e furon forse le <lb/>difficolt&agrave; dello sperimentare e l'incertezza dei resultati, che non gli dettero <lb/>animo di proseguire i tentativi ne'semi, dai quali nonostante sperava che <lb/>verrebbe dimostrato non esser necessario il concorso dell'aria, per ridestar <lb/>negli stessi semi e negli ovi, come nelle fiamme, gli spiriti della vita. </s></p><p type="main">

<s>Sentite le difficolt&agrave; dello sperimentare al modo boyleiano, il Malpighi <lb/>scelse una via pi&ugrave; facile, bench&egrave; non fosse cos&igrave; diretta: pens&ograve; di sottrarre <pb xlink:href="020/01/1683.jpg" pagenum="558"/>i semi dall'azione dell'aria, tenendoli immersi nell'acqua di un vaso, alla <lb/>quale soprannotava uno straterello di olio. </s>

<s>I semi, ch'eran di vario genere, <lb/>si videro presto cominciare a risolversi in bolle, e a render torbida l'acqua: <lb/>dopo venti giorni erano affatto corrotti, senza dar segno di vegetazione. </s>

<s>&ldquo; Vi&shy;<lb/>gesima transacta die, aqua foetentissima erat, conclusaque semina corrupta <lb/>absque vegetatione &rdquo; (De sem. </s>

<s>veget. </s>

<s>cit, pag. </s>

<s>108). </s></p><p type="main">

<s>Pareva si dimostrasse da questa esperienza la necessit&agrave; dell'aria per <lb/>vegetare, ma tante difficolt&agrave; si potevano contrapporre a una tal conclusione, <lb/>che il Malpighi stesso avendole presentite lasci&ograve; la questione indecisa. </s>

<s>L'aveva <lb/>per&ograve; il Borelli risoluta con gran confidenza, e gi&agrave; posta per fondamento alla <lb/>sua teoria, essendo chiaro che i termometri cotiledonari non avrebbero po&shy;<lb/>tuto, senza l'intervento dell'aria, esercitare sul germe i loro uffici, pi&ugrave; sot&shy;<lb/>tilmente spiegati nella propos. </s>

<s>CLXXXI, che il Borelli stesso formulava: <lb/>&ldquo; praecipuam causam vegetationis plantarum esse aerem &rdquo; (De motu anim, <lb/>P. II cit., pag. </s>

<s>371). </s></p><p type="main">

<s>Dietro una tanta autorit&agrave; nella scienza si dur&ograve; a credere che l'aria con&shy;<lb/>corresse nella germogliazione colla sua elasticit&agrave;, messa in gioco dalle al&shy;<lb/>ternative del caldo e del freddo, infintanto che Guglielmo Homberg non <lb/>torn&ograve; a tentare quei pneumatici esperimenti, innanzi alle difficolt&agrave; de'quali <lb/>erasi arretrato il Boyle. </s>

<s>Pi&ugrave; fortunato dell'Inglese, o pi&ugrave; destro, il nuovo <lb/>sperimentatore francese riusc&igrave; a far germogliare i semi di varie piante nel <lb/>vuoto, dietro il qual fatto pose contro il Borelli queste due conclusioni: <lb/>&ldquo; I. </s>

<s>Que ni le ressort de l'air, ni sa pesanteur ne sont point la cause prin&shy;<lb/>cipale de la germination des plantes, puisque les graines germent dans le <lb/>vuide. </s>

<s>II. </s>

<s>Que l'air est cependant au moins une cause accidentelle de cette <lb/>germination, quisque d'une m&egrave;me quantite de graines de la m&egrave;me esp&egrave;ce, <lb/>il en avoit germ&eacute; un bien plus grand nombre dans l'air que dans le vuide &rdquo; <lb/>(Collection acad., T. </s>

<s>I cit., pag. </s>

<s>184, 85). </s></p><p type="main">

<s>Sulla fine del secolo XVIII si trov&ograve; ch'eran false queste conclusioni <lb/>dell'Homberg, e ch'era invece vera la proposizion del Borelli, modificata <lb/>per&ograve; col sostituire ai giochi elastici dell'aria, imparati dall'arte santoriana, <lb/>un'azione pi&ugrave; sottile e pi&ugrave; intima, rivelata da una scienza che apparve nuova. </s>

<s><lb/>Ma come al tornar del giorno pieno precede un incerto albore crepuscolino, <lb/>cos&igrave; avvenne allo splendido sole di quella scienza. </s></p><p type="main">

<s>Chenelmo Dygby lesse nel collegio di Gresham, il d&igrave; 23 Gennaio 1660, <lb/>una dissertazione, che fu dal patrio idioma tradotta in latino col titolo <emph type="italics"/>De <lb/>vegetatione plantarum.<emph.end type="italics"/> Ivi narra com'aves<gap/>e reso fertilissimo un campo, <lb/>spargendovi sopra sostanze terree mescolate con nitro. </s>

<s>Si dir&agrave; forse, poi sog&shy;<lb/>giunge, ch'&egrave; lo stesso nitro, attratto dalle radici, quello che ha prodotto <lb/>l'ubert&agrave; della messe? </s>

<s>Niente affatto, perch&egrave; sarebbe presto esaurito, n&egrave; po&shy;<lb/>trebbe somministrar materia a tanta progenie. </s>

<s>&ldquo; Salis nitrum est ibi instar <lb/>magnetis quod attrahit similem salem, quo aer redditur faecundus. </s>

<s>Et hinc <lb/>Cosmopolita ansam arripiebat dicendi quod <emph type="italics"/>in aere occultum quoddam vi&shy;<lb/>tae alimentum sit.<emph.end type="italics"/> In tali aere, qui hoc <emph type="italics"/>benigno igne<emph.end type="italics"/> maxime impraegna-<pb xlink:href="020/01/1684.jpg" pagenum="559"/>tus est, salubrem producimus vitam..... Hic sal est alimentum pulmonum <lb/>et nutrimentum spirituum..... Hic igitur spiritus qui est in aere attrahi&shy;<lb/>tur, veluti per quendam magnetem, per salinum liquorem, quem semen <lb/>imbibit et cuius plenum est..... Huic sali <emph type="italics"/>omnium rerum seminales vir&shy;<lb/>tutes<emph.end type="italics"/> inclusae sunt..... &rdquo; (Amstelodami 1669, pag. </s>

<s>54-57): enimmi alllora, <lb/>e lungo tempo da poi, ma che la Chimica moderna ha felicemente inter&shy;<lb/>pretati. </s></p><pb xlink:href="020/01/1685.jpg"/><p type="main">

<s><emph type="center"/>CAPITOTO XIV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dei Minerali<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della sede nettunica del regno minerale. </s>

<s>&mdash; II. </s>

<s>Della sede plutonica del regno minerale. </s>

<s>&mdash; III. </s>

<s>Della <lb/>generazion dei cristalli, e di ci&ograve; che intorno alle forme cristalline fu osservato e speculato dagli <lb/>Accademici del Cimento. </s>

<s>&mdash; IV. Dell'origine e de'progressi della Cristallografia fuori dell'Ac&shy;<lb/>cademia del Cimento. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>A quei, che ingannati da fallaci esperienze, ammettevano potersi le piante <lb/>nutrir di sola acqua pura, rimaneva il dovere di rispondere a chi gli avesse <lb/>interrogati come mai l'acqua stessa riesca a trasformarsi nelle solide fibre <lb/>delle foglie, della corteccia e del legno; e come mai valga una sostanza in&shy;<lb/>sipida e inodora a infondere tanta soavit&agrave; ne'frutti, e tant'olezzo ne'fiori. </s>

<s><lb/>Si rispondeva nonostante, perch&egrave; di parole fu sempre gran dovizia, con ar&shy;<lb/>gomenti, che ritraevano tutt'insieme de'difetti provenienti dalle difficolt&agrave; <lb/>della cosa, e dalla ignoranza della Chimica: alcuni per&ograve;, come il Bonnet per <lb/>esempio, negarono esser l'acqua unico alimento alla vita vegetativa, e se al&shy;<lb/>cuni semi furono a spettacolo offerti dal Du-Hamel lietamente germogliati <lb/>e cresciuti nel muschio inumidito, nella segatura del legno o nella bamba&shy;<lb/>gia, ci&ograve; avvien, diceva l'Autore della <emph type="italics"/>Contemplazion della Natura,<emph.end type="italics"/> &ldquo; perch&egrave; <lb/>molte di tali materie o trasmutansi insensibilmente in terra, o contengono <lb/>attualmente parti terree, o perch&egrave; l'acqua, da cui vengono innaffiate, &egrave; pre&shy;<lb/>gna di tali particole, che gli organi delle piante estraggono, preparano o si <lb/>assimilano &rdquo; (Traduz. </s>

<s>cit., T. I, pag. </s>

<s>185). </s></p><p type="main">

<s>Cos&igrave; venivasi nelle piante a riconoscere quella intima relazione, che le <lb/>stringe col regno minerale; relazione messa gi&agrave; in grande evidenza dalle <pb xlink:href="020/01/1686.jpg" pagenum="561"/>combustioni de'tronchi, de'rami e delle stesse foglie nelle ceneri delle quali, <lb/>lisciviate, s'ammirarono l'eleganti variet&agrave; delle forme cristalline. </s>

<s>L'esperienze <lb/>intorno a questi, che si chiamarono <emph type="italics"/>Sali fattizi,<emph.end type="italics"/> incominciate nel periodo <lb/>primo dall'Accademia del Cimento, si perfezionarono nel periodo ultimo per <lb/>opera di Franceso Redi, il quale raccolse in XX aforismi il resultato de'suoi <lb/>diligentissimi studi. </s></p><p type="main">

<s>Si vedevano dunque cos&igrave; manifestamente ritornare al regno minerale i <lb/>cadaveri delle piante, come vi ritornavano in egual modo i cadaveri degli <lb/>animali. </s>

<s>Un'assai ovvia osservazione dall'altra parte, che cio&egrave; gli animali <lb/>stessi nutronsi delle sostanze gi&agrave; preparate ne'vegetanti, mentre che i ve&shy;<lb/>getanti si nutrono immediatamente dalla terra, scopriva facile alle menti dei <lb/>Filosofi e dei volgari quell'ingradarsi sempre a maggiore altezza e a dignit&agrave;, <lb/>che fanno i tre grandi regni della Natura. </s></p><p type="main">

<s>Rimasero per&ograve; di cos&igrave; fatti passaggi dalla materia bruta alla organiz&shy;<lb/>zata affatto occulte le ragioni e i modi, infin tanto che il benefico Micro&shy;<lb/>scopio non venne a diradare alquanto il velo di que'misteri. </s>

<s>Apparvero <lb/>allora molte delle particelle minerali informi, perch&egrave; forse non riusc&igrave; a raf&shy;<lb/>figurarle la vista naturale, nemmeno avvalorata dall'arte, ma in alcune al&shy;<lb/>tre di quelle particelle si riconobbero figure superficiali ben definite, e con&shy;<lb/>terminanti lo spazio in angoli e in lati condotti a regola di squisitissima <lb/>geometria. </s>

<s>Negli stami per&ograve;, di che s'intessono gli organi alle piante e agli <lb/>animali, si videro quelle angolosit&agrave; sparire per ridursi a prendere costante&shy;<lb/>mente una figura otricellare o sferoidea. </s></p><p type="main">

<s>Or perch&egrave; i solidi, in prendere le loro angolosit&agrave;, si vedono ritornare <lb/>alla sfera, convien dire che questa sia il subietto generale di tutte le figure <lb/>poliedriche, cosicch&egrave; il definito per esempio nel triangolo e nel quadrato, <lb/>nella piramide e nel cubo, si trovi indefinitamente contenuto nella sfera e <lb/>nel cerchio. </s>

<s>Di qui vedesi esser mirabilmente l'Istiologia illustrata dalla Geo&shy;<lb/>metria, perciocch&egrave; nella cellula si comprendono indeterminate le particolari <lb/>virt&ugrave; del cristallo. </s>

<s>La determinata figura perci&ograve; di questo non permette altro <lb/>incremento che per apposizione di parti ugualmente determinate, mentre <lb/>dalla indefinita forma della cellula possono uscire le indefinite variet&agrave; di <lb/>tutte le altre forme, che si trovano in lei virtualmente comprese. </s></p><p type="main">

<s>La scienza dei minerali non &egrave; dunque, come potrebbe sembrare, aliena <lb/>dalla scienza dei viventi, perch&egrave; lo studio del cristallo conduce o pu&ograve; facil&shy;<lb/>mente condurre allo studio della cellula, e poniamo che si trovino, in am&shy;<lb/>bedue i casi, difficolt&agrave; insuperabili all'ingegno e all'industria dell'uomo, &egrave; <lb/>un fatto oramai sperimentato in Filosofia che sono i paragoni di scoperte <lb/>nuove sempre fecondi. </s></p><p type="main">

<s>Vien forse da queste considerazioni, le quali non si possono da noi ac&shy;<lb/>cennare che in fretta, qualche lume d'idee per rispondere a chi volesse sa&shy;<lb/>pere se giovi nello studio della Storia naturale incominciar dagli animali o <lb/>dai minerali, dall'alto gradatamente scendendo in basso, o facendo a ritroso <lb/>il viaggio. </s>

<s>Il proposto quesito &egrave; simile a quell'altro: se giovi nello studio <pb xlink:href="020/01/1687.jpg" pagenum="562"/>della geometria incominciar dal circolo o dal triangolo, tenendo via sintetica <lb/>o analitica: questione di metodo irresolubile in logica, ma che facilmente si <lb/>risolve nel pratico insegnamento. </s></p><p type="main">

<s>Comunque sia, s'&egrave; da noi tenuto il primo di questi metodi: si &egrave; in&shy;<lb/>cominciato cio&egrave; dal narrar le faticose conquiste dell'ingegno nello studio <lb/>della vita animale, perch&egrave; sono in essa eminentemente comprese le vite dei <lb/>sottoposti ordini naturali, come son le figure poliedriche eminentemente tutte <lb/>comprese nella sfera, o come son, nelle virt&ugrave; della cellula, a s&igrave; grande al&shy;<lb/>tezza sublimate le virt&ugrave; dei cristalli. </s></p><p type="main">

<s>Nella storia delle osservazioni e delle esperienze, fatte dalla scienza in&shy;<lb/>torno a questi stessi cristalli, s'assolve il presente argomento secondo i limiti <lb/>e l'ordine che ci siamo prescritti. </s>

<s>Il rimanente, che pu&ograve; concernere i mi&shy;<lb/>nerali, si riduce alle loro origini in seno e sulla superficie della gran madre <lb/>Terra, la quale venne per le subite vicende a deporveli in due vari modi. </s>

<s><lb/>Costituiscono perci&ograve; questi due modi al regno come due cospicue e distinte <lb/>sedi, in riconoscer le quali essendosi lungamente e faticosamente studiata la <lb/>scienza, non rimane a noi, prima di trattar de'cristalli, che a narrar colla <lb/>solita brevit&agrave; il lento e faticoso progredire di quelli studi. </s></p><p type="main">

<s>Incominciano cos&igrave; fatti studi col propor che si fece il problema dell'ori&shy;<lb/>gine dei corpi marini, i quali si ritrovan dispersi per i continenti, o depo&shy;<lb/>sti sulle alte cime dei monti, e dal vario modo come fu risoluto quel pro&shy;<lb/>blema dipendono, delle nuove scienze che siam per narrare, gli arretramenti <lb/>e i progressi. </s>

<s>Dalle tradizioni antiche s'introdusse con Teofrasto l'opinione <lb/>che fosse nella terra una virt&ugrave; plastica, simile a quella del mare, e fu, nei <lb/>primi restauramenti scientifici, il Falloppio che accolse, e nel suo trattato <lb/><emph type="italics"/>De metallis seu fossilibus<emph.end type="italics"/> dette autorit&agrave; e diffuse una tale falsa opinione. </s>

<s><lb/>Giorgio Agricola, che non molto dopo venne fuori a trattare dello stesso <lb/>argomento, ammetteva nel VII libro <emph type="italics"/>De natura fossilium<emph.end type="italics"/> l'esistenza di un <lb/>succo lapidescente, il quale, entrando per tutti i pori, gli riempie di tutto <lb/>s&egrave;, e ne modella gl'incavi. </s>

<s>&ldquo; Cum Natura, poi soggiunge, lapides arborum <lb/>similes procreet, diligenter videndum est an corticem et medullam aliaque <lb/>habeant, quae si absunt non stipites in lapides conversi sunt, sed Na&shy;<lb/>tura fecit lapides stirpium simillimos &rdquo; (De natura fossilium, Basileae 1546, <lb/>pag. </s>

<s>327, 28). </s></p><p type="main">

<s>Ebbero il Falloppio e l'Agricola alle loro ipotesi molti seguaci, i quali <lb/>non sentirono a professarle gran repugnanza, in tempi che s'ammetteva dai <lb/>pi&ugrave; ne'vermi, e in alcune piante, la generazione spontanea. </s>

<s>Argomentavano <lb/>infatti costoro che la materia, la quale d&agrave; vita a un insetto, pu&ograve; men dif&shy;<lb/>ficilmente plasmarsi a comporre il nicchio a una Conchiglia, o a un Echino. </s>

<s><lb/>Parve nonostante ad alcuni quella ipotesi dissennata, e il Fracastoro fu primo <lb/>a profferire il suo giudizio in privato, e il Cesalpino in pubblico, scrivendo <lb/>nel I libro <emph type="italics"/>De metallicis<emph.end type="italics"/> che le conchiglie e altri avanzi marini furono ivi <lb/>deposte dalle acque, le quali poi si ritirarono lasciando arido il continente. <lb/></s>

<s>&ldquo; Hoc enim modo censere, poi ne conclude, magis consonum est rationi, <pb xlink:href="020/01/1688.jpg" pagenum="563"/>quam putare vim animalem, intra lapides, rudimenta animalium ac planta&shy;<lb/>rum gignere, ut quidam putant &rdquo; (Romae 1596, pag. </s>

<s>5). </s></p><p type="main">

<s>Veniva pochi anni dopo a dar maggior forza al ragionamento del Ce&shy;<lb/>salpino Fabio Colonna, il quale, invocando il filosofico assioma che la Na&shy;<lb/>tura nulla fa a caso, dimostrava la falsit&agrave; dell'opinione di Teofrasto. </s>

<s>Inutili <lb/>infatti sarebbero i denti senza le mascelle, e i nicchi, che non han da co&shy;<lb/>prire, e le ossa, che non hanno da sostentar nessun membro animale. </s>

<s>&ldquo; Den&shy;<lb/>tes sine maxilla, testacea sine animali, ossa unica (nonnisi omnia coniuncta <lb/>cum ipso animali) in proprio elemento Natura nunquam fecit: quomodo in <lb/>alieno nunc potuisset fecisse est credendum? </s>

<s>Ossa enim ex eodem seminali <lb/>excremento ortum habere simul cum animali ipsa experientia et Natura do&shy;<lb/>cuit, tam in homine, quam in animalibus sanguine praeditis, et ex semine <lb/>initium habentibus, ac etiam quibusdam aliis: quomodo in subterraneis ter&shy;<lb/>restribus semen hoc inveniri asseritur? </s>

<s>qua experientia? </s>

<s>Hoc si daretur et <lb/>hominem sponte oriri esset observatum vel animalia, ut bos, equus et si&shy;<lb/>milia &rdquo; (Dissertatio De glossopetris, appendix ad tract. <emph type="italics"/>De purpura,<emph.end type="italics"/> Ro&shy;<lb/>mae 1616, pag. </s>

<s>32). </s></p><p type="main">

<s>Comparve nel 1622 alla luce la descrizione del Museo Calzolari, lasciata <lb/>a mezzo per causa di morte da Benedetto Ceruti, e condotta a termine da <lb/>Andrea Chiocchi, il quale, trattando <emph type="italics"/>De lapideis rebus a Natura effigie do&shy;<lb/>natis,<emph.end type="italics"/> divulg&ograve; sulla proposta questione quella, ch'egli chiama <emph type="italics"/>Magni Fra&shy;<lb/>castori sententiam.<emph.end type="italics"/> Racconta come Torello Sarayna, giureconsulto e archeo&shy;<lb/>logo veronese, scavando il patrio monte da quella parte, d'onde sgorga la <lb/>fontana cos&igrave; detta del <emph type="italics"/>Ferro,<emph.end type="italics"/> vi trovasse con sua grande maraviglia sepolte <lb/>conchiglie, ostriche, con molte altre spoglie di marini animali. </s>

<s>Non sapendo <lb/>come spiegare il fatto interrog&ograve; il celebre concittadino suo Girolamo Fraca&shy;<lb/>storo, il quale rispose aversi della proposta questione tre diverse sentenze. </s>

<s><lb/>La prima di coloro, che dicevano essere quegli animali stati trasportati col&agrave; <lb/>dal Diluvio; sentenza per&ograve; ch'egli giudicava poco probabile, perch&egrave; la uni&shy;<lb/>versale inondazione non fu d'acque venute di sotto dal mare, ma di sopra <lb/>dal cielo, e poi perch&egrave; si potrebbe a quel modo spiegar l'esistenza dei corpi <lb/>marini sulle vette, ma no alle falde dei monti. </s></p><p type="main">

<s>Era la seconda sentenza quella di coloro, che tenevano con Teofrasto, <lb/>ai quali rispondeva il Fracastoro cos&igrave; argomentando: O le sostanze lapidee, <lb/>formate dal succo plastico a imitazione delle parti animali, furono un giorno <lb/>viventi o no: Se furono viventi, allora perch&egrave; non si vedono tuttavia rivi&shy;<lb/>vere simili produzioni? </s>

<s>Dir poi che non furono mai viventi, e che solo imi&shy;<lb/>tarono l'esteriori forme animali, &egrave; in aperta contradizione col senso, veden&shy;<lb/>dosi che le conchiglie fossili, per esempio, hanno tutte le parti delle con&shy;<lb/>chiglie vive e vere, con questa sola differenza ch'essendosi corrotte mancano <lb/>le parti molli. </s></p><p type="main">

<s>&ldquo; Cum hactenus, prosegue a dire il Chiocchi, magni Fracastori senten&shy;<lb/>tiam recitasset Sarayna, qua aliorum Phylosophorum sibi hac in re non <lb/>probari placita docebat, subiecit. </s>

<s>Ergo se dicebat existimare haec olim vera <pb xlink:href="020/01/1689.jpg" pagenum="564"/>animantia fuisse illuc iactata a mari et in mari enata. </s>

<s>&rdquo; Questa poi con&shy;<lb/>clude &egrave; la dottrina dell'eccellentissimo Fracastoro, che raccoglie in s&egrave; il va&shy;<lb/>lore di molte e classiche testimonianze, rappresentando egli medico, filosofo, <lb/>poeta e astronomo le persone e il divino ingegno d'Ippocrate, di Aristotile, <lb/>di Platone, di Virgilio e di Tolomeo. (Descriptio Musaei Calceolari, Vero&shy;<lb/>nae 1622, pag. </s>

<s>409). </s></p><p type="main">

<s>Comunque sia, erano i progressi della scienza mal fondati sopra l'au&shy;<lb/>torit&agrave; di un grand'uomo, quando a confortar le ragioni mancavano l'espe&shy;<lb/>rienze dei fatti. </s>

<s>Coteste esperienze, alle quali non si prevedevano da nessuno <lb/>ancora possibili i modi, ebbero nella gloriosa Accademia fiorentina i prin&shy;<lb/>cipii, com'ora accenneremo, e come meglio vedremo di poi. </s></p><p type="main">

<s>Fu, qualche miglio in distanza da Livorno, nell'anno 1666, pescato un <lb/>gran pesce del genere dei Cani, il capo del quale, fatto per ordine del Gran&shy;<lb/>duca venire a Firenze, fu consegnato a Niccol&ograve; Stenone, nuovo accademico <lb/>del Cimento, perch&egrave; lo sezionasse. </s>

<s>Carlo Dati, concorso fra gli altri allo spet&shy;<lb/>tacolo, vi riconobbe una gran somiglianza con quella testa di Lamia, fatta <lb/>incidere in rame e descritta dal Mercati nella Metalloteca sua Vaticana: di <lb/>che fece consapevole lo Stenone, a cui, perch&egrave; se ne potesse giovare a'suoi <lb/>studii, prest&ograve; il rame stesso inciso insieme col manoscritto. </s>

<s>L'Autore di que&shy;<lb/>sto, come si sa dalle passate storie, riponeva fra i metalli <emph type="italics"/>idiomorfi<emph.end type="italics"/> anche <lb/>le Glossopietre, le quali, perciocch&egrave; troppo somigliavano ai denti delle La&shy;<lb/>mie, cos&igrave;, perch&egrave; non l'avessero gl'inesperti a confondere insieme, ne fa&shy;<lb/>ceva notare le differenze: &ldquo; Video namque Glossopetras magnas et Lamiae <lb/>piscis dentes confundi etiam a curiosis. </s>

<s>Similitudo errorem subornavit, quae <lb/>tanta est ut, qui utrorumque ortum non noverit, nihil suspicetur; qui utrin&shy;<lb/>que notas non contulerit, non dignoscat..... Quod inter dentes et Glosso&shy;<lb/>petras illas discriminis est, exiguum sane. </s>

<s>Crassiores plerumque Glossopetrae, <lb/>tenuiores dentes, et mollius nitent, ut inter osseam et lapideam Glossopetra&shy;<lb/>rum materiam ex aspectu iudicium capiamus. </s>

<s>Unus quoque et perpetuus <lb/>dentium color candidus, vel aetate flavescens, Glossopetrae variant &rdquo; (Metal&shy;<lb/>lotheca vatic. </s>

<s>cit., pag. </s>

<s>333, 34). </s></p><p type="main">

<s>Leggendo lo Stenone nel manoscritto queste parole, s'accorse dell'in&shy;<lb/>ganno, che s'era fatto il Mercati, in creder che le notate accidentali variet&agrave; <lb/>fra i denti delle Lamie e le Glossopietre importassero fra loro qualche sostan&shy;<lb/>zial differenza, e fu da ci&ograve; condotto a entrare nella questione, cos&igrave; lungamente <lb/>agitata, fra chi diceva esser le stesse Glossepietre prodotte dalla terra, e chi <lb/>sosteneva invece essere avanzi di antichi animali. </s>

<s>Da varie osservazion&igrave;, fra le <lb/>quali la pi&ugrave; importante si &egrave; che i fossili e i viventi si ritrovan simili in tutte le <lb/>loro pi&ugrave; minime parti, trae il prudente uomo, non bene in tutto rassicurato <lb/>dalle troppo scarse esperienze, le seguenti sei conclusioni, alle quali d&agrave; il <lb/>modesto titolo di <emph type="italics"/>congetture.<emph.end type="italics"/> Nella I e nella II si argomenta non poter es&shy;<lb/>sere i fossili prodotti dalla terra, perch&egrave; non si vede nelle parti intorno, ri&shy;<lb/>mosse se molli, o nella deformata figura dei creduti vegetanti se quelle stesse <lb/>parti son dure, nessun evidente segno di accrescimento, come osservasi per <pb xlink:href="020/01/1690.jpg" pagenum="565"/>esempio nelle radici degli alberi &ldquo; quae in terra duriori mille modis intor&shy;<lb/>tae et compressae a figura recedunt &rdquo; (Canis carchariae dissectum caput, <lb/>Myologiae sperimen. </s>

<s>cit., pag. </s>

<s>94). Nella III, nella IV e nella V congettura <lb/>s'ammettono le stratificazioni alluvionali, in che s'affalda la superficie ter&shy;<lb/>restre, e nella VI finalmente concludesi: &ldquo; Nihil obstare videtur quominus <lb/>animalium partibus similia corpora, quae e terris eruuntur, pro animalium <lb/>partibus habeantur &rdquo; (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>Poco tempo dopo che lo Stenone cos&igrave; con gran prudenza fiosofava, <lb/>un Pittor sic&igrave;liano usciva calorosamente fuori a decidere la controversia, <lb/>prendendo per sua pi&ugrave; sicura scorta la Filosofia del senso comune. </s>

<s>Agostino <lb/>Scilla pubblicava in Napoli, nel 1670, un libretto intitolato <emph type="italics"/>Vana specula&shy;<lb/>zione disingannata dal senso,<emph.end type="italics"/> dove si proponeva principalmente di dimo&shy;<lb/>strare il vero essere delle Glossopietre, di che trovasi largamente seminata <lb/>l'isola di Malta. </s>

<s>&ldquo; Rimetto la causa, egli scrive, e la decisione di essa fran&shy;<lb/>camente a cotest'Isola candidissima, che non vuole mica addossati miracoli <lb/>finti, essendo bene provveduta de'veri e sodi, che la Natura abbondante&shy;<lb/>mente in essa ha depositato, come mostrer&ograve; nel luogo della dichiarazione <lb/>d'alcune sue bellissime medaglie, se piacer&agrave; al Signore. </s>

<s>Udiamola in cor&shy;<lb/>tesia e incolpiamo noi medesimi se ingannare ci vogliamo. </s>

<s>Essa agli occhi <lb/>nostri fedelmente parla, affermandoci che la Natura non ha avuto parte di <lb/>generazione, nella sua marga, di denti, di echini, d'ossa, di vertebre, come <lb/>pur ora dalle stesse cose l'osserveremo &rdquo; (pag. </s>

<s>111). Le osservazioni pro&shy;<lb/>cedono con senno non solo, ma con rettitudine di metodo sperimentale, in&shy;<lb/>fiorata di antica e di moderna erudizione. </s>

<s>Parevano perci&ograve; dover riuscir con&shy;<lb/>cludenti ai Filosofi, e tutt'insieme persuasive alle genti volgari, ma in effetto <lb/>seguit&ograve; ancora la vana speculazione a prevalere sul senso. </s></p><p type="main">

<s>Ai Peripatetici, tuttavia ostinati in credere alle generazioni spontanee <lb/>degl'infimi esseri viventi, arridevano meglio delle nuove dottrine le antiche, <lb/>che il Gassendo riferiva cos&igrave; nel II Tomo del suo Syntagma filosofico: &ldquo; Cae&shy;<lb/>teri fere haec referunt aut ad mundi animam, aut universi ad naturam, <lb/>quae cum eadem ubique sit, et rerum omnium quos ubique contineat lapi&shy;<lb/>des efformat ex succo idoneo in mediis continentibus referentes externa spe&shy;<lb/>cie conchas et pisces, quos procreare eadem solet in medio ac dissito mari &rdquo; <lb/>(editio cit., pag. </s>

<s>104). </s></p><p type="main">

<s>Fra'nostri uno de'pi&ugrave; fervorosi seguaci di questa opinione &egrave; da anno&shy;<lb/>verare Filippo Bonanni, che le altrui autorit&agrave; confortava con osservazioni sue <lb/>proprie, e con ragioni, che dovevano allora essere seducenti. </s>

<s>Diceva parere <lb/>impossibile che sieno reliquie di animali le cos&igrave; dette ossa dei giganti, non <lb/>essendoci memoria che abbiano mai vissuto al mondo creature cos&igrave; smisu&shy;<lb/>rate, e fuori de'consueti ordini naturali. </s>

<s>Che se convien di qui persuadersi <lb/>non poter quelle gigantesche ossa esser altro che un gioco della Natura, <lb/>perch&egrave; non potr&agrave; l'argomento applicarsi ai testacei e alle innumereroli altre <lb/>reliquie de'corpi marini, che si trovano qua e l&agrave; disperse ne'continenti? <lb/></s>

<s>&ldquo; Onde mi restringo a credere, cos&igrave; conclude, generarsi gran parte de'te-<pb xlink:href="020/01/1691.jpg" pagenum="566"/>stacei dalla Terra, con l'anima vegetativa, che perfezioni loro la forma, e <lb/>distribuisca l'alimento: animati dal Supremo Signore, quando ne vede la <lb/>materia disposta, quasi <emph type="italics"/>ludens in orbe tarrarum,<emph.end type="italics"/> ma con gioco non inde&shy;<lb/>gno della dignit&agrave; di lui, poich&egrave; tutto &egrave; operare di perfettissima Sapienza, e <lb/>di Provvidenza infinita &rdquo; (Ricreazione dell'occhio cit., pag. </s>

<s>82). </s></p><p type="main">

<s>In Francia rinnovell&ograve;, sui principii del secolo XVIII, le idee riferite dal <lb/>Gassendo un anonimo Autore di un libro intitolato <emph type="italics"/>Nouveau voyage d'Ita&shy;<lb/>lie,<emph.end type="italics"/> dove, nelle lettere XXVI e XXX, si tratta delle origini de'corpi marini <lb/>ritrovati scavando sulle cime dei monti. </s>

<s>Il Vallisnieri se ne scandalizz&ograve;, e <lb/>offeso nell'onor nazionale scriveva cos&igrave;, ardente di zelo: &ldquo; Mi credeva, se <lb/>Dio mio aiuti, che in Francia pi&ugrave; alcuno non si trovasse, che opinioni s&igrave; <lb/>rancide e s&igrave; abominevoli sostenesse, o che altre ne desse continuamente in <lb/>luce, s&igrave; mal fondate, che a un solo crollo trabocchino e a terra cadano, per&shy;<lb/>ch&egrave; tanto di noi si burlano, e parlano della Filosofia d'Italia come si par&shy;<lb/>lerebbe di quella de'Lapponi e degl'Irochesi, se incominciassero a filosofare, <lb/>come il nostro insigne letterato, signor abate Conti, ud&igrave; con le sue proprie <lb/>orecchie nella loro reale Accademia, quando fecero l'elogio al morto Mar&shy;<lb/>tino Poli, speziale romano, e membro illustre della detta reale Accademia &rdquo; <lb/>(De'corpi marini che su'monti si trovano, Venezia 1727, pag. </s>

<s>16). </s></p><p type="main">

<s>Aveva ragione di esclamar cos&igrave; il Vallisnieri, e di rinfacciare a quei <lb/>Francesi, dispregiatori dell'Italiana filosofia, che quel loro modo di filoso&shy;<lb/>fare era un rinnovellar le antiche vanit&agrave; delle forze plastiche, e delle gene&shy;<lb/>razioni spontanee, dal Redi e dal Malpighi, italiani, a cui aggiungeva s&egrave; me&shy;<lb/>desimo per terzo, cacciate via dalla scienza con tante dimostrative esperienze, <lb/>e con tanto solidi ragionamenti. </s>

<s>Cosicch&egrave; pu&ograve; giustamente dirsi essere stato <lb/>precipuo merito della scienza italiana se, a mezzo il secolo XVIII, s'accett&ograve; <lb/>senza controversie da tutti la sentenza pronunziata da quel Giovanni Bian&shy;<lb/>chi, meglio conosciuto sotto il nome di Jano Planco, il quale, nel catalogo <lb/>de'Lincei premesso al <emph type="italics"/>Fitobasanos<emph.end type="italics"/> del Colonna, scrisse a proposito delle <lb/>piante fossili escavate in alcuni nostri terreni: &ldquo; certissimum est ipsum esse <lb/>vere lignum, quaemadmodum sunt verae marinae testae cornua illa Ham&shy;<lb/>monis, et omnia marina fossilia, quae in montibus reperiuntur &rdquo; (Floren&shy;<lb/>tiae 1744, pag. </s>

<s>XXXIII). </s></p><p type="main">

<s>Conquistatasi faticosamente questa prima parte del vero, rimaneva a ri&shy;<lb/>solvere l'altra ben pi&ugrave; diffic&igrave;le questione: come mai le conchiglie e gli altri <lb/>fossili fossero potuti risalire ai monti dalle basse giaciture dei mari. </s>

<s>Quando <lb/>ai problemi naturali si cercavano prima di tutto le soluzioni ne'libri dei Fi&shy;<lb/>losofi, si rispondeva al proposto problema de'corpi marini sui monti in due <lb/>vari modi, secondo che di Platone o di Aristotile erano i libri via via con&shy;<lb/>sultati. </s>

<s>Il primo de'due solenni Maestri, ammettendo essere i monti alla <lb/>Terra congeniti, non lasciava a rispondere se non che o la Natura imita fra <lb/>terra le produzioni proprie dell'acqua, o che sien quelle marine produzioni <lb/>state deposte ne'continenti dalle acque diluviali. </s></p><p type="main">

<s>Le tradizioni bibliche, miste colle platoniche, conciliarono molti seguaci <pb xlink:href="020/01/1692.jpg" pagenum="567"/>a questa seconda opinione, ma trovarono altri pi&ugrave; spedito il dire che la Na&shy;<lb/>tura o il caso danno talvolta alle pietre quelle cos&igrave; bizzarre forme, che le <lb/>rendon tanto simili agli animali. </s>

<s>Primeggia fra costoro il Falloppio, il quale, <lb/>nel cap. </s>

<s>IV del suo trattato <emph type="italics"/>De metallis seu fossilibus,<emph.end type="italics"/> proponendosi la que&shy;<lb/>stione <emph type="italics"/>Terra quomodo generetur,<emph.end type="italics"/> risponde sull'autorit&agrave; di Platone ch'&egrave; ge&shy;<lb/>nerata la Terra dalle fumose esalazioni calde e secche, come gli par di po&shy;<lb/>terlo persuadere ai lettori con una cos&igrave; fatta esperienza: &ldquo; Accipiatis terram <lb/>ponetisque eam ipsam in vase aliquo vitreo, quod habeat orificium angu&shy;<lb/>stum, et latum sit in fundo, mediaque sui parte. </s>

<s>Postea ponatis portionem <lb/>terrae in ipso, et operculo superaddito ponatis vas ad ignem, et sinite ut <lb/>calor exagitet terram illam, et videbitis quod ascendet vapor terrestris, et <lb/>post aliquod tempus cernetis concrescere aliquid terraei circa osculum va&shy;<lb/>sis, quod non aliunde oritur quam ex fumoso illo vapore. </s>

<s>&rdquo; Come altrimenti, <lb/>poi soggiunge, s'intenderebbe la generazione dei monti sulla Terra, nati in&shy;<lb/>sieme con lei? (Opera omnia, Francofurti 1584, pag. </s>

<s>327). </s></p><p type="main">

<s>Aristotile, questa volta pi&ugrave; che dal proprio ingegno lasciatosi consigliare <lb/>alle osservazioni dei fatti, ne conclude una dottrina assai pi&ugrave; sana della pla&shy;<lb/>tonica, e della quale solamente oggid&igrave; si comprende la verit&agrave; e l'importanza. </s>

<s><lb/>Il secondo capitolo del I libro Dei meteorologici comincia con queste parole, <lb/>nelle quali il Filosofo raccoglie il frutto delle osservazioni, che si potevano <lb/>fare allora sulla superfice terrestre, comparate con quelle, che si ricavavano <lb/>dalle relazioni degli scrittori pi&ugrave; antichi, o dai naturali rimasti monumenti. <lb/></s>

<s>&ldquo; Non semper autem eadem loca terrae neque aquosa sunt, neque arida, <lb/>sed permutantur secundum fluviorum generationes et defectus. </s>

<s>Quapropter <lb/>et quae sunt circa continentem permutantur, et quae circa mare, et non <lb/>semper haec quidem terra, haec autem mare perseverant omni tempore, sed <lb/>fit mare quidem ubi arida, ubi autem nunc mare hic iterum terra &rdquo; (Ope&shy;<lb/>rum, T. VI cit., fol. </s>

<s>21). </s></p><p type="main">

<s>Veniva da queste dottrine naturale la soluzione del tanto agitato pro&shy;<lb/>blema, e fu il Cesalpino uno de'primi a proporla ai desiderosi, e a divul&shy;<lb/>garla nel suo libro II <emph type="italics"/>De metallicis,<emph.end type="italics"/> dove, trattando delle Conchiglie, delle <lb/>Belenniti e delle Glossopietre, &ldquo; neque mirandum, dice, in mediterraneis et <lb/>montibus altissimis reperiri animalia maritima in lapides conversa: non enim <lb/>absurdum est ubique mare extitisse, imo necessarium, ut tradit Aristotiles &rdquo; <lb/>(pag. </s>

<s>133). </s></p><p type="main">

<s>Deriv&ograve; dalle medesime fonti aristoteliche in sostanza la sua ipotesi an&shy;<lb/>che il Fracastoro, il quale diceva essere i monti un agglomerato di arene <lb/>gettate dalle onde, rimaste in secco ritirandosi il mare. </s>

<s>Il Chiocchi infatti, <lb/>nella citata descrizione del Museo Calzolari, dop'aver detto come, secondo il <lb/>Sarayna, esso Fracastoro credeva che i corpi fossili fossero stati un giorno <lb/>veri viventi, e che le acque marine gli avessero cos&igrave; deposti fra terra, nel <lb/>ridursi ne'loro bacini; &ldquo; sed haec dependere aiebat, poi soggiunge il De&shy;<lb/>scrittore, ex maiori cognitione: Montes onim omnes a mari factos fuisse <lb/>asseverabat, primum iactata arena in cumulos, fuisseque olim mare ubi nunc <pb xlink:href="020/01/1693.jpg" pagenum="568"/>montes extant. </s>

<s>Mox, eodem recedente, detectos fuisse montes et insulas, quod <lb/>et in dies videtur fieri, quando et Aegyptus tota mari olim obruta fuerit, et <lb/>in littoribus etiam Italiae, ut circa Ravennam apparet, ubi longe abest ab <lb/>eo quod olim fuerit passuum centum &rdquo; (pag. </s>

<s>409). </s></p><p type="main">

<s>A queste del Falloppio, del Cesalpino e del Fracastoro si riducevano <lb/>principalmente le ipotesi immaginate, fra la prima met&agrave; del secolo XVI e <lb/>la seconda met&agrave; del secolo appresso, a spiegar l'origine dei continenti, e la <lb/>loro distinzione in monti ed in valli, ma s'aggiungevano a queste stesse, <lb/>derivate da Platone e da Aristotile, altre ipotesi, ora suggerite dalla fanta&shy;<lb/>sia, e ora pi&ugrave; consigliatamente dall'osservazione dei fatti. </s>

<s>Parve a Ferrante <lb/>Imperato che si venisse da tutte queste a proporre altrettante cause con&shy;<lb/>correnti ciascuna, secondo il suo proprio modo di operare, a far mutar fac&shy;<lb/>cia alla terra, ed espresse la sua opinione in un <emph type="italics"/>Discorso sopra le muta&shy;<lb/>zioni dei paesi,<emph.end type="italics"/> che forma il cap. </s>

<s>IV del VII libro della sua Storia naturale. <lb/></s>

<s>&ldquo; E prima, ivi egli dice, della commutazion di terra e mare di molte e molte <lb/>miglia in Paesi petrosi ne abbiamo ampissima testimonianza nella Puglia. </s>

<s>Il <lb/>trasmutarsi il paese piano in montuoso &egrave; cosa che facilmente avviene alle <lb/>piane, che alte sieno, mentre dal corso dei torrenti si fanno profondit&agrave; grandi <lb/>e valli. </s>

<s>L'alzarsi la terra in alto, nel modo che fanno le posteme nel corpo <lb/>degli animali e delle piante, e il dar vegetazione alle pietre, onde possano <lb/>li monti alzarsi, non &egrave; cosa fuori di sperienza e di ragione: manifestamente <lb/>in molte pietre si vede la virt&ugrave; vegetale. </s>

<s>Veggonsi inoltre monti da incendii <lb/>sotterranei avvenuti, come ai nostri tempi nella Campania, nel tenimento di <lb/>Pozzuoli, abbiam visto di un monte fatto dalle ceneri di fuoco sotterraneo &rdquo; <lb/>e soggiunge l'azione dei terremoti, del flusso marino, che solleva le arene <lb/>in monti, come si vede nel Belgio. (Venezia 1672, pag. </s>

<s>175-77). </s></p><p type="main">

<s>Aveva insomma la scienza progredito infino a mezzo il secolo XVII, e <lb/>del problema geologico in discorso eran le soluzioni che se ne sapevano <lb/>dare quelle raccolte e riferite, com'abbiamo udito, da Ferrante Imperato. </s>

<s><lb/>Mancava a quelle dottrine il fondamento delle osservazioni, che si paravan <lb/>cos&igrave; difficili a farsi per la smisurata ampiezza, e per le varie accidentalit&agrave; <lb/>presentate dalla superfice terrestre, l'edifizio della quale trovasi tanto spesso <lb/>circondato o ricoperto da manifeste rovine. </s>

<s>Non aveva nessuno ancora, per <lb/>comprendere in uno sguardo e per comparar fra loro le diverse regioni geo&shy;<lb/>logiche, istituito nessun viaggio, e de'varii fatti, sui quali principalmente si <lb/>fondavano alcune delle ipotesi pi&ugrave; sicure, se ne stavano tutti allora alle no&shy;<lb/>tizie lasciate ne'loro libri dagli scrittori pi&ugrave; antichi. </s></p><p type="main">

<s>Lo Stenone fu il primo a sentire il bisogno di questi scientifici viaggi, <lb/>e a manifestarne in pubblico il desiderio, quando, nel descriver l'anatomia <lb/>del capo della Carcaria, tocc&ograve; la questione delle Glossopietre dell'isola di <lb/>Malta, sopra l'osservazion delle quali avanz&ograve; quelle sei congetture, che con&shy;<lb/>tenevano il fecondo germe di una scienza novella. </s>

<s>Fu una gran ventura che <lb/>fosse cotesto germe deposto in seno all'Accademia del Cimento, la quale, <lb/>educatasi per lungo tempo all'arte dell'esperienze fisiche e delle naturali <pb xlink:href="020/01/1694.jpg" pagenum="569"/>osservazioni intorno a tante cose, che appariscono o che si producono sopra <lb/>la terra; ora stendeva con generoso ardimento il pensiero a far soggetto dei <lb/>suoi nuovi studii la Terra stessa, nelle sue prime origini, e nella sua pre&shy;<lb/>sente struttura. </s>

<s>Cooperava a quell'istituto, nella stessa fiorentina Accademia, <lb/>il Borelli, quando, ad istanza del cardinale Leopoldo, descriveva la <emph type="italics"/>Historia <lb/>et meteorologia incendii aetnaei,<emph.end type="italics"/> e vi cooperava altres&igrave; il Viviani, quando <lb/>dimostrava al Granduca le utilit&agrave; grandi, che verrebbero allo Stato dall'ap&shy;<lb/>plicare quegli stessi studii scientifici all'economia. </s>

<s>Ci permettano perci&ograve; i <lb/>Lettori che poniamo sotto i loro occhi la seguente scrittura, nella quale, <lb/>portando il Viviani l'esempio delle cave del vetriolo, voleva estendere i suoi <lb/>avvedimenti economici a tutti gli altri minerali della Toscana, sulle incerte <lb/>giaciture de'quali sarebbe per venir tanta luce da quella nuova scienza, che <lb/>pur allora in Firenze s'instituiva: </s></p><p type="main">

<s>&ldquo; Il serenissimo Granduca potrebbe, con suo grandissimo utile ed onore, <lb/>benefizio universale di tutto lo Stato, ed impiego di gran quantit&agrave; de'suoi <lb/>sudditi, e con pochissima spesa, rendere lo Stato abbondante d'ogni sorta <lb/>metalli, minerali e mezzi minerali, senz'aver bisogno di cercarli in paesi <lb/>stranieri, con l'estrazione dei denari dello Stato, anzi, con l'estrazione di <lb/>detta roba introdurre il danaro di fuori. </s>

<s>Il modo sarebbe tale: &rdquo; </s></p><p type="main">

<s>&ldquo; Ci sono in molti luoghi dello Stato di S. A. S. miniere d'ogni sorte, <lb/>e miniere abbondanti, quali se ne giacciono neglette ed infruttuose. </s>

<s>Per&ograve; <lb/>potrebbe il serenissimo Granduca eleggere un Sopraintendente generale di <lb/>tutte le miniere dello Stato, ma che fosse persona intelligente in tale affare, <lb/>con assegnarli <emph type="italics"/>cavatto<emph.end type="italics"/> nel negozio, a fine che, volendo utilizzare s&egrave; mede&shy;<lb/>simo, per necessit&agrave;, apporterebbe utile maggiore a Sua Altezza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per rimettere in piedi le fabbriche per ogni sorta miniere, con poca <lb/>spesa ed in breve tempo, si potrebbe fare in questo modo: Si ritrovano due <lb/>miniere di vitriolo, una a Stazzema, che &egrave; la migliore e pi&ugrave; abbondante, <lb/>l'altra alla Striscia. </s>

<s>Basterebbe mettere andanti ed incamminare questi due <lb/>edifizi, che con il solo ritratto di questi, in pochi anni, si pianterebbero le <lb/>fabbriche necessarie per tutte le altre miniere. </s>

<s>Perch&egrave; il vitriolo si potrebbe <lb/>fare di esquisitezza tale, che sarebbe stimato per tutto il mondo migliore di <lb/>ogni altro, e con pochissima spesa, o di gran lunga minore di quella face&shy;<lb/>vano per il passato, quando facevano il vitriolo ordinario, con risparmio di <lb/>legne, di vasi, con pi&ugrave; facilit&agrave;, ed in quella quantit&agrave; che si volesse. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Nello Stato di S. A. S., compresa Lucca, Massa, Carrara e la Luni&shy;<lb/>giana, si esiter&agrave; in circa migliaia 200 di vitriolo l'anno. </s>

<s>Il prezzo corrente <lb/>&egrave; di scudi 30 il migliaio; onde migliaia 200 vitriolo farebbero la somma di <lb/>scudi 600, e questi si guadagnerebbero nello Stato. </s>

<s>Per Francia poi e per <lb/>Alessandria ci sarebbe l'esito di altre tre in quattrocento migliaia. </s>

<s>Ma sup&shy;<lb/>poniamo che fuori si esitasse sol tanto vitriolo, che bastasse per pagare <lb/>tutte le spese, resterebbero in ogni modo li scudi 600 annui netti e liberi <lb/>di spese. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per mettere in piedi gli edifizi detti di vitriolo, con poca spesa si pu&ograve; <pb xlink:href="020/01/1695.jpg" pagenum="570"/>fare, perch&egrave; l'edifizio di Stazzema, qual'&egrave; delli signori Carnesecchi inven&shy;<lb/>tori della miniera, si potrebbe mettere andante con facilit&agrave;, mentre le mu&shy;<lb/>raglie sono ancora in essere, ed in parte coperte; sicch&egrave; basterebbe coprire <lb/>quella parte che manca, fare una caldaia di piombo con il suo fornello, e <lb/>due vasche di legno e una fornace per calcinare la vena, che cos&igrave; l'edifizio <lb/>sarebbe aggiustato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; L'edifizio poi della Striscia si potrebbe rimettere in ordine, mentre <lb/>si lavorasse quello di Stazzema, a causa che il vitriolo della Striscia si cava <lb/>da una terra, quale avanti sia stagionata vuole stare riposata sotto un ca&shy;<lb/>pannone, quasi due anni, ma la vena, che si cava a Stazzema, in pochi giorni <lb/>si calcina, e si pu&ograve; mettere in opera, e la vena &egrave; in tanta copia, che si pu&ograve; <lb/>fare tutta quella quantit&agrave; del vitriolo che si vuole. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Alla Striscia ci &egrave; abbondanza grandissima di legna; a Stazzema an&shy;<lb/>cora ci sono legne forti in quantit&agrave;, che senza pregiudizio delli edifizi del <lb/>ferro, che sono in quel paese, si potrebbero adoperare, stante che le fabbri&shy;<lb/>che del ferro non si possono servire se non di carbon dolce, e per fare il <lb/>vitriolo sono necessarie le legne forti, perch&egrave; le dolci, come faggio e casta&shy;<lb/>gno de'quali si serve la maggioranza, non son buone per fare il vitriolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Li boschi si possono eternare con il modo di tagliarli, onde sarebbe <lb/>necessario che quello, che fosse eletto Sopraintendente generale di tutte le <lb/>miniere, avesse anche la sopraintendenza di tutte le boscaglie appartenenti <lb/>a dette miniere, che con li boschi si manterrebbero, s'aprirebbero molte <lb/>fabbriche di miniere d'ogni sorte, con utile considerabile del serenissimo <lb/>Granduca, benefizio pubblico, comodo del privato, e senza danno di alcuno. </s>

<s>&rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. CXXXVI, c. </s>

<s>89, 90). </s></p><p type="main">

<s>S'accennava di sopra che a riconoscere questi pubblici benefizi e que&shy;<lb/>sti comodi privati, i quali dai pi&ugrave; attivi esercizi della metallurgia sareb&shy;<lb/>bero per provenire alla Toscana, avea dato eccezionale eccitamento la nuova <lb/>scienza, che s'istituiva allora nell'Accademia di lei; scienza, che propone&shy;<lb/>vasi d'investigar la particolare struttura della superficie terrestre, in seno <lb/>alla quale scavando, si trovano qua e l&agrave; dispersi i vari generi di minerali. </s>

<s><lb/>S'accennava inoltre che, fra gli Accademici fiorentini, colui che, presa oc&shy;<lb/>casione dai denti delle Carcarie, riconosciuti fossili nelle glossopietre di Malta, <lb/>dette inizio ai nuovi studii, era stato lo Stenone, a cui perci&ograve; il Granduca <lb/>e il cardinale Leopoldo commisero il primo ufficio di esaminare, e di de&shy;<lb/>scrivere la struttura geologica del suolo toscano. </s></p><p type="main">

<s>Ebbe per prima cosa lo Stenone a notar questo fatto singolare, che <lb/>cio&egrave;, dovunque, apparisce la superficie terrestre composta di strati, gli uni <lb/>soprapposti agli altri, e benissimo discernibili fra loro per una quasi inter&shy;<lb/>ruzione di continuit&agrave;, e talvolta per una diversa struttura, nella quale in <lb/>ogni modo riconoscendo le chiare note di un sedimento, ebbe perci&ograve; a con&shy;<lb/>cluderne, in conferma delle dottrine aristoteliche, tante volte sull'arida essersi <lb/>disteso e poi ritirato il mare, quanti di quegli strati era dato d'annoverare. </s>

<s><lb/>Presa la stratigrafia dunque per principal fondamento alle sue congetture, <pb xlink:href="020/01/1696.jpg" pagenum="571"/>pens&ograve; che ne'primi loro stati naturali ciascuno di quei sedimenti giacesse <lb/>in sito orizzontale, e che il trovarli inclinati, e in altri modi sconvolti, fosse <lb/>per effetto di cause perturbatrici, alle quali attribuiva tutte le ineguaglianze <lb/>e le accidentalit&agrave; di figura, che si osservano qua e l&agrave; sulla faccia della Terra. </s>

<s><lb/>Risaputo, per relazioni avutene dagli amici, tale esser pure la struttura di <lb/>tutte le altre pi&ugrave; lontane regioni terrestri, stabil&igrave; sui sedimenti alluvionali <lb/>una generale scienza geologica, che particolarmente applicata alla Toscana <lb/>dette per conclusione essere il suolo di lei passato per sei distinte vicende: <lb/>due volte fluido, due volte piano e secco, due volte aspro. </s></p><p type="main">

<s>Il soggetto delle nuove scoperte e delle nuove speculazioni voleva avere <lb/>una forma, per presentarsi innanzi all'illustre Accademia, e lo Stenone <lb/>avrebbe desiderato di dargliela italiana, ma intanto che, maturandosi la no&shy;<lb/>tizia delle cose, sarebbe egli di nazione straniera venuto nell'uso della no&shy;<lb/>stra lingua a maggior perfezione, per non indugiar di troppo, distese del <lb/>Trattato un <emph type="italics"/>prodromo<emph.end type="italics"/> in latino col titolo <emph type="italics"/>De solido intra solidum natura&shy;<lb/>liter contento.<emph.end type="italics"/> Ivi cos&igrave; scriveva in principio, rivolgendo il discorso al Gran&shy;<lb/>duca: &ldquo; Et haec quidem italico idiomate extendere coeperam, tum quod tibi <lb/>ita placere intelligerem, tum quo pateret illustri Academiae, quae suorum <lb/>me numero adscripsit, me ut minime dignum tali honore ita maxime avi&shy;<lb/>dum esse testandi conatus, quibus in al&igrave;quam etruscae linguae cognitionem <lb/>pervenire allaboro. </s>

<s>Nec aegre fero impositam mihi necessitatem differendi <lb/>eamdem scriptionem. </s>

<s>Ut enim instans iter mihi promittit cumulatiorem no&shy;<lb/>titiam rerum quaestioni illustrandae inserventium; sic temporis mora feli&shy;<lb/>ciores in linguae studio progressus mihi pollicetur. </s>

<s>&rdquo; Il manoscritto, fatto <lb/>diligentemente copiare, fu consegnato in mano del Viviani, che faceva allora <lb/>da segretario dell'Accademia, e che di proprio pugno scrisse alla copia l'in&shy;<lb/>titolazione, dopo la quale aggiunse: &ldquo; Questo fu stampato sotto la mia cura <lb/>in Firenze nel 1669 &rdquo; (MSS. Cim., T. XXXII, c. </s>

<s>1). </s></p><p type="main">

<s>Il promesso trattato in lingua italiana non ebbe sventuratamente l'ese&shy;<lb/>cuzione, disanimato forse l'Autore dalla poca accoglienza, che si fece a que&shy;<lb/>sto Prodromo. </s>

<s>Vedremo gli esempi e le ragioni di ci&ograve; nel progresso di <lb/>questa storia, ma intanto esaminiamo la nuova scienza geologica, che quasi <lb/>vaticinio incompreso vi s'annunziava. </s></p><p type="main">

<s>Dicemmo che aveva quella nuova scienza per lo Stenone il fondamento <lb/>nella stratigrafia, e perch&egrave; l'ordine de'soprapposti strati alluvionali vede&shy;<lb/>vasi qua e l&agrave; perturbato, per trovare il filo, da non smarrirsi in tanta con&shy;<lb/>fusione, ricorse argutamente l'Autore all'esame delle materie fossili. </s>

<s>Gli <lb/>sugger&igrave; un tale esame alcune note distintive, e gli forn&igrave; gli opportuni ar&shy;<lb/>gomenti per concluder dell'et&agrave; di uno strato, e se concorressero a formarlo, <lb/>insieme con le marine, altre acque di fiume. </s></p><p type="main">

<s>Trovato anche insieme il modo da riconoscer per queste note paleon&shy;<lb/>tologiche che un medesimo strato, deposto originalmente in sito orizzontale, <lb/>qua rimaneva depresso o inclinato, l&agrave; spostato o sconvolto, incominci&ograve; lo <lb/>Stenone a pensare da quali agenti potess'esser naturalmente prodotto un <pb xlink:href="020/01/1697.jpg" pagenum="572"/>tale effetto, n&egrave; seppe riconoscervene altri pi&ugrave; efficacemente operativi del <lb/>fuoco e dell'acqua. </s>

<s>&ldquo; Primus modus est stratorum violenta in altum excus&shy;<lb/>sio, sive eam producat praeceps incendium halituum subterraneorum, sive <lb/>idem efficiat violenta aeris elisio propter ingentes alias in vicinia ruinas.... <lb/>Posterior modus est spontaneus stratorum superiorum delapsus, seu ruina, <lb/>quando, subducta materia inferiori seu fundamento, superiora rimas agere <lb/>coeperint, unde pro cavitatum et rimarum varietate varius diffractorum stra&shy;<lb/>torum situs sequitur, dum quaedam horizonti parallela manent, alia ad il&shy;<lb/>lum perpendicularia fiunt, pleraque obliquos angulos cum ea constituunt, <lb/>nonnulla in arcus inflectuntur, materia eorum tenaci existente &rdquo; (pag. </s>

<s>31, 32). <lb/>Questa sudduzion di materia, per cui, rimasti gli strati orizzontali senza fon&shy;<lb/>damento, rovinano, &egrave;, dice lo Stenone, principalmente operata dall'acque, che <lb/>sciolgono e portan via le materie terrose, ma pu&ograve; talvolta produrla anche <lb/>il fuoco, il quale, liquefacendo le materie solide, le fa scorrere altrove. </s>

<s>Cos&igrave; <lb/>i due potentissimi agenti trasformatori della superfice terrestre, di nature <lb/>discordi e di modi, si riscontrano negli effetti. </s></p><p type="main">

<s>Proposti cos&igrave; fatti principii, si passa dall'Autore a risolvere il problema <lb/>tanto controverso dell'origine de'monti, la quale origine egli naturalmente ri&shy;<lb/>conosce dal mutato ordine degli strati. </s>

<s>&ldquo; Quod mutatus stratorum situs praeci&shy;<lb/>pua montium origo sit inde patet, quod in qualibet congerie montium conspi&shy;<lb/>ciantur: I. </s>

<s>Ingentia plana in quorumdam vertice. </s>

<s>II. </s>

<s>Multa strata horizonti <lb/>parallela. </s>

<s>III. </s>

<s>Ab eorumdem lateribus strata varia varie ad horizontem incli&shy;<lb/>nata. </s>

<s>IV. </s>

<s>In oppositis collium lateribus ruptorum stratorum facies, mate&shy;<lb/>riae et figurae omnimodam convenientiam demonstrantes. </s>

<s>V. </s>

<s>Nud&igrave; stratorum <lb/>limbi. </s>

<s>VI. </s>

<s>Ad radices eiusdem congeriei disruptorum stratorum fragmenta, <lb/>partim in colles congesta, partim per vicinos agros dispersa &rdquo; (pag. </s>

<s>32). </s></p><p type="main">

<s>Quest'aspetto generale, che presentano all'osservatore geologo i monti, <lb/>vien dallo Stenone esemplificato nella Toscana, le sei distinte et&agrave; geologiche <lb/>della quale son per l'Autore stesso illustrate dalle sei seguenti Figure: <lb/>&ldquo; Esibet autem figura XI planum perpendiculare Etruriae, quo tempore <lb/>strata lapidea etiam num integra et horizonti parallela erant. </s>

<s>Figura XII <lb/>ingentes cavitates, sive ignium sive aquarum vi exesas, intactis superioribus <lb/>stratis. </s>

<s>Figura XIII a disruptis stratis superioribus ortos montes et valles. </s>

<s><lb/>Figura XIV a mare facta nova strata in dictis vallibus. </s>

<s>Figura XV ex novis <lb/>stratis consumptam partem inferiorum stratorum, intactis superioribus. </s>

<s>Fi&shy;<lb/>gura XVI, disruptis superioribus stratis arenaceis, productos ibi colles et <lb/>valles &rdquo; (ibi, Explicatio figurarum). <lb/><figure id="id.020.01.1697.1.jpg" xlink:href="020/01/1697/1.jpg"/></s></p><p type="caption">

<s>Figura 11.<pb xlink:href="020/01/1698.jpg" pagenum="573"/><figure id="id.020.01.1698.1.jpg" xlink:href="020/01/1698/1.jpg"/></s></p><p type="caption">

<s>Figura 12.<lb/><figure id="id.020.01.1698.2.jpg" xlink:href="020/01/1698/2.jpg"/></s></p><p type="caption">

<s>Figura 13.<lb/><figure id="id.020.01.1698.3.jpg" xlink:href="020/01/1698/3.jpg"/></s></p><p type="caption">

<s>Figura 14.<lb/><figure id="id.020.01.1698.4.jpg" xlink:href="020/01/1698/4.jpg"/></s></p><p type="caption">

<s>Figura 15.<lb/><figure id="id.020.01.1698.5.jpg" xlink:href="020/01/1698/5.jpg"/></s></p><p type="caption">

<s>Figura 16.</s></p><p type="main">

<s>Ora, quella nuova scienza, che dicevasi instituita dagli Accademici del <lb/>Cimento, si vede per queste immagini rappresentata ai nostri occhi in tutta <lb/>la sua verit&agrave;, e in tutta la sua vita, ma allora, e per lungo tempo di poi, <lb/>parvero quelle sei figure come tanti geroglifici egiziani. </s>

<s>Il Prodromo dello <lb/>Stenone rimase da tutti dimenticato, e di quella illustre Accademia, nella <lb/>quale fu letto, principe il cardinale Leopoldo, fu negata perfin l'esistenza. </s></p><p type="main">

<s>Questo dall'altra parte era un frutto precoce, maturato sopr'un albero <lb/>esotico ne'frequentatissimi orti accademici, all'ombra de'quali mollemente <lb/>seduto insegnava il Cartesio a fabbricar con la fantasia non la Terra sola, <lb/>ma l'Universo. </s>

<s>Tommaso Burnet non ard&igrave; di stendere tanto al largo l'ali <lb/>dell'immaginoso suo ingegno, ma della formazion della Terra in particolare <pb xlink:href="020/01/1699.jpg" pagenum="574"/>si compiacque di aver immaginato un pi&ugrave; bel sistema di quello dell'applau&shy;<lb/>dito Maestro. </s>

<s>Legga, chi vuole in tutta la sua integrit&agrave; veder rappresentarsi <lb/>innanzi la nuova architettura cosmica comparata con la cartesiana, il cap. </s>

<s>IV <lb/>del II libro <emph type="italics"/>Telluris theoria sacra,<emph.end type="italics"/> dove infin dal titolo si promette che sar&agrave; <lb/>dall'Autore notato &ldquo; discrimen hypothesi nostrae ab illa Cartesii, et in ipsius <lb/>defectus animadvertitur &rdquo; (Londini 1681, pag. </s>

<s>181) </s></p><p type="main">

<s>&Egrave; la teoria della terra dall'Autore inglese appellata <emph type="italics"/>sacra,<emph.end type="italics"/> perch&egrave; non <lb/>ha nelle naturali osservazioni il fondamento, ma nella lettura dei Libri santi, <lb/>dai quali apertamente raccogliesi aver nel suo pi&ugrave; interno seno la Terra <lb/>un'immensa accolta di acque, sotto il nome di <emph type="italics"/>abisso,<emph.end type="italics"/> dalle rotte fonti del <lb/>quale si produsse il noetico diluvio. </s>

<s>Or il Burnet, tutto intento a dimostrar <lb/>che cotesto fatto tenuto per miracoloso non era punto fuori degli ordini na&shy;<lb/>turali, immagin&ograve; che l'antidiluviana superfice terrestre fosse solida, polita e <lb/>liscia, girata tutto intorno e sopraincombente all'abisso. </s>

<s>Al sole poi si spacc&ograve; <lb/>cotest'arida crosta, come la belletta delle paludi, e facendo gli ardenti raggi, <lb/>penetrati addentro per le fessure, evaporare il liquido sottoposto, venne tutto <lb/>a ridursi in frantumi, che rimasero cos&igrave; sommersi nell'acque diluviali. </s>

<s>&ldquo; Ex <lb/>altera parte etiam notandum est hanc terram, exteriorem solis ardoribus con&shy;<lb/>tinuo expositam, progressu temporis et saeculorum magis exsiccam aridam&shy;<lb/>que devenisse, et deglutinatis partibus, prae nimia siccitate, et se contrahen&shy;<lb/>tibus in plurimis locis secessisse, unde tandem factum est ex una parte com&shy;<lb/>page telluris hoc modo labefactata, ex altera vaporibus auctis infra terram <lb/>et maiori vi et vehementia se dilatantibus, Tellus decreto tempore et conspi&shy;<lb/>rantibus causis, per quandam speciem terraemotus rupta, dissiluerit, moli&shy;<lb/>bus illis sive fragmentis, in quae distracta erat in subiectam abyssum, vario <lb/>modo et situ delabentibus &rdquo; (ibid., pag. </s>

<s>52). </s></p><p type="main">

<s>Di qui concluse facilmente il Burnet l'origine naturale dei monti, e <lb/>come venisse la Terra a distinguersi in oceani e in continenti, con super&shy;<lb/>ficie aspre da per tutto e ineguali. </s>

<s>&ldquo; Nempe cum fatiscebat et in plura <lb/>fragmenta disrupta in abyssum delapsa est ea compages, uti partes fragmen&shy;<lb/>torum quae aquis quomodocumque eminebant, rationem habuerunt aridae <lb/>atque terrae habitabilis; ita istius aridae partes, quocumque modo eminen&shy;<lb/>tiores caeteris, montium et collium rationem generalem subierunt &rdquo; (ibid., <lb/>pag. </s>

<s>94). Questa &egrave; per&ograve; l'origine dei monti, che si possono secondo il Bur&shy;<lb/>net chiamare primarii: gli altri secondarii crede che sien l'effetto di pi&ugrave; <lb/>minuti stritolamenti prodotti dalle concussioni, nel rovinar gi&ugrave; negli abissi. <lb/></s>

<s>&ldquo; Nempe cum primum inferiores partes fragmenti descendendo contingebant <lb/>fundum abyssi, vel forsan etiam superficiem, ex subita illa motus obstruc&shy;<lb/>tione orta est magna concussio et vibratio per totum fragmentum, atque inde <lb/>denuo dissiliunt et varie disrumpuntur ipsius partes. </s>

<s>Atque ab hac concus&shy;<lb/>sione et secunda disruptione ortas esse existimo innumeras illas inaequali&shy;<lb/>tates superficiei terrarum: colles, declives agros, planities multiformes, val&shy;<lb/>les &rdquo; (ibid., pag. </s>

<s>95). </s></p><p type="main">

<s>Il favorevole incontro, che trovarono cos&igrave; fatte fantasie, comparato col-<pb xlink:href="020/01/1700.jpg" pagenum="575"/>l'abbandono, in che furono lasciate le sapienti dottrine stenoniane, &egrave; cosa <lb/>che fa stupire, ma Bernardino Ramazzini fra'nostri, nel cap. </s>

<s>IV del suo <lb/>trattato <emph type="italics"/>De fontium mutinensium admiranda scaturigine,<emph.end type="italics"/> tutto in pensiero <lb/>di ritrovar l'antica costituzione e la forma del suolo, da cui vedeva scaturir <lb/>quelle sue maravigliose fonti modanesi, dop'aver accennato alle rivoluzioni <lb/>geologiche, le notizie delle quali attingevano gli eruditi dai libri platonici e <lb/>dalle bibliche tradizioni, fa menzione delle teorie del Burnet, e poi cos&igrave; to&shy;<lb/>sto soggiunge: &ldquo; Huiusmodi excogitatum, utut pro novo accipiatur, non no&shy;<lb/>strorum sed antiquiorum temporum constat esse figmentum. </s>

<s>Franciscus Pa&shy;<lb/>tritius, vir eruditione sat clarus, in quodam libello suo <emph type="italics"/>De antiquorum <lb/>rethorica,<emph.end type="italics"/> italico idiomate conscripto, ac Venetiis impresso per Franciscum <lb/>Sanensem anno 1562, dialogo primo, satis lepidam narrationem habet, quam <lb/>refert Julium Strozzam a comite Ballhassare Castilioneo audivisse, illum <lb/>vero a philosopho quodam abyssino in Hispania accepisse &rdquo; (Patavii 1713, <lb/>pag. </s>

<s>59, 60). E seguita il Ramazzini a riassumere in poche parole la storia <lb/>del filosofico romanzo, la quale poi, perch&egrave; crede che debba molto ricreare <lb/>i lettori, trascrive a verbo dall'originale citato dialogo del Patrizio. </s></p><p type="main">

<s>I ciechi ammiratori del Burnet, scoperti essere invece gli ammiratori di <lb/>un Abissino studioso degli antichissimi etiopici annali, rimasero delusi e <lb/>svergognati, e molti fra'nostri e fra gli stranieri si compiacquero, dopo il <lb/>Ramazzini, per attizzar sempre pi&ugrave; il fuoco ai rossori della vergogna, di <lb/>comparare con quello elegantemente riferito dal Patrizio il filosofico romanzo <lb/>burneziano. </s>

<s>Il Vallisnieri, ch'&egrave; uno de'pi&ugrave; zelanti in sostituir le osservazioni <lb/>sensate alle vane speculazioni, scrive di certi che troppo si confidavano di <lb/>cos&igrave; fatte vanit&agrave;, per spiegar le origini e le vicende subite dalla superfice <lb/>terrestre: &ldquo; Cadono in certo modo costoro, senza avvedersene, quasi nel so&shy;<lb/>gno galante o nel romanzo bizzarro (almeno cos&igrave; a me pare) dello stato del <lb/>mondo avanti il diluvio del famoso Burnet, o di quel sapiente Abissino rap&shy;<lb/>portato per dire pi&ugrave; cose belle che vere dal dottissimo Francesco Patrizio <lb/>nel suo dialogo fra Giulio Strozza e il conte Baldassarre da Castiglione. </s>

<s>Si <lb/>contenti di sentirlo, perciocch&egrave; le servir&agrave; almeno di un onesto e gentile di&shy;<lb/>vertimento. </s>

<s>Voleva che la Terra fosse gi&agrave; senza monti, e nel centro tutta <lb/>vota e cavernosa, nella cui superfice fossero scavate spelonche e ripostigli, <lb/>dagli uomini abitati e dagli animali, per gli cui usi erano le acque e l'aria <lb/>sparse per le medesime. </s>

<s>Ma insuperbiti gli uomini e fattisi intollerabili, <lb/>Giove al di sopra co'fulmini e Plutone al di sotto co'terremoti, cominci&ograve; a <lb/>scuotere e crollare orribilmente le sue radici, col quale orrendo fulmina&shy;<lb/>mento e crollamento, aprendo in molti luoghi la Terra e rompendola, ella <lb/>cadde tutta nelle proprie caverne di sotto, e s&egrave; medesima assorse e riemp&igrave;, <lb/>dal che avvenne ch'ella e minor divenne, e si allontan&ograve; dal cielo..... (De <lb/>corpi marini ecc. </s>

<s>cit., pag. </s>

<s>63). </s></p><p type="main">

<s>Essendosi cos&igrave;, dal Vallisnieri e da parecchi altri eloquenti oratori, pro&shy;<lb/>nunziato il giudizio, riconosciuto dai pi&ugrave; savi giustissimo, intorno al sistema <lb/>del Burnet, che veniva a qualificarsi a parole e a dimostrarsi in fatti per <pb xlink:href="020/01/1701.jpg" pagenum="576"/>un romanzo; si potrebbe credere che rinsaviti i cultori della scienza tor&shy;<lb/>nassero indietro a rivolgere almeno sul dimenticato Stenone uno sguardo. </s>

<s><lb/>Ma &egrave; singolare che gl'illusi occhi loro si compiacessero piuttosto in vagheg&shy;<lb/>giare una nuova ipotesi, la quale veniva a infondere una certa apparente <lb/>solidit&agrave; nelle vane fantasie del Burnet, per l'osservazioni di alcuni fatti, al&shy;<lb/>trimenti per&ograve; rappresentati da quel vero esser loro, in che gli avea colti, e <lb/>dichiarati innanzi agli Accademici fiorentini, la sagacia dello stesso Stenone. </s></p><p type="main">

<s>Giovanni Woodward, connazionale al Burnet, pubblicava in Londra <lb/>nel 1695 un libro intitolato <emph type="italics"/>An essay towards the natural history of the <lb/>Earth.<emph.end type="italics"/> Credeva l'Autore di poter dare il titolo di Storia naturale al suo si&shy;<lb/>stema, perch&egrave; muove dall'osservazion degli strati, in che trov&ograve; affaldarsi do&shy;<lb/>vunque la superfice terrestre. </s>

<s>Ma poi, ripensando a ci&ograve; che potesse esser <lb/>causa di cotesta singolare stratificazione, non gli occorse nulla di meglio alla <lb/>fantasia dell'universale Diluvio, il quale, erompendo dagli abissi, disciolse le <lb/>materie terree, e poi le depose a quel modo che l'escavazioni oggid&igrave; ce lo <lb/>fanno vedere. </s>

<s>A chi gli opponeva come potessero le acque avere una tale <lb/>virt&ugrave; solvente, anche delle materie lapidefatte o metalliche, rispondeva che <lb/>per divino decreto fu sospesa la legge della coesione molecolare, e soggiun&shy;<lb/>geva essere pure in quel breve tempo sospesa la legge di gravit&agrave; a chi do&shy;<lb/>mandava come mai sostanze, di tanto pi&ugrave; gran peso specifico dell'acqua, <lb/>potessero esser cos&igrave; venute a sollevarsi in alto dai loro bassi fondi marini. </s></p><p type="main">

<s>Ma come si conciliavano le storie naturali con questi fatti miracolosi? </s>

<s><lb/>Quale scientifica dimostrazione si dava dell'esistenza dell'abisso a coloro, i <lb/>quali sapevano che ai tempi biblici si credeva esser la Terra una falda, o <lb/>una piana isola galleggiante sul mare, e che l'idea delle sotterranee acque <lb/>diluviali erompenti era nata dal fatto di quelle scavate fontane, simili ai no&shy;<lb/>stri pozzi cos&igrave; detti artesiani? </s>

<s>Era facile a riconoscer, dietro queste consi&shy;<lb/>derazioni, come il sistema del Woodward non avea veramente nulla, che gli <lb/>meritasse il titolo di Storia naturale, e nonostante quelle cos&igrave; leggere osser&shy;<lb/>vazioni stratigrafiche e paleontologiche, credute nuove, riuscirono cos&igrave; se&shy;<lb/>ducenti, da rendere accettevole in parte le nuove fantasie, e da indurre gli <lb/>stessi pi&ugrave; severi ingegni a perdonare all'immaginoso Inglese i manifesti pa&shy;<lb/>ralogismi. </s>

<s>Anche fra'nostri Italiani Jano Planco per esempio si professa se&shy;<lb/>guace di lui, e lo stesso Vallisnieri, bench&egrave; ne repudi risolutamente la vana <lb/>speculazione, e nelle sensate osservazioni riconosca l'imperfezione e l'errore, <lb/>incerto in che modo risolvere il gran problema geologico, cos&igrave; desiderosa&shy;<lb/>mente allora dalla scienza richiesto, non vede, in mezzo a tante tenebre, <lb/>venir altra, bench&egrave; languida luce, che dalle pagine wowardiane. </s>

<s>Non par che <lb/>nemmen egli si accorga esser cotesta luce un incerto riflesso della splendida <lb/>face accesa nel Prodromo dello Stenone, in cui &egrave; la stratigrafia rappresen&shy;<lb/>tata nel suo esser vero, e non come l'effetto di un unico Diluvio, secondo <lb/>quel che diceva il Woodward in manifesta contradizione coi fatti nataturali; <lb/>ma come il deposto da successive alluvioni, che fecero pi&ugrave; volte mutar fac&shy;<lb/>cia alla Terra. </s></p><pb xlink:href="020/01/1702.jpg" pagenum="577"/><p type="main">

<s>L'unico merito dunque, ch'ebbe il libro del Woodward, fu quello di <lb/>rendere accettabile ai negligenti delle scientifiche tradizioni o ai ritrosi quella <lb/>parte di scienza stenoniana, che riconosceva per uno de'massimi efficienti <lb/>geologici le acque diluviali, d'onde venne a costituirsi al regno mineralo&shy;<lb/>gico la sua prima e principale nettunica sede. </s>

<s>Ora &egrave; a narrar da chi, e in <lb/>che modo si mettesse in evidenza sperimentale la seconda parte di quella <lb/>medesima scienza stenoniana, che l'altro massimo efficiente geologico rico&shy;<lb/>nobbe nel fuoco, e come d'ambedue le parti, riunite da'moderni insieme e <lb/>coltivate con assiduo studio amoroso, venisse ad erigersi in mezzo alla Sto&shy;<lb/>ria naturale quel nuovo maraviglioso edifizio, sulle pareti del quale e nel&shy;<lb/>l'interno, come in bene appropriati loculi, depose la Natura stessa di sua <lb/>propria mano le varie specie dei minerali. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Giova, nell'introdursi a trattare questa seconda importantissima parte <lb/>della presente storia, far pi&ugrave; diligente attenzione a quella particolare effi&shy;<lb/>cienza, che s'attribuisce al fuoco nella Geologia stenoniana. </s>

<s>Nella descrizione <lb/>anatomica del capo della Carcaria era gi&agrave; l'Autore ricorso col pensiero a <lb/>quell'isole, che raccontavano gli Storici essersi vedute emergere dal mare, <lb/>per impeto di sotterranei incendi, perch&egrave;, applicando una simile origine plu&shy;<lb/>tonica a Malta, venisse ad aversi qualche buona ragion naturale dell'esi&shy;<lb/>stenza dei tanti avanzi marini, che si trovan dispersi qua e l&agrave; sull'arida su&shy;<lb/>perfice di lei &ldquo; Si credimus historiis e medio mari novae subsiluere insulae, <lb/>et quis Melitae prima incunabula novit? </s>

<s>Forsan mari olim supposita ea terra <lb/>canum marinorum latibulum fuit, quorum dentes, coenoso fundo olim inse&shy;<lb/>pulti, mutato fundi situ per subterraneorum halituum praeceps incendium, <lb/>modo in media insula reperiuntur &rdquo; (pag. </s>

<s>109, 10). </s></p><p type="main">

<s>Vedemmo gi&agrave; come nel <emph type="italics"/>Prodromo<emph.end type="italics"/> s'attribuisse la rottura degli strati <lb/>lapidei a due forze: una naturale o di gravit&agrave;, e l'altra violenta, consi&shy;<lb/>stente nelle scosse prodotte dai fuochi sotterranei, per cui vennero a solle&shy;<lb/>varsi in alto gli stessi strati scommossi. </s>

<s>Di que'fuochi, soggiunge poi lo <lb/>Stenone, se ne vedono presso i monti sassosi gl'indizi manifesti. </s>

<s>&ldquo; Vel in <lb/>ipsis montibus saxeis, vel in eorumdem vicinia evidentissima ignis subter&shy;<lb/>ranei indicia reperiuntur &rdquo; (pag. </s>

<s>33). N&egrave; per la sola spinta di basso in alto <lb/>concorrono potentemente cotesti fuochi a sollevar la terra sulle alture dei <lb/>monti, ma anche altrimenti, accumulandone talvolta le materie per egestione. <lb/></s>

<s>&ldquo; Possunt et aliter montes produci ut egestione ignium, cineres et saxa cum <lb/>sulphure atque bitumine eructantium, nec non pluviarum et torrentium im&shy;<lb/>petu, quo strata saxea, caloris et frigoris vicissitudinibus, iam tum fixa in <lb/>praeceps devolvuntur; strata vero terrea, magnis ardoribus, rimas agentia <lb/>in varias partes resolvuntur. </s>

<s>Unde patet duo esse summa genera montium <pb xlink:href="020/01/1703.jpg" pagenum="578"/>colliumque; primum eorum quod e stratis componitur, quorum binae spe&shy;<lb/>cies sunt, dum in quibusdam strata saxea, in aliis terrea strata abundant; <lb/>alterum genus eorum est, qui ex stratorum fragmentis et abrasis partibus <lb/>confuse et nullo ordine exsurgunt &rdquo; (ibid.). </s></p><p type="main">

<s>Bench&egrave; la teoria plutonica de'sollevamenti sia cos&igrave; dallo Stenone chia&shy;<lb/>ramente espressa, nonostante, in quel descriver ch'ei fa, per una pratica <lb/>applicazione de'pi&ugrave; generali principii, la carta geologica della Toscana, tra&shy;<lb/>scura affatto le forze endogene, per attribuire alla sola forza di gravit&agrave; la <lb/>rottura degli strati lapidescenti e terrosi, sotto i quali <emph type="italics"/>ingentes cavitates <lb/>formatae erant.<emph.end type="italics"/> Di queste cavit&agrave;, sebben sieno talvolta gli efficienti i sot&shy;<lb/>terranei fuochi liquefattori, per lo pi&ugrave; lo Stenone ne attribuisce l'opera al&shy;<lb/>l'azione dissolutiva delle acque, cosicch&egrave;, nella nuova istituzione geologica <lb/>del nostro Accademico del Cimento, il Nettunismo pareva avere una preva&shy;<lb/>lenza. </s>

<s>N&egrave; &egrave; a fare di ci&ograve; le maraviglie, perch&egrave;, quanto evidenti nell'esser <lb/>loro e nel prepotente modo di operare gli si mostravano le acque superfi&shy;<lb/>ciali, altrettanto incerta apparivagli l'esistenza di quel fuoco centrale, di cui <lb/>da sole le relazioni di alcuni fatti storici era dato di argomentare gli effetti. </s>

<s><lb/>Simone Maioli, ne'suoi <emph type="italics"/>Dies caniculares<emph.end type="italics"/> pubblicati in Roma nel 1597, ri&shy;<lb/>serb&ograve; il colloquio XVI a trattare dei monti, e ne descrive verso la fine al&shy;<lb/>cuni, nati per forza d'ignee sotterranee esplosioni e di terremoti, secondo <lb/>che gli descrivon nelle loro storie Teofrasto, Tacito, Plinio e altri antichi <lb/>scrittori. </s>

<s>Ma voleva lo Stenone fondar la sua scienza sulle naturali osserva&shy;<lb/>zioni de'fatti, e non sull'autorit&agrave; degli uomini, e perci&ograve; s'indusse con gran <lb/>riserbo, e come per semplice congettura, ad ammettere il sollevamento del&shy;<lb/>l'isola di Malta, per impulso di sotterraneo incendio su dalle acque del mare. </s></p><p type="main">

<s>Erano dall'altra parte tuttavia vive in Toscana alcune tradizioni, rima&shy;<lb/>ste in non troppo onorata fama appresso i fervorosi innovatori delle scienze <lb/>sperimentali, perch&egrave; quel Ferdinando granduca, a cui ora lo Stenone inti&shy;<lb/>tola il suo Prodromo, era quello stesso, a cui ventott'anni prima Giovanni <lb/>Nardi aveva dedicata la sua fisica Prolusione <emph type="italics"/>De igne subterraneo.<emph.end type="italics"/> E perch&egrave; <lb/>la ipotesi di lui, dopo un secolo preciso rinnovellata da un altro Italiano, &egrave; <lb/>da tutti oramai risonosciuta meritevole di onoranze nelle pagine della Sto&shy;<lb/>ria, non rincresca ai Lettori di trattenersi qui brevemente con noi a esami&shy;<lb/>nare le principali idee espresse intorno a cos&igrave; nuovo, e tanto lubrico sog&shy;<lb/>getto, dal Fisico fiorentino. </s></p><p type="main">

<s>Incomincia l'Autore a dimostrar la sua tesi dai fatti, o com'egli si <lb/>esprime, dagli esperimenti: &ldquo; Dari ignem subterraneum experimentis con&shy;<lb/>firmatur &rdquo; (Florentiae 1641, pag. </s>

<s>2), e si riducon questi esperimenti a no&shy;<lb/>tare che non ci &egrave; regione continentale o insulare sulla superfice terrestre, <lb/>in cui non si veggano incendi attuali, o non si trovino scritte memorie, o <lb/>non si osservino manifesti indizi d'incendi passati. </s>

<s>Cita di queste scritte me&shy;<lb/>morie storiche gli Autori, ai quali aggiunge il suffragio de'sacri testi, dei <lb/>Mitologi e dei Poeti. </s>

<s>Passando quindi a farla da fisico, investiga di que'fuo&shy;<lb/>chi sotterranei l'indole e la natura, ch'ei riconosce non punto dissimile dal <pb xlink:href="020/01/1704.jpg" pagenum="579"/>fuoco elementare, e a cui egli assegna per sua natural sede le cavernosit&agrave; <lb/>della terra, delle quali si trattiene a dimostrar l'esistenza. </s></p><p type="main">

<s>Erano per&ograve; cos&igrave; fatte opinioni tutte di secondaria importanza, rispetto <lb/>a un'altra, la soluzion della quale massimamente si desiderava, e ch'era <lb/>intorno a riconoscer la causa efficiente e l'origine di ci&ograve; che, per i monti <lb/>ignivomi e per altre scaturigini di fuoco, si teneva per manifesto. </s>

<s>E qui il <lb/>Nardi, prima di profferir l'opinione sua propria, si trattiene a confutar quella <lb/>di coloro, i quali alla compressione degli spiriti aerei e delle acque discor&shy;<lb/>renti per le segrete viscere della terra attribuivan la causa degli incendi in <lb/>essa latenti. </s>

<s>Credeva di aver tanto da dimostrare la falsit&agrave; di una tale ipo&shy;<lb/>tesi, per l'esempio delle trombe idrauliche e degli schioppi pneumatici, nei <lb/>quali due strumenti, alla forte pressione prodotta nel cacciar dell'embolo, <lb/>n&egrave; l'acqua per&ograve; n&egrave; l'aria concepiscono aumento di calore. </s>

<s>&ldquo; Non minus <lb/>falsum praeterea, est quod illa maris vel spiritus <emph type="italics"/>arctatio<emph.end type="italics"/> ignem generet, <lb/>contrarium nam experimur in hydraulicis, nec non in bellicis tormentis, <lb/>flatu solo artificiose compresso pyrii pulveris vicem supplente, quae neque <lb/>ignem, neque calorem inde concipiunt &rdquo; (ibid., pag. </s>

<s>26). </s></p><p type="main">

<s>Se gli avesse alcuno mostrata sotto gli occhi l'esperienza del fuoco, <lb/>che di fatto s'apprende all'esca, per la forte compressione dell'aria, nel cos&igrave; <lb/>detto <emph type="italics"/>Acciarino pneumatico,<emph.end type="italics"/> forse il Nardi sarebbesi ricreduto, ed egli pe&shy;<lb/>ripatetico scomunicato avrebbe dato l'esempio a tanti ortodossi pi&ugrave; recenti, <lb/>i quali, non avendo saputo riconoscer la naturale origine del calor centrale <lb/>nella compressione della materia attrattavi d'ogni parte, andarono a fanta&shy;<lb/>sticar che la Terra fosse un giorno un tizzone acceso, spentosi alla super&shy;<lb/>fice a poco a poco. </s>

<s>&Egrave; da scusarsi dunque esso Nardi se al vero naturale <lb/>intraveduto dagli altri sostitu&igrave; quella sua fantastica opinione, invocatrice della <lb/>superna benefica mano dell'Onnipotente, la quale, affinch&egrave; non ne avesse <lb/>il mondo a ricevere nocumento, releg&ograve; come in una carcere il fuoco giu <lb/>nelle tartaree caverne. </s></p><p type="main">

<s>Il difetto, che contenevano in s&egrave; tanto l'ipotesi del Peripatetico antico, <lb/>quanto quelle de'Novatori moderni, dava luogo a promovere un'altra que&shy;<lb/>stione intorno al mantenersi i sotterranei fuochi perenni. </s>

<s>Chi riconosce la <lb/>vera causa di loro nel premersi, che necessariamente fa la materia in con&shy;<lb/>seguenza dell'attrazion centrale, d&agrave; la nuova questione implicitamente per <lb/>gi&agrave; risoluta, essendo chiaro dover quegli stessi sotterranei incendi durare <lb/>quanto durer&agrave; la presente costituzion della Terra. </s>

<s>Tutte le Geogonie per&ograve;, <lb/>che professan l'ipotesi di un primitivo globo infocato, son per rispondere <lb/>al quesito costrette di ricorrere alle coibenze degli strati superficiali. </s>

<s>Ma que&shy;<lb/>sta risposta, se non c'inganniamo, sembra a noi non punto meno meschina <lb/>di quella data dal Nardi, il quale, ricercando ai tartarei fuochi il pascolo che <lb/>gli mantenga, come il combustibile mantiene gli altri fuochi elementari, si <lb/>lusing&ograve; di averlo trovato in quel che, secondo l'espressione biblica, &egrave; detto <lb/><emph type="italics"/>pinguedine della terra.<emph.end type="italics"/></s></p><p type="main">

<s>Credeva questa stessa pinguedine il Nardi sufficiente a produrre per s&egrave; <pb xlink:href="020/01/1705.jpg" pagenum="580"/>sola l'effetto desiderato, anche senza ricorrere, com'altri facevano, alle pin&shy;<lb/>guedini dell'acqua, ossia ai bitumi, e ci&ograve; argomentava dall'osservar che tal&shy;<lb/>volta son pi&ugrave; attivi di quegli a mare i vulcani fra terra. </s>

<s>Non vo'nonostante <lb/>negar, poi soggiunge, &ldquo; et mari inesse pinguedinem, et uberem hinc quan&shy;<lb/>doque accessisse fomitem flagrantibus ignibus, verum neque individua fuit <lb/>illa comes fidaque sodalis. </s>

<s>Nam et Vesevi atque Aetnae fatiscunt quando&shy;<lb/>que incendia, adeo ut impune licuerit curiosis vel craterum intima scrutari <lb/>viscera. </s>

<s>Quod si mons uterque maris vicinia nunquam destituitur, neque <lb/>tamen perpetuo flagrat, quas ministrabit opes maris pinguedo distantissimis <lb/>ignibus? </s>

<s>&rdquo; (ibid, pag. </s>

<s>49). </s></p><p type="main">

<s>I moderni Geologi che, dall'avere osservato essere i vulcani attivi per <lb/>lo pi&ugrave; disposti lungo i lidi marini, attribuirono all'acque per sotterranee vie <lb/>comunicanti col mare un'azione simile a quella non in tutto osata negare <lb/>dal Nardi: per questa e per altre non poche verit&agrave; che vi si trovano adom&shy;<lb/>brate, e quali fecondabili germi disperse, tengono la fisica prolusione <emph type="italics"/>De <lb/>igne subterraneo,<emph.end type="italics"/> come una prima e antica reliqua della loro scienza, in <lb/>onore. </s>

<s>Ma i contemporanei e i successivi seguaci degl'istituti sperimentali <lb/>derisero da principio, e poi facilmente dimenticarono, quasi fossero tutte <lb/>allo stesso modo eterodosse, le dottrine di chi chiamava il moto della terra <lb/><emph type="italics"/>damnata impostura<emph.end type="italics"/> (pag. </s>

<s>68) e diceva i vitrei organi applicati ad uso di <lb/>termometro <emph type="italics"/>malo omine a Sanctorio Sanctorio olim fabrefacta<emph.end type="italics"/> (pag. </s>

<s>62). </s></p><p type="main">

<s>&Egrave; notabilissimo nonostante che, facendosi Galileo ammiratore delle nuove <lb/>speculazioni del Nardi, ne raccomandasse ai discepoli e agli amici, fra'quali <lb/>Francesco Rinuccini, la lettura, specialmente dei <emph type="italics"/>problemata centum<emph.end type="italics"/> inve&shy;<lb/>stigati nel cap. </s>

<s>L dal proprio ingegno dell'Autore, e gli promette che &ldquo; in <lb/>una lettura di poco pi&ugrave; di un'ora vedr&agrave; la soluzione di tanti ammirabili ef&shy;<lb/>fetti della Natura, che un solo mi ha messo in disperazione d'intenderlo, <lb/>con la contemplazione del tempo di tutta mia vita &rdquo; (Alb. </s>

<s>VII, 363). Tanto <lb/>sono anzi in Galileo notabili queste espressioni, che le hanno alcuni credute <lb/>un'ironia. </s>

<s>Ma che sieno invece la significazione di un sentimento vero vien <lb/>confermato dal vedere esso Galileo esprimersi al medesimo modo con altri <lb/>amici e scolari suoi, raccomandando a loro la rara eccellenza del libro del <lb/>Nardi, ond'&egrave; che Fulgenzio Micanzio rispondeva, dietro queste raccomanda&shy;<lb/>zioni: &ldquo; Cosa commendata da V. S. non pu&ograve; essere che rara ed eccellente, <lb/>onde ne ho curiosit&agrave; suprema &rdquo; (Campori, Carteggio galil., Modena 1881, <lb/>pag. </s>

<s>574) </s></p><p type="main">

<s>Con la medesima sincerit&agrave; e persuasione aveva pure Galileo raccoman&shy;<lb/>dato il libro <emph type="italics"/>De igne subterraneo<emph.end type="italics"/> a Vincenzio Renieri, il quale per&ograve;, giu&shy;<lb/>dicandone in modo tutto diverso, rimproverava dolcemente il Maestro di <lb/>avergli fatto perdere il tempo a rileggere i cento problemi &ldquo; ne'quali, cos&igrave; <lb/>esprimesi in una lettera indirizzata allo stesso Galileo da Pisa, per la de&shy;<lb/>bolezza del mio ingegno non ho saputo trovare quelle maraviglie, che ella <lb/>mi accenna. </s>

<s>Pu&ograve; essere che ci&ograve; derivi dall'avermi io gi&agrave; presupposto che <lb/>il credere la Terra essere piena di fuoco sia un paradosso, e che per&ograve; io <pb xlink:href="020/01/1706.jpg" pagenum="581"/>non arrivi alle altre belle sottigliezze ne'problemi racchiuse. </s>

<s>Ma io sono di <lb/>un ingegno cos&igrave; tardo, che stimo non essere differenza tra chi per vedere <lb/>quaranta o cinquanta monti gettar fiamme crede esserne piena tutta la Terra, <lb/>e tra chi, per veder fumare cinque o sei cammini di Pisa, credesse che le <lb/>case di dentro abbruciassero tutte &rdquo; (Alb. </s>

<s>X, 410). </s></p><p type="main">

<s>Se fossero tali difficolt&agrave; del Renieri giunte alle orecchie dello Stenone, <lb/>non sarebbero forse state quelle, che lo fecero andare in ammetter l'esi&shy;<lb/>stenza del fuoco sotterraneo cos&igrave; cauto, essendo, come la sent&igrave; molto giudi&shy;<lb/>ziosamente Galileo, non improbabile congettura di un incendio interno alla <lb/>terra il vederlo per tante bocche vomitato al di fuori. </s>

<s>Non era dunque il <lb/>fatto in s&egrave;, che teneva la mente dell'Autor del Prodromo agitata dal dub&shy;<lb/>bio: erano i modi e le ragioni del fatto, intorno a che sentiva, o avrebbe <lb/>potuto sentire la debolezza degli argomenti addotti dal peripatetico Nardi, <lb/>seppure, negli ultimi tempi dell'Accademia del Cimento, non era la Fisica <lb/>prolusione di lui gi&agrave; defunta, e nella granducale biblioteca sepolta. </s></p><p type="main">

<s>Da che pu&ograve; avere origine quel calore si intenso, che liquef&agrave; le lapidee <lb/>materie e sublima gli stessi metalli? </s>

<s>Qual'&egrave; quel pascolo, che nelle riposte <lb/>viscere della Terra lo rende perenne? </s>

<s>Opera egli in aprirsi al di fuori le <lb/>vie, e in ridurre gli strati alluvionali in frantumi immediatamente per la sua <lb/>propria virt&ugrave; dilatatrice, o mediatamente per l'aria, o per vapore che tona <lb/>orribilmente ed esplode? </s>

<s>Eran tutti questi problemi, che si proponevano <lb/>alla mente dello Stenone, e giacch&egrave; le vie sperimentali da risolverli erano <lb/>chiuse, non rimaneva a far altro che attenersi giudizionsamente alle conget&shy;<lb/>ture, il momento delle quali nel presente proposito sent&igrave; pi&ugrave; debole che in <lb/>altre sue geologiche speculazioni. </s>

<s>Ma il Plutonismo in ogni modo &egrave; per il <lb/>nostro Accademico fiorentino la seconda attivissima efficienza delle trasfor&shy;<lb/>mazioni superficiali del Globo; efficienza sopra la predicata verit&agrave; della quale <lb/>ci bisognarono ancora settant'anni, prima che uscisse fuori qualcuno a ri&shy;<lb/>volgervi l'attenzione. </s></p><p type="main">

<s>Vedemmo come in questo lasso di tempo, dannosamente neglette le <lb/>teorie stenoniane, non rimanesse altro vestigio di scienza, che nel libro del <lb/>Woodward, qualche languido riflesso del quale eccitava pi&ugrave; vivo il deside&shy;<lb/>rio di scoprir comecchessia la luce del vero. </s>

<s>Grandissime difficolt&agrave; per&ograve; si <lb/>presentavano a tutti coloro, che volevano non fabbricar romanzi ma istituire <lb/>una scienza nuova, nella quale dall'altra parte si salvassero le bibliche tra&shy;<lb/>dizioni di un unico diluvio di quaranta giorni: per cui anzi le difficolt&agrave; ri&shy;<lb/>ducendo nell'impossibilit&agrave; di giungere all'intento desiderato, i pi&ugrave; savi si <lb/>attennero al partito di preparar le fondamenta e il materiale, intanto che, <lb/>col progredir degli studi, sarebbe venuto il tempo di fabbricar l'edifizio. </s></p><p type="main">

<s>Due illustri uomini abbiamo da annoverar fra costoro in Italia: Luigi <lb/>Ferdinando Marsili e Anton Maria Vallisnieri. </s>

<s>Il primo, uomo di armi, si <lb/>tratteneva nelle militari escursioni ad osservare ci&ograve; che di pi&ugrave; notabile gli <lb/>presentasse, in distanti regioni, la superfice terrestre, con intenzione d'in&shy;<lb/>vestigarne l'<emph type="italics"/>organica struttura.<emph.end type="italics"/> Si proponeva poi di raccogliore il frutto di <pb xlink:href="020/01/1707.jpg" pagenum="582"/>tali investigazioni in un trattato &ldquo; in cui spero, cos&igrave; egli stesso si esprime, <lb/>di non avanzar cosa non fondata sul fatto, senza lasciarmi trasportare dal <lb/>genio o dal capriccio di vane ipotesi, contento di riferire il veduto, perch&egrave; <lb/>altri, dediti e avvezzi a queste precise determinazioni, vi lavorino sopra e vi <lb/>fabbrichino a loro talento &rdquo; (Lettera in appendice al tratt. </s>

<s>del Vallisnieri <lb/><emph type="italics"/>De'corpi marini ecc.,<emph.end type="italics"/> ediz. </s>

<s>cit., pag. </s>

<s>144). </s></p><p type="main">

<s>Di questa struttura organica della Terra, che voleva ridurre il Marsili <lb/>a trattazione compiuta, avea gi&agrave; ricavato uno splendido saggio da quella co&shy;<lb/>stante disposizione di strati sopra strati, in che trov&ograve; che da per tutto si <lb/>ammassicciano i monti. </s>

<s>Era stato per&ograve; in queste stratigrafiche osservazioni, <lb/>lasciamo andar lo Stenone, prevenuto dal Woodward, e v'attendevano con&shy;<lb/>temporaneamente Giovanni Scheuchzer e il Vallisnieri. </s>

<s>Ma seppe bene aprirsi <lb/>il Marsili, attiguo a questo, un altro campo che tutti, sbigottiti dalle diffi&shy;<lb/>colt&agrave; e giudicandolo una temeraria audacia dell'ingegno, lasciarono inesplo&shy;<lb/>rato. </s>

<s>Il Boyle, &egrave; vero, avea scritta e pubblicata una dissertazione <emph type="italics"/>De fundo <lb/>maris,<emph.end type="italics"/> ma non erano in essa altro che i primi tentativi, somiglianti a quelli <lb/>di un notatore inesperto, che non sa perdere di vista la linea fiduciosa <lb/>del lido. </s></p><p type="main">

<s>Il nostro Bolognese dunque fu il primo, che os&ograve; esplorare la struttura <lb/>geologica dell'ampio e velato seno del mare, incitato dal desiderio di verifi&shy;<lb/>care una sua congettura, se cio&egrave; fossero anche que'bassi fondi, come le al&shy;<lb/>ture montane, costruiti di strati sopra strati. </s>

<s>Ebbe di qui origine l'<emph type="italics"/>Histoire <lb/>physique de la mer,<emph.end type="italics"/> della quale opera, intanto che per mancanza di osser&shy;<lb/>vazioni indugiavasi la pubblicazione, eseguita poi in Amsterdam nel 1725; <lb/>fece l'Autore stesso nella patria lingua un <emph type="italics"/>Ristretto,<emph.end type="italics"/> in forma di lettera in&shy;<lb/>dirizzata a Cristino Martinelli. </s>

<s>In essa, accennando in principio a'suoi nuovi <lb/>intrapresi tentativi, cos&igrave; si esprimeva: &ldquo; Il motivo, che stimolommi a tali <lb/>tentativi, fu quello di volere indagare dentro la struttura dell'alveo marit&shy;<lb/>timo se vi fosse un'organica disposizione corrispondente a quella da me ri&shy;<lb/>trovata nella parte consistente sassosa, per cui formasi il continente della <lb/>Terra, giacch&egrave;, avendo io avuto ne'tanti miei viaggi ed impieghi il comodo <lb/>di poter misurare, e per cos&igrave; dire anatomizzare in buon numero le parti <lb/>della medesima, formai non cos&igrave; piccola idea di voler dimostrare l'organica <lb/>struttura di questo globo terrestre, mediante una serie assai numerosa di <lb/>osservazioni, massimamente nella parte montuosa che, nel suo corso inter&shy;<lb/>rotto entro lo spazio d'Europa, ho in gran parte ocularmente osservato &rdquo; <lb/>(Venezia 1711, pag. </s>

<s>2, 3). </s></p><p type="main">

<s>Delle cinque parti in fatti, in ch'&egrave; distinto questo <emph type="italics"/>Saggio fisico della <lb/>storia naturale del mare,<emph.end type="italics"/> riserbandosi la prima a descriver la natura del <lb/>fondo, dice l'Autore d'aver verificato in essa la struttura che sospettava, <lb/>cio&egrave; &ldquo; di strati sopra strati, corrispondenti a quei che ho gi&agrave; riscontrati nei <lb/>monti dei continenti, ed una tale corrispondenza giovami assai per avanzare <lb/>con pi&ugrave; fondamento il mio sistema circa la dimostrazione dell'organica strut&shy;<lb/>tura del globo terreno &rdquo; (ivi, pag. </s>

<s>23). Anche nell'esteriore aspetto, e nel-<pb xlink:href="020/01/1708.jpg" pagenum="583"/>l'andamento, si rassomigliano, prosegue a dire il Marsili, coi continenti i <lb/>bassi fondi marini, che pur &ldquo; variano or piani, ora inarcati, ora irregolari, <lb/>ora con alvei, che conducono dal continente fiumi perenni sotterranei d'acque <lb/>dolci, ora con monti isolati, che rimangono alcune volte coperti da diverse <lb/>altezze d'acque, ed altre volte spuntano appena fuori della medesima, oppure <lb/>s'inalzano formando isole visibili &rdquo; (ivi, pag. </s>

<s>24). </s></p><p type="main">

<s>Il sistema per&ograve; <emph type="italics"/>circa la dimostrazione dell'organica struttura del globo <lb/>terreno,<emph.end type="italics"/> a stabilire il quale dovevano, come di sopra udimmo, servir questi <lb/>studi intorno alla struttura geologica de'bassi fondi marini, non fu dal Mar&shy;<lb/>sili, che si sappia, condotto alla sua perfezione. </s>

<s>Ci&ograve; forse avvenne perch&egrave;, <lb/>nel 1726, il Vallisnieri pubblicando la sua lezione accademica <emph type="italics"/>Dell'origine <lb/>delle fonti,<emph.end type="italics"/> l'avea corredata di dottissime annotazioni, per giunta alle quali <lb/>descrisse la nuova scoperta, ch'egli e lo Scheuchzer avevano fatta, di quella <lb/>ch'eran soliti chiamare <emph type="italics"/>anatomica composizione dei monti e delle valli.<emph.end type="italics"/><lb/>&ldquo; Quantunque i moderni naturali Filosofi, scrive esso Vallisnieri in princi&shy;<lb/>pio della detta <emph type="italics"/>Giunta,<emph.end type="italics"/> facilmente intender possano ci&ograve; che, intorno la strut&shy;<lb/>tura nuovamente scoperta de'monti, tutti a strati sopra strati mirabilmente <lb/>composti, mi sono preso la briga di raccontare; nulladimeno per rendere pi&ugrave; <lb/>agevole l'intendimento, anche a quelli che non gli hanno osservati .... ho <lb/>determinato di porre le figure di molti tolte dal naturale, giacch&egrave; mi si pre&shy;<lb/>senta la sorte di averle elegantissime dal signor Giovanni Scheuchzero, <lb/>grande istorico della Natura, delle quali ora, in passando per Padova, con <lb/>un discorso <emph type="italics"/>Dell'origine dei monti<emph.end type="italics"/> me ne fa un pregiatissimo dono &rdquo; (Ve&shy;<lb/>nezia 1726, pag. </s>

<s>100). </s></p><p type="main">

<s>Le figure orografiche sono in una medesima tavola rappresentate in sei <lb/>distinti quadretti, che il Vallisnieri illustra nella sua <emph type="italics"/>Giunta<emph.end type="italics"/> con assai brevi <lb/>parole descrittive, e contento in rappresentare agli occhi e alla mente dei <lb/>suoi lettori l'<emph type="italics"/>anatomia,<emph.end type="italics"/> non si cura punto di quella, che si potrebbe chia&shy;<lb/>mare <emph type="italics"/>fisi<gap/>logia<emph.end type="italics"/> della Terra. </s>

<s>&ldquo; Se il globo terrestre, cos&igrave; egli stesso dichiara <lb/>la sua intenzione, avanti l'universale diluvio fosse formato di strati o di <lb/>varie cortecce, com'&egrave; al presente; se tutti fossero orizzontali, o ci fosse l'al&shy;<lb/>tezza e la struttura de'monti che ora veggiamo; se tutti sieno seguiti nel <lb/>precipitarsi le parti terrestri, conforme le leggi di gravit&agrave;, nel fine del di&shy;<lb/>luvio; come di poi si sieno rotti, altri inalzati, altri abbassati, altri in mille <lb/>guise rivoltati, piegati e sconvolti; o se sieno stati formati da pi&ugrave; inonda&shy;<lb/>zioni, o da pi&ugrave; rovine e terremoti dislogati e disguisati; non &egrave; questo il <lb/>luogo di ricercarlo, contentandomi di avere solamente esposto ci&ograve; che m'aspet&shy;<lb/>tava per lo stabilimento del mio problema dell'origine delle fontane &rdquo; (ivi, <lb/>pag. </s>

<s>108). </s></p><p type="main">

<s>De'proposti problemi geologici dunque si protesta il Vallisnieri di non <lb/>aver voluto risolver che questo solo, lasciando all'altrui industria l'eserci&shy;<lb/>tarsi intorno ai rimanenti. </s>

<s>N'era fra questi uno per&ograve;, stato fin allora assai <lb/>dibattuto, ma che trovava facile e concludentissima risoluzione a solo volger <lb/>lo sguardo sopra queste tavole ori<gap/>ognostiche. </s>

<s>Anche il Guglielmini, per ci-<pb xlink:href="020/01/1709.jpg" pagenum="584"/>tare uno de'pi&ugrave; prossimi e autorevoli esempi, era stato sedotto dall'error <lb/>comune, cos&igrave; pensando e scrivendo dell'origine de'monti e delle valli. </s>

<s>&ldquo; Se <lb/>si considera la parte pi&ugrave; alta della Terra, cio&egrave; quella che noi chiamiamo <lb/>montuosa, si pu&ograve; ben facilmente comprendere che le spaccature, le quali in <lb/>essa da per tutto si trovano, per lo fondo delle quali scorrono i rivi, i tor&shy;<lb/>renti ed i fiumi, e che sono come termini divisorii d'una montagna dal&shy;<lb/>l'altra; &egrave; facile, dico, comprendere ch'esse sono state fatte dalla forza delle <lb/>acque, che le ha scavate col corso &rdquo; (Della natura de'fiumi, Vol. </s>

<s>I, Mi&shy;<lb/>lano 1821, pag, 348). Ma il Vallisnieri, confermando le dimenticate dottrine <lb/>dello Stenone, argomentava sicuramente dalla stratigrafia de'monti, e sen&shy;<lb/>tenziosamente ne concludeva: &ldquo; le valli, particolarmente ne'luoghi montuosi, <lb/>non sono formate da altro, se non da interrompimento o divisione degli <lb/>strati, o dalla rottura o piegatura de'medesimi &rdquo; (Giunta cit., pag. </s>

<s>108). </s></p><p type="main">

<s>Qual si fosse per&ograve; la causa di una tale rottura o piegatura, il Valli&shy;<lb/>snieri, come dianzi da lui stesso udimmo, lo lasciava alla investigazione dei <lb/>sagaci Naturalisti, fra'quali sorse, non molti anni dopo, Anton Lazzero Moro. </s>

<s><lb/>Tutto in istudio di ricercar l'origine de'crostacei, e de'corpi marini, che si <lb/>ritrovan sui monti (nel qual problema si rinchiudeva in germe la moderna <lb/>Geologia) comprese il Moro che non avrebbero avuto i travagli della mente <lb/>nessun conforto, infintanto che dell'origine di quegli stessi monti si ragio&shy;<lb/>nasse dai gran Maestri a quel modo che faceva il Guglielmini. </s>

<s>E perch&egrave; la <lb/>voce dello Stenone era sventuratamente rimasta fra le chiuse pareti dell'Ac&shy;<lb/>cademia del Cimento, non rimaneva altro che i disegni stratigrafici aggiunti <lb/>alla lezione accademica del Vallisnieri, da cui potessero pigliare eccitamento <lb/>e scorta gl'ingegni meditativi. </s></p><p type="main">

<s>Considerando dunque attentamente il Moro cotesti disegni, e suppo&shy;<lb/>nendo che gli strati pietrosi rappresentati dovessero essere, nella prima loro <lb/>e natural disposizione, tutti livellati all'orizzonte, intravide sagacemente la <lb/>ragione di quelle loro curvosit&agrave;, di quelle loro contorsioni e rotture, ammet&shy;<lb/>tendo l'esistenza di una forza, che pingesse con variata gagliardia di mo&shy;<lb/>mento dall'interno del terrestre globo all'esterno. </s>

<s>Or, in qual cosa potrebbe <lb/>meglio risedere cotesta forza endogena, che nel fuoco sotterraneo, di cui ave&shy;<lb/>vano ammessa l'esistenza, e riconosciuta altres&igrave; l'efficacia, tanti scrittori, <lb/>dall'antico Platone al moderno francese autore del <emph type="italics"/>Voyage d'Italie,<emph.end type="italics"/> citato <lb/>dal Vallisnieri? </s></p><p type="main">

<s>Ebbe da queste idee origine quel trattato in folio, che vide la luce in <lb/>Venezia nel 1740 col titolo <emph type="italics"/>De'crostacei, e degli altri marini corpi, che si <lb/>trovano sui monti,<emph.end type="italics"/> distinto in due libri, nel primo de'quali si confuta il <lb/>Nettunismo del Burnet e del Woodward, e nel secondo si stabilisce la teo&shy;<lb/>ria vulcanica nuova, per applicarla, cos&igrave; formulata, alla soluzione del prin&shy;<lb/>cipale problema: &ldquo; Gli animali e i vegetabili marini, le cui spoglie o reli&shy;<lb/>quie in oggi o sopra o sotto certi monti si trovano, nati, nutriti e cresciuti <lb/>nelle marine acque, innanzi che que'monti sopra la superfice del mare si <lb/>alzassero; allora l&agrave; furono spinti, dove ora esistono per lo pi&ugrave; impietriti, <pb xlink:href="020/01/1710.jpg" pagenum="585"/>quando que'monti, uscendo dal seno della Terra coperta d'acqua; s'alza&shy;<lb/>rono a quelle altezze, in cui ora si veggono &rdquo; (pag. </s>

<s>231). </s></p><p type="main">

<s>Sollecito di fare apparire al mondo in questa formulata proposizione <lb/>una scoperta originale, il Moro commemora l'anonimo Autor francese del <lb/>Viaggio nuovo d'Italia, e l'opinione di quei citati dal Woodward, i quali <lb/>dicevano essersi formate tutte l'isole, e le altre terre abitabili a quel modo, <lb/>che si formaron Rodi, e Tera, e Terasia, per impeto di terremoti e di sot&shy;<lb/>terranee sollevazioni. </s>

<s>Dello Stenone non fa nessun motto: eppure queste <lb/>dugent'undici pagine in folio, in che si squaderna il secondo libro del Moro. </s>

<s><lb/>non contengono altro insomma che un commentario prolisso, o una verbo&shy;<lb/>sissima esplicazione del concetto stenoniano, di cui giova qui ripetere le for&shy;<lb/>mali espressioni: <emph type="italics"/>Forsitan mari olim supposita ea terra canum marino&shy;<lb/>rum latibulum fuit, quorum dentes coenoso fundo olim insepulti, mutato <lb/>fundi situ per subterraneorum halituum praeceps incendium, modo in <lb/>media insula reperiuntur.<emph.end type="italics"/></s></p><p type="main">

<s>Quel che lo Stenone pensava cos&igrave; in particolare dell'isola di Malta, il <lb/>Moro l'applic&ograve; a tutte le isole, e ai continenti, e l'ipotesi delle Glossopietre <lb/>estese in forma di tesi a tutti i corpi marini. </s>

<s>La nuova teoria plutonica in&shy;<lb/>fatti si fonda dal pi&ugrave; recente Autore sopra le osservazioni dell'Isola nuova, <lb/>nata nell'arcipelago nel 1707; sopra il Monte nuovo, nato nel 1538 presso <lb/>Pozzuolo; sopra il Vesuvio e sopra l'Etna, che danno argomento alle de&shy;<lb/>scrizioni storiche de'primi capitoli del secondo libro. </s></p><p type="main">

<s>Uno de'principali meriti, ch'ebbe il Moro nel promovere la nuova <lb/>scienza, consiste nell'aver richiamata l'attenzione de'Geologi sopra gli ef&shy;<lb/>fetti delle forze endogene, l'attivit&agrave; delle quali troppo debolmente si faceva <lb/>concorrere nella Dinamica terrestre dello Stenone. </s>

<s>Vedemmo come, nel de&shy;<lb/>scrivere la Geologia della Toscana, attribuisse l'insigne uomo la rottura degli <lb/>strati al loro proprio peso, che per le avvenute escavazioni si sentiva sotto <lb/>mancare il sostegno, e poniamo che si spiegassero bene a cotesto modo le <lb/>varie inclinazioni prese da quegli stessi strati, e i patiti dislocamenti, era <lb/>per&ograve; difficile a intendere come si fossero potuti cos&igrave; contorcere violente&shy;<lb/>mente e incurvare, a quel modo che gli avea veduti e descritti il Vallisnieri. <lb/></s>

<s>&ldquo; Se alcuno (esce perci&ograve; cos&igrave; il Moro a dar perfezione alle teorie stenoniane) <lb/>sia che chiegga come abbiano potuto in tante guise incurvarsi questi pie&shy;<lb/>trosi strati, io rispondo che, a somiglianza di ci&ograve; che tante volte &egrave; stato ve&shy;<lb/>duto farsi dal Mongibello e dal Vesuvio, la materia di quegli strati lique&shy;<lb/>fatta, fu prima da'monti superiori vomitata, e nelle vicine valli, e fors'anco <lb/>nelle acque, che di prima quelle regioni coprivano, distesa. </s>

<s>Fu dipoi o in&shy;<lb/>nanzi che indurasse o dopo indurata, ma di nuovo da'sotterranei fuochi <lb/>ammollita, fu dico da questi all'insuso qua e l&agrave; inegualmente sospinta, e <lb/>dove le forze del fuoco impellente furono maggiori e pi&ugrave; continuate, l&agrave; pi&ugrave; <lb/>alta, dove minori furon le forze e non continuate, l&agrave; pi&ugrave; bassa venne quella <lb/>materia a trovarsi &rdquo; (ivi, pag. </s>

<s>280). </s></p><p type="main">

<s>Difficilmente si sarebbe potuta spiegare, per solo avvallarsi del soggia-<pb xlink:href="020/01/1711.jpg" pagenum="586"/>cente terreno, l'origine di quelle immense volte di pietra, indicate con la <lb/>lettera B nel primo disegno del Vallisnieri, e con le lettere A e C nel se&shy;<lb/>condo, per cui cos&igrave; facile il Moro trov&ograve; nelle forze endogene la causa na&shy;<lb/>turale del fatto: &ldquo; Questi strati, egli dice, furono all'ins&ugrave; spinti dalla forza <lb/>del fuoco, in guisa che nelle parti di mezzo delle concavit&agrave; l'urto fu mag&shy;<lb/>giore, che nelle altre parti, ma non tale per&ograve;, che il fuoco sbucato sia fino <lb/>a diromperli &rdquo; (ivi, pag. </s>

<s>281). </s></p><p type="main">

<s>Com'aveva il Woodward conferito a mantener viva la prima grande <lb/>efficienza geologica, riconosciuta dallo Stenone nell'acqua; cos&igrave; il Moro, per <lb/>questo sue divulgate dottrine, s'acquist&ograve; il merito, come si diceva, di aver, <lb/>non solo resuscitata dall'oblio, ma resa pi&ugrave; evidente altres&igrave; quella seconda <lb/>efficienza, che lo Stenone stesso riconosceva nel fuoco. </s>

<s>Il danno era per&ograve; che <lb/>non si facevano quelle due stesse efficienze, secondo che il Maestro della <lb/>nuova scienza insegnava, concorrere insieme, ma come il Woodward a sole <lb/>le acque diluviali attribuiva sulla superfice terrestre le subite trasformazioni; <lb/>cos&igrave; il Moro le attribuiva a soli gl'incendi sotterranei. </s></p><p type="main">

<s>Il Vallisnieri, bench&egrave; non volesse andar tanto innanzi, s'era pur fatto <lb/>intendere che gli strati pietrosi fossero un impostime delle acque, e il Moro <lb/>voleva invece che fossero materie allo stesso modo deposte, ma vomitate dai <lb/>fuochi. </s>

<s>&ldquo; Ben dice dunque, cos&igrave; scrive esso Moro, il signor Vallisnieri che <lb/>i monti fatti a strati, cio&egrave; i monti secondarii, paion tutti fatti in pi&ugrave; volte, <lb/>e che paion simili a que'tavolati e bellette, che da'torbidi fiumi ne'luoghi <lb/>bassi depongonsi. </s>

<s>Avvertasi per&ograve; che quando il Vallisnieri dice che <emph type="italics"/>appari&shy;<lb/>scono i monti formati, come d'una crosta sopra un'altra crosta, ognuna <lb/>delle quali sia stata lasciata in forma di posatura da varie inondazioni <lb/>in tempi a noi ignoti seguite;<emph.end type="italics"/> intendersi non debbe che quelle inondazioni <lb/>sieno state di acqua, ma solamente di quelle materie, bench&egrave; non cos&igrave; pens&ograve; <lb/>il Vallisnieri, di cui ognuna di quelle croste &egrave; composta. </s>

<s>Imperciocch&egrave; na&shy;<lb/>cquero a principio delle cose, cacciati da sotterranei fuochi fuor del seno <lb/>della Terra, i monti primarii, ed alzatisi sopra la superfice dell'acqua, che <lb/>dianzi il tutto copriva, dalle aperte loro bocche e caverne vomitarono varie <lb/>sorte di materie, le quali o a guisa di fiumi scorrendo, o a guisa di pioggia <lb/>dall'alto cadendo, si avvallarono e distesero, una dopo l'altra e una sopra <lb/>l'altra, alle falde di que'monti, giusta il modo che veggiamo tenersi tavolta <lb/>dal Vesuvio, dall'Etna e da altri somiglianti monti fiammiferi, e cos&igrave; ven&shy;<lb/>nero a formare in que'bassi luoghi moltissimi tavolati e posature composte <lb/>qual d'una sorta, qual d'un'altra, e qual di varie sorte di materia. </s>

<s>Da nuovi <lb/>fuochi poi accesi sotterra furono que'tavolati e posature all'ins&ugrave; cacciati, e <lb/>indi si formarono que'monti, che secondarii per me si appellano, e che os&shy;<lb/>serv&ograve; il Vallisnieri essere tutti fatti a strati &rdquo; (ivi, pag. </s>

<s>271, 72). </s></p><p type="main">

<s>I progressi della Geologia dunque non si potevano altrimenti sperare, <lb/>che dall'attemperamento di questa esagerata teoria plutonica colla nettunica, <lb/>ma non era venuto ancora il tempo del fecondo connubio. </s>

<s>Quattro anni dopo <lb/>che il Moro avea, sulle osservazioni e sull'esperienze, stabilito e reso pub-<pb xlink:href="020/01/1712.jpg" pagenum="587"/>blico il suo sistema, l'alito cartesiano che, spinto fuori sulle duttili onde del <lb/>Burnet e del Woodward, le avea enfiate nelle variopinte bolle dei loro si&shy;<lb/>stemi, torn&ograve; in Francia a spirar sul Buffon, che quelle aeree bolle trasform&ograve; <lb/>in una bomba lanciata nello spazio dagl'incendi del sole. </s>

<s>Raffreddandosi ivi <lb/>a poco a poco &ldquo; i vapori che prima si erano distesi, come veggiamo disten&shy;<lb/>dersi le code delle comete, si condensarono a poco a poco, e deposero al <lb/>tempo stesso un loto misto di materie sulfuree e saline, una parte delle <lb/>quali pel moto delle acque s'insinu&ograve; nelle fenditure perpendicolari, dove <lb/>form&ograve; i metalli e i minerali, il resto rimase nella superfice della Terra. </s>

<s><lb/>Adunque nello stato primiero della Terra era l'interno del globo composto <lb/>d'una materia vetrificata, come l'arena, che non &egrave; altro che un tritume di <lb/>vetro, e al di sopra di questa arena galleggiarono le parti pi&ugrave; leggere. </s>

<s>Ogni <lb/>cosa era coperta da uno strato di acqua, nata da'vapori condensati, che de&shy;<lb/>pose da per tutto una belletta mista di tutte quelle materie, che possono <lb/>sublimarsi e svaporare per la violenza del fuoco, e l'aria si form&ograve; coi va&shy;<lb/>pori pi&ugrave; sottili che, per la leggerezza loro, si svilupparono dalle acque e le <lb/>sormontarono. </s>

<s>Tale era lo stato del globo, quando l'azione del flusso e ri&shy;<lb/>flusso, e quella de'venti e del calore del sole cominciarono ad alterare la <lb/>superfice della Terra. </s>

<s>Il moto diurno e quello del flusso e riflusso primie&shy;<lb/>ramente sollevarono le acque sotto i climi meridionali, e queste rapirono e <lb/>portarono seco verso l'equatore il loto, le crete, le arene, ed elevando le <lb/>parti dell'equatore abbassarono per avventura a poco a poco quelle dei poli, <lb/>perciocch&egrave; le acque disfecero bentosto e ridussero in polvere le pomici e <lb/>le altre parti spugnose della materia vetrificata, ch'erano nella superfice; <lb/>scavarono delle valli, ed alzarono delle eminenze, che in decorso diventarono <lb/>continenti, e cagionarono tutte l'inuguaglianze, che osservansi alla superfice <lb/>della Terra &rdquo; (Teoria della Terra, Opere, Vol. </s>

<s>I, Venezia 1820, pag. </s>

<s>313, 14). </s></p><p type="main">

<s>Cos&igrave;, dopo lo Stenone, il Marsili, il Vallisnieri e il Moro, seguitavasi a <lb/>delirare in Francia, bench&egrave; altrove non mancassero provvidamente alcuni, <lb/>che s'inspiravan piuttosto al senno italiano. </s>

<s>In Germania furono tradotti i <lb/>due libri <emph type="italics"/>De'crostacei,<emph.end type="italics"/> e nel 1751 pubblicati in Lipsia. </s>

<s>In Inghilterra Odoardo <lb/>King proponeva nel 1767 innanzi alla Societ&agrave; regia una soluzione del famoso <lb/>problema dell'esistenza de'corpi marini sui monti, che si not&ograve; riscontrar <lb/>con quella data del Geologo nostro veneziano. </s>

<s>Vien perci&ograve; da alcuni Italiani <lb/>accusato l'Inglese di plagio: ma senz'avere ancora veduta l'opera di Laz&shy;<lb/>zero Moro non poteva il King essersi sentito fecondare l'ingegno da quelle <lb/>parole con le quali termina lo Stenone di descriver l'anatomia del capo della <lb/>Carcaria? </s>

<s>Non era egli naturalissimo che venisse fatto a quel di Londra, <lb/>come a quel di Venezia, di passare dall'isola di Malta a tutte l'isole della <lb/>Terra, e dalle Glossopietre a tutte le altre spoglie de'viventi nell'acqua ri&shy;<lb/>trovate poi sotterra? </s>

<s>&Egrave; da un'altra parte a riflettere che sui principii del <lb/>secolo XVIII tutti i grandi Anatomici, specialmente trattando degli organi <lb/>de'sensi, additavano continuamente queste pagine stenoniane, dove son tante <lb/>le sentenze quante son le parole, e in ogni sentenza ritrovasi, o esplicita-<pb xlink:href="020/01/1713.jpg" pagenum="588"/>mente annunziata, o in germe, qualche grande scoperta. </s>

<s>Consultavano al&shy;<lb/>tres&igrave; quelle pagine gli antiquarii, i quali ritrovavano in esse investigate le <lb/>origini delle antichit&agrave; o naturali o manufatte, che si scavan di sottoterra. </s>

<s><lb/>Or chi potrebbe negare che l'antiquario King non avesse piuttosto derivata <lb/>di qui, che ricopiata dal Moro la geologica soluzione del suo problema? </s></p><p type="main">

<s>Comunque sia, poco presso a chiudersi il secolo, che felicemente si <lb/>apriva col Marsili, col Vallisnieri e col Moro, la nuova scienza delle super&shy;<lb/>ficiali trasformazioni del globo veniva con proprio nome salutata, e a grande <lb/>onore accolta fra le maggiori sorelle a partecipare dello storico regno della <lb/>Natura. </s>

<s>Par che la Geologia sia nata adulta in paese straniero, ma chi at&shy;<lb/>tentamente l'osserva vi riconosce le infantili fattezze, con le quali nella fio&shy;<lb/>rentina Accademia fu esposta. </s>

<s>Si effigiava ivi dallo Stenone la Terra, se&shy;<lb/>condo che le osservazioni fatte sul suolo toscano gli avevano dimostrato, <lb/>come composta di strati sopra strati deposti dalle torbide acque diluviali. </s>

<s><lb/>Furono quelle inondazioni tante, ritirandosi il mare e poi tornando a rico&shy;<lb/>prir l'arida e a imporvi nuova materia, quanti di quegli strati se ne pos&shy;<lb/>sono annoverare affaldati intorno al nucleo del Globo. </s>

<s>Tale pure &egrave; la stra&shy;<lb/>tigrafia, nel suo essere e nella sua natura, che ci vien descritta dai Geologi <lb/>moderni, i quali riconobbero il vero prenunziato gi&agrave; dallo Stenone, in mezzo <lb/>alle seduttrici aberrazioni del Woodward e dello stesso Lazzero Moro. </s>

<s>&Egrave; no&shy;<lb/>tabile come il nostro Accademico fiorentino, nel difficile cimento di conci&shy;<lb/>liare le tradizioni bibliche con le osservazioni naturali, uscisse destramente <lb/>salvo di l&agrave;, dove l'inesperto Inglese, costretto ad ammettere un unico di&shy;<lb/>luvio di pochi giorni, e perci&ograve; un'unica deposizione delle materie, avea mi&shy;<lb/>seramente fatto naufragio. </s>

<s>Lo Stenone, anche in ci&ograve; seguito da molti mo&shy;<lb/>derni, ritrov&ograve; la causa semplicissima e naturale di quelle molteplici e ripetute <lb/>alluvioni, che venivano all'occhio dell'osservatore dimostrate dai fatti. </s>

<s>&ldquo; Quod <lb/>si quis dixerit in terra centrum gravitatis non semper idem esse cum cen&shy;<lb/>tro figurae, sed modo ab una, modo ab altera eius parte recedere, prout ca&shy;<lb/>vitates subterraneae variis locis creverint; facilem rationem afferre licet cur <lb/>fluidum, initio rerum omnia tegens, certa loca arida reliquerit, iterumque <lb/>redierit ad illa occupanda &rdquo; (Prodromus cit., pag. </s>

<s>72). </s></p><p type="main">

<s>Lo Stenone insegn&ograve; che i monti e le valli niente altro son che l'effetto <lb/>della rottura degli strati, e bench&egrave; il Buffon, a mezzo il secolo XVIII, so&shy;<lb/>gnasse intorno a ci&ograve; non meno stranamente de'buoni uomini antichi, i Geo&shy;<lb/>logi oggid&igrave; confermano essere la dottrina stenoniana la vera. </s>

<s>Hanno solo <lb/>riconosciuto in lei il bisogno di venire in parte emendata, sostituendo alla <lb/>forza di gravita le forze endogene, messe in tanta evidenza da Lazzero Moro. </s></p><p type="main">

<s>Coloro che dissero maravigliati esser nata e cresciuta la Geologia tra <lb/>la fine del secolo XVIII e il principio del secolo appresso, dovrebbero con&shy;<lb/>siderare che se crebbe in quel tempo, era gi&agrave; da molto tempo nata in To&shy;<lb/>scana, e che apparve il maraviglioso incremento dal congiunger felicemente <lb/>insieme, o per dir meglio, dall'infondere in quella dello Stenone la scienza <lb/>del Moro. </s>

<s>Agli stranieri, e specialmente ai Francesi, si d&agrave; da molti il me-<pb xlink:href="020/01/1714.jpg" pagenum="589"/>rito di aver questa stessa scienza abbellita coi sistemi, dai quali si astennero <lb/>i Nostri o si mostrarono sempre assennatamente pi&ugrave; sobrii. </s>

<s>Sorse dopo il <lb/>Buffon la splendida fantasia del La-Place, che lungamente e universalmente <lb/>sedusse gl'ingegni, ma che ora si dissipa anch'essa al tocco dell'esperienza, <lb/>come le altre bolle enfiate dagli spiriti cartesiani. </s></p><p type="main">

<s>Le ipotesi de'due Francesi ora commemorati avevano principalmente in <lb/>mira di accomodarsi e di spiegare due fatti: il calor centrale e la figura <lb/>ellissoidea della Terra, e perci&ograve; immaginarono un globo tutto internamente <lb/>compreso dal fuoco, e da lui reso molle e pastoso. </s>

<s>L'esperienza e il cal&shy;<lb/>colo dimostrano invece che dovette il globo terrestre esser solido in prin&shy;<lb/>cipio, com'&egrave; al presente. </s>

<s>Nacque l'inganno dal credere che una sfera di <lb/>solido vetro, per esempio, o di metallo, girata velocemente intorno al suo <lb/>asse, e per lunghissimo tempo, non dovesse, anche senza esser molle, ri&shy;<lb/>gonfiare nell'equatore in modo simile, e proporzionale a quello, che ha de&shy;<lb/>formata la Terra. </s>

<s>&Egrave; da un'altra parte simile un tale inganno a quello, che <lb/>facevasi il Moro e i geologi dopo lui, i quali crederono che non potessero <lb/>essere state le stratificazioni pietrose cos&igrave; contorte e incurvate, se non che <lb/>quando si trovavan tuttavia plastiche e molli, per l'azione liquefattrice dei <lb/>fochi. </s>

<s>Eppure si vedono tutti i giorni gli architravi di pietra incurvarsi nei <lb/>nostri edifizi sotto il peso delle muraglia. </s>

<s>Gl'insensibili momenti delle forze <lb/>continuamente operanti, accumulati dal tempo, producono questi e moltis&shy;<lb/>simi altri fatti naturali, che alcuni invece attribuiscono a cause immaginarie. </s></p><p type="main">

<s>Dicemmo che da questo vizio d'immaginar ci&ograve;, che non si arriva a co&shy;<lb/>noscer di fatto, si astennero i nostri Italiani, e perch&egrave; vogliono gli stranieri <lb/>attribuirlo piuttosto a difetto d'ingegno, venga anche quest'altro esempio a <lb/>dimostrare i buoni effetti del prudente consiglio. </s>

<s>In fin da quando il Bo&shy;<lb/>relli, per gli eccitamenti avuti dal cardinale Leopoldo de'Medici, apriva in <lb/>Sicilia, ma sempre come Accademico del Cimento, un nuovo campo alla Pa&shy;<lb/>leontologia, si proponeva a sciogliere il problema delle cos&igrave; dette <emph type="italics"/>ossa de'gi&shy;<lb/>ganti,<emph.end type="italics"/> le quali pi&ugrave; abbondantemente che altrove si ritrovarono sparse in <lb/>Toscana per la valle superiore dell'Arno, e per i colli volterrani. </s>

<s>Lo Ste&shy;<lb/>none riconosciuto il fatto che coteste erano ossa di animali vissuti sotto altro <lb/>cielo, disse che, venuti qua in servizio dell'esercito di Annibale, morti o <lb/>naturalmente o in guerra, vi restaron sepolti. </s>

<s>&ldquo; Certum est transiisse illac <lb/>Annibalem, antequam ad lacum Trasimenum cum Romanis confligeret; cer&shy;<lb/>tum est extitisse in ipsius exercitu iumenta africana, et immensae magni&shy;<lb/>tudinis elephantes turrigenos; certum est, dum a montibus fesulanis descen&shy;<lb/>deret nimia aquarum alluvie, periisse in locis paludosis magnam partem <lb/>animalium oneribus vehendis destinatorum &rdquo; (ibid., pag. </s>

<s>64). </s></p><p type="main">

<s>Queste ragioni dello Stenone furono poi ripetute da molti, ma il pro&shy;<lb/>blema incontr&ograve; bene altre difficolt&agrave;, quando si ritrovarono elefanti e mam&shy;<lb/>mouth fossili in Russia e in Siberia. </s>

<s>Incredibile &egrave; l'affaccendamento di co&shy;<lb/>loro, che volevano spiegar come mai dalle regioni equatoriali fossero emigrati <lb/>col&agrave; presso il polo quadrupedi cos&igrave; ponderosi e inerti; indicibile &egrave; l'attivit&agrave; <pb xlink:href="020/01/1715.jpg" pagenum="590"/>de'Filosofi in assottigliar l'ingegno per ritrovar la ragione di tanta avve&shy;<lb/>nuta variet&agrave; di climi. </s>

<s>Mentre uno perci&ograve; si profonda negli abissi della terra, <lb/>e un altro si sublima agli spazii celesti, un nostro Italiano trova da risol&shy;<lb/>vere il problema in questa semplice e naturalissima osservazione, che cio&egrave; <lb/>&ldquo; la temperatura de'luoghi situati fuori dei tropici non dipende esclusiva&shy;<lb/>mente dalla maggiore o minore distanza dall'equatore, ma &egrave; variamente mo&shy;<lb/>dificata da cause meteoriche, la massima delle quali &egrave; lo spirare di certi <lb/>venti &rdquo; (Brocchi, Conchiologia fossile, Vol. </s>

<s>I, Milano 1843, pag. </s>

<s>386). Or <lb/>perch&egrave; queste cause meteoriche dipendono dall'ampiezza de'mari, rispetto <lb/>ai continenti, e dalle relative posizioni dei gioghi montani, il solo variato <lb/>aspetto della superfice terrestre induce necessariamente una variazione del <lb/><gap/>lima, il quale poteva porci&ograve; esser tale un giorno in Siberia e in Russia, <lb/>qual'&egrave; oggid&igrave;, o non molto differente, nelle regioni affricane. </s></p><p type="main">

<s>La causa tanto agitata del cos&igrave; detto <emph type="italics"/>periodo glaciale,<emph.end type="italics"/> e intorno a che <lb/>gli stranieri fantasticarono in s&igrave; strani modi, vien naturalmente risoluta da <lb/>questa proposizione del Brocchi, a cui dobbiamo altres&igrave; la dottrina degli spon&shy;<lb/>tanei abbassamenti e sollevamenti del livello del mare con che venivansi a <lb/>spiegare le vicende delle allagazioni e dei ritiramenti di lui meglio che con <lb/>l'ipotesi dello Stenone. </s>

<s>Vero &egrave; che il Brocchi non s'era in tutto ancora de&shy;<lb/>liberata la mente dal supposto del violento operare dei cataclismi pensando <lb/>che &ldquo; essendosi <emph type="italics"/>subitaneamente<emph.end type="italics"/> abbassato il livello del mare si riducesse <lb/>nell'odierno suo letto &rdquo; (ivi, pag. </s>

<s>383) ma furon queste idee per inevitabile <lb/>conseguenza logica portate nella scienza dallo Stenone, ridotto fra l'angustie <lb/>della cronologia biblica, e dal Moro a cui fu principalmente inspirata la teo&shy;<lb/>ria plutonica dal subitaneo apparirgli sotto gli occhi le nuove Isole greche. </s></p><p type="main">

<s>In qualunque modo si conferma sempre meglio per questi esempi il <lb/>proposito nostro, ch'era quello di dimostrare com'avessero gl'Italiani le prime <lb/>parti, cos&igrave; nell'istituire, come nel coltivare la Geologia, le due massime effi&shy;<lb/>cienze della quale, riconosciute da Niccol&ograve; Stenone e da Lazzero Moro, fu&shy;<lb/>rono in tutte le loro particolarit&agrave; messe in evidenza dagli studiosi dei nostri <lb/>giorni. </s>

<s>Ci siamo intrattenuti in questa seconda parte del presente capitolo a <lb/>trattare della seconda efficienza plutonica, riguardandola come sede del regno <lb/>minerale nelle vene metalliche e nei cristalli. </s>

<s>Furono infatti i due Autori <lb/>ora commemorati i primi che, alle immaginarie e favolose origini degli stessi <lb/>metalli, specialmente preziosi, e delle gemme, sostituirono le investigate cause <lb/>naturali. </s>

<s>Fu per essi altres&igrave; messa finalmente in chiaro la cos&igrave; dubbia ori&shy;<lb/>gine de'cristalli, e s'incominci&ograve; allora a filosofare pi&ugrave; sanamente intorno <lb/>alle ragioni delle loro forme geometriche, ci&ograve; ch'essendo di principale im&shy;<lb/>portanza nella Mineralogia, ci consiglia a trattenerci pi&ugrave; di proposito, nel <lb/>seguente articolo, sopra un tale argomento. </s></p><pb xlink:href="020/01/1716.jpg" pagenum="591"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Come spesso avviene che l'abito non trasformato seguiti a far mante&shy;<lb/>nere, nelle domestiche e nelle civili consuetudini, i trasformati titoli della <lb/>persona; cos&igrave; non di rado avviene de'vocaboli, rispetto alle idee. </s>

<s>Abbiamo <lb/>di ci&ograve; un notabile esempio nel vocabolo stesso <emph type="italics"/>cristallo,<emph.end type="italics"/> il quale, perch&egrave; <lb/>vale ai Greci quanto <emph type="italics"/>ghiaccio indurito,<emph.end type="italics"/> si seguit&ograve; a credere che tal si fosse <lb/>davvero la natura propria del minerale. </s>

<s>Il fatto, che sembra incredibile a chi <lb/>non ha ben misurata la forza dell'abitudine, o non ha ben riconosciuta la <lb/>tirannia, che sul pensiero esercitano le parole, fu sanzionato dall'antico padre <lb/>de'Naturalisti, Cecilio Plinio, il quale, nel cap. </s>

<s>Il del libro XXXVII delle <lb/>sue Storie, avendo fatto prima motto di alcuni effetti del calore &ldquo; contraria, <lb/>soggiunge, huic causa crystallum facit, gelu vehementiori concreto. </s>

<s>Non alicubi <lb/>certe reperitur, quam ubi maxime hybernae nives rigent, glaciemque esse <lb/>certum est, unde et nomen Gracei dedere &rdquo; (Hagenoae 1518, fol. </s>

<s>CCLXXIX <lb/>ad terg.). </s></p><p type="main">

<s>In ogni modo avendo la cosa, per chi dava luogo al senno, apparenza <lb/>di paradosso, quegli altri che davan luogo piuttosto all'autorit&agrave; de'maggiori, <lb/>si studiavano di salvarla col ricorrere a certe mendicate lusinghiere espe&shy;<lb/>rienze. </s>

<s>Volevano che a mettere un cristallo sulla lingua ne sentisse il si&shy;<lb/>ziente il medesimo refrigerio, che a mettervi sopra un pezzetto di gelo, e <lb/>dall'aver forse osservato per caso che qualche untuosa lamina cristallina, <lb/>per effetto di capillarit&agrave;, galleggia sull'acqua, ne vollero inferire esser que&shy;<lb/>sta una propriet&agrave; generale, che i cristalli tutti hanno comune col ghiaccio. </s></p><p type="main">

<s>Quando cominciarono ad apparire sull'orizzonte d'Italia gli albori cre&shy;<lb/>puscolari della Scienza sperimentale, quel buon senese Vannoccio Biringucci, <lb/>che fu primo a richiamar l'attenzione sui minerali del ricco suolo toscano, <lb/>e ad accennare alle utilit&agrave;, che se ne ricaverebbero, per l'esercizio delle <lb/>arti, per l'economia dello Stato, e per gli usi della guerra; metteva, cos&igrave; <lb/>scrivendo, un poco di senno in quelle scapestrate idee, che s'avevano dagli <lb/>studiosi di Plinio intorno all'origine dei cristalli. </s>

<s>&ldquo; Cominciandomi a dirvi <lb/>del cristallo, vi dico che &egrave; una pietra trasparente, lucida e chiara, compo&shy;<lb/>sta dalla Natura con predominio acqueo, talch&egrave; da molti, contr'all'ordine <lb/>delle cose naturali, &egrave; stato creduto che la Natura l'abbi generato di pura <lb/>acqua per forza d'una potente e perpetua frigidit&agrave;, ch'&egrave; continuamente in <lb/>que'monti e luoghi dov'el si trova, ne'quali mai le acque e le nevi, per <lb/>li grandissimi freddi, disghiacciar non si possono. </s>

<s>E questa tal loro opinione <lb/>han cerca di provar con dire che il cristallo ancor ritiene la natura del&shy;<lb/>l'acqua ghiacciata, qual'&egrave;, oltre a quel che dimostra nell'aspetto, che s'el <lb/>si mette nell'acqua, come ancor fa il ghiaccio, vi galleggia sopra, senza an&shy;<lb/>dare a fondo. </s>

<s>Ed anco dicono di pi&ugrave; che si usa metterne sotto la lingua <pb xlink:href="020/01/1717.jpg" pagenum="592"/>de'sizienti per la sua frigidit&agrave; ed umidit&agrave; che rende, e ch'ello spegne la <lb/>siccit&agrave; della sete. </s>

<s>Ma queste cose, ancor che fosser tutte, che non sono, con&shy;<lb/>siderando non concludono che sia acqua, perch&egrave; il medesimo ancora sarebbe <lb/>del diamante e del berillo, e per&ograve; non mi par da credere ch'el sia acqua <lb/>pura gelata, e fatta indissolubile come dicono, perch'&egrave; pietra cos&igrave; dalla na&shy;<lb/>tura generata. </s>

<s>E di poi, se questo fosse, in que'luoghi dove spesso piove, <lb/>e tante nevi che mettono per freddo tutte ghiacciassero e non disghiaccias&shy;<lb/>sero mai, e sempre si convertissero in cristallo, vi sarebbero maggiori le <lb/>montagne del cristallo, che quelle delle pietre &rdquo; (De la Pirotecnia, libri X, <lb/>Venezia 1540, fol. </s>

<s>37, 38). </s></p><p type="main">

<s>Faceva eco al nostro Senese dalla lontana Germania, pochi anni dopo, <lb/>Giorgio Agricola, il quale, nel libro VI <emph type="italics"/>De natura fossilium,<emph.end type="italics"/> trattando del&shy;<lb/>l'origine de'cristalli, dimostra con le ragioni e con l'esperienza esser falsa <lb/>l'opinione de'seguaci di Plinio, che dicevano essere essi cristalli generati <lb/>sotto terra dalle acque indurite nel gelo, perch&egrave; se ci&ograve; fosse &ldquo; in frigidis&shy;<lb/>simis quibusque regionibus, in quibus non rivi modo, sed etiam maximi <lb/>amnes usque ad vada glaciantur, plurima fierent ac solis calore liquescerent <lb/>rursus, quorum neutrum fieri videmus &rdquo; (Basileae 1546, pag. </s>

<s>282). &Egrave; falso <lb/>altres&igrave;, soggiunge l'Agricola, che il ghiaccio indurito per anni e per secoli <lb/>sui monti si trasformi finalmente in cristallo, perch&egrave;, sebbene in cadendo <lb/>mostri di essere cos&igrave; duro come la stessa pietra, &ldquo; etiam ipsa tandem solis <lb/>liquescit calore. </s>

<s>Igitur crystallus est succus, quem, sicut in libris <emph type="italics"/>De ortu <lb/>et causis subterrancorum<emph.end type="italics"/> scripsi, frigus intra terram conglutinavit &rdquo; (ibid.). </s></p><p type="main">

<s>In Italia, prima della instaurazione del metodo sperimentale, furono man&shy;<lb/>tenute vive queste tradizioni della scienza dal Cesalpino, il quale ripudiava <lb/>l'opinion di coloro, che dicevano essere i cristalli ghiaccio impietrito per la <lb/>semplicissima ragione che i luoghi, dove nascono quegli stessi metalli, come <lb/>il diamante per esempio e simili altri, &ldquo; non in Septemtrione sunt, sed in <lb/>India, Arabia et calidioribus regionibus &rdquo; (De metallicis cit., pag. </s>

<s>36). Dopo <lb/>la detta instaurazione uno de'pi&ugrave; autorevoli nella scienza, che trattassero <lb/>dell'origine dei cristalli, fu Tommaso Bartholin nel suo libro <emph type="italics"/>De nivis usu <lb/>medico,<emph.end type="italics"/> dove, proponendosi nel cap. </s>

<s>XV di spiegare il detto di Plutarco, che <lb/>cio&egrave; non sieno altro le pietre se non che terra indurita dal freddo, &ldquo; an <lb/>hinc, soggiunge, patrocinium invenient qui crystallos ex glacie derivant? </s>

<s>&rdquo; <lb/>(Hafniae 1661, pag. </s>

<s>102). E seguita a riferir le contrarie opinioni degli Au&shy;<lb/>tori, da Plinio a'suoi tempi, cos&igrave; all'ultimo concludendo il discorso: &ldquo; Nos <lb/>chrystallum ita generari credimus sicut, in cryptis et locis subterraneis, ex <lb/>stillicidio aquarum lapides frigore concrescunt &rdquo; (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>Le incrostazioni pietrose del carbonato calcare le credeva dunque il <lb/>Bartholin una trasformazione, sub&igrave;ta per via del freddo cos&igrave; intenso dal&shy;<lb/>l'acque, e allo stesso modo credeva che si generassero i cristalli. </s>

<s>Il valen&shy;<lb/>t'uomo, in tempi ne'quali non aveva ancora la Chimica rivelato il mistero <lb/>degli stillicidi pietrificanti, toglieva all'ipotesi pliniana quella sua prima ap&shy;<lb/>parente stranezza col richiamar l'attenzione su questo fatto, dal quale forse <pb xlink:href="020/01/1718.jpg" pagenum="593"/>rimasero pur sedotti gli Accademici fiorentini, come pare che si rilevi dalle <lb/>seguenti parole da loro scritte nella prefazione all'<emph type="italics"/>Esperienze intorno agli <lb/>artificiali agghiacciamenti.<emph.end type="italics"/> &ldquo; Sul fondamento adunque, essi dicono, dello <lb/>strano passaggio, che fanno l'acque e i pi&ugrave; di tutti gli altri liquori nel con&shy;<lb/>gelare, non &egrave; mancato chi creda che, dove il freddo lavora col&agrave; nelle sue <lb/>miniere co'materiali pi&ugrave; proprii, arrivi a condizionare le acque purissime a <lb/>ricever cos&igrave; fatta tempera, che e'le formi eziandio in rocche durissime di <lb/>cristalli, ed in gioie di varii colori, secondo la varia tintura che possono dar <lb/>loro i fumi de'minerali vicini, e sino arrivino all'invincibil saldezza dello <lb/>stesso diamante. </s>

<s>E Platone fu di questo parere, che da'rimasugli delle acque, <lb/>ond'ei credeva nel segreto della Terra crearsi l'oro, il diamante s'ingene&shy;<lb/>rasse, che perci&ograve; nel Timeo ramo dell'oro vien nominato il diamante da <lb/>quel divino Filosofo &rdquo; (Saggi di nat. </s>

<s>esp. </s>

<s>cit., pag. </s>

<s>78). </s></p><p type="main">

<s>In un libro, in cui sempre severamente s'osserva il precetto di non <lb/>riferir se non ci&ograve; che resulta manifesto per l'esperienza, fa gran maraviglia <lb/>quest'ossequioso trattenimento intorno a un platonico concetto, che doveva <lb/>allo squisito senso de'nostri Accademici scoprirsi alieno dal vero sperimen&shy;<lb/>tale. </s>

<s>La maraviglia per&ograve; scema per una parte, e cresce per l'altra a chi <lb/>senta annunziarsi all'orecchio che la Cristallografia, allora quasi sconosciuta, <lb/>ebbe nell'ultimo periodo di quella stessa Accademia, nella quale erano state <lb/>gi&agrave; scritte le sopra riferite parole, la sua principale e pi&ugrave; intensa cultura. </s>

<s><lb/>Lo Stenone infatti rivoltosi, in mezzo allo studio de'cristalli, di cui pi&ugrave; qua <lb/>narreremo i progressi, a ricercar la loro origine rimasta lungamente cos&igrave; <lb/>controversa, fu primo a riconoscerla simile a quella de'sali, formulando cos&igrave; <lb/>in questa proposizione la sua sentenza: &ldquo; fluidum, in quo crystallus con&shy;<lb/>crescit, eodem modo se habet ad crystallum, quomodo aqua comunis se habet <lb/>ad salia &rdquo; (Prodromus cit, pag. </s>

<s>45). </s></p><p type="main">

<s>Si pu&ograve; facilmente provar questa proposizione, dice l'Autore, da ci&ograve; che <lb/>nelle concrezioni i cristalli e i sali hanno di comune, ma per non divagar <lb/>da que'termini prescritti a un Prodromo, pensa di ridur tutte le prove nella <lb/>descrizione della seguente, che a lui par bellissima osservazione sperimen&shy;<lb/>tale; &ldquo; experimentum recitabo, quod mihi perpulchrum visum est: In eo&shy;<lb/>dem lapide variis in locis recedentes ab invicem lamellae eius crystallis ple&shy;<lb/>nae erant, quarum nonnullae aqueae, aliae lucidissimae, quaedam albae, <lb/>multae amethistinae erant, sibi invicem immixtae sine ulla colorum cenfu&shy;<lb/>sione, eodem omnino modo quo vitriolum et alumen in eadem aqua disso&shy;<lb/>luta, post consumptam aquae partem, seorsim c<gap/>ncrevisse singula, absque <lb/>ulla partium miscela, hic facta salium experimenta demonstrant &rdquo; (ibid.). </s></p><p type="main">

<s>Dimostravano cio&egrave;, secondo lo Stenone, questi esperimenti che l'acqua <lb/>non &egrave; la genitrice immediata dei cristalli, quasi ch'ella presti a loro della <lb/>sua propria costanza, ma &egrave; solo il mestruo del succo lapideo, che si depone <lb/>in forme regolari, come, sciolti prima nell'acqua stessa, vi si vedono deporre <lb/>allo stesso modo i varii sali. </s>

<s>Cos&igrave; con questa generosa rivendicazione del <lb/>vero un Accademico del Cimento emendava i falli de'suoi predecessori, ma <pb xlink:href="020/01/1719.jpg" pagenum="594"/>infelicemente sparsa la sua voce al vento rimase intera, specialmente negli <lb/>stranieri, la ragion delle accuse, che il Boerhaave avvent&ograve; contro i Nostri <lb/>sanguinosissime, mettendoli alla pari con Paracelso. </s></p><p type="main">

<s>Agli stillicidii pietrificanti del Bartholin i seguaci dell'antica ipotesi pli&shy;<lb/>niana erano venuti via via, per salvarla, ad aggiungere nuovi argomenti, <lb/>opportunamente suggeriti a loro dall'esperienze dei salci e delle zucche nu&shy;<lb/>trite di sola acqua, secondo le descrizioni dell'Helmont e del Boyle. </s>

<s>N&egrave; a <lb/>ci&ograve; solo contenti, entrarono nel campo della Chimica ad additare agl'incre&shy;<lb/>duli, nelle acque mescolate alle distillazioni, il principio generatore degli olii. </s>

<s><lb/>Fu ci&ograve; che dette occasione al Boerhaave d'inveire contro l'ignoranza di co&shy;<lb/>storo e di tutti gli altri, che dicevano trar da sola l'acqua tutti i corpi sen&shy;<lb/>sibili la necessaria materia ai loro nascimenti. </s>

<s>&ldquo; Attamen etiam cavendi hic <lb/>errores sunt, quoniam praememorata iam et alia quaedam suscitaverunt opi&shy;<lb/>nionem inter Chemicos ac si aqua sola materies foret unde corpora sensi&shy;<lb/>bilia cuncta nascerentur. </s>

<s>Fuerunt enim qui scripsere inter principes Chemi&shy;<lb/>cos quod aqua, gelu primo defaecatissima reddita, per longum tempus, deinde <lb/>autem nunquam regelascens, sed semper sensim increscente frigore constricta, <lb/>densata, ponderosior reddita, tandem in veram crystallum montanam transi&shy;<lb/>ret. </s>

<s>Quin id narrant audacter in montibus Helvetiorum glacialibus, ad pla&shy;<lb/>gas horum boreales, ubi regelascens nunquam per saecula glacies ita tran&shy;<lb/>sformari dicitur: de quibus Paracelsus atque Academia Cimentina videantur &rdquo; <lb/>(Elementa Chemiae, T. I, Lugd. </s>

<s>Batav. </s>

<s>1732, pag. </s>

<s>593). </s></p><p type="main">

<s>La scoperta poi fattasi che il ghiaccio non &egrave; capace di ricevere ulte&shy;<lb/>rior grado di freddo, ma inalterabilmente si rimane, per qualunque tempo <lb/>e in qualunque ambiente, sempre nel medesimo stato, fin&igrave; per toglier via <lb/>dalle menti l'errore. </s>

<s>Martin Kaehler, uno de'Linneidi upsaliensi, lesse in&shy;<lb/>nanzi all'illustre Preside, il d&igrave; 22 Dicembre 1747, una dissertazione intito&shy;<lb/>lata <emph type="italics"/>Crystallorum generatio,<emph.end type="italics"/> la quale valse con la Chimica del Boerhaave <lb/>a diffondere nella scienza la verit&agrave; delle dottrine stenoniane, concludendo, <lb/>anche il Medico linneano, la generazione de'cristalli lapidei da questi due <lb/>prestabiliti principii: &ldquo; I. </s>

<s>Quod crystallissatio salibus competit, nullique cor&shy;<lb/>pori quantum novimus alii. </s>

<s>II. </s>

<s>Quod omnis crystallissatio fit in aqua &rdquo; (Amoe&shy;<lb/>nitates acad. </s>

<s>cit., pag. </s>

<s>438). </s></p><p type="main">

<s>La dottrina dello Stenone per&ograve; che cio&egrave; ogni cristallizzazione si faccia <lb/>nell'acqua, o per <emph type="italics"/>via umida,<emph.end type="italics"/> era una conseguenza di quel predominio che <lb/>egli dava all'efficienza nettunica. </s>

<s>Lazzero Moro invece, il quale non ricono&shy;<lb/>sceva altra efficienza geologica, che la vulcanica, fu primo ad ammettere la <lb/>generazion naturale dei cristalli per quella, che si suol dire <emph type="italics"/>via secca,<emph.end type="italics"/> ap&shy;<lb/>poggiandosi alle proprie teorie e a certe esperienze intorno ai cristalli arti&shy;<lb/>ficialmente ottenuti per via di fusione, che aveva allora lette nell'ottavo <lb/>tomo del Giornale dei Letterati d'Italia. </s>

<s>Nel cap. </s>

<s>XII del II libro <emph type="italics"/>De'cro&shy;<lb/>stacei<emph.end type="italics"/> il fatto osservato e descritto dal Vallisnieri, che cio&egrave; negli strati lapi&shy;<lb/>pei dei monti si ammirano cristalli e cristalloidi, &egrave; cos&igrave; dallo stesso Lazzero <lb/>Moro spiegato, applicandovi il suo sistema: &ldquo; Si sa che un cocentissimo fuoco <pb xlink:href="020/01/1720.jpg" pagenum="595"/>ha forza di molte materie convertire in cristallo, il perch&egrave;, sendo veemen&shy;<lb/>tissimo il fuoco che nelle viscere della terra si nutre, non &egrave; fuor di ragione <lb/>attribuire al medesimo la formazione di quei cristalli, che negli accennati <lb/>strati si ammirano &ldquo; (pag. </s>

<s>277, 78). </s></p><p type="main">

<s>Cos&igrave; la verace dottrina della generazion de'cristalli, sia per soluzione, <lb/>sia per fusione, trionf&ograve; all'ultimo sopra l'errore, che avea lungamente sog&shy;<lb/>giogati gl'ingegni, ai quali proponevasi nulladimeno a risolvere un altro <lb/>problema concernente la ragione di quelle forme geometriche, secondo le <lb/>quali si vede sempre assettarsi la cristallizzabile materia, o stemperata in un <lb/>liquido o risoluta dal fuoco. </s>

<s>I lunghi e faticosi studi, intrapresi per riuscire <lb/>al difficile intento, forniscono il soggetto a un importantissima storia, a cui <lb/>servire essendo i documenti di qualit&agrave; diversa siam costretti a distinguerli <lb/>in acroamatici e in esoterici. </s>

<s>Riponiamo fra'primi non quelli soli, che rima&shy;<lb/>sero manoscritti, ma quegli altri eziandio, che manoscritti andarono prima <lb/>attorno, e poi furono dati alle stampe, come la Storia naturale dell'Impe&shy;<lb/>rato, e la Metalloteca del Mercati; e riponiamo pure in quell'ordine quei <lb/>documenti storici, ch'essendo usciti in pubblico infino dalle loro origini, <lb/>qual sarebbe il Prodromo dello Stenone, rimasero come luce riverberata in <lb/>s&egrave; stessa dalle opache pareti della chiusa lanterna. </s>

<s>Toccheremo con brevit&agrave; <lb/>questa prima storia, che appartien tutta all'Italia, e pi&ugrave; propriamente alla <lb/>Toscana, per passar poi ad accennare a quell'altra, che si diffonde in pi&ugrave; <lb/>ampio teatro, e che rende visibile il suo progresso, come raggio di luce che <lb/>si veda per gli aperti spazii rifletter da specchio a specchio. </s></p><p type="main">

<s>Quel Torricelli, che instituiva in Firenze nelle sale medicee la Fisica <lb/>sperimentale, trovando ne'varii soggetti naturali fecondo campo, ed eserci&shy;<lb/>zio degno a'suoi studii, non lasci&ograve; indietro di considerare i cristalli. </s>

<s>Geome&shy;<lb/>tra eccellentissimo e discepolo di Galileo, ch'era solito dire aver la Natura <lb/>scritto il suo libro con caratteri geometrici, non vide meglio che nelle figure <lb/>cristalline questi stessi caratteri espressi, ond'&egrave; che, sentitosi potentemente <lb/>allettare verso quelli l'ingegno, si volse ad interpetrarli con gli esercizi del&shy;<lb/>l'arte. </s>

<s>I minerali, che pi&ugrave; di frequente gli erano occorsi ad esaminare col <lb/>Microscopio della perlina, di cui, come si sa, egli fu l'inventore e l'arte&shy;<lb/>fice; ridotti in minime particelle, trov&ograve; configurati in cubi, in ottaedri e in <lb/>dodecaedri. </s>

<s>E perch&egrave; nella successione di queste forme gli parve un passar <lb/>dal semplice al composto, volle nell'arte sua geometrica ritrovar le ragioni <lb/>e gli ordini di un tal passaggio. </s>

<s>Cos&igrave; gli vennero facilmente dimostrate va&shy;<lb/>rie proposizioni intorno ai solidi poliedri inscritti e circoscritti, lusingato da <lb/>una dolce speranza, e da un geloso desiderio che fossero nuove. </s>

<s>Non assi&shy;<lb/>curandosene per&ograve;, volle trepidamente interrogar del fatto Michelangiolo Ricci, <lb/>a cui inviava da Firenze le dette geometriche dimostrazioni, insieme con la <lb/>notizia di ci&ograve;, che aveva nuovamente osservato intorno alle forme cristalline <lb/>di alcuni minerali, come del sale ridotto in parallelepipedi, e della marche&shy;<lb/>sita in dodecaedri. </s>

<s>Il Ricci cos&igrave;, il d&igrave; 13 Agosto del 1645, rispondeva da <lb/>Roma al riverito maestro, e al carissimo amico: </s></p><pb xlink:href="020/01/1721.jpg" pagenum="596"/><p type="main">

<s>&ldquo; Sono piaciute assaissimo le proposizioni degl'inscritti e circoscritti, <lb/>ottaedri, dodecaedri, cubi, ecc., e poich&egrave; ella pare che nella sua mi accenni <lb/>che le fosse grato di sapere se altri abbia preoccupato il luogo di primo in&shy;<lb/>ventor di quelle, rispondo che l'abate Maurolico ha considerate le medesime <lb/>cose in tutti i casi possibili, con particolar brevit&agrave;. </s>

<s>E per darne a V. S. <lb/>qualche saggio, dell'iscrizione dell'ottaedro nel cubo, cos&igrave; dice: <emph type="italics"/>coniunge <lb/>sex basium cubi centra per duodecim rectas, quae quidem inclusum octae&shy;<lb/>drum configurabimus.<emph.end type="italics"/> E volendo iscrivere il cubo nell'ottaedro, cos&igrave; dice: <lb/><emph type="italics"/>octo triangulorum centra continua per duodecim lineas, quippe quae et <lb/>latera inclusi cubi erunt.<emph.end type="italics"/> Quanto alle osservazioni poi del sale ridotto in <lb/>parallelepipedi, e alle marchesite in dodecaedri per opera di natura, delle <lb/>prime mi ricordo averne fatta osservazione molti anni sono. </s>

<s>Mi dice il signor <lb/>Antonio che nell'Istoria naturale di Ferrante Imperato vi si contengono rare <lb/>forme e stravaganti di varie pietre e minerali, dove trovansi ancora soggetti <lb/>per altre bellissime considerazioni &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, c. </s>

<s>146, 47). </s></p><p type="main">

<s>Quel signor Antonio, a cui il Ricci qui accenna, &egrave; l'aretino Nardi, au&shy;<lb/>tore delle <emph type="italics"/>Scene accademiche,<emph.end type="italics"/> in una delle quali fa delle Storie naturali <lb/>dell'Imperato, vedute da lui manoscritte, quell'elogio che i nostri lettori al&shy;<lb/>trove hanno inteso. </s>

<s>La notizia data da Antonio Nardi relativa alle descrizioni <lb/>de'cristalli, che si potevano leggere nell'opera manoscritta, faceva risalire a <lb/>un mezzo secolo innanzi quelle osservazioni, alle quali come nuovo si cre&shy;<lb/>deva d'essere entrato il Torricelli, e il giudizio dello stesso Nardi, dianzi ri&shy;<lb/>ferito dal Ricci, era giustamente fondato sopra ci&ograve;, che aveva letto nel li&shy;<lb/>bro XXIV delle dette Storie naturali, ai capitoli II, III e IV, dove intorno <lb/>alle cristallizzazioni, o agl'<emph type="italics"/>ingemmamenti,<emph.end type="italics"/> come gli chiama l'Autore, si leg&shy;<lb/>gono cose nuove per que'tempi, e tuttavia notabili per i nostri. </s></p><p type="main">

<s>Nel secondo di que'capitoli ora detti intitolato <emph type="italics"/>Variet&agrave; di figure negli <lb/>ingemmamenti,<emph.end type="italics"/> &ldquo; dunque nelle dette spezie, si legge, come anco in altre <lb/>differenze di pietre si veggono determinate maniere di consistenza e di figura, <lb/>e altre sono in figura di dado, come una spezie di marchesita, e il topazio <lb/>d'Alemagna, che se ne veggono molti ingemmamenti accostati insieme, per&shy;<lb/>ciocch&egrave; ciascun di essi &egrave; in forma di cubo, di cui un angolo affonda nella <lb/>madre, come radice nella terra. </s>

<s>Altre sono in forma dodecaedra, che &egrave; il <lb/>corpo composto di superfice cinquangole, qual'&egrave; l'ingemmamento dello sta&shy;<lb/>gno, ed una spezie di marchesita. </s>

<s>Altre sono in forma di colonnetta, che nel <lb/>suo fine s'appunta, come alcune spezie di cristalli; altri in forme pirami&shy;<lb/>dali &rdquo; (Venezia 1672, pag. </s>

<s>558, 59). </s></p><p type="main">

<s>Nel capitolo III, intitolato <emph type="italics"/>Cristallo e figure diverse cristalline,<emph.end type="italics"/> il no&shy;<lb/>stro Autore, in mezzo alla predominante ipotesi pliniana, cos&igrave; scrive della <lb/>natura e dell'origine dei cristalli: &ldquo; Il cristallo &egrave; spezie d'ingemmamento <lb/>duro, di chiarezza e trasparenza perfetta, simile nell'effigie ad acqua agghiac&shy;<lb/>ciata, limpida. </s>

<s>Si apprende in gemme nell'umor petrigno, non altrimenti che <lb/>gli zuccheri e sali negli umori della lor sostanza partecipi: s'ingemma e <lb/>vegeta in figura seangola &rdquo; (ivi, pag. </s>

<s>559). </s></p><pb xlink:href="020/01/1722.jpg" pagenum="597"/><p type="main">

<s>Se in questo capitolo dice l'Imperato cose, che porgerebbero secondo <lb/>il Nardi <emph type="italics"/>soggetto per altre bellissime considerazioni,<emph.end type="italics"/> nel seguente cap. </s>

<s>IV <lb/>descrive quelle <emph type="italics"/>Forme cristalline diverse,<emph.end type="italics"/> che al Nardi stesso parvero <emph type="italics"/>rare <lb/>e stravaganti.<emph.end type="italics"/> &ldquo; Sono altre spezie cristalline tra le quali l'una &egrave; che, con <lb/>la fattezza e progresso delle punte, rassembra un riccio marino, di cui cia&shy;<lb/>scun raggio &egrave; in forma di colonnetta seangola, che nel suo fine s'appunta: <lb/>nasce nelli sassi delle vene piombine. </s>

<s>Simili alli raggi detti si ritrovano altri <lb/>ingemmamenti di lunghezza e grossezza, che giungono al dito umano, in <lb/>figura seangola, che nello stremo s'appunta, ed avviene che ad una colon&shy;<lb/>netta maggiore s'attacchino alle volte d'intorno molte colonnette minori. </s>

<s><lb/>Sono dette colonnette di trasparenza e chiarezza notabili ... Oltre delle dette <lb/>sono le forme olivari, con numero di sei facce e grossezza delle colonnette <lb/>dette, ma diverse nell'essere dall'una e l'altra parte appuntate nel modo di <lb/>nocciolo.... Vi sono altre forme cristalline, tra le quali &egrave; l'ingemmamento <lb/>in forma di pigna, perciocch&egrave;, siccome nel frutto pineo nascono dal torso <lb/>di mezzo le squame ristrette insieme nelli piccoli, ed ingrossan di mano in <lb/>mano sinch&egrave; vengano nelli nodi apparenti; nell'istesso modo li rai di questa <lb/>spezie cristallina si partono da principii ristretti, ingrossandosi fino alla prima <lb/>parte apparente, ove si distingue la loro forma seangola, ed indi finalmente si <lb/>appuntano in forma piramidata nell'istesso numero di facce &rdquo; (ivi, pag. </s>

<s>560). </s></p><p type="main">

<s>Quando nel 1668 lo Stenone, in appendice alla descrizione anatomica <lb/>del capo della Carcaria, avea avanzate quelle sue prime congetture geologi&shy;<lb/>che, per le quali veniva ad iniziarsi nell'Accademia fiorentina una nuova <lb/>scienza intorno alla struttura superficiale della terra, e alle produzioni mi&shy;<lb/>neralogiche di lei, n&egrave; ancora erano alla pubblica notizia queste cose scritte <lb/>dall'Imperato intorno alla natura e alle forme de'cristalli; il cardinale Leo&shy;<lb/>poldo, che aveva di cos&igrave; fatte carte manoscritte procurato diligente raccolta, <lb/>rileggendo un giorno la sopra citata lettera del Ricci mostr&ograve; alla presenza <lb/>del Viviani, dello Stenone e del Dati, una vivissima curiosit&agrave; di sapere quel <lb/>che nelle sue Storie avesse scritto, in quel soggetto cos&igrave; lodato dal Nardi, <lb/>lo sconosciuto Naturalista napoletano. </s>

<s>Allora il Dati, ch'era stato generoso <lb/>d'offerire allo Stenone, accademico collega suo, inciso in rame il capo della <lb/>Lamia, disse che, fra gl'iconismi illustrativi della medesima Metalloteca va&shy;<lb/>ticana, n'erano parecchi altri rappresentanti variatissime figure di minerali, <lb/>bench&egrave; avesse l'Autore lasciato di descriverle, forse perch&egrave; non ebbe tempo <lb/>di dar perfezione all'ultimo Armario, a cui si dovevano riferir senza dub&shy;<lb/>bio quegli stessi iconismi. </s>

<s>Entrati a questa notizia col cardinale Leopoldo, <lb/>lo Stenone e il Viviani in gran desiderio di vederli, il Dati stesso present&ograve; <lb/>nell'Accademia que'cinque bellissimi rami incisi, e le impressioni de'quali <lb/>posson ora tutti vedere eseguite da pag. </s>

<s>372-77 dell'edizi&ograve;ne dell'opera del <lb/>Mercati, con tanto amore e con tanta scienza curata dal Lancisi. </s></p><p type="main">

<s>A pagina 372 &egrave; rappresentata una figura cristallina ottaedrica, la quale <lb/>grandeggia scolpita in mezzo ad altre pi&ugrave; piccole isomorfe, incise nel me&shy;<lb/>desimo rame, a illustrare la qual figura il Lancisi stesso cos&igrave; scrive in nota: <pb xlink:href="020/01/1723.jpg" pagenum="598"/>&ldquo; Figura haec adamussim exprimit formam aluminis octaedricam, quam <lb/>Auctor fortasse, postquam librum hunc conscripsisset, oblata occasione obser&shy;<lb/>vavit, atque proinde incidendam curavit, ideo nihil mirum si in capite <emph type="italics"/>De <lb/>alumine<emph.end type="italics"/> huic iconi spatium non reliquerit. </s>

<s>&rdquo; A pag. </s>

<s>374, nel rame su cui <lb/>furono incise varie forme cristalline appartenenti a varie specie di minerali, <lb/>tutti per&ograve; di un medesimo tipo, &egrave; sotto scolpita l'iscrizione <emph type="italics"/>Lapis multan&shy;<lb/>gulus<emph.end type="italics"/> e <emph type="italics"/>Lapis crystallinus <foreign lang="greek">poluecago<gap/>w</foreign>;<emph.end type="italics"/> son le parole che si leggono scolpite <lb/>sotto l'altro rame impresso a pag. </s>

<s>376 rappresentante un bellissimo gruppo <lb/>di cristalli simili a quel topazio di Alemagna, di cui diceva l'Imperato <emph type="italics"/>ve&shy;<lb/>dersi molti ingemmamenti accostati insieme, perciocch&egrave; ciascuno di essi &egrave; <lb/>in forma di cubo, di cui un angolo affonda nella madre, come radice <lb/>nella terra.<emph.end type="italics"/> A pag. </s>

<s>377 un altro rame rappresenta varie modificazioni delle <lb/>figure di quel cristallo &ldquo; qui componitur, secondo ch'esprimesi lo Stencne, <lb/>ex duabus pyramidibus hexagonis, et columna intermedia itidem hesagona &rdquo; <lb/>(Prodromus cit., pag. </s>

<s>37). Il Mercati lo chiama <emph type="italics"/>Lapis diconus,<emph.end type="italics"/> e il Lancisi <lb/>appone in nota: &ldquo; Qui hic lapis diconus a Mercato inscribitur extat apud <lb/>Imperatum nomine <emph type="italics"/>Ingemmamenti cristallini olivari ed appuntati in ambo <lb/>le parti. </s>

<s>&rdquo;<emph.end type="italics"/> L'ultimo iconismo cristallografico Vaticano ricorre nella medesima <lb/>pagina sotto il precedente, e nello stesso rame &egrave; fatta incidere l'iscrizione: <lb/><emph type="italics"/>Adamantes sponte Naturae formati.<emph.end type="italics"/></s></p><p type="main">

<s>A tal vista e a tali presentissimi esempi della geometrizzante Natura il <lb/>Viviani e lo Stenone si sentirono nascere un desiderio vivissimo di quelli <lb/>studii, a cui le parole del cardinale Leopoldo venivano ad aggiungere sti&shy;<lb/>moli potentissimi. </s>

<s>Degli esercizi cristallografici del primo non abbiamo altro <lb/>documento che in qualche notarella manoscritta, come per esempio sarebbe <lb/>questa: &ldquo; I diamanti rozzi, che si trovano in alcuni monti d'Armenia ed <lb/>altrove, hanno tutti figura di ottaedro &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>5). <lb/>Ma le speculazioni del Viviani uscirono associate con quelle dello Stenone, <lb/>il quale, nel Prodromo <emph type="italics"/>De solido intra solidum naturaliter contento,<emph.end type="italics"/> sta&shy;<lb/>bil&igrave; i nuovi fondamentali principii alla Cristallografia. </s></p><p type="main">

<s>Muovono le speculazioni stenoniane dal fatto che in un medesimo li&shy;<lb/>quido posson formarsi cristalli di figure diverse, d'onde ne conseguiva che <lb/>il moto della cristallizzabile materia &ldquo; quo versus iam formatae crystalli plana <lb/>determinantur, non oritur a communi quadam causa motus in fluido am&shy;<lb/>biente, sed in qualibet crystallo mutatur &rdquo; (pag. </s>

<s>42). Le figure dunque per <lb/>ciascun cristallo sono prestabilite dalla Natura, e non resta a investigare alla <lb/>scienza se non che le ragioni e i modi, come la materia si dispone in quelle <lb/>date inclinazioni di linee e di piani, e s'aggiunge via via allo stesso prefor&shy;<lb/>mato cristallo per ridurlo al suo ordinario incremento. </s>

<s>Si riconoscono dallo <lb/>Stenone quelle ragioni e que'modi in due speciali virt&ugrave;, una delle quali dia <lb/>regola, e l'altra impulso meccanico al moto. </s>

<s>Crede che la prima dipenda da <lb/>un fluido sottile, esalante dallo stesso nucleo cristallino, come quello che <lb/>esala dal magnete; la seconda poi da null'altro pensa provenire, che dal <lb/>turbato equilibrio idrostatico del liquido ambiente. </s>

<s>&ldquo; In crystalli incremento <pb xlink:href="020/01/1724.jpg" pagenum="599"/>geminus motus considerandus est: unus quo efficitur ut certis crystalli locis <lb/>et non aliis apponatur materia crystallina, quem ego motum permeanti fluido <lb/>subtili adscribendum suspicor, et allato magnetis exemplo illustrandum; alter <lb/>quo apposita crystallo nova materia crystallina in planum extenditur, qui a <lb/>fluido ambiente determinandus est. </s>

<s>Sic ubi super magnetem exsurrexerint <lb/>fila ferrca, aeris motu quod ab uno decutitur alteri accedit &rdquo; (pag. </s>

<s>43, 44). </s></p><p type="main">

<s>Di qual natura sia il fluido sottile rassomigliato al magnetico, dalla po&shy;<lb/>larit&agrave; del quale dipendono le regolate e invariabili inclinazioni delle linee <lb/>e de'piani cristallini, lo Stenone espressamente non dice, ma s'intende esser <lb/>l'etere, da cui faceva anche il Newton nascere l'attrazione molecolare. </s>

<s>Co&shy;<lb/>munque sia, crede il Nostro che per opera di quel fluido etereo si facciano <lb/>le rifrazioni, bench&egrave; lasci decidere la questione a ingegni pi&ugrave; sottili. </s>

<s>&ldquo; An <lb/>dictum fluidum illud sit cuius ope refractio peragitur, an vero fluidum ali&shy;<lb/>quod sit inde diversum, ingeniosioribus examinandum relinquo &rdquo; (pag. </s>

<s>42). </s></p><p type="main">

<s>Trasparisce di qui, come da un rado velo, la figura del Viviani, a cui <lb/>sempre era solito di rimettersi lo Stenone, quando troppo addentro entra&shy;<lb/>vasi nelle sottigliezze geometriche. </s>

<s>Di questa causa delle rifrazioni, dipen&shy;<lb/>denti da un fluido etereo, che s'impola nei cristalli, ne scrisse poco dopo <lb/>lo stesso Viviani a Erasmo Bartholin, quando questi gli annunzi&ograve; la sco&shy;<lb/>perta della duplice refrazione, che subisce il raggio incidente attraverso allo <lb/>spato d'Islanda. </s>

<s>Il Bartholin ben conobbe che nelle diottriche speculazioni <lb/>del Geometra fiorentino si troverebbe non difficilmente la ragione del nuovo <lb/>fatto spettacoloso, ond'&egrave; che, a sollecitar l'amico a studiar meglio la cosa, <lb/>dietro le pi&ugrave; precise osservazioni riscontrate con l'esperienza, gli mandava <lb/>a Firenze, il d&igrave; 23 Aprile del 1672, l'opuscolo sull'inusitata refrazione, con <lb/>un frustolo del cristallo che la produce. </s>

<s>&ldquo; Mitto opusculum de crystallo quo&shy;<lb/>dam islandico, figurae et refractionis inusitatae, una cum frustulo eiusdem <lb/>crystalli, cuius phaenomena nemo te magis mirabitur, qui naturam refrac&shy;<lb/>tionum optime calles &rdquo; (MSS. Gal., T. CXLV, c. </s>

<s>222). Da questo lampeg&shy;<lb/>giar d'idee intorno alle propriet&agrave; diottriche dei cristalli s'intravede quell'am&shy;<lb/>pia e intensa cultura, che sarebbesi data nell'Accademia del Cimento alla <lb/>Cristallografia, se avesse per avventura avuto effetto la divisata Dissertazione <lb/>stenoniana, della quale sola ci &egrave; rimasto il Prodromo. </s></p><p type="main">

<s>Proceduti fin qui, non possiamo non soffermarci a indagare i segreti <lb/>sentimenti, che avranno suscitato queste storie nell'animo de'nostri Lettori, <lb/>ne'quali, anche Italiani, &egrave; oramai ingerita la persuasione che, fatto il prin&shy;<lb/>cipe Leopoldo cardinale, si chiudessero le porte alla gloriosa Accademia. </s>

<s>In <lb/>ogni modo, specialmente gli stranieri, attribuiranno a uno de'soliti vanti <lb/>esagerati il dire che la Geologia e la Cristallografia, fra gli autori delle quali <lb/>&egrave; un miracolo a sentire oggid&igrave; pronunziare un nome italiano, furono due <lb/>scienze istituite nella nostra Accademia del Cimento. </s>

<s>Ma perch&egrave; son le no&shy;<lb/>stre asserzioni fondate sempre sopra documenti certissimi, non resta agli <lb/>oppositori a far altro, se non che a dimostrare come quegli stessi documenti <lb/>sono stati da noi o male intesi, o male applicati. </s></p><pb xlink:href="020/01/1725.jpg" pagenum="600"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>In tanto che la Critica (se pure la non ha da pensare ad altro che a <lb/>queste cose) attender&agrave; a trovare argomenti da negare o da riformare la sto&shy;<lb/>ria qui addietro da noi narrata, procedendo addiritto per le nostre vie, pas&shy;<lb/>seremo a dir dell'origine e dei progressi, che fece la Cristallografia fuori <lb/>dell'Accademia del Cimento. </s>

<s>E quanto all'origine, a noi par che non prima <lb/>distintamente apparisca che nelle pagine del Cesalpino, il quale osserva che, <lb/>nello scindere i corpi duri, alcune particelle escono naturalmente ordinate, <lb/>come in quelli che si risolvono in scaglie, altre irregolari, come avvien per <lb/>esempio quando si rompe un sasso a furia di colpi da una mazza di ferro. <lb/></s>

<s>&ldquo; Potest vero, poi soggiunge, et divisio fieri in coagulatione, dum humida <lb/>adhuc sunt corpora. </s>

<s>Si enim in coagulatione partes in diversa tendant, di&shy;<lb/>visionem fieri necesse est, et pro divisione figuras determinatas, perinde ac <lb/>in exsiccatione soli palustris, scinditur enim in multas rimas, unde figurae <lb/>diversae contingunt. </s>

<s>Simile quid contingere putandum est in crystalli coa&shy;<lb/>gulatione. </s>

<s>Succus enim lapidescens cum totum spacium impleat loci in quo <lb/>est, in coagulatione discedentibus in diversa partibus terrenis, et ad latera <lb/>saxi continentis attractis agglutinatisque, figuram quoque faciet in concretis <lb/>lapillis, quae apta nata sit spacium replere. </s>

<s>Si igitur non uniformiter, sed <lb/>vario modo divisiones contingunt, etiam varietate figurarum implebitur spa&shy;<lb/>cium. </s>

<s>Si autem uniformiter, quod ob puritatem succi contingit, necesse est <lb/>unum genus figurae oriri in omnibus, quae apta nata sit spacium implere &rdquo; <lb/>(De metallicis cit., pag. </s>

<s>97, 98). </s></p><p type="main">

<s>Le figure geometriche atte nate a riempire senza vuoto intermedio uno <lb/>spazio, prosegue a dire il Cesalpino, son tre: il triangolo, il quadrato e l'esa&shy;<lb/>gono. </s>

<s>Ma perch&egrave; la concrezione di quel succo lapideo, che si suppone esser <lb/>purissimo, si fa per una occulta tendenza verso il centro, egli &egrave; questo stesso <lb/>centro troppo remoto dagli angoli di un quadrato composto di quattro altri <lb/>quadrati accostati insieme. </s>

<s>Dall'altra parte ad accostare insieme tanti trian&shy;<lb/>goli equilateri, che s'appuntino essi pure in un centro comune, non viene <lb/>a comporsi un nuovo triangolo, ma un esagono, &ldquo; relinquitur igitur ut sola <lb/>hexagona fiat &rdquo; (ibid., pag. </s>

<s>98). </s></p><p type="main">

<s>Citava in proposito il nostro Peripatetico l'autorit&agrave; del Maestro, che <lb/>nel III <emph type="italics"/>De coelo<emph.end type="italics"/> avea cos&igrave; scritto: &ldquo; In planis tres figurae videntur implere <lb/>locum, triangulus, quadratus et sexangulus &rdquo; (Arist., Op., T. V, Venetiis 1560, <lb/>fol. </s>

<s>229). Ma trattandosi di una questione geometrica, si sovvennero i lettori <lb/>di quel che, intorno alle propriet&agrave; degl'isoperimetri, aveva dimostrato, nel <lb/>V libro delle <emph type="italics"/>Collezioni matematiche,<emph.end type="italics"/> Pappo Alessandrino. </s>

<s>Nella prefazione <lb/>al libro, che Federigo Commandino urbinate avea divulgato in lingua latina, <lb/>il Matematico antico richiamava l'attenzione di suo figlio Ermodoro e dei let-<pb xlink:href="020/01/1726.jpg" pagenum="601"/>tori sul maraviglioso artificio geometrico dei favi. </s>

<s>Crede che, avendo Dio sa&shy;<lb/>pientissimo infusa l'intelligenza nelle api, esse scegliessero quella struttura <lb/>esagonale per riuscire a due principali intenti, quali erano di riporre il miele <lb/>in celle della pi&ugrave; capace figura e tale, che permettesse di accostarsi alle altre <lb/>simili celle, senza lasciarvi alcuno spazio vuoto intermedio, dove s'avessero <lb/>a introdurre esseri o elementi nocivi. </s>

<s>Bench&egrave; dunque tra le figure isoperi&shy;<lb/>metre la nostra scienza geometrica, dice Pappo, dimostri essere il circolo la <lb/>pi&ugrave; capace di tutte, le api nulladimeno, le quali non hanno in mente altro <lb/>che l'utilit&agrave; e la fuga dai pericoli, si condussero a eseguire per matematica <lb/>necessit&agrave; la figura esagonale. </s>

<s>&ldquo; Cum igitur tres figurae sint, quae per seipsas <lb/>locum circa idem punctum consistentem replere possunt, triangulum scilicet, <lb/>quadratum et hexagonum, apes illam quae ex pluribus angulis constat, ad <lb/>structuram sapienter delegerunt, utpote suspicantes eam plus mellis capere <lb/>quam utramque reliquarum. </s>

<s>Et apes quidem illud tantum, quod ipsis utile <lb/>est cognoscunt, videlicet hexagonum quadrato et triangulo esse maius, et <lb/>plus mellis capere posse, nimirum aequali materia in constructionem uniu&shy;<lb/>scuiusque consumpta. </s>

<s>Nos vero, qui plus sapientiae quam apes hebere pro&shy;<lb/>fitemur, aliquid etiam magis insigne investigabimus. </s>

<s>Figurarum enim plana&shy;<lb/>rum, quae cum aequilaterae et aequiangulae sint ambitum aequalem habent, <lb/>ea semper maior est, quae ex pluribus angulis constat, circulus vero omnium <lb/>est maximus, si modo aequali ipsis ambitu comprehendatur &rdquo; (Bononiae 1660, <lb/>pag. </s>

<s>114). </s></p><p type="main">

<s>Queste idee applicate all'ipotesi cristallogenica del Cesalpino ingerirono <lb/>facilmente l'opinione che, infusa la Divina Sapienza come nelle api cos&igrave; nel <lb/>succo lapideo, questo nel coagularsi in cristalli, per non lasciare gli spazii <lb/>vuoti e per adattarsi in luogo della maggior possibile capacit&agrave;, fosse neces&shy;<lb/>sariamente condotto a prendere struttura esagonale. </s></p><p type="main">

<s>Eran tali le meno irragionevoli dottrine professate intorno alla Cristal&shy;<lb/>lografia, sui principii del secolo XVII, quando il Keplero scopr&igrave; quella me&shy;<lb/>desima struttura esagonale ne'fiocchi della neve. </s>

<s>La cosa apparve nuova e <lb/>inaspettata, perch&egrave; lo stesso Cesalpino aveva giusto negato essere i cristalli <lb/>acqua congelata, fra le altre, principalmente per questa ragione, perch&egrave; il <lb/>ghiaccio non piglia mai figura sessangolare &ldquo; sed figuram conservat vel con&shy;<lb/>tinentis corporis vel rotundam, aut fortuitam, qualis est in gutta cum in <lb/>grandinem congelatur &rdquo; (De met. </s>

<s>cit., pag. </s>

<s>96). </s></p><p type="main">

<s>&Egrave; notabile, ci permettano i lettori la breve digressione, che ottantun'anno <lb/>dopo il Keplero Gian Domenico Cassini si credesse di essere stato il primo <lb/>ad osservare un'altra cosa nuova e inaspettata nelle figure della neve, ma <lb/>&egrave; ben assai pi&ugrave; notabile che fosse la novit&agrave; accolta, e come tale divulgata <lb/>dall'Accademia parigina. </s>

<s>&ldquo; Il y a long-tems que l'on s&ccedil;ait que la neige est <lb/>exagone: mais on n'avoit peut &ecirc;tre point encore observ&eacute; que les six rayons <lb/>dont chaque floccon est compos&eacute;, sont souvent comme autant de petites <lb/>branches garnies de fevilles, et que quelques floccons forment comme une <lb/>espece de fleur. </s>

<s>Ce que M. </s>

<s>Cassini a remarqu&eacute; en considerant avec un mi-<pb xlink:href="020/01/1727.jpg" pagenum="602"/>croscope la neige, qui tomba le premier jour de ce mois (Fevrier 1692). Il <lb/>ne se trouve pas ici assez de place pour en faire la description, mais les <lb/>deux figures, que l'on en donne, feront comprendre tout d'un coup ce qu'un <lb/>long discours ne pourroit peut-&egrave;tre pas si bien expliquer &rdquo; (Collection academ., <lb/>T. I, a Djion 1754, pag. </s>

<s>261, 62). Le due accademiche figure per&ograve; non giun&shy;<lb/>sero per nulla nuove a chi, infin dal 1661, ne avea vedute elegantemente <lb/>impresse ben sei di quelle medesime stelle piumate o di quelle rosette fio&shy;<lb/>rite nella tavola che precede al trattato <emph type="italics"/>De figura nivis<emph.end type="italics"/> di Erasmo Bartho&shy;<lb/>lin. </s>

<s>Ma pi&ugrave; s'ebbero a maravigliare della nuova proposta coloro, che nello <lb/>schematismo VIII della Micrografia dell'Hook, pubblicata nel 1665, s'erano <lb/>trattenuti a contemplare il maraviglioso spettacolo di quelle ventotto e pi&ugrave; <lb/>figure, rappresentanti in vario modo la neve nelle sue stelle cristalline e <lb/>ne'fiori. </s></p><p type="main">

<s>Il Keplero, che non aveva allora i necessarii diottrici strumenti, non <lb/>giunse a penetrare una cos&igrave; sottile e complicata struttura, tutto intento dal&shy;<lb/>l'altra parte ad usar le sottigliezze del suo ingegno geometrico in ricercar <lb/>l'origine nella neve di que'sei perfettissimi raggi di stella, sufficienti per s&egrave; <lb/>soli ad eccitare ne'contemplanti la maraviglia. </s>

<s>Le correnti opinioni, che si <lb/>diceva di sopra, gli fecero prima rivolgere il pensiero agli apiarii, ma la ra&shy;<lb/>gione che s'adduceva dalla geometria di Pappo non sembravagli concludente, <lb/>perch&egrave; diceva che, se gl'industriosi insetti avessero voluto veramente eleg&shy;<lb/>gere le celle pi&ugrave; capaci, sarebbero dovuti andare a formarle circolari, senza <lb/>badar tanto all'economia dello spazio, quasi che in tutto l'alveare non ne <lb/>rimanesse altro che quello. </s>

<s>&ldquo; Sed non sufficit haec ratio, nam si capacita&shy;<lb/>tem quaerunt, cur non quaelibet sibi rotumdum fingit nidum? </s>

<s>quid opus <lb/>est minutias loci consectari, quasi nullum in toto alveari restet spacium? </s>

<s>&rdquo; <lb/>(De nive sexangula, Francofurti 1611, pag. </s>

<s>11). </s></p><p type="main">

<s>Si presentavano, insieme con questo delle api, a considerare al Keplero <lb/>altri simili esempi, come quello de'grani chiusi nelle mele granate che tutti <lb/>si trovano anch'essi in figura di poliedri regolari. </s>

<s>Parendo inconveniente <lb/>agli alberi un'anima, come una intelligenza alle api, fu anzi questo secondo <lb/>fatto, riconosciuto aver la sua causa nella compressione, che crescendo si <lb/>fanno gli stessi grani, rinchiusi nella mela, a vicenda; fu questo fatto di&shy;<lb/>ciamo che indusse esso Keplero ad attribuire a una simile compressione la <lb/>figura esagonale, che vengono a prendere le celle ceree de'favi, sostituendo <lb/>nell'un caso e nell'altro alla elezion della mente un ceca necessit&agrave; della ma&shy;<lb/>teria. </s>

<s>&ldquo; Has igitur rationes materialem necessitatem respicientes puto suffi&shy;<lb/>cere ut hoc loco non existimem philosophandum de perfectione et pulchri&shy;<lb/>tudine, vel nobilitate figurae rhombicae, neque satagendum ut esseutia ani&shy;<lb/>mulae, quae est in ape, ex contemplatione figurae quam fabricatur, eliciatur. </s>

<s><lb/>Idem de malo punico intelligendum. </s>

<s>Apparet necessitas materialis, quae <lb/>acinos producit ad rhombicum succedente incremento. </s>

<s>Itaque vanum est de <lb/>essentia animae in hac arbore cogitare, quae rhombicum potissimum effi&shy;<lb/>ciat &rdquo; (ibid.). </s></p><pb xlink:href="020/01/1728.jpg" pagenum="603"/><p type="main">

<s>Dagli alveari e dai pomi granati passando al propostosi soggetto, do&shy;<lb/>mandava a s&egrave; medesimo il Keplero se a una simile necessit&agrave; materiale si <lb/>dovessero attribuir le figure impresse nella neve. </s>

<s>Si risovvenne, in mezzo a <lb/>queste dubbiose ricerche, di quel che aveva sentito dire ad alcuni gioiellieri, <lb/>che cio&egrave; si trovano i diamanti naturalmente lavorati in forma di perfettis&shy;<lb/>simo ottaedro. </s>

<s>Se ci&ograve; fosse vero, cos&igrave; ragionava, non sarebbe improbabile il <lb/>credere che fosse impressa nel vapore salito dalla terra una figura regolare, <lb/>simile a quella che impresse sottoterra al diamante, ricavandola dal suo fe&shy;<lb/>condissimo seno, la formatrice Natura. </s>

<s>&ldquo; Aiunt gemmarii naturalia in ada&shy;<lb/>mantibus inveniri octaedra perfectissimae et limatissimae formae. </s>

<s>Id si est, <lb/>multum nos confirmat. </s>

<s>Nam facultas animalis, quae in terra indidit adamanti <lb/>formam octaedri, ex penitissimo sinu suae naturae depromptam, eadem cum <lb/>vapore progressa de terra figuram eamdem indidit, et nivi ex vapore illo <lb/>consistenti &rdquo; (ibid., pag. </s>

<s>20). </s></p><p type="main">

<s>Parendogli pi&ugrave; ragionevole questa seconda ipotesi, volle il Keplero pa&shy;<lb/>ragonarla pi&ugrave; diligentemente con quella prima, e riconoscendo la debolezza <lb/>degli argomenti dedotti dalle figure geometriche, atte a riempire uno spazio, <lb/>per non rendersi chiara la ragione del doversi al triangolo e al quadrato <lb/>preferire l'esagono; e non potendosi persuadere perch&egrave; s'avesse dagli iso&shy;<lb/>perimetri a escludere in ogni modo il circolo, inclin&ograve; a credere che la figura <lb/>stellata della neve, come quella de'cristalli, non dipendesse da necessit&agrave; della <lb/>materia, ma che piuttosto risultasse tale e non altra perch&egrave; &ldquo; ipsa huius <lb/>formatricis natura in intimo sinu suae essentiae particeps est sexanguli &rdquo; <lb/>(ibid., pag. </s>

<s>22), </s></p><p type="main">

<s>Quella stessa Natura per&ograve;, che &egrave; cos&igrave; esperta ed esercitata della Geo&shy;<lb/>metria, non si restringe a una forma sola, com'&egrave; la sessangolare impressa <lb/>nella neve e l'ottaedrica nel diamante, ma varia il suo lavoro passando ad <lb/>altre forme, come alla dodecaedra e alla icosaedra, in ch'io vidi, dice il <lb/>Keplero, configurati alcuni esempi di minerali, visitando il Museo di Dresda. <lb/></s>

<s>&ldquo; Itaque verisimile est hanc facultatem formatricem pro diverso humore di&shy;<lb/>versam fieri &rdquo; (ibid., pag. </s>

<s>24). Concludendo poi il discorso per quel che <lb/>pi&ugrave; particolarmente concerne la neve, si rivolge ai Chimici, per proporre a <lb/>loro il quesito se forse anche in essa neve ritrovisi qualche sale, che la in&shy;<lb/>formi e la renda partecipe della sua propria figura. </s>

<s>&ldquo; Dicant igitur Chymici <lb/>an in nive sit aliquid salis, et quodnam salis genus, et quam illud alias in&shy;<lb/>duat figuram &rdquo; (ibid.). </s></p><p type="main">

<s>Cos&igrave;, intorno all'origine delle figure cristalline, proponeva il Keplero <lb/>due ipotesi: una che riconosceva quella stessa origine dalla necessit&agrave; della <lb/>materia, e l'altra che attribuiva il fatto all'essere le particelle materiali gi&agrave; <lb/>preformate in tale o tale altro modo dalle stesse mani geometrizzanti della <lb/>Natura. </s>

<s>Inclinava il Keplero stesso, com'abbiamo udito, a questa seconda <lb/>ipotesi, ma lasciava la decisione ai dotti, ch'ei comprendeva tutti nella per&shy;<lb/>sona di quel Giovan Matteo Wacker, a cui particolarmente, in trattar <emph type="italics"/>De <lb/>nive sexangula,<emph.end type="italics"/> rivolgeva il discorso. </s></p><pb xlink:href="020/01/1729.jpg" pagenum="604"/><p type="main">

<s>Uno de'principali fra que'dotti, che tornarono sull'argomento, fu nel <lb/>suo libro delle Meteore il Cartesio, il quale si sent&igrave; dal proprio genio por&shy;<lb/>tato a scegliere la prima ipotesi, perch&egrave; la seconda non lasciava gran campo <lb/>aperto ai giochi e alle arguzie dell'ingegno. </s>

<s>Dop'aver trovata e detta la ra&shy;<lb/>gione del mutare apparenza, che fanno i sei denti o le appuntate fila, delle <lb/>quali ogni globulo di neve s'irraggia, &ldquo; aegre tantummodo, poi soggiunge, <lb/>poteram coniiciere quidnam in aere libero turbantibus ventis adeo accurate <lb/>hos sex dentes formare, et circa singula grana disponere potuisset, donec <lb/>tandem in mentem venit facillime fieri potuisse ut ventos nonnulla ex iis <lb/>granis versus aliquam nubem expulerit, eaque infra illam vel ultra suspensa <lb/>aliquandiu detinuerit, atque ibi procul dubio ita disponi debuisse, ut sin&shy;<lb/>gula sex aliis in eodem plano sitis cingerentur, quia talis est ordo naturae &rdquo; <lb/>(Dissertatio De methodo, Francofurti ad M. 1692, pag. </s>

<s>159). </s></p><p type="main">

<s>Che tale veramente sia l'ordine della Natura, che cio&egrave; intorno a ogni <lb/>granello ghiacciato se ne dispongano altri sei simili, d'onde venga a risul&shy;<lb/>tarne la desiderata figura esagonale, il Cartesio lo vede chiaro cos&igrave;, da non <lb/>aver bisogno di alcuna dimostrazione. </s>

<s>Ma Erasmo Bartholin attese appunto <lb/>a scrivere il suo Discorso <emph type="italics"/>De figura nivis<emph.end type="italics"/> per spiegar con geometriche de&shy;<lb/>scrizioni questo passo delle dottrine cartesiane. </s>

<s>Prese per esempio i favi del <lb/>miele e, supposte a principio le cellule circolari, dimostr&ograve; come intorno a <lb/>ciascuna cellula disponendosene altre sei compresse continuamente dall'ape, <lb/>ch'entra ed esce, per la duttilit&agrave; della cera, come per una necessit&agrave; della <lb/>materia, vengano esse cellule a stringersi l'una contro l'altra, riempiendo <lb/>gl'interstizi rimasti fra circoli e circoli, i quali perci&ograve; si trasformano in po&shy;<lb/>ligoni esagonali. </s></p><p type="main">

<s>Questa dimostrazione de'favi l'applic&ograve; il Bartholin, ci&ograve; che dall'altra <lb/>parte era il suo principale intento, alla neve, la quale egli col Cartesio cre&shy;<lb/>deva fosse conformata a principio in granuli o in glomi di ghiaccio, che, <lb/>premuti insieme dalla forza dei venti a contrasto della nube, venissero a <lb/>trasformare in esagono quel che intorno ad essi era prima un perfettissimo <lb/>cerchio. </s>

<s>&ldquo; Id enim in globulo cereo fieri animadvertimus. </s>

<s>Legibus hisce na&shy;<lb/>turae ratis per totum ambitum observans sex cuspides optime ordinari pos&shy;<lb/>sunt forma hexagona, qualem stellula refert. </s>

<s>Idque quod patitur unus glo&shy;<lb/>morum intelligimus de omnibus eadem ratione nubem constituentibus &rdquo; (De <lb/>figura nivis, Hafniae 1661, pag. </s>

<s>37). </s></p><p type="main">

<s>Non dubita il Filosofo e Matematico cartesiano di estendere questa me&shy;<lb/>desima generazion materiale alle figure, che prendono nel congelarsi i me&shy;<lb/>talli liquefatti, non per&ograve; gettati alla rinfusa, ma ne'debiti modi. </s>

<s>Soggiunge <lb/>anzi esser questa stessa la causa meccanica, che produce le figure geome&shy;<lb/>triche ne'cristalli, la materia lapidea de'quali, agitata da forze intestine, vien <lb/>compressa nelle varie sue parti. </s>

<s>&ldquo; Certe si plumbum liquefactum, ceram <lb/>aut quamcunque materiam mollem humidamque incertis legibus proijcias, <lb/>infinita genera figurarum irregularium describentur, sed si modulum adhi&shy;<lb/><gap/>ris accomodabunt sese ad datam formam, tepore languescentes partes, <pb xlink:href="020/01/1730.jpg" pagenum="605"/>obstante vel cogente duritie materiae. </s>

<s>Non secus evenit crystallis, salibus, <lb/>aliisque, ubi vis interna motum partibus addit, partes quoque singulae pres&shy;<lb/>sae invicem figuram ordinant &rdquo; (ibid., pag. </s>

<s>26, 27). </s></p><p type="main">

<s>Sarebbero forse prevalse queste cartesiane fantasie nella scienza, se una <lb/>maggiore autorit&agrave; di quella di Erasmo Bartholin non avesse richiamata l'at&shy;<lb/>tenzione de'Mineralogisti sopra quelle particole primigenie della materia, <lb/>uscite dal fecondo seno della formatrice Natura, e ad ammetter le quali tanto <lb/>inclinava il matematico ingegno di Giovanni Keplero. </s>

<s>Tommaso Willis, da <lb/>ci&ograve; che aveva letto in fine alla dissertazione <emph type="italics"/>De nive sexangula,<emph.end type="italics"/> che cio&egrave; le <lb/>figure della neve sieno forse dovute a un sale rimescolato fra gli elementi <lb/>dell'acqua, si condusse di speculazione in speculazione ad ammettere che si <lb/>debbano agli stessi sali, <emph type="italics"/>qui constanti ritu efformantur<emph.end type="italics"/> come gli avevano <lb/>dimostrato le varie esperienze, attribuire i principii formativi di tutti quanti <lb/>i corpi. </s>

<s>Ma perch&egrave; in alcuni di questi, come ne'vegetabili e negli animali, <lb/>son le figure assai pi&ugrave; varie e pi&ugrave; complicate, s'aggiunge la informatrice <lb/>virt&ugrave; dello spirito, ch'&egrave; rispetto al sale quel ch'&egrave; il compasso rispetto alla <lb/>riga nel descriver che fa il Geometra artificiosamente le sue figure. </s>

<s>&ldquo; Ete&shy;<lb/>nim, in corporum naturalium figuris determinandis, <emph type="italics"/>spiritus<emph.end type="italics"/> ac <emph type="italics"/>sal<emph.end type="italics"/> habent <lb/>se uti <emph type="italics"/>circinus<emph.end type="italics"/> ac <emph type="italics"/>regula<emph.end type="italics"/> in describendis figuris mathematicis &rdquo; (De fermen&shy;<lb/>tis, Op. </s>

<s>omnia, T. I, Lugduni 1681, pag. </s>

<s>60). Son dunque i sali, original&shy;<lb/>mente configurati dalla stessa Natura, dopo lo spirito, il secondo elemento <lb/>informativo della materia. </s>

<s>&ldquo; Sunt enim sales isti elementa velut secunda et <lb/>ab eorum in corporibus insitione propriae et nativae rerum figurae pluri&shy;<lb/>mum dependent, quare et ipsi configuratione quadam elementari primitus <lb/>a Natura imbuuntur &rdquo; (ibid.). </s></p><p type="main">

<s>Avevano le dottrine del Willis, come tutti i sistemi, assai dell'imma&shy;<lb/>ginario, ma da quella parte che insegnavano essere i sali originalmente pre&shy;<lb/>figurati, e non venuti a circoscriversi regolarmente a quel modo per neces&shy;<lb/>sit&agrave; materiale, eran vere, e conferirono a dimostrarle come tali gli Anatomici <lb/>nostri italiani scopritori dell'organo del gusto. </s>

<s>I sali artificialmente ricavati <lb/>dalle ceneri delle piante e dell'erbe, per lo pi&ugrave; comestibili agli uomini e <lb/>agli animali, lisciviate nella prima Accademia medicea, fecero balenare alla <lb/>mente di Lorenzo Bellini il pensiero, che le variet&agrave; degli angoli ora acuti, <lb/>ora ottusi, e delle superfice ora aspre, ora levigate, producessero la variet&agrave; <lb/>de'sapori, variamente titillando le papille nervee, ch'egli avea nuovamente <lb/>scoperte nella muccosa linguale. </s>

<s>Concorreva l'immaginazione a rendergli lo <lb/>spettacolo pi&ugrave; giocondo, lusingandolo di aver ritrovato, anche negli altri ge&shy;<lb/>neri di sali che si sentono al gusto dolci, amari, acri, salsi, acidi &ldquo; deter&shy;<lb/>minatam asperitatem aut levitatem, obtusulos angulos, acutulosve, plures <lb/>paucioresve cuspidulas easque breviores aut longiores &rdquo; (Gustus organum, <lb/>Bononiae 1665, pag. </s>

<s>67). </s></p><p type="main">

<s>Se riuscirono per&ograve; queste osservazioni immaginarie, e inutili a stabilir <lb/>la teoria fisiologica del senso, giovarono non poco ai progressi della Cristal&shy;<lb/>lografia, essendo stato il Bellini condotto a concluder da quelle stesse osser-<pb xlink:href="020/01/1731.jpg" pagenum="606"/>vazioni &ldquo; unumquemque salem certo quodam modo conformatum esse, et <lb/>talem hanc extimam habitudinem adeo sibi esse propriam et connaturalem, <lb/>ut nunquam eamdem posse exuere et sua sponte dum insensiles particulae <lb/>coagmentantur, invicem in eius figurae crassiuscusculam massam confluere &rdquo; <lb/>(ibid., pag. </s>

<s>66). </s></p><p type="main">

<s>A confermare questa importantissima conclusione soccorre opportuno, <lb/>prosegue a dire esso Bellini, il Microscopio, o come a lui piace meglio chia&shy;<lb/>marlo l'<emph type="italics"/>Engiscopio,<emph.end type="italics"/> il quale rivela in ogni frustolo di sale la figura impressa <lb/>a tutta intera la mole. </s>

<s>Non adducendo per&ograve; il Nostro della fatta esperienza <lb/>nessun esempio particolare, lasciava il campo aperto al Leeuwenhoeck, il <lb/>quale sper&ograve; a principio di coglier le figure distinte nelle minime particelle <lb/>saline, nell'atto stesso che vanno a deporsi giu dal liquido solvente. </s>

<s>Ma per&shy;<lb/>ch&egrave; non era da assicurarsi di aver veduto il vero, per le illusioni che la luce <lb/>attraversando il liquido poteva fare all'occhio; sul sal comune superficial&shy;<lb/>mente osservato, sul nitro, e con pi&ugrave; curioso spettacolo sopra lo zucchero <lb/>verific&ograve; l'esperienze microscopiche accennate dal Bellini. </s>

<s>&ldquo; Tum et istud cre&shy;<lb/>dendum est exigua salia, licet millies exiliora sint quam ut ope Microscopii <lb/>conspiciatur, figura tamen convenire cum salibus in molem capaciorem con&shy;<lb/>cretis, haud secum quam in sale communi, in nitro et in permultis salibus <lb/>evenire videmus. </s>

<s>Quin idem observatur in saccharo, quod vulgo candiense <lb/>vel creticum appellatur. </s>

<s>Cum enim saccarum illud, aeri prius humidiori <lb/>expositum, iterum in suppedaneo siccaretur, nonnunquam mulierculas de <lb/>obfuscato sacchari splendore conquerentes audivi. </s>

<s>Cum in obfuscationis istius <lb/>rationem inquirerem, animadverti sacchari superficiem ab aere humidiore <lb/>nonnihil resolutam vel liquefactam fuisse. </s>

<s>Dum autem per calorem ignis ite&shy;<lb/>rum duresceret, incredibilem exiguarum particularum copiam, quarum per&shy;<lb/>multae cum maioribus sacchari partibus figura conveniebant, spisseseendo <lb/>coivisse. </s>

<s>Haec vero exiguarum particularum imagines sacchari splendorem <lb/>obscurabat &rdquo; (Epistolae physiol., Epist. </s>

<s>XXII, Delphis 1719, pag. </s>

<s>200, 1). </s></p><p type="main">

<s>Carlo Fracassati &egrave; un altro degli anatomici, collega al Bellini nella sco&shy;<lb/>perta dell'organo del gusto, e con lui concorso a riconoscerne l'eccitamento <lb/>dalle particelle saline, di che si compongono i corpi saporosi. </s>

<s>Dalla fisiolo&shy;<lb/>gia trasportato anch'egli nel campo della cristallografia, non gli parve ra&shy;<lb/>gionevole ammettere l'ipotesi del Bartholin, per non veder come si possa a <lb/>molte figure cristalline applicare il meccanismo della struttura dei favi. </s>

<s>Non <lb/>si pu&ograve;, secondo lui, la questione risolvere altrimenti che per via delle os&shy;<lb/>servazioni microscopiche, e delle esperienze sopra la cristallizzazione, le quali <lb/>anche diligentemente instituite poco insegnerebbero, egli dice, &ldquo; ni creda&shy;<lb/>mus initio constitutum ut in rebus ipsis quaedam figura confletur, ac prae&shy;<lb/>sertim in salibus, quae perpetuo retineatur. </s>

<s>Haecque cum minima sit in pri&shy;<lb/>mis particulis ac moleculis, sensum eatenus deinde non fugiat, quatenus <lb/>mutua adaptatione in eadem semper conspiratione partium coordinatione <lb/>sensibilis ac eadem figura ex pluribus minimis emergat, adeo ut cubus <lb/>evidens minimis cubis originem debeat, et figura aliqua regularis a mi-<pb xlink:href="020/01/1732.jpg" pagenum="607"/>nimis eiusdem rationis resultet &rdquo; (De lingua, cum Malpighi, Op. </s>

<s>T. II cit., <lb/>pag. </s>

<s>184). </s></p><p type="main">

<s>Conferma il Fracassati il fatto di questa molecolare struttura ne'cri&shy;<lb/>stalli con pi&ugrave; ragioni, la prima e principale delle quali si desume dai corpi <lb/>organici, che si vedono essere anch'essi composti di molte altre pi&ugrave; piccole <lb/>membra simili, come per esempio le fibre muscolari e i lobi polmonari ri&shy;<lb/>sultanti dalla testura di moltissime altre pi&ugrave; piccole fibre, e di pi&ugrave; piccoli <lb/>lobi, secondo che poco fa ha dimostrato, egli dice, l'anatomia del Malpighi. </s>

<s><lb/>Questi dall'altra parte sono i modi tenuti dalla Natura, che dalle piccole cose <lb/>assorge alle grandi. </s>

<s>&ldquo; Igitur valde probabile videtur in multis, conciliante <lb/>assensum experimento, obviam rerum figuram, saliumque praecipue, simili <lb/>ac minime interius latitanti respondere &rdquo; (ibid.). </s></p><p type="main">

<s>Agli esperimenti, che conciliano assenso a queste cose, aggiunge il Fra&shy;<lb/>cassati quello del fuoco, il quale, essendo per la sua virt&ugrave; dissolvente cos&igrave; <lb/>efficace analista della materia, non &egrave; nulladimeno capace di distruggere le <lb/>latitanti particelle saline informatrici de'varii corpi. </s>

<s>Conchiude perci&ograve; da que&shy;<lb/>sto fatto, come da chiarissimo argomento, &ldquo; esse quasdam texturas primi&shy;<lb/>genias, quibus entia differant, quae alias convenirent, quarum coordinatio <lb/>debeat manere. </s>

<s>Inde sales forte in cineribus suis, licet passi sint ab igne, <lb/>ubi in aqua fluxerint, ad suam redeunt figuram. </s>

<s>Ipsa vegetabilia et mordi&shy;<lb/>cus se tueri videbis, ac factam ab igne divisionem umbratili parere coaliti <lb/>nemo, qui Vulcano mereat, redivivam e pulvere suo Quercetani rosam igno&shy;<lb/>rat, ut hoc portento e cineribus veram quilibet palingenesim possit suspi&shy;<lb/>cari. </s>

<s>Ipse Davissonus resinam abietinam distillaturus ad collum cucurbitae <lb/>imagines abictis affabre effietas notabat &rdquo; (ibid., pag. </s>

<s>185) </s></p><p type="main">

<s>Qui, dall'officina sperimentale del Fisico ci par essere trasportati nelle <lb/>sotterranee grotte del mago, alle incantazioni del quale non far&agrave; maraviglia <lb/>che rimanessero allucinati i peripatetici, se vi rimase cos&igrave; indegnamente preso <lb/>anche il Fracassati. </s>

<s>Filippo Bonanni, che fu de'peripatetici pi&ugrave; reputati a'suoi <lb/>tempi, ammettendo col Willis che si debbano alle insite particelle saline at&shy;<lb/>tribuir le figure varie de'corpi, non sapeva provar meglio l'assunta propo&shy;<lb/>sizione che con questi argomenti, i quali riferiremo qui con le stesse parole <lb/>dell'Autore, perch&egrave; servano di qualche ricreazione ai nostri affaticati lettori. <lb/></s>

<s>&ldquo; E per non porre qui quel tutto (dice nelle <emph type="italics"/>Osservazioni delle chiocciole,<emph.end type="italics"/><lb/>dop'aver testualmente riferita la sentenza del Willis) che lungamente vi sa&shy;<lb/>rebbe da scriverne in prova, baster&agrave; ricordare alcune sperienze, dalle quali <lb/>si ha che siccome estratto da qualche sostanza per via del fuoco il sale fisso <lb/>nelle ceneri, cos&igrave; il volatile ne'vapori forma la figura medesima in cui era. </s>

<s><lb/>E quanto al volatile, verissimo &egrave; che nelle fredde notti del verno fa una <lb/>foglia di ghiaccio su'vetri delle finestre coll'umido accidentale, che seco esce <lb/>da'rami verdi che si ardono, e stampa con essa l'immagine dell'albero onde <lb/>&egrave; tratto. </s>

<s>Quanto poi al fisso, vero &egrave; che abbruciandosi erbe o rami di al&shy;<lb/>bero e fattane acqua imbevuta del sale delle lor ceneri, se queste con quella <lb/>si porranno in un vaso aperto al sereno del verno che le aggeli, si vedr&agrave; <pb xlink:href="020/01/1733.jpg" pagenum="608"/>nella crosta del ghiaccio la figura dell'albero di cui &egrave; quella cenere. </s>

<s>Giovan <lb/>Daniello Horstio dal sale dell'assenzio vide nata l'immagine della sua pianta. </s>

<s><lb/>Olao Borricchio dal proprio sale trasse e di&egrave; a vedere ottimamente espressa <lb/>la figura d'una quasi selvetta di cipressi. </s>

<s>E lasciando quante altre riferir si <lb/>potrebbono tutte degne a sapersi, vaglia per tutte quella celebre, che v&agrave; per <lb/>bocca di molti col nome di <emph type="italics"/>Rosa polonica,<emph.end type="italics"/> mostrata al famoso Quercetano <lb/>da un Medico pollacco, il quale sapeva s&igrave; perfettamente estrarre i sali e con&shy;<lb/>servare gli spiriti delle piante in ampolle di vetro ben chiuse che, ricercato <lb/>di far germogliare una rosa, preso il vaso ove teneva chiuso il sale di questo <lb/>fiore, vi accost&ograve; la fiamma di una lucerna per intiepidirlo alquanto. </s>

<s>Allora <lb/>quella impalpabile cenere, mettendosi in moto, si vedeva sorgere e aprirsi in <lb/>una specie di rosa, che a poco a poco crescesse, rappresentando in s&egrave; tutte <lb/>le parti del fiore. </s>

<s>Quella ombratile figura per&ograve;, ricadendo la cenere in fondo, <lb/>si disfece, rimossa che fu dal vaso la fiamma &rdquo; (Roma 1681, pag. </s>

<s>303, 4). </s></p><p type="main">

<s>Il Bellini, giova dirlo per onor della scienza, sent&igrave; con il Fracassati che <lb/>sarebbe questa rinascenza dalle ceneri dimostrativa della indistruttibile figura <lb/>de'sali, <emph type="italics"/>si a veritate non recederet,<emph.end type="italics"/> cos&igrave; questo che si racconta della Rosa <lb/>polonica, con altri simili fatti, come l'olivo risorto nelle foglie e ne'rami <lb/>dall'olic rinchiuso in quella boccetta miracolosa data in dono a Ferdinando <lb/>Gonzaga. </s>

<s>&ldquo; Sed quidquid isthaec sint, seu vera seu falsa narrentur, &rdquo; con&shy;<lb/>clude esso Bellini (Gustus org. </s>

<s>cit, pag. </s>

<s>59), per dimostrar la primigenia e <lb/>indistruttibile figura de'sali non occorre andare a cercare altre prove, quando <lb/>il microscopio rivela quella stessa figura cos&igrave; evidente agli occhi di tutti. </s>

<s>Il <lb/>Leeuwenhoeck fece, come dicemmo, di questa evidenza di fatto promessa <lb/>dal Bellini pubblica e solenne testimonianza, ond'&egrave; che il Boerhaave defi&shy;<lb/>niva non molti anni dopo come cosa accertata oramai, e fuori di ogni con&shy;<lb/>troversia &ldquo; crystallisationem salium esse collectionem elementorum salino&shy;<lb/>rum eiusdem speciei in glebas unitas, et semper stabilis figurae, propriae <lb/>uni singulari sali &rdquo; (Elem. </s>

<s>Chemiae cit., T. II, pag. </s>

<s>334). </s></p><p type="main">

<s>Ci si permetta, a questo punto della nostra Storia, una breve sosta, per <lb/>considerare i fatti ora esposti, dai quali riconoscesi l'efficacia che, in pre&shy;<lb/>parar la certezza di questa boeraviana definizione, ebbe, contro le prevalenti <lb/>fantasie del Cartesio, la teoria fisiologica del gusto speculata dagli Anatomici <lb/>nostri italiani. </s>

<s>L'ipotesi per&ograve; del Bellini e del Fracassati, che cio&egrave; le varie <lb/>saporose affezioni si dovessero unicamente ai sali variamente configurati nei <lb/>cibi; ipotesi, che parve nata all'occasione della scoperta delle papille nervee <lb/>sopra la lingua, era fra noi alquanto pi&ugrave; antica, e risale forse alle prime <lb/>prove sperimenteli instituite in Firenze sui cos&igrave; detti sali faltizi. </s></p><p type="main">

<s>Comunque sia, di quell'immaginata causa delle varie figure saline in <lb/>produr sulla lingua le affezioni varie del gusto, ne discorreva, come di cosa <lb/>gi&agrave; convenuta, il Magalotti in una sua lettera scritta il d&igrave; 8 Gennaio 1660 <lb/>da Roma al priore Orazio Ricasoli Rucellai. </s>

<s>E perch&egrave; nelle eleganti parole <lb/>del Segretario della fiorentina Accademia si trovano accennate le principali <lb/>dottrine che, in mezzo al trionfante cartesianismo, si professavano allora dai <pb xlink:href="020/01/1734.jpg" pagenum="609"/>Nostri intorno alla natura de'sali, alle loro liquazioni e ad altri particolari ef&shy;<lb/>fetti; non dispiacer&agrave; di veder quelle stesse parole trascritte qui ai nostri Let&shy;<lb/>tori, i quali sentiranno gusto dell'ingegnose arguzie dell'Autore in risolvere <lb/>un problema curioso, in tempi, in cui la Fisiologia medica pur allora nasceva. </s></p><p type="main">

<s>Passato dunque da Firenze a soggiornare alquanto in Roma il nostro <lb/>conte Lorenzo, si trov&ograve; mal'affetto da una eruzione cutanea, che con i mo&shy;<lb/>lesti e dolorosi pruriti gli tolse affatto per pi&ugrave; notti la dolce quiete del sonno. </s>

<s><lb/>I medici l'attribuivano a un ribollimento di sangue, occasionato dal mutare <lb/>aria e cibi, e specialmente i vini, cos&igrave; gravi in Roma rispetto a quei cos&igrave; deli&shy;<lb/>cati di Firenze. </s>

<s>In una di quelle moleste notti perci&ograve;, tutta intera passata in&shy;<lb/>sonne, il Magalotti, riconoscendo essere il suo malore principalmente occasio&shy;<lb/>nato dai vini, ne specul&ograve; cos&igrave; il modo, come poi scrisse all'amico suo Rucellai: </s></p><p type="main">

<s>&ldquo; Noi vegghiamo per esperienze, diceva, non vi esser sostanza alcuna in <lb/>natura, da cui non si estragga il suo sale, e questo in ciascuna ritener co&shy;<lb/>stantemente una determinata figura. </s>

<s>Cosi riconosciamo non solo nei puri <lb/>sali, cio&egrave; a dire nel comune, nell'ammoniaco, nel nitro e nell'allume, ma <lb/>universalmente nell'erbe tutte e nelle piante, e talora nelle pietre, ne'mi&shy;<lb/>nerali, e finalmente nelle stesse gioie. </s>

<s>Siccome dunque di ciascheduna so&shy;<lb/>stanza &egrave; una sola determinata figura nelle particelle del suo sale, non sar&agrave; <lb/>lontano dalla probabilit&agrave; il credere che diverse viti possano avere diversit&agrave; <lb/>di figure ne'loro sali, perciocch&egrave;, se vorremo rifondere la differenza de'loro <lb/>sapori in quella di dette figure, bisogner&agrave; che queste sieno diversissime, e <lb/>niente meno differiranno fra loro le figure de'sali delle viti e dell'uve, di <lb/>ci&ograve; si differiscano da quelle d'alcun altro frutto, avvengach&egrave; assai minor di&shy;<lb/>vario sia tra i sapori del moscadello e d'un granato dolce, di quel che si <lb/>corra tra la nostra uva di messer Alemanno, ed un abrostino forte. </s>

<s>Ma <lb/>quand'anco V. S. Ill.ma volesse controvertermi questo ragionamento, della <lb/>verit&agrave; o falsit&agrave; del quale pur l'esperienza potrebbe chiarirci con l'estrazione <lb/>de'sali di varie viti o uve, e tuttavia volesse credere analoghe le figure dei <lb/>sali di tutte le uve di Europa e del mondo; non potr&agrave; V. S. Ill.ma negarmi <lb/>che diversi sieno i minerali, di cui son pregni i terreni sotto diversi climi. </s>

<s><lb/>Cos&igrave; la Tolfa ha miniere di allume, e senza estendere un minerale per tutto un <lb/>clima, che saria cosa ridicola, gli metto avanti tutti quei paesi, dove vi hanno <lb/>acque termali, e ritrover&agrave; che in un circuito di poche miglia, nella nostra <lb/>Toscana, ne abbiamo sopra quaranta vene tutte gravide di diverse miniere. </s>

<s><lb/>Sar&agrave; vero dunque che nell'uve d'un paese, e in quelle di un altro, si ritrovi <lb/>diversit&agrave; di sali, se non per loro natura, almeno per lo finissimo permischia&shy;<lb/>mento di quelli, che sono proprii de'minerali portati da questi terreni. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Considerata questa verit&agrave;, io considero ancora il vino, che &egrave; il liquore <lb/>che da quell'uva si spreme, gravido anch'egli de'medesimi sali. </s>

<s>E se un <lb/>vino si concede essere sparso di differenti sali da quei di un altro, se non <lb/>per loro natura, come dicemmo, almeno per l'infusione de'minerali suc&shy;<lb/>chiati dalla diversit&agrave; de'terreni; bisogner&agrave; dunque che, bevendosi una tal <lb/>sorte di vino, nel chilo ancora molto del suo sale si stemperi, e con esso <pb xlink:href="020/01/1735.jpg" pagenum="610"/>trapassi per le vene lattee e pe'vasi toracici, e finalmente entri anch'esso <lb/>in carriera con la massa del sangue a fare il suo corso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E consideri V. S. che, liquandosi un sale, e'non si fonde mica in <lb/>acqua o in altro umore pi&ugrave; tenue, ma e'si rimane nel primo esser suo uno, <lb/>incorruttibile ed eterno, cio&egrave; a dire in un atomo di una tal figura. </s>

<s>E perci&ograve; <lb/>quand'e'pare che un sale nell'acqua o in altro liquore si stemperi, non sono <lb/>gli atomi minimi figurati del sale quei che si struggono, ma si &egrave; la massa <lb/>del sale, che si fonde: cio&egrave; molti di quegli atomi minimi, che insieme uniti <lb/>e legati, nel lapillarsi, erano ricresciuti in corpicelli di figure similari, mol&shy;<lb/>lificandosi per via dell'umore quel glutine che in s&igrave; fatta guisa strignevali, <lb/>gli uni dagli altri si sciolgono, e mischiandosi fra atomo e atomo dell'acqua, <lb/>ossivvero ficcandosi tra'vacuetti e interstizii di quelli, per modo che poco o <lb/>nulla chiuggano il passaggio alla luce, che pur per quei vani passando facea <lb/>parer limpida e trasparente l'acqua; alla nostra vista s'occultano. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cos&igrave; per l'appunto, poich&egrave; e'sono mischiati col sangue, non altri&shy;<lb/>menti si liquano, ma ritengono tuttavia la loro figura, al modello della quale <lb/>vanno stampando il cavo per quei meati pi&ugrave; angusti, di dove e'passano <lb/>nel fare il corso della circolazione. </s>

<s>Venga ora un altro vino di differente <lb/>paese, colore e sapore, e perci&ograve; imbevuto e pregno di sali diversi Egli &egrave; <lb/>certo che ogni volta che questi non s'adattino con la loro figura al cavo o <lb/>alla stampa impressa da'sali di un altro vino in quelle venuzze sottilissime <lb/>capillari, incalzata con impeto la massa del sangue dove galleggiano dal moto <lb/>della sistole, dovranno in quelle violenti schizzature di sangue penetrare ad&shy;<lb/>dentro, e s&igrave; sforzare gli orifizi angustissimi ed i canali di quelle fila di vene, <lb/>incavandole d'altra forma per rendersele permeabili nel loro corso. </s>

<s>E suc&shy;<lb/>cedendo ci&ograve; no nei vasi pi&ugrave; grandi ma solo nelle vene finissime, sottilissime, <lb/>capillari ed esterne, quindi avviene che quivi si sentano le punture di que&shy;<lb/>gli aculei di sale, i quali moltissimi di essi, anzi che stamparle della loro <lb/>forma e figura, squarciandole si estrinsecano, e rimanendo fuori della vena <lb/>e del corso dell'altro sangue, restano sotto il velo sottilissimo dell'epider&shy;<lb/>mide con qualche stilla di sangue, derivata dal piccolo squarcio di quelle <lb/>fibre, s'infiammano e pungono, onde poi, col grattare rompendosi il sud&shy;<lb/>detto velo, si cava, dir&ograve; cos&igrave;, con quell'atometto di sale, quella spina che <lb/>punge &rdquo; (MSS. Cim., T. XXIV, c. </s>

<s>62, 63). </s></p><p type="main">

<s>Apparisce chiaro da questo documento come, infin da mezzo il se&shy;<lb/>colo XVII, si professasse con sicurezza in Firenze quella verit&agrave; dei nativi e <lb/>inalterabili elementi salini che, combattuta dai cartesiani e dai peripatetici, <lb/>si ridusse appena in salvo fra gl'insegnamenti del Boerhaave, alquanti anni <lb/>dopo il cominciar del secolo appresso. </s>

<s>Rimaneva in ogni modo a sapere <lb/>come si potessero comporre insieme gli stabili elementi salini a rappresen&shy;<lb/>tare la sempre stabile figura della gleba. </s>

<s>Il problema apparteneva alle ra&shy;<lb/>gioni della pura Geometria, e fu il primo a risolverlo geometricamente Gian <lb/>Domenico Guglielmini. </s>

<s>Ei riconobbe che le tante e s&igrave; varie figure dei sali <lb/>si potevano tutte ridurre a prismi e ad ottaedri, ossia a piramidi, essendo <pb xlink:href="020/01/1736.jpg" pagenum="611"/>chiaro ch'esso ottaedro risulta di due simili figure piramidali congiunte in&shy;<lb/>sieme per la superfice quadrata delle loro basi. </s>

<s>Mettersi a dimostrar che un <lb/>prisma si riduce in altri pi&ugrave; piccoli prismi sarebbe, dice il Guglielmini, &ldquo; un <lb/>accendere fiaccole al sole, posciach&egrave; ognun sa che i parallelepipedi, colle di&shy;<lb/>visioni eguali de'lati, delle basi e delle altezze, si dividono in altri simili ed <lb/>eguali fra di s&egrave;, onde di otto cubi piccoli se ne fa un grande di lato dop&shy;<lb/>pio ad uno de'primi; con ventisette se ne forma un altro triplicato pari&shy;<lb/>mente di lato, e cos&igrave; degli altri, il che s'adatta a spiegare la composizione <lb/>del Sal comune, del Sal gemma, di tutte le spezie di vitriolo e del tartaro. </s>

<s><lb/>E i prismi, come quello del Salnitro, sono composti d'altri pi&ugrave; piccoli di <lb/>base, o esagona o triangolare equilatera, posciach&egrave; in questa figura l'esa&shy;<lb/>gona si risolve, dai quali ordinatamente disposti, tanto nella base quanto nel&shy;<lb/>l'altezza, ne nascono i prismi esagoni osservati nel Nitro &rdquo; (Riflessioni filos. </s>

<s><lb/>delle figure dei sali, Bologna 1688, pag. </s>

<s>32). </s></p><p type="main">

<s>Pi&ugrave; difficile poteva sembrare la composizione piramidale della gleba, ri&shy;<lb/>sultante da pi&ugrave; piccole figure piramidali degli elementi salini, ed &egrave; perci&ograve; <lb/>che il Guglielmini si trattien pi&ugrave; di proposito in questo particolare, illu&shy;<lb/>strando in un'appendice geometrica questo suo, per s&egrave; dall'altra parte assai <lb/>spiegato discorso: &ldquo; Egli &egrave; chiaro, ei dice, che dividendo i lati d'un qua&shy;<lb/>drato secondo la stessa misura, e connettendo i punti corrispondenti de'lati <lb/>opposti con linee rette, resta esso spartito in piccoli quadretti tanti di nu&shy;<lb/>mero, quanto importa il quadrato delle misure di uno de'lati. </s>

<s>Quindi &egrave; che <lb/>dalla divisione in parti eguali resta divisa l'area del primo in quattro mi&shy;<lb/>nori quadretti, che ponno essere basi delle piramidi, che fra poco dirovvi. </s>

<s><lb/>Egli &egrave; altres&igrave; manifesto che dividendo i lati d'una piramide quadrata nel <lb/>mezzo, e facendo passare per li punti della divisione un piano, si lascia al <lb/>di sopra una piramide simile all'intera, ed eguale ad una di quelle, che <lb/>terminando colle loro cime ne'punti predetti, hanno per base uno de'pic&shy;<lb/>cioli quadrati che di sopra vi mentovava. </s>

<s>Queste co'loro vertici lasciano al <lb/>di sopra uno spazio simile ed eguale alla base di una di esse, dentro del <lb/>quale colla punta all'ingiu pu&ograve; situarsi un'altra piramide, di cui sulla base <lb/>rovesciata posa l'altra piramide eguale, che poco fa vi dissi essere tagliata <lb/>dal piano al di sopra. </s>

<s>Ecco adunque come di sei piramidi, quattro delle quali <lb/>restano situate colla sua base in un medesimo piano, un'altra rivoltata al&shy;<lb/>l'ingiu riempie parte dello spazio, che fra le quattro prime rimane, e l'ul&shy;<lb/>tima si posa sopra la base di questa; pu&ograve; formarsi una piramide maggiore <lb/>simile in tutto e per tutto a ciascuna delle componenti &rdquo; (ivi, pag. </s>

<s>22, 23). </s></p><p type="main">

<s>Cos&igrave;, congiunta alle fisiche osservazioni del Bellini e del Fracassati la <lb/>geometria del Guglielmini, venivano a stabilirsi, fuori dell'Accademia del <lb/>Cimento, le fondamenta alla scienza dei cristalli, per quel che particolar&shy;<lb/>mente concerne il materiale adattamento della loro figura. </s>

<s>Rimaneva a saper <lb/>ci&ograve; che, pur fuori dell'Accademia del Cimento, si pensasse intorno alla causa, <lb/>che dispone a configurarsi in tale e in tale altro modo le disperse parti&shy;<lb/>celle della materia. </s>

<s>Il Willis non par che attribuisse quella causa se non al <pb xlink:href="020/01/1737.jpg" pagenum="612"/>restringersi i pori del liquido di soluzione, per cui vengono gli elementi sa&shy;<lb/>lini ad accostarsi sempre pi&ugrave; strettamente fra loro, infin tanto che, per la <lb/>sopravvenuta azione del freddo prodottosi dallo stesso liquido evaporante, <lb/>non si riduce quel primo legger contatto a farsi pi&ugrave; stabilmente tenace. <lb/></s>

<s>&ldquo; Postea, si liquor iste aliquatenus evaporetur ut meatibus et poris eius <lb/>nonnihil constrictis salis corpuscula sibi invicem approximentur, se mutuo <lb/>prehendunt et externo frigore constipante una coeunt, et mediis in undis in <lb/>crystallos suae naturae proprias figurantur &rdquo; (De ferment. </s>

<s>cit., pag. </s>

<s>59, 60). </s></p><p type="main">

<s>Dell'esistenza di questi pori nel liquido, e della loro azione come ricet&shy;<lb/>tacoli del sale risoluto, avevano fatto soggetto alle loro prove sperimentali <lb/>gli Accademici fiorentini (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>639), i <lb/>quali, com'apparisce dai loro Diarii manoscritti, e specialmente da quello <lb/>raccolto nella Parte I del Tomo II, s'occuparono altres&igrave; d'investigar <emph type="italics"/>l'au&shy;<lb/>mento di peso specifico delle soluzioni.<emph.end type="italics"/> Ond'&egrave; che quel si riteneva dall'In&shy;<lb/>glese, e da tutti insieme con lui, per semplice ipotesi, i Nostri s'erano, infin <lb/>dal 1657, studiati di confermarlo coll'esperienze. </s></p><p type="main">

<s>Lo Stenone, come vedemmo, al vago nome di <emph type="italics"/>spirito<emph.end type="italics"/> immaginato dal <lb/>Willis sostitu&igrave; la pi&ugrave; probabile esistenza di un fluido etereo, e l'opera del <lb/>compasso, nel descriver le figure saline, pi&ugrave; propriamente la riconobbe nelle <lb/>polarit&agrave; magnetiche di quello stesso fluido, esalato dalla materia cristalliz&shy;<lb/>zante. </s>

<s>Neglettesi queste idee stenoniane, il Guglielmini se le rivide balenare <lb/>alla mente, quando pens&ograve; che le particelle figurate &ldquo; ponno ricevere il moto <lb/>o dal sole o dal lume, ne'corpi che sono senz'anima, o da questa in quelli <lb/>che ne sono dotati &rdquo; (ivi, pag. </s>

<s>32, 33). Se non fossero rimaste le tradizioni <lb/>della scienza italiana dannosamente chiuse fra le pareti dell'Accademia fio&shy;<lb/>rentina, il nostro Fisico di Bologna, che vedemmo in altre occasioni aver <lb/>idee a quelle del Newton cos&igrave; conformi, preveniva senza dubbio l'Inglese <lb/>nel dimostrare i principii dell'attrazione molecolare. </s>

<s>A questa egli invece, <lb/>prevalendo in Italia la dottrina galileiana della forza del vacuo, sostitu&igrave; la <lb/>pressione dell'aria, che attragga e tenga le molecole cristalline, come le cop&shy;<lb/>pette attraggon la carne o come si tengono insieme due lamine di vetro <lb/>lisce e talmente adattate, che non vi resti aria di mezzo. </s>

<s>&ldquo; Se adunque, egli <lb/>dice, vi prover&ograve; essere i pori del sale cotanto piccoli che neghino l'ingresso <lb/>all'aria, sar&agrave; la pressione di questa, esercitata egualmente per ogni verso, <lb/>la cagione dell'adesione delle di lui parti, bench&egrave; queste in sole linee una <lb/>coll'altra si tocchino &rdquo; (ivi, pag. </s>

<s>30). </s></p><p type="main">

<s>Venne poco dopo il Newton il quale, sperimentando che due lamine di <lb/>vetro lisce si tengono unite insieme anche nel vuoto, band&igrave; dalla Fisica l'ipotesi <lb/>galileiana, per mettere in pi&ugrave; chiara evidenza quella dello Stenone, le magne&shy;<lb/>tiche azioni speculate dal quale comparvero sotto la nuova forma delle attra&shy;<lb/>zioni e delle repulsioni molecolari. </s>

<s>L'applicazione di una tale dottrina neu&shy;<lb/>toniana alla Cristallografia consiste nel supporre che le particelle saline, <lb/>prima di associarsi, si trovassero notanti in mezzo al liquido, dispostevi l'una <lb/>rispe<emph type="italics"/>i<emph.end type="italics"/>to all'altra secondo misurati intervalli, e secondo ordini certi; cosicch&egrave; <pb xlink:href="020/01/1738.jpg" pagenum="613"/>agissero a vicenda con forze uguali o disuguali fra loro, secondo che si tro&shy;<lb/>vassero poste a uguale o a disuguale distanza. </s>

<s>Cos&igrave; intendesi come sempre <lb/>vengano a comporsi le particelle in ordini simili, e come, senza queste forze <lb/>attrattive, o elle debbano concorrere a caso o andarsene confusamente di&shy;<lb/>sperse. </s>

<s>&ldquo; Quum liquor sale quovis imbutus, evaporatus est, quod aiunt, ad <lb/>cuticulam et deinde refrixit, sal continuo concrescit in figuras aliquas regu&shy;<lb/>lares. </s>

<s>Ex quo apparet salis particulas, antequam concrescerent, iam in li&shy;<lb/>quore illo aequis interiectis intervallis, certisque ordinibus dispositas, inna&shy;<lb/>tasse, et consequenter eas in se invicem egisse vi aliqua, quae aequalis sit <lb/>in intervallis aequalibus in iuaequalibus inaequalis. </s>

<s>Nam tali quidem vi illae <lb/>se in consimiles ordines usquequaque disponent, sine ea autem circumnata&shy;<lb/>bunt dispersim quaquaversus; itemque sine ullo ordine, ut forte ceciderit, <lb/>concurrent &rdquo; (Opera omnia optica, Patavii 1773, pag. </s>

<s>158). </s></p><p type="main">

<s>Venivano queste neutoniane dottrine a confermare e a rendere tutt'in&shy;<lb/>sieme la ragione di quel che diceva il Willis del ristringimento de'pori nel <lb/>liquido evaporante, per cui quasi spremute, e costrette d'uscir fuori da'loro <lb/>loculi troppo angusti, son costrette a deporsi le risolute particelle del sale. </s>

<s><lb/>Il Newton insegnava invece che, restringendosi i pori al liquido raffreddato, <lb/>le particelle che prima gli riempivano vengono ad accostarsi cos&igrave; da ridursi <lb/>nella loro sfera di attrazione, e perci&ograve; tornano a ricomporsi in quel mede&shy;<lb/>simo ordine, che avevano prima di essere sciolte. </s>

<s>Applicando poi il Boer&shy;<lb/>haave queste dottrine alle soluzioni, fece rilevar l'importanza grande, che ha <lb/>il calore nel governo delle loro leggi, e come male si confidassero i Chi&shy;<lb/>mici, trascurando quell'elemento, di poter definire la quantit&agrave; del sale re&shy;<lb/>solubile in una data misura di acqua. </s>

<s>&ldquo; Inde igitur rursum liquet faculta&shy;<lb/>tem aquae qua solvit sales pendere partim ex sale et aqua partim vero ex <lb/>copia ignis, qui se adiungit tam sali quam aquae. </s>

<s>Quare etiam colligo defi&shy;<lb/>niri haud posse, ut omnes fere Chemici voluerunt, quantum salis in aqua <lb/>queat dissolvi, nisi quam accuratissime simul definiatur quantus calor simul <lb/>fuerit adhibitus inter dissolvendum &rdquo; (Elementa Chemiae, T. </s>

<s>I cit., pag. </s>

<s>575). </s></p><p type="main">

<s>Dovendosi a questo punto, secondo i limiti che ci siamo prescritti, ar&shy;<lb/>restare la presente Storia, coloro che si compiacciono de'progressi fatti dalla <lb/>moderna Cristallografia confesseranno facilmente a non altro poi ridursi que&shy;<lb/>sti stessi ammirati progressi, che allo svolgimento delle dottrine, storica&shy;<lb/>mente da noi fin qui esposte, e il pi&ugrave; pieno e compendioso esempio delle <lb/>quali ci &egrave; offerto dallo Stenone. </s>

<s>A chi va oggid&igrave; orgoglioso del suo gran sa&shy;<lb/>pere in fatto di scienze sperimentali, compassionando la bonaria semplicit&agrave; <lb/>e l'ignoranza degli avi, potrebbero forse qualche poco giovare questa e le <lb/>altre Storie passate; felici chiamandoci noi e sodisfatti dei nostri studi, se <lb/>valessero a persuadere gl'illusi che i frondosi rami lussureggianti sotto <lb/>questo nostro sole attinsero gi&agrave; il nutrimento da quelle antiche radici, le <lb/>quali, specialmente sotto il suolo d'Italia, si vanno a ricongiungere nell'al&shy;<lb/>bero della scienza, invisibili, ma pur cos&igrave; sempre efficacemente operanti. <pb xlink:href="020/01/1739.jpg"/></s></p><pb xlink:href="020/01/1740.jpg"/><p type="main">

<s><emph type="center"/>INDICI<emph.end type="center"/><pb xlink:href="020/01/1741.jpg"/></s></p><pb xlink:href="020/01/1742.jpg"/><p type="main">

<s><emph type="center"/>INDICE DEI CAPITOLI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>CAPITOLO I.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dell'Anatomia nello studio della vita animale.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle istituzioni anatomiche di Galeno, e delle prime instaurazion&igrave; dell'arte, per opera <lb/>del Berengario e del Vesalio <emph type="italics"/>Pag.<emph.end type="italics"/> 7 </s></p><p type="main">

<s>II Dell'anatomia descrittiva instituita dal Falloppio, e proseguita dall'Eustacbio, dal&shy;<lb/>l'Acquapendente e dal Casserio &rdquo; 13 </s></p><p type="main">

<s>III Delle vivisezioni praticate da Realdo Colombo e come s'incominciassero ad applicare le <lb/>leggi della Fisica a spiegar le funzioni della vita. </s>

<s>&rdquo; 22 </s></p><p type="main">

<s>IV Dell'Anatomia della Scuola iatromeccanica &rdquo; 30 </s></p><p type="main">

<s>V Della Scuola iatromeccanica italiana, e dei limiti naturalmente imposti ai progressi del&shy;<lb/>l'Anatomia &rdquo; 35 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO II.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dei moti muscolari.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle prime ipotesi proposte a rendere la ragione dei moti muscolari, e particolar&shy;<lb/>mente dell'ipotesi del Cartesio <emph type="italics"/>Pag.<emph.end type="italics"/> 43 </s></p><p type="main">

<s>II Di altre varie ipotesi principalmente speculate dai nostri Italiani &rdquo; 50 </s></p><p type="main">

<s>III Dei moti volontarii, e dei naturali &rdquo; 63 </s></p><p type="main">

<s>IV Della meccanica dei moti muscolari &rdquo; 73 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO III.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dei moti del cuore.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della struttura muscolare del cuore; dei moti di sistole e di diastole <emph type="italics"/>Pag.<emph.end type="italics"/> 84 </s></p><p type="main">

<s>II Delle forze motive del cuore, e della loro misura; del moto del sangue per le arterie <lb/>e per le vene &rdquo; 96 </s></p><p type="main">

<s>III Delle leggi idrauliche applicate ai moti del sangue &rdquo; 111 </s></p><pb xlink:href="020/01/1743.jpg" pagenum="618"/><p type="main">

<s><emph type="center"/>CAPITOLO IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del circolo del sangue.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Del circolo polmonare <emph type="italics"/>Pag.<emph.end type="italics"/> 124 </s></p><p type="main">

<s>II Del circolo universale &rdquo; 136 </s></p><p type="main">

<s>III Delle esperienze e delle osservazioni, che dimostrano la verit&agrave; del circolo universale &rdquo; 143 </s></p><p type="main">

<s>IV Del sistema arveiano in Italia, e della trasfusione del sangue &rdquo; 152 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO V.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Della respirazione.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle cause motive, degli organi e dei modi della respirazione <emph type="italics"/>Pag.<emph.end type="italics"/> 164 </s></p><p type="main">

<s>II Dell'azione dell'aria inspirata sul sangue dei polmoni &rdquo; 174 </s></p><p type="main">

<s>III Della respirazione dei neonati; del problema arveiano &rdquo; 186 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Della nutrizione.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle varie dottrine professate dai Fisiologi intorno alla digestione, e delle esperienze <lb/>in proposito di Lazzero Spallanzani <emph type="italics"/>Pag.<emph.end type="italics"/> 199 </s></p><p type="main">

<s>II Della scoperta delle vie del chilo per le vene lattee del Mesenterio &rdquo; 209 </s></p><p type="main">

<s>III Della scoperta del Ricettacolo del chilo, e del Canale toracico &rdquo; 217 </s></p><p type="main">

<s>IV Della scoperta dei vasi linfatici; delle esequie al Fegato defunto &rdquo; 229 </s></p><p type="main">

<s>V Dell'opera data particolarmente dai nostri Italiani allo studio dei vasi bianchi &rdquo; 238 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dei sensi.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Del tatto, del gusto e dell'odorato <emph type="italics"/>Pag.<emph.end type="italics"/> 251 </s></p><p type="main">

<s>II Dell organo dell'udito; dell'orecchio medio, ossia della Cassa del timpano &rdquo; 264 </s></p><p type="main">

<s>III Dell'orecchio interno, ossia del Labirinto &rdquo; 276 </s></p><p type="main">

<s>IV Del senso dell'udito &rdquo; 285 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Anc&ograve;ra Dei sensi.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Dell'organo della vista; delle membrane dell'occhio <emph type="italics"/>Pag.<emph.end type="italics"/> 300 </s></p><p type="main">

<s>II Degli umori di rifrangenza nell'occhio &rdquo; 321 </s></p><p type="main">

<s>III Del senso della vista &rdquo; 334 </s></p><pb xlink:href="020/01/1744.jpg" pagenum="619"/><p type="main">

<s><emph type="center"/>CAPITOLO IX.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Degli ordinamenti naturali.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Degli ordinamenti degli animali <emph type="italics"/>Pag.<emph.end type="italics"/> 351 </s></p><p type="main">

<s>II Dell'ordinamento delle piante &rdquo; 360 </s></p><p type="main">

<s>III Dell'ordinamento dei minerali &rdquo; 369 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO X.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>De'Mammiferi e degli uccelli.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della generazione dag'i svolgimenti embrionali dell'uovo <emph type="italics"/>Pag.<emph.end type="italics"/> 378 </s></p><p type="main">

<s>II De'moti locali: del passo e del volo &rdquo; 395 </s></p><p type="main">

<s>III Di alcune questioni concernenti le funzioni digestive ne'quadrupedi ruminanti, e negli <lb/>uccelli gallinacci; delle vescicole pneumatiche negli uccelli &rdquo; 406 </s></p><p type="main">

<s>IV Di cerle piu notabili differenze negli organi dei sensi: degli strumenti della voce e del <lb/>canto &rdquo; 418 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO XI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dei pesci.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Degli organi, e degli esercizi del nuoto <emph type="italics"/>Pag.<emph.end type="italics"/> 430 </s></p><p type="main">

<s>II Della respirazione branchiale, e del circolo del sangue &rdquo; 439 </s></p><p type="main">

<s>III. </s>

<s>Degli organi dei sensi &rdquo; 452 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO XII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Degl'Insetti.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della generazione spontanea, e delle varie esperienze istituite per dimostrarla falsa <emph type="italics"/>Pag.<emph.end type="italics"/> 465 </s></p><p type="main">

<s>II Della Micrografia, e delle particolari applicazioni di lei alla scoperta degli organi della <lb/>respirazione &rdquo; 478 </s></p><p type="main">

<s>III Degli organi de'sensi, e particolarmente degli occhi &rdquo; 487 </s></p><p type="main">

<s>IV De'fenomeni di fosforescenza, segnatamente nelle lucciole marine, e nelle terrestri &rdquo; 495 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO XIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Delle piante.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle principali funzioni nutritive: delle forze concorrenti a produr l'ascesa dei succhi; <lb/>dell'azione, e delle propriet&agrave; delle foglie. <emph type="italics"/>Pag.<emph.end type="italics"/> 508 </s></p><p type="main">

<s>II Del circolo della linfa, e della respirazione &rdquo; 523 </s></p><p type="main">

<s>III Dell'ufficio dei fiori, della distinzione dei sessi, e della fecondazione dei semi &rdquo; 531 </s></p><p type="main">

<s>IV Della germinazione: dell'uso dei lobi e delle foglie seminali: dell'azione dell'aria, e <lb/>dei semi posti a germogliare nel vuoto &rdquo; 549 </s></p><pb xlink:href="020/01/1745.jpg" pagenum="620"/><p type="main">

<s><emph type="center"/>CAPITOLO XIV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dei Minerali.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della sede nettunica del regno minerale <emph type="italics"/>Pag.<emph.end type="italics"/> 560 </s></p><p type="main">

<s>II Della sede plutonica del regno minerale &rdquo; 577 </s></p><p type="main">

<s>III Della generazion dei cristalli, e di ci&ograve; che intorno alle forme cristalline fu osservato e <lb/>speculato dagli Accademici del Cimento &rdquo; 591 </s></p><p type="main">

<s>IV Dell'origine e dei progressi della Cristallografia, fuori dell'Accademia del Cimento &rdquo; 600 </s></p><pb xlink:href="020/01/1746.jpg"/><p type="main">

<s><emph type="center"/>INDICE ALFABETICO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>DEGLI AUTORI E DELLE COSE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Co'numeri s'accenna alle pagine.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="bold"/>Achilli<gap/>i Alessandro<emph.end type="bold"/> annoverato fra'primi osservatori dei moti pupillari 315. </s></p><p type="main">

<s><emph type="bold"/>Acipensero,<emph.end type="bold"/> pesce, organo dell'odorato di lui descritto dal Morgagni 461. </s></p><p type="main">

<s><emph type="bold"/>Acquapendente (d') Girolamo Fabrizi<emph.end type="bold"/> anatomico 19, suoi errori di meccanica muscolare 74, scopre <lb/>le valvole delle vene 146, sue idee retrograde intorno al circolo del sangue 143, sue osservazioni <lb/>importanti intorno alla figura, e alla disposizione della membrana del Timpano 256, quale uso <lb/>egli assegni agli organi interni dell'udito 288, primo cultore dell'Anatomia comparata 357, a <lb/>quali organi attribuisca la direzione del volo negli uccelli 404, come non scoprisse nulla di nuovo <lb/>negli organi della ruminazione 408, propone i tre problemi, ne'quali concludesi la meccanica del <lb/>nuoto de'pesci 431, ammette la generazione spontanea 496. </s></p><p type="main">

<s><emph type="bold"/>Acquedutto<emph.end type="bold"/> scoperto dal Falloppio nell'interno dell'orecchio 379. </s></p><p type="main">

<s><emph type="bold"/>Acqueo,<emph.end type="bold"/> umore dell'occhio: esperienze intorno alla sua generazione 330, sua quantit&agrave; relativa a <lb/>quella degli altri umori 332. </s></p><p type="main">

<s><emph type="bold"/>Acustico,<emph.end type="bold"/> nervo degli uccelli, descritto dallo Scarpa 422. </s></p><p type="main">

<s><emph type="bold"/>Aggiunti Niccol&ograve;,<emph.end type="bold"/> come spieghi il modo del salir la linfa ne'vasi delle piante 512. </s></p><p type="main">

<s><emph type="bold"/>Aldovrandi Ulisse,<emph.end type="bold"/> come ordini la sua storia degli uccelli 354, osserva non esser vero che la coda <lb/>negli uccelli faccia l'ufficio del timone nelle navi 403. </s></p><p type="main">

<s><emph type="bold"/>Ali,<emph.end type="bold"/> nell'esercizio del volo, rassomigliate da Aristotile ai remi 4<gap/>0. </s></p><p type="main">

<s><emph type="bold"/>Anastomosi<emph.end type="bold"/> fra le estremit&agrave; venose e le arteriose, perch&egrave; messe in dubbio dall'Harvey e dal <lb/>Pecquet 148. </s></p><p type="main">

<s><emph type="bold"/>Angeli Stefano,<emph.end type="bold"/> suo giudizio intorno alla Miologia stenoniana 37. </s></p><p type="main">

<s><emph type="bold"/>Antenne,<emph.end type="bold"/> intorno alla bocca degli insetti, credute da alcuni organi di sensi speciali 487. </s></p><p type="main">

<s><emph type="bold"/>Antiperipatias,<emph.end type="bold"/> libro nel quale Marc'Aurelio Severino dimostra che i pesci hanno le trachee e i <lb/>polmoni 443. </s></p><p type="main">

<s><emph type="bold"/>Aorta<emph.end type="bold"/> ascendente e discendente ne'pesci a quali vasi corrisponda nei polmonati 450. </s></p><p type="main">

<s><emph type="bold"/>Api<emph.end type="bold"/> costruiscono i favi esagonali 601, non gli costruiscono per lume d'intelligenza, ma secondo il <lb/>Keplero per necessit&agrave; materiale 602. </s></p><p type="main">

<s><emph type="bold"/>Aranzio Giulio Cesare<emph.end type="bold"/> descrive i particolari organi inservienti alla circolazione del sangue nel feto, <lb/>ed emenda Galeno 190. </s></p><p type="main">

<s><emph type="bold"/>Arena Filippo<emph.end type="bold"/> primo a professsare in Italia il sistema sessuale delle piante 549. </s></p><p type="main">

<s><emph type="bold"/>Aria,<emph.end type="bold"/> primi riconosciuti effetti di lei nella respirazione 166, refrigera, secondo il Cesalpino, il calor <lb/>naturale del sangue 166, perch&egrave;, secondo il Borelli e il Fracassati, sia necessaria alla vita dei <lb/>pesci 446, se sia necessaria alla germogliazione dei semi 558. </s></p><p type="main">

<s><emph type="bold"/>Aristotile,<emph.end type="bold"/> come dia definitiva sentenza del primato tra il cuore e il fegato, giudicando dalla loro <lb/>sede 126 </s></p><p type="main">

<s><emph type="bold"/>Aromatari Giuseppe,<emph.end type="bold"/> suoi pensieri intorno alla germogliazione dei semi 552, primo a riconoscers <lb/>l'uso delle foglie seminali 553. </s></p><p type="main">

<s><emph type="bold"/>Arte della pittura<emph.end type="bold"/> in servizio della Storia naturale 3<gap/>3. </s></p><p type="main">

<s><emph type="bold"/>Arterie,<emph.end type="bold"/> la loro virt&ugrave; pulsante vien partecipata dal sangue 99. </s></p><p type="main">

<s><emph type="bold"/>Asellio Gaspero,<emph.end type="bold"/> suoi dubbi intorno al circolo polmonare 136, racconta in che modo riusci a sco&shy;<lb/>prire le vene lattee 213. </s></p><p type="main">

<s><emph type="bold"/>Aura seminale,<emph.end type="bold"/> sola, secondo il Graaf, fecondatrice 389. </s></p><pb xlink:href="020/01/1747.jpg" pagenum="622"/><p type="main">

<s><emph type="bold"/>Baglivi Giorgio,<emph.end type="bold"/> sua teoria dei moti muscolari 59, insegna il modo dl osservare il circolo del sangue <lb/>nelle rane 140, suoi errori intorno alla causa, per cui l'aria introduces&igrave; ne'polmoni 174, e intorno <lb/>all'azione dell'aria sul sangue 186. </s></p><p type="main">

<s><emph type="bold"/>Baliani Giovan Batista,<emph.end type="bold"/> come spieghi in che modo l'animale si muova 50, preferisce le sue fanta&shy;<lb/>tasie alle verit&agrave; scoperte dall'Harvey 157. </s></p><p type="main">

<s><emph type="bold"/>Bartholin Tommaso<emph.end type="bold"/> dimostra il Canal toracico in due cadaveri umani 226, sua nuova storia dei <lb/>Vasi linfatici 232. </s></p><p type="main">

<s><emph type="bold"/>Basilio Magno,<emph.end type="bold"/> fa menzione di un'esperienza concernente la respirazion degl'insetti 482. </s></p><p type="main">

<s><emph type="bold"/>Beccaria Giovan Batista,<emph.end type="bold"/> attribuisce la fosforescenza marina a un'azione elettrica 502, riconosce <lb/>nell'elettricit&agrave; il principio visibile della vita 506. </s></p><p type="main">

<s><emph type="bold"/>Bellini Lorenzo,<emph.end type="bold"/> sue teorie de'moti muscolari 57, come spieghi l'alternarsi dei moti del cuore 95, <lb/>applica al sangue, fluente dalla aperta vena, gli effetti delle acque de'fiumi nel rompersi degli <lb/>argini 115, rassomiglia l'azion dell'aria sul sangue dei polmoni all'azione dell'aria stessa sul&shy;<lb/>l'uovo 185, racconta come gli occorresse di scoprir sulla lingua le papille nervee del gusto 257. </s></p><p type="main">

<s><emph type="bold"/>Benedetti Giovan Batists,<emph.end type="bold"/> primo ad applicare le lenti cristalline al foro della Camera oscura, per <lb/>meglio rassomigliar lo strumento artificiale all'occhio 339, suo problema meccanico intorno al <lb/>girar delle trottole 399. </s></p><p type="main">

<s><emph type="bold"/>Berengario Jacopo da Carpi,<emph.end type="bold"/> suoi commentarii all'Anatomia del Mondino 10, sua Isagoge 11, sua <lb/>teoria de'moti muscolari 45, come conge<gap/>turasse dover esser costrutto il cuore 87, come sosti&shy;<lb/>tuisse le sue proprie immaginazioni alla dimostrata verit&agrave; del circolo polmonare 129, ammette <lb/>con Galeno il setto medio perforato 130, primo inventore de'due primi ossicini dell'udito 270, <lb/>descrive le membrane dell'occhio 302. </s></p><p type="main">

<s><emph type="bold"/>Bernoulli Giovanni<emph.end type="bold"/> censura un teorema di Meccanica muscolare dimostrato dallo Stenone 57, av&shy;<lb/>verte un error del Borelli 76. </s></p><p type="main">

<s><emph type="bold"/>Bils Lodovico,<emph.end type="bold"/> suo Dutto rorifero 228. </s></p><p type="main">

<s><emph type="bold"/>Boheraave Ermanno<emph.end type="bold"/> confuta l'opinione di chi dic<gap/>va tutte le sostanze generarsi dall'acqua 594, come <lb/>definisca i sali 608, primo a far notare l'efficacia del calore nelle soluzioni 613, sua teoria della <lb/>digestione 205. </s></p><p type="main">

<s><emph type="bold"/>Bonanni Filippo<emph.end type="bold"/> crede che le reliquie fossili animali siano un gioco della Natura 565. </s></p><p type="main">

<s><emph type="bold"/>Bonnet Carlo,<emph.end type="bold"/> sue esperienze sopra la respirazione delle foglie 530, sull'uso proprio delle foglie se&shy;<lb/>minali 556, nega che le piante si nutriscano di sola acqua 560. </s></p><p type="main">

<s><emph type="bold"/>Borelli Gian Alfonso<emph.end type="bold"/> promette due libri preparatorii alla teoria de'moti animali 31, sua teorica dei <lb/>moti muscolari 55, risponde alle obiezioni dello Stenone 56, si riscontra colla celebre esperienza <lb/>del Galvani 61, &egrave; primo a dimostrare da che resulti la macchina dei moti muscolari 76, dimo&shy;<lb/>stra che l'aria entra nel petto dilatandosi il torace 173, sua controversia col Malpighi intorno <lb/>all'uso dei polmoni 183, sua teoria meccanica della respirazione 18<gap/>, come sciogliesse il pro&shy;<lb/>blema harveiano 195, conferma le osservazioni harveiane intorno alla digestione meccanica degli <lb/>uccelli 202, suo giudizio intorno al trattato del Glisson <emph type="italics"/>Anatome Hepatis<emph.end type="italics"/> 244. </s></p><p type="main">

<s><emph type="bold"/>Bot<gap/>llo Leonardo<emph.end type="bold"/> crede avere scoperta nel cuore una via nuova al sangue 191, perch&egrave; fosse ma&shy;<lb/>giudicato dal Flourens 192. </s></p><p type="main">

<s><emph type="bold"/>Boyle Reberto<emph.end type="bold"/> dimostra sperimentalmente che l'aria irrompe spontanea nel dilatato torace 172, primo <lb/>a tentar la soluzione del problema harveiano 194, sua esperienza a dimostrar che l'aria &egrave; nel <lb/>cessaria alla vita dei pesci 444. </s></p><p type="main">

<s><emph type="bold"/>Branchie de'pesci,<emph.end type="bold"/> loro uso secondo il Rondelezio 442, descritte dal Perrault 450. </s></p><p type="main">

<s><emph type="bold"/>Brocchi Giovan Batista,<emph.end type="bold"/> come risolva due celebri problemi geologici 590. </s></p><p type="main">

<s><emph type="bold"/>Buffen,<emph.end type="bold"/> qual falso criterio si proponga in ordinar la Natura 360, sua Teoria della Terra 587. </s></p><p type="main">

<s><emph type="bold"/>Burnet Tommaso,<emph.end type="bold"/> sua Teoria sacra della Terra 574. </s></p><p type="main">

<s><emph type="bold"/>Camerarius Bodolf'Jacopo,<emph.end type="bold"/> primo a proporre in pubblico il sistema sessuale delle piante 539, con&shy;<lb/>fronta la generazion delle piante con quella degli animali 540. </s></p><p type="main">

<s><emph type="bold"/>Camper Pietro<emph.end type="bold"/> dimostra che Galeno non sezion&ograve; mai cadaveri umani 380. </s></p><p type="main">

<s><emph type="bold"/>Canale,<emph.end type="bold"/> come dal Petit scoperto nell'occhio 326. </s></p><p type="main">

<s><emph type="bold"/>Canali<emph.end type="bold"/> semicircolari dell'orecchio descritti dal Falloppio 283. </s></p><p type="main">

<s><emph type="bold"/>Canalicmlo<emph.end type="bold"/> della vescica natatoria non in tutti i pesci ha origine dallo stomaco 435. </s></p><p type="main">

<s><emph type="bold"/>Canani Giovan Batista,<emph.end type="bold"/> primo a scoprire le valvole delle vene 144. </s></p><p type="main">

<s><emph type="bold"/>Capillari,<emph.end type="bold"/> fenomeni applicati dal Borelli a spiegare il moto del sangue nelle vene 107. </s></p><p type="main">

<s><emph type="bold"/>Caprifico,<emph.end type="bold"/> fico silvestre 543. </s></p><p type="main">

<s><emph type="bold"/>Caraffella,<emph.end type="bold"/> in cui il liquido sale e scende al variare della temperatura, applicata da Galileo e dal <lb/>Castelli alla fisiologia vegetabile e animale 27. </s></p><p type="main">

<s><emph type="bold"/>Cartes<gap/>o <gap/>enato<emph.end type="bold"/> introduce i suoi vizii filosofici anche nell'Anatomia 34, sua teoria dei moti musco-<pb xlink:href="020/01/1748.jpg" pagenum="623"/>lari 47, contradice all'Harveio intorno alla regola dei moti del cuore 92, argomenti di questa sua <lb/>contradizione 93, &egrave; prevenuto dal Cesalpino 94, sua ipotesi intorno all'effetto dell'aria sui pol&shy;<lb/>moni 167, sua teoria della digestione 200, ammette l'esistenza di un muscolo sfintere intorno <lb/>alla pupilla 316, propone il modo d<gap/> osservare le immagini rovesciate nell'occhio 344. </s></p><p type="main">

<s><emph type="bold"/>Casserio Giulio,<emph.end type="bold"/> anatomico 21 </s></p><p type="main">

<s><emph type="bold"/>Cassini Gian Domenico<emph.end type="bold"/> osserva le galle della quercie 470. </s></p><p type="main">

<s><emph type="bold"/>Celso Cornelio<emph.end type="bold"/> descrive le membrane dell'occhio 301. </s></p><p type="main">

<s><emph type="bold"/>Cesalpino Andrea<emph.end type="bold"/> conferma il circolo polmonare del sangue 133, &egrave; il primo ad asserire che tutti i <lb/>vasi hanno origine dal cuore 141, non conobbe il ritorno del sangue arterioso per le vene 142, <lb/>quale ei credesse esser l'uso dell'aria ne'polmoni 166, crede che le meseraiche conducano il chilo <lb/>mescolato col sangue 212, non pu&ograve;, secondo il Borelli, attribuirsegli la scoperta dell'Harvey 242, <lb/>propone in Botanica il primo sistema razionale 362, come ordini i Minerali 371, riconosce nelle <lb/>piante organi simili a quelli degli animali 509, rassomiglia l'ascender della linfa ne'vasi delle <lb/>piante all'ascender dell'olio nelle lucerne 510, primo a riconoscere le somiglianze, che passano <lb/>fra i semi delle piante, e le uova degli animali 551. </s></p><p type="main">

<s><emph type="bold"/>Chiocciola dell'orecchio,<emph.end type="bold"/> invenzione di lei attribuita ad Empedocle e ad Aristotile 382, descritta dal&shy;<lb/>l'Eustachio 382, organo delle particolari percezioni de'suoni, secondo il Cotunnio 299. </s></p><p type="main">

<s><emph type="bold"/>Cicale,<emph.end type="bold"/> organo con cui producono il suono descritto dal Casserio 488. </s></p><p type="main">

<s><emph type="bold"/>Cigno,<emph.end type="bold"/> organi del canto scoperti dall'Aldovrandi in questo uccello 427. </s></p><p type="main">

<s><emph type="bold"/>Cigoli Lodovico,<emph.end type="bold"/> sua teoria della vista 342. </s></p><p type="main">

<s><emph type="bold"/>Ciliari,<emph.end type="bold"/> corpi dell'occhio 309, loro struttura 311. </s></p><p type="main">

<s><emph type="bold"/>Cimento Accademici (del),<emph.end type="bold"/> loro esperienze intorno alla digestione delle galline e delle anatre 202. </s></p><p type="main">

<s><emph type="bold"/>Circolazione<emph.end type="bold"/> dei pianeti paragonata a quella del sangue 125, della linfa ne'vasi delle piante 524. </s></p><p type="main">

<s><emph type="bold"/>Circolo cartesiano<emph.end type="bold"/> concernente l'aria inspirata 170. </s></p><p type="main">

<s><emph type="bold"/>Civetta,<emph.end type="bold"/> occhio di lei scelto dal Briggs per osservare l'inversione delle immagini 344. </s></p><p type="main">

<s><emph type="bold"/>Coda<emph.end type="bold"/> degli uccelli serve secondo Aristotile a dirigere il volo, come il timone dirige il corso alle <lb/>navi 403, dei pesci, organo essenziale del nuoto 439. </s></p><p type="main">

<s><emph type="bold"/>Cole Guglielmo,<emph.end type="bold"/> suo teorema idraulico applicato al moto del sangue 119. </s></p><p type="main">

<s><emph type="bold"/>Colombo Realdo,<emph.end type="bold"/> suo trattato <emph type="italics"/>De re anatomica<emph.end type="italics"/> 17, dimostra l'utilit&agrave; della vivisezione 23, scopre <lb/>negli animali vivi che i moti del cuore si fanno diversamente da quel che avea detto il Vesa&shy;<lb/>lio 91, come scoprisse che l'arteria vibra quando il ventricolo &egrave; in quiete 96, dimostra il circolo <lb/>polmonare 132, come enumeri le membrane dell'occhio 303. </s></p><p type="main">

<s><emph type="bold"/>Colonna Fabio<emph.end type="bold"/> ordina le piante secondo il fiore e il frutto 364, come argomenti contro chi ammet&shy;<lb/>teva le reliquie fossili marine essere generate dalla terra 563. </s></p><p type="main">

<s><emph type="bold"/>Conchiglie<emph.end type="bold"/> credute generarsi dal limo della terra 476. </s></p><p type="main">

<s><emph type="bold"/>Cornelio Tommaso<emph.end type="bold"/> dimostra esser falso, contro il Cartesio, che il calor del sangue produca i moti <lb/>del cuore 94, eseguisce l'esperienza galenica creduta impossibile dall'Harveio 99, primo a me&shy;<lb/>ditare e a sperimentare intorno agli usi dell'aria nella respirazione 175, &egrave; il primo a fare espe&shy;<lb/>rienza che il forame ovale nei neonati si obliter&agrave; dopo qualche tempo 197, sua teorica della di&shy;<lb/>gestione 203, rivendica le funzioni del Fegato 247, suoi paradossi intorno alla generazione 386. </s></p><p type="main">

<s><emph type="bold"/>Coroide,<emph.end type="bold"/> da che argomentasse il Mariotte esser ella, e non la retina, organo precipuo della visione 345. </s></p><p type="main">

<s><emph type="bold"/>Cotunnio Domenico,<emph.end type="bold"/> sua teorica dell'udito 298. </s></p><p type="main">

<s><emph type="bold"/>Cristalli,<emph.end type="bold"/> secondo Plinio, originati dal ghiaccio 591, come fosse ripudiata questa opinione da Van&shy;<lb/>noccio Biringucci 591, e come da Giorgio Agricola 592, come si figurano secondo il Cesalpino 600, <lb/>hanno, secondo il Keplero, figure prestabilite dalla Natura 603, si formano, secondo Erasmo Bar&shy;<lb/>tholin, come i favi delle api, dalla necessit&agrave; della materia 604. </s></p><p type="main">

<s><emph type="bold"/>Cristallino dell'occhio,<emph.end type="bold"/> sua figura desunta dalle osservazioni 328, desunta dai principii diottrici 329, <lb/>creduto da alcuni Antichi organo essenziale della visione 335, fa, secondo il Plater, da occhiale <lb/>alla retina 339, ragione della sua particolar figura nell'occhio dei pesci 453. </s></p><p type="main">

<s><emph type="bold"/>Cristallografia,<emph.end type="bold"/> sua prima cultura nell'Accademia del Cimento 593, suoi principii stabiliti dallo <lb/>Stenone 598. </s></p><p type="main">

<s><emph type="bold"/>Croone Guglielmo,<emph.end type="bold"/> sua trattato dei moti muscolari 38, in che secondo lui consista la causa di quei <lb/>moti 55, primo a misurare la potenza dei muscoli 75. </s></p><p type="main">

<s><emph type="bold"/>Cuore,<emph.end type="bold"/> suoi moti involontarii 64, come si spieghino dal Borelli 65, &egrave; per Ippocrate un muscolo molto <lb/>forte 84, con quali argomenti provasse Galeno che non &egrave; altrimenti un muscolo 85, il Vesalio &egrave; <lb/>incerto della sua struttura, e il Colombo nega che sia muscolare 86, suo maraviglioso artificio <lb/>descritto dal Borelli 88, &egrave; composto di fibre aggomitola'o 89, &egrave; tessuto, secondo il Vesalio, come <lb/>i vimini di un canestro 90, come si possano dal colore, secondo l'Harveio, riconoscere le fasi <lb/>de'suoi moti 92, ritmo de'suoi moti 95, suoi moti dimostrati dall'Harveio farsi contrariamente <lb/>a quelli delle arterie 97, misura delle sue forze secondo il Borelli 101, &egrave; il sole del Microcosmo 125. </s></p><pb xlink:href="020/01/1749.jpg" pagenum="624"/><p type="main">

<s><emph type="bold"/>Dati Carlo<emph.end type="bold"/> invia a Tommaso Bartholin l'epistole malpighiane <emph type="italics"/>De pulmonibus<emph.end type="italics"/> 2<gap/>8, descrive la sto&shy;<lb/>ria del manoscritto della Metalloteca vaticana 373. </s></p><p type="main">

<s><emph type="bold"/>Digby Chenelmo<emph.end type="bold"/> presente l'azione chimica dell'essigeno dell'aria nella germogliazione dei semi 558. </s></p><p type="main">

<s><emph type="bold"/>Digestione degli animali,<emph.end type="bold"/> esperienze di Lazzero Spallanzani 206, esperienze particolari del medesimo <lb/>fatto sull'uomo 208. </s></p><p type="main">

<s><emph type="bold"/>Disseminazione delle piante,<emph.end type="bold"/> suo meccanismo 550. </s></p><p type="main">

<s><emph type="bold"/>Dodart Dionirio,<emph.end type="bold"/> sua teoria della voce e della modulazione dei tuoni 425. </s></p><p type="main">

<s><emph type="bold"/>Drebbelio Cornelio,<emph.end type="bold"/> sua nave sottomarina 178. </s></p><p type="main">

<s><emph type="bold"/>Du-Verny Giuseppe<emph.end type="bold"/> riconosce la vera natura dei vasi sanguigni nei pesci 451. </s></p><p type="main">

<s><emph type="bold"/>Ecphrasis,<emph.end type="bold"/> titolo dato a un libre, dove Fabio Colonna descrive molte piante nuove 363. </s></p><p type="main">

<s><emph type="bold"/>Elettriclt&agrave;,<emph.end type="bold"/> invocata a spiegare la fosforescenza marina 497. </s></p><p type="main">

<s><emph type="bold"/>Engiscopio,<emph.end type="bold"/> strumento diottrico, usato da Lorenzo Bellini per osservar le figure dei sali 606. </s></p><p type="main">

<s><emph type="bold"/>Epatico-acquosi (dutti),<emph.end type="bold"/> prima scoperti con questa denominazione da Olao Rudbeck 230. </s></p><p type="main">

<s><emph type="bold"/>Esperienza galenica<emph.end type="bold"/> creduta dall'Harveio impossibile a praticarsi 98, del Vesalio intorno al riattivar <lb/>l'uso de'polmoni 168. </s></p><p type="main">

<s><emph type="bold"/>Etere elettrico<emph.end type="bold"/> applicato dal Newten a spiegar la causa dei moti muscolari 60. </s></p><p type="main">

<s><emph type="bold"/>Eustachio Bartolommeo,<emph.end type="bold"/> sue Tavole anatomiche 18, sostiene che Galeno descrisse il corpo dell'uomo, <lb/>e non delle scimmie 280, se si possa attribuirgli il merito di avere scoperto il Canale toracico 241. </s></p><p type="main">

<s><emph type="bold"/>Faber Giovanni<emph.end type="bold"/> scopre gli organi della ruminazione 408. </s></p><p type="main">

<s><emph type="bold"/>Fabry Gnorato,<emph.end type="bold"/> suoi giudizi intorno alla prima scoperia del Canale toracico 223, sua smania d'ap&shy;<lb/>propriarsi le altrui scoperte 224 </s></p><p type="main">

<s><emph type="bold"/>Fagioli,<emph.end type="bold"/> esperienze fatte dal Bonnet intorno alla loro germogliazione 556. </s></p><p type="main">

<s><emph type="bold"/>Falloppio Gabbriello,<emph.end type="bold"/> come si risolvesse a scrivere le sue Osservazioni anatomiche 14, suoi precetti <lb/>di Anatemia 16, dimostra, dall'esame degli ossi, che Galeno descrisse lo scheletro delle scimmie 279. </s></p><p type="main">

<s><emph type="bold"/>Farfalle,<emph.end type="bold"/> fosforescenza scoperta ne'loro occhi 566. </s></p><p type="main">

<s><emph type="bold"/>Fegato,<emph.end type="bold"/> epigrafe di Tommaso Bartholin da porsi sul suo tumulo 232, rivendicato nella sua dignit&agrave; <lb/>dal Van-Horne 234. </s></p><p type="main">

<s><emph type="bold"/>Fernelio Giovanni<emph.end type="bold"/> argomenta dalla ragione, e non dal senso, che le meseraiche portano il chilo al <lb/>Fegato 210. </s></p><p type="main">

<s><emph type="bold"/>Ferrein Antonio,<emph.end type="bold"/> sua teorica della voce 427. </s></p><p type="main">

<s><emph type="bold"/>Fiamma,<emph.end type="bold"/> che arde in mezzo all'aria, paragonata<gap/>al polmone che respira 176. </s></p><p type="main">

<s><emph type="bold"/>Fico<emph.end type="bold"/> addotto per un<gap/> de'pi&ugrave; validi argomenti contro la sessualit&agrave; delle piante 544, sua vera inf<gap/>re&shy;<lb/>scenza da chi prima scoperta 544. </s></p><p type="main">

<s><emph type="bold"/>Finck Giovanni<emph.end type="bold"/> &egrave; creduto da Claudio Beriguardo primo dimostratore del Canale toracico 239. </s></p><p type="main">

<s><emph type="bold"/>Finextra rotonda,<emph.end type="bold"/> nell'interno dell'or<gap/>hio, sua vera figura 277, non &egrave; aperta ma chiusa da una <lb/>apposita membrana 278, usi di lei secondo l'Ingrassia 291, secondo il Valsalva 297, nell'or<gap/>chio <lb/>degli uccelli descritta dallo Scarpa 420. </s></p><p type="main">

<s><emph type="bold"/>Fiore delle piante,<emph.end type="bold"/> ufficio di lui secondo il Malpighi 536, secondo il Grew 537. </s></p><p type="main">

<s><emph type="bold"/>Fisiologia del cuore<emph.end type="bold"/> ebbe origine dalle vivisezioni del Colombo, proseguite dall'Harveio 24. </s></p><p type="main">

<s><emph type="bold"/>Fitobasano,<emph.end type="bold"/> libro dove si descrivono le nuove piante scoperte da Fabio Colonna 363. </s></p><p type="main">

<s><emph type="bold"/>Foglie nelle piante<emph.end type="bold"/> servono, secondo il Malpighi, a concuocere gli alimenti 520, s'imlevono del&shy;<lb/>l'umidit&agrave; dell'aria 521, servono alla traspiraziene 522, aiuta<gap/>e l'ascesa dei succo nutritizi<gap/> 523. <lb/>foglie seminali, loro usi sperimentati dal Malpighi 553, loro ufficii nella germagliazione, secondo <lb/>il Borelli 554, sono organi non accessorii, ma necessarii 555. </s></p><p type="main">

<s><emph type="bold"/>Folli Francesco<emph.end type="bold"/> <gap/>arra come gli sovvenisse il pensiero di trasfondere il sangue da un animale in <lb/>un altro 158. </s></p><p type="main">

<s><emph type="bold"/>Forame ovale<emph.end type="bold"/> nel feto si richiude dopo qualche tempo 196. </s></p><p type="main">

<s><emph type="bold"/>Forami,<emph.end type="bold"/> aperti sulla superfice dei pesci <gap/>63. </s></p><p type="main">

<s><emph type="bold"/>Fosforescenza marina,<emph.end type="bold"/> come spiegata dal Cartesio 496, come dal Borelli 497, delle carni dei pesci <lb/>sperimentata dal Boyle, e confermata nell'Accademia del Cimento 503. </s></p><p type="main">

<s><emph type="bold"/>Fracassati Carlo,<emph.end type="bold"/> anatomico, allevato dal Borelli 31, propone la sua nu<gap/>va Medicina infusoria 160. </s></p><p type="main">

<s><emph type="bold"/>Fracastoro Girolamo,<emph.end type="bold"/> opinioni varie riferite da lui intorno all'origine dei corpi marini, che si tro&shy;<lb/>vano fossili dispersi nei continenti 563. </s></p><p type="main">

<s><emph type="bold"/>Fuoco<emph.end type="bold"/> centrale della Terra ammesso da Galileo e negato dal Reni<gap/>ri 580. </s></p><p type="main">

<s><emph type="bold"/>Galeno,<emph.end type="bold"/> grande Maestro di Anatomia 9, primo a conoscer gli ufficii de'muscoli 44, come dimostri <lb/>il circolo polmenare del sangue 127, sue osservazioni intorno a certi organi inservienti alla cir&shy;<lb/>colazione del sangue nel feto 188, idee attribuitegli intorno alla respirazione dei pesci 441. </s></p><pb xlink:href="020/01/1750.jpg" pagenum="625"/><p type="main">

<s><emph type="bold"/>Galileo<emph.end type="bold"/> deriv&ograve; dall'Acquapendente e dal Santorio un certo amore per l'Anatomia, e per la Medi&shy;<lb/>cina 25, dimostra il teorema fondamentale della Meccanica animale 77, spiega da che nasca la <lb/>stanchezza, che sentesi nelle nostre membra 79, sua teoria meccanica delle funi applicate al <lb/>meccanismo del cuore 89, sua faliace instituzione intorno alla vista 341, sue osservazioni intorno <lb/>alle piante 511, come spieghi il maturarsi dei frutti 512. </s></p><p type="main">

<s><emph type="bold"/>Galle della querce,<emph.end type="bold"/> loro generazione descritta 475. </s></p><p type="main">

<s><emph type="bold"/>Galvani Luigi,<emph.end type="bold"/> sua teoria elettrica dei moti muscolari 61, come invochi l'azione del fluido elettrico <lb/>a spiegare i moti necessarii dei muscoli, e i volontarii 70. </s></p><p type="main">

<s><emph type="bold"/>Gangli dei nervi<emph.end type="bold"/> descritti dal Lancisi 68. </s></p><p type="main">

<s><emph type="bold"/>Gassendo Pietro<emph.end type="bold"/> crede che il passo de'quadrupedi si faccia commutando diagonalmente i piedi 397, <lb/>per quali ragioni negasse l'udito ai pesci 459, sue dottrine intorno alla generazion degl'insetti 472. </s></p><p type="main">

<s><emph type="bold"/>Geologia moderna<emph.end type="bold"/> &egrave; una esplicazione de'concetti esposti nell'Accademia del Cimento da Niecol&ograve; <lb/>Stenone 588. </s></p><p type="main">

<s><emph type="bold"/>Gesner Currado,<emph.end type="bold"/> primo a ordinar le piante secondo il fiore e il frutto 362. </s></p><p type="main">

<s><emph type="bold"/>Ghiandole sierose,<emph.end type="bold"/> prima scoperte da Olao Rudbeck 239, conglobate, studiate prima e descritte dal <lb/>Malpighi 249. </s></p><p type="main">

<s><emph type="bold"/>Glisson Francesco,<emph.end type="bold"/> usi assegnati da lui alla linfa 237, ammette nell'animale un quinto genere di <lb/>vasi 238. </s></p><p type="main">

<s><emph type="bold"/>Glottide,<emph.end type="bold"/> precipuo strumento della voce, secondo Galeno e il Berengario 422. </s></p><p type="main">

<s><emph type="bold"/>Graaf Begnero,<emph.end type="bold"/> suo trattato <emph type="italics"/>De mulierum organis<emph.end type="italics"/> 388. </s></p><p type="main">

<s><emph type="bold"/>Grew Neemia<emph.end type="bold"/> presenta alla R. </s>

<s>Societ&agrave; di Londra la sua Anatomia delle piante 514, esamina e giu&shy;<lb/>dica l'Anatomia fitologica del Malpighi 515 e 517. </s></p><p type="main">

<s><emph type="bold"/>Grilli,<emph.end type="bold"/> organi e meccanismo, con cui producono il suono, descritti dal Casserio 488. </s></p><p type="main">

<s><emph type="bold"/>Guglielmini Domenico<emph.end type="bold"/> dimostra co'principii idraulici le leggi del moto del sangue per le arterie 105, <lb/>e per le vene 110, conferma un teorema di Guglielmo Colo 120, confuta l'opinione della fiamma <lb/>vitale 156, primo ad applicar la Geometria alle figure cristalline 610. </s></p><p type="main">

<s><emph type="bold"/>Gusto,<emph.end type="bold"/> propria sede dell'organo ritrovata dal Bellini 257, e dal Fracassati 258. </s></p><p type="main">

<s><emph type="bold"/>Hales Stefano<emph.end type="bold"/> intraprende esperienze, per trovar la ragione dei moti muscolari 59, misura la forza <lb/>impulsiva del cuore 103, sperimenta sulle perdite di velocita del sangue, nel passare dal tronco <lb/>ai rami 121. </s></p><p type="main">

<s><emph type="bold"/>Haller Alberto<emph.end type="bold"/> compie la teoria dell'irritabilit&agrave; dei muscoli proposta dal Bellini 58, come spiegi i <lb/>moti muscolari, indipendenti dalla volont&agrave; 70, sperimenta la verit&agrave; del Teorema belliniano, re&shy;<lb/>lativo all'emissione del sangue 118. </s></p><p type="main">

<s><emph type="bold"/>Harvey Guglielmo,<emph.end type="bold"/> se la scoperta del circolo del sangue gli possa essere stata ispirata da Galeno 137, <lb/>sua opiniono intorno all'uso dell'aria ne'polmoni 167, primo a descrivere il circolo sanguigno <lb/>nel feto 194, sue opinioni intorno alla digestione degli uccelli 201, nega le vene lattee 216, come <lb/>professasse anch'egli il falso principio della generazione spontanea 497, sue esperienze sopra la <lb/>respirazione degl'insetti 482. </s></p><p type="main">

<s><emph type="bold"/>Hegardt Cornelio,<emph.end type="bold"/> primo a spiegar, nel sistema sessuale, la frutescenza del fico 548. </s></p><p type="main">

<s><emph type="bold"/>Hire (de la) Filippo<emph.end type="bold"/> scopre i tre occhi in fronte alle mosche 491. </s></p><p type="main">

<s><emph type="bold"/>Hodierna Giovan Batista,<emph.end type="bold"/> primo a descrivere l'occhio delle mosche 489. </s></p><p type="main">

<s><emph type="bold"/>Homberg Guglielmo<emph.end type="bold"/> trova germogliare i semi anche nel vuoto 558. </s></p><p type="main">

<s><emph type="bold"/>Idrauliche,<emph.end type="bold"/> leggi del moto de'liquidi nelle trombe, applicate dal Borelli ai moti del cuore 112, e del <lb/>sangue 113. </s></p><p type="main">

<s><emph type="bold"/>I<gap/>hmor Natana<gap/>le<emph.end type="bold"/> dimostra i moti della respirazione d<gap/>pendere dal torace 169. </s></p><p type="main">

<s><emph type="bold"/>Immagini rovesciate<emph.end type="bold"/> sulla retina, da chi primo sperimentate 343. </s></p><p type="main">

<s><emph type="bold"/>Imperato Ferrante,<emph.end type="bold"/> sue Storie naturali 355, cause da lui assegnate alle variazioni della superfice <lb/>terrestre 568, sue osservazioni e descrizioni di varie forme cristalline 596. </s></p><p type="main">

<s><emph type="bold"/>Incudine,<emph.end type="bold"/> origine di questo nome dato a uno degli assicini dell'udito 268. </s></p><p type="main">

<s><emph type="bold"/>Insetti fastidiosi,<emph.end type="bold"/> loro generazione dall'uovo 478, loro occhi riscontrano per ogni parte con quelli <lb/>degli animali superiori 493, esperienze otticbe fatte con la cornea dei loro occhi dal Puget, e <lb/>descritte dal Reaumur 494. </s></p><p type="main">

<s><emph type="bold"/>Insetto,<emph.end type="bold"/> perch&egrave; cosi denominato 495. </s></p><p type="main">

<s><emph type="bold"/>Iride dell'occhio,<emph.end type="bold"/> origine del nome 311, ragione del suo vario colore 312, non ha rigirato intorno al <lb/>foro pupillare nessun muscolo sfintere 317, sua struttura striata 318, qual sia lo stato suo natu&shy;<lb/>rale, se quando &egrave; contratta, o quando &egrave; dilatata <emph type="italics"/>ivi.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="bold"/>Jatromatematica,<emph.end type="bold"/> scuola instituita in Italia, suoi pregi e sua insufficienza riconosciuta, 40. </s></p><pb xlink:href="020/01/1751.jpg" pagenum="626"/><p type="main">

<s><emph type="bold"/>Keill Iacopo,<emph.end type="bold"/> come misuri la forza muscolare del cuore 102, calcola in qual proporzione stia la somma <lb/>delle luci de'rami sanguigni, rispetto a quella del tronco 121. </s></p><p type="main">

<s><emph type="bold"/>Keplero Giovanni,<emph.end type="bold"/> come emendasse la teorica della visione data dal Porta 340. </s></p><p type="main">

<s><emph type="bold"/>King Oloardo,<emph.end type="bold"/> probabilmente attinse dallo Stenone le sue teorie geologiche 387, </s></p><p type="main">

<s><emph type="bold"/>Klein Iacopo Teodoro<emph.end type="bold"/> crede di aver ritrovate tutte le parti dell'organo uditorio dei pesci 464. </s></p><p type="main">

<s><emph type="bold"/>Lamia,<emph.end type="bold"/> pesce anatomizzato dallo Stenone 373. </s></p><p type="main">

<s><emph type="bold"/>Lamina spirale<emph.end type="bold"/> dell'orecchio, organo precipuo, secondo il Duverney, dell'udito 295. </s></p><p type="main">

<s><emph type="bold"/>Lancisi Giovan Maria,<emph.end type="bold"/> sua teorica dei moti muscolari 67, applica al cuore la meccanica galileiana <lb/>delle funi 90. </s></p><p type="main">

<s><emph type="bold"/>Lapilli<emph.end type="bold"/> nell'orecchio dei pesci 463. </s></p><p type="main">

<s><emph type="bold"/>Laringe inferiore<emph.end type="bold"/> negli uccelli scoperta dall'Aldovrandi 427, confermata dalle esperienze del Perrault 428. </s></p><p type="main">

<s><emph type="bold"/>Lattee vene,<emph.end type="bold"/> da chi prima scoperte nell'uomo 215. </s></p><p type="main">

<s><emph type="bold"/>Lauro,<emph.end type="bold"/> germogliazione delle bacche di lui sperimentata dal Borelli 553. </s></p><p type="main">

<s><emph type="bold"/>Leeuwenoeck Antonio<emph.end type="bold"/> osserva la circolazione del sangue nella coda delle anguille 150. </s></p><p type="main">

<s><emph type="bold"/>Lenticolare,<emph.end type="bold"/> ossicino dell'udito, storia della sua scoperta 273. </s></p><p type="main">

<s><emph type="bold"/>Linfa,<emph.end type="bold"/> sua ascesa nelle piante, come spiegata dal Mariotte e dal Perrault 519, viaggio di lei nelle <lb/>piante descritto dal Malpighi 525. </s></p><p type="main">

<s><emph type="bold"/>Lingua<emph.end type="bold"/> dei pesci 454, &egrave; in questi animali organo del gusto, secondo il Rondelezio 454, non ha le <lb/>papille nervee del gusto, secondo il Fracassati 455. </s></p><p type="main">

<s><emph type="bold"/>Linneo Carlo,<emph.end type="bold"/> suo metodo di ordinare le piante 368, confessa di non aver saputo scoprir la causa <lb/>della fosforescenza marina, prima del Vianelli 501, sua filosofia botanica dei s<gap/>ssi 546. </s></p><p type="main">

<s><emph type="bold"/>Lower Riccardo<emph.end type="bold"/> fa esperienze sulla trasfusione del sangue 160. </s></p><p type="main">

<s><emph type="bold"/>Lucciole,<emph.end type="bold"/> come perdano il lume nel vuoto, secondo le esperienze degli Accademici del Cimento 503, <lb/>organi della loro fosforescenza descritti dal Malpighi 505. </s></p><p type="main">

<s><emph type="bold"/>Lusitano Amato,<emph.end type="bold"/> sua mendace esperienza per dimostrar le valvole delle vene 144. </s></p><p type="main">

<s><emph type="bold"/>Magalotti Lorenzo,<emph.end type="bold"/> suo discorso intorno ai vasi linfatici, e al circolo glissoniano 244-47, ammette la <lb/>generazione dei vermi dalla vita delle piante 471. </s></p><p type="main">

<s><emph type="bold"/>Magiotti Raffaello<emph.end type="bold"/> inizia la Jatromatematica insieme con Galileo e col Castelli 28, suggerisce al <lb/>Borelli un principio fisico, per spiegare i moti animali 53 e 55, primo a diffondere in Italia la <lb/>scoperta del circolo del sangue 155, esorta Galileo a trattar dell'incesso degli animali 397. </s></p><p type="main">

<s><emph type="bold"/>Magnol Pietro,<emph.end type="bold"/> suoi criterii seguiti nell'ordinare le piante 365. </s></p><p type="main">

<s><emph type="bold"/>Malpighi Marcello,<emph.end type="bold"/> chiamato dal Borelli allo studio dell'anatomia 33, come dimostri che i nervi <lb/>son tubolari 54, rivendica a se la scoperta delle fibre spirali del cuore 89, fa primo uso delle <lb/>iniezioni, per dimostrar le anastomosi de'vasi arteriosi coi venosi 149, osserva il circolo del sangue <lb/>nelle vene 149, sua teorica intorno all'uso dei polmoni 181, intravede le vere funzioni dell'aria <lb/>inspirata sul sangue 184, conferma l'esistenza delle uova nelle femmine dei quadrupedi 389, <lb/>dimostra esser dall'uovo anche la generazione dei vermi delle galle 474, scopre le trachee nelle <lb/>piante 513, presenta la sua prima idea dell'Anatomia delle piante alla R. </s>

<s>Societ&agrave; di Londra 514, <lb/>scrive altri trattati sull'Anatomia delle piante 515, causa del disordine tenuto nella pubblicazione <lb/>di questi trattati, e quale altro ordine avrebbe probabilmente dato a loro l'Autore 516, sue espe&shy;<lb/>rienze sopra l'uso delle foglie seminali 556. </s></p><p type="main">

<s><emph type="bold"/>Mantice,<emph.end type="bold"/> rassomigliato, prima da Aristotile e poi dal Cartesio, al polmone 168. </s></p><p type="main">

<s><emph type="bold"/>Marini,<emph.end type="bold"/> corpi ritrovati nei continenti, loro origine secondo il Falleppio, l'Agricola e il Cesalpino 562. </s></p><p type="main">

<s><emph type="bold"/>Mariotte Edmondo<emph.end type="bold"/> descrive una sua nuova esperienza intorno alla vista 344. </s></p><p type="main">

<s><emph type="bold"/>Marsili Luigi Ferdinando,<emph.end type="bold"/> suo saggio fisico della Storia naturale del mare 582. </s></p><p type="main">

<s><emph type="bold"/>Martello,<emph.end type="bold"/> origine di questo nome imposto a uno degli ossicini dell'udito 268. </s></p><p type="main">

<s><emph type="bold"/>Mascagni Paolo,<emph.end type="bold"/> a che attribuisce il moto della linfa 250. </s></p><p type="main">

<s><emph type="bold"/>Mattioli Pier Andrea<emph.end type="bold"/> nega la sessualit&agrave; dalle piante 535. </s></p><p type="main">

<s><emph type="bold"/>Mayow Giovanni<emph.end type="bold"/> dice che l'aria inspirata, operante sul sangue, &egrave; di natura nitro salina 180. </s></p><p type="main">

<s><emph type="bold"/>Membrana<emph.end type="bold"/> tesa nell'interna cavit&agrave; dell'orecchio da chi prima scoperta 265, del timpano, da chi prima <lb/>fosse cos&igrave; denominato <emph type="italics"/>ivi,<emph.end type="italics"/> come e chi lo trovasse compaginato di pi&ugrave; pellicole soprapposte, 266 </s></p><p type="main">

<s><emph type="bold"/>Mercati Michele,<emph.end type="bold"/> come ordini i minirali 376, varie forme cristalline esibite dagli iconismi di lui. </s>

<s>598. </s></p><p type="main">

<s><emph type="bold"/>Mercuriale Girolamo,<emph.end type="bold"/> sue nuove osservazioni anatomiche nel ventricolo dei ruminanti 407. </s></p><p type="main">

<s><emph type="bold"/>Mersenne Marino<emph.end type="bold"/> divulga l'invenzione drebbelliana delle navi sottomarine 178. </s></p><p type="main">

<s><emph type="bold"/>Meseraiche vene,<emph.end type="bold"/> valvole scoperte in esse dal Colombo 211. </s></p><p type="main">

<s><emph type="bold"/>Metalloteca vaticana<emph.end type="bold"/> di Michele Mercati 375. </s></p><p type="main">

<s><emph type="bold"/>Michelini Famiano,<emph.end type="bold"/> suo sistema di Medicina 30, annunzia a Galileo e al Baliani la scoperta del oir&shy;<lb/>colo del sangue 156. </s></p><pb xlink:href="020/01/1752.jpg" pagenum="627"/><p type="main">

<s><emph type="bold"/>Michelotti Pierantonio,<emph.end type="bold"/> difficolt&agrave; da lui promosse contro il calcolo delle forze del cuore fatto dal <lb/>Keil 104, &egrave; primo a diffidar dell'applicazione delle leggi idrauliche al moto del sangue 117. </s></p><p type="main">

<s><emph type="bold"/>Micrografia,<emph.end type="bold"/> suoi progressi nelle applicazioni allo studio degl'insetti 479, opera di R. </s>

<s>Hoohe 481, <lb/>dove vi si trovano descritti gli occhi delle mosche 490. </s></p><p type="main">

<s><emph type="bold"/>Minerali,<emph.end type="bold"/> come Aristotile gli distingua per le loro diverse origini 369. </s></p><p type="main">

<s><emph type="bold"/>Molinetti Antonio,<emph.end type="bold"/> come spieghi l'adattamento dell'occhio a veder distintintamente nelle varie di&shy;<lb/>stanze 349. </s></p><p type="main">

<s><emph type="bold"/>Montanari Ceminiano<emph.end type="bold"/> descrive la trasfusione del sangue da un agnello in un cane decrepito 161. </s></p><p type="main">

<s><emph type="bold"/>Morgagni Giovan Batista,<emph.end type="bold"/> qual uso egli assegni ai gangli nervosi 249, scopre esser la membrana <lb/>del timpano composta di pi&ugrave; pellicole soprapposte 266. dimostra contro il Mariotte che l'organo <lb/>precipuo della visione &egrave; la retina, e non la cor<gap/>dea 347. </s></p><p type="main">

<s><emph type="bold"/>Mero Lazzaro,<emph.end type="bold"/> suo trattato dei crostacei marini <gap/>84, suo sistema geologico &egrave; uno svolgimento delle <lb/>idee dello Stenone 585. </s></p><p type="main">

<s><emph type="bold"/>Muscoli,<emph.end type="bold"/> non possono nel contrarsi rassomigliarsi alle funi inumidite 52. </s></p><p type="main">

<s><emph type="bold"/>Muscolo minimo,<emph.end type="bold"/> trovato dall'Eustachio nell'osso pietrose 274, casseriano, scoperto anche dall'Acqua&shy;<lb/>pendente nell'interno dell'orecchio 275. </s></p><p type="main">

<s><emph type="bold"/>Nardi Antonio,<emph.end type="bold"/> de'primi in Italia ad accogliere la scoperta del circolo del sangue 155, crede collo <lb/>Harvey che gl'insetti respirino dagli anelli del ventre e se ne assicura coll'esperienza 483. </s></p><p type="main">

<s><emph type="bold"/>Nardi Giovanni,<emph.end type="bold"/> suo trattato <emph type="italics"/>De igne subterraneo<emph.end type="italics"/> 578, lettura di questo trattato raccomandata ai <lb/>suoi discepoli da Galileo 580. </s></p><p type="main">

<s><emph type="bold"/>Nervi,<emph.end type="bold"/> non sono, secondo T. Bartholini, canali, 49, ottici, se siano perforati 320, loro inserzione ec&shy;<lb/>centrica 334. </s></p><p type="main">

<s><emph type="bold"/>Neve,<emph.end type="bold"/> le figure cristalline di lei fu creduto essere stato il primo a osservarle G. D. </s>

<s>Cassini 601, loro <lb/>origine come spiegata dal Cartesio 6<gap/>4. </s></p><p type="main">

<s><emph type="bold"/>Newton Isacco<emph.end type="bold"/> applica il principio delle attrazioni e delle repulsioni molecolari alla formazione dei <lb/>cristalli 613. </s></p><p type="main">

<s><emph type="bold"/>Nitro,<emph.end type="bold"/> sale, ristoratore, secondo il Digby, dell'aria viziata nella respirazione 179. </s></p><p type="main">

<s><emph type="bold"/>Nollet<emph.end type="bold"/> confessa di avere scoperte le lucciole marine dopo il Vianelli 591. </s></p><p type="main">

<s><emph type="bold"/>Notatoio<emph.end type="bold"/> dei pesci, da chi prima scoperto 433. </s></p><p type="main">

<s><emph type="bold"/>Occhio,<emph.end type="bold"/> sua iconografia 333, suo adattamento a vedere in varie distanze, come spiegato 349. </s></p><p type="main">

<s><emph type="bold"/>Ocelli<emph.end type="bold"/> e occhi del bombice, descritti dal Malpighi 490. </s></p><p type="main">

<s><emph type="bold"/>Odorato,<emph.end type="bold"/> qual credessero che ne fosse lo strumento gli antichi 259, come, secondo il Molinetti, si <lb/>moltiplichi nei canaliculi dell'osso cribroso 251, dei pesci, loro organo descritto 460. </s></p><p type="main">

<s><emph type="bold"/>Odori,<emph.end type="bold"/> loro natura descritta da A. </s>

<s>Nardi 260, osservazioni intorno ad essi fatte dal Magalotti 262. </s></p><p type="main">

<s><emph type="bold"/>Olivari<emph.end type="bold"/> corpi, nome dato dal Falloppio ai gangli dei nervi 67. </s></p><p type="main">

<s><emph type="bold"/>Olmi,<emph.end type="bold"/> vermi annidati nelle loro foglie 469. </s></p><p type="main">

<s><emph type="bold"/>Ordinamenti<emph.end type="bold"/> animali secondo Aristotile 352. </s></p><p type="main">

<s><emph type="bold"/>Orecchio<emph.end type="bold"/> dei pesci, cosi volgarmente dette, sono i loro polmoni 447. </s></p><p type="main">

<s><emph type="bold"/>Orecchio<emph.end type="bold"/> esterno variamente configurato nei varii animali 419. </s></p><p type="main">

<s><emph type="bold"/>Ossiciui<emph.end type="bold"/> dell'udito prima commemorati dal Berengario 267, da chi prima veramente scoperti 269, <lb/>dell'udito ne'pesci, descritti dal Severino 458. </s></p><p type="main">

<s><emph type="bold"/>Ossicino<emph.end type="bold"/> dell'udito negli uccelli, descritto dallo Scarpa 420. </s></p><p type="main">

<s><emph type="bold"/>Palme,<emph.end type="bold"/> loro sessualit&agrave; 534. </s></p><p type="main">

<s><emph type="bold"/>Papille<emph.end type="bold"/> nervee ritrovate dal Malpighi sopra la lingua 254, qual sia il loro uso 255, sopra la cute in <lb/>che modo le scoprisse il Malpighi <emph type="italics"/>ivi.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="bold"/>Paracelso<emph.end type="bold"/> riconosce nell'aria l'elixir della vita 177. </s></p><p type="main">

<s><emph type="bold"/>Passo<emph.end type="bold"/> dei quadrupedi, come si faccia secondo Aristotile e secondo l'Acquapendente 396, come secondo <lb/>Galileo e secondo il Borelli 398. </s></p><p type="main">

<s><emph type="bold"/>Pecquet Giovanni,<emph.end type="bold"/> a quali momenti riduca le forze motrici del sangue ne'vasi 100, conferma il moto <lb/>circ<gap/>lare del sangue supposto dall'Harvey 147, narra come scoprisse il ricettacolo del chilo 219-21. </s></p><p type="main">

<s><emph type="bold"/>Peli<emph.end type="bold"/> negli occhi degl'insetti, scoperti dal Vallisnieri 492. </s></p><p type="main">

<s><emph type="bold"/>Perrault Claudio<emph.end type="bold"/> crede che tutti gli organi dei sensi negl'insetti si riducano a quello del tatto 492. </s></p><p type="main">

<s><emph type="bold"/>Pesci artificiall<emph.end type="bold"/> costruiti dal Magiotti, per dimostrar la meccanica dei loro moti 432; naturali, loro <lb/>respirazione negata da Aristotile 440, affermata da Galeno <emph type="italics"/>ivi,<emph.end type="italics"/> circolo del loro sangue, secondo <lb/>il Perrault 449, papille nervee del gusto dove risiedano in essi 455, loro organi che servono <lb/>all'udito e all'<gap/>fatto, secondo il Casserio 457, alcuni di essi nascono spontaneamente, secondo il <lb/>Rondelezio 496. </s></p><pb xlink:href="020/01/1753.jpg" pagenum="628"/><p type="main">

<s><emph type="bold"/>Petali,<emph.end type="bold"/> nome imposto da Fabio Colonna alle foglie colorite dei fiori 542. </s></p><p type="main">

<s><emph type="bold"/>Pettine,<emph.end type="bold"/> nell'occhio degli uccelli 419. </s></p><p type="main">

<s><emph type="bold"/>Peyer Giovan Currado,<emph.end type="bold"/> sua Mericologia 409, obiezioni fatte contro lei e risposte 411. </s></p><p type="main">

<s><emph type="bold"/>Piante,<emph.end type="bold"/> come siano ordinate in un libro attribuito ad Aristotile 361. </s></p><p type="main">

<s><emph type="bold"/>Pietruzze<emph.end type="bold"/> nel ventricolo degli uccelli, loro uso secondo l'Harvey 412, secondo il Borelli 413. </s></p><p type="main">

<s><emph type="bold"/>Pigmento<emph.end type="bold"/> delle tuniche dell'occhio 312. </s></p><p type="main">

<s><emph type="bold"/>Pinne,<emph.end type="bold"/> come siano ne'pesci precipuo organo del nuoto 438. </s></p><p type="main">

<s><emph type="bold"/>Piater Felice<emph.end type="bold"/> enumera le membrane dell'occhio 303. </s></p><p type="main">

<s><emph type="bold"/>Plinio,<emph.end type="bold"/> sua storia naturale 353. </s></p><p type="main">

<s><emph type="bold"/>Polline,<emph.end type="bold"/> creduto pieno di granellini di zolfo 545. </s></p><p type="main">

<s><emph type="bold"/>Polmoni,<emph.end type="bold"/> se i loro moti siano spontanei o necessarii 167. </s></p><p type="main">

<s><emph type="bold"/>Pontedera Gi<gap/>lie,<emph.end type="bold"/> suoi argomenti contro il sistema sessuale delle piante 543. </s></p><p type="main">

<s><emph type="bold"/>Problema<emph.end type="bold"/> curioso di Meccanica animale risoluto prima dall'Acquapendente e poi dal Borelli 78, <lb/>arveiano, come proposto e risoluto 187. </s></p><p type="main">

<s><emph type="bold"/>Problemi<emph.end type="bold"/> varii di Meccanica animale risoluti dal Borelli 81. </s></p><p type="main">

<s><emph type="bold"/>Punctum saliens,<emph.end type="bold"/> da che rappresentato, secondo l'Hales, nel seme delle piante 546. </s></p><p type="main">

<s><emph type="bold"/>Punto<emph.end type="bold"/> cieco nell'occhio, da che dipenda 345. </s></p><p type="main">

<s><emph type="bold"/>Pupilla,<emph.end type="bold"/> sua mobilit&agrave; 513, il Porta e poi l'Acquapendente, avutane la notizia dal Sarpi, la divulgano <lb/>nei loro libri 314. </s></p><p type="main">

<s><emph type="bold"/>Ramazzini Bernardino<emph.end type="bold"/> nota che il sistema geogonico del Burnet riscontra con un romanzo filosofico <lb/>narrato da Francesco Patrizio 575. </s></p><p type="main">

<s><emph type="bold"/>Rane,<emph.end type="bold"/> loro generazione spontanea affermata dai Gesuiti, e negata dagli Accademici fiorentini 498. </s></p><p type="main">

<s><emph type="bold"/>Ray Giovanni<emph.end type="bold"/> attende ad ordinare le piante secondo i soli frutti 365. </s></p><p type="main">

<s><emph type="bold"/>Reaumur (de) Renato Antonio Ferchaud<emph.end type="bold"/> conferma le dottrine del Malpighi intorno alla generazione <lb/>dei vermi nelle galle 475, contradice al Malpighi in alcune cose relative alla respirazione degli <lb/>insetti 485. </s></p><p type="main">

<s><emph type="bold"/>Recchi Nard'Antonio,<emph.end type="bold"/> sue storie naturali del Messico 364. </s></p><p type="main">

<s><emph type="bold"/>Redi Francesco<emph.end type="bold"/> approva, intorno alla digestione, le dottrine di Tommaso Cornelio 205, suo sistema <lb/>della generazione ovarica 390, sue esperienze per dimostrar che le pietruzze nel ventricolo degli <lb/>uccelli non si r<gap/>solvono in chilo 414, crede che i vermi sulle piante siano generati dalla vita <lb/>vegetativa 473, pensa che tutti gli alberi e l'erbe abbiano il maschio e la femmina 534. </s></p><p type="main">

<s><emph type="bold"/>Respirazione<emph.end type="bold"/> animale, singolari idee di Stefano Lorenzini intorno ad essa 448, delle piante 528. </s></p><p type="main">

<s><emph type="bold"/>Reticolo<emph.end type="bold"/> sulla cute delle foglie, simile al malpighiano sulla pelle degli animali 529. </s></p><p type="main">

<s><emph type="bold"/>Retina<emph.end type="bold"/> dell'occhio, sua struttura secondo il Valsalva 319. </s></p><p type="main">

<s><emph type="bold"/>Reversivo, nerve,<emph.end type="bold"/> suo uso nella formazion della voce dimostrato da R. </s>

<s>Colombo 422. </s></p><p type="main">

<s><emph type="bold"/>Rombo,<emph.end type="bold"/> come non sia veramente questa la figura degli elementi muscolari 77. </s></p><p type="main">

<s><emph type="bold"/>Rondelezio Guglielmo,<emph.end type="bold"/> come ordini la storia naturale dei pesci 354, canone sperimentale formulato <lb/>da lui 441. </s></p><p type="main">

<s><emph type="bold"/>Rosa polonica<emph.end type="bold"/> del Quercetano 608. </s></p><p type="main">

<s><emph type="bold"/>Rudbeck Olao,<emph.end type="bold"/> come fosse uno degli scopritori del Canale toracico 227. </s></p><p type="main">

<s><emph type="bold"/>Ruschi Giovan Batista,<emph.end type="bold"/> come preparasse al Petit la scoperta del Canal <emph type="italics"/>godronn&eacute;<emph.end type="italics"/> nell'occhio 325. </s></p><p type="main">

<s><emph type="bold"/>Ruysch Federigo<emph.end type="bold"/> dimostra al Bils, che le negava, le valvole ne'linfatici 236, scopre nell'occhio la <lb/>membrana detta ruischiana dal nome di lui 308. </s></p><p type="main">

<s><emph type="bold"/>Sacculo embrionale,<emph.end type="bold"/> qualificato dall'Harvey per un uovo 385. </s></p><p type="main">

<s><emph type="bold"/>Sagredo Gian Francesco,<emph.end type="bold"/> sua teoria della vista 341. </s></p><p type="main">

<s><emph type="bold"/>Sali,<emph.end type="bold"/> Sono secondo il Willis i principii formativi di tutti i corpi 605, son gli strumenti eccitatori del <lb/>gusto <emph type="italics"/>ivi,<emph.end type="italics"/> hanno secondo il Bellini figure primigenie 606, &egrave; in essi, come nelle altre cose, insita <lb/>una loro propria e distinta figura, secondo il Fracassati 607, fissi nelle ceneri e volatili ne'vapori, <lb/>formano secondo Filippo Bonanni le figure de'corpi ai quali erano appartenuti 608, come a loro, <lb/>residenti nei vini, attribuisca il Magalotti la causa di una sua mala affezione cutanea 609, come <lb/>si spiegasse in vari modi l'adesione delle loro particelle nella composizione del tutto 612. </s></p><p type="main">

<s><emph type="bold"/>Salto,<emph.end type="bold"/> negli animali, sua teoria meccanica 82. </s></p><p type="main">

<s><emph type="bold"/>Sangue<emph.end type="bold"/> non pu&ograve; far enfiare i muscoli per moverli 52. </s></p><p type="main">

<s><emph type="bold"/>Santorio Sant<gap/>rre<emph.end type="bold"/> dimostra che la retina, per ritener le immagini, dee essere opaca 342. </s></p><p type="main">

<s><emph type="bold"/>Sarpi Paolo<emph.end type="bold"/> se gli si possa attribuir la scoperta delle valvole delle vene 146, non conobbe il circolo <lb/>del sangue 153, osserva la variabile grandezza della pupilla 313. </s></p><p type="main">

<s><emph type="bold"/>Schelhammer Cristoforo,<emph.end type="bold"/> sua teoria dell'udito 294. </s></p><p type="main">

<s><emph type="bold"/>Scilla Agostino,<emph.end type="bold"/> suoi retti giudizi intorno all'origine delle glossopietre di Malta 565. </s></p><pb xlink:href="020/01/1754.jpg" pagenum="629"/><p type="main">

<s><emph type="bold"/>Sclerotica<emph.end type="bold"/> dell'occhio, sua composizione anatomica 304, da che sia resa trasparente nella parte an&shy;<lb/>teriore della cornea 306. </s></p><p type="main">

<s><emph type="bold"/>Semicircolari<emph.end type="bold"/> canali nell'organo auditorio dei pesci 462. </s></p><p type="main">

<s><emph type="bold"/>Servet Michele,<emph.end type="bold"/> suo libro <emph type="italics"/>Christianismi restitutio<emph.end type="italics"/> 134, come descrive il circolo polmonare 135, <lb/>confrontato col Colombo 139, di cui ripete le dottrine apprese nella sua scuola 140. </s></p><p type="main">

<s><emph type="bold"/>Sessualit&agrave;<emph.end type="bold"/> delle piante professata dal Valentin, dal Vaillant, dal Bradley e da altri anteriori al Linneo 541. </s></p><p type="main">

<s><emph type="bold"/>Setto<emph.end type="bold"/> medio del cuore dimostrato dal Colombo essere imperforato 138, membranoso del vestibolo, <lb/>organo precipuo dell'udito, secondo il Cotunnio 298. </s></p><p type="main">

<s><emph type="bold"/>Sifone idrostatico<emph.end type="bold"/> applicato al moto del sangue per le vene 106. </s></p><p type="main">

<s><emph type="bold"/>Spallanzani Lazzero<emph.end type="bold"/> verifica che il moto del sangue ora si conferma ora no alle leggi idrauliche 122, <lb/>conclusione importantissima di lui, relativa all'applicazione di queste leggi 123, primo a osservare <lb/>il circolo del sangue negli animali caldi 151, primo o scoprire il circolo coronario 152, sue espe&shy;<lb/>rienze sopra la digestione 207, sue esperienze per dimostrar che le pietruzze ne'ventricoli degli <lb/>uccelli non fanno, in triturare i cibi, l'ufficio dei denti 414, propone alcune esperienze intorno <lb/>alla germogliazione dei semi, fatte gi&agrave; dal Malpighi 557. </s></p><p type="main">

<s><emph type="bold"/>Spermazzoi,<emph.end type="bold"/> loro scoperta e loro usi nell'opera della generazione 392, negati da molti, n'&egrave; confermata <lb/>l'esistenza dal Vailisnieri 394. </s></p><p type="main">

<s><emph type="bold"/>Spiriti vitali,<emph.end type="bold"/> loro origine e natura 51. </s></p><p type="main">

<s><emph type="bold"/>Staffa,<emph.end type="bold"/> ossicino dell'udito, questioni intorno alla sua prima invenzione 271, quali si creda esser<gap/>e <lb/>stati i veri inventori 272. </s></p><p type="main">

<s><emph type="bold"/>Stami,<emph.end type="bold"/> fanno, secondo il Grew, ne'fiori, l'ufficio tutt'insieme di maschi e di femmine 538. </s></p><p type="main">

<s><emph type="bold"/>Stenone Niccol&ograve;,<emph.end type="bold"/> suo <emph type="italics"/>Specimen Myologiae<emph.end type="italics"/> 36, difficolt&agrave; opposte da lui alla teorica del Borelli intorno <lb/>ai moti muscolari 56, primo a descrivere l'anatomia del cuore 86, primo a professare l'ovologia 386, <lb/>concetto ch'egli ebbe della respirazione 447, sue congetture intorno all'origine dei corpi marini <lb/>sui monti 564, suo Prodromo geologico perch&egrave; scritto in latino 571. </s></p><p type="main">

<s><emph type="bold"/>Stimmate<emph.end type="bold"/> negl'insetti scoperte dal Malpighi 484. </s></p><p type="main">

<s><emph type="bold"/>Strumenti,<emph.end type="bold"/> per mezzo dei quali muovesi il corpo animale, 72. </s></p><p type="main">

<s><emph type="bold"/>Strumento<emph.end type="bold"/> del gran vacuo inventato dal Borelli 504. </s></p><p type="main">

<s><emph type="bold"/>Swammerdam Giovanni,<emph.end type="bold"/> sua esperienza per dimostrar la propulsione dell'aria nel respirare 171, <lb/>come si lusingasse di avere egli il primo sciolto il problema arveiano 295, dimostra le valvole <lb/>dei linfatici 236. </s></p><p type="main">

<s><emph type="bold"/>Tatto,<emph.end type="bold"/> suo strumento secondo gli antichi 253. </s></p><p type="main">

<s><emph type="bold"/>Teofrasfo<emph.end type="bold"/> nega la sessualit&agrave; delle piante 533. </s></p><p type="main">

<s><emph type="bold"/>Termometro Santoriano<emph.end type="bold"/> applicato dal Borelli all'ascesa del succo nelle piante 519. </s></p><p type="main">

<s><emph type="bold"/>Terre<emph.end type="bold"/> continentali e mari, loro avvicendamento secondo Aristotile 567. </s></p><p type="main">

<s><emph type="bold"/>Testicoli femminei,<emph.end type="bold"/> e loro usi secondo il Berengario 383. </s></p><p type="main">

<s><emph type="bold"/>Timone<emph.end type="bold"/> delle navi, suo uso applicato dal Borelli al volo degli uccelli 405. </s></p><p type="main">

<s><emph type="bold"/>Timpano<emph.end type="bold"/> secondario, nome imposto dallo Scarpa alla finestra rotonda dell'orecchio 299. </s></p><p type="main">

<s><emph type="bold"/>Torace,<emph.end type="bold"/> moti di lui studiati dall'Acquapendente sopra gli uccelli 415. </s></p><p type="main">

<s><emph type="bold"/>Torricelli Evangelista,<emph.end type="bold"/> come precorresse alla istituzione iatromeccanica 28, strumenti per uso me&shy;<lb/>dico inventati da lui 29, sue osservazioni intorno alle figure dei cristalli 595. </s></p><p type="main">

<s><emph type="bold"/>Toscana,<emph.end type="bold"/> sue varie et&agrave; geologiche rappresentate dallo Stenone 572. </s></p><p type="main">

<s><emph type="bold"/>Tournefort Giuseppe,<emph.end type="bold"/> suo metodo di ordinare le piante 367. </s></p><p type="main">

<s><emph type="bold"/>Trachee<emph.end type="bold"/> polmonari scoperte dal Malpighi negl'insetti 484, nelle piante, e loro usi 518. </s></p><p type="main">

<s><emph type="bold"/>Tuba eustachiana,<emph.end type="bold"/> nome imposto dal Valsalva a un acquedotto scoperto dall'Eustachio 280, sua in&shy;<lb/>venzione attribuita ad Aristotile 281, com'ella sovvenga apportuna al senso nei sordi 289, fal&shy;<lb/>loppiana, descritta dal suo proprio inventore 383. </s></p><p type="main">

<s><emph type="bold"/>Tuoni<emph.end type="bold"/> della voce, come variamente modulati secondo l'Acquapendente 424. </s></p><p type="main">

<s><emph type="bold"/>Udito,<emph.end type="bold"/> suo pi&ugrave; intimo organo come funzioni secondo l'Eustachio 287, come creduto volontario dal&shy;<lb/>l'Acquapendente 290, esiste anche ne'pesci, secondo il Rondelezio 456, organi da lui descritti <emph type="italics"/>ivi.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="bold"/>Ulmo Antonio<emph.end type="bold"/> seziona le galline in servizio dell'Aldovrandi 381. </s></p><p type="main">

<s><emph type="bold"/>Umore,<emph.end type="bold"/> che inonda l'orecchio interno, scoperto dal Valsalva 284, che riempie tutto il Labirinto, sco&shy;<lb/>perto dal Cotunnio <emph type="italics"/>ivi,<emph.end type="italics"/> acqueo dell'occhio trovato dai primi anatomici scarso 322, suo poter re&shy;<lb/>frangente 338, vitreo, sua tunica propria 324, suoi usi, secondo l'Acquapendente 338, cristallino, <lb/>sua struttura lamellare 327, del Morgagni 327, vaginale e ghiandole che lo secernono 391. </s></p><p type="main">

<s><emph type="bold"/>Untuesit&agrave;,<emph.end type="bold"/> a che fine sullata dalla superficie dei pesci 452. </s></p><p type="main">

<s><emph type="bold"/>Uovo<emph.end type="bold"/> gallinaceo, perch&egrave; scelto dall'Harvey a soggetto de'suoi studi embriologici 382. </s></p><p type="main">

<s><emph type="bold"/>Utere<emph.end type="bold"/> delle galline 381, nelle cerve trovato chiuso dall'Harvey 384. </s></p><pb xlink:href="020/01/1755.jpg" pagenum="630"/><p type="main">

<s><emph type="bold"/>Valli<emph.end type="bold"/> sulla superficie terrestre, come formate 584. </s></p><p type="main">

<s><emph type="bold"/>Vallianieri Antonio<emph.end type="bold"/> si meraviglia degli errori rinnovellati in Francia intorno all'origine dei corpi <lb/>marini sui monti 566, compendia elegantemente il romanzo geologico raccontato da Francesco <lb/>Patrizio 575. </s></p><p type="main">

<s><emph type="bold"/>Valsalva Anton Maria<emph.end type="bold"/> esamina e descrive pi&ugrave; diligentemente la Tuba eustachiana 280, sue esperienze <lb/>per dimostrar come la luce operi sopra la retina 348. </s></p><p type="main">

<s><emph type="bold"/>Valvele<emph.end type="bold"/> delle vene, loro efficacia in promovere il corso del sangue, dimostrata dal Borelli 108, loro <lb/>esistenza perch&egrave; negata dal Vesalio 144, perch&egrave; dal Falloppio 145, dei vasi linfatici, da chi prima <lb/>scoperti 235. </s></p><p type="main">

<s><emph type="bold"/>Van-Horne Giovanni<emph.end type="bold"/> racconta come riuscisse a scoprire il canale toracico 221, medita sul sistema <lb/>della generaziono dell'uomo e dei quadrupedi dall'uovo 337, suo Prodromo al trattato della ge&shy;<lb/>nerazione 338. </s></p><p type="main">

<s><emph type="bold"/>Ventricoli<emph.end type="bold"/> della laringe, loro usi nel modulare i tuoni, secondo il Morgagni 427, dei ruminanti, nomi <lb/>a loro imposti da Aristotile 406. </s></p><p type="main">

<s><emph type="bold"/>Verle Giovan Batista,<emph.end type="bold"/> sua anatomia artifiziale dell'occhio 310. </s></p><p type="main">

<s><emph type="bold"/>Vesalio Andrea,<emph.end type="bold"/> suoi sette libri di anatomia contro Galeno 12, suo esame alle osservazioni anatomiche <lb/>del Falloppio 18, sua teoria dei moti muscolari 45, come descriva la struttura del cuore 88, come <lb/>si approprii certe idee di Galeno 130, e del Berengario 131, primo a designaro il forame ovale <lb/>nel feto 189, si appropria la scoperta degli ossicini dell'udito, poi subito rivendicato dagl'Italiani <lb/>all'Achillini e al Berengario 268, a quante ei riduca le parti componenti l'occhio 302, confessa <lb/>di avere errato nel detorminare, rispetto agli umori, la quantit&agrave; dell'acqueo nell'occhio 323. </s></p><p type="main">

<s><emph type="bold"/>Vescica notatoria<emph.end type="bold"/> de'pesci, usi di lei accennati prima dal Rondelezio 431, poi da Galileo 432, &egrave; in&shy;<lb/>nata in lei l'ar<gap/>a secondo il Cornelio <emph type="italics"/>ivi,<emph.end type="italics"/> meato d'onde esce da lei l'aria contenutavi, scoperto <lb/>dagli Accademici del Cimento 433, canaliculo che la mette in comunicazione coll'esterno, scoperto <lb/>dal Fracassati <emph type="italics"/>ivi,<emph.end type="italics"/> creduta servire alla respirazione dall'Harvey e dal Mersenno 434, sfintere di <lb/>lei, che secondo il Borelli la comprime e la dilata 435, mancante in alcuni pesci, da che venga <lb/>supplita 436. </s></p><p type="main">

<s><emph type="bold"/>Vescicole pn<gap/>nmatiche<emph.end type="bold"/> nel ventre degli uccelli osservate dall'Acquapendente 416, dimostrate dal&shy;<lb/>l'Harvey 417, loro usi nella respirazione 418. </s></p><p type="main">

<s><emph type="bold"/>Vespucci A<gap/>erigo<emph.end type="bold"/> accenna alla Storia naturale del Nuovo Mondo 353. </s></p><p type="main">

<s><emph type="bold"/>Vianelli Giuseppe<emph.end type="bold"/> racconta come scoprisse nelle lucciole la causa della fosforescenza marina 498. </s></p><p type="main">

<s><emph type="bold"/>Vidio Guido<emph.end type="bold"/> ammette il circolo polmonare 136, designa i mescoli ordinati ai moti del torace 173. </s></p><p type="main">

<s><emph type="bold"/>Vista,<emph.end type="bold"/> come si faccia, dimostrato sperimentalmente, prima da Leonardo da Vinci 336, e poi dal <lb/>Porta 337. </s></p><p type="main">

<s><emph type="bold"/>Viviani Vi<gap/>io,<emph.end type="bold"/> qual parte egli avesse nella Miologia dello Stenone 36, suo discorso intorno ai <lb/>minerali della Toscana 569, &egrave; sollecitato da Erasmo Bartholin a studiare il fatto della duplice <lb/>rifrazione 599. </s></p><p type="main">

<s><emph type="bold"/>Vocali, nervi,<emph.end type="bold"/> dimostrati dalle vivisazioni di R. </s>

<s>Colombo 423. </s></p><p type="main">

<s><emph type="bold"/>Velo<emph.end type="bold"/> degli uccell&igrave;, sua meccanica secondo l'Acquapendente 401, secondo il Borelli 402, uso delle penne <lb/>nell'esercizio di lui <emph type="italics"/>ivi.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="bold"/>Volontaril,<emph.end type="bold"/> moti de'muscoli, applicati al cuore, come il Cartesio gli spieghi 63. </s></p><p type="main">

<s><emph type="bold"/>Volta Alessandro<emph.end type="bold"/> dimostra essere l'elcttricit&agrave; galvanica insufficiente causa dei moti muscolari 71. </s></p><p type="main">

<s><emph type="bold"/>Vuote,<emph.end type="bold"/> esperienze del Boyle, per concluder se nascano in esso nuovi viventi 557. </s></p><p type="main">

<s><emph type="bold"/>Wahibom Gustavo<emph.end type="bold"/> risponde alle difficolt&agrave; promosse dal Pontedera, e da altri, contro il sistema ses&shy;<lb/>suale delle piante 547. </s></p><p type="main">

<s><emph type="bold"/>Willis Tommase<emph.end type="bold"/> dice che l'aria inspirata riaccende il sangue 180, nega esister nei pesci un nervo <lb/>che presieda all'udito 462. </s></p><p type="main">

<s><emph type="bold"/>Woodward Giovanni,<emph.end type="bold"/> sua storia naturale della Terra 576. </s></p><p type="main">

<s><emph type="bold"/>Zona<emph.end type="bold"/> scoperta nell'occhio da Gotofredo Zinn 326. </s></p><p type="main">

<s><emph type="bold"/>Zone<emph.end type="bold"/> dei canali semicircolari, quale uso abbiano nell'orecchio a produrre, secondo il Valsaiva, il <lb/>senso dell'udito 296. </s></p><p type="main">

<s><emph type="bold"/>Zucchere,<emph.end type="bold"/> figure cristalline osservate sulla superficie di lui col Microscopio 606. <pb xlink:href="020/01/1756.jpg"/><pb xlink:href="020/01/1757.jpg"/></s></p><pb xlink:href="020/01/1758.jpg"/><p type="main">

<s>Finito di stampare in Bologna presso la <lb/>Libreria Editrice Forni nel Giugno 1970 </s></p><pb xlink:href="020/01/1759.jpg"/></chap><chap><p type="main">

<s>350478 Storia Del Metodo Sperimentale Italia </s></p><p type="main">

<s><emph type="center"/>THE SOURCES OF SCIENCE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Editor-in-Chief: Harry Woolf<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Willis K. </s>

<s>Shepard Professor of the History of <lb/>Science, The Johns Hopkins University<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="020/01/1760.jpg"/><p type="main">

<s><emph type="center"/><emph type="bold"/><emph type="italics"/>Storia del Metodo<emph.end type="italics"/><emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/><emph type="italics"/>Sperimentale in Italia<emph.end type="italics"/><emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>by RAFFAELLO CAVERNI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>in Six Volumes<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Volume IV<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>THE SOURCES OF SCIENCE, NO. 134<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT CORPORATION<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>NEW YORK LONDON 1972<emph.end type="center"/></s></p><pb xlink:href="020/01/1761.jpg"/><p type="main">

<s><emph type="center"/>Reproduced here is the Florence edition of 1891-1900.<emph.end type="center"/></s></p><figure id="id.020.01.1761.1.jpg" xlink:href="020/01/1761/1.jpg"/><p type="main">

<s><emph type="center"/>Copyright &copy; 1972 by Johnson Reprint Corporation All rights reserved<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT CORPORATION<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>111 Fifth Avenue, New York, N.Y. 10003, U.S.A.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT COMPANY LTD.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Shipton Group House, 24/28 Oval Road, London, NW1 7DD, England<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Printed in Italy<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="020/01/1762.jpg"/><p type="main">

<s><emph type="center"/>DEL METODO SPERIMENTALE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>APPLICATO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>ALLA SCIENZA DEL MOTO DEI GRAVI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>PARTE PRIMA<emph.end type="center"/><pb xlink:href="020/01/1763.jpg"/></s></p><pb xlink:href="020/01/1764.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO I.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Della Scienza del moto nel secolo XVI<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle prime istituzioni statiche nella Scuola peripatetica, e nella alessandrina &mdash; II. </s>

<s>Dei principii <lb/>statici di Giordano Nemorario: de'manoscritti di Leonardo da Vinci, e delle fonti, dalle quali <lb/>deriv&ograve; in essi la Scienza del moto. </s>

<s>&mdash; III. </s>

<s>Delle dottrine statiche degli Antichi promosse nello <lb/>Note manoscritte di Leonardo da Vinci. </s>

<s>&mdash; IV. </s>

<s>Di alcuni pi&ugrave; notabili teoremi e problemi di <lb/>Meccanica dimostrati, e risoluti da Leonardo da Vinci. </s>

<s>&mdash; V. </s>

<s>Dei principii dinamici professati <lb/>da Leonardo da Vinci intorno alle leggi della caduta dei gravi, e della teoria de'proietti. </s>

<s>&mdash; <lb/>VI. </s>

<s>Degli altri principali Autori, che promossero la Meccanica dopo la prima met&agrave; del se&shy;<lb/>colo XVI. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Gli studi del Filosofo intorno ai tre grandi regni della Natura, per dare <lb/>un'idea de'quali abbiamo scritto il III Tomo della nostra Storia, si ridu&shy;<lb/>cono insomma, in una sentenza sola concludendo il lungo discorso, a inve&shy;<lb/>stigare le leggi del moto, da cui risulta ai varii corpi l'essere, e in cui ma&shy;<lb/>nifestasi, a noi che non ne sappiamo altro, la vita. </s>

<s>Che se le stesse fisiche <lb/>discipline hanno per loro particolar soggetto il moto, che atteggia in varie <lb/>guise la materia, e si trasforma in elettricit&agrave;, in luce e in calore, bene &egrave; a <lb/>dir che avessero i Peripatetici gran ragione di sentenziar col loro Maestro, <lb/>che ignorato il moto veniva necessariamente a ignorarsi la Natura. </s>

<s>Ond'&egrave; <lb/>facile dietro ci&ograve; a congetturare, anche prima di averne avuto dai documenti <lb/>storici la certezza, che dovette aver la Meccanica una delle prime e pi&ugrave; di&shy;<lb/>ligenti culture nella naturale Filosofia degli antichi. </s></p><p type="main">

<s>Si fece anche della Meccanica, come di tutte le discipline applicabili <lb/>agli usi della vita, una distinzione in pratica e in razionale, e quella per <pb xlink:href="020/01/1765.jpg" pagenum="8"/>logica necessit&agrave;, come in altri simili esempi s'osserva, dovette precedere a <lb/>questa. </s>

<s>Come gli uomini, ne'loro primi esercizi delle arti manuali, incomin&shy;<lb/>ciassero a servirsi della leva per inalzare pi&ugrave; facilmente i pesi, o del cuneo <lb/>per spezzarli e renderli pi&ugrave; maneggevoli, o del martello per ficcare adden&shy;<lb/>tro lo stesso cuneo, e per via della penetrazione congiungere stabilmente <lb/>insieme pi&ugrave; corpi; non &egrave; facile a dire, ma s'ingannerebbe grandemente co&shy;<lb/>lui, che credesse doversi attribuir l'invenzione di questa e di altre simili <lb/>macchine all'industria, e all'ingegno della tale o tale altra particolare per&shy;<lb/>sona. </s>

<s>Investigar dunque l'origine di cos&igrave; fatti meccanici ritrovati non si <lb/>rende per questo solo difficile, perch&egrave;, di tempi cos&igrave; lontani, ci mancano gli <lb/>storici documenti, ma perch&egrave; le prime origini delle cose, come vedesi per <lb/>l'esempio delle piante e degli animali, si trovano nelle virt&ugrave; de'loro semi <lb/>latenti, cosicch&egrave;, non esplicate ancora in s&egrave; medesime, si rendono perci&ograve; <lb/>inesplicabili a noi. </s>

<s>Di qui viene ch'essendo noi stessi ciechi a quella impe&shy;<lb/>netrabile vista, siamo soliti di lusingarci col dire che la pratica &egrave; cieca. </s></p><p type="main">

<s>La razionale cultura dell'ingegno, nell'esercizio delle arti meccaniche, <lb/>si rassomiglia insomma alla cultura delle piante, la quale incomincia allora <lb/>che, sviluppatosi il seme da'suoi invogli, si rende nella definita forma delle <lb/>sue parti riconoscibile allo stesso cultore, che non sa, n&egrave; si cura d'investi&shy;<lb/>gare il mistero della nuova mirabile apparizione. </s>

<s>I Filosofi pure ebbero a <lb/>incominciare allora a coltivar la scienza dei pesi, che furono dalle arti ma&shy;<lb/>nuali esercitati que'primi e pi&ugrave; semplici strumenti, da rendere applicabili o <lb/>da moltiplicare le forze, che l'uomo stesso ritrovava in s&egrave;, o che studiavasi <lb/>di ricavare dai moti degli animali e dai mondani elementi. </s></p><p type="main">

<s>A voler dire chi fossero que'primi antichi Filosofi s'incontrano le me&shy;<lb/>desime difficolt&agrave;, che a voler mettersi a designare delle cose i primi prin&shy;<lb/>cipii, i quali poniamo pure che ne'civili antichissimi consorzii, rispetto a <lb/>quella particolare scienza di che si tratta, fossero svolti; la distinta e pi&ugrave; <lb/>chiara notizia nulladimeno ci s'adombra dalla lontananza dei tempi, o ci ri&shy;<lb/>mane affatto ignorata per mancanza di documenti. </s>

<s>Talete Milesio, Pitagora, <lb/>Aristeo, Ippocrate di Chio e Archita non sono altro per noi che apparizioni <lb/>d'ombre senza persona, o, per pi&ugrave; vera e meglio appropriata immagine, <lb/>invisibili rivi, delle sotterranee acque menate dai quali ci possiamo solamente <lb/>accorgere dall'ingrossare della corrente. </s>

<s>Presso a quattrocento anni prima <lb/>dell'era volgare si divise quella corrente in due grandi fiumi, i quali, mi&shy;<lb/>rabile a dire, in tanto correre in lungo si sono scavati gli alvei cos&igrave; profondi <lb/>che, attraversati e rimescolati con innumerevoli altre ubertose sorgenti in&shy;<lb/>contrate per via, serbano ancora in mezzo le loro proprie vestigia distinte <lb/>a chi d'alto gli rimira dai colli alle foci. </s></p><p type="main">

<s>Platone e Aristotile sono i due grandi fiumi, che da XXIII secoli ri&shy;<lb/>corrono a irrigare tutte intere alla scienza le membra, e avendo le due onde <lb/>fluenti qualit&agrave; varia e moto quasi contrario par che sieno provvidamente <lb/>ordinate a mantenere, in quelle stesse membra, perenne il circolo della vita. </s>

<s><lb/>Quel di Stagira, pi&ugrave; giovane e discepolo dell'Ateniese, fa nella storia della <pb xlink:href="020/01/1766.jpg" pagenum="9"/>Meccanica la prima comparsa, perch'egli usc&igrave; fuori a insegnarla in un trat&shy;<lb/>tatello, che porta scritto in fronte il nome di lui, e dell'autenticit&agrave; del quale <lb/>non lasciano dall'altra parte a dubitare le distintive note del filosofico in&shy;<lb/>gegno. </s>

<s>A leggere infatti le prime parole, nelle quali Aristotile definisce le <lb/>facolt&agrave; dell'arte meccanica, si rivelano aperti i principii professati da lui <lb/>intorno all'arte e all'ingegno dell'uomo che, non arrestato dalle difficolt&agrave;, <lb/>trionfa vittorioso sopra la stessa reluttante Natura. </s>

<s>La Meccanica perci&ograve; defi&shy;<lb/>niscesi dal Filosofo, di questa vittoria dell'ingegno dell'uomo, come il pi&ugrave; <lb/>proprio e pi&ugrave; splendido esempio. </s>

<s>&ldquo; Quando igitur quippiam praeter natu&shy;<lb/>ram oportuerit facere, difficultate sua haesitationem praestat, arteque indi&shy;<lb/>get, quam ob rem eam artis partem, quae huiusmodi succurrit difficulta&shy;<lb/>tibus, Mechanicam appellamus &rdquo; (Arist., Quaest. </s>

<s>mech. </s>

<s>Operum, T. XI, <lb/>Venetiis 1560, fol. </s>

<s>27). </s></p><p type="main">

<s>I Meccanici, che poi pi&ugrave; saviamente seguitarono altri instituti, riconob&shy;<lb/>bero anche in queste idee i viziosi peripatetici principii, e Galileo primo fra <lb/>gli altri dimostr&ograve; non essere nelle macchine punto vero che vi trionfino <lb/>l'ingegno e l'arte dell'uomo, quasi ingannando la Natura &ldquo; istinto della <lb/>quale, anzi fermissima constituzione, &egrave; che niuna resistenza possa esser su&shy;<lb/>perata da forza, che di quella non sia pi&ugrave; potente &rdquo; (Alb. </s>

<s>XI, 85). </s></p><p type="main">

<s>Da un tal vizioso fermento compresa la Meccanica aristotelica, sembre&shy;<lb/>rebbe che ne fosse per riuscire tutta intera la massa corrotta, n&egrave; fa perci&ograve; <lb/>maraviglia che Galileo stesso se lo credesse, e che lo facesse credere a tutta <lb/>la sua scuola. </s>

<s>S'ingannava per&ograve;, cos&igrave; giudicando, quell'autorevolissimo Mae&shy;<lb/>stro della nuova scienza del moto, e appariranno dal processo della nostra <lb/>Storia manifesti ai lettori i dannosissimi effetti di quell'inganno. </s>

<s>Ma giova <lb/>intanto accennare alla ragione perch&egrave; la massima parte delle Questioni ari&shy;<lb/>stoteliche, con gran maraviglia di chi sa meditarle, risolute dall'Autore con&shy;<lb/>forme al vero, si rimanessero provvidamente immuni dal contagio peripate&shy;<lb/>tico. </s>

<s>Quella ragione poi da null'altro dipende che dalla natura propria delle <lb/>trattate questioni, le quali partecipano tutto insieme, come lo stesso Aristo&shy;<lb/>tile avverte, della scienza matematica e della naturale. </s>

<s>&ldquo; Sunt autem haec <lb/>neque naturalibus omnino quaestionibus eadem, neque seiungata valde; ve&shy;<lb/>rum mathematicarum contemplationum, naturaliumque communia &rdquo; (Quaest. </s>

<s><lb/>cit., fol. </s>

<s>27). Ma perch&egrave; la matematica &egrave; prevalente, ecco ci&ograve; che salva la <lb/>pi&ugrave; gran parte di quelle stesse meccaniche questioni dal temuto contagio, e <lb/>che le imprime delle indelebili note del vero. </s></p><p type="main">

<s>Tutto il fondamento infatti della nuova istituzione meccanica &egrave;, secondo <lb/>Aristotile, riposto nelle ammirande dignit&agrave;, e nelle propriet&agrave; geometriche del <lb/>circolo, che si rappresentano alla viva mente di lui nel primo mettersi a <lb/>penetrare i misteriosi effetti del vette. </s>

<s>Come mai, si domanda, un gran peso, <lb/>impossibile a sollevar con la mano, si rende cos&igrave; facilmente trattabile, usan&shy;<lb/>dovi quello strumento? </s>

<s>E risponde il Filosofo: &ldquo; Omnium autem huiusmodi <lb/>causae principium habet circulus &rdquo; (ibid., fol. </s>

<s>28). Circolare infatti &egrave; il moto <lb/>della Libbra, alla quale riducesi il Vette, e perch&egrave; nel Vette stesso risol-<pb xlink:href="020/01/1767.jpg" pagenum="10"/>vonsi finalmente i moti di quasi tutti gli altri meccanici strumenti, &egrave; perci&ograve; <lb/>che tutta quanta la scienza, di che si tratta, &egrave; misteriosamente compresa <lb/>nelle propriet&agrave; del cerchio. </s>

<s>&ldquo; Ea igitur, quae circa Libram fiunt, ad circu&shy;<lb/>lum referuntur, quae vero circa Vectem ad ipsam Libram: alia autem fere <lb/>omnia, quae circa mechanicas motiones fiunt, ad Vectem &rdquo; (ibid.). </s></p><p type="main">

<s>Penetriamo dunque, prosegue a ragionare Aristotile, se vogliamo inten&shy;<lb/>dere le ragioni del moto, il meccanismo dello stesso circolo, il quale intanto <lb/>ci si presenta come generato dalla composizione di due moti. </s>

<s>E perch&egrave; qui <lb/>massimamente s'asconde quel mistero, che vuol rivelare alla nostra mente <lb/>il Filosofo, incomincia dal far notare che, della detta composizione, l'effetto <lb/>resultante &egrave; diverso, secondo che le parti componenti hanno o no una de&shy;<lb/>finita proporzione fra loro. </s>

<s>Se quella proporzione esiste, la resultante del <lb/>moto &egrave; una linea retta, altrimenti &egrave; una curva. </s>

<s>La prima conclusione &egrave; di <lb/>tanta importanza nella storia della Meccanica, che vogliamo invitar l'Autore <lb/>stesso a dimostrarcela, tanto pi&ugrave; che il processo geometrico di lui ha tutta <lb/>la facilit&agrave; e la chiarezza desiderabile in un Antico. </s></p><p type="main">

<s>&ldquo; Sit enim proportio, dice Aristotile, secundum quam latum fertur, <lb/>quam habet AB ad AC (fig. </s>

<s>1), et A quidem feratur versus B, AB vero <lb/><figure id="id.020.01.1767.1.jpg" xlink:href="020/01/1767/1.jpg"/></s></p><p type="caption">

<s>Figura 1.<lb/>subter feratur versus MC: latum autem sit A <lb/>quidem ad D, ubi autem est AB versus E. </s>

<s><lb/>Quoniam igitur lationis erat proportio quam <lb/>AB habet ad AC necesse est et ad AE hanc <lb/>habere proportionem. </s>

<s>Simile igitur est propor&shy;<lb/>tione parvum quadrilaterum maiori. </s>

<s>Quamo&shy;<lb/>brem et eadem illorum est diameter, et A erit <lb/>ad F. </s>

<s>Eodem etiam ostendetur modo ubicum&shy;<lb/>que latio deprehendatur, semper enim supra diametrum erit. </s>

<s>Manifestum <lb/>igitur quod id, quod secundum diametrum duabus fertur lationibus, acces&shy;<lb/>satio secundum laterum proportionem fertur &rdquo; (ibid., ad t.). Il quadrilatero <lb/>&egrave; in questo caso figurato rettangolo, ma il Teorema aristotelico &egrave; generale, <lb/>e si applica indifferentemente dall'Autore anche al parallelogrammo, per <lb/>la diagonale di cui si fa, pur come dianzi, la resultante del moto, secondo <lb/><figure id="id.020.01.1767.2.jpg" xlink:href="020/01/1767/2.jpg"/></s></p><p type="caption">

<s>Figura 2.<lb/>la proporzione de'lati che rappresentano le <lb/>componenti. </s>

<s>Disegnatosi infatti il parallelo&shy;<lb/>grammo BEC (fig. </s>

<s>2), come vedesi al fol. </s>

<s>29 <lb/>delle citate Questioni meccaniche, son tali le <lb/>chiarissime parole ivi da Aristotile scritte per <lb/>illustrarlo: &ldquo; Si quidem igitur in proportione <lb/>feratur quam habet BE, EC, fertur utique <lb/>secundum diametrum ubi BC. &rdquo; </s></p><p type="main">

<s>Chi ha letto quel che continuamente si ripete oramai da tutti, dopo il <lb/>Lagrange, che cio&egrave; fu Galileo il primo a comporre e a decomporre le forze <lb/>nel rettangolo, e il Varignon a far pi&ugrave; generalmente lo stesso nel paralle&shy;<lb/>logrammo, dee provar necessariamente gran maraviglia de'sopra allegati due <pb xlink:href="020/01/1768.jpg" pagenum="11"/>chiarissimi testi, ma per non precorrere alla storia de'fatti importantissimi, <lb/>che dipendono da questo ora accennato, seguitiamo Aristotile, il quale va <lb/>dimostrandoci il fondamento suo meccanico stabilito nell'ammirande pro&shy;<lb/>priet&agrave; del cerchio. </s>

<s>Ha principio il moto, di cui servesi la Geometria per de&shy;<lb/>scrivere la mistica figura, dal centro, il quale, essendo in s&egrave; consistente in <lb/>un semplice punto, si espande al di fuori, quasi per una violenta esplosione, <lb/>che via via rallenta la sua prima foga a proporzione della distanza. </s>

<s>Quella <lb/>forza esplosiva poi, mentre tende a rifuggire per linea retta dal centro, ferma <lb/>stando questa linea in uno de'suoi estremi, rigira con l'altro tutt'intorno <lb/>allo stesso centro, e cos&igrave; da due moti, uno naturale per la circonferenza e <lb/>l'altro violento per il diametro, e non aventi fra loro nessuna proporzione <lb/>definita, vien secondo Aristotile a descriversi quella linea curva, indefinita&shy;<lb/>mente ritornante in s&egrave; stessa, ch'&egrave; il cerchio. </s></p><p type="main">

<s>La meccanica della Libbra, come udimmo dianzi dire dal Nostro, ha la <lb/>sua causa in questa dignit&agrave; del circolo, e perch&egrave; a quello strumento ridu&shy;<lb/>cesi il Vette, ch'&egrave; una Libbra di braccia ineguali, qual'&egrave; dunque la ragione <lb/>della sua potenza, se non che la maggior velocit&agrave; del braccio pi&ugrave; lungo com&shy;<lb/>pensa la maggior gravit&agrave; del peso applicato al braccio pi&ugrave; corto? </s>

<s>&ldquo; Ipse <lb/>vectis est in causa librae existens, spartum inferne habens in inaequalia di&shy;<lb/>visa. </s>

<s>Hypomochlion enim est spartum, ambo namque stant ut centrum. </s>

<s>Quo&shy;<lb/>niam autem ab aequali pondere celerius movetur maior earum, quae a cen&shy;<lb/>tro sunt, duo vero pondera quod movet et quod movetur; quod igitur motum <lb/>pondus ad movens, longitudo patitur ad longitudinem. </s>

<s>Semper autem quanto <lb/>ab hypomochlio distabit magis, tanto facilius movebit. </s>

<s>Causa autem est quo&shy;<lb/>niam quae plus a centro distat, maiorem describit circulum, quare ab eadem <lb/>potentia plus separabitur movens illud, quod plus ab hypomochlion dista&shy;<lb/>bit &rdquo; (ibid., fol. </s>

<s>30 ad t.). </s></p><p type="main">

<s>Riducendo il detto aristotelico in forme pi&ugrave; precise, se ne raccoglie <lb/>ch'essendo le velocit&agrave; proporzionali agli spazii, o alle distanze dal centro, <lb/>la potenza e la resistenza, applicate alle due estreme parti dello strumento, <lb/>stanno reciprocamente come quelle stesse distanze. </s>

<s>Ma questa, che dall'al&shy;<lb/>tra parte &egrave; facile conclusione geometrica, non era il principale intento del <lb/>nostro Filosofo, all'arguto ingegno del quale riserbavasi a investigar la causa, <lb/>perch&egrave; il braccio pi&ugrave; corto della leva sia in ogni modo sempre il pi&ugrave; tardo. </s>

<s><lb/>La speculata genesi meccanica del circolo &egrave; quella appunto che preparavasi <lb/>per la risposta. </s>

<s>Imperocch&egrave; il raggio pi&ugrave; corto, essendo pi&ugrave; vicino al cen&shy;<lb/>tro, e venendo perci&ograve; pi&ugrave; fortemente attratto da esso, &egrave; men libero ne'suoi <lb/>moti di quel che non sia il pi&ugrave; lungo; ond'&egrave; ragionevole che, essendo meno <lb/>spedito, anche a proporzione riesca sempre pi&ugrave; tardo. </s>

<s>&ldquo; Si autem duobus <lb/>ab eadem potentia latis hoc quidem plus repellatur, illud vero minus, ra&shy;<lb/>tioni consentaneum est tardius moveri quod plus repellitur eo, quod repel&shy;<lb/>litur minus. </s>

<s>Quod videtur accidere maiori et minori illarum, quae ex cen&shy;<lb/>tro circulos describunt. </s>

<s>Quoniam enim propius est manentis eius quae minor <lb/>est extremum quam id quod est maioris, veluti retractum in contrarium ad <pb xlink:href="020/01/1769.jpg" pagenum="12"/>medium, tardius fertur minoris extremum. </s>

<s>Omni quidem igitur circulum <lb/>describenti istuc accidit, ferturque eam, quae secundum naturam est latio&shy;<lb/>nem, secundum circumferentiam: illam vero praeter naturam in transver&shy;<lb/>sum et secundum centrum. </s>

<s>Maiorem autem semper eam, quae praeter na&shy;<lb/>turam est, ipsa minor fertur, quia enim centro est vicinior quod retrahit, <lb/>vincitur magis &rdquo; (ibid., fol. </s>

<s>29). </s></p><p type="main">

<s>Prestabiliti questi generalissimi e fecondi principii di statica razionale, <lb/>passa Aristotile a dimostrare quel che aveva prima accennato, che cio&egrave; tutti <lb/>i moti, i quali si fanno intorno alle Macchine, si riducono in fine alla leva. </s>

<s><lb/>Sono, oltre essa leva e la libbra, gli strumenti meccanici informati della <lb/>nuova scienza, la Troclea e il Polispasto, l'Asse nel peritrochio e il Cuneo. </s>

<s><lb/>La potenza meccanica dell'Asse, la quale si governa secondo le lunghezze <lb/>delle scitale o dei bracci della Leva, a cui viene immediatamente applicata <lb/>la forza; gli fu occasione d'inganno intorno agli usi della Troclea, credendo <lb/>che tanto avesse questo strumento maggior virt&ugrave; di sollevare i pesi, quanto <lb/>fosse maggiore il suo raggio. </s>

<s>In questo falso supposto si propone a risol&shy;<lb/>vere la cos&igrave; formulata IX Questione: &ldquo; Cur ea, quae per maiores circulos <lb/>tolluntur et trahuntur, facilius et citius moveri contingit, veluti maioribus <lb/>Trochleis quam minoribus, et scytalis similiter? </s>

<s>&rdquo; (ibid., fol. </s>

<s>32 ad t). &Egrave; que&shy;<lb/>sto stesso errore quello altres&igrave;, che vizia la risoluta Questione XVIII, intorno <lb/>al determinar le ragioni che passano tra la potenza e il peso nel Polispasto. </s></p><p type="main">

<s>&Egrave; certamente un tale errore in Aristotile notabilissimo, rivelandosi chia&shy;<lb/>ramente alla mente di ognuno che la Troclea &egrave; una Libbra di braccia <lb/>eguali. </s>

<s>Ma &egrave; da avvertir che l'inganno ha giusto nella stessa Libbra la sua <lb/>prima radice. </s>

<s>S'incominciano infatti le meccaniche Questioni dal domandar <lb/>come mai le Bilance di braccia pi&ugrave; lunghe sieno pi&ugrave; diligenti. </s>

<s>Si conferma <lb/>il supposto qui dall'Autore per vero, osservando che i moti negli strumenti <lb/>pi&ugrave; grandi sono assai meglio visibili, perch&egrave; le braccia pi&ugrave; lunghe fanno <lb/>maggiore la declinazione. </s>

<s>Un altro fatto per&ograve; sembrava confermare tutto il <lb/>contrario, cio&egrave; che si scelgono i piccoli <emph type="italics"/>Saggiatori<emph.end type="italics"/> dagli orefici come pi&ugrave; <lb/>squisiti delle grandi Bilance usate dai rivenditori delle merci pi&ugrave; vili. </s>

<s>L'os&shy;<lb/>servazione fu fatta contro il Filosofo nel VII libro dei Quesiti da Niccol&ograve; <lb/>Tartaglia, il quale concluse da'suoi nuovi statici principii che ogni sorta di <lb/>peso far&agrave; il medesimo effetto in ogni sorta di Libbra (Venezia 1546, fol. </s>

<s>77). <lb/>L'errore insomma di Aristotile &egrave; manifesto, ma giova, a quietar l'animo di <lb/>coloro i quali n'hanno fatto cos&igrave; gran caso, osservare che, pur dall'analisi <lb/>dei Moderni, resulta esser tanto pi&ugrave; mobile la Bilancia, quanto sono pi&ugrave; <lb/>lunghe le sue braccia. </s></p><p type="main">

<s>Comunque sia, l'Asse nel peritrochio &egrave; ben da Aristotile nella Que&shy;<lb/>stione XIII ridotto alla Leva, il maggior braccio della quale &egrave; costituito nelle <lb/>scitale o nei manubrii, tanto pi&ugrave; potenti a sollevare il peso, quanto sono <lb/>pi&ugrave; lunghi, perciocch&egrave; riescono in moversi altrettanto pi&ugrave; veloci. </s>

<s>E bench&egrave; <lb/>tant&igrave; sieno stati fra i Meccanici i dissidii, hanno i pi&ugrave; nulladimeno dato ra&shy;<lb/>gione al Maestro antico in ridurre anche il Cuneo alle ragioni del Vette. </s></p><pb xlink:href="020/01/1770.jpg" pagenum="13"/><p type="main">

<s>Le arti manuali, accomodando ai loro particolari esercizi gli strumenti, <lb/>riuscirono a modificarli cos&igrave;, da non esser facile a riconoscerli nella sempli&shy;<lb/>cit&agrave; dei loro principii, ma Aristotile, che ha professato di riguardare come <lb/>principalissimo degli strumenti la Leva, non s'inganna, e nell'uso delle Ta&shy;<lb/>naglie, per esempio, secondo che si legge nella XXI Questione, dimostra che <lb/>tutta l'efficacia dipende dall'essere le Tanaglie stesse composte di due Vetti, <lb/>nell'articolazion de'quali consista l'ipomoclio. </s>

<s>Del resto, per tacere di altri <lb/>non meno rilevanti argomenti, le forze centrifughe e le resistenze dei solidi <lb/>allo spezzarsi, che per Galileo si svolsero in una scienza nuova, se son Que&shy;<lb/>stioni in Aristotile o non bene o non completamente risolute, giovarono nul&shy;<lb/>ladimeno a richiamare a s&egrave;, infino dalle prime istituzioni della scienza, l'at&shy;<lb/>tenzione degli studiosi. </s></p><p type="main">

<s>Tale era insomma la nuova scienza meccanica insegnata ai Peripatetici <lb/>dal loro Maestro, il quale occorre primo a commemorar nella storia, pi&ugrave; <lb/>per dignit&agrave;, che per tempo. </s>

<s>Gli Accademici, di questi argomenti, che pare&shy;<lb/>vano aggirarsi nel trivio delle arti manuali, non udirono trattarne mai alla <lb/>divina eloquenza di Platone. </s>

<s>Ma quando nella scuola di Alessandria quelle <lb/>matematiche contemplazioni, dallo stesso Platone tanto raccomandate, ebbero <lb/>cos&igrave; larga e cos&igrave; intensa cultura, si giudic&ograve; non indegno del Filosofo il trat&shy;<lb/>tenersi sull'ali dell'ingegno a specular dall'alto secondo qual ragione la <lb/>Geometria governi il moto dei corpi. </s></p><p type="main">

<s>Primo e solenne Maestro di Matematiche in cotesta scuola sedeva Eu&shy;<lb/>clide, fra'molti libri scritti dal quale se ne annovera uno trattante <emph type="italics"/>De pon&shy;<lb/>deribus.<emph.end type="italics"/> Quali siano precisamente i principii meccanici ivi professati non &egrave; <lb/>possibile averne certezza, essendo anche questa, insieme con la maggior <lb/>parte delle opere dell'Autore, andata smarrita, ma un teorema, che da al&shy;<lb/>cuni s'attribuisce a lui, ne farebbe ragionevolmente congetturare che la <lb/>Meccanica dell'Alessandrino fosse informata a quegli stessi principii, che <lb/>furono poi svolti dal nostro Siracusano. </s>

<s>Il teorema infatti, che dicesi Eucli&shy;<lb/>deo, tanto ritrae della scienza meccanica di Archimede, che alcuni compila&shy;<lb/>tori delle opere di lui, come per esempio il Rivault, lo inserirono, cos&igrave; for&shy;<lb/>mulato, in appendice al libro I Degli equiponderanti: &ldquo; Si fuerint duae <lb/>quantitates in aequilibrio, quae ambae vel ambarum una radiis adhaeserint: <lb/>a centris autem gravitatum carumdem in radios quibus appenduntur per&shy;<lb/>pendiculares agantur; incident haec in radiorum puncta, a quibus si appen&shy;<lb/>sae fuerint eaedem quantitates, ita ut iam radiis non toto corpore adhae&shy;<lb/>reant, sed tantum ab illis punctis appendeant; manebunt in aequilibrio &rdquo; <lb/>(Archimedis Opera per D. Rivaltum, Parisiis 1615, pag. </s>

<s>186). </s></p><p type="main">

<s>L'Autore delle XIII proposizioni <emph type="italics"/>De ponderibus,<emph.end type="italics"/> conosciuto sotto il <lb/>nome di Giordano Nemorario, fece del teorema ora formulato la proposi&shy;<lb/>zione sua IX, conclusa da tutt'altri principii, e il commentator di Giordano, <lb/>dimostrando anch'egli in un altro modo la cosa, terminava la dimostrazione <lb/>con le parole: &ldquo; Hic explicit secundum aliquos liber Euclidis <emph type="italics"/>De ponderi&shy;<lb/>bus &rdquo;<emph.end type="italics"/> (De ponderibus cit., pag. </s>

<s>24). </s></p><pb xlink:href="020/01/1771.jpg" pagenum="14"/><p type="main">

<s>Se fosse dunque del citato teorema statico Euclide veramente l'autore, <lb/>parrebbe si dovesse a lui la prima applicazione dei centri di gravit&agrave; agli <lb/>equiponderanti. </s>

<s>Ma qualunque sia la ragion del primato, intorno a che poco <lb/>gioverebbe a noi il disputare, giacch&egrave; la nuova istituzione non ci &egrave; altri&shy;<lb/>menti nota che per le tradizioni archimedee, nel nostro Siracusano perci&ograve; <lb/>conviene investigarne l'indole e la natura. </s></p><p type="main">

<s>E quanto all'indole &egrave; facile avvedersi che si conforma al Platonismo <lb/>alessandrino, cos&igrave; autorevolmente introdotto nelle Matematiche da Euclide, <lb/>la Meccanica del quale, come quella del Nostro, &egrave; schiva d'implicarsi vil&shy;<lb/>mente nelle passioni della materia. </s>

<s>Nei corpi infatti, astraendo da tutto il <lb/>resto, non si considera da quegli Autori altro che il peso, non come qua&shy;<lb/>lit&agrave; degli stessi corpi, ma come quantit&agrave; matematicamente, secondo tutte le <lb/>altre quantit&agrave;, computabile in numeri o in linee. </s>

<s>La ponderosit&agrave; perci&ograve;, cos&igrave; <lb/>in astratto considerata, fa indipendente la Meccanica alessandrina dalla mole <lb/>universale dei corpi materiali, ossia dalla Terra, al mezzo della quale essi <lb/>corpi non tendono, per rivolgersi piuttosto l&agrave; dove potente gli chiama un <lb/>loro proprio e particolar centro, in cui si raccolgono, e da cui par che vir&shy;<lb/>tualmente si dispensino i pesi. </s></p><p type="main">

<s>L'indole di questa Scuola si par dunque diversa dalla Peripatetica, al <lb/>Maestro della quale udimmo poco fa dire che le Questioni meccaniche par&shy;<lb/>tecipano della scienza matematica e della naturale. </s>

<s>Ma perch&egrave; la naturale i <lb/>Platonici l'avevano a schifo, reputandone indegno a un Filosofo lo studio, <lb/>si guardavano dalle dottrine peripatetiche come da un contagio, per conferma <lb/>e per prova di che &egrave; notabile che non si trovi citato quasi mai il nome di <lb/>Aristotile dagli Scrittori alessandrini. </s>

<s>Durarono infino a tutto il secolo XVII, <lb/>in cos&igrave; fatte questioni, gli esempii della divisione fra le due scuole, ma per&shy;<lb/>ch&egrave; lo Stagirita s'era meglio apposto al vero, si pu&ograve; dir che la scienza mec&shy;<lb/>canica, com'ebbe da lui i principii, cos&igrave; avesse anche secondo lui le per&shy;<lb/>fezioni. </s></p><p type="main">

<s>L'asserita sentenza ha bisogno in ogni modo di prove, perch&egrave;, mentre <lb/>da una parte non vien suffragata dalle antiche tradizioni, specialmente pla&shy;<lb/>toniche, le due grandi autorit&agrave; di Galileo e del Cartesio dall'altra, si det&shy;<lb/>tero il pi&ugrave; sollecito studio di contradirla. </s>

<s>Ma bench&egrave; non appariscano di <lb/>quelle prove espresse le vestigia, si desumono nulladimeno con sufficiente <lb/>certezza dalle leggi, che governano il logico progredir del pensiero, dalle <lb/>quali si conclude non dovere in altro consistere le meccaniche istituzioni <lb/>archimedee che in una esplicazione de'concetti del Filosofo Stagirita. </s>

<s>N&egrave; ci&ograve; <lb/>si creda perch&egrave; s'inducesse il Siracusano a contradire all'indole della sua <lb/>scuola, ma perch&egrave; Aristotile stesso pose per fondamento della sua scienza <lb/>meccanica una delle pi&ugrave; ammirabili dignit&agrave; della Geometria. </s></p><p type="main">

<s>Questa dignit&agrave; infatti vedemmo essere costituita nel cerchio, la descri&shy;<lb/>zione del quale resulta, secondo il Filosofo, dalla composizione di due moti, <lb/>uno diretto secondo il raggio, e che muove dal centro, e l'altro applicato <lb/>all'estremit&agrave; del raggio stesso. </s>

<s>La forza, che produce quel primo moto, <pb xlink:href="020/01/1772.jpg" pagenum="15"/>l'aveva Aristotile qualificata per violenta, quasi che il cerchio fosse gene&shy;<lb/>rato per esplosione del centro. </s>

<s>Ma intorno alla causa del secondo moto, di <lb/>quello cio&egrave; che naturalmente conduce in giro l'estremit&agrave; del raggio, l'Au&shy;<lb/>tore delle Meccaniche questioni non s'era bene spiegato. </s>

<s>Ora incominciano <lb/>di qui le laboriose speculazioni della Scuola alessandrina, rappresentata per <lb/>noi in Archimede, di cui solo alcuni libri salvati e gli scrittori antichi ci <lb/>hanno trasmesso qualche notizia. </s></p><p type="main">

<s>Da che dunque potrebbe esser meglio resa evidente la forza applicata <lb/>all'estremit&agrave; del raggio, ragionava Archimede, che da un peso posto nel suo <lb/>estremo? </s>

<s>Siasi, per esempio, esso raggio esplicato in fino in A (fig. </s>

<s>3), dove <lb/><figure id="id.020.01.1772.1.jpg" xlink:href="020/01/1772/1.jpg"/></s></p><p type="caption">

<s>Figura 3.<lb/>giunto, il peso P lo devii dalla sua dirittura, <lb/>per condurlo in giro. </s>

<s>S'esplichi ancora il rag&shy;<lb/>gio infino in B per altrettanto spazio, e ivi <lb/>pure s'applichi un peso Q, che faccia forza <lb/>di deviarlo e di menarlo in volta come quel <lb/>primo. </s>

<s>Perch&egrave; B, ritrovandosi a una distanza <lb/>doppia di A, &egrave; secondo Aristotile attratto al <lb/>centro O con la met&agrave; della violenza, sembra <lb/>dunque ragionevole che quello abbia bisogno <lb/>della met&agrave; della forza necessaria a questo, per <lb/>venir deviato dal suo retto cammino: e in&shy;<lb/>somma P conviene essere il doppio pi&ugrave; pe&shy;<lb/>sante di <expan abbr="q.">que</expan> </s></p><p type="main">

<s>Proseguendo il ragionamento, scendeva <lb/>come corollario da questa proposizione che, <lb/>applicando in C un peso R eguale a P, e in D un peso S eguale a Q, le <lb/>estremit&agrave; de'due diametri, pareggiate ne'loro contrarii moti, dovessero per&shy;<lb/>manere in equilibrio. </s>

<s>Tale appunto &egrave; il fondamento statico della Libbra, <lb/>d'onde venne immediatamente condotto Archimede a quello della Leva, per&shy;<lb/>ch&egrave; considerando i due cerchi saldati insieme, e BD come una linea sola, <lb/>perciocch&egrave; P, per esempio, &egrave; tanto bene equilibrato dal peso R in C, quanto <lb/>dal peso S in D, ne conseguiva dunque, essendo applicabile il caso, non <lb/>alla doppia sola, ma a qualunque proporzione; che dovessero avere i pesi <lb/>fra loro la reciproca ragione delle distanze. </s></p><p type="main">

<s>Questo fondamentale teorema dava il modo a sciogliere il problema, <lb/>tanto dai Meccanici desiderato, <emph type="italics"/>Datum pondus data potentia movere;<emph.end type="italics"/> pro&shy;<lb/>blema che, cos&igrave; in sesto luogo formulato da Pappo nell'VIII libro delle sue <lb/><emph type="italics"/>Collezioni,<emph.end type="italics"/> gli suggeriva le seguenti parole, premesse alla soluzione come <lb/>per nota: &ldquo; Hoc enim est quadragesimum inventum mechanicum Archime&shy;<lb/>dis, in quo fertur dixisse: <emph type="italics"/>Da mihi ubi consistam et Terram commovebo &rdquo;<emph.end type="italics"/><lb/>(Pappi Alexandrini Collect., Bononiae 1660, pag. </s>

<s>460). E rispetto a'due cer&shy;<lb/>chi saldati insieme, che poi in pratica venivano a trasformarsi in quell'or&shy;<lb/>gano meccanico cos&igrave; detto il <emph type="italics"/>Timpano,<emph.end type="italics"/> Pappo stesso, che ne aveva fatta <lb/>l'applicazione moltiplicandone secondo la lunghezza dei raggi la potenza al <pb xlink:href="020/01/1773.jpg" pagenum="16"/>saepissime imputat Galeno, dum ipsum suis delusum simiis multa afferre et <lb/>comminisci ait quae, si humana cadavera secuisset, aliter protulisset &rdquo; (ibi, <lb/>pag. </s>

<s>510). </s></p><p type="main">

<s>Cos&igrave; veniva chiaramente dimostrato dai fatti che tanto Galeno quanto <lb/>il Vesalio erano due uomini, come tutti gli altri, soggetti ad errori; onde <lb/>avendosi per cosa certa essere stata l'Anatomia fino a quel tempo coltivata <lb/>da uomini e non da Dei, nell'imperfezione umana, in ch'era rimasta, dava <lb/>certissima speranza a tutti e prometteva il merito debito a chiunque ne fa&shy;<lb/>vorisse i progressi, per cui il Falloppio stesso, ad avvivar la speranza di con&shy;<lb/>seguir pi&ugrave; facilmente un tal merito, dettava a chi si volesse dare agli eser&shy;<lb/>cizii dell'arte i precetti seguenti: </s></p><p type="main">

<s>&ldquo; I. </s>

<s>Quae non connata sunt facile ac leviter dividi. </s>

<s>II. </s>

<s>Quae connata <lb/>sunt difficillime, nisi maxima adhibita diligentia, dividenda esse. </s>

<s>III. </s>

<s>Nihil <lb/>lacerandum. </s>

<s>IV. </s>

<s>Quod summe est necessarium et difficile ut sciamus quae <lb/>sit una pars, quae vero plures: ne plures partes simul iunctas constituamus <lb/>unam esse, nec ex una plures faciamus. </s>

<s>V. </s>

<s>Quis sit ordo in dissectione obser&shy;<lb/>vandus: possumus enim vario modo incipere et mutare ordinem. </s>

<s>Aut enim <lb/>habemus rationem dignitatis, et tunc incipimus a dignioribus ut a corde, a <lb/>cerebro; aut dirigimus ordinem ad duiturnitatem materiae, et incipimus ab <lb/>iis partibus quae citius pereunt et putrescunt, aut respicimus collocationem <lb/>et situm partium, ut quando extimas prius secamus servato ordine usque <lb/>ad intimas, aut spectamus usum toti corpori exhibitum, et tunc a duriori&shy;<lb/>bus incipit ars, utpote ac quae totum corpus fulciunt. </s>

<s>VI. </s>

<s>Ut cognoscamus <lb/>quibus instrumentis nunc haec particula nunc illa sit dividenda, cui adhi&shy;<lb/>bendi opera ministri, cui minime. </s>

<s>VII. </s>

<s>Ut cognoscamus quae particulae sint <lb/>dividendae et inspiciendae in vivis animalibus, quae vero in mortuis et qua <lb/>ratione; quaedam enim partes etiam mortuae omnia integra reservant, quae&shy;<lb/>dam vero vel nihil vel parum admodum retinent illius quod sensu est per&shy;<lb/>cipiendum &ldquo; (Institutiones anatom. </s>

<s>inter Op. </s>

<s>omnia cit., pag. </s>

<s>521). </s></p><p type="main">

<s>Nella duplice opera delle <emph type="italics"/>Osservazioni<emph.end type="italics"/> anatomiche e delle <emph type="italics"/>Istituzioni,<emph.end type="italics"/><lb/>si rendeva dunque per due conti il Falloppio benemerito de'progressi del&shy;<lb/>l'Anatomia: prima, per aver salvato dagli attentati del Vesalio, che voleva <lb/>reciderle, le pi&ugrave; antiche tradizioni galeniche della scienza; poi, per aver mo&shy;<lb/>strato che alla via gloriosamente corsa dallo stesso Vesalio non era posto il <lb/>termine nelle scoperte di lui, ma che restava molto ancora a scoprire a chi <lb/>vi si fosse rivolto con studio amoroso, com'egli ne'suoi due libri anatomici <lb/>insegnava coi fatti e coi precetti. </s></p><p type="main">

<s>Ma i precetti a dir vero accennano all'arte gi&agrave; progredita, la quale si <lb/>studia di giungere alla sua perfezione per quella via gi&agrave; segnata dai primi <lb/>maestri, senza cercare o saper trovar modo da renderla pi&ugrave; diritta e pi&ugrave; <lb/>aperta. </s>

<s>Vedremo di ci&ograve; l'esempio ne'principali Anatomisti, che successero <lb/>al Falloppio, mettendo in pratica i precetti di lui, mentre che Realdo Co&shy;<lb/>lombo, il quale porgeva nuovi argomenti all'Anatomia per progredire, ri&shy;<lb/>maneva incompreso e per lungo tempo dimenticato. <pb xlink:href="020/01/1774.jpg" pagenum="17"/>cipio meccanico rimangon deluse, non riducendosi la tanto desiderata dimo&shy;<lb/>strazione, alle mani di Archimede, che a un ingegnosissimo gioco della <emph type="italics"/>Com&shy;<lb/>posizion delle forze parallele.<emph.end type="italics"/></s></p><p type="main">

<s>Come Aristotile dette alla Meccanica la prima ala nella composizione <lb/>delle forze angolari, cos&igrave; Archimede la forn&igrave; di questa seconda, l'invenzione <lb/>della quale gli occorse nelle prime speculazioni <emph type="italics"/>De libra.<emph.end type="italics"/> I pesi infatti, che <lb/>s'equilibrano distribuiti nel Timpano, secondo la precedente figura terza, <lb/>sono una scomposizione dell'unico peso, che grava nel centro. </s>

<s>E dall'altra <lb/>parte, essendo chiaro che, anche tolti i pesi Q, R, rimane tuttavia il sistema <lb/>equilibrato, pu&ograve; perci&ograve; il peso totale venire altres&igrave; decomposto ne'due P <lb/>ed S. </s>

<s>Ma qual'&egrave; il fondamento, e la regola di questa operazione? </s>

<s>non altra <lb/>che il primo postulato dell'Autore: <emph type="italics"/>Petimus aequalia pondera ab aequa&shy;<lb/>libus distantiis aequiponderare.<emph.end type="italics"/> Archimede insomma lasci&ograve; la scienza in <lb/>quella medesima sete, in che l'aveva lasciata Aristotile, e cos&igrave; per l'uno <lb/>come per l'altro Maestro il fondamento statico riducesi a un fatto, che bi&shy;<lb/>sogna ammettere per evidenza sperimentale, ma che la Geometria confessa <lb/>di non avere argomenti da poterlo dimostrare. </s>

<s>Era quel fatto sperimentale, <lb/>per Aristotile, che i cerchi di pi&ugrave; gran raggio son pi&ugrave; veloci, e per Archi&shy;<lb/>mede che, posti ad uguali distanze nella Libbra, s'equiponderano insieme <lb/>due pesi eguali. </s></p><p type="main">

<s>L'arguto Siracusano avr&agrave; ripensato che il Filosofo studiavasi di rendere <lb/>la ragione della maggior velocit&agrave; nel circolo di raggio maggiore, col consi&shy;<lb/>derar ch'egli &egrave; meno violentemente attratto e avvinto nel centro, ma il fe&shy;<lb/>condo principio era, specialmente a que'tempi, pi&ugrave; difficile a dimostrare <lb/>della sua conseguenza, per cui, a ci&ograve; che potevasi cos&igrave; facilmente mettere <lb/>in dubbio, parve pi&ugrave; prudente consiglio all'Autore Degli equiponderanti so&shy;<lb/>stituire la certezza di un fatto. </s></p><p type="main">

<s>Notabile cosa &egrave; in questo particolare che quel di Siracusa s&igrave; mostri <lb/>meno platonico dell'altro di Stagira, il quale aveva fatta meccanica la stessa <lb/>Geometria. </s>

<s>Le aristoteliche speculazioni perci&ograve; intorno ai moti generatori del <lb/>cerchio erano conformissime al genio di Archimede, e, se ne fu sviato dal <lb/>nuovo processo che i centri di gravit&agrave; venivano a introdur nel trattato degli <lb/>equilibrii, vi torn&ograve; poi pi&ugrave; di proposito, per raccoglierne quel pregevolis&shy;<lb/>simo frutto, che egli espose nel libro Delle spirali. </s>

<s>L'accennata origine rende <lb/>meno inaspettato il nuovo abito, sotto cui si presenta la geometrica tratta&shy;<lb/>zione, che &egrave; per noi il terzo libro meccanico scritto dal nostro Siracusano. </s></p><p type="main">

<s>Aristotile erasi contentato di accennare cos&igrave; alle leggi dei moti equa&shy;<lb/>bili: &ldquo; Citius enim bifariam dicitur, sive enim in minori tempore aequalem <lb/>pertrausit locum, citius fecisse dicimus; seu, in aequali, maiorem &rdquo; (Quaest. </s>

<s><lb/>cit., fol. </s>

<s>28 ad t.). Ma Archimede ne fa, nelle due prime proposizioni, sog&shy;<lb/>getto a matematica dimostrazione, riferendo la prima che, se sieno le velo&shy;<lb/>cit&agrave; eguali, gli spazii percorsi saranno proporzionali ai tempi, e la seconda <lb/>che, se sieno i tempi eguali, le velocit&agrave; torneranno proporzionali agli spazii. </s></p><p type="main">

<s>L'applicazione di queste leggi de'moti equabili si fa alla generazione <pb xlink:href="020/01/1775.jpg" pagenum="18"/>meccanica della spirale, la quale ci vuol poco a intendere come fosse sug&shy;<lb/>gerita ad Archimede dalla generazione meccanica del cerchio aristotelico, <lb/>che, lasciando impresse le vestigia del punto portato dai due moti equabil&shy;<lb/>mente fatti e nello stesso tempo per la circonferenza e per il raggio, ver&shy;<lb/>rebbe evidentemente a disegnare la spirale archimedea. </s>

<s>La mirabile gene&shy;<lb/>razione meccanica di questa curva, che insomma contenevasi latente nelle <lb/>Questioni meccaniche, fu, insieme col principio della composizione delle forze <lb/>angolari attinto alle medesime aristoteliche Questioni, conclusa da Archi&shy;<lb/>mede in que'suoi teoremi, che riuscirono alla intelligenza dei Matematici <lb/>tanto astrusi. </s>

<s>La concisione dello scrittore parve che fosse causa di ci&ograve;, ben&shy;<lb/>ch&egrave; unica e vera causa fosse piuttosto la Scuola alessandrina, la quale, sde&shy;<lb/>gnosa di partecipar con la Peripatetica, tenne ascosa la chiave di quel mi&shy;<lb/>stero, infintantoch&egrave; in un novello Archimede non venne, dopo tanti secoli, <lb/>a ritrovarla il Torricelli. </s></p><p type="main">

<s>Ha l'illustre Discepolo di Galileo una scrittura intitolata <emph type="italics"/>Dimostrazione <lb/>della XVIII proposizione di Archimede delle Linee spirali colla dottrina <lb/>del moto di Galileo,<emph.end type="italics"/> dove, dopo di aver col principio della composizione <lb/>delle forze ortogonali dimostrata la promessa proposizione archimedea, sog&shy;<lb/>giunge: &ldquo; Nell'istesso modo per appunto si dimostra la verit&agrave; delle due se&shy;<lb/>guenti proposizioni nel maraviglioso libro Delle spirali. </s>

<s>A noi baster&agrave; di avere <lb/>accennato per qual via Archimede possa esser venuto in cognizione d'una <lb/>verit&agrave; tanto astrusa, e per cos&igrave; dire inopinabile, come la addotta. </s>

<s>Credo certo <lb/>che l'Autore a bello studio volesse occultare ed inviluppare la dimostrazione <lb/>del Teorema, a segno tale che non si potesse conoscere da che origine <lb/>glien'era derivata la cognizione. </s>

<s>Per&ograve; nel corso di tanti secoli non fu mai <lb/>capita evidentemente questa passione della spirale, non per altro che per la <lb/>mancanza della dottrina del moto, nota benissimo fino a'suoi tempi all'Ar&shy;<lb/>chimede antico, ma pubblicata solamente nei nostri dal Moderno &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. XXVIII, c. </s>

<s>113). </s></p><p type="main">

<s>Credeva dunque il Torricelli, come poi il Lagrangia e altri, che la re&shy;<lb/>gola di comporre i moti fosse un mistero riserbatosi in petto da Archimede, <lb/>e poi rivelato da Galileo nella proposizione II del IV Dialogo delle due Nuove <lb/>Scienze, ma il fatto &egrave; che Aristotile aveva insegnata gi&agrave; quella medesima <lb/>regola pi&ugrave; di venti secoli prima, e che Archimede la presupponeva nelle <lb/>sue dimostrazioni come nota oramai a tutti, bench&egrave; non da tutti intesa, e <lb/>perci&ograve; n&egrave; approvata, ond'&egrave; che non intesa pure e non approvata torn&ograve; per <lb/>tanti secoli la scienza meccanica, che s'annunziava nel libro Delle spirali. </s>

<s><lb/>Maestro dunque di questa scienza non si rendeva Archimede che nel trat&shy;<lb/>tato Degli equiponderanti, e, per quegli antichi che lo poterono studiare, nel <lb/>trattato <emph type="italics"/>De libra.<emph.end type="italics"/> La determinazione del centro dei gravi, che l&agrave; si dava per <lb/>unico fondamento meccanico, essendo principio troppo astratto, si porgeva <lb/>male applicabile a far giusto giudizio fra la proporzione dello strumento e <lb/>la potenza motrice. </s>

<s>E se la Statica n'ebbe a risentire vantaggio, fu quando <lb/>il Torricelli rivest&igrave; l'astratta ponderosit&agrave; archimedea delle qualit&agrave; generali <pb xlink:href="020/01/1776.jpg" pagenum="19"/>di tutti i corpi, considerando i loro centri in relazione col centro della <lb/>Terra. </s></p><p type="main">

<s>Di qui si comprende come non dovesse venire alla Statica, dal trattato <lb/>Degli equipondenti, grande impulso a progredire. </s>

<s>Prese la Scuola alessan&shy;<lb/>drina, conoscendo che l'impedimento veniva dalla troppo rigorosa osser&shy;<lb/>vanza dei precetti platonici, seco medesima consiglio di temperar quel ri&shy;<lb/>gore, condescendendo in qualche cosa lo spirito alla materia, ond'&egrave; che <lb/>Herone fu, secondo Pappo, di sentimento che la Meccanica razionale dovesse <lb/>consistere, no nella Geometria sola e nell'Aritmetica, ma eziandio nelle fisi&shy;<lb/>che ragioni. </s>

<s>&ldquo; Sentit Hero mechanicus, et rationalem quidem partem ex <lb/>geometria et arithmetica et ex phisicis rationibus constare &rdquo; (Collectiones <lb/>mathem. </s>

<s>cit, pag. </s>

<s>442). Nonostante, se ben si considerano gli effetti di que&shy;<lb/>sta generosa deliberazione presa dal Meccanico alessandrino, si trovano tanto <lb/>sterili, da non aggiungere in sostanza nulla di pi&ugrave; all'opera fatta da Archi&shy;<lb/>mede intorno alla Libbra. </s></p><p type="main">

<s>Alle considerazioni, dalle quali dipende la verit&agrave; cos&igrave; conclusa e asse&shy;<lb/>rita, porgono argomento le stesse Collezioni matematiche di Pappo, l'ottavo <lb/>libro delle quali &egrave; un nitidissimo specchio dei progressi, che fece la Mec&shy;<lb/>canica nella Scuola alessandrina dai tempi di Filone e di Herone infino a <lb/>quelli dell'Autore, che corona l'opera degli antichi con le sue proprie in&shy;<lb/>venzioni. </s>

<s>Al trattatello delle Macchine premette poche parole, dove dice che <lb/>essendogli i libri antichi capitati alle mani tutti guasti, mancanti del prin&shy;<lb/>cipio o del termine, ha creduto bene in servigio degli studiosi di reinte&shy;<lb/>grarli, esponendo in un breve discorso le figure, gli usi e i nomi di quelle <lb/>meccaniche facolt&agrave;, per le quali un dato peso vien mosso da una data po&shy;<lb/>tenza. </s>

<s>&ldquo; Traditum autem est ab Herone et Philone qua de causa praedictae <lb/>facultates in unam reducantur naturam, quamquam figuris multum inter se <lb/>distantes. </s>

<s>Nomina igitur haec sunt: Axis in peritrochio, Vectis, Polyspaston, <lb/>Cuneus, et praeter haec quae appellatur infinita Cochlea &rdquo; (ibid., pag. </s>

<s>482). </s></p><p type="main">

<s>S'aspetterebbe a tali espressioni il Lettore di vedere in che modo s'in&shy;<lb/>formino, le cinque macchine annoverate, a un principio solo che le riduca <lb/>tutte a un'unica natura, perch&egrave; nell'invenzione di quel tale principio con&shy;<lb/>sistono insomma i progressi della Statica. </s>

<s>Ma l'aspettazione in singolar modo <lb/>&egrave; delusa, terminandosi da Pappo la breve descrizione di ciascuno strumento <lb/>ora col dire che qual sia la ragione tra la potenza e la resistenza <emph type="italics"/>deinceps <lb/>ostendemus,<emph.end type="italics"/> ora affermando esser la tale o tale altra quella ragione, <emph type="italics"/>ut osten&shy;<lb/>demus,<emph.end type="italics"/> e intanto, senza poi dimostrar nulla, si chiude il libro. </s></p><p type="main">

<s>Potrebb'essere in ogni modo, tanti pericoli hanno corso nell'approdare <lb/>infino a noi queste carte, che, come si sono avute le Collezioni matemati&shy;<lb/>che mancanti dei due primi libri, cos&igrave; qualcun altro ne fosse venuto a man&shy;<lb/>care oltre all'ottavo, ma tutto d&agrave; indizio che l&agrave; dove la trattazione mecca&shy;<lb/>nica ci &egrave; rimasta fosse il termine naturale. </s>

<s>Da un'altra parte non mantenne <lb/>Pappo le sue promesse, perch&egrave; le gli vennero a mancare in Filone e in <lb/>Herone, non per essere i loro libri mutilati, ma per l'insufficienza de'prin-<pb xlink:href="020/01/1777.jpg" pagenum="20"/>cipii scienziali a progredire tant'oltre. </s>

<s>Si torna perci&ograve; a quel che si diceva <lb/>pi&ugrave; sopra ridursi la Statica degli Alessandrini ai principii archimedci della <lb/>Libbra, ci&ograve; che dalle stesse Collezioni di Pappo ha la conferma. </s></p><p type="main">

<s>Il Timpano infatti e le Ruote dentate son l'uniche macchine, nelle quali <lb/>matematicamente si dimostri la ragion che passa fra la potenza e la resi&shy;<lb/>stenza. </s>

<s>&ldquo; Hero autem Alexandrinus, constructionem eius in libro qui insci&shy;<lb/>bitur <foreign lang="greek">Baroulxon</foreign> manifestissime explicavit, sumpto lemmate quod demonstra&shy;<lb/>vit in Mechanicis, ubi etiam de quinque facultatibus disserit, videlicet de <lb/>Cuneo, Vecte, Cochlea, Polyspasto et Axe &rdquo; (ibid., pag. </s>

<s>460). E dop'avere <lb/>applicata la detta macchina a produrre un effetto particolare, che consisteva <lb/>nel potersi per mezzo di lei movere un peso di mille seicento talenti, con <lb/>la sola potenza di ottocento, perch&egrave; il diametro del Timpano era doppio di <lb/>quello del suo proprio asse; &ldquo; hoc enim problema, immediatamente sog&shy;<lb/>giunge, demonstratum est ab Herone in Mechanicis, et alia quam plurima <lb/>problemata utilissima et vitae nostrae rationibus conducentia conscripta sunt &rdquo; <lb/>(ibid.). Ma il problema, se vero &egrave; quel che Pappo stesso pi&ugrave; sotto afferma, <lb/>era stato risoluto prima da Archimede nel suo trattato <emph type="italics"/>De libra.<emph.end type="italics"/> E perch&egrave; <lb/>da questo immediatamente dipendeva l'altro problema delle ruote dentate, <lb/>il Collettore alessandrino aggiunge di sua propria mano al troppo scarso cor&shy;<lb/>redo della Meccanica il seguente teorema: &ldquo; Ponatur Tympanum quidem A <lb/>dentium sexaginta, Tympanum vero B dentium quadraginta: dico, ut velo&shy;<lb/>citas Tympani A ad velocitatem Tympani B, ita esse dentium B multitudi&shy;<lb/>nem ad multutudinem dentium A &rdquo; (ibid., pag. </s>

<s>478). </s></p><p type="main">

<s>L'infelice tentativo, del resto, fatto da Pappo stesso intorno al piano in&shy;<lb/>clinato, e l'avere alle quattro macchine aristoteliche aggiunta la Coclea, che <lb/>malamente riducevasi al Cuneo, sono anzi argomenti, che aggiungono valore <lb/>al nostro discorso, da cui volevasi concludere che la Scuola alessandrina non <lb/>promosse punto pi&ugrave; la Statica da quel grado, in cui l'aveva lasciata Ari&shy;<lb/>stotile nelle sue Questioni. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Al Liceo di Alessandria succede nel VII secolo la Scuola araba, il sen&shy;<lb/>sualismo della quale fa le pi&ugrave; vigorose contrapposizioni con lo spiritualismo <lb/>filosofico di Platone. </s>

<s>E perch&egrave; le umane discipline erano strette oramai a <lb/>tal partito o da rinunziare affatto a ogni magistero di scienza, o da scegliere <lb/>fra l'Accademia e il Peripato, si comprende facilmente come all'indole e ai <lb/>costumi degli Arabi s'affacessero meglio gl'istituti di questo, che poneva <lb/>all'intelletto la precedenza del senso. </s>

<s>Quando perci&ograve; la gente nuova avesse <lb/>coltivato pi&ugrave; la sapienza, che l'utile e il piacere, ci si potrebbe aspettare <lb/>che, riprese le aristoteliche tradizioni, dovesse la Meccanica venir per loro <lb/>promossa da quella quasi immobilit&agrave;, in che l'avevano trattenuta gli anti-<pb xlink:href="020/01/1778.jpg" pagenum="21"/>chi. </s>

<s>Nonostante, bench&egrave; non sia pervenuto alla nostra notizia nessuno arabo <lb/>autore, che scrivesse intorno all'arte e alla scienza dei pesi, non si pu&ograve; per <lb/>questo affermar da noi che ne fosse a quel tempo negletto lo studio. </s>

<s>Anzi <lb/>il vedere i manifesti profitti di lui nell'applicazione di quella scienza a di&shy;<lb/>scipline affini, che dal fecondo connubio vengono a ricevere il loro incre&shy;<lb/>mento, sarebbe prova certa di non scarsa cultura. </s>

<s>S'intende da noi dire di <lb/>Alhazen, autore di un trattato di Ottica, dove la luce si considera come un <lb/>corpo, che velocissimo si muove nello spazio, e che percotendo negli altri <lb/>corpi si riflette e si rifrange con certe leggi meccaniche, per dimostrar le <lb/>quali fa sapiente e libero uso della regola aristotelica, che insegna a decom&shy;<lb/>porre una sola in due forze angolari. </s>

<s>Chi poi pensa a quel che verr&agrave; coi <lb/>fatti a dimostrarci la storia, che cio&egrave; dall'uso di quella regola riconosce <lb/>massimamente la Meccanica i suoi progressi, vedr&agrave; come sia forse da dire <lb/>addirittura abbondante quella cultura di lei appresso gli Arabi, che dianzi ci <lb/>contentammo di giudicar non iscarsa. </s></p><p type="main">

<s>Le ricercate utilit&agrave; e i comodi sensuali della vita, il predominante prin&shy;<lb/>cipio peripatetico, che dovesse cio&egrave; la Natura sottostare e quasi pigliar legge <lb/>dal filosofico ingegno, non ci permettono di pensare che gli Arabi trascu&shy;<lb/>rassero lo studio e l'esercizio di quelle macchine, ch'erano il trionfo della <lb/>potenza dell'uomo sulle ritrosie della materia, e a geometrizzare intorno alle <lb/>quali s'erano volti gli Alessandrini per una singolare combattuta condiscen&shy;<lb/>denza. </s>

<s>Quelle Questioni aristoteliche dall'altra parte, senza divagare in spe&shy;<lb/>culazioni, che apparivano inutili a chi non sapeva apprenderle come belle; <lb/>trovavano esplicatissimo il principio statico universale applicabile a trovar <lb/>la pi&ugrave; giusta proporzione tra la potenza delle varie maniere di strumenti <lb/>motori, e la resistenza del peso mosso: ond'&egrave; che ragionevolmente pu&ograve; cre&shy;<lb/>dersi essere la scienza dei pesi coltivata in quella Scuola un commento pi&ugrave; <lb/>o meno dotto del maraviglioso segreto usato dalla Natura in moltiplicare le <lb/>forze per la loro applicazione immediata ai moti circolari. </s></p><p type="main">

<s>La Scuola latina, che poi successe, fra le tradizioni universali della <lb/>scienza attinta dagli Arabi accolse anche quella parte, che concerne le isti&shy;<lb/>tuzioni meccaniche, i canoni selettissimi delle quali noi li riconosciamo for&shy;<lb/>mulati in quelle XIII proposizioni <emph type="italics"/>De ponderibus,<emph.end type="italics"/> che vanno sotto il nome <lb/>di Giordano Nemorario, e che, dopo aver servito per tre secoli di testo ma&shy;<lb/>noscritto, sopra cui, passando da Aristotile, si faceva uno studio superiore <lb/>della scienza; furono nel 1523, da Pietro Appiano matematico tedesco, di&shy;<lb/>vulgate a gran benefizio per le pubbliche stampe. </s></p><p type="main">

<s>Che sia Giordano peripatetico si rivela infino dalle prime parole, nelle <lb/>quali professa di voler trattare de'pesi come di una scienza, che da una <lb/>parte &egrave; soggetta alla Geometria, e dall'altra alla Filosofia naturale. </s>

<s>Incomin&shy;<lb/>ciano perci&ograve; le investigazioni di lui, come quelle di Aristotile, dal moto cir&shy;<lb/>colare della Libbra, e il fatto misterioso del pesar pi&ugrave; i gravi, quanto pi&ugrave; <lb/>si dilungano dal centro, gli si presentava a considerare sotto l'aspetto pi&ugrave; <lb/>semplice, bench&egrave; poi infine torni al medesimo, dell'alleggerirsi che fanno <pb xlink:href="020/01/1779.jpg" pagenum="22"/>gli stessi gravi quanto pi&ugrave; discendono nel semicerchio. </s>

<s>Perch&egrave; nel braccio <lb/>della Bilancia AB (fig. </s>

<s>4) il grave A pesa pi&ugrave;, come l'esperienza dimostra, <lb/><figure id="id.020.01.1779.1.jpg" xlink:href="020/01/1779/1.jpg"/></s></p><p type="caption">

<s>Figura 4.<lb/>che quando sia sceso in C? &mdash; La causa ef&shy;<lb/>ficiente di ci&ograve;, ragionava argutamente Giordano, <lb/>non pu&ograve; consistere in altro che nel particolar <lb/>modo della discesa, la quale da una parte si fa <lb/>in gi&ugrave;, e dall'altra per traverso. </s>

<s>Ecco i due <lb/>moti di Aristotile presentarsi sotto le loro vere <lb/>sembianze; ecco una grande rivelazione: la di&shy;<lb/>scesa del grave nel circolo resulta dalla composi&shy;<lb/>zione di due forze, una naturale diretta al centro <lb/>della Terra, e l'altra violenta e diretta al centro <lb/>dello strumento. </s>

<s>&ldquo; Iste descensus est mixtus ex <lb/>descensu naturali et violento &rdquo; (De ponderibus cit., pag. </s>

<s>4). E poich&egrave; il <lb/>moto naturale &egrave; tanto pi&ugrave; impedito, quanto ha in s&egrave; misto pi&ugrave; del violento; <lb/>in C il corpo &egrave; pi&ugrave; leggero che in A, e in D pi&ugrave; leggero che in C, per&shy;<lb/>ch&egrave;, nella discesa pel maggiore arco, &egrave; maggior parte di violenza che nella <lb/>discesa per l'arco minore. </s>

<s>&ldquo; Potest ex hoc ostendi quod pondus in Libra <lb/>tanto fit levius quanto plus descendit in semicirculo. </s>

<s>Incipiat igitur mobile <lb/>descendere a termino semicirculi et descendat continue: dico tunc quod <lb/>maior arcus circuli plus contrariatur rectae lineae quam minor, et casus <lb/>gravis per arcum maiorem plus contrariatur casui gravis, qui per rectam <lb/>fieri debet, quam casus per arcum minorem; patet: ergo maior est violen&shy;<lb/>tia in motu secundum arcum maiorem, quam secundum minorem &rdquo; (ibid.). </s></p><p type="main">

<s>Da questo medesimo principio dipende la soluzione del medesimo pro&shy;<lb/>blema sotto l'altra forma, in che piacque di presentarlo ad Aristotile, per&shy;<lb/>ch&egrave; cio&egrave; il corpo sia pi&ugrave; grave e pi&ugrave; velocemente discenda nel circolo pi&ugrave; <lb/>grande, che nel minore? </s>

<s>Perch&egrave;, risponde Giordano, essendo nel maggior <lb/>circolo minore l'obliquit&agrave;, vi &egrave; meno di violenza, e la discesa perci&ograve; &egrave; pi&ugrave; <lb/>naturale. </s>

<s>&ldquo; Eodem syllogismo necesse est pondus gravius esse quodammodo <lb/>et velocius descendere quod movetur in circulo maiori, quia, ut prius pro&shy;<lb/>batur, minus obliquatur quam in circulo minori, et per consequens minus <lb/>habet violentiae: quia igitur minus distat descensus in circulo maiori a <lb/>descensu naturali, qui fit per lineam rectam, quam qui est in circulo mi&shy;<lb/>nori, dicatur descensus rectior, idest plus tendens ad rectitudinem, atque <lb/>in circulo minori, ob rationem oppositam, obliquior descensus &rdquo; (ibid., <lb/>pag. </s>

<s>5). </s></p><p type="main">

<s>Cos&igrave; veniva Giordano a ritrovar nelle cause naturali quella ragione, che <lb/>Aristotile ricavava dalle arguzie del proprio ingegno, e che da Archimede <lb/>si faceva tutta consistere nel fatto sperimentale degli equilibrii. </s>

<s>E perch&egrave; <lb/>anco il Matematico tedesco sentiva che si sarebbero potute fare a lui le dif&shy;<lb/>ficolt&agrave;, che poi si fecero a Galileo, &egrave; sollecito di prevenirle con dire che si <lb/>pu&ograve; del grave in quiete ragionare come se si movesse, essendo che nell'uno <lb/>e nell'altro stato patisce le medesime contrariet&agrave; e la quiete stessa pu&ograve; ri-<pb xlink:href="020/01/1780.jpg" pagenum="23"/>guardarsi come il termine del moto. </s>

<s>&ldquo; Grave igitur in parte inferiori, sive <lb/>moveatur sive quiescat, levius est secundum situm &rdquo; (ibid.). </s></p><p type="main">

<s>Quel che Giordano diceva dell'essere un corpo pi&ugrave; leggero o pi&ugrave; grave <lb/><emph type="italics"/>secondo il sito<emph.end type="italics"/> si traduce ora, nel linguaggio pi&ugrave; accetto ai moderni, nella <lb/>parola <emph type="italics"/>momento,<emph.end type="italics"/> la quantit&agrave; del quale &egrave; varia secondo la varia distanza del <lb/>corpo dal punto di sospensione, o secondo il progresso che scendendo fa <lb/>nella perpendicolare. </s>

<s>Da cos&igrave; nuovi e fecondi principii trae l'Autore sette <lb/>importantissime conclusioni, che per le cose da dimostrare servono di <emph type="italics"/>po&shy;<lb/>stulati.<emph.end type="italics"/> &ldquo; Prima est: omnis ponderosi motum ad medium esse &rdquo; (ibid.), <lb/>ossia al centro terrestre, e ci&ograve; veniva a ridurre nel vero esser loro le astratte <lb/>ponderosit&agrave; di Archimede. </s>

<s>Il secondo postulato che dice: &ldquo; quanto gravius <lb/>tanto velocius descendere &rdquo; (ibid.) si pu&ograve; giudicare pi&ugrave; lubrico che falso, <lb/>intendendosi non della libera discesa, che si fa con moto accelerato, ma di <lb/>quella, che si fa nelle Macchine equabilmente. </s></p><p type="main">

<s>I postulati per&ograve; che seguitano contengono in s&egrave; il germe di una scienza <lb/>nuova intorno ai momenti dei gravi scendenti sopra varie inclinazioni dei <lb/>piani. </s>

<s>&ldquo; Tertia, gravius esse in descendendo, quanto eiusdem motus ad me&shy;<lb/>dium est rectior. </s>

<s>Quarta, secundum situm gravius esse, quanto in eodem <lb/>situ minus obliquus est descensus. </s>

<s>Quinta, obliquiorem autem descensum <lb/>minus capere de directo in eadem quantitate &rdquo; (ibid.). Da questa conclu&shy;<lb/>sione e dalla seconda s'argomenta che la gravit&agrave; <emph type="italics"/>secundum situm,<emph.end type="italics"/> o come <lb/>altrimenti si dice il <emph type="italics"/>momento,<emph.end type="italics"/> &egrave; il prodotto del peso moltiplicato per la quan&shy;<lb/>tit&agrave; della discesa naturale, d'ond'&egrave; facile confermare quello che poco fa si <lb/>diceva, che cio&egrave; si contengono in questi principii statici di Giordano i ger&shy;<lb/>mogli di una scienza nuova. </s>

<s>E infatti, immaginando un corpo scendere ora <lb/>sopra l'inclinazione AB (fig. </s>

<s>5), ora sopra la AC, ora sopra la AD, percioc&shy;<lb/><figure id="id.020.01.1780.1.jpg" xlink:href="020/01/1780/1.jpg"/></s></p><p type="caption">

<s>Figura 5.<lb/>ch&egrave;, pervenuto al sito della ugualit&agrave;, che il VII postu&shy;<lb/>lato dice <emph type="italics"/>esse acquidistantiam superficiei orizontis,<emph.end type="italics"/> ha <lb/>raggiunta la medesima quantit&agrave; del discenso naturale <lb/>AE; avr&agrave; perci&ograve; in ogni caso eguale momento. </s>

<s>Ora es&shy;<lb/>sendo questo il principio fondamentale, a cui s'in&shy;<lb/>forma e da cui quasi totalmente dipende la Meccanica <lb/>galileiana, basterebbe l'aver fatto osservar ci&ograve; senz'al&shy;<lb/>tro a provar che dallo stesso Giordano muovono le <lb/>lontane e occulte radici a quella che, dopo quattro <lb/>secoli, pubblicamente s'intitolava <emph type="italics"/>Scienza Nuova.<emph.end type="italics"/></s></p><p type="main">

<s>Ma perch&egrave; meglio si confermi fin d'ora un fatto <lb/>che, nel primo annunziarsi in questa Storia, trova il conflitto della comune <lb/>opinione, vedasi come da questi statici principii del Nemorario concludasi <lb/>direttamente la verit&agrave; di un teorema dimostrato in varii modi dai Meccanici <lb/>del secolo XVI, e che Galileo nonostante si lusing&ograve; di aver dato per nuovo. </s></p><p type="main">

<s>Sieno sopra i due piani inclinati MO, MR (fig. </s>

<s>6) aventi la medesima <lb/>altezza MN posti due gravi P e Q, e si cerchi qual relazione debba passar <lb/>fra loro e gli stessi piani, perch&egrave; possano scendere con eguali momenti. <pb xlink:href="020/01/1781.jpg" pagenum="24"/>Prese AS, CF, nelle due oblique eguali, quel che <emph type="italics"/>capiunt de directo in ea&shy;<lb/>dem quantitate<emph.end type="italics"/> saranno le due perpendicolari AB, CD, per cui saranno <lb/><figure id="id.020.01.1781.1.jpg" xlink:href="020/01/1781/1.jpg"/></s></p><p type="caption">

<s>Figura 6.<lb/>espressi i momenti da <lb/>P.AB, e da q.CD. </s>

<s>E <lb/>perch&egrave; si vuole che tali <lb/>due momenti tornino e&shy;<lb/>guali, avremo dunque <lb/>P:Q=CD:AB. </s>

<s>Si com&shy;<lb/>pongano i due triangoli <lb/>ABS, CDF, dai quali ri&shy;<lb/>caveremo le due seguenti <lb/>equazioni: CD:CF= <lb/>MN:MR; AB:AS=MN:MO, d'onde CD:AB=MO:MR e perci&ograve; P:Q <lb/>=MO:MR. </s></p><p type="main">

<s>Ma perch&egrave; il principale intento del Nemorario era quello di dimostrare <lb/>il principio statico, ossia il fondamento a tutte le macchine, da Aristotile ri&shy;<lb/>posto nella Leva, a quest'unico strumento fa, nella proposizione VIII, l'ap&shy;<lb/>plicazione immediata delle sue dottrine. </s>

<s>Erano state preparate gi&agrave; queste <lb/>dottrine, per servire pi&ugrave; appropriatamente alla detta VIII proposizione, nella <lb/>proposizione I, nella quale si considerano piuttosto le velocit&agrave;, che gli spazii <lb/>percorsi nella naturale discesa: &ldquo; Inter quaelibet duo gravia (cos&igrave; quella <lb/>I proposizione &egrave; formulata) est velocitas descendendo proprie et ponderum <lb/>eodem ordine sumpta proportio, descensus autem, et contrarii motus, pro&shy;<lb/>partio eadem, sed permutata &rdquo; (ibid., pag. </s>

<s>6). </s></p><p type="main">

<s>Sia la Leva DE (fig. </s>

<s>7) sostenuta in A come centro. </s>

<s>La potenza da D <lb/>discendendo in M, fa risalire da E in F la resistenza, ma la proporzione in <lb/><figure id="id.020.01.1781.2.jpg" xlink:href="020/01/1781/2.jpg"/></s></p><p type="caption">

<s>Figura 7.<lb/>ogni modo &egrave; la medesima, ben&shy;<lb/>ch&egrave; permutata. </s>

<s>Or supposto che <lb/>la discesa della prima sia DM, e <lb/>l'ascesa della seconda EF, rap&shy;<lb/>presentati coi pesi P e Q il mo&shy;<lb/>tore e il mosso, sar&agrave; dunque il <lb/>momento di quello P.DM e di <lb/>questo q.EF, che nel caso dell'e&shy;<lb/>quilibrio. </s>

<s>daranno la proporzione <lb/>P:Q=EF:DM. </s>

<s>Ma perch&egrave; i <lb/>triangoli ADM, AEF son simili P:Q=AE:AD, che vuol dire la resistenza <lb/>s'equilibra con la potenza, quando son reciprocamente proporzionali alle <lb/>due braccia della leva, o alle due distanze dal punto d'appoggio o alla velo&shy;<lb/>cit&agrave; virtuale dell'ascesa da una parte e della discesa dall'altra. </s></p><p type="main">

<s>&Egrave; facile ora scoprire che il principio statico del Cartesio &egrave; un imme&shy;<lb/>diato e legittimo corollario di questa dimostrazione. </s>

<s>Supponiamo infatti che <lb/>AM sia pi&ugrave; lunga il doppio di AF, DM sar&agrave; pure il doppio di EF, e P sar&agrave; <lb/>met&agrave; del peso di <expan abbr="q.">que</expan> Di qui &egrave; che, considerando la potenza ora collocata in <pb xlink:href="020/01/1782.jpg" pagenum="25"/>M, ora in F, tanto ci vuole a sollevare Q in F, quanto P in D; ossia la <lb/>met&agrave; del peso ad un'altezza doppia. </s></p><p type="main">

<s>Per poi far vedere il Nemorario che il suo principio statico generale <lb/>s'applica alla soluzione di altri varii problemi, non contento di far soggetto <lb/>alla sua IX proposizione il teorema <emph type="italics"/>De ponderibus<emph.end type="italics"/> di Euclide, lo promove <lb/>cos&igrave; nella seguente sua X proposizione: &ldquo; Si canonium fuerit symmetrum <lb/>magnitudine et substantiae eiusdem, dividaturque in duas partes inaequales, <lb/>et suspendatur in termino minoris portionis pondus quod faciat canonium <lb/>parallelum epipedo orizontis, proportio ponderis illius, ad superabundantiam <lb/>ponderis maioris portionis canonii ad minorem, est sicut proportio totius ca&shy;<lb/>nonii ad duplum longitudinis minoris portionis &rdquo; (ibid., pag. </s>

<s>24). </s></p><p type="main">

<s>Sia AB (fig. </s>

<s>8) il cannone omogeneo e uniforme, diviso in due parti <lb/>disuguali nel punto C, da cui si tenga sospeso. </s>

<s>Appendasi dall'estremit&agrave; A <lb/><figure id="id.020.01.1782.1.jpg" xlink:href="020/01/1782/1.jpg"/></s></p><p type="caption">

<s>Figura 8.<lb/>un pezzo di cannone omogeneo <lb/>e uniforme al primo, e di tal <lb/>peso che valga a ridurre il can&shy;<lb/>none AB orizzontale. </s>

<s>Presa dal <lb/>centro una distanza CD=AC <lb/>in modo che DB sia la diffe&shy;<lb/>renza che passa fra la maggiore e la minor parte della divisione <lb/>fatta nel cannon livellato, e considerando il peso di questa diffe&shy;<lb/>renza concentrato in E, come quello del cannone pendulo concen&shy;<lb/>trato in F, dimostra il Nemorario, che le condizioni del richiesto <lb/>equilibrio sono espresse dall'equazione F:E=AB:2AC. </s></p><p type="main">

<s>La concisione del trattatello di Giordano, e lo stretto ordine matema&shy;<lb/>tico, con cui procede, ci fanno ragionevolmente supporre che fosse scritto <lb/>per servire di testo alle lezioni di Statica, alle quali precedevano le Que&shy;<lb/>stioni di Aristotile. </s>

<s>La condensata scienza e la fecondit&agrave; dei concetti lascia&shy;<lb/>vano dall'altra parte ampio e libero campo ai lettori di svolgere le propo&shy;<lb/>ste dottrine in teoremi nuovi, o di servirsene per argomento a risolvere <lb/>nuovi problemi. </s>

<s>Nei secoli XIV e XV fu creduto che mancassero cos&igrave; fatti <lb/>lettori, e che si riducessero le lezioni di Meccanica razionale alle Questioni <lb/>aristoteliche, all'oracolo delle quali sarebbe stato un sacrilegio aggiunger <lb/>nulla o detrarre. </s>

<s>S'inger&igrave; una cos&igrave; fatta opinione per non s'aver notizia di <lb/>nessuno autore di Meccanica in que'tempi, e per essersi fatto concetto che <lb/>fosse quella un'epoca d'ignoranza universale. </s>

<s>Ma chi ha penetrato mai nelle <lb/>scuole di quell'antica gente? </s>

<s>Chi ha esaminate le loro scritture, quelle par&shy;<lb/>ticolarmente che servivano per le lezioni, e nelle quali i Maestri esplicavano <lb/>a s&egrave; medesimi i loro pensieri? </s>

<s>Chi potesse veder le carte di tanti Filosofi <lb/>solitarii di que'tempi, e saper quello che il vigoroso ingegno rivel&ograve; a loro <lb/>degli effetti naturali, si confesserebbe forse che sono almeno in gran parte <lb/>temerarii i correnti giudizi. </s></p><p type="main">

<s>Il secolo nostro ne ha avuto un singolarissimo esempio in Leonardo da <lb/>Vinci, sui manoscritti scientifici del quale, dopo tre secoli, il mondo lette-<pb xlink:href="020/01/1783.jpg" pagenum="26"/>rato ha da poco fa aperti gli occhi. </s>

<s>&Egrave; il soggetto per la nostra Storia tanto <lb/>importante, che non si pu&ograve; trascurar di dire per quali avventurose vicende <lb/>quell'uomo tanto ammirato per l'eccellenza delle sue pitture e sculture, e <lb/>per le stupende opere d'ingegneria pratica, si sia ora venuti a riconoscerlo <lb/>per un solenne maestro di teorie. </s>

<s>L'importanza poi dell'argomento tanto <lb/>per noi pi&ugrave; cresce, in quanto che, di quelle teorie, le concernenti la Mec&shy;<lb/>canica son pi&ugrave; ammirabili di tutte; ond'&egrave; che Leonardo, riappiccando il filo <lb/>delle tradizioni agli ultimi studiosi di Giordano, lo protrae non solo infino <lb/>al secolo XVI, ma par che con valido braccio lo lanci anche al di l&agrave; di <lb/>Galileo. </s></p><p type="main">

<s>La storia avventurosa de'manoscritti vinciani, infino al 1784, si pu&ograve; <lb/>leggere cos&igrave; compilata dall'Autore del ragionamento premesso ai Disegni di <lb/>Leonardo da Vinci, incisi e pubblicati in quell'anno stesso in Milano da Carlo <lb/>Giuseppe Gerli: &ldquo; De'codici della Biblioteca ambrosiana ecco ci&ograve; che ne <lb/>scrive il signor mariette in una nota alla sua Lettera al signor conte di Cay&shy;<lb/>lus, che &egrave; la LXXXIV fra le Lettere pittoriche (Tomo II, pag. </s>

<s>171), e con <lb/>cui concorda il Bosca, nella Storia della Biblioteca ambrosiana: &rdquo; </s></p><p type="main">

<s>&ldquo; Lasci&ograve; Leonardo i suoi disegni a Francesco Melzi, dopo la cui morte <lb/>furono cos&igrave; trascurati, che Lelio Gavardi d'Asola, parente stretto di Aldo <lb/>Manuzio, maestro in quella casa, ebbe tutto l'agio di prenderseli. </s>

<s>S'impadron&igrave; <lb/>di tredici volumi, parte in folio e parte in 4&deg;, e portolli a Firenze con spe&shy;<lb/>ranza di venderli cari al granduca Francesco de'Medici, ma essendo questi <lb/>inaspettatamente morto, Lelio si vide deluso, e compreso dal rimorso pens&ograve; <lb/>a farne la restituzione, pregando a tale oggetto Gio. </s>

<s>Ambrogio Mazzenta, <lb/>gentiluomo milanese, ch'ei ritrov&ograve; in Pisa, a volere riportare quei libri ai <lb/>signori Melzi. </s>

<s>Cos&igrave; fu fatto, ma tenendone questi poco conto, abbench&egrave; av&shy;<lb/>visati del pregio da Pompeo Leoni celebre scultore, sei ne lasciarono in dono <lb/>al Mazzenta. </s>

<s>Di questi, uno ne fu donato a Carlo Emanuele duca di Savoia, <lb/>un altro n'ebbe il pittore Ambrogio Figini, i cui disegni furono poi ven&shy;<lb/>duti al signor Giuseppe Smith, ed uno ne ottenne il cardinale Federigo Bor&shy;<lb/>romeo, che ne arricch&igrave; la Biblioteca ambrosiana da lui instituita. </s>

<s>&Egrave; questo <lb/>un tomo in folio coperto di velluto rosso, che vi si vede tuttora. </s>

<s>Leonardo <lb/>vi tratta de'lumi e delle ombre, da matematico e da pittore. </s>

<s>I tre altri vo&shy;<lb/>lumi, che erano in mano del Mazzenta, passarono a Pompeo Leoni sum&shy;<lb/>mentovato, il quale ne compose un sol volume ben grosso, che conteneva, <lb/>per quel che si dice, 1750 disegni. </s>

<s>Di questo pregevole volume fece acqui&shy;<lb/>sto il conte Galeazzo Arconati, che nel 1637 ne fe dono alla mentovata Bi&shy;<lb/>blioteca ambrosiana, con tutto quello che aveva potuto raccogliere dal me&shy;<lb/>desimo maestro, consistente in dodici volumi, mostrando il pi&ugrave; generoso <lb/>disinteresse, poich&egrave; ricus&ograve; di venderli per tremila doppie al re d'Inghilterra, <lb/>siccome apparisce dalla marmorea epigrafe, a lui posta in un salone della <lb/>Biblioteca medesima. </s>

<s>Quanto ai sette volumi, che si riserbarono i Melzi, si <lb/>crede che fossero mandati in Spagna a Filippo II, che si piccava d'esserne <lb/>intendente. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/1784.jpg" pagenum="27"/><p type="main">

<s>&ldquo; A quanto dice il Mariette noi non abbiamo che aggiungere, se non <lb/>che, oltre i mentovati codici dati alla Biblioteca dall'Arconati e dal Mazzenta, <lb/>uno ve n'&egrave; in 16&deg; donatole dal conte Orazio Archinto, nel 1674. &rdquo; (pag. </s>

<s>8). </s></p><p type="main">

<s>Il documento pubblicato a pag. </s>

<s>131, 32 da Carlo Amoretti (Memorie <lb/>storiche ecc., Milano 1804) racconta con qualche variet&agrave; la parte ch'ebbe <lb/>in questo fatto il Mazzenta, ma perch&egrave; non &egrave; cosa per noi di grande im&shy;<lb/>portanza basti il sapere che, infino dal 1637, si trovarono nella Biblioteca <lb/>ambrosiana raccolti di Leonardo quattordici volumi manoscritti. </s>

<s>A quel pi&ugrave; <lb/>grosso di tutti, messo insieme dal Leoni, fu dato, per la mole e per la con&shy;<lb/>gerie dei disegni e delle descrizioni, il nome di <emph type="italics"/>Atlantico:<emph.end type="italics"/> gli altri, non <lb/>avendo, per la confusione delle materie comune a tutti, nessun titolo pro&shy;<lb/>prio, si distinsero in capriccioso ordine con le lettere dell'alfabeto. </s>

<s>Si fece <lb/>forse questa designazione ai codici, quand'ebbero a mutar domicilio e pa&shy;<lb/>drone: forse, attesa la diligenza dei bibliotecari ambrosiani, la cosa &egrave; pi&ugrave; <lb/>antica, ma in ogni modo il Venturi, che sent&igrave; primo il dovere di citare con <lb/>fedelt&agrave; le fonti, alle quali aveva attinto i suoi <emph type="italics"/>Saggi,<emph.end type="italics"/> dee aver trovata quel&shy;<lb/>l'alfabetica designazione gi&agrave; fatta. </s></p><p type="main">

<s>Comunque sia di ci&ograve;, a noi solo importa sapere quali siano le tradi&shy;<lb/>zioni dell'antica scienza, che si trovano disperse per coteste carte avventu&shy;<lb/>rosamente cos&igrave; raccolte. </s>

<s>Che scienza naturale veramente dentro ci fosse, era <lb/>una voce vaga, echeggiante insomma quella messa fuori gi&agrave; dal Vasari, ma <lb/>da qualche po'd'Ottica in fuori, che traspariva dal pubblico trattato Della <lb/>pittura in servigio dell'arte, nessun aveva notati di altro, in soggetto scien&shy;<lb/>tifico, o trascritto gli autentici documenti. </s></p><p type="main">

<s>Dalle carte vinciane, per varie parti d'Europa disperse, s'incominci&ograve;, <lb/>nel secolo XVIII, a pubblicare disegni o da artisti o da signori dilettanti <lb/>dell'arte, e il Caylus, il Grozart, il Mariette, l'Harundel e l'Hollar ne ri&shy;<lb/>portarono di grandissime lodi. </s>

<s>Si riscossero a quegli applausi gl'Italiani, che <lb/>si ricordarono essere la loro Biblioteca ambrosiana doviziosissima di cos&igrave; fatti <lb/>lavori, usciti dalla penna o dalla matita di un tanto Autore, e Baldassarre <lb/>Oltrocchi, bibliotecario, sollecit&ograve; e fu largo de'suoi consigli al pittor mila&shy;<lb/>nese Giuseppe Gerli, che scelse da varii codici le pi&ugrave; belle e, per la loro <lb/>curiosit&agrave;, le pi&ugrave; notabili figure. </s></p><p type="main">

<s>Fu alla pubblicazione, che avvenne come si disse in Milano nel 1784, <lb/>premesso un Ragionamento molto erudito, e da cui forse vennero le prime <lb/>e pi&ugrave; precise e pi&ugrave; particolari notizie di Leonardo come inventore di stru&shy;<lb/>menti della scienza e dell'arte, o come cultore delle matematiche applicate. </s>

<s><lb/>Si diceva aver trovato, squadernando que'sapienti volumi, nuove proposte <lb/>di fontane e di varie trombe, per tirar acqua or co'soffietti, or co'vapori, <lb/>or colle secchie attaccate a una fune perpetua: vi si vedevano immaginate <lb/>navicelle a ruota, da andare a ritroso della corrente, e vi s'accennava a <lb/>quella barca, che appar&igrave; poi disegnata nella Tavola XLVII illustrativa del <lb/>trattato Del moto e della misura dell'acqua (Bologna 1828), nella quale i <lb/>galeotti dovevano, invece dei remi, menare un manubrio applicato a una <pb xlink:href="020/01/1785.jpg" pagenum="28"/>ruota dentata, che per via di rocchetti e di altre ruote dentate faceva vol&shy;<lb/>gere un'<emph type="italics"/>elice,<emph.end type="italics"/> come ne'piroscafi della nuova invenzione. </s>

<s>S'ammirava la <lb/>grande arte meccanica di Leonardo applicata alla ballistica e alla tattica <lb/>&ldquo; siccome scorgesi nelle moltissime macchine per tirare e alzar pesi, per <lb/>gittar sassi, formare e stender ponti, e nelle armi che ha immaginate s&igrave; per <lb/>offendere che per difendersi, fra le prime delle quali sono da annoverarsi i <lb/>carri falcati &rdquo; (pag. </s>

<s>3). </s></p><p type="main">

<s>&ldquo; Non solo per&ograve; attese, poi si soggiunge, alle arti distruggitrici, ma <lb/>pens&ograve; anche alle utili, e veggonsi suoi disegni d'un telaro da far nastri, <lb/>d'una gran cesoia, d'un congegno da torcer fili, d'un girarrosto a fumo, <lb/>d'una macchina da purgar porti e da formar lime, e d'altri utili ritrovati. </s>

<s><lb/>Vedonsi pure alcune figure, che sembrano destinate a spiegare l'acustica, i <lb/>fenomeni dell'eco e l'Ottica, intorno alla quale moltissimo ha disegnato e <lb/>scritto, e un disegno pur v'&egrave;, che direbbesi un Canocchiale &rdquo; (ivi, pag. </s>

<s>4). </s></p><p type="main">

<s>Ai curiosi, che s'intrattenevano piacevolmente a squadernare il volume <lb/>in folio del Gerli, per ridere sgangheratamente di quelle caricature, e per <lb/>ammirar quegli uomini il dorso, le braccia e i piedi de'quali aveva strana&shy;<lb/>mente Leonardo impennati di ali, rimaneva largo campo d'immaginar la <lb/>scienza acustica e ottica e il Canocchiale e tante altre cose, che dicevasi <lb/>avere inventate quel fecondo e mirabilissimo ingegno. </s>

<s>Or chi pu&ograve; mai pre&shy;<lb/>scrivere le vie per l'aria ai voli infaticabili della immaginazione? </s></p><p type="main">

<s>Furono in queste esaltazioni di mente trovati dai Francesi i Lombardi <lb/>a tempo della conquista, e perch&egrave; ogni patria gloria dei conquistati doveva <lb/>esser mancipio dei conquistatori, fu cos&igrave; decretato dei manoscritti di Leo&shy;<lb/>nardo da Vinci. </s>

<s>Fossero stati intorno a ci&ograve; gl'Italiani pi&ugrave; silenziosamente <lb/>operosi, e meno loquaci, non sarebbero stati forse provocati i vincitori, che <lb/>avevano le mani al ferro e non ai libri, ad entrare nell'Ambrosiana per con&shy;<lb/>culcar la cresta che di l&agrave; rizzavano i vinti. </s>

<s>Che poi non fosse quello vera&shy;<lb/>mente amore ai libri e alla scienza si conferma dal fatto che, svolti appena <lb/>i codici da chi gli ebbe in consegna, e rifiutatone uno perch&egrave; pareva appar&shy;<lb/>tener piuttosto a Luca Pacioli che a Leonardo, da nessun Francese furono <lb/>per lungo tempo mai pi&ugrave; aperti. </s>

<s>E messi sulla bilancia i dodici da una parte, <lb/>e il Codice atlantico dall'altra, perch&egrave; nella mole e nel peso non era molto <lb/>grande la differenza, furono ripartite le spoglie fra l'Istituto e la nazionale <lb/>Biblioteca di Parigi. </s></p><p type="main">

<s>Gli spogliati insorgevano con parole irosamente impotenti contro l'inde&shy;<lb/>gna usurpazione, ma alcuni de'pi&ugrave; savi, tornando alla coscenza, si consi&shy;<lb/>gliarono di ristorare il danno, e di riparare al patrio onore coi fatti. </s>

<s>Giovan <lb/>Batista Venturi corre da Bologna a Parigi dietro i predatori, e l&agrave;, dove nel&shy;<lb/>l'Istituto nazionale avevano allora allora posata una parte della preda, si <lb/>mette con diligente studio a ricercarla, perch&egrave; di un tesoro egualmente in&shy;<lb/>fruttuoso, o sepolto a Milano o a Parigi, potesse usufruirne la scienza uni&shy;<lb/>versale. </s>

<s>Cos&igrave;, intanto che meditava di far opera pi&ugrave; lunga e pi&ugrave; compiuta, <lb/>per sodisfare al sollecito desiderio di quei generosi, che nell'amor degli stu-<pb xlink:href="020/01/1786.jpg" pagenum="29"/>dii comuni a tutti volevano veder sopita la imparit&agrave; delle gare municipali, <lb/>s'affrett&ograve; di dar fuori in Parigi, nel 1797, il suo <emph type="italics"/>Essai sur les ouvrages <lb/>physico-matematiques de Leonard de Vinci.<emph.end type="italics"/></s></p><p type="main">

<s>Ha il Venturi, come gli altri suoi connazionali, preoccupato il giudizio <lb/>intorno alla straordinaria eccellenza scientifica di Leonardo, fondata insomma <lb/>sopra la rumorosa fama che ne correva, ma non bene accertata ancora coi <lb/>fatti. </s>

<s>Traspariscono gl'indizi di quella mente preoccupata infino dalle prime <lb/>pagine, nelle quali si vuol Leonardo fare precursor del Copernico, mentre <lb/>egli in verit&agrave; non professa che la semplice rotazione diurna della Terra, im&shy;<lb/>mobile nel suo centro, conforme a quell'opinione, comune a molti allora e <lb/>ne'secoli precedenti, che si distinse col nome di semicopernicismo. </s>

<s>Al va&shy;<lb/>loroso Fisico e Matematico di Bologna mancavano di pi&ugrave; i criterii storici ne&shy;<lb/>cessari a dare il giusto merito alle speculazioni di Leonardo, comparandole <lb/>con le tradizioni pi&ugrave; antiche e con la scienza moderna, d'onde avvenne che <lb/>alcune cose rimasero incerte nel <emph type="italics"/>Saggio,<emph.end type="italics"/> e alcune altre a parer nostro fu&shy;<lb/>rono male intese. </s>

<s>Per scegliere qualche esempio, che si riferisca al nostro <lb/>particolare argomento, in quella prima nota tradotta dal Venturi al &sect; VII <lb/>non sembra a noi che s'abbia per nulla a intendere della Leva angolare, <lb/>non trattandosi in verit&agrave; d'altro che di una bellissima applicazione delle <lb/>forze composte, per cui la Leva si dice da Leonardo <emph type="italics"/>reale,<emph.end type="italics"/> essendo la forza, <lb/>attualmente a lei applicata, risoluta nelle due, che si chiamano con molta <lb/>propriet&agrave; le <emph type="italics"/>Leve potenziali.<emph.end type="italics"/> Fa veramente gran maraviglia che non rico&shy;<lb/>noscesse lo stesso Venturi il principio statico della Leva angolare nella nota <lb/>seguente, nella quale si dimostra che il momento del peso pendulo appli&shy;<lb/>cato all'estremit&agrave; di un filo o di una verga, la quale un contrappeso va sol&shy;<lb/>levando con pi&ugrave; o meno forza, &egrave; proporzionale al seno dell'angolo dell'in&shy;<lb/>clinazione fatto dalla stessa verga con la linea verticale. </s></p><p type="main">

<s>La traduzione francese e la parafrasi delle Note manoscritte che ai sem&shy;<lb/>plici e rozzi modi del popolano da Vinci sostituiva l'artificioso linguaggio degli <lb/>scienziati moderni, conferiva efficacemente a confermar sempre pi&ugrave; l'opinione <lb/>che si trovasse in que'solitarii manoscritti da quel miracolo d'ingegno divi&shy;<lb/>nata la scienza fisica matematica dei nostri tempi. </s>

<s>L'andar cos&igrave; a genio del <lb/>pubblico fece al <emph type="italics"/>Saggio<emph.end type="italics"/> del Venturi riscotere applausi universali, ch'eccitarono <lb/>altri in Italia ad imitarne, quant'era a loro possibile, gli esempi. </s>

<s>Nella Va&shy;<lb/>ticana trovavasi una copia manoscritta del trattato Della pittura, di cui il Du&shy;<lb/>fresne non aveva pubblicato che un saggio, e Guglielmo Manzi, nel 1817, <lb/>s'affrett&ograve; di darlo alle stampe nuovamente corretto e intero. </s>

<s>Possedeva, pure <lb/>in Roma, la Barberiniana il libro <emph type="italics"/>Del moto e misura dell'acqua,<emph.end type="italics"/> che il <lb/>p. </s>

<s>Luigi Maria Arconati domenicano aveva, infino dal 1643, finito di tra&shy;<lb/>scrivere e di ordinare sulle note sparse di Leonardo, e Francesco Cardinali <lb/>lo pubblic&ograve; in Bologna nel 1828, raccogliendolo nel Tomo X de'pi&ugrave; scelti <lb/>Idraulici d'Italia. </s></p><p type="main">

<s>S'aspettava intanto con gran desiderio che il Venturi mantenesse la <lb/>promessa di dar compieta l'opera, della quale il pubblico aveva con tanta <pb xlink:href="020/01/1787.jpg" pagenum="30"/>avidit&agrave; accolto il Saggio, ma perch&egrave; le speranze oramai venivano meno, Gu&shy;<lb/>glielmo Libri, infino dal 1630, pens&ograve; di supplire all'importantissimo ufficio. </s>

<s><lb/>Erano gi&agrave; quindici anni che il Codice atlantico aveva fatto ritorno in patria, <lb/>rimanendo tuttavia gli altri dodici suoi minori fratelli in perpetuo esilio nel&shy;<lb/>l'Istituto parigino; e in Milano, dove si ritrovava nella primavera del detto <lb/>anno 1630, attendeva il futuro nostro Storico delle Matematiche, con grande <lb/>alacrit&agrave;, a trascrivere dallo stesso Atlantico quel che sembravagli pi&ugrave; impor&shy;<lb/>tante, e a dilucidarne, come sapeva meglio, i disegni. </s>

<s>Si rec&ograve; poi nella se&shy;<lb/>guente estate a Parigi, per scotere ai dodici Manoscritti dell'Istituto la pol&shy;<lb/>vere lasciatavi cader sopra per pi&ugrave; di trent'anni. </s></p><p type="main">

<s>La scienza universale, che di fatto ritrov&ograve; sparsa per quelle neglette <lb/>carte, parve allo stesso Libri superar quella, che andavasi diffondendo dalla <lb/>fama, e scrivendo a Gino Capponi gli diceva avervi trovato di tutto: fisica, <lb/>matematica, astronomia, storia, filosofia, novelle, meccanica, da parergli un <lb/>vero prodigio; ch'era quello insomma un divino ingegno, creatore della Fi&shy;<lb/>losofia sperimentale in Italia (Lettere di G. Capponi, Vol. </s>

<s>I, Firenze 1882, <lb/>pag. </s>

<s>299, 308). Di qui i ferventi propositi di dar, sotto migliori forme, ese&shy;<lb/>cuzione al primo progetto del Venturi; propositi che si sfogarono, come nu&shy;<lb/>voloni di estate in poche stille di pioggia, in quella prolissa enumerazione <lb/>delle tante cose pensate e fatte da Leonardo, e in quella spruzzagliatella di <lb/>note, trascritte e apposte al II libro della Storia delle Matematiche in Italia. </s></p><p type="main">

<s>La fama di Leonardo enciclopedico cos&igrave; cresceva, sempre pi&ugrave; andando, <lb/>che d'ogni parte scrittori venivano con pi&ugrave; risonanti parole a ripetere le <lb/>maraviglie scritte dal Libri. </s>

<s>Alla fine di queste declamazioni per&ograve; voci pi&ugrave; <lb/>sommesse e assennate parevano domandare e dire ai declamatori: ma fa&shy;<lb/>teci un po'leggere e veder co'nostri occhi quel che il grand'uomo ha scritto <lb/>e disegnato nella sua integrit&agrave; originale, giacch&egrave; le poche stille sparse dal <lb/>Venturi e dal Libri n'accendono pi&ugrave; che mai viva la sete. </s></p><p type="main">

<s>Ebbero buona volont&agrave; di rispondere a questi onestissimi desiderii al&shy;<lb/>cuni Italiani, mettendo mano nel 1872 a pubblicare il Codice atlantico, che <lb/>da vent'anni in que &egrave; rimasto nel suo primo principio, mentre in Parigi <lb/>Carlo Ravaisson-Mollien ha gi&agrave; compiuta la trascrizione e il commento ai <lb/>dodici manoscritti dell'Istituto, e Gianpaolo Richter ha dato, da dieci anni, <lb/>al pubblico in Londra raccolte e ordinate le note del Nostro, le quali, ben&shy;<lb/>ch&egrave; insomma trattino di tutto, escludendovisi le cose d'argomento fisico&shy;<lb/>matematico, s'intitolarono <emph type="italics"/>Scritti letterarii.<emph.end type="italics"/></s></p><p type="main">

<s>Se non tutto dunque &egrave; ormai sotto gli occhi del pubblico studioso tanta <lb/>parte degli scritti di Leonardo, da poter farne il pi&ugrave; giusto giudizio, che con&shy;<lb/>fermi o rettifichi quello corso gi&agrave; per la fama infino dai tempi del Vasari. <lb/></s>

<s>&Egrave; per prima cosa, in tal proposito, da osservare che la variet&agrave; e la molti&shy;<lb/>plicit&agrave; degli argomenti scientifici &egrave; il carattere proprio di quasi tutti gli scrit&shy;<lb/>tori di quella et&agrave;, permettendo la ristretta economia della scienza di allora <lb/>a un uomo solo di potere attendere a coltivarla in ogni sua parte. </s>

<s>Nei libri <lb/><emph type="italics"/>De rerum varietate,<emph.end type="italics"/> per esempio, di Girolamo Cardano &egrave; una enciclopedia <pb xlink:href="020/01/1788.jpg" pagenum="31"/>ben pi&ugrave; larga, e qua e l&agrave; pi&ugrave; profonda di quel che non sia nelle Note di <lb/>Leonardo, le proposte di macchinamenti e di capricciosi ingegni, che si leg&shy;<lb/>gono nelle quali, non sono molto pi&ugrave; maravigliose di quell'altre, che si <lb/>leggono scritte nelle due Magie del Porta. </s>

<s>Egli &egrave; un fatto insomma che se <lb/>quegli scritti, i quali sono usciti oggidi fuori tanto accarezzati, e in cos&igrave; ni&shy;<lb/>tide vesti, fossero stati impressi in volumoni in folio, a mezzo il secolo XVI, <lb/>avrebbe il loro Autore incontrata la medesima sorte de'suoi contemporanei, <lb/>de'quali nessuno apprezza le perle, mentre di Leonardo si fa gran conto <lb/>anco delle quisquiglie. </s></p><p type="main">

<s>Chi trova il gusto del vero in queste considerazioni facilmente si ac&shy;<lb/>corge che la naturale grandezza della figura viene alquanto esagerata dalle <lb/>fumose esalazioni, che s'interpongono fra lei e l'occhio di chi la rimira <lb/>ond'&egrave; nostro principal dovere il rimovere quelle caligini, perch&egrave; la vista ci <lb/>si renda sincera. </s>

<s>Dir Leonardo creatore della scienza sperimentale &egrave; una tale <lb/>iperbole, da non si perdonar cos&igrave; facilmente a uno Storico delle Matemati&shy;<lb/>che, perch&egrave; la creazione sarebbe nell'uomo un'assurdit&agrave;, piuttosto che un <lb/>vero e proprio prodigio, ed &egrave; ufficio della storia quello di dimostrare come <lb/>i creduti prodigi si riducono all'ordine naturale svelando l'occulta causa <lb/>che gli ha prodotti. </s></p><p type="main">

<s>Nelle tradizioni scientifiche dei secoli precedenti al XVI si scoprirebbero <lb/>le fonti naturali, da cui deriv&ograve; la variet&agrave; enciclopedica delle dottrine pro&shy;<lb/>fessate da un Artista di que'tempi, ma per non divagar di troppo dal no&shy;<lb/>stro argomento, ci contenteremo di dire che, nella Scuola peripatetica e nella <lb/>Alessandrina, riassunte da Giordano Nemorario, si trovan naturalmente com&shy;<lb/>presi i fecondi principii, da cui concluse i suoi maravigliosi teoremi di Mec&shy;<lb/>canica razionale Leonardo da Vinci. </s>

<s>La composizione infatti delle forze pa&shy;<lb/>rallele e delle angolari, le velocit&agrave; virtuali, i momenti de'gravi lungo i piani <lb/>inclinati erano cose insegnate da quelle antiche scuole: tutte insomma, verso <lb/>la fine del XV secolo, venivano ai Matematici apparecchiate le vie, da con&shy;<lb/>dur la scienza del moto a suoi pi&ugrave; liberi e pi&ugrave; spediti progressi. </s></p><p type="main">

<s>Chi per&ograve; seguitasse a leggere il seguente nostro &sect; III tornerebbe in&shy;<lb/>dietro a farci questa osservazione: non eran pervenute le tradizioni scien&shy;<lb/>tifiche, che voi dite, anche al Cardano, al Tartaglia, al Maurolico, al Com&shy;<lb/>mandino e a tanti altri illustri Matematici di quel secolo? </s>

<s>Or come mai <lb/>Leonardo, nelle Meccaniche, sorvola in molte cose a tutti costoro, e in al&shy;<lb/>cune altre, ci&ograve; che pare incredibile, allo stesso Galileo, e va a raggiungere <lb/>il Torricell&igrave;, il Viviani e il Borelli? </s>

<s>Anche ammessa dunque l'efficacia delle <lb/>tradizioni par rimanga sempre e in ogni modo un prodigio che un semplice <lb/>Artista siasi cos&igrave; potuto avvantaggiare sopra tanti valorosi filosofici ingegni. </s></p><p type="main">

<s>L'osservazione giustissima costringendoci a confessare che la cultura di <lb/>quei tempi non era alla scienza, a cui giunse Leonardo, magistero sufficiente, <lb/>fa rivolgere il nostro pensiero a cercare e a riconoscere altrove quel che ne <lb/>supplisca al difetto, nel magistero stesso dell'esperienza. <emph type="italics"/>La isperientia,<emph.end type="italics"/> dice <lb/>il nostro popolano di Vinci, <emph type="italics"/>non falla mai, ma sol fallano,<emph.end type="italics"/> dice audace-<pb xlink:href="020/01/1789.jpg" pagenum="32"/>mente rivolgendosi ai Filosofi, <emph type="italics"/>i vostri giuditii<emph.end type="italics"/> (Libri, Histoire des Mathem., <lb/>T. III, Paris 1840, pag. </s>

<s>235). </s></p><p type="main">

<s>Non &egrave; l'esperienza, che l'Autore qui professa di seguitare, il metodo <lb/>artificioso dei moderni, ma &egrave; quell'ardore di voler tutto mettere a cimento, <lb/>e di tutto certificarsi con le prove di fatto, che la Natura stessa infonde <lb/>nell'animo dei fanciulli, e a cui poi le scuole insegnano a sostituire le ar&shy;<lb/>guzie dell'ingegno. </s>

<s>Ecco ci&ograve; che rende singolare nella storia letteraria del <lb/>secolo XVI Leonardo da Vinci; ecco a che principalmente riducesi la feli&shy;<lb/>cit&agrave; di quell'ingegno: all'esser cio&egrave; rimasto franco dalla tirannia delle sco&shy;<lb/>lastiche discipline. </s>

<s>Mentre gli altri generalmente andavano tronfii di ripetere <lb/>quel che avevano letto ne'libri dei Filosofi, per cui argutamente gli chiama <lb/><emph type="italics"/>recitatori<emph.end type="italics"/> e <emph type="italics"/>trombetti,<emph.end type="italics"/> egli interpetra la Natura medesima con l'esperienza, <lb/>maestra a loro stessi che in Filosofia si facevano maestri. </s>

<s>E ci si mette, <lb/>come si diceva, con quell'ardore instancabile che &egrave; innato ai fanciulli, dei <lb/>quali par che serbi, aggiunta alla vigoria delle membra e alla tenacit&agrave; del <lb/>volere, la squisitezza dei sensi. </s>

<s>Le accidentali variet&agrave; per esempio della di&shy;<lb/>scesa dei gravi, prodotte dalla resistenza dell'aria secondo la figura del corpo <lb/>cadente e il modo com'&egrave; rivolta e diretta al centro quella stessa figura, con <lb/>tante altre minuzie, che occorrono ad osservare in quello sperimento, sem&shy;<lb/>brano cose a nessun altro possibili che alla pazienza infinita di Leonardo. </s></p><p type="main">

<s>Coloro per&ograve;, che proclamano il grand'uomo non discepolo d'altri che <lb/>della sua propria esperienza, profferiscono sentenza non vera, avendosi per <lb/>certo ch'egli aveva studiato con Aristotile, Archimede e Euclide, sotto la di&shy;<lb/>sciplina del grande amico suo Luca Pacioli. </s>

<s>Non la sola Natura dunque, ma <lb/>l'arte altres&igrave; concorse a educare nel popolano di Vinci l'ingegno, e special&shy;<lb/>mente l'arte del calcolo algebrico, intorno al quale &egrave; notabile essere stato <lb/>egli de'primi a far uso delle lettere minuscule dell'alfebeto. </s>

<s>Quel che per&ograve; <lb/>potrebbesi affermare per vero &egrave; che l'uso di rappresentare in pittura gli <lb/>atti pi&ugrave; naturali della persona condusse Leonardo a inventare quei segni, <lb/>che si praticano anche oggid&igrave; per distinguere le quantit&agrave; positive e le ne&shy;<lb/>gative. </s>

<s>Il <emph type="italics"/>no<emph.end type="italics"/> infatti esprimesi naturalmente con la rotazione orizzontale del <lb/>capo, nel quale atto si fa pi&ugrave; cospicua la linea descritta dalla bocca chiusa. </s>

<s><lb/>La linea orizzontale perci&ograve;, a indicar le quantit&agrave; negative, &egrave; il taglio della <lb/>bocca stessa, che silenziosamente nega. </s>

<s>Il <emph type="italics"/>si<emph.end type="italics"/> invece si suole esprimere ro&shy;<lb/>tando il capo verticalmente, e in quell'atto la linea pi&ugrave; cospicua &egrave; quella <lb/>disegnata dal profilo del naso. </s>

<s>Dalla linea verticale perci&ograve; veniva suggerita <lb/>naturalmente la distinzione delle quantit&agrave; positive. </s>

<s>Ma perch&egrave; potevasi fa&shy;<lb/>cilmente confonder quel segno con altri segni comuni, come quello per esem&shy;<lb/>pio dell'unit&agrave; e dell'<emph type="italics"/>i,<emph.end type="italics"/> per evitar la confusione, aggiunse Leonardo al profilo <lb/>del naso i due occhi, ossia due punti, che ricongiunti insieme, nella fretta <lb/>dello scrivere, dal continuato tratto della penna, vennero a compor la nota <lb/>crocellina. </s></p><p type="main">

<s>Le tradizioni dunque scientifiche, apprese a scelti libri, congiunte con <lb/>la discrezione del senno popolare, e dalle naturali esperienze illustrate e <pb xlink:href="020/01/1790.jpg" pagenum="33"/>promosse formano quel pi&ugrave; vero e pi&ugrave; compiuto magistero, da cui fu per <lb/>le vie della scienza guidato l'elettissimo ingegno di Leonardo da Vinci. </s>

<s>E <lb/>che tale sia veramente la qualit&agrave; e la natura di quel magistero, come po&shy;<lb/>trebbesi dimostrare in tutti gli altri scientifici argomenti, cos&igrave; &egrave; facile a ve&shy;<lb/>rificarsi particolarmente nel nostro, dietro le cose da noi sopra discorse, dalle <lb/>quali insomma resulta che, nei principii statici divulgati dalle scuole a quei <lb/>tempi, era come in germe rinchiusa la nuova scienza di Galileo. </s>

<s>Meditando <lb/>Leonardo e illustrando coll'esperienza cotesti fecondissimi principii, non fa <lb/>dunque maraviglia che s'incontrasse in alcuni di quei teoremi, concernenti <lb/>le leggi dei momenti, delle velocit&agrave; e dei tempi de'corpi gravi, disposti a <lb/>scendere per i piani inclinati e per gli archi dei cerchi, che poi fecero pub&shy;<lb/>blica e solenne mostra al mondo nelle proposizioni del III Dialogo delle due <lb/>Nuove scienze. </s></p><p type="main">

<s>Che poi in questo incontro dei due grandi ingegni Toscani non ci sia <lb/>nulla di miracoloso e di straordinario, si prova per altri esempi, ne'quali <lb/>il medesimo fatto avvenne per manifesta via naturale, come nel Tartaglia <lb/>per esempio, da cui il teorema che i pesi di due corpi gravi su due piani <lb/>egualmente alti ma variamente inclinati sieno proporzionali alle lunghezze <lb/>degli stessi piani &egrave; immediatamente concluso, nella Questione X del suo trat&shy;<lb/>tatello <emph type="italics"/>De ponderositate,<emph.end type="italics"/> dai principii statici del Nemorario. </s>

<s>Claudio Beri&shy;<lb/>guardi nel VI de'suoi Circoli pisani, Parte III, pone i teoremi fondamentali <lb/>della Meccanica galileiana, dicendo di essersi incontrato in quelle dimostra&shy;<lb/>zioni, &ldquo; XX annis antequam illi (Galileo e il Torricelli) de re quidquam <lb/>vulgassent &rdquo; (Patavii 1660, pag. </s>

<s>307). E noi gli prestiamo pienissima fede, <lb/>avendo potuto ritrovare anch'egli, il Beriguardo, venti anni prima della pub&shy;<lb/>blicazione dei Dialoghi dei Due massimi sistemi, come Leonardo e il Tar&shy;<lb/>taglia e altri, nella scienza anteriore al secolo XVI, i principii a quelle na&shy;<lb/>turalissime conclusioni. </s></p><p type="main">

<s>Dell'altro che fu magistero a Leonardo per&ograve;, consistente nell'esperienza, <lb/>e da cui si disse doversi principalmente riconoscere la superiorit&agrave;, che egli <lb/>ottenne fra'contemporanei e i discendenti; si possono nel presente soggetto <lb/>i molti esempii ridurre a uno solo. </s>

<s>Quella superiorit&agrave; infatti, chi ben con&shy;<lb/>sidera, ha la sua occulta causa motiva nel principio della composizion delle <lb/>forze, che il popolano da Vinci riconosce nel suo senno sperimentale esser <lb/>vera contro le cavillose dubitazioni degli scienziati. </s>

<s>Il Cardano per esempio, <lb/>nel cap. </s>

<s>X <emph type="italics"/>De motibus mirabilibus,<emph.end type="italics"/> che &egrave; parte del IX libro Dei paralipo&shy;<lb/>meni, fa un chiarissimo commento del teorema di Aristotile concernente i <lb/>due moti, che risultano dalla diagonale del rettangolo, ma poi, nella propo&shy;<lb/>sizione LIX dell'<emph type="italics"/>Opus novum,<emph.end type="italics"/> passando a farne l'applicazione ai proietti, <lb/>si rimane incerto se le forze, che distraggono il mobile in due diverse parti, <lb/>serbino la loro propria natura componendosi in un unico moto. </s>

<s>Il Tarta&shy;<lb/>glia ripudi&ograve; risolutamente il teorema aristotelico, e bench&egrave; il Benedetti si <lb/>sforzasse di ritener la scienza sul retto sentiero, Galileo non l'ammise che <lb/>nel caso delle direzioni ortogonali, e pure anche in questo particolare non <pb xlink:href="020/01/1791.jpg" pagenum="34"/>ne seppe far uso, come sventuratamente non ne sepper far uso il Torri&shy;<lb/>celli, il Viviani e il Borelli, se non in qualche caso straordinario e, come <lb/>cavalli che adombrino, condotti a mano dalla Geometria per vie trasversali. </s></p><p type="main">

<s>Sar&agrave; questo notabilissimo punto di storia da noi trattato nelle sue par&shy;<lb/>ticolarit&agrave; a suo tempo, e vedremo allora le ragioni per cui diffidarono quei <lb/>grandi ingegni di por mano al filo, che gli avrebbe potuti sicuramente gui&shy;<lb/>dare nei pi&ugrave; intricati meccanici labirinti. </s>

<s>Ma perch&egrave; insomma quelle ragioni <lb/>si riducono a filosofici cavilli, il Popolano di Vinci, non curandoli, s'attiene <lb/>all'esperienza, la quale, in vario modo ripetuta, gli conferm&ograve; la verit&agrave; an&shy;<lb/>tica, che cio&egrave; qualunque moto, che si rappresenti per la diagonale, si com&shy;<lb/>pone di due altri proporzionali ai lati del rettangolo o del parallelogrammo. </s></p><p type="main">

<s>Ecco scoperta l'occulta causa naturale di quel che, leggendo per le pre&shy;<lb/>ziose Note manoscritte, faceva prima stupire come di un miracolo nuovo; <lb/>ed ecco in che modo dalle tradizioni, comuni a tutti, e dalla esperienza, pro&shy;<lb/>pria e singolare a Leonardo, derivasse naturalmente quella maravigliosa <lb/>scienza del moto, della quale, scegliendo qua e l&agrave;, poniamo innanzi ai no&shy;<lb/>stri Lettori in ordine questo seguente Saggio. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Giova prima di tutto sapere qual concetto, da metafisico e tutt'insieme <lb/>da immaginoso artista, si fosse della forza e degli effetti di lei formato Leo&shy;<lb/>nardo: &ldquo; Forza dico essere una virt&ugrave; spirituale, una potenza invisibile, la <lb/>quale, per accidentale esterna violenza, &egrave; causata dal moto e collocata e in&shy;<lb/>fusa nei corpi, i quali sono dal loro naturale uso ritratti e piegati, dando a <lb/>questi vita attiva di maravigliosa potenza, che costringe tutte le create cose <lb/>a mutazione di forma e di sito. </s>

<s>Corre con furia alla sua desiderata morte, <lb/>e vassi diversificando mediante le cagioni. </s>

<s>Tardit&agrave; la fa grande, e prestezza <lb/>la fa debole; nasce per violenza, e muore per libert&agrave;. </s>

<s>E quanto &egrave; maggiore <lb/>pi&ugrave; presto muore e si consuma. </s>

<s>Scaccia con furia ci&ograve; che si oppone a sua <lb/>disfazione; desidera vincere, occidere la sua cagione, il suo contrasto e muore <lb/>vincendo. </s>

<s>S&egrave; stessa occide, fassi pi&ugrave; potente dove trova maggiore contrasto, <lb/>e caccia con furia ci&ograve; che si oppone alla sua morte. </s>

<s>Ogni cosa volentieri <lb/>fugge la sua morte. </s>

<s>Essendo costretta, ogni cosa costringe, nessuna cosa <lb/>senza lei si muove. </s>

<s>Il corpo, dov'essa giunge, nasce. </s>

<s>Non cresce n&egrave; in peso <lb/>n&egrave; in forma: nessuno moto fatto da lei fia durabile. </s>

<s>Cresce nelle fatiche, e <lb/>manca per riposo. </s>

<s>Il corpo dov'&egrave; costretta &egrave; fuori di libert&agrave;, e spesso ge&shy;<lb/>nera, mediante il moto, nuova forza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La forza &egrave; causata dal moto e infusa nel peso, e similmente il corpo <lb/>&egrave; causato dal moto e infuso nel peso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La forza &egrave; causa del moto, e il moto &egrave; causa della forza, e il moto <lb/>infonde la forza e il colpo nel peso, mediante l'obietto. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/1792.jpg" pagenum="35"/><p type="main">

<s>&ldquo; La forza in alcuno effetto, quando si disf&agrave;, si trasferisce in questo <lb/>corpo, che fugge dinanzi, e genera mediante il movimento il colpo di mag&shy;<lb/>giore efficacia, e dopo s&egrave; fa ruina, com'appare nel moto della pallotta, ch'&egrave; <lb/>cacciata dalla forza della bombarda. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La forza non si estende se non in tre effetti, i quali ne contengono <lb/>infiniti, i quali effetti sono tirare, spingere e fermare. </s>

<s>E detta forza pu&ograve; na&shy;<lb/>scere in due diversi modi: il primo si &egrave; per lo subito accrescimento d'un <lb/>corpo raro a un denso, come la moltiplicazione del fuoco nella bombarda, <lb/>il quale, non si trovando in vacuo recipiente loco al suo accrescimento, corre <lb/>con furia a pi&ugrave; ampio sito, scacciando ogni ostacolo che si oppone al suo <lb/>desiderio, e questo medesimo fa il corso dell'acqua e del vento, che scac&shy;<lb/>cia ogni ostacolo che si oppone. </s>

<s>Secondo, &egrave; quello che si crea ne'corpi pie&shy;<lb/>gati e storti fuori di loro natura, come il balestro e altre simili macchine. </s>

<s>&rdquo; <lb/>(Ravaisson-Mollien, Les Munuscr. </s>

<s>de Leonard ecc., MSS. A., Paris 1871, <lb/>fol. </s>

<s>34 a tergo). </s></p><p type="main">

<s>In queste parole ci sembra che sien comprese tutte quelle variet&agrave; di <lb/>effetti e di modi, ne'quali pu&ograve; esplicarsi la forza o per gl'impulsi naturali <lb/>della gravit&agrave;, o per quei preternaturali, come Galileo direbbe, della elasti&shy;<lb/>cit&agrave; dei solidi e de'liquidi: effetti e modi che furono soggetti di specula&shy;<lb/>zioni e di esperienze al nostro Leonardo. </s></p><p type="main">

<s>Il primo e pi&ugrave; ovvio aspetto, secondo il quale s'appresenti a conside&shy;<lb/>rare la forza, &egrave; quello del peso dei corpi gravitanti verso il centro terrestre, <lb/>la quale gravitazione &egrave; nel concetto del Vinci un'appetenza, un desiderio, <lb/>che hanno tutti i gravi di scendere a ritrovar la loro quiete. </s>

<s>&ldquo; Ogni peso <lb/>desidera di scendere al centro per la via pi&ugrave; breve, e dov'&egrave; maggiore pon&shy;<lb/>derosit&agrave; ivi &egrave; maggiore desiderio, e quella cosa che pi&ugrave; pesa, essendo li&shy;<lb/>bera, pi&ugrave; presto cade &rdquo; (ivi, fol. </s>

<s>35). </s></p><p type="main">

<s>Si sente queste parole render per eco la proposizione I del Nemora&shy;<lb/>rio, il quale dicemmo essere stato il primo a riguardare i pesi, non in <lb/>astratto secondo Archimede, ma nella loro realt&agrave;, e come attratti e diretti <lb/>al centro terrestre. </s>

<s>Leonardo mirabilmente illustra questo concetto. </s>

<s>Egli im&shy;<lb/>magina che la Terra, per qualsivoglia cagione, venga a essere ridotta in <lb/>frantumi confusamente dispersi per lo spazio, e dice che ciascuno di questi <lb/>frantumi scenderebbe verso il centro e lo trapasserebbe di altrettanto spa&shy;<lb/>zio, reciprocando le sue vibrazioni sempre e sempre minori, infintanto che <lb/>non avesse trovato presso a quel centro il conveniente suo collocamento, a <lb/>quel modo medesimo che noi vediamo per esperienza avvenire nel pendolo. <lb/>(Venturi, <emph type="italics"/>Essai<emph.end type="italics"/> cit., pag. </s>

<s>9). </s></p><p type="main">

<s>Piuttosto che trattenerci qui in estatica ammirazione intorno alla legge <lb/>dell'inerzia dei movimenti, e intorno all'oscillazione de'Pianeti dall'uno al&shy;<lb/>l'altro apside delle loro orbite come sogn&ograve; di aver letto in queste espres&shy;<lb/>sioni di Leonardo il Venturi, richiameremo l'attenzione de'nostri Lettori <lb/>sopra la questione famosa <emph type="italics"/>De lapsu lapidis circa centrum mundi,<emph.end type="italics"/> che do&shy;<lb/>vette incominciare ad agitarsi fra gli scienziati infino dal terminar del se-<pb xlink:href="020/01/1793.jpg" pagenum="36"/>colo XV. </s>

<s>Il Nostro la risolve a quel modo, che pochi anni dopo la risolvettero <lb/>il Tartaglia e il Maurolico, de'quali cos&igrave; scriveva il Benedetti per risposta a <lb/>un amico che, in mezzo alle peripatetiche controversie, lo aveva interrogato <lb/>intorno a quella stessa questione. </s>

<s>&ldquo; De illo, de quo me interrogas, dico Ni&shy;<lb/>colaum Tartaleam nec non Franciscum Maurolicum recte sensisse, male vero <lb/>Alexandrum Piccolomineum, et exemplum Maurolici optimum esse quod ta&shy;<lb/>men, si capere non potes, crede saltem authoritatibus talium virorum, qui <lb/>tantum in iis scientiis superant ipsum Alexandrum Piccolomineum, quan&shy;<lb/>tum a Sole caetera superantur astra. </s>

<s>Lapis igitur ille transiret centrum re&shy;<lb/>diretque cum diminutione tamen motus impressi, eo ferme modo ut scri&shy;<lb/>bunt iudiciosissimi illi viri, donec post multas reditiones sursum deorsumque <lb/>quiesceret circa centrum mundi &rdquo; (Liber spec., Venetiis 1599, pag. </s>

<s>368). </s></p><p type="main">

<s>Si sarebbe senza dubbio dal Benedetti, se avesse potuto veder mano&shy;<lb/>scritte quelle Note, che ora ci son sotto gli occhi, annoverato primo Leo&shy;<lb/>nardo fra quegli <emph type="italics"/>iudiciosissimi viri,<emph.end type="italics"/> e Galileo affermando &ldquo; di poter credere <lb/>che, quando il globo terrestre fosse perforato per il centro, una palla d'ar&shy;<lb/>tiglieria scendendo per tal pozzo acquisterebbe sino al centro tal impeto di <lb/>velocit&agrave;, che trapassato il centro la spingerebbe in su per altrettanto spa&shy;<lb/>zio, quanto fosse stato quello della caduta, diminuendo sempre la velocit&agrave; <lb/>oltre al centro con decrementi simili agli incrementi acquistati nello scen&shy;<lb/>dere &rdquo; (Alb. </s>

<s>I, 250); mentre coglieva dal Benedetti stesso il frutto gi&agrave; ma&shy;<lb/>turo avrebbe dovuto fra s&egrave; pensare ch'egli era stato allegato sull'albero di <lb/>una scienza pi&ugrave; antica. </s></p><p type="main">

<s>In quella stessa scienza, ch'&egrave; da noi cos&igrave; poco conosciuta, e perci&ograve; di&shy;<lb/>sprezzata, il desiderio di confermare le tradizioni sacre de'rivolgimenti, che <lb/>sarebbero per avvenire sulla superfice terrestre, introduceva un'altra que&shy;<lb/>stione intorno alla variabilit&agrave; del punto, a cui s'ammetteva oramai che d'ogni <lb/>parte tendessero i gravi. </s>

<s>Leonardo, il quale non poteva rimanersi indiffe&shy;<lb/>rente innanzi a un problema cos&igrave; strettamente connesso co'principii mec&shy;<lb/>canici ch'ei professava, considerando che il centro di gravit&agrave; di un corpo <lb/>dipende dalla sua figura ne concludeva perci&ograve; che la Terra, cos&igrave; per conti&shy;<lb/>nue vicende trasformabile, doveva necessariamente variare il punto della sua <lb/>attrazione. </s>

<s>&ldquo; Ogni grave, egli dice, tende al basso, e le cose alte non re&shy;<lb/>steranno in loro altezza, ma col tempo tutte discenderanno e cos&igrave; col tempo <lb/>il Mondo rester&agrave; sferico, e per conseguenza fia tutto coperto dall'acqua &rdquo; <lb/>(Del moto dell'acqua, Bologna 1828, pag. </s>

<s>282). In questo caso il centro della <lb/>gravit&agrave; della Terra torner&agrave; a un medesimo col centro della figura, ma in&shy;<lb/>tanto che si dispone il Mondo a questo suo finale assettamento, quello stesso <lb/>centro canger&agrave; sensibilmente di sito, &ldquo; e ci&ograve; principalmente, dice Leonardo, <lb/>per due mutazioni alla sua superfice: l'una si varia ogni sei ore, e l'altra <lb/>&egrave; fatta in molte migliaia di anni, e quella di sei ore nasce dal flusso e ri&shy;<lb/>flusso del mare, l'altra deriva dalla consumazione delle montagne, per li <lb/>moti dell'acqua, nati dalle pioggie e dal continuo corso de'fiumi. </s>

<s>Mutasi <lb/>adunque il sito al centro del Mondo e non il centro al sito, perch&egrave; tal cen-<pb xlink:href="020/01/1794.jpg" pagenum="37"/>tro &egrave; immobile, e il sito di continuo si muove di moto rettilineo, e non sar&agrave; <lb/>mai curvilineo &rdquo; (ivi, pag. </s>

<s>285). </s></p><p type="main">

<s>Se avesse il Venturi potuto consultar questo passo, sarebbesi facilmente <lb/>accorto che, nella Nota infrancesata al &sect; I del suo <emph type="italics"/>Essai,<emph.end type="italics"/> Leonardo ammet&shy;<lb/>tave, come tanti altri che lo avevano preceduto, la rotazione della Terra in <lb/>s&egrave; stessa, ma non intorno a un centro posto fuori di lei. </s>

<s>Sarebbe stato piut&shy;<lb/>tosto utile osservare, a quel proposito della linea descritta dai gravi cadenti <lb/>in relazione con la vertigine terrestre, come, facendo Leonardo una felicis&shy;<lb/>sima applicazione della Spirale archimedea, avesse poi dato agli stessi scien&shy;<lb/>ziati moderni maggior sodisfazione di Galileo. </s>

<s>E perch&egrave;, dal comparare in&shy;<lb/>sieme la scienza di questi due grandi uomini, risulta gran parte della Storia, <lb/>e de'frutti che si possono raccogliere dalla Storia; &egrave; bene esaminar pi&ugrave; da <lb/>presso come, ambedue partendo dai medesimi principii, s'incontrassero perci&ograve; <lb/>necessariamente nelle medesime conclusioni. </s></p><p type="main">

<s>Quasi fosse vero quel ch'esso Galileo si studi&ograve; d'insinuare, e riusc&igrave; a <lb/>persuadere che cio&egrave;, ne'dieci e pi&ugrave; secoli precedenti a lui, la scienza del <lb/>moto non avesse fatto progressi, si lusing&ograve; d'essere egli venuto il primo a <lb/>riappiccare le tradizioni a quel filo, lungamente rimasto nella Scuola ales&shy;<lb/>sandrina interciso, o per dir meglio avviluppato in un nodo, precipua causa <lb/>fra quelle che arrestarono il suo svolgimento. </s>

<s>Consisteva quel nodo nella <lb/>proposizione IX dell'VIII libro di Pappo, e Galileo si compiacque di averlo <lb/>egli finalmente sciolto, dimostrando che, per condurre un grave sopra un <lb/>piano perfettamente orizzontale, non ci era bisogno di nessuna potenza, e <lb/>che tutta la gran mole della sua Scienza nuova aveva potuto progredire <lb/>tant'oltre, principalmente per aver tolto quell'impedimento alla ruota. </s></p><p type="main">

<s>Che fosse questa davvero, come si diceva, una dolce lusinga fattasi dal <lb/>gran Maestro se n'ebbero ad accorgere i discepoli stessi, quelli almeno che <lb/>non rimasero abbarbagliati agl'improvvisi fulgori, fra'quali altrove citammo <lb/>Michelangiolo Ricci, al giudizio del quale ci piace ora aggiungere l'altro di <lb/>Antonio Nardi. </s>

<s>Nella veduta I della V scena intitolata <emph type="italics"/>Giudizi sopra alcuni <lb/>Filosofi,<emph.end type="italics"/> cos&igrave; esso Nardi scriveva al proposito nostro: &ldquo; Il Galileo &egrave; stato <lb/>de'primi, che ha praticato il modo di accoppiare le fisiche e le matemati&shy;<lb/>che discipline: fugli scorta il Benedetti &rdquo; (MSS. Gal., T. XX, pag. </s>

<s>633), di <lb/>che appunto l'argomento in discorso pu&ograve; servire di presentissimo esempio. <lb/><figure id="id.020.01.1794.1.jpg" xlink:href="020/01/1794/1.jpg"/></s></p><p type="caption">

<s>Figura 9.</s></p><p type="main">

<s>Nel cap. </s>

<s>XIV infatti del Libro delle specu&shy;<lb/>lazioni il Benedetti dimostra che una sfera, la <lb/>quale tocchi il piano orizzontale in un punto, pu&ograve; <lb/>esser qua e l&agrave; per quello stesso piano condotta, <lb/>senz'alcuna difficolt&agrave; o resistenza. </s>

<s>&ldquo; Rei exem&shy;<lb/>plum, cos&igrave; dice l'Autore, in carta describere pos&shy;<lb/>sumus, mediante figura circulari 9 hic subscripta <lb/>ANEU, contigua lineae rectae BD in puncto A, <lb/>unde EOA perpendicularis erit ipsi BD, et tan&shy;<lb/>tum ponderis habebimus a parte AUE, quantum <pb xlink:href="020/01/1795.jpg" pagenum="38"/>ab ipsa ANE. </s>

<s>Nunc igitur, si imaginabimur ductum esse centrum versus N, <lb/>per lineam ON parallelam ipsi AB, clarus nobis erit quod, absque ulla diffi&shy;<lb/>cultate aut resistentia, idem ducemus, quia huiusmodi centrum ab inferiori <lb/>parte ad superiorem nunquam mutabit situm respectu distantiae seu inter&shy;<lb/>valli, quae inter ipsum lineamque AB intercedit &rdquo; (editio cit., pag. </s>

<s>155). </s></p><p type="main">

<s>Ma le tradizioni di questa parte scienziale, raccolte nel suo libro e cos&igrave; <lb/>chiaramente esposte dal Benedetti, erano anche pi&ugrave; antiche, come appari&shy;<lb/>sce dalla proposizione XL dell'<emph type="italics"/>Opus Novum<emph.end type="italics"/> del Cardano cos&igrave; formulata: <lb/>&ldquo; Omne corpus sphaericum tangens planum in puncto movetur ad latus <lb/>per quamcumque vim, quae medium dividere potest &rdquo; (Operum, T. IV cit., <lb/>pag. </s>

<s>480). Ed &egrave; la ragione di ci&ograve; secondo l'Autore, come secondo il Bene&shy;<lb/>detti, che il centro di gravit&agrave; della sfera in moversi non sale n&egrave; scende, <lb/>ond'&egrave; ch'essa sfera non ha da superare altra resistenza da quella infuori <lb/>contrappostale dal mezzo dell'aria. </s>

<s>Quanto all'attrito poi, che potrebbe na&shy;<lb/>scer dal contatto col piano, &egrave; anco questo impedimento cessato dal suppo&shy;<lb/>sto che lo stesso contatto si faccia matematicamente in un punto, ond'&egrave; <lb/>che, per aversi maggior possibile corrispondenza fra la Geometria e la Fi&shy;<lb/>sica, richiedesi dal Cardano &ldquo; planum esse ex durissima materia, quae nullo <lb/>modo cedat &rdquo; (ibid.). Ma perch&egrave; difficile era troppo trovar materia s&igrave; dura, <lb/>e pi&ugrave; difficile che mai girare attorno un corpo in perfettissima sfera, sov&shy;<lb/>venne al Cardano stesso il felicissimo pensiero di dimostrar fisicamente il <lb/>teorema meccanico per via di quella esperienza de'corpi penduli, descritta <lb/>gi&agrave; nel libro <emph type="italics"/>De subtilitate.<emph.end type="italics"/> Coll'allungare il filo diviene il pendolo, bench&egrave; <lb/>gravissimo, sempre pi&ugrave; mobile, e giunge a un punto da venir mosso per <lb/>qualunque leggerissimo soffio, intantoch&egrave; <emph type="italics"/>praecantatione moveri videtur<emph.end type="italics"/><lb/>(Lugduni 1580, pag. </s>

<s>97). La ragione di ci&ograve; la riconosce l'Autore nell'esser <lb/>l'arco simile del maggior cerchio pi&ugrave; in rettitudine orizzontale di quel che <lb/>non sia il minore, e di qui la gran facilit&agrave; a venir mosso il pendolo grave <lb/>con tanto poca forza, da parer che quasi ubbidisca per incanto al soffio <lb/>della parola. </s></p><p type="main">

<s>Son questi principii fondamentali espressi dai sopra citati Autori con <lb/>tanta precisione, e con tanta evidenza, da persuader facilmente ognuno che <lb/>dovesser essere gi&agrave; prestabiliti nella scienza del moto, come legittimo frutto <lb/>dei teoremi archimedei e delle proposizioni del Nemorario. </s>

<s>Un corpo infatti, <lb/>secondo quelle dottrine, permane in equilibrio, infintanto che il centro della <lb/>gravit&agrave; non perda il suo sostegno, rimovendosi dal sito della uguaglianza, <lb/>che dallo stesso Nemorario ponesi <emph type="italics"/>esse aequidistantiam superficiei orizon&shy;<lb/>tis.<emph.end type="italics"/> In piena conformit&agrave; delle quali dottrine il nostro Leonardo, nel trattato <lb/>Della pittura pubblicato dal Manzi, cos&igrave; scriveva: &ldquo; Il moto &egrave; creato dalla <lb/>distruzione del bilico, cio&egrave; dalla inegualit&agrave;, imperocch&egrave; nessuna cosa per s&egrave; <lb/>si muove che non esca del suo bilico, e quella si fa pi&ugrave; veloce, che pi&ugrave; si <lb/>muove dal detto bilico &rdquo; (Roma 1817, pag. </s>

<s>169). </s></p><p type="main">

<s>Scendeva direttamente da questi principii quella conclusione, che Gali&shy;<lb/>leo pose contro Pappo, ma che il Cardano e il Benedetti avevano, come ve-<pb xlink:href="020/01/1796.jpg" pagenum="39"/>demmo, posta assai prima di lui, e prima di tutti loro Leonardo, il quale, <lb/>con quasi le medesime parole che si leggono nell'<emph type="italics"/>Opus novum<emph.end type="italics"/> e nel <emph type="italics"/>Li&shy;<lb/>ber speculationum,<emph.end type="italics"/> aveva lasciato scritto cos&igrave; nelle sue Note: &ldquo; Qualunque <lb/>cosa si trova in piano suolo e perfetto, che il suo polo non si trova in fra <lb/>parti uguali di pesi, mai si fermer&agrave;: lo esempio si vede in quelli che sdruc&shy;<lb/>ciolano per lo diaccio, che mai si fermano se le parti non tornano equidi&shy;<lb/>stanti al loro centro. </s>

<s>Al contrario, il corpo sferico perfetto posto sul piano <lb/>perfetto non avr&agrave; alcun movimento, se gi&agrave; non glielo darai, e la ragione si <lb/>&egrave; che tutte le sue parti sono di pari distanza al centro, onde sempre rimane <lb/>in bilancia, e la bilancia, che ha le sue braccia uguali di peso e di lun&shy;<lb/>ghezza, sta senza moto. </s>

<s>Essendo, in detto corpo sferico, eguale l'uno suo <lb/>mezzo all'altro, ancora lui fia senza moto &rdquo; (MSS. A. cit., fol. </s>

<s>21, 22). </s></p><p type="main">

<s>Dietro questo principio, cos&igrave; nello schietto linguaggio del Popolano da <lb/>Vinci formulato, il gran Maestro della scienza del moto pass&ograve; a concludere <lb/>la legge dei momenti dei gravi lungo i piani inclinati, con pi&ugrave; felice aggres&shy;<lb/>sione di Pappo, e a dimostrar le propriet&agrave; generali dei movimenti dei corpi, <lb/>d'onde immediatamente scendeva la verit&agrave; dei nuovi teoremi. </s>

<s>Leonardo <lb/>muove dai medesimi principii e giunge alle medesime conclusioni. </s>

<s>E perch&egrave; <lb/>insomma i pensieri di lui procedono dalle proposizioni del Nemorario, non <lb/>&egrave; maraviglia se si svolgono in simile ordine a quello del Tartaglia, il quale <lb/>anch'egli, con pi&ugrave; felici auspici di Pappo, s'apparecchiava a dimostrar la <lb/>variet&agrave; de'momenti ne'pesi per varie obliquit&agrave; di linee scendenti, sul fon&shy;<lb/>damento della seguente Questione, ch'&egrave; la nona del suo opuscolo <emph type="italics"/>De pon-<emph.end type="italics"/><lb/><figure id="id.020.01.1796.1.jpg" xlink:href="020/01/1796/1.jpg"/></s></p><p type="caption">

<s>Figura 10.<lb/><emph type="italics"/>derositate:<emph.end type="italics"/> &ldquo; Aequalitas declinationis identitas ponde&shy;<lb/>ris. </s>

<s>&rdquo; (Editio cit., fol. </s>

<s>6 ad t.). </s></p><p type="main">

<s>Similmente Leonardo, disegnando questa che con <lb/>molta propriet&agrave; chiama <emph type="italics"/>Bilancia<emph.end type="italics"/> (fig. </s>

<s>10), cos&igrave; con tali <lb/>parole sottoscrittevi la dichiara: &ldquo; Se li pesi e le braccia <lb/>e li moti (ossia le velocit&agrave; virtuali) sono uguali in obli&shy;<lb/>quit&agrave;, essi pesi non moveranno l'uno l'altro. </s>

<s>&mdash; Li pesi <lb/>eguali mantengono la gravit&agrave; eguale nella obliquit&agrave; egua&shy;<lb/>le &rdquo; (Les Manuscr. </s>

<s>E., Paris 1888, fol. </s>

<s>58 ad t.). </s></p><p type="main">

<s>Or se la obliquit&agrave; &egrave; disuguale, con qual proporzione varier&agrave; il peso? </s>

<s><lb/>Ecco il problema pi&ugrave; importante e pi&ugrave; difficile del primo, che nuovamente <lb/>voleva essere risoluto. </s>

<s>Il Tartaglia lo sciolse con la Geometria, e con la Geo&shy;<lb/>metria pure, bench&egrave; in vario modo, lo sciolse come presto vedremo anche <lb/>Leonardo, ma volle per assicurarsi meglio del vero far precedere alla ma&shy;<lb/>tematica l'esperienza, nella quale riusc&igrave; pi&ugrave; felicemente dello Stevino, del <lb/>Beriguardo e di altri, che si vollero quasi un secolo dopo metter per la me&shy;<lb/>desima via. </s>

<s>I primi tentativi dee averli fatti con la Bilancia sopra descritta, <lb/>variando obliquit&agrave; e lunghezza ad uno de'bracci di lei, ma perch&egrave; difficile <lb/>troppo riusciva l'aggiustare i pesi, e senza errore computarne i momenti, <lb/>gli sovvenne il felice pensiero di ricorrere alla Bilancia idrostatica, nella <lb/>quale il peso dell'acqua &egrave; giustissimamente compartito nell'uno e nell'al-<pb xlink:href="020/01/1797.jpg" pagenum="40"/>tro braccio dalla stessa Natura. </s>

<s>&ldquo; L'acqua ABS (fig. </s>

<s>11) non avr&agrave; movi&shy;<lb/>mento, perch&egrave; intanto pesa l'acqua AB, quanto l'acqua AS, e la linea BS <lb/><figure id="id.020.01.1797.1.jpg" xlink:href="020/01/1797/1.jpg"/></s></p><p type="caption">

<s>Figura 11.<lb/>&egrave; piana, e l'acqua piana par s&egrave; non si <lb/>muove &rdquo; (Del moto dell'acqua cit., pag. </s>

<s>436). <lb/>Ora il peso <emph type="italics"/>p<emph.end type="italics"/> dell'acqua AS, chiamata *s la <lb/>sezione nel punto A comune ai due tubi, <lb/>&egrave; *s. </s>

<s>AS; e il peso P dell'acqua AB &egrave; *s. </s>

<s>AB. </s>

<s><lb/>Essendo perci&ograve; i due pesi eguali, s'avr&agrave; <lb/>la proporzione P:<emph type="italics"/>p<emph.end type="italics"/>=AB:AS com'espres&shy;<lb/>siva, nel moderno nostro linguaggio, del <lb/>resultato medesimo, a cui per cos&igrave; facile e sicura via fu condotto Leonardo. </s></p><p type="main">

<s>Ebbe esso Leonardo altres&igrave; dalla medesima Bilancia idrostatica la dimo&shy;<lb/>strazione sperimentale di un altro teorema, che gli serv&igrave; per rispondere al <lb/>seguente propostosi quesito: Se l'acqua, che cala uno dito per miglio, cam&shy;<lb/>mina uno miglio per ora, quanto camminer&agrave; ella calando due dita? </s>

<s>&rdquo; (Les <lb/>Manuscr. </s>

<s>A. cit., fol. </s>

<s>27 ad t.). Galileo, non avendo trovato modo a dimo&shy;<lb/>strarlo, ci&ograve; che poi fece il Torricelli, suppose quel teorema, da cui si diceva <lb/>dipendere la risposta al quesito di Leonardo, come vero, per cui procedeva <lb/>nel suo trattato Della scienza meccanica cos&igrave; asseverantemente, ma senza <lb/>alcuna dimostrazione, nel suo discorso: &ldquo; Se avremo i piani elevati AC, <lb/><figure id="id.020.01.1797.2.jpg" xlink:href="020/01/1797/2.jpg"/></s></p><p type="caption">

<s>Figura 12.<lb/>AD, AE (fig. </s>

<s>12) sopra di essi non sar&agrave; spinto un <lb/>dato corpo grave, se non con violenza, la quale mag&shy;<lb/>giore si richieder&agrave; per moverlo sopra la linea AD, <lb/>che sopra la AC, e maggiore ancora sopra la AE <lb/>che sopra l'AD, il che procede per avere egli mag&shy;<lb/>gior impeto di andare al basso per la linea AE che <lb/>per l'AD, e per la AD che per l'AC; sicch&egrave; po&shy;<lb/>tremo concludere i corpi gravi aver maggior resi&shy;<lb/>stenza ad esser mossi sopra piani elevati diversa&shy;<lb/>mente, secondo che l'uno sar&agrave; pi&ugrave; o meno elevato <lb/>dell'altro &rdquo; (Alb. </s>

<s>XI, 114). </s></p><p type="main">

<s>Per Leonardo si trasforma il piano AE in un tubo comunicante col <lb/>tubo AB, e perch&egrave; piegandosi esso tubo AE in AD, in AC, ecc., le pres&shy;<lb/>sioni misurate dall'altezza del livello del liquido nel tubo verticale diminui&shy;<lb/>scono via via come le perpendicolari EF, DC, CH, n'ebbe perci&ograve; a con&shy;<lb/>cludere sperimentalmente, dall'idrostatica facendo legittimo passagggio alla <lb/>statica, che gl'impeti di scendere o le velocit&agrave; di un medesimo grave sopra <lb/>un piano variamente inclinato stanno come le altezze perpendicolari, o come <lb/>i seni delle elevazioni. </s>

<s>Applicando poi il teorema al sopra propostosi que&shy;<lb/>sito ne concludeva la seguente verissima risposta: &ldquo; Quell'acqua, la quale <lb/>caler&agrave; un'oncia per miglio, avr&agrave; di movimento un quarto di braccio per un <lb/>tempo (cio&egrave; per un tempo di musica): quella, che avr&agrave; due once per miglio, <lb/>avr&agrave; di movimento mezzo braccio per tempo, e cos&igrave; quella che cala quat&shy;<lb/>tr'once si mover&agrave; un braccio per tempo &rdquo; (Moto dell'acqua cit., pag. </s>

<s>432). </s></p><pb xlink:href="020/01/1798.jpg" pagenum="41"/><p type="main">

<s>Tanto vide Leonardo farsi in questi giochi idrostatici la Natura da s&egrave; <lb/>medesima rivelatrice delle leggi del moto, che ritornando alla Bilancia, rap&shy;<lb/>presentata nella nostra figura XI, vi ritrov&ograve; la pi&ugrave; chiara conferma delle <lb/>supposte verit&agrave; del Nemorario. </s>

<s>&ldquo; L'acqua ricevuta nell'angolo supino occu&shy;<lb/>per&agrave; tanto pi&ugrave; dell'una faccia che dell'altra, quanto l'una faccia fia pi&ugrave; <lb/>obliqua dell'altra &rdquo; (Manuscr. </s>

<s>A. cit, fol. </s>

<s>22). E ci&ograve; parve al Nostro la pi&ugrave; <lb/>bella dimostrazione sperimentale di ci&ograve;, che in quarto luogo supponevasi dallo <lb/>stesso Nemorario: &ldquo; Secundum situm gravius esse, quanto in eodem situ <lb/>minus obliquus est descensus &rdquo; (De pond. </s>

<s>cit., praefatio). </s></p><p type="main">

<s>Se si fanno in A, seguitava a ragionare Leonardo degli effetti della Bi&shy;<lb/>lancia, i due pesi equilibrio, dunque l'impeto di discendere che ha l'acqua <lb/>AS &egrave; in quel punto eguale all'impeto discensivo dell'acqua AB, come di <lb/>qualunque altr'acqua avesse anche maggiore e maggiore obliquit&agrave;, purch&egrave; <lb/>attingesse superiormente al livello della orizzontale SB prolungata, nel qual <lb/>fatto riconosceva lo stesso Leonardo una dimostrazione sperimentale pi&ugrave; fa&shy;<lb/>cile e pi&ugrave; conclusiva di quella, che immagin&ograve; Galileo, perch&egrave; gli fosse con <lb/>minore difficolt&agrave; concesso per teoricamente vero quel suo principio mecca&shy;<lb/>nico fondamentale, che cio&egrave; &ldquo; i gradi di velocit&agrave; di un mobile, discendente <lb/>con moto naturale dalla medesima sublimit&agrave; per piani in qualsivoglia modo <lb/>inclinati, all'arrivo all'orizzonte son sempre eguali, rimossi gl'impedimenti &rdquo; <lb/>(Alb. </s>

<s>XIII, 177). </s></p><p type="main">

<s>Apparve questa verit&agrave; alla mente di Leonardo in tanta evidenza, da <lb/>fargli pronunziar sotto forma del pi&ugrave; certo teorema quello, che sarebbe po&shy;<lb/>tuto sembrare un paradosso, che cio&egrave;, scendendo un corpo in varii modi, <lb/>deviato per obliquit&agrave; di linee e di rimbalzi, giunge al suo termine orizzon&shy;<lb/>tale, come se fosse senz'altro impedimento sempre andato a diritto a ritro&shy;<lb/>var quello, che &egrave; il sito dell'egualit&agrave;, secondo l'espressione del Nemorario. <lb/></s>

<s>&ldquo; Ogni movimento fatto dalla forza conviene che faccia tal corso, quanto &egrave; <lb/>la proporzione della cosa mossa con quella che muove, e se ella trover&agrave; <lb/>resistente opposizione finir&agrave; la lunghezza del suo debito viaggio per circolar <lb/>moto o per altri varii risaltamenti e balzi, i quali computato il tempo e il <lb/><figure id="id.020.01.1798.1.jpg" xlink:href="020/01/1798/1.jpg"/></s></p><p type="caption">

<s>Figura 13.<lb/>viaggio fia come se il corso fosse stato senz'alcuna <lb/>contradizione &rdquo; (ivi, fol. </s>

<s>60 ad t.). </s></p><p type="main">

<s>Dall'applicazione di questi veri principii riu&shy;<lb/>sciva dimostrato uno dei teoremi pi&ugrave; fondamentali <lb/>della Meccanica, relativo alla proporzione dei tempi <lb/>che passa a scendere un grave o per l'obliqua o <lb/>per la perpendicolare. </s>

<s>Sia AB (fig. </s>

<s>13) questa per&shy;<lb/>pendicolare, lungo la quale abbia a cadere il grave L, <lb/>e AC l'obliqua, per la quale abbia pure a scendere <lb/>il grave M, che si suppone essere il medesimo o di <lb/>pari peso con L. </s>

<s>Non solo, per i posti principii, i <lb/>due corpi hanno eguale velocit&agrave; ne'punti L, M, ma ne'punti O, P; Q, R, e <lb/>in tutti gli altri infiniti che si potrebbero determinare con condur linee <pb xlink:href="020/01/1799.jpg" pagenum="42"/>infinite parallele alla orizzontale, cosicch&egrave; pu&ograve; dirsi essere AB, AC due rette <lb/>che si compongono d'infiniti momenti velocitativi fra s&egrave; tutti eguali. </s>

<s>Ma <lb/>per la definizione di Aristotile nelle Questioni meccaniche, e per i teoremi <lb/>di Archimede <emph type="italics"/>De spiralibus,<emph.end type="italics"/> dove le velocit&agrave; sono eguali i tempi convien <lb/>che sieno proporzionati agli spazii, dunque il tempo della discesa del grave <lb/>L, al tempo della discesa del grave M star&agrave; come la AB alla AC; teorema <lb/>che Leonardo stesso formulava con queste parole: &ldquo; Tanto cader&agrave; pi&ugrave; pre&shy;<lb/>sto il peso L che il peso M, quanto la linea AB entra nella linea AC &rdquo; (ivi <lb/>fol. </s>

<s>33). </s></p><p type="main">

<s>Bench&egrave; fosse questo, insieme con gli altri teoremi sopra narrati, una <lb/>nuova rivelazione che Leonardo veniva a fare alla scienza, non era ancora <lb/>esaurita la fecondit&agrave; di quella Bilancia, che per la facilit&agrave; de'liquidi ad ub&shy;<lb/>bidir docilmente a tutti i minimi impulsi, e per quella loro destrezza, di&shy;<lb/>ciam cos&igrave;, a sottrarsi agl'impedimenti, si rendeva leggibilissimo esemplare <lb/>del moto degli altri gravi. </s>

<s>L'esattissimo livellamento, che in ogni caso si <lb/>osserva nei due tubi comunicanti, era un fatto particolare, il quale general&shy;<lb/>mente applicato a tutti i corpi si poteva tradurre in quell'altro fondamentale <lb/>principio meccanico, che cio&egrave;, secondo l'espressioni stesse di Galileo, &ldquo; l'im&shy;<lb/>peto acquistato da un grave in qualsivoglia luogo del suo moto sia tanto <lb/>che basterebbe a ricondurlo a quell'altezza, d'onde si parti &rdquo; (Alb. </s>

<s>I, 27, 28). <lb/>E Leonardo, in eguale e pi&ugrave; piena sentenza: &ldquo; Il corpo che scende per AB <lb/>(nella posta addietro figura XI) risalir&agrave; in S alla medesima linea orizzontale, <lb/>come nel tubo pieno di acqua &rdquo; (Manuscr. </s>

<s>A. cit, fol 22). </s></p><p type="main">

<s>Si fece opposizione a Galileo, mettendo in conto le perdite di velocit&agrave; <lb/>subite dal grave per via dell'urto violento e degli attriti; ingiusta e inutile <lb/>opposizione, perch&egrave; quello stesso teorema galileiano si dava solamente per <lb/>vero nel caso che venissero rimossi tutti gl'impedimenti, di che la Bilan&shy;<lb/>cia idrostatica, per la fluidit&agrave; dell'acqua, ne porgeva il pi&ugrave; bello e pi&ugrave; di&shy;<lb/>mostrativo esempio. </s>

<s>Leonardo in ogni modo par che neghi a qualunque <lb/>causa accidentale il potere in nulla minorare quella virt&ugrave;, che vale a riso&shy;<lb/>spingere tanto in su il grave, quant'era in gi&ugrave; prima disceso. </s>

<s>&ldquo; Oh mira&shy;<lb/>bile giustizia di te Primo Motore! Tu non hai voluto mancare a nessuna <lb/>potenzia: loro ordini egualit&agrave; de'suoi necessarii effetti, conciossiach&egrave; se una <lb/>potenzia debba cacciare cento braccia una cosa vinta da lei, e questa nel <lb/>suo ubbidire trovi intoppo, hai ordinato che la potenza del colpo ricausi <lb/>nuovo movimento, il quale per diversi balzi ricuperi la intera somma del <lb/>suo debito viaggio. </s>

<s>E se tu misurerai la linea fatta dai detti balzi, tu tro&shy;<lb/>verai essere di tale lunghezza, qual sarebbe a trarre colla medesima forza <lb/>una simile cosa libera per l'aria. </s>

<s>Questa esperienza farai con una piccola <lb/>ballotta di vetro battuta sopra un suolo di pietra viva e piana, e abbi una <lb/>lancia lunga segnata di diversi colori, e quando hai spettatori fa'tenere l'asta <lb/>a uno, e pon mente da alquanto lontano ne'balzi a che colori ella s'alza di <lb/>mano in mano a ogni balzo nell'altezza dell'asta, e notali. </s>

<s>E se saranno i <lb/>notatori quanti i balzi, pi&ugrave; facilmente ognuno terr&agrave; a mente il suo. </s>

<s>Ma <pb xlink:href="020/01/1800.jpg" pagenum="43"/>fa'che l'asta sia piuttosto ferma da capo o in un buso da pi&egrave;, perch&egrave; chi <lb/>la tenesse in mano occuperebbe la veduta ai giudicatori, e fa'che il primo <lb/>balzo si facci in mezzo a due angoli retti, acci&ograve; la palla caggi sempre in un <lb/>medesimo loco, perch&egrave; meglio fieno notate l'altezze de'balzi nell'asta. </s>

<s>Poi <lb/>fa'trarre da quella medesima potenzia questa ballotta per libero tratto, e <lb/>nota il luogo dove percote, e misura, e troverai il secondo viaggio essere <lb/>compagno al primo &rdquo; (ivi, fol. </s>

<s>24). </s></p><p type="main">

<s>Ne'pendoli, secondo Leonardo, ne'quali l'impeto dell'ascesa non &egrave; re&shy;<lb/><figure id="id.020.01.1800.1.jpg" xlink:href="020/01/1800/1.jpg"/></s></p><p type="caption">

<s>Figura 14.<lb/>stituito dall'elasticit&agrave; dell'urto, ma <lb/>dagl'impeti precedenti via via ac&shy;<lb/>cumulati nella discesa, deve il fatto <lb/>sopra notato verificarsi anche con <lb/>maggiore esattezza, intanto che, se <lb/>il pendolo casca da A (fig. </s>

<s>14) giun&shy;<lb/>ger&agrave; in E con tale acquisto di forza, <lb/>da poter risalire per essa infino in D <lb/>a ritrovare l'orizzontale AD, dalla <lb/>quale s'era partito. </s>

<s>Nel medesimo <lb/>modo sar&agrave; vero che risalir&agrave; lo stesso pendolo in B o in F, dop'esser caduto <lb/>dai punti G, C nelle orizzontali GB, CF. </s></p><p type="main">

<s>Nella totale escursione per l'emiciclo il grave pendulo ha dunque in G <lb/>e in B velocit&agrave; uguali, ci&ograve; che si concludeva da Leonardo, considerando che <lb/>sono uguali le condizioni del moto tanto nell'ascesa, quanto nella discesa, <lb/>non essendo, secondo il Nemorario la quiete altro che il termine dello stesso <lb/>moto, cosicch&egrave;, incomincino le reciprocazioni o da A o da D, le mosse di <lb/>discendere in ogni modo sono state precedute dagli atti del salire. </s>

<s>&ldquo; Il moto <lb/>naturale fu prima accidentale, cio&egrave; la pietra che cade fu prima portata e <lb/>gettata in alto &rdquo; (ivi, fol. </s>

<s>31 ad t.); alle quali parole di Leonardo cos&igrave; fanno <lb/>quest'altre di Galileo da commento: &ldquo; Quando voi reggete in mano una <lb/>pietra non altro fate che imprimerli tanta virt&ugrave; impellente all'ins&ugrave;, quanta <lb/>&egrave; la facolt&agrave; della sua gravit&agrave; traente in gi&ugrave; &rdquo; (Alb. </s>

<s>XIII, 160). </s></p><p type="main">

<s>Essendo dunque in N e in B nell'arco descritto dal pendolo le due ve&shy;<lb/>locit&agrave; eguali, consider&ograve; Leonardo che eguali pure sarebbero state quelle ve&shy;<lb/>locit&agrave;, quando il peso A fosse caduto per la perpendicolare AG, o per l'obli&shy;<lb/>qua AB, d'onde n'ebbe a formulare la seguente Nota a modo di teorema: <lb/>&ldquo; Il peso A, dopo esser disceso per C, E risalir&agrave; in B con quella velocit&agrave; <lb/>che avrebbe una palla uguale, che fosse scesa da A in B per la linea di&shy;<lb/>ritta AB &rdquo; (Manuscr. </s>

<s>A. cit., fol. </s>

<s>26). </s></p><p type="main">

<s>Appartiene al medesimo ordine di speculazioni anche quest'altra con&shy;<lb/>clusione cos&igrave; espressa in una delle solite Note vinciane, che il Venturi tra&shy;<lb/>scrisse dall'appendice al manoscritto B: &ldquo; Il corpo grave A scende pi&ugrave; veloce <lb/>per l'arco ACE che per la corda AE, perch&egrave; in AC comincia la sua discesa, <lb/>come per la perpendicolare &rdquo; (<emph type="italics"/>Essai<emph.end type="italics"/> cit., pag. </s>

<s>18). Devesi senza dubbio Leo&shy;<lb/>nardo essersi certificato di questa notizia, sperimentando intorno alla discesa <pb xlink:href="020/01/1801.jpg" pagenum="44"/>di qualche pallottola dentro alla cassa di un vaglio, come pure si legge che <lb/>facevano Guidubaldo del Monte e Galileo, ma le espressioni <emph type="italics"/>in AC comin&shy;<lb/>cia la sua discesa come per la perpendicolare<emph.end type="italics"/> contengono un germe di <lb/>dimostrazione, ch'&egrave; poi quella, della quale s'ebbe per qualche tempo a con&shy;<lb/>tentare lo stesso Galileo. </s>

<s>Divisi infatti da Leonardo l'arco e la corda in due <lb/>parti eguali ne'punti C e H di mezzo, consider&ograve; che la scesa per AC, ben&shy;<lb/>ch&egrave; pi&ugrave; lunga, &egrave; nonostante pi&ugrave; precipitosa che per AH, e ne concluse per&shy;<lb/>ci&ograve;, come nella Lettera galileiana allo Staccoli, che la velocit&agrave; gi&agrave; concepita <lb/>pel vantaggio di AC &egrave; pi&ugrave; potente per conservare l'acquisto fatto che non <lb/>&egrave; la declivit&agrave; della rimanente parte HE della corda a ristorare il danno della <lb/>perdita gi&agrave; fatta (Alb. </s>

<s>VI, 369, 70). </s></p><p type="main">

<s>I saggi, che abbiamo dati fin qui, sembrano a noi sufficienti per di&shy;<lb/>mostrare la fecondit&agrave; di quei principii statici, che si professavano ai tempi, <lb/>ne'quali Leonardo attendeva a'suoi studii, e confermano tutto insieme quel <lb/>che si diceva che cio&egrave; potevasi derivare da quelli stessi principii la miglior <lb/>parte della Meccanica galileiana. </s>

<s>Le proposizioni del Nemorario per&ograve; avevano <lb/>un intendimento assai pi&ugrave; modesto, ed era quello di stabilire una legge sta&shy;<lb/>tica generale, da poter applicarsi alle macchine, per saper secondo qual'or&shy;<lb/>dine si corrisponda in esse la resistenza del mobile con la potenza del mo&shy;<lb/>tore. </s>

<s>Leonardo architetto non poteva negligere quello studio, per fondamento <lb/>al quale pose le velocit&agrave; virtuali di Aristotile e del Nemorario, mentre dal&shy;<lb/>l'altra parte cereava di trarre quel maggior profitto possibile dai teoremi <lb/>archimedei Degli equiponderanti. </s>

<s>Fu il Libri il primo a notar che venivano <lb/>per i manoscritti vinciani que'teoremi promossi, infino a ricercar co'me&shy;<lb/>todi de'moderni il centro della gravit&agrave; della piramide (Histoire des mathem., <lb/>T. III, Paris 1840, pag. </s>

<s>44), ma perch&egrave; non sono in tale argomento le dif&shy;<lb/>ficolt&agrave; della Fisica punto minori di quelle della Geometria, scegliamo, come <lb/>pi&ugrave; proprii di questi Saggi, alcuni fatti, che sembravano al volgo e agli <lb/>stessi dotti miracolosi, ma che Leonardo naturalmente spiegava, applican&shy;<lb/>dovi il principio che un corpo, o pi&ugrave; corpi congiunti insieme nella pi&ugrave; strana <lb/>posizione e figura, permangono in stabile equilibrio, quando il centro di gra&shy;<lb/>vit&agrave; del tutto vada a cader giusto sul punto che gli fa da sostegno. </s>

<s>&ldquo; Quel <lb/>peso unito, che fia sostenuto in mezzo, e il rimanente stia sospeso, di qua&shy;<lb/><figure id="id.020.01.1801.1.jpg" xlink:href="020/01/1801/1.jpg"/></s></p><p type="caption">

<s>Figura 15.<lb/>lunque strana forma si vuole, che sem&shy;<lb/>pre si stabilir&agrave; sopra il suo sostentacolo <lb/>in equilibrio, e qualche volta le estremit&agrave; <lb/>non fieno uguali al centro del peso. </s>

<s>Ver&shy;<lb/>bigratia: sia AB (fig. </s>

<s>15) uno pezzo di <lb/>riga, il quale posi solamente la estremit&agrave; <lb/>A, e il resto stia sospeso. </s>

<s>Questo fia im&shy;<lb/>possibile a fare, se prima tu non unisci <lb/>e congiungi con esso il peso CB, il quale <lb/>faccia tal contrapposto, che resti in mezzo <lb/>fra C, B, e verr&agrave; questo peso a fermarsi in sul polo A, e lo strumento di <pb xlink:href="020/01/1802.jpg" pagenum="45"/>sotto (fig. </s>

<s>16) &egrave; sottoposto a simile ragione &rdquo; (Manuscr. </s>

<s>A. cit., fol. </s>

<s>33 ad t.). <lb/>Questi semplici e naturali esempi dell'equilibrio stabile dei corpi furono poi <lb/><figure id="id.020.01.1802.1.jpg" xlink:href="020/01/1802/1.jpg"/></s></p><p type="caption">

<s>Figura 16.<lb/>da Leonardo informati di artistica eleganza <lb/>in quelle figurine ondeggianti, che torna&shy;<lb/>rono un secolo dopo nella mente del Vi&shy;<lb/>viani a dar di s&egrave; pubblico e curioso spet&shy;<lb/>tacolo nel teatro della scienza meccanica: <lb/>delle quali figurine e di altre forme pi&ugrave; <lb/>bizzarre di corpi gravi sospesi Leonardo <lb/>stesso cos&igrave; in una breve nota svelava il <lb/>mistero agli attoniti ammiratori. </s>

<s>&ldquo; Il cen&shy;<lb/>tro di ciascuno peso sospeso si stabilisce sotto il suo sostentacolo &rdquo; (Ra&shy;<lb/>vaisson-Mollien, Manuscr. </s>

<s>B., Paris 1883, fol. </s>

<s>18). </s></p><p type="main">

<s>Ma passiamo a vedere come facesse il Nostro l'applicazione di questi e <lb/>degli altri sopra accennati principii statici al moto delle macchine. </s>

<s>L'alte&shy;<lb/>razione, che subisce un peso nel dilungarsi pi&ugrave; o meno il punto della sua <lb/>sospensione dal centro, e che comunemente chiamasi <emph type="italics"/>momento,<emph.end type="italics"/> da Leonardo <lb/>&egrave; distinto col nome di <emph type="italics"/>peso accidentale.<emph.end type="italics"/> &ldquo; Il peso accidentale, egli dice, se <lb/>posto in bilancia contro al peso naturale vale quanto esso peso naturale, e <lb/>questo si prova mediante il peso, che di loro riceve il polo della Bilancia, <lb/>il quale si carica tanto pi&ugrave; del peso accidentale che del naturale, quanto il <lb/>braccio maggiore di tal bilancia eccede il braccio minore &rdquo; (Mollien, Manus. </s>

<s>E., <lb/>Paris 1888, fol. </s>

<s>59). </s></p><p type="main">

<s>Da questo principio generale conclude Leonardo i varii teoremi, e rac&shy;<lb/>coglie i dati necessarii a risolvere alcuni problemi concernenti la Libbra, <lb/><figure id="id.020.01.1802.2.jpg" xlink:href="020/01/1802/2.jpg"/></s></p><p type="caption">

<s>Figura 17.<lb/>degli uni e degli altri de'quali propo&shy;<lb/>niamo ai Lettori i seguenti Saggi: &ldquo; I <lb/>pesi eguali, mutati per eguale distan&shy;<lb/>zia dal centro ovvero polo della Bilan&shy;<lb/>cia, terranno gli estremi della Bilancia <lb/>equidistanti al sostentacolo della Bilan&shy;<lb/>cia: cio&egrave; se i pesi M, N (fig. </s>

<s>17), ap&shy;<lb/>piccati in C, A, e'siano d'egual peso <lb/>ed egual distanza al polo della Bilan&shy;<lb/>cia S, e che tu li scosti da esso polo infino in D, B, se le fieno <lb/>uguali distanzie, rimarran gli estremi della Bilancia in equilibrio &rdquo; <lb/><figure id="id.020.01.1802.3.jpg" xlink:href="020/01/1802/3.jpg"/></s></p><p type="caption">

<s>Figura 18.<lb/>(Manuscr. </s>

<s>A. cit., fol. </s>

<s>52 ad t). &mdash; <lb/>&ldquo; Domando se le due braccia della <lb/>Bilancia saranno compartite in parti <lb/>eguali e in A, B, C, D, E (fig. </s>

<s>18) <lb/>fia posto per ciascheduno una lib&shy;<lb/>bra, quante libbre li far&agrave; resistenzia <lb/>in F? </s>

<s>Farai cos&igrave;: a fare resistenzia a una libbra posta in F, B <lb/>fa resistenzia a due, C a tre, D a quattro, ed E a cinque, che <pb xlink:href="020/01/1803.jpg" pagenum="46"/>tutta la somma fa resistenzia a quindici libbre poste in F &rdquo; (ivi, fol. </s>

<s>5). &mdash; <lb/>&ldquo; Se una Bilancia avr&agrave; un peso, il quale sia per lunghezza a similitudine <lb/><figure id="id.020.01.1803.1.jpg" xlink:href="020/01/1803/1.jpg"/></s></p><p type="caption">

<s>Figura 19.<lb/>d'uno de'suoi bracci, cio&egrave; MN (fig. </s>

<s>19), <lb/>che sia di sei libbre, quante libbre poste <lb/>in F li faranno resistenza? </s>

<s>Dico che tre <lb/>libbre fiano a sufficienza, imperocch&egrave; se <lb/>il peso MN sar&agrave; lungo quanto uno dei <lb/>bracci, potrai stimare che sia collocato <lb/>in mezzo al braccio della Bilancia nel <lb/>punto A: adunque, se in A fia sei lib&shy;<lb/>bre, altre sei libbre poste in R li farebbero resistenza, e se si tirer&agrave; al&shy;<lb/>trettanto innanzi insino allo estremo della Bilancia, nel punto R, tre libbre <lb/>li faranno resistenza &rdquo; (ivi). </s></p><p type="main">

<s>Quest'ultimo problema appartiene all'ordine di quelli, di cui si dice che <lb/>Euclide abbia dato il primo esempio, promosso dal Nemorario nelle sue ul&shy;<lb/>time proposizioni, come altrove accennammo. </s>

<s>E perch&egrave; la data soluzione &egrave; <lb/>vera, sia applicato il bastone MN a contatto del braccio della Libbra, sia so&shy;<lb/>speso a fila pi&ugrave; o meno lunghe, eguali o diseguali, si cred&egrave; il Nemorario <lb/>stesso di dover con la seguente proposizione III assicurare intorno a ci&ograve; i <lb/>dubitanti: &ldquo; Cum fuerint appensorum pondera aequalia, non motum faciet, <lb/>in aequilibri, appendiculorum inaequalitas &rdquo; (De pond. </s>

<s>cit., pag. </s>

<s>11). Leo&shy;<lb/>nardo dimostr&ograve; la medesima proposizione in una Nota, che dice: &ldquo; Ogni <lb/>corpo di lunga figura, d'eguale grossezza e peso, sospeso ne'suo estremi da <lb/>due corde attaccate nelli estremi d'egual braccia della Bilancia, bench&egrave; esse <lb/>corde siano di varie lunghezze, nientedimeno sempre le Bilance staranno <lb/>nella linea della egualit&agrave;. </s>

<s>La ragione si &egrave; che se tiri perpendicolare una li&shy;<lb/>nea, che passa sotto il centro della Bilancia, essa linea ancora passer&agrave; per <lb/>lo centro del sostenuto peso &rdquo; (Manuscr. </s>

<s>C. cit., fol. </s>

<s>7). </s></p><p type="main">

<s>Fu il Nemorario quello altres&igrave; che messe primo in campo la questione <lb/>lasciata indietro da Aristotile intorno alla bilancia di braccia eguali, che, ri&shy;<lb/>mossa per violenza dalla posizione orizzontale, per s&egrave; naturalmente vi ri&shy;<lb/>torna; questione, che fu forse delle pi&ugrave; agitate fra'Meccanici infino al ter&shy;<lb/>minar del secolo XVII, e cos&igrave; da Leonardo anch'essa risoluta: &ldquo; La Bilan&shy;<lb/>cia di braccia e pesi eguali, rimossa dal sito della egualit&agrave;, far&agrave; braccia e <lb/>pesi ineguali, onde necessit&agrave; la costringe a racquistare la perduta egualit&agrave; <lb/>di braccia e di pesi. </s>

<s>Provasi per la IIa di questo, e si prova perch&egrave; il peso <lb/>pi&ugrave; alto &egrave; pi&ugrave; rimoto dal centro del circonvolubile, che il peso pi&ugrave; basso, <lb/>e pertanto ha pi&ugrave; debole sostentacolo, onde pi&ugrave; facilmente discende e lieva <lb/>in alto la opposita parte del peso congiunto allo estremo del braccio mi&shy;<lb/>nore &rdquo; (Manuscr. </s>

<s>E. cit., fol. </s>

<s>59). Chi volesse avere la pi&ugrave; chiara dimostra&shy;<lb/>zione di fatto che la scienza del moto di Leonardo da Vinci &egrave; lo svolgi&shy;<lb/>mento di una scienza anteriore collazioni il senso di questa Nota con le <lb/>proposizioni II e VII dell'antico Giordano, e alla proposizione X di lui ag&shy;<lb/>giunga questa Nota vinciana per corollario: &ldquo; Per saggiare un uomo e ve-<pb xlink:href="020/01/1804.jpg" pagenum="47"/>der se elli ha giudizio vero della natura dei pesi, domandali in che luogo <lb/>si debba tagliare uno dei bracci eguali della Bilancia, e fare che il tagliato <lb/>appiccato allo estremo del suo rimanente facci contrappeso al braccio suo <lb/>opposito con precisione, la qual cosa mai &egrave; possibile, e se elli ti divide il <lb/>sito, lui &egrave; tristo matematico &rdquo; (Manuscr. </s>

<s>M., fol. </s>

<s>68 ad t.). </s></p><p type="main">

<s>Le proposizioni statiche intorno alla Bilancia, che abbiamo fin qui dai <lb/>manoscritti vinciani raccolte e ordinate, son tutte dipendenti dal principio <lb/>che la Bilancia stessa si carica tanto pi&ugrave; del peso accidentale, che del na&shy;<lb/>turale, quanto il braccio maggiore eccede il braccio minore. </s>

<s>Questo prin&shy;<lb/>cipio per&ograve; si poneva come un semplice fatto sperimentale, senz'altra mate&shy;<lb/>matica dimostrazione, la quale non fu poi da Leonardo trascurata, quando <lb/>pass&ograve; a trattare del Vette, ch'&egrave; pure una Bilancia a braccia disuguali, e nel <lb/>quale distingue col nome proprio di <emph type="italics"/>leva<emph.end type="italics"/> il braccio, che rimane dalla parte <lb/>della potenza, e col nome di <emph type="italics"/>contralleva<emph.end type="italics"/> quell'altro, a cui viene applicata <lb/>la resistenza. </s>

<s>&ldquo; Tanto sar&agrave; maggiore, cos&igrave; dice, il moto del motore nello <lb/>estremo della leva, che il moto del mobile nella contralleva, quanto il mo&shy;<lb/>bile fia di maggior peso naturale. </s>

<s>&mdash; Tanto s'aggiunge di peso accidentale <lb/><figure id="id.020.01.1804.1.jpg" xlink:href="020/01/1804/1.jpg"/></s></p><p type="caption">

<s>Figura 20.<lb/>al motore, posto nello estremo <lb/>della leva, quanto il mobile, po&shy;<lb/>sto nello estremo della contral&shy;<lb/>leva, lo eccede di peso naturale. </s>

<s><lb/>Provasi, e diremo che il moto <lb/>del motore si ha dal D ad M <lb/>(fig. </s>

<s>20), e quel del mobile dal&shy;<lb/>l'E all'F. </s>

<s>Dico che tanto sar&agrave; <lb/>maggiore il moto DM che il mo&shy;<lb/>to EF, quanto il peso accidentale <lb/>di Q eccede il peso P, il quale lo eccede per uno &rdquo; (ivi, fol. </s>

<s>58). </s></p><p type="main">

<s>Suppone l'Autore, in questo caso particolare, che DA sia il doppio di <lb/>AE, e che perci&ograve; per l'equilibrio il peso Q debba stare al peso P come due <lb/>sta ad uno, ma la legge medesima &egrave; cos&igrave; generalmente formulata in que&shy;<lb/>st'altra Nota: &ldquo; Quella proporzione, che avr&agrave; in s&egrave; la lunghezza della leva <lb/>colla sua contralleva, tale proporzione troverai nella qualit&agrave; de'loro pesi, e <lb/>simile nella tardit&agrave; del moto, e nella qualit&agrave; del cammino fatto da ciascuna <lb/>loro estremit&agrave;, quando fieno pervenute alla permanente altezza del loro polo &rdquo; <lb/>(Manuscr. </s>

<s>A. cit., fol. </s>

<s>45). &mdash; &ldquo; Il peso applicato nella stremit&agrave; della lieva, <lb/>fatta di qualunque materia si sia, lever&agrave; tanto pi&ugrave; peso nel fine della contro <lb/>lieva, che il peso di s&egrave;, quanto la controlieva entra nella lieva &rdquo; (ivi, fol. </s>

<s>47). </s></p><p type="main">

<s>Dal principio della Leva dipende, secondo Aristotile, la legge statica di <lb/>tutte le altre macchine, ci&ograve; che nel Timpano, nell'Asse in peritrochio, e <lb/>nella stessa Troclea semplice rendevasi evidente, bench&egrave; il Filosofo non si <lb/>accorgesse ch'essendo essa Troclea semplice una Bilancia di braccia eguali <lb/>non pu&ograve; la potenza in essa avere nessun vantaggio sopra la resistenza. </s>

<s>Del <lb/>facile errore accortisi gli Alessandrini lo emendarono, e Pappo, descrivendo <pb xlink:href="020/01/1805.jpg" pagenum="48"/>il Polispasto, dice per evidente prova sperimentale che tanto pi&ugrave; facilmente <lb/>si sollevano con tale strumento i pesi &ldquo; quanto plura membra funis inflecte&shy;<lb/>tur &rdquo; (Coll. </s>

<s>mat. </s>

<s>cit., pag. </s>

<s>484), bench&egrave; non renda ivi di ci&ograve; nessuna ra&shy;<lb/>gione, lusingando al solito i suoi lettori con le sole promesse. </s></p><p type="main">

<s>Leonardo s'esercit&ograve; molto nelle sue Note in descrivere varie composi&shy;<lb/>zioni di Polispasti, e in determinare le richieste proporzioni tra i pesi da <lb/>sollevarsi e le potenze motrici, di che pu&ograve; aversi un'idea da queste nostre <lb/>spigolature. </s>

<s>Incomincia dal porre per fondamento quella verit&agrave;, che da molti <lb/>Peripatetici si negava, e perci&ograve; cos&igrave; risolutamente sentenzia: &ldquo; Nessuno <lb/>corpo ponderoso lever&agrave; in Bilancia circolare, con forza del suo semplice peso, <lb/>pi&ugrave; peso di s&egrave; medesimo. </s>

<s>Bilancia circolare chiamo la rotella, ovver carru&shy;<lb/>cola, colla quale si trae l'acqua de'pozzi, colla quale non si lever&agrave; mai pi&ugrave; <lb/>peso che si pesi quello che attigne l'acqua. </s>

<s>&mdash; Ogni peso levato col mezzo <lb/>della Bilancia circolare si raddoppia nel sostentacolo d'essa Bilancia. </s>

<s>Questa <lb/><figure id="id.020.01.1805.1.jpg" xlink:href="020/01/1805/1.jpg"/></s></p><p type="caption">

<s>Figura 21.<lb/>proposizione chiaramente si comprende <lb/>ancora nelle carrucole dei pozzi, imperoc&shy;<lb/>ch&egrave;, se uno v'attinghi una secchia di <lb/>peso di cento libbre, bisogna che l'attigni&shy;<lb/>tore ve ne metti all'opposita parte cento <lb/>una libbra, e tutto esso peso rimane a <lb/>sostentacolo d'essa carrucola. </s>

<s>&mdash; Se rad&shy;<lb/>doppi la corda che sostiene le venti lib&shy;<lb/>bre (fig. </s>

<s>21), F ne sosterr&agrave; 10, e cos&igrave; D <lb/>altre 10. Se tu vuoli che C tiri le 10 lib&shy;<lb/>bre, che si caricheranno in D, dai a C <lb/>libbre undici, e lever&agrave; le dieci di D. </s>

<s>Adun&shy;<lb/>que il sostentacolo FD sostiene libbre 21. <lb/>&mdash; Se tu vuoli incordare le taglie in quattro doppii, le quali taglie abbino <lb/>a levare 20 libbre di peso, dico che la girella Z (fig. </s>

<s>22) sosterr&agrave; 10 lib&shy;<lb/>bre, e 10 ne sosterr&agrave; la girella K, le quali si trasferiscono a'sua superiori <lb/><figure id="id.020.01.1805.2.jpg" xlink:href="020/01/1805/2.jpg"/></s></p><p type="caption">

<s>Figura 22.<lb/>sostentacoli, cio&egrave; Q piglia da Z 5 <lb/>libbre, e cinque ne piglia ancora <lb/>F da Z, e 5 da K, e questo me&shy;<lb/>desimo K ne d&agrave; 5 a Q, e chi vo&shy;<lb/>lessi vincere le 5 di Q ne metta <lb/>6 nel contrappeso X, e mettendo <lb/>in nell'ultimo loco 6 contra 5, e <lb/>ciascuna delle quattro corde, che <lb/>sostengono le 20 libbre, non sen&shy;<lb/>tendo per s&egrave; se non 5 libbre, quella <lb/>libbra di pi&ugrave; ch'io metto nella <lb/>corda QX, non trovando in nessuna delle apposite corde pari peso a s&egrave;, <lb/>tutte le vince e tutte le muove &rdquo; (Manuscr. </s>

<s>A. cit., fol. </s>

<s>62). Di qui conclude <lb/>lo stesso Leonardo che &ldquo; il peso applicato alle taglie con quattro girelle star&agrave; <pb xlink:href="020/01/1806.jpg" pagenum="49"/>in equilibrio col quarto del peso applicato alla corda del primo moto &rdquo; <lb/>(Manus. </s>

<s>C. cit, fol. </s>

<s>7 ad t.), ci&ograve; che traducesi nel linguaggio dei Meccanici <lb/>moderni: la resistenza sta alla potenza, come quattro, ossia come il numero <lb/>de'tratti di fune, sta ad uno. </s></p><p type="main">

<s>Rispetto al Cuneo, forse pi&ugrave; saviamente di alcuni moderni, pens&ograve; Leo&shy;<lb/>nardo non esservi buone ragioni da contradire Aristotile, che lo strumento <lb/>ridusse alla Leva, ond'&egrave; che, nella Scienza meccanica degli antichi, le mag&shy;<lb/>giori incertezze versano intorno alla Vite. </s>

<s>Pappo la rassomigli&ograve; a un Cuneo <lb/><emph type="italics"/>expers percussionis,<emph.end type="italics"/> e Galileo, come si lusing&ograve; di essere stato il primo a <lb/>notar l'errore del Matematico alessandrino, rispetto alla potenza necessaria <lb/>a sollevare un peso sopra un piano inclinato; cos&igrave; pure si lusing&ograve; di aver <lb/>egli ridotto il primo la ragion della vite a quella dei piani pi&ugrave; o meno obli&shy;<lb/>qui. </s>

<s>Quel primato per&ograve; &egrave; bene pi&ugrave; antico, e infintantoch&egrave; non produca al&shy;<lb/><figure id="id.020.01.1806.1.jpg" xlink:href="020/01/1806/1.jpg"/></s></p><p type="caption">

<s>Figura 23.<lb/>cuno la fede di documenti anteriori, par che <lb/>giustamente sia dovuto a Leonardo. </s>

<s>Una sua <lb/>Nota infatti s'intitola <emph type="italics"/>Della ragion della vite,<emph.end type="italics"/><lb/>e sotto un disegno (fig. </s>

<s>23) rappresentante <lb/>un peso posato sulla orizzontale in faccia a <lb/>varie obliquit&agrave; di piani, si legge scritto: <lb/>&ldquo; Tanto quanto il peso &egrave; pi&ugrave; presso al primo grado di facilit&agrave;, che all'ul&shy;<lb/>timo, tanto fia pi&ugrave; agevole a montare &rdquo; (Manuscr. </s>

<s>A. cit., fol. </s>

<s>42 ad t.). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>A misurare i progressi fatti da Leonardo nella scienza del moto, per <lb/>quel fecondo svolgersi dei principii, che si trovavano professati nella Statica <lb/>degli Autori pi&ugrave; antichi, si resta senza dubbio maravigliati, e coloro, i quali <lb/>andavano ripetendo esser la Meccanica in que'secoli rimasta immobile nei <lb/>libri di Archimede, si trovano oramai costretti di confessare, che la comune <lb/>opinione gli aveva ingannati. </s>

<s>Ma i confessati inganni e le maraviglie prese, <lb/>per le cose fin qui discorse, tanto dovrebbero pi&ugrave; crescere nella mente e <lb/>nell'animo dei nostri Lettori, tuttavia ripensando alle nuove cose, che siamo <lb/>per riferire, dalle quali apparir&agrave; che quell'Uomo, il quale confessava di es&shy;<lb/>sere <emph type="italics"/>senza lettere,<emph.end type="italics"/> non emula solamente il gran Galileo, ma lo vince, e quel <lb/>ch'&egrave; pi&ugrave; mirabile vince altres&igrave; gli stessi valorosissimi matematici della <lb/>scuola di lui. </s></p><p type="main">

<s>Non fa perci&ograve; maraviglia che molti dei teoremi, i quali si trovano nelle <lb/>Note vinciane conclusi, apparissero una miracolosa rivelazione di un inge&shy;<lb/>gno quasi divino. </s>

<s>E l'essere, come si diceva, quei teoremi conclusi e assai <lb/>raramente dimostrati, o per dir meglio, il non vedere espressamente formu&shy;<lb/>lati quei principii, dai quali si conducono con logico ordine dall'Autore le <pb xlink:href="020/01/1807.jpg" pagenum="50"/>dimostrazioni, fu potissima causa che s'ingerisse quella cos&igrave; fatta opinione <lb/>in tutti rimasti alla superficiale lettura istupiditi. </s></p><p type="main">

<s>D'investigare cotesti cos&igrave; spesso taciuti principii e di scoprire quel lo&shy;<lb/>gico ordine, con che deve Leonardo averli condotti alle conclusioni, &egrave; stato <lb/>lo studio nostro principale, da cui ci &egrave; felicemente venuto l'intendere la <lb/>natural ragione di quello, che sarebbe altrimenti rimasto un mistero. </s>

<s>Erano <lb/>dall'altra parte cos&igrave; fatti principii, che per noi si riducono principalmente <lb/>alla composizion delle forze nel rettangolo e nel parallelogrammo, assai an&shy;<lb/>tichi e, per essere stati insegnati da Aristotile, largamente diffusi. </s>

<s>Ma i pe&shy;<lb/>ripatetici, inetti, e gli altri diffidenti fecer s&igrave; che con danno gravissimo della <lb/>scienza si rimanessero nelle Questioni meccaniche sterili o con frutti scarsi <lb/>ed agresti. </s></p><p type="main">

<s>Fra i non inetti, e i non diffidenti a quei tempi, Leonardo non fu cer&shy;<lb/>tamente il solo, ma il principale e il meglio conosciuto da noi, che abbiamo <lb/>finalmente avuto la ventura di poter, come cosa pubblica, leggere i suoi <lb/>manoscritti. </s>

<s>E perch&egrave; Galileo e i discepoli di lui, tutt'altro che inetti, fu&shy;<lb/>rono per&ograve; diffidenti, ecco naturalmente scoperta la recondita ragione del <lb/>perch&egrave; Filosofi cos&igrave; valorosi si trovino bene spesso senza vantaggio sopra <lb/>l'illetterato artista di Vinci, e talora rimangan anzi da lui superati e vinti. </s>

<s><lb/>Ma &egrave; bene lasciar le parole e venire ai fatti. </s></p><p type="main">

<s>Ecco il primo saggio, che ci si offre, della fruttuosa applicazione fatta <lb/>da Leonardo del principio delle forze composte alla dimostrazion del se&shy;<lb/>guente teorema: &ldquo; Sia la leva AT (fig. </s>

<s>24) il suo punto d'appoggio in A, <lb/><figure id="id.020.01.1807.1.jpg" xlink:href="020/01/1807/1.jpg"/></s></p><p type="caption">

<s>Figura 24.<lb/>un peso O attaccato in T, e la forza <lb/>N, che ha da tenere il peso O in <lb/>equilibrio. </s>

<s>Tira AB perpendicolare <lb/>a BO e AC perpendicolare a CT: <lb/>quella proporzione avr&agrave; N ad O che <lb/>la linea AB alla linea AC &rdquo; (Ma&shy;<lb/>nuscr. </s>

<s>E cit., fol. </s>

<s>65). I termini qui <lb/>di mezzo fra la conclusione e il <lb/>principio non &egrave; difficile ritrovarli in <lb/>ci&ograve;: che considerando Leonardo la <lb/>linea AT come la diagonale del ret&shy;<lb/>tangolo rappresentatrice di tutta la <lb/>forza, che distrae dal suo punto d'appoggio la leva, decompone quella stessa <lb/>forza unica in due: AB orizzontale misuratrice della forza traente N, e AC <lb/>verticale misuratrice della forza gravitante O per cui son veramente le con&shy;<lb/>dizioni dell'equilibrio date dall'equazione N:O=AB:AC, conforme a quel <lb/>che dalle Note dell'Autore s'&egrave; di sopra trascritto. </s></p><p type="main">

<s>Si faceva da ci&ograve; Leonardo via a proporre un altro teorema, i corollarii <lb/>del quale s'applicavano utilmente alla desiderata dimostrazion matematica <lb/>di alcune verit&agrave;, gi&agrave; prima conosciute per sola esperienza. </s>

<s>&ldquo; Sia un peso <lb/>sostenuto da una corda attaccata in A (fig. </s>

<s>25). Dalla posizione perpendi-<pb xlink:href="020/01/1808.jpg" pagenum="51"/>colare AB sia ritirato esso peso in AM, per mezzo di una forza F, la dire&shy;<lb/><figure id="id.020.01.1808.1.jpg" xlink:href="020/01/1808/1.jpg"/></s></p><p type="caption">

<s>Figura 25.<lb/>zion della quale formi un angolo retto con AM: <lb/>tanto sar&agrave; minore la forza F del peso M, quanto <lb/>AC &egrave; minore di AM &rdquo; (Venturi, <emph type="italics"/>Essai<emph.end type="italics"/> cit., pag. </s>

<s>17). </s></p><p type="main">

<s>I mezzi termini di questa dimostrazione, ta&shy;<lb/>ciuti al solito da Leonardo, si ritrovano nella pro&shy;<lb/>priet&agrave; del parallelogrammo delle forze, di cui dee <lb/>cos&igrave; l'Autore aver fatto libero uso e sicuro. </s>

<s>Pro&shy;<lb/>lunghisi nella stessa XXV figura AM di una quan&shy;<lb/>tit&agrave; MD a piacere, e si rappresenti per essa il peso <lb/>del grave M che, per la costruzione del paralle&shy;<lb/>logrammo EF, si decompone in due: uno secondo <lb/>la natural direzione dei gravi ME, e l'altro MF, <lb/>diretto al punto, a cui trae il peso F. </s>

<s>Le con&shy;<lb/>dizioni dell'equilibrio tra il grave pendulo M, e <lb/>la potenza F che lo travia dalla verticale, sono evi&shy;<lb/>dentemente date dall'equazione F:M=MF:ME. </s>

<s><lb/>Conducasi ora la orizzontale AC, la quale sia in C incontrata dal prolunga&shy;<lb/>mento di EM. </s>

<s>I due triangoli simili AMC, MED danno la proporzione <lb/>ED:ME=AC:AM. </s>

<s>E perch&egrave; ED=MF &egrave; perci&ograve;, in piena conformit&agrave; con <lb/>la proposizione di Leonardo, F:M=AC:AM. </s></p><p type="main">

<s>Da ci&ograve; concludevasi che, per tener sollevato il grave pendulo nella si&shy;<lb/>tuazione orizzontale, nel qual caso AC e AM sono uguali; dee essere F di <lb/>pari forza col peso M che, rappresentato dall'intero raggio del cerchio, <lb/>quando scende per l'arco e giunge per esempio ne'punti N, M, diminuisce <lb/>il momento suo totale a proporzione delle linee AH, AC, che sono i seni <lb/>degli angoli dell'inclinazione fatta dal filo, o dal braccio di leva inginoc&shy;<lb/>chiata in A, con la linea verticale. </s></p><p type="main">

<s>Fu a dare in pubblico queste conclusioni primo fra i Matematici il Be&shy;<lb/>nedetti, nel cap. </s>

<s>II del suo trattato <emph type="italics"/>De mechanicis,<emph.end type="italics"/> e Galileo l'applic&ograve; util&shy;<lb/>mente come lemma, senza darne dimostrazione. </s>

<s>Come lemma pure, ancora <lb/>supposto vero, ne fece il medesimo uso il Torricelli, il quale abbrevi&ograve; e in&shy;<lb/>form&ograve; della sua solita eleganza il teorema galileiano. </s>

<s>Prolunghisi nella me&shy;<lb/>desima figura XXV la tangente MF in P, e conducasi la orizzontale PR. </s>

<s>I <lb/>triangoli simili ACM, FPR danno la proporzione AC:AM=FR:FP e <lb/>perci&ograve; F:M=FR:FP. </s>

<s>Ora permanendo il grave M ugualmente bene in <lb/>equilibrio o sia, come dianzi, sospeso al filo AM, o posato sul piano FP; <lb/>dunque ne conclude il Torricelli: &ldquo; Momentum totale gravis, ad momen&shy;<lb/>tum quod habet in plano inclinato, est ut longitudo ipsius plani inclinati ad <lb/>perpendiculum &rdquo; (De motu gravium, Florentiae 1644, pag. </s>

<s>101). </s></p><p type="main">

<s>Il processo di Leonardo &egrave; facile persuadersi che dovesse esser simile <lb/>a questo, con tal differenza per&ograve; che, mentre il Torricelli ammetteva per <lb/>lemma supposto vero che &ldquo; quando grave circumfertur a semidiametro <lb/>AG=AM, manente puncto A, tunc momentum totale eius, hoc est mo-<pb xlink:href="020/01/1809.jpg" pagenum="52"/>mentum, quod habet in situ G, ad momentum quod habet in situ M, est <lb/>ut AG=AM:AC &rdquo; (ibid.), Leonardo invece ammetteva questo medesimo <lb/>come corollario di una sua proposizione gi&agrave; dimostrata, facendo, come s'&eacute; <lb/>veduto, uso del parallelogrammo delle forze stimato una falsa regola dal Tor&shy;<lb/>ricelli stesso e da Galileo. </s>

<s>Ond'&egrave; che l'Uomo del popolo, a cui l'ordine del <lb/>variare i gravi i loro momenti secondo l'obliquit&agrave; de'piani era stato rive&shy;<lb/>lato dal fatto fisico della Bilancia idrostatica, ora &egrave; il primo a darne mate&shy;<lb/>matica dimostrazione, non meno elegante di quella dello stesso Torricelli e <lb/>pi&ugrave; compiuta. </s></p><p type="main">

<s>Che fossero veramente i processi di Leonardo in proposito simili ai tor&shy;<lb/>ricelliani si conferma dal vedere che l'uno e l'altro Autore deducono, dalla <lb/><figure id="id.020.01.1809.1.jpg" xlink:href="020/01/1809/1.jpg"/></s></p><p type="caption">

<s>Figura 26.<lb/>medesima proposizione, i medesimi <lb/>corollari. </s>

<s>&Egrave; il primo di questi il se&shy;<lb/>guente, illustrato dalla figura 26 rap&shy;<lb/>presentante una sfera, all'estremo <lb/>diametro della quale &egrave; tangente, e <lb/>perci&ograve; perpendicolare, CP piano in&shy;<lb/>clinato. </s>

<s>Prolungata la orizzontale PF <lb/>in D, e condotta ED, i triangoli si&shy;<lb/>mili EDP, CPF danno la proporzione <lb/>PC:CF=EP:DP. &ldquo; Hinc colligi&shy;<lb/>tur, dice il Torricelli, momentum <lb/>sphaerae gravis super diversas pla&shy;<lb/>norum elevationes semper esse ut li&shy;<lb/>nea illa horizzontalis, quae a contactu <lb/>in ipsa sphaera ducitur, posita sem&shy;<lb/>per diametro pro momento maximo, sive totali &rdquo; (ibid., pag. </s>

<s>102-3). </s></p><p type="main">

<s>Leonardo, invece della corda intera, prende la met&agrave;, e prende il raggio <lb/>invece del diametro, formulando cos&igrave;, nella sua solita schietta semplicit&agrave;, il <lb/>corollario torricelliano: &ldquo; Se P sia il polo, dove la palla tocca il suo piano; <lb/>quanto fia maggiore spazio da N a P, tanto fia pi&ugrave; veloce il suo corso &rdquo; <lb/>(Manuscr. </s>

<s>A cit., fol. </s>

<s>52). Ci&ograve; fa l'Autore di questa Nota, perch&egrave; non aveva <lb/>come il Torricelli di mira quest'altro elegantissimo teorema, che si conclu&shy;<lb/>deva dal moltiplicar per la circonferenza EDP i due termini EP, DP del&shy;<lb/>l'ultima proporzione; teorema che, nel trattato <emph type="italics"/>De motu ac momentis<emph.end type="italics"/> in&shy;<lb/>cominciato a compilar dal Viviani, come vedremo a suo luogo, &egrave; proposto <lb/>sotto questa forma: &ldquo; Momentum totale sphaerae gravis EDP, ad momen&shy;<lb/>tum partiale in hoc situ, est ut tota sphaerae superficies ad armillam, aut <lb/>ad zonam sphaericam descriptam ab arcu inferiori DP, quem subtendet corda <lb/>orizontalis DP ducta ex puncto P, in quo sphaera planum tangit, si sphaera <lb/>revolvatur circa diametrum horizontali DP parallelam &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. XXXVII, c. </s>

<s>91). </s></p><p type="main">

<s>La poco diversa via tenuta da Leonardo fu per&ograve; anch'essa all'Autore <lb/>occasione feconda di rappresentare il principale teorema sotto una forma <pb xlink:href="020/01/1810.jpg" pagenum="53"/>nuova, la quale non sarebbe stata indegna dello stesso Torricelli, anche per <lb/>la sua sola geometrica eleganza. </s>

<s>Condotta la PS parallela ad AN, e l'AS <lb/>parallela alla PN, gli apparve chiaro che l'intero momento della sfera o <lb/>ruota posata sul piano orizzontale stava al momento della stessa ruota sul <lb/>piano obliquo CP come la linea AP, ad AS, la quale AS misura la distanza <lb/>del centro A dal punto del sostegno suo naturale sul prolungamento di AN. </s>

<s><lb/>Che se fosse la via anche di pi&ugrave; inclinata, e la ruota la toccasse per esem&shy;<lb/>pio in Q, quanto viene a crescere AR sopra AS, altrettanto si fa lo scen&shy;<lb/>dere pi&ugrave; precipitoso. </s>

<s>Il nuovo processo insomma che, sgombrate le vie dagli <lb/>errori di Pappo, &egrave; il pi&ugrave; diretto, conduce a riguardar la sfera come sospesa <lb/>dal punto A, quando posa in perfetto piano, e come sospesa dai punti S, R, <lb/>quando con minore o maggior impeto tende a scendere in basso. </s>

<s>Ma per&shy;<lb/>ch&egrave; parole anco pi&ugrave; ornate delle nostre non &egrave; possibile che riescano a quella <lb/>stupenda chiarezza, che resulta dallo schietto linguaggio dell'Autore, ecco <lb/>come i nuovi, e a que'tempi sublimi concetti, sieno resi in questa breve e <lb/>semplice Nota: &ldquo; Se il peso fia in A, la sua vera e retta resistenza sarebbe <lb/>AB, e in qualunque parte la ruota tocca terra li fia suo polo, e quella parte, <lb/>che resta maggiore e fuori d'esso polo, quella cade. </s>

<s>Essendo SP il polo, <lb/>chiaro appare pesare pi&ugrave; ST che SM, onde conviene che la parte ST cag&shy;<lb/>gia in basso, e vinca e levi SM, e movasi alla china con furia. </s>

<s>E se esso <lb/>polo fussi in Q, tanto quanto AR &egrave; maggiore di AS, tanto correrebbe per <lb/>s&egrave; la ruota pi&ugrave; forte alla china, che facesse il polo in Q che in P &rdquo; (Ma&shy;<lb/>nuscr. </s>

<s>A cit., fol. </s>

<s>21 ad t.). </s></p><p type="main">

<s>Chi volesse veramente persuadersi dell'efficacia di questa mirabile con&shy;<lb/>cisione sopra le prolisse e ornate dimostrazioni de'Meccanici, venuti in tempi <lb/>a noi tanto meno lontani, collazioni di grazia la Nota vinciana con quel che <lb/>scrive nelle sue <emph type="italics"/>Dimostrazioni fisico-matematiche delle sette proposizioni<emph.end type="italics"/><lb/>Donato Rossetti. </s>

<s>Egli, con l'intenzione d'illustrare le dottrine galileiane, <lb/>dalle condizioni dell'equilibrio di una sfera, posata sopra un piano perfet&shy;<lb/>tamente orizzontale, passa a determinare i momenti sopra varie inclinazioni <lb/>di piani, e gli trova proporzionali ai seni degli angoli, fatti con la verticale <lb/>dal raggio della ruota o della sfera al punto della sua tangenza col piano; <lb/>ossia, secondo l'espression dell'Autore, &ldquo; come la distanza alla distanza del <lb/>centro di gravit&agrave; dall'impedimento &rdquo; (Firenze 1668, pag. </s>

<s>14), da Leonardo <lb/>chiamato col nome di <emph type="italics"/>polo.<emph.end type="italics"/> Ma bench&egrave; sieno i processi dimostrativi ne'due <lb/>Autori uguali, e simili le stesse loro figure illustrative, chi, volendo aver <lb/>chiara e piena intelligenza di quelle cose, non preferirebbe d'impararle piut&shy;<lb/>tosto dalla rozza Nota del Pittore da Vinci, che dall'elaborato libro del Ma&shy;<lb/>tematico di Livorno? </s></p><p type="main">

<s>Le belle teorie meccaniche, relative al momento dei gravi sopra i piani <lb/>inclinati, furon dunque uno de'pi&ugrave; preziosi frutti, che raccolse Leonardo <lb/>dall'uso di decomporre le forze. </s>

<s>Ma perch&egrave;, ritrovata una volta la via, a chi <lb/>per essa si mette i recapiti sono inaspettatamente frequenti; cos&igrave; avvenne <lb/>felicemente anche al Nostro, che riusc&igrave; a dimostrare altri teoremi, ignorati <pb xlink:href="020/01/1811.jpg" pagenum="54"/>per l'avanti e per lungo tempo di poi. </s>

<s>&Egrave; uno de'pi&ugrave; importanti e de'pi&ugrave; <lb/>desiderati fra i detti teoremi quello della ragion varia della percossa, secondo <lb/>che viene il colpo obliquamente o a diritto. </s>

<s>Il Cardano proponendosi di di&shy;<lb/>chiarare nell'<emph type="italics"/>Opus novum<emph.end type="italics"/> &ldquo; quanta proportione decedat ictus in obliquum <lb/>parietem, ab eo qui est ad perpendiculum &rdquo; (Operum, T. IV cit., pag. </s>

<s>520), <lb/>ne conclude essere quella proporzione secondo gli angoli dell'incidenza, e <lb/>tanto aveva la cosa lusingh&igrave;ero aspetto di verit&agrave;, che fu la medesima carda&shy;<lb/>nica conclusione ammessa senz'alcun dubbio anche da Galileo. </s>

<s>Nella re&shy;<lb/>staurata scienza fu primo a riconoscer l'errore il Torricelli, fatto accorto <lb/>tutto insieme dalla Fisica e dalla Geometria: dietro lui poi il Borelli mosse <lb/>pi&ugrave; sicuro i suoi passi. </s>

<s>E perch&egrave; la via lunga, segnata da Galileo al Bo&shy;<lb/>relli, fu compendiosamente, a partir dal medesimo principio e giungere al <lb/>medesimo termine, percorsa dal solo Leonardo; giova accennar di volo ai <lb/>progressi fatti dalla scuola galileiana, perch&egrave; pi&ugrave; efficace riesca, colla scienza <lb/>sparsa per le solitarie Note vinciane, l'invidioso confronto. </s></p><p type="main">

<s>Rimeditava un giorno il Torricelli queste parole scritte nella I Gior&shy;<lb/>nata de'<emph type="italics"/>Due massimi sistemi:<emph.end type="italics"/> &ldquo; Fate conto che tutte le linee parallele, che <lb/>voi vedete partirsi dai termini A, B (fig. </s>

<s>27) sieno i raggi, che sopra la <lb/>linea CD vengono ad angoli retti: inclinate ora la medesima CD, sicch&egrave; <lb/><figure id="id.020.01.1811.1.jpg" xlink:href="020/01/1811/1.jpg"/></s></p><p type="caption">

<s>Figura 27.<lb/>penda come DO: non vedete voi che buona <lb/>parte di quei raggi, che ferivano la CD, pas&shy;<lb/>sano senza toccar la DO? Adunque, se la DO <lb/>&egrave; illuminata da manco raggi, &egrave; ben ragionevole <lb/>che il lume ricevuto da lei sia pi&ugrave; debole &rdquo; <lb/>(Alb. </s>

<s>I, 92). L'argomento fisico, nella mente <lb/>matematica del Lettore, si trasformava facil&shy;<lb/>mente in geometrico, e giacch&egrave; l'obliquit&agrave; DO <lb/>riceve tanta parte de'raggi, quanti ne cadono <lb/>sulla perpendicolare DM; dunque, n'ebbe a <lb/>concludere, la quantit&agrave; del lume ricevuto sulla <lb/>parete eretta sta alla quantit&agrave; del lume sul&shy;<lb/>l'inclinata, come l'intero seno sta al seno dell'angolo dell'incidenza. </s>

<s>Riguar&shy;<lb/>dando poi quei raggi come composti d'innumerevoli corpuscoli in moto, <lb/>applic&ograve; quella legge fotometrica all'analoga legge meccanica della percossa. </s></p><p type="main">

<s>Pubblicatisi appresso i Dialoghi delle Due nuove scienze, altre rimedi&shy;<lb/>tate parole ivi lette suggerirono alla Geometria del Torricelli, intorno a ci&ograve;, <lb/>idee pi&ugrave; precise. </s>

<s>Diceva cos&igrave; nel IV di que'Dialoghi Galileo: &ldquo; Se la posi&shy;<lb/>tura del corpo, che riceve la percossa, sar&agrave; tale che il moto del percuziente <lb/>la vada a investire ad angoli retti, l'impeto del colpo sar&agrave; il massimo. </s>

<s>Ma <lb/>se il moto verr&agrave; obliquamente, e come diciam noi a scancio, il colpo sar&agrave; <lb/>pi&ugrave; debole, e pi&ugrave; e pi&ugrave; secondo la maggiore obliquit&agrave;, perch&egrave; in oggetto <lb/>in tal modo situato, ancorch&egrave; di materia sodissima, non si spenge e ferma <lb/>tutto l'impeto e moto del percuziente, il quale sfuggendo passa oltre, con&shy;<lb/>tinuando almeno in qualche parte a moversi sopra la superficie del resi-<pb xlink:href="020/01/1812.jpg" pagenum="55"/>stente opposto &rdquo; (Alb, XIII, 246). La qual considerazione, introdotta da Ga&shy;<lb/>lileo nella yolgare notizia della percossa, apr&igrave; nel Torricelli la mente a <lb/>geometrizzare in questa guisa. </s>

<s>Sia DB la percossa diretta sulla parete resi&shy;<lb/>stente BF (fig. </s>

<s>28) e AB l'obliqua. </s>

<s>&ldquo; Tanto adunque, dice il Torricelli, sar&agrave; <lb/><figure id="id.020.01.1812.1.jpg" xlink:href="020/01/1812/1.jpg"/></s></p><p type="caption">

<s>Figura 28.<lb/>di moto parallelo nella linea AB rispetto alla BF, <lb/>quanto &egrave; la linea CB. </s>

<s>Ma di questo non facciamo <lb/>stima, perch&egrave; moltiplicato non aiuta, e diminuito non <lb/>debilita il momento, mentre l'altro impeto non al&shy;<lb/>terato resti il medesimo. </s>

<s>Di perpendicolare poi nella <lb/>stessa sar&agrave; quanto la linea AC, e la linea del colpo <lb/>sar&agrave; maggiore o minore, secondo che nello stesso <lb/>tempo sar&agrave; la linea AC maggiore o minore.... Si <lb/>cava di qui per corollario che la incidenza perpen&shy;<lb/>dicolare ha la maggior forza, essendo come il seno <lb/>totale;... la proiezione parallela non ha niente, es&shy;<lb/>sendo la forza sua come seno nullo; l'incidenza di trenta gradi ha la met&agrave; <lb/>della forza totale, essendo il seno suo la met&agrave; del semidiametro &rdquo; (De motu <lb/>grav., Florentiae 1644, pag. </s>

<s>241, 42). </s></p><p type="main">

<s>Fu il Borelli per&ograve; il primo che, nella proposizione XLV del suo trat&shy;<lb/>tato <emph type="italics"/>De vi percussionis,<emph.end type="italics"/> applic&ograve; direttamente al teorema il principio della <lb/>composizione delle forze ortogonali, riguardando AB come la diagonale del <lb/>rettangolo risoluta nelle due potenze AE, AC, la seconda delle quali, per <lb/>essere perpendicolare alla superfice che ha da ricevere il colpo, &egrave; la sola <lb/>efficace. </s>

<s>Dall'avere usato questo processo dimostrativo s'inger&igrave; forse nello <lb/>stesso Borelli la persuasione d'essere egli stato il primo a dimostrar &ldquo; la <lb/>misura precisa del momento delle percosse fatte in diverse inclinazioni, le <lb/>quali non son misurate dagli angoli dell'incidenza, come taluno mostra di <lb/>credere, ma dai loro seni retti &rdquo; (Risposta alle considerazioni fatte sopra il <lb/>libro della percossa, Messina 1667, pag. </s>

<s>11). </s></p><p type="main">

<s>Mentre dunque nel 1667, quando si scrivevano queste parole, matema&shy;<lb/>tici cos&igrave; valorosi, quali erano il Riccioli e l'Angeli, partecipavano agli er&shy;<lb/>rori del Cardano e di Galileo; Leonardo da Vinci aveva gi&agrave; da un secolo <lb/>e mezzo prima dimostrato matematicamente il vero, servendosi dell'argo&shy;<lb/>mento medesimo del celebrato Autore <emph type="italics"/>De vi percussionis.<emph.end type="italics"/> E perch&egrave; le ve&shy;<lb/>rit&agrave; non comuni agli uomini son per tutti di faticosa inquisizione, avendo&shy;<lb/>sene per le Note vinciane visibili le vestigia, giova ricercar le vie, per le <lb/>quali si condusse felicemente l'Autore alla riuscita. </s></p><p type="main">

<s>Fu anch'egli a principio lusingato dall'apparente verit&agrave;, e ritenne per <lb/>certo che l'effetto del colpo sempre riuscisse proporzionale al semplice an&shy;<lb/>golo dell'incidenza, come apparisce dalla seguente Nota: &ldquo; Se la ballotta C <lb/>(fig. </s>

<s>29) correr&agrave; per la linea CB, percoter&agrave; la linea AG, e far&agrave;, colla linea <lb/>del suo corso che passa al suo centro e con la linea del loco percosso, lo <lb/>angolo CAG, e quante volte questo angolo acuto entra nell'angolo retto, <lb/>tanto fia il colpo pi&ugrave; debole che non si conviene alla sua fuga, imperocch&egrave; <pb xlink:href="020/01/1813.jpg" pagenum="56"/>il primo grado del colpo si &egrave; infra angoli eguali, che lo fa nel percotere <lb/><figure id="id.020.01.1813.1.jpg" xlink:href="020/01/1813/1.jpg"/></s></p><p type="caption">

<s>Figura 29.<lb/>della linea AE, l'ultimo grado si &egrave; nella linea <lb/>AC, e il mezzano &egrave; nella linea AF &rdquo; (Manuscr. </s>

<s><lb/>A cit., fol. </s>

<s>22). </s></p><p type="main">

<s>Quelle delicate poi e precise esperienze <lb/>dinamiche proprie, alla sola arte pazientissima <lb/>di Leonardo, lo fecero entrare in sospetto che <lb/>la percossa seguitasse tutt'altra legge da que&shy;<lb/>sta, avvertendo che, nella inclinazione di 45 <lb/>gradi, serba ancora il colpo tanta virt&ugrave;, da <lb/>non parer dimidiata. </s>

<s>Quel pi&ugrave; giusto mezzo <lb/>fu dal sagace sperimentatore trovato, quando la linea dell'incidenza s'avvi&shy;<lb/>cina ai trenta gradi; ci&ograve; che gli fu scorta a scoprire la legge geometrica <lb/>dei seni. </s></p><p type="main">

<s>Prima per&ograve; di trascrivere ai nostri Lettori la Nota, dove quella legge <lb/>meccanica &egrave; formulata, per confortare di qualche prova ci&ograve; che pu&ograve; cre&shy;<lb/>dersi essere stato asserito da noi per dubitabile congettura, giova dar un sag&shy;<lb/>gio di altre esperienze di Leonardo, che si riferiscono al presente soggetto. <lb/></s>

<s>&ldquo; I pesi d'eguale materia ed eguale altezza e di varii pesi, posati sopra il <lb/>tenero fango, faranno in fra loro eguale profondit&agrave; d'impressione &rdquo; (Manuscr. </s>

<s><lb/>C cit., fol. </s>

<s>7 ad t.). </s></p><p type="main">

<s>Che tornino le pressioni e le percosse indipendenti dalla base, e sola&shy;<lb/>mente proporzionali alle altezze, &egrave; un fatto che non fu bene avvertito nem&shy;<lb/>men dai Meccanici del secolo XVII. </s>

<s>Aveva Galileo confusamente accennato <lb/>a ci&ograve;, quando avvert&igrave; che il minor colpo fatto dalle frecce torte dipendeva <lb/>da ci&ograve;, che &ldquo; il centro della loro gravit&agrave;, non rispondendo alla cuspide per <lb/>la linea del moto, non cessa di proseguire alquanto, torcendosi d'avvantag&shy;<lb/>gio l'asta lanciata &rdquo; (Alb. </s>

<s>XIV, 321), ma pure Isacco Vossio, nel 1663, a <lb/>una sua meccanica conclusione gi&agrave; dimostrata ebbe a soggiungere questo <lb/>corollario. </s>

<s>&ldquo; Quare autem pondus premens in longum, non vero in latum, <lb/>extendi debeat, huius rei ratio est manifesta, quia nempe omnis pressio fit <lb/>a perpendiculari pondere. </s>

<s>Sola perpendicularis designat corporis prementis <lb/>mensuram. </s>

<s>Plurimum itaque falluntur, qui putant quomodocunque dupli&shy;<lb/>cato mallei pondere duplicari quoque percussionem. </s>

<s>Nisi duplicetur ferri <lb/>longitudo non potest duplicari percussio &rdquo; (De motu marium, Appendix <lb/>Hagae Comitis 1663, pag. </s>

<s>163, 64). </s></p><p type="main">

<s>Fra gl'ingannati, qui voluti ammonire dal Vossio, era da fare una par&shy;<lb/>ticolare eccezione rispetto a Leonardo, il quale aveva cos&igrave; in un'altra sua <lb/>Nota lasciato scritto: &ldquo; Se lascerai cadere uno martello di una libbra cento <lb/>volte l'altezza di uno braccio sopra una verga di piombo, e poi tolli uno <lb/>martello d'altro peso che sia della grossezza del martello, e sia tanto lungo <lb/>che pesi cento libbre, e fallo medesimamente cadere l'altezza d'uno braccio <lb/>sopra una verga di piombo simile alla prima; e vedrai quanto la verga del <lb/>colpo unito fia pi&ugrave; trafitta che la prima &rdquo; (Manuscr. </s>

<s>A cit., fol. </s>

<s>4). </s></p><pb xlink:href="020/01/1814.jpg" pagenum="57"/><p type="main">

<s>Soggiungeva il Vossio nel corollario citato una curiosa osservazione <lb/>teorica, in piena conformit&agrave; con la pratica, che cio&egrave; volendo aggiungere al <lb/>ferro percuziente un manico, come si fa nel martello, perch&egrave; pi&ugrave; valido ne <lb/>riesca e pi&ugrave; sicuro il colpo, convien che il ferro stesso sia leggermente in&shy;<lb/>curvato. </s>

<s>&ldquo; Observandum tamen si scapum ligneum inserere velis, incurvan&shy;<lb/>dum esse leniter ferrum. </s>

<s>Quando enim manus ducit malleum in circulum, <lb/>pars superior mallei aliquantum a manu recedit, et pressionem facit extra <lb/>circulum quem describit. </s>

<s>Ut vero tota pressio et totum pondus premat in <lb/>loco debito, necessario ita incurvandum est ferrum, ut nulla eius portio ver&shy;<lb/>setur extra circulum, per quem ducendus sit malleus &rdquo; (Appendix, sit., <lb/>pag. </s>

<s>164). </s></p><p type="main">

<s>Nel trattar di cos&igrave; fatto strumento, cio&egrave; del martello, Galileo nella <lb/><emph type="italics"/>Scienza meccanica<emph.end type="italics"/> si passa assai leggermente di questa argutissima osser&shy;<lb/>vazione vossiana, per trattenersi a redarguire Aristotile, il quale voleva &ldquo; la <lb/>ragion del mirabile effetto della percossa ridurre alla lunghezza del manu&shy;<lb/>brio o manico del martello &rdquo; (Alb. </s>

<s>XI, 124). Leonardo invece, dottamente <lb/>commenta le dottrine aristoteliche, e in alcuni suoi teoremi enuncia e di&shy;<lb/>mostra come sia vero, e secondo qual proporzione la maggiore o minore <lb/>lunghezza del manico del martello cooperi efficacemente a rendere o mag&shy;<lb/>giore e minore la percossa. </s>

<s>&ldquo; Se darai un colpo coll'asta MS (fig. </s>

<s>30) nel <lb/><figure id="id.020.01.1814.1.jpg" xlink:href="020/01/1814/1.jpg"/></s></p><p type="caption">

<s>Figura 30.<lb/>loco N, tenendo M in mano, <lb/>tanto quanto MN entra in MS, <lb/>tante volte il colpo fia minore <lb/>che se lo dessi colla lunghezza <lb/>di MS, imperocch&egrave; MS fa tanta <lb/>lieva dopo N, che il colpo non <lb/>&egrave; di troppa valetudine &rdquo; (Ma&shy;<lb/>nuscr. </s>

<s>A cit., fol. </s>

<s>4) ad t.). La <lb/>valetudine dunque del colpo, <lb/>fatto dal menar della verga MS, tenuta in mano in M come si farebbe del <lb/>manico di un martello, &egrave; secondo Leonardo e secondo Aristotile proporzio&shy;<lb/>nale alla lunghezza del manico stesso. </s>

<s>Il colpo infatti &egrave; maggiore o minore <lb/>secondo la maggiore o minore velocit&agrave; del perenziente, la quale ne'punti N, <lb/>P, S della verga &egrave; manifestamente proporzionale alle lunghezze MN, MP, <lb/>MS. Ond'&egrave; che se, per esempio, MN &egrave; un terzo di tutta la lunghezza della <lb/>verga e MP la met&agrave;, il colpo fatto ne'due punti P, N star&agrave; a quello fatto <lb/>in S, come la met&agrave; e come un terzo. </s>

<s>&ldquo; Il movimento fatto nel terzo di <lb/>qualunque asta entrer&agrave; tre volte nel moto da capo, e il moto fatto dal mezzo <lb/>dell'asta entrer&agrave; due volte nel moto ultimo &rdquo; (ivi, fol. </s>

<s>7). </s></p><p type="main">

<s>Tali sono i teoremi dimostrati intorno alla forza della percossa da Leo&shy;<lb/>nardo, i quali noi abbiamo voluto preporre al principale, perch&egrave; agli stu&shy;<lb/>pefatti della tanta scienza di un tale uomo ne sia manifesta l'origine e la <lb/>preparazione. </s>

<s>Fu dunque quel fondamentale teorema cos&igrave;, un secolo prima <lb/>del Torricelli, formulato: &ldquo; Due pesi d'eguale qualit&agrave; caduti da eguale al-<pb xlink:href="020/01/1815.jpg" pagenum="58"/>tezza daranno tanto minore colpo l'uno dell'altro, quanto la linea della ca&shy;<lb/>duta lia pi&ugrave; obliqua all'uno che all'altro: cio&egrave; quanto la linea AC (nella <lb/>precedente figura XXVIII) entra nella linea AB, tanto il peso B dar&agrave; mi&shy;<lb/>nore colpo che il peso C &rdquo; (ivi, fol. </s>

<s>4 ad t.): ci&ograve; che nel pi&ugrave; proprio lin&shy;<lb/>guaggio matematico riesce alla forma, sotto alla quale fu cos&igrave; esposto dal <lb/>Borelli quello stesso teorema: &ldquo; Si corpus aliquod moveatur inclinato motu <lb/>ad superficiem alterius corporis omnino quiescentis, vis et energia percus&shy;<lb/>sionis obliquae, ad absolutam percussionem perpendicularem, eamdem pro&shy;<lb/>portionem habet quam sinus anguli incidentiae, ad sinum totum &rdquo; (De vi <lb/>percuss., Bononiae 1667, pag. </s>

<s>89). </s></p><p type="main">

<s>Il felice e maraviglioso incontro fra il Matematico di Messina e il Pit&shy;<lb/>tor<gap/> da Vinci consegue naturalmente dall'avere i due Autori professati i <lb/>medesimi principii. </s>

<s>Il secondo per&ograve;, che fidatosi non della sola autorit&agrave; di <lb/>Aristotile, ma della propria esperienza, aveva que'medesimi principii estesi <lb/>alla composizion delle forze, con qualunque angolo s'incontrassero insieme <lb/>nel parallelogrammo; ebbe il vantaggio sul primo, e su tutti gli altri della <lb/>Scuola galileiana che, troppo ossequiosi al Maestro, reputarono non valer <lb/>quella regola meccanica altro che per le forze composte ad angolo retto, <lb/>nelle quali veramente la potenza dell'ipotenusa equivale alla somma delle <lb/>potenze de'due cateti. </s>

<s>Quando poi il Varignon e il Newton vinsero cos&igrave; fatti <lb/>galileiani pregiudizii, si trov&ograve; la Scienza in mano la chiave da aprir certe <lb/>vie rimaste fin allora inaccesse, intanto che s'ebbe a poter gloriare del titolo <lb/>di <emph type="italics"/>Meccanica nuova.<emph.end type="italics"/></s></p><p type="main">

<s>Il Torricelli e il Viviani particolarmente s'erano tanto confidati nelle <lb/>forze del loro ingegno, rese gagliarde dalla scienza di Galileo, che un se&shy;<lb/>colo prima degli stranieri tentarono quelle novit&agrave; meccaniche, delle quali <lb/>cos&igrave; il Torricelli stesso scriveva in una sua lettera al Ricci: &ldquo; Questa set&shy;<lb/>timana (la prima dell'anno 1643) ho trovato una cosa di Meccanica che &egrave; <lb/>totalmente nuova &rdquo; (Lettere, per Giovanni Ghinassi, Faenza 1864, pag. </s>

<s>16). <lb/>Il Viviani imitatore ed emulo del Torricelli tent&ograve; pure, oltre questa cosa <lb/>nuova in Meccanica che consisteva nel determinar le pressioni esercitate da <lb/>una trave appoggiata a un muro, altre simili meccaniche novit&agrave;, e fu il primo <lb/>che si proponesse a risolvere il problema della tension delle funi gravate <lb/>di pesi. </s>

<s>Ma perch&egrave; non erano cos&igrave; fatti problemi risolubili per altro, che <lb/>per l'uso del parallelogrammo, rimasero alle mani del Torricelli e del Vi&shy;<lb/>viani o una delusione o una violenza fatta all'ingegno, intanto che la Mec&shy;<lb/>canica nuova in Italia risale propriamente ai tempi di Leonardo. </s>

<s>Si trovano <lb/>per quelle sue mirabili Note apertissimi di ci&ograve; gli esempii, e perch&egrave; si veda <lb/>chiara la somiglianza che passa fra l'antica scienza italiana e la nuova ri&shy;<lb/>sorta, ci tratterremo, come sufficienti per questo Saggio, intorno ai due sopra <lb/>citati problemi, comparando i modi, tenuti nel risolverli da Leonardo, con <lb/>quegli altri, che tennero i due ora commemorati valorosi discepoli di Galileo. </s></p><p type="main">

<s>Il problema delle funi caricate di pesi propostosi dal Viviani si trova <lb/>da lui stesso scritto in una sua Nota in questa forma: &ldquo; I fili CFA (fig. </s>

<s>31) <pb xlink:href="020/01/1816.jpg" pagenum="59"/>BA cavalchino i chiodi C, B, e sieno date le lunghezze CA, AB, ed al punto A <lb/>legato un peso G. </s>

<s>Si cerca che pesi deano attaccarsi alle estremit&agrave; M, N, <lb/><figure id="id.020.01.1816.1.jpg" xlink:href="020/01/1816/1.jpg"/></s></p><p type="caption">

<s>Figura 31.<lb/>acciocch&egrave; il peso G non iscorra <lb/>da parte alcuna, e che i fili CA, <lb/>AB non allunghino o accorcino, <lb/>e che proporzione abbiano tra <lb/>di loro i pesi G, M, N &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXIII, fol. </s>

<s>26). </s></p><p type="main">

<s>La soluzione del problema, <lb/>che non si ritrova data qui dal&shy;<lb/>l'Autore, dipende da una pro&shy;<lb/>posizione pi&ugrave; generale, che pu&ograve; <lb/>essere cos&igrave; formulata: Concor&shy;<lb/>rano le due funi CA, AB nel <lb/>nodo A, da cui penda il grave G. </s>

<s><lb/>Si domanda con quale sforzo siano tese esse funi dai punti C e B, a cui sono <lb/>stabilmente fisse per i loro due capi? </s>

<s>&mdash; Facendo uso del parallelogrammo <lb/>delle forze, la Meccanica nuova insegna a procedere cos&igrave;: Sul prolungamento <lb/>delle due linee CA, AB costruiscasi il parallelogrammo HO, di cui la dia&shy;<lb/>gonale AG rappresenti il peso G e i lati AH, AO le tensioni delle due funi. </s>

<s><lb/>Chiamate T, T&prime; queste tensioni, avremo T:T&prime;=sen GAO:sen GAH. </s>

<s>Con&shy;<lb/>dotta dal punto B l'orizzontale BF, e prolungata la verticale AG infino in D, <lb/>avremo sen GAO=sen DAF sta ad FD; come sen GAH=sen DAB sta a DB, <lb/>e perci&ograve; T:T&prime;=FD:DB. </s>

<s>Moltiplicando ambedue i termini di questa se&shy;<lb/>conda ragione per AD/2, avremo che le tensioni delle due corde AB, FA stanno <lb/>reciprocamente come i triangoli FAD, DAB. </s></p><p type="main">

<s>Questa della Nuova meccanica &egrave; la conclusione medesima, a cui giunse <lb/>per le medesime vie, con la meccanica sua antica, Leonardo, il quale, chia&shy;<lb/>mando i due ora detti triangoli <emph type="italics"/>angoli chiusi,<emph.end type="italics"/> cos&igrave; propriamente si esprime <lb/>in una sua Nota: &ldquo; Il grave sospeso nell'angolo delle corde divide il peso <lb/>a esse corde in tal proporzione, qual'&egrave; la proporzione delli angoli inclusi <lb/>infra le dette corde, e la linea centrale di tal peso. </s>

<s>Provasi, e sia l'angolo <lb/>della detta corda BAC, nel quale &egrave; sospeso il grave alla corda AG. </s>

<s>Sia dun&shy;<lb/>que tagliato esso angolo nel sito della egualit&agrave; dalla linea FB. </s>

<s>Di poi tira <lb/>la perpendicolare DA all'angolo A, che sia in continuo diretto colla corda <lb/>AG, e quella proporzione che ha lo spazio DF col DB, avr&agrave; il peso che <lb/>sente la corda BA col peso che sente la corda FA &rdquo; (Manuscr. </s>

<s>B cit., fol. </s>

<s>66 <lb/>ad t.). Di qui venivasi facilmente alla final conclusione enunciata, perch&egrave; <lb/>DF e DB son le basi di due triangoli, che hanno la medesima altezza AD e <lb/>&ldquo; nei triangoli d'eguale altezza, dice Leonardo stesso nella sua Geometria, <lb/>fia la medesima proporzione qual'&egrave; quella della loro base &rdquo; (Ravaisson&shy;<lb/>Mollien Man. </s>

<s>K., Paris 1888, fol. </s>

<s>86 ad t.). </s></p><p type="main">

<s>Chiamato per brevit&agrave; <foreign lang="greek">a</foreign> l'angolo FAD, <foreign lang="greek">a</foreign>&prime; l'altro angolo adiacente DAB, <pb xlink:href="020/01/1817.jpg" pagenum="60"/>il parallelogrammo misuratore della tensione delle due funi, in relazione col <lb/>peso G che le aggrava, d&agrave; G:T=sen (<foreign lang="greek">a</foreign>+<foreign lang="greek">a</foreign>&prime;):sen <foreign lang="greek">a</foreign>; G:T&prime;=sen <lb/>(<foreign lang="greek">a</foreign>+<foreign lang="greek">a</foreign>&prime;):sen <foreign lang="greek">a</foreign>&prime;. </s>

<s>Ond'&egrave; che, se sen <foreign lang="greek">a</foreign>&prime;=<emph type="italics"/>o<emph.end type="italics"/> la Ia di queste due equazioni <lb/>d&agrave; G=T e la IIa d&agrave; T&prime;=<emph type="italics"/>o<emph.end type="italics"/>:ci&ograve; vuol dire che se dei due tratti di corda <lb/>l'uno si mantiene obliquo, e l'altro si riduce in direzion verticale, a que&shy;<lb/>sto solo, nulla cooperandovi l'altro, &egrave; affidato tutto il peso: corollario im&shy;<lb/>portante, non lasciato indietro da Leonardo. </s>

<s>&ldquo; Quando la linea intercentrica <lb/>(ha cos&igrave; in una sua Nota) non taglia l'angolo fatto dal concorso delle due <lb/>corde, che sostengono il grave; allora, sola una di esse corde &egrave; sostenitrice <lb/>di tutto il grave. </s>

<s>Provasi, e sia prima che la linea intersecatrice DG tagli <lb/>l'angolo A fatto dal concorso delle due corde AB, AF, che sostengono il <lb/>grave, per la qual linea l'angolo BAF &egrave; diviso in due triangoli BAD, DAF. </s>

<s><lb/>Noi abbiamo provato come tal proporzione hanno li pesi sostenuti dalle due <lb/>corde, nelle quali si divide il peso G, quale &egrave; la proporzione che hanno li <lb/>detti due triangoli fra loro. </s>

<s>Ma nella figura FDAG la linea intercentrica non <lb/>taglia l'angolo del concorso delle due corde che sostengono il peso, ma passa <lb/>per l'una delle dette corde, e per questo resta un sol triangolo col quale <lb/>non si pu&ograve; dar proporzione, perch&egrave; in una cosa sola non si d&agrave; proporzione. </s>

<s><lb/>Egli &egrave; dunque necessario confessare che tutto il peso sia in tutta la corda, <lb/>d'onde passa la detta linea intercentrica &rdquo; (Manuscr. </s>

<s>E cit., fol. </s>

<s>68). O in <lb/>altre parole, come lo stesso Autore nostro altrove si esprime: &ldquo; Se due <lb/>corde concorreranno alla sospensione di un grave, e che l'una sia diritta e <lb/>l'altra obliqua; essa obliqua non sostiene parte alcuna d'esso peso &rdquo; (ivi, <lb/>fol. </s>

<s>70). </s></p><p type="main">

<s>Se i due angoli <foreign lang="greek">a</foreign>, <foreign lang="greek">a</foreign>&prime; sono uguali, resulta da quelle due medesime equa&shy;<lb/>zioni, dateci di sopra dalla risoluzione del parallelogrammo, T=T&prime;=G/2; <lb/>altro corollario cos&igrave; espresso da Leonardo: &ldquo; Le due corde eguali, che da <lb/>eguale altezza alla sospensione d'un medesimo grave concorrano, sempre <lb/>fieno in fra loro d'obliquit&agrave; eguale, ed egualmente cariche di quel peso che <lb/>per loro si sostiene &rdquo; (ivi, fol. </s>

<s>67 ad t.). </s></p><p type="main">

<s>Per la semplice inspezione della figura XXXI, che abbiamo seguitato <lb/>fin qui ad avere sott'occhio, facilmente si mostra, anche senza ricorrere alle <lb/>vie analitiche, che facendosi l'angolo FAB sempre pi&ugrave; ottusso vanno via via <lb/>le tensioni delle funi a farsi maggiori, rispetto al peso rappresentato dalla <lb/>diagonale AG del parallelogrammo, n&egrave; pu&ograve; quell'angolo sparire, e ridursi <lb/>i due distinti tratti di corda in dirittura, se non a condizione che la diago&shy;<lb/>nale stessa svanisca, e che perci&ograve; il peso G riducasi a nulla: nuovo e pi&ugrave; <lb/>che mai importante corollario formulato cos&igrave; da Leonardo: &ldquo; Mai la corda, <lb/>di qualunque grossezza o potenza, posta nel sito della egualit&agrave;, colli suoi <lb/>opposti estremi si potr&agrave; dirizzare, avendo alcuno peso in mezzo alla sua lun&shy;<lb/>ghezza &rdquo; (ivi, fol. </s>

<s>60 ad t.). E perch&egrave; la nuova e inaspettata rivelazione della <lb/>Matematica poteva ai volgari ingegni apparire strana, si studi&ograve; perci&ograve; Leo&shy;<lb/>nardo di persuaderli cos&igrave; del vero, applicando il teorema gi&agrave; formulato in <pb xlink:href="020/01/1818.jpg" pagenum="61"/>generale a un esempio particolare. </s>

<s>&ldquo; Impossibile fia, egli dice, a dirizzare <lb/>una corda che la lunghezza sua fia 100 braccia, e sia sospesa in fra due <lb/>carrucole di 100 braccia d'intervallo, e a ciascuna testa sia appiccato uno <lb/>peso di 1000 libbre. </s>

<s>Dico che se tu appiccherai uno peso in mezzo a detta <lb/>corda, che pesi cento libbre, che la corda si romper&agrave; prima ch'ell'alzi, di&shy;<lb/>rizzandosi, il suo peso nel sito della ugualit&agrave;. </s>

<s>E'pare quasi impossibile a <lb/>dire che duemila libbre di peso, che &egrave; attaccato in nelli estremi della corda, <lb/>non debba elevare dugento libbre, cio&egrave; il peso della corda e quello che &egrave; <lb/>posto in mezzo alla corda &rdquo; (Manuscr. </s>

<s>A cit., fol. </s>

<s>51 ad t.). </s></p><p type="main">

<s>A persuadere la verit&agrave; di un tale apparente paradosso si sceglie da Leo&shy;<lb/>nardo una via indiretta, per la quale, poste quelle e certe altre particolari <lb/>condizioni, si viene a concludere che, per tender la corda, non mille libbre <lb/>di peso ci bisognerebbero, ma ventimila, intantoch&egrave; la corda stessa, prima <lb/>che tesa, dovrebbe necessariamente essere a tanto sforzo strappata. </s>

<s>I mezzi <lb/>termini della conclusione si trovano dal Nostro ne'principii statici del vette, <lb/>in un modo simile a quel del Borelli, nella proposizione sua LXV della <lb/>I Parte <emph type="italics"/>De motu animalium.<emph.end type="italics"/> &Egrave; questa proposizione cos&igrave; dall'Autore suo <lb/>formulata: &ldquo; Nulla potentia finita poterit sublevare aut retinere quamlibet <lb/>exiguam resistentiam, usque ad situm horizontalem &rdquo; (Romae 1680, pag. </s>

<s>124). <lb/>Sia R (fig. </s>

<s>32) una potenza, la quale, tirando obliquamente per la dire&shy;<lb/><figure id="id.020.01.1818.1.jpg" xlink:href="020/01/1818/1.jpg"/></s></p><p type="caption">

<s>Figura 32.<lb/>zione AC, costringe il peso T a salire sempre rasente <lb/>il regolo CD. </s>

<s>Dice ch'essendo AH proporzionale alla <lb/>potenza, e HD proporzionale al peso stesso non potr&agrave; <lb/>essere sollevato pi&ugrave; su del punto H, e li giunto si <lb/>far&agrave; l'equilibrio. </s>

<s>Potrebbe la dimostrazione rendersi <lb/>pi&ugrave; speditamente sicura, applicandovi il principio <lb/>della composizion delle forze, imperocch&egrave; la potenza <lb/>AH pu&ograve; decomporsi nelle due DH, ZH, della seconda <lb/>delle quali &egrave; rintuzzata l'azione dalla resistenza del <lb/>regolo. </s>

<s>Di qui si vede che potrebbe essere un peso <lb/>anche sollevato in O, purch&egrave; interceda fra lui e la <lb/>potenza la relazione di OD ad OA, e si vede inoltre <lb/>che la direzione della potenza stessa, qualunque ella <lb/>si sia, non potr&agrave; mai essere quella di AD, se non a condizione che il peso <lb/>da sollevarsi sia nullo. </s></p><p type="main">

<s>Il Borelli per&ograve; tiene nel dimostrare quest'altra via, quale dalle sue se&shy;<lb/>guenti parole vien disegnata. </s>

<s>&ldquo; Quod vero absoiute resistentia T perduci aut <lb/>retineri non possit in horizontali DA, patet, quia T in D solummodo mo&shy;<lb/>veri potest per DC tangentem circulum radio AD descriptum, et sic linea <lb/>tractionis AD per vectis DA fulcumentum A transiret, ed ideo potentia R <lb/>sustinere non posset exiguam resistentiam T &rdquo; (ibid., pag. </s>

<s>125). Considera <lb/>insomma il Borelli che AD sia un vette, e che la direzione della potenza <lb/>passi per il suo punto d'appoggio, nel qual caso non pu&ograve; veramente il vette <lb/>stesso venir sollevato e ridotto in positura orizzontale, se non che da una <pb xlink:href="020/01/1819.jpg" pagenum="62"/>potenza infinita. </s>

<s>Abbiamo infatti, riguardando uno de'bracci della leva come <lb/>contratto nel punto A, T:R=<emph type="italics"/>o<emph.end type="italics"/>:AD d'onde R=T.AD/<emph type="italics"/>o<emph.end type="italics"/>=&inf;. </s></p><p type="main">

<s>Leonardo procede nella sua dimostrazione in un modo simile a questo, <lb/>se non che suppone che l'altro braccio del vette sia ridotto, non a un punto <lb/>matematico, ma a una piccolissima estensione, la quale determinata, bench&egrave; <lb/>non conduca alla necessit&agrave; di una potenza infinita, la richiede nulladimeno <lb/>talmente grande, da vincere di gran lunga qualunque natural resistenza, che <lb/>le possa fare una fune. </s></p><p type="main">

<s>Sia la met&agrave; di questa fune rappresentata da AR (fig. </s>

<s>33), e sia OD il <lb/>diametro della girella, ch'essa fune cavalca, per esser tenuta tesa dal grave <lb/><figure id="id.020.01.1819.1.jpg" xlink:href="020/01/1819/1.jpg"/></s></p><p type="caption">

<s>Figura 33.<lb/>pendulo Q, mentr'&egrave; gravata <lb/>in A da un pi&ugrave; piccolo peso <lb/>P. Leonardo, come il Bo&shy;<lb/>relli, deduce le relazioni, che <lb/>debbon passare fra i due <lb/>detti pesi per l'equilibrio, <lb/>dalle leggi del vette, uno <lb/>de'bracci del quale sia po&shy;<lb/>sto nella lunghezza della fu&shy;<lb/>ne, e l'altro nel raggio della <lb/>rotella, il centro della quale <lb/>fa da fulcro alla stessa leva. </s>

<s>D&agrave; dunque quella legge statica P:Q=DO:AR, <lb/>ossia Q=AR/DO.P, e per tutta intera la fune, con i due pesi eguali che la <lb/>tirano da'suoi capi, 2Q=2.AR/DO.P. </s>

<s>Passando ora a fare di questa for&shy;<lb/>mula l'applicazione numerica; perch&egrave; ponesi da Leonardo P=100, AR <lb/>=200, DO=1; sar&agrave; dunque 2Q=400X100=40,000, d'onde Q= <lb/>20,000. </s></p><p type="main">

<s>Tal'&egrave; appunto il discorso di Leonardo nella seguente forma da lui pro&shy;<lb/>priamente espresso, dop'avere affermato essere impossibile a far tendere una <lb/>corda da due pesi di mille libbre, che la tirino fortemente da una parte e <lb/>dall'altra: &ldquo; La ragione di questo si &egrave;, che il peso, posto in mezzo alla <lb/>corda, fa quello medesimo offizio al contrappeso delle mille libbre, che fa&shy;<lb/>rebbe altrettanto peso appiccato nella estremit&agrave; di una leva, che fosse lunga <lb/>50 braccia. </s>

<s>Adunque, per sapere la verit&agrave; di questo effetto, cio&egrave; se gli &egrave; <lb/>possibile che il peso delle 2000 libbre pu&ograve; dirizzare la corda, misura il dia&shy;<lb/>metro del sodo della girella, che sostiene il peso delle mille libbre, e guarda <lb/>quante volte la met&agrave; d'esso diametro entra dal mezzo della girella al mezzo <lb/>del peso delle cento libbre, sopra la linea RA. </s>

<s>E quanto detta parte del <lb/>diametro, cio&egrave; OR, entra dugento volte insino al di sopra del mezzo della <lb/>corda; altrettanto fa l'altro mezzo, che dice 400. Adunque d&igrave;: 400 via 100 <lb/>fa quarantamila, e poi v'&egrave; il peso della corda, che la regola del suo peso <pb xlink:href="020/01/1820.jpg" pagenum="63"/>di sotto. </s>

<s>In effetto la corda, in molta lunghezza, non si dirizzer&agrave;, se non si <lb/>rompe &rdquo; (Manuscr. </s>

<s>A cit., fol. </s>

<s>51 ad t.). </s></p><p type="main">

<s>S'esercit&ograve; anche Galileo intorno a questo meccanico problema, ma l'im&shy;<lb/>possibilit&agrave; di dirizzare una corda in linea orizzontale, da qualunque immensa <lb/>forza sia tirata, non sapendo come Leonardo far uso del parallelogrammo, <lb/>che rende per s&egrave; medesimo l'apparente stranezza evidente, si lusing&ograve; di poter <lb/>concluderla dal principio statico generale de'momenti uguali alle velocit&agrave; <lb/>moltiplicate per i pesi. </s>

<s>&ldquo; Intendete per ora, cos&igrave; scrive nella IV giornata <lb/>delle Due nuove scienze, questa linea AB (fig. </s>

<s>34) passando sopra i due <lb/>punti fissi e stabili A, B, aver nelle estremit&agrave; sue pendenti come vedete <lb/><figure id="id.020.01.1820.1.jpg" xlink:href="020/01/1820/1.jpg"/></s></p><p type="caption">

<s>Figura 34.<lb/>due immensi pesi eguali C, <lb/>D, li quali, tirandola con <lb/>grandissima forza, la fac&shy;<lb/>ciano star veramente tesa <lb/>direttamente, essendo essa <lb/>una semplice linea senza <lb/>veruna gravit&agrave;. </s>

<s>Or qui vi <lb/>soggiungo e dico che, se <lb/>dal mezzo di quella, che <lb/>sia il punto E, voi sospenderete qualsivoglia piccolo peso, quale sia que&shy;<lb/>sto H; la linea AB ceder&agrave;, ed inclinandosi verso il punto F, ed in conse&shy;<lb/>guenza allungandosi, costringer&agrave; i due gravissimi pesi C, D a salire in alto, <lb/>il che in tal guisa vi dimostro &rdquo; (Alb. </s>

<s>XIII, 264). Descrive, per la dimo&shy;<lb/>strazione, Galileo, co'due raggi AE, BE, fissi ne'loro centri A, B, le due por&shy;<lb/>zioni di cerchio EG, EM, e per provar possibile che il piccolo peso II ha <lb/>virt&ugrave; di scendere, come per esempio sarebbe in F, e perci&ograve; di far risalire <lb/>i due grandissimi pesi C e D, per tratti uguali a FL, FI; ricorre al prin&shy;<lb/>cipio statico de'momenti, il quale dovrebbe, nel caso dell'equilibrio, dare <lb/>l'equazione C:H=EF:FI. </s>

<s>Ma perch&egrave; EF ha maggior proporzione a FI <lb/>di quel che non ha C ad H, il che Galileo si studia di dimostrare, resta che <lb/>il piccolissimo peso abbia tanta viri&ugrave; di moto in basso, da sollevare i due <lb/>grandissimi in alto: &ldquo; resta manifesto cio&egrave;, dice lo stesso Galileo, che la <lb/>linea AB partir&agrave; dalla rettitudine orizzontale. </s>

<s>E quel che avviene alla retta <lb/>AB priva di gravit&agrave;, mentre si attacchi in E qualsivoglia minimo peso H, <lb/>avviene alla stessa corda AB, intesa di materia pesante, senza l'aggiunta di <lb/>alcun altro grave, poich&egrave; vi si sospende il peso stesso della materia compo&shy;<lb/>nente essa corda &rdquo; (ivi, 265). </s></p><p type="main">

<s>Al Viviani, come vedremo pi&ugrave; di proposito altrove, entr&ograve; poi qualche <lb/>scrupolo di questa galileiana dimostrazione, n&egrave; gli parve che la tangente e <lb/>la secante si movessero in tale ordine fra loro, da rendere le velocit&agrave; com&shy;<lb/>parabili. </s>

<s>Il dubbio dall'altra parte non era senza giusto motivo, reso anche <lb/>pi&ugrave; manifesto per l'uso del parallelogrammo, da cui resulta che la ragion <lb/>del peso C al peso II non &egrave; quella delle linee EF:FI, posta da Galileo, ma <lb/>s&igrave; veramente quell'altra delle linee EF:AE. </s></p><pb xlink:href="020/01/1821.jpg" pagenum="64"/><p type="main">

<s>Notabile che Leonardo, il quale si serv&igrave; di questa medesima costruzione <lb/>galileiana, col diretto e immediato intento di dimostrare che, in qualunque <lb/>sorta di movimento, allora si stabilisce il sistema in equilibrio, che gli spa&shy;<lb/>zii tornano reciprocamente proporzionali ai pesi; rimanesse, come Galileo, <lb/>ingannato, reputando che gli allungamenti delle secanti e della tangente, co&shy;<lb/>mune ai due archi de'cerchi, potessero servire per la pi&ugrave; giusta misura delle <lb/>velocit&agrave;, con le quali i due ponderosi gravi C, D risalgono, e il corpicciolo H <lb/>discende. </s>

<s>&ldquo; Se la corda AB, egli dice, sia tesa da due forze uguali C, D, <lb/>poni nel mezzo della corda in E un piccolo peso H. </s>

<s>Egli scender&agrave; infino <lb/>in F, e far&agrave; salire nel medesimo tempo i due pesi C, D. </s>

<s>Col raggio AE tira <lb/>l'arco EG, il moto del peso C sar&agrave; IF. </s>

<s>Il peso H scender&agrave; infintanto che non <lb/>si riduca alla proporzione H:C=IF:EF &rdquo; (Venturi, <emph type="italics"/>Essai<emph.end type="italics"/> cit., pag. </s>

<s>17). </s></p><p type="main">

<s>Se avesse preso per filo, da non smarrirsi per la intricata via, il paral&shy;<lb/>lelogrammo, si sarebbe Leonardo, come negli altri casi, felicemente incon&shy;<lb/>trato nel vero, ma bench&egrave; riconoscesse quella regola per certa, ebbe nono&shy;<lb/>stante questa volta a trovare qualche difficolt&agrave; nel bene applicarla. </s>

<s>Di simili <lb/>difficolt&agrave;, dall'altra parte s'incontrarono bene spesso anche i moderni a dover <lb/>fare esperienza, di che il problema della trave appoggiata al muro, accen&shy;<lb/>nato di sopra, offre in proposito un singolarissimo esempio. </s>

<s>Dopo l'instau&shy;<lb/>razione della Scienza meccanica fu, come si disse, il Torricelli il primo a <lb/>fare una tal nuova e pericolosa prova, e bench&egrave; debba essere altrove que&shy;<lb/>sto per noi argomento a pi&ugrave; lungo discorso, basti qui il dir tanto intorno <lb/>al modo tenuto in risolver quel meccanico problema dal discepolo di Galileo, <lb/>quanto giovi a paragonarlo con quell'altro modo proseguito da Leonardo. </s></p><p type="main">

<s>Cos&igrave; dunque esso Torricelli, presa un giorno la penna in mano, col&shy;<lb/>l'intenzione di mettere in bella forma il suo pensiero; ne lasciava in una <lb/>notarella manoscritta interrotto il costrutto, dop'avere appena accennato al <lb/>suo assunto: &ldquo; Fra gli effetti della Meccanica, degni di essere osservati, uno <lb/><figure id="id.020.01.1821.1.jpg" xlink:href="020/01/1821/1.jpg"/></s></p><p type="caption">

<s>Figura 35.<lb/>se ne trova, non avvertito ancora da alcuno che io sappia, ep&shy;<lb/>pur da esso possono derivar cognizioni di qualche momento e <lb/>di molta curiosit&agrave;. </s>

<s>Sia AB (fig. </s>

<s>35) un muro eretto al piano del&shy;<lb/>l'orizzonte BC, e sia AC una trave appoggiata al muro. </s>

<s>Chiara <lb/>cosa &egrave; che, mentre ella star&agrave; assai eretta, come AC, pochissima <lb/>forza che, posta in C, spinga verso B baster&agrave; per reggerla, il <lb/>che non accader&agrave;, quando la trave sia pi&ugrave; in&shy;<lb/>clinata, come la DE. Ora, per contemplar ci&ograve;, <lb/>supponghiamo per ora che AC sia una linea, e <lb/>che in A e in C siano due potenze eguali, e <lb/>che la A prema perpendicolarmente in gi&ugrave; verso <lb/>B, ma la C spinga orizzontalmente verso E. </s>

<s><lb/>Cercasi la proporzione del momento, che averanno queste due forze, e dico <lb/>che la forza A alla C sar&agrave; come la linea CB alla BA, permutatamente prese. </s>

<s><lb/>Per provar questo bisogner&agrave; discorrere pi&ugrave; a lungo .... Ora in cambio delle <lb/>due potenze si potr&agrave;, come nelle macchine della Meccanica, ed in particolare <pb xlink:href="020/01/1822.jpg" pagenum="65"/>nella lieva, considerare in A un peso, ed in C la potenza come sopra..... <lb/>(MSS. Gal. </s>

<s>Disc., T. XXXVII, c. </s>

<s>87). </s></p><p type="main">

<s>Nell'attendere a compilare il trattato torricelliano <emph type="italics"/>De motu ac momen&shy;<lb/>tis<emph.end type="italics"/> voleva il Viviani raccogliere anche questo fra gli altri teoremi, rendendo <lb/>intelligibile il pensiero dell'Autore coll'osservar ch'&egrave; la conclusione di lui <lb/>dedotta dalla Meccanica galileiana, considerando l'angolo retto B cos&igrave; dispo&shy;<lb/>sto, che l'ipotenusa riesca parallela all'orizzonte. </s>

<s>Di qui &egrave; che venendo, in <lb/>tal disposizione della segnata figura, ed aver le due linee oblique AB, BC <lb/>la medesima altezza, un grave che per essa scenda ha gl'impeti reciproca&shy;<lb/>mente proporzionali alle loro lunghezze. </s></p><p type="main">

<s>Ecco come pensava il Viviani di spiegare e rendere in forma i concetti <lb/>del Torricelli: &ldquo; In angulo recto ABC, e perpendiculari AB et horizzontali <lb/>BC constituto, concipiatur quaecumque subtensa AC, vel quaedam hasta so&shy;<lb/>lida, omni tamen gravitate carens et inflexibilis. </s>

<s>In A, et in C, sint duae <lb/>acquales potentiae, quam altera deorsum premat iuxta directionem perpen&shy;<lb/>diculi AB, altera autem impellat iuxta directionem horizontalem CB, contra <lb/>angulum B. </s>

<s>Dico momentum patentiae in A, ad momentum potentiae in C, <lb/>esse in ratione latorum permutatim sumptorum, nempe ut CB ad BA. &rdquo; </s></p><p type="main">

<s>&ldquo; Ad hoc probandum ponatur, non amplius latus BC, sed hypothenusa, <lb/>sive AC, esse horizontaliter constituta, ita ut planum trianguli ABC cum <lb/>aliquo verticalium congruat, angulo B deorsum spectante, productisque BA, <lb/>BC, in angulis A, C concipiantur aequalia pondera A, C. </s>

<s>Per ea, quae de&shy;<lb/>monstravit magnus Galilaeus in suo Mechanicae tractatu, aliisque aggressio&shy;<lb/>nibus, et hic Auctor ad initium sui libelli <emph type="italics"/>De motu<emph.end type="italics"/> confirmavit, momentum <lb/>gravis A directive per planum AB, ad momentum aequalis gravis C directive <lb/>per planum CB, est reciproce ut CB ad BA &rdquo; (ivi, c. </s>

<s>104 ad t.). </s></p><p type="main">

<s>Non era possibile per&ograve; che a quel sottile giudizio del Viviani non sem&shy;<lb/>brasse questa una troppo gran violenza fatta ai principii statici galileiani, <lb/>per accomodarli in qualche modo alla soluzion del problema; nonostante, <lb/>proponendosi un caso simile, non par che sapesse trovar, di questa, via <lb/>molto migliore. </s></p><p type="main">

<s>&ldquo; Sia il muro a piombo AB (scrive esso Viviani in una sua Nota au&shy;<lb/>tografa) ed il pavimento BC, ed un corrente DE si vadi appoggiando come <lb/>si vede in varie positure e inclinazioni. </s>

<s>Si cerca con che proporzione vadia <lb/>questo grave violentando i detti piani sopra i quali si appoggia. </s>

<s>&mdash; Credo <lb/>che il peso, che sente il piano AB, al peso che sente il pavimento, stia omo&shy;<lb/>logamente come l'altezza del muro del toccamento del corrente fino a terra, <lb/>nel luogo B, alla lunghezza del pavimento, dal detto B fino all'altro tocca&shy;<lb/>mento sopra di esso &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXIII, c. </s>

<s>30). </s></p><p type="main">

<s>L'opinione cos&igrave; espressa non si trova qui confortata da nessuna dimo&shy;<lb/>strazione, ma che fosse fondata, come si disse, sulla statica galileiana, pu&ograve; <lb/>confermarsi da un'altra Nota, nella quale il Viviani stesso conclude le pro&shy;<lb/>porzioni delle varie spinte del corrente contro il muro, nelle sue varie in&shy;<lb/>clinazioni, dagl'impeti che farebbe un grave supposto scendervi sopra, come <pb xlink:href="020/01/1823.jpg" pagenum="66"/>su due varie obliquit&agrave; di un medesimo piano. </s>

<s>Or perch&egrave; i gravi uguali A, D <lb/>posti sopra le oblique eguali AC, DE hanno impeti proporzionali alle altezze <lb/>AB, DB, applica il Viviani questa ragion meccanica dei momenti a qualun&shy;<lb/>que altra potenza, e perci&ograve; anche alla spinta data al muro dal corrente, che <lb/>in varia giacitura gli si appoggia. </s>

<s>&ldquo; Quod vero de momentis aequalium gra&shy;<lb/>vium super codem aequali plano AC, DE, intelligatur quoque de momentis <lb/>aequalium potentiarum quarumlibet, per directiones AC, DE &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. XXXVII, c. </s>

<s>105). </s></p><p type="main">

<s>Se il trapasso, dai momenti sopra i piani inclinati a qualunque potenza <lb/>operi in quelle direzioni, sia da concedersi al Viviani, ne dubitarono ragio&shy;<lb/>nevolmente i Matematici venuti di poi, i quali, divulgatasi la notizia del pro&shy;<lb/>blema proposto dal Torricelli, vi applicarono a risolverlo la regola del pa&shy;<lb/>rallelogrammo delle forze. </s>

<s>Il modo pi&ugrave; conveniente per&ograve; di quella applicazione <lb/>gli pose in impaccio, ond'&egrave; che ne dettero soluzioni varie, e forse non meno <lb/>incerte di quelle date dai due commemorati discepoli di Galileo, concluden&shy;<lb/>dole dalle dottrine statiche del loro Maestro. </s></p><p type="main">

<s>Pu&ograve;, comunque sia, per facilitar la questione, osservarsi che, se ne'due <lb/>punti di appoggio A e C, rappresentati da noi nella solita figura XXXV, <lb/>s'intendano applicate due forze orizzontali, eguali e contrarie alle due spinte, <lb/>il corrente rimarr&agrave; tuttavia in equilibrio, cosicch&egrave; &egrave; il punto C del pavi&shy;<lb/>mento, che ne sostien sopr&agrave; s&egrave; tutto il peso. </s>

<s>L'una o l'altra poi di quelle <lb/>spinte eguali pu&ograve; facilmente determinarsi, decomponendole ne'lati del paral&shy;<lb/>lelogrammo, da che, chiamata S la detta spinta, P il peso del corrente inteso <lb/>raccolto nel suo centro di gravit&agrave;, <foreign lang="greek">f</foreign> l'angolo ch'egli fa col muro di appoggio, <lb/><emph type="italics"/>a<emph.end type="italics"/> la sua lunghezza, <emph type="italics"/>b<emph.end type="italics"/> la parte di lui che resta dal centro di gravit&agrave; al punto <lb/>di contatto col pavimento; s'ottiene la relazione S:P=(<emph type="italics"/>a&mdash;b<emph.end type="italics"/>) tang.<foreign lang="greek">f</foreign>:<emph type="italics"/>a.<emph.end type="italics"/><lb/>Che se il corrente stesso &egrave; omogeneo e uniforme, e <emph type="italics"/>b<emph.end type="italics"/> perci&ograve; &egrave; uguale alla <lb/>met&agrave; di <emph type="italics"/>a,<emph.end type="italics"/> il valore della spinta &egrave; dato da P.(tang.<foreign lang="greek">f</foreign>)/2=P.(BC)/2; ossia essa <lb/>spinta &egrave; uguale al peso del grave che si appoggia, moltiplicato per la met&agrave; <lb/>della sua proiezione ortogonale. </s></p><p type="main">

<s>Ora &egrave; da vedere in che modo fosse questo medesimo problema risoluto <lb/>da Leonardo, che fu primo a proporlo ai Meccanici, un secolo prima del <lb/>Torricelli. </s>

<s>Non avendo nemmen egli, come i moderni, trovato conveniente <lb/>modo di applicarvi il principio della composizion delle forze, si lasci&ograve;, fin <lb/>dove seppero, condurre all'Aritmetica e alla Geometria, e poi, abbandonato <lb/>da loro, ripos&ograve; l'affaticata mente nell'esperienza. </s>

<s>&ldquo; Quello corpo, del quale <lb/>la continua larghezza &egrave; superata dalla lunghezza, conviene che dia di s&egrave; <lb/>eguale carico ai due sua estremi contatti, quando fieno equidistanti al cen&shy;<lb/>tro come F, E (fig. </s>

<s>36), ma quando il corpo star&agrave; per linea perpendicolare <lb/>dico il contatto della inferiore stremit&agrave; ricevere sopra s&egrave; tutto il di sopra <lb/>posto carico, e la superiore niente pesa al suo apposito contatto, come ap&shy;<lb/>pare in GE. </s>

<s>Ma se detto corpo fia colle due estremit&agrave; di discordante distanza <lb/>a detto centro, sar&agrave; di discordante peso, imperocch&egrave; la parte, che pi&ugrave; se li <pb xlink:href="020/01/1824.jpg" pagenum="67"/>avvicina, pi&ugrave; carica, e la pi&ugrave; lontana si fa pi&ugrave; lieve, come appare in A, C. <lb/><figure id="id.020.01.1824.1.jpg" xlink:href="020/01/1824/1.jpg"/></s></p><p type="caption">

<s>Figura 36.<lb/>Adunque, se nella prima proposizione si di&shy;<lb/>mostra il detto peso compartirsi ne'due estre&shy;<lb/>mi contatti, e cos&igrave; nella seconda il basso E <lb/>ricever&agrave; tutto, e il G niente; adunque &egrave; ne&shy;<lb/>cessario confessare, per ragione geometrica e <lb/>arismetrica, che quel peso, che si trova tra <lb/>l'uno e l'altro modo, partecipi de'due estremi, <lb/>come A, C. </s>

<s>Se il peso AE fia 4 braccia e 8 <lb/>libbre, e che tu lo penda in modo, che non <lb/>sia tutto nel punto E, e n&egrave; compartito per <lb/>met&agrave; in FE, anzi si trovi in mezzo alla linea <lb/>FE, cio&egrave; sopra il punto C; dico per ragion di <lb/>Arismetrica che se il peso, stando per lo ritto, <lb/>d&agrave; 8 libbre di carico al punto E, e stando intieramente a diacere glie ne <lb/>d&agrave; 4; or piglia il mezzo che &egrave; infra 4 e 8, che &egrave; 6: adunque il punto sia <lb/>B e CA sia due fra forza e peso, e per ragion geometrica si trova che, <lb/>tolta la base del triangolo ACE, e quella partita per met&agrave; nel punto D, dico <lb/>sempre DE darsi a A, e cos&igrave; DF darsi in E. DE &egrave; simile a AB, e cos&igrave; DF <lb/>&egrave; simile a BE &rdquo; (Manuscr. </s>

<s>B cit., fol 63). </s></p><p type="main">

<s>Non in tutti i casi per&ograve; vale questa ragione geometrica, perch&egrave; DF non <lb/>&egrave; <emph type="italics"/>simile,<emph.end type="italics"/> ossia uguale a BE, se non che quando il triangolo AEF &egrave; equila&shy;<lb/>tero, e il corrente &egrave; perci&ograve; inclinato di 60 gradi sul pavimento. </s>

<s>Nonostante <lb/>vuol Leonardo che questa sia regola generale, e che sia da seguirsi per qua&shy;<lb/>lunque inclinazione, com'egli dice di aver trovato coll'esperienza. </s>

<s>&ldquo; Io trovo <lb/>per esperienza che il legno AE dar&agrave; tanto di s&egrave; men carico nel punto E, <lb/>quanto &egrave; la met&agrave; della basa del triangolo AEC: cio&egrave; se la mazza sar&agrave; 6 brac&shy;<lb/>cia e pesi 6 libbre, e la met&agrave; della sua base ED sia uno braccio, dico che <lb/>il bastone dar&agrave; di s&egrave; peso al punto E cinque, e una libbra ne va in forza <lb/>nel loco, dove s'appoggia A &rdquo; (ivi, fol. </s>

<s>14 ad t.). </s></p><p type="main">

<s>&Egrave; chiaro dunque che Leonardo, confondendo le spinte orizzontali con <lb/>l'unica verticale, fa quelle variar fra loro secondo l'inclinazione dell'asta <lb/>appoggiata al sostegno, ond'&egrave; che, chiamando S la spinta data dall'asta <lb/>stessa in A, S&prime; l'altra data in E, e ritenute le solite denominazioni <emph type="italics"/>a,<emph.end type="italics"/> <foreign lang="greek">f</foreign> poste <lb/>di sopra, le relazioni fra S, S&prime; sarebbero secondo Leonardo espresse dal&shy;<lb/>l'equazione S:S&prime;=tang.<foreign lang="greek">f</foreign>:2<emph type="italics"/>a<emph.end type="italics"/>&mdash;tang.<foreign lang="greek">f. </foreign></s></p><p type="main">

<s>Notabile &egrave; a questo proposito l'ingegnoso modo, con che spesso il No&shy;<lb/>stro sa tradurre in formule matematiche i resultati delle esperienze. </s>

<s>Le re&shy;<lb/>gole, ch'egli d&agrave; in varie Note del manoscritto C, per determinar l'altezza <lb/>di un liquido, in un vaso chiuso, dall'ampiezza e dalla forma del getto, ce <lb/>ne offrirebbero un esempio singolarissimo. </s>

<s>Ma perch&egrave; questo appartiene a <lb/>un soggetto alquanto diverso dal presente, termineremo il nostro Saggio col <lb/>proporre ai lettori un altro problema di Meccanica che, essendo stato prima <lb/>secondo noi risoluto dallo stesso Leonardo per esperienza, fu da lui poi ri-<pb xlink:href="020/01/1825.jpg" pagenum="68"/>dotto a regola generale geometrica. </s>

<s>&ldquo; La infima bassezza dell'arco, che fa <lb/><figure id="id.020.01.1825.1.jpg" xlink:href="020/01/1825/1.jpg"/></s></p><p type="caption">

<s>Figura 37.<lb/>la corda pi&ugrave; lunga che lo spazio che &egrave; infra <lb/>i sua sostentacoli, sostenuta ne'sua stremi da <lb/>due varie altezze, toccher&agrave; terra tanto pi&ugrave; <lb/>presso al minore sostentacolo, che al maggiore, <lb/>quanto il maggiore riceve dentro a s&egrave; l'altezza <lb/>del minore. </s>

<s>Verbigrazia, se il sostentacolo AB <lb/>(fig. </s>

<s>37) entra due volte in nel maggiore so&shy;<lb/>stentacolo ED, lo spazio, che resta infra CB, <lb/>entra ancora due volte in DC &rdquo; (Manuscr. </s>

<s>A <lb/>cit., fol. </s>

<s>48). </s></p><p type="main">

<s>Bench&egrave; per&ograve;, considerato il consueto or&shy;<lb/>dine del procedere di Leonardo, siasi da noi <lb/>affermato che probabilmente questo teorema <lb/>meccanico fu per lui prima il frutto dell'esperienza, le speculate teorie dei <lb/>pesi attaccati alle funi dovettero nulladimeno venire a dargliene la conferma. </s>

<s><lb/>Negli esempii da noi sopra recati il peso G della figura XXXI si supponeva <lb/>cos&igrave; fisso in A, che le funi CA, AB rimanessero sempre di lunghezza inva&shy;<lb/>riabile. </s>

<s>Ora volle Leonardo, proseguendo l'amato esercizio, veder come pro&shy;<lb/>cedesse il fatto, quando lo stesso peso fosse libero di scorrere per la fune, <lb/>infintantoch&egrave; non si fosse adagiato al suo naturale equilibrio, come sarebbe <lb/>per esempio a infilarvi un anello di ferro. </s></p><p type="main">

<s>Dir, come ne concludono analiticamente i Moderni, che dal dover es&shy;<lb/>sere la direzione della gravit&agrave; dell'anello perpendicolare all'ellise da lui de&shy;<lb/>scritta nello sorrere per la fune, ne concludesse anche Leonardo che la linea <lb/>intercentrica dee divider l'angolo fatto dalla stessa fune in due parti uguali; <lb/>sarebbe forse un esagerar di troppo le naturali virt&ugrave; di quell'ingegno, ma <lb/>in ogni modo, o per esperienza, come crediamo noi, o per altre vie, egli <lb/>riusc&igrave; benissimo a conoscere quella verit&agrave;, o vogliam dire geometrica, o di <lb/>semplice fatto. </s></p><p type="main">

<s>Sieno dunque A e B (fig. </s>

<s>38) i due punti variamente alti, e a cui <lb/>stanno fissi i capi della fune AEB, nella quale &egrave; stato infilato il pesante <lb/><figure id="id.020.01.1825.2.jpg" xlink:href="020/01/1825/2.jpg"/></s></p><p type="caption">

<s>Figura 38.<lb/>anello E. </s>

<s>Per risolvere il problema conduce <lb/>Leonardo per E la orizzontale DC, sopra la <lb/>quale abbassa le due perpendicolari AC, BD. </s>

<s><lb/>Dovendo la linea intercentrica EF, per le ri&shy;<lb/>conosciute condizioni dell'equilibrio, dividere <lb/>l'angolo AEB in due parti uguali, cio&egrave; in AEF <lb/>=EAC, e in FEB=EBD, i due triangoli <lb/>simili, o <emph type="italics"/>angoli chiusi uguali,<emph.end type="italics"/> come il Nostro <lb/>gli chiama, ACE, BED daranno AC:BD= <lb/>CE:ED; proporzione sopra la quale, anche <lb/>graficamente, si potr&agrave; risolvere il problema <lb/>in un modo forse pi&ugrave; facile e pi&ugrave; spedito di quello stesso suggeritoci dal <pb xlink:href="020/01/1826.jpg" pagenum="69"/>Bossut, o da altri Matematici moderni. </s>

<s>&ldquo; Quel corpo ponderoso, cos&igrave; pro&shy;<lb/>priamente esprimesi Leonardo, che fia sospeso infra la corda, della quale i <lb/>sua estremi fieno attaccati a due sostentacoli di diversa altezza, giacer&agrave; infra <lb/>eguali angoli, de'quali le loro base fieno tanto pi&ugrave; larghe l'una che l'altra, <lb/>quanto gli estremi della corda fieno fermi pi&ugrave; alti l'uno che l'altro &rdquo; (ivi, <lb/>fol. </s>

<s>48). </s></p><p type="main">

<s>Or &egrave; facile vedere che, riguardando la fune come aggravata dal suo <lb/>proprio peso, si possa facilmente ridurre alle condizioni dell'antecedente <lb/>questo secondo esempio, in cui la fune stessa &egrave; aggravata da un peso stra&shy;<lb/>niero. </s>

<s>E di qu&igrave; &egrave; a concludere all'ultimo quanto nella Geometria e nella <lb/>esperienza, sapientemente contemperate insieme, sapesse ritrovar valido ar&shy;<lb/>gomento di progredire la scienza meccanica di Leonardo da Vinci, speculata <lb/>dalle naturali virt&ugrave; del proprio ingegno, e diretta da tutta quella scienza, che <lb/>si poteva avere al suo tempo. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Ai magnificatori del divino ingegno, ai troppo creduli della miracolosa <lb/>potenza dell'uomo, che crea da s&egrave; medesimo nuove scienze, senza prece&shy;<lb/>denti tradizioni, e senza un primo maestro; si rivolge in particolare l'ar&shy;<lb/>gomento di questa storia, la quale ci sovviene opportuna a confermare il <lb/>fatto, che l&agrave; dove venivano a mancar le anteriori istituzioni e i principii, da <lb/>attingervi il vero in essi concluso, andava anche il divino ingegno di Leo&shy;<lb/>nardo da Vinci brancolando, insieme con gli altri, fra le tenebre dell'igno&shy;<lb/>ranza e dell'errore. </s>

<s>Per la Statica erano date quelle istituzioni e posti quei <lb/>principii da Aristotile, da Archimede, e da Giordano Nemorario, che segnano, <lb/>secondo noi, nella storia della scienza tre distinte epoche progressive, e fu <lb/>mostrato di sopra come, giovandosi di quegli utilissimi documenti, sapesse <lb/>ingegnosamente Leonardo applicarli alla teoria delle macchine, e a'momenti <lb/>dei gravi sopra i piani inclinati; e come fedelmente, proseguendo la regola <lb/>di decomporre le forze, insegnata da Aristotile e messa gi&agrave; in uso in certi <lb/>problemi ottici da Alazeno e da Vitellione; riuscisse mirabilmente ad assog&shy;<lb/>gettar la pi&ugrave; ritrosa parte della Meccanica alle docili discipline della Geo&shy;<lb/>metria. </s></p><p type="main">

<s>Alla Dinamica per&ograve; corse la sorte alquanto diversa. </s>

<s>Bench&egrave; avesse le <lb/>prime mosse da Archimede, furono per&ograve; cos&igrave; deboli e cos&igrave; lontane, da non <lb/>risentirne l'impulso, se non che tra il finir del secolo XVI, e il principiar <lb/>del seguente, per opera precipua del Benedetti e di Galileo. </s>

<s>&Egrave; perci&ograve; che <lb/>Leonardo, studioso delle archimedee tradizioni, seppe sgombrarsi la mente <lb/>dagli errori aristotelici intorno al&igrave;e qualit&agrave; e alle cause, che rendono i corpi <lb/>o gravi o leggeri, riconoscendole facilmente dal vario impulso dei mezzi; ma <lb/>da'moti equabili in fuori, non riusc&igrave; con l'aiuto delle matematiche a saper <pb xlink:href="020/01/1827.jpg" pagenum="70"/>nulla di pi&ugrave; de'contemporanei intorno alle leggi dei corpi gravi natural&shy;<lb/>mente cadenti e dei proietti. </s>

<s>La stessa mirabile pazientissima diligenza delle <lb/>esperienze, se pot&egrave; farlo accorto di qualche peripatetico errore, non valse <lb/>nulladimeno a rivelargli il vero, lungo tempo dopo riserbato alle scoperte <lb/>del Cavalieri e di Galileo. </s>

<s>A confermar le quali cose, e a provar l'assunto <lb/>propostoci contro chi temerariamente asseriva esser la Scienza meccanica <lb/>una creazione della mente di Leonardo da Vinci, convien ricorrere ai docu&shy;<lb/>menti, dimostrativi da una parte dell'efficacia, e dall'altra del difetto delle <lb/>tradizioni. </s></p><p type="main">

<s>Notabilissimo esempio di cos&igrave; fatta efficacia ci si porge in quel che <lb/>s'accennava della naturale gravit&agrave; e leggerezza, intorno a che aveva Aristo&shy;<lb/>tile insegnato moltissimi errori, qual sarebbe per esempio quello che ogni <lb/>corpo, nel suo proprio luogo, &egrave; grave come l'aria nell'aria, e l'acqua nel&shy;<lb/>l'acqua, e che a ciascun corpo l'esser grave e leggero &egrave; per una assoluta <lb/>propriet&agrave; della Natura. </s>

<s>Dimostr&ograve; invece Archimede non essere, nella gra&shy;<lb/>vit&agrave; e nella leggerezza de'corpi, nulla di assoluto, ma tutto aver relazione <lb/>e dipendenza dalla qualit&agrave; del mezzo, la circumpulsion del quale lascia ca&shy;<lb/>dere il grave s'&egrave; vinta dal peso di lui, e lo fa al contrario salire se, sopra <lb/>quello stesso peso, riman vincitrice. </s>

<s>In sentenza de'quali savi documenti, <lb/>appresi dalla lettura dei Libri archimedei, andava cos&igrave; ripetendo anche il <lb/>nostro Leonardo: &ldquo; Li moti degli elementi gravi non sono al centro, per <lb/>andare ad esso centro, ma perch&egrave; il mezzo ove essi sono non li pu&ograve; resi&shy;<lb/>stere, e quando l'elemento trova resistenza nel suo elemento, il suo corpo <lb/>pi&ugrave; non pesa, n&egrave; cerca pi&ugrave; di andare al centro &rdquo; (Del moto dell'acqua cit., <lb/>pag. </s>

<s>281). E pi&ugrave; sotto ripete, anche pi&ugrave; spiegatamente, cos&igrave; lo stesso con&shy;<lb/>cetto: &ldquo; La terra &egrave; grave nella sua sfera, ma tanto pi&ugrave; quanto essa sar&agrave; <lb/>in elemento pi&ugrave; lieve. </s>

<s>Il fuoco &egrave; lieve nella sua sfera, e tanto pi&ugrave;, quanto <lb/>esso sar&agrave; in elemento pi&ugrave; grave. </s>

<s>L'acqua &egrave; grave e lieve, e tanto pi&ugrave; grave <lb/>quanto essa sar&agrave; in elemento pi&ugrave; lieve, e tanto pi&ugrave; lieve quanto essa sar&agrave; <lb/>in elemento pi&ugrave; grave. </s>

<s>Sicch&egrave; nessuno elemento semplice ha la sua gravit&agrave; <lb/>o levit&agrave; nella sua propria sfera. </s>

<s>E se la vessica piena d'aria pesa pi&ugrave; nelle <lb/>bilance, ch'essendo vuota, questo &egrave; perch&egrave; tale aria &egrave; condensata, e con&shy;<lb/>densar si potrebbe il fuoco, che sarebbe pi&ugrave; grave che l'aria o eguale all'aria, <lb/>e forse pi&ugrave; grave che l'acqua, e forse eguale alla terra &rdquo; (ivi, pag. </s>

<s>282). </s></p><p type="main">

<s>A mostrar che, da una medesima fonte, salirono queste acque vive, <lb/>giova comparar le dottrine del Nostro con quelle, che ha in certe sue abboz&shy;<lb/>zate scritture Galileo. </s>

<s>Ma perch&egrave; queste stesse galileiane scritture, date ora <lb/>alla luce, non sono altro che una giovanile esercitazion dell'Autore sopra le <lb/><emph type="italics"/>Speculazioni<emph.end type="italics"/> del Benedetti, pensiamo di trascriver qui le parole del Mate&shy;<lb/>matico di Venezia, che sembrano a noi copiate da un pi&ugrave; antico esemplare <lb/>caduto quasi un secolo prima sotto gli occhi del popolano di Vinci. </s>

<s>Nel trat&shy;<lb/>tatello <emph type="italics"/>Disputationes de quibusdam placitis Aristotelis,<emph.end type="italics"/> al cap. </s>

<s>XXVI, cos&igrave; <lb/>si legge: &ldquo; Omne corpus esse in loco proprio grave, ut Aristoteli placuit, <lb/>non est admittendum..... Exemplum, quod ipse de utre inflato proponit, <pb xlink:href="020/01/1828.jpg" pagenum="71"/>debuisset saltem ei oculos ad veritatem, quae clarissime fulget, inspiciendam, <lb/>aperire. </s>

<s>Verissimum est utrem inflatum plus ponderis habere quam vacuum, <lb/>aut quando aer in eo non est per vim inclusus. </s>

<s>Ratio autem huius rei est <lb/>quia, quando inflatus est, ea quantitas aeris, in eum per vim iniecti, mino&shy;<lb/>rem occupat locum, quam si eidem libere vagari permitteretur, unde vio&shy;<lb/>lenter quodammodo condensata est, et quia corpus densum in minus denso <lb/>semper descendit, et minus densum in magis denso ascendit. </s>

<s>Hanc ob cau&shy;<lb/>sam uter inflatus plenus corpore magis denso, quam est medium quod eum <lb/>circumdat, descendit, non quia aer in aere, aut aqua in aqua sit gravis &rdquo; <lb/>(Editio cit., pag. </s>

<s>85). </s></p><p type="main">

<s>Come le fonti, da cui s'attinsero queste dottrine nel secolo del Bene&shy;<lb/>detti, ossia della instaurazion della scienza, e in quello di Leonardo che la <lb/>preparava, erano le archimedee; cos&igrave; di l&agrave; s'appresero nel medesimo tempo <lb/>le facili ragioni matematiche dei moti equabili. </s>

<s>&ldquo; Se una potenzia (ha cos&igrave; <lb/>una delle solite Note vinciane) mover&agrave; un corpo in alquanto tempo un al&shy;<lb/>quanto spazio, la medesima potenzia mover&agrave; la met&agrave; di quel corpo nel me&shy;<lb/>desimo tempo due volte quello spazio, ovvero la medesima virt&ugrave; mover&agrave; la <lb/>met&agrave; di quel corpo per tutto quello spazio nella met&agrave; di quel tempo &rdquo; (Ra&shy;<lb/>vaisson-Mollien, Manuscr. </s>

<s>F, Paris 1889, fol. </s>

<s>26). </s></p><p type="main">

<s>Le difficolt&agrave; maggiori frugavano pi&ugrave; vivamente il desiderio di sapere <lb/>il vero intorno ai moti accelerati, principalmente da poi che alcuni, imbe&shy;<lb/>vuti delle dottrine archimedee, dall'aver colto Aristotile in fallo circa ai gravi <lb/>e ai leggeri, entrarono in gran sospetto che si fosse il Filosofo parimente <lb/>ingannato, quando sentenzi&ograve; che le velocit&agrave; dei gravi cadenti son propor&shy;<lb/>zionali alla potenza dei loro pesi. </s>

<s>Sembrava che l'esperienze da farsi in mezzo <lb/>all'aria, per chiarir cos&igrave; fatti dubbii, non fossero molto pi&ugrave; difficili di quel&shy;<lb/>l'altre fatte gi&agrave; in mezzo all'acqua, ma s'ebbe presto a riconoscere l'illu&shy;<lb/>sione, quando, lasciando andare da qualche altura varie sorte di corpi, se ne <lb/>volle con gli occhi, o con poco opportuni strumenti, misurar, per compa&shy;<lb/>rarle fra loro, le varie velocit&agrave; delle cadute. </s>

<s>Il vero si nascondeva agli spe&shy;<lb/>rimentatori, or qua or l&agrave; rifuggendo ai due eccessi, intanto che, tutti allo <lb/>stesso modo ingannati in osservar le misure degli spazii e dei tempi, par&shy;<lb/>vero ad alcuni quelle misure cos&igrave; grandi da venire in conferma della legge <lb/>peripatetica, mentre altri credettero di trovarle fra loro cos&igrave; poco differenti. </s>

<s><lb/>da pronunziar la sentenza contraria, che cio&egrave; due gravi, diversamente pe&shy;<lb/>santi, giungono in cadute eguali a toccar nel medesimo istante la terra. </s></p><p type="main">

<s>Leonardo volle entrare di mezzo nella questione che, movendo al trion&shy;<lb/>fante Peripaticismo cos&igrave; nuovo e valido assalto, doveva a que'tempi agitarsi <lb/>tra'Filosofi e i Matematici con gran fervore. </s>

<s>Si facevano i Matematici forti <lb/>dell'autorit&agrave; di Archimede e anche il Nostro, bench&egrave; non dubitasse di poter <lb/>logicamente fare il trapasso dalla Statica alla Dinamica, consentendo con Ari&shy;<lb/>stotile che, cos&igrave; nelle Macchine come nelle libere cadute, fossero le velocit&agrave; <lb/>proporzionali ai momenti dei pesi, si persuase nulladimeno che il discordar <lb/>cos&igrave; come facevano l'esperienze da questa legge, dipendesse tutto acciden-<pb xlink:href="020/01/1829.jpg" pagenum="72"/>talmente dalle varie resistenze del mezzo, il quale se pu&ograve;, essendo acqua, o <lb/>impedire affatto la velocit&agrave; del galleggiante o ridurla in verso contrario; potr&agrave; <lb/>similmente, essendo aria, colla sua resistenza varia, alterare in vario modo <lb/>la velocit&agrave; del grave che discende per essa. </s>

<s>&ldquo; Sempre la potenzia del motore, <lb/>egli dice, debba essere proporzionata al peso del suo mobile, e alla resistenza <lb/>del mezzo per il quale il peso si muove. </s>

<s>Ma di tale azione non si pu&ograve; dare <lb/>scienza, se prima non si d&agrave; la quantit&agrave; della condensazione dell'aria percossa <lb/>da qualunque mobile, la quale condensazione sar&agrave; di maggiore o minor <lb/>densit&agrave; secondo la maggiore o minor velocit&agrave;, che ha in s&egrave; il mobile che la <lb/>preme, come ci mostra il volar degli uccelli, li quali, col suono delle loro <lb/>alie battendo l'aria, fanno il suono pi&ugrave; grave o pi&ugrave; acuto, secondo il pi&ugrave; <lb/>tardo o veloce moto delle loro alie &rdquo; (Manuscr. </s>

<s>E cit., fol. </s>

<s>23 ad t.). </s></p><p type="main">

<s>Per giunger dunque ad avere e a dare la desiderata scienza dell'azione <lb/>dell'aria sulle libere cadute dei corpi, attese il nostro Leonardo con solle&shy;<lb/>cito studio alle fisiche propriet&agrave; di lei, e ne consegu&igrave; in parte quella noti&shy;<lb/>zia, che s'annunzi&ograve; un secolo e pi&ugrave; dopo da Galileo e dal Torricelli per una <lb/>nuova grande scoperta. </s>

<s>L'elasticit&agrave; dell'aereo elemento intorno alla quale <lb/>si seguit&ograve; a dubitare da molti infino a mezzo il secolo XVII, veniva dimo&shy;<lb/>strata con l'esperienze medesime de'moderni negli Spiritali del Porta, e il <lb/>Cardano l'applicava, come si vedr&agrave; meglio in seguito, alla caduta dei gravi, <lb/>illustrando il sopra esposto concetto di Leonardo. </s>

<s>Quanto al peso, l'aveva <lb/>benissimo esso Leonardo riconosciuto nell'esperienza aristotelica dell'aria <lb/>condensata nel pallone di vetro, ma non si arrest&ograve; il progresso di una tale <lb/>notizia per lui, che attendeva a scoprir le fisiche propriet&agrave; di quello ele&shy;<lb/>mento, in mezzo a cui naturalmente discendono tutti i gravi. </s>

<s>L'artificiale <lb/>condensazione dell'aria stessa dentro il pallone chiuso, e la misura di lei <lb/>rivelatagli da una squisita bilancia, lo condussero, in mezzo a questi suoi prin&shy;<lb/>cipali intenti meccanici, a scoprir la naturale condensazione dell'aria per <lb/>certe sottilissime vie, delle quali, divagando un poco dal diritto nostro cam&shy;<lb/>mino, segneremo qui ai Lettori la traccia. </s></p><p type="main">

<s>Trov&ograve; dunque che un corpo intero pesa pi&ugrave; di quando sia ridotto in <lb/>frantumi, e che una fune avvolta in matassa &egrave; alquanto pi&ugrave; leggera che se <lb/>venga distesa. </s>

<s>Il fatto in s&egrave; curioso ritrov&ograve; per Leonardo una facile ragion <lb/>naturale nelle varie resistenze dell'aria, le quali si fanno o maggiori o mi&shy;<lb/>nori, secondo che maggiore o minore &egrave; il volume del corpo, o &egrave; pi&ugrave; o men <lb/>lata la superficie dell'immersione. </s>

<s>Quando per esempio la fune &egrave; avvolta, <lb/>la resistenza s'estende a tutta la superficie della matassa, mentre, quando <lb/>&egrave; distesa, non trova altra resistenza che nel suo infimo capo, a quel modo <lb/>che resiste l'acqua solamente contro la piccola base inferiore di un lungo <lb/>e sottil cilindro, che s'immerga nel vaso. </s>

<s>&ldquo; Molti piccoli corpi ponderosi, <lb/>cos&igrave; scrive il Nostro, giunti insieme uniti fieno di maggior peso che a essere <lb/>separati: cio&egrave;, se torrai raspatura di piombo o vetro pesto e pesali, e poi <lb/>li fondi insieme, troverai questi essere cresciuti &rdquo; (Manuscr. </s>

<s>A cit., fol. </s>

<s>4). <lb/>E in un'altra Nota: &ldquo; se peserai una corda distesa, e poi la pesi avvolta, tro-<pb xlink:href="020/01/1830.jpg" pagenum="73"/>verai di maggior peso la distesa che l'avvolta, perch&egrave; l'avvolta trova mag&shy;<lb/>gior resistenza &rdquo; (ivi, fol. </s>

<s>34). </s></p><p type="main">

<s>Ora in queste cos&igrave; delicate e minuziose esperienze, ripetute da Leo&shy;<lb/>nardo in tanti modi e tante volte, ebbe a trovare con sua grande sorpresa <lb/>che, da un giorno a un altro, e da una stagione a un'altra, il peso sulla <lb/>Bilancia variava, ci&ograve; che, essendo i corpi medesimi, e medesimi i modi del <lb/>trattarli, non poteva attribuirsi ad altro, che a qualche variazione subita nella <lb/>densit&agrave; dell'aria, e perci&ograve; nel peso dell'atmosfera. </s>

<s>E perch&egrave; osserv&ograve; che suc&shy;<lb/>cedevano cos&igrave; fatte variazioni spesso al variarsi lo stato del cielo, da sereno <lb/>per esempio a piovoso, gli si ebbe facilmente a trasformare quella delica&shy;<lb/>tissima bilancia delle esperienze in un vero e proprio <emph type="italics"/>Barometro.<emph.end type="italics"/> Tale &egrave; <lb/>per noi quello strumento <emph type="italics"/>da conoscere la costituzione e la densit&agrave; dell'aria, <lb/>e quand'&egrave; che il tempo si dispone alla pioggia,<emph.end type="italics"/> pubblicato dal Venturi <lb/>nel &sect; XIII del suo <emph type="italics"/>Essai<emph.end type="italics"/> (pag. </s>

<s>28), e da lui, perch&egrave; forse credeva non poter <lb/>Leonardo giungere a tanto, giudicato, come quello dell'Alberti o di altri pi&ugrave; <lb/>antichi, un Igrometro. </s></p><p type="main">

<s>Le vie dall'altra parte, che condussero il Nostro a partecipare alla <lb/>grande invenzione del Torricelli, come noi le abbiamo investigate; son na&shy;<lb/>turali, n&egrave; mancherebbero altre simili esperienze a confermar questa fede <lb/>nei dubitanti. </s>

<s>Candido Del Buono scopr&igrave; nell'Accademia del Cimento come <lb/>un corpo caldo ha sulla bilancia maggior leggerezza ch'essendo freddo. </s>

<s>Il <lb/>fatto era stato scoperto lungo tempo prima, e sperimentato dal Nostro, il <lb/>quale not&ograve; cos&igrave; nelle pagine di un suo manoscritto: &ldquo; Sperimento come <lb/>il caldo fa lieve i corpi ponderosi. </s>

<s>&mdash; L'una delle due cose di pari peso <lb/>posta sopra la bilancia, quella che fia infocata fia pi&ugrave; lieve che l'altra fredda. </s>

<s><lb/>Questa prova farai con due pallotte di rame appiccate a due fili di ferro <lb/>colle bilance. </s>

<s>L'una delle due metti in foco, e fa'rovente, e quando dal <lb/>foco &egrave; fatta rossa tirala fuori dal foco, acciocch&egrave; il vapore del calore che si <lb/>leva non ispingessi in alto il peso, e vederai che quella pallotta, che prima <lb/>essendo fredda era di pari peso coll'altra, esser per lo calore fatta leggera &rdquo; <lb/>(Manuscr. </s>

<s>A cit., fol. </s>

<s>57). </s></p><p type="main">

<s>Il Borelli ridusse questa medesima esperienza, rimasta una semplice <lb/>curiosit&agrave; nel Del Buono, a farsi dimostrativa del peso dell'aria, alterato dal&shy;<lb/>l'azion del calore, nella proposizione LXI <emph type="italics"/>De motionibus naturalibus,<emph.end type="italics"/> dal&shy;<lb/>l'Autore stesso cos&igrave; formulata: &ldquo; Trutinae aequilibratae una lanx excalefacta, <lb/>sursum elevatur, extrusa a pondere aeris, reliquam lanceam ambientis. </s>

<s>&rdquo; Ora <lb/>era naturalissimo che Leonardo, tutto intento a studiare gli effetti della den&shy;<lb/>sit&agrave; dell'aria ne'moti naturali, attribuisse il fatto della leggerezza de'corpi <lb/>caldi alle cause medesime, alle quali gli veniva attribuendo il Borelli, e che <lb/>perci&ograve; gli conferisse anco questa notizia per l'invenzione dello strumento, <lb/>da conoscer le varie costituzioni dell'atmosfera. </s></p><p type="main">

<s>Comunque sia di ci&ograve;, ritornando al proposito nostro, vedremo quel che <lb/>decidesse Leonardo, in ordine alla fervorosa questione insorta a'suoi tempi <lb/>delle velocit&agrave;, con cui scendono i corpi di vario peso e d'ugual materia la-<pb xlink:href="020/01/1831.jpg" pagenum="74"/>sciati andare da una medesima altezza. </s>

<s>La sentenza si trova cos&igrave; decisamente <lb/>scritta dall'Autore in questa sua Nota: &ldquo; Se due palle di una medesima <lb/>materia, che l'una sia il doppio peso dell'altra, cadendo in un tempo da <lb/>una medesima altezza, non cader&agrave; prima altrettanto tempo la maggiore che <lb/>la minore &rdquo; (Manuscr. </s>

<s>A cit., fol. </s>

<s>34). </s></p><p type="main">

<s>La matematica scienza del moto non poteva per&ograve; contentarsi di una <lb/>sentenza la quale, bench&egrave; sia cos&igrave; pronunziata in forma assoluta, si riteneva <lb/>nonostante dalla sola parte negativa; ond'&egrave; che volendo il coscienzioso scien&shy;<lb/>ziato adempire al debito suo, formul&ograve; dietro l'esperienze, e dietro i calcoli <lb/>della resistenza opposta dall'aria al velocitarsi dei gravi cadenti, una nuova <lb/>legge, la quale stava di mezzo fra quella insegnata da Aristotile, e l'altra <lb/>riformata dai Matematici novelli. </s>

<s>Dicevano questi che se caderanno da una <lb/>medesima altezza due corpi sferici d'ugual materia, ma l'un de'quali abbia <lb/>doppio diametro dell'altro, le velocit&agrave; della loro discesa in ogni modo sa&shy;<lb/>ranno uguali. </s>

<s>I Peripatetici invece, volendo mantenere per assolutamente <lb/>vera la sentenza del loro Maestro, affermavano che, dovendo essere le velo&shy;<lb/>cit&agrave; proporzionali ai pesi, i quali stanno nei corpi sferici come i cubi dei <lb/>raggi, dee dunque la maggiore e pi&ugrave; ponderosa sfera scendere otto volte <lb/>pi&ugrave; veloce della minore. </s>

<s>Leonardo ne conclude che le disputate differenze <lb/>delle velocit&agrave;, negli esempii citati, non sono n&egrave; cos&igrave; piccole da reputarsi per <lb/>nulle, n&egrave; son cos&igrave; grandi, che stieno come i cubi, ma come i semplici raggi <lb/>delle sfere, o come i loro diametri. </s>

<s>&ldquo; Se cader&agrave; dall'alto in basso due di&shy;<lb/>seguali corpi sferici, e ponderosi d'egual materia e caduta, tanto cader&agrave; pi&ugrave; <lb/>presto l'uno che l'altro, quanto il diametro dell'uno entra nell'altro &rdquo; (ivi, <lb/>fol. </s>

<s>32). </s></p><p type="main">

<s>Ecco data cos&igrave; scienza dell'azion dell'aria sulle cadute de'corpi: frutto <lb/>di lunghi calcoli e di pazientissime esperienze. </s>

<s>Riman per&ograve; tuttavia fermo <lb/>nella mente di Leonardo l'assoluto principio aristotelico, che cio&egrave; <emph type="italics"/>sempre <lb/>la potenzia del motore debba essere proporzionata al peso del suo mobile.<emph.end type="italics"/><lb/>Cerca perci&ograve; nuove esperienze, che gli confermino la creduta verit&agrave; di cos&igrave; <lb/>fatto principio, e facilmente le trova ne'doviziosi ripostigli del suo ingegno <lb/>inventivo. </s>

<s>Se si scelgano tali figure di corpi, cos&igrave; fra s&egrave; ragionava, nelle <lb/>quali, aumentandosi il peso, la resistenza fatta a loro dall'aria rimanga sem&shy;<lb/>pre la stessa, dovr&agrave; in tal caso verificarsi esattamente quella legge, che ve&shy;<lb/>niva dianzi alterata nelle forme sferiche, per non potersi in esse moltiplicar <lb/>cos&igrave; la quantit&agrave; di materia, che non si venga anche insieme ad aumentare <lb/>la superfice del resistente. </s>

<s>I cilindri e i prismi si possono quanto si vuole <lb/>crescer di peso, allungandoli sulla medesima base, e saranno perci&ograve; cos&igrave; fatte <lb/>figure opportunissime per l'esperienze, perch&egrave;, presa per esempio un'asta <lb/>lunga tre braccia, e segata in due pezzi, l'uno d'un braccio e l'altro di due, <lb/>se si lasceranno questi due pezzi cadere da una medesima altezza, e per lo <lb/>lungo, cosicch&egrave; avendo le basi eguali trovino nel fender l'aria le resistenze <lb/>pure eguali; quel di due braccia andr&agrave; doppiamente veloce di quell'altro. </s>

<s><lb/>La teoria, pensa Leonardo stesso, che debba esattamente riscontrare con <pb xlink:href="020/01/1832.jpg" pagenum="75"/>l'esperienza. </s>

<s>&ldquo; Se dividerai, egli dice, uno pezzo d'asta di tre braccia d'eguale <lb/>grossezza e peso in due parti, e l'un de'pezzi sia due braccia e l'altro uno <lb/>braccio, e lascieraigli cadere per ritto in un medesimo tempo da una me&shy;<lb/>desima altezza, cader&agrave; altrettanto pi&ugrave; presto l'uno che l'altro &rdquo; (ivi, fol. </s>

<s>34). </s></p><p type="main">

<s>Ma perch&egrave; nessun creda ch'egli siasi in cos&igrave; pensare ingannato, descrive <lb/>altrove i modi pi&ugrave; particolari dell'esperienza, e par che inviti scongiurando <lb/>i lettori a ripeterla, perch&egrave; si persuadano co'loro proprii occhi che cos&igrave;, <lb/>com'ei la trova di fatto e la descrive, sta propriamente la cosa. </s>

<s>&ldquo; Se vuoi <lb/>provare quanto cade pi&ugrave; presto uno peso d'una oncia che uno di due once, <lb/>cadendo da una medesima altezza, farai cos&igrave;: Piglia due pezzi di sughero <lb/>d'una medesima grossezza e di duplicata lunghezza, cio&egrave; che quello che pesa <lb/>due once sia pi&ugrave; lungo altrettanto che l'altro, e falli gittare a uno dall'al&shy;<lb/>tezza di un campanile, in un medesimo tempo, e poni l'occhio a quello mi&shy;<lb/>nore che rimane indietro, notando con l'occhio i segni del muro, ovver delle <lb/>pietre d'onde passa, e quando sentirai dare il botto in terra delle due once, <lb/>nota in qual pietra del campanile il peso d'un oncia s'incontrava, e poi mi&shy;<lb/>sura quanta via aveva fatta l'oncia, quando le due once dettono il botto in <lb/>terra &rdquo; (ivi, fol. </s>

<s>30 ad t.). </s></p><p type="main">

<s>Raccogliesi da tali autentici documenti che i progressi fatti da Leo&shy;<lb/>nardo, in questa parte della scienza del moto, consistono unicamente nel&shy;<lb/>l'aver considerata e calcolata l'azione dell'aria, che accidentalmente perturba <lb/>la legge peripatetica, da lui stesso ritenuta per certa, delle velocit&agrave; propor&shy;<lb/>zionali alle quantit&agrave; della materia. </s>

<s>Per quelle considerazioni per&ograve;, se pot&egrave; <lb/>vantaggiarsene la Fisica o la Meteorologia, la Dinamica si rimase immobile <lb/>nell'errore antico, come si rimase pure immobile in esso, per Leonardo, <lb/>quand'ei si propose di passare a sciogliere quest'altro quesito: &ldquo; Se uno <lb/>peso cade dugento braccia, quanto cader&agrave; elli pi&ugrave; presto le seconde cento <lb/>braccia, che le prime? </s>

<s>&rdquo; (ivi, fol. </s>

<s>32 ad t.). </s></p><p type="main">

<s>La soluzione, che se ne dava allora da tutti, e che dur&ograve; a darsi da tutti <lb/>fino ai tempi di Galileo, aveva il suo fondamento sopra l'esperienza della <lb/>percossa, tanto in s&egrave; lusinghiera che nessuno ancora sospettava della falla&shy;<lb/>cia. </s>

<s>Si teneva dunque per certissimo che la maggiore o minor trafitta di&shy;<lb/>pendesse dalla maggiore o minor velocit&agrave; del percuziente, o dalla maggiore <lb/>o minore altezza della discesa, la quale, essendo per esempio doppia, ren&shy;<lb/>desse precisamente sul percosso doppio il suo effetto. </s>

<s>Cos&igrave; venivano lusin&shy;<lb/>gandosi i Matematici di avere sperimentalmente conclusa la legge, che le <lb/>velocit&agrave;, nelle naturali cadute dei gravi, son semplicemente proporzionali agli <lb/>spazii. </s></p><p type="main">

<s>Non seppe dal numero dei lusingati sottrarsi nemmeno il nostro Leo&shy;<lb/>nardo, il quale, in una sua Nota, lasciavaci cos&igrave; scritto: &ldquo; Per definire il <lb/>discenso o inegualit&agrave; degl'intervalli delle ballotte dico in prima, per la IX di <lb/>questo, che il discenso di ciascuna ballotta, dividendolo a gradi eguali per <lb/>altezza, che in ogni grado di esso moto essa ballotta acquista un grado di <lb/>velocit&agrave;, onde questa tale proporzione di gradi di velocit&agrave; fia proporzione <pb xlink:href="020/01/1833.jpg" pagenum="76"/>continua arismetrica, perch&egrave; si proporziona insieme li eccessi ovver differen&shy;<lb/>zie delle velocit&agrave;. </s>

<s>Onde concludo che tali spazii saranno eguali, perch&egrave; sem&shy;<lb/>pre eccedono ovver superano l'uno l'altro con eguale accrescimento &rdquo; (Libri, <lb/>Histoire cit., T. III, pag. </s>

<s>212). </s></p><p type="main">

<s>Persuaso che l'assegnata proporzione aritmetica fra gli spazii e i tempi <lb/>fosse la vera, pensava Leonardo stesso a renderla con qualche ingegno evi&shy;<lb/>dente, ci&ograve; ch'ei pensava potersi fare nella seguente maniera: &ldquo; Caccia ven&shy;<lb/>ticinque pallotte d'egual peso in un cannone, in modo che stiano una sopra <lb/>l'altra perpendicolari, e mettile in un luogo alto, e distoppa con un filo, e <lb/>sta'da pi&egrave;, ma el moto non ti lascer&agrave; conoscere gli spazii puri. </s>

<s>E cos&igrave; se <lb/>AB (fig. </s>

<s>39) ha fatto in un grado di tempo un grado di discenso, BC, per <lb/>essere pi&ugrave; veloce, avr&agrave; fatto un grado di pi&ugrave; di moto, e cos&igrave; CD, per essere <lb/>pi&ugrave; veloce, e v&agrave; seguitando &rdquo; (Del moto delle acque cit., pag. </s>

<s>363). </s></p><p type="main">

<s>La proposta era bella, quando non fosse per&ograve; venuto a guastarla quella <lb/>massima difficolt&agrave;, confessata dallo stesso Proponente, che cio&egrave; il moto troppo <lb/><figure id="id.020.01.1833.1.jpg" xlink:href="020/01/1833/1.jpg"/></s></p><p type="caption">

<s>Fig.39.<lb/><figure id="id.020.01.1833.2.jpg" xlink:href="020/01/1833/2.jpg"/></s></p><p type="caption">

<s>Figura 40.<lb/>veloce non lasciava all'osservatore co&shy;<lb/>noscere gli spazii puri. </s>

<s>Si dette dunque <lb/>Leonardo a pensare a un modo come si <lb/>potesse arrestare il moto delle pallotte, <lb/>nell'atto stesso che ritenevano una certa <lb/>natural proporzione gl'intervalli del loro <lb/>discenso, cosicch&egrave;, colte in tale stato di <lb/>quiete, se ne potesse a bell'agio, e pre&shy;<lb/>cisamente come stavano in natura, ritro&shy;<lb/>var le misure. </s>

<s>L'invenzione, che ha per <lb/>verit&agrave; pi&ugrave; del capriccio che dell'ingegno, <lb/>&egrave; descritta dall'Autore in questo modo: <lb/>&ldquo; Sia posta in piedi per linea perpen&shy;<lb/>dicolare l'asse MN (fig. </s>

<s>40), e sia, con <lb/>terra mista con cimatura, bene interrata, <lb/>alla quale sia congiunto, ad uso di libro, <lb/>l'asse OP, e si possa serrare subito con <lb/>due corde come vedi, ed all'estremo di <lb/>essa asse interrata sia messo il pi&egrave; d'una <lb/>cerbottana, stoppata da pi&egrave; e piena di pallotte <lb/>di egual peso e figura. </s>

<s>Poi, ferma bene la cer&shy;<lb/>bottana e l'asse interrata, subito lascia andare il contrappeso, e le due asse <lb/>si serreranno, e le pallotte che cadevano tutte si ficcheranno in essa terra, <lb/>e potrai poi misurare la proporzione della variet&agrave; delli loro intervalli &rdquo; (ivi, <lb/>pag. </s>

<s>364). </s></p><p type="main">

<s>Se fosse stata questa esperienza messa dall'Inventore in pratica, e avesse <lb/>ottenuto l'effetto che s'immaginava, si sarebbe dovuto senza dubbio togliere <lb/>da quell'inganno, in cui persisteva, perch&egrave; gl'intervalli delle pallotte, rima&shy;<lb/>ste murate nell'assicella, gli avrebbero facilmente mostrato di serbar fra loro <pb xlink:href="020/01/1834.jpg" pagenum="77"/>una proporzione assai diversa dall'aritmetica. </s>

<s>Ma i principii, da concluderne <lb/>la vera legge della caduta dei gravi, non erano nella Scienza dinamica an&shy;<lb/>cora posti, e l'error della mente affascinava anche a Leonardo lo stesso <lb/>chiaro lume degli occhi. </s>

<s>Il fatto mirabilmente conferma la legge logica del <lb/>pensiero, alla quale doveva naturalmente soggiacere anche il Nostro, che <lb/>cio&egrave; non si d&agrave; progresso, dove mancano le tradizioni, come non si d&agrave; svol&shy;<lb/>gimento organico della vita vegetativa o della animale, dove manchino i <lb/>germi. </s>

<s>L'esperienza stessa, e sia pur diligente e destra, non vale, come non <lb/>vale a un campo non seminato qualunque pi&ugrave; sottile arte della cultura. </s>

<s>Dove <lb/>per&ograve; un germoglio si giace abbandonato e latente, in qualche pi&ugrave; remota <lb/>parte del suolo, chi n'ha l'industria l'educa, e pare ai meno esperti o ai <lb/>negligenti che abbia nelle sterili zolle, quella mano educatrice, miracolosa&shy;<lb/>mente infusa la vita. </s>

<s>Nel soggetto, che &egrave; della caduta dei gravi, ci offre Leo&shy;<lb/>nardo stesso di ci&ograve; che si dice per allegoria il pi&ugrave; proprio e pi&ugrave; notabile <lb/>esempio, in cui pur si verifica che, se al venirgli meno la scienza dei mag&shy;<lb/>giori v&agrave; brancolando anch'egli per le tenebre insieme con gli altri; l&agrave; dove, <lb/>di quella scienza prefulgevali un raggio, ebbe pi&ugrave; acuta vista di Calileo. </s></p><p type="main">

<s>Ritorniamo indietro a ripensare al nostro sperimentatore, che ora sale <lb/>sull'alta cima di un campanile, per lasciar di l&igrave; cadere a terra le variamente <lb/>ponderose sfere di piombo, e i prismi di sughero; ora, affidato ad altri il <lb/>manuale ufficio, scende a pi&egrave; della torre, per osservar colla pi&ugrave; grande at&shy;<lb/>tenzione quanto l'uno de'cadenti scenda pi&ugrave; veloce dell'altro. </s>

<s>Un fatto sin&shy;<lb/>golarissimo ebbe a notare in queste esperienze, ed era che si vedeva il grave <lb/>andare a battere un po'in distanza dalla base della torre, cosicch&egrave; sempre <lb/>dava in terra quel che pareva piuttosto dover dare a dirittura nel muro. </s>

<s><lb/>S'aggiungeva costantemente al fatto che la divergenza del punto della ca&shy;<lb/>duta dal perpendicolo rimaneva dalla plaga orientale, ci&ograve; che facilmente fece <lb/>nascere nell'arguto Osservatore il sospetto, che s'avesse la causa del suo <lb/>stupore a riconoscer nel moto circonvolubile della Terra. </s></p><p type="main">

<s>S'applic&ograve; pertanto Leonardo con tutto il suo studio a ritrovare una con&shy;<lb/>ferma e una dimostrazione delle sue congetture nella Meccanica, e in simili <lb/>altri fatti rappresentabili per esperienze. </s>

<s>Le fila della pioggia, che mostrano <lb/>scendere obliquamente dall'alto a chi di rincontro a loro cammina, furono <lb/>forse il principio alle idee, che si svolsero in quell'acuto meditativo pen&shy;<lb/>siero. </s>

<s>Ei volle ad arte sottoporsi quelle piovose fila alla pi&ugrave; comoda contem&shy;<lb/>plazione, facendo fluir l'acqua dal sottil foro di un vaso, ora equabilmente <lb/>mosso, ora tenuto fermo, e mosso invece il soggiacente piano, che ha da <lb/>ricever l'artificiosa pioggia cadente. </s>

<s>In una Nota, che s'intitola <emph type="italics"/>Del moto <lb/>dell'immobile, che versa con moto continuo sopra sito mobile; ovvero es&shy;<lb/>sendo mobile quel che versa;<emph.end type="italics"/> cos&igrave; si legge: &ldquo; Il moto del liquido il qual <lb/>versa per il fondo del vaso mobile sar&agrave; per linea retta situata per obliquo, <lb/>la quale obliquit&agrave; fia di tanto maggiore o minore declinazione, quanto il <lb/>moto del vaso che la genera sar&agrave; di maggiore o minore velocit&agrave; &rdquo; (Ravais&shy;<lb/>son-Mollien, Manuscr. </s>

<s>G, Paris 1890, fol. </s>

<s>54). </s></p><pb xlink:href="020/01/1835.jpg" pagenum="78"/><p type="main">

<s>Si vede a illustrar questa Nota disegnato in margine il vaso che, stando <lb/>quieto verserebbe verticalmente il filo liquido AB (fig. </s>

<s>41), mentre mosso <lb/><figure id="id.020.01.1835.1.jpg" xlink:href="020/01/1835/1.jpg"/></s></p><p type="caption">

<s>Figura 41.<lb/>in direzion parallela al piano orizzontale BC fa risultarne, <lb/>da'due composti insieme, il moto obliquo AC, ch'&egrave; la dia&shy;<lb/>gonale del rettangolo costruito. </s>

<s>Passando a farne poi la me&shy;<lb/>ditata applicazione, vedeva Leonardo in quel vaso la Terra <lb/>ch'&egrave; il recipiente di tutti i gravi cadenti; la sublimit&agrave; del <lb/>foro di efflusso gli rappresentava l'altezza della Torre, che si <lb/>muove in oriente sul suo piano terrestre, e la linea BC gli <lb/>misurava la distanza orientale che fa dal perpendicolo il punto, <lb/>dove v&agrave; a battere il grave caduto dalla sommit&agrave; dell'edifizio. </s></p><p type="main">

<s>Supponiamo, cos&igrave; di speculazione in speculazione si con&shy;<lb/>duceva l'alta mente di Leonardo, che il grave non trovi in <lb/>C impedimento, n&egrave; in altro piano pi&ugrave; profondo, ma libero <lb/>prosegua la sua discesa; qual sar&agrave; il termine e la linea del suo viaggio? </s>

<s>A <lb/>risolvere il nuovo arduo problema, che illuse il gran Galileo al ritentarne <lb/>che fece un secolo dopo la prova, il Nostro si chiar&igrave; bene della verit&agrave; di un <lb/>principio meccanico, illustrato verso la met&agrave; del secolo XVII dal Gassendo, <lb/>sotto il nome <emph type="italics"/>Del moto impresso dal motore traslato.<emph.end type="italics"/> Propostosi questo <lb/>principio da cui n'ebbe a concludere che, rivolgendosi attorno la Terra con <lb/>gli elementi, la linea della libera caduta &egrave; sempre retta, riusc&igrave; il nostro Mate&shy;<lb/>matico a dimostrare che la risultante di questo moto diretto e del circonvo&shy;<lb/>lubile, a cui soggiace nello scendere il grave, &egrave; un'elica, che parte dal prin&shy;<lb/>cipio del moto stesso per ritornar continua al centro del mondo. </s></p><p type="main">

<s>Tanta parte di scienza pellegrina, e che si direbbe davvero una crea&shy;<lb/>zione da chi non considera in Leonardo il discepolo di Archimede, &egrave; come <lb/>lampo di viva luce riflessa da questa Nota: <emph type="italics"/>&ldquo; Del moto della freccia so-<emph.end type="italics"/><lb/><figure id="id.020.01.1835.2.jpg" xlink:href="020/01/1835/2.jpg"/></s></p><p type="caption">

<s>Figura 42.<lb/><emph type="italics"/>spinta dall'arco.<emph.end type="italics"/> La freccia tratta dal centro <lb/>del mondo alla suprema parte degli elementi <lb/>s'alzer&agrave; e discender&agrave; per una medesima linea <lb/>retta, ancorch&egrave; li elementi sieno in moto circon&shy;<lb/>volubile intorno al centro degli elementi. </s>

<s>&mdash; La <lb/>gravit&agrave;, che per li circonvolubili elementi di&shy;<lb/>scende, sempre ha il suo moto per la rettitudine <lb/>di quella linea, che dal principio del moto al <lb/>centro del mondo si estende. </s>

<s>&mdash; Le otto linee <lb/>(fig. </s>

<s>42) colle otto divisioni, nelle quali esse son <lb/>compartite, hanno a dimostrare una sola linea, <lb/>e quella &egrave; retta, per la quale il peso, che per <lb/>li circonvolubili elementi dicende, passa per cia&shy;<lb/>scuna delle otto sue partizioni, la qual linea al fine ritorna al medesimo sito <lb/>d'onde ella si divise. </s>

<s>Il moto del grave ha dupla denominazione, cio&egrave; cur&shy;<lb/>vit&agrave;, elica rettilinea &rdquo; (Manuscr. </s>

<s>G cit., fol. </s>

<s>54). </s></p><p type="main">

<s>In un'altra Nota descrive, pi&ugrave; particolarmente cos&igrave;, il moto del grave, <pb xlink:href="020/01/1836.jpg" pagenum="79"/>a dimostrar che la linea passata da lui &egrave; veramente l'elica sopraddetta: <lb/>&ldquo; Il mobile discendente dalla suprema parte della sfera del fuoco far&agrave; moto <lb/>retto infino alla Terra, ancora che li elementi fussero in continuo moto cir&shy;<lb/>convolubile intorno al centro del mondo. </s>

<s>Provasi, e sia che il grave che <lb/>discende per li elementi sia B, (nella precedente figura XLII) che si mova <lb/>dall'A, per discendere al centro del mondo M. </s>

<s>Dico che tal grave, ancora <lb/>che facci discenso curvo a modo di linea elica, che mai si svier&agrave; dal suo <lb/>discenso rettilineo, il quale &egrave; in continuo processo infra il loco, d'onde si <lb/>divise, al centro del mondo, perch&egrave; se si part&igrave; dal punto A e discese al B, <lb/>nel tempo che discese in B e fu portato in D, il sito della A &egrave; scivolato <lb/>in C, e cos&igrave; D mobile si trova nella rettitudine che s'estende infra C e il <lb/>centro del mondo M. </s>

<s>Se il mobile discende dal D all'F, C principio del <lb/>moto, in nel medesimo tempo, si move dal C all'E; e se F discende in H, <lb/>e'si volta in G, e cos&igrave; in ventiquattr'ore il mobile discende alla Terra sotto <lb/>il loco d'onde prima si divise, e tal moto &egrave; composto. </s>

<s>Se il mobile discende <lb/>dalla suprema all'infima parte degli elementi in ventiquattr'ore, il moto suo <lb/>fia composto di retto e curvo.. Retto dico, perch&egrave; mai non si svier&agrave; dalla <lb/>linea brevissima, che s'estende dal loco d'onde si divise al centro degli ele&shy;<lb/>menti, e si fermer&agrave; nello stremo infimo di tal rettitudine, la qual sempre <lb/>sta per zenit sotto il loco, d'onde tal mobile si divise. </s>

<s>E tal moto in s&egrave; &egrave; <lb/>curvo con tutte quante le parti della linea, e per conseguenza &egrave; al fine curvo <lb/>con tutta la linea. </s>

<s>E di qui nasce che il sasso gettato dalla Torre non per&shy;<lb/>cota nel lato d'essa Torre, prima che in terra &rdquo; (ivi, fol. </s>

<s>55). </s></p><p type="main">

<s>Accennammo di sopra che nelle nuove Istituzioni della Scienza mecca&shy;<lb/>nica Galileo concluse dal principio della composizione dei moti la natura <lb/>della curva, che descriverebbe il mobile menato in volta dalla rotazion della <lb/>Terra, mentre egli tende a scendere al centro con velocit&agrave; accelerata, e disse <lb/>che probabilmente doveva quella tal curva essere un mezzo cerchio. </s>

<s>L'er&shy;<lb/>rore incredibile in tale e tanto Maestro lev&ograve; un grande scandolo nel mondo <lb/>della scienza, a rimediare al quale non giovarono n&egrave; le scuse dello stesso <lb/>Galileo, n&egrave; lo zelo de'suoi discepoli, che fecero per verit&agrave; peggio che mai a <lb/>dire essere quelle cose, nel II dialogo dei Due massimi sistemi, state scritte <lb/>dall'Autore per celia. </s>

<s>Dovevano invece confessare che l'origine di un tale er&shy;<lb/>rore proveniva dall'inesperienza del risolvere e del comporre insieme due moti, <lb/>per cui non pot&egrave; Galileo stesso accorgersi della fallacia ascosta nell'ammetter <lb/>che resultasse in mezzo cerchio un moto misto del circolare e del retto. </s></p><p type="main">

<s>Se dunque l'Autore delle sopra recate Note manoscritte pot&egrave;, in un se&shy;<lb/>colo in cui si disse che la Meccanica non era nata, restar di tanto superiore <lb/>al gran Galileo nel rappresentar per un elice la linea descritta dai corpi <lb/>gravi cadenti, va principalmente di tutto ci&ograve; debitore a quella perizia, che <lb/>egli ebbe nel trattar la regola della diagonale ne'rettangoli, e nei paralle&shy;<lb/>logrammi. </s>

<s>Nasce altres&igrave; dall'uso di questa regola la superiorit&agrave; che ottenne <lb/>il Matematico di Vinci sopra quello di Arcetri, non solo per rispetto alla <lb/>proposizion principale di che si tratta, ma agli stessi corollarii di lei. </s></p><pb xlink:href="020/01/1837.jpg" pagenum="80"/><p type="main">

<s>Galileo, dal moversi realmente in circolo il grave che scende, ne con&shy;<lb/>cluse il paradosso che l'accelerazione, veduta farsi da lui in linea retta, non <lb/>era che un'illusione, mentre Leonardo, con grande maraviglia di chi vi pensa, <lb/>argoment&ograve; da quel moto la ragione di un fatto, che veniva inaspettatamente <lb/>a confermar le ragionevoli congetture della rotazione terrestre. </s>

<s>Tanto poi <lb/>pi&ugrave; cresce una tal maraviglia in chi rammemora i lunghi e faticosi progressi <lb/>fatti dalla scienza, prima di giungere a scoprir quella deviazione orientale <lb/>nella caduta dei gravi, che s'era gi&agrave; rivelata da due secoli e mezzo alle teo&shy;<lb/>rie e alle esperienze di Leonardo da Vinci. </s></p><p type="main">

<s>Andate quelle esperienze e quelle teorie in dimenticanza, con la mag&shy;<lb/>gior parte delle tradizioni scientifiche del secolo XVI, s'incominciarono sotto <lb/>false apparenze a rivelar di nuovo, poco prima che giungesse alla sua met&agrave; <lb/>il secolo appresso, alle osservazioni, che sul cader dei gravi dalla sommit&agrave; <lb/>del campanile di Pisa, institu&igrave; nel 1641 Vincenzio Renieri. </s>

<s>Accortosi che, <lb/>accelerandosi il moto, le sfere gravi incominciavano a non scender pi&ugrave; a <lb/>perpendicolo, attribu&igrave; l'effetto alla resistenza del mezzo (Alb. </s>

<s>X, 410, 11), <lb/>di che apertosene con Galileo gli fu da lui risposto osservasse meglio, perch&egrave; <lb/>forse quel deviar del grave dal suo cadente era una illusione (ivi, pag. </s>

<s>144). <lb/>Nel 1679 in Inghilterra si verific&ograve; che il Renieri non s'era punto illuso, ma <lb/>l'Hook attribu&igrave; il fatto a una causa molto diversa. </s>

<s>Un secolo appresso il <lb/>D'Alembert in Francia dimostr&ograve; che, rivolgendosi la Terra attorno, un corpo <lb/>lanciato verso il zenit non dovrebbe, tornando in gi&ugrave;, dare esattamente nel <lb/>punto da cui s'era partito. </s>

<s>Fu la congettura confermata da G. B. </s>

<s>Gugliel&shy;<lb/>mini nel 1791, facendo in Bologna cadere i gravi dalla cima della Garisenda, <lb/>ond'ei raccolse dalle sue esperienze una tale celebrit&agrave;, da non si potere egua&shy;<lb/>gliare a quella, che l'antico Leonardo sarebbesi meritata. </s></p><p type="main">

<s>Ha questo tratto di storia in s&egrave; tanto del maraviglioso, da dare, in cosa <lb/>s&igrave; remota dai sensi, giusto motivo a coloro, che attribuirono al precursore <lb/>dell'Hook, del D'Alembert e del Guglielmini il titolo di divino, ma noi di <lb/>tale esagerata eccellenza scoprimmo le cause naturali nelle antoriori prepa&shy;<lb/>razioni, ch'ebbe la scienza dell'uomo ammirato, al mancar delle quali ci <lb/>hanno provato i fatti esser venuta meno ogni adorata divinit&agrave; dell'ingegno. </s>

<s><lb/>Que'fatti, che ci hanno fin qui servito di prova all'intento, concernevano la <lb/>legge della caduta dei gravi, dalla quale dipendendo la legge dei proietti <lb/>siam sicuri di trovare in ordine ad essa Leonardo non sorvolar coll'ingegno <lb/>agli errori, che si commettevano dai Matematici de'suoi tempi. </s></p><p type="main">

<s>Era il primo di quegli errori che la traiettoria andasse, per qualche <lb/>tratto dal suo principio, in linea retta, cosicch&egrave;, ne'tiri di punto in bianco, <lb/>procedesse il proietto, appena uscito dall'obice, per esattissima linea oriz&shy;<lb/>zontale. </s>

<s>Conseguiva da ci&ograve; che dovesse il proietto stesso, per qualche tempo, <lb/>sottrarsi alla sua gravit&agrave; naturale, e Leonardo, insieme con gli altri, non <lb/>dubit&ograve; di ammetter per vera una tale falsissima conclusione. </s>

<s>&ldquo; Ogni grave, <lb/>egli dice, che si muove per il sito della egualit&agrave;, non pesa se non per la <lb/>linea del suo moto. </s>

<s>Provasi nella prima parte che fa il moto della pallotta <pb xlink:href="020/01/1838.jpg" pagenum="81"/>della bombarda, il quale moto &egrave; nel sito della egualit&agrave; &rdquo; (Manuscr. </s>

<s>G cit., <lb/>fol. </s>

<s>77). Rallentandosi poi la prima concepita foga, il proietto comincia a <lb/>declinare per una linea curva, creduta anche dal Nostro simile a un'arco <lb/>di cerchio, per ridursi finalmente alla linea verticale, come tutti i gravi na&shy;<lb/>turalmente cadenti. </s>

<s>Volendo infatti insegnare a conoscere quanto sia tratto <lb/>il vino pi&ugrave; alto o pi&ugrave; basso dal rinchiuso vasello, dice che si riceva il vino <lb/>stesso &ldquo; quando &egrave; caduto fuori del vasello, e dopo che la sua curvazione <lb/>s'&egrave; ridotta alquanto perpendicolare linea &rdquo; (Manuscr. </s>

<s>C cit., fol. </s>

<s>6 ad t.). </s></p><p type="main">

<s>La traiettoria dunque sarebbe per Leonardo una curva, che comincia e <lb/>termina per linea retta, ma la questione cos&igrave;, secondo le idee di que'tempi, <lb/>dall'Autor risoluta, riguardava piuttosto la teoria che la pratica, alla quale <lb/>principalmente importava di saper qual'&egrave;, in essa traiettoria, il punto a cui <lb/>corrisponde la massima percossa. </s>

<s>Il Nostro determina giusto quel punto nel <lb/>mezzo del cammin retto, fatto per l'aria dal corpo ponderoso. </s>

<s>&ldquo; Il mezzo <lb/>del retto cammino fatto da'ponderosi corpi, che per violento moto discor&shy;<lb/>rono per l'aria, fia di maggiore potenza e di maggiore percussione nel suo <lb/>opposito contrasto, che nessun altra parte d'esso corso &rdquo; (Manuscr. </s>

<s>A cit., <lb/>fol. </s>

<s>43 ad t.). </s></p><p type="main">

<s>La ragione di questo teorema &egrave; conclusa dai predominanti principii pe&shy;<lb/>ripatetici, secondo i quali &egrave; l'aria che ora seconda, ora impedisce il moto <lb/>al proietto: principii, che sostituiti alla virt&ugrave; impressa e alla forza d'iner&shy;<lb/>zia, non per&ograve; cessano di esser falsi, bench&egrave; Leonardo gl'illustri con inge&shy;<lb/>gnosi commenti. </s>

<s>Sia A (fig. </s>

<s>43) l'obice, ABC il sito della egualit&agrave;, o la per&shy;<lb/>fetta linea orizzontale. </s>

<s>S'ammette da Leonardo che il proietto prosegua in <lb/><figure id="id.020.01.1838.1.jpg" xlink:href="020/01/1838/1.jpg"/></s></p><p type="caption">

<s>Figura 43.<lb/>quella linea per un certo tratto <lb/>il suo viaggio, come sarebbe <lb/>infino in C, di dove poi inco&shy;<lb/>mincia a declinare. </s>

<s>Il punto <lb/>B di mezzo del cammin retto <lb/>AC sarebbe quello della massima velocit&agrave;, ci&ograve; che dall'Autore cos&igrave; si dimo&shy;<lb/>stra: &ldquo; La ragione di questo si &egrave; che, quando il peso si parte dalla forza <lb/>del suo motore, bench&egrave; essa dipartita sia in primo grado di sua potenza, <lb/>nientedimeno, trovando l'aria senza moto, egli si trova in primo grado di <lb/>sua resistenza. </s>

<s>E bench&egrave; essa aria sia di maggiore somma di resistenza, che <lb/>non &egrave; la potenza del peso sospinto da lei, nondimeno, percotendone piccola <lb/>parte, viene in rimanente vincitore, onde la caccia dal suo sito, e nel cac&shy;<lb/>ciarla impedisce alquanto la sua velocit&agrave; Essendo adunque quest'aria so&shy;<lb/>spinta, ella ne sospinge e caccia dell'altra, e genera dopo s&egrave; circolari mo&shy;<lb/>vimenti, de'quali il peso mosso in essa &egrave; sempre centro, a similitudine <lb/>de'circoli fatti nell'acqua, che si fanno centro del loco percosso dalla pie&shy;<lb/>tra. </s>

<s>E cos&igrave;, cacciando l'uno circolo l'altro, l'aria, ch'&egrave; dinanzi al suo mo&shy;<lb/>tore tutta per quella linea, &egrave; preparata al movimento, il quale tanto pi&ugrave; cre&shy;<lb/>sce, quanto pi&ugrave; s'appressa il peso che la caccia. </s>

<s>Onde, trovando esso peso <lb/>men resistenzia d'aria, con pi&ugrave; velocit&agrave; raddoppia il suo corso, a similitudine <pb xlink:href="020/01/1839.jpg" pagenum="82"/>della barca tirata per l'acqua, la quale si muove con difficolt&agrave; nel primo <lb/>moto, bench&egrave; il suo motore sia nella pi&ugrave; potente forza. </s>

<s>E quando essa acqua <lb/>con arcate onde comincia a pigliare moto, la barca seguitando esso moto <lb/>trova poca resistenza, onde si move con pi&ugrave; facilit&agrave;. </s>

<s>Similmente, la ballotta <lb/>trovando poca resistenzia, seguita il principiato corso, infino a tanto che, <lb/>abbandonata alquanto dalla prima forza, comincia a debolire e declinare, <lb/>onde, mutando corso, la preparata fuga fattali dinanzi dalla fuggente aria, <lb/>non li servono pi&ugrave;, e quanto pi&ugrave; declina, pi&ugrave; trova varia resistenzia d'aria, <lb/>e pi&ugrave; si tarda, insino a tanto che, ripigliando il moto naturale, si rif&agrave; di <lb/>pi&ugrave; velocit&agrave;. </s>

<s>La barca torcendosi ritarda ancora lei suo corso. </s>

<s>Ora io con&shy;<lb/>chiuggo, per la ragione della VIII proposizione, che quella parte del moto, <lb/>che si trova tra la prima resistenzia dell'aria, e il principio della sua de&shy;<lb/>clinazione; sia di maggiore potenzia, e che questo &egrave; il mezzo del cammino, <lb/>il quale &egrave; fatto per l'aria con retta e diritta linea &rdquo; (ivi, fol. </s>

<s>43 ad t.) </s></p><p type="main">

<s>Di qui, e dalle cose sopra esposte, raccogliesi che Leonardo, nel trattar <lb/>de'proietti e della caduta naturale dei gravi, non ne seppe troppo pi&ugrave; avanti <lb/>de'suoi contemporanei, i quali lasciarono la scienza a quel punto, a cui <lb/>l'aveva ridotta Aristotile ne'suoi insegnamenti. </s>

<s>Questo avvenne dall'altra <lb/>parte per logica necessit&agrave;, non potendosi concluder nulla dal falso, com'&egrave; <lb/>impossibile il progredire col&agrave; dove manchi fermezza al pi&egrave; mosso. </s>

<s>Nella Mec&shy;<lb/>canica peripatetica per&ograve;, misto al falso, si conteneva molta parte del vero, <lb/>da cui seppe il Nostro levarsi sublime con l'ala del matematico ingegno. </s>

<s>A <lb/>confermare il qual fatto, cos&igrave; importante alla storia scientifica del secolo XVI, <lb/>giova aggiungere agli esempii sopra recati alcuni altri concernenti la resi&shy;<lb/>stenza dei corpi solidi allo spezzarsi. </s></p><p type="main">

<s>Galileo si vant&ograve; di avere, intorno a questo soggetto, istituita una scienza <lb/>nuova, la quale non &egrave; per&ograve; altro che una pi&ugrave; larga, e pi&ugrave; corretta esplica&shy;<lb/>zione di ci&ograve; che si propose di risolvere Aristotile qua e l&agrave; nelle sue varie <lb/>Questioni. </s>

<s>Nella XXV, applicandosi dal Filosofo la teoria del vette, si rende <lb/>la ragione del perch&egrave; tanto pi&ugrave; facilmente si tribbi un legno, appoggiandovi <lb/>il ginocchio nel mezzo, quanto le mani, che lo tengono per le due estremit&agrave;, <lb/>son pi&ugrave; remote dallo stesso ginocchio, e Leonardo, passando dalla volgare <lb/>curiosit&agrave; dell'esempio a cercar l'utile che se ne potrebbe ricavar per le co&shy;<lb/>struzioni, &ldquo; trovo, egli dice, che uno peso posto sopra una asse, sospesa <lb/>infra due pilastri, f&adot; calare in mezzo detta asse uno braccio: l'asse &egrave; quattro <lb/>braccia, e il peso &egrave; lontano da uno pilastro braccia due. </s>

<s>Se tu fai che detto <lb/>peso non sia distante pi&ugrave; d'uno braccio, quanto caler&agrave; detta asse sotto il <lb/>soprapposto peso? </s>

<s>&ldquo; (Manuscr. </s>

<s>A ci., fol. </s>

<s>48). E sullo stesso argomento, in <lb/>un'altra Nota, si legge: &ldquo; Fa esperienza: se uno legno sottile, sospeso per <lb/>traverso sopra due sostentacoli ne'sua estremi, regge dieci libbre; che reg&shy;<lb/>ger&agrave; una trave di medesima proporzione? </s>

<s>e guarda se la regola delle tre <lb/>cose ti serve, perch&egrave; la sperienza fa buona regola &rdquo; (ivi, fol. </s>

<s>33). </s></p><p type="main">

<s>L'aristotelica Questione XXVI intende a rispondere al perch&egrave; tanto son <lb/>pi&ugrave; fragili i legni, quanto sono pi&ugrave; lunghi, e anche la ragion di ci&ograve;, cos&igrave; <pb xlink:href="020/01/1840.jpg" pagenum="83"/>dal Filosofo come da Galileo, concludesi dalla teoria della leva, sull'estre&shy;<lb/>mit&agrave; della quale tanto pi&ugrave; s'aggrava il peso, quant'ella va sempre pi&ugrave; lunga. </s>

<s><lb/>Dietro i quali statici principii Leonardo pure formula i suoi teoremi, e ri&shy;<lb/>sponde ai proposti quesiti. </s>

<s>&ldquo; Se una lancia di venti braccia regge dieci lib&shy;<lb/>bre, uno braccio d'essa, della medesima grossezza, ne regger&agrave; dugento, im&shy;<lb/>perocch&egrave; tanto quanto l'asta corta entra nella lunga, tante volte sostiene pi&ugrave; <lb/>peso che la lunga &rdquo; (ivi, fol. </s>

<s>49 ad t). &mdash; &ldquo; Se una lancia lunga cento sue <lb/>grossezze regge venti libbre, che regger&agrave; una di cinque grossezze della me&shy;<lb/>desima asta? </s>

<s>Tanto quanto cinque entra in cento, tanto l'asta di cento gros&shy;<lb/>sezze regger&agrave; men peso, che l'asta di cinque grossezze &rdquo; (ivi, fol. </s>

<s>48 ad t.). </s></p><p type="main">

<s>Nel trattato meccanico delle resistenze de'solidi allo spezzarsi una que&shy;<lb/>stione manca in Aristotile, ed &egrave; quella che riguarda le funi, intorno a che <lb/>fu veramente Leonardo il primo a darne una scienza nuova, che in molte <lb/>parti si riscontra col vero, lungo tempo dopo insegnato da Galileo. </s>

<s>Nel I dia&shy;<lb/>logo delle Due nuove scienze si dimostra che la tegnenza dei canapi dipende <lb/>dallo strignimento delle tortuosit&agrave;, per cui si collegano le separate fila tanto <lb/>tenacemente &ldquo; che di non molti giunchi, neanco molto lunghi, sicch&egrave; poche <lb/>sono le spire, con le quali tra di loro s'intrecciano; si compongono robu&shy;<lb/>stissime funi &rdquo; (Alb. </s>

<s>XIII, 14). Dagli effetti medesimi della quale artificiosa <lb/>struttura stabilisce Leonardo la seguente legge sperimentale: &ldquo; Trovo che <lb/>tanto quanto elleno (le funi) scemano nell'avvoltarsi, tanto sono pi&ugrave; potenti <lb/>che prima &rdquo; (Manuscr. </s>

<s>A cit., fol. </s>

<s>49). </s></p><p type="main">

<s>Un inganno in questo proposito si reputava da Galileo che fosse prima <lb/>di lui stato a tutti comune, e consisteva nel credere che tanto fossero pi&ugrave; <lb/>resistenti le funi, quanto sono pi&ugrave; corte. </s>

<s>Fu anche Leonardo un tempo di <lb/>questa falsa opinione, come da alcune sue Note chiaramente apparisce. </s>

<s>In <lb/>una di esse cos&igrave; domanda: &ldquo; Se una corda d'uno braccio regge cento lib&shy;<lb/>bre, quante libbre regger&agrave; una corda della medesima grossezza, che sia lunga <lb/>cento braccia? </s>

<s>&rdquo; (ivi, fol. </s>

<s>5). La risposta al quesito &egrave; data cos&igrave; dall'Autore <lb/>in un'altra Nota: &ldquo; Tanto quanto la minor lunghezza della corda entra nella <lb/>maggiore, tanto &egrave; pi&ugrave; forte ch'essa maggiore &rdquo; (ivi, fol. </s>

<s>49). Il galileiano <lb/>Salviati dimostr&ograve; a Simplicio che questa proposizione era <emph type="italics"/>falsa non che <lb/>impossibile<emph.end type="italics"/> (Alb. </s>

<s>XIII, 121), ma Leonardo s'avvide poi da s&egrave; medesimo del&shy;<lb/>l'inganno, senz'altro maestro che la propria ragione e la propria esperienza, <lb/>dalle quali ebbe poi a concluderne, come Galileo e come l'Aggiunti, che <lb/>&ldquo; ogni gravit&agrave; sospesa &egrave; tutta per tutta la lunghezza della corda, che la so&shy;<lb/>stiene, ed &egrave; tutta in ogni parte di quella &rdquo; (Manuscr. </s>

<s>E cit., fol 32 ad t.). </s></p><p type="main">

<s>Un'altra questione relativa alle resistenze, trascurata da Aristotile e da <lb/>Galileo, fu trattata da Leonardo, il quale solo pot&egrave; conoscerne l'importanza, <lb/>da giungere alle conclusioni medesime de'Meccanici moderni. </s>

<s>La questione <lb/>riguarda quella specie di resistenza, oppost&agrave; al libero moto dagli attriti, che <lb/>nascono tra la superfice del mobile, e quella del piano che lo sostiene, cos&igrave; <lb/>raccogliendo in Nota il frutto delle diligenti esperienze: &ldquo; Sia A (fig. </s>

<s>44) <lb/>il corpo confregato, ovvero strascinato dal Motore B; CD sia il piano pulito, <pb xlink:href="020/01/1841.jpg" pagenum="84"/>dove esso corpo &egrave; confregato. </s>

<s>Sono le confregazioni de'corpi di quattro sorte, <lb/>delle quali la prima si &egrave;, quando due corpi sono puliti e piani, come qui &egrave; <lb/><figure id="id.020.01.1841.1.jpg" xlink:href="020/01/1841/1.jpg"/></s></p><p type="caption">

<s>Figura 44.<lb/>proposto. </s>

<s>La seconda &egrave;, quando il corpo <lb/>strascinato &egrave; pulito, e il piano dove si <lb/>muove &egrave; aspro. </s>

<s>La terza &egrave;, quando il <lb/>corpo strascinato &egrave; aspro, e il piano dove <lb/>si muove &egrave; pulito. </s>

<s>Il quarto modo &egrave; quando <lb/>il corpo strascinato, e il piano dove si strascina, &egrave; aspro. </s>

<s>D&agrave; l'esperienza <lb/>che la cosa pulita, strascinata per pulito piano, resiste nel moto al suo mo&shy;<lb/>tore con potenza eguale alla quarta parte della sua gravezza, e delle altre <lb/>seguenti due sorte tanto &egrave; a movere la cosa aspra sopra piano pulito, quanto <lb/>la cosa pulita sopra piano aspro. </s>

<s>La confregazione de'corpi puliti mancher&agrave; <lb/>tanto pi&ugrave; di resistenza e di peso, quanto il sito dove si muove &egrave; meno obli&shy;<lb/>quo, essendo il motore sopra o sotto il suo mobile &rdquo; (Saggio del Codice atlan&shy;<lb/>tico, Milano 1872, fol. </s>

<s>195). <lb/><figure id="id.020.01.1841.2.jpg" xlink:href="020/01/1841/2.jpg"/></s></p><p type="caption">

<s>Figura 45.</s></p><p type="main">

<s>Per determinar pi&ugrave; particolarmente questa legge, <lb/>segnate in una quarta di cerchio varie obliquit&agrave; di piani, <lb/>cos&igrave; delle resistenze varie incontrate da un corpo, che <lb/>lunghessi scenda, ne assegna Leonardo in numeri i gradi <lb/>proporzionali: &ldquo; N (fig. </s>

<s>45) d&agrave; di s&egrave; resistenza eguale <lb/>al quarto della sua gravit&agrave; naturale; M resiste per l'ot&shy;<lb/>tavo della sua gravit&agrave;; O resiste per un sedicesimo; P <lb/>non resiste, perch&egrave; in lui l'O ha consumato la sua con&shy;<lb/>fregazione. </s>

<s>Ma a dire meglio N resiste per un quarto del <lb/>suo peso naturale; M resiste per un mezzo quarto; O resiste per un quarto <lb/>del sopraddetto quarto; P non resiste nulla, perch&egrave; il quarto del quarto <lb/>s&igrave; consuma nel moto fatto dall'O al P &rdquo; (Manuscr. </s>

<s>E cit., fol. </s>

<s>78 ad t.). </s></p><p type="main">

<s><emph type="center"/>VI.<emph.end type="center"/></s></p><p type="main">

<s>Il promesso Saggio dei varii trattati meccanici, gli elementi dei quali <lb/>si ritrovan senz'ordine dispersi, e in frettolose Note accennati ne'Manoscritti <lb/>di Leonardo da Vinci; &egrave;, secondo la nostra possibilit&agrave;, e l'intento della nostra <lb/>Storia, a questo punto compiuto. </s>

<s>I meditativi Lettori penseranno fra s&egrave; me&shy;<lb/>desimi che, seguitando la Scienza del moto ad esser promossa dagli altri <lb/>Autori, che si dettero a coltivarla in quel tempo, con tal valido impulso <lb/>quale abbiamo fin qui veduto; avrebbe il primo instaurato edifizio vinto in <lb/>grandezza e in decoro quel nuovo, che disegn&ograve; la mente di Galileo. </s></p><p type="main">

<s>Il fatto &egrave; per&ograve; che non furono que'successivi progressi punto propor&shy;<lb/>zionati all'impulso, che pareva dover ricevere la scienza dall'opera di Leo&shy;<lb/>nardo, la quale opera ebbe veramente in s&egrave; qualche cosa di straordinario. </s>

<s><lb/>Le ragioni di ci&ograve; le abbiamo di sopra esposte nel nostro lungo discorso, e <pb xlink:href="020/01/1842.jpg" pagenum="85"/>si riducono in somma all'aver saputo felicemente congiungere il singolaris&shy;<lb/>simo uomo la scienza della scuola coll'esperienza e col senno popolare. </s>

<s>Nei <lb/>contemporanei e nei successori si rivel&ograve; varia l'indole dell'ingegno, secondo <lb/>che varia era la mistura de'due elementi educativi. </s>

<s>V'erano da una parte <lb/>i soli addetti alla scuola, i quali giurando nelle parole del Maestro si ren&shy;<lb/>devano perci&ograve; inabili a qualunque progresso, e v'erano dall'altra i disce&shy;<lb/>poli della propria esperienza e del proprio senno, i quali essendo privi di <lb/>lettere mancavano del necessario strumento da comunicare alla scienza qua&shy;<lb/>lunque progresso. </s>

<s>Partecipava anche Leonardo alle condizioni di questi tali, <lb/>e di qu&igrave; avvenne che tanti documenti, i quali avrebbe potuto dare util&shy;<lb/>mente agli studiosi, riuscirono in gran parte inefficaci. </s>

<s>Diciamo in gran parte, <lb/>perch&egrave; ci sembra inverosimile che tante speculazioni e tante scoperte si vo&shy;<lb/>lessero tutte rimaner chiuse nella mente di chi le pens&ograve;, e ne'volumi di chi <lb/>le scrisse. </s>

<s>Tanta fiamma non v'era cenere che bastasse a tenerla sotto s&egrave; <lb/>d'ogni canto sopita. </s></p><p type="main">

<s>Si diffondevano quelle speculazioni nelle stesse controversie, che l'uomo <lb/>del senno popolare e delle proprie esperienze aveva cos&igrave; spesso co'Filosofi <lb/>in libris, contro i quali scriveva: &ldquo; Me inventore disprezzano; quanto mag&shy;<lb/>giormente loro, non inventori ma trombetti e recitatori delle altrui opere, <lb/>dovranno essere biasimati? </s>

<s>&rdquo; (Libri, Histoire cit., T. III, pag. </s>

<s>238). Si dif&shy;<lb/>fondevano quelle scoperte in quelli stessi, che n'erano pubblici testimoni <lb/>di veduta, e che ne facevan uso ora nell'esercizio delle arti, ora a spetta&shy;<lb/>colo de'curiosi, com'altrove dicemmo essere avvenuto dell'invenzione della <lb/>Camera oscura. </s>

<s>N&egrave; all'esperienza per esempio della caduta dei gravi dalle <lb/>sommit&agrave; degli edifizii, eretti in mezzo a popolose citt&agrave;, potevano mancare <lb/>pubblici testimonii, oltre a quelli che davan mano allo sperimentatore, e <lb/>che, partecipando con lui alla scoperta del vero, si facevan gloria nel di&shy;<lb/>vulgarlo. </s></p><p type="main">

<s>Essendo tali i precipui e pi&ugrave; attivi, e si pu&ograve; dire i soli organi della <lb/>diffusione, molte parti di scienza speculata, e non intesa dai comunali inge&shy;<lb/>gni, si dovette necessariamente arrestare ne'manoscritti informi dell'Autore, <lb/>cosicch&egrave; rimaneva l'opera promotrice affidata tutta a que'pochi, ch'essendo <lb/>pure educati nelle scuole avevano dai libri imparato a pensar da s&egrave;, e sa&shy;<lb/>pevan con l'arte della parola significare agli altri i loro pensieri. </s>

<s>Delle scuole, <lb/>nelle quali insegnavansi le discipline, che formano il principale argomento <lb/>di questa storia, n'erano come vedemmo due separate e distinte coi nomi <lb/>di Peripatetica e di Alessandrina, dell'una delle quali sedeva autorevole e <lb/>solenne maestro Archimede, e dell'altra un pi&ugrave; prossimo promotore, Gio&shy;<lb/>dano Nemorario. </s>

<s>Nella educazion popolare di Leonardo non si conosceva <lb/>distinzion di partito, saggiamente imbevendo, da qualunque fonte gli deri&shy;<lb/>vasse, il vero, ma nelle menti educate sotto le pi&ugrave; regolari discipline dei <lb/>Maestri era impossibile che facessero insieme consorzio Aristotile e Platone. </s>

<s><lb/>Come in tutti gli altri rami di scienza, cos&igrave; avvenne anche in questa del <lb/>moto che alcuni attesero a professarla coi metodi platonici, sull'esempio di <pb xlink:href="020/01/1843.jpg" pagenum="86"/>Archimede, altri invece seguitando i prevalenti metodi peripatetici sull'esem&shy;<lb/>pio del Nemorario. </s>

<s>Fu il prevaler di questi una buona ventura ai progressi <lb/>della Statica in particolare, perch&egrave; i principii archimedei erano assai pi&ugrave; ri&shy;<lb/>stretti nella cerchia de'loro impulsi, come il nostro discorso lo dimostrava <lb/>di sopra con le ragioni, e come ora si vedr&agrave; confermato dai fatti. </s></p><p type="main">

<s>Nella prima met&agrave; del secolo XVI ebbe la Statica due cultori insigni, e <lb/>che rappresentano in s&egrave; scolpitamente impressa la varia indole delle due <lb/>Scuole. </s>

<s>Francesco Maurolico proponeva nel trattato <emph type="italics"/>De momentis aequali&shy;<lb/>bus<emph.end type="italics"/> i suoi teoremi, concludendoli dai principii archimedei, e Niccol&ograve; Tarta&shy;<lb/>glia, nell'VIII libro de'suoi <emph type="italics"/>Quesiti,<emph.end type="italics"/> dimostrava sui principii del Nemorario <lb/>le generali proposizioni concernenti quella, ch'egli chiama <emph type="italics"/>Scienzia dei pe&shy;<lb/>sci.<emph.end type="italics"/> Vuole ora l'ordine della nostra Storia, e l'importanza del negletto ar&shy;<lb/>gomento, che ci tratteniam brevemente in esaminar la varia opera data a <lb/>questi matematici studii dai due Promotori. </s></p><p type="main">

<s>De'quattro libri di che si compone il maurolicano trattato <emph type="italics"/>De momentis <lb/>aequalibus,<emph.end type="italics"/> la dimostrazione de'principii statici ricorre propriamente nel <lb/>primo. </s>

<s>&Egrave; da notar che cominci&ograve; il nostro Autore a introdur nella scienza <lb/>la parola <emph type="italics"/>momento,<emph.end type="italics"/> consacrata poi dall'uso generale nel significato cos&igrave; dal <lb/>Maurolico stesso definito: &ldquo; Momentum est vis ponderis a spatio quopiam <lb/>contra pendentis, unde ponderum aequalium momenta possunt esse inaequa&shy;<lb/>lia, et e contra continget momentorum aequalium pondera esse inaequalia &rdquo; <lb/>(Archimedis monum. </s>

<s>ex traditione Maurolici, Panormi 1685, pag. </s>

<s>86). Ri&shy;<lb/>corre altres&igrave; in questo trattato la prima dimostrazion matematica del prin&shy;<lb/>cipio statico generale, che cio&egrave; i momenti stanno in ragion composta degli <lb/>spazii e dei pesi. </s></p><p type="main">

<s>La proposizione &egrave; conclusa con assai spedito processo dal principio ar&shy;<lb/>chimedeo: &ldquo; Si gravia reciproca sint distantiis, quibus absunt centra ipso&shy;<lb/>rum a puncto quodam in recta linea coniungente centra posito, punctum <lb/>illud est commune centrum gravium &rdquo; (ibid., 99), d'onde per corollario de&shy;<lb/>riva: &ldquo; gravia aeque ponderantia reciproca sunt spatiis, e quibus pendent &rdquo; <lb/>(ibid., 100). Da questi premessi teoremi, e dalla definizion de'momenti, si <lb/>fa via l'Autore a dimostrare che &ldquo; quam multiplex est pondus ponderis ad <lb/>idem spatium, tam multiplex est momentum momenti &rdquo; (102), da che imme&shy;<lb/>diatamente concludonsi le due proposizioni, &ldquo; Gravia ab aequis spatiis pen&shy;<lb/>dentia sunt momentis proportionalia; Gravium aequalium, ab inaequalibus <lb/>spatiis ponderantium, momenta sunt ad invicem sicut spatia &rdquo; (ibid., 103); <lb/>proposizioni, che compongonsi nell'altra fondamentale, cos&igrave; formulata: &ldquo; Mo&shy;<lb/>mentorum ratio componitur ex ratione ponderum, et ex ratione spatiorum, <lb/>a quibus gravia pendent &rdquo; (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>Il manoscritto di quel primo libro, in cui s'espongono ordinatamente <lb/>dall'Autore le matematiche dimostrazioni di questi teoremi, &egrave; sottoscritto da <lb/>Castelbuono nel d&igrave; 6 di Dicembre, marted&igrave;, dell'anno 1547, come parte in&shy;<lb/>tegrante di un'opera, che attendeva a raccogliere e ad illustrare i patrii mo&shy;<lb/>numenti di scienza lasciati dall'antico Archimede. </s>

<s>Rimase una tale opera <pb xlink:href="020/01/1844.jpg" pagenum="87"/>lungo tempo sconosciuta, fuor che agli eredi del defunto Autore, ultimo dei <lb/>quali fu il marchese di Campotondo. </s>

<s>Colto egli stesso e la sua famiglia da <lb/>lunghe infermit&agrave;, gli sovveniva di cure mediche e di medicinali uno Spe&shy;<lb/>ziale messinese, di nome Lorenzo di Tommaso, che, venuto finalmente a far <lb/>col marchese il conto del suo avere, n'ebbe a ricevere volentieri in paga&shy;<lb/>mento, amante della letteratura com'egli era, i libri e i manoscritti del ce&shy;<lb/>lebre Antenato. </s>

<s>Gli parvero fra questi da pregiare principalmente i <emph type="italics"/>Monu&shy;<lb/>menti archimedei,<emph.end type="italics"/> e sovvenuto dal Senato messinese, a cui voleva dedicarli, <lb/>di moneta, e da Gian Alfonso Borelli, professore in quello studio, di consi&shy;<lb/>gli, per quel che riguarda la scienza; dette mano nel 1670 a pubblicarli, <lb/>per le stampe di Paolo Bonacota. </s>

<s>Era nel 1672 giunta quasi a termine l'im&shy;<lb/>pressione, quando per i tumulti civili, costretti ad esular Lorenzo di Tom&shy;<lb/>maso e il Borelli, s'impossess&ograve; di quelle abbandonate carte il Regio Fisco, <lb/>che fece di Messina trasportarle a Palermo. </s>

<s>Quietati poi nel 1681 i tumulti, <lb/>e tornata la citt&agrave; sotto il giogo spagnuolo, un signor messinese, zelante delle <lb/>patrie lettere, sotto il nome di Cillenio Esperio, riscatt&ograve; da Palermo le con&shy;<lb/>fiscate carte de'suoi concittadini, fra le quali ebbe a trovar, senza principio <lb/>e senza fine, i fogli gia stati impressi dal Bonacota. </s>

<s>Non sapendo ancora <lb/>nulla delle subite vicende, si rivolse a due padri gesuiti, dai quali ebbe in <lb/>risposta le notizie per noi riferite. </s>

<s>Premesse le lettere dei detti gesuiti al&shy;<lb/>l'Opera, ei la volle far reimprimere a sue spese, e reintegrare in Palermo, <lb/>di dove usc&igrave; nel 1685 col titolo di <emph type="italics"/>Archimedis siracusani monumenta omnia <lb/>mathematica, quae extant, ex traditione Francisci Maurolici.<emph.end type="italics"/></s></p><p type="main">

<s>Si raccoglie da queste notizie ch'essendo venute le tradizioni mauroli&shy;<lb/>cane alla luce, quand'era giunta alla sua piena maturit&agrave; la fiorente Scuola <lb/>galileiana, tornarono affatto inutili ai progressi della scienza, ond'&egrave; che ri&shy;<lb/>mase l'opera promotrice tutta affidata ai pubblici documenti, che s'ebbero <lb/>dal Tartaglia. </s>

<s>L'opuscolo postumo <emph type="italics"/>De ponderositate,<emph.end type="italics"/> pubblicato nel 1565 in <lb/>Venezia da Curzio Troiano, &egrave; importante per la storia, perch&egrave; si rivela in <lb/>esso come l'Autore tenesse dietro a commentare il Nemorario, con quel fer&shy;<lb/>vente amor di discepolo, che il Maurolico stesso faceva intorno al suo grande <lb/>Siracusano, ma &egrave; superfluo come documento di scienza, perch&egrave; tutte le pro&shy;<lb/>posizioni meccaniche quivi dimostrate trovano ne'<emph type="italics"/>Quesiti e invenzioni,<emph.end type="italics"/> pub&shy;<lb/>blicati dallo stesso Tartaglia nel 1546, amplissimo svolgimento. </s></p><p type="main">

<s>Nell'ottavo di que'libri s'insegna, come si disse, la Scienza dei pesi, <lb/>e non &egrave; altro insomma che un trattatello di Statica generale, ordinatamente <lb/>condotto di proposizione in proposizione sui postulati del Nemorario, ai quali, <lb/>segnando nell'antica scienza peripatetica un notabile progresso, s'aggiunge <lb/>domandando &ldquo; ne sia concesso niun corpo esser grave in s&egrave; medesimo, cio&egrave; <lb/>l'acqua nell'acqua, il vino nel vino, l'olio nell'olio, l'aere nell'aere non <lb/>essere di alcuna gravit&agrave; &rdquo; (Quesiti e invenzioni, Venezia 1546, fol. </s>

<s>85 t.). </s></p><p type="main">

<s>Che intenda veramente l'Autore di mettersi egli a ordinare la scienza, <lb/>della quale i precedenti scrittori non avevano fatto altro che porre i prin&shy;<lb/>cipii, lo dichiara cos&igrave; a don Diego Hurtado di Mendoza, interlocutore del dia-<pb xlink:href="020/01/1845.jpg" pagenum="88"/>logo, che aveva domandato qual costrutto si potrebbe cavare da tale scienza. <lb/></s>

<s>&ldquo; Li costrutti, risponde Niccol&ograve;, che di tale scienza si potriano cavare, saria <lb/>quasi impossibile a poterli a Vostra Signoria esprimere, ovver connumerare: <lb/>nondimeno io vi riferir&ograve; quelli, che per al presente a me sono manifesti. </s>

<s><lb/>E pertanto dico che, per vigore di tale scienza, egli &egrave; possibile a conoscere <lb/>e misurare con ragione la virt&ugrave; e potenza di tutti quelli strumenti mecca&shy;<lb/>nici, che dai nostri antichi sono stati ritrovati per augumentare la forza <lb/>dell'uomo nell'elevare, condurre, ovver spingere avanti ogni gran peso &rdquo; <lb/>(ivi, fol. </s>

<s>81). </s></p><p type="main">

<s>Or perch&egrave; la virt&ugrave; e la potenza di tutti gli strumenti meccanici trova, <lb/>secondo Aristotile e il Nemorario, la ragion della sua misura nelle leggi del <lb/>Vette e della Libbra, il Tartaglia, fedel seguace delle dottrine di quegli Au&shy;<lb/>tori, attende a stabilire i fondamenti alla Statica, dimostrando che s'equili&shy;<lb/>brano allora insieme la potenza e la resistenza quando son le forze recipro&shy;<lb/>camente proporzionali alle distanze. </s>

<s>Incomincia perci&ograve; anch'egli, come il <lb/>Maurolico, a stabilir la legge principalissima dei momenti, concludendola da <lb/>due proposizioni simili a quelle date dal Matematico siciliano. </s>

<s>L'una dice: <lb/>&ldquo; La proporzione della grandezza dei corpi di un medesimo genere, e quella <lb/>della lor potenzia &egrave; una medesima &rdquo; (ivi, fol. </s>

<s>86); l'altra: &ldquo; Se saranno <lb/>due corpi semplicemente eguali di gravit&agrave;, ma ineguali per vigor del sito, <lb/>ovver posizione, la proporzione della loro potenzia e quella della lor velo&shy;<lb/>cit&agrave; necessariamente sar&agrave; una medesima &rdquo; (ivi, fol. </s>

<s>87). Di qui immediata&shy;<lb/>mente ne conseguiva esser le potenze stesse in ragion composta delle velo&shy;<lb/>cit&agrave; e delle moli. </s>

<s>Ma perch&egrave; le velocit&agrave; son proporzionali agli spazii, ossia <lb/>agli archi descritti dagli estremi bracci della Leva e della Bilancia, e gli archi <lb/>hanno la ragion medesima dei raggi, ossia delle distanze dal centro al punto <lb/>della sospensione dei pesi; ne conclude perci&ograve; il Tartaglia che le potenze <lb/>o le forze stanno in ragion composta dei pesi, e delle distanze delle loro <lb/>sospensioni dal centro dei movimenti. </s>

<s>Di qui &egrave; che, avendosi pesi eguali, i <lb/>loro momenti nella Bilancia sono come le lunghezze dei bracci da cui stanno <lb/>pendenti, ci&ograve; che vien dal Tartaglia stesso formulato nel modo seguente: <lb/>&ldquo; La proporzione della potenza de'corpi semplici, eguali in gravit&agrave;, ma ine&shy;<lb/>guali per vigor del sito, ovver posizione, e quella della loro distanza dal <lb/>sparto, ovver centro della Libra, s'approvano essere eguali &rdquo; (ivi, fol. </s>

<s>88). </s></p><p type="main">

<s>Se mantengonsi i pesi tuttavia eguali, e sopra pi&ugrave; le braccia della Bi&shy;<lb/>lancia sono eguali, concludesi da quel generale principio che i momenti o <lb/>le potenze son parimente per riuscire fra loro eguali, ci&ograve; che viene dimo&shy;<lb/>strato dal Nostro nella V proposizione: &ldquo; Quando che la posizione di una <lb/>Libbra di braccia eguali sia nel sito della egualit&agrave;, e nella estremit&agrave; del&shy;<lb/>l'uno e l'altro braccio vi sieno appesi corpi semplicemente eguali in gra&shy;<lb/>vit&agrave;, tal Libbra non si separer&agrave; dal sito della egualit&agrave;, e se per caso la sia <lb/>da qualche altro peso, nell'uno dei detti bracci imposto, separata dal sito <lb/>della egualit&agrave;, ovvero con la mano; remosso quel tal peso ovver mano la <lb/>Libbra di necessit&agrave; ritorner&agrave; al detto sito della egualit&agrave; &rdquo; (ivi ad t.). </s></p><pb xlink:href="020/01/1846.jpg" pagenum="89"/><p type="main">

<s>Se mantenendosi tuttavia le distanze eguali i pesi son per&ograve; differenti, <lb/>il maggiore avr&agrave; necessariamente maggior momento, e verr&agrave; perci&ograve; turbato <lb/>alla Libbra l'equilibrio, come procede a dimostrare il Tartaglia nella sua <lb/>VI proposizione: &ldquo; Quando che la posizione di una Libbra di braccia eguali <lb/>sia nel sito della egualit&agrave;, e che nella estremit&agrave; dell'uno e dell'altro brac&shy;<lb/>cio vi sieno appesi corpi semplicemente ineguali di gravit&agrave;; dalla parte dove <lb/>sar&agrave; il pi&ugrave; grave sar&agrave; forzata a declinare perfino alla linea della direzione &rdquo; <lb/>(ivi, fol. </s>

<s>90). Se al contrario i pesi sono eguali, ma le distanze dal centro <lb/>son differenti, la Bilancia traboccher&agrave; dalla parte del braccio maggiore. </s>

<s>&ldquo; Se <lb/>li bracci della Libbra saranno ineguali, e che nella estremit&agrave; di cadauno di <lb/>quelli vi sieno appesi corpi semplicemente eguali in gravit&agrave;, dalla parte del <lb/>pi&ugrave; lungo braccio tal Libbra far&agrave; declinazione &rdquo; (ivi, fol. </s>

<s>92). </s></p><p type="main">

<s>Son tutte queste proposizioni dall'Autore ordinate alla maggior con&shy;<lb/>clusione finale, ed &egrave;: che essendo varie le distanze, e tutt'insieme anche i <lb/>pesi, quelle stanno in reciproca proporzione di questi. </s>

<s>&ldquo; Se li bracci della <lb/>Libbra, cos&igrave; propriamente si esprime nella sua VIII proposizione il Tarta&shy;<lb/>glia, saranno proporzionali alli pesi in quella imposti, talmente che nel brac&shy;<lb/>cio pi&ugrave; corto sia appeso il corpo pi&ugrave; grave; quelli tai corpi ovver pesi sa&shy;<lb/>ranno egualmente gravi, secondo tal posizione ovver sito &rdquo; (ivi ad t.): ci&ograve; <lb/>che dall'altra parte &egrave; la version letterale della VIII del Nemorario: &ldquo; Si <lb/>fuerint brachia Librae proportionalia ponderibus appensorum, ita ut in bre&shy;<lb/>viori gravius appendatur, aeque gravia erunt secundum situm &rdquo; (De pond. </s>

<s><lb/>cit., fol. </s>

<s>21). </s></p><p type="main">

<s>Risedendo in questa proposizione il principio fondamentale a tutta la <lb/>Statica, si sentiva perci&ograve; ragionevolmente il bisogno di dimostrarla con tutto <lb/>il rigor matematico, ci&ograve; che fu primo a fare come si disse Archimede nei <lb/>suoi Equiponderanti. </s>

<s>E qui giova osservare, a dichiarar meglio le parole, che <lb/>soggiunger&agrave; il Tartaglia dopo la sua dimostrazione, come nell'Archimede <lb/>del Rivault e di altri le due proposizioni, dove si dimostra che, o commen&shy;<lb/>surabili o incommensurabili che sieno le grandezze, si equilibrano allora che <lb/>stanno in ragion reciproca delle distanze; ricorrono in ordine numerate per <lb/>la VI e per la VII. </s>

<s>Altri compilatori per&ograve;, escludendo da una tal dignit&agrave; <lb/>negli Equiponderanti le due prime proposizioni, perch&egrave; non son veramente <lb/>altro che la petizione I e II; incominciavano piuttosto a numerarle da quella <lb/>che, secondo il Rivault, &egrave; la III, cosicch&egrave; la VI e la VII tornavano, in que&shy;<lb/>sto pi&ugrave; ragionevole ordinamento, la IV e la V. </s></p><p type="main">

<s>Ordinava cos&igrave; i teoremi al suo Archimede anche il Tartaglia, e perci&ograve; <lb/>nel compiacersi di aver data dimostrazione della legge, che governa il moto <lb/>delle Macchine, concludendola da principii diversi, ma non per&ograve; punto men <lb/>matematicamente precisi di quelli del Siracusano; fa dir cos&igrave; a Don Diego <lb/>Mendoza che, dietro l'enunciata proposizione VIII, era stato con gran pia&shy;<lb/>cere ad ascoltarne il ragionamento: &ldquo; Questa &egrave; una assai bella proposizione, <lb/>ma el mi pare, se ben mi ricordo, che Archimede Siracusano ne ponga una <lb/>simile, ma el non mi pare che lui la dimostri per questo vostro modo. <pb xlink:href="020/01/1847.jpg" pagenum="90"/><emph type="italics"/>Niccol&ograve;.<emph.end type="italics"/> Vostra Signoria dice la verit&agrave;, anzi di tal proposizione lui ne fa due <lb/>proposizioni, e queste sono la quarta e la quinta di quel Libro, dove tratta <lb/>delli centri delle cose gravi, e in effetto tai due proposizioni lui le dimostra <lb/>succintamente per li suoi principii da lui per avanti posti e dimostrati. </s>

<s>E <lb/>perch&egrave; tali suoi principii ovver argomenti non si convegneriano in questo <lb/>trattato, per esser materia alquanto diversa da quella, n'&egrave; parso in questo <lb/>luoco di dimostrare tal proposizione con altri principii ovver argomenti, pi&ugrave; <lb/>convenienti in questo loco &rdquo; (Quesiti e inv. </s>

<s>cit., fol. </s>

<s>93). </s></p><p type="main">

<s>Il Tartaglia, divulgando col suo commento la dimostrazione de'princi&shy;<lb/>pii statici co'nuovi argomenti del Nemorario, apriva un pi&ugrave; largo campo <lb/>alla scienza, e pareva perci&ograve; che dovessero gli studiosi mostrargliene la de&shy;<lb/>bita riconoscenza. </s>

<s>Ma invece lo abbandonarono, entrati in sospetto della so&shy;<lb/>lidit&agrave; matematica di quel modo di argomentare, comparato con quello pi&ugrave; <lb/>risoluto dell'antico Archimede. </s>

<s>Concorreva a confermare il sospetto la nausea, <lb/>che s'incominciava a sentire oramai delle dottrine peripatetiche, specialmente <lb/>da poi che il Benedetti era con la sua grande autorit&agrave; venuto ad appor la <lb/>nota di falso al principio, da cui il Nemorario stesso e il Tartaglia avevano <lb/>conclusa la legge dei momenti. </s>

<s>Nel cap. </s>

<s>I delle <emph type="italics"/>Disputationes de quibusdam <lb/>placitis Aristotelis,<emph.end type="italics"/> dop'aver confutato quel che nelle varie sue Opere il Fi&shy;<lb/>losofo insegna relativamente ai corpi della medesima specie e figura, che <lb/>scendono con velocit&agrave; proporzionali alle grandezze; cos&igrave; il Matematico vene&shy;<lb/>ziano soggiunge: &ldquo; Alii quoque permulti eamdem opinionem retinuerunt, <lb/>et omnium postremus Nicolaus Tartalea, secunda propositione vigesimi noni <lb/>Quaesiti octavi libri, ubi profitetur se demonstratione probare hanc propo&shy;<lb/>sitionem veram existere, neque videt quam magna resistentiarum sit diffe&shy;<lb/>rentia, quae, tam ex diversitate figurarum quam ex magnitudinum varie&shy;<lb/>tati, oriri potest, quas quidem diversitates non consideravit quidem &rdquo; (Liber <lb/>specul. </s>

<s>cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Il giudizio per&ograve;, con buona pace del Benedetti, &egrave; inconsiderato, non fa&shy;<lb/>cendo distinzione fra la libera caduta de'corpi in mezzo all'aria, e la loro <lb/>pressione sugli organi delle Macchine, n&egrave; avvertendo che, se la legge ari&shy;<lb/>stotelica &egrave; falsa nei moti, &egrave; per&ograve; verissima nei momenti. </s>

<s>Cosicch&egrave; la II pro&shy;<lb/>posizione dell'ottavo libro de'<emph type="italics"/>Quesiti<emph.end type="italics"/> corrisponde perfettamente alla XXXVIII <lb/>del I libro <emph type="italics"/>De momentis aequilibus,<emph.end type="italics"/> che dice: &ldquo; Gravium aequalium ab <lb/>inaequalibus spatiis pendentium momenta sunt ad invicem sicut spatia &rdquo; <lb/>(editio cit., pag. </s>

<s>103): tanto essendo il dire col Tartaglia che le potenze son <lb/>proporzionali alle velocit&agrave;, quanto dir col Maurolico che i momenti son pro&shy;<lb/>porzionali agli spazii. </s>

<s>Che se si tien per verissimo questo, non si vede la <lb/>ragione perch&egrave; quello, come il Benedetti vuole, s'abbia a imputare di falso. </s></p><p type="main">

<s>Comunque sia, fu della Dinamica il Tartaglia alquanto pi&ugrave; benemerito <lb/>che della Statica, non avendo insomma intorno a questa fatt'altro, che espli&shy;<lb/>care e illustrare le proposizioni del Nemorario. </s>

<s>La teoria de'proietti prin&shy;<lb/>cipalmente si pu&ograve; dire che ha i principii da lui, perch&egrave; gli studii di Leo&shy;<lb/>nardo da Vinci non si riducono a pi&ugrave;, che a poche regole sperimentali. <pb xlink:href="020/01/1848.jpg" pagenum="91"/>L'occasione, ch'ebbe il nostro Bresciano di far della Ballistica una scienza <lb/>nuova, fu propriamente quella di rispondere al desiderio de'principi de'suoi <lb/>tempi e de'capitani, per sola pratica conduttori in campo di quelle arti&shy;<lb/>glierie, con che dovevano miseramente offendersi insieme, e desolarsi le citt&agrave; <lb/>italiane. </s></p><p type="main">

<s>Che fosse veramente tale quella detta occasione, ce lo attesta con le <lb/>sue proprie parole il Tartaglia, nell'atto di dedicare a Francesco Maria <lb/>della Rovere, duca di Urbino, il libro, in cui distese ordinatamente il primo, <lb/>e affatto nuovo trattato della Scienza del moto. </s>

<s>In quella Lettera infatti, <lb/><emph type="italics"/>data in Venetia in le case nuove di S. Salvatore, alli XX di Dicem&shy;<lb/>bre M. D. XXXVIII,<emph.end type="italics"/> cos&igrave; appunto scrive: &ldquo; Habitando in Verona l'anno <lb/>M. D. XXXI, illustrissimo signor Duca, mi fu adimandato da un mio intimo <lb/>e cordiale amico, peritissimo bombardiere in Castel vecchio, uomo attem&shy;<lb/>pato e copioso di molte virt&ugrave;, il modo di mettere a segno uno pezzo di ar&shy;<lb/>tiglieria al pi&ugrave; che pu&ograve; tirare. </s>

<s>E abbench&egrave; in tale arte io non avessi pratica <lb/>alcuna, perch&egrave; in vero, eccellentissimo Duca, giammai discargheti (scaricai) <lb/>artiglieria, archibuso, bombarda n&egrave; schioppo, nientedimeno, desideroso di <lb/>servir l'amico, gli promisi di dargli in breve risoluta risposta. </s>

<s>E di poi che <lb/>ebbi ben masticata e ruminata tal materia, gli conclusi e dimostrai con ra&shy;<lb/>gioni naturali e geometrice qualmente bisognava che la bocca del pezzo <lb/>stesse elevata talmente, che guardasse rettamente a 45 gradi sopra l'oriz&shy;<lb/>zonte &rdquo; e dice che si serviva per far ci&ograve; di una squadra, o come pi&ugrave; pro&shy;<lb/>priamente si direbbe da noi di un archipenzolo, colla quarta del cerchio <lb/>divisa in dodici gradi, insegnando che l'obice torner&agrave; giusto eretto a 45 gradi, <lb/>quando, posto il lato pi&ugrave; lungo di essa squadra in dirittura con l'asse del <lb/>cannone, il filo a piombo batter&agrave; sul mezzo del quadrante, ossia nel sesto <lb/>grado. </s>

<s>Poi prosegue cos&igrave; la narrazione: &ldquo; La qual conclusione a esso parve <lb/>aver qualche consonantia, pur circa ci&ograve; dubitava alquanto, parendo a lui che <lb/>tal pezzo guardasse troppo alto. </s>

<s>Il che procedeva per non esser capace delle <lb/>nostre ragioni, n&egrave; in le matematiche ben corroborato, nientedimeno con al&shy;<lb/>cuni esperimenti particolari infine si verific&ograve; totalmente cos&igrave; essere. </s>

<s>&rdquo; </s></p><p type="main">

<s>Prosegue poi con lo stesso tenore il Tartaglia a raccontare che questo <lb/>suo intimo amico, a cui egli aveva cos&igrave; insegnato a fare il tiro della mag&shy;<lb/>gior volata, inclinando l'asse dell'obice a mezza squadra, ebbe una scom&shy;<lb/>messa con un suo compagno d'arme, il quale sosteneva che, a voler raggiun&shy;<lb/>ger quella maggior volata, conveniva inclinare il pezzo due punti pi&ugrave; basso. </s></p><p type="main">

<s>&ldquo; E sopra di questo, poi soggiunge il Tartaglia, fu deposta una certa <lb/>quantit&agrave; di danari, e finalmente venneno alla sperienzia, e fu condotta una <lb/>colubrina da 20 a Santa Lucia in campagna, e cadauno di loro tir&ograve; secondo <lb/>la proposta, senza alcuno avvantaggio di polvere n&egrave; di palla, onde quello, <lb/>che tir&ograve; secondo la nostra determinazione, tir&ograve; di lontano, secondo che ne <lb/>fu referto, pertiche 1972 da piedi sei per pertica alla veronese; l'altro, che <lb/>tir&ograve; li due punti pi&ugrave; basso, tir&ograve; di lontano solamente pertiche 1872. Per la <lb/>qual cosa tutti li Bombardieri ed altri si verificarono della nostra determi-<pb xlink:href="020/01/1849.jpg" pagenum="92"/>nazione, che avanti di questa esperienzia stasevano (stavano) ambigui, imo, <lb/>la maggior parte avevano contraria opinione, parendoli che tal pezzo guar&shy;<lb/>dasse troppo alto. </s>

<s>&rdquo; </s></p><p type="main">

<s>Incoraggiato fervorosamente il Tartaglia in veder che alle sue divina&shy;<lb/>zioni di matematica astratta rispondevano cos&igrave; bene i fatti sperimentati, volle <lb/>penetrare pi&ugrave; addentro in questa materia, nella quale ebbe a scoprir nuove <lb/>altre cose non pi&ugrave; pensate prima di lui. </s>

<s>&ldquo; Et incominciai (son sue proprie <lb/>parole) a raziocinare la specie dei moti, che in un corpo grave potesse acca&shy;<lb/>dere, onde trovai quelle esser due: videlicet naturale et violento.... Da poi <lb/>investigai con ragion geometrica dimostrativa la qualit&agrave; de'transiti, ovver <lb/>moti violenti dei detti corpi gravi, secondo li varii modi che possono essere <lb/>eietti, ovver tirati violentemente per aere. </s>

<s>Oltra di questo mi certificai, con <lb/>ragioni geometrice dimostrative, qualmente tutti i tiri di ogni sorte di ar&shy;<lb/>tiglierie erano fra loro simili, e conseguentemente proporzionali, e simil&shy;<lb/>mente le distanzie loro.... Oltra di questo, con ragioni evidentissime, co&shy;<lb/>nobbi qualmente un pezzo di artiglieria posseva per due diverse vie, ovvero <lb/>elevazioni, percotere in un medesimo luogo. </s>

<s>&rdquo; </s></p><p type="main">

<s>Esamineremo pi&ugrave; particolarmente a suo luogo ci&ograve; che trovasse la scienza <lb/>de'proietti di vantaggiarsi in queste raziocinazioni e in queste esperienze <lb/>del Tartaglia, ma perch&egrave; fin d'ora apparisca non tutte essere state una va&shy;<lb/>nit&agrave; della mente, e una illusione degli occhi, giova osservare come fu il <lb/>Nostro, il quale present&igrave; la fallacia che s'ascondeva ne'giudizii comuni ai <lb/>suoi tempi, secondo i quali si riteneva potersi cos&igrave; furiosamente cacciare un <lb/>proietto, da farlo per qualche tratto del suo cammino procedere in linea <lb/>retta. </s>

<s>Udimmo di sopra Leonardo partecipare con tutti gli altri a questo <lb/>gravissimo errore, quando disse che, ne'tiri di punto in bianco, il moto <lb/>della palla della bombarda &egrave; <emph type="italics"/>nel sito della egualit&agrave;,<emph.end type="italics"/> ma il Tartaglia, giu&shy;<lb/>stamente considerando che qualunque sia la furia del moto violento, non <lb/>pu&ograve; la cacciata palla mai sottrarsi agli stimoli del moto naturale, consent&igrave; <lb/>che si dicesse impropriamente retta quella, che, sebbene insensibilmente, <lb/>conveniva che in ogni modo procedesse per linea curva. </s></p><p type="main">

<s>Partendosi l'Autore della <emph type="italics"/>Scientia nuova<emph.end type="italics"/> da questo verissimo princi&shy;<lb/>pio, si sarebbe con buoni auspicii incamminato verso la scoperta delle traiet&shy;<lb/>torie, ma le ignorate leggi dei moti naturali ebbero infelicemente ad arre&shy;<lb/>star que'progressi. </s>

<s>Ammise anch'egli, come tutti gli altri, che il velocitarsi <lb/>dei gravi cadenti fosse dovuto alle attrazioni, e alle impulsioni del mezzo, e <lb/>come tutti gli altri pure, argomentando dagli effetti della percossa, ne con&shy;<lb/>cluse che le velocit&agrave; delle cadute son proporzionali agli spazii. </s></p><p type="main">

<s>I progressi insomma, che fece per opera del Tartaglia la Dinamica, si <lb/>riducono principalmente ai proietti, intorno ai quali inizi&ograve; veramente il no&shy;<lb/>stro Bresciano una Scienza nuova. </s>

<s>Le altre parti della Meccanica non eb&shy;<lb/>bero da lui che assai scarsa cultura, e da non si pararagonar certamente <lb/>con quella di Leonardo da Vinci, mostratasi al nostro esame cos&igrave; larga ed <lb/>intensa Non fu una tal larghezza imitata forse a que'tempi meglio che dal <pb xlink:href="020/01/1850.jpg" pagenum="93"/>Cardano, per i varii trattati meccanici del quale &egrave; notabile che si trovin ri&shy;<lb/>dotte nel filo delle correnti tradizioni molte dottrine, rimaste sorrenate ne'Ma&shy;<lb/>noscritti vinciani. </s>

<s>E perch&egrave; il fatto &egrave; importante a persuader coloro, i quali <lb/>si credono che il grande Artista si ritrovasse in mezzo al fiume della scienza <lb/>senza nulla ricever dall'onda che viene, e senza dar nulla all'onda che v&agrave;, <lb/>&egrave; bene che si confermi con qualche esempio. </s></p><p type="main">

<s>Per primo de'quali ci piace addur quello della elasticit&agrave; dell'aria, e <lb/>della sua efficacia sulla caduta dei gravi. </s>

<s>Nella scarsa nostra erudizione sto&shy;<lb/>rica non abbiam saputo, di quel fatto fisico che tanto dette a dubitare ai <lb/>Saggi, trovar altro documento anteriore a quello portoci da una delle sopra <lb/>trascritte Note di Leonardo, nella quale si diceva non si poter dare scienza <lb/>del moto dei gravi, <emph type="italics"/>se prima non si d&agrave; la quantit&agrave; della condensazione <lb/>dell'aria, percossa da qualunque mobile, la qual condensazione sar&agrave; di <lb/>maggiore o minore densit&agrave;, secondo la maggiore o minore velocit&agrave;, che <lb/>ha in s&egrave; il mobile che la preme.<emph.end type="italics"/> Or vien da un tal chiarissimo documento <lb/>provocata la domanda, se veramente fu Leonardo il primo a scoprire il fatto <lb/>del condensamento dell'aria, o s'ei la ricev&egrave; piuttosto dalle tradizioni scien&shy;<lb/>tifiche de'suoi tempi. </s>

<s>Per risposta di che pu&ograve; opportunamente osservarsi <lb/>come il Cardano, a cui si pu&ograve; credere che non fossero mai venuti sott'oc&shy;<lb/>chio i manoscritti vinciani, applica, nella proposizione CX del suo <emph type="italics"/>Opus no&shy;<lb/>vum,<emph.end type="italics"/> il fatto del condensarsi l'aria a proporzion che il corpo, con pi&ugrave; o <lb/>men grayezza cadendo, sotto di s&egrave; la preme, per conciliare il falso princi&shy;<lb/>pio aristotelico con gli apparenti resultati dell'esperienza. </s></p><p type="main">

<s>Nel II libro <emph type="italics"/>De subtilitate,<emph.end type="italics"/> entrando l'Autore, a proposito degli elementi, <lb/>a trattare dell'aria, riferisce il detto di coloro che, reputandola lieve in s&egrave; <lb/>stessa, ne concludevano perci&ograve; che vien mossa dalla sua propria forma, per <lb/>cui, usciti dalla man del motore, si vede conservarsi tuttavia il moto im&shy;<lb/>presso ai proietti. </s>

<s>Intorno a che soggiunge esser quattro le opinioni &ldquo; quas <lb/>nullus expositor intellexit, et maxime Aristotelis, quem adeo iactant opinio&shy;<lb/>nem &rdquo; (Lugduni 1580, pag. </s>

<s>90). La quale opinione aristotelica, passando il <lb/>Cardano in quarto luogo ad esporre, dice che consisteva nell'ammetter la <lb/>comunicazione e la partecipazion del moto al proietto, dall'ondoso moto aereo <lb/>concentrico al proiciente, il qual moto, estinguendosi a poco a poco nel diffon&shy;<lb/>dersi sempre pi&ugrave; al largo, abbandona finalmente il mobile nella sua quiete. </s>

<s><lb/>Dopo che torna a ripetere non aver nessuno prima di lui saputo intendere <lb/>il testo aristotelico, inteso gi&agrave; benissimo, come vedemmo, ed esposto in que&shy;<lb/>sta medesima cardanica sentenza da Leonardo. </s></p><p type="main">

<s>Un altro esempio del consentimento che passa fra le idee dei due ce&shy;<lb/>lebri uomini, da che ragionevolmente per noi se ne conclude dover avere <lb/>avute in qualche modo comuni le tradizioni, ci si porge dal moto dei corpi <lb/>pendoli, intorno ai quali udimmo dianzi ragionar l'Autore delle Note ma&shy;<lb/>noscritte cos&igrave;, come fa l'Autore del II libro <emph type="italics"/>De subtilitate:<emph.end type="italics"/> &ldquo; At vero, cum <lb/>impellitur, tanta ferme vi redit ad medium, quanta ab illo depulsum est. </s>

<s><lb/>Igitur cum ea vi iam depulsum sit a medio, gratia exempli, per cubiti spa-<pb xlink:href="020/01/1851.jpg" pagenum="94"/>tium, tantumdem descendere in contrariam partem necessarium erit, atque <lb/>ita continuo ac alternato reditu tardissime conquiescere &rdquo; (ibid., pag. </s>

<s>97). </s></p><p type="main">

<s>Chi poi volesse facilmente persuadersi che il Cardano non lasci&ograve; forse <lb/>inesplorata nessuna parte di quell'ampio soggetto, che la Meccanica presen&shy;<lb/>tava alle speculazioni di Leonardo, non ha a far altro che svolgere le pagine <lb/>dell'<emph type="italics"/>Opus novum,<emph.end type="italics"/> dove della Statica e della Dinamica si trovano proposti e <lb/>dimostrati i pi&ugrave; importanti teoremi. </s>

<s>Il Filosofo non procede in tutti sicuro, <lb/>come l'Artista, per le ragioni, altre volte accennate, dell'aver diffidato o del <lb/>non essersi ben chiarita in mente la regola di risolvere i moti, a che ag&shy;<lb/>giungevasi il prevaler nella mente di lui le speculate teorie ai fatti speri&shy;<lb/>mentati. </s>

<s>I principali esempii di quelle incertezze, che poi condussero anche <lb/>il Cardano nell'errore comune, si possono desumere dalle proposizioni LXXII <lb/>e CXVIII, dove, attendendo l'Autore a ricercare in qual proporzione stanno <lb/>i pesi scendenti sopra varie declivit&agrave; di piani, e le percosse sopra varie obli&shy;<lb/>quit&agrave; di pareti, riduce quelle stesse proporzioni agli angoli, piuttosto che ai <lb/>seni. </s>

<s>La fallacia del ragionamento di lui consisteva nel concluder ch'essendo <lb/>per l'orizzontale il peso e la percossa nulli, e per il perpendicolo quello to&shy;<lb/>tale, e questa del massimo effetto; si compartissero giustamente secondo le <lb/>varie declivit&agrave; i gradi di mezzo. </s></p><p type="main">

<s>Il Cardano aveva, insieme con gli altri usciti dalle pubbliche scuole, <lb/>pi&ugrave; fiducia nelle filosofiche virt&ugrave; del ragionamento, che nell'esperienza, ma <lb/>Leonardo, il quale la pensava altrimenti, ritrov&ograve; nell'esperienza stessa, come <lb/>vedemmo, la sua salvezza. </s>

<s>Forse non ebbe n&egrave; anch'esso Cardano, in propo&shy;<lb/>sito delle percosse, a trascurar di ricorrere ai fatti, i quali non valsero nulla&shy;<lb/>dimeno a farglisi benefici rivelatori del vero, per un inganno che nascon&shy;<lb/>devasi sotto. </s>

<s>Consisteva quell'inganno nel deviar che fa il mobile dalla sua <lb/>giusta dirittura l'aria, dalla foga di lui innanzi innanzi compressa; sottilissimo <lb/>inganno possibile solo a scoprirsi dalla sagacia sperimentale di Vincenzio <lb/>l&igrave;enieri, e un secolo prima da quella di Leonardo da Vinci. </s>

<s>&ldquo; La percussione, <lb/>egli dice, d'ogni grave sferico non far&agrave; cicatrice che abbian proporzione in <lb/>fra loro, qual'&egrave; quella dell'obliquit&agrave; de'siti dov'essi percotono. </s>

<s>&mdash; Quel che <lb/>si propone non mancherebbe merito che non fussi integralmente confermo <lb/>dall'esperienza, se non fosse la fissa condensazione dell'aria sospinta dal fu&shy;<lb/>rore della pallotta, la quale, non sendo in s&egrave; veloce come il moto fatto da tal <lb/>motore che la caccia, si viene a condensare, e tanto pi&ugrave; si condensa, quanto <lb/>&egrave; pi&ugrave; cacciata, e per questo accade che percote poi tale pallotta con linea, <lb/>che non sia centrale &rdquo; (Ravaisson-Mollien, Manuscr. </s>

<s>L, Paris 1890, fol. </s>

<s>44). </s></p><p type="main">

<s>La inferiorit&agrave; nell'arte sperimentale, a paragone di quella che appari&shy;<lb/>sce cos&igrave; sottile in questa Nota di Leonardo, si rivela forse pi&ugrave; manifesta nel <lb/>fatto della libera caduta dei gravi, intorno a che il Cardano, nella proposi&shy;<lb/>zione XIII, non sa far altro che commentare le pi&ugrave; volgari dottrine, dimo&shy;<lb/>strando che le parti anteriori del mezzo resistono, mentre invece le poste&shy;<lb/>riori, entrando a riempire il vacuo, aiutano alla velocit&agrave; del mobile il moto. </s>

<s><lb/>Da ci&ograve; poi conclude, nella XXXI, la ragione del perch&egrave;, verso la fine, vada <pb xlink:href="020/01/1852.jpg" pagenum="95"/>il grave cadente sempre pi&ugrave; accelerandosi, che in altra parte del tempo. </s>

<s><lb/>Nella scienza poi dei moti violenti si solleva mirabilmente il Cardano sopra <lb/>la volgare schiera, principalmente per aver notato che la parte di mezzo <lb/>della traiettoria non &egrave; circolare, come dicevano Leonardo stesso e il Tarta&shy;<lb/>glia &ldquo; sed quasi linea, quae parabolae ferme imitatur &rdquo; (De subtil. </s>

<s>cit., <lb/>pag. </s>

<s>96), e poi per aver combattuto l'antico errore del mezzo, che conserva <lb/>anche fuor del motore al mobile l'impulso del moto, sostituendogli franca&shy;<lb/>mente l'altra vera sentenza, che cio&egrave; &ldquo; illud quod movet est impetus acqui&shy;<lb/>situs &rdquo; (ibid., pag. </s>

<s>93). </s></p><p type="main">

<s>La forza d'inereia trasparisce di qui, nel lungo decorrere della storia <lb/>da Aristotile in poi, per la prima volta, bench&egrave; ne'moti dei pendoli l'avesse <lb/>Leonardo in qualche modo avvertita, e l'avesse posta il Cardano stesso, come <lb/>dianzi s'&egrave; inteso, in pi&ugrave; espressa forma. </s>

<s>Notabile &egrave; come una tal notizia, <lb/>senza la quale era affatto impossibile che si spedisse alla Dinamica il passo, <lb/>si chiarisse cos&igrave; alle menti nel breve tratto di tempo interceduto fra le prime <lb/>speculazioni del Cardano e le ultime del Benedetti; che bisognasse a questi <lb/>aguzzare l'ingegno per rispondere a chi domandava come mai, date le prime <lb/>mosse a un pendolo, per esempio, o a una ruota, non perseverino perpetui <lb/>nel moto, come pur dovrebbero fare per necessaria legge della loro inerzia. </s></p><p type="main">

<s>Di qui si vede che gl'incerti albori crepuscolari son gi&agrave; passati, e che <lb/>il sole incomincia a vibrare oramai sull'orizzonte scoperti i suoi primi raggi, <lb/>prima di rivolgersi a contemplare i quali nelle speculazioni del Benedetti, <lb/>giova fissare in Guidubaldo del Monte quell'indivisibile punto, che distin&shy;<lb/>gue i pi&ugrave; vivi e intensi riflessi dell'aurora dalla luce diretta del giorno. </s></p><p type="main">

<s>Il maraviglioso impulso, che vennero a dare ai progressi delle Matema&shy;<lb/>tiche nel secolo XVI le resuscitate tradizioni archimedee, sollecit&ograve; le infa&shy;<lb/>ticabili cure di Federigo Comandino a cercar dovunque, a tradurre e a com&shy;<lb/>mentare i libri di tanti altri Matematici antichi, cosicch&egrave; deplorava Guidubaldo <lb/>nella morte di lui la perdita di que'medesimi celeberrimi uomini Archita, <lb/>Euclide, Apollonio e Archimede stesso, i quali parve essere a un tratto tor&shy;<lb/>nati a rivivere nell'Urbinate. </s>

<s>&ldquo; Ille autem, poi soggiunge nella prefazione <lb/>al <emph type="italics"/>Mechanicorum liber<emph.end type="italics"/> (Pisauri 1577), perpetuo in aliarum mathematicarum <lb/>explicationem versans, mechanicam facultatem aut penitus praetermisit, aut <lb/>modice attigit. </s>

<s>Quapropter in hoc studium ardentius ego incumbere coepi. </s>

<s>&rdquo; </s></p><p type="main">

<s>La parola <emph type="italics"/>Meccanica<emph.end type="italics"/> non ha per&ograve; per Guidubaldo quella estensione di <lb/>significato, che ha ora per noi, e ch'ebbe in effetto per Leonardo da Vinci, <lb/>per il Cardano e per il Tartaglia, ma si restringeva a significare il trattato <lb/>delle Macchine, alla descrizion delle quali insomma riducevasi tutta la scienza. </s>

<s><lb/>Lo studio delle facolt&agrave; meccaniche, a cui dice di essersi ardentemente rivolto <lb/>il Nostro, &egrave; dunque assai limitato, ma pur era, pi&ugrave; che altri mai, bisognoso <lb/>di speciale attenzione sulla fine del secolo XVI, perch&egrave;, nel vastissimo campo <lb/>aperto dai tre grandi uomini sopra commemorati, rimanevasi unico quasi <lb/>negletto. </s></p><p type="main">

<s>Pappo infatti e Vitruvio si erano contentati a descriver le Macchine, e <pb xlink:href="020/01/1853.jpg" pagenum="96"/>ad insegnare il modo di disporne cos&igrave; gli organi, che valessero a produrre <lb/>il massimo effetto: dalla Scuola alessandrina e dalla Peripatetica s'era gi&agrave; <lb/>conclusa, e con matematiche dimostrazioni confermata la legge statica ge&shy;<lb/>nerale, ma come poi si applicasse una tal legge, eminentemente rappresen&shy;<lb/>tata nella Leva, a tutte le altre Macchine, era un desiderio che Guidubaldo, <lb/>col suo ardente studio, si dette a sodisfare, specialmente in coloro &ldquo; qui ex <lb/>Pappo, ex Vitruvio et aliis didicerint quid sit Vectis, quid Trochlea, quid <lb/>Axis in peritrochio, quid Cuneus, quid Cochlea, quomodoque, ut pondera <lb/>moveri possint, aptari debeant; adhuc tamen accidentia permulta, quae <lb/>inter potentiam et pondus vectis virtute illis insint instrumentis, perdiscere <lb/>cupiunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>L'intenzion dell'Autore, corrispondente ai bisogni reclamati allora dagli <lb/>studiosi, era dunque quella di dimostrare come alla virt&ugrave; del Vette si ridu&shy;<lb/>cano le accidentali relazioni, che passano tra la potenza e il peso negli altri <lb/>strumenti, e infatti si coronan le proposizioni di ciascun trattato col dire e <lb/>col ripetere: &ldquo; Ex his manifestum est ita esse pondus ad potentiam, ipsum <lb/>pondus sustinentem, sicut spatium potentiae moventis ad spatium ponderis <lb/>moti &rdquo; (Mechan. </s>

<s>lib. </s>

<s>cit., fol. </s>

<s>82 t.). E perch&egrave; gli spazii sono in ogni caso <lb/>proporzionali ai tempi, un altro importantissimo corollario si deduce dai di&shy;<lb/>mostrati teoremi, ed &egrave;: &ldquo; quo pondus facilius movetur, eo quoque tem&shy;<lb/>pus maius esse; quo vero difficilius, eo minor esse, et e converso &rdquo; (ibid., <lb/>fol. </s>

<s>105 t.): propriet&agrave; generale di tutte le Macchine, che l'Autore stesso ap&shy;<lb/>plica cos&igrave; alla Coclea in particolare: &ldquo; Ex his manifestum est quo plures <lb/>sunt helices, et quo longiores sunt scytalae, sive manubria, pondus ipsum, <lb/>facilius quidem, tardius autem moveri &rdquo; (ibid., fol. </s>

<s>123). A torto dunque <lb/>rimproverava Galileo l'<emph type="italics"/>inganno universale<emph.end type="italics"/> dei Meccanici, ch'ei pretendeva <lb/>di esser <expan abbr="ve&ntilde;uto">vennuto</expan> egli primo a scoprire al mondo ignorante, col dimostrargli <lb/>come quel che si acquista nella forza si scapita nel tempo (Alb. </s>

<s>XI, 85, 87). <lb/>Il trattato galileiano Delle macchine non differisce sostanzialmente da quello <lb/>di Guidubaldo, in qualche parte emendato dietro il progredir, che in un <lb/>mezzo secolo aveva fatto la scienza. </s></p><p type="main">

<s>Concernono principalmente quegli emendamenti la teoria del piano in&shy;<lb/>clinato, intorno alla quale l'Autor del Libro delle meccaniche ripete l'er&shy;<lb/>rore antico di Pappo salutato da lui, insieme con Archimede, per suo rive&shy;<lb/>rito maestro. </s>

<s>&ldquo; Ego enim, in hac praesertim facultate, Archimedis vestigiis <lb/>haerere semper volui. </s>

<s>&rdquo; Maestro poi sopra tutti i maestri riconosce osse&shy;<lb/>quioso il grande Aristotile, di cui non fece Archimede stesso ch'esplicar le <lb/>dottrine, e applicarle ad esempii particolari. </s>

<s>&ldquo; Archimedi saepius fuit mecha&shy;<lb/>nicae disciplinae rudimenta explanare, propterea ad magis particularia enu&shy;<lb/>cleanda descendere voluit &rdquo; (In duos Archim. </s>

<s>libros paraphrasis, Pisauri 1588, <lb/>pag. </s>

<s>4). In Guidubaldo insomma non &egrave; da aspettarsi nessuna novit&agrave; della <lb/>scienza, ch'egli crede esser benissimo dagli antichi trattata. </s>

<s>E se alcuno si <lb/>sentisse intorno a ci&ograve; movere qualche dubbio, riducasi solo alla memoria <lb/>que'grandi nomi di Aristotile e di Archimede, e se lo vedr&agrave; a un tratto <pb xlink:href="020/01/1854.jpg" pagenum="97"/>dissipar dalla mente. </s>

<s>&ldquo; Ambiget fortasse quispiam numquid haec principia <lb/>recte ab illis fuerint pertractata, sed statim omnis cessat dubitandi occasio, <lb/>si tantorum virorum praestantia ad memoriam revocetur &rdquo; (ibid., pag. </s>

<s>5). </s></p><p type="main">

<s>In Giovan Batista Benedetti per&ograve;, da cui propriamente s'instaura una <lb/>scienza nuova, hanno le parole un tuono molto diverso. </s>

<s>Confessa anch'egli <lb/>in Aristotile ammirabile la sapienza, ma benche senta il gran pericolo, che <lb/>si correva a'suoi tempi in contraddire ai placiti venerati, &ldquo; in medium, egli <lb/>francamente dice nella prefazioncella alle <emph type="italics"/>Disputazioni,<emph.end type="italics"/> quaedam proferre <lb/>non dubitavi, in quibus me inconcussa Mathematicae philosophiae basis, cui <lb/>semper insisto, ab eo dissentire coegit &rdquo; (Specul. </s>

<s>liber cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Versano principalmente i dissensi intorno a ci&ograve; che il Filosofo aveva <lb/>ne'suoi varii libri insegnato degli accidenti, che accompagnano il moto, e <lb/>delle cause, che velocitano i gravi. </s>

<s>Avverte sapientemente la fallacia delle <lb/>dottrine peripatetiche, in sentenziare che le velocit&agrave; son proporzionali ai pesi, <lb/>consistere nel non avere abbastanza considerato la gran differenza della re&shy;<lb/>sistenza opposta dal mezzo alla caduta de'gravi di figura varia, e di varii <lb/>volumi: e dop'avere, in una bene ordinata serie di capitoli, dimostrato se&shy;<lb/>condo qual proporzione i mezzi stessi variati alterino la legge dei moti; ne <lb/>conclude, con gran maraviglia di chi sente annunziarsi una cosa tanto <lb/>nuova, &ldquo; quod, in vacuo, corpora eiusdem materiae aequali velocitate mo&shy;<lb/>verentur &rdquo; (ibid., pag. </s>

<s>174). </s></p><p type="main">

<s>Le porte della verit&agrave;, rimaste dai peripatetici insegnamenti per s&igrave; lun&shy;<lb/>ghi secoli imprunate, una volta rese cos&igrave; felicemente sgombre dovevano con&shy;<lb/>durre il Benedetti a consegnare di propria mano allo stesso Galileo la chiave, <lb/>da entrare addirittura ne'pi&ugrave; riposti vestiboli del tempio. </s>

<s>Il Cardano e lo <lb/>Scaligero avevano fatto fare alla Dinamica il primo passo, dando, fra le varie <lb/>opinioni degli antichi, la preferenza a quella, che ammetteva moversi, anche <lb/>fuor del motore, il mobile per intrinseca virt&ugrave; rimastagli impressa, e non <lb/>per estrinseca impulsione del mezzo, ma ne'moti naturali non avevano sa&shy;<lb/>puto ancora vedere come si potesse convenientemente applicare questa legge <lb/>dell'inerzia. </s>

<s>Il Benedetli per&ograve;, nel cap. </s>

<s>XXIV delle sopra citate Disputazioni, <lb/>rimeditava quel s&igrave; fecondo principio professato dal Nemorario, non essere <lb/>altro cio&egrave; la quiete se non che il termine del moto, e poi mirabilmente com&shy;<lb/>mentato da Leonardo con dire, che <emph type="italics"/>la pietra che cade fu prima portata <lb/>e gettata in alto,<emph.end type="italics"/> e non facendo perci&ograve; alcuna distinzione fra moto violento <lb/>e naturale, n'ebbe logicamente a concluder che nasceva anche questo da <lb/>una certa impressione &ldquo; ex impetuositate recepta a dicto mobili, quae im&shy;<lb/>pressio et impetuositas, in motibus rectis naturalibus, continuo crescit &rdquo; (ibid., <lb/>pag. </s>

<s>184). E ci&ograve;, in altre parole e in altra forma, voleva appunto dire che <lb/>le velocit&agrave; sono proporzionali ai tempi. </s>

<s>La qual nuova forma introdotta nei <lb/>semplicissimi teoremi archimedei, dai quali per facile corollario scendeva <lb/>stare gli spazii in ragion composta delle velocit&agrave; e dei tempi, veniva mira&shy;<lb/>bilmente a scoprirsi in quella gran verit&agrave;, conclusa e al mondo attonito an&shy;<lb/>nunziata da Galileo, che cio&egrave; gli spazii non vanno altrimenti, come dicevasi <pb xlink:href="020/01/1855.jpg" pagenum="98"/>da tutti, secondo i semplici tempi, ma secondo i quadrati di quegli stessi <lb/>tempi. </s></p><p type="main">

<s>A questi poi, che sono i principali, s'aggiungono altri meriti dovuti <lb/>nell'instaurare la scienza all'insigne Matematico veneziano, quali sarebbero <lb/>quello di avere illustrate molte delle Questioni aristoteliche, dimostrando per <lb/>esempio come il Cuneo e le Taglie si r&igrave;ducono propriamente alle ragioni <lb/>del Vette; quello di aver prefinita la misura giusta alla lunghezza del brac&shy;<lb/>cio, nella Leva angolare, e nelle direzioni oblique di avere insegnato a com&shy;<lb/>putarne il momento rotatario; quello di aver posto il principio matematico <lb/>alle forze centrifughe, argutamente osservando, <emph type="italics"/>id quod a nemine adhuc, <lb/>quod sciam est observatum<emph.end type="italics"/> (pag. </s>

<s>286), che cio&egrave;, bench&egrave; sia il mobile pre&shy;<lb/>potentemente menato in giro dal motore, tende nonostante a rifuggire in <lb/>linea retta, non verso il centro del mondo, ma in direzione della tangente. </s>

<s><lb/>Da molte altre parti di questo trattatello <emph type="italics"/>De mechanicis<emph.end type="italics"/> scaturiscono vivi <lb/>raggi di luce, a illuminare alla scienza gl'incerti sentieri. </s></p><p type="main">

<s>&Egrave; a questo punto terminato il Prologo del nostro Dramma, ne'perso&shy;<lb/>naggi del quale, e specialmente degli ultimi compariti in scena, fissando gli <lb/>spettatori lo sguardo, gli riconosceranno quasi tutti, d'abito e di nazione, <lb/>italiani. </s>

<s>Simeone Stevino, unico forse fra gli stranieri che vi si fosse intruso, <lb/>ha dovuto modestamente ritirarsi in disparte, riconoscendo d'essere stato <lb/>prevenuto nell'azion principale dal Cardeno e dal Tartaglia, l'un de'quali <lb/>aveva gi&agrave;, per matematiche ragioni, concluso che s'equilibran due pesi sopra <lb/>due varie obliquit&agrave; di piani, le lunghezze de'quali stien come gli stessi pesi; <lb/>e l'altro era venuto a dimostrare ai Meccanici il vero principio della com&shy;<lb/>posizion delle forze, bench&egrave; mostrasse di non sapere in nessun caso come <lb/>applicarlo agli esempii. </s></p><p type="main">

<s>Cos&igrave; stando i fatti, fin qui da noi lungamente discorsi, non pu&ograve; non <lb/>recarci gran maraviglia quel che leggesi appresso a un celebrato Storico <lb/>delle Matematiche, non ridursi cio&egrave; l'opera, data allo studio della Mecca&shy;<lb/>nica dagli scienziati del secolo XVI, che a certi prolissi commentarii sulle <lb/>Questioni aristoteliche. </s>

<s>&ldquo; Les travaux des savans du seizieme si&egrave;cle, sur la <lb/>Mecanique, dice Stefano Montucla, ne consistent presque qu'en de prolixes <lb/>commentaires sur les Questions mecaniques d'Aristote &rdquo; (Tome I, An. </s>

<s>VII, <lb/>pag. </s>

<s>689). E altrove avea gi&agrave; il medesimo Autore mostrato un gran disprezzo <lb/>per il Filosofo, dicendo che la maggior parte delle spiegazioni meccaniche <lb/>di lui son false, e che la prima e fondamentale, dedotta dalle dignit&agrave; del <lb/>circolo, &ldquo; est tout-a-fait ridicule &rdquo; (ivi, pag. </s>

<s>187). </s></p><p type="main">

<s>Nel secolo XVIII eran pur troppo tali i correnti giudizii dei Matema&shy;<lb/>tici; giudizii, a formulare e a confermar ne'quali le menti, avevano avuto <lb/>gran parte Galileo e il Cartesio, ambiziosi di tenere il principato della scienza, <lb/>e gelosi di dividerne con qualsivoglia altri il potere. </s>

<s>Ma pure al primo esce <lb/>pi&ugrave; qua e pi&ugrave; l&agrave; ingenuamente di bocca la confessione di aver trovato in <lb/>Aristotile il principio a certe sue meccaniche speculazioni, che sarebbero al&shy;<lb/>trimenti rimaste forse senza progressi. </s>

<s>Cos&igrave; la nuova scienza delle resistenze <pb xlink:href="020/01/1856.jpg" pagenum="99"/>dei solidi confessa aver avuto in lui il motivo dalle Questioni meccaniche <lb/>del Filosofo &ldquo; mentre vuol render la ragione onde avvenga che i legni, <lb/>quanto son pi&ugrave; lunghi, tanto son pi&ugrave; deboli &rdquo; (Alb. </s>

<s>XIII, 125), e mentre <lb/>in altra Questione risponde al perch&egrave; &ldquo; manco fatica si ricerchi a rompere <lb/>un legno, tenendo le mani nell'estremit&agrave;, cio&egrave; remote assai dal ginocchio, <lb/>che se le tenessimo vicine &rdquo; (ivi, pog. </s>

<s>134), riducendo, come Galileo nella <lb/>II Giornata delle Due nuove scienze, la causa di questi fatti a quella ge&shy;<lb/>neralissima delle Leve, il principio statico che governa le quali, e che con&shy;<lb/>siste nel compensarsi la tardit&agrave; del resistente dalla velocit&agrave; del movente, <lb/>confessa Galileo stesso essere stato Aristotile il primo a proporlo e a dimo&shy;<lb/>strarlo (ivi, pag. </s>

<s>264). N&egrave; gli parve quella dimostrazione punto ridicola, come <lb/>nou parve tale a Leonardo da Vinci, il quale anzi, in tempi che prevalevano <lb/>le dottrine del Nemorario, elesse di tornar cos&igrave; all'antico modo di ragionar <lb/>del Filosofo: &ldquo; Quella cosa, che fia pi&ugrave; lontana al suo firmamento, manco <lb/>da essa fia sostenuta. </s>

<s>Essendo manco sostenuta, pi&ugrave; fia partecipevole di sua <lb/>libert&agrave;, e perch&egrave; il peso libero sempre discende, adunque quella estremit&agrave; <lb/>dell'asta d'essa Bilancia, che fia pi&ugrave; distante al suo firmamento, perch&egrave; &egrave; <lb/>ponderosa, pi&ugrave; presto che alcuna parte di s&egrave; discender&agrave; &rdquo; (Manuscr. </s>

<s>N.o 2038, <lb/>Paris 1891, fol. </s>

<s>2 t.). </s></p><p type="main">

<s>In ogni modo a nessuno mai parve ridicola la Questione XXIV &ldquo; quam <lb/>ob causam maior circulus aequalem minori circumvolvitur lineam, quando <lb/>circa idem centrum fuerint positi &rdquo; (Arist., operum T. XI cit., fol. </s>

<s>35 t.). <lb/>Il Benedetti, che fu forse il primo a torturar nel curioso quesito l'ingegno, <lb/>disse nel cap. </s>

<s>XXII del suo trattatello <emph type="italics"/>De mechanicis<emph.end type="italics"/> che il moto del mi&shy;<lb/>nor circolo della ruota non &egrave; tutto progressivo, ma in parte anche regres&shy;<lb/>sivo, e Galileo, che fra tutti disse ammirabile questo problema, rifiutata la <lb/>prima spiegazione affacciataglisi alla mente, ripetuta poi da alcuni Francesi, <lb/>che cio&egrave; fossero i punti della circonferenza minore, tirati dalla maggiore, <lb/>strascicati per qualche tratto (Alb. </s>

<s>XIII, 27); and&ograve; a immaginare un gioco <lb/>de'vacui interposti, quasi la maggiore circonferenza fosse, rispetto a&igrave;la mi&shy;<lb/>nore, una corda elastica stirata. </s></p><p type="main">

<s>&Egrave; un fatto per&ograve;, notabilissimo per la nostra Storia, che volle Galileo a <lb/>grande studio tenere occulte le pi&ugrave; prossime e pi&ugrave; ubertose fonti, dalle <lb/>quali derivavagli, specialmente in Italia, a que'suoi tempi la scienza. </s>

<s>Le ve&shy;<lb/>locit&agrave; virtuali e la ragion de'pesi alle lunghezze dei piani inclinati, che po&shy;<lb/>nevano da una parte il principio, e dall'altra venivano a dare alla Statica <lb/>l'incremento; la regola della composizione dei moti, e le forze d'inerzia, <lb/>applicate prima ai proietti e poi alle naturali cadute dei gravi, per cui si <lb/>aprivano cos&igrave; facili le vie alla Dinamica; volle l'ambizioso Autore dei Dia&shy;<lb/>loghi fare apparire al mondo come dottrine nuove, gelosamente tacendo il <lb/>nome del Benedetti, e dispettosamente protestandosi di non saper quel che <lb/>s'avessero detto il Cardano e il Tartaglia nei loro libri. </s></p><p type="main">

<s>In tempi, che il Peripato regnava quasi universale e assoluto nelle <lb/>scuole, e che non riducevansi le scienze naturali ad altro, che a prolissi e <pb xlink:href="020/01/1857.jpg" pagenum="100"/>nebulosi commentarii intorno ai placiti del Filosofo; non riusc&igrave; difficile a <lb/>Galileo far apparire agli occhi degli spettatori d'un abito e d'un colore quei <lb/>tre o quattro, che si sarebbero da viste pi&ugrave; sincere facilmente scorti in mezzo <lb/>alla turba volgare. </s>

<s>Fu poi tanto destro l'ingegno e tanto fortunata l'opera <lb/>di quell'uomo in produrre una cos&igrave; fatta illusione, che dura tuttavia dopo <lb/>tre secoli, e durer&agrave; chi sa quanto, a far velo ai giudizii degli uomini. </s></p><p type="main">

<s>Comunque sia, &egrave; debito principale della nostra Storia lo scoprire l'in&shy;<lb/>ganno, e seguendo il filo delle tradizioni dimostrare come per legge natu&shy;<lb/>rale si sia svolto il pensiero. </s>

<s>Le creazioni, cos&igrave; facilmente attribuite agl'in&shy;<lb/>gegni, si possono ammettere per una iperbole, il qual modo per&ograve; di dire, <lb/>che piace a tanti, non essendo consentito alla scientifica precisione, ci sug&shy;<lb/>gerisce il prudente consiglio d'andar a ricercar la scintilla, che sempre per <lb/>necessit&agrave; seconda qualche gran fiamma. </s>

<s>E perch&egrave; si saranno accorti i Let&shy;<lb/>tori che il proposito nostro s'&egrave; in questo primo discorso incominciato gi&agrave; a <lb/>mandare ad effetto, proseguiremo in egual modo nelle singole trattazioni di <lb/>questa prima parte della Storia della Meccanica, per nostra gloria quasi tutta <lb/>italiana, soffermando il passo ne'Dialoghi delle Due nuove scienze, dai quali, <lb/>come da editto pubblicamente affisso, si promulgano al mondo le leggi <lb/>del moto. </s></p><pb xlink:href="020/01/1858.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO II.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dei Baricentri<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della invenzione del centro di gravit&agrave; nei solidi. </s>

<s>&mdash; II. </s>

<s>Dei quattro libri centrobrarict di Paolo <lb/>Guldino, e della Geometria degl'indivisibili di Bonaventura Cavalieri. </s>

<s>&mdash; III. </s>

<s>Delle risposte del <lb/>Cavalieri alle opposizioni fattegli dal Guldino, e come la Regola centrobrarica avesse dal Me&shy;<lb/>todo degl'indivisibili la sua prima matematica dimostrazione. </s>

<s>&mdash; IV. </s>

<s>Delle nuove dimostrazioni <lb/>della Regola centrobrarica che, primi, vennero a dare alle scienze matematiche in Italia Anto&shy;<lb/>nio Nardi e Vincenzio Viviani. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Le leggi del moto, che dicemmo essere state solennemente promulgate <lb/>dai primi Dialoghi di Galileo, segnano un'epoca novella nella storia della <lb/>Meccanica. </s>

<s>Ma l'epoca che la precede incomincia anch'essa dal medesimo <lb/>fatto delle cadute dei gravi, considerate sotto quel pi&ugrave; semplice aspetto, che <lb/>ci si presentano tutti i giorni nell'esperienze comuni. </s>

<s>Si vede ogni corpo <lb/>sempre per naturale necessit&agrave; cadere, quando gli venga meno il sostegno, <lb/>e o cada liberamente o sia sostenuto, &egrave; un sottilissimo filo quello che segna <lb/>la libera via, o che impedisce la tendenza del moto. </s>

<s>L'osservazione ovvia al <lb/>volgo e insignificante fu principio fecondo di scienza al Filosofo che, consi&shy;<lb/>derando come si poteva di qualunque peso impedir la caduta, col sostenerlo <lb/>per via di un semplicissimo filo; ebbe a concluderne che nella direzione <lb/>verticale di lui si raccoglieva dunque, alla caduta stessa, d'ogni parte il <lb/>conato. </s>

<s>Altre esperienze poi fecero questa prima importante notizia progre&shy;<lb/>dire pi&ugrave; oltre, imperocch&egrave;, vedendo rimanersi ugualmente bene nella sua <lb/>quiete il grave, da qualunque punto della sua superficie si tenesse sospeso, <lb/>non fu difficile, con l'aiuto della Geometria, concluderne che il conato del <pb xlink:href="020/01/1859.jpg" pagenum="102"/>cadente raccoglievasi tutto, non in una sottil linea, come dianzi pareva, ma <lb/>in un indivisibile punto, qual si viene a determinare dall'intersecamento delle <lb/>due verticali, che penetrano dentro il peso pendulo, or in una ora in un'altra <lb/>delle variate sue positure. </s>

<s>Dette perci&ograve; a quel punto l'artificioso linguaggio <lb/>dei Matematici il nome di <emph type="italics"/>Baricentro,<emph.end type="italics"/> o di Centro di gravit&agrave;, e dal consi&shy;<lb/>derarne le varie propriet&agrave; e gli effetti ebbe principio quella, che ai nostri <lb/>Italiani, i quali si dettero, primi nel secolo XVI, a coltivarla, piacque chia&shy;<lb/>mar col nome di Scienza dei pesi. </s></p><p type="main">

<s>Secondo l'uso volgare il permanere qualunque corpo sospeso in equi&shy;<lb/>librio si significa col dire ch'egli sta in bilancia, ci&ograve; che, mentre da una <lb/>parte rivela aver avuto l'artificioso strumento la sua prima origine da un <lb/>fatto naturale, dimostra dall'altra come dai centri di gravit&agrave; si pigliassero i <lb/>principii fondamentali alla Statica. </s>

<s>I pesi infatti, che s'impongono di qua e <lb/>di l&agrave; ne'bacini, si raccolgono come in centro nel fulcro della Libbra, e vi <lb/>rimangon sospesi in quiete infin tanto che non venga a mancare esso ful&shy;<lb/>cro. </s>

<s>Il trattato archimedeo perci&ograve; degli Equiponderanti non &egrave;, nella sua prima <lb/>parte, che l'esplicazione di questo stesso concetto, bench&egrave; la prevalente Geo&shy;<lb/>metria soggioghi e par che abbia quasi licenziata l'esperienza da'suoi an&shy;<lb/>tichi servigi. </s></p><p type="main">

<s>Il soggetto dall'altra parte veniva per s&egrave; stesso a vestire schietto abito <lb/>geometrico, dipendendo la giusta posizione del centro dalla forma propria <lb/>del corpo, n&egrave; portando le nuove inquisizioni altra differenza che del consi&shy;<lb/>derare come pesanti quelle particelle, che si riguardavano solo come per <lb/>ogni verso distese a occupare lo spazio. </s>

<s>Cos&igrave; confermasi l'idea di quello <lb/>stretto connubio, che passa fra la Meccanica e le Matematiche; idea che gi&agrave; <lb/>ci si rappresentava alla mente chiarissima, infin da quando udimmo Aristo&shy;<lb/>tile porre per fondamento alla scienza i moti generatori del cerchio. </s>

<s>Sarebbe <lb/>stato anzi giovevole il commemorar queste cose a coloro, a cui giunsero, a <lb/>mezzo il secolo XVII, inaspettati i servigi che, nel Metodo centrobrarico, ve&shy;<lb/>niva a rendere la Meccanica stessa alla Geometria. </s></p><p type="main">

<s>Ma per procedere ordinatamente nel nostro discorso &egrave; da tornare a <lb/>quel trattato Degli equiponderanti, in cui dimostrava Archimede essere una <lb/>medesima cosa il centro naturale dei gravi, e il centro artificiale della Lib&shy;<lb/>bra, matematicamente concludendo le leggi statiche dal principio dei Bari&shy;<lb/>centri. </s>

<s>La nuova istituzione archimedea per&ograve; non giovava allo studio della <lb/>Statica sola, ma conferiva mirabilmente ai progressi di tutta intera la Scienza <lb/>del moto, la quale veniva a rendersi cos&igrave; tanto pi&ugrave; semplice nelle sue la&shy;<lb/>boriose dimostrazioni, considerando le disperse virt&ugrave; come tutte insieme <lb/>raccolte in un punto. </s>

<s>Se ci fosse la comparazione permessa, diremmo perci&ograve; <lb/>che la Baricentrica &egrave;, nella Scienza del moto, quel ch'&egrave; il cuore nella vita <lb/>dell'animale, ond'ei si pu&ograve; intendere com'ella debba nella storia apparire <lb/>la prima, quasi <emph type="italics"/>punctum saliens<emph.end type="italics"/> in mezzo alle altre non discernibili parti <lb/>dell'embrione. </s></p><p type="main">

<s>Cos&igrave; essendo, si riduceva tutto lo studio a cercare, e a segnar le vie di <pb xlink:href="020/01/1860.jpg" pagenum="103"/>giungere in quegli intimi penetrali, dove risiede il cuore impulsivo del moto <lb/>in tutti i gravi. </s>

<s>&Egrave; perci&ograve; che Archimede, dop'avere nel I libro dimostrata <lb/>la natura e le propriet&agrave; del punto, intorno a cui d'ogni parte si radunano <lb/>i pesi; passa immediatamente a cercare e a segnar quelle pi&ugrave; riposte vie <lb/>geometriche, che possono condurre a trovar quel punto preciso, bench&egrave; il <lb/>primo instituito insegnamento del grande Maestro lasci in vivo desiderio gli <lb/>studiosi di vederlo compiuto. </s></p><p type="main">

<s>I teoremi infatti, che ricorrono nella seconda met&agrave; del I libro, via via <lb/>dimostrati, concernono le sole figure piane circoscritte da linee rette, e il <lb/>II libro si consacra tutto alla ricerca del centro di gravit&agrave; ne'piani curvi&shy;<lb/>linei o, come saremmo tentati di chiamarli, triangoloidi parabolici. </s>

<s>Con <lb/>ci&ograve;, qual dopo tanti secoli e dopo tante vicende pervenne alle mani dei Ma&shy;<lb/>tematici, si chiude dall'Autore il trattato Degli equiponderanti. </s></p><p type="main">

<s>Gli studiosi lettori, fra'quali abbiamo noi Italiani da annoverarne, in&shy;<lb/>fino a mezzo il secolo XVI, distintamente tre de'pi&ugrave; insigni, si trovavano da <lb/>quella fida scorta abbandonati col&agrave;, dove speravano che sarebbero venuti a <lb/>riuscire gli ultimi passi. </s>

<s>Imperocch&egrave; quale importanza potevano per s&egrave; stesse <lb/>avere le superfice, se non in ordine ai solidi, i quali soli son propriamente <lb/>ponderosi? </s>

<s>Alla invenzione perci&ograve; del centro di gravit&agrave; de'triangoli si po&shy;<lb/>teva attendere com'a studio, ordinato a facilitar la ricerca del centro di gra&shy;<lb/>vit&agrave; nella piramide, e i baricentri ne'trapezii e nelle sezioni del cono si po&shy;<lb/>tevano desiderare per venir pi&ugrave; facilmente introdotti alle pi&ugrave; complicate <lb/>risoluzioni dei centri di gravit&agrave; ne'prismi e nelle conoidi. </s>

<s>Or a veder che <lb/>in quelle superfice piane, per s&egrave; medesime imponderanti, s'assolve tutta <lb/>quanta l'intenzion dell'Autore, se ne dovettero fare due congetture: o che <lb/>fosse venuto a mancare il III libro, dove avrebbe Archimede dato il suo <lb/>trattato Degli equiponderanti compiuto; o che, contento ad averne posti i <lb/>principii, lasciasse alla esercitazione degli studiosi le non difficili desiderate <lb/>conclusioni. </s></p><p type="main">

<s>Quanto ai solidi infatt&igrave;, che si dicono di rivoluzione, era ovviamente <lb/>dimostrabile che nella sfera e nel cilindro i centri di gravit&agrave; corrispondono <lb/>ai centri delle grandezze. </s>

<s>Maggiore difficolt&agrave; &egrave; vero incontravasi rispetto al <lb/>cono, le quali difficolt&agrave; venivano nonostante ad appianarsi, riguardando quel <lb/>solido come una piramide a base poligonare di un numero infinito di lati: <lb/>ond'&egrave; che riducevasi cos&igrave; la questione alla ricerca del centro nella piramide <lb/>stessa, la quale, in qual si voglia modo si presenti composta, &egrave; risolubile <lb/>sempre in altre minori piramidi a base triangolare. </s>

<s>Ma la baricentrica in&shy;<lb/>qui&sgrave;izion del triangolo pareva a questo principale intento presa a far dall'Au&shy;<lb/>tore in que'teoremi del I libro Dagli equiponderanti, perch&egrave;, proseguendo <lb/>simili vie, si potessero pi&ugrave; facilmente condurre gli studios&igrave; al baricentrico di <lb/>ogni solido piramidale. </s></p><p type="main">

<s>Comunque siasi raggiunsero veramente gl'istituti archimedei, nella <lb/>Scuola matematica di Luca Pacioli, questo intento, come si dimostra per <lb/>l'esempio insigne di Leonardo da Vinci, di cui solo ci rimangono i docu-<pb xlink:href="020/01/1861.jpg" pagenum="104"/>menti. </s>

<s>&ldquo; Il centro di ogni gravit&agrave; piramidale, cos&igrave; leggesi in una delle so&shy;<lb/>lite Note, &egrave; nel quarto del suo assi, verso la base, e se dividerai l'assis per <lb/>quattro eguali, e intersegherai due degli assi di tal piramide, tale interse&shy;<lb/>gamento verr&agrave; nel predetto quarto &rdquo; (Manuscr. </s>

<s>F cit., fol. </s>

<s>51). </s></p><p type="main">

<s>Guglielmo Libri che fu, come si disse, il primo a fermar l'attenzione <lb/>su queste Note, e a fissare gli occhi sopra le due figure appostevi per illu&shy;<lb/>strarle, si cred&egrave; di poter raccogliere da que'segni che Leonardo &ldquo; decom&shy;<lb/>posait les pyramides en plans paralleles a la base, comme on le fait a pre&shy;<lb/>sent &rdquo; (Histoire des Matem., T. III cit., pag. </s>

<s>41 in nota). La conclusione <lb/>per&ograve; sembra a noi temeraria, perch&egrave; ne'detti iconismi, e specialmente nel <lb/>secondo, niente altro fa l'Autore che rappresentare all'occhio quell'interse&shy;<lb/>camento de'due assi, condotti sulle respettive basi da due vertici opposti, <lb/>da cui diceva determinarsi alla piramide il preciso punto del centro. </s>

<s>&Egrave; ci&ograve; <lb/>dall'altra parte pienamente conforme con gli istituti archimedei, l&agrave; dove <lb/>s'insegna a trovare il centro di gravit&agrave; ne'triangoli; istituti, ch'ebbe a se&shy;<lb/>guir fedelmente anche il nostro Leon&agrave;rdo, a cui, ripetiamo, parerci teme&shy;<lb/>rario l'attribuire il metodo degl'indivisibili, che s'ebbe necessariamente a <lb/>introdur nella scienza, dopo la Geometria nuova del Cavalieri. </s>

<s>E perch&egrave; la <lb/>questione, a cui ha dato motivo il Libri, &egrave; di troppo grande importanza nella <lb/>Storia, non increscer&agrave; d'intrattenervi attorno brevemente il discorso. </s></p><p type="main">

<s>Il processo dimostrativo, che nel I libro Degli equiponderanti si pro&shy;<lb/>poneva, per le ricerche ulteriori, ad esempio, incomincia dalla proposi&shy;<lb/>zione XIII, nella quale dimostra Archimede che il centro della gravit&agrave; del <lb/>triangolo si trova nella bissettrice condotta dall'angolo opposto sopra la base. </s>

<s><lb/>Poi si passa, per facile via, alla proposizione XIV, che insegna a determi&shy;<lb/>nare il punto preciso del centro ricercato nell'intersezione di due delle dette <lb/>bissettrici, da due diversi angoli condotte nello stesso triangolo sopra cia&shy;<lb/>scuna delle due contrapposte basi. </s>

<s>D'onde con facile dimostrazione geome&shy;<lb/>trica si viene a concluderne, nel secondo lemma che segue, essere prefinito <lb/>il centro di gravit&agrave; nel triangolo dalla prima delle tre parti, in che s'in&shy;<lb/>tenda, a movere dalla base, essere stata divisa una bissettrice. </s></p><p type="main">

<s>Per procedere alla ricerca del centro della gravit&agrave; nella piramide il fa&shy;<lb/>cile ordine dunque, che si suggeriva dagl'insegnamenti di Archimede, era <lb/>questo: trovato il centro di due delle facce triangolari del solido, condurre <lb/>dai vertici opposti due linee, nell'intersezion delle quali dovendosi ritrovar <lb/>tutta insieme raccolta la gravit&agrave; piramidale, si dimostrava per Geometria, in <lb/>un modo simile a quello del citato lemma archimedeo, che la detta interse&shy;<lb/>zione facevasi ne'tre quarti della linea, che movendo dal vertice, va a ter&shy;<lb/>minar nel centro della opposta base triangolare. </s></p><p type="main">

<s>Or chi attende a cos&igrave; fatti processi dimostrativi facilmente ritrova che <lb/>dipendono ambedue dalla proposizione XIII del I Degli equiponderanti, posta <lb/>la quale, se ne concludono tutte le altre come facilissimi corollarii. </s>

<s>Diceva <lb/>quella proposizione: &ldquo; Cuiuscumque trianguli centrum gravitatis est in recta <lb/>linea, quae ab angulo in mediam basim ducitur &rdquo; (Archim. </s>

<s>op. </s>

<s>cit., pag. </s>

<s>177), <pb xlink:href="020/01/1862.jpg" pagenum="105"/>alla quale, nell'omologo processo inquisitivo del centro della gravit&agrave; nella <lb/>piramide, corrisponde l'altra proposizione dai promotori di Archimede, come <lb/>per esempio dal Maurolico, cos&igrave; formulata: &ldquo; Recta, quae a vertice pyrami&shy;<lb/>dis in eius centrum agitur, producta, cadit in centrum basis triangulae &rdquo; <lb/>(De mom. </s>

<s>aequal. </s>

<s>cit., pag. </s>

<s>169). </s></p><p type="main">

<s>Il modo per&ograve; di dimostrare le due proposizioni &egrave; molto diverso appresso <lb/>agli Autori antichi, e ai moderni. </s>

<s>Si confrontino di grazia le due varie di&shy;<lb/>mostrazioni faticosamente condotte, e ambedue, per indiretta via, degli as&shy;<lb/>surdi concluse nel trattato di Archimede, con la facile, e non men matema&shy;<lb/>tica dimostrazione, che per via degl'indivisibili oggid&igrave; se ne d&agrave; dai Matematici, <lb/>i quali, considerando un triangolo come composto d'infinite linee ponderose, <lb/>tutte parallele alla base; da uno de'pi&ugrave; elementari teoremi di Geometria, e <lb/>dal postulato primo Degli equiponderanti, immediatamente ne concludono <lb/>dovere al triangolo essere il centro di gravit&agrave; nella linea, ch'essendo bisset&shy;<lb/>trice alla base, &egrave; tutt'insieme bissettrice delle altre infinite condotte a lei <lb/>parallele. </s>

<s>Si confronti dall'altra parte il lungo ordine delle proposizioni, che <lb/>precedono alla XIV citata nel IV libro maurolicano <emph type="italics"/>De momentis aequali&shy;<lb/>bus,<emph.end type="italics"/> con lo spedito processo dei Moderni, i quali, ritrovato il centro di gra&shy;<lb/>vit&agrave; del triangolo, dal riguardar la piramide come composta d'infiniti triangoli <lb/>paralleli alla base (dalla quale movendo s'assottigliano sempre pi&ugrave; infintan&shy;<lb/>toch&egrave; non vanno a morir nel vertice) immediatamente ne concludono dover <lb/>la gravit&agrave; del solido raccogliersi tutta intorno alla linea condotta dal vertice <lb/>stesso sopra il centro della contrapposta base triangolare. </s></p><p type="main">

<s>Or pretendeva il Libri che tale, qual'&egrave; in uso appresso ai Matematici <lb/>moderni, fosse il processo inquisitivo del centro della gravit&agrave; nella piramide <lb/>praticato da Leonardo da Vinci. </s>

<s>Ma perch&egrave; l'asserzione dello Storico delle <lb/>Matematiche in Italia non &egrave; in sostanza fondata che sopra un inganno del&shy;<lb/>l'occhio frettolosamente da lui gettato sulla citata pagina del manoscritto <lb/>vinciano, vuol la ragion critica, e vuole il senso comune che si facciano i <lb/>Matematici del secolo XV e XVI discepoli di Archimede, e seguaci de'suoi <lb/>metodi antichi, piuttosto che discepoli e seguaci de'metodi nuovi del Cava&shy;<lb/>lieri. </s>

<s>N&egrave; vale a rimoverci da questa nostra opinione l'autorit&agrave; del Torri&shy;<lb/>celli, il quale, proponendosi di trovar la quadratura della parabola col me&shy;<lb/>todo degl'indivisibili, cos&igrave; scriveva in quella sua breve prefazione al trattato: <lb/>&ldquo; Quod autem haec Indivisibilium Geometria novum penitus inventum sit, <lb/>non ausim affirmare. </s>

<s>Crediderim potius veteres Geometras hac methodo usos <lb/>in inventione theorematum difficillimorum, quamquam in demonstrationibus <lb/>aliam viam magis probaverint, sive hoc ad occultandum artis arcanum, sive <lb/>ne ulla invidis detractoribus proferretur occasio contradicendi &rdquo; (Opera <lb/>geom., P. II, Florentiae 1644, pag. </s>

<s>56). </s></p><p type="main">

<s>Questi occulti arcani dell'arte antica per&ograve;, che ben si pu&ograve; intendere <lb/>corn'entrassero negl'insegnamenti della morale, della politica e della religione, <lb/>non si vede per qual motivo s'avessero da'sapienti a osservare nelle mate&shy;<lb/>matiche discipline. </s>

<s>Anche a proposito della composizione dei moti vedemmo <pb xlink:href="020/01/1863.jpg" pagenum="106"/>come il Torricelli stesso credesse aver voluto Archimede tener occulta la <lb/>regola ai profani, mentr'&egrave; un fatto che s'insegnava pubblicamente da Ari&shy;<lb/>stotile, e, da chi l'avesse saputa intendere, si praticava senza misteri. </s>

<s>Tro&shy;<lb/>vandosene in quelle medesime aristoteliche Questioni i germi, l&agrave; dove si <lb/>dice essere il cerchio generato dall'esplosione del centro, non negheremmo <lb/>che potessero gli Antichi avere avuto qualche idea del metodo degli indivi&shy;<lb/>sibili: non cos&igrave; chiara per&ograve;, da applicarla, anche ne'pi&ugrave; semplici casi, a. </s>

<s>quel <lb/>modo che si fa dai moderni; ond'&egrave; che ci confermiamo, con riverenza del <lb/>Torricelli e del Libri, nel nostro sentimento, che cio&egrave; Leonardo proseguisse <lb/>ne'suoi studii baricentrici i metodi antichi, com'&egrave; certo che gli prosegui&shy;<lb/>rono altri matematici di que'tempi, fra'quali &egrave; il Maurolico uno de'pi&ugrave; <lb/>insigni. </s></p><p type="main">

<s>Al IV libro <emph type="italics"/>De momentis aequalibus,<emph.end type="italics"/> scritto per supplire al difetto o <lb/>alla iattura del III archimedeo Degli equiponderanti, premette il Matematico <lb/>messinese una prefazioncella, nella quale, per avvertire il lettore della sua <lb/>intenzione, ch'era quella di passare alla ricerca dei centri di gravit&agrave; nei so&shy;<lb/>lidi, dice di esser rimasto sorpreso da gran maraviglia, in trovar che ne'li&shy;<lb/>bri di Archimede non si lasciava luogo all'importante argomento. </s>

<s>&ldquo; Nam, <lb/>poi soggiunge, quamvis memorati centri inventio facilis sit in sphaera, faci&shy;<lb/>lis in solidis, quae vulgo regularia dicuntur, et centrum omnis prismatis sit <lb/>centrum ipsum rectilinei quod basibus medium et parallelum interiacet; <lb/>tamen centrum pyramidis non minori industria quam centrum plani trian&shy;<lb/>gularis, ne dicam maiori, exquiri poterat &rdquo; (Archim. </s>

<s>monum. </s>

<s>cit., pag. </s>

<s>156). </s></p><p type="main">

<s>Si rivela da queste espressioni del Maurolico il processo della sua mente, <lb/>il quale come in Leonardo consiste nell'applicare i teoremi archimedei, con&shy;<lb/>cernenti i triangoli, alle piramidi. </s>

<s>Ma l'arte matematica dell'Autore supera <lb/>di gran lunga quella de'contemporanei, nonch&egrave; degli antichi, come pu&ograve; ve&shy;<lb/>dersi dall'ordine delle proposizioni, e dal nuovo aspetto, sotto cui le pre&shy;<lb/>senta. </s>

<s>S'accennava di sopra due essere le diverse vie che, in ricercare il <lb/>centro della gravit&agrave; ne'piani triangolari e ne'solidi piramidali, tennero i Ma&shy;<lb/>tematici, secondo il modo antico o il moderno. </s>

<s>Il Maurolico procede o addita <lb/>agli studiosi una via di mezzo, tutta nuova, speditissima, e di mirabile riu&shy;<lb/>scita. </s>

<s>Dato un triangolo, come per esempio ABC (fig. </s>

<s>46), ne considera la <lb/><figure id="id.020.01.1863.1.jpg" xlink:href="020/01/1863/1.jpg"/></s></p><p type="caption">

<s>Figura 46.<lb/>gravit&agrave; divisa in tre parti eguali, e racc&ograve;lte in <lb/>tre cerchi o dischi, concentrati ciascuno negli <lb/>angoli. </s>

<s>S'ha dai pi&ugrave; elementari teoremi Degli <lb/>equiponderanti che il centro de'due gravi A e <lb/>B riesce in G, punto di mezzo della linea AB, <lb/>ond'&egrave; che, condotta la GC, perciocch&egrave; gravano <lb/>in uno degli estremi di lei due dischi, e nell'al&shy;<lb/>tro estremo C il terzo, avremo il comun centro <lb/>de'tre gravi, ch'&egrave; il centro medesimo del trian&shy;<lb/>golo, stabilito in H per modo, che stia CH ad HG, come due sta ad uno. </s>

<s>A <lb/>cos&igrave; facile conclusione elegante conduce per diritta via la proposizione XXXVI <pb xlink:href="020/01/1864.jpg" pagenum="107"/>del II libro <emph type="italics"/>De momentis aequalibus,<emph.end type="italics"/> cos&igrave; formulata: &ldquo; Si fuerint tria gravia <lb/>aequalia, quorum gravitatis centra iungantur per tres rectas, centrum com&shy;<lb/>mune illorum erit centrum facti trianguli &rdquo; (Archim. </s>

<s>monum. </s>

<s>cit., pag. </s>

<s>132). </s></p><p type="main">

<s>Conduce per analoghe vie, con pari facilit&agrave; ed eleganza, a ritrovare il <lb/>centro d'ogni gravit&agrave; piramidale la proposizione XVI che, nel IV libro mau&shy;<lb/>rolicano, si pone dall'Autore in questa forma: &ldquo; Si fuerint quatuor gravia <lb/><figure id="id.020.01.1864.1.jpg" xlink:href="020/01/1864/1.jpg"/></s></p><p type="caption">

<s>Figura 47.<lb/>aequalia, quorum centra, non in uno <lb/>plano posita, per sex rectas conficiant <lb/>pyramidem trilateram; centrum factae <lb/>pyramidis erit commune centrum qua&shy;<lb/>tuor gravium &rdquo; (ibid., pag. </s>

<s>169). Se <lb/>s'intenda infatti la gravit&agrave; della pira&shy;<lb/>mide ABCD (fig. </s>

<s>47) divisa in quat&shy;<lb/>tro parti eguali raccolte in quattro <lb/>sfere, concentrate in ciascuno dei <lb/>quattro angoli solidi; il centro di gra&shy;<lb/>vit&agrave; delle tre A, B, C sar&agrave; in M, da <lb/>cui condotta la MD gravata in uno <lb/>estremo dall'unico peso D, e dall'al&shy;<lb/>tro da tre simili pesi, verr&agrave; a dare <lb/>in T il comun centro, che &egrave; il centro <lb/>stesso della piramide, cosicch&egrave; per <lb/>legge statica interceda la relazione TD:MT=3:1; ci&ograve; che significa es&shy;<lb/>sere la MT, di tutta intera la MD, una quarta parte. </s></p><p type="main">

<s>I Matematici precedenti erano, come si mostr&ograve; per l'esempio di Leo&shy;<lb/>nardo, riusciti alla medesima facile conclusione, ma il Maurolico, essendosi <lb/>per precipuo intento prefisso di promovere Archimede, prosegue oltre a com&shy;<lb/>pier l'opera lasciata a mezzo dal suo autore e maestro. </s>

<s>Il secondo libro Degli <lb/>equiponderanti &egrave; ordinato alla ricerca del centro di gravit&agrave; nelle sezioni dei <lb/>conoidi parabolici; ricerca che s'assolve tutta nella proposizione VIII, per <lb/>la quale si dimostra concentrarsi in detta sezione il peso tutto intorno al <lb/>diametro, &ldquo; ita ut pars ipsius, quae est ad verticem, sit sesquialtera partis, <lb/>quae est versus basim &rdquo; (Archim., Opera cit., pag. </s>

<s>207). Ma il Maurolico, <lb/>dal piano passando al solido rotondo, com'era dianzi passato alla piramide <lb/>dal semplice triangolo, primo fra'Matematici di cui ci sieno rimasti i docu&shy;<lb/>menti, dimostr&ograve;, nell'ultimo libro del suo trattato, la seguente proposizione, <lb/>quasi volesse coronar di lei tutta l'opera sua: &ldquo; Centrum gravitatis para&shy;<lb/>bolici conoidis axem ita dividit, ut pars, quae ad verticem, reliquae ad basim <lb/>sit dupla &rdquo; (Archim. </s>

<s>monum. </s>

<s>cit, pag. </s>

<s>177). </s></p><p type="main">

<s>Veniva cos&igrave; alla Meccanica dai nostri Matematici italiani, fioriti tra il <lb/>finir del XV secolo e il cominciar del secolo appresso, aperto un nuovo <lb/>eampo, che forse ebbe qualche cultura dagli antichi, ma che poi, per quel <lb/>cos&igrave; lungo abbandono, ebbesi sventuratamente a tornar sodo. </s>

<s>Di quelle eser&shy;<lb/>citazioni per&ograve; o fu affatto perduta la memoria, o se ne trovarono solo assai <pb xlink:href="020/01/1865.jpg" pagenum="108"/>pi&ugrave; tardi i documenti. </s>

<s>Bench&egrave; il Maurolico per esempio fosse de'primi ad <lb/>esser conosciuto e, raccogliendosene nel 1575 in Venezia gli Opuscoli ma&shy;<lb/>tematici, s'annunziasse in fine all'opera, fra le altre lucubrazioni proprie <lb/>all'Autore, anche i quattro libri <emph type="italics"/>De momentis aequalibus,<emph.end type="italics"/> &ldquo; in quorum po&shy;<lb/>stremo, vi si diceva, de centris solidorum ab Archimede omissis agitur, et <lb/>de centro solidi parabolici &rdquo;; vedemmo nonostante come se ne indugiasse <lb/>infino al 1685 la pubblicazione. </s></p><p type="main">

<s>Anche passata dunque di qualche anno la prima met&agrave; del secolo XVI, <lb/>seguitava Archimede a far dir di s&egrave; i Matematici, fra'quali Federigo Com&shy;<lb/>mandino, che avrebbe voluto vedere applicarsi il gran Maestro siracusano <lb/>alla desiderata ricerca dei centri di gravit&agrave; ne'solidi. </s>

<s>Si sentiva inclinato <lb/>piuttosto ad accusar l'Autore Degli equiponderanti di negligenza, per aver <lb/>lasciata l'opera incompiuta, che a lamentarne, attraverso al fluttuare de'se&shy;<lb/>coli, la iattura, quando quel cardinale Cervini, che fu poi papa Marcello II, <lb/>gli regal&ograve; un esemplare Delle galleggianti pubblicate nel 1549 per cura di <lb/>Niccol&ograve; Tartaglia, dall'antico testo greco novamente tradotte in latino. </s></p><p type="main">

<s>Mentre studiosamente attendeva a rimeditare il Trattato archimedeo, per <lb/>emendarlo degli errori e per commentarlo a comun benefizio degli studiosi, <lb/>s'abbatt&egrave;, passando al II libro, a leggere la dimostrazione del teorema II. </s>

<s><lb/>Proponendosi ivi l'Autore di determinar le condizioni dell'equilibrio idro&shy;<lb/>statico in una porzione di conoide parabolico immerso, fra gli altri principii <lb/>premessi alla conclusione v'ebbe, con sua gran sorpresa, a leggere anche <lb/>questo: &ldquo; Sumatur autem centrum gravitatis portionis totius, quod nimirum <lb/>sit in puncto R diametrum ita dividente, ut totus diameter sit sesquialter <lb/>partis, quae est ad verticem, vel haec pars sit dupla eius, quae ad basim &rdquo; <lb/>(Archim., Opera cit., pag. </s>

<s>506). </s></p><p type="main">

<s>Dunque, cominci&ograve; allora a riformare, cos&igrave; ragionando, i suoi primi giu&shy;<lb/>dizii il Commandino, non dee esser vero che trascurasse Archimede lo stu&shy;<lb/>dio del centro di gravit&agrave; ne'solidi, trovandosene qui geometricamente defi&shy;<lb/>nita la misura nel conoide parabolico. </s>

<s>In ogni modo, o dee averne trattato <lb/>egli stesso, il Matematico sicuracusano, o qualcun altro prima di lui, non <lb/>essendo possibile dar cos&igrave; confidentemente l'enunciato teorema, senz'averne <lb/>prima avuto certezza di dimostrazione. </s>

<s>Ma perch&egrave; insomma la dimostrazione, <lb/>che pur s'argomentava dover esservi di fatto, nella Geometria antica non <lb/>si trovava, pens&ograve; il matematico urbinate di supplir secondo le sue forze al <lb/>difetto. </s>

<s>&ldquo; Cum autem ad hoc scribendum aggressus essem (cos&igrave; prosegue <lb/>con le sue proprie parole esso Commandino il racconto) allatus est ad me <lb/>liber Francisci Maurolici messanensis, in quo Vir ille doctissimus, et in iis <lb/>disciplinis exercitatissimus, affirmabat se de centro gravitatis corporum so&shy;<lb/>lidorum conscripsisse. </s>

<s>Cum hoc intellexissem, sustinui me paulisper taci&shy;<lb/>tusque expectavi dum opus clarissimi Viri, quem semper honoris caussa <lb/>nomino, in lucem proferretur. </s>

<s>Mihi enim exploratissimum erat F. </s>

<s>Mauroli&shy;<lb/>cum multo doctius et exquisitius hoc disciplinarum genus scriptis suis tra&shy;<lb/>diturum &rdquo; (De centro grav. </s>

<s>Praef., pag. </s>

<s>III-IV). Ma perch&egrave; l'opera a com-<pb xlink:href="020/01/1866.jpg" pagenum="109"/>parire indugiava, e quasi presago che, se gli si fosse di cent'anni prolungata <lb/>ancora la vita, non sarebbe stato pure a tempo a vederla; dette risoluta <lb/>mano a scrivere quel trattato <emph type="italics"/>De centro gravitatis solidorum,<emph.end type="italics"/> che venne <lb/>alla prima pubblica notizia dei Matematici nel 1565 in Bologna. </s></p><p type="main">

<s>Ivi, in XXX ordinate proposizioni, s'investigano dall'Autore i centri <lb/>della gravit&agrave; ne'solidi terminati da superficie piane, specialmente nella pi&shy;<lb/>ramide e ne'suoi frusti: poi si passa alla medesima inquisizione ne'tre re&shy;<lb/>golari corpi rotondi, nella sfera cio&egrave;, nel cilindro e nel cono. </s>

<s>Quanto agli <lb/>altri corpi terminati da superfice miste, in parte piane cio&egrave; e in parte ro&shy;<lb/>tonde, lasci&ograve; il Commandino in gran desiderio la scienza, contento a solo il <lb/>conoide parabolico, in cui pareva avergli Archimede assegnata alle nuove <lb/>speculazioni la meta. </s></p><p type="main">

<s>Aveva il Matematico urbinate insomma, con lo spengerla solamente in <lb/>parte, accesa pi&ugrave; vivamente che mai la sete del sapere. </s>

<s>Aggiungevasi poi, <lb/>al difetto del trattato nell'estensione, qualche difetto qua e l&agrave; nella condotta <lb/>de'particolari teoremi, e Guidubaldo del Monte, per esempio, bench&egrave; cos&igrave; <lb/>affezionato e riverente al Maestro, pur francamente confessava al p. </s>

<s>Clavio <lb/>che l'ultima <emph type="italics"/>De centro gravitatis solidorum<emph.end type="italics"/> &ldquo; non era buona, per non <lb/>essere universale &rdquo; (Alb. </s>

<s>VIII, 2). La pr&ograve;posizione, a cui qui si accenna, &egrave; <lb/>la XXX del trattato, e ha per soggetto la ricerca del centro di gravit&agrave;, no <lb/>nelle conoidi intere, ma nelle loro porzioni. </s></p><p type="main">

<s>Soggiungeva Guidubaldo, nelle sopra citate parole indirizzate in una <lb/>lettera a Galileo, dop'avere commemorato il Clavio: &ldquo; il qual padre mi <lb/>mand&ograve; poi la sua dimostrazione assai diversa da questa di V. S. &rdquo; (ivi). <lb/>Ne'principii dell'anno 1588, in cui si scrivevano queste parole, era esso Ga&shy;<lb/>lileo dunque, bench&egrave; giovanissimo, uno dei Matematici che attendevano alla <lb/>baricentrica de'solidi, iniziata dal Commandino. </s>

<s>La mano stessa dell'Autore <lb/>gi&agrave; vecchio volle di questi sparsi teoremi intessere una corona, per appen&shy;<lb/>derla all'estrema parete del grande edifizio delle Due nuove scienze. </s>

<s>Ivi, <lb/>quasi in lapide monumentale, fece al suo Salviati scolpire cos&igrave; fatte parole, <lb/>a perpetua memoria: &ldquo; Queste sono alcune proposizioni attenenti al centro <lb/>di gravit&agrave; dei solidi, le quali in sua giovent&ugrave; and&ograve; ritrovando il nostro Acca&shy;<lb/>demico, parendogli che quello, che in tal materia aveva scritto Federigo <lb/>Commandino, non mancasse di qualche imperfezione. </s>

<s>Credette dunque con <lb/>queste proposizioni, che qui vedete scritte, poter supplire a quello, che si <lb/>desiderava nel libro del Commandino,.... con pensiero di andar seguitando <lb/>cotal materia, anco negli altri solidi non tocchi dal Commandino, ma incon&shy;<lb/>tratosi dopo alcun tempo nel libro del signor Luca Valerio, sommo geome&shy;<lb/>tra, e veduto com'egli risolve tutta questa materia, senza niente lasciare in&shy;<lb/>dietro, non seguit&ograve; pi&ugrave; avanti, bench&egrave; le aggressioni sue sieno per istrade <lb/>molto diverse da quelle del signor Valerio &rdquo; (Alb. </s>

<s>XIII, 266). </s></p><p type="main">

<s>Il libro dell'Autore onorificamente qui commemorato usc&igrave; in Roma <lb/>nel 1604, col titolo <emph type="italics"/>De centro gravitatis solidorum, libri tres.<emph.end type="italics"/> Scrive nella <lb/>prefazione il Valerio come, vivamente dolendosi che dovesse la Geometria <pb xlink:href="020/01/1867.jpg" pagenum="110"/>stare in desiderio di conseguire una notizia cos&igrave; degna, qual'era quella dei <lb/>centri di gravit&agrave; nei solidi, lasciati indietro dal Commandino; incorasse una <lb/>viva speranza, non atterrito dai lassi di lui, di poter supplire al difetto. </s>

<s>E <lb/>perci&ograve; &ldquo; cum ante exercitationis causa omnium quae proposui solidorum, <lb/>excepto conoide parabolico, centra gravitatis aliis viis indagassem; postea <lb/>non solum parabolici, sed ante me tentata nemini hyperbolici conoidis et <lb/>frusti utriusque et portionis utriusque conoidis, et portionis frusti et hemi&shy;<lb/>sphaerii et hemisphaeroidis, et cuiuslibet portionis sphaerae, et sphaeroidis <lb/>uno et duobus planis parallelis abscissae centra gravitatis adinveni, multa <lb/>autem ex his duplici, quaedam triplici via &rdquo; (Praefatio libri cit, pag. </s>

<s>2). </s></p><p type="main">

<s>Dopo XXXIV anni che il campo baricentrico dei solidi era, per ogni <lb/>sua pi&ugrave; remota parte, stato percorso dal Valerio, per cui quietava senz'altri <lb/>desiderii la Geometria nel nuovo riconquistato possesso; Galileo cred&egrave; me&shy;<lb/>ritevoli di essere risaputi dal pubblico i suoi studii giovanili. </s>

<s>E perch&egrave; ri&shy;<lb/>conosceva egli stesso consistere tutta la ragion di quel merito nel solo essere <lb/>le sue aggressioni per istrade molto diverse da quelle del Professor di ma&shy;<lb/>tematiche nel ginnasio romano, la curiosit&agrave; c'invita a cercar quel che, per <lb/>la gloria di un tant'uomo, si ritrovasse nel metodo galileiano veramente <lb/>di nuovo. </s></p><p type="main">

<s>Anche al primo sguardo nessuna novit&agrave; si vede apparire nella sostanza, <lb/>procedendosi col metodo degl'inscritti e dei circoscritti sulle orme, che al <lb/>Maurolico, al Commandino e al Valerio aveva gi&agrave; segnate Archimede ne'suoi <lb/>pi&ugrave; antichi teoremi. </s>

<s>Tutto il merito dunque, che attribuiscesi Galileo, non <lb/>pu&ograve; consistere in altro, che in qualche accidentalit&agrave; introdotta ne'pi&ugrave; triti <lb/>processi dimostrativi, i quali perch&egrave; insomma, nell'Appendice al quarto dia&shy;<lb/>logo delle Due nuove scienze, s'informano al I Lemma e alla proposizione I, <lb/>baster&agrave; esaminar questa, per dar retto giudizio di tutto il resto. </s></p><p type="main">

<s>Incominciarono le difficolt&agrave; da certi Fiorentini amici dell'Autore, i quali, <lb/>dop'avere attentamente letta la dimostrazione del Lemma, dissero &ldquo; di non <lb/>ci aver l'intera satisfazione, non tollerando volentieri quel doppio modo di <lb/>considerare le medesime grandezze in diverse bilance &rdquo; (Alb. </s>

<s>VI, 2). Gali&shy;<lb/>leo non era forse infin d'allora tale, da metter in dubbio il valore del suo <lb/>proprio ingegno, ma pi&ugrave; per farsi conoscere da loro, che per consultarne <lb/>l'oracolo, si rivolse a due de'pi&ugrave; famosi Matematici che si conoscessero al&shy;<lb/>lora; al padre Clavio e. </s>

<s>a Guidubaldo Del Monte. </s>

<s>Questi insomma approv&ograve; <lb/>con plauso, ma il Clavio rispondeva &ldquo; non gli dar fastidio quel doppio modo <lb/>di considerare le medesime grandezze in diverse bilance, perch&egrave; Archimede <lb/>fa quasi il medesimo nella propos. </s>

<s>VI del libro I Degli equiponderanti &rdquo; <lb/>(Alb. </s>

<s>VIII, 3), diceva per&ograve; doversi, per non incorr&egrave;re in un circolo vizioso, <lb/>dimostrare, e non semplicemente supporre, essere uno medesimo il centro <lb/>di gravit&agrave; nelle due bilance. </s></p><p type="main">

<s>In cinquant'anni, quanti intercessero fra queste controversie e la pub&shy;<lb/>blicazione degli ultimi Dialoghi, Galileo non trov&ograve; nelle sue prime giova&shy;<lb/>nili dimostrazioni nulla che fosse da correggere, e perci&ograve;, in quella forma <pb xlink:href="020/01/1868.jpg" pagenum="111"/>ch'ebbero da principio, solennemente le espose al pubblico giudizio. </s>

<s>Le cri&shy;<lb/>tiche del Clavio e de'Fiorentini amici della giovent&ugrave; dell'Autore tornarono <lb/>in campo pi&ugrave; vigorose che mai, ond'&egrave; che il Viviani, cos&igrave; geloso della glo&shy;<lb/>ria del suo Maestro, ben conoscendo che le promosse difficolt&agrave; non erano <lb/>affatto prive di fondamento, proponeva di dimostrare il medesimo lemma <lb/>galileiano in quest'altra maniera. </s></p><p type="main">

<s>&ldquo; Si magnitudines quotcumque sese aequaliter excedentes, quarum <lb/>excessus minimae eorum sit aequalis, ln eadem linea secta ex distantiis <lb/>aequalibus suspensae fuerint; omnium ita suspensarum eentrum gravitatis <lb/>ita dividet libram, ut pars versus minores magnitudines, ad partem versus <lb/>maiores sit dupla. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ex distantiis aequalibus magnitudines, quales dictae sunt, suspendan&shy;<lb/>tur 1, 2, 3, 4, 5, 6, sitque FI (fig. </s>

<s>48) dupla ipsius IE, et eidem aequales <lb/><figure id="id.020.01.1868.1.jpg" xlink:href="020/01/1868/1.jpg"/></s></p><p type="caption">

<s>Figura 48.<lb/>ponantur IN, ND, DM, MO. </s>

<s><lb/>Quia itaque magnitudo 2 <lb/>dupla est magnitudinis 1, <lb/>estque FI ipsius EI simi&shy;<lb/>liter dupla; erit I centrum gravitatis compositae ex istis magnitudinibus <lb/>1+2. Suspensa est itaque magnitudo 3 in puncto I; suspensa est autem <lb/>in D magnitudo 3: ex punctis ergo D, I aequales pendent magnitudines. </s>

<s>Est <lb/>autem DN, ipsi NI distantiae, aequalis: equiponderant ergo ex puncto N <lb/>magnitudines 1+2+3. Est autem FN dupla ipsius DN, suntque magni&shy;<lb/>tudines 1, 2, 3 in puncto N suspensae. </s>

<s>In puncto autem C suspenditur ma&shy;<lb/>gnitudo 4, suntque dictae magnitudines ad magnitudinem 4 in sesquialtera <lb/>ratione. </s>

<s>Item et CD ipsius DN est sesquialtera: suspensis itaque magnitudi&shy;<lb/>nibus 3, 2, 1 in N, et magnitudiues 4 in C, erit omnium centrum gravitatis <lb/>in D. </s>

<s>Et est FD ipsius DC dupla: suspensae sunt igitur in D magnitudines <lb/>4, 3, 2, 1, in B autem maguitudo 5, quae illarum est dimidium. </s>

<s>Estque BM <lb/>ipsius MD dupla: ergo magnitudinum 5, 4, 3, 2, 1, ita suspensarum, cen&shy;<lb/>trum gravitatis erit M. </s>

<s>Est autem FM dupla MB: pendent ergo ex M ma&shy;<lb/>gnitudines 5, 4, 3, 2, 1, ex A autem 6. Suntque hae magnitudines in ra&shy;<lb/>tione 5 ad 2, et rursus AO ad OM est ut 5 ad 2, est enim BO aequalis OM, <lb/>et AB sesquialtera BO. </s>

<s>Aequiponderabunt igitur magnitudines omnes sic di&shy;<lb/>spositae in puncto O, et est FO dupla ad AO, nam OD dupla est OB, et DF <lb/>dupla BA. </s>

<s>Quare patet propositum &rdquo; (MSS. Gal. </s>

<s>Disc., T. LXIV, c. </s>

<s>98). </s></p><p type="main">

<s>Condotta cos&igrave; la dimostrazione, come il Viviani la proponeva, sarebbe <lb/>da una parte riuscita assai pi&ugrave; semplice e pi&ugrave; chiara di quella di Galileo, <lb/>mentre si veniva dall'altra a cessare ogni difficolt&agrave;, e a rimovere ogni ac&shy;<lb/>cusa di petizion di principio, e di soverchio abuso de'metodi archimedei. </s>

<s><lb/>Confermava dunque, cos&igrave;, il Discepolo sviscerato quelle difficolt&agrave; e quelle <lb/>accuse, che si davano al suo Maestro, il quale tornava perci&ograve; giudicato non <lb/>giusto estimatore de'proprii meriti, per comun sentenza de'benevoli e degli <lb/>avversarii. </s></p><p type="main">

<s>Da queste considerazioni s'accende in noi pi&ugrave; viva la curiosit&agrave; di pe-<pb xlink:href="020/01/1869.jpg" pagenum="112"/>netrare addentro nell'animo di Galileo, per vedervi ci&ograve; che lo movesse a <lb/>pubblicar, cos&igrave; fuori di proposito, quell'appendice al IV de'Dialoghi trat&shy;<lb/>tanti unicamente del moto. </s>

<s>Scrisse nel 1686 in una lettera a Elia Diodati <lb/>che le dette conclusioni <emph type="italics"/>De centro gravitatis solidorum<emph.end type="italics"/> erano state ritro&shy;<lb/>vate da lui &ldquo; essendo d'et&agrave; di ventun'anno, e di due di studi di geome&shy;<lb/>tria &rdquo; (MSS. Gal., P. V, T. VI, c. </s>

<s>73). Per questa et&agrave;, senza dubbio, quelle <lb/>matematiche conclusioni son molto: si direbbe anzi che son troppo e tali <lb/>che, se si dovesse dai fiori di primavera argomentare ai frutti dell'autunno, <lb/>si direbbe che quel giovane in Geometria fosse per riuscir davvero un Ar&shy;<lb/>chimede novello. </s>

<s>Le lusinghiere speranze per&ograve; andarono fallite, perch&egrave; ai <lb/>giusti giudici s'appresentano i volumi di Galileo, ricchi di tante altre belle <lb/>cose, alquanto poveri per&ograve; di Geometria. </s>

<s>Ora, a ripensare ai lassi nella curva <lb/>descritta dai gravi cadenti e nella corda tesa; alla insufficienza in trovar la <lb/>matematica dimostrazione delle leggi dei pendoli; a quelle stesse stentate e <lb/>avvolte dimostrazioni date negli ultimi due Dialoghi del moto dall'Autore <lb/>gi&agrave; vecchio di settant'anni; quelle fatte a ventuno potevano, non solo reg&shy;<lb/>g&egrave;re, ma rimaner superiori al confronto. </s></p><p type="main">

<s>Altri motivi, ch'ebbe l'Autore di dar quell'appendice ai dialoghi delle <lb/>Due nuove scienze, si diranno in altro proposito, concludendo intanto che <lb/>per quelle galileiane dimostrazioni non fu la Baricentrica punto oltre pro&shy;<lb/>mossa dall'opera del Commandino, cosicch&egrave; tutto il merito ne rimane a <lb/>Luca Valerio. </s>

<s>Dopo il Valerio, il Torricelli ne coltiv&ograve; lo studio da pari suo, <lb/>e il Cavalieri col suo metodo nuovo additava in cielo la stella, a segno della <lb/>quale potrebbero i Matematici correr sicuri quel mare, in tutta la sua smi&shy;<lb/>surata ampiezza, nei pi&ugrave; temuti seni riposti. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Mancavano dieci anni, per raggiungere la sua met&agrave;, al secolo XVI, e <lb/>in Vienna d'Austria erano gi&agrave; appariti due grossi volumi in folio, l'Autor <lb/>de&igrave; quali, straniero all'Italia, presumeva baldanzosamente di aver costruita <lb/>una nuova nave, che per s&egrave; sola bastasse a correre l'ampio mare che si <lb/>diceva. </s>

<s>Era imposto a quella nave il nome di <emph type="italics"/>Centrobrarica,<emph.end type="italics"/> e il nocchiero <lb/>di lei Paolo Guldin affidavasi al meccanico impulso delle sue vele, per appro&shy;<lb/>dar facile e sicuro ai pi&ugrave; lontani e infrequentati lidi della Geometria. </s></p><p type="main">

<s>Se si potesse, in argomento cos&igrave; serio, dar qualche parte alla poesia, <lb/>si direbbe che restarono a quel fatto i Matematici maravigliati, come le Ninfe <lb/>e Nettuno stesso, quando primo Giason dal Pelio spinse nel mar gli abeti. </s>

<s><lb/>Ma era una maraviglia, che s'ebbe presto a spengere nei pi&ugrave; meditativi, i <lb/>quali ripensarono che il fatto era bene pi&ugrave; antico, avendone dato il primo <lb/>esempio Aristotile nella genesi meccanica del circolo, e poi Archimede nella <lb/>genesi meccanica della Spirale. </s>

<s>Il connubio stretto dall'altra parte fra la <pb xlink:href="020/01/1870.jpg" pagenum="113"/>scienza del moto e la scienza dello spazio non poteva giunger nuovo a nes&shy;<lb/>suno, che riflettesse come giusto il moto non si rende commensurabile e <lb/>parvente, che per via dello spazio, e l'avventuroso incontro fra la Mecca&shy;<lb/>nica e la Geometria nella Centrobrarica era prestabilito dall'eterna legge <lb/>della natura, che le gravit&agrave; son proporzionate alle moli. </s></p><p type="main">

<s>Abbiamo voluto far balenare alla mente de'nostri lettori queste idee, <lb/>perch&egrave; intanto si persuadano quanto la Centrobrarica abbia bisogno, e sia <lb/>meritevole di storia. </s>

<s>Si narrer&agrave; da questa, con quella brevit&agrave; che le &egrave; pre&shy;<lb/>scritta, i principii e i progressi della invenzione ammirata, e si mostrer&agrave; <lb/>come s'ingannasse il Guldino in pretendere che la sua Regola per s&egrave; sola <lb/>bastasse, e che potesse anzi col suo pratico meccanismo supplir non solo, <lb/>ma sopravvincere le alte speculazioni matematiche del Cavalieri. </s></p><p type="main">

<s>E prima di tutto, quanto ai principii, si volle da alcuno riconoscerli <lb/>lontanissimi in Pappo, il quale aveva assai bene illustrato il concetto dei <lb/>centri gravitativi, e ne avea data un'assai chiara e precisa definizione che, <lb/>senza nulla aggiungere o levare, il Commandino e Guidubaldo tradussero <lb/>ne'loro libri. </s>

<s>Nella prefazione al libro VII delle Matematiche collezioni il <lb/>valoroso Geometra d'Alessandria pone innanzi a contemplare in uno sguardo <lb/>le principali opere di Euclide e di Apollonio, e ammirando la fecondit&agrave; dei <lb/>ritrovati, e la bellezza delle speculazioni, vien comparandole con le misere <lb/>frivolezze de'suoi tempi. </s>

<s>Io poi, prosegue a dire l'Autore inspirato ai pla&shy;<lb/>tonici precetti alessandrini, essendomi dato infin da giovane allo studio delle <lb/>Matematiche, e avendo trovati avviliti gl'ingegni nelle questioni naturali, ne <lb/>presi gran vergogna, e sentii in me che avrei potuto metter fuori qualche <lb/>cosa di meglio. </s>

<s>E per mostrare, o mio figlio Ermodoro, ch'io non sia ve&shy;<lb/>nuto a mani vuote innanzi a te e ai lettori, v'annunzier&ograve; intanto un teo&shy;<lb/>rema, che contiene in s&egrave; molti altri bellissimi teoremi concernenti le linee, <lb/>le superfice e i solidi: teorema che nessuno ancora ha dimostrato, ma che <lb/>io con ragioni geometriche prover&ograve; nel XII libro di questi Elementi. </s>

<s>Il teo&shy;<lb/>rema dunque &egrave; tale: &ldquo; Perfectorum utrorumque ordinum proportio com&shy;<lb/>posita est ex proportione amphismatum, et rectarum linearum similiter ad <lb/>axes ductarum a punctis, quae in ipsis gravitatis centra sunt: imperfecto&shy;<lb/>rum autem proportio composita est ex proportione amphismatum, et circum&shy;<lb/>ferentiarum a punctis, quae in ipsis sunt centra gravitatis, factarum. </s>

<s>Harum <lb/>circumferentiarum proportio dividitur in proportionem ductarum linearum <lb/>et earum quas continent ipsarum extrema ad axes &rdquo; (Mathem. </s>

<s>collect. </s>

<s>cit., <lb/>pag. </s>

<s>252). </s></p><p type="main">

<s>I progressi fatti poi dalla Centrobrarica suggeriscono di queste parole <lb/>dell'antico Pappo, lungamente rimaste enimmatiche, una tale interpetrazione, <lb/>che l'enunciato alessandrino teorema viene a fare esatto riscontro con quel&shy;<lb/>l'altro dimostrato in tempi assai pi&ugrave; recenti da Giann'Antonio Rocca e dal <lb/>Torricelli, e dal quale scende, per corollario immediato, la Regola del Gul&shy;<lb/>dino. </s>

<s>Per perfetti infatti dell'uno e dell'altro ordine si pu&ograve; intendere i so&shy;<lb/>lidi di rivoluzione generati da superfice regolari circoscritte da linee rette, <pb xlink:href="020/01/1871.jpg" pagenum="114"/>come i triangoli e i quadrati, o da linee curve come i cerchi e le ellissi. </s>

<s><lb/>Cos&igrave; fatti solidi dunque, dice Pappo, star fra loro in ragion composta delle <lb/>superfice genitrici e delle linee condotte dal centro di gravit&agrave; all'asse di ro&shy;<lb/>tazione, o delle circonferenze da esse linee come raggi descritte. </s>

<s>La mede&shy;<lb/>sima regola poi, soggiunge il Collettore alessandrino, vale anche per le su&shy;<lb/>perfice imperfette o irregolari, e per evitare intorno a ci&ograve; ogni causa di <lb/>errore, avverte che il raggio della circonferenza si compone della linea con&shy;<lb/>dotta all'asse dal centro di gravit&agrave; sulla superfice circonvolubile, la qual <lb/>linea vuol essere dalla sua estrema parte prolungata infino a toccar l'asse <lb/>di rotazione. </s>

<s>Si direbbe, in pi&ugrave; brevi parole, essere il raggio della circon&shy;<lb/>ferenza, ch'entra nella detta ragione, la perpendicolare condotta dal centro <lb/>di gravit&agrave; sopra l'asse. </s>

<s>Tale &egrave;, secondo noi, uno dei significati che si pos&shy;<lb/><figure id="id.020.01.1871.1.jpg" xlink:href="020/01/1871/1.jpg"/></s></p><p type="caption">

<s>Figura 49.<lb/>son dare alle parole <emph type="italics"/>Harum circumferentiarum <lb/>proportio dividitur in proportionem ductarum <lb/>linearum, et earum quas continent ipsarum <lb/>extrema ad axes;<emph.end type="italics"/> significato che s'illustra dalla <lb/>figura 49, per la quale si mostra com'essendo <lb/>in D il centro di gravit&agrave; della superfice ABC <lb/>circonvolubile all'asse EF, la lunghezza del rag&shy;<lb/>gio della circonferenza si compone <emph type="italics"/>ductae lineae<emph.end type="italics"/><lb/>DH, e della estremit&agrave; di lei verso l'asse, HG. </s></p><p type="main">

<s>Dicemmo che il significato delle parole di Pappo ebbe solo nella pi&ugrave; <lb/>recente scienza una interpetrazione, perch&egrave; veramente, prima che si descri&shy;<lb/>vesse la Regola guldiniana, pareva impossibile a indovinarsi, e ci&ograve; tanto pi&ugrave;, <lb/>per esser venuto a mancare il XII libro di quegli Elementi, ne'quali pro&shy;<lb/>metteva il Matematico alessandrino che avrebbe dato del proposto teorema <lb/>la desiderata dimostrazione. </s>

<s>Noi siam dunque persuasi che si trovi in Pappo <lb/>promossa la Regola centrobrarica, o che vi si trovi almeno annunziato il <lb/>teorema, da cui potere immediatamente concluderlo, e siamo persuasi al&shy;<lb/>tres&igrave; che non fosse stato difficile ad esso Pappo dimostrar quel teorema, se <lb/>non con il metodo del Rocca e del Torricelli, con quell'altro almeno che, <lb/>secondo gli ordini antichi, vedremo essere stato tenuto da Antonio Nardi. </s></p><p type="main">

<s>Non possiamo per&ograve; consentir con coloro, i quali vollero dire che avesse <lb/>il Guldino tolta la sua Regola dal citato passo del Matematico greco, s&igrave; perch&egrave; <lb/>quel passo non si porge di facile intelligenza, se non a cui fosse la detta <lb/>Regola nota, s&igrave; perch&egrave; pi&ugrave; prossima e pi&ugrave; scoperta, nel libro di un suo <lb/>contemporaneo e connazionale, era la fonte, a cui attinse il Gesuita tedesco <lb/>le acque da riempirne il suo fiume. </s></p><p type="main">

<s>Giovanni Keplero, aiutandosi della Fisica, promosse in modo nuovo, <lb/>sopra quella degli antichi la moderna Geometria. </s>

<s>Crediamo in dir cos&igrave; di <lb/>aver bene qualificata, se non c'inganniamo, l'indole geometrica di quell'in&shy;<lb/>gegno, in cui sempre le immaginose apprensioni del sensibile precorrevano <lb/>e preparavano, come fiore il frutto, le sublimi concezioni dell'intelletto. </s>

<s>Il <lb/>libro di lui, pubblicato in Lintz nel 1615, s'intitola <emph type="italics"/>Nova Stereometria do-<emph.end type="italics"/><pb xlink:href="020/01/1872.jpg" pagenum="115"/><emph type="italics"/>liorum,<emph.end type="italics"/> e la seconda parte, <emph type="italics"/>Stereometriae archimedeae supplementum,<emph.end type="italics"/> co&shy;<lb/>mincia con queste parole, nelle quali dichiara l'Autore com'avessero avuto <lb/>origine le novit&agrave; da s&egrave; introdotte nella scienza stereometrica degli antichi. <lb/></s>

<s>&ldquo; Hucusque Archimedes et Geometrae veteres progressi sunt, inquirentes <lb/>naturam et dimensiones figurarum ordinatarum rectilinearum et curvilinea&shy;<lb/>rum, quaeque ab iis solida proximo gradu gignuntur. </s>

<s>Caeterum, quia figura <lb/>Dolii longius a regularibus excurrit, operae praetium me facturum putavi, <lb/>si genesim illius et cognatarum, gradusque cognationis earum cum regula&shy;<lb/>ribus, eadem quasi Tabella comprehensa, ob oculos exhiberem &rdquo; (Nova Ste&shy;<lb/>reometria, Lincii 1615, fol. </s>

<s>16 t.). </s></p><p type="main">

<s>Si contengono in questa Tavola descritte molte figure di corpi rotondi <lb/>che non avendo avuto ancora un nome proprio dalla scienza, lo derivano <lb/>per similitudine o dalle arti fabbrili o dalla stessa natura, come quel per <lb/>esempio di anello, di fascia, di fuso; di oliva, di pera e di mela. </s>

<s>Non &egrave; in <lb/>cos&igrave; fatti corpi nulla che tutt'insieme possa rassomigliarsi alla perfezion <lb/>della sfera, del cilindro o del cono, ma il Keplero ingegnosamente pens&ograve; di <lb/>ridurre a queste forme regolari le parti, se non potevasi il tutto. </s>

<s>Cos&igrave; apriva <lb/>alle Matematiche una via che, passando per gl'indivisibili del Cavalieri, do&shy;<lb/>veva gloriosamente condurre al calcolo infinitesimale. </s></p><p type="main">

<s>Sia per esempio ABCE (fig. </s>

<s>50) la curva che, rivolgendosi intorno al&shy;<lb/><figure id="id.020.01.1872.1.jpg" xlink:href="020/01/1872/1.jpg"/></s></p><p type="caption">

<s>Figura 50.<lb/>l'asse AE, abbia generato un solido, a cui, per la somi&shy;<lb/>glianza col frutto naturale, d&agrave; il Keplero il nome di Pera. </s>

<s><lb/>Condotte le linee DF, CG, BH perpendicolari all'asse, divi&shy;<lb/>deranno queste la curva genitrice in porzioni di curve re&shy;<lb/>golari e di linee rette, in modo tale che si potr&agrave; tutto il <lb/>solido riguardar composto di una callotta sferica, poi di <lb/>un tronco di cono, con la base minore in basso, poi di un <lb/>altro simile tronco, con la base minore in alto, e cos&igrave; di <lb/>seguito, infintantoch&egrave; dalle risolute parti, regolarmente mi&shy;<lb/>surabili, non resulti nella composizione la misura del tutto. </s></p><p type="main">

<s>Fu questo metodo resolutivo applicato altres&igrave; dal Kep&shy;<lb/>lero a una nuova misura stereometrica, dalla quale doveva immediatamente <lb/>conseguire la regola del Guldino. </s>

<s>S'immagini un cilindro di materia duttile, <lb/>del quale sia fatta una ciambella. </s>

<s>La misura del nuovo solido di rivoluzione <lb/><figure id="id.020.01.1872.2.jpg" xlink:href="020/01/1872/2.jpg"/></s></p><p type="caption">

<s>Figura 51.<lb/>&egrave; senza dubbio quella stessa del cilindro, ma <lb/>&egrave; per&ograve; da pensar che, mentre si mantien certa <lb/>nella trasformazione e inalterata la base, ha <lb/>dovuto dagli opposti lati, per ragion meccanica, <lb/>variare l'altezza. </s>

<s>Sia infatti in GCD (fig. </s>

<s>51) <lb/>rappresentata una sezione della detta ciambella <lb/>composta d'infiniti minimi dischi come EFD. </s>

<s><lb/>Nel piegamento, cos&igrave; violentemente sub&igrave;to, tutti i dischi dalla parte di D <lb/>si sono dilatati, e dalla parte di E compressi, cosicch&egrave; la prima naturale <lb/>altezza del cilindro, nel trasformarsi in ciambella, dall'esterno &egrave; cresciuta, <pb xlink:href="020/01/1873.jpg" pagenum="116"/>e dall'interno &egrave; diminuita. </s>

<s>Di qui &egrave; che, per non fare errore in cos&igrave; lubrica <lb/>materia, prenderemo, dice il Keplero, quella misura nelle parti di mezzo, e <lb/>potr&agrave; cos&igrave; riguardarsi la ciambella stessa come generata dalla rivoluzione <lb/>del disco EFD, intorno al punto A come a suo centro. </s>

<s>Per la pi&ugrave; esatta <lb/>misura poi della solidit&agrave;, prenderemo, come nel cilindro, la base moltipli&shy;<lb/>cata per l'altezza, ma non sar&agrave; questa altezza la raddirizzata circonferenza <lb/>descritta dal raggio AD, perch&egrave; eccessiva; n&egrave; sar&agrave; l'altra pi&ugrave; interna circon&shy;<lb/>ferenza descritta dal raggio AE, perch&egrave; difettiva, ma s&igrave; propriamente quella <lb/>descritta dal raggio AF, supposto che sia in F il centro del disco, e di tutti <lb/>gli altri infiniti che compongono il cilindro. </s>

<s>Ci&ograve; &egrave; dal Keplero stesso messo <lb/>cos&igrave; in forma di proposizione, che &egrave; la XVIII della citata sua Stereometria <lb/>nuova: &ldquo; Omnis annulus sectionis circularis, vel ellipticae, est aequalis <lb/>cylindro, cuius altitudo aequat longitudinem circumferentiae, quam centrum <lb/>figurae circumductae descripsit; basis vero eadem est cum sectione annuli &rdquo; <lb/>(ibid., fol. </s>

<s>20 t.). </s></p><p type="main">

<s>La proposizione cos&igrave; esposta non voleva dall'Autore lasciarsi indimo&shy;<lb/>strata, ma il modo &egrave; affatto fisico o meccanico, e non punto geometrico, e <lb/>consiste insomma nel far considerare quel che dall'altra parte &egrave; ovvio alla <lb/>pi&ugrave; volgare esperienza, che cio&egrave;, incurvandosi una verga diritta, tanto ven&shy;<lb/>gon le parti di lei a rimaner pi&ugrave; compresse, quanto son pi&ugrave; vicine al cen&shy;<lb/>tro di curvatura. </s>

<s>&ldquo; Annulo enim GCD sed integro (cos&igrave; propriamente dice <lb/>il Keplero) ex centro spacii A secto in orbiculos infinitos ED, cosque mini&shy;<lb/>mos, quilibet eorum tanto erit tenuior versus centrum A, quanto pars eius <lb/>ut E fuerit propior centro A quam est F, et recta per F ipsi ED perpen&shy;<lb/>dicularis in plano secante: tanto etiam crassior versus exteriora D. </s>

<s>Extre&shy;<lb/>mis vero dictis, scilicet D, E, simul sumptis, duplum sumitur eius crassitiei, <lb/>quae est in orbiculorum medio &rdquo; (ibid.). </s></p><p type="main">

<s>Poi soggiungesi un corollario, in cui fa l'Autore osservare che vale la <lb/>medesima regola per la misura di altre simili ciambelle, qualunque sieno <lb/>le figure della loro sezione, &ldquo; dummodo in plano per AD ad annulum recto <lb/>sectionis partes, eis et ultra F, fuerint aequales, aequaliterque sitae hinc et <lb/>inde, quod explorabimus in figura sectionis quadrata &rdquo; (ibid.). </s></p><p type="main">

<s>Era dunque la Regola kepleriana limitata alle figure perfette, nelle quali <lb/>sole &egrave; possibile a determinarsi con precisione il centro della grandezza. </s>

<s>Sov&shy;<lb/>venne in questo al Guldino una felicissima idea, che gli fece senza limiti <lb/>approvar quel concetto, e fu di sostituire il centro di gravit&agrave; al centro di <lb/>figura. </s>

<s>Si trattava infatti di ridurre la quantit&agrave; di materia, variamente di&shy;<lb/>stribuita, in un punto solo di mezzo, per cui argutamente pens&ograve; dover me&shy;<lb/>glio servire all'uopo la Meccanica, con le sue leggi degli equiponderanti, <lb/>che non la Geometria con la regola delle sue ci<gap/>coscrizioni. </s></p><p type="main">

<s>Nel 1635 aveva il Guldino pubblicato il suo primo libro della Centro&shy;<lb/>brarica, che trattava della semplice invenzione del centro di gravit&agrave; nelle <lb/>superfice e ne'solidi. </s>

<s>L'opera, bench&egrave; pi&ugrave; estesa, &egrave; pure nel valor mate&shy;<lb/>matico assai inferiore a quella, non del Valerio solo, ma e dello stesso Com-<pb xlink:href="020/01/1874.jpg" pagenum="117"/>mandino primo conosciuto iniziator della scienza. </s>

<s>Nel 1640 comparve, pure <lb/>in Vienna d'Austria, il secondo libro della stessa Centrobrarica, in cui l'Au&shy;<lb/>tore esplicava in questa nuova forma il concetto, che si diceva essergli fe&shy;<lb/>licemente sovvenuto in rimeditare il teorema XVIII della Stereometria nuova <lb/>del Keplero: &ldquo; Partes rotundae quantitatis, quo longius distant a centro seu <lb/>axe rotationis, eo plus etiam quantitatis seu potestatis describunt, cum maio&shy;<lb/>rem faciant circuitum: et contra quo magis partes ad axem rotationis acce&shy;<lb/>dunt, hoc minorem faciunt ambitum, minusque quantitatis efficiunt. </s>

<s>Inve&shy;<lb/>nire ergo oportet aliquod medium, ita ut partes hinc inde, hoc est extrorsum <lb/>et introrsum, sive ultra et eis descriptae, aliquo modo aequentur. </s>

<s>Hoc au&shy;<lb/>tem fiet si linea illa circularis, quae in quantitatem rotundam ducenda erit, <lb/>accipiatur ea quam in rotatione describit centrum gravitatis magnitudinis <lb/>rotundae, quae est sola et unica. </s>

<s>Hoc enim centrum, cum magnitudinis cuius <lb/>centrum dicitur circa se contineat partes aequalium momentorum in motu <lb/>recto quidem ac perpendiculari; describet undique atque efficiet rursus par&shy;<lb/>tes quantitatis, seu potestatis inde genitae, similiter aequalium momentorum, <lb/>ita ut centrum gravitatis effectae potestatis denuo sit in linea, quam in hoc <lb/>motu recto descripsit recta ex centro gravitatis magnitudinis motae, ad eam <lb/>perpendiculariter educta &rdquo; (Centrobraryca, Viennae 1640, pag. </s>

<s>146). </s></p><p type="main">

<s>Ecco dunque in che consiste il progresso della invenzione del Guldino: <lb/>il Keplero aveva detto che la misura del solido di rivoluzione GCD, nel <lb/>passato nostro LI iconismo, &egrave; data dal prodotto della superfice EFD, che si <lb/>vuol di perfetta figura come il cerchio o il quadrato, per la circonferenza <lb/>descritta dalla linea AF, supposto essere in F il centro della superfice stessa, <lb/>dalla quale ha da generarsi il solido rotondo. </s>

<s>Il Guldino viene ora a dare <lb/>una regola simile, che vale generalmente qualunque forma abbia la super&shy;<lb/>ficie rotante, e annunzia che il corpo generatosi da cos&igrave; fatta rotazione &egrave; <lb/>misurato dal prodotto della detta superfice per la circonferenza descritta <lb/>dalla linea AF, supposto per&ograve; che segni F il centro della gravit&agrave;, e non <lb/>della figura. </s></p><p type="main">

<s>Il passo guldiniano, da cui questa nuova Regola resulta, lo abbiamo <lb/>trascritto dal capitolo VIII del detto libro II; capitolo, che &egrave; in forma di <lb/>proposizione, alla quale seguitano quattro corollarii Conclude in questi l'Au&shy;<lb/>tore le varie regole particolari, che scendono dalla generalissima ne'casi, <lb/>che si vogliano paragonare fra loro le misure di due solidi rotondi R, R&prime; ge&shy;<lb/>nerati da due figure diverse. </s>

<s>Chiamate F, F&prime; queste figure e C, C&prime; le cir&shy;<lb/>conferenze descritte da'loro centri di gravit&agrave; nell'andare attorno, la regola <lb/>centrobrarica si conclude nell'equazione R:R=FC:F&prime;C&prime;, che il Gul&shy;<lb/>dino, nel suo corollario terzo, formula con queste parole: &ldquo; Si tam quan&shy;<lb/>titates rotundae quam viae sive radii rotationis sint inaequales, sequitur ul&shy;<lb/>terius potestatum proportionem esse compositam ex ratione quantitatis rotatae <lb/>unius ad quantitatem rotatam alterius, et ex ratione viae vel radii illius unius, <lb/>ad viam vel radium huius alterius (ibid., pag. </s>

<s>148). </s></p><p type="main">

<s>Se di questa nuova ragione stereometrica non hanno ancora i Matema-<pb xlink:href="020/01/1875.jpg" pagenum="118"/>tici finito di ammirare la semplicit&agrave; e la bellezza, s'immagini qual dovesse <lb/>essere l'animo dell'inventore, disposto, per l'indole propria e del suo soda&shy;<lb/>lizio, a magnificare e a vantar sopra gli altri ogni minima cosa. </s>

<s>Che &egrave; mai <lb/>la Stereometria nuova del Keplero, appetto alla sua Baricentrica? </s>

<s>L'Autore <lb/>della stereometria delle botti aveva ben tentata la misura di quelli, e di tanti <lb/>altri solidi di rivoluzione, ma perch&egrave; non seppe riconoscer l'uso, che po&shy;<lb/>teva farsi dei centri di gravit&agrave;, <emph type="italics"/>cursum non tenuit, tentatisque excidit ausis.<emph.end type="italics"/><lb/>Cos&igrave; appunto scriveva il Guldino, a pag. </s>

<s>297 del II tomo, nella prefazione <lb/>al suo III libro centrobrarico pubblicato nel 1641. </s></p><p type="main">

<s>In quel medesimo anno, congiunto al III, pubblicava pure esso Gul&shy;<lb/>dino il IV e ultimo libro, alla fin del quale soggiungeva un capitolo inti&shy;<lb/>tolato: <emph type="italics"/>Perpenduntur quaedam ex Nova geometria Bonaventurae Cava&shy;<lb/>lieri desumpta.<emph.end type="italics"/> In cinque proposizioni, alcune delle quali corredate di scolii, <lb/>si censurano ivi dall'Autore altrettante proposizioni dimostrate nella Geo&shy;<lb/>metria degl'indivisibili dal Cavalieri. </s>

<s>Ma gi&agrave; le sollecitudini del Gesuita te&shy;<lb/>desco, in vantar l'eccellenza dell'opera sua sopra quella del nostro Italiano, <lb/>erano incominciate infin dalla prima pubblicazione del libro II, dove il proe&shy;<lb/>mio &egrave; principalmente ordinato dall'Autore a glorificar s&egrave; e ad opprimere <lb/>il suo rivale. </s>

<s>Lo accusava di plagio, per non aver fatto altro che imitare, e <lb/>appropriarsi il metodo del Keplero e di Bartolommeo Sovero, e compassio&shy;<lb/>nava que'tanto sudati studii che, per non esservisi saputa riconoscer la di&shy;<lb/>gnit&agrave; de'baricentri, non erano riusciti ad altro, che a dar qualche forma <lb/>geometrica ai pi&ugrave; astrusi paralogismi. </s></p><p type="main">

<s>Il Cavalieri, combattuto da tante altre parti, prese nuovo coraggio al <lb/>poderoso assalto, gi&agrave; presago che i posteri, pi&ugrave; retti giudici, avrebbero sulla <lb/>sua Geometria posata la corona della gloria. </s>

<s>Mentre perci&ograve; il Guldino si sfo&shy;<lb/>gava in esaltar tutto s&egrave; e il suo istituto, sentiva il Cavalieri in coscienza il <lb/>dovere di difendere il vero, e s'apparecchiava a farlo con tante ragioni, che <lb/>gli tenevano la mente e l'animo in gran tumulto. </s>

<s>Avrebbe voluto rispon&shy;<lb/>dere all'Autore della Centrobrarica, appena levati gli occhi dal libro, che <lb/>lui piuttosto non aveva fatto altro che proseguire i metodi del Keplero, e <lb/>che l'accusa data al Maestro col dire &ldquo; analogiis et coniecturis multum tri&shy;<lb/>buisse, non scientifice semper conclusisse et insuper sua omnia obscura pro&shy;<lb/>posuisse &rdquo; (Centrobr. </s>

<s>cit., T. II, pag. </s>

<s>322) si dovevano pi&ugrave; giustamente ri&shy;<lb/>versar sul discepolo ingrato. </s>

<s>Dove sono infatti, domandava fra s&egrave; il Cavalieri, <lb/>in questa opera del Guldino i fondamenti matematici? </s>

<s>Si procede anche qui <lb/>per analogie e per congetture, che son quelle medesime del Keplero, perch&egrave;, <lb/>sebbene vi si sia sostituito il centro di gravit&agrave; al centro della figura, la ra&shy;<lb/>gione ultima insomma si riduce al fatto della verga diritta trasformata in <lb/>ciambella. </s>

<s>Vero &egrave; che non si d&agrave; matematica dimostrazione della Stereome&shy;<lb/>tria nuova, ma qual matematica dimostrazione conforta le conclusioni della <lb/>Centrobrarica? </s>

<s>Tutto si fa consistere in dare a vedere ai lettori come i re&shy;<lb/>sultati della Regola nuova riscontrano esattamente con i teoremi di Euclide <lb/>e di Archimede. </s>

<s>S'accusano gl'indivisibili di nessuna riuscita, eppur potreb-<pb xlink:href="020/01/1876.jpg" pagenum="119"/>besi facilmente dimostrare che si trova in essi uno de'pi&ugrave; solidi fondamenti <lb/>a quell'edifizio centrobrarico, che il suo Autore ha lasciato per aria. </s></p><p type="main">

<s>Se il Keplero propone tutte le sue cose oscure, seguitava a ragionare <lb/>fra s&egrave; il Cavalieri, non si lusinghi per&ograve; della semplicit&agrave; della sua Regola il <lb/>Guldino. </s>

<s>&Egrave; molto facile a dire: dato il centro di gravit&agrave; di qualunque su&shy;<lb/>perfice irregolare si ha, per sicura e spedita via, la misura del solido ro&shy;<lb/>tondo. </s>

<s>Come pu&ograve; ritrovarsi quel centro? </s>

<s>se in modo geometrico, risolvendo <lb/>la proposta superfice in tanti triangoli, e componendo in uno i centri par&shy;<lb/>ziali; mentre non sarebbe a confidar da una parte che riuscisse quella via <lb/>veramente sicura, dovrebbesi confessare dall'altra che non tornerebbe punto <lb/>spedita. </s>

<s>Facile senza dubbio s'avrebbe il centro di gravit&agrave;, in qualunque <lb/>superfice pi&ugrave; irregolare, dalla intersezione di due perpendicoli; ma pure il <lb/>modo sarebbe affatto meccanico, bench&egrave; assai confacevole col metodo, che <lb/>regola tutta la Centrobrarica del Guldino. </s></p><p type="main">

<s>Dovevano questi tumultuosi ragionamenti uscire in forma di pubblica <lb/>scrittura dalla mente del Cavalieri, e a dir come e quando ci&ograve; avvenisse ha <lb/>da attender ora la nostra Storia. </s>

<s>E perch&egrave; dalla Geometria degli indivisibili <lb/>piglia la narrazione il suo principio e la sua maggiore importanza, non in&shy;<lb/>crescer&agrave; ai Lettori l'esser tenuti brevemente in discorso di quell'Opera, ch'&egrave; <lb/>pure uno de'monumenti pi&ugrave; insigni della Scienza italiana. </s></p><p type="main">

<s>Muovono dal Keplero anche le nuove speculazioni del Cavalieri. </s>

<s>Tor&shy;<lb/>niamo con lo sguardo indietro sulla nostra L figura. </s>

<s>Pu&ograve; la linea DE fisi&shy;<lb/>camente riguardarsi come un arco di cerchio, e le CD, CB come linee rette; <lb/>ma se poteva ci&ograve; facilmente concedersi al Keplero, per la pratica misura <lb/>delle botti, non reggeva per&ograve; il postulato al pi&ugrave; rigoroso istituto geometrico. </s>

<s><lb/>Perch&egrave; si potessero quelle linee geometricamente riguardar come rette, non <lb/>conveniva prenderle in quantit&agrave; definita, come l'Autore della Stereometria <lb/>nuova faceva, ma s&igrave; ridurle alla loro ultima divisione, o renderle <emph type="italics"/>indivisi&shy;<lb/>bili,<emph.end type="italics"/> come piaceva dire al Cavalieri. </s></p><p type="main">

<s>Della matematica precisione di questo metodo s'erano dall'altra parte <lb/>confidati anche i geometri antichi, allora che intendevano studiosi ad aver <lb/>tanto pi&ugrave; prossima al vero la quadratura del circolo, quanto fossero mag&shy;<lb/>giori i lati de'poligoni inscritti e dei circoscritti, d'onde per legittimo ragio&shy;<lb/>namento scendeva poter riguardarsi matematicamente come retta la indivisi&shy;<lb/>bile porzioncella di un arco. </s>

<s>Il Cavalieri insomma divideva la linea flessuosa <lb/>ABCDE in un numero infinito di tratti, infinitamente moltiplicando le pa&shy;<lb/>rallele, condotte perpendicolari all'asse dal Keplero; cosicch&egrave; di tutte in&shy;<lb/>sieme queste parallele venisse quasi a intessersi la proposta superfice, come <lb/>di tutti insieme i piani paralleli descritti, veniva per simil modo il solido di <lb/>rotazione a compaginarsi. </s>

<s>&ldquo; Hinc manifestum est figuras planas nobis ad <lb/>instar telae parallelis fiilis contextae concipiendas esse: solida vero, ad instar <lb/>librorum, qui parallelis foliis coacervantur &rdquo; (Exercit. </s>

<s>geom., Bononiae 1647, <lb/>pag. </s>

<s>3). </s></p><p type="main">

<s>Il nuovo metodo dall'altra parte prometteva assai bene di s&egrave;, col dif-<pb xlink:href="020/01/1877.jpg" pagenum="120"/>fondere sugli antichi teoremi euclidei una maravigliosa chiarezza. </s>

<s>La misura <lb/>della superfice di un rettangolo, per esempio, e della solidit&agrave; di un cilindro, <lb/>si rendeva ora assai facile a intendere come fossero date dal prodotto delle <lb/>basi per le altezze, perch&egrave; quelle basi rappresentano il primo filo e la prima <lb/>pagina, da cui, per la soprapposizione di altrettanti simili fili e pagine quanti <lb/>son punti indivisibili nell'altezza, viene ad aversi tutto insieme il tessuto <lb/>della superfice, e tutta intiera la coacervazion del volume. </s>

<s>Prometteva altres&igrave; <lb/>quel metodo, che procede per via della division delle parti, di alleggerir <lb/>molte di quelle difficolt&agrave;, che l'antica geometria ritrovava in considerare il <lb/>tutto, quasi come si esperimenta di un gran sasso che, malagevole ad esser <lb/>mosso dalla forza di un gigante, ridotto in minutissima polvere, &egrave; sollevato <lb/>dalla pi&ugrave; leggera aura di vento. </s></p><p type="main">

<s>Incoraggiato dunque da cos&igrave; belle promesse, dietro la regola generale <lb/>che &ldquo; figurae tam planae quam solidae sunt in ratione omnium suorum <lb/>indivisibilium collective &rdquo; (ibid., pag. </s>

<s>6), messe il Cavalieri in ordine, tra il <lb/>finir dell'anno 1621 e il cominciar del seguente, una serie di proposizioni, <lb/>e ne compose un trattatello, che il di 22 Marzo del 1622 spediva da Milano <lb/>a Firenze a Galileo. </s>

<s>Accompagnava il plico una lettera, nella quale, dopo <lb/>alcune avvertenze fatte intorno al principio e al modo di dimostrar per via <lb/>degli indivisibili quelle varie proposizioni, si finiva con queste parole: &ldquo; Di <lb/>grazia mi favorisca di dirmene il suo parere, che lo sto aspettando con gran <lb/>desiderio &rdquo; (Campori, Carteggio galil., Modena 1881, pag. </s>

<s>191). </s></p><p type="main">

<s>Galileo, che tutto allora era dietro a rimeditare sopra quegli infiniti <lb/>istanti di tempo, secondo i quali crescono le velocit&agrave; nei moti accelerati, <lb/>vide in quelle infinite linee, di che il Cavalieri intesseva le superfice, ma&shy;<lb/>ravigliosamente specchiati in immagine viva i suoi pensieri, e facendosi agli <lb/>indivisibili punti di una linea verticale, presa per l'altezza di un triangolo, <lb/>rappresentare gl'infiniti istanti di tempo decorsi, e alla orizzontale, presa <lb/>per base, l'ultimo grado della velocit&agrave; acquistatasi dal mobile nella caduta; <lb/>tirata dalle estremit&agrave; di tal base e di tale altezza un'obliqua, dal triangolo <lb/>ch'indi nasceva vedevasi sotto gli occhi rappresentati i tre efficienti del moto. </s>

<s><lb/>Lo spazio infatti rappresentato dalla superfice triangolare riusciva proporzio&shy;<lb/>nale al prodotto dell'altezza per la base, ossia della velocit&agrave; per il tempo, se&shy;<lb/>condo le leggi per altra via gi&agrave; scoperte, e il corollario fondamentale, che cio&egrave;, <lb/>movendo un grave dalla quiete e proseguendo poi equabilmente il suo libero <lb/>moto naturale, secondo il grado della velocit&agrave; ultimamente acquistata, pas&shy;<lb/>serebbe in tempo eguale uno spazio doppio; appariva visibile nel rettangolo, <lb/>che costruito sopra la medesima base triangolare, in eguale altezza, esso <lb/>pure in superfice riesce doppio. </s></p><p type="main">

<s>Allettato dalla bellezza di questi nuovi processi dimostrativi, mentre atten&shy;<lb/>deva Galileo a metterli in forma, nei primi libri che abbozzava allora <emph type="italics"/>De <lb/>motu,<emph.end type="italics"/> s'era voluto dimenticar dell'Inventore, entrato in gran desiderio che <lb/>quel trattato degli indivisibili si potesse dir suo. </s>

<s>Chi avrebbe osato mai di <lb/>negarglielo, se fosse uscito a dire che quegli stessi pensieri erano prima <pb xlink:href="020/01/1878.jpg" pagenum="121"/>passati per la sua mente? </s>

<s>Deliberava intanto di starsene in silenzio, e il <lb/>Cavalieri che, in cinque mesi, non aveva avuta la desiderata risposta, tor&shy;<lb/>nava, con lettera del d&igrave; 11 di Agosto, a manifestar l'ardentissima sete, che <lb/>gli era convenuto di sopportare, sperando, diceva, che &ldquo; finalmente io sii di <lb/>questo da lei graziato. </s>

<s>&rdquo; Nel Dicembre appresso la grazia ancora non era <lb/>ricevuta, e gli era solo, per mezzo del padre Castelli, fatto sapere che chi <lb/>aveva a darla non poteva <emph type="italics"/>per le sue grandissime occupazioni &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>198). <lb/>Pass&ograve; tutto l'inverno in silenzio, e la primavera seguente tornava il Cava&shy;<lb/>lieri con accorata preghiera, a scrivere queste parole: &ldquo; Spero dunque dalla <lb/>benignit&agrave; sua che, dal tempo che li togliono i suoi alti pensieri d'altre sue <lb/>pi&ugrave; necessarie occupazioni, sceglier&agrave; alcuna parte per dare un'occhiata a <lb/>questo mio trattatello &rdquo; (ivi, pag. </s>

<s>201). </s></p><p type="main">

<s>Ma chi poteva persuadersi che in pi&ugrave; di un anno non avesse trovato <lb/>Galileo qualche ora di tempo, per dare una scorsa al trattato, o pochi mi&shy;<lb/>nuti almeno per scriver da s&egrave;, senz'altro mediatore, che l'aveva ricevuto? </s>

<s><lb/>La semplicit&agrave; del Cavalieri non doveva essere poi tanta, da non sospettar <lb/>che qualche cosa ci doveva esser sotto, e dopo tre anni e pi&ugrave; di pena final&shy;<lb/>mente ebbe il segreto: Galileo attendeva a scrivere egli stesso un trattato <lb/>Degli indivisibili, e non voleva esser prevenuto da un suo discepolo. </s></p><p type="main">

<s>Il Cavalieri, contento che fosse il soggetto reputato di tanta importanza, <lb/>aspettava che venisse in luce l'opera del Maestro, a cui il d&igrave; 29 Febbraio 1626 <lb/>scriveva da Roma: &ldquo; Si ricordi dell'opera sua Degli indivisibili, che gi&agrave; de&shy;<lb/>termin&ograve; di comporre &rdquo; (Alb. </s>

<s>IX, 100). Non tralasciava per&ograve; il primo intra&shy;<lb/>preso studio, e dalle superfice era passato a trattar de'solidi, scrivendo il <lb/>libro in lingua italiana, &ldquo; acci&ograve;, diceva a Galileo, se le pare bene, ancora <lb/>lei cos&igrave; faccia del suo Degli indivisibili &rdquo; (Campori, Cart. </s>

<s>cit., pag. </s>

<s>243). </s></p><p type="main">

<s>Tanto s'esercit&ograve; il Cavalieri intorno a scrivere quel suo libro, che il <lb/>d&igrave; 17 Dicembre 1627 dava di Parma a Galileo la nuova &ldquo; come gi&agrave; un mese <lb/>fa inviai l'opera, che gi&agrave; componevo, qual V. S. sa, a monsignor Ciampoli, <lb/>avendola terminata nel miglior modo che ho saputo e potuto &rdquo; (Alb. </s>

<s>IX, 121). <lb/>Un anno e pochi mesi dopo, gi&agrave; eletto pubblico professore di Matematiche <lb/>nello studio di Bologna, mandava a quei Signori come saggio di s&egrave; i VII li&shy;<lb/>bri della sua nuova Geometria, per cui, a rispondere alle imputazioni del <lb/>Guldino, dichiarava la precedenza del libro suo manoscritto sopra quello <emph type="italics"/>De <lb/>curvi et recti proportione promota<emph.end type="italics"/> del Sovero, invocando testimonii di ci&ograve; <lb/>gl'illustrissimi Senatori dell'inclita citt&agrave; di Bologna, ai quali, dice nella III <lb/>delle citate esercitazioni geometriche, &ldquo; misi, eodem anno 1629, dictae Geo&shy;<lb/>metriae VII libros, etsi manuscriptos, attamen absolutos &rdquo; (pag. </s>

<s>183). </s></p><p type="main">

<s>S'aspettava tuttavia con desiderio l'opera, che Galileo aveva determi&shy;<lb/>nato di comporre sopra questo medesimo argomento, ma, giunti all'anno 1632, <lb/>non s'era altro veduto di lui che l'applicaziene fatta degli indivisibili a di&shy;<lb/>mostrar, nella II Giornata dei Due massimi sistemi, il teorema del moto equa&shy;<lb/>bile, che in tempo eguale all'accelerato passa uno spazio doppio (Alb. </s>

<s>I, 252). <lb/>Nelle passioni, a cui fu soggetto l'animo dell'Autore per questa pubblica-<pb xlink:href="020/01/1879.jpg" pagenum="122"/>zione, s'attuti lo spirito che traboccando voleva invadere gli altrui dominii, <lb/>n&egrave;, dedicandosi poi tutto alle speculazioni del moto, seppe veder come si <lb/>raccoglierebbe di l&igrave; tanto frutto, da compensare in coscienza i rimorsi del&shy;<lb/>l'usurpato. </s>

<s>Rimasto dunque il metodo dagl'indivisibili in libert&agrave; del suo le&shy;<lb/>gittimo inventore, s'apparecchiava questi, senza pi&ugrave; lungamente indugiare, <lb/>a pubblicarlo. </s>

<s>E giacch&egrave; andava Galileo per ogni parte annunziando la pros&shy;<lb/>sima stampa della dottrina del moto, tanto desiderata, il Cavalieri scrive&shy;<lb/>vagli cos&igrave; il d&igrave; 10 di Gennaio del 1634 da Bologna: &ldquo; La vorrei ben pre&shy;<lb/>gare, se le venisse a taglio, che si compiacesse toccare qualche cosa ancora <lb/>della dottrina degli indivisibili, come gi&agrave; alcuni anni sono aveva pensiero, <lb/>in grazia della mia Geometria, che glie ne resterei obbligatissimo: credo che <lb/>dal dialogizzare potr&agrave; far nascere l'occasione, perci&ograve; sperer&ograve; di esserne fa&shy;<lb/>vorito &rdquo; (Alb. </s>

<s>X, 4). </s></p><p type="main">

<s>Il Cavalieri andava con ragione rammemorando gli anni passati, ne'quali <lb/>la bellezza del nuovo metodo aveva cos&igrave; sedotta la mente di Galileo, n&egrave; sa&shy;<lb/>rebbesi aspettato mai che il primo fervente amore si fosse convertito in al&shy;<lb/>trettanta freddezza di odio. </s>

<s>Nel Luglio del 1634 erano gi&agrave; finiti di stampare <lb/>in Bologna i primi cinque libri della Geometria degl'indivisibili, e man&shy;<lb/>datigli a Galileo perch&egrave;, avendone agio, <emph type="italics"/>gliene desse un poco d'occhiata<emph.end type="italics"/><lb/>(Alb. </s>

<s>X, 48), n'ebbe a gustar l'Autore dalla risposta il primo amaro sag&shy;<lb/>gio di quella inaspettata mutazione. </s>

<s>Dicevasi in tal risposta, fatta sulla fine <lb/>del Settembre del 1634, non sembrargli il nuovo metodo del tutto impro&shy;<lb/>babile, ma che ci avevano per&ograve; molte difficolt&agrave;, la prima e pi&ugrave; forte delle <lb/>quali consisteva in questa, che noi ora diremo come fosse nata nella mal <lb/>disposta mente dell'oppositore. </s></p><p type="main">

<s>Intendasi il mezzo cerchio AFB (fig. </s>

<s>52), il cui centro C, ed intorno ad <lb/>esso il parallelogrammo rettangolo ADEB, e dal centro ai punti D, E siano <lb/>le linee rette CD, CE. </s>

<s>Figurandoci poi il semidiametro CF perpendicolare a <lb/><figure id="id.020.01.1879.1.jpg" xlink:href="020/01/1879/1.jpg"/></s></p><p type="caption">

<s>Figura 52.<lb/>una delle due AB, DE immobile, intendiamo <lb/>intorno a quello girarsi tutta questa figura. <lb/></s>

<s>&Egrave; manifesto che dal triangolo CDF sar&agrave; ge&shy;<lb/>nerato un cono, e dal triangoloide ADF un <lb/>cilindro scavato da un emisferio, a cui si <lb/>pu&ograve;, per la somiglianza, dare il nome di <lb/>cratere o di scodella. </s>

<s>Luca Valerio aveva, per <lb/>servirsene come lemma alla proposizione XII <lb/>del II libro <emph type="italics"/>De centro gravitatis,<emph.end type="italics"/> dimostrato che, non solo la solidit&agrave; di tutto <lb/>il cratere e quella di tutto il cono sono eguali, ma che, condotto a qualsi&shy;<lb/>voglia punto un piano secante parallelo alla base DE, sono altres&igrave; eguali fra <lb/>loro le due porzioni. </s>

<s>Anzi, non le porzioni sole generate per esempio dalla <lb/>figura GAI, e dal triangolo CHP, ma lo stesso circolo descritto dal raggio HP <lb/>e l'armilla o nastro descritto dalla linea GI, relative basi delle due sezioni, <lb/>si serbano costantemente fra loro eguali. </s></p><p type="main">

<s>La dimostrazione del Valerio consisteva nel condurre moltissime linee <pb xlink:href="020/01/1880.jpg" pagenum="123"/>come la GN, le quali nel cono e nel cratere segassero piccolissime porzioni, <lb/>ch'ei dimostrava essere eguali, per concluder poi l'eguaglianza del tutto dal&shy;<lb/>l'eguaglianza delle singole parti. </s>

<s>Aveva il processo di quella dimostrazione, <lb/>col metodo degl'indivisibili, una somiglianza, che volle Galileo irragionevol&shy;<lb/>mente ridurre a un'assoluta identit&agrave;, argomentando allo stesso modo dover <lb/>esser fra loro eguali le due ultime porzioni nelle divisioni del Valerio, e le <lb/>due esaustioni, secondo il metodo del Cavalieri. </s>

<s>Ma perch&egrave; sono evidente&shy;<lb/>mente quelle due esaustioni l'orlo della scodella e l'apice del cono, condur&shy;<lb/>rebbe dunque il metodo degl'indivisibili, diceva Galileo, all'assurda conse&shy;<lb/>guenza che fossero insieme eguali una linea lunghissima e un punto. </s></p><p type="main">

<s>Rispondeva il Cavalieri, scoprendo nel sillogismo di Galileo una fallacia, <lb/>la quale consisteva nel voler dedurre la medesima illazione dalle variate pre&shy;<lb/>messe. </s>

<s>Nell'ultima divisione infatti le due quantit&agrave; comparate dal Valerio <lb/>mantengono sempre la loro prima natura di solidi, e perci&ograve; vale la conclu&shy;<lb/>sione dell'eguaglianza: non vale per&ograve;, quando de'due solidi uno sia trasfor&shy;<lb/>mato in un punto, e l'altro in una linea. </s>

<s>Che se conducasi l'argomento a <lb/>rigor di logica, l'applicazione degl'indivisibili al Lemma del Valerio conduce <lb/>alla verit&agrave;, e non all'assurdo. </s>

<s>&ldquo; Nel suo esempio infatti (per citar le parole <lb/>proprie che il Cavalieri us&ograve; nel risponder&egrave; a Galileo) gl'indivisibili sono piani, <lb/>e di questi rimangono sempre parti eguali, detraendo parti eguali dal cono <lb/>e dalla scodella; e perch&egrave; per arrivare all'ultima esinanizione di questi, cio&egrave; <lb/>all'annullare i piani, basta levarvi una dimensione; perci&ograve; parmi che con <lb/>ragione si dica che queste ultime esinanizioni sono eguali, essendo noi ar&shy;<lb/>rivati al nullo piano, tanto nel cono, quanto nella scodella &rdquo; (Alb. </s>

<s>X, 56). </s></p><p type="main">

<s>Diceva insomma il Cavalieri esser tanto vera la eguaglianza fra zero e <lb/>zero, a cui conducono gl'indivisibili, quanto &egrave; vera l'eguaglianza fra quan&shy;<lb/>tit&agrave; e quantit&agrave;, a cui conduceva il metodo del Valerio, e confortava il suo <lb/>retto modo di ragionare con quest'altro geometrico esempio. </s>

<s>Nel semicer&shy;<lb/>chio AFB (fig. </s>

<s>52 prec.) l'eguaglianza fra ARXRB e QR2 &egrave; la medesima <lb/>per tutte le altre infinite linee, che si volessero, al di qua e al di l&agrave;, con&shy;<lb/>durre a RQ parallele, n&egrave; una tale costante eguaglianza per questo cessa, <lb/>perch&egrave; uno de'segmenti riesca il massimo, e l'altro, insieme con la perpen&shy;<lb/>dicolare, riducasi a nulla, facendo ABX0 e 0X0 insieme equazione ve&shy;<lb/>rissima. </s></p><p type="main">

<s>Dopo questa risposta, fatta in una lettera del d&igrave; 2 Ottobre 1634, ne sov&shy;<lb/>vennero al Cavalieri altre, non meno persuasive, che torn&ograve; a scrivere a Ga&shy;<lb/>lileo in una seconda lettera del d&igrave; 19 Dicembre. </s>

<s>Diceva che, intessendosi <lb/>secondo il suo metodo le superfice dal moto delle basi, non si possono attri&shy;<lb/>buire a queste le propriet&agrave; di quelle, come non si possono alla spola in quiete <lb/>attribuire le medesime propriet&agrave; della spola che si muove, &ldquo; perch&egrave; il prin&shy;<lb/>cipio e termine del moto non &egrave; moto &rdquo; (Campori, Carteggio cit., pag. </s>

<s>423). <lb/>N&egrave; perch&egrave; s'intessano le superfice di linee e i solidi s'affaldino di piani, vien <lb/>per questo che debbano essere necessariamente eguali le superfice involgenti <lb/>e le moli. </s>

<s>Prendiamo per esempio il parallelepipedo, fatto da tre linee pro-<pb xlink:href="020/01/1881.jpg" pagenum="124"/>porzionali, come 1, 2, 4, e il cubo, fatto dalla media. </s>

<s>Saranno ambedue le <lb/>solidit&agrave; date da 8, essendo a questo numero eguali tanto la potenza 23 quanto <lb/>il prodotto 1X2X4. Ma mentre la superfice del cubo &egrave; data da 4X6=24; <lb/>la superfice del parallelepipedo &egrave; data invece da 2+2+2X4+2X8=28. <lb/>&ldquo; Siccome dunque, ne conclude il Cavalieri, sta l'eguaglianza delle solidit&agrave; <lb/>con le diseguaglianze delle superfice ambienti; cos&igrave; sta l'egualit&agrave; di tutti i <lb/>piani di due solidi con la disegualit&agrave; di tutte le linee che giaccione nelle <lb/>superfice ambienti, senza alcun pregiudizio, essendo ci&ograve; conforme alle mie <lb/>definizioni &rdquo; (ivi). </s></p><p type="main">

<s>Questi argomenti per&ograve; non valsero a persuader Galileo, incocciato oramai <lb/>con quegli indivisibili, ai quali aveva fatto in principio cos&igrave; lieta accoglienza. </s>

<s><lb/>N&egrave; sapendo in che modo ricoprire innanzi al Cavalieri quella sua cocciutag&shy;<lb/>gine, gli veniva scrivendo che la vecchiaia non gli permetteva d'intender <lb/>cose tanto difficili, a che rispondeva il buon Frate non doversi attribuir ci&ograve; <lb/>alla vecchiaia di chi leggeva, ma s&igrave; piuttosto alla debolezza dell'ingegno di <lb/>chi aveva scritto (ivi, p. </s>

<s>429). In ogni modo, s'annunziava il d&igrave; 12 Marzo 1635 <lb/>che di quello scritto da parecchi anni sarebbe finita la stampa fra due o <lb/>tre settimane (ivi, pag. </s>

<s>432). E fu davvero felicemente finita in Bologna, di <lb/>dove si divulg&ograve; col titolo <emph type="italics"/>Geometria indivisibilibus continuorum nova qua&shy;<lb/>dam ratione promota.<emph.end type="italics"/></s></p><p type="main">

<s>Tre anni dopo gli Elzeviri in Leida pubblicavano i quattro dialoghi <lb/>Delle due nuove scienze. </s>

<s>Il Cavalieri non s'aspettava forse che la preghiera, <lb/>fatta quattro anni prima all'Autore di dir cio&egrave; qualche cosa degl'indivisi&shy;<lb/>bili in grazia della sua Geometria; fosse esaudita, ma non avrebbe pensato <lb/>mai che quella sua povera Geometria avesse dovuto ricevere il tradimento <lb/>di sentirsi chiamata complice nella dimostrazion di un assurdo. </s></p><p type="main">

<s>Nel primo di que'dialoghi galileiani si risolve la questione della <emph type="italics"/>Ruota <lb/>di Aristotile,<emph.end type="italics"/> dicendo che la circonferenza, svolta dalla ruota stessa nel mo&shy;<lb/>versi, era l'espansione o la distrazione del suo centro. </s>

<s>L'assurdit&agrave; perci&ograve;, <lb/>che conseguiva da una tal soluzione, del dover esser cio&egrave; un punto e una <lb/>linea eguali, ammettendo la dottrina dell'interpozion de'vacui, si sarebbe <lb/>potuta sciogliere da Galileo con l'esempio di una minuta gocciola d'acqua <lb/>saponata, che insufflata diventa un gran pallone. </s>

<s>Ma lasciando gli argomenti <lb/>fisici, per attenersi ai matematici, chiama, invece della bolla del sapone, a <lb/>rendergli il servigio di mostrar probabile il paradosso, la Geometria del <lb/>Cavalieri. </s>

<s>&ldquo; Vedendo di non ci poter fare altro per ora, prover&ograve; di quie&shy;<lb/>tare, egli dice, o almeno temperare una improbabilit&agrave; con un'altra simile <lb/>o maggiore, come talvolta una maraviglia s'attutisce con un miracolo &rdquo; <lb/>(Alb. </s>

<s>XIII, 30). E passa a descrivere la generazione della scodella e del <lb/>cono, per poi concluderne, dall'applicarvi il metodo degl'indivisibili, che la <lb/>circonferenza, ossia punti infiniti, sono uguali a un punto solo. </s></p><p type="main">

<s>Avevagli il Cavalieri dimostrato, con argomenti matematici da persua&shy;<lb/>dere il pi&ugrave; indocile ostinato intelletto, che l'equazione, chiamata C per bre&shy;<lb/>vit&agrave; la circonferenza, non &egrave; C=0, come se ne voleva concluder paralogiz-<pb xlink:href="020/01/1882.jpg" pagenum="125"/>zando, ma CX0=0; verissima e non assurda, anco quando C rappre&shy;<lb/>sentasse qualcuno degl'immensi orbi celesti. </s>

<s>Or come mai Galileo ostinarsi <lb/>cos&igrave; contro la verit&agrave; conosciuta? </s>

<s>Che ci fosse in quel giudizio passione, ce <lb/>l'hanno fatto sospettar facilmente le cose addietro narrate, ma non &egrave; facile <lb/>scoprir l'occulta origine di quella passione, se non forse applicandovi la nota <lb/>favola della volpe che, non potendo giunger di terra al bel grappolo del&shy;<lb/>l'uva si vendicava con dire che la non era matura. </s></p><p type="main">

<s>Sembrer&agrave; l'applicazione ingiuriosa, ma &egrave; ben assai pi&ugrave; ingiurioso il <lb/>modo pensato dagli sviscerati amici di Galileo, per salvare il venerato nome <lb/>di lui dall'ingiuria. </s>

<s>Fra'dotti familiari colloqui, che tenevano insieme in Roma <lb/>Stefano Gradi, bibliotecario della Vaticana, il fiorentino abate Ottavio Fal&shy;<lb/>conieri e il conte Giulio Montevecchi, cadde un giorno il ragionamento sopra <lb/>questo discorso, che fa degl'infiniti il Salviati galileiano. </s>

<s>Di ci&ograve; che fu al&shy;<lb/>lora dagli amici disputato il Gradi stesso scrisse una dissertazione episto&shy;<lb/>lare latina, che il Viviani accolse con grande amorevolezza e, di sua propria <lb/>mano copiata, la inser&igrave; gelosamente fra le sue carte. </s></p><p type="main">

<s>Ebbero prima di tutto a convenire i tre dotti uomini nella sentenza che <lb/>la dimostrazione del punto eguale a una linea era addirittura un paradosso. <lb/></s>

<s>&ldquo; Alioquin eadem opera, dicevano, lineam aequalem superficici, et superfi&shy;<lb/>ciem corpori, ac proinde punctum ipsum, hoc est rem nullius mensurae, <lb/>quantitati trinae dimensae statuemus aequalem. </s>

<s>Quod, queso, quid aliud est <lb/>quam omni philosophiae, omnique rectae rationi manifestam inferre vim, et <lb/>ipsam rerum universitatem ad chaos, imo ad nihilum antiquum, redigere? </s>

<s>&rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. CXXXVII, c. </s>

<s>32 t.). </s></p><p type="main">

<s>Soggiungevano poi, pure d'unanime consenso, i tre Filosofi amici che <lb/>il ragionamento del Salviati era un paralogismo, e adducendo altri matema&shy;<lb/>tici esempii riuscivano insomma, bench&egrave; inconsapevoli, a confermar con si&shy;<lb/>mili argomenti la fallacia scoperta nel discorso di Galileo dal Cavalieri. </s>

<s>Pas&shy;<lb/>savano oltre ad esaminar le ragioni di coloro, che intendevano di salvar la <lb/>logica galileiana con l'esempio autorevolissimo del Valerio. </s>

<s>&ldquo; Verum nihil <lb/>alteri cum altero commune: ibi enim (in prop. </s>

<s>XII l&igrave;bri II <emph type="italics"/>De centro gra&shy;<lb/>vitatis<emph.end type="italics"/>) Author ille gravissimus aequalitatem inter craterem et conum de&shy;<lb/>ducit ex eo, quod per quaedam plana, basi cylindri aequidistantia, dividitur <lb/>conus quidem in plures cylindros, crater vero in totidem orbes cylindricos <lb/>(voco orbes cylindricos solidum illud, quod restat ex maiore cylindro, si mi&shy;<lb/>nor cylindrus eiusdem axis ab eo auferatur) ita ut unicuique cylindro com&shy;<lb/>ponenti conum respondeat orbis cylindricus eiusdem magnitudinis. </s>

<s>Recte <lb/>autem ex aequalitate singularum partium aequalitas consurgit universarum, <lb/>et sic, ex aequalitate cylindrorum et orbium cylindricorum, aequalitas cra&shy;<lb/>teris et coni, prout in Elementis..... &rdquo; </s></p><p type="main">

<s>&ldquo; In casu autem, quo de agimus, ad nullam recte institutam argumen&shy;<lb/>tandi rationem Salviati collectio reduci potest. </s>

<s>Vel enim punctum et circum&shy;<lb/>ferentia, de quorum aequalitate ille pronunciat, concurrunt tanquam partes <lb/>ad componendum integraliter craterem et conum, et tunc argumentum non <pb xlink:href="020/01/1883.jpg" pagenum="126"/>procedit, quia cum sine illis hae duae quantitates aequales inter se sint, ex <lb/>eorum quae inaequalia sunt additione inaequalia fiunt, vel saltem, cum ae&shy;<lb/>qualitas huiusmodi dubia et in quaestione sit, dubia quoque fiat necesse est <lb/>compositarum ex illis quantitatum aequalitas, et ita nihil inde potest inferri <lb/>ad conclusionis quaesitae resolutionem. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Multo minus argumentum procederet si, ut res est, nec punctum ad <lb/>conum, nec circumferentia ad craterem, tanquam partes integrales, concur&shy;<lb/>runt. </s>

<s>Tunc enim non bene resultat aequalitas residui duorum aequalium ex <lb/>utrinque ablatorum aequalitate: nam ad verificandum axioma de veritate <lb/>residui ex aequalitate ablatorum a totis aequalibus, necesse est ut illa tota <lb/>aequalia, quae invicem comparantur, a suo quoque ablato et residuo, tan&shy;<lb/>quam a partibus integralibus, componantur; alioquin si quis auferat ex ali&shy;<lb/>qua triremi modium frumenti, eandemque quantitatem ex aliquo parvo lin&shy;<lb/>tre, concludere poterit lintrem esse triremi aequalem. </s>

<s>Ex quibus apparet <lb/>sine dubio mens Galilei, in illo Dialogo, nequaquam sic affecta exactam ad <lb/>severas geometricas leges doctrinam tradere intendat &rdquo; (fol. </s>

<s>33 t. </s>

<s>et 34). </s></p><p type="main">

<s>Or quale altra dunque potrebb'essere l'intenzion di un Geometra, che <lb/>tratta di Geometria? </s>

<s>E rispondono in strana sentenza i tre galileiani romani: <lb/>quella di parlar da Poeta, l'industria del quale &ldquo; in hoc omnis posita est <lb/>ut delectet intelligentem. </s>

<s>Quapropter non video quamobrem ingenuae Gali&shy;<lb/>laei nostri urbanitati non licuerit, in hoc suo paradoxo aequalitatis inter li&shy;<lb/>neam et punctum, eumdum ludum ludere, quem olim in suis <emph type="italics"/>De agricul&shy;<lb/>tura<emph.end type="italics"/> lusit Hesiodus, ubi ait: <emph type="italics"/>Stulti, nesciunt enim quam maius sit dimidium <lb/>toto &rdquo;<emph.end type="italics"/> (ibid., fol. </s>

<s>34 t.). </s></p><p type="main">

<s>Il ripiego di questi non &egrave; per&ograve; meno strano di quello usato da altri ga&shy;<lb/>lileiani, quando asserirono essere stato scritto ne'Dialoghi Del mondo per <lb/>celia che i cadenti si muovono in un mezzo cerchio, per andar dalla super&shy;<lb/>fice al centro della Terra mossa. </s>

<s>Quasi che il dire aver Galileo trattata la <lb/>scienza da poeta e da burla non sia oltraggio maggiore che a confessare i <lb/>passionati errori di lui, ch'era pur un uomo come tutti gli altri. </s></p><p type="main">

<s>Da un tal giusto criterio guidati, e scorti dai fatti svelatici dal sopra <lb/>allegato commercio epistolare, ignoto ai disputanti romani; noi crediamo che <lb/>il ragionamento intorno all'eguaglianza della linea e del punto fosse posto <lb/>da Galileo per far onta alla nuova Geometria del Cavalieri, della quale e <lb/>del Calcolo infinitesimale, con la pronunziata sentenza che degli infiniti &ldquo; non <lb/>si pu&ograve; dire uno esser maggiore o minore o eguale all'altro &rdquo; (Alb. </s>

<s>XIII, 35), <lb/>si venivano a recidere i teneri stami vitali. </s></p><p type="main">

<s>Che fosse veramente ceco l'odio di Galileo, in menar cos&igrave; attorno la <lb/>falce, lo prova il non aver pensato e salvar l'onor suo da una manifesta <lb/>contradizione. </s>

<s>Egli aveva, come si disse, prediletti gl'Indivisibili, e ne'dialo&shy;<lb/>loghi dei Due massimi sistemi gli aveva assunti alla gloria di dimostrare in <lb/>Meccanica uno dei principali teoremi. </s>

<s>Se avesse poi avuto qualche ragione <lb/>di repudiarli conveniva dirlo in tutt'altra maniera che da Poeta didattico o <lb/>satirico, o almeno per prudenza tacere. </s>

<s>Eppure, mentre nel I dialogo si sen-<pb xlink:href="020/01/1884.jpg" pagenum="127"/>tenzia, come ora udimmo, non si poter dare un infinito maggiore di un altro, <lb/>nel III, trascrivendosi le cose scritte nel 1622, vi si legge conclusa una delle <lb/>prime e principali verit&agrave; meccaniche dall'essere le infinite linee di un trian&shy;<lb/>golo la met&agrave; delle infinite linee di un parallelogrammo della medesima base <lb/>e della medesima altezza. </s>

<s>&ldquo; Hoc enim motu ex quiete accelerato iuxta pa&shy;<lb/>rallelas trianguli conficitur; illud vero iuxta parallelas parallelogrammi quae, <lb/>dum fuerint infinitae, duplae sunt ad parallelas infinitas trianguli &rdquo; (ivi, <lb/>pag. </s>

<s>200). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Quando il Cavalieri attendeva a dar pi&ugrave; compiuta che fosse possibile <lb/>la prima edizione della sua Geometria, perch&egrave; <expan abbr="d&imacr;ceva">dinceva</expan>: &ldquo; non so se pi&ugrave; stam&shy;<lb/>per&ograve; di simili materie, che sono da molti aborrite, da pochi viste, e da po&shy;<lb/>chissimi apprezzate &rdquo; (Campori, Carteggio cit., pag. </s>

<s>429), era forse ancora <lb/>lontano dal sospettar che tra que'pochi sarebbe da annoverar lo stesso Ga&shy;<lb/>lileo, a cui scriveva quelle parole. </s>

<s>Ma correvano da tre anni oramai per le <lb/>mani di tutti i dialoghi Delle due nuove scienze, in cui il discorso degli infi&shy;<lb/>niti e del loro uso da farsi nelle Matematiche vi pareva inserito apposta, per&shy;<lb/>ch&egrave; fosse universalmente aborrita e disprezzata quella povera nuova Geo&shy;<lb/>metria. </s>

<s>Il Guldino se ne prevalse, e fra gli argomenti, nella prefazione al <lb/>II libro centrobrarico raccolti per dimostrar falso il metodo degl'indivisibili, <lb/>l'autorevole giudizio di Galileo, trattandosi di un tanto maestro contro il suo <lb/>discepolo, fu nelle destre mani dell'avversario uno de'pi&ugrave; potenti. </s>

<s>&ldquo; Gali&shy;<lb/>leus profecto in eodem dialogo <emph type="italics"/>De motu locali,<emph.end type="italics"/> disputans de infinito, de pro&shy;<lb/>prietatibus finitorum, quas infinitis applicare minime liceat; contra ipsum <lb/>concludit &rdquo; (Centrobr., T. II cit., pag. </s>

<s>3). </s></p><p type="main">

<s><emph type="italics"/>Amicus Plato,<emph.end type="italics"/> rispondeva fra s&egrave; medesimo il Cavalieri, sette anni prima <lb/>di dirlo in pubblico, <emph type="italics"/>sed magis amica veritas<emph.end type="italics"/> (Exerc. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>181), <lb/>per la sacrosanta difesa della quale verit&agrave;, piuttosto che di s&egrave; stesso, revo&shy;<lb/>cava tutte a s&egrave; le virt&ugrave; del proprio ingegno. </s>

<s>Voleva rispondere al Guldino <lb/>l'ammirata celebrit&agrave; del quale pi&ugrave; noceva alla sua causa che non le addotte <lb/>ragioni, e perch&egrave; non s'avesse, come per lo pi&ugrave; nelle controversie accade, <lb/>a perdere inutilmente il tempo in parole, attendeva a dimostrar la bont&agrave; del <lb/>suo metodo dai frutti dati, e dai tanti pi&ugrave; che avrebbe potuto dare. </s></p><p type="main">

<s>Erano in gran fama di matematici valorosi a quei tempi, oltre al Tor&shy;<lb/>ricelli, l'aretino Antonio Nardi, e il reggiano Giann'Antonio Rocca, i quali <lb/>voleva il Cavalieri chiamar commiliti alla difesa del vero, pregandoli a dar <lb/>fuori qualche saggio de'loro studii, e confortandoli a proseguirli, perch&egrave; <lb/>dell'applicazione del nuovo metodo vedessero il Guldino e il mondo gli <lb/>effetti. </s></p><p type="main">

<s>Il Nardi attendeva a raccogliere i suoi sparsi teoremi in un libro, che <pb xlink:href="020/01/1885.jpg" pagenum="128"/>avrebbe voluto intitolare <emph type="italics"/>Ricercate geometriche,<emph.end type="italics"/> e il Rocca, stato gi&agrave; in Pia&shy;<lb/>cenza discepolo dell'Autor degl'indivisibili, aveva con quel metodo sciolto il <lb/>problema della relazione stereometrica, che passa tra il fuso parabolico e il <lb/>cilindro circoscritto. </s>

<s>Ma il Torricelli era tutto allora in sollecito studio di <lb/>raccogliere, per darle alle stampe, le sue varie opere geometriche, fra le <lb/>quali sapeva il Cavalieri esserne molte trattate col metodo nuovo: ond'&egrave; che, <lb/>cogliendo l'occasione di rispondere allo stesso Torricelli, che gli avea man&shy;<lb/>date certe sue nuove dimostrazioni del centro di gravit&agrave; in un segmento di <lb/>sferoide, rendendo facilissimi e spediti i lunghi e faticosi processi del Vale&shy;<lb/>rio; cos&igrave; in una lettera del d&igrave; 3 Gennaio 1643 scriveva da Bologna, dichia&shy;<lb/>rando le sue intenzioni di rispondere al Guldino, e chiedendo all'opera, dal <lb/>valoroso amico, aiuto e consiglio. </s></p><p type="main">

<s>&ldquo; Se mi &egrave; parsa maravigliosa la prima sua speculazione, questa seconda <lb/>del modo di ritrovare i centri di gravit&agrave;, mi &egrave; parsa pur sommamente bella. </s>

<s><lb/>Ma infatti il padre. </s>

<s>Guldini battezza tutte queste cose, trovate per gl'indivi&shy;<lb/>sibili, come provate solo per modo meccanico, e non veramente dimostra&shy;<lb/>tivo. </s>

<s>Ho di gi&agrave; visto il suo secondo tomo della Centrobrarica, nel quale, ben&shy;<lb/>ch&egrave; sia assai grosso, non consuma per&ograve; pi&ugrave; che nove ovvero dieci carte per <lb/>la contradizione alla mia Geometria, della quale dice non aver visto se non <lb/>queste poche cose, che egli prende a impugnare, riserbandosi a miglior tempo <lb/>il confutare il resto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Incominciando dunque dalla prima proposizione del I libro, che &egrave; di <lb/>trovare il vertice di una figura, il che eseguisco io con far movere equidi&shy;<lb/>stantemente una retta o piano, sino che tocchi la figura, oppone esser modo <lb/>meccanico, ma vedrei un poco volentieri che, in cosa cos&igrave; universale, mi <lb/>somministrasse egli miglior modo, quale, se io non m'inganno, stimo esser <lb/>difficilissimo, mentre non si discenda alle specie delle figure. </s>

<s>Passa poi, senza <lb/>vedere altro del primo, al secondo libro, ed ivi a bocca aperta biasima le <lb/>differenti petizioni, e la I e III proposizione, pronunziandole per false asso&shy;<lb/>lutamente: il tutto perch&egrave; gl'infiniti indivisibili non si danno <emph type="italics"/>actu,<emph.end type="italics"/> ma solo <lb/><emph type="italics"/>potentia<emph.end type="italics"/> nel continuo, e poi perch&egrave; sono infiniti, e per&ograve; incomparabili. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Tralasciato poi il resto, passa ai nuovi fondamenti del VII libro, oppo&shy;<lb/>nendo a quella supposizione delle figure egualmente analoghe come a cosa <lb/>meccanica, e che non finirebbe mai. </s>

<s>E sebbene, per levare ogni ombra a <lb/>chi avesse dubbio per questo non finir mai, soggiungo un'altra dimostra&shy;<lb/>zione dell'istesso, quanto alle figure piane, conforme allo stile di Archimede; <lb/>finalmente cavilla pure anche contro di questa, mostrando che io non posso <lb/>spezzare le figure tanto diverse e stravaganti in pi&ugrave; pezzi, che fanno a mio <lb/>proposito; onde conclude la mia Geometria non aver sussistenza alcuna. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora io son risoluto, con la occasione dell'Opusculo di Trigonometria <lb/>con le tavole de'seni e logaritmi, che io stampo in grazia di questi scolari; <lb/>di aggiungervi un poco di risposta. </s>

<s>E perch&egrave; egli stima questa mia maniera <lb/>infruttuosa, mi saria molto caro se io potessi o accennare o mostrare quei <lb/>trovati maravigliosi, ai quali &egrave; arrivata Lei, con l'aggiunta della sottigliezza <pb xlink:href="020/01/1886.jpg" pagenum="129"/>del suo ingegno. </s>

<s>Questo per&ograve; che io dico intendo sia per non detto, quando <lb/>a lei paresse altrimenti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma volendosi compiacere di farmi questo favore, parmi che in due <lb/>modi ci&ograve; potesse farsi; cio&egrave;, o essendo Lei per stampare le sue speculazioni <lb/>in breve, che ella v'inserisse ancora le cose trovate per gl'indivisibili, in <lb/>grazia mia; ovvero che ella le diffondesse ed inviasse a me, in forma di let&shy;<lb/>tera, e che si contentasse che io le inserissi nella mia risposta, precisamente <lb/>come me le mandasse, e come cose sue, e sotto il suo nome, e non in altro <lb/>modo; cio&egrave; nel modo stesso che le farebbe stampar Lei, acci&ograve; il Padre nel <lb/>medesimo tempo vedesse il frutto di quelli, conoscesse il mondo il valore <lb/>di V. S., e che gl'indivisibili sono accetti ai Geometri d'incomparabile va&shy;<lb/>lore; bench'egli dica non essere approvati dai Geometri. </s>

<s>Per&ograve; sia questo <lb/>per non detto, quando ella non ci abbia gusto o comodit&agrave; di farlo, n&egrave; nel&shy;<lb/>l'uno n&egrave; nell'altro modo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se il signor Antonio Nardi avesse stampato le sue <emph type="italics"/>Ricercate geome&shy;<lb/>triche,<emph.end type="italics"/> mi saria stato molto caro e molto a proposito; ma, non avendo io <lb/>con lui corrispondenza di lettere, non ho campo di pregarnelo, come volen&shy;<lb/>tieri farei. </s>

<s>E se mai ella avesse occasione di scrivergli, riceverei a sommo <lb/>favore che ella glie ne desse qualche motivo. </s>

<s>Spero ancora che il signor <lb/>Giovanni Antonio Rocca mi far&agrave; grazia di due o tre proposizioni, ritrovate <lb/>pur da lui per gl'indivisibili, e che sono veramente molto singolari, e molto <lb/>a proposito per rispondere al detto Padre, siccome ora intender&agrave;: intendo <lb/>pure di pubblicarle, com'&egrave; il dovere, sotto il nome suo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Imperocch&egrave; deve sapere che il detto Padre ha ritrovato una bellis&shy;<lb/>sima cosa, poich&egrave; &egrave; universale per tutte le figure solide, che nascono per <lb/>rivoluzione intorno all'asse, e per le superfice curve descritte pure dalle linee <lb/>o rette o curve, che s'intendano pure generarsi per rivoluzione intorno l'asse, <lb/>alle quali non sono ancora arrivati gl'indivisibili, e quello che importa &egrave; as&shy;<lb/>sai pi&ugrave; facile da intendersi, che lo spezzamento degl'indivisibili, e questo <lb/>consiste tutto in questa proposizione: <emph type="italics"/>&ldquo; Se sar&agrave; trovato il centro di gra&shy;<lb/>vit&agrave; della figura, piano o linea che si sia da rivolgersi, moltiplicando la <lb/>circonferenza, descritta nella intera rivoluzione dal centro di gravit&agrave;, nella <lb/>figura piana o linea revoluta, si produrr&agrave; la solidit&agrave; del corpo o la su&shy;<lb/>perfice descritta. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Questo gran principio &egrave; lasciato dal Padre senza alcuna dimostrazione, <lb/>e dice di volerlo solo provare <emph type="italics"/>ab indutione,<emph.end type="italics"/> cio&egrave; che le conclusioni cavate <lb/>da esso son vere, concorrendo con quelle di Euclide e di Archimede. </s>

<s>Il che <lb/>parmi, quand'io non avessi altra cosa in mia difesa, che mi somministri la <lb/>risposta adeguata per il detto Padre, poich&egrave; ancor le mie proposizioni con&shy;<lb/>cordano, e per&ograve; dovranno per lui stimarsi veri anco i miei principii. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E poich&egrave; anco al signor Rocca sovvenne due anni sono una simil <lb/>cosa, poich&egrave; dimostr&ograve; che il momento della parabola librata intorno la base, <lb/>con un parallelogrammo applicato all'istessa base, al momento del paralle&shy;<lb/>logrammo &egrave; come il solido descritto dalla parabola, cio&egrave; il fuso parabolico <pb xlink:href="020/01/1887.jpg" pagenum="130"/>al cilindro fatto dal parallelogrammo; perci&ograve; ne cav&ograve; di qua che il fuso al <lb/>cilindro ha la proporzione composta, come si dimostra essere il momento al <lb/>momento di due pesi, della proporzione della parabola al parallelogrammo, <lb/>e della distanza del centro di gravit&agrave; della parabola dall'asse della rivolu&shy;<lb/>zione alla distanza del centro di gravit&agrave; del parallelogrammo dal detto asse. </s>

<s><lb/>La quale, quando il parallelogrammo si supponga dell'istessa altezza con la <lb/>parabola, sar&agrave; come 4 a 5, siccome la parabola al parallelogrammo &egrave; come <lb/>2 a 3, quali compongono la proporzione di 8 a 15, cio&egrave; del fuso al cilindro, <lb/>siccome appunto trova anco il detto Padre. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E perch&egrave; le distanze dei centri dall'asse della rivoluzione sono come <lb/>le circonferenze da loro descritte, e la dimostrazione, dal signor Rocca <lb/>fatta per gl'indivisibili, s'adatta ad ogni altra figura piana; perci&ograve; &egrave; mani&shy;<lb/>festo che il signor Rocca viene virtualmente ad aver dimostrato che questi <lb/>corpi rotondi, come generalmente anch'esso Padre gli chiama, hanno la pro&shy;<lb/>porzion composta della proporzione delle figure geometriche, e delle circon&shy;<lb/>ferenze descritte dai centri, d'onde finalmente si prova facilmente che la so&shy;<lb/>lidit&agrave; di un qualunque corpo rotondo &egrave; il prodotto della circonferenza fatta <lb/>dal centro, moltiplicata nella figura genitrice. </s>

<s>Cosa che il Padre lascia senza <lb/>dimostrazione, e perci&ograve; calzer&agrave; bene che gl'indivisibili facciano questo ser&shy;<lb/>vigio, almeno quanto ai solidi, sebbene stimo l'istesso potersi anco provare <lb/>per la circoscrizione ed inscrizione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto poi alle superfice, descritte da linee rette, si cava detto prin&shy;<lb/>cipio per la misura del circolo, superfice, e frusto di superfice datoci da Ar&shy;<lb/>chimede, e da questi si trasferisce alla superfice della sfera ed altre super&shy;<lb/>fice curve per l'inscrizione e circoscrizione delle rette. </s>

<s>Sicch&egrave; ella intende <lb/>quanto sia bello questo principio, e quanto a me torni a proposito il pro&shy;<lb/>varlo con la invenzione del signor Rocca, per gl'indivisibili, come diceva <lb/>di sopra. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora perch&egrave; il Padre, avendo incontrata questa maniera veramente <lb/>bella, par che voglia sbandire, non solo dalla persona propria, ma da ogni <lb/>altra, gl'indivisibili, &egrave; necessario che io gli mostri che, se questa maniera <lb/>avanza gl'indivisibili in qualche cosa, ancor questi avanzano quelli in qual&shy;<lb/>che altra. </s>

<s>E per tralasciare l'infinit&agrave; dei solidi, ai quali essi continuamente <lb/>s'estendono, mi vado indovinando che il modo di trovare il centro di gra&shy;<lb/>vit&agrave; dei solidi, e massime da lei accennatomi, sia uno degli avanzi. </s>

<s>Simil&shy;<lb/>mente non mi pare da sprezzare la misura del fuso iperbolico, supposta la <lb/>quadratura dell'iperbola, da esso Padre non ritrovata, ed insomma in molte <lb/>altre, per non parlare anco delle cose fisiche, parmi che gl'indivisibili pos&shy;<lb/>sano avvantaggiar quel modo, com'ella sa meglio di me, i quali, se in qualche <lb/>modo si adattassero alle superfice curve, non vi saria che desiderarvi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se ella dunque si disponesse a farmi questo favore, ella farebbe un <lb/>segnalato servigio agl'indivisibili, ed a me ancora. </s>

<s>E perch&egrave; la somma delle <lb/>difficolt&agrave; fattemi dal Padre si riduce all'incomprensibilit&agrave; degl'infiniti, ed <lb/>alla superposizione da farsi di una figura spezzata sopra un'altra eguale <pb xlink:href="020/01/1888.jpg" pagenum="131"/>innumerabili volte, che pare pure impossibile; la vorrei pregare, bench&egrave; abbi <lb/>diverse cose da dire in risposta, se gli sovvenisse qualche cosa, che potesse <lb/>maggiormente mettere in chiaro la risposta a queste due cose, la quale non <lb/>sovvenisse a me, mi vogli onorare di darmene un poco di motivo, poich&egrave; e <lb/>la mia continua infermit&agrave; m'impedisce la totale applicazione, <emph type="italics"/>et plura vi&shy;<lb/>dent oculi plures, quam solus ocellus,<emph.end type="italics"/> e chi &egrave; sopra il gioco pare che veda <lb/>meglio i colpi che chi gioca, oltre la sua incomparabile sottigliezza d'inge&shy;<lb/>gno, che pu&ograve; giungere dove la mia debolezza di corpo e di mente non pos&shy;<lb/>sono arrivare, e con pregarla a scusarmi le bacio affettuosamente le mani. </s>

<s>&rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>144-52). </s></p><p type="main">

<s>Non sembra che si curasse il Torricelli di assottigliar l'ingegno per sug&shy;<lb/>gerire al Cavalieri la risposta alle due dette obiezioni del Guldino, non si <lb/>offendendo sostanzialmente per esse i principii della Matematica, ma insti&shy;<lb/>gava l'amico ad attutire l'arroganza del Gesuita, col dimostrargli la falsit&agrave; <lb/>di parecchie proposizioni, che si trovavano nel suo libro. </s>

<s>Argoment&ograve; <emph type="italics"/>ab in&shy;<lb/>dutione<emph.end type="italics"/> l'Autore della Centrobrarica, dal veder che il centro, nella super&shy;<lb/>fice conica e nel frusto di cono, &egrave; il medesimo che nella figura piana gene&shy;<lb/>ratrice; doversi ci&ograve; verificare anche ne'frusti di sfera, di sferoide e di conoide <lb/>parabolico. </s>

<s>L'analogia aveva tanto del verisimile, che fu creduta esser quella <lb/>la verit&agrave;, anche dal Cavalieri, ma entrato poi in sospetto di ci&ograve;, dietro il <lb/>teorema torricelliano del centro di gravit&agrave; della superfice di un frusto sfe&shy;<lb/>rico, ritrov&ograve; false le proposizioni guldiniane, e ne dette al Torricelli stesso <lb/>avviso, per lettera del d&igrave; 23 Aprile 1643, mandandogliene la dimostrazione, <lb/>che fu poi pubblicata da pag. </s>

<s>236-38 della II Esercitazione geometrica. </s>

<s>Do&shy;<lb/>veva questa accusa di falsit&agrave; essere uno degli argomenti da inserirsi nella <lb/>Risposta, intorno alla quale scriveva cos&igrave; il Cavalieri da Bologna il d&igrave; 22 Set&shy;<lb/>tembre di quel medesimo anno 1643, per sodisfare alla curiosit&agrave;, che di sa&shy;<lb/>perne qualche cosa gli aveva il Torricelli mostrata pochi giorni prima. </s></p><p type="main">

<s>&ldquo; Cammino assai lentamente nella risposta al Guldini, non essendo an&shy;<lb/>cora al fine del I dialogo, poich&egrave; mi son risoluto, ad imitazione del Galileo, <lb/>di rispondergli in dialogo, avendolo onorato con introdurvi per interlocutori <lb/>il padre don Benedetto, un signor Cesare Marsili, gentiluomo bolognese, <lb/>morto un pezzo fa, che fu amico mio e si dilettava della Matematica, ed un <lb/><emph type="italics"/>Gesulpa Geniuldus,<emph.end type="italics"/> anagramma di <emph type="italics"/>Paulus Guldinus.<emph.end type="italics"/> In questo per&ograve; si con&shy;<lb/>tiene la parte difensiva, siccome in altro sar&agrave;, non dir&ograve; l'offensiva, ma l'esame <lb/>del fondamento del Guldino da lui non provato, la dimostrazione di quello <lb/>per gl'indivisibili e senza, ed altre cose, che mostreranno il frutto, che si <lb/>cava dagl'indivisibili. </s>

<s>In un altro poi, che sar&agrave; il terzo Dialogo, metter&ograve; <lb/>quelle poche cose, che mi &egrave; accaduto di trovare in diverse materie, eziandio <lb/>senza gl'indivisibili, acci&ograve; non periscano &rdquo; (ivi, c. </s>

<s>182, 83). </s></p><p type="main">

<s>Dopo un mese, quel I dialogo era gi&agrave; finito, e l'Autore significava per <lb/>lettera al Torricelli il desiderio che aveva di mandarglielo, perch&egrave; gli desse <lb/>un'occhiata, e gliene dicesse il suo senso (ivi, c. </s>

<s>185). Bench&egrave; fosse tutto <lb/>allora in studio di curar le sue opere geometriche, delle quali era quasi a <pb xlink:href="020/01/1889.jpg" pagenum="132"/>mezzo la stampa, il Torricelli rispose che volentieri avrebbe veduto quel dia&shy;<lb/>logo in difesa degl'indivisibili, e il d&igrave; 8 Gennaio 1644, con una lettera, nella <lb/>quale si dicevano queste cose, il Cavalieri accompagnavagli il manoscritto: </s></p><p type="main">

<s>&ldquo; In conformit&agrave; di quello, che io gliene scrissi, confidato nella sua amo&shy;<lb/>revoleza, gl'invio questo primo dialogo, per contenersi in esso materia prin&shy;<lb/>cipalmente di controversia in cosa, della quale ella &egrave; benissimo, per non dire <lb/>pi&ugrave; di me, informata. </s>

<s>So che ella vi trover&agrave; di molte imperfezioni, ma spero <lb/>che mi avr&agrave; in parte per iscusato, sapendo di quanto pregiudizio mi sia allo <lb/>speculare la continua mia infermit&agrave; corporale..... So che le dimostrazioni <lb/>o lemmi, che quivi dimostro, potevano forse apportarsi in miglior modo, e <lb/>con pi&ugrave; chiarezza; tuttavia, dovendo esser vista principalmente da que&igrave;li, che <lb/>hanno intesa la mia Geometria, ai quali le indirizzo, spero che supereranno <lb/>facilmente le difficolt&agrave; che incontreranno. </s>

<s>Vi ho inserito alcuni discorsi fatti <lb/>dal Marsigli, con un poca di libert&agrave; filosofica, acci&ograve; anche i puri Filosofi vi <lb/>abbiano qualche cosa per il gusto loro, sebbene di poco momento. </s>

<s>Anzi so <lb/>che a molte cose daranno del naso, come alla composizione del continuo <lb/>d'indivisibili, alle immagini e lumi, che si riducono a un punto, il che da <lb/>me &egrave; stato messo per un certo ghiribizzo, e come cosa ammirabile: o che <lb/>si riducano o no ad un punto, &egrave; degno di considerazione &rdquo; (ivi, 186, 87). </s></p><p type="main">

<s>Rispose il Torricelli di aver letto con piacere il Dialogo e di approvare <lb/>le risposte fattevi al Guldino, e avendo intanto gi&agrave; riveduti e licenziati per <lb/>la stampa i foglietti della prima parte delle Opere geometriche, come pri&shy;<lb/>maticcio anticipato frutto, gl'inviava a Bologna all'amico. </s>

<s>Si comprendevano <lb/>in que'foglietti i due libri <emph type="italics"/>De solidis sphaeralibus,<emph.end type="italics"/> e il Cavalieri in leggerli <lb/>ci vedeva mirabilmente promossa la Geometria antica, piuttosto che la nuova. </s>

<s><lb/>Incominci&ograve; a dubitare allora che le belle speranze concepute, ed espresse <lb/>nella prima lettera del d&igrave; 3 Gennaio 1643, volessero rimanersi deluse, e che <lb/>s'avesse a rinnovare l'esempio di Galileo, tanto pi&ugrave; che il Torricelli gli aveva <lb/>scritte certe difficolt&agrave; contro il metodo degl'indivisibili, venute, ei diceva, <lb/>da un gran Matematico di Francia. </s>

<s>Con paterna sollecitudine, non delle spe&shy;<lb/>culazioni sue proprie, ma della matematica verit&agrave;, che vedeva cos&igrave; chiara <lb/>risplendergli nella mente, l'Autore della Geometria nuova trov&ograve; a quella diffi&shy;<lb/>colt&agrave; dell'Anonimo francese facile la risposta. </s>

<s>Ebbe anzi a maravigliarsi che <lb/>a nessuno de'suoi oppositori, nemmeno al Guldino stesso, non fosse sov&shy;<lb/>venuta un'altra difficolt&agrave;, che, in antivedere le offese, era sovvenuta spon&shy;<lb/>tanea allo stesso difensore; difficolt&agrave; ch'era di grande apparenza, e che il <lb/>Cavalieri volle mettere innanzi al Torricelli insieme con la risposta, per mo&shy;<lb/>strar quanto fosse, in mezzo al fiero combattimento, sicuro della vittoria: </s></p><p type="main">

<s>&ldquo; La difficolt&agrave; dunque (cos&igrave; dicevasi dallo stesso Cavalieri, in una let&shy;<lb/>tera del d&igrave; 5 Aprile 1644, che poi, voltata in latino, fu inserita da pag. </s>

<s>238-40 <lb/>della III Esercitazione) consiste in questo. </s>

<s>Sia HD (fig. </s>

<s>53) perpendicolare <lb/>ad AG, ed AD minore, e DG maggiore di essa DH. </s>

<s>Giunte poi le HG, HA, <lb/>sia regola HD, e di tutte le linee del triangolo HAD se ne prendano quante <lb/>si voglia KB, IC.... e per K, I tirinsi le KM, IL parallele ad AG, e le <pb xlink:href="020/01/1890.jpg" pagenum="133"/>LE, MF parallele ad HD. &Egrave; dunque manifesto che la KB &egrave; eguale ad MF, <lb/><figure id="id.020.01.1890.1.jpg" xlink:href="020/01/1890/1.jpg"/></s></p><p type="caption">

<s>Figura 53.<lb/>ed IC ad LE, e in conseguenza che <lb/>a quante si voglia si estenderanno in <lb/>tal modo nel triangolo HAD: cio&egrave;, <lb/>dir&agrave; alcuno, a tutte le linee del trian&shy;<lb/>golo HAD troveremo eguali tutte le <lb/>linee del triangolo HDG, onde questi <lb/>triangoli saranno eguali, eppure son <lb/>diseguali, dunque.... &rdquo; </s></p><p type="main">

<s>&ldquo; Ora a questo dubbio direi che, <lb/>intendendo noi prese nel triangolo HAD tutte le di lui linee di retto tran&shy;<lb/>sito, che sono tante quanti sono i punti di retto transito della AD; altret&shy;<lb/>tanti punti, ma di obliquo transito, prendiamo nella AH, ed altrettante pa&shy;<lb/>rallele ad AG, ed in conseguenza altrettante nel triangolo HDG parallele ad <lb/>HD, le quali in conseguenza non sono tante, quanti sono i punti di retto <lb/>transito della maggiore di DA, DG, cio&egrave; quante sono tutte le linee del trian&shy;<lb/>golo HDG, cio&egrave; non sono tante infinit&agrave; di linee queste, come quelle, e per&ograve;, <lb/>non si prendendo in ambedue questi triangoli per questa via tutte le loro <lb/>linee di retto transito, non si conclude bene l'egualit&agrave; di detti triangoli. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Parmi che ci&ograve;, per una certa analogia, si possi dare ad intendere con <lb/>la tela, poich&egrave; intendendo HAG essere pur di tela, AG regola dell'ordito, <lb/>ed HD del tessuto, essendo nel triangolo HAD cento fili di tessuto, saranno <lb/>cento ancora i punti segnati in HA, da'quali per l'ordito stesi cento fili <lb/>noteranno cento punti in HG, e cento parallele ad HD nel tessuto del trian&shy;<lb/>golo HDG. </s>

<s>Ma il tessuto di esso HDG porta molti pi&ugrave; fili, cio&egrave; per esempio <lb/>trecento, essendo DG tripla di DA; dunque di questi trecento fili non ne <lb/>prendiamo se non cento, e cos&igrave; allo stesso modo negl'infiniti &rdquo; (ivi, c. </s>

<s>198-200). </s></p><p type="main">

<s>Due mesi, dop'aver ricevuta questa difficolt&agrave; con la sua soluzione, che <lb/>aiutandosi cos&igrave; de'fisici esempii si rendeva anche ai meno acuti d'ingegno <lb/>assai intelligibile; il Torricelli spediva da Firenze al Cavalieri i foglietti gi&agrave; <lb/>stampati della II parte delle Opere geometriche, contenenti la risoluzione <lb/>de'due problemi della misura della parabola, e del Solido acuto iperbolico. </s>

<s><lb/>Quanto alla parabola, si proponevano dal fecondo ingegno geometrico del&shy;<lb/>l'Autore venti varii modi di trovarne la quadratura, i primi dieci secondo <lb/>i metodi antichi, e gli altri per la nuova Geometria degl'indivisibili. </s>

<s>Nella <lb/>prefazione a questa II parte del trattato <emph type="italics"/>De dimensione parabolae<emph.end type="italics"/> il Tor&shy;<lb/>ricelli esaltava il metodo nuovo, da cui breve, diretto e affermativo scendeva <lb/>il modo di dimostrare moltissimi teoremi, imperscrutabili agli antichi, con&shy;<lb/>cludendo con queste parole: &ldquo; Haec enim est in mathematicis spinetis via <lb/>vere regia, quam primus omnium aperuit, et ad publicum bonum com&shy;<lb/>planavit mirabilium inventorum macbinator Cavalerius &rdquo; (Florentiae 1644, <lb/>pag. </s>

<s>56). </s></p><p type="main">

<s>Il Cavalieri respir&ograve; in leggere cos&igrave; fatte parole, e prese subito la penna <lb/>in mano per ringraziare il Torricelli dell'aver cos&igrave; onorata la sua persona. <pb xlink:href="020/01/1891.jpg" pagenum="134"/>Poi soggiungeva, in questa medesima lettera, che &egrave; del d&igrave; 15 Giugno, dopo <lb/>aver dimostrata la sua compiacenza in veder de'suoi metodi esposto cos&igrave; <lb/>bel frutto sotto gli occhi de'suoi tanti contradittori: &ldquo; Confesso che il ve&shy;<lb/>derla astenersene nell'opera De'solidi sferali mi gener&ograve; qualche timore di <lb/>restar privo di cos&igrave; gloriosa testimonianza, ma ora veggo che ella ha fatto <lb/>davvantaggio &rdquo; (MSS. Gal., T. cit., fol. </s>

<s>209 a t.). </s></p><p type="main">

<s>La compiacenza era nel Cavalieri tanto pi&ugrave; giustamente sentita, in quanto <lb/>che vedeva rimediarsi dal Torricelli il grave danno, che era derivato alla <lb/>sua Geometria dai nuovi dialoghi di Galileo. </s>

<s>E in vero, senza una tale e <lb/>tanta autorit&agrave; del Discepolo, che in Geometria reputavasi meritamente su&shy;<lb/>periore a quella del Maestro, forse la italiana Geometria degl'indivisibili ri&shy;<lb/>maneva soggiogata per chi sa quanto tempo dalla Centrobrarica del Guldino. <lb/></s>

<s>&Egrave; perci&ograve; ch'esso Cavalieri, bench&egrave; di continuo tormentato dalla podagra, <lb/>prendeva da quelle torricelliane proposizioni animo di proseguire a com&shy;<lb/>battere per l'amore del vero, e per le glorie scientifiche dell'Italia, e dopo <lb/>avere, il d&igrave; 13 marzo 1644, annunziato al Torricelli di aver dato principio a <lb/>stampare il I Dialogo, in risposta alle soverchierie del Guldino (ivi, fol. </s>

<s>197), <lb/>dopo sei mesi, in mezzo a quegli spasimi atroci, che lo rendevano affranto <lb/>ma non vinto, tornava in altra lettera, tra accorato e lieto, a dargli questa <lb/>nuova: &ldquo; &Egrave; stampato il I dialogo, ma il II e il III, non solo non &egrave; stam&shy;<lb/>pato, ma neanche composto: insomma io sono in stato di far poco &rdquo; (ivi, <lb/>fol. </s>

<s>211). </s></p><p type="main">

<s>La morte del Guldino, avvenuta in Gratz sulla fine dell'anno 1643, ma <lb/>della quale non ebbe il Cavalieri notizia, se non che nella primavera se&shy;<lb/>guente, fecero all'intrapresa opera mutar proposito e forma, volendo il pio <lb/>e gentile animo dell'Autore osservare il precetto naturale del <emph type="italics"/>parce sepulto.<emph.end type="italics"/><lb/>E giacch&egrave; la forma del dialogo lo conduceva ad affogare in una superfluit&agrave; <lb/>di parole le idee, scelse, anche per risparmiar tempo e fatica, di espor le <lb/>medesime cose in discorso disteso, ond'&egrave; che, negletti i primi fogli stam&shy;<lb/>pati e dismessa la cura di proseguir sull'andamento di quelli, si trasforma&shy;<lb/>rono i tre meditati dialoghi in quelle sei geometriche Esercitazioni, che vi&shy;<lb/>dero nel 1647 la prima luce in Bologna. </s>

<s>Il trasformato stile non detrasse <lb/>per&ograve; nulla alla efficacia della prima intenzione, che era quella di rispon&shy;<lb/>dere al Guldino, e di attutirne la filosofica baldanza. </s>

<s>E perch&egrave; il tornar sopra <lb/>cose scritte dodici anni fa poteva riuscire oscuro a chi le avesse dimenti&shy;<lb/>cate, tanto pi&ugrave; che della Geometria degl'indivisibili, nel 1647, a testimo&shy;<lb/>nianza dell'Autore, <emph type="italics"/>nulla amplius inveniebantur penes bibliopolas exem&shy;<lb/>plaria,<emph.end type="italics"/> pens&ograve; il Cavalieri di premettere alla esercitazione apologetica due <lb/>altre esercitazioni, nelle quali s'esponesse compendiosamente l'uno e l'al&shy;<lb/>tro metodo: quello cio&egrave; che trattava gl'indivisibili collettivamente presi, e <lb/>in che ponevansi le fondamenta al Calcolo integrale, e l'altro, che quegli <lb/>stessi indivisibili riguardava distributivamente presi, insegnando a calcolar, <lb/>come oggid&igrave; si direbbe, le quantit&agrave; nei loro differenziali. </s></p><p type="main">

<s>Segue immediatamente la III Esercitazione, nella quale si propone l'Au-<pb xlink:href="020/01/1892.jpg" pagenum="135"/>tore di volere esaminar le difficolt&agrave; fatte contro gli esposti metodi dal Gul&shy;<lb/>dino, e nelle prime parole premesse al trattato si compendia cos&igrave; dal Ca&shy;<lb/>valieri stesso la importante storia letteraria, da noi precedentemente ne'suoi <lb/>particolari narrata: &ldquo; Dum eas omnes, quas in hucusque declaratam indivi&shy;<lb/>sibilium doctrinam difficultates evulgarat Guldinus, mente obvolvebam, ac <lb/>pleniori rationum volumine, quae responsionis loco afferre posse videbantur, <lb/>retexere aggrediebar, quinimo et iam ipsius Operis aliquot folia praelo com&shy;<lb/>mississem; repente cum fama tum litteris amicorum nunciatum est ipsum, <lb/>de Geometria quidem benemeritum, fato concessisse. </s>

<s>Indolui vehementer, <lb/>cum ob publicum Reipublicae litterariae damnum, tum ob mihi praereptam <lb/>laboris pene confecti materiam, quam viventi conseveram. </s>

<s>Mors enim ipsa, <lb/>ingrato me silentio damnans, multa vetuit prodere, quae disserendi campus <lb/>opportunior, si vixisset, aperuerat &rdquo; (Exercit. </s>

<s>cit., pag. </s>

<s>177). </s></p><p type="main">

<s>Quel largo campo infatti, che si voleva alle disputazioni aprire il Cava&shy;<lb/>lieri, ne'tre dialoghi divisati nelle lettere da noi sopra alligate al Torricelli; <lb/>si restrinse, morto il Guldino, in que'XV compendiosi capitoli della III geo&shy;<lb/>metrica Esercitazione. </s>

<s>Lasceremo addietro l'esame di ci&ograve; che in tali capi&shy;<lb/>toli ordinatamente discorre il Cavalieri a confutar gli argomenti, dall'Autor <lb/>della Centrobrarica accampati contro la nuova Geometria, e ci tratterremo <lb/>piuttosto intorno all'ultimo, ch'&egrave; il pi&ugrave; importante per la nostra Storia, e in <lb/>cui si dimostra quale utilit&agrave; avrebbe potuto ricavar dagl'indivisibili l'Au&shy;<lb/>tore stesso della Centrobrarica, che pubblicamente gli avea repudiati. </s>

<s>Per <lb/>concluder poi che questa utilit&agrave; era la maggiormente desiderabile, dop'aver <lb/>notato che il Guldino lasciava la sua Regola senza il conforto di nessuna <lb/>matematica ragione, volle il Cavalieri mostrar come a tanta necessit&agrave; sov&shy;<lb/>venissero i suoi principii opportuni. </s>

<s>E qui, per aggiungere alle sue proprie <lb/>speculazioni il suffragio e l'opera di Matematici valorosi, adduceva in propo&shy;<lb/>sito un lemma di Giann'Antonio Rocca, da cui facilmente scendeva dimo&shy;<lb/>strata la Regola guldiniana. </s>

<s>L'importanza del corollario conferisce tanta <lb/>dignit&agrave; alla proposizion principale, che giova risalire alle origini di essa <lb/>proposizione, in questo breve cenno di storia. </s></p><p type="main">

<s>Un Gesuita fiammingo, mosso dalla fama, che del valore del Cavalieri <lb/>in cose geometriche s'era fino oltre monte diffusa, gli scrisse una volta, pro&shy;<lb/>ponendogli a risolvere questo problema: Essendo un parallelogrammo cir&shy;<lb/>coscritto ad una parabola, e rivolgendosi questa e quello intorno alla base, <lb/>come ad asse comune, si domanda la ragione che avranno insieme le mi&shy;<lb/>sure dei due solidi cos&igrave; generati, del cilindro cio&egrave; e del fuso. </s>

<s>Poi soggiun&shy;<lb/>geva di aver egli stesso, il Matematico fiammingo, gi&agrave; risoluto il problema, <lb/>e di aver trovato essere il fuso la met&agrave; del cilindro circoscritto. </s></p><p type="main">

<s>Essendo il Cavalieri alquanti anni dopo tutto intento a raccogliere pro&shy;<lb/>blemi geometrici per la sua Centuria, gli occorse, in mezzo a quella eletta <lb/>variet&agrave;, di tornar sul problema gi&agrave; propostogli da quel Fiammingo, e appli&shy;<lb/>candovi il metodo degl'indivisibili trov&ograve; che, delle quindici parti del cilin&shy;<lb/>dro, il fuso non ne conteneva che otto. </s>

<s>Dava di ci&ograve; avviso a Galileo, per <pb xlink:href="020/01/1893.jpg" pagenum="136"/>lettera del d&igrave; 25 Gennaio 1636, dop'avergli accennato al modo di quadrare <lb/>la volta a crociera: &ldquo; Mi &egrave; anche venuto trovato che essendo un parallelo&shy;<lb/>grammo circoscritto ad una parabola, e rivolgendosi quella intorno alla base, <lb/>il cilindro generato dal parallelogrammo &egrave; come 15 a 8, bench&egrave; un padre <lb/>Gesuita fiammingo mi scrivesse di aver ritrovato essere tra quelli propor&shy;<lb/>zione doppia. </s>

<s>L'uno e l'altro poi di questi problemi &egrave; da me dimostrato <lb/>per i principii della mia Geometria &rdquo; (Alb. </s>

<s>X, 325). </s></p><p type="main">

<s>Cinque anni dopo, cio&egrave; sulla fine dell'anno 1640, essendosi Giann'An&shy;<lb/>tonio Rocca, sotto le discipline del Cavalieri, dato con grande applicazione <lb/>allo studio della Geometria, volle provarsi a risolvere quel medesimo pro&shy;<lb/>blema, proposto gi&agrave; al suo Maestro dal Gesuita fiammingo, e vi riusc&igrave; per <lb/>una via facilissima, e in tutto nuova. </s>

<s>Si prepar&ograve; a quell'intento un bellis&shy;<lb/>simo Lemma, che dal Torricelli, avutone notizia dal Cavalieri nella prima <lb/>lettera da noi dianzi trascritta, fu, per servirsene a uno de'venti modi da <lb/>ritrovar la quadratura della Parabola, reso per la prima volta pubblicamente <lb/>noto sotto questa forma: &ldquo; Si figura plana super aliqua sui recta linea figu&shy;<lb/>ram ipsam secante libretur, erunt momenta segmentorum figurae ut sunt <lb/>solida rotunda ab ipsis segmentis, circa secantem lineam revolutis, descri&shy;<lb/>pta &rdquo; (Operum geom., P. II cit., pag. </s>

<s>76). <lb/><figure id="id.020.01.1893.1.jpg" xlink:href="020/01/1893/1.jpg"/></s></p><p type="caption">

<s>Figura 54.</s></p><p type="main">

<s>Sieno le figure piane qualun&shy;<lb/>que ACDB, AEFB (fig. </s>

<s>54) revo&shy;<lb/>lubili intorno all'asse AB, a cui si <lb/>conducano a piacere le CIE, DHF <lb/>perpendicolari. </s>

<s>Considerate queste <lb/>linee come ponderose, e come aventi <lb/>ne'respettivi centri L, N i l&ograve;ro pesi <lb/>raccolti, si avr&agrave;, chiamando con M, <lb/>M&prime; i momenti delle dette grandezze <lb/>librate intorno ai punti H, I, M:M&prime;= <lb/>DHXLH:HFXHM=DH2:HF2, <lb/>che &egrave; altres&igrave; eguale a CoDH:CoHF, <lb/>stando, per gli Elementi, i circoli <lb/>come i quadrati dei raggi. </s></p><p type="main">

<s>Essendo poi queste cos&igrave; trovate <lb/>relazioni vere, non solo per la linea <lb/>CIE, ma per le infinite altre, che si potessero condurre alla DHF parallele, ne <lb/>conseguir&agrave; che la somma dei momenti M sta alla somma dei momenti M&prime;, <lb/>come stanno le somme de'circoli descritti dalle infinite linee condotte per&shy;<lb/>pendicolari all'asse AB nell'una e nell'altra delle due volubili rappresen&shy;<lb/>tate figure. </s>

<s>Percioch&egrave; ora di queste somme di circoli infiniti si compaginano <lb/>i solidi rotondi dalle dette figure piane generati, accennando con R, R&prime; que&shy;<lb/>sti solidi, e colla cifra &int;, che ci rammemori l'origine del calcolo integrale, <lb/>la somma di tutti i detti momenti. </s>

<s>avremo R:R&prime;=&int;M:&int;M&prime;; equazione <lb/>che rende appunto dimostrato il proposto lemma del Rocca. </s></p><pb xlink:href="020/01/1894.jpg" pagenum="137"/><p type="main">

<s>Si passava di qui a un corollario che, a risolvere il problema stereome&shy;<lb/>trico del fuso parabolico e del cilindro circoscritto, serviva di pi&ugrave; prossima <lb/>preparazione immediata. </s>

<s>Sia infatti O il comun centro di N e di L, e si <lb/>conduca OP perpendicolare all'asse: si ha per facile dimostrazione che la <lb/>somma dei momenti N, L &egrave; eguale alla somma delle grandezze CI, DH mol&shy;<lb/>tiplicata per OP. </s>

<s>Se si assommino ora, invece di due soli, tutti gl'infiniti <lb/>momenti della superfice ACDB, la somma di tutte le infinite grandezze si <lb/>raccoglier&agrave; in un punto per esempio in O, che sar&agrave; il centro di gravit&agrave; di <lb/>essa superfice, la quale chiameremo S. </s>

<s>Procedendo allo stesso modo per <lb/>l'altra superfice S&prime;, sia il centro di gravit&agrave; di lei in Q e sia PQ la pi&ugrave; breve <lb/>distanza di questo stesso centro dall'asse: avremo dunque &int;M=SXOP, <lb/>&int;M&prime;=S&prime;XPq. </s>

<s>I quali due valori, sostituiti nel precedente Lemma, <lb/>davano al Rocca, per quel corollario importante che si diceva, R:R&prime;= <lb/>SXOP:S&prime;XPQ, ci&ograve; che significa avere i due solidi rotondi la ragion <lb/>composta delle due figure genitrici, e della distanza del centro di gravit&agrave; <lb/>di ciascuna dall'asse di rotazione. </s></p><p type="main">

<s>Preparatosi cos&igrave; l'argomento, s'usava in tal maniera dal Rocca a risol&shy;<lb/>vere il propostosi problema. </s>

<s>Sieno il rettangolo AS, che chiameremo R, e <lb/>la parabola ATB, che chiameremo P, le due figure genitrici del cilindro C <lb/>e del fuso F. </s>

<s>Se in O, Q rispondono i due centri delle dette figure, e son <lb/>perci&ograve; OP, PQ le respettive distanze dall'asse di rotazione, avremo dunque, <lb/>per le cose ultimamente dimostrate, C:F=RXOP:PXPq. </s>

<s>Ma la <lb/>ottava archimedea del II <emph type="italics"/>De aequiponderantibus<emph.end type="italics"/> (Opera cit., pag. </s>

<s>207) d&agrave; <lb/>OP:PQ=5:4, e la XXIV <emph type="italics"/>De quadratura paraboles<emph.end type="italics"/> (ibid., pag. </s>

<s>441) <lb/>d&agrave; R:P=3:2, perci&ograve; se ne conclude C:F=15:8. </s></p><p type="main">

<s>&ldquo; His demonstratis (cos&igrave; nel cap. </s>

<s>XIV della III Esercitazione ripigli&ograve; il <lb/>costrutto il Cavalieri) remanet ostendendum quomodo ex his inferatur re&shy;<lb/>gula Guldini, quo ad figuras planas, earumque potestates, quod nunc pate&shy;<lb/>fiet &rdquo; (pag. </s>

<s>232). Sieno nella precedente figura il rettangolo AS e la figura <lb/>qualunque AEFB le due seperfice genitrici. </s>

<s>Avremo, per le cose gi&agrave; dimo&shy;<lb/>strate dal Rocca, che i due solidi rotondi generati hanno la ragion composta <lb/>del rettangolo e dell'altra superfice irregolare nelle distanze OP, PQ de'loro <lb/>centri dall'asse. </s>

<s>E perch&egrave; i raggi stanno come le circonferenze, avremo <lb/>dunque R:R&prime;=ASXCaOP:AEFBXCa<expan abbr="Pq.">Pque</expan> Rappresentando R un <lb/>cilindro sar&agrave; perci&ograve; eguale ad ABXCoBS=ABXBS/2XCaBS= <lb/>ABXBSXCaOP, perch&egrave; il rettangolo d&agrave; BS=2 OP.Ma ABXBS= <lb/>AS, dunque sar&agrave; R=ASXCaOP, e perci&ograve; anche R&prime;=AEFBXCa<expan abbr="Pq.">Pque</expan> <lb/>&ldquo; Hoc autem, conclude il Cavalieri, est conforme regulae Guldini &rdquo; (ibid., <lb/>pag. </s>

<s>233). </s></p><pb xlink:href="020/01/1895.jpg" pagenum="138"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Il Rocca, col dimostrato Lemma, e il Torricelli, con la seconda parte <lb/>delle Opere geometriche, avevano dunque assai generosamente corrisposto <lb/>ai desiderii del Cavalieri, e cooperato efficacemente con lui in difendere la <lb/>Geometria degl'indivisibili dagl'insulti del Guldino. </s>

<s>Rimaneva, de'tre chia&shy;<lb/>mati alla difesa, il Nardi, il quale per&ograve; sembra che diffidasse dell'assoluta <lb/>bont&agrave; dei metodi nuovi. </s>

<s>Trasparisce una tal diffidenza da certe parole scritte <lb/>nella Veduta XLII della Scena VI, le quali crediam bene di sottoporre alla <lb/>considerazione degli studiosi. </s></p><p type="main">

<s>&ldquo; In grazia dei Matematici, egli ivi dice, ho posto accademicamente che <lb/>le linee, i punti e le superfice siano in atto ne'corpi, come parti veraci e <lb/>componenti, da che ne seguirebbe l'aver quei termini propria esistenza, e <lb/>nulla vieterebbe potersi da qualche forza separar dal soggetto, e da qualche <lb/>suprema potersi separar tutti. </s>

<s>Quindi si darebbe uno spazio ed un numero <lb/>infinito, il che repugna alle cose poste. </s>

<s>Diciamo dunque che i punti, le linee <lb/>e le superfice, in tanto sono cosa reale, in quanto sono modi o termini dei <lb/>corpi. </s>

<s>Onde, come cosa reale, si riferiscono alle qualit&agrave;, e si dividono alcuni <lb/>di loro per accidente, come il giallo alla divisione dell'oro, e dirassi un corpo <lb/>comporsi e misurarsi d'infinite superfice, come quasi l'oro dalle infinite su&shy;<lb/>perfice in atto o in potenza che, per accidente, agguagliano tutta la super&shy;<lb/>fice di quello. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E cos&igrave; anche per esempio una superfice dividesi alla divisione d'un <lb/>corpo, come lungo e largo, ma la stessa, come mancante di profondit&agrave;, &egrave; un <lb/>nulla, e dal nulla non si pu&ograve; comporre cosa alcuna, bench&egrave; si moltiplichi <lb/>per qualsivoglia numero finito e anche infinito, se dar si potesse: &egrave; ben <lb/>vero poi che il giallo non riducesi alla ragione del quanto, come riduconsi <lb/>la linea e la superfice al corpo. </s>

<s>Ora il Galilei, bench&egrave; parli molto ambiguo <lb/>degli infiniti di atto e di potenza, di numero e di mole, come anche del con&shy;<lb/>tinuo e del congiunto, e di altri somiglianti principii, contuttoci&ograve; si lascia <lb/>intendere essere i corpi composti d'infiniti indivisibili attuali, e nello stesso <lb/>modo contenersi, ed esser distinti l'uno dall'altro i punti in una periferia, <lb/>come i lati nel perimetro di un poligono, ma questi principii, con altre con&shy;<lb/>seguenze, hanno bisogno di ridursi a buon senso. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, <lb/>pag. </s>

<s>970, 71). </s></p><p type="main">

<s>Questo ragionamento del s&igrave; valoroso matematico amico suo, se dette <lb/>occasione al Torricelli di scrivere <emph type="italics"/>De doctrina indivisibilium non temere <lb/>usurpanda<emph.end type="italics"/> (Fabroni, Vitae Ital., Vol. </s>

<s>I, Pisis 1778, pag. </s>

<s>375), non valse <lb/>per&ograve; a persuadergli che, per mancare le superfice di profondit&agrave;, come si <lb/>diceva, non se ne potessero comporre i solidi, e per protestare contro que&shy;<lb/>sta opinione, nella II parte <emph type="italics"/>De dimensione parabolae,<emph.end type="italics"/> entrava francamente <pb xlink:href="020/01/1896.jpg" pagenum="139"/>per quella via regia apertagli innanzi dal Cavalieri. </s>

<s>Questa pubblica prova <lb/>per&ograve; &egrave; posteriore all'altra, che si desume dai privati commerci epistolari, <lb/>ne'quali si lesse come, non avendo familiarit&agrave; col Nardi, esso Cavalieri pre&shy;<lb/>gasse il Torricelli a voler dar motivo all'amico d'entrare a pigliar le difese <lb/>della nuova Geometria contro la presunzion del Guldino. </s></p><p type="main">

<s>Non manc&ograve; il Torricelli di far l'impostogli ufficio, e fu per questa oc&shy;<lb/>casione ch'ebbe il Nardi la prima notizia della Centrobrarica, come il Tor&shy;<lb/>ricelli stesso l'avea poco fa avuta da quella lettera da Bologna del d&igrave; 3 Gen&shy;<lb/>naio 1643 da noi trascritta di sopra, essendo un fatto in tal proposito assai <lb/>notabile, che tanto s'esercitassero i nostri Matematici intorno a dar ragio&shy;<lb/>nevole fondamento a quella Regola meccanica universale, senz'aver mai po&shy;<lb/>tuto, per la sua rarit&agrave;, leggere l'opera del Gesuita tedesco. </s></p><p type="main">

<s>Il Nardi dunque informato della questione, contento di aver avuto di li <lb/>l'impulso a'suoi studii geometrici, si tenne, quanto fosse possibile, in di&shy;<lb/>sparte dai litiganti. </s>

<s>Concorse nonostante a confermare quelle accuse di fal&shy;<lb/>sit&agrave;, che l'Autor della Geometria nuova volea ritorcere contro alcune pro&shy;<lb/>posizioni della Centrobrarica. </s>

<s>Era una di queste proposizioni quella del centro <lb/>di gravit&agrave; di un segmento sferico, o di un emisferio, che il Torricelli, ad <lb/>istanza del Cavalieri, determin&ograve; in un punto assai diverso da quello, che <lb/>una geometrica fallacia avea suggerito al Guldino. </s>

<s>Propostosi questo mede&shy;<lb/>simo problema baricentrico al Nardi, s'incontr&ograve; per altra via nella conclu&shy;<lb/>sione torricelliana, cos&igrave; lasciando scritto in quel suo ampio Teatro accade&shy;<lb/>mico, nell'ultima Scena, che s'intitola <emph type="italics"/>Pi&ugrave; vedute in una:<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Essere il centro di gravit&agrave; d'una superfice emisferica nel mezzo del&shy;<lb/>l'asse, in che sbagliossi il Guldino, provasi da me facilmente con dividere <lb/>detto asse in particelle eguali, e ciascuna minore della distanza che l'avver&shy;<lb/>sario vuole dal mezzo. </s>

<s>Quindi, tirati piani paralleli alla base, per dette <lb/>divisioni si tagliano parti eguali di superfice, quali, per essere uniforme&shy;<lb/>mente gravi, peseranno egualmente, ed aver&agrave; ciascuna il centro dentro i <lb/>termini della sua particella di asse, e quindi dedurrassi facilmente l'assurdo. </s>

<s><lb/>Trovasi anche facilmente il centro delle superfice coniche e cilindriche, come <lb/>anche col Teorema generale meccanico, quello della mezza periferia, ed in <lb/>questo osservasi la medesima analogia, da chi ben l'intende, che nella su&shy;<lb/>perfice emisferica. </s>

<s>Con l'aiuto poi di queste invenzioni si discende alle pi&ugrave; <lb/>particolari proposte intorno alla stessa materia &rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, <lb/>pag. </s>

<s>1360). </s></p><p type="main">

<s>Si rivela ai sagaci lettori da queste parole il genio geometrico del Nardi, <lb/>il quale, avuta la notizia della Regola guldiniana, rimasta per l'inventore <lb/>una cosa puramente meccanica; prov&ograve; una viva compiacenza in trovar che <lb/>la ragion matematica cos&igrave; da tutti desiderata scendeva chiarissima dalle sue <lb/>proprie invenzioni. </s>

<s>Erano quelle invenzioni novelli frutti menati dall'albero <lb/>antico, a pi&egrave; del quale rampollava un gran principio, che il Nardi stesso <lb/>chiama <emph type="italics"/>Della trasformazion delle figure.<emph.end type="italics"/> Questa trasformazione dunque, che <lb/>ne'libri del Keplero e del Guldino apparve a tutti i Geometri nuova, la vide <pb xlink:href="020/01/1897.jpg" pagenum="140"/>il Nostro, in s&egrave; e nelle sue mirabili conseguenze, espressa da quel I teo&shy;<lb/>rema archimedeo, in cui il circolo s'insegna a trasformare in un triangolo. </s>

<s><lb/>Cos&igrave; parevagli che si venisse quel teorema a svolgere in tutte le propriet&agrave; <lb/>de'triangoli, dimostrate da Euclide nel VI libro Degli elementi, e perci&ograve; escla&shy;<lb/>mava, in fine alla XXV veduta della II Scena, dop'averne dimostrate le <lb/>feconde applicazioni: &ldquo; Ora questo gran principio, cio&egrave; la I Della misura <lb/>del cerchio e la sua proporzionale, che altro sono in effetto, se non la <lb/>I del VI e la sua proporzionale? </s>

<s>&rdquo; (MSS. cit., pag. </s>

<s>329). </s></p><p type="main">

<s>La Centrobrarica insomma, che i loro Autori avevano derivata da stra&shy;<lb/>niere sorgenti, veniva il Nardi a dimostrare com'ella scaturisse dalle stesse <lb/>pi&ugrave; sincere fonti della Geometria, s&igrave; per le linee, s&igrave; per le superfice comun&shy;<lb/>que poste, e di qualunque figura, revolubili intorno all'asse. </s>

<s>A che altro <lb/>accennano gli antichi teoremi euclidei della superfice piana del circolo, e <lb/>della convessa del cilindro, se non alla manifesta trasformazione di quelle <lb/>stesse superfice rotonde in due rettangoli, l'uno de'quali sia costruito sulla <lb/>circonferenza e sulla met&agrave; del raggio, e l'altro sulla circonferenza descritta <lb/>dalla base, e sull'altezza della linea che, menata in giro alla sua parallela <lb/>immobile, descrive quella cilindrica superfice? </s></p><p type="main">

<s>N&egrave; una tale trasformabilit&agrave; delle superfice curve in rette si verifica solo <lb/>nelle due citate proposizioni, ma in quell'altre eziandio, dice il Nardi, con&shy;<lb/>cernenti le superfice coniche, o de'frusti di coni. </s>

<s>Sia la linea AB (fig. </s>

<s>55) <lb/>revolubile intorno all'asse CD. </s>

<s>Se si prende in E il mezzo della linea AB, <lb/><figure id="id.020.01.1897.1.jpg" xlink:href="020/01/1897/1.jpg"/></s></p><p type="caption">

<s>Figura 55.<lb/>e si conduce EF perpendicolare a CD, la superfice cos&igrave; <lb/>descritta sar&agrave; eguale a quella del cilindro. </s>

<s>Per la XVI <lb/>archimedea infatti <emph type="italics"/>De sphaera et cylindro<emph.end type="italics"/> (Opera cit., <lb/>pag. </s>

<s>38), si ha <foreign lang="greek">p</foreign>.AB(AC+BD)=<foreign lang="greek">p</foreign>.2 EFXAB <lb/>=CaEFXAB. </s>

<s>Se poi la linea s'inclina fino a <lb/>toccare in H l'asse di rotazione, la superfice rotata <lb/>riuscir&agrave; conica, e avr&agrave; per misura, secondo la Geome&shy;<lb/>tria antica, CaBDXBH/2=CaEF&prime;XBH, che esat&shy;<lb/>tamente risponde con la Regola nuova. </s>

<s>Ma ascoltiamo <lb/>le parole proprie del Nardi che, nella citata Veduta <lb/>XXV del suo scientifico Panorama, ci distese in po&shy;<lb/>che parole, e sotto il titolo di <emph type="italics"/>Teorema generale mec&shy;<lb/>canico,<emph.end type="italics"/> il primo trattato compiuto di Geometria centrobrarica. </s></p><p type="main">

<s>&ldquo; Tal Teorema, egli dice, fu proposto, per quanto intendo, senza dimo&shy;<lb/>strazione, dal padre Guldino, e deducesi da certa regola del Keplero. </s>

<s>E ben&shy;<lb/>ch&egrave; io non abbia veduta l'Opera sua, mi vien detto nondimeno essere in <lb/>sostanza questo: <emph type="italics"/>Se sar&agrave; trovato il centro di gravit&agrave; della linea, o figura <lb/>piana da rivolgersi, moltiplicando la circonferenza, descritta secondo la <lb/>intera rivoluzione dal centro di gravit&agrave;, nella linea revoluta o figura piana, <lb/>si produrr&agrave; la superfice descritta o la solidit&agrave; del corpo. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Questo teorema ha molti casi, quali tutti dal Metodo della trasforma-<pb xlink:href="020/01/1898.jpg" pagenum="141"/>zione delle figure facilmente si mostrano. </s>

<s>E facendomi dalle linee, saranno <lb/>o rette o curve: se rette, o semplici o composte: se semplici, o perpendico&shy;<lb/>lari o parallele o inclinate all'asse della rivoluzione. </s>

<s>Le perpendicolari o toc&shy;<lb/>cheranno o segheranno o saranno disgiunte dall'asse. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se la linea perpendicolare tocchi l'asse, descriver&agrave; un cerchio, e in <lb/>questo si verifica, per le cose da noi dimostrate, la proposizione. </s>

<s>Se lo se&shy;<lb/>ghi, avverr&agrave; lo stesso, bench&egrave; la parte minore resti oziosa. </s>

<s>Se sia disgiunta, <lb/>descriver&agrave; una fascia circolare, in cui anche si trova, per le cose da noi <lb/>dette, la verit&agrave; della proposta, ma la retta parallela all'asse descriver&agrave; una <lb/>superfice cilindrica, qual'&egrave; manifesto che eguaglia ad un rettangolo sotto <lb/>essa linea, e sotto la periferia descritta dalla distanza dell'asse. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che se la stessa retta s'inclini, mantenendo il suo centro la stessa <lb/>distanza dall'asse, descriver&agrave; una porzione di conica superfice eguale alla <lb/>cilindrica, il che raccogliesi dalle nostre invenzioni, e dalla XV ancora del <lb/>I Della sfera e cilindro. </s>

<s>E se inclinandosi tocchi l'asse, descriver&agrave; una su&shy;<lb/>perfice conica eguale, per le cose insegnate, ad un triangolo rettangolo, di <lb/>cui l'altezza s'agguagli alla linea revoluta, e la base alla periferia descritta <lb/>dalla perpendicolare dall'altro estremo della linea nell'asse. </s>

<s>Adunque il ret&shy;<lb/>tangolo, sotto la medesima linea e sotto la met&agrave; della periferia suddetta, sar&agrave; <lb/>eguale alla conica superfice. </s>

<s>Ma questa met&agrave; vien descritta dalla perpendi&shy;<lb/>colare, che congiunge l'asse al centro di gravit&agrave; di essa linea, com'&egrave; pa&shy;<lb/>lese. </s>

<s>Se poi la medesima linea inclinandosi seghi l'asse, farannosi due su&shy;<lb/>perfice coniche, ove ha luogo la ragione me&shy;<lb/>desima. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di qui passeremo alla teoria dei casi <lb/>composti. </s>

<s>Siano le tre linee rette GD, DC, CF <lb/>(fig. </s>

<s>56) revolute intorno all'asse HB: dico <lb/><figure id="id.020.01.1898.1.jpg" xlink:href="020/01/1898/1.jpg"/></s></p><p type="caption">

<s>Figura 56.<lb/>che la superfice descritta da esse &egrave; eguale ad <lb/>un rettangolo contenuto sotto di esse linee, <lb/>come una, e sotto la periferia descritta dalla <lb/>perpendicolare, che congiunge l'asse e il cen&shy;<lb/>tro della loro gravit&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Poniamo, per dare esempio di tutti i casi possibili, che la linea DG <lb/>sia inclinata all'asse, e che <lb/>DC sia parallela, e che CF <lb/>sia perpendicolare al mede&shy;<lb/>simo asse. </s>

<s>Divisa DC egual&shy;<lb/>mente in A, tirisi all'asse la <lb/>perpendicolare AB, e trovisi <lb/>il rettangolo MS (fig. </s>

<s>57) <lb/><figure id="id.020.01.1898.2.jpg" xlink:href="020/01/1898/2.jpg"/></s></p><p type="caption">

<s>Figura 57.<lb/>eguale alla superfice cilindrica <lb/>descritta da DC, qual rettan&shy;<lb/>golo abbia il lato MN eguale <lb/>a DC. </s>

<s>Adunque l'altro lato <pb xlink:href="020/01/1899.jpg" pagenum="142"/>MT sar&agrave; eguale alla periferia descritta da AB. Parimente, divisa DG egual&shy;<lb/>mente in E (fig. </s>

<s>56 prec.), tirisi EH perpendicolare all'asse, e trovisi il ret&shy;<lb/>tangolo NP eguale alla porzione di superfice conica descritta da DG. </s>

<s>Dun&shy;<lb/>que se il lato NO, posto a dirittura con MN, s'agguagli a DG, anche OP <lb/>s'agguaglier&agrave; alla periferia descritta da HE. </s>

<s>Sia SY l'eccesso di NS sopra <lb/>OP, e dividasi SY in R, sicch&egrave; RY ad RS si trovi come MN ad NO, e <lb/>compiscasi il rettangolo MQ, con prodursi OP, e tirarsi RQ parallela ad <lb/>MO. </s>

<s>Adunque il rettangolo MQ s'agguaglier&agrave; ai due MS, NP, poich&egrave; eguali <lb/>sono i rettangoli TR, RP. &rdquo; </s></p><p type="main">

<s>&ldquo; Cada ora in AB perpendicolare EV e congiungansi i punti E, A, e <lb/>trovato il centro comune della gravit&agrave; delle rette GD, DC, sia L, da cui per&shy;<lb/>pendicolare in AB cade LZ. </s>

<s>Sar&agrave; dunque come AL ed LE, ovvero come GD <lb/>a DC, cos&igrave; AZ a YV; ovvero RS ad RY, e per&ograve; la periferia descritta da BZ, <lb/>cio&egrave; da IL, sar&agrave; eguale alla retta NR, onde, moltiplicata per GD e DC come <lb/>una, cio&egrave; per MO, former&agrave; il rettangolo MQ eguale a due rettangoli MS, <lb/>NP, il che bisognava dimostrare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Nello stesso modo si prover&agrave; che, trovato il centro di gravit&agrave; delle <lb/>due GC, DC come una, e di CF, il rettangolo contenuto sotto tutte tre come <lb/>una, e sotto la periferia descritta dalla perpendicolare da esso centro nel&shy;<lb/>l'asse, s'agguaglia alla superfice nata dalla rivoluzione di dette due linee. </s>

<s><lb/>E quello che in tre, in tutte le altre linee in infinito, con lo stesso metodo, <lb/>si prover&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Passiamo alle linee curve, le quali o sono curve uniformi o difformi. </s>

<s><lb/>Chiamo uniformi quelle, che sono curve verso la stessa parte; difformi <lb/>quelle, che verso le contrarie parti. </s>

<s>Ora le difformi si riducono, come com&shy;<lb/>poste, alle uniformi, onde, provata la mede&shy;<lb/>sima verit&agrave; in queste, anche in quelle si pro&shy;<lb/>ver&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia dunque la curva GAC (fig. </s>

<s>58) da <lb/>rivolgersi intorno all'asse HB, e di essa curva <lb/>sia centro di gravit&agrave; L. </s>

<s>Dico che la superfice <lb/>descritta dalla sua rivoluzione s'agguaglia al <lb/>rettangolo sotto una eguale a GAC, e sotto <lb/>la periferia descritta da LB perpendicolare in <lb/>HB. </s>

<s>Intendansi sottese al concavo di essa curva <lb/><figure id="id.020.01.1899.1.jpg" xlink:href="020/01/1899/1.jpg"/></s></p><p type="caption">

<s>Figura 58.<lb/>molte rette, che abbiano i medesimi termini colla curva, ed anche al con&shy;<lb/>vesso, nello stesso modo, altre rette si circoscrivano. </s>

<s>E nulla importa qual <lb/>posizione abbia la linea curva verso HB. &rdquo; </s></p><p type="main">

<s>&ldquo; Ora perch&egrave;, nella figura da noi posta, accade che il concavo suo ri&shy;<lb/>miri l'asse, avverr&agrave; che il centro delle inscritte linee, V, sia pi&ugrave; verso al&shy;<lb/>l'asse, che il centro Z delle circoscritte, restando di mezzo il centro L della <lb/>curva. </s>

<s>E s'avverta che tutti questi centri si sono posti in una retta, perch&egrave; <lb/>nulla importa il considerare l'esser sotto o sopra di essa, ma solo attendesi <lb/>la distanza dell'asse. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/1900.jpg" pagenum="143"/><p type="main">

<s>&ldquo; Ci&ograve; avvertito, dico apparir la verit&agrave; della proposta, perch&egrave; se dices&shy;<lb/>simo che la superfice descritta dalla curva non s'agguagliasse al rettangolo <lb/>sotto di essa e della periferia descritta da LB, avverria che o fosse mag&shy;<lb/>giore o minore. </s>

<s>Se maggiore, ne sia determinato l'eccesso. </s>

<s>E perch&egrave; le cir&shy;<lb/>coscritte rette GD, DC...., avendo i medesimi termini con la curva verso <lb/>la stessa parte, sono maggiori della curva; avverr&agrave; che, moltiplicandosi le <lb/>circoscrizioni delle linee rette, eccedano queste la curva di meno, che la su&shy;<lb/>perfice descritta da queste eccede il rettangolo sopraddetto, e cos&igrave; poi av&shy;<lb/>verr&agrave; che il rettangolo contenuto sotto queste circoscritte, e sotto la perife&shy;<lb/>ria descritta da LB, fosse minore dell'altro sotto la curva, e sotto la medesima <lb/>periferia, il che &egrave; assurdo, trovandosi le circoscritte pi&ugrave; lontane dall'asse, <lb/>che non &egrave; la curva, quale anche &egrave; minore di quelle. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La stessa maniera serve per provare che non pu&ograve; esser minore, e <lb/>pi&ugrave; brevemente, per le cose da noi dimostrate altrove. </s>

<s>Concluderassi che, <lb/>per mantenersi la stessa analogia delle inscritte e circoscritte rette alla curva, <lb/>in ogni moltiplicazione intorno a trasformarsi in punti, anche in tal caso la <lb/>proporzionale conclusione avr&agrave; luogo. </s>

<s>&rdquo; (MSS. cit., pag. </s>

<s>314-21). </s></p><p type="main">

<s>La premeditata elezione del metodo antico degl'inscritti e dei circoscritti <lb/>condusse il Nardi a dimostrare quest'ultimo teorema all'assurdo, mentre, <lb/>proseguendo il metodo nuovo, avrebbe potuto dare un'assai facile dimostra&shy;<lb/>zione diretta, considerando la curva, qualunque ella si fosse, come compo&shy;<lb/>sta d'indivisibili particelle che, essendo rette, riducevano questo al caso pre&shy;<lb/>cedente. </s>

<s>Le linee infatti DG, DC, CF della passata figura LVI, indivisibilmente <lb/>moltiplicate, purch&egrave; sempre si rimangano nel medesimo piano giacenti, sono <lb/>atte a rappresentar l'andamento di qualunque specie di curva. </s></p><p type="main">

<s>Ma pure, moltiplicandosi pi&ugrave; e pi&ugrave; le linee inscritte e circoscritte, in&shy;<lb/>torno a ridurle in punti, il metodo antico, come nella quadratura del cir&shy;<lb/>colo, viene a riscontrarsi col nuovo, e il Nardi, nelle parole ultimamente ci&shy;<lb/>tate, par che giusto voglia accennare a questo incontro. </s>

<s>&Egrave; perci&ograve; forse che, <lb/>passando, dai rotondi generati da linee, a trattar de'rotondi generati da su&shy;<lb/>perfice, non si sentirebbe punto ritroso di prendere a fondamento e a prin&shy;<lb/>cipio delle sue speculazioni quel Lemma del Rocca, di cui gli avea il Torri&shy;<lb/>celli dato notizia, ammirandone la bellezza. </s>

<s>Ma pur non men bello sembrava <lb/>al Nardi il Metodo della trasformazion delle figure, e tra per l'amore alle <lb/>proprie invenzioni, e per rendere il processo dimostrativo uniforme, seguit&ograve; <lb/>a far vedere com'anche per i solidi rotondi derivi dalla Geometria antica la <lb/>Centrobrarica nuova. </s></p><p type="main">

<s>Quel Metodo, che condusse il Nostro a tante nuove conclusioni, quali <lb/>invano si desidera di veder distese nel libro delle <emph type="italics"/>Ricercate geometriche,<emph.end type="italics"/> ha, <lb/>nelle particolari applicazioni alla Centrobrarica, come accennammo, il suo <lb/>fondamento in questo teorema, che da Archimede si pone per principio alla <lb/>dimensione del circolo: &ldquo; Omnis circulus aequalis est triangulo rectangulo, <lb/>cuius radius est par uni eorum, quae sunt circa rectum angulum, circum&shy;<lb/>ferentia vero basi &rdquo; (Opera cit., pag. </s>

<s>128). </s></p><pb xlink:href="020/01/1901.jpg" pagenum="144"/><p type="main">

<s>Ora &egrave; davvero, come parve al Nardi, maravigliosamente bello il modo, <lb/>che offre questo archimedeo teorema, di trasformar le figure, le quali si ri&shy;<lb/>ducono ne'pi&ugrave; semplici casi o a rettangoli, che generano <lb/>cilindri, o a triangoli, che rotati descrivono coni. </s>

<s>Rap&shy;<lb/>presenti AB (fig. </s>

<s>59) uno di questi rettangoli revolubile <lb/>intorno al lato CB: il rotondo cilindrico nato da cos&igrave; fatta <lb/>rivoluzione &egrave; noto aver per misura CoEBXBC eguale, <lb/>per il citato teorema archimedeo, ad EB/2XCaEBXBC <lb/>=EBXBCXCaEB/2. Se ora sia G il centro di gra&shy;<lb/>vit&agrave; del rettangolo, da cui si conduca GD perpendicolare <lb/>all'asse, CaEB/2 sar&agrave; eguale a CaGD, ond'&egrave; che per tal <lb/>metodo geometrico viene il solido cilindrico a trasfor&shy;<lb/><figure id="id.020.01.1901.1.jpg" xlink:href="020/01/1901/1.jpg"/></s></p><p type="caption">

<s>Figura 59.<lb/>marsi nel parallelepipedo EBXBCXCaGD, il quale perci&ograve; ha per base <lb/>il rettangolo genitore AB, e per altezza la circonferenza descritta dal centro <lb/>di gravit&agrave;, come pel metodo centrobrarico. </s></p><p type="main">

<s>Sia poi revolubile intorno al medesimo asse CB il triangolo CEB: il <lb/>cono cos&igrave; descritto ha per misura CoEBXCB/3 che, per il citato <lb/>principio <lb/>archimedeo, &egrave; eguale ad EB/2XCaEBXCB/3=EBXCaGDXCB/3, man&shy;<lb/>tenuta la costruzion precedente. </s>

<s>Abbassata ora la bissettrice CP, suppongasi <lb/>in N il centro di gravit&agrave; del triangolo, da cui si conduca la perpendicolare <lb/>NO. </s>

<s>I triangoli simili e la posizion di quel centro, danno 3:2=GD:NO= <lb/>CaGD:CaNO, d'onde CaGD=3 CaNO/2; valore che, sostituito nella supe&shy;<lb/>riore misura geometrica ultimamente trovata, d&agrave; il cono trasformato nel <lb/>prisma triangolare EBXCB/2XCaNO, conforme alla Regola centrobrarica. </s>

<s><lb/>Ma perch&egrave; le parole proprie del Nardi, nella loro original concisione, sono <lb/>assai pi&ugrave; efficaci, seguitiamo a trascriverle fedelmente ai nostri Lettori: </s></p><p type="main">

<s>&ldquo; Passiamo alle superfice rivoltate intorno ad un asse. </s>

<s>E qui avverti&shy;<lb/>sco primieramente essere stato dimostrato dal sottilissimo G. </s>

<s>Antonio Rocca <lb/>che i solidi rotondi hanno la proporzione delle figure genitrici, e delle cir&shy;<lb/>conferenze descritte dai centri, da che ci riscontriamo con la proposta di <lb/>sopra fatta. </s>

<s>Ma per far noi uniforme il metodo di dimostrare i prodotti delle <lb/>superfice, e quelli delle linee, prenderemo il principio dai pi&ugrave; semplici casi, <lb/>proponendo un rettangolo AEBC (fig. </s>

<s>prec.), il quale si pu&ograve; intendere ri&shy;<lb/>volgersi intorno ad un lato o intorno ad altro asse disgiunto. </s>

<s>Se intorno ad <lb/>un lato, descrive un cilindro, ed a questo s'agguaglia, com'&egrave; facile a in&shy;<lb/>tendersi dalle cose da noi dimostrate, un prisma contenuto da tre rettan&shy;<lb/>goli e da due triangoli laterali, anch'essi rettangoli. </s>

<s>Ciascuno di questi trian-<pb xlink:href="020/01/1902.jpg" pagenum="145"/>goli s'agguaglia al cerchio base del cilindro, e il rettangolo, che fa angolo <lb/>retto con l'altra base del prisma, &egrave; lo stesso che AEBC, ma l'altro sud&shy;<lb/>detto rettangolo si contiene sotto la retta CB, e sotto la periferia descritta <lb/>dal doppio di GD, posto esser GD la retta, che dal centro del rettangolo <lb/>cade perpendicolare in CB. &rdquo; </s></p><p type="main">

<s>&ldquo; Adunque &egrave; manifesto, per gli Elementi, che il solido, sotto AEBC e <lb/>sotto la periferia descritta da GD, s'agguaglia al prisma. </s>

<s>E lo stesso &egrave; vero <lb/>nei parallelogrammi non rettangoli revoluti, poich&egrave; l'eccesso di uno estremo <lb/>compensa il difetto dell'altro nei solidi prodotti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che se tirato sia nel rettangolo AEBC il diametro CE, e si rivolga <lb/>il triangolo CEB intorno all'asse CB, descriver&agrave; un cono, che al cilindro del <lb/>rettangolo ha la ragione di uno a tre. </s>

<s>Adunque un solido sotto detto trian&shy;<lb/>golo, e sotto la periferia descritta da GD, aver&agrave; al cono la ragione di tre a <lb/>due, quale &egrave; la medesima che quella della linea GD alla linea, che perpen&shy;<lb/>dicolare cade dal centro del triangolo in CB. </s>

<s>E cos&igrave; le comuni regole dei <lb/>solidi, nati dalla rivoluzione dei piani, avranno luogo anche in questo caso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora se il rettangolo s'intende rivolgersi disgiunto, ma parallelo con <lb/>un suo lato all'asse, descriver&agrave; un anello cilindrico, e se inclinato descrive&shy;<lb/>rallo conico: e qui le proporzionali cose avvengono che nelle linee revolute. </s>

<s><lb/>Onde, supponendo di scrivere a persone perite, non m'intertengo pi&ugrave;, e pas&shy;<lb/>sandomene alle superfice contenute da rette pi&ugrave; irregolarmente poste, od a <lb/>curve linee, dico che, mediante la circoscrizione di rettangoli o parallelo&shy;<lb/>grammi, s'otterr&agrave; l'intento. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E prendiamo in esempio la parabola, a cui sia circoscritto il paral&shy;<lb/>lelogrammo, com'anche alla usanza archimedea altri minori parallelogrammi <lb/>siano inscritti e circoscritti, perch&egrave;, rivoltate tutte queste figure intorno alla <lb/>base parabolica, si descriver&agrave; dal parallelogrammo un cilindro, dalla parabola <lb/>un fuso, e dalle figure inscritte e circoscritte descriverannosi due solidi com&shy;<lb/>posti di cilindri e di anelli cilindrici. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La proporzione poi del cilindro, descritto dal parallelogrammo, al so&shy;<lb/>lido descritto dalla figura circoscritta alla parabola, o a quello descritto dalle <lb/>inscritte, si trover&agrave; col metodo sopra usato esser composta della proporzione <lb/>del parallelogrammo alla figura, e della linea, che dal centro va, a quella <lb/>del centro di quelle, e ci&ograve; insino all'ultimo. </s>

<s>Adunque anche il cilindro al <lb/>fuso sar&agrave; nella stessa proporzione. </s>

<s>Ora il parallelogrammo alla parabola &egrave; <lb/>come 6 a 4, per le cose da noi dimostrate. </s>

<s>E la linea dal centro suo, a <lb/>quella del centro di questa, &egrave; come 5 a 4, come da Archimede si dimostra. </s>

<s><lb/>Adunque il cilindro al fuso sar&agrave; come 30 a 16 o come 15 a 8. &rdquo; </s></p><p type="main">

<s>&ldquo; Che se la parabola e il rettangolo si rivolgano per la cima di essa, <lb/>vedrassi in un tratto essere il cilindro al solido come 5 a 4. Finalmente, se <lb/>la mezza parabola si rivolge insieme col parallelogrammo, che quella com&shy;<lb/>prenda intorno ad una parallela all'asse e segante la acuta parabolica; sar&agrave; <lb/>nello stesso modo la proporzione dei solidi nota. </s>

<s>Ma sono quasi impossibili <lb/>le investigazioni a priori di cotali materie per il metodo antico, e bisogna <pb xlink:href="020/01/1903.jpg" pagenum="146"/>ridursi al nuovo, col quale anche a priori dimostrasi questa universalissima <lb/>proposta meccanica. </s>

<s>&rdquo; (MSS. cit., pag. </s>

<s>321-26). </s></p><p type="main">

<s>In queste ultime espressioni del Nardi si d&agrave; la dovuta importanza alla <lb/>Regola centrobrarica, della quale si dice poter aversi prova a priori, ossia <lb/>matematica, e non solamente fisica, com'erasi avuta dal Keplero e dal Gul&shy;<lb/>dino, in que'loro impropriamente chiamati teoremi. </s>

<s>Il metodo della trasfor&shy;<lb/>mazion delle figure aveva all'Autore offerti di quelle matematiche dimostra&shy;<lb/>zioni gli esempi sopra recati, ma i centri di gravit&agrave; introdottivi partecipavano <lb/>ancora qualche cosa del meccanico ai nuovi processi dimostrativi, ond'&egrave; che <lb/>il Nardi, il quale voleva assolutamente renderli geometrici, pens&ograve; di sostituire <lb/>a quelli stessi centri di gravit&agrave; il <emph type="italics"/>centro della potenza.<emph.end type="italics"/> Intendeva per que&shy;<lb/>sto nome significato quel che'&egrave; oggid&igrave; nel comun linguaggio dei Matema&shy;<lb/>tici, estendendolo a qualunque prodotto di quantit&agrave; numeriche o lineari, da <lb/>cui giusto vien la potenza di produr da linee superfice, e da superfice so&shy;<lb/>lidit&agrave; di corpi. </s>

<s>Cos&igrave; tornava la Meccanica centrobrarica del Guldino, per <lb/>opera del Nostro, non solo, diciam cos&igrave;, trasposta negli orti, ma qual novello <lb/>ramo inoculata nel grande albero antico della Geometria. </s></p><p type="main">

<s>&ldquo; Veramente maravigliosa (cos&igrave; proseguesi nel manoscritto l'interrotto <lb/>ragionamento) sembra la suddetta Regola generalissima con la sua prova <lb/>intorno alla potenza delle linee e superfice rivoltate in giro. </s>

<s>Mancagli non&shy;<lb/>dimeno il riducimento dal meccanico al geometrico, con ridurre il centro <lb/>della gravit&agrave; al centro della potenza. </s>

<s>Dico centro della gravit&agrave; d'una super&shy;<lb/>fice il definito altre volte, ma centro della potenza dico il punto dentro alla <lb/>sua superfice o suo concavo, da cui, tirata una retta perpendicolare all'asse <lb/>di qualsivoglia rivoluzione descrive essa retta, con un suo estremo, una pe&shy;<lb/>riferia eguale all'altezza di un solido, che per base abbia la superfice di <lb/>un solido voltata poi in giro, ed al solido da quella superfice descritto sia <lb/>eguale. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il centro dunque della potenza sar&agrave; in effetto lo stesso che quello <lb/>della gravit&agrave;, ma sar&agrave; dato per termini geometrici. </s>

<s>Il centro poi della figura <lb/>sar&agrave; talvolta diverso da quello della potenza, poich&egrave; per esempio dirassi: nel <lb/>mezzo cerchio il centro della figura &egrave; nel mezzo della sua base; nel cerchio <lb/>poi e nel parallelogrammo conviene in uno l'un centro e l'altro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se finalmente vogliamo definire nelle linee il centro della potenza, <lb/>diremo esser quel punto, dentro alla linea o suo concavo, da cui tirata una <lb/>retta perpendicolare all'asse di qualsivoglia rivoluzione descriva essa retta <lb/>con un suo estremo una periferia eguale al lato di un rettangolo, il qual <lb/>rettangolo sia eguale alla superfice descritta dalla linea voltata in giro, ed <lb/>abbia l'altro suo lato eguale ad essa linea. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, quanto alla generale dimostrazione in tutti i suoi casi da noi <lb/>apportata, non lasceremo d'avvertire com'ella &egrave; tutta fondata nella prima <lb/>proposta della misura del cerchio, ond'&egrave; quasi un corollario suo e della sua <lb/>proporzionale. </s>

<s>Dico dunque che le line rette voltate in giro non possono <lb/>descrivere se non cerchi e sue fasce, superfice coniche e cilindriche, poich&egrave; <pb xlink:href="020/01/1904.jpg" pagenum="147"/>non possono aver se non tre situazioni rispetto all'asse della rivoluzione. </s>

<s><lb/>Agguagliato dunque ad un triangolo noto o rettangolo il cerchio in quello <lb/>trasformato, agguaglieremo anco la sua fascia e settore, come parimente la <lb/>superfice conica e sua parte, e la cilindrica, che &egrave; un rettangolo. </s>

<s>Saputa poi <lb/>la potenza d'una retta, si sa quella di due e quante vogliamo, poich&egrave; que&shy;<lb/>sto non si riduce ad altro, se non che i rettangoli uguali hanno reciproche <lb/>le basi e le altezze. </s>

<s>Dall'applicar poi, di fuori e di dentro alle curve, rette, <lb/>si prova della potenza delle curvo quella che delle rette. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E passando alla potenza delle superfice, noi sappiamo, con la analo&shy;<lb/>gia della I suddetta della misura del cerchio, che un rettangolo, voltato in&shy;<lb/>torno alla base o ad una parallela alla base, descrive un cilindro o un anello <lb/>cilindrico, e questi s'agguagliano, trasformati, ad un prisma o parallelepi&shy;<lb/>pedo retto. </s>

<s>Saputo la potenza di un rettangolo, sapremo quella di due o <lb/>pi&ugrave;, poich&egrave; ci&ograve; non si riduce ad altro, se non che i parallelepipedi uguali <lb/>hanno reciproche le basi e le altezze. </s>

<s>Quindi, passando alle inscrizioni e <lb/>circoscrizioni di rettangoli o parallelogrammi alle piane figure, s'otterr&agrave; pro&shy;<lb/>porzionalmente lo stesso che nelle stesse linee. </s>

<s>Tanto importa un principio <lb/>grande, mentre bene applicar si sappia. </s>

<s>Ora, questo gran principio, cio&egrave; la <lb/>I della misura dal cerchio e la sua proporzionale, che altro sono in effetto, <lb/>se non la I del VI e le sue proporzionali? </s>

<s>&rdquo; (MSS. cit., pag. </s>

<s>326-29). </s></p><p type="main">

<s>A ripensar che le conseguenze di questo gran principio archimedeo, con <lb/>le bellissime applicazioni di lui al modo di trasformar le figure, si dimo&shy;<lb/>strarono dal Nardi nel libro delle Ricercate geometriche, e in quello delle <lb/>Scene accademiche, l'uno rimasto tuttavia manoscritto e l'altro a quel che <lb/>sembra perduto; si pu&ograve; facilmente intendere quale documento importante <lb/>sia venuto a mancare alla storia della Scienza italiana. </s>

<s>Quanto al presente <lb/>proposito poi si comprender&agrave; qual grave danno dovesse venire a risentirne <lb/>la Centrobrarica, la quale seguitava a rimanere nei quattro libri del Gul&shy;<lb/>dino senz'alcun fandamento di Geometria. </s>

<s>Vero &egrave; bene che il Cavalieri vi <lb/>avea sufficientemente supplito, ma &egrave; pure un fatto notabilissimo che quel <lb/>XIV capitolo, con tutta la III geometrica Esercitazione, furono parole in Ita&shy;<lb/>lia gettate al vento. </s>

<s>Gl'indivisibili avevano avuto un colpo mortale dai Dia&shy;<lb/>loghi di Galileo, e perci&ograve; i seguaci del potentissimo uomo, bench&egrave; si sentis&shy;<lb/>sero allettati allo splendore e alla bellezza del vero, o s'astennero nonostante, <lb/>come il Nardi, dal professarli, o gli professarono con riserbo, come il Tor&shy;<lb/>ricelli e il Viviani. </s>

<s>Nelle opere matematiche di questo si legge un tal sen&shy;<lb/>timento non meno espresso, che nelle opere di quello, imperocch&egrave;, nella <lb/>IX proposizione <emph type="italics"/>De maximis et minimis,<emph.end type="italics"/> dop'avere in una prima maniera <lb/>dimostrato che la parabola &egrave; sesquialtera al triangolo della medesima base <lb/>e della medesima altezza, cos&igrave; il Viviani stesso soggiunge per monito al let&shy;<lb/>tore: &ldquo; Ut hoc loco ex adverso indirectae antiquorum viae per duplicem <lb/>positionem luce clarius pateat quantum facilitatis, brevitatis atque evidentiae <lb/>nanciscatur a nova directaque methodo, <emph type="italics"/>recte tamen cauteque usurpata,<emph.end type="italics"/><lb/>acutissimi geometrae Cavalerii, per indivisibilium doctrinam, nobis amicis-<pb xlink:href="020/01/1905.jpg" pagenum="148"/>simam; ex hac alteram accipe eiusdem theorematis demonstrationem &rdquo; (Flo&shy;<lb/>rentiae 1659, pag. </s>

<s>35). </s></p><p type="main">

<s>L'applicazione per&ograve; degl'indivisibili &egrave; fatta qui, come ne'teoremi tor&shy;<lb/>ricelliani, rispetto ai pi&ugrave; semplici casi elementari del metodo, ma le proposi&shy;<lb/>zioni, in che quello stesso metodo via via si svolge, e sempre pi&ugrave; altamente <lb/>s'ingrada, sembravano ai Galileiani audacie temerarie dell'ingegno. </s>

<s>Ad imi&shy;<lb/>tazione perci&ograve; del Maestro come non vollero entrar nell'alto della Geometria <lb/>in VII libri, cos&igrave; non si curarono di leggerne il compendio nelle due prime <lb/>Esercitazioni, insiem con le quali ebbe a trovarsi esclusa dalla lettura an&shy;<lb/>che la III contro il Guldino. </s></p><p type="main">

<s>Di qui &egrave; dato intendere come, morti il Cavalieri, il Torricelli e il Nardi, <lb/>venisse della Centrobrarica, nella Scuola galileiana, a perdersi quasi ogni me&shy;<lb/>moria. </s>

<s>Ebbero gran parte in quell'oblio le difficolt&agrave;, che trovarono a penetrar <lb/>fra noi i due Tomi in folio stampati a Vienna. </s>

<s>Vedemmo come il Cavalieri <lb/>stesso ne avesse avuto notizia solamente due anni da poi, che furono pub&shy;<lb/>blicati, e rispondeva cos&igrave; al Torricelli, che con grande istanza gli avea ri&shy;<lb/>chiesti: &ldquo; Circa il libro del Guldini non posso dirle altro, se non che qua <lb/>in Bologna non se ne trovano, essendo venuto solo quello che ho io, ed un <lb/>altro, che fu comprato da un altro. </s>

<s>Ma credo che a Venezia se ne trove&shy;<lb/>ranno, poich&egrave; di l&agrave; vennero questi due. </s>

<s>&Egrave; stampato in Vienna dell'Austria <lb/>nel 1640 &rdquo; (MSS. Gal. </s>

<s>Disc., XLI, fol. </s>

<s>161). Ma non sembra fosse rimasto <lb/>in Venezia altro esemplare del libro desiderato, cosicch&egrave; forse il Torricelli <lb/>non lo vide se non che assai tardi, com'&egrave; certo che non lo aveva ancora <lb/>veduto il Nardi, quando scrisse le vedute della II Scena. </s>

<s>Ventisei anni dopo <lb/>par che seguitasse tuttavia fra noi la penuria, giacch&egrave; il Viviani, avendone <lb/>data la commissione in Roma a Matteo Campani, questi gli rispondeva il <lb/>d&igrave; 18 Gennaio 1670: &ldquo; Il libro del Guldino da mons&ugrave; Biagio non si trova, <lb/>n&egrave; io ho potuto ancora far diligenza altrove, per la mia indisposizione &rdquo; (ivi, <lb/>Disc., T. CXLV, fol. </s>

<s>127). </s></p><p type="main">

<s>Della Centrobrarica insomma, oltrepassata di alcuni anni la met&agrave; del <lb/>secolo XVII, non si sapeva nulla di pi&ugrave; da'Nostri di quel che avessero per <lb/>caso sentito dire dagli altri, ond'&egrave; che giova a noi raccontare dai discorsi <lb/>di chi e come si venisse a riaccendere nell'ingegno de'Matematici italiani <lb/>la fiamma, rimasta spenta o sopita nelle Esercitazioni del Cavalieri, e nelle <lb/>Scene del Nardi. </s></p><p type="main">

<s>Ne'primi giorni di Aprile del 1656 Erasmo Bartholin, venuto a viag&shy;<lb/>giare in Italia, capit&ograve; in Padova, dov'era poco prima da Firenze giunto an&shy;<lb/>che il Viviani. </s>

<s>Incontratisi insieme i due Matematici amici, e caduto com'&egrave; <lb/>naturale il discorso intorno agli amati studii, disse il Bartholin che il padre <lb/>Guldin gesuita aveva, nella II parte della sua Centrobrarica, proposto senza <lb/>per&ograve; dimostrarlo un gran teorema universale, e soggiungeva che l'avea ri&shy;<lb/>cavato da un manoscritto greco di Pappo alessandrino. </s></p><p type="main">

<s>La medesima notizia era venuta in quel tempo anche alle orecchie del <lb/>Borelli, il quale, forse due mesi prima di diventargli cos&igrave; fiero e ostinato <pb xlink:href="020/01/1906.jpg" pagenum="149"/>nemico, ne dette amichevole avviso al Viviani, soggiungendo in che egli cre&shy;<lb/>desse consistere quel teorema guldiniano, e formulandogli ne'suoi veri e <lb/>precisi termini la Regola centrobrarica. </s></p><p type="main">

<s>Parve al Viviani l'annunziata verit&agrave; bellissima, e tutto allora in ammi&shy;<lb/>razione de'sublimi concetti di Apollonio e di Aristeo, i perduti libri de'quali <lb/>si disponeva a divinare, sent&igrave; nascersi vivissimo il desiderio di ricercar quella <lb/>Regola centrobrarica nelle carte greche del Matematico antico. </s>

<s>La cosa per&ograve; <lb/>si rendeva assai difficile, trattandosi di un manoscritto. </s>

<s>Poi seppe che il Bar&shy;<lb/>tholin era stato male informato, e che il libro, da cui si diceva aver rica&shy;<lb/>vata la sua invenzione il Gesuita tedesco, correva oramai per le mani di <lb/>tutti tradotto in lingua latina, e commentato dal Commandino. </s></p><p type="main">

<s>Il curioso riscontro del nuovo nell'antico pass&ograve; per alquanti anni inos&shy;<lb/>servato, n&egrave; sapremmo noi dire chi fosse il primo, a cui occorresse di farlo. </s>

<s><lb/>Non fu certamente il Cavalieri, in man del quale avrebbe quella nota po&shy;<lb/>tuto fare un bellissimo gioco, perch&egrave;, nel ritorcer le accuse contro il Gul&shy;<lb/>dino, lo avrebbe potuto tacciare qual plagiario di Pappo, con pi&ugrave; acuta <lb/>ferita, che dicendolo imitator del Keplero. </s>

<s>Bench&egrave; dunque il Bartholin fran&shy;<lb/>tendesse, dee aver pure attinta a'suoi connazionali o ai vicini quella noti&shy;<lb/>zia, che, alteratasi di discorso in discorso e gi&agrave; penetrata in Italia, venne <lb/>finalmente a scoprirsi al Viviani sotto l'aspetto del vero. </s></p><p type="main">

<s>Le matematiche Collezioni erano state tradotte, come dicemmo, dal Com&shy;<lb/>mandino, il quale, sopraggiunto dalla morte, avendo lasciata inedita e in <lb/>alcune parti imperfetta la sua versione, non si risolverono perci&ograve; gli eredi <lb/>di pubblicarla, infin tanto che il duca Francesco Maria Della Rovere non <lb/>venne a interporvi l'autorevole sua mediazione, ordinandone in Urbino la <lb/>stampa a sue proprie spese. </s>

<s>Il Viviani dunque si dette con gran diligenza <lb/>a cercare il Volume, e nelle parole, con le quali si chiude al VII libro quella <lb/>lunga erudita prefazione, parvegli aver trovato quel che cercava, riducendo <lb/>all'espressa formula del Borelli l'enimmatico senso. </s></p><p type="main">

<s>C'&egrave; fra le carte dello stesso Viviani (MSS. cit. </s>

<s>Disc., T. XCVIII, fol. </s>

<s>161) <lb/>tuttavia rimasta la copia, che di sua propria mano fece del passo di Pappo, <lb/>e com'ei par che se lo volesse per pi&ugrave; comoda meditazione sottoporre in <lb/>quel foglio sott'occhio, cos&igrave; noi pensiamo di trascriver qui, nella sua inte&shy;<lb/>gra fedelt&agrave;, il testo, perch&egrave; possano i nostri lettori aver pi&ugrave; comoda e pi&ugrave; <lb/>facile intelligenza dell'arguto commento: &ldquo; Perfectorum utrorumque ordi&shy;<lb/>num proportio composita est ex proportione amphismatum, et rectarum li&shy;<lb/>nearum similiter ad axes ductarum a punctis, quae in ipsis gravitatis centra <lb/>sunt: imperfectorum autem proportio composita est ex proportione amphi&shy;<lb/>smatum, et circumferentiarum a punctis, quae in ipsis sunt centra gravita&shy;<lb/>tis, factorum. </s>

<s>Harum circumferentiarum proportio dividitur in proportionem <lb/>ductarum linearum, et earum quas continent ipsarum extrema ad axes .... <lb/>angulorum .... &rdquo; (Collectiones cit., pag. </s>

<s>252). </s></p><p type="main">

<s>Quest'ultimo periodo, che per la corruzione del testo &egrave; di pi&ugrave; difficile <lb/>intelligenza, serv&igrave; al Viviani di chiave per aprire il chiuso degli altri, inter-<pb xlink:href="020/01/1907.jpg" pagenum="150"/>petrandolo nella seguente guisa, e illustrando l'interpetrazione con l'appo&shy;<lb/>sta figura, per noi in ordine LXa, nella quale MN, RS rappresentano due <lb/>superfice qualunque, i centri di gravit&agrave; delle quali A, C sien revolubili at&shy;<lb/><figure id="id.020.01.1907.1.jpg" xlink:href="020/01/1907/1.jpg"/></s></p><p type="caption">

<s>Figura 60.<lb/>torno all'asse BD, in distanze varie e per vario <lb/>angolo di rotazione: &ldquo; Harum circumferentiarum <lb/>proportio dividitur in proportionem ductarum li&shy;<lb/>nearum AB, GD et in proportionem angulorum <lb/>ABE, GDF earumdem linearum a centro gravitatis <lb/>extremorum amphismatum ad axem rotationis <lb/>ductarum &rdquo; (MSS. T. cit., fol. </s>

<s>163). </s></p><p type="main">

<s>L'interpretazione dall'altra parte risponde <lb/>conformissima con la Regola centrobrarica, perch&egrave;, <lb/>rimanendo le due superfice sempre per la mede&shy;<lb/>sima base ai due solidi cilindrici, o ai due pri&shy;<lb/>smatici, in cui vengono trasformati; le circonferenze, che ne misuran le re&shy;<lb/>lative altezze, tornan maggiori o minori, secondo che sono i centri di <lb/>gravit&agrave; A, G pi&ugrave; o meno distanti, o per maggiore o minore angolo intorno <lb/>all'asse rotati. </s>

<s>La distinzione perci&ograve; di <emph type="italics"/>perfetti<emph.end type="italics"/> e d'<emph type="italics"/>imperfetti<emph.end type="italics"/> appella, se&shy;<lb/>condo il Viviani, al grado della rotazione, la quale, se sia fatta per tutto il <lb/>circolo intera, genera il rotondo perfetto, e lo genera imperfetto se, prima <lb/>di ritornare in s&egrave;, il moto rotatorio si arresta. </s>

<s>A questi poi si accomodano, <lb/>secondo l'interpetre, gli altri sensi, cos&igrave; in questa nota autografa dichiarati: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Amphisma, amphismatis.<emph.end type="italics"/> Pro hac voce amphisma intelligit fortasse <lb/>Pappus omne id quod circa manentem axem circumfertur, vel circumver&shy;<lb/>titur, vel circumducitur, aut circum rotatur, vel illud sit linea in plano, in <lb/>quo est axis manens, vel superficies plana figurata in plano, in quo idem <lb/>axis repertur. </s>

<s>Si linea, in ipsa circumrotatione describit superficiem rotun&shy;<lb/>dam, quam voco annularem. </s>

<s>Si superficies plana, hoc est figura plana, so&shy;<lb/>lidum rotundum vel clausum vel apertum ad instar annuli describet. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pro illa voce <emph type="italics"/>ordo<emph.end type="italics"/> intelligit forsan unumquodque horum producto&shy;<lb/>rum a rotantibus, nempe vel rotundum superficie annulari, vel rotundum <lb/>solidum annulare clausum vel apertum. <emph type="italics"/>Perfectus ordo<emph.end type="italics"/> forsan est id quod <lb/>amphismate in integra ac perfecta rotatione describitur. </s>

<s>Nos autem dicimus <lb/>superficiem annularem vel annulum. </s>

<s>Imperfectus vero ordo, quod ab im&shy;<lb/>perfecta, non integra, sed partiali, fit rotatione, et quod voco sectorem, vel <lb/>superficiem annularem, vel annulum &rdquo; (ibid., fol. </s>

<s>162). </s></p><p type="main">

<s>Sarebbero cos&igrave; le cose per ogni verso assai bene accomodate, quando <lb/>nell'ultimo trascritto periodo avesse veramente voluto esprimer Pappo quel <lb/>che il Viviani v'intende, e quando, in corrispondenza alle voci greche del <lb/>testo, fossero dal Commandino rese le latine <emph type="italics"/>imperfectum<emph.end type="italics"/> e <emph type="italics"/>perfectum,<emph.end type="italics"/> le <lb/>quali, avendo il radicale nel verbo <emph type="italics"/>perficio,<emph.end type="italics"/> sono atte nate a significare o <lb/>la cosa manca o ridotta alla sua perfezione. </s>

<s>In qualunque modo, &egrave; il com&shy;<lb/>mento non indegno del divinator di Apollonio e di Aristeo, il qual divina&shy;<lb/>tore, nella estrema vecchiezza ritornando indietro su queste cose con la lunga <pb xlink:href="020/01/1908.jpg" pagenum="151"/>memoria, si compiacque di essere stato egli il primo a togliere agli strani <lb/>versi il velame. </s>

<s>Un giovane studente di Firenze gli venne un giorno a pro&shy;<lb/>por la stereometria del pinnacolo delle due piramidi erette sulla piazza di <lb/>S. </s>

<s>Maria Novella, che parendogli assai bello e nuovo problema, si dette vo&shy;<lb/>lentieri a scioglierlo, servendosi della Regola centrobrarica, da lui stesso <lb/>chiamata &ldquo; quell'ammirando universale teorema, che assai oscuramente ac&shy;<lb/>cenn&ograve; Pappo Alessandrino, senza gi&agrave; dimostrarlo, ma per&ograve; interpetrato da <lb/>me, 50 e pi&ugrave; anni sono corsi, ed allora anche da me provato in pi&ugrave; modi &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. XCII, fol. </s>

<s>29). </s></p><p type="main">

<s>Al buon vecchio quasi ottuagenario dee per&ograve;, nello scrivere quel nu&shy;<lb/>mero 50, aver fatto fallo o la memoria o la penna, perch&egrave; da lui stesso <lb/>altrove &egrave; stato scritto il giorno, in ch'ebbe della Centrobrarica dal Barto&shy;<lb/>lino la prima notizia, e il mese, in ch'egli attese a esercitarsi in trovar quelle <lb/>dimostrazioni, ch'eran venute a mancare in Pappo e nel Guldino, e che <lb/>formavano dianzi, nella scrittura del Nostro intorno al pinnacolo delle Pi&shy;<lb/>ramidi fiorentine, il secondo oggetto della sua compiacenza. </s></p><p type="main">

<s>Cotali importanti documenti, per cui viene a precisarsi questa crono&shy;<lb/>logia, e a confermarsi la storia da noi sopra accennata, si ricavano dal se&shy;<lb/>guente poscritto a una lettera autografa dello stesso Viviani, e da lui diretta <lb/>a Erasmo Bartholin da Padova, il di 3 Giugno del 1656: &ldquo; Non voglio man&shy;<lb/>care, ivi si legge, di dar parte a V. S. come, nello speculare alcune mate&shy;<lb/>rie geometriche meccaniche, mi &egrave; sortito ritrovare la dimostrazione, ed an&shy;<lb/>che in pi&ugrave; modi, di un gran teorema universale, del quale tre mesi sono <lb/>con V. S. mi diede notizia il signor Giovanni Alfonso Borelli, gi&agrave; matema&shy;<lb/>tico di Pisa, come proposto, ma non dimostrato dal padre Guldini gesuita <lb/>nella II parte della sua Centrobrarica, e pens&ograve; che sia quel medesimo, del <lb/>quale V. S. mi accenn&ograve; che detto Padre aveva cavato da un manoscritto <lb/>greco di Pappo, perch&egrave;, ricercando detto signor Borelli qual potess'essere <lb/>quel principio del Guldini o teorema, del quale V. S. mi aveva discorso <lb/>quando lei fu qua, mi rispose che credeva potess'esser questo, cio&egrave;: che <lb/>rivoltandosi qualunque figura piana regolare intorno una retta linea, come <lb/>asse della rivoluzione, proponeva il Guldini che il solido rotondo o annulare <lb/>descritto da detta figura fosse uguale ad un cilindro, che ha per base la <lb/>detta figura, e per altezza una linea uguale alla periferia descritta nella ri&shy;<lb/>voluzione dal centro di gravit&agrave; della detta figura, soggiungendo per&ograve; che non <lb/>lo dimostrava, e non sapeva che fosse stato provato nemmeno da altri. </s>

<s>Io <lb/>dunque su questo e su quel principio, del quale intender&agrave; V. S.; lo dimo&shy;<lb/>stro in pi&ugrave; modi assai belli, e pi&ugrave; genericamente proposti, cio&egrave; di qualun&shy;<lb/>que figura piana, bench&egrave; irregolare, e per ottener questo mi &egrave; convenuto <lb/>trovare una mano di lemmi nuovi, e ne ho poi dedotto una quantit&agrave; di altri <lb/>teoremi bellissimi, oltre all'avere ancora con tale occasione speculato sopra <lb/>la misura delle superfice curve con qualche acquisto, e certamente vi saria <lb/>da fare un trattato molto curioso &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLII, fol. </s>

<s>11, 12). </s></p><p type="main">

<s>L'avere inteso dal Borelli, ignaro delle Scene del Nardi e dimentico <pb xlink:href="020/01/1909.jpg" pagenum="152"/>delle Esercitazioni del Cavalieri, che il teorema guidiniano da nessuno an&shy;<lb/>cora era stato dimostrato, fece nascere nel Viviani il desiderio di mettersi <lb/>egli, che si credeva il primo, alla prova, e riuscitagli felicemente feconda <lb/>ne dava sollecito avviso al Bartholin, perch&egrave; quel Borelli, divenutogli in que&shy;<lb/>sto mezzo tempo acerbissimo nemico, non avesse a vantarsi di averlo pre&shy;<lb/>venuto. </s>

<s>Il principio, su cui la dimostrazion si fondava, e che accennavasi <lb/>nell'allegato poscritto, par che sia rivelato dal seguente titolo, scritto in <lb/>fronte a una delle tre centrobrariche proposizioni, occorse all'Autore le prime <lb/>nell'esercitarsi intorno alla ricerca dei Massimi e dei minimi elementi: <lb/>&ldquo; Elementum maximum, pro dimensione rotundarum superficierum et so&shy;<lb/>lidorum &rdquo; (MSS. Gal. </s>

<s>Disc., T. LXXXIII, fol. </s>

<s>112). </s></p><p type="main">

<s>Informe, e a gran fatica leggibile &egrave; il citato manoscritto: i fogli son <lb/>nella cucitura del volume slocati, e ne mancano alcuni, in cui dee avere il <lb/>Viviani lasciata scritta la dimostrazione del primo teorema controbrarico fon&shy;<lb/>damentale, concernente le superfice descritte dalla rotazione delle semplici <lb/>linee. </s>

<s>Bench&egrave; nel metodo proseguito dal Nostro si ponesse cos&igrave; fatto teorema <lb/>per principale, come si &egrave; detto, gli dovea pure riuscir di assai facile dimo&shy;<lb/>strazione, tanto pi&ugrave; che bastava alla somma delle cose il considerar quelle <lb/>linee come rette, e in qualunque modo rivolte verso l'asse. </s>

<s>Se perpendico&shy;<lb/>lari, la figura descritta &egrave; un circolo o un nastro tondo, se parallele, &egrave; una <lb/>superfice cilindrica, ed &egrave; finalmente conica, se la retta revolubile &egrave; comun&shy;<lb/>que inclinata. </s>

<s>Per tutti questi tre casi la trasformazion del rotondo geome&shy;<lb/>trico nel retto centrobrarico &egrave; data immediatamente dagli Elementi, e se ne <lb/>sar&agrave; in poche parole spedito il Viviani come, richiamandosi agli antichi teo&shy;<lb/>remi di Euclide e di Archimede, se n'era gi&agrave; molto prima spedito il Nardi. </s></p><p type="main">

<s>Faceva a questa prima proposizione centrobrarica seguito l'altra, la quale, <lb/>dal caso delle linee semplici passandosi alle linee composte, veniva dall'Au&shy;<lb/>tore stesso cos&igrave; formulata: &ldquo; Si in eodem plano, in quo axis rotationis re&shy;<lb/>peritur, ad alteram axis partem fuerint quotvis rectae lineae terminatae, <lb/>utcumque positae, ac circa axem fiat rotatio plani, in quo assumptae rectae <lb/>insunt: erit aggregatum superficierum omnium, ab ipsis rectis in rotatione <lb/>descriptarum, aequale aggregato totidem rectangulorum, quorum bases sint <lb/>ipsae rectae datae, altitudines vero singulae sint aequales illi peripheriae, <lb/>quae a datarum rectarum communi cen&shy;<lb/>tro gravitatis, in eadem rotatione, descri&shy;<lb/>bitur &rdquo; (ibid.). </s></p><p type="main">

<s>Si abbiano a principio, per proceder <lb/>con pi&ugrave; facile ordine, due sole linee CD, <lb/>PF (fig. </s>

<s>61), comunque poste rispetto al&shy;<lb/>l'asse AB, e, divise ambedue in mezzo nei <lb/>punti M, N, sia trovato in O il loro cen&shy;<lb/>tro, con la nota legge degli Equiponde&shy;<lb/>ranti, che d&agrave; ON stare ad OM, reciproca&shy;<lb/>mente come CD sta a PF. Condotte, dai <lb/><figure id="id.020.01.1909.1.jpg" xlink:href="020/01/1909/1.jpg"/></s></p><p type="caption">

<s>Figura 61.<pb xlink:href="020/01/1910.jpg" pagenum="153"/>tre notati punti centrali, perpendicolari all'asse le tre linee MR, OS,NT, e <lb/>da M e da N abbassate le MZ, NV sopra OS, &ldquo; iam, prosegue cos&igrave; propria&shy;<lb/>mente il Viviani il suo ragionamento, cum ex hypothesi sit ut CD ad PF, <lb/>ita reciproce NO ad OM, vel, in similibus triangulis NOV, MOZ, ut VO ad OZ; <lb/>erit rectangulum sub PF, VO aequale rectangulo sub CD, ZO. &rdquo; </s></p><p type="main">

<s>&ldquo; Et quoniam rectangulum sub CD in OS aequale est rectangulis sub <lb/>CD in ZS vel in MR, et sub eadem CD in OZ, hoc est sub PF in ON, quod <lb/>ipsi sub CD in OZ aequale modo ostendimus; addito communi rectangulo <lb/>sub PF in OS, erunt duo simul rectangula sub CD in OS, et sub PF in OS <lb/>aequalia tribus simul rectangulis sub CD in MR, sub PF in OV, et sub <lb/>PF in OS. &rdquo; </s></p><p type="main">

<s>&ldquo; Sed hae duo postrema rectangula conficiunt unum tantum sub PF <lb/>in VS; ergo illa duo rectangula simul, sub CD in OS et sub PF in OS, <lb/>aequantur duobus simul sub CD in MR, et sub PF in VS, vel in NT. &rdquo; </s></p><p type="main">

<s>&ldquo; Sed ut sunt horum omnium rectangulorum latera OS, MR, NT, ita <lb/>sunt circulares peripheriae ab ipsis lateribus tanquam radiis in rotatione <lb/>descriptae; ergo et duo rectangula simul, hoc est sub CD in peripheriam a <lb/>radio SO, et sub PF in eamdem peripheriam, aequalia sunt duobus simul <lb/>rectangulis sub CD in peripheriam a radio RM, et sub PF in peripheriam <lb/>a radio TN. &rdquo; </s></p><p type="main">

<s>&ldquo; Sed rectangulum sub CD in peripheriam a radio RM aequale osten&shy;<lb/>dimus (theor. </s>

<s>I) superficiei descriptae a recta CD in sua rotatione, et simi&shy;<lb/>liter rectangulum sub PF in peripheriam a radio NT aequale esse superfi&shy;<lb/>ciei descriptae in rotatione a recta PF; ergo eadem simul rectangula, nempe <lb/>sub CD et sub PF in totidem peripherias aequales ei quae puncto O primo <lb/>invento describitur, aequantur praedictis superficiebus, ab eisdem rectis CD, <lb/>PF in rotatione descriptis circa axem AB, quod memento &rdquo; (ibid., fol. </s>

<s>112, <lb/>et 115). </s></p><p type="main">

<s>Sian ora, cos&igrave; soggiunge il Viviani per la sua dimostrazione, oltre a CD <lb/>e a PF, altre simili linee, come GH, IL, comunque poste esse pure rispetto <lb/>all'asse, purch&egrave; giacenti nel medesimo piano, e rispondenti dalla medesima <lb/>parte. </s>

<s>Divisa anche GH in mezzo, e congiunto questo punto con O, sia Q <lb/>il comun centro delle due grandezze CD, EF da una parte, e di GH dal&shy;<lb/>l'altra. </s>

<s>Costruite le parti come dianzi, si giunger&agrave; per una simile via a una <lb/>simile conclusione, a dimostrar cio&egrave; che l'aggregato delle superfice, descritte <lb/>dalle dette tre linee nella loro simultanea rotazione, eguaglia altrettanti ret&shy;<lb/>tangoli aventi ciascuno una di queste linee per base, e per altezza tutti la <lb/>medesima circonferenza descritta dal raggio, che dal punto Q vada, per la <lb/>via pi&ugrave; breve, a ritrovar l'asse. </s></p><p type="main">

<s>Divisa similmente IL nel mezzo, e congiunto questo punto con Q, sia <lb/>Y il centro di gravit&agrave;, intorno a cui si equilibrano le tre grandezze da una <lb/>parte con questa quarta dall'altra. </s>

<s>Sar&agrave; facile, con lo stesso processo, il di&shy;<lb/>mostrare che le superfice descritte insieme dalle quattro dette linee sono <lb/>eguali ad altrettanti rettangoli, eretti su ciascuna di esse, a una altezza che, <pb xlink:href="020/01/1911.jpg" pagenum="154"/>per tutte, s'agguagli alla circonferenza descritta da quel raggio, che va dal <lb/>punto Y a raggiunger l'asse. </s></p><p type="main">

<s>Sien pure proposte quante altre linee si voglia, sar&agrave; sempre vera per <lb/>tutte quella conclusione, che per le quattro date &egrave; dal Viviani cos&igrave; formu&shy;<lb/>lata: &ldquo; Aggregatum igitur superficierum a rectis CD, EF, GH, IL in rota&shy;<lb/>tione factarum, quaecumque illae sint, vel armillares, vel cilindricae vel co&shy;<lb/>nicae, aequale est aggregato totidem rectangulorum super easdem bases CD, <lb/>EF, GH, IL, et quorum singulae altitudines sint aequales peripheriae a com&shy;<lb/>muni earumdem rectarum centro gravitatis Y in ipsa rotatione descriptae. </s>

<s><lb/>Quod erat demonstrandnm &rdquo; (ibid., fol. </s>

<s>113). </s></p><p type="main">

<s>Da questa seconda proposizione, applicandovi il metodo degl'indivisibili, <lb/>fa, quasi da corollario, scendere il Viviani la terza: &ldquo; Rotundum solidum, <lb/>a quacumque figura plana circa axem rotante genitum, aequale est cylin&shy;<lb/>drico, cuius basis sit ipsa plana figura, altitudo vero aequalis sit peripheriae <lb/>ab illius gravitatis centro descriptae &rdquo; (ibid., fol. </s>

<s>114). </s></p><p type="main">

<s>Sia ABC (fig. </s>

<s>62) quella qualunque figura piana revolubile intorno al&shy;<lb/>l'asse EF, e s'immagini che siano sopr'essa disegnate, a piacer nostro, e <lb/><figure id="id.020.01.1911.1.jpg" xlink:href="020/01/1911/1.jpg"/></s></p><p type="caption">

<s>Figura 62.<lb/>quali tutte insieme concentrate in D, innume&shy;<lb/>revoli grandezze lineari, parallele, &Egrave; chiaro che <lb/>verr&agrave; dal loro aggregato nella rotazione descritto <lb/>l'aggregato di altrettante superfice, le quali <lb/>riusciranno o cilindriche o coniche, secondo la <lb/>direzione scelta e data da noi a quelle stesse <lb/>linee, che l'hanno generata. </s>

<s>&ldquo; Sed aggregatum <lb/>omnium simul figurarum aequidistantium ab <lb/>his omnibus rectis, in rotatione descriptum, <lb/>aequalem esse demonstravimus aggregato totidem rectangulorum, quorum <lb/>bases sint ipsae rectae, altitudines vero singulae sint aequales peripheriae <lb/>a centro D descriptae; et primum aggregatum rotundum solidum constituit, <lb/>secundum vero cylindricum facit super basi ABC in altitudine circumfe&shy;<lb/>rentiae a puncto D; ergo ipsum solidum solido ipsi cylindrico aequale est, <lb/>quod erat demonstrandum &rdquo; (ibid.). </s></p><p type="main">

<s>Altre proposizioni centrobrariche si trovano qua e l&agrave; dal Viviani dimo&shy;<lb/>strate ne'suoi manoscritti, come nel tomo XCV della collezione citata, nei <lb/>primi fogli del quale la dimostrazione della Regola guldiniana conducesi in <lb/>altro modo da quello ora esposto, e vi si trova notato il corollario, dall'al&shy;<lb/>tra parte a concludersi facilissimo, che se cio&egrave; le superfice MN, RS (nella <lb/>passata figura LX) son proporzionali alle distanze AB, DC &ldquo; rotundae ma&shy;<lb/>gnitudines, quae ab ipsis fient, erunt inter se ut quadrata distantiarum ea&shy;<lb/>rum &rdquo; (fol. </s>

<s>3 t.). </s></p><p type="main">

<s>Di tutte queste proposizioni poi messe in ordine compose il Viviani un <lb/>trattatello di Centrobrarica, ch'egli intendeva di preparar per le stampe. </s>

<s>Sa&shy;<lb/>rebbe quel trattatello, per esser venuto il primo a sottoporre all'edifizio gul&shy;<lb/>diniano il suo matematico fondamento, riuscito utilissimo all'universale, e <pb xlink:href="020/01/1912.jpg" pagenum="155"/>di particolar gloria per la scienza italiana. </s>

<s>Ma meditando l'Autore cose forse <lb/>maggiori, erasi oramai condotto all'estrema vecchiezza, senza dar n&egrave; di que&shy;<lb/>ste n&egrave; di quelle alcuna pubblica sodisfazione, quando un Cardinale, che aveva <lb/>a sue proprie spese fatta erigere una nuova Tipografia, gli mostr&ograve; il desi&shy;<lb/>derio di stampar qualche cosa delle tante scritture di lui sconosciute. </s>

<s>Per <lb/>rispondere al quale invito prese un giorno il Viviani la penna in mano, con <lb/>l'intenzione di far recapitare all'Eminentissimo innominato questa lettera <lb/>scritta: </s></p><p type="main">

<s>&ldquo; Son gi&agrave; molti anni che io mi trovo distese tre mie antiche operette <lb/>di Geometria, l'una intitolata <emph type="italics"/>De tetragonismicis,<emph.end type="italics"/> l'altra <emph type="italics"/>De centrobraricis,<emph.end type="italics"/><lb/>divisa ciascuna in due libri, e la terza <emph type="italics"/>De terebratione solidorum,<emph.end type="italics"/> e di tutte <lb/>&egrave; gi&agrave; gran tempo che sono intagliate le figure in bossolo gi&agrave; ben fatte. </s>

<s>E <lb/>perch&egrave; in questa et&agrave; mia cadente di LXXIV anni e in continuo moto per <lb/>le campagne, in servizio di questa serenissima Altezza, quand'io non mi <lb/>trovi in letto malato, io dispero oramai di poter perfezionare molte altre di <lb/>quelle, che sono abbozzate, e perci&ograve; io desidero di veder fuori almeno que&shy;<lb/>ste tre insieme, ma specialmente sotto il benigno patrocinio dell'Eminenza <lb/>V. R.ma, mentre per&ograve; si compiacesse di farmi degna di tanto onore. </s>

<s>Queste <lb/>dunque farei prontamente copiare assai ben corrette, e quando me ne desse <lb/>la permissione, le invierei una per volta, insieme con le figure, affinch&egrave; <lb/>V. Emin. </s>

<s>si contentasse ancora di far qualche pregio a tali opere con i no&shy;<lb/>bilissimi caratteri della sua nuova Stamperia &rdquo; (MSS. cit., T. CI, fol. </s>

<s>124). </s></p><p type="main">

<s>&Egrave; scritta in fronte a questa bozza, pure autografa, la nota: <emph type="italics"/>Questa let&shy;<lb/>tera non la mandai e non....<emph.end type="italics"/> cosicch&egrave; il trattatello centrobrarico del Vi&shy;<lb/>viani riman tuttavia un desiderio di tutti coloro, che avrebbero voluto ve&shy;<lb/>der qualche pubblico documento dell'importantissima opera data, prima degli <lb/>stranieri, dai Matematici nostri intorno alle ammirate novit&agrave; del Guldino. </s></p><pb xlink:href="020/01/1913.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO III.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Degli Equiponderanti<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della legge delle equiponderanze dimostrata col principio delle velocit&agrave; virtuali. </s>

<s>&mdash; II. </s>

<s>Della legge <lb/>delle equiponderanze dimostrata coi principii archimedei. </s>

<s>&mdash; III. </s>

<s>Della teoria de'momenti ap&shy;<lb/>plicata a dimostrar la legge degli equiponderanti. </s>

<s>&mdash; IV. </s>

<s>Delle Bilancie di braccia eguali e delle <lb/>condizioni del loro equilibrio, nel caso delle forze o parallele o convergenti al centro terrestre. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Nella scienza de'centri di gravit&agrave; fu detto, e si conferma dalla storia <lb/>del capitolo precedente, che si compendia tutta intera la scienza meccanica, <lb/>ond'&egrave; che di questa &egrave; riconosciuto solenne maestro al mondo Archimede. </s>

<s><lb/>Come nel trattato del nostro Siracusano s'applicassero i baricentrici, a di&shy;<lb/>mostrar la legge dell'equilibrio fra'pesi, s'&egrave; gi&agrave; scritto da noi nell'intro&shy;<lb/>durre il discorso intorno alla presente parte storica, e fu mostrato allora <lb/>quanto, per i matematici specialmente italiani del secolo XVI, venissero l'ar&shy;<lb/>chimedee dottrine ad essere largamente promosse. </s>

<s>S'accenn&ograve; anco insieme <lb/>ad un'altra fonte pi&ugrave; antica, dalla quale si deriv&ograve; in quel secolo non men <lb/>larga vena di scienza, e come, in mezzo agli aperti dissidii, si sapessero con&shy;<lb/>giungere insieme, in tacito e pi&ugrave; fecondo connubio, gl'insegnamenti del <lb/>Matematico di Siracusa con quelli del Filosofo di Stagira. </s></p><p type="main">

<s>Di queste attrazioni, diciam cos&igrave;, e di queste repulsioni, dalle quali par <lb/>che resulti la vita dell'intelletto, com'&egrave; certo che resulta la vita della ma&shy;<lb/>teria, ci offre in proposito un notabilissimo esempio quel Leonardo da Vinci, <lb/>i manoscritti del quale, che unici per avventura ci son rimasti, specchiano <lb/>la mente dell'Autore e quella tutto insieme de'Matematici de'suoi tempi. <pb xlink:href="020/01/1914.jpg" pagenum="157"/>Si ripeteva da questi il principio statico del Nemorario, riducendolo a dire <lb/>che il peso, applicato all'estremit&agrave; di un raggio pi&ugrave; lungo, ha maggior mo&shy;<lb/>mento, perch&egrave; il maggior circolo volge pi&ugrave; da presso al retto discenso; prin&shy;<lb/>cipio non voluto approvare da Leonardo per concludente, perch&eacute;, attaccato <lb/>il peso a un filo avvolto all'estremit&agrave; del raggio per l'altro capo, bench&egrave; <lb/>non faccia il suo viaggio circolare ma retto, pur si vede scendere allo stesso <lb/>modo, e vincere un egual peso, che stia similmente pendulo dal raggio pi&ugrave; <lb/>corto. </s>

<s>&ldquo; Dice il Pelacane che il maggior braccio di questa bilancia (appel&shy;<lb/>lando alla figura disegnata in margine del foglio) cadr&agrave; pi&ugrave; presto che il <lb/>minore, perch&egrave; il suo descenso descrive il suo quarto circolo pi&ugrave; diritto che <lb/>non fa il minore, e perch&egrave; i pesi desiderano cadere perpendicolare linea. </s>

<s><lb/>Quanto esso circolo pi&ugrave; si torcer&agrave;, pi&ugrave; si ritarder&agrave; il moto. </s>

<s>La figura getta <lb/>per terra questa ragione perch&egrave; il discenso de'suoi pesi non vanno per cir&shy;<lb/>colo; eppure cala il peso del maggiore braccio &rdquo; (Ravaisson-Mollien, Manus. </s>

<s><lb/>N.0 2038 italien de la Bibliot. </s>

<s>nationale, Paris 1891, fol. </s>

<s>2 t.). </s></p><p type="main">

<s>L'obiezione a dir vero avrebbe trovata una assai facile risposta nel Pe&shy;<lb/>lacane, e in tutti gli altri, che avevano imparato dal Nemorario a misurare <lb/>la quantit&agrave; della discesa, no nell'obliqua o circolare o retta, ma nella per&shy;<lb/>pendicolare, alla quale dovevasi, per gl'insegnamento dello stesso Giordano, <lb/>ridurre una tal discesa, o fosse il grave affisso al raggio o libero vi pen&shy;<lb/>desse da un filo. </s>

<s>Ma fu in ogni modo la proposta difficolt&agrave; giudicata da Leo&shy;<lb/>nardo di tanta forza, da farlo andare in cerca di un altro principio, da cui <lb/>concluder la legge statica fondamentale tanto desiderata. </s>

<s>Di questo principio <lb/>dall'altra parte non si sarebbe potuto negar la verit&agrave; da nessuno, che non <lb/>patisse difetto o di ragione o di esperienza, consistendo insomma nell'affer&shy;<lb/>mar che un peso tanto &egrave; men sostenuto, quanto &egrave; pi&ugrave; lontano dal suo so&shy;<lb/>stegno. </s>

<s>Era da ci&ograve; facile concluder la ragione perch&egrave; il peso stesso quanto <lb/>&egrave; applicato al braccio della Bilancia pi&ugrave; lungo, altrettanto abbia a moversi <lb/>pi&ugrave; veloce. </s>

<s>&ldquo; Quella cosa che fia pi&ugrave; lontana al suo firmamento, manco da <lb/>esso fia sostenuta. </s>

<s>Essendo manco sostenuta, pi&ugrave; fia partecipevole di sua li&shy;<lb/>bert&agrave;. </s>

<s>E perch&egrave; il peso libero sempre discende, adunque quella estremit&agrave; <lb/>dell'asta d'essa Bilancia, che fia pi&ugrave; distante al suo firmamento, perch&egrave; &egrave; <lb/>ponderosa, pi&ugrave; presto che alcuna parte di s&egrave; discender&agrave; &rdquo; (ivi). </s></p><p type="main">

<s>La teoria vinciana prende dunque il principio da Archimede, dalle dot&shy;<lb/>trine di cui si deduce che un peso &egrave; tanto men sostenuto, quanto il suo <lb/>centro di gravit&agrave; &egrave; pi&ugrave; distante dal suo sostegno, ma nel passar poi a con&shy;<lb/>cluderne la legge della equiponderanza bisognava dire che due gravi si fa&shy;<lb/>rebbero allora insieme equilibrio, quando l'uno e l'altro fossero disposti a <lb/>scendere nel medesimo tempo. </s>

<s>Cos&igrave; venivano da varie parti a riscontrarsi <lb/>Archimede e Aristotile; il principio baricentrico e quello delle velocit&agrave; vir&shy;<lb/>tuali, celebrandosi fra le due scuole discordi quel clandestino connubio, il <lb/>portato del quale ebbe, sul cominciar del secolo XVII, ostetrici che lo espo&shy;<lb/>sero al mondo maravigliato. </s></p><p type="main">

<s>Che tali, cio&egrave; ostetrici della scienza statica e non veri genitori, si fos-<pb xlink:href="020/01/1915.jpg" pagenum="158"/>sero lo Stevino, il Galileo e il Cartesio manifesto apparisce dalla storia del <lb/>capitolo I di questo tomo, ond'&egrave; che, lasciando oramai di tornare indietro <lb/>sopra la legittimit&agrave; della origine, ci tratterremo ad esaminare il parto, ri&shy;<lb/>volgendoci prima di tutto col&agrave;, dove nelle sue pagine celebrate ci fu espo&shy;<lb/>sto da Galileo. </s></p><p type="main">

<s>Il libro, in cui il principio statico professato da Galileo fece, non la <lb/>prima, ma la pi&ugrave; solenne sua pubblica mostra fu quello dei Massimi sistemi, <lb/>dove disputandosi nella Giornata seconda intorno alle resistenze, che oppon&shy;<lb/>gono i gravi all'essere sollevati, si conclude per l'esempio della Stadera do&shy;<lb/>vere ivi i pesi resister con forza diversa da quella della semplice gravit&agrave;. </s>

<s><lb/>Or da che altro mai pu&ograve; scaturire questa forza ristoratrice, se non dal moto, <lb/>cosicch&egrave; &ldquo; la velocit&agrave; del mobile meno grave compensi la gravit&agrave; del mo&shy;<lb/>bile pi&ugrave; grave e meno veloce? </s>

<s>&rdquo; (Alb. </s>

<s>I, 237). </s></p><p type="main">

<s>S'immagini infatti di avere a pesare una balla di lana o di seta: &ldquo; il <lb/>moversi lo spazio di cento dita il romano, nel tempo che la balla si muove <lb/>per un sol dito, &egrave; l'istesso che il dire esser la velocit&agrave; del moto del romano <lb/>cento volte maggiore della velocit&agrave; del moto della balla. </s>

<s>Ora, prosegue a <lb/>dire il Salviati galileiano, fermatevi bene nella fantasia come principio vero <lb/>e notorio che la resistenza, che viene dalla velocit&agrave; del moto, compensa <lb/>quello che dipende dalla gravit&agrave; di un altro mobile, sicch&egrave; in conseguenza <lb/>tanto resiste all'esser frenato un mobile d'una libbra, che si muova con <lb/>cento gradi di velocit&agrave;, quanto un altro mobile di cento libbre, la cui velo&shy;<lb/>cit&agrave; sia d'un grado solo &rdquo; (ivi). </s></p><p type="main">

<s>Le resistenze dunque non sono in semplice ragion de'pesi, ma in ra&shy;<lb/>gion composta delle velocit&agrave; e de'pesi, ond'&egrave; che, nel caso degli equipon&shy;<lb/>deranti, essendo quelle resistenze eguali, dovranno le velocit&agrave; stare in reci&shy;<lb/>proca proporzione degli stessi pesi. </s>

<s>&Egrave; qui dunque formulato da Galileo quel <lb/>principio statico, che si disse <emph type="italics"/>delle velocit&agrave; virtuali,<emph.end type="italics"/> di che trattando il La&shy;<lb/>grange, nell'introduzione alla sua celebre <emph type="italics"/>Mecanique analitique,<emph.end type="italics"/> scriveva: <lb/>&ldquo; il ne paroit pas que les Geometres, qui ont pr&eacute;c&egrave;d<gap/> Galil&egrave;e, en aient eu <lb/>connoissance, et je crois pourvoit en attribuer la d&egrave;couverte a cet Auteur &rdquo; <lb/>(Paris 1788, pag. </s>

<s>8). </s></p><p type="main">

<s>Pare incredibile che uno Scrittore tanto grave possa aver sentenziato <lb/>essere il detto principio statico rimasto ignoto ai precursori di Galileo, quando <lb/>Galileo stesso lo dichiara come cosa <emph type="italics"/>notissima e dimostrata da Aristotile <lb/>nelle sue Questioni meccaniche<emph.end type="italics"/> (Alb. </s>

<s>XIII, 265). Chi poi rammemora le <lb/>cose, da noi scritte nel cap. </s>

<s>I di questo tomo, sa come di fatto il principio <lb/>delle velocit&agrave; virtuali, appresso ai matematici de'secoli anteriori al XVII, <lb/>fosse veramente notissimo e dimostrato. </s></p><p type="main">

<s>In ogni modo, professandosi tale dottrina in quel libro galileiano tanto <lb/>famoso, veniva, come face, a risplendere sul moggio e a farsi perci&ograve; pi&ugrave; <lb/>scoperto segno agli applausi e alle contradizioni. </s>

<s>Il Cartesio, fra tanti con&shy;<lb/>tradittori il pi&ugrave; valido e il pi&ugrave; infervorato di tutti, non sapendo trovar ra&shy;<lb/>gione di accusar come assolutamente falso il principio professato da Galileo, <pb xlink:href="020/01/1916.jpg" pagenum="159"/>lo accusava come difettoso ed incerto, proponendone un altro che riusciva, <lb/>secondo lui, nella generale applicazione alle condizioni dell'equilibrio in tutte <lb/>le macchine, pi&ugrave; semplice e pi&ugrave; sicuro. </s>

<s>Consisteva in sostanza il principio <lb/>cartesiano nel sostituire gli spazii alle velocit&agrave;, rappresentandosi sotto que&shy;<lb/>sta forma assai seducente, che cio&egrave; tanta forza ci vuole a sollevare un peso <lb/>di cento libbre all'altezza di due piedi, quanto a sollevare un peso di du&shy;<lb/>gento libbre all'altezza di un piede solo. </s>

<s>A cos&igrave; fatta legge volle poi dimo&shy;<lb/>strar l'Autore che s'informavano tutte le macchine, nello spiegar le quali, <lb/>in quel trattatello <emph type="italics"/>De mechanica<emph.end type="italics"/> pubblicato postumo, incominciava con que&shy;<lb/>ste parole: &ldquo; Machinarum harum omnium inventio unico tantum principio <lb/>innititur, quod nimirum iisdem viribus quibus pondus v. </s>

<s>g. </s>

<s>100 librarum <lb/>in duorum pedum altitudinem attolli potest, iisdem inquam aliud quoque <lb/>200 librarum in unius pedis altitudinem possit elevari &rdquo; (Amstelodami 1704, <lb/>pag. </s>

<s>13). </s></p><p type="main">

<s>Essendo il moto delle macchine uniforme, e sempre nei moti uniformi <lb/>rispondendo in egual tempo le velocit&agrave; agli spazii, il principio del Cartesio <lb/>non differiva adunque dal galileiano che per una semplice accidentalit&agrave; della <lb/>forma, e noi vedemmo come fosse una tale trasformazione fatta gi&agrave;, nella <lb/>Meccanica aristotelica, dal Nemorario. </s>

<s>Nonostante, per quella smania che <lb/>aveva il Filosofo francese di soverchiare il nostro Italiano, si studiava di <lb/>persuadere agli amici che, col mettere in conto le velocit&agrave; piuttosto che gli <lb/>spazii, mentre si veniva da una parte a rendere pi&ugrave; difficile la Scienza mec&shy;<lb/>canica, le si poneva dall'altra per fondamento un principio o non affatto <lb/>vero o dubbioso. </s></p><p type="main">

<s>Quanto alle difficolt&agrave; si compiaceva, in una Epistola al Mersenno, di <lb/>averle cessate in gran parte, mettendo in considerazione due sole, invece di <lb/>tre dimensioni, e faceva in ci&ograve; principalmente consistere la fina arte usata <lb/>in distendere il suo statico trattatello. </s>

<s>&ldquo; Quod si celeritatis considerationem <lb/>cum spatii consideratione iungere voluissem, habuissem necesse tres dimen&shy;<lb/>siones virtuti isti tribuere: ut vero illam excluderem duas tantum illi tri&shy;<lb/>bui. </s>

<s>Et si quid artis in ulla exigui huius <emph type="italics"/>De statica<emph.end type="italics"/> scripti parte ostendi, <lb/>velim sciant me nusquam plus quam in hoc ostendisse &rdquo; (Epistolae Pars I, <lb/>Francof. </s>

<s>ad Moenum 1692, pag. </s>

<s>229). </s></p><p type="main">

<s>Il principio statico di Galileo, poi soggiunge il Cartesio stesso in un'al&shy;<lb/>tra sua lettera al Mersenno, non solo viene a rendere la Statica pi&ugrave; com&shy;<lb/>plicata, ma che &egrave; peggio sta fondato sul falso: falso essendo che a raddop&shy;<lb/>piare una data velocit&agrave; si richieda sempre una forza precisamente doppia. <lb/></s>

<s>&ldquo; Quantum vero ad id quod Galileus de Bilance et Vecte scripsit, optime <lb/>quidem explicat quod ita sit, sed non cur ita sit, sicut per principium meum <lb/>explico. </s>

<s>Qui vero dicunt debuisse me cum Galileo celeritatem considerare, <lb/>non vero spatium, ut machinarum rationem redderem, inter nos puto eos <lb/>id temere dicere, nec quicquam in hac materia intelligere. </s>

<s>Et quamvis cla&shy;<lb/>rissimum sit opus esse maiore vi ad corpus aliquod celerrime, quam lente <lb/>attollendum, nihilominus falsum est vim debere exacte duplam ad duplican-<pb xlink:href="020/01/1917.jpg" pagenum="160"/>dam celeritatem, et facillimum est contrarium probare &rdquo; (Epistolae Pars II, <lb/>ibid., pag. </s>

<s>255) </s></p><p type="main">

<s>Tace qui il Cartesio la facile prova, ma in un'altra epistola, indirizzata <lb/>essa pure al Mersenno, dice che pu&ograve; dedursi dal fatto della Bilancia in equi&shy;<lb/>librio, sul piattello della quale chi getta una piccola moneta vede moversi <lb/>il braccio in basso assai lentamente, ma a gettarvi una moneta doppia si <lb/>osserva farsi allora la declinazione pi&ugrave; che doppiamente sollecita. </s>

<s>&ldquo; Si bi&shy;<lb/>lanci in aequilibrio constitutue imposueris nummum aliquod, quod illi mo&shy;<lb/>mentum dare possit, tum enim admodum lente deprimetur, cum contra si <lb/>eiusdem istius ponderis duplum imposueris, decidet plus quam duplo citius &rdquo; <lb/>(ibid., pag. </s>

<s>320). </s></p><p type="main">

<s>Le varie proporzioni di moto nella Bilancia si concludevan dunque per <lb/>il Cartesio da un semplice fatto sperimentale, ond'&egrave; che venivasi male a <lb/>proposito invocando la Fisica a decidere una questione di Matematica pura. </s>

<s><lb/>Era una tal questione risoluta gi&agrave; da Galileo, quand'egli dimostr&ograve; &ldquo; che il <lb/>cadente, partendosi dalla quiete passa per tutti gl'infiniti gradi di tardit&agrave; &rdquo; <lb/>(Alb. </s>

<s>I, 34). La teoria cos&igrave; formulata doveva esser quella che venisse a in&shy;<lb/>formare il fatto sperimentale invocato dal Cartesio, correggendo i facili in&shy;<lb/>ganni che, rispetto ai moti della Bilancla, si poteva far l'occhio, ma ripu&shy;<lb/>diando una certezza matematica per attenersi a una fisica fallacia, s'ostin&ograve; <lb/>il Cartesio stesso a negar quel che delle velocit&agrave; iniziali aveva sapientemente <lb/>concluso Galiteo. </s>

<s>&ldquo; Sciendum enim est, quidquid in contrarium dicant Ga&shy;<lb/>lileus et alii nonnulli, corpora quae descendere, vel quocumque modo mo&shy;<lb/>veri incipiunt, non transire per omnes tarditatis gradus, sed a primo instanti <lb/>aliquantam velocitatem obtinere, quae postea multum augetur &rdquo; (Epistol., <lb/>P. II cit., pag. </s>

<s>115). </s></p><p type="main">

<s>Il Mersenno, a cui si dirigevano queste parole, domandava la prova di <lb/>cos&igrave; fatta sentenza, ma perch&egrave; il Cartesio non l'aveva pronta, e conosceva <lb/>forse che non sarebbe riuscito mai a trovarla, si scusava rispondendo non <lb/>aver inteso di negare assolutamente che il mobile passi per tutti gl'infiniti <lb/>gradi di tardit&agrave; &rdquo; sed vero dixi non posse id, nisi praecognita gravitatis na&shy;<lb/>tura, determinari &rdquo; (ibid., pag. </s>

<s>122). Non si capiva per&ograve; come mai non si <lb/>potesse determinare il moto iniziale di un grave, senza preconoscere la na&shy;<lb/><figure id="id.020.01.1917.1.jpg" xlink:href="020/01/1917/1.jpg"/></s></p><p type="caption">

<s>Figura 63.<lb/>tura della gravit&agrave;, ond'&egrave; perci&ograve; che il Mersenno citava la <lb/>dimostrazione di Galileo, la quale concludevasi, senz'altre <lb/>prenozioni, dai principii certissimi della Geometria. </s>

<s>Cos&igrave; in <lb/>fatti, rappresentandosi con i lati di un triangolo gli ele&shy;<lb/>menti del moto, procede nella Giornata II dei Due massimi <lb/>sistemi quella galileiana dimostrazione: &ldquo; Essendo posto il <lb/>termine A (fig. </s>

<s>63) come momento minimo di velocit&agrave;, <lb/>cio&egrave; come stato di quiete, e come primo instante del tempo <lb/>susseguente AD, &ecaron; manifesto che, avanti l'acquisto del <lb/>grado di velocit&agrave; DH fatto nel tempo AD, si &egrave; passato <lb/>per altri infiniti gradi minori e minori guadagnati negli <pb xlink:href="020/01/1918.jpg" pagenum="161"/>infiniti instanti, che sono nel tempo DA, corrispondenti agli infiniti punti, <lb/>che sono nella linea DA. </s>

<s>Per&ograve; per rappresentare la infinit&agrave; dei gradi di <lb/>velocit&agrave;, che precedono al grado DH, bisogna intendere infinite linee sempre <lb/>minori e minori, che s'intendano tirate dagli infiniti punti della linea DA <lb/>parallele alla DH, la quale infinit&agrave; di linee ci rappresenta in ultimo la su&shy;<lb/>perfice del triangolo AHD. </s>

<s>E cos&igrave; intenderemo qualsivoglia spazio passato <lb/>dal mobile con moto che, cominciando dalla quiete, si vadia uniformemente <lb/>accelerando, aver consumato ed essersi servito di infiniti gradi di velocit&agrave; <lb/>crescenti conforme alle infinite linee che, cominciando dal punto A, s'in&shy;<lb/>tendono tirate parallele alla linea HD &rdquo; (Alb. </s>

<s>I, 252). Il Cartesio, che anche <lb/>la Matematica voleva soggiacesse alle finzioni del suo cervello, cos&igrave; rispon&shy;<lb/>deva al Mersenno per infirmare la conclusione di Galileo: &ldquo; Non possum <lb/>definire qua velocitate unumquodque grave descendere incipiat: quaestio <lb/>enim est tantum de facto, quae pendet ex celeritate materiae subtilis. </s>

<s>Haec <lb/>autem celeritas in initio tantumdem aufert de proportione celeritatis qua <lb/>corpora descendunt, quantum exiguum triangulum AHD de triangulo ABC, <lb/>si supponatur linea HD repraesentare primum velocitatis momentum et BC <lb/>ultimum &rdquo; (Epistol., P. II cit, pag. </s>

<s>127). </s></p><p type="main">

<s>Ma intanto che l'invidioso rivale si schermiva cos&igrave; d'ogni parte, per <lb/>riparare ed eludere i colpi dell'avversario, non si avvedeva che alcuni altri <lb/>attendevano tacitamente ad aguzzare un'arme, da cui riceverebbero, senza <lb/>presente rimedio, eguale offesa i due combattenti. </s>

<s>Sia infatti che s'equi&shy;<lb/>ponderino due gravi quando sono reciprocamente proporzionali alle velocit&agrave; <lb/>o agli spazii, di un effetto in atto s'adduceva, cos&igrave; da Galileo come dal Car&shy;<lb/>tesio, una cagione in potenza. </s>

<s>Non era questa volta un rivale, che faceva <lb/>l'obiezione contro le professate dottrine dell'avversario, ma era un disce&shy;<lb/>polo affezionato che, persuaso di difendere il vero, contradiceva al suo pro&shy;<lb/>prio maestro. </s>

<s>Antonio Nardi, dop'avere in una delle sue scene dimostrate <lb/>alcune verit&agrave; generali appartenenti alla Statica, cos&igrave; soggiungeva: <lb/><figure id="id.020.01.1918.1.jpg" xlink:href="020/01/1918/1.jpg"/></s></p><p type="caption">

<s>Figura 64.</s></p><p type="main">

<s>&ldquo; Si raccorr&agrave; che male si persuadono i Mecca&shy;<lb/>nici comunemente compensarsi, in una Bilancia di <lb/>disuguali braccia, le velocit&agrave; del moto con la gran&shy;<lb/>dezza del momento, onde cercano di render ragione <lb/>perch&egrave; questi pesi disuguali da distanze reciproca&shy;<lb/>mente disuguali pesino ugualmente. </s>

<s>Ma ci&ograve; non &egrave; <lb/>in vero cagione dell'equilibrio, perch&egrave; cos&igrave; discor&shy;<lb/>rendo s'adduce di un effetto in atto una cagione in <lb/>potenza. </s>

<s>Il Galilei nel libro Delle galleggianti dice <lb/>cos&igrave;: <emph type="italics"/>Sia al vaso larghissimo EIDF<emph.end type="italics"/> (fig. </s>

<s>64) <emph type="italics"/>con&shy;<lb/>tinuata l'angustissima canna ICAB, ed intendasi <lb/>in essi infusa l'acqua sino al livello LGH, la quale <lb/>in questo stato si quieter&agrave;, non senza maraviglia di <lb/>alcuno, che non capir&agrave; cos&igrave; subito come esser possa<emph.end type="italics"/><pb xlink:href="020/01/1919.jpg" pagenum="162"/><emph type="italics"/>che il grave carico della gran mole d'acqua GD, premendo abbasso, non <lb/>sollevi e scacci la piccola quantit&agrave; dell'altra contenuta dentro alla canna CL, <lb/>dalla quale gli vien contesa e impedita la scesa. </s>

<s>Ma tal maraviglia ces&shy;<lb/>ser&agrave;, se noi cominceremo a fingere l'acqua GD essersi abbassata solamente <lb/>sino a Q, e considereremo poi ci&ograve; che aver&agrave; fatto l'acqua CL, la quale <lb/>per dare luogo all'altra, che si &egrave; scemata dal livello GH sino al livello Q, <lb/>dover&agrave; per necessit&agrave; essersi nell'istesso tempo alzata dal livello L sino <lb/>in AB, e essser la salita LB tanto maggiore della scesa GQ, quant'&egrave; <lb/>l'ampiezza del vaso GD maggiore della larghezza della canna LC, che <lb/>insomma &egrave; quanto l'acqua GD &egrave; pi&ugrave; della LC. </s>

<s>Ma essendo che il mo&shy;<lb/>mento della velocit&agrave; del moto in un mobile compensa quello della gravit&agrave; <lb/>di un altro, qual maraviglia sar&agrave; se la velocissima salita della poca <lb/>acqua CL resister&agrave; alla tardissima scesa della molta GD?<emph.end type="italics"/> Sino a qui il <lb/>mio Maestro &rdquo; (MSS. Gal. </s>

<s>Dis., T. XX, pag. </s>

<s>861, 62). </s></p><p type="main">

<s>Avendo fin qui il Nardi repudiato il principio delle velocit&agrave; virtuali, se&shy;<lb/>guita nel suo discorso ad assegnar dell'equilibrio idrostatico una causa di&shy;<lb/>versa, come ad una causa diversa attribuiva l'equiponderanza dei pesi nella <lb/>Stadera. </s>

<s>Abbiamo inteso gi&agrave; qual si fosse di questo repudio il motivo, ma <lb/>ora ci rimane ad esaminar se egli fosse ragionevole e giusto. </s></p><p type="main">

<s>L'obiezione non era punto nuova, come nuova non era la dottrina, e <lb/>perci&ograve; il Nemorario, a cui primo fu fatta, rispondeva argutamente col dire <lb/>ch'essendo la quiete il termine del moto si potevano attribuire a quella le <lb/>passioni di questo. </s>

<s>Si noti come Leonardo da Vinci esplicasse questo con&shy;<lb/>cetto, affermando che la pietra che cade fu prima portata in alto, e perch&egrave; <lb/>accennavasi infin d'allora che i pensieri medesimi di Giordano e di Leo&shy;<lb/>nardo si riscontravano in Galileo, vediamo come la scienza antica avesse <lb/>dalla nuova il suo pi&ugrave; chiaro commento. </s></p><p type="main">

<s>Svolgiamo le pagine, nelle quali &egrave; scritta la III Giornata, per soffermar <lb/>l'attenzione col&agrave; dove il Sagredo considera che la virt&ugrave; impressa al proietto, <lb/>contrastando continuamente con la gravit&agrave;, quando questa riman vincitrice <lb/>su quella intercede la quiete, che &egrave; il termine dell'ascesa e il principio della <lb/>discesa, e vuol da questo dedurne la causa dell'accelerazione del moto. </s>

<s>Op&shy;<lb/>pone Simplicio che l'arguto pensiero non &egrave; concludente e non sodisfa, se <lb/>non a que'moti naturali che son preceduti da un moto violento, per cui il <lb/>Sagredo medesimo domanda se pu&ograve; nel proietto imprimersi una virt&ugrave; che <lb/>sia molta o sia poca, sicch&egrave; possa essere scagliato in alto cento braccia, ed <lb/>anche venti o quattro o uno: ci&ograve; che avendo Simplicio affermato gli vien <lb/>su quel fondamento fatta una tale risposta: </s></p><p type="main">

<s>&ldquo; E non meno potr&agrave; cotal virt&ugrave; impressa di cos&igrave; poco superar la re&shy;<lb/>sistenza della gravit&agrave;, che non l'alzi pi&ugrave; di un dito, e finalmente pu&ograve; la <lb/>virt&ugrave; del proiciente esser solamente tanta che pareggi per l'appunto la re&shy;<lb/>sistenza della gravit&agrave;, sicch&egrave; il mobile sia non cacciato in alto, ma solamente <lb/>sostenuto. </s>

<s>Quando dunque voi reggete in mano una pietra che altro fate <lb/>voi che l'imprimerli tanta virt&ugrave; impellente all'ins&ugrave; quanta &egrave; la facolt&agrave; della <pb xlink:href="020/01/1920.jpg" pagenum="163"/>sua gravit&agrave; traente in gi&ugrave;? </s>

<s>E questa vostra virt&ugrave; non continuate voi di con&shy;<lb/>servargliela impressa, per tutto il tempo che voi la sostenete in mano? </s>

<s>Si <lb/>diminuisce ella forse per la lunga dimora, che voi la reggete? </s>

<s>E questo <lb/>sostentamento, che vieta la scesa al sasso, che importa che sia fatto pi&ugrave; dalla <lb/>vostra mano che da una tavola, o da una corda, dalla quale ei sia sospeso? </s>

<s><lb/>Certo niente. </s>

<s>Concludete pertanto, signor Simplicio, che il precedere alla ca&shy;<lb/>duta del sasso una quiete lunga o breve o momentanea non fa differenza <lb/>alcuna, sicch&egrave; il sasso non parta sempre affetto da tanta virt&ugrave; contraria alla <lb/>sua gravit&agrave;, quanto appunto bastava a tenerlo in quiete &rdquo; (Alb. </s>

<s>XIII, 160). </s></p><p type="main">

<s>Aveva Galileo applicato alla Statica questi suoi principii l&agrave; dove, nel <lb/>trattato della Scienza meccanica, volle confermare le conclusioni archimedee <lb/>concernenti l'equilibrio della leva con l'invocare il principio delle velocit&agrave; <lb/>virtuali. </s>

<s>&ldquo; Avendo noi mostrato, egli ivi dice, come i momenti di pesi dise&shy;<lb/>guali vengono pareggiati dall'essere contrariamente in distanze che abbiano <lb/>la medesima proporzione di essi, non mi pare da doversi passar con silen&shy;<lb/>zio un'altra congruenza di probabilit&agrave;, dalla quale pu&ograve; essere ragionevolmente <lb/>confermata la medesima verit&agrave;. </s>

<s>Perciocch&egrave; considerisi la libbra DE (fig. </s>

<s>65) <lb/>divisa in parti diseguali nel punto A, e i pesi della medesima proporzione <lb/>che hanno le distanze AD, AE, alternamente sospesi dai punti D, E. &Egrave; gi&agrave; <lb/><figure id="id.020.01.1920.1.jpg" xlink:href="020/01/1920/1.jpg"/></s></p><p type="caption">

<s>Figura 65.<lb/>manifesto come l'uno contrappo&shy;<lb/>ser&agrave; l'altro e, conseguentemente, <lb/>come, se a uno di essi fosse ag&shy;<lb/>giunto un minimo momento di <lb/>gravit&agrave;, si moverebbe al basso inal&shy;<lb/>zando l'altro. </s>

<s>Sicch&egrave; aggiunto in&shy;<lb/>sensibil peso al grave P si mover&agrave; <lb/>la Libbra, discendendo dal punto D <lb/>verso M, e ascendendo l'altra estre&shy;<lb/>mit&agrave; E in F. </s>

<s>E perch&egrave;, per fare abbassare il P, ogni minima gravit&agrave; accre&shy;<lb/>sciutali &egrave; bastante, per&ograve;, non tenendo noi conto di questo insensibile, non <lb/>faremo differenza dal potere un peso sostenere un altro al poterlo muovere &rdquo; <lb/>(Alb. </s>

<s>XI, 95). </s></p><p type="main">

<s>Entrando dunque bene addentro ai pensieri di Galileo, i quali eran poi <lb/>quelli di Giordano, di Leonardo e di tutti gli altri, che avevano accolte e <lb/>illustrate le pi&ugrave; antiche dottrine di Aristotile, si vede bene come per essi <lb/>non &egrave; altro la quiete se non un moto iniziale, cosicch&egrave; venivano insomma a <lb/>dar delle velocit&agrave; virtuali una definizione identica a quella dei moderni, i quali <lb/>dicon giusto velocit&agrave; virtuale esser &ldquo; celle qu'un corps en &eacute;quilibre est <lb/>dispose &agrave; recevoir, en cas que l'&eacute;quilibre vienne &agrave; &egrave;tre rompu; c'est a dire <lb/>la vitesse que ce corps prendroit reelllement dans le premier instant de son <lb/>mouvement &rdquo; (Lagrange, Mechan. </s>

<s>anal. </s>

<s>cit, pag. </s>

<s>8). </s></p><p type="main">

<s>Or come mai si domander&agrave;, essendo una tal definizione del Lagrange <lb/>universalmente approvata, per avere il suo fondamento ne'pi&ugrave; certi princi&shy;<lb/>pii matematici, pot&egrave; il Nardi, ch'era pure cos&igrave; studioso discepolo di Gali-<pb xlink:href="020/01/1921.jpg" pagenum="164"/>leo, metterla in dubbio, e bandir le velocit&agrave; virtuali dall'ingerirsi delle sta&shy;<lb/>tiche dimostrazioni? </s>

<s>Soccorre facile e pronta la risposta a una tale domanda <lb/>sulle labbra di coloro, che ripensano come i principii, a cui s'informa la <lb/><emph type="italics"/>Mechanique analitique<emph.end type="italics"/> del Matematico torinese erano ai tempi del Nardi, <lb/>negl'insegnamenti dello stesso Galileo, o ambigui o apertamente ripudiati <lb/>per falsi. </s>

<s>Vedemmo di questa ambiguit&agrave;, nel capitolo precedente, gli esem&shy;<lb/>pii, e insegnandosi dal Maestro non si poter trattare degl'indivisibili allo <lb/>stesso modo che delle quantit&agrave; finite, com'era possibile che allignasse nella <lb/>sua scuola il Calcolo infinitesimale o qualcuna delle sue pi&ugrave; feconde appli&shy;<lb/>cazioni? </s>

<s>Se i moti iniziali infatti, o i primi istanti di tempo in un grave <lb/>sostenuto a un braccio di leva o pi&ugrave; lungo o pi&ugrave; corto, son, come si con&shy;<lb/>clude per la dottrina di Galileo, tutti egualmente disposti, per non ci essere <lb/>un infinito o un infinitesimo maggiore o minore di un altro; com'era pos&shy;<lb/>sibile confermare le leggi statiche col principio delle velocit&agrave; virtuali? </s>

<s>Ne <lb/>sarebbe conseguito l'assurdo che un peso nella Libbra, a qualunque distanza <lb/>dal sostegno serbasse sempre eguale momento. </s></p><p type="main">

<s>Questi ragionamenti incominciati nella mente del Nardi s'ebbero poi a <lb/>fare anche dal Torricelli e dal Viviani, i quali presero risoluzione di ban&shy;<lb/>dire addirittura dalla Statica il principio delle velocit&agrave; virtuali. </s>

<s>Il primo dei <lb/>due commemorati Geometri infatti, proponendosi di dimostrar che due gravi <lb/>posati sopra due varie obliquit&agrave; di piani della medesima altezza, se sono <lb/>omologamente proporzionali alle lunghezze di quegli stessi piani, hanno i <lb/>momenti eguali, caus&ograve; d'imitar Galileo (il quale in occasione di dimostrare <lb/>un suo principio supposto aveva allora allora trovata la proporzione mede&shy;<lb/>sima di que'momenti col principio delle velocit&agrave; virtuali) per attenersi pi&ugrave; <lb/>sicuramente a un principio affatto diverso, concludendo l'equilibrio fra i <lb/>detti corpi costituiti sopra varie declivit&agrave; dal dimostrar che nuovamente fa&shy;<lb/>ceva &ldquo; centrum commune gravitatis eorum descendere non posse, sed in <lb/>eadem semper horizontali linea, quantumlibet gravia moveantur, reperiri &rdquo; <lb/>(Oper. </s>

<s>geom., Pars I cit., pag. </s>

<s>100). </s></p><p type="main">

<s>Il Viviani poi d&agrave; del notabile fatto esempii pi&ugrave; positivi. </s>

<s>Nel tomo IV, <lb/>parte V de'manoscritti di Galileo, son raccolte insieme e cucite alla rinfusa <lb/>fettucce e frustuli di carte, nelle quali riconoscono facilmente gli esperti il <lb/>carattere calligrafico, giovanile, dello stesso Viviani. </s>

<s>Vi son notati pensieri <lb/>di vario soggetto scientifico, che il diligente discepolo scriveva in fretta, come <lb/>gli venivano alla memoria, e secondo ch'egli stesso diceva <emph type="italics"/>ad mentem Ga&shy;<lb/>lilei.<emph.end type="italics"/> Nella prima faccia del foglio 26, in mezzo ad altre notarelle del pi&ugrave; <lb/>svariato argomento, alcune delle quali assai curiose, si legge: &ldquo; L'impeto <lb/>che ha un grave nel voler discendere &egrave; tanto, quanto &egrave; forza che basti per <lb/>sostenerlo. </s>

<s>&rdquo; Ma passando poi di qui al foglio 39 la nostra attenzione &egrave; ri&shy;<lb/>volta a leggere con qualche maraviglia quest'altra nota: &ldquo; Pensare se &egrave; vero <lb/>che per ritenere un peso serva tanta forza, quanta ne fa quello per scen&shy;<lb/>dere: come si far&agrave; per rimanerne sicuri? </s>

<s>&rdquo; </s></p><p type="main">

<s>La prima importante notizia che di qui ricava il lettore sarebbe che Ga-<pb xlink:href="020/01/1922.jpg" pagenum="165"/>lileo stesso fosse entrato in sospetto della verit&agrave; del principio statico da lui <lb/>professato, Anzi, quando s'avesse a credere che fossero tutte queste note <lb/>veramente scritte dal Viviani <emph type="italics"/>ad mentem Galilei,<emph.end type="italics"/> verrebbe quella prima <lb/>irresoluta notizia a confermarsi nella certezza, giacch&egrave; quivi stesso, a tergo <lb/>del foglio 41, leggesi un frammento di Dialogo dove, mettendosi dal Sagredo <lb/>in dubbio il principio delle velocit&agrave; virtuali, per esser duro ad apprendere <lb/>come una cosa che non &egrave; ancora possa produrre un effetto presente, il Sal&shy;<lb/>viati, ossia Galileo cos&igrave; risponde: &ldquo; V. S. ha molto ben ragione di dubitare <lb/>ed io ancora, non restando ben sodisfatto di simile discorso, trovai di quie&shy;<lb/>tarmi per un altro verso molto semplice e speditivo. </s>

<s>&rdquo; </s></p><p type="main">

<s>Questo modo pi&ugrave; semplice e speditivo, che il Salviati passa a proporre, <lb/>in sostituzion di quello delle velocit&agrave; virtuali, sembra essere stato suggerito <lb/>da ci&ograve; che, nella Parafrasi ai due libri archimedei <emph type="italics"/>De aequiponderantibus,<emph.end type="italics"/><lb/>dice cos&igrave; proemiando Guidubaldo del Monte: &ldquo; Sint duo pondera A, B in <lb/>aliquo vecte, A maius, B minus quorum simul ita in vecte dispositorum sit <lb/>centrum gravitatis C. </s>

<s>Sit autem sub vecte inter C, A fulcimentum in D, et <lb/>quoniam pondera A, B penes C gravitatis centrum inclinantur, tunc C deor&shy;<lb/>sum naturaliter movebitur ac per consequens pondus quoque B movebi&shy;<lb/>tur &rdquo; (Pisauri 1588, pag. </s>

<s>2). La dimostrazione fatta nel frammento di dia&shy;<lb/>logo dal Salviati &egrave; fondata sui fatti statici descritti in queste parole di Gui&shy;<lb/>dubaldo. </s></p><p type="main">

<s>Ma &egrave; egli veramente quel frammento di dialogo fra il Sagredo e il <lb/>Salviati scritto secondo l'intenzione di Galileo? </s>

<s>La nota autografa apposta <lb/>in margine dal Viviani <emph type="italics"/>di questo ho l'originale<emph.end type="italics"/> farebbe anzi credere che <lb/>Galileo stesso avesse di sua propria mano distesa l'interlocuzione, e che il <lb/>Viviani non avesse fatto altro che copiarla. </s>

<s>Anche noi, avendo creduto da <lb/>principio che le cose stessero propriamente cos&igrave;, come ci si rappresentavano, <lb/>asserimmo nel Discorso preliminare a questa Storia che Galileo aveva inten&shy;<lb/>zione di riformare il dialogo delle Due nuove scienze, per sostituirvi un altro <lb/>principio statico diverso da quello delle velocit&agrave; virtuali, ma poi, svolgendo <lb/>le carte propriamente appartenenti allo zelante discepolo, scoprimmo che <lb/>quella sostituzione aveva inteso di farla egli di suo proprio moto, e non per <lb/>copia avutane o per desiderio espressogli dal Maestro. </s>

<s>Il seguente documento, <lb/>che noi trascriviamo qui nella sua integrit&agrave;, mette in chiaro le cose nei loro <lb/>pi&ugrave; minuti particolari. </s></p><p type="main">

<s>&ldquo; Trovandomi un giorno, scrive di sua propria mano il Viviani, a ra&shy;<lb/><figure id="id.020.01.1922.1.jpg" xlink:href="020/01/1922/1.jpg"/></s></p><p type="caption">

<s>Figura 66.<lb/>gionamento di varie materie con un tal <lb/>Simplicio patrizio anconitano, pass&ograve; que&shy;<lb/>sti ad interrogarmi sopra il seguente <lb/>dubbio meccanico, il quale per meglio <lb/>esplicare rappresenter&ograve; con alquanto di <lb/>figura nel modo appresso: Sia sostenuta <lb/>nel punto C (fig. </s>

<s>66) la Libbra di brac&shy;<lb/>cia disuguali, AC maggiore, CB minore: <pb xlink:href="020/01/1923.jpg" pagenum="166"/>cercasi la cagione onde avvenga che, posti nell'estremit&agrave; due pesi eguali <lb/>A, B, la Libbra non resti in quiete o in equilibrio, ma inclini dalla parte <lb/>del braccio maggiore trasferendosi come in EF. &rdquo; </s></p><p type="main">

<s>&ldquo; La ragione, che comunemente se ne assegna, &egrave; perch&egrave; la velocit&agrave; del <lb/>peso A nello scendere sarebbe maggiore della velocit&agrave; del peso B, per esser <lb/>la distanza CA maggiore della distanza CB, onde il mobile A, eguale quanto <lb/>al peso al B, lo supera quanto al momento della velocit&agrave;, e per&ograve; gli pre&shy;<lb/>vale e scende sollevando l'altro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Qui dubitasi circa il valore di tal ragione, la quale par che non ab&shy;<lb/>bia forza di concludere, perch&egrave; &egrave; ben vero che il momento di un grave <lb/>s'accresce congiunto con velocit&agrave; sopra il momento d'un grave eguale, che <lb/>sia costituito in quiete, ma che, posti ambedue in quiete, cio&egrave; dove non sia <lb/>neppur moto, non che velocit&agrave; maggiore di un'altra, quella maggioranza, <lb/>che ancora non &egrave; ma ancora ha da essere, possa produrre un effetto pre&shy;<lb/>sente, ha qualche durezza nel potersi apprendere, sentendovisi veramente <lb/>difficolt&agrave; notabile. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; A cos&igrave; fatta istanza sovvennemi di subito rispondere, alla presenza <lb/>ancora di amico caro, che fu il signor Cosimo Galilei, il quale io adduco in <lb/>testimonio, in ogni caso che il Signor patrizio, scordandosi aver ricevuto da <lb/>me tal risposta e credendosela propria, in qualche occasione se ne vestisse; <lb/>che con molto apparente ragione S. S. Ecc.ma dubitava, non restando ancor <lb/>io ben sodisfatto di tal discorso, ma che io credevo ben di poter quietarlo, <lb/>con una ragione potissima, semplicissima e spedita, senza supporre altro che <lb/>la prima e comunissima notizia meccanica, cio&egrave; che tutte le cose gravi vanno <lb/>all'ingi&ugrave; in tutte le maniere che gli vien permesso, e che quando possono <lb/>scendere, bench&egrave; per minimo spazio, sempre se ne ingegnano. </s>

<s>Per esempio, <lb/>quando nella suddetta libbra AB si pongono due pesi eguali, se questa si <lb/>lascer&agrave; andare liberamente, fin che non trovi intoppo, se ne caler&agrave; al cen&shy;<lb/>tro comune delle cose gravi, mantenendo sempre il centro della sua gra&shy;<lb/>vit&agrave;, che &egrave; il punto di mezzo D, nella retta che da esso v&agrave; al centro uni&shy;<lb/>versale, poich&egrave; un grave in tanto si muove e scende naturalmente, in quanto <lb/>il suo centro di gravit&agrave; pu&ograve; acquistare e scendere verso il centro comune. </s>

<s><lb/>Ma se in questo moto della Libbra si opporr&agrave; un intoppo sotto il centro D, <lb/>il moto si fermer&agrave;, restando la Libbra co'suoi pesi in equilibrio, non po&shy;<lb/>tendo il loro centro di gravit&agrave; comune D calare a basso. </s>

<s>Ma se l'intoppo <lb/>si metter&agrave; fuori del centro D, come sarebbe in C, tale intoppo non fermer&agrave; <lb/>la Bilancia, ma il centro D devier&agrave; dalla perpendicolare, per la quale cam&shy;<lb/>minava, e cos&igrave; scender&agrave; come gli &egrave; permesso dal sostegno C, cio&egrave; per <lb/>l'arco DO. &rdquo; </s></p><p type="main">

<s>&ldquo; Insomma questa Libbra con i due pesi eguali nell'estremit&agrave; &egrave; un <lb/>corpo solo, ed un grave solo, il cui centro di gravit&agrave; &egrave; il punto D, e que&shy;<lb/>sto solo corpo grave scender&agrave; sempre quando e quanto potr&agrave;, e la sua scesa <lb/>sar&agrave; regolata dal centro di gravit&agrave; suo proprio, e quando se gli sottopone <lb/>il sostegno C, il centro D cala in O, seguitando anche di moversi fino al <pb xlink:href="020/01/1924.jpg" pagenum="167"/>perpendicolo, sicch&egrave; quello che scende &egrave; tutto il corpo aggregato e compo&shy;<lb/>sto della Libbra e suoi pesi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La risposta adunque propria ed adeguata all'interrogazione perch&egrave; <lb/>inclini la Libbra sospesa fuori del centro, &egrave; perch&egrave;, come quella che &egrave; una <lb/>sola macchina, trovandosi qualche poco in libert&agrave;, scende e si avvicina quanto <lb/>pi&ugrave; pu&ograve; al centro comune di tutti i gravi, essendo massima indubitabile che, <lb/>qualunque volta una macchina di uno o pi&ugrave; gravi abbia il suo comun cen&shy;<lb/>tro di gravit&agrave; costituito in luogo, che possa per qualche parte, bench&egrave; mi&shy;<lb/>nimo, far qualche acquisto verso il comun centro dei gravi, cio&egrave; della Terra; <lb/>sempre si muova e discenda. </s>

<s>E quando tal centro col muoversi non possa <lb/>subito far qualche acquisto <emph type="italics"/>deorsum,<emph.end type="italics"/> se ne stia infallibilmente in una per&shy;<lb/>petua quiete. </s>

<s>&rdquo; (MSS, Gal. </s>

<s>Dis., T. CXXXV, fol. </s>

<s>8, 9). </s></p><p type="main">

<s>Ora, nel citato volume manoscritto di Galileo, trovandosi messo in forma <lb/>di dialogo questo medesimo discorso, illustrato da eguale figura e con le <lb/>stesse stessissime lettere di richiamo, s'ha scoperto l'inganno da quella <lb/>mano propria che l'aveva tessuto. </s>

<s>Quel giocar poi con la finzione e addi&shy;<lb/>mesticarsi con la menzogna, che non troverebbe in giudici severi cos&igrave; fa&shy;<lb/>cile scusa, &egrave; la pi&ugrave; giusta misura da estimar quanto fosse nel Viviani lo <lb/>zelo di salvar l'onore e la gloria del suo adorato Maestro. </s>

<s>Avrebbe voluto <lb/>che fosse sotto il solo nome di lui raccolta tutta intera la scienza, la quale, <lb/>per esser senza mende, fosse andata esente da qualunque censura. </s>

<s>I mano&shy;<lb/>scritti rivelano nello sviscerato Discepolo queste intenzioni, delle quali si far&agrave; <lb/>a suo tempo disamina pi&ugrave; diligente contentandoci per ora di quel frammento <lb/>di dialogo, in cui poco fa c'incontrammo. </s></p><p type="main">

<s>Conosceva il Viviani che qualunque dottrina avesse avuto per fonda&shy;<lb/>mento il principio delle quantit&agrave; infinitamente piccole era in Galileo una <lb/>contradizione, la quale pi&ugrave; che altrove appariva manifesta col&agrave;, dove ne'dia&shy;<lb/>loghi delle Due nuove scienze trattavasi di applicare agli equiponderanti il <lb/>principio delle velocit&agrave; virtuali. </s>

<s>Finse perci&ograve; il Viviani che l'Autore avesse <lb/>per s&egrave; medesimo pensato di riformare il dialogo, a quel modo ch'esibivasi <lb/>dalla supposta copia, coll'intenzion d'inserirla a suo luogo nella prima ri&shy;<lb/>stampa. </s>

<s>L'essersi messo intorno a ci&ograve; con tanto ardore, da non curare il <lb/>pericolo certissimo di trovarsi convinto di menzogna, sarebbe fra gli altri <lb/>uno de'pi&ugrave; chiari segni che il Viviani partecipava con le idee del Nardi e <lb/>del Torricelli, che fossero cio&egrave; da repudiar nella Statica le velocit&agrave; virtuali, <lb/>essendo il principio matematico infinitesimale, in ch'elle trovavano sicurezza, <lb/>a que'tempi, immaturi a comprendere l'importanza della Geometria del Ca&shy;<lb/>valieri; ambiguamente esposto da chi non l'avesse, come Galileo, aperta&shy;<lb/>mente negato. </s></p><p type="main">

<s>E qui, presso a chiudere questo cenno di storia, la quale risale al Tar&shy;<lb/>taglia, al Nemorario, e anzi molto pi&ugrave; su, non possiamo non rammemorare <lb/>ai Lettori, perch&egrave; riconoscano quanto sia alieno dal vero, il giudizio che, <lb/>per essere pronunziato da un celebre Autore, fu ripetuto e tuttavia si ri&shy;<lb/>pete da molti. </s>

<s>Il Lagrange dunque, dop'avere accennato a quelle velocit&agrave;, <pb xlink:href="020/01/1925.jpg" pagenum="168"/>che danno virt&ugrave; di moto, e sul principio delle quali si stabil&igrave; quel suo in&shy;<lb/>signe analitico Libro, immediatamente soggiunge: &ldquo; Pour peu qu'on exa&shy;<lb/>mine les conditions de l'equilibre dans le levier et dans les autres machi&shy;<lb/>nes, il est facile de reconno&icirc;tre la verit&eacute; de ce principe: cependan<emph type="italics"/>t<emph.end type="italics"/> il ne <lb/>paro&icirc;t pas que les Geometres qui ont pr&eacute;c&eacute;d&eacute; Galilee, en aient eu connois&shy;<lb/>sance, et je crois pouvoir en attribuer la decouverte &agrave; cet Auteur &rdquo; (Mechan. </s>

<s><lb/>analit. </s>

<s>cit., pag. </s>

<s>8). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Galileo per verit&agrave; non fece mai cenno di credersi o di volersi far credere <lb/>Autore della scoperta, la quale egli anzi francamente, come vedemmo, attri&shy;<lb/>buisce ad Aristotile. </s>

<s>In ogni modo per&ograve; tanto <emph type="italics"/>dans son traite<emph.end type="italics"/> Della scienza <lb/>meccanica, quanto <emph type="italics"/>dans ses dialogues sur le mouvement,<emph.end type="italics"/> citati dallo stesso <lb/>Lagrange, le velocit&agrave; virtuali non hanno se non che una parte secondaria, <lb/>e s'adducono per una certa <emph type="italics"/>congruenza e probabilit&agrave;, dalla quale pu&ograve; es&shy;<lb/>sere ragionevolmente confermata<emph.end type="italics"/> (Alb. </s>

<s>XI, 95) la legge delle equiponde&shy;<lb/>ranze, gi&agrave; dall'Autore ivi dimostrata secondo il metodo di Archimede. </s>

<s>Ga&shy;<lb/>lileo dunque, cos&igrave; in principio della <emph type="italics"/>Scienza meccanica,<emph.end type="italics"/> come nel II dialogo <lb/>Delle due nuove scienze, pone per principale fondamento alla statica il teo&shy;<lb/>rema VI <emph type="italics"/>De acquiponderantibus:<emph.end type="italics"/> &ldquo; Commensurabiles magnitudines ex di&shy;<lb/>stantiis reciprocis, eamdem rationem habentibus quam pondera, aequiponde&shy;<lb/>rant &rdquo; (Opera cit., pag. </s>

<s>165). Gli si dovrebbe intorno a ci&ograve; confermare il <lb/>merito di aver resa pi&ugrave; semplice e pi&ugrave; generale la dimostrazione archime&shy;<lb/>dea, se non fosse stato prevenuto dallo Stevino, di cui quella dello stesso <lb/>Galileo &egrave; una imitazione perfetta. </s></p><p type="main">

<s>Il Matematico di Bruges, nel suo libro <emph type="italics"/>Des elemens de Statique,<emph.end type="italics"/> pub&shy;<lb/>blicato verso la fine del secolo XVI, dimostra in due varii modi, corrispon&shy;<lb/>denti ai teoremi VI e VII di Archimede, questa sua prima e fondamentale <lb/>proposizione: &ldquo; De deux pesanteurs equilibres la plus pesante a telle raison <lb/>a la plus legere, comme le long rayon au cort &rdquo; (Ouvres mathematique, <lb/>Leyde 1634, pag. </s>

<s>436). </s></p><p type="main">

<s>Incomincia dal primo modo, che suppone i due gravi commensurabili, <lb/>e invece di suppor, come fa Archimede, una linea imponderabile uniforme&shy;<lb/>mente gravata di pesi eguali, immagina che sia da equilibrare un solido pon&shy;<lb/><figure id="id.020.01.1925.1.jpg" xlink:href="020/01/1925/1.jpg"/></s></p><p type="caption">

<s>Figura 67.<lb/>deroso omogeneo e uniforme, come un <lb/>prisma per esempio o un cilindro. </s>

<s>Sia <lb/>dunque ABCD (fig. </s>

<s>67) questo cilindro, <lb/>che si suppone essere di sei libbre, uni&shy;<lb/>formemente compartite per i piani EF, <lb/>GH, IK, LM, NO condotti paralleli alla <lb/>base, e secanti l'asse PQ ne'punti R, <pb xlink:href="020/01/1926.jpg" pagenum="169"/>S, T, V, X. </s>

<s>Si prenda AM per il peso maggiore, che ha da equiponderare <lb/>all'altro minore LC. &Egrave; chiaro ch'essendo X il centro di gravit&agrave; di questo, <lb/>e S il centro di gravit&agrave; di quello, si potranno i due pesi riguardar come <lb/>bilanciati agli estremi della linea SX sostenuta in T, centro di gravit&agrave; di <lb/>tutto il solido, cosicch&egrave; sia TX il maggior braccio di tal Bilancia, e TS il <lb/>minore. </s></p><p type="main">

<s>Ora, prosegue a dir lo Stevino, &ldquo; il faut demonstrer que la pesanteur <lb/>majeure LD est a la moindre LC comme le long rayon TX au plus court TS &rdquo; <lb/>ci&ograve; che si fa dall'Autore in assai facile modo, perch&egrave; i due cilindri LD, LC, <lb/>avendo basi eguali, stanno come le altezze PV, VQ, le quali stanno come 4:2. <lb/>Ma anche TX sta a ST come due sta ad uno, ossia come 4:2, dunque <lb/>LD:LC=TX:ST. </s></p><p type="main">

<s>Se poi si vuol dividere il cilindro equilibrato in due parti incommen&shy;<lb/>surate e incommensurabili, la conclusione &egrave; la medesima, come passa a di&shy;<lb/>mostrar lo Stevino nel suo secondo esempio, supponendo ch'esso cilindro, <lb/><figure id="id.020.01.1926.1.jpg" xlink:href="020/01/1926/1.jpg"/></s></p><p type="caption">

<s>Figura 68.<lb/>rappresentato in AC (fig. </s>

<s>68), sia dal <lb/>piano EF, parallelo alla base AD, se&shy;<lb/>gato in due porzioni qualunque AF, <lb/>EC. </s>

<s>Sia poi condotto l'asse GH: nei <lb/>punti M, met&agrave; dello stesso GH, K <lb/>met&agrave; di GI, L met&agrave; di IH saranno co&shy;<lb/>stituiti i centri di gravit&agrave; del solido <lb/>intero e della maggiore e della minor <lb/>parte di lui. </s>

<s>Poste le quali cose &ldquo; il faut demonstrer que comme le corps <lb/>ou pesanteur (les quels sont icy de mesme &agrave; cause de leur proportion, car <lb/>comme le corps EFDA au corps EFCB ainsi la pesanteur de celuy-la a ce&shy;<lb/>luy-cy, d'autant que la colomne est de tout cost&eacute; de pesanteur uniforme) de <lb/>EFDA a EFCB, ainsi le long rayon ML au plus court MK &rdquo; (ivi, pag. </s>

<s>437): <lb/>e ci&ograve; fa l'Autore in tre articoli, che si possono compilare nel modo seguente. </s></p><p type="main">

<s>Avendo i due cilindri le basi eguali saranno proporzionali alle altezze <lb/>o alle loro met&agrave;, per cui avremo AF:EC=KI:IL. </s>

<s>Se ora a MH e a MG <lb/>eguali s'aggiunga KM otterremo una nuova eguaglianza HK=MG+KM, <lb/>dal primo termine della quale tolto GK, e dall'altro KI, essendo le quantit&agrave; <lb/>tolte eguali, eguali pure saranno le rimanenti, le quali facilmente si ridu&shy;<lb/>cono a IH/2=IL=KM: all'una e all'altra delle quali due ultime quan&shy;<lb/>tit&agrave; eguali aggiungendo IM s'avr&agrave; ML=KI. </s>

<s>Cos&igrave; preparate le cose, un <lb/>passo solo conduce all'ultima conclusione, perch&egrave; l'eguaglianza AF:EC= <lb/>KI:IL, sostituitovi ML a KI, e KM ad IL, si trasforma nell'altra AF:EC= <lb/>ML:KM, come dovevasi dimostrare. </s></p><p type="main">

<s>&ldquo; On pourroit encor, soggiunge lo Stevino, repliquer que cesta demon&shy;<lb/>stration tient lieu entre les corps de matiere uniforme, et qui font ensemble <lb/>una colomne, pour a quoy subvenir s'ensuit la regle generale .... &rdquo; (ivi) e <lb/>passa a dimostrar che vale la medesima regola anco se i corpi son disformi, <pb xlink:href="020/01/1927.jpg" pagenum="170"/>sempre equilibrandosi anch'essi allora, che i loro pesi stanno reciprocamente <lb/>alle lunghezze dei raggi. </s></p><p type="main">

<s>Chi ora da questi elementi di Statica dello Stevino passa a leggere di&shy;<lb/>mostrato, nella Scienza meccanica di Galileo &ldquo; come pesi diseguali pesino <lb/>egualmente sospesi da distanze diseguali, le quali abbiano contraria propor&shy;<lb/>zione di quella, che essi pesi si ritrovano avere &rdquo; (Alb. </s>

<s>XI, 92) trova i me&shy;<lb/>desimi modi, variati di s&igrave; leggere accidentalit&agrave;, ch'&egrave; pur forza di confessare <lb/>esser questa galileiana dimostrazione, come si diceva, perfettamente imitata <lb/>da quella del Matematico olandese. </s></p><p type="main">

<s>Nella seconda Giornata Delle due nuove scienze si pone per fondamento <lb/>alle dimostrazioni delle resistenze dei solidi, e come principio noto &ldquo; quello <lb/>che nelle Meccaniche si dimostra tra le passioni del Vette, che noi chia&shy;<lb/>miamo Leva, cio&egrave; che nell'uso della Leva la forza alla resistenza ha la pro&shy;<lb/>porzion contraria di quella, che hanno le distanze tra il sostegno e le me&shy;<lb/>desime forza e resistenza &rdquo; (Alb. </s>

<s>XIII, 112). Alla qual proposta del Salviati <lb/>soggiungendo Simplicio essere stato dimostrato ci&ograve; da Aristotile, il Salviati <lb/>stesso risponde: &ldquo; Voglio che gli concediamo il primato nel tempo, ma nella <lb/>fermezza della dimostrazione parmi che se gli debba per grand'intervallo <lb/>anteporre Archimede, da una sola proposizione del quale, dimostrata da esso <lb/>negli Equiponderanti, dipendono le ragioni, non solamente della Leva, ma <lb/>della maggior parte degli altri strumenti meccanici. </s></p><p type="main">

<s>Si conferma di qui quel che altrove si disse che cio&egrave; il principio ari&shy;<lb/>stotelico delle velocit&agrave; virtuali era creduto da Galileo aver minore fermezza <lb/>di quell'altro posto da Archimede negli Equiponderanti, e perci&ograve;, volendo <lb/>quasi lemma ai suoi nuovi teoremi ridurre alla memoria la dimostrazione <lb/>di quel principio archimedeo, lo fa, Galileo, in modo tanto simile a quello <lb/>prima tenuto nella Scienza meccanica, che, nelle Opere, i Fiorentini editori <lb/>di queste, rimandano i lettori ai principii della sopra detta Giornata seconda <lb/>Del moto. </s></p><p type="main">

<s>La fama acquistata dall'Autore fece credere a tutti essere stato egli il <lb/>primo a metter mano nella dimostrazione degli Equiponderanti, rendendola <lb/>assai pi&ugrave; semplice, e comprendendo in una le due proposizioni archimedee. </s>

<s><lb/>Ma l'intento principale di Galileo era quello di cessar certe difficolt&agrave;, che <lb/>egli ebbe a sentir promosse contro a s&egrave; stesso, infin da quando s'esercitava <lb/>da giovane intorno ai Baricentri, da coloro i quali &ldquo; non tolleravano volen&shy;<lb/>tieri quel doppio modo di considerare le medesime grandezze in diverse Bi&shy;<lb/>lance &rdquo; (Alb. </s>

<s>VI, 2). </s></p><p type="main">

<s>Rappresentandoci infatti nuovamente sott'occhio la figura LXVII e ri&shy;<lb/>guardando le linee AD, EF, GH, ecc., come pesanti, e ordinatamente disposte <lb/>sulla lunghezza della linea PQ, la Bilancia sospesa in I si risolve da Archi&shy;<lb/>mede in altre due Bilance, l'una sospesa in G e l'altra in N, ed era ci&ograve; <lb/>che mal si tollerava dai Fiorentini oppositori di Galileo. </s></p><p type="main">

<s>Nelle nuove dimostrazioni il difetto si rendeva meno sensibile, ma pur <lb/>rimaneva sempre, ond'&egrave; che non valsero le sollecitudini dello stesso Galileo <pb xlink:href="020/01/1928.jpg" pagenum="171"/>e dello Stevino a quietar lo spirito degl'intolleranti. </s>

<s>Il Mariotte, per citarne <lb/>uno de'pi&ugrave; celebri, nella seconda parte del suo <emph type="italics"/>Moto delle acque,<emph.end type="italics"/> propone <lb/>un principio statico generale da applicarsi al moto de'fluidi; principio che <lb/>egli insomma riduce a quello delle velocit&agrave; virtuali, dicendo che allora si <lb/>equilibrano due corpi quando o urtandosi o movendosi l'uno in modo da <lb/>far necessariamente movere anche l'altro le velocit&agrave; stanno reciprocamente <lb/>alle moli. </s>

<s>&ldquo; De-la, egli dice, on prouve facilement le principe de Mechani&shy;<lb/>que qui a et&eacute; mal prouv&eacute; par Archimede, par Galilee et par plusieurs Au&shy;<lb/>teurs, scavoir que lorsqu'en une Balance les poids sont reciproques &agrave; leurs <lb/>distances du centre de la Balance, ils font equilibre &rdquo; (Oeuvres, T. II, a la <lb/>Haye 1740, pag. </s>

<s>357). </s></p><p type="main">

<s>L'Huyghens pi&ugrave; moderatamente si content&ograve; di dire che, nella proposi&shy;<lb/>zione fondamentale della Meccanica, Archimede &ldquo; tacite ponit quid de quo <lb/>iure aliquo possumus dubitare &rdquo; (Opera varia, Vol. </s>

<s>I, Lugd. </s>

<s>Batav., pag. </s>

<s>282), <lb/>e giacch&egrave; anche a lui sembrava che n&egrave; lo Stevino n&egrave; Galileo non avessero <lb/>tolto affatto il difetto, s'ingegn&ograve; di salvare il principato al teorema archi&shy;<lb/>medeo, tenendo nel dimostrarlo altro modo. </s>

<s>Chiede perci&ograve; ne sia concesso <lb/>a lui, come all'Autore antico, due cose; la prima: che due pesi eguali, attac&shy;<lb/>cati alle estremit&agrave; di due braccia di leva eguali, si fanno equilibrio, e la se&shy;<lb/>conda che la Bilancia di braccia diseguali cariche d'egual peso inclina dalla <lb/>parte del braccio pi&ugrave; lungo. </s>

<s>A questi aggiunge l'Huyghens un terzo postu&shy;<lb/>lato ed &egrave; che, come fu concesso ad Archimede essere imponderabile la linea, <lb/>cos&igrave; concedasi a lui essere imponderabile il piano, che fa il medesimo offi&shy;<lb/>cio di sostenere i pesi per l'equilibrio. </s></p><p type="main">

<s>Poi prepara l'Huyghens due lemmi di tanto facile dimostrazione, che <lb/>il primo si riduce a un fatto, e il secondo non si potrebbe altrimenti dimo&shy;<lb/>strare che dagli assurdi, che ne conseguono. </s>

<s>&Egrave; quella prima lemmatica pro&shy;<lb/>posizione dall'Autore cos&igrave; formulata: &ldquo; Si super planum horizontale, quod <lb/>imponitur lineae rectae quae id dividit in duas partes, applicetur pondus, <lb/>vis quam illud pondus habebit ad deflectendum planum partem versus ad <lb/>quam applicatur, erit maior quam si positum sit prope dictam lineam &rdquo; (ibid., <lb/>pag. </s>

<s>283). Il secondo poi di que'lemmi si pone dall'Autore stesso sotto la <lb/>seguente forma: &ldquo; Si planum horizontale oneratum plurimis ponderibus ma&shy;<lb/>neat in aequilibrio impositum lineae rectae quae id secat in duas partes, cen&shy;<lb/>trum gravitatis plani sic onerati erit in ipsa linea recta &rdquo; (ibid., pag. </s>

<s>283, 84). </s></p><p type="main">

<s>Di questo e dell'altro Lemma si serve l'Huyghens per dimostrar la <lb/>proposizione sua principale, cos&igrave; formulata: &ldquo; Duo gravia commensurabilia <lb/>appensa ad extremitates brachiorum Librae erunt in aequilibrio, si brachia <lb/>sint in ratione reciproca gravium &rdquo; (ibid., pag. </s>

<s>284). </s></p><p type="main">

<s>Sieno i due detti gravi conmmensurabili A e B (fig. </s>

<s>69), e sia con essi <lb/>la Libbra CE talmente disposta, che il minor braccio CD abbia al suo mag&shy;<lb/>giore DE quella proporzione medesima, che ha reciprocamente il maggior <lb/>peso A a B suo minore: &ldquo; dico Libram esse in aequilibrio appenso A ad <lb/>extremum C, et B ad extremum E, si CE sustineatur in D. &rdquo; </s></p><pb xlink:href="020/01/1929.jpg" pagenum="172"/><p type="main">

<s>Nel piano orizzontale, per cui passa CE, si conducano ad essa CE, per&shy;<lb/>pendicolari in C e in E, le due linee KM, LG, e presa EF=CD si con&shy;<lb/>ducano per i punti F, D le linee GK, ML che, facendo con la Libbra CE <lb/>una mezza squadra, s'intersechino in N ad angolo retto. </s></p><p type="main">

<s>Cos&igrave; fatto, se il peso A sta a B come per esempio 9 sta a 4, si distri&shy;<lb/>buiscano ad ordinati intervalli le nove parti di A sulla linea KM, e le quat&shy;<lb/><figure id="id.020.01.1929.1.jpg" xlink:href="020/01/1929/1.jpg"/></s></p><p type="caption">

<s>Figura 69.<lb/>tro parti di B sulla linea LG, e da <lb/>ciascuna porzion de'pesi cos&igrave; distri&shy;<lb/>buiti si conducano sulla LM altret&shy;<lb/>tante linee perpendicolari. </s>

<s>Si dimostra <lb/>facilmente che i pesi dell'una parte <lb/>si equilibrano con quelli dell'altra <lb/>intorno alla linea LM, sopra la quale <lb/>si dee trovar pure il comun centro <lb/>di gravit&agrave; per le cose gi&agrave; dimostrate <lb/>nel II lemma. </s>

<s>&ldquo; Sed centrum gravi&shy;<lb/>tatis etiam est in linea CE, quoniam <lb/>evidens est planum etiam futurum <lb/>in aequilibrio si in hac linea susti&shy;<lb/>neatur. </s>

<s>Erit ergo centrum gravitatis <lb/>punctum commune illis duabus lineis <lb/>LM, et CE, scilicet punctum D, in quo, si planum sustineatur, manet in <lb/>aequilibrio. </s>

<s>Patet ergo veritas theorematis &rdquo; (ibid., pag. </s>

<s>286). </s></p><p type="main">

<s>La dimostrazione ugeniana, bench&egrave; cos&igrave; elaborata, &egrave; nonostante meno <lb/>comprensiva di quella dello Stevino, non essendo applicabile se non che alle <lb/>quantit&agrave; commensurabili, e pur qui come l&agrave; &egrave; qualche cosa che gli schifil&shy;<lb/>tosi non saprebbero tollerare. </s>

<s>Un altro Matematico non men valoroso del&shy;<lb/>l'Huyghens si volle perci&ograve; provare se forse gli riusciva di contentarli, affi&shy;<lb/>dandosi alla maravigliosa efficacia, allora allora incominciatasi a sperimentare, <lb/>del principio della composizion delle forze. </s>

<s>Il Newton dunque nel I libro <lb/>Dei principii matematici propose della legge degli Equiponderanti una nuova <lb/>dimostrazione che, ridotta alla sua maggiore semplicit&agrave;, procede nel modo <lb/>seguente. <lb/><figure id="id.020.01.1929.2.jpg" xlink:href="020/01/1929/2.jpg"/></s></p><p type="caption">

<s>Figura 70.</s></p><p type="main">

<s>S&igrave;a OK (fig. </s>

<s>70) il minore, o <lb/>OL il maggior braccio della Bilan&shy;<lb/>cia KL, dagli estremi L, K della <lb/>quale pendano i pesi P ed A. </s>

<s><lb/>Fatto centro in O, e con un rag&shy;<lb/>gio eguale ad OL, si descriva un <lb/>cerchio, che tagli il filo KA nel <lb/>punto D, da cui conducasi a DO <lb/>la linea DC perpendicolare. </s>

<s>Presa <lb/>per misura del peso A la lunghezza <lb/>della linea DC, si decomponga con <pb xlink:href="020/01/1930.jpg" pagenum="173"/>la regola del parallelogrammo la forza rappresentata da essa DC nelle due forze <lb/>DM, DC, quella rintuzzata dalla resistenza del centro O, e questa unica ri&shy;<lb/>masta nella sua libera azione. </s>

<s>I triangoli simili DAC, OKD danno AD:DC= <lb/>OD:OK, e perci&ograve; DC=ADXOK/OD. </s>

<s>Ma considerando che DC trae in di&shy;<lb/>rezione perpendicolare al braccio di leva OD, eguale per costruzione al brac&shy;<lb/>cio OL, &egrave; certo che fa forza come se fosse un peso applicato in L nella <lb/>direzione del filo LP, e non potr&agrave; perci&ograve; stabilirsi la macchina in equilibrio, <lb/>se non a patto che sia P=DC. </s>

<s>Ponendo perci&ograve; nel valore di essa DC <lb/>superiormente determinato, A invece di AD e OL invece di OD, avremo <lb/>P=AXOK/OL ossia A:P=OL:OK. &ldquo; Pondera igitur A et P, ne con&shy;<lb/>clude il Newton, quae sunt reciproce ut radii in directum positi OK et OL, <lb/>idem pollebunt, et sic consistent in aequilibrio, quae est proprietas notis&shy;<lb/>sima Librae, Vectis et Axis in peritrochio &rdquo; (Princ. </s>

<s>mathem., T. I, Gene&shy;<lb/>vae 1739, pag. </s>

<s>28). </s></p><p type="main">

<s>Si oppose anche a questa neutoniana proposizione che il dimostrar <lb/>l'equilibrio nella leva diritta, col ridurla a torta ed incurva, non sembrava <lb/>modo da doversi con facilt&agrave; tollerare. </s>

<s>Ma il Newton insomma usciva, cos&igrave;, <lb/>in pubblico uno de'primi e il pi&ugrave; autorevole di tutti nell'applicare alla Sta&shy;<lb/>tica i principii della <emph type="italics"/>Meccanica nuova,<emph.end type="italics"/> de'quali facendo quell'uso, che poi <lb/>videsi cos&igrave; largamente fare al Varignon, si poteva per essi dimostrar la ra&shy;<lb/>gion delle equiponderanze in modo, che anche gl'intolleranti vi s'avessero <lb/>finalmente a quietare. </s></p><p type="main">

<s>Riducendosi infatti sull'esempio del Newton i pesi a forze rappresen&shy;<lb/>tate da linee, abbiasi la Bilancia AB (fig. </s>

<s>71), nella quale sia AG il brac&shy;<lb/>cio minore, e GB il maggiore, tirato questo in gi&ugrave; dalla forza BQ, come <lb/><figure id="id.020.01.1930.1.jpg" xlink:href="020/01/1930/1.jpg"/></s></p><p type="caption">

<s>Figura 70.<lb/>quello &egrave; tirato dalla forza AP, ambedue <lb/>fra s&egrave; parallele, come son parallele fra <lb/>loro le direzioni dei liberi pesi archimedei. </s>

<s><lb/>Applicate ai punti A, B, nella direzione di<lb/>AB, due forze AM, BN eguali e contrarie' <lb/>e nei parallelogrammi MP, NQ, gi&agrave; co&shy;<lb/>struiti, condotte le diagonali XA, YB, che <lb/>prolungate s'incontrino in S, da cui si<lb/>conduca SG parallela ad AP, dimostra&shy;<lb/>rono assai facilmente i novelli Meccanici <lb/>successeri del Newton che questa stessa <lb/>linea SG rappresenta una forza equipol&shy;<lb/>lente alle due AP, BQ in reciproca ragion delle quali stanno le braccia BG, <lb/>GA della Bilancia AB, nel punto G intersegata. </s>

<s>Se dunque SG tira in dire&shy;<lb/>zione contraria alle due BQ, AP il sistema permarr&agrave; in equilibrio, e perci&ograve; <lb/>essendo P, Q, due pesi pendoli dai fili AP, BQ, secondo il metodo archi&shy;<lb/>medeo, la Bilancia stessa rimarr&agrave; per le medesime ragioni equilib<gap/>ta, se <pb xlink:href="020/01/1931.jpg" pagenum="174"/>nel punto G, distante da A e da B reciprocamente come i pesi ivi appli&shy;<lb/>cati, consiste il suo proprio sostegno. </s></p><p type="main">

<s>Nella composizione dunque e nella risoluzione delle forze parallele si <lb/>giudic&ograve; che avesse finalmente la teoria degli Equiponderanti ritrovata la sua <lb/>pi&ugrave; precisa dimostrazione, e le antiche difficolt&agrave; sommosse contro i seguaci <lb/>di Archimede ebbero a risiedere, come risiede colui che furiosamente era <lb/>insorto contro una persona al primo riconoscerla ch'ei fa sott'abito trasfor&shy;<lb/>mato. </s>

<s>Si voleva dire cio&egrave; che il teorema VI <emph type="italics"/>De aequiponderantibus<emph.end type="italics"/> &egrave; di&shy;<lb/>mostrato da Archimede col principio della composizione e della risoluzione <lb/>delle forze parallele, ond'&egrave; che i Matematici fiorentini oppositori di Galileo <lb/>durarono nelle opposizioni infin tanto che, sotto il seducente abito nuovo, <lb/>non riconobbero ascondersi la persona stessa del venerando Siracusano. </s>

<s>I <lb/>pesi infatti per lui son qualit&agrave; astratte dalla pi&ugrave; vile materia; sono in&shy;<lb/>somma forze geometricamente commensurabili, che agiscono insieme paral&shy;<lb/>lele. </s>

<s>La linea dunque GH, alla quale consideriamo ridotto il solido AC nella <lb/>figura LXVIII, &egrave; sollecitata da tante forze eguali e parallele quanti sono in <lb/>essa punti materiali, e saranno perci&ograve; dette forze in numero proporzionale <lb/>alla lunghezza di lei. </s>

<s>La resultante poi c'insegnano i Meccanici novelli <lb/>essere equipollente alla somma di tutte le componenti (alle quali riesce pa&shy;<lb/>rallela) applicata in M giusto mezzo della linea GH. </s>

<s>Se sia dunque essa GH <lb/>sospesa in M per un filo rimarr&agrave; in equilibrio, e in cos&igrave; fatto discorso, chi <lb/>ben considera, si trasforma la prima petizion di Archimede: <emph type="italics"/>aequalia pon&shy;<lb/>dera ab aequalibus distantiis aequiponderare.<emph.end type="italics"/></s></p><p type="main">

<s>Avrebbero preteso alcuni che il postulato s'avesse a dimostrare, ma <lb/>qual dimostrazione, di grazia, ne hanno fatta i moderni? </s>

<s>Supponiamo che <lb/>nella rappresentata figura LXXI, AP e AQ siano eguali, e che il punto G <lb/>torni nel giusto mezzo della Bilancia AB equilibrata dalla forza SG eguale <lb/>e contraria alle dette altre due: qual ragione rendono i moderni dell'equi&shy;<lb/>librio? </s>

<s>Null'altra da quella in fuori suggerita a tutti dal senso comune, <lb/>che cio&egrave; due forze eguali e contrarie si elidono a vicenda. </s>

<s>Ora questo, che <lb/>&egrave; il postulato della Meccanica moderna, &egrave; il postulato altres&igrave; della Mec&shy;<lb/>canica antica, perch&egrave;, dando alla Bilancia forma di una carrucola, per la <lb/>gola della quale passi una fune con due pesi eguali penduli ai capi; &egrave; ma&shy;<lb/>nifesto che <emph type="italics"/>aequalia pondera ab aequalibus distantiis aequiponderare<emph.end type="italics"/> val <lb/>precisamente quanto a dire che si fanno insieme equilibrio due forze eguali <lb/>e contrarie. </s></p><p type="main">

<s>Passando ora al teorema VI Degli equiponderanti, soggetto a tante e <lb/>cos&igrave; lunghe contradizioni, sieno trasformati i pesi in forze parallele, e si ve&shy;<lb/>dr&agrave; facilmente, come si diceva, che il metodo di Archimede &egrave; quel mede&shy;<lb/>simo tenuto da'Moderni nel risolvere e ricomporre insieme pi&ugrave; forze paral&shy;<lb/>lele. </s>

<s>Ritorniamo indietro anche un'altra volta sulla figura LXVIII, e la linea <lb/>GH equilibrata in M suppongasi divisa in due differenti parti ponderose <lb/>GI, IH sollecitate da tante forze parallele quanti punti materiali si compren&shy;<lb/>dono in ciascuna di esse. </s>

<s>La resultante della forza GI, eguale alla loro <pb xlink:href="020/01/1932.jpg" pagenum="175"/>somma e ad esse parallela, &egrave; applicata in K, com'&egrave; applicata in L la resul&shy;<lb/>tante delle forze IH. </s>

<s>Se poi anche tali due forze cos&igrave; resultate si compon&shy;<lb/>gano con la medesima regola, tutte le potenze sollecitatrici si riducono a <lb/>una sola applicata in M, punto distante da K e da L reciprocamente alle <lb/>forze applicate in L e in K. </s>

<s>Questo processo dunque &egrave; identico a quello <lb/>dello Stevino e di Galileo, e come senza difetto s'approva ora dai moderni, <lb/>cos&igrave; dovevasi allora passare agli antichi senza difetto. </s></p><p type="main">

<s>Anche la Baricentrica tutta &egrave; stabilita da Archimede sul principio della <lb/>composizion delle forze parallele, com'&egrave; per s&egrave; manifesto nel circolo, nel <lb/>rettangolo e in tutte le altre figure, nelle quali il centro della gravit&agrave; &egrave; quel <lb/>medesimo del centro della grandezza, e com'&egrave; facile altres&igrave; riscontrar nel <lb/>trangolo e nelle varie superficie, che ne dipendono. </s>

<s>Nel triangolo ABC per <lb/>esempio (figura LXIII addietro) le infinite linee ponderose parallele alla base <lb/>possono rappresentarsi da altrettante forze applicate al mezzo di ciascuna <lb/>linea, e proporzionali alla lunghezza di lei, cosicch&egrave; la composizion di tutte <lb/>queste forze, dalle quali nasce la gravit&agrave; del triangolo, ci dar&agrave; una resul&shy;<lb/>tante unica applicata a un punto della bissettrice, che sia dal vertice A di&shy;<lb/>stante per due terzi. </s>

<s>&Egrave; apertissimo dunque che si riducono allo stesso la <lb/>invenzion del baricentrico nella superfice triangolare, e la invenzion del cen&shy;<lb/>tro delle forze parallele, che la sollecitano tutte insieme per farla o ponde&shy;<lb/>rar sul sostegno o libera cadere. </s></p><p type="main">

<s>L'identit&agrave; de'due metodi, come si riscontra nelle superficie, cos&igrave; &egrave; fa&shy;<lb/>cile riscontrarla ne'solidi da quelle stesse superfice compaginati, ond'&egrave; che <lb/>la Meccanica antica troverebbe nella moderna la sua pi&ugrave; stabile conferma <lb/>e la sua pi&ugrave; sicura difesa, quando fosse vero per&ograve; che venissero i pesi ben <lb/>rappresentati da forze tutte in direzioni fra loro parallele. </s>

<s>Le platoniche <lb/>astrattezze archimedee furono da tutti i Matematici concordemente appro&shy;<lb/>vate e imitate nelle loro meccaniche dimostrazioni, infintantoch&egrave;, incomin&shy;<lb/>ciatasi sulla fine del secolo XVI a instaurare la nuova scienza, non si pens&ograve; <lb/>che non eran da tenere oramai pi&ugrave; lungamente chiuse le orecchie alle voci <lb/>di colui, che si sentiva per amor del vero doversi riconoscere di quella stessa <lb/>scienza primo Autore, il quale aveva sentenziato nelle sue <emph type="italics"/>Questioni<emph.end type="italics"/> essere <lb/>da educar la Meccanica con matematiche contemplazioni, non disgiunte dalle <lb/>questioni naturali. </s>

<s>Volendosi perci&ograve; da'Meccanici moderni celebrar tra la <lb/>Fisica e la Geometria il connubio secondo il prescritto antichissimo rito, co&shy;<lb/>nobbero che, tendendo i gravi al centro della Terra a cui sono uniti, non <lb/>potevano le loro direzioni esser parallele ma convergenti. </s></p><p type="main">

<s>Cos&igrave; essendo, i presidii, che si diceva aver ritrovati nella moderna l'an&shy;<lb/>tica scienza archimedea, vennero improvvisamente a mancarle, e s'ebbe essa <lb/>stessa a veder trasformata in altra ne'suoi fondamentali teoremi e ne'suoi <lb/>corollarii immediati. </s>

<s>Come fosse tentata e divisata una tale trasformazione <lb/>&egrave; ci&ograve; che noi vogliamo brevemente narrare ai lettori sui documenti, che son <lb/>potuti venire alla nostra notizia. </s></p><p type="main">

<s>Ne'primi giorni del Novembre dell'anno 1635, Giovanni di Beaugrand, <pb xlink:href="020/01/1933.jpg" pagenum="176"/>gentiluomo francese e studiosissimo delle Matematiche, viaggiando in Italia <lb/>si diresse a Firenze con la principale intenzione di conoscere di persona il <lb/>famosissimo Galileo, e di trattenersi qualche ora in ragionamento con lui. </s>

<s><lb/>Salito infatti ad Arcetri disse, per dar qualche saggio de'suoi studii, eh'egli <lb/>avea tempo fa dimostrata una proposizione affatto nuova, che cio&egrave; i gravi <lb/>mutan peso, scemandolo quanto pi&ugrave; si avvicinano al centro della Terra. </s>

<s>Ri&shy;<lb/>mase Galileo sorpreso da questa notizia e mostr&ograve; vivissimo desiderio di ve&shy;<lb/>der come si potesse dimostrare una proposizione tanto straordinaria. </s>

<s>Il Beau&shy;<lb/>grand, sceso in Firenze, scrisse di citt&agrave; una lettera, in data del d&igrave; 3 Novembre <lb/>sopraddetto, la quale terminava con queste parole: &ldquo; Le mando il compen&shy;<lb/>dio della dimostrazione, ch'io ho fatta qualche tempo fa delle proporzioni <lb/>delle varie gravit&agrave; d'un corpo grave secondo i suoi varii intervalli dal cen&shy;<lb/>tro della Terra, di che parlassimo insieme nella mia ultima visita, e che <lb/>mi mostr&ograve; aggradire di vederla. </s>

<s>Sar&ograve; contentissimo che passi per il suo <lb/>esame, al quale la sottometto &rdquo; (Alb. </s>

<s>X, 120). </s></p><p type="main">

<s>Non ci &egrave; rimasto documento n&egrave; dell'esposto processo dimostrativo n&egrave; <lb/>del giudizio, che ne fu dato: questo solo si sa che, passando il Beaugrand <lb/>a Roma, Galileo scrisse raccomandandolo con gran lodi al padre Benedetto <lb/>Castelli. </s>

<s>Rimase il Castelli innamorato degli amabilissimi modi del Genti&shy;<lb/>luomo, e quanto ai discorsi, con lui tenuti in soggetto matematico, cos&igrave; ne <lb/>scriveva il d&igrave; 30 dello stesso mese in una lettera a Galileo: &ldquo; Ieri poi il <lb/>congresso secondo fu lunghissimo, ed avessimo ragionamento di diverse ma&shy;<lb/>terie. </s>

<s>Mi raccont&ograve; diversi titoli di trattati che ha fra le mani, e in partico&shy;<lb/>lare mi disse che trattava delle meccaniche e de'centri di gravit&agrave;, e che, <lb/>dove da'passati scrittori erano considerati i pesi come discendenti paralleli, <lb/>che lui li maneggiava come concorrenti nel centro della Terra, come real&shy;<lb/>mente sono &rdquo; (ivi, pag. </s>

<s>124). </s></p><p type="main">

<s>Prosegue a dire il Castelli a Galileo essergli sembrata quella una sot&shy;<lb/>tilissima speculazione, e come ripensandoci sopra fosse rimasto confuso dalla <lb/>conseguenza che sarebbe scesa necessariamente da quei principii. </s>

<s>Tanto si <lb/>sent&igrave; la mente ripiena delle nuove idee che, poco essendo una lettera scritta, <lb/>se ne sfog&ograve; con l'amico e discepolo suo Antonio Nardi, ne'ragionamenti col <lb/>quale espose il teorema del Beaugrand e i corollari ch'egli stesso vedeva ne <lb/>sarebbero conseguiti. </s>

<s>Ben conobbe il Nardi che, ammettendosi le direzioni <lb/>dei pesi non parallele ma convergenti, mentre s'allargava il campo alla Mec&shy;<lb/>canica nuova, veniva ad esser l'antica ne'suoi fondamentali principii modi&shy;<lb/>ficata, e pensava come potesse ci&ograve; farsi, distendendo cos&igrave;, come si leggono <lb/>nella VI Scena accademica, i suoi pensieri. </s></p><p type="main">

<s>&ldquo; Nel principio dei superficiali equilibrii suppone Archimede che pesi <lb/>eguali da distanze eguali pesino egualmente, ma non cos&igrave; da diseguali. </s>

<s>Di&shy;<lb/>mandasi tal principio concedere senz'altra prova, come che il comun giu&shy;<lb/>dizio e l'esperienza lo manifesti, almeno nell'equidistanza della Libbra dal <lb/>piano orizzontale. </s>

<s>Ma chiunque sapesse che la dimostrazione sua pende im&shy;<lb/>mediatamente da un altro pi&ugrave; universale principio, che cio&egrave; i gravi tendono <pb xlink:href="020/01/1934.jpg" pagenum="177"/>al centro loro, saprebbe anco pi&ugrave; chiaramente le conclusioni, che da quello <lb/>rampollano. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; I gravi dunque tendere al centro &egrave; principio indubitabile per il senso, <lb/>ed anco per la ragione, poich&egrave; a comporre una naturale sfera o un mon&shy;<lb/>dano corpo, qual'&egrave; la Terra, par necessario che ad un punto le parti sue <lb/>cospirino, e per il contrario vediamo che, mentre disciorre una tal compo&shy;<lb/>sizione si deva, tutte le parti del composto dal comun centro di essa com&shy;<lb/>posizione si allontanano, come nel fuoco, cio&egrave; nelle materie quali perfetta&shy;<lb/>mente risolvonsi, appare. </s>

<s>Quando dunque un particolar corpo arda e disciol&shy;<lb/>gasi avviene che le parti sue, dal comune loro centro allargandosi, acquistino, <lb/>insieme con la rarit&agrave;, leggerezza, e per trovarsi in un mezzo pi&ugrave; di loro <lb/><figure id="id.020.01.1934.1.jpg" xlink:href="020/01/1934/1.jpg"/></s></p><p type="caption">

<s>Figura 72.<lb/>denso sono premute all'ins&ugrave;, onde propriet&agrave; del fuoco <lb/>giudicasi l'andare in alto, bench&egrave; ci&ograve; da straniera ca&shy;<lb/>gione gli avvenga, poich&egrave; il proprio suo &egrave; d&igrave; disten&shy;<lb/>dersi per ogni banda. </s>

<s>Ma forse anco da straniera, oltre <lb/>alla propria cagione, avviene il tendere ad un comun cen&shy;<lb/>tro le cose gravi, di che per ora non occorre trattare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In quel cambio suppongasi il globo ABC (fig. </s>

<s>72) <lb/>rappresentare il Globo terrestre, il cui centro D, e il <lb/>diametro AC. </s>

<s>Prendasi fuori del globo qualsivoglia <lb/>punto H, onde scenda la perpendicolare HD in AC, e <lb/>parallela ad AC intendasi EGI, che in G tagli DH. </s>

<s>Di <lb/>nuovo siano EGI le braccia eguali di una Bilancia: il <lb/>sostegno sia H, sicch&egrave; G sia il centro dei momenti delle braccia, onde in H <lb/>si rifletta il peso composto della Bilancia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Basti ora sapere al Meccanico risedere nel punto D o l&agrave; almeno ten&shy;<lb/>dere una virt&ugrave;, che a s&egrave; rapisca la linea EGI, naturale o matematica che <lb/>quella fingiamo, di maniera che, se ritenuta ella non fosse, s'unirebbe il <lb/>punto suo G col punto D. </s>

<s>E se li punti, che compongono al modo loro EGI, <lb/>non fossero fortemente congiunti, ne seguirebbe che ciascuno di loro a di&shy;<lb/>rittura si tirasse al centro, di maniera che al punto G toccherebbe il luogo <lb/>D, e di mano in mano i pi&ugrave; prossimi a G otterrebbero i luoghi pi&ugrave; pros&shy;<lb/>simi a D intorno a cui s'unirebbero. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Immaginiamoci dunque dal punto D partirsi le linee DE, DI, e cos&igrave; <lb/>altre di mezz&ograve;, infinite, in EG, GI, e saranno eguali e similmente ritire&shy;<lb/>ranno i punti E, I verso il centro D, e lo stesso s'intender&agrave; delle altre tutte <lb/>in EG, GI, sicch&egrave; niuna di esse braccia prevaleria all'altra, poich&egrave; scambie&shy;<lb/>volmente si rintuzzano i loro momenti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma se da EG si tagli la EF, eguale ad FG, avverr&agrave; che, essendo FG <lb/>minore il doppio di GI e cos&igrave; similmente minori le linee, che dal centro in <lb/>lei terminano; cio&egrave; essendo il triangolo GDF la met&agrave; del triangolo GDI, sar&agrave; <lb/>ancora il momento di quello minore il doppio del momento di questo, e <lb/>perci&ograve; l'estremit&agrave; I sar&agrave; tirata nel punto, in s&egrave; mobile, G verso il centro, <lb/>sino a che arrivi alla linea della direzione HGD, ov'&egrave; il pi&ugrave; vicin luogo che <pb xlink:href="020/01/1935.jpg" pagenum="178"/>possa il punto I ottener verso D, e cos&igrave; per il contrario verr&agrave; in alto re&shy;<lb/>spinta la FE. &rdquo; </s></p><p type="main">

<s>&ldquo; Immaginiamoci dunque che la EG sia composta di diseguale spes&shy;<lb/>sezza di punti, di maniera che per esempio FG, la quale si pone la met&agrave; <lb/>di EG, sia il doppio pi&ugrave; densa di FE. </s>

<s>Adunque nel caso nostro il doppio <lb/>pi&ugrave; linee o atti lineari al centro ritireranno FG, che non ritireranno GK, <lb/>eguale e contrapposta a FG. </s>

<s>Adunque di nuovo tutto il momento composto <lb/>di EDG sar&agrave; sesquialtero del momento di GDI, e quindi il punto E si abbas&shy;<lb/>ser&agrave;, e l'altro si alzer&agrave;. </s>

<s>Ma perch&egrave; il triangolo EDF &egrave; eguale all'altro, si&shy;<lb/>mile e similmente in GI, qual sia KDI, avverr&agrave; che, se tagliamo la parte FE <lb/>e resti FG, si compensino i momenti, perch&egrave; EF pesa una parte di quelle <lb/>di che GI o EG &egrave; due. </s>

<s>Perci&ograve;, quando sia come la distanza GI alla distanza <lb/>GF, cos&igrave; il momento GE al momento GI, si far&agrave; l'equilibrio. </s>

<s>E perch&egrave;, come <lb/>la distanza GI alla distanza GF, cos&igrave; puossi fare in infinito una distanza GI <lb/>ad un'altra in GF; quindi, se dalle suddette distanze pendano come da fon&shy;<lb/>damento simili pesi, o se in esse si sospendano similmente gli stessi trian&shy;<lb/>goli FDE, IDG resteranno come prima compensati i momenti, poich&egrave; i <lb/>pesi reciprochi informano le distanze proporzionalmente. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. XX, pag. </s>

<s>853-56). </s></p><p type="main">

<s>Come tutte le sue speculazioni cos&igrave; anche questa il Nardi comunic&ograve; al <lb/>Torricelli, il quale ebbe a concluderne che &ldquo; quando noi ammettiamo che <lb/>i pesi nella Libbra abbiano inclinazione verso il centro della Terra, siccome <lb/>naturalmente l'hanno, e non che le linee di detta inclinazione ne'pesi siano <lb/>parallele fra loro, secondo che comunemente si suppone; ne seguir&agrave; che non <lb/>ci sia Libbra orizzontale con braccia disuguali, e con pesi con reciproca pro&shy;<lb/>porzione della lunghezza delle braccia, sicch&egrave; detti pesi facciano equilibrio &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>112 a t.) </s></p><p type="main">

<s>Dimostra il Torricelli questa sua proposizione in due maniere, la prima <lb/>delle quali consiste nel provare l'impossibilit&agrave; del supposto che la Libbra <lb/><figure id="id.020.01.1935.1.jpg" xlink:href="020/01/1935/1.jpg"/></s></p><p type="caption">

<s>Figura 73.<lb/>stia orizzontale, &ldquo; imperocch&egrave; sia, egli dice, pri&shy;<lb/>mieramente la Libbra AB (fig. </s>

<s>73) ed in essa i <lb/>punti A e B siano egualmente distanti dal centro <lb/>della Terra E, al quale inclinano secondo le rette <lb/>AE, BE. </s>

<s>Facciasi BC a CA reciprocamente come <lb/>il peso A al peso B, i quali pesi come ancora le <lb/>braccia della Libbra si suppongono disuguali fra <lb/>di loro ed il centro della Libbra sar&agrave; C. Dopo, si <lb/>congiunga la ECD, la quale non pu&ograve; essere per&shy;<lb/>pendicolare alla Libbra AB, perch&egrave; il triangolo <lb/>isoscele AEB, sega la base AB in parti disuguali. </s>

<s><lb/>Adunque posto che CD rappresenti la trutina, con <lb/>la quale si sospende la Libbra dal suo centro, detta trutina deve direttamente <lb/>guardare il centro della Terra E e non sar&agrave; la trutina perpendicolare alla <lb/>Libbra, e in conseguenza la Libbra non &egrave; orizzontale. </s>

<s>Il che ecc. </s>

<s>&rdquo; (ivi, c. </s>

<s>113). </s></p><pb xlink:href="020/01/1936.jpg" pagenum="179"/><p type="main">

<s>Passando alla seconda maniera abbiasi la medesima Libbra AB (fig. </s>

<s>74) <lb/>con pesi di differente gravit&agrave; reciprocamente proporzionali alle braccia AC, <lb/><figure id="id.020.01.1936.1.jpg" xlink:href="020/01/1936/1.jpg"/></s></p><p type="caption">

<s>Figura 74.<lb/>BC, e l'uno posto a una distanza BE dal cen&shy;<lb/>tro della Terra e l'altro a una distanza AE <lb/>minore. </s></p><p type="main">

<s>&ldquo; Dal centro C della Libbra si tirino, <lb/>dice il Torricelli, le perpendicolari CF, CG alle <lb/>linee delle inclinazioni dei pesi al centro della <lb/>Terra, e si tagli BH eguale ad AE, e si giun&shy;<lb/>gano le CE, CH. </s>

<s>Aver&agrave; il triangolo CEB al <lb/>triangolo CEA, cio&egrave; la base BC alla base CA, <lb/>maggior proporzione che il triangolo CHB al medesimo triangolo CEA, cio&egrave; <lb/>l'altezza CG all'altezza FG. &rdquo; </s></p><p type="main">

<s>&ldquo; Si supponga inoltre un peso in B eguale al peso in A, e sar&agrave; il mo&shy;<lb/>mento del peso maggiore in B al momento del peso minore, pure in B, <lb/>come la mole alla mole, cio&egrave; come la mole del peso in A alla mole del peso <lb/>minore in B, ovvero come BC a CA, per la costruzione. </s>

<s>Ma il momento del <lb/>medesimo peso maggiore in B al momento del suo eguale in A &egrave; come la <lb/>perpendicolare CG alla perpendicolare CF, per le cose dichiarate da Giovan <lb/>Batista de'Benedetti nelle sue <emph type="italics"/>Speculazioni matematiche,<emph.end type="italics"/> al trattato della <lb/>Meccanica al Cap. </s>

<s>III, ovvero IV; adunque ha maggior proporzione il mo&shy;<lb/>mento del peso maggiore in B al momento del peso minore in B, che il <lb/>medesimo momento del peso maggiore in B al momento del peso in A, e <lb/>per conseguenza il momento del peso minore in B e il momento del peso <lb/>in A non sono eguali e non fanno equilibrio, ma &egrave; maggiore il momento <lb/>del peso in A e per&ograve; si muter&agrave; la Libbra, il che si doveva provare. </s>

<s>Onde <lb/>resta provato che non ci sia Libbra di braccia ineguali, la quale stia oriz&shy;<lb/>zontalmente in equilibrio con i pesi, che abbiano reciproca proporzione con <lb/>le braccia della medesima Libbra &rdquo; (ivi, c. </s>

<s>113 a t.). </s></p><p type="main">

<s>Queste meccaniche proposizioni son parti di un trattatello, che il Tor&shy;<lb/>ricelli stesso preparava per risolvere finalmente un problema antico, e in&shy;<lb/>torno a cui gli Autori, nel secolo XVI, avevano cos&igrave; lungamente e senza <lb/>nulla concluderne disputato: il problema delle condizioni dell'equilibrio nelle <lb/>Bilance o nella Libbra di braccia eguali. </s>

<s>Alla questione, promossa gi&agrave; da <lb/>Aristotile, presero fervorosa parte il Cardano, il Tartaglia e il Del Monte, <lb/>che le parteciparono perci&ograve; la celebrit&agrave; del loro nome, ond'&egrave; che, tra per <lb/>questo e tra per la pratica importanza dello strumento cos&igrave; spesso invocato <lb/>a geloso giudice del valor delle merci pi&ugrave; preziose, non si vuol passar in <lb/>silenzio nella Storia degli equiponderanti. </s>

<s>Ma perch&egrave; la matematica soluzion <lb/>del problema dipende in gran parte dalla teoria de'momenti, e dal pi&ugrave; giu&shy;<lb/>sto modo di computarli, faremo di una tal teoria e delle applicazioni di lei <lb/>a dimostrar la legge delle equiponderanze primo soggetto alla seguente parte <lb/>del nostro discorso. </s></p><pb xlink:href="020/01/1937.jpg" pagenum="180"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Fu notato altrove da noi che la parola <emph type="italics"/>momento<emph.end type="italics"/> s'introdusse nel lin&shy;<lb/>guaggio meccanico dal Maurolico, consacrandola a significar propriamente <lb/>lo sforzo di un peso <emph type="italics"/>a spatio quopiam contra pendentis.<emph.end type="italics"/> Si dee al Mate&shy;<lb/>matico messinese altres&igrave; la prima dimostrazione, condotta sui principii archi&shy;<lb/>medei, che cio&egrave; stanno i momenti in ragion composta delle distanze e dei <lb/>pesi. </s>

<s>Se la ragion del primato per&ograve; vuol concedersi quanto al linguaggio, <lb/>non sarebbe da far lo stesso quanto all'assoluta sostanza della cosa signi&shy;<lb/>ficata, perch&egrave; il Nemorario, illustrando la Meccanica aristotelica, aveva gi&agrave; <lb/>insegnato a computar quelli che si chiamaron momenti nei gravi posati so&shy;<lb/>pra i loro sostegni, contro i quali fanno, secondo il sito, maggiore o mi&shy;<lb/>nore lo sforzo computabile dal prodotto della mole per la quantit&agrave; del <lb/>discenso. </s></p><p type="main">

<s>Nell'uno e nell'altro metodo il computo in conclusione torna allo stesso, <lb/>ma in quello proseguito dal Nemorario si venivano a cansar certi difficili <lb/>incontri, i quali dal Maurolico o non preveduti o non affrontati, condussero <lb/>a naufragar tanti, che s'erano volentieri voluti imbarcar con lui. </s>

<s>Volendo <lb/>il diligente Raccoglitore de'Monumenti archimedei definir com'abbiasi a in&shy;<lb/>tendere l'equiponderar de'pesi dai loro sostegni nel compararne insieme i <lb/>momenti; &ldquo; gravia vero, egli dice, aeque pendere, sive aeque ponderare, <lb/>dicuntur cum ab aliquo puncto appensa ita pendent, ut recta, quae gravi&shy;<lb/>tatum centra vel appensionum puncta coniungit, horizonti aequidistet. </s>

<s>&rdquo; <lb/>(Monum. </s>

<s>archim. </s>

<s>cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Qui per&ograve; si riguarda la leva nel caso pi&ugrave; comune e particolare, in cui <lb/>le due braccia di lei sieno disposte in linea retta, e le direzioni de'pesi o <lb/>delle forze sieno ad esse braccia perpendicolari. </s>

<s>Ma poniamo che le dette <lb/>braccia sian curve o che facciano angolo fra loro: poniamo che, pur essendo <lb/>rette, non sia alla loro rettitudine la direzione delle forze ortogonale: come <lb/>si deve computare il momento in questi casi possibili e naturali, e in cui <lb/>viene a mancar la regola insegnata dell'equidistanza dall'orizzonte della li&shy;<lb/>nea, che congiunge i centri di gravit&agrave; de'pesi o i punti delle loro sospen&shy;<lb/>sioni? </s>

<s>Il Maurolico non sa risolvere dalla mente i dubbi penosi, e perci&ograve; <lb/>giova narrar da chi e come si diffondesse la benefica luce sopra questi incerti <lb/>segnati sentieri. </s></p><p type="main">

<s>Facendo per maggior chiarezza distinto questo passo storico in due parti, <lb/>secondo che l'anomalia si riguarda nella leva o nella direzione della forza <lb/>applicata, e incominciando dalla prima, diciamo che al difetto del Maurolico <lb/>avrebbero ben saputo supplire i contemporanei o i predecessori che s'eser&shy;<lb/>citarono in quel medesimo studio. </s>

<s>Leonardo da Vinci, che oramai &egrave; uno dei <lb/>pi&ugrave; conosc&igrave;ut&igrave;, s&igrave; propone a risolvere l'importante qucsito nel vario sforzo <pb xlink:href="020/01/1938.jpg" pagenum="181"/>che fa, per mover la ruota, un medesimo peso attaccato in varii punti della <lb/>circonferenza, e dice ch'essendo il detto peso ora attaccato per esempio <lb/><figure id="id.020.01.1938.1.jpg" xlink:href="020/01/1938/1.jpg"/></s></p><p type="caption">

<s>Figura 75.<lb/>in A (fig. </s>

<s>75), ora in B, condotte le perpendicolari <lb/>AC, BD sopra la orizzontale ZQ, lo sforzo o il mo&shy;<lb/>mento del peso in A sta allo sforzo o al momento <lb/>del medesimo peso in B, come OC sta ad OD, ci&ograve; <lb/>che nel potente linguaggio popolare del Nostro &egrave; <lb/>cos&igrave; espresso: &ldquo; La ruota essendo co'sua estremi <lb/>egualmente distante al suo centro, tutti i pesi posti <lb/>nella sua circonferenza faranno tale forza in essa, <lb/>quale farebbero simili pesi posti sotto loro perpendi&shy;<lb/>colare sopra la linea della egualit&agrave; QZ &rdquo; (Ravaisson-Mollien, Manuscr. </s>

<s>N.02038 <lb/>ital., Paris 1891, fol. </s>

<s>2 t.). </s></p><p type="main">

<s>Che il bel teorema non si rimanesse nella scienza di Leonardo chiuso <lb/>e infecondo, ma che ne'contemporanei e ne'successori immediati fosse dif&shy;<lb/>fuso, ce lo attesta il Cardano, il quale nel suo I libro <emph type="italics"/>De subtilitate<emph.end type="italics"/> segue <lb/>la medesima regola per computar, ne'varii punti della circonferenza, il mo&shy;<lb/><figure id="id.020.01.1938.2.jpg" xlink:href="020/01/1938/2.jpg"/></s></p><p type="caption">

<s>Figura 76.<lb/>mento vario di un peso, che si supponga at&shy;<lb/>taccato a un raggio circonvolubile al centro. </s>

<s><lb/>Sia questo centro B (fig. </s>

<s>76) e si supponga il <lb/>peso ora collocato in C, ora in F, dai quali due <lb/>punti sien condotte le CB, FP perpendicolari <lb/>alla linea della direzione, ossia alla verticale <lb/><expan abbr="Aq.">Aque</expan> Ne conclude il Cardano che il momento <lb/>del peso in C &egrave; tanto maggiore del momento <lb/>del medesimo peso in F, quanto CB &egrave; mag&shy;<lb/>giore distanza di FP. &ldquo; Manifestum est in sta&shy;<lb/>teris, et in his qui pondera elevant, quod <lb/>quanto magis pondus a trutina eo magis grave <lb/>videtur. </s>

<s>Sed pondus in C distat a trutina quan&shy;<lb/>titate BC lineae, et in F quantitate FP. </s>

<s>Sed CB est maior FP ex XVa tertii <lb/>Elementorum Euclidis, igitur, lance posita in C, gravius pondus videbitur <lb/>quam in F &rdquo; (Operum T. III, Lugduni 1663, pag. </s>

<s>370). </s></p><p type="main">

<s>&Egrave; questo il metodo, che si tiene ancora per computare i momenti, de&shy;<lb/>rivato da Aristotile secondo gli ordini archimedei. </s>

<s>Ma il Cardano v'aggiunse <lb/>l'altra dimostrazione secondo il metodo del Nemorario, concludendo essere <lb/>in C il corpo pi&ugrave; pesante che in F, perch&egrave; in egual tempo quello si muove <lb/>al centro per maggiore spazio di questo. </s>

<s>&ldquo; Ut autem cognoscamus quod C <lb/>sit gravius in eo situ quam in F, necessarium est ut in aequali tempore <lb/>moveatur per maius spatium versus centrum &rdquo; (ibid.). </s></p><p type="main">

<s>Prende per la dimostrazione il Cardano due archi FG, CE eguali, e con&shy;<lb/>dotte le GO, EM perpendicolari ad AQ, e le FL, CS perpondicolari a GO, <lb/>SM, per gli Elementi geometrici ne conclude essere, CS ossia BM, mag&shy;<lb/>giore di FL, ossia di OP. &ldquo; Dum igitur Libra movetur ex C in E pondus <pb xlink:href="020/01/1939.jpg" pagenum="182"/>descendit per BM lineam, seu proprinquus centro redditur quam esset in C. </s>

<s><lb/>Et dum movetur per spatium arcus FG descenditque per OP et BM maior <lb/>est OP. Igitur, supposito etiam quod in aequali tempore transiret ex C in <lb/>E et ex F in G, adhuc velocius descendit ex C quam ex F. </s>

<s>Igitur gravius <lb/>est in C quam in F &rdquo; (ibid.). </s></p><p type="main">

<s>Furono questi teoremi, cos&igrave; dal Cardano come e dal Tartaglia, dimo&shy;<lb/>strati per servirsene a risolvere la questione delle Bilance, e in proposito <lb/>pure di tal questione si presero ad esaminar da Guidubaldo Del Monte, il <lb/>quale ebbe a notarli di errore. </s>

<s>Non mi posso persuadere, diceva, che la ra&shy;<lb/>gion vera dell'essere il grave in C (nella sopra apposta figura LXXVI) pi&ugrave; <lb/>peso che in F, consista nell'esser CB maggiore di FP &ldquo; cum potius signum, <lb/>quam vera causa esse videatur &rdquo; (Mechanicorum liber, Pisauri 1577, fol. </s>

<s>9 t.). <lb/>Gli faceva anche ombra quel leggere nel Cardano la dimostrazione condotta <lb/>col principio de'<emph type="italics"/>momenti virtuali,<emph.end type="italics"/> considerandovisi il peso che fa il suo <lb/>sforzo in C, e in F &ldquo; non quatenus est in C, et in F, sed quatenus a <lb/>punctis C, F recedit &rdquo; (ibid.). Negava assolutamente poi che il massimo <lb/>peso s'acquisti dal corpo quand'&egrave; attaccato sulla circonferenza all'estremit&agrave; <lb/>del semidiametro orizzontale: &ldquo; ostendam falsum esse pondus in C gravius <lb/>esse quam in alio situ &rdquo; (ibid.). </s></p><p type="main">

<s>Dimostrava Guidubaldo non essere quel punto C, ma un altro che fosse <lb/>al centro B pi&ugrave; vicino, d'onde veniva a concluderne la falsit&agrave; della regola <lb/>del Cardano. </s>

<s>Si faceva tutta l'efficacia della dimostrazione dipendere dal ri&shy;<lb/>guardar le direzioni de'pesi come convergenti al centro della Terra, e non <lb/>come parallele: perch&egrave; in fatti se sia in T il detto centro, da cui si con&shy;<lb/>duca CT, questa come obliqua tirer&agrave; meno della perpendicolare TV e per&shy;<lb/>ci&ograve; in V, avr&agrave; il grave maggior momento che in C, bench&egrave; la distanza da <lb/>AQ sia minore a quel punto che a questo. </s></p><p type="main">

<s>Conseguiva di qui non essere nel secondo de'due sopra commemorati <lb/>teoremi del Cardano le due linee FL, CS alle PO, BM parallele, per cui, <lb/>ci&ograve; negando, veniva a rovinare tutta quella cardanica dimostrazione, alle <lb/>mani di coloro che la tenevan per vera &ldquo; nisi fortasse dixerint haec, omnia, <lb/>propter maximam a centro mundi usque ad nos distantiam, adeo insensi&shy;<lb/>bilem esse, ut propter insensibilitatem tanquam vera supponi possint &rdquo; (ibid., <lb/>fol. </s>

<s>15 t.). </s></p><p type="main">

<s>La diritta logica del ragionamento avrebbe dovuto dunque condurre <lb/>alla conclusione che i teoremi del Cardano son solamente veri nel suppo&shy;<lb/>sto che le direzioni dei pesi, per la gran lontananza dal centro della Terra, <lb/>sieno sensibilmente parallele, ma Guidubaldo vuol pronunziarne della fal&shy;<lb/>sit&agrave; sentenza assoluta, non rimovendosi dal suo giudizio, nemmen quando <lb/>egli si vede scorto da quegli stessi reputati falsi principii alla desiderata <lb/>conquista del vero. </s>

<s>&ldquo; Ex ipsorum quin etiam rationibus ac falsis supposi&shy;<lb/>tionibus iam declaratos Librae effectus ac motus deducere ac manifestare <lb/>libet, ut quanta sit veritatis efficacia appareat, quippe ex falsis etiam elu&shy;<lb/>cescere contendit &rdquo; (ibid., fol. </s>

<s>25 t.). Che nella Bilancia di braccia eguali <pb xlink:href="020/01/1940.jpg" pagenum="183"/>e col punto di sospensione al di sopra, rimossa dall'orizzonte, il lato pi&ugrave; <lb/>alto abbia maggior momento lo prova anche Guidubaldo, applicandovi i teo&shy;<lb/>remi del Cardano, dall'esser maggiore la distanza del centro, e maggiore <lb/>la quantit&agrave; del discenso, ma invece di argomentar di qui, secondo la buona <lb/>Logica che non potevano non esser veri que'repudiati teoremi, dice esser <lb/>tanta della verit&agrave; l'efficacia ch'ella risplende anche in mezzo all'errore. </s></p><p type="main">

<s>Quella logica, che nel libro <emph type="italics"/>Mechanicorum,<emph.end type="italics"/> cos&igrave; ragionando l'Autore, <lb/>a giudizio di tutti i savii faceva difetto, s'instaur&ograve; nella scienza dal Bene&shy;<lb/>detti, il quale dette autorit&agrave; ai teoremi del Cardano e di Leonardo da Vinci, <lb/>dimostrando nel capitolo I della sua Meccanira, dal supposto comunemente <lb/>approvato delle forze parallele, che &ldquo; omne pondus positum in extremitate <lb/>alicuius braehii Librae maiorem aut minorem gravitatem habet, pro diversa <lb/>ratione situs ipsius brachii &rdquo; (Speculationum lib. </s>

<s>cit., pag. </s>

<s>111); cosicch&egrave;, <lb/>come passa a dimostrar nel capitolo II, la proporzione del peso, in Q (nella <lb/>precedente figura LXXV) al medesimo peso in B &ldquo; erit quemadmodum to&shy;<lb/>tius brachii OQ ad partem OD &rdquo; (ibid., pag. </s>

<s>142). Di qui ne conclude la <lb/>regola, che conferma la gi&agrave; insegnata da Leonardo, esser cio&egrave; la perpendi&shy;<lb/>colare, condotta dal centro sulla direzione del peso, quella &ldquo; quae nos du&shy;<lb/>cit in cognitionem quantitatis virtutis illius &rdquo; (ibid., pag. </s>

<s>143). </s></p><p type="main">

<s>La regola di computare i momenti, quando i centri di gravit&agrave; dei pesi <lb/>o i loro punti di sospensione non si ritrovano sopra la medesima linea oriz&shy;<lb/>zontale, veniva cos&igrave; insegnata dal Benedetti con matematica certezza, e po&shy;<lb/>niamo che non fosse in verit&agrave; l'insegnamento affatto nuovo, confer&igrave; nono&shy;<lb/>stante a confermar quello, che avevano detto alcuni suoi predecessori. </s>

<s>Nessuno <lb/>per&ograve;, che si sappia, aveva risposto ancora a quell'altro quesito: come sia, <lb/><figure id="id.020.01.1940.1.jpg" xlink:href="020/01/1940/1.jpg"/></s></p><p type="caption">

<s>Figura 77.<lb/>cio&egrave;, da computare il momento, <lb/>quando le forze non agiscono <lb/>in direzione perpendicolare ma <lb/>obliqua, come per esempio AC <lb/>(fig. </s>

<s>77), che s'intenda applicata <lb/>all'estremo braccio OA di una <lb/>Libbra. </s>

<s>Ricorrendo al principio <lb/>dei moti composti riesce facilis&shy;<lb/>sima la risoluzione del propo&shy;<lb/>sto problema, perch&egrave;, presa la <lb/>linea AC per la misura di tutta intera la detta forza, e costruito sopr'essa <lb/>linea il rettangolo AECD, il lato AE sta per la pi&ugrave; giusta misura della virt&ugrave; <lb/>che rimane. </s></p><p type="main">

<s>Quando per&ograve; quel modo di risolvere un moto in due non era fra'Mec&shy;<lb/>canici in uso, il determinar con matematica certezza quanto, dal tirare obli&shy;<lb/>quo, rimetta del suo intero valore una forza, era problema superiore all'arte <lb/>di un comunale geometra, e nonostante quel Benedetti, che aveva insegnato <lb/>a computar le distanze, qualunque fosse il punto della sospensione, insegna <lb/>ora a conputar, dovunque ella sia diretta, la intensit&agrave; che rimane alla forza, <pb xlink:href="020/01/1941.jpg" pagenum="184"/>e dice &ldquo; debere deprehendi a perpendicularibus, quae a centro Librae ad <lb/>lineas inclinationis exiliunt &rdquo; (ibid.). </s></p><p type="main">

<s>Secondo una tal regola dunque, prolungata la AC, e da O condotta al <lb/>OH perpendicolare sopra questo prolungamento, se con AO si rappresenta <lb/>tutto il valor della forza, OH &egrave; la misura giusta di quel che in lei rimane <lb/>di attivo, ci&ograve; che fa esatto riscontro con la regola desunta dalla risoluzione <lb/>del moto, essendo che i triangoli simili AEC, OHA danno AC:AE=OA:OH. </s></p><p type="main">

<s>Nella instaurazion della scienza, felicemente avvenuta sui principii del <lb/>secolo XVII, si trovarono dunque fra gl'insegnamenti del Benedetti le re&shy;<lb/>gole pi&ugrave; sicure per computare i momenti, e veniva, cos&igrave;, a rendersi possi&shy;<lb/>bile il promovere o il correggere i falli de'teoremi pi&ugrave; antichi. </s>

<s>Il Cartesio <lb/>per verit&agrave;, preferendo di misurar gli spazii nella quantit&agrave; delle discese ver&shy;<lb/>ticali, a modo del Nemorario e del Tartaglia, piuttosto che considerare i <lb/>moti pi&ugrave; o men veloci negli archi dei cerchi; non sent&igrave; n&egrave; il bisogno n&egrave; <lb/>l'utilit&agrave; delle regole insegnate dal Matematico nostro veneziano, ma Gali&shy;<lb/>leo ne ricav&ograve; gran profitto, e deve alla loro sapiente applicazione se la sua <lb/>Scienza meccanica s'avvantaggia da molte parti sopra quella di Guidubaldo. </s></p><p type="main">

<s>Il fondamento a quella Scienza meccanica, com'apparisce da ci&ograve; che se <lb/>n'&egrave; detto addietro a varie occasioni, &egrave; posto da Galileo nella teoria dei mo&shy;<lb/>menti, ch'egli, quasi con le medesime parole del Maurolico, definisce &ldquo; quel&shy;<lb/>l'impeto di andare al basso, composto di gravit&agrave;, posizione o altro, dal che <lb/>possa essere tal propensione cagionata &rdquo; (Alb. </s>

<s>XI, 90). Mentre per&ograve; il Mau&shy;<lb/>rolico non aveva considerato quella posizione, se non che nel caso pi&ugrave; co&shy;<lb/>mune e particolare de'centri di gravit&agrave; o delle sospensioni in una medesima <lb/>linea orizzontale, Galileo contempla anche il caso che quegli stessi centri si <lb/>trovino a varie altezze, per essere le braccia della Bilancia o incurve o an&shy;<lb/>golari, e rammemora perci&ograve; la Regola del Benedetti ai lettori, avvertendoli <lb/>&ldquo; come le distanze si devono misurare con linee perpendicolari, le quali dal <lb/>punto della sospensione caschino sopra le rette, che dai centri della gravit&agrave; <lb/>de'pesi si tirano al centro comune delle cose gravi &rdquo; (ivi, pag. </s>

<s>91). </s></p><p type="main">

<s>Il fondamento statico scelto da Galileo era senza dubbio d'assai pi&ugrave; ge&shy;<lb/>nerale applicazione di quell'altro, volutosi preferir dal Cartesio, ma riusciva <lb/>all'intelligenza alquanto pi&ugrave; duro, essendo pi&ugrave; facilmente disposta a conce&shy;<lb/>der che un corpo tanto maggior momento acquisti quanto pi&ugrave; scende, di <lb/>quel che non sia a conceder che un simile corpo, tanto acquisti maggior gra&shy;<lb/>vit&agrave; quanto pi&ugrave; si dilunga dal centro della sua sospensione. </s>

<s>Vedemmo gli <lb/>sforzi che, incominciando da Aristotile, fecero per rivelare il mistero i Ma&shy;<lb/>tematici antichi, e i Moderni pure avrebbero desiderato che Galileo avesse <lb/>fatto lo stesso. </s>

<s>La questione &egrave; vero era pi&ugrave; filosofica che matematica, ma <lb/>perch&egrave; sentivasi che, se non utile, adornare la scienza di cos&igrave; fatte specu&shy;<lb/>lazioni sarebbe stato almen bello; qualcuno della Scuola galileiana si prov&ograve;, <lb/>non diciam di supplire al difetto, ma di esplicare in altra forma e di ri&shy;<lb/>durre pi&ugrave; direttamente alla Statica alcuni concetti del Maestro. </s></p><p type="main">

<s>Noi vogliamo rammemorare ai Lettori in tal proposito i pensieri di An-<pb xlink:href="020/01/1942.jpg" pagenum="185"/>tonio Nardi, il quale, dopo aver, nel passo poco addietro, addotto, insegnato <lb/>a computare i momenti dal composto di tutte insieme le linee radiose di <lb/>forza appuntate da una parte nel centro terrestre, e dall'altra in tutte le <lb/>particelle materiali della Bilancia; e dop'avere osservato che, inclinandosi <lb/>essa Bilancia, vanno i momenti di lei dall'infinito a terminare nel zero, sog&shy;<lb/>giunge quanto appresso: </s></p><p type="main">

<s>&ldquo; Poich&egrave;, sebbene il peso &egrave; lo stesso, la forza nondimeno &egrave; divisa, onde <lb/>stanno insieme il pesar pi&ugrave; e il forzar meno, e per il contrario ancora. </s>

<s>Di <lb/>pi&ugrave;, se alcuno prenda qualche bacchetta, e in un ginocchio piegar la voglia, <lb/>prover&agrave; diverso effetto se verso il mezzo o se verso un estremo la forzi, <lb/>poich&egrave; in questo caso meno piegher&agrave; con egual virt&ugrave; la pi&ugrave; corta, che la <lb/>pi&ugrave; lunga parte di essa bacchetta. </s>

<s>Quindi raccor devesi che, facendosi la <lb/>forza secondo la profondit&agrave; di essa bacchetta, pi&ugrave; resiste la stessa profon&shy;<lb/>dit&agrave; all'impeto, quale informa la minore, che a quello che informa la mag&shy;<lb/>gior lunghezza, poich&egrave; maggiore ragione ha a quella che a questa. </s>

<s>Quindi <lb/>&egrave; palese che l'atto e l'impeto, siccome corpo non &egrave;, cos&igrave; occupa senza te&shy;<lb/>ner luogo tutto un corpo, e si moltiplica in esso cos&igrave;, che maggiore &egrave; nel <lb/>maggiore che nel minor soggetto, quando per&ograve; uguale la sua cagione si <lb/>fosse. </s>

<s>E se un soggetto fosse privo d'ogni momento ed atto pi&ugrave; si move&shy;<lb/>rebbe da uguale impeto, mentre grande, che mentre piccolo il soggetto fosse, <lb/>il che un paradosso parrebbe, se l'esperienza non l'approvasse, anco nelle <lb/>cose che straniero momento ottengono. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di gi&agrave; &egrave; noto che con la stessa forza pi&ugrave; lontano lanciamo una me&shy;<lb/>diocre palla di sasso, che una galla o un grano di arena. </s>

<s>Dicono alcuni che <lb/>la galla e il grano di arena non ponno romper l'aria, ma questa &egrave; sempli&shy;<lb/>cit&agrave;, poich&egrave; per il solo romper l'aria si deve attendere la solidit&agrave; del corpo, <lb/>qual'&egrave; la galla o il grano di arena, e se questi corpi non romponla, viene, <lb/>non per difetto della solidit&agrave; loro, ma per incapacit&agrave; di ricever l'impeto, <lb/>nata o per la piccolezza o per la rarit&agrave;, che alla piccolezza riducesi, del sog&shy;<lb/>getto, a che concorre l'aria, per quella parte che risguarda il pi&ugrave; o meno <lb/>veloce rompersi, e massime dai minimi leggeri e cadenti corpi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quest'altra esperienza anco mirabilmente conferma il parer nostro, <lb/>poich&egrave; di due travi disuguali di lunghezza, ma uguali in grossezza, mentre <lb/>galleggiano placidamente nell'acqua, si spinger&agrave; e si tirer&agrave; pi&ugrave; validamente <lb/>la pi&ugrave; lunga da forze eguali e parallele al piano dell'orizzonte, che non si <lb/>far&agrave; la pi&ugrave; corta. </s>

<s>Ma in aria, non cos&igrave; sempre avverr&agrave;, poich&egrave; il momento <lb/>dalle cose intorno al centro impressoli non &egrave; pi&ugrave; pareggiato dall'ambiente, <lb/>onde talvolta accader&agrave; che la forza straniera impressali sia molto minore <lb/>della gravit&agrave; sua. </s>

<s>Ma se due forze eccedano due diseguali solidi, e non <lb/>affetti da altro sensibil momento, farassi proporzionalmente maggiore effetto <lb/>nel maggiore, il che vedesi nelle bombarde e negli schioppi. </s>

<s>&rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. XX, pag. </s>

<s>857, 58). </s></p><p type="main">

<s>Illustrare, cos&igrave; come faceva il Nardi, la teoria de'momenti nell'astruso <lb/>concetto delle forze incorporee, che misteriosamente si moltiplicano a pro-<pb xlink:href="020/01/1943.jpg" pagenum="186"/>porzione della quantit&agrave; della materia, era non bello solo, ma necessario, spe&shy;<lb/>cialmente a que'tempi, ne'quali si voleva stabilir la scienza sopra pi&ugrave; fermi <lb/>principii, e infonderle un vigor nuovo di vita. </s>

<s>Il fondamonto naturale per&ograve; <lb/>era da ritrovar nella Matematica, ma bench&egrave; avesso Galileo trattato co'mo&shy;<lb/>menti molta parte della Scienza meccanica, misurandoli dal prodotto del peso <lb/>per la distanza, la matematica dimostrazione nulladimeno di questo fonda&shy;<lb/>mental teorema, fecondissimo di tanti corollarii, era quella che, ne'primi <lb/>decennii del secolo XVII, quando ancora non era nemmen conosciuto il trat&shy;<lb/>tato del Maurolico, pi&ugrave; vivamente da tutti si desiderava. </s></p><p type="main">

<s>Alla fine del terzo di quei decennii quel che di Meccanica aveva pub&shy;<lb/>blicamente insegnato Galileo si riduceva ne'dialoghi Dei due massimi Si&shy;<lb/>stemi, nel secondo dei quali, avendo asserito il Salviati che due momenti <lb/>si eguagliano allora insieme quando si eguagliano i prodotti delle velocit&agrave; <lb/>per i pesi, il Sagredo cos&igrave; gli domanda: &ldquo; Ma credete voi che la velocit&agrave; <lb/>ristori per l'appunto la gravit&agrave;? </s>

<s>cio&egrave; che tanto sia il momento e la forza <lb/>di un mobile v. </s>

<s>g. </s>

<s>di quattro libbre di peso, quanto quella di un di cento, <lb/>qualunque volte quello avesse cento gradi di velocit&agrave;, e questo quattro gradi <lb/>solamente? </s>

<s>&rdquo; (Alb. </s>

<s>I, 237). Il che voleva dire in altre parole: credete voi <lb/>che i momenti stiano veramente in ragion composta delle velocit&agrave; e dei pesi? </s>

<s><lb/>A che risponde il Salviati: &ldquo; Certo s&igrave;, come io vi potrei con molte espe&shy;<lb/>rienze provare &rdquo; (ivi), fra le quali molte esperienze sceglie quella notissima <lb/>della stadera, nella quale veramente si vede che la maggior velocit&agrave; del pic&shy;<lb/>colo romano compensa il legger moto della gravissima balla. </s></p><p type="main">

<s>Ma questo era insomma un rendere pi&ugrave; ardente la sete, che gi&agrave; ne <lb/>aveva accesa Archimede, a cui, domandandosi perch&egrave; due pesi eguali equi&shy;<lb/>ponderino da due eguali distanze, rispondeva con pi&ugrave; ragione di Galilao, ri&shy;<lb/>mandando i curiosi alla disciplina delle esperienze volgari. </s>

<s>Il progresso di <lb/>tanti secoli esigeva con pi&ugrave; diritto matematiche dimostrazioni, e giacch&egrave; lo <lb/>stesso Galileo non aveva corrisposto al comun desiderio, pens&ograve; di supplirvi <lb/>opportunamente uno de'suoi primi discepoli, Niccol&ograve; Aggiunti. </s>

<s>Egli, precor&shy;<lb/>rendo di quasi un mezzo secolo al Mariotte ed altri Matematici, avea tentato <lb/>una pi&ugrave; generale dimostrazione delle leggi dei momenti, riducendoli cos&igrave; a <lb/>quella che, in qualunque condizion del mobile, o stabilmente sospeso o libe&shy;<lb/>ramente mosso, ebbe proprio nome di <emph type="italics"/>quantit&agrave; di moto.<emph.end type="italics"/> Abbiamo detto che <lb/>tent&ograve; di fare quel che certamente avrebbe messo ad effetto, se cos&igrave; giovane non <lb/>l'avesse alla scienza rapito la morte. </s>

<s>Ma quel che in ogni modo pu&ograve; respi&shy;<lb/>golarsi dalle informi carte lasciate da lui, in quella parte che fu senza dubbio <lb/>scritta fra l'anno 1632 e il 1635, basta per farci argomentare a qual maggior <lb/>grado di perfezione sarebbe giunta la scienza del moto infino da'suoi principii, <lb/>se la Fisica di Galileo avesse avuto il conforto della Geometria dell'Aggiunti. </s></p><p type="main">

<s>Il valoroso giovane precursore del Mariotte e del Borelli, nelle sparse <lb/>pagine del suo trattato, primaticcio frutto di quella, che poi si chiam&ograve; da <lb/>Galileo Scienza nuova, incominci&ograve; dal definire i modi e le sperimentate leggi, <lb/>secondo le quali i corpi in moto operano la percossa. </s></p><pb xlink:href="020/01/1944.jpg" pagenum="187"/><p type="main">

<s>&ldquo; La percossa del grave, egli dice, che discendendo percote l'addiman&shy;<lb/>deremo <emph type="italics"/>percossa naturale. </s>

<s>Percossa violenta<emph.end type="italics"/> intenderemo quella del grave, <lb/>che ascendendo percote. <emph type="italics"/>Percossa media<emph.end type="italics"/> diremo quella del grave, che mo&shy;<lb/>vendosi orizzontalmente percote. <emph type="italics"/>Percossa composta<emph.end type="italics"/> diremo quella di quel <lb/>grave, il cui moto naturale &egrave; accelerato da motore estrinseco, e con tal moto <lb/>accelerato percota. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La percossa opera con la velocit&agrave; e con la copia della materia, in <lb/>cui s'imprime detta velocit&agrave;, e per&ograve; se caderanno dalla medesima altezza <lb/>due gravi disuguali dell'istessa materia, come due palle di ferro disuguali, <lb/>le loro percosse saranno disuguali, e maggiore sar&agrave; la percossa della mag&shy;<lb/>gior palla, bench&egrave; ambedue discendano con la medesima velocit&agrave; &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>95). </s></p><p type="main">

<s>Ora questo, che sembrava essere approvato dall'esperienza, si voleva <lb/>dall'Aggiunti confermare con la teoria, dimostrando che i momenti, o pi&ugrave; <lb/>in generale le quantit&agrave; di moto, son matematicamente proporzionali al pro&shy;<lb/>dotto delle velocit&agrave; per le quantit&agrave; della materia. </s>

<s>La proposizione era quella <lb/>stessa XXVII dimostrata quarant'anni dopo nel trattato <emph type="italics"/>De vi percussionis,<emph.end type="italics"/><lb/>e come ivi il Borelli la conclude dalle due proposizioni precedenti, cos&igrave; <lb/>avrebbe voluto fare l'Aggiunti, proponendosi di dimostrar come, essendo le <lb/>moli eguali, i momenti stanno in ragione delle velocit&agrave;, ed essendo le ve&shy;<lb/>locit&agrave; uguali stanno essi momenti in diretta ragion delle moli. </s></p><p type="main">

<s>La prima di queste proposizioni non si trova a suo luogo, e invece se <lb/>ne legge nel manoscritto un'altra, che potrebbesi dire un corollario di <lb/>lei, se non fosse una falsit&agrave; manifesta o una di quelle arguzie delle quali <lb/>si trova nelle speculazioni dell'Aggiunti pi&ugrave; di un esempio. </s>

<s>La detta pro&shy;<lb/>posizione, che tiene nel citato manoscritto il luogo della prima, &egrave; cos&igrave; for&shy;<lb/>mulata: &ldquo; Anco la sola velocit&agrave; senza il peso opera ed ha momento &rdquo; (ivi <lb/>a tergo). Aveva Aristotile sentenziato &ldquo; che senza l'inerenza del suo sog&shy;<lb/>getto non pu&ograve; n&egrave; essere n&egrave; anco immaginarsi alcun movimento &rdquo; sentenza <lb/>che, ripetuta da Simplio nel II dialogo Dei due massimi sistemi, &egrave; dal Sa&shy;<lb/>gredo ivi approvata per vera. </s>

<s>Volle nonostante l'Aggiunti, cos&igrave; argutamente <lb/>discorrendo, contradire al giudizio di Aristotile e di Galileo, ci&ograve; che avrebbe <lb/>avuto il diritto di fare, quando non avesse contradetto insieme alla ragion <lb/>matematica, perch&egrave; se una delle quantit&agrave; componenti il momento &egrave; zero, dee <lb/>necessariamente il momento stessa ridursi a zero: </s></p><p type="main">

<s>&ldquo; Che la velocit&agrave;, senza il peso, operi ed abbia forza, &egrave; manifesto nei <lb/>venti, i quali, non essendo altro che aria mossa nell'aria (perch&egrave; un grave <lb/>in un mezzo ugualmente grave in specie ad esso, come dimostra Archimede, <lb/>non ha peso alcuno in detto mezzo) adunque tutta la forza del vento na&shy;<lb/>sce dalla sola velocit&agrave;, con la quale si muove l'aria. </s>

<s>&Egrave; ancora manifesto <lb/>nelle percosse violente perch&egrave;, facendosi la percossa violenta dal grave al&shy;<lb/>l'ins&ugrave;, ed essendo l'inclinazione del grave all'ingi&ugrave;, l'effetto dunque della <lb/>percossa non pu&ograve; nascere dal peso, cio&egrave; dalla propensione all'ingi&ugrave;, ma s&igrave; <lb/>bene dalla velocit&agrave; impressagli all'ins&ugrave;. </s>

<s>&Egrave; finalmente questo stesso manife-<pb xlink:href="020/01/1945.jpg" pagenum="188"/>sto nella percossa media, ovvero orizzontale, nella quale, movendosi il grave <lb/>parallelo all'orizzonte, l'effetto che resulta da tal movimento non verr&agrave; dal <lb/>suo peso, cio&egrave; dalla sua inclinazione al centro, ma dall'impulso laterale ov&shy;<lb/>vero orizzontale, al quale il peso ovver moto all'ingi&ugrave; non osta, ma neanco <lb/>opera n&egrave; coopera &rdquo; (ivi). </s></p><p type="main">

<s>La proposizione II, che immediatamente segue, &egrave; cos&igrave; formulata: &ldquo; La <lb/>medesima volocit&agrave;, nelle maggiori e minori quantit&agrave; di materia, opera pi&ugrave; <lb/>o meno potentemente, secondo la proporzione della materia &rdquo; (ivi a tergo). <lb/>Vi si doveva intendere premessa la dimostrazione di un lemma, che si legge <lb/>altrove nel manoscritto, e che risponde alla proposizione XXXVII del I libro <lb/>maurolicano <emph type="italics"/>De momentis:<emph.end type="italics"/> &ldquo; Gravia ab aequis spatiis pendentia sunt mo&shy;<lb/>mentis proportionalia &rdquo; (Monum. </s>

<s>archim. </s>

<s>cit., pag. </s>

<s>103); proposizione da&shy;<lb/>taci dall'Aggiunti sotto quest'altra forma: &ldquo; Due gravi della medesima ma&shy;<lb/>teria omogenea, attaccati nell'istesso punto della Bilancia, hanno i loro <lb/>momenti proporzionali alle moli &rdquo; (MSS. cit., fol. </s>

<s>100). </s></p><p type="main">

<s>Supponesi, per le cose da dimostrare, essersi gi&agrave; previamente dimostrato <lb/>ch'essendo le distanze reciproche alle moli i momenti sono eguali, ci&ograve; che <lb/>in via analitica conduce ora noi in due passi alla conclusione, perch&egrave;, chia&shy;<lb/>mate D <emph type="italics"/>d<emph.end type="italics"/> le distanze, M <emph type="italics"/>m<emph.end type="italics"/> le moli, Q <emph type="italics"/>q<emph.end type="italics"/> i momenti, essere DM=<emph type="italics"/>dm<emph.end type="italics"/> val <lb/>quanto dire Q=<emph type="italics"/>q,<emph.end type="italics"/> e dall'equazione Q:<emph type="italics"/>q<emph.end type="italics"/>=DM:<emph type="italics"/>dm,<emph.end type="italics"/> se D=<emph type="italics"/>d,<emph.end type="italics"/> si con&shy;<lb/>clude immediatamente l'annunziato teorema. </s>

<s>Ma l'Aggiunti per le antiche <lb/>vie lunghe cos&igrave; procede: </s></p><p type="main">

<s>&ldquo; Nella Bilancia AB (fig. </s>

<s>78), il cui centro sia C, pendano dal mede&shy;<lb/>simo punto M li due gravi I, G, dico ecc. </s>

<s>Come sta la mole G alla mole I, <lb/><figure id="id.020.01.1945.1.jpg" xlink:href="020/01/1945/1.jpg"/></s></p><p type="caption">

<s>Figura 78.<lb/>cos&igrave; stia la distanza CB alla distanza <lb/>CM, e la distanza DC facciasi eguale <lb/>a CM. </s>

<s>Poi attacchisi in B il peso K, <lb/>eguale ad I, ed in D il peso F eguale <lb/>a G. </s>

<s>Perch&egrave; le distanze son recipro&shy;<lb/>che alle moli, il momento di K &egrave; <lb/>uguale al momento di F, cio&egrave; al mo&shy;<lb/>mento di G, essendo G ed F pesi <lb/>eguali in distanze eguali. </s>

<s>Ma il mo&shy;<lb/>mento di K al momento di I ha la proporzione della distanza BC alla di&shy;<lb/>stanza CM, cio&egrave; della mole G alla mole I: adunque ancora il momento di G <lb/>al momento di I ha la proporzione della mole C alla mole I, il che dove&shy;<lb/><figure id="id.020.01.1945.2.jpg" xlink:href="020/01/1945/2.jpg"/></s></p><p type="caption">

<s>Figura 79.<lb/>vamo dimostrare &rdquo; (ivi a tergo). </s></p><p type="main">

<s>Ci&ograve; premesso, passa l'Ag&shy;<lb/>giunti a dimostrare che, se sa <lb/>ranno due solidi B, A (fig. </s>

<s>79) <lb/>mobili di uguali velocit&agrave; nel&shy;<lb/>l'orizzonte CD, fatti della stessa <lb/>materia ma disuguale, il mo&shy;<lb/>mento dell'uno al momento del-<pb xlink:href="020/01/1946.jpg" pagenum="189"/>l'altro sta come la quantit&agrave; della materia dell'uno alla quantit&agrave; della materia <lb/>dell'altro. </s>

<s>&ldquo; Imperocch&egrave;, egli dice, alzisi nel punto D la linea DE perpendico&shy;<lb/>lare all'orizzonte, e detta linea intendasi come una leva convertibile intorno <lb/>al punto fisso F, preso nel mezzo di essa. </s>

<s>Di poi alzisi dal punto E la linea <lb/>EH, la quale, passando per la girella volubile intorno al punto K, discenda <lb/>perpendicolarmente in I. Dopo, intendansi attaccati alla linea HI due gravi <lb/>N, M dell'istessa materia, i quali siano di figura simile ed eguali alli so&shy;<lb/>lidi A, B, l'uno all'uno e l'altro all'altro, e la loro velocit&agrave; nella perpen&shy;<lb/>dicolare HI sia uguale alla velocit&agrave; delli A, B nella linea CD. Adunque, per <lb/>l'assioma, la forza e momento dell'uno sar&agrave; uguale al momento e forza <lb/>dell'altro a s&egrave; uguale. </s>

<s>Posto dunque che N sia uguale ad A, se il mobile A <lb/>far&agrave; forza in D, perch&egrave; la linea EH vien tirata dalla forza del grave N &egrave; <lb/>come se N fosse attaccato in E, e facesse la medesima forza per la linea <lb/>EH, ch'egli fa per la linea CI. </s>

<s>Ma le distanze FE, FD sono eguali, e la ve&shy;<lb/>locit&agrave; e quantit&agrave; della materia &egrave; uguale nell'uno e nell'altro mobile, dun&shy;<lb/>que il momento del grave N pendente nella linea HI appunto sar&agrave; uguale <lb/>al momento del mobile A posto in D, e per l'istessa ragione la forza o mo&shy;<lb/>mento del grave M pendente dalla linea. </s>

<s>HI sar&agrave; uguale al momento del <lb/>mobile B, che faccia forza in D. </s>

<s>E perci&ograve; come stanno fra loro i momenti <lb/>de'gravi M, N, cos&igrave; tra di loro stanno i momenti de'mobili B, A. </s>

<s>Ma per&shy;<lb/>ch&egrave; li gravi M, N son dell'istessa materia, e pendenti dal medesimo punto, <lb/>sar&agrave; il momento di M al momento di N come la mole M alla mole N. </s>

<s>Adun&shy;<lb/>que anco il momento di B al momento di A star&agrave; come la mole M alla <lb/>mole N, cio&egrave; come la mole di B alla mole di A, essendo l'una eguale al&shy;<lb/>l'una e l'altra all'altra &rdquo; (ivi, fol. </s>

<s>96). </s></p><p type="main">

<s>Sopra questa dimostrazione trover&agrave; forse da ridir qualche cosa chi ha <lb/>fatto l'abito oramai ai metodi nuovi, ma era pure conforme al nostro isti&shy;<lb/>tuto il dimostrare per qualche esempio qual si fosse l'incerto e faticoso eser&shy;<lb/>cizio dell'ali, prima che potesse il pensiero spiegar, come ora noi lo vediamo, <lb/>per l'aria il suo libero volo. </s>

<s>In ogni modo concludendo l'Aggiunti dalle sue <lb/>proposizioni che le quantit&agrave; di moto stanno in ragion composta delle velo&shy;<lb/>cit&agrave; e delle moli, e che perci&ograve;, stando queste velocit&agrave; e queste moli in re&shy;<lb/>ciproca ragione fra loro, esse quantit&agrave; sono eguali, veniva a sostituire un <lb/>principio universale di Meccanica a quello che il Mariotte diceva essere stato <lb/>mal provato da Archimede e da Galileo. </s></p><p type="main">

<s>Giovanni Wallis, sopra questo principio universale dell'ugualit&agrave; dei mo&shy;<lb/>menti, fond&ograve; nel 1670 l'edifizio della sua Statica, applicando alle macchine <lb/>principali le leggi della Libbra. </s>

<s>Scrisse intorno a questa, nella I parte del <lb/>suo trattato <emph type="italics"/>De motu,<emph.end type="italics"/> un libro particolare, la XII proposizion del quale si <lb/>espone cos&igrave; in s&egrave; e ne'suoi corollarii: &ldquo; Si idem sit Librae centrum atque <lb/>centrum motus, quae ex illa libera pendent gravia, aut etiam alias directe <lb/>vel subsunt vel incumbunt, in ea ratione ponderant, seu gravant sua re&shy;<lb/>spectiva brachia, caeteris paribus, quae ex rationibus ponderum et distan&shy;<lb/>tiarum punctorum applicationis a communi Librae et motus centre compo-<pb xlink:href="020/01/1947.jpg" pagenum="190"/>nitur. </s>

<s>Adeoque, si distantiae sint aequales, in ratione ponderum; si pondera <lb/>sint aequalia, in ratione distantiarum; si vel utraque sint aequalia vel sint <lb/>reciproce proportionalia, aequiponderant. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Idem intellige de viribus aliis, nempe in ea ratione movendo pollent <lb/>quae componitur ex rationibus virium et distantiarum a communi centro <lb/>motus et Librae, sive quod huius instar est, quibus directe applicantur vi&shy;<lb/>res &rdquo; (Londini 1670, pag. </s>

<s>82). </s></p><p type="main">

<s>Cos&igrave; fatti principii s'applicavano ugualmente bene, qualunque relazione <lb/>avessero fra loro le braccia della Libbra, propostasi innanzi alla mente come <lb/>oggetto di matematica contemplazione. </s>

<s>Ma quando questa Libbra mentale <lb/>veniva a scendere a'suoi pratici esercizii, e a farsi perci&ograve; materiata, s'ebbe <lb/>a riconoscere un intestino conflitto fra la teoria e l'esperienza, specialmente <lb/>in quella Bilancia di braccia eguali intorno agli effetti della quale tenevano <lb/>aperti gli occhi i compratori delle merci preziose, sollecitando la scienza a <lb/>suggerir la ragione e il modo di assicurarsi dal pericolo delle frodi. </s>

<s>Le sol&shy;<lb/>lecite cure, ch'essa scienza volentieri si prese, perch&egrave; si regolassero con <lb/>equa lance i contratti, sono antichissime e meritevoli di una pagina propria <lb/>nella storia delle Equiponderanze; pagina che noi ora vogliamo spiegar sotto <lb/>gli occhi dei nostri Lettori, dop'aver detto della regola de'momenti dal&shy;<lb/>l'ignorar la quale o dal professarla dipendono in gran parte. </s>

<s>come si di&shy;<lb/>ceva sulla fine dell'altra parte di questo discorso, alle speculazioni che pas&shy;<lb/>siamo a narrare o i corti voli o i provvidi avvedimenti. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Aristotile incomincia dalle Bilance le sue Meccaniche questioni, a ri&shy;<lb/>solver le quali accenna essere stato consigliato dal dovere dl scoprir le frodi, <lb/>che andavano macchinando i venditori di porpora, ora col non mettere nel <lb/>giusto mezzo lo sparto, ora coll'aggiungere all uno o all'altro bacino pez&shy;<lb/>zetti di piombo o barbe e nodi di legno: &ldquo; ligni enim gravior illa est pars <lb/>in qua est radix: nodus vero radix quaedam est &rdquo; (Operum, T. XI cit., <lb/>fol. </s>

<s>30). La ragione del quanto e del come cos&igrave; facendo defraudavano i detti <lb/>e simili altri venditori si not&ograve; che non seppe il Filosofo dedurla da'suoi veri <lb/>principii, cosicch&egrave; da capo cominciando le censure, i baldanzosi avversarii, <lb/>senza voler risparmiar nulla, le condussero fino in fondo. </s>

<s>Diremo di queste <lb/>censure poi per trattenerci ora intorno alla seconda meccanica questione, <lb/>che non si pot&egrave; n&egrave; anch'essa liberar da censure nuove e pi&ugrave; forti. </s></p><p type="main">

<s>&ldquo; Cur, domanda Aristotile sempre in proposito delle Bilance di braccia <lb/>eguali, siquidem sursum fuerit spartum, quando deorsum lato pondere quis&shy;<lb/>piam id amovet rursum ascendit Libra:-si autem deorsum constitutum fue&shy;<lb/>rit non ascendit sed manet? </s>

<s>&rdquo; (ibid.). Sia la Bilancia BC (fig. </s>

<s>80) per il <lb/>suo mezzo D superiormente sospesa in A: perch&egrave; abbassata a forza da C <pb xlink:href="020/01/1948.jpg" pagenum="191"/>in E, rimossa appena la mano, torna da questa forzata nella prima sua po&shy;<lb/><figure id="id.020.01.1948.1.jpg" xlink:href="020/01/1948/1.jpg"/></s></p><p type="caption">

<s>Figura 80.<lb/>sizion naturale? </s>

<s>E risponde Ari&shy;<lb/>stotile, supposto che sia ADM il <lb/>perpendicolo: &ldquo; quia DH maior <lb/>est dimidio &rdquo; (ibid.) e perci&ograve; dal <lb/>suo stesso maggior peso &egrave; quella <lb/>maggior parte costretta a scendere <lb/>nuovamente in basso. </s></p><p type="main">

<s>Tutt'altrimenti avviene, pro&shy;<lb/>segue a dire il Filosofo, quando <lb/>il punto di sospensione sia sotto <lb/>alla Bilancia CN come per esem&shy;<lb/>pio in M (fig. </s>

<s>81) perch&egrave; rimo&shy;<lb/>vendo essa Bilancia in OR, se sia <lb/>MD il perpendicolo, &ldquo; plus dimidio fit Librae quae deorsum est pars DO, <lb/><figure id="id.020.01.1948.2.jpg" xlink:href="020/01/1948/2.jpg"/></s></p><p type="caption">

<s>Figura 81.<lb/>quam quod perpendiculum secet: qua&shy;<lb/>propter non ascendit; elevata enim <lb/>pars levior est: ablato igitur onere, <lb/>necesse est manere &rdquo; (ibid. </s>

<s>ad tergum). </s></p><p type="main">

<s>Fra'primi e pi&ugrave; conosciuti pro&shy;<lb/>motori di Aristotile, nel secolo XVI, <lb/>Niccol&ograve; Tartaglia illustr&ograve;, nell'una e <lb/>nell'altra parte della Questione i con&shy;<lb/>cetti del Filosofo, e solo si compiacque <lb/>di aver dato della prima &ldquo; ragione al&shy;<lb/>quanto pi&ugrave; chiara et miglior figura &rdquo; <lb/>(Quesiti e invenzioni cit., fol. </s>

<s>79 a t.). <lb/>La seconda parte della proposta aristo&shy;<lb/>telica ha da queste precise parole la <lb/>pi&ugrave; piena conferma e il pi&ugrave; spiegato commento: &ldquo; Per essere adunque la <lb/>elevata parte DR di menor quantit&agrave; della inclinata OD, viene a esser pi&ugrave; <lb/>debole, ovver men potente di lei, e per&ograve; non &egrave; atta n&egrave; sofficiente a poterla <lb/>urtare e sforzare a farla ascendere al suo primo loco in C, come fece nella <lb/>passata, anzi quella rester&agrave; cos&igrave; inclinata al basso e la retener&agrave; lei cos&igrave; in <lb/>aere elevata &rdquo; (ivi, fol. </s>

<s>80). </s></p><p type="main">

<s>Cos&igrave; Aristotile per&ograve; come il Tartaglia peccano nel risolvere la Que&shy;<lb/>stione, commettendo nella prima parte impropriet&agrave;, e nella seconda un pa&shy;<lb/>tentissimo errore. </s>

<s>Guidubaldo del Monte si pot&egrave; salvare dall'uno e dall'altro <lb/>fallo, dimostrando la sua II e III proposizione <emph type="italics"/>De libra<emph.end type="italics"/> col principio de'cen&shy;<lb/>tri di gravit&agrave;, i quali, secondo che riescon sotto o sopra al punto della so&shy;<lb/>spensione, rendono alla macchina e al corpo o stabile o no l'equilibrio. </s></p><p type="main">

<s>Nella detta proposizione II, che corrisponde al primo caso della Que&shy;<lb/>stione aristotelica, considera Guidubaldo che, rimossa la Libbra, il centro di <lb/>gravit&agrave; D nella precedente figura LXXX s'&egrave; dovuto trasferire in G fuori <pb xlink:href="020/01/1949.jpg" pagenum="192"/>del perpendicolo, &ldquo; et quoniam AG horizzonti non est perpendicularis, ma&shy;<lb/>gnitudo ex ponderibus E, H composita in hoc situ minime persistet, sed <lb/>deorsum, secundum eius centrum gravitatis G, per circumferentiam GD mo&shy;<lb/>vebitur, donec AG horizonti fiat perpendicularis, scilicet donec AG in AD <lb/>redeat &rdquo; (Mechanic. </s>

<s>lib., Pisauri 1677, fol. </s>

<s>4). La nuova dimostrazione, mo&shy;<lb/>vendo da principii pi&ugrave; sicuri, &egrave; pi&ugrave; propria di quella di Aristotile e pi&ugrave; pre&shy;<lb/>cisa, perch&egrave;, mentre la ragion del Filosofo si faceva principalmente dipen&shy;<lb/>dere dal peso delle braccia della Bilancia, quella di Guidubaldo astrae da <lb/>questa material condizione, ed &egrave; perci&ograve; applicabile al caso, in cui secondo <lb/>gl'istituti archimedei si considerino i pesi sostenuti da leve imponderabili. </s></p><p type="main">

<s>Quanto al secondo caso della detta Question meccanica lo stesso Gui&shy;<lb/>dubaldo, nella proposizione sua III, sempre scorto da quella fida regola ba&shy;<lb/>ricentrica, corregge il gravissimo errore di Aristotile, inconsideratamente ri&shy;<lb/>petuto, come udimmo, dal Tartaglia: e perciocch&egrave;, rimossa la Bilancia in OR, <lb/>nell'antecedente figura LXXXI, il centro di gravit&agrave; s'&egrave; dovuto trasferire in <lb/>G, e GM perci&ograve; non pi&ugrave; riesce perpendicolare all'orizzonte &ldquo; magnitudo, <lb/>dunque di qui ne conclude, ex O, R ponderibus composita, in hoc situ <emph type="italics"/>mi&shy;<lb/>nime manebit,<emph.end type="italics"/> sed secundum eius gravitatis centrum G deorsum per cir&shy;<lb/>cumferentiam GH movebitur &rdquo; (ibid., fol. </s>

<s>5). </s></p><p type="main">

<s>&Egrave; ora una cos&igrave; fatta conclusione manifestamente contraria a quella di <lb/>Aristotile, il quale aveva detto nel sopra allegato testo che, rimossa la Bi&shy;<lb/>lancia dal sito suo orizzontale, ivi <emph type="italics"/>necesse est manere.<emph.end type="italics"/> Notabile &egrave; a questo <lb/>proposito che Guidubaldo, invece di reclamare contro l'errore scoperto, si <lb/>lusinghi di ridurre i falsi sensi del Filosofo alle pi&ugrave; chiare espressioni del <lb/>vero. </s>

<s>&ldquo; Aristotelis quoque ratio hic perspicua erit: si enim punctum D (nella <lb/>preposta figura LXXXI) ubi OR, DM se invicem secant; erit DO maior DR, <lb/>et quoniam DM perpendiculum, secundum ipsum Aristotilem, Libram OR <lb/>in partes inaequales dividit, et maior pars est versus O, hoc est DO: Libra <lb/>OR ex parte O deorsum movebitur, cum id quod plus est deorsum fera&shy;<lb/>tur &rdquo; (ibid., fol. </s>

<s>25 ad t.). </s></p><p type="main">

<s>Si pu&ograve; facilmente concedere, supposto che la ponderosit&agrave; della Bilancia <lb/>resulti non da'pesi soli ma e dalle braccia, che la ragion di Aristotile sia <lb/>da questo commento resa fin qui perspicua: ma quel che segue bench&egrave; <lb/>Guidubaldo non faccia vista, e non sospetti che se n'abbiano ad avvedere i <lb/>sagaci lettori, la rende apertamente contradittoria, perch&egrave; mentre l&agrave; nelle <lb/>Questioni meccaniche si diceva che, rimosso in O (nella passata fig. </s>

<s>LXXXI) <lb/>lo strumento, <emph type="italics"/>necesse est ibi manere,<emph.end type="italics"/> qui, nel libro <emph type="italics"/>Mechanicorum,<emph.end type="italics"/> si sog&shy;<lb/>giunge cos&igrave;, descrivendo con tutta la pi&ugrave; desiderabile precisione le condi&shy;<lb/>zioni e gli effetti degl'instabili equilibrii: &ldquo; Similiter ex dictis quoque eli&shy;<lb/>ciemus Libram OR, centrum habens infra libram, quo magis a situ CN <lb/>distabit velocius moveri. </s>

<s>Centrum enim gravitatis G, quo magis a puncto D <lb/>distat, eo velocius pondus ex O, R ponderibus Libraque OR compositum <lb/>movebitur, donec angulus CGO rectus evadat: adhuc insuper velocius mo&shy;<lb/>vebitur quo Libram a centro D magis distabit &rdquo; (ibid.). </s></p><pb xlink:href="020/01/1950.jpg" pagenum="193"/><p type="main">

<s>La riverenza, o forse pi&ugrave; veramente il timore di non avere a scanda&shy;<lb/>lizzare o provocarsi l'odio degli adoratori del Nume, consigli&ograve; a Guidubaldo <lb/>la prudenza di questa logica, ma il Benedetti, senza tante paure e senza <lb/>tanti riguardi, disse a chi lo voleva sapere che Aristotile, nella seconda parte <lb/>della sua seconda meccanica Questione, &ldquo; toto coelo aberrat, quia necessa&shy;<lb/>rium est ut Libra omnino cadat &rdquo; (Specul. </s>

<s>liber cit., pag. </s>

<s>154). </s></p><p type="main">

<s>Procedendo con la medesima libert&agrave; in esaminar la prima parte della <lb/>Questione, tutt'altro che commentare ossequiosamente il testo, come fa Gui&shy;<lb/>dubaldo, argutamente il Benedetti notava che, non deducendola dalla gene&shy;<lb/>ralit&agrave; de'principii, non poteva risolvere Aristotile la sua stessa propostasi <lb/>questione, che con certe sue difettose ragioni. </s>

<s>Causa, diceva, del tornare <lb/>dalla posizion violenta alla naturale la Libbra, &ldquo; non solum est maior quan&shy;<lb/>titas ponderis brachiorum, quae iam praetergressa est ultra verticalem li&shy;<lb/>neam, sed etiam est longitudo brachii elevati, quae ultra verticalem lineam <lb/>reperitur, unde eius extremi pondus redditur gravius in proportione &rdquo; (ibid.): <lb/>ci&ograve; che mostrasi dal Benedetti stesso anche pi&ugrave; evidente, abbassando dal <lb/>punto H, nella figura LXXX, la verticale HQ, e da E conducendo la oriz&shy;<lb/>zontale EQ, per esser dalla differenza delle due linee EM, MQ esattamente <lb/>misurata la differenza dei due momenti. </s></p><p type="main">

<s>Voleva cos&igrave; confermare il Matematico veneziano l'utilit&agrave; della Regola <lb/>delle distanze dal perpendicolo, per risolvere con precisione sicura questa e <lb/>altre simili statiche questioni, e perch&egrave; vedemmo non essere, a mezzo il se&shy;<lb/>colo XVI, quella Regola nuova, si potrebbe congetturare che, in ridurre a <lb/>maggior precisione e in correggere i primi aristotelici quesiti dall'errore, <lb/>non fossero stati n&egrave; Guidubaldo n&egrave; il Benedetti stesso dei primi. </s>

<s>Vengono <lb/>ora le congetture a ridursi a certezza di fatti, per le Note di Leonardo da <lb/>Vinci, in una delle quali si legge: &ldquo; La Bilancia di braccia e pesi eguali, <lb/>rimossa dal sito della egualit&agrave;, far&agrave; braccia e pesi ineguali, onde necessit&agrave; <lb/>la costringe a racquistare la perduta egualit&agrave; di braccia e di pesi. </s>

<s>Provasi <lb/>per la II di questo, e si prova, perch&egrave; il peso pi&ugrave; alto &egrave; pi&ugrave; remoto dal <lb/>centro del circonvolubile, che il peso pi&ugrave; basso, e pertanto ha pi&ugrave; debole <lb/>sostentamento, onde pi&ugrave; facilmente discende e leva in alto la opposta parte <lb/>del peso congiunto allo estremo del braccio minore &rdquo; (Manuscr. </s>

<s>E cit., <lb/>fol. </s>

<s>59). Ora, perch&egrave; la distanza del peso H, nella solita figura LXXX, dal <lb/>circonvolubile, ossia da qualunque punto della linea verticale, &egrave; MQ, e la <lb/>distanza del peso E &egrave; manifestamente EM, veniva dunque la prima parte <lb/>della Questione seconda di Aristotile risoluta da Leonardo, prima che dal <lb/>Benedetti, con la maggior possibile precisione, applicandovi la Regola dei <lb/>momenti. </s></p><p type="main">

<s>N&egrave; la seconda parte della medesima Questione, che si proponeva dal <lb/>gran Maestro della Meccanica a tutti gli studiosi di allora, poteva passare <lb/>alla scienza di Leonardo inosservata. </s>

<s>Cos&igrave; infatti si legge in quest'altra sua <lb/>Nota, tenendo, nel computar la variet&agrave; dei momenti la stessa regola seguita <lb/>di sopra: &ldquo; Quanto lo estremo della superiore parte della Bilancia s'avvi-<pb xlink:href="020/01/1951.jpg" pagenum="194"/>cina pi&ugrave; alla linea perpendicolare, che non fa lo estremo della parte infe&shy;<lb/>riore, tanto pi&ugrave; lungo e ponderoso si trover&agrave; il braccio inferiore che il su&shy;<lb/>periore, essendo l'asse d'egual qualit&agrave; &rdquo; (Manuscr. </s>

<s>Ash. </s>

<s>N.02038, Paris 1891, <lb/>fol. </s>

<s>3). Tornando dunque indietro alla figura LXXXI, prolungata la perpen&shy;<lb/>dicolare da una parte e dall'altra, e da essa, con le linee RP, OQ, misurate <lb/>le distanze di R, e di O, dice Leonardo, esser di tanto maggior momento <lb/>O, di R, quanto &egrave; pi&ugrave; lunga la distanza OQ della distanza PR, com'era per <lb/>ripeter poi, sulla costruzione medesima, il Benedetti. </s></p><p type="main">

<s>Nella ora letta Nota il manoscritto vinciano non si spiega pi&ugrave; avanti, <lb/>n&egrave; noi ci siamo abbattuti a leggere altrove qual si fosse l'opinione di Leo&shy;<lb/>nardo intorno allo stato o al moto della Bilancia OR, se cio&egrave; la si rimanga <lb/>a quel modo inclinata, come, con Aristotile, diceva il Tartaglia, o s'ella se&shy;<lb/>guiti a scendere infino a capovolgersi perpendicolare, come dalle teorie dei <lb/>centri di gravit&agrave; ebbe a concluderne Guidubaldo. </s>

<s>Noi siamo certi che anche <lb/>Leonardo, leggendo il testo, deve aver come il Benedetti esclamato che il <lb/>Filosofo <emph type="italics"/>toto coelo aberrat,<emph.end type="italics"/> ed &egrave; la nostra certezza fondata nel saper che lo <lb/>stesso Leonardo aveva benissimo divisate le condizioni del vario equilibrio, <lb/>il quale pu&ograve; allora solamente, diceva, essere stabile &ldquo; quando il centro di <lb/>gravit&agrave; di ciascuno peso sospeso si stabilisca sotto il suo sostentacolo &rdquo; (Ma&shy;<lb/>nuscr. </s>

<s>B cit., fol. </s>

<s>18 a tergo). Quando dunque il centro di gravit&agrave; riman <lb/>sopra al sostentacolo stesso, come in quel secondo caso della Bilancia, non <lb/>pu&ograve; essere in essa alcuna stabilit&agrave;, e perci&ograve; tutt'altro che rimanere segui&shy;<lb/>ter&agrave;, sempre pi&ugrave; precipitando, la sua discesa. </s></p><p type="main">

<s>Fra le Questioni, promosse da Aristotile intorno all'equilibrio delle Bi&shy;<lb/>lance di braccia eguali, se n'agitava, infino dagli stessi tempi di Leonardo <lb/>da Vinci, un'altra, lasciata dal Filosofo addietro, e in proposito della quale <lb/>finge Niccol&ograve; Tartaglia di avere avuto col signore ambasciator di Mendoza <lb/>il seguente colloquio: <emph type="italics"/>&ldquo; Signor ambasciator.<emph.end type="italics"/> Ma se ben me aricordo voi <lb/>dicesti anchora, nel principio del nostro ragionamento, che Aristotile pre&shy;<lb/>termette over tace una questione sopra delle dette Libre, di non puoca im&shy;<lb/>portantia, over speculatione: hor ditime che question &egrave; questa. <emph type="italics"/>Nicol&ograve;.<emph.end type="italics"/> Se <lb/>vostra Signoria ben se aricorda della sua seconda questione, in questa ivi in&shy;<lb/>terrogatamente adimanda et consequentemente dimostra perch&egrave; causa, quando <lb/>chel sparto sera di sopra della Libra, et che luno di brazzi di quella da qual&shy;<lb/>che peso s&igrave;a portato over spinto a basso, remosso che sia over levato via <lb/>quel tal peso, la detta Libra di nuovo reascende e ritorna al suo primo luoco. </s>

<s><lb/>Et sel detto sparto &egrave; di sotto della detta Libra, et che medesimamente luno <lb/>di suoi brazzi sia da qualche peso pur portato over spinto a basso, remosso, <lb/>over levado che sia via quel tal peso, la detta Libra non riascende n&egrave; ri&shy;<lb/>torna al suo primo luoco, come che fu nellaltra positione, ma rimane di <lb/>sotto cio&egrave; a basso. </s>

<s>Hor dico che lui pretermette over tace unaltra questione, <lb/>che in questo luoco se convegnaria, di molta maggior speculatione di ca&shy;<lb/>dauna delle sopradette, la qual question &egrave; questa: Perch&egrave; causa, quando <lb/>chel sparto &egrave; precisamente in essa Libra, e che lun di brazzi di quella sia <pb xlink:href="020/01/1952.jpg" pagenum="195"/>da qualche peso portato, over urtado a basso, remosso, over levado che sia <lb/>via quel tal peso, la detta Libra di nuovo reascende al suo primo luoco, <lb/>si come che fa anchora quella che ha il sparto di sopra da lei &rdquo; (Quesiti et <lb/>inventioni cit., fol. </s>

<s>79). </s></p><p type="main">

<s>La questione, che qui Niccol&ograve; proponeva all'Ambasciator come nuova, <lb/>era stata messa in campo tre secoli avanti da Giordano Nemorario, il quale <lb/>formulava cos&igrave; la seconda delle sue XIII proposizioni <emph type="italics"/>De ponderibus:<emph.end type="italics"/> &ldquo; Cum <lb/>fuerit aequilibris aequalis, aequis ponderibus appensis, ab aequalitate non <lb/>recedet: et si ab aequidistantia separetur, ad aequalitatis situm revertetur &rdquo; <lb/>(Editio cit., pag. </s>

<s>9). </s></p><p type="main">

<s>Dimostrava il Matematico tedesco questa sua proposizione con la va&shy;<lb/>riet&agrave; dei momenti, computati nella quantit&agrave; del discenso verticale, secondo <lb/>il suo proprio instituto, cecamente seguito, come accennavano le sopra ci&shy;<lb/>tate parole, dal Tartaglia, il quale non seppe avvedersi che, sebben fosse <lb/>quella istituita regola giusta, veniva nonostante al caso male applicata. </s>

<s>In&shy;<lb/>torno a ci&ograve; i Matematici precedenti dovevano avere avuto qualche contro&shy;<lb/>versia, come apparisce dalle Note di Leonardo, il quale non si poteva per&shy;<lb/>suadere della verit&agrave; della proposizion di Giordano, a quel modo che facevano <lb/>tanti altri a'suoi tempi, sull'autorit&agrave; del Maestro. </s>

<s>Il popolano di Vinci, edu&shy;<lb/>catosi l'ingegno fuor della Scuola, seguitava piuttosto l'infallibile autorit&agrave; <lb/>della Geometria, ta quale gli ragionava che, se la Libbra &egrave; di braccia e di <lb/><figure id="id.020.01.1952.1.jpg" xlink:href="020/01/1952/1.jpg"/></s></p><p type="caption">

<s>Figura 82.<lb/>pesi eguali, sospesa nel suo centro di gravit&agrave;, deve <lb/>in qualunque posizione rimanere equilibrata, sem&shy;<lb/>pre serbando, i pesi, eguali i loro momenti. </s></p><p type="main">

<s>La dimostrazione era chiara, computando con <lb/>la regola delle distanze orizzontali dal circonvolubile <lb/>quegli stessi momenti, perch&egrave; rimossa la Libbra ZQ <lb/>(fig. </s>

<s>82) in BM, per esempio, o in AN, essendo i <lb/>momenti BXOD con MXOR, e AXOC con <lb/>NXOP esattamente eguali, dee l&igrave; dove fu lasciata <lb/>rimanere in perfetto equilibrio. </s>

<s>La teoria dall'altra parte veniva a Leonardo <lb/>confermata dall'esperienza della ruota o del cerchio girato intorno al suo polo. </s></p><p type="main">

<s>Per dimostrare poi pi&ugrave; chiaramente la cosa, in un tempo solo, con le <lb/>ragioni e coi fatti, immaginava Leonardo di avere una tavoletta di basi ret&shy;<lb/>tangolari, esattamente impolata nel suo centro di gravit&agrave; e di figura, e cos&igrave; <lb/>sotto, il titolo <emph type="italics"/>Sperientia della Bilancia,<emph.end type="italics"/> scriveva: &ldquo; Questa Bilancia rester&agrave; <lb/>dove tu la lasci, come fa il cerchio intorno al suo polo. </s>

<s>Per tutte le ragioni <lb/>dette questa Bilancia non si mover&agrave; dal suo sito, avendo rispetto al centro <lb/>del mondo &rdquo; (Manuscr. </s>

<s>G cit., fol. </s>

<s>78 a tergo). Poi, per dichiarar meglio il <lb/>suo pensiero, ch'egli accenna di aver notato anche altrove; sotto l'ultima <lb/>di queste righe soggiunge: </s></p><p type="main">

<s>&ldquo; Se la ponderazione della Bilancia sar&agrave; fatta in polo vicino al punto <lb/>matematico, che si fa centro della gravit&agrave; della Bilancia; allora le braccia <lb/>eguali della Bilancia resteranno in quella obliquit&agrave;, che la mano dell'uomo <pb xlink:href="020/01/1953.jpg" pagenum="196"/>la lascer&agrave;. </s>

<s>Provasi, perch&egrave; la linee BD (fig. </s>

<s>83), nel mezzo della quale &egrave; <lb/><figure id="id.020.01.1953.1.jpg" xlink:href="020/01/1953/1.jpg"/></s></p><p type="caption">

<s>Figura 83.<lb/>situato il centro matematico della Bilancia, divide la <lb/>quantit&agrave; della Bilancia nelli due triangoli BCD, DBE, <lb/>li quali sono infra loro simili e eguali in figura e <lb/>in peso, sol si variano nella situazione. </s>

<s>Ma per tal <lb/>variazione non si variano li pesi dalla linea centrale <lb/>del polo BD, perch&egrave; l'angolo superiore C del trian&shy;<lb/>golo BCD &egrave; tanto remoto dalla linea centrale BD, <lb/>quanto si sia l'angolo E, come mostra la linea EP, <lb/>e perch&egrave; &egrave; provato non dare noia da essere pi&ugrave; alto <lb/>l'un peso che l'altro, cio&egrave; l'angolo C che l'an&shy;<lb/>golo E &rdquo; (ivi). </s></p><p type="main">

<s>Ma per far la dimostrazione anche pi&ugrave; precisa <lb/>riduceva Leonardo tutto il peso de'due triangoli <lb/>eguali ne'loro centri di gravit&agrave; N, E, d'onde condotte le NM, EF perpen&shy;<lb/>dicolari alla linea centrale BD, si rende manifesto che, rimanendo fra loro <lb/>in qualunque posizione l'egualit&agrave; dei due triangoli rettangoli BMN, EFD, <lb/>anche le distanze EF, MN si serbano in qualunque modo fra loro eguali. </s>

<s><lb/>Ci&ograve; che laconicamente disse Leonardo in queste parole sottoscritte alle pre&shy;<lb/>cedenti: &ldquo; Noi abbiamo concluso che tal Bilancia non avr&agrave; moto, essendo <lb/>il suo centro matematico in mezzo a tutti li oppositi pesi fra loro eguali &rdquo; (ivi). </s></p><p type="main">

<s>Questo riguardar le cose sotto vario aspetto, come ci rivelano le addotte <lb/>Note, per meglio certificarsi di aver veduto il vero, &egrave; indizio manifeste delle <lb/>contradizioni che dovette patire Leonardo dai seguaci del Nemorario, i quali <lb/>uscirono poi dalle private disputazioni in pubblico nelle Opere del Tarta&shy;<lb/>glia e del Cardano. </s>

<s>Nell'ottavo libro dei Quesiti il primo de'due detti Ma&shy;<lb/><figure id="id.020.01.1953.2.jpg" xlink:href="020/01/1953/2.jpg"/></s></p><p type="caption">

<s>Figura 84.<lb/>tematici dimostra la proposizione II di Giordano <lb/>concludendola, come Giordano stesso, dalla inegua&shy;<lb/>lit&agrave; dei momenti virtuali che, rimossa la Bilancia <lb/>dalla orizzontale, sollecitano la caduta de'due pesi. </s></p><p type="main">

<s>Sia la Bilancia orizzontale AB (fig. </s>

<s>84) ri&shy;<lb/>mossa in DC: vuol dimostrare il Tartaglia che ivi <lb/>non rimarr&agrave;, perch&egrave; il peso D avendo maggior mo&shy;<lb/>mento di C, viene a ridurla in basso. </s>

<s>Che il mo&shy;<lb/>mento di D sia veramente maggiore di C lo prova, <lb/>perch&egrave; avendo a scendere per eguale spazio, come <lb/>per esempio D in E, e C in F, D acquista maggiore quantit&agrave; del descenso <lb/>essendo IH maggiore di GF. </s></p><p type="main">

<s>&ldquo; Dico che il corpo B, scrive il Tartaglia, stante quel nel punto D viene <lb/>a esser pi&ugrave; grave, secondo il sito, del corpo A, stante quello in ponto C, <lb/>perch&egrave; il decenso del detto corpo B dal ponto D nel ponto E &egrave; pi&ugrave; rettto <lb/>del decenso del corpo A dal ponto C nel ponto F, per la seconda parte <lb/>della quarta petitione, perch&egrave; capisse pi&ugrave; della linea della diretione, cio&egrave; che <lb/>nel discendere il detto corpo B dal ponto D nel ponto E, lui capisse over <pb xlink:href="020/01/1954.jpg" pagenum="197"/>piglia della linea della diretione la parte IH, ed il corpo A, nel discendere <lb/>dal ponto C nel ponto F, lui caperia della detta linea della diretione la parte <lb/>GF. </s>

<s>E perch&egrave; la parte IH &egrave; maggiore della linea over parte CF, per la <lb/>17a diffinizione, pi&ugrave; obliquo sar&agrave; il decenso dal ponto C al ponto F di quello <lb/>dal ponto D al ponto E. Onde, per la seconda parte della quarta petitione, <lb/>il corpo B in tal positione sar&agrave; pi&ugrave; grave secondo il sito del corpo A..... <lb/>E per&ograve; al detto corpo B far&agrave; reascendere il detto corpo A al ponto A, suo <lb/>primo et condecente luoco, et lui medesimamente discendar&agrave; nel ponto B, <lb/>pur suo primo et condecente luoco, cio&egrave; nel sito della egualit&agrave;. </s>

<s>nel qual <lb/>sito li detti dui corpi se trovarano egualmente gravi secondo el sito, et per&shy;<lb/>ch&egrave; sono anchora simplicemente egualmente gravi se conservarano nel detto <lb/>luoco &rdquo; (fol. </s>

<s>89 a tergo). </s></p><p type="main">

<s>Fu detto da alcuni, e ripetuto da molti, che il Cardano sent&igrave; anch'egli, <lb/><figure id="id.020.01.1954.1.jpg" xlink:href="020/01/1954/1.jpg"/></s></p><p type="caption">

<s>Figura 85.<lb/>degli effetti della Bilancia rimossa dalla oriz&shy;<lb/>zontale, come il Nemorario commentato da que&shy;<lb/>ste parole del Tartaglia. </s>

<s>Ma nel libro I <emph type="italics"/>De <lb/>subtilitate,<emph.end type="italics"/> che &egrave; il luogo propriamente citato <lb/>da costoro, si conclude intorno alla seconda <lb/>Question meccanica di Aristotile con dire che <lb/>non &egrave; ci&ograve; dimostrato da Giordano, n&egrave; inteso. </s>

<s><lb/>Consisteva quel discorso nel provare che in F <lb/>(fig. </s>

<s>85) il peso della Bilancia CD &egrave; men grave <lb/>che in C, per la giusta ragione della inegua&shy;<lb/>lit&agrave; dei momenti, cos&igrave; misurati dalle distanze <lb/>FP, CB, come dai discensi OP, BM, e dopo <lb/>questo soggiunge: &ldquo; Ex hoc autem demon&shy;<lb/>stratur quod dicit Philosophus quod, si aequalia sint pondera in F et C, <lb/>Libra tamen sponte redit ad situm CD, ubi trutina sit AB. </s>

<s>Nec hoc de&shy;<lb/>monstrat Jordanus nec intellexit &rdquo; (Op. </s>

<s>T. III cit., pag. </s>

<s>369). </s></p><p type="main">

<s>&Egrave; chiaro dunque di qui che il discorso del Cardano tendeva a ritrovar <lb/>la vera ragion matematica della prima parte della seconda Questione aristo&shy;<lb/>telica, relativa alle condizioni dell'equilibrio nella Bilancia sospesa dalla parte <lb/>di sopra. </s>

<s>Passa poi a trattare dell'altro caso, quando cio&egrave; il sostegno ri&shy;<lb/>manga al disotto, e dice che, abbassatosi il peso in R, &ldquo; non solum non re&shy;<lb/>vertitur ad situm CD, imo magis R descendit versus Q, et F ascendit ver&shy;<lb/>sus A, ut experimento patet. </s>

<s>Hoc etiam Jordanus non demonstravit &rdquo; (ibid.). </s></p><p type="main">

<s>Ed &egrave; vero che Giordano non lo dimostr&ograve;, perch&egrave; non era il suo intento, <lb/>ma &egrave; curioso che si dica essere stato ci&ograve; dimostrato da Aristotile, il quale, <lb/>come udimmo dalla lettura del testo, avea asserito tutto il contrario da quel <lb/>che il Cardano stesso diceva essere per esperienza manifesto. </s>

<s>Non si sa poi <lb/>dove si legga il nuovo principio statico attribuito al Filosofo che cio&egrave; il mag&shy;<lb/>giore angolo, fatto dalla trutina con le braccia, renda maggiore da quella <lb/>parte il peso della Bilancia. </s>

<s>&ldquo; Aristotiles dicit hoc contingere quum trutina <lb/>est supra Libram, quia angulus QBF metae maior est angulo QBR. </s>

<s>Et si-<pb xlink:href="020/01/1955.jpg" pagenum="198"/>militer, quum trutina fuerit QB, erit meta AB, et tunc angulus BBA maior <lb/>erit angulo FBA. </s>

<s>Sed maior angulus reddit gravius pondus, igitur, dum tru&shy;<lb/>tina superius est, F erit gravius R, ideo F trahet Libram versus C; et, dum <lb/>fuerit inferius, R erit gravius quam F, ideo trahet Libram versus Q &rdquo; (ibid.). </s></p><p type="main">

<s>Aristotile aveva detto invece che R <emph type="italics"/>necesse est manere,<emph.end type="italics"/> e avea detto <lb/>contro la ragion matematica e contro l'esperienza. </s>

<s>Ma se fa bene il Car&shy;<lb/>dano a gettare un velo sulle vergogne del Padre, non era per&ograve; necessario <lb/>il far mendace vista al mondo che quel velo posticcio fosse l'abito proprio <lb/>e naturale. </s>

<s>Avrebbe in qualunque modo fatto assai meglio a difendere la <lb/>verit&agrave;, senza accettazion di persona; ci&ograve; che l'avrebbe fatto meno ligio ad <lb/>Aristotile, e pi&ugrave; giusto con Giordano, la seconda proposizion del quale fu <lb/>lui che non la dimostr&ograve; e non la intese. </s>

<s>Fra quelle cardaniche speculazioni <lb/>infatti non si trova nemmeno un cenno dell'equilibrio della Bilancia, non <lb/>sospesa n&egrave; sopra n&egrave; sotto, ma nel suo proprio centro. </s></p><p type="main">

<s>Il Cardano insomma e il Tartaglia, l'uno fedel seguace del Nemorario <lb/>e l'altro capriccioso interpetre di Aristotile, sono gli esemplari de'matema&shy;<lb/>tici di poco anteriori, co'quali ebbe Leonardo le sue controversie, decise <lb/>oramai, sopra le riferite cose, nel giudizio de'nostri matematici Lettori. </s>

<s>Ma <lb/>la risoluzion finale dipende da considerazioni un poco pi&ugrave; sottili, per dir <lb/>delle quali, a complemento di questa storia, ci convien ritornare indietro ai <lb/>colloqui, ch'ebbe Giovanni di Beugrand in Roma con Benedetto Castelli. </s></p><p type="main">

<s>Dop'avere inteso dal Matematico francese che i corpi, avvicinandosi al <lb/>centro della Terra, diventano sempre men gravi, maravigliato il Nostro di <lb/>quella novit&agrave; incominci&ograve; a pensare fra s&egrave; alle strane conseguenze, una delle <lb/>quali, scriveva a Galileo pochi giorni di poi, &egrave; questa: &ldquo; che io non so pi&ugrave; <lb/>dove sia il centro di gravit&agrave; di una sfera, poich&egrave;, intesa segata la sfera in <lb/>due parti eguali da un piano orizzontale, essendo la parte che &egrave; verso il <lb/>centro pi&ugrave; vicina al centro della Terra, che non &egrave; l'altro emisfero; sar&agrave; <lb/>ancora meno grave, e dovendo il centro di gravit&agrave; del composto di tutti e <lb/>due gli emisferi essere nella linea che congiunge il loro centro di gravit&agrave;, <lb/>e in quel punto di essa, che la divide in modo che la parte che tocca al <lb/>minor peso, alla parte che tocca al maggior peso abbia la proporzione re&shy;<lb/>ciproca che ha il maggior peso al minore; &egrave; manifesto che il centro di gra&shy;<lb/>vit&agrave; di tutta la sfera non pu&ograve; essere nel centro di magnitudine, come si <lb/>pensa che sia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma quello che accresce in me la maraviglia &egrave; che, portando la me&shy;<lb/>desima sfera pi&ugrave; verso il centro della Terra, si van continuamente mutando <lb/>le proporzioni delle distanze dei due emisferi, e cos&igrave; il centro della gravit&agrave; <lb/>del composto dei due emisferi si ander&agrave; sempre mutando, n&egrave; mai si potr&agrave; <lb/>determinare il centro di gravit&agrave; di una sfera, senza la relazione della lon&shy;<lb/>tananza dei centri di gravit&agrave; dei due emisferi dal centro della Terra. </s>

<s>&rdquo; <lb/>(Alb. </s>

<s>X, 121, 22). </s></p><p type="main">

<s>Avendo comunicato poi il Castelli cos&igrave; fatti pensieri, che gli passavano <lb/>per la mente, al Nardi, questi, dop'aver riformata la Statica archimedea, <pb xlink:href="020/01/1956.jpg" pagenum="199"/>come si vide, raccolse dal suo discorso alcuni quesiti e corollari importanti, <lb/>dai quali dovea dipendere quella final risoluzione del problema della Bilan&shy;<lb/>cia, che poco fa si diceva. </s>

<s>Se i pesi variano, ragionava fra s&egrave; esso Nardi, <lb/>secondo le distanze dal centro terrestre, non &egrave; dunque il primo postulato <lb/>di Archimede. <emph type="italics"/>Petimus aequalia pondera ab aequalibus distantiis aequi&shy;<lb/>ponderare,<emph.end type="italics"/> vero assolutamente, ma nel solo caso che la Bilancia stia oriz&shy;<lb/>zontale. </s>

<s>E qui gli si riduceva alla memoria la seconda proposizion di Gior&shy;<lb/>dano, l'enunciato della quale aveva fin allora, come Leonardo, creduto falso, <lb/>ma che ora vedeva esser salvo, non gi&agrave; dalle ragioni addotte dallo stesso <lb/>Giordano, ma perch&egrave; il peso sollevato, essendo pi&ugrave; distante dal centro della <lb/>Terra, &egrave; pi&ugrave; grave, e dee far perci&ograve; tornare la Bilancia alla prima sua po&shy;<lb/>sizione orizzontale, bench&egrave; l'eccessiva distanza da noi a quell'infimo centro <lb/>ne impedisca di vederne con gli occhi l'effetto. </s>

<s>Che poi i corpi pesino tanto <lb/>pi&ugrave;, quanto da quello stesso centro del mondo son pi&ugrave; distanti, come il <lb/>Beaugrand aveva detto al Castelli, sembrava al Nardi molto probabile: sem&shy;<lb/>brava probabile cio&egrave; che intorno al centro della Terra, mantenessero i corpi <lb/>la ragion medesima di egualit&agrave;, che intorno al centro della Bilancia, nella <lb/>quale pure si osserva che tanto son pi&ugrave; pesi quanto son pi&ugrave; lontani. </s></p><p type="main">

<s>Di questi pensieri ci lasci&ograve; il Nardi stesso scritta la memoria dopo il <lb/>discorso, altrove da noi disteso, e nel quale, riguardando le forze conver&shy;<lb/>genti, presentava sotto un nuovo punto di vista gli antichi teoremi archi&shy;<lb/>medei. </s>

<s>&ldquo; Molti e importanti quesiti e corollari, egli dice, dal presente di&shy;<lb/>scorso si potrebbero fare e raccorre, onde per esempio cercherassi se pesi <lb/>eguali, disegualmente rimossi dal centro, pesin disegualmente, e se pi&ugrave; pe&shy;<lb/>sino i pi&ugrave; lontani. </s>

<s>Quando ci&ograve; sia vero, non sar&agrave; assolutamente vera la prima <lb/>domanda di Archimede. </s>

<s>Pare certamente probabile che, se il punto G (fig. </s>

<s>86) <lb/><figure id="id.020.01.1956.1.jpg" xlink:href="020/01/1956/1.jpg"/></s></p><p type="caption">

<s>Figura 86.<lb/>s'intenda trasportato nel centro D, mantenghino i pesi <lb/>in E e in I le stesse ragioni di egualit&agrave; in detto centro <lb/>che fuori, e cos&igrave; il piccolo lontano contrappeser&agrave; al <lb/>grande vicino, l&agrave; dove nel centro D mancheranno in <lb/>tutto di momento i gravi, che ivi si quietano. </s>

<s>Scorgesi <lb/>di qui che vera saria l'opinione di quelli, i quali vole&shy;<lb/>vano che la linea EI, non parallela ad AC per qualche <lb/>violenza, dovesse, tolta tal violenza, ritornar parallela, <lb/>ma la ragione di ci&ograve; essi ad altro non molto felicemente <lb/>riferivano. </s>

<s>&Egrave; ben vero che ad essi conveniva asserire, <lb/>concordemente con tutti quelli i quali la stessa opinione <lb/>approvavano, che la lontananza dal centro cos&igrave; ecces&shy;<lb/>siva impedisce tal effetto, non altrimenti che impedisce all'occhio il veder <lb/>l'inclinazione delle due linee, che dagli estremi della Bilancia concorrono <lb/>prodotte nel centro. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>873). </s></p><p type="main">

<s>Apparisce da questo documento che i pensieri del Beaugrand e del Ca&shy;<lb/>stelli vennero a ridestare le controversie intorno all'equilibrio della Bilancia, <lb/>nella quale sieno collocati i centri delle grandezze; pensieri e controversie <pb xlink:href="020/01/1957.jpg" pagenum="200"/>che il Nardi comunic&ograve; al Torricelli, in sul punto ch'era questi per dimo&shy;<lb/>strare i venti modi varii di quadrar la Parabola. </s>

<s>Le rumorose novit&agrave; veni&shy;<lb/>vano a mettere qualche scrupolo in que'torricelliani teoremi, che l'Autore <lb/>avea condotti secondo gl'instituti archimedei, seguiti anche da Galileo, ma <lb/>non curando cos&igrave; fatte sottigliezze, reputate inutili e inefficaci, mantenne, per <lb/>le medesime ragioni di Leonardo che, o fossero i pesi pi&ugrave; alti o pi&ugrave; bassi <lb/>nella Libbra, o fosse essa Libbra orizzontale o inclinata, s'equiponderino le <lb/>gravit&agrave;, quand'hanno reciproca ragione alle distanze, o quand'esse gravit&agrave; <lb/>sono eguali e sono appese a distanze parimente eguali. </s>

<s>Fra i supposti infatti <lb/>premessi al trattato <emph type="italics"/>De dimensione parabolae<emph.end type="italics"/> pose in VI luogo anche que&shy;<lb/>sto: &ldquo; Aequalia gravia ex aequalibus distantiis aequiponderant, sive Libra <lb/>ad horizontem parallela fuerit sive inclinata; et gravia eandem reciproce ra&shy;<lb/>tionem habentia quam distantiae aequiponderant, sive Libra sit ad horizon&shy;<lb/>tem parallela sive inclinata &rdquo; (Opera geom. </s>

<s>cit., P. II, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Bench&egrave; dunque, poco prima del 1644, avesse il Torricelli deliberato di <lb/>badare a s&egrave; e non si divagar la mente nelle sottilit&agrave; propostegli dal Nardi, <lb/>e nelle altrui controversie (maluimus rei nostrae servire quam aliorum con&shy;<lb/>troversiae demonstrationem accommodare), venne per&ograve; presto il tempo che <lb/>s'ebbe a trovar messo su quelle stesse vie, a grande industria scansate, e <lb/>a compiacer del buon termine a cui si vide condotto. </s>

<s>La pi&ugrave; efficace occa&shy;<lb/>sione di quel ravviarsi col&agrave;, dove le speculazioni dello stesso Nardi gli aveano <lb/>accennato, fu questa che ora diremo. </s></p><p type="main">

<s>Il Cartesio, per applicare alle macchine quello ch'egli chiamava suo <lb/>nuovo principio statico, aveva, in poche parole francesi, disteso un tratta&shy;<lb/>tello, che and&ograve; lungamente attorno manoscritto, pubblicato postumo nell'ori&shy;<lb/>ginale, e poi dal Poisson, insieme con altre operette del medesimo Autore, <lb/>nel 1704 in Amterdam tradotto in latino. </s>

<s>Il Mersenno mand&ograve; cotesto ma&shy;<lb/>noscritto meccanico al Torricelli, il quale non intendendo il francese se ne <lb/>faceva tradur qualche cosa al Viviani, che ne prese in tale occasione copia, <lb/>inserita poi ne'primi fogli del Tomo CXI dei Discepoli di Galileo. </s>

<s>Il titolo <lb/>&egrave; <emph type="italics"/>Les Mechaniques,<emph.end type="italics"/> poco sotto al quale si legge: <emph type="italics"/>&ldquo; Mechanice prima prin&shy;<lb/>cipia explicat<emph.end type="italics"/> des engins, par l'aide des quels on peut, avec petite force, <lb/>lever un tardeau fort pesant &rdquo; (fol. </s>

<s>1). </s></p><p type="main">

<s>Nell'ultimo capitoletto, ch'&egrave; il VI, <emph type="italics"/>Du Levier,<emph.end type="italics"/> dop'aver dimostrate le <lb/>condizioni dell'equilibrio nello strumento, riguardando le forze naturali che <lb/>lo sollecitano come convergenti al centro del mondo, l'Autore cos&igrave; conclude: <lb/>&ldquo; De quoy on peut resondre toutes les difficultes de la Balance nestre, qu'n <lb/>point indivisibile, ainsy que iay suppose pour le Levier, si les bras sont pen&shy;<lb/>dues de part et d'autre, celuy qui sera le plus bas se doit tousiours tro&shy;<lb/>vuer le plus pesant, en sorte que le centre de la gravit&egrave; n'est pas.... et <lb/>immoble en casque corps, ainsy que l'avoient suppos&egrave; les ancines, ce que <lb/>personne encore, que ie sathe, n'a remarqu&egrave; (ivi, fol. </s>

<s>5 a tergo). </s></p><p type="main">

<s>Ora al significato di queste parole s'ebbe facilmente a risovvenire il <lb/>Torricelli delle speculazioni del Nardi, con le quali e co'pensieri medesimi <pb xlink:href="020/01/1958.jpg" pagenum="201"/>del Castelli si riscontravano queste vantate novit&agrave; cartesiane. </s>

<s>Incominci&ograve; a <lb/>dubitare allora se a introdur cos&igrave; fatte novit&agrave; nella scienza fosse stato primo <lb/>il Beaugrand o il Cartesio, quando un giorno gli occorse di tornare a svol&shy;<lb/>gere il libro <emph type="italics"/>Mecanicorum<emph.end type="italics"/> di Guidubaldo del Monte. </s>

<s>Si lev&ograve; dalla medita&shy;<lb/>zione di quelle pagine maravigliato che i suoi maestri Galileo, e il padre <lb/>don Benedetto, avessero potuto credere al Beaugrand, che si vantava di es&shy;<lb/>sere stato il primo, dopo tutti i passati scrittori (Alb. </s>

<s>X, 121) a maneggiare <lb/>i pesi, non come paralleli ma come converganti, mentre Guidubaldo, cin&shy;<lb/>quant'ott'anni prima che venisse a insegnarla un Francese, aveva dato ag'Ita&shy;<lb/>liani, e a chiunque fosse piaciuto di ascoltarla, questa lezione: </s></p><p type="main">

<s>&ldquo; In quocunque enim situ pondus aliquod constituatur, si naturalem <lb/>eius ad propium locum motionem spectemus, cum recta ad eum suapte na&shy;<lb/>tura moveatur, supposita totius universi figura eiusmodi erit: ut semper <lb/>spatium, per quod naturaliter movetur, rationem habere videatur lineae a <lb/>circumferentia ad centrum productae. </s>

<s>Non igitur naturales descensus recti <lb/>cuiuslibet soluti ponderis per lineas fieri possunt inter se parallelas. </s>

<s>cum <lb/>omnes in centrum mundi conveniant &rdquo; (Editio cit., fol. </s>

<s>15 a t.). E come <lb/>cos&igrave; convenienti avea riguardate quelle direzioni de'pesi nel trattare ivi <emph type="italics"/>De <lb/>libra,<emph.end type="italics"/> mettendosi in mezzo a quelle controversie, dalle quali s'era fin allora <lb/>astenuto il Torricelli, ma che ora tornavano ad allettarlo, perch&egrave; avea sco&shy;<lb/>perto in Italia il maestro a quel Cartesio e a quel Beugrand, ch'eran ve&shy;<lb/>nuti a farsi maestri di novit&agrave; agl'Italiani e al mondo. </s></p><p type="main">

<s>Guidubaldo dunque propugnava, come Leonardo da Vinci, l'opinione <lb/>dell'equilibrio indifferente della Bilancia, contro la proposizione di Gior&shy;<lb/>dano e contro il quesito del Tartaglia, scoprendo la fallacia, che s'ascon&shy;<lb/>deva nel loro discorso; fallacia, che egli diceva consistere nel riguardar, per <lb/>le premesse, i pesi come liberi, e nel riguardarli poi come congiunti, ve&shy;<lb/>nendo alla conclusione. </s>

<s>Con la loro stessa regola di computare i momenti, <lb/>soggiungeva l'arguto censore, si dimostra che l'equilibrio non &egrave; nella Bi&shy;<lb/>lancia di Giordano stabile ma indifferente, perch&egrave;, mentre il peso D (nella <lb/>retro apposta figura LXXXIV) discende per l'arco DE, il peso C riascende <lb/>per un arco eguale CL, e son pure eguali MG, HI, quantit&agrave; dell'ascesa e <lb/>del descenso. </s>

<s>&ldquo; Qualis ergo erit propensio unius ad motum deorsum, talis <lb/>etiam erit resistentia alterius ad motum sursum; resistentia scilicet violen&shy;<lb/>tiae ponderis in C in ascensu naturali potentiae ponderis in D in descensu <lb/>contra nitendo opponitur, cum sit ipsi aequalis, quo enim pondus in D na&shy;<lb/>turali potentia deorsum velocius descendit, eo tardius in C violenter ascendit, <lb/>quare neutrum ipsorum alteri praeponderabit, cum ab aequali non proveniat <lb/>actio. </s>

<s>Non igitur pondus in D pondus in C sursum movebit &rdquo; (ibid., fol. </s>

<s>18 a t.). </s></p><p type="main">

<s>Cos&igrave; veniva bene confutato, co'suoi proprii argomenti, il Tartaglia, il <lb/>quale aveva dimostrato dover esser maggiore il momento del peso pi&ugrave; alto, <lb/>e che perci&ograve; era necessario tornasse la Bilancia a stabilirsi nel suo primo <lb/>equilibrio, mentre sanamente applicando quella regola ne conseguiva dover <lb/>essa Bilancia anzi rimanere, serbando, in qualunque posizione i pesi eguali <pb xlink:href="020/01/1959.jpg" pagenum="202"/>i momenti. </s>

<s>Avrebbe cos&igrave; Guidubaldo raggiunto, per le medesime vie di Leo&shy;<lb/>nardo l'intento, ma perch&egrave; non stimava, come vedemmo, quella regola di <lb/>computare i momenti per buona, cerc&ograve; altro modo alle sue dimostrazioni. </s>

<s><lb/>Mentre cos&igrave; cercava, conformando il discorso agli effetti della Natura, che fa <lb/>convergere i pesi al centro del mondo, s'abbatt&egrave; a dover concluderne una <lb/>verit&agrave; inaspettata, ehe cio&egrave; nello scendere la Bilancia s'aggrava. </s></p><p type="main">

<s>Siano D, E (fig. </s>

<s>87) i due pesi in<gap/>orno al centro C, e posto in S il <lb/>centro della Terra siano DS, ES le loro direzioni: &ldquo; quare, si ut rei veri&shy;<lb/><figure id="id.020.01.1959.1.jpg" xlink:href="020/01/1959/1.jpg"/></s></p><p type="caption">

<s>Figura 87.<lb/>tas est, ponderis descensus magis <lb/>minusve obliquus dicetur secun&shy;<lb/>dum recessum et accessum ad <lb/>spatia per lineas DS, ES designata, <lb/>iuxta naturales ipsorum ad pro&shy;<lb/>pria loca lationes, conspicuum est <lb/>minus obliquum esse descensum <lb/>ipsius E per EG, quam ipsius D, <lb/>per DA.... quare in E pondus <lb/>magis gravitabit quam in D, quod est penitus op&shy;<lb/>positum eius, quod ipsi ostendere conati sunt &rdquo; (ibi, <lb/>fol. </s>

<s>19 a t.). </s></p><p type="main">

<s>La conclusione contradiceva a Giordano e al <lb/>Tartaglia, i quali avevano voluto dimostrare che, in&shy;<lb/>vece il peso in E &egrave; meno grave, ma contradiceva <lb/>altres&igrave; alle intenzioni stesse dell'Autore, le quali <lb/>erano quelle di provar che i due pesi, comunque <lb/>volti, serbano eguali i momenti. </s>

<s>Guidubaldo perci&ograve; <lb/>ebbe a rifiutar quella sua conclusione, e perch&egrave; in&shy;<lb/>somma non era possibile salvar nella Bilancia l'in&shy;<lb/>differenza dell'equilibrio, se non a patto che fos&shy;<lb/>sero le forze parallele, si trov&ograve; costretto ad ammet&shy;<lb/>tere il supposto antico di Archimede e di Leonardo. </s>

<s><lb/>Disse che, quando i pesi D, E son liberi di se&shy;<lb/>condar gli effetti della Natura, le direzioni son convergenti, ma che son pa&shy;<lb/>rallele, quando si trovano nello strumento artificiosamente congiunti. </s>

<s>&ldquo; In&shy;<lb/>surgent autem fortasse contra nos: si igitur, dicent, pondus in E gravius est <lb/>pondere in D, Libra DE in hoc situ minime persistet, quod equidem tueri <lb/>proposuimus, sed in EG movebitur. </s>

<s>Quibus respondemus plurimum referre <lb/>sive consideremus pondera quatenus sunt invicem disiuncta, sive quatenus <lb/>sunt sibi invicem connexa: alia est enim ratio ponderis in E sine connexione <lb/>ponderis in D, alia vero eiusdem alteri ponderi connexa, ita ut alterum sine <lb/>altero moveri non possit, nam ponderis in E, quatenus est sine alterius pon&shy;<lb/>deris connexione, rectus naturalis descensus est per lineam ES; quatenus <lb/>vero connexum est ponderi in D, eius naturalis descensus non erit amplius <lb/>per lineam ES, sed per lineam CS parallelam &rdquo; (ibid.). </s></p><pb xlink:href="020/01/1960.jpg" pagenum="203"/><p type="main">

<s>Ebbe facilmente il Torricelli a scoprire il paralogismo di questo discorso, <lb/>perch&egrave; anche stando i due pesi connessi dovevano essere le loro forze con&shy;<lb/>correnti, e perci&ograve; il peso in E doveva, per le ragioni di Guidubaldo, cio&egrave; <lb/>per la variet&agrave; della discesa, essere in qualunque modo il pi&ugrave; grave. </s>

<s>Se non <lb/>che mancava a determinarsi la quantit&agrave;, e nell'uno e nell'altro peso, la pro&shy;<lb/>porzione di quella discesa, ci&ograve; che sarebbesi potuto fare, conducendo ne'punti <lb/>E, D al cerchio due tangenti, come fu da questa stessa figura del Nostro, <lb/>suggerito al Cartesio, ma il Torricelli, ricordandosi del Benedetti, segu&igrave; la <lb/>pi&ugrave; spedita via segnatagli da lui. </s></p><p type="main">

<s>In un luogo delle sue Meccaniche, da noi citato di sopra, dop'avere inse&shy;<lb/>gnato il Matematico veneziano che la regola per determinar la quantit&agrave; di <lb/>una forza obliquamente diretta, rispetto alla ortogonale, era quella di con&shy;<lb/>dur dal centro una perpendicolare alla direzione, soggiunge: &ldquo; Hinc quoque <lb/>corollarium quoque sequetur quod, quanto propinqius erit centrum Librae <lb/>centro regionis elementaris, tantum quoque minus erit grave &rdquo; (Specul. </s>

<s><lb/>lib. </s>

<s>cit., pag. </s>

<s>143). </s></p><p type="main">

<s>Dal caso della Bilancia orizzontale, qui contemplato dal Benedetti, passa <lb/>il Torricelli ad applicare il teorema al caso della Bilancia inclinata, e non <lb/><figure id="id.020.01.1960.1.jpg" xlink:href="020/01/1960/1.jpg"/></s></p><p type="caption">

<s>Figura 88.<lb/>solamente conferma la conclusione di Guidu&shy;<lb/>baldo, che cio&egrave; il peso in E &egrave; pi&ugrave; grave che <lb/>in D, ma dimostra in qual proporzione sia <lb/>l'un peso minore dell'altro, preparandosi a <lb/>ci&ograve; fare le vie con questo Lemma: Abbiasi il <lb/>triangolo ABC (fig. </s>

<s>88), in cui sia il lato AB <lb/>minore del lato BC, e sia BD bissettrice. </s>

<s>Con&shy;<lb/>ducansi dal punto D, ai detti lati, DF e DE perpendicolari; sar&agrave; ABXDF <lb/>=BCXED; ossia AB:BC=ED:DF. </s></p><p type="main">

<s>&ldquo; Ora posto, dice il Torricelli, che B figuri il centro, ed AC una Lib&shy;<lb/>bra di braccia eguali, con due pesi eguali nelle estremit&agrave; A, C, i cui mo&shy;<lb/>menti o gravit&agrave; son misurate dalle perpendicolari DF, DE, siccome dichiara <lb/>Giov. </s>

<s>Battista de'Benedetti nel suo libro Delle speculazioni matematiche, <lb/>capitolo III ovvero IV; ne segue che il momento del peso in A, al momento <lb/>del peso in C, sia reciprocamente come la retta BC alla retta AB, cio&egrave; re&shy;<lb/>ciprocamente come la distanza dei pesi dal centro della Terra. </s>

<s>E di qui ab&shy;<lb/>biamo, non solamente che il peso pi&ugrave; vicino al centro, mentre &egrave; nella Lib&shy;<lb/>bra, pesa pi&ugrave; del meno vicino, ma sappiamo ancora in qual proporzione pi&ugrave; <lb/>pesa &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>112). </s></p><p type="main">

<s>Abbiamo voluto citar piuttosto il passo manoscritto, che quello pubbli&shy;<lb/>cato dal Grandi nelle note a Galileo (Alb. </s>

<s>XIV, 121), non solo perch&egrave; la <lb/>pubblicazione di lui, in alcune parti infedele, nuoce alla chiarezza, ma per&shy;<lb/>ch&egrave;, seguitando a leggere nello stesso manoscritto, trovasi dal Torricelli, con <lb/>la considerazione delle forze centrali, risoluto pi&ugrave; sottilmente che possa de&shy;<lb/>siderarsi il problema meccanico da Aristotile proposto nella sua prima Que&shy;<lb/>stione. </s>

<s>Il Tartaglia ne discorse a lungo nel VII libro de'suoi Quesiti, accu-<pb xlink:href="020/01/1961.jpg" pagenum="204"/>sando di falso il detto del Filosofo, che cio&egrave; le Bilanee di braccia pi&ugrave; lunghe <lb/>siano pi&ugrave; diligenti, e fa ivi notare che, per quella maggior diligenza, si eleg&shy;<lb/>gono anzi dagli orefici i piccoli Saggiatori. </s>

<s>Conclude il suo lungo discorso <lb/>con dire che, essendo le Bilance pi&ugrave; piccole pi&ugrave; esenti dalle passioni della <lb/>materia, rispondono perci&ograve; meglio alle intenzioni del Geometra, secondo le <lb/>quali hanno eguale mobilit&agrave; cos&igrave; le lunghe braccia come le corte &ldquo; perch&egrave; <lb/>ogni sorte di peso, posto in qualsivoglia sorte di Libra, far&agrave; inclinar quella <lb/>de continuo, per fino a tanto che quella sia gionta all'ultimo over pi&ugrave; basso <lb/>luoco, che quella inclinar si possa &rdquo; (fol. </s>

<s>77 a tergo). </s></p><p type="main">

<s>Ma questo si verifica nel caso della Bilancia <emph type="italics"/>folle,<emph.end type="italics"/> ch'&egrave; il pi&ugrave; temuto <lb/>vizio dello strumento, e i Saggiatori non per questo son agili, <emph type="italics"/>perch&egrave; pi&ugrave; <lb/>se accostano over approprinquano alle parti della Libra ideale,<emph.end type="italics"/> ma per&shy;<lb/>ch&egrave; la loro leggerezza conferisce a fare avvicinar pi&ugrave; che sia possibile il <lb/>centro di gravit&agrave; al punto di appoggio, cosicch&egrave;, senz'andar ne'difetti del&shy;<lb/>l'equilibrio indifferente, ne partecipano de'vantaggi. </s></p><p type="main">

<s>Il Benedetti perci&ograve; correggeva Aristotile con altre ragioni dedotte dalla <lb/>natura del Vette, perch&egrave;, in due Bilance solamente differenti per la lun&shy;<lb/>ghezza delle braccia, il peso &egrave; nel braccio pi&ugrave; lungo pi&ugrave; ponderoso, &ldquo; et <lb/>hac de causa movebit ad partem inferiorem maiori cum agilitate brachium: <lb/>multo magis etiam illud ipsum deprimet, idest maiorem etiam angulum fa&shy;<lb/>ciet &rdquo; (Specul. </s>

<s>lib. </s>

<s>cit., pag. </s>

<s>153). </s></p><p type="main">

<s>Il Torricelli poi dimostr&ograve;, come necesaria conseguenza delle forze con&shy;<lb/>vergenti, che appena inclinata la Bilancia dal suo preponderante questo ac&shy;<lb/>cresce il momento con proporzion maggiore nel braccio pi&ugrave; lungo, che nel <lb/>pi&ugrave; corto, e di qui la ragion vera dei vantaggi da Aristotile predicati. </s>

<s>&ldquo; Inol&shy;<lb/>tre (cos&igrave; ripigliasi nel manoscritto torricelliano il costrutto che si lasci&ograve; di <lb/>sopra interrotto) possiamo dedurne un'altra verit&agrave;, che non si cammina con <lb/><figure id="id.020.01.1961.1.jpg" xlink:href="020/01/1961/1.jpg"/></s></p><p type="caption">

<s>Figura 89.<lb/>la medesima proporzione nella Libbra grande <lb/>e nella piccola sempre. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia una Libbra AB (fig. </s>

<s>89) ed una <lb/>minore CD, il cui centro comune sia in E, <lb/>ambedue con braccia eguali e con pesi eguali, <lb/>e l'estremit&agrave; F rappresenti il centro della <lb/>Terra, al quale tendono naturalmente i pesi <lb/>per linee non parallele, ma convergenti in F. </s>

<s><lb/>E perch&egrave; il peso A al peso B ha, secondo il <lb/>suo momento, la proporzione reciproca di BF <lb/>ad FA, ed il momento del peso C al momento <lb/>del peso D &egrave; come la DF alla CF, e la BF <lb/>alla CF ha maggior ragione che la DF alla <lb/>medesima FC (suppongo che la Libbra sia totalmente obliqua, che il punto <lb/>A sia il pi&ugrave; vicino al centro F e poi il punto C, e poi E e poi D e B sia il <lb/>pi&ugrave; lontano) ed essendo FC maggiore di FA, sar&agrave; per conseguenza molto <lb/>maggiore la ragione di BF ad FA, che di DF a FC; cio&egrave; maggiore ragione <pb xlink:href="020/01/1962.jpg" pagenum="205"/>del momento di A rispetto al momento del peso B, che del peso C al <lb/>peso D. &rdquo; </s></p><p type="main">

<s>&ldquo; E questa speculazione ci fa intendere un segreto vantaggio, che ha <lb/>la Libbra grande sopra la piccola, nel mostrare la inegualit&agrave; di due pesi, <lb/>che stiano appesi alle estremit&agrave; di quella Libbra. </s>

<s>Imperocch&egrave;, sebbene stando <lb/>in equilibrio, o diciamo in sito orizzontale, le due Libbre, la maggiore e la <lb/>minore, non cammina la proporzione della maggior proporzione de'momenti <lb/>nella Libbra maggiore che nella minore; tuttavia, ponendosi che un peso <lb/>sia maggiore dell'altro, il maggiore rimove la Libbra dal sito orizzontale, <lb/>ed indi acquista il maggior peso molto maggior momento nella Libbra grande <lb/>che nella piccola, siccome si &egrave; dimostrato di sopra, ed in conseguenza ci mo&shy;<lb/>stra pi&ugrave; apertamente l'inegualit&agrave;. </s>

<s>Nelle Libbre per&ograve; materiali nel punto del&shy;<lb/>l'equilibrio nasce un certo ritardamento dal tocco che si fa, il quale impe&shy;<lb/>disce pi&ugrave; la Libbra maggiore che la minore &rdquo; (fol. </s>

<s>112). </s></p><p type="main">

<s>Avendo pi&ugrave; sopra mostrato qual si fosse l'origine di queste specula&shy;<lb/>zioni del Torricelli, giova soggiunger che un'origine simile dovettero aver <lb/>le speculazioni del Cartesio, a cui aveva riferito il Mersenno le conclusioni <lb/>dello stesso Torricelli, e il modo da lui tenuto in computare i momenti nella <lb/><figure id="id.020.01.1962.1.jpg" xlink:href="020/01/1962/1.jpg"/></s></p><p type="caption">

<s>Figura 90.<lb/>Bilancia considerate le forze co&shy;<lb/>me dirette al centro della Terra. <lb/></s>

<s>&ldquo; Quantum ad id quod de Bilance <lb/>scribis, rispondeva Renato all'ami&shy;<lb/>co, in eorum sum sententia qui <lb/>dicunt pondera esse in aequilibrio, <lb/>quando sunt in ratione reciproca <lb/>linearum perpendicularium, quae <lb/>ducuntur a centro Librae in lineas <lb/>rectas, quae extremitates brachiorum centro Terrae <lb/>connectunt &rdquo; (Epist., T. II cit., pag. </s>

<s>93). E fu in <lb/>questa sentenza condotto e in essa confermato da <lb/>un ragionamento, simile a quello, a cui il Torricelli <lb/>aveva nel <emph type="italics"/>Mechanicorum liber<emph.end type="italics"/> ritrovato, come si <lb/>disse, il principio. </s>

<s>Riduciamoci perci&ograve; alla memoria <lb/>il discorso, in cui dianzi dimostravasi da Guidubaldo <lb/>che il pi&ugrave; basso peso nella Bilancia prepondera al <lb/>pi&ugrave; alto, e rappresentiamoci nuovamente sott'occhio <lb/>l'iconismo illustrativo (fig. </s>

<s>90). Diceva che il peso in <lb/>E ha la discesa pi&ugrave; retta del peso D, perch&egrave; l'an&shy;<lb/>golo SEG &egrave; pi&ugrave; acuto di SDA e ci&ograve; dee naturalmente <lb/>aver suggerito al Cartesio l'uso delle due tangenti, <lb/>che venivano cos&igrave; a rappresentargli i due pesi come <lb/>posati sopra due piani, in cui le Meccaniche avevano <lb/>insegnato gi&agrave; a computar, fra la gravezza assoluta e la relativa, la propor&shy;<lb/>zion del momento. </s></p><pb xlink:href="020/01/1963.jpg" pagenum="206"/><p type="main">

<s>Non altrimenti infatti da questo primo avvio procede, nell'epist. </s>

<s>LXXVIII <lb/>della I parte, quella cartesiana dimostrazione, nella quale si dice essere la <lb/>gravit&agrave; relativa del peso D all'assoluta come il perpendicolo DI sta al piano <lb/>inclinato DH, e allo stesso modo essere le due gravit&agrave; di E come EF sta <lb/>ad EL. </s>

<s>Ma perch&egrave; CM &egrave; stata condotta perpendicolare a MS, i triangoli si&shy;<lb/>mili ELF, CEM daranno EF:EL=CM:CE. </s>

<s>Simili parimente essendo i <lb/>due triangoli DHI, DIC si avr&agrave; per essi DI:DH=IC:DC. Ond'&egrave; che, se <lb/>siano i pesi assolutamente eguali, ossia se EL=DH, avendo la Bilancia le <lb/>due braccia CE, DC uguali, le due dette ragioni si ridurranno in quest'una <lb/>EF:DI=CM:IC. </s>

<s>Ora prosegue a dimostrare il Cartesio, in modo simile <lb/>a quello del Torricelli, che CM:IC=DS:ES. &ldquo; Pondus autem, quod est <lb/>in E, se habet ad pondus, quod est in D, ut CM:IC, ergo ut DS:ES. </s>

<s>Unde <lb/>liquet centrum gravitatis duorum ponderum D, E, simul iunctorum per li&shy;<lb/>neam DE, non esse in puncto C, sed inter C et E, ex. </s>

<s>gr. </s>

<s>in puncto R, in <lb/>quod suppono cadere lineam illam, quae dividit angulum DSE in duas ae&shy;<lb/>quales partes. </s>

<s>Hoc enim posito, notum est in Geometria lineam DR esse <lb/>ad RE ut DS ad ES, ita ut debeant pondera in D et E sustineri a puncto R, <lb/>ut in aequilibrio maneant in eo in quo sunt loco. </s>

<s>Verum, si supponatur <lb/>linea DE aliquanto magis aut minus inclinata super horizontem, aut si suppo&shy;<lb/>nantur pondera haec in alia a Terra distantia, oportebit illa ab alio puncto <lb/>sustineri ut sint in aequilibrio, et sic illorum centrum gravitatis non est sem&shy;<lb/>per in eodem puncto &rdquo; (Fancof. </s>

<s>1692, pag. </s>

<s>226, 27). E cos&igrave; quel che asse&shy;<lb/>riva l'Autore in fine alle sue <emph type="italics"/>Mechaniques<emph.end type="italics"/> &egrave; matematicamente qui dimo&shy;<lb/>strato. </s></p><p type="main">

<s>Veniva dunque dal Cartesio e dal Torricelli, per queste loro matematiche <lb/>dimostrazioni, confermato quel che contro Giordano e il Tartaglia aveva da <lb/>quella sua meccanica speculazione concluso gi&agrave; Guidubaldo, ond'&egrave; che sem&shy;<lb/>brava aversi finalmente decisa, da tre cos&igrave; grandi autorit&agrave; nella scienza, la <lb/>causa della II proposizion <emph type="italics"/>De ponderibus,<emph.end type="italics"/> rimasta accusata di falsit&agrave; nel suo <lb/>enunciato e nelle sue ragioni. </s>

<s>La Bilancia di braccia e di pesi eguali, ri&shy;<lb/>mossa dalla natural sua posizione orizzontale, non rimane, come diceva Leo&shy;<lb/>nardo, n&egrave; ritorna, come voleva Giordano: non indifferente anzi n&egrave; stabile, <lb/>ma folle, seguita a scender gi&ugrave; infin tanto che non si posi nel perpendicolo, <lb/>tirata e vinta dalla maggior gravit&agrave; che, avvicinandosi al centro della Terra, <lb/>acquista il peso pi&ugrave; basso. </s></p><p type="main">

<s>La questione per&ograve; non era semplicemente matematica, e pur come ma&shy;<lb/>tematica pareva che si potesse risolvere in diversa maniera, perch&egrave;, rima&shy;<lb/>nendo i pesi orizzontali, scemano com'avea concluso il Benedetti, tanto pi&ugrave; <lb/>di momento, quanto il centro della Bilancia s'avvicina pi&ugrave; al centro del <lb/>mondo: mentre, rimanendo immobile essa Bilancia e sol variandosi intorno <lb/>a lei la posizione de'pesi, questi, quanto son men lontani dal comun cen&shy;<lb/>tro dei gravi, tanto pi&ugrave; crescono, come dalla regola del Benedetti stesso re&shy;<lb/>sulta, i loro momenti. </s></p><p type="main">

<s>Sembrerebbe dunque che si dovesse ricavar la legge dal primo fatto, <pb xlink:href="020/01/1964.jpg" pagenum="207"/>in cui tutta la macchina si muove, o non dal secondo, in cui si move sola <lb/>una parte, e che ne sia perci&ograve; da concludere aver la gravit&agrave; diretta, e non <lb/>reciproca ragione delle distanze. </s>

<s>Si volle nonostante il Torricelli tener fermo <lb/>a questa seconda, perch&egrave; s'accomodava con una sua certa idea singolare, <lb/>che cio&egrave; fosse natura propria dei gravi quella, non di tendere, ma di rifug&shy;<lb/>gire dal centro. </s>

<s>Sarebbe perci&ograve; quella comunemente chiamata gravit&agrave; da dir <lb/>piuttosto leggerezza, intorno alla quale scrisse due eloquenti lezioni, coll'in&shy;<lb/>tendimento di dimostrare agli Accademici fiorentini &ldquo; non esser possibile <lb/>che gli elementi vadano al centro, primieramente perch&egrave; non possono arri&shy;<lb/>varvi, e secondariamente perch&egrave; arrivandovi sarebbe un distruggere s&egrave; me&shy;<lb/>desimi &rdquo; (Lezioni accad., Milano 1823, pag. </s>

<s>148). Quanto pi&ugrave; dunque si di&shy;<lb/>lungano i corpi dal centro della Terra tanto pi&ugrave;, secondo il Torricelli, en&shy;<lb/>trando nella loro propria region naturale, divengono leggeri, ossia scemano <lb/>di quel momento che violentemente trattenevali in basso. </s></p><p type="main">

<s>Il Cartesio, incerto intorno al modo di definir le cose secondo il suo <lb/>proprio sistema, giacch&egrave; Guidubaldo l'avea condotto a concluder che le gra&shy;<lb/>vit&agrave; stanno in reciproca ragione delle distanze, si studiava di confortare le <lb/>matematiche dimostrazioni con l'esperienze, osservando i grossi uccelli &ldquo; ut <lb/>grues, ciconias etc. </s>

<s>multo facilius volare in altiore aere quam inferius &rdquo; <lb/>(Epist. </s>

<s>LXXIII cit., pag. </s>

<s>215), non per altro, diceva, che per ritrovarsi co&shy;<lb/>lass&ugrave; pi&ugrave; legger&igrave;, e lo stesso notava de'cos&igrave; detti aquiloni o cervi volanti. </s>

<s><lb/>Nulla ha per&ograve; maggiore efficacia a confermarlo in quella sua opinione di <lb/>un'esperienza eseguita dal suo amico Mersenno, il quale, avendo fatto tirar <lb/>verso il zenit palle da gran cannoni, e non vedendole tornare a basso, do&shy;<lb/>mandava maravigliato dove fassero andate, e a lui rispondeva il Cartesio che <lb/>dovevano esser lass&ugrave; divenute tanto leggere, da andar disperse com'al vento <lb/>le foglie. </s>

<s>&ldquo; Denique, si experimentum illud quod a teipso factum fuisse mihi <lb/>significasti, et de quo alii etiam nonnulli scripserunt, verum sit, nempe glo&shy;<lb/>bos maiorum tormentorum versus zenith recta explosorum non recidere, col&shy;<lb/>ligere licet ictus eos in tantam altitudinem ferri, atque a Terrae centro adeo <lb/>elongari, ut omnem suam gravitatem inde deperdant &rdquo; (ibid.). </s></p><p type="main">

<s>Queste, francamente parlando, son puerili semplicit&agrave;, come quegli del <lb/>Torricelli, trattenendosi sulla superfice e nell'interno della Terra, si direb&shy;<lb/>bero filosofi capricci se, pigliando dalla luce, dal calore e dal suono gli <lb/>esempii (Lez. </s>

<s>cit., pag. </s>

<s>147), non avessero le leggi della loro diffusione po&shy;<lb/>tuto portare a concluder, per gli spazii celesti, direttamente la legge neuto&shy;<lb/>niana della gravitazion de'pianeti in reciproca ragion de'quadrati delle di&shy;<lb/>stanze dai loro centri attrattivi. </s>

<s>Questionandosi per&ograve; de'corpi componenti <lb/>questa bassa regione elementare, sembrava a molti, che pi&ugrave; sanamente ra&shy;<lb/>gionavano sull'andare di Antonio Nardi, assai ragionevole che intorno al <lb/>centro della Terra serbassero i pesi proporzioni simili a quelle, che si ve&shy;<lb/>dono osservare intorno al centro della Bilancia. </s></p><p type="main">

<s>Il concetto delle forze attrattive, che venivasi a chiarir sempre meglio, <lb/>pigliava ardore dagli inavvertiti spiriti aristotelici, i quali avevano pronun-<pb xlink:href="020/01/1965.jpg" pagenum="208"/>ziato essere nel centro della Libbra un'attrazion simile a quella, che si di&shy;<lb/>ceva avere il centro della Terra. </s>

<s>E perci&ograve;, come ammetteva il Filosofo essere <lb/>a proporzione delle distanze men sostenuto il peso nell'artificiale strumento; <lb/>cos&igrave; sembrava ragionevole che dovesse avvenir nella macchina naturale, ossia <lb/>nella Terra, in cui pure si avveri che, tanto pi&ugrave; crescano i pesi di momento, <lb/>quanto pi&ugrave; si dilungano dal centro. </s>

<s>Il Castelli e il Viviani fra'nostri furono <lb/>di questo sentimento, e ne dettero dimostrazione, il primo in appendice a <lb/>una lettera a Galileo (Alb. </s>

<s>X, 125-27), e il secondo in un suo foglio ma&shy;<lb/>noscritto pubblicato dal padre Grandi (Alb. </s>

<s>XIV, 120). Sostenne questa opi&shy;<lb/>nione in Francia il Fermat, contro validi oppositori, e la professarono molti <lb/>altri, fra'quali pi&ugrave; autorevole di tutti fu il Newton, che formulava cos&igrave;, <lb/>ne'<emph type="italics"/>Principii matematici,<emph.end type="italics"/> la proposizione IX del III libro: &ldquo; Gravitatem, <lb/>pergendo a superficiebus planetarum, deorsum decrescere in ratione distan&shy;<lb/>tiarum a centro quam proxime &rdquo; (Genevae 1742, pag. </s>

<s>53); proposizione, <lb/>che viene ad essere dimostrata dalla LXXIII del I libro, supposto che serbi <lb/>in s&egrave; da per tutto uguale densit&agrave; la materia componente il pianeta. </s></p><p type="main">

<s>Se cos&igrave; &egrave;, dopo tante vicende fortunose, la proposizion di Giordano &egrave; <lb/>salva, almeno nel suo pronunziato. </s>

<s>La Bilancia violentemente rimossa si ri&shy;<lb/>stabilisce nel suo primo equilibrio orizzontale, perch&egrave; il peso che riman sopra <lb/>acquista maggior momento, non gi&agrave; dalla maggior rettitudine della discesa <lb/>nel cerchio, ma dalla maggior distanza che, rispetto al peso di sotto, lo se&shy;<lb/>para dal centro della regione elementare. </s></p><p type="main">

<s>Se tutte le acque scendessero ai fiumi, la loro ubert&agrave; sarebbe propor&shy;<lb/>zionale alle piogge, e cos&igrave; avverrebbe del fiume della scienza, se tutte le <lb/>speculazioni entrassero nell'aperto alveo, che mena e regola la corrente. </s>

<s>Ma <lb/>come molte acque rimangono stagnanti o vanno per sotterranei rigagnoli <lb/>disperse, cos&igrave; avvien delle idee, di che ci porgono un singolare esempio le <lb/>cose fin qui discorse, essendo che tanto lavorio di mente, fatto da quegli <lb/>insigni matematici intorno alle propriet&agrave; della Bilancia, o si rimanesse nei <lb/>manoscritti o si riducesse in libri, non per tempo venuti alla luce. </s>

<s>Di qui <lb/>&egrave; che questa parte della scienza degli equilibrii, verso l'anno 1667, era si <lb/>pu&ograve; dire a quel punto, in cui l'avea lasciata, quasi un secolo prima, Gui&shy;<lb/>dubaldo del Monte. </s></p><p type="main">

<s>Geminiano Montanari infatti, professore nello studio di Bologna, dettava <lb/>in quell'anno a'suoi scolari una lezione intorno agli effetti delle Bilance, <lb/>dimostrati in sette matematiche proposizioni, nelle quali si concludeva dover <lb/>essere una Libbra, che abbia il punto di sospensione nel centro, in condi&shy;<lb/>zione di equilibrio indifferente. </s>

<s>E bench&egrave; fosse questa, come si sa, l'opi&shy;<lb/>nione di Guidubaldo, teneva nonostante il Montanari in approvarla altro <lb/>modo, ch'era quello di far vedere com'avendo in qualunque posizione l'un <lb/>peso e l'altro egual distanza dalla verticale, condotta per il punto del cir&shy;<lb/>convolubile, hanno perci&ograve; eguali i momenti, secondo il ragionamento stesso <lb/>che avea fatto due secoli prima Leonardo da Vinci. </s></p><p type="main">

<s>L'anno dopo che fu dettata questa lezione, l'autografo della quale &egrave; <pb xlink:href="020/01/1966.jpg" pagenum="209"/>inserito dal foglio 128-31 del tomo XIX de'Manoscritti del Cimento, Donato <lb/>Rossetti pubblicava in Firenze le sue <emph type="italics"/>Dimostrazioni fisico-matematiche delle <lb/>VII proposizioni,<emph.end type="italics"/> nella II delle quali, con principii statici che avevano l'ap&shy;<lb/>parenza di nuovi, si tornava a discorrere degli effetti delle Bilance, propo&shy;<lb/>nendosi a risolvere il problema sotto questa forma: &ldquo; Si pigli una Bilancia, <lb/>che abbla uguali le braccia, all'estremit&agrave; delle quali si appendino i pesi <lb/>uguali, e si costituisca inclinata all'orizzonte: si fermi, e dopo si lassi in <lb/>sua libert&agrave;. </s>

<s>L'esperienza insegna che in tal sito non si fermi, ma che si <lb/>porti con le braccia parallele all'orizzonte. </s>

<s>Cercasi la causa di tal movi&shy;<lb/>mento &rdquo; (pag. </s>

<s>9). </s></p><p type="main">

<s>Se bastasse la sola considerazione dei centri di gravit&agrave;, dovrebbe la Bi&shy;<lb/>lancia, dice il Rossetti, rimanere, ma perch&egrave; il fatto dimostra che ritorna, <lb/>&egrave; da ricercar di ci&ograve; la ragione in qualche altra cosa diversa, dipend&egrave;nte da <lb/>questo, ch'egli vuole gli sia concesso, che cio&egrave; &ldquo; un corpo prema e graviti <lb/>sopra un altro, non solo per il proprio momento, ma ancora per tutto il <lb/>momento degli altri corpi, che uno sopra l'altro l'aggravano &rdquo; (ivi, pag. </s>

<s>4). <lb/>Ammesso questo, poi soggiunge, &ldquo; se ne deduce, levati gl'impedimenti, che <lb/>ogni settore di globo sar&agrave; sem&shy;<lb/>pre in peso assoluto eguale ad <lb/>un altro settore a s&egrave; medesi&shy;<lb/>mamente eguale &rdquo; (ivi). </s></p><p type="main">

<s>Se ora siano GD, ND, LD <lb/>(fig. </s>

<s>91) tre linee, che s'appun&shy;<lb/>tano nel centro della Terra D, <lb/>facendo gli angoli GDN, NDL <lb/>eguali, e sia la Bilancia EF so&shy;<lb/>spesa nel suo centro di gravit&agrave; <lb/>in C, supposte le due braccia <lb/>CE, CF eguali e i pesi in E e <lb/>in F eguali, rimarr&agrave; EF nella <lb/>perfetta linea orizzontale, per&shy;<lb/>ch&egrave; il settore GDN, avendo ca&shy;<lb/><figure id="id.020.01.1966.1.jpg" xlink:href="020/01/1966/1.jpg"/></s></p><p type="caption">

<s>Figura 91.<lb/>pacit&agrave; uguale a quella del settore NDL, vengono EC, e CF ugualmente pre&shy;<lb/>mute dall'una parte e dall'altra. </s></p><p type="main">

<s>Ma s'inclini la Bilancia, e si lasci nella posizione AB: il peso A serba <lb/>tuttavia il momento medesimo del peso B, ma i settori HDN, NDM sono <lb/>disuguali e perci&ograve;, aggiungendo quegli uguali momenti a questi disuguali <lb/>settori, si farebbe contro la causa degli equilibrii. </s>

<s>&ldquo; Adunque non pu&ograve; la <lb/>Bilancia stessa, ne conclude il Rossetti, fermarsi in questa inclinazion di set&shy;<lb/>tori, uno maggiore dell'altro, ed &egrave; necessario che si riduca all'orizzontale <lb/>EF, nel qual posto solo aggiunge i suoi momenti uguali ai momenti uguali <lb/>degli uguali settori NDL, NDG &rdquo; (ivi, pag. </s>

<s>16). </s></p><p type="main">

<s>Entrato il Rossetti, per via specialmente della spiegazione de'fenomeni <lb/>di capillarit&agrave;, in gare letterarie col Montanari, questi pubblic&ograve; in Bologna <pb xlink:href="020/01/1967.jpg" pagenum="210"/>nel 1669, sotto il nome del suo discepolo Ottavio Finetti, un libro apologe&shy;<lb/>tico col titolo di <emph type="italics"/>Prostasi fisico-matematica,<emph.end type="italics"/> dove, dopo la stampa della sopra <lb/>commemorata Lezione <emph type="italics"/>Degli effetti delle bilance,<emph.end type="italics"/> si facevano alcune consi&shy;<lb/>derazioni intorno a ci&ograve; che degli equilibrii aveva nella II delle sue propo&shy;<lb/>sizioni dimostrato lo stesso Rossetti. </s>

<s>Si diceva che se CB ha maggior mo&shy;<lb/>mento di AC dee necessariamente seguitare a scendere, e non a risalire <lb/>all'orizzonte, e quanto all'efficacia de'centri di gravit&agrave; e all'esperienza, da <lb/>cui la speculazione pigliava il fondamento, cos&igrave; si diceva: </s></p><p type="main">

<s>&ldquo; &Egrave; manifesto che il signor Rossetti s'inganna in credere che, quando <lb/>un corpo &egrave; sospeso per il centro di gravit&agrave; sua, non resti in ogni sito equi&shy;<lb/>librato, il che nel suo caso succederebbe sempre, purch&egrave; li tre punti del&shy;<lb/>l'asse e degli estremi fossero in una linea retta a capello. </s>

<s>Ma il fatto sta <lb/>che niuna Bilancia buona ha questi tre punti in linea retta, ma bens&igrave; quello <lb/>di mezzo &egrave; d'alquanto superiore agli altri due, onde da ci&ograve; nascono gli ef&shy;<lb/>fetti considerati. </s>

<s>E se il signor Rossetti, nel fare l'esperienze sue, avesse <lb/>bene avvertito alla vera struttura delle Bilance, non avrebbe ricercato infino <lb/>al ccntro della Terra la cagione di quegli effetti &rdquo; (pag. </s>

<s>42). </s></p><p type="main">

<s>Erano il Montanari e il Rossetti stati ascritti all'Accademia del Cimento, <lb/>in quell'ultimo periodo che seguitava a presiederla, gi&agrave; fatto cardinale, il <lb/>principe Leopoldo, il quale volle sentire intorno a quelle controversie delle <lb/>Bilance il giudizio del Viviani. </s>

<s>Rispose questi che il Montanari, come fisico <lb/>matematico, ragionava bene, perch&egrave;, attendendo alla smisurata distanza che <lb/>&egrave; dalla superfice al centro della Terra, si possono le direzioni dei pesi ri&shy;<lb/>guardar come parallele, e perci&ograve;, se il punto di sospensione &egrave; nel centro o <lb/>vicinissimo al centro, la Bilancia &egrave; in condizione di equilibrio indifferente, <lb/>com'&egrave; confermato dalla pi&ugrave; facile esperienza. </s>

<s>Ma l'esperienza del Rossetti <lb/>diceva liberamente essere una fallacia, perche, se rimosso uno de'pesi la <lb/>vedeva tornare all'orizzonte, non poteva esser per altro, se non che per <lb/>aversi il punto di sospensione costituito pi&ugrave; in alto del centro. </s>

<s>Notava inol&shy;<lb/>tre che s'introducevano da lui le direzioni convergenti fuor di proposito, <lb/>perch'essendo il pi&ugrave; basso peso il pi&ugrave; grave ne doveva seguire un effetto <lb/>contrario. </s></p><p type="main">

<s>Restava cos&igrave; confermata l'accusa del Montanari, che cio&egrave; il Rossetti non <lb/>aveva bene avvertito alla vera struttura delle Bilance, e il Viviani stesso <lb/>ebbe in questa occasione a fare esperienza del difetto che, di queste cogni&shy;<lb/>zioni intorno al principio delle equiponderanze, era in parecchi altri a quei <lb/>tempi, come si mostrer&agrave; dal seguente fatto, col quale siam per chiudere <lb/>nella nostra Storia questo episodio. </s></p><p type="main">

<s>Aveva posto pi&ugrave; volte mente il Viviani a quell'ondeggiare, che fanno <lb/>le Bilance prima di ristabilirsi in equilibrio, e il lungo ago gli si rappre&shy;<lb/>sentava nella viva immaginazione qual persona folle e ubriaca. </s>

<s>Gli venne di <lb/>qui il pensiero di quella macchinetta spettacolosa che, senza conoscerne l'in&shy;<lb/>ventore, si descrive in quasi tutti i trattati di Fisica, per dar l'esempio e <lb/>mostrar la ragione dell'equilibrio stabile ne'corpi sospesi; esempio rappre-<pb xlink:href="020/01/1968.jpg" pagenum="211"/>sentato in un fantoccio, con due contrappesi in una mano e nell'altra, che <lb/>posato sulla punta di un pi&egrave;, su qualunque sostegno, va balenando qua e l&agrave; <lb/>n&egrave; casca mai. </s>

<s>Di contro all'abbozzato disegno scriveva il Viviani stesso di <lb/>sua propria mano in un foglio: &ldquo; Tutto il segreto dentro la figuretta ondeg&shy;<lb/>giante sul bilico senza mai cadere, bench'ella non sia collegata col soste&shy;<lb/>gno, ma solamente vi posi colla punta, sta che il centro di gravit&agrave; del compo&shy;<lb/>sto si trova sempre sotto il punto del sostegno &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLIII, <lb/>fol. </s>

<s>64). Era il segreto stesso tanto tempo prima scoperto da Leonardo da <lb/>Vinci: <emph type="italics"/>il centro di ciascuno peso sospeso ci stabilisce sotto il suo sosten&shy;<lb/>tacolo,<emph.end type="italics"/> eppure Giuseppe Ferroni, valoroso fisico e matematico, discepolo del <lb/>Viviani, veduta con sua gran maraviglia in Bologna, dov'era allora profes&shy;<lb/>sore nel collegio dei gesuiti, una di quelle figurine ondeggianti in casa Co&shy;<lb/>spi, non seppe, con tutta la sua scienza n&egrave; con quella de'suoi colleghi, ren&shy;<lb/>dersi la ragione di quel fatto spettacoloso. </s></p><p type="main">

<s>&ldquo; Ho visto in casa del marchese Cospi, perci&ograve; scriveva al Viviani, una <lb/>statuetta di legno di un Maestro, la quale, tenendo in mano un'asta rigida <lb/>con due contrappesi, ed avendo nel piede una punta ferrata di trottola, posta <lb/>su un candeliere di legno, su quello si gira, facendo molti ondeggiamenti, <lb/>come se volesse cadere, ma per&ograve; sempre si mantiene in piedi. </s>

<s>Io pensai <lb/>che questo equilibrio nascesse dal centro della gravit&agrave;, qual fosse nella punta <lb/>di ferro, che le serve d&igrave; polo per raggirarsi, ma conobbi di aver fallito, per&shy;<lb/>ch&egrave;, avendo provato a sospendere la statuetta da detta punta di ferro, non <lb/>stava equilibrata, ma prevalevano i contrappesi. </s>

<s>Onde mi sono immaginato <lb/>vi sia dentro qualche artifizio di argento vivo, quale scorra in que'tanti on&shy;<lb/>deggiamenti per l'asta de'contrappesi. </s>

<s>So questa invenzione esser venuta <lb/>di Firenza, onde la stimo parto dell'ingegno di V. S. illustrissima. </s>

<s>Sono som&shy;<lb/>mamente bramoso di saperne l'arcano, onde fo ricorso alla sua gentilezza, <lb/>pregandola si compiaccia di spiegarmelo. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLVI, <lb/>fol. </s>

<s>281). </s></p><p type="main">

<s>Il Viviani compiacque al discepolo e all'amico, ma &egrave; notabile che si <lb/>servisse per la spiegazione di un esempio men naturale di quello delle Bi&shy;<lb/>lance, e che volesse sostituire alla dottrina de'centri di gravit&agrave;, di cos&igrave; fa&shy;<lb/>cile applicazione ne'comuni strumenti da pesare, le pi&ugrave; complicate teorie <lb/>de'centri di oscillazione dei pendoli. </s>

<s>Il Ferroni in ogni modo vedeva come <lb/>si potesse far dipendere il segreto da pi&ugrave; alti principii de'vulgari, e cos&igrave; <lb/>rispondeva, per significare la sua gratitudine alla liberalit&agrave; del Maestro: </s></p><p type="main">

<s>&ldquo; Mi &egrave; stata graditissima la sua spiegazione, la quale ho notificata ad <lb/>alcuni di questi lettori di Filosofia, e perch&egrave; mi domandano la sua lettera, <lb/>io per sodisfare a tutti in un colpo ho risoluto di far venire in collegio, di <lb/>casa del bali Cospi, il fantoccio barcollante, e farlo vedere a tutta questa <lb/>nostra numerosa scolaresca, che pochissimi di loro l'hanno veduto, e con <lb/>quella occasione farvi sopra l'eruditissima spiegazione della sua lettera. </s>

<s>Ser&shy;<lb/>virommi della sua similitudine molto calzante del vaso cupo dondolante sulla <lb/>punta di un coltello, sulla schiena superiore del qual vaso s'inchiodasse un <pb xlink:href="020/01/1969.jpg" pagenum="212"/>fantoccio. </s>

<s>Conforme i suoi insegnamenti <lb/>ridurr&ograve; la macchina al pendolo, ma per <lb/>pi&ugrave; facile intelligenza degli scolari, la ri&shy;<lb/>durr&ograve; al pendolo composto di asta rigida <lb/>ABC (fig. </s>

<s>92), la di cui asta BC, di sotto <lb/>al B centro del moto, se si divaricasse in <lb/>due aste de'contrappesi del fantoccio bar&shy;<lb/>collante, farebbe sulla punta B la supe&shy;<lb/>riore asta BA quegli ondeggiamenti, che <lb/>fa la macchinetta ammirata &rdquo; (ivi, fol. </s>

<s>282). <lb/><figure id="id.020.01.1969.1.jpg" xlink:href="020/01/1969/1.jpg"/></s></p><p type="caption">

<s>Figura 92.</s></p><pb xlink:href="020/01/1970.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle Macchine<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della natura delle Macchine e del modo di operar del Vette, dell'Asse nella ruota, e delle Taglie; <lb/>del Cuneo e della Vite. </s>

<s>&mdash; II. </s>

<s>Delle proporzioni tra la resistenza, e la potenza necessaria a sol&shy;<lb/>levare i gravi, per via dei piani inclinati. </s>

<s>&mdash; III. </s>

<s>Delle censure di Alessandro Marchetti sopra <lb/>i teoremi di Galileo e del Torricelli del momento dei gravi su i piani inclinati: della etero&shy;<lb/>dossia meccanica di Giovan Francesco Vanni, e delle difficolt&agrave;, che trovarono in confutarla i <lb/>Galileiani. </s>

<s>&mdash; IV. </s>

<s>Delle confutazioni speculate dai Matematici stranieri, e della questione in&shy;<lb/>torno alla composizion dei momenti, proposta in Roma per rispondere ai sofismi del Vanni: <lb/>degli errori di Luc'Antonio Porzio confutati dal Grandi. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>A definir l'essere e le propriet&agrave; naturali di quegli ingegni ritrovati dal&shy;<lb/>l'arte e dall'industria dell'uomo ora per isgravarsi, ora per esercitar pi&ugrave; <lb/>facilmente le forze nel maneggio dei pesi, giova ripensare a quegli atti, che <lb/>comunemente si fanno, e che, sebben passino inavvertiti dal volgo, il Filo&shy;<lb/>sofo nonostante piglia per fondamento alle sue speculazioni. </s>

<s>Chiunque vuol <lb/>dalle sue spalle deporre qualche cosa, che gliele aveva aggravate con fati&shy;<lb/>cosa molestia, o la getta a posar per terra o l'attacca a qualche mensola. </s>

<s><lb/>Il piano suolo dunque direttamente, e gli oggetti fermati in esso e sopr'esso <lb/>elevati son le macchine pi&ugrave; naturali, che i primi uomini ebbero a trovar <lb/>negli aperti campi, e ne'rami degli alberi sporgenti. </s>

<s>L'essenza poi di co&shy;<lb/>teste macchine, che la Natura spontanea offeriva agli affaticati, si vede non <lb/>in altro insomma consistere che nell'uso dei sostegni. </s></p><p type="main">

<s>I corpi per&ograve;, cos&igrave; ben sostenuti, si rimanevano tuttavia immobili, e a <lb/>colui, che, per suo desiderio o per suo bisogno, gli avesse voluti traslocare, <pb xlink:href="020/01/1971.jpg" pagenum="214"/>conveniva riprenderseli nuovamente di l&agrave;, dove aveagli o posati o sospesi, <lb/>riaggravandosi di tutta quella prima deposta fatica le braccia e gli omeri. </s>

<s><lb/>Il non poter sempre durare una tal fatica, e il desiderio innato di allegge&shy;<lb/>rirla affin&ograve; l'industria, e sugger&igrave; i primi esercizi dell'arte. </s>

<s>Dovett'essere il <lb/>pi&ugrave; ovvio di questi suggerimenti quello di traslocare il pesante corpo posato <lb/>in piano col rotolarlo, ci&ograve; che serviva bene, quando si voleva mettere da una <lb/>parte piuttosto che da un'altra, ma non gi&agrave;, quando fosse stato bisogno di <lb/>sollevarlo pi&ugrave; in alto. </s>

<s>S'ebbe a sperimentare anzi che, dove l&agrave; bastava una <lb/>piccolissima forza, qui era invece necessit&agrave; di mettercela tutta. </s>

<s>Doveva es&shy;<lb/>servi dunque, tra questo massimo e quel minimo, una via di mezzo, ed era <lb/>ci&ograve; appunto che si cercava, perch&egrave; ben riconoscendo non esser possibile a <lb/>sollevare un peso senza fatica, n&egrave; potendo per natura scansarla, si cercava <lb/>l'arte di alleggerirla o di ridurla almen tale, che si potesse durare. </s></p><p type="main">

<s>S'apr&igrave; da questi desiderii la mente, la quale intese che, a rotolare il <lb/>grave sul piano, ci voleva piccolissima forza, perch&egrave; rimaneva tutto sul suo <lb/>sostegno, e che a sollevarlo ce ne bisognava grandissima, perch&egrave; nulla oramai <lb/>pi&ugrave; gli serviva di appoggio. </s>

<s>Bene essendosi di qui compresa la ragion della <lb/>maggiore e della minore difficolt&agrave; del moto, sugger&igrave; l'arte che quello si cer&shy;<lb/>cava si sarebbe facilmente potuto ritrovare <lb/>col far s&igrave; che il grave, se non tutto, fosse <lb/>almeno sostenuto dalla macchina in parte, <lb/>e si lasciasse il resto alle forze del motore. </s></p><p type="main">

<s>S'otteneva l'intento con l'inclinare pi&ugrave; <lb/>o meno il piano sull'orizzonte, e secondo <lb/>quella maggiore o minore inclinazione si <lb/>compartivano, fra la potenza e la resistenza, <lb/>le virt&ugrave; a talento dell'arte. </s>

<s>Sia AB (fig. </s>

<s>93) <lb/>il piano e AD il perpendicolo: a rotolare <lb/>un grave sopra AB richiedesi piccolissima, <lb/>anzi nessuna forza, se fosse possibile ri&shy;<lb/>movere ogni sorta d'impedimenti, perch&egrave; <lb/>la macchina resiste per s&egrave; a tutto il peso. </s>

<s><lb/>Ma a sollevar quello stesso grave per AD, <lb/><figure id="id.020.01.1971.1.jpg" xlink:href="020/01/1971/1.jpg"/></s></p><p type="caption">

<s>Figura 93.<lb/>si richiede tutta intera la forza necessaria, <lb/>perch&egrave; la macchina nulla ne sostenta. </s>

<s>Fra B e D son segnate infinite le vie <lb/>di mezzo, e quanto pi&ugrave; si sale, tanto <lb/>meno resiste la macchina al peso, e pi&ugrave; <lb/>perci&ograve; ne rilascia alle forze del motore. </s></p><p type="main">

<s>Dal piano passando alla mensola, o <lb/>di qualunque sia forma e comunque sia <lb/>posto, al fulcro, ebbe l'arte a essere <lb/>scorta da esperienze simili e da simili <lb/><figure id="id.020.01.1971.2.jpg" xlink:href="020/01/1971/2.jpg"/></s></p><p type="caption">

<s>Figura 94.<lb/>ragionamenti, quando volle provarsi a sollevare i pesi, esercitandovi at&shy;<lb/>torno la Leva. </s>

<s>Sia in C (fig. </s>

<s>94) ad essa Leva il fulcro, e sia in B col-<pb xlink:href="020/01/1972.jpg" pagenum="215"/>locato il peso: facilissime esperienze dimostrarono che, facendosi forza in A <lb/>a una distanza da C eguale a quella di B, si durava fatica quanto a tenere <lb/>il peso in mano, o quanto a riprenderlo dalla mensola, dove s'era attac&shy;<lb/>cato, e rimetterselo sulle braccia. </s>

<s>Ritirando per&ograve; B verso C si sentiva alle&shy;<lb/>viare via via la fatica, infin tanto che, giunto in C, non ci voleva forza di <lb/>nulla. </s>

<s>S'ebbe anche di qui perci&ograve; a riconoscere che fra il tutto e il nulla <lb/>v'erano le vie di mezzo, la ragion delle quali dipendeva dalla maggiore o <lb/>minor distanza dal sostegno, secondo la qual distanza si potevano a piacer <lb/>dell'arte compartire, fra la potenza e la resistenza, i respettivi momenti. </s>

<s><lb/>Quanto pi&ugrave; debole si sentiva il motore, tanto pi&ugrave; studiavasi di caricarsi di <lb/>men peso per s&egrave;, e di lasciarlo piuttosto sul sostegno, pigliando giusta re&shy;<lb/>gola dalle distanze, giacch&egrave; l'esperienza gli avea insegnato che tanto pi&ugrave; resi&shy;<lb/>ste la macchina, quanto ha il peso pi&ugrave; vicino al centro del moto, e tanto <lb/>men fatica si dura, quanto gli si resiste di pi&ugrave; lontano. </s></p><p type="main">

<s>La Leva e il Piano inclinato sono i due esemplari, a cui s'informano, <lb/>e da cui dipendono le altre macchine conosciute e descritte dalla scienza <lb/>ne'suoi trattati, giacch&egrave; derivano dalla prima l'Asse in peritrochio e il Po&shy;<lb/>lispasto, e dalla seconda il Cuneo e la Coclea. </s>

<s>Que'Filosofi perci&ograve;, che al <lb/>sopra detto modo ragionavano, investigarono l'intima costituzione di tutt'e <lb/>sei le potenze meccaniche, e facilmente ne riconobbero le propriet&agrave; nelle <lb/>ragioni e negli usi. </s></p><p type="main">

<s>Fruga i nostri Lettori la curiosit&agrave; di sapere se fossero que'Filosofi, o <lb/>gli antichi del tempo di Archimede, o i moderni del tempo di Galileo, per <lb/>dar sodisfazione alla qual curiosit&agrave; rispondiamo essere stati coloro, che pi&ugrave; <lb/>espressamente riducevano le virt&ugrave; delle macchine al sostegno, Filosofi sco&shy;<lb/>nosciuti di que'tempi di mezzo, ne'quali speculava Leonardo da Vinci. </s>

<s>Il <lb/>fondamento statico di Lui, come si rifer&igrave; nella prima parte del precedente <lb/>discorso, &egrave; riposto nel principio notissimo che <emph type="italics"/>quella cosa, che fia pi&ugrave; lon&shy;<lb/>tana dal suo firmamento, manco da esso fia sostenuta,<emph.end type="italics"/> d'onde se ne con&shy;<lb/>cludono le leggi dell'equilibrio tra la potenza e la resistenza dei gravi so&shy;<lb/>spesi. </s>

<s>Quanto ai gravi posati sui piani, vedemmo nel capitolo primo di que&shy;<lb/>sto Tomo come Leonardo, immaginando di aver la ruota di un carro, che <lb/>si muova su per un'erta, determinasse con geometrica precisione quel che <lb/>va del peso al sostegno, e quel che rimane a tirare alle forze dell'uomo o <lb/>del cavallo. </s></p><p type="main">

<s>Investigata cos&igrave; la natura delle macchine nelle sue ragioni, era facile <lb/>secondo la verit&agrave; a comprenderne gli usi, imperocch&egrave; s'immagini di aver, <lb/>nella passata figura XCIII, qualche corpo pesante A, il quale si voglia, ser&shy;<lb/>vendosi del piano inclinato, sollevare a un'altezza possibile alle nostre forze. </s>

<s><lb/>Sia quello scelto piano AM, e sopr'esso tirisi il grave, per mezzo della fune <lb/>AE, che passi in E, per la gola della puleggia ivi affissa. </s>

<s>Giunto A in M &egrave; <lb/>scorsa tanto di fune EH, quanto &egrave; la lunghezza AM, e s'&egrave; cos&igrave; conseguito <lb/>l'intento. </s>

<s>Volendosene ora esaminare il modo, si trover&agrave; che, se avessimo <lb/>avuto forza pari alla resistenza, e n&egrave; perci&ograve; bisogno alcuno di macchina, sa-<pb xlink:href="020/01/1973.jpg" pagenum="216"/>rebbesi il peso A potuto sollevare in quel medesimo atto e tempo all'al&shy;<lb/>tezza AD, com'&egrave; facile a intendere immaginando che A, invece di posar sul <lb/>piano pendesse libero in F della puleggia. </s>

<s>Ma intanto, bench&egrave; siasi fatt'uso <lb/>della macchina, &egrave; tanto piccola l'altezza CM, a cui siamo giunti, quanto pic&shy;<lb/>cola era la forza applicata. </s></p><p type="main">

<s>Le medesime proporzioni si osservano nella Leva, perch&egrave;, posto per <lb/>esempio il peso in D (nella figura XCIV poco addietro rappresentata) e a <lb/>una maggior distanza dal fulcro applicata in A la potenza, se avessimo avuto <lb/>forze sufficienti si sarebbe, senza altr'uso di macchina, nel medesimo atto <lb/>e nel medesimo tempo, sollevato il peso infino in E, mentre non siam riu&shy;<lb/>sciti a portarlo pi&ugrave; su che in F, a un'altezza tanto minore di E, quanto le <lb/>nostre facolt&agrave; si trovarono inferiori al bisogno. </s>

<s>Non &egrave; dunque vero, s'ebbe <lb/>a concluderne di qui, che per gli strumenti meccanici s'avvalorin le forze, <lb/>e che se ne moltiplichi l'effetto, vedendosi secondo i meriti, n&egrave; pi&ugrave; n&egrave; meno, <lb/>retribuita la pi&ugrave; giusta mercede. </s>

<s>Sicch&egrave; insomma, bene esaminate le cose, <lb/>si trov&ograve; non ci prestar le macchine altro servizio, che di render, quantun&shy;<lb/>que piccole, efficaci le nostre forze e, non avendo a dispor del tutto, potere <lb/>almeno renderne fruttuosa una parte. </s></p><p type="main">

<s>Tale &egrave; il luminoso concetto che investe le Meccaniche di Leonardo, ma <lb/>che negli Autori succeduti a lui apparisce alquanto meno sincero. </s>

<s>Aveva <lb/>Guidubaldo fatto notare che &ldquo; quo pondus facilius movetur, eo quoque tem&shy;<lb/>pus maius esse; quo vero difficilius, eo minus esse &rdquo; (Mechanic. </s>

<s>lib. </s>

<s>cit., <lb/>fol. </s>

<s>105 a t.), e Galileo faceva da questo fatto dipendere la natura degli stru&shy;<lb/>menti meccanici, e la ragione de'loro effetti, &ldquo; perch&egrave;, avendo noi scarsit&agrave; <lb/>di forza e non di tempo &rdquo; (Alb. </s>

<s>XI, 36), supplisce con l'abbondanza di que&shy;<lb/>sto la macchina al difetto di quella. </s>

<s>S'ebbe di qui a formulare il meccanico <lb/>aforismo: <emph type="italics"/>quel che s'acquista in forza si perde in tempo,<emph.end type="italics"/> ci&ograve; che dai ra&shy;<lb/>gionamenti riferiti di sopra non appare assolutamente vero, essendosene tut&shy;<lb/>t'altrimenti concluso che nulla s'acquista di forza e nulla si perde di tempo. </s>

<s><lb/>Quell'aforismo, che certamente non s'avvera n&egrave; nel Piano inclinato n&egrave; nella <lb/>Leva, Guidubaldo lo applic&ograve; alla Troclea, all'Asse nella ruota e alla Vite, <lb/>d'onde &egrave; facile a comprendersi che la considerazione del tempo, non sov&shy;<lb/>vien dall'essenza della macchina, ma dal particolar modo com'&egrave; disposta, <lb/>che, senza nulla variar degli organi, permette di ripetere e di continuare i <lb/>primi intrapresi esercizi. </s>

<s>Il Peritrochio infatti &egrave; una Leva continua, com'&egrave; un <lb/>piano continuo la Coclea: e la Taglia stessa &egrave; una fune continuamente tesa. </s></p><p type="main">

<s>La natura delle Macchine sembra dunque essere stata assai meglio de&shy;<lb/>finita da Leonardo, che non da Guidubaldo o da Galileo, ond'&egrave; facile aspet&shy;<lb/>tarsi che dovesse avere il primo qualche vantaggio sugli altri due, anche <lb/>nell'investigarne la ragion degli effetti. </s>

<s>Quanto al Piano che, secondo il con&shy;<lb/>cetto dello stesso Leonardo, &egrave; la Macchina essenziale, e a cui si riduce infine <lb/>la stessa Leva; quel vantaggio apparisce dalle cose dette nel capitolo I di <lb/>questo Tomo assai manifesto, e si farebbe manifesto altres&igrave; per le altre mac&shy;<lb/>chine secondarie, se fosse qui o altrove, nella nostra Storia, luogo a trattar <pb xlink:href="020/01/1974.jpg" pagenum="217"/>di proposito della Scienza meccanica di Leonardo da Vinci. </s>

<s>Si vedr&agrave; non&shy;<lb/>stante nel seguente compendioso discorso ricorrerne pi&ugrave; di un esempio. </s></p><p type="main">

<s>Richiederebbe l'ordine logico che si facesse primo il piano, e le due <lb/>Macchine che ne dipendono, naturale soggetto a quel discorso, e che si <lb/>venisse poi a dir della Leva e delle altre due Macchine, che pur da essa de&shy;<lb/>rivano. </s>

<s>Ma non pu&ograve; la storia degli svolgimenti del pensiero adattarsi all'or&shy;<lb/>dine di un trattato, che suppone il pensiero stesso gi&agrave; svolto. </s>

<s>Ci&ograve; necessa&shy;<lb/>riamente conduce a far ultimo quel ch'era primo, e ci consiglia a cominciar <lb/>dal Vette, e dagli strumenti che hanno forma di lui. </s></p><p type="main">

<s>Quando il punto di sospensione &egrave; nel mezzo, si applicano immediata&shy;<lb/>mente al Vette le leggi delle equiponderanze, delle quali Aristotile pose i <lb/>principii, e Archimede poi ne dett&ograve; al mondo geometrica dimostrazione. </s>

<s>Si <lb/>poteva per&ograve; disporre lo strumento in altri due modi, o ponendo il peso tra <lb/>la potenza e il sostegno, o la potenza fra il sostegno e il peso. </s>

<s>Di questi due <lb/>nuovi generi di Leva non si trova fatta chiara distinzione appresso agli An&shy;<lb/>tichi, bench&egrave; la XXIX Questione aristotelica proponga a considerare un esem&shy;<lb/>pio, che imitasi cos&igrave; spesso ne'manuali esercizi. </s>

<s>Perch&egrave;, domanda il Filo&shy;<lb/>sofo, trasportandosi un peso pendente da un legno, posato coll'estremit&agrave; <lb/>sulle spalle a due uomini, si senton questi egualmente aggravati, se il peso <lb/>&egrave; nel mezzo, ma, se riman da una parte, se ne sente pi&ugrave; addosso il pi&ugrave; vi&shy;<lb/>cino? </s>

<s>Forse perch&egrave;, risponde, il legno &egrave; un Vette, il peso &egrave; il fu&igrave;cro, e un <lb/>degli uomini fa da potenza e l'altro da resistenza? </s>

<s>&ldquo; An quoniam Vectis <lb/>quidem lignum efficitur, pondus vero hypomochlion, qui autem proprior est <lb/>ponderi ex iis qui illud gestant, id quod movetur, alter vero portantium <lb/>quod movet &rdquo; (Operum, T. XI cit., fol. </s>

<s>38). </s></p><p type="main">

<s>La questione in sostanza era ben risoluta, se non che, per non trasfi&shy;<lb/>gurar di troppo la natura delle cose, giovava lasciare al peso rappresentar <lb/>la propria qualit&agrave; di resistenza; a uno degli uomini il fulcro, e all'altro il <lb/>motore. </s>

<s>Cos&igrave; veniva ben distinto il secondo genere di Leva, che poi, come <lb/>Aristotile insomma fa, si riduce alle medesime leggi del primo. </s>

<s>La distinzion <lb/>chiara per&ograve; della nuova forma e le ragioni della trasformazione s'incomin&shy;<lb/>ciarono a dimostrar dai Meccanici del secolo XV, ma non apparvero forse <lb/>prima alla luce, che ne'libri del Benedetti e di Guidubaldo del Monte. </s>

<s>Que&shy;<lb/>sti, come lemma preparatorio al suo trattatello <emph type="italics"/>De trochlea,<emph.end type="italics"/> consider&ograve;, nelle <lb/>proposizioni II e III <emph type="italics"/>De vecte,<emph.end type="italics"/> gli altri due modi di usar lo strumento, di&shy;<lb/>versi dall'ordinario descritto da Archimede, e, nel caso che sia il peso nel <lb/>mezzo, dimostr&ograve; in due maniere che la potenza e la resistenza hanno ragion <lb/>reciproca delle distanze dal fulcro. </s>

<s>Galileo imit&ograve; Guidubaldo, alla seconda <lb/>maniera del quale s'accosta la dimostrazione che, nella <emph type="italics"/>Scienza meccanica,<emph.end type="italics"/><lb/>vien proposta per lemma al capitolo <emph type="italics"/>Delle taglie<emph.end type="italics"/> (Alb. </s>

<s>XI, 104, 5). </s></p><p type="main">

<s>Tengono i due Autori il medesimo modo, tenuto gi&agrave; da Leonardo, ma <lb/>egli &egrave; pi&ugrave; agile e, in quella sua naturale <lb/>semplicit&agrave;, pi&ugrave; elegante di loro. </s>

<s>Sia AD <lb/>(fig. </s>

<s>95) una Leva di primo genere col ful&shy;<lb/><figure id="id.020.01.1974.1.jpg" xlink:href="020/01/1974/1.jpg"/></s></p><p type="caption">

<s>Figura 95.<pb xlink:href="020/01/1975.jpg" pagenum="218"/>cre in C, e co'pesi A, D in equilibrio, secondo la nota proporzione D:A= <lb/>AC:CD. </s>

<s>Si trasporti A in B, in distanza eguale dal centro: non verr&agrave; per <lb/>questo alterata in nulla quella prima equiponderanza, la ragion della quale, <lb/>posta BC invece di CA, e B invece di A, sar&agrave; espressa in quest'altra forma <lb/>D:B=BC:CD. </s>

<s>Nella seconda maniera di Guidubaldo, e in quella che <lb/>imit&ograve; da lui Galileo, si riducono le lunghe parole a questo breve discorso, <lb/>che si legge scritto cos&igrave; in una Nota di Leonardo: </s></p><p type="main">

<s>&ldquo; Se la lieva &egrave; doppia della contrallieva, tanto fa al motore avere il <lb/>peso in mezzo alla lieva, quanto nel termine della contrallieva. </s>

<s>Provasi, e <lb/>sia CD la lieva, CA la contrallieva, la quale &egrave; per la met&agrave; d'essa lieva. </s>

<s>E <lb/>se il peso sar&agrave; applicato nel mezzo della lieva in B, allora tanto ne sentir&agrave; <lb/>il sito C, quanto ne sente D, perch&egrave; le distanze CB, e DB, ch'el sostengono, <lb/>sono uguali, e per la nona di questo libro tal fia la proporzione de'pesi, che <lb/>sente li sostentacoli del peso da lor sostenuto, qual'&egrave; quella delle distanze, <lb/>che hanno li centri de'sostentacoli dal centro del grave sospeso. </s>

<s>Adunque <lb/>&egrave; concluso che C, D sostentacoli si caricano ugualmente di B peso. </s>

<s>Oltre a <lb/>di questo, se il peso B fia trasmutato tanto al di l&agrave; del fine della lieva, <lb/>quanto era di qua, il motore D sentir&agrave; tanto peso del grave trasmutato, <lb/>quanto esso si sentissi di prima. </s>

<s>Provasi: CD lieva del motore D &egrave; doppia <lb/>alla contrallieva del mobile A, adunque D motore sente la met&agrave; del mobile, <lb/>come sentire solea, quando esso mobile era in B, e cos&igrave; &egrave; concluso il nostro <lb/>intento &rdquo; (Manuscr. </s>

<s>G cit., fol. </s>

<s>63). </s></p><p type="main">

<s>Riman qui Leonardo nel solo modo di dimostrare superiore a Guidu&shy;<lb/>baldo, ma altrove, ci&ograve; che pi&ugrave; importa, lo vince, quando sia per inusitati <lb/>sentieri da giungere alla scoperta del vero. </s>

<s>Le proposizioni VIII e IX <emph type="italics"/>De <lb/>vecte<emph.end type="italics"/> son manifestamente false, e farebbe gran maraviglia che non avessero <lb/>l'esperienze fatto ravveder de'suoi errori l'Autore, se avesse saputo il modo <lb/>di applicare all'estremo braccio della leva inclinata la giusta direzione della <lb/>potenza. </s>

<s>&ldquo; Sit vectis AB (fig. </s>

<s>96), <lb/><figure id="id.020.01.1975.1.jpg" xlink:href="020/01/1975/1.jpg"/></s></p><p type="caption">

<s>Figura 96.<lb/>egli dice, horizonti aequidistans, cu&shy;<lb/>ius fulcimentum C, pondus autem <lb/>BD, eiusdem vero gravitatis centrum <lb/>sit supra vectem uhi H, sitque po&shy;<lb/>tentia sustinens in A. </s>

<s>Moveatur dein&shy;<lb/>de Vectis AB in EF, sitque pondus <lb/>motum in FG: dico primum mino&shy;<lb/>rem potentiam E sustinere pondus <lb/>FG, vecte EF, quam potentia in A <lb/>pondus BD, vecte AB.... Sit deinde <lb/>vectis in QR, et pondus in QS, cuius centrum gravitatis sit O: dico maio&shy;<lb/>rem requiri potentiam in R ad sustinendum pondus QS, quam in A, ad <lb/>pondus BD &rdquo; (Mechanic., lib. </s>

<s>cit., fol. </s>

<s>44, 45). </s></p><p type="main">

<s>La ragione di questi asserti la fa Guidubaldo dipendere dalle interse&shy;<lb/>zioni delle perpendicolari condotte sulle Leve dai centri di gravit&agrave; dei pesi, <pb xlink:href="020/01/1976.jpg" pagenum="219"/>le quali perpendicolari, nel peso orizzontale BD, precidono il braccio di leva <lb/>in I, ma nel peso sollevato in FG lo precidono in M pi&ugrave; vicino, e nel peso <lb/>abbassato in QI lo precidono in T, pi&ugrave; lontano dal fulcro di quel che non <lb/>sia I. </s>

<s>Da questa variet&agrave; di distanze, cos&igrave; misurate, conclude Guidubaldo la <lb/>variet&agrave; dei momenti, ma Leonardo, seguendo in ci&ograve; la regola vera, ch'era <lb/>quella di porre i pesi <emph type="italics"/>sotto la loro perpendicolare sopra la linea della ugua&shy;<lb/>lit&agrave;,<emph.end type="italics"/> se questa linea della ugualit&agrave; &egrave; AB, abbassate sopr'essa, dai due cen&shy;<lb/>tri K, O, le perpendicolari KY, TX, avrebbe sicuramente detto essere CY <lb/>e CX, e non CM e CT le distanze dal centro, per le quali s'ha, rispetto a <lb/>CI, da misurare la variet&agrave; del momento che subisce il peso o pi&ugrave; alto o pi&ugrave; <lb/>basso. </s>

<s>Si sarebbe di qui facilmente scoperta la fallacia, che s'ascondeva nel <lb/>discorso, per cui concludevasi da Guidubaldo dover essere in QI il grave <lb/>pi&ugrave; ponderoso, quando non gli fosse in pi&ugrave; diritto e sicuro modo rivelato <lb/>il vero dall'esperienza, come doveva essergli occorso nel trattar dell'Asse <lb/>nel peritrochio. </s></p><p type="main">

<s>Di questa macchina non lasciarono gli Antichi altro documento, da quel <lb/>che si legge nell'ottavo libro delle Collezioni di Pappo, dove il Matematico <lb/>alessandrino si limita a descrivere brevemente gli organi, chiamando asse <lb/>il cilindro, intorno a cui s'avvolge la fune che ha da tirare il peso, timpano <lb/>la ruota attraversata nel suo centro dall'asse, e scitale dall'ufficio le leve <lb/>confitte sulla circonferenza della stessa ruota, le quali valgono per noi quanto <lb/>a dire manubrii. </s>

<s>Rimase perci&ograve; ai moderni l'ufficio di dare scienza dell'arte, <lb/>e Guidubaldo del Monte, fra'primi e pi&ugrave; conosciuti, dimostr&ograve; questa facile <lb/>proposizione: &ldquo; Potentia pondus sustinens Axe in peritrochio ad pondus, <lb/>eamdem habet proportionem, quam semidiameter Axis ad semidiametrum <lb/>tympani, una cum scytala &rdquo; (Mechan., lib. </s>

<s>cit., fol. </s>

<s>107). </s></p><p type="main">

<s>Le difficolt&agrave; cominciarono quando, costituendosi la potenza in un altro <lb/>peso, la scitala usciva fuori della sua prima posizione orizzontale. </s>

<s>Vennero <lb/>allora l'esperienze a far veder chiaramente che quella stessa potenza va&shy;<lb/>riava il momento, e Guidubaldo, applicandovi la regola de'centri di gravit&agrave;, <lb/>riusc&igrave; a dimostrare il fatto e la causa, ma non le giuste proporzioni di una <lb/>tal variazione. </s>

<s>Quelle esperienze per&ograve;, pi&ugrave; giudiziosamente consultate che <lb/>nelle proposizioni VIII e IX <emph type="italics"/>De vecte,<emph.end type="italics"/> rivelarono all'Autore il vero, almeno <lb/>in una sua parte pi&ugrave; rilevante, ponendo mente alla differenza che passa, <lb/>quando si fa l'equilibrio della macchina vincere a un peso morto, o a una <lb/>potenza animata, come son le mani e le braccia dell'uomo. </s>

<s>In questo caso, <lb/>o tirando l'un manubrio o l'altro, la fatica &egrave; sempre la stessa, perch&egrave; la <lb/>forza non &egrave; diretta secondo il perpendicolo, ma secondo la circonferenza. <lb/></s>

<s>&ldquo; Tunc eademmedet potentia, vel in F vel in T constituta, idem pondus <lb/>sustinere poterit, cum semper, in cuiuscumque extremitate scytalae ponatur, <lb/>ab eodem centro aequidistans fuerit, ac secundum eamdem circumferentiam <lb/>ab eodem centro aequaliter semper distantem propensionem habeat. </s>

<s>Neque <lb/>enim, sicuti pondus, proprio nutu magis in centrum ferri exoptat quam cir&shy;<lb/>culariter moveri, cum utrumque seu quemlibet alium motum nullo prorsus <pb xlink:href="020/01/1977.jpg" pagenum="220"/>respiciat discrimine. </s>

<s>Propterea non eodem modo res se habet, sive pondera, <lb/>sive animatae potentiae iisdem locis, eodem munere obeundo, fuerint consti&shy;<lb/>tutae &rdquo; (ibid., fol. </s>

<s>109). </s></p><p type="main">

<s>Galileo, dietro i documenti che s'avevano oramai studiando nelle Mec&shy;<lb/>caniche del Benedetti, illustr&ograve; e ridusse a matematica precisione il concetto <lb/>di Guidubaldo, che cio&egrave; &ldquo; se nella medesima circonferenza fosse applicata <lb/>forza animata, la quale avesse momento di far impeto per tutti i versi, po&shy;<lb/>tria far l'effetio, costituita in qualsivoglia luogo di detta circonferenza, ti&shy;<lb/>rando non al basso, ma in traverso secondo la contingente &rdquo; (Alb. </s>

<s>XI, 101), <lb/>perch'essendo la tangente perpendicolare al raggio serba, per le cose dimo&shy;<lb/>strate dal Benedetti, tutta intera la sua potenza. </s>

<s>Si riduce in conclusione a <lb/>queste e a poche altre semplici considerazioni quel che, esplicando e di pi&ugrave; <lb/>facili parole ornando il trattato di Guidubaldo, trov&ograve; da aggiungere Galileo <lb/>nella scienza meccanica dell'Asse nella ruota. </s>

<s>Ma passando alle Taglie non <lb/>promove proprio di nulla la scienza del suo predecessore, fedelmente e in <lb/>tutto seguitata da lui, bench&egrave; fosse facile a riconoscerla in s&egrave; cos&igrave; difettosa. </s></p><p type="main">

<s>La seconda proposizione <emph type="italics"/>De trochlea,<emph.end type="italics"/> nel libro di Guidubaldo, &egrave; cos&igrave; <lb/>formulata: &ldquo; Si funis orbiculo trochleae ponderi alligatae circumducatur, al&shy;<lb/>tero eius extremo alicubi religato, al&shy;<lb/>tero vero a potentia pondus susti&shy;<lb/>nente apprehenso, erit potentia pon&shy;<lb/>deris subdupla &rdquo; (fol. </s>

<s>64 t.). Figurata <lb/>in BCD (fig. </s>

<s>97) la rotella, dall'asse <lb/>E dalla quale penda il peso A, soste&shy;<lb/>nuto dalle funi FB, GD, una delle <lb/>quali sia fissa in F e sia all'altra ap&shy;<lb/>plicata la potenza, dimostra Guidu&shy;<lb/>baldo quella sua proposizione, condu&shy;<lb/>cendo il diametro DB, in cui vede rap&shy;<lb/>presentarsi una Leva di secondo genere <lb/>col sostegno in B, colla resistenza po&shy;<lb/>sta nel mezzo E, e con la potenza ap&shy;<lb/>plicata in D, la quale, per le cose di&shy;<lb/><figure id="id.020.01.1977.1.jpg" xlink:href="020/01/1977/1.jpg"/></s></p><p type="caption">

<s>Figura 97.<lb/>mostrate <emph type="italics"/>De vecte,<emph.end type="italics"/> dee stare al peso come BE a BD o come uno sta a due. </s></p><p type="main">

<s>Galileo, avendo anch'egli premessa per servir di lemma, come dicemmo, <lb/>la dimostrazione delle condizioni dell'equilibrio nella Leva di secondo ge&shy;<lb/>nere, l'applica, ad imitazione di Guidubaldo, alla girella sostenuta da due <lb/>funi, e poi soggiunge: &ldquo; Abbiamo fin qui esplicato come, col mezzo della <lb/>Taglia, si possa duplicar la forza. </s>

<s>Resta che, con maggior brevit&agrave; che sia <lb/>possibile, dimostriamo il modo di crescerla secondo qual si voglia moltipli&shy;<lb/>cit&agrave;, e prima parleremo della moltiplicit&agrave; secondo i numeri pari, e poi <lb/>impari, e per dimostrar come si possa aumentare la forza in proporzione <lb/>quadrupla, proporremo la seguente speculazione, come lemma delle cose se&shy;<lb/>guenti &rdquo; (Alb. </s>

<s>XI, 108, 9). </s></p><pb xlink:href="020/01/1978.jpg" pagenum="221"/><p type="main">

<s>Il lemma, che passa a dimostrar Galileo, &egrave; la proposizione VI formu&shy;<lb/>lata cos&igrave; da Guidubaldo: &ldquo; Sint duo vectes AB, CD (fig. </s>

<s>98) bifariam divisi <lb/>in E, F, quorum fulcimenta sint in B, D; sitque pondus G in E, F utrique <lb/><figure id="id.020.01.1978.1.jpg" xlink:href="020/01/1978/1.jpg"/></s></p><p type="caption">

<s>Figura 98.<lb/>vecti appensum, ita ut ex utroque <lb/>aequaliter ponderet, duaeque sint po&shy;<lb/>tentiae in A, C aequales pondus su&shy;<lb/>stinentes; dico unamquamque poten&shy;<lb/>tiam in A, C subquadruplam esse pon&shy;<lb/>deris G &rdquo; (Mechan., lib. </s>

<s>cit., fol. </s>

<s>70). <lb/>La facile dimostrazione &egrave; uguale nel&shy;<lb/>l'uno e nell'altro Autore, com'&egrave; ugua&shy;<lb/>le l'applicazione che da ambedue se <lb/>ne fa, quando una girella di sopra <lb/>sostiene altre due girelle di sotto, i diametri delle quali fanno l'ufficio, e <lb/>seguon perci&ograve; le leggi statiche de'due vetti proposti. </s>

<s>Provasi con analogo <lb/>discorso che, se i vetti son tre, la potenza &egrave; un sesto, se son quattro, &egrave; <lb/>un ottavo del peso, &ldquo; atque ita deinceps in infinitum &rdquo; (ibid.). </s></p><p type="main">

<s>&ldquo; Passando ora, dice Galileo, alla dichiarazione del modo di moltipli&shy;<lb/>care la forza secondo i numeri dispari, e facendo principio dalla proporzione <lb/>tripla, prima metteremo avanti la presente speculazione, come che dalla sua <lb/>intelligenza dipenda tutto il presente negozio &rdquo; (Alb. </s>

<s>XI, 111). La specula&shy;<lb/>zione consiste nella proposizione IV da Guidubaldo cos&igrave; formulata: &ldquo; Sit <lb/>vectis AB (nella precedente figura) cuius fulcimentum sit B, qui bifariam <lb/>dividatur in E, sitque pondus G in E appensum, duaeque sint potentiae ae&shy;<lb/>quales in E, A pondus G sustinentes: dico unamquamque potentiam in E, A <lb/>ponderis G subtriplam esse (Mechan., lib. </s>

<s>cit., fol. </s>

<s>67 a t.). </s></p><p type="main">

<s>Serve anche questa proposizione ad ambedue gli Autori di lemma a <lb/>dimostrar che la potenza &egrave; un terzo della resistenza, quando alla girella in&shy;<lb/>feriore, da cui pende il peso, ne sovrasti una superiore congiuntale per una <lb/>corda, un capo della quale sia fermato alla stessa girella inferiore, e sia al&shy;<lb/>l'altro applicata la virt&ugrave; motrice. </s>

<s>Con ragioni analoghe a queste si dimo&shy;<lb/>stra da Guidubaldo il modo e la ragione di ridurre a un quinto, a un set&shy;<lb/>timo, a un nono, e cosi di seguito la forza applicata alla fune, rispetto a <lb/>quella, che assolutamente bisognerebbe per sollevare senz'altra macchina il <lb/>peso. </s>

<s>&Egrave; poi sollecito di far notare in corollarii che si deducono via via dalle <lb/>dimostrate proposizioni, come al diminuir della forza corrisponde sempre una <lb/>lunghezza maggiore nel viaggio; cosicch&egrave; non si riduce essa forza per esem&shy;<lb/>pio alla met&agrave;, o a un terzo, senza ch'ella non abbia contrariamente a per&shy;<lb/>correre il doppio o il triplo dello spazio. </s>

<s>In conformit&agrave; di che Galileo, dopo <lb/>aver dimostrato il modo e le ragioni di ridur per le Taglie a met&agrave; la fatica <lb/>soggiunge: &ldquo; E qui, come negli altri strumenti s'&egrave; fatto e ne'seguenti si <lb/>far&agrave;, non passeremo senza considerazione come il viaggio, che fa la forza, <lb/>venga ad essere doppio del movimento del peso &rdquo; (Alb. </s>

<s>XI, 107). </s></p><p type="main">

<s>Il Cartesio, descrivendo nelle sue Meccaniche le propriet&agrave; della Troclea, <pb xlink:href="020/01/1979.jpg" pagenum="222"/>faceva notar, come cosa nuova e importante, che le virt&ugrave; della macchina <lb/>non nascono dalla Troclea in s&egrave; stessa, ma dalla fune, la quale, avvolta so&shy;<lb/>lamente di sotto, se la potenza tira in su, o di sotto e di sopra, se si vuol <lb/>farla tirare in gi&ugrave;, percorre uno spazio doppio di quello, che nello stesso <lb/>tempo si percorre dal peso. </s>

<s>&ldquo; Observandum quoque est vires illas non a <lb/>Trochlea proficisci, sed tantummodo a funis motu illius, qui ponderi est <lb/>motus duplo &rdquo; (Editio cit., pag. </s>

<s>15). In una delle sue Epistole poi diceva <lb/>essere una sciocchezza quella di Guidubaldo, che riduceva la Troclea alla <lb/>natura del Vette. </s>

<s>&ldquo; In Trochea autem ineptum mihi videtur Vectem quae&shy;<lb/>rere, quod, si bene memini, Guidonis Ubaldi figmentum est &rdquo; (Epist., P. II <lb/>cit., pag. </s>

<s>93). </s></p><p type="main">

<s>L'accusa insolente &egrave; stata oramai giudicata dai Matematici moderni, i <lb/>quali, bench&egrave; considerino pi&ugrave; volentieri le tensioni delle funi, non credon <lb/>per&ograve; che sia ridicolo il riconoscere nella Troclea le virt&ugrave; stesse del Vette. </s>

<s><lb/>Pi&ugrave; giudiziosa dunque di quella del Cartesio sembrer&agrave; a tutti la delibera&shy;<lb/>zione presa da un nostro Italiano, se non precursore certamente contempo&shy;<lb/>raneo al Filosofo francese, il qual nostro Autore, intendendo che sia la po&shy;<lb/>tenza applicata alle funi, pensava di avere a dimostrar le proposizioni delle <lb/>Taglie meglio di Guidubaldo. </s></p><p type="main">

<s>Niccol&ograve; Aggiunti sanamente ragionava non poter essere le virt&ugrave;, dove <lb/>manchi la natura del Vette, la quale par che essenzialmente sia posta nel <lb/>sostegno. </s>

<s>&ldquo; Se il peso G, egli dice (nella precedente figura XCVIII), sar&agrave; <lb/>sostenuto dalle forze A, C, il sostegno in B sosterr&agrave; quel che avanza a dette <lb/>forze, perch&egrave; il sostegno B non fa forza in su ma solo ritien che la leva, <lb/>dalla parte B, non si muova in gi&ugrave;. </s>

<s>Sicch&egrave;, quando le sole forze A, C fos&shy;<lb/>sero bastanti a sostenere il peso G (come sempre avvien nelle Taglie) il so&shy;<lb/>stegno non opera cosa alcuna &rdquo; (MSS. Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>91). </s></p><p type="main">

<s>Persuaso dunque che debba esser cos&igrave;, come la mente gli ragionava, <lb/>che cio&egrave; nelle taglie operino solamente le forze applicate alle funi, a dimo&shy;<lb/>strare il particolar modo di cos&igrave; fatta operazione s'apparecchiava l'Aggiunti <lb/>il seguente teorema: &ldquo; Sia la <lb/>superfice parallelogramma o ret&shy;<lb/>tangola AB (fig. </s>

<s>99) orizzontale, <lb/>ed in essa sia la linea ED, che <lb/>divida nel mezzo FB, AI, ed essa <lb/>ancora sia divisa in mezzo col <lb/>punto C, dal quale ereggasi la <lb/>CH perpendicolare al piano AB. </s>

<s><lb/>Intendasi la detta linea ED mo&shy;<lb/>bile intorno al punto C, come <lb/>una bilancia di braccia uguali, <lb/>ed al moto di essa intendasi con&shy;<lb/>seguentemente mobile la super&shy;<lb/>fice AB. </s>

<s>Intendansi poi distese <lb/><figure id="id.020.01.1979.1.jpg" xlink:href="020/01/1979/1.jpg"/></s></p><p type="caption">

<s>Figura 99.<pb xlink:href="020/01/1980.jpg" pagenum="223"/>secondo le linee equidistanti AF, ED, IB, le corde NAFM, XEDK, QIBR, e <lb/>dalla parte AI penda attaccato il cilindro grave NQ, il quale sia sospeso da <lb/>tutt'e tre le corde in sito orizzontale e parallelo alla AI. Dall'altra parte <lb/>della FB pendano, dai tre capi delle corde, i tre gravi U, S, T eguali in <lb/>mole e in peso ciascuno a ciascuno, e tra tutti e tre di egual peso che il <lb/>cilindro <expan abbr="Nq.">Nque</expan> &rdquo; </s></p><p type="main">

<s>&ldquo; Essendo dunque i tre gravi pendenti, come se fossero attaccati co'loro <lb/>centri di gravit&agrave; ugualmente distanti l'un dall'altro, dunque, per la V di <lb/>Archimede, il centro della gravezza composta di tutti e tre sar&agrave; nel punto <lb/>D, sicch&egrave; tutto il peso di tutti e tre gravita massimamente in D, esercitando <lb/>l'istessa gravit&agrave;, attaccati ne'punti F, D, B, come se tutti e tre fossero at&shy;<lb/>taccati in D, e cos&igrave; il cilindro NQ &egrave; come se fosse attaccato solamente in <lb/>E, e l'istesso peso sente la libbra ED, quando il cilindro pende dai punti <lb/>A, E, I, come quando pende da E solamente. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Essendo dunque in questo modo pesi uguali attaccati in distanze uguali <lb/>dalla libbra ED, si far&agrave; l'equilibrio, e la colonna equiponderer&agrave; alli tre pesi. </s>

<s><lb/>Ma i tre pesi attaccati in F, D, B gravitano a parte, come appesi tutti in&shy;<lb/>sieme al punto D, e la colonna sospesa come prima in A, E, I gravita come <lb/>sospesa solamente dal punto E; dunque anco in questo stato il peso S non <lb/>pu&ograve; se non sostenere del peso NQ, attaccato in egual distanza a quella <lb/>d'onde egli stesso &egrave; sospeso; non pu&ograve; dico sostenere se non quella parte, <lb/>che sar&agrave; uguale a lui medesimo. </s>

<s>Ma il peso di esso &egrave; una terza parte del <lb/>cilindro NQ, per il supposto, ponendo tutti e tre eguali a tutto NQ, adun&shy;<lb/>que il peso S sostiene la terza parte del peso <expan abbr="Nq.">Nque</expan> Adunque le rimanenti <lb/>due terze parti son sostenute dalli pesi U, T. </s>

<s>Ma questi sono tra loro uguali, <lb/>e costituiti nel medesimo modo rispetto alla libbra ED, dunque sostengono <lb/>ugualmente, e per&ograve; anch'essi sostengono una terza parte del cilindro &rdquo; (ivi). </s></p><p type="main">

<s>Seguita a questa proposizione un corollario, in cui dichiara l'Autore la <lb/>sua intenzione di applicare i dimostrati principii alle Taglie. </s>

<s>&ldquo; Dal che rac&shy;<lb/>cogliesi, egli dice, che se, invece delli tre pesi pendenti ed eguali, s'inten&shy;<lb/>deranno applicate tre forze eguali, una per una alle corde NA, XE, QI, che <lb/>per appunto sostenessero il grave NQ orizzontalmente; ciascuna di queste <lb/>forze &egrave; uguale alla terza parte del peso sostenuto. </s>

<s>Di qui, s'io non erro, <lb/>dimostrer&ograve; meglio del signor marchese Guidubaldo le proposizioni delle Ta&shy;<lb/>glie, considerando nelle corde che sostengono il peso essere applicate forze <lb/>eguali tra di loro. </s>

<s>La qual considerazione sar&agrave; verissima, perch&egrave; finalmente <lb/>la sola forza, ch'&egrave; posta nel capo della corda che s'avvolge alle girelle, &egrave; <lb/>quella che tien per tutto tirata la corda, e che si va per tutto insinuando <lb/>in essa, come a suo luogo dichiareremo, e dimostreremo le proposizioni delle <lb/>Taglie, senza considerare in esse i sostegni, come fa Guidubaldo, i quali non <lb/>pare che vi abbiano luogo &rdquo; (ivi, fol. </s>

<s>90). </s></p><p type="main">

<s>La meccanica delle Taglie veniva, per cos&igrave; fatte considerazioni, ridotta <lb/>alla sua perfezione, raggiuntasi assai presto in Italia por opera di Guidu&shy;<lb/>baldo e dell'Aggiunti. </s>

<s>Ma sulla fine del secolo XV si comprendevano insieme <pb xlink:href="020/01/1981.jpg" pagenum="224"/>le specu&igrave;azioni dei due Autori dai Matematici di quei tempi, che gli avevano <lb/>preceduti, com'apparisce dai documenti rimastici ne'manoscritti di Leonardo <lb/>da Vinci. </s>

<s>Riconoscendo anche nelle Taglie la natura propria a tutte le mac&shy;<lb/>chine, facevano consistere la loro essenzial virt&ugrave; nel sostegno, il quale in <lb/>questo caso &egrave; la mensola che sostenta il peso, non immediatamente, ma me&shy;<lb/>diante un filo o una fune a cui si attacca. </s>

<s>Riprendendosi in mano cotesto <lb/>filo, si veniva a riprendere anche tutta insieme la prima deposta fatica, ma, <lb/>sperimentando e ragionando a quel modo che facevasi dianzi intorno al Piano <lb/>e alla Leva, s'ebbe a riconoscere facilmente che si poteva esercitar, non <lb/>avendola tutta, una forza parziale coll'incaricarsi di una parte del peso, ri&shy;<lb/>lasciandone a sostenere alla mensola il resto. </s>

<s>Cos&igrave;, supposto che sia GF nella <lb/>precedente figura 97, una mensola, alla quale sieno attaccati i due capi G, F <lb/>della corda GCF, che infilata in una puleggia o in un anello sostenga il peso A <lb/>di sotto, lasciando fermo il capo F e solo prendendo l'altro capo G in mano, <lb/>si sentir&agrave; questa alleggerita della met&agrave; dello sforzo. </s></p><p type="main">

<s>Facilissimo era poi trovar modo di far sostenere alla mensola qualun&shy;<lb/>que altra parte del peso maggiore della met&agrave;, col moltiplicar, per mezzo di <lb/>una traversa ferma di sopra, alle corde i punti di appoggio, e per mezzo di <lb/>un'altra traversa di sotto i punti di attacco. </s>

<s>S'immagini infatti di aver fer&shy;<lb/>mata in ACB (fig. </s>

<s>100) la traversa AB, la quale possa nella sua lunghezza <lb/>dar luogo a pi&ugrave; punti di appoggio, e da quel di mezzo C penda la corda <lb/><figure id="id.020.01.1981.1.jpg" xlink:href="020/01/1981/1.jpg"/></s></p><p type="caption">

<s>Figura 100.<lb/>CD, alla quale sia in D legata la tra&shy;<lb/>versa EF, che sostiene il peso G nel <lb/>suo mezzo. </s>

<s>Presi i quattro punti di <lb/>appoggio O, M, N, I e P, H, L, K re&shy;<lb/>spettivi punti di attacco delle corde <lb/>OP, MH, NL, IK, &egrave; facile intendere <lb/>come sciolta la CD le quattro che la <lb/>suppliscono sostengano ciascuna la <lb/>quarta parte di tutto il peso, cosic&shy;<lb/>ch&egrave; se il capo della fune O sia so&shy;<lb/>stenuto dal braccio di un uomo, que&shy;<lb/>sto, per sostenere il grave pendente, non ha da far che sola una quarta parte <lb/>dello sforzo. </s>

<s>E perch&egrave; si pu&ograve; a piacere moltiplicare il numero delle corde, <lb/>s'intende come si pu&ograve; a piacere incaricarsi di qualunque piccolo peso, la&shy;<lb/>sciandone tutto il resto al sostegno. </s></p><p type="main">

<s>Andava per&ograve; cos&igrave; bene il discorso, quando si trattava di sostenere, ma <lb/>trattandosi di movere, non era questo lo strumento adattato al bisogno. </s>

<s>Vo&shy;<lb/>levano essere le funi, non fisse, ma scorrevoli, e comunicantisi la forza l'una <lb/>all'altra, ci&ograve; che facilmente s'otteneva, fissando ne'punti R, S, T, U altret&shy;<lb/>tante girelle, sulle quali scorrendo, si continuasse una fune dall'uno all'al&shy;<lb/>tro suo estremo. </s></p><p type="main">

<s>Era questa la natura delle Taglie, che rappresentavasi nelle specula&shy;<lb/>zioni di Leonardo, il quale, ritraendo nel suo modo di dimostrare il modo <pb xlink:href="020/01/1982.jpg" pagenum="225"/>stesso come gli s'eran venuti a svolgere nella mente i pensieri, quasi sem&shy;<lb/>pre disegna disposte come nella figura C le carrucole, che hanno a servir <lb/>d'esempio alle sue proposizioni. </s>

<s>Veniva cos&igrave; benissimo a riconoscersi lo stru&shy;<lb/>mento in ci&ograve; che ha di comune con le altre macchine, che pigliano la loro <lb/>virt&ugrave; dai sostegni, e in ci&ograve; che gli &egrave; proprio, e lo rende una macchina par&shy;<lb/>ticolare, per l'uso che vi si fa delle funi, le quali, avendo ugual tensione <lb/>nell'equilibrio, una piccola forza, che sopraggiungasi alla potenza, <emph type="italics"/>tutte le <lb/>vince,<emph.end type="italics"/> dice Leonardo stesso nel suo potente linguaggio, <emph type="italics"/>e tutte le muove.<emph.end type="italics"/><lb/>L'espressione &egrave; resa dall'Aggiunti in quelle parole, poco dianzi citate, nelle <lb/>quali diceva che <emph type="italics"/>la sola forza, posta nel capo della corda che s'avvolge <lb/>alle girelle, &egrave; quella che tien per tutto tirata la corda, e che si va per <lb/>tutto insinuando in essa.<emph.end type="italics"/></s></p><p type="main">

<s>Era dunque bisogno venisse dimostrato che la forza s'insinua in tutta <lb/>la lunghezza della fune? </s>

<s>Senza dubbio: e se Galileo ne tratt&ograve; in modo fisico, <lb/>fu l'Aggiunti il primo a darne matematica dimostrazione, com'apparisce da <lb/>ci&ograve; che si legge nel capitolo V del nostro II Tomo a pag. </s>

<s>215. Sembra che <lb/>rimanesse intorno a ci&ograve; ingannato, a principio, anche Leonardo, ma poi si <lb/>persuase del vero cos&igrave; espresso in una Nota, da noi anche altrove trascritta: <lb/><emph type="italics"/>Ogni gravit&agrave; sospesa &egrave; tutta per tutta la lunghezza della corda, che la <lb/>sostiene, ed &egrave; tutta in ogni parte di quella.<emph.end type="italics"/> D'ond'&egrave; facile intendere come, <lb/>seguitando a correre l'errore, che cio&egrave; non per tutta la lunghezza si diffonda <lb/>nella fune la forza uguale, non poteva Guidubaldo professare il principio <lb/>cos&igrave; semplice delle tensioni, a cui suppl&igrave; con la ragion certissima del Vette. </s>

<s><lb/>Non era questo dunque un commettere errore, e tanto meno, come impu&shy;<lb/>dentemente volle dire il Cartesio, uno scorrere in ridicolezze, ma piuttosto <lb/>era un difetto inevitabile a una scienza, alla quale era rotto il filo delle pi&ugrave; <lb/>prossime tradizioni, e che, rimasta alle forze di un uomo solo, rendeva ine&shy;<lb/>vitabili altri e maggiori difetti. </s>

<s>Nel <emph type="italics"/>Liber mechanicorum<emph.end type="italics"/> del nostro Urbi&shy;<lb/>nate si suppon sempre, in qualunque disposizione di Taglie, che le funi ti&shy;<lb/>rino fra loro parallele, ci&ograve; che non sempre nella pratica si avvera, e bench&egrave; <lb/>fosse facile sperimentare che quella perpendicolar direzion delle forze tor&shy;<lb/>nava pi&ugrave; vantaggiosa, la necessit&agrave; nonostante portava a dover tirare spesso <lb/>in direzione obliqua. </s></p><p type="main">

<s>In questo caso l'esperienza stessa mostrava che le relazioni fra la re&shy;<lb/>sistenza e la potenza variavano, al variarsi l'angolo dell'obliquit&agrave;, ma con <lb/>qual ordine si facesse una tal variazione non era facile a Guidubaldo il di&shy;<lb/>mostrarlo, n&egrave; a Galileo, i quali perci&ograve; non vollero nemmen tentare l'arduo <lb/>problema. </s>

<s>Al difetto, in cui lasciarono i due Matematici la scienza, aveva <lb/>come vedemmo largamente supplito Leonardo, il quale, con la regola della <lb/>composizion delle forze, facendo rappresentare il peso alla diagonale, deter&shy;<lb/>minava la tension delle funi a proporzione de'due lati opposti nel paralle&shy;<lb/>logrammo. </s>

<s>Veniva cos&igrave;, un secolo e mezzo prima del Varignon, ridotta alla <lb/>sua pi&ugrave; desiderabile perfezione la teoria delle Taglie, e nella fune gravata <lb/>da pesi, ridotta alle pi&ugrave; certe leggi della Statica, s'incominci&ograve; a riconoscere <pb xlink:href="020/01/1983.jpg" pagenum="226"/>una delle pi&ugrave; usate e pi&ugrave; importanti macchine elementari, sconosciuta a <lb/>Pappo e agli altri matematici antichi. </s>

<s>Quella Meccanica dunque che, sui <lb/>principii del secolo XVIII, si volle dire novella, era nel XVI gi&agrave; bene adulta, <lb/>e con proprio nome fra le sorelle scienze distinta. </s></p><p type="main">

<s>Simeone Stev&igrave;no, raccogliendo e sponendo al pubblico le tradizioni, fino <lb/>allora rimaste nelle private scuole e nei manoscritti, dette a quella scienza <lb/>il nome di <emph type="italics"/>Spartostatica, ou de l'Art ponderaire par Cordages.<emph.end type="italics"/> La mac&shy;<lb/>china funicolare ha secondo l'Autore, come tutti gli altri meccanici stru&shy;<lb/>menti, le sue statiche e certissime leggi, le quali dipendono da un principio, <lb/>che si suppone verissimo e noto, e che, non avendo perci&ograve; altro bisogno <lb/>che di essere spiegato, si risolve in tanti distinti corollarii. </s>

<s>Nel III si sup&shy;<lb/>pone di avere un peso colonnare AB (fig. </s>

<s>101) sostenuto, per il suo centro <lb/>di gravit&agrave; C, da due forze, una diretta secondo CD, e l'altra secondo CE. <lb/><figure id="id.020.01.1983.1.jpg" xlink:href="020/01/1983/1.jpg"/></s></p><p type="caption">

<s>Figura 101.<lb/>Dato il peso della colonna, il quale agisce <lb/>secondo la perpendicolare CI, e dati gli an&shy;<lb/>goli DCI, ECI, si vuol determinare il grado <lb/>della forza, che s'ha da fare in D e in E, <lb/>per sostenere il grave sospeso. </s>

<s>A far ci&ograve;, <lb/>rappresentando la lunghezza della linea CI <lb/>la gravezza totale, si conduca dal punto I <lb/>la IH parallela a CE, &ldquo; comme CI a CH, <lb/>dice lo Stevino, ainsi le poids de la colomne <lb/>entiere au poids qui avient en D. </s>

<s>Et de <lb/>mesme maniere trouvera-on le poids, qui advient in E, en menant de I jus&shy;<lb/>ques a CE la ligne IK parallele a DC, et disant: comme l'elevation droite <lb/>CI a l'elevation oblique CK, ainsi lo poids de la colomne au poids qui advient <lb/>sur E &rdquo; (Oeuvres mathem. </s>

<s>cit., pag. </s>

<s>505). </s></p><p type="main">

<s>Qui poi osserva l'Autore ch'essendo sempre CK=HI non &egrave; necessa&shy;<lb/>rio descrivere tutto intero il parallelogrammo, avendosi gli elementi che <lb/>bisognano a risolvere il problema dal triangolo IHC, &ldquo; avec le quel on dira: <lb/>comme CI a CH, ainsi le poids de la colomne au poids qui advient sur D. <lb/>D'avantage CI a IH ainsi le poids de la colomne au poids, qui advient sur E. </s>

<s><lb/>Derechef comme CH a HI, ainsi le poids, qui advient sur D. au poids qui <lb/>advient sur E &rdquo; (ivi). Nel corollario V s'applicano i medesimi principii, e <lb/>la medesima regola che ne deriva, al caso che AB riducasi in un peso sfe&shy;<lb/>roideo infilato e pendolo da una fune, ai due capi della quale gli sforzi ne&shy;<lb/>cessarii per far la debita resistenza son tuttavia proporzionali ai lati del <lb/>triangolo, che insiste sulla perpendicolare, presa per misura dello stesso peso <lb/>assoluto. </s></p><p type="main">

<s>Precede la Spartostatica nelle Meccaniche dello Stevino a un altro trat&shy;<lb/>tato, che ha pure un distinto nome di <emph type="italics"/>Trocheologia,<emph.end type="italics"/> nella prefazioncella <lb/>alla quale il Matematico del conte Maurizio di Naussau cos&igrave; dice: &ldquo; Apres <lb/>que Son Excellence eust leu un livre intitul&eacute; <emph type="italics"/>Delle fortificazioni di Bo&shy;<lb/>naiuto Lorini,<emph.end type="italics"/> et illec veu un traite touchant les poulies, et ce seulement <pb xlink:href="020/01/1984.jpg" pagenum="227"/>par elevations perpendiculaires a l'horizon, par le moyen des forces atti&shy;<lb/>rantes du haut en bas directement, ce qu&igrave; n'arrive pas tousiours en la <lb/>practique, il a est&eacute; quant et quant desidereux de scavoir la propriete d'icel&shy;<lb/>les, qui est necessaire pour scavoir quelle force est requise, pour elever <lb/>quelque pesanteur &rdquo; (ivi, pag. </s>

<s>509). Per soddisfare al qual desiderio dice lo <lb/>Stevino di aver dato mano a scrivere la sua Trocheologia, la quale avrebbe <lb/>potuto risparmiare al Varignon un secolo dopo quella sua <emph type="italics"/>Memoire sur les <lb/>poulies,<emph.end type="italics"/> ch'ebbe qual cosa nuova chi l'ammir&ograve; e chi la contraddisse. </s></p><p type="main">

<s>Applicando dunque il vecchio Matematico di Bruges alle tensioni delle <lb/>funi oblique nella Troclea la regola del parallelogrammo delle forze, inse&shy;<lb/>gnata gi&agrave; nella Spartostatica al V corollario, immagina che siano CN, MC <lb/>(fig. </s>

<s>97 a pag. </s>

<s>220) le direzioni delle forze, che sostengono il grave A pen&shy;<lb/>dente dalla puleggia, e dice che, prolungate quelle direzioni, si debbono in&shy;<lb/>contrare in C in un medesimo punto della perpendicolare KC, sopra la quale <lb/>determinato un punto K, e da esso condotta la KI parallela a NC, il desi&shy;<lb/>derato quesito delle relazioni che passano fra le potenze M, N e la resi&shy;<lb/>stenza A &egrave; sciolto dalle seguenti equazioni: KC:KI:IC=A:N:M. <lb/>&ldquo; Comme ces 3 lignes l'une a l'autre KC, KI, IG, ainsi les pesanteurs de A, <lb/>qui eschoit sur CN, qui eschoit en M &rdquo; (ivi, pag. </s>

<s>510). </s></p><p type="main">

<s>Si disse chc in questa Spartostatica steviniana si raccoglievano le er&shy;<lb/>ranti tradizioni di una scienza anteriore, e della quale non ci &egrave; noto altro <lb/>documento dai manoscritti di Leonardo, che la coltiv&ograve;, non per consolar&shy;<lb/>sene semplicemente l'ingegno meditativo, ma per consultarla utilmente nelle <lb/>pratiche applicazioni, di che ci offron le Taglie un importantissimo esem&shy;<lb/>pio. </s>

<s>Essendo la potenza, che ha da vincere e da movere tutte le funi, le <lb/>braccia degli operai, che ne tirano a stratte il capo, si dubitava se in quelle <lb/>stratte si venisse a fare troppo gran violenza al sostegno, intorno a che ri&shy;<lb/>pensando Leonardo si propose a sciogliere il seguente <emph type="italics"/>&ldquo; Quesito delli pesi <lb/>che discendono.<emph.end type="italics"/> Domandasi se delli pesi, che discendono in fra le carru&shy;<lb/>cole, se dan di s&egrave; pi&ugrave; o men peso alli poli delle Taglie nel discendere, che <lb/>nello stare fermi &rdquo; (Manuscr. </s>

<s>G cit, fol. </s>

<s>17 a tergo). </s></p><p type="main">

<s>Per dar di ci&ograve; la desiderata risolu&shy;<lb/>zione, s'applic&ograve; Leonardo stesso a fare <lb/>una esperienza bellissima, pi&ugrave; semplice, <lb/>e meglio accomodata alle speculazioni di <lb/>alcuni matematici moderni, di quel che <lb/>non fossero le due secchie nella bilancia <lb/>descritta da Galileo (Alb. </s>

<s>XIII, 309) per <lb/>misurare la forza della percossa. </s>

<s>&ldquo; Il peso <lb/>grave che libero discende, cos&igrave; Leonardo <lb/>formula la sua proposizione, non d&agrave; di s&egrave; <lb/>peso ad alcuno sostentacolo. </s>

<s>Provasi: A <lb/>(fig. </s>

<s>102) &egrave; uno, e B due; seguita che M <lb/>sostiene solamente due, perch&egrave; l'eccesso <lb/><figure id="id.020.01.1984.1.jpg" xlink:href="020/01/1984/1.jpg"/></s></p><p type="caption">

<s>Figura 102.<pb xlink:href="020/01/1985.jpg" pagenum="228"/>che ha 2B sopra uno, &egrave; uno, il quale uno, non avendo chi il sostenga in A, <lb/>discende libero. </s>

<s>Adunque non ha sostantacolo, e non avendo sostentacolo, <lb/>non li &egrave; proibito il moto. </s>

<s>Adunque M stremo della Bilancia non sente tale <lb/>eccesso, perch&egrave; chi cade non &egrave; sostenuto &rdquo; (ivi, fol. </s>

<s>13 a t.). </s></p><p type="main">

<s>Confermavano sempre pi&ugrave; questi fatti sperimentali Leonardo nell'opi&shy;<lb/>nione che pigliassero le Taglie virt&ugrave; di movere dalle funi, e che non si ri&shy;<lb/>ducessero perci&ograve; se non che dalla lontana alla natura del Vette, della quale <lb/>cosi strettamente partecipa l'Asse nella rota. </s>

<s>Appartengono, comunque sia, <lb/>ambedue i detti strumenti all'ordine di quelle macchine, che sostengono per <lb/>sospensione dentro un'area assai circoscritta del piano, a cui si riducono <lb/>insomma esse Macchine tutte, come a elemento primario, e le varie accli&shy;<lb/>vit&agrave; del quale son che danno ora maggiore, ora minore virt&ugrave; di movere al <lb/>Cuneo e alla Vite. </s>

<s>Le leggi statiche di questi principali organi motori fu&shy;<lb/>rono, com'apparisce dall'ottavo libro di Pappo, dagli antichi poco ben co&shy;<lb/>nosciute, e dovendosi ora narrar da noi come e quando venissero i moderni <lb/>ad averne la desiderata notizia, si dovrebbe incominciare dal Piano inclinato. </s>

<s><lb/>Da lui anzi, come da principal fondamento meccanico, avrebbe dovuto mo&shy;<lb/>vere il nostro discorso, ma le ragioni che ce ne sviarono allora ci consi&shy;<lb/>gliano a non ridurci in via, se non che dopo aver detto di quel poco, che <lb/>dallo stesso piano inclinato distingue nell'operare il Cuneo e la Vite. </s></p><p type="main">

<s>Aristotile, nella sua XVII Questione <lb/>meccanica ridusse le virt&ugrave; del Cuneo a <lb/>quelle del Vette, cos&igrave; dicendo: &ldquo; Sit <lb/>Cuneus ubi ABC (fig. </s>

<s>103), quod vero <lb/>cuneo scinditur DEFG: Vectis igitur fit <lb/>ipsa AB, pondus vero ipsius B inferior <lb/>pars, hypomochlion autem DG, huic au&shy;<lb/>tem contrarius vectis BC. </s>

<s>Percussa igi&shy;<lb/>tur AC, utroque illorum utitur vecte: <lb/>scindit enim ipsum B &rdquo; (Operum, T. XI <lb/>cit., fol. </s>

<s>33 a tergo). N&egrave; altro par che <lb/>s'aggiungesse dagli Antichi a dichiarar <lb/><figure id="id.020.01.1985.1.jpg" xlink:href="020/01/1985/1.jpg"/></s></p><p type="caption">

<s>Figura 103.<lb/>meglio la natura, e a spiegar gli effetti dello strumento, giacch&egrave; Pappo, li&shy;<lb/>mitandosi a darne al solito una brevissima descrizione, fa notar solamente <lb/>cos&igrave; in generale che &ldquo; quanto Cunei angulus minor est, tanto facilius agit &rdquo; <lb/>(Collectiones mathem. </s>

<s>cit., pag. </s>

<s>486). </s></p><p type="main">

<s>Guidubaldo fra'moderni &egrave; de'primi, che siasi studiato di cogliere da <lb/>varii aspetti la versatile natura del Cuneo, e dop'avere accennato all'opi&shy;<lb/>nion di Aristotile soggiunge sembrargli assai pi&ugrave; conveniente il ridurre il <lb/>modo dell'operare dello strumento a quello di una Leva di secondo genere, <lb/>cosicch&egrave;, se sia ABC il Cuneo, come nella precedente figura, e GDEF il <lb/>corpo da scindersi verso le duo opposte parti IG, RD. &ldquo; IG movebitur a <lb/>puncto I vecte AB, cuius fulcimentum B. </s>

<s>Punctum enim I tangit pondus, <lb/>et instrumenta movent per contactum. </s>

<s>Similiter RD movebitur ab R vecte <pb xlink:href="020/01/1986.jpg" pagenum="229"/>CB, cuius fulcimentum B, et uterque vectis utrique resistit in B, ita ut po&shy;<lb/>tius fulcimenti vice fungalur, quam movendi ponderis, qnod ipsum hoc quo&shy;<lb/>que modo manifestum erit &rdquo; (Mechanic. </s>

<s>lib. </s>

<s>cit., fol. </s>

<s>113). </s></p><p type="main">

<s>Parve anche al Benedetti, acutamente esaminando la Questione aristo&shy;<lb/>telica, che i due lati del Cuneo operassero a modo di una Leva, non di <lb/>primo genere, com'avea detto il Filosofo, ma di secondo, se non che dispo&shy;<lb/>neva al motore al mobile e all'ipomoclio, diversamente da Guidubaldo, i <lb/>luoghi e gli ufficii, sembrando in verit&agrave; poco probabile il costituire in B il <lb/>fulcro che, aprendosigli innanzi il corpo scindibile, rimane per lo pi&ugrave; libero <lb/>da qualunque contatto. </s>

<s>Considerando poi l'acuto Matematico veneziano che <lb/>la forza dalla testa del Cuneo si diffonde ne'punti I, R, applic&ograve; quivi la po&shy;<lb/>tenza, in M, termine della parte scissa, costitu&igrave; la resistenza, e nelle parti <lb/>scindibili, che immediatamente succedono, suppose l'ipomoclio. </s>

<s>&ldquo; Oportet <lb/>nunc imaginari duos Vectes in hunc modum ut puncta I, R ligni sint loco <lb/>extremi ipsius Vectis, et T, X loco virtutis applicatae, et resistentia circa <lb/>punctum M, et pars K, quasi immediata post M versus extremitatem FE <lb/>ligni, sit loco hypomochlii. </s>

<s>Hinc fiet ut quanto longiores erunt lineae IMK, <lb/>et RMK tanto quoque facilius virtutes T, X impellent I, R &rdquo; (Specul., <lb/>lib. </s>

<s>cit., pag. </s>

<s>162). </s></p><p type="main">

<s>Guidubaldo per&ograve; fu forse il primo, che riguardasse il Cuneo sotto un <lb/>altro aspetto, in quanto cio&egrave; le parti del corpo scindibile strisciano sopra i <lb/>lati insinuantisi come sopra due piani inclinati. </s>

<s>&ldquo; Quoniam autem totus Cu&shy;<lb/>neus scindendo movetur, possumus idcirco eumdem alio quoque modo consi&shy;<lb/>derare, videlicet dum ingreditur id quod scinditur nihil aliud esse nisi pondus <lb/>supra planum horizonti inclinatum movere &rdquo; (Mechan., lib. </s>

<s>cit., fol. </s>

<s>113, 14). <lb/>Condotta da B ad AC la BH perpendicolare, osserva che il moto del Cuneo <lb/>si fa nella direzione BH, e il moto delle parti scindibili nella direzione GD, <lb/>cosicch&egrave;, quando esso Cuneo sia entrato tutto, s'&egrave; la potenza mossa quanto <lb/>BH, e la resistenza quanto AC, d'onde immediatamente ne conclude: &ldquo; quo <lb/>minor est angulus eo facilius movet ac scindit &rdquo; (ibid., fol. </s>

<s>115 a t.). </s></p><p type="main">

<s>Il Cartesio poi consider&ograve; il Cuneo propriamente cosi, com'&egrave; rappresen&shy;<lb/>tato nelle relazioni fra il motore e il mobile da quel Guidone Ubaldo, sulla <lb/>scienza del quale volle versare il ridicolo: &ldquo; Facultas Cunei ABC, dice nel <lb/>cap. </s>

<s>III Delle meccaniche, per se nunc facile intelligitur ex illis, quae de <lb/>Plano inclinato iamiam dicta sunt. </s>

<s>Vis enim, qua deorsum pellitur, ita se <lb/>movet, ut, cum propellat secundum lineam BH (nell'ultima nostra figura) <lb/>et lignum aliudve corpus scindendum non hiscit, vel quoque sarcina quam <lb/>attollit non elevatur, nisi iuxta lineam AC, ita ut vis qua Cuneus pellitur <lb/>seu deprimitur eamdem habere debeat rationem ad ligni huius vel sarcinae <lb/>resistentiam, quam habet linea AC ad lineam BH &rdquo; (editio cit., pag. </s>

<s>17). </s></p><p type="main">

<s>La meccanica del Cuneo cos&igrave;, come dal Cartesio, dopo Guidubaldo, vien <lb/>divisata, riuscirebbe semplicissima, ma i Matematici posteriori, meglio esa&shy;<lb/>minando il fatto, v'ebbero a ritrovare un tal complicato concorso di cause, <lb/>da disperar di venirne a capo, e, anche invocando quella taumaturga ope-<pb xlink:href="020/01/1987.jpg" pagenum="230"/>razione della composizion delle forze, quel che insomma seppero dirne ri&shy;<lb/>ducesi a questo: Incominciatasi a far la scissione per <lb/>esempio di un legno dai punti, dove le parti scisse <lb/>contrastano con i lati del Cuneo, si alzino sopr'essi <lb/>lati due perpendicolari, le quali, supponendosi il trian&shy;<lb/>gono VV&prime;T (fig. </s>

<s>104) isoscele, s'incontreranno in un <lb/>medesimo punto H della bissettrice TT&prime;. </s>

<s>Presa poi sopra <lb/>questa una lunghezza PH a rappresentare la forza insi&shy;<lb/>nuatrice, si prolunghino le due dette perpendicolari in <lb/>R&prime;, R, e costruiscasi il parallelogrammo, in cui anche <lb/><figure id="id.020.01.1987.1.jpg" xlink:href="020/01/1987/1.jpg"/></s></p><p type="caption">

<s>Figura 104.<lb/>si tiri la diagonale R&prime;R, che intersechi in I l'altra dia&shy;<lb/>gonale PH. </s>

<s>Dai triangoli simili RIH, TT&prime;V, R&prime;IP si avranno queste due <lb/>equazioni HI=HR T&prime;V/TV, IP=HR&prime;V&prime;T&prime;/TV, le quali sommate insieme, e, per <lb/>essere come s'&egrave; detto il Cuneo isoscele, posto HR=HR&prime;, e T&prime;V+T&prime;V&prime;=VV&prime;, <lb/>saranno HI+IP=HR VV&prime;/TV. </s>

<s>E perch&egrave; HI+IP=HP, che s'&egrave; detto rap&shy;<lb/>presentar la potenza, se ne conclude dunque di qui dover esser questa stessa <lb/>potenza, alla resistenza HR, come VV&prime;, che &egrave; la testa del Cuneo, a TV, che <lb/>&egrave; uno de'suoi lati. </s></p><p type="main">

<s>Al Cuneo ridusse Pappo la Vite, la quale niente altro &egrave; per lui &ldquo; quam <lb/>assumptus Cuneus expers percussionis &rdquo; (Collect. </s>

<s>cit., pag. </s>

<s>486). Guidubaldo <lb/>ripet&egrave; la sentenza medesima fra'moderni, ma perch&egrave; il Cuneo si riduce per <lb/>lui al Piano inclinato, cos&igrave; dunque riducesi anche la Vite, com'egli stesso <lb/>dimostra nella II <emph type="italics"/>De Cochlea<emph.end type="italics"/> cos&igrave; proposta: &ldquo; Si fuerit Cochlea helices <lb/>habens aequales, dico has nihil aliud esse praeter planum horizonti inclina&shy;<lb/>tum circa cylindrum revolutum &rdquo; (Mechan., lib. </s>

<s>cit., fol. </s>

<s>124). </s></p><p type="main">

<s>Le leggi statiche per&ograve; del piano elicale, essendo quelle medesime del <lb/>piano svolto, se ne rimette intorno a ci&ograve; il Nostro a quello, che nelle Ma&shy;<lb/>tematiche collezioni era stato insegnato da Pappo. </s>

<s>&ldquo; Quomodo autem hoc <lb/>ad Libram reducatur manifestum est ex nona octavi libri eiusdem Pappi &rdquo; <lb/>(ibid., fol. </s>

<s>124 a tergo). Da questa IX proposizione del Matematico alessan&shy;<lb/>drino incomincia la storia del Piano inclinato, che &egrave; poi la storia stessa della <lb/>Coclea, a narrar la quale distintamente si riserba, per quella prima dignit&agrave; <lb/>meccanica, la seguente seconda parte del nostro discorso. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>&Egrave; quella nona proposizione, alla quale rimanda Guidubaldo i lettori de&shy;<lb/>siderosi d'intendere in che modo si riducano le ragioni del Piano inclinato <lb/>a quelle della Libbra, cos&igrave;, nell'ottavo libro delle Collezioni matematiche, <lb/>formulata: &ldquo; Dato pondere a data potentia ducto in plano horizonti paral-<pb xlink:href="020/01/1988.jpg" pagenum="231"/>lelo, et altero plano inclinato, quod ad subiectum planum datum angulum <lb/>efficiat, invenire potentiam, a qua pondus in plano inclinato ducatur &rdquo; (Edi&shy;<lb/>tio cit., pag. </s>

<s>458). Nel testo greco, e nella versione del Commandino che <lb/>abbiamo sott'occhio, si costruisce dall'Autore il problcma e si risolve, ma <lb/>non dispiacer&agrave; ai nostri Lettori che si sostituisca al discorso di lui quello <lb/>di un suo studioso, pi&ugrave; chiaro e pi&ugrave; spedito, e che piglia accidentalmente <lb/>importanza, per essere stato fatto da uno sconosciuto fiorentino discepolo di <lb/>Galileo. </s></p><p type="main">

<s>Cosimo Noferi lasci&ograve; fra'suoi manoscritti un compendio e un commento <lb/>alle Meccaniche di Pappo, alle quali si pone per principio e per fondamento <lb/>la proposizione nona sopra accennata, ridotta a quest'altra semplice e chia&shy;<lb/>rissima forma: <emph type="italics"/>&ldquo; Pappi<emph.end type="italics"/> De Mechanica <emph type="italics"/>propositio I.<emph.end type="italics"/> Potentia C (fig. </s>

<s>105) <lb/><figure id="id.020.01.1988.1.jpg" xlink:href="020/01/1988/1.jpg"/></s></p><p type="caption">

<s>Figura 105.<lb/>moveat pondus A in <lb/>plano horizontali NM: <lb/>quaeritur quae poten&shy;<lb/>tia movebit idem pon&shy;<lb/>dus A in plano incli&shy;<lb/>nato secundum an&shy;<lb/>gulum HMN. </s>

<s>Tangat <lb/>planum HM circulus <lb/>GLX ad ipsum ere&shy;<lb/>ctus, et iuncta EL, <lb/>quae erit perpendicu&shy;<lb/>laris, ducatur EH parallela plani NM, et ab L mittatur perpendicularis LF, <lb/>et fiat ut GF ad FE, ita pondus A ad pondus B, et potentia C ad poten&shy;<lb/>tiam D. </s>

<s>Dico potentias ambas D, C movere pondus A per planum HM. &rdquo; </s></p><p type="main">

<s>&ldquo; Quia ergo ut GF ad FE, ita A ad B, ergo, suspensis his ponderibus <lb/>in E, A, et in G, B, aequiponderabunt fulcimento F, tamquam nixo plano <lb/>horizontali. </s>

<s>Sed pondus A movebatur a potentia C in plano NM, ergo in <lb/>plano HM movebitur ab utrisque potentiis D, C &rdquo; (MSS. Gal. </s>

<s>Disc., T. VII, <lb/>fol. </s>

<s>39 a tergo). </s></p><p type="main">

<s>Il trovare uno de'pi&ugrave; immediati discepoli, e uno de'pi&ugrave; prossimi pre&shy;<lb/>cursori di Galileo a trattenersi tuttavia intorno ai paralogismi di Pappo, ci <lb/>fa ripensare alla sterilit&agrave; della Scuola alessandrina, in comparazione con la <lb/>Pitagorica rinvigorita di novella giovent&ugrave; da Giordano Nemorario, e da'se&shy;<lb/>guaci di lui cos&igrave; validamente promossa. </s>

<s>Appartiene al numero di questi se&shy;<lb/>guaci Leonardo da Vinci, ne'manoscritti del quale la statica del Piano in&shy;<lb/>clinato vien ridotta a quella maggior perfezione, che si possa desiderare dai <lb/>Matematici odierni. </s>

<s>Cos&igrave; fatte dimostrate verit&agrave;, che nel lontano e riposto <lb/>campo, dove noi le vediam rifiorire, par che riposino in pace solitaria, si <lb/>educarono sotto l'aperto cielo contrastate da coloro, che preferivano le lu&shy;<lb/>cerne e le serre alla luce e ai tiepori del sole. </s>

<s>Pochi uscirono vittoriosi dalla <lb/>lotta, ceme Leonardo, e son cotesti pochi a noi sconosciuti, ma quegli altri <lb/>che, verso la met&agrave; del secolo XVI, lasciarono nelle pubbliche carte impressa <pb xlink:href="020/01/1989.jpg" pagenum="232"/>della loro mente l'effige, si vedono uscir fuori dal combattimento con l'abito <lb/>lacerato, o rimasto sozzo nel cader nella polvere e nello strisciar per il fango. </s>

<s><lb/>Il Cardano e il Tartaglia sono i due pi&ugrave; famosi fra costoro, e il campo, dove <lb/>ebbero a combattere, a risorgere e a ricadere, &egrave; smisurato, ma noi ci pro&shy;<lb/>poniamo qui di restringer quella misura a un punto, che &egrave; quel segnato, <lb/>dove si diceva dianzi, nelle Collezioni di Pappo. </s></p><p type="main">

<s>Difficile, prima del Commandino, la lettura del testo greeo, il Matema&shy;<lb/>tico d'Alessandria non era saputo. </s>

<s>E dall'altra parte le XIII Proposizioni <lb/>del Nemorario, dove si dimostravan le leggi delle discese rette e oblique dei <lb/>gravi, incoravano una dolce speranza nei promotori d'aver facile a risolvere <lb/>il famoso problema della proporzion del peso di una sfera pendula al discen&shy;<lb/>dente per un piano acclive. </s>

<s>Il Cardano nell'<emph type="italics"/>Opus novum<emph.end type="italics"/> proponeva giusto <lb/>in tal forma la questione: &ldquo; Proportionem ponderis sphaerae pendentis ad <lb/>descendentem per acclive planum invenire &rdquo; (Operum, T. IV cit., pag. </s>

<s>496). <lb/>E si credeva di avere a ritrovar la desiderata verit&agrave; con un discorso di que&shy;<lb/>sta fatta: Per mover la sfera nel piano orizzontale non ci vuol forza di nulla, <lb/>ma per sollevarla nel perpendicolo ci bisogna una forza, che sia uguale a <lb/>tutto il peso. </s>

<s>Fra il tutto e il nulla sono le vie di mezzo, per comparar le <lb/>quali si doveva cercare un termine di confronto. </s>

<s>Il Cardano, che s'era cos&igrave; <lb/>avviato bene, a questo punto incespica, e invece di pigliar per termine di <lb/>confronto la discesa verticale, fatta in un dato tempo dalla sfera libera ca&shy;<lb/>dente, come pareva che suggerissero gl'insegnamenti del Nemorario, prese <lb/>la rettitudine dell'angolo, che la discesa fa con l'orizzontale, cosicch&egrave; in&shy;<lb/>somma, nel risolvere il problema, gli vennero scambiati gli angoli con i seni. </s>

<s><lb/>Ecco qual'&egrave; la forma propria e la conclusione del suo ragionamento: </s></p><p type="main">

<s>&ldquo; Sit sphaera aequalis ponderi G (fig. </s>

<s>106) in puncto B, quae debeat <lb/>trahi super BE acclive planum BO ad perpendiculum plani BF. </s>

<s>Quia ergo <lb/>in BO movetur a quantitate modica, ut per <lb/><figure id="id.020.01.1989.1.jpg" xlink:href="020/01/1989/1.jpg"/></s></p><p type="caption">

<s>Figura 106.<lb/>dicta superuis, erit per communem animi sen&shy;<lb/>tentiam, vis quae movebit G per BO nulla; per <lb/>dieta vero G movebitur ad F semper a costanti <lb/>vi aequali G, et per BE a costanti vi aequali K, <lb/>sicut per BD a costanti vi aequali H. Ergo, <lb/>per ultimam petitionem, cum termini servent <lb/>quoad partem eamdem rationem singuli per se, <lb/>et motum per BO sit a nulla vi, erit proportio <lb/>G ad K velut proportio vis, quae movet per BF, <lb/>ad vim quae movet per BE, et velut anguli per <lb/>EBO facti ad angulum EBO. </s>

<s>Et ita vis, quae <lb/>movet sphaeram per BF, et est, ut dictum est, G, ad vim, quae movet per <lb/>BD, et est K, est ex supposito, ut FBO ad DBO. </s>

<s>Igitur proportio difficul&shy;<lb/>tatis motus per BD, ad idem per BO, est veluti H ad K, quod erat demon&shy;<lb/>strandum &rdquo; (ibid.). </s></p><p type="main">

<s>Questo cardanico teorema, che cio&egrave; la gravit&agrave; assoluta sta alla relativa <pb xlink:href="020/01/1990.jpg" pagenum="233"/>nel piano inclinato come l'angolo retto sta all'angolo fatto con l'orizzonte <lb/>dallo stesso piano, doveva esser quello comunemente dimostrato dai Mate&shy;<lb/>matici contemporanei, e dai predecessori, male deducendolo dai principii sta&shy;<lb/>tici del Nemorario. </s>

<s>Imperocch&egrave; si dovevano, secondo que'principii, compu&shy;<lb/>tare i momenti per la discesa virtuale del grave nel diretto, ossia per i seni <lb/>e non per gli angoli delle inclinazioni. </s>

<s>S'era Leonardo ben saputo delibe&shy;<lb/>rare da questo errore, a cui poi, insieme con la volgar turba dei Matema&shy;<lb/>tici, rimase preso anco il Cardano, ma il Tartaglia, esercitandosi intorno alle <lb/>XIII proposizioni <emph type="italics"/>De ponderibus,<emph.end type="italics"/> e ragionando intorno ad esse a dovere, fu <lb/>condotto alla conclusion vera, che si desiderava, e fu il primo a dar pub&shy;<lb/>blica dimostrazione delle leggi dell'equilibrio de'gravi, in atto di scendere <lb/>lungo i piani inclinati. </s>

<s>Di quelle giovanili esercitazioni lasci&ograve; il Matematico <lb/>bresciano memoria in un opuscolo, intitolato <emph type="italics"/>Jordani opusculum<emph.end type="italics"/> De pon&shy;<lb/>derositate <emph type="italics"/>Nicolai Tartaleae studio correctum,<emph.end type="italics"/> pubblicato postumo, com'al&shy;<lb/>trove si disse, nel 1565 in Venezia. </s>

<s>In cotesto opuscolo la questione X &egrave; <lb/>cos&igrave; proposta: &ldquo; Si per diversarum obliquitatum vias duo pondera descen&shy;<lb/>dant, fiantque declinationum et ponderum una proportio, eodem ordine <lb/>sumpta, una erit utriusque virtus in declinando &rdquo; (fol. </s>

<s>7). E nel risolverla <lb/>ch'e'fa &egrave; sollecito di avvertire i Lettori, ch'egli &egrave; venuto a salvare dal co&shy;<lb/>mune naufragio, come, trattando di declinazioni, non intende di quelle degli <lb/>angoli, ma delle linee o de'seni: &ldquo; dico non angulorum, sed linearum usque <lb/>ad aequidistantem resecationem, in qua aequaliter sumunt de directo &rdquo; (ibid.). </s></p><p type="main">

<s>Le giovanili esercitazioni <emph type="italics"/>De ponderositate<emph.end type="italics"/> furono poi dal medesimo <lb/>Tartaglia pi&ugrave; ampiamente svolte, e in pi&ugrave; piacevole forma ridotte fra'<emph type="italics"/>Que&shy;<lb/>siti,<emph.end type="italics"/> nel IX libro de'quali la XV proposizione cos&igrave; procede in dialogo, fra <lb/>Nicol&ograve; e il signor don Diego ambasciator cesareo in Venezia. <emph type="italics"/>&ldquo; Nicol&ograve;.<emph.end type="italics"/> Se <lb/>dui corpi gravi descendano per vie de diverse obliquit&agrave;, et che la propor&shy;<lb/>tione delle declinationi delle due vie e della gravit&agrave; de detti corpi sia fatta <lb/>una medesima, tolta per el medesimo ordine; anchora la virt&ugrave; de luno e <lb/>laltro de detti dui corpi gravi, in el descendere, sar&agrave; una medesima. <emph type="italics"/>Am&shy;<lb/>basciator.<emph.end type="italics"/> Questa propositione mi par bella e <lb/>per&ograve; datime anchora un essempio chiaro, acci&ograve; <lb/>che meglio mi piaccia. <emph type="italics"/>Nicol&ograve;.<emph.end type="italics"/> Sia la linea ABC <lb/>(fig. </s>

<s>107) equidistante al horizonte et sopra di <lb/>quella sia perpendicolarmente eretta la linea BD, <lb/>et dal ponto D descendano de qua et de la le <lb/>due vie over linee DA et DC et sia la DC di <lb/>maggior obliquit&agrave;. </s>

<s>Per la proportione adunque <lb/>delle lor declinationi, non dico delli lor angoli <lb/>ma delle linee per fin alla equidistante reseca&shy;<lb/>tione, in la quale equalmente summono del di&shy;<lb/>retto. </s>

<s>Sia adunque la lettera F supposta per un <lb/>corpo grave, posto sopra la linea DC, et un al&shy;<lb/>tro la lettera H sopra la linea DA, et sia la <lb/><figure id="id.020.01.1990.1.jpg" xlink:href="020/01/1990/1.jpg"/></s></p><p type="caption">

<s>Figura 107.<pb xlink:href="020/01/1991.jpg" pagenum="234"/>proporzione della semplice gravit&agrave; del corpo F alla semplice gravit&agrave; del corpo <lb/>H s&igrave; come quella della DC alla DA: dico li detti dui corpi gravi essere in <lb/>tai siti over luochi di una medesima virt&ugrave; over potentia &rdquo; (Ediz. </s>

<s>cit., fol. </s>

<s>97). </s></p><p type="main">

<s>La promessa dimostrazione si conclude dalla proposizion precedente cos&igrave; <lb/>annunziata: &ldquo; La equalit&agrave; della declinatione &egrave; una medesima equalit&agrave; de <lb/>peso &rdquo; (ivi, fol. </s>

<s>96 a tergo), e da Leonardo, come si rifer&igrave; altrove: &ldquo; li pesi <lb/>eguali mantengono le gravit&agrave; eguali nelle obliquit&agrave; eguali &rdquo; (MSS. E, fol. </s>

<s>58). <lb/>Il Tartaglia lo dimostra assai facilmente dai professati principii perch&egrave;, posto <lb/>il medesimo peso ora in E ora F, sul medesimo declivio DC, scendendo per <lb/>tratti uguali EC, FG, si accosta ugualmente al comun centro dei gravi, es&shy;<lb/>sendo i due diretti FM, EN eguali, e perci&ograve; serbano sempre eguali i mo&shy;<lb/>menti. </s>

<s>&ldquo; Adunque il detto corpo ponderoso si essendo nel ponto F come <lb/>nel ponto E in quantit&agrave; over decensi equali capir&agrave; equalmente del diretto, <lb/>sar&agrave; di una medesima gravit&agrave; in qual si voglia di quelli &rdquo; (Quesiti cit., <lb/>fol. </s>

<s>97). Di qui scende immediatamante che le due obliquit&agrave; DC, DA, pren&shy;<lb/>dendo ugualmente del diretto DB, debbono le gravit&agrave; E, H, star come le <lb/>quantit&agrave; delle respettive discese, ossia come DC ad AD, ed &egrave; tanto la con&shy;<lb/>clusione, come si diceva, immediata e diretta, che, volendosi provare il Tar&shy;<lb/>taglia a dimostrarla, non sa trovare altri termini, che quelli della riduzione <lb/>agli assurdi. </s>

<s>Nonostante, dop'essere stato pazientemente don Diego ad ascol&shy;<lb/>tare, ebbe a dire verso Nicol&ograve;, che aveva appena allora finito il suo di&shy;<lb/>scorso: &ldquo; Questa &egrave; stata una bella speculatione et me e piaciuta assai &rdquo; <lb/>(ivi, fol. </s>

<s>97 a tergo). </s></p><p type="main">

<s>Piacque poi il teorema anche a Simeone Stevino, il quale, dato mano <lb/>a costruire quella nuova Bilancia, trov&ograve; che veramente i fatti rispondevano <lb/>alle speculazioni, perch&egrave; legate le due sfere H, F a un filo, scorrevole sulla <lb/>puleggia P, se le gravit&agrave; di esse sfere son proporzionali <emph type="italics"/>per il medesimo <lb/>ordine,<emph.end type="italics"/> come diceva il Tartaglia, ai lati del triangolo DC, DA, si fanno in&shy;<lb/>sieme equilibrio. </s>

<s>Allettato il Matematico di Bruges da un'invenzione, che <lb/>nella sua semplicit&agrave; ebbe a ritrovar tanto bella, si mise dietro amorosa&shy;<lb/>mente ad accarezzarla, e gli riusc&igrave; di aggiungerle nuova bellezza, ch'egli <lb/>stesso poi descrisse cos&igrave; nel teorema XI della sua Statica: </s></p><p type="main">

<s>&ldquo; Soit accomod&egrave; a l'entour <lb/>du triangle ABC (fig. </s>

<s>108) un <lb/>entour de 14 globes egaux en <lb/>pesanteur, en grandeur, et equi&shy;<lb/>distans comme D, E, F, G, H, I, <lb/>K, L, M, N, O, P, Q, R, enfilez <lb/>d'une ligne passant par leurs <lb/>centres, ainsi qu'ils puissent tour&shy;<lb/>ner sur leurs subdits centres, et <lb/>qu'il y puisse avoir 2 globes sur <lb/>le coste BC, et 4 sur BA: alors, <lb/>comme ligne a ligne, ainsi le <lb/><figure id="id.020.01.1991.1.jpg" xlink:href="020/01/1991/1.jpg"/></s></p><p type="caption">

<s>Figura 108.<pb xlink:href="020/01/1992.jpg" pagenum="235"/>nombre des glohes au nombre des globes. </s>

<s>Qui aussi en S, T, V soyent trois <lb/>poincts fermes, dessus lesquels la ligne ou le filet puisse couler, et que les <lb/>deux parties au dessus dei triangle soyent paralleles aux costez d'iceluy AB, <lb/>BC, tellement que le tout puisse torner librement, et dans accrochement, <lb/>sur les dists costez AB, BC. &rdquo; </s></p><p type="main">

<s>&ldquo; Si la pouvoir des poids D, R, Q, P n'estoit egal au pouvoir des deux <lb/>globes E, F, l'un coste sera plus pesant que l'autre, donc, s'il est possible, <lb/>que les 4 D, R, Q, P soyent plus pesans que les deux, E, F. </s>

<s>Mais les 4 O, <lb/>N, M, L sont egaux aux 4 G, H, I, K, parquoy le coste des 8 globes D, R, <lb/>Q, P, O, N, M, L sera plus pesant selon leur disposition, que non pas <lb/>les 6 E, F, G, H, I, K. </s>

<s>Et puisque la partie plus pesante emporte la plus <lb/>legere, les 8 globes descenderont, et les autres 6 monteront. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Qui il soit ainsi donc et que D vienne ou O est presentement, et <lb/>ainsi des autres. </s>

<s>Voire que E, F, G, H viennent ou sont maintenant P, Q, <lb/>R, D, aussi I, K ou sont maintenant E, F. </s>

<s>Ce neont moins l'entour des <lb/>globes aura la mesma disposition qu'auparavant, et par mesme raison les <lb/>8 globes aurent le dessus en pesanteur, et en tombant feront revenir 8 au&shy;<lb/>tres en leurs places, et ainsi ce mouvement n'auroit aucunne fin, ce qui est <lb/>absurde. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Et de mesme sera la demonstration de l'autre cost&eacute;. </s>

<s>La partie donc <lb/>de l'entour D, R, Q, P, O, N, M, L sera en equilibre avec la partie E, F, <lb/>G, H, I, K. </s>

<s>Qui si on oste des deux costez les pesanteurs egales, et qui <lb/>ont mesme desposition, comme sont les 4 globes O, N, M, L d'une part, et <lb/>les 4 G, H, I, K d'autre part; les 4 restans D, R, Q, P seront et demeu&shy;<lb/>reront en equilibre avec le 2 E, F, parquoy E aura un pouvoir duble au <lb/>pouvoir de D. </s>

<s>Comme donc le cost&eacute; BA 2 au cost&eacute; BC 1, ainsi le pouvoir <lb/>de E au pouvoir de D. &rdquo; (Oeuvres mathem. </s>

<s>cit., pag. </s>

<s>448). </s></p><p type="main">

<s>Tanto in questa dimostrazione sperimentale dello Stevino, quanto nel <lb/>teorema del Tartaglia, la conclusione si verifica, anche quando uno de'lati <lb/>del triangolo &egrave; verticale, essendo anzi questo stesso lato verticale la misura <lb/>immediata e diretta della discesa. </s>

<s>Ma lo Stevino stesso cred&egrave; bene di do&shy;<lb/>verne avvertire i Lettori con questo corollario: &ldquo; Soit mantenant l'un des <lb/>costez du triangle comme BD, qui est moitie du l'autre AB, perpendicu&shy;<lb/>laire a AC come cy joignant, le globe D, qui est double a G sera encor <lb/>en equilibre avec E, car, comme le coste AB a BC, ainsi le globe D au <lb/>globe E &rdquo; (ivi). </s></p><p type="main">

<s>Il Lagrange, nell'introduzione alla sua Meccanica analitica, volle in par&shy;<lb/>ticolar modo rammemorare ai matematici de'suoi tempi questa dimostra&shy;<lb/>zion dello Stevino &ldquo; parce qu'elle, ei dice, est tres-ingenieuse, et qu'elte est <lb/>d'ailleurs peu connue &rdquo; (Editio cit., pag. </s>

<s>5). Sarebbe stata nonostante que&shy;<lb/>sta meritevole commemorazione del Matematico italiano assai pi&ugrave; efficace, <lb/>se non avesse lasciato di avvertir che l'olandese Autor <emph type="italics"/>Des elemens de Sta&shy;<lb/>tique<emph.end type="italics"/> suppone gi&agrave; noto il teorema del Tartaglia, senza il quale tutte le in&shy;<lb/>gegnose eleganze sarebbero rimaste una veste senza persona, o per pi&ugrave; pro-<pb xlink:href="020/01/1993.jpg" pagenum="236"/>prio dire una fisica fuor di luogo in quel libro di matematica. </s>

<s>Cosicch&egrave; <lb/>insomma non intende lo Stevino di dimostrare, ma di confermare con una <lb/>bella esperienza la bellissima <emph type="italics"/>speculatione<emph.end type="italics"/> del nostro Matematico di Brescia. </s></p><p type="main">

<s>Pietro Herigon, per rendere quella intenzione pi&ugrave; sincera e pi&ugrave; mani&shy;<lb/>festa, fece alla dimostrazione fisica precedere la matematica, componendo <lb/>insieme e riducendo a pi&ugrave; compendiosa semplicit&agrave; il teorema del Tartaglia e <lb/>l'esperienza dello Stevino. </s>

<s>Nel trattatello di Meccanica, compreso nel III Tomo <lb/>del <emph type="italics"/>Corso matematico,<emph.end type="italics"/> la proposizione VIII &egrave; cos&igrave; formulata: &ldquo; Si recta, a <lb/>vertice trianguli ad basim ducta, sit perpendicularis horizonti, pondera su&shy;<lb/>per lateribus trianguli, habentia eamdem proportionem quam latera, aequi&shy;<lb/>ponderant &rdquo; (Paris 1644, pag. </s>

<s>300). </s></p><p type="main">

<s>Sia D (fig. </s>

<s>109) il grave sul piano AC equilibrato dall'altro grave G, <lb/>che libero scende lungo CB. </s>

<s>Presa AE=CB, l'ascesa virtuale del primo <lb/>sar&agrave; EF, e la discesa del secondo nel me&shy;<lb/>desimo tempo sar&agrave; CB, e deve, per i prin&shy;<lb/>cipii statici professati dal Tartaglia, aversi <lb/>D:G=CB:EF=AC:AE, ossia CB, per <lb/>costruzione. </s>

<s>&ldquo; Hinc perspicuum est, dice <lb/>propriamente l'Herigonio, pondus D ad <lb/>pondus, quo in lineam CB gravitat, habere <lb/>eamdem proportionem quam AC ad CB &rdquo; <lb/>(ibid.). <lb/><figure id="id.020.01.1993.1.jpg" xlink:href="020/01/1993/1.jpg"/></s></p><p type="caption">

<s>Figura 109.</s></p><p type="main">

<s>A confermar coi fatti, e a render di pi&ugrave; facile intelligenza la mecca&shy;<lb/>nica proposizion con gli esempii, il parigino Compilator della scienza mate&shy;<lb/>matica universale di allora, cos&igrave; soggiunge: &ldquo; Si pondera habentia eamdem <lb/>proportionem, quam habent trianguli, non essent situ aequilibra, sequere&shy;<lb/>tur fieri posse motum continuum circa triangulum. </s>

<s>Atqui hoc est absurdum, <lb/>cum Natura nihil suscipiat quod non exequatur, igitur, pondera, habentia <lb/>eamdem proportionem quam latera trianguli, sunt situ aequilibra &rdquo; (ibid., <lb/>pag. </s>

<s>303). Il moto continuo che ne seguiredbe lo dimostra l'Herigonio a <lb/>modo dello Stevino, se non che trasforma i globi infilati in un tubo pieno <lb/>d'acqua, disposto come si rappresentavan dianzi quegli stessi quattordici globi <lb/>nella figura steviniana. </s>

<s>Il liquido dunque, per non incorrere nell'assurdit&agrave; <lb/>del moto perpetuo, dee essere in A e in C in equilibrio, ossia debbono es&shy;<lb/>sere ivi le due pressioni uguali. </s>

<s>&ldquo; Cum igitur aqua tubi non perpetuo mo&shy;<lb/>veatur, necesse est potentiam descensus aquae tubi AB esse aequalem po&shy;<lb/>tentiae descensus tubi BC, quod erat demonstrandum &rdquo; (ibid., pag. </s>

<s>305). </s></p><p type="main">

<s>Queste tradizioni della scienza non fu solo l'Herigonio a raccoglierle, <lb/>ma lo imitarono anche altri di que'tempi, fra quali si gloria di essere stato <lb/>il primo Claudio Beriguardi. </s>

<s>Nella terza parte de'suoi <emph type="italics"/>Circoli pisani,<emph.end type="italics"/> cir&shy;<lb/>colo VI, confessa che della discesa dei gravi trattarono accuratamente Ga&shy;<lb/>lileo e il Torricelli, ma soggiunge ch'egli stesso aveva concluso quelle me&shy;<lb/>desime verit&agrave; da altri principii &ldquo; XX annis antequam illi de ea re quidquam <lb/>vulgassent &rdquo; (Patavii 1660, pag. </s>

<s>307). Non dice per&ograve;, come sarebbe stato <pb xlink:href="020/01/1994.jpg" pagenum="237"/>giusto dovere, che quei principii erano stati posti, e pubblicamente profes&shy;<lb/>sati pi&ugrave; di altri vent'anni avanti, e descrive quale speculazione sua propria <lb/>l'esperienza dello Stevino, che cio&egrave; sei globi uguali infilati son necessarii <lb/>per fare equilibrio a due altri simili globi, se i lati del triangolo su cui ri&shy;<lb/>posano stanno come tre a uno. </s>

<s>Soggiunge, cosa dall'altra parte assai ovvia <lb/>a sovvenire in mente a ciascuno, e notata gi&agrave; come si vide da Leonardo, e <lb/>un secolo dopo dall'Herigonio, che si dimostrerebbe lo stesso, quando fosse <lb/>il triangolo un tubo pieno di acqua o d'argento vivo. </s></p><p type="main">

<s>Cos&igrave; fatte esperienze variabili in tante guise erano tutte una bella con&shy;<lb/>ferma del teorema del Tartaglia che, sebben sotto altra forma, compariva <lb/>in sostanza un secolo dopo nella statica del Cartesio. </s>

<s>Il famoso principio in&shy;<lb/>fatti che tanta forza ci vuole a sollevare un peso di due libbre all'altezza <lb/>di un braccio, quanto un peso di una libbra sola all'altezza di due brac&shy;<lb/>cia, si riduce, come altrove avvertimmo, a dire che sono i momenti uguali, <lb/>quando s'uguagliano i prodotti dei descensi retti per le loro respettive moli, <lb/>d'ond'ebbe il Tartaglia a concluder la sua bella speculazione, a quel modo <lb/>che poi fece il Cartesio, perch&egrave;, rivolgendo lo sguardo sulla figura CIX, &egrave; <lb/>facile vedere che la scesa verticale del peso G &egrave; uguale ad AC, e l'ascesa <lb/>di D &egrave; uguale a BC, e perci&ograve; dall'essere DXCD=GXAC ne viene <lb/>D:G=AC:CB, cio&egrave;, dice lo stesso Cartesio, &ldquo; minor vis requiritur ad <lb/>pondus D, iuxta lineam AC trahendum, quam secundum lineam CB; hoc est, <lb/>si AC sit dupla lineae CB, vis tantum dimidia requiritur &rdquo; (Epist., Pars. </s>

<s>I <lb/>cit., pag. </s>

<s>212). </s></p><p type="main">

<s>La riduzione del principio cartesiano a quello, che ne concluse il Tar&shy;<lb/>taglia dai principii del Nemorario, fu efficacemente espressa da Giovanni <lb/>Wallis nella sua VIII proposizione <emph type="italics"/>De motuum declivivitate,<emph.end type="italics"/> dove dimostra <lb/>che i momenti si compongono della ragion delle altezze e delle moli. </s>

<s>&ldquo; Cum <lb/>enim ea ratione plus ponderant gravia, caeteris paribus, qua sunt maioris <lb/>ponderis, quoque plus descenditur; ea ratione ponderabunt utriusque ratione <lb/>habita qua pollent eorum, secundum utramque considerationem, descensus <lb/>ascensusve, hoc est ea quae ex ponderum et altitudinum rationibus compo&shy;<lb/>nitur &rdquo; (De motu cit., pag. </s>

<s>39). E lo prova con l'esempio della Leva e del <lb/>Piano inclinato, dove si vede che i due gravi D e G, nella solita figura ul&shy;<lb/>timamente rappresentata, si equiponderano, quando stanno i loro pesi reci&shy;<lb/>procamente come le quantit&agrave; dell'ascesa e della discesa virtuale. </s>

<s>Conclude <lb/>poi di qui la XXI proposizione, che dice: &ldquo; Grave ponderat, pro varia ascen&shy;<lb/>suum descensuumve obliquitate, in ratione rectorum sinuum inclinationis ad <lb/>horizontem, sive complementi obliquitatis &rdquo; (ibid., pag. </s>

<s>54). </s></p><p type="main">

<s>Tale essendo l'ubert&agrave; del frutto raccolto dai seguaci della Scuola peri&shy;<lb/>patetica, sterili sembreranno al confronto gli studii di chi, in grazia del Com&shy;<lb/>mandino, pot&egrave; tutti vedere in Pappo misurati i progressi della Scuola ales&shy;<lb/>sandrina. </s>

<s>Dopo le Meccaniche di Guidubaldo il primo pubblico documento <lb/>in proposito s'ha dalla Filosofia magnetica di Niccol&ograve; Cabeo, il quale invoca <lb/>le leggi statiche della discesa dei gravi ne'piani inclinati a risolvere un que-<pb xlink:href="020/01/1995.jpg" pagenum="238"/>sito, che gli si propone intorno alla perpetuit&agrave; del moto, possibile ad otte&shy;<lb/>nersi dalle virt&ugrave; perpetuamente attrattive del magnete. </s>

<s>S'applica perci&ograve; ad <lb/>esaminar diligentemente la proposizione IX dell'ottavo libro delle matema&shy;<lb/>tiche Collezioni, e facilmente si avvede che l'assunto preso dall'Autore, per <lb/>concluder la sua proposizione, era falso, perch&egrave;, per movere il peso nel&shy;<lb/>l'orizzonte, tutt'altro che bisognarvi maggior forza che a moverlo su per <lb/>l'acclivio, non ci vuol anzi forza di nulla, come, per i teoremi del Cardano <lb/>e del Benedetti, era a tutti oramai notissimo. </s>

<s>Fa notare di pi&ugrave; il Cabeo l'as&shy;<lb/>surdo, che conseguirebbe manifestissimo dalle posizioni di Pappo, perch&egrave;, se <lb/>nella figura CV, la potenza P deve stare al peso E come EF ad FG, &ldquo; si <lb/>HM accedat ad perpendicularem, requireretur potentia maxima, et, si sit <lb/>omnino perpendicularis, infinita, quod est impossibile &rdquo; (Coloniae 1629, <lb/>pag. </s>

<s>342). Se nell'equazione infatti P=EXEF/FG, FG riducesi a zero, do&shy;<lb/>vrebbe tornar P uguale all'infinito. </s></p><p type="main">

<s>Perch&egrave; dunque da un principio falso non poteva conseguirne il vero, <lb/>propone il Cabeo una soluzion del problema diversa da quella di Pappo, e <lb/>perch&egrave; insomma non si trattava d'altro, che di trovar la forza necessaria a <lb/>far risalire il grave sopra l'acclivit&agrave; del piano HM, considera questa forza <lb/>applicata in I all'estremit&agrave; di una leva di secondo genere, che abbia in F <lb/>o in L il fulcro, e in E la resistenza. </s>

<s>Le note leggi del Vette, applicate al <lb/>piano inclinato, davano dunque risoluto il problema col far come FI ad FE, <lb/>cos&igrave; il peso alla potenza, che ha da sollevarlo. </s>

<s>Che se questa ragione non <lb/>piace &ldquo; quia vere etiam ipsa suas habet difficultates, donec exactius exami&shy;<lb/>netur, hanc aliam habeto &rdquo; (ibid., pag. </s>

<s>343), ma la nuova, che si propone, <lb/>sembra andare anche pi&ugrave; lontana dal vero, per raggiungere il quale sarebbe <lb/>allo stesso Cabeo stato meglio deliberarsi affatto dalla costruzione, e dalla <lb/>geometrica dimostrazione di Pappo. </s></p><p type="main">

<s>Cos&igrave; giudiziosamente avea fatto Galileo, a cui sorti perci&ograve; di dare il <lb/>primo la ragion del piano inclinato, derivandola dai principii della Scuola <lb/>alessandrina che, reputata da lui unica legittima, gli fece ingiustamente dire, <lb/>nell'accingersi a trattar delle proporzioni dei moti di un medesimo mobile <lb/>sopra diversi piani inclinati, che quella era questione &ldquo; a Philosophis nul&shy;<lb/>lis, quod sciam, pertractata &rdquo; (Alb. </s>

<s>XI, 56). Consiste la nuova dimostrazione <lb/>nel trapassar, dai gravi sostenuti dal braccio di <lb/>una Libbra, a considerarli come sostenuti dalla re&shy;<lb/>sistenza di un piano, appropriando a questo le note <lb/>condizioni dell'equilibrio di quella. </s>

<s>Se dal braccio <lb/>AB di una Leva (fig. </s>

<s>110) penda in B un peso, que&shy;<lb/>sto eserciter&agrave; il suo momento totale, mentre esso <lb/>braccio rimanga in AB livellato. </s>

<s>Ma se inclinisi in <lb/>AC, il momento parziale di C, rispetto al totale in B, <lb/>sar&agrave;, secondo il noto teorema del Benedetti, come <lb/>la porzione AD, precisa dalla perpendicola CD, a <lb/><figure id="id.020.01.1995.1.jpg" xlink:href="020/01/1995/1.jpg"/></s></p><p type="caption">

<s>Figura 110.<pb xlink:href="020/01/1996.jpg" pagenum="239"/>tutta intera la AB. </s>

<s>Se s'immagini ora nel punto C essere applicato un piano <lb/>EF, perpendicolare ad AC, tanto fa al grave a pendere dal braccio della <lb/>Leva, quanto a riposare sul piano, per scendere lungo il quale esercita ugual <lb/>momento che lungo l'arco del cerchio. </s>

<s>Dunque anche il momento parziale di <lb/>C, posato sul piano EF, sar&agrave; al momento totale come AD ad AC, ossia AB, <lb/>e come EG sta ad EF, per la similitudine dei triangoli. </s>

<s>&ldquo; Per&ograve; concluderemo, <lb/>scrive Galileo, questa universal proposizione col dire: sopra il piano la forza <lb/>al peso avere la medesima proporzione che la perpendicolare, dal termine <lb/>del piano tirata all'orizzonte, alla lunghezza di esso piano &rdquo; (ivi, pag. </s>

<s>118). </s></p><p type="main">

<s>Correva attorno questa galileiana dimostrazione manoscritta, prima del&shy;<lb/>l'anno 1615, sotto il nome del Vieta, cosa creduta da molti, come dal Ba&shy;<lb/>liani (Alb. </s>

<s>XVI, 105) anche in Italia, ma bench&egrave; pi&ugrave; seducente era nondi&shy;<lb/>meno pi&ugrave; lubrica di quella del Tartaglia. </s>

<s>Attribuisce Alessandro Marchetti <lb/>a questa lubricit&agrave;, del&igrave;a quale vedremo nella seguente parte del nostro di&shy;<lb/>scorso gli esempii, l'aver Galileo tenuto altro modo nell'aggiunta postuma <lb/>al terzo dialogo Delle due nuove scienze. </s>

<s>Ivi, come lo stesso Tartaglia, sug&shy;<lb/>geritogli forse dall'Herigonio, di cui siam certi aver esso Galileo fra'suoi <lb/>libri il Corso matematico (Alb. </s>

<s>X, 211, 28); dimostra esser due gravi con&shy;<lb/>giunti insieme in equilibrio, quando le ascese e le discese virtuali nel per&shy;<lb/>pendicolo stanno reciprocamente fra loro come i pesi. </s>

<s>&ldquo; Mentrech&egrave; dunque <lb/>il grave D (nella passata figura CIX) movendosi da A in C, resiste solo nel <lb/>salire lo spazio perpendicolare CB, ma che l'altro G scende a perpendicolo, <lb/>necessariamente quanto tutto lo spazio AC, e che tal proporzione di salita <lb/>e scesa si mantiene sempre l'istessa, poco o molto che sia il moto dei detti <lb/>mobili, per esser collegati insieme; possiamo assertivamente affermare che, <lb/>quando debba seguire l'equilibrio, cio&egrave; la quiete tra essi mobili, i momenti, <lb/>le velocit&agrave; o le lor propensioni al moto, cio&egrave; gli spazii che da loro si pas&shy;<lb/>serebbero nel medesimo tempo, devon rispondere reciprocamente alle loro <lb/>gravit&agrave; &rdquo; (Alb. </s>

<s>XIII, 176). Posto il qual principio, professato dal Tartaglia, <lb/>la conclusione era necessariamente la medesima, cosicch&egrave; il teorema del Ma&shy;<lb/>tematico di Brescia aveva un secolo dopo dal Fiorentino la sua pi&ugrave; solenne <lb/>conferma. </s></p><p type="main">

<s>Era venuto per&ograve; in quel tempo il Nardi a mettere scrupolo intorno alle <lb/>discese, e alle velocit&agrave; virtuali, invocando il logicale assioma che <emph type="italics"/>a posse ad <lb/>esse non valet illatio,<emph.end type="italics"/> n&egrave; parendo ragionevole il trattar di una cosa da farsi, <lb/>come se fosse gi&agrave; fatta. </s>

<s>Persuaso anche il Torricelli che dalle propensioni <lb/>al moto non si potesse ragionevolmente argomentare al moto, ebbe a cer&shy;<lb/>care altro principio cos&igrave; formulato: &ldquo; Duo gravia simul coniuncta ex se <lb/>moveri non posse, nisi centrum commune gravitatis ipsorum descendat &rdquo; <lb/>(Op. </s>

<s>geom., P. </s>

<s>I cit., pag. </s>

<s>99); principio che si trov&ograve; opportuno a dimo&shy;<lb/>strare il teorema del Tartaglia, e fecondo di altre bellissime conseguenze. </s></p><p type="main">

<s>Se sopra i due piani CM, CN (fig. </s>

<s>111) diversamente inclinati, e insi&shy;<lb/>stenti sulla medesima orizzontale MN, sien posati due corpi tali, che i loro <lb/>pesi stiano come le linee CM, CN, bilanciati insieme poseranno in equilibrio, <pb xlink:href="020/01/1997.jpg" pagenum="240"/>ossia non avranno motivo d'andar n&egrave; in su n&egrave; in gi&ugrave;. </s>

<s>&ldquo; Ostendemus enim <lb/>centrum commune gravitatis eorum descendere non posse, sed in eadem <lb/><figure id="id.020.01.1997.1.jpg" xlink:href="020/01/1997/1.jpg"/></s></p><p type="caption">

<s>Figura 111.<lb/>semper horizontali linea, quantumlibet gra&shy;<lb/>via moveantur, reperiri &rdquo; (ivi, pag. </s>

<s>100). <lb/>Suppongasi infatti che non rimangano i <lb/>due corpi bilanciati, ma che l'uno risalga <lb/>da A in E, mentre l'altro scende da B in <lb/>D, per egual tratto. </s>

<s>Si farebbe ci&ograve; mani&shy;<lb/>festamente senza motivo, perch&egrave; il centro <lb/>di gravit&agrave; ch'essendo in A e in B costituiti i due corpi si trova sopra la linea <lb/>orizzontale AB, nella nuova posizione E, D in essa linea orizzontale rimane, <lb/>ci&ograve; che si dimostra dal Torricelli cos&igrave; con la sua solita facilit&agrave; elegante. </s>

<s>Si <lb/>ha per supposizione E:D=AC:CB. </s>

<s>E da E condotta EF parallela a CB, <lb/>AC:CB=AE:EF=BD:EF=GD:EG. </s>

<s>Ma se E e D stanno recipro&shy;<lb/>camente come GD a EG il loro comun centro di gravit&agrave; &egrave; in G, ch'&egrave; pure <lb/>un punto della orizzontale AB niente pi&ugrave; alto o pi&ugrave; basso del primo, e per&shy;<lb/>ci&ograve; la Bilancia, nelle condizioni supposte, &egrave; in stato d'equilibrio indifferente. </s></p><p type="main">

<s>Se fosse il lato CB a perpendicolo, il peso B graviterebbe lungh'esso <lb/>col suo momento totale, e dal general teorema ora dimostrato ne consegui&shy;<lb/>rebbe immediatamente che &ldquo; momentum totale gravis ad momentum, quod <lb/>habet in plano inclinato, est ut longitudo ipsius plani inclinati ad perpen&shy;<lb/>diculum (ibid., pag. </s>

<s>101). Il Torricelli per&ograve; ne fa una dimostrazione distinta, <lb/>per condur la quale, entrato oramai in diffidanza del principio delle velo&shy;<lb/>cit&agrave; virtuali, &egrave; costretto di tornare agl'istituti meccanici di Galileo, conclu&shy;<lb/>dendo dalla statica della Libbra quella del piano inclinato, col processo me&shy;<lb/>desimo, che s'illustrava dianzi dalla CX figura. </s></p><p type="main">

<s>Fu l'esempio del Torricelli efficacissimo sopra la Scuola galileiana, dalla <lb/>quale, banditisi i moti potenziali, non rimaneva altro modo per comparare <lb/>i momenti da quello in fuori di misurarli dalle <lb/>gravit&agrave; attuali, esercitate sul braccio orizzontale <lb/>e inclinato della Leva. </s>

<s>Il Borelli volle dare alla <lb/>dimostrazione una forma nuova, costruendola <lb/>nella seguente maniera. </s>

<s>Sia TFR (fig. </s>

<s>112) una <lb/>Leva angolare col braccio TF parallelo all'oriz&shy;<lb/>zonte, e con l'altro eguale FR comunque sol&shy;<lb/>levato, e abbia in F essa Leva il suo fulcro. </s>

<s><lb/>Sopra T e sopra R si alzino in ciascun de'due <lb/>bracci le perpendicolari, che prolungate s'in&shy;<lb/><figure id="id.020.01.1997.2.jpg" xlink:href="020/01/1997/2.jpg"/></s></p><p type="caption">

<s>Figura 112.<lb/>contreranno in D, come pure s'incontreranno <lb/>in E i prolungamenti di TF e di DR, venendosi cos&igrave; a disegnare il triangolo <lb/>rettangolo DTE, dal funicolo TDR teso lungo il qual triangolo, sian congiunti <lb/>due pesi, uno pendulo in T, e l'altro posato in R sul declivio del piano DE, <lb/>e si vogliano determinare le condizioni del loro equilibrio. </s></p><p type="main">

<s>Tanto essendo al grave R il venir sostenuto dal piano DE, quanto dal <pb xlink:href="020/01/1998.jpg" pagenum="241"/>braccio FR, e al grave T il pendere dal funicolo DT o dal braccio FT, le <lb/>richieste condizioni dell'equilibrio saranno, nell'uno e nell'altro caso, le <lb/>stesse. </s>

<s>Ma per le note leggi della Leva, abbassata la perpendicolare RH, si <lb/>ha che R sta a T come TF, ossia FR, sta ad FH. &ldquo; Et quia, per conclu&shy;<lb/>der con le parole medesime del Borelli, similia sunt duo triangula FRH et <lb/>DTE, latera sunt proportionalia, nempe FR ad FH erit ut ED ad DT, et <lb/>proinde pondus R ad T erit ut ED ad DT &rdquo; (De motu anim., P. I, Ro&shy;<lb/>mae 1688, pag. </s>

<s>121). </s></p><p type="main">

<s>Anche il Viviani, in uno de'suoi primi esercizii, aguzz&ograve; l'ingegno per <lb/>concluder dalla statica della Leva, in qualche altro modo, la proposizione da <lb/>lui stesso cos&igrave; formulata: &ldquo; Il momento totale del grave al momento ch'egli <lb/>ha, essendo posato sopra un piano obliquo, ha quella proporzione che la <lb/>lunghezza del detto piano inclinato al suo perpendicolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia la lunghezza CI (fig. </s>

<s>113) parallela al piano dell'orizzonte, dal <lb/>cui estremo C penda obliquamente, se&shy;<lb/><figure id="id.020.01.1998.1.jpg" xlink:href="020/01/1998/1.jpg"/></s></p><p type="caption">

<s>Figura 113.<lb/>condo qualunque inclinazione, il piano <lb/>CB, il cui perpendicolo BL, e sopra qual&shy;<lb/>sivoglia parte D del detto piano CB si <lb/>posi il grave A, ritenuto dal piano DM <lb/>attaccato al piano CB: dico il momento <lb/>totale del grave A, al momento ch'egli ha <lb/>posato sopra il piano inclinato CB, avere <lb/>quella proporzione che ha la lunghezza <lb/>del piano CB al suo perpendicolo BL. &rdquo; </s></p><p type="main">

<s>&ldquo; Cada dall'estremo C la perpendicolare CE, uguale a CD, e giungasi <lb/>ED, e si prolunghi. </s>

<s>E perch&egrave; l'angolo CED &egrave; uguale all'angolo CDE, sar&agrave; <lb/>CED minore d'un retto, e perci&ograve; la ED prodotta concorrer&agrave; con CI. </s>

<s>Con&shy;<lb/>corra per esempio in H, e sia H centro della Libbra, il cui braccio HC. &Egrave; <lb/>manifesto che il grave A, posato sopra MD, far&agrave; forza per scendere obli&shy;<lb/>quamente verso DM, e per&ograve; far&agrave; forza allo ingi&ugrave; contro il braccio della Lib&shy;<lb/>bra CH. </s>

<s>Tanto dunque sar&agrave; il momento, con che il grave A spinge l'osta&shy;<lb/>colo CD, quanto &egrave; il momento, con cui sforza ad abbassarsi il braccio della <lb/>Libbra CH. </s>

<s>Ma rispetto alla Libbra il momento del grave A posato in C al <lb/>momento del medesimo posato in D ha quella proporzione che la distanza <lb/>CH alla distanza FH, dunque il momento del grave A, posato in C, cio&egrave; il <lb/>momento totale, a quello ch'egli ha pesato in D verso DM, &egrave; come la CH <lb/>alla FH, e perci&ograve; come la CE alla DF, cio&egrave; come la CD alla DF, e perci&ograve; <lb/>come la CB alla BL, il che dovevasi dimostrare &rdquo; (MSS. Cim., T. XXXIV, <lb/>fol. </s>

<s>207, 8). </s></p><p type="main">

<s>Dicemmo che questo trapassar dalle leggi dell'equilibrio nella leva alle <lb/>proporzioni del moto sui piani inclinati, di che dette forse Galileo i primi <lb/>esempii, bench&egrave; seducente era lubrico, com'ebbe il Viviani stesso a sperimen&shy;<lb/>tar nell'eleggere a questa sua dimostrazione i mezzi termini, i quali manife&shy;<lb/>stamente contengono una fallacia. </s>

<s>Perch&egrave; se il grave A fa forza di abbassare <pb xlink:href="020/01/1999.jpg" pagenum="242"/>la Libbra nella direzione CD, il suo momento comparato con quello, che egli <lb/>ha nella direzione CE, non sta come CH ad HF, ma ad HN condotta da H <lb/>perpendicolare sopra CB, secondo la regola insegnata dal Benedetti. </s>

<s>Di una <lb/>tal costruzione fa gran maraviglia che non si servissero, e che non ne co&shy;<lb/>noscessero l'importanza que'sagaci galileiani, perch&egrave; riducendosi a quella, <lb/>che si usa per decompor le forze, avrebbe potuto condur per una via di&shy;<lb/>retta e sicura a concluder l'intento. </s>

<s>Dalla similitudine infatti de'triangoli <lb/>HNC, CLB si sarebbe immediatamente dedotto che HC sta ad HN, ossia la <lb/>forza diretta alla obliqua, o com'altrimenti vuol dirsi il momento totale nel <lb/>perpendicolo al parziale sul piano inclinato, come BC sta a BL. </s></p><p type="main">

<s>Dev'essersi per&ograve; il Viviani facilmente accorto di quella sua fallacia, <lb/>quand'egli, primo nella Scuola galileiana impar&ograve; a decomporre il momento <lb/>totale ne'due parziali, l'un de'quali s'esercita contro, e l'altro lungo il piano <lb/>inclinato; ci&ograve; che, passatosi fin allora senza considerazione, costituiva quella <lb/>lubricit&agrave;, che si diceva essere per tornare pericolosa a chi, argomentando <lb/>dalla Libbra, avesse voluto imitare gli esempii di Galileo. </s></p><p type="main">

<s>Nell'aggiunta postuma alla terza giornata Delle due nuove scienze si <lb/>accennava al fecondo principio, di cui disse bene il Lagrange: &ldquo; il paruit <lb/>que Galilee n'a pas connu toute l'importance &rdquo; (Mechan. </s>

<s>anal. </s>

<s>cit., pag. </s>

<s>8), <lb/>considerando nel triangolo BEF (fig. </s>

<s>114) &ldquo; il moto del mobile, per esem&shy;<lb/>pio all'ins&ugrave; da B in E, esser composto del trasversale orizzontale BF, e del <lb/><figure id="id.020.01.1999.1.jpg" xlink:href="020/01/1999/1.jpg"/></s></p><p type="caption">

<s>Figura 114.<lb/>perpendicolare FE, ed essendo che, quanto <lb/>all'orizzontale, nessuna &egrave; la resistenza del <lb/>medesimo all'esser mosso, non facendo con <lb/>tal moto perdita alcuna, nemmeno acquisto, <lb/>in riguardo della propria distanza dal comun <lb/>centro delle cose gravi, che nell'orizzonte <lb/>si conserva sempre l'istessa; resta la resi&shy;<lb/>stenza esser solamente rispetto al dover sa&shy;<lb/>lire la perpendicolare FE &rdquo; (Alb. </s>

<s>XIII, 176). Ma il Torricelli, nel corollario <lb/>alla proposizione II <emph type="italics"/>De motu gravium,<emph.end type="italics"/> proponendosi di risolvere il problema <lb/>di Pappo, che per i falli di Guidubaldo e del Cabeo dice esser divenuto a <lb/>quei tempi famoso, faceva una costruzione e un ragionamento, da cui pote&shy;<lb/>vasi facilmente concludere la quantit&agrave;, in che il momento totale di un grave <lb/>si comparte sul piano ne'suoi momenti parziali. </s>

<s>Rappresenti, egli dice, la <lb/>verticale BC quello stesso momento totale, e dalla sua estremit&agrave; C si ab&shy;<lb/>bassi la CD perpendicolare all'obliqua BE: il segmento BD misura la po&shy;<lb/>tenza necessaria a ritenere il grave sopra il declivio, ed &egrave; cos&igrave; manifesta&shy;<lb/>mente ne'suoi veri termini risoluto il problema famoso. </s></p><p type="main">

<s>Ne'lati BC, BD del triangolo CBD s'hanno dunque prefigurati il mo&shy;<lb/>mento totale nel perpendicolo, e il momento della discesa lungo il declivio: <lb/>or che altro pu&ograve; essere il terzo lato CD, che retto insiste sopr'esso decli&shy;<lb/>vio, se non che la misura, con cui il grave scendendo preme sul suo soste&shy;<lb/>gno? </s>

<s>Le proporzioni dunque de'moti, in che si risolve la gravit&agrave; totale, son <pb xlink:href="020/01/2000.jpg" pagenum="243"/>date dalla similitudine de'due triangoli BCD, EBF, dalla quale concludesi <lb/>immediatamente che, rappresentando, l'ipotenusa BE essa gravit&agrave; totale, i <lb/>due cateti danno la misura giusta delle due gravit&agrave; parziali, la verticale EF <lb/>rappresentando l'impeto dello scendere, e la orizzontale la pressione eser&shy;<lb/>citata dal grave sul piano che gli soggiace. </s></p><p type="main">

<s>Sarebbe la similitudine de'due detti triangoli potuta valer di matema&shy;<lb/>tica dimostrazione, per chi avesse avuto dimestichezza con la regola di de&shy;<lb/>comporre i momenti, come ve l'aveva Leonardo da Vinci, nelle Note del <lb/>quale si trovano con sicurezza proposti tutti que'teoremi che, negletti da <lb/>Galileo e dal Torricelli, si diceva, e or ora lo vedremo, essere stato il primo <lb/>a dimostrarli laboriosamente il Viviani. </s>

<s>&ldquo; Il grave uniforme, cos&igrave; annunzia <lb/>Leonardo la sua proposizione, che discende per obliquo divide il suo peso <lb/>in due varii aspetti. </s>

<s>Provasi, e sia AB (fig. </s>

<s>115) mobile situato per la obli&shy;<lb/>quit&agrave; ABC: dico che il peso del grave AB comparte la sua gravit&agrave; per due <lb/>aspetti: cio&egrave; per la linea BC e per la linea <lb/><figure id="id.020.01.2000.1.jpg" xlink:href="020/01/2000/1.jpg"/></s></p><p type="caption">

<s>Figura 115.<lb/>BM (perpendicolare a BC) &rdquo; (Manuscr. </s>

<s>G cit., <lb/>fol. </s>

<s>75). La dimostrazione, per la quale rimanda <lb/>Leonardo al suo trattato di Statica, a cui era <lb/>ormai dal Nemorario consacrato il titolo di <emph type="italics"/>Li&shy;<lb/>bro dei pesi,<emph.end type="italics"/> si doveva concludere immediata&shy;<lb/>mente dalla costruzion del triangolo delle forze, <lb/>di cui rivelasi in quest'altra Nota tutta l'arte e la scienza: &ldquo; Il grave, che <lb/>non pesa inverso il centro del mondo, sempre pesa in due o pi&ugrave; lochi. </s>

<s>Pro&shy;<lb/>vasi, e sia il grave AB, il quale non pesa per la linea centrale BE, adunque <lb/>pesa alli due sostentacoli BC, BM &rdquo; (ivi, fol. </s>

<s>76 a tergo), i quali due so&shy;<lb/>stentacoli fanno equilibrio all'impeto discensivo del grave e al gravitativo <lb/>di lui sul piano inclinato, secondo la proporzionale misura delle loro lun&shy;<lb/>ghezze lineari BE, EC, presa la BC per misura dell'impeto totale. </s></p><p type="main">

<s>Se l'angolo BCM &egrave; semiretto le due linee BE, EC tornano uguali, ci&ograve; <lb/>che vuol dir compartirsi in quel caso il momento totale ugualmente ne'due <lb/>parziali; corollario che Leonardo stesso prometteva avrebbe concluso dalla <lb/>proposizion principale in quel Libro, dove egli aveva intenzione di dimo <lb/>strarla. </s>

<s>&ldquo; Il perch&egrave; e'l quanto &egrave; maggiore il peso pi&ugrave; all'uno che all'altro <lb/>aspetto, e che obliquit&agrave; fia quella che comparte due pesi per egual parte, <lb/>sar&agrave; detto nel libro <emph type="italics"/>Delli pesi &rdquo;<emph.end type="italics"/> (ivi, fol. </s>

<s>75). </s></p><p type="main">

<s>Il Viviani, in maneggiar queste regole poco esperto, n&egrave; fidandosi d'al&shy;<lb/>tra scorta che di quella di Galileo, riusc&igrave; alle medesime conclusioni di Leo&shy;<lb/>nardo, ma quanto pi&ugrave; laboriosamente si giudichera dai nostri Lettori, alla <lb/>pubblica notizia dei quali rendiamo la seguente scrittura, viva immagine di <lb/>una pupilla, che al primo trasparir di mezzo alle nuvole un raggio chiaro <lb/>di luce, si volge a lui per accoglierlo con letizia desiderosa. </s>

<s>In un angolo <lb/>del foglio 16 del Tomo CXIII dei Discepoli di Galileo leggesi cos&igrave; scritto <lb/>dal Viviani di propria mano: &ldquo; Questa corrisponde a quella del Galileo, che <lb/>prova che l'impeto composto di due moti equabili, perpendicolare ed oriz-<pb xlink:href="020/01/2001.jpg" pagenum="244"/>zontale, &egrave; uguale in potenza a tutt'e due: Credo che il momento totale sia <lb/>uguale in potenza al momento gravitativo, e al momento discensivo insieme <lb/>presi. </s>

<s>Cos&igrave; &egrave; veramente, e lo provo qui sotto, dopo la quarta di queste mie <lb/>seguenti proposizioni. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Proposizione I.<emph.end type="italics"/> Il momento totale di un grave, al momento discen&shy;<lb/>sivo sopra un piano, sta come il piano inclinato alla elevazione del mede&shy;<lb/>simo piano. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Poich&egrave;, quando il peso A al C (fig. </s>

<s>116) sta come l'inclinata BA alla <lb/>BC perpendicolare, i pesi hanno momento uguale di discendere. </s>

<s>Ma C eser&shy;<lb/><figure id="id.020.01.2001.1.jpg" xlink:href="020/01/2001/1.jpg"/></s></p><p type="caption">

<s>Figura 116.<lb/>cita il suo momento totale, dunque C &egrave; la <lb/>misura del momento discensivo di A per BA. </s>

<s><lb/>Ma il totale di A al totale di C sta come A <lb/>a C, e si &egrave; dimostrato che il totale di C &egrave; il <lb/>medesimo che il discensivo di A; dunque il <lb/>totale di A al discensivo del medesimo sopra <lb/>BA sta come la AB, piano inclinato, alla BC <lb/>perpendicolare, che &egrave; la sua elevazione. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Proposizione II.<emph.end type="italics"/> Il momento discensivo di un grave per un piano, <lb/>al discensivo del medesimo sopra altro piano, sta in proporzione reciproca&shy;<lb/>mente de'medesimi piani. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia altro piano BD, e sia un grave D uguale all'A. </s>

<s>Sar&agrave; il discen&shy;<lb/>sivo di A per BA, al totale di A, cio&egrave; di D, come CB a BA, per l'antece&shy;<lb/>dente, ed il totale di D, al discensivo di D per BD, come DB a BC, per la <lb/>medesima antecedente. </s>

<s>Adunque <emph type="italics"/>ex aequo,<emph.end type="italics"/> per la perturbata, il discensivo <lb/>di A per BA, al discensivo di D cio&egrave; del medesimo A per BD, star&agrave; come <lb/>BD a BA. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Proposizione III.<emph.end type="italics"/> Il momento discensivo di un grave per un piano <lb/>inclinato, al gravitativo sopra il medesimo piano, sta come la elevazione del <lb/>piano alla orizzontale. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se i due piani BA, AF (fig. </s>

<s>117) fanno angolo retto in A, &egrave; chiaro <lb/>che il momento discensivo di un grave, posto in A, che tocchi tutt'e due <lb/><figure id="id.020.01.2001.2.jpg" xlink:href="020/01/2001/2.jpg"/></s></p><p type="caption">

<s>Figura 117.<lb/>i piani, cio&egrave; che il discensivo per BA &egrave; il me&shy;<lb/>desimo del gravitativo sulla FA, ed il discensivo <lb/>della FA &egrave; il medesimo del gravitativo sulla BA. </s>

<s><lb/>Stante questo, e quanto di l&agrave;, cio&egrave; posto che <lb/>il grave A al C stia come il piano AB al per&shy;<lb/>pendicolare BC, tirata per B la BE perpendico&shy;<lb/>lare a BA, cio&egrave; parallela ad AF, &egrave; chiaro che il momento discensivo di un <lb/>grave E, uguale allo A, per BE, &egrave; uguale al discensivo dello A per FA, es&shy;<lb/>sendo ugualmente inclinato l'uno che l'altro, cio&egrave; il gravitativo di A sopra <lb/>FA, per la precedente riflessione, ossia il discensivo di A per BA, al di&shy;<lb/>scensivo di E per BE, sta come la BE alla BA, per la II. </s>

<s>Adunque il discen&shy;<lb/>sivo di A per BA al gravitativo di A sopra BA, star&agrave; come la EB alla BA, <lb/>cio&egrave; come la BC, perpendicolare all'orizzonte, alla CA orizzontale. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2002.jpg" pagenum="245"/><p type="main">

<s><emph type="italics"/>&ldquo; Corollario.<emph.end type="italics"/> Quando l'angolo dell'inclinazione sar&agrave; mezzo retto, allora <lb/>il discensivo di un grave sar&agrave; uguale al gravitativo, perch&egrave; la perpendico&shy;<lb/>lare torna uguale alla orizzontale. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Proposizione IV.<emph.end type="italics"/> Il momento totale di un grave, al momento gravi&shy;<lb/>tativo del medesimo sopra un piano inclinato, sta come il piano inclinato <lb/>alla orizzontale. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Positis iisdem,<emph.end type="italics"/> il totale di A al discensivo di A per BA, sta come la <lb/>AB alla BC, per la I, e il discensivo di A per BA, al gravitativo di A so&shy;<lb/>pra BA, sta come la BC alla CA per la III. </s>

<s>Adunque <emph type="italics"/>ex aequo<emph.end type="italics"/> il totale <lb/>di A al gravitativo del medesimo sopra BA stanno come BA ad AC. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario.<emph.end type="italics"/> Onde se il momento totale di un grave come A si porr&agrave; <lb/>che sia misurato per esempio dal piano inclinato AB, il momento descen&shy;<lb/>sivo del medesimo per detto piano sar&agrave; misurato dalla BC, ed il gravitativo <lb/>dalla AC, per la I e per la III di questo foglio. </s>

<s>Ma la AB, &egrave; in potenza <lb/>uguale alle BC, AC, adunque il momento totale di un grave &egrave; sempre uguale <lb/>al momento gravitativo, di esso sopra un piano col momento discensivo per <lb/>il medesimo piano. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Proposizione V.<emph.end type="italics"/> Che i momenti discensivi di un grave per diverse <lb/>inclinazioni di piani stiano come i seni retti delle elevazioni de'medesimi <lb/>piani, si dimostra da Galileo e dal Torricelli nel corollario della III <emph type="italics"/>De motu <lb/>gravium.<emph.end type="italics"/> Ma che i momenti gravitativi di un grave, sopra diverse inclina&shy;<lb/>zioni di piani, siano come i seni retti degli angoli de'complementi delle ele&shy;<lb/>vazioni de'medesimi piani, cos&igrave; dalla nostra precedente si deduce; &rdquo; </s></p><p type="main">

<s>&ldquo; Poich&egrave; il momento gravitativo di A sopra AC, (fig. </s>

<s>118) al suo to&shy;<lb/>tale momento, sta come la DC alla CA, per la precedente, ed il totale di <lb/>A, cio&egrave; di B, che &egrave; uguale ad A, al gravitativo di B <lb/><figure id="id.020.01.2002.1.jpg" xlink:href="020/01/2002/1.jpg"/></s></p><p type="caption">

<s>Figura 118.<lb/>sopra BC, sta come la CA, cio&egrave; come la CB alla CE, <lb/>per la medesima; adunque <emph type="italics"/>ex aequo<emph.end type="italics"/> il gravitativo di <lb/>A sopra AC, al gravitativo del medesimo A sopra BC, <lb/>star&agrave; come CD a CE, che sono i seni retti de'compi&shy;<lb/>menti degli angoli delle elevazioni ACE, BCE. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario.<emph.end type="italics"/> Di qui si ricava che nelle inclina&shy;<lb/>zioni, che <emph type="italics"/>aequaliter distant a semicirculo,<emph.end type="italics"/> sempre <lb/>il gravitativo sopra un piano &egrave; uguale al discensivo <lb/>per l'altro, e il discensivo al gravitativo, perch&egrave; il <lb/>seno retto dell'uno &egrave; uguale al seno del complemento dell'altro &rdquo; (ivi, <lb/>fol. </s>

<s>16, 17). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Con le cinque proposizioni dal Viviani, al modo ora esposto dimostrate, <lb/>veniva la Statica del piano inclinato, nella scuola galileiana, a ridursi alla <lb/>sua perfezione, e perch&egrave; doveva sopr'essa posarsi il fondamento a tutto l'edi-<pb xlink:href="020/01/2003.jpg" pagenum="246"/>fizio meccanico, giovarono provvidamente a confermarla da una parte le sot&shy;<lb/>tili disamine, e le temerarie contradizioni dall'altra. </s>

<s>Alessandro Marchetti <lb/>mandava fuori in Firenze nel 1669 un trattato <emph type="italics"/>De resistentia solidorum,<emph.end type="italics"/> a <lb/>cui poneva per fondamento un principio &ldquo; quo nullum aliud fortasse fir&shy;<lb/>mius in mechanicis reperias unquam &rdquo; (pag. </s>

<s>XI) e che solo, senz'altra mac&shy;<lb/>china, dice essergli stato sufficiente a sollevar la mole, ch'egli veniva a met&shy;<lb/>tere in pubblica mostra. </s>

<s>Quel fondamento, al dir del macchinatore, frutto <lb/>di meditazioni alte e profonde, consisteva nella proposizione <emph type="italics"/>Momenta gra&shy;<lb/>vium proportionem habent compositam ex proportionibus ponderum et <lb/>longitudinum<emph.end type="italics"/> (ivi) che, felicemente occorsagli a dimostrare, ebbe a fargli <lb/>menare il vanto di una grande scoperta. </s>

<s>Comunicata a Lorenzo Bellini, amico <lb/>suo e collega nello studio pisano, la novit&agrave; preziosa, &ldquo; suscipit ipse hilari <lb/>vultu, favet utrique nostrum fortuna, ostendimus ambo, diversa tamen ra&shy;<lb/>tiocinatione, quam deinde nobis invicem exibemus &rdquo; (ivi). </s></p><p type="main">

<s>La iattanza desta in noi una gran maraviglia, la quale di poco si dimi&shy;<lb/>nuisce, anche ripensando alle condizioni di quei tempi, perch&egrave;, sebbene sia <lb/>vero che non erano ancora nel 1669 pubblicate le proposizioni del Mauro&shy;<lb/>lico n&egrave; quelle dell'Aggiunti, e che i trattati, in cui il Barrow e il Wallis <lb/>applicavano alla statica le teoria de'momenti non potessero essere al Mar&shy;<lb/>chetti e al Bellini ancora noti; nota era al mondo scientifico la borelliana <lb/>proposizione XXVII <emph type="italics"/>De vi percussionis,<emph.end type="italics"/> e pi&ugrave; noto che mai, nella proposi&shy;<lb/>zione XVIII <emph type="italics"/>De dimensione Parabolae<emph.end type="italics"/> il Lemma geometrico del Rocca in&shy;<lb/>vocato dal Torricelli. </s>

<s>In ogni modo la vantata scoperta del nuovo fondamento <lb/>meccanico sembra a noi una puerilit&agrave;, perch&egrave; la proposizion che i momenti <lb/>si compongono delle distanze e delle moli si conclude immediatamente dal <lb/>supposto che due pesi uguali e ugualmente distanti dal sostegno si fanno <lb/>insieme equilibrio o, come si vuol dire, hanno uguale il momento, il quale <lb/>chiamato M &egrave; espresso dalla formula M=PXD, intendendosi per P il <lb/>peso, e per D la distanza. </s>

<s>Per un altro peso <emph type="italics"/>p,<emph.end type="italics"/> e per un'altra distanza <emph type="italics"/>d,<emph.end type="italics"/><lb/>il momento <emph type="italics"/>m<emph.end type="italics"/> &egrave; parimenti espresso da <emph type="italics"/>m<emph.end type="italics"/>=<emph type="italics"/>p<emph.end type="italics"/>X<emph type="italics"/>d<emph.end type="italics"/> e queste due equazioni <lb/>contengono in s&egrave; dimostrata la proposizion del Marchetti, con i suoi corol&shy;<lb/>larii che essendo uguali le distanze i momenti stanno come i pesi, e che, se <lb/>essi pesi stanno reciprocamente come le distanze, i momenti sono uguali: <lb/>corollarii supposti per veri dallo stesso Marchetti, e sopra i quali ei conduce <lb/>nel seguente modo la sua dimostrazione. </s></p><p type="main">

<s>Se dagli estremi della Libbra AC <lb/><figure id="id.020.01.2003.1.jpg" xlink:href="020/01/2003/1.jpg"/></s></p><p type="caption">

<s>Figura 119.<lb/>(fig. </s>

<s>119) sostenuta in B, pendano in equi&shy;<lb/>librio le moli E, F, si avr&agrave; per i principii <lb/>archimedei F:E=AB:BC. </s>

<s>Intendasi <lb/>appesa all'estremo A una terza mole D: <lb/>sar&agrave; per la ragione identica D:F=D:F, <lb/>DXF:FXE=ABXD:BCXF. </s>

<s>Ma i <lb/>momenti M.oD, M.oE, supposti i pesi D, E <lb/>attaccati ai medesimi punti della Libbra, <pb xlink:href="020/01/2004.jpg" pagenum="247"/>stanno come le moli D, E, e il momento di E &egrave; uguale al momento di F, dunque <lb/>MoD:MoF=ABXD:BCXF, &ldquo; momentum scilicet D ad E, hoc est F in <lb/>composita est proportione ex rationibus D ad F et AB ad BC &rdquo; (ibid., pag. </s>

<s>2). </s></p><p type="main">

<s>Il Bellini us&ograve; un artificio simile per dimostrare la sua proposizione, <lb/>&ldquo; Momenta inaequalium facultatum, ab inaequalibus longitudinibus penden&shy;<lb/>tium, sunt in ratione composita ponderum et longitudinum &rdquo; (Opera omnia, <lb/>P. II, Venetiis 1703, pag. </s>

<s>88), e fu perci&ograve; chiamato dal Marchetti a parte&shy;<lb/>cipare al merito di aver gettato quelle <emph type="italics"/>Fondamenta universae scientiae de <lb/>motu,<emph.end type="italics"/> con le quali si pretendeva di dar fermezza all'edifizio meccanico del <lb/>Torricelli e di Galileo. </s>

<s>Nel 1674 usciva in Pisa, col detto titolo prosuntuoso, <lb/>un libricciolo di poche paginette in 24&deg;, nella prefazione al quale cos&igrave; diceva <lb/>il Marchetti rivolgendosi al suo lettore: &ldquo; Causam huius inscriptionis sta&shy;<lb/>tim intelliges, agnosces enim hisce inniti, non ea solum quae primus omnium <lb/>circa eiusmodi subiectum excogitavit maximus, admirabilis ac toto orbe ce&shy;<lb/>leberrimus Galileus, sed et quae rursus illis addidit eximius vir Evangeli&shy;<lb/>sta Torricellius, aliique insignes huius saeculi Mathematici, immo et innu&shy;<lb/>mera propemodum, quae in diem alii etiam moliri possunt. </s>

<s>Fecit haec <lb/>memoratus Galileus, et, dicam libere id quod sentio, non satis firme, quod <lb/>vel ex eo evinci potest quia, in posthuma editione suorum operum, ipse no&shy;<lb/>vis ratiociniis ea fulcire conatus est. </s>

<s>Idipsum fecerat Torricellius, aliique <lb/>etiam tentarunt, sed quorum nullus, nisi mea me opinio fallat, exacte prae&shy;<lb/>stitit, omnes namque satis quidem probabiliter ratiocinati sunt, sed neces&shy;<lb/>sarias, et quales decuit vere geometricas, demonstrationes nemo exhibuit. </s>

<s><lb/>An tales itaque ego exhibuerim tu ipse iudica &rdquo; (pag. </s>

<s>6). </s></p><p type="main">

<s>Galileo e il Torricelli, in queste parole rimproverati, avrebbero potuto <lb/>rispondere al petulante discepolo che avevano molto bene considerate le cose, <lb/>dette quali egli si vanta di essere stato il primo; e noi in altra occasione <lb/>trascriveremo a giustificarli i teoremi, che lasciarono ambedue manoscritti, <lb/>per dimostrar che i momenti stanno in ragion composta delle distanze e dei <lb/>pesi, non con intenzione di applicarli ai piani inclinati, ma alle resistenze <lb/>dei solidi allo spezzarsi. </s></p><p type="main">

<s>La prima vera geometrica dimostrazione che, secondo il Marchetti, non <lb/>fu, tale quale si conveniva, esibita dal Torricelli, &egrave; questa: che pesi uguali, <lb/>sopra uguali piani variamente inclinati, hanno i momenti proporzionali ai <lb/>perpendicoli. </s>

<s>La proposta, ch'&egrave; la III torricelllana <emph type="italics"/>De motu,<emph.end type="italics"/> dovrebbe a ri&shy;<lb/>gore di geometria essere dimostrata cos&igrave;, come il Marchetti stesso voleva <lb/>insegnare a fare ai due celeberrimi esi&shy;<lb/>mii maestri, nella prefazione al suo li&shy;<lb/>bricciolo commemorati. </s>

<s>Sia il grave sfe&shy;<lb/>rico G, col centro in H, posato ora sul <lb/>piano AC (fig. </s>

<s>120) e ora sul medede&shy;<lb/>simo piano, ma abbassatosi da CE in DF. </s>

<s><lb/>Tirate in ciascuna figura da H le ver&shy;<lb/>ticali HN, e dai punti di contatto I, K <lb/><figure id="id.020.01.2004.1.jpg" xlink:href="020/01/2004/1.jpg"/></s></p><p type="caption">

<s>Figura 120.<pb xlink:href="020/01/2005.jpg" pagenum="248"/>le orizzontali IL, KM, le due coppie di triangoli simili IHL, CAE, e KMH, <lb/>DEF danno le due proporzioni LI:IH=EC:CA, KH:KM=ED:DF, <lb/>e perci&ograve; LI:KM=EC:DF. </s>

<s>Ma perch&egrave; LI sta ad MK come il momento <lb/>di G sepra AC sta al momento del medesimo peso sopra ED, &ldquo; ergo mo&shy;<lb/>mentum ponderis G supra CA, ad momentum eiusdem ponderis supra DE, <lb/>in eadem est proportione, in qua CE est ad DF &rdquo; (ibid., pag. </s>

<s>11, 12). </s></p><p type="main">

<s>La solita macchina, operatrice dei primi maravigliosi effetti in sollevar <lb/>la mole <emph type="italics"/>De resistentia solidorum,<emph.end type="italics"/> &egrave; che gioca qui nelle mani dell'Autore, <lb/>per raddirizzare e confermare il teorema torricelliano de'momenti dei gravi <lb/>sopra i piani inclinati, la dimostrazion del quale &egrave;, come apertamente si <lb/>vede, conclusa dal principio gi&agrave; dimostrato che stanno essi momenti in ra&shy;<lb/>gion composta delle distanze e dei pesi. </s>

<s>Galileo e il Torricelli, tutto attri&shy;<lb/>buendo l'impeto del discendere ai pesi, non badarono alle distanze, e non <lb/>fecero perci&ograve; distinzione fra l'essere il centro di gravit&agrave; nel piano o sopra <lb/>il piano, nel primo dei quali due casi il grave come, se pendesse dal cen&shy;<lb/>tro della Libbra, non esercita momento propriamente detto, mentre nel se&shy;<lb/>condo caso &egrave; come se pendesse da un braccio della stessa Libbra. </s>

<s>Cos&igrave;, nei <lb/>due sopra addotti esempii, altro &egrave; avere la sfera G il centro di gravit&agrave; in <lb/>I o in K nel piano, altro &egrave; averlo in H sopra il piano, non sentendo nel <lb/>primo caso altr'impeto che quello della discesa naturale obliqua, ed eser&shy;<lb/>citando nel secondo un vero e proprio momento, misurabile dal prodotto del <lb/>peso G per la distanza IL o MK. </s></p><p type="main">

<s>Il Marchetti per&ograve; non sta a richiamar l'attenzione sopra questo esame <lb/>particolare, lasciandone la cura a un giovane suo discepolo, Giuseppe Vanni, <lb/>che nel 1688 pubblicava in Firenze sua patria una esercitazione meccanica <lb/><emph type="italics"/>De'momenti de'gravi sopra a'piani.<emph.end type="italics"/> Ivi &ldquo; mi maraviglio bene, egli dice, <lb/>e non so per qual destino, che ancor quel grand'uomo d'Evangelista Tor&shy;<lb/>ricelli, nella seconda proposizione del primo libro Dei moti, per altro certa, <lb/>parlando dei gravi similmente posti si servisse d'una dimostrazione, nella <lb/>quale due cose egli afferma che non mi paiono vere. </s>

<s>Dice in primo luogo <lb/>che, se il peso A (fig. </s>

<s>121) al peso D sta come AB a BC, il momento del <lb/>peso A &egrave; uguale al momento del peso D, ci&ograve; che n&egrave; &egrave; vero, n&egrave; si deduce <lb/><figure id="id.020.01.2005.1.jpg" xlink:href="020/01/2005/1.jpg"/></s></p><p type="caption">

<s>Figura 121.<lb/>com'egli afferma dalla sua prece&shy;<lb/>dente. </s>

<s>Perciocch&egrave; nella prima consi&shy;<lb/>dera i pesi co'centri delle lor gravit&agrave; <lb/>nel piano, cio&egrave; posti, come s'&egrave; defi&shy;<lb/>nito, nel piano, e nella seconda gli <lb/>pone sopra il piano, cosa che varia <lb/>di gran lunga i momenti: anzi nel <lb/>primo caso i gravi, come noi dimostreremo, non hanno momento alcuno, e <lb/>nel secondo il pi&ugrave; delle volte l'esercitano. </s>

<s>Secondariamente pronunzia che il <lb/>momento del grave C, al momento del grave D, sta come la mole alla mole, <lb/>essendosi dimostrato, nella seconda di questo, aver proporzion composta della <lb/>mole alla mole, e della distanza alla distanza &rdquo; (pag. </s>

<s>37, 38). </s></p><pb xlink:href="020/01/2006.jpg" pagenum="249"/><p type="main">

<s>Queste non son per&ograve; altro che sottigliezze di effetti, dipendenti dalla <lb/>particolar figura del corpo disposto a scendere ora strisciando, ora rivolgen&shy;<lb/>dosi in s&egrave; stesso o ruzzolando, e Galileo e il Torricelli non sempre usano <lb/>la parola momento in senso proprio, come lo defin&igrave; il Maurolico, ma lo fanno <lb/>pi&ugrave; spesso sinonimo d'impeto o di, qualunque egli sia, conato al moto, il <lb/>quale impeto o conato totale, non variandosi in un medesimo mobile per <lb/>variar di posizione o di figura, anche gl'impeti parziali rimangon gli stessi, <lb/>e perci&ograve; la questione &egrave; lasciata a decidere al principio della composizion <lb/>delle forze, di bene altra efficacia della macchina dei momenti costruita dal <lb/>Marchetti e dal Vanni. </s></p><p type="main">

<s>Se di quella sicurissima regola di decomporre le forze avesse saputo <lb/>far uso Vitale Giordano, si sarebbe facilmente ravveduto della insussistenza <lb/>delle sue obiezioni contro il lemma della proposizione II del Torricelli, e le <lb/>sue nubi &ldquo; quae videntur obscuritatis nescio quid ac dubii praecedentis theo&shy;<lb/>rematis conclusioni offundere &rdquo; (Fundam. </s>

<s>doctrinae motus, Romae 1688, <lb/>pag. </s>

<s>1) gli si sarebbero d'un tratto dissipate dalla mente, perch&egrave; il mo&shy;<lb/>mento totale del peso sostenuto orizzontalmente dal braccio della Libbra si <lb/>decompone sul piano in due, uno, che solo rimane attivo, e l'altro che si <lb/>rintuzza dalla resistenza del piano. </s>

<s>Ma il Giordano che non sapeva vedere <lb/>in che modo e in qual precisa quantit&agrave; le parti rispondessero al tutto, per&shy;<lb/>ci&ograve; oppose che non pu&ograve; il momento del peso, sostenuto dal solo vette, es&shy;<lb/>sere il medesimo di quello sostenuto tutt'insieme dal vette e dal declivio, <lb/>sopra il quale egli scende. </s></p><p type="main">

<s>Dall'aver dunque trascurata la regola dei moti composti, e non quella <lb/>dei momenti, dipendeva la lubricit&agrave; della prima galileiana dimostrazione, fe&shy;<lb/>delmente imitata dal Torricelli, il quale, se non si fosse contentato di dir <lb/>cos&igrave; in generale che il grave &egrave; in parte abbandonato al proprio impeto, e <lb/>in parte &egrave; sostenuto dal piano obliquo; non avrebbe dato al Giordano, mes&shy;<lb/>sosi su per quel lubrico, occasione di cader cos&igrave; tante volte com'egli fece. </s>

<s><lb/>Maravigliosa perci&ograve; apparir&agrave;, anco da questa parte, la scienza di Leonardo <lb/>da Vinci, che fra tanti insidiosi agguati procede sicura, e che ora d&agrave; sodi&shy;<lb/>sfazione al Marchetti, dimostrando come lui la proposizione del grave sfe&shy;<lb/>rico ruzzolante con la regola dei momenti; ora d&agrave; sodisfazione al Vanni, <lb/>considerando il grave che non ruzzola, ma che striscia su&igrave; piano, e pure, <lb/>in mezzo alte variate cause accidentali, mostra essere una medesima la ve&shy;<lb/>rit&agrave; dell'effetto. </s>

<s>Cotesta sua sicurezza vedemmo nascere dall'aver saputo com&shy;<lb/>partire la gravit&agrave; per due aspetti, ci&ograve; che, non essendosi saputo fare n&egrave; da <lb/>Galileo n&egrave; dal Torricelli, provoc&ograve; prima i restauri del Marchetti inutili e <lb/>inefficaci, e poi la famosa demolizione della Statica antica, tentata dal ge&shy;<lb/>suita lucchese Giovan Francesco Vanni. </s></p><p type="main">

<s>Antonio Magliabecchi, bibliotecario del granduca di Firenze, mand&ograve; un <lb/>giorno del 1684 a cotesto Gesuita lucchese, che allora insegnava in Roma, <lb/>il libricciolo del Marchetti Dei fondamenti della scienza universale del moto, <lb/>dove leggendo il Vanni che Galileo e il Torricelli avevano dimostrata la <pb xlink:href="020/01/2007.jpg" pagenum="250"/>proposizion dei momenti sopra i piani inclinati, <emph type="italics"/>non satis firme,<emph.end type="italics"/> prese ardir <lb/>di soggiungere ch'era affatto impossibile dar fermezza a ci&ograve; che non sussi&shy;<lb/>ste. </s>

<s>Pochi giorni dopo andava attorno per Roma un foglietto in 24&deg; di quat&shy;<lb/>tro sole paginette stampate, la prima delle quali portava scritto in fronte: <lb/>&ldquo; Specimen libri De momentis gravium, Auctore I. F. V. lucensi, ad illu&shy;<lb/>strissimum et eruditissimum D. </s>

<s>Antonium Magliabechium Sereniss. </s>

<s>M. D. </s>

<s><lb/>Etruriae Bibliothecarium. </s>

<s>&rdquo; Poi subito sotto si rivolgeva l'Autore allo stesso <lb/>Magliabecchi, per annunziargli che la intenzion della sua breve scrittura era <lb/>quella di dimostrar come la proposizione che il momento totale sta al par&shy;<lb/>ziale sul piano, reciprocamente come il piano stesso sta al perpendicolo, cre&shy;<lb/>duta da Galileo, dal Torricelli e da tanti altri esimi Matematici vera, era una <lb/>falsit&agrave; manifesta. </s>

<s>Il ragionamento procedeva cos&igrave;, come noi compendiosa&shy;<lb/>mente lo ridurremo da ci&ograve; che leggesi nel citato foglietto volante. </s></p><p type="main">

<s>Sia il piano inclinato XNC (fig. </s>

<s>122) di cui si prolunghi la base oriz&shy;<lb/>zontale NC della quantit&agrave; CO, uguale ad XN, e sopra O eretto il perpendi&shy;<lb/>colo ZO, uguale a NC, s'appoggi l'altro piano ZC, che far&agrave; per la costru&shy;<lb/><figure id="id.020.01.2007.1.jpg" xlink:href="020/01/2007/1.jpg"/></s></p><p type="caption">

<s>Figura 122.<lb/>zione l'angolo XCZ retto, dentro il quale s'im&shy;<lb/>magini posato il grave sferico IFH. </s>

<s>Il peso totale <lb/>si compartir&agrave; ugualmente nelle due direzioni <lb/>FI, IH, condotte dal centro I ai punti di con&shy;<lb/>tatto, e perci&ograve; perpendicolari ai due piani tan&shy;<lb/>genti. </s>

<s>Chiamati ora M. </s>

<s>T il momento totale, <lb/>M. XC, M.ZC i momenti parziali sopra i piani <lb/>XC, ZC, si dovrebbe, secondo il teorema dimo&shy;<lb/>strato da Galileo e dal Torricelli, avere le due <lb/>proporzioni M.T:M.XC=XC:XN, M.T:M.ZC <lb/>=XC:NC, le quali composte darebbero M.T:M.XC+M.ZC=XC:XN+NC; <lb/>cio&egrave;, dice il Vanni, &ldquo; momentum totale ad momenta partialia, simul sumpta, <lb/>est ut hypothenuse XC ad latera XN, et NC, in directum posita eiusdem trian&shy;<lb/>guli XNC. </s>

<s>Atqui hypothenusa XC non est aequalis lateribus XN, NC, sed <lb/>est illis minor, ergo, si totale momentum ad partialia sit ut XC ad XN et <lb/>NC, momentum totale non aequatur, sed est minus momentis partialibus <lb/>simul sumptis. </s>

<s>Ergo momentum totale, ad momentum super plano declivi XC, <lb/>non est ut longitudo plani XC ad perpendiculum XN &rdquo; (Romae 1684, pag. </s>

<s>3). </s></p><p type="main">

<s>&Egrave; indicibile la confusione che venne a mettere in tutto il mondo ma&shy;<lb/>tematico questo argomento del Vanni, in cui ora, a noi che abbiamo dime&shy;<lb/>stichezza col parallelogrammo delle forze, &egrave; tanto facile scoprire il paralo&shy;<lb/>gismo. </s>

<s>Ma non era allora cos&igrave;: l'arguto oppositore concludeva contro la <lb/>proposizione di Galileo da un princip&igrave;o insegnato dallo stesso Galileo, che <lb/>cio&egrave; &ldquo; si aliquod mobile duplici motu aequabili moveatur, nempe horizon&shy;<lb/>tali et perpendiculari, impetus, seu momentum lationis ex utroque motu <lb/>compositae, erit potentia aequalis ambobus momentis priorum motum &rdquo; <lb/>(Alb. </s>

<s>XIII, 234). Questa galileiana risponde alla XLI <emph type="italics"/>De vi percussionis,<emph.end type="italics"/><lb/>dove il Borelli avverte che il moto resultante per XC (nella precedente <pb xlink:href="020/01/2008.jpg" pagenum="251"/>figura CXXII) &egrave; uguale alla somma dei due componenti, fatti per la oriz&shy;<lb/>zontale NC e per la verticale XN, non in lunghezza, ma solamente in po&shy;<lb/>tenza. </s>

<s>&ldquo; Hic vero XC non est aequalis longitudine, set potentia tantum, mo&shy;<lb/>tibus XN et NC, propter angulum rectum &rdquo; (Bononiae 1667, pag. </s>

<s>85). </s></p><p type="main">

<s>Il Borelli, dietro gl'insegnamenti di Galileo, s'illudeva con le potenze <lb/>che producono i quadrati <emph type="italics"/>propter angulum rectum:<emph.end type="italics"/> era chiaro per&ograve; che si <lb/>trattava di forze, la potenza delle quali non pu&ograve; consistere in altro che nello <lb/>spingere un grave in un dato tempo per uno spazio determinato, ond'&egrave; che, <lb/>secondo esso Borelli, si misura quella stessa potenza dal prodotto della ve&shy;<lb/>locit&agrave; motrice per la quantit&agrave; di materia mossa. </s>

<s>Siano al peso, rappresen&shy;<lb/>tato in C nell'ultima figura, applicate due forze, una delle quali abbia virt&ugrave; <lb/>di trasportarlo equabilmente in un minuto secondo da C in N, per la oriz&shy;<lb/>zontale, e l'altra di sollevarlo da N in X, nello stesso tempo, per la verti&shy;<lb/>cale: saranno quelle due potenze come le velocit&agrave;, o come gli spazii pas&shy;<lb/>sati, ossia come le lunghezze NC, XN, e sar&agrave; pure come la lunghezza XC <lb/>la resultante de'due moti composti, o il tutto rispetto alle sue parti. </s>

<s>Se dun&shy;<lb/>que queste, sommate insieme, debbono uguagliarsi a quella, come dimostra&shy;<lb/>vano Galileo e il Borelli, essere la potenza XC uguale alla somma delle due <lb/>potenze NC e XN non voleva altro dire, fuor di ogni altra ambage, se non <lb/>ch'essere l'ipotenusa uguale alla somma de'due cateti. </s>

<s>Ma perch&egrave; questo <lb/>&egrave; manifestamente falso, e a un tal passo inevitabilmente conduce il suppo&shy;<lb/>sto che il momento totale stia al parziale come il piano sta al perpendicolo, <lb/>dunque concludeva il Vanni quel supposto teorema non pu&ograve; esser vero. </s></p><p type="main">

<s>Sembrava gl&igrave; si dovesse da tutti rispondere esser piuttosto falso che il <lb/>momento totale debba equivalere alla somma dei due parziali, ma illudeva <lb/>cos&igrave; il male applicato assioma che il tutto &egrave; uguale alle parti, e sopra i pi&ugrave; <lb/>prevaleva cos&igrave; grande l'autorit&agrave; di Galileo, che non si vollero in generale <lb/>ascoltar le ragioni, con le quali il Mersenno si studiava di ridurre al vero <lb/>le menti. </s>

<s>Com'&egrave; possibile, diceva nella prefazione alla sua Meccanica, che <lb/>un martello, sceso con la velocit&agrave; XC, faccia ugual percossa su C a quella <lb/>di un altro, che scenda con la velocit&agrave; XN+NC, tanto pi&ugrave; grande, se &egrave; <lb/>vero che sia tanto maggior l'impeto di un corpo, quanto va pi&ugrave; veloce? </s>

<s><lb/>Che dunque il moto per XC sia uguale alla somma dei moti per XN e NC <lb/>&ldquo; est ex mente Galilei pag. </s>

<s>250 Dialogorum, quod tamen minime verum <lb/>esse videtur &rdquo; (Parisiis 1644). </s></p><p type="main">

<s>Aveva il Vanni insomma proposto a sciogliere ai Matematici sbigottiti <lb/>questo dilemma: o &egrave; falso il teorema del moto per l'ipotenusa composto <lb/>dei due per i cateti, come si dimostra da Galileo nella IV giornata Delle due <lb/>nuove scienze, o &egrave; falso l'altro teorema della proporzion dei momenti di un <lb/>medesimo grave nel declivio e nel perpendicolo, com'&egrave; da Galileo stesso ivi <lb/>dimostrato nell'aggiunta postuma alla III Giornata. </s>

<s>L'audace oppositore, ap&shy;<lb/>provando quello per vero, ripudi&ograve; questo come falso e, ritornando indietro <lb/>un secolo e mezzo a intromettersi nella questione fra il Tartaglia e il Car&shy;<lb/>dano, ripet&egrave; con costui che il peso nel perpendicolo sta al peso nel piano <pb xlink:href="020/01/2009.jpg" pagenum="252"/>inclinato come l'angolo dell'elevazione sta all'angolo retto. </s>

<s>In un libricciolo <lb/>di poche pagine uscito fuori anonimo in Roma nel settembre del 1686 col <lb/>titolo <emph type="italics"/>Exegeses physico mathematicae de momentis gravium, de Vecte ac <lb/>de motu aequabiliter accelerato,<emph.end type="italics"/> si studi&ograve; di dare apparenza di vero a quel <lb/>ripudiato cardanico teorema, confermandolo poi nel 1693 con nuovi paralo&shy;<lb/>gismi in un altro libretto di maggior mole, <lb/>uscito pure in Roma a nome dell'Autore, <lb/>col titolo <emph type="italics"/>Investigatio momentorum,<emph.end type="italics"/> e in <lb/>cui la XXVI proposizione cos&igrave; viene annun&shy;<lb/>ziata: &ldquo; Si globi G et D (fig. </s>

<s>123) deti&shy;<lb/>neantur immoti a potentia Q, per filum <lb/>DQG, cuius una pars sit normalis horizonti, <lb/>altera sit parallela plano declivi AC, ac sup&shy;<lb/>ponamus conatum quam adhibet potentia Q <lb/><figure id="id.020.01.2009.1.jpg" xlink:href="020/01/2009/1.jpg"/></s></p><p type="caption">

<s>Figura 123.<lb/>nullatenus differre a conatibus simul sumptis quos adhibent potentiae D, G, <lb/>globus G ad globum D est ut angulus elevationis A ad rectum B &rdquo; (pag. </s>

<s>65). </s></p><p type="main">

<s>Lo <emph type="italics"/>Specimen<emph.end type="italics"/> del Vanni era come il lampo precursore alla folgore del&shy;<lb/>l'<emph type="italics"/>Esegesi,<emph.end type="italics"/> avventata, per distruggerlo dalle fondamenta, contro l'antico edi&shy;<lb/>fizio meccanico condotto da Galileo al pi&ugrave; alto fastigio; ond'&egrave; che tutti co&shy;<lb/>loro, i quali vi si riparavano sotto, o che uscivano di quando in quando fuori <lb/>per ammirarlo, furiosi insorsero contro il mago, che aveva con le malefiche <lb/>arti condensato nel sereno aere la inaspettata procella. </s>

<s>E qui, come sempre <lb/>suole avvenire in simili casi, l'insurrezione si sfogava, secondo l'indole della <lb/>persona o la qualit&agrave; dell'ingegno in varia maniera. </s>

<s>I pi&ugrave;, per assicurarsi <lb/>del pericolo, si stavano contenti a ricercare e a mettere a nuova prova la <lb/>stabilit&agrave; del fondamento, mentre alcuni altri volevano anche pi&ugrave; avanti en&shy;<lb/>trare addentro all'officina del mago, per spezzar quelle filosofiche ampolle, <lb/>dalle quali si faceva esalare il malefico fiato. </s>

<s>Del primo modo d'insorgere, <lb/>specialmente in Italia, s'ebbero molti esempii, ma pochi del secondo, per&shy;<lb/>ch&egrave;, sebben fosse facile a riconoscer quella per una vipera, difficile riusciva <lb/>a scoprir la borsa e i canali, d'onde stilla il veleno, come apparir&agrave; dai fatti <lb/>che ora riferiremo. </s></p><p type="main">

<s>Vedemmo come il lampo minaccioso del Vanni, prima che a nessun al&shy;<lb/>tro, si scoprisse agli occhi del Magliabechi, il quale, rimasto a un tratto cos&igrave; <lb/>abbarbagliato, volle interpellare il giudizio di varii suoi dotti amici, fra'quali <lb/>Antonio Monfort, che cos&igrave; gli rispondeva il di 10 Settembre 1685 da Na&shy;<lb/>poli: &ldquo; Le rendo infinite grazie dell'opuscolo del signor Vanni, il quale non <lb/>l'ho veduto prima di oggi. </s>

<s>In quanto al mio giudizio so che sar&agrave; molto de&shy;<lb/>bole, ma perch&egrave; V. S. illustrissima comanda cos&igrave;, non posso se non ob&shy;<lb/>bedire. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il Galileo ed anco Renato, nella II parte delle Lettere, epist. </s>

<s>LXXII, <lb/>vogliono che il momento del grave D per l'inclinata AC (nella precedente <lb/>figura) sia al momento medesimo per la perpendicolare CB, come la CB alla <lb/>AC, e per conseguenza, quando si uniranno i due triangoli come vuole il <pb xlink:href="020/01/2010.jpg" pagenum="253"/>p. </s>

<s>Vanni, non si compartiscono i due momenti sopra le loro ipotenuse in <lb/>modo, che uniti si eguaglino al momento totale, ma sempre saranno mag&shy;<lb/>giori di quello, siccome li due lati del triangolo rettangolo avanzano l'ipo&shy;<lb/>tenusa. </s>

<s>Ora il Padre doveva dimostrare che li due suddetti momenti non <lb/>possono esser maggiori del momento totale, per aver poi luogo la sua con&shy;<lb/>seguenza. </s>

<s>Dir&agrave; il Padre che questo &egrave; noto <emph type="italics"/>lumine naturae,<emph.end type="italics"/> ma con sua li&shy;<lb/>cenza non par cos&igrave;, quando tanti grandi uomini, non solo non l'hanno co&shy;<lb/>nosciuto per tale, ma ne hanno dimostrato il contrario, che nell'unione dei <lb/>triangoli, per lo scambievole impedimento, cessano li momenti per l'incli&shy;<lb/>nata, e totalmente il peso si riduce sopra le basi NC, CO della figura del <lb/>Padre. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Prego V. S. Ill.ma a restar servito che questo giudizio, qualunque egli <lb/>sia, resti fra noi, perch&egrave; non vorrei briga con costoro, i quali, bench&egrave; siano <lb/>amici infruttuosi, son per&ograve; nemici efficaci &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXII, <lb/>fol. </s>

<s>77). </s></p><p type="main">

<s>Se fosse, senza alcuna paura delle gesuitesche inimicizie, proceduto il <lb/>Monfort avanti, forse avrebbe risoluta la questione ne'suoi veri termini, ma <lb/>mettendo dubbii intorno al II teorema del IV Dialogo del moto, sarebbe ve&shy;<lb/>nuto ad attaccar briga tutt'insieme co'gesuiti e coi galileiani, i quali, messi <lb/>in grande imbarazzo dal dilemma del Vanni, non potevan far altro che con&shy;<lb/>fermare il vero, senza saper scoprire la fallacia nei ragionamenti, che vo&shy;<lb/>levano dargli apparenza di falso. </s></p><p type="main">

<s>La mattina del d&igrave; 28 Aprile 1685 il Viviani riceveva da Roma una let&shy;<lb/>tera, dove un tal Girolamo Pollini gli scriveva, fra le altre, queste parole: <lb/>&ldquo; Coll'occasione che ieri l'altro mi fu dato un foglietto da un mio amico <lb/>stampato, che io gli mando copiato, di un certo Francesco Spoleti di Luci&shy;<lb/>gnano, dottore di medicina, quale adesso si ritrova in Venezia, ho volsuto <lb/>cercare l'origine per il quale fu stampato, ed ieri appunto trovai il p. </s>

<s>Gio&shy;<lb/>van Francesco Vanni lucchese, gesuita nel Collegio romano, che mi don&ograve; <lb/>il presente foglietto stampato da lui, che io gl'invio (lo <emph type="italics"/>Specimen,<emph.end type="italics"/> che tien <lb/>luogo de'fogli 69, 70 nel Tomo CXLVII de'<emph type="italics"/>Discepoli<emph.end type="italics"/> fra i manoscritti del <lb/>Viviani) il quale padre mi disse di vantaggio che il dottissimo Galileo e il <lb/>Torricelli si sono molto ingannati nel dimostrare le sue proposizioni, par&shy;<lb/>ticolarmente <emph type="italics"/>De vecte,<emph.end type="italics"/> e che esso ha una dottrina contraria ad essi, quale <lb/>mi mostr&ograve; manoscritta, quale per il tempo cos&igrave; breve, diss'egli, non volse <lb/>che si leggesse, ma solo qualche proposizione, dicendo che fra poco l'avrebbe <lb/>stampata, avendo la licenza di poterla stampare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Prego la bont&agrave; di V. S. Ecc.ma di riflettere alla proposta del padre <lb/>Gesuito, ed alla risposta dello Spoleti, dicendo esso Gesuito che lo Spoleti <lb/>non abbia arrivato al fondo della proposizione di detto Padre, ma che esso <lb/>prova bene, ma non conclude alcuna cosa contro la propria proposizione &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. CXLVI, fol. </s>

<s>276). </s></p><p type="main">

<s>Il foglietto dello Spoleti, che noi leggiamo fra i manoscritti del Viviani <lb/>copiato dal Pollini, s'intitolava <emph type="italics"/>De momento gravis in plano inclinato, di-<emph.end type="italics"/><pb xlink:href="020/01/2011.jpg" pagenum="254"/><emph type="italics"/>cato Christinae Succorum Reginae a Francisco Spoleti lucignanensi.<emph.end type="italics"/> In <lb/>una prefazioncella prometteva l'Autore ai lettori avrebbe a loro provato, con <lb/>metodo nuovo, che il momento del grave sul piano obliquo sta al suo mo&shy;<lb/>mento totale come il perpendicolo all'ipotenusa &ldquo; non solum ad hanc fir&shy;<lb/>mandam doctrinam, verum etiam ut falsitatis arguam propositionem nuper <lb/>editam Romae a Mathematico lucensi, qui hac in re hallucinatos ait excel&shy;<lb/>lentissimos Magistros, censetque momenta gravis in duobus planis inclina&shy;<lb/>tis, simul sumpta, esse aequalia suo momento totali, quod falsum ostendam &rdquo; <lb/>(MSS. Gal., T. CXLVI, foI. 277). </s></p><p type="main">

<s>Applicando infatti le formule generali ai <lb/>numeri, suppone lo Spoleti essere NCO (fig. </s>

<s>124) <lb/>sette ulne, delle quali NC=ZO ne contenga <lb/>tre, e CO=NX ne contenga quattro. </s>

<s>Calcolati <lb/>poi convenientemente co'logaritmi gli elementi <lb/>trigonometrici in questione, conclude: &ldquo; Hinc <lb/>patet momenta sphaerae I in planis inclinatis <lb/>XC, ZC simul sumpta ad suum momentum to&shy;<lb/>tale non esse ut 1 ad 1, sicut Mathematicus <lb/>lucensis volebat, sed ut 7 ad 5, nempe ut ver&shy;<lb/><figure id="id.020.01.2011.1.jpg" xlink:href="020/01/2011/1.jpg"/></s></p><p type="caption">

<s>Figura 124.<lb/>ticalis XN et verticalis ZO (eguale alla orizzontale NC) ad hypothenusam XC, <lb/>quod erat ostendendum &rdquo; (ivi, fol. </s>

<s>279). </s></p><p type="main">

<s>Questo numerico esempio dello Spoleti confermava senza dubbio il teo&shy;<lb/>rema di Galileo e del Tartaglia, ma aveva ragione il Vanni a dire che non <lb/>concludeva alcuna cosa contro il suo argomento, perch&egrave;, per far ci&ograve;, sarebbe <lb/>convenuto provare come mai il tutto non debba essere eguale alle parti, con&shy;<lb/>tro l'assioma, e contro il teorema II dimostrato da Galileo nella sua IV gior&shy;<lb/>nata Del moto. </s>

<s>Un Galileiano perci&ograve; non poteva far altro che ostinarsi a <lb/>mantenere il vero contro i liberi sofismi, come presso a poco fa colui che <lb/>la mente combattuta riposa nell'evidenza dei fatti. </s>

<s>S'attenne a questo par&shy;<lb/>tito un altro Gesuita, ch'ebbe educato l'ingegno a una scuola diversa da <lb/>quella del Vanni, il fiorentino Giuseppe Ferroni, il quale scriveva cos&igrave; da <lb/>Siena il d&igrave; 9 Luglio 1687 al suo amato maestro Vincenzio Viviani: </s></p><p type="main">

<s>&ldquo; Il mio scolare, dottor Pier Antonio Morozzi, com'Ella avr&agrave; potuto co&shy;<lb/>noscere, &egrave; un angelo d'ingegno e di costumi, ed io ho pensato di fargli <lb/>onore con fargli stampare a suo nome, senza mentovarmi, un problema. </s>

<s>Ri&shy;<lb/>pensando qual problema dar gli potessi, mi &egrave; sovvenuto il foglio volante del <lb/>p. </s>

<s>Domenico (cos&igrave;) Vanni lucchese Del momento dei gravi discendenti sopra <lb/>i piani inclinati, e della sua Esegesi, ove, con discorsi filosofici che non hanno <lb/>alcuno odore di Geometria, pretende di gettare a terra la dottrina <emph type="italics"/>De motu<emph.end type="italics"/><lb/>del nostro gran maestro Galileo, e di stampare un foglio volante in rispo&shy;<lb/>sta. </s>

<s>Egli mena troppa galloria, vedendo che niun risponde alla sua obie&shy;<lb/>zione. </s>

<s>Penso rispondere, e con sua buona licenzia valermi dei moti equipol&shy;<lb/>lenti, come V. S. Ill.ma m'insegn&ograve; in Firenze, e soggiungere per i momenti <lb/>dei gravi una dimostrazione, presa in parte da alcuni manoscritti del p. </s>

<s>Egi-<pb xlink:href="020/01/2012.jpg" pagenum="255"/>dio Gottignes, ma da me variata in gran parte, e accomodata al mio intento. </s>

<s><lb/>Ma perch&egrave; in Geometria non mi fido di me, la mando qui a V. S. Ill.ma, <lb/>acci&ograve; mi faccia grazia di esaminarla, e vedere se sta a martello, e quando <lb/>pur vi stia mi faccia grazia di motterla in pi&ugrave; chiarezza, ed in miglior lume. </s>

<s><lb/>Non ardirei incomodarla di tanto, se non sapessi che l'amore di V. S. Ill.ma<lb/>verso il nostro riverito maestro Galileo gli fosse per addolcire la noia &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. CXLVII, fol. </s>

<s>19). </s></p><p type="main">

<s>La proposizione meccanica inclusa in questa lettera del Ferroni veniva <lb/>cos&igrave; formulata: &ldquo; Potentia, pondus sustinens in plano inclnato AC (fig. </s>

<s>125), <lb/><figure id="id.020.01.2012.1.jpg" xlink:href="020/01/2012/1.jpg"/></s></p><p type="caption">

<s>Figura 125.<lb/>ad potentiam idem pondus sustinendum <lb/>in perpendiculari CE, seu momentum <lb/>gravis in plano inclinato, ad momantum <lb/>absolutum, est reciproce ut perpendicu&shy;<lb/>laris CE ad inclinatam AC &rdquo; (ivi, fol. </s>

<s>20). <lb/>La dimostrazione si allunga e si raggira <lb/>per i pi&ugrave; elementari teoremi euclidei, <lb/>ma si spedisce in sostanza in poche pa&shy;<lb/>role, considerando HIL come una leva angolare col fulcro in I, con la po&shy;<lb/>tenza applicata in H, in direzione parallela ad AC, e con la resistenza in <lb/>L, cosicch&egrave; si avr&agrave;, per le notissime leggi archimedee, che sta la detta po&shy;<lb/>tenza alla sua respettiva resistenza come IL sta ad IH, o, per la similitu&shy;<lb/>dine de'triangoli, come CE sta ad AC. </s></p><p type="main">

<s>Il proposito manifestato dal Ferroni di valersi dei moti equipollenti, in&shy;<lb/>segnatigli dal Viviani nelle cinque sopra riferite proposizioni, sarebbe riu&shy;<lb/>scito efficacissimo per soggiunger, dopo la verit&agrave; conclusa dalla leva ango&shy;<lb/>lare, al Vanni una risposta, quando si fosse per&ograve; quella equipollenza intesa <lb/>a dovere. </s>

<s>Ma perch&egrave; vi si manteneva salva la falsa dottrina galileiana, che <lb/>il momento per l'ipotenusa fosse uguale in potenza alla somma de'momenti <lb/>per i cateti, era impossibile al Ferroni e al Viviani, e a qualunque altro di <lb/>quella setta, il rispondere in modo che non ripetesse il Vanni stesso a loro <lb/>quel che avea detto allo Spoleti, che cio&egrave; ragionavano bene, ma che contro <lb/>il suo argomento non concludevano niente. </s>

<s>Di qui &egrave; che lo zelo del Viviani, <lb/>rinfocolato da tanti, se ce ne fosse stato bisogno, che si rivolgevano a lui, <lb/>s'ebbe a rimanere inerte in difender da que&shy;<lb/>sta parte l'onor del suo Nume, e sopportare <lb/>in pace i sacrileghi insulti, e lasciar menar <lb/>galloria a chi vedeva fuggirglisi innanzi i pau&shy;<lb/>rosi. </s>

<s>Anche lo zelante Discepolo, ritirato in di&shy;<lb/>sparte, mentre si faceva attorno cos&igrave; grande <lb/>schiamazzo, meditava fra s&egrave;, e poi scriveva cos&igrave; <lb/>di rincontro a una figura, che rammentava <lb/>quella del Vanni: &ldquo; Il grave A (fig. </s>

<s>126) po&shy;<lb/>sato su due piani inclinati BC, BD violenta sul&shy;<lb/>l'uno e sull'altro, e compartisce il suo peso <lb/><figure id="id.020.01.2012.2.jpg" xlink:href="020/01/2012/2.jpg"/></s></p><p type="caption">

<s>Figura 126.<pb xlink:href="020/01/2013.jpg" pagenum="256"/>o momento parte sul piano BC, e parte sul BD. </s>

<s>Cerca con che proporzione <lb/>sian divisi questi momenti in differenti inclinazioni di piano, e variandosi <lb/>l'angolo DBC da acuto a retto e da retto a ottuso &rdquo; (MSS. Gal. </s>

<s>Disc., T. <lb/>CXIII, fol. </s>

<s>30 a tergo). </s></p><p type="main">

<s>Non molto tempo dopo lasciava cos&igrave; in un altro foglio il Viviani stesso <lb/>abbozzato quel che cercando aveva trovato: &ldquo; Sia la sfera A, nella mede&shy;<lb/>sima figura, che posi nell'angolo de'due piani DB, BC. e sia DC orizzon&shy;<lb/>tale, BE perpendicolare, e DG parallela ad EB, ed EF a CB. </s>

<s>Dico il mo&shy;<lb/>mento gravitativo di A sopra CB, al gravitativo sopra DB, stare come DB <lb/>ad EF, <emph type="italics"/>vel ad BG, vel ut EII ad EI parallelae ipsis planis, vel ut EL <lb/>ad EM perpendiculares iisdem planis,<emph.end type="italics"/> cio&egrave; come i seni retti de'comple&shy;<lb/>menti delle inclinazioni de'piani. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Poich&egrave; il gravitativo sopra BC al totale sta come EC a CB, ovvero <lb/>come DE ad EF, ed il totale, al gravitativo sopra DB, sta come BD a DE; <lb/>cos&igrave; <emph type="italics"/>ex aequo in ratione perturbata,<emph.end type="italics"/> come il gravitativo sopra BC, al gra&shy;<lb/>vitativo sopra DB, cos&igrave; la DB alla EF. </s>

<s>Ma EF &egrave; uguale a GB, per&ograve; il gravi&shy;<lb/>tativo al gravitativo sta come DB a BG, ovvero EH ad HB <emph type="italics"/>vel ad EI. </s>

<s>Sed <lb/>duetis perpendicularibus EL, EM, triangula EHL, EIM fiunt similia, et <lb/>propterea, ut EH ad EI, ita EL ad EM, quae sunt sinus recti comple&shy;<lb/>mentarum angulorum ECB, EDB elevationum &rdquo;<emph.end type="italics"/> (ivi, fol. </s>

<s>18). </s></p><p type="main">

<s>Ecco messa cos&igrave; dallo stesso Viviani a partito la dottrina dei moti equi&shy;<lb/>pollenti, ma quale argomento somministrava per rispondere al Vanni? </s>

<s>Nuovo <lb/>era senza dubbio e bello il meccanico teorema che le pressioni si compar&shy;<lb/>tono sui due piani proporzionalmente ai coseni degli angoli delle elevazioni, <lb/>ma qual'&egrave; la terza linea che rappresenta la pressione totale, proporzional&shy;<lb/>mente comparabile con le due trovate pressioni parziali? </s>

<s>Noi sappiamo es&shy;<lb/>sere quella terza linea la EB, diagonale del parallelogrammo EIBH, ma il <lb/>Viviani avversava questa dottrina, reputandola falsa, perch&egrave;, non essendo <lb/>l'angolo EIB retto, non potevano i moti per EI e per IB essere eguali a <lb/>quello fatto per EB, che non &egrave; ipotenusa, come EI e IB non sono cateti; <lb/>n&egrave; perci&ograve; alla potenza di quella si pu&ograve; dire uguale la somma delle potenze <lb/>di questi. </s>

<s>Essendo per&ograve; cos&igrave;, come Galileo insegnava nel teorema II Dei <lb/>proietti, ben comprendeva il Viviani che, tutt'altro che confutare, anzi si <lb/>confermava l'obiezione del Vanni, per cui a risolverla, tentando altra via, <lb/>disputavasi intanto in Roma intorno al modo di computare i momenti. </s>

<s>Non <lb/>vuol di quelle dispute passarsi la nostra Storia, ma prima di dir di loro <lb/>giova veder quel che se ne pensasse in proposito dai Matematici stranieri. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Aveva il Vanni stesso mandato il suo <emph type="italics"/>Specimen<emph.end type="italics"/> agli eruditi di Lipsia, <lb/>che lo inserirono ne'loro atti di Novembre dell'anno 1684, con la ri&shy;<lb/>sposta, nella quale, bench&egrave; si affermasse non essere assurdo che i momenti <pb xlink:href="020/01/2014.jpg" pagenum="257"/>parziali sommati insieme eccedano il momento totale del globo posato sui <lb/>due piani, la dimostrazione nonostante che se ne dava non era quella pro&shy;<lb/>prio che faceva al caso; ond'&egrave; che parve a molti si confermasse, invece di <lb/>rispondere all'obiezione. </s>

<s>Furono di questo parere due grandi uomini Goti&shy;<lb/>fredo Leibniz e Iacopo Bernoulli, che cercavan perci&ograve; di dar sodisfazione ai <lb/>curiosi, e di rassicurare la scienza in altri modi. </s>

<s>Come per&ograve; vi riuscissero, <lb/>si vedr&agrave; da quel che ora diremo. </s></p><p type="main">

<s>Nel 1685 gli eruditi di Lipsia accoglievano nei loro atti una scrittura <lb/>del Leibniz, che s'intitolava: <emph type="italics"/>Demonstratio geometrica Regulae, apud sta&shy;<lb/>ticos receptae, de momentis gravium in planis inclinatis, nuper in dubium <lb/>vocatae, et solutio casus elegantis, in Actis nov. </s>

<s>1684, pag. </s>

<s>512, propositi, <lb/>De globo duobus planis angulum rectum facientibus simul incumbente, <lb/>quantum unumquodque planorum prematur determinans.<emph.end type="italics"/> (Opera omnia, <lb/>T. III, Genevae 1768, pag. </s>

<s>176). Incomincia ivi l'Autore dal confermar la <lb/>verit&agrave; contradetta dal Vanni, dimostrando che due corpi son allora insieme <lb/>in perfetto equilibrio, quando le loro gravit&agrave; son proporzionali alle lunghezze <lb/>dei piani, e lo fa servendosi del medesimo principio, e ragionando allo stesso <lb/>modo, che aveva fatto, nella proposizione sua I. <emph type="italics"/>De motu gravium,<emph.end type="italics"/> il Tor&shy;<lb/>ricelli. </s>

<s>Il non farsi motto di un uomo, e di un trattato, nella Scienza mec&shy;<lb/>canica tanto celebre, dette occasione di maraviglia a molti, i quali s'avranno <lb/>tanto pi&ugrave; a maravigliare di ci&ograve; che ora diremo. </s></p><p type="main">

<s>Speditosi di quella torricelliana dimostrazione, il Leibniz passa a risol&shy;<lb/>vere il caso proposto dal Vanni, prendendo per suo primo e principale ar&shy;<lb/>gomento il principio che due sono i momenti esercitati dal grave sul piano <lb/>inclinato. </s>

<s>&ldquo; Statim autem patet (quod etiam ab admodum R. P. Kochanskio, <lb/>in actis Junii 1685, recte notatum video) globum in plano aliquo inclinato <lb/>duplex exercere momentum; unum quod decliviter descendere tendit, alte&shy;<lb/>rum quo planum declive premit, quae duo simul obsolutum, seu totale gra&shy;<lb/>vis momentum constituunt &rdquo; (ibid.). Cotesti due momenti erano stati, come <lb/>vedemmo, designati coi nomi di <emph type="italics"/>momento discensivo<emph.end type="italics"/> e di <emph type="italics"/>momento gravi&shy;<lb/>tativo<emph.end type="italics"/> sul piano dal Viviani, il quale aveva altres&igrave; dimostrato, nelle sue Cin&shy;<lb/>que proposizioni, il primo stare al totale come XN ad XC (nella fig. </s>

<s>127), <lb/><figure id="id.020.01.2014.1.jpg" xlink:href="020/01/2014/1.jpg"/></s></p><p type="caption">

<s>Figura 127.<lb/>ed il secondo, al medesimo momento totale, star <lb/>come NC alla stessa XC. </s>

<s>Il Leibniz invece, per&shy;<lb/>suaso che questo momento gravitativo sia la dif&shy;<lb/>ferenza che passa fra il totale e il discensivo, lo <lb/>fa proporzionale a XC-XN. &ldquo; Itaque, in nostro <lb/>casu, ob duas causas, planum alterutrum, ut <lb/>XFC, a globo I premi intelligitur: prima est <lb/>quod globus I, descendere tendens in plani XFC, <lb/>linea FC, momento quod sit ad totale ut XN <lb/>ad XC, quemadmodum demonstravimus, aget re&shy;<lb/>liquo, quod erit ad totale ut XC-XN ad XC, in ipsum planum declive XFC, <lb/>a quo sustentatur &rdquo; (ibid., pag. </s>

<s>176, 77). </s></p><pb xlink:href="020/01/2015.jpg" pagenum="258"/><p type="main">

<s>L'errore, di cui pare incredibile non si dovesse avvedere un tale e tanto <lb/>Matematico, era stato, com'abbiamo letto, insegnato gi&agrave; negli Atti lipsiensi <lb/>dal padre Kochanski, che anzi il Leibniz altamente loda, e affettuosamente <lb/>ringrazia come colui &ldquo; qui viam iam tum designavit, cui recte insistendo, <lb/>ad determinationem pressionis cuiuscumque plani perveniri poterat &rdquo; (ibid., <lb/>pag. </s>

<s>178). Ma perch&egrave; il Kochanski era discepolo, e promotore degl'insegna&shy;<lb/>menti del nostro piacentino Paolo Casati, par che il Leibniz abbia voluto <lb/>eleggere i due Gesuiti a maestri. </s></p><p type="main">

<s>In quel medesimo anno 1684, in cui il padre Vanni spacciava in Roma <lb/>il suo foglietto volante, uscivano in Lione gli otto libri della Meccanica del <lb/>Casati. </s>

<s>Nel cap. </s>

<s>XV del I libro, proponendosi l'Autore di trattar dell'equi&shy;<lb/>librio de'corpi sospesi da una o pi&ugrave; funi, offriva il primo esempio di cos&igrave; <lb/>fatti problemi che, risoluti gi&agrave; francamente da Leonardo e dallo Stevino, <lb/>crano dalla nuova scuola, per la troppa facilit&agrave;, reputati fallaci. </s>

<s>Penda il <lb/>grave A (fig. </s>

<s>128) dalle due funi AB, AC, fisse ne'punti B e C. </s>

<s>Considera <lb/>il Casati separatamente i due sforzi, e prima, nel funicolo AC, risolve il mo&shy;<lb/>mento totale in due, uno libero e l'altro impedito. </s>

<s>Per il teorema galileiano <lb/><figure id="id.020.01.2015.1.jpg" xlink:href="020/01/2015/1.jpg"/></s></p><p type="caption">

<s>Figura 128.<lb/>secondo De'proietti, dice che, se il momento <lb/>totale &egrave; AC, il libero &egrave; AE, ma l'impedito <lb/>non pu&ograve; essere altro che la differenza tra <lb/>questi due, la quale essendo PC, dunque il <lb/>grave A sforza da questa parte la fune con <lb/>due momenti uguali ad AP+PC. Simil&shy;<lb/>mente, dall'altra parte, essendo AD=AQ <lb/>il momento libero, e QB l'impedito, il grave <lb/>far&agrave; forza sulla fune con momento uguale <lb/>ad AQ+BQ, intantoch&egrave;, se fossero i due <lb/>funicoli di ugual lunghezza, la somma dei <lb/>quattro momenti riuscirebbe doppia a quella <lb/>di tutto il peso. </s>

<s>Conobbe a questo punto il Casati che il suo ragionamento lo <lb/>avea condotto a un assurdo, e bench&egrave; non avesse saputo scoprire ascondersi <lb/>la fallacia in ci&ograve; principalmente che i due momenti impediti non son pro&shy;<lb/>porzionali alle differenze PC, QB, ma s&igrave; veramente alle perpendicolari CE, <lb/>DB; una inspirazione venutagli dalle tradizioni, rimaste nell'Herigonio in&shy;<lb/>tercise, gli fece provvidamente corregger l'errore, costruendo su'due lati <lb/>AR=AD, e AG=AE il parallelogrammo RG, e dicendo che a questi due <lb/>momenti parziali s'attempera il totale rappresentato dalla diagonale AN dello <lb/>stesso parallelogrammo. </s></p><p type="main">

<s>S'accorgono i Lettori che questa, aperta anche pi&ugrave; largamente dal Ca&shy;<lb/>sati, come or ora vedremo, era la vera via regia, da condursi a risolvere il <lb/>paralogismo del Vanni, ma a correr per essa il Leibniz non s'era bene an&shy;<lb/>cora accomodato i calzari. </s>

<s>Come il Kochaski aveva imparato di qui a mi&shy;<lb/>surare il momento gravitativo sul piano inclinato; cos&igrave; il Leibniz stesso tra&shy;<lb/>sform&ograve; facilmente questa costruzione in modo, che BA, AC rappresentassero, <pb xlink:href="020/01/2016.jpg" pagenum="259"/>non due funi, ma due piani, e la sfera A, dianzi pendula, s'immagin&ograve; rin&shy;<lb/>chiusa dentro l'angolo BAC, come ritenutavi fra due sponde. </s></p><p type="main">

<s>Procedendo il Matematico tedesco con un ragionamento similissimo a <lb/>quello del nostro Piacentino, s'ebbe a incontrar nel medesimo assurdo, che <lb/>cio&egrave; i quattro momenti parziali tornavan doppi al totale, a che, come trov&ograve; <lb/>il Nostro rimedio applicandovi la Regola del parallelogrammo delle forze, <lb/>sostitu&igrave; lo Straniero, che di quella diffidava, un'altra Regola, da lui detta <lb/><emph type="italics"/>Degli alternativi,<emph.end type="italics"/> che consisteva insomma nel ridurre un caso di Meccanica <lb/>alle condizioni di un gioco d'azzardo. </s>

<s>&ldquo; Verum, cum quatuor premendi cau&shy;<lb/>sis simul sumptis bis integretur momentum totale; patet illas, sic absolute <lb/>sumptas, non esse compatibiles, nec <emph type="italics"/>cumulative<emph.end type="italics"/> sed, ut post dicam, tantum <lb/><emph type="italics"/>elective,<emph.end type="italics"/> sive <emph type="italics"/>alternative<emph.end type="italics"/> componendas, alioqui effectus globi in plano maior <lb/>esset momento globi totalis absoluti. </s>

<s>Cum vero manifestum sit duas semper <lb/>causas in quolibet plano, aequali ratione, in considerationem venire debere, <lb/>nec tamen integras retineri posse; adhibenda est <emph type="italics"/>Regula alternativorum,<emph.end type="italics"/><lb/>quae in iure accrescendi, in aestimatione aleae ludentium, eiusque casibus <lb/>locum habet, hoc est utriusque momenti sumendum est dimidium, seu, quod <lb/>eodem redit, medium inter ipsa aritmeticum, sive dimidium summae ex am&shy;<lb/>bobus &rdquo; (ibid., pag. </s>

<s>178). Cos&igrave;, conclude il Leibniz, &egrave; tolta quella difficolt&agrave;, <lb/>che avea fatto arretrare e rivolgere altrove il Casati (di cui per&ograve;, come del <lb/>Torricelli, non si fa il minimo cenno) perch&egrave; la met&agrave; della somma, presa <lb/>secondo la proposta regola metafisica, riduce uguali al totale i quattro de&shy;<lb/>signati momenti parziali. </s></p><p type="main">

<s>Non erano, sull'esempio del Leibniz, disposti gli altri Matematici ad ap&shy;<lb/>provare la Regola del parallelogrammo, ch'era quasi la pietra del paragone, <lb/>per scoprir che quello del Vanni era peltro; ma &egrave; pur notabile come Ja&shy;<lb/>copo Bernoulli vi si riducesse molto d'appresso, e giungesse perci&ograve; il primo <lb/>a dar, con qualche matematica ragionevolezza, alla famosa difficolt&agrave; la ri&shy;<lb/>sposta desiderata, la quale, sotto il mese di Febbraio del 1686, s'inser&igrave; con <lb/>questo titolo a pag. </s>

<s>96 negli Atti degli eruditi di Lipsia: &ldquo; Jacobi Bernoulli <lb/>solutio difficultatis contra propositionem quamdam me&shy;<lb/>chanicam aut. </s>

<s>J. F. V. lucensi proposita 1685. &rdquo; </s></p><p type="main">

<s>Si raccolse poi questa scrittura fra le opere dell'Au&shy;<lb/>tore, pubblicate nel 1744 in Ginevra, dove, da pag. </s>

<s>245-47 <lb/>del I Tomo, si trascrive lo <emph type="italics"/>Specimen<emph.end type="italics"/> del Vanni, insieme <lb/>con la breve censura fatta da un Matematico, a nome del&shy;<lb/>l'Accademia, in tal modo per&ograve; che parve al Bernoulli non <lb/>risolvere l'obiezione. </s>

<s>Diceva quel matematico Censore es&shy;<lb/>ser possibile che i momenti sui piani si compongano in&shy;<lb/>sieme, da eccedere il momento del grave assoluto, e lo <lb/>provava supponendo che uno di essi piani, per esempio AC <lb/>(fig. </s>

<s>129) fosse verticale, nel qual caso &ldquo; utique momenta <lb/>in ambobus planis in unum addita non possunt aequari <lb/>uni ex ipsimet, totum parli, quod tamen, secundum obiicientis sontentiam, <lb/><figure id="id.020.01.2016.1.jpg" xlink:href="020/01/2016/1.jpg"/></s></p><p type="caption">

<s>Figura 129.<pb xlink:href="020/01/2017.jpg" pagenum="260"/>fieri deberet: momentum enim in plano verticali utique est ipsum momen&shy;<lb/>tum gravis absolutum &rdquo; (pag. </s>

<s>247). </s></p><p type="main">

<s>Il Bernoulli giustamente negava che il momento nel piano verticale <lb/>AC fosse assoluto, perch&egrave; la direzione IH gli riesce obliqua, come riesce <lb/>obliqua la direzione IF all'altro piano XC, cosicch&egrave;, n&egrave; in questo n&egrave; in <lb/>quello, il momento &egrave; propriamente tutto, ma &egrave; diminuito, e potrebbe dire <lb/>alcuno perci&ograve; che, sebben nel tutto i due momenti eccedano il momento <lb/>del grave assoluto, diminuiti nonostante lo possono eguagliare &ldquo; quod Au&shy;<lb/>thorem obiectionis in sua potius opinione confirmaret &rdquo; (ivi, pag. </s>

<s>249). </s></p><p type="main">

<s>Dovendosi dunque cercare altrove, nell'argomento del Vanni, la frode, <lb/>crede il Bernoulli di averla scoperta in ci&ograve; che si confondono insieme dal&shy;<lb/>l'oppositore il peso e il momento del peso. </s>

<s>Son queste due cose ben assai <lb/>differenti, come si vede, egli dice, per esempio nel Vette, in cui, bench&egrave; il <lb/>peso rimanga il medesimo, cresce o scema nonostante il momento, secondo <lb/>che maggiore o minore &egrave; la lunghezza del braccio. </s>

<s>Cos&igrave; pure, secondo le <lb/>varie inclinazioni, cresce o scema il peso, con cui preme un grave il piano <lb/>sottoposto, n&egrave; difficile &egrave;, soggiunge lo stesso Bernoulli, a determinarne il <lb/>momento, attendendo a ci&ograve; che <lb/>accade, quando scendono, il cor&shy;<lb/>po, e il piano tutt'a un tempo <lb/>che lo sostiene. </s></p><p type="main">

<s>Se il sostegno &egrave; orizzon&shy;<lb/>tale comeK (fig.130), e la scesa <lb/>&egrave; per un tratto verticale, come <lb/>KL, a voler che il grave non <lb/>sia abbandonato dal suo soste&shy;<lb/>gno, bisogna che corrano am&shy;<lb/>bedue ugualmente veloci. </s>

<s>Al&shy;<lb/>trimenti per&ograve; avviene se il corpo <lb/>&egrave; sostenuto da due piani, come <lb/><figure id="id.020.01.2017.1.jpg" xlink:href="020/01/2017/1.jpg"/></s></p><p type="caption">

<s>Figura 130.<lb/>XC, ZC (fig. </s>

<s>131) perch&egrave;, mentre il globo I per <lb/>esempio scende equabilmente da I in L, per lo <lb/><figure id="id.020.01.2017.2.jpg" xlink:href="020/01/2017/2.jpg"/></s></p><p type="caption">

<s>Figura 131.<lb/>spazio IL=CP, il piano XC &egrave; sceso in QP per uno spazio, misurato dalla <lb/>linea brevissima CQ, ond'&egrave; che, stando i momenti come le velocit&agrave;, e come <lb/>gli spazii, il momento sopra XC, che significheremo con M.XC, &egrave; alla met&agrave; <lb/>del peso P del globo come CP a <expan abbr="Cq.">Cque</expan> In pari modo M.ZC:P/2=CP:CR. </s>

<s><lb/>E di qui, essendo CR=CQ, P=(M.XC+M.ZC)/CP CQ, ossia M.XC+ <lb/>M.ZC:P=CP:Cq. </s>

<s>&ldquo; Adeoque momentum globi super utroque plano, <lb/>simul sumptum, est ad totum ipsius ponderis, seu ad momentum absolu&shy;<lb/>tum, ut CP ad <expan abbr="Cq.">Cque</expan> Est vero CP maior CQ, igitur momentum ec. </s>

<s>quod erat <lb/>demonstrandum &rdquo; (ibid., pag. </s>

<s>249). </s></p><p type="main">

<s>Il Viviani trascrisse di sua propria mano questa scrittura del Bernoulli, <pb xlink:href="020/01/2018.jpg" pagenum="261"/>che si trova inserita ne'fogli 77, 78 del tomo CXXXII de'Discepoli di Ga&shy;<lb/>lileo, dove alla figura sono apposte in lapis le linee da noi punteggiate, e <lb/>in margine, con una crocellina per segno di richiamo, all'ultima ragione <lb/>scritta CP:AQ &egrave; soggiunto: &ldquo; vel ut IC ad IF, vel ut FC ad CO &rdquo; e ci&ograve; <lb/>vorrebbe dire che la somma dei momenti parziali di tanto eccede il totale, <lb/>di quanto il totale stesso eccede il solo momento gravitativo. </s></p><p type="main">

<s>A rispondere alla nostra curiosit&agrave; di saper qual giudizio facesse di que&shy;<lb/>sta bernulliana soluzione il Viviani, non abbiamo altro argomento che la tra&shy;<lb/>scritta postilla, ma possiamo congetturare che non gli sodisfacesse, come <lb/>quella che portava a concludere contro i principii di Galileo, ai quali non <lb/>era possibile in ogni modo ridurre l'osservazione che cos&igrave; faceva il Ber&shy;<lb/>noulli stesso in un suo corollario: &ldquo; Concludimus, quo acutiorem angulum <lb/>ambo plana constituunt, eo magis, et quo obtusiorem eo minus momenta <lb/>partialia excessura esse momentum totale, ratione rectae CP ad <expan abbr="Cq;">Cque</expan> illo <lb/>casu existente maiore, hoc minore, donec tandem apertura anguli tanta fiat, <lb/>ut ambo plana coalescant in unum horizontalem, quo facto, coincident quo&shy;<lb/>que CQ et CR cum CP, sustinebitque planum non nisi ipsum momentum <lb/>globi absolutum &rdquo; (ibid., pag. </s>

<s>250). </s></p><p type="main">

<s>Nella meccanica del Casati avrebbero potuto, questo teorema e questo <lb/>corollario del Bernoulli, trovare il loro pieno e pi&ugrave; chiaro commento, inten&shy;<lb/>dendo che la sopra allegata figura CXXVIII rappresenti in AB e in AC due <lb/>piani inclinati, nell'angolo fatto dai quali, posato il globo A, vien questo <lb/>sollecitato da due momenti, l'uno per AG e l'altro per AR, che si com&shy;<lb/>pongono insieme nella diagonale AN del parallelogrammo. </s>

<s>N&egrave; sarebbe da cos&igrave; <lb/>fatta costruzione immediatamente resultato che la somma dei momenti, nei <lb/>due piani, sta al momento totale come AG+AR, ossia AG+GN, sta ad <lb/>AN, qualunque poi si fosse l'angolo BAC. </s></p><p type="main">

<s>Aveva il Casati, come accennammo, presentita in questa conclusione la <lb/>difficolt&agrave; stessa del Vanni, la quale egli risolse, unico e primo, un anno <lb/>avanti che fosse fatta, con le sue vere e proprie ragioni. </s>

<s>Com'&egrave; possibile, <lb/>cos&igrave; gli pass&ograve; per la mente la prima ombra del dubbio, che, dovendo es&shy;<lb/>sere il tutto eguale alle parti, sia una cos&igrave; fatta e necessaria uguaglianza <lb/>rappresentata dalle linee AG+GN, e dalla AN, se questa evidentemente &egrave; <lb/>minore di que&igrave;le? </s>

<s>Poi trov&ograve; che doveva di necessit&agrave; esser cos&igrave;, perch&egrave; i due <lb/>moti si elidono, o, come s'era espresso Giovan Marco Marci, matematico di <lb/>Praga, nel suo libro <emph type="italics"/>De proportione motus,<emph.end type="italics"/> si contrariano, ed elidendosi e <lb/>contrariandosi diminuiscono il loro effetto: or come potrebbero, diminuendo, <lb/>ragguagliarsi, se non fossero originariamente maggiori? </s></p><p type="main">

<s>Che poi la terribile difficolt&agrave; trovi, in questa semplicissima ragion delle <lb/>collisioni, la sua risposta, lo spiega il Casati stesso richiamando l'attenzione <lb/>sul parallelogrammo delle forze, in cui si vede, egli dice, che la resultante <lb/>&egrave; maggiore, quanto minore &egrave; l'angolo, e al contrario, avvicinandosi in quel <lb/>caso le componenti alla concorrenza, e in questo all'apposizione. </s>

<s>&ldquo; Qua in <lb/>re plurimum interest quam invicem habeant inclinationem directiones mo-<pb xlink:href="020/01/2019.jpg" pagenum="262"/>tuum in diversa abeuntium: quo enim acutiorem angulum constituunt, eo <lb/>longius provehitur mobile, ut, AB, <lb/>AC (fig. </s>

<s>132) in acutum angulum <lb/>coeuntibus, mobile ex A in D ve&shy;<lb/>nit, quo vero obtusior fuerit angu&shy;<lb/>lus, eo etiam brevius est iter ipsius <lb/>mobilis .... ut ipsa motuum natura <lb/><figure id="id.020.01.2019.1.jpg" xlink:href="020/01/2019/1.jpg"/></s></p><p type="caption">

<s>Figura 132.<lb/>postulat, qui nimirum sibi invicem magis adversantur, magisque in diversa <lb/>abeunt, se magis elidunt &rdquo; (Mechanic., libri cit., pag. </s>

<s>103, 4). </s></p><p type="main">

<s>Se il Bernoulli dunque costrinse il Vanni a ricredersi in forza di una <lb/>matematica dimostrazione, non facile ad arrivarsi da tutti, e non sfuggevole <lb/>a tutte le cavillazioni; lo avea il Casati gi&agrave; convinto con ragioni tanto sem&shy;<lb/>plici e chiare, da non riluttarvi, se non chi patisse difetto di senso comune, <lb/>o avesse la mente stravolta da pregiudizii, com'avvenne a que'Matematici <lb/>romani, i quali s'accennava dianzi essere entrati in disputa intorno al modo <lb/>di computare i momenti. </s></p><p type="main">

<s>Vitale Giordano, pubblicando in Roma nel 1687 una sua dissertazione <lb/>sopra questo argomento, dop'aver nell'avvertenza detto al Lettore essere il <lb/>fine del suo discorso quello di rispondere all'Autor dell'Esegesi fisico ma&shy;<lb/>tematica <emph type="italics"/>De momentis gravium,<emph.end type="italics"/> soggiunge: &ldquo; Existimavit quidam non modo <lb/>subtilem Anonymi doctrinam hoc sophismate laborare, quod in ea compo&shy;<lb/>nantur momenta gravium per additionem, cum sint revera componenda per <lb/>multiplicationem, verum etiam Isaacum Barrow ac R. P. </s>

<s>Casatum sibi adsti&shy;<lb/>pulari. </s>

<s>&rdquo; Aveva il Casati, nel sopra citato capitolo della sua Meccanica, scritto <lb/>queste precise parole: &ldquo; Re autem ipsa quod ex iis componitur momentum, <lb/>non ex ipsorum momentorum additione conflatur, sed ex ipsis temperatur &rdquo; <lb/>(pag. </s>

<s>103). Se dunque non per addizione, vollero concluderne i disputanti, <lb/>per moltiplicazione si compongono i momenti, non badando a quel che di <lb/>pi&ugrave; importante era negli insegnamenti del Matematico piacentino, il quale, <lb/>dopo avere affermato che il momento della resultante non &egrave; uguale alla <lb/>somma delle componenti, soggiunge <emph type="italics"/>sed ex ipsis temperatur,<emph.end type="italics"/> andando nella <lb/>diagonale del parallelogrammo. </s></p><p type="main">

<s>Il Giordano, pregato da'suoi scolari, <emph type="italics"/>tota ferme Europa longe dissitis,<emph.end type="italics"/><lb/>a volere, in grazia loro e per utilit&agrave; della Repubblica letteraria, pronun&shy;<lb/>ziare la sua sentenza, dimostr&ograve;, bench&egrave; con falsi teoremi, che non si pote&shy;<lb/>vano per moltiplicazione comporre i momenti, e che in tale assurdo non in&shy;<lb/>corse il Casati, per le opere del quale attentamente leggendo, &ldquo; nusquam <lb/>inveni verbum quod eo spectet, ut momenta gravium componantur per mul&shy;<lb/>tiplicationem &rdquo; (Dissert. </s>

<s>cit., pag. </s>

<s>4): quel che per&ograve; pi&ugrave; importava non seppe <lb/>nemmen egli, il Giordano, come gli altri, intendere il significato del tempe&shy;<lb/>rarsi i momenti nella diagonale del parallelogrammo, n&egrave; prevalersi perci&ograve; <lb/>di quella dottrina, unica efficace a rispondere ai paralogismi del Vanni, che <lb/>era il fine del discorso, scritto dal professore nell'Archiginnasio romano. </s></p><p type="main">

<s>Ebbe ancora a indugiare questa risposta infin verso alla fine del secolo, <pb xlink:href="020/01/2020.jpg" pagenum="263"/>quando l'autorit&agrave; del Newton, e le insistenze del Varignon riuscirono final&shy;<lb/>mente a persuadere i Matematici di ci&ograve;, che avevano praticato Leonardo, lo <lb/>Stevino e altri pochi, in cos&igrave; eletto modo per&ograve; che il Casati stim&ograve; essere a <lb/>tutti notissima la Regola del parallelogrammo. </s>

<s>&ldquo; Notum omnibus est mo&shy;<lb/>tum, qui ex AB et AC (nella precedente figura) componitur, non fieri ex <lb/>earum additione, sed temperari ad lineam AD, quae dimetiens est paralle&shy;<lb/>logrammi, quod ex earumdem linearum AB, AC longitudine, ac mutua in&shy;<lb/>clinatione, formam desumit &rdquo; (Mech., pag. </s>

<s>103). </s></p><p type="main">

<s>Veniva di qui, contro la seconda proposizione meccanica del IV dialogo <lb/>di Galileo, solennemente confermata quella sentenza di condanna, pronun&shy;<lb/>ziata gi&agrave; dal Mersenno, e il dilemma famoso del Vanni, intorno a cui suda&shy;<lb/>rono inutilmente un Leibniz e un Viviani, si sapeva sciogliere oramai da <lb/>chiunque avesse nelle scuole matematiche appresi i primi elementi. </s></p><p type="main">

<s>Mentre che i Matematici si travagliavano cos&igrave; affannosamente, come ap&shy;<lb/>parisce dai fatti narrati, per salvar la verit&agrave; del teorema, dimostrato gi&agrave; dal <lb/>Tartaglia, contro chi veniva nella Meccanica a rinnovellare gli errori del Car&shy;<lb/>dano; s'insorgeva con altri sofismi a turbar la pace della scienza, preso ar&shy;<lb/>dire dall'esempio del Vanni. </s>

<s>Il Cartesianismo, dominante nella Scuola fisico&shy;<lb/>matematica napoletana, sugger&igrave; a Luc'Antonio Porzio una nuova costruzione <lb/>meccanica, riguardando i perpendicoli non <lb/>paralleli, come comunemente si fa, ma quali <lb/>sono in realt&agrave; convergenti al centro ter&shy;<lb/>restre, secondo che il Cartesio stesso sem&shy;<lb/>pre scrupolosamente osserva nel descriver <lb/>gli effetti delle Macchine. </s>

<s>Essendo cos&igrave;, non <lb/>&egrave; vero, diceva il Porzio, ci&ograve; che insegna il <lb/>Maestro che, se cio&egrave; CA (fig. </s>

<s>133) &egrave; dop&shy;<lb/>pia di CB, per far salire il peso sul piano <lb/><figure id="id.020.01.2020.1.jpg" xlink:href="020/01/2020/1.jpg"/></s></p><p type="caption">

<s>Figura 133.<lb/>ci voglia la met&agrave; della forza, necessaria a <lb/>ritirarlo in su per il perpendicolo, perch&egrave;, <lb/>sottilmente ragionando, quella proporzion <lb/>tra la forza e il peso trovasi alquanto di&shy;<lb/>versa da quella, che nelle sue Meccaniche <lb/>assegna il Cartesio. </s>

<s>Il ragionamento era <lb/>tale qual si pu&ograve; argomentare dalla seguente <lb/>nota dell'Autore: </s></p><p type="main">

<s>&ldquo; Nel piano, secante o tangente la Terra <lb/>DCE (fig. </s>

<s>134), sia AB secante o tangente <lb/>un cerchio massimo, alla quale, dal centro <lb/>C, si tiri la perpendicolare CD. </s>

<s>Egli &egrave; ma&shy;<lb/>nifesto che, se altra sfera I sia collocata <lb/>sopra varii punti del piano gi&agrave; detto, e in <lb/>modo che sempre AB sia tangente di un <lb/>certo cerchio massimo IH, quando questa <lb/><figure id="id.020.01.2020.2.jpg" xlink:href="020/01/2020/2.jpg"/></s></p><p type="caption">

<s>Figura 134.<pb xlink:href="020/01/2021.jpg" pagenum="264"/>sfera sar&agrave; collocata sopra il punto D, la linea CD prolungata divider&agrave; il <lb/>cerchio massimo IH in due parti uguali, e se il cerchio avesse gravit&agrave; si do&shy;<lb/>vrebbe fare equilibrio tra i segmenti eguali. </s>

<s>Quando ella sar&agrave; sopra il punto <lb/>F, la linea CF prolungata segher&agrave; il cerchio massimo IH in parti diseguali, <lb/>e se i segmenti diseguali fossero gravi non si potrebbero tra loro fare equi&shy;<lb/>librio, lo che agevolmente si dimostra. </s>

<s>E da ci&ograve; facilmente ancora si pu&ograve; <lb/>provare che, se per un piano caggia una sfera grave, sempre in dato punto <lb/>una sua porzione contraster&agrave; e ripugner&agrave; alla caduta, ma non sar&agrave; ella ba&shy;<lb/>stevole a far l'equilibrio in quel punto. </s>

<s>Qual porzione, mentre scende la <lb/>sfera, sempre si fa vie pi&ugrave; e pi&ugrave; grande, finch&egrave;, giunta la sfera al punto <lb/>D, cesser&agrave; per la linea AB l'impeto di gravit&agrave;, imperocch&egrave; in D la met&agrave; <lb/>della sfera appunto contraster&agrave;, e ripugner&agrave; ad ogni moto, che di qua e di <lb/>l&agrave; dal punto D potesse fare la sfera, cio&egrave; in D si fa l'equilibrio sulla linea <lb/>AB &rdquo; (Opera omnia, T. II, Neapoli 1736, pag. </s>

<s>233, 34). </s></p><p type="main">

<s>Da queste considerazioni ebbe il Porzio a concluderne che la sfera IHF, <lb/>posata sul piano inclinato AB, venendo a esser segata dal perpendicolo CFH <lb/>nelle parti disuguali HIL, HLF, avr&agrave; tant'impeto di scendere quant'&egrave; l'ec&shy;<lb/>cesso dell'una parte sull'altra, perch&egrave; il menisco HLFH riman sostenuto dal <lb/>perpendicolo stesso, che lo attraversa per il centro, lasciando alla sua libera <lb/>caduta il resto. </s>

<s>Di qui il teorema del Tartaglia, per pi&ugrave; di un secolo appro&shy;<lb/>vatosi da tanti insigni Matematici di tutto il mondo, veniva dal Porzio, nella <lb/>sua proposizione XIII <emph type="italics"/>De motu corporum,<emph.end type="italics"/> cos&igrave; riformato: &ldquo; Pondus abso&shy;<lb/>lutum datae sphaerae uniformis insistentis dato puncto plani, quod appellant <lb/>inclinatum, ad eiusdem gravitatem relativam, quam dicunt, sive partialem; <lb/>minorem habet rationem ea, quam longitudo dati plani habet ad perpendi&shy;<lb/>culum &rdquo; (Op., T. cit., pag. </s>

<s>137). </s></p><p type="main">

<s>Aveva anche l'obiezione del Porzio senza dubbio qualche cosa di se&shy;<lb/>ducente, perch&egrave; pareva non si potesse negare essere il solo menisco HLFH <lb/>la parte sostenuta del peso. </s>

<s>Per scoprire per&ograve; la frode conveniva dimostrare <lb/>la vera direzione del fulcro, ci&ograve; che riusciva assai difficile a chi non avesse <lb/>uso del parallelogrammo. </s>

<s>Di qui &egrave; che inutilmente, in una sua Epistola di&shy;<lb/>vulgata in Roma, vi si prov&ograve; Vitale Giordano, il quale a quello del Porzio <lb/>sostitu&igrave; un altro pi&ugrave; grave errore, volutosi matematicamente dimostrar da <lb/>lui nel <emph type="italics"/>Fondamentum doctrinae motus gravium,<emph.end type="italics"/> dove, dopo di aver nella <lb/>VII proposizione asserito. </s>

<s>&ldquo; Pondus totale gravis, ad momentum quod ha&shy;<lb/>bet in plano declivi, est ut longitudo ipsius plani declivis ad perpendicu&shy;<lb/>lum &rdquo; (Romae 1688, pag. </s>

<s>38), passa a provar, nelle proposizioni seguenti, <lb/>che pu&ograve; il peso totale, al momento nel piano, ora aver maggiore, e ora mi&shy;<lb/>nor proporzione del declivio al perpendicolo. </s></p><p type="main">

<s>Non mancarono alcuni della scuola del Marchetti, i quali ebbero a no&shy;<lb/>tare che il vizio, nei ragionamenti del Giordano, consisteva nel paragonare <lb/>il peso, espresso da una linea, col momento, espresso da un rettangolo; ma <lb/>infatti tanta poca sicurt&agrave; dagli errori e tanta incertezza nel rispondere alle <lb/>obiezioni da null'altro dipendeva, che dal non si saper risolvere i quesiti, <pb xlink:href="020/01/2022.jpg" pagenum="265"/>applicandovi il principio della composizion delle forze. </s>

<s>Nei primi anni del <lb/>secolo XVIII incominci&ograve; quel principio a divulgarsi nei Matematici, e Guido <lb/>Grandi pot&egrave;, con la sua Epistola mathematica <emph type="italics"/>De momentis gravium in <lb/>planis inclinatis,<emph.end type="italics"/> ravviar la scienza ne'suoi retti sentieri. </s></p><p type="main">

<s>Bisognava dimostrar contro il Porzio che la direzione del fulcro, da cui <lb/>&egrave; sostenuto il grave sul piano inclinato, si dee prender secondo il perpen&shy;<lb/>dicolo condotto dal centro di gravit&agrave; sul piano, e non al centro terrestre. </s>

<s><lb/>Per far ci&ograve; premette il Grandi per lemma alla sua dimostrazione il princi&shy;<lb/>pio della comp&ograve;sizion delle forze, le quali essendo due, come AB, AC (nella <lb/>passata figura CXXXII) sollecitanti il punto A in quelle due direzioni, dice, <lb/><emph type="italics"/>id quod, notissimum est,<emph.end type="italics"/> essere allora quel punto in equilibrio, quando una <lb/>terza forza AH, uguale alla diagonale AD del parallelogrammo, tiri in verso <lb/>contrario. </s></p><p type="main">

<s>Ci&ograve; premesso, abbiasi la sfera grave K (fig. </s>

<s>135) sollecitata da due forze, <lb/>l'una KQ nella direzion della gravit&agrave; naturale, e l'altra KR diretta secondo <lb/>la fune PK, che fa forza alla stessa sfera, affinch&egrave; la <lb/>non debba cadere. </s>

<s>Perch&egrave; dunque ella potesse ivi rima&shy;<lb/>nere in equilibrio, bisognerebbe applicare in K una terza <lb/>forza, uguale e contraria alla diagonale KM del paralle&shy;<lb/>logrammo. </s>

<s>Ma questa forza &egrave; sostituita dalla resistenza <lb/>del piano AB, dunque il piano &egrave; premuto nella direzione, <lb/>e con forza proporzionale alla linea KM, la quale gli &egrave; <lb/>perpendicolare. </s>

<s>&ldquo; Quare, cos&igrave; propriamente il Grandi con&shy;<lb/>clude, cum haec sit plano perpendicularis ad contactum, <lb/>demonstratum erit actionem sustinentis plani iuxta dic&shy;<lb/>tam perpendicularem exerceri &rdquo; (Lucae 1711, pag. </s>

<s>25). <lb/><figure id="id.020.01.2022.1.jpg" xlink:href="020/01/2022/1.jpg"/></s></p><p type="caption">

<s>Figura 135.</s></p><p type="main">

<s>Ma co'Matematici del secolo XVIII fece la scienza <lb/>tali progressi, da non temere oramai pi&ugrave; di cos&igrave; fatte <lb/>contradizioni, ond'&egrave; che sopra questo statico fondamento <lb/>venne a confermarsi sempre pi&ugrave; la Dinamica, della quale &egrave; tempo che si <lb/>cominci la storia. </s></p><pb xlink:href="020/01/2023.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO V.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle libere cadute dei gravi<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della legge di Aristotile che le velocit&agrave; dei cadenti son proporzionali ai pesi, e come prima si tro&shy;<lb/>vasse quella legge contraria alle esperienze, e poi si dimostrasse contraria alla ragione, e si <lb/>verificasso finalmente che tutti i corpi nel vuoto scendono ugualmente veloci. </s>

<s>&mdash; II. </s>

<s>Delle cause <lb/>acceleratrici del moto, e come Galileo fosse il primo a concluder la legge matematica d&igrave; un <lb/>tale acceleramento dai principii del Benedetti. </s>

<s>&mdash; III. </s>

<s>Della forza d'inerzia applicata ai moti na&shy;<lb/>turali, e delle leggi dei moti accelerati geometricamente dimostrate da Galileo e dal Baliani. </s>

<s>&mdash; <lb/>IV. </s>

<s>Dei pretendenti o dei contradittori di Galileo, e come si confermassero, per l'esperienze del <lb/>Riccioli e per i teoremi dell'Huyghens, le leggi galileiane dei gravi cadenti. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Dagl'insegnamenti aristotelici ebbero le due parti, in che distinguesi <lb/>la Scienza del moto, variamente efficaci gl'impulsi, perch&egrave;, mentre la Sta&shy;<lb/>tica era giunta per questi alla sua quasi total perfezione, la Dinamica, dopo <lb/>pochi passi fatti a gran pena, rimanevasi tuttavia implicata in gravissimi er&shy;<lb/>rori. </s>

<s>Le variet&agrave; della fortuna si parteciparono dalle prime speculazioni del <lb/>Maestro a quelle de'lontani e numerosi suoi discendenti, un poco senza dub&shy;<lb/>bio per vizioso contagio, e un poco perch&egrave; cos&igrave; portava il naturale anda&shy;<lb/>mento delle cose. </s>

<s>Del quale andamento chi volesse mettersi a ricercare i <lb/>principii gli troverebbe facilmente in ci&ograve;, che Aristotile poneva per fonda&shy;<lb/>mento alla Statica la Geometria, e alla Dinamica invece dava nuove leggi, <lb/>non ricavate dai fatti naturali, ma dalle pi&ugrave; infelici arguzie del filosofico <lb/>ingegno. </s></p><p type="main">

<s>I libri, che s'intitolano <emph type="italics"/>Physicorum,<emph.end type="italics"/> son quelli principalmente, in cui <lb/>il Filosofo lascia alle sue arguzie pi&ugrave; libero il freno, e proponendosi, nel <pb xlink:href="020/01/2024.jpg" pagenum="267"/>quarto dei detti fisici libri, di contradire agli Autori, che lo avevano prece&shy;<lb/>duto e che ammettevano l'esistenza del vacuo, come quello ch'&egrave; necessario <lb/>a intendere le osservate passioni del moto; impone capricciosamente alla Na&shy;<lb/>tura s&igrave; fatte leggi, da ridurla in ogni modo a concludere i suoi proprii ar&shy;<lb/>gomenti. </s>

<s>Consisteva uno de'cos&igrave; fatti argomenti nel provar che, dandosi il <lb/>vacuo, non sarebbe possibile il moto locale, perch&egrave; dovrebbe la traslazione <lb/>farsi in un istante, mentre il moto stesso non &egrave; che una successione cau&shy;<lb/>sata dall'impulso, e regolata dalla maggiore o minore resistenza del mezzo. </s>

<s><lb/>La ragione poi di una tal resistenza &egrave;, secondo il Filosofo, che v&agrave; un corpo <lb/>tanto pi&ugrave; o meno veloce quanto &egrave; pi&ugrave; raro o pi&ugrave; denso il mezzo, dentro al <lb/>quale si muove. </s>

<s>&ldquo; Sit enim B, egli dice nel 70&deg; testo del IV libro, quidem <lb/>aqua, D vero aer: quanto ergo subtilior est aer aqua, et incorporalior, tanto <lb/>citius A per D movebitur quam per B. </s>

<s>Habet ergo eandem rationem secun&shy;<lb/>dum quam distat aer ab aqua, velocitas ad velocitatem &rdquo; (Operum, T. IV, <lb/>Venetiis 1560, fol. </s>

<s>129 ad t.). Ma nel vuoto la rarit&agrave; &egrave; infinita, dunque an&shy;<lb/>che la velocit&agrave; ivi dentro &egrave; infinita. </s></p><p type="main">

<s>Da quest'altra argomentazione si rivela anche meglio la temerit&agrave; del&shy;<lb/>l'ingegno, che vuol ridurre le leggi della Natura alle sue proprie ragioni. </s>

<s><lb/>Dall'ammettere il vacuo, diceva, ne conseguirebbe in ogni modo che le ve&shy;<lb/>locit&agrave; di qualunque peso fossero uguali, ma questo &egrave; impossibile, dunque <lb/>il vacuo non pu&ograve; darsi. </s>

<s>Le prove di una tale impossibilit&agrave; poi le desumeva <lb/>il Filosofo dai fatti, per i quali non ha dubbio di affermar che manifesta&shy;<lb/>mente si vede essere le velocit&agrave; sempre proporzionali ai pesi. </s>

<s>&ldquo; Videmus <lb/>corpora, quae sunt magis ponderosa, sive gravia sive levia, cum fuerint in <lb/>aliis dispositionibus in capitulo figurae, eodem modo moveri in aequali loco <lb/>velocius secundum proportiones eorum ad invicem. </s>

<s>Ergo sequitur ut talis <lb/>sit dispositio eorum in vacuo etiam. </s>

<s>Sed hoc est impossibile, quoniam non <lb/>potest aliquis dicere qua de causa expellitur in eo velocius, quoniam hoc in <lb/>plano est necessarium. </s>

<s>Quod enim est fortius velocius dividit illud: illud <lb/>enim quod movetur aut illud quod cedit, aut per suam figuram dividit, aut <lb/>per suum pondus. </s>

<s>A quo sequitur ut motus omnium corporum sit aequalis <lb/>in velocitate, quod est impossibile &rdquo; (ibid., fol. </s>

<s>135 ad t.). </s></p><p type="main">

<s>Stabilite cos&igrave; dal Filosofo le due leggi della caduta dei gravi, quali sono: <lb/>che vanno per varii mezzi le velocit&agrave; alle rarezze proporzionali, e che, in <lb/>un medesimo mezzo, hanno esse velocit&agrave; la proporzion diretta dei pesi, si <lb/>approvarono cecamente da tutti infintanto che, risorto nel secolo XV Archi&shy;<lb/>mede, i fatti che, conforme alle verit&agrave; naturali, si dimostrano da lui nel <lb/>trattato Delle galleggianti, non vennero provvidamente a fare almeno in parte <lb/>ravvedere gl'illusi. </s>

<s>S'ebbe allora con gran maraviglia a notare un manife&shy;<lb/>sto errore nella fondamentale dottrina del Filosofo, il quale insegnava essere <lb/>ne'corpi una leggerezza positiva, e che ciascuno pesava nel suo proprio ele&shy;<lb/>mento. </s>

<s>Resultava invece dai teoremi archimedei niente altro essere la leg&shy;<lb/>gerezza che una certa diminuzione della gravit&agrave; assoluta, la quale fa risa&shy;<lb/>lire un corpo, non per naturale attivit&agrave;, ma per la patita circumpulsione del <pb xlink:href="020/01/2025.jpg" pagenum="268"/>mezzo. </s>

<s>Galileo, in alcune sue esercitazioni preparatorie ai trattati Del moto, <lb/>applicava direttamente a illustrar questi effetti della gravit&agrave; positiva i teo&shy;<lb/>remi archimedei (Opere, ediz. </s>

<s>naz., T. I, Firenze 1890, pag. </s>

<s>346-52, 363-66) <lb/>e pi&ugrave; di un mezzo secolo dopo istituivano gli Accademici del Cimento due <lb/>belle esperienze, <emph type="italics"/>per provar che non v'&egrave; leggerezza positiva<emph.end type="italics"/> (Saggi di na&shy;<lb/>turali esper., Firenze 1841, pag. </s>

<s>131-35). Ma erano gli ostinati. </s>

<s>Peripatetici <lb/>a que'tempi oramai ridotti a s&igrave; pochi, che sembrano quelle descrizioni quasi <lb/>lussureggiare nel libro de'nostri Fisici fiorentini. </s>

<s>L'opera di costoro era in&shy;<lb/>cominciata gi&agrave; infino da Leonardo, e la proseguirono valorosamente il Car&shy;<lb/>dano, il Tartaglia, il Benedetti, dai quali tutti ammettevasi, contro il Filo&shy;<lb/>sofo, quasi senza contradizione, che l'aria nell'aria, come l'acqua nell'acqua, <lb/>non pesi. </s></p><p type="main">

<s>Le medesime benefiche istituzioni archimedee avevano altres&igrave; fatti de&shy;<lb/>stri gl'ingegni a scoprir, nel primo de'riferiti argomenti di Aristotile, le <lb/>fallacie, delle quali ebbe non difficilmente a persuadersi quello stesso Sim&shy;<lb/>plicio galileiano, a cui diceva il Salviati &ldquo; che quando fosse vero che l'istesso <lb/>mobile in mezzi di differente sottilit&agrave; e rarit&agrave;, ed insomma di diversa ce&shy;<lb/>denza, quali per esempio son l'acqua e l'aria, si movesse con velocit&agrave; nel&shy;<lb/>l'aria maggiore che nell'acqua, secondo la proporzione della rarit&agrave; dell'aria <lb/>a quella dell'acqua; ne seguirebbe che ogni mobile, che scendesse per aria, <lb/>scenderebbe anco nell'acqua. </s>

<s>Il che &egrave; tanto falso, quanto che moltissimi corpi <lb/>scendono nell'aria che nell'acqua, non pur non discendono, ma sormontano <lb/>all'ins&ugrave; &rdquo; (Alb. </s>

<s>XIII, 68). </s></p><p type="main">

<s>Del secondo aristotelico argomento si dimostra pure da Galileo la fal&shy;<lb/>sit&agrave; in pi&ugrave; luoghi delle sue Opere, con lunghi ragionamenti, che si com&shy;<lb/>pendiano in questa breve nota, ritrovata da noi manoscritta: &ldquo; Contempletur <lb/>quod quemadmodum gravia omnia supra horizonte quiescunt, licet maxima <lb/>vel minima; ita in linaeis inclinatis eadem velocitate moventur, quemadmo&shy;<lb/>dum et in ipso quoque perpendiculo, quod bonum erit demonstrare dicendo <lb/>quod, si gravius velocius, sequeretur quod gravius tardius, iunctis gravibus <lb/>inaequalibus. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Movebuntur autem eadem celeritate, non solum gravia inaequalia et <lb/>homogenea sed et eterogenea, ut lignum et plumbum. </s>

<s>Cum enim antea <lb/>ostensum fuerit magna et parva homogenea aequaliter moveri, dicas: sit B <lb/>sphaera lignea, et A plumbea, adeo magna, ut cum in medio habeat cavi&shy;<lb/>tatem pro B, sit tamen gravior quam sphaera solida lignea ipsi A aequalis, <lb/>ita ut per adversarium velocius moveatur quam B. Ergo, si in cavitate illa <lb/>ponatur B, tardius movebitur A, quam cum erat levior, quod est absurdum. </s>

<s>&rdquo; <lb/>(MSS. Gal., P. V, T. II, fol. </s>

<s>147). </s></p><p type="main">

<s>Ma forse, meglio di qualunque pi&ugrave; sottil ragionamento, veniva la fal&shy;<lb/>lacia del Filosofo scoperta dalle giornaliere esperienze dei domestici pi&ugrave; <lb/>abietti, quando gettano dalle finestre la spazzatura, le variet&agrave; degli oggetti <lb/>raccolti nella quale si vedono quasi a un tempo cadere a terra, se non gli <lb/>turbi o non gli dissipi il vento. </s>

<s>All'aristotelica sentenza nonostante, che cio&egrave; <pb xlink:href="020/01/2026.jpg" pagenum="269"/>siano le velocit&agrave; proporzionali alle grandezze, dava grande apparenza di ve&shy;<lb/>rit&agrave; la Statica, confondendosi facilmente i pesi con i momenti, i quali son <lb/>senza dubbio, nelle macchine, proporzionali alle velocit&agrave; o alle distanze. </s></p><p type="main">

<s>Bench&egrave; per tutto il secolo XVI, come vedremo, si persistesse dannosa&shy;<lb/>mente dai Matematici in questo errore, nonostante i primi nuovi seguaci di <lb/>Archimede incominciarono a dubitar, nel secolo avanti, che, come s'era in <lb/>altre parti manifestamente scoperto l'errore, cos&igrave; fosse almen qualche cosa <lb/>d'improprio in quest'altra sentenza del Filosofo, nella quale francamente si <lb/>pronunziava essere le velocit&agrave; proporzionali alle grandezze. </s>

<s>Le pi&ugrave; triviali <lb/>esperienze, come si faceva dianzi osservare, contradicevano a quel <emph type="italics"/>videmus<emph.end type="italics"/><lb/>del Maestro, perch&egrave; invece gli occhi facevan vedere a tutti molto diversa&shy;<lb/>mente. </s>

<s>Si vollero perci&ograve; istituire in proposito esperienze pi&ugrave; diligenti, e noi <lb/>narrammo quelle fatte da Leonardo da Vinci, il quale n'ebbe sentenziosa&shy;<lb/>mente a concludere il fatto che <emph type="italics"/>due palle di una medesima materia, che <lb/>una sia il doppio peso dell'altra, cadendo in un tempo da una medesima <lb/>altezza, non cadr&agrave; prima altrettanto tempo la maggiore che la minore.<emph.end type="italics"/></s></p><p type="main">

<s>A chi prima udi pronunziare una tal sicura sentenza, tanto aliena dalle <lb/>prevalenti opinioni, parve quasi vedere un lampo abbagliante sotto un cielo <lb/>nuvoloso, ma erano i nuvoli gi&agrave; dissipati dal rinascente Sole archimedeo, <lb/>verso cui non fu Leonardo solo a rivolgere gli occhi. </s>

<s>Hanno molti creduto <lb/>cos&igrave;, ma sarebbe da dire improvvido il benefizio della Natura, se al soprav&shy;<lb/>venire i tiepori di una nuova primavera facesse, anche in remota selva ed <lb/>incolta, aprire un fiore solo e allegare un sol frutto. </s>

<s>Non mancarono eru&shy;<lb/>diti, i quali accennarono a un Bellaso, a un Michele Varrone o a qualcun <lb/>altro, ma il Libri not&ograve; e trascrisse un documento, dal quale apparisce es&shy;<lb/>sersi, intorno al fatto della caduta dei gravi, scoperto l'errore aristotelico <lb/>anche da altri Filosofi contemporanei a Leonardo. </s></p><p type="main">

<s>&Egrave; quel documento ricavato da certe <emph type="italics"/>Questioni sull'Alchimia<emph.end type="italics"/> scritte, <lb/>infino dal 1544, da Benedetto Varchi, ma che videro solamente nel 1827 in <lb/>Firenze la luce, per solo fine di condir forse con questo tanti altri insipidi <lb/>testi di lingua. </s>

<s>Il Libri pone il Varchi nel numero di Giovanni Rucellai, <lb/>poeta naturalista delle api, di Bernardino Baldi, cronista dei Matematici an&shy;<lb/>tichi, e di Bernardo Bontalenti, architettore di macchine maravigliose, di&shy;<lb/>cendo dello Storico fiorentino &ldquo; qui etudie avec soin la chute des graves &rdquo; <lb/>(Histoire des Mathem., T. III cit., pag. </s>

<s>199) e accennando a un passo delle <lb/>Lezioni di lui, stampate in Firenze da Filippo Giunti nel 1590, per mostrar <lb/>che l'Autore ben conobbe &ldquo; l'influence de le couleur des surfaces sur <lb/>l'absorption des rayons calorifiques &rdquo; (ivi). Dee essere il passo, a cui il Li&shy;<lb/>bri accenna, senza dubbio quello che &egrave; cos&igrave; scritto nella lezion <emph type="italics"/>Dei colori,<emph.end type="italics"/><lb/>unica di fisico argomento: &ldquo; E chi non l'ha veduto non crederebbe o ma&shy;<lb/>lagevolmente che un pezzo di cristallo ardesse tutti gli altri colori, dal bianco <lb/>in fuori &rdquo; (pag. </s>

<s>259). </s></p><p type="main">

<s>Il giudizio per&ograve;, che dette intorno al Varchi come scienziato il Libri, <lb/>&egrave; assai diverso da quello di Galileo, dalla bocca del quale lo raccolse, e cos&igrave; <pb xlink:href="020/01/2027.jpg" pagenum="270"/>ne serb&ograve; memoria in una Nota il Viviani: &ldquo; Il Varchi dice quel che non <lb/>intende, e per&ograve; non intende quel che dice &rdquo; (MSS. Gal., P. V, T. IV, fol. </s>

<s>26). <lb/>Sembra a noi che ambedue i giudici vadano negli eccessi, perch&egrave;, sebbene <lb/>sia vero che il Varchi non abbia n&egrave; qualit&agrave; n&egrave; meriti di scienziato, sent&igrave; <lb/>nonostante gusto della scienza, che desideroso raccolse da coloro, i quali po&shy;<lb/>tevano insegnargliela o ne'libri o a viva voce, e seppe scegliere con libert&agrave; <lb/>quelle opinioni, che gli parvero pi&ugrave; vere, come dimostr&ograve; nel fatto della ca&shy;<lb/>duta dei gravi, intorno a che non studi&ograve; con senno, come dice il Libri, ma <lb/>con senno approv&ograve; i resultati delle esperienze altrui, e il giudizio di quei <lb/>pochi, i quali dicevano esser quella, come tutte le altre verit&agrave; naturali, da <lb/>apprender, non dai libri di Aristotile, ma dalla osservazione dei fatti. </s>

<s>&ldquo; E <lb/>sebbene, egli scrive, il costume dei Filosofi moderni &egrave; di creder sempre e <lb/>non provar mai tutto quello che si trova scritto ne'buoni Autori, e massi&shy;<lb/>mamente in Aristotile, non &egrave; per&ograve; che non fosse e pi&ugrave; sicuro e pi&ugrave; dilet&shy;<lb/>tevole fare altrimenti, e discendere qualche volta alle sperienze in alcune <lb/>cose, come v. </s>

<s>g. </s>

<s>nel movimento delle cose gravi, nella qual cosa e Aristo&shy;<lb/>tile e tutti li altri Filosofi, senza mai dubitarne, hanno creduto e affermato <lb/>che, quanto una cosa sia pi&ugrave; grave, tanto pi&ugrave; tosto discende, il che la prova <lb/>dimostra non esser vero. </s>

<s>E se io non temessi d'allontanarmi troppo dalla <lb/>proposta materia mi distenderei pi&ugrave; lungamente in provare questa opinione, <lb/>della quale ho trovato alcuni altri, e massimamente il reverendo padre (non <lb/>men detto Filosofo che buon Teologo) fra Francesco Beato, metafisico di <lb/>Pisa, e messer Luca Ghini, medico e semplicista singolarissimo, oltre la <lb/>grande, non solamente cognizione, ma pratica dei Minerali tutti quanti, se&shy;<lb/>condo che a me parve, quando gli udii da lui pubblicamente nello Studio <lb/>di Bologna &rdquo; (<emph type="italics"/>Alchimia<emph.end type="italics"/> cit., pag. </s>

<s>54). </s></p><p type="main">

<s>Se dunque il Ghini e il Beato erano gi&agrave; convinti della falsit&agrave; che, quanto <lb/>una cosa &egrave; pi&ugrave; grave, tanto pi&ugrave; tosto discenda, per prove fatte quand'era <lb/>il Varchi ancora giovane studente; convien dir che fossero le loro esperienze <lb/>o contemporanee o di poco posteriori a quelle di Leonardo, il quale aveva <lb/>insomma concluso esser l'errore aristotelico solamente accidentale, e n&ograve; nella <lb/>sostanza, perch&egrave; se due gravi omogenei e uniformi, bench&egrave; di vario peso, <lb/>dispongansi cos&igrave; che trovino cadendo resistenza uguale nel mezzo, si ve&shy;<lb/>dranno, diceva, andar con velocit&agrave; proporzionali alle potenze, cosicch&egrave; <emph type="italics"/>quella <lb/>cosa che pi&ugrave; pesa, essendo libera, pi&ugrave; presto cade.<emph.end type="italics"/></s></p><p type="main">

<s>Correva dunque, sui principii del secolo XVI, l'opinione fra i pi&ugrave; li&shy;<lb/>beri ingegni che fossero solo da attribuire alle resistenze del mezzo le ano&shy;<lb/>malie osservate nella legge aristotelica, ond'&egrave; che, sperimentando i pi&ugrave; da <lb/>piccole altezze, e osservando che fra due corpi cadenti di vario peso, ma <lb/>uniformi e omogenei, le differenze del tempo sono insensibili, argutamente <lb/>introducendo gli effetti dell'elasticit&agrave; dell'aria, pensarono di conciliar la se&shy;<lb/>ducente dottrina del Filosofo coi fatti sperimentali apertamente contarii, di&shy;<lb/>cendo che le resistenze opposte ai cadenti dal mezzo son direttamente pro&shy;<lb/>porzionali ai pesi. </s>

<s>Il Cardano dette forma scientifica a questo pensiero nella <pb xlink:href="020/01/2028.jpg" pagenum="271"/>proposizione CX del suo <emph type="italics"/>Opus novum,<emph.end type="italics"/> che cos&igrave; formulava: &ldquo; Si duae sphae&shy;<lb/>rae ex eadem materia descendant in aere, eodem temporis momento ad pla&shy;<lb/>num veniunt &rdquo; (Operum, T. IV cit., pag. </s>

<s>515). </s></p><p type="main">

<s>Piacque l'ingegnosa cardanica dimostrazione, e s'introdusse nella scienza <lb/>di coloro, i quali professavano, in sul finir del secolo, i pi&ugrave; liberi e i pi&ugrave; <lb/>creduti sani principii di Filosofia naturale. </s>

<s>Son fra questi pi&ugrave; insigni pro&shy;<lb/>fessori da annoverare il Moleto e il Benedetti, il primo dei quali dettava <lb/>dalla cattedra padovana, a cui sarebbe per succedere Galileo, alcune lezioni <lb/>di Meccanica, che avevan per uno de'principali argomenti a trattar della <lb/>caduta dei gravi, secondo le pi&ugrave; accurate osservazioni dei fatti. </s>

<s>Per poi me&shy;<lb/>glio divulgar le nuove dottrine pens&ograve; il Moleto stesso di dare a loro forma <lb/>di dialogo, e finse, per salvarsi dall'ira peripatetica, che uscissero cos&igrave; fatte <lb/>novit&agrave; di bocca a un gran personaggio, a un Principe reale, che sta l'Au&shy;<lb/>tore ascoltando ossequioso, bench&egrave; non punto stupidamente ne approvi ogni <lb/>detto. </s>

<s>Son dunque gl'interlocutori <emph type="italics"/>P,<emph.end type="italics"/> che vuol dire il Principe, e <emph type="italics"/>A,<emph.end type="italics"/> ossia <lb/>l Autore: e perch&egrave; crediamo che sia un tale importantissimo documento alla <lb/>maggior parte dei nostri Lettori ignoto, pensiamo di trascrivere intanto, dal&shy;<lb/>l'Appendice ai Manoscritti galileiani, questo primo passo, che concerne le <lb/>velocit&agrave;, secondo le quali si muovono, attraverso a qualche resistenza del <lb/>mezzo, i varii gravi: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; Or il grave, movendosi naturalmente, pu&ograve; muoversi con mag&shy;<lb/>giore e con minore velocit&agrave; rispetto al mezzo, poich&egrave; per un mezzo pi&ugrave; sot&shy;<lb/>tile si muove con maggior velocit&agrave;, e per un mezzo pi&ugrave; crasso con meno. </s>

<s><lb/>Il che tutto pu&ograve; V. S. intenderlo benissimo con le cose che si muovono al&shy;<lb/>l'ingi&ugrave; per l'acqua, e con quelle per l'aria. </s>

<s>Laddove, se V. S. piglier&agrave; una <lb/>profondit&agrave; d'acqua di cento passi, e vi lascer&agrave; andare un grave, ed osser&shy;<lb/>ver&agrave; il tempo che consumer&agrave; a toccare il fondo, e noteralla da parte, e di <lb/>nuovo piglier&agrave; un'altezza di cento passi parimente e vi lascer&agrave; andare un <lb/>grave del peso, sostanza e figura dell'altro, e terr&agrave; conto del tempo, che <lb/>consumer&agrave; nel venire a basso; trover&agrave; questo tempo essere molto minore <lb/>dell'altro. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; Perch&egrave; vuole V. A. che il grave sia della stessa sostanza, peso <lb/>e figura dell'altro? </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; Per levar le cagioni da dubitare. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; E che dubbio pu&ograve; esserci intorno a questo? </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; Grandissimo, perciocch&egrave; Aristotile ha dato cagione da dubi&shy;<lb/>tare, dicendo che per uno stesso mezzo la velocit&agrave; delle cose, che si muo&shy;<lb/>vono per movimento naturale, essendo della stessa natura e figura, &egrave; sic&shy;<lb/>come le potenze loro. </s>

<s>Cio&egrave;, se dalla cima di un'alta torre n&ograve;i lasceremo <lb/>venir gi&ugrave; due palle, l'una di piombo di venti libbre, e l'altra parimenti di <lb/>piombo d'una libbra, che il movimento della maggiore sar&agrave; venti volte pi&ugrave; <lb/>veloce di quello della minore. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; Questo mi pare assai ragionevole, anzi, quando mi fosse do&shy;<lb/>mandato per principio, lo concederei. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2029.jpg" pagenum="272"/><p type="main">

<s><emph type="italics"/>P.<emph.end type="italics"/> &mdash; Vossignoria s'ingannerebbe: anzi vengono tutti in uno stesso <lb/>lempo, e di ci&ograve; se n'&egrave; fatta la prova, non una volta, ma molte. </s>

<s>E v'&egrave; di <lb/>pi&ugrave; che una palla di legno, o pi&ugrave; o men grande d'una di piombo, lasciata <lb/>venir gi&ugrave; d'una stessa altezza, nello stesso tempo con quella di piombo, di&shy;<lb/>scendono e trovano la terra o il suolo nello stesso momento di tempo. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; Se l'A. V. non mi dicesse di averne fatta la prova io nol cre&shy;<lb/>derei; e come si pu&ograve; salvare Aristotile? </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; Molti si sono sforzati di salvarlo diversamente, ma infatti mal <lb/>si pu&ograve; salvare. </s>

<s>Anzi, per dire a V. S. il tutto, io credei un giorno di aver <lb/>trovato il modo di salvarlo, ma poi, pensando meglio al fatto, cos&igrave; non fu. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; Tuttavia non pu&ograve; essere che non sia ingegnoso ed arguto, e <lb/>perci&ograve; l'A. V. sia servita a dirlo. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; Per compiacerla lo dir&ograve;, ma prima dichiarer&ograve; alcuni principii <lb/>che mi bisognano. </s>

<s>&Egrave; chiara cosa appresso che quanto pi&ugrave; un grave si muove <lb/>per proprio movimento, come il sasso col discendere, tanto pi&ugrave; venghi ve&shy;<lb/>locitandosi; laddove chi presupponesse uno spazio infinito, infinita sarebbe <lb/>per quello la velocit&agrave; del grave. </s>

<s>Se dunque presupponessimo che nel con&shy;<lb/>cavo della Luna fosse un grandissimo sasso, prima che fosse nella superfice <lb/>della terra si sarebbe fatto di movimento molto veloce. </s>

<s>Pu&ograve; di questa ve&shy;<lb/>locit&agrave; V. S. certificarsene, oltre l'autorit&agrave; dei Filosofi, in questo modo. </s>

<s>Potr&agrave; <lb/>pigliare una palla o di sasso o di piombo o di ferro o d'altra materia grave, <lb/>e lasciar venir gi&ugrave; questa palla da due diverse altezze, la quale percota in <lb/>due resistenti d'egual natura, e vedr&agrave; che quella, che verr&agrave; dal luogo pi&ugrave; <lb/>alto, far&agrave; maggiore effetto nel resistente, che quella che verr&agrave; dalla minore <lb/>altezza: e non essendo la stessa cosa cresciuta di peso, adunque converr&agrave; <lb/>dire il maggiore effetto venir dalla maggiore velocit&agrave;. </s>

<s>Appresso stante a que&shy;<lb/>sto principio, se noi faremo d'una stessa altezza venire due palle di disu&shy;<lb/>guale grandezza, e siano della stessa materia, &egrave; manifesto che la maggiore <lb/>nello stesso resistente far&agrave; maggiore effetto che la minore. </s>

<s>Adunque sar&agrave; <lb/>venuta con maggiore velocit&agrave; che la minore: adunque non si muovono con <lb/>egual velocit&agrave;, che &egrave; quello che si vuole. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; Ho inteso la ragione di V. A. ed in vero par che possa sal&shy;<lb/>vare Aristotile, n&egrave; saprei per ora trovarvi l'inganno, se non vi pensassi su. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; L'inganno &egrave; facile da scoprire, poich&egrave; la maggior percossa della <lb/>maggior palla non nasce dalla velocit&agrave; del movimento, essendo che il senso <lb/>osserva essere il movimento eguale, ma nasce dal peso, il che si pu&ograve; pro&shy;<lb/>vare cos&igrave;. </s>

<s>Lasciamo venir da alto, e da due diverse distanze due palle della <lb/>medesima materia, ma di disugual peso, e venga la minore dalla maggiore <lb/>altezza, la quale ecceda la minore nel triplo o nel quadruplo, e facciamo <lb/>che la minore di due once venghi da un'altezza di cento passi, e la mag&shy;<lb/>giore di due o tre libbre venghi non pi&ugrave; da alto, che da quattro o cinque <lb/>passi: qual crede V. S. che nello stesso resistente far&agrave; maggiore effetto e <lb/>percossa? </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; E chi dubita che la maggiore, e cos&igrave; dimostra l'esperienza? </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2030.jpg" pagenum="273"/><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; E ci&ograve; di dove &egrave; se non dal maggior peso? </s>

<s>e con tutto ci&ograve; con <lb/>maggior velocit&agrave; discende la minore, poich&egrave; da maggiore altezza viene. </s>

<s>Essi <lb/>poi sforzato Girolomo Cardano, nel libro suo <emph type="italics"/>Delle proporzioni,<emph.end type="italics"/> di mostrare <lb/>che due palle di disegual grandezza, messe in pari altezza, sieno per venir <lb/>gi&ugrave; nello stesso tempo. </s>

<s>Ma, perch&egrave; la dimostrazione sua non mi piace in&shy;<lb/>teramente, io lascio di dirla a V. S. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; Anzi voglio supplicare V. A. che me la dica, per vedere l'er&shy;<lb/>rore d'un uomo cos&igrave; famoso. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; Io non voglio dire che sia errore, ma ho solo detto che non <lb/>mi piace, e dirolla per sodisfare a V. S. </s>

<s>Egli dice: sieno due palle, A mag&shy;<lb/>giore, e B minore (fig 136) ed il diametro di A sia di tre palmi v. </s>

<s>g. </s>

<s>o <lb/>qual altra misura si voglia, e quello di B uno della stessa misura, e sieno <lb/><figure id="id.020.01.2030.1.jpg" xlink:href="020/01/2030/1.jpg"/></s></p><p type="caption">

<s>Figura 136.<lb/>della medesima materia, e sieno mosse con egual <lb/>distanza da CD, il quale sia il piano dove sieno per <lb/>dare. </s>

<s>Dico che, lasciate andare nello stesso tempo, <lb/>che parimente nello stesso tempo daranno nel piano <lb/>CD, poich&egrave; il diametro del corpo A &egrave; triplo al dia&shy;<lb/>metro del corpo B. </s>

<s>Adunque il corpo A al corpo B <lb/>sar&agrave; come 27 a uno, poich&egrave; le sfere hanno la pro&shy;<lb/>porzione fra di loro che i cubi de'loro diametri, per <lb/>l'ultima del XII di Euclide. </s>

<s>Adunque la gravit&agrave; di A <lb/>alla gravit&agrave; di B &egrave; come di 27 a uno. </s>

<s>Ma perch&egrave; <lb/>ogni peso, nel discender suo, condensa l'aria in quel <lb/>grado, ch'egli pesa, come l'aria sotto A &egrave; 27 volte pi&ugrave; densa che l'aria <lb/>sotto B, per&ograve; il peso A, avendo da passare aria pi&ugrave; densa, forza &egrave; che pi&ugrave; <lb/>peni nel discender suo. </s>

<s>Adunque, essendo la proporzione di A a B come <lb/>27 a uno, e tale essendo la potenza di A a B, seguirebbe che, quando non <lb/>avesse impedimento, che si dovesse movere nella velocit&agrave; di 27 a uno. </s>

<s>Ora, <lb/>l'impedimento di A all'impedimento di B &egrave; come 27 a uno; adunque uguale <lb/>&egrave; l'impedimento alla potenza, e per&ograve; seguir&agrave; che il movimento loro debba <lb/>essere in egual tempo. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; Se il Cardano la mette cos&igrave; facile e chiara, come V. A. l'ha <lb/>detto, a me pare una bella dimostrazione, n&egrave; saprei, per quel ch'io me ne <lb/>intenda, dire se non che fosse interamente e per ogni parte bella. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; A me piace pi&ugrave;, adesso che l'ho detta a V. S., che quando la <lb/>lessi appresso dell'Autore. </s>

<s>E quel che a me non piaceva era quella densit&agrave;, <lb/>perch&egrave; non son ben capace che l'aria si condensi secondo il peso. </s>

<s>Che si <lb/>condensi ancora si potrebbe dubitare. </s>

<s>Ma concedendo che l'aria si condensi, <lb/>e si condensi secondo il peso, la dimostrazione corre benissimo, ed &egrave; bella <lb/>e ingegnosa. </s>

<s>Quanto al condensarsi dell'aria molti par che lo concedano, e <lb/>particolarmente nelle cose de'movimenti, perch&egrave;, quando non si concedesse <lb/>tal condensazione, saremmo sforzati a concedere il vacuo, cosa tanto odiosa <lb/>alla Natura; la quale pi&ugrave; presto comporta che le cose gravi ascendano, che <lb/>ammettere quello. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2031.jpg" pagenum="274"/><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; E come potr&agrave; V. A. mostrare che la Natura ammette piutto&shy;<lb/>sto che le cose gravi ascendano, che il vacuo? </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; In molti modi potrei mostrarlo a V. S., ma poich&egrave; questo non <lb/>&egrave; il suo luogo, per&ograve; sar&agrave; bene soprassedere alquanto. </s>

<s>&rdquo; (Opusc. </s>

<s>scientifici, <lb/>T. II, fol. </s>

<s>3-6). </s></p><p type="main">

<s>Della bella proposizion del Cardano, cos&igrave; chiaramente espostaci da Sua <lb/>Altezza in questo dialogo del Moleto, dette il Benedetti dimostrazione non <lb/>meno bella, nel cap. </s>

<s>XI delle sue <emph type="italics"/>Disputazioni.<emph.end type="italics"/> Per provar ivi che &ldquo; cor&shy;<lb/>pora, licet inaequalia, eiusdem materiae et figurae, si resistentias habuerint <lb/>ponderibus proportionales, aequaliter movebuntur &rdquo; (Specul. </s>

<s>cit., pag. </s>

<s>175); <lb/>immagina di avere un corpo sferico omogeneo, la gravit&agrave; del quale raccolta <lb/>nel suo centro gli partecipi nel cadere un certo grado d'impulso, uguale <lb/>a quello che risentirebbe una Bilancia nel suo centro, a distanze eguali dal <lb/>quale fossero sospesi due altri corpi sferici, che pesassero ciascuno la met&agrave; <lb/>del maggiore. </s>

<s>La cosa &egrave; chiara per s&egrave;, dice il Benedetti, perch&egrave; i corpi <lb/>tanto pesano separati, quanto congiunti, ed essendosi supposto che le resi&shy;<lb/>stenze tornino ad essi pesi proporzionali, &egrave; dunque vero quel che si diceva, <lb/>che cio&egrave; i due corpi &ldquo; tam separata quam coniuncta candem velocitatem <lb/>retinerent &rdquo; (ibid.). </s></p><p type="main">

<s>Non si comprende per&ograve; come si possa questa conciliare con la propo&shy;<lb/>sizion precedente &ldquo; quod in vacuo corpora eiusdem materiae aequali velo&shy;<lb/>citate moverentur &rdquo; (ibid., pag. </s>

<s>174), che si dimostra dal Benedetti in modo <lb/>simile a quello di dianzi, osservando che nel vuoto tanto il centro di gra&shy;<lb/>vit&agrave; del peso congiunto, quanto il centro della Bilancia nelle due met&agrave; se&shy;<lb/>parate, sentendo uguale impulso, e non avendo nulla che impedisca a loro <lb/>il moto, debbono andare ugualmente veloci; perch&egrave; da ci&ograve; che dimostra l'Au&shy;<lb/>tore stesso nel cap. </s>

<s>XI ne sarebbe stato da concluder piuttosto che si do&shy;<lb/>vrebbe nel vuoto la legge aristotelica esattamente verificare; vi si dovrebbe <lb/>cio&egrave; vedere le velocit&agrave; tanto varie, quanto varie ai cadenti son le grandezze. </s></p><p type="main">

<s>La mente del Matematico veneziano non sembra a noi che serbi, in&shy;<lb/>torno a questo punto, la sua ordinaria serenit&agrave;: si direbbe anzi addirittura <lb/>ch'ella sta affannosamente fluttuante fra l'errore antico e la verit&agrave; nuova, <lb/>perch&egrave;, mentre nel libro <emph type="italics"/>De resolutione omnium Euclidis problematum<emph.end type="italics"/> par <lb/>che vi si trovi per la prima volta, come fece osservare il Libri in una Nota <lb/>al III Tomo della sua Storia, &ldquo; la consideration de la gravit&egrave; proportionnelle <lb/>a la masse &rdquo; (pag. </s>

<s>122), ci&ograve; che confermerebbe la conclusione delle velo&shy;<lb/>cit&agrave; uguali nel vuoto; i due primi capitoli delle <emph type="italics"/>Disputazioni<emph.end type="italics"/> non lasciano <lb/>luogo a dubitare che il Benedetti torn&ograve; a considerare le velocit&agrave; proporzio&shy;<lb/>nali ai pesi, come legge naturale verissima in s&egrave;, bench&egrave; alterabile per la <lb/>varia resistenza, e per l'attitudine varia, che hanno le varie figure de'corpi <lb/>a penetrare la crassizie dei mezzi. </s>

<s>Accennando infatti, nel cap. </s>

<s>I, gli errori <lb/>di Aristotile, ch'egli si disponeva a confutare, soggiunge che anche altri, <lb/>fra'quali il Tartaglia, tennero quella opinione che cio&egrave; due corpi della me&shy;<lb/>desima specie e della medesima figura serbino esatta proporzione con le ve-<pb xlink:href="020/01/2032.jpg" pagenum="275"/>locit&agrave; nei loro moti: opinione non per altro falsa, dice il Benedetti, se non <lb/>perch&egrave; non considerarono costoro &ldquo; quam magna resistentiarum sit diffe&shy;<lb/>rentia quae, tam ex diversitate figurarum, quam ex magnitudinum varietate <lb/>exoriri potest &rdquo; (Specul. </s>

<s>cit., pag. </s>

<s>168). Nel seguente capitolo poi si spiega <lb/>meglio il concetto dell'Autore, il quale vuol concluder dal suo ragionamento <lb/>che, se le velocit&agrave; non sono, come dovrebbero essere per ragion naturale, <lb/>proporzionali ai pesi, ci&ograve; da null'altro dipende, se non perch&egrave; quella pro&shy;<lb/>porzione &egrave; alterata dalla inegualit&agrave; della figura, alla quale non ugualmente <lb/>resiste il mezzo, o da una qualche varia direzione del moto rispetto alla linea <lb/>perpendicolare. </s>

<s>&ldquo; Quotiescumque igitur duo corpora unam eandemque re&shy;<lb/>sistentiam ipsorum superficiebus aut habebunt aut recipient, eorum motus <lb/>inter seipsos eodem plane modo proportionati consurgent, quo erunt ipso&shy;<lb/>rum virtutes moventes &rdquo; (ibid, pag. </s>

<s>169). </s></p><p type="main">

<s>Non veniva dunque il Benedetti in tal proposito nulla insegnando di <lb/>meglio di quel che si potesse legger da tutti, ne'libri del Cardano, e tali <lb/>insegnamenti erano quelli insomma, che autorevolmente si davano, sul finir <lb/>del secolo XVI, agli studiosi della scienza del moto. </s>

<s>Era fra questi studiosi <lb/>Jacopo Mazzoni, il quale, venuto a professare Filosofia nello Studio pisano, <lb/>richiamava l'attenzione de'suoi discepoli sopra il libro del Matematico di <lb/>Venezia, di cui compendiava, nel cap. </s>

<s>XVIII del suo <emph type="italics"/>Preludio,<emph.end type="italics"/> le confuta&shy;<lb/>zioni de'molti errori, detti in Fisica e in Matematica da Aristotile, ramme&shy;<lb/>morando in particolare gli argomenti, per cui dimostravasi non esser vero <lb/>&ldquo; corpora, eadem specie et figura praedita, per idem medium mota, eamdem <lb/>plane proportionem in suorum motuum velocitatibus, quam in suis magni&shy;<lb/>tudinibus habent, retinere &rdquo; (In universam Plat. </s>

<s>et Arist. </s>

<s>philosophiam prae&shy;<lb/>ludia, Venetiis 1597, pag. </s>

<s>192). </s></p><p type="main">

<s>Era fra i giovani, uditori in Pisa a que'tempi, anche Galileo, in cui ri&shy;<lb/>conoscendo il Mazzoni una singolare attitudine dell'ingegno a penetrare la <lb/>scienza del moto, raccomandavagli il libro del Benedetti, e glie ne spiegava <lb/>in privato le speculazioni. </s>

<s>Sent&igrave; il giovane alunno, da quelle vive parole del <lb/>Maestro e dalla lettura che gli suggeriva, instillarglisi il primo ineffabile gu&shy;<lb/>sto della libert&agrave; nel pensare, e perch&egrave; i fervorosi consigli e gli esempii effi&shy;<lb/>caci gli avean fatto deliberar nell'animo non doversi credere oramai pi&ugrave; al&shy;<lb/>l'autorit&agrave; di Aristotile, dunque, ne concludeva, nemmeno a quella di nessun <lb/>altro Filosofo, non eccettuato lo stesso Benedetti, quando si riconosca an&shy;<lb/>ch'egli traviar dalla rettitudine delle verit&agrave; naturali. </s></p><p type="main">

<s>Studiando Galileo, con questa libera libert&agrave; propostasi, i varii capitoli <lb/>delle <emph type="italics"/>Disputazioni,<emph.end type="italics"/> ebbe a notar che il X e l'XI, se non si contradicevano, <lb/>per lo meno non erano conseguenti, perch&egrave;, ammessa pure l'ipotesi delle <lb/>resistenze a proporzione dei pesi, non era possibile che, cos&igrave; nel vuoto come <lb/>nel pieno, le velocit&agrave;, come cercavasi di dimostrare, tornassero uguali. </s>

<s>Ri&shy;<lb/>meditava perci&ograve; fra s&egrave; quale delle due propos&igrave;zioni potess'esser la vera, e <lb/>giacch&egrave; anche il Benedetti, lasciandosi andare ad ammettere per ipotesi le <lb/>resistenze proporzionali ai pesi, pareva averci qualche gran dubbio; e giac-<pb xlink:href="020/01/2033.jpg" pagenum="276"/>ch&egrave; il principio della condensazione e della elasticit&agrave; dell'aria, come dal Mo&shy;<lb/>leto, a quel che faceva dire a Sua Altezza, cos&igrave; anche da Galileo malvolen&shy;<lb/>tieri si concedevano al Cardano; e perci&ograve; tratteneva esso Galileo il meditativo <lb/>pensiero sopra quel che leggeva proposto, e poi dimostrato <emph type="italics"/>Quod in vacuo <lb/>corpora eiusdem materiae aequali velocitate moverentur,<emph.end type="italics"/> ci&ograve; ch'essendo <lb/>vero condannerebbe la legge aristotelica per falsa, non accidentalmente. </s>

<s>come <lb/>da tutti s'era fin'allora insegnato, non escluso lo stesso Benedetti, ma per <lb/>falsa nella sostanza. </s>

<s>Le speculazioni per&ograve;, in argomento tanto sottile, vole&shy;<lb/>vano essere aiutate dall'esperienza, e il discepolo del Mazzoni, divenutogli <lb/>in Pisa gi&agrave; collega, stava, tutto baldanzoso della nuova Filosofia, intorno alla <lb/>base del Campanile, per osservar quando due sfere dello stesso metallo, ma <lb/>di varia grandezza, lasciate da scolari o da amici andar dall'alto della torre <lb/>a un tempo, giungessero in terra. </s></p><p type="main">

<s>Intorno a questo passo della vita scientifica di Galileo son corse, e cor&shy;<lb/>rono tuttavia, certe opinioni, della falsit&agrave; o della impropriet&agrave; delle quali &egrave; <lb/>debito nostro avvertire i Lettori. </s>

<s>E prima di tutto si crede fossero queste <lb/>fatte in Pisa le prime esperienze, che invece s'&egrave; veduto essere state inco&shy;<lb/>minciate un secolo prima, intantoch&egrave; sopr'esse il Cardano ritrov&ograve; e condusse <lb/>quella sua celebre proposizione, riscontrata pubblicamente in Padova, per <lb/>tacere altri esempii, dal Moleto coi fatti. </s>

<s>Dette il Riccioli inoltre autorit&agrave; a <lb/>quell'altra opinione, largamente diffusa dal Wolf, che cio&egrave; Galileo, speri&shy;<lb/>mentando da troppo piccole altezze, n&egrave; potendo perci&ograve; accorgersi di nessuna <lb/>sensibile differenza, dicesse giunger due palle di piombo, una piccola e l'al&shy;<lb/>tra grande, a toccar nel medesimo istante il piano sottoposto. </s>

<s>&Egrave; da osser&shy;<lb/>var per&ograve; contro i detti di costoro, come apparir&agrave; meglio dal progresso del <lb/>nostro discorso, che, sebben Galileo ritenesse come vero quel sincronismo, <lb/>fu condotto per&ograve; a pronunziare una tal sentenza da tutt'altre ragioni, che <lb/>da quelle delle esperienze, alla diligenza delle quali, bench&egrave; fossero l'altezze <lb/>piccole, non era sfuggita l'osservazione che la minore sfera rimanevasi an&shy;<lb/>cora indietro di qualche palmo, quando gi&agrave; la maggiore avea dato sul pa&shy;<lb/>vimento. </s>

<s>A persuadersi poi che dovesser essere quelle galileiane esperienze <lb/>delle pi&ugrave; diligenti, dopo le diligentissime istituite da Leonardo da Vinci, <lb/>giova leggere quel capitolo <emph type="italics"/>De motu<emph.end type="italics"/> dove, proponendosi lo stesso Galileo <lb/>di scoprir l'errore dei Filosofi, i quali dicevano esser l'aria inclusa la causa <lb/>per cui i lievi si muovono in principio pi&ugrave; velocemente dei gravi, cos&igrave; in <lb/>terzo luogo, fra gli altri modi, argomenta: &ldquo; Si multum aeris, quod in ligno <lb/>est, illud velocius facit, ergo semper velocius. </s>

<s>dum fuerit in aere movebi&shy;<lb/>tur. </s>

<s>Experientia tamen contrarium ostendit: verum enim est lignum in prin&shy;<lb/>cipio sui motus ocius ferri plumbo; attamen paulo post adeo acceleratur <lb/>motus plumbi, ut lignum post se relinquat, et, si ex alta turri demittantur, <lb/>per magnum spatium praecedat: et de hoc saepe periculum feci &rdquo; (Le Opere <lb/>di Galileo, ediz. </s>

<s>naz., T. </s>

<s>I cit., pag. </s>

<s>334). </s></p><p type="main">

<s>Riconoscendo benissimo Galileo doversi cos&igrave; fatte differenze di moto at&shy;<lb/>tribuire alle varie resistenze del mezzo, che si rendon sensibili anche quando, <pb xlink:href="020/01/2034.jpg" pagenum="277"/>essendo omogenei e uniformi i cadenti, son per&ograve; di grandezze diverse; con&shy;<lb/>fermavasi in quel che, per semplice speculazione, avea gi&agrave; concluso col Be&shy;<lb/>nedetti, che cio&egrave; nel vuoto, dove quelle stesse resistenze son nulle, cos&igrave; la <lb/>grande e la piccola sfera di piombo, come quella di piombo e l'altra simile <lb/>di legno, passerebbero in tempi uguali sempre uguale uno spazio. </s>

<s>Essendo <lb/>il fatto ritrovato cos&igrave;, per ragioni e per esperienze, certissimo, cercava Ga&shy;<lb/>lileo la causa di un effetto tanto singolare, e intorno a cui tutti prima di <lb/>lui avevano fatto naufragio. </s>

<s>Dopo lunghe meditazioni gli parve di non poter <lb/>risolvere altrimenti il problema, se non con ammettere &ldquo; che di ciaschedun <lb/>corpo grave cadente sia una da Natura determinata velocit&agrave;, sicch&egrave; l'ac&shy;<lb/>crescergliela o diminuirgliela non si possa, se non con usargli violenza &rdquo; <lb/>(Alb. </s>

<s>XIII, 65). </s></p><p type="main">

<s>Ecco rivelato alla scienza per la prima volta un gran vero, ed ecco <lb/>tolto ai progressi di lei un grande impedimento: i pesi non son proporzio&shy;<lb/>nali alla semplice gravit&agrave;, ma s&igrave; alla gravit&agrave; moltiplicata per la <emph type="italics"/>massa,<emph.end type="italics"/> per <lb/>cui, in qualunque ponderoso, la forza che ne velocita la caduta si mantiene <lb/>invariabile. </s>

<s>Cos&igrave; la legge aristotelica veniva da Galileo a dimostrarsi falsa, <lb/>non accidentalmente, ma nella sua causa, e scoprivasi finalmente l'insidiosa <lb/>fallacia; intanto che, mentre appariva da una parte chiarissimo, come mai <lb/>una sfera di piombo e un frustulo di lei dovessero andare ugualmente ve&shy;<lb/>locitati, cadendo, si scoprivan facilmente dall'altra i paralogismi dell'antica <lb/>Filosofia. </s></p><p type="main">

<s>Qui consiste il vero merito di Galileo, non saputo riconoscere, n&egrave; per&shy;<lb/>ci&ograve; degnamente apprezzare da tanti ciechi ammiratori di lui, contenti a farlo, <lb/>dopo un secolo, ripetitore dal campanile di Pisa delle esperienze di Leonardo <lb/>e di Luca Ghini. </s>

<s>E perch&egrave; l'origine e il progresso della nuova galileiana <lb/>rivelazione non manchino del loro debito documento, ridurremo alla memo&shy;<lb/>ria dei nostri Lettori queste parole, estratte dal Discorso scritto in risposta <lb/>a un libro peripatetico di Antonio Rocco. </s></p><p type="main">

<s>&ldquo; Incontratomi, dice Galileo, nel testo di Aristotile, nel quale egli per <lb/>manifesta suppone la sua proposizione, subito sentii gran repugnanza nel&shy;<lb/>l'intelletto come potesse essere che un corpo, dieci o venti volte pi&ugrave; grave <lb/>dell'altro, dovesse cadere a basso con decupla o vigecupla velocit&agrave;, e mi <lb/>sovvenne aver veduto nelle tempeste mescolatamente cadere piccoli grani di <lb/>grandine con mezzani e con grandi dieci e pi&ugrave; volte, e non questi antici&shy;<lb/>pare il loro arrivo in terra; n&egrave; meno esser credibile che i piccoli si fosser <lb/>mossi un pezzo avanti ai grandissimi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di qui, passando col discorso pi&ugrave; oltre, mi formai un'assioma, da <lb/>non essere revocato in dubbio da nessuno, e supposi qualsivoglia corpo grave <lb/>discendente aver nel suo moto un grado di velocit&agrave;, da natura limitato ed <lb/>in maniera prefisso, che il volerglielo alterare col crescergli la velocit&agrave; o <lb/>diminuirgliela non si potesse fare, senza usargli violenza, per ritardargli o <lb/>concitargli il detto suo limitato corso naturale. </s>

<s>Fermato questo discorso, mi <lb/>figurai colla mente due corpi eguali in mole e in peso, quali fossero per <pb xlink:href="020/01/2035.jpg" pagenum="278"/>esempio due mattoni, li quali da una medesima altezza in un medesimo <lb/>istante si partissero. </s>

<s>Questi non si pu&ograve; dubitare che scenderanno con pari <lb/>velocit&agrave;, cio&egrave; coll'assegnata loro dalla Natura, la quale, se da qualche altro <lb/>mobile dee loro essere accresciuta, &egrave; necessario che esso con maggior velo&shy;<lb/>cit&agrave; si muova. </s>

<s>Ma se si figureranno i mattoni nello scendere unirsi ed at&shy;<lb/>taccarsi insieme, quale di loro sar&agrave; quello che, aggiungendo impeto all'altro, <lb/>gli raddoppi la velocit&agrave;, stante che ella non pu&ograve; essere accresciuta da un <lb/>sopravveniente mobile, se con maggior velocit&agrave; non si muove? </s>

<s>Convien dun&shy;<lb/>que concedere che il composto di due mattoni non alteri la loro prima ve&shy;<lb/>locit&agrave; &rdquo; (Alb. </s>

<s>II, 315, 16). </s></p><p type="main">

<s>Sentesi di qui echeggiare, quasi nelle medesime parole, il concetto del <lb/>Benedetti, ma Galileo recide con la sua solita arte, o a dir meglio nasconde <lb/>anche questo filo delle pi&ugrave; prossime tradizioni, bench&egrave; non riuscisse ad arre&shy;<lb/>stare il corso alla logica della Natura, la quale con pari liberalit&agrave; porgeva <lb/>quello stesso filo per guida anche ad altri ingegni speculativi. </s>

<s>Abbiam fra <lb/>questi da annoverare Giovan Marco, matematico di Praga, e Giovan Ba&shy;<lb/>tista Baliani, il quale, pubblicando per la prima volta in Genova nel 1638 un <lb/>suo trattatello <emph type="italics"/>De motu gravium<emph.end type="italics"/> raccontava nella prefazione come nel 1611, <lb/>essendo per patria legge prefetto alla Rocca di Savona, la comodit&agrave; di quel&shy;<lb/>l'altura e l'avere a mano le palle dei cannoni militari lo invogliassero a far <lb/>esperienze della caduta dei gravi. </s>

<s>Ebbe da cos&igrave; fatte esperienze ripetute pi&ugrave; <lb/>volte che due de'suddetti globi, uno di una libbra e l'altro di cinquanta, <lb/>giungevano a toccare il suolo <emph type="italics"/>in indivisibili temporis momento.<emph.end type="italics"/> (De motu <lb/>natur., editio 2a, Genuae 1646, pag. </s>

<s>5). </s></p><p type="main">

<s>Incominci&ograve; allora a pensare che i fatti non concordavano con le dot&shy;<lb/>trine della maggior parte dei Filosofi, ond'&egrave; che volle veder se la legge da <lb/>loro approvata si verificasse, almeno ne'corpi di differente gravit&agrave; in spe&shy;<lb/>cie. </s>

<s>Ma fatti andar gi&ugrave; dall'alto della Rocca due globi, uno di piombo e <lb/>l'altro di cera, trov&ograve; che questo rimaneva s&igrave; all'altro indietro, di un tale <lb/>spazio per&ograve; da non serbar proporzione alcuna con le differenti gravezze. <lb/></s>

<s>&ldquo; Porro, cum ex experimentis satis superque liqueret in naturali motu gra&shy;<lb/>vium proportionem gravitatum communiter creditam non servari, in eam <lb/>descendi sententiam ut arbitrarer fortasse gravitatem se habere ut agens, <lb/>materiam vero, seu mavis materiale corpus, ut passum, et proinde gravia <lb/>moveri iuxta proportionem gravitatis ad materiam, et ubi sine impedimento <lb/>naturaliter perpendiculari motu ferantur moveri aequaliter, quia ubi plus <lb/>est gravitatis plus pariter sit materiae, seu materialis gravitatis &rdquo; (ibid., <lb/>pag. </s>

<s>6, 7). </s></p><p type="main">

<s>Penetrando bene addentro al significato di queste parole, ben si com&shy;<lb/>prende come, dicendo il Baliani che le due sfere omogenee si vedevan ca&shy;<lb/>dere <emph type="italics"/>in indivisibili temporis momento,<emph.end type="italics"/> non intendeva escludere qualche pic&shy;<lb/>cola real differenza di moto, la quale accidentalmente nascesse dall'impedi&shy;<lb/>mento del mezzo, in conformit&agrave; della quale intenzione gli abbiamo sentito <lb/>espressamente dire che allora due corpi, comunque tra loro differenti, si <pb xlink:href="020/01/2036.jpg" pagenum="279"/>moverebbero di moto uguale, <emph type="italics"/>ubi sine impedimento<emph.end type="italics"/> (ci&ograve; che solo pu&ograve; av&shy;<lb/>venire nel vuoto) <emph type="italics"/>naturaliter perpendiculari motu ferantur.<emph.end type="italics"/> In questo stato <lb/>di assoluta libert&agrave; da tutti gl'impedimenti considerava anche Giovan Marco <lb/>le cadute de'corpi, quando asseriva: &ldquo; motum, quatenus a gravitate proce&shy;<lb/>dit, eiusdem speciei seu gradus, eadem celeritate fieri in omnibus, quan&shy;<lb/>tumvis mole, figura, pondere a se differant &rdquo; (De proportione motus, Pra&shy;<lb/>gae 1639, P.). </s></p><p type="main">

<s>Non ebbe questa considerazione il gesuita Niccol&ograve; Cabeo, il quale, tro&shy;<lb/>vandosi nella quaresima del 1636 a predicare in Genova, strinse amicizia <lb/>col Baliani che, discorrendo degli amati suoi studi, si era pi&ugrave; volte espresso <lb/>(per formular la legge naturale nella sua essenza, consistente nell'aver cia&shy;<lb/>ciascuna divisa particella materiale il medesimo impulso discensivo di tutta <lb/>insieme la mole) dicendo che qualunque corpo dovrebbe cader dall'alto <lb/>ugualmente veloce. </s>

<s>Intese il Cabeo quel discorso senza alcuna discrezione, <lb/>e perch&egrave; forse ridusse le sue esperienze a lasciarseli cadere dall'una e dal&shy;<lb/>l'altra mano, scrisse di avere sperimentato che un pezzo di piombo e <emph type="italics"/>fru&shy;<lb/>stum panis<emph.end type="italics"/> cadevano nel medesimo tempo. </s></p><p type="main">

<s>Incontr&ograve; un caso simile a Galileo che, secondo le intenzioni medesime <lb/>del Baliani, si esprimeva nei medesimi modi in privato coi discepoli e con <lb/>gli amici, e poi, lusingandosi di dover essere inteso dai giudiziosi, cos&igrave; pub&shy;<lb/>blicamente scriveva nella II Giornata dei Due massimi sistemi: &ldquo; Palle di <lb/>una, di dieci, di cento, di mille libbre tutte misureranno le medesime cento <lb/>braccia nello stesso tempo &rdquo; (Alb. </s>

<s>I, 245). Era fra quegli scolari, che aveva <lb/>prima ascoltato e poi letto Galileo, Vincenzio Renieri, il quale si trovava a <lb/>professare le Matematiche in Pisa, quando nel 1641 gli giunse notizia del&shy;<lb/>l'esperienze del Cabeo. </s>

<s>E perch&egrave; queste, com'&egrave; facile indovinare, si tene&shy;<lb/>vano per incredibili, come per dubbiose s'avevano quelle di Galileo; per <lb/>certificarsi della verit&agrave; dei fatti s'istituirono, ne'primi giorni di Marzo di <lb/>quell'anno 1641, dal campanile di Pisa opportune esperienze, delle quali il <lb/>Renieri, dopo pochi giorni, scriveva allo stesso Galileo cos&igrave; per lettera il re&shy;<lb/>sultato: </s></p><p type="main">

<s>&ldquo; Abbiamo qui avuto occasione di fare una esperienza di due gravi ca&shy;<lb/>denti dall'alto di diversa materia, cio&egrave; uno di legno e uno di piombo, ma <lb/>della stessa grandezza; perch&egrave; un tal Gesuita scrive che scendono nello stesso <lb/>tempo, e con pari velocit&agrave; arrivano a terra, ed un tale Inglese affermava che <lb/>il Liceti componeva di ci&ograve; un problema, e ne rendeva la ragione. </s>

<s>Ma final&shy;<lb/>mente abbiamo trovato il fatto in contrario, perch&egrave; dalla cima del campa&shy;<lb/>nile del. </s>

<s>Duomo tra la palla di piombo e quella di legno vi corrono tre brac&shy;<lb/>cia almeno di differenza. </s>

<s>Si fecero anche esperienze di due palle di piombo, <lb/>una della grandezza eguale a una ordinaria di artiglieria, e l'altra da mo&shy;<lb/>schetto, e si vedeva tra la pi&ugrave; grossa e la pi&ugrave; piccola, dall'altezza dello <lb/>stesso campanile, esservi un buon palmo di differenza, del quale la pi&ugrave; <lb/>grossa anticipava la pi&ugrave; piccola &rdquo; (Alb. </s>

<s>X, 410). </s></p><p type="main">

<s>Galileo si compiacque di queste esperienze, che diceva sovvenire a con-<pb xlink:href="020/01/2037.jpg" pagenum="280"/>ferma delle sue dottrine, ci&ograve; che giunse nuovo, e contrario a quel che si <lb/>aspettava il Renieri, il quale credeva di aver anzi trovato che i fatti contra&shy;<lb/>dicevano a quel che aveva udito dire al suo Maestro o letto nel sopra ci&shy;<lb/>tato luogo dei dialoghi Del mondo. </s>

<s>Galileo allora dichiar&ograve; meglio in qual <lb/>senso si dovesse interpetrare quel luogo, in cui intendevasi formular la legge <lb/>assolutamente, astraendo dalle accidentalit&agrave; prodotte dall'impedimento del <lb/>mezzo, gli effetti del quale, da che solo potevano dipendere le differenze <lb/>nelle varie cadute sperimentate, diceva di aver minutamente considerati e <lb/>discorsi nel primo dialogo Dei moti, alla lettura del quale, se voleva avere <lb/>intera scienza di quelle cose, rimandava il Renieri. </s></p><p type="main">

<s>Il Renieri per&ograve; rispondeva ingenuamente di non avere avuto ancora <lb/>tempo in due anni di leggere il libro con quell'attenzione, che richiedevan <lb/>le proposizioni ivi matematicamente dimostrate. </s>

<s>&ldquo; L'ultimo Dialogo di V. S. E. <lb/>non &egrave; stato da me letto, se non in qua e in l&agrave;, perch&egrave; l'estate passata, che <lb/>avrei potuto attendervi con diligenza, ella sa come io stetti, e di poi non ho <lb/>avuto tempo di poterlo vedere con quella applicazione, che ricercano le di&shy;<lb/>mostrazioni che sono in esso. </s>

<s>So che &egrave; verissimo che due gravi differenti in <lb/>specie, bench&egrave; uguali di mole, non serbano proporzione alcuna di gravit&agrave; <lb/>nello scendere, anzi che per esempio nell'acqua il legno si mover&agrave; al con&shy;<lb/>trario del piombo, e per&ograve; fino da principio mi risi della esperienza del Ge&shy;<lb/>suita, che affermava che il piombo <emph type="italics"/>et frustum panis,<emph.end type="italics"/> per dire com'egli <lb/>scrive, si movevano con egual velocit&agrave; al centro. </s>

<s>Ma che due gravi ineguali <lb/>di peso, ma della stessa materia, cadendo dalla stessa altezza a perpendi&shy;<lb/>colo, abbiano ad arrivare con diversa velocit&agrave; e in diverso tempo al cen&shy;<lb/>tro, mi pareva d'aver da lei udito o letto, che ora non mi ricordo, non poter <lb/>essere &rdquo; (ivi, pag. </s>

<s>414). </s></p><p type="main">

<s>Soggiungeva il Renieri a queste parole, scritte il d&igrave; 20 di Marzo, che <lb/>nelle prossime vacanze di Pasqua avrebbe atteso finalmente alla lettura del <lb/>libro, e mandando, secondo le altrui promesse e i desiderii proprii, la cosa <lb/>ad effetto, avr&agrave; trovato quel che Galileo discorre a lungo delle difficolt&agrave; in&shy;<lb/>contrate dai cadenti al loro libero velocitarsi, nel mezzo, e si sar&agrave; persuaso <lb/>di aver franteso, quando gli parve aver udito dire al Maestro non essere <lb/>assolutamente possibile che due gravi della stessa materia, cadendo dalla <lb/>stessa altezza per l'aria, in diverso tempo arrivino al centro. </s></p><p type="main">

<s>Non cos&igrave; per&ograve;, a dispetto della ragione e dei fatti, se ne volle persua&shy;<lb/>dere il Cabeo, il quale pubblicando in due volumoni in folio, nel 1646, i <lb/>suoi Commentarii sui quattro libri meteorologici di Aristotile, torna nel primo <lb/>libro sulla questione se di tutti i cadenti le velocit&agrave; siano uguali, e come <lb/>avesse a dimostrare il teorema pi&ugrave; certo di Geometria cos&igrave; scrive: &ldquo; Sint <lb/>primo duo gravia eiusdem rationis, ut duo plumbea, sive omnino similem <lb/>habeant figuram, ut quod ambo sint sphaerica, sive non, quae simul ex edito <lb/>loco decidant: dico simul physice ex quacumque altitudine ad terram per&shy;<lb/>venire. </s>

<s>Hoc multis experimentis et ego ipse sum expertus et alii etiam <lb/>experti sunt, et semper omnino aequali tempore descendere deprehendi, <pb xlink:href="020/01/2038.jpg" pagenum="281"/>etiamsi unum esset unius unciae, alterum quinquaginta, nec quolibet po&shy;<lb/>sito magno discrimine in pondere potest notari sensibile discrimen in casu &rdquo; <lb/>(In libros meteor. </s>

<s>Arist., T. I, Romae 1646, pag. </s>

<s>97). </s></p><p type="main">

<s>Non contento di ci&ograve;, il Cabeo, con la sua solita temeraria franchezza <lb/>poco appresso asserisce non due soli globi di piombo grandemente diversi <lb/>di mole, &ldquo; Sed etiam globos valde impares in materia, ut plumbeum et li&shy;<lb/>gneum, et dispares in figura, ut quadratum seu piramidale et rotundum, si <lb/>simul ex edito loco, tranquillo coelo, cadant, ambo simul ad terram perve&shy;<lb/>nire, ita ut quantumcumque sit discrimen ponderis non possit notari sensi&shy;<lb/>bile discrimen temporis quo ad terram allidunt &rdquo; (ibid.). Non ignora quel <lb/>che andavano dicendo alcuni doversi tener conto, in cos&igrave; fatti esperimenti, <lb/>della resistenza dell'aria, ma, guardate, rispondeva il Cabeo, quanto son varii <lb/>i cervelli degli uomini! chi vuol che l'aria acceleri il moto, e chi vuole che <lb/>lo ritardi. </s>

<s>Ma lasciamo i discorsi e atteniamoci ai fatti, tante volte da me <lb/>sperimentati, i quali ci persuadono &ldquo; aerem nihil efficere in isto motu nec <lb/>pro nec contra velocitatem &rdquo; (ibid., pag. </s>

<s>68). </s></p><p type="main">

<s>Non pot&egrave;, in leggere queste cose, Giovan Batista Riccioli tenersi dal <lb/>rimproverare il suo confratello, per essersi cos&igrave; ostinatamente messo a im&shy;<lb/>pugnare la verit&agrave; conosciuta, e nel II Tomo dell'Almagesto nuovo pubbli&shy;<lb/>camente confessa che, per quanto si studiasse di persuadere il Cabeo con <lb/>addurre i certissimi fatti in contrario &ldquo; nunquam ex ea opinione per me <lb/>divelli potuit &rdquo; (Bononiae 1651, pag. </s>

<s>382). Prosegue poi a dire che quella <lb/>opinione, cos&igrave; asseveranteinente professata nel libro Delle meteore, era af&shy;<lb/>fatto temeraria, perch&egrave; ivi non si dice da che altura furon fatti gli esperi&shy;<lb/>menti, sebben giurasse d'esser certo, il Riccioli, che da quelli fatti insieme <lb/>nel 1634 in Ferrara dal Campanile della chiesa del Ges&ugrave;, non bene alta <lb/>24 metri &ldquo; nunquam adduci potuit ut eam vel ullam inaequalitatem admit&shy;<lb/>teret, aut discrimen in lapsis &rdquo; (ibid.). </s></p><p type="main">

<s>A concluder qualche cosa di certo ci bisognavano altezze maggiori, ond'&egrave; <lb/>che, venuto il Riccioli a insegnare nel Collegio della sua Compagnia di Ges&ugrave; <lb/>in Bologna, rivolse lieto lo sguardo alla torre degli Asinelli, che poi ritrov&ograve; <lb/>tanto comoda a esperimentar le cadute dei gravi <emph type="italics"/>perinde ac si ad hunc <lb/>finem esset constituta.<emph.end type="italics"/> Di lass&ugrave;, fra gli altri, tuttavia memorabili nella sto&shy;<lb/>ria per la loro straordinaria diligenza, istitu&igrave; quella IV classe di esperimenti <lb/><emph type="italics"/>pro duorum gravium diversi ponderis descensu inaequali,<emph.end type="italics"/> che andavano <lb/><emph type="italics"/>ad hominem<emph.end type="italics"/> contro il Cabeo, e contro tutti coloro ch'ei credeva tenesser <lb/>con lui. </s></p><p type="main">

<s>Molto fallace, incomincia a dire il Riccioli, &egrave; questo modo di sperimen&shy;<lb/>tare, se non vi si usi una grande circospezione, la quale si fa principal&shy;<lb/>mente consister da lui nello sceglier due corpi che, avendo differente peso, <lb/>incontrino nonostante nell'aria una medesima resistenza. </s>

<s>Eragli a principio, <lb/>come a Leonardo, venuto in mente di usar cilindri o prismi della medesima <lb/>base e di differente altezza, ma, rotando questi intorno al loro centro di gra&shy;<lb/>vit&agrave;, rendevano troppo incerto il tempo della caduta, e perci&ograve; scelse piut-<pb xlink:href="020/01/2039.jpg" pagenum="282"/>tosto due globi di argilla fresca, i quali, avendo ambedue uguale diametro, <lb/>scavandone uno intorno al centro, riducevasi sotto pari volume la met&agrave; pi&ugrave; <lb/>leggero dell'altro, che pesava esattamente vent'once. </s></p><p type="main">

<s>Cos&igrave; preparati, si lasciavano nello stesso tempo cadere i due globi dalla <lb/>maggiore altura della torre degli Asinelli, lungo le pareti della quale de&shy;<lb/><figure id="id.020.01.2039.1.jpg" xlink:href="020/01/2039/1.jpg"/></s></p><p type="caption">

<s>Figura 137.<lb/>scrivan le due linee GI, OD (fig. </s>

<s>137), in cui i due punti I, D <lb/>designano il pavimento, e G, O i merli della torre. </s>

<s>Furono l'espe&shy;<lb/>rienze ripetute pi&ugrave; volte: nel Maggio del 1640, nell'Agosto del 1645, <lb/>nell'Ottobre del 1648, e ultimamente nel 1650, sempre alla pre&shy;<lb/>senza di molti testimoni, che il Riccioli cita per nome, i pi&ugrave; ge&shy;<lb/>suiti, fra'quali due destinati ad ottenere una meritata celebrit&agrave; nella <lb/>scienza; Francesco Maria Grimaldi, assiduo sempre e diligentissimo <lb/>cooperatore, e Paolo Casati. </s>

<s>&ldquo; Siquidem, cos&igrave; descriveva il Riccioli <lb/>stesso il resultato di queste esperienze, globus argillaceus levior <lb/>seu 10 unciarum, eodem momento quo argillaceus alter eiusdem <lb/>molis sed unciarum 20 demissus fuit ex O, apparuit adhuc in F <lb/>distans a pavimento I pedes saltem 15, eo momento quo gravior <lb/>pavimentum idem percusserat in D, et iam in sexcenta fragmina <lb/>dissiluerat &rdquo; (ibid., pag. </s>

<s>387). </s></p><p type="main">

<s>Fra i testimoni invocati, e i curiosamente concorsi a spettacolo di que&shy;<lb/>ste esperienze &ldquo; aderant, dice il Riccioli stesso, tres aut quatuor Philoso&shy;<lb/>phiae aut Theologiae magistri, qui cum Galilaeo aut Cabeo et Arriaga exi&shy;<lb/>stimaverant duo quaelibet gravia, dimissa simul ex eadem altitudine quan&shy;<lb/>tacumque, descendere ad terram eodem physico temporis momento. </s>

<s>At statim <lb/>opinionem hanc deposuerunt &rdquo; (ibid.). </s></p><p type="main">

<s>Era dunque anche il Riccioli dell'opinion del Renieri, e, argomentando <lb/>da quel che aveva trovato scritto ne'dialoghi Dei due massimi sistemi, po&shy;<lb/>neva senza eccezione Galileo nel novero del Cabeo e dell'Arriaga. </s>

<s>I dialo&shy;<lb/>ghi Del moto o non furono dall'illustre Sperimentator bolognese mai letti <lb/>o secondando gl'istituti della sua setta si serb&ograve; ritroso a quelle dottrine, <lb/>giacch&egrave; dalle XIII classi di esperimenti descritti intorno alla caduta dei gravi, <lb/>ne deduce alcuni teoremi, nell'ultimo de'quali, trovandosi costretto a pro&shy;<lb/>fessar contro lo stesso Aristotile, non sa pi&ugrave; dove andare a ritrovare il vero <lb/>smarrito. </s>

<s>&ldquo; Quoniam vero difficile reddi potest ratio a priori cur effectus <lb/>velocitatis ad velocitatem non servet proportionem, quam habet causa ad <lb/>causam, nempe gravitas ad gravitatem; hinc factum ut non pauci ex iam <lb/>nominatis putarint per se duo quaelibet gravia, quantumvis differentia in <lb/>pondere, aequaliter descendere, si removeantur quae per accidens unum <lb/>eorum retardant &rdquo; (ibid., pag. </s>

<s>396). Ci&ograve; reputasi dal Riccioli impossibile, <lb/>perch&egrave; supponeva nel suo discorso che si volesser rimovere tutti gl'impe&shy;<lb/>dimenti esterni, considerando i gravi sempre moversi in mezzo all'aria, ma <lb/>Galileo e i <emph type="italics"/>pauci ex iam nominatis<emph.end type="italics"/> intendevano che il principale, anzi l'unico <lb/>impedimento al moto dei gravi, fosse l'aria stessa, per rimover la quale sup&shy;<lb/>ponevano il vuoto. </s></p><pb xlink:href="020/01/2040.jpg" pagenum="283"/><p type="main">

<s>Accennammo gi&agrave; alla dimostrazione geometrica del Benedetti, e ora sog&shy;<lb/>giungeremo quell'altra fisica, che dettero contemporaneamente i due grandi <lb/>Maestri del moto in Alemagna e in Italia. </s>

<s>Giovan Marco scriveva cos&igrave; nel <lb/>suo capitolo <emph type="italics"/>De inaequalium ponderum lapsu:<emph.end type="italics"/> &ldquo; Quia ergo retardatio mo&shy;<lb/>tus est a medio, quo medium magis resistit divisioni eo minor velocitas <lb/>motus, maior autem excessus tarditatis in minori, propterea quod aucta re&shy;<lb/>sistentia eadem differentia in minori intervallo. </s>

<s>E contra minuitur excessus <lb/>in medio magis raro. </s>

<s>Itaque si detur corpus infinitae raritatis, cuiusmodi <lb/>vacuum, quia nulla resistentia, nulla quoque erit inaequalitas motus &rdquo; (De <lb/>propor. </s>

<s>motus, Pragae 1639, P3). </s></p><p type="main">

<s>Nella medesima forma argomentava il Salviati nella giornata prima Delle <lb/>due nuove scienze (Alb. </s>

<s>XIII, 75) e nel Discorso contro il peripatetico Rocco, <lb/>cos&igrave; dicendo: &ldquo; Tuttavolta che noi vediamo che con l'attenuare e allegge&shy;<lb/>rire il mezzo, anco nel mezzo dell'aria, che pure &egrave; corporeo e perci&ograve; resi&shy;<lb/>stente, arriviamo a vedere due mobili, sommamente differenti di peso, per <lb/>un breve spazio moversi di velocit&agrave; niente o pochissimo differenti, le quali <lb/>poi siamo certi farsi diverse, non per le gravit&agrave; che sempre son le stesse, <lb/>ma per gl'impedimenti e ostacoli del mezzo, che sempre s'augumentano; <lb/>perch&egrave; non dobbiamo tener per fermo che, rimossa del tutto la gravit&agrave;, la <lb/>crassizie e tutti gli altri impedimenti del mezzo pieno, nel vacuo, i metalli <lb/>tutti, le pietre, i legni ed insomma tutti i gravi si movesser colla stessa ve&shy;<lb/>locit&agrave;? </s>

<s>&rdquo; (Alb. </s>

<s>II, 328). </s></p><p type="main">

<s>Con tale intenzione s'asseriva pure ne'dialoghi Del mondo, e nel primo <lb/>Del moto che non solo una lacrima di piombo avrebbe a moversi veloce, <lb/>come una palla di artiglieria, ma un grano di rena, come una macina di <lb/>guado (Alb. </s>

<s>XIII, 67). Venendo per&ograve; a farne esperienza non si trova se&shy;<lb/>guirne cos&igrave; puntualmente l'effetto, per gl'impedimenti dell'aria, i quali son <lb/>poi dallo stesso Galileo ridotti alle loro pi&ugrave; giuste ragioni. </s>

<s>&ldquo; L'esperienza, <lb/>egli dice, fatta con due mobili quanto pi&ugrave; si possa differenti di peso, col <lb/>farli scendere da un'altezza, per osservare se la velocit&agrave; loro sia uguale, <lb/>patisce qualche difficolt&agrave;, imperocch&egrave; se l'altezza sar&agrave; grande, il mezzo che <lb/>dall'impeto del cadente dee essere aperto e lateralmente spinto, di molto <lb/>maggior pregiudizio sar&agrave; al piccol momento del mobile leggerissimo, che alla <lb/>violenza del gravissimo, per lo che per lungo spazio il leggero rimarr&agrave; in&shy;<lb/>dietro, e nell'altezza piccola si potrebbe dubitare se veramente non vi fusse <lb/>differenza, o pur se ve ne fosse, ma inosservabile &rdquo; (ivi, pag. </s>

<s>86, 87). </s></p><p type="main">

<s>Per scansar le quali difficolt&agrave;, non vedendo ancora possibile il modo di <lb/>levar affatto l'aria di mezzo, fu condotto Galileo all'ingegnosissimo partito <lb/>di renderne poco sensibili gl'impedimenti &ldquo; col fare scendere i mobili sopra <lb/>un piano declive, non molto elevato sopra l'orizzontale, che sopra questo, <lb/>non meno che nel perpendicolo, potr&agrave; scorgersi quello che facciano i gravi <lb/>differenti di peso. </s>

<s>E passando pi&ugrave; avanti ho anco voluto liberarmi da qual&shy;<lb/>che impedimento, che potesse nascer dal contatto di essi mobili sul detto <lb/>piano declive, e finalmente ho preso due palle, una di piombo e una di su-<pb xlink:href="020/01/2041.jpg" pagenum="284"/>ghero; quella ben pi&ugrave; cento volte pi&ugrave; grave di questa, o ciascuna di loro <lb/>attaccate a due sottili spaghetti eguali, lunghi quattro o cinque braccia, le&shy;<lb/>gati ad alto. </s>

<s>Allontanata poi l'una e l'altra palla dallo stato perpendicolare, <lb/>gli ho dato l'andare nell'istesso momento, ed esse scendendo per le circon&shy;<lb/>ferenze dei cerchi descritti dagli spaghi, eguali loro semidiametri, e passate <lb/>oltre al perpendicolo, son poi per le medesime strade ritornate indietro. </s>

<s>E <lb/>reiterando ben cento volte per lor medesime le andate e le tornate, hanno <lb/>sensatamente mostrato come la grave va talmente sotto il tempo della leg&shy;<lb/>gera, che n&egrave; in ben cento vibrazioni n&egrave; in mille anticipa il tempo di un <lb/>minimo momento, ma camminano con passo ugualissimo &rdquo; (ivi, pag. </s>

<s>87). </s></p><p type="main">

<s>Dice di essere anche il Baliani ricorso al medesimo efficacissimo espe&shy;<lb/>rimento dimostrativo delle velocit&agrave; sempre uguali, in corpi delle pi&ugrave; diffe&shy;<lb/>renti gravit&agrave; specifiche, fatti vibrare ne'pendoli. </s>

<s>&ldquo; Globos in gravitate et in <lb/>materia inaequales appendi funiculis aequalibus, et agitatos animadverti mo&shy;<lb/>veri tempore aequali, et hoc servare adeo fideliter ut globus plumbeus dua&shy;<lb/>rum unciarum, alter librarum duarum; ferreus librarum 34 et lapideus <lb/>40 circiter, nec non et lapis informis, quorum funiculi, comprehensis ipso&shy;<lb/>rum semidiametris, aequales essent, uno et eodem temporis spatio moveren&shy;<lb/>tur, et vibrationes easdem numero darent hinc inde sive motus unius globi <lb/>fieret per aequale spatium, sive per inaequale &rdquo; (De motu natur. </s>

<s>cit., pag. </s>

<s>6). </s></p><p type="main">

<s>Notava per&ograve; Galileo, e l'avr&agrave; pure dovuto notare il Baliani, scorgersi <lb/>anche in quelle esperienze l'operazione del mezzo dal diminuire assai pi&ugrave; <lb/>presto &ldquo; le vibrazioni del sughero che quelle del piombo &rdquo; (Alb. </s>

<s>XIII, 87) <lb/>per toglier la quale inesattezza, che avrebbe potuto forse mettere qualche <lb/>scrupolo nella conclusione, il Newton fece tornire due scatolette sferiche di <lb/>legno uguale, e di uguale diametro, e l'una emp&igrave; di trucioli pur di legno <lb/>e l'altra del medesimo peso di oro diligentemente curando di situarlo nel <lb/>centro dell'oscillazione. </s>

<s>&ldquo; Pyxides ab aequalibus pedum undecim filis pen&shy;<lb/>dentes constituebant pendula, quoad pondus, figuram et aeris resistentiam, <lb/>omnino paria; et paribus oscillationibus iuxta positae, ibant una et redibant <lb/>diutissime &rdquo; (Principia mathem., T. III, Genevae 1742, pag. </s>

<s>33). Speriment&ograve; <lb/>poi con altri corpi della pi&ugrave; varia natura, e n'ebbe sempre i medesimi re&shy;<lb/>sultati. </s>

<s>&ldquo; Rem tentavi in auro, argento, plumbo, vitro, arena, sale communi, <lb/>ligno, aqua, tritico &rdquo; (ibid.). </s></p><p type="main">

<s>Sembra che dovessero quelle prime esperienze di Galileo e del Baliani <lb/>coi pendoli, rese dal Newton poi s&igrave; perfette, essere sufficienti a dimostrar <lb/>che una medesima &egrave; la velocit&agrave; nel composto e nella materia divisa, e che <lb/>dipendon le differenze dalla sola resistenza del mezzo. </s>

<s>Ma Galileo non si <lb/>content&ograve; di questo, e prevenendo il male inteso pensiero del Riccioli e del <lb/>Renieri si trattenne con assai lungo e spiegato discorso, nel Io dialogo Delle <lb/>due nuove scienze, a mostrar come ogni differenza di moto, da lui benis&shy;<lb/>simo ne'varii casi osservata prima de'suoi contradittori, dipendeva dai varii <lb/>impedimenti dell'aria. </s></p><p type="main">

<s>E quanto alle esperienze del Riccioli coi cadenti di ugual natura e vo-<pb xlink:href="020/01/2042.jpg" pagenum="285"/>lume, ma differenti di peso, dalle quali esperienze costantemente resultava <lb/>andar sempre il pi&ugrave; grave alquanto pi&ugrave; veloce dell'altro, aveva gi&agrave; Galileo <lb/>resa la ragione di questa anomalia, osservando che, se l'altezza sar&agrave; grande, <lb/>il mezzo, che dall'impeto del cadente dee essere aperto e lateralmente spinto, <lb/>di molto maggior pregiudizio sar&agrave; al pi&ugrave; piccolo momento del mobile pi&ugrave; <lb/>leggero, che alla maggior violenza del pi&ugrave; grave (Alb. </s>

<s>XIII, 86). </s></p><p type="main">

<s>Quanto poi all'esperienza del Renieri, con le sfere cadenti omogenee e <lb/>varie, non solo di peso, ma di volume, aveva pure Galileo matematica&shy;<lb/>mente dimostrato come dall'impedimento minore, che viene a ricever dal&shy;<lb/>l'aria la maggior palla, dipendesse l'anticipare sopra la minore di quel <emph type="italics"/>buon <lb/>palmo.<emph.end type="italics"/> Ammesso che le resistenze sien proporzionali alle superfice, riduce&shy;<lb/>vasi la dimostrazione ai principii della Geometria &rdquo; la quale c'insegna che <lb/>molto maggior proporzione &egrave; tra la mole e la mole, nei solidi simili, che tra <lb/>le loro superfice &rdquo; (ivi, pag. </s>

<s>92). E per&ograve; il pi&ugrave; piccol corpo, avendo mag&shy;<lb/>gior superfice del grande, a proporzion del peso diminuito, &egrave; disposto per&shy;<lb/>ci&ograve; a ricevere anche maggiore impedimento. </s></p><p type="main">

<s>Nel Discorso altre volte citato si spiega intorno a ci&ograve; Galileo col Rocco <lb/>non men chiaramente di quel che facesse il Salviati con Simplicio. </s>

<s>&ldquo; Nei <lb/>corpi della medesima materia, e simili di figura, cotal impedimento non ri&shy;<lb/>ceverebbe augumento n&egrave; diminuzione, per crescimento o diminuzione di <lb/>grandezza, tuttavolta che le lor superfice crescessero e calassero colla me&shy;<lb/>desima proporzione. </s>

<s>Ma perch&egrave; le superfice dei solidi simili, no nell'istessa <lb/>proporzione, ma in minore, cio&egrave; in subsesquialtera di quella di essi solidi, <lb/>crescono e calano; per&ograve;, diminuendo assai pi&ugrave; la grandezza e peso del so&shy;<lb/>lido, che non dimuisce la superfice, l'impedimento vien tuttavia crescendo <lb/>a proporzione della virt&ugrave;, cio&egrave; della gravit&agrave; del solido, dalla quale l'impe&shy;<lb/>dimento dell'aderenza della superfice dee essere superato..... E cos&igrave;, se <lb/>noi anderemo suddividendo e scemando sempre con proporzion maggiore la <lb/>mole corporea che la superficiale, cio&egrave; diminuendo quella in sesquialtera <lb/>proporzione di questa, ci ridurremo ad una polverizzazione di particole cos&igrave; <lb/>minime, che la mole e gravit&agrave; loro diverr&agrave; piccolissima, in comparazione <lb/>delle loro superfice, le quali potranno esser mille volte maggiori di quello <lb/>che converrebbe, acci&ograve; fusse l'impedimento dell'aderenza colla medesima <lb/>proporzione superato dalla gravit&agrave; de'loro corpuscoli, e queste saranno quei <lb/>minimi atomini della sottilissima arena, che intorbida l'acqua, e non calano <lb/>se non in molte ore quello spazio, che un sassetto quanto una noce passa <lb/>in una battuta di polso &rdquo; (Alb. </s>

<s>II, 324, 25). </s></p><p type="main">

<s>Ritornando Galileo, dop'avere scritto questo Discorso e dop'aver gi&agrave; <lb/>pubblicati i IV dialoghi Del moto, sopra questo argomento, s'incontr&ograve; in un <lb/>assai facile, ma elegante teorema formulato cos&igrave; in una sua Nota: &ldquo; D'una <lb/>palla grande ne fo palline: la superfice delle palline tutte &egrave; tanto maggiore <lb/>della superfice della grande, quanto il diametro della grande supera il dia&shy;<lb/>metro della piccola &rdquo; (MSS. Gal., P. V, T. IV, fol. </s>

<s>29). </s></p><p type="main">

<s>Trovasi la dimostrazione di ci&ograve; scritta in un altro foglio, applicandola <pb xlink:href="020/01/2043.jpg" pagenum="286"/>per pi&ugrave; facile esempio ai cubi, piuttosto che alle sfere, e cos&igrave; ragionando, <lb/>dietro i pi&ugrave; elementari principii della Stereometria: &ldquo; Il numero de'cubi, <lb/>ne'quali uno si risolve, &egrave; il numero delle parti, che son nel lato del cubo <lb/>che si risolve, come, per esempio, diviso il lato del cubo in tre o quattro <lb/>parti, i cubi, che da esse parti si faranno, saranno 27 o 64, ed avendo ogni <lb/>cubo sei quadrati in superfice, moltiplicando 27 per 6, e 64 pur per 6, <lb/>averemo i numeri dei quadrati, che son superfice dei detti cubi. </s>

<s>Tutte le <lb/>superfice dei piccoli cubi risoluti prese insieme, alla superfice del cubo grande <lb/>risoluto, hanno la medesima proporzione che il numero delle parti del lato <lb/>che si sega, all'uno, e cos&igrave; tutte le superfice dei 27 cubi, alla superfice del <lb/>primo massimo cubo, saranno triple, e tutte le superfice delli 64 cubetti, <lb/>prese insieme, saranno quadruple della superfice dell'intero gran cubo, es&shy;<lb/>sendo che il lato di questo fu diviso in tre parti, per cavarne li 27 cubi, <lb/>ed in 4, per cavarne li cubi 64 &rdquo; (ivi, fol. </s>

<s>19). </s></p><p type="main">

<s>Doveva il teorema, nel riordinamento che meditava di dar Galileo ai <lb/>dialoghi Delle due nuove scienze, inserirsi nel Io stampato, l&agrave; dove si trat&shy;<lb/>tava d&igrave; questo soggetto, per meglio dichiarar la legge della resistenza dei <lb/>mezzi nelle cadute dei gravi, e gi&agrave; avevalo reso generale, considerando il <lb/>maggior cubo diviso in qualunque numero di parti, e aveva gi&agrave; distesa la <lb/>bozza del frammento dialogizzato, dove, dopo la dimostrazion del Salviati, <lb/>cos&igrave;, lodato avendo la bellezza e l'utilit&agrave; del teorema, dovea soggiungersi <lb/>dal Sagredo: &ldquo; Mi par di notare un altro modo di potere, in una sola e <lb/>semplice operazione, ritrovare l'eccesso delle superfice di molti solidi, tra <lb/>di loro simili ed uguali, sopra la superfice di un solo, pur simile, ma uguale <lb/>a tutti quelli. </s>

<s>Questo mi par che ci venga dato dalla radice cuba del nu&shy;<lb/>mero de'piccoli solidi, come per esempio: la superfice di mille palline quanto <lb/>&egrave; maggiore della palla sola, eguale e simile a tutte quelle eguali e simili <lb/>tra di loro? </s>

<s>diremo esser maggiore dieci volte, per esser dieci la radice cuba <lb/>di mille, e dieci volte il diametro della grande conterr&agrave; il diametro della <lb/>piccola &rdquo; (ivi, fol. </s>

<s>38). </s></p><p type="main">

<s>Ma gi&agrave; nei Dialoghi stampati, anche senza queste aggiunte, si contene&shy;<lb/>vano ampiamente svolte le dottrine della resistenza dell'aria nei cadenti di <lb/>varia specie e di varia mole, che, divulgatesi nel mondo della scienza, si <lb/>vollero riscontrar con nuove e pi&ugrave; diligenti esperienze. </s>

<s>Il Mersenno scriveva, <lb/>in proposito di queste sperimentate dottrine galileiane, al Cartesio, il quale <lb/>cos&igrave; rispondeva: &ldquo; Supponis pondus quod ex gravi materia constat, et cui <lb/>proinde aer minus obstat, sed omissis experimentis de turre Argentinensi, <lb/>illic enim neminem notum habeo, ausim asserere pondus ex gravi materia <lb/>constans citius descensurum quam aliud ex leviori. </s>

<s>Atque ex duobus eius&shy;<lb/>dem materiae et figurae ponderibus illud celerius descensurum, quod est <lb/>crassius &rdquo; (Epist., P. II cit., pag. </s>

<s>301). </s></p><p type="main">

<s>Nella teoria delle resistenze, del resto, come abbiamo ora letto, appro&shy;<lb/>vata, ritrov&ograve; per&ograve; il Cartesio in Galileo falsa questa proposizione: &ldquo; non es&shy;<lb/>sere sfera s&igrave; grande, n&egrave; di materia s&igrave; grave, che la renitenza del mezzo, <pb xlink:href="020/01/2044.jpg" pagenum="287"/>ancorch&egrave; tenuissimo, non raffreni la sua accelerazione, e che, nella conti&shy;<lb/>nuazion del moto, non la riduca alla equabilit&agrave; &rdquo; (Alb. </s>

<s>XIII, 95). Perci&ograve;, in <lb/>quella medesima lettera sopra citata in risposta al Mersenno, dop'aver con&shy;<lb/>sentito che possa dopo qualche spazio l'accelerazione ridursi insensibile, di&shy;<lb/>mostra il Cartesio l'impossibilit&agrave; di un'assoluta uguaglianza matematica fra <lb/>gl'impulsi accelerativi e le resistenze sempre crescenti, &ldquo; et proinde, cos&igrave; <lb/>conclude il discorso, celeritas semper augebitur, neque tamen unquam, ut <lb/>dixi, ccloritas tantum minuetur a resistentia aeris quantum accipit a gravi&shy;<lb/>tate incrementi, unde liquet ex sana Malhesi falaam esse propositionem <emph type="italics"/>Ga&shy;<lb/>lilei &rdquo;<emph.end type="italics"/> (Epist. </s>

<s>cit., pag. </s>

<s>300). </s></p><p type="main">

<s>Falsa pure fu dimostrata la proposizione di Galileo dall'Huyghens e dal <lb/>Newton, da cui nonostante ebbero le dottrine della caduta dei gravi la loro <lb/>pi&ugrave; autorevole conferma. </s>

<s>Nello scolio alla proposizione XL del III libro <emph type="italics"/>Dei <lb/>principii<emph.end type="italics"/> s'hanno descritte le pi&ugrave; diligenti esperienze intorno ai gravi, di <lb/>vario peso e di vario volume, lasciati andar dal comignolo della chiesa di <lb/>San Paolo di Londra, e nel mese di Giugno del 1710 dall'Autore stesso os&shy;<lb/>servati. </s></p><p type="main">

<s>I precedenti sperimentatori non avevano operato mai soli, ma sempre <lb/>con l'aiuto di uno almeno o di pi&ugrave; compagni, i quali non sempre erano <lb/>cos&igrave; destri, come, con quasi militar disciplina aveva il Riccioli ridotti i suoi <lb/>frati, che s'esercitavan da lui a pronunziare in dialetto bolognese i numeri <lb/><emph type="italics"/>un, du, tri....<emph.end type="italics"/> con suono tanto veloce, da tener dietro al moto dei velo&shy;<lb/>cissimi pendoli oscillanti. </s>

<s>Erano per tale esercizio divenuti s&igrave; esperti che, <lb/>venendosi a fare il riscontro tra le vibrazioni contate da quelli di sopra la <lb/>torre, e le contate in terra dallo stesso Riccioli, si trov&ograve; sempre, nei ripe&shy;<lb/>tuti esperimenti &ldquo; nunquam discrimen inter nos fuisse unius integrae vi&shy;<lb/>bratiunculae, quod scio vix creditum iri a quibusdam, et tamen verissime <lb/>ita fuisse testor &rdquo; (Almag., T. II cit., pag. </s>

<s>385). </s></p><p type="main">

<s>Non tutti potendo istituire una cos&igrave; disciplinata milizia, il Newton trov&ograve; <lb/>ingegnosamente il modo di far da s&egrave; solo, col posare i gravi, consistenti in <lb/>due palloni di vetro, uno pien di mercurio e l'altro d'aria, su un'assicella <lb/>che, rovesciata, facevali ambedue cader nel medesimo tempo. </s>

<s>Il sostegno che, <lb/>venendo meno all'assicella, doveva farla cos&igrave; traboccare, si levava di terra, <lb/>per mezzo di un fil di ferro, il quale, nell'atto stesso che si tirava, dava <lb/>l'andare al pendolo. </s>

<s>&ldquo; Tabula lignea ad unum eius terminum polis ferreis <lb/>suspendebatur, ad alterum pessulo ligneo incumbebat, et globi duo, huic ta&shy;<lb/>bulae impositi, simul demittebantur, subtrahendo pessulum ope fili ferrei ad <lb/>terram usque demissi, et eodem temporis momento pendulum ad minuta <lb/>secunda oscillans, per filum illud ferreum tractum, demitteretur et oscillare <lb/>inciperet &rdquo; (T. III cit., pag. </s>

<s>332). </s></p><p type="main">

<s>Ripet&egrave; gli esperimenti, dal medesimo luogo, il solertissimo Hauksbec, <lb/>e il d&igrave; 25 Aprile del 1719 il Desaguliers gl&igrave; riprese, ripetendogli il d&igrave; 14 di <lb/>Luglio di quel medesimo anno, secondo che apparisce dal N.o 362 delle <emph type="italics"/>Fi&shy;<lb/>losofiche transazioni,<emph.end type="italics"/> e secondo riferisce nel sopra citato scolio il Newton, <pb xlink:href="020/01/2045.jpg" pagenum="288"/>il quale racconta come, per aver globi della maggior leggerezza possibile, <lb/>che pi&ugrave; degli altri risentissero nel cadere gl'impedimenti dell'aria, s'accon&shy;<lb/>ciasse esso Desaguliers di propria mano vessiche suine. </s>

<s>&ldquo; Tempora autem <lb/>mensurabantur pendulis, ad dimidia minuta secunda oscillantibus. </s>

<s>Et eorum, <lb/>qui in terra stabant, unus habebat horologium cum elatere ad singula mi&shy;<lb/>nuta secunda, quater vibrante. </s>

<s>Alius habebat machinam aliam affabre con&shy;<lb/>structam, cum pendulo etiam ad singula minuta secunda quater vibrante. </s>

<s><lb/>Et similem machinam habebat unus eorum, qui stabant in summitate Tem&shy;<lb/>pli. </s>

<s>Et haee instrumenta ita formabantur, ut motus eorum pro lubitu vel <lb/>inciperet, vel sisteretur &rdquo; (ibid., pag. </s>

<s>335). </s></p><p type="main">

<s>Veniva da tali esperienze, pi&ugrave; precise di tutte le precedenti, che abbia <lb/>in tal proposito a raccontare la storia, e insuperabili forse ai futuri speri&shy;<lb/>mentatori; a confermarsi direttamente il teorema del Newton, che cio&egrave; in <lb/>qualunque fluido <emph type="italics"/>caeteris paribus<emph.end type="italics"/> le resistenze son proporzionali alla den&shy;<lb/>sit&agrave;, e indirettamente, e per necessaria conseguenza, veniva anche insieme <lb/>a confermarsi il teorema di Galileo. </s></p><p type="main">

<s>Ma il teorema galileiano della caduta dei gravi si concludeva in somma <lb/>nella proposizione che, levato ogni impedimento, ossia nel vuoto, i corpi, di <lb/>qualunque mole e di qualunque specie, si vedrebbero ivi andare ugualmente <lb/>veloci. </s>

<s>Non era questa per&ograve; altro che un'induzione dall'esperienze fatte in <lb/>mezzi via via sempre pi&ugrave; rari, giacch&egrave; l'esperienza diretta &ldquo; &egrave; forse, diceva <lb/>Galileo, impossibile a farsi &rdquo; (Alb. </s>

<s>II, 327): </s></p><p type="main">

<s>Occorse finalmente l'invenzione della Macchina pneumatica, presentita <lb/>in quel <emph type="italics"/>forse,<emph.end type="italics"/> e il Boyle, percorrendo quasi tutto il campo della Fisica, non <lb/>avrebbe lasciata questa parte indietro, se avesse potuto procurarsi tubi di <lb/>vetro della necessaria lunghezza. </s>

<s>Il Newton in ogni modo volle, come gli <lb/>era possibile, fare il primo esperimento, il quale per&ograve; non riusc&igrave; decisivo, <lb/>perch&egrave;, in altezze inferiori a un metro, si vedono anche in mezzo all'aria <lb/>cadere in un tempo i corpi gravi e i leggeri. </s>

<s>Il Desaguliers allora attese a <lb/>costruire una colonna di tubi congiunti insieme con mastice, e sostenuti <lb/>su su da traverse di legno, fissate da una parte e dall'altra, come i gradi <lb/>di una scala, a due staggi eretti sulla base della macchina, cosicch&egrave; pot&egrave; <lb/>comporne un tubo andante di vetro lungo presso a quattro metri. </s>

<s>Fattosi <lb/>in cotesto tubo il vuoto, nel Settembre del 1717, si dette pubblico spetta&shy;<lb/>colo, essendovi presente il Re, e il principe di Walles, i quali videro ma&shy;<lb/>ravigliati cader nello stesso tempo una ghinea e un bocconcello di carta. </s></p><p type="main">

<s>Il Gravesande descrisse poi, con la sua solita minuziosa diligenza, una <lb/>macchina &ldquo; qua duo corpora in vacuo eodem momento demittuntur &rdquo; (Phy&shy;<lb/>sices elem., T. II, Leidae 1748, pag. </s>

<s>618-24) perch&egrave; veramente la maggior <lb/>difficolt&agrave;, e la cura pi&ugrave; necessaria per la precisione dell'esperienza, consiste <lb/>nel lasciare i due corpi a un tempo: ci&ograve; che in questa macchina s'otteneva <lb/>per mezzo di una morsetta, un labbro della quale essendo elastico, s'allon&shy;<lb/>tanava dall'altro immobile, per mezzo di un filo di ferro. </s>

<s>Erano anzi que&shy;<lb/>ste morsette sei, disposte intorno al centro di un esagono, per cui, fatto <pb xlink:href="020/01/2046.jpg" pagenum="289"/>addentare a ciascuna di esse o la medesima coppia o differenti coppie com&shy;<lb/>poste di un grave e di un leggero, introdotte tutte insieme, cos&igrave; saldate sulla <lb/>lamina esagonale, nella sommit&agrave; del tubo, che veniva per ci&ograve; esattamente <lb/>chiuso; si poteva sei volte, col non far altro che girare una vite, la quale <lb/>riducesse a basso ora una morsa ora un'altra, ripetere sei volte lo spetta&shy;<lb/>coloso esperimento. </s>

<s>Era il tubo del resto costruito di pezzi saldati insieme <lb/>con cera, e montato come quello del Desaguliers, bench&egrave; l'altezza della <lb/>colonna non aggiungesse bene a due metri. </s></p><p type="main">

<s>Anche il Wolf, nel cap. </s>

<s>I del II tomo della Fisica sperimentale, dove <lb/>tratta <emph type="italics"/>De lapsu corporum gravium,<emph.end type="italics"/> descrisse un apparecchio per lasciare <lb/>andare a un tempo i due cadenti nel tubo vuoto; apparecchio, che consi&shy;<lb/>steva in una specie di staffa, formata dalla congiunzione di due lamine ela&shy;<lb/>stiche, che si potevano separare e cos&igrave; lasciavano in abbandono i corpi ivi <lb/>sopra posati, tutte le volte che, per mezzo di un filo, da potersi tirar di <lb/>fuori, si venivano ad allontanare gli elastri &rdquo; (Versio latina, Venetiis 1756, <lb/>pag. </s>

<s>15-18). </s></p><p type="main">

<s>Si tolgono ora gli sperimentatori d'ogni sollecitudine col capovolgere il <lb/>tubo, in cui sieno stati posti gli oggett&igrave;, prima di fare il vuoto, e col chiu&shy;<lb/>dere, per mezzo di una chiavetta, l'ingresso all'aria, la quale, riammessa a <lb/>poco per volta, fa notar sempre maggiore la differenza fra la caduta del corpo <lb/>grave e del leggero. </s>

<s>Cos&igrave;, dopo due secoli, la speculazione del Benedetti <lb/><emph type="italics"/>quod in vacuo corpora aequali velocitate moverentur,<emph.end type="italics"/> si riduceva al pi&ugrave; <lb/>certo fatto sperimentale. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>La semplice osservazione, ovvia a tutti, senz'altro artificio di macchi&shy;<lb/>namenti, dava certezza di questo fatto: che anche in mezzo all'aria i corpi <lb/>gravi resi, con l'andare, a vincere ogni impedimento sempre pi&ugrave; validi, <lb/>tanto si vanno pi&ugrave; affrettando nel loro moto, quanto pi&ugrave; si dilungano dal <lb/>loro principio. </s>

<s>Rimaneva al Filosofo per&ograve; l'ufficio d'investigar le cause di <lb/>cos&igrave; fatto acceleramento, intorno a che ebbero gli Antichi tanto poco ragio&shy;<lb/>nevoli, e cos&igrave; strane opinioni, che dal troppo debole impulso ricevuto non <lb/>molto ebbe a progredire la scienza, quando vennesi a restaurare in tempi <lb/>a noi meno lontani. </s></p><p type="main">

<s>Leonardo da Vinci, com'attribuiva al mezzo la causa del ritardarsi il <lb/>moto nei liberi cadenti, cos&igrave; attribuiva alla medesima causa il velocitarsi, <lb/>perch&egrave; il grave, diceva, mette nel cadere in circolar moto ondoso l'aria, <lb/>attraverso alla quale egli passa &ldquo; e cos&igrave;, cacciando l'un circolo l'altro, <lb/>l'aria, che &egrave; dinanzi al suo motore, tutta per quella linea &egrave; preparata al <lb/>movimento, il quale tanto pi&ugrave; cresce, quanto se le appressa il peso che la <lb/>caccia. </s>

<s>Onde, trovando esso peso men resistenza d'aria, con pi&ugrave; velocit&agrave; rad-<pb xlink:href="020/01/2047.jpg" pagenum="290"/>doppia suo corso, a similitudine della barca tirata per l'acqua &rdquo; (Manuscr. </s>

<s>A <lb/>cit., fol. </s>

<s>43 ad t.). </s></p><p type="main">

<s>Il Tartaglia trovava quelle medesime tradizioni, ch'erano venute prima <lb/>a inspirare la scienza di Leonardo, col quale anch'egli dimostra che, messa <lb/>l'aria sotto il cadente in moto, questa muove innanzi a s&egrave; l'altr'aria con&shy;<lb/>tigua, &ldquo; ita ut illa mota gravitatem descendentem impediat minus, unde gra&shy;<lb/>vius efficitur et cadentia amplius impelli, ita ut iam non impellantur, sed <lb/>etiam trahant. </s>

<s>Sicque fit ut illius gravitas tractu illorum adiuvatur, et mo&shy;<lb/>tus eorum gravitate ipsius augetur, unde et velocitatem illius continue mul&shy;<lb/>tiplicare constat &rdquo; (Opusc. <emph type="italics"/>De ponderositate<emph.end type="italics"/> cit., fol. </s>

<s>14). </s></p><p type="main">

<s>Ripete anche il Cardano, nella proposizione XIII dell'<emph type="italics"/>Opus novum,<emph.end type="italics"/> le <lb/>medesime cose, dimostrando che &ldquo; in omni corpore mobili in medio partes <lb/>medii resistunt obviae, aliae impellunt &rdquo; (Op. </s>

<s>omnia, T. IV cit, pag. </s>

<s>477), <lb/>ma nella XXX e XXXI proposizione della medesima Opera comincia ad ap&shy;<lb/>parire un raggio incerto di luce che consola, come dopo una notte lunga <lb/>l'albeggiare del giorno. </s>

<s>L'acceleramento non dipende solo dalla causa estrin&shy;<lb/>seca del mezzo, ma dalla intrinseca della gravit&agrave;, la qual causa motiva &ldquo; cum <lb/>sit perpetua, et a principio aeterno, quod per dicta aequaliter movet, igitur <lb/>motus ille fiet velocior in fine, quam in alia parte temporis &rdquo; (ibid.). Secondo <lb/>questo cardanico concetto il moto accelerato non sarebbe altro dunque che <lb/>l'equabile, a cui sopraggiungon via via sempre nuovi impulsi equabilmente <lb/>crescenti; concetto sottilissimo e, come si diceva, albore di un nuovo sole, <lb/>che a quegli occhi sonnolenti per&ograve; non si discerneva ancora ben dalle te&shy;<lb/>nebre. </s>

<s>Di qui &egrave; che i seguaci del Cardano non seppero accoglier, delle dot&shy;<lb/>trine di lui, se non quelle sole, che si confacevano meglio con le correnti <lb/>opinioni, come accadde a quel Principe nel dialogo del Moleto, che noi ri&shy;<lb/>prendiamo in mano per seguitare a trascriverlo ai nostri Lettori: </s></p><p type="main">

<s>&ldquo; Vorrei intendere, dice l'Autore a Sua Altezza, se fosse possibile di&shy;<lb/>mostrare perch&egrave; il grave, quanto pi&ugrave; discende, tanto pi&ugrave; viene velocitandosi, <lb/>perch&egrave; mi pare di avere sentito dire non so che di luogo..... &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; Dir&ograve; a V. S. intorno a ci&ograve; molte sono state le opinioni, ma le <lb/>famose sono l'una del luogo, l'altra del movimento, la terza rispetto al <lb/>modo, e questa par che abbia del dimostrativo. </s>

<s>Quanto al luogo, molti hanno <lb/>detto che il luogo &egrave; cagione della velocit&agrave; del grave, e cos&igrave; del lieve, di&shy;<lb/>cendo che il grave appetisce l'andare al luogo suo, e per&ograve; quanto a quello <lb/>pi&ugrave; si appressa, tanto pi&ugrave; si velocita, per arrivar pi&ugrave; presto a quello. </s>

<s>Il che <lb/>non pare che possa essere vero, essendo che, quando cos&igrave; fosse, nel grave <lb/>verrebbe ad essere una virt&ugrave; conoscente, cosa fuori del ragionevole. </s>

<s>L'altra <lb/>&egrave; del movimento, perciocch&egrave;, essendo il movimento l'atto del mobile, e l'atto <lb/>essendo la perfezion della cosa, adunque, quando il grave si muove &egrave; nella <lb/>sua perfezione. </s>

<s>Ma chi &egrave; gi&agrave; in atto segue l'operazione, che da quell'atto <lb/>viene, con pi&ugrave; facilit&agrave; nell'ultimo, che nel principio e nel mezzo; adunque, <lb/>cominciando il grave a moversi, non si muove con quella facilit&agrave;, che fa dopo <lb/>che si sar&agrave; mosso per alquanto di spazio, essendo che viene alterandosi di <pb xlink:href="020/01/2048.jpg" pagenum="291"/>mano in mano, e per&ograve;, quanto pi&ugrave; si mover&agrave;, con tanto pi&ugrave; facilit&agrave; verr&agrave; <lb/>a moversi, e per consequente con tanto pi&ugrave; velocit&agrave;. </s>

<s>Da dove &egrave; che con pi&ugrave; <lb/>velocit&agrave; si move nel fine, che nel principio e nel mezzo. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A.<emph.end type="italics"/> &mdash; Questa mi pare dimostrazione, e nella quale non &egrave; cosa al&shy;<lb/>cuna da negare, e parmi simile alle ragioni, che si dicono nelle morali, che, <lb/>come l'uomo ha acquistato l'abito delle virt&ugrave;, le fa senza fatica, e quanto <lb/>pi&ugrave; opera, tanto pi&ugrave; apprende. </s>

<s>&Egrave; simile ancora a quello che diciamo del&shy;<lb/>l'intendere, che l'intelletto non s'affatica nell'intendere, e son certo che, se <lb/>Franceschino che suona l'organo di S. Barbera, non sentisse il travaglio del <lb/>corpo, che quanto pi&ugrave; sonasse, tanto pi&ugrave; sonerebbe: ma &egrave; forza che all'ul&shy;<lb/>timo le membra s'affatichino. </s>

<s>Ci&ograve; non pu&ograve; avvenire al grave, poich&egrave; le parti <lb/>sue non s'affaticano nel discendere, per esser cosa inanimata, e per&ograve;, come <lb/>V. A. ha detto, e bene, pi&ugrave; e pi&ugrave; si velocita dall'attivarsi pi&ugrave; e pi&ugrave; col <lb/>discendere, ed io quanto a me mi contenterei di questa sola ragione. </s>

<s>Ma se <lb/>V. A., per suo contento, vuol dire l'altra, io l'udir&ograve; volentieri. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; P.<emph.end type="italics"/> &mdash; Poich&egrave; si &egrave; nominata, &egrave; bene dirla, perch&egrave; acquieta non meno <lb/>della pur ora detta, ed &egrave; messa dal Cardano. </s>

<s>S'ha da provare che il grave <lb/>discendendo, quanto pi&ugrave; discende, tanto pi&ugrave; si far&agrave; veloce nel movimento <lb/>suo, essendo tale il movimento suo naturale. </s>

<s>Si presuppone con verit&agrave; che <lb/>l'aria sia l'impedimento al movimento del grave, poich&egrave;, come prova Ari&shy;<lb/>stotile, quando dal concavo della Luna infino al centro dell'universo non <lb/>fosse corpo di sorta alcuna, o fosse il luogo vacuo, il movimento si farebbe <lb/>in istante. </s>

<s>Ma quanto pi&ugrave; l'aria &egrave; presso, tanto pi&ugrave; si condensa, e quanto <lb/>pi&ugrave; &egrave; condensata, tanto pi&ugrave; resiste al movimento del grave. </s>

<s>Adunque, men&shy;<lb/>tre il grave si muove, quanto pi&ugrave; &egrave; lontano dal luogo, dove ha da andare, <lb/>tanto pi&ugrave; ha d'impedimento, poich&egrave; tanto pi&ugrave; aria ha da passare, e per con&shy;<lb/>sequente condensata dal peso del grave, e per&ograve; pi&ugrave; tardi sar&agrave; il movimento. </s>

<s><lb/>Ma quanto pi&ugrave; discender&agrave;, tanto meno aver&agrave; d'impedimento, e per&ograve; pi&ugrave; ve&shy;<lb/>loce sar&agrave;. </s>

<s>Giugniamo a questo che se noi intenderemo il grave A (fig. </s>

<s>138) <lb/><figure id="id.020.01.2048.1.jpg" xlink:href="020/01/2048/1.jpg"/></s></p><p type="caption">

<s>Figura 138.<lb/>nel concavo della Luna, inteso per DE, nel <lb/>dispiccarsi da quel luogo, intendendo il piano <lb/>della Terra essere FG, aver&agrave; il cilindro ABH <lb/>d'aria densa da passare, e dopo lui non <lb/>sar&agrave; aria che le succeda. </s>

<s>Ma quando il corpo <lb/>A sar&agrave; venuto nel B, oltre che aver&agrave; solo <lb/>il cilindro BH da passare, che resister&agrave; meno <lb/>di quel che faceva ABH; aver&agrave; l'aria AB <lb/>che, succedendogli per ragione del vacuo, <lb/>verr&agrave; con l'impulso suo a velocitare il mo&shy;<lb/>mento del grave. </s>

<s>E per consequente, quanto <lb/>pi&ugrave; discender&agrave;, tanto maggiore impulso <lb/>aver&agrave;, e minore resistenza, e per&ograve; maggiore sar&agrave; sempre la sua velocit&agrave;. </s>

<s><lb/>Laddove, quando sar&agrave; in H, sar&agrave; di maggior velocit&agrave;, che quand&ograve; sar&agrave; <lb/>in B, per le allegate ragioni. </s>

<s>E cos&igrave; &egrave; vero che, quanto pi&ugrave; il grave di-<pb xlink:href="020/01/2049.jpg" pagenum="292"/>scender&agrave;, con tanto maggior velocit&agrave; si mover&agrave;. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Appendice cit., <lb/>fol. </s>

<s>6-8). </s></p><p type="main">

<s>Non si decide bene dalla forma del dialogo se preferiscasi quest'ultima <lb/>ragione del luogo, a quella precedentemente detta <emph type="italics"/>del modo<emph.end type="italics"/> giudicandosi <lb/>forse l'una e l'altra ugualmente dimostrativa: questa per l'autorit&agrave; del Car&shy;<lb/>dano, ma quella per una certa ragione, che acquietava la mente, perch&egrave; ve&shy;<lb/>devasi sotto una veste simbolica trasparir qualche effigie del vero. </s>

<s>Notabile <lb/>che, in alcuni pensieri di Galileo copiati dal Viviani, si trovi quasi il me&shy;<lb/>desimo concetto espresso in forme simili a quelle del Moleto. </s></p><p type="main">

<s>&ldquo; La forza del vento, diceva, non subito imprime la massima velocit&agrave; <lb/>alla nave, ma successivamente e con tempo, avvegnach&egrave; nel principio la <lb/>trovi immota, e di mano in mano opera sopra il mobile continuamente ef&shy;<lb/>fetto di maggiore velocit&agrave;. </s>

<s>N&egrave; dobbiamo porre alcuna differenza tra gl'im&shy;<lb/>pulsi dati per intervalli, e quello che vien conferito con forza continuata, <lb/>perch&egrave; siccome tra gl'impulsi interrotti nessuna variet&agrave; si deve considerare, <lb/>se talvolta in dieci minuti di tempo si dieno venti scosse o trenta, o cento <lb/>o mille; cos&igrave; neanche pu&ograve; cadere alcuna alterazione tra quelli e l'impulso <lb/>continuato, non essendo questo altro che una frequentissima moltitudine di <lb/>spinte, cio&egrave; infinite, dentro allo stesso tempo. </s>

<s>Non basta dunque che il mo&shy;<lb/>bile, il mezzo e la facolt&agrave; sieno sempre le stesse a fare l'introduzione di una <lb/>tanta celerit&agrave;, ma vi vuole, partendosi il mobile dalla quiete, una succes&shy;<lb/>sione di tempo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In simil guisa penso io che proceda il negozio nei mobili naturali, <lb/>partendosi dalla quiete, dove da qualche impedimento erano ritenuti, purch&egrave; <lb/>il mezzo sia sempre lo stesso, lo stesso il mobile, e la stessa la gravit&agrave; mo&shy;<lb/>vente. </s>

<s>Tuttavia essa gravit&agrave; sul principio opera sopra un mobile non abi&shy;<lb/>tuato di moto alcuno, ma poi successivamente va operando sopra mobile <lb/>affetto di velocit&agrave;, onde, operando essa virt&ugrave; nel modo stesso, muove p&igrave;&ugrave;, <lb/>perch&egrave; accresce moto sopra mobile, ch'ella ritrova in moto. </s>

<s>&rdquo; (MSS. Gal., <lb/>P. V, T. IV, fol. </s>

<s>14 a tergo). </s></p><p type="main">

<s>Se non era questo il formato concetto del vero, n'era per&ograve; il germe <lb/>fecondo, che ora diremo come si venisse a svolgere e ad apparire. </s>

<s>All'aria, <lb/>infino a mezzo il secolo XVI, s'attribuiva dai pi&ugrave; il mantenersi tuttavia in <lb/>moto il proietto, anche uscito fuori e abbandonato dal proiiciente, ma il Car&shy;<lb/>dano, esaminando nel libro <emph type="italics"/>De subtilitate<emph.end type="italics"/> intorno a ci&ograve; le varie opinioni, <lb/>per prima egli annovera quella della virt&ugrave; rimasta impressa nel mobile, come <lb/>il calore nell'acqua; &ldquo; sed nos (poi all'ultimo conclude, dop'avere esposte <lb/>altre tre varie opinioni) indigemus prima, quae est simplicissima, et etiam <lb/>non tantas difficultates patitur, et cum supponitur quod omne quod mo&shy;<lb/>vetur ab aliquo movetur, verissimum est, sed illud quod movet est im&shy;<lb/>petus acquisitus, sicut calor in aqua, qui est ibi praeter naturam ab igne in&shy;<lb/>ductus, et tamen, igne sublato, manum tangentibus exurit &rdquo; (Lugduni 1580, <lb/>pag. </s>

<s>93). </s></p><p type="main">

<s>La divisione che si faceva tra il moto naturale e il violento, creduti <pb xlink:href="020/01/2050.jpg" pagenum="293"/>sull'autorit&agrave; di Aristotile di natura diversa, non lasciava al Cardano appli&shy;<lb/>care ai cadenti il verissimo principio della forza, che rimane impressa nei <lb/>proietti, e bench&egrave; ne avesse pur qualche sentore, come apparisce dalla <lb/>XXXI proposizione, da noi poco addietro citata, pure il passo, che dovea <lb/>ridur la scienza alle mani di Galileo, non fu fatto da altri, prima che dal <lb/>Benedetti. </s>

<s>Nel cap. </s>

<s>XXIV Delle disputazioni, dop'aver confutato Aristotile <lb/>con dir che l'aria, tutt'altrimenti che mantenere il moto nel proiiciente, anzi <lb/>glielo impedisce, &ldquo; huiusmodi, soggiunge, corporis separatim a primo mo&shy;<lb/>vente velocitas oritur a quadam naturali impressione, ex impetuositate re&shy;<lb/>cepta a dicto mobili, quae impressio et impetuositas, in motibus rectis na&shy;<lb/>turalibus, continuo crescit, cum perpetuo in se causam moventem, idest <lb/>propensionem eundi ad locum, et a natura assignatum habeat &rdquo; (Specul. </s>

<s><lb/>lib. </s>

<s>cit., pag. </s>

<s>184). </s></p><p type="main">

<s>Ecco finalmente scoperta, e rivelata la vera causa fisica dell'accelerarsi <lb/>i cadenti, ne'quali riman la virt&ugrave; della gravit&agrave; impressa, dopo il principio <lb/>del moto, come riman la virt&ugrave; del proiiciente impressa tuttavia nel proietto. </s>

<s><lb/>Aristotile dunque, cos&igrave; prosegue il Benedetti a spiegare il suo pensiero, non <lb/>doveva dire che, quanto pi&ugrave; s'avvicina il corpo al termine <emph type="italics"/>ad quem,<emph.end type="italics"/> ma <lb/>piuttosto che, quanto pi&ugrave; si dilunga dal termine <emph type="italics"/>a quo,<emph.end type="italics"/> tanto pi&ugrave; cadendo <lb/>si fa veloce, &ldquo; quia tanto maior fit semper impressio, quanto magis move&shy;<lb/>tur naturaliter corpus, et continuo novum impetum recipit, cum in se mo&shy;<lb/>tus causam contineat, quae est inclinatio ad locum suum eundi, extra quem <lb/>per vim consistit &rdquo; (ibid.). </s></p><p type="main">

<s>Chi dubitasse ancora se quei primi scritti galileiani <emph type="italics"/>De motu<emph.end type="italics"/> siano ve&shy;<lb/>ramente, come noi gli qualificammo, esercitazioni sopra i libri del Benedetti, <lb/>pu&ograve; con facilit&agrave; persuadersene, rileggendo quel capitolo. </s>

<s>&ldquo; In quo causa ac&shy;<lb/>celerationis motus naturalis in fine, in medio affertur &rdquo; (Opere, ediz. </s>

<s>naz. </s>

<s><lb/>cit., pag. </s>

<s>315-23) che &egrave; un lungo e luminoso commento delle parole ulti&shy;<lb/>mamente citate dal libro <emph type="italics"/>Delle disputazioni.<emph.end type="italics"/></s></p><p type="main">

<s>La quiete del grave fuori del centro &egrave; una violenza, secondo il Bene&shy;<lb/>nedetti, simile a quella fatta allo stesso grave, che la mano o la fionda git&shy;<lb/>tano in su, dilungandolo dal suo centro, cosicch&egrave; i due moti di scesa e di <lb/>salita, bench&egrave; in apparenza contrarii, dipendono dalla medesima causa, e <lb/>nell'uno e nell'altro &egrave; della naturalit&agrave; e della violenza la medesima pro&shy;<lb/>porzione. </s>

<s>In piena conformit&agrave; con le quali speculazioni scriveva Galileo: <lb/>&ldquo; Io non credo che voi fuste renitenti a concedermi che l'acquisto dei gradi <lb/>di velocit&agrave; del sasso, cadente dallo stato di quiete, possa farsi col medesimo <lb/>ordine, che la diminuzione e perdita dei medesimi gradi, mentre da virt&ugrave; <lb/>impellente fusse ricacciato in su alla medesima altezza &rdquo; (Alb. </s>

<s>XIII, 158). <lb/>Conseguiva di qui che un tal grave &ldquo; non persista per verun tempo quanto <lb/>in alcun medesimo grado di velocit&agrave; &rdquo; (ivi) e che l'accelerazione dipenda <lb/>dall'essere la virt&ugrave; impressa superata e vinta dalla gravit&agrave; prevalente: che <lb/>sono i principii da Galileo premessi alla dimostrazion della legge, secondo <lb/>la quale si fa la detta accelerazione rispetto agli spazii e ai tempi. </s>

<s>La grande <pb xlink:href="020/01/2051.jpg" pagenum="294"/>scoperta scaturiva dalle medesime fonti, come vedremo, dop'averne ricer&shy;<lb/>cati e brevemente corsi i sotterranei diverticoli. </s></p><p type="main">

<s>I pi&ugrave; Antichi, per l'insufficienza dei sensi a giudicare la proporzion <lb/>degli spazii, in moti tanto veloci, e per la mancanza dei necessari strumenti, <lb/>non ebbero forse speranza di ritrovar la legge dell'acceleramento dei gravi. </s>

<s><lb/>I naturali effetti della percossa incominciaron poi a ingerir nell'animo qual&shy;<lb/>che lusinga perch&egrave;, vedendosi per esperienza che quanto un grave cade pi&ugrave; <lb/>d'alto, produce tanto pi&ugrave; valido colpo, e sembrando assai verosimile che, <lb/>rimanendosi la gravit&agrave; la stessa, si dovesse alla sola velocit&agrave; la maggior forza <lb/>acquistata; fu pensato che questa potess'essere di quella stessa velocit&agrave; la <lb/>pi&ugrave; giusta misura. </s>

<s>S'informano a cos&igrave; fatti pensieri in ogni modo quelle <lb/>proposizioni intorno ai moti accelerati, che primo venne in pubblico a di&shy;<lb/>mostrar nella sua <emph type="italics"/>Nuova scientia<emph.end type="italics"/> il Tartaglia. </s></p><p type="main">

<s>&ldquo; El si suppone, egli dice, che il corpo ugualmente grave vada pi&ugrave; ve&shy;<lb/>loce, dove fa, ovvero faria, per comun sentimento, maggiore effetto in un <lb/>resistente. </s>

<s>&mdash; Quanto pi&ugrave; un grave, egualmente grave, verr&agrave; da grande altezza <lb/>di moto naturale, tanto maggiore effetto far&agrave; in un resistente &rdquo; (In Vene&shy;<lb/>tia 1537, fol. </s>

<s>11 a tergo). </s></p><p type="main">

<s>Date queste definizioni e fatte queste ipotesi, passa l'Autore a dimo&shy;<lb/>strar le due seguenti proposizioni, nelle quali si conclude insomma tutta la <lb/>nuova scienza dei moti accelerati. </s>

<s>&Egrave; la prima proposizione cos&igrave; formulata: <lb/>&ldquo; Ogni corpo ugualmente grave nel moto naturale, quanto pi&ugrave; el se ander&agrave; <lb/>aluntanando dal suo principio, ovvero approprinquando al suo fine, tanto <lb/>pi&ugrave; ander&agrave; veloce &rdquo; (ivi, fol. </s>

<s>12), e la seconda: &ldquo; Tutti li corpi egual&shy;<lb/>mente gravi, simili ed eguali, dal principio delli loro movimenti naturali si <lb/>partiranno da egual velocit&agrave;, ma giongendo al fine di tali lor movimenti, <lb/>quello, che avr&agrave; transito per pi&ugrave; lungo spazio, ander&agrave; pi&ugrave; veloce &rdquo; (ivi, <lb/>fol. </s>

<s>13 a t.). </s></p><p type="main">

<s>Che siano le velocit&agrave; proporzionali agli spazii fu creduto, come vedemmo, <lb/>anche da Leonardo da Vinci, il quale propose quella sua esperienza della <lb/>tavoletta lutata, da ritenere in s&egrave; impressi i globi cadenti nelle loro varie <lb/>stazioni. </s>

<s>Bench&egrave; si comprenda come non si potesse un tale strumento far a <lb/>nessun pi&ugrave; esperto sperimentatore rivelator fedele de'ricercati effetti natu&shy;<lb/>rali, non si sa per&ograve; se si volgesse Leonardo a fare esperienze della percossa, <lb/>che all'ingegno fecondamente inventivo di lui si sarebbero presentate a fare <lb/>in varie maniere, come per esempio deducendo la proporzion della forza <lb/>dall'intensit&agrave; del suono, dallo stritolamento, dalle ripercussioni e da simili <lb/>altri effetti, che si sogliono variamente produrre dai varii corpi percossi. </s>

<s>Ma <lb/>com'era possibile a ritrovar le misure proporzionali tra il fragore prodotto <lb/>o il numero de'frantumi, in che riducesi per esempio un piatto di porcel&shy;<lb/>lana, sotto i colpi di una palla di piombo lasciata ora cader da un'altezza, <lb/>ora da un'altra doppia o tripla? </s>

<s>S'intende come la difficolt&agrave; dovess'essere, <lb/>a qualunque arte sperimentale, specialmente a que'tempi, insuperabile, ben&shy;<lb/>ch&egrave; non si creda da noi fosse stato per sfuggire alla diligenza di Leonardo <pb xlink:href="020/01/2052.jpg" pagenum="295"/>l'osservazione del fatto, che cio&egrave; i frantumi di una sfera di argilla secca, <lb/>per esempio, o di un vuoto globo di vetro, venuti dall'altezza di venti metri, <lb/>fanno segno d'esser l'effetto di un colpo qualche cosa pi&ugrave; del doppio di <lb/>quello, dai medesimi corpi risentito nel cader dall'altezza di soli dieci metri. </s></p><p type="main">

<s>Tanto in qualunque modo lusingava la semplicit&agrave; della serie dei numeri <lb/>naturali, assegnata per legge agl'incrementi degli spazii, e tanto verosimile <lb/>appariva essere gli effetti delle percosse proporzionali alle altezze, che nei <lb/>primi anni del secolo XVII si trov&ograve; sedotto da una tal fallacia anche Gali&shy;<lb/>leo, il quale pubblicamente confess&ograve; essergli da principio sembrata cosa da <lb/>non si mettere in dubbio &ldquo; che quel grave, che viene dall'altezza di sei <lb/>braccia, non abbia e percota con impeto doppio di quello, che ebbe, sceso <lb/>che fu tre braccia, e triplo di quello che ebbe alle due, e sescuplo dell'avuto <lb/>nello spazio di uno &rdquo; (Alb. </s>

<s>XIII, 161). Cosicch&egrave;, dietro questi fatti speri&shy;<lb/>mentali creduti verissimi, ebbe anch'egli, insieme con tutti gli altri, a de&shy;<lb/>finire: &ldquo; Moto uniformemente accelerato esser quello, nel quale la velocit&agrave; <lb/>andasse crescendo, secondo che cresce lo spazio che si va passando &rdquo; (ivi). </s></p><p type="main">

<s>Ora &egrave; da veder come Galileo riuscisse felicemente il primo a scoprir <lb/>la fallacia, che si conteneva in questa definizione, argomentando dalle pro&shy;<lb/>priet&agrave; de'moti uniformi, benissimo conosciute anco agli Antichi, e dimo&shy;<lb/>strate da Archimede nel libro Delle spirali. </s>

<s>Resultando da cosi fatte propo&shy;<lb/>sizioni com'avendosi le velocit&agrave; proporzionali agli spazii i tempi sono uguali, <lb/>si scopriva l'addotta definizione falsa e impossibile, quanto che il moto si <lb/>faccia in un istante, come Galileo stesso dimostrava col seguente evidentis&shy;<lb/>simo ragionamento: &ldquo; Quando le velocit&agrave; hanno la medesima proporzione <lb/>che gli spazii passati o da passarsi, tali spazii vengono passati in tempi eguali. </s>

<s><lb/>Se dunque le velocit&agrave;, con le quali il cadente pass&ograve; lo spazio di quattro brac&shy;<lb/>cia, furon doppie delle velocit&agrave;, con le quali pass&ograve; le due prime braccia (sic&shy;<lb/>come lo spazio &egrave; doppio dello spazio) adunque i tempi di tali passaggi sono <lb/>uguali. </s>

<s>Ma passare il medesimo mobile le quattro braccia e le due nell'istesso <lb/>tempo non pu&ograve; aver luogo, fuor che nel moto istantaneo, e noi vediamo che <lb/>il grave cadente fa suo moto in tempo, ed in minore passa le due braccia, <lb/>che le quattro; adunque &egrave; falso che la velocit&agrave; sua cresca come lo spazio &rdquo; <lb/>(ivi, pag. </s>

<s>161, 62). </s></p><p type="main">

<s>Scopertasi cos&igrave; la fallacia, e l'impossibilit&agrave; della proposizion del Tarta&shy;<lb/>glia e di tutti coloro, che tenevano insiem con lui essere ne'cadenti le ve&shy;<lb/>locit&agrave; proporzionali agli spazii, &egrave; ammirabile la facilit&agrave; e la prontezza, con la <lb/>quale, applicando Galileo ai teoremi dei moti equabili le dottrine del Bene&shy;<lb/>detti, si trov&ograve; in mano la vera legge dei moti accelerati. </s>

<s>Se i tempi sono <lb/>eguali, le velocit&agrave; stanno come gli spazi, e se le velocit&agrave; sono uguali, gli <lb/>spazi stanno come i tempi. </s>

<s>Se sono gli spazi uguali, le velocit&agrave; son recipro&shy;<lb/>che dei tempi: essendo poi gli spazi diversi, hanno questi la ragion compo&shy;<lb/>sta delle velocit&agrave;, e dei tempi passati. </s></p><p type="main">

<s>Queste quattro proposizioni, dimostrate da Galileo nel I libro Dei mo&shy;<lb/>vimenti locali con gli antichi processi archimedei, si deducono a colpo d'oc-<pb xlink:href="020/01/2053.jpg" pagenum="296"/>chio, facendo uso dei simboli algebrici, dalle due equazioni V=S/T, <emph type="italics"/>v=s/t,<emph.end type="italics"/><lb/>intendendovi per V, <emph type="italics"/>v<emph.end type="italics"/> due diverse velocit&agrave;, come per S, <emph type="italics"/>s,<emph.end type="italics"/> e per T, <emph type="italics"/>t<emph.end type="italics"/> due <lb/>spazi, e due tempi diversi. </s>

<s>D'immediata conclusione di qui &egrave; pure la pro&shy;<lb/>porzione S:<emph type="italics"/>s<emph.end type="italics"/>=V.T:<emph type="italics"/>v.t,<emph.end type="italics"/> che rende dimostrato il teorema IV Dei moti <lb/>equabili, intorno al quale Galileo cos&igrave; meditava: Secondo la dottrina del Be&shy;<lb/>nedetti il moto accelerato non &egrave; altro che lo stesso moto equabile, <emph type="italics"/>qui con&shy;<lb/>tinuo novum impetum recipit.<emph.end type="italics"/> Or se fosse vero questo supposto, che cio&egrave; <lb/>gl'impeti o le velocit&agrave; crescono come i tempi, ne conseguirebbe che gli spazi <lb/>sarebbero proporzionali ai quadrati dei tempi. </s></p><p type="main">

<s>Facendo uso de'simboli algebrici, noi vediamo di una tal conseguenza <lb/>la dimostrazione immediata, sostituendo la ragione di T:<emph type="italics"/>t<emph.end type="italics"/> a quella di V:<emph type="italics"/>v<emph.end type="italics"/><lb/>nella proporzione ultimamente scritta, la quale vien perci&ograve; a trasformarsi in <lb/>quest'altra S:<emph type="italics"/>s<emph.end type="italics"/>=T2:<emph type="italics"/>t<emph.end type="italics"/>2. </s>

<s>Ma Galileo, senza simboli, ragionava allo stesso <lb/>modo in quest'altra forma, che il Viviani, nella sua nativa semplicit&agrave;, ci <lb/>conserv&ograve; trascritta: &ldquo; Quando la velocit&agrave; &egrave; l'istessa ed uniforme, gli spazi <lb/>passati hanno fra loro la medesima proporzione dei tempi, e quando il tempo <lb/>&egrave; lo stesso, e le velocit&agrave; differenti, gli spazi passati son fra di loro come esse <lb/>velocit&agrave;. </s>

<s>Quando dunque la velocit&agrave; crescesse secondo la proporzione del&shy;<lb/>l'allungamento del tempo, gli spazi passati crescerebbero con doppia pro&shy;<lb/>porzione di quella che cresce il tempo &rdquo; (Alb. </s>

<s>XIV, 322). Ebbe poi lo stesso <lb/>argomento pi&ugrave; nobile forma nel III dialogo Delle due nuove scienze, dove <lb/>cos&igrave; concludesi la proposizione II: &ldquo; Verum, in quarta propositione primi <lb/>libri, demonstratum est mobilium, aequabili motu latorum, spatia peracta <lb/>habere inter se rationem compositam ex ratione velocitatum, et ex ratione <lb/>temporum. </s>

<s>Hic autem ratio velocltatum est eadem cum ratione temporum; <lb/>ergo ratio spatiorum peractorum dupla est ratione temporum, quod erat de&shy;<lb/>monstrandum &rdquo; (Alb. </s>

<s>XIII, 168, 69). </s></p><p type="main">

<s>Intorno al nuovo teorema, cos&igrave; con inaspettata facilit&agrave; dimostrato, non <lb/>sarebbe da metter dubbio, quando fosse stato vero il supposto del Bene&shy;<lb/>detti, il qual supposto sembrava dall'altra parte a Galileo assai conforme <lb/>con gl'istituti della Natura, in tutte le altre sue ammirabili operazioni, &ldquo; in <lb/>quibus exarandis uti consuevit mediis primis, simplicissimis, facillimis &rdquo; (ivi, <lb/>pag. </s>

<s>154). Volle nonostante averne il parere del Sarpi, a cui cos&igrave; scriveva di <lb/>Padova, il d&igrave; 16 Ottobre del 1604: &ldquo; Ripensando circa le cose del moto, nelle <lb/>quali, per dimostrare gli accidenti da me osservati, mi mancava principio <lb/>totalmente indubitabile, da poter porlo per assioma, mi son ridotto ad una <lb/>proposizione, la quale ha molto del naturale e dell'evidente, e questa sup&shy;<lb/>posta dimostr&ograve; poi il resto: cio&egrave; gli spazi passati dal moto naturale essere <lb/>in proporzione doppia dei tempi, e per conseguenza gli spazi passati in tempi <lb/>eguali essere come i numeri impari ab unitate, e le altre cose. </s>

<s>Il principio <lb/>&egrave; questo: che il mobile naturale vada crescendo di velocit&agrave; con quella pro&shy;<lb/>porzione, che si discosta dal principio del suo moto..... Aver&ograve; caro che <lb/>V. S. M. R. lo consideri un poco, e me ne dica il suo parere &rdquo; (Alb. </s>

<s>VI, 24, 25). </s></p><pb xlink:href="020/01/2054.jpg" pagenum="297"/><p type="main">

<s>Qualunque si fosse il parere del Sarpi, il pi&ugrave; autorevole giudice nono&shy;<lb/>stante, trattandosi di un fatto, era l'esperienza, alla quale non manc&ograve; di ri&shy;<lb/>correre Galileo, sperando di ritrovare a'suoi dubbi definitiva risoluzione. </s>

<s>La <lb/>via pi&ugrave; diretta sarebbe stata quella di osservare, nella successione dei tempi, <lb/>gli spazi passat&igrave;, mentre un grave liberamente scende lungo le mura di qual&shy;<lb/>che alta torre, ma la prospettiva facilmente inganna l'osservatore, se non <lb/>essendo l'altezza tale, da poter la virt&ugrave; del mobile vincere le resistenze, non <lb/>&egrave; l'occhio cos&igrave; disposto &ldquo; ut angulorum disparitate minime decipiatur &rdquo; <lb/>(Alb. </s>

<s>XI, 53). E perch&egrave; trovava Galileo difficile il sodisfare a cos&igrave; fatte co&shy;<lb/>modit&agrave;, pens&ograve; di attendere ad altre esperienze, le quali, bench&egrave; per una via <lb/>meno diretta, lo conducessero al fine desiderato. </s>

<s>E per prima cosa gli oc&shy;<lb/>corse di rivolgersi ad esaminare gli effetti della percossa, ma l'ebbe a tro&shy;<lb/>vare implicata in insuperabili difficolt&agrave; e aver gli effetti di lei piuttosto pro&shy;<lb/>porzione con l'infinito. </s></p><p type="main">

<s>Torn&ograve; allora col pensiero a que'piani inclinati, che aveva dianzi trovati <lb/>cos&igrave; comodi, quando trattavasi di dimostrare che corpi di qualunque mole e <lb/>di qualunque specie vanno ugualmente veloci, perch&egrave;, mentre da una parte <lb/>essi gravi cos&igrave; lentamente scendendo ricevono dall'aria minore impedimento, <lb/>danno dall'altra tutto l'agio all'osservatore di esaminare, in tempi tanto pi&ugrave; <lb/>lunghi, le proporzioni degli spazi passati. </s>

<s>Disposto perci&ograve; un regolo lungo <lb/>dodici braccia, con una delle sue estremit&agrave; elevata un braccio o due sul <lb/>piano dell'orizzonte, e per diminuire l'attrito incollatavi sopra una carta pe&shy;<lb/>cora bene stirata, vi lasciava scendere una perfetta sfera di bronzo, e per <lb/>via di una clessidra a acqua &ldquo; esaminando il tempo di tutta la lunghezza <lb/>col tempo della met&agrave;, e con quello di due terzi o dei tre quarti, o in con&shy;<lb/>clusione con qualunque altra divisione, per esperienze ben cento volte re&shy;<lb/>plicate (afferma cos&igrave; Galileo) sempre s'incontrava gli spazi passati esser tra <lb/>di loro come i quadrati dei tempi &rdquo; (Alb. </s>

<s>XIII, 172). </s></p><p type="main">

<s>Chiudesi la descrizione dell'esperienza col dire che &ldquo; tali operazioni <lb/>molte e molte volte replicate giammai non differivano di un notabile mo&shy;<lb/>mento &rdquo; (ivi, pag. </s>

<s>173), ci&ograve; che noi c'induciamo a credere difficilmente, <lb/>con buona pace di Galileo, s&igrave; rispetto alla misura degli spazi, passati sul <lb/>regolo con resistenze sempre difformi, s&igrave; rispetto alla misura dei tempi, presa <lb/>con strumenti tanto imperfetti, e quando ancora s'ignoravan le leggi del&shy;<lb/>l'efflusso dei liquidi dai fori dei vasi. </s>

<s>Vero &egrave; bene che, secondo osserva il <lb/>Wolf, essendosi scelta <emph type="italics"/>una gran secchia,<emph.end type="italics"/> &ldquo; tempus a corpore labento in&shy;<lb/>sumptum, admodum parvum, aqua ad modicam altitudinem interea fidit, <lb/>proindeque res perinde se habuit, ac si in vase ad eamdem semper altitu&shy;<lb/>dinem aqua mansisset, et invariata celeritate iugiter effluxisset &rdquo; (Physica <lb/>experim., Vol. </s>

<s>II, Venetiis 1756, pag. </s>

<s>2): vero &egrave; bene che, secondo udiremo <lb/>dire tra poco allo stesso Galileo, si pesava l'acqua <emph type="italics"/>con una bilancia cos&igrave; <lb/>esatta, che tirava ad un sessantesimo di grano,<emph.end type="italics"/> ma come computare le <lb/>perdite per evaporazione, per aderenza alle pareti dei vasi, e per tanti altri <lb/>accidenti dovuti al visco del liquido, e alle cause capillari? </s>

<s>Eppure dovevano <pb xlink:href="020/01/2055.jpg" pagenum="298"/>tali minime cause concorrere efficacemente in alterar la misura di que'mi&shy;<lb/>nimi tempi, ci&ograve; che ben riconosciuto da que'due valorosi sperimentatori che <lb/>furono il Ricci e il Torricelli, gli fece restar muti innanzi al Mersenno, il <lb/>quale diceva &ldquo; esser difficilissimo il certificarsi dell'esattezza dell'esperienza <lb/>fatta da Galileo, e riferita a c. </s>

<s>175 del suo libro Del moto &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. XLII, fol. </s>

<s>116). </s></p><p type="main">

<s>Si poteva il pericolo manifesto d'incorrere in simili inesattezze dir con <lb/>dolce lusinga di averlo superato a parole, come fa in questo dialogo il Sal&shy;<lb/>viati, il quale s'era nonostante, nell'altro Dialogo, gi&agrave; tradito, quando si <lb/>volle cimentare coi fatti. </s>

<s>Ivi, per confondere i Peripatetici, si proponeva di <lb/>trovare il preciso tempo della caduta di una palla di artiglieria dall'orbe <lb/>lunare; tempo che, conosciutasi la distanza dalla Luna a noi, e trovato per <lb/>esperienza il tempo, che impieg&ograve; il mobile a passare uno spazio dato, si de&shy;<lb/>terminava facilmente in numeri, supposta, come da Galileo si credeva, la <lb/>gravit&agrave; costante, applicandovi la nuova legge scoperta dei moti accelerati. </s>

<s><lb/>Ora l'esperienza, dice il Salviati stesso nel II dialogo Dei due massimi si&shy;<lb/>stemi, di averla fatta, e, avendola anche pi&ugrave; volte replicata, di aver sempre <lb/>trovato che una palla di cento libbre &ldquo; scende dall'altezza di cento braccia <lb/>in cinque minuti secondi d'ora &rdquo; (Alb. </s>

<s>I, 246). </s></p><p type="main">

<s>Non dicendosi per&ograve; il modo come l'operazione fu fatta, si cred&egrave; da <lb/>tutti, specialmente prima di aver letta l'esperienza descritta nel III dialogo <lb/>Delle due nuove scienze, che avesse Galileo adoperato il pendolo, per la mi&shy;<lb/>sura dei tempi, e che avesse direttamente osservati gli spazi nelle libere ca&shy;<lb/>dute verticali. </s>

<s>Fu tra coloro, che ingerirono una tale opinione, il Riccioli, <lb/>il quale, attendendo nel 1634 in Ferrara a fare insieme col Cabeo espe&shy;<lb/>rienze intorno alle cadute dei gravi, cred&egrave; di averne ricavata la legge na&shy;<lb/>turale che vadano gl'incrementi degli spazi in serie continuamente tripla, <lb/>cio&egrave; come i numeri 1, 3, 9, 27, ecc. </s>

<s>Non aveva per&ograve; letti ancora i dialoghi <lb/>Dei due massimi sistemi, proibiti dalla sacra Congregazione dell'Indice, ma, <lb/>avutane poi nel 1640 licenza, vi trov&ograve;, per quegl'incrementi degli spazi, <lb/>formulata una legge alquanto diversa, da lui creduta semplicemente speri&shy;<lb/>mentale, e ch'era quella della serie de'numeri impari <emph type="italics"/>ab unitate.<emph.end type="italics"/></s></p><p type="main">

<s>Stava incerto in quale dei due resultati sperimentali consistesse l'er&shy;<lb/>rore, quando s'abbatt&egrave; a leggere di quella palla di artiglieria di cento lib&shy;<lb/>bre, che passa le cento braccia in cinque minuti secondi. </s>

<s>Si risovvenne al&shy;<lb/>lora che uno de'suoi globi di argilla era sceso dai merli della torre degli <lb/>Asinelli, cio&egrave; per braccia 187, in quattro minuti secondi e venti terzi, &ldquo; cer&shy;<lb/>tusque eram in mei temporis numeratione nullum sensibilem errorem fuisse &rdquo; <lb/>(Almag. </s>

<s>novum, T. II cit., pag. </s>

<s>386), per cui concluse dover esser senza <lb/>dubbio l'errore nelle esperienze di Galileo. </s>

<s>Avr&agrave; egli, incominci&ograve; allora a <lb/>ripensare fra s&egrave; il Riccioli, sbagliato Galileo nell'osservare gli spazi o nel <lb/>misurare i tempi? </s>

<s>Gli pareva per verit&agrave; difficile che si dovesse una palla <lb/>di cento libbre portare cos&igrave; per gusto sulla cima di un'alta torre, e che si <lb/>potesse di lass&ugrave; maneggiare con la destrezza necessaria, per la precisione <pb xlink:href="020/01/2056.jpg" pagenum="299"/>dell'esperienza, ed essendo, anche per le grandi citt&agrave;, cos&igrave; fatte torri assai <lb/>rare, avrebbe dovuto Galileo nominar quella, ch'ei trov&ograve; meglio accomodata <lb/>al bisogno. </s>

<s>Pure, non passando per la mente al Riccioli il possibile uso dei <lb/>piani inclinati, non seppe rimoversi dal suo primo supposto, che cio&egrave; fossero <lb/>quelle galileiane osservazioni fatte nelle cadute perpendicolari, le quali, per&shy;<lb/>ciocch&egrave; sembravano men difficili a contrassegnar lungo il muro della torre <lb/>secondo i vari intervalli, di quel che non fosse difficile aggiustar le lun&shy;<lb/>ghezze ai pendoli; al tempo di questi, &ldquo; non exacto ad primi mobilis tem&shy;<lb/>pus, et fixarum transitum per medinm coeli &rdquo; (ibid.), volle esso Riccioli at&shy;<lb/>tribuir piuttosto gli sbagli nelle esperienze di Galileo. </s></p><p type="main">

<s>I dialoghi Delle due nuove scienze, attentamente considerati, avrebbero <lb/>potuto servire all'Autore dell'Almagesto nuovo di commento, per fargli in&shy;<lb/>tendere perch&egrave; Galileo non nominasse la torre, che non era necessaria, e <lb/>come si potesse con facilit&agrave;, e senza punto pregiudicare alla precisione delle <lb/>esperienze, far uso di una palla di cento libbre. </s>

<s>Avrebbe congetturato in&shy;<lb/>somma che quella palla di ferro si faceva, in una comoda stanza a pian ter&shy;<lb/>reno, su un lungo regolo leggermente inclinato, risalir, per poi lasciarla <lb/>scendere, con tal debole impulso, da non eccedere, bench&egrave; cos&igrave; grave di cento <lb/>libbre, le forze muscolari di un Filosofo. </s></p><p type="main">

<s>Dal tempo delle scese del grave lungo il piano inclinato si poteva ar&shy;<lb/>gomentare il tempo della scesa nel perpendicolo, o per via del teorema terzo <lb/>del terzo dialogo Delle due nuove scienze (Alb. </s>

<s>XIII, 179) o anche meglio, <lb/>per via di un altro teorema, che, sebben non si trovi fra gli altri dimo&shy;<lb/>strato nel dialogo ora detto, formulavasi cos&igrave; dallo stesso Galileo nel suo <lb/>primo trattato manoscritto: &ldquo; Si ex eodem puncto horizontis ducatur per&shy;<lb/>pendiculus et planum inclinatum, et in plano inclinato sumatur quodlibet <lb/>punctum, a quo in plano perpendicularis linea usque ad perpendiculum pro&shy;<lb/>trahatur; lationes in parte perpendiculi, inter horizontem <lb/>et occursum perpendicularis intercepta, et in parte plani <lb/>inclinati inter eamdem perpendicularem et horizontalem <lb/>intercepta, eodem tempore absolvuntur &rdquo; (MSS. Gal., P. V, <lb/>T. II, fol. </s>

<s>180). </s></p><p type="main">

<s>S'immagini essere AC (fig. </s>

<s>139) la lunghezza del de&shy;<lb/>clivio sul quale sia stato trovato scendere un grave in un <lb/><figure id="id.020.01.2056.1.jpg" xlink:href="020/01/2056/1.jpg"/></s></p><p type="caption">

<s>Figura 139.<lb/>tempo gi&agrave; misurato: per sapere a qual punto, pur par&shy;<lb/>tendosi da C, sarebbe lo stesso grave sceso nel perpendi&shy;<lb/>colo in quel medesimo tempo, &ldquo; tirate, insegna cos&igrave; a fare <lb/>il Salviati al Sagredo, da A la perpendicolare sopra la CA, <lb/>prolungando essa e la CB fino al concorso in D: quello <lb/>sar&agrave; il punto cercato &rdquo; (Alb. </s>

<s>I, 32). </s></p><p type="main">

<s>Questo solo senz'altro sarebbe stato sufficiente per computare il tempo, <lb/>che spenderebbe una palla di artiglieria a scendere infino a noi dal mondo <lb/>della Luna, ma Galileo, per pigliare a fondamento della sua costruzione un <lb/>dato sperimentale pi&ugrave; specioso, volle ridurre la distanza DC alle cento brac-<pb xlink:href="020/01/2057.jpg" pagenum="300"/>cia, o sia per far credere di essere veramente salito a quell'altezza, o sia <lb/>per frugar pi&ugrave; vivamente l'animo di coloro, che dovevano esser curiosi di <lb/>saper com'avesse fatto a indovinare con tanta precisione in quanto tempo <lb/>un grave scende gi&ugrave; da un campanile, senz'esserne mai salito in cima a <lb/>farne le prove. </s>

<s>Comunque sia, trovatosi T, tempo della discesa per la lun&shy;<lb/>ghezza perpendicolare CD; il tempo incognito X della discesa per le cento <lb/>braccia, essendo gli spazi come i quadrati dei tempi, veniva dato dall'equa&shy;<lb/>zione DC:T2=100:X2=T2.100/DC, ossia X=T.&radic;100/DC, che Galileo, <lb/>come udimmo, trov&ograve; uguale a cinque minuti secondi. </s></p><p type="main">

<s>Il Riccioli, persuaso che la scoperta della legge dell'incremento degli <lb/>spazi, secondo la serie dei numeri impari, fosse il frutto dell'esperienza; era <lb/>alieno dall'indovinar che per tali vie indirette si fosse condotto Galileo a <lb/>sciogliere il suo dinamico problema, com'era alieno dal creder che, per mi&shy;<lb/>surare i tempi, seguitasse a far uso della Clessidra, all'imperfezion della <lb/>quale, e non ai male aggiustati pendoli, progettati da Galileo stesso, ma non <lb/>saputi ridurre alla pratica, si dee principalmente l'esorbitante errore del&shy;<lb/>l'aver egli fatto penar cinque interi secondi un grave a scender per sole <lb/>cento braccia. </s>

<s>E perch&egrave; alieni dal creder cos&igrave; son pur anche coloro, i quali <lb/>fanno Galileo inventor del pendolo misuratore del tempo, lasceremo, a per&shy;<lb/>suadergli meglio del loro inganno, le congetture, per venire alla certezza <lb/>dei fatti. </s></p><p type="main">

<s>Leggendo il Baliani il II dialogo Dei due massimi sistemi, era entrato <lb/>in gran curiosit&agrave; di sapere com'avesse fatto Galileo a trovar quelle cento <lb/>braccia in cinque secondi. </s>

<s>Cred&egrave; anch'egli, come il Riccioli, che avesse os&shy;<lb/>servate la cadute dirette, e che ne avesse misurato il tempo col pendolo, ma <lb/>non essendone certo, interrog&ograve; Galileo stesso, il quale indugio a rispondere, <lb/>come vedremo in altra occasione, sette anni, e finalmente, nel d&igrave; primo di <lb/>Agosto del 1639, rispondeva alle richieste dell'amico, le quali si riducevano <lb/>a due: al tempo della discesa per le cento braccia, e al saper qual parte <lb/>sia questo tempo di un giorno sidereo. </s>

<s>&ldquo; Quanto alla prima operazione, dice <lb/>Galileo, la scesa di quella palla, che io fo scendere per quel canale, ad ar&shy;<lb/>bitrio nostro inclinato, ci dar&agrave; tutti i tempi, non solo delle cento braccia, <lb/>ma di qualsivoglia altra quantit&agrave; di caduta perpendicolare, atteso che, co&shy;<lb/>m'ella medesima sa e dimostra, la lunghezza del detto canale, o vogliamo <lb/>dire piano inclinato, &egrave; media proporzionale tra la perpendicolare elevazione <lb/>di detto piano, e la lunghezza di tutto lo spazio perpendicolare, che nel <lb/>medesimo tempo si passerebbe dal mobile cadente &rdquo; (Lettere, Pisa 1864, <lb/>pag. </s>

<s>41). </s></p><p type="main">

<s>Alla seconda richiesta rispondeva Galileo proponendo l'uso dei pendoli, <lb/>difficile a ridursi in pratica, perch&egrave; supponeva fosse ritrovato il numero <lb/>delle vibrazioni, fatte da un pendolo di qualunque lunghezza in 24 ore si&shy;<lb/>deree, ond'&egrave; che soggiungeva cos&igrave; Galileo stesso, riconoscendo non esser <lb/>quello altro che un bel progetto: &ldquo; Vero &egrave; che noi pofremo passare a pi&ugrave; <pb xlink:href="020/01/2058.jpg" pagenum="301"/>esatte misure con avere veduto ed osservato qual sia il flusso dell'acqua per <lb/>un sottile cannello, perch&egrave;, raccogliendo ed avendo pesata quanta ne passa <lb/>v. </s>

<s>g. </s>

<s>in un minuto, potremo poi, col pesare la passata nel tempo della scesa <lb/>per il canale, trovare l'esattissima misura e quantit&agrave; di esso tempo, serven&shy;<lb/>doci massime di una Bilancia cos&igrave; esatta, che tira ad un sessantesimo di <lb/>grano &rdquo; (ivi, pag. </s>

<s>43). </s></p><p type="main">

<s>Resi oramai certi che i congetturati processi di Galileo sono i veri, si <lb/>vede da qual radice dovessero inevitabilmente provenire gli errori, ma si <lb/>aggiungeva di pi&ugrave;, contro la desiderata precisione dell'esperienza, l'uso dei <lb/>piani inclinati. </s>

<s>Il Riccioli non volle lasciare indietro nemmeno questa classe <lb/>di esperimenti, e ai gradi di una scala di pietra, AD (fig. </s>

<s>140) alto sul pa&shy;<lb/>vimento undici once e mezzo di piede romano antico, AE, alto un piede, <lb/>dieci once e mezzo, AF, alto due piedi e 50 once, appoggiava ora un ca&shy;<lb/><figure id="id.020.01.2058.1.jpg" xlink:href="020/01/2058/1.jpg"/></s></p><p type="caption">

<s>Figura 140.<lb/>nale, ora un regolo lungo 35 piedi, e per quello <lb/>faceva scendere l'acqua, e per questo corpi di <lb/>varia specie, come globi di legno e di argilla. </s>

<s><lb/>L'acqua, nelle tre varie disposizioni del regolo <lb/>in DC, EC, FC, lo passava in 15&Prime;, 40&tprime;; 9, 10; <lb/>6, 40: il globo di legno, nelle tre simili di&shy;<lb/>sposizioni, passava il regolo in 18&Prime;, 0&tprime;; 11, <lb/>0; 8, 10, e il globo di argilla in 19&Prime;, 0&tprime;; <lb/>12, 0; 8, 59. Ora &egrave; facile argomentare di qui <lb/>al notabile indugio prodotto dagli attriti, vedendosi l'acqua, che ne risente <lb/>meno, scendere assai pi&ugrave; veloce. </s>

<s>Che se il globo di argilla, bench&egrave; pi&ugrave; <lb/>grave, procedeva nonostante men frettoloso, dipendeva, dice il Riccioli, uni&shy;<lb/>camente da ci&ograve;, &ldquo; quia fricatione magis continua descendebat per canalem, <lb/>et ligneus saltitando sua levitate ulterius promovebatur &rdquo; (Almag. </s>

<s>novum, <lb/>T. II cit., pag. </s>

<s>393). </s></p><p type="main">

<s>Se dunque Galileo trov&ograve; che una palla di artiglieria scende cento brac&shy;<lb/>cia in cinque secondi, mentre si sa che ella la scenderebbe in qualche cosa <lb/>meno di tre secondi e mezzo, s'intende da che dovesse dipender l'errore, <lb/>che, in computo cos&igrave; sottile, &egrave; da dire esorbitante. </s>

<s>E perch&egrave; l'esorbitanza, <lb/>concorrendovi le medesime cause, doveva pure ritrovarsi ne'risultati del&shy;<lb/>l'esperienza descritta nel III dialogo Delle due nuove scienze, dicano dun&shy;<lb/>que i nostri Lettori qual fede sia da dare allo stesso Galileo, quando volle <lb/>asserir, l&agrave;, che gli spazi passati dalla palla di bronzo rispondevano esatta&shy;<lb/>mente ai quadrati dei tempi. </s>

<s>Di non esser creduto se l'aspettava egli stesso, <lb/>e che facendone altri esperienze pi&ugrave; diligenti avrebbero trovato falso il suo <lb/>detto. </s>

<s>Si contentava perci&ograve; di aver proposto innanzi a chi avesse saputo bene <lb/>usarlo un bello artificio, &ldquo; il quale, scriveva al Baliani, penso che ella sti&shy;<lb/>mer&agrave; squisitissimo, ancorch&egrave; poi, volendo sperimentare se quello che io <lb/>scrissi delle cento braccia in cinque secondi sia vero, lo trovasse falso, per&shy;<lb/>ch&egrave;, per manifestare la estrema gofferia di quegli, che scriveva ed assegnava <lb/>il tempo della caduta della palla d'artiglieria dall'orbe lunare, poco importa <pb xlink:href="020/01/2059.jpg" pagenum="302"/>che i cinque minuti delle cento braccia siano o no giusti &rdquo; (Lettere cit., <lb/>pag. </s>

<s>43). </s></p><p type="main">

<s>Ecco, dal loro proprio Autore, qualificata l'indole delle esperienze ga&shy;<lb/>lileiane, nel descriver le quali si pu&ograve; dir veramente, come disse in altro <lb/>proposito Stefano Gradi, ch'egli parl&ograve; da poeta. </s>

<s>Il fondamento della verit&agrave; <lb/>era per Galileo nella Matematica, e per sempre meglio confermarla invo&shy;<lb/>cava la Geometria, dalla quale, dopo quelle prime rivelazioni che s'&egrave; detto <lb/>di sopra, incominciano a pigliar forma i nuovi teoremi. </s>

<s>Il moto per&ograve;, come <lb/>ha leggi sue proprie, cos&igrave; ha proprii i principii, dal congiungere i quali con <lb/>quelli della Geometria riusc&igrave; Galileo, come da fecondo connubio, a far na&shy;<lb/>scere una Scienza nuova. </s>

<s>&Egrave; uno de'pi&ugrave; fondamentali, tra que'meccanici prin&shy;<lb/>cipii, e de'pi&ugrave; necessarii a condurre le nuove dimostrazioni, quello cos&igrave; detto <lb/>dell'inerzia, intorno a che, prima di proseguire pi&ugrave; oltre, ha da fare una <lb/>breve sosta il passo frettoloso della nostra Storia. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Il Newton poneva per terza definizione al primo libro De'principii ma&shy;<lb/>tematici di Filosofia naturale che fosse nella materia insita una virt&ugrave; di re&shy;<lb/>sistere, per la quale ciascun corpo, quanto &egrave; in s&egrave;, persevera nel suo primo <lb/>stato o di quiete o di moto uniformemente diretto. </s>

<s>&ldquo; Unde etiam vis insita <lb/>nomine significantissimo <emph type="italics"/>Vis inertiae<emph.end type="italics"/> dici possit &rdquo; (Editio cit., pag. </s>

<s>4). Il <lb/>corpo dunque non esercita questa forza, che per resistere alle mutazioni di <lb/>stato, a cui tenterebbe di ridurlo qualche forza straniera, ond'&egrave; un tale <lb/>esercizio tutt'insieme resistenza e impeto. </s></p><p type="main">

<s>L'aver trovato il nome da dare alla cosa, valse al Newton per una sco&shy;<lb/>perta, che gli si attribu&igrave; facilmente, quando, dietro una tanta autorit&agrave;, di&shy;<lb/>venne fra'Matematici quella frase di un uso comune. </s>

<s>Accennarono poi alcuni <lb/>eruditi che l'invenzione risaliva al Cartesio, e avrebbero pi&ugrave; giustamente <lb/>dovuto avvertire che su un tal principio d'inerzia era fondata la dimostra&shy;<lb/>zione data da Galileo della legge dei moti accelerati. </s>

<s>Chiunque per&ograve; ha senno <lb/>s'avvedr&agrave; facilmente come, trattandosi non di un fatto fisico, ma di un con&shy;<lb/>cetto, che trov&ograve; nel Newton una definizione appropriata agli instituti mate&shy;<lb/>matici della sua Filosofia, non poteva non essere quel concetto pi&ugrave; antico <lb/>del Cartesio e di Galileo. </s>

<s>La prima indole sua metafisica vale a confermar&shy;<lb/>gli una tale nota di antichit&agrave;, perch&egrave; dal desiderio, innato in ogni creatura, <lb/>di conservarsi nella sua propria esistenza, presero i Filosofi uno de'princi&shy;<lb/>pali argomenti a dimostrare l'immortalit&agrave; dell'anima umana. </s>

<s>Vollero dire <lb/>alcuni che fosse questo sentimento della nostra immortalit&agrave;, e gli sperimen&shy;<lb/>tati istinti della conservazione della propria vita negli animali, che fecero <lb/>anche alla materia bruta attribuire un sentimento simile e un simile istinto, <lb/>ma risolverono altri sapientemente la questione, risalendo alla Causa prima, <pb xlink:href="020/01/2060.jpg" pagenum="303"/>la quale a ogni creato effetto, insieme con l'essere, partecipa anche le virt&ugrave; <lb/>necessarie per conservarsi nell'esistenza. </s></p><p type="main">

<s>Imbevute le menti di cos&igrave; fatti principii di Filosofia universale, si ap&shy;<lb/>plicarono dai Matematici, per tacito consenso, alla particolare scienza del <lb/>moto, intantoch&egrave;, a mezzo il secolo XVI, era cos&igrave; ben chiaro e cos&igrave; ben per&shy;<lb/>suaso dover un corpo messo in moto perseverare in esso, che si proponeva <lb/>al Benedetti a risolvere il seguente quesito: &ldquo; An motus circularis alicuius <lb/>molae molendinariae, si super aliquod punctum quasi mathematicum quie&shy;<lb/>sceret, posset esse perpetuus, cum aliquando esset mota, supponendo ettam <lb/>eandem esse perfecte rotundam et levigatam &rdquo; (Specul, lib. </s>

<s>cit., pag. </s>

<s>285). <lb/>Si rispondeva non poter essere un tal moto perpetuo, e neanco lungamente <lb/>duraturo, perch&egrave;, oltre alla resistenza dell'aria ci &egrave; la violenza fatta alle <lb/>parlicelle materiali, che compongono il corpo, alle quali particelle repugna <lb/>il moto circolare e vertiginoso, essendo loro naturale inclinazione l'andar <lb/>per linea retta. </s>

<s>&ldquo; Unde tanto magis contra suammet naturam volvuntur, ita <lb/>ut secundum naturam quiescant, quia cum eis proprium sit, quando sunt <lb/>motae, eundi recta, quanto violentius volvuntur, tanto magis una resistit <lb/>alteri, et quasi retro revocat eam quam antea reperitur habere &rdquo; (ibid.). </s></p><p type="main">

<s>In un'altra Lettera al medesimo Paolo Capra, che gli avea proposto <lb/>questo primo quesito, torna il Benedetti sullo stessso argomento, applicando <lb/>la forza d'inerzia, non a soli i moti violenti ma altresi ai naturali, d'onde <lb/>venne Galileo scorto a ritrovare la prima dimostrazione geometrica dei moti <lb/>accelerati, come vedremo or ora, dop'avere in uno sguardo comprese quelle <lb/>vie, che conducono a diritto sulle soglie della Filosofia neutoniana. </s></p><p type="main">

<s>Galileo dunque, secondo l'opinione oramai invalsa a'suoi tempi, ripe&shy;<lb/>teva, a proposito delle vibrazioni di un pendolo, che potrebbero perpetuarsi <lb/>&ldquo; e creder&ograve;, egli dice, che lo farebbero, se si potesse levare l'impedimento <lb/>dell'aria &rdquo; (Alb. </s>

<s>I, 250). Ma nella II lettera intorno alle macchie solari, ren&shy;<lb/>deva anche pi&ugrave; esplicito, e nella sua massima precisione, il concetto, cos&igrave; <lb/>scrivendo: &ldquo; Rimossi tutti gl'impedimenti esterni, un grave, nella super&shy;<lb/>fice sferica e concentrica della Terra, sar&agrave; indifferente alla quiete ed ai mo&shy;<lb/>vimenti verso qualunque parte dell'orizzonte, ed in quello stato si conser&shy;<lb/>ver&agrave;, nel quale una volta sar&agrave; posto, cio&egrave;, se sar&agrave; stato messo in istato di <lb/>quiete, quello conserver&agrave;, e se sar&agrave; posto in movimento, v. </s>

<s>g. </s>

<s>verso occi&shy;<lb/>dente, nell'istesso si manterr&agrave; &rdquo; (Alb. </s>

<s>III, 418): cosicch&egrave;, rimeditando esso <lb/>Galileo sopra la nuova legge scoperta <emph type="italics"/>spatia ut quadrata temporum,<emph.end type="italics"/> ne con&shy;<lb/>cludeva quel che leggesi in questa nota: &ldquo; L'impeto contribuito ad un mobile <lb/>&egrave; probabile che sia eterno, e che eternamente si moverebbe, quando il mobile <lb/>non avesse propensione verso alcuna parte &rdquo; (MSS. Gal., P. V, T. 4, fol. </s>

<s>29). </s></p><p type="main">

<s>In un'altra nota autografa, apposta alla dimostrazion del teorema, che <lb/>lo spazio, passato equabilmente dal mobile con l'ultimo grado di velocit&agrave; <lb/>acquistata, &egrave; doppio del primo spazio passato dallo stesso mobile accelera&shy;<lb/>tamente, partendosi dalla quiete; &ldquo; Huic demonstrationi, scrive, necessarium <lb/>mihi videtur ostendisse antea motum horizontalem progredi in infinitum &rdquo; <pb xlink:href="020/01/2061.jpg" pagenum="304"/>(MSS. Gal., P. V, T. II, fol. </s>

<s>181). Ma la dimostrazione era difficile a de&shy;<lb/>dursi dai principii naturali, secondo i quali non si poteva ragionare altri&shy;<lb/>menti da quel che poi fece Galileo stesso nel III dialogo Delle due nuove <lb/>scienze, dove tutta la dimostrazione dell'eternit&agrave; del moto equabile si ridu&shy;<lb/>ceva a questa ragion semplicissima: &ldquo; si enim est aequabilis, non debilita&shy;<lb/>tur, aut remittitur, et multo minus tollitur &rdquo; (Alb. </s>

<s>XIII, 201). </s></p><p type="main">

<s>L'Aggiunti, fra le sue sollecitudini di confermare dimostrativamente le <lb/>dottrine galileiane, dop'aver detto che ogni minima forza vale a movere un <lb/>sfera grave in un perfettissimo piano orizzontale, cos&igrave; ragionando conclude <lb/>un suo lemma, premesso alla soluzione di un problema, di cui a suo tempo <lb/>i Lettori ammireranno la novit&agrave; curiosa: &ldquo; Se la forza movente sar&agrave; estrin&shy;<lb/>seca, e dopo l'impulso abbandona il mobile, detto mobile si mover&agrave;, rimosso <lb/>l'impedimento del mezzo, sempre con la medesima velocit&agrave;, perch&egrave;, a voler <lb/>che si movesse pi&ugrave; tardi, bisognerebbe crescere la resistenza, e a voler che <lb/>si movesse pi&ugrave; presto, bisognerebbe crescere l'inclinazione a quel moto. </s>

<s>Ma <lb/>n&egrave; l'una n&egrave; l'altra si cresce, mentre il motore &egrave; estrinseco, e il mezzo senza <lb/>impedimento; adunque durer&agrave; sempre a moversi di velocit&agrave; uniforme &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. 18, fol. </s>

<s>97). </s></p><p type="main">

<s>Anche il Cartesio, in una delle sue lettere al Mersenno, dop'avergli <lb/>detto che, per dimostrar la legge dei moti accelerati, supponeva che il mo&shy;<lb/>bile una volta mosso perseverasse nel suo moto, soggiungeva: &ldquo; idque in <lb/>Physica mea demonstraturum me spero &rdquo; (Epist., P. III cit., pag. </s>

<s>298, 99). <lb/>Ma poi ebbe nell<gap/> Metafisica invece a ricercare i principii alla sua dimo&shy;<lb/>strazione, e gli ritrov&ograve; nella immutabilit&agrave; di Dio e delle leggi della Natura. <lb/></s>

<s>&ldquo; Harum prima est unamquamque rem, quatenus est simplex et indivisa, <lb/>manere quantum in se est in eodem semper statu, nec unquam mutari, nisi <lb/>a causis externis. </s>

<s>Ita, si pars aliqua materiae sit quadrata, facile nobis per&shy;<lb/>suademus illam perpetuo mansuram esse quadratam, nisi quid aliunde adve&shy;<lb/>niat, quod eius figuram mutet. </s>

<s>Si quiescat, non credimus illam unquam in&shy;<lb/>cepturam moveri, nisi ab aliqua causa ad id impellatur. </s>

<s>Nec ulla maior ratio <lb/>est, si moveatur, cur putemus ipsam unquam sua sponte, et a nullo alio <lb/>impeditam motum illum suum intermissuram. </s>

<s>Atque ideo concludendum est <lb/>id quod movetur, quantum in se est, semper moveri &rdquo; (Principia Philos., <lb/>Amstelodami 1650, pag. </s>

<s>51, 52). </s></p><p type="main">

<s>Chi pensi ora alla diffusione, ch'ebbero questi principii di Filosofia car&shy;<lb/>tesiana, concludenti in s&egrave; le tradizioni del secolo precedente, si persuader&agrave; <lb/>facile di quel che si diceva, non aver cio&egrave; fatto altro il Newton che attri&shy;<lb/>buire alla materia una virt&ugrave; di resistere alle cause esterne, che venissero <lb/>&agrave; perturbarla dal suo primo stato, e dare a quella virt&ugrave; il nome significan&shy;<lb/>tissimo di Forza d'inerzia. </s>

<s>Ond'&egrave; ch'essendosi dimostrato come, anche senza <lb/>nome distinto, era benissimo conosciuta e insegnata nel secolo XVI questa <lb/>propriet&agrave; della materia, &egrave; tempo che si veda quanto si giovasse Galileo di <lb/>cos&igrave; fatto insegnamento, per condur la sua prima dimostrazione geometrica, <lb/>e concluderne di l&igrave; le principali propriet&agrave; dei moti accelerati. </s></p><pb xlink:href="020/01/2062.jpg" pagenum="305"/><p type="main">

<s>Aveva il Benedetti messo innanzi cos&igrave; agli studiosi del suo libro Delle <lb/>speculazioni: &ldquo; Omne corpus grave, aut sui natura, aut vi motum, in se <lb/>recipit impressionem aut impetum motus, ita ut, separatum a virtute mo&shy;<lb/>vente, per aliquod temporis spatium ex seipso moveatur &rdquo; (Editio cit., <lb/>pag. </s>

<s>286, 87), e in quest'impeto rimasto nel mobile impresso riconosceva <lb/>la causa acceleratrice del moto. </s>

<s>Suppongasi, ragionava dietro ci&ograve; Galileo, che <lb/>abbia il mobile, partendosi dalla quiete in A (fig. </s>

<s>141), percorso lo spazio <lb/><figure id="id.020.01.2062.1.jpg" xlink:href="020/01/2062/1.jpg"/></s></p><p type="caption">

<s>Figura 141.<lb/>AB in.un primo tempo, e che, giunto in B, sia sottratto agl'im&shy;<lb/>pulsi continui della gravit&agrave; in qualunque modo, come per esem&shy;<lb/>pio rivolgendo in direzione orizzontale il suo corso. </s>

<s>Proseguir&agrave;, <lb/>secondo gl'insegnamenti del Benedetti, il conceputo moto spon&shy;<lb/>taneamente, passando uno spazio che, aggiuntovi poi quello, per <lb/>cui sarebbe spinto dalla propria gravit&agrave;, se gli fosse rimasta im&shy;<lb/>pressa, ossia se non avesse deviato dalla prima direzion perpen&shy;<lb/>dicolare, dee esser nel secondo tempo necessariamente maggior che <lb/>nel primo. </s>

<s>Il secondo viaggio BE insomma, fatto in parte spon&shy;<lb/>taneamente dal mobile, e in parte per impulso della propria gra&shy;<lb/>vit&agrave;, si vede dover esser necessariamente maggiore del primo AB, <lb/>ma Galileo voleva saper di pi&ugrave; qual ne fosse precisamente l'ec&shy;<lb/>cesso. </s></p><p type="main">

<s>Il progresso fatto per solo impulso di gravit&agrave;, e che vien rap&shy;<lb/>presentato dalla linea continua DE, si comprende come dovess'es&shy;<lb/>sere uguale nel primo e nel secondo tempo, che pur si suppongono <lb/>uguali, ond'&egrave; che tutto si riduceva a sapere la quantit&agrave; dello spa&shy;<lb/>zio, passato dal mobile con la spontaneit&agrave; del suo moto, e che si <lb/>distingue con la linea BD punteggiata. </s>

<s>Per saper dunque qual <lb/>parte dello spazio AB sia lo spazio BD, Galileo cos&igrave; ragionava: <lb/>Partendosi dalla quiete A rappresentata da zero, suppongasi che, <lb/>giunto in B, abbia il mobile acquistato nel primo tempo 5 gradi <lb/>di velocit&agrave;, cosicch&egrave;, divisa la linea AB in cinque parti, la prima <lb/>contenga uno spazio, la seconda due, e cos&igrave; di seguito in fino alla <lb/>quinta, che ne conterr&agrave; cinque, e saranno perci&ograve; tutti insieme gli <lb/>spazi 0+1+2+3+4+5=15. Ora, giunto il mobile in B, <lb/>si suppone che con moto uniforme prosegua spontaneamente, nel <lb/>secondo tempo uguale al primo, con la velocit&agrave; iniziale ulterior&shy;<lb/>mente acquistata uguale a 5: cosicch&egrave; i termini da sommarsi, che <lb/>dianzi erano sei, da zero a cinque, ora son pur sei, ma tutti eguali a 5, e <lb/>perci&ograve; la somma degli spazii contenuti nella linea BD sar&agrave; uguale a 30. &rdquo; E <lb/>perci&ograve;, cos&igrave; Galileo conclude il suo ragionamento, movendosi il mobile per <lb/>altrettanto spazio, ma con velocit&agrave; equabile, e qual'&egrave; quella del sommo <lb/>grado 5, dover&agrave; passare spazio doppio di quello, che pass&ograve; nel tempo acce&shy;<lb/>lerato, che cominci&ograve; dallo stato di quiete &rdquo; (Alb. </s>

<s>I, 251). </s></p><p type="main">

<s>Se dunque BD &egrave; il doppio di AB, e se DE gli &egrave; uguale, lo spazio BE, <lb/>passato dal mobile nel secondo tempo, sar&agrave; tre volte pi&ugrave; grande dello spa-<pb xlink:href="020/01/2063.jpg" pagenum="306"/>zio AB passato nel primo. </s>

<s>Con un ragionamento simile seguitava a dimo&shy;<lb/>strar Galileo che EK, KR, spazi passati dal mobile nel IIIo e nel IVo tempo, <lb/>erano cinque e sette volte pi&ugrave; grandi dello spazio AB, cosicch&egrave; ne conclu&shy;<lb/>deva che i ricercati eccessi stavano come la serie de'numeri impari 3, 5, 7.... <lb/>E giacch&egrave; numerati, nella linea della caduta AR, gli spazi ordinatamente ai <lb/>tempi, si vede che, se alla fine del Io lo spazio &egrave; 1, alla fine del IIo &egrave; 4, <lb/>del IIIo &egrave; 9, del IVo &egrave; sedici; si confermava per la nuova dimostrazione quel <lb/>ch'era riuscito Galileo a dimostrare per altre vie, che cio&egrave; crescono gli <lb/>spazi come i quadrati dei tempi. </s></p><p type="main">

<s>Nel 1622 il Cavalieri propose, come altrove vedemmo, il suo metodo <lb/>degl'indivisibili a Galileo, il quale lo trov&ograve; opportunissimo a rendere anche <lb/>pi&ugrave; perfette queste dimostrazioni per via geometrica, facendo rappresentare <lb/>gl'infiniti istanti, contenuti in un tempo quanto, agl'infiniti punti contenuti <lb/>in una linea, e gli spazi alle infinite linee di che si contenesse, secondo il Ca&shy;<lb/>valieri, una superfice. </s>

<s>Perci&ograve; al Sagredo che, servendosi di numeri deter&shy;<lb/>minati, avea concluso il sopra riferito ragionamento, il Salviati soggiungeva: <lb/>&ldquo; Voi mi avete fatto venire in mente di aggiungere qualche cosa di pi&ugrave;, <lb/>imperocch&egrave;, essendo nel moto accelerato l'agumento continuo, non si pos&shy;<lb/>sono compartire i gradi della velocit&agrave;, la quale sempre cresce, in numero <lb/>alcuno determinato, perch&egrave; mutandosi di momento in momento son sempre <lb/>infiniti: per&ograve; meglio potremo esemplificare la nostra intenzione, figurandoci <lb/>un triangolo &rdquo; (Alb. </s>

<s>I, 251, 52). </s></p><p type="main">

<s>La dimostrazione delle propriet&agrave; dei moti accelerati riusciva, per que&shy;<lb/>sta nuova via geometrica, di una facilit&agrave; e di un'evidenza maravigliosa, im&shy;<lb/><figure id="id.020.01.2063.1.jpg" xlink:href="020/01/2063/1.jpg"/></s></p><p type="caption">

<s>Figura 142.<lb/>perocch&egrave;, figurandoci essere quel triangolo AFH (fig. </s>

<s>142) <lb/>si pu&ograve; immaginare che le parti uguali AC, CD, DE, EF, <lb/>prese sopra il lato AF perpendicolare, rappresentino i tempi, <lb/>e che le linee CG, DK, EI, FH, orizzontalmente condotte <lb/>parallele alla base FH, rappresentino le velocit&agrave; via via <lb/>crescenti, per le propriet&agrave; dei triangoli simili, a propor&shy;<lb/>zione dei tempi. </s>

<s>Gli spazi perci&ograve;, che si sa avere la ragion <lb/>composta delle velocit&agrave; e dei tempi, saranno rappresentati <lb/>dai triangoli ACG, ADK, AEI, AFH, aventi AC, AD, AE, <lb/>AF per altezze, e CG, DK, EI, FH per loro respettive basi; <lb/>per cui, chiamandosi per brevit&agrave; S, S&prime;, S&Prime; quegli stessi spazi, <lb/>o i triangoli a cui sono proporzionali, sar&agrave; S:S&prime;:S&Prime;= <lb/>ACXCG:ADXDK:AEXEI, e perch&egrave; AC:AD:AE= <lb/>CG:DK:EI, dunque S:S&prime;:S&Prime;=AC2:AD2:AE2, ossia gli spazi stanno <lb/>come i quadrati dei tempi. </s>

<s>Dai trapezi inoltre CK, DI, EH, che si potranno <lb/>significare per brevit&agrave; con T, T&prime;, T&Prime;, verranno rappresentati gl'incrementi <lb/>degli spazi via via decorsi, e perch&egrave; T=3CGXCD/2, T&prime;=5CGXDE/2, <lb/>T&Prime;=7CGXEF/2, e perci&ograve; T:T&prime;:T&Prime;....=3:5:7.... </s></p><pb xlink:href="020/01/2064.jpg" pagenum="307"/><p type="main">

<s>Ma ascoltiamo lo stesso Galileo, il quale, prima di esporsi in pubblico, <lb/>s'esercitava cos&igrave;, verso il 1622, a distendere i suoi pensieri: </s></p><p type="main">

<s>&ldquo; Io suppongo, e forse potr&ograve; dimostrarlo, che il grave cadente natu&shy;<lb/>ralmente vada continuamente accrescendo la sua velocit&agrave;, secondo che ac&shy;<lb/>cresce la distanza dal termine onde si parti, come v. </s>

<s>g., partendosi il grave <lb/>dal punto A (nella precedente figura) e cadendo per la linea AB, suppongo <lb/>che il grado di velocit&agrave; nel punto D sia tanto maggiore che il grado di ve&shy;<lb/>locit&agrave; in C, quanto la distanza DA &egrave; maggiore della CA, e cos&igrave; il grado di <lb/>velocit&agrave; in E essere al grado di velocit&agrave; in D, come EA a DA:e cos&igrave; in <lb/>ogni punto della linea AB trovarsi con gradi di velocit&agrave; proporzionali alle <lb/>distanze dei medesimi punti dal termine A. </s>

<s>Questo principio mi par molto <lb/>naturale, e che risponda a tutte le esperienze, che veggiamo negli strumenti <lb/>e macchine, che operano percotendo, dove il percuziente fa tanto maggiore <lb/>effetto, quanto da pi&ugrave; grande altezza casca, e supposto questo principio dimo&shy;<lb/>strer&ograve; il resto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Faccia la linea AH qualunque angolo con la AF e per li punti, C, D, <lb/>E, F sieno tirate le parallele CG, DK, EI, FH:e perch&egrave; le linee FH, EI, <lb/>DK, CG sono tra di loro come le FA, EA, DA, CA; adunque le velocit&agrave; <lb/>nei punti F, E, D, C sono come le linee FH, EI, DK, CG; vanno dunque <lb/>continuamente crescendo i gradi di velocit&agrave; in tutti i punti della linea AF, <lb/>secondo l'incremento delle parallele tirate da tutti i medesimi punti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Inoltre, perch&egrave; la velocit&agrave;, con la quale il mobile &egrave; venuto da A in D, <lb/>&egrave; composta di tutti i gradi di velocit&agrave; avuti in tutti i punti della linea AD, <lb/>e la velocit&agrave;, con che ha passata la linea AC, &egrave; composta di tutti i gradi <lb/>di velocit&agrave;, che ha avuto in tutti i punti della linea AC; adunque la velo&shy;<lb/>cit&agrave;, con che ha passata la linea AD, alla velocit&agrave;, con che ha passata la <lb/>linea AC, ha quella proporzione che hanno tutte le linee parallele, tirate da <lb/>tutti i punti della linea AD, sino alla AK, a tutte le parallele tirate da tutti <lb/>i punti della linea AC sino alla AG, e questa proporzione &egrave; quella che ha <lb/>il triangolo ADK al triangolo ACG, cio&egrave; il quadrato AD al quadrato AC. &rdquo; </s></p><p type="main">

<s>&ldquo; Adunque la velocit&agrave;, con che si &egrave; passata la linea AD, alla velocit&agrave; <lb/>con che &egrave; passata la linea AC, ha doppia proporzione di quella, che ha DA <lb/>a CA. </s>

<s>E perch&egrave; la velocit&agrave; alla velocit&agrave; ha contraria proporzione di quella, <lb/>che ha il tempo al tempo, imperocch&egrave; il medesimo &egrave; crescere la velocit&agrave; <lb/>che scemare il tempo;; adunque il tempo del moto in AD al tempo del moto <lb/>in AC ha sudduplicata proporzione di quella, che ha la distanza AD alla di&shy;<lb/>stanza AC. </s>

<s>Le distanze dunque dal principio del moto sono come i quadrati <lb/>dei tempi, e dividendo gli spazi passati in tempi uguali, sono come i nu&shy;<lb/>meri impari ab unitate, che risponde a quello che ho sempre detto, e con <lb/>esperienze osservato, e cos&igrave; tutti i veri si rispondono. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E se queste cose son vere, io dimostro che la velocit&agrave; nel moto vio&shy;<lb/>lento va decrescendo con la medesima proporzione, con la quale, nella me&shy;<lb/>desima linea retta, cresce nel moto naturale. </s>

<s>Imperocch&egrave; sia il principio del <lb/>moto violento il punto B ed il fine il termine A. </s>

<s>E perch&egrave; il proietto non <pb xlink:href="020/01/2065.jpg" pagenum="308"/>passa il termine A, adunque l'impeto, che ha avuto in B, fu tanto, quanto <lb/>poteva cacciarlo fino al termine A, e l'impeto, che il medesimo proietto ha <lb/>in F, &egrave; tanto, quanto pu&ograve; cacciarlo al medesimo termine A, essendo il me&shy;<lb/>desimo proietto in E, D, C si trova congiunto con impeto potente a spin&shy;<lb/>gerlo al medesimo termine A, n&egrave; pi&ugrave; n&egrave; meno. </s>

<s>Dunque l'impeto va giu&shy;<lb/>stamente calando, secondo che scema la distanza del mobile dal termine A. </s>

<s><lb/>Ma secondo la medesima delle distanze dal termine A va crescendo la ve&shy;<lb/>locit&agrave;, quando il medesimo grave cader&agrave; dal punto A, come di sopra si &egrave; <lb/>supposto, e confrontato con le altre prime nostre osservazioni e dimostra&shy;<lb/>zioni; adunque &egrave; manifesto quello che volevamo provare. </s>

<s>&rdquo; (MSS. Gal., P. V, <lb/>T. II, fol. </s>

<s>128). </s></p><p type="main">

<s>Un altro confronto, fra le prime dimostrazioni date in numeri determi&shy;<lb/>nati, e queste nuove condotte col metodo degli indivisibili, non fu lasciato <lb/>indietro da Galileo, ne'<emph type="italics"/>Massimi sistemi,<emph.end type="italics"/> dove, dopo di aver costituito il trian&shy;<lb/>golo per la scala delle velocit&agrave;, suppone che il mobile, invece di partir dalla <lb/>quiete, movesse da A (nella solita ultima figura) con una velocit&agrave; iniziale <lb/>AM, eguale a FH, e con quella medesima seguitasse per tutto il tempo AF. <lb/>&Egrave; manifesto che il triangolo AFH s'&egrave; raddoppiato, trasformandosi nel ret&shy;<lb/>tangolo AFHN, e per&ograve; &ldquo; se il mobile che cadendo si &egrave; servito dei gradi di <lb/>velocit&agrave; accelerata, conforme al triangolo AFH, ha passato in tanto tempo <lb/>un tale spazio, &egrave; ben ragionevole e probabile che, servendosi delle velocit&agrave; <lb/>uniformi, e rispondenti al parallelogrammo, passi con moto equabile, nel me&shy;<lb/>desimo tempo, spazio doppio al passato dal moto accelerato &rdquo; (Alb. </s>

<s>I, 553). </s></p><p type="main">

<s>In questi dialoghi Dei due massimi sistemi la nuova Scienza galileiana <lb/>del moto appariva sull'orizzonte, come aurora, che precedeva agli altri Dia&shy;<lb/>loghi, e intanto serv&igrave; quell'insolito albore di scorta ai vigili e d'impulso <lb/>agl'irresoluti. </s>

<s>Fra questi &egrave; da annoverare de'primi lo stesso Cavalieri, il <lb/>quale dalla fecondit&agrave; del suo metodo ricav&ograve; un'altra dimostrazione dei moti <lb/>accelerati, pi&ugrave; bella di quella stessa, che avea suggerita allo stesso Galileo, <lb/>considerando i gradi delle velocit&agrave;, piuttosto che nel triangolo, in un cir&shy;<lb/>colo, il centro del quale rappresenti la quiete, e le onde concentriche, in <lb/>che si diffonde al largo, le varie velocit&agrave;, le quali sono infinite. </s>

<s>&ldquo; Ora per&shy;<lb/>ch&egrave; pare impossibile, dice l'Autore dello <emph type="italics"/>Specchio ustorio,<emph.end type="italics"/> il sommare infi&shy;<lb/>nite circonferenze, io mi prevaglio dell'area dello stesso cerchio, e ne cavo <lb/>le proporzioni delle aggregate velocit&agrave;, incominciando dal centro o dalla <lb/>quiete, e procedendo fino alla circonferenza estrema, cio&egrave; fino al massimo, <lb/>avendo dimostrato io nella mia Geometria che qual proporzione hanno i cer&shy;<lb/>chi fra loro, tale anco l'hanno tutte le circonferenze descrittibili sopra il <lb/>centro dell'uno, a tutte le circonferenze descrittibili sopra il centro dell'al&shy;<lb/>tro. </s>

<s>Perci&ograve;, se nel nostro cerchio, nel quale voglio misurare le aggregate <lb/>velocit&agrave; con la distanza di un terzo del semidiametro, per esempio, descri&shy;<lb/>ver&ograve; un cerchio, la cui circonferenza mi rappresenti un tal grado di velo&shy;<lb/>cit&agrave;, sapr&ograve; che qual proporzione ha il cerchio grande al piccolo, tale ancora <lb/>l'averanno tutte le circonferenze concentriche del cerchio grande, a tutte le <pb xlink:href="020/01/2066.jpg" pagenum="309"/>circonferenze concentriche del piccolo; cio&egrave; tutti i gradi di velocit&agrave;, acqui&shy;<lb/>stati nel trapassare dalla quiete al grado massimo, a tutti i gradi acquistati <lb/>passando dall'istessa quiete al grado intermedio, che abbiamo preso. </s>

<s>Ma i <lb/>cerchi sono tra loro come i quadrati de'semidiametri, dunque anche dette <lb/>velocit&agrave; cresceranno secondo l'incremento de'quadrati de'semidiametri. </s>

<s>Ma <lb/>con qual proporzione cresce la velocit&agrave; nel mobile, crescono anche li spazi <lb/>decorsi dall'istesso mobile, com'&egrave; ragionevole chi acquista altrettanta velo&shy;<lb/>cit&agrave;, quanta si trovava avere, guadagna ancora forza di trapassare altret&shy;<lb/>tanto spazio, quanto faceva, e cos&igrave; nelle altre proporzioni; adunque gli spazi <lb/>decorsi dal mobile, nel quale si vanno aggregando le velocit&agrave;, saranno come <lb/>i quadrati de'semidiametri de'cerchi, ne'quali si possono considerare dette <lb/>velocit&agrave;, cio&egrave; come i quadrati dei tempi, quali intenderemo nel semidiame&shy;<lb/>tro del dato cerchio. </s>

<s>Se quello dunque si supponesse diviso in cinque parti <lb/>uguali, posto che il quadrato dell'una di queste parti fosse uno, il quadrato <lb/>di due sarebbe quattro, di tre nove, di quattro sedici, e tal proporzione <lb/>avrebbero i cinque cerchi descritti sopra questi semidiametri, e perci&ograve;, sot&shy;<lb/>traendo ciascun antecedente dal suo conseguente, resterebbono questi nu&shy;<lb/>meri 1, 3, 5, 7, che mostrerebbono la progressione del minimo cerchio e <lb/>delli seguenti residui o armille, che ci rappresentano i gradi acquistati dal <lb/>mobile continuamente ne'suddetti tempi eguali &rdquo; (Bologna 1650, ediz. 2

a, <lb/>pag. 

95-97). </s></p><p type="main">

<s>Ma non era il proposito del Cavalieri quello di trattare del moto, di cui <lb/>tocca incidentemente, per confermare l'utilit&agrave;, che potrebbe venire alla Mec&shy;<lb/>canica dall'applicarvi i metodi della nuova Geometria. </s>

<s>Due trattati di quella <lb/>Scienza, della quale s'eran gi&agrave; ne'dialoghi Dei due massimi sistemi posti i <lb/>principii, apparvero contemporanei a quello pubblicato da Galileo in Leyda <lb/>nel 1638, e son gli Autori di que'trattati Del moto il nostro Giovan Batti&shy;<lb/>sta Baliani, e l'alemanno Giovan Marco Marci. </s>

<s>Ebbero tutt'e tre i valentuo&shy;<lb/>mini meriti proprii, che i giusti estimatori riconosceranno meglio dal pro&shy;<lb/>gresso della nostra Storia, la quale intanto si limita qui a dire quel che <lb/>avessero ciascuno di proprio o di comune intorno al modo di dimostrar la <lb/>legge dei moti accelerati. </s></p><p type="main">

<s>Galileo, nelle due prime proposizioni del III dialogo, e nello scolio alla <lb/>proposizione XXIII, non segue altro metodo, che quello degl'indivisibili, e <lb/>perci&ograve;, repudiata la prima maniera da lui tenuta avanti al 1623, cio&egrave; quando <lb/>ancora non aveva avuto notizia della Geometria nuova del Cavalieri, s'at&shy;<lb/>tenne a questa seconda, come quella, che, sostituendo il nuovo calcolo dif&shy;<lb/>ferenziale, rendeva essa sola trattabile con precisione una parte della Mate&shy;<lb/>matica, nella quale s'introducevano gl'infiniti. </s></p><p type="main">

<s>E qui non si vorrebbe da noi tornare sull'odioso argomento del rim&shy;<lb/>proverare l'ingratitudine, con la quale Galileo rimerit&ograve; la Geometria nuova <lb/>dei prestati servigi, ma non si pu&ograve; lasciare inavvertita una cosa, necessaria <lb/>a intendere quel che non intesero que'dotti uomini romani, presieduti da <lb/>Stefano Gradi, i quali, per levar di mezzo ogni occasione di accusa, e per <pb xlink:href="020/01/2067.jpg" pagenum="310"/>fare sparire le contradizioni, manifeste ne'dialoghi Delle due nuove scienze, <lb/>non videro con la mente affascinata que'teoremi, e que'problemi, che pro&shy;<lb/>cedono ivi dimostrati e risoluti con gli schietti metodi del Cavalieri. </s></p><p type="main">

<s>Sembrerebbe la cosa incredibile, se non avessimo, oltre ai recati nel <lb/>capitolo II, nuovi documenti di ci&ograve;, in una scrittura dello stesso Gradi, con&shy;<lb/>servataci dal Viviani, l'intenzione della quale scrittura rivelasi dalle prime <lb/>parole, con le quali incomincia: &ldquo; Videtur assignari posse non insufficiens <lb/>causa etiam a priori eius aequalitatis. </s>

<s>quam in motu naturaliter accelerato <lb/>crescentis per singula momenta velocitatis clarissimus Galieus, in egregio <lb/>suo de hac materia tractatu, supponit, nec alia probatione firmare videtur, <lb/>quam quae a convenentia quadam ac Naturae in similibus operibus consue&shy;<lb/>tudine duci potest &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXII, fol. </s>

<s>92). </s></p><p type="main">

<s>Per assegnare la causa sufficiente di quelle egualit&agrave; di moto accelerato <lb/>prende il Gradi la linea AB (fig. </s>

<s>143), divisa in parti uguali determinate, <lb/><figure id="id.020.01.2067.1.jpg" xlink:href="020/01/2067/1.jpg"/></s></p><p type="caption">

<s>Figura 143.<lb/>per la scala dei tempi, secondo i quadrati de'quali <lb/>crescon gli spazi, &ldquo; ita ut toto tempore AB spatium <lb/>loci confectum a dato corpore sit aequale rectangulis <lb/>ACD, ECF, GEH, BGI contentis a figura denticulata <lb/>ABL. </s>

<s>Ita sine dubio eveniret, si dicta motus velocitas, <lb/>in dato corpore perseverans, nonnisi per assignata in&shy;<lb/>tervalla sua caperet incrementa. </s>

<s>Quod si talia intervalla <lb/>in eodem tempore duplo minora essent, et consequen&shy;<lb/>ter prima velocitas AD duplo maior poneretur eadem <lb/>figura ABL, minutioribus sine dubio denticulis incisa <lb/>esset, et ad trianguli ABL naturam propius accederet, <lb/>idque semper magis ac magis ita eveniret, quo minor prima velocitas esset, <lb/>et quo plura adeoque breviora intervalla idem illud temporis spatium se&shy;<lb/>carent &rdquo; (ivi, fol. </s>

<s>95). </s></p><p type="main">

<s>Ora, fa certo gran maraviglia che il Gradi, galileiano s&igrave; dotto, amico <lb/>al Viviani e a Michelangiolo Ricci estimatissimo, si mettesse a discorrere <lb/>cos&igrave;, per supplire al difetto di Galileo, il quale aveva, nella giornata II Dei <lb/>massimi sistemi, fatto fra il Sagredo e il Salviati discorrere in quel mede&shy;<lb/>simo modo, per assegnar quella medesima causa dell'equalit&agrave; del moto ac&shy;<lb/>celerato, che il Gradi si proponeva di assegnare a priori. </s>

<s>Anche il Sagredo <lb/>infatti, che determinava co'numeri conseguenti dall'uno al cinque le cre&shy;<lb/>scenti velocit&agrave;, se fosse dall'aritmetica passato alla geometria, avrebbe rap&shy;<lb/>presentati gli spazi col triangolo denticulato, ma il Salviati soggiungeva a <lb/>quel discorso che l'addentellatura si viene a ridurre all'uguaglianza della <lb/>linea AL del triangolo, non facendo crescere le velocit&agrave; secondo numeri de&shy;<lb/>terminati, ma secondo le infinite linee, che contessono la superfice del trian&shy;<lb/>golo stesso, come insegnava a fare il Cavalieri, le nuove dottrine del quale <lb/>son, con sottil arte da Galileo velate di s&igrave; strano mistero, da rintuzzar l'acume <lb/>del Gradi e de'suoi amici e colleghi. </s></p><p type="main">

<s>Quale efficacia avessero propriamente le tradizioni della scienza italiana <pb xlink:href="020/01/2068.jpg" pagenum="311"/>sulla mente di Giovan Marco, &egrave; difficile a indovinare in scrittore, che par <lb/>simile a una di quelle montagne, mal discernibile ad occhio nudo nella pro&shy;<lb/>spettiva aerea del lontano orizzonte. </s>

<s>Comunque sia per&ograve;, dal principio che <lb/>la virt&ugrave; locomotiva cresce in quel modo, che cresce il triangolo <emph type="italics"/>sibi simile <lb/>manens,<emph.end type="italics"/> dimostra la sua XII proposizione: &ldquo; Incrementa velocitatis ratio&shy;<lb/>nem habent quam temporum quadrata &rdquo; (De proport. </s>

<s>motus cit., fol. </s>

<s>19 <lb/>a tergo), e pur col modesimo principio dimostra l'altra proposizione XVIII: <lb/>&ldquo; Velocitas in fine motus, aequabili tempore, per spatium movet duplum <lb/>velocitatis eodem motu collectae &rdquo; (ibid., fol. </s>

<s>25). </s></p><p type="main">

<s>Ma il Baliani, seguendo altra via, che in una lettera al Castelli chiama <lb/>egli stesso <emph type="italics"/>molto stravagante,<emph.end type="italics"/> riusc&igrave; a dimostrare la medesima proposizione, <lb/>concludendola dalle propriet&agrave; dei pendoli di varia lunghezza. </s>

<s>&ldquo; Iam ante <lb/>plures annos, cos&igrave; ci racconta l'Autore la storia di queste sue meccaniche <lb/>speculazioni, mihi visus sum assequi causam accelerationis motus, dum adhuc <lb/>mobile a motore impellitur; quia nimirum mobili moto imprimatur impetus <lb/>causa motus subsequentis, ex quo in secundo tempore adsunt duo motores, <lb/>unde est velocior, et impetus maior. </s>

<s>In tertio tempore sunt duo itidem mo&shy;<lb/>tores, et alter, puta impetus maioris virtutis, unde motus adhuc celerior, et <lb/>ita deinceps. </s>

<s>Non vero ex hoc constabat qua proportione talis acceleratio <lb/>fieret. </s>

<s>Interdum, dum pendulorum motus perquirerem, praeter expectatio&shy;<lb/>nem se se mihi obtulit eorum longitudines diuturnitatibus in duplicata re&shy;<lb/>spondere ratione, de quo in prioris libri praefatione, ex quo demum nihil <lb/>minus cogitanti mihi in sexta propositione eiusdem deducere contigit mo&shy;<lb/>tum tali pacto accelerari, ut in secundo tempore sit prioris triplum, in ter&shy;<lb/>tio quintuplum, et deinceps iuxta numerorum imparum progressionem &rdquo; (De <lb/>motu natur. </s>

<s>cit., pag. </s>

<s>99). </s></p><p type="main">

<s>Per dimostrare la VI proposizione citata, e che si formula <emph type="italics"/>Lineae de&shy;<lb/>scensus gravium, dum naturali motu perpendiculariter feruntur, sunt in <lb/>duplicata ratione diuturnitatum,<emph.end type="italics"/> l'Autore suppone come cosa vera di fatto <lb/>l'isacronismo dei pendoli, rimossi per qualunque ampiezza nella quarta del <lb/>cerchio, e principalmente ritien come certo per esperienza che &ldquo; Pendulo&shy;<lb/>rum inaequalium longitudines sunt ut <lb/>quadrata vibrationum &rdquo; (ibid., pag. </s>

<s>15). </s></p><p type="main">

<s>S'aggiungono ai supposti quattro <lb/>petizioni, la prima delle quali &egrave; che le <lb/>porzioni delle vibrazioni, fatte da due <lb/>pendoli di varia lunghezza, sieno in cia&shy;<lb/>scuno proporzionali alle stesse vibrazioni <lb/>intere, a quelle cio&egrave; che farebbero per <lb/>tutta intera la quarta del cerchio, come <lb/>per esempio, se sieno due pendoli, uno <lb/>di lunghezza AB (fig. </s>

<s>144), l'altro di <lb/><figure id="id.020.01.2068.1.jpg" xlink:href="020/01/2068/1.jpg"/></s></p><p type="caption">

<s>Figura 144.<lb/>lunghezza AE, chiede gli sia concesso <lb/>che il tempo della intera vibrazione BII <pb xlink:href="020/01/2069.jpg" pagenum="312"/>stia al tempo della intera vibrazione EI, come il tempo della parzial vibra&shy;<lb/>zione BC sta al tempo di EF. </s>

<s>Nelle petizioni II e III vuole il Baliani che la <lb/>circonferenza si riguardi come un poligono di moltissimi lati, e crede non <lb/>doverglisi negare che, data una linea di qualunque lunghezza, non si possa <lb/>descrivere una circonferenza tanto ampia, che quella stessa linea non trovi <lb/>da rettificarsi in una qualche porzione della detta circonferenza. </s>

<s>Che se <lb/>questo non gli si neghi, gli verr&agrave; ultimamente concesso che i cadenti ser&shy;<lb/>bino nel moto retto e nel circolare la medesima proporzione. </s>

<s>Dietro ci&ograve;, <lb/>ecco come facilmente il Baliani dimostra il suo teorema. </s></p><p type="main">

<s>Sieno KM, LN, nella detta figura, due spazi verticali passati da due <lb/>gravi ne'tempi O, P: convien dimostrare essere KM:LN=O2:P2. </s>

<s>Si de&shy;<lb/>scrivano le due quarte di cerchio HCB, IFE con raggi di tal lunghezza, che <lb/>gli archi BC, EF si possano riguardare come due linee rette uguali a KM, <lb/>LN, e s'immagini che i gravi cadenti per queste linee siano le sfere pen&shy;<lb/>dole H, I, sollevate in B, E Il tempo per BC dunque sar&agrave; O, e per EF <lb/>sar&agrave; P, ond'&egrave; che, per la IIIa supposizione, avremo AB:AE=O2:P2. </s>

<s>Ma <lb/>per la somiglianza de'triangoli ABC, AEF abbiamo AB:AE=BC:EF, e <lb/>BC=KM, EF=LN, dunque KM:LN=O2:P2, come volevasi dimo&shy;<lb/>strare. </s></p><p type="main">

<s>L'altra proposizione, corollario di questa, che &egrave; formulata: &ldquo; Gravia na&shy;<lb/>turali motu descendunt semper velocius, ea ratione ut temporibus aequalibus <lb/>descendant per spatia semper maiora, iuxta proportionem quam habent im&shy;<lb/>pares numeri ab unitate inter se &rdquo; (ibid., pag. </s>

<s>25); si dimostra dal Baliani <lb/>in modo grafico, ma evidentissimo, in questa maniera: &ldquo; Sieno le linee <lb/>uguali AB, BC, CD (fig. </s>

<s>145) a rappresentare i tempi uguali, e i quadrati <lb/><figure id="id.020.01.2069.1.jpg" xlink:href="020/01/2069/1.jpg"/></s></p><p type="caption">

<s>Figura 145.<lb/>AE, AF, AG rappresentino gli spazi. </s>

<s>Si vede <lb/>che al primo tempo AB corrisponde il solo qua&shy;<lb/>drato AE; al secondo tempo AC corrisponde il <lb/>quadrato AF, composto d'altri quattro pi&ugrave; pic&shy;<lb/>coli quadrati tutti uguali ad AE, e al terzo tempo <lb/>AD corrisponde il quadrato AG, che de'quadrati <lb/>piccoli uguali ad AE ne comprende evidente&shy;<lb/>mente nove. </s>

<s>Cosicch&egrave;, essendo 1, 2, 3.... i <lb/>tempi, gli spazi respettivamente passati son co&shy;<lb/>me 1, 4, 9...., e perci&ograve; gli incrementi come <lb/>1, 3, 5...., secondo la serie de'numeri impari <lb/>ab unitate. </s></p><p type="main">

<s>Si compiaceva seco stesso il Baliani della facilit&agrave;, con la quale era riu&shy;<lb/>scito a dimostrar quel medesimo di Galileo, senza farsi imitator di nessuno, <lb/>ma, venendo a istituire fra'due Autori il confronto, troppo bene se ne ri&shy;<lb/>conosceva la differenza, e quanto rimanesse indietro la fisica sperimentale <lb/>dell'uno alla matematica rigorosa dell'altro. </s>

<s>Galileo stesso, tanto pi&ugrave; viva&shy;<lb/>mente eccitato dall'emulazione, ne faceva rilevare queste differenze, e ardi&shy;<lb/>menti chiamava i supposti del Baliani, e le petizioni errori. </s>

<s>Di ci&ograve; scriveva <pb xlink:href="020/01/2070.jpg" pagenum="313"/>in una lettera al Ren&igrave;eri (Campori, Carteggio eit., pag. </s>

<s>539) la quale non &egrave; <lb/>pervenuta alla nostra notizia, ma vi supplisce una scrittura, che il Viviani <lb/>fece in Arcetri, essendo ospite in casa il Maestro, che glie la dettava, e che <lb/>perci&ograve; si dice essere stata scritta <emph type="italics"/>ad mentem Galilaei.<emph.end type="italics"/> &Egrave; intitolata <emph type="italics"/>Sopra i <lb/>principii del Baliani,<emph.end type="italics"/> a cui dal Censore si rivolge cos&igrave; il discorso: </s></p><p type="main">

<s>&ldquo; &Egrave; la nostra intenzione investigare e dimostrare geometricamente ac&shy;<lb/>cidenti e passioni, che accaggiono ai mobili gravi naturalmente e libera&shy;<lb/>mente discendenti sopra spazi retti differenti, o di lunghezza o d'inclinazione, <lb/>o d'ambedue insieme. </s>

<s>Nel venir poi alla elezione dei principii, sopra i quali <lb/>deve esser fondata la scienza, prendete come chiara notizia accidenti, i quali <lb/>niuna connessione hanno con moti fatti sopra linee non rette, non di asse&shy;<lb/>gnabile inclinazione, n&egrave; che in esse le diverse lunghezze operino quello, che <lb/>operano nelle linee rette, ma in tutto e per tutto cose differentissime, lo che <lb/>mi par grave errore, e tanto maggiore, quanto che e'se ne tira dietro un <lb/>altro non minore. </s>

<s>Mi dichiaro: voi pigliate come principio noto e indubi&shy;<lb/>tato le vibrazioni del medesimo pendolo farsi tutte sotto tempi uguali, siano <lb/>elle di qualsivoglia grandezza. <emph type="italics"/>Item<emph.end type="italics"/> supponete i tempi delle vibrazioni di <lb/>pendoli diseguali esser tra di loro in suddupla proporzione delle lunghezze <lb/>dei loro fili, assunto veramente ardito. </s>

<s>E da questo, che supponete accadere <lb/>nei mobili discendenti per circonferenze di cerchi, volete raccorre quello che <lb/>occorre nei moti retti. </s>

<s>Ma se io non erro, assai meno obliquamente si po&shy;<lb/>teva ottener l'intento, discorrendo cos&igrave;: &rdquo; </s></p><p type="main">

<s>&ldquo; La linea AB (fig. </s>

<s>146) intendasi rappresentare il filo pendente, e, <lb/>stando fermo il termine supremo A, intendasi il mobile posto in B dise&shy;<lb/>gnare l'arco del quadrante BC. Similmente, preso A<emph type="italics"/>b<emph.end type="italics"/> come pendolo minore, <lb/><figure id="id.020.01.2070.1.jpg" xlink:href="020/01/2070/1.jpg"/></s></p><p type="caption">

<s>Figura 146.<lb/>sia l'arco del quadrante <emph type="italics"/>bc<emph.end type="italics"/> quello, che descri&shy;<lb/>verebbe il mobile posto in <emph type="italics"/>b,<emph.end type="italics"/> e d'essi qua&shy;<lb/>dranti siano le corde suttese BC, <emph type="italics"/>bc,<emph.end type="italics"/> ed in&shy;<lb/>tendansi le tangenti orizzontali BD, <emph type="italics"/>bd<emph.end type="italics"/> alle <lb/>perpendicolari CD, <emph type="italics"/>cd.<emph.end type="italics"/> Ora, essendo le due <lb/>declinazioni in tutto e per tutto simili, molto <lb/>ragionevolmente si pu&ograve; prendere, e come prin&shy;<lb/>cipio noto supporre, che le proporzioni dei <lb/>moti, che accadessero farsi sopra le rette AB, <lb/>BC, per l'arco CB, fossero le medesime, che <lb/>nella minor figura per le linee analoghe A<emph type="italics"/>b, <lb/>bc,<emph.end type="italics"/> onde, permutando, il moto per l'arco <emph type="italics"/>cb,<emph.end type="italics"/><lb/>al moto per l'arco CB abbia la medesima proporzione, che il moto per la <lb/>perpendicolare <emph type="italics"/>ab,<emph.end type="italics"/> al moto per la perpendicolare AB, onde, pigliando per <lb/>supposto che i tempi per gli archi siano in suddupla proporzione delle <lb/>lunghezze dei fili, gi&agrave; &egrave; manifesto che con altrettanta verit&agrave; si pu&ograve; supporre <lb/>che i tempi per le perpendicolari A<emph type="italics"/>b,<emph.end type="italics"/> AB siano in suddupla proporzione <lb/>delle lunghezze A<emph type="italics"/>b,<emph.end type="italics"/> AB. </s>

<s>E cos&igrave; si viene a schivare la supposizione assai <lb/>dura, come appresso diremo, che i moti per le parti minime delli archi siano <pb xlink:href="020/01/2071.jpg" pagenum="314"/>come se fosser fatti per linee rette, assunto come dico assai duro, imperoc&shy;<lb/>ch&egrave; con gran ragione pu&ograve; il lettore domandare che gli sia assegnata la quan&shy;<lb/>tit&agrave; dell'arco, che V. S. chiama minima, sicch&egrave;, per esempio, ella intenda <lb/>l'arco esser minimo fino che non giunga alla met&agrave; di un grado. </s>

<s>Inoltre, <lb/>sarebbe stato necessario dichiararsi quale delle stesse linee rette si deva <lb/>prendere per gli archi minimi, cio&egrave; se quella, che, partendosi dal medesimo <lb/>punto dell'arco, tocca la circonferenza, oppure la sega come corda di esso <lb/>arco minimo, oppure &egrave; una delle altre molte, che dal medesimo punto primo <lb/>possono tirarsi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Da queste molte linee pare che venga esclusa la tangente necessa&shy;<lb/>riamente, imperocch&egrave;, considerando nella figura passata la tangente dell'arco <lb/>BC nel punto B; che viene ad essere la orizzontale BD, manifesta cosa &egrave; <lb/>che il mobilo, posto sopra di essa, in nessuna parte si mover&agrave;, ma bene, <lb/>posto in qualsivoglia punto dell'arco BC remoto dal B, discender&agrave; egli in B. </s>

<s><lb/>Essendo dunque la discrepanza tra la tangente e l'arco tanto grande, per <lb/>quanto appartiene al moto, quanto &egrave; differente la quiete dal moto; con poca <lb/>o niuna probabilit&agrave; si potr&agrave; supporre che il moversi dal punto C, per la <lb/>tangente o per l'arco, siano l'istessa cosa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma vegghiamo un'altra disparit&agrave; massima. </s>

<s>Niuno negher&agrave; i moti del <lb/>medesimo mobile, fatti sopra piani di diversa inclinazione, esser tra di loro <lb/>differenti, e che in conseguenza un moto, il quale, cominciato sopra una tale <lb/>inclinazione debba di parte in parte trapassar sopra altrettante altre diverse <lb/>inclinazioni, sar&agrave; sommamente differente da quello, che sopra una stessa in&shy;<lb/>clinazione deve andarsi continuando. </s>

<s>Ora, nella circonferenza del quadrante <lb/>CB, tante sono le diverse inclinazioni, quante le tangenti, e queste sono <lb/>quante i punti, cio&egrave; infinite, per lo che anco in qualsivoglia piccola parte <lb/>della circonferenza, siccome vi sono infiniti punti, vi sono anche infinite in&shy;<lb/>clinazioni, per la mutazione delle quali non si pu&ograve; dire che il moto per <lb/>l'arco possa esser simile, non che l'istesso, che per una medesima inclina&shy;<lb/>zione sola. </s>

<s>&rdquo; (MSS. Gal., P. V, T. IV, fol. </s>

<s>36-38). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Il Discorso di Galileo non sembra che fosse mandato al Baliani, a cui <lb/>era indirizzato, ma egli ebbe sentore di quelle censure, divulgatesi in Ge&shy;<lb/>nova fra gli amici di Daniele Spinola, il quale cos&igrave; scriveva a Galileo stesso <lb/>in una sua del di 25 Marzo 1639: &ldquo; Ho da pregiarmi poi grandemente che <lb/>qualche pensiero, venutomi circa il libro del signor Baliani, sia stato da <lb/>V. S. autenticato nella lettera scritta ultimamente al p. </s>

<s>d. </s>

<s>Vincenzo, impe&shy;<lb/>rocch&egrave;, tacendo del rimanente, quelle sue supposizioni mi son sempre parse <lb/>alquanto difficili da concedere &rdquo; (Campori, Carteggio cit., pag. </s>

<s>539). Di qui <lb/>si passava a fare il confronto fra i due emuli Autori della Scienza del moto, <pb xlink:href="020/01/2072.jpg" pagenum="315"/>e si avviliva l'uno, spesso con passionato giudizio, per secondare le gloriose <lb/>inclinazioni dell'altro. </s>

<s>Lo stesso Spinola scriveva nel seguente Agosto al me&shy;<lb/>desimo Galileo: &ldquo; Veramente i supposti del signor Giovan Batista appresso <lb/>di ognuno han mestieri di gagliarda dimostrazione..... Or considerisi qual <lb/>piacere si pu&ograve; cavare dalle proposizioni fondate sopra di essi, le quali molti <lb/>stimano che non sian del tutto sue, perch&egrave; si vede di dove ponno esser <lb/>tolte. </s>

<s>Ma nel libro di V. S. son congiunte la chiarezza, la facilit&agrave;, la novit&agrave;, <lb/>il diletto, il profitto e la maraviglia in ogni cosa &rdquo; (ivi, pag. </s>

<s>546). </s></p><p type="main">

<s>Tale era il giudizio che sentiva di s&egrave; il Baliani fare a'suoi concittadini, <lb/>e dovette sentir rammarico, pi&ugrave; che delle lodi esagerate del suo rivale, delle <lb/>odiosit&agrave; calunniose, in chi sembrava dover piuttosto inclinare alla benevo&shy;<lb/>lenza. </s>

<s>Poteva consolarsi de'pi&ugrave; assennati giudizi di coloro, i quali dicevano <lb/>aver tenuto i due Autori due vie diverse, e ora rimanere indietro l'uno, <lb/>ora precedere all'altro; ma, vinto da un sentimento d'ira vendicatrice, volle <lb/>con le calunnie rispondere ai calunniosi, e dire che anzi Galileo aveva preso <lb/>da lui, n&egrave; mancarono animi disposti ad accogliere quelle suggestioni. </s></p><p type="main">

<s>Fu tra costoro de'primi il Cabeo, il quale nel suo libro primo sulla <lb/>Meteorologia di Aristotile si maravigli&ograve; come Galileo si fosse pubblicamente <lb/>vantato di essere egli venuto il primo ad annunziare al mondo la ritrovata <lb/>misura nell'impeto dei cadenti. </s>

<s>&ldquo; Melius dixisset se nusquam legisse aut <lb/>scivisse ab aliquo mensuratum, nam et ego et ali mecum mensuraverant, <lb/>et fateor me ab ipso hoc non didicisse &rdquo; (T. </s>

<s>I cit., pag. </s>

<s>92). Intende per <lb/>quegli altri, ch'ebbe soci nelle operazioni, il Baliani, il quale alcuni anni <lb/>pi&ugrave; tardi citava questo passo del Cabeo al Mersenno, per testimoniare le sue <lb/>pretensioni di aver prevenuto Galileo. </s>

<s>Al quale annunzio esso Mersenno ri&shy;<lb/>spondeva cos&igrave; con lettera del d&igrave; 25 Ottobre 1647, da Parigi: &ldquo; Ho gran <lb/>gusto che V. S. m'abbia imparato per l'ultima sua che Galileo non sia il <lb/>primo, che ha osservato la proporzione del moto dei corpi gravi, che ca&shy;<lb/>scano gi&ugrave;, perch&egrave; io pubblicher&ograve; a tutti quanti che in ci&ograve; siete stato il primo <lb/>osservatore, come l'ha confermato il P. </s>

<s>Cabeo nel luogo citato da voi nelle <lb/>sue <emph type="italics"/>Meteore &rdquo;<emph.end type="italics"/> (Baliani, Opere diverse, Genova 1666, pag. </s>

<s>10). </s></p><p type="main">

<s>Dovevano esser passati pochi anni, da che il medesimo Mersenno aveva <lb/>ricevuto lettere di un altro, che nella scoperta legge dei moti accelerati pre&shy;<lb/>tendeva il primato su Galileo. </s>

<s>Il Cartesio infatti gli scriveva, un luned&igrave; mat&shy;<lb/>tina, che un tal D. B. era venuto a riprendersi i dialoghi Dei due massimi <lb/>sistemi, che gli aveva portato a leggere il sabato sera, cosicch&egrave; non potette <lb/>avere che per sole trent'ore il libro fra le mani. </s>

<s>&ldquo; Integrum tamen evolvi.... <lb/>Cogitationum mearum nonnullas hic illic sparsas animadverti, atque inter <lb/>alias duae sunt, quas ad te scripsisse me opinor, nempe spatia, quae cor&shy;<lb/>pora gravia desc<gap/>ndendo percurrunt, esse ad se invicem ut quadrata tem&shy;<lb/>porum, quae descendendo impendunt.... altera est vibrationes eiusdem fu&shy;<lb/>nis pari fere temporis spatio fieri, quamvis aliae aliis longe maiores esse <lb/>possint &rdquo; (Epist., P. II cit., pag. </s>

<s>219). In un'altra Epistola, indirizzata pure <lb/>al Mersenno, accenna il Cartesio stesso a un Innominato che, se non &egrave; Ga-<pb xlink:href="020/01/2073.jpg" pagenum="316"/>lileo, &egrave; in ogni modo oratoriamente rivestito di un abito, che non si diffe&shy;<lb/>renzia in nulla da quello di Galileo, di cui dice che &ldquo; supponit mecum id <lb/>quod semel moveri coepit sponte sua pergere in motu, etiam absque novo <lb/>impulsu, donec ab aliqua causa exteriori impediatur, et proinde corpus ali&shy;<lb/>quod, semel motum in vacuo, motum iri in aeternum, sed in aere aliter se <lb/>res habet, propterea quod aeris resistentia eius motum paulatim minuit. </s>

<s><lb/>Praeterea supponit corpus aliquod gravitate sua singulis momentis deorsum <lb/>impelli, atque ita in vacuo celeritatem motus perpetuo augeri, secundum <lb/>proportionem a me antea observatam, quam illi plus decem retro annos <lb/>explicui, hoc enim ab eo tempore in adversariis meis notatum reperio &rdquo; <lb/>(ibid., pag. </s>

<s>299). </s></p><p type="main">

<s>Mancando a questa oratoria esercitazione in forma epistolare la data, <lb/>non &egrave; possibile assegnar l'anno preciso, in cui il Cartesio not&ograve; fra'suoi ri&shy;<lb/>cordi l'anno della scoperta, che nel libro de'ricordi di Galileo, per certis&shy;<lb/>simo documento, &egrave; il 1604, quando il Filosofo francese, nato nel 1596, era <lb/>ancora fanciullo. </s>

<s>Quelle nuove scoperte verit&agrave; intorno alle leggi dei moti <lb/>accelerati ora le chiama il Cartesio sue <emph type="italics"/>cogitazioni,<emph.end type="italics"/> ora sue <emph type="italics"/>osservazioni,<emph.end type="italics"/><lb/>lasciando noi che leggiamo incerti se si tratti di matematiche speculazioni <lb/>o d'esperienze. </s>

<s>Ma perch&egrave; a sperimentare il fatto mancava anche a lui l'arte, <lb/>e mancavano gli strumenti, non potevano essere quelle sue altro che cogi&shy;<lb/>tazioni, fondate come quelle di Galileo sul principio dell'inerzia della mate&shy;<lb/>ria, e sul supposto che le velocit&agrave;, via via sopraggiunte al mobile, siano pro&shy;<lb/>porzionali ai tempi. </s>

<s>Nella seconda infatti delle Epistole sopra commemorate <lb/>il ragionamento dell'Autore &egrave; tale: &ldquo; Supponatur molem plumheam gravi&shy;<lb/>tatis suae vi cadere, et statim, post primum quo coepit descendere momen&shy;<lb/>tum, Deus totam eius gravitatem adimat, ita ut moles ista gravior non sit <lb/>aere aut pluma: nihilominus perget descendere in vacuo, quandoquidem <lb/>incoepit moveri, neque porro ratio reddi potest cur deberet quiescere..... <lb/>Verum non amplius augebitur eius celeritas, et si postmodum Deus ad mo&shy;<lb/>mentum reddit huic moli plumbeae totam, quam ante habuerat, gravitatem, <lb/>et momento post eam illi iterum adimat, annon liquet secundo hoc momento <lb/>molem hanc plumbeam, haud minus quam primo, impulsum iri ab eadem <lb/>illa vi gravitatis, et proinde motus eius dupla velocitate auctus erit, idemque <lb/>fiet in tertio, quarto et quinto momentis? </s>

<s>&rdquo; (ibid., pag. </s>

<s>298, 99). </s></p><p type="main">

<s>&Egrave; questo, come dicemmo, il ragionamento medesimo, che faceva anche <lb/>Galileo, cosicch&egrave; ambedue i Filosofi, dai principii gi&agrave; posti dal Benedetti, e <lb/>divenuti oramai nella scientifica istituzione universali, giungevano alle me&shy;<lb/>desime conclusioni: ci&ograve; che, mentre toglie da una parte ogni maraviglia <lb/>nata dal pensare a un fortuito incontro, fa comprender dall'altra quanto <lb/>irragionevolmente chiamasse il Cartesio sue cogitazioni le cose lette in Ga&shy;<lb/>lileo, non ripensando che, portati i semi sulle libere ali dei venti, possono <lb/>cader qui come l&agrave;, un poco prima o un poco dopo, e bench&egrave; d'una origine, <lb/>germogliar solitari, crescere separati e vivere sconosciuti. </s>

<s>Ma il Cartesio, che <lb/>presumeva di esser nato spontaneo, senza seme, e che perci&ograve; credeva di non <pb xlink:href="020/01/2074.jpg" pagenum="317"/>avere nessun simile a s&egrave;, chiamava sue certe virt&ugrave;, ch'egli stesso, e gli altri <lb/>ne'quali s'abbatteva a ritrovarle, avevano partecipate dai generanti. </s></p><p type="main">

<s>Queste frettolose considerazioni che, in universale applicate, togliereb&shy;<lb/>bero via le contese del mio e del tuo, nella storia delle scoperte cos&igrave; fre&shy;<lb/>quenti; si dovrebbero applicare, se fosse il caso, anche al Baliani. </s>

<s>Diciamo <lb/>se fosse il caso, perch&egrave; lo sdegnato Genovese si serv&igrave;, a persuadere pi&ugrave; fa&shy;<lb/>cilmente nel Cabeo, nel Mersenno e negli altri cos&igrave; fatti, le sue ragioni, del&shy;<lb/>l'equivoco, che nasceva dal non distinguere nella caduta dei gravi le sem&shy;<lb/>plici velocit&agrave; osservate dalla legge delle loro proporzioni, potendo intorno a <lb/>quelle citar testimoni i Savonesi, i quali avevano veramente veduto cader <lb/>dall'alto della loro rocca a scientifico esercizio, le palle dei cannoni parec&shy;<lb/>chi anni prima, che si leggessero i dialoghi Dei due massimi sistemi. </s></p><p type="main">

<s>Prima per&ograve; di essere entrato in queste gare, incitatovi dagli odiosi pa&shy;<lb/>ragoni, e principalmente dagl'ingiusti giudizi de'suoi concittadini, aveva il <lb/>Baliani stesso confessato il vero al Castelli, raccontandogli cos&igrave; in una let&shy;<lb/>tera da Savona, del d&igrave; 20 Febbraio 1627, com'avuta da Galileo la notizia <lb/>che l'incremento degli spazi nelle cadute naturali dei gravi &egrave; secondo la <lb/>serie de'numeri impari, gli occorresse senz'altro, per una via nuova e ina&shy;<lb/>spettata, di ritrovar ora la dimostrazione: &ldquo; Facendo il trattato dei solidi, <lb/>cos&igrave; propriamente egli dice, avvenne che senza cercarla mi riusc&igrave; a parer <lb/>mio ben dimostrata una proposizione, per una via molto stravagante, la <lb/>quale il signor Galileo m'avea detta per vera, senza per&ograve; addurmene la di&shy;<lb/>mostrazione, ed &egrave; che i corpi di moto naturale vanno aumentando la velo&shy;<lb/>cit&agrave; loro con la proporzione 1, 3, 5, e cos&igrave; in infinito &rdquo; (Alb. </s>

<s>IX, 142). </s></p><p type="main">

<s>La question del primato fra i pretendenti &egrave; cos&igrave; dunque definitivamente <lb/>decisa a favore di Galileo, alla compiuta gloria del quale rimane ancora a <lb/>veder come venisse finalmente a confermarsi la verit&agrave; di quella legge dei <lb/>moti accelerati, ch'egli ebbe il primo scoperta e dimostrata. </s>

<s>Non manca&shy;<lb/>rono, com'&egrave; da credere, nemmeno intorno a questa novit&agrave; i dubbi e le con&shy;<lb/>tradizioni, di alcune delle quali, come di quelle del Cabeo, ci vorremmo <lb/>volentieri passare, per non essere provocate che dal mal animo o dalla igno&shy;<lb/>ranza. </s>

<s>Nel I libro de'commentari sulla Meteorologia aristotelica fa dir l'Au&shy;<lb/>tore a Galileo &ldquo; velocitatem temporibus aequalibus crescere iuxta numeros <lb/>impares &rdquo; (T. </s>

<s>I cit., pag. </s>

<s>94) e costruendo il triangolo dimostra che invece <lb/>crescono come la serie de'numeri naturali, non avvedendosi esser questa <lb/>la supposizione, che lo stesso Galileo fa, e che di l&igrave; ne conseguiva non star <lb/>le velocit&agrave;, ma gl'incrementi degli spazi come la serie de'numeri impari. </s>

<s><lb/>A suggello poi di questa sua interpetrazione o maliziosa o ignorante, avendo <lb/>sotto gli occhi il triangolo, che gli rappresentava crescere ordinatamente le <lb/>velocit&agrave; da zero a un grado determinato, dice di non sapere quanta &egrave; la <lb/>velocit&agrave; &ldquo; qua quodlibet grave motum incipit &rdquo; e finisce col rimanere incerto <lb/>&ldquo; utrum possim facere triangulum velocitatis &rdquo; (ibid.). </s></p><p type="main">

<s>I dubbi, d'onde aspettava la verit&agrave; la sua conferma, volevan movere da <lb/>animi ben pi&ugrave; retti, e da ingegni pi&ugrave; meditativi, ai quali non potevano man-<pb xlink:href="020/01/2075.jpg" pagenum="318"/>car di ci&ograve; le occasioni, principalmente perch&egrave; le difficolt&agrave; di eseguirle non <lb/>lasciavano aver quella piena fede che bisognava nell'esperienze, cosicch&egrave; <lb/>ai fatti della Natura s'andava a ricercar la certezza nelle speculazioni della <lb/>Geometria. </s>

<s>Ma perch&egrave; questa stessa Geometria, bench&egrave; costituita di numeri <lb/>e di linee, s'implicava nelle passioni della materia, non poteva perci&ograve; por&shy;<lb/>gere nessun sicuro asilo alla mente, che si studiava di pellegrinare dal senso. </s>

<s><lb/>De'penosi travagli di lei in vedersi scoperto falso quel che cos&igrave; confidente&shy;<lb/>mente riteneva per vero, giova qui recar qualcuno de'pi&ugrave; notabili esempi, <lb/>il primo de'quali ci si presenta nella storia, poco dopo che le nuove leggi <lb/>dinamiche furono annunziate nei dialoghi Dei due massimi sistemi. </s></p><p type="main">

<s>Pietro Carcavil, di Parigi, mandava a Galileo, nel Maggio dell'anno 1637, <lb/>alcune carte di un suo amico, che non nomina, ma che sappiamo essere il <lb/>Fermat, il quale cos&igrave;, dop'aver dimostrato essere un'elice, e non un semi&shy;<lb/>cerchio, la linea descritta dai cadenti, incominciava le censure sopra gli altri <lb/>teoremi galileiani: &ldquo; De linea seu helice, quam describit grave naturaliter <lb/>descendens secundum proportionem motus a Galilaeo assignatam, a nobis <lb/>multa probata sunt, sed quia accuratius perpendenti haec proportio gravium <lb/>naturaliter descendentium non satis patet, imo geometricis demonstrationi&shy;<lb/>bus repugnare videtur, aliquam in experiendo fallaciam irrepsisse facile cre&shy;<lb/>diderim. </s>

<s>Quis autem rationem sensibus non praetulerit? </s>

<s>Propositionem geo&shy;<lb/>metricam huic experientiae repugnantem, praemisso postulatu, conspicemus. </s>

<s><lb/>Postulatum hoc sit: Nullum motum fieri absque celeritate corporis moti &rdquo; <lb/>(MSS. Gal., P. V, T. VII, fol. </s>

<s>98). </s></p><p type="main">

<s>Vuol da questo postulato il Fermat dimostrare esser falso quel che Ga&shy;<lb/>lileo dice del mobile che, partendosi dalla quiete, acquista via via velocit&agrave;, <lb/>mentre si muove, perch&egrave;, egli cos&igrave; argomenta, o si fa quell'acquisto nel <lb/>primo istante o in tempo determinato. </s>

<s>Se nel primo istante, come dunque <lb/>si parte dalla quiete? </s>

<s>Se in qualche tempo determinato, perch&egrave; cos&igrave; e non <lb/>prima n&egrave; dopo? </s>

<s>E perch&egrave; da questo principio, che cio&egrave;, partendosi dalla <lb/>quiete per giungere a un moto determinato, passa il mobile per tutti gl'in&shy;<lb/>finiti gradi delle velocit&agrave; intermedie, si dimostra da Galileo la proporzione <lb/>dei moti accelerati, ne conclude il Fermat &ldquo; non potest igitur constare Ga&shy;<lb/>lilaei propositio &rdquo; (ibid.). </s></p><p type="main">

<s>Galileo rispose a queste e a simili altre difficolt&agrave;, promosse dal mede&shy;<lb/>simo Censore, in una lettera, indirizzata al Carcavil stesso il d&igrave; 5 Giugno <lb/>di quell'anno 1637, da Arcetri, e son le risposte di lui, mirabil cosa, com&shy;<lb/>pendiate cos&igrave; in questo discorso che faceva il Cartesio in una delle sue epi&shy;<lb/>stole al Mersenno: &ldquo; Quod ait Galileus corpora descendentia transire per <lb/>omnes tarditatis gradus, haud puto vulgo fieri, sed non esse impessibile quin <lb/>id fiat aliquando. </s>

<s>Aberrat vero D. </s>

<s>Fermat in argumento quo utitur ad illum <lb/>refellendum, cum dicit <emph type="italics"/>acquiritur velocitas, vel in primo instanti, vel in <lb/>tempore aliquo determinato,<emph.end type="italics"/> neutrum enim verum est, et utendo terminos <lb/>scholae dici potest quod <emph type="italics"/>acquiritur in tempore inadacquate sumpto.<emph.end type="italics"/> Deni&shy;<lb/>que, quidquid ille dicit de gradibus celeritatis motus potest, eodem modo, <pb xlink:href="020/01/2076.jpg" pagenum="319"/>dici de gradibus latitudinis trianguli ABC (fig. </s>

<s>147), et tamen haud credo <lb/>negaturum il um quin inter punctum A et lineam BC reperiuntur latitudi&shy;<lb/><figure id="id.020.01.2076.1.jpg" xlink:href="020/01/2076/1.jpg"/></s></p><p type="caption">

<s>Figura 147.<lb/>nes omnes ipsa BC minores &rdquo; (Epistol., P. II cit., pag. </s>

<s>249). </s></p><p type="main">

<s>Le censure del Fermat sulla legge galileiana de'moti <lb/>accelerati, e le risposte di Galileo stesso e del Cartesio ri&shy;<lb/>masero per qualche tempo ne'privati commerci scientifici <lb/>di quegli Autori, cosicch&egrave; le prime delle dette censure, <lb/>pubblicamente note, vennero da quel Baliani, il quale ve&shy;<lb/>demmo quanto si fosse compiaciuto di aver ritrovato della <lb/>detta legge galileiana una nuova dimostrazione. </s>

<s>Notabile <lb/>che poi confessasse di essersi messo a dimostrar quel teo&shy;<lb/>rema, non perch&egrave; lo credesse vero, ma per emulare o per prevenire, in <lb/>una esercitazione geometrica, Galileo rimasto ingannato, diceva, da fallaci <lb/>esperienze, alle quali, chi saviamente supplisca con la ragione, troverebbe <lb/>non crescer veramente gli spazi secondo la serie dei numeri impari, ma se&shy;<lb/>condo quella piuttosto dei numeri naturali. </s>

<s>Il discorso, che faceva il Mate&shy;<lb/>matico genovese, per provare il suo assunto, si riduce al seguente. </s></p><p type="main">

<s>Sia da A (fig. </s>

<s>148) passato un mobile in E, indipendentemente dall'im&shy;<lb/>peto acquistato per la forza d'inerzia, la quale incominci ad agire in E. &Egrave; <lb/><figure id="id.020.01.2076.2.jpg" xlink:href="020/01/2076/2.jpg"/></s></p><p type="caption">

<s>Figura 148.<lb/>chiaro che tanto maggiori sa&shy;<lb/>ranno le parti, in che s'intende <lb/>esser diviso lo spazio AE, quanto <lb/>saranno pi&ugrave; piccole. </s>

<s>Suppongasi <lb/>che siano dieci, e che il mobile abbia in tre tempi uguali successivamente <lb/>passati gli spazi AB, BC, CD. Quante, in questi spazi, si troveranno ad AE <lb/>particelle uguali? </s>

<s>Sar&agrave; facile a dar di ci&ograve; la risposta, sommando la serie <lb/>de'numeri naturali da uno infino a dieci; da 11 infino a 20, e da 21 infino <lb/>a 30. E perch&egrave; la prima somma d&agrave; 55, la seconda 155, e la terza 255, delle <lb/>particelle uguali ad AE se ne conteranno in AB 55, in BC 155, in CD 255. <lb/>Gl'incrementi dunque degli spazi AB, BC, CD staranno come 55; 155; 255, <lb/>ossia come 11; 31; 51, con qualche notabile differenza dalla serie de'numeri <lb/>impari. </s>

<s>Ora, se non in dieci, ma in cento parti, dividasi lo spazio AE, si <lb/>trover&agrave;, come dianzi operando, contenersene in AB, di quelle centesime <lb/>5050; in BC 15050; in CD 25050, procedenti nella serie de'numeri 101, <lb/>301, 501, pochissimo differente da quella de'numeri impari ab unitate. </s></p><p type="main">

<s>Da un tal discorso poi il Baliani stesso trae questa conclusione: &ldquo; Au&shy;<lb/>getur igitur, ni fallor, motus iuxta progressionem arithmeticam, non nume&shy;<lb/>rorum imparium ab unitate hucusque creditam, sed naturalem. </s>

<s>At nihilo&shy;<lb/>minus cum fere idem effectus subsequatur, ob insensibilem discrepantiam, <lb/>mirandum non est creditum fuisse spatia esse in duplicata ratione tempo&shy;<lb/>rum, quando quidem, etiamsi verum praecise fortasse non sit, est attamen <lb/>adeo veritati proximum, ut veritatem in adhibitis experimentis sensus per&shy;<lb/>cipere nequiverit: quamobrem excusandi sunt quicumque ita censuerunt. </s>

<s><lb/>Ego autem modo veritatem delitescentem detexisse spero, causam nimirum, <pb xlink:href="020/01/2077.jpg" pagenum="320"/>qua huiusmodi proportio emanat aperuisse, et insuper quales errores fue&shy;<lb/>rint in suppositionibus et experimentis hucusque habitis, quod an re vera <lb/>consecutus fuerim aliorum sit iudicium &rdquo; (De motu natur. </s>

<s>cit., pag. </s>

<s>113). </s></p><p type="main">

<s>De'chiamati a dare il loro giudizio alcuni, come Onorato Fabry, rispo&shy;<lb/>sero stranamente che, tanto poteva esser vera l'ipotesi galileiana, quanto <lb/>un'altra diversa, ch'egli stesso, il Fabry, proponeva, e secondo la quale sa&shy;<lb/>rebbero gl'incrementi degli spazi come la serie de'numeri 4, 8, 16, 32, 64...: <lb/>quella, cio&egrave; l'ipotesi galileiana, &ldquo; ad usum omnino adhibenda est, &rdquo; ma vo&shy;<lb/>lendo ridurre il fatto alla vera causa dell'accelerazione, &ldquo; mea certe, non <lb/>modo praeferenda est, verum etiam necessario tenenda &rdquo; (Dial. </s>

<s>physici De <lb/>motu Terrae, Lugduni 1665, pag. </s>

<s>68). </s></p><p type="main">

<s>Altri per&ograve; di pi&ugrave; senno, come il Mariotte, traevano dal discorso del Ba&shy;<lb/>liani verissimo una conclusione affatto diversa, riducendola a confermare la <lb/>legge galileiana, la quale, perciocch&egrave; &egrave; solo allora esattamente dimostrabile <lb/>quando il tempo e lo spazio son per via degl'indivisibili rappresentati dagli <lb/>infiniti punti di una linea, e dalle infinite linee di un triangolo; par che <lb/>dunque sia da tener per la pi&ugrave; vera la serie de'numeri impari, alla quale <lb/>tanto pi&ugrave; ci si avvicinava, quanto pi&ugrave; lo spazio AE, nel sopra riferito esem&shy;<lb/>pio dello stesso Baliani, riducevasi in minime parti. </s></p><p type="main">

<s>Nel terzo Discorso sul moto delle acque, parte seconda, per far inten&shy;<lb/>dere in che modo abbiasi a concepire l'acceleramento, immagina il Mariotte <lb/>un leggerissimo corpo veloce, che a furia di ripetuti urti commove un pe&shy;<lb/>santissimo corpo dalla sua quiete, e dice che, se al primo urto passa una <lb/>linea, al secondo ne passer&agrave; due, al terzo tre, e cos&igrave; di seguito secondo la <lb/>serie de'numeri naturali. </s>

<s>&ldquo; Or si l'on prend plusieurs nombres de suite, <lb/>commen&ccedil;ant &agrave; l'unit&eacute;, comme 1, 2, 3, 4, etc., iusques a 20, et q'on compte <lb/>20 momens; la somme de cette progression sera 210; et si on compte 40 mo&shy;<lb/>mens, selon la meme progression iusques a 40, la somme de ces derniers <lb/>nombres sera 820, qui est quadruple au peu pres de 210, somme des 20 pre&shy;<lb/>miers nombres, mais a l'infini cette derniere somme sera quadruple de la <lb/>premiere precisement, parce que la proportion du defaut diminue touiurs: <lb/>ce que Galileo a aussi conclu dans son Traite de l'acceleration du mouve&shy;<lb/>ment des corps qui tombent &rdquo; (Oeuvres, T. II a l'Haye 1740, pag. </s>

<s>393). </s></p><p type="main">

<s>Doveva esser questa pure la conclusione del discorso del Baliani, e se <lb/>fu irragionevolmente diversa, &egrave; da attribuire in gran parte al bisogno sen&shy;<lb/>titosi in que'tempi, in cui mancavano esperienze sicure, di addimesticare <lb/>con la verit&agrave; i ritrosi ad ammetterla, perch&egrave; gl'incrementi degli spazi, fa&shy;<lb/>cendoli come la serie de'numeri impari, sembravano eccessivi. </s>

<s>Fu da ragioni <lb/>simili mosso a dubitare degl'insegnamenti di Galileo uno de'discepoli di lui <lb/>pi&ugrave; valorosi, Antonio Nardi, il quale proponeva perci&ograve; di sostituire al trian&shy;<lb/>golo la parabola, facendo crescere le velocit&agrave; come le radici dei tempi, co&shy;<lb/>sicch&egrave; la ragione per esempio di due a uno si riducesse a quella di &radic;8 a <lb/>&radic;4, ch'esso Nardi scrive R. </s>

<s>Q 8 a R. </s>

<s>Q 4, non essendosi ancora quel segno del <lb/>radicale introdotto nell'uso. </s>

<s>Sostituita dunque, secondo questa nuova ipotesi, <pb xlink:href="020/01/2078.jpg" pagenum="321"/>&radic;T:&radic;<emph type="italics"/>t<emph.end type="italics"/> alla ragione di V:<emph type="italics"/>v,<emph.end type="italics"/> l'equazione S:<emph type="italics"/>s<emph.end type="italics"/>=V.T:<emph type="italics"/>v.t<emph.end type="italics"/> si trasforma <lb/>nell'altra S:<emph type="italics"/>s<emph.end type="italics"/>=T&radic;T:<emph type="italics"/>t<emph.end type="italics"/> &radic;<emph type="italics"/>t<emph.end type="italics"/>=&radic;T3:&radic;<emph type="italics"/>t<emph.end type="italics"/>3, che conclude essere gli spazi <lb/>come le radici dei cubi de'tempi. </s></p><p type="main">

<s>&ldquo; La nuova scienza del Galileo intorno al moto dei cadenti e dei pro&shy;<lb/>ietti, leggesi nella veduta XLII della seconda Scena, s'appoggia tutta a due <lb/>principii: l'uno che il moto orizzontale sia uguale, l'altro che il moto dei <lb/>cadenti riceva nuova aggiunta di velocit&agrave;, secondo la ragione dei tempi. </s>

<s>Du&shy;<lb/>bito nondimeno che questo secondo principio non bene con l'esperienza con&shy;<lb/>cordi, sicch&egrave; non tanto si velociti un cadente, quanto da esso principio se&shy;<lb/>gue. </s>

<s>N&egrave; l'esperienza della palla sdrucciolante per un canale si reputa da me <lb/>sicura, oltrech&egrave; il moto di essa &egrave; composto di due, mentre, scendendo, si <lb/>ruzzola per il sostegno e, per l'aderenza al <gap/>nale, in s&egrave; stessa. </s>

<s>E siccome, <lb/>per l'aderenza e sostegno, quella riesce pi&ugrave; tarda di un'altra, che per l'aria <lb/>discenda; cos&igrave;, mediante la complicazione de'due moti, e per premere obli&shy;<lb/>quamente sopra il canale, pu&ograve; da principio rendersi meno veloce dell'altra <lb/>suddetta. </s>

<s>Dunque in tale esperienza qualche cosa desidero, e massime che il <lb/>sostegno e l'aderenza al canale non solo pu&ograve; ritardar la palla, ma anco di fatto <lb/>la rattiene dallo scorrere, mentre sia il canale poco all'orizzonte inclinato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Alcuno dunque pensar potrebbe che nel III dialogo Del moto, a c. </s>

<s>170 <lb/>(<emph type="italics"/>nella prima edizione di Leyda<emph.end type="italics"/>) la velocit&agrave; EB (fig. </s>

<s>149) alla velocit&agrave; I non <lb/><figure id="id.020.01.2078.1.jpg" xlink:href="020/01/2078/1.jpg"/></s></p><p type="caption">

<s>Figura 149.<lb/>fosse come la retta EB alla retta I, o come due ad uno, ma <lb/>come R. </s>

<s>Q 8 a R. </s>

<s>Q 4. Sicch&egrave;, in cambio di prendere un <lb/>triangolo AEB, si prendesse una semiparabola, di cui la cima <lb/>A, la semibase EB, e l'asse AB. </s>

<s>Ma ricevendosi che i gravi <lb/>s'affrettino come vuole il Galileo, ne segue che lo spazio <lb/>trascorso in un dato tempo, il che sopra accennammo, al <lb/>trascorso nella prima met&agrave; di esso tempo, sia come quattro <lb/>a uno, e successivamente come i quadrati dei tempi. </s>

<s>Anche <lb/>ne segue che i tempi del moto uguale e dell'affrettato siano <lb/>uguali, quando il massimo grado di velocit&agrave; dell'affrettato <lb/>sia doppio di qualsivoglia grado dell'uguale. </s>

<s>Ma dalla nuova <lb/>ipotesi segue che i tempi del moto uguale e dell'affrettato <lb/>siano uguali, quando il massimo grado di velocit&agrave; dell'af&shy;<lb/>frettato sia sesquialtero di qualsivoglia grado dell'uguale. </s>

<s><lb/>Inoltre segue che lo spazio trascorso in un dato tempo, al <lb/>trascorso nella prima met&agrave; di esso tempo, sia come 8 a <lb/>R. </s>

<s>Q 8, onde avrebbe minor ragione che tre ad uno, e gli <lb/>spazi trascorsi dal cadente in tempi uguali saranno come i cubi delle R. </s>

<s>Q <lb/>di essi tempi, cio&egrave; come R. </s>

<s>O 1, R. </s>

<s>Q 8, R. </s>

<s>Q 27, R. </s>

<s>Q 64. &rdquo; </s></p><p type="main">

<s>&ldquo; Considerisi la discrepanza tra le conclusioni dell'una e dell'altra ipo&shy;<lb/>tesi, e non &egrave; dubbio che coloro, i quali ascrivevano a cattive osservazioni <lb/>il credere che i gravi s'affrettino cadendo, si sottoscriverebbero pi&ugrave; all'ul&shy;<lb/>tima che all'altra ipotesi, per parere almeno di non avere essi errato cos&igrave; <lb/>all'ingrosso nelle loro osservazioni. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>973, 74). </s></p><pb xlink:href="020/01/2079.jpg" pagenum="322"/><p type="main">

<s>Negli stessi discepoli dunque di Galileo quella che, annunziata prima <lb/>nei dialoghi Del mondo, e poi dimostrata negli altri dialoghi Del moto, si <lb/>chiama ora per noi col nome di <emph type="italics"/>legge,<emph.end type="italics"/> non aveva pi&ugrave; valore che di una <lb/>semplice <emph type="italics"/>ipotesi,<emph.end type="italics"/> pi&ugrave; dipendente da un supposto principio, che da un fatto <lb/>sperimentato. </s>

<s>Si conferma insomma da ci&ograve; quel che si diceva, che cio&egrave; le <lb/>incertezze e i dubbi, in <expan abbr="ammetter&etilde;">ammetterem</expan> nell'accelerazione dei gravi quella nuova <lb/>proporzione degli incrementi, dipendevano principalmente dal non esser riu&shy;<lb/>scito ancora nessuno a farne osservazioni dirette, per le quali si potessero <lb/>persuadere di fatto i ritrosi essere una falsit&agrave; quel che si teneva per assai <lb/>ragionevole, e che sembrava essere cos&igrave; ben confermato dagli effetti delle <lb/>percosse. </s>

<s>Le esperienze infatti proposte, e poeticamente descritte nel III dia&shy;<lb/>logo Delle due nuove scienze, vedemmo quanto, mettendosi a praticarle, do&shy;<lb/>vessero andar soggette a fallacie: opinione autorevolmente confermata dalle <lb/>sopra riferite parole del Nardi. </s>

<s>Il Baliani pure, bench&egrave; ne fosse dallo stesso <lb/>Galileo messo in sospetto, non si cur&ograve; di verificare se quella palla di ferro <lb/>metteva a scendere per lo spazio di cento braccia precisamente cinque mi&shy;<lb/>nuti secondi di tempo. </s>

<s>Argomentasi ci&ograve; da una lettera di lui, scritta da Ge&shy;<lb/>nova il 16 di Settembre del 1639, e indirizzata ad Arcetri, dove, riferendo <lb/>l'esperienza di una palla di moschetto, che, lasciata cader dall'alto albero <lb/>di una nave fatta vogar dalla ciurma velocissimamente, si vedeva con gran <lb/>maraviglia di tutti battere, senza punto rimanerne in dietro, a pi&egrave; dell'al&shy;<lb/>bero stesso; soggiunge: &ldquo; eppure, essendo l'albero alto pi&ugrave; di sessanta brac&shy;<lb/>cia, massime che la galea &egrave; grossa, cio&egrave; la nostra Capitana, per ragione la <lb/>palla dovea star per aria pi&ugrave; di tre minuti secondi &rdquo; (Alb. </s>

<s>X, 370). </s></p><p type="main">

<s>Anche il Fermat e il Cartesio, come per le loro proprie testimonianze <lb/>pi&ugrave; sopra udimmo, fecero dell'accelerarsi dei gravi <emph type="italics"/>prove<emph.end type="italics"/> e <emph type="italics"/>osservazioni,<emph.end type="italics"/><lb/>che si trovarono riscontrar con la legge formulata da Galileo, ma non di&shy;<lb/>cendoci il particolar modo che, in provare e in osservare, fu da loro tenuto, <lb/>&egrave; da creder che di poco differisse, nella struttura e nell'efficacia, da ci&ograve; che <lb/>nello stesso proposito sugger&igrave; l'industria al Gassendo. </s>

<s>Fu il celebre Filo&shy;<lb/>sofo parigino uno de'difensori pi&ugrave; strenui della legge galileiana contro i pa&shy;<lb/>ralogismi del gesuita Pietro Casr&eacute;e, a cui indirizzava tre eruditissime epi&shy;<lb/>stole, che videro la pubblica luce sotto il titolo <emph type="italics"/>De proportione, qua gravia <lb/>accelerantur.<emph.end type="italics"/> Risponde ivi agli argomenti dell'avversario con matematiche <lb/>ragioni, ma per quel che s'appartiene alle esperienze in particolare, &ldquo; obser&shy;<lb/>vationes, egli dice, a Galilaeo recitatas praetereo: ad meas quod spectat, <lb/>quotquot mihi licuit et quantum licuit peragere, illam proportionem semper <lb/>exhibuerunt &rdquo; (De proportione etc., Parisiis 1646, pag. </s>

<s>230). </s></p><p type="main">

<s>Quali poi si fossero queste esperienze, e come fossero particolarmente <lb/>condotte, l'aveva scritto gi&agrave; il Gassendo nell'epistola I, dove si leggon tre <lb/>vari modi proposti dall'Autore per confermare sperimentalmente che gli <lb/>spazi passati dai gravi liberamente cedenti son proporzionali ai quadrati delle <lb/>velocit&agrave; o dei tempi. </s>

<s>Il primo modo incominciava allora a rendersi famoso <lb/>per le controversie, alle quali sarebbe tra gl'Idrometri andato soggetto: con-<pb xlink:href="020/01/2080.jpg" pagenum="323"/>troversie, che non temute dal Gassendo, lo lasciaron sicuro nell'approvare <lb/>il fatto, che le velocit&agrave; del flusso di un liquido dal foro aperto in un vaso <lb/>son proporzionali alle radici delle altezze. </s>

<s>Prendi, egli perci&ograve; dice, uno dei <lb/>cos&igrave; fatti vasi cilindrici, e infusavi acqua infino a una certa altezza, mante&shy;<lb/>nutavi costante, supponiamo che aperto il foro tu ne abbi attinto un fiasco <lb/>in un minuto. </s>

<s>&ldquo; Ut deinde tempore eodem, et per idem foramen, exsiliant <lb/>duo congii, et aqua proinde sit duplo compressior, ad quamnam usque al&shy;<lb/>titudinem adaugendus erit, complendusve cylindrus? </s>

<s>Ad duplam ne solum? </s>

<s><lb/>Non sane sed omnino ad quadruplam. </s>

<s>Et ut exsiliant tres, ad triplam ne? </s>

<s><lb/>Haudquaquam profecto, sed ad nonuplam. </s>

<s>Et ut exsiliant quatuor, ad qua&shy;<lb/>druplam ne? </s>

<s>Minime gentium, sed ad sexdecuplam &rdquo; (ibid., pag. </s>

<s>36). </s></p><p type="main">

<s>Il secondo modo, o non &egrave; da noi bene inteso, o contiene in s&egrave; una fal&shy;<lb/>lacia, consistendo nel proporre un peso pendolo, in cui s'esperimenta, dice <lb/><figure id="id.020.01.2080.1.jpg" xlink:href="020/01/2080/1.jpg"/></s></p><p type="caption">

<s>Figura 150.<lb/>il Gassendo, che, rimanendosi la fune <lb/>ugualmente lunga, le velocit&agrave; delle oscil&shy;<lb/>lazioni crescono come i quadrati dei pesi <lb/>uguali, che devono aggiungersi al primo, <lb/>perch&egrave; se ne solleciti il moto. </s>

<s>Passando <lb/>perci&ograve; al terzo modo, immagina l'Autore <lb/>di avere pi&ugrave; pendoli disposti lungo la <lb/>medesima linea verticale AQ (fig. </s>

<s>150) <lb/>crescenti in lunghezza via via come i <lb/>quadrati de'numeri naturali, cosicch&egrave;, <lb/>essendo AM uno, sia AO quattro, AQ <lb/>nove, ecc. </s>

<s>Rimossi tutti insieme per un <lb/>angolo uguale dal perpendicolo, in modo <lb/>che si trovino in diritta linea, come per <lb/>esempio sull'obliqua AG, &ldquo; observa&shy;<lb/>mus, dice il Gassendo, tempus quo glo&shy;<lb/>bus secundus pervenit ad O esse duplum <lb/>temporis, quo primus pervenit ad M, et <lb/>tempus, quo tertius ad Q, triplum &rdquo; <lb/>(ibid., pag. </s>

<s>40). Ma per costruzione lo spazio circolare GQ, o il retto PQ <lb/>che gli corrisponde, &egrave; nonuplo, e lo spazio EO o NO &egrave; quadruplo dello spa&shy;<lb/>zio CM o LM passato dal pendolo nel primo tempo. </s></p><p type="main">

<s>Che sia veramente cos&igrave;, cio&egrave; che gli spazi stanno come i quadrati dei <lb/>tempi, &egrave; confermato, soggiunge quivi il Gassendo stesso, da un altro fatto, <lb/>che a me sperimentando &ldquo; observare licuit, constitutam pilam supra planum <lb/>libellatum oppositumque ad M, ad O, ad Q, dum percuteretur propellere&shy;<lb/>turque o globis incurrentibus, assequi velocitatem excurrereque, non iuxta <lb/>numeros quadratos, quales sunt CM, EO, GQ, sed iuxta radices ipsorum, <lb/>qualia sunt et tempora unum, duo, tria &rdquo; (ibid., pag. </s>

<s>41). </s></p><p type="main">

<s>Chiunque ora chiuda, lette queste belle proposizioni, il libro, e pene&shy;<lb/>tri con l'immaginazione dentro il segreto gabinetto sperimentale del Gas-<pb xlink:href="020/01/2081.jpg" pagenum="324"/>sendo, scoprir&agrave; facilmente che il Filosofo faceva conto di aver veduto con gli <lb/>occhi del corpo quel che avea chiaramente speculato con la luce dell'intel&shy;<lb/>letto. </s>

<s>Quali strumenti usava l'Autore, o suggeriva a chi avesse voluto imi&shy;<lb/>tarlo, per la pi&ugrave; esatta misura di cos&igrave; minimi tempi? </s>

<s>Non si fa menzione <lb/>d'altro misuratore, che delle arterie pulsanti, ond'&egrave; che l'esperienza vera, <lb/>da dimostrar che quella del Gassendo non poteva essere altro che immagi&shy;<lb/>naria, consisterebbe nel mettere un ignorante degli elementi della Meccanica, <lb/>per veder ci&ograve; che riuscisse a sapere delle differenze de'tempi, impiegati dai <lb/>pendoli a passar per gli archi CM, EO, GQ, con gran diligenza toccandosi <lb/>e attentamente ascoltandosi i polsi. </s></p><p type="main">

<s>Cos&igrave; fatti generi d'esperienze si lusingarono tanti altri, da Galileo al <lb/>Gassendo, di averle eseguite, ma quand'anco avessero avuto per caso una <lb/>buona riuscita, non era da riposare in esse con fede, come non cred&egrave; di <lb/>avervi a riposare il Fermat, conscio che a lui mancavano gli strumenti ne&shy;<lb/>cessari per osservare cos&igrave; sfuggevoli, e pur necessariamente concludenti mi&shy;<lb/>nuzie de'tempi. </s>

<s>Non si ridusse il prezioso cronometro praticabile, con indi&shy;<lb/><figure id="id.020.01.2081.1.jpg" xlink:href="020/01/2081/1.jpg"/></s></p><p type="caption">

<s>F. 151.<lb/>cibile pertinacia e solerzia, che per l'industria di Giovan Batista Ric&shy;<lb/>cioli, a cui primo si deve l'aver, con esattezza maravigliosa, confer&shy;<lb/>mata la teoria galileiana con i fatti sperimentati. </s></p><p type="main">

<s>Ritorniamo alla storia, da noi lasciata altrove interrotta nel II tomo <lb/>dell'Almagesto nuovo, per le pagine del quale si leggeva come fosse <lb/>l'Autore entrato in sospetto che, nel prescrivere le proporzioni de'moti <lb/>accelerati, fosse incorso Galileo in qualche fallacia. </s>

<s>Vedemmo quali <lb/>fossero di quel sospetto i ragioneveli motivi, e com'avesse speranza il <lb/>Riccioli, pi&ugrave; diligentemente sperimentando, di ritrovare per gl'incre&shy;<lb/>menti degli spazi una serie aritmetica, diversa da quella de'numeri <lb/>impari. </s>

<s>A conseguir poi una tal maggior diligenza sperimentale si con&shy;<lb/>fidava principalmente l'Autore nell'uso dei pendoli, da lui stesso, <lb/>com'altrove diremo, con laboriosissima industria ritrovati aggiustatis&shy;<lb/>simi, e volendo studiare il moto nel suo libero esercizio, e non vio&shy;<lb/>lentemente costretto ne'piani inclinati o nei pendoli a rispondere alle <lb/>intenzioni, e a secondare le comodit&agrave; dell'arte; ritornava con desiderio, <lb/>come a strumento di nessun altro atto meglio a rappresentare gli effetti <lb/>della Natura, alla torre degli Asinelli. </s></p><p type="main">

<s>Disegnata dunque nell'altezza della gran Torre una linea NH <lb/>(fig. </s>

<s>151) e preparato un pendolo cos&igrave; lungo, che ad ogni vibrazione <lb/>batteva dieci terzi di minuto, cerc&ograve; il Riccioli, col suo fido compagno <lb/>Francesco Maria Grimaldi, qual si fosse l'altezza, da cui un globo di <lb/>argilla cadeva in cinque delle dette vibrazioni, e trov&ograve; con ripetute <lb/>prove essere quella precisa altezza BH di dieci piedi romani antichi. </s>

<s><lb/>Passarono poi i due sperimentatori a cercar l'altra altezza, necessaria <lb/>perch&egrave; il medesimo globo dovesse gi&ugrave; da essa cadere in tempo doppio, <lb/>e trovarono essere 40 piedi, l'intervallo dei quali &egrave; segnato dalla linea <lb/>KH. </s>

<s>Di l&igrave;, via via ascendendo pi&ugrave; in alto, trovarono passare il cadente le <pb xlink:href="020/01/2082.jpg" pagenum="325"/>linee LH, MH, NH, di 90, di 160 e di 250 piedi, in quindici, in venti, in <lb/>venticinque vibrazioni, ossia in tempo triplo, quadruplo e quintuplo di quel <lb/>primo. </s></p><p type="main">

<s>Venendo dopo ci&ograve; il Riccioli, con trepido desiderio, a fare il conto de&shy;<lb/>gl'incrementi subiti, per decider se procedevano secondo la serie da Galileo <lb/>proposta, o secondo quell'altra, ch'egli aveva sospettata pi&ugrave; vera, al vedersi <lb/>tornar sotto la punta della penna 10&mdash;40=30, 90&mdash;40=50, 160&mdash;90= <lb/>70, 250&mdash;160=90, precisamente insomma secondo la serie de'numeri im&shy;<lb/>pari; ebbe a rimanerne stupito. </s>

<s>E tuttavia fermo in credere che fosse riu&shy;<lb/>scito Galileo alla sua scoperta, per diritta via sperimentale, non si poteva <lb/>dar pace come, da esperienze cos&igrave; imperfette e necessariamente fallaci, avesse <lb/>potuto quell'uomo cos&igrave; puntualmente coglier nel vero. </s></p><p type="main">

<s>Gli pass&ograve; per la mente il sospetto che qualche errore fosse scorso, o <lb/>nelle osservazioni sue proprie o in quelle del Grimaldi, e perci&ograve; volle ripe&shy;<lb/>tere l'esperienza, servendosi di un altro pendolo, che batteva un minuto <lb/>secondo preciso di tempo sidereo. </s>

<s>N&egrave; contento ancora, prov&ograve; in altri modi, <lb/>e sempre costantemente riducevasi il conto a dire che gli spazi crescono se&shy;<lb/>condo la serie de'numeri impari, e che perci&ograve; vanno veramente come i qua&shy;<lb/>drati dei tempi. </s>

<s>&ldquo; Ergo ad p. </s>

<s>Bonaventuram Cavalerium, in bononiensi uni&shy;<lb/>versate primarium Matheseos professorem, et quondam Galilaei alumnum, <lb/>me contuli, cum p. </s>

<s>Grimaldo, ipsique narravi consensum meorum experi&shy;<lb/>mentorum cum experimentis Galilaei, quoad hanc quidem proportionem, <lb/>neque enim ille, chiragra simul et podagra lectulo aut sellulae affixus, in&shy;<lb/>teresse ipsis poterat. </s>

<s>Incredibile autem dictu est quantopere ex nostra hac <lb/>contextatione fuerit exhilaratus &rdquo; (Almag. </s>

<s>novum, T. II cit., pag. </s>

<s>386). </s></p><p type="main">

<s>Il Cavalieri, cos&igrave; devotamente affezionato al suo Maestro, ripensava, in <lb/>mezzo ai dolori atroci della podagra, alla consolazione che avrebbe dovuto <lb/>provare a una tal notizia il buon vecchio, il quale avrebbe potuto dire di <lb/>morir contento, dop'essere stato fatto finalmente certo che la sua Nuova <lb/>scienza non era una semplice ipotesi, ma un fatto reale, e che le sue pro&shy;<lb/>posizioni Del moto non erano da rassomigliare alle conclusioni dimostrate <lb/>da Archimede circa la spirale, vere solamente in astratto &ldquo; per non ri&shy;<lb/>trovarsi in natura mobile, che in quella maniera spiralmente si muova &rdquo; <lb/>(Alb. </s>

<s>VII, 157). </s></p><p type="main">

<s>Nel 1651 si divulgarono l'esperienze del Riccioli, rimaste fin'allora so&shy;<lb/>lamente note ai familiari e agli amici, e per quelle varie descrizioni, che si <lb/>leggevano nel II tomo dell'Almagesto nuovo, si mostrava la verit&agrave; presa da <lb/>cos&igrave; sottil arte, e avvinta da cos&igrave; stretti legami, che nessuno os&ograve; poi pi&ugrave; di <lb/>mettere in dubbio se l'accelerazione dei gravi, qual consegue dal supporre <lb/>crescenti le velocit&agrave; come i tempi, fosse un fatto fisico o una matematica <lb/>esercitazione. </s>

<s>Sotto questo duplice abito, fisico matematico, fece la Scienza <lb/>del moto la sua prima e solenne comparsa nell'<emph type="italics"/>Orologio oscillatorio<emph.end type="italics"/> del&shy;<lb/>l'Huyghens, la seconda parte del quale, a stabilir le leggi della discesa dei <lb/>gravi, incomincia dal dimostrare i teoremi di Gelileo. </s>

<s>Consistendo i princi-<pb xlink:href="020/01/2083.jpg" pagenum="326"/>pii, da'quali si concludono quelle leggi o si dimostrano que'teoremi, nella <lb/>forza di gravit&agrave;, e nella forza d'inerzia, riguard&ograve; ingegnosamente l'Huyghens <lb/>gli spazi acceleratamente passati come la resultante unica di due moti. </s></p><p type="main">

<s>Sia spinto il mobile A (fig. </s>

<s>152), da qualsivoglia forza, nella direzione <lb/>AB: se fingasi un tal mobile senza peso, o se gli effetti della gravit&agrave; di lui <lb/>siano dal sostentamento di qualche piano impediti, proceder&agrave; esso mobile <lb/><figure id="id.020.01.2083.1.jpg" xlink:href="020/01/2083/1.jpg"/></s></p><p type="caption">

<s>Figura 152.<lb/>per tutta la linea AB equabilmente. </s>

<s>Ma suppongasi <lb/>che la gravit&agrave; liberamente eserciti il suo impulso <lb/>discensivo, come quando un corpo vien gettato per <lb/>aria: allora, se nel mentre che con equabile moto <lb/>il proietto &egrave; passato in B, la gravit&agrave; sua naturale <lb/>l'ha fatto scendere infino in C, non &egrave; la linea del <lb/>moto la somma delle due AB, BC, ma una linea <lb/>di mezzo, che s'intravede facilmente dover essere <lb/>una curva, bench&egrave; non importi ora a noi di sapere <lb/>a quale specie appartenga. </s>

<s>Se non &egrave; per&ograve; la tra&shy;<lb/>sversale descritta dal moto del proietto la somma <lb/>delle due componenti, s'avvicina ad esser tale, via <lb/>via che la linea AB tende a dirigersi nel perpendicolo, come per esempio, <lb/>immaginando che ella declini sempre pi&ugrave; in basso, volgendosi intorno al <lb/>punto A come a suo centro. </s>

<s>Quando infatti essa AB &egrave; orizzontale, la re&shy;<lb/>sultante del moto &egrave; AC, ma &egrave; AC&prime;, quando B siasi abbassato in B&prime;, e, ri&shy;<lb/>dottosi finalmente in B&Prime;, sopra un punto della verticale; la resultante allora <lb/>del moto &egrave; AC&Prime;=AB&Prime;+B&Prime;C&Prime;, ossia &egrave; uguale alla somma per l'appunto <lb/><figure id="id.020.01.2083.2.jpg" xlink:href="020/01/2083/2.jpg"/></s></p><p type="caption">

<s>Figura 153.<lb/>delle due componenti. </s>

<s>Se ora nella naturale discesa <lb/>dei gravi, cos&igrave; conclude l'Huyghens il ragionamento, <lb/>&ldquo; scorsim, uti diximus, duos motus consideremus, <lb/>alterumque ab altero nullo modo impediri cogitemus, <lb/>hinc iam accelerationis gravium cadentium causam <lb/>legesque reperire licebit &rdquo; (Opera varia, Vol. </s>

<s>I, <lb/>Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>52). </s></p><p type="main">

<s>Sia infatti lo spazio verticale, percorso dal mo&shy;<lb/>bile nel primo tempo, uguale ad AB (fig. </s>

<s>153) il <lb/>quale &ldquo; dimidium est eius spatii, quod pari tempore <lb/>transiret motu aequabili cum velocitate, quam acqui&shy;<lb/>sivit ultimo casus momento &rdquo; come dimostra l'Huy&shy;<lb/>ghens nella II proposizione (ibid., pag. </s>

<s>54). Dunque <lb/>nel secondo tempo il moto &egrave; composto dell'orizzon&shy;<lb/>tale BC, doppio ad AB, e del verticale CD=AB, <lb/>cosicch&egrave;, dovendo nella perpendicolare la resultante <lb/>essere uguale alla somma delle componenti, sar&agrave; <lb/>BE=3AB. </s>

<s>Nel punto E, da cui comincia a decor&shy;<lb/>rere il terzo tempo, il moto equabile, in quel medesimo tempo assoluto, <lb/>sar&agrave;, per la detta II proposizione, EF=4AB. Ora, componendosi questo con <pb xlink:href="020/01/2084.jpg" pagenum="327"/>qu&egrave;llo della gravit&agrave; costante FG, ch'&egrave; perci&ograve; uguale ad AB, far&agrave; resultarne <lb/>il terzo moto EH=5AB: ond'&egrave; che, proseguendosi per il quarto, per il <lb/>quinto, e per tutti gli altri tempi, il medesimo ragionamento, se ne con&shy;<lb/>clude essere gl'incrementi degli spazi come la serie de'numeri impari, e gli <lb/>spazi stessi perci&ograve; come i quadrati de'tempi decorsi. </s></p><p type="main">

<s>I cinque libri dell'<emph type="italics"/>Orologio oscillatorio<emph.end type="italics"/> ebbero, specialmente appresso <lb/>agli stranieri, maggior diffusione de'quattro dialoghi Delle due nuove scienze, <lb/>s&igrave; perch&egrave; la lingua latina, in cui furono originalmente scritti quelli, era d'in&shy;<lb/>telligenza universale, s&igrave; perch&egrave;, avendo l'Olandese derivata nella sua la <lb/>scienza dell'Italiano, s'attingeva di l&agrave;, con pari utile e con comodit&agrave; mag&shy;<lb/>giore, che a risalire alle prime faticose sorgenti. </s>

<s>S'inger&igrave; da ci&ograve; l'opinione <lb/>che avesse Galileo conclusa la legge dei cadenti dai medesimi principii uge&shy;<lb/>niani, per cui il Newton, stabilite nella forza d'inerzia le <emph type="italics"/>Leggi<emph.end type="italics"/> del moto, <lb/>e nel principio della composizione delle forze conclusi i <emph type="italics"/>Corollari<emph.end type="italics"/> &ldquo; per le&shy;<lb/>ges duas primas, soggiungeva, et corollaria duo prima Galilaeus invenit de&shy;<lb/>scensum gravium esse in duplicata ratione temporum &rdquo; (Principia mathem., <lb/>T. </s>

<s>I cit., pag. </s>

<s>45, 46). Ora si sa dai nostri Lettori quanto fossero i processi <lb/>galileiani alieni dal far uso de'moti composti, per cui il fatto del Newton, <lb/>se mostra da una parte quanto poco si leggessero i libri di Galileo nel loro <lb/>originale, conferma dall'altra come a lui solo, di unanime consenso, in mezzo <lb/>alle pretensioni del Cartesio, s'attribuisse la scoperta, ond'&egrave; che nessun'al&shy;<lb/>tra espressione si conforma col vero storico forse meglio di quella, che chiama <lb/><emph type="italics"/>galileiane<emph.end type="italics"/> le leggi dei gravi cadenti. </s></p><pb xlink:href="020/01/2085.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle scese dei gravi lungo i piani inclinati<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Dei principii fondamentali, da cui si dimostra la scienza dei moti inclinati, e di una supposizione <lb/>fatta in proposito da Galileo. </s>

<s>&mdash; II. </s>

<s>Ordinamento e pubblicazione del primo Libro galileiano <lb/><emph type="italics"/>De motu,<emph.end type="italics"/> contenente i teoremi dimostrati infino all'anno 1602. &mdash; III. </s>

<s>Ordinamento e pubbli&shy;<lb/>cazione del secondo Libro galileiano <emph type="italics"/>De motu,<emph.end type="italics"/> incominciato nel 1604, e nel 1609 rimasto inter&shy;<lb/>rotto, per le ragioni che qui si diranno. </s>

<s>&mdash; IV. </s>

<s>Ordinamento delle proposizioni lasciate mano&shy;<lb/>scritte da Galileo, per condurre in una terza maniera il suo trattato <emph type="italics"/>De motu.<emph.end type="italics"/> &mdash; V. </s>

<s>Dei teoremi <lb/>concernenti i Moti locali, ordinati da Galileo per la stampa, e delle critiche fatte dal Cartesio <lb/>contro essi. </s>

<s>&mdash; VI. </s>

<s>Di ci&ograve; che pu&ograve; dirsi nuovo nel trattato di Galileo, che qui paragonasi con <lb/>quello del Baliani, e dell'opera data da altri Autori stranieri, come dal Mariotte e dall'Huy&shy;<lb/>ghens, intorno al medesimo soggetto del moto dei gravi per i piani inclinati. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>L'attributo, che si d&agrave; alle scoperte dei Fisici o alle speculazioni dei <lb/>Filosofi, desumendolo dal particolar nome di un uomo, &egrave;, a volere esser <lb/>giusti, una impropriet&agrave;, che si pu&ograve; solo salvare nella convenzion del linguag&shy;<lb/>gio, e che viene a ridursi, in pi&ugrave; rigorosi termini, a una falsit&agrave;, nel tribu&shy;<lb/>nale della giustizia, ogni volta che si vogliono quelle attribuzioni fare esclu&shy;<lb/>sive, come Galileo e il Cartesio pretendevano nelle loro speculazioni e nelle <lb/>loro scoperte. </s>

<s>Perch&egrave;, nell'ordine intellettuale, &egrave; un consorzio non meno <lb/>stretto, n&egrave; men necessario di quel che sia negli ordini civili, e perci&ograve; da <lb/>uno e da un altro autore piglia nome questa o quella parte della scienza, <lb/>come piglia nome dal gerarca o dal padre una societ&agrave; religiosa o una fa&shy;<lb/>miglia. </s></p><p type="main">

<s>Dir dunque galileiane le leggi della caduta dei gravi non si deve in&shy;<lb/>tendere a quel modo che tanti fanno, quasi fossero uscite spontanee quelle <pb xlink:href="020/01/2086.jpg" pagenum="329"/>verit&agrave; naturali dalla solitaria mente di Galileo, il quale &egrave; padre nella scienza, <lb/>come fu padre nella famiglia, e non potrebbe esser tale nell'una e nell'al&shy;<lb/>tra, senza esser disceso dagli avi, e senz'aver celebrato un connubio. </s>

<s>Ha la <lb/>precedente storia narrato chi fossero quegli avi, e qual si fosse il rito di <lb/>quel connubio per ci&ograve;, che particolarmente concerne i primi fondamenti posti <lb/>alla Dinamica, e perch&egrave; il medesimo Architettore sopra una s&igrave; ben fondata <lb/>base dette mano a costruir l'edifizio, ha la nostra storia a narrare con quali <lb/>strumenti, e con quale industria fosse condotto. </s>

<s>L'essersi mostrato alla pub&shy;<lb/>blica vista quel monumento della scienza in abito, in corporatura o in ti&shy;<lb/>tolo di nuovo, lusingava l'Autore, e seduceva gli spettatori, ma lo spetta&shy;<lb/>colo era simile a quello di colui che, non avendo saputo dianzi distinguere <lb/>il calice dall'altro verde, vede ora, a ripassar pel medesimo giardino, la so&shy;<lb/>litaria fronda scoppiata nelle fragranze del fiore. </s></p><p type="main">

<s>Tornando dall'immagine specchiata indietro all'oggetto reale, s'incon&shy;<lb/>tra questo, secondo la nostra intenzione, nel III dialogo Delle due nuove <lb/>scienze; fiore aperto, a cui, perch&egrave; non si creda una incantevole apparizione, <lb/>giova riconoscer la boccia e la pianticella madre che l'ha generato. </s></p><p type="main">

<s>In quel III Dialogo, che si diceva, legge il Protagonista agli altri inter&shy;<lb/>locutori una serie di teoremi, scritti in altra lingua, e posti sotto altra forma, <lb/>nei quali teoremi, dalle proporzioni del moto per la verticale, si passa a <lb/>dimostrar geometricamente le proporzioni del moto nelle direzioni oblique. </s>

<s><lb/>E perch&egrave; una tale obliquit&agrave; di direzione non pu&ograve; il mobile prenderla, se <lb/>non per qualche violenza, che lo costringa a moversi contro l'inclinazione <lb/>sua naturale, &egrave; perci&ograve; che la nuova scienza attende a dimostrar le leggi, se&shy;<lb/>condo le quali i gravi scendono lungo i piani inclinati. </s>

<s>Se si considerino <lb/>per&ograve; in queste scese i semplici impeti, o s'attenda solamente a ritrovare la <lb/>proporzion dei momenti, la Scienza nuova si riduce all'antica, e la pianti&shy;<lb/>cella madre, di che simboleggiando si diceva, scopresi ne'principii statici di <lb/>Giordano Nemorario, e la boccia del fiore tanto ammirato nei negletti <emph type="italics"/>Que&shy;<lb/>siti<emph.end type="italics"/> del Tartaglia. </s></p><p type="main">

<s>Esplicatesi infatti le medesime questioni, e dimostrato con la sola no&shy;<lb/>vit&agrave; del processo, diverso un poco da quello del Tartaglia, che gl'impeti nel <lb/>perpendicolo e nell'obliqua hanno ragion reciproca delle lunghezze, Galileo, <lb/>introducendosi alle sue nuove speculazioni, cos&igrave; scriveva: &ldquo; Ex his facile <lb/>erit aliquorum problematum solutionem assequi, qualia haec sunt: primo, <lb/>datis duobus planis inclinatis, quorum rectus descensus idem sit, invenire <lb/>proportionem celeritatum eiusdem mobilis &rdquo; (Alb. </s>

<s>XI, 61). </s></p><p type="main">

<s>Il linguaggio stesso, come sentono echeggiarsi nelle orecchie i Lettori, <lb/>&egrave; quello del Nemorario, che primo apr&igrave; le vie al Tartaglia di ritrovar la <lb/>proporzione tra l'impeto nell'obliquo e nel retto descenso; impeto che, ri&shy;<lb/>guardato come causa efficiente della celerit&agrave;, trasformava il teorema dello <lb/>stesso Tartaglia in quest'altro concluso ivi cos&igrave; da Galileo: &ldquo; Constat ergo <lb/>eiusdem mobilis, in diversis inclinationibus, celeritates esse inter se, permu&shy;<lb/>tatim, sicut obliquorum descensuum, aequales rectos descensus comprehen-<pb xlink:href="020/01/2087.jpg" pagenum="330"/>dentium, longitudines &rdquo; (ibid., pag. </s>

<s>62). E perch&egrave; le celerit&agrave; hanno ragion <lb/>contraria alle tardit&agrave;, ossia ai tempi, rimanendo gli spazi i medesimi, dun&shy;<lb/>que i tempi, nell'obliquo e nel retto descenso, stanno come le lunghezze <lb/>non permutate: &ldquo; erit ergo sicut tarditas ad tarditatem, ita linea ad li&shy;<lb/>neam &rdquo; (ibid.). </s></p><p type="main">

<s>Chi si risovviene delle cose lette nel capitolo I di questo Tomo, sa che <lb/>a una tal conclusione era, dai medesimi principii, giunto anche Leonardo <lb/>da Vinci, e perch&egrave; di l&agrave;, cio&egrave; dall'essere i tempi, nel perpendicolo e nel&shy;<lb/>l'obliqua di uguali altezze, come gli spazi, si svolge quasi tutta intera la <lb/>serie dei teoremi galileiani, i quali dipenderebbero perci&ograve; unicamente dalla <lb/>Statica del Nemorario e del Tartaglia; scarsi e limitati alle sole cadute di&shy;<lb/>rette apparirebbero i frutti della Dinamica nuova. </s>

<s>Eppure, al primo entrare <lb/>allo studio del Trattato galileiano, si rivela esser l'intenzion dell'Autore <lb/>tutta diversa, perch&egrave; i primi teoremi, che s'incontrano dimostrati, e da cui <lb/>dipendono gli altri, son puramente dinamici, e progredendo oltre nella let&shy;<lb/>tura non &egrave; possibile non accorgersi della sollecitudine di chi scrive, in non <lb/>derivar mai <emph type="italics"/>ex mechanicis,<emph.end type="italics"/> ossia dalla statica, quant'&egrave; possibile, i principii <lb/>alle sue dimostrazioni. </s></p><p type="main">

<s>Di questo notabilissimo fatto, e delle sue ragioni, le cose che siamo per <lb/>dire ci renderanno certi, ma intanto non si pu&ograve; non ripensare al modo, come <lb/>potesse Galileo rendere indipendente la sua Dinamica dai principii gi&agrave; sta&shy;<lb/>biliti in una scienza anteriore, perch&egrave; ci&ograve; sembrerebbe evidentemente un <lb/>voler raccogliere i frutti dai novelli rami recisi dal tronco. </s>

<s>Essendo per&ograve; <lb/>questa intenzione dell'audace cultore contraria affatto alle leggi della Na&shy;<lb/>tura, non sarebbe stata in nessun modo riuscibile se, mettendosi a recidere <lb/>alla rigogliosa pianta lo stelo, non avesse salvata la pi&ugrave; profonda radice, dalla <lb/>quale s'argoment&ograve; di fare scoppiare le nuove fronde. </s></p><p type="main">

<s>Galileo infatti, nel bandire dalla sua Scienza nuova il teorema del Tar&shy;<lb/>taglia, non pot&egrave; fare a meno di ridursi a professar quel principio, da cui, <lb/>come da radice, era germogliato esso teorema; principio, il quale noi sap&shy;<lb/>piamo consistere nell'ammetter che, per le varie obliquit&agrave;, i momenti dei gravi <lb/>siano allora uguali, quando <emph type="italics"/>aequaliter capiunt de directo.<emph.end type="italics"/> E perch&egrave; i mo&shy;<lb/>menti o gl'impeti, quali cause efficienti, supponeva ragionevolmente Galileo <lb/>che fossero proporzionali alle velocit&agrave;, come a loro effetti immediati; e perci&ograve; <lb/>il principio statico del Nemorario si trasforma, nelle semplici parole e non <lb/>punto nella sostanza, in quest'altro, da cui si fa dipendere tutta la nuova <lb/>scienza galileiana: &ldquo; Accipio gradus velocitatis eiusdem mobilis, super di&shy;<lb/>versas planorum inclinationes acquisitos, tunc esse aequales, cum eorumdem <lb/>planorum elevationes aequales sint &rdquo; (Alb. </s>

<s>XIII, 163). </s></p><p type="main">

<s>Da ci&ograve;, senz'avere altrimenti bisogno d'invocare il teorema del Tarta&shy;<lb/>glia, si concludeva la dimostrazione dei tempi proporzionali agli spazi, per&shy;<lb/>ch&egrave;, supponendo un medesimo mobile o due mobili uguali movere dalla <lb/>quiete in A (fig. </s>

<s>154), e l'uno scendere per la diritta AB e l'altro per la <lb/>obliqua AC, perciocch&egrave; nei punt&igrave; D, E; F, G; H, I ecc., resecati dalle re-<pb xlink:href="020/01/2088.jpg" pagenum="331"/>spettive linee condotte parallele alla orizzontale BC, gl'impeti o le velocit&agrave; <lb/>sono uguali, in quanto che le scese AD, AE; AF, AG; AH, AI ecc., tutte <lb/><figure id="id.020.01.2088.1.jpg" xlink:href="020/01/2088/1.jpg"/></s></p><p type="caption">

<s>Figura 154.<lb/><emph type="italics"/>capiunt aequaliter de directo;<emph.end type="italics"/> dunque, nei moti <lb/>per tutta l'AB, e per tutta l'AC, son le velocit&agrave; <lb/>uguali. </s>

<s>Ma dove sono le velocit&agrave; uguali, gli spazi <lb/>son proporzionali ai tempi, e perci&ograve; il tempo per <lb/>AB, al tempo per AC, sta come la linea AB alla <lb/>linea AC. </s></p><p type="main">

<s>Tale essendo il processo di Galileo tradisce <lb/>le sue intenzioni di rendere la scienza nuova in&shy;<lb/>dipendente dall'antica, alla quale, non solamente <lb/>appartiene il supposto delle velocit&agrave; uguali nel&shy;<lb/>l'egual rettitudine del descenso, ma i teoremi al&shy;<lb/>tres&igrave;, che concernono i moti equabili, dai quali <lb/>accidentalmente derivano gli accelerati. </s>

<s>La Dina&shy;<lb/>mica nuova insomma si fondava sopra questi tre massimi principii: che le <lb/>velocit&agrave; siano in ragion diretta degli spazi e reciproca dei tempi; che sian <lb/>proporzionali agl'impeti, e che si trovino sempre uguali in qualunque obli&shy;<lb/>quit&agrave;, quando le scese rette siano uguali. </s>

<s>Il primo principio, che non ne <lb/>avrebbe avuto bisogno, &egrave; in s&egrave; e nelle sue conseguenze dimostrato da Ga&shy;<lb/>lileo in quelle sei proposizioni dei moti equabili, che precedono al trattato <lb/>dei moti accelerati; il secondo tiene in s&egrave; impressa la nota dell'evidenza, <lb/>ma il terzo non ha d'altronde il suffragio che dall'aver condotto Leonardo <lb/>da Vinci e il Tartaglia a conseguenze vere. </s>

<s>Poteva, per questo e per la sua <lb/>propria ragionevolezza, quel supposto approvarsi, ma a Galileo, che sopra <lb/>lui solo erigeva la gran mole, sembrava conveniente saggiarne meglio la <lb/>solidit&agrave;, perch&egrave;, vacillando quello, ne vacillava tutto intero l'edifizio costruito, <lb/>come su regola, sul supposto che le medesime leggi governino il moto nel <lb/>perpendicolo e nei piani inclinati. </s>

<s>&ldquo; Id autem, quod demonstratum est in <lb/>lationibus peractis in perpendiculis, intelligatur etiam itidem contingere in <lb/>planis utcumque inclinatis, in iisdem enim assumptum est accelerationis <lb/>gradus eadem ratione augeri &rdquo; (Alb. </s>

<s>XIII, 173, 74). </s></p><p type="main">

<s>Le cure per&ograve;, poste dall'Istitutore in confermare quel suo fondamento, <lb/>non appariscono proporzionate al bisogno, perch&egrave; non si limitano ad altro, <lb/>che a descrivere un'esperienza, per la quale alle gi&agrave; probabili ragioni si <lb/>viene a crescere tanto la probabilit&agrave;, &ldquo; che poco gli manchi all'agguagliarsi <lb/>ad una ben necessaria dimostrazione &rdquo; (ivi, pag. </s>

<s>164). &Egrave; quella esperienza <lb/>desunta dalle vibrazioni del pendolo, in cui si osserva che sormonta quasi <lb/>a quella medesima altezza, d'onde fu sceso, ed &egrave; da credere che vi arrive&shy;<lb/>rebbe precisamente, quando si togliessero gl'impedimenti dell'aria e del filo. <lb/></s>

<s>&ldquo; Dal che possiamo veracemente concludere, dice Galileo, che l'impeto acqui&shy;<lb/>stato nel punto B (fig. </s>

<s>155) dalla palla, nello scendere per l'arco CB, fu <lb/>tanto, che bast&ograve; a risospingersi per un simile arco BD alla medesima al&shy;<lb/>tezza &rdquo; (ivi). </s></p><pb xlink:href="020/01/2089.jpg" pagenum="332"/><p type="main">

<s>Per rendere poi questa dimostrazione sperimentale anche pi&ugrave; conclu&shy;<lb/>dente, immagina l'Autore che, rimosso il filo in AC, e di l&igrave; lasciato andare, <lb/><figure id="id.020.01.2089.1.jpg" xlink:href="020/01/2089/1.jpg"/></s></p><p type="caption">

<s>Figura 155.<lb/>incontri in E un chiodo, co&shy;<lb/>sicch&egrave; sia costretto di risa&shy;<lb/>lir dall'opposta parte, de&shy;<lb/>scrivendo un arco di cer&shy;<lb/>chio con un raggio EB pi&ugrave; <lb/>corto del primo, e vuol che <lb/>poi si abbassi anche di pi&ugrave; <lb/>quell'ostacolo, come in F, da <lb/>far risalire il grave pendulo <lb/>per un arco appartenente a <lb/>un circolo descritto anche <lb/>da minor raggio, e nono&shy;<lb/>stante si osserva che l'im&shy;<lb/>peto, conceputo in B per la <lb/>discesa dal medesimo pun&shy;<lb/>to C, fa in tutt'e tre i casi <lb/>risalire il pendolo stesso nei <lb/>punti D, G, I, situati con C sulla medesima linea orizzontale. </s>

<s>Sarebbe il <lb/>fatto riuscito meglio dimostrativo coi sifoni pieni di acqua, che servirono cos&igrave; <lb/>bene al medesimo intento a Leonardo da Vinci, come vedemmo, n&egrave; a Ga&shy;<lb/>lileo sfugg&igrave; l'appropriatissimo esempio, quando nel I dialogo Dei due mas&shy;<lb/>simi sistemi, a confermare la verit&agrave; della sentenza che l'impeto acquistato <lb/>dal mobile in qualsivoglia luogo del suo moto &egrave; tanto, che basterebbe a ri&shy;<lb/>condurlo all'altezza d'onde si part&igrave;; dop'avere invocata l'esperienza del pen&shy;<lb/>dolo, soggiunge: &ldquo; Mostrami l'istesso l'acqua, che, scendendo per un sifone, <lb/>rimonta altrettanto, quanto fu la sua scesa &rdquo; (Alb. </s>

<s>I, 28). </s></p><p type="main">

<s>Anzi &egrave; a notare che in questo primo Dialogo, dove si pongono i prin&shy;<lb/>cipii a uno special trattato di Meccanica, concernente il moto della Terra <lb/>in particolare, Galileo s'intrattiene a dimostrare il supposto delle velocit&agrave; <lb/>uguali, dopo cadute uguali, pi&ugrave; a lungo e con maggior variet&agrave; e valore di <lb/>argomenti di quel che non faccia nel III dialogo Delle due nuove scienze, <lb/>dove quello stesso principio &egrave; supposto a trattare in tutta la sua generalit&agrave; <lb/>la scienza del moto. </s>

<s>Forse la ragione, per cui parve che Galileo stesso se <lb/>ne passasse qui con troppa leggerezza, &egrave; perch&egrave; credeva di averne detto al&shy;<lb/>trove abbastanza: e infatti gli attori dei <emph type="italics"/>Due massimi sistemi<emph.end type="italics"/> s'intratten&shy;<lb/>gono nelle loro prime interlocuzioni a confermare i principii della Mecca&shy;<lb/>nica, dipendenti da quel discorso, che si fa da pag. </s>

<s>29-32 dell'edizione, da <lb/>noi tenuta sott'occhio. </s>

<s>Chi volesse poi di un tal discorso avere in poche pa&shy;<lb/>role condensata la sostanza, legga la seguente nota manoscritta: <emph type="italics"/>&ldquo; Miran&shy;<lb/>dum:<emph.end type="italics"/> numquid motus per perpendiculum AD (fig. </s>

<s>156) velocior sit quam <lb/>per inclinationem AB? </s>

<s>Videtur esse, nam aequalia spacia citius conficiun&shy;<lb/>tur per AD, quam AB; attamen videtur et non esse, nam, ducta horizon-<pb xlink:href="020/01/2090.jpg" pagenum="333"/>tali BC, tempus per AB, ad tempus per AC, est ut AB ad AC. </s>

<s>Ergo eadem <lb/><figure id="id.020.01.2090.1.jpg" xlink:href="020/01/2090/1.jpg"/></s></p><p type="caption">

<s>Figura 156.<lb/>momenta velocitatis per AB et per AC: est enim una ca&shy;<lb/>demque velocitas illa, quae, temporibus inaequalibus, spa&shy;<lb/>cia transit inaequalia eamdem quam tempora rationem ha&shy;<lb/>bentia &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>164 a tergo). </s></p><p type="main">

<s>Il teorema fondamentale dei tempi proporzionali agli <lb/>spazi nella verticale e nell'obliqua ugualmente elevate, &egrave; qui <lb/>come l&agrave; concluso dallo stesso supposto principio, ma ne'dia&shy;<lb/>loghi Del mondo &egrave; la supposizione, messa per fondamento ai <lb/>dialoghi Del moto, fatta dipendere da un'altra supposizione, <lb/>tolta la quale, rovinerebbe necessariamente ogni scienza dei <lb/>moti naturali e dei proietti. </s>

<s>Abbiamo poco fa udito consi&shy;<lb/>stere una tal supposizione nell'ammetter che l'impeto della <lb/>scesa sia bastante a far risalire il mobile alla medesima al&shy;<lb/>tezza, di che d&agrave; Galileo, a varie occasioni, nelle varie sue <lb/>Opere, tal dimostrazione, da non si mettere in dubbio per <lb/><figure id="id.020.01.2090.2.jpg" xlink:href="020/01/2090/2.jpg"/></s></p><p type="caption">

<s>Figura 157.<lb/>nessuno, che specialmente gli abbia concesso esser nei <lb/>moti accelerati le velocit&agrave; proporzionali ai tempi. </s>

<s>In quel <lb/>discorso infatti, trascritto a pag. </s>

<s>307 nel capitolo addietro, <lb/>si sovverranno i Lettori come, dal suppor <emph type="italics"/>che il grave <lb/>cadente naturalmente vada continuamente accrescendo <lb/>la sua velocit&agrave;, secondo che accresce la distanza dal <lb/>termine onde si part&igrave;,<emph.end type="italics"/> se ne concludesse che il mobile <lb/>in C, in D, in E (fig. </s>

<s>157) e negli altri infiniti punti <lb/>della linea AB, ha per la caduta acquistato tale impeto, <lb/>da ricondursi in A al suo primo principio. </s></p><p type="main">

<s>Sperava Galileo di poter forse dimostrare quel suo <lb/>supposto, da cui diceva conseguir questo effetto, ma la <lb/>sua dimostrazione, che cio&egrave; si velocitino i gravi proporzio&shy;<lb/>natamente ai tempi, rimase per l'Autore e per noi un desiderio, non so&shy;<lb/>disfatto che in parte e indirettamente dagli Accademici del Cimento, i quali <lb/>narrano di aver fatto una tale esperienza: &ldquo; Una pallina di vetro piena, <lb/>lasciata dall'altezza di 50 parti, arriv&ograve; con la riflessione maggiore a gradi <lb/>48, mancandoli, per arrivare d'ond'ella partissi dalla quiete, due gradi soli, <lb/>che potevano importare un soldo in circa del nostro braccio a panno fio&shy;<lb/>rentino. </s>

<s>Da questa esperienza vien quasi confermata la conclusione del Ga&shy;<lb/>lileo, che un grave, nell'infimo termine della sua scesa, abbia acquistato tan&shy;<lb/>t'impeto, che basti a ricondurlo alla medesima orizzontale, dove egli principi&ograve; <lb/>suo moto, potendo probabilmente dirsi che l'impedimento del mezzo, come <lb/>il medesimo Galileo dice seguire nei pendoli, ed il cedere, bench&egrave; pochissimo, <lb/>del grave cadente e del piano, ov'egli venne a riflettersi; abbian dato mo&shy;<lb/>tivo alla detta palla, e sieno stati causa che ella non si riduca con la rifles&shy;<lb/>sione precisamente alla medesima altezza di parti 50. &rdquo; (Targioni, Notizie <lb/>delle scienze fisiche in Toscana, T. II, P. II, Firenze 1780, pag. </s>

<s>667, 68). </s></p><pb xlink:href="020/01/2091.jpg" pagenum="334"/><p type="main">

<s>Nelle esperienze degli Accademici fiorentini, e nel ragionamento di Ga&shy;<lb/>lileo, le proiezioni e i rimbalzi si consideravano fatti nella linea verticale, <lb/>ma ci&ograve; a poco giovava senza dimostrar che lo stesso avviene e si verifica <lb/>nelle linee oblique, e nei piani inclinati. </s>

<s>Contemplandosi, in mezzo a que&shy;<lb/>ste galileiane speculazioni, un tal caso, si sarebbe molto pi&ugrave; per tempo giunti <lb/>a far l'importantissima osservazione dell'isocronismo del ramo ascendente <lb/>col discendente nella traiettoria, e sarebbero le due scienze dei moti natu&shy;<lb/>rali e dei proietti nate a un parto, mentre invece, per passare a concluder <lb/>la potenza degl'impeti a far risalire il mobile per il medesimo tratto di via <lb/>comunque obliqua, fu costretto Galileo a far indietro anche un'altra volta <lb/>ritorno alla statica antica, computando gl'impeti secondo la quantit&agrave; del di&shy;<lb/>scenso retto, e ci&ograve; per l'unica ragione che un grave, in tanto solo acquista <lb/>momento, in quanto che movendosi s'avvicina al suo centro. </s>

<s>Ond'&egrave; che <lb/>l'impeto dello scendente per il piano AII, nella precedente figura, giunto <lb/>che sia al termine H, &egrave; uguale all'impeto acquistato dal medesimo mobile, <lb/>dopo la scesa perpendicolare AF &ldquo; perch&egrave; in effetto ambedue si sono avvi&shy;<lb/>cinati al centro ugualmente &rdquo; (Alb. </s>

<s>I, 28, 29). </s></p><p type="main">

<s>La ragione ultima del supposto galileiano riducesi in somma a questa, <lb/>pubblicamente esposta con s&igrave; gran solennit&agrave; in quel libro, che annunziava <lb/>la nuova Scienza del moto, la quale sembrava al suo Autore potersi fon&shy;<lb/>dare con sicurezza sopra un tal ragionevolissimo assunto, come quello, da <lb/>cui s'eran dedotte le approvatissime leggi dei momenti dei gravi sopra i <lb/>piani inclinati. </s>

<s>Nonostante, ai dimentichi o ai non curanti delle preparazioni <lb/>fatte nei dialoghi Del mondo al libro Dei moti locati, parvero quelle espe&shy;<lb/>rienze del pendolo, sulle quali sole si tratteneva, e per le quali sole si vo&shy;<lb/>leva conquistar l'assenso dei Lettori, principio non conveniente a una trat&shy;<lb/>tazione, che procedeva del resto con tutto il rigore della Geometria, ond'&egrave; <lb/>che, al primo apparire in Leyda del volume famoso, si lev&ograve; contro lui una <lb/>voce universale, che diceva esser la nuova scienza un'illusione o in difetto, <lb/>perch&egrave; posata sopra non vero o poco stabile fondamento. </s></p><p type="main">

<s>Quella voce poi si diffuse dai varii Scrittori con tenor vario, secondo <lb/>che movevano le opposizioni o dall'amore o dall'odio alla Scienza nuova. </s>

<s><lb/>Il Cabeo, pronto sempre a dimostrar falsa una sentenza, purch&egrave; Galileo <lb/>l'avesse pronunziata, non rimase, nemmeno in questa occasione, indietro nel <lb/>suo poco lodevole ufficio, e formulato l'assunto che, in una medesima oriz&shy;<lb/>zontale, gl'impeti acquistati dal cadente, per l'obliqua o per il perpendi&shy;<lb/>colo, sono uguali. </s>

<s>&ldquo; puto, soggiunge, ego hoc falsum, et ex principiis eiusdem <lb/>Auctoris evidenter confutari &rdquo; (Comment. </s>

<s>in Meteor. </s>

<s>Arist., T. </s>

<s>I cit., pag. </s>

<s>92). <lb/>Gli argomenti per&ograve; son tali, da mostrar che il Censore non aveva le prime <lb/>notizie elementa<gap/>i della Meccanica, consistendo nel dir che l'impeto, vale&shy;<lb/>vole a far risalir da B (nella fig. </s>

<s>155 poco addietro) il pendolo in I, dev'es&shy;<lb/>ser maggiore dell'altr'impeto, che basta a farlo risalire in D, perch&egrave; il viag&shy;<lb/>gio BI &egrave; pi&ugrave; erto del viaggio BD, e si fa con pi&ugrave; celere moto. </s></p><p type="main">

<s>Queste del Cabeo eran pure le ragioni del Cazr, secondo che riferisce, <pb xlink:href="020/01/2092.jpg" pagenum="335"/>per confutarle, il Gassendo. </s>

<s>&ldquo; Inquis, cum neque ex terminis notum sit, neque <lb/>ulla sufficiente experientia confirmatum, imo cum rationes etiam non de&shy;<lb/>sint, quibus oppositum probabilius reddatur, nempe gradus velocitatis per <lb/>longius planum acquisitos gradibus per brevius planum acquisitos esse mi&shy;<lb/>nores; id a Galilaeo non peti, sed debuerat demonstrari, cum praesertim <lb/>maxima pars subsequentium theorematum hoc unico postulato nitantur. </s>

<s>Quid <lb/>enim certi ex incertis concludi potest aut ex principio, ut ipsemet Galilaeus <lb/>agnoscit, verisimili tantum ac probabili, demonstrari? </s>

<s>&rdquo; (De proportione qua <lb/>gravia accelerantur, Epist. </s>

<s>I cit., pag. </s>

<s>21). Il Mersenno era pure di questo <lb/>sentimento, e diceva in Roma a Michelangiolo Ricci &ldquo; che l'assunto primo <lb/>fatto dal Galileo era bisognoso di prove, e perci&ograve; o probabile o improbabile, <lb/>ed in conseguenza le proposizioni sei seguenti osserva esser tanto lontane <lb/>dall'evidenza geometrica, quant'&egrave; impossibile aver certezza di una conclu&shy;<lb/>sione dedotta da verosimile assunto &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>116). <lb/>Ripeteva cos&igrave; dicendo il Censore quel che gli aveva pochi anni prima scritto <lb/>il Cartesio in una sua Epistola, nella quale, fra le parecchie altre cose no&shy;<lb/>tate contro a quello che novamente aveva letto nel Galileo, era anche que&shy;<lb/>sta: &ldquo; Supponit etiam velocitatis gradus eiusdem corporis in diversis planis <lb/>esse aequales, quando aequales sunt istorum planorum elevationes. </s>

<s>Hoc vero <lb/>ille non probat, neque exacte verum est. </s>

<s>Et quia sequentia omnia ex dua&shy;<lb/>bus hisce hypothesibus dependent, dici potest illum in aere aedificasse &rdquo; <lb/>(Epist., P. II cit., pag. </s>

<s>243, 44). </s></p><p type="main">

<s>Nel Mersenno e nel Cartesio, come nel Cabeo e nel Cazr, non erano <lb/>scevri da passione cos&igrave; fatti giudizi, ma che fossero comuni, lo conferma <lb/>l'esservi anche i pi&ugrave; amorevoli a Galileo, bench&egrave; per diverso motivo, con&shy;<lb/>corsi. </s>

<s>Il Viviani cos&igrave; scriveva a proposito de'suoi studii giovanili: &ldquo; Appena <lb/>ebbi scorsi i primi Elementi, che, impaziente di vederne l'applicazione, pas&shy;<lb/>sai alla scienza dei moti naturali, nuovamente promossa dal Galileo, e che <lb/>allora appunto era uscita alla luce, ed arrivato a quel principio supposto <lb/>che le velocit&agrave; dei mobili naturalmente per piani di una medesima eleva&shy;<lb/>zione siano uguali fra loro, dubitai, non gi&agrave; della verit&agrave; dell'assunto, ma <lb/>della evidenza di poterlo suppor come noto &rdquo; (Scienza universale delle pro&shy;<lb/>porzioni, Firenze 1674, pag. </s>

<s>99). </s></p><p type="main">

<s>Nel medesimo tempo che il Viviani, attendeva allo studio delle Matema&shy;<lb/>tiche il giovane principe Leopoldo dei Medici, sotto la direzione di Famiano <lb/>Michelini, il quale scriveva a Galileo che S. A. aveva difficolt&agrave; in ammet&shy;<lb/>tere per certo l'assunto, che si supponeva nel bellissimo libro Del moto, e <lb/>lo pregava perci&ograve; a volergliene mandar la dimostrazione, perch&egrave; senz'essa <lb/>pareva al suo regio alunno &ldquo; di andare al buio, ancorch&egrave; quelle esperienze, <lb/>che Ella pone nel libro, siano poco meno che dimostrazione &rdquo; (MSS. Gal., <lb/>P. VI, T. XIII, fol. </s>

<s>112). </s></p><p type="main">

<s>Fu il supposto meccanico dimostrato da Galileo, come narreremo in <lb/>quest'altra parte della nostra Storia, e n'ebbero il Viviani, il principe Leo&shy;<lb/>poldo e tutti gli altri a rimaner sodisfatti, ma perch&egrave; intanto s'aspettava che <pb xlink:href="020/01/2093.jpg" pagenum="336"/>occorresse di fare una seconda edizione dei dialoghi Delle due nuove scienze, <lb/>per inserirvi la dimostrazione tanto desiderata, il Torricelli, che nel 1644 <lb/>dava alla luce il suo celebre libro <emph type="italics"/>De motu gravium,<emph.end type="italics"/> scriveva cos&igrave; nel proe&shy;<lb/>mio, dop'aver formulato quello stesso supposto galileiano. </s>

<s>&ldquo; Ex hac peti&shy;<lb/>tione dependet quasi universa illius doctrina de motu, tum accelerato, tum <lb/>proiectorum. </s>

<s>Si quis de principio dubitet, de iis, quae inde consequntur, cer&shy;<lb/>tam omnino scientiam non habebit &rdquo; (Opera geom., P. </s>

<s>I cit., pag. </s>

<s>98). So <lb/>bene, prosegue il Torricelli a dire, che Galileo ritrov&ograve; negli ultimi anni della <lb/>sua vita di quel supposto la dimostrazion matematica, ma perch&egrave; rimane <lb/>tuttavia inedita, vi suppliremo noi nel presente trattato &ldquo; ut appareat quod <lb/>Galilei suppositio demonstrari potest, et quidem immediate, ex illo theore&shy;<lb/>mate, quod pro demonstrato ex mechanicis ipse desumit in se, in secunda <lb/>parte sextae propositionis De motu accelerato. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il teorema, a cui qui si accenna, &egrave; il seguente: Siano AB, AD (fig. </s>

<s>158) <lb/>due piani di lunghezza uguale, l'uno elevato secondo DF, l'altro secondo <lb/><figure id="id.020.01.2093.1.jpg" xlink:href="020/01/2093/1.jpg"/></s></p><p type="caption">

<s>Figura 158.<lb/>BE. &ldquo; Supponit Galileus, dice il Torricelli, <lb/>pro demonstrato, momentum in plano AB, <lb/>ad momentum in plano AD, esse ut BE ad <lb/>DF &rdquo; (ibid.). Ora &egrave; cosa veramente singo&shy;<lb/>lare che il Torricelli non si avvedesse es&shy;<lb/>sere il teorema, in quella stessa VI propo&shy;<lb/>sizione da lui citata, non gi&agrave; supposto, ma <lb/>benissimo dimostrato in questo modo: <lb/>&ldquo; Constat ex meis Elementis mechanicis <lb/>momentum ponderis super plano secundum <lb/>lineam ABC (nella medesima figura) elevato, ad momentum suum totale, esse <lb/>ut BE ad BA, vel ad DA; eiusdemque ponderis momentum super elevatione <lb/>AD, ad totale suum momentum, esse ut DF ad DA, vel BA. </s>

<s>Ergo eiusdem pon&shy;<lb/>deris momentum super plano secundum DA inclinato, ad momentum super <lb/>inclinatione secundum ABC, est ut linea DF ad lineam BE &rdquo; (Alb. </s>

<s>XIII, 182). </s></p><p type="main">

<s>La dimostrazione, come ognun vede, &egrave; legittima, perch&egrave;, chiamato M.o il <lb/>momento, dalle due equazioni M.oAB:M.oBE=BE:AB; M.oAD:M.oDF= <lb/><figure id="id.020.01.2093.2.jpg" xlink:href="020/01/2093/2.jpg"/></s></p><p type="caption">

<s>Figura 159.<lb/>DF:AD, si conclude il teorema, come allo stesso <lb/>modo lo concluse il Viviani nella seguente sua <lb/>Nota: &ldquo; Sint gravia A, D (fig. </s>

<s>159) aequalia et <lb/>plana AC, DE aequalia. </s>

<s>Jam momentum A per <lb/>AC, ad momentum A per AB, est ut AB ad <lb/>AC, vel ad DE: et momentum A, vel D, per <lb/>DB, ad momentum D per DE, est ut DE ad <lb/>DB. </s>

<s>Ergo ex aequo momentum absolutum pon&shy;<lb/>deris A per AC, ad momentum absolutum pon&shy;<lb/>deris D per DE, est ut AB ad DB, vel ut altitu&shy;<lb/>dinem planorum &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXVII, <lb/>fol. </s>

<s>105). </s></p><pb xlink:href="020/01/2094.jpg" pagenum="337"/><p type="main">

<s>Or essendo cos&igrave;, fa, ripetiamo, gran maraviglia che il Torricelli dicesse <lb/>di non essersi mai incontrato in un simile teorema: <emph type="italics"/>nos in huiusmodi theo&shy;<lb/>rema non incidimus,<emph.end type="italics"/> e ch'egli credesse perci&ograve; di essere stato il primo a <lb/>dimostrarlo, come fece nella sua III proposizione, in modo per&ograve; men sem&shy;<lb/>plice di quello di Galileo, e meno diretto. </s>

<s>Che i momenti insomma sui piani <lb/>di lunghezza uguale, ma variamente inclinati, stiano come i seni degli an&shy;<lb/>goli delle elevazioni, si suppone &egrave; vero da Galileo nel trattato Delle mac&shy;<lb/>chine, ma no nel secondo processo dimostrativo della proposizione VI Dei <lb/>moti accelerati, dove anzi ne d&agrave; una bella dimostrazione, che pass&ograve;, non si <lb/>sa come, di vista al Torricelli, e che, per servirsene a risolvere il problema <lb/>delle pressioni fatte dalla trave appoggiata al muro, fu raccolto nelle sue <lb/>cose meccaniche dal Viviani. </s></p><p type="main">

<s>Avvertito ci&ograve;, che fa accorti i saggi poter cecuzzire talvolta anche le <lb/>linci, proseguiamo oltre a leggere nel libro <emph type="italics"/>De motu gravium,<emph.end type="italics"/> per trattener <lb/>particolarmente la nostra attenzione intorno a ci&ograve;, che riguarda gli usi e le <lb/>necessit&agrave; dell'invocato supposto galileiano. </s>

<s>Dop'avere, nella IV proposizione, <lb/>dimostrato dalla precedente che i tempi, nelle varie inclinazioni ugualmente <lb/>alte, son come gli spazi, sovvenne al Torricelli un'altra dimostrazione, alla <lb/>quale premette queste parole: &ldquo; Praecedens theorema poterat demonstrari <lb/>sine ulla suppositione. </s>

<s>Demonstrat enim Galileus, in propos. </s>

<s>VI De motu <lb/>accelerato, tempora lationum per chordas omnes in circulo aequalia esse. </s>

<s><lb/>Idque tribus modis probat. </s>

<s>In primo et tertio subest principium suum non <lb/>satis evidens; in secundo vero nihil supponitur, praeter iam dictum theorema <lb/>mechanicum. </s>

<s>Quod si, ipso teste, demonstratum antea fuerat, ex ipso imme&shy;<lb/>diate, tamquam corollarium, necessaria illatio suae tertiae propositionis, imo <lb/>et suae petitionis demonstrari poterat &rdquo; (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>107). </s></p><p type="main">

<s>Accenna insomma il Torricelli a un partito che, se avesse saputo Ga&shy;<lb/>lileo destramente afferrarlo, lo avrebbe condotto a dimostrare il suo terzo <lb/>fondamental teorema, che cio&egrave; i tempi per l'inclinata e per la perpendico&shy;<lb/>lare stanno come le lunghezze, senza alcuna supposizione. </s>

<s>Consisterebbe <lb/>quel partito nel movere dal teorema meccanico, e per esso dimostrare, come <lb/>lo stesso Galileo fa nel secondo modo della sua VI proposizione, che le corde <lb/>al diametro nel cerchio sono equidiuturne. </s>

<s>Dimostrato ci&ograve;, la proposizione <lb/>terza, per la quale bisogn&ograve; invocare il supposto, nella teoria dei moti ac&shy;<lb/>celerati ne scendeva per legittimo corollario immediato. </s></p><p type="main">

<s>A far che dunque tutto nel terzo dialogo Delle due nuove scienze pro&shy;<lb/>cedesse per legittima dimostrazione, bastava, secondo il Torricelli, dare ai <lb/>teoremi galileiani un ordine alquanto diverso, qual sarebbe il seguente. </s>

<s>Ai due <lb/>primi teoremi dimostrativi della legge dei moti accelerati, e ai loro corol&shy;<lb/>lari, specialmente al II del II teorema, che dice essere i tempi impiegati a <lb/>percorrere due spazi qualunque proporzionali all'uno dei detti spazi, e alla <lb/>media fra ambedue; dovrebbe seguitare il teorema meccanico, da cui si di&shy;<lb/>mostrerebbe quella, che ricorre in ordine la VI nel trattato di Galileo. </s>

<s>A <lb/>questa succederebbe l'altra proposizione che, nello stesso trattato galileiano, <pb xlink:href="020/01/2095.jpg" pagenum="338"/>le viene anteposta, e che concerne i tempi proporzionali alle lunghezze delle <lb/>scese oblique, sopra la qual proposizione erigendosi tutto il meccanico edi&shy;<lb/>fizio, verrebbe questo, senza che nessuno avesse ragione di dubitarne, a ri&shy;<lb/>posar sul pi&ugrave; solido fondamento. </s></p><p type="main">

<s>Il Torricelli mostra, nell'<emph type="italics"/>aliter<emph.end type="italics"/> alla proposizione sua IV, in che modo, <lb/>cos&igrave; disponendosi le cose, si verrebbe a concluder la desiderata verit&agrave; fon&shy;<lb/>damentale alla nuova Scienza galileiana, tutto dimostrando, senza nulla sup&shy;<lb/>porre, ma si pu&ograve; l'esempio di lui rendere anche pi&ugrave; spedito nella forma <lb/>che segue: Sia ADB (fig. </s>

<s>160) il piano inclinato, e sia la lunghezza perpen&shy;<lb/><figure id="id.020.01.2095.1.jpg" xlink:href="020/01/2095/1.jpg"/></s></p><p type="caption">

<s>Figura 160.<lb/>dicolare AC media proporzionale fra AB e AD. Avremo, <lb/>per il II sopra citato corollario alla proposizione II Dei <lb/>moti accelerati (Alb. </s>

<s>XIII, 173), T.oAB:T.oAD= <lb/>AB:AC. </s>

<s>Congiunti i punti D, C ne resulta il triangolo <lb/>rettangolo ADC, in cui, circoscrittogli il mezzo cerchio, <lb/>il lato AD si dimostra dal teorema meccanico essere ad <lb/>AC equidiuturno. </s>

<s>Ond'&egrave; che a T.oAD sostituito il suo <lb/>uguale T.oAC nella sopra scritta ragione, si verr&agrave; sen&shy;<lb/>z'altro ad avere T.oAB:T.oAC=AB:AC, ossia che i tempi nella per&shy;<lb/>pendicolare e nell'obliqua stanno come le loro rispettive lunghezze. </s></p><p type="main">

<s>Ripensando a queste cose, direbbesi da tutti insieme col Torricelli es&shy;<lb/>sere stata una mala ventura di Galileo quella di non aver conosciuto, e di <lb/>non aver messo in esecuzione un cos&igrave; bello espediente. </s>

<s>Che se parve acco&shy;<lb/>starvisi, quando dettava al Viviani il teorema inserito postumo nel III dia&shy;<lb/>logo Del moto, troppo tardi direbbero venne l'inspirazione al buon vecchio. </s></p><p type="main">

<s>In cos&igrave; fatti sentimenti eravamo anche noi, quando, svolgendo il se&shy;<lb/>condo Tomo della Parte quinta dei Manoscitti galileiani, ci abbattemmo a <lb/>leggere una proposizione, che ritraeva in s&egrave; l'ordine propriamente divisato <lb/>dal Torricelli: si dimostrava cio&egrave; in essa che i tempi son proporzionali alle <lb/>lunghezze dei piani ugualmente elevati dop'aver dal teorema meccanico con&shy;<lb/>cluso l'isocronismo per le corde dei cerchi. </s>

<s>Fummo a un tratto soprappresi <lb/>da tanta maraviglia, che non sapendo allora come attutirla, s'and&ograve; a pen&shy;<lb/>sare fra noi che fossero quelle cose dettate da Galileo a qualcuno de'suoi <lb/>pi&ugrave; familiari, come l'ultimo progressivo svolgimento de'suoi pensieri. </s>

<s>Ma ci <lb/>dovemmo poi persuadere che quello scritto era autografo, da mostrar che <lb/>non impigrita punto dalla vecchiezza fosse la mano, la quale, guidata an&shy;<lb/>cora dalla libera vista, faceva correre la penna sicura. </s></p><p type="main">

<s>Seguitando avanti e indietro a squadernare il volume, tutti sopra pen&shy;<lb/>siero di queste cose, ebbe quella prima nostra maraviglia a crescere anche <lb/>di pi&ugrave; all'incontrarci in un'altra proposizione autografa, nella quale, col me&shy;<lb/>desimo processo ma in modo alquanto diverso, dimostravasi, dal Teorema <lb/>meccanico, e dalla propriet&agrave; delle corde isocrone, che le tardit&agrave; di due gravi <lb/>scendenti per due varie obliquit&agrave; di piani ugualmente elevati erano propor&shy;<lb/>zionali alle lunghezze delle discese. </s>

<s>In quel contrapporre le tardit&agrave; alle ce&shy;<lb/>lerit&agrave;, causate dai momenti, ci parve riconoscere l'esercizio delle ali giova-<pb xlink:href="020/01/2096.jpg" pagenum="339"/>nette, prima di spiegare i liberi voli, e il frammento, pubblicato nel Tomo XI <lb/>a pag. </s>

<s>56-62 dall'Alb&egrave;ri, ci confermava nell'opinione, che i ritrovati processi <lb/>dimostrativi, creduti degli ultimi, erano invece dei primi tempi. </s></p><p type="main">

<s>Allora, a uno de'quesiti, che ci avevano tante volte tenuto in angustia, <lb/>cominci&ograve; ad apparire la speranza di una risposta. </s>

<s>Avendo letto quel che <lb/>scriveva Galileo, nel 1602, a Guidubaldo del Monte, delle leggi dei moti dei <lb/>gravi scendenti per la quarta di un cerchio, e ripensando che quella era <lb/>una delle ultime proposizioni, che suppone le parecchie altre dimostrate nel <lb/>libro Dei moti locali; si domandava a noi stessi: forse che la serie dei teo&shy;<lb/>remi, i quali nel III dialogo Delle due nuove scienze si recitano dal Sal&shy;<lb/>viati, fu dall'Accademico ordinata infino dal 1602? Ma come &egrave; possibile ci&ograve;, <lb/>se non era ancora dimostrata la legge dei moti accelerati, la quale non occorse <lb/>prima del 1604, come si sa per certissimi documenti? </s>

<s>Eppure &egrave; un fatto <lb/>che aveva due anni prima Galileo dimostrato esser nelle scese dei gravi per <lb/>i cerchi l'arco brachistocrono della corda sottesa; proposizione che doveva <lb/>necessariamente conseguire da altre proposizioni, fra le quali, non potendo <lb/>essere le due prime del secondo libro inserito nel Dialogolo terzo, sembrava <lb/>che la conclusion meccanica scritta a Guidubaldo non potess'esser condotta <lb/>al modo, che si legge nel Dialogo ora detto, dove supponesi dimostrata la <lb/>proporzion dei tempi impiegati a percorrere acceleratamente in una mede&shy;<lb/>sima direzione due spazi. </s>

<s>Ma perch&egrave; da questo in fuori non ha quella <lb/>XXXVI proposizione stampata nient'altro di dinamico, si pensava che, di&shy;<lb/>mostrato in altro modo e da tutt'altri principii concluso il corollario secondo <lb/>della II proposizione Dei moti accelerati, poteva la detta proposizione XXXVI, <lb/>anche dalla statica sola, senza difficolt&agrave;, derivarsi. </s>

<s>Ritrovato perci&ograve; che s'ebbe, <lb/>fra quelle confuse carte galileiane, il Teorema, dove dall'isocronismo di due <lb/>corde, variamente inclinate al diametro perpendicolare di un cerchio, si con&shy;<lb/>cludeva essere i tempi della discesa per le due varie altezze, come una di <lb/>esse altezze alla media fra tutt'e due; non ci parve mancar altro per dire <lb/>di aver ritrovata la serie e il processo dimostrativo di quei teoremi, che, <lb/>pieno di compiacente maraviglia per la inaspettata verit&agrave; dimostrata, Galileo, <lb/>per lettera del d&igrave; 29 del Novembre 1602, annunziava a Guidubaldo del Monte. </s></p><p type="main">

<s>Preso animo di qui a proseguire le nostre investigazioni, per rispon&shy;<lb/>dere ai varii quesiti, che gli uni dagli altri ci rampollavano nella mente fe&shy;<lb/>condi, si volle sapere qual relazione avesse con le annunziate a Guidubaldo <lb/>quella proposizione, nella quale dicemmo d'esserci prima abbattuti, e che <lb/>per dimostrar come i tempi, nella perpendicolare e nell'obliqua alte ugual&shy;<lb/>mente son proporzionali alle lunghezze, procedeva propriamente a quel modo, <lb/>che suggerivasi dal Torricelli, per evitar qualunque supposto. </s>

<s>Si pens&ograve; da <lb/>principio che fosse una tal proposizione dimostrata, per sostituirsi a quella <lb/>delle <emph type="italics"/>tardit&agrave;,<emph.end type="italics"/> fra i teoremi nel Settembre del 1602 gi&agrave; prima ordinati, ma <lb/>poi ci accorgemmo che quella stessa proposizione faceva parte di altre ri&shy;<lb/>trovate da noi manoscritte, le quali accennavano a un trattato assai pi&ugrave; <lb/>compiuto, e mostravano un andamento diverso dal primo: ci accorgemmo <pb xlink:href="020/01/2097.jpg" pagenum="340"/>insomma che Galileo riformava, e riordinava il primo libro dopo le scoperte <lb/>leggi dei moti accelerati. </s></p><p type="main">

<s>La curiosit&agrave; per&ograve;, sodisfatta cos&igrave; da una parte, accresceva piuttosto che <lb/>diminuire quella prima presa maraviglia dall'altra, perch&egrave;, certificati ora&shy;<lb/>mai due essere stati i varii modi di procedere senza nulla supporre, non si <lb/>sapeva intendere come, nel render solennemente pubblico il suo trattato <lb/>Dei movimenti locali, Galileo ripudiasse que'due primi rigorosi processi per <lb/>eleggerne un terzo, che moveva da una supposizione, e che doveva metter <lb/>perci&ograve; negli animi tanto scandolo, e nelle menti tanto scompiglio. </s></p><p type="main">

<s>Desiderosi dunque d'intendere la ragione di cos&igrave; strano ripudio, si tor&shy;<lb/>nava, con pi&ugrave; diligenza che mai, a quel manoscritto meccanico laberinto, <lb/>tenendo in mano, per filo da non ismarrirci, la proposizione fondamentale <lb/>dei tempi lungo i piani ugualmente elevati, dalla qual proposizione dipen&shy;<lb/>dono tutte le altre appartenenti a quel secondo libro, che dopo la teoria dei <lb/>moti accelerati era, come dicemmo, la riforma e il riordinamento del primo <lb/>annunziato gi&agrave; nella sopra citata lettera a Guidubaldo. </s>

<s>Da un teorema, tor&shy;<lb/>nando per quelle zibaldate carte innanzi e indietro, correndo e ricorrendo <lb/>faticosamente per le difformi facce di que'fogli, a cercar l'altro, che ne sa&shy;<lb/>rebbe dovuto seguitare, secondo l'intrapreso ordine dimostrativo, si trova&shy;<lb/>vano i principii statici conserti coi dinamici a dar giusta misura, e quasi <lb/>bellezza di moto all'andamento delle proposizioni. </s>

<s>A un tratto ci troviamo <lb/>dalla statica abbandonati, e ci accorgiamo che l'Autore la scansa, come per&shy;<lb/>sona a cui si creda esser sotto la veste ascosta un'arme insidiosa. </s>

<s>Ma per&shy;<lb/>ch&egrave; non ce ne rimanga alcun dubbio, ce l'ha Galileo stesso di mano pro&shy;<lb/>pria lasciato scritto. </s>

<s>Dimostrato un teorema <emph type="italics"/>ex mechanicis,<emph.end type="italics"/> secondo il solito <lb/>modo, lo assale un dubbio molesto se quel ch'&egrave; proprio dei moti equabili <lb/>possa convenire agli accelerati, e senz'altro risolve e imperiosamente dice <lb/>a s&egrave; stesso: <emph type="italics"/>Demonstra aliter sic,<emph.end type="italics"/> e da l&igrave; innanzi rimane a condur le pro&shy;<lb/>posizioni la Dinamica sola. </s></p><p type="main">

<s>Sodisfatti, per avere scoperto il motivo di ci&ograve; che ci aveva prima de&shy;<lb/>stato cos&igrave; gran maraviglia, teniam dietro all'Autore nella presa risoluzione, <lb/>e riconosciamo in quei manoscritti il teorema fondamentale concluso dal <lb/>nuovo supposto; teorema che doveva indegnamente supplantare i bei teo&shy;<lb/>remi, derivati dalla teoria meccanica dei momenti. </s>

<s>Di qui dunque comincia <lb/>una nuova riforma, e si d&agrave; ordine a un trattato nuovo, che &egrave; il terzo ma&shy;<lb/>noscritto, e che solo rimane a Galileo per preparazione immediata a quello, <lb/>che vedr&agrave; finalmente in Leyda la pubblica luce. </s>

<s>La stampa risponde talvolta <lb/>con leggere variet&agrave; al manoscritto, ma pi&ugrave; spesso se ne dilunga con variet&agrave; <lb/>notabilissima, e utile di essere collazionata, perch&egrave; sovente, con l'intenzione <lb/>di spiegar meglio il concetto, s'avvolge ne'ricorsi, e si smembra negl'in&shy;<lb/>cisi. </s>

<s>Cosicch&egrave; lo stampato, che &egrave; il quarto, non ci dispensa che solo in parte <lb/>dal far conoscere ai nostri lettori anche quel terzo libro, o terzo modo di <lb/>trattare dei movimenti locali, rimasto fin qui, insieme con gli altri due, non <lb/>visto fra gli studiati manoscritti di Galileo. </s></p><pb xlink:href="020/01/2098.jpg" pagenum="341"/><p type="main">

<s>Dir que'libri non visti, o meglio non visti i materiali e i disegni la&shy;<lb/>sciatici per costruirli, non parr&agrave; forse credibile a chi sa essere stati man&shy;<lb/>dati, pochi anni addietro, per tutto il mondo trombetti a convocare mano&shy;<lb/>scritti galileiani, e non potr&agrave; persuadersi costui che siasi atteso con tanta <lb/>industria a raccoglier <emph type="italics"/>Lettere<emph.end type="italics"/> di fuori, non curando in casa i teoremi, e a <lb/>mettere in pubblica mostra gli <emph type="italics"/>Scampoli,<emph.end type="italics"/> lasciando chiuse le stoffe negli <lb/>armadi. </s>

<s>Eppur, ne'primi volumi dell'<emph type="italics"/>Edizion nazionale,<emph.end type="italics"/> ne'quali le opere <lb/>di Galileo ricorrono in ordine cronologico, avrebbero dovuto trovar luogo il <lb/>primo Libro, anteriore al 1602, e il secondo riformato tra il 1604 e il 1609, <lb/>n&egrave; ritrovandoveli, e ripensando che dovevano aver gl'Italiani eletto all'opera <lb/>alcuni de'pi&ugrave; valorosi in questa specialit&agrave; di studii, s'incominciava a dubi&shy;<lb/>tare di esserci noi stessi ingannati, quando, meglio esaminando i fastosi <lb/>volumi nazionali, ci parve che non fosse l'edizione diretta da quella propria <lb/>e particolare scienza richiesta al bisogno, e che fossero principalmente <lb/>rivolte le cure degli egregi editori a mettere i punti e le virgole al loro <lb/>posto, a restituir le dieresi e altri segni esquisiti, come farebbe un acca&shy;<lb/>demico della Crusca, a cui fosse dato a curare qualche prezioso testo di <lb/>lingua. </s></p><p type="main">

<s>Ritrovatici dunque a correr soli questo mar periglioso, raddoppiammo <lb/>le nostre industrie in cercar d'ogni parte argomenti, e in accomodarli al <lb/>nostro bisogno, perch&egrave; valessero tutti insieme a ridurci la fragile barca in <lb/>porto. </s>

<s>Daremo il nome di formali ad alcuni di quegli argomenti, e di ma&shy;<lb/>teriali agli altri, intendendo per i primi quelli, che consistono nel concetto, <lb/>a cui s'informano le varie proposizioni. </s>

<s>Dal progressivo concettuale svolgi&shy;<lb/>mento si desume con certezza logica il relativo ordine cronologico e nume&shy;<lb/>rico della serie de'teoremi, ma gli altri argomenti, che si dissero materiali, <lb/>mentre da una parte servono di riscontro per l'ordine relativo, sovvengono <lb/>dall'altra necessari a determinare il tempo assoluto, rivelatoci massimamente <lb/>dalla data certissima dei commerci epistolari. </s></p><p type="main">

<s>A far materiale riscontro alla cronologia presunta dalla logica, ci han <lb/>servito non poco le forme calligrafiche, e le stesse varie tinte dell'inchio&shy;<lb/>stro. </s>

<s>&Egrave; a tutti noto come la mano che scrive risenta variet&agrave; dagli anni, a <lb/>quel modo che la risentono i moti di tutte le altre membra, e come pu&ograve; <lb/>ciascuno fare esperienza in s&egrave; stesso, confrontando con quelle scritte a <lb/>trent'anni le carte scritte a cinquanta. </s>

<s>Sarebbe la differenza senza dubbio <lb/>assai pi&ugrave; notabile, se si facesse il confronto fra la calligrafia della prima <lb/>giovent&ugrave;, con quella dell'ultima vecchiezza, ma ci siam tenuti ai vent'anni, <lb/>che son lo spazio intercesso fra queste scritture, lasciate nel 1610, e non <lb/>riprese di proposito fino al 1630, come si parr&agrave; a suo luogo da certissimi <lb/>documenti. </s>

<s>I teoremi dimostrati tra il 1602 e il 1610 sono scritti con in&shy;<lb/>chiostro pi&ugrave; chiaro, e con agili forme rotonde. </s>

<s>Nel 1630, la vista affievolita <lb/>cos&igrave;, che sarebbesi tra pochi anni affatto spenta, aveva bisogno di segni me&shy;<lb/>glio scolpiti: l'inchiostro perci&ograve; &egrave; nero, le linee grosse, le forme quadrate. </s>

<s><lb/>A noi quasi pareva di veder viva la mano, che in tante carte del detto <pb xlink:href="020/01/2099.jpg" pagenum="342"/>Tomo II torna, dopo vent'anni, a scrivere sotto un teorema l'enunciazione, <lb/>in quella forma propria che l'originale serber&agrave; per la prossima stampa. </s></p><p type="main">

<s>D'altre particolarit&agrave; non terremo in discorso i Lettori, i quali le in&shy;<lb/>tenderanno assai meglio, vedendole in atto nella pubblicazione, e nella sto&shy;<lb/>ria di quei primi teoremi, intorno ai quali, per istituire una delle sue nuove <lb/>scienze, esercit&ograve; Galileo le sue matematiche speculazioni. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Nella Lettera, scritta da Padova il d&igrave; 29 di Novembre del 1602, e che <lb/>s'&egrave; pi&ugrave; volte commemorata, dava Galileo a Guidubaldo del Monte notizia di <lb/>alcune esperienze di moti, che avendo apparenza di straordinari, e giudican&shy;<lb/>dosi perci&ograve; dalla volgare opinione incredibili, diceva essergli stati confermati <lb/>dalla Geometria, la quale eragli nello stesso tempo venuta a rivelare que&shy;<lb/><figure id="id.020.01.2099.1.jpg" xlink:href="020/01/2099/1.jpg"/></s></p><p type="caption">

<s>Figura 161.<lb/>st'altre, non meno inopinabili conclusioni. <lb/></s>

<s>&ldquo; Sia dal cerchio BDA (fig. </s>

<s>161) il diame&shy;<lb/>tro BA eretto all'orizzonte, e dal punto A <lb/>fino alla circonferenza tirate linee <emph type="italics"/>utcum&shy;<lb/>que<emph.end type="italics"/> AF, AE, AD, AC. Dimostro, dice Gali&shy;<lb/>leo, mobili uguali cadere in tempi uguali, <lb/>e per la perpendicolare BA, e per gli piani <lb/>inclinati, secondo le linee CA, DA, EA, FA, <lb/>sicch&egrave;, partendosi nell'istesso momento dalli <lb/>punti B, C, D, E, F arriveranno nell'istesso <lb/>momento al termine A, e sia la linea FA <lb/>piccola quanto esser si voglia. </s>

<s>E forse anco <lb/>pi&ugrave; inopinabile parer&agrave; questo pur da me <lb/>dimostrato, che, essendo la linea SA non <lb/>maggiore della corda di una quarta, e le linee SI, IA <emph type="italics"/>utcumque,<emph.end type="italics"/> pi&ugrave; presto <lb/>fa il modesimo mobile il viaggio SIA, partendosi da S, che il viaggio solo <lb/>IA, partendosi da I &rdquo; (Alb. </s>

<s>VI, 23). </s></p><p type="main">

<s>Le annunziate proposizioni dipendevano da principii gi&agrave; noti, e da ve&shy;<lb/>rit&agrave; legittimamente di l&igrave; concluse con sottili matematici ragionamenti, che <lb/>s'andarono, come rigagnoli in un fiume, a disperdere fra i teoremi inseriti <lb/>nel III dialogo Delle due nuove scienze. </s>

<s>E perch&egrave; la scienza universale della <lb/>Natura &egrave; irrigata da quest'acque vive, non pu&ograve; chi cammina lungo le sponde <lb/>ad ammirare, e a cogliere i frutti dell'ubertosa campagna, non tener desi&shy;<lb/>deroso dietro i passi di colui, che viene ora a mostrar d'onde salga la be&shy;<lb/>nefica fonte, e a segnar quali sieno del primo formatosi ruscelletto i lontani <lb/>smarriti sentieri. </s></p><p type="main">

<s>PROPOSITIO I. &mdash; &ldquo; Momenta gravitatis eiusdem mobilis supra plano in-<pb xlink:href="020/01/2100.jpg" pagenum="343"/>clinato, et in perpendiculo, permutatim respondent longitudini et elevationi <lb/>eiusdem plani. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sit ad horizontem AB (fig. </s>

<s>162) planum inclinatum CA, in quo su&shy;<lb/><figure id="id.020.01.2100.1.jpg" xlink:href="020/01/2100/1.jpg"/></s></p><p type="caption">

<s>Figura 162.<lb/>matur quodcumquo punctum C, et, dimissa perpendi&shy;<lb/>culari ad horizontem CB, sit plani CA altitudo seu ele&shy;<lb/>vatio. </s>

<s>Dico momentum gravitatis mobilis D, super plano <lb/>CA, ad totale suum momentum in perpendiculo CB, <lb/>esse ut altitudo CB ad eiusdem plani longitudinem CA &rdquo; <lb/>(MSS. Gal., P. V, T. II, fol. </s>

<s>179). Per la dimostrazione <lb/>di ci&ograve; rimanda Galileo al suo trattato Della scienza mec&shy;<lb/>canica, che doveva dunque nel 1602 esser noto, bench&egrave; <lb/>andasse attorno anonimo e manoscritto. </s>

<s>&ldquo; Id autem ex Mechanicis probatum <lb/>est &rdquo; (ibid.). </s></p><p type="main">

<s>PROPOSITIO II. &mdash; &ldquo; Momenta gravitatis eiusdem mobilis, super diver&shy;<lb/>sas planorum inclinationes, habent inter se permutatim eamdem rationem, <lb/><figure id="id.020.01.2100.2.jpg" xlink:href="020/01/2100/2.jpg"/></s></p><p type="caption">

<s>Figura 163.<lb/>quam eorumdem planorum longitudines, dum eidem <lb/>elevationi respondeant. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sint diversae planorum inclinationes AB, AC <lb/>(fig. </s>

<s>163) quae eidem elevationi AD respondeant. </s>

<s><lb/>Dico momentum gravitatis eiusdem mobilis super <lb/>AB, ad momentum gravitatis super AC, eamdem <lb/>habere rationem quam longitudo AC habet ad lon&shy;<lb/>gitudinem AB. </s>

<s>Ex antecedenti enim momenta gra&shy;<lb/>vitatis super AB, ad totale momentum in perpen&shy;<lb/>diculo AD, est ut AD ad AB. </s>

<s>Totale vero momen&shy;<lb/>tum per AD, ad momentum per AC, est ut CA <lb/>ad AD. Ergo, ex aequali, in analogia perturbata, momentum per AB, ad <lb/>momentum per AC, erit ut longitudo AC ad longitudinem AB. </s>

<s>Quod erat <lb/>demonstrandum &rdquo; (ibid.). </s></p><p type="main">

<s>PROPOSITIO III. &mdash; &ldquo; Sit ad horizontalem AH (fig. </s>

<s>164) perpendicula&shy;<lb/><figure id="id.020.01.2100.3.jpg" xlink:href="020/01/2100/3.jpg"/></s></p><p type="caption">

<s>Figura 164.<lb/>ris BC, et inclinata BD, in qua sumatur <lb/>BE, et ex E, ad BD, perpendicularis aga&shy;<lb/>tur EF, ipsi BC occurrens in F. </s>

<s>Demon&shy;<lb/>strandum sit tempus per BE aequari <lb/>tempori per BF. &rdquo; </s></p><p type="main">

<s>&ldquo; Ducatur ex E perpendicularis ad <lb/>AB, quae sit EG, et quia impetus per <lb/>BE, ad impetum per EG, est ut EG ad <lb/>BE, ut supra demonstratur, ut autem <lb/>EG ad BE, ita BE ad BF, ob similitudi&shy;<lb/>nem triangulorum GEB, BEF; ergo, ut <lb/>BF spacium, ad spacium BE, ita impetus <lb/>per BF ad impetum per BE. </s>

<s>Ergo eodem tempore fiet motus per BF et <lb/>per BE &rdquo; (ibid., fol. </s>

<s>147 ad terg.). </s></p><pb xlink:href="020/01/2101.jpg" pagenum="344"/><p type="main">

<s>La dimostrazione, che Galileo sar&agrave; per mettere in miglior forma in <lb/>quest'altro Libro, dandocela pi&ugrave; distesa, va qui succinta, come quella che <lb/>doveva solo servire per memoria all'Autore, e che poteva anche cos&igrave; ba&shy;<lb/>stare agli esperti di queste materie, i quali non occorreva fare avvertiti che <lb/>l'impeto per EG &egrave; uguale all'impeto per BF, essendo ambedue quelle linee <lb/>dirette nel perpendicolo. </s>

<s>N&egrave; si richiama, per questi stessi motivi, il teorema <lb/>che nel libro Dei moti equabili si suppone essere stato gi&agrave; dimostrato, e da <lb/>cui dipende quella final conclusione, che cio&egrave;, essendo per BE e per BF <lb/>gl'impeti o le velocit&agrave; proporzionali agli spazi, i tempi necessariamente deb&shy;<lb/>bono essere uguali. </s></p><p type="main">

<s>Era l'attenzione di Galileo dalla dimostrata similitudine dei triangoli <lb/>GBE, EBF richiamata piuttosto ad avvertire un fatto, che non poteva esser <lb/>senza ragioni, e ci lasciava di una tale singolar avvertenza il documento <lb/>scritto in questa Nota. </s>

<s>&ldquo; Advertas cur cadentia ex B (nella preallegata figura) <lb/>sint semper una in locis sibi respondentibus, ut EF, ita ut angulus BEF <lb/>sit aequalis angulo FBH &rdquo; (ibid., fol. </s>

<s>57 ad terg.). Il costrutto, lasciato nel <lb/>manoscritto a questo punto interrotto, si compieva facilmente coll'osservare <lb/>che, come l'angolo BEF &egrave; uguale all'angolo FBH, cos&igrave; l'angolo EFB &egrave; <lb/>uguale all'angolo GBE, intanto che se, data la lunghezza BE si voglia sa&shy;<lb/>pere come dirigere la EF, che, incontrando la verticale BC prefinisca in essa <lb/>lo spazio BF sincrono alla data BE, si dee per quella direzione prender l'an&shy;<lb/>golo BEF uguale a FBH, che &egrave; l'angolo fatto dalla linea BC con la oriz&shy;<lb/>zontale. </s>

<s>Se sia data invece BF e si voglia da F dirigere sopra EB una linea, <lb/>che tagli nella BD una porzione EB sincrona alla BF, l'angolo BFE della <lb/>direzione dev'essere uguale a GBE, ch'&egrave; pur l'angolo fatto dalla stessa EB <lb/>con la orizzontale. </s>

<s>Son dunque date le direzioni, in ambedue i casi, dagli <lb/>angoli permutatamente fatti dalle linee EB, BF colla orizzontale: nuova av&shy;<lb/><figure id="id.020.01.2101.1.jpg" xlink:href="020/01/2101/1.jpg"/></s></p><p type="caption">

<s>Figura 165.<lb/>vertita conclusione elegante, che si <lb/>verifica anche quando BC, a simili&shy;<lb/>tudine di BD, sia obliqua, come Ga&shy;<lb/>lileo passa cos&igrave; a dimostrare. </s></p><p type="main">

<s>PROPOSITIO IV. &mdash; Infra horizon&shy;<lb/>tem AB (fig. </s>

<s>165), ex eodem puncto C, <lb/>sint duae rectae aequales utcumque <lb/>inclinatae CD, CE, et ex terminis D, E, <lb/>ad horizontem perpendiculares, agantur DA, EB, et lineae CD a puncto D <lb/>costituatur angulus CDF angulo BCE aequalis. </s>

<s>Dico ut DA ad BE ita esse <lb/>DC ad CF. &rdquo; </s></p><p type="main">

<s>&ldquo; Ducatur perpendicularis CG: et quia CDF aequatur angulo BCE, et <lb/>rectus G recto B, erit ut DC ad CG, ita CE ad EB. </s>

<s>Est autem CD ipsi CE <lb/>aequalis; ergo CG aequatur BE. </s>

<s>Et cum angulus CDF angulo BCE sit ae&shy;<lb/>qualis, et angulus FCD communis, reliquus ad duos rectos DFC reliquo DCA <lb/>aequabitur, et anguli ad A, et G sunt recti. </s>

<s>Ergo triangulus ADC triangulo <lb/>CGF est similis, quare, ut AD ad DC, ita GC ad CF, et permutando, ut AD <pb xlink:href="020/01/2102.jpg" pagenum="345"/>ad CG, hoc est ad BE, ita DC ad CF, quod erat probandum &rdquo; (idid., fol. </s>

<s>148 <lb/>ad terg.). </s></p><p type="main">

<s>Il semplice Lemma geometrico s'applica alla Meccanica con questo, che <lb/>immediatamente da Galileo si soggiunge, quasi in forma di corollario. </s>

<s>&ldquo; Cum <lb/>autem impetus per CD, ad impetum per CF, sit ut perpendiculus AD ad <lb/>perpendiculum BE; constat motus per CD et CF eodem tempore absolvi. </s>

<s><lb/>Itaque distantiae, quae in diversis inclinationibus eodem tempore conficiun&shy;<lb/>tur, determinantur per lineam, quae, ut facit DF, lineis inclinatis occurrit <lb/>secundum angulos aequales illis, quos inclinatae ad horizontem constituunt, <lb/>permutatim sumptos &rdquo; (ibid.). </s></p><p type="main">

<s>Nemmen qui Galileo, a cui dovevano rimanere queste scritture per suo <lb/>uso privato, &egrave; sollecito di sminuzzar cos&igrave; il pane della Scienza, come quando <lb/>sar&agrave; per metterlo innanzi ai Simplicii sopra il pubblico desco, certissimo che <lb/>i Sagredi, ai quali soli intendeva allora di rivolgere il discorso, avrebbero <lb/>da s&egrave; medesimi, per la prima Proposizione facilmente compreso ch'essendo <lb/>M.oCD:M.oAD=AD:DC, e M.oCE:M.oBE=BE:CE, da queste due <lb/>equazioni, nelle quali M.oAD=M.oBE, DC=CE, e M.oCE=M.oCF si <lb/>concludeva legittimamente essere i momenti stessi o gl'impeti per CD o <lb/>per CF proporzionali alle due perpendicolari AD, BE, come ivi, senza trat&shy;<lb/>tenersi a dimostrarlo, si ammette. </s>

<s>Questa concisione, che sarebbe ai buoni <lb/>intenditori tanto meglio piaciuta delle molte parole, &egrave; serbata pure nella <lb/><figure id="id.020.01.2102.1.jpg" xlink:href="020/01/2102/1.jpg"/></s></p><p type="caption">

<s>Figura 166.<lb/>seguente bellissima proposizione, feconda <lb/>di altre nuove bellissime conseguenze. </s></p><p type="main">

<s>PROPOSITIO V. &mdash; &ldquo; Sit GD (fig. </s>

<s>166) <lb/>erecta ad horizontem, DF vero inclinata; <lb/>dico eodem tempore fieri motum ex G in <lb/>D, et ex F in D. &rdquo; </s></p><p type="main">

<s>&ldquo; Momentum enim super FD est idem <lb/>ac super tangentem in E, quae ipsi FD sit <lb/>parallela. </s>

<s>Ergo momentum super FD, ad <lb/>totale momentum, erit ut CA ad AB, idest <lb/>AE. </s>

<s>Verum ut CA ad AE, ita ID ad DA, <lb/>et dupla FD ad duplum DG; ergo momen&shy;<lb/>tum super FD, ad totale momentum super <lb/>GD, est ut FD ad GD. </s>

<s>Ergo eodem tempore <lb/>fiet motus per FD, et GD &rdquo; (ibid., fol. </s>

<s>152). </s></p><p type="main">

<s>I nostri Lettori riconoscono facilmente in questa una di quelle costru&shy;<lb/>zioni, con le quali i Matematici, da Leonardo da Vinci al Torricelli, s'ar&shy;<lb/>gomentarono di concludere dalla Libbra le leggi statiche dei momenti sopra <lb/>i piani inclinati. </s>

<s>Costituito infatti il piano dalla tangente LN, elevata di NM <lb/>sopra la orizzontale LM, i triangoli simili LMN, AEC conducono per la via <lb/>piana a quel punto, a cui di slancio salt&ograve; Galileo, il quale pure ivi sottin&shy;<lb/>dende un corollario, d'altra parte di facilissima derivazione, dop'avere osser&shy;<lb/>vato che le dimostrate propriet&agrave; della corda DF convengono altres&igrave; a DO, <pb xlink:href="020/01/2103.jpg" pagenum="346"/>e a un'altra corda qualunque. </s>

<s>Ora se GP, GQ sono uguali, e similmente <lb/>inclinate alle DF, DO, i moti per queste &egrave; evidente dover essere i mede&shy;<lb/>simi dei moti per quelle, cosicch&egrave; insomma si riduce l'accennato Corollario <lb/>a dire che in qualunque corda si conduca dall'estremit&agrave; D o dalla sommit&agrave; <lb/>C del diametro a un punto della circonferenza, si spedisce il moto nel me&shy;<lb/>desimo tempo come se cadesse il mobile per tutta la lunghezza verticale del <lb/>diametro stesso. </s>

<s>Le quali cose cos&igrave; ben predisposte conducono Galileo a di&shy;<lb/>mostrar la seguente proposizione fondamentale. </s></p><p type="main">

<s>PROPOSITIO VI. &mdash; &ldquo; Sit planum horizontis secundum lineam ABC (fig. </s>

<s>167) <lb/>ad quam sint duo plana inclinata secundum lineas DB, DA. </s>

<s>Dico idem mo&shy;<lb/><figure id="id.020.01.2103.1.jpg" xlink:href="020/01/2103/1.jpg"/></s></p><p type="caption">

<s>Figura 167.<lb/>bile tardius moveri per DA, quam per <lb/>DB, secundum rationem longitudinis <lb/>DA ad longitudinem DB. &rdquo; </s></p><p type="main">

<s>&ldquo; Erigatur enim ex B perpendicu&shy;<lb/>laris ad horizontem, quae sit BE: ex D <lb/>vero, ipsi BD perpendicularis, DE oc&shy;<lb/>curcens BE in E, et circa BDE trian&shy;<lb/>gulum circulus describatur, qui tanget <lb/>AC in puncto B, ex quo, ipsi AD pa&shy;<lb/>rallela, ducatur BF, et connectatur FD. </s>

<s><lb/>Patet tarditatem per FB esse consimilem tarditati per DA. </s>

<s>Quia vero tempore <lb/>eodem movetur mobile per DB et FB, patet velocitates per BD, ad velocita&shy;<lb/>tes per BF, esse ut DB ad FB, ita ut semper iisdem temporibus duo mo&shy;<lb/>bilia, ex punctis D, F venientia, linearum DB, FB partes, integris lineis DB, <lb/>FB proportione respondentes, peregerint. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cum vero angulus BFD, in portione, angulo DBA ad tangentem sit <lb/>aequalis, angulus vero DBF alterno BDA; aequiangula erunt triangula BFD, <lb/>ABD, et, ut BD ad BF, ita AD ad DB. </s>

<s>Ergo ut AD ad DB, ita velocitas <lb/>per DB ad velocitatem per DA, et ex opposito tarditas per DA, ad tardita&shy;<lb/>tem per BD. &rdquo; </s></p><p type="main">

<s>&ldquo; Si hoc ponatur, reliqua demonstrari possunt. </s>

<s>Ponatur igitur augeri <lb/>et imminui motus velocitatem secundum proportionem, qua augentur et <lb/>minuuntur gravitatis momenta, et cum constet eiusdem mobilis momenta <lb/>gravitatis super plano DB, ad momenta super plano DA, esse ut longitudo <lb/>DA ad longitudinem DB; idcirco velocitatem per DB, ad velocitatem per DA, <lb/>esse ut AD ad DB &rdquo; (ibid., fol. </s>

<s>34). </s></p><p type="main">

<s>Il linguaggio stesso accenna, come si disse, essere stata delle prime a <lb/>dimostrarsi questa proposizione, nella quale <emph type="italics"/>tardit&agrave;,<emph.end type="italics"/> o <emph type="italics"/>diuturnit&agrave;,<emph.end type="italics"/> come ad <lb/>altri piacque dir meglio, si chiama quello, che poi Galileo, nel perfezionato <lb/>esercizio della sua scienza, chiamer&agrave; sempre col nome di <emph type="italics"/>tempo.<emph.end type="italics"/> A questo <lb/>ultimamente trascritto. </s>

<s>come a teorema antecedentemente dimostrato, accenna <lb/>il discorso pubblicatosi dall'Alb&egrave;ri (Tomo XI, pag. </s>

<s>61, 62), da cui si con&shy;<lb/>ferma che, posto essere i tempi come le lunghezze delle oblique ugualmente <lb/>elevate, <emph type="italics"/>reliqua demonstrari possunt.<emph.end type="italics"/></s></p><pb xlink:href="020/01/2104.jpg" pagenum="347"/><p type="main">

<s>La prima cosa, che occorreva a dimostrare, per servirsene nel progresso <lb/>delle altre dimostrazioni, era che i tempi, per due spazi ugualmente diretti, <lb/>son proporzionali a uno dei detti spazi e alla media fra ambedue. </s>

<s>Ci&ograve; po&shy;<lb/>tevasi immediatamente dedurre dalla legge dei moti accelerati, ma non es&shy;<lb/>sendo questa ancora a Galileo nota, fu costretto a far del facile corollario <lb/>un elaborato teorema, a cui convenne di pi&ugrave; chiamare in aiuto un lemma <lb/>geometrico, che ritrovasi manoscritto a tergo del folio 172 nel citato codice, <lb/>e che corrisponde al primo lemma premesso alla XXXVI proposizione stam&shy;<lb/>pata (Alb. </s>

<s>XIII, 214). Noi potremmo rimandar l&agrave; i Lettori, se in due parole <lb/><figure id="id.020.01.2104.1.jpg" xlink:href="020/01/2104/1.jpg"/></s></p><p type="caption">

<s>Figura 168.<lb/>non si riducesse qui alla loro memoria. </s>

<s>Per ritrovare <lb/>infatti le relazioni, che passano fra le tre linee AS, <lb/>AB, AC nella figura 168, basta congiungere insieme i <lb/>due punti B, C, d'onde nascono i due triangoli SBC, <lb/>BCA che, riconosciuti simili, danno AB:AC=AC:AS, <lb/>in che consiste il Lemma geometrico, che s'invoca per <lb/>condur la seguente proposizione. </s></p><p type="main">

<s>PROPOSITIO VII. &mdash; &ldquo; Posteaquam (in antecedenti <lb/>propos. </s>

<s>V et eius corollario) ostensum fuerit tempora <lb/>per AB, AC esse aequalia, demonstrabitur tempus per <lb/>AD, ad tempus per AE, esse ut DA ad mediam inter DA, AE. &rdquo; </s></p><p type="main">

<s>&ldquo; Nam tempus per DA, ad tempus per AC, est ut DA ad AC lineam: <lb/>Tempus autem per AC, idest per AB ad tempus AE, est ut lina AB ad AE, <lb/>hoc est AS ad AD. </s>

<s>Ergo ex aequali, in analogia perturbata, tempus per AD, <lb/>ad tempus AE, est ut linea AS ad lineam AC. </s>

<s>Cumque AC, ex demonstra&shy;<lb/>tis, sit media inter SA, AB, et ut SA ad AB, ita DA ad AE; ergo tempus <lb/>per AD, ad tempus per AE, est ut DA ad mediam inter DA, AE, quod erat <lb/>probandum &rdquo; (ibid., fol. </s>

<s>147). </s></p><p type="main">

<s>Si sottintende da Galileo, anche dopo questa, un facile corollario, in <lb/>cui si dimostra che, non solo nelle direzioni verticali, ma e nelle oblique <lb/>corre la medesima proporzione dei tempi. </s>

<s>Avendosi infatti le oblique AC, AD <lb/>(fig. </s>

<s>169) se AR &egrave; media fra AB, AG, condotte dai punti G, R le due oriz&shy;<lb/>zontali GE, RN, &egrave; facile vedere che, in virt&ugrave; dei triangoli simili, venutisi a <lb/>descrivere dalle dette orizzontali parallele, AT e AN son medie proporzio&shy;<lb/>nali fra AC, AF, e AD, AE. </s>

<s>Ed essendo pure, in virt&ugrave; dei triangoli simili, <lb/><figure id="id.020.01.2104.2.jpg" xlink:href="020/01/2104/2.jpg"/></s></p><p type="caption">

<s>Figura 169.<lb/>fra AR e AG, AB, nella verticale, come fra <lb/>AT e AC, AF, nell'obliqua, la medesima pro&shy;<lb/>porzion degli spazi; &egrave; chiaro che la medesima <lb/>proporzione si serber&agrave; pure dei tempi. </s>

<s>In <lb/>ogni modo si suppongon da Galileo facil&shy;<lb/>mente note queste meccaniche propriet&agrave;, nella <lb/>proposizione, che cos&igrave; passa a dimostrare. </s></p><p type="main">

<s>PROPOSITIO VIII. &mdash; &ldquo; Sint ad horizon&shy;<lb/>tem DB (in eadem figura 169) quotcumque <lb/>lineae ab eadem altitudine A demissae AB, <pb xlink:href="020/01/2105.jpg" pagenum="348"/>AC, AD, et sumpto quolibet puncto G, per ipsum horizonti parallela sit GFE, <lb/>sitque media inter GA, AB ipsa AR, et per R altera parallela RTN. </s>

<s>Constat <lb/>lineas AT, AN esse medias inter CA, AF, et DA, AE. </s>

<s>Dico quod si absuma&shy;<lb/>tur AB esse tempus, quo mobile cadit ex A io B, tempus RB esse illud, <lb/>quo conficitur GB; TC vero esse tempus ipsius CF, et ND ipsius ED. &rdquo; </s></p><p type="main">

<s>&ldquo; Id autem constat, nam, cum AR sit media inter BA, AG, sitque BA <lb/>tempus casus totius AB; tempus AR erit tempus casus per AG. </s>

<s>Ergo reli&shy;<lb/>quum temporis RB erit tempus casus per GB, post AG, et idem dicetur de <lb/>aliis temporibus TC, ND, et lineae FC, ED. &rdquo; </s></p><p type="main">

<s>&ldquo; Patet insuper tempora casuum per GB, FC, ED esse ut lineas GB, <lb/>FC, ED. </s>

<s>Non tamen a magnitudinibus linearum GB, FC, ED esse determi&shy;<lb/>nandas eorumdem temporum quantitates si temporis mensura ponatur AB, <lb/>in quo tempore conficiatur linea AB, sed desumendas esse a lineis RB, <lb/>TC, ND &rdquo; (ibid., fol. </s>

<s>178). </s></p><p type="main">

<s>L'avvertimento &egrave; importante, e sembra che Galileo l'abbia fatto a s&egrave; <lb/>stesso, dop'averne sperimentata la fallacia, nella quale essendo egli prima <lb/>incorso, si trov&ograve; impedita la via di giungere alla sua final conclusione. </s>

<s>Que&shy;<lb/>sta conclusione si sa dalla Lettera a Guidubaldo esser quella che, per le <lb/>corde spezzate, il tempo speso da un mobile per giungere da un punto della <lb/>circonferenza all'infimo contatto di lei col piano orizzontale, sopra cui sup&shy;<lb/>ponesi eretta, &egrave; pi&ugrave; breve che per la corda intera. </s>

<s>Per giunger felicemente <lb/>a concluder ci&ograve; le otto sopra dimostrate proposizioni servivano quasi tutte <lb/>di principii necessari e di mezzi: una per&ograve; mancavane ancora, per la quale <lb/><figure id="id.020.01.2105.1.jpg" xlink:href="020/01/2105/1.jpg"/></s></p><p type="caption">

<s>Figura 170.<lb/>si dimostrasse che, partendosi un mobile per esempio <lb/>in D (fig. </s>

<s>170) dalla quiete, giunto in B, deve avere <lb/>acquistata la velocit&agrave; medesima, come se fosse venuto <lb/>per l'obliqua AE, o per qualunque altra che, movendo <lb/>pure da A, risalisse a toccare un punto della orizzon&shy;<lb/>tale DE prolungata. </s>

<s>La dimostrazione sarebbe per dare <lb/>in seguito a Galileo gran faccenda, ma egli intanto se <lb/>n'espediva, supponendola inclusa, e facilmente deri&shy;<lb/>vabile per corollario da quest'altro teorema, che si <lb/>propone cos&igrave; e si dimostra. </s></p><p type="main">

<s>PROPOSITIO IX. &mdash; &ldquo; Tempora casuum in planis, <lb/>quorum eadem sit altitudo, eamdem inter se servant <lb/>rationem, sive illis idem impetus praecedat, sive ex quiete incipiant. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sint plana AB, AC (in supra signata figura) quorum eadem altitudo. </s>

<s><lb/>Extenso autem BA utcumque in D, fiat casus ex D per ambo AC, AB. </s>

<s>Dico <lb/>tempus per AC, ad tempus per AB, esse in eadem ratione, ac si principium <lb/>casus foret in A. </s>

<s>Sit enim ipsarum BD, DA media DF, et ducta parallela <lb/>ex F erit GE media inter CE, AE. </s>

<s>Facto igitur principio lationis ex D, tem&shy;<lb/>pora casuum per AC, AB erunt inter se ut AG, AF. </s>

<s>Quod si casus inci&shy;<lb/>piat ex A, erunt tempora per AC, AB inter se ut AC, AB lineae. </s>

<s>Ergo pa&shy;<lb/>tet proposituum &rdquo; (ibid., fol. </s>

<s>38). </s></p><pb xlink:href="020/01/2106.jpg" pagenum="349"/><p type="main">

<s>Cos&igrave; tutto, con matematica legge preordinato a dimostrare l'ultima <lb/>proposizione annunziata nella lettera a Guidubaldo, nient'altro rimaneva a <lb/>fare a Galileo, che premetter due lemmi geometrici, che sono il II e il III <lb/>premessi alla XXXIX proposizione stampata, e che si leggono manoscritti <lb/>l'uno al foglio 163, e l'altro al foglio 172 del citato volume. </s>

<s>&Egrave; il primo dei <lb/>detti lemmi stampati quello gi&agrave; premesso alla VII proposizione, da noi pub&shy;<lb/>blicatasi nelle pagine poco addietro, cosicch&egrave;, tutte insomma ricomposte le <lb/>membra, danno quasi abito di persona e atteggiamento di vita alla verit&agrave; <lb/>cos&igrave; ultimamente annunziata. </s></p><p type="main">

<s>PROPOSITIO X. &mdash; &ldquo; Sit circuli circumferentia AIS (fig. </s>

<s>171), et diame&shy;<lb/><figure id="id.020.01.2106.1.jpg" xlink:href="020/01/2106/1.jpg"/></s></p><p type="caption">

<s>Figura 171.<lb/>ter AB ad horizontem erectum, et ducatur <lb/>SA, non maior subtendente quadrante, et a <lb/>terminis S, A aliae duae ad quodcumque <lb/>punctum I: dico mobile ex termino S ferri <lb/>per duas SI, IA lineas tempore breviori, <lb/>quam per SA, ex eodem termino S, vel per <lb/>solam AI, ex termino I. &rdquo; </s></p><p type="main">

<s>&ldquo; Ducta sit per S ipsi AB perpendi&shy;<lb/>cularis .... &rdquo; (ibid., fol. </s>

<s>163) e seguita come <lb/>nello stampato (Alb. </s>

<s>XIII, 216, 17) con <lb/>qualche leggerissima differenza nelle pa&shy;<lb/>role. </s>

<s>Ed ecco per quali vie, rimaste in mezzo <lb/>a tanto fervore di studii galileiani, nella <lb/>storia della Scienza fin qui non segnate, si <lb/>condusse Galileo, <emph type="italics"/>senza trasgredire i termini meccanici,<emph.end type="italics"/> a dimostrare le sue <lb/>inopinabili conclusioni. </s>

<s>Erano que'termini meccanici ridotti alla Statica, e <lb/>l'Autore, nelle dieci proposizioni che compongono quel suo primo trattato <lb/><emph type="italics"/>De motu,<emph.end type="italics"/> non si serve n&egrave; poteva servirsi d'altro argomento. </s>

<s>Ma, istituitasi <lb/>nel 1604 la Dinamica nuova, s'aprirono alla Scienza altre pi&ugrave; late vie, e si <lb/>pot&egrave; giungere per pi&ugrave; diretti e piani sentieri al medesimo intento deside&shy;<lb/>rato, ch'era quello di dimostrare il brachistocronismo dei gravi scendenti <lb/>per le molteplici corde inflesse e sottese a una quarta di cerchio. </s>

<s>Essendo <lb/>questo dunque il termine fisso, rimaneva nel teorema meccanico tuttavia <lb/>fermo il principio, cosicch&egrave; venivasi la trasformazione a subire dal solo mezzo, <lb/>e da ci&ograve; dipendon principalmente le note distintive di quel secondo Libro <lb/>che, raccolto dai Manoscritti galileiani e ordinato, si porge ora alla notizia <lb/>e all'esame dei nostri meditativi Lettori. </s></p><pb xlink:href="020/01/2107.jpg" pagenum="350"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Chi, dalle nuove aure menato, s'asside nella mirabile navicella a cor&shy;<lb/>rere questo lucido mare aperto da Galileo, s'accorge che una vela, bench&egrave; <lb/>rimanga alquanto pi&ugrave; sotto alla maestra, &egrave; nondimeno la pi&ugrave; frequente nel&shy;<lb/>l'opera, e in render agile il corso forse la pi&ugrave; efficace di tutte le altre. </s>

<s>&Egrave; <lb/>facile agli studiosi della Scienza meccanica, vogliam dire passando al senso <lb/>proprio dal figurato, accorgersi che, nella massima parte dei teoremi gali&shy;<lb/>leiani, chi conduce innanzi le dimostrazioni, e pi&ugrave; efficacemente le volge alla <lb/>loro final conclusione, &egrave; la legge dei tempi, che si passano dal mobile in <lb/>percorrer due spazi ugualmente diretti. </s>

<s>Abbiamo veduto per quali vie lun&shy;<lb/>ghe e tortuose fosse dovuto passar Galileo, prima di giungere, nella sopra <lb/>trascritta proposizione VII, a quella conclusione, che ora invece vedeva scen&shy;<lb/>dere per corollario immediato dal principio dinamico, sentenziosamente da <lb/>lui stesso formulato in queste parole: &ldquo; Momenta velocitatum cadentis ex <lb/>sublimi sunt inter se ut radices distantiarum peractarum, nempe in subdu&shy;<lb/>pla ratione illarum &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>164 a tergo). </s></p><p type="main">

<s>Di qui &egrave; che, avendo le velocit&agrave; la medesima proporzione dei tempi, se <lb/>cada il mobile da A in B (fig. </s>

<s>172) o da A in C, per due spazi diversi, ma se&shy;<lb/>condo la medesima linea AL diretti, avremo T.oAB:T.oAC=&radic;AB:&radic;AC= <lb/>AB:&radic;AB.AC, che &egrave; quel che appunto proponevasi di dimostrar Galileo <lb/><figure id="id.020.01.2107.1.jpg" xlink:href="020/01/2107/1.jpg"/></s></p><p type="caption">

<s>Figura 172.<lb/>stesso, co'principii statici, nella detta sua VII pro&shy;<lb/>posizione. </s></p><p type="main">

<s>Incomincia perci&ograve; questo secondo Libro, dietro <lb/>i principii dinamici riformato, dal dimostrare le pro&shy;<lb/>priet&agrave; generali dei moti accelerati, per derivarne di <lb/>l&igrave; gli opportuni corollari. </s>

<s>Ma non abbiamo trovate <lb/>scritte le proposizioni preparate a questo particolare <lb/>intento di servir come d'introduzione al nuovo trat&shy;<lb/>tato. </s>

<s>Forse, tutto in sollecitudine di ridurre intanto <lb/>alle forme pi&ugrave; convenienti il teorema fondamentale <lb/>dei tempi, nelle oblique ugualmente elevate, propor&shy;<lb/>zionali agli spazi; non attese Galileo a distendere <lb/>quelle prime dimostrazioni relative alle libere ca&shy;<lb/>dute dei gravi, riserbandosi a farlo dopo che, dallo stesso ora detto fonda&shy;<lb/>mentale, si sarebbe svolta la serie di tutti gli altri teoremi. </s>

<s>Quando poi, per <lb/>ridursi sotto gli occhi compiuto il disegno del suo trattato, prese risoluzione <lb/>di porre a questa serie i primi termini tralasciati, era gi&agrave; venuto il Cava&shy;<lb/>lieri a proporgli il suo Metodo degli indivisibili, secondo il quale condusse <lb/>Galileo stesso le proposizioni, che si ricopian dal Manoscritto, per ridurle <lb/>qui ne'primi ordini di questo secondo Libro, resa la ragione ai Lettori del <lb/>commesso anacronismo. </s></p><pb xlink:href="020/01/2108.jpg" pagenum="351"/><p type="main">

<s>PROPOSITIO I. &mdash; &ldquo; Absumo eam esse cadentis mobilis per lineam AL <lb/>(nella precedente figura 172) accelerationem, ut, pro ratione spatii peracti, <lb/>crescat velocitas, ita ut velocitas in C, ad velocitatem in B, sit ut spacium <lb/>CA ad spacium BA. &rdquo; </s></p><p type="main">

<s>&ldquo; Cum autem haec ita se habeant, ponatur AX, cum AL angulum con&shy;<lb/>tinens, sumptisque partibus AB, BC, CD, DE .... aequalibus, protrahantur <lb/>BM, CN, DO, EP.... Si itaque cadentis per AL velocitates, in B, C, D, E <lb/>locis, se habent ut distantiae AB, AC, AD, AE; ergo se quoque habent ut <lb/>lineae BM, CN, DO, EP. &rdquo; </s></p><p type="main">

<s>&ldquo; Quia vero velocitas augetur consequenter in omnibus punctis lineae <lb/>AE, et non tantum in adnotatis B, C, D, ergo velocitates illae omnes sese <lb/>respiciunt ut lineae, quae, ab omnibus dictis punctis lineae AE, ipsis BM, <lb/>CN, DO aequidistanter producuntur. </s>

<s>Ipsae autem infinitae sunt et consti&shy;<lb/>tuunt triangulum AEP: ergo velocitates, in omnibus punctis lineae AB, ad <lb/>velocitates in omnibus punctis lineae AC, ita se habent ut triangulus ABM <lb/>ad triangulum ACN, et sic de reliquis, hoc est in duplicata proportione li&shy;<lb/>nearum AB, AC &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>35 a tergo). </s></p><p type="main">

<s>Si vede bene che questa proposizione &egrave; compendiata da quell'altra scrit&shy;<lb/>tura italiana, che si pubblic&ograve; nel capitolo precedente, per adattarla alle forme <lb/>proprie, e al succinto andamento dei nuovi teoremi. </s>

<s>Ma che Galileo vera&shy;<lb/>mente la scrivesse con la particolare intenzione di premetterla al secondo <lb/>libro Dei movimenti locali, si conferma dal soggiungersi immediatamente il <lb/>seguente corollario, che ricorre, per questo e per gli altri simili trattati, con <lb/>assidua vicenda, quasi moto di spola a tesser le fila della lunga tela. </s></p><p type="main">

<s>COROLLARIUM. &mdash; &ldquo; Quia vero, pro ratione incrementi accelerationis, <lb/>tempora, quibus motus ipsi fiunt, debent imminui; ergo tempus, quo mo&shy;<lb/>bile permeat AB, ad tempus, quo permeat AC, est ut AB linea ad eam, <lb/>quae inter AB, AC media proportionalis existit &rdquo; (ibid.). </s></p><p type="main">

<s>Il metodo degl'Indivisibili, applicato a dimostrar la legge fondamentale <lb/>dei moti accelerati, si porgeva altres&igrave; opportuno a dimostrarne le conseguenze <lb/>pi&ugrave; rilevanti, compendiate in questa, che qui si soggiunge </s></p><p type="main">

<s>PROPOSITIO II. &mdash; &ldquo; Factus sit motus, ex A (fig. </s>

<s>173) usque B, natu&shy;<lb/><figure id="id.020.01.2108.1.jpg" xlink:href="020/01/2108/1.jpg"/></s></p><p type="caption">

<s>Figura 173.<lb/>raliter acceleratus: Dico quod, si velocitas, in omnibus <lb/>punctis AB, fuisset eadem ac reperitur in puncto B, du&shy;<lb/>plo citius fuisset peractum spacium AB, quia velocitates <lb/>omnes, in singulis punctis AB lineae, ad totidem velocita&shy;<lb/>tes, quarum unaquaeque esset aequalis velocitati BC, eam&shy;<lb/>dem haberent rationem, quam triangulus ABC ad rectan&shy;<lb/>gulum ABCD. &rdquo; </s></p><p type="main">

<s>COROLLARIUM I. &mdash; &ldquo; Sequitur ex hoc, quod, si ad <lb/>horizontem CB fuerit planum BA elevatum, sitque BC <lb/>dupla ad BA, mobile, ex A in B, et successive, ex B in C, temporibus aequa&shy;<lb/>libus esse perventurum, nam, postquam est in B, per reliqua BC, uniformi <lb/>velocitate et eadem movetur, qua in ipsomet termino B, post casum AB. &rdquo; </s></p><pb xlink:href="020/01/2109.jpg" pagenum="352"/><p type="main">

<s>COROLLARIUM II. &mdash; &ldquo; Patet rursus totum tempus per ABC, ad tempus <lb/>per AB, esse sesquialterum &rdquo; (ibid., fol. </s>

<s>181). </s></p><p type="main">

<s>Le proposizioni III e IV, che contengono in s&egrave; dimostrato il principio <lb/>meccanico, son le medesime della I e II, scritte nel primo Libro, e si pre&shy;<lb/>mettono qui come necessarie a concluderne la proposizione V, che &egrave; la V <lb/>di quello stesso primo Libro, corredata per&ograve; di un elegante corollario. </s>

<s>Fu <lb/>un tal corollario suggerito a Galileo dall'essersi, in cercare i mezzi termini <lb/>della detta V proposizione, incontrato nel seguente teorema: Sia CDA (fig. </s>

<s>174) <lb/><figure id="id.020.01.2109.1.jpg" xlink:href="020/01/2109/1.jpg"/></s></p><p type="caption">

<s>Figura 174.<lb/>un circolo, a cui giunga nel punto A la AF tan&shy;<lb/>gente. </s>

<s>Se si conducano dal punto di contatto le due <lb/>corde AC, AD, e presa AB=AD, si abbassino da <lb/>B, D alla AF due perpendicolari, s'avr&agrave; la propor&shy;<lb/>zione DF:EB=AD:AC. </s></p><p type="main">

<s>Facendo ora il trapasso dalla Geometria alla <lb/>Meccanica, considerando la AF orizzontalmente di&shy;<lb/>retta, e AD, AC quali due piani inclinati, il dimo&shy;<lb/>strato teorema geometrico, insieme con la detta pro&shy;<lb/>posizione V, davan facile modo a Galileo di risolver <lb/>questo meccanico teorema: Sopra il piano AC trovare il punto, da cui par&shy;<lb/>tendosi un mobile, giunga in A nel medesimo tempo, che vi giungerebbe <lb/>quel medesimo mobile, partendosi da D sull'altro piano; imperocch&egrave; la cer&shy;<lb/>cata lunghezza AC s'&egrave; trovato esser quarta proporzionale dopo DF, EB, AD, <lb/>ed essere di pi&ugrave; una corda che, partendosi dal medesimo infimo punto del <lb/>diametro a un punto della medesima circonferenza, si sa, per la dimostrata <lb/>proposizione V, dover essere alla corda AD tautocrona, per cui soggiungesi <lb/>da Galileo cos&igrave; a quella stessa V proposizione, per modo di corollario: </s></p><p type="main">

<s>&ldquo; Collige, existentibus planis inaequaliter inclinatis AD, AC, atque data <lb/>longitudine AD, inveniri posse, in plano AC, portionem, quae eodem tem&shy;<lb/>pore cum DA peragatur. </s>

<s>Ducto enim perpendiculo DF, et, posita AB ae&shy;<lb/>quali AD, ducto perpendiculo BE, fiat, ut DF ad EB, ita DA ad AC, erit&shy;<lb/>que tempus per CA aequalc tempori per DA &rdquo; (ibid., fol. </s>

<s>47). </s></p><p type="main">

<s>Cos&igrave; nuovamente preparate le cose, nel corollario della prima proposi&shy;<lb/>zione, nel teorema meccanico, e in questo ultimo del tautocronismo delle <lb/>corde nel cerchio; passava felicemente Galileo, senza nulla supporre, a di&shy;<lb/>mostrar questa, che &egrave; in ordine la VI proposizione del Libro, e che pu&ograve; <lb/>considerarsi rispetto all'altre come la canocchia, dalla quale si dovr&agrave; trarre <lb/>e compilare il lungo filo. </s></p><p type="main">

<s>PROPOSITIO VI. &mdash; &ldquo; Tempus casus per planum inclinatum, ad tempus <lb/>sasus per lineam suae altitudinis, est ut eiusdem plani longitudo ad longi&shy;<lb/>tudinem suae altitudinis. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sit planum inclinatum BA (fig. </s>

<s>175) ad lineam horizontis AC, sitque <lb/>linea altitudinis perpendicularis BC: Dico tempus casus, quo mobile move&shy;<lb/>tur per BA, ad tempus, in quo cadit per BC, esse ut BA ad BC. &rdquo; </s></p><p type="main">

<s>&ldquo; Erigatur perpendicularis ad horizontem ex A, quae sit AD, cui oc-<pb xlink:href="020/01/2110.jpg" pagenum="353"/>currat in D perpendicularis ad AB ducta ex B, quae sit BD, et circa trian&shy;<lb/><figure id="id.020.01.2110.1.jpg" xlink:href="020/01/2110/1.jpg"/></s></p><p type="caption">

<s>Figura 175.<lb/>gulum ABD circulus describatur. </s>

<s>Et quia DA, <lb/>BC ambae sunt ad horizontem perpendiculares, <lb/>constat tempus casus per DA, ad tempus casus <lb/>per BC, esse ut media inter DA, BC ad ipsam <lb/>BC. </s>

<s>Tempus autem casus per DA aequatur <lb/>tempori casus per BA: media vero inter DA <lb/>et BC, est ipsa AB; ergo patet propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s>COROLLARIUM. &mdash; &ldquo; Ex hoc sequitur ca&shy;<lb/>suum tempora per plana inclinata, quorum <lb/>eadem sit altitudo, esse inter se ut eorumdem <lb/>planorum longitudines. </s>

<s>Si enim fuerit aliud planum inclinatum BE, tempus <lb/>casus per BA, ad tempus casus per BC est ut BA linea ad BC. </s>

<s>Tempus vero <lb/>per BE, ad tempus per BC, est ut BE ad BC; ergo, ex aequali, patet pro&shy;<lb/>positum &rdquo; (ibid., fol. </s>

<s>60). </s></p><p type="main">

<s>Preordinato, in queste proposizioni, e specialmente nella bellissima ul&shy;<lb/>tima, l'andamento di tutto il resto, procedeva Galileo innanzi per raggiun&shy;<lb/>gere il suo finale intento, lieto nella propria coscienza di non aver trasgre&shy;<lb/>dito i termini meccanici, in conformit&agrave; de'quali soggiungeva la seguente <lb/>proposizione, dando miglior forma a quella in terzo luogo, nel I Libro, gi&agrave; <lb/>dimostrata: </s></p><p type="main">

<s>PROPOSITIO VII. &mdash; &ldquo; Si ex eodem puncto horizontis ducatur perpendicu&shy;<lb/>lus et planum inclinatum, et in plano inclinato sumatur quodlibet punctum, <lb/>a quo in plano perpendicularis linea usque ad perpendiculum protrahatur; <lb/>lationes, in parte perpendiculi inter horizontem et occursum perpendicula&shy;<lb/>ris intercepta, et in parte plani inclinati inter eamdem perpendicularem et <lb/>horizontalem intercepta, eodem tempore absolvuntur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sint, ex eodem puncto B horizontalis AH (fig. </s>

<s>176), perpendicularis <lb/>BC, et planum inclinatum BD. </s>

<s>Sumpto quolibet puncto E, ex eo, ad EB, <lb/><figure id="id.020.01.2110.2.jpg" xlink:href="020/01/2110/2.jpg"/></s></p><p type="caption">

<s>Figura 176.<lb/>perpendicularis agatur EF, occurrens <lb/>perpendiculo in puncto F: Dieo lationes <lb/>per BF, et per EB, eodem tempore con&shy;<lb/>fici. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Demittatur, ex eodem puncto E, <lb/>perpendicularis ad horizontem, EG, quae <lb/>erit perpendiculo BF parallela, et angu&shy;<lb/>lus GEB coalterno EBF aequalis, et rec&shy;<lb/>tus BGE recto BEF: quare aequiangula <lb/>erunt triangula GEB, BEF, et, ut GE ad <lb/>EB, ita EB ad BF. </s>

<s>Ut autem GE ad EB, <lb/>ita momentum gravitatis mobilis in plano <lb/>BD, ad totale suum momentum in perpendiculo BC. </s>

<s>Habet igitur distantia <lb/>EB, ad distantiam BF, eamdem rationem, quam gravitatis momentum super <lb/>planum EB, ad totale momentum super perpendiculum BF: quare eodem <pb xlink:href="020/01/2111.jpg" pagenum="354"/>tempore conficiuntur lationes per EB et BF &rdquo; (MSS. Gal., P. V, T. II, <lb/>fol. </s>

<s>180). </s></p><p type="main">

<s>Il lieto e libero progresso delle proposizioni, a questo punto, si arresta, <lb/>perch&egrave;, ripensando Galileo intorno al principio meccanico invocato nell'ul&shy;<lb/>tima parte di questa dimostrazione, per concluderne efficacemente l'intento, <lb/>dubita se, essendo il moto del grave lungo il piano e nel perpendicolo acce&shy;<lb/>lerato, possa legittimamente applicarsi in questo caso il teorema dei moti <lb/>equabili, che cio&egrave;, avendosi le velocit&agrave; uguali, i tempi sono proporzionali agli <lb/>spazi. </s>

<s>Perci&ograve;, dopo la proposizione VII, ora ultimamente trascritta, rivela <lb/>cos&igrave; la penosa tenzione dei suoi nuovi dubbi, e la subitanea presa risolu&shy;<lb/>zione di dare altro indirizzo ai suoi pensieri: </s></p><p type="main">

<s>&ldquo; Necessariam hanc propositionem ad praecedentem existimo. </s>

<s>Velocita&shy;<lb/>tes mobilium, quae in aequali momento incipiunt motum, sunt semper inter <lb/>se in eadem proportione, ac si aequabili motu progrederent, ut verbi gra&shy;<lb/>tia mobile per AC (fig. </s>

<s>177) incipit motum cum momento, ad momentum <lb/><figure id="id.020.01.2111.1.jpg" xlink:href="020/01/2111/1.jpg"/></s></p><p type="caption">

<s>Figura 177.<lb/>per CB, ut CB ad AC. </s>

<s>Si aequabili motu progredere&shy;<lb/>tur, tempus per AC, ad tempus per CB, esset ut AC <lb/>ad CB, quod in accelerato dubito quidem, et ideo de&shy;<lb/>monstra aliter sic: &rdquo; </s></p><p type="main">

<s>PROPOSITIO VIII. &mdash; &ldquo; Tempus per AC (in eadem <lb/>figura) ad tempus per CB, ex praecedentibus, est ut <lb/>linea AC, ad lineam CB. </s>

<s>Sed etiam ad tempus CD habet <lb/>eamdem rationem, cum CB sit media inter AC, DC; ergo <lb/>tempora CD, CB erunt aequalia &rdquo; (ibid., fol. </s>

<s>177). </s></p><p type="main">

<s>Qui dunque si rimane questo secondo Libro, mosso con s&igrave; lieti auspici, <lb/>interrotto, e le belle meccaniche dimostrazioni, che lo componevano, son la&shy;<lb/>sciate dall'Autore in abbandono, come farebbe l'Artefice degli elaborati or&shy;<lb/>gani di una macchina in costruzione, la quale vuol essere riformata sopra <lb/>altro modello. </s>

<s>E perch&egrave; il fulcro, diciamo cos&igrave; di una tal macchina consi&shy;<lb/>steva nella VII sopra scritta proposizione, soggetta ai dubbi nati intorno alla <lb/>proposizione seguente, e per le medesime ragioni; doveva la riforma inco&shy;<lb/>minciare di l&igrave;, e in altri modi fuor dei meccanici, e con principii diversi da <lb/>quelli, che son proprii dei moti equabili, conveniva dimostrar che, in piani <lb/>ugualmente alti ma variamente inclinati, i tempi delle cadute son propor&shy;<lb/>zionali agli spazi. </s></p><p type="main">

<s>La prima difficolt&agrave;, che doveva pararsi innanzi alla mente di Galileo, <lb/>in ridur le cose alle sue intenzioni, consisteva nell'aver riconosciuto impos&shy;<lb/>sibile a rendere i moti accelerati indipendenti dagli equabili, cosicch&egrave; non <lb/>rimaneva a far altro, per quietare i dubbi e per rendere legittime le con&shy;<lb/>clusioni, che dimostrar come l'una qualit&agrave; di moto ritorni nell'altra. </s>

<s>Per <lb/>far ci&ograve;, non essendo istituita ancora la Geometria degl'Indivisibili, bisognava <lb/>contentarsi alle approssimazioni, attribuendo alle piccole particelle quante <lb/>quel che non &egrave; proprio a rigore che delle infinitesime. </s></p><p type="main">

<s>Siano AB (fig. </s>

<s>178) perpendicolare e AC inclinata comprese fra le oriz-<pb xlink:href="020/01/2112.jpg" pagenum="355"/>zontali AM, BC, e dividasi tutta la detta AB nelle porzioncelle AE, EG, GI, <lb/>IL .... conducendo da ogni punto di divisione altrettante orizzontali, come <lb/>DE, FG, HI.... Credeva Galileo di poter leggittimamente riguardar come <lb/><figure id="id.020.01.2112.1.jpg" xlink:href="020/01/2112/1.jpg"/></s></p><p type="caption">

<s>Figura 178.<lb/>equabile il moto fatto per i brevi tratti AE, AD; <lb/>EG, DF; GI, FH; ... cosicch&egrave;, quando fosse vero <lb/>che in E e in D le velocit&agrave; sono uguali, se ne <lb/>concluderebbe che il tempo per AE sta al tempo <lb/>per AD come lo spazio AE sta allo spazio AD, <lb/>d'onde, dal semplice passando al composto, tor&shy;<lb/>nerebbe altres&igrave; dimostrato, scansando i modi mec&shy;<lb/>canici e i repentini passaggi dai moti equabili agli <lb/>accelerati, che il tempo per tutta la AB sta al <lb/>tempo per tutta la AC, come la lunghezza AB <lb/>perpendicolare sta alla lunghezza AC obliqua. </s></p><p type="main">

<s>Il modo di toglier dunque ogni dubbio, che <lb/>potesse nascere intorno ai processi dimostrativi <lb/>delle prime proposizioni, credeva Galileo che fosse cos&igrave; ritrovato, quando <lb/>gli si concedesse da tutti per vero che in D e in E, in F e in G, in H e <lb/>in I, e in somma, in tutti i punti ugualmente distanti dall'orizzonte, le <lb/>velocit&agrave; nel perpendicolo e nell'obliqua fossero uguali. </s>

<s>Ma questo dall'al&shy;<lb/>tra parte era il principio, da cui s'era fatta dipendere la Statica antica, la <lb/>verit&agrave; della quale nessuno avrebbe osato negare, come nessuno aveva messo <lb/>ancora dubbio intorno al modo di computare i momenti, secondo l'uso del <lb/>Nemorario, del Cardano e del Tartaglia, moltiplicando per le discese rette <lb/>le quantit&agrave; della materia. </s>

<s>Supponevasi di pi&ugrave; &egrave; vero da Galileo che le ve&shy;<lb/>locit&agrave; fossero proporzionali ai momenti, ma nemmeno intorno a ci&ograve; pareva <lb/>che potesse nascer dubbio, dovendo esser necessariamente le cause propor&shy;<lb/>zionali agli effetti. </s>

<s>Non fidandosi nonostante di s&egrave; medesimo, ed essendo <lb/>la cosa di tanta importanza, volle Galileo stesso averne il parere da uno <lb/>dei pi&ugrave; grandi Matematici, che si conoscessero allora in Italia, e il d&igrave; 5 di <lb/>Giugno del 1609 scriveva da Padova a Roma una lettera a Luca Valerio, <lb/>comunicandogli i due supposti, e interrogandolo se credeva che, senz'altra <lb/>prova, si potessero ammetter per veri. </s>

<s>Indugi&ograve; il Valerio infino al d&igrave; 18 del <lb/>seguente mese di Luglio, per farvi pi&ugrave; riposata considerazione, <lb/><figure id="id.020.01.2112.2.jpg" xlink:href="020/01/2112/2.jpg"/></s></p><p type="caption">

<s>Figura 179.<lb/>e finalmente rispose che, per principii di una scienza di mezzo, <lb/>non gli sembravano i due proposti punto oscuri, ma gli si ren&shy;<lb/>devano anzi chiarissimi a quel lume di metafisica &ldquo; che, mol&shy;<lb/>tiplicandosi la virt&ugrave; della causa sufficiente, &egrave; necessario si <lb/>moltiplichi la quantit&agrave; dell'effetto, secondo la medesima pro&shy;<lb/>porzione &rdquo; (Alb. </s>

<s>VII, 46). </s></p><p type="main">

<s>&ldquo; Dunque (soggiungeva poco appresso lo stesso Valerio, <lb/>riducendo ai casi particolari le generalit&agrave; del suo discorso) se <lb/>l'impeto e l'inclinazione della gravit&agrave; del corpo A (fig. </s>

<s>179), <lb/>sopra il piano inclinato all'orizzonte secondo l'angolo B, si <pb xlink:href="020/01/2113.jpg" pagenum="356"/>supponga esser doppio dell'impeto della gravit&agrave; del medesimo A sopra il <lb/>piano inclinato all'orizzonte secondo l'angolo C, maggiore dell'angolo B, e <lb/>tali due diversi impeti nascano dalla gravit&agrave; di A, limitata verso la produ&shy;<lb/>zione dell'impeto diversamente, per le diverse inclinazioni dei detti piani; <lb/>si vede per immediata conseguenza che la velocit&agrave; del moto naturale di A, <lb/>sopra il piano meno inclinato, sar&agrave; doppia della velocit&agrave; del moto della me&shy;<lb/>desima A sopra quell'altro piano pi&ugrave; inclinato. </s>

<s>Dunque il vigore della causa <lb/>immediata della doppia velocit&agrave;, che &egrave; l'impeto o l'inclinazione alla doppia <lb/>velocit&agrave;, doveva esser doppia dell'inclinazione alla mezza velocit&agrave;, secondo <lb/>la maggiore inclinazione dell'altro piano &rdquo; (ivi, pag. </s>

<s>47). </s></p><p type="main">

<s>A confermare la ragionevelezza di questo discorso, interrompendo per <lb/>un poco il filo alla storia, giova osservare come inconsapevolmente si ri&shy;<lb/>scontrasse con quell'altro discorso, che faceva il Torricelli, quando venne <lb/>il Mersenno a promovere di fatto le difficolt&agrave; sospettate da Galileo. </s>

<s>Nello <lb/>scolio alla proposizione II <emph type="italics"/>De motu gravium<emph.end type="italics"/> aveva scritto l'Autore: &ldquo; Sup&shy;<lb/>ponimus hic, cum ipso Galileo, velocitates in diversis planorum inclinatio&shy;<lb/>nibus ita esse, ut sunt momenta, quando eadem fuerit moles &rdquo; (Op. </s>

<s>geom. </s>

<s><lb/>cit, P. I, pag. </s>

<s>104). Ora, avendo il Mersenno letto il trattato torricelliano, <lb/>scriveva da Parigi all'Autore stesso, fra le parecchie altre cose che non gli <lb/>erano piaciute, anche queste: &ldquo; Supponis cum Galileo velocitates in diver&shy;<lb/>sis planorum inclinationibus ita esse, ut sunt momenta, quando fuerit eadem <lb/>moles. </s>

<s>Si quis negaverit hanc hypothesim, ob paralogismum et confusionem <lb/>momentorum, seu gravitationum, cum ipsis motibus; quomodo suppositum <lb/>probare possit, ne forte corruant quaecumque Galileus se probaturum exi&shy;<lb/>stimavit, aut tu ipse in illius gratiam addideris? </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. XLI, <lb/>fol. </s>

<s>68 ad t.). </s></p><p type="main">

<s>A queste difficolt&agrave; e a queste accuse rispondeva cos&igrave;, per s&egrave; e per Galileo, <lb/>il Torricelli con i medesimi argomenti, che il comun senso aveva suggeriti al <lb/>Valerio: &ldquo; Quod ego suppono pag. </s>

<s>104, cum Galileo, adeo manifestum mihi vi&shy;<lb/>detur, ut sine ulla dubitatione loco principii admitti et concedi posse videatur. </s>

<s><lb/>Ratio physica est. </s>

<s>Si fuerint a diversis planis duae sphaerae, exempli gratia, <lb/>vitreae et aequales, postquam ostendero momentum unius ad momentum al&shy;<lb/>terius esse duplum, quis non concedat et velocitatem ad velocitatem esse du&shy;<lb/>plam? </s>

<s>Dupla enim causa duplum effectum parere debet in eodem sub&igrave;ecto. </s>

<s><lb/>Moles supponuntur aequeles, eiusdemque materiae, virtus vero, quae im&shy;<lb/>pellit alteram molem, dupla demonstratur virtutis alterius. </s>

<s>Ergo, si dupla <lb/>virtus est, duplam proculdubio velocitatem efficiet &rdquo; (ivi, T. LX, fol. </s>

<s>76). </s></p><p type="main">

<s>Bello &egrave; quel che il Torricelli soggiunge, per prevenire le difficolt&agrave; e <lb/>per confermare la dottrina galileiana che le velocit&agrave;, nelle scese naturali dei <lb/>gravi, sono indipendenti dai loro pesi, concludendo in queste parole la sua <lb/>lunga dimostrazione: &ldquo; Virtus minor, ad minus pondus a se movendum, <lb/>eamdem habet rationem, quam virtus maior ad maius pondus a se moven&shy;<lb/>dum &rdquo; (ibid., fol. </s>

<s>76 ad t.). Ma &egrave; da tornare al Valerio, per veder quel che <lb/>egli sentisse di quell'altro importante supposto comunicatogli da Galileo. </s></p><pb xlink:href="020/01/2114.jpg" pagenum="357"/><p type="main">

<s>Egli dava, nel riconoscerne la naturale evidenza, la pi&ugrave; decisa e pi&ugrave; <lb/>concludente dimostrazione fra le molte che, dai Matematici posteriori, a in&shy;<lb/>cominciare dallo stesso Galileo infino all'Huyghens, furono speculate, e pro&shy;<lb/>poste a verificare le prime fatte supposizioni. </s>

<s>Si desumeva per esso Valerio <lb/>la detta dimostrazione dal principio della composizione dei moti, considerando <lb/>l'impeto della scesa per l'obliqua AC (fig. </s>

<s>180) come prodotto dalla forza <lb/><figure id="id.020.01.2114.1.jpg" xlink:href="020/01/2114/1.jpg"/></s></p><p type="caption">

<s>Figura 180.<lb/>AC, la quale venga decomposta nella verticale BC e nella <lb/>orizzontale AB. </s>

<s>E perciocch&egrave; per questa la forza impel&shy;<lb/>lente &egrave; nulla, non riman dunque attivo altro che l'im&shy;<lb/>peto per BC, e perci&ograve; essendo le cadute o per AC o <lb/>per BC del medesimo effetto, si vede come debbano <lb/>essere in B e in A le velocit&agrave; uguali. </s>

<s>E perch&egrave; son <lb/>documento assai importante alla storia dei moti com&shy;<lb/>posti e a quella del famoso supposto meccanico, rife&shy;<lb/>riamo le parole proprie, che soggiungeva alle sopra trascritte il valoroso pro&shy;<lb/>fessore nell'Arciginnasio romano. </s></p><p type="main">

<s>&ldquo; Per quanto poi si riferisce alla seconda supposizione, scriveva a Ga&shy;<lb/>lileo, questa non mi si rende men chiara della prima, perciocch&egrave; essendo il <lb/>moto del corpo grave D, nella figura precedente, mosso per l'AC all'oriz&shy;<lb/>zonte AB, mobile verso l'AB, e l'altro per una perpendicolare all'orizzonte, <lb/>essa ancor mobile; cosa chiara &egrave; che, quando D sar&agrave; in A, avr&agrave; acquistato <lb/>tanto impeto o inclinazione a velocemente muoversi, che &egrave; la quantit&agrave; del&shy;<lb/>l'effetto (in quanto effetto, dico, di quella parte del moto composto, che si <lb/>fa per la perpendicolare mobile eguale alla stabile CB) quanto avrebbe acqui&shy;<lb/>stato, se D si fosse mosso per la sola perpendicolare CB, e ci&ograve; dico in vi&shy;<lb/>gore del sopra detto principio &rdquo; (Alb. </s>

<s>VIII, 47, 48). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Rassicurato dunque cos&igrave; Galileo che, supponendosi noti i due principii <lb/>sottoposti all'autorevole giudizio di Luca Valerio, si poteva sopr'essi, sen&shy;<lb/>z'altro bisogno di ricorrere al Teorema meccanico, stabilire con sicurezza il <lb/>nuovo architettato edifizio; nell'estate del 1609 dette mano a condurlo se&shy;<lb/>condo quest'altro meditato disegno, lusingandosi che sarebbe senz'alcuna <lb/>contradizione approvato. </s>

<s>Le due prime proposizioni perci&ograve; del II Libro ri&shy;<lb/>manevano ferme, come il primo anello, da cui doveva dipendere la lunga <lb/>catena, senz'altro intermedio delle due seguenti proposizioni meccaniche, le <lb/>quali venivano perci&ograve; repudiate come sospette di fallacia in concludere da <lb/>esse le ragioni dei moti accelerati. </s>

<s>Dovevano in loro luogo supplire i due <lb/>principii supposti, dai quali si verrebbe a dimostrare il Teorema fondamen&shy;<lb/>tale, che cio&egrave; i tempi nel perpendicolo e nell'obliqua hanno la proporzione <lb/>delle loro lunghezze lineari. </s></p><pb xlink:href="020/01/2115.jpg" pagenum="358"/><p type="main">

<s>Premesso dunque il trattato Dei moti equabili, e le dette proposizioni <lb/>Ia e IIa Dei moti accelerati, la IIIa, che doveva immediatamente seguitare in <lb/>questo terzo libro galileiano <emph type="italics"/>De motu,<emph.end type="italics"/> era cos&igrave; formulata, e dalla fatta <lb/>supposizione delle velocit&agrave; uguali, dopo cadute uguali, nel seguente modo <lb/>condotta: </s></p><p type="main">

<s>PROPOSITIO III. &mdash; &ldquo; Si in perpendiculo et in plano inclinato, quorum <lb/>eadem sit altitudo, feratur idem mobile, tempora lationum erunt inter se ut <lb/>plani inclinati, et perpendiculi longitudines. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sint ad planum horizontis CB (fig. </s>

<s>181) perpendicularis AB, et pla&shy;<lb/>num inclinatum AC, quorum eadem sit altitudo, nempe ipsa perpendicula&shy;<lb/><figure id="id.020.01.2115.1.jpg" xlink:href="020/01/2115/1.jpg"/></s></p><p type="caption">

<s>Figura 181.<lb/>ris AB, et per ipsam descendat idem mobile. </s>

<s>Dico <lb/>tempus lationis per AB, ad tempus lationis per <lb/>AC, esse ut longitudo AB, ad longitudinem AC. &rdquo; </s></p><p type="main">

<s>&ldquo; Cum enim assumptum sit, in inclinato de&shy;<lb/>scensu, volocitatis momenta eadem semper repe&shy;<lb/>riri in punctis aequaliter ab horizonte distanti&shy;<lb/>bus, iuxta perpendiculares distantias continue <lb/>augeri secundum rationem elongationis perpen&shy;<lb/>dicularis a linea horizontali, in qua fuit lationis <lb/>initium; constat quod, producta linea horizontali <lb/>AM, quae ipsi BC erit parallela, sumptisque in <lb/>perpendiculari AB quotcumque punctis E, G, I, <lb/>L, et per ipsis ductis parallelis horizonti ED, GF, <lb/>IH, LK, erit mobilis per AB momentum, seu gradus velocitatis in puncto E <lb/>idem cum gradu velocitatis lati per AC in puncto D, cum punctorum E, D <lb/>eadem sit distantia perpendicularis ab horizonte AM, et similiter concludatur <lb/>in punctis F, G idem esse velocitatis momentum, et rursus in punctis H, I, <lb/>et K, L, et C, B. </s>

<s>Et quia velocitas semper intenditur pro ratione elongationis <lb/>a termino A, constat in latione AB tot esse velocitatis gradus, seu momenta <lb/>diversa, quot sunt in eadem linea AB puncta magis a termino A distantia, <lb/>quibus totidem in linea AC respondent, et per parallelas lineas determinantur, <lb/>in quibus iidem sunt gradus velocitatis. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sunt igitur in linea AB quasi innumerabilia quaedam spaciola, qui&shy;<lb/>bus multitudine quidem aequalia, et bina sumpta, in eamdem rationem re&shy;<lb/>spondentia, alia signant in AC, per lineas innumeras parallelas, ex punctis <lb/>lineae AB ad lineam AC extensas. </s>

<s>Intercepta nam AD, DF, EH ad spacia <lb/>AE, EG, GI respondent singula singulis ad rationem AC ad AB, suntque <lb/>in singulis binis sibi respondentibus iidem velocitatis gradus. </s>

<s>Ergo, ex prae&shy;<lb/>cedentibus, tempora omnia simul sumpta lationum omnium per AB, ad tem&shy;<lb/>pora omnia similiter accepta lationum omnium per AC, eamdem hubebunt <lb/>rationem quam spacia omnia lineae AB, ad spacia omnia lineae AC. </s>

<s>Hoc <lb/>autem idem esse ac tempus casus per AB ad tempus casus per AC; idest <lb/>ut linea AB ad AC, quod erat demonstrandum &rdquo; (MSS. Gal., P. V, T. II, <lb/>fol. </s>

<s>179). </s></p><pb xlink:href="020/01/2116.jpg" pagenum="359"/><p type="main">

<s>Di quel che si dava nel II Libro per corollario ne fa in questo l'Au&shy;<lb/>tore una proposizione distinta, che immediatamente succede alla sopra scritta, <lb/>in quarto luogo, e in tal forma: </s></p><p type="main">

<s>PROPOSITIO IV. &mdash; &ldquo; Tempora lationum per diversas lineas inclinatas, <lb/>quarum eadem sit altitudo perpendicularis, sunt inter se ut earumdem li&shy;<lb/>nearum longitudines. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sint ad horizontem BD (fig. </s>

<s>182) diversa plana inclinata AB, AC, <lb/><figure id="id.020.01.2116.1.jpg" xlink:href="020/01/2116/1.jpg"/></s></p><p type="caption">

<s>Figura 182.<lb/>quorum eadem sit altitudo AD perpendicularis. </s>

<s>Dico <lb/>tempus casus per AB, ad tempus casus per AC, esse <lb/>ut AB longitudo, ad longitudinem AC. &rdquo; </s></p><p type="main">

<s>&ldquo; Ex antecedenti enim tempus casus per AB, <lb/>ad tempus casus per perpendicularem AD, est ut AB <lb/>linea ad lineam AD, et, per eamdem, ut AC linea <lb/>ad ipsam AD, ita tempus casus per AC, ad tempus <lb/>casus per AD. Ergo, ex aequali, ut longitudo AB <lb/>ad longitudinem AC, ita tempus casus per AB. ad <lb/>tempus casus per AC &rdquo; (ibid., fol. </s>

<s>179 ad t.). </s></p><p type="main">

<s>L'altra proposizione fondamentale concernente <lb/>il tautocronismo delle corde nei cerchi, che nel primo e nel secondo Libro <lb/>si concludeva direttamente dal Teorema meccanico, escluso ora questo Teo&shy;<lb/>rema, conveniva dimostrarla in altro modo, che la VIII proposizione del II <lb/>Libro avrebbe offerto in s&egrave; pronto e spedito. </s>

<s>Imperocch&egrave; se nel triangolo <lb/>ADC (fig. </s>

<s>183), rettangolo in D, il tempo per AD &egrave; uguale al tempo per <lb/><figure id="id.020.01.2116.2.jpg" xlink:href="020/01/2116/2.jpg"/></s></p><p type="caption">

<s>Figura 183.<lb/>AC, bastava circoscrivere il mezzo cerchio ADC al detto <lb/>triangolo rettangolo, perch&egrave; fosse all'occhio insieme e <lb/>alla mente manifesto che la caduta per la corda AD, e <lb/>per il diametro AC si spediscono nel medesimo tempo. </s>

<s><lb/>Volle Galileo nonostante dar cos&igrave; altra macchina a una <lb/>proposizione, che doveva al suo intento essere della <lb/>massima importanza. </s></p><p type="main">

<s>PROPOSITIO V. &mdash; &ldquo; Si in circulo, ad horizontem <lb/>erecto, a puncto sublimi quocumque ducantur lineae rectae, usque ad circum&shy;<lb/>ferentiam, per quas cadant gravia quotcumque, omnia tem&shy;<lb/><figure id="id.020.01.2116.3.jpg" xlink:href="020/01/2116/3.jpg"/></s></p><p type="caption">

<s>Figura 184.<lb/>poribus aequalibus ad terminos suos pervenient. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sit enim circumferentia ad horizontem erecta ABEC <lb/>(fig. </s>

<s>184), punctum sublime A, a quo lineae quotcumque, <lb/>ad circumferentiam usque, protrahantur AE, AB, et per <lb/>ipsas cadant mobilia: Dico, temporibus aequalibus, illa <lb/>perventura esse ad terminos E, B. &rdquo; </s></p><p type="main">

<s>&ldquo; Sit enim AC per centrum ducta, cui ex B per&shy;<lb/>pendiculasis sit BD. </s>

<s>Patet AB mediam esse proportiona&shy;<lb/>lem inter CA, AD, quare, ex demonstratis, tempus, quo <lb/>mobile ex A cadit in C, ad tempus casus ex A in D, est <lb/>ut linea BA, ad lineam AD. &rdquo; </s></p><pb xlink:href="020/01/2117.jpg" pagenum="360"/><p type="main">

<s>&ldquo; Verum, similiter, ex demonstratis, tempus casus ex A in B, ad tem&shy;<lb/>pus casus ex A in D, est ut BA ad AD. </s>

<s>Ergo tempora casuum AB, AC <lb/>erunt aequalia, cum eamdem, ad idem tempus casus, habeant rationem. </s>

<s>Et <lb/>similiter de reliquis omnibus demonstratur. </s>

<s>Ergo patet propositum &rdquo; (ibid., <lb/>fol. </s>

<s>48). </s></p><p type="main">

<s>&Egrave; soggiunto a questa proposizione un Corollario, a cui non avrebbe <lb/>pensato di supplire nel trattato a stampa il Viviani, se l'avesse qui trovato <lb/>nel Manoscritto. </s>

<s>Vedremo tra poco come si sian bene incontrati, bench&egrave; <lb/>inconsapevolmente, il Discepolo col Maestro. </s></p><p type="main">

<s>COROLLARIUM. &mdash; &ldquo; Ex his colligitur gravia eodem tempore pertransire <lb/>plana inaequalia, et inaequaliter inclinata, dum, quam proportionem habet <lb/>longitudo maioris plani, ad longitudinem alterius, eamdem duplicatam habeat <lb/>perpendicularis maioris plani, ad perpendicularem minoris. </s>

<s>Cum enim qua&shy;<lb/>dratum AE sit aequale rectangulo CAF, quadratum vero BA rectangulo <lb/>CAD; rectangulum vero CAF, ad rectangulum CAD, est ut FA ad AD; ergo <lb/>FA ad AD est ut quadratum EA, ad quadratum BA. </s>

<s>Ratio igitur perpendicu&shy;<lb/>laris FA, ad perpendicularem DA, dupla est rationis EA ad AB. etc. </s>

<s>&rdquo; (ibid.). </s></p><p type="main">

<s>Non mancava che aggiungere a questa V la proposizione IX del I Li&shy;<lb/>bro, con i tre Lemmi geometrici ivi gi&agrave; preparati, per concludere il princi&shy;<lb/>pale intento, qual era quello di dimostrare il brachistocronismo dell'arco <lb/>rispetto alle corde inflesse e sottese, a quel modo che fu mantenuto in tutte <lb/>le varie forme di trattati, dal primo, composto nel 1604, infino all'ultimo <lb/>mandato nel 1638 alle stampe. </s>

<s>La somma dunque dei principali teoremi, che <lb/>qualificarono questo III Libro, e che lo distinguono nella mossa e nell'an&shy;<lb/>damento dai precedenti, si riduceva alle cinque proposizioni, in parte sopra <lb/>accennate, e in parte trascritte, dalle quali s'&egrave; detto come un passo solo <lb/>condurrebbe Galileo alla sua finale intenzione. </s>

<s>Ma si conteneva in quei teo&shy;<lb/>remi un rigoglio giovanile di vita, che voleva scoppiare in numerosi ram&shy;<lb/>polli, i nodi germinativi de'quali s'ascondevano latenti nella ultima trascritta <lb/>proposizione V, nel corollario di lei, e nella proposizione IX del I Libro. </s>

<s><lb/>Basta rivolger l'occhio sulla figura 184, qui poco addietro impressa, e ri&shy;<lb/>chiamarsi alla mente le nozioni, ch'ella doveva illustrare, per vedervi sotto <lb/>annidati due varii germi, da ciascun de'quali si svolgerebbe un proprio e <lb/>distinto ordine di teoremi. </s>

<s>Le inclinate AB, AE infatti, per le quali s'im&shy;<lb/>magina da Galileo avere le loro scese i gravi, ora si considerano in quanto <lb/>sono corde di un cerchio, come si fa nella proposizione, ora in quanto son <lb/>piani, adattati comunque all'uso di sostentare i corpi cadenti, come si fa <lb/>nell'immediato corollario ivi soggiunto. </s>

<s>Dal riguardar le cose sotto quel <lb/>primo aspetto, si rappresentavano alla mente, come raggio di luce in varie <lb/>parti riflesso e diffratto, i teoremi e i problemi concernenti i varii casi dei <lb/>piani, da un mobile passati in tempi o pi&ugrave; lunghi o pi&ugrave; brevi; mentre, dal <lb/>riguardar le cose sotto quell'altro aspetto, nasceva la curiosit&agrave; di saper le <lb/>leggi, a cui vanno soggette le scese, secondo che i piani variamente incli&shy;<lb/>nati son di uguale o differente lunghezza. </s>

<s>La IX proposizione poi, che bi-<pb xlink:href="020/01/2118.jpg" pagenum="361"/>sogn&ograve; a Galileo aggiungere, nel primo e negli altri trattati, per ritrovare in <lb/>qual proporzione stia il tempo, che impiega un mobile a scendere per due <lb/>piani inflessi, era la pi&ugrave; feconda di tutte, come quella che rendevasi trasfor&shy;<lb/>mabile in una numerosa elegante variet&agrave; di casi. </s></p><p type="main">

<s>In quelle cinque proposizioni dunque, che s'&egrave; detto di sopra, e nelle <lb/>altre due, l'una delle quali preparava immediatamente, e l'altra concludeva <lb/>la finale intenzion dell'Autore, ch'era quella di dimostrar come la scesa per <lb/>l'arco &egrave; pi&ugrave; breve che per le corde; si rappresentava, per dir cos&igrave;, il nudo <lb/>tronco, che, dai tre detti nodi scoppiando, si dovea rivestire via via di no&shy;<lb/>velli rami e di fronde. </s>

<s>L'opera dedita ad aggiungere all'albero della Nuova <lb/>scienza questo decoro, fu per Galileo lunga, perch&egrave; distratta dalle maravi&shy;<lb/>gliose scoperte celesti, e interrotta dai casi fortunosi della vita. </s>

<s>Posto nel <lb/>1609 il nuovo fondamento, sulle due ipotesi comunicate a Luca Valerio, e <lb/>riformate le due proposizioni fondamentali concernenti il tempo della scesa <lb/>per le oblique di uguale altezza, e il tautocronismo delle corde, con che rap&shy;<lb/>presentavasi della Nuova scienza, come dicevasi, il nudo tronco; non fece <lb/>altro Galileo, infino al 1630, che derivar qualche ramo ora dall'uno, ora <lb/>dall'altro centro germinativo. </s>

<s>Son di una tale opera rimaste segnate, nei <lb/>Manoscritti galileiani, le disperse vestigia, le quali noi intendiamo di rasse&shy;<lb/>gnare nei tre detti ordini distinti, secondo che le cose via via dimostrate <lb/>dipendono, come da loro principio, o dalla V proposizione e dal corollario <lb/>di lei in questo III libro, o dalla IX proposizione del primo. </s></p><p type="main">

<s>Incominciando dal dar ordine in questo terzo Trattato ai teoremi, con&shy;<lb/>cernenti il tempo nelle corde dei cerchi, e che si derivano dalla V propo&shy;<lb/>sizione fondamentale come corollarii, si deve alla detta ultima proposizione <lb/>trascritta far succedere immediatamente le due seguenti: </s></p><p type="main">

<s>PROPOSITIO VI. &mdash; &ldquo; Si in circulo, cuius diameter sit ad perpendicnlum, <lb/>ducatur linea, quae ad diametrum non pertingat, motus per ipsam citius <lb/>absolvetur, quam per diametrum perpendicularem. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Circuli ad horizontem erecti esto diameter perpendicularis AB (fig. </s>

<s>185): <lb/><figure id="id.020.01.2118.1.jpg" xlink:href="020/01/2118/1.jpg"/></s></p><p type="caption">

<s>Figura 185.<lb/>De plano DF, ad diametrum non pertingente, <lb/>quod tempus descensus in eo sit brevius, demon&shy;<lb/>stratur ducto plano DB, quod et longius erit, et <lb/>minus declive, quam DF: ergo tempus per DF <lb/>brevius, quam per DB, hoc est, per AB &rdquo; (MSS. <lb/>Gal., P. V, T. II, fol. </s>

<s>164). </s></p><p type="main">

<s>PROPOSITIO VII. &mdash; &ldquo; Si in circulo, cuius <lb/>diameter sit ad perpendiculum, ducatur linea, <lb/>quae a diametro secetur, motus per ipsam tardius <lb/>absolvetur, quam per diametrum perpendicula&shy;<lb/>rem. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In praecedenti enim figura sit linea qua&shy;<lb/>libet DE, et quia ipsa erit longior quam DB, et magis inclinata, propositum <lb/>fit manifestum &rdquo; (ibid.). </s></p><pb xlink:href="020/01/2119.jpg" pagenum="362"/><p type="main">

<s>Dipendenti dalla V proposizione fondamentale, e conseguenze immediate <lb/>di lei, son queste altre due proposizioni, che ordiniamo qui sotto, e che i <lb/>Lettori, nella materia e nella forma troveranno eleganti. </s></p><p type="main">

<s>PROPOSITIO VIII. &mdash; Motuum, qui a dato puncto, usque ad datam li&shy;<lb/>neam, per lineas rectas conficiuntur, ille brevissimo tempore absolvitur, qui <lb/>in recta fit abscindens de data linea partem aequalem ei parti lineae hori&shy;<lb/>zontalis, quae per datum punctum usque ad datam lineam producitur, quae <lb/>inter datum punctum et occursum intercipitur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sit datum punctum A (fig. </s>

<s>186), et linea quaecumque BDC, et per A <lb/>horizonti aequidistans AB, quae lineae BD in B occurrat, et interceptae AB <lb/><figure id="id.020.01.2119.1.jpg" xlink:href="020/01/2119/1.jpg"/></s></p><p type="caption">

<s>Figura 186.<lb/>ponatur aequalis BD. </s>

<s>Dico motum per AD <lb/>absolvi tempore breviori, quam per quam&shy;<lb/>cumque aliam lineam, ex puncto A, ad <lb/>quodcumque punctum lineae BDC, pro&shy;<lb/>ductam. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ducatur ad BA perpendicularis AC, <lb/>et ex D, ad ipsam BC perpendicularis DE, <lb/>occurrens AC in E. </s>

<s>Et quia, in triangulo <lb/>aequicruri ABD, anguli BAD, BDA sunt <lb/>aequales, ergo reliqua ad rectos, nempe EAD, EDA aequales pariter erunt, <lb/>et linea EA, aequalis ipsi ED. &rdquo; </s></p><p type="main">

<s>&ldquo; Si itaque, centro E, intervallo EA, circulus describatur, transibit per <lb/>D, ubi lineam BDC tanget. </s>

<s>Quare lineae omnes, quae supra et infra AD, <lb/>usque ad lineam BC, producuntur, ultra circumferentiam circuli extendun&shy;<lb/>tur, ex quo patet propositum &rdquo; (ibid., fol. </s>

<s>127, ad t.). </s></p><p type="main">

<s>PROPOSITIO IX. &mdash; &ldquo; Sit linea horizontalis AC (fig. </s>

<s>187), perpendiculus <lb/>vero BG, et in AC accipiatur quodcumque C: Dico quod, si mobile debet <lb/><figure id="id.020.01.2119.2.jpg" xlink:href="020/01/2119/2.jpg"/></s></p><p type="caption">

<s>Figura 187.<lb/>ex C ad lineam perpendiculi, per unicam lineam <lb/>moveri, ad eam perveniet tempore brevissimo, si <lb/>veniat per CE, quae lineam BE, ipsi BC aequa&shy;<lb/>lem, adsumit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Centro enim B, intervallo BE, circulus de&shy;<lb/>scribatur, ductisque CF, et CG utcumque, patebit <lb/>motum per CE citius absolvi quam per CF, aut <lb/>CG. </s>

<s>Si enim ducatur tangens circulum ICH, et <lb/>ipsi CF parallela ELH, erit LE brevior quam CF. </s>

<s><lb/>Sed tempus per CE aequatur tempori per LE, <lb/>ergo .... &rdquo; </s></p><p type="main">

<s>&ldquo; Similiter, ducta EHI ipsi CG parallela et <lb/>aequali, constat CG longiorem esse HE. </s>

<s>At tem&shy;<lb/>pus per CE aequater tempori per HE, ergo patet <lb/>propositum &rdquo; (ibid., fol. </s>

<s>140). </s></p><p type="main">

<s>Queste quattro, con alcun'altra che forse <lb/>ci &egrave; passata d'occhio, sono le proposizioni dimo-<pb xlink:href="020/01/2120.jpg" pagenum="363"/>strate da Galileo, per svolgere il concetto principale, espresso nella quinta <lb/>proposizione di questo Libro. </s>

<s>Il corollario di lei dette luogo pure a espli&shy;<lb/>carsi in altri, non men curiosi e importanti quesiti, com'&egrave; quello di trovare <lb/>in qual proporzione stiano i tempi dei cadenti su due piani variamente incli&shy;<lb/><figure id="id.020.01.2120.1.jpg" xlink:href="020/01/2120/1.jpg"/></s></p><p type="caption">

<s>Figura 188.<lb/>nati, e ora uguali in lunghezza, ora differenti. </s>

<s>Appar&shy;<lb/>tiene al primo caso un teorema, dimostrato in due varie <lb/>maniere, all'una delle quali &egrave; premesso il seguente <lb/>Lemma: </s></p><p type="main">

<s>&ldquo; Sint tres lineae utcumque A, D, E (fig. </s>

<s>188) et <lb/>inter A, D media proportionalis sit B; inter A, E me&shy;<lb/>dia proportionalis sit C; inter E, D tandem media sit G: <lb/>Dico, ut C ad B, ita esse G ad D. &rdquo; </s></p><p type="main">

<s>&ldquo; Quia enim B est media inter A, D, erit quadratum <lb/>B aequale rectangulo A.D. </s>

<s>Similiter quadratum C ae&shy;<lb/>quale rectangulo A.E. Igitur, ut rectangulus A.E, ad <lb/>rectangulum A.D, ita quadratum C, ad quadratum B. </s>

<s><lb/>Ut autem rectangulus A.E, ad rectangulum A.D, ita <lb/>linea E, ad D. </s>

<s>Ut vero linea E, ad lineam D, ita qua&shy;<lb/>dratum G, ad quadratum D: urgo, ut quadratum C, ad <lb/><figure id="id.020.01.2120.2.jpg" xlink:href="020/01/2120/2.jpg"/></s></p><p type="caption">

<s>Figura 189.<lb/>quadratum B, ita quadratum G, ad quadratum D, et, ut <lb/>C ad B, ita G ad D &rdquo; (ibid., fol. </s>

<s>37). </s></p><p type="main">

<s>Dietro il qual Lemma, ecco in che modo Galileo di&shy;<lb/>mostra in qual proporzione stieno i tempi delle cadute di <lb/>un medesimo grave sopra due piani ugualmente lunghi, <lb/>ma variamente inclinati. </s></p><p type="main">

<s>PROPOSITIO X. &mdash; &ldquo; Sint plana aequalia AB, CB (fig. </s>

<s>189) <lb/>inaequaliter inclinata, et altitudo inclinationis plani AB sit <lb/>BE; ipsius vero BC sit BD. </s>

<s>Dico tempus casus super BA, <lb/>ad tempus casus per BC, esse ut media proportionalis in&shy;<lb/>ter DB, BE, ad ipsam BE. &rdquo; </s></p><p type="main">

<s>&ldquo; Accipiatur FB ipsis CB, AB aequalis, et ipsarum <lb/>FB, BD media sit BS: ipsarum vero FB, BE media sit BR. </s>

<s><lb/>Et quia tempus casus FB, ad tempus casus BD, est ut SB ad BD; tempus <lb/>vero casus BD, ad tempus casus BC, ut BD ad BC; ergo, ex aequali, tem&shy;<lb/>pus casus BF, ad tempus casus BE, ut SB ad BE. </s>

<s>Et convertendo, tempus <lb/>casus BE, ad tempus casus BF, ut BE ad BS. &rdquo; </s></p><p type="main">

<s>&ldquo; Similiter autem demonstrabitur, ut tempus casus BF, ad tempus ca&shy;<lb/>sus BA, ita linea RB ad BA, aut BC: ergo, ex aequali, in analogia pertur&shy;<lb/>bata, ut tempus casus BC, ad tempus casus BA, ita RB ad SB. </s>

<s>Et conver&shy;<lb/>sim, ut tempus casus BA, ad tempus casus BC, ita SB ad BR. </s>

<s>Ex Lemmate <lb/>vero antecedenti, ut SB ad BR, ita media inter DB, BE ad ipsam BE; quare <lb/>patet propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Aliter absque Lemmate. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sit BI (fig. </s>

<s>190) media inter BD, BE, et IS parallela ed DC: et quia, <pb xlink:href="020/01/2121.jpg" pagenum="364"/>ut tempus per BA, ad tempus per BE, ita linea BA, ad lineam BE: ut au&shy;<lb/><figure id="id.020.01.2121.1.jpg" xlink:href="020/01/2121/1.jpg"/></s></p><p type="caption">

<s>Figura 190.<lb/>tem tempus BE, ad tempus BD, ita linea BE ad BI; ut <lb/>autem tempus BD, ad tempus BC, ita linea BD ad BC, hoc <lb/>est BI ad BS; ergo, ex aequali, ut tempus per BA ad <lb/>tempus per BC, ita linea AB, seu BC, ad BS, hoc est <lb/><figure id="id.020.01.2121.2.jpg" xlink:href="020/01/2121/2.jpg"/></s></p><p type="caption">

<s>Figura 191.<lb/>DB ad BI, seu IB ad BE, quod erat pro&shy;<lb/>bandum &rdquo; (ibid., fol. </s>

<s>37). </s></p><p type="main">

<s>Dai piani di lunghezze uguali, pas&shy;<lb/>sando a quelli di lunghezze differenti, di&shy;<lb/>mostrava Galileo quest'altra proposizione: </s></p><p type="main">

<s>PROPOSITIO XI. &mdash; &ldquo; Sint plana quaecumque inclinata <lb/>AB, AC (fig. </s>

<s>191) et perpendiculus AE, cui, ad rectos an&shy;<lb/>gulos, BG, et sit inter CA, AD media AF: Dico tempus per <lb/>AB, ad tempus per AC, esse ut BA ad AF. &rdquo; </s></p><p type="main">

<s>&ldquo; Nam, tempus per AB, ad tempus per AD, est ut AB <lb/>ad AD: tempus vero per AD, ad tempus per AC, est ut AD <lb/>ad AF: ergo, ex aequali, tempus per AB, ad tempus per AC, est ut AB ad <lb/>AF, quod erat ostendendum &rdquo; (ibid., fol. </s>

<s>58). </s></p><p type="main">

<s>Di qui, cio&egrave; dall'essere T.oAB:T.oAC=AB:AF, avendosi AF= <lb/>&radic;AC.AD, viene T.oAB:T.oAC=AB&radic;AC:AC&radic;AD.E perch&egrave; AC:AD= <lb/>AE:AG, resterebbe di qui dimostrata, a quel modo che leggesi nel trattato <lb/>a stampa, la proposizione V, la formula della quale trovasi autografa a tergo <lb/>del foglio 35, dove si fa del teorema l'applicazione a un caso numerico, posto <lb/>AB uguale a 8, AC uguale a 20, e AG, AE, altezze perpendicolari, uguali a <lb/>4 e a 16. Galileo calcola la formula T.oAC:T.oAB=&radic;AC2.AG:&radic;AB2.AE, <lb/>ponendo per AC, AG, AB, AE i respettivi valori numerici, e trova T.oAC: <lb/>T.oAB=&radic;1600:&radic;1024=10:8; conclusione scritta in testa al citato fo&shy;<lb/>glio, che dice: &ldquo; Tempo per AC, al tempo per AB, &egrave; come 10 a 8. &rdquo; </s></p><p type="main">

<s>Venne in altro modo confermata a Galileo la proposta verit&agrave;, suppo&shy;<lb/>nendo che i piani AB, AC sian corde di cerchi, perch&egrave; si sa, in questo caso, <lb/>doverne, per le cose gi&agrave; dimostrate, resultare l'uguaglianza dei tempi. </s>

<s>Tale <lb/>sembra infatti fosse l'intenzione, ch'egli ebbe, nel soggiungere cos&igrave;, per <lb/>modo di corollario, alla sopra riferita XI proposizione: </s></p><p type="main">

<s>&ldquo; Ratio temporis AC, ad tempus AB (in semicirculo ABC) componitur <lb/>ex ratione AC ad AB, et altitudinis AG, ad mediam inter altitudines AG, <lb/>AE, quae ratio est eadem cum ratione BA ad AC. </s>

<s>Quadratum enim AB, ad <lb/>quadratum AC, est ut AG ad AE, nempe, ut rectangulus HAG, ad rectan&shy;<lb/>gulum HAE. </s>

<s>Sed ratio composita ex CA ad AB, et ex AB ad CA, est ratio <lb/>aequalitatis, ergo fit propositum &rdquo; (ibid., fol. </s>

<s>35). </s></p><p type="main">

<s>Di pi&ugrave; fecondo svolgimento dicemmo essere la proposizione IX del I li&shy;<lb/>bro, concernente i tempi delle scese per due varie inflessioni di piani; pro&shy;<lb/>posizione, che Galileo dimostra qui in altro modo, e pone sotto un altro <lb/>aspetto, forse per prepararsi pi&ugrave; facile la via a dimostrar, ne'varii casi da <lb/>contemplarsi, le varie proporzioni del moto. </s></p><pb xlink:href="020/01/2122.jpg" pagenum="365"/><p type="main">

<s>PROPOSITIO XII. &mdash; &ldquo; Sit AC (fig. </s>

<s>192) perpendicularis ad horizontem <lb/>CD, ponaturque inclinata BD, fiatque motus ex A per ABD: Dico tempus per <lb/><figure id="id.020.01.2122.1.jpg" xlink:href="020/01/2122/1.jpg"/></s></p><p type="caption">

<s>Figura 192.<lb/>BC, post casum AB, ad tempus per BD, post <lb/>eumdem casum AB, esse ut linea BC ad BD. &rdquo; </s></p><p type="main">

<s>&ldquo; Ducatur AF parallela DC, et protrahatur <lb/>DB ad F. </s>

<s>Erit iam tempus casus per FBD, ad <lb/>tempus casus per ABC, ut FD linea, ad lineam <lb/>AC. </s>

<s>Est autem tempus casus per FB, ad tempus <lb/>casus per AB, ut linea FB ad lineam AB, ergo <lb/>tempus casus reliquae BC, post AB, ad tempus <lb/>casus reliquae BD, post FB, erit ut reliqua BC, <lb/>ad reliquam BD. </s>

<s>Sed tempus casus per BD, post <lb/>FB, est idem cum tempore per BD, post AB, <lb/>cum AF sit horizonti aequidistans; ergo patet <lb/>propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s>COROLLARIUM. &mdash; &ldquo; Colligitur autem ex hoc, quod tempora casuum per <lb/>BC, et per BD, sive fiat principium motus ex termino B, sive praecedat <lb/>motus ex eadem tamen altitudine, eamdem inter se servant rationem, nempe <lb/>eam, quae est lineae BC ad BD &rdquo; (ibid., fol. </s>

<s>68). </s></p><p type="main">

<s>Uno dei primi, e pi&ugrave; curiosi quesiti, relativi a questa dimostrata pro&shy;<lb/>posizione, era tale: Poniamo che un grave partendosi dalla quiete A (nella <lb/>precedente figura) scenda perpendicolare infino in B, dove giunto, ora se&shy;<lb/>guiti per la sua prima dirittura BC, ora s'infletta secondo BD, terminando <lb/>in ambedue i casi il viaggio nella medesima orizzontale DC: si vuol sapere <lb/>in qual proporzione stiano i tempi delle due scese. </s>

<s>Rispondesi a ci&ograve; con la <lb/>seguente, cos&igrave; da Galileo proposta e dimostrata: </s></p><p type="main">

<s>PROPOSITIO XIII. &mdash; &ldquo; Fiat motus per ABC, et per duas AB, BD: sit <lb/>RA media inter CA, AB, et ipsi DC parallela ducatur RS: Dico iam tem&shy;<lb/>pus per ABC, ad tempus per ABD, esse ut linea AC, ad lineam AR cum SD. &rdquo; </s></p><p type="main">

<s>&ldquo; Si enim protrahatur BD usque ad occursum cum AF, horizonti DC <lb/>parallela, erit FS media inter DF, FB. Et, ut CA ad AR, ita tempus per <lb/>CA, ad tempus per AB: ita ut, si ponatur AC tempus per AC, erit AR <lb/>tempus per AB, et RC tempus per BC. &rdquo; (In fatti CA:AR=T.oAC:T.oAB. </s>

<s><lb/>Ma tempo AC uguale AC, dunque AR=T.oAB. </s>

<s>Di pi&ugrave; AR=AC&mdash;RC= <lb/>T.oAC&mdash;RC:dunqueT.oAC&mdash;T.oAB=RC. </s>

<s>Or perch&egrave; T.oAC&mdash;T.oAB= <lb/>T.oBC, sar&agrave; dunque, come Galileo ha concluso, T.oBC=RC). &ldquo; Et sinili&shy;<lb/>ter SD demonstrabitur esse tempus per BD, post casum ex F, vel ex A, <lb/>ex quo patet tempus per totam AC, ad tempus per duas ABD, esse ut AR <lb/>cum RC, ad AR cum SD &rdquo; (ibid., fol. </s>

<s>56). </s></p><p type="main">

<s>Altro caso, pi&ugrave; semplice di quello ora proposto, ma pi&ugrave; conducevole al <lb/>finale intendimento di questo trattato, era la proporzione dei tempi passati <lb/>dai gravi nello scendere per la flessura di due piani distinti, come per esem&shy;<lb/>pio, prima per AB (fig. </s>

<s>193) e poi per BC, ci&ograve; che Galileo fa in due varii <lb/>modi, dopo il primo dei quali si trova notato cos&igrave; nel Manoscritto: &ldquo; Huic <pb xlink:href="020/01/2123.jpg" pagenum="366"/>praemittenda videtur sequens propositio: Si linea, in qua fiat latio ex quiete, <lb/><figure id="id.020.01.2123.1.jpg" xlink:href="020/01/2123/1.jpg"/></s></p><p type="caption">

<s>Figura 193.<lb/>dividatur utcumque, tempus lationis prioris par&shy;<lb/>tis, ad tempus lationis secundae partis, est ut <lb/>ipsamet prima pars, ad excessum, quo eadem <lb/>pars superatur a media inter totam, et ipsam <lb/>primam partem &rdquo; (ibid., fol. </s>

<s>49). Questa, come <lb/>si sovverranno facilmente i nostri Lettori, &egrave; la <lb/>proposizione XI del trattato a stampa, di assai <lb/>facile conclusione dalla nota legge dei moti ac&shy;<lb/>celerati, che cio&egrave; i tempi stanno come le radici <lb/>degli spazi. </s>

<s>Abbiamo infatti nel presente caso <lb/>T.oEB:T.oBC=EB:&radic;EB.BC=EB:&radic;(EB(CE&mdash;EB)), ch'esprime in <lb/>cifra quel che intendeva Galileo di dire col suo discorso. </s>

<s>Questa proposizione <lb/>poi, che &egrave; come si &egrave; detto l'XI del trattato a stampa, non fu solamente pre&shy;<lb/>messa, ma sostituita alla seguente manoscritta: </s></p><p type="main">

<s>PROPOSITIO XIV. &mdash; &ldquo; Fiat latio per plana inflexa AB, BC (in praece&shy;<lb/>denti figura) et invenienda sit ratio temporis casus per AB, ad tempus ca&shy;<lb/>sus per BC, post casum AB. &rdquo; </s></p><p type="main">

<s>&ldquo; Ducatur horizontalis AE, cui CB producta occurrat in E, et ipsarum <lb/>CE, EB media sit ED. </s>

<s>Dico tempus per AB, ad tempus per BC, esse ut AB <lb/>ad BD. &rdquo; </s></p><p type="main">

<s>&ldquo; Tempus enim per AB, ad tempus per EB, est ut AB ad EB: tem&shy;<lb/>pus vero per EB, ad tempus per BC, est ut EB ad BD: ergo tempus per <lb/>AB, ad tempus per BC, est ut AB ad BD, quod erat demonstrandum &rdquo; <lb/>(ibid., fol. </s>

<s>49). </s></p><p type="main">

<s>La medesima proposizione si trova cos&igrave; altrimenti dimostrata, ed &egrave;, tra <lb/><figure id="id.020.01.2123.2.jpg" xlink:href="020/01/2123/2.jpg"/></s></p><p type="caption">

<s>Figura 194.<lb/>le notabili differenze, da osservar la forma teo&shy;<lb/>rematica, sostituita alla problematica. </s></p><p type="main">

<s>&ldquo; Sit FG (fig. </s>

<s>194) horizontalis, et ex su&shy;<lb/>blimi A fiat motus per ABF, et, protracta AB <lb/>usque ad D, sit media inter DA, AB ipsa AC, <lb/>et horizonti aequidistans sit CE: Dico tempus <lb/>per AB, ad tempus per BF, esse ut AB, ad BE. &rdquo; </s></p><p type="main">

<s>&ldquo; Nam tempus per AB, ad tempus per BD, <lb/>est ut AB ad BC. </s>

<s>Tempus vero per BD, post AB, <lb/>ad tempus per BF, post AB, est ut BD ad BF, <lb/>idest BC ad BE. Ergo, ex aequali, tempus per AB, ad tempus per BF, est <lb/>ut AB ad BE &rdquo; (ibid., fol. </s>

<s>126). </s></p><p type="main">

<s>Sarebbe stato il soggetto, senza dubbio, di altre simili esplicazioni fe&shy;<lb/>condo, le quali per&ograve;, se conferivano ad aggiungere una lussuriosa ricchezza <lb/>alla Scienza del moto, avrebbero divagato l'Autore dal suo principale intento, <lb/>e perci&ograve;, coi Lemmi geometrici preparatorii, e con la proposizione X del <lb/>primo, si chiudeva da Galileo anche questo terzo Trattato manoscritto. </s></p><pb xlink:href="020/01/2124.jpg" pagenum="367"/><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Dicemmo come fossero le proposizioni, da noi sopra ordinate in forma <lb/>di trattato, dimostrate interrottamente da Galileo, in certe ore di quiete dai <lb/>travagli dell'animo, e di riposo dallo studio delle cose celesti, quando nel 1630, <lb/>ritiratosi in pace solitaria nell'amena suburbana villa di Bellosguardo, an&shy;<lb/>nunziava agli amici, come a Niccol&ograve; Aggiunti &ldquo; l'acquisto conseguito nella <lb/>Scienza del moto &rdquo; (Alb. </s>

<s>IX, 215). Abbiamo di un tale acquisto, che si do&shy;<lb/>veva essere steso a vario, e pi&ugrave; largo soggetto, un documento curioso nelle <lb/>stesse carte galileiane, e particolarmente nella 78a e nella 93a del citato vo&shy;<lb/>lume, sulla prima delle quali leggesi, a quel modo che fu data alle stampe, <lb/>la proposizione XXIX manoscritta sul tergo di una lettera, indirizzata all'Au&shy;<lb/>tore il d&igrave; 10 di Gennaio di quell'anno 1630, da un amico, per invitarlo a <lb/>pranzo nella sua prossima villa delle Rose; e la proposizione XXXIV, scritta <lb/>pure dalla propria mano di Galileo, sul rovescio di quell'altra carta citata, <lb/>che &egrave; una lettera indirizzatagli di que'giorni da un signore della famiglia <lb/>Galletti. </s></p><p type="main">

<s>Mentre cos&igrave; attendeva all'opera di esplicar meglio il trattato, e dai primi <lb/>e principali teoremi dedurre le conseguenze o pi&ugrave; curiose o pi&ugrave; importanti, <lb/>era venuto il tempo di raccogliere finalmente i materiali dispersi, e nel corso <lb/>di quasi trent'anni gi&agrave; preparati, per dar mano a costruire il nuovo pre&shy;<lb/>meditato edifizio. </s>

<s>Tre abbiamo veduto essere stati i disegni, che vuol ora <lb/>Galileo prendere in esame, per elegger quello, che sar&agrave; giudicato meritevole <lb/>di essere esposto alla pubblica vista. </s>

<s>Procedevano i primi due in perfetta <lb/>regola, senz'altre supposizioni, da quelle in fuori che il comun senso appro&shy;<lb/>verebbe come verit&agrave; per s&egrave; chiare e naturali, e si poneva al terzo per fon&shy;<lb/>damento un supposto, che l'Autore stesso credeva, se non necessario, al&shy;<lb/>meno utile il dimostrarlo. </s>

<s>Il motivo di questo, che fu per comune giudizio <lb/>un progredire in peggio, si disse essere stato il dubbio se, dalle propriet&agrave; <lb/>dei moti equabili si potessero legittimamente concludere quelle dei moti ac&shy;<lb/>celerati; dubbio che fece lasciare a Galileo la diritta via regia, come cavallo <lb/>che subito adombra. </s></p><p type="main">

<s>Poi s'ebbe a persuader del suo inganno, specialmente quando rivolse <lb/>l'attenzione sopra quel teorema, che lasci&ograve; nel foglio 163 manoscritto, e che <lb/><figure id="id.020.01.2124.1.jpg" xlink:href="020/01/2124/1.jpg"/></s></p><p type="caption">

<s>Figura 195.<lb/>fu collocato in ordine il XXV nella serie delle <lb/>proposizioni, che compongono il trattato a stampa. </s>

<s><lb/>Succedendo il moto equabile per la orizzontale CF <lb/>(fig. </s>

<s>195) al moto accelerato per l'obliqua AB, e <lb/>per la perpendicolare AC, se BE sia la met&agrave; di <lb/>AB, e DC la met&agrave; di AC, si ha per quella XXV <lb/>proposizione T.oAB:T.oEB=AB:EB; T.oAC:T.oDC=AC:DC. </s></p><pb xlink:href="020/01/2125.jpg" pagenum="368"/><p type="main">

<s>Se si supponga ora che in B e in C le velocit&agrave; siano uguali, i tempi <lb/>dei moti per la orizzontale CF staranno come gli spazi, e perci&ograve; dall'essere <lb/>essi tempi equabilmente passati per le EB, DC come le linee stesse EB, DC, <lb/>vedeva Galileo venir legittimamente conclusa, dalle due soprascritte propor&shy;<lb/>zioni, la proposizione fondamentale, che cio&egrave;, come le linee AB, AC stanno <lb/>pure i tempi dei moti, per quelle stesse linee accelerati. </s></p><p type="main">

<s>Che fossero veramente tali i pensieri, passati per la mente di Galileo, <lb/>e in virt&ugrave; dei quali ebbesi a ravveder del suo inganno, oltre a quel che si <lb/>legge nel III Dialogo, dopo la III proposizione, si conferma dalla seguente <lb/>Nota rimastaci manoscritta: </s></p><p type="main">

<s>&ldquo; Spatia motus accelerati ex quiete, et spatia motuum aequabilium, ad <lb/>motus acceleratos consequentia, et temporibus iisdem confecta, eamdem inter <lb/>se retinent rationem. </s>

<s>Sunt enim haec spatia dupla illorum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Tempora vero et gradus velocitatum acquisitarum eamdem inter se <lb/>habent rationem. </s>

<s>Haec enim ratio subdupla est rationis spatiorum dictorum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Spatia motus accelerati AB, AC (fig. </s>

<s>196), motuum aequabilium con&shy;<lb/>sequentium BE, CD, eamdem cum illis habent rationem: sunt enim dupla <lb/><figure id="id.020.01.2125.1.jpg" xlink:href="020/01/2125/1.jpg"/></s></p><p type="caption">

<s>Figura 196.<lb/>illorum. </s>

<s>Tempora per AB, AC sunt inter se ut gradus <lb/>velocitatis in B et in C. </s>

<s>Ratio vero haec subdupla est <lb/>rationis BA ad AC, vel BE ad CD &rdquo; (ibid., fol. </s>

<s>79 ad t.). </s></p><p type="main">

<s>A confermare anche in altro modo le corrispondenze <lb/>tra i moti equabili e gli accelerati, sembra che fosse preso <lb/>a dimostrare da Galileo quest'altro teorema, diligente&shy;<lb/>mente copiatoci dal Viviani, e di cui s'ha l'auttentica <lb/>copia nel Volume che citeremo. </s>

<s>Leggesi ivi cos&igrave;: &ldquo; Dei <lb/>moti fatti in tempi eguali, gli spazi stanno come le velocit&agrave;; Dei fatti con <lb/>velocit&agrave; uguale, gli spazi stanno come i tempi; Dei fatti in spazi eguali, le <lb/>velocit&agrave; risponderanno contrariamente ai tempi &rdquo; (MSS. Gal., P. V, T. IV, <lb/>fol. </s>

<s>5). </s></p><p type="main">

<s>Son queste, cos&igrave; annunziate proposizioni, le prime da Galileo stesso di&shy;<lb/>mostrate nel primo libro Dei moti locali, di facile conseguenza dal principio, <lb/>per s&egrave; evidente, che cio&egrave; un moto si dice essere tanto pi&ugrave; veloce, quanto <lb/>&egrave; pi&ugrave; corto il tempo, e lo spazio &egrave; pi&ugrave; lungo. </s>

<s>Chiamate perci&ograve; V, S, T; <lb/><emph type="italics"/>v, s, t<emph.end type="italics"/> due diverse velocit&agrave;, due diversi spazi, e due tempi diversi, vien quello <lb/>stesso principio espresso dalle formule V=S:T; <emph type="italics"/>v=s:t<emph.end type="italics"/>, dalle quali, se <lb/>S=<emph type="italics"/>s,<emph.end type="italics"/> immediatamente si conclude la terza delle proposizioni sopra enun&shy;<lb/><figure id="id.020.01.2125.2.jpg" xlink:href="020/01/2125/2.jpg"/></s></p><p type="caption">

<s>Figura 197.<lb/>ciate, che cio&egrave;, essendo gli spazi uguali, le velocit&agrave; ri&shy;<lb/>spondono contrariamente ai tempi. </s></p><p type="main">

<s>Ma Galileo trov&ograve; che potevansi cos&igrave; le medesime <lb/>cose dimostrare dal principio dei moti accelerati nel <lb/>perpendicolo AB (fig. </s>

<s>197), e nell'inclinata AC, sopra <lb/>la quale si prenda una lunghezza AE uguale ad AB. </s>

<s><lb/>Chiamata M la media tra AC, AE, s'hanno, per le note <lb/>leggi dei moti accelerati, le due proporzioni T.&prime;AB:T.oAE=AE:M; <pb xlink:href="020/01/2126.jpg" pagenum="369"/>V.aAE:V.aAC=AE:M. Ond'e che, supposto V.aAC=V.aAB, immediata&shy;<lb/>mente se ne conclude di qui T.oAB:T.oAE=V.aAE:V.aAB, come in&shy;<lb/>tendeva Galileo stesso di dimostrare con questo suo pi&ugrave; lungo discorso. </s></p><p type="main">

<s>&ldquo; Posta la parte AE eguale alla AB, il tempo per AB, al tempo per AC, <lb/>sta come AB ad AC, cio&egrave; AE ad AC. </s>

<s>Ma come il tempo per AE, al tempo <lb/>per AC, cos&igrave; la media tra le AE, AC alla AC; dunque, come il tempo per <lb/>AB, al tempo per AE, cos&igrave; la AB, cio&egrave; la AE, alla detta media. </s>

<s>Ma, come <lb/>la velocit&agrave; per AC, alla velocit&agrave; per AE, cos&igrave; la medesima media alla AE; <lb/>adunque, la velocit&agrave; per AB, che &egrave; la medesima che la velocit&agrave; per AC, alla <lb/>velocit&agrave; per AE, sta come la AE a quella medesima. </s>

<s>Adunque &egrave; manifesto <lb/>che i tempi per le uguali AB, AE rispondono contrariamente alle velocit&agrave; <lb/>per le medesime, il che bisognava dimostrare &rdquo; (ivi). </s></p><p type="main">

<s>Restavano di qui confermate le verit&agrave;, da Galileo espresse nel ragiona&shy;<lb/>mento illustrato dianzi dalla figura 195, che cio&egrave; i moti equabili e gli acce&shy;<lb/>lerati serbano la medesima proporzione fra gli spazi e i tempi, ond'&egrave; che <lb/>veniva tolta di qui ogni ombra a quel dubbio, che lo aveva fatto arretrare, <lb/>e che lo avea consigliato, ai dimostrati teoremi, di sostituire un supposto <lb/>bisognoso di dimostrazione. </s></p><p type="main">

<s>Nel metter dunque in ordine le proposizioni, che dovevano comporre il <lb/>trattato da inserirsi nel III Dialogo, per dar finalmente alla luce la nuova <lb/>Scienza del moto, si crederebbe che, ripresa la fiducia antica del Teorema <lb/>meccanico, volesse Galileo ritornar sulla dirittura della prima via abbando&shy;<lb/>nata, dimostrativamente concludendo da quello stesso Teorema la proposi&shy;<lb/>zione fondamentale delle proporzionalit&agrave; fra i tempi e gli spazi, nei declivi <lb/>ugualmente elevati, a quel modo che aveva fatto nel II Libro, immeritata&shy;<lb/>mente repudiato, e dove tutto, in bel geometrico modo, si dimostrava senza <lb/>alcuna temeraria supposizione. </s></p><p type="main">

<s>Eppure i primi, ch'ebbero fra mano il volume stampato in Leyda, tro&shy;<lb/>varono la proposizione III, dimostrata col principio supposto, quale fu co&shy;<lb/>municato a Luca Valerio, condotta in sostanza a quel modo, che la III del <lb/>III Libro, se non che nel metodo degl'Indivisibili si rendeva pi&ugrave; ferma, e <lb/>si riduceva pi&ugrave; esatta. </s>

<s>Per segno poi della fatta riconciliazione col Teorema <lb/>meccanico non rimaneva altro che la VI proposizione, nella quale, fra i varii <lb/>modi di dimostrare il tautocronismo delle scese per le corde dei cerchi, si met&shy;<lb/>teva in secondo luogo anche quello derivato <emph type="italics"/>ex mechanicis.<emph.end type="italics"/> (Alb. </s>

<s>XIII, 182). </s></p><p type="main">

<s>L'elezione insomma, fra i tre tentati disegni del trattato Dei moti lo&shy;<lb/>cali, cadde per Galileo sul III, a cui pose per fondamenti, come vedemmo, <lb/>i teoremi dimostrativi delle leggi dei moti accelerati, e il supposto che, in <lb/>uguali discese rette, le velocit&agrave; dei cadenti, per qualunque declivio, sono <lb/>uguali. </s>

<s>Riconobbe pur troppo anche da s&egrave; stesso Galileo l'imprudenza dello <lb/>stabilire il fondamento alla sua Scienza nuova sopra un principio non certo, <lb/>e in margine alla proposizione III del III Libro, nella quale faceva la prima <lb/>applicazione del detto supposto, scrisse, appellando alla relativa figura, che <lb/>per noi &egrave; la 181, &ldquo; credo esse utile, si non necessarium, demonstrasse mo-<pb xlink:href="020/01/2127.jpg" pagenum="370"/>bile in D esse eiusdem momenti, quod in E &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>88). <lb/>Ma si ridusse tutta quella dimostrazione nel fatto sperimentale dei pendoli, <lb/>che risalgono alla medesima altezza orizzontale, da cui furono scesi. (Alb. </s>

<s><lb/>XIII, 164, 65). </s></p><p type="main">

<s>Delle proposizioni, che compongono il terzo trattato manoscritto, non ne <lb/>fu nello stampato lasciata addietro nessuna nella sostanza, ma furono quasi <lb/>tutte rifuse. </s>

<s>Talvolta un teorema si umilia al grado di corollario, e tal altra <lb/>un corollario si esalta alla dignit&agrave; di teorema. </s>

<s>Non sempre per&ograve;, in cos&igrave; fare, <lb/>si riducono le cose in meglio, giudice il Viviani, il quale avrebbe voluto ve&shy;<lb/>der trattata, per esempio, la proposizione VI, stampata, in altro modo, e non <lb/>sapendo nulla del corollario alla V proposizione del III libro manoscritto, e <lb/>credendo che avesse Galileo per inavvertenza cos&igrave; lasciate le cose in difetto, <lb/>vi suppl&igrave; di suo in una Nota, che l'Alb&egrave;ri pubblic&ograve; a pag. </s>

<s>184 del citato <lb/>Tomo XIII. </s></p><p type="main">

<s>Anche la proposizione VIII del II Libro, bench&egrave; solennemente promessa <lb/>nel I dialogo Dei due massimi sistemi (Alb. </s>

<s>I, 32), non apparisce esplicita <lb/>nel III dialogo Delle scienze nuove, bench&egrave; si derivi per facile corollario <lb/>dalla IX, stampata in quel Dialogo stesso. </s></p><p type="main">

<s>Le proposizioni principali hanno, anco in questo stampato, quei tre cen&shy;<lb/>tri evolutivi da noi notati nel III Libro, e dai quali sembrava si dovesse far <lb/>dipendere la bene ordinata serie dei teoremi, ma Galileo non sempre osserva <lb/>quest'ordine. </s>

<s>Si direbbe anzi che non osserva ordine alcuno, nel distribuire <lb/>le parti accessorie e le mediane del suo trattato, e quel lasciare un soggetto, <lb/>per passare a un altro, e poi tornare ancora indietro sopra quel primo, fu <lb/>una delle precipue ragioni, per cui parvero le dimostrate cose, specialmente <lb/>ad alcuni poco benevoli, oscure e prolissamente noiose. </s></p><p type="main">

<s>Prese giusto da questa prolissit&agrave; motivo il Cartesio di dire che non ebbe <lb/>la pazienza di leggere le galileiane dimostrazioni, bench&egrave;, pur cos&igrave; come <lb/>stavano, avesse fiducia che fossero vere. </s>

<s>&ldquo; De geometricis demonstrationi&shy;<lb/>bus, quibus liber eius refertus est, scriveva cos&igrave; del libro di Galileo in una <lb/>delle sue Epistole al Mersenno, nihil dico; non enim potui a me impetrare ut <lb/>illas legerem, et quidem crediderim veras esse omnes &rdquo; (Pars. </s>

<s>II cit., pag. </s>

<s>244). <lb/>In semplicemente legger per&ograve; l'enunciato dei varii proposti teoremi disse di <lb/>avervi questo notato come certo, che non era cio&egrave; punto necessario essere <lb/>un gran Geometra per ritrovarli, e che non s'andava, nel condurre il ra&shy;<lb/>gionamento, per le vie pi&ugrave; spedite. </s>

<s>&ldquo; Hoc enim observavi, propositiones inspi&shy;<lb/>ciendo, non esse opus ut quisquam sit magnus Geometra ad illas invenien&shy;<lb/>das &rdquo; (ibid.). </s></p><p type="main">

<s>Il giudizio &egrave; forse uno dei pi&ugrave; giusti, che uscissero dalla mente del <lb/>Cartesio, perch&egrave;, appetto alla Geometria, cos&igrave; largamente promossa da lui, <lb/>questa di Galileo doveva sembrare una esercitazione da scolaretti. </s>

<s>Ma &egrave; a <lb/>pensar che il Trattato galileiano, uscito alla pubblica luce nel 1638, e dal <lb/>Cartesio stesso letto qualche anno dopo, s'era incominciato a comporre nei <lb/>princiqii del secolo, quando la Geometria non conosceva altri promotori che <pb xlink:href="020/01/2128.jpg" pagenum="371"/>il Commandino, il Valerio, e Guidubaldo. </s>

<s>Si dovrebbero dunque i teoremi, <lb/>scritti nel III dialogo delle due Nuove scienze, paragonare con quelli dimo&shy;<lb/>strati da cos&igrave; fatti Autori, e non con gli altri, che poterono, quarant'anni <lb/>dopo, venir sublimati sulle ali della nuova analisi cartesiana. </s>

<s>Istituito da que&shy;<lb/>sta parte il confronto, non par che Galileo rimanga di gran lunga inferiore <lb/>ai Matematici, che lo avevano preceduto. </s>

<s>Si direbbe anzi che gli avanza per <lb/>una certa elegante facilit&agrave;, come si pu&ograve; argomentare da alcuni esempi di <lb/>teoremi puramente geometrici, nei quali s'incontr&ograve; pi&ugrave; volte l'Autore, cer&shy;<lb/>cando i mezzi alle sue meccaniche dimostrazioni. </s></p><p type="main">

<s>Ripensando alle propriet&agrave; geometriche delle linee, tessenti la figura, <lb/>sopra la quale erasi dimostrato il corollario alla XI del III libro, vide sca&shy;<lb/>turirne questo teorema: che cio&egrave; la corda esterna, dalla estremit&agrave; della quale <lb/>sia condotta una perpendicolare al diametro, &egrave; media proporzionale fra la <lb/><figure id="id.020.01.2128.1.jpg" xlink:href="020/01/2128/1.jpg"/></s></p><p type="caption">

<s>Figura 198.<lb/>corda interna tutta intera, e il segmento di lei rimasto tra <lb/>la sommit&agrave; del cerchio, e la perpendicolare stessa interse&shy;<lb/>cante. </s>

<s>Cos&igrave;, come aveva riconosciuto una tale geometrica <lb/>propriet&agrave;, con le ragioni di lei, Galileo notava, in mezzo ai <lb/>Teoremi di Meccanica, nel suo manoscritto: &ldquo; AB (fig. </s>

<s>198) <lb/>est media inter CA, AD, nam rectangulus CAD aequatur <lb/>rectangulo HAG. </s>

<s>Si enim ducatur HC, erit triangulus ACH <lb/>simile triangulo ADG &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>35). </s></p><p type="main">

<s>Quest'altre geometriche relazioni deve averle ricono&shy;<lb/>sciute Galileo, in mezzo alle proposizioni di Meccanica, di&shy;<lb/>mostrative dei tempi delle scese per le corde dei cerchi, e <lb/>dop'avere, in testa al foglio 58 del citato volume, notato <emph type="italics"/>haec non est motus <lb/>materia,<emph.end type="italics"/> cos&igrave; soggiunge: &ldquo; Sit IC (fig. </s>

<s>199) perpendicularis ad diametrum <lb/>circuli AB, ductaque a puncto A quaecumque linea circumferentiae et per&shy;<lb/><figure id="id.020.01.2128.2.jpg" xlink:href="020/01/2128/2.jpg"/></s></p><p type="caption">

<s>Figura 199.<lb/>pendiculari CI occurrens, ut AID, <lb/>AD, ADI, dico rectangulum DAI rec&shy;<lb/>tangulo BAC esse aequale. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si enim iungatur recta DB, <lb/>erit angulus in semicirculo, ad pun&shy;<lb/>ctum D, rectus, estque angulus C <lb/>quoque rectus, communis autem an&shy;<lb/>gulus ad A. </s>

<s>Ergo triangulorum ae&shy;<lb/>quiangulorum DAB, CAI latera erunt <lb/>proportionalia, utque BA ad AD, ita <lb/>IA ad AC. </s>

<s>Ergo patet propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s>Si riferisce probabilmente alla <lb/>medesima origine quest'altro teo&shy;<lb/>rema di Geometria, cos&igrave; proposto <lb/>da Galileo e cos&igrave; dimostrato: &ldquo; Sit circulus, cuius diameter AB (fig. </s>

<s>200) <lb/>et ipsi parallela tangens CE, et ex termino B quaelibet linea BO in circulo <lb/>applicetur. </s>

<s>Dico perpendiculares, quae a termino B et O, ipsi BO, accomo-<pb xlink:href="020/01/2129.jpg" pagenum="372"/>dantur, protractas, de linea CE partem, diametro circuli aequalem, semper <lb/><figure id="id.020.01.2129.1.jpg" xlink:href="020/01/2129/1.jpg"/></s></p><p type="caption">

<s>Figura 200.<lb/>intercipere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Jungantur enim A, O, et extendatur ad <lb/>tangentem in F, quae ad BO erit perpendicularis, <lb/>cui ex B parallela sit BE: demonstrandum FE <lb/>diametro circuli esse aequalem. </s>

<s>Id autem constat, <lb/>quia in parallelogrammo ABEF latera AB, FE <lb/>opposita aequalia sunt, ex Elementis. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Vel dicas quod ducta, ex O, OG parallela <lb/>ipsi AB, et BG perpendiculari ad BO, abscindet <lb/>semper OG aequalis diametro circuli, quod patet <lb/>ex triangulis AOB, OBG similibus, et aequali&shy;<lb/>bus &rdquo; (ibid., fol. </s>

<s>68). </s></p><p type="main">

<s>Ritornando al Cartesio, e ai giudizi di lui <lb/>scritti in confidenza al Mersenno, &egrave; da osservare <lb/>di pi&ugrave; che, nei teoremi galileiani, non si tratta <lb/>di semplice Geometria pura, ma di Geometria <lb/>applicata alla Scienza del moto, ci&ograve; che impor&shy;<lb/>tava un assai maggiore difficolt&agrave;, per esser cose, <lb/>delle quali i predecessori o non ne avevano dati <lb/>alcuni o pochissimi esempi. </s>

<s>Di qui &egrave; che spesso, <lb/>per assicurarsi meglio delle verit&agrave; di quelle nuove conclusioni, riduceva Ga&shy;<lb/>lileo le astratte generalit&agrave; ai casi concreti, e invocava l'Aritmetica a far ri&shy;<lb/>scontro colla Geometria. </s>

<s>Cos&igrave; fatte applicazioni ricorrono nel citato mano&shy;<lb/>scritto galileiano frequenti, ond'&egrave; che pi&ugrave; volte occorse all'Autore, anche <lb/>in mezzo a cos&igrave; fatti aritmetici esercizi, di ritrovare alcuni teoremi nuovi, <lb/>e nella loro semplicit&agrave; eleganti. </s>

<s>Tale sarebbe per esempio il seguente, cos&igrave; <lb/>formulato al foglio 35: &ldquo; In numeris, ab unitate consequentibus, summa <lb/>cuiuslibet multitudinis, ad aliam summam alterius multitudinis, si ab utra&shy;<lb/>que dimidium maximi numeri auferatur, est ut quadratum multitudinis unius <lb/>ad quadratum alterius multitudinis. </s>

<s>&rdquo; </s></p><p type="main">

<s>Per la dimostrazione per&ograve; non si fa dell'Algebra altr'uso, che in appa&shy;<lb/>renza, chiamando <emph type="italics"/>ab<emph.end type="italics"/> la somma dei numeri in serie naturale, da 1 a 8, e <lb/><emph type="italics"/>ac<emph.end type="italics"/> la somma di un'altra simile serie, da 1 a 6, e notando che il Teorema <lb/>generale formulato si verifica esattamente nelle particolarit&agrave; del preso esem&shy;<lb/>pio numerico. </s>

<s>&ldquo; Summa enim <emph type="italics"/>ab<emph.end type="italics"/> est 36: ablato dimidio 8, remanet 32. <lb/>Summa <emph type="italics"/>ac<emph.end type="italics"/> est 21: ablato dimidio 6, remanet 18. Et 32 ad 18 est ut qua&shy;<lb/>dratum multitudinis <emph type="italics"/>ab,<emph.end type="italics"/> nempe 64, ad quadratum multitudinis <emph type="italics"/>ac,<emph.end type="italics"/> quod <lb/>est 36 &rdquo; (ibid.). </s></p><p type="main">

<s>Sia pure che, per ritrovare cos&igrave; fatti Teoremi di Geometria e di Aritme&shy;<lb/>tica, non ci fosse bisogno di essere gran Matematici, ma non poteva il Car&shy;<lb/>tesio negare che non fosse Galileo stato il primo ad applicare la Geometria <lb/>e l'Aritmetica a quel modo, per dimostrare le nuove propriet&agrave; e i varii e <lb/>complicati effetti del moto. </s></p><pb xlink:href="020/01/2130.jpg" pagenum="373"/><p type="main">

<s>Un'altra delle ragioni, per cui non piaceva al Cartesio stesso quel trat&shy;<lb/>tato galileiano, era perch&egrave;, nel dimostrar quei tanti teoremi, non teneva le <lb/>vie pi&ugrave; compendiose. </s>

<s>&ldquo; Observavi eum maxime compendiosas vias non <lb/>sectari &rdquo; (Epist. </s>

<s>cit., pag. </s>

<s>244). E anche questo giudizio cartesiano &egrave; vero, <lb/>suffragato da quello degli stessi nostri Lettori, i quali avranno gi&agrave; fatto in <lb/>s&egrave; medesimi il confronto fra la elegante snellezza delle dimostrazioni, stese <lb/>nei tre libri manoscritti, con quelle date a stampa uggiosamente pesanti. </s></p><p type="main">

<s>Il Salviati, cos&igrave; nell'attuale occasione del ragionare, come nel riferire <lb/>le cose gi&agrave; prima ragionate, aveva da una parte riguardo ai Sagredi, i quali <lb/>si sarebbero potuti facilmente condurre per le vie compendiose, ma ripen&shy;<lb/>sava dall'altra ai Simplicii, che avendo le gambe deboli e corte conveniva <lb/>condur per le vie piane, e perci&ograve; inevitabilmente pi&ugrave; lunghe. </s>

<s>E perciocch&egrave;, <lb/>non al Cartesio solo, ma a tutti i Matematici rappresentati in Gian Fran&shy;<lb/>cesco Sagredo, si vede che sarebbero piaciute meglio le dimostrazioni, quali <lb/>uscirono di primo getto, che non le rifatte per la stampa (inutili del resto <lb/>ai Simplicii, ai quali, per quanto fosse sminuzzato, rimarrebbe sempre quel <lb/>solido cibo indigesto) crediamo di aver fatto cosa grata ai sopraddetti Mate&shy;<lb/>matici, e di avere anche in parte provveduto alla gloria di Galileo, nel dare <lb/>alla luce i tre libri <emph type="italics"/>De motu,<emph.end type="italics"/> nelle loro forme originali. </s></p><p type="main">

<s><emph type="center"/>VI.<emph.end type="center"/></s></p><p type="main">

<s>Il trattato Dei moti locali, intorno a cui ha avuto occasione d'intrat&shy;<lb/>tenersi fin qui lungamente la nostra Storia, contiene in s&egrave;, e rappresenta <lb/>una di quelle due scienze, che Galileo era solito chiamare col titolo di nuove. </s>

<s><lb/>Molti, che questo titolo gli concessero cecamente, crederono, e l'Autore stesso <lb/>si studi&ograve; con arte di confermarli in quella loro opinione, che cio&egrave; s'avessero <lb/>tali novit&agrave; a intendere in senso assoluto, quasi che si fossero alle insegnate <lb/>dottrine posti i principii, oltre all'averne svolte le conseguenze. </s>

<s>Dicemmo <lb/>altrove come fosse questa una vana lusinga, e una incredibile presunzione, <lb/>confortando il nostro detto coi fatti, dai quali ci venne dimostrato aver avuto <lb/>la scienza del moto, nel secolo XVI, certezza di principii, e speranza lieta <lb/>di futuri progressi. </s></p><p type="main">

<s>Il seme, da cui germin&ograve; la scienza di Galileo, vedemmo essere stato il <lb/>Teorema meccanico del Tartaglia: e perciocch&egrave; s'era a comun benefizio, per <lb/>mezzo del libro dei <emph type="italics"/>Quesiti e inventioni,<emph.end type="italics"/> un tal fecondo seme largamente <lb/>disperso, non pareva credibile ne dovesse nascere un filo solo. </s>

<s>Vero &egrave; che, <lb/>come spesso avviene ai seminatori del campo, un granello va a cader sulla <lb/>pietra, e se lo beccano gli uccelli dell'aria: un'altro cade in terra mal fon&shy;<lb/>data, e germoglia, ma poi presto, per mancanza di umore, si secca, cosic&shy;<lb/>ch&egrave; quello solo, che va a cadere in ben disposto terreno, nasce e cresce e <lb/>matura nella spiga. </s></p><pb xlink:href="020/01/2131.jpg" pagenum="374"/><p type="main">

<s>Cos&igrave; fatte buone disposizioni, dal figurato passando al senso proprio, <lb/>non si debbono tanto intender dipendere dalle qualit&agrave; della mente, quanto <lb/>dal fine accidentale, che s'erano proposti di conseguire gli Autori, per al&shy;<lb/>cuni dei quali riducevasi tutto quel fine in promovere in qualche modo il <lb/>teorema del Tartaglia, mentre Galileo, essendosi prefisso per termine il bra&shy;<lb/>chistocronismo degli archi rispetto alle corde, dovette necessariamente pas&shy;<lb/>sare per la lunga e ordinata serie delle proposizioni intermedie. </s></p><p type="main">

<s>Di qui avvenne ch'essendo, nelle poche menti disposte a riceverlo e a <lb/>fecondarlo, medesimo il seme, uno dei grani spunt&ograve; appena: o come si vuol <lb/>dire in senso proprio non fu da qualche Autore promosso il Teorema mec&shy;<lb/>canico oltre alle sue prime conseguenze, mentre ebbe per qualche altro uno <lb/>svolgimento assai pi&ugrave; largo, bench&egrave; lontano dal raggiunger l'estensione, a <lb/>cui fu ridotto da Galileo, il quale &egrave; perci&ograve;, nell'istituire la nuova scienza, <lb/>il maggiore, ma non il solo. </s>

<s>I concorrenti si riducono per noi a questi due <lb/>principali: a Claudio Beriguardi cio&egrave;, e a Giovan Batista Baliani, che, giu&shy;<lb/>dicati dai pi&ugrave; imitatori o emuli non solo, ma plagiari di Galileo, appariscono <lb/>ora innanzi alla Storia nella verit&agrave; del loro aspetto, in quanto rappresen&shy;<lb/>tano le varie disposizioni delle menti aperte a ricevere il seme della scienza, <lb/>che la provvida Mano superna sparge largamente, e diffonde per tutto l'aperto <lb/>campo sottoposto, e non in qualche chiuso e privilegiato orticello. </s></p><p type="main">

<s>Quando, nel VI della III parte dei <emph type="italics"/>Circoli pisani,<emph.end type="italics"/> si lesse che l'Autore <lb/>asseriva di aver dimostrato le propriet&agrave; del moto, nelle rette e nelle obli&shy;<lb/>que discese dei gravi, vent'anni prima che Galileo e il Torricelli avessero <lb/>pubblicato nulla intorno a quello argomento; molti se ne risero, avendo per <lb/>cosa impossibile che il losco Peripatetico fosse penetrato a veder tanto ad&shy;<lb/>dentro, quanto l'acuto Linceo. </s>

<s>Quando apparve in Genova il trattato <emph type="italics"/>De <lb/>motu naturali,<emph.end type="italics"/> in quel tempo medesimo, che in Leida si pubblicarono i <lb/>dialoghi Delle due nuove Scienze, sempre fermi costoro nel medesimo pen&shy;<lb/>siero, che cio&egrave;, a ricever le arcane rivelazioni della Scienza del moto, non <lb/>ci fosse altro cervello capace, che quello di Galileo, dissero che il Baliani <lb/>lo avea ricopiato. </s>

<s>E perch&egrave; non aveva ci&ograve; alcuna apparente verosimiglianza, <lb/>essendo le due pubblicazioni contemporanee, tennero per cosa certa che il <lb/>Genovese avesse avuto fra mano il trattato galileiano manoscritto, nonostante <lb/>che, del gratuito asserto, sia dimostrata la falsit&agrave; dalla storia narrata qui <lb/>addietro. </s>

<s>Se fosse mai stato a loro noto, avrebbero, del libro di Giovan Marco <lb/>Tedesco, fatto il medesimo commento, non avvedendosi che, cos&igrave;, male si <lb/>spiegava il fatto dipendente piuttosto da quella causa naturale, da noi sopra <lb/>proposta, che cio&egrave;, partendo Autori d'indole, di studii e di patria diversi dai <lb/>medesimi principii, dovevano necessariamente riuscire alle medesime conse&shy;<lb/>guenze, almeno pi&ugrave; prossime e pi&ugrave; immediate. </s>

<s>Ci&ograve; che si induce dalla ra&shy;<lb/>gione, vien confermato dal fatto che, consistendo quel principio, come pi&ugrave; <lb/>volte s'&egrave; detto, nel Teorema meccanico, e le immediate conseguenze di lui <lb/>riducendosi nel passar dai momenti alle velocit&agrave;, e da queste ai tempi; si <lb/>videro riscontrarsi inconsapevoli insieme, in tal processo dimostrativo, gli <pb xlink:href="020/01/2132.jpg" pagenum="375"/>Autori, come sconosciuti pellegrini che, tendendo a un medesimo luogo, si <lb/>incontrano per la medesima via. </s></p><p type="main">

<s>Il Beriguardi infatti, dop'aver dimostrato che il medesimo grave tanto <lb/><figure id="id.020.01.2132.1.jpg" xlink:href="020/01/2132/1.jpg"/></s></p><p type="caption">

<s>Figura 201.<lb/>&egrave; pi&ugrave; ponderoso nel perpendicolo BC (fig. </s>

<s>201) che nel <lb/>declivio AC, quanto la linea AC &egrave; maggiore di BC, con&shy;<lb/>sidera molto ragionevolmente che questo ponderar di&shy;<lb/>verso del medesimo globo, per la sola ragione del venir <lb/>collocato su due piani diversi, &ldquo; non videtur provenire <lb/>posse, nisi a virtute, qua celerius movetur per BC, <lb/>quam per AC, secundum permutatam laterum propor&shy;<lb/>tionem &rdquo; (Circuli pisani, editio 2a, Patavii 1660, pag. </s>

<s>310). <lb/>Di qui perci&ograve; ne conclude che, supposto esser AC tripla di BC, la velocit&agrave; <lb/>nella perpendicolare deve contrariamente esser tripla dell'altra nell'inclinata. </s></p><p type="main">

<s>Vede l'Autore, da una tal conclusione, derivarsi un corollario di tanta <lb/>importanza, che stabilisce il primo passo, da progredire oltre liberamente <lb/>per la scienza galileiana. </s>

<s>Se, come s'&egrave; supposto dianzi essere AC tripla di <lb/>BC, cos&igrave; suppongasi ora essere la stessa BC tripla di CD, partendosi il mo&shy;<lb/>bile dal punto C, dov'era in quiete, passer&agrave; i due spazi CB, CD nel mede&shy;<lb/>simo tempo. </s>

<s>Che se volesse, poi soggiunge, alcuno determinare graficamente <lb/>il punto D, non dovrebbe far altro che condurre da B, estremit&agrave; della perpen&shy;<lb/>dicolare, la normale DB all'inclinata, dalla qual normale si verrebbe a descri&shy;<lb/>vere il triangolo BCD, ch'essendo simile ad ABC darebbe AC:BC=BC:CD. </s></p><p type="main">

<s>Questa dimostrazione, condotta su particolari dati numerici, si ridur&shy;<lb/>rebbe assai facilmente alla sua generalit&agrave;, ragionando in un modo simile a <lb/>quello dell'Autore. </s>

<s>Imperocch&egrave;, chiamata V la velocit&agrave; per la perpendico&shy;<lb/>lare, <emph type="italics"/>v<emph.end type="italics"/> la velocit&agrave; per la inclinata, abbiamo V:<emph type="italics"/>v<emph.end type="italics"/>=AC:BC. </s>

<s>Per trovar <lb/>poi il punto D, dove sar&agrave; giunto il grave sull'obliqua, nel tempo che il me&shy;<lb/>desimo grave avrebbe passata la diretta BC, diremo ch'essendo i tempi <lb/>uguali debbon essere le velocit&agrave; proporzionali agli spazi, per cui, chiamata X <lb/>la lunghezza CD incognita, avremo V:<emph type="italics"/>v<emph.end type="italics"/>=BC:X, e perci&ograve; AC:BC= <lb/>BC:X. Ora, tirata da B la BD, perpendicolare ad AC, i triangoli simili ABC, <lb/>BCD danno AC:BC=BC:CD; dunque X=CD. </s></p><p type="main">

<s>Le meccaniche propriet&agrave; del circolo, che apparvero, come veramente <lb/>sono, maravigliose, scendevano dimostrate di qui per corollario immediato, <lb/>perch&egrave;, circoscritto al triangolo rettangolo DCB un mezzo cerchio, il tauto&shy;<lb/>cronismo, concluso per la precedente proposizione, veniva a riferirsi a CD, <lb/>come corda, e a CB come a diametro di quel medesimo cerchio. </s>

<s>Il Beri&shy;<lb/>guardi non accenna per verit&agrave; a questo progresso, che conduceva molto ad&shy;<lb/>dentro alla scienza galileiana Giovan Marco, il quale, dalla XIII sua propo&shy;<lb/>sizione dimostrativa dell'equidiuturnit&agrave; per la verticale e per l'inclinata, <lb/>ambedue prefinite dalla perpendicolare, che da quella giunge a questa; passa <lb/>a concluder, nella XV: &ldquo; Motus, ex eodem puncto, per lineas subtensas, <lb/>sunt aequales motus per diametrum eiusdem circuli &rdquo; (De prop. </s>

<s>motus cit., <lb/>fol. </s>

<s>23 ad t.). </s></p><pb xlink:href="020/01/2133.jpg" pagenum="376"/><p type="main">

<s>Vedemmo come fossero questi memorabili teoremi, nel primo Libro di <lb/>Galileo, ordinati a servire di Lemmi, per dimostrare il fondamento alla nuova <lb/>Dinamica, che cio&egrave; i tempi, nelle scese da uguali altezze, stanno come gli <lb/>spazi. </s>

<s>Ora, n&egrave; il Beriguardi n&egrave; Giovan Marco progredirono tant'oltre nelle <lb/>loro meccaniche speculazioni, rimanendosi di gran lunga indietro, non a Ga&shy;<lb/>lileo solo, ma al Baliani, il trattatello del quale procede nelle sue dimostra&shy;<lb/>zioni in un modo tanto simile a quello, che si osserva nel primo Manoscritto <lb/>galileiano, da dar qualche apparenza di verit&agrave; a quel che si diceva dianzi <lb/>calunnioso commento. </s>

<s>Se non che, farebbesi forse meglio a rassomigliare i <lb/>processi del Baliani a quelli del Torricelli, cos&igrave; nella eleganza dei modi, come <lb/>nell'elezione degli ordini dimostrativi. </s>

<s>Che se allo stesso Torricelli, in voler <lb/>render la scienza indipendente da qualunque ipotesi, occorse di ritornar sulle <lb/>tracce, e quasi indovinare i primi modi tenuti da Galileo, senz'averne ve&shy;<lb/>duti i Manoscritti, ma condottovi dalla logica dei pensieri; diciamo che que&shy;<lb/>sto stesso incontr&ograve; nello speculare al Baliani, cosicch&egrave; l'identit&agrave; dei profes&shy;<lb/>sati principii, e il comune studio di proseguire in Geometria le vie pi&ugrave; <lb/>compendiose, conducessero i due Autori alle conseguenze medesime nella <lb/>sostanza e nelle forme. </s></p><p type="main">

<s>Apriamo, per passar dalle parole ai fatti, il citato trattatello <emph type="italics"/>De motu <lb/>naturali,<emph.end type="italics"/> pubblicato la prima volta, nel 1638, dal Matematico genovese, e <lb/>troveremo, come principal cosa da notare, che mentre Galileo in principio <lb/>si fa Autore del Teorema meccanico, e poi lo repudia come sospetto; il Ba&shy;<lb/>liani lo riguarda come un vero matematico, o per dimostrazione o per na&shy;<lb/>turale evidenza, cos&igrave; chiaro, da scriversi in quarto luogo fra i postulati sotto <lb/>una tal forma: &ldquo; Momentum gravis super plano inclinato est ad ipsius gra&shy;<lb/>vitatem ut perpendicularis ad inclinatam, si ab eodem puncto ducta sint ad <lb/>idem planum orizontale dicta perpendicularis et dictum planum inclinatum, <lb/>et proinde tali casu proportio gravitatis ad momentum est reciproca propor&shy;<lb/>tione linearum super quibus grave movetur &rdquo; (De motu natur., edizio 2a, <lb/>Genuae 1646, pag. </s>

<s>15, 16). Da questo, e dall'altro postulato gi&agrave; premesso, <lb/>che cio&egrave; il momento sta al momento del solido grave, come la velocit&agrave; sta <lb/>alla velocit&agrave;, ne conclude il Baliani che le velocit&agrave; stesse, nel perpendicolo <lb/>e nell'obliqua, stanno reciprocamente come le lunghezze. </s></p><p type="main">

<s>Questa proposizione, che &egrave; l'XI del I libro, &egrave; ordinata dall'Autore al&shy;<lb/>l'altra fondamental proposizione dei tempi proporzionali alle lunghezze del&shy;<lb/>l'obliqua e della perpendicolare, al qual uso &egrave; premessa altres&igrave; in XVII luogo, <lb/>la soluzione del seguente, per altre vie oramai ben noto Problema: &ldquo; Data <lb/>linea perpendiculari, per quam grave descendat, cui annectatur linea, seu <lb/>planum declinans; in declinante reperire punctum, quo grave perveniat eo <lb/>tempore, quo pertransiverit perpendiculum &rdquo; (ibid., pag. </s>

<s>34). </s></p><p type="main">

<s>Sia il piano inclinato AC, nell'ultima rappresentata figura 201, elevato <lb/>all'altezza BC sopra il piano orizzontale AB, e si voglia sapere a qual punto <lb/>si trover&agrave; un grave scendente per AC, mentre un altro simile grave, par&shy;<lb/>titosi dal medesimo punto C, abbia percorso tutto intero il perpendicolo CB. <pb xlink:href="020/01/2134.jpg" pagenum="377"/>Condotta la BD perpendicolare ad AC, sar&agrave; D il punto cercato, imperocch&egrave; <lb/>abbiamo, dice il Baliani, per le cose gi&agrave; dimostrate, che la velocit&agrave;, lungo <lb/>AC, sta alla velocit&agrave;, lungo CB, come CB sta ad AC. </s>

<s>Ma perch&egrave;, essendo CD <lb/>terza proporzionale dopo AC, CB, si ha CB:AC=CD:CB, dunque le ve&shy;<lb/>locit&agrave;, nel piano inclinato e nel perpendicolo, stanno come CD a CB, ossia, <lb/>come gli spazi passati. </s>

<s>Ma quando le velocit&agrave; stanno come gli spazi, i tempi <lb/>sono uguali, dunque &egrave; vero quel che si diceva, che cio&egrave; i tempi per CD e <lb/>per CB sono uguali. </s></p><p type="main">

<s>Da questa proposizione ne deduce, per facile corollario, l'Autore, come <lb/>Giovan Marco e come il Torricelli, il tautocronismo fra le corde e il diame&shy;<lb/>tro, circoscrivendo al triangolo rettangolo CDB un semicerchio, d'onde s'apre <lb/>la via a dimostrar quest'altra proposizione, ch'&egrave; il fondamento, su cui posa <lb/>la nuova Scienza del moto: &ldquo; Si duo gravia descendunt, alterum quidem <lb/>perpendiculariter, alterum vero super plano declinante, pervenient ad idem <lb/>planum orizontale, tali ratione, ut sit eadem proportio inter diuturnitates <lb/>eorum, quae inter perpendicularem et declinantem &rdquo; (ibid., pag. </s>

<s>36). </s></p><p type="main">

<s>Propostasi innanzi la medesima figura 201, a dimostrar che il tempo <lb/>per AC sta al tempo per CB, come AC linea sta a CB, procede spedita&shy;<lb/>mente sicuro il Baliani in questa maniera: Perciocch&egrave; abbiamo, per le gi&agrave; <lb/>dimostrate leggi dei moti accelerati, che CD:AC=T.oCD2:T.oAC2 e per <lb/>una delle proposizioni antecedenti, che T.oCD=T.oCB, ne conseguiranno <lb/>dunque le relazioni CD:AC=T.oCB2:T.oAC2=CDXAC:AC2. </s>

<s>Ma <lb/>perch&egrave; i triangoli simili ABC, BCD danno CB2=CDXAC, sar&agrave; T.oCB2: <lb/>T.oAC2=CB2:AC2, e perci&ograve; anche i semplici tempi per CB e per AC sta&shy;<lb/>ranno come le semplici linee CB, AC. </s></p><p type="main">

<s>Il fondamento alla Scienza nuova era dunque posto anche dal Baliani, <lb/>con questa proposizione, la quale &egrave; conclusa, come si vede, da principii di&shy;<lb/>versi, ed &egrave; condotta in diverso modo da quella di Galileo. </s>

<s>Ma perch&egrave; s'as&shy;<lb/>solvevano, in stabilire un tal fondamento, le intenzioni del Matematico ge&shy;<lb/>novese, ei non d&agrave; alla sua scienza tutta l'estensione della scienza galileiana, <lb/>a confronto della quale, se rimane inferiore rispetto alla materia, vince per&ograve; <lb/>l'esaltato emulo suo rispetto alla elegante semplicit&agrave; della forma. </s>

<s>Dicemmo, <lb/>e lo ripetiamo, che in ci&ograve; il Baliani, meglio che a Galileo, si rassomiglia al <lb/>Torricelli, col trattato del quale, che si compone, secondo la stessa modesta <lb/>espression dell'Autore, delle respigolature fatte nel dovizioso campo gali&shy;<lb/>leiano, si riduceva al suo perfezionamento in Italia la nuova istituita Scienza <lb/>del moto. </s></p><p type="main">

<s>Oltremonti per&ograve; avveniva quel che suole avvenire, la mattina, agli abi&shy;<lb/>tanti delle valli occidentali, che si trovano innanzi rischiarata la via, e cam&shy;<lb/>minano in mezzo al chiaro giorno, senza pensar che anche quella, bench&egrave; <lb/>giunga ai loro occhi diffusa, &egrave; la luce viva del sole. </s>

<s>Edmondo Mariotte leg&shy;<lb/>geva un giorno, innanzi all'accademica Assemblea parigina, una certa sua <lb/>dissertazioncella, con la quale s'argomentava di rendere la ragione del perch&egrave; <lb/>una corda di liuto, mossa, faccia spontaneamente risonare le altre corde tese <pb xlink:href="020/01/2135.jpg" pagenum="378"/>all'unisono o all'ottava. </s>

<s>Fra i molti dotti, ivi convenuti, il solo Cristiano Huy&shy;<lb/>ghens sent&igrave; che quella era la ragione medesima data da Galileo, e lo disse <lb/>all'Autore, il quale si scus&ograve; asseverando che il libro di Galileo non l'aveva <lb/>mai letto. </s>

<s>Poi, messosi per curiosit&agrave;, dopo qualche tempo, a leggere, &ldquo; J'ai <lb/>trouv&eacute; en effet que ses pens&eacute;es &eacute;toient tellement conformes aux miennes, <lb/>sur ce suiet, que vous pouviez croire, avec beaucoup de raison, que j'avois <lb/>emprunt&eacute; de lui ce que j'en avois &eacute;crit &rdquo; (Oeuvres, T. II, a l'Haye 1740, <lb/>pag. </s>

<s>558). </s></p><p type="main">

<s>Rivolgeva queste precise parole il Mariotte all'Huyghens stesso, in una <lb/>lettera, scritta da Dijon il d&igrave; primo del Febbraio 1668, per dedicare al fu&shy;<lb/>turo Autore dell'<emph type="italics"/>Orologio oscillatorio<emph.end type="italics"/> alcune sue proposizioni sul moto dei <lb/>pendoli e dei corpi gravi, le quali, bench&egrave; confessi essere in sostanza quelle <lb/>medesime gi&agrave; dimostrate da Galileo, &ldquo; il y a pourtant una difference toute <lb/>enti&egrave;re entre les fa&ccedil;ons de d&eacute;montrer, et l'ordre et suite des propositions, <lb/>comme vous le pourrez juger facilement, s'il vous pla&igrave;t de lire l'ecrit ci&shy;<lb/>joint. </s>

<s>Car vous verrez que dans ma premi&egrave;re proposition je donne, ou crois <lb/>donner, la vraie cause de l'acceleration du mouvement, au lieu que Galilee <lb/>se contente de la supposer et d'enfaire une d&eacute;finition; que dans ma V je <lb/>prouve ce qu'il prend pour principe, et qu'il demande lui &egrave;tre accord&eacute; au <lb/>commencement de son Trait&eacute;; et que dans ma VIII je donne la proportion <lb/>du tems par le c&ograve;t&eacute; du quarr&eacute;, avec le tems par les 2 c&ograve;tez de l'octogone, et <lb/>par celui des 3 c&ograve;tez du dodecagone, ce qu'il n'a pas fait &rdquo; (ivi, pag. </s>

<s>558, 59). </s></p><p type="main">

<s>Se abbia propriamente il Mariotte, com'ei vorrebbe far credere, data in <lb/>quella sua I proposizione la vera causa dell'accelerazione del moto, lo la&shy;<lb/>sciamo giudicare ai nostri Lettori, perch&eacute; a noi sembra non aver fatto altro <lb/>il Matematico francese che mettere in altra forma i concetti stessi di Gali&shy;<lb/>leo, i quali rimangono, cos&igrave; per l'uno come per l'altro Autore, indipenden&shy;<lb/>temente dalle parole usate a significarli, non pi&ugrave; che una semplice defini&shy;<lb/>zione. </s>

<s>Quanto al vantarsi poi di aver dato dimostrazione di quel che, nel <lb/>Trattato galileiano, si chiede ne sia concesso come noto, non si vede troppo <lb/>giusta ragion di tal vanto, essendo stato fatto ci&ograve;, tanti anni prima, con <lb/>pubblica solennit&agrave;, dal Baliani e dal Torricelli, e avendo anzi il Gassendo <lb/>divulgata in Francia la notizia che quella tanto desiderata dimostrazione era <lb/>stata fatta dallo stesso Galileo, per inserirsi, occorrendo di ristamparlo, nel <lb/>suo III dialogo Del moto. </s></p><p type="main">

<s>Qualche cosa nonostante di nuovo e di singolare &egrave; nella VII proposi&shy;<lb/>zione, nella quale s'insegna dal Mariotte a calcolare la proporzion del tempo, <lb/>scendendo il grave per la sottesa a una quarta di cerchio, per i due lati <lb/>dell'ottagono, e per i tre del dodecagono, a fin di concluderne il brachisto&shy;<lb/>cronismo degli archi rispetto alle corde. </s>

<s>Ostentava, in ordine a ci&ograve;, l'eccel&shy;<lb/>lenza del suo proprio trattato, in confronto di quello di Galileo, il quale, se <lb/><emph type="italics"/>il n'a pas fait,<emph.end type="italics"/> non &egrave; da apporglielo a difetto, avendo egli tenuto altre vie <lb/>pi&ugrave; generali, e diciamolo francamente, pi&ugrave; matematiche di quelle proseguite <lb/>dall'Accademico parigino. </s>

<s>Si pu&ograve; aggiungere anzi che la VIII proposizione del <pb xlink:href="020/01/2136.jpg" pagenum="379"/>francese Autore <emph type="italics"/>Du mouvement des pendules<emph.end type="italics"/> dipende dalla precedente, che <lb/><figure id="id.020.01.2136.1.jpg" xlink:href="020/01/2136/1.jpg"/></s></p><p type="caption">

<s>Figura 202.<lb/>si deriva per corollario dalla XIV, ordinata da <lb/>noi di sopra, nel pubblicare il III libro galileiano. </s></p><p type="main">

<s>La detta VII proposizione infatti, nel trattato del <lb/>Mariotte, &egrave; cos&igrave; formulata: &ldquo; Soit AB (fig. </s>

<s>202) per&shy;<lb/>pendiculaire &agrave; l'horison; AC, BD perpendiculaires &agrave; <lb/>AB, et AE le quart de la ligne; et soit FED quelcon&shy;<lb/>que ligne entre les deux paralleles AC, BD: je dis que <lb/>le tems par FE, EB sera &eacute;gal au tems par AE, ED. </s>

<s><lb/>Mais si AE est moindre que le quart de AB, le tems <lb/>par AE, ED, sera plus grand que par FE, EB. </s>

<s>Mais <lb/>si AE est plus que le quart, le tems par FE, EB sera <lb/>le plus grand &rdquo; (Ouvres, T. II cit., pag. </s>

<s>564, 65). </s></p><p type="main">

<s>La dimostrazione si deriva per legittimo e immediato discorso, come <lb/>s'&egrave; detto, dalla XIV del III libro manoscritto di Galileo, dalla quale, prese <lb/>FG, AH medie proporzionali fra FD, FE, e AB, AE, si hanno l'equazioni <lb/>T.oAE:T.oED=AE:EG; T.oFE:T.oEB=FE:EH, che danno per com&shy;<lb/>posizione T.oAE+T.oED:T.oED=AE+FG:EG; T.oFE+T.oEB: <lb/>T.oEB=FE+EH:EH. </s>

<s>Ma perch&egrave; T.oFD=EG, e T.oEB=EH, sar&agrave; <lb/>T.oAE+T.oED:T.oFE+T.oEB=AE+EG:FE+EH. </s></p><p type="main">

<s>Vien di qui dimostrato il teorema del Mariotte, ne'suoi tre casi di&shy;<lb/>stinti, imperocch&egrave;, quanto al primo, se AE, e perci&ograve; anche EF, son la quarta <lb/>parte precisa delle AB, GD, sono altres&igrave; respettivamente uguali alle EH, EG, <lb/>e perci&ograve; T.oAE+T.oED=T.oEF+T.oEB. </s>

<s>Essendo nel secondo caso as&shy;<lb/>sai facile dimostrare che AE+EG>FE+EH,
e nel terzo che AE+EG &lt;<lb/>FE+EH, se ne conclude, rispetto all'uno e all'altro propostosi caso, dalla <lb/>formulata equazione, l'intento. </s></p><p type="main">

<s>Soggiunge a ci&ograve; poi il Mariotte il seguente Scolio, che serve efficace&shy;<lb/>mente di Lemma alla VIII proposizione: &ldquo; On prouvera le meme, si les <lb/>deux lignes AEB, FED sont toutes deux inclin&eacute;es: et l'on peut conclure, <lb/>par ce qui est dit au troisieme cas, qu'un poids commen&ccedil;ant sa descent par <lb/>une ligne perpendiculaire, ou peu inclin&eacute;e, et la finissan par une beaucoup <lb/>inclin&eacute;e, fait le tems plus court que s'il commen&ccedil;oit et finissoit au contraire, <lb/><figure id="id.020.01.2136.2.jpg" xlink:href="020/01/2136/2.jpg"/></s></p><p type="caption">

<s>Figura 203.<lb/>si la perpendiculaire et l'inclin&egrave;e sont &eacute;gales, et <lb/>meme, quand la perpendiculaire et l'inclin&eacute;e se&shy;<lb/>roient un peu plus grandes que l'inclin&eacute;e et la <lb/>perpendisulaire &rdquo; (ivi, pag. </s>

<s>565). </s></p><p type="main">

<s>Dietro le quali cose, ecco in che modo con&shy;<lb/>duce il Mariotte la sua VIII proposizione, corri&shy;<lb/>spondente alla XXXVI di Galileo. </s>

<s>Siano alla me&shy;<lb/>desima quarta di cerchio BDEC (fig. </s>

<s>203) inscritti <lb/>il lato BC del quadrato, i due lati BF, FC del&shy;<lb/>l'ottagono, e i tre lati BD, DE, EC del dodeca&shy;<lb/>gono, e s'immagini che scenda per essi da B un <pb xlink:href="020/01/2137.jpg" pagenum="380"/>grave per giungere all'infimo punto C dello stesso quadrante, eretto sul piano <lb/>dell'orizzonte, in modo che AC gli riesca perpendicolare. </s>

<s>S'argomenta dal&shy;<lb/>l'ultima fatta considerazione, e osservando che la scesa per BFC &egrave; meno <lb/>inclinata in principio, e pi&ugrave; inclinata nel termine di quel che non sia BC; <lb/>come pure che l'altra scesa per BDEC &egrave; meno inclinata in principio e <lb/>pi&ugrave; inclinata nel suo termine di quel che non sia la scesa per BFC; s'ar&shy;<lb/>gomenta, diciamo, che pi&ugrave; breve per BFC che non per BC, e pi&ugrave; breve <lb/>ancora per BDEC che non per BFC sar&agrave; il tempo della scesa di quel mede&shy;<lb/>simo grave. </s>

<s>Cosicch&egrave;, venendo ai calcoli numerici, si troverebbe, dice il Ma&shy;<lb/>riotte, che, essendo il tempo per BC centomila, quello per BFC sar&agrave; 93,758, <lb/>e quello per BDEC 93,072, presso a poco. </s>

<s>&ldquo; D'ou l'on peut conclure, cos&igrave; <lb/>termina l'Autore la sua dimostrazione, que le tems par quatre soutendantes <lb/>de suite sera encore plus court, et enfin que par la circonference BC il <lb/>sera le plus court de tous, et pourroit etre au tems par BC comme 93 a 100, <lb/>ou 13 a 14 a peu pres &rdquo; (ivi, pag. </s>

<s>565). </s></p><p type="main">

<s>Questo trattatello <emph type="italics"/>Du mouvement,<emph.end type="italics"/> in VIII proposizioni, con una con&shy;<lb/>clusione relativa all'isocronismo dei pendoli, fu nel 1668 dedicato, come di&shy;<lb/>cemmo, all'Huyghens, il quale, pubblicando cinque anni dopo il suo <emph type="italics"/>Orolo&shy;<lb/>gio oscillatorio,<emph.end type="italics"/> veniva con tanto pi&ugrave; valide forze del Mariotte a promovere <lb/>la Scienza del moto. </s>

<s>Doveva anch'egli partire dai medesimi principii, dei <lb/>quali riconobbe con imparziale giudizio primo autore Galileo, se non che <lb/>dei modi da lui tenuti in dimostrarli non &egrave; sodisfatto. </s>

<s>Era a quel tempo <lb/>gi&agrave; venuta alla luce l'aggiunta postuma al III dialogo delle Due nuove <lb/>scienze, dove si dimostrava quel che s'era prima supposto, che cio&egrave; sono <lb/>uguali le velocit&agrave; sopra piani diversamente inclinati, ma della medesima al&shy;<lb/>tezza, e questa galileiana dimostrazione all'Huyghens <emph type="italics"/>parum firma videtur,<emph.end type="italics"/><lb/>per cui crede di dovergliene sostituire un'altra. (Horol. </s>

<s>oscill., Lib. </s>

<s>II, pro&shy;<lb/>posizione VI, Opera varia, T. </s>

<s>I cit., pag. </s>

<s>62, 63). </s></p><p type="main">

<s>Parve inoltre anche all'Autore dell'<emph type="italics"/>Horologio,<emph.end type="italics"/> come al Cartesio, che non <lb/>tenesse l'Accademico nostro fiorentino le vie pi&ugrave; compendiose, specialmente <lb/>in dimostrare quel teorema &ldquo; cui reliqua omnia, quae de descensu super <lb/>planis inclinatis tradidit, superstruuntur &rdquo; (ibid., pag. </s>

<s>63). &Egrave; quel galileiano <lb/>teorema, a cui qui si accenna, il III, che nel pubblico trattato Dei moti lo&shy;<lb/>cali riman tuttavia concluso dal principio supposto. </s>

<s>Ma l'Huyghens, avendo <lb/>gi&agrave; prima dato dimostrazione di quello stesso supposto, osservava che, dalle <lb/><figure id="id.020.01.2137.1.jpg" xlink:href="020/01/2137/1.jpg"/></s></p><p type="caption">

<s>Figura 204.<lb/>propriet&agrave; dei moti equabili succedentisi agli accelerati, <lb/>s'aveva una dimostrazione assai pi&ugrave; semplice e pi&ugrave; spe&shy;<lb/>dita di quella stessa data da Galileo, bench&egrave; con l'aiuto <lb/>degli Indivisibili. </s></p><p type="main">

<s>Scenda infatti il grave per AB (fig. </s>

<s>204) e per AC. <lb/>S'ha, per le propriet&agrave; del moto equabile dopo l'ac&shy;<lb/>celerato, dimostrate nella I proposizione di Galileo, che <lb/>la velocit&agrave; in B &egrave; uguale a 2.AB/T.oAB, e che la velocit&agrave; in C &egrave; uguale a 2.AC/T.oAC. <pb xlink:href="020/01/2138.jpg" pagenum="381"/>Ma, secondo che suppone esso Galileo o secondo che volle l'Huyghens di&shy;<lb/>mostrare, le velocit&agrave; in B e in C sono uguali, dunque T.oAB:T.oAC= <lb/>AB:AC, che &egrave; il fondamento alla nuova scienza del moto, sostituito nella VII <lb/>del II libro dell'<emph type="italics"/>Orologio oscillatorio<emph.end type="italics"/> alla III del III dialogo delle Due nuove <lb/>scienze. </s></p><p type="main">

<s>Cos&igrave; fatte sostituzioni per&ograve;, concernenti la forma piuttosto che la so&shy;<lb/>stanza, non detraggono che in assai piccola parte a Galileo il merito di es&shy;<lb/>sere egli stato il primo a mettere in ordine di trattato que'teoremi, che <lb/>l'Huyghens e il Mariotte, per tacere di altri, resero con le loro speculazioni <lb/>d'altre nuove mirabili conseguenze fecondi. </s></p><pb xlink:href="020/01/2139.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle scese dei gravi per gli archi dei cerchi<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle varie esperienze e delle teorie, che persuasero essere i tempi delle scorse dei gravi, nelle <lb/>concavit&agrave; dei cerchi e nei pendoli, per qualunque ampiezza di arco, uguali. </s>

<s>&mdash; II. </s>

<s>Delle nuove <lb/>esperienze e delle teorie, che dimostrarono non essere i tempi dello corse e delle ricorse dei <lb/>cadonti, per le concavit&agrave; dei cerchi e nei pendoli, esattamente uguali. </s>

<s>&mdash; III. </s>

<s>Delle leggi delle <lb/>cadute dei gravi per archi di cerehi simili, e delle loro applicazioni al problema del pendolo a <lb/>secondi. </s>

<s>&mdash; IV. </s>

<s>Di ci&ograve; che operarono i Discepoli di Galileo, e s<gap/>guatamente il Viviani. </s>

<s>per dare <lb/>scienza delle supposte propriet&agrave; dei pendoli disugnali. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>L'argomento storico del capitolo precedente ha in s&egrave; un'importanza, <lb/>ch'&egrave; sfuggita forse all'attenzione dei nostri Lettori, ma che a noi preme di <lb/>far osservare. </s>

<s>Si riferisce una tale importanza al sodisfar che le narrate sto&shy;<lb/>rie fanno alla curiosit&agrave; di coloro, i quali, essendo passati per la lunga serie <lb/>delle proposizioni, di che si compila il trattato galileiano Dei moti locali, in&shy;<lb/>serito nel III dialogo Delle due nuove scienze, domandano, appena usciti <lb/>fuori dalla faticosa lettura, qual potesse essere stata l'intenzion dell'Autore <lb/>in raggirarsi prolissamente intorno a cos&igrave; fatte speculazioni, che, ridotte a <lb/>quelle sole, dalle quali verrebbe propriamente promossa la Scienza, si pote&shy;<lb/>vano tanto pi&ugrave; efficacemente concludere in un piccol numero di teoremi. </s></p><p type="main">

<s>La curiosit&agrave;, che dee senza dubbio aver frugato tutti i Lettori del trat&shy;<lb/>tato a stampa, vien ora ad essere sodisfatta in chi rammemora i primi ma&shy;<lb/>noscritti sul medesimo argomento, ne'quali s'incominciava dallo stabilire le <lb/>leggi dei moti accelerati, per concluderne brevemente, previi i necessarii <lb/>Lemmi, il brachistocronismo degli archi rispetto alle sottese dei cerchi. </s>

<s>Quel <pb xlink:href="020/01/2140.jpg" pagenum="383"/>che sta di mezzo vedemmo non esser altro che una soprabbondanza di or&shy;<lb/>dito, messo in mezzo alle rare fila dal tessitore, quando impose altro nome, <lb/>e volle riserbare ad altr'uso l'inaspettatamente riuscita eccellenza della tela. </s>

<s><lb/>Per servirsi d'altra immagine a significare il medesimo concetto, si direbbe <lb/>che avvenne a Galileo come a colui, che, correndo la ruota, vede uscire un'an&shy;<lb/>fora dall'argilla posta in sul tornio, per ridurla alle semplici forme di un <lb/>orciolo. </s>

<s>La curiosa trasformazione apparisce evidente a chi paragona il primo <lb/>trattatello manoscritto, l'intenzion del quale era quella di concluder che il <lb/>tempo per gli archi &egrave; pi&ugrave; breve che per le corde inflesse, con l'ultimo trat&shy;<lb/>tato a stampa, in cui proponevasi l'Autore di dimostrare le propriet&agrave; dei <lb/>moti locali, a fine d'instaurarne una Scienza nuova. </s></p><p type="main">

<s>&Egrave; dunque manifesta di qui l'origine storica di quel III dialogo Del moto, <lb/>che form&ograve; l'ammirazione del mondo: &egrave; manifesto cio&egrave; che, dall'esercitarsi <lb/>Galileo intorno alle propriet&agrave; meccaniche dei cerchi, fu condotto a ritrovare <lb/>i principii e le conseguenze nuove della Scienza universale dei moti. </s>

<s>Ora &egrave; <lb/>notabile che questa universalit&agrave; si riduca infine e torni alle particolarit&agrave; delle <lb/>prime intenzioni, giacch&egrave; si vede che anche il trattato, a cui s'impose il <lb/>titolo Dei moti locali, si corona con la proposizione XXXVI, nella quale si <lb/>dimostra che la via pi&ugrave; breve di giungere da un punto all'altro, non &egrave; per <lb/>la rettitudine della corda, ma per l'arco sotteso. </s>

<s>Quella XXXVI proposizione <lb/>dunque, che non &egrave; pi&ugrave; la finale intenzion del trattato, vi riman nulladimeno <lb/>una delle principali; ond'&egrave; che la sua propria dignit&agrave; c'invita a ricercarne <lb/>l'origine, e a indagarne il fine, che nel libro di Galileo, come il nostro di&shy;<lb/>scorso confermer&agrave;, non apparisce. </s>

<s>Anche il Cartesio perci&ograve; dettesi a indo&shy;<lb/>vinare, e si cred&egrave; che il fine della detta proposizione, e di tutto anzi il trat&shy;<lb/>tato, che ne preparava le conclusioni; fosse quello di dimostrare l'isocronismo <lb/>dei pendoli. </s>

<s>&ldquo; Caeterum, cos&igrave; scriveva al Mersenno, nel far la critica al libro <lb/>di Galileo, tertium suum Dialogum non alio consilio scripsisse mihi videtur, <lb/>quam ut rationem redderet cur eiusdem chordae vibrationes sint inter se <lb/>aequales, quod tamen non praestat, sed solum concludit pondera citius de&shy;<lb/>scendere secundum arcum circuli, quam secundum eiusdem arcus chordam &rdquo; <lb/>(Epist., P. II cit., pag. </s>

<s>244). </s></p><p type="main">

<s>Nessun'altra divinazione dette mai me&shy;<lb/>glio di questa nella cruna del vero, essendo <lb/>che Galileo stesso, rivelando i segreti suoi <lb/>pensieri a Guidubaldo Del Monte, dica esser <lb/>passate per la sua mente le cose proprie a <lb/>quel modo, che avea scritto il Cartesio. </s>

<s>Nella <lb/>lettera infatti del d&igrave; 20 di Novembre del <lb/>1602, dop'aver dato allo stesso Guidubaldo <lb/>notizia delle dimostrate proposizioni concer&shy;<lb/>nent&igrave; il tempo della scesa per l'arco, e per <lb/><figure id="id.020.01.2140.1.jpg" xlink:href="020/01/2140/1.jpg"/></s></p><p type="caption">

<s>Figura 205.<lb/>le inflesse corde sottese; il medesimo Gali&shy;<lb/>leo immediatamente soggiunge: &ldquo; Sin qui ho dimostrato senza trasgredire <pb xlink:href="020/01/2141.jpg" pagenum="384"/>i termini meccanici, ma non posso spuntare a dimostrare come gli archi <lb/>SIA (fig. </s>

<s>205), IA sieno passati in tempi uguali, che &egrave; quello che cerco &rdquo; <lb/>(Alb. </s>

<s>VI, 23). </s></p><p type="main">

<s>Essendoci cos&igrave; dunque certificati che l'occasione d'istituire la Scienza <lb/>nuova del moto venne veramente a Galileo dall'essersi voluto mettere a di&shy;<lb/>mostrare l'isocronismo dei pendoli, si pu&ograve; dir che la storia della Dinamica <lb/>incominci dalla storia di una tale scoperta. </s>

<s>Una tradizione volgare, avva&shy;<lb/>lorata dall'autorit&agrave; del Viviani, narra che ci&ograve; avvenne nel Duomo di Pisa, <lb/>attendendo ivi al dondolar lungo e lento di una lampada sospesa. </s></p><p type="main">

<s>&ldquo; Trovavasi il Galileo, scrive esso Viviani nella sua <emph type="italics"/>Storia dell'appli&shy;<lb/>cazione del pendolo all'Orologio,<emph.end type="italics"/> in et&agrave; di vent'anni in circa, intorno al&shy;<lb/>l'anno 1583, nella citt&agrave; di Pisa, dove per consiglio del padre s'era applicato <lb/>agli studii della Filosofia e della Medicina, ed essendo un giorno nel Duomo <lb/>di quella citt&agrave;, come curioso ed accortissimo ch'egli era, caddegli in mente <lb/>di osservare, dal moto di una lampana che era stata allontanata dal perpen&shy;<lb/>dicolo, se per avventura i tempi delle andate e tornate di quelle, tanto per <lb/>gli archi grandi, che per i mediocri e per i minimi, fossero uguali, paren&shy;<lb/>dogli che il tempo per la maggior lunghezza dell'arco grande potesse forse <lb/>restar contraccambiato dalla maggior velocit&agrave;, con che per esso vedeva mo&shy;<lb/>vere la lampana, come per linea nelle parti superiori pi&ugrave; declive. </s>

<s>Sovven&shy;<lb/>negli dunque, mentre questa andava quietamente movendosi, di far di quelle <lb/>andate e tornate un esamine, come suol dirsi, alla grossa, per mezzo delle <lb/>battute del proprio polso, e con l'aiuto ancora del tempo della Musica, nella <lb/>quale egli gi&agrave; con gran profitto erasi esercitato, e per allora con questi tali <lb/>riscontri parvegli non aver falsamente creduto della egualit&agrave; di quei tempi &rdquo; <lb/>(Alb. </s>

<s>XIV, 342). </s></p><p type="main">

<s>Nella <emph type="italics"/>Vita di Galileo,<emph.end type="italics"/> e in varie scritture inedite, come in quella <emph type="italics"/>Del <lb/>votamento dei vasi<emph.end type="italics"/> o <emph type="italics"/>Delle clessidre<emph.end type="italics"/> (MSS. Gal., T. CXVIII, fol. </s>

<s>6), e in <lb/>quell'altra da noi in parte pubblicata a pag. </s>

<s>303, 4 del I Tomo di questa <lb/>nostra Storia, ripete il Viviani il medesimo commento, che tale e non altro <lb/>&egrave; per noi propriamente il nome, che si meritan cos&igrave; fatte narrazioni. </s>

<s>In que&shy;<lb/>st'ultima citata scrittura inedita per&ograve; soggiunge esso Viviani le seguenti pa&shy;<lb/>role, con la storica verit&agrave; forse meglio conformi: &ldquo; Nella medesima et&agrave; sua <lb/>giovanile, quando Galileo studiava Filosofia, che fu pure intorno al 1580, si <lb/>chiar&igrave;, con l'aiuto di questo suo Pendolo, della falsit&agrave; di que'due pronun&shy;<lb/>ziati di Aristotile, con l'un dei quali egli afferma vedersi che due mobili di <lb/>gravit&agrave; diverse discendono per l'istesso mezzo con velocit&agrave; proporzionali alle <lb/>medesime gravit&agrave; loro: con l'altro che l'istesso mobile si muove per di&shy;<lb/>versi mezzi con velocit&agrave; continuamente proporzionali alle lor densit&agrave; o gra&shy;<lb/>vezze, facendone. </s>

<s>per chiarirsi della verit&agrave; del primo, varie esperienze nel&shy;<lb/>l'aria con diversi gravi lasciati cader nell'istesso tempo dall'altezza del <lb/>campanile di Pisa, e per riscontro del secondo varie altre prove nell'aria e <lb/>nell'acqua, indagata prima industriosamente la proporzione delle densit&agrave; o <lb/>gravit&agrave; in specie di tali fluidi &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>62). </s></p><pb xlink:href="020/01/2142.jpg" pagenum="385"/><p type="main">

<s>Ora, sembra a noi che questa di confutare gli errori aristotelici fosse <lb/>la pi&ugrave; naturale e la pi&ugrave; ragionevole occasione a Galileo di scoprire l'iso&shy;<lb/>cronismo dei pendoli. </s>

<s>Come, a sperimentare che i gravi, di qualunque ma&shy;<lb/>teria e di qualunque mole, scendono ugualmente veloci, Galileo stesso, non <lb/>sodisfatto de'piani inclinati, per evitare ogni attrito, ricorresse ai pendoli, <lb/>fu da noi fatto avvertire altrove, citandone gli opportuni documenti. </s>

<s>Era <lb/>perci&ograve; naturalissimo che in cos&igrave; fatte esperienze, nelle quali si trattava di <lb/>comparare le velocit&agrave; di due pendoli diversi, si accorgesse il sagace Speri&shy;<lb/>mentatore della equidiuturnit&agrave; delle loro vibrazioni, come ingenuamente narra <lb/>di essersi, a una simile occasione, abbattuto il Baliani a fare la medesima <lb/>scoperta. </s>

<s>Dop'avere, nella prefazione al primo libro <emph type="italics"/>De motu,<emph.end type="italics"/> detto in che <lb/>modo gli occorresse di sperimentare che i gravi, comunque fossero ponde&shy;<lb/>rosi, lasciati cader per un eguale spazio perpendicolare, lo passavano tutti <lb/>nel medesimo tempo, &ldquo; institi adhuc, soggiunge il Matematico genovese, et <lb/>globos, in gravitate et in materia inaequales, appendi funiculis aequalibus, <lb/>et agitatos animadverti moveri tempore aequali, et hoc servare adeo fideli&shy;<lb/>ter, ut globus plumbeus duarum unciarum, alter librarum duarum, f&egrave;rreus <lb/>librarum 34, et lapideus quadraginta circiter, nec non et lapis informis, quo&shy;<lb/>rum funiculi, comprehensis ipsorum semidiametris, aequales essent; uno et <lb/>eodem temporis spatio moverentur, et vibrationes easdem numero darent <lb/>hinc inde, sive motus unius globi fieret per aequale spatium, sive per inae&shy;<lb/>quale, ita ut qui maiori impetu iactabatur, et sic maius spatium percurre&shy;<lb/>bat, illud tanto velocius pertransiret &rdquo; (Editio secunda cit., pag. </s>

<s>6). </s></p><p type="main">

<s>Dice il Baliani essergli felicemente occorsa una tale scoperta nel 1611, <lb/>quando l'esperienze proprie, per determinar la legge dei gravi cadenti, l'eb&shy;<lb/>bero fatto accorto degli altrui inveterati errori. </s>

<s>Ma Galileo, come, allo stesso <lb/>modo sperimentando, aveva parecchi anni prima scoperto quei medesimi er&shy;<lb/>rori; cos&igrave;, parecchi anni prima del Baliani, ebbe occasione di avvertir che <lb/>le varie ampiezze dei corpi oscillanti eran passate da loro nei medesimi tempi. </s>

<s><lb/>Vuol giustizia perci&ograve; che debbasi a lui, a Galileo, la precedenza nel merito <lb/>della scoperta, la quale non avvenne per quelle quasi romantiche avventure <lb/>giovanili, alle quali ci fa ripensare il Viviani, ma per i meditati esercizi del&shy;<lb/>l'uomo pi&ugrave; maturo, e della mente aperta a ricevere, o a risentire almeno, <lb/>gl'influssi delle scientifiche tradizioni. </s></p><p type="main">

<s>Alcune delle pi&ugrave; singolari propriet&agrave; del moto dei gravi, costretti a scen&shy;<lb/>der per un arco di cerchio, appesi a una fune fissa nella sua sommit&agrave;, e <lb/>libera alla sua estremit&agrave; inferiore; erano state sagacemente avvertite dai <lb/>nostri Matematici del secolo XVI, e vedremo tra poco come da cos&igrave; fatte <lb/>esperienze delicatissime avesse principio e impulso a progredire la Scienza <lb/>meccanica di Leonardo da Vinci. </s>

<s>Il Cardano poi iniziava nel suo libro <emph type="italics"/>De <lb/>subtilitate<emph.end type="italics"/> questa nuova Scienza da un'occasione sovvenutagli simile a quella <lb/>di Galileo e del Baliani perch&egrave;, ripensando anch'egli alla difficolt&agrave; di mo&shy;<lb/>vere un grave posat in piano orizzontale, si volse a paragonare il fatto con <lb/>quella grandissima facilit&agrave;, con la quale si pu&ograve; imprimere un tal simile moto <pb xlink:href="020/01/2143.jpg" pagenum="386"/>al medesimo grave, tenendolo sospeso, ed ebbe di qui motivo a sciogliere <lb/>un problema, che fu poi posto per fondamento alla Meccanica galileiana. <lb/></s>

<s>&ldquo; Cum per aequidistantem finitori lineam tam difficulter gravia moveantur, <lb/>cur est quod, suspensa, facile adeo impelluntur, ut annulus filo suspensus <lb/>sponte videatur moveri? </s>

<s>&rdquo; (Lugduni 1580, pag. </s>

<s>97). </s></p><p type="main">

<s>La causa di ci&ograve;, dice il Cardano, &egrave; perch&egrave;, quando il grave &egrave; posato, <lb/>la forza dee sostenerlo e moverlo, mentre, quando &egrave; sospeso, non dee far <lb/>che moverlo solo. </s>

<s>E pur cos&igrave; movendolo, &ldquo; tanta ferme vi redit ad medium, <lb/>quanta ab illo depulsum est: igitur, cum ea vi iam depulsum sit a medio, <lb/>gratia exempli, per cubiti spatium, tantumdem descendere in contrariam par&shy;<lb/>tem necessarium erit, atque ita continuo ac atternato reditu tardissime con&shy;<lb/>quiescere &rdquo; (ibid.). </s></p><p type="main">

<s>Si trovano in queste parole, come i nostri Lettori s'accorgono facil&shy;<lb/>mente, incluse le fondamentali dottrine dei pendoli, i quali ondeggiando <lb/>risalgon <emph type="italics"/>ferme<emph.end type="italics"/> alla medesima altezza, d'onde furono scesi, e vi risalireb&shy;<lb/>bero puntualmente, quando non ricevessero impedimento dal mezzo, cosicch&egrave; <lb/>nel vuoto quegli ondeggiamenti, che nell'aria vanno a morir tardissimi, con&shy;<lb/>tinuerebbero ivi perpetui. </s>

<s>Cotali pensieri, che fanno esatto riscontro con <lb/>quelli di Galileo (Alb. </s>

<s>I, 250), non sono qui dal Cardano espressi, ma s'ar&shy;<lb/>gomentano facilmente da ci&ograve; che il medesimo Autore insegna nella XL pro&shy;<lb/>posizione dell'<emph type="italics"/>Opus novum,<emph.end type="italics"/> dove dice che una perfetta sfera, per moversi <lb/>in piano perfettamente orizzontale, non ha bisogno d'altra forza da quella <lb/>in fuori &ldquo; quae potest scindere aerem &rdquo; (Operum. </s>

<s>T. IV cit., pag. </s>

<s>480). </s></p><p type="main">

<s>Soggiunge il Cardano, nel citato libro <emph type="italics"/>De subtilitate,<emph.end type="italics"/> al medesimo pro&shy;<lb/>posito, un'altra osservazione importante, ed &egrave; che l'anello grave sospeso a <lb/>un filo si move tanto pi&ugrave; facilmente, quanto il filo stesso &egrave; pi&ugrave; lungo. </s>

<s>La <lb/>ragione di ci&ograve;, illustrata dall'Autore con apposita figura, e confortata dagli <lb/>invocati teoremi della sua Geometria, si conclude insomma col dire ch'es&shy;<lb/>sendo il filo pi&ugrave; lungo riesce a proporzione pi&ugrave; ampio l'arco descritto, e <lb/>perci&ograve; il grave, in ugual tratto, men si discosta dalla tangente orizzontale, <lb/>d'onde la facilit&agrave; del suo moto maggior che nell'altro appeso a un filo pi&ugrave; <lb/>corto, il quale &egrave; necessario che &ldquo; a centro Terrae magis ascendat &rdquo; (pag. </s>

<s>97). </s></p><p type="main">

<s>Ravviandoci ora al nostro primo ragionamento, diciamo che le consi&shy;<lb/>derazioni dei pendoli, in mezzo alle meccaniche speculazioni, potevano na&shy;<lb/>turalmente sovvenire a Galileo dagli esempi degli anteriori Maestri della <lb/>Scienza, anche senza l'avventuroso incontro nel Duomo di Pisa, immagi&shy;<lb/>nato forse da chi si dette a credere che nessun altro avesse pensato mai di <lb/>ritrovare scienza di cos&igrave; fatti moti per gli archi dei cerchi, ond'ebbe a fa&shy;<lb/>voleggiarne l'origine prima dalle lampade ondeggianti. </s>

<s>Non sembra che Ga&shy;<lb/>lileo avesse parte in ingerire una tale opinione, perch&egrave;, anche l&agrave; dove sa&shy;<lb/>rebbe caduto opportuno di accennare a ci&ograve;, che dette prossima occasione <lb/>alla scoperta, ne tace, e dice anzi per bocca del Sagredo che &ldquo; avendo ben <lb/>mille volte posto cura alle vibrazioni in particolare delle lampade pendenti <lb/>in alcune chiese da lunghissime corde, inavvertentemente mosse da alcuno, <pb xlink:href="020/01/2144.jpg" pagenum="387"/>il pi&ugrave; che io cavassi da tale osservazione fu l'improbabilit&agrave; dell'opinione di <lb/>quelli, che vogliono che simili moti vengano mantenuti, e continuati dal <lb/>mezzo, cio&egrave; dall'aria &rdquo; (Alb. </s>

<s>XIII, 100). </s></p><p type="main">

<s>Se la storia dunque ha da fondarsi sui documenti, si dovrebbe dire che <lb/>Galileo stesso nega di avere imparato l'isocronismo dalle lampade oscillanti, <lb/>dalle quali solo prese occasione di riconoscer l'impossibilit&agrave; dell'opinione <lb/>aristotelica intorno all'aria, che produce e mantiene il moto ai proietti. </s>

<s>Quanto <lb/>al moto dei gravi naturalmente cadenti, come i corpi appesi a un filo, piut&shy;<lb/>tosto che striscianti lungo un piano, gli servissero a sperimentar le leggi <lb/>delle cadute, e a scoprire le altre non meno inverosimili opinioni del Filo&shy;<lb/>sofo, lo dice in questo stesso Dialogo poco avanti, quasi volesse da s&egrave; me&shy;<lb/>desimo Galileo confermar che fu dall'usare i pendoli in cos&igrave; fatte esperienze, <lb/>che gli occorse di avvertire l'ugual tempo delle loro maggiori o minori <lb/>oscillazioni. </s></p><p type="main">

<s>Comunque sia, il primo autentico documento, in cui facciasi menzione <lb/>dello scoperto isocronismo, &egrave; una lettera del 1602 indirizzata a Guidubaldo <lb/>del Monte, quando Galileo non era semplice scolare, ma professore in Pa&shy;<lb/>dova, dove non s'esercitava per suo giovanile diletto intorno alla Musica, <lb/>ma insegnava alla giovent&ugrave;, d'ogni parte del mondo convenutavi, la Mate&shy;<lb/>matica. </s>

<s>Appartengono a cotesti tempi alcune scritture del professor pado&shy;<lb/>vano, dalle quali giusto apparisce ch'egli studiava allora intorno alle pro&shy;<lb/>priet&agrave; del moto, sgombrandosi innanzi le vie dagli aristotelici errori. </s>

<s>Starebbe <lb/>perci&ograve; anche questo a confermar l'opinione che fosse la scoperta fatta in <lb/>quel tempo, o poco prima che ne desse lo Scopritore avviso a Guidubaldo, <lb/>a cui parve impossibile che per pochi gradi e per l'intero quadrante pas&shy;<lb/>sasse un mobile tanto differente lunghezza di via nel medesimo tempo. </s>

<s>Volle <lb/>nonostante ricorrere alle esperienze, facendo scendere alcune pallottoline den&shy;<lb/>tro uno scatolone, e confermando dal fatto quella prima impossibilit&agrave; giu&shy;<lb/>dicata col semplice discorso. </s></p><p type="main">

<s>Galileo importunamente insisteva per persuadere al celebre Matematico <lb/>che la cosa non era impossibile, e, invece di servirsi dello scatolone, fallace <lb/>o per non essere ben pulito, <lb/>o per non essere esattamen&shy;<lb/>te girato in cerchio; lo con&shy;<lb/>sigliava a tener quel mede&shy;<lb/>simo modo, col quale diceva <lb/>di essersi egli stesso con tan&shy;<lb/>ta certezza chiarito del ve&shy;<lb/>ro. </s>

<s>&ldquo; Piglio, scriveva nella ci&shy;<lb/>tata Lettera, data da Padova <lb/>il d&igrave; 20 Novembre 1602, due <lb/><figure id="id.020.01.2144.1.jpg" xlink:href="020/01/2144/1.jpg"/></s></p><p type="caption">

<s>Figura 206.<lb/>fili sottili, lunghi ugualmente due o tre braccia l'uno, e <lb/>sieno AB (fig. </s>

<s>206), EF (fig. </s>

<s>207), e gli appicco a due <lb/><figure id="id.020.01.2144.2.jpg" xlink:href="020/01/2144/2.jpg"/></s></p><p type="caption">

<s>Figura 207.<lb/>chiodetti A, E, e nell'altre estremit&agrave; B, F lego due palle di piombo uguali, <pb xlink:href="020/01/2145.jpg" pagenum="388"/>sebben niente importa se fossero disuguali, rimovendo poi ciascuno dei detti <lb/>fili dal suo perpendicolo, ma uno assai, come saria per l'arco CB, e l'altro <lb/>pochissimo, come saria per l'arco IF. </s>

<s>Gli lasci&ograve; poi nell'istesso tempo andare <lb/>liberamente, e l'uno comincia a descrivere archi grandi simili al BCD, e <lb/>l'altro ne descrive de'piccoli, simili al FIG, ma non per&ograve; consuma pi&ugrave; <lb/>tempo il mobile B a passare tutto l'arco BCD, che si faccia l'altro mobile <lb/>F a passare l'arco FIG &rdquo; (Alb. </s>

<s>VI, 20, 21). </s></p><p type="main">

<s>Il modo di assicurarsi della verit&agrave; di questo fatto Galileo lo riduce prin&shy;<lb/>cipalmente a numerare le vibrazioni grandi e le piccole, ma poi ne soggiunge <lb/>un altro, in cui si chiama giudice il senso della vista. </s>

<s>Questo secondo modo, <lb/>oltre ad essere meno tedioso, si rendeva assai pi&ugrave; concludente, e fu grande <lb/>sventura dello Sperimentatore il non dargli che un'importanza secondaria, <lb/>per cui non us&ograve; forse in praticarlo la debita diligenza. </s>

<s>Ci&ograve; che i fatti da <lb/>narrare confermeranno trasparisce intanto dalle seguenti parole che Galileo <lb/>prosegue a scrivere a Guidubaldo: </s></p><p type="main">

<s>&ldquo; Il mobile B passa per lo grand'arco BCD, e ritorna per lo mede&shy;<lb/>simo BCB, e poi ritorna verso D, e va per 500 e 1000 volte reiterando le <lb/>sue reciprocazioni. </s>

<s>L'altro parimente va da E in G, e di poi torna in F, e <lb/>parimente far&agrave; molte reciprocazioni, e nel tempo ch'io numero <emph type="italics"/>v, g,<emph.end type="italics"/> le prime <lb/>cento grandi reciprocazioni BCD, DCB, ecc., un altro osservatore numera <lb/>cento altre reciprocazioni per FIG piccolissime, e non ne numera pure una <lb/>sola di pi&ugrave;; segno evidentissimo che ciascheduna particolare di esse gran&shy;<lb/>dissime BCD consuma tanto tempo, quanto ognuna delle minime particolari <lb/>FIG. </s>

<s>Or se tutta la BCD vien passata in tanto tempo, in quanto la FIG, <lb/>ancora le loro met&agrave;, che sono le cadute per gli archi disuguali della mede&shy;<lb/>sima quarta, saranno fatte in tempi uguali. </s>

<s>Ma anco, senza stare a nume&shy;<lb/>rar altro, V. S. Ill.ma vedr&agrave; che il mobile F non far&agrave; le sue piccolissime <lb/>reciprocazioni pi&ugrave; frequenti, che il mobile B le sue grandissime, ma sempre <lb/>anderanno insieme &rdquo; (ivi, pag. </s>

<s>21). </s></p><p type="main">

<s>Lusingandosi ora Galileo che fossero queste sue esperienze tanto esatte, <lb/>da non si mettere in dubbio la verit&agrave; del nuovo fatto scoperto, erasi dato <lb/>con grande studio a ricercarne la matematica dimostrazione, persuaso doversi <lb/>corrispondere amichevolmente insieme la Fisica e la Geometria. </s>

<s>E giunto, <lb/>per quelle vie che sono ai nostri Lettori oramai ben note, a dimostrar le <lb/>ammirabili propriet&agrave; delle corde, sperava che un breve passo lo dovesse fe&shy;<lb/>licemente condurre alla desiderata dimostrazione dell'isocronismo per gli ar&shy;<lb/>chi, ci&ograve; che a far dianzi l'udimmo accoratamente dire a Guidubaldo <emph type="italics"/>non <lb/>esser potuto spuntare.<emph.end type="italics"/> L'espressione, nella propriet&agrave; del linguaggio toscano, <lb/>era efficacissima a significar la mente e l'animo di Galileo, il quale tanto <lb/>era certo del fatto, da non sospettar nemmeno dalla lontana che non si po&shy;<lb/>tesse, senza trasgredire i termini meccanici, dimostrarlo, perch&egrave; non era esat&shy;<lb/>tamente vero; ma ne dava tutta la colpa alla sua propria insufficienza, co&shy;<lb/>sicch&egrave;, invocando altri principii, tenendo altre vie, facendo insomma nuovi <lb/>sforzi, sperava di riuscire a dimostrar con meccaniche ragioni che le corse <pb xlink:href="020/01/2146.jpg" pagenum="389"/>e le ricorse per gli archi di qualunque ampiezza si spediscono dai pendoli <lb/>tutte nei medesimi tempi. </s></p><p type="main">

<s>Trent'anni dopo quegli sforzi fatti, e i progrediti esercizi intorno alla <lb/>Scienza del moto, erano riusciti a niente, cosicch&egrave;, volendo alla fin dei dia&shy;<lb/>loghi Dei due massimi sistemi render solennemente noto al mondo il pro&shy;<lb/>gramma delle sue meccaniche scoperte, intanto che meditava di raccoglierle <lb/>insieme in un Libro a parte, annunziava tra le altre maravigliose propriet&agrave; <lb/>del pendolo, &ldquo; che fa le sue vibrazioni con l'istessa frequenza, o pochissimo <lb/>o quasi insensibilmente differente, sien elleno fatte per archi grandissimi o <lb/>per piccolissimi dell'istessa circonferenza &rdquo; soggiungendo di essersi per ri&shy;<lb/>petute esperienze assicurato che &ldquo; se noi rimoveremo il pendolo dal perpen&shy;<lb/>dicolo uno, due, o tre gradi solamente, oppure lo rimoveremo 79, 80, o an&shy;<lb/>che sino a una quarta intera, lasciato in sua libert&agrave;, far&agrave; nell'uno e nell'altro <lb/>caso le sue vibrazioni con la medesima frequenza &rdquo; (Alb. </s>

<s>I, 487). </s></p><p type="main">

<s>Dop'avere ripetuto cos&igrave;, senz'altre nuove osservazioni, quel che tren&shy;<lb/>t'anni prima avea scritto a Guidubaldo del Monte, Galileo, come corollario <lb/>dipendente dall'isocronismo dei pendoli, annunziava la bellissima conclusione <lb/>che, fatto un arco con una tavola ben pulita e liscia, come sarebbe la cassa <lb/>di un vaglio, e posta una palla in qual si voglia punto della sua concavit&agrave;, <lb/>arriva al termine infimo, sempre, di dovunque movesse, in tempi uguali: <lb/>soggiungeva poi a questi pur per simili corollarii delle propriet&agrave; del pen&shy;<lb/>dolo, il tautocronismo per le corde, e il brachistocronismo per gli archi (ivi, <lb/>pag. </s>

<s>488). </s></p><p type="main">

<s>Sembrerebbe di qui che, per ragione meccanica della sua scoperta, non <lb/>essendo dopo tanto tempo e dopo tante fatiche potuto spuntar Galileo a tro&shy;<lb/>vare una dimostrazione diretta, s'acquetasse finalmente a far valere per gli <lb/>archi il tautocronismo ritrovato verissimo per le corde. </s>

<s>La congettura &egrave; ve&shy;<lb/>rificata da chiarissimi documenti posteriori, come dalle celebri Lettere al <lb/>Carcaville (Alb. </s>

<s>VII, 158) e a Lorenzo Realio (ivi, pag. </s>

<s>168) ma pi&ugrave; solen&shy;<lb/>nemente dal primo dialogo Delle due nuove scienze, dove cos&igrave; espressamente <lb/>si legge: &ldquo; E quanto al primo dubbio che &egrave; se veramente e puntualissi&shy;<lb/>mamente l'istesso pendolo fa tutte le sue vibrazioni massime, mediocri e mi&shy;<lb/>nime, sotto tempi precisamente eguali, io mi rimetto a quello, che intesi gi&agrave; <lb/>dal nostro Accademico, il quale dimostra bene che il mobile, che discen&shy;<lb/>desse per le corde suttese a qual si voglia arco, le passerebbe necessaria&shy;<lb/>mente tutte in tempi eguali, tanto le suttese sotto cent'ottanta gradi, cio&egrave; <lb/>tutto il diametro, quanto le suttese di cento, di sessanta, di due, di mezzo <lb/>e di quattro m&igrave;nuti, intendendo che tutte vadano a terminar nell'infimo <lb/>punto toccante il piano orizzontale &rdquo; (Alb. </s>

<s>XIII, 98). </s></p><p type="main">

<s>Quel giovane, cos&igrave; scrupoloso di trasgredire i termini meccanici, ora <lb/>dunque da vecchio s'&egrave; fatto di pi&ugrave; rilasciata coscienza, la quale non avreb&shy;<lb/>begli dovuto consentire cos&igrave; facile il trapasso dalle propriet&agrave; meccaniche <lb/>delle corde alle analoghe propriet&agrave; meccaniche per gli archi sottesi. </s>

<s>Che se <lb/>avesse dovuto ridurlo ai termini del dovere, conveniva piuttosto suggerirgli <pb xlink:href="020/01/2147.jpg" pagenum="390"/>questa per la pi&ugrave; sicura via da tenere: ammetter cio&egrave; che, in tanto si po&shy;<lb/>tessero dire isocroni gli archi, in quanto si confondono con le corde, le quali <lb/>solo s'&egrave; riuscito a dimostrare isocrone: e insomma non asserire cos&igrave; con&shy;<lb/>fidentemente che, per tutta la quarta del cerchio, vanno le vibrazioni eguali, <lb/>ma quelle sole fatte per un piccolo numero di gradi. </s>

<s>Che se non tenne Ga&shy;<lb/>lileo dietro alla severa logica di questo discorso, si deve alla persuasione che <lb/>fossero puntualissime le sue esperienze, le quali non avendo potuto altri&shy;<lb/>menti dimostrare, e non convenendogli di confessar al pubblico la sua in&shy;<lb/>sufficienza, com'avea fatto da giovane e in privato con Guidubaldo; s'attenne <lb/>al partito di far dell'isocronismo dei pendoli un corollario alla VI proposi&shy;<lb/>zione del II libro Dei moti locali. </s></p><p type="main">

<s>Nella fallacia di cos&igrave; fatte delicatissime esperienze incorsero altres&igrave; il <lb/>Baliani e Giovan Marco, il primo dei quali non profess&ograve; l'isocronismo, che <lb/>quale un semplice supposto sperimentale, ponendolo cos&igrave; formulato per uno <lb/>dei fondamenti alle sue meccaniche proposizioni: &ldquo; Aequipendulorum eorum&shy;<lb/>dem vibrationes sunt aequidiuturnae etiamsi inaequales &rdquo; (De motu cit., <lb/>pag. </s>

<s>15). Ma il Matematico tedesco volle provarsi a darne diretta dimostra&shy;<lb/>zione matematica, con l'apparato di quattro lemmi, premessi in servigio al <lb/>suo XXIV teorema <emph type="italics"/>De proportione motus,<emph.end type="italics"/> proposto in tal forma: &ldquo; Perpen&shy;<lb/>diculum, ex quolibet puncto eiusdem circuli, <lb/>aequali tempore recurrit in suam stationem. <lb/></s>

<s>&rdquo; Nel circolo TUXB (fig. </s>

<s>208), col centro in <lb/>A, sollevato il perpendicolo AT o in AB, o in <lb/>AD, o in AF, o in qual si voglia altra minore <lb/>altezza, dimostra l'Autore che tanto da B, <lb/>quanto da D o da F, ricorre in T esso perpen&shy;<lb/>dicolo alla sua prima stazione, sempre nel <lb/>medesimo tempo. </s>

<s>Il ragionamento muove in <lb/>parte da principii dimostrati, e in parte da <lb/>principii supposti, ma la conclusione non &egrave;, e <lb/>non poteva esser altro che uno sforzo dell'inge&shy;<lb/><figure id="id.020.01.2147.1.jpg" xlink:href="020/01/2147/1.jpg"/></s></p><p type="caption">

<s>Figura 208<lb/>gno. </s>

<s>Le velocit&agrave; in B, in D e in F son proporzionali ai seni AB, CD, EF, <lb/>che in uguali archi intercetti vanno via via scemando di lunghezza, ma cre&shy;<lb/>scono le proporzioni fra loro, avendo CD a EF maggior ragione che AB a <lb/>CD, cosicch&egrave; l'incremento da una parte e il decremento dall'altra riducono <lb/>all'egualit&agrave; costante la fine del moto. </s>

<s>&ldquo; At vero quia ad singula puncta, <lb/>mutata sinuum ratione, mutatur quoque ratio velocitatis; maior enim propor&shy;<lb/>tio CD ad EF, quam AB ad CD, erit quoque maior proportio arcus D F ad <lb/>ad FH quam arcus BD ad DF. </s>

<s>Quia ergo, cum hoc sinuum et arcuum decre&shy;<lb/>mento, continuo augetur illorum proportio, minuitur vero distantia termi&shy;<lb/>norum motus; necesse est demum absumi et deficere, illoque deficiente, mo&shy;<lb/>tum coaequari &rdquo; (fol. </s>

<s>I, 2). </s></p><p type="main">

<s>Lusingavasi Giovan Marco di aver dato cos&igrave; buona dimostrazion mate&shy;<lb/>matica dell'isocronismo dei pendoli, ingannato dalle osservazioni dei fatti, <pb xlink:href="020/01/2148.jpg" pagenum="391"/>intorno ai quali abbiamo dianzi veduto come fossero similmente tratti in <lb/>inganno Galileo e il Baliani. </s>

<s>Che fosse da un'altra parte una tale osserva&shy;<lb/>zione veramente ingannatrice, lo conferma l'esempio del pi&ugrave; diligente spe&shy;<lb/>rimentatore, che si conoscesse a quei tempi, il quale pubblic&ograve; solennemente <lb/>di aver per ripetuti sperimenti scoperto che, oscillando i pesi penduli a un <lb/>filo, passano i maggiori e i minori archi descritti in tempi sempre fra loro <lb/>uguali. </s></p><p type="main">

<s>Giovan Batista Riccioli era nel 1629 professore in Parma, nel collegio <lb/>dei gesuiti, quando un giorno gli scrisse il Cabeo da Ferrara, pregandolo a <lb/>fare esperienza se due pendoli, del medesimo peso e della medesima altezzza, <lb/>ritirati a ugual distanza dal perpendicolo, e poi di l&igrave; lasciati ambedue a un <lb/>tempo, andavano e ritornavano sempre di pari passo. </s>

<s>Ebbe esecuzion la ri&shy;<lb/>chiesta in compagnia di Daniello Bartoli e di Alfonso Iseo, i quali ritrova&shy;<lb/>rono essere propriamente cos&igrave;, come il Cabeo aveva a loro annunziato. </s></p><p type="main">

<s>Stava allora il Riccioli tutto in sollecito studio di ritrovare le propor&shy;<lb/>zioni delle cadute dei gravi, ma a condur la difficile impresa vivamente <lb/>sentiva il bisogno di uno strumento, da misurare esatte le minuzie del <lb/>tempo. </s>

<s>Le pulsazioni delle arterie, i flussi dell'acqua o della polvere nelle <lb/>clessidre, e simili altri cronometri allora in uso, gli reputava tanto fallaci, <lb/>da non si confidar che le proporzioni cos&igrave; misurate, nemmen prossimamente, <lb/>rispondessero alle vere. </s>

<s>Occorsogli poi per avventura di fare, agl'inviti del <lb/>Cabeo, le sopra dette esperienze, &ldquo; tunc suspicari coepi, scrive lo stesso Ric&shy;<lb/>cioli, oscillationes eiusdem perpendiculi quaslibet aequales esse quibuslibet <lb/>in tempore, quod postea (ci&ograve; che a pag. </s>

<s>386 del II tomo dello stesso <emph type="italics"/>Alma&shy;<lb/>gesto nuovo,<emph.end type="italics"/> dice essere avvenuto in Ferrara nel 1634) iteratis accuratius <lb/>experimentis, perdidici. </s>

<s>Necdum enim tum ad manus meas pervenerant dia&shy;<lb/>logi Galilaei <emph type="italics"/>De mundi systemate,<emph.end type="italics"/> ubi, dialogo II, idem affirmatur, nec <lb/>D. </s>

<s>Joannis Baptistae Baliani opusculum <emph type="italics"/>De motu naturali solidorum:<emph.end type="italics"/> illos <lb/>enim biennio, hoc decennio post tantummodo legi &rdquo; (Almag. </s>

<s>novi, T. I, Bo&shy;<lb/>noniae 1651, pag. </s>

<s>84). </s></p><p type="main">

<s>Gli esperimenti, dai quali dice il Riccioli di avere appresso il fatto an&shy;<lb/>nunziato, son descritti nell'appresso proposizione I del cap. </s>

<s>XX del II libro, <lb/>la quale, richiamando i Lettori addietro alla figura 207 per rammemorare <lb/>a loro che <emph type="italics"/>vibrazione semplice<emph.end type="italics"/> chiama l'Autore la semplice andata da F <lb/>in G, e <emph type="italics"/>vibrazione composta<emph.end type="italics"/> la detta andata col ritorno da G in H, un poco <lb/>pi&ugrave; sotto ad F; &egrave; cos&igrave; formulata: &ldquo; Perpendiculi eiusdem quaelibet vibratio <lb/>simplex cuilibet vibrationi simplici, et quaelibet composita cuilibet compo&shy;<lb/>sitae ad sensum aequalis est in tempore sui motus, per se, seu est aequi&shy;<lb/>diuturna, seu, graece, <emph type="italics"/>isochrona &rdquo;<emph.end type="italics"/> (ibid., pag. </s>

<s>85). </s></p><p type="main">

<s>Numerammo, poi si legge per la dimostrazione, nelle notti del 19 e <lb/>20 Maggio, e del 2 Giugno, il numero delle vibrazioni fatte da un pendolo <lb/>dal punto del passaggio della Spiga, al punto del passaggio di Arturo al <lb/>medesimo meridiano, e trovammo due volte vibrazioni semplici 3212, e una <lb/>volta 3214. &ldquo; At si vibrationes eiusdem perpendiculi inaequali tempore sen-<pb xlink:href="020/01/2149.jpg" pagenum="392"/>sibiliter fierent, non posset non esse magna differentia in numero illarum, <lb/>post multas saltem vibrationes se prodiens. </s>

<s>Nusquam autem se prodit, ergo <lb/>ad sensum sunt aequales in tempore &rdquo; (ibid.). </s></p><p type="main">

<s>Soggiunge immediatamente il Riccioli a queste parole ch'egli intende <lb/>dire dell'uguaglianza assoluta, escluse le cause accidentali. </s>

<s>&Egrave; notabile poi che <lb/>riduca queste cause accidentali al vento, &ldquo; qui ex adverso flaret, aut aliud <lb/>quidpiam extraordinarium perpendiculum incitaret, aut retardaret &rdquo; (ibid.). <lb/>Dicemmo esser ci&ograve; notabile, perch&egrave; la temuta causa perturbatrice in verit&agrave; <lb/>non esiste, essendo, come Galileo aveva gi&agrave; pubblicamente insegnato, del <lb/>tutto impossibile il far fare a un pendolo le vibrazioni sotto altri tempi, da <lb/>quelli per naturale necessit&agrave; determinati &ldquo; salvo che con allungargli o ab&shy;<lb/>breviargli la corda &rdquo; (Alb. </s>

<s>I, 487). </s></p><p type="main">

<s>Dal non aver riconosciuta la natura meccanica dello strumento dipende <lb/>pure l'altra inutile scrupolosaggine dal Riccioli osservata nelle sue espe&shy;<lb/>rienze, qual &egrave; quella di tenere esattissimo conto del peso del pendolo e delle <lb/>sue sospensure. </s>

<s>Pu&ograve; essere il peso accidentalmente notato nelle esperienze <lb/>di colui che sa ridurre il pendolo composto al semplice, e che &egrave; ben per&shy;<lb/>suaso essere le vibrazioni maggiori pi&ugrave; diuturne, essendo che un maggior <lb/>peso conferisce alla maggior duratura delle vibrazioni ampie: ma nella mente <lb/>del Riccioli che professava l'isocronismo assoluto, e che tanto era ancora <lb/>lontano dal presentir la teoria de'centri di oscillazione, quel notare il peso <lb/>del grave ondeggiante, e della sua catena, era senza alcuna ragione, e un <lb/>impaccio di pi&ugrave;, volontariamente frappostosi alla facilit&agrave;, e talvolta anco al&shy;<lb/>l'esattezza delle esperienze. </s>

<s>Non l'arte insomma, ma la scienza fu che fece <lb/>difetto in ci&ograve; al solertissimo Sperimentatore. </s></p><p type="main">

<s>Galileo aveva dell'assoluta uguaglianza dei pendoli assegnata un'altra <lb/>causa perturbatrice, la quale, perciocch&egrave; non appariva avversa alle approvate <lb/>verit&agrave; della scienza, riusc&igrave; molto pi&ugrave; seducente di quella falsa assegnata dal <lb/>Riccioli. </s>

<s>Si riduce quell'accennata causa perturbatrice al mezzo dell'aria &ldquo; la <lb/>quale resistendo all'essere aperta, ritarda qualche poco, e impedisce il moto <lb/>del pendolo, ma l'impedimento &egrave; ben poco, di che &egrave; argomento il numero <lb/>grande delle vibrazioni, che si fanno avanti che il mobile si fermi del tutto &rdquo; <lb/>(Alb. </s>

<s>I, 250). Or essendo da tutti quest'impedimento riconosciuto reale, e <lb/>dal fatto qui notato da Galileo argomentandosi alla sua piccolezza, questa <lb/>era tale da lusingar che a lei sola si dovessero attribuir quelle piccole ine&shy;<lb/>guaglianze, notabili all'esperienze pi&ugrave; diligenti e pi&ugrave; delicate. </s>

<s>Di qui s'in&shy;<lb/>tende perch&egrave;, nella prima met&agrave; del secolo XVI, la maggior parte e i pi&ugrave; au&shy;<lb/>torevoli fra i Fisici e i Matematici professassero, astraendo dalle piccole cause <lb/>perturbatrici, dipendenti dalle resistenze del mezzo, con Gal&igrave;leo, col Baliani <lb/>e con Giovan Marco, l'isocronismo assoluto. </s></p><p type="main">

<s>Per citare di quei Fisici, e di quei Matematici qualche esempio, il Mer&shy;<lb/>senno, in un libro, in cui ordinava e dava solenne pubblicit&agrave; a molte dot&shy;<lb/>trine per la massima parte da lui attinte ai libri, o nei familiari colloqui con <lb/>gli Scienziati italiani, cos&igrave; scriveva: &ldquo; Recursus fili AB (fig. </s>

<s>209), a quovis <pb xlink:href="020/01/2150.jpg" pagenum="393"/>puncto quadrantis BD, vel BC, redeuntes, sunt proxime isocroni, hoc est <lb/>fiunt aequali tempore, nam, sive globulum <lb/>ex B ad G, vel ad E, vel ad D traxeris, <lb/>tempus, quo descendit a G ad B, prope&shy;<lb/>modum aequale est tempori, quo descendit <lb/>a G ad B. </s>

<s>Dixi <emph type="italics"/>propemodum<emph.end type="italics"/> et <emph type="italics"/>prox ime,<emph.end type="italics"/><lb/>quod aer, a D ad B interiectus, magis <lb/>impediat globum B ex D, quam aer, inter <lb/>E et B interpositus, globum ex E rede&shy;<lb/><figure id="id.020.01.2150.1.jpg" xlink:href="020/01/2150/1.jpg"/></s></p><p type="caption">

<s>Figura 209<lb/>untem &rdquo; (Cogitata physico mat., Parisiis 1644, pag. </s>

<s>10). Cos&igrave; fatto impe&shy;<lb/>dimento avvertiva il Mariotte essere altres&igrave; maggiore o minore, secondo la <lb/>maggiore o minor virt&ugrave; del peso specifico del pendolo in superarlo, cosic&shy;<lb/>ch&egrave; da certi calcoli, istituiti nella proposizione VIII del suo trattato <emph type="italics"/>Du mou&shy;<lb/>vement,<emph.end type="italics"/> conclude che se il pendolo stesso &egrave; d'oro &ldquo; et que la resistance <lb/>de l'air n'augmente le tems de sa ch&ucirc;te par 90 degrez que de 1/13, les gran&shy;<lb/>des et les petites vibrations seront egales. </s>

<s>Mais soit que le poids soit de bois <lb/>ou de plumb, les vibrations par un arc de 30 degrez et au-dessous seront <lb/>sensiblement egales &rdquo; (Oeuvres, T. II cit., pag. </s>

<s>566). </s></p><p type="main">

<s>Le teorie per&ograve; del Mariotte erano per s&egrave; medesime insufficienti a de&shy;<lb/>cidere la questione dell'isocronismo dei pendoli circolari, la qual questione, <lb/>prima che pubblicasse l'Huyghens il suo <emph type="italics"/>Orologio oscillatorio,<emph.end type="italics"/> veniva ri&shy;<lb/>messa al giudizio unico delle esperienze. </s>

<s>Queste, non molti anni dopo pas&shy;<lb/>sata la prima met&agrave; del secolo XVII, riuscirono finalmente a confermare i <lb/>dubbi di quei pochi, che contradissero a Galileo, o ai primi seguaci di lui, <lb/>concludendo, come si narrer&agrave; in quest'altra parte del nostro discorso, che <lb/>l'isocronismo assoluto, nelle scese per gli archi dei cerchi, repugna alla <lb/>verit&agrave; dei fatti, con maggior diligenza che non si fosse fatto fin allora, os&shy;<lb/>servati. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Guidubaldo del Monte, a cui primo Galileo annunziava la sua scoperta, <lb/>fu anche il primo a contradirla, parendogli irragionevole che, &ldquo; pigliandosi <lb/>una quarta di cerchio lunga cento miglia, due mobili uguali possano pas&shy;<lb/>sarla uno tutta, e l'altro un palmo solo in tempi uguali &rdquo; (Alb. </s>

<s>VI, 22). <lb/>Soggiungeva, a conferma della sua contradizione, un'esperienza, che Gali&shy;<lb/>leo stesso, per le gi&agrave; accennate ragioni, reputava fallace. </s>

<s>Nonostante, nel <lb/>dialogo ultimo Dei due massimi sistemi, descriveva l'Autore l'esperienza <lb/>medesima di Guidubaldo, suggerendo di farla, con una palla ben rotonda e <lb/>tersa, dentro la cassa di un vaglio, e affermando, com'avrebbe fatto della <lb/>proposizion matematica pi&ugrave; certamente dimostrata, che &ldquo; posta la palla in <lb/>qualsivoglia luogo, o vicino o lontano dall'infimo termine B (immaginando <lb/>che DEGB, nella precedente figura, rappresenti la quarta della concavit&agrave; cir&shy;<lb/>colare), come mettendola nel punto G, ovvero in E o in D, e lasciata in li-<pb xlink:href="020/01/2151.jpg" pagenum="394"/>bert&agrave;, in tempi uguali o insensibilmente differenti arriver&agrave; al termine B, par&shy;<lb/>tendosi dal G o dall'E o dal D, o da qualsivoglia altro luogo &rdquo; (Alb. </s>

<s>I, 488). </s></p><p type="main">

<s>Se una tal formulata proposizione fosse puramente teorica o sperimen&shy;<lb/>tale, non &egrave; difficil decidere a chi ripensa che mancavano, cos&igrave; a Galileo come <lb/>a Guidubaldo, gli strumenti necessari a misurar, nella scesa del grave o dal <lb/>punto G o dal punto D, l'uguaglianza o la differenza dei tempi; e dall'al&shy;<lb/>tra parte potevasi avere ugualmente dubbio della perfetta forma circolare, <lb/>cos&igrave; nello scatolone, come nella cassa del vaglio. </s>

<s>Fu la sola teoria dunque <lb/>che resist&egrave; alle contradizioni, alle quali non si sarebbe potuto dare per ve&shy;<lb/>rit&agrave; risposta definitiva nemmeno dalle esperienze pi&ugrave; accurate, come dovet&shy;<lb/>tero senza dubbio esser quelle istituite dagli Accademici del Cimento, a cui <lb/>parve in principio che avesse avuto ragion Guidubaldo, e poi confermarono <lb/>l'assoluta proposizione annunziata di sopra da Galileo. </s>

<s>Sperimentando infatti <lb/>la prima volta il d&igrave; 29 Dicembre 1661, trovarono che &ldquo; le corse e ricorse <lb/>d'una palla d'avorio, fatte per un canal circolare, non sono equitemporanee, <lb/>ma le maggiori sono pi&ugrave; veloci, e le minori pi&ugrave; tarde &rdquo; (Targioni, Noti&shy;<lb/>zie ecc. </s>

<s>cit., T. II, P. II, pag. </s>

<s>669, 70). Il d&igrave; 7 del Gennaio appresso, tor&shy;<lb/>nando a ripetere la medesima esperienza, scrissero gli Accademici, nel loro <lb/>solito Diario, di avere invece trovato che &ldquo; le corse e ricorse d'una palla <lb/>nel canale circolare, sia quella di metallo o di avorio, maggiore o minore, <lb/>sono equitemporanee &rdquo; e che &ldquo; sia la palla di metallo o d'avorio, grande o <lb/>piccola, fa ugual numero di vibrazioni in tempi uguali &rdquo; (ivi, pag. </s>

<s>670). </s></p><p type="main">

<s>Ben s'accorsero que'solertissimi Sperimentatori che l'eleggere questo <lb/>modo era un voler andar, senza vantaggio, ad affrontare le incertezze ine&shy;<lb/>vitabili prodotte dagli attriti, e dalla imperfetta rotondit&agrave; del canale, e tor&shy;<lb/>naron perci&ograve; con savio consiglio ai funependoli. </s>

<s>Ma perch&egrave; pareva a loro <lb/>che di questi avesse dato certezza di scienza Galileo, e non si potevano in&shy;<lb/>durre a sottoporre al cimento le dottrine del venerato Maestro, se non che <lb/>quando altri avesse sollevato intorno a quelle qualche temibile dubbio, giova <lb/>a noi accennare ad alcuni di quei primi e pi&ugrave; autorevoli, che, avendo con <lb/>diligenza osservate le corse e le ricorse dei pendoli, trovarono che non tutte <lb/>erano equidiuturne, e che le dottrine di Galileo perci&ograve; non rispondevano <lb/>esattamente alla verit&agrave; dei fatti sperimentati. </s></p><p type="main">

<s>Citeremo fra que'liberi censori di Galileo, o fra quegli spregiudicati os&shy;<lb/>servatori dei fatti naturali, Gotifredo Wendelin, e Niccol&ograve; Cabeo, l'efficacia <lb/>dei quali in diffondere la notizia delle loro esperienze si dee forse, piutto&shy;<lb/>sto che a loro stessi, all'opera del Riccioli. </s>

<s>Nell'Almagesto nuovo infatti, <lb/>pi&ugrave; facilmente che ne'libri del Matematico straniero, a noi rari, o nelle di&shy;<lb/>sperse epistole e nelle erudite dissertazioni di lui, lessero gl'Italiani che alle <lb/>cause dell'inuguaglianza dei pendoli &ldquo; addit Vendelinus, si pendulum attol&shy;<lb/>latur ultra gradus 40, aut 45 vibrationes eius, esse longioris temporis &rdquo; <lb/>(T. </s>

<s>I cit., pag. </s>

<s>85). </s></p><p type="main">

<s>Poco pi&ugrave; avanti, in questo medesimo cap. </s>

<s>XX del libro II, si cita dal <lb/>Riccioli il trattato del Wendelin <emph type="italics"/>De ecclipsibus, et idea Tabularum atlan-<emph.end type="italics"/><pb xlink:href="020/01/2152.jpg" pagenum="395"/><emph type="italics"/>ticarum,<emph.end type="italics"/> per mostrar come ivi, in prefinir la misura alla lunghezza del pen&shy;<lb/>dolo che batte i secondi, non fosse stato esso Wendelin col Langreno e con <lb/>altri molto esatto, e richiamando all'esame altre sentenze, in tal proposito <lb/>soggiunte, il Riccioli stesso cos&igrave; scrive: &ldquo; Non ostendit autem quomodo vera <lb/>sint quae subnectit: <emph type="italics"/>Etsi autem verum non est aeque diuturnas esse omnes <lb/>eiusdem suspensurae oscillationes, verum autem est hyeme, hoc est sole <lb/>perigeo, plures una hora fieri, quam estate, seu sole apogeo<emph.end type="italics"/> Et nisi forte <lb/>putet ob Terrae motum eas incitari, concitato motu diurno ob accessum ad <lb/>Solem, retardari autem in recessu, quod etiam Keplero, Longomontano et <lb/>Bullialdo placuisse docebimus; concedit tamen Vendelinus: <emph type="italics"/>Si utrinque pen&shy;<lb/>dulum extra lineam perpendiculi sui extrahatur ad gradus 10, conficere <lb/>oscillationes plurimas, et in longissimum tempus isochronas, seu aeque <lb/>diuturnas, et ad omnem sensum aequales &rdquo;<emph.end type="italics"/> (ibid., pag. </s>

<s>88). </s></p><p type="main">

<s>Il Riccioli non crede all'esperienza del Wendelin, che cio&egrave; nell'in&shy;<lb/>verno faccia pi&ugrave; frequenti il pendolo le sue vibrazioni che nell'estate, per&shy;<lb/>ch&egrave;, non essendosi ancora scoperto che la causa del misterioso effetto era <lb/>dovuta alla dilatazion del calore, per cui le sospensure metalliche s'allun&shy;<lb/>gano e s'accorciano al variare delle stagioni, s'attribuiva il fatto al moto <lb/>della Terra, con tanta ostinazione negato dal Riccioli stesso, il quale per&ograve; <lb/>non sembra ritroso a concedere al Wendelin l'altra osservazione, di non <lb/>minore importanza, perch&egrave; riduceva alle precision del vero le dottrine di <lb/>Galileo; che cio&egrave; il moto dei pendoli non &egrave; uguale per tutta l'ampiezza del <lb/>quadrante, ma quando solo si riduce alle vibrazioni piccole, come dentro a <lb/>una diecina di gradi. </s></p><p type="main">

<s>Quanto al Cabeo, egli instituiva nel I libro de'suoi Commenti meteo&shy;<lb/>rologici una questione sui pendoli, revocando a uno a uno a sottile e rigo&shy;<lb/>roso esame i documenti galileiani, ma pi&ugrave; di proposito trattenendosi sopra <lb/>quello, in cui si asserisce essere uguali in tempo le vibrazioni di due pen&shy;<lb/>doli di ugual lunghezza, bench&egrave; uno sia grave e l'altro leggero. </s>

<s>Nel primo <lb/>dialogo infatti Delle due nuove scienze aveva, pi&ugrave; chiaramente che altrove, <lb/>espressa cos&igrave; questa sua dottrina, comparando insieme due pendoli sospesi <lb/>a ugual lunghezza di filo, ma uno di sughero e l'altro di piombo: </s></p><p type="main">

<s>&ldquo; Slargato il pendolo del piombo v. </s>

<s>g. </s>

<s>cinquanta gradi dal perpendi&shy;<lb/>colo, e di l&igrave; lasciato in libert&agrave;, scorre, e passando oltre al perpendicolo quasi <lb/>altri cinquanta, descrive l'arco di quasi cento gradi, e ritornando per s&egrave; <lb/>stesso indietro, descrive un altro minore arco, e continuando le sue vibra&shy;<lb/>zioni, dopo gran numero di quelle, si riduce finalmente alla quiete. </s>

<s>Cia&shy;<lb/>scheduna di tali vibrazioni si fa sotto tempi uguali, tanto quella di novanta <lb/>gradi, quanto quella di cinquanta o di venti, di dieci, di quattro; sicch&egrave; in <lb/>conseguenza la velocit&agrave; del mobile vien sempre languendo, poich&egrave;, sotto <lb/>tempi eguali, va passando successivamente archi sempre minori a minori. </s>

<s><lb/>Un simile, anzi l'istesso effetto, fa il sughero pendente da un filo altret&shy;<lb/>tanto lungo, salvo che in minor numero di vibrazioni si conduce alla quiete, <lb/>come meno atto, mediante la sua leggerezza, a superar l'ostacolo dell'aria. <pb xlink:href="020/01/2153.jpg" pagenum="396"/>Con tutto ci&ograve; tutte le vibrazioni grandi e piccole si fanno sotto tempi <lb/>eguali tra di loro, ed eguali ancora ai tempi delle vibrazioni del piombo &rdquo; <lb/>(Alb. </s>

<s>XIII, 88). </s></p><p type="main">

<s>Ora, osserva il Cabeo che questo, cos&igrave; francamente asserito da Galileo, <lb/>pu&ograve; ammettersi <emph type="italics"/>si rudi minerva et crassiori mensura examinetur,<emph.end type="italics"/> ma, se <lb/>si vuol discutere con pi&ugrave; esatti e pazienti esperimenti, si trover&agrave; manifesta&shy;<lb/>mente falso. </s>

<s>&ldquo; Si enim, ex aequali filo, duo valde inaequalia pondera suspen&shy;<lb/>dantur, et remotis illis a perpendiculo utrumque omnino eodem temporis <lb/>puncto liberetur, post primas undationes statim incipiunt dissentire, nec so&shy;<lb/>lum aequales, quoad magnitudinem, undationes non faciunt, sed nec aequa&shy;<lb/>les quoad tempus, et sicut gravius longiora spatia metitur, ita etiam longiori <lb/>mora producitur &rdquo; (Editio cit., pag. </s>

<s>99). E soggiunge di aver fatto di ci&ograve;, <lb/>per s&egrave; stesso e per altri, esperienza con due palle di piombo, ambedue so&shy;<lb/>spese a ugual lunghezza di filo, ma l'una pesa 60 scrupoli, e l'altra 15, e <lb/>di aver trovato che, mentre questa faceva 115 vibrazioni, quell'altra pi&ugrave; pe&shy;<lb/>sante ne faceva appena cento nel medesimo tempo. </s></p><p type="main">

<s>S'interrompe a questo punto dal Cabeo il ragionamento, per significare <lb/>ai Lettori un suo dubbio intorno al modo di misurar la lunghezza del filo, <lb/>d'onde potrebbe in parte dipendere la differenza fra l'esperienze di Galileo <lb/>e le sue proprie. </s>

<s>Avendo la palla di piombo, di 60 scrupoli, assai maggior <lb/>diametro dell'altra, di soli scrupoli 12, <emph type="italics"/>si dee prender la lunghezza del filo <lb/>insino a tutto il corpo grave pendente, o insino al centro di esso?<emph.end type="italics"/> Questo <lb/>medesimo quesito, in questa medesima forma, fu proposto da Giovanni Pie&shy;<lb/>roni a Galileo (Alb. </s>

<s>X, 68), il quale non seppe che si rispondere con cer&shy;<lb/>tezza di scienza, essendo troppo ancora lontana la soluzion del problema dei <lb/>centri di oscillazione. </s>

<s>Nonostante, udimmo poco fa dire al Baliani doversi <lb/>misurare i fili nella loro lunghezza <emph type="italics"/>comprehensis semidiametris<emph.end type="italics"/> dei corpi <lb/>di varia mole da essi fili pendenti, ci&ograve; che anche al Cabeo parve esser <emph type="italics"/>magis <lb/>secundum naturam rerum,<emph.end type="italics"/> e ne seguiron gli esempi gli stessi Accademici <lb/>del Cimento, i quali usarono di sospender palline di oro a tenuissimi fili di <lb/>seta, per avere il centro dell'oscillazione costituito nel centro della figura. </s></p><p type="main">

<s>Ma Galileo, intorno a ci&ograve; incerto, per fare esperienza dell'isocronismo <lb/>di due pendoli di vario peso, sceglieva corpi di differente gravit&agrave; specifica, <lb/>quali erano il sughero e il piombo, riducendoli sotto ugual forma e volume, <lb/>e cos&igrave; rendevasi sicuro della ugual lunghezza delle loro sospensure, o s&igrave; <lb/>avessero a computar fino alla superficie o insino al centro del corpo grave <lb/>pendente. </s></p><p type="main">

<s>Comunque sia, questo, dice il Cabeo, m'hanno costantemente dimostrato <lb/>le mie esperienze, al contrario di quelle descritte da Galileo, &ldquo; pondus sci&shy;<lb/>licet minus leve plures exhibuisse, eodem tempore, vibrationes &rdquo; (Comment. </s>

<s><lb/>meteor., T. </s>

<s>I cit., pag. </s>

<s>100). Il Riccioli conferm&ograve; poi solennemente i risul&shy;<lb/>tati sperimentali del suo Collega, nelle proposizioni V, VI e VII del cap. </s>

<s>XX <lb/>del II libro dell'Almagesto nuovo, dove piuttosto che Galileo si prende di <lb/>mira il Baliani, il quale, come vedemmo, concluse l'uguaglianza dei pendoli <pb xlink:href="020/01/2154.jpg" pagenum="397"/>dall'essere tutte uguali le ondulazioni dei corpi di vario peso, come di globi <lb/>di piombo di due once o di due libbre, e di un pezzo di pietra informe, <lb/>purch&egrave; tutti pendenti da uguali lunghezze. </s></p><p type="main">

<s>La detta V proposizione, che contiene in s&egrave; le altre due, &egrave; cos&igrave; formu&shy;<lb/>lata: &ldquo; Duorum perpendiculorum, in omnibus aequalium praeter quam in <lb/>gravitate, illud quod gravius est diutius in motu perseverat, et intra aequale <lb/>tempus plures numero vibrationes peragit &rdquo; (T. </s>

<s>I cit., pag. </s>

<s>85). Questa, in&shy;<lb/>sieme con le altre due, &ldquo; est, dice il Riccioli, contra Balianum, qui, si al&shy;<lb/>titudo perpendiculorum sit aequalis, vibrationes eorum aequidiuturnas pu&shy;<lb/>tat. </s>

<s>Sed ergo non possum ocu&igrave;is meis non credere &rdquo; (ibid., pag. </s>

<s>85, 86). </s></p><p type="main">

<s>Il senso della vista, a cui non si poteva non credere, aveva al Riccioli <lb/>e al Cabeo testimoniato del vero, ma, dimostrando la falsit&agrave; dell'isocroni&shy;<lb/>smo in due pendoli di differente peso, veniva anche insieme a farne argo&shy;<lb/>mentare la falsit&agrave; dell'isocronismo assoluto, in pendoli di peso uguale, o nel <lb/>medesimo pendolo, per via di un ragionamento, ch'era riserbato a farsi a <lb/>un collega dei due commemorati sperimentatori, come or ora vedremo. </s>

<s>Fa <lb/>perci&ograve; gran maraviglia che rimanesse intorno a ci&ograve; allucinato il Riccioli, il <lb/>quale non avrebbe affermato quell'assoluto isocronismo, se, piuttosto che <lb/>servirsi delle osservazioni astronomiche, si fosse rivolto a farne esperienze <lb/>dirette, sull'andare di quelle che gli avean messo sotto gli occhi la verit&agrave; <lb/>dei fatti formulati nelle tre sopra dette proposizioni. </s></p><p type="main">

<s>Il Cabeo per&ograve;, proseguendo nella citata Questione a discutere intorno <lb/>ai professati insegnamenti di Galileo, afferm&ograve; rimanergli in dubbio se del <lb/>medesimo pendolo le vibrazioni maggiori e le minori si spediscano precisa&shy;<lb/>mente nel medesimo tempo, perch&egrave; da certe esperienze istituite in proposito <lb/>appariva in que'moti ondulatorii una, piccola s&igrave;, ma pur sensibile diffe&shy;<lb/>renza. </s>

<s>&ldquo; Ego, si rem mathematice definire vellem, adhuc, ut verum fatear, <lb/>fere sto in ancipiti; nam, si duo aequalia pondera pendeant ex aequali filo, <lb/>et alterum illorum moveatur per arcus decem graduum, et alterum per ar&shy;<lb/>cus triginta quinque graduum, etiam si in initio simul incedant, tamen, post <lb/>mulias undationes, patebit dissentire &rdquo; (Comment. </s>

<s>meteor., lib. </s>

<s>I cit., pag. </s>

<s>100). <lb/>Soggiunge esser vero che il dissenso &egrave; assai piccolo, non trovandosi la diffe&shy;<lb/>renza di una vibrazione, se non che dopo un lunghissimo tempo, ma chi <lb/>avesse preso Galileo alla parola, rimovendo l'un dei pendoli per dieci gradi <lb/>e l'altro, non per trentacinque soli, ma per settanta o ottanta; avrebbe le <lb/>disegualit&agrave; in tali moti veduto apparirgli innanzi molto pi&ugrave; presto. </s>

<s>E per&shy;<lb/>ciocch&egrave; questo modo di sperimentare, di cui Galileo, nelle sue relazioni con <lb/>Guidubaldo, non seppe riconoscere l'efficacia, non potevan mancar altri che <lb/>lo eleggessero come il pi&ugrave; facile di tutti, e il pi&ugrave; risolutivo; &egrave; perci&ograve; che <lb/>sarebbero bastate le osservazioni del Wendelin, del Cabeo e del Riccioli, <lb/>anche senz'altro, per mettere in trepida sollecitudine gli Accademici del <lb/>Cimento. </s></p><p type="main">

<s>Trattandosi dell'onore dell'adorato Maestro, &egrave; facile indovinare che il <lb/>pi&ugrave; affaccendato di tutti gli Accademici fosse il Viviani, del quale facemmo, <pb xlink:href="020/01/2155.jpg" pagenum="398"/>a pag. </s>

<s>319 del I tomo della nostra Storia, note alcune esperienze di due pen&shy;<lb/>doli d&igrave; uguale lunghezza, e sospesi dal medesimo sostegno, che fatto vibrare <lb/>l'uno si vede spontaneamente incominciare a moversi anche l'altro. </s>

<s>Rife&shy;<lb/>rimmo allora cos&igrave; fatte esperienze come istituite a fine di confermare il <lb/>fatto di quella maravigliosa simpatia dei pendoli scoperta dall'Huyghens, e <lb/>ora soggiungiamo che forse il Viviani prese occasione da Galileo di osservar <lb/>le medesime cose, e di scoprirne l'occulte e pi&ugrave; probabili ragioni. </s></p><p type="main">

<s>Nel primo dialogo infatti Delle due nuove scienze s'istituisce la dot&shy;<lb/>trina dei pendoli per applicarla alla soluzione di alcuni problemi di Musica, <lb/>e principalmente a quello delle due corde tese all'unisono, delle quali vi&shy;<lb/>brando una, per esempio in un cembalo, fa questa tremar l'aria che le &egrave; <lb/>appresso, i cui tremori si distendono per grande spazio, e vanno a urtare <lb/>tutte le altre corde del medesimo strumento. </s>

<s>&ldquo; Ma la corda, che &egrave; tesa al&shy;<lb/>l'unisono con la tocca, essendo disposta a far le sue vibrazioni sotto il <lb/>medesimo tempo, comincia al primo impulso a muoversi un poco, e so&shy;<lb/>praggiungendogli il secondo, il terzo, il ventesimo e pi&ugrave; altri, e tutti negli <lb/>aggiustati e periodici tempi, riceve finalmente il medesimo tremore, che la <lb/>prima tocca, e si vede chiarissimamente andar dilatando le sue vibrazioni <lb/>giusto allo spazio della sua motrice &rdquo; (Alb. </s>

<s>XIII, 101). </s></p><p type="main">

<s>Or perch&egrave; Galileo rassomigliava il vibrar delle corde sonore al vibrar <lb/>di due pendoli muti, di ugual lunghezza di filo, era naturale sovvenisse in <lb/>mente al meditativo Viviani che, a quel modo che l'aria comunica il suo <lb/>moto alla corda quieta, e disposta a vibrare nei medesimi tempi; cos&igrave; avve&shy;<lb/>nisse dell'aria commossa dall'un pendolo, che comunica il suo proprio moto <lb/>all'altro pendolo quieto, ma disposto pure a vibrar sotto i medesimi tempi <lb/>anch'esso, perch&egrave; sospeso a lunghezza uguale di filo. </s></p><p type="main">

<s>Il simpatico mistero si trovava dunque, nel fatto e nelle sue pi&ugrave; pro&shy;<lb/>babili ragioni, involuto nelle parole di Galileo, e il Viviani, forse alla noti&shy;<lb/>zia della osservazione ugeniana comunicatagli dal principe Leopoldo, lo sciolse <lb/>da que'suoi involucri, e se lo pose a contemplare innanzi agli occhi svelato, <lb/>nelle descritte danze dei due pendoli uguali. </s>

<s>Diceva intanto a s&egrave; stesso, in <lb/>mezzo a cos&igrave; belle scientifiche contemplazioni: &ldquo; Anche questo dar&agrave; modo <lb/>di conoscere se i pendoli sono equidiuturni &rdquo; (MSS. Cim., T. X, fol. </s>

<s>47). </s></p><p type="main">

<s>Questa espressione, lasciamo andare tutte le altre questioni, che si po&shy;<lb/>trebbero movere intorno al curioso fatto osservato dall'Huyghes, e alla parte <lb/>che v'ebbero i Nostri nello spiegarlo; ci rivela che nell'Accademia fioren&shy;<lb/>tina, specialmente per opera del Viviani, si discuteva intorno all'isocronismo <lb/>dei pendoli, e si pensava ai modi pi&ugrave; accomodati per risolverne i dubbi. </s>

<s>Si <lb/>fu uno di questi modi, e forse dei primi, quello di far correre e ricorrere <lb/>le palline gravi dentro canali semicircolari, e non avendone avuta sodisfa&shy;<lb/>zione, come si vide, si volsero gli Accademici a sperimentare i libramenti <lb/>di varii liquidi dentro i rami dei loro sifoni, giacch&egrave; ritenevasi allora da tutti <lb/>quel che avea cos&igrave; lasciato scritto il Mersenno, in un luogo delle sue <emph type="italics"/>Nuove <lb/>osservazioni:<emph.end type="italics"/> &ldquo; Quod autem de funependulis audisti .... possis etiam referre <pb xlink:href="020/01/2156.jpg" pagenum="399"/>ad vibrationes hydrargirii a tubo quopiam descendentis &rdquo; (T. III, Parisiis 1647, <lb/>pag. </s>

<s>159). E bench&egrave; queste vibrazioni, o libramenti, fatti per discese rette <lb/>e non circolari, fossero propriamente isocroni, come ne concluse il Newton <lb/>nel corollario I della proposizione XLIV dimostrata nel II libro dei suoi <lb/><emph type="italics"/>Principii<emph.end type="italics"/> (edizione cit., pag. </s>

<s>357); ebbero nonostante i nostri Accademici a <lb/>raccogliere anche di qui poco di certo, come apparisce dalle seguenti re&shy;<lb/>lazioni: </s></p><p type="main">

<s>&ldquo; A'd&igrave; 23 Novembre 1661, leggesi in uno dei Diarii, osservati i libra&shy;<lb/>menti, che fa l'acqua infusa in un sifone di vetro, con gli suoi rami per&shy;<lb/>pendicolari al fondo; si trovarono equitemporanei tanto quelli che avevano <lb/>origine da maggiore altezza, che gli altri di minore.... A'd&igrave; 24 detto, i li&shy;<lb/>bramenti dell'argento vivo, nel sifone di braccia perpendicolari, sono equi&shy;<lb/>temporanei fra di loro, e con quelli dell'acqua infusa alla medesima altezza <lb/>dell'argento vivo &rdquo; (Targioni, Notizie ecc., T. II cit., pag. </s>

<s>647). </s></p><p type="main">

<s>Corrisponderebbero queste esperienze, come si vede, a quelle dei fu&shy;<lb/>nependoli di vario peso o specifico, o assoluto, e parevano confermare le <lb/>osservazioni di Galileo e del Baliani, ritrovate false dal Cabeo e dal Riccioli. </s>

<s><lb/>Di qui dunque avranno dovuto a principio argomentar gli Accademici la ve&shy;<lb/>rit&agrave; dell'isocronismo galileiano, nel medesimo pendolo o in pendoli uguali, <lb/>ma poi vennero a infirmar la logica dell'argomento altre esperienze, dalle <lb/>quali ebbero gli Accademici stessi a ricavar che i libramenti dell'argento <lb/>vivo, in sifoni della medesima altezza &ldquo; non sono equitemporanei, anzi li <lb/>massimi son pi&ugrave; tardi dei mezzani, e questi ancor pi&ugrave; tardi dei minimi &rdquo; <lb/>(ivi, pag. </s>

<s>651). </s></p><p type="main">

<s>Veniva questo fatto a confermare l'esperienze del Wendelin divulgate <lb/>dall'opera del Riccioli, per cui stavano gli Accademici in gran trepidazione <lb/>d'aver a confessar finalmente i falli di Galileo. </s>

<s>Lasciati addietro perci&ograve; gli <lb/>altri modi, i quali avevano ritrovati tanto incerti, vennero nella final deci&shy;<lb/>sione di sperimentare direttamente, com'esso Wendelin aveva fatto, sui pesi <lb/>ondeggianti dai fili. </s>

<s>Ma come assicurarsi che anche questi secondano i moti <lb/>dei pendoli con l'argento vivo, facendo pi&ugrave; tarde delle mezzane e delle mi&shy;<lb/>nime le loro massime vibrazioni? </s>

<s>Venne allora in mente al Viviani di co&shy;<lb/>struir quel Cronometro, rappresentato in disegno nel libro dei <emph type="italics"/>Saggi,<emph.end type="italics"/> e coi <lb/>moti di lui, i quali per forza della molla, fra gli ugualmente scompartiti <lb/>denti della ruota, erano obbligati a farsi sempre uguali; comparare i moti <lb/>osservati nei pendoli liberamente oscillanti. </s>

<s>L'esperienze corrisposero esat&shy;<lb/>tamente con quelle dei libramenti dell'argento vivo sopra descritti, come, <lb/>sotto i d&igrave; 29 Novembre 1661, si registr&ograve; nel Diario con queste precise pa&shy;<lb/>role: &ldquo; Esaminato ugual numero di vibrazioni dell'istesso pendolo grandi <lb/>e piccole, si trova che in tempi uguali, dati dalle vibrazioni di un altro pen&shy;<lb/>dolo, lasciato andare sempre dalla medesima altezza, ne vanno pi&ugrave; delle mi&shy;<lb/>nime che delle maggiori, e di queste pi&ugrave; che delle massime. </s></p><p type="main">

<s>Rimase l'importantissima Nota al foglio 156 del II tomo dei Manoscritti <lb/>del Cimento, infino al 1780, anno in cui il Targioni la pubblic&ograve; a pag. </s>

<s>390 <pb xlink:href="020/01/2157.jpg" pagenum="400"/>del II tomo, parte II, delle citate <emph type="italics"/>Notizie degli aggrandimenti delle scienze <lb/>fisiche, avvenuti in Toscana.<emph.end type="italics"/> Cosicch&egrave; non era, prima del Targioni, pubbli&shy;<lb/>camente noto, di questo sperimental lavorio degli Accademici fiorentini, se <lb/>non che quel cenno, che se ne faceva cos&igrave; nel libro dei <emph type="italics"/>Saggi di naturali <lb/>esperienze:<emph.end type="italics"/> &ldquo; Qui par luogo di dire che l'esperienza ci avea mostrato (come <lb/>fu anche avvertito dal Galileo, dopo l'osservazione che, prima d'ogni altro, <lb/>ei fece, intorno all'anno 1583, della loro prossima ugualit&agrave;) non tutte le vi&shy;<lb/>brazioni del pendolo correre in tempi precisamente tra loro uguali, ma quelle, <lb/>che di mano in mano si accostano alla quiete, spedirsi in pi&ugrave; breve tempo, <lb/>che non fanno le prime, come si dir&agrave; a suo luogo &rdquo; (Firenze 1841, pag. </s>

<s>21). </s></p><p type="main">

<s>La promessa per&ograve; non fu mantenuta, non facendosi del pendolo, in <lb/>tutto il Libro, altra parola. </s>

<s>Sconsigli&ograve; dal proposito il Principe dell'Accade&shy;<lb/>mia e i Colleghi il Viviani, trepido per l'onore dell'adorato Maestro, il qual <lb/>Viviani, costretto a passare al Segretario quel cenno sopra trascritto, gli sug&shy;<lb/>ger&igrave; le parole incluse fra parentesi, nelle quali, per salvar Galileo, non per&shy;<lb/>don&ograve; al pudore di fornicar pubblicamente con la menzogna. </s>

<s>Fra tanti timidi <lb/>e ciechi adoratori del Nume &egrave; da lodare massimamente Paolo Frisi, il quale, <lb/>con la molta scienza che aveva di quelle cose, giudicando secondo, che ri&shy;<lb/>chiedeva il dovere, il Soggetto elogiato, e lasciando di ripetere inutilmente, <lb/>anzi dannosamente le solite declamazioni; scriveva con filosofica libert&agrave; in <lb/>questo proposito: &ldquo; Non pu&ograve; ammettersi quanto si legge negli att&igrave; dell'Ac&shy;<lb/>cademia del Cimento che il Galileo erasi accorto di qualche disuguaglianza dei <lb/>tempi delle maggiori e minori vibrazioni &rdquo; (Elogio di Galileo, Livorno 1775, <lb/>pag. </s>

<s>96, in nota). </s></p><p type="main">

<s>Non era il Frisi di quelli che magnifican Galileo, senz'averlo mai letto, <lb/>ma cercando per le opere maggiori e minori di lui i tanti luoghi, dove si <lb/>parla delle propriet&agrave; dei pendoli, trov&ograve;, come troverebbero tutti i diligenti <lb/>lettori, che sempre vi si professa il pi&ugrave; assoluto isocronismo. </s>

<s>Poteva il Vi&shy;<lb/>viani attaccarsi a quel che si legge nel II dialogo Dei massimi sistemi, al <lb/>luogo da noi sopra citato, dove si accenna all'impedimento dell'aria, che <lb/><emph type="italics"/>ritarda qualche poco<emph.end type="italics"/> il moto del pendolo: e, perch&egrave; nelle vibrazioni pi&ugrave; <lb/>ampie quell'impedimento &egrave; maggiore, argomentarne che dunque le mag&shy;<lb/>giori fra quelle stesse vibrazioni sono, almeno insensibilmente, secondo Ga&shy;<lb/>lileo, pi&ugrave; tarde delle minori. </s>

<s>Ma che l'argomento, cos&igrave; artificiosamente con&shy;<lb/>dotto, non fosse secondo le finali espresse intenzioni di chi avea scritto quel <lb/>Dialogo, poteva riconoscerlo il Viviani dalla collazione con le seguenti pa&shy;<lb/>role, nelle quali alla dottrina dell'isocronismo dei pendoli si poneva da Ga&shy;<lb/>lileo stesso l'ultimo e pi&ugrave; solenne suggello: </s></p><p type="main">

<s>&ldquo; Sospendansi, egli dice nel IV dialogo Delle nuove scienze, due fili, <lb/>egualmente unghi e di lunghezza di quattro o cinque braccia, due palle di <lb/>piombo eguali, e, attaccati i detti fili in alto, si rimuovano ambedue le palle <lb/>dallo stato perpendicolare, ma l'una si allontani per ottanta o pi&ugrave; gradi, e <lb/>l'altra non pi&ugrave; che quattro o cinque; sicch&egrave;, lasciata in libert&agrave; l'una, scenda, <lb/>e trapassando il perpendicolo descriva archi grandissimi di 160, 150, 140 <pb xlink:href="020/01/2158.jpg" pagenum="401"/>gradi ecc. </s>

<s>diminuendoli a poco a poco; ma l'altra, scorrendo liberamente, <lb/>passi archi piccoli di 10, 8, 6 ecc. </s>

<s>diminuendoli essa pure a poco a poco. </s>

<s><lb/>Qui primieramente dico che, in tanto tempo passer&agrave; la prima li suo&igrave; gradi <lb/>180, 160 ecc., in quanto l'altra li suoi 10, 8 ecc. </s>

<s>Dal che si fa manifesto <lb/>che la velocit&agrave; della prima palla sar&agrave; 16 e 18 volte maggiore della velocit&agrave; <lb/>della seconda, sicch&egrave;, quando la velocit&agrave; maggiore pi&ugrave; dovesse essere im&shy;<lb/>pedita dall'aria che la minore, pi&ugrave; rade dovriano esser le vibrazioni negli <lb/>archi grandissimi di 180 o 160, che nei piccolissimi di 10, 8, 4, ed anche <lb/>di 2, e di 1. Ma a questo repugna l'esperienza. </s>

<s>Imperocch&egrave;, se due com&shy;<lb/>pagni si metteranno a numerare le vibrazioni, l'uno le grandissime e l'altro <lb/>le piccolissime, vedranno che ne numereranno, non pur le diecine, ma le <lb/>centinaia ancora, senza discordar di una, anzi di un sol punto. </s>

<s>E questa os&shy;<lb/>servazione ci assicura congiuntamente delle due proposizioni, cio&egrave; che le <lb/>massime e le minime vibrazioni si fanno tutte, a una a una, sotto tempi <lb/>eguali, e che l'impedimento e ritardamento dell'aria non opera pi&ugrave; nei moti <lb/>velocissimi, che nei tardissimi &rdquo; (Alb. </s>

<s>XIII, 231). </s></p><p type="main">

<s>Si persuaderanno anche i pi&ugrave; ritrosi, dietro la lettura di questo certis&shy;<lb/>simo documento, che l'esperienze degli Accademici fiorentini non confer&shy;<lb/>mavano, come avrebbe voluto far credere il Viviani, ma riformavano le dot&shy;<lb/>trine di Galileo, e del benefizio di una tale riforma va debitrice la scienza <lb/>galileiana, come si disse, al Riccioli. </s>

<s>Se non fossero le parole di lui venute <lb/>a mettere il sospetto nei Nostri, stimolandogli a ritornare ai fatti, perch&egrave; <lb/>fossero meglio esaminati, non si sarebbe forse all'infallibile Nume, dai ge&shy;<lb/>losi custodi del tempio, turbata cos&igrave; la pace dei venerandi riposi. </s></p><p type="main">

<s>Una tale efficacia del Riccioli era naturale che si dovesse far sentire <lb/>anche pi&ugrave; valida ai liberi ingegni, come per esempio al padre Francesco <lb/>Lana, il quale incominci&ograve; giusto a sospettar della verit&agrave; dell'assoluto isocro&shy;<lb/>nismo professato da Galileo, ripensando a quelle tre proposizioni intorno ai <lb/>pendoli di ugual lunghezza, ma di peso diverso, formulate, come si disse, <lb/>dallo stesso Riccioli nel citato luogo dell'Almagesto. </s>

<s>Perch&egrave;, domandava a <lb/>s&egrave; medesimo, il pendolo pi&ugrave; grave fa in ugual tempo minor numero di vi&shy;<lb/>brazioni dell'altro pendolo pi&ugrave; leggero? </s>

<s>E veniva al Lana la risposta, non <lb/>data ancora da nessuno, dal ripensar che forse, pi&ugrave; lungamente durando il <lb/>pendolo pi&ugrave; grave nelle vibrazioni sue pi&ugrave; larghe, eran queste pi&ugrave; diuturne <lb/>di quelle, fatte dall'altro pendolo pi&ugrave; leggero, che si riduce pi&ugrave; presto a <lb/>languir nelle vibrazioni pi&ugrave; strette. </s>

<s>Pareva il felice pensiero essergli confer&shy;<lb/>mato dalle esperienze, quando nel 1668 s'abbatt&egrave; a leggere, nel libro degli <lb/>Accademici fiorentini, il passo che poco sopra abbiamo trascritto. </s>

<s>Non tro&shy;<lb/>vandovi espresso nulla, entr&ograve; in gran curiosit&agrave; di sapere come i celebri Spe&shy;<lb/>rimentatori si fossero assicurati di quelle disuguaglianze, e dal cenno, che ivi <lb/>se ne fa, dicendosi che, per ridurlo alla desiderata uguaglianza di moto, <emph type="italics"/>fu <lb/>stimato bene applicare il pendolo all'orivolo,<emph.end type="italics"/> congettur&ograve;, com'era il vero, <lb/>che avessero gli Accademici comparate le variet&agrave; delle libere oscillazioni con <lb/>quelle costrette a farsi nello strumento sempre per archi uguali. </s></p><pb xlink:href="020/01/2159.jpg" pagenum="402"/><p type="main">

<s>Or perch&egrave;, cos&igrave; essendo, giudicava il Lana il suo metodo sperimentale <lb/>assai pi&ugrave; sicuro, lo descriveva perci&ograve; in una lettera del d&igrave; 9 Maggio 1668, <lb/>diretta da Brescia a quegli Accademici, che dunque non credeva a quel tempo <lb/>gi&agrave; morti, come temerariamente fu detto e ripetuto da tanti, ma ch'ei sa&shy;<lb/>peva proseguir anzi, bench&egrave; dispersi, pi&ugrave; largamente che mai gli studi spe&shy;<lb/>rimentali sotto la presidenza del cardinale Leopoldo dei Medici. </s>

<s>&ldquo; L'espe&shy;<lb/>rienze poi, scriveva il Lana dop'avere ossequiosamente introdotto il discorso, <lb/>che mi hanno mostrato non compirsi le vibrazioni in tempi uguali, sono le <lb/>seguenti: &rdquo; </s></p><p type="main">

<s>&ldquo; Servendomi di due pendoli, uno de'quali corrispondeva nelle sue sem&shy;<lb/>plici vibrazioni ad un minuto secondo, l'altro ad un mezzo secondo, li alzai <lb/>ad un medesimo grado del suo arco, minore di 45 gradi. </s>

<s>Mentre il primo <lb/>comp&igrave; 64 vibrazioni semplici, il secondo ne comp&igrave; 129, e perch&egrave; ne doveva <lb/>compire solo 128, la diversit&agrave; stimai provenirne perch&egrave; il pendolo pi&ugrave; alto <lb/>era molto pi&ugrave; pesante, onde continuava a scorrere archi grandi, quando l'altro <lb/>pi&ugrave; leggero aveva notabilmente diminuito li suoi archi. </s>

<s>Ci&ograve; mi fu confer&shy;<lb/>mato dalla seguente esperienza: Lasciai cadere il pendolo pi&ugrave; lungo dall'al&shy;<lb/>tezza di gradi 60, e l'altro dall'altezza di gradi 30: mentre quello compi&egrave; <lb/>20 vibrazioni, questo ne compi&egrave; 41. &rdquo; </s></p><p type="main">

<s>&ldquo; Pi&ugrave; chiara mi parve l'esperienza seguente: Lasciai cadere il maggior <lb/>pendolo dall'altezza di gradi 20, ed il minore da quella di gradi 30. Quindi <lb/>accadeva che gli archi di questo pendolo, come quello che era pi&ugrave; leggero, <lb/>ed era anche caduto da maggiore altezza; si andavano impiccolendo pi&ugrave; no&shy;<lb/>tabilmente, che non facevano gli archi dell'altro pendolo pi&ugrave; pesante, e ca&shy;<lb/>duto da minore altezza, e che, dopo 100 vibrazioni, incominciarono a descri&shy;<lb/>vere archi uguali. </s>

<s>In tutto questo tempo le vibrazioni dell'uno e dell'altro <lb/>andavano di concerto, compiendosi nel medesimo tempo una semplice del&shy;<lb/>l'uno, mentre si compiva una composta dell'altro, ma poi tosto gli archi <lb/>del minor pendolo incominciarono a farsi minori di quelli, ch'erano scorsi <lb/>dal maggiore, e nel medesimo tempo parimente incominciarono ad essere <lb/>pi&ugrave; veloci, sicch&egrave;, dopo altre 100 vibrazioni del maggiore, il minore ne com&shy;<lb/>p&igrave;va 201. &rdquo; </s></p><p type="main">

<s>&ldquo; Rimanevami alcun sospetto che la predetta disuguaglianza potesse <lb/>provenire dal maggior peso, ovvero altezza di un pendolo, in riguardo del&shy;<lb/>l'altro, perch&egrave;, sospesi due pendoli dalla medesima altezza, l'uno di legno <lb/>pesante scrupoli 16 1/2, l'altro di metallo, scrupoli 22 1/2, e lasciati cadere <lb/>l'uno e l'altro da una medesima altezza, avveniva che il primo, per essere <lb/>meno pesante e di maggior mole, incominci&ograve; subito a scorrer gli archi molto <lb/>minori dell'altro, e medesimamente in pi&ugrave; breve tempo compivali, e per <lb/>certificarmi che ci&ograve; non provenisse da qualche disuguaglianza nella lunghezza <lb/>del filo, che in misurarlo avesse ingannato l'occhio, lasciai cadere li mede&shy;<lb/>simi pendoli da inuguali altezze, cio&egrave; quello di legno da una minore, e l'altro <lb/>di metallo da una maggiore. </s>

<s>E perch&egrave; gli archi maggiori si vanno dimi&shy;<lb/>uendo pi&ugrave; notabilmente di quello, che facciano li minori, quindi accadeva <pb xlink:href="020/01/2160.jpg" pagenum="403"/>che il pendolo di metallo, caduto da maggiore altezza, andava pi&ugrave; notabil&shy;<lb/>mente diminuendo i suoi archi, e, con la sua proporzione, anche i tempi <lb/>delle ondazioni erano pi&ugrave; brevi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In queste e in altre simili esperienze ho sempre osservato che un <lb/>pendolo precorre all'altro, solo allorquando le ondazioni si fanno in archi <lb/>minori, checchessia del maggior peso, e della maggior mole, purch&egrave; i fili <lb/>siano uguali. </s>

<s>&rdquo; (MSS. Cim., T. XXV, fol. </s>

<s>11, 12). </s></p><p type="main">

<s>Si conclude in queste ultime parole il fatto, non bene osservato da Ga&shy;<lb/>lileo nelle sue prime esperienze descritte a Guidubaldo del Monte, che cio&egrave;, <lb/>lasciati andare due pendoli, bench&egrave; di diverso peso, purch&egrave; di lunghezze <lb/>uguali, nello stesso tempo e dalla stessa parte, si vedono andar di pari passo <lb/>infin tanto che fanno le vibrazioni di uguale, o di poco differente ampiezza <lb/>di arco, ma al diminuirsi quest'ampiezza notabilmente pi&ugrave; nell'uno che nel&shy;<lb/>l'altro, si vede sempre preceder quello, che va per archi minori. </s>

<s>La costanza <lb/>di questo fatto osservato fece proporre al Lana, nel suo tomo secondo <emph type="italics"/>Ma&shy;<lb/>gisterii Naturae et Artis,<emph.end type="italics"/> il seguente esperimento, che &egrave; in ordine il XIX, <lb/>nel cap. </s>

<s>I del V libro: &ldquo; Unius eiusdemque penduli singulae vibrationes <lb/>non sunt omnino aequidiuturnae, sed successive minori ac minori temporis <lb/>spatio absolvuntur &rdquo; (Brixiae 1686, pag. </s>

<s>342). &rdquo; </s></p><p type="main">

<s>La certezza, che aveva il Lana del fatto, avrebbe desiderato si parte&shy;<lb/>cipasse altres&igrave; alla ragione del fatto, ma non seppe, come tant&igrave; altri, in che <lb/>meglio riconoscerla che negli impedimenti dell'aria, per cui credeva che il <lb/>perfetto isocronismo s'avesse a osservare nel vuoto. </s>

<s>&ldquo; Mi sarebbe cosa gra&shy;<lb/>tissima, scriveva nei principii della citata lettera agli Accademici fiorentini, <lb/>il sapere con quale artificio si sono assicurati che l'ondazioni del pendolo <lb/>siano inuguali di tempo, poich&egrave; se fosse con l'applicazione del pendolo al&shy;<lb/>l'oriolo, averei qualche dubbio che ci&ograve; fosse bastante a provare l'intento, <lb/>e stimerei piuttosto che ne potesse certificare l'esperienza fatta nel vuoto, <lb/>in cui parmi che tutte le vibrazioni dovrebbero compirsi in tempi uguali, e <lb/>di ci&ograve; volentieri ne riceverei alcuna prova da lor altri Signori, la quale an&shy;<lb/>che servirebbe a fine di conoscere quanta sia la resistenza dell'aria, in pa&shy;<lb/>ragone della mole e peso del pendolo, che a me, in un pendolo di piombo <lb/>pesante scrupoli 8, gr. </s>

<s>39, le cui vibrazioni composte si facevano in un <lb/>minuto secondo; &egrave; stata in proporzione di 10,638 ad 1. Ed in un altro, di <lb/>mistura poco pi&ugrave; grave dell'acqua, cio&egrave; 16 volte in circa pi&ugrave; leggera del <lb/>piombo, e 4 volte maggiore nella sua superfice di quello fosse la superfice <lb/>del precedente pendolo di piombo, fu come 156 a 1 &rdquo; (MSS. cit., fol. </s>

<s>11). </s></p><p type="main">

<s>Le prove nel vuoto, richieste agli Accademici fiorentini dal Lana, erano <lb/>state parecchi anni prima tentate in varii modi coi libramenti de'liquidi nei <lb/>sifoni, e direttamente coi funependoli, ma i resultati delle esperienze riu&shy;<lb/>scirono sempre incerti. </s>

<s>&ldquo; I libramenti dell'acqua in un sifone ritorto, leg&shy;<lb/>gesi in uno dei Diarii sotto il d&igrave; 2 Gennaio 1662, dopo fatto il vuoto, pare <lb/>che durino pi&ugrave; che quando vi &egrave; l'aria &rdquo; (Targioni, Notizie cit., T. II, <lb/>pag. </s>

<s>651). </s></p><pb xlink:href="020/01/2161.jpg" pagenum="404"/><p type="main">

<s>Al fol. </s>

<s>78 del tomo X dei Manoscritti del Cimento vedesi, di mano del <lb/>Viviani, disegnata la camera del vuoto, dalla v&ocirc;lta della <lb/>quale pende un filo con una pallina (fig. </s>

<s>210), e bench&egrave; <lb/>non sianvi scritte altre dichiarazioni, s'argomenta pure <lb/>da quei semplici segni, per s&egrave; stessi eloquenti, la non <lb/>riuscita intenzione degli Sperimentatori. </s>

<s>Il Boyle ripet&egrave; <lb/>poi con la massima diligenza lo stesso esperimento, per <lb/>mezzo della sua Macchina pneumatica, sotto la campana <lb/>della quale, dop'averne aspirata l'aria, facendo oscillar <lb/>un pendolo, ne comparava le oscillazioni con quelle fatte <lb/>da un altro pendolo in mezzo all'aria aperta. </s>

<s>&ldquo; Verum, <lb/>n'ebbe per&ograve; a concluder l'Autore, ex facto hoc esperi&shy;<lb/>mento parum didicimus, nisi quod discrimen inter mo&shy;<lb/>tum penduli istiusmodi in communi aere, atque in aere <lb/><figure id="id.020.01.2161.1.jpg" xlink:href="020/01/2161/1.jpg"/></s></p><p type="caption">

<s>Figura 210<lb/>valde rarefacto in vasis, vix sensibile sit &rdquo; (Nova Experim. </s>

<s>Op. </s>

<s>omnia, T. <lb/>I, Venetiis 1697, pag. </s>

<s>61). </s></p><p type="main">

<s>Non essendosi dunque potuto decidere con l'esperienza se le disugua&shy;<lb/>glianze osservate nei pendoli nascevano, come probabilmente si sospettava, <lb/>dall'impedimento dell'aria, presentivasi del fatto una causa pi&ugrave; riposta, la <lb/>quale s'ebbe finalmente scoperta, invocatosi dai Fisici il valido aiuto della <lb/>Geometria. </s>

<s>Fu il fortunato discopritore Cristiano Huyghens, il quale, mes&shy;<lb/>sosi addentro alla questione infino dal 1656, la dette nel 1673, con mirabile <lb/>opera matematica, risoluta. </s>

<s>Ei non ebbe a dubitar punto se le massime oscil&shy;<lb/>lazioni son pi&ugrave; tarde delle minime, essendosene bene assicurato con questo, <lb/>ch'egli dice facile esperimento: &ldquo; Nam si pendula duo, pondere et longitu&shy;<lb/>dine aequalia, alterum procul a perpendiculo, alterum parumper dimovea&shy;<lb/>tur, simul dimissa, non diu in partes easdem una ferri cernentur, sed prae&shy;<lb/>vertet illud, cuius exiliores erunt recursus &rdquo; (Horologium, Opera varia, Vol. </s>

<s>I, <lb/>Lugduni Batav. </s>

<s>1724, pag. </s>

<s>12). L'esperienza ugeniana &egrave;, come si ramme&shy;<lb/>moreranno i nostri Lettori, quella proposta in secondo luogo da Galileo a <lb/>Guidubaldo del Monte, e poi ripetuta dal Cabeo. </s>

<s>Che se questo ne rimase <lb/>in dubbio, e quell'altro disse di non essersi accorto, in pendoli cos&igrave; oscil&shy;<lb/>lanti, di nessuna disuguaglianza di moto, non &egrave; da attribuire ad altro, che <lb/>alla poca perizia, o alla poca diligenza nell'osservare, e, per le preconcette <lb/>idee della mente, al non aver voluto credere alla testimonianza degli occhi. </s></p><p type="main">

<s>Fu quella certissima sperimentata disuguaglianza, che indusse l'Huy&shy;<lb/>ghens ad applicare il pendolo alle ruote degli orologi, come v'avea indotto <lb/>in quel medesimo tempo il Viviani per quelle stesse ragioni, ma il Mate&shy;<lb/>matico olandese, pi&ugrave; libero nel pensare del Nostro, persuaso dall'esperienze <lb/>del Boyle e dalle poco sodisfacenti teorie del Mariotte non si potere attri&shy;<lb/>buire all'aria, n&egrave; a nessun altra estrinseca causa gli effetti sperimentati, pe&shy;<lb/>netr&ograve; addentro alla natura delle cose, e sagacemente scopr&igrave; che Galileo fu, <lb/>prima che dai fatti, ingannato dalle speculazioni. </s>

<s>&ldquo; Mensura enim temporis <lb/>certa atque aequalis pendulo semplici natura non inerat, cum latiores excur-<pb xlink:href="020/01/2162.jpg" pagenum="405"/>sus angustioribus tardiores observentur, sed Geometria duce diversam ab ea, <lb/>ignotamque antea penduli suspensionem reperimus, animadversa lineae cuius&shy;<lb/>dam curvatura, quae ad optatam aequalitatem illi conciliandam, mirabili plane <lb/>ratione, comparata est &rdquo; (Horol. </s>

<s>oscill., Op. </s>

<s>varia cit., T. I, pag. </s>

<s>30). </s></p><p type="main">

<s>La curva tautocrona insomma scopr&igrave; l'Huyghens che non era il cir&shy;<lb/>colo, come credevasi da Galileo, e da tutti gli altri dietro lui, ma la Cicloide, <lb/>per la quale, oscillando il pendolo, serba l'isocronismo assoluto. </s>

<s>Che se, <lb/>infino dai tempi del Wendelin, si osserv&ograve; l'uguaglianza del moto verificarsi <lb/>nelle piccole digressioni, e fisicamente poi si spieg&ograve; il fatto col dire che i <lb/>piccoli archi pochissimo differiscono dalle corde suttese; ora, per i teoremi <lb/>ugeniani, si riduceva la fisica alla precision matematica, dicendosi esatta&shy;<lb/>mente isocroni i pendoli semplici, le vibrazioni dei quali si fanno per un <lb/>circolo osculatore alla cicloide. </s>

<s>E cos&igrave; venne finalmente la Geometria a to&shy;<lb/>gliere d'ogni sollecitudine Galileo, rivelandogli, dopo settantun anno, che <lb/>se non era spuntato, senza trasgredire i termini meccanici, a dimostrar che <lb/>i gravi, per qualunque punto della quarta di un cerchio cadendo, giungono <lb/>al basso nel medesimo tempo; era perch&egrave; il falso, per qualunque argomento <lb/>della retta ragione, non si poteva ridurre al vero. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Annunziando l'Huyghens a Lodovico XIV le nuove scoperte propriet&agrave; <lb/>meccaniche della Cicloide, si compiaceva di aver dato finalmente alla Nau&shy;<lb/>tica e all'Astronomia il tanto desiderato esatto misuratore del tempo. </s>

<s>Il Vi&shy;<lb/>viani meditava pochi anni prima di comparire innanzi alla medesima regia <lb/>Maest&agrave;, per rivendicar que'meriti al suo Galileo, ripetendo al re di Francia <lb/>quel ch'avea nel 1654 scritto al principe Leopoldo di Toscana, che cio&egrave; Ga&shy;<lb/>lileo, nella sua giovent&ugrave; &ldquo; con la sagacit&agrave; del suo ingegno invent&ograve; quella <lb/>semplicissima e regolata misura del tempo, per mezzo del pendolo .... della <lb/>quale invenzione si valse poi in varie esperienze, e misure di tempi e moti, <lb/>e fu il primo che le applicasse alle osservazioni celesti, con incredibile acqui&shy;<lb/>sto della Astronomia e Geografia &rdquo; (Alb. </s>

<s>XV, 331, 32). </s></p><p type="main">

<s>I vanti del Viviani furono ripetuti, e si ripetono tuttavia da tutti, fuor <lb/>che da noi, fatti accorti dalla passata storia che, chiunque avesse inteso far <lb/>del pendolo galileiano un misuratore del tempo, si sarebbe trovato alle mani <lb/>uno strumento fallace. </s>

<s>Non s'accorse l'ammirato Inventore della fallacia, <lb/>perch&egrave;, contro i gratuiti asserti e le correnti opinioni, ei non fece uso mai <lb/>di un tale strumento, e solo negli ultimi anni della sua vita lo proponeva, <lb/>nei pi&ugrave; incomodi e impraticabili esercizi, al Baliani, posponendolo nonostante <lb/>alle volgari clessidre. </s></p><p type="main">

<s>Questo, che sar&agrave;, cos&igrave; al primo annunzio, dispettosamente ripudiato dai <lb/>lettori dell'elogio di Galileo, &egrave; quel che ora intende di venire innanzi a nar&shy;<lb/>rare la nostra Storia, la quale, avendo gi&agrave; frugato per i giovanili scritti mi-<pb xlink:href="020/01/2163.jpg" pagenum="406"/>nori, e cercate le due maggiori opere distese in dialogo, ha trovato sempre <lb/>le propriet&agrave; del pendolo descritte come una meccanica speculazione, o come <lb/>una estatica contemplazione delle maraviglie della Natura, ma non mai come <lb/>un artificio dell'uomo, per servirsene alle pi&ugrave; giuste misure del tempo. </s></p><p type="main">

<s>Facemmo, a pagine 301, 302 del nostro I tomo, avvertire che, primo a <lb/>servirsi del pendolo per uso cronometrico, fu il Santorio, e non avremmo <lb/>risospinta indietro la vista cos&igrave; lontano, se non ci premesse di confessare <lb/>ai lettori l'errore, in cui allora cademmo, in dar lo strumento santoriano, <lb/>da una delle antiche misure denominato <emph type="italics"/>Cotyla,<emph.end type="italics"/> per un automa, mentre <lb/>era il dito che, movendo o da una parte o da un'altra l'indice per un certo <lb/>numero di gradi, faceva rotare ora a destra ora a sinistra un cilindro, da <lb/>cui svolgendosi, o su cui avvolgendosi il filo del pendolo, si poteva a pia&shy;<lb/>cere aggiustarlo alla misura corrispondente al numero segnato dalla punta <lb/>dell'indice stesso sopra la mostra. </s>

<s>Il Santorio insomma apparisce nella storia <lb/>il primo, che applicasse il pendolo agli usi pratici, mentre Galileo si trat&shy;<lb/>teneva sterilemente a contemplarne la teoria. </s>

<s>Ma perch&egrave;, da chi tutto vuole <lb/>attribuire a quell'uomo, adorato come divino, anche questa distinzione &egrave; ne&shy;<lb/>gata, &egrave; ben lasciare i rettorici discorsi a chi se ne diletta, per ridurci alla <lb/>severa e schietta conclusione dei fatti. </s></p><p type="main">

<s>Nell'Aprile del 1632 Galileo mandava in dono una copia dei dialoghi <lb/>Dei due massimi sistemi al Baliani, il quale, come in altra occasione accen&shy;<lb/>nammo, attentamente leggendo, ebbe a rimaner sorpreso della precision della <lb/>misura ivi assegnata al tempo di un grave, che sia liberamente sceso per <lb/>lo spazio di cento braccia, e gli venne gran curiosit&agrave; di sapere com'avesse <lb/>fatto Galileo a ritrovar che quello spazio era passato nel preciso tempo di <lb/>cinque minuti secondi. </s>

<s>Ringraziando perci&ograve; del dono, scriveva da Genova, il <lb/>d&igrave; 23 del detto mese, una lettera, nella quale, dop'essersi professato obbli&shy;<lb/>gatissimo per le tante cose nuove bellissime chiaramente spiegate nel libro, <lb/>esprimeva cos&igrave; all'Autore il suo desiderio: </s></p><p type="main">

<s>&ldquo; Io riceverei a gran favore che V. S. mi desse conto del modo, con <lb/>che ha ritrovato che il grave scende per cento braccia in cinque secondi. </s>

<s><lb/>Altre volte io tentai l'impresa, per mezzo di una palla attaccata ad una fu&shy;<lb/>nicella, tanto lunga che le sue vibrazioni durassero un secondo per appunto, <lb/>n&egrave; mi &egrave; finora riuscito di trovar qual sia la lunghezza precisa della fune.... <lb/>Di questo orologio, che misurasse i secondi, io mi do ad intendere che me <lb/>ne servirei a pi&ugrave; usi; e in misurar le grandi distanze, per mezzo della dif&shy;<lb/>ferenza del tempo, che &egrave; fra la vista e l'udito, se pure &egrave; vero, come credo, <lb/>che tal differenza sia proporzionata alle distanze, onde facendo sparar un'ar&shy;<lb/>tiglieria lontano circa 30 miglia, purch&egrave; io possa vederne il fuoco e sentirne <lb/>il tuono, dalla lor differenza verrei in cognizione della distanza precisamente; <lb/>e in ritrovare i gradi della longitudine, mediante il moto della Luna, ancor&shy;<lb/>ch&egrave; non vi sia ecclissi, atteso che, con un oriolo cos&igrave; esatto, si ritroverebbe <lb/>precisamente la differenza della distanza della Luna a qualche stella, e del&shy;<lb/>l'un meridiano all'altro, calcolandovi per&ograve; le anomalie di essa Luna, e molte <pb xlink:href="020/01/2164.jpg" pagenum="407"/>cose simili. </s>

<s>Che perci&ograve; io la prego a dirmi il modo di misurare i secondi &rdquo; <lb/>(Alb. </s>

<s>IX, 266, 67). </s></p><p type="main">

<s>L'orologio cos&igrave; ideato era proprio quello, che si ricercava per la solu&shy;<lb/>zione di tanti problemi o curiosi o utili, e in tutti i modi bellissimi e nuovi, <lb/>n&egrave; poteva il Baliani immaginarsi che non fossero quelle medesime idee pas&shy;<lb/>sate per la mente inventiva di Galileo. </s>

<s>Colui, fra s&egrave; pensava, il quale ha <lb/>prefiniti i tempi al cadere dei gravi, e il periodo al Gioviali, inventore e <lb/>magnificatore delle propriet&agrave; del pendolo, deve aver sicurissimo il modo di <lb/>misurar col pendolo un minuto secondo, ed egli spero me lo dir&agrave;, ma il de&shy;<lb/>siderio non fu sodisfatto. </s></p><p type="main">

<s>Due anni e mezzo dopo, Giovanni Pieroni, che si trovava in Austria, e <lb/>che s'esercitava nell'Astronomia, scrivendo da Vienna il d&igrave; 4 Gennaio 1635 <lb/>allo stesso Galileo, gli diceva di certe sue osservazioni fatte sopra le stelle <lb/>fisse, e poi soggiungeva: &ldquo; Io son dietro a farne cento altre, che a suo tempo <lb/>le comunicher&ograve;, ma mi sarebbe di grandissimo vantaggio in esse sapere da <lb/>V. S. quanto vada lungo un pendolo per misurare uno o alquanti secondi <lb/>di tempo, o se la lunghezza si prende insino o tutto il corpo grave pen&shy;<lb/>dente, o insino al centro di esso. </s>

<s>Per&ograve;, se piacesse a V. S. darmene noti&shy;<lb/>zia, non potrei dirle quanto grato favore mi farebbe, e potrebbe dirmelo alla <lb/>misura del braccio di cost&igrave;, perch&egrave; io la ritenga meco esatta &rdquo; (Alb. </s>

<s>X, 68). </s></p><p type="main">

<s>Nemmeno il Pieroni ebbe a questa sua istante domanda la desiderata <lb/>risposta, e se volesse saper qualcuno chi ci abbia chiarito di una tale no&shy;<lb/>tizia, la contraria verit&agrave; della quale potrebbe risultar forse dai privati com&shy;<lb/>merci epistolari rimasti a noi sconosciuti, risponderemo francamente che, <lb/>contro l'opinion del Baliani, del Pieroni e di tutti, Galileo non aveva avuto <lb/>infin allora il pensiero di applicare il pendolo alle osservazioni celesti, e <lb/>tanto meno aveva conceputa la speranza di risolvere il problema della lun&shy;<lb/>ghezza da dare al filo, perch&egrave; il pendolo stesso batta esattamente un mi&shy;<lb/>nuto secondo. </s></p><p type="main">

<s>La pi&ugrave; certa soluzione infatti di quel problema dipende, come si sa, <lb/>dalla legge delle proporzioni, che passano fra due varie lunghezze di pen&shy;<lb/>doli, e la durata o il numero delle vibrazioni fatte da ciascuno nei mede&shy;<lb/>simi tempi; legge che voleva prima esser conosciuta in s&egrave; stessa, per poi <lb/>venire applicata a risolvere la questione proposta. </s>

<s>Or si comprende bene <lb/>quanto sia necessario il saper nei presenti dubbi come e quando riuscisse <lb/>Galileo a scoprir che i tempi delle vibrazioni dei pendoli stanno come le <lb/>radici delle lunghezze dei fili. </s>

<s>Il Baliani dice di essersi abbattuto a caso a <lb/>osservare il fatto, istituendo nel 1611 quelle sue esperienze intorno al moto <lb/>dei pendoli di vario peso, per concluderne dal loro isocronismo che le ve&shy;<lb/>locit&agrave; non sono proporzionate alle moli. </s>

<s>In mezzo a queste osservazioni dei <lb/>pendoli di lunghezze uguali, gli venne voglia di sperimentare in pendoli di <lb/>lunghezze differenti, &ldquo; in quibus peragendis illud, egli dice, praeter expecta&shy;<lb/>tionem sese mihi obtulit, quod, quotiescumque globi penderent ex funicu&shy;<lb/>lis inaequalibus, ita inaequali motu ferebantur, ut longitudines funiculorum <pb xlink:href="020/01/2165.jpg" pagenum="408"/>durationibus motuum in duplicato ratione responderent &rdquo; (De motu natur. </s>

<s><lb/>cit., pag. </s>

<s>6). </s></p><p type="main">

<s>Galileo, in nessuno dei libri pubblicati da lui infino al 1632 o a qual&shy;<lb/>che anno di poi, fa motto di questa insigne legge, sperimentalmente sco&shy;<lb/>perta dal Baliani. </s>

<s>Anzi si conclude da un luogo della giornata quarta Dei <lb/>due massimi sistemi che l'Autore credeva allora fossero i tempi delle vi&shy;<lb/>brazioni proporzionali alle semplici lunghezze dei pendoli, come, nell'asta <lb/>accomodata a temperare il tempo degli orologi, fanno i pesi di piombo a <lb/>dilungarli o a ritirarli pi&ugrave; verso il centro. </s>

<s>&ldquo; Qui la virt&ugrave; movente &egrave; la me&shy;<lb/>desima, cio&egrave; il contrappeso, i mobili sono i medesimi piombi, e le vibra&shy;<lb/>zioni loro son pi&ugrave; frequenti, quando son pi&ugrave; vicini al centro, cio&egrave; quando <lb/>si muovono per minori cerchi. </s>

<s>Sospendansi pesi eguali da corde diseguali <lb/>e, rimossi dal perpendicolo, lascinsi in libert&agrave;. </s>

<s>Vedremo gli appesi a corde <lb/>pi&ugrave; brevi fare lor vibrazioni sotto pi&ugrave; brevi tempi, come quelli, che si muo&shy;<lb/>vono per cerchi minori &rdquo; (Alb. </s>

<s>I, 487). Ond'&egrave; chiaro che i tempi per gli <lb/>archi son, secondo questo discorso, non proporzionali alle radici, ma alle <lb/>semplici lunghezze dei raggi. </s></p><p type="main">

<s>Si posson di qui tutti facilmente persuadere che colui, il quale versava <lb/>in cos&igrave; fatti errori, non era in grado di risolvere i quesiti propostigli dal <lb/>Baliani e dal Pieroni. </s>

<s>Troppo erano per&ograve; quei quesiti importanti, e tali da <lb/>meritar che vi esercitasse attorno Galileo la sua scienza, la quale nel 1537 <lb/>parve esaurita. </s>

<s>Aveva gi&agrave; riconosciuto allora il suo inganno in paragonare <lb/>ai moti equabili dei pesi nell'orologio a ruote i moti accelerati dei pendoli, <lb/>i quali non potevano sottrarsi alle leggi universali dei gravi cadenti, di cui <lb/>i tempi son anche proporzionati alle radici, e non ai semplici spazi passati. </s>

<s><lb/>Notabile &egrave; che Galileo, rispetto alle cadute per gli archi dei cerchi, incor&shy;<lb/>resse in quei medesimi crrori, che fu egli il primo a scoprire nelle cadute <lb/>rette dei gravi: per&ograve; &egrave; pi&ugrave; notabile che, spendendo tanta scienza matematica <lb/>intorno a queste cadute verticali, si rimettesse per quelle circolari alla sem&shy;<lb/>plice esperienza. </s>

<s>Ma l'arte sperimentale aveva troppo corte le ali per sol&shy;<lb/>levar l'ingegno a risolvere con precisione matematica il problema della lun&shy;<lb/>ghezza, che vuol avere un pendolo per battere i secondi; ond'&egrave; che, dovendosi <lb/>far d'esso pendolo un misuratore del tempo, confidatosi tutto nella falsa legge <lb/>dell'isocronismo, fond&ograve; sopr'essa un progetto, in cui, senza poter andare pi&ugrave; <lb/>avanti per non avere scienza delle propriet&agrave; dei pendoli di varia lunghezza, <lb/>esaur&igrave;, come si disse, Galileo le forze del proprio ingegno. </s>

<s>Non parvero queste <lb/>per&ograve; punto deboli a quell'Uomo, che si lusingava dover lo stesso Orologio <lb/>a minuti secondi, quando pure alcuno l'avesse saputo trovare, rimanersi in&shy;<lb/>feriore a quel suo squisito <emph type="italics"/>Misuratore del tempo,<emph.end type="italics"/> che gli incor&ograve; la speranza <lb/>di aver per esso a risolvere con sicurezza il problema delle longitudini. </s></p><p type="main">

<s>Sotto il d&igrave; 6 di Giugno di quell'anno 1637 abbiamo infatti scritta a <lb/>Lorenzo Realio, ch'era uno dei deputati dagli Olandesi ad esaminar la pro&shy;<lb/>posta di Galileo intorno al modo di trovare le longitudini, una lettera, nella <lb/>quale &egrave; nitidamente specchiata la scienza galileiana dei pendoli nei loro usi <pb xlink:href="020/01/2166.jpg" pagenum="409"/>pratici, dedotti dalla teoria, la quale anche qui, con manifesta trasgressione <lb/>di ogni termine di Meccanica e di Logica, si riduce a concludere il tauto&shy;<lb/>cronismo deg&igrave;i archi dal tautocronismo delle corde (Alb. </s>

<s>VII, 168). Vi si <lb/>professa pure il pi&ugrave; assoluto isocronismo delle vibrazioni, invocando per con&shy;<lb/>fermarlo quell'esperienza, che fece chiaramente vedere il contrario all'Huy&shy;<lb/>ghens, e a tutti coloro che non vogliano negar fede ai loro occhi proprii <lb/>(ivi, pag. </s>

<s>169). Sopra questo principio, che nonostante da Galileo si d&agrave; per <lb/>verissimo e stabile, &egrave; fondata la nuova invenzione di misurar i minimi tempi, <lb/>&ldquo; perch&egrave; fatta una volta tanto, con pazienza, la numerazione delle vibrazioni, <lb/>che si fanno in un giorno naturale, misurato colla rivoluzione di una stella <lb/>fissa; s'aver&agrave; il numero delle vibrazioni d'un'ora, d'un minuto o d'altra <lb/>minor parte. </s>

<s>Potrassi ancora, fatta questa prima esperienza col pendolo di <lb/>qualsivoglia lunghezza, crescerlo o diminuirlo, sicch&egrave; ciascheduna vibrazione <lb/>importi il tempo di un minuto secondo, imperocch&egrave; le lunghezze di tali pen&shy;<lb/>doli mantengono fra di loro duplicata proporzione di quella dei tempi, come <lb/>per esempio: posto che un pendolo di lunghezza di quattro palmi faccia in <lb/>un dato tempo mille vibrazioni, quando noi volessimo la lunghezza d'un <lb/>altro pendolo, che nell'istesso tempo, facesse duplicato numero di vibrazioni, <lb/>bisogna che la lunghezza del pendolo sia la quarta parte della lunghezza <lb/>dell'altro. </s>

<s>Ed insomma, come si pu&ograve; vedere coll'esperienza, la moltitudine <lb/>delle vibrazioni dei pendoli di lunghezze diseguali &egrave; sudduplicata di esse <lb/>lunghezze &rdquo; (Alb. </s>

<s>VII, 170). </s></p><p type="main">

<s>La legge &egrave; dunque formulata qui molto diversamente da quel che, cin&shy;<lb/>que anni prima, si fosse fatto nella IV giornata dei Massimi sistemi, ma <lb/>come e a qual felice occasione si fosse Galileo ravveduto del suo errore non <lb/>si cura di dirlo, non essendo dell'indole di quell'uomo, come in simili altri <lb/>casi notammo, il far pur vista di avere sbagliato. </s>

<s>Questo solo ci dice che <lb/>fu una tal legge scoperta e verificata per via dell'esperienza: e perch&egrave; in <lb/>quel tempo, cio&egrave; nel 1637, attendeva a metter in ordine, per darlo alle <lb/>stampe, il manoscritto del primo dialogo delle Scienze nuove, ivi ebbero so&shy;<lb/>lenne pubblicit&agrave; i fatti osservati, che non avevano, a volere esser giusti, nes&shy;<lb/>sun diritto d'essere esposti al mondo come nuovi, essendosi incontrato in <lb/>essi, infino dal 1611, il Baliani, e avendoli il Mersenno, in un suo libro <lb/>stampato in francese in Roma nel 1636, gi&agrave; divulgati. </s></p><p type="main">

<s>Nuovo sarebbe stato il problema del pendolo a secondi, che pareva aversi <lb/>risoluto nelle sopra scritte parole al Realio, per cui fa a prima vista gran <lb/>maraviglia il non veder quella soluzione inserita nei dialoghi del Moto, l&agrave; <lb/>dove specialmente sperava d'avercela a trovare il Baliani. </s>

<s>&ldquo; Anzi che in <lb/>quelli (nei dialoghi del Sistema) V. S. dice qualche cosa, di che io sperava <lb/>che ne dovesse dar pi&ugrave; distinto conto in questi, cio&egrave; di aver osservato che <lb/>il grave discende, di moto accelerato, per cento braccia in cinque minuti <lb/>secondi di ora; sperava dico che dovesse dir con che ragione si &egrave; assicu&shy;<lb/>rata che sian cinque secondi, e massime dove d&agrave; conto di altre esperienze <lb/>fatte in simil materia &rdquo; (Alb. </s>

<s>X, 353). </s></p><pb xlink:href="020/01/2167.jpg" pagenum="410"/><p type="main">

<s>Chi non si sarebbe infatti aspettato che, stabilitasi la legge dei quadrati <lb/>dei tempi proporzionali alle lunghezze dei pendoli, non avesse Galileo appli&shy;<lb/>cato il corollario de'quadrati delle vibrazioni, ad esse lunghezze reciproca&shy;<lb/>mente proporzionali, a dar regola matematica per trovar la lunghezza del <lb/>pendolo, che batte i secondi? </s>

<s>E invece s'applica a risolvere un problema <lb/>di pura curiosit&agrave;, qual'&egrave; quello &ldquo; di saper la lunghezza di una corda pen&shy;<lb/>dente da qualsivoglia grandissima altezza &rdquo; (Alb. </s>

<s>XIII, 99). N&egrave; il discorso <lb/>in materia de'pendoli s'introduce in questo primo dialogo per applicare ad <lb/>essi, nel terzo, le conclusioni intorno ai moti locali, le quali si rimangono <lb/>ivi perci&ograve; una sterile esercitazione, ma per spiegare il fatto assai trito &ldquo; delle <lb/>due corde tese all'unisono, che al suono dell'una l'altra si muove &rdquo; (ivi, <lb/>pag. </s>

<s>98) e per mostrare il modo, col quale l'occhio ancora possa ricrearsi <lb/>nel vedere i medesimi scherzi, che sente l'udito nelle varie consonanze mu&shy;<lb/>sicali (ivi, pag. </s>

<s>109). </s></p><p type="main">

<s>Certo una tal negligenza, in soggetto tanto importante, e ad una delle <lb/>pi&ugrave; grandi utilit&agrave;, che s'aspettavano da Galileo la Dinamica, la Nautica e <lb/>l'Astronomia preferire gli scherzi della Musica, fa gran maraviglia, la quale <lb/>ci vien tolta dal pensar che non bastava la notizia di un semplice principio <lb/>sperimentale, per ricavarne una regola matematica. </s>

<s>Che se fosse quel prin&shy;<lb/>cipio per s&egrave; bastato, non aveva bisogno di ricorrere a Galileo quel Baliani, <lb/>il quale aveva parecchi anni prima scoperto che le lunghezze dei pendoli <lb/>stanno come i quadrati dei tempi delle vibrazioni. </s>

<s>Conveniva dunque ridurre <lb/>questo fatto a un calcolo, il quale, bench&egrave; fosse assai semplice, era nono&shy;<lb/>stante cos&igrave; sottile, da sfuggire all'arte dello stesso Galileo. </s>

<s>A chi non lo <lb/>crederebbe faremo intanto avvertire una impropriet&agrave; di linguaggio, scorsa <lb/>nella Lettera al Realio, che poi nel Dialogo si ripete, dicendosi l&agrave; <emph type="italics"/>che la <lb/>moltitudine delle vibrazioni dei pendoli di lunghezze diseguali &egrave; suddu&shy;<lb/>pla di esse lunghezze,<emph.end type="italics"/> e qu&agrave;, che <emph type="italics"/>le lunghezze delle corde hanno fra loro <lb/>la proporzione, che hanno i quadrati dei numeri delle vibrazioni, che si <lb/>fanno nel medesimo tempo.<emph.end type="italics"/> La parola <emph type="italics"/>reciproca,<emph.end type="italics"/> che si legge nell'edizione <lb/>dell'Alb&egrave;ri, in carattere corsivo, &egrave; una correzione introdottavi da una copia <lb/>dell'edizione di Leyda postillata dal Viviani. </s></p><p type="main">

<s>L'impropriet&agrave; del linguaggio, che in due cos&igrave; insigni scritture non si <lb/>potrebbe facilmente passare per una semplice inavvertenza, &egrave; indizio e causa <lb/>di una confusion nelle idee, della quale ci porge Galileo stesso l'esempio, <lb/>quando, poco dopo d'aver annunziata la legge, che governa il moto dei pen&shy;<lb/>doli di varia lunghezza, si propon di ricavarne la soluzione di questo pro&shy;<lb/>blema, per render visibile il gioco delle consonanze musicali: S'abbiano tre <lb/>pendoli, e si cerchi quali debban essere le loro lunghezze, perch&egrave;, mentre <lb/>il pi&ugrave; lungo fa due vibrazioni, il mezzano ne faccia tre, e il pi&ugrave; corto quat&shy;<lb/>tro. </s>

<s>Questo otterremo, dice il Salviati, &ldquo; quando il pi&ugrave; lungo contenga sedici, <lb/>palmi, o altre misure, delle quali il mezzano ne contenga nove, e il minore <lb/>quattro &rdquo; (Alb. </s>

<s>XIII, 109). Ma qui &egrave; un error di calcolo manifesto, perch&egrave;, <lb/>se i numeri delle vibrazioni son 2, 3, 4, e debbono le lunghezze reciproca-<pb xlink:href="020/01/2168.jpg" pagenum="411"/>mente stare come i quadrati di questi numeri, non saranno dunque 16, 9 e 4, <lb/>ma 36 16 e 9. Fu il primo il Viviani a notare lo sbaglio, e, a pag. </s>

<s>107 di <lb/>una copia dell'edizione di Leyda, scrisse di propria mano in margine, con <lb/>insolita libert&agrave;, la seguente postilla: </s></p><p type="main">

<s>&ldquo; Quando i numeri delle vibrazioni, fatte nel medesimo tempo dai tre <lb/>fili pendoli, differenti in lunghezza, sono queste: cio&egrave; 2, 3, 4 come gli pone <lb/>il signor Galileo, dovendo tali lunghezze stare in proporzione reciproca dei <lb/>quadrati di detti numeri, staranno come questi numeri 9, 4 2 1/4, cio&egrave; 16, <lb/>7 1/9, 4, onde, dove qui al quarto verso dicesi <emph type="italics"/>nove,<emph.end type="italics"/> &egrave; errore di calcolo, e <lb/>deve dire <emph type="italics"/>sette e un nono.<emph.end type="italics"/> Che se le lunghezze dei fili de'tre pendoli fos&shy;<lb/>sero quali le pone sopra il signor Galileo, cio&egrave; fossero 16, 9, 4, i tempi delle <lb/>loro uniche vibrazioni sarebbero 4, 3, 2: i numeri delle vibrazioni, fatte <lb/>nel medesimo tempo, sarebbero 3, 4, 6, onde gl'incontri di esse seguireb&shy;<lb/>bero ad ogni 3 vibrazioni del lungo, 4 del mezzano e 6 del corto, e non ad <lb/>ogni 2, 3, 4, com'ei dice &rdquo; (MSS. Gal., P. V, T. IX). </s></p><p type="main">

<s>L'errore non &egrave;, come il Viviani voleva credere, materiale del calcolo, <lb/>ma formale della regola, male istituita a ben condurlo, ond'&egrave; che Galileo, <lb/>veduta la difficolt&agrave; di spuntare a risolvere il problema del pendolo, che batte <lb/>i secondi, annunziato gi&agrave; nella lettera al Realio, ridusse l'ambita invenzione <lb/>del suo nuovo Misuratore del tempo per gli usi nautici quale ei lo descrisse <lb/>per gli usi astronomici nelle <emph type="italics"/>Operazioni,<emph.end type="italics"/> che son l'unica prima scrittura, <lb/>nella quale si parli di proposito del pendolo, per uso di Cronometro. </s>

<s>E per&shy;<lb/>ch&egrave; una tale scrittura &egrave; del 1639, come apparisce da certissimo documento <lb/>(Alb. </s>

<s>VII, 193) ecco una dimostrativa conferma di ci&ograve;, che abbiamo ad altre <lb/>occasioni asserito, che cio&egrave;, non prima del 1637, cominci&ograve; a pensar Galileo <lb/>di far de'pendoli quelle cronometriche applicazioni, delle quali annunziava <lb/>nel 1639 il definitivo progetto. </s>

<s>Consisteva un tal progetto nel servirsi di un <lb/>pendolo di qualunque lunghezza, e, fallacemente supposto che facesse tutte <lb/>le sue vibrazioni uguali, contare il numero delle fatte da lui in 24 ore si&shy;<lb/>deree, &ldquo; imperocch&egrave; da esse, in tutte l'altre osservazioni di tempi, potremo <lb/>avere la quantit&agrave; loro in ore, minuti, secondi, terzi, ecc., operando con la <lb/>regola aurea &rdquo; (Alb. </s>

<s>V, 374). </s></p><p type="main">

<s>Cos&igrave; essendo, non si trovava ora dunque Galileo chiusa in tutto la bocca, <lb/>come nel 1632, e nel 1635, quando il Baliani e il Pieroni erano venuti a <lb/>proporgli i loro quesiti. </s>

<s>E perci&ograve; al primo commemorato, che nel principio <lb/>del Luglio 1639 era venuto a ripetere la dimenticata domanda, fatta con <lb/>tanta istanza sette anni avanti all'occasione del vedersi smarrita la speranza <lb/>d'avere a ritrovar nei dialoghi Del moto descritto lo strumento, con cui si <lb/>potesse ognuno certificare essere il tempo speso da un mobile a passar cento <lb/>braccia precisamente cinque secondi; Galileo, ora liberale dell'acquistata <lb/>scienza, rispondeva con lettera del d&igrave; primo Agosto di quel medesimo anno, <lb/>dove, dopo aver detto come, facendo uso de'suoi teoremi, si fosse assicu&shy;<lb/>rato del tempo assoluto della scesa del mobile per quello spazio, passa a <lb/>propor l'altro modo da tenersi per ritrovare il tempo relativo. </s></p><pb xlink:href="020/01/2169.jpg" pagenum="412"/><p type="main">

<s>&ldquo; Ci&ograve; otterremo, scriveva, dalla ammirabile propriet&agrave; del pendolo, che <lb/>&egrave; di fare tutte le sue vibrazioni, grandi e piccole, sotto tempi eguali. </s>

<s>Si ri&shy;<lb/>cerca, <emph type="italics"/>pro una vice tantum,<emph.end type="italics"/> che due, tre o quattro amici, curiosi e pazienti, <lb/>avendo appostata una stella fissa, che risponde contro a qualche segno sta&shy;<lb/>bile, preso un pendolo di qualsivoglia lunghezza, vadano numerando le sue <lb/>vibrazioni per tutto il tempo del ritorno della medesima fissa al primo luogo, <lb/>e questo sar&agrave; il numero delle vibrazioni di 24 ore. </s>

<s>Dal numero di queste <lb/>potremo ritrovare il numero delle vibrazioni di qualsivogliano altri pendoli <lb/>minori e minori a nostro piacimento, sicch&egrave;, se v. </s>

<s>g. </s>

<s>le numerate da noi <lb/>nelle 24 ore fossero state per esempio 234,567, pigliando un altro pendolo <lb/>pi&ugrave; breve, nel quale uno numeri per esempio 800 vibrazioni, mentre che <lb/>l'altro misurasse 156 delle maggiori, gi&agrave; avremo, per la regola aurea, il nu&shy;<lb/>mero delle vibrazioni di tutto il tempo delle 24 ore. </s>

<s>E se con queste vi&shy;<lb/>brazioni vorremo sapere il tempo della scesa per il canale, potremo, con la <lb/>medesima agevolezza, ritrovare non solo i minuti primi, secondi e terzi, ma <lb/>quarti e quinti, e quanto pi&ugrave; ci piacer&agrave; &rdquo; (Lettere di Galileo, Pisa 1864, <lb/>pag. </s>

<s>42). </s></p><p type="main">

<s>Cos&igrave; fatte minuzie erano pi&ugrave; per&ograve; a lussuria di calcolo, che per servire <lb/>alla precisione delle esperienze, per le quali sarebbesi massimamente desi&shy;<lb/>derato che fosse giusto il numero delle vibrazioni, contate nel tempo delle <lb/>24 ore da que'due o tre o quattro amici. </s>

<s>Ma dove ritrovar tanta resistenza <lb/>al disagio, o tanta durazione nella lunga pazienza? </s>

<s>E quando pure si fos&shy;<lb/>sero ritrovate cos&igrave; rare virt&ugrave;, nell'abito corporeo e nelle disposizioni del&shy;<lb/>l'animo, chi sarebbesi potuto ripro ne<gap/>tere tanta infallibilit&agrave; del senso, da <lb/>assicurarsi che, di quelle tante migliaia di vibrazioni, nemmen una gliene <lb/>fosse sfuggita all'attenzion della vista? </s>

<s>Furon quelle riflessioni, che, alle <lb/>sopra lasciate interrotte, suggeriron le parole seguenti: &ldquo; Vero &egrave; che noi <lb/>potremo passare a pi&ugrave; esatta misura, con avere veduto ed osservato qual sia <lb/>il flusso dell'acqua per un sottile cannello, perch&egrave;, raccogliendo ed avendo <lb/>pesata quanta ne passa v. </s>

<s>g. </s>

<s>in un minuto, potremo poi, col pesare la pas&shy;<lb/>sata nel tempo della scesa per il canale, trovare l'esattissima misura e quan&shy;<lb/>tit&agrave; di esso tempo, servendosi massimamente di una bilancia cos&igrave; esatta, che <lb/>tira ad un sessantesimo di grano &rdquo; (ivi, pag. </s>

<s>43). </s></p><p type="main">

<s>Ecco dunque dove vanno a finire tutte le declamate eccellenze di quel <lb/>Misuratore del tempo, con cui si ritroverebbero infallibilmente, in mezzo al&shy;<lb/>l'incerto mare, i naviganti olandesi; ecco dove va a sfumar la gloria del&shy;<lb/>l'ambita invenzione! a dir che, rispetto al pendolo, son pi&ugrave; esatta misura <lb/>le clessidre, e, in tanto fasto di novit&agrave;, tornare indietro a Proclo e a Cleo&shy;<lb/>mede. </s>

<s>Sentiva il Baliani questi rimproveri nella sua propria coscienza po&shy;<lb/>tenti, e s'infervorava sempre pi&ugrave; in voler aver quel pendolo a secondi, da <lb/>cui sperava la felice risoluzione di tanti bei problemi di Ottica, di Acustica, <lb/>di Goografia, di Astronomia e di Nautica, i quali tutti Galileo, a scusar s&egrave;, <lb/>e a giustificarsi di ci&ograve; che aveva scritto per verificare la legge delle cadute <lb/>dei gravi, sacrificava agl'ignobili vasi sgocciolanti. </s></p><pb xlink:href="020/01/2170.jpg" pagenum="413"/><p type="main">

<s>Nei giorni, in cui recapit&ograve; questa lettera di Firenze, si trovava di pas&shy;<lb/>saggio in Genova il p. </s>

<s>Niccol&ograve; Cabeo, a cui si rivolse il Baliani, pregandolo <lb/>a voler usar di tutto il suo studio, e di tutta la sua pazienza, per veder di <lb/>ricavar da que'documenti galileiani la misura giusta del pendolo oscillante <lb/>a ogni minuto secondo. </s>

<s>Tornato il Cabeo a Ferrara, si dette con indicibile <lb/>assiduit&agrave; all'opera, e in poco pi&ugrave; di una settimana si lusing&ograve; di averla con&shy;<lb/>dotta a buon termine, scrivendo a Genova, e mandandone la misura. </s>

<s>Lieto <lb/>il Baliani di aver finalmente conseguito lo strumento, che gli potrebbe &ldquo; ser&shy;<lb/>vire per un Orologio da misurar molte cose, che richiedano tempo breve &rdquo; <lb/>(Alb. </s>

<s>X, 360) ne dava, per lettera del d&igrave; 19 Agosto, avviso a Galileo, dicen&shy;<lb/>dogli essere stato il Cabeo, che, reputato atto a ci&ograve;, &ldquo; e a molto maggior <lb/>cosa &rdquo; (ivi) l'aveva, pregatone, sodisfatto del suo desiderio. </s></p><p type="main">

<s>Galileo cominci&ograve; a quell'avviso a ripensar curiosamente com'avesse fatto <lb/>esso Cabeo a ritrovare una tal misura, e il d&igrave; primo del seguente Settembre <lb/>significava cos&igrave; al Baliani il suo pensiero: &ldquo; In risposta alla gratissima del <lb/>19 del passato mese, dico che, quanto a misurare il tempo con un pendolo <lb/>aggiustato a fare le sue vibrazioni in un minuto secondo, si avanza la fa&shy;<lb/>tica del fare il calcolo con la semplice operazione della regola aurea, avendo <lb/>una volta tenuto conto del numero delle vibrazioni di qualsivoglia pendolo, <lb/>fatte in 24 ore, la quale osservazione &egrave; necessario che il p. </s>

<s>Cabeo abbia <lb/>fatta con un pendolo di qualsiasi lunghezza, e da esso cavatone, con l'in&shy;<lb/>venzione delle medie, la lunghezza del pendolo di un minuto secondo &rdquo; (Let&shy;<lb/>tere di Gal. </s>

<s>cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Ma che cosa &egrave; questa <emph type="italics"/>invenzion delle medie,<emph.end type="italics"/> domandava a s&egrave; stesso il <lb/>Baliani, a cui era venuta da Ferrara la misura, non per&ograve; il modo usato in <lb/>ritrovarla. </s>

<s>Rispondeva perci&ograve; a Galileo non saper dirgli, in proposito di quel <lb/>modo, altro che questo: &ldquo; Il calcolo del padre Cabeo credo che sia fatto al <lb/>modo di V. S., che cos&igrave; io gli suggerii, quando egli era qui, non per&ograve; tanto <lb/>esattamente, da numerare le vibrazioni fatte in 24 ore, ma credo in una o <lb/>due ore solamente, in qualunque lunghezza del pendolo, col farci poi il conto <lb/>per la regola aurea, come V. S. dice &rdquo; (Alb. </s>

<s>X, 365). </s></p><p type="main">

<s>La regola aurea per&ograve;, cos&igrave; usata intorno a pendoli di qualunque lun&shy;<lb/>ghezza, non poteva bastar per s&egrave; sola a ritrovar la prefinita misura del pen&shy;<lb/>dolo a secondi, altro che per via di ripetuti tentativi, allungando o occor&shy;<lb/>ciando il filo, trovato battere una certa misura del tempo, infino a ridurlo <lb/>a un secondo preciso; nei quali tentativi consisteva quella, che Galileo chia&shy;<lb/>mava <emph type="italics"/>invenzion delle medie.<emph.end type="italics"/> Se dovea dunque il Cabeo seguitar necessa&shy;<lb/>riamente questa via di prova, non c'era, secondo lo stesso Galileo, nessun'al&shy;<lb/>tra regola matematicamente sicura. </s>

<s>Le parole perci&ograve; scritte nella lettera al <lb/>Realio non dovettero aver, nella mente dello scrittore, il significato, che <lb/>sembrava esservi espresso, che cio&egrave;, trovato il numero delle vibrazioni fatte <lb/>in un minuto secondo da un pendolo di qualunque lunghezza, si potesse, <lb/>dal teorema ivi opportunamente invocato, che cio&egrave; <emph type="italics"/>la moltitudine delle vi&shy;<lb/>brazioni dei pendoli di lunghezze diseguali &egrave;<emph.end type="italics"/> reciprocamente <emph type="italics"/>sudduplicata<emph.end type="italics"/><pb xlink:href="020/01/2171.jpg" pagenum="414"/><emph type="italics"/>di esse lunghezze;<emph.end type="italics"/> dedurne la lunghezza del pendolo a secondi: imperocch&egrave; <lb/>l'operazione fatta con questa regola si riduceva alla certezza di un calcolo <lb/>aritmetico, consistente nel moltiplicar la misura del pendolo arbitrario per <lb/>il quadrato del numero delle vibrazioni, fatte da lui in un minuto secondo. </s></p><p type="main">

<s>Essendo insomma Galileo persuaso non si poter risolvere il problema <lb/>del pendolo, determinatamente lungo, altro che per ripetute esperienze fatte <lb/>col pendolo di qualunque lunghezza, ne concludeva che in precisione era <lb/>questo suo orologio superiore a quello dell'altro, e che perci&ograve; male il Ba&shy;<lb/>liani aveva provveduto al suo bisogno, dando la preferenza alla invenzione <lb/>del Cabeo, che va inevitabilmente sottoposta a qualche errore, &ldquo; il quale, <lb/>bench&egrave; piccolo, moltiplicato secondo il numero delle molte vibrazioni, pu&ograve; <lb/>partorire notabile errore, il che non accade nelle vibrazioni, non obbligate <lb/>alla lunghezza del filo, che, molte centinaia di volte replicata, ci deve dare <lb/>la misura del tempo; sicch&egrave; ogni piccolo errore, preso nella lunghezza del <lb/>pendolo, va molte centinaia di volte moltiplicato, mentre nell'altra mia ope&shy;<lb/>razione l'errore non pu&ograve; nascere salvo che dal numerare le vibrazioni, delle <lb/>quali una sola parte di una sola vibrazione pu&ograve; essere presa pi&ugrave; o meno del <lb/>giusto &rdquo; (Lettere di Gal. </s>

<s>cit., pag. </s>

<s>48). </s></p><p type="main">

<s>Questo, che dice qui Galileo, &egrave; come il pi&ugrave; distinto suggello a confer&shy;<lb/>mar ch'ei non doveva conoscere altro modo, che tentare e ritentare per via <lb/>della esperienza, perch&egrave;, se avesse saputa la regola del calcolo, istituita die&shy;<lb/>tro le ragioni, che serbano insieme i pendoli, tra i tempi del loro vibrare <lb/>e le lunghezze dei fili; non avrebbe avuto alcun dubbio che, tanto il pen&shy;<lb/>dolo obbligato, quanto quello non obbligato a lunghezza, sarebbero andati <lb/>soggetti ai medesimi errori, dipendenti unicamente dagli sbagli nel nume&shy;<lb/>rare le vibrazioni fatte in 24 ore, e nel dedurne di l&igrave; il numero delle vi&shy;<lb/>brazioni fatte in un minuto secondo, potendo esser l'une, e perci&ograve; anche <lb/>l'altre, prese, come Galileo stesso dianzi diceva, pi&ugrave; o meno del giusto. </s>

<s>Se <lb/>chiamata L infatti l'arbitraria lunghezza del pendolo, e N2 il quadrato del <lb/>numero delle vibrazioni, da lui fatte in un minuto secondo, la cercata lun&shy;<lb/>ghezza X dell'orologio a secondi vien rappresentata dalla formula X=LN2; <lb/>&egrave; chiaro che tutta l'esattezza, cos&igrave; di questa come dell'operazione di Gali&shy;<lb/>leo, dipende dal valore di N, non avendo L nessuna difficolt&agrave; a dare a chiun&shy;<lb/>que la voglia la precisa lunghezza sua lineare. </s></p><p type="main">

<s>Or perch&egrave; da nessuna parte dei consultati commerci epistolari resulta <lb/>chiaro se il modo tenuto dal Cabeo fosse propriamente quello congetturato <lb/>da Galileo, n&egrave; il Baliani a lui scrisse quanta fosse la ritrovata misura del <lb/>pendolo, rimarremo qui in gran curiosit&agrave; di saper la parte pi&ugrave; importante <lb/>di questa storia, se il Cabeo stesso, pubblicando i suoi commentari sulla Me&shy;<lb/>teorologia di Aristotile, non fosse venuto a darci la desiderata notizia. </s>

<s>Nella <lb/>Questione ultimamente citata, nella quale si richiamavano a sottile esame le <lb/>dottrine galileiane intorno ai pendoli di uguale lunghezza, dop'avere il Cabeo <lb/>concesso che, per esser piccole le disuguaglianze osservate, si potevano i moti <lb/>di quegli stessi pendoli reputare isocroni, cos&igrave; soggiunge: &ldquo; Ex hoc habe-<pb xlink:href="020/01/2172.jpg" pagenum="415"/>tur utilissimum sane instrumentum, vel potius Horologium, ad mensuran&shy;<lb/>dum tempora brevissima, ita ut ex serico filo suspendendo globulum plum&shy;<lb/>beum, non solum tibi possis instruere Horologium, quo minuta secunda <lb/>metiaris, sed etiam 3, 4, immo et 5 unius secundae poteris metiri. </s>

<s>Ego mihi <lb/>comparavi, satis pertinaci labore, mensurando integram horam, longitudinem <lb/>fili penduli exactissime, qua unam habeo secundam. </s>

<s>Longitudo fili est un&shy;<lb/>ciarum 9 pedis romani antiqui &rdquo; (Editio cit., T. I, pag. </s>

<s>100). </s></p><p type="main">

<s>La notizia &egrave; importante, perch&egrave; sappiamo ora di certo che la quantit&agrave; <lb/>della misura del pendolo a secondi, reputata dal Cabeo e creduta dal Baliani <lb/>esattissima, era nove once di piede romano antico, ossia un palmo, che, se&shy;<lb/>condo le comuni tavole di riduzione, corrisponderebbe a 0m, 223. L'enorme <lb/>sbaglio, che non poteva solo dipendere dalla poco esatta misura dell'ora, <lb/>presa forse dagli orologi scioterici o dalle clessidre, farebbe credere che di&shy;<lb/>pendesse piuttosto dalla mala corrispondenza di quei tentativi, ai quali era, <lb/>secondo Galileo, necessario si riducesse l'osservatore, per conseguire il suo <lb/>intento. </s>

<s>Dal sopra trascritto passo per&ograve; non s'argomenta nulla in proposito, <lb/>ma nel II tomo di quelia stessa Opera meteorologica ci toglie intorno a ci&ograve; <lb/>l'Autore ogni dubbio. </s>

<s>Dice anzi che, nel provarsi ad allungare e ad accor&shy;<lb/>ciare il pendolo, per ridurlo alla desiderata misura, si accorse di un fatto <lb/>inaspettato, che cio&egrave; la frequenza delle vibrazioni non diminuiva a proporzion <lb/>dei fili accorciati. </s>

<s>Dop'aver trovato con la regola di Galileo che un pendolo <lb/>faceva per esempio quattro vibrazioni in un minuto secondo, credeva che, <lb/>per avere una vibrazione sola, bastasse ridurlo quattro volte pi&ugrave; lungo, e <lb/>trov&ograve; invece, con sua gran sorpresa, che si dovea allungare molto di pi&ugrave;, <lb/>cosicch&egrave;, se un palmo avesse dato un secondo preciso, per avere un minuto <lb/>primo, tutt'altro che 60 palmi disse di non aver trovato ancora un filo tanto <lb/>lungo, che gli fosse bastato al bisogno. </s>

<s>&ldquo; Imminuto filo penduli fiunt qui&shy;<lb/>dem undationes incitatiores, at non inci'antur ad rationem imminuti fili, ita <lb/>ut, si filium fiat dimidio brevius, et undatio duplo fiat incitatior, non hoc <lb/>inquam sequitur, nam pendulum, cuius filum sit palmare, unam fere absumit <lb/>secundam singulis undationibus, et tamen filum sexaginta palmorum non <lb/>unum explet integrum minutum. </s>

<s>Immo nullam hactenus taniam fili longi&shy;<lb/>tudinem habere potui, quae integrum daret minutum &rdquo; (pag. </s>

<s>289). </s></p><p type="main">

<s>Tale fu la cultura, e tali furono i frutti, che raccolse il Cabeo dal suo <lb/>pertinace lavoro, dai consigli del Baliani, e dagli insegnamenti di Galileo. </s>

<s><lb/>Non sapendo il pubblico nulla di cos&igrave; fatti consigli, e di cos&igrave; fatti insegna&shy;<lb/>menti, rimasti nei privati commerci epistolari, ebbe a far le maraviglie di <lb/>tanto errore e di tanta ignoranza, di che al Cabeo solo rest&ograve; a sopportare <lb/>l'accusa. </s>

<s>&ldquo; Quae omnia non impediunt, scriveva il Mersenno dopo aver letto, <lb/>ne'commentari alla Meteorologia aristotelica, il passo ora copiato, quin fieri <lb/>nequeat ut filum palmare secundum minutum fere duret, cum vix secundi <lb/>respondeat dimidio, adeo ut ostenderit Cabeus se non satis exacte duratio&shy;<lb/>nes funependuli examinasse, neque rationem temporum duplicatam nosse, <lb/>ut clarum est ex eodem loco, quod eo magis admiror quod illam rationem <pb xlink:href="020/01/2173.jpg" pagenum="416"/>ex Galilaeo didicisse debuerit, quem toties refellere conatus est, quodque ex <lb/>nostris <emph type="italics"/>Harmonicis,<emph.end type="italics"/> Romae decennio prostantibus antequam suum in Me&shy;<lb/>teora volumen ederet, rationem illam funependulorum discere potuit &rdquo; (Re&shy;<lb/>flexiones phisico-malhem., Parisiis 1647, pag. </s>

<s>158) </s></p><p type="main">

<s>Forse il Cabeo non aveva letto altro che nell'ultima giornata dei Mas&shy;<lb/>simi sistemi, dove s'insinua la falsa dottrina dei tempi proporzionali alle <lb/>semplici lunghezze dei pendoli. </s>

<s>Ma poniamo che avesse appreso, dal primo <lb/>dialogo delle Nuove scienze o dagli <emph type="italics"/>Armonici,<emph.end type="italics"/> che que'tempi sono invece <lb/>proporzionali alle radici delle lunghezze; non gli sarebbe per&ograve; bastata que&shy;<lb/>sta notizia a conseguire una misura del pendolo pi&ugrave; giusta, come non bast&ograve; <lb/>al Baliani e a Galileo, dei quali avrebbe avuto pi&ugrave; ragione di maraviglia si <lb/>il Mersenno. </s>

<s>Vien tolta ogni occasione di maraviglia per&ograve; dal ripensar le cause, <lb/>che resero cos&igrave; incerti nella dottrina, e cos&igrave; mal sicuri nella pratica quei tre, <lb/>che primi in Italia dettero opera insieme a risolvere il problema del pendolo <lb/>a secondi; cause che si riducono, come tante volte abbiam detto, al non aver <lb/>nessuno di essi penetrate le matematiche ragioni di un fatto, ch'ebbe a ri&shy;<lb/>manersi perci&ograve; fra la non superabile angusta cerchia delle esperienze. </s></p><p type="main">

<s>In quel medesimo anno 1638, in cui Galileo e il Baliani si confessa&shy;<lb/>vano impotenti all'impresa, e vi faceva il Cabeo cos&igrave; infelice riuscita, si stam&shy;<lb/>pava in Praga un libro, rivelatore di quella scienza dei pendoli, ch'era <lb/>venuta meno ai nostri Italiani. </s>

<s>Giovan Marco, nella XXVIII proposizione <emph type="italics"/>De <lb/>proportione motus,<emph.end type="italics"/> era il primo che, da principii matematici, venisse a di&shy;<lb/>mostrare <emph type="italics"/>Motus circulorum sunt in ratione suorum temporum, quam habent <lb/>diametri ad se duplicatam<emph.end type="italics"/> (fol. </s>

<s>37 ad t.). </s></p><p type="main">

<s>I principii matematici, che servon come di lemmi alla dimostrazione, son <lb/>pur essi dall'Autore matematicamente dimostrati in altre proposizioni ante&shy;<lb/>cedenti, fra le quali &egrave; la XIII del trattato, coll'aggiunta di un corollario, che <lb/><figure id="id.020.01.2173.1.jpg" xlink:href="020/01/2173/1.jpg"/></s></p><p type="caption">

<s>Figura 211<lb/>manca alla proposizione III del primo libro manoscritto di <lb/>Galileo. </s>

<s>Essendo AB (fig. </s>

<s>211) verticale e AC obliqua, pre&shy;<lb/>cisa in C dalla BC condottale perpendicolare, si dimostra in <lb/><figure id="id.020.01.2173.2.jpg" xlink:href="020/01/2173/2.jpg"/></s></p><p type="caption">

<s>Figura 212<lb/>quel manoscritto galileiano che, a move&shy;<lb/>re da A, si passano dal mobile i due spazi <lb/>AB, AC nel medesimo tempo, e Giovan <lb/>Marco soggiunge che nel medesimo tem&shy;<lb/>po anche si passerebbe la BC, essen&shy;<lb/>do in C il principio del moto, perch&egrave;, <lb/>costruito il parallelogrammo AD, la BC, <lb/>in virt&ugrave; del teorema galileiano, &egrave; isocro&shy;<lb/>na a CD, e perci&ograve; anche ad AB, ond'&egrave; <lb/>che AB, AC, BC sono isocrone insieme. </s>

<s>L'altra proposi&shy;<lb/>zione, pi&ugrave; prossimo lemma a quella da dimostrare, &egrave; la <lb/>XXVI, che cio&egrave; i tempi per gli archi simili son propor&shy;<lb/>zionali ai tempi per i seni corrispondenti. </s></p><p type="main">

<s>Dietro ci&ograve;, ecco insomma come Giovan Marco, con eleganza spedita, <pb xlink:href="020/01/2174.jpg" pagenum="417"/>dimostra che il tempo per l'arco CD (fig. </s>

<s>212), di cui il seno &egrave; CE, sta al <lb/>tempo per l'arco BF, di cui il seno &egrave; BG, come la radice di AC sta alla <lb/>radice di AB. </s>

<s>Abbiamo To.CD:To.BF=To.CE:To.BG, e perch&egrave; CE &egrave; <lb/>isocrona ad AC, e BG isocrona ad AB, To.CD:To.BF=To.AC:To.AB. </s>

<s><lb/>Ma il tempo per AC sta al tempo per AB, come la radice di AC sta alla <lb/>radice di AB; dunque, secondo queste medesime radici, che son quelle delle <lb/>altezze dei pendoli, o delle lunghezze dei raggi, stanno anche i tempi per <lb/>gli archi simili da loro descritti. </s></p><p type="main">

<s>Di qui, mentre il Cabeo andava fra le tenebre brancolando a cercar <lb/>l'esatto misuratore dei secondi minuti, e Galileo conveniva non si potere <lb/>andar altro che brancolando, ricavava Giovan Marco la regola matemati&shy;<lb/>camente sicura. </s>

<s>Supponiamo, diceva, di aver trovato che un pendolo, preso <lb/>di tal lunghezza che si giudichi alcun poco maggiore della richiesta, fa 1200 <lb/>vibrazioni in un'ora, o 20 in un minuto, e si voglia ridurlo a farne preci&shy;<lb/>samente 60 in quel medesimo tempo. </s>

<s>&Egrave; certo che tanto dovr&agrave; essere pi&ugrave; <lb/>frequente questo di quello, quanto 60 &egrave; maggior numero di 20, o tre &egrave; mag&shy;<lb/>giore di uno. </s>

<s>Or perch&egrave; le altezze dei pendoli stanno, secondo il dimostrato <lb/>teorema, come i quadrati dei tempi, diremo che la maggiore altezza sta nel <lb/>presente caso alla minore, come il quadrato di tre sta al quadrato di uno, <lb/>e avremo perci&ograve; questa stessa minore altezza, ch'&egrave; la conveniente a un oro&shy;<lb/>logio a secondi, riducendo a un nono la nota altezza maggiore. </s>

<s>&ldquo; Sumatur <lb/>quaecumque productio fili, aliquanto tamen longior, quo minus cito a motu <lb/>conquiescat, numereturque huius escursus per spatium unius horae qua&shy;<lb/>drantis, et sint v. </s>

<s>g. </s>

<s>300, eruntque spatio horae unius 1200. Quod si ergo <lb/>fiat ut quadratum temporis, nimirum trium secundorum, idest 9 ad 1, ita <lb/>longitudo fili ad minorem, erit huius motus aequalis secundo &rdquo; (ibid., fol. </s>

<s>63). </s></p><p type="main">

<s>Essendo il libro del Matematico di Praga rimasto in Italia e in Francia <lb/>per molti anni sconosciuto, non ebbero gl'insegnamenti di lui qu&agrave; dai monti <lb/>nessuna efficacia, ma pur la soluzion del problema del pendolo a secondi <lb/>dipendeva dalle dottrine di Galileo e del Baliani cos&igrave; immediata, che non <lb/>trovarono difficolt&agrave; i discepoli a conseguirla da quegli stessi principii, posti <lb/>cos&igrave; stabilmente dai loro proprii maestri. </s>

<s>Da commemorare fra quei disce&shy;<lb/>poli uno dei primi &egrave; Benedetto Castelli, il quale, nel secondo libro Della mi&shy;<lb/>sura delle acque correnti, dedicato manoscritto infino dal 1642 a Cosimo gran <lb/>principe di Toscana, proponeva per gli usi idrometrici il pendolo, di cui di&shy;<lb/><figure id="id.020.01.2174.1.jpg" xlink:href="020/01/2174/1.jpg"/></s></p><p type="caption">

<s>Figura 213<lb/>ceva &ldquo; si devono numerare le vibrazioni, <lb/>che si fanno mentre dura l'opera, e saran&shy;<lb/>no tanti minuti secondi, quando per&ograve; il <lb/>filo sia lungo tre piedi romani &rdquo; (Bologna <lb/>1660, pag. </s>

<s>80). Il Mersenno poi, pubbli&shy;<lb/>cando nel 1644 in Parigi il suo libro <emph type="italics"/>Co&shy;<lb/>gitata physico-mathematica,<emph.end type="italics"/> cos&igrave;, a pro&shy;<lb/>posito del pendolo misuratore del tempo, <lb/>in quella sua general prefazione, scriveva: &ldquo; Si enim filum illud AB (fig. </s>

<s>213) <pb xlink:href="020/01/2175.jpg" pagenum="418"/>tripedale fuerit, globuli, ad punctum G vel F aut aliud quodvis usque ad C vel <lb/>D erecti, recursus per semicircumferentiam DBC, tempus unius secundi <lb/>consumit, recursus vero a D ad B, vela C ad B, semisecundum &rdquo; (pag. </s>

<s>9). </s></p><p type="main">

<s>Tre piedi romani, ossia 0m, 885, e tre piedi parigini, ossia 0m, 972, son <lb/>misure del pendolo a secondi straordinariamente pi&ugrave; giuste di quelle date <lb/>dal Cabeo pochi anni prima, della quale aggiustatezza &egrave; da riconoscere la <lb/>ragione nell'avere il Castelli e il Mersenno non operato a caso, ma dietro <lb/>quella regola matematicamente certa, che conseguiva, come dicemmo, dai <lb/>teoremi di Galileo e dai supposti del Baliani, immediata. </s>

<s>Non bastava per&ograve; <lb/>la semplice regola matematica, sopra la quale proporre la soluzion teorica <lb/>del problema, ci&ograve; che solo erasi contentato di far Giovan Marco; bisognava <lb/>di pi&ugrave; venire ai casi pratici, ed avere in effetto misurate le vibrazioni, fatte <lb/>da qualunque lunghezza di pendolo in una certa esatta durata di tempo. </s>

<s><lb/>Deve ci&ograve; necessariamente essere stato operato dal Castelli e dal Mersenno, <lb/>ma come non lo sappiamo: non sappiamo cio&egrave; se fu quel tempo misurato <lb/>dal moto delle stelle, come insegnava Galileo, o dai flussi delle polveri e dei <lb/>liquidi, o dagli appulsi delle ombre alle linee gnomoniche, secondo si crede <lb/>aver fatto il Cabeo. </s></p><p type="main">

<s>In quel medesimo tempo per&ograve; del Castelli s'esercitava intorno a ri&shy;<lb/>durre alla sua pratica soluzione il problema del pendolo a secondi un no&shy;<lb/>stro insigne Sperimentatore, che ne lasci&ograve; pubblica e particolare notizia del <lb/>modo, e che, sebben avverso per istituto, si professava nulladimeno in quel <lb/>caso anch'egli discepolo di Galileo. </s>

<s>Giovan Batista Riccioli, proponendosi nel <lb/>II libro del I tomo dell'Almagesto nuovo di trattar delle oscillazioni dei pen&shy;<lb/>doli, e delle loro applicazioni alla misura dei tempi, concludeva cos&igrave; le brevi <lb/>parole premesse nel cap. </s>

<s>XX al suo trattatello: &ldquo; Quae igitur, per meipsum, <lb/>et ope sociorum, ad satietatem usque expertus sum, una cum selectis ex <lb/>Galileo et Baliano, recensebo &rdquo; (Bononiae 1651, pag. </s>

<s>84). </s></p><p type="main">

<s>Da Galileo e dal Baliani dice di aver principalmente appreso, e di aver <lb/>poi confermato co'suoi proprii esperimenti che le varie lunghezze di due <lb/>pendoli stanno reciprocamente come i quadrati dei numeri delle vibrazioni, <lb/>d'onde conseguono <emph type="italics"/>duo insignia problemata,<emph.end type="italics"/> il primo dei quali &egrave; che, dato <lb/>il numero delle vibrazioni e la lunghezza di un pendolo, si pu&ograve; di l&igrave; otte&shy;<lb/>nerne la lunghezza dell'altro. </s>

<s>Ricava di qui il Riccioli la regola per la mi&shy;<lb/>sura del pendolo a secondi, ma non avrebbe potuto per s&egrave; medesima quella <lb/>stessa regola condurre all'intento, senza premetter la soluzione di un altro <lb/>problema, qual era quello di ritrovare il tempo del primo mobile, o del giorno <lb/>solare conveniente a tutto il moto o alle singole vibrazioni di un pendolo <lb/>dato. </s>

<s>Conveniva dunque ricorrere a una misura di confronto, la quale si po&shy;<lb/>teva ottener da quei modi, che pi&ugrave; erano in uso appresso agli antichi, come <lb/>dalle pulsazioni delle arterie, dalle Clessidre, e dagli Orologi solari. </s>

<s>Volle il <lb/>Riccioli esaminar ciascuno di questi tre modi, che gli si porgevano per la <lb/>pratica facili e pronti, ma che poi ebbe a rifiutar, non essendo nessun di <lb/>loro trovato esatto. </s></p><pb xlink:href="020/01/2176.jpg" pagenum="419"/><p type="main">

<s>Quanto ai polsi, aveva letto nella proposizione LVIII dell'<emph type="italics"/>Opus novu<gap/><emph.end type="italics"/><lb/>del Cardano che &ldquo; in hora sunt pulsus arteriarum quatuor millia ictuum <lb/>in homine prope temperamentum: (Operum, T. </s>

<s>V cit, pag. </s>

<s>489); alla qua <lb/>sentenza del celebre medico, e del fisico valoroso, parve sottoscrivere anche <lb/>il Keplero, quando, nell'Epitome astronomica, per comparar le frazioni del <lb/>l'ora equinoziale ai polsi dell'uomo, concludeva, dopo ripetute osservazion <lb/>fatte intorno al loro numero in varii individui: &ldquo; Breviter, in una hora qua&shy;<lb/>tuor millia, plus minus &rdquo; (Lentiis 1618, pag. </s>

<s>279). Ma il Riccioli, riducendo <lb/>alle vibrazioni di un pendolo, fatte in un minuto, le pulsazioni osservate in <lb/>un gran numero di persone, appartenenti al suo proprio sodalizio; trov&ograve; che <lb/>differivano dalle 50 alle 85. Pens&ograve; in tale incertezza di fare esperienza delle <lb/>Clessidre, ma, comparate anch'esse con le vibrazioni di un pendolo, fatte in <lb/>un quarto d'ora, trov&ograve; che ne rispondevano di quelle stesse vibrazioni ora <lb/>pi&ugrave; ora meno, ond'&egrave; che, sperando di conseguire una maggiore esattezza, <lb/>si dette, insieme col p. </s>

<s>Francesco Maria Grimaldi, a costruire, con la mag&shy;<lb/>gior possibile diligenza, un orologio solare. </s>

<s>&ldquo; Sed quia umbrae ad lineas <lb/>horarias appulsus non potest discerni adeo axacte, ut non formidemus de <lb/>aliquorum secundorum errore, ideo, dimisso hoc modo, ad alios me con&shy;<lb/>tuli &rdquo; (Almag. </s>

<s>Novi, T. </s>

<s>I cit., pag. </s>

<s>86). </s></p><p type="main">

<s>I modi, a cui s'ebbe finalmente a rivolgere il Riccioli furon quelli che <lb/>erano stati proposti da Galileo, e i tre o quattro amici pazienti, ch'egli ri&shy;<lb/>chiedeva all'operazione, e che rimasero in vita sua non pi&ugrave; che una lusin&shy;<lb/>ghiera speranza, gli trov&ograve; il Riccioli stesso fra'suoi pi&ugrave; giovani confratelli. </s>

<s><lb/>Ne scelse fra questi nove, ch'egli addestr&ograve; con gesuitica disciplina, e dal <lb/>mezzogiorno del d&igrave; 2 Aprile 1642 al mezzogiorno del di appresso, gli tenne <lb/>vigili in assidua opera diligente a contare il numero delle vibrazioni fatte <lb/>nelle 24 ore da un pendolo, lungo 3972 centesime di oncia di piede romano <lb/>antico. </s>

<s>Si davano la muta di mezz'ora in mezz'ora, e per evitar la lunga <lb/>pronunzia dei numeri pi&ugrave; grossi gettavano, a ogni sessanta vibrazioni con&shy;<lb/>tate, una fava o altro calcolo in una cestella. </s>

<s>Si trov&ograve; dunque, alla fine del&shy;<lb/>l'operazione, riducendo il giorno solare al sidereo, che un calcolo, ossia ses&shy;<lb/>santa vibrazioni, erano state fatte dal pendolo in 3576 minuti terzi. </s></p><p type="main">

<s>Cos&igrave; fatto, non bisognava altro a risolvere il problema della lunghezza <lb/>del pendolo a secondi, che applicare alla regola teorica i numeri trovati. </s>

<s>E <lb/>perch&egrave;, chiamata L la lunghezza del pendolo arbitrario, ed N il numero delle <lb/>vibrazioni da lui fatte in un certo tempo; chiamata L'la cercata lunghezza <lb/>del pendolo a secondi, ed N&prime; il numero delle vibrazioni, che in quel mede&shy;<lb/>simo tempo si vorrebbe che fosser fatte da lui; la detta regola &egrave; espressa <lb/>da L&prime;=LN2/N.2, facendosi dunque L=3867, N=60, N&prime;=3576/60, s'ebbe <lb/>L&prime;=3867X36002/35762. </s>

<s>&ldquo; Ergo, si quadratum numeri 3600, quod est 12,960,000, <lb/>ducatur per altitudinem centesimarum 3867, fiet summa 50,416,320,000, quae <lb/>divisa per quadratum tertiorum 3576, qnod est 12,787,776, relinquit cente-<pb xlink:href="020/01/2177.jpg" pagenum="420"/>simas unciarum 3927; hoc est pedes 3, uncias 3, et 27/100 &rdquo; (ibid., pag. </s>

<s>87). <lb/>E tale &egrave;, secondo il Riccioli, la precisa lunghezza del pendolo misurator dei <lb/>secondi. </s></p><p type="main">

<s>Se il piede romano antico fosse precisamente tale, quale ce lo danno <lb/>le comuni Tavole di riduzione, corrispondente cio&egrave; a 0m, 295, un dodicesimo <lb/>di lui, ossia un'oncia, equivarrebbe a 0m, 025, presso a poco, e un cente&shy;<lb/>simo d'oncia a 0m, 00025; cosicch&egrave; 3927 centesime, quante ha trovato il <lb/>Riccioli dovere andar lungo il pendolo oscillante a ogni secondo, tornereb&shy;<lb/>bero prossimamente 0m, 98175. Non siam certi per&ograve; se quali le Tavole ce <lb/>le danno fossero le riduzioni esatte del piede romano antico, secondo il Ric&shy;<lb/>cioli, il quale ne tratt&ograve; particolarmente nel XII libro della Geografia nuova <lb/>riformata, designandolo col nome proprio di <emph type="italics"/>Piede vespasianeo.<emph.end type="italics"/> Ma nel mar&shy;<lb/>gine inferiore della pag. </s>

<s>58 del I tomo dell'Almagesto esib&igrave;, della met&agrave; di <lb/>lui, la precisa lunghezza lineare, scrivendo: &ldquo; Est autem vera longitudo se&shy;<lb/>mipedis romani antiqui quantam vides in sequenti schemate R. &rdquo; La lun&shy;<lb/>ghezza R, quivi rappresentata, &egrave; divisa in sei parti equivalenti alle sei once, <lb/>sopra le quali riportata, con la maggior diligenza possibile, una riga, ci parve <lb/>che corrispondessero ciascuna a 0m, 026 prossimamente. </s>

<s>D'onde parrebbe che <lb/>le 3927 centesime si dovessero ridurre a 1m, 02102, ch'&egrave; misura alcun poco <lb/>maggiore di quell'altra ricavata dalle Tavole di riduzione. </s></p><p type="main">

<s>Consistendo lo strumento, usato all'operazione, in un globo di ferro <lb/>sospeso a una catena di ferro, e resultandone perci&ograve; un pendolo composto, <lb/>non si possono le sopra calcolate misure, in qualunque modo ridotte, rife&shy;<lb/>rire a quelle convenienti al pendolo semplice, le quali si sa che, per la lati&shy;<lb/>tudine di Bologna, sono 0m, 993. Ma comunque sia aveva ragione il Riccioli <lb/>di compiacersi, non solo d'essere stato egli il primo, ma di aver dato, della <lb/>lunghezza del pendolo a secondi, la misura pi&ugrave; giusta di qualunque altro <lb/>s'esercitasse a calcolarla in quel tempo o poco dipoi. </s>

<s>&ldquo; Gavisus sum autem <lb/>cum, post aliquot annos, audivi perpendiculi oscillationes ab aliis Astrono&shy;<lb/>mis adhibitas, nimirum a Michaele Florentio Langreno, ut ex literis ad me <lb/>ab ipso datis didici, a Gottefrido Vendelino, a p. </s>

<s>Athanasio Kirchero, a Mer&shy;<lb/>senno et aliis, sed non constat omnes aeque accuratos fuisse in mensuris <lb/>perpendiculi determinandis. </s>

<s>Nam, ut una vibratio uni secundo temporis ae&shy;<lb/>quivaleat, Mersennus requirit funiculum pedum 3, sed parisiensium. </s>

<s>Kir&shy;<lb/>cherus autem filum 3 pedum cum dimidio, non adiecto pondere, cui fere <lb/>subscribit Vendelinus &rdquo; (ibid., pag. </s>

<s>88). Le cause dell'incertezza e dell'er&shy;<lb/>rore, dipendenti principalmente dal non saper determinare il centro del&shy;<lb/>l'oscillazione, e dal reputar le vibrazioni maggiori isocrone alle minori, erano <lb/>a tutti questi sperimentatori comuni, non eccettuato lo stesso Riccioli, il <lb/>quale si dilung&ograve; nonostante dal vero assai meno degli altri, per la incom&shy;<lb/>parabile diligenza da lui usata nelle osservazioni. </s></p><pb xlink:href="020/01/2178.jpg" pagenum="421"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Al Riccioli dunque si debbono, intorno agli usi del pendolo, attribuire <lb/>quei meriti, che un opinione universalmente invalsa attribuisce a Galileo, <lb/>l'opera del quale in proposito ci ha mostrato la storia essere stata incredi&shy;<lb/>bilmente debole e scarsa. </s>

<s>Del difetto, che ritrovavasi negli insegnamenti del <lb/>Maestro, n'ebbero a risentire anche i primi Discepoli, i quali &egrave; notabilis&shy;<lb/>sima cosa che, esercitandosi cos&igrave; valorosamente in svolgere e in confermare <lb/>i varii teoremi dei movimenti locali, non promovessero nemmen d'un passo, <lb/>rispetto al pendolo, i principii galileiani. </s>

<s>Svolgendo infatti i manoscritti e i <lb/>pubblici trattati del Castelli, del Renieri, del Cavalieri, del Nardi e di simili <lb/>altri, non ci siamo abbattuti mai a trovare in essi una proposizione mecca&shy;<lb/>nica intorno a quello argomento, e il Torricelli stesso, nel suo celebre trat&shy;<lb/>tato, non fa del moto dei gravi penduli da fili nemmeno un semplice motto. </s>

<s><lb/>Solamente ci &egrave; occorso, in consultare i manoscritti di lui, di notare una pro&shy;<lb/>posizione, delle feconde conseguenze della quale per&ograve; non par che si cu&shy;<lb/>rasse l'Autore, contento a considerarne alcuna della minore importanza. </s>

<s>&Egrave; <lb/>la detta proposizione cos&igrave; messa in formula, e cos&igrave; dimostrata: </s></p><p type="main">

<s>&ldquo; Quod libet pondus a qualibet potentia moveri; vel nullum pondus <lb/>pendens tam magnum esse, ut ab omni minima potentia non moveatur. </s>

<s>&rdquo; <lb/><figure id="id.020.01.2178.1.jpg" xlink:href="020/01/2178/1.jpg"/></s></p><p type="caption">

<s>Figura 214</s></p><p type="main">

<s>&ldquo; Sit pondus A (fig. </s>

<s>214) suspensum filo BA, <lb/>intelligaturque pondus esse ut ipsa BA. </s>

<s>Detur <lb/>iam potentia BC, et ducatur perpeudiculum CD: <lb/>dico pondus A a data potentia moveri usque in <lb/>D. </s>

<s>Ducatur tangens FDE, horizontalis FH ubicu&shy;<lb/>mque, et perpendicularis EH ubicumque. </s>

<s>Eritq&shy;<lb/>ue, ut BD ad BC, ita FE ad EH. </s>

<s>Ergo pondus <lb/>sustinetur a potentia in D, puncto plani; quare et&shy;<lb/>iam in D, puncto quadrantis, et propterea in <lb/>quolibet puncto arcus AD movetur &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. XXXVII, fol. </s>

<s>97). </s></p><p type="main">

<s>Sembrava che dovesse di qu&igrave; concluderne <lb/>il Torricelli quel corollario importante, che avea condotto Giovan Marco a <lb/>instituire le prime teorie dei pendoli, che cio&egrave;, essendo BD a BC come FE <lb/>ad EH, il peso pendulo nel perpendicolo A sta allo stesso pendolo, rimos&shy;<lb/>so nella posizione D, come il seno totale sta al seno dell'angolo dell'incli&shy;<lb/>nazione. </s>

<s>Ma, come dicemmo, non ha di una tal conclusione l'Autore nem&shy;<lb/>meno il minimo pensiero. </s></p><p type="main">

<s>Notabile &egrave; che Niccol&ograve; Aggiunti, in una Nota pubblicata dal Nelli nel <lb/>suo <emph type="italics"/>Saggio di storia letteraria,<emph.end type="italics"/> si fosse qualche anno prima proposto di di&shy;<lb/>mostrar questo medesimo del Torricelli, e nel medesimo modo, per servir&shy;<lb/>sene come lemma a concludere il suo assunto, che &ldquo; se un pendolo grave sar&agrave; <pb xlink:href="020/01/2179.jpg" pagenum="422"/>rimosso dal suo perpendicolo durer&agrave; a moversi alternamente in perpetuo &rdquo; <lb/>(Lucca 1759, pag. </s>

<s>89). L'intenzion dell'Autore era quella di confermar con <lb/>matematiche ragioni ci&ograve; che aveva semplicemente asserito come probabile <lb/>Galileo, nella giornata II Dei massimi sistemi (Alb. </s>

<s>I, 250), ma si poteva <lb/>pure utilmente promovere il teorema a dimostrare altre propriet&agrave; mecca&shy;<lb/>niche del pendolo, ci&ograve; che qui trascura di fare anche l'Aggiunti. </s></p><p type="main">

<s>I primi esercizi, intorno a questo cos&igrave; negletto argomento, fatti nella <lb/><figure id="id.020.01.2179.1.jpg" xlink:href="020/01/2179/1.jpg"/></s></p><p type="caption">

<s>Figura 215<lb/>Scuola galileiana, incominciano dal Viviani, il quale ci <lb/>lasciava fra i suoi manoscritti questo notabilissimo do&shy;<lb/>cumento: &ldquo; La violenza che patisce il filo AB (fig. </s>

<s>215), <lb/>essendo stirato dal grave A, credo che sia tale, quale <lb/>&egrave; il momento del medesimo grave, movendosi per il <lb/>piano BA, cio&egrave; che la forza fatta dal grave al filo nel <lb/>luogo AB, alla forza fatta al filo nel luogo BC, che &egrave; <lb/>la forza totale, sia come il momento del medesimo grave <lb/>sopra un piano inclinato quanto BA, al momento totale <lb/>per la perpendicolare BC. </s>

<s>Credo ancora che la somma <lb/>dei due momenti del grave A, l'uno per la dirittura <lb/>del filo BA, l'altro per la tangente AE, sia uguale al <lb/>momento totale. </s>

<s>Inventa un modo per esperimentarlo &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. CXIII, fol, 30 a tergo). </s></p><p type="main">

<s>Tanto senti il Viviani al bisogno la Matematica inesperta, che volle aver <lb/>refugio nell'esperienza. </s>

<s>E che cosa gli doveva l'esperienza dimostrare? </s>

<s>que&shy;<lb/>sto n&egrave; pi&ugrave;, n&egrave; meno: che cio&egrave; la somma dei momenti parziali &egrave; uguale al <lb/>momento totale. </s>

<s>Ora, si risovverranno i Lettori delle famose obiezioni del <lb/>Vanni, dietro le quali si tirer&agrave; la memoria quell'altre analoghe parole, la&shy;<lb/>sciateci scritte dallo stesso Viviani, a proposito del momento dei gravi so&shy;<lb/>pra i piani inclinati: <emph type="italics"/>credo che il momento totale sia uguale in potenza <lb/>al momento gravitativo, e al momento discensivo insieme presi.<emph.end type="italics"/> La falla&shy;<lb/>cia, che s'asconde in quella parola <emph type="italics"/>potenza,<emph.end type="italics"/> &egrave; nota oramai a chi ha letto <lb/>la nostra Storia, e dietro quella fallacia, felicemente dal caso emendata, riu&shy;<lb/>sc&igrave; all'Autore delle <emph type="italics"/>Cinque proposizioni<emph.end type="italics"/> a dimostrar secondo qual propor&shy;<lb/>zione, nelle discese oblique, si compartano i momenti dei gravi. </s></p><p type="main">

<s>Nel medesimo modo, e non gi&agrave; per via della esperienza, si sarebbe <lb/>forse potuto dar matematica dimostrazione di ci&ograve; che il Viviani credeva <lb/>esser vero nella proposta questione del pendolo, essendo la forza, che stira <lb/>il filo nella direzione AB, comparabile col momento gravitativo sul piano in&shy;<lb/>clinato, come l'altra forza, diretta secondo la tangente AE, &egrave; pur compara&shy;<lb/>bile col momento discensivo. </s>

<s>Questo, nelle dette <emph type="italics"/>Cinque proposizioni<emph.end type="italics"/> si dimo&shy;<lb/>stra proporzionale al seno, e quello al coseno dell'angolo dell'inclinazione, <lb/>ci&ograve; ch'&egrave; pur vero, secondo che il Viviani credeva, nel pendolo, come si <lb/>dimostrerebbe, facendo uso del principio della composizion delle forze, im&shy;<lb/>perocch&egrave;, se la perpendicolare AF, qual diagonale del parallelogrammo, rap&shy;<lb/>presenta il momento totale, i lati AE, AD, che corrispondono ai momenti <pb xlink:href="020/01/2180.jpg" pagenum="423"/>parziali, stanno a quella stessa diagonale come il seno e il coseno dell'an&shy;<lb/>golo DAF, uguale all'angolo dell'inclinazione, stanno al seno totale. </s></p><p type="main">

<s>Si diceva che sarebbe il Viviani potuto riuscire a questa medesima con&shy;<lb/>clusione importante dietro ci&ograve; ch'era stato dimostrato da lui del momento <lb/>dei gravi sopra i piani inclinati, ma non siam certi che vi si provasse, e, <lb/>se dovessimo dare intorno a ci&ograve; il nostro giudizio, sarebbe che quella sua <lb/>scienza del pendolo si rimase, almeno per qualche tempo, un semplice <emph type="italics"/>credo.<emph.end type="italics"/><lb/>Or una tale incertezza nel Viviani, e negli altri pi&ugrave; immediati discepoli di <lb/>Galileo, si contrappone, in modo che fa stupire, con la sicurezza della scienza <lb/>di Leonardo da Vinci, nei manoscritti del quale si trova, come si rifer&igrave; a suo <lb/>luogo, dimostrato il teorema delle forze sollecitanti il pendolo, per ridurlo <lb/>alla sua prima stazione perpendicolare. </s>

<s>Ebbero, come quasi sempre, le spe&shy;<lb/>culazioni principio dall'esperienza, la quale, bench&egrave; sembri delicatissima, era <lb/>nonostante assai meglio dimostrativa di quell'altra impossibile, che si pro&shy;<lb/>poneva d'inventare il Viviani. </s></p><p type="main">

<s>La figura disegnata a tergo del foglio 76 del Manoscritto G, e che noi <lb/><figure id="id.020.01.2180.1.jpg" xlink:href="020/01/2180/1.jpg"/></s></p><p type="caption">

<s>Figura 216<lb/>imitiamo nella figura 216, s'illustra <lb/>da Leonardo con queste parole: &ldquo; Il <lb/>peso ventilante da destra a sinistra, <lb/>e da sinistra a destra, si fa tanto pi&ugrave; <lb/>grave al suo appendiculo, d'esso ap&shy;<lb/>pendiculo, quanto esso appendiculo &egrave; <lb/>meno obliquo. </s>

<s>&rdquo; E a tergo del seguente foglio 79 un'altra Nota, nello stesso <lb/>proposito, cos&igrave; dice: &ldquo; Il grave ventilante, per qualunque aspetto, avr&agrave; tanto <lb/>pi&ugrave; o men gravezza, intorno alla fronte che ha l'asta della Bilancia, quanto <lb/>la congiunzione, che ha l'appendiculo del peso col braccio della bilanc&igrave;a, <lb/>sar&agrave; pi&ugrave; vicino all'angolo retto. </s>

<s>&rdquo; Il modo dell'esperienza &egrave; assai chiaro, <lb/>essendo alle due estremit&agrave; A, C della Bilancia di braccia uguali, sostenuta <lb/>in B, penduli, da due fili di ugual lunghezza, i pesi uguali D, E. </s>

<s>Nella quiete, <lb/>o nella posizione verticale di questi pesi, permane l'equilibrio, ma, rimosso <lb/>per esempio il peso D in F, l'altro contrappeso E la vince, con tanto per&ograve; <lb/>minor prevalenza, quanto l'angolo FAD, fatto dall'appendicolo FA con la <lb/>fronte A della Bilancia, &egrave; pi&ugrave; vicino all'angolo retto. </s></p><p type="main">

<s>Dimostrava dunque la bella e delicata esperienza che il grave in F pesa <lb/>meno sulla Bilancia che in D, ma secondo qual precisa proporzione si di&shy;<lb/>minuisce il momento non era l'esperienza per s&egrave; stessa atta a rivelarlo con <lb/>regola certa; ond'&egrave;, che rivolgendosi a trattar la cosa con le leggi matema&shy;<lb/>tiche del moto, si condusse Leonardo a specular quel teorema, da noi posto <lb/>a pagine 51 di questo tomo. </s>

<s>Deriva da quel teorema per corollario la pro&shy;<lb/>porzione del moto di un grave cadente lungo un piano inclinato; propor&shy;<lb/>zione conclusa in modo somigliantissimo a quello tenuto da Galileo, il quale <lb/>per&ograve;, considerando il peso sostenuto dal braccio di una leva, piuttosto che <lb/>da un filo, si precluse, a dimostrar le propriet&agrave; meccaniche del pendolo, quel <lb/>trapasso, che felicemente fu fatto da Leonardo. </s></p><pb xlink:href="020/01/2181.jpg" pagenum="424"/><p type="main">

<s>Venendo cos&igrave; la scienza galileiana dei pendoli a mancar del suo mec&shy;<lb/>canico fondamento, rimase tutta raccomandata alle esperienze, sterili per s&egrave; <lb/>medesime d'ogni frutto migliore. </s>

<s>I frutti infatti che s'ebbero, e si not&ograve; an&shy;<lb/>che altrove, furono alcune curiose applicazioni alla Musica, e alla misura <lb/>delle altezze, ci&ograve; che veniva dannosamente a sedur col diletto, e a traviar <lb/>dall'utile, come si pu&ograve; confermare da questo esempio. </s>

<s>A un Matematico di <lb/>Roma, allettato da quel modo che s'insegna nel primo dialogo Delle due <lb/>nuove scienze, per dedur dalle semplici vibrazioni la lunghezza di una corda <lb/>pendente; venne un giorno il capriccio d'inventar qualche altra cosa di si&shy;<lb/>mile, per misurar le altezze, servendosi di un filo. </s>

<s>Non riuscitogli per&ograve; il <lb/>desiderio, si rivolse a Michelangiolo Ricci, il quale dava cos&igrave;, del modo come <lb/>avea sodisfatto l'amico, la seguente notizia in una lettera, scritta il d&igrave; 18 Giu&shy;<lb/>gno 1643 al Torricelli: </s></p><p type="main">

<s>&ldquo; Li giorni addietro un amico mio voleva misurare certe altezze, con <lb/>l'aiuto di un filo, e venne a consultare meco, per trovar qualche mezzo alla <lb/><figure id="id.020.01.2181.1.jpg" xlink:href="020/01/2181/1.jpg"/></s></p><p type="caption">

<s>Figura 217<lb/>consecuzione del suo intento. </s>

<s>Fattavi un poco di ri&shy;<lb/>flessione, dimostrai che il filo ABC (fig. </s>

<s>217), essendo <lb/>attaccato a due capi, e che per esso scorra qualche <lb/>peso, detto peso incurver&agrave; il filo in angolo, facendo <lb/>gli angoli ABE, CBD uguali sopra la retta EBD, tirata <lb/>nel punto B parallela all'orizzonte. </s>

<s>L'avvertenza di <lb/>questo fu bastante all'amico per conseguire il suo <lb/>pensiero, ed alla sagacit&agrave; di V. S. l'aver detto questo sar&agrave; pi&ugrave; che troppo, <lb/>per farle intendere dimostrativamente che la cosa vada cos&igrave; &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. XLII, fol. </s>

<s>136). </s></p><p type="main">

<s>Il teorema si sovverranno i Lettori essere stato dimostrato da Leonardo, <lb/>in quelle Note da noi trascritte a pagine 68 e 69 di questo tomo, ond'&egrave; che <lb/>molti stupiranno del fortuito incontro fra il semplice Artista di Vinci, e il <lb/>valoroso Matematico di Roma. </s>

<s>Bene &egrave; per&ograve; pi&ugrave; da stupire che il Discepolo <lb/>di Galileo facesse argomento unico e principale, nella dottrina dei pesi pen&shy;<lb/>denti da fili, quel che il Discepolo del Nemorario riguardava come cosa se&shy;<lb/>condaria, e data quasi per mescere all'utile qualche diletto. </s>

<s>Ma qual utile, <lb/>a promover la scienza, ricavasse il Ricci da quel suo teorema, lo lasciamo al <lb/>giudizio di chi rimedita i fatti di questa Storia. </s></p><p type="main">

<s>Sarebbe superfluo l'intrattener pi&ugrave; lungamente il discorso a dimostrar <lb/>che, nella prima met&agrave; del secolo XVII, veniva la vera scienza del moto dei <lb/>gravi per gli archi dei cerchi a mancar nella Scuola galileiana, n&egrave; par si <lb/>accorgessero i seguaci di lei del difetto, se non allora che sentiron vivo il <lb/>bisogno d'invocare i principii di quella stessa scienza a regolar gli strumenti <lb/>misuratori esatti dei minimi tempi. </s>

<s>Ritorniamo con la memoria a Firenze, <lb/>quando il principe Leopoldo dei Medici poneva il Viviani e il Borelli quasi <lb/>pietre angolari, prima di dar forma all'edifizio della gloriosa sperimentale <lb/>Accademia. </s>

<s>Riducendosi principalmente gl'istituti di lei a promovere la Fi&shy;<lb/>sica galileiana, si fecero primi soggetti all'esperienze le misure della velo-<pb xlink:href="020/01/2182.jpg" pagenum="425"/>cit&agrave; del suono e della luce. </s>

<s>Ma quali si avevano allora strumenti, che ser&shy;<lb/>vissero all'uso? </s>

<s>Erano &egrave; vero infin dal 1651 resi pubblicamente noti gli <lb/>strumenti, e i metodi del Riccioli, ma riuscivano difficilmente praticabili agli <lb/>osservatori o poco attenti o poco esperti, e in conclusione tornavano fallaci. </s></p><p type="main">

<s>Il fatto, di cui s'ebbe finalmente a persuadere lo stesso Viviani, che <lb/>cio&egrave; non tutte le vibrazioni d'un medesimo pendolo sono esattamente uguali, <lb/>ma che le minori si spediscono in tempo sensibilmente pi&ugrave; breve delle mag&shy;<lb/>giori; gli fece, verso il 1656, immaginare quell'Orologio a ruote, mosse dal&shy;<lb/>l'elaterio di una molla, e regolate dal pendolo, di cui, nel secondo capitolo <lb/>del nostro primo tomo, fu narrata la storia. </s>

<s>L'Huyghens meditava allora <lb/>intorno a una simile invenzione, ch'ebbe pubblicit&agrave; in quel medesimo <lb/>anno 1657, quando si metteva gi&agrave; in uso il Cronometro fiorentino. </s>

<s>La no&shy;<lb/>tizia, che &egrave; per riuscire delle pi&ugrave; importanti nella Storia della Meccanica, e <lb/>delle invenzioni italiane, vuol trattener qui, ne'suoi particolari, il nostro <lb/>discorso. </s></p><p type="main">

<s>L'esattezza dello strumento, che s'immaginava di costruire il Viviani, <lb/>dipendeva dalla misura esatta dei pendoli, che si dovevano adattare, e so&shy;<lb/>stituir l'uno all'altro, secondo che si voleva, per esempio un secondo per <lb/>ogni vibrazione, o qualche altra parte osservabile di lui. </s>

<s>Con qual regola <lb/>dunque si dovrebbero precisare queste misure? </s>

<s>Aveva il Riccioli insegnata <lb/>gi&agrave; quella regola, e l'aveva altresi messa in pratica, ma, poniamo che fosse <lb/>vera, non aveva altro suffragio che i fatti, dal Riccioli stesso trovati riscon&shy;<lb/>trar con l'esperienze di Galileo e del Baliani. </s>

<s>Se fu sentito mai quel difetto <lb/>della scienza galileiana, che fu pi&ugrave; volte da noi lamentato, si fu questa una <lb/>delle pi&ugrave; efficaci occasioni per dover riconoscerlo, e per risolversi ad emen&shy;<lb/>darlo. </s>

<s>Si trattava dall'altra parte di applicar quella regola a risolvere un <lb/>problema di una tal precisione, da non sperar mai di conseguirla, senza il <lb/>magistero supremo della Geometria. </s></p><p type="main">

<s>I primi esercizi, fatti dal Viviani a geometrizzare quel che nel I dia&shy;<lb/>logo delle Nuove scienze si dice essere stato per esperienza scoperto intorno <lb/>ai tempi delle oscillazioni, in relazione con la lunghezza dei pendoli; appa&shy;<lb/>riscono da una di quelle postille alla copia dell'edizione di Leyda, che &egrave; il <lb/>tomo IX della Parte V de'Manoscritti di Galileo. </s>

<s>Ivi, a pi&egrave; della pag. </s>

<s>97, <lb/>cos&igrave;, di mano propria del Viviani, si legge: &ldquo; Adunque, di due pendoli dise&shy;<lb/>guali, il tempo per l'arco dell'uno, al tempo per l'arco dell'altro, sta come <lb/>il tempo pel seno dell'uno, al tempo pel seno di un arco simile dell'altro, <lb/>i quali seni formano un sol piano inclinato, e per i quali i mobili natural&shy;<lb/>mente discendenti scorrono in tempi, che hanno suddupla proporzione di <lb/>essi seni. </s>

<s>Or, perch&egrave; questi son proporzionali ai loro raggi, che sono le lun&shy;<lb/>ghezze dei pendoli, dunque, ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s>Supposto ben dimostrato il principio, la conseguenza &egrave; matematicamente <lb/>vera, e si somiglia molto alla proposizione di Giovan Marco, resa molto pi&ugrave; <lb/>semplice, e pi&ugrave; bella. </s>

<s>Imperocch&egrave;, se il tempo per BD (fig. </s>

<s>218) sta al tempo <lb/>per BE come il tempo per BF sta al tempo per BG, i quali tempi stanno <pb xlink:href="020/01/2183.jpg" pagenum="426"/>come le radici degli spazi; essendo la radice di BF alla radice di BG, come <lb/><figure id="id.020.01.2183.1.jpg" xlink:href="020/01/2183/1.jpg"/></s></p><p type="caption">

<s>Figura 218<lb/>la radice di AB &egrave; alla radice di CB, ne vien per legit&shy;<lb/>tima conseguenza che, come tali radici, le quali son le <lb/>lunghezze dei pendoli; cos&igrave; stieno i tempi delle vibra&shy;<lb/>zioni per gli archi simili. </s></p><p type="main">

<s>Ma come i tempi per gli archi simili sieno pro&shy;<lb/>porzionali ai tempi per i seni corrispondenti, non si <lb/>accenna da qual principio lo concluda il Viviani. </s>

<s>Forse <lb/>proponevasi di darne altrove, o in altro tempo, la dimo&shy;<lb/>strazione, la quale doveva, come nel trattato di Giovan <lb/>Marco, dipendere dal teorema, che il momento totale <lb/>del pendolo nel perpendicolo sta al momento parziale <lb/>dello stesso pendolo, fuori del perpendicolo, come il seno <lb/>totale sta al seno dell'angolo dell'inclinazione. </s>

<s>Ma per&shy;<lb/>ch&egrave; intorno a questo teorema il Viviani stesso versava, come vedemmo, in <lb/>qualche incertezza rispetto al compartire giustamente il momento totale nel <lb/>discensivo per la tangente all'arco, e nel gravitativo, secondo la direzione <lb/>del filo; &egrave; assai probabile che la dimostrazione, accennata nella detta postilla, <lb/>si rimanesse ivi incompiuta, e che pensasse l'Autore di sostituirle quell'altra <lb/>meno matematica e pi&ugrave; lunga, nella quale c'incontreremo fra poco. </s></p><p type="main">

<s>Ma intanto la Geometria, nel definir quelle relazioni tra le semplici li&shy;<lb/>nee e i quadrati, rivelava alla mente del Viviani l'equazione della parabola, <lb/>per la quale si significherebbero, in nuovo modo elegante, le meccaniche <lb/>propriet&agrave; dei pendoli, facendo alle ordinate rappresentare i tempi delle vi&shy;<lb/>brazioni, e alle ascisse le lunghezze dei fili. </s>

<s>Del qual pensiero, appena sov&shy;<lb/><figure id="id.020.01.2183.2.jpg" xlink:href="020/01/2183/2.jpg"/></s></p><p type="caption">

<s>Figura 219<lb/>venutogli, lasci&ograve; scritta il Viviani stesso la <lb/>seguente memoria: &ldquo; Se le linee OA, OC, <lb/>OE (fig. </s>

<s>219) rappresentano i tempi delle <lb/>vibrazioni di diverse lunghezze, le linee AB, <lb/>GD, HF, ecc., del trilineo parabolico ABI, <lb/>di cui vertice sia I, rappresentano le lun&shy;<lb/>ghezze dei fili: cio&egrave;, se la vibrazione di un <lb/>tempo AO vuole lunghezza di filo quanto <lb/>AB, la vibrazione del tempo CO vorr&agrave; lunghezza del filo quanto GD, ed il <lb/>tempo EO lunghezza di filo quanto HF, e questo perch&egrave; le lunghezze dei fili <lb/>sono tra loro come i quadrati dei tempi delle vibrazioni, siccome le linee AB, <lb/>GD, HF sono tra loro, <emph type="italics"/>ob parabolam,<emph.end type="italics"/> come i quadrati delle AO, CO, EO, ecc. </s>

<s><lb/>Di qui si potr&agrave; cavare la fabbrica di uno strumento, che dia le lunghezze <lb/>de'fili dei cercati tempi &rdquo; (MSS. Cim., T. X, fol. </s>

<s>49). </s></p><p type="main">

<s>L'idea di questo strumento, cos&igrave; sovvenuta, fece nella mente del Vi&shy;<lb/>viani definir la forma del Cronometro, per servire all'esperienze della ve&shy;<lb/>locit&agrave; del suono e della luce, il qual Cronometro, come sappiamo, indicava <lb/>sopra la medesima mostra variamente i tempi, secondo le lunghezze varie <lb/>dei fili applicati. </s>

<s>Quello strumento dunque, da trovar giuste e speditamente <pb xlink:href="020/01/2184.jpg" pagenum="427"/>cos&igrave; fatte lunghezze, era parte essenziale dell'invenzione, e fu perci&ograve; l'In&shy;<lb/>ventore sollecito di mandar l'idea conceputa ad effetto. </s>

<s>Abbiamo il docu&shy;<lb/>mento di ci&ograve; nella seguente scrittura, nella quale la descrizion del Trilineo <lb/>parabolico si fa dipendere dai suoi proprii principii matematici, sostituiti alle <lb/>semplici e fuggitive osservazioni di Galileo. </s></p><p type="main">

<s>&ldquo; Il Galileo, nel primo dialogo delle due nuove scienze meccaniche, a <lb/>faccia 96 dell'edizione di Leida del 1638, dice, in persona del Salviati, cos&igrave;: <lb/><emph type="italics"/>Quanto poi alla proporzione de'tempi delle uniche vibrazioni di mobili, <lb/>pendenti da fila di differente lunghezza, le replicate esperienze, colle quali <lb/>ciascuno pu&ograve; sodisfarsi, mi han dimostrato che sono essi tempi in propor&shy;<lb/>zione suddupla delle lunghezze delle fila, ovver le lunghezze sono in dupla <lb/>proporzione dei tempi, cio&egrave; sono come i quadrati di essi tempi.<emph.end type="italics"/> Tal pro&shy;<lb/>priet&agrave; non la fortifica l'Autore con alcuna dimostrazione, bastandogli forse <lb/>l'esperienza, ch'ei ne doveva aver fatta con diverse proporzioni cognite di <lb/>fili, e come di fatti riesce, e ciascuno pu&ograve; con somma facilit&agrave; assicurarsene. </s>

<s><lb/>Nondimeno, per tentar di convalidarla con qualche ragione, almeno proba&shy;<lb/>bile, se non chiarissima, io la discorro in tal guisa: &rdquo; </s></p><p type="main">

<s>&ldquo; TEOREMA I. &mdash; Considerinsi AB, AC (fig. </s>

<s>220) essere due differenti <lb/><figure id="id.020.01.2184.1.jpg" xlink:href="020/01/2184/1.jpg"/></s></p><p type="caption">

<s>Figura 220<lb/>fila, in un medesimo perpendicolo, con gravi <lb/>eguali appesi alle loro estremit&agrave; B, C, ed al&shy;<lb/>lontanati dal medesimo perpendicolo per ar&shy;<lb/>chi simili BD, CE, non maggiori degli archi <lb/>BF, CG de'quadranti dei loro cerchi. </s>

<s>La&shy;<lb/>scinsi da D e da E in loro libert&agrave;: dico <lb/>prima che il tempo della vibrazione del pen&shy;<lb/>dolo AD, per l'arco DB, al tempo della vi&shy;<lb/>brazione del pendolo AE, per l'arco simile <lb/>EC, ha suddupla proporzione della lunghezza <lb/>del proprio filo AD, alla lunghezza del pro&shy;<lb/>prio filo AE. &rdquo; </s></p><p type="main">

<s>&ldquo; Imperocch&egrave;, essendo FB, GC archi simili, e similmente posti, e pro&shy;<lb/>porzionali ai loro semidiametri AB, AC, posti nella medesima dirittura; par <lb/>ragionevole che il tempo della caduta di un mobile da A in B, al tempo <lb/>della scorsa del medesimo per l'arco del proprio quadrante, abbia da avere <lb/>in tutto simile proporzione a quella della caduta del mobile, pel raggio mi&shy;<lb/>nore da A in C, al tempo della scorsa per l'arco GC del proprio quadrante, <lb/>non vi essendo ragione per cui tali proporzioni debbano differire. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E similmente par ragionevole che, essendo tanto gli archi FB, GC, <lb/>che gli archi DB, EC, simili e similmente posti, il tempo della scorsa del <lb/>mobile per l'arco FB del quadrante maggiore, al tempo della scorsa per <lb/>l'arco proprio DB, abbia da esser la stessa che quella del tempo della scorsa <lb/>per l'arco GC del quadrante minore, al tempo della scorsa pel proprio arco <lb/>EC, proporzionale al GC, come il DB all'FB; onde verrebbe per l'ugualit&agrave; <lb/>che il tempo per AB, al tempo per DB, fosse come Il tempo per AC, al <pb xlink:href="020/01/2185.jpg" pagenum="428"/>tempo per l'arco EC: e, permutando, che il tempo per AB, al tempo per <lb/>AC, stesse come il tempo per l'arco DB, al tempo per l'arco EC. </s>

<s>Ma il <lb/>tempo per AB al tempo per AC ha suddupla proporzione di AB ad AC; <lb/>adunque anche il tempo per DB, al tempo per EC, avrebbe suddupla pro&shy;<lb/>porzione dell'AB all'AC, che son le lunghezze de'fili dei pendoli. </s>

<s>Ma cia&shy;<lb/>scuna vibrazione di ciascun di essi pendoli, larghe o strette che sieno, nel <lb/>proprio cerchio passa in tempi uguali, come la esperienza il dimostra, adun&shy;<lb/>que par manifesto quanto senz'altra prova asser&igrave; il Galileo, cio&egrave; che i tempi <lb/>hanno suddupla proporzione delle lunghezze delle fila, ovvero che le lun&shy;<lb/>ghezze hanno dupla proporzione dei tempi, cio&egrave; sono come i quadrati dei <lb/>tempi. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>63). </s></p><p type="main">

<s>Soggiunge immediatamente il Viviani che questa bella propriet&agrave;, cos&igrave; <lb/>dimostrata, gli somministr&ograve; la fabbrica di quello strumento, di cui gli era <lb/>gi&agrave; venuta l'idea, e che qui prosegue a descrivere con quelle stesse parole, <lb/>da noi trascritte a pag. </s>

<s>328, 29 del nostro primo Tomo. </s>

<s>A complemento <lb/>della qual descrizione aggiungeremo qui quel che suggerisce il Viviani per&shy;<lb/>ch&egrave;, chiunque non si trovasse altro a mano che una semplice riga e una <lb/>catenella, potesse, pi&ugrave; facilmente e con maggior brevit&agrave;, conseguire il me&shy;<lb/>desimo intento. </s></p><p type="main">

<s>&ldquo; Ma con pi&ugrave; brevit&agrave; conseguiremo, egli dice, l'istesso, senza macchina, <lb/>mediante una riga CD (fig. </s>

<s>221) la di cui met&agrave; CE sia divisa in 60 parti <lb/><figure id="id.020.01.2185.1.jpg" xlink:href="020/01/2185/1.jpg"/></s></p><p type="caption">

<s>Figura 221<lb/>eguali, da E sino in C, e mediante <lb/>ancora d'un sol filo di catenuzza <lb/>formata di piccolissimi anelli. </s>

<s>Per&shy;<lb/>ch&egrave;, tenuta essa riga CD orizzontal&shy;<lb/>mente, e fermato in C uno dei capi <lb/>del detto filo di catena, e questo <lb/>lasciato far la sacca sua naturale <lb/>CMHD, che forma sempre parabola, <lb/>fatto passar rasente il punto D, ed <lb/>allontanato talmente che di tal sacca <lb/>la massima altezza EF, la qual passa <lb/>pel punto di mezzo E, dov'&egrave; il <lb/>numero 60, sia appunto uguale al <lb/>filo AB (del pendolo che batte i secondi) quivi presentato, e poi questo <lb/>portato or in G, al numero 30, or in L, al numero 20; le intersecazioni <lb/>H, M di esso filo colla catenuzza daranno, fuor della sacca, le lunghezze HI, <lb/>MN, che dovranno avere i pendoli cercati &rdquo; (ivi, fol. </s>

<s>64). </s></p><p type="main">

<s>Lo strumento era cos&igrave; ben preparato agli usi di prefinir le misure dei <lb/>pendoli, dietro i principii matematici dimostrati ne&igrave; I Teorema, in cui &egrave; no&shy;<lb/>tabile che sentisse il Viviani di aver dato ragione <emph type="italics"/>probabile,<emph.end type="italics"/> ma non chia&shy;<lb/>rissima. </s>

<s>Questa confessata insufficienza conferma la nostra congettura, che <lb/>cio&egrave; quella prima dimostrazione, accennata a pi&egrave; della pagina 97 dell'edi&shy;<lb/>zione di Leyda, rimanesse incompiuta, per non aversi certezza dei momenti, <pb xlink:href="020/01/2186.jpg" pagenum="429"/>in cui si comparte l'assoluta gravit&agrave; del pendolo, rimosso dalla stazion sua <lb/>perpendicolare. </s>

<s>Versando in tale incertezza, anche il Borelli non seppe pro&shy;<lb/>porre altra dimostrazione, da quella che fu poi scritta in ordine la XCII nel <lb/>trattato <emph type="italics"/>De vi percussionis<emph.end type="italics"/> (Bononiae 1667, pag. </s>

<s>212, 13) e nella quale, dal <lb/>suppor, come il Viviani fa, ch'essendo le lunghezze de'raggi proporzionali <lb/>alle ampiezze degli archi, fossero altres&igrave; proporzionali i tempi, si concludeva <lb/>che questi per essi archi erano proporzionali alle radici delle altezze dei pen&shy;<lb/>doli. </s>

<s>A confermar poi la somiglianza del processo dimostrativo, in ambedue <lb/>gli Autori, sovvien la considerazione che ambedue suppongono essere nello <lb/>stesso pendolo <emph type="italics"/>itus et reditus aequitemporaneos<emph.end type="italics"/> (ivi, pag. </s>

<s>212), e ci&ograve; con&shy;<lb/>ferma che gli Accademici fiorentini non si persuasero delle disuguaglianze <lb/>delle libere vibrazioni, se non da poi che l'ebbero comparate con quelle, <lb/>fatte sempre per uguale ampiezza d'arco, nell'Orologio. </s></p><p type="main">

<s>Di questo Orologio dunque era stata, nel Teorema I, speculata dal Vi&shy;<lb/>viani la teoria, e non rimaneva altro, per metterlo in uso, che a trovar la <lb/>precisa lunghezza del filo AB (nella precedente figura) corrispondente a un <lb/>secondo. </s>

<s>Come gli stessi Accademici fiorentini risolvessero l'importante pro&shy;<lb/>blema lo vedremo tra poco, per non perder di mira quello stesso Viviani, <lb/>a cui preme di seguitare a dar dimostrazione delle conclusioni supposte da <lb/>Galileo, e specialmente di quella, che le lunghezze dei pendoli stanno reci&shy;<lb/>procamente come i quadrati de'numeri delle vibrazioni fatte nei medesimi <lb/>tempi. </s>

<s>Furono a quest'effetto preparati altri due teoremi, ai quali si pre&shy;<lb/>mette dall'Autore un discorso, nelle sue prime parti da noi trascritto a <lb/>pag. </s>

<s>303, 304 del nostro I Tomo, ma che ora vogliam dar per compiuto, <lb/>affinch&egrave; possa chi legge paragonare i fiori del rettorico elogio con i frutti <lb/>della semplice Storia. </s></p><p type="main">

<s>&ldquo; Nella medesima et&agrave; sua giovanile, prosegue dunque il Viviani a dire <lb/>di Galileo, quando studiava Filosofia, che fu intorno al 1580, si chiar&igrave;, col&shy;<lb/>l'aiuto di questo suo pendolo, della falsit&agrave; di que'due pronunziati di Ari&shy;<lb/>stotile, con l'un de'quali egli afferma vedersi che due mobili di gravit&agrave; di&shy;<lb/>versa discendono per lo stesso mezzo con velocit&agrave; proporzionali alle medesime <lb/>gravit&agrave; loro; con l'altro, che lo stesso mobile si muove per diversi mezzi <lb/>con velocit&agrave; continuamente proporzionali alle loro densit&agrave; e gravezze, facen&shy;<lb/>done, per chiarirsi della verit&agrave; del primo, varie esperienze nell'aria, con di&shy;<lb/>versi gravi lasc&igrave;ati cader nello stesso tempo dall'altezza del campanile di Pisa, <lb/>e, per riscontro del secondo, varie altre prove nell'aria e nell'acqua, inda&shy;<lb/>gata prima industriosamente la proporzione delle densit&agrave; e gravit&agrave; in specie <lb/>di tali fluidi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Da queste, e da mille altre fallacie degli scrittori antichi, scoperte dal <lb/>libero ed inventivo ingegno del nostro Accademico, veramente linceo; ebbe <lb/>la prima origine, e il natale in Toscana questa libert&agrave; di filosofare, ch'egli <lb/>us&ograve; sempre, e che si propal&ograve; poi per Italia, e per tutte le Universit&agrave; del&shy;<lb/>l'Europa, dove in oggi tanto fiorisce, e con la quale si son fatti finora s&igrave; <lb/>gran progressi in ogni parte della Fisica, dell'Astronomia, dell'Anatomia, e <pb xlink:href="020/01/2187.jpg" pagenum="430"/>di ogni altra pi&ugrave; nobile facolt&agrave;. </s>

<s>Ond'&egrave; che meritamente l'ingegnoso Gas&shy;<lb/>sendo lo riconosce e commenda per padre della vera Filosofia, a confusione <lb/>di quegli ingrati Italiani, e di alcuni altri oltre a'monti, i quali, bench&egrave; di <lb/>professione religiosa, non sapendo occultar la propria passione, gli si dimo&shy;<lb/>strarono nemici capitalissimi con gli scritti e co'fatti, stimati da loro a lui <lb/>sommamente pregiudicevoli, quantunque poi sien risultati in gloria al me&shy;<lb/>mesimo, ed a loro di biasimo, e vituperio appresso i veri sapienti, e senza <lb/>passione.... Ma lasciando tale digressione, vengo alla dimostrazione delle <lb/>conclusioni supposte dal Galileo, e prima pongo il seguente Lemma: &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Se due grandezze omogenee ed eguali, sono divise in differente nu&shy;<lb/>mero di parti eguali, il numero delle parti della prima, al numero delle <lb/>parti della seconda, sta reciprocamente come una sola parte della seconda <lb/>ad una sola parte della prima. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Siano AB, CD (fig. </s>

<s>222) le due date grandezze omogenee, eguali, <lb/><figure id="id.020.01.2187.1.jpg" xlink:href="020/01/2187/1.jpg"/></s></p><p type="caption">

<s>Figura 222<lb/>e la prima AB sia divisa in qualun&shy;<lb/>que numero di parti eguali AE, EF, <lb/>FG, GH, HI, IL, LB, e la seconda CD <lb/>in altro qualunque numero di parti <lb/>uguali CM, MN, ND. </s>

<s>Dico che il nu&shy;<lb/>mero delle parti della prima AB, al <lb/>numero delle parti della seconda CD, <lb/>sta come una sola parte CM della <lb/>seconda ad una sola parte AE della <lb/>prima. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Essendo il numero delle parti in AB differente dal numero delle parti <lb/>in CD, pongasi che il numero maggiore sia in AB, ed al numero minore, <lb/>che &egrave; in BD, prendasi eguale il numero AG, talmente che tante parti eguali <lb/>siano in AG, che in CD. </s>

<s>Avr&agrave; dunque il numero delle parti in AB, al nu&shy;<lb/>mero delle parti in CD, la medesima proporzione che il numero delle parti <lb/>in AB al numero delle parti in AG, cio&egrave; che la grandezza AB alla AG, cio&egrave; <lb/>che la grandezza CD, posta uguale alla AB, alla grandezza AG, cio&egrave;, che la <lb/>summultiplice grandezza CM alla ugualmente summultiplice grandezza AE, <lb/>che &egrave; quello che si doveva dimostrare &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>62). </s></p><p type="main">

<s>Il Lemma stesso, facendo uso dell'analisi, si dimostrerebbe efficacemente <lb/>in due parole, perch&egrave;, chiamando A, A'le due grandezze omogenee, uguali; <lb/>N il numero delle parti, in cui si vuol divisa l'una, N&prime; il numero delle parti, <lb/>in cui s'intende esser divisa l'altra, e P una sola parte di quella, P'una <lb/>sola parte di questa; le due equazioni A/N&prime;=P, A&prime;/N&prime;=P&prime; danno N:N&prime;= <lb/>P&prime;:P. </s>

<s>In simile spedito modo si dimostrerebbe che i numeri delle vibra&shy;<lb/>zioni stanno rcciprocamente come i tempi, e da questo e dal Teorema I si <lb/>concluderebbe, con pari facilit&agrave;, che le lunghezze dei pendoli stanno reci&shy;<lb/>procamente come i quadrati de'numeri delle vibrazioni. </s>

<s>Compia infatti un <lb/>numero N di vibrazioni un pendolo, mentre un altro, nel medesimo tempo <foreign lang="greek">q</foreign>, <pb xlink:href="020/01/2188.jpg" pagenum="431"/>ne compie N&prime;. </s>

<s>Il tempo T di una vibrazione del primo sar&agrave; T=<foreign lang="greek">q</foreign>/N e il <lb/>tempo T&prime; d'una vibrazione del secondo sar&agrave; T&prime;=<foreign lang="greek">q</foreign>/N&prime;, d'onde T:T&prime;= <lb/>N&prime;:N, e anche T2:T&prime;2=N&prime;2:N2. </s>

<s>Chiamate ora L, L&prime; le lunghezze dei <lb/>pendoli corrispondenti, essendo stato dianzi dimostrato, nel trascritto Teo&shy;<lb/>rema I, che L:L&prime;=T2:T&prime;2, immediatamente se ne conclude L:L&prime;= <lb/>N&prime;2:N2. </s>

<s>Ma il Viviani, proseguendo i metodi antichi, ha bisogno di quel pi&ugrave; <lb/>lungo discorso, che ora leggeremo, per dimostrare i due seguenti teoremi, <lb/>che sono il II e il III del suo trattatello <emph type="italics"/>Dei pendoli di lunghezze disuguali.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; TEOREMA II. &mdash; <emph type="italics"/>I numeri delle vibrazioni di due pendoli disuguali, <lb/>fatte dentro a un medesimo tempo, sono fra loro in proporzione reciproca <lb/>dei tempi delle uniche vibrazioni de'medesimi pendoli, ed anche in reci&shy;<lb/>proca proporzione della somma dei tempi di eguali numeri di vibrazioni <lb/>di essi pendoli.<emph.end type="italics"/> &mdash; Imperocch&egrave;, passandosi le singolari vibrazioni di ciascun <lb/>pendolo, considerate in s&egrave;, in tempi uguali, il numero delle vibrazioni del <lb/>primo pendolo, al numero delle vibrazioni del secondo, star&agrave; come il nu&shy;<lb/>mero de'tempi uguali del numero delle vibrazioni del primo al numero dei <lb/>tempi uguali del numero delle vibrazioni del secondo. </s>

<s>Ma, per il supposto, <lb/>il tempo del numero delle vibrazioni del primo &egrave; uguale al tempo del nu&shy;<lb/>mero delle vibrazioni del secondo, poich&egrave; quelle del primo si son poste pas&shy;<lb/>sate nel medesimo tempo che quelle del secondo; adunque, per l'antece&shy;<lb/>dente Lemma, il numero de'tempi uguali delle vibrazioni del primo, al <lb/>numero de'tempi uguali delle vibrazioni del secondo, cio&egrave;, pel dimostrato <lb/>qui a principio, il numero delle vibrazioni del primo, al numero delle vi&shy;<lb/>brazioni del secondo, sta come il tempo dell'unica vibrazione del secondo <lb/>al tempo dell'unica vibrazione del primo: e, presi di questi tempi gli egual&shy;<lb/>mente molteplici, come la somma de'tempi uguali di un numero di vibra&shy;<lb/>zioni del primo pendolo alla somma de'tempi uguali d'egual numero di vi&shy;<lb/>brazioni del secondo, il che si doveva dimostrare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; TEOREMA III. &mdash; <emph type="italics"/>Le lunghezze delle corde de'pendoli hanno fra loro <lb/>la proporzione reciproca, che hanno i quadrati de'numeri delle vibrazioni, <lb/>che si fanno nel medesimo tempo da essi pendoli. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Essendosi provato nel passato teorema che il numero delle vibrazioni <lb/>del primo dei pendoli, al numero delle vibrazioni del secondo, fatte in un <lb/>medesimo tempo, sta reciprocamente come il tempo dell'unica vibrazione <lb/>del secondo al tempo dell'unica vibrazione del primo, &egrave; manifesto che, an&shy;<lb/>che il quadrato del medesimo numero delle vibrazioni del primo, al qua&shy;<lb/>drato del medesimo numero delle vibrazioni del secondo, fatte in un me&shy;<lb/>desimo tempo, sta reciprocamente come il quadrato del tempo dell'unica <lb/>vibrazione del secondo al quadrato del tempo dell'unica vibrazione del primo. </s>

<s><lb/>Ma, per il Teorema I, il quadrato del tempo dell'unica vibrazione del se&shy;<lb/>condo, al quadrato del tempo dell'unica vibrazione del primo, sta come la <lb/>lunghezza del secondo alla lunghezza del primo; adunque anche il quadrato <pb xlink:href="020/01/2189.jpg" pagenum="432"/>del suddetto numero delle vibrazioni del primo, al quadrato del suddetto nu&shy;<lb/>mero delle vibrazioni del secondo, fatte in quel medesimo tempo, sta come <lb/>la lunghezza del filo del secondo alla lunghezza del filo del primo: onde, <lb/>permutando queste proporzioni e convertendo i termini, la lunghezza del filo <lb/>del primo, alla lunghezza del filo del secondo, sta come il quadrato del nu&shy;<lb/>mero delle vibrazioni del secondo al quadrato del numero delle vibrazioni <lb/>del primo, il che dovevasi dimostrare &rdquo; (ivi). </s></p><p type="main">

<s>Volle il Viviani stesso fare l'applicazioni numeriche di questo dimostrato <lb/>Teorema, calcolando le varie lunghezze dei fili, supposto esser cento la lun&shy;<lb/>ghezza di quello, che in un dato tempo fa cento vibrazioni. </s>

<s>Perch&egrave; ne fa&shy;<lb/>cesse 90, in quel medesimo tempo, trov&ograve; che il filo doveva esser lungo <lb/>123 37/81; perch&egrave; ne facesse 80, lungo 156 1/4; perch&egrave; ne facesse 70, lungo <lb/>204 4/49, e perch&egrave; ne facesse 60, lungo 277 7/9. Per aver poi 110 vibrazioni <lb/>trov&ograve; dover essere la lunghezza del pendolo 82 78/121, e per averne 120 do&shy;<lb/>veva essere la lunghezza del filo 69 4/9 di quelle medesime parti. </s>

<s>Si vedono <lb/>questi numeri scritti in colonne lungo una linea, che rappresenta il filo di <lb/>un pendolo disegnato nel foglio 51 del X tomo dei manoscritti del Cimento. </s>

<s><lb/>A sinistra &egrave; la colonna dei <emph type="italics"/>Numeri di vibrazioni fatte nel medesimo tempo,<emph.end type="italics"/><lb/>e a destra, nei punti corrispondenti, l'altra colonna dei <emph type="italics"/>Numeri delle lun&shy;<lb/>ghezze dei fili.<emph.end type="italics"/></s></p><p type="main">

<s>Questo trattatello <emph type="italics"/>Dei pendoli,<emph.end type="italics"/> il quale &egrave; il primo, che occorra a com&shy;<lb/>memorar nella Storia della Meccanica in Italia, aveva nella mente del Vi&shy;<lb/>viani una duplice intenzione: quella cio&egrave; di supplire ai difetti gravi della <lb/>Scienza galileiana, e l'altra di stabilir bene le teorie, da costruirvi sopra il <lb/>Cronometro, che doveva nella Corte medicea servire alle esperienze della <lb/>velocit&agrave; del suono e della luce. </s>

<s>Essendosi dunque tutto cos&igrave; bene prestabi&shy;<lb/>lito, come siam fin qui venuti narrando, non mancava a far altro, per met&shy;<lb/>tere il detto Cronometro in uso, che a trovar la lunghezza del pendolo a <lb/>secondi, perch&egrave; si potesse ricavar di l&igrave;, o col calcolo o per via dello stru&shy;<lb/>mento, le lunghezze delle fila convenienti a dar la richiesta misura delle <lb/>pi&ugrave; sottili minuzie dei tempi. </s>

<s>Era stato l'importante problema risoluto, come <lb/>si disse, dal Riccioli, e per risoluto ritenevasi pure nella Scuola galileiana, <lb/>come si par dall'esempio del Castelli. </s>

<s>Ma perch&egrave; dubitavasi, in cos&igrave; fatte <lb/>misure, di quella precisione, che si voleva per le nuove accademiche espe&shy;<lb/>rienze, ne di&egrave; il principe Leopoldo, sul cominciar dell'anno 1657, commis&shy;<lb/>sione al Borelli, gi&agrave; professore nello Studio pisano. </s>

<s>Pens&ograve; il peritissimo Astro&shy;<lb/>nomo di dedurre il numero delle vibrazioni, fatte in ventiquattr'ore da un <lb/>pendolo di qualunque lunghezza, in pi&ugrave; squisito e pi&ugrave; facile modo di quello <lb/>suggerito da Galileo, ed eseguito dai pazientissimi sodali del gesuita Ric&shy;<lb/>cioli; dal contar quelle sole vibrazioni fatte in tempo, che il sole scorre su&igrave; <lb/>circolo equinoziale per tutta la lunghezza del suo diametro apparente, la qual <lb/>lunghezza essendo, per le diligentissime osservazioni degli Astronomi, nota, <lb/>dava sicuro il calcolo delle vibrazioni, che da quello stesso pendolo si sa&shy;<lb/>rebbero dovute fare in tutto il tempo delle ventiquattr'ore sideree. </s>

<s>Dietro <pb xlink:href="020/01/2190.jpg" pagenum="433"/>ci&ograve;, e dietro la dimostrata legge che le lunghezze dei pendoli stanno reci&shy;<lb/>procamente come i quadrati dei numeri delle vibrazioni, era dal Borelli, con <lb/>metodi nuovi, risoluto il problema dell'Orologio a secondi. </s></p><p type="main">

<s>Non apparendo, che per noi si sappia, da nessuna parte della Storia, si <lb/>comprende di quanta curiosit&agrave;, e di quanta importanza debba riuscir la no&shy;<lb/>tizia del resultato dei calcoli del Borelli, applicati a dar nel Cronometro fio&shy;<lb/>rentino le pi&ugrave; precise misure dei pi&ugrave; minuziosi intervalli dei tempi. </s>

<s>Ci por&shy;<lb/>gono i primi cenni di questa cos&igrave; desiderata notizia le seguenti parole, scritte <lb/>da Pisa, il di 14 Aprile 1657, dallo stesso Borelli al principe Leopoldo, in <lb/>una lettera pubblicata fra le altre, che raccolse Angelo Fabbroni: &ldquo; Intanto <lb/>invio a V. A. S. le misure squisite delle lunghezze dei pendoli corrispon&shy;<lb/>denti a minutissimi tempi orarii, le quali lunghezze le ho aggiustate, con <lb/>quanta maggior diligenza ho potuto, il giorno di questo Equinozio passato, <lb/>numerando diligentemente pi&ugrave; e pi&ugrave; volte le vibrazioni di tali pendoli nel <lb/>transito del disco solare mandato da uno squisito perfetto Telescopio, il qual <lb/>modo &egrave; il pi&ugrave; squisito e certo, che si possa in tal proposito usare &rdquo; (Let&shy;<lb/>tere inedite, T. II, Firenze 1775, pag. </s>

<s>60). </s></p><p type="main">

<s>Sembra che il Borelli abbia voluto soprabbondare nel rispondere al que&shy;<lb/>sito, ch'era strettamente quello di cercar la misura della lunghezza del pen&shy;<lb/>dolo a secondi, perch&egrave; se ne sarebbe di l&igrave; facilmente, per via del Trilineo <lb/>parabolico inventato dal Viviani, ricavata la misura di tutti gli altri pendoli <lb/>minori. </s>

<s>Il Borelli invece mandava precise tutt'esse misure, le quali poi <lb/>eran quelle, che si dovevano direttamente applicare al Cronometro, rispar&shy;<lb/>miando la fatica di calcolarle, o lasciandone solamente la cura di confron&shy;<lb/>tarle nello strumento. </s>

<s>Dall'altra parte era assai facile dedur di l&igrave; la lun&shy;<lb/>ghezza del pendolo a secondi, presa per fondamento ad aggiustar quelle dette <lb/>misure. </s></p><p type="main">

<s>Il medesimo modo, che porgevasi al Principe e al Viviani s&igrave; certo, ser&shy;<lb/>virebbe anche a noi, desiderosi di scoprire un tal fondamento, da cui dedur <lb/>la misura del pendolo a secondi, ritrovata per le nuove osservazioni astro&shy;<lb/>nomiche del Borelli; se apparisse dalla lettera edita dal Fabbroni la quan&shy;<lb/>tit&agrave; delle varie lunghezze ivi accennate. </s>

<s>Ma non aggiungendosi dall'editore <lb/>l'importante notizia, dubitammo che il Borelli stesso avesse mandate quelle <lb/>misure, prese sulla lunghezza di qualche filo o di qualche strisciola di carta, <lb/>la quale, acclusa nella lettera, fosse andata smarrita. </s>

<s>Ci occorse, in mezzo <lb/>a cos&igrave; fatti dubbii, il pensiero che doveva il Principe aver consegnate le ri&shy;<lb/>cevute misure al Viviani, il quale aveva a metterle in uso, e ci sembr&ograve; per <lb/>questo probabile che, ad evitare il pericolo di un tal facile smarrimento, ne <lb/>avesse preso e lasciato scritto pi&ugrave; stabile ricordo. </s>

<s>La congettura venne pre&shy;<lb/>sto e felicemente a verificarsi, cercando, secondo questa nostra intenzione, <lb/>per i Manoscritti del Cimento, nel X tomo dei quali ci occorse a leggere, <lb/>nel noto carattere del Viviani, cos&igrave;, sulla prima spaziosa faccia del foglio 191: </s></p><p type="main">

<s>&ldquo; Lunghezze mandate dal signor Borelli al serenissimo principe Leo&shy;<lb/>poldo: &rdquo; </s></p><pb xlink:href="020/01/2191.jpg" pagenum="434"/><p type="main">

<s>&ldquo; AB, lunghezza del pendolo, la cui vibrazione &egrave; dieci minuti secondi di <lb/>un'ora, sicch&egrave; sei vibrazioni di AB fanno un secondo, e 360 fanno un primo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; AC, 15&tprime;; sicch&egrave; 4 AC fanno un secondo, e 240 vibrazioni di AC <lb/>fanno un primo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; AD, 20&tprime;; sicch&egrave; 3 AD fanno un secondo, e 180 un primo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; AE, 25&tprime;; sicch&egrave; 2 2/5 AE fanno un secondo, e 140 un primo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; AF, 30&tprime;; sicch&egrave; 2 AF fanno un secondo, e 120 un primo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Notisi che in questi il signor Borelli intende per vibrazione una sola <lb/>andata, od un solo ritorno del pendolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>Ma rimase anche di qui la nostra principale speranza delusa, non ap&shy;<lb/>parendo, da nessuna parte del Manoscritto, delle indicate lunghezze vesti&shy;<lb/>gio. </s>

<s>Ci venne allora voglia di consultare l'originale, da cui doveva aver tra&shy;<lb/>scritta quella lettera il Fabbroni, e lo trovammo facilmente, nella citata <lb/>raccolta dei Manoscritti del Cimento, ai fogli 65 e 66 del Tomo XVI. </s>

<s>A tergo <lb/>del precedente foglio 64, bianco nella sua prima faccia, si not&ograve; tracciata una <lb/>linea orizzontale, divisa in parti disugualmente nei punti contrassegnati dalle <lb/>lettere A, B, C ... la qual linea ci apparve prima interrotta nella <gap/>ucitura, <lb/>ma poi trovammo che passava di sotto alla piegatura de'detti fogli 65 e 66, <lb/>per andare a continuarsi nella medesima direzione sulla prima faccia del fo&shy;<lb/>glio 67, procedendo nelle divisioni segnate con le lettere D, E, e, com'era <lb/>cominciata con la lettera A, cos&igrave; terminava con la lettera F. </s></p><p type="main">

<s>La corrispondenza di queste lettere, con quelle indicateci dal Viviani, <lb/>sarebbe per s&egrave; medesima bastata a farci accorti dover esser ivi quella linea <lb/>tracciata per rappresentar le lunghezze dei pendoli, quando non fossero ve&shy;<lb/>nute a toglierci d'ogni dubbio le sottoscritte dichiarazioni: &ldquo; AB, lunghezza <lb/>di pendolo, la cui vibrazione &egrave; dieci minuti terzi di ora. </s>

<s>&mdash; AC, pendolo, la <lb/>vibrazione del quale &egrave; quindici minuti terzi. </s>

<s>&mdash; AD, di venti minuti terzi; <lb/>AE, di venticinque minuti terzi; AF, pendolo, una sola vibrazione del quale <lb/>&egrave; trenta minuti terzi. </s>

<s>&rdquo; </s></p><p type="main">

<s>Sulle lunghezze della linea AF, disegnata nel foglio del Borelli, prese <lb/>dunque il Viviani, per fare esperienza del suo Cronometro, le misure dei <lb/>pendoli, ma non trov&ograve; praticabile altro che quella dei mezzi secondi, per&shy;<lb/>ch&egrave;, come poi fece scrivere nel libro dei <emph type="italics"/>Saggi,<emph.end type="italics"/> &ldquo; tutti gli altri pi&ugrave; corti <lb/>riescono cos&igrave; veloci, che gli occhi non gli p&ograve;sson seguire &rdquo; (Firenze 1841, <lb/>pag. </s>

<s>22). Qui per verit&agrave; non s'intende come mai i pendoli, pi&ugrave; corti di <lb/>quello dei mezzi secondi, si dicano andar tanto veloci, da non poter esser <lb/>seguiti dagli occhi, tanto pi&ugrave; che non era necessario osservarne direttamente <lb/>i moti, venendo questi comunicati all'indice, moventesi regolarmente pi&ugrave; <lb/>lento sulla mostra dell'Orologio. </s>

<s>Comunque sia, rigettate per inutili le mi&shy;<lb/>sure dei dieci, dei quindici, dei venti e de'venticinque terzi, trovava il Vi&shy;<lb/>viani le altre divisioni, comprese fra un secondo intero e la met&agrave; di lui, <lb/>per mezzo del suo Trilineo parabolico, la massima ordinata del quale, d'onde <lb/>prendevano regola tutte le altre, s'aveva, con assai facile calcolo, definita <lb/>da una qualunque delle misure descritte dallo stesso Borelli. </s></p><pb xlink:href="020/01/2192.jpg" pagenum="435"/><p type="main">

<s>Il modo insomma tenuto dal Viviani &egrave; quello stesso, che si porge pa&shy;<lb/>rato a noi, se vogliamo sapere quant'egli mettesse lunga, tra la riga e il <lb/>vertice della catenuzza, la linea corrispondente alla lunghezza del pendolo a <lb/>secondi. </s>

<s>Possiamo anche noi infatti tornare sul foglio del Borelli, che ci &egrave; <lb/>rimasto, e da una delle misure calcolate da lui riuscire, con pari facilit&agrave;, <lb/>alla medesima conclusione. </s></p><p type="main">

<s>Noi ci siamo provati, e misurando, con la maggior diligenza che ci sia <lb/>stata possibile, la lunghezza della linea AF conveniente a un mezzo secondo, <lb/>ci &egrave; sembrato corrispondesse a 0m, 289; cosicch&egrave; la lunghezza di tutto il pen&shy;<lb/>dolo di un secondo, quale fu ritrovata dal Borelli, e quale fu dal Viviani ap&shy;<lb/>plicata al Cronometro usato alle pi&ugrave; delicate esperienze degli Accademici <lb/>del Cimento, sarebbe di 1m, 156, come resulta dal moltiplicar 0m, 289, che <lb/>&egrave; la data altezza del pendolo dei mezzi secondi, per il quadrato del tempo <lb/>doppio. </s>

<s>Difficile &egrave; vero, per la grossezza delle linee e de'punti segnati dalla <lb/>penna del Borelli, e per la difficolt&agrave; di mettere in piano il foglio, ritrarre <lb/>le misure esatte. </s>

<s>Ma perch&egrave; in somma non potrebbe l'errore importar altro <lb/>che qualche millimetro, vien questa lunghezza del pendolo a secondi a riu&shy;<lb/>scire in ogni modo eccessiva, e pi&ugrave; aberrante dal vero di quella stessa da&shy;<lb/>taci dal Riccioli. </s>

<s>Non &egrave; possibile, massimamente per esserci <gap/>imaste ignote <lb/>le particolarit&agrave; dei modi tenuti nelle osservazioni, computare le complicate <lb/>cause di questi errori, ma le principali, e che furono ad ambedue i Mate&shy;<lb/>matici nostri comuni, si riducono al ritener che fecero per isocrone cos&igrave; le <lb/>massime come le minime vibrazioni, e al non aver saputo ridurre al suo <lb/>vero centro oscillatorio il pendolo composto. </s></p><p type="main">

<s>Comunque sia, non doveva, cos&igrave; come vollero gli Accademici fiorentini, <lb/>rilasciarsi questa loro opera, data intorno alla costruzione dell'Orologio, alle <lb/>curiose indagini della Storia, n&egrave; par che facesse bene il Viviani a sacrificar <lb/>l'invenzione alla gloria del suo Maestro. </s>

<s>Il Cronometro, ch'egli istituiva sulle <lb/>dimostrate teorie, e ch'egli costruiva secondo le regole dell'arte, piuttosto <lb/>che <emph type="italics"/>sull'andare di quello di Galileo,<emph.end type="italics"/> era sull'andar di quell'altro, che im&shy;<lb/>maginava l'Huyghens qualche mese dopo, e che s'esegu&igrave; in Olanda nel me&shy;<lb/>desimo tempo. </s></p><pb xlink:href="020/01/2193.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle resistenze dei solidi<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle proposizioni dimostrate da Galileo nel secondo dialogo delle due Nuove Scienze. </s>

<s>&mdash; II. </s>

<s>Dei <lb/>trattati di Francesco Blondel, di Vincenzio Viviani e di Alessandro Marchetti. </s>

<s>&mdash; III. </s>

<s>Delle con&shy;<lb/>troversie insorte fra Alessandro Marchetti e Guido Grandi. </s>

<s>&mdash; IV. Dell'applicazione della teo&shy;<lb/>ria dei momenti. </s>

<s>&mdash; V. </s>

<s>Delle osservazioni dei fatti, e delle esperienze concorse a promovere <lb/>la nuova scienza di Galileo. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>L'altra Scienza nuova, che si compiaceva di avere istituita Galileo, dopo <lb/>quella dei Moti locali, concerne le dimostrazioni delle virt&ugrave; dei solidi, nel <lb/>resistere allo spezzarsi, o gravati dal proprio peso o da pesi stranieri. </s>

<s>Ben&shy;<lb/>ch&egrave; sia per&ograve;, da questa parte, la novit&agrave; pi&ugrave; apparente, non &egrave; che mancas&shy;<lb/>sero nemmen qui le tradizioni rimaste salve, a comun benefizio degli stu&shy;<lb/>diosi, in quei meccanici <emph type="italics"/>Quesiti,<emph.end type="italics"/> ne'quali raccoglieva Aristotile la preziosa <lb/>eredit&agrave; di una scienza pi&ugrave; antica. </s>

<s>Nel XVI si domanda perch&egrave; tanto sien pi&ugrave; <lb/>deboli i legni, quanto sono pi&ugrave; lunghi, cosicch&egrave; un fuscello, lungo per esem&shy;<lb/>pio un cubito, sostenuto a un estremo, si mantiene diritto, e al contrario <lb/>una verga, lunga cento cubiti, dall'altro suo estremo liberamente pendente, <lb/>piegasi in basso. </s>

<s>&ldquo; An quia, risponde il Filosofo, et vectis et onus et hypo&shy;<lb/>mochlion, in levando, ipsa fit ligni proceritas? </s>

<s>Prior namque illius pars ceu <lb/>hypomochlion fit; quod vero in extremo est, pondus. </s>

<s>Quamobrem quanto <lb/>extensius fuerit id quod ab hypomochlio est, tanto inflecti necesse est ma&shy;<lb/>gis &rdquo; (Operum cit., T. XI, fol. </s>

<s>33). </s></p><p type="main">

<s>Vuol dire insomma Aristotile: Se i due legni AB, CD (fig. </s>

<s>223) son so&shy;<lb/><figure id="id.020.01.2193.1.jpg" xlink:href="020/01/2193/1.jpg"/></s></p><p type="caption">

<s>Figura 223<lb/>stenuti in A, C, rimanendo in B, D liberi, e <lb/>se si riguardino i loro pesi concentrati nei <lb/>due punti di mezzo E, F, il primo opera con <lb/>la leva AE, e l'altro con la leva CF, tanto <lb/>pi&ugrave; lunga, e perci&ograve; s'inflette costretto d'ub&shy;<lb/>bedire a una forza maggiore. </s></p><pb xlink:href="020/01/2194.jpg" pagenum="437"/><p type="main">

<s>Il solido resistente ha, nel proposto Quesito, da una parte sola l'ap&shy;<lb/>poggio, onde, a dar compiuta risoluzione di questa Scienza, par che voglia <lb/>Aristotile stesso considerare il caso della resistenza, quando il legno ha l'ap&shy;<lb/>poggio in ambedue gli estremi, come avviene allora che, per tribbiarlo, un <lb/>lo tiene di qua e di l&agrave; con le mani, e lo sforza nel mezzo, puntandovi il <lb/>piede o il ginocchio &ldquo; Cur eiusdem magnitudinis lignum facilius genu fran&shy;<lb/>gitur, si quispiam aeque deductis manibus, extrema comprehendens, frege&shy;<lb/>rit, quam si iuxta genu? </s>

<s>&rdquo; (ibid.). Pone qui Aristotile il principio verissimo <lb/>che la minima resistenza del solido CD, sostenuto da ambedue gli estremi, <lb/>come nella precedente figura, sia nel mezzo, e che fuori da questo mezzo <lb/>si faccia quella prima resistenza sempre minore, perch&egrave; minore &egrave; la leva <lb/>della forza. </s>

<s>&ldquo; Genu centrum est: quanto autem remotius a centro fuerit, <lb/>facilius movetur quodcumque: moveri autem quod frangitur necesse est &rdquo; <lb/>(ibid.). Tale &egrave; la ragione perch&egrave;, a sforzarlo in F nel mezzo, pi&ugrave; facilmente <lb/>il legno si spezzi, che a sforzarlo in II. </s></p><p type="main">

<s>Chi ripensi ora a quei tempi, nei quali i divulgati insegnamenti aristo&shy;<lb/>telici venivano dai teoremi di Archimede in gran parte emendati, e valida&shy;<lb/>mente promossi, non creder&agrave; possibile che i discepoli di Luca Pacioli la&shy;<lb/>sciassero questa nuova scienza delle resistenze del tutto incolta. </s>

<s>A conferma <lb/>di che basterebbero i teoremi di Leonardo da Vinci, e le disperse specula&shy;<lb/>zioni dei contemporanei e degli immediati successori di lui: teoremi e spe&shy;<lb/>culazioni che, giusto per essere state disperse o nei pubblici libri non bene <lb/>schiarite, resero, come si diceva, le novit&agrave; di Galileo pi&ugrave; apparenti. </s></p><p type="main">

<s>Queste novit&agrave;, che nel 1638 fecero la loro pubblica e solenne comparsa, <lb/>erano gi&agrave; infino dal 1609 uscite dalla mente dell'Autore, il quale ne lasci&ograve; <lb/>cos&igrave; autentico documento in una scrittura, d'altre simili e contemporanee <lb/>verit&agrave; scoperte, rivelatrice importante: &ldquo; E pure ultimamente ho finito di <lb/>ritrovare tutte le conclusioni, con le sue dimostrazioni, attenenti alle forze <lb/>e resistenze dei legni di diverse lunghezze, grossezze e figure; e quanto sien <lb/>pi&ugrave; deboli nel mezzo che negli estremi, e quanto maggior peso sosterranno <lb/>se quello sar&agrave; distribuito per tutto il legno, anzi che in un sol luogo, e qual <lb/>figura doveria avere acci&ograve; fosse per tutto egualmente gagliardo: la quale <lb/>Scienza &egrave; molto necessaria nel fabbricare macchine ed ogni sorta di edifi&shy;<lb/>zio, n&egrave; vi &egrave; alcuno che ne abbia trattato &rdquo; (Alb. </s>

<s>VI, 69). </s></p><p type="main">

<s>Hanno tutte le conclusioni qui accennate la loro dimostrazione nel <lb/>II dialogo delle due Scienze nuove, in forma di trattato, che a rivelar gli <lb/>influssi delle tradizioni pi&ugrave; antiche si divide in due parti, corrispondenti ai <lb/>due detti Quesiti aristotelici, nell'un de'quali si considera il solido appog&shy;<lb/>giato a un solo, e nell'altro ai suoi due estremi. </s>

<s>A dare scienza di queste <lb/>passioni della materia bisognava definir prima la natura della forza, che re&shy;<lb/>siste alla separazione delle particelle materiali; forza che per Galileo si ri&shy;<lb/>duce a due capi: &ldquo; l'uno dei quali &egrave; quella decantata repugnanza, che ha <lb/>la Natura all'ammettere il vacuo: per l'altro bisogna, non bastando questo <lb/>del vacuo, introdur qualche glutine, visco o colla, che tenacemente colleghi <pb xlink:href="020/01/2195.jpg" pagenum="438"/>le particole, delle quali esso corpo &egrave; composto &rdquo; (Alb. </s>

<s>XIII, 15). La forza <lb/>cos&igrave; definita &egrave; quella, che oggid&igrave; si chiama di <emph type="italics"/>coesione,<emph.end type="italics"/> la quale Galileo ap&shy;<lb/>plic&ograve; al legno, come al vetro e al marmo, e a simili altri corpi duri, cosic&shy;<lb/>ch&egrave;, distratte appena le particelle, la rottura in tutti, allo stesso modo, ne <lb/>segue a un tratto e immediata. </s></p><p type="main">

<s>Per misurar poi i varii gradi della potenza, necessaria a fare una tal <lb/>distrazione, Galileo stesso ricorse alla Statica, secondo i principii della quale <lb/>si possono avere gli equivalenti di qualunque forza dal prodotto del peso <lb/>per l'altezza verticale a cui vien sollevato. </s>

<s>Supponiamo che il solido AB <lb/>(fig. </s>

<s>224) sia col suo lato CB aderente ad altra materia, dalla quale si vo&shy;<lb/><figure id="id.020.01.2195.1.jpg" xlink:href="020/01/2195/1.jpg"/></s></p><p type="caption">

<s>Figura 224<lb/>glia staccarlo. </s>

<s>Si pu&ograve; operare in due modi: o <lb/>col tirare perpendicolarmente alla linea del con&shy;<lb/>tatto, o col sollevare essa linea da una parte, <lb/>facendo appoggio dall'altra, cosicch&egrave; ci sarebbe <lb/>nel primo caso bisogno di una potenza assoluta, <lb/>ossia uguale alla resistenza, e nel secondo ba&shy;<lb/>sterebbe quella sola potenza, che &egrave; respettiva <lb/>agli effetti della leva. </s>

<s>La proporzione, che passa <lb/>fra l'una e l'altra potenza di rompere un medesimo solido, la conclude Galileo <lb/>dal detto fondamento statico in modo, che in sostanza riducesi al seguente: </s></p><p type="main">

<s>Se la linea CB, aderente prima alla EH, si supponga essere stata stac&shy;<lb/>cata in tutti i suoi punti per distanze tutte eguali a BH, la forza che ha <lb/>prodotto l'effetto &egrave; manifestamente quella, che &egrave; necessaria a sollevare al&shy;<lb/>l'altezza BH tutti i punti materiali contenuti nella linea CB. </s>

<s>E perch&egrave; que&shy;<lb/>sti punti son tanti, quanto &egrave; lunga la linea stessa CB, sar&agrave; dunque, per il <lb/>detto principio statico misurata la proposta forza dal prodotto CB2XBH. </s></p><p type="main">

<s>Nel caso per&ograve; che si fosse procurata la medesima rottura, applicando <lb/>la forza in B, e facendo rivolgere la linea CB intorno a C come a centro, <lb/>il favor della leva diminuisce notabilmente quella prima forza assoluta, e <lb/>con qual proporzione, comparata con la respettiva, pu&ograve; facilmente conclu&shy;<lb/>dersi, considerando il punto B sollevato in BI, a un'altezza uguale alla BH. </s>

<s><lb/>Gli altri punti di mezzo fra B e C saranno sollevati per altezze via via sem&shy;<lb/>pre minori, corrispondenti alle ordinate nel triangolo CBI, per cui sar&agrave; data <lb/>la misura della nuova forza dal prodotto di queste stesse ordinate per il nu&shy;<lb/>mero dei punti mater&igrave;ali contenuti in BC, ossia da CB2XBI/2=CB2XBH/2. <lb/>La cosa pu&ograve; ridursi alla maggiore esattezza matematica considerando BH, <lb/>BI come distanze infinitesime, e sufficienti a produrre la rottura del solido, <lb/>cosicch&egrave; quella prima forza contemplata sta a questa seconda, come BH sta a <lb/>BH/2. E perch&egrave; la forza necessaria a separare le particelle materiali &egrave; uguale <lb/>e contraria alla forza, con cui le particelle stesse resistono all'essere sepa&shy;<lb/>rate, dunque la resistenza <emph type="italics"/>assoluta<emph.end type="italics"/> &egrave; doppia della <emph type="italics"/>respettiva.<emph.end type="italics"/> &ldquo; E questa, <lb/>dice Galileo, sia la nostra prima proposizione &rdquo; (Alb. </s>

<s>XIII, 117). </s></p><pb xlink:href="020/01/2196.jpg" pagenum="439"/><p type="main">

<s>Posto cos&igrave; alla nuova Scienza il suo fondamento &ldquo; conviene ora, sog&shy;<lb/>giunge lo stesso Galileo, che cominciamo a investigare secondo qual pro&shy;<lb/>porzione vada crescendo il momento della propria gravit&agrave;, in relazione alla <lb/><figure id="id.020.01.2196.1.jpg" xlink:href="020/01/2196/1.jpg"/></s></p><p type="caption">

<s>Figura 225<lb/>propria resistenza all'essere spezzato, in un pri&shy;<lb/>sma o cilindro grave, mentre stando parallelo al&shy;<lb/>l'orizzonte si va allungando, il qual momento <lb/>trovo andar crescendo in duplicata proporzione <lb/>dell'allungamento, cio&egrave; secondo i quadrati delle <lb/>lunghezze &rdquo; (ivi, pag. </s>

<s>118). La dimostrazione <lb/>riducesi alla seguente, supponendo essere AD <lb/>(fig. </s>

<s>225) la sezione di un solido prismatico fisso <lb/>nel muro AC con la sua base. </s>

<s>Tutto il peso <lb/>della detta sezione, che si pu&ograve; riguardar come <lb/>raccolto nel suo centro di gravit&agrave; H, &egrave; dato da <lb/>CDXAC, cosicch&egrave;, condotta la HI=CD/2 perpendicolare alla base, sar&agrave; il <lb/>momento, a cui debbon resistere le particelle materiali AC aderenti al muro, <lb/>CDXACXCD/2. Se ora la sezione stessa s'immagini prolungata in E, co&shy;<lb/>sicch&egrave; i pesi delle sue particelle d'ogni parte si raccolgano in M, il nuovo <lb/>momento, a cui debbon resistere i punti di attacco al sostegno, si trover&agrave; <lb/>allo stesso modo di dianzi uguale a CFXACXCF/2. Stanno dunque vera&shy;<lb/>mente le due resistenze come CD2 a CF2, secondo che diceva di aver tro&shy;<lb/>vato Galileo. </s></p><p type="main">

<s>Procedendo oltre a dimostrare, secondo i posti principii, le ragioni del <lb/>resistere allo spezzarsi rasente il muro, a cui siano stati affissi per le loro <lb/>basi di varia grandezza, due cilindri di lunghezze uguali, come per esempio <lb/>A, B (fig. </s>

<s>226), osserva l'Autore che &ldquo; se consideriamo l'assoluta e sem&shy;<lb/><figure id="id.020.01.2196.2.jpg" xlink:href="020/01/2196/2.jpg"/></s></p><p type="caption">

<s>Figura 226<lb/>plice resistenza, che risiede nelle basi, <lb/>cio&egrave; nei cerchi EF, DC, all'essere strap&shy;<lb/>pati, facendogli forza col tirarli per di&shy;<lb/>ritto; non &egrave; dubbio che la resistenza del <lb/>cilindro B &egrave; tanto maggiore che quella <lb/>del cilindro A, quanto il cerchio EF &egrave; <lb/>maggiore del CD, perch&egrave; tanto pi&ugrave; sono <lb/>le fibre, i filamenti o le parti tenaci, che <lb/>tengono unite le parti dei solidi. </s>

<s>Nel far forza per&ograve; per traverso ci serviamo <lb/>di due leve, delle quali le parti o distanze, dove si applicano le forze, sono <lb/>le linee DG, FH; i sostegni sono nei punti D, F, ma le altre parti o di&shy;<lb/>stanze, dove son poste le resistenze, sono i semidiametri dei cerchi DC, EF, <lb/>perch&egrave; i filamenti, sparsi per tutte le superficie dei cerchi, &egrave; come se tutti si <lb/>riducessero nei centri &rdquo; (ivi, pag. </s>

<s>119, 20). </s></p><p type="main">

<s>Cos&igrave; dunque la resistenza respettiva del cilindro B sar&agrave; tanto maggiore <pb xlink:href="020/01/2197.jpg" pagenum="440"/>della resistenza respettiva del cilindro A, quanto il prodotto della superficie <lb/>del circolo di raggio OF per esso raggio, &egrave; maggiore del prodotto della su&shy;<lb/>perficie del circolo di raggio ID per il medesimo raggio. </s>

<s>Ma le superficie <lb/>dei circoli stanno come i quadrati dei raggi, dunque star&agrave; la prima resi&shy;<lb/>stenza alla seconda come OF3 ad ID3, o come anche EF3 a CD3: ossia, come <lb/>Galileo propriamente si esprime, la resistenza all'esser rotti i due cilindri <lb/>&ldquo; cresce in triplicata proporzione dei diametri delle loro grossezze, cio&egrave; delle <lb/>loro basi &rdquo; (ivi, pag. </s>

<s>119). </s></p><p type="main">

<s>Stabiliti questi fondamentali teoremi della prima parte del suo Trat&shy;<lb/>tato, Galileo si trattiene a risolvere alcuni quesiti, e a dedurne alcuni corol&shy;<lb/><figure id="id.020.01.2197.1.jpg" xlink:href="020/01/2197/1.jpg"/></s></p><p type="caption">

<s>Figura 227<lb/><figure id="id.020.01.2197.2.jpg" xlink:href="020/01/2197/2.jpg"/></s></p><p type="caption">

<s>Figura 228<lb/>larii, o curiosi in s&egrave; stessi, o utili per le <lb/>loro applicazioni, come sarebbe per esem&shy;<lb/>pio: perch&egrave; una verga pi&ugrave; resista all'esser <lb/>rotta, facendo forza secondo la sua lar&shy;<lb/>ghezza, che secondo la grossezza? </s>

<s>Abbiasi <lb/>la riga BE (fig. </s>

<s>227): chi volesse romperla <lb/>cos&igrave; ritta troverebbe molto maggior resi&shy;<lb/>stenza che a romperla posta per piatto, <lb/>come nella figura 228, di che la ragione <lb/>apparisce chiara dai posti principii, per&shy;<lb/>ch&egrave;, mentre in ambedue i casi la resi&shy;<lb/>stenza assoluta &egrave; la medesima, essendo le <lb/>medesime le superficie aderenti, la resi&shy;<lb/>stenza respettiva &egrave; tanto maggiore nella <lb/>prima posizione che nella seseconda, quanto AB, o la sua met&agrave; che serve <lb/>di contralleva, &egrave; maggiore della met&agrave; di CD. </s></p><p type="main">

<s>Quest'altra curiosa e importante novit&agrave; si conclude pure dagli stessi <lb/>principii: sia il cilindro vuoto AE ugualmente lungo, e ugualmente peso del <lb/>cilindro massiccio IN (fig. </s>

<s>229): chi si volesse provare a stroncar questi due <lb/>solidi, facendo forza in E, N contro le basi AB, IL aderenti, troverebbe molto <lb/><figure id="id.020.01.2197.3.jpg" xlink:href="020/01/2197/3.jpg"/></s></p><p type="caption">

<s>Figura 229<lb/>maggior difficolt&agrave; nel primo che nel <lb/>secondo, e ci&ograve; perch&egrave;, mentre in am&shy;<lb/>bedue la resistenza assoluta &egrave; la mede&shy;<lb/>sima, la resistenza respettiva nell'uno <lb/>per&ograve; &egrave; tanto minore della resistenza <lb/>respettiva dell'altro, quanto il diame&shy;<lb/>tro IL, o la met&agrave; di lui che fa da con&shy;<lb/>tralleva, &egrave; minore della met&agrave; di AB. <lb/>Ond'&egrave; a concluder di qui con Galileo <lb/>che &ldquo; le resistenze di due cilindri eguali, ed egualmente lunghi, l'uno dei <lb/>quali sia vuoto e l'altro massiccio, hanno tra di loro la medesima propor&shy;<lb/>zione che i loro diametri &rdquo; (ivi, pag. </s>

<s>145). </s></p><p type="main">

<s>L'utilit&agrave; di questa conclusione, nelle opere dell'arte, &egrave; abbellita per Ga&shy;<lb/>lileo dal contemplare il provvido e sapiente magistero della Natura nel fab-<pb xlink:href="020/01/2198.jpg" pagenum="441"/>bricar le leggere ossa ai volanti per l'aria, o i gracili calami, sopra i quali <lb/>ondeggiano al vento le pingui spighe nei campi. </s>

<s>Considera inoltre l'Autore <lb/>di questa nuova Scienza che le resistenze dei solidi non mantengono la pro&shy;<lb/>porzione delle grandezze, come nella Geometria, nella quale non si muta <lb/>propriet&agrave; alle figure simili; cosicch&egrave; s'ingannerebbe molto colui, il quale <lb/>credesse che, a raddoppiare a un cilindro la base e la lunghezza, dovesse <lb/>tuttavia serbare una resistenza uguale alla prima. </s>

<s>La ragione di ci&ograve; si vede <lb/>nei professati principii chiarissima, perch&egrave; sebben nel cilindro doppio sia rad&shy;<lb/>doppiate la leva, e siano altres&igrave; raddoppiati i filamenti o i punti di attacco, <lb/>la contralleva nonostante &egrave; cresciuta meno del doppio, e tanto meno quanto <lb/>minore di due &egrave; la sua propria radice. </s>

<s>Di qui sapientemente conclude Galileo <lb/>la ragione del non riuscire secondo i modelli le macchine in grande, e come <lb/>sarebbe impossibile all'arte fabbricare edifizii grandissimi, e alla Natura al&shy;<lb/>beri o animali di smisurata grandezza, se gi&agrave; non si togliesse materia molto <lb/>pi&ugrave; dura e resistente della consueta, o non si volessero cos&igrave; deformare le <lb/>ordinarie figure, da metterle in vista di orribili mostri (ivi, pag. </s>

<s>128, 29). </s></p><p type="main">

<s>Venivano queste considerazioni ad accennare a un'altra Scienza nuova, <lb/>che sarebbe tra non molto per istituire il Borelli, e della quale intanto sem&shy;<lb/>bra che volesse il Viviani, con queste parole, preconizzare i natalizii: </s></p><p type="main">

<s>&ldquo; Fra le molte ed ammirabili conclusioni, avvertite e dimostrate dal <lb/>Galileo, bellissima ed utilissima &egrave; quella in materia di resistenza dei corpi <lb/>solidi, a caso per cos&igrave; dire conosciuta e messa in opera dall'Arte, ma prima <lb/>e pi&ugrave; altamente dalla sovrana maestra Natura, la quale, bisognosa in alcuni <lb/>suoi macchinamenti di diminuire assai il peso, ma meno assai la gagliardia <lb/>di alcuni corpi, di lor natura molto gravi; ha industriosamente trovatane la <lb/>maniera e messala ad effetto, e questo ella ha osservato, come acutamente <lb/>avvertisce il medesimo Galileo, nelle ossa degli animali, le quali, come di <lb/>materia per s&egrave; stessa assai grave, era necessario per certo rispetto farle <lb/>quanto fosse pi&ugrave; possibile leggere negli uccelli, per facilitare il potersi so&shy;<lb/>stenere per aria, e che nel medesimo tempo fossero gagliarde e robuste, ed <lb/>in particolare quelle delle ali, acci&ograve; con forza a volont&agrave; potessero battere le <lb/>medesime ali, che in larghi spazi s'aprono e si dilatano; dovecch&egrave; negli ani&shy;<lb/>mali terrestri, non era necessaria tanta leggerezza, ma bene un'altra sorta <lb/>di robustezza. </s>

<s>Sono perci&ograve; con somma provvidenza fatte da Dio le ossa degli <lb/>uccelli con gran cavit&agrave; e con sottile corteccia, ma non cos&igrave; quelle dei ret&shy;<lb/>tili che, rispetto alla grossezza, hanno dentro poco vacuo. </s>

<s>Dico fatto ci&ograve; molto <lb/>provvidamente, perch&egrave; dovendo i terrestri esercitare i movimenti loro tra <lb/>sassi e sterpi, dove si corre pericolo di urtare, era necessario l'ossa loro <lb/>essere resistenti alle forze, alle quali l'ossa, quanto pi&ugrave; cave, tanto meno <lb/>sono resistenti. </s>

<s>Ma nei volatili, ch'esercitano il loro velocissimo corso per <lb/>il liquido dell'aria, come liberi dal pericolo delli ur<gap/>i, la resistenza non era <lb/>cos&igrave; necessaria, ma bene la leggerezza &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>18). </s></p><p type="main">

<s>Le riferite conclusioni che il Viviani, cos&igrave; discorrendo, applicava alla <lb/>Meccanica animale, appartengono, come si diceva, alla prima parte del Trat-<pb xlink:href="020/01/2199.jpg" pagenum="442"/>tato galileiano, dove si considerano i momenti e le resistenze dei prismi e <lb/>cilindri solidi, l'una estremit&agrave; dei quali sia posta immobile, e solo nell'al&shy;<lb/>tra sia applicata la forza di un peso premente. </s>

<s>&ldquo; Ora voglio, soggiunge <lb/>lo stesso Galileo, che discorriamo alquanto dei medesimi prismi e cilindri, <lb/>quando fossero sostenuti da ambedue le estremit&agrave; &rdquo; (Alb. </s>

<s>XIII, 132): e pro&shy;<lb/>postasi la questione aristotelica del legno, tenuto per i due capi con le mani <lb/>a fin di spezzarlo, puntandovi contro il ginocchio; considerati, come il Fi&shy;<lb/>losofo fa, gli effetti della leva, ne riduce i momenti, con questo fondamen&shy;<lb/>tale teorema, alle loro pi&ugrave; giuste proporzioni: &ldquo; Se nella lunghezza di un <lb/>cilindro si noteranno due luoghi, sopra i quali si voglia far la frazione di <lb/>esso cilindro, le resistenze di detti due luoghi hanno fra di loro la mede&shy;<lb/>sima proporzione che i rettangoli fatti dalle distanze di essi luoghi contra&shy;<lb/>riamente presi &rdquo; (ivi, pag. </s>

<s>135). </s></p><p type="main">

<s>Or perch&egrave; quello che dicesi dei cilindri si applica ugualmente ai prismi, <lb/>se sar&agrave; dunque una trave prismatica DB (fig. </s>

<s>230), sostenuta nelle sue te&shy;<lb/>state, com'ai palchi delle stanze; e se le resistenze vanno colle dimostrate <lb/><figure id="id.020.01.2199.1.jpg" xlink:href="020/01/2199/1.jpg"/></s></p><p type="caption">

<s>Figura 230<lb/>proporzioni crescendo dal mezzo di qua <lb/>e di l&agrave; verso i sostegni, si potrebbe dun&shy;<lb/>que levar della grossezza di essa trave <lb/>non piccola parte, con alleggerimento <lb/>del peso, con abbellimento del palco, <lb/>e con qualche diminuzione del prezzo. </s>

<s><lb/>Provoc&ograve; un tal pensiero in Galileo la <lb/>soluzione di un problema, che si pre&shy;<lb/>sentava alla sua speculazione di una no&shy;<lb/>vit&agrave; e di una bellezza maravigliosa, e che consisteva &ldquo; nel ritrovar quale <lb/>figura dovrebbe aver quel tal solido, che in tutte le sue parti fosse egual&shy;<lb/>mente resistente, tal che non pi&ugrave; facile fosse ad esser rotto da un peso, che <lb/>lo premesse nel mezzo, che in qualsivoglia altro luogo &rdquo; (ivi, pag. </s>

<s>136, 37). </s></p><p type="main">

<s>Trov&ograve; felicemente la desiderata figura segando la detta trave prisma&shy;<lb/>tica BD lungo il filo della parabola FNB, cosicch&egrave; il solido parabolico, che <lb/>indi ne nasce, sia d'ugual resistenza cos&igrave; nella base AD, come in CO, e in <lb/>qualunque altra sezione. </s>

<s>A dimostrar che ci&ograve; sia il vero s'apparecchia Galileo <lb/>con questo Lemma: &ldquo; Se saranno due Libre o Leve divise dai loro sostegni <lb/>in modo, che le due distanze, dove si hanno a costituire le potenze, abbiano <lb/>tra di loro doppia proporzione delle distanze, dove saranno le resistenze, le <lb/><figure id="id.020.01.2199.2.jpg" xlink:href="020/01/2199/2.jpg"/></s></p><p type="caption">

<s>Figura 231<lb/>quali resistenze stiano fra loro come <lb/>le loro distanze; le potenze sostenenti <lb/>saranno eguali &rdquo; (ivi, pag. </s>

<s>138). </s></p><p type="main">

<s>Si pu&ograve; la dimostrazione galile&shy;<lb/>iana ridurre cos&igrave; a maggior brevit&agrave; <lb/>e chiarezza: Siano le due leve AB, <lb/>CD (fig. </s>

<s>231), aventi i loro fulcri <lb/>in E, F, e si chiamino R, R&prime; le resi-<pb xlink:href="020/01/2200.jpg" pagenum="443"/>stenze applicate in C, A; P, P&prime; le potenze applicate in D, B: sup; osto che <lb/>sia (I) EB:FD=AE2:FC2; (II) AE:FC=R&prime;:R, convien dimostrare <lb/>che P=P&prime;. </s>

<s>Si prenda sul braccio della Leva EB la lunghezza GE media <lb/>proporzionale fra EB, FD: avremo (III) EG2:FD2=AE2:FC2; e anche <lb/>insieme (IV) EB2:EG1=AE2:FC2. </s>

<s>Ma abbiamo per le propriet&agrave; del Vette, <lb/>e per la IIIa, la Va R:P=DF:FC=GE:AE, e pure, per la propriet&agrave; <lb/>del Vette (VI) R&prime;:P&prime;=BE:AE, e per la IIIa e la IVa R:R&prime;=GE:BE; <lb/>dunque la Va e la VIa daranno P:P&prime;=AE:AE, ossia P=P&prime; come do&shy;<lb/>vevasi dimostrare. </s></p><p type="main">

<s>Inteso ci&ograve;, torniamo con Galileo indietro sulla figura CCXXX a consi&shy;<lb/>derar la trave prismatica ridotta, col filo della sega, al solido parabolico <lb/>DOGBCA, che &egrave; quello che si dice esser per tutto di ugual potenza in re&shy;<lb/>sistere a un peso che lo prema. </s>

<s>Avendo infatti la resistenza da pareggiare <lb/>con la leva BA, alla resistenza da pareggiarsi con la leva BC, la medesima <lb/>proporzione che il rettangolo DA al rettangolo OC, la quale proporzione &egrave; <lb/>la medesima di quella che ha la linea AF alla NC; chiamata dunque come <lb/>dianzi R&prime; la prima resistenza, ed R la seconda, sar&agrave; R&prime;:R=AB:BC. </s>

<s>Ma <lb/>le propriet&agrave; della parabola danno AB:BC=AF2:NC2 e perci&ograve;, per le con&shy;<lb/>clusioni del precedente Lemma, preparato gi&agrave; per applicarsi al caso presente, <lb/>la potenza, che ha di resistere AB, sar&agrave; uguale alla potenza di CO, e di qual <lb/>si voglia altra sezione condotta nella trave parabolica parallela alla base. </s>

<s>Or <lb/>perch&egrave;, per le cose dimostrate dai Matematici antichi, il solido parabolico <lb/>cos&igrave; rimasto &egrave; due terzi di tutto il prisma da cui fu segato, ne conclude <lb/>perci&ograve; Galileo che nella trave, diminuita di un terzo del suo peso, non &egrave; <lb/>per&ograve; menomata per nulla quella prima potenza che aveva essendo intera. </s></p><p type="main">

<s>La conclusione &egrave; bellissima, anzi veramente maravigliosa, mentre che <lb/>per&ograve; si rimanga nei libri alla contemplazion dei Filosofi, i quali possono con <lb/>la mente astrarre dalla materia. </s>

<s>Ma Galileo si lusingava di esser col suo Teo&shy;<lb/>rema venuto a suggerire una utilissima applicazione alle costruzioni, spe&shy;<lb/>cialmente navali, vedendosi &ldquo; come con diminuzion di peso di pi&ugrave; di tren&shy;<lb/>tatre per cento si posson fare i travamenti, senza diminuir punto la loro <lb/>gagliardia, il che, nei navigli grandi in particolare, per regger le coverte, <lb/>pu&ograve; essere di utile non piccolo, attesoch&egrave; in cotali fabbriche la leggerezza <lb/>importa infinitamente &rdquo; (ivi, pag. </s>

<s>140). </s></p><p type="main">

<s>Le contradizioni, ch'ebbe per ci&ograve; a patir Galileo dai Meccanici poste&shy;<lb/>riori, si diranno pi&ugrave; qua: per ora non son da passare inosservati i due <lb/>modi, ch'egli propone per descrivere una parabola. </s>

<s>Not&ograve; il Cartesio che quei <lb/>modi son puramente meccanici &ldquo; et secundum Geometriam accuratam falsi &rdquo; <lb/>(Epist. </s>

<s>cit., P. II, pag. </s>

<s>243) ci&ograve; che sapevasi benissimo anche da Galileo, ma <lb/>tant'era la fiducia che aveva di esser venuto colle sue teorie a recare non <lb/>piccola utilit&agrave; all'arte, che scelse i due detti modi perch&egrave; <emph type="italics"/>sopra tutti gli <lb/>altri speditissimi<emph.end type="italics"/> (Alb. </s>

<s>XIII, 144), e perch&egrave; la sega in mano dell'operaio &egrave; <lb/>impossibile che vada a filo dell'accurata Geometria. </s>

<s>S'aggiungeva la com&shy;<lb/>piacenza della novit&agrave; non saputa che da quei pochissimi, ai quali fosse per <pb xlink:href="020/01/2201.jpg" pagenum="444"/>avventura capitato il Manoscritto di Guidubaldo del Monte, dove dice che la <lb/>linea dei proietti si rassomiglia a quella disegnata da una catenuzza, pen&shy;<lb/>dula nelle sue estremit&agrave; da due punti fissi orizzontali, e che l'esperienza di <lb/>tal moto proiettizio &ldquo; si pu&ograve; far pigliando una palla tinta d'inchiostro, e <lb/>tirandola sopra un piano di una tavola, il qual stia quasi perpendicolare al&shy;<lb/>l'orizzonte &rdquo; (Libri Histoire des Mathem., T. IV, Paris 1841, pag. </s>

<s>397). </s></p><p type="main">

<s>N&egrave; furon queste sole le notizie in tal congiuntura partecipatesi a Gali&shy;<lb/>leo: l'applicazione delle propriet&agrave; dei pendoli al vibrare delle corde sonore, <lb/>e la soluzion del problema famoso relativo alla corda tocca, che fa simpa&shy;<lb/>ticamente tremare le altre corde unisone e quiete, son cose che si legge&shy;<lb/>vano per le neglette carte scoperte dal Libri, pi&ugrave; di trent'anni prima, che <lb/>si vedessero trasposte nel terzo dialogo delle due Nuove Scienze. </s>

<s>E qui ca&shy;<lb/>drebhe in proposito il dire qual parte avesse Galileo nelle esperienze dei <lb/>proietti descritte da Guidubaldo, e qual giudizio facesse delle teorie in pro&shy;<lb/>posito o delle opinioni di lui. </s>

<s>Ma perch&egrave; dovremo di ci&ograve; tenere altrove par&shy;<lb/>ticolare discorso, richiameremo l'attenzione dei nostri Lettori intorno a ci&ograve;, <lb/>che lo stesso Guidubaldo ivi insegna della resistenza delle corde tirate da pesi. </s></p><p type="main">

<s>&ldquo; Una corda che sostenta un peso, egli dice, tanto sostiene essendo <lb/>corta, quanto lunga. </s>

<s>&Egrave; ben vero che nella lunga, prima per la sua gravit&agrave;, <lb/>poi perch&egrave; nella lunga ci possono esser molte parti deboli, pu&ograve; esser che <lb/>ella si tronchi pi&ugrave; facilmente e da minor peso, ma se, dove ella si stronca <lb/>per la sua distrazione, la corda fosse sostenuta poco di sopra, e poco di sotto <lb/>fosse stato il peso, senza dubbio ella medesimamente si sarebbe stroncata, <lb/>perch&egrave; si sarebbe nel medesimo modo distratta &rdquo; (ivi, pag. </s>

<s>398). Chi ora <lb/>collazionasse queste parole con quelle che si leggono in Galileo, nella II gior&shy;<lb/>nata delle Scienze nuove a pag. </s>

<s>121 della citata edizione, non ci troverebbe <lb/>altra differenza che nell'essere dialogizzate. </s></p><p type="main">

<s>L'importanza di queste verit&agrave;, delle quali ebbe forse a persuadersi Gui&shy;<lb/>dubalde dop'avere scritto il suo trattato Delle meccaniche, in mezzo ai pre&shy;<lb/>valenti errosi messi in campo dal Simplicio galileiano, consigli&ograve; l'Aggiunti <lb/>di specular quella sua sottilissima dimostrazione, che si riferi a pag. </s>

<s>215, 16 <lb/><figure id="id.020.01.2201.1.jpg" xlink:href="020/01/2201/1.jpg"/></s></p><p type="caption">

<s>Figura 232<lb/>del nostro II Tomo. </s>

<s>Anche il Tor&shy;<lb/>ricelli, bench&egrave; vedesse assai chiaro <lb/>che la forza di un uomo, applicata <lb/>in B (fig. </s>

<s>232) a un capo della corda <lb/>di qualunque lunghezza, si propaga uguale di tratto in tratto infino all'altro <lb/>capo C, a cui il peso da tirarsi &egrave; raccomandato; non cred&egrave; nonostante inu&shy;<lb/>tile spendervi attorno qualche discorso. </s></p><p type="main">

<s>&ldquo; Io considero qui primieramente, egli dice, che tutta la corda BC aver&agrave; <lb/>la medesima tensione in ogni sua parte, cio&egrave; tanto sar&agrave; tirata nel princi&shy;<lb/>pio B, quanto nel mezzo D, e quanto verso il fine C. </s>

<s>Questo &egrave; assai chiaro, <lb/>astraendo per&ograve; da qualche variet&agrave;, che potesse fare il peso della corda, ed <lb/>anco astraendo dalla differenza, che potesse nascere dal toccamento della <lb/>corda sopra il piano a lei sottoposto, che per&ograve; la considereremo in aria, e <pb xlink:href="020/01/2202.jpg" pagenum="445"/>senza la gravit&agrave; propria. </s>

<s>Nondimeno si pu&ograve; con qualche discorso dimo&shy;<lb/>strare cos&igrave;: &rdquo; </s></p><p type="main">

<s>&ldquo; L'uomo traente conferisce al punto B tanta forza, quanta ne ha esso <lb/>uomo: il punto B tira poi con tanta forza il punto E suo congiunto, quanta <lb/>ne ha esso B, cio&egrave; quanta &egrave; la forza dell'uomo, e il punto E tira il punto <lb/>F suo congiunto con quanta ne ha esso E, cio&egrave; quanta &egrave; la forza dell'uomo, <lb/>e cos&igrave; si pu&ograve; andar discorrendo di tutti i punti, cio&egrave; di tutta la corda BC, <lb/>e concluderemo che l'ultimo punto C, e perci&ograve; il gran sasso A, vien tirato <lb/>con altrettanta forza per appunto, con quanta vien tirato il punto B, cio&egrave; <lb/>con la forza dell'uomo traente, non accresciuta n&egrave; diminuita. </s>

<s>Concludiamo <lb/>dunque questo principio: che qualunque volta averemo una lunghezza, cio&egrave; <lb/>una estensione di punti continuati, e che il primo di essi punti venga ti&shy;<lb/>rato o spinto con una tal forza, anco tutti gli altri successivamente saranno <lb/>tirati o spinti con la medesima forza, senza accrescerla n&egrave; diminuirla, ma <lb/>trasmettendola sino al fine &rdquo; (MSS. Gal., T. XXXVII, fol. </s>

<s>123). </s></p><p type="main">

<s>La medesima conclusione scende da un principio dinamico pi&ugrave; gene&shy;<lb/>rale, ed &egrave; che la forza comunicata non varia di grado non variando la ve&shy;<lb/>locit&agrave; nella sezione costante, come si suppone avere la corda BC, che tira <lb/>il sasso. </s>

<s>Ma se da D per esempio verso C la corda &egrave; pi&ugrave; sottile o pi&ugrave; grossa, <lb/>che da D verso B, allora, essendo le velocit&agrave; in ragion reciproca delle se&shy;<lb/>zioni, la forza non si propaga pi&ugrave; eguale, e restando indietro le parti meno <lb/>veloci si separano necessariamente dalle altre sempre in punti determinati. </s>

<s><lb/>Nascon di qui certi fatti maravigliosi, che in alcuni moderni scrittori ebbero <lb/>apparenza di nuovi, ma che furono molto prima osservati dal Viviani, e in <lb/>alcune sue Note autografe cos&igrave; descritti: </s></p><p type="main">

<s>&ldquo; Il peso A (fig. </s>

<s>233) di cinque libbre stia attac&shy;<lb/><figure id="id.020.01.2202.1.jpg" xlink:href="020/01/2202/1.jpg"/></s></p><p type="caption">

<s>Figura 233<lb/>cato dalla sottilissima fune BC, e al medesimo peso stia <lb/>pendente un'altra simil cordicella BF: dico potersi dar <lb/>caso che, nel tirar questa a basso con forza, ella si <lb/>stianti e rimanga la corda BC salda e illesa col peso A, <lb/>e ci&ograve; seguir&agrave; per mezzo di una stratta, che si dia alla <lb/>funicella BF con un colpo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma pi&ugrave; maraviglia sar&agrave;, quando anco la corda BF <lb/>sia pi&ugrave; forte e pi&ugrave; grossa della superiore BC, perch&egrave; &egrave; <lb/>certo che, tirando a basso da F, questa si romper&agrave; nella <lb/>parte BC. </s>

<s>Nondimeno si potr&agrave; fare che si rompa la pi&ugrave; forte BF, che in B <lb/>vi sia attaccato un peso tale, che appena sia retto dalla sottil corda BC. </s>

<s>Que&shy;<lb/>sto si conseguir&agrave; per mezzo dell'asta infilata nel muro D, e alla corda nella <lb/>estremit&agrave; F, sulla quale asta o bastone si dia un colpo col maglio ra&shy;<lb/>sente F. &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>29). </s></p><p type="main">

<s>Potrebbero questi fatti passar per semplici giochi, se non avessero una <lb/>seria applicazione nelle funi da sostener pesi, o da sollevarli per via delle <lb/>Macchine; ci&ograve; che saviamente consigli&ograve; Galileo di farne argomento nel trat&shy;<lb/>tar delle resistenze. </s>

<s>Non poteva egli reputare innocuo l'error di Simplicio <pb xlink:href="020/01/2203.jpg" pagenum="446"/>in creder che tanto fossero le corde pi&ugrave; valide a sostenere, quanto fossero <lb/>state pi&ugrave; corte, avendo, insiem con lo stesso Guidubaldo, dovuto riconoscere <lb/>che, dal versare intorno a ci&ograve; o nell'errore o nel dubbio, nacque l'imper&shy;<lb/>fezione, in cui si lasci&ograve; la meccanica delle Taglie. </s></p><p type="main">

<s>Il trattato Delle resistenze dei solidi nel II dialogo galileiano &egrave; dunque <lb/>cos&igrave;, nella novit&agrave; del suo argomento, compiuto, n&egrave; resta a far altro, in mezzo <lb/>alle ammirazioni, che a notarne i difetti. </s>

<s>Chi, non frastornato dal lungo cla&shy;<lb/>mor degli applausi, esamina tranquillamente, s'accorge prima di tutto di un <lb/>disordine nel succedersi delle proposizioni, le ultime delle quali hanno re&shy;<lb/>lazione strettissima con le prime. </s>

<s>Il difetto, &egrave; vero, scomparisce nella forma <lb/>del dialogo, ed &egrave; perci&ograve; il dialogo stesso che toglie precisione al trattato, <lb/>intanto che avvenne in questo quel che nell'altro proposito dei Moti locali, <lb/>che cio&egrave;, per dare inutile sodisfazione ai Simplicii, n'ebbero i Sagredi a ri&shy;<lb/>maner mal contenti. </s></p><p type="main">

<s>Giova ricercar nella Storia di questo mal contento un esempio, che ci <lb/>occorre nella prima lettura del Dialogo, dove, propostosi il caso che si vo&shy;<lb/>glia sollevare un masso, per via di una Leva, si domanda qual parte sia del <lb/>peso totale quella, che vien sostenuta dal soggetto piano, e quale quell'al&shy;<lb/>tra, che grava nell'estremit&agrave; della stessa Leva (Alb. </s>

<s>XIII, 415). Il problema <lb/>era per s&egrave; di facilissima soluzione e spedita, perch&egrave; supposto essere A (fig. </s>

<s>234) <lb/>il masso da sollevarsi con l'appoggio in N, &egrave; manifesto che la resistenza ap&shy;<lb/><figure id="id.020.01.2203.1.jpg" xlink:href="020/01/2203/1.jpg"/></s></p><p type="caption">

<s>Figura 234<lb/>plicata in C, all'estremit&agrave; della <lb/>Leva di primo genere GNC, &egrave; la <lb/>stessa potenza della Leva di se&shy;<lb/>condo genere CHB, che ha l'ap&shy;<lb/>poggio in B sul terreno, e il <lb/>peso in H nell'intersezione della <lb/>verticale AH fatta scendere dal <lb/>centro di gravit&agrave; del masso. </s>

<s>Cosicch&egrave;, abbassata da C perpendicolarmente <lb/>la CF sopra la orizzontale BF, e prolungata la AH in O, si rendono, in virt&ugrave; <lb/>dei triangoli CBF, HBO, simili le due Leve CHB, FOB, ond'&egrave; che avremo, <lb/>chiamata A la potenza, e C la resistenza, A:C=BF:BO. </s>

<s>Questa stessa <lb/>resistenza dunque, applicata in C all'estremit&agrave; della contralleva NC, avr&agrave; alla <lb/>potenza G della Leva la relazione cos&igrave; espressa: A.BO/BF:G=GN:NC, ossia <lb/>A/G=GN.BF/NC.BO, che vuol dire &ldquo; il momento di tutto il peso, al momento della <lb/>potenza in G, avere la proporzione composta della distanza GN alla distanza <lb/>NC, e della FB alla BO &rdquo; (ivi, pag. </s>

<s>115, 16) come Galileo si proponeva di <lb/>dimostrare. </s></p><p type="main">

<s>Ma vedasi come quella galileiana dimostrazione, illustrata da una figura <lb/>poco precisa, e nelle successive edizioni anche pi&ugrave; deturpata; s'aggiri per <lb/>vie pi&ugrave; lunghe e faticose, non per altro fine che di renderla di pi&ugrave; facile <lb/>intelligenza: e intanto usciva fuori un Matematico gesuita a mostrare quel <pb xlink:href="020/01/2204.jpg" pagenum="447"/>mal contento che si diceva. </s>

<s>Volle il Viviani difendere il suo Maestro nella <lb/>seguente postilla, inserita fra le pagine 112, 113 della citata edizione di <lb/>Leida: </s></p><p type="main">

<s>&ldquo; Quando il Galileo dice: <emph type="italics"/>la potenza in B alla potenza in C sta come <lb/>la FO alla OB,<emph.end type="italics"/> egli intende di quelle potenze, che resistono alle forze del <lb/>sasso, le quali vengono fatte ed esercitate nei punti C, B, sul Vette o sul <lb/>terreno, per le direzioni delle perpendicolari all'orizzonte, che passano per <lb/>detti punti C, B, nella guisa che tutto il sasso fa la sua forza di discendere <lb/>col suo centro di gravit&agrave; per il perpendicolo AO: ed in tal maniera intesa <lb/>la sua dimostrazione cammina benissimo, e non merita di essere incolpata <lb/>d'alcuno errore dal reverendo padre G..... Che se poi altri volesse inten&shy;<lb/>dere che le forze o potenze, delle quali parla il Galileo nella sua medesima <lb/>dimostrazione, e le quali resistono alle forze del sasso, agissero per altre di&shy;<lb/>rezioni diverse da quelle dei detti perpendicoli; allora converrebbe discorrere <lb/>le cose diversamente, come il Galileo stesso averebbe saputo fare, e far bene, <lb/>in seguito di tale nuova e diversa ipotesi, senza che il detto Padre se ne <lb/>pigliasse pensiero &rdquo; (MSS. Gal., P. V, T. IX). </s></p><p type="main">

<s>Ma in verit&agrave; non si tratta d'ipotesi: si tratta di principii, che non pos&shy;<lb/>sono essere punto diversi da quelli, che Galileo stesso professa e insegna <lb/>nelle sue <emph type="italics"/>Meccaniche,<emph.end type="italics"/> dalle cose dimostrate nelle quali si concluderebbe, <lb/>checch&egrave; se ne dica il Viviani, essere per lo meno una impropriet&agrave; riguar&shy;<lb/>dare come potenza il fulcro della Leva, e non distinguere il genere delle due <lb/>macchine nella variet&agrave; delle loro applicazioni. </s></p><p type="main">

<s>Cos&igrave; fatte impropriet&agrave; nel significare i concetti si vedrebbero forse evi&shy;<lb/>tate, se potessimo aver sott'occhio i primi getti, che fece Galileo di quelle <lb/>sue dimostrazioni, quando non pensava ancora di renderle in cos&igrave; inefficace <lb/>modo pepolari. </s>

<s>Ci sarebbe, comunque sia, rimasto di quella prima e pi&ugrave; ap&shy;<lb/>propriata maniera pubblico documento, quando avesse il Salviati mantenuta <lb/>la promessa, fatta sulla sera della prima Giornata, di comparire la mattina <lb/>appresso innanzi agli interlocutori, per trattar con essi delle resistenze dei <lb/>solidi allo spezzarsi, recando seco <emph type="italics"/>alcuni fogli,<emph.end type="italics"/> dov'aveva per ordine notati <lb/>i teoremi e problemi attenenti a quel soggetto (Alb. </s>

<s>XIII, 94). </s></p><p type="main">

<s>A quest'annunzio incorammo la speranza di avere a ritrovar que'fogli <lb/>tra i Manoscritti, i quali ci porgerebbero materia a riordinare, e occasione <lb/>a render pubblicamente noto ai Lettori il primo trattato galileiano Delle re&shy;<lb/>sistenze, come facemmo del primo trattato Dei movimenti locali. </s>

<s>Ma furono <lb/>questa volta le nostre ricerche meno felici, perch&egrave; non fu possibile di que'fo&shy;<lb/>gli ritrovarne altro che pochi, e delle cose dimostrate in altri le semplici <lb/>conclusioni. </s></p><p type="main">

<s>Notabile &egrave; tra que'fogli uno, in cui fu scritto il teorema delle condi&shy;<lb/>zioni generali dell'equilibrio della Leva, quando il grave non &egrave; sollevato di <lb/>peso, ma da una estremit&agrave; si appoggia sul suolo; teorema, che appartiene <lb/>al trattato <emph type="italics"/>Della scienza meccanica,<emph.end type="italics"/> d'onde lo trasse l'Autore, per metterlo <lb/>in dialogo in principio alla seconda giornata delle due Nuove Scienze. </s>

<s>Fa <pb xlink:href="020/01/2205.jpg" pagenum="448"/>perci&ograve; maraviglia che l'Alb&egrave;ri, il quale fu primo a reintegrare colla dimo&shy;<lb/>strazione della Leva archimedea quel trattato galileiano, lasciasse da questa <lb/>parte la reintegrazione incompleta, come l'hanno lasciata gli editori novelli, <lb/>che troppo spesso seguono, senz'avvedersene, le vestigia di lui. </s>

<s>Quel teo&shy;<lb/>rema dunque, ch'&egrave; quasi un corollario alla terza proposizione <emph type="italics"/>De aequipon&shy;<lb/>derantibus,<emph.end type="italics"/> fu da Galileo dialogizzato sopra questa scrittura, della quale, <lb/>come di tutto il trattato delle Meccaniche, non &egrave; rimasto se non che la copia: </s></p><p type="main">

<s>&ldquo; Se sia un solido sopra l'orizzonte, e questo si deva alzare, &egrave; cosa <lb/>chiara che, se piglieremo una leva, che abbia il suo sostegno, che, a volerlo <lb/>equilibrare, bisogner&agrave;, volendo prima sollevarlo, mettere dall'altra parte della <lb/>lieva potenza tale, che abbia al peso assoluto di detto solido la medesima <lb/>proporzione, che hanno tra loro le parti di detta lieva, ma contrariamente <lb/>prese. </s>

<s>Ma se ci contenteremo di alzarne una parte, e che il rimanente si <lb/>posi in terra, in questo caso, mentre si comincia ad alzarne una parte, sem&shy;<lb/>pre va scemando il peso sopra la lieva, e va crescendo in terra. </s>

<s>Per&ograve; si di&shy;<lb/>mostrer&agrave; che detto peso, alla potenza che deve equilibrarlo, in qualsivoglia <lb/>sito che sar&agrave; detto solido, abbi proporzione composta di quella, che hanno <lb/>tra di loro le parti della lieva, cio&egrave; quella che &egrave; dal fulcro verso il solido, <lb/>e di quella, che ha la linea parallela all'orizzonte, compresa tra la perpen&shy;<lb/>dicolare che casca dove tocca la lieva nel solido, e dove tocca il solido in <lb/>terra, a quella che &egrave; compresa tra la perpendicolare che casca a detta linea <lb/>dal centro di gravit&agrave; di detto solido, e dove tocca detto solido la detta linea <lb/>orizzontale. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia il solido A (nella precedente figura) il quale sia equilibrato dalla <lb/>lieva GC, sostenuta nel punto N, e che posi in terra nel punto B: dico che <lb/>il peso assoluto di detto solido, in qualsivoglia sito, ha alla potenza posta in <lb/>G una proporzione composta di quella, che ha la GN alla NC, e di quella <lb/>di FB alla BO. &rdquo; </s></p><p type="main">

<s>&ldquo; Facciasi, come la BF alla BO, cos&igrave; NC ad un'altra che sia H, e ti&shy;<lb/>risi AO dal centro della gravit&agrave; del solido perpendicolare alla BF orizzon&shy;<lb/>tale. </s>

<s>Perch&egrave; dunque la potenza, che sostiene il solido A nel punto C, alla <lb/>potenza che sostiene il medesimo nel punto B, ha la proporzione che ha la <lb/>linea BH alla HC, sendo detto solido sostenuto nelli due punti C, B; sar&agrave;, <lb/>componendo tutt'e due le potenze, cio&egrave; il peso assoluto del solido A, che &egrave; <lb/>l'istesso alla potenza C, come FB alla BO, cio&egrave; come CN alla H. </s>

<s>Ma la po&shy;<lb/>tenza di C, a quella di G, &egrave; come GN alla NC; adunque <emph type="italics"/>ex aequali,<emph.end type="italics"/> in pro&shy;<lb/>porzion perturbata, il peso A alla potenza G ha la proporzione di GN alla <lb/>H, che &egrave; composta di quella, che ha la GN alla NC, e di quella di NC alla H, <lb/>cio&egrave; di BF alla BO, che &egrave; quello etc. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per voler poi trovare la quantit&agrave;, moltiplichinsi insieme le due ante&shy;<lb/>cedenti, cio&egrave; la GN per la BF, e la NC per la BO, e cos&igrave; sar&agrave; noto che <lb/>potenza ci bisogni in qualsivoglia sito. </s>

<s>&rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>27). </s></p><p type="main">

<s>Quali siano, dopo questo, gli altri fogli, da'quali tradusse Galileo nei <lb/>Dialoghi i dimostrati teoremi, si vedr&agrave; nel processo di questo nostro discorso, <pb xlink:href="020/01/2206.jpg" pagenum="449"/>e bench&egrave; questi, come si diceva dianzi, sian pochi alle nostre speranze, e al <lb/>desiderio degli studiosi, son sufficienti nulladimeno a confermare quello, che <lb/>solo congetturando s'annunziava, che cio&egrave; si vedrebbero in queste prime <lb/>forme dimostrative evitate le impropriet&agrave; e le tediose lungaggini dei teoremi <lb/>dialogizzati. </s>

<s>Ma si vengono altres&igrave;, leggendo que'fogli, a scoprir cose bene <lb/>assai pi&ugrave; importanti: Alla seconda parte del trattato si pone per fondamento, <lb/>come altrove avvertimmo, la proposizione che le resistenze in due punti di&shy;<lb/>versi del medesimo cilindro &ldquo; hanno fra di loro la medesima proporzione <lb/>che i rettangoli fatti dalle distanze di essi luoghi contrariamente presi &rdquo; (ivi, <lb/>pag. </s>

<s>135). Il teorema per&ograve; apparisce in questa parte del Dialogo galileiano <lb/>difettoso per pi&ugrave; ragioni: prima di tutto, perch&egrave; si suppone, senza dimo&shy;<lb/>strarlo, che la proporzion dei momenti sia composta delle distanze e dei pesi; <lb/>e poi, perch&egrave; non risponde direttamente alla Questione aristotelica che lo <lb/>avea provocato, a risolver la quale bisognava piuttosto dimostrare in qual <lb/>ragione stia la medesima forza del ginocchio, rispetto alla resistenza opposta <lb/>ne'varii punti fuor del mezzo del legno che si vuole spezzato. </s></p><p type="main">

<s>Concorsero zelanti a supplire ai difetti del Maestro Michelangiolo Ricci, <lb/>il Torricelli, il Viviani e il Marchetti, quest'ultimo compiacendosi di aver <lb/>data dimostrazione della composizion dei momenti, e quegli altri di aver di&shy;<lb/>rettamente risoluta la Questione aristotelica, concludendo che, supposto esser <lb/>rigido il legno e troncativo secondo l'ipotesi galileiana, gli sforzi fatti nelle <lb/>varie parti di lui dal ginocchio, fuori del mezzo, stanno omologamente come <lb/>i rettangoli delle distanze dai punti, dove le mani lo tengon preso: d'onde <lb/>il bellissimo corollar&igrave;o che la scala dei momenti dei detti sforzi &egrave; nelle <lb/>linee parallele al diametro di una Parabola ordinaria, che abbia per base la <lb/>lunghezza dello stesso legno, compresa fra i due estremi punti di appoggio. </s></p><p type="main">

<s>Or si diceva dunque che, leggendo in quei fogli rimasti in mano al <lb/>Salviati, si scopre con gran maraviglia avere per s&egrave; medesimo Galileo gi&agrave; <lb/>pensato di dimostrar tutto quello, che soggiunsero i quattro sopra comme&shy;<lb/>morati discepoli di lui, per rendere il teorema delle resistenze del solido ap&shy;<lb/>poggiato alle sue due estremit&agrave; d'ogni parte compiuto: n&egrave;, senza attribuirlo <lb/>alla forma del dialogo, e al desiderio di rendere quelle matematiche diffi&shy;<lb/>colt&agrave; di facile intelligenza a tutti, si comprenderebbe perch&egrave; Galileo volesse <lb/>darci le laboriose scoperte mutilate cos&igrave; nella loro parte migliore. </s></p><p type="main">

<s>Di vederle ora finalmente reintegrate non pu&ograve; non nascere vivo il de&shy;<lb/>siderio in chi ama questi nuovi studii galileiani, e noi volentieri sodisfaremo <lb/>pi&ugrave; qua agli studiosi, quando ce ne porger&agrave; l'occasione il discorso. </s>

<s>Intanto, <lb/>quasi per caparra di quello che si promette, daremo fuori uno di quei fogli <lb/>manoscritti che, sebben non contenga nulla di pi&ugrave; di quel che si legge nel <lb/>Dialogo, quanto alla materia; giova nonostante nella sua forma a confermar <lb/>ci&ograve; che s'&egrave; detto pi&ugrave; volte, che cio&egrave; nella matematica precisione del primo <lb/>trattato si vedrebbero sparire in gran parte le impropriet&agrave; ingannatrici, e <lb/>cessare i tedii impazienti della mente, che vorrebbe correre spedita alla con&shy;<lb/>clusione, e importunamente si vede trattenuta in parole. </s></p><pb xlink:href="020/01/2207.jpg" pagenum="450"/><p type="main">

<s>Manca a quel foglio il Lemma, che Galileo non scrive, perch&egrave; non &egrave; <lb/>suo, ma &egrave;, cos&igrave; formulata, la III manifestazione del I dei due Lemmi pre&shy;<lb/>messi da Archimede alla proposizione XI Delle spirali: &ldquo; Si similes figurae <lb/>describantur ab omnibus, quae sese aequali invicem superant, et ab iis quae <lb/>sunt illarum maximae aequales; quae sane fiunt ab aequalibus maximae, <lb/>eorum quae fiunt ab iis quae sese aequaliter excedunt, minora sunt quam <lb/>tripla: sublata vero figura, quae describitur a maxima, reliquarum sunt plus <lb/>quam tripla &rdquo; (Opera omnia cit., pag. </s>

<s>365). </s></p><p type="main">

<s>Supposto questo che cio&egrave;: se quante linee si vogliono si eccederanno <lb/>egualmente, e l'eccesso sia eguale alla minima di quelle, ed altrettante siano <lb/>ciascheduna eguale alla massima, i quadrati di tutte queste saranno meno <lb/>che tripli dei quadrati di quelle che si eccedono, ma i medesimi saranno <lb/>pi&ugrave; che tripli di quegli altri che restano, trattone il quadrato della massima; <lb/>ecco come Galileo aveva, secondo l'espression del Salviati, <emph type="italics"/>altra volta di&shy;<lb/>mostrata<emph.end type="italics"/> (ivi, pag. </s>

<s>140) la sua proposizione, per applicarla al solido paea&shy;<lb/>bolico di ugual resistenza, e cos&igrave; confermare contro i dubitanti l'asserto che <lb/>egli sia veramente due terzi del prisma, da cui fu segato: </s></p><p type="main">

<s>&ldquo; Sit parabola CBA (fig. </s>

<s>235), parallelogrammo CP inscripta: dico pa&shy;<lb/><figure id="id.020.01.2207.1.jpg" xlink:href="020/01/2207/1.jpg"/></s></p><p type="caption">

<s>Figura 235<lb/>rallelogrammum parabolae esse se&shy;<lb/>squialter; hoc est esse triplum reli&shy;<lb/>qui spacii ABP extra parabolam. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si enim non sit, aut erit maius <lb/>aut minus. </s>

<s>Sit primo maius: exces&shy;<lb/>sus autem, quo spacium PC maius <lb/>est quam triplum spacii APB, vo&shy;<lb/>cetur X, divisoque parallelogrammo <lb/>continue in spacia aequalia, per li&shy;<lb/>neas ipsis AC, PB parallelas, devenie&shy;<lb/>mus ad spacia, quorum unum ipso X <lb/>erit minus, quale sit OB, et per puncta, ubi reliquae parallelae lineam para&shy;<lb/>bolae secant, ducantur aequidistantes ipsi AP, donec figura quaedam spacio <lb/>relicto extra parabolam circumscribatur, constans ex parallelogrammis AG, <lb/>KE, LF, MH, NI, OB, quae figura spacium APB extra parabolam minori <lb/>quantitate superabit quam sit X, cum superet idem quantitate adhuc minori <lb/>parallelogrammo OB. </s>

<s>Ergo idem parallelogrammum CP maius erit quam <lb/>triplum dictae figurae circumscriptae, quod est impossibile. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Non est ille minus quam triplum: nam cum DA ad AZ sit ut qua&shy;<lb/>dratum DE ad quadratum ZG; ut autem DA ad AZ, ita parallelogrammum <lb/>DK, seu KE, ad parallelogrammum KZ; ergo, ut quadratum ZG ad quadra&shy;<lb/>tum DE (ita quadratum AK ad quadratum AL) ita parallelogrammum AG <lb/>ad parallelogrammum KE. &rdquo; </s></p><p type="main">

<s>&ldquo; Similiter ostendemus reliqua parallelogramma LF, MH, NI, OB esse <lb/>inter se ut quadrata linearum AK, AL, AM, AN, AO, AP sese aequaliter <lb/>excedentium, et quorum excessus minimae AK est aequalis. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2208.jpg" pagenum="451"/><p type="main">

<s>&ldquo; Cum itaque sint huiusmodi spacia ut quadrata linearum sese aequa&shy;<lb/>liter excedentium, quarum excessus minimae est aequalis; si sint alia toti&shy;<lb/>dem numero, magnitudine vero unumquodque maximo OB aequalia, pa&shy;<lb/>rallelogrammum nempe CP componentia, constat haec ad spacia, a sese <lb/>aequaliter excedentium linearum, minora esse quam tripla. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Dico praeterea non esse minus parallelogrammum CP quam triplum, <lb/>ad idem spacium APB. </s>

<s>Si enim CP dicatur esse minus, sit defectus X, et <lb/>figura similiter inscr batur, constans ex parallelogrammis KQ, LR, MS, NT, <lb/>OU, quae sint ut quadrata linearum sese aequaliter excedentium etc., quae <lb/>deficiat a dicto spacio minori quantitate quam sit X (cum deficiat per mi&shy;<lb/>norem quam sit OB) quae erit adhuc maior quam tertia pars parallelogrammi <lb/>CP, quod pariter est falsum, cum sit minor. </s>

<s>&rdquo; (MSS. Gal., P. V, T. II, <lb/>fol. </s>

<s>102 a tergo). </s></p><p type="main">

<s>La conclusione, nel foglio che veniva a mancare, &egrave; taciuta, come quella <lb/>che occorrerebbe alla mente dei Lettori spontanea, perch&egrave; avendo provato <lb/>non poter essere il triangolo mistilineo ABP n&egrave; maggiore n&egrave; minore della <lb/>terza parte del parallelogrammo CP scendeva dunque senz'altro che do&shy;<lb/>vess'essere eguale. </s>

<s>Si collazioni ora di grazia questa dimostrazione con quella <lb/>inserita nel Dialogo, e che comprende quasi mezza la pagina 140, la 141, 42 <lb/>e un terzo della 143 dell'edizion dell'Alb&egrave;ri, e si vedr&agrave; quanto lo sminuz&shy;<lb/>zare le cose per renderle pi&ugrave; chiare noccia, in queste matematiche propo&shy;<lb/>sizioni, alla chiarezza. </s></p><p type="main">

<s>Che se di questa chiarezza l'ordine &egrave; causa principale la libert&agrave; del dia&shy;<lb/>logo a ogni passo l'infrange, e non &egrave; perci&ograve; maraviglia se, avendo Galileo <lb/>incominciato in margine a numerare le proposizioni, fa dopo l'VIII cessare <lb/>anche questa guida al Lettore. </s>

<s>Ne'quei numeri, giusto per far l'ufficio di <lb/>guida e d'indice, avrebbero reso piccolo servigio, specialmente in ramme&shy;<lb/>morare e in dovere ad altri indicar questo o quello dei dimostrati teoremi. </s>

<s><lb/>Un tal bisogno fu che consigliava al Viviani di proseguire a segnar sopra <lb/>la copia da lui postillata l'interrotta numerazione infino alla XV, perch&egrave; <lb/>spesso occorrevagli di citarle nell'esercitarsi che fece intorn&ograve; a quello stesso <lb/>argomento. </s>

<s>E perch&egrave; anche noi, nel dover dirne la storia, ci troveremo <lb/>nel medesimo caso, abbiam voluto condurre a termine la detta numera&shy;<lb/>zione, della quale intendiamo servirci per togliere ogni equivoco, e per <lb/>non esser costretti a ripeter sempre le formule, spesso spesso non brevi, <lb/>di Galileo. </s></p><p type="main">

<s>L'equivoco, che potrebbe nuocere alla chiarezza delle cose da dire, e <lb/>che perci&ograve; preme a noi di evitare, pu&ograve; nascer dal credere che si debbano <lb/>mettere in ordine tutte le proposizioni dimostrate, mentre Galileo stesso inco&shy;<lb/>minci&ograve; a numerar quelle sole attenenti alla meccanica delle resistenze, la&shy;<lb/>sciando indietro le altre di pura Geometria. </s></p><p type="main">

<s>Seguitando dunque anche noi quegli esempii, raccoglieremo qui ordi&shy;<lb/>nate le proposizioni o abbiano forma loro propria, o si trovino involte nel <lb/>conversevole discorso del Salviati. </s>

<s>Il primo dei numeri, che apponiamo a <pb xlink:href="020/01/2209.jpg" pagenum="452"/>ciascuna, appella alla edizione di Leida, e l'altro, che gli segue appresso, a <lb/>quella dell'Alb&egrave;ri. </s></p><p type="main">

<s>PROPOSIZIONE I. &mdash; &ldquo; Figuriamoci il prisma solido ABCD, fitto in un <lb/>muro dalla parte AB, e nell'altra estremit&agrave; s'intenda la forza del peso E:... <lb/>il momento della forza E, posta in C, al momento della resistenza, che ha <lb/>nella grossezza del prisma, ha la medesima proporzione che la lunghezza CB <lb/>alla met&agrave; della BA &rdquo; (114, 116). </s></p><p type="main">

<s>PROPOSIZIONE II. &mdash; &ldquo; Intendasi una riga AD, la cui lunghezza sia AC, <lb/>e la grossezza assai minore CB: si cerca perch&egrave;, volendola romper per ta&shy;<lb/>glio, resister&agrave; al gran peso T, ma posta per piatto non resister&agrave; all'X mi&shy;<lb/>nore del T &rdquo; (116, 118). </s></p><p type="main">

<s>PROPOSIZIONE III. &mdash; &ldquo; I momenti delle forze dei prismi o cilindri ugal&shy;<lb/>mente grossi, ma disegualmente lunghi, son tra di loro in duplicata pro&shy;<lb/>porzione di quella delle loro lunghezze &rdquo; (117, 119). </s></p><p type="main">

<s>PROPOSIZIONE IV. &mdash; &ldquo; Nei prismi e cilindri egualmente lunghi, ma <lb/>disegualmente grossi, la resistensa all'esser rotti cresce in triplicata propor&shy;<lb/>zione dei diametri delle loro grossezze, cio&egrave; delle loro basi &rdquo; (118, 119). </s></p><p type="main">

<s>PROPOSIZIONE V. &mdash; &ldquo; Dei prismi e cilindri, di diversa lunghezza e gros&shy;<lb/>sezza, le resistenze all'esser rotti hanno proporzione composta della propor&shy;<lb/>zione dei cubi de'diametri delle lor basi, e della proporzione delle loro <lb/>lunghezze, permutatamente prese &rdquo; (121, 122). </s></p><p type="main">

<s>PROPOSIZIONE VI. &mdash; &ldquo; Dei cilindri e prismi simili i momenti compo&shy;<lb/>sti, cio&egrave; resultanti dalle loro gravit&agrave; e dalle loro lunghezze, che sono come <lb/>leve, hanno tra di loro proporzione sesquialtera di quella, che hanno le re&shy;<lb/>sistenze delle medesime loro basi &rdquo; (122, 123). </s></p><p type="main">

<s>PROPOSIZIONE VII. &mdash; &ldquo; Dei prismi o cilindri simili gravi un solo e unico <lb/>&egrave; quello, che si riduce, gravato dal proprio peso, all'ultimo stato tra lo <lb/>spezzarsi e il sostenersi intero &rdquo; (124, 155). </s></p><p type="main">

<s>PROPOSIZIONE VIII. &mdash; &ldquo; Dato un cilindro o prisma di massima lun&shy;<lb/>ghezza, da non esser dal suo proprio peso spezzato, e data una lunghezza <lb/>maggiore, trovar la grossezza d'un altro cilindro o prisma che, sotto la <lb/>data lunghezza, sia l'unico e massimo resistente al proprio peso &rdquo; (125, <lb/>126). </s></p><p type="main">

<s>PROPOSIZIONE IX. &mdash; &ldquo; Dato il cilindro AC, qualunque si sia il suo mo&shy;<lb/>mento verso la sua resistenza, o data qualsiasi lunghezza DE, trovar la gros&shy;<lb/>sezza del cilindro, la cui lunghezza sia DE, e il suo momento verso la sua <lb/>resistenza ritenga la medesima proporzione, che il momento del cilindro AC <lb/>alla sua &rdquo; (128, 128). </s></p><p type="main">

<s>PROPOSIZIONE X. &mdash; &ldquo; Dato un prisma o cilindro col suo peso, ed il <lb/>peso massimo sostenuto da esso, trovare la massima lunghezza, oltre alla <lb/>quale prolungato, dal solo suo proprio peso si romperebbe &rdquo; (131, 131). </s></p><p type="main">

<s>PROPOSIZIONE XI. &mdash; &ldquo; Il cilindro, che gravato dal proprio peso sar&agrave; <lb/>ridotto alla massima lunghezza, oltre alla quale pi&ugrave; non si sosterrebbe, o <lb/>sia retto nel mezzo da un solo sostegno, ovvero da due nelle estremit&agrave;, po-<pb xlink:href="020/01/2210.jpg" pagenum="453"/>tr&agrave; essere lungo il doppio di quello che sarebbe fitto nel muro, cio&egrave; soste&shy;<lb/>nuto in un sol termine &rdquo; (132, 132). </s></p><p type="main">

<s>PROPOSIZIONE XII. &mdash; &ldquo; Se nella lunghezza d'un cilindro si noteranno <lb/>due luoghi, sopra i quali si voglia far la frazione di esso cilindro, le resi&shy;<lb/>stenze dei detti due luoghi hanno fra di loro la medesima proporzione, <lb/>che i rettangoli fatti dalle distanze di essi luoghi, contrariamente presi &rdquo; <lb/>(135, 135). </s></p><p type="main">

<s>PROPOSIZIONE XIII. &mdash; &ldquo; Dato il peso massimo retto dal mezzo di un ci&shy;<lb/>lindro o prisma, dove la resistenza &egrave; minima, e dato un peso maggiore di <lb/>quello, trovare nel detto cilindro il punto, nel quale il dato peso maggiore <lb/>sia retto come massimo &rdquo; (136, 136). </s></p><p type="main">

<s>PROPOSIZIONE XIV. &mdash; &ldquo; Il prisma, segato diagonalmente, ottiene contraria <lb/>natura del prisma intero, cio&egrave; che meno resiste all'essere spezzato sopra il <lb/>termine C, che sopra l'A, dalla forza posta in B, quanto la lunghezza CB <lb/>&egrave; minore della BA &rdquo; (138, 137). </s></p><p type="main">

<s>PROPOSIZIONE XV. &mdash; &ldquo; Nella faccia di un prisma sia segnata la linea pa&shy;<lb/>rabolica, secondo la quale sia segato esso prisma: dico tal solido esser per <lb/>tutto egualmente resistente &rdquo; (140, 139). </s></p><p type="main">

<s>PROPOSIZIONE XVI. &mdash; &ldquo; Le resistenze di due cilindri eguali ed egual&shy;<lb/>mente lunghi, l'uno dei quali sia vuoto e l'altro massiccio, hanno tra di loro <lb/>la medesima proporzione che i loro diametri &rdquo; (147, 145). </s></p><p type="main">

<s>PROPOSIZIONE XVII. &mdash; &ldquo; Data una canna vuota, trovare un cilindro <lb/>pieno uguale ad essa &rdquo; (148, 146). </s></p><p type="main">

<s>PROPOSIZIONE XVIII. &mdash; &ldquo; Trovare qual proporzione abbiano le resistenze <lb/>di una canna e di un cilindro, qualunque siano, purch&egrave; egualmente lun&shy;<lb/>ghi &rdquo; (148, 146). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Non oziosamente si disse avere il Viviani preso in mano il lapis, a pro&shy;<lb/>seguire la numerazione di queste proposizioni, ma per ridursele pi&ugrave; facil&shy;<lb/>mente alla memoria, e indicarle ne'suoi studiosi esercizii. </s>

<s>Abbiamo docu&shy;<lb/>mento certo che cominciarono questi esercizii infino dal 1644, e che vi ritorn&ograve; <lb/>sopra, interrompendo spesso l'opera sua, ma non intiepidendo nel suo primo <lb/>fervore. </s>

<s>Quel che via via gli occorreva a notare, si per ridurre le dottrine <lb/>del suo Maestro pi&ugrave; compiute e pi&ugrave; corrette, s&igrave; per applicarle a pi&ugrave; ampio <lb/>soggetto, rendendole di nuove o curiose o utili conseguenze feconde; scri&shy;<lb/>veva, secondo il suo solito, sopra foglietti sciolti, che poi alla rinfusa si rac&shy;<lb/>coglievano insieme in un inserto. </s>

<s>Erano materiali preziosi e abbondanti, per <lb/>comporre delle resistenze dei solidi un trattato perfetto, il quale per&ograve;, per i <lb/>casi della vita distratta in tante altre cure, e per l'indole propria dell'Autore, <lb/>si rimase per sempre informe, e se ne pot&egrave; poco giovare la scienza, e sola&shy;<lb/>mente dopo quelle lunghe avventure, che si narreranno in questa Storia. </s></p><pb xlink:href="020/01/2211.jpg" pagenum="454"/><p type="main">

<s>Intanto, nel 1661, Francesco Clousier pubblicava in Parigi una lettera <lb/>di Francesco Blondel, sottoscritta il di 12 Agosto 1657, e indirizzata a Paolo <lb/>Wrz &ldquo; in qua, dicevasi nel frontespizio, famosa Galilaei propositio discuti&shy;<lb/>tur circa naturam lineae, qua trabes secari debent, ut sint aequalis ubique <lb/>resistentiae, et in qua lineam illam, non quidem parabolicam, ut ipse Gali&shy;<lb/>laeus arbitratus est, sed ellipticam esse demonstratur. </s>

<s>&rdquo; </s></p><p type="main">

<s>La scoperta del Blondel era come un saggio, che si dava al pubbico <lb/>di studii pi&ugrave; ampii, fatti sopra Galileo, intantoch&egrave; ne aveva l'illustre Ma&shy;<lb/>tematico francese composto gi&agrave;, nel 1649, un libro <emph type="italics"/>De resistentia solidorum,<emph.end type="italics"/><lb/>ch'egli avrebbe voluto intitolare <emph type="italics"/>Galilaeus promotus.<emph.end type="italics"/> &ldquo; Ayant, scriveva in <lb/>un suo Discorso apologetico nel 1661, pour ce suiet compos<gap/> le livre, que <lb/>vous avez veu prest a estre donn<gap/> au public. </s>

<s>Il y a plus de douze ans, que <lb/>j'appelle <emph type="italics"/>Galilaeus promotus, De resistentia solidorum,<emph.end type="italics"/> et que pouvant quel&shy;<lb/>que jour estre mis en <gap/> miere &rdquo; (Recueil de plusieurs traietez de Mathem., <lb/>Paris 1673, pag. </s>

<s>60). Quel giorno per&ograve; non venne mai, e vedremo perch&egrave; <lb/>il Blondel revocasse quel suo primo fervoroso pensiero, com'attesta il Leib&shy;<lb/>niz in una sua lettera autografa al Grandi: &ldquo; Blondellus librum De resisten&shy;<lb/>tia solidorum composuerat, sed, re melius comperta, cum ego Parisiis age&shy;<lb/>rem, idest paulo post annum 1672, totum revocarat &rdquo; (MSS. Cim., T. XXIX, <lb/>fol. </s>

<s>287). Cosicch&egrave; non ebbe il pubblico degli studii del Blondel intorno alla <lb/>resistenza dei solidi altro che le proposizioni, nelle quali si dimostra esser <lb/>l'ellittico e no il parabolico il solido atto a resistere ugualmente per tutto <lb/>alla pressione di un peso. </s></p><p type="main">

<s>Se fossero, com'asserirono alcuni, queste dimostrazioni approdate per <lb/>tempo in Italia a dare impulso agli ingegni, non si potrebbe affermar con <lb/>certezza, ma non sembra che avesse il Viviani, per esempio, bisogno di tali <lb/>impulsi stranieri: e dall'altra parte, in mezzo a studii cos&igrave; primaticci e ope&shy;<lb/>rosi, era naturale gli si rivelasse spontaneo alla mente l'errore del Maestro, <lb/>dalle dottrine stesse insegnate dal quale concludevasi facilmente esser da <lb/>segar la trave, perch&egrave; ugualmente resista, non secondo il filo della parabola, <lb/>ma secondo quel dell'ellisse, e anzi di altre curve, e di quella stessa pa&shy;<lb/>rabolica, che si mettesse con la superficie terminata da lei in piano, piut&shy;<lb/>tosto che eretta. </s></p><p type="main">

<s>Professa di essersi condotto a queste medesime conclusioni Alessandro <lb/>Marchetti, non per altro impulso che per quello venutogli direttamente dalla <lb/>lettura del Dialogo galileiano, incominciata a farsi da lui con pi&ugrave; attenzione <lb/>nel 1659. &ldquo; Aveva io, egli dice, nello studiare il Galileo intorno alla ugual <lb/>resistenza del solido parabolico in ogni sua parte, osservato come da tal pro&shy;<lb/>posizione il Salviati, principale tra i personaggi dal medesimo Galileo intro&shy;<lb/>dotti a parlare in quel suo dialogo, deduce per corollario che potrebbero <lb/>fabbricarsi i travamenti delle navi con diminuzione di peso di pi&ugrave; di 33 <lb/>per cento, senza diminuire punto la loro gagliardia, al che, facendo io qual&shy;<lb/>che attenta e matura riflessione, e considerando che i suddetti travamenti <lb/>non si appoggiano a un sostegno solo, come il solido parabolico, del quale <pb xlink:href="020/01/2212.jpg" pagenum="455"/>esso Galileo aveva, poco innanzi la suddetta, ammiranda invero e del suo su&shy;<lb/>blime ingegno degnissima, propriet&agrave; dimostrato, ma vengon retti in ambe&shy;<lb/>due le loro estremit&agrave;, ancorch&egrave; io mi persuadessi che potesse esser vero, <lb/>che anche questi secondo la linea parabolica fossero in ogni lor parte egual&shy;<lb/>mente resistenti, per vederlo affermato con tanta franchezza da un s&igrave; gran&shy;<lb/>d'Uomo; pur nondimeno volli meglio certificarmene per mezzo di qualche <lb/>evidente dimostrazione, alla quale avendo io pi&ugrave; volte pensato e ripensato, <lb/>e non potendone venire a capo, incolpava da principio il corto mio inten&shy;<lb/>dimento, quasi che egli fosse incapace di penetrar col&agrave;, ove con una sola <lb/>occhiata della sua eccelsa mente aveva, col dedurre dalla detta proposizione <lb/>quel corollario, penetrato il divino ingegno del Galileo. </s>

<s>Ma disingannatomi <lb/>finalmente, e conosciuto, e con geometrica evidenza provato, che non il so&shy;<lb/>lido parabolico, sostenuto in ambedue i suoi estremi termini, non era per <lb/>tutto egualmente resistente, ma che di lui neanche verificavasi la suddetta <lb/>propriet&agrave;, quando viene appoggiato a un sostegno solo, se non in caso che <lb/>egli si consideri come nulla pesante (cosa che pu&ograve; ben da noi immaginarsi, <lb/>ma non giammai ottenersi, mettendo in opera le dette travi, per essere que&shy;<lb/>ste necessariamente materiali, e per&ograve; sempre congiunte col proprio peso) <lb/>presi animo, non solo di speculare o dimostrare alcune altre proposizioni a <lb/>tal materia appartenenti, ma di mandarle manoscritte, dalla mia villa di Pon&shy;<lb/>tormo, dove io allora mi ritrovava, a Firenze, al non mai lodato abbastanza <lb/>mio gran maestro G. A. Borelli, per sentirne da lui il suo dottissimo e sin&shy;<lb/>cerissimo parere. </s>

<s>Ed avendomi egli prontamente risposto, e non solo appro&shy;<lb/>vato le suddette proposizioni, ma consigliatomi di pi&ugrave; a specularne delle <lb/>nuove, io di buona voglia mi accinsi all'opera, quale, a dir vero, non senza <lb/>molto studio e fatica ridussi al fine desiderato &rdquo; (<emph type="italics"/>Lettera, nella quale si <lb/>ribattono le ingiuste accuse del P. D. G. G., Lucca 1711, pag. </s>

<s>27, 28<emph.end type="italics"/>). <lb/>La fatica per&ograve;, soggiungeva nella prefazione al libro da darsi alla luce, <lb/>essergli stata non poco alleviata dall'invenzione della composizion dei mo&shy;<lb/>menti, per la quale, se prima conveniva dare allo stesso libro il titolo di <lb/><emph type="italics"/>Galileo ampliato,<emph.end type="italics"/> ora poteva, senz'altro, sostituirglisi quello <emph type="italics"/>Della resistenza <lb/>dei solidi.<emph.end type="italics"/> &ldquo; Hinc haud immerito ex hoc libello expunctus titulus <emph type="italics"/>Galilaeus <lb/>ampliatus,<emph.end type="italics"/> eiusque vice iure substitutus <emph type="italics"/>De resistentia solidorum &rdquo;<emph.end type="italics"/> (Flo&shy;<lb/>rentiae 1669, pag. </s>

<s>IX). </s></p><p type="main">

<s>Messa dunque cos&igrave; in ordine l'opera laboriosa, si presenta un giorno <lb/>il Marchetti innanzi al cardinale Leopoldo, offerendogli il manoscritto, ed <lb/>esprimendogli il desiderio di dedicarne la stampa all'Eminenza Sua Sere&shy;<lb/>nissima. </s>

<s>Alla nuova l'animo del Viviani entr&ograve; in gran tumulto: egli va&shy;<lb/>gheggiava da lungo tempo il proposito di raccogliere in un volume tutte le <lb/>cose scritte a illustrar le dottrine del suo Maestro, specialmente attinenti <lb/>alle resistenze dei solidi, e premessavi la vita di Galileo dedicar tutto a <lb/>Luigi XIV di Francia, in riconoscenza dei ricevuti onori e delle munificenze. </s>

<s><lb/>L'opera del Marchetti avrebbe resa inutile, o solamente secondaria la mi&shy;<lb/>glior parte dell'opera sua, e non vedendo perci&ograve; altro rimedio al suo danno <pb xlink:href="020/01/2213.jpg" pagenum="456"/>va al Cardinale stesso, supplicandolo a interporre la sua autorit&agrave;, per otte&shy;<lb/>ner dal Marchetti la dilazione della stampa per alquanti mesi. </s>

<s>Il Marchetti, <lb/>soggiogato, tacque alla proposta, e s'intese che tacendo volesse acconsen&shy;<lb/>tire &ldquo; di che, scrisse poi, dal signor Lorenzo Bellini, e particolarmente dal <lb/>signor Gio. </s>

<s>Alfonso Borelli fui agramente ripreso &rdquo; (ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>Queste e altre simili espressioni darebbero gran fondamento al sospetto <lb/>che soffiasse, con enfiate guance, nella fiamma il Borelli, avido di vendetta <lb/>contro il Viviani, ch'egli accusava di avere stimolato, e concorso con lo Ste&shy;<lb/>none a prevenire, nella Miologia, la nuova Scienza dei moti animali. </s>

<s>Gli era <lb/>forse venuto alle orecchie che il Viviani stesso avesse presa, dalle resistenze <lb/>dei corpi duri, occasione d'entrare in argomento delle resistenze delle ossa <lb/>e delle membra, ci&ograve; che poi era il vero, com'apparisce da certe note, e spe&shy;<lb/>cialmente da quella, nella quale si propose: &ldquo; Consideretur magna vis in <lb/>impellendo, dum crura ad coxas angulos obtusos faciunt &rdquo; (MSS. Gal., P. V, <lb/>T. VII, fol. </s>

<s>38) rassomigliando la forza delle membra a quella stessa di un <lb/>legno, secondo un simile angolo inflesso. </s></p><p type="main">

<s>In qualunque modo, non s'intende a che pro rich&igrave;edere l'indugio di <lb/>alquanti mesi, quando, a dar forma all'opera, non sarebbero al Viviani ba&shy;<lb/>stati altrettanti anni: n&egrave;, risolvendosi ancora di porvi mano, pregava Carlo <lb/>Dati di tornare al principe Leopoldo, per veder di prolungare ancora di pi&ugrave; <lb/>quell'indugio. </s>

<s>Rispose il Principe sentir gran passione di questo negozio; <lb/>avrebbe fatto il possibile, ma che non voleva comandare. </s>

<s>Ci&ograve; che inteso il <lb/>Viviani depose affatto il pensiero, e, per provvedere in qualche modo alla <lb/>iattura, raccolse le sue carte in un fascio, e and&ograve; a farle riconoscere, con <lb/>la propria firma e con l'impression del sigillo, a Sua Altezza, &ldquo; il che, scri&shy;<lb/>veva allo stesso Marchetti, riuscir&agrave; di mia somma quiete e sodisfazione, per <lb/>poter far constar, con aprirlo a chi e quando occorresse, che io non m'era <lb/>mosso n&egrave; per iattanza, n&egrave; per impedire il proseguimento de'suoi intenti &rdquo; <lb/>(<emph type="italics"/>Lettera pubblicata dal Grandi nella Risposta apol., Lucca 1712, pag. </s>

<s>75<emph.end type="italics"/>). <lb/>Avvisava nel tempo stesso Francesco Blondel, ch'era allora in viaggio per <lb/>l'Italia, scrivesse al Colbert per quali penose avventure avea dovuto deporre <lb/>il pensiero di dedicare il libro su Galileo al Re di Francia. </s></p><p type="main">

<s>Un lampo fuggitivo venne poco dopo a rallegrare al Viviani la faccia <lb/>rannuvolata: la luce lusinghiera appariva attraverso alle parole di questa <lb/>lettera, che il Marchetti scriveva il d&igrave; 14 Febbraio 1668 al cardinale Leo&shy;<lb/>poldo: </s></p><p type="main">

<s>&ldquo; Tre mesi di proroga, domandatami dal signor Carlo Dati per ordine <lb/>di V. A. R. intorno alla pubblicazion del mio libro di resistenze, son gi&agrave; <lb/>spirati da molti giorni. </s>

<s>Ne d&ograve; parte, com'&egrave; mio debito, alla R. A. V. ed in&shy;<lb/>sieme la supplico vivamente, e con ogni maggiore ossequio di umilt&agrave;, a farlo <lb/>sapere al signor Viviani, acci&ograve;, se egli &egrave; all'ordine, come credo, con la sua <lb/>Opera, possiamo, con quelle condizioni e cautele che pi&ugrave; parranno conve&shy;<lb/>nevoli a V. A. R., dare ambedue principio unitamente alla stampa: se no, <lb/>io con buona grazia di V. A. R., e sotto il benigno auspicio del suo nome <pb xlink:href="020/01/2214.jpg" pagenum="457"/>gloriosissimo, comincer&ograve; ogni volta a stampare la mia, nella quale, per la&shy;<lb/>sciare anco libero il campo al signor Viviani di potere con suo comodo ed <lb/>a sua voglia ampliare le dottrine di Galileo, ed inserirle nella sua Vita, <lb/>com'ei desidera, tacer&ograve; il titolo di <emph type="italics"/>Galileo ampliato,<emph.end type="italics"/> n&egrave; mi servir&ograve; d'al&shy;<lb/>cuno principio di quel grand'uomo, come innanzi mi ero proposto, ma solo, <lb/>con fondamenti proprii miei, tratter&ograve;, senza pur farne alcuna menzione, della <lb/>resistenza dei corpi duri &rdquo; (MSS. Cim, T. XIX, fol. </s>

<s>144). </s></p><p type="main">

<s>Intese il Cardinale che il Marchetti si dichiarasse di voler trattar nel <lb/>suo libro materie non toccate da Galileo, cosicch&egrave;, essendo le opere dei due <lb/>concorrenti di argomento diverso, si potessero stampare ambedue insieme, <lb/>senza che l'una recasse all'altra nessun pregiudizio. </s>

<s>Lieto di veder che final&shy;<lb/>mente riusciva a buon termine il geloso negozio, ne di&egrave; sollecito avviso al <lb/>Viviani, il quale subito, con l'animo ravvivato, revocava cos&igrave; dal Blondel la <lb/>datagli commissione: &ldquo; Molto opportunamente risolse V. S. illustrissima di <lb/>non scrivere all'eccellentissimo signor Colbert intorno a quel suo partico&shy;<lb/>lare, se non dopo arrivato a Roma, poich&egrave;, con la medesima mia lettera e <lb/>sotto quella fede da lei promessami nel rimanente, devo dirle come in que&shy;<lb/>sti giorni il serenissimo Cardinale mi ha significato di aver avuto infallibile <lb/>certezza che quell'Amico ha variato affatto pensiero, e non tratta punto di <lb/>resistenze de'corpi duri, n&egrave; fa mai menzione del trattato di Galileo, e nem&shy;<lb/>meno lo nomina. </s>

<s>Tanto, e niente pi&ugrave; mi ha partecipato S. A., dicendo non <lb/>saper altro, onde, essendo cos&igrave;, non vedo che io debba qua far istanza di <lb/>sospensione, ma lascerolla uscire fuori, ed io da qui avanti, con l'animo che <lb/>V. S. illustrissima per sua bont&agrave; me ne ha dato, ripiglier&ograve; le fatiche di <lb/>quella <emph type="italics"/>Vita,<emph.end type="italics"/> e ander&ograve; seguitando ad ordinare e distendere il restante di quella <lb/>materia informe, che io le feci vedere &rdquo; (<emph type="italics"/>Lettera pubblicata dal Grandi <lb/>nella Risposta apol. </s>

<s>cit., pag. </s>

<s>83, 84<emph.end type="italics"/>). </s></p><p type="main">

<s>Un anno, e qualche mese dopo, vede il Viviani stesso comparirsi in&shy;<lb/>nanzi un libretto in ottavo, legato in foglio, sopravi scritto: <emph type="italics"/>dono dell'Au&shy;<lb/>tore,<emph.end type="italics"/> e, svolta per curiosit&agrave; la copertina, posa sul frontespizio gli occhi ran&shy;<lb/>nuvolati:.... era il trattato del Marchetti <emph type="italics"/>De resistentia solidorum,<emph.end type="italics"/> uscito <lb/>allora allora alla luce in Firenze dalla tipografia di Vincenzio Vangelisti. </s>

<s>Le <lb/>figure stesse intercalate nel testo gli rivelarono amaramente che il cardinale <lb/>Leopoldo aveva frantese l'espressioni del Marchetti, e ch'erano ambedue ri&shy;<lb/>masti ugualmente ingannati nel creder che non si trattasse l&igrave; n&egrave; di Gali&shy;<lb/>leo, n&egrave; di resistenze dei corpi duri. </s>

<s>Leggendo poi pi&ugrave; attentamente, e con <lb/>animo oramai rassegnato, ebbe anzi a maravigliarsi del riscontro che notava <lb/>fra le principali di quelle proposizioni e le sue proprie, intantoch&egrave;, come il <lb/>Blondel, vedute le cose del Viviani; cos&igrave; il Viviani stesso revoc&ograve; per sem&shy;<lb/>pre le sue, vedute le cose del Marchetti. </s></p><p type="main">

<s>Questa conclusione &egrave; tutt'affatto contraria a quella dei partigiani, un <lb/>dei quali pi&ugrave; infervorato di tutti, ammirava la mortificazione che allora fece <lb/>il Viviani stesso &ldquo; della curiosit&agrave;, che naturalmente nascer gli dovette nel <lb/>cuore, di leggere il trattato del Marchetti, e riscontrarlo nelle cose pi&ugrave; prin-<pb xlink:href="020/01/2215.jpg" pagenum="458"/>cipali, per sapere se in parte o in tutto l'avesse prevenuto, ed in qual modo <lb/>impugnasse lo sbaglio preso da Galileo &rdquo; (Grandi, Risposta apol. </s>

<s>cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Noi invece, vedendo che il Viviani abbandon&ograve; per sempre il proposito, con <lb/>s&igrave; fervorose espressioni ultimamente comunicate al Blondel, teniamo che ci&ograve; <lb/>non fosse n&egrave; per volubilit&agrave;, n&egrave; per ignavia, ma perch&egrave;, riscontrando il Mar&shy;<lb/>chetti nelle parti principali, conobbe che veramente lo aveva prevenuto, e che <lb/>s'era mirabilmente riscontrato seco nell'impugnare lo sbaglio preso da Galileo. </s></p><p type="main">

<s>Nello scolio infatti alla proposizione LXXXIII del I libro, l'Autore <emph type="italics"/>De <lb/>resistentia solidorum<emph.end type="italics"/> cos&igrave; scriveva: &ldquo; Hic fortasse non abs re erit animad&shy;<lb/>vertere quod, licet solidum parabolicum, abstrahendo a momento suae gra&shy;<lb/>vitatis, sit ubique aequalis resistentiae, quemadmodum in suis dialogis osten&shy;<lb/>dit Galileus, et nos etiam paulo inferius alia via ostensi sumus; si tamen <lb/>illius pondus consideretur, magis magisque semper resistit, quam magis ma&shy;<lb/>gisque peragendae fractionis locus eius vertici proximior est &rdquo; (Floren&shy;<lb/>tiae 1669, pag. </s>

<s>60). </s></p><p type="main">

<s>Le vie tenute dal Marchetti, per dimostrar che il solido parabolico, sup&shy;<lb/>posto senza peso, &egrave; di ugual resistenza, sono speditissime, e l&agrave; dove Galileo <lb/>premette un lemma e faticosamente, come vedemmo, s'aggira, il Marchetti, <lb/>col principio della composizion dei momenti gi&agrave; dimostrato, e dietro il di&shy;<lb/>mostrato teorema che i momenti delle resistenze delle sezioni, aventi basi <lb/>uguali e differenti altezze, stanno come i quadrati di esse altezze, cos&igrave;, in <lb/>due parole, conclude la sua proposizione. </s></p><p type="main">

<s>Sia il solido parabolico DB (fig. </s>

<s>236) e OB una sua parte: posto che <lb/><figure id="id.020.01.2215.1.jpg" xlink:href="020/01/2215/1.jpg"/></s></p><p type="caption">

<s>Figura 236<lb/>i pesi F, G equivalgano col loro mo&shy;<lb/>mento ai momenti delle resistenze delle <lb/>sezioni AD, CO, che chiameremo M.oAD, <lb/>M.oCO, abbiamo M.oAD:M.oCO= <lb/>F.AB:G.CB. </s>

<s>Ma per le cose dimo&shy;<lb/>strate M.oAD:M.oCO=AF2:NG2, e in <lb/>virt&ugrave; della parabola AF2:NC2=AB:CB, <lb/>dunque AB:CB=F.AB:G.CB. <lb/>&ldquo; Ergo F ad G, hoc est resistentia so&shy;<lb/>lidi DB, ad resistentiam solidi OB, proportionem habet aequalitatis &rdquo; (ibid.). <lb/><figure id="id.020.01.2215.2.jpg" xlink:href="020/01/2215/2.jpg"/></s></p><p type="caption">

<s>Figura 237</s></p><p type="main">

<s>Il Viviani a principio, non sapendosi distaccare <lb/>dalle orme di Galileo, aveva pensato di sostituire un <lb/>altro lemma, cos&igrave; intitolato da lui stesso e cos&igrave; scritto: <lb/><emph type="italics"/>&ldquo; Lemma pro propositione XV Galilei, pag. </s>

<s>140, ali&shy;<lb/>ter demonstranda, et ope infrascripti lemmatis ge&shy;<lb/>neralis:<emph.end type="italics"/> In parabola ABC (fig. </s>

<s>237), ductis ordina&shy;<lb/>tis AC, EF, et inter partes diametri CB, BE sumpta BH <lb/>media proportionalis, ductis BG, HI, semper erit ut AC <lb/>ad CG ita EF ad IH. </s>

<s>Nam recta CB ad BE, vel qua&shy;<lb/>dratum CB ad quadratum BH, est ut quadratum AC <lb/>ad quadratum EF. </s>

<s>Est etiam linea AC ad FE ut li-<pb xlink:href="020/01/2216.jpg" pagenum="459"/>nea CB ad BH, vel ut CG ad IH, et, permutando, AC ad CG ut EF ad IH, <lb/>quod erat etc. </s>

<s>&rdquo; (MSS. Gal., P. V, T. VII, fol. </s>

<s>54). </s></p><p type="main">

<s>Ma ebbe poi anche il Viviani a ritrovare non difficilmente quell'altra <lb/>macchina, della quale non era nessun'altra pi&ugrave; valida <emph type="italics"/>ad attollendam hanc <lb/>molem:<emph.end type="italics"/> e come il Marchetti, che proemiando cos&igrave; si esprimeva, erasi nelle <lb/>due prime proposizioni dell'uno e dell'altro libro accomodata cos&igrave; fatta mac&shy;<lb/>china ai bisogni; cos&igrave; avevasela al medesimo intento apparecchiata il Viviani <lb/>stesso in questo, ch'egli intitola <emph type="italics"/>Lemma generale:<emph.end type="italics"/> &ldquo; Se A (fig. </s>

<s>238) equi&shy;<lb/>libri B, e D equilibri C, sempre il peso A al peso D ha la ragion compo&shy;<lb/><figure id="id.020.01.2216.1.jpg" xlink:href="020/01/2216/1.jpg"/></s></p><p type="caption">

<s>Figura 238<lb/>sta della distanza GE alla EH, del <lb/>peso B al peso C, o resistenza B <lb/>alla C, e della distanza LF alla FI &rdquo; <lb/>(ivi, fol. </s>

<s>52). Possono vederne i Let&shy;<lb/>tori la dimostrazione trascritta nel <lb/>trattato del Grandi (Alb. </s>

<s>XIV, 16), ma <lb/>l'intralciato ragionamento si com&shy;<lb/>pendia e si dichiara per l'applica&shy;<lb/>zione delle propriet&agrave; generali della <lb/>Leva, dalle quali abbiamo A:B= <lb/>GE:EH; C:D=FL:FI. </s>

<s>Moltiplicate poi insieme queste due proporzioni, <lb/>e con l'identica B:C=B:C, danno A.B.C:B.C.D, ossia A:D= <lb/>GE.B.LF:HE.C.FI, com'erasi proposto di dimostrare il Viviani. </s></p><p type="main">

<s>Deduce da questo il Viviani stesso un altro Lemma pi&ugrave; particolare, per <lb/>servire all'uso di quelle dimostrazioni, da trattarsi specialmente con la teo&shy;<lb/><figure id="id.020.01.2216.2.jpg" xlink:href="020/01/2216/2.jpg"/></s></p><p type="caption">

<s>Figura 239<lb/>ria dei momenti, ed &egrave; cos&igrave; formu&shy;<lb/>lato: &ldquo; Se saranno le due libbre <lb/>AB, CD (fig. </s>

<s>239) coi sostegni E, <lb/>F, e con le contralleve AE, CF <lb/>eguali tra loro, e con i pesi e re&shy;<lb/>sistenze G, H, che tra loro stiano <lb/>come le leve EB, FD omologa&shy;<lb/>mente; dico che, se in B, D si <lb/>appenderanno i pesi I, L, che equi&shy;<lb/>librino le resistenze G, H; che i <lb/>detti pesi I, L saranno uguali &rdquo; (ivi, fol. </s>

<s>66). La dimostrazione, che s'ha <lb/>trascritta dal Grandi nel luogo citato, pag. </s>

<s>17, si conduce direttamente e <lb/>con gran facilit&agrave; dagli stessi principii della Leva, i quali danno I:G= <lb/>AE:EB; L:H=CF:FD. </s>

<s>Ma per supposizione G:H=EB:FD, dun&shy;<lb/>que I:L=AE:CF. </s>

<s>E pure &egrave; per supposizione AE=CF, dunque I=L. </s></p><p type="main">

<s>Ora, dietro queste dimostrate propriet&agrave; generali del momento dei pesi <lb/>nella Libbra, e dietro la proposizione III di Galileo, dalla quale avevasi per <lb/>facile corollario che i moment&igrave; delle sez&igrave;oni ugualmente larghe e differen&shy;<lb/>temente alte stanno come i quadrati delle altezze; ecco come il Viviani, mo&shy;<lb/>vendo dai principii medesimi posti gi&agrave; dal Marchetti, fosse proceduto con <pb xlink:href="020/01/2217.jpg" pagenum="460"/>maraviglioso riscontro per le medesime vie di lui, e fosse giunto perci&ograve;, ben&shy;<lb/>ch&egrave; con pi&ugrave; complicato discorso, alle medesime conclusioni: In un foglio, <lb/>inserito poi tra la pag. </s>

<s>140 e 141 della pi&ugrave; volte citata edizione di Leida, <lb/>postillata dal Viviani, il postillatore cos&igrave; di sua propria mano aveva scritto: <lb/><emph type="italics"/>Per la faccia 240 della prima edizione di Leida; la proposizione del so&shy;<lb/>lido parabolico senza bisogno del Lemma:<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Il momento della resistenza della sezione AD (fig. </s>

<s>240) a quello della <lb/>CO, ha la proporzione composta della sezione AD alla CO, ovvero dell'al&shy;<lb/>tezza AF all'altezza CN, e della leva della AD, alla leva della CO, ovvero <lb/><figure id="id.020.01.2217.1.jpg" xlink:href="020/01/2217/1.jpg"/></s></p><p type="caption">

<s>Figura 240<lb/>della medesima AF alla CN. </s>

<s>Ma tali due <lb/>proporzioni compongono quella del qua&shy;<lb/>drato AF al quadrato CN, cio&egrave; della <lb/>leva BA alla BC; adunque il momento <lb/>della resistenza della sezione AD, al mo&shy;<lb/>mento della resistenza della sezione CO, <lb/>sta come la leva BA alla leva BC, o <lb/>come il momento di un grave appeso <lb/>in B dalla distanza BA, al momento del <lb/>medesimo grave appeso in B dalla distanza BC. E, permutando, il momento <lb/>della resistenza della sezione AD, al momento di un grave appeso in B, dalla <lb/>distanza BA, sta come il momento della resistenza della sezione CO, al mo&shy;<lb/>mento del medesimo grave appeso in B dalla distanza BC. &rdquo; </s></p><p type="main">

<s>&ldquo; Se dunque sar&agrave; appeso in B, dalla distanza BA, un grave, il di cui <lb/>momento pareggi appunto il momento della resistenza della sezione AD, an&shy;<lb/>che il momento del medesimo grave, appeso in B dalla distanza BC, pareg&shy;<lb/>ger&agrave; il momento della resistenza della sezione CN. </s>

<s>E perci&ograve; questo solido <lb/>parabolico, nel considerarlo senza peso, si pu&ograve; dire che sia per tutto ugual&shy;<lb/>mente resistente, perch&egrave; tanto il momento della resistenza della maggior se&shy;<lb/>zione AD, quanto quello di ogni altra minore sezione CO, &egrave; pareggiato dal <lb/>momento di un medesimo grave assoluto posto in B, or dalla distanza BA, <lb/>ed ora dalla distanza BC. Onde, per render vera la proposizione del Galileo <lb/>posta a faccia 140, basta considerare che quel suo solido parabolico sia senza <lb/>peso, e che i varii momenti della resistenza delle sue varie sezioni sian posti <lb/>a cimento dei movimenti di un medesimo grave assoluto appeso alle estre&shy;<lb/>mit&agrave; delle lunghezze, che stanno fuori del muro. </s>

<s>&rdquo; (MSS. Gal., P. V, T. IX). </s></p><p type="main">

<s>Ecco, come il Viviani avesse <emph type="italics"/>impugnato la sbaglio di Galileo:<emph.end type="italics"/> nel cor&shy;<lb/>regger poi questo sbaglio erano pure proceduti ambedue gli Autori, incon&shy;<lb/>sapevoli, nello stessissimo modo. </s>

<s>In un altro foglietto infatti, inserito nella <lb/>citata copia di Leida, e propriamente applicato alla pag. </s>

<s>141, il Viviani stesso <lb/>cos&igrave; aveva scritto: </s></p><p type="main">

<s>&ldquo; Pongasi ora che tal solido parabolico AFDOG (nella precedente figura) <lb/>sia con peso, ora fuori del muro quanto AB, ora quanto CB. </s>

<s>Il momento <lb/>della resistenza della sezione AD, al momento della resistenza della sezione <lb/>CO, sta come il quadrato AF al quadrato CN. </s>

<s>Ma il momento del grave so-<pb xlink:href="020/01/2218.jpg" pagenum="461"/>lido ADGB, al momento del grave COGB, avendo ragion composta di quella <lb/>fra il solido e il solido, cio&egrave; del cubo AF al cubo CN, e di quella della leva <lb/>AB alla leva BC, cio&egrave; di quella del quadrato AF al quadrato CN, le quali <lb/>due ragioni compongono quella del quadrato cubo AF al quadrato cubo CN, <lb/>e la proporzione del quadrato AF al quadrato CN &egrave; suddupla sesquialtera <lb/>del quadrato cubo AF al quadrato cubo CN; adunque anche la proporzione <lb/>del momento della resistenza della sezione AD, al momento della resistenza <lb/>della sezione CO, &egrave; suddupla sesquialtera della proporzione del momento del <lb/>grave solido FAG, al momento del grave solido NCG &rdquo; (ivi). </s></p><p type="main">

<s>La conclusione di questo teorema dipende manifestamente da due prin&shy;<lb/>cipii: il primo dei quali, chiamati M.oAD, M.oOC i momenti delle resistenze <lb/>delle due sezioni, &egrave; espresso dall'equazione M.oAD:M.oOC=AF2:CN2, <lb/>che corrisponde precisamente con la LXXXII del Marchetti, bench&egrave; si met&shy;<lb/>tano le ascisse, ossia le lunghezze in luogo dei quadrati delle ordinate: &ldquo; So&shy;<lb/>lidi parabolici, et ex eo abscissae portionis momenta resistentiarum sunt inter <lb/>se ut longitudines &rdquo; (De resistentia solid. </s>

<s>cit., pag. </s>

<s>57). </s></p><p type="main">

<s>L'altro principio premesso dal Viviani &egrave; che i momenti del solido pa&shy;<lb/>rabolico e della sua parte stanno come le quinte potenze delle basi, o delle <lb/>loro altezze, avendo le larghezze uguali, ci&ograve; che corrisponde pure esatta&shy;<lb/>mente con la LXXXIII dello stesso Marchetti: &ldquo; Solidi parabolici, et ex eo <lb/>abscissae portionis momenta ponderum sunt in quintupla proportione basis <lb/>ad basim &rdquo; (ibid., pag. </s>

<s>58): che vuol dire, chiamati M.oS, M.oS&prime; i momenti <lb/>di tutto il solido e della sua porzione, M.oS:M.oS&prime;=AF5:CN5. </s>

<s>Inalzata <lb/>ora questa a quadrato, e l'altra dei momenti delle resistenze delle sezioni <lb/>alla quinta potenza, si ha M.oAD5:M.oCO5=M.oS2:M.oS2, ossia M.oAD: <lb/>M.oCO=M.oS2/5:M.oS&prime;2/5, che &egrave; la proporzion <emph type="italics"/>suddupla sesquialtera<emph.end type="italics"/> se&shy;<lb/>condo la conclusion del Viviani; o anche M.oS:M.oS&prime;=M.oAD5/2:M.oCO5/2, <lb/>che &egrave; la ragion <emph type="italics"/>dupla sesquialtera,<emph.end type="italics"/> sotto la qual forma, dalle due citate pro&shy;<lb/>posizioni LXXXII e LXXXIII, concludesi cos&igrave; la medesima verit&agrave; dal Mar&shy;<lb/>chetti: &ldquo; Ex duabus hisce propositionibus facile elicitur Solidi parabolici, et <lb/>ex eo abscissae portionis momenta ponderum esse inter se in dupla sesquial&shy;<lb/>tera proportione momentorum resistentiarum &rdquo; (ibid., pag. </s>

<s>59). </s></p><p type="main">

<s>Passando a esaminare altre parti di minore curiosit&agrave;, o di minore im&shy;<lb/>portanza, ebbe pure a trovare il Viviani, tra le proposizioni del Marchetti e <lb/>le sue, simili riscontri, che lo fecero con tranquillo animo e con sereno giu&shy;<lb/>dizio finalmente persuaso essere per riuscire superflua, almeno nella so&shy;<lb/>stanza, l'opera sua, dopo quella del suo rivale. </s>

<s>Altre parti del suo ingegno, <lb/>non per questo avvilito n&egrave; stanco, dedicherebbe, in rendimento di grazie, <lb/>al Re di Francia, e dignitosamente ritiratosi cos&igrave; da parte pose fine alla <lb/>controversia. </s></p><pb xlink:href="020/01/2219.jpg" pagenum="462"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Sui principii del secolo XVIII, quando gi&agrave; il Viviani dormiva da sette <lb/>anni nel sonno della pace, si risvegli&ograve; quel fuoco che, non sopito ma spento <lb/>oramai, si credeva sotto le ceneri del sepolcro. </s>

<s>Fu Guido Grandi che rinfo&shy;<lb/>col&ograve; quelle ire, mostrando di aver sotto la cappa del monaco nascosta la <lb/>spada per difendere il suo Maestro, come ei diceva, ma veramente per of&shy;<lb/>fendere il Marchetti, nell'insegnamento delle Matematiche nello Studio pi&shy;<lb/>sano, suo rivaleggiante collega. </s>

<s>Nel 1710 pubblicava esso Grandi per la se&shy;<lb/>conda volta un libro intitolato <emph type="italics"/>Quadratura circuli et hyperbolae,<emph.end type="italics"/> nella <lb/>prefazione al quale, fra i varii esempii di Matematici illustri, che inconsa&shy;<lb/>pevoli s'erano riscontrati nelle medesime conclusioni, cita anche quello del <lb/>Marchetti, il quale, nel dimostrare la composizion dei momenti si riscontr&ograve; <lb/>con Galileo, col Cavalieri e col Torricelli, e nel trattare delle resistenze dei <lb/>solidi col Blondel &ldquo; qui idem Galilaei sphalma de solido parabclico aequalis <lb/>ubique resistentiae, etiam cum utrimque fulcitur, prior detexit &rdquo; (ibid., <lb/>pag. </s>

<s>XIII). </s></p><p type="main">

<s>L'orlo della coppa, se non esalava le fragranze del buon liquore, non <lb/>mandava per&ograve; il fetor del veleno, che raccoglieva nel fondo, e che dalle <lb/>esperte narici del Marchetti fu troppo bene sentito. </s>

<s>Incominci&ograve; a lamentar&shy;<lb/>sene con gli amici, e fece, perch&egrave; circolasse in Corte, innanzi alla quale <lb/>massimamente gli doleva di venire accusato, per essere il libro della Qua&shy;<lb/>dratura del circolo dedicato al principe Gian Gastone; una scrittura per di&shy;<lb/>mostrare che in verit&agrave; non aveva tolto nulla n&egrave; dal Cavalieri n&egrave; dal Blon&shy;<lb/>dello. </s>

<s>Il Principe e i cortigiani al gran romore che ogni giorno cresceva pi&ugrave; <lb/>levarono le orecchie, e per intendere il diritto o il torto di questa lite si <lb/>rivolsero al Grandi, che ne scrisse perci&ograve; la seguente <emph type="italics"/>Informatione:<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Il signor dottore Alessandro Marchetti, da due passi dell'Opera del <lb/>p. </s>

<s>Grandi, ultimamente stampata e dedicata al serenissimo principe Giovan <lb/>Gastone, piglia motivo di lamentarsi e tenersi offeso: L'uno &egrave; nella prefa&shy;<lb/>zione, pag. </s>

<s>XII, &sect; <emph type="italics"/>Nonnulli,<emph.end type="italics"/> e l'altro &egrave; verso il mezzo dell'Opera da pag. </s>

<s>29 <lb/>a pag. </s>

<s>34. &rdquo; </s></p><p type="main">

<s>&ldquo; Pretende nel primo luogo che il p. </s>

<s>Grandi abbia voluto far credere <lb/>che l'opera <emph type="italics"/>De resistentia solidorum<emph.end type="italics"/> del suddetto signor Marchetti fosse da <lb/>altri rubata. </s>

<s>Al che risponde il p. </s>

<s>Grandi non esser mai stata questa la sua <lb/>intenzione, n&egrave; potersi ci&ograve; dedurre dalle sue parole: anzi apparire il contra&shy;<lb/>rio dallo stesso contesto. </s>

<s>Persino nella prima stampa di quest'Opera aveva <lb/>il p. </s>

<s>Grandi asserito che, in materie matematiche, <expan abbr="&emacr;ra">erra</expan> facilissimo che gli <lb/>Autori s'incontrassero nel dire le medesime cose, come confessa essere tal&shy;<lb/>volta a lui stesso avvenuto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In questa nuova impressione aveva motivo di mostrare ci&ograve; pi&ugrave; evi&shy;<lb/>dentemente con varii esempii. </s>

<s>Fra questi, dop'aver nominato mons&ugrave; di Fer-<pb xlink:href="020/01/2220.jpg" pagenum="463"/>mat, il signor Viviani, il Guldino e Grogorio di S. Vincenzio, nomina con <lb/>lode il signor Marchetti, chiamandolo <emph type="italics"/>praeclarum illum Poetam, nostrique <lb/>pisani Licei Mathematicum,<emph.end type="italics"/> ed accennando alla sfuggita il Teorema del <lb/>momento dei gravi, che si era attribuito, e che poi il Viviani fece vedere <lb/>pubblicamente che prima era stato detto da Galileo, dal Cavalieri, da Anto&shy;<lb/>nio Rocca e dal Torricelli; difende che ci&ograve; potesse accadere, senza che possa <lb/>sospettarsi averlo egli dai suddetti rubato, <emph type="italics"/>cum tamen id citra ullam plagii <lb/>suspicionem eventus facillime suadeat. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Poi passa al libro <emph type="italics"/>De resistentia solidorum<emph.end type="italics"/> di esso Marchetti, dove <lb/>questi cerca di confutare una proposizione di Galileo, e correggerne lo sba&shy;<lb/>glio preso in tal materia da quel grand'Uomo, il che dice il p. </s>

<s>Grandi es&shy;<lb/>sere stato stampato otto anni prima da mons&ugrave; Blondel, che lo stesso sba&shy;<lb/>glio scopr&igrave;, e lo emend&ograve; allo stesso modo; e dice che dodici anni avanti <lb/>avea per ci&ograve; scritto un volume <emph type="italics"/>De resistentia solidorum<emph.end type="italics"/> intitolato <emph type="italics"/>Galilaeus <lb/>promotus,<emph.end type="italics"/> che il Marchetti dice nella sua prefazione aver egli prima posto <lb/>al suo libro, e sotto il qual nome fu dal Rossetti citato: cose tutte di fatto <lb/>indubitabile, e che pu&ograve; mostrarsi co'libri allora stampati. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quindi passa ad altri esempii, da m. </s>

<s>Ischyrnhausen, m. </s>

<s>Wallis, m. </s>

<s>Leib&shy;<lb/>niz, m. </s>

<s>De l'Hopital, m. </s>

<s>Parent, al p. </s>

<s>Intieri, e finalmente si dichiara di non <lb/>essere stata sua intenzione di pregiudicare perci&ograve; in nulla alla gloria di quei <lb/>celebratissimi Uomini, con queste parole, che sono a pag. </s>

<s>XV: <emph type="italics"/>Cum autem <lb/>nihil inventionis gloriae praeiudicet quod quis se ab aliis praeoccupatum <lb/>deprehendat, quia semper invenisse acum&igrave;nis est, primum invenisse for&shy;<lb/>tunae; non erit opinor qui haec a me superius notata fuisse suspicetur, <lb/>ut clarissimorum virorum inventis quidquam propterea detraherem, sed <lb/>unice ut facilem hunc in rebus geometricis consensum pluribus exemplis <lb/>confirmarem.<emph.end type="italics"/> Dal che &egrave; chiarissimo non essere stata intenzione del p. </s>

<s>Grandi <lb/>n&egrave; di offendere in ci&ograve; il Marchetti, n&egrave; di pregiudicargli in conto alcuno, n&egrave; <lb/>di asserire che quel libro fosse da lui rubato: il che non sarebbe stato a <lb/>proposito del suo argomento, che era solo dell'incontrarsi casualmente i <lb/>Matematici nel dire le medesime cose. </s>

<s>&rdquo; (MSS. Cim., T. XXIX, fol. </s>

<s>311, 12). </s></p><p type="main">

<s>Accompagnava il Grandi questa Informazione con una sua lettera, scritta <lb/>il d&igrave; 22 Maggio 1711 da Pisa, nella quale, detto di aver risaputo della scrit&shy;<lb/>tura che il Marchetti avea sparsa nella Corte medicea, con intenzione di farla <lb/>stampare, soggiungeva riserbarsi per&ograve; &ldquo; di rispondere pi&ugrave; individualmente <lb/>alle sue querele, quando avr&ograve; fortuna di vedere la sopra nominata Scrit&shy;<lb/>tura, e di difendere que'passi, ch'egli pretende di accusare di errore &rdquo; <lb/>(ivi, fol. </s>

<s>303). </s></p><p type="main">

<s>Dopo pochi mesi usciva quella desiderata Scrittura in pubblico da Lucca, <lb/>in forma di Lettera dedicata a Bernardo Trevisano, che, procuratore di <lb/>S. Marco, era uso con <emph type="italics"/>ragione e con dritto a librar l'altrui colpa e il <lb/>merto. (Sonetto premesso alla Lettera).<emph.end type="italics"/> Rispondeva contro le accuse del <lb/>Grandi che, quanto alla composizion dei momenti, era verissimo che il Ca&shy;<lb/>valieri l'aveva dimostrata prima di lui, &ldquo; con altro metodo per&ograve; diverso, <pb xlink:href="020/01/2221.jpg" pagenum="464"/>egli dice, dal mio, e senza che in quel tempo veduto avessi la sua dimo&shy;<lb/>strazione &rdquo; <emph type="italics"/>(Lettera nella quale si ribattono le accuse date dal P. D. G. G., <lb/>Lucca 1711, pag. </s>

<s>20).<emph.end type="italics"/> Per quel poi particolarmente riguarda il Blondel, <lb/>reca documenti a provar ch'egli avea gi&agrave;, infino dal 1659, notato lo sbaglio <lb/>di Galileo, due anni prima che il Matematico francese pubblicasse la sua <lb/>Epistola al Vulzio. </s>

<s>Quanto poi al <emph type="italics"/>Galileo promoto<emph.end type="italics"/> del medesimo Autore, non <lb/>essendo stato mai pubblicato &ldquo; come poteva io, ne conclude il Marchetti <lb/>stesso, averlo veduto, n&egrave; pure avutone alcun sentore, ond'io potessi pi&shy;<lb/>gliarne, non dir&ograve; i pensieri e le dimostrazioni, ma n&egrave; anche lo stesso ti&shy;<lb/>tolo? </s>

<s>&rdquo; (ivi, pag. </s>

<s>23). </s></p><p type="main">

<s>A un animo generoso, e non punto pregiudicato, sarebbero dovute que&shy;<lb/>ste risposte bastare per buone ragioni, ma il Grandi, lette per le pubbliche <lb/>stampe queste cose, mand&ograve; ad effetto la promessa di <emph type="italics"/>rispondere indivi&shy;<lb/>dualmente alle querele,<emph.end type="italics"/> pubblicando in Lucca nel 1712 un libro intitolato <lb/><emph type="italics"/>Risposta apologetica alle apposizioni fatte dal signor Alessandro Marchetti, <lb/>nella sua Lettera diretta a Bernardo Trevisano.<emph.end type="italics"/> Fu allora che tir&ograve; fuori <lb/>l'arme rimasta, nella prefazione al libro <emph type="italics"/>Della quadratura del circolo,<emph.end type="italics"/> ar&shy;<lb/>tificiosamente coperta sotto il finto velo delle parole, e non solo conferm&ograve; <lb/>contro il Marchetti le accuse di plagio, ma soggiunse che in quell'avevaci <lb/>di suo era tutto pieno di errori. </s>

<s>Il Marchetti usc&igrave; a fare le sue difese in <lb/>un Discorso, diretto al medesimo Trevisano, e pubblicato in Lucca nel 1714, <lb/>dimostrando come gli errori fossero da attribuirsi piuttosto al suo avversario. </s></p><p type="main">

<s>L'importanza dell'argomento non ci dispensa dall'entrar giudici in que&shy;<lb/>sta lite, ma prima vogliam dire che, secondo per lo pi&ugrave; avviene fra i liti&shy;<lb/>ganti, anche fra questi due fu l'ultimo a tacere colui che aveva meno ra&shy;<lb/>gione. </s>

<s>E perch&egrave; tale all'imparzial nostro giudizio apparisce il Grandi, egli, <lb/>non perdonando al sepolcro, riepilog&ograve; le irragionevoli accuse quattro anni <lb/>dopo la morte del Marchetti, quando nel 1718 compil&ograve; le informi note del <lb/>Viviani nel trattato <emph type="italics"/>Delle resistenze.<emph.end type="italics"/> Siam perci&ograve; dal filo dell'argomento <lb/>condotti a dire di una tale compilazione, e prima di tutto dei motivi che <lb/>s'ebbe di farla, risalendo cos&igrave; ai principii col nostro discorso. </s></p><p type="main">

<s>Quando il Viviani protest&ograve; al Marchetti di aver levato affatto il pen&shy;<lb/>siero di concorrere con lui, prima di avere in quella medesima Lettera detto <lb/>del deposito delle sue carte nelle mani del principe Leopoldo, che le sot&shy;<lb/>toscrisse e le leg&ograve;, fermandone la legatura col suo sigillo; aveva asserito <lb/>che molte di quelle conclusioni le aveva gi&agrave; comunicate a pi&ugrave; d'uno, che <lb/>pur vive, e che erano ventitre o ventiquattr'anni che aveva cominciato ad <lb/>applicar la mente a quelle discipline, quando lui che veniva ora a concor&shy;<lb/>rere seco era tuttavia fanciullo. </s></p><p type="main">

<s>Le affermazioni erano sincere, e si pu&ograve; per prima loro testimonianza <lb/>citare il Magalotti, il quale si gloriava cos&igrave; dicendo: &ldquo; Per tre anni ebbi in <lb/>sorte di essere tosoriere de'preziosi concetti del signor Vincenzio Viviani, <lb/>onde appresso di lui <emph type="italics"/>si trovan molte gioie care e belle,<emph.end type="italics"/> che nelle opere <lb/>stampate del Galileo non si veggono, e che ben presto verranno in luce &rdquo; <pb xlink:href="020/01/2222.jpg" pagenum="465"/><emph type="italics"/>(Lettere scientifiche ed erudite, Firenze 1721, pag. </s>

<s>2).<emph.end type="italics"/> S'accenna in que&shy;<lb/>ste parole, che dovettero essere scritte nel 1668, evidentemente al trattato <lb/>Delle resistenze, per conferma di che, e dell'aver veramente veduto un tale <lb/>trattato, il Magalotti, in quella sua prima Lettera scientifica, applica alcuni prin&shy;<lb/>cipii ivi supposti, e una proposizione ivi pur dimostrata, per risolvere al priore <lb/>Orazio Rucellai, che glielo aveva proposto, il problema: perch&egrave; in tempo <lb/>di neve si fiacchino pi&ugrave; facilmente i rami agli ulivi, e a simili altre piante. </s></p><p type="main">

<s>I villici attribuivano il caso, osservato giusto in que'giorni in certe pos&shy;<lb/>sessioni del Rucellai, alla neve venuta a piombo, ma il Megalotti, sovvenen&shy;<lb/>dosi di aver letto nei fogli manoscritti del Viviani &ldquo; che la cedenza della <lb/>materia dei solidi altera la proporzione delle loro resistenze, a segno tale <lb/>che un medesimo ferro sar&agrave; ora pi&ugrave; ora meno resistente, secondo la diffe&shy;<lb/>renza della tempera &rdquo; (MSS. Gal., P. V, T. VII, fol. </s>

<s>29) applic&ograve; questo prin&shy;<lb/>cipio ai rami degli ulivi con dire che, avendo il freddo altrerata la loro tem&shy;<lb/>pera, ne aveva fatto altres&igrave; variare i momenti delle resistenze. </s>

<s>Rassomigliava <lb/>poi cos&igrave; fatte alterazioni, prodotte dal freddo nel legno, alle alterazioni pro&shy;<lb/>dotte dall'argento vivo, che penetra dentro l'oro, e come questo, ridotto per <lb/>esempio in forma di cilindro e ficcato nel muro, resisterebbe al proprio peso <lb/>alquant&ograve; meno di un altro cilindro uguale, ma di oro schietto; cos&igrave; per so&shy;<lb/>miglianza affermava che, meno dei naturali, resistono allo spezzarsi i rami <lb/>penetrati dal freddo. </s></p><p type="main">

<s>Volendo ora il Magalotti dare ad intendere la proporzion delle varia&shy;<lb/>zioni di cos&igrave; fatte resistenze, comparate con quelle dei cilindri dell'oro, ora <lb/>puro, ora alterato nella sua naturale gravit&agrave; in specie, per l'inzuppamento <lb/>dell'argento vivo; dice che si potrebbero in ambedue i casi reggere i detti <lb/>solidi da s&egrave; stessi, purch&egrave; &ldquo; il quadrato della lunghezza del cilindro del&shy;<lb/>l'oro inzuppato, al quadrato della lunghezza del cilindro dell'oro puro, stia <lb/>reciprocamente come la gravit&agrave; in specie dell'oro puro, alla gravit&agrave; in spe&shy;<lb/>cie dell'oro inzuppato, siccome dimostra il signor Vincenzio Viviani &rdquo; (Let&shy;<lb/>tere cit., pag. </s>

<s>7). </s></p><p type="main">

<s>Il Grandi, ne'manoscritti ch'ebbe a mano, ritrov&ograve; sotto questa forma, <lb/>del teorema, il semplice enunciato: <emph type="italics"/>Allora i cilindri orizzontalmente fitti <lb/>nel muro, che sieno d'uguale grossezza, ma di differente gravit&agrave; in spe&shy;<lb/>cie, sono d'egual momento verso le loro resistenze, quando i quadrati <lb/>delle loro lunghezze hanno reciproca proporzione delle gravit&agrave; in specie, <lb/>ovvero che le lunghezze hanno reciproca proporzione delle gravit&agrave; asso&shy;<lb/>lute<emph.end type="italics"/> (Alb. </s>

<s>XIV, 31). Il Compilatore suppl&igrave; di suo alla dimostrazion che man&shy;<lb/>cava, ma che il Magalotti attesta essere stata fatta, e noi, dietro gl'indizii <lb/>di lui, crediamo che facilmente procedesse cos&igrave;, in maniera forse pi&ugrave; con&shy;<lb/>forme col rimanente di quella ivi suggerita dallo stesso Grandi: </s></p><p type="main">

<s>Sia GF (fig. </s>

<s>241) la sezione del cilindro dell'oro puro, HM quella dello <lb/>inzuppato, che manterr&agrave; nonostante uguale grossezza. </s>

<s>Si vuol sapere qual <lb/>proporzione debbano avere le lunghezze massime EF, IM verso i pesi asso&shy;<lb/>luti o in specie, a cui que'solidi han da resistere. </s></p><pb xlink:href="020/01/2223.jpg" pagenum="466"/><p type="main">

<s>Applicato al centro di gravit&agrave; B il peso P, la resistenza sar&agrave; P.AB, <lb/>come pure, applicato al centro D il peso P&prime;, la resistenza sar&agrave; P&prime;.CD. Ora, <lb/>perch&egrave; debbono queste due resistenze respettive essere eguali, avremo P:P&prime;= <lb/><figure id="id.020.01.2223.1.jpg" xlink:href="020/01/2223/1.jpg"/></s></p><p type="caption">

<s>Figura 241<lb/>CD:AB=IM:EF, che vuol dire che le <lb/>lunghezze hanno ragion reciproca dei pesi <lb/>assoluti. </s>

<s>Chiamati poi V, V&prime; i volumi dei <lb/>due cilindri o delle loro sezioni, e G, G&prime; le <lb/>loro gravit&agrave; in specie, sar&agrave; G.V:G&prime; V&prime;= <lb/>IM:EF, ossia G:G&prime;=V&prime;.IM:V.EF.Ma <lb/>perch&egrave; V=EF.EG, V&prime;=IM.IH, ed EG= <lb/>IH; sar&agrave; dunque G:G&prime;=IM2:EF2, ossia <lb/>che le gravit&agrave; in specie stanno reciproca&shy;<lb/>mente come i quadrati delle lunghezze, se&shy;<lb/>condo avea concluso il Viviani in quel suo <lb/>manoscritto Delle resistenze, veduto dal Ma&shy;<lb/>galotti. </s></p><p type="main">

<s>Quella Lettera scientifica al Rucellai sarebbe dunque venuta opportuna <lb/>ad attestare della reale esistenza di un tal Manoscrito, ma si fece pubbli&shy;<lb/>camente nota troppo tardi, perch&egrave; se ne potesse persuadere l'animo sospet&shy;<lb/>toso del Marchetti, il quale anzi reput&ograve;, e poi disse al pubblico essere stata <lb/>un'impostura l'andare il Viviani con quell'involto di carte sotto il braccio <lb/>al Cardinale dei Medici, e, facendogliele vedere cos&igrave; alla grossa e alla sfug&shy;<lb/>gita, dargli ad intendere che conteneva un'opera simile alla sua, ci&ograve; che <lb/>concludeva non essere altro &ldquo; che un mero vanto, o che, confrontando egli <lb/>le sue fatiche con le mie, e conoscendole di gran lunga inferiori, am&ograve; an&shy;<lb/>ch'egli meglio di sopprimerle, che di pubblicarle &rdquo; <emph type="italics"/>(Lettera in cui si ri&shy;<lb/>batton le accuse ecc., pag. </s>

<s>25).<emph.end type="italics"/> E come fossero queste al glorioso nome del <lb/>Viviani leggere ingiurie, soggiungeva che per invidia s'era astutamente messo <lb/>a impedirgli per molto tempo la pubblicazion del suo libro, intanto che, con <lb/>suo grave danno, avesse il Blondel in Francia a prevenirlo. </s></p><p type="main">

<s>Volarono le calunniose querele largamente attorno a titillare le orec&shy;<lb/>chie, e a insinuarsi nell'animo dei Matematici, fra'quali il Leibniz scriveva <lb/>cos&igrave; in una lettera al Grandi: &ldquo; Clarissimum Marchettum audivi quaeri de <lb/>insigni Viro, et mihi olim amico, Vincentio Viviano, quod hic illum multos <lb/>ante annos aeditionem libri <emph type="italics"/>De resistentia solidorum<emph.end type="italics"/> diu differre coegerit. </s>

<s><lb/>Ego meum iudicium hic non intorpono, neque Vivianum, quamtumvis ami&shy;<lb/>cum, excusarem, si quid in ea re humani passus esset &rdquo; (MSS. Cim., T. XXIX, <lb/>fol. </s>

<s>287). </s></p><p type="main">

<s>Non voleva il Leibniz coscenziosamente farsi giudice, per mancanza di <lb/>prove, che il Grandi aveva gi&agrave; in mano infin da quando si dette a scrivere <lb/>la sua <emph type="italics"/>Risposta apologetica,<emph.end type="italics"/> a pag. </s>

<s>88, della quale, dop'avere accennato che, <lb/>dal silenzio tenuto dal Viviani con gli stessi suoi pi&ugrave; familiari, s'incomin&shy;<lb/>ci&ograve; a dubitare se veramente avesse atteso a trattare delle Resistenze dei so&shy;<lb/>lidi; soggiunge che il medesimo signor abate Jacopo Panzanini, nipote ed <pb xlink:href="020/01/2224.jpg" pagenum="467"/>erede dello stesso Viviani, non ne era punto informato, ma che poi, fattagli <lb/>istanza da chi aveva interessi in questa causa, finalmente ritrov&ograve; il Ma&shy;<lb/>noscritto in quell'argomento, e con i contrassegni corrispondenti con la de&shy;<lb/>scrizione fattane da suo zio al Marchetti, quando lo avvis&ograve; per lettera del <lb/>deposito di quello stesso suo Manoscritto, e della recognizione impressavi <lb/>dalla mano e dal sigillo del cardinale Leopoldo. </s>

<s>La lettera, con cui il Pan&shy;<lb/>zanini annunziava al Grandi la scoperta, fu scritta da Firenze il d&igrave; 24 No&shy;<lb/>vembre 1711; e incomincia con queste parole: </s></p><p type="main">

<s>&ldquo; Al mio ritorno di villa scrissi altra lettera a V. P. Rev.ma, ed ora che <lb/>ho avuto tempo di ricercar meglio gli scritti del signor Vincenzio Viviani <lb/>mio zio, posso aggiungerle che ho trovate alcune sue fatiche in tre fascetti, <lb/>che uno intorno le Resistenze dei corpi solidi, altro sopra le Galleggianti, <lb/>ed altro di varie speculazioni meccaniche, quali portano nel frontespizio la <lb/>firma del fu serenissimo principe cardinale Leopoldo, sotto il d&igrave; 2 Marzo 1667 <lb/><emph type="italics"/>ab Incarnatione,<emph.end type="italics"/> e sono infilzati in un cordone di seta, annodato e segnato <lb/>col sigillo dell'A. S. Rev.ma, che non pu&ograve; revocarsi in dubbio la vera esi&shy;<lb/>stenza dei medesimi in quel tempo &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLVIII, fol. </s>

<s>169). </s></p><p type="main">

<s>Venuto il Grandi nelle prossime vacanze del Natale a Firenze, dette a <lb/>quelle carte una scorsa in casa del Panzanini, trascrivendone qualche cosa, <lb/>che poi pubblic&ograve; nella sua <emph type="italics"/>Risposta apologetica.<emph.end type="italics"/> Ma sentito dalla lettera del <lb/>Leibniz che s'erano negli animi insinuate le orgogliose querele del Mar&shy;<lb/>chetti, e trovandosi oramai cos&igrave; impegnato in difendere la causa del suo <lb/>Maestro, giudic&ograve; non esserci altro pi&ugrave; efficace modo, che di pubblicare il <lb/>Manoscritto felicemente ritrovato, dietro il quale giudicherebbero i Matema&shy;<lb/>tici se era impostura quel che il Viviani diceva di avere speculato intorno <lb/>alle Resistenze dei solidi, e se erano quelle speculazioni spregevoli, e da non <lb/>venire in confronto con quelle dello stesso Marchetti. </s>

<s>Fatto al Panzanini <lb/>motto di questa sua intenzione, mentre pensava al modo di mandarla ad <lb/>effetto, gli si fa innanzi Benedetto Bresciani, che attendeva allora in Firenze <lb/>con Tommaso Bonaventuri a fare una nuova edizione delle opere di Galileo, <lb/>fra le quali il trattato Delle resistenze si potrebbe inserire come commento. </s>

<s><lb/>Acconsent&igrave; il Grandi, e fece, per mezzo dello stesso Bresciani, richiedere il <lb/>Manoscritto al Panzanini, il quale anzi raccolse, insieme con quello delle <lb/>Resistenze, gli altri trattati di suo zio, della consegna dei quali dava cos&igrave;, <lb/>per lettera del d&igrave; 27 Giugno 1713, avviso allo stesso Grandi: </s></p><p type="main">

<s>&ldquo; Ho consegnato, secondo la richiesta fattami dal signor Benedetto Bre&shy;<lb/>sciani, gli tre fascetti consaputi di Vincenzio Viviani, avendomi rappresen&shy;<lb/>tato che V. Rev.za si sia esibita di distendere quelle proposizioni in essi <lb/>enunciate, con ridurle in buona forma. </s>

<s>E potendo queste servir di moto alla <lb/>sua fecondissima mente, per crearne infinite altre, ben volentieri io ne sono <lb/>contento, e vado fra me stesso considerando la bella sorte toccata a mio <lb/>zio di aver, dopo la sua morte, un sostenitore della sua gloria di s&igrave; alto va&shy;<lb/>lore: ricompensa a mio credere centuplicata del zelo s&igrave; premuroso, che aveva <lb/>verso il suo Maestro &rdquo; (ivi, fol. </s>

<s>171). </s></p><pb xlink:href="020/01/2225.jpg" pagenum="468"/><p type="main">

<s>Le carte dunque, ch'ebbe sott'occhio il Grandi a esaminare, e che ci <lb/>son tuttavia rimaste raccolte nel Tomo VII della V parte dei Manoscritti di <lb/>Galileo, contenevano proposizioni mutilate, informi e senz'ordine, parte scritte <lb/>in latino, e parte in italiano: lemmi preparati, ma de'quali non appariva la <lb/>diretta intenzione; pensieri sparsi, propositi di tentar cose nuove, espressi <lb/>sentenziosamente in parole, o per via di semplici abbozzate figure. </s>

<s>Difficile <lb/>cavar di li costrutto a un teorema perfetto, o pensiamo a un intero trat&shy;<lb/>tato. </s>

<s>Suppl&igrave; felicemente il Grandi, col suo valor matematico, alla dimostra&shy;<lb/>zione di molti teoremi, nel Manoscritto solamente accennati, ma dove s'in&shy;<lb/>voca l'esperienza a conforto della Geometria, non seppe ben comprendere <lb/>il suo Autore, n&egrave; farne perci&ograve; rilevare quel che, sopra Galileo e il Mar&shy;<lb/>chetti, aveva di pi&ugrave; nuovo e importante. </s></p><p type="main">

<s>Si propone per esempio, fra gli altri, a risolvere questi problemi: &ldquo; Cur <lb/>lignum horizontale facilius inflectatur quam inclinatum, et de proportione <lb/>diversarum inclinationum. </s>

<s>&mdash; Cur prisma triangulare facilius inflectatur su&shy;<lb/>perficie deorsum spectante, quam angulo. </s>

<s>&mdash; Non omne pondus, quod po&shy;<lb/>test inflectere lignum, potest quoque frangere: Lignum enim inflexum minus <lb/>trahitur, quam horizontaliter distentus, cum <lb/>ad angulum obtusum trahatur &rdquo; (MSS. Gal., <lb/>P. V, T. VII, fol. </s>

<s>38). Di cos&igrave; fatti quesiti <lb/>e pensieri compil&ograve; il Grandi la sua LXXVIII <lb/>proposizione (Alb. </s>

<s>XIV, 67), che illustr&ograve; di <lb/>considerazioni sue proprie, le quali egli dice <lb/>darebbero campo &ldquo; a molte particolari spe&shy;<lb/>culazioni, alle quali per ora non posso ap&shy;<lb/>plicare &rdquo; (ivi, pag. </s>

<s>68). Ma il Viviani, me&shy;<lb/>glio che alle speculazioni, aveva pensato, <lb/>nell'incertezza del caso, d'interpellar l'espe&shy;<lb/>rienza, accennata in queste due semplici <lb/>figure 242 e 243, la prima delle quali s'il&shy;<lb/><figure id="id.020.01.2225.1.jpg" xlink:href="020/01/2225/1.jpg"/></s></p><p type="caption">

<s>Figura 242<lb/><figure id="id.020.01.2225.2.jpg" xlink:href="020/01/2225/2.jpg"/></s></p><p type="caption">

<s>Figura 243<lb/>lustra dalla nota seguente: &ldquo; Sperimenta <lb/>questo: cio&egrave; con che proporzione de'pesi <lb/>A, B si faccia l'equilibrio della libbra o <lb/>leva DE orizzontale &rdquo; (MSS. Gal., P. V, T. <lb/>VII, a tergo del fol. </s>

<s>24). </s></p><p type="main">

<s>Perch&egrave; in questi, e in altri simili se&shy;<lb/>gni, di che son piene parecchie facce del <lb/>Manoscritto, s'ascondeva come si disse l'ori&shy;<lb/>ginalit&agrave; dei pensieri del Viviani, non sa&shy;<lb/>pendoli il Grandi interpetrare, veniva a perdere, nella difesa della sua causa, <lb/>l'argomento migliore. </s>

<s>N&egrave; solo si mettevano cos&igrave; alla luce le medesime cose, <lb/>ch'erano nel Marchetti, ma si lasciava ben assai pi&ugrave; completo del nuovo ap&shy;<lb/>parire il libro di lui, che aveva le proposizioni del famoso solido parabolico <lb/>mancante nella compilazione del Grandi. </s>

<s>Mancano qui pure altre proposizioni, <pb xlink:href="020/01/2226.jpg" pagenum="469"/>per cui vengono a concludersi dietro un supposto alcuni fra i principali <lb/>Teoremi. </s>

<s>Tale sarebbe per esempio il LVII, che &egrave; del prisma parabolico <lb/>d'ugual resistenza, e nella presente causa di massima importanza: Teorema <lb/>per&ograve; che qui non conclude, se non ammesso il non dimostrato che cio&egrave; i <lb/>momenti de'pesi uguali, gravanti in varie parti fuori del mezzo un cilin&shy;<lb/>dro, sostenuto nelle sue estremit&agrave;; stanno direttamente come i rettangoli <lb/>delle distanze. </s></p><p type="main">

<s>Non aveva il Viviani tralasciata questa dimostrazione: l'aveva anzi, come <lb/>vedremo a suo luogo, resa generalissima in modo, da applicarsi per fonda&shy;<lb/>mento alle molte proposizioni del suo trattato, rimaste in aria nella compi&shy;<lb/>lazione del Grandi, la quale vien perci&ograve; notata di un difetto gravissimo, da <lb/>cui va senza dubbio esente il Marchetti. </s></p><p type="main">

<s>Fu un grande inganno di esso Grandi quel di credere che, nelle sole <lb/>carte ritrovate dal Panzanini, consistesse tuttoci&ograve; che delle Resistenze dei <lb/>solidi aveva speculato il Viviani, e quell'inganno rec&ograve; alla causa che difen&shy;<lb/>deva gravissimo danno. </s>

<s>Videro quelle ordinate speculazioni, nel 1718, in Fi&shy;<lb/>renze la luce, inserite nel III Tomo delle opere di Galileo, ma qual effetto <lb/>ebbe l'intenzione di chi avea condotto il faticoso lavoro? </s>

<s>Si veniva senza <lb/>dubbio a purgare il Viviani dalla calunnia che fingesse di avere un trattato <lb/>Delle resistenze, e che volesse pubblicarlo per impedire i progressi al Mar&shy;<lb/>chetti, ma chi leggeva alla II giornata di Galileo il nuovo commento non <lb/>poteva non giudicarlo superfluo, dopo quello dello stesso Marchetti: e perch&egrave; <lb/>le novit&agrave;, per le quali si sarebbe potuto distinguer quello stesso commento, <lb/>rimanevano nell'opera del Compilatore affogate o spente, inferior nell'am&shy;<lb/>piezza del soggetto, nella concisione delle dimostrazioni, e nell'ordine delle <lb/>parti. </s>

<s>Ma nell'animo del Grandi prevaleva il pensiero di s&egrave;, a quello che <lb/>doveva aver del Viviani, e parve perci&ograve; che avesse presa principalmente <lb/>quella fatica, per scagliar l'ultima pietra sulla tomba del suo nemico. </s>

<s>L'atto <lb/>che sa d'empio, era mosso e guidato da quella irragionevolezza, che risul&shy;<lb/>ter&agrave; dall'esame delle controversie insorte fra i due Matematici professori <lb/>nello studio di Pisa. </s></p><p type="main">

<s>Fermo in quel pregiudizio, comune a tanti, che fosse Galileo infallibile <lb/>oracolo di ogni verit&agrave; matematica, non poteva patire il Grandi che si dicesse <lb/>avere sbagliato il divino Uomo circa all'ugual resistenza del solido parabo&shy;<lb/>lico: ci&ograve; egli reputava una vera <emph type="italics"/>calunnia,<emph.end type="italics"/> di che volle agramente ripren&shy;<lb/>dere il Marchetti e il Blondel (Alb. </s>

<s>XIV, 86), contrapponendo alla loro au&shy;<lb/>dacia l'esempio del Viviani, il quale con buona pace dimostr&ograve; che tutto il <lb/>male si rimediava, ponendo il solido con la superfice parabolica in piano <lb/>piuttosto che eretta, come per inavvertenza doveva averla disegnata lo stesso <lb/>Galileo. </s></p><p type="main">

<s>I nostri Lettori, i quali hanno oramai i documenti in mano, sanno <lb/>come si trovassero mirabilmente il Marchetti e il Blondel col Viviani con&shy;<lb/>cordi nel correggere quel trascorso: che se l'Autore <emph type="italics"/>De resistentia solido&shy;<lb/>rum<emph.end type="italics"/> scrisse nella sua prefazione <emph type="italics"/>Salviatus illic veri specie fuit deceptus<emph.end type="italics"/><pb xlink:href="020/01/2227.jpg" pagenum="470"/>il Postillatore dell'edizione di Leida scrisse in margine, di rincontro alla <lb/>proposiz&igrave;one formulata dallo stesso Salviati, <emph type="italics"/>falsa,<emph.end type="italics"/> dichiarandosi come si <lb/>rendesse vera, cosiderata la figura in astratto e qual puramente geometrica, <lb/>e conclucendo nel modo medesimo del Marchetti, come si vide, che l'er&shy;<lb/>rore di Galileo non in altro consisteva che nel volere applicare le propriet&agrave; <lb/>di un solido senza peso alla travatura delle navi, per necessit&agrave; naturale <lb/>pesanti. </s></p><p type="main">

<s>Anzi il Viviani, che in riconoscere gli sbagli del suo Maestro non cre&shy;<lb/>deva punto di calunniarlo, ebbe a notare parecchie altre proposizioni par&shy;<lb/>tecipanti la falsit&agrave; medesima di quella famosa corretta dal Marchetti, di cui <lb/>bene spesso si mostra pi&ugrave; sottile e pi&ugrave; libero censore. </s>

<s>&Egrave; notabile, fra gli <lb/>altri esempii di cos&igrave; fatte censure, quella che liberamente egli esercit&ograve; in&shy;<lb/>torno alla proposizione XIV, manifestamente falsa nel suo principio, e per&shy;<lb/>ci&ograve; nella sua conclusione. </s>

<s>Dice ivi Galileo: &ldquo; Questo DB (fig. </s>

<s>244) &egrave; un <lb/><figure id="id.020.01.2227.1.jpg" xlink:href="020/01/2227/1.jpg"/></s></p><p type="caption">

<s>Figura 244<lb/>prisma (il Viviani vi aggiunge: <lb/><emph type="italics"/>senza peso)<emph.end type="italics"/> la cui resistenza al&shy;<lb/>l'essere spezzato nell'estremit&agrave; <lb/>AD, da una forza premente nel <lb/>termine B, &egrave; tanto minore della <lb/>resistenza, che si troverebbe nel <lb/>luogo CI, quanto la lunghezza <lb/>CB &egrave; minore della BA &rdquo; (Alb. </s>

<s><lb/>XIII, 137): che vuol dire avere <lb/>le resistenze reciproca propor&shy;<lb/>zione delle lunghezze, con fal&shy;<lb/>sit&agrave; manifesta. </s>

<s>N&egrave; par credibile che Galileo non s'accorgesse dello sbaglio, <lb/>perch&egrave;, segato dal piano DMB il prisma nel mezzo, dice pi&ugrave; sotto che la <lb/>resistenza AD sta alla resistenza CO, come il rettangolo AD sta al rettan&shy;<lb/>golo CO. </s>

<s>Se ora per questa medesima ragione le resistenze AD, CI debbono <lb/>stare come i rettangoli son dunque esse resistenze insieme uguali, e dovreb&shy;<lb/>bero esser perci&ograve; uguali altres&igrave; le lunghezze AB, CB: cosa tanto assurda, <lb/>da far avveduto chiunque che sarebbe dovuto il ragionamento procedere in <lb/>quest'altra maniera: </s></p><p type="main">

<s>Applicati in B due pesi P.P&prime; la resistenza della sezione AD &egrave; uguale <lb/>ad AB.P, ed &egrave; per somigliante ragione CB.P&prime; la resistenza della sezione <lb/>CI. </s>

<s>Ma perch&egrave; sono le due resistenze uguali, dunque P:P&prime;=CB:AB, e <lb/>perci&ograve; stanno i pesi e non le resistenze, come Galileo diceva, in proporzione <lb/>reciproca delle lunghezze. </s></p><p type="main">

<s>Il Viviani insomma, cos&igrave; rettamente come dovevasi ragionando, not&ograve; in <lb/>quella sua cartuccia, inserita fra la pag. </s>

<s>138 e 139 della edizione di Leida, <lb/>riferendosi alla detta proposizione qual si legge nel testo: &ldquo; &Egrave; falsa cos&igrave; pro&shy;<lb/>nunziata: le resistenze del medesimo prisma o cilindro fitti nel muro, con&shy;<lb/>siderati senza peso, sono fra loro come i pesi attaccati alle estremit&agrave;, che <lb/>siano bastanti a spezzargli, i quali pesi hanno fra loro la proporzion reci-<pb xlink:href="020/01/2228.jpg" pagenum="471"/>proca delle lunghezze fuori del muro. </s>

<s>Vera cos&igrave;: gli equivalenti la mede&shy;<lb/>sima resistenza assoluta (ossia i pesi assoluti da noi sopra significati con <lb/>P.P&prime;) di un cilindro o prisma senza peso, fitti in un muro da diverse lun&shy;<lb/>ghezze, hanno proporzione reciproca delle lunghezze &rdquo; (MSS. Gal., P. V, <lb/>T. IX). E rendendo la galileiana proposizione anche pi&ugrave; generale, avrebbe <lb/>volentieri voluto sostituire, a quella falsa messa in bocca al Salviati, que&shy;<lb/>st'altra pi&ugrave; conforme col vero, cos&igrave; formulata: &ldquo; I minimi pesi bastanti a <lb/>pareggiar da diverse lunghezze la medesima resistenza della sezion verticale <lb/>di un cilindro o prisma o altro qualunque solido, senza peso, fitto in un <lb/>muro, sono fra loro in reciproca proporzione delle medesime lunghezze &rdquo; (ivi). </s></p><p type="main">

<s>&Egrave; lecito di qui argomentare quanto fosse il Viviani docile a pigliare stu&shy;<lb/>pidamente contro le calunnie del Blondel e del Marchetti le difese di Ga&shy;<lb/>lileo, ricorrendo allo strattagemma di riguardare il solido parabolico posato <lb/>in piano. </s>

<s>Si poteva la strana idea sopportare nel Grandi, infintanto che il <lb/>teorema del Prisma parabolico, sostenuto dalle due parti, gli occorse a no&shy;<lb/>tare nel primo frettoloso esame del Manoscritto, separatamente dagli altri: <lb/>ma quando attese di proposito e con pace a metter ordine a tutto il trat&shy;<lb/>tato, dalle relazioni che aveva quel teorema con altri simili ivi dimostrati <lb/>si sarebbe dovuto avveder che il Viviani, tutt'altro che insorgere avverso, <lb/>si trovava col Marchetti e col Blondel, per riuscir con loro a un termine, <lb/>sulla dirittura del medesimo sentiero. </s></p><p type="main">

<s>Hanno nel primo aspetto gl'incontri dei tre Autori qualche cosa di ma&shy;<lb/>raviglioso, ma &egrave; il Grandi stesso che ci toglie ogni maravigl&igrave;a, avvertendo <lb/>nella prefazione al suo libro <emph type="italics"/>Della quadratura del circolo,<emph.end type="italics"/> che in Matema&shy;<lb/>tica, a partire dai medesimi principii, chiunque retto ragiona non solo &egrave; <lb/>facile ma &egrave; necessario s'incontri nelle medesime conclusioni. </s>

<s>Ebbero il Blon&shy;<lb/>del, il Viviani e il Marchetti comune lo studio sul Galileo, non fatto super&shy;<lb/>ficialmente e in fretta, come quel del Cartesio, il quale &egrave; curioso che, no&shy;<lb/>tando tante altre verit&agrave; di errore, del solido parabolico di ugual resistenza <lb/>convenisse con lo stesso Galileo che <emph type="italics"/>verum est vere<emph.end type="italics"/> (Epist. </s>

<s>cit., P. II, pag. </s>

<s>243) <lb/>ad eccezione di tutto il rimanente. </s>

<s>I tre sopra commemorati videro invece, <lb/>al medesimo chiaro lume della Geometria, ch'era falso, e, scorti dalla me&shy;<lb/>desima infallibile guida a investigare la verit&agrave; della cosa, non poterono non <lb/>incontrarsi nella medesima conclusione, che cio&egrave; il solido parabolico pesante, <lb/>tanto pi&ugrave; resiste, quanto la forza lo preme pi&ugrave; presso al vertice, in ragion <lb/>dupla sesquialtera dei momenti dei pesi ai momenti delle resistenze. </s></p><p type="main">

<s>Come procedessero d'ugual passo il Viviani e il Marchetti, in questa <lb/>investigazione, gi&agrave; di sopra si vide: e si pu&ograve; con certezza argomentare che <lb/>fossero queste stesse le vie tenute dal Blondel. </s>

<s>Scopertosi ora non essere pro&shy;<lb/>priamente parabolica la figura del solido, che ugualmente resiste, era natura&shy;<lb/>lissimo che si proponesse ai tre Autori, nel medesimo tempo, il quesito: qual <lb/>altra dunque dovrebb'essere quella vera figura? </s>

<s>E non poteva far altro la <lb/>Geometria che rispondere: la ellittica, come di fatti dimostr&ograve; il Marchetti nella <lb/>proposizione XXXIX del II libro, e il Viviani nella XCVI del suo trattato. </s></p><pb xlink:href="020/01/2229.jpg" pagenum="472"/><p type="main">

<s>Ma la dimostrazione di ci&ograve; era facile vedere che si applicava a parec&shy;<lb/>chi altri solidi &ldquo; quae, cum nixa sint super extremitatibus, aequaliter re&shy;<lb/>sistunt ponderi, quod intra fulcimentum sit appensum &rdquo; (MSS. Gal., P. V, <lb/>T. VII, fol. </s>

<s>59), fra'quali solidi annovera lo stesso Viviani, in questo luogo <lb/>citato, il Prisma parabolico, il Semicilindrico e base circolare, il Semicilin&shy;<lb/>drico a base elittica, e le volte, che abbian per centina un semicerchio e <lb/>una semiellisse, o due semiellissi di egual diametro orizzontale, e di diverso <lb/>diametro perpendicolare. </s></p><p type="main">

<s>Ecco dunque com'ebbe origine nel Viviani l'invenzion di quel prisma <lb/>parabolico, che s'immagin&ograve; il Grandi essere stata fatta per servire appunto <lb/>&ldquo; a confutare la calunnia opposta al Galileo, prima da m. </s>

<s>Blondello in Fran&shy;<lb/>cia, e poi dal signor Marchetti in Italia &rdquo; (Alb. </s>

<s>XIV, 87): ecco quanto ri&shy;<lb/>dicolo apparisca lo stesso Grandi, quando ci descrive il Viviani, che si mette <lb/>attorno a duplicare il Cuneo galileiano, e poi lo raddoppia di nuovo, <emph type="italics"/>per <lb/>maggiore stabilit&agrave; e vaghezza!<emph.end type="italics"/> (ivi, pag. </s>

<s>86). Ma, mentre il Valentuomo si <lb/>trattiene in queste ridicolezze, e per mostrare la maggiore fecondit&agrave; dell'in&shy;<lb/>gegno del Viviani, sopra quel del Marchetti, ordina le varie proposizioni con&shy;<lb/>cernenti la variet&agrave; delle forme dei solidi di resistenze uguali; non s'avvede <lb/>che manca ad esse proposizioni il fondamento, e che quello che vi si sot&shy;<lb/>topone non &egrave; il loro proprio. </s></p><p type="main">

<s>Le XCV, XCVI infatti, questa degli emi&shy;<lb/>cilindri di base circolare o di base ellittica <lb/>(Alb. </s>

<s>XIV, 87), quella del Prisma elittico <lb/>QM (fig. </s>

<s>245), sostenuto alle sue estremit&agrave; <lb/><figure id="id.020.01.2229.1.jpg" xlink:href="020/01/2229/1.jpg"/></s></p><p type="caption">

<s>Figura 245<lb/>M, N (ivi, pag. </s>

<s>86), si concludono da tali <lb/>due principii: che i pesi uguali pendenti <lb/>da I, L stanno come i rettangoli MI.IN, <lb/>ML.LN, e che i momenti delle resistenze <lb/>delle sezioni AB.CD son proporzionali alle <lb/>basi GB, HD. </s>

<s>Come alla conclusione mancasse, negli <lb/>ordinamenti del Grandi, quel primo fondamento, gi&agrave; <lb/>lo dicemmo: ora &egrave; da soggiungere che il secondo ivi <lb/>indicato non &egrave; il suo proprio. </s>

<s>Per verificare infatti l'as&shy;<lb/>serta proporzion dei momenti delle sezioni, s'indica <lb/>la proposizione II: <emph type="italics"/>I momenti delle resistenze, nelle se&shy;<lb/>zioni dei solidi, le di cui basi siano disuguali ed eguali <lb/>le altezze, sono come le medesime basi<emph.end type="italics"/> (ivi, pag. </s>

<s>14), <lb/>la qual proposizione prende valore dalla prima, che <lb/>dice: <emph type="italics"/>I momenti di resistenza della medesima sezione, <lb/>o di sezioni uguali, sono tra di loro come le distanze <lb/>del centro di gravit&agrave; di esse dal sostegno<emph.end type="italics"/> (ivi). <lb/><figure id="id.020.01.2229.2.jpg" xlink:href="020/01/2229/2.jpg"/></s></p><p type="caption">

<s>Figura 246</s></p><p type="main">

<s>Il Grandi, invocando i principii della Leva, dice questa proposizion del <lb/>Viviani evidente, e tale senza dubbio sarebbe, mentre che si trattasse delle <lb/>resistenze respettive, perch&egrave;, avendosi le due sezioni AC, EH (fig. </s>

<s>246) con <pb xlink:href="020/01/2230.jpg" pagenum="473"/>le altezze AD, EG uguali, e con i centri di gravit&agrave; in O, M, le leve fa&shy;<lb/>vorevoli ON, MR producono momenti di forza uguali ad AB.AD.NO, <lb/>EF.EG.RM; onde, chiamate R.R&prime; le resistenze delle dette sezioni, se ne <lb/>conclude R:R&prime;=AB.AD.NO:EP.EG.RM=AB:EF. </s></p><p type="main">

<s>Ma nelle sezioni AB, CD del Prisma parabolico, rappresentato nella <lb/>figura 245, si tratta di resistenze assolute, dove non &egrave; perci&ograve; favore alcuno <lb/>di Leva, e nonostante asserisce il Viviani anche di esse: &ldquo; Momenta resi&shy;<lb/>stentiarum sectionum solidi, quarum bases sint inaequales, aequales vero <lb/>altitudines, sunt inter se ut ipsae bases &rdquo;, avvertendo che ci&ograve; si avvera &ldquo; in <lb/>omnibus sectionum figuris, quarum centra gravitatis axes dividant in eadem <lb/>ratione &rdquo; (MSS. Gal., P. V, T. VII, fol. </s>

<s>56). Anzi la stessa proposizione I, <lb/>che s'&egrave; riferita dianzi secondo la traduzione del Grandi, nell'originale &egrave; <lb/>cos&igrave; formulata: &ldquo; Momenta resistentiarum eiusdem sectionis, vel aequalium <lb/>sectionum, sunt inter se ut distan&shy;<lb/>tiae centri gravitatis &icirc;psarum a ful&shy;<lb/>cimento &rdquo; (ibid.), ed &egrave; nel Mano&shy;<lb/>scritto illustrata da varie coppie di <lb/>figure uguali, come di triangoli o <lb/>di ellissi, ora posate sul sostegno <lb/>con l'apice, ora con la base. </s>

<s>Cos&igrave;, <lb/>il momento della resistenza, nel <lb/>triangolo ABC (fig. </s>

<s>247), sta al mo&shy;<lb/><figure id="id.020.01.2230.1.jpg" xlink:href="020/01/2230/1.jpg"/></s></p><p type="caption">

<s>Figura 247<lb/>mento della resistenza, nel mede&shy;<lb/>simo triangolo posto secondo DEF, come HG sta ad LF, distanza dei centri <lb/>di gravit&agrave; dal sostegno. </s>

<s>Similmente, ne'rettangoli AC, EH (fig. </s>

<s>248), aventi le <lb/><figure id="id.020.01.2230.2.jpg" xlink:href="020/01/2230/2.jpg"/></s></p><p type="caption">

<s>Figura 248<lb/>basi BC, DH uguali, i momenti stanno <lb/>come i quadrati delle altezze AB, ED, <lb/>e pure ne'rettangoli o ellissi o al&shy;<lb/>tro, aventi le altezze AC, ED uguali <lb/>(fig. </s>

<s>249), i momenti delle resistenze <lb/>stanno come le basi. </s></p><p type="main">

<s>Queste, che noi col Grandi ab&shy;<lb/>biam chiamate proposizioni, il Viviani <lb/>le intitola <emph type="italics"/>Lemmata universalia pro <lb/>resistentiis<emph.end type="italics"/> in servigio principalmente <lb/>delle proposizioni concernenti i solidi di resistenze uguali. </s>

<s>Essendo perci&ograve; <lb/>di tanta importanza nel Trattato quei Lemmi, pens&ograve; bene l'Ordinatore di <lb/><figure id="id.020.01.2230.3.jpg" xlink:href="020/01/2230/3.jpg"/></s></p><p type="caption">

<s>Figura 249<lb/>esso Trattato di suppli&rgrave;e alle dimostra&shy;<lb/>zioni, che non si trovan nel Manoscritto, <lb/>ma non ebbe il pensiero nessun buono <lb/>effetto, per le accennate ragioni del ve&shy;<lb/>nir meno l'invocato favor della Leva <lb/>nelle resistenze assolute delle varie di&shy;<lb/>segnate sezioni, i centr&igrave; di gravit&agrave; delle quali battono a perpendicolo sul <pb xlink:href="020/01/2231.jpg" pagenum="474"/>sostegno. </s>

<s>Dovette dunque il Viviani, a confortare i suoi Lemmi, avere invo&shy;<lb/>cato un diverso principio, che non s'intenderebbe, senza attribuirlo all'animo <lb/>preoccupato, come il Grandi non indovinasse esser quello dei momenti delle <lb/>forze proporzionali alle velocit&agrave; moltiplicate per i pesi. </s></p><p type="main">

<s>Cos&igrave;, per esempio, nelle sopra disegnate figure triangolari 247, la re&shy;<lb/>sistenza &egrave; vinta, quando il centro di gravit&agrave; &egrave; portato da H e da L in G <lb/>e in F, fuori del sostegno, a che fare ci bisognan due forze, atte a movere <lb/>il medesimo peso triangolare, l'una con la velocit&agrave; HG, l'altra con la ve&shy;<lb/>locit&agrave; LF; ond'&egrave; ch'esse forze saranno, come conclude il Viviani, propor&shy;<lb/>zionali a queste due distanze. </s>

<s>Similmente, nelle sezioni rettangolari di ugual <lb/>base e di differente altezza, rappresentate dianzi nella figura 248, i momenti <lb/>delle forze, che vincono le resitenze assolute, sono AB.BC.MP, ED.DH.OQ, <lb/>e perci&ograve;, avendosi MP=AB/2, OQ=ED/2, torneranno i detti momenti pro&shy;<lb/>porzionali ai quadrati delle respettive altezze, e proporzionali alle basi tor&shy;<lb/>neranno nelle sezioni AD, EF, rappresentate nell'ultima figura 249, per es&shy;<lb/>sere gli spazi ON, MP, che misuran le velocit&agrave; uguali, ambedue la met&agrave; <lb/>delle altezze rettangolari uguali. </s></p><p type="main">

<s>L'universalit&agrave; di questi Lemmi, dal Viviani applicati ai solidi ugual&shy;<lb/>mente resistenti, conduceva a concludere che infinite posson essere le varie <lb/>figure di cos&igrave; fatti solidi, non che quelle tre, per le quali il Grandi (Rispo&shy;<lb/>sta apol. </s>

<s>cit., pag. </s>

<s>129) mena vanto di superiorit&agrave; del suo Autore, sopra <lb/>l'unico solido ellittico proposto dal Marchetti. </s>

<s>S'annovera tra quelle tre <lb/>figure il Cuneo triangolare, di che certo, essendo cosa di si facile conse&shy;<lb/>guenza, non avrebbe tenuto conto lo stesso Viviani. </s>

<s>Sono di quella facilit&agrave; <lb/>indizio le due stesse varie maniere di dimostrare la proposizione, alle quali <lb/>due maniere dell'Autore ne aggiunge il Grandi una terza, che non &egrave; pure <lb/>da rassomigliar a quest'altra, quale pu&ograve; aversi per via diretta: </s></p><p type="main">

<s>Sia il Cuneo triangolare AC (fig. </s>

<s>250), sporgente fuori del muro, ora <lb/><figure id="id.020.01.2231.1.jpg" xlink:href="020/01/2231/1.jpg"/></s></p><p type="caption">

<s>Figura 250<lb/>quanto DO, ora quanto QD, e il peso <lb/>G pareggi, col suo momento G.DO, <lb/>la resistenza R della sezione AB, men&shy;<lb/>tre l'altro peso H pareggia, col mo&shy;<lb/>mento H.DQ, la resistenza R&prime; della <lb/>sezione FE. </s>

<s>Considerando che, per via <lb/>di uno de'Lemmi universali gia di&shy;<lb/>mostrati, le resistenze delle sezioni <lb/>aventi uguali altezze stanno come le <lb/>basi AI, NE, o come le lunghezze OD, <lb/>QD, avremo R:R&prime;=G.DO:H.DQ <lb/>=DO:DQ e perci&ograve; G=H. </s></p><p type="main">

<s>Il discorso lungo, fin qui da noi <lb/>intrattenuto sulle controversie insorte fra i due Professori pisani, per deci&shy;<lb/>der delle ragioni del primato, e dei modi cen cui si vollere, circa al solido <pb xlink:href="020/01/2232.jpg" pagenum="475"/>parabolico di ugual resistenza, riformare e promovere i teoremi di Galileo; <lb/>ci ha portato a concludere che fossero d'ogni parte irragionovoli i giudizii <lb/>del Grandi. </s>

<s>Ma perch&egrave; l'odio divampa al largo con le sue fiamme voraci, <lb/>ritroveremo una pari irragionevolezza, quando esso Grandi, non contento di <lb/>avere accusato il Marchetti di plagio, passa a fare un sottile esame di altre <lb/>varie proposizioni di lui, per voler notarle vergognosamente di errore. </s></p><p type="main">

<s>Nel II capitolo della I parte della <emph type="italics"/>Risposta apologetica<emph.end type="italics"/> l'Autore, per to&shy;<lb/>gliere al Marchetti il vanto di aver egli il primo dimostrata la composizion <lb/>dei momenti, cita la proposizione VI del dialogo II, e dice che ivi Galileo <lb/>&ldquo; suppone evidentemente la ragione de'momenti composta di quella dei pesi <lb/>e delle lunghezze onde dipendono, e se ne serve al proposito della resi&shy;<lb/>stenza dei solidi: sebbene egli ne deduce una conclusione alquanto diversa <lb/>da quella del signor Marchetti, il quale, esaminando lo stesso soggetto nella <lb/>proposizione XI del I libro Della resistenza dei solidi, mostra che la ragion <lb/>de'momenti ne'solidi simili &egrave; <emph type="italics"/>duplicata<emph.end type="italics"/> di quella delle resistenze, quando <lb/>il Galileo l'ha detta di sopra <emph type="italics"/>sesquialtera,<emph.end type="italics"/> verificandosi per&ograve; in diverso senso <lb/>l'una e l'altra proposizione, come si pu&ograve; supporre, da che in questo par&shy;<lb/>ticolare non ha preteso il mio dottissimo Avversario di corregger sbaglio <lb/>veruno nel Galileo &rdquo; (pag. </s>

<s>37, 38). </s></p><p type="main">

<s>Qui per&ograve; sembra strano che un'assoluta verit&agrave; matematica abbia ad <lb/>accomodarsi a diverso senso, e giacch&egrave; ambedue gli Autori accolgono le me&shy;<lb/>desime ipotesi, e muovono dai medesimi principii, si vedeva impossibile che <lb/>una proporzione fosse tutto insieme sesquialtera e duplicata. </s>

<s>Certi dunque <lb/>che doveva la verit&agrave; essere o da una parte o dell'altra, e scevri dai pre&shy;<lb/>giudizii del Grandi, e di tanti altri insieme con lui, che una conclusione sia <lb/>vera perch&egrave; Galileo l'ha dimostrata; abbiamo voluto meglio esaminare la <lb/>cosa, e ci pare aver trovato che la ragione sia dalla parte del Marchetti, il <lb/>quale avrebbe potuto perci&ograve; a tutto diritto correggere in Galileo un altro <lb/>sbaglio, meno assai perdonabile del primo. </s></p><p type="main">

<s>Siano i due cilindri simili AB, CD (fig. </s>

<s>251): Galileo dice, nella sua <lb/>VI proposizione, che i loro momenti &ldquo; hanno tra di loro proporzione se&shy;<lb/><figure id="id.020.01.2232.1.jpg" xlink:href="020/01/2232/1.jpg"/></s></p><p type="caption">

<s>Figura 251<lb/>squialtera di quella, che hanno le resistenze <lb/>delle loro basi &rdquo; (Alb. </s>

<s>XIII, 123) e il Mar&shy;<lb/>chetti invece formula la sua XI proposizione: <lb/>&ldquo; Solidorum inter se similium momenta pon&shy;<lb/>derum in duplicata sunt proportione resi&shy;<lb/>stentiarum &rdquo; (pag. </s>

<s>10). Chiamati C, C&prime; i due <lb/>detti cilindri, e M.o C, M.o C&prime; i loro mo&shy;<lb/>menti, convengono ambedue gli Autori nello <lb/>stabilire l'equazione (A) M.o C:M.o C&prime;= <lb/>C.AB:C&prime;.CD. </s>

<s>Ma perch&egrave; C, C&prime; stanno come i cubi dei diametri D, D&prime; delle <lb/>basi o delle altezze proporzionali, Galileo ha per prima conclusione (B) M.oC: <lb/>M.oC&prime;=D3:D&prime;3, e il Marchetti (C) M.oC:M.oC&prime;=AB1:CD1=D1:D&prime;1, <lb/>d'onde nasce la diversit&agrave; della conclusione finale, perch&egrave; chiamate R, R&prime; le <pb xlink:href="020/01/2233.jpg" pagenum="476"/>resistenze, essendo pure per ambedue gli Autori (D) R:R&prime;=D2:D&prime;2, cu&shy;<lb/>bando questa, e quadrando la (B), si ottiene M.oC2:M.oC&prime;2=R3:R&prime;3, ossia <lb/>M.oC:M.oC&prime;=R3/2:R&prime;3/2, che &egrave; la ragione sesquialtera di Galileo: mentre <lb/>la (D) quadrata, e la (C) danno M.oC:M.oC&prime;=R2:R&prime;2, che &egrave; la ragion <lb/>duplicata del Marchetti. </s></p><p type="main">

<s>Or perch&egrave; tutta la question si riduce a saper se AB &egrave; uguale a CD, <lb/>per cui si possano le due quantit&agrave; eliminare dalla seconda ragione di (A), <lb/>o se sono diverse, per cui debbano rimaner nella (C) come fattori, chiun&shy;<lb/>que abbia meno scienza del Grandi, ma miglior senso comune, senza mezzi <lb/>termini, decide esser vera la proposizion del Marchetti, e falsa addirittura <lb/>quella di Galileo. </s>

<s>&ldquo; La forza della leva AB, egli dice, &egrave; eguale alla forza <lb/>della leva CD, e questo perch&egrave; la lunghezza AB, al semidiametro della base B, <lb/>ha la medesima proporzione, per la similitudine dei cilindri, che la lun&shy;<lb/>ghezza CD al semidiametro della base D &rdquo; (Alb. </s>

<s>XIII, 123, 24); n&egrave; s'av&shy;<lb/>vedeva il grand'Uomo che, mentre nelle similitudini de'cilindri la ragione <lb/>&egrave; diretta, nella forza della leva e inversa, e che AB, e CD nella (A) non <lb/>rappresentano le leve, ma le semplici lunghezze delle leve, le quali perci&ograve; <lb/>non compongono da s&egrave; sole i momenti delle forze. </s></p><p type="main">

<s>Erano state gi&agrave; da noi fatte e scritte queste avvertenze, quando, tor&shy;<lb/>nando a svolgere, nel T. IX della P. </s>

<s>V dei Manoscritti di Galileo, le po&shy;<lb/>stille del Viviani al secondo dialogo delle Nuove scienze, fu trattenuta la <lb/>nostra attenzione sopra un foglietto, in testa al quale il Postillatore stesso <lb/>scriveva: <emph type="italics"/>Propos. </s>

<s>VI del Galileo generalmente e diversamente enunciata, <lb/>per esser quella non vera.<emph.end type="italics"/></s></p><p type="main">

<s>Il pi&ugrave; autorevole giudice che si potesse desiderare aveva dato dunque <lb/>sentenza contro Galileo, e aveva gi&agrave; deciso a favor del Marchetti, togliendo <lb/>insieme ogni refugio a quei dissennati, i quali non dubitavano di sacrifi&shy;<lb/>care all'amore del vero la vana gloria di un uomo. </s>

<s>Dicevano costoro, e si <lb/>ripeteva dal Grandi, ch'era possibile salvar la VI proposizione di Galileo da <lb/>ogni nota di errore, intendendo delle <emph type="italics"/>resistenze assolute<emph.end type="italics"/> quel che ivi si dice <lb/>dei momenti, ma il Viviani soggiunge che non verrebbesi a togliere la fal&shy;<lb/>sit&agrave;, nemmeno cos&igrave; benignamente interpetrando la detta proposizione, la <lb/>quale pu&ograve; solo esser vera a quel modo, che dal Marchetti fu poi pronun&shy;<lb/>ziata. </s>

<s>&ldquo; E per chi dubitasse, dice nella sua postilla il Viviani, che l'enun&shy;<lb/>ziazione del Galileo si dovesse intendere cos&igrave;: cio&egrave; che i momenti gravanti <lb/>dei cilindri simili hanno proporzion sesquialtera di quella, che hanno le re&shy;<lb/>sistenze assolute per&ograve;, e non i momenti loro resistenti; pur si prova che, <lb/>volendo paragonare il rispetto dei momenti gravanti con quello delle resi&shy;<lb/>stenze assolute, l'enunziazione sia profferita diversamente cos&igrave;, cio&egrave;: <emph type="italics"/>I mo&shy;<lb/>menti gravanti dei solidi simili son fra loro in doppia proporzione delle <lb/>resistenze assolute delle basi. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>L'esser proceduto a diritto il Marchetti, senza fare n&egrave; queste osserva&shy;<lb/>zioni n&egrave; questi confronti, rivela nell'animo di lui riverenza molto maggiore <lb/>di quella, che non mostrasse di avere in s&egrave; il Grandi, che, riprensore cos&igrave; <pb xlink:href="020/01/2234.jpg" pagenum="477"/>zelante dei calunniatori del divino Uomo, non ebbe poi scrupolo di mettersi <lb/>nel numero di loro, quando vide aver di l&igrave; meglio libero il braccio, per av&shy;<lb/>ventare al nemico le saette avvelenate. </s>

<s>S'argomenta e si prova ci&ograve; dal modo <lb/>che tenne in censurare la II proposizione del libro II <emph type="italics"/>De resistentia soli&shy;<lb/>dorum,<emph.end type="italics"/> e le molte altre dipendenti da lei, tutte dal Grandi allo stesso modo <lb/>notate di false, perch&egrave; fondate, egli dice, sul falso supposto, &ldquo; cio&egrave; che la <lb/>resistenza d'un solido prismatico fitto nel muro, alla resistenza nel mezzo <lb/>di esso, in caso che retto sia dall'una o dall'altra parte, sia in ragion sud&shy;<lb/>dupla, cio&egrave; come uno sta a due &rdquo; (Risposta apol. </s>

<s>cit., pag. </s>

<s>118). </s></p><p type="main">

<s>Ora &egrave; da osservar che il Marchetti divide, come Galileo, dietro le pi&ugrave; <lb/>antiche tradizioni aristoteliche, il suo trattato in due parti, alla seconda delle <lb/>quali, che &egrave; de'solidi retti nelle due loro estremit&agrave;, pone per fondamento <lb/>il supposto dal medesimo Galileo, cio&egrave; &ldquo; che il cilindro che, gravato dal <lb/>proprio peso, sar&agrave; ridotto alla massima lunghezza, oltre alla quale pi&ugrave; non <lb/>si sosterrebbe, o sia retto nel mezzo da un solo sostegno, ovvero da due <lb/>nelle estremit&agrave;, potr&agrave; essere lungo il doppio di quello, che sarebbe fitto nel <lb/>muro, cio&egrave; sostenuto in un sol termine &rdquo; (Alb. </s>

<s>XIII, 132). </s></p><p type="main">

<s>Parve ai due Autori la cosa per s&egrave; tanto manifesta nelle note leggi <lb/>degli equiponderanti, che non ci videro nessun bisogno di dimostrarla, e <lb/>dall'altra parte non ritrovarono ragione al&shy;<lb/>cuna di dubitare che, se per esempio il ci&shy;<lb/>lindro AB (fig. </s>

<s>252), confitto con la sua <lb/><figure id="id.020.01.2234.1.jpg" xlink:href="020/01/2234/1.jpg"/></s></p><p type="caption">

<s>Figura 252<lb/>base A nel muro, e il cilindro BC, confit&shy;<lb/>tovi con la sua base C, resistono al proprio <lb/>peso, non debbano altres&igrave; resistere attestati <lb/>insieme i due cilindri in B (fig. </s>

<s>253), com&shy;<lb/>ponenti un cilindro solo AC doppiamente <lb/>lungo, non venendosi per questo avvicina&shy;<lb/><figure id="id.020.01.2234.2.jpg" xlink:href="020/01/2234/2.jpg"/></s></p><p type="caption">

<s>Figura 253<lb/>mento a far altro, che a favorire anzi la <lb/>virt&ugrave; di resistere alla rottura, col contatto <lb/>adesivo delle due superficie BE, e col re&shy;<lb/>ciproco appoggio delle testate. </s></p><p type="main">

<s>Incominciarono i dubb&icirc; a nascere, quan&shy;<lb/>do la chiarezza dei fatti venne a intorbidarsi <lb/>agitata dalle speculazioni, imperocch&egrave;, con&shy;<lb/>siderati i cilindri AB, BC della figura 252 <lb/>senza peso, e fatti rappresentare i momenti delle resistenze dai pesi uguali <lb/>P, Q, operanti col favor delle leve uguali AB, BC; si domandava se attestati <lb/>i due cilindri si dovevano i pesi P, Q unire insieme, o se bastava un solo <lb/>di essi a rappresentare le parti congiunte: sarebbe lo stesso che domandare <lb/>se in B, nella figura 253, le due linee BE, BE si son fuse in una, o se, per <lb/>la semplice congiunzione, si mantengan distinte. </s>

<s>E giacch&egrave;, considerate le <lb/>gravit&agrave; dei due cilindri AB, BC riunite nei loro centri, i pesi P, Q son la <lb/>met&agrave; dei pesi di essi cilindri, si riduceva la domanda a sapere se il peso R, <pb xlink:href="020/01/2235.jpg" pagenum="478"/>pendente dal mezzo del cilindro doppio a rappresentarne la resistenza, sia <lb/>uguale alla somma dei pesi P, Q, o ad uno di essi solo. </s>

<s>Che se sia uguale <lb/>alla somma, e la resistenza in B patisca perci&ograve; doppia violenza, non potrebbe <lb/>esser vero il supposto di Galileo, se non a patto che il cilindro AC sia pi&ugrave; <lb/>sottile o pi&ugrave; corto. </s></p><p type="main">

<s>Fu il dubbio primo a nascere nella mente del Viviani, il quale si pose <lb/>perci&ograve; innanzi a risolvere cos&igrave; il quesito: &ldquo; Se il cilindro AB, nell'ultima <lb/>figura 253, fitto nel muro, &egrave; bastante a spezzare in B, cio&egrave; a superare la <lb/>resistenza B, col proprio peso e con la leva AB, aggiungendo dall'altra parte <lb/>altrettanto cilindro BC, pare che la medesima resistenza B venga violentata <lb/>da doppia forza, e che, per spezzarsi col sostegno in mezzo, voglia essere <lb/>la met&agrave; pi&ugrave; sottile, o di lunghezza media proporzionale tra AB e BD met&agrave; <lb/>di AB &rdquo; (MSS. Gal., P. V, T. VII, fol. </s>

<s>29). </s></p><p type="main">

<s>Rimaste queste cose lungamente sepolte nei manoscritti, &egrave; notabile che <lb/>entrasse nel medesimo filo delle speculazioni, sulla fine del secolo XVII, un <lb/>celebre matematico francese, Filippo De-la-Hire, che nel suo <emph type="italics"/>Trait&eacute; de Me&shy;<lb/>canique<emph.end type="italics"/> risolve con nostra gran meraviglia le questioni della Libbra, avuto <lb/>riguardo ai pesi che tendono al centro della Terra, in quel modo che ve&shy;<lb/>demmo averle gi&agrave; risolute il Torricelli nei manoscritti suoi sconosciuti. </s>

<s>L'Ac&shy;<lb/>cademico parigino dunque, trattando nella sua proposizione CXXVI <emph type="italics"/>De la <lb/>resistance des solides,<emph.end type="italics"/> scrive cos&igrave; a proposito della proposizione XI di Ga&shy;<lb/>lileo: &ldquo; Il dit que ce cylindre doit se rompre de m&ecirc;me, soit qu'il soit sou&shy;<lb/>tenu par son milieu, ou par ses extremitez: mais il n'a pas fait assez d'at&shy;<lb/>tention &agrave; ce qu'il a avanc&eacute;, et s'il s'&eacute;toit donn&eacute; la peine d'en suivre la <lb/>d&eacute;monstration jusqu'&agrave; la fin, il auroit trouv&eacute; que, dans sa supposition des <lb/>liens, ce cylindre ne doit avoir que la moyenne proportionelle entre AB (nel&shy;<lb/>l'ultima nostra figura), et sa moiti&eacute; DB &rdquo; (A Paris 1695, pag. </s>

<s>483). </s></p><p type="main">

<s>La dimostrazione si pu&ograve;, per brevit&agrave; e per maggiore chiarezza, ridurre alla <lb/>forma seguente: Sia il cilindro ABC sostenuto nel suo mezzo B, come si rap&shy;<lb/>presenta nella figura ora citata: il momento <lb/>della sua resistenza, chiamata B la base <lb/>dello stesso cilindro, sar&agrave; B.AD.DB. </s>

<s>Ab&shy;<lb/>biasi poi un altro cilindro di ugual gros&shy;<lb/>sezza, e perci&ograve; di ugual base, ma talmente <lb/><figure id="id.020.01.2235.1.jpg" xlink:href="020/01/2235/1.jpg"/></s></p><p type="caption">

<s>Figura 254<lb/>lungo che la met&agrave; sua EG (fig. </s>

<s>254) sia media proporzionale tra AD, DB: il <lb/>momento della resistenza in E sar&agrave; uguale a B.EG.EG. </s>

<s>Ma EG.EG, ossia EG2, <lb/>&egrave; per supposizione uguale ad AD.DB, dunque le due resistenze sono uguali. </s></p><p type="main">

<s>Dir che Galileo non si <emph type="italics"/>donn&eacute; la peine<emph.end type="italics"/> di condurre alla sua final con&shy;<lb/>clusione una dimostrazione cos&igrave; fondamentale, doveva secondo il Grandi pa&shy;<lb/>rere un'altra calunnia: eppure, per offendere il Marchetti egli approva le <lb/>censure del De-la-Hire, salutato ossequiosamente col nome di <emph type="italics"/>profondissimo <lb/>Geometra,<emph.end type="italics"/> e con lui ripete &ldquo; che, dall'essere un cilindro retto nel mezzo <lb/>equilibrato con la sua resistenza, non doveva il Galileo inferire che il me&shy;<lb/>desimo reggere si dovesse appoggiato a due sostegni nelle sue estremit&agrave;, e <pb xlink:href="020/01/2236.jpg" pagenum="479"/>che piuttosto dovea dire che la lunghezza d'un cilindro, da reggersi sopra <lb/>due sostegni, esser debba mezzana proporzionale tra quella lunghezza, che <lb/>si pu&ograve; reggere pendente da un muro, e la doppia della medesima &rdquo; (Ri&shy;<lb/>sposta apol. </s>

<s>cit., pag. </s>

<s>122): d'onde, contro il Marchetti, conclude che la re&shy;<lb/>sistenza di un solido prismatico fitto nel muro, alla resistenza nel mezzo di <lb/>esso, non sta come uno a due, ma come uno a quattro, e che son perci&ograve; <lb/>da correggere tutte le proposizioni <emph type="italics"/>De resistentia solidorum,<emph.end type="italics"/> dipendenti <lb/>dalla seconda del secondo libro, col duplicare il conseguente delle proposi&shy;<lb/>zioni, ivi dall'Autore assegnate. </s></p><p type="main">

<s>Rispondeva il Marchetti, per difendere s&egrave; dalle accuse e insieme anche <lb/>Galileo, dimostrasse il suo Avversario perch&egrave; mai il peso B della figura 253 <lb/>debba esser la somma dei due pesi P, Q pendenti nella precedente figura, <lb/>e non piuttosto uguale a uno di essi solo, essendo che da un tal supposto <lb/>non dimostrato pigli tutta la virt&ugrave; di concludere la proposizion del De-la&shy;<lb/>Hire. </s>

<s>E giacch&egrave; la dignit&agrave; di Galileo vedeva essere cos&igrave; avvilita dal suo stesso <lb/>Difensore zelante, egli &egrave; il Marchetti il primo che, cogliendone di qui l'oc&shy;<lb/>casione, pensi a salvarla dalle apparenti contradizioni. </s></p><p type="main">

<s>Sui principii del primo dialogo delle Nuove Scienze leggesi descritto il <lb/>fatto di una colonna di marmo che, posata presso la sua estremit&agrave; sopra <lb/>due pezzi di trave, si ruppe a sottoporle un terzo simile sostegno nel mezzo <lb/>(Alb. </s>

<s>XIII, 9). &ldquo; Or dal successo, da Galileo raccontato, osserva il Marchetti, <lb/>e dalla cagione dal medesimo assegnatane, pare che quel grand'Uomo si <lb/>desse a credere che la resistenza di un medesimo cilindro, appoggiato nel <lb/>mezzo ad un solo sostegno, sia minore della resistenza del medesimo appog&shy;<lb/>giato a due ne'suoi punti estremi, il che &egrave; poi tutto il contrario di quello <lb/>che lo stesso Galileo afferma nella proposizione XI del secondo dialogo &rdquo; <lb/>(Discorso cit., pag. </s>

<s>59, 60). </s></p><p type="main">

<s>Essendo questo insomma il principo, posto per fondamento alla Scienza <lb/>delle resistenze dei solidi appoggiati su due sostegni, premeva troppo al Mar&shy;<lb/>chetti di confermarlo, almeno con l'autorit&agrave; di Galileo, e perci&ograve; impiega l'ul&shy;<lb/>tima parte del suo <emph type="italics"/>Discorso apologetico,<emph.end type="italics"/> da pag. </s>

<s>58 a pag. </s>

<s>68, a provar che <lb/>le teorie professate nel secondo dialogo non contradicono alle esperienze de&shy;<lb/>scritte nel primo, s&igrave; perch&egrave; le due travi, che facevano alla pesante colonna <lb/>da sostegni, non essendo punti indivisibili non dovevano segnare le distanze <lb/>precise dal mezzo; s&igrave; perch&egrave;, non essendo la colonna un cilindro perfetto, <lb/>ma, come tutte le altre colonne materiali erette per i nostri edifizi, essendo <lb/>sensibilmente pi&ugrave; grossa da una parte che da un'altra, il centro di gravit&agrave; <lb/>non doveva riuscire appunto nel mezzo della figura, dove si dice esserle stato <lb/>sottoposto quel terzo sostegno, per maggior sicurezza. </s></p><p type="main">

<s>Quanto poi al principio, da cui s'informa la proposizion del De-la-Hire, <lb/>con tanto ardore proseguita dal Grandi, faceva argutamente osservare esso <lb/>Marchetti che il peso del cilindro EGF nella figura 254 &ldquo; allora tutto si rac&shy;<lb/>coglie ed esercita la sua energia sul proprio centro di gravit&agrave;, quando pende <lb/>in aria liberamente, senza esser retto da alcun sostegno, il che non succede <pb xlink:href="020/01/2237.jpg" pagenum="480"/>nel caso, nel quale il cilindro EGF &egrave; appoggiato ne'suoi estremi a due so&shy;<lb/>stegni, i quali vengono a scemarli la met&agrave; del suo peso &rdquo; (Discorso cit., <lb/>pag. </s>

<s>56). Accusava perci&ograve; di falsi i modi di dimostrare del De-la-Hire e del <lb/>Grandi, i quali, nel computare il momento della parte EG del cilindro, pren&shy;<lb/>dono per leva favorevole EG, mentre dovrebbe esser quella vera leva la di&shy;<lb/>stanza del centro di gravit&agrave; di esso EG dal suo proprio sostegno. </s>

<s>Cos&igrave; se <lb/>ne concluderebbe che tutto il cilindro EF, appoggiato dalle sue estremit&agrave;, <lb/>&egrave; lungo e grosso quanto AC appoggiato solo nel mezzo, come lo rappresenta <lb/>la figura 253, e come fu supposto da Galileo. </s></p><p type="main">

<s>La forza di queste ragioni non poteva non essere presentita dal Grandi, <lb/>il quale, trovandosi la mente gi&agrave; tentata dai dubbii, ne volle avere il giudi&shy;<lb/>zio del Leibniz. </s>

<s>Rispondeva il celebre Matematico, letto il libro del Mar&shy;<lb/>chetti: &ldquo; Haerebam in primis in eius demonstratione, quando accedebat ad <lb/>solidum utrinque fultum. </s>

<s>Sane, cum tunc ruptura alicubi fit in medio, con&shy;<lb/>tingit aliqua veluti extritio, quae non est obvia, cum solidum ex muro proie&shy;<lb/>ctum est, et rumpitur prope murum &rdquo; (MSS. Cim., T. XXIX, fol. </s>

<s>287). </s></p><p type="main">

<s>Questa osservazione consigli&ograve; forse il Grandi a tenere una via di mezzo, <lb/>in risolvere la questione, dicendo che la proposizione del De-la-Hire &egrave; vera, <lb/>quando il solido semplicemente si appoggia con le sue estremit&agrave; sui soste&shy;<lb/>gni. </s>

<s>&ldquo; Quando poi, soggiunge, i termini di un solido fossero immobilmente <lb/>fitti in due pareti, ed impegnativi dentro, allora cresce il doppio di prima <lb/>la resistenza di esso solido, perch&egrave;, do&shy;<lb/>vendosi spezzare, dovrebbe rompersi an&shy;<lb/>cora vicino ai due sostegni, le quali due <lb/>frazioni equivalgono appunto alla rottura <lb/>del mezzo, come mostra il p. </s>

<s>Host&egrave;, li&shy;<lb/>bro II, propos. </s>

<s>LIX e LXII <emph type="italics"/>Della costru&shy;<lb/>zion dei vascelli,<emph.end type="italics"/> d'onde in tal caso si <lb/>verifica esattamente la proposizione del <lb/>Galileo &rdquo; (Risposta apol. </s>

<s>cit., pag. </s>

<s>122, 23). </s></p><p type="main">

<s>La proposizione LIX, che qu&igrave; il <lb/>Grandi cita dal II libro della <emph type="italics"/>Theorie<emph.end type="italics"/><lb/><figure id="id.020.01.2237.1.jpg" xlink:href="020/01/2237/1.jpg"/></s></p><p type="caption">

<s>Figura 255<lb/><emph type="italics"/>de la costruction des vaisseux<emph.end type="italics"/> di Paolo Host&eacute;, &egrave; cos&igrave; formulata: &ldquo; Si le <lb/>poids C (fig. </s>

<s>255), en faisant l'ouverture FNG, fait aussi les ouvertures AML, <lb/>BHI, ces deus ouvertures prises ensemble <lb/>vaudront autant que l'ouverture FNG &rdquo; <lb/>(A Lyon 1697, pag. </s>

<s>114): di che la dimo&shy;<lb/>strazione &egrave; ovvia, dietro i primi elementi <lb/>della Geometria, essendo l'angolo FNE= <lb/>AML, come pure, per simili ragioni, l'an&shy;<lb/>golo GNE=IHB. </s></p><p type="main">

<s>Questa LIX proposizione per&ograve; di&shy;<lb/>pende dalla XVII, che poteva forse il <lb/><figure id="id.020.01.2237.2.jpg" xlink:href="020/01/2237/2.jpg"/></s></p><p type="caption">

<s>Figura 256<lb/>Grandi citare pi&ugrave; opportunamente, perch&egrave;, date due travi, una AC (fig. </s>

<s>256), <pb xlink:href="020/01/2238.jpg" pagenum="481"/>appoggiata nel mezzo E, e gravata dai pesi A, C ne'suoi estremi; l'altra <lb/>MO, perfettamente uguale alla AC, ma appoggiata dalle due parti M, O, e <lb/>caricata nel mezzo dal peso N; dimostra l'Host&eacute; &ldquo; que la vitesse de la puis&shy;<lb/>sance N est moins grande que la vitesse des poids A, C &rdquo; (ivi, pag. </s>

<s>101). <lb/>E nel corollario alla seguente propos&igrave;zione XVIII, nella quale dimostra che <lb/>la velocit&agrave; del peso N, sta alla velocit&agrave; dei pesi A, C, come il coseno del&shy;<lb/>l'angolo della met&agrave; dell'apertura sta al seno totale; osserva che, se l'aper&shy;<lb/>tura &egrave; infinitesima, o come diremmo volgarmente se la trave &egrave; semplice&shy;<lb/>mente <emph type="italics"/>incrinata,<emph.end type="italics"/> il peso N sar&agrave; uguale alla somma dei pesi A, C. &ldquo; Si on <lb/>fait l'ouverture de la poutre infinement petite, la vitesse de la puissance N <lb/>sera egale &agrave; la vitesse des poids A, C; c'est pourquoi la puissance N sera <lb/>egale aux poids A, C &rdquo; (ivi, pag. </s>

<s>102). </s></p><p type="main">

<s>Cos&igrave; essendo, occorre ora a domandare se citasse opportunamente il <lb/>Grandi queste proposizioni dell'Host&eacute; a decider tra il De-la-Hire e il Mar&shy;<lb/>chetti la differenza, incominciata da un semplice dubbio del Viviani intorno <lb/>alla proposizione XI di Galileo. </s>

<s>&Egrave; facile a rispondere che non pu&ograve; nel pre&shy;<lb/>sente giudizio nulla valere l'autorit&agrave; dell'Host&eacute;, il quale ammette ipotesi e <lb/>professa principii tutt'affatto diversi da quelli di Galileo, e perci&ograve; del De&shy;<lb/>la-Hire e del Marchetti. </s>

<s>Lo fa avvertire l'Autore stesso nella prefazione a <lb/>questo secondo libro, dove, dopo aver detto che il desiderio di fare accorti <lb/>gli Stati di tante inutili spese, nel provvedere alla stabilit&agrave; delle navi da <lb/>guerra, gli avea fatto intraprendere la fatica di ricercar la teorica delle loro <lb/>costruzioni; soggiunge di non aver ignorato che Galileo l'avea prevenuto, <lb/>nel trattar l'argomento, &ldquo; quoique les voyes que j'ai tenues soient tout a <lb/>fait differentes &rdquo; (ivi, pag. </s>

<s>94). La qual differenza apparisce notabile dalla <lb/>proposizione XXV, in cui si dimostra che la scala dei momenti dei pesi uguali <lb/>attaccati ad una libbra, sostenuta ne'suoi estremi, sta nel triangolo, mentre <lb/>per Galileo sta nella parabola. </s></p><p type="main">

<s>Al giudizio dunque del Matematico francese, male a proposito invocato <lb/>dal Grandi, potremo sostituire quello del nostro italiano Mariano Fontana, il <lb/>quale, avendo nel primo de'suoi tre libri <emph type="italics"/>Della dinamica<emph.end type="italics"/> preso ad esami&shy;<lb/>nar sottilmente la proposizione del De-la-Hire, con la quale s'accorda <emph type="italics"/>il ce&shy;<lb/>lebre geometra Guidone Grandi,<emph.end type="italics"/> sentenza che <emph type="italics"/>questi s'ingannano senza, <lb/>dubbio, e che il Galileo ha ragione.<emph.end type="italics"/> Gli argomenti da provar ci&ograve; si ridu&shy;<lb/>cono principalmente a quelli, con i quali il Marchetti si studiava di salvare <lb/>i principii ch'egli professava dalle fallacie de'due contradittori ora comme&shy;<lb/>morati &ldquo; l'errore dei quali, dice il Fontana, ha origine dalla supposizione, <lb/>la quale essi fanno, che tutto il peso del prisma EF, nella nostra figura 254, <lb/>sia riunito nel suo centro di gravit&agrave; in G.... Ma, da quanto fu dimostrato <lb/>di sopra, chiaro apparisce che non &egrave; permesso, nel presente caso, di sup&shy;<lb/>porre tutto il peso del prisma EF nel suo centro di gravit&agrave;. </s>

<s>I due segmenti <lb/>EG, GF formano due sistemi, e questi sono in una vera opposizione l'uno <lb/>contro l'altro. </s>

<s>Quindi si pu&ograve; bene supporre che il peso di ciascun segmento <lb/>sia nel suo centro di gravit&agrave;, ma non gi&agrave; che i pesi dei due segmenti siano <pb xlink:href="020/01/2239.jpg" pagenum="482"/>riuniti nel centro di gravit&agrave; del prisma.... Veramente &egrave; singolare che uo&shy;<lb/>mini forniti di tanto ingegno, e di cos&igrave; squisita dottrina, non vedessero che <lb/>altro effetto dee fare il peso tutto riunito in G, ed il peso stesso distribuito <lb/>nella lunghezza del prisma &rdquo; (Pavia 1790, pag. </s>

<s>306, 7). Il qual discorso si <lb/>pu&ograve; concluder col dire che, riducendo in G il centro, il prisma si considera <lb/>come se dovesse rimanere intero, e non disposto alla rottura. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Risulta da tutto il precedente discorso il mal animo, e il perverso giu&shy;<lb/>dizio del Grandi verso il Marchetti, ma abbiamo voluto riserbare alla pre&shy;<lb/>sente parte del nostro capitolo l'esame di un'altra accusa di plagio, perch&egrave; <lb/>ci porge occasione a un argomento speciale, e importante in questa storia <lb/>Delle resistenze. </s></p><p type="main">

<s>L'Autore dunque <emph type="italics"/>De quadratura circuli,<emph.end type="italics"/> in quel luogo della sua pre&shy;<lb/>fazione, da noi altrove citato, incominci&ograve; maliziosamente dall'accennare al <lb/>teorema meccanico de'momenti composti delle distanze e dei pesi: e perch&egrave; <lb/>di ci&ograve; il Marchetti menava vanto come di una scoperta sua propria, egli al <lb/>contrario, per attutirne la baldanza, citava un passo dalla <emph type="italics"/>Scienza delle pro&shy;<lb/>porzioni,<emph.end type="italics"/> dove il Viviani dichiara essere stato il detto teorema Dei momenti <lb/>insegnato gi&agrave;, e messo in uso da Galileo, dal Cavalieri, dal Rocca e dal Tor&shy;<lb/>ricelli. </s>

<s>Poi soggiunge l'Autore di quella Prefazione, facendo vista di volere <lb/>scusare il Marchetti: <emph type="italics"/>cum tamen id citra ullam plagii suspicionem eventu <lb/>facillimum suadeat obvia cuilibet ex primis vulgatisque Mechanicae prin&shy;<lb/>cipiis dictae propositionis deductio.<emph.end type="italics"/> Ma il velo, tolto a queste parole da lui <lb/>stesso, che con tant'arte ce lo aveva messo, mentre lo rende colpevole della <lb/>pi&ugrave; scaltra e pi&ugrave; vile ipocrisia, viene a confermar sempre meglio l'irragio&shy;<lb/>nevolezza di quelle accuse, che vedemmo non aver provocate altro che l'odio. </s></p><p type="main">

<s>Proponiamoci prima di tutto quel che scrisse il Viviani nella sua <emph type="italics"/>Scienza <lb/>universale delle proporzioni,<emph.end type="italics"/> in quel luogo citato dal Grandi, cio&egrave; dopo la <lb/>conclusione V che dice: <emph type="italics"/>Quorumcumque gravium a quibuslibet distantiis <lb/>suspensorum momenta sunt in ratione composita ex ratione distantiarum <lb/>et ex ratione gravitatum. </s>

<s>&rdquo;<emph.end type="italics"/> Questo teorema, ivi si legge, fu dimostrato dal&shy;<lb/>l'acutissimo matematico il padre Bonaventura Cavalieri, e da lui stampato <lb/>nel 1647, alla proposizione VI della sua quinta <emph type="italics"/>Esercitazione geometrica,<emph.end type="italics"/><lb/>bench&egrave; di tal conclusione si fosse prima servito un tal Giovanni Antonio <lb/>Rocca, insigne Geometra e discepolo di detto Padre, in un suo proprio lemma <lb/>meccanico, il quale fu poi riferito dal Torricelli, in pi&egrave; della proposizione XVIII <lb/>delle sue <emph type="italics"/>Quadrature della parabola.....<emph.end type="italics"/> Ma per&ograve; questa medesima con&shy;<lb/>clusione molto prima era nota al nostro Galileo, come apparisce da quel suo <lb/>teorema meccanico, nel trattato <emph type="italics"/>Delle resistenze,<emph.end type="italics"/> premesso come lemma al <lb/>problema che propone: <emph type="italics"/>Dato il peso massimo retto dal mezzo d'un ci-<emph.end type="italics"/><pb xlink:href="020/01/2240.jpg" pagenum="483"/><emph type="italics"/>lindro o prisma, dove la resistenza &egrave; minima, e dato un peso maggiore di <lb/>quello, trovare nel detto cilindro il punto, nel quale il dato peso maggiore <lb/>sia retto come peso massimo:<emph.end type="italics"/> dove manifestamente si riconosce tal quinta <lb/>conclusione, ed ancora il mezzo per dimostrarla &rdquo; (Firenze 1674, pag. </s>

<s>8, 9). </s></p><p type="main">

<s>Potrebb'essere che il Viviani s'inducesse a fare questi cenni storici del <lb/>Teorema meccanico dei momenti, per levare ogni vana presunzione dall'animo <lb/>del Marchetti: non apparisce da nessuna parte del suo discorso per&ograve; che fosse <lb/>propriamente questa la sua intenz&igrave;one, della quale nonostante si fa interpetre <lb/>il Grandi, per aver, nell'offendere il comune nemico, un ausiliario cos&igrave; potente. </s>

<s><lb/>Il Marchetti, che sotto la pelle dell'agnello, della quale s'era coperto l'Autore <lb/>della Quadratura del circolo, sapeva bene nascondersi l'arti insidiose del lupo, <lb/>intese che Galileo, il Cavalieri e il Torricelli gli venivano proposti, per rinfac&shy;<lb/>ciargli la temerit&agrave; di essersi appropriata un'invenzione, della quale si ricono&shy;<lb/>scevano quelli per primi autori. </s>

<s>E perch&egrave; si sentiva, per solo avere ignorata la <lb/>storia, la coscienza franca intorno a ci&ograve; di ogni colpa volontaria, ne volle far <lb/>pubblica confessione in modo, che, se non in ogni incidente, nel merito prin&shy;<lb/>cipale della causa per&ograve; noi giudici imparziali abbiam dovuto riconoscerne l'in&shy;<lb/>nocenza. </s>

<s>Affinch&egrave; poi la promessa imparzialit&agrave; del giudizio apparisca sincera, <lb/>e venga ad aver perci&ograve; sull'animo e nella mente dei nostri Lettori maggiore <lb/>efficacia, vogliamo che le difese, prima di sentirle uscire dalla bocca dell'im&shy;<lb/>putato, resultino in favore a lui dal diligente esame dei fatti. </s></p><p type="main">

<s>E per cominciare da Galileo, la proposizione, nella quale da lui dice <lb/>il Viviani essere invocato il Teorema dei momenti, &egrave; la XII, cos&igrave; formulata: <lb/>&ldquo; Se nella lunghezza d'un cilindro si noteranno due luogh&igrave;, sopra i quali <lb/>si voglia far la frazione di esso cilindro, le resistenze di detti due luoghi <lb/>hanno tra di loro la medesima proporzione, che i rettangoli fatti dalle di&shy;<lb/>stanze di essi luoghi, contrariamente presi &rdquo; (Alb. </s>

<s>XIII, 135). </s></p><p type="main">

<s>Proponi&agrave;moci la medesima <lb/>figura galileiana, per noi la 257, <lb/>nella quale A, B rappresentano i <lb/>minimi pesi atti a rompere il ci&shy;<lb/>lindro AB in C, come E, F rap&shy;<lb/>presentan pure i minimi pesi, per <lb/>rompere in D: abbiamo, per la <lb/>teoria della leva, A:B=BC:AC, <lb/>E:F=BD:AD, le quali due <lb/><figure id="id.020.01.2240.1.jpg" xlink:href="020/01/2240/1.jpg"/></s></p><p type="caption">

<s>Figura 257<lb/>equazioni danno per composizione ciascuna A+B:B=BA:AC; E+F:F= <lb/>BA:AD; d'onde s'ha, permutando, A+B:E+F=B/F:AC/AD. </s>

<s>Ma per le <lb/>supposte cose, e per ragione del Vette &ldquo; come la forza B alla F, cos&igrave;, <lb/>dice Galileo, sta reciprocamente la linea DB alla BC &rdquo; (ivi) e perci&ograve;, sosti&shy;<lb/>tuendo nell'ultima B/F il suo uguale DB/BC, si viene alla proposta conclusione <lb/>A+B:E+F=BD.AD:AC.BC. </s></p><pb xlink:href="020/01/2241.jpg" pagenum="484"/><p type="main">

<s>Diceva il Viviani, come dianzi udimmo, che in questo processo dimo&shy;<lb/>strativo di Galileo si riconosce la conclusion dei momenti, <emph type="italics"/>ed ancora il mezzo <lb/>di dimostrarla.<emph.end type="italics"/> E infatti, se per momento s'intende, com'esso Galileo nella <lb/><emph type="italics"/>Scienza meccanica<emph.end type="italics"/> insegna, <emph type="italics"/>quell'impeto di andare al basso composto di <lb/>gravit&agrave; e di posizione<emph.end type="italics"/> (Alb. </s>

<s>XI, 90), i prodotti B.BC, F.BD rappresen&shy;<lb/>tano due momenti Mo.B, Mo.F uguali, perch&egrave; i due pesi B, F, operando colle <lb/>distanze BC, BD, s'&egrave; supposto che producano effetti uguali. </s>

<s>Abbiamo dunque <lb/>Mo.B:Mo.F=B.BC:F.BD; equazione, che tiene in s&egrave; scritta la scoperta <lb/>del Marchetti dei momenti proporzionali ai prodotti delle distanze e dei pesi. </s></p><p type="main">

<s>Ma poteva il Marchetti rispondere che in Galileo si riconosce il Teo&shy;<lb/>rema ne'suoi principii, non per&ograve; nella forma della conclusione, in dar la <lb/>qual forma poteva tuttavia compiacersi l'Autor <emph type="italics"/>De resistentia solidorum<emph.end type="italics"/> di <lb/>essere stato il primo. </s>

<s>Or che avrebbero mai detto e fatto il Grandi e il Vi&shy;<lb/>viani, se avessero saputo che Galileo, anche in mettere in espressa forma <lb/>la conclusione aveva prevenuto e superato il Marchetti? </s>

<s>Nessuno par che <lb/>fin qui abbia avuto notizia dei pochi rimasti fra que'fogli, dove il Salviati <lb/>diceva di aver per ordine notati i teoremi e problemi attenenti alle Resi&shy;<lb/>stenze, e colui stesso, che gli raccolse nel Volume in cui noi gli abbiamo <lb/>trovati, mettendo innanzi il foglietto che doveva venir dopo, poneva e s&egrave;, e <lb/>chiunque avesse superficialmente svolte le dotte carte in grande difficolt&agrave; di <lb/>ricavarne il costrutto. </s>

<s>&Egrave; tempo perci&ograve; che diamo ai nostri Lettori la gi&agrave; <lb/>promessa sodisfazione, negata al Viviani, al Grandi e ai tanti altri Galile&shy;<lb/>iani sviscerati, trascrivendo dall'autografo il Teorema famoso cos&igrave; formulato: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Ponderum, in Libra suspensorum, momenta habent rationem com&shy;<lb/>positam ex ratione ipsorum ponde&shy;<lb/>rum, et ex ratione distantiarum.<emph.end type="italics"/> &mdash; <lb/>Pendeant pondera DE et F (fig. </s>

<s>258) <lb/>ex d&igrave;stantiis AB, BC: dico momen&shy;<lb/>tum ponderis DE, ad momentum pon&shy;<lb/>deris F, habere rationem compositam <lb/>ex rationibus ponderis DE ad pen&shy;<lb/><figure id="id.020.01.2241.1.jpg" xlink:href="020/01/2241/1.jpg"/></s></p><p type="caption">

<s>Figura 258<lb/>dus F, et distantiae AB, ad distantiam BC &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>40). </s></p><p type="main">

<s>La dimostrazione muove da due principii: il primo dei quali &egrave; quello, <lb/>che il Viviani riconobbe nella XII proposizione del II dialogo delle Scienze <lb/>nuove, dichiarata da noi pi&ugrave; sopra, e l'altro, che immediatamente deriva <lb/>dalle propriet&agrave; del Vette, gli effetti del quale son proporzionali alle forze ap&shy;<lb/>plicate nelle medesime, o in eguali distanze. </s>

<s>Presa perci&ograve; del maggior peso <lb/>DE tanta parte DO, che, avendosi per l'uno dei proposti principii F:OD= <lb/>AB:BC, il momento di F sia uguale a quello di DO, avendosi per l'altro <lb/>dei premessi principii M.oOD:M.oDE=OD:DE; se si ponga in questa <lb/>equazione M.oOD=M.oF, e OD=F.BC/AB, si giunge alla conclusione <lb/>M.oF:M.oDE=F.BC:DE.AB, alla quale pure giunge Galileo, mettendo <lb/>in quest'altra forma il suo discorso: </s></p><pb xlink:href="020/01/2242.jpg" pagenum="485"/><p type="main">

<s>&ldquo; Ut enim AB ad BC, ita fiat pondus F ad pondus DO: cum ergo pon&shy;<lb/>dera F et DO habeant rationem distantiarum AB, BC permutatam, erit mo&shy;<lb/>mentum ponderis F aequale momento ponderis DE. </s>

<s>Cum igitur sint tria <lb/>pondera utcumque ED, F et DO, erit ratio ponderis ED ad DO composita <lb/>ex ratione ED ad F, et F ad DO. &rdquo; </s></p><p type="main">

<s>&ldquo; Ut autem pondus ED ad pondus DO, ita momentum ED ad momen&shy;<lb/>tum DO: pendent enim ex eodem puncto. </s>

<s>Igitur, cum momentum DO sit <lb/>aequale momento F, ratio momenti ED, ad momentum F, erit composita <lb/>ex ratione ponderis ED, ad pondus F, et ponderis F ad pondus DO. &rdquo; </s></p><p type="main">

<s>&ldquo; Factum est autem pondus F, ad pondus DO, ut distantia AB ad distan&shy;<lb/>tiam BC; ergo patet momentum ponderis ED, ad momentum ponderis F <lb/>habere rationem compositam ex rationibus ponderum ED, F, et distantiarum <lb/>AB, BC &rdquo; (ibid.). </s></p><p type="main">

<s>Seguita un corollario, che serve per lemma a un'altra proposizione, nel&shy;<lb/>l'intender la quale s'aggiunger&agrave; nei nostri Lettori, alla maraviglia dell'aver <lb/>Galileo lasciata indietro quella prima proposizione importante, la maraviglia <lb/>dell'averne anche insieme lasciata una seconda, per s&egrave;, e per le sue appli&shy;<lb/>cazioni al trattato delle resistenze, assai bella. </s></p><p type="main">

<s>&ldquo; Quod si suspendatur, cos&igrave; dice quel corollario, ex puncto S (nella <lb/>medesima fig. </s>

<s>258), facta distantia BS aequali distantiae BC, pondus T ae&shy;<lb/>quale ponderi F, erit eius momentum momento F aequale, et similiter pon&shy;<lb/>derum ED et T momenta habebunt rationem compositam ex ponderibus <lb/>ED, T, et ex distantiis AB, BS. &rdquo; </s></p><p type="main">

<s>&ldquo; Sit modo cylindrus EGT (fig. </s>

<s>259), respondens Librae ABCD, utcum&shy;<lb/><figure id="id.020.01.2242.1.jpg" xlink:href="020/01/2242/1.jpg"/></s></p><p type="caption">

<s>Figura 259<lb/>que sectum in SG: dico momentum <lb/>totius cylindri pendentis ex C, ad mo&shy;<lb/>mentum frusti EG pendentis ex B, <lb/>esse ut rectangulus DCA, ad rectan&shy;<lb/>gulum DBA. &rdquo; </s></p><p type="main">

<s>&ldquo; Ex demonstratis enim momen&shy;<lb/>tum ponderis EGT, ad momentum pon&shy;<lb/>deris EG, habet rationem compositam ex pondere EGT ad pondus EG, et <lb/>distantiae CD ad distantiam DB. </s>

<s>Pondus autem EGT, ad pondus EG, est <lb/>ut linea AC ad AB; ergo momentum ponderis EGT, ad momentum ponde&shy;<lb/>ris GE, habet rationem compositam ex CD ad DB, et ex CA ad AB, quae <lb/>est rectanguli DCA, ad rectangulum DBA &rdquo; (ibid.). </s></p><p type="main">

<s>Rimaste queste cose ne'Manoscritti sconosciute, non si poteva a tutto <lb/>diritto negare al Marchetti il vanto di aver egli il primo esplicato, e pre&shy;<lb/>messo in for&mgrave;a al suo libro Delle resistenze il Teorema meccanico dei mo&shy;<lb/>menti: cosicch&egrave; o cessa, o viene ad essere infirmata quell'accusa di pla&shy;<lb/>gio, mossagli incontro dal Viviani e dal Grandi, per quello che s'appartiene <lb/>a Galileo. </s></p><p type="main">

<s>Quanto poi al Torricelli, &egrave; verissimo che, alla proposizione XVIII del <lb/>secondo libro Delle quadrature della parabola, soggiungeva il Lemma, in cui <pb xlink:href="020/01/2243.jpg" pagenum="486"/>il Rocca servivasi per dimostrarlo di questo principio: che cio&egrave;, se sia data <lb/>una linea retta ponderosa sostenuta in un punto, che la divida in due parti, <lb/>il momento dell'una al momento dell'altra &ldquo; habebit rationem compositam <lb/>ex ratione magnitudinum, et ex ratione distantiarum &rdquo; (Opera geom., P. II <lb/>cit., pag. </s>

<s>77): ma n&egrave; dall'uno, n&egrave; dall'altro Autore per&ograve; si dimostrava per&shy;<lb/>ch&egrave; dovesse aversi quella detta ragione. </s>

<s>Anzi lo stesso Torricelli aveva dato <lb/>al Marchetti, e a Giuseppe Vanni suo discepolo, come altrove accennammo, <lb/>occasione di esser ripreso intorno alla seconda proposizione <emph type="italics"/>De motu gra&shy;<lb/>vium,<emph.end type="italics"/> nella quale si pronunzia che il momento del grave scendente per <lb/>l'un piano inclinato sta al momento del discendente per l'altro, <emph type="italics"/>ut moles <lb/>ad molem<emph.end type="italics"/> (ibid., P. I, pag. </s>

<s>100), mentre la ragion vera di essi momenti &egrave; <lb/>composta dei pesi assoluti, e delle distanze. </s></p><p type="main">

<s>Bench&egrave; quella seconda torricelliana proposizione sia vera, e si possano <lb/>in qualche modo salvare i principii di mezzo, ivi invocati per dimostrarla, <lb/>&egrave; per&ograve; un fatto notabilissimo che il Torricelli, in due teoremi lasciatici ma&shy;<lb/>noscritti, mostr&ograve; di esser davvero scorso in quegli errori, pubblicamente <lb/>notati nella meccanica Esercitazione del Vanni. </s></p><p type="main">

<s>&Egrave; il primo dei due detti Teoremi proposto dall'Autore in questa forma: <lb/>&ldquo; Se due pesi di diversa gravit&agrave; in specie, ma di mole eguali, saranno po&shy;<lb/>sti a distanze disuguali dal centro, il peso assoluto del primo, al peso as&shy;<lb/>soluto del secondo, aver&agrave; la proporzione composta della proporzione, che ha <lb/>la gravit&agrave; in specie del primo alla gravit&agrave; in specie del secondo, e della <lb/>proporzione, che ha la distanza del primo alla distanza del secondo dal <lb/>centro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Siano i due pesi <emph type="italics"/>ut ponitur<emph.end type="italics"/> L, O (fig. </s>

<s>260) il centro C, e le distanze <lb/>disuguali OC, CL. Facciasi, come la gravit&agrave; del primo O, alla gravit&agrave; del <lb/><figure id="id.020.01.2243.1.jpg" xlink:href="020/01/2243/1.jpg"/></s></p><p type="caption">

<s>Figura 260<lb/>secondo L; cos&igrave; la linea A <lb/>alla B; e, come la distanza <lb/>del primo, alla distanza del <lb/>secondo, cos&igrave; la linea B alla <lb/>D: dico che il peso asso&shy;<lb/>luto di O, all'assoluto di L, <lb/>&egrave; come la linea A alla D. &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXVII, fol. </s>

<s>77). </s></p><p type="main">

<s>Per rendere, in poche parole e pi&ugrave; chiara, la dimostrazion dell'Autore, <lb/>chiaminsi G.O, G.L le gravit&agrave; dei due pesi, e D.O, D.L le loro distanze: <lb/>abbiamo, secondo il supposto, G.O:G.L=A:B; D.O:D.L=B:D. </s>

<s><lb/>Moltiplicando termine per termine fra loro queste due proporzioni, o poi eli&shy;<lb/>minando la quantit&agrave; B dalla seconda ragione, se ne conclude immediata&shy;<lb/>mente G.OXD.O:G.LXD.L=A:D. </s></p><p type="main">

<s>Ora, &egrave; di qui manifesto che, essendo per la fatta supposizione le moli, <lb/>ossia i volumi uguali, questa prima scritta ragione rappresenta la composi&shy;<lb/>zion dei momenti, e son perci&ograve; essi momenti che stanno come A a D, e <lb/>non i pesi assoluti, come diceva il Torricelli. </s></p><p type="main">

<s>L'errore, incredibile in tanto Uomo e in tanto facile argomento, fu no-<pb xlink:href="020/01/2244.jpg" pagenum="487"/>tato gi&agrave; dal Viviani, quando, nel raccogliere anche queste fra le altre tor&shy;<lb/>ricelliane proposizioni, rimaste senz'ordine e senza forma nei manoscritti; <lb/>la metteva per la X nel trattato, ch'egli aveva preso a compilare <emph type="italics"/>De molu <lb/>ac momentis,<emph.end type="italics"/> avvertendo ch'era stata da lui &ldquo; fatta latina, e corretta col <lb/>mutare per tutto le parole <emph type="italics"/>peso assoluto,<emph.end type="italics"/> dicendo <emph type="italics"/>momento,<emph.end type="italics"/> ed aggiungendo <lb/>alla parola <emph type="italics"/>gravit&agrave;<emph.end type="italics"/> sempre <emph type="italics"/>in specie,<emph.end type="italics"/> perch&egrave;, se in luogo di momento dicesse <lb/>peso assoluto, ed in luogo di gravit&agrave; in specie dicesse solamente gravit&agrave;, tutta <lb/>la proposizione e dimostrazione &egrave; falsa &rdquo; (ivi, fol. </s>

<s>95). Onde a renderla vera <lb/>il Viviani stesso intendeva cos&igrave; di proporla: &ldquo; Si duo pondera diversae gra&shy;<lb/>vitatis in specie, sed aequalium molium, appensa fuerint in aequalibus a <lb/>centro distantiis, momentum primi ponderis, ad momentum secundi, habe&shy;<lb/>bit rationem compositam ex ratione gravitatis in specie primi, ad gravita&shy;<lb/>tem in specie secundi, et ex proportione distantiae primi, ad distantiam se&shy;<lb/>cundi &rdquo; (ivi). </s></p><p type="main">

<s>L'altro Teorema, soggiunto nel manoscritto del Torricelli a dimostrare <lb/>la ragion dei momenti, da qualunque distanza pendano i gravi, e qualun&shy;<lb/>que sia la loro gravit&agrave; specifica, e il loro volume; vien proposto dall'Autore <lb/>in questa forma: &ldquo; Se saranno due solidi di gravit&agrave; diversa in specie, di <lb/>mole disuguali, posti in distanze disuguali dal centro, e se si far&agrave; come la <lb/>gravit&agrave; del primo, alla gravit&agrave; del secondo, cos&igrave; l'A al B, e come la mole <lb/>del primo, alla mole del secondo, cos&igrave; B al C, e come la distanza del primo, <lb/>alla distanza del secondo, cos&igrave; C al D; aver&agrave; il peso assoluto del primo, al <lb/>peso assoluto del secondo, la proporzione che ha l'A al D. &rdquo; </s></p><p type="main">

<s>&ldquo; Sia il primo A, il secondo B, il centro C; e siano le linee D, E, F, G, <lb/>come si suppone: dico che il peso assoluto di A, al peso assoluto di B, &egrave; <lb/>come D a G &rdquo; (ivi, fol. </s>

<s>77). </s></p><p type="main">

<s>&Egrave; facile scoprire anche in questo un errore simile a quello scoperto <lb/>nel Teorema precedente, imperocch&egrave;, chiamate G.A, V.A, D.A; G.B, <lb/>V.B, D.B, le gravit&agrave; in specie, le moli o i volumi e le distanze di A e <lb/>di B, si hanno le tre equazioni G.A:G.B=D:E; V.A:V.B=E:F; <lb/>D.A:D.B=F:G, le quali moltiplicate insieme, ed eliminato il comun <lb/>prodotto EXF nella seconda ragione, concludono G.AXV.AXD.A: <lb/>G.BXV.BXD.B=D:G. Ora, perch&egrave; G.AXV.A, G.BXV.B <lb/>sono uguali ai pesi assoluti di A e di B, &egrave; manifesta la falsit&agrave; della propo&shy;<lb/>sta torricelliana, e come essi pesi assoluti, non semplicemente, ma molti&shy;<lb/>plicati per le distanze, ossia i loro momenti, abbiano come D a G le loro <lb/>ragioni. </s></p><p type="main">

<s>Il Viviani perci&ograve;, che raccolse anche questa seconda proposizione, per <lb/>metterla in ordine la XI nel trattato torricelliano <emph type="italics"/>De motu ac momentis,<emph.end type="italics"/><lb/>notava in margine al suo manoscritto di averla &ldquo; fatta latina, corretta come <lb/>la passata, perch&egrave; era falsa al modo scritto dall'Autore &rdquo; (ivi, fol. </s>

<s>96), onde <lb/>egli avrebbe voluto renderla alla verit&agrave;, pronunziandola in quest'altra ma&shy;<lb/>niera: &ldquo; Si fuerint duo solida A, B, diversae gravitatis in specie et inae&shy;<lb/>qualium molium, ex inaequalibus a centro C distantiis appensa, et fiat ut <pb xlink:href="020/01/2245.jpg" pagenum="488"/>gravitas specifica primi A, ad specificam secundi B, ita linea D ad E, et, ut <lb/>distantia primi ad distantiam secundi, ita E ad F, et, ut moles primi A, ad <lb/>molem secundi B, ita F ad G; erit momentum primi, ad momentum se&shy;<lb/>cundi, ut D ad G &rdquo; (ivi). </s></p><p type="main">

<s>Insufficientemente dunque il Rocca, e male a proposito il Torricelli si <lb/>citavano quali premostratori del Teorema dei momenti, cosicch&egrave; non restava <lb/>altro che il Cavalieri a dar valore all'argomento del Grandi. </s>

<s>Nella V Eser&shy;<lb/>citazione geometrica si pu&ograve; dir che veramente apparisca, cos&igrave;, nella sua pi&ugrave; <lb/>espressa e pi&ugrave; ordinata forma, il Teorema, che dovea levar tanto romore: <lb/>&ldquo; Quorumcumque gravium, a quibus libet distantiis suspensorum, momenta <lb/>sunt in ratione composita ex ratione distantiarum, et gravitatum &rdquo; (Bono&shy;<lb/>niae 1647, pag. </s>

<s>336). L'Autore premette, a dimostrar questa, due altre pro&shy;<lb/>posizioni, la prima delle quali facilmente conclude, dalle propriet&agrave; del Vette, <lb/>ch'essendo uguali le distanze, i momenti son proporzionali ai pesi; e la se&shy;<lb/>conda, ch'essendo uguali i pesi, i momenti son proporzionali alle distanze. </s></p><p type="main">

<s>Ci&ograve; premesso, abbiansi, dice il Cavalieri, due pesi E, D (fig. </s>

<s>261) ap&shy;<lb/>plicati nelle estremit&agrave; della Libbra CB, sostenuta in A. </s>

<s>Prendasi un terzo <lb/><figure id="id.020.01.2245.1.jpg" xlink:href="020/01/2245/1.jpg"/></s></p><p type="caption">

<s>Figura 261<lb/>peso F, uguale ad E, e si sospenda <lb/>in G, a una distanza AG uguale ad AB: <lb/>avremo per la prima M.oF:M.oD= <lb/>F:D, e per la seconda, M.oE:M.oF= <lb/>AC:AG. </s>

<s>Moltiplicate queste due equa&shy;<lb/>zioni, eliminato M.oF da ciascun ter&shy;<lb/>mine della prima ragione, e ad AG <lb/>sostituito AB, ad F, E; si giunge in ultimo ad avere M.oE:M.oD= <lb/>CA.E:AB.D, nella quale concludesi l'intenzione del Cavalieri, da lui stesso <lb/>cos&igrave; espressa: &ldquo; Momentum E, ad momentum D, est in ratione composita ex <lb/>ratione CA ad AB, et ex ratione gravitatis E, ad gravitatem D &rdquo; (ibid.). </s></p><p type="main">

<s>Rispose il Marchetti, in sentirsi indicare questa dimostrazione, pubbli&shy;<lb/>cata da un Matematico tanto celebre ventidue anni prima della sua, che il <lb/>metodo per&ograve; era diverso, e che non aveva allora veduto il libro del Cava&shy;<lb/>lieri (Lettera cit., pag. </s>

<s>20). Il Grandi gli rinfacci&ograve; ch'ei l'aveva <emph type="italics"/>esistente <lb/>nella sua libreria<emph.end type="italics"/> (Risposta cit., pag. </s>

<s>31), n&egrave; valse il rispondere che non <lb/>tutti si leggono i libri, che s'hanno per i palchetti, perch'esso Grandi ne&shy;<lb/>gasse fede a quelle buone ragioni. </s></p><p type="main">

<s>Ora, il nostro giudizio &egrave; alquanto diverso, e, se il Marchetti confess&ograve; <lb/>ingenuamente di non aver lette le Esercitazioni geometriche, crediamo di&shy;<lb/>cesse la verit&agrave;, confortata dall'esempio di certi altri fatti, ricorsi indietro <lb/>in questa nostra Storia. </s>

<s>Si rammemoreranno i Lettori di ci&ograve;, che dicemmo <lb/>nel II capitolo baricentrico, a proposito del teorema del Guldino, rimasto <lb/>ignoto al Borelli e al Viviani, bench&egrave; avesse fatta pubblica e s&igrave; battagliera <lb/>comparsa nella III Esercitazione del Cavalieri. </s>

<s>Com'&egrave; dunque certo che il <lb/>Borelli e il Viviani non avevano letto il libro nel 1656; cos&igrave; pu&ograve; credersi <lb/>che non l'avesse letto il Marchetti, seguitando l'esempio de'suoi maggiori, <pb xlink:href="020/01/2246.jpg" pagenum="489"/>i quali, male insinuati da Galileo, non facevano troppo buon viso all'Au&shy;<lb/>tore della Geometria degl'indivisibili. </s></p><p type="main">

<s>Comunque sia, venivano i fatti a decidere la controversia del primato, <lb/>e perci&ograve; il Marchetti, il quale sentivasi forse, meglio che dal suo Avversa&shy;<lb/>rio, rimproverare dalla propria coscienza la vanagloria dell'aver descritta in&shy;<lb/>nanzi al suo libro la mirabile invenzione occorsagli del meccanico Teorema; <lb/>si volse a dire &ldquo; che non del detto Teorema, per s&egrave; medesimo considerato <lb/>feci io gran caso, n&egrave; della sua invenzione e dimostrazione sperai gran lode, <lb/>ma bens&igrave; dell'avere io avvertito quanto egli a maraviglia giovar potevami <lb/>a dimostrar brevemente e facilmente, non solo tante mie nuove proposizioni <lb/>intorno alla resistenza dei corpi duri, ma eziandio quelle stesse, le quali con <lb/>altro mezzo, e con assai maggior lunghezza e difficolt&agrave;, aveva gi&agrave; dimostrate <lb/>il gran Galileo &rdquo; (Lettera cit., pag. </s>

<s>22). </s></p><p type="main">

<s>Il Grandi, che, a confettar d'aloe sulla lingua del suo avversario anche <lb/>quest'ultima compiacenza, non aveva materia, e di quella che poteva avere <lb/>non seppe far uso, contrappose insipide ragioni, riducendosi, per confrontar <lb/>la lunghezza e la brevit&agrave;, infino a contar le linee spese nelle dimostrazioni <lb/>dai due Autori. </s>

<s>Che se avesse ricercato, o si fosse saputo prevalere degli argo&shy;<lb/>menti, avrebbe potuto provar contro il Marchetti che, anche prima di lui, il <lb/>Torricelli e il Viviani, e anzi il medesimo Galileo, in certi fogli smarriti, ave&shy;<lb/>vano promossa la nuova Scienza istituita nel II dialogo delle Scienze nuove, <lb/>applicandovi il Teorema dei momenti. </s>

<s>Noi, per render di cos&igrave; belle, e cos&igrave; im&shy;<lb/>portanti notizie rifiorita la nostra Storia, faremo quello che avrebbe dovuto fare <lb/>lo stesso Grandi, incominciando dal riferire un Teorema sconosciuto al pub&shy;<lb/>blico, dove il Torricelli promoveva le dottrine della proposizione XII galileiana. </s></p><p type="main">

<s>&Egrave; questa proposizione, come <lb/>altre volte s'&egrave; detto, il fonda&shy;<lb/>mento alla parte seconda del Trat&shy;<lb/>tato, che &egrave; delle resistenze dei so&shy;<lb/>lidi, appoggiati nelle loro estremit&agrave; <lb/>a due sostegni: e bench&egrave; nella <lb/>figura, che nella nostra 262 ri&shy;<lb/>torna sott'occhio, e nella dichia&shy;<lb/>razione di Galileo non apparisca <lb/><figure id="id.020.01.2246.1.jpg" xlink:href="020/01/2246/1.jpg"/></s></p><p type="caption">

<s>Figura 262<lb/>tale, &egrave; pur assai facile ridurvela, essendo manifesto che rimangono le proposte <lb/>condizioni inalterate, mettendo in A, B i sostegni, e facendo da D, C pendere <lb/>due pesi uguali alla somma di A, B, e di E, F. </s>

<s>Intese la detta proposi&shy;<lb/>zione XII cos&igrave; trasformata il Torri&shy;<lb/>celli, quando scrisse: &ldquo; Il Galileo mo&shy;<lb/>stra che preso il punto A (fig. </s>

<s>263) <lb/>nel mezzo, ed il B n&ograve; nel mezzo, la <lb/>resistenza in A, alla resistenza in B, <lb/>sia come reciprocamente il rettan&shy;<lb/>golo CBD al rettangolo CAD. &rdquo; <lb/><figure id="id.020.01.2246.2.jpg" xlink:href="020/01/2246/2.jpg"/></s></p><p type="caption">

<s>Figura 263</s></p><pb xlink:href="020/01/2247.jpg" pagenum="490"/><p type="main">

<s>&ldquo; E stante questo, immediatamente soggiunge, sia attaccato in A il peso <lb/>F, e sia tale che basti per romper l'asta, cio&egrave; sia uguale alla resistenza, che <lb/>essa ha in A. </s>

<s>Sia poi un altro peso H, uguale all'F, ma attaccato in B: dico <lb/>che il momento del peso F, al momento di H, sta come il rettangolo CAD <lb/>al rettangolo CBD. &rdquo; </s></p><p type="main">

<s>&ldquo; Intendasi il peso E tale, che sia uguale alla resistenza dell'asta in B: <lb/>perciocch&egrave; per momento qui intendiamo la proporzione, che ha l'attivit&agrave; o <lb/>forza del peso attaccato verso la resistenza dell'asta; averanno dunque li <lb/>pesi E ed F, ne'siti loro, egual momento e virt&ugrave; verso l'asta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, perch&egrave; E ed H sono nello stesso sito, sar&agrave; il momento E, al <lb/>momento H, come la mole E alla mole H; cio&egrave; la mole E alla mole F; <lb/>cio&egrave; la resistenza di B alla resistenza di A; cio&egrave; il rettangolo, per Galileo, <lb/>CAD al rettangolo GBD. &Egrave; dunque vero che il momento E, cio&egrave; il mo&shy;<lb/>mento F uguale, ha la medesima proporzione al momento H, che ha il ret&shy;<lb/>tangolo CAD al rettangolo CBD. &rdquo; </s></p><p type="main">

<s>&ldquo; Intendansi ora due altri pesi uguali fra loro I ed L (fig. </s>

<s>264), e si <lb/>attacchino dai punti A, B. &Egrave; chiaro che il momento F, al momento I, per <lb/><figure id="id.020.01.2247.1.jpg" xlink:href="020/01/2247/1.jpg"/></s></p><p type="caption">

<s>Figura 264<lb/>essere nel medesimo sito, sta come <lb/>la mole alla mole, ossia, come il mo&shy;<lb/>mento H al momento L. Adunque, <lb/>permutando, come il momento F al <lb/>momento H, cos&igrave; il momento I al mo&shy;<lb/>mento L. <emph type="italics"/>Vel sic melius:<emph.end type="italics"/> momen&shy;<lb/>tum I ad F est ut moles ad molem. </s>

<s><lb/>Ergo, permutando, momentum I, ad <lb/>momentum L, ut momentum F ad <lb/>H; nempe ut rectangulus CAD ad rectangulum CBD. &rdquo; (MSS. Gal. </s>

<s>Disc, <lb/>T. XXXVII, fol. </s>

<s>65). </s></p><p type="main">

<s>Veniva cos&igrave; dunque il Torricelli ad arricchire la Scienza galileiana delle <lb/>resistenze di un altro bel Teorema, cio&egrave; che i momenti dei pesi uguali, pre&shy;<lb/>menti un'asta sostenuta agli estremi in varii punti della sua lunghezza, son <lb/>direttamente proporzionali ai rettangoli descritti con le distanze dai due so&shy;<lb/>stegni. </s>

<s>Comunic&ograve;, come tutte le altre speculazioni, anche questa al suo gio&shy;<lb/>vane amico e discepolo in Roma Michelangiolo Ricci, il quale,, eccitato cos&igrave; <lb/>dagli esempii del Maestro a speculare su quel medesimo argomento offertogli <lb/>dalla proposizione XII di Galileo, s'accorse che il problema proposto nella <lb/>seguente XIII, e per risolvere il quale Galileo stesso era ricorso al semicer&shy;<lb/>chio, si scioglieva con mirabile facilit&agrave; e speditezza, applicandovi invece la <lb/>parabola, notissima propriet&agrave; della quale &egrave; che le linee condotte parallele al <lb/>diametro segan la base in modo, da riuscir tutte e sempre proporzionali <lb/>ai rettangoli costruiti sulle sezioni. </s></p><p type="main">

<s>A dimostrar perci&ograve; al Torricelli che non infruttuose erano riuscite le <lb/>sue premure, e non inefficaci gli esempii, cos&igrave; scrivevagli il d&igrave; 18 Luglio 1643, <lb/>lo stesso Ricci, in una lettera da Roma: &ldquo; E poich&egrave; vedo che V. S. &egrave; cos&igrave; <pb xlink:href="020/01/2248.jpg" pagenum="491"/>proprizio al mio profitto, non voglia gravarsi di leggere la infrascritta di&shy;<lb/>mostrazione, la quale, quando mi venga approvata da V. S., mi render&ograve; si&shy;<lb/>curo, non solo della bont&agrave; della dimostrazione, ma assieme d'aver ben capita <lb/>la materia delle resistenze del Galileo, intorno alla quale versa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia dato il prisma o cilindro AB (fig. </s>

<s>265), nel quale, preso ad arbi&shy;<lb/><figure id="id.020.01.2248.1.jpg" xlink:href="020/01/2248/1.jpg"/></s></p><p type="caption">

<s>Figura 265<lb/>trio il punto E, sia quivi sostenuto il peso L <lb/>come peso massimo. </s>

<s>Dato poi un altro peso G, <lb/>si cerca di trovare nel prisma AB il luogo, <lb/>dove il peso G sia retto come peso massimo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sulla lunghezza AB s'intenda descritta <lb/>la parabola ADB, il cui diametro DC, e ad esso <lb/>sia parallela la FE. </s>

<s>Si faccia, come il peso G <lb/>al peso L, cos&igrave; la retta EF alla parte HC del <lb/>diametro DC, e dal punto H si tiri la HI pa&shy;<lb/>rallela alla BA, e dal punto I la KI parallela <lb/>al diametro DC: dico il punto K essere il punto <lb/>cercato, perch&egrave; il peso G al peso L si &egrave; fatto <lb/>come la FE alla HC, ovvero KI, cio&egrave;, come il <lb/>rettangolo BEA al rettangolo AKB; cio&egrave;, come <lb/>la resistenza in K, alla resistenza in E. Dunque, permutando, il peso G, <lb/>alla resistenza in K, ha la proporzione del peso L alla resistenza in E, che <lb/>sono uguali per il supposto, e per&ograve; il peso G sar&agrave; sostenuto in K come peso <lb/>massimo. </s>

<s>Il che ecc. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>11, 12). </s></p><p type="main">

<s>Il Torricelli, non solo approv&ograve; la proposizione del Ricci, ma ebbe a <lb/>ringraziarlo come colui, ch'era venuto con quella sua parabola a rivelargli <lb/>un'altra cosa bellissima, da mettersi per corollario al Teorema dianzi rife&shy;<lb/>rito, cio&egrave; che i momenti dei pesi uguali prementi l'asta, o, come il Viviani <lb/>incominci&ograve; a dire, la <emph type="italics"/>Scala<emph.end type="italics"/> di essi momenti &egrave; in una parabola, che insiste <lb/><figure id="id.020.01.2248.2.jpg" xlink:href="020/01/2248/2.jpg"/></s></p><p type="caption">

<s>Figura 266<lb/>come su base sulla lunghezza stessa dell'asta. </s>

<s>Gli <lb/>pass&ograve; di qui l'agile pensiero a quell'altra para&shy;<lb/>bola, che Galileo diceva esser descritta da una ca&shy;<lb/>tena che faccia saccaia, e si compiacque di aver <lb/>avuto a ritrovare in quel suo Teorema, e nel co&shy;<lb/>rollario suggeritogli dal Ricci, la dimostrazione <lb/>desiderata. </s></p><p type="main">

<s>Sia la catena ACB (fig. </s>

<s>266): pens&ograve; il Tor&shy;<lb/>ricelli che ciascuno anello di lei, come per esem&shy;<lb/>pio E, F, fossero ivi scesi, trasportativi dai punti <lb/>G, H con forze, misurate dai pesi di essi anelli <lb/>moltiplicati per le velocit&agrave; GE, HF: cosicch&egrave;, chiamate F, F&prime; cotali forze, <lb/>e P il peso, in ciascuno degli anelli uguale, fosse F=P.GE, F&prime;=P.HF, <lb/>ossia F:F&prime;=GE:HF. </s>

<s>Ma perch&egrave; sono queste forze evidentemente uguali <lb/>ai momenti, ch'eserciterebbero gli stessi anelli, se si considerassero come in&shy;<lb/>filati nella linea AB; e stanno, per il dimostrato Teorema, essi momenti come <pb xlink:href="020/01/2249.jpg" pagenum="492"/>i rettangoli AGB, AHB; dunque F:F&prime;=AGB:AHB, e perci&ograve; AGB:AHB= <lb/>GE:HF. </s>

<s>Dunque la linea curva AECFB, in che disponesi la catena, &egrave; ve&shy;<lb/>ramente, come Galileo diceva, una parabola. </s>

<s>Tale &egrave; l'esplicato discorso, che <lb/>si condensa dal Torricelli in questa sua Nota: &ldquo; Funis, seu catenula ACB <lb/>pendens, parabolam format, quia unaquaeque portio pendens descendit pro <lb/>ratione sui momenti &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXVII, fol. </s>

<s>81). </s></p><p type="main">

<s>Rimaste queste speculazioni lungo tempo sepolte nella cassetta, dove <lb/>gelosamente si deposero i manoscritti del Torricelli, il Viviani, a cui non <lb/>era stato consegnato ancora il deposito prezioso, era per s&egrave; medesimo (non <lb/>punto meno studioso de'dialoghi di Galileo, di quel che si fossero il Tor&shy;<lb/>ricelli stesso e il Ricci) entrato in quel medesimo filo di speculazioni, e, cre&shy;<lb/>dendosi di essere stato il primo, era per altre vie riuscito a dimostrare i <lb/>medesimi teoremi. </s>

<s>Scrisse perci&ograve; in fronte a una sua carta questo titolo: <lb/><emph type="italics"/>Theorema a nullo, quod sciam, demonstratum comprehendens illud quo&shy;<lb/>que, quod ostenditur a Galileo, ad fac. </s>

<s>136, secundi dialogi De resisten&shy;<lb/>tia corporum solidorum<emph.end type="italics"/> (MSS, Gal., T. CXVII, fol. </s>

<s>22). Il Teorema poi &egrave; <lb/>cos&igrave; formulato: </s></p><p type="main">

<s>&ldquo; Sia il peso D (fig. </s>

<s>267) appeso al mezzo C della leva AB, sostenuta <lb/>negli estremi A, B, ed egual peso E penda dal punto F, fuori del mezzo di AB: <lb/><figure id="id.020.01.2249.1.jpg" xlink:href="020/01/2249/1.jpg"/></s></p><p type="caption">

<s>Figura 267<lb/>dico che il momento di <lb/>D in C, al momento di <lb/>E in F, sta omologa&shy;<lb/>mente come il rettan&shy;<lb/>golo ACB al retrangolo <lb/>AFB &rdquo; (ivi). La dimo&shy;<lb/>strazione &egrave; molto ela&shy;<lb/>borata, coll'intenzione <lb/>di renderla comprensiva <lb/>della XII di Galileo, della <lb/>quale vedemmo come il Torricelli invece avesse fatta la sua un semplice <lb/>corollario. </s></p><p type="main">

<s>&ldquo; Prolunghisi, prosegue il Viviani, tal linea AB dall'una e dall'altra <lb/>parte, cosicch&egrave; AG, BH siano uguali fra loro ed alle met&agrave; AC, CB, ed in <lb/>H penda I met&agrave; del peso D, ed in G penda il peso L met&agrave; del medesimo <lb/>peso D, che il momento di D in C sar&agrave; ugual momento de'due L, I posti <lb/>in G, H. </s>

<s>Si faccia poi come FA ad AG, cos&igrave; L ad M, che il momento di <lb/>M sar&agrave; uguale al momento di L. </s>

<s>Si faccia ancora come FB a BH, cos&igrave; <gap/><lb/>ad N, che il momento di N sar&agrave; uguale al momento di I; onde il momento <lb/>di ambedue L, I, in G, H, cio&egrave; il momento di D in C sar&agrave; uguale al mo&shy;<lb/>mento di ambedue M, N in F. </s>

<s>Ora il peso M all'L sta come GA ad AF, <lb/>ed il peso L cio&egrave; l'I al peso N sta come FB a BH, cio&egrave; a GA; dunque, <lb/>per la ragione perturbata, il peso M all'N sta come BF ad FA, ed i pesi <lb/>M, N ad N come BA ad FA &rdquo; (ivi). </s></p><p type="main">

<s>Dalle equazioni M:L=GA:AF; I:N=FB:GA composta per mol-<pb xlink:href="020/01/2250.jpg" pagenum="493"/>tiplicazione la M:N=FB:FA, e da questa per somma la M+N:N= <lb/>FB+FA:FA, ossia M+N:N=AB:FA; ecco come il Viviani procede in <lb/>questa sua dimostrazione: Si ha per supposto N:2I=BH:2FB, la quale, <lb/>a moltiplicarla con l'ultima ritrovata, d&agrave; M+N:2I=AB.BH:2FB.FA. </s>

<s><lb/>Ma perch&egrave; 2I=E, BH=HC/2=AB/2, sar&agrave; M+N:E=AB2:4BF.FA, <lb/>ossia M+N:E=(AB/2)2:BF.FA. </s>

<s>E perch&egrave; AB=AC=CB, dunque <lb/>M+N:E=AC.CB:BF.FA. Ora, essendo che i pesi M+N, E, attac&shy;<lb/>cati al medesimo punto F, stanno come i loro momenti, e per le cose gi&agrave; di&shy;<lb/>mostrate M.oD=M.o(M+N), dunque in ultima conclusione M.oD:M.oE= <lb/>AC.CB:BF.FA. </s></p><p type="main">

<s>A chi poi desiderasse avere la dimostrazione ne'modi, e secondo il lin&shy;<lb/>guaggio proprio dell'Autore, sodisfaremo seguitando cos&igrave; a trascrivere di l&agrave;, <lb/>dove sopra lasciammo interrotto il manoscritto: </s></p><p type="main">

<s>&ldquo; Ma i pesi M, N al doppio di I, cio&egrave; ai pesi L, I, cio&egrave; al solo peso E <lb/>hanno ragion composta della M, N alla N, cio&egrave;, pel dimostrato adesso, di BA <lb/>ad AF, e di N al doppio di I, cio&egrave; di HB al doppio di BF, cio&egrave; di HC ov&shy;<lb/>vero BA al quadruplo di BF; e la ragion composta di BA ad AF, e di BA <lb/>al quadruplo di BF ha quella del quadrato BA al rettangolo di AF nel qua&shy;<lb/>druplo di BF; adunque i pesi M, N al peso E stanno come il quadrato di <lb/>BA al rettangolo di AF nel quadruplo di BF: o, presi i suqquadrupli di <lb/>tali spazi, come il quadrato di BC, cio&egrave; il rettangolo BCA al rettangolo BFA. </s>

<s><lb/>Ma il momento dei pesi M, N in F, al momento del peso E in F, sta come <lb/>il composto dei pesi M. </s>

<s>N al peso E, cio&egrave;, pel provato adesso, come il ret&shy;<lb/>tangolo BCA al rettangolo BFA, ed il momento de'pesi M, N in F si prov&ograve; <lb/>uguale al momento del peso D in C; adunque anche il momento del peso <lb/>D in C, al momento dell'egual peso E in F, sta come il rettangolo BCA al <lb/>rettangolo BFA, il che ecc. </s>

<s>&rdquo; (ivi). </s></p><p type="main">

<s>Avvertiva nell'intitolazione il Viviani che questa sua era comprensiva <lb/>della XII di Galileo, la quale infatti deriva per corollario dalla equazione <lb/>M+N:E=AC.CB:AF.FB, postovi E=D; corollario dal Viviani stesso <lb/>cos&igrave; formulato: &ldquo; Di qui si cava che i pesi M, N ed il peso D, che hanno <lb/>momenti uguali, hanno ragion reciproca dei rettangoli ACB, AFB &rdquo; (ivi). </s></p><p type="main">

<s>Derivavasi pure dal Viviani di qui un altro corollario, nel quale si ri&shy;<lb/>scontrava col Torricelli, come s'era riscontrato nel dimostrare la proposi&shy;<lb/>zione principale. </s>

<s>Quel corollario era dall'Autore messo in questa forma: &ldquo; La <lb/>scala dei momenti de'pesi uguali G, H, nella precedente nostra figura 266, <lb/>attaccati ad una Libbra, sostenuta ne'suoi estremi A, B, sta nelle linee EG, <lb/>FH della parabola ACB, parallele al diametro, essendo la libbra AB base di <lb/>detta parabola &rdquo; (MSS. Gal., P. V, T. VII, fol. </s>

<s>61). </s></p><p type="main">

<s>Incontratosi il Grandi in questo corollario, staccato dalla sua proposi&shy;<lb/>zione, lo inser&igrave; per il teorema LIV nel trattato Delle resistenze, supplendo <lb/>cos&igrave; di suo alla dimostrazione, che in quella parte del manoscritto si tro-<pb xlink:href="020/01/2251.jpg" pagenum="494"/>vava mancare: &ldquo; imperocch&egrave; i detti momenti sono come i rettangoli AGB, <lb/>AFB fatti dalle parti di essa Libbra, come dimostra il Galileo nella propo&shy;<lb/>sizione XIII. </s>

<s>Ma a questi rettangoli sono proporzionali le linee GE, HF, ti&shy;<lb/>rate nella parabola parallele al diametro, dunque ecc. </s>

<s>&rdquo; (Alb. </s>

<s>XIV, pag. </s>

<s>79). </s></p><p type="main">

<s>Per quella che qui il Grandi chiama proposizione XIII s'intende vera&shy;<lb/>mente, secondo la segnatura incominciata da Galileo, la XII, nella quale che <lb/>non si dimostri essere i momenti come i rettangoli AGB, AFB lo seppero <lb/>molto bene il Torricelli e il Viviani, i quali altrimenti non si sarebbero af&shy;<lb/>faticati, n&egrave; compiaciutisi di avere essi i primi ritrovato il nuovo teorema. </s>

<s>La <lb/>compiacenza poi da parte di esso Viviani era troppo giusta, perch&egrave;, da quel <lb/>ch'ei credeva <emph type="italics"/>a nullo demonstratum,<emph.end type="italics"/> gli venivano felicemente concluse le <lb/>proposizioni dei solidi di resistenze uguali, della Scala dei momenti nella pa&shy;<lb/>rabola, e di tante altre belle dottrine aggiunte alle galileiane, che nell'opera <lb/>del Grandi si rimangono come rivi senza sorgente, non scoprendosi quella <lb/>unica da lui indicata, a chi si metta pi&ugrave; diligentemente a cercare, cos&igrave; ma&shy;<lb/>nifesta. </s></p><p type="main">

<s>Quando Lodovico Serenai consegn&ograve; i manoscritti torricelliani al Viviani, <lb/>questi, nel mettere all'ordine il trattato <emph type="italics"/>De motu ac momentis,<emph.end type="italics"/> ebbe a di&shy;<lb/>singannarsi, ritrovando per que'fogli quel ch'egli credeva non aver nessun <lb/>altro dimostrato prima di lui. </s>

<s>Abbattutosi poi in quella Nota, nella quale, <lb/>dalla Scala dei momenti de'pesi in una Libbra sostenuta dalle due parti, si <lb/>concludeva essere la linea, in che disponesi la catena una parabola; scrisse <lb/>in margine: <emph type="italics"/>Questa io la tralascio, perch'&egrave; di Galileo.<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., <lb/>T. XXXVII, fol. </s>

<s>81). </s></p><p type="main">

<s>Ma dove ha dimostrato, dai principii meccanici, Galileo, avrebbe potuto <lb/>domandare il Torricelli al suo discepolo, amico e collega, che la sacca di una <lb/>fune o di una catena &egrave; in figura di parabola? </s>

<s>Nel secondo dialogo delle <lb/>Scienze nuove, dopo la XV proposizione, null'altro si fa che affermare, die&shy;<lb/>tro ci&ograve; che apparisce alla vista: &ldquo; la catenella si piega in figura parabolica &rdquo; <lb/>(Alb. </s>

<s>XIII, 144). </s></p><p type="main">

<s>Or chi sa come sarebbero rimasti i due interlocutori, se fosse entrato <lb/>qualcuno in mezzo a loro, mostrando una carta autografa, dalla quale ma&shy;<lb/>nifestamente apparisse che Galileo aveva gi&agrave; da s&egrave; dimostrato il Teorema <lb/>da ambedue creduto una loro propria invenzione; che ne avea dedotta per <lb/>corollario la scala parabolica de'momenti dei pesi uguali attaccati nella lun&shy;<lb/>ghezza di una Libbra, e che ne aveva pure indi concluso dovere in figura <lb/>di parabola insenarsi, rilasciata dai due capi fissi, una catena? </s></p><p type="main">

<s>Quella carta autografa, che non videro mai i due Discepoli zelanti, pu&ograve; <lb/>essere ora alla notizia di tutti che, andando a squadernare il secondo tomo <lb/>della parte quinta dei Manoscritti di Galileo, fermino sul foglio 43 la loro <lb/>attenzione. </s>

<s>Ivi apparir&agrave; grandeggiare in campo una figura, da noi rappre&shy;<lb/>sentata nella 268, sottovi scritte, da una parte del foglio, sentenziosamente <lb/>cos&igrave; queste righe: &ldquo; Il grave in G preme con manco forza che in S, se&shy;<lb/>condo la proporzione del rettangolo FGC al rettangolo FSC &rdquo;: ci&ograve; ch'esat-<pb xlink:href="020/01/2252.jpg" pagenum="495"/>tamente corrisponde col Teorema <emph type="italics"/>a nullo quod siam demonstratum,<emph.end type="italics"/> in cui <lb/>il Viviani, come Galileo, ma dopo Galileo non saputo, asserisce che il mo&shy;<lb/>mento del peso in G, al momento del medesimo peso in S, sta omologa&shy;<lb/>mente come il rettangolo FGC al rettangolo FSC. </s></p><p type="main">

<s>Le linee ST, GD, nella figura galileiana, accennano evidentemente che <lb/>i momenti dei pesi in S e in G son proporzionali ad esse linee condotte <lb/><figure id="id.020.01.2252.1.jpg" xlink:href="020/01/2252/1.jpg"/></s></p><p type="caption">

<s>Figura 268<lb/>parallele al diametro AQ della curva FAC, la qual <lb/>curva essere intesa per quella, in cui si piega la <lb/>catena, e dover essere parabolica, &egrave; dichiarato <lb/>espressamente dalla Nota scritta in capo al fo&shy;<lb/>glio, che cos&igrave; dice: &ldquo; Passi la catenella per i <lb/>punti F, C, e, dato lo scopo Z, tira tanto la ca&shy;<lb/>tena che passi per Z, e troverai la distanza SC, <lb/>e l'angolo della elevazione. </s>

<s>Dimostrasi che, sic&shy;<lb/>come &egrave; impossibile tirar la catena in retto; cos&igrave; <lb/>essere impossibile che il proietto vadia mai per <lb/>diritto, se non nella perpendicolare in su, come <lb/>anco la catena a piombo si stende in retto. </s>

<s>Sic&shy;<lb/>come la parabola del proietto &egrave; descritta da due <lb/>moti, orizzontale e perpendicolare; cos&igrave; la cate&shy;<lb/>nella resulta da due sforzi: orizzontale da chi la <lb/>tira nella estremit&agrave;, e perpendicolare <emph type="italics"/>deorsum<emph.end type="italics"/><lb/>dal proprio peso. </s>

<s>&rdquo; </s></p><p type="main">

<s>Queste note furono scritte verso il 1637, che vuol dire un ventisette o <lb/>vent'ott'anni dopo essere stati scritti que'fogli, nei quali erano secondo il <lb/>Salviati, messi in ordine di trattato i teoremi e problemi delle Resistenze, <lb/>fra'quali teoremi doveva essere dimostrato anche quello dei pesi uguali pre&shy;<lb/>menti in varii punti la lunghezza di un'asta, con momenti proporzionali <lb/>direttamente ai rettangoli delle distanze dagli appoggi; intorno a che Gali&shy;<lb/>leo avea prevenuta l'industria del Torricelli e del Viviani, il quale a pag. </s>

<s>105 <lb/>della sua <emph type="italics"/>Scienza delle proporzioni<emph.end type="italics"/> (Firenze 1674), facendosi a indovinar <lb/>come Galileo deducesse che la sacca naturale delle catenuzze s'adatta sem&shy;<lb/>pre alle linee paraboliche, colse cos&igrave; nel vero com'avesse avuto sott'occhio <lb/>il manoscritto da noi sopra citato. </s>

<s>Ma la parabola de'proietti, venuta come <lb/>vedremo, ad esercitare l'ingegno dello stesso Galileo in su gli ultimi anni <lb/>de'suoi studii meccanici, gli fece revocare alla mente le prime antiche spe&shy;<lb/>culazioni, sperando che alla Dinamica nuova fosse per recare qualche lume <lb/>la statica delle resistenze. </s></p><p type="main">

<s>Era sen&zgrave;a dubbio significantissima l'analogia tra la catena e il proietto, <lb/>che non si possono tirare in linea retta, per non esser possibile spogliar del <lb/>loro peso naturale la palla scagliata, e gli anelli tesi da qualunque forza: <lb/>com'era pure assai lusinghiero il pensiero del Torricelli, che fossero cio&egrave; i <lb/>pesi in T e in D scesi da S e da G, trattivi con forze proporzionali alle <lb/>linee ST, GD, condotte parallele al diametro della parabola. </s>

<s>Ma non sem-<pb xlink:href="020/01/2253.jpg" pagenum="496"/>bra che l'analogia pi&ugrave; regga, quando, dalla Statica trapassando ai pi&ugrave; as&shy;<lb/>soluti principii della Dinamica, Galileo rassomiglia i moti, che fanno piegar <lb/>la catena, ai medesimi moti, da'quali resulta la linea dei proietti. </s>

<s>Che se, <lb/>in considerare la scesa degli anelli, gli spazi ST, GD non son passati stati&shy;<lb/>camente con moto equabile, ma dinamicamente con moto accelerato, non <lb/>sarebbe possibile dimostrar che la curva FAC &egrave; una parabola, a quel modo <lb/>che, se le cose da lui supposte fossero state esattamente vere, era riuscito <lb/>a dimostrare il Torricelli. </s></p><p type="main">

<s>Forse del confidarsi che si potesse con matematica esattezza la catena&shy;<lb/>ria rassomigliare alla traiettoria fu sconfortato Galileo dall'esperienza, de&shy;<lb/>scrivendo coi metodi geometrici una parabola, e adattandovi sopra pendente <lb/>una catenuzza. </s>

<s>Osserv&ograve; che tali adattamenti si fanno via via pi&ugrave; precisi, <lb/>che la curva &egrave; pi&ugrave; tesa, cosicch&egrave;, mentre prima aveva assolutamente sen&shy;<lb/>tenziato, come udimmo, che la catenella <emph type="italics"/>si piega in figura parabolica,<emph.end type="italics"/> ora, <lb/>temperando il discorso, soggiunge che <emph type="italics"/>si piega in linee, le quali assai si <lb/>avvicinano alle paraboliche<emph.end type="italics"/> (Alb. </s>

<s>XIII, 163). Fa a questa opinione di Ga&shy;<lb/>lileo bel riscontro quella dell'Huyghens, il quale, in descrivere nella sua <lb/><emph type="italics"/>Astroscopia<emph.end type="italics"/> l'antenna, che porta in alto la lente, dice del filo che, racco&shy;<lb/>mandato da un capo a essa lente per moverla, scende gi&ugrave; con l'altro alle <lb/>mani dell'osservatore: &ldquo; Quae ad eius flexum attinent, Geometriae ratio&shy;<lb/>nibus experimentisque expendi possunt: nempe contentum filum, flexu illo <lb/>exiguo, parabolicam lineam tam prope exprimit, ut pro vera absque errore <lb/>habeat &rdquo; (Opera varia cit., pag. </s>

<s>268). </s></p><p type="main">

<s>Cos&igrave; l'Huyghens dunque come Galileo ritenevano che fosse la catenaria <lb/>una parabola, specialmente quand'&egrave; piccolo il flesso. </s>

<s>Ci&ograve; dall'altra parte &egrave; <lb/>confermato assai bene dall'analisi, comparando l'equazioni delle due curve, <lb/>che per l'una &egrave; X:X&prime;=<emph type="italics"/>y2:y&prime;2<emph.end type="italics"/>, e per l'altra X:X&prime;=<emph type="italics"/>yc:y&prime;c&prime;<emph.end type="italics"/>, inten&shy;<lb/>dendosi per <emph type="italics"/>c, c&prime;<emph.end type="italics"/> i tratti, che son compresi fra il principio delle ascisse e <lb/>il fine delle ordinate, i quali tratti &egrave; manifesto che tanto pi&ugrave; si accostano <lb/>con esse ordinate, quanto il flesso &egrave; minore, o la catena &egrave; pi&ugrave; distesa. </s></p><p type="main">

<s>Ritornando ora col&agrave;, d'onde siam deviati col nostro discorso, son tali <lb/>i teoremi e tali le conclusioni della teoria dei momenti applicata alle resi&shy;<lb/>stenze da Galileo, dal Torricelli e dal Viviani: teoremi e conclusioni, che <lb/>si sarebbero dovuti citare dal Grandi, se avesse voluto con argomenti rin&shy;<lb/>tuzzare la gloria, che il suo rivale menava d'essere stato, a maneggiar quella <lb/>teoria egli il primo fra tutti. </s>

<s>Ma perch&egrave; esso Grandi far ci&ograve; o non pot&egrave; o <lb/>non seppe, resta a concludersi dunque il nostro lungo ragionamento con <lb/>dire, che irragionevoli appariscono da ogni parte le censure di lui contro <lb/>quel trattato <emph type="italics"/>De resistentia solidorum,<emph.end type="italics"/> meditato dal Marchetti e scritto in <lb/>gran parte ne'tempi delle vacanze autunnali, passate ora nella paterna casa <lb/>di Empoli, ora nella prossima villa di Pontormo, ai verdi campi della quale, <lb/>e ai pioppi pampinosi, memorie dolcissime della nostra fanciullezza, ci sia <lb/>permesso di mandare un saluto. </s></p><pb xlink:href="020/01/2254.jpg" pagenum="497"/><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Le cose, ne'precedenti articoli di questo capitolo esposte intorno alle <lb/>Resistenze, non sono state altro che di speculazioni, alle quali si vedeva <lb/>d'alto precedere l'infallibile scorta della Geometria. </s>

<s>Tale, dall'altra parte, <lb/>&egrave; stata sempre la legge storica del pensiero, che concepisce le forme astratte, <lb/>prima di considerarle incarnate nella materia, come per un esempio insi&shy;<lb/>gne, e appropriatissimo al caso dell'Archimede novello, pu&ograve; vedersi nelle <lb/>opere dell'Archimede antico. </s>

<s>Come dunque, alla Statica e alla Idrostatica <lb/>archimedea, che considerano la gravit&agrave; ne'solidi, e la fluidit&agrave; nei liquidi <lb/>astrattamente dalle altre passioni della materia, successero le due nuove <lb/>Scienze, che vollero richiamare le matematiche astrazioni a rispondere alla <lb/>presente realt&agrave; dei fatti; cos&igrave; avvenne della Scienza delle resistenze dei corpi <lb/>allo spezzarsi. </s></p><p type="main">

<s>Fu dei primi a dar mano all'opera Paolo Wrz, o Vulzio, come lo chia&shy;<lb/>marono i nostri Italiani, se ha da credersi al Leibniz, il quale, dop'avere <lb/>accennato al libro delle Resistenze, che il Blondel avea revocato, soggiunge <lb/>cos&igrave;, nella citata lettera autografa al Grandi: &ldquo; Paulus Wurzius, qui ductor <lb/>exercitus apud Batavos, paulo post initium Belli gallici, idest paulo post eum&shy;<lb/>dem annum 1672, obiit, idem argumentum tractarat per experimenta, quae <lb/>Galilaeo hand consona deprehenderat, sed scheda eius periere &rdquo; (MSS. Cim., <lb/>T. XXIX, fol. </s>

<s>287). </s></p><p type="main">

<s>Che tra i teoremi galileiani e gli sperimenti non fosse per passare quella <lb/>consonanza, si vedeva per necessit&agrave; conseguente dalla legge sopra accennata, <lb/>ma il Viviani ne aveva riconosciute le intime cause speciali, forse prima del <lb/>Vulzio, quando scrisse nella seguente nota: &ldquo; Pare che in questa Scienza <lb/>delle resistenze si deva astrarre la flessibilit&agrave; dei corpi, che fanno molla, po&shy;<lb/>tendo questi alterare le proporzioni investigate, siccome la temperie e varie <lb/>crudezze di metalli &rdquo; (MSS. Gal., P. V, T. VII, fol. </s>

<s>29). </s></p><p type="main">

<s>Apparisce da altre Note sparse per queste medesime carte manoscritte, <lb/>e dal Grandi secondo noi, nelle <emph type="italics"/>Definizioni<emph.end type="italics"/> premesse al Trattato e nelle <lb/><emph type="italics"/>Supposizioni,<emph.end type="italics"/> non bene ordinate; che il Viviani aveva gi&agrave; pensato di ritro&shy;<lb/>vare, per via di esperimenti opportuni, le relazioni che passano fra la re&shy;<lb/>sistenza assoluta e la respettiva in varie qualit&agrave; di corpi, sperando cos&igrave; di <lb/>poter ridurre le verit&agrave; della Geometria a consentire in qualche modo con <lb/>le verit&agrave; naturali. </s>

<s>&ldquo; Si sperimenti, egli scrive, quanto peso ci voglia a strap&shy;<lb/>pare i cilindri di vetro per diritto a piombo, attaccando al termine inferiore <lb/>tanto peso, che faccia lo strappamento. </s>

<s>&mdash; Di qui si cava la <emph type="italics"/>tariffa<emph.end type="italics"/> delle <lb/>resistenze assolute di uguali sezioni di metalli, e si pu&ograve; provare se doppia <lb/>sezione voglia doppio peso, come la ragione ce ne persuade &rdquo; (Alb. </s>

<s>XIV, 5). </s></p><p type="main">

<s>La particolare scelta delle materie, fatta dal Viviani per le sue espe&shy;<lb/>rienze, aveva un fine importantissimo nella decisione dell'ipotesi ammessa <pb xlink:href="020/01/2255.jpg" pagenum="498"/>da Galileo, perch&egrave; i metalli duri, e specialmente il vetro, pareva che si po&shy;<lb/>tessero proporre per gli esempii delle rotture, che si fanno istantanee. </s>

<s>Ma <lb/>quando il Viviani stesso ebbe a sperimentare, nell'Accademia del Cimento, <lb/>che anche il vetro cede alle forze del calore, <emph type="italics"/>per lo ficcamento de'volanti <lb/>corpiccioli del fuoco nell'esterna porosit&agrave;<emph.end type="italics"/> (Saggi cit., pag. </s>

<s>118), entr&ograve; in so&shy;<lb/>spetto che dovesse similmente cedere alle forze di un peso; sospetto, che <lb/>si verific&ograve; con quella bella esperienza, descritta poi nel citato libro dei <emph type="italics"/>Saggi,<emph.end type="italics"/><lb/>dove si legge che, adattati due vasi di vetro, uno conico l'altro piramidale, <lb/>negl'incastri di una grossa tavola, essendo vuoti, tornando a rimetterveli <lb/>pieni di argento vivo, non v'entravano al segno di prima, <emph type="italics"/>secondo che la <lb/>forza del peso gli distendeva &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>125). </s></p><p type="main">

<s>Lo stesso vetro dunque, n'ebbe di qui a concludere il Viviani, &egrave; di <lb/>que'corpi, che fanno molla, e si dovrebbe perci&ograve;, secondo i propositi scritti, <lb/>astrarre anche questo dalla Scienza matematica delle resistenze, cosicch&egrave; <lb/>non vedeva a qual mai corpo in natura si potessero adattare le ipotesi e i <lb/>teoremi di Galileo. </s>

<s>Parrebbero queste conclusioni contradire a uno di quei <lb/>supposti, premessi al suo Trattato in tal forma: &ldquo; La separazione delle due <lb/>superfice del solido, tenuto per traverso, si fa nel medesimo istante, tanto <lb/>nei punti remoti dal sostegno, che nei vicini, e che in quelli di mezzo, stante <lb/>che tale separazione si fa con moto regolare dell'una superfice, che si muove <lb/>dall'altra che sta ferma &rdquo; (Alb. </s>

<s>XIV, 9). Ogni contradizione per&ograve; sparisce, <lb/>penetrando addentro alla intenzione del Viviani, il quale, professando l'ipo&shy;<lb/>tesi e i teoremi galileiani come formule astratte, si proponeva di ridurle poi <lb/>ai casi particolari della tale o tale altra materia resistente, introducendovi <lb/>quelle, ch'ei chiamava <emph type="italics"/>tariffe,<emph.end type="italics"/> e i moderni <emph type="italics"/>coefficienti sperimentali.<emph.end type="italics"/> Il sa&shy;<lb/>piente istituto, il quale mirabilmente si conforma con quello proseguito og&shy;<lb/>gid&igrave;, dopo tanti pericoli, dalla Scienza, non ebbe effetto per quelle avven&shy;<lb/>ture, che si son gi&agrave; narrate nella nostra Storia. </s></p><p type="main">

<s>Apprese nonostante da'familiari colloqui col Viviani sembrano nel ca&shy;<lb/>pitolo XVIII della Meccanica le osservazioni del Mersenno (Parisiis 1644, <lb/>pag. </s>

<s>62-68), il quale poi, nel III tomo delle Riflessioni fisiche matematiche, <lb/>faceva notar che il ferro e gli altri metalli, anzi tutti i corpi, s'inflettono <lb/>prima di rompersi: difficolt&agrave; per chi tratta delle resistenze, <emph type="italics"/>quam et ipse <lb/>Galileus vitavit.<emph.end type="italics"/> E bench'egli si presumesse di aver proposte le cose con <lb/>certezza di dimostrazione, &ldquo; examine diligenti egent, quod inibunt, quibus <lb/>otium et voluntas adfuerit &rdquo; (Parisiis 1647, pag. </s>

<s>151). </s></p><p type="main">

<s>Il primo, a cui venne questa volont&agrave;, ed ebbe quest'ozio, sembra es&shy;<lb/>sere stato il Mariotte, il quale narra nel trattato <emph type="italics"/>Du mouvement des eaux<emph.end type="italics"/><lb/>di aver fatto, insieme col signor Hubin, un'altra bella esperienza, dopo quella <lb/>de'nostri Accademici fiorentini, di un filo di vetro grosso un quarto di linea <lb/>e lungo quattro piedi, che stirato si allungava, e lasciato ritornava allo stato <lb/>di prima. </s>

<s>Ebbe di qui a persuadersi il Mariotte, come il Viviani, non v'es&shy;<lb/>ser corpo, per quanto credasi rigido e duro, che si rompa a un tratto, senza <lb/>prima cedere o pi&ugrave; o meno alla forza del peso. </s>

<s>Ma mentre il Nostro non <pb xlink:href="020/01/2256.jpg" pagenum="499"/>si cred&egrave; per questo di dover bandire l'ipotesi galileiana dal Trattato delle <lb/>resistenze, il Francese dettesi a speculare, e a sperimentare per sostituir&shy;<lb/>vene un'altra. </s></p><p type="main">

<s>Supposto dunque che siano tutti i corpi duri intessuti di fibre, le quali <lb/>cedano alquanto alla forza, che tenterebbe di romperle, pens&ograve; il Mariotte <lb/>che le resistenze, specialmente respettive, dovevano avere effetti diversi da <lb/>quelli ammessi da Galileo, secondo il quale i momenti di esse resistenze non <lb/>variano, per variar la potenza dei punti di attacco, che in ciascuno secondo <lb/>lui &egrave; assoluta, ma per solo variar la distanza dal fulcro nella contralleva: <lb/>mentre veramente attendendo alla maggior e minor tensione delle fibre, che <lb/>debb<gap/>n rompersi tutte insieme, il momento varia, si per la distanza dal ful&shy;<lb/>cro, e s&igrave; per la potenza, che non pu&ograve;, rispetto alla naturale testura del corpo <lb/>resistente, mantenersi assolutamente uguale in ogni parte della stessa con&shy;<lb/>tralleva. </s></p><p type="main">

<s>Spiegava il Mariotte assai bene cos&igrave; il suo concetto: Abbiasi la Libbra <lb/>ACB (figura 269), col fulcro in C, ed essendo BC a CE come dodici a uno, <lb/>sospendansi in E, in D, a una distanza DC doppia di EC, e in A, a una <lb/><figure id="id.020.01.2256.1.jpg" xlink:href="020/01/2256/1.jpg"/></s></p><p type="caption">

<s>Figura 269<lb/>distanza AC doppia di DC, i tre <lb/>pesi I, H, G, ciascuno uguale a <lb/>dodici libbre, ai quali tutt'e tre <lb/>far&agrave; perci&ograve; equilibrio in B il peso <lb/>F, che sia di sette libbre. </s>

<s>Questo <lb/>sarebbe conforme con l'ipotesi di <lb/>Galileo, secondo la quale le resi&shy;<lb/>stenze rappresentate da I, H, G, operanti c&igrave;ascuna col peso assoluto di do&shy;<lb/>dici libbre, non per altro variano i loro momenti, che per variare le distanze <lb/>delle contralleve EC, CD, CA dal loro punto di appoggio. </s></p><p type="main">

<s>Succede per&ograve; la cosa molto diversamente, soggiunge il Mariotte, quando <lb/>le resistenze non son rappresentate da pesi, che operino ciascuno con as&shy;<lb/>soluta potenza indipendentemente gli uni dagli altri, ma da fibre, che ven&shy;<lb/>gano stirate con varia violenza, e l'una delle quali non si rompe, se non <lb/>si rompe nello stesso tempo anche l'altra. </s>

<s>Rappresenti ACPQ (fig. </s>

<s>270) un <lb/><figure id="id.020.01.2256.2.jpg" xlink:href="020/01/2256/2.jpg"/></s></p><p type="caption">

<s>Figura 270<lb/>solido, stabilmente congiunto con <lb/>la contralleva DC per via delle tre <lb/>corde uguali, e di ugual resistenza <lb/>DI, GL, HM, in distanze CA, CE, <lb/>CB dal fulcro, che stieno fra loro, <lb/>e con la leva CF, come i pesi con&shy;<lb/>siderati di sopra. </s>

<s>Si supponga che, <lb/>a voler rompere ciascuna di esse corde, si debba prima distrarla per due <lb/>linee dallo stato attuale. </s>

<s>A che fare, attaccato in F, sia bastante il peso R <lb/>di quattro libbre; e si supponga altresi, ci&ograve; che &egrave; assai verosimile e con&shy;<lb/>fermato dalle esperienze, che le tensioni siano proporzionali alle forze ten&shy;<lb/>denti: egli &egrave; chiaro, dice il Mariotte, che bisogneranno due libbre in R per <pb xlink:href="020/01/2257.jpg" pagenum="500"/>distendere due linee la corda GL, essendo sola, e una libbra solamente per <lb/>distendere allo stesso modo la corda HM. </s>

<s>Ma perch&egrave;, quando la corda DI &egrave; <lb/>distratta due linee, la corda GL non &egrave; distratta che una linea sola, e la <lb/>corda HM una mezza linea; ne segue, per la seconda delle fatte supposizioni, <lb/>che, quando si tirano tutte insieme, un peso d'una libbra in circa sar&agrave; ba&shy;<lb/>stante a fare equilibrio con la tensione della corda GL, tesa non pi&ugrave; di una <lb/>linea, e sole quattr'once basteranno, per fare equilibrio con la tensione HM, <lb/>bench&egrave; la resistenza assoluta di quest'ultima sia una libbra. </s>

<s>Cosicch&egrave;, per <lb/>ridurre le tre corde in questo stato, baster&agrave; porre in R poco pi&ugrave; di cinque <lb/>libbre, e non sette, come vorrebbesi per Galileo. </s></p><p type="main">

<s>Per riscontrare la verit&agrave; di questo ragionamento istitu&igrave; il Mariotte, alla <lb/>presenza del Carcavy, del Roberval e dell'Huyghens, alcune esperienze con <lb/>cilindri di legno secco, e con cannelli di vetro, e sempre afferma di aver <lb/>trovato che, per la pi&ugrave; giusta misura delle loro resistenze respettive, non <lb/>bisognava prendere la proporzione della lunghezza alla met&agrave;, ma a un terzo <lb/>poco pi&ugrave; della grossezza. </s>

<s>Cosicch&egrave;, trattando nel secondo Discorso della <lb/>parte quinta <emph type="italics"/>Del moto delle acque,<emph.end type="italics"/> delle forze di resistenza dei condotti, <lb/>avuto riguardo alla materia e alla pressione, renunzi&ograve; all'ipotesi, e alle con&shy;<lb/>seguenze ch'indi ne trasse Galileo, di cui cos&igrave; parla l'Autore, nell'intro&shy;<lb/>durre il citato Discorso: </s></p><p type="main">

<s>&ldquo; Galil&eacute;e a fait un Trait&eacute; de la resistance des solides, ou il explique <lb/>&agrave; sa mani&egrave;re la force, que doit avoir un poids, lorsqu'il est suspendu &agrave; <lb/>l'extremit&eacute; d'un solide fich&eacute; dans un mur. </s>

<s>Comme si le mur est AB (fig. </s>

<s>271) <lb/><figure id="id.020.01.2257.1.jpg" xlink:href="020/01/2257/1.jpg"/></s></p><p type="caption">

<s>Figura 271<lb/>et le solide CDEF, et que le poids G soit suspendu <lb/>en F par la corde FG, il dit que la longueur FD est <lb/>comme le bras d'un levier, et que l'epaisseur CD est <lb/>comme le contre-levier, en sorte que, si on vouloit <lb/>separer une partie, qui est en C, et que sa resistance <lb/>absolue f&ugrave;t de 10 livres, il faudroit que le poids G <lb/>f&ugrave;t seulement de 2 livres, si la longueur FD etoit 5 <lb/>fois plus grande que DC. </s>

<s>Mais en considerant une au&shy;<lb/>tre partie comme I, &eacute;galement distante de C et D, il <lb/>ne faudroit qu'une livre en G, parce que le levier FD seroit alors 10 fois <lb/>plus grand que le contre-levier DI. </s>

<s>Et parce qu'il suppose que la rupture se <lb/>fait en m&egrave;me tems dans toutes les parties de CD, dont les unes sont entre <lb/>D et I, et les autres entre I et C, il pretend qu'il faut consid&eacute;rer l'augmen&shy;<lb/>tation de la force du poids, selon la raison de FD &agrave; la moienne distance DI, <lb/>ce qui pourtant repugne a plusieurs experiences, que j'ai faites avec des <lb/>solides de bois et de verre, ou j'ai trouv&eacute; qu'il faloit prendre la raison de FD <lb/>a une ligne moindre que DI, comme le quart de DC, ou le tiers, et non <lb/>de FD &agrave; la moiti&eacute; de DC &rdquo; (Oeuvres, T. II, A la Haye 1740, pag. </s>

<s>461). </s></p><p type="main">

<s>Il ragionamento e le conclusioni del Mariotte sedussero i Matematici, e <lb/>giacch&egrave; il Francese aveva tentata una dimostrazione, ma non os&ograve; di ridurla <lb/>a tutto il rigore della Geometria, se ne assunse l'incarico il Leibniz in una <pb xlink:href="020/01/2258.jpg" pagenum="501"/>Dissertazione, inserita, per il mese di Luglio 1684, negli Atti degli Eruditi <lb/>di Lipsia. </s>

<s>Incomincia a fare osservare l'Autore che due corpi coerenti non <lb/>si staccano a un tratto, come pu&ograve; giudicarsi per l'esempio di un bastone, <lb/>che si piega, prima di rompersi, o di una corda, che si distende, prima di <lb/>strapparsi. </s>

<s>Anzi che qualunque materiata forma, per quanto rigidissima, s'in&shy;<lb/>fletta a ogni legger colpo, si dimostra nel suono, il quale non per altro si pro&shy;<lb/>duce, che per le reciprocate vibrazioni, bench&egrave; insensibili, del corpo risonante. </s>

<s><lb/>Lo stesso vetro &egrave; flessibile, a quel che pare da'filamenti di lui, e bench&egrave; mas&shy;<lb/>siccio si contrae e si dilata al calore, e sotto un peso che non leggermente <lb/>lo prema, come si legge nel libro degli Sperimenti fiorentini. </s>

<s>Le parti pure <lb/>delle piante e degli animali ci son dall'Anatomia descritte come tessili. </s></p><p type="main">

<s>&ldquo; Consideremus ergo, prosegue a dire il Leibniz, velut fibras quasdam, <lb/>quae partes corporum connectant, et intelligamus trabem MC (fig. </s>

<s>272) pa&shy;<lb/>rieti, vel substentaculo DE plurimis fibrarum plexibus alligari in punctis <lb/><figure id="id.020.01.2258.1.jpg" xlink:href="020/01/2258/1.jpg"/></s></p><p type="caption">

<s>Figura 272<lb/>A, H, B, et aliis intermediis innumeris. </s>

<s>Appenso iam pon&shy;<lb/>dere in C, movebitur nonnihil trabs circa fulcrum A, et <lb/>punctum trabis B, a pariete discedens, a puncto parietis B <lb/>veniet ad punctum a pariete distans M, secumque tra&shy;<lb/>hens fibram, quae parieti annectitur, eam tendet instar <lb/>chordae, sive ultra naturalem suum statum extendet &rdquo; <lb/>(Opera omnia, T. III, Genevae 1768, pag. </s>

<s>163). Lo stesso <lb/>avverr&agrave; di qualunque altro punto H, ma la fibra HK sar&agrave; <lb/>stirata con tanto minor forza della fibra BM, quanto il <lb/>quadrato di AH &egrave; minore del quadrato di AB. </s></p><p type="main">

<s>Da questa proposizione, che cio&egrave; i momenti delle re&shy;<lb/>sistenze fatte dalle varie fibre son proporzionali ai qua&shy;<lb/>drati delle distanze dal fulcro, piglia ogni valore la teoria <lb/>leibniziana, la quale perci&ograve; si dimostra dall'Autore con un <lb/>matematico discorso, che noi riduciamo cos&igrave; a poche pa&shy;<lb/>role. </s>

<s>Supposto, com'&egrave; ragionevole, e com'&egrave;, dice il Leib&shy;<lb/>niz, dimostrato altrove, che le forze sieno proporzionali <lb/>alle tensioni, e che queste siano proporzionali alle lunghezze, a cui son ri&shy;<lb/>dotte le fibre, il momento M.oF della forza di resistenza, che fa la fibra BM, <lb/>sar&agrave; evidentemente AB.BM, come, per ugual ragione, il momento M.oF&prime; <lb/>della forza, che fa la fibra HK, sar&agrave; AH.HK. </s>

<s>E perch&egrave; la similitudine dei <lb/>triangoli d&agrave; BM:HK=AB:AH, sar&agrave; dunque M.oF:M.oF&prime;=AB2:AH2. </s></p><p type="main">

<s>&Egrave; questa, come si vede, l'equazione a una parabola, che piacque al <lb/>Leibniz di descrivere dentro il quadrato SN, preso a rappresentare, con le <lb/>infinite linee tutte uguali a SR delle quali s'intesse, la resistenza assoluta <lb/>della trave. </s>

<s>Se si sega il lato RN in F, in modo da avere RN:FN=AB:AH, <lb/>e se da F si conduce alla parabola, parallela all'asse delle ascisse, la FQ, <lb/>avremo, per le propriet&agrave; di essa parabola, RS:FQ=NR2:FN2, ond'&egrave; <lb/>M.oF:M.oF&prime;=RS:Fq; che vuol dir che, se RS rappresenta la resistenza <lb/>in B, FQ rappresenta la resistenza in H. </s></p><pb xlink:href="020/01/2259.jpg" pagenum="502"/><p type="main">

<s>Si pu&ograve; la medesima conclusione applicare a tutti gl'infiniti punti, com&shy;<lb/>presi fra R ed N, da ciascun de'quali condotte le ordinate alla parabola, si <lb/>verr&agrave; di tutte insieme a tessere la superficie del trilineo parabolico concavo <lb/>NRSQN, il quale servir&agrave; perci&ograve; a rappresentare la resistenza respettiva della <lb/>trave, come il quadrato SN, allo stesso trilineo circoscritto, s'era preso dianzi <lb/>a reppresentare la resistenza assoluta. </s>

<s>Ma il trilineo &egrave; la terza parte del <lb/>quadrato, dunque anche la resistenza respettiva &egrave; la terza parte dell'asso&shy;<lb/>luta. </s>

<s>&ldquo; Generaliter ergo, conclude il Leibniz la sua dimostrazione, pondus, <lb/>trabem parallelepipedam directe evellens, erit, ad pondus abrumpens trans&shy;<lb/>verse seu per modum vectis, ut longitudo vectis, ad tertiam partem crassi&shy;<lb/>tiei trabis &rdquo; (ibid., pag. </s>

<s>164). </s></p><p type="main">

<s>Alcuni Autori di Meccanica resero pi&ugrave; semplice questa dimostrazion <lb/>leibniziana, introducendovi il centro di gravit&agrave;, ma potevasi invece applicare <lb/>il centro delle forze parallele, che conduce alla medesima conclusione per <lb/>una via, la quale, essendo la pi&ugrave; diretta, &egrave; anche perci&ograve; la pi&ugrave; conveniente <lb/>e la pi&ugrave; spedita. </s>

<s>Sia infatti P il peso che, applicato all'estremit&agrave; di una leva <lb/>lunga quant'uno de'lati del quadrato MC, opera con momento uguale alla <lb/>potenza, che sar&agrave; perci&ograve; espressa da P.AB. </s>

<s>La resultante di tutte le forze <lb/>parallele resistenti &egrave; data da BM.AB/2, che &egrave; la somma di tutte le fibre, o <lb/>infinite linee, di cui si tesse il triangolo ABM, il quale si pu&ograve; per maggior <lb/>precisione riguardare come infinitesimo, e il punto di applicazione della detta <lb/>resultante sar&agrave; in H, a due terzi dalla linea AB, a partire dal fulcro. </s>

<s>Sar&agrave; <lb/>perci&ograve; il momento della resistenza BM.AB/2X2AB/3, che, dovendo per l'equi&shy;<lb/>librio essere uguale al momento delle potenza, dar&agrave; P.AB=BM.AB.AB/3. <lb/>e fatto Q=BM.AB, P=Q/3. Ma perch&egrave; Q &egrave; manifestamente la somma di <lb/>tutte le forze uguali, che concorrono a fare la resistenza assoluta, e P dal&shy;<lb/>l'altra parte rappresenta la forza della resistenza respettiva; questa &egrave; dun&shy;<lb/>que la terza parte di quella. </s></p><p type="main">

<s>Suppongasi ora che il peso del quadrato materiale SN sia quel che ci <lb/>vuole per strappare direttamente la trave MC dalla parete AB, con la quale <lb/>era prima coerente: per aver la quantit&agrave; del peso, che applicato in C &egrave; ne&shy;<lb/>cessario a troncar la medesima trave per traverso, ossia col far girare il <lb/>lato AM intorno al centro A, bisogna secondo Galileo segare il quadrato lungo <lb/>la linea retta NS, e, secondo il Leibniz, lungo il filo della parabola SQN, <lb/>e il peso del trilineo concavo NRSQN, secondo l'uno Autore, o il peso del <lb/>triangolo RSN, secondo l'altro, daranno quello che si cercava. </s></p><p type="main">

<s>La maggior parte dei Matematici, specialmente stranieri, prefer&igrave; l'ipo&shy;<lb/>tesi leibniziana, della quale il Varignon, in una delle pubbliche adunanze, <lb/>tenute nel 1702 dall'Accademia di Parigi, diceva che, sebbene la gli sem&shy;<lb/>brasse <emph type="italics"/>tres vraisemblables, pourroit n'etre pas encore au gr&edot; de tout le<emph.end type="italics"/><pb xlink:href="020/01/2260.jpg" pagenum="503"/><emph type="italics"/>monde.<emph.end type="italics"/> Giacomo Bernoulli infatti dirigeva, sotto il d&igrave; 12 Marzo 1705, a quella <lb/>medesima Accademia una lettera, nella quale, dopo avere accennato alle <lb/>nuove ipotesi, che il Mariotte e il Leibniz volevano sostituire alla galileiana. </s>

<s><lb/>soggiuge: &ldquo; Mais aucun de ces Auteurs ne considerant les corps comme <lb/>sujets &agrave; compression, et sur-tout leur hypothese des tensions des fibres, pro&shy;<lb/>portionnelles aux forces tendantes, ne s'accordant pas precisement avec la <lb/>Nature &rdquo; (Opera, T. II, Genevae 1744, pag. </s>

<s>978). </s></p><p type="main">

<s>Sar&agrave; pur troppo vero che le tensioni delle fibre, nello strapparsi natu&shy;<lb/>ralmente i solidi, non sono proporzionali alle forze tendenti, ma &egrave; falso che <lb/>nessuno de'due Autori commomerati non consideri i corpi come soggetti a <lb/>compressione, leggendosi cos&igrave; espressamente scritto dal Mariotte, in quel suo, <lb/>da noi sopra citato Discorso: &ldquo; Cela &eacute;tant suppose, si DCEF (nella prece&shy;<lb/>dente nostra figura 271) est un b&agrave;ton quarr&eacute; fich&eacute; dans un mur, on peut <lb/>concevoir que depuis D jusqu'a I, qui est la moiti&eacute; de l'epaisseur DC, les <lb/>parties se pressent par le poids G: celle, qui sont proches de D, davantage <lb/>que celles vers I; et que depuis I jusques a C, elles s'etendent &rdquo; (Oeu&shy;<lb/>vres cit. </s>

<s>pag. </s>

<s>465). </s></p><p type="main">

<s>Tale &egrave; l'espresso concetto del Mariotte, bench&egrave; pochi sian per conce&shy;<lb/>dergli che il punto della distinzion tra le fibre stirate e le compresse sia <lb/>nella precisa met&agrave; della grossezza DC del bastone; e tanto meno sien di&shy;<lb/>sposti a concedere quel che il Mariotte stesso soggiunge e ammette come <lb/>verosimile, che cio&egrave; &ldquo; ces pressemens resistent autant que les extensions, <lb/>et qu'il faut un m&egrave;me poids pour les faire &rdquo; (ivi). </s></p><p type="main">

<s>Ora, in correggere specialmente la prima di queste ipotesi, tutt'altro <lb/>che verosimile, consiste il merito e la novit&agrave; della <emph type="italics"/>Veritable hypothese de <lb/>la resistance des solides,<emph.end type="italics"/> come al Bernoulli stesso udiremo confessar tra <lb/>poco, nel concludere il suo discorso, il quale piglia valore dal suppor che <lb/>sia medesimo l'effetto della rottura, e sia uguale la forza necessaria, tanto <lb/>a portar la trave BD (fig. </s>

<s>273) con la sua base da AB in AF, facendola gi&shy;<lb/>rar sul sostegno A, quanto a farla indietreggiare in GF, strisciandola sullo <lb/><figure id="id.020.01.2260.1.jpg" xlink:href="020/01/2260/1.jpg"/></s></p><p type="caption">

<s>Figura 273<lb/>stesso sostegno, cosicch&egrave;, nel triangolo BSF, <lb/>sian comprese tutte le fibre stirate, e nel <lb/>triangolo GSA tutte le fibre compresse. </s>

<s>Die&shy;<lb/>tro la quale ipotesi dimostra il Bernoulli che <lb/>la forza di produr tali effetti di compres&shy;<lb/>sione e di distrazione &egrave; quella medesima, <lb/>che potrebbe estendere le fibre tutte in&shy;<lb/>sieme comprese nel triangolo BAF, o com&shy;<lb/>primere tutte le altre, comprese nel trian&shy;<lb/>golo GAF, ci&ograve; ch'egli fa nel IV lemma, cos&igrave; propriamente da lui formu&shy;<lb/>lato: &ldquo; La m&egrave;me force, qui fait plier une poutre ou perche ABCD de AB <lb/>en GF, en etendant une partie de ses fibres de la quantit&eacute; du triangle <lb/>BSF, et comprimant l'autre de la quantit&eacute; du triangle ASG; seroit capable <lb/>d'&egrave;tendre l'assemblage de toutes les fibres sur l'apui A de la qnantit&egrave; du <pb xlink:href="020/01/2261.jpg" pagenum="504"/>triangle ABF, ou bien de comprimer cet assemblage sur l'apui B ou F de <lb/>la quantit&eacute; du triangle BAG, ou FAG &rdquo; (Opera cit., pag. </s>

<s>982). </s></p><p type="main">

<s>In virt&ugrave; di questo Lemma si scioglie dal Bernoulli stesso, con l'aiuto <lb/>dell'analisi infinitesimale, il primo dei due problemi da lui promessi in prin&shy;<lb/>cipio della sua Lettera, concludendo che la forza, sufficiente a rompere a <lb/>diritto la trave, sta a quella, necessaria per romperla a traverso, come la <lb/>lunghezza AD sta a una quarta proporzionale, che &egrave; sempre minore della <lb/>terza parte della grossezza AB. &ldquo; Ce qui s'accorde avec les experiences de <lb/>mr. </s>

<s>Mariotte, qu'a toujours trouv&eacute; cette quantit&eacute; moindre que le tiers, et <lb/>plus grande que le quart de la l auteur AB &rdquo; (ivi, pag. </s>

<s>988). </s></p><p type="main">

<s>Sarebbe l'opera del Bernoulli riuscita proficua, quando i fondamenti, <lb/>posti a quella sua analisi, fossero andati esenti da tutte le pi&ugrave; giudiziose <lb/>censure. </s>

<s>Ma insorsero il Bullinger e il Parent, i quali opposero, fra le altre <lb/>cose, che sebben sia lo stesso, geometricamente parlando o rispetto alla sem&shy;<lb/>plice situazione, il considerar la testata della trave, prima trasferita in AF <lb/>e poi in GF, o il considerarla come portata a un tratto in GF; non &egrave; per&ograve; <lb/>vero che possa la medesima forza indifferentemente operare o l'uno o l'al&shy;<lb/>tro effetto. </s>

<s>Conclusero perci&ograve; i due savi e valorosi Censori che la soluzione <lb/>del difficile problema era da sperar, non dall'analisi, ma dalla esperienza. </s></p><p type="main">

<s>Fu questa via, tra'Nostri, dop'essersi lungamente intrattenuto in eser&shy;<lb/>citaziani geometriche, e in speculazioni loquaci, approvata e proposta agli <lb/>studiosi, in fine alle <emph type="italics"/>Istituzioni<emph.end type="italics"/> meccaniche, dal Grandi, quand'una delle <lb/>principali questioni, ch'egli ebbe col Marchetti, parve che decisamente ve&shy;<lb/>nisse a risolversi dall'esperienze, fatte in Padova dal Poleni. </s>

<s>Si rammemo&shy;<lb/>reranno i nostri Lettori che, nella proposizione III del secondo libro <emph type="italics"/>De re&shy;<lb/>sistentia solidorum,<emph.end type="italics"/> professava l'Autore essere la resistenza del prisma <lb/>appoggiato ai due estremi doppia della resistenza del medesimo prisma af&shy;<lb/>fisso a una parete: contro la qual supposizione, fatta prima da Galileo, il <lb/>Grandi, animato dal De-la-Hire, prese a dimostrar che, non doppia era la <lb/>detta resistenza, ma quadrupla, e secondo alcuni calcoli anche ottupla del&shy;<lb/>l'altra. </s>

<s>Or perch&egrave; non poteva la mente desiderosa del vero assoluto acquie&shy;<lb/>tarsi in tali incertezze, volle il Poleni esaminare i fatti, e sperimentando sopra <lb/>un prisma di abete, e sopra varii cilindri di cera e di vetro, raccolse da <lb/>queste sue esperienze, come il Grandi stesso riferisce nelle <emph type="italics"/>Istituzioni<emph.end type="italics"/> ci&shy;<lb/>tate, che <emph type="italics"/>la proporzione dei pesi, ne'casi supposti, &egrave; sempre vicina alla <lb/>proporzione di uno a quattro<emph.end type="italics"/> (Firenze 1739, pag. </s>

<s>160). </s></p><p type="main">

<s>Nel medesimo tempo o poco prima Pietro van Musschenbroek istituiva <lb/>in Olanda esperienze simili a quelle del nostro Poleni, costruendo perci&ograve; <lb/>una Macchina particolare. </s>

<s>Anzi, tanto sent&igrave; il Professore ultraiettino la ne&shy;<lb/>cessit&agrave; dell'argomento, che tutto volle percorrere il campo della nuova <lb/>Scienza galileiana, intorno alla quale scrisse, e pubblic&ograve; in Leida nel 1699 <lb/>una elaboratissima dissertazione intitolata <emph type="italics"/>Introductio ad cohaerentiam cor&shy;<lb/>porum firmorum.<emph.end type="italics"/> Concede che sia una tal coerenza dovuta all'attrazione <lb/>molecolare, ma in che consista, e da che dipenda una tal misteriosa forza <pb xlink:href="020/01/2262.jpg" pagenum="505"/>attrattiva non trova che sia detto da quella nuova Filosofia, della quale esplica <lb/>le dottrine, che specialmente si leggono ne'dialoghi di Galileo, ne'discorsi <lb/>idraulici del Mariotte, e nelle scritture accademiche del Leibniz e del Ber&shy;<lb/>noulli. </s>

<s>E giacch&egrave; egli pur conviene con i tre ultimi Autori commemorati <lb/>che tutti i corpi sono pi&ugrave; o meno flessibili, &ldquo; quaenam proportio aut pro&shy;<lb/>portiones, essendo cos&igrave; poi domanda, erunt inter cohaerentiam absolutam <lb/>et respectivam? </s>

<s>&rdquo; (pag. </s>

<s>528). Il Mariotte, soggiunge, ritrov&ograve; quella propor&shy;<lb/>zione essere di tre o di quattro a uno, n&egrave; si pu&ograve; negare che talvolta non <lb/>sia cos&igrave;, come ci risult&ograve; da varii nostri esperimenti, &ldquo; verum plurimas alias <lb/>proportiones dari etiam ex illis constabit, et quidem aliquando esse ut 8 <lb/>ad 1: immo omnes intermedias inter 3 ad 1, et 18 ad 1 obtinere, quod <lb/>probat Mariotti assertum non esse universale &rdquo; (ibid). </s></p><p type="main">

<s>N&egrave; si confidi, prosegue a dire il Musschenbroek, di aver nulla di uni&shy;<lb/>versale asserito ne'suoi teoremi il Leibniz, perch&egrave;, sebben sia vero talvolta <lb/>che gli allungamenti delle fibre son proporzionali alle forze traenti, per lo <lb/>pi&ugrave; si osserva che, moltiplicandosi i pesi non si moltiplicano a proporzion <lb/>le estensioni, come si vede per la seguente esperienza. </s>

<s>Presa una corda da <lb/>violino, lunga tre piedi, si fece tirar da pesi ora di 2, ora di 4, di 6, e di <lb/>otto libbre, e si osserv&ograve; essere i respettiv&igrave; allungamenti 9, 17, 23, 27 linee, <lb/>mentre dovevano essere 9, 18, 27, 36 linee, se fosse stata vera l'ipotesi <lb/>leibniziana delle forze proporzionali alle tensioni (ivi, pag. </s>

<s>530). </s></p><p type="main">

<s>&ldquo; Sequitur ex his, ne conclude l'Autore, non dari in Natura unam re&shy;<lb/>gulam universalem exponentem proportionem eamdem inter cohaerentiam <lb/>respectivam et absolutam, qualem Geometrae dare annisi sunt, cum diver&shy;<lb/>sissima esse debeat proportio pro varia corporum flexibilitate, quemadmo&shy;<lb/>dum revera experientia evincit. </s>

<s>Si Philosophi, antequam operam huic doctri&shy;<lb/>nae navassent, prius plurima tentamina accurata instituissent, multis peper&shy;<lb/>cissent laboribus, neque unquam uni universali regulae incubuissent. </s>

<s>Quot <lb/>enim fere diversa corpora dantur, totidem diversae proportiones inter cohae&shy;<lb/>rentiam absolutam et respectivam deprehenduntur &rdquo; (ibid., pag. </s>

<s>534). A <lb/>questa diversit&agrave; di proporzioni corrispondevano quelle, che il Viviani chia&shy;<lb/>mava <emph type="italics"/>tariffe,<emph.end type="italics"/> ond'&egrave; notabile che, nella sentenza approvata oramai da tutti i <lb/>Fisici e da tutti i Matematici, dopo tanti pericoli fatti, si riscontrassero, nel <lb/>mezzo e nel principio del faticoso cammino di quasi due secoli, l'olandese <lb/>Alunno del Newton, e il fiorentino Discepolo di Galileo. </s></p><pb xlink:href="020/01/2263.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO IX.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>De'proietti<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Di ci&ograve; che specularono il Tariaglia, il Cardano e il Benedetti, e come fossero, sui principii del se&shy;<lb/>colo XVII, promosse da Guidubaldo del Monte quelle speculazioni. </s>

<s>&mdash; II. </s>

<s>De progressi fatti da <lb/>Galileo: com'ei credesse la linea descritta dai proietti esser, nella sua parte curva, circolare. </s>

<s><lb/>e come primo il Cavalieri la dimostrasse parabolica. </s>

<s>&mdash; III. </s>

<s>Della prima parte del quarto Dia&shy;<lb/>logo galileiano; ossia della misura degl'impeti in ciascun punto della parabola. </s>

<s>&mdash; IV. </s>

<s>Della <lb/>seconda e terza parte del trattato galileiano; ossia della massima ampiezza dei tiri a mezza <lb/>squadra, e della costruzione delle Tavole ballistiche. </s>

<s>&mdash; V. </s>

<s>Delle difficolt&agrave; mosse contro la teo&shy;<lb/>ria del moto parabolico, e di alcune esperienze istituite per confrantarle co'teoremi di questa <lb/>nuova Scienza. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Nel trattato Delle resistenze consisteva l'altra Scienza nuova, che s'isti&shy;<lb/>tuiva da Galileo, dopo quella Dei moti locali, e noi ne abbiamo voluto di&shy;<lb/>scorrere nella nostra Storia, con ordine diverso da quello che tenne ne'suoi <lb/>dialoghi l'Autore, ma che meglio si conforma coi tempi, e con l'origine delle <lb/>speculazioni. </s>

<s>Vedemmo infatti come fossero, nel 1604, gi&agrave; posti al trattato <lb/><emph type="italics"/>De motu<emph.end type="italics"/> i fondamenti, mentre solamente cinque anni dopo s'incomincia ad <lb/>aver le prime notizie delle proposizioni dimostrate intorno al resistere dei <lb/>corpi duri. </s></p><p type="main">

<s>Si comprendono nella general denominazione di moti i cos&igrave; detti natu&shy;<lb/>rali e i violenti, i quali hanno nei detti dialeghi un discorso distinto s&igrave;, ma <lb/>nella successione non interrotto, e da Galileo composto con tale artificio, da <lb/>parer che la Scienza dei gravi naturalmente cadenti fosse nata a un parto <lb/>con quella de'proietti. </s>

<s>Venuti alla luce i tre dialoghi tutti insieme, il pub&shy;<lb/>blico, che con tanto applauso gli accolse, non si cur&ograve; di sapere come si con&shy;<lb/>cepisse, o secondo qual ordine si svolgessero gli organi al nuovo parto ma&shy;<lb/>raviglioso, e fu perci&ograve; facilmente creduto dai Lettori quel che pi&ugrave; premeva <lb/>all'Autor di far credere, che cio&egrave; nei foglietti, recati seco dal Salviati per <lb/>leggerli nella terza e nella quarta Giornata agl'interlocutori, fossero scritti <pb xlink:href="020/01/2264.jpg" pagenum="507"/>insieme i teoremi dimostrativi delle propriet&agrave; dei moti naturali, e dei vio&shy;<lb/>lenti: ond'essendo propriamente la scienza di questi incominciata dalla di&shy;<lb/>mostrazione delle traiettorie paraboliche, si veniva destramente a insinuare <lb/>che anche una tale dimostrazione facesse parte delle dottrine pi&ugrave; antiche, <lb/>comprese nel trattato Dei moti locali. </s>

<s>Dai fatti diligentemente esaminati per&ograve; <lb/>si scopre che i teoremi, per i quali si veniva a far della manuale arte bal&shy;<lb/>listica una terza Scienza nuova, non occorsero al pensiero di Galileo che <lb/>in sugli ultimi anni della sua vita scientifica, a appariscono ne'suoi libri <lb/>come improvvisi raggi di sol vespertino, che sia rimasto tutto il di nuvoloso. </s>

<s><lb/>Ma perch&egrave;, per essere un frutto serotino, non vuol dire perci&ograve; che sia di&shy;<lb/>fettoso, e suole anzi di pi&ugrave; acquistare di pregio, rimarrebbe l'industria usata <lb/>da Galileo per farlo apparir primaticcio un mistero, se non ci fosse rivelato <lb/>dalla storia, che siam per narrare, e che insomma si riduce tutta e procede <lb/>dalla scoperta delle Traiettorie paraboliche. </s></p><p type="main">

<s>In qual difetto si rimanesse intorno a ci&ograve; la Scienza del moto, la quale <lb/>aveva pure tant'oltre progredito, sulla fine del secolo XV, per gl'impulsi <lb/>avuti da Ciordano Nemorario; si mostra con l'esempio di Leonardo da Vinci, <lb/>le dottrine del quale intorno ai proietti sono oramai note ai nostri Lettori, <lb/>cosicch&egrave;, nel 1537, ebbe <gap/>n secolo prima di Galileo ogni ragione il Tarta&shy;<lb/>glia d'intitolare il suo libro <emph type="italics"/>Scientia nuova.<emph.end type="italics"/> Le proposizioni per&ograve;, che qui <lb/>concernono le traiettorie, sono false nella loro radice, concludendosi nella <lb/>quinta del primo libro, cos&igrave; formulata: &ldquo; Niun corpo egualmente grave pu&ograve; <lb/>andare per alcun spacio di tempo, over di luoco, di moto naturale e violente <lb/>insieme misto &rdquo; (Vinegia 1537, fol. </s>

<s>15 a tergo). Scende questa dalla prima <lb/>difettosa, e dalla terza, manifestamente falsa nell'asserire che &ldquo; quanto pi&ugrave; <lb/>un corpo egualmente grave se andara luntanando dal suo principio, over <lb/>proprinquando al suo fine nel moto violente, tanto pi&ugrave; andar&agrave; pigro e tardo &rdquo; <lb/>(ivi, fol. </s>

<s>13 a tergo). </s></p><p type="main">

<s>S'incontra nonostante al primo aprire del libro, nell'Epistola dedica&shy;<lb/>toria a Francesco Maria Della Rovere, duca di Urbino, una vera novit&agrave;, la <lb/>promessa dimostrazione scientifica della quale apparisce meravigliosa, che <lb/>cio&egrave;, <emph type="italics"/>per mettere a segno un pezzo de artiglieria, al pi&ugrave; che pu&ograve; tirare, <lb/>bisognava che la bocca del pezzo stesse ellevata talmente, che guardasse <lb/>rettamente a 45 gradi sopra al orizonte<emph.end type="italics"/> (ivi, fol. </s>

<s>3). </s></p><p type="main">

<s>Narra il Tartaglia come, a lui di queste cose inesperto, fosse proposto <lb/>il problema da un cordiale amico suo, <emph type="italics"/>peritissimo bombardiere in Castel <lb/>vecchio,<emph.end type="italics"/> e come gli occorresse in tale occasione, per aggiustare l'inclina&shy;<lb/>zione del pezzo, d'inventare una Squadra di legno &ldquo; over di alcun metallo <lb/>(come l'Autore stesso ce la descrive nel suo <emph type="italics"/>Primo quesito<emph.end type="italics"/>) fatta con di&shy;<lb/>ligentia, la quale ha interchiuso uno quadrante, cio&egrave; una quarta parte dun <lb/>cerchio, e tutto quel spacio vol esser diviso prima in 12 parti equali, e que&shy;<lb/>ste 12 parti li chiamaremo ponti. </s>

<s>Anchora cadauna di queste tai parti over <lb/>ponti vol esser anchora divisa in altre 12 parti equali, le qual parti chia&shy;<lb/>maremo menuti, e questi menuti si segnano con lineete alquanto pi&ugrave; corte <pb xlink:href="020/01/2265.jpg" pagenum="508"/>di quelle delli ponti. </s>

<s>Fatto questo bisogna ficare uno pironcino di ferro, over <lb/>di ottone, precisamente nel centro del quadrante, e a quel tal pironcino attac&shy;<lb/>carvi uno perpendicolo girabile, cio&egrave; uno fil di seta o daltro con un piom&shy;<lb/>bino da capo &rdquo; (Quesiti et Inventioni, Venetia 1546, fol. </s>

<s>5). </s></p><p type="main">

<s>Di un tale strumento, il quale <emph type="italics"/>gi&agrave; pi&ugrave; di cent'anni,<emph.end type="italics"/> scriveva nel 1641 <lb/>il Torricelli a pag. </s>

<s>227 della prima parte delle Opere geometriche, <emph type="italics"/>&egrave; stato <lb/>in uso, ed &egrave; ancora l'unico regolatore dei Bombardieri,<emph.end type="italics"/> si servi il Tarta&shy;<lb/>glia per eseguir l'esperienza del massimo tiro, che mostr&ograve;, contro la comune <lb/>opinione, avvenir veramente allora quando, infilata la pi&ugrave; lunga delle due <lb/>gambe della Squadra nella bocca del cannone, il perpendicolo batteva nel <lb/>sesto punto. </s>

<s>Confermavano dunque i fatti quel che, dice il Tartaglia stesso <lb/>al Duca d'Urbino, <emph type="italics"/>dimostrai con ragioni naturale et geometrice, di poi che <lb/>hebbi ben masticata e ruminata tal materia,<emph.end type="italics"/> le quali ragioni naturali e <lb/>geometriche sono esposte nel secondo libro, alla VIII proposizione che dice: <lb/>&ldquo; Se una medema possansa eiettara, over tirara corpi egualmente gravi si&shy;<lb/>mili et eguali in diversi modi violentemente per aere. </s>

<s>Quello che far&agrave; il suo <lb/>transito elevato a 45 gradi sopra a l'orizonte fara etiam il suo effetto pi&ugrave; <lb/>lontan dal suo principio sopra il pian dell'orizzonte, che in qualunque altro <lb/>modo elevato &rdquo; (Scientia n. </s>

<s>cit., fol. </s>

<s>27 a tergo). </s></p><p type="main">

<s>Chiunque s'abbatta a udire una tal proposta, per que'tempi s&igrave; nuova, <lb/>corre curiosamente trepido a leggerno la dimostrazione, ma rimane com'un <lb/>che sogni, e che, mentre stende le braccia all'oggetto desiderato, si desta. </s>

<s><lb/>Le ragioni geometriche del Tartaglia consistono nel suppor che le traietto&shy;<lb/>rie si compongano di moto violento schietto, in parte retto, e in parte curvo, <lb/>e di moto naturale lungo la tangente all'estremo punto della curva: le ra&shy;<lb/>gioni naturali poi si riducono a invocar l'assioma che, fra due massima&shy;<lb/>mente contrari, &egrave; sempre un luogo di mezzo. </s>

<s>Dietro le quali due ragioni, <lb/>e dietro il fatto accomodatizio che cio&egrave; il termine del moto violento nella <lb/>verticale &egrave; pi&ugrave; al di sopra, e nella orizzontale pi&ugrave; al di sotto dell'orizzonte, <lb/>che in tutte le altre inclinazioni intermedie; cos&igrave; procede il Tartaglia e con&shy;<lb/>clude il suo proprio discorso: </s></p><p type="main">

<s>&ldquo; Perch&egrave; evidentemente sapemo che, se un corpo egualmente grave <lb/>sar&agrave; eietto, over tirato violentemente per il pian de l'orizzonte, quel andara <lb/>a terminare il suo moto violento pi&ugrave; sotto a l'orizonte, che in qualunque <lb/>modo elevato, ma se lo andaremo allevando pian piano sopra a l'orizonte <lb/>per un tempo andara terminando il detto suo moto violente pur sotto a l'ori&shy;<lb/>zonte, ma continuando tal elevatione evidentemente sapemo che a tempo <lb/>terminara di sopra al detto orizonte, et poi, quanto pi&ugrave; se andara elevando <lb/>tanto pi&ugrave; andara a terminare pi&ugrave; in alto, e finalmente, giongendo alla per&shy;<lb/>pendicolare sopra al orizonte, quel terminara pi&ugrave; in alto over pi&ugrave; lontano <lb/>di sopra al detto piano del orizonte, che in qualunque modo ellevato: onde <lb/>seguiria, per le antecedenti propositioni over argumentationi, che gli sia una <lb/>ellevatione cos&igrave; conditionata, chel debbia far terminare precisamente in el <lb/>proprio piano del orizonte, la qual argumentatione essendo vera se verifi-<pb xlink:href="020/01/2266.jpg" pagenum="509"/>cara realmente al senso, etiam al intelletto, in quella ellevatione, che &egrave; media <lb/>fra quelle due massimamente contrarie in terminatione et questa ellevatione <lb/>media &egrave; quando il detto transito, over moto violente dun corpo egualmente <lb/>grave, &egrave; allevato alli 45 gradi sopra al orizonte &rdquo; (ivi, fol. </s>

<s>29). </s></p><p type="main">

<s>Nessuno si crederebbe che, a determinare l'inclinazione del pezzo, per <lb/>avere il tiro della massima volata, fosse condotto il Tartaglia da cos&igrave; fatto <lb/>strano discorso, ond'&egrave; pi&ugrave; ragionevole il pensare che indovinasse il vero, <lb/>argomentando piuttosto dall'attenta osservazione dei fatti. </s>

<s>Basta guardare, <lb/>quando fanno tra loro alle sassate per le strade i monelli, che sempre get&shy;<lb/>tano il sasso <emph type="italics"/>a mezz'aria,<emph.end type="italics"/> e i pi&ugrave; esperti cos&igrave; puntualmente, com'avessero <lb/>in mano la Squadra. </s></p><p type="main">

<s>Pi&ugrave; difficile per&ograve; sembrava a indovinare dai fatti un'altra verit&agrave;, di&shy;<lb/>pendente dalla prima scoperta, e bench&egrave; Galileo, promettendo di dimostrare <lb/>che sono uguali fra loro i tiri, quando le elevazioni superano o mancano <lb/>dalla semiretta per angoli uguali, dicesse ci&ograve; <emph type="italics"/>forse per l'esperienza non &egrave; <lb/>stato osservato<emph.end type="italics"/> (Alb. </s>

<s>XIII, 251), il Tartaglia, non per osservazioni sperimen&shy;<lb/>tali, ma per ragioni evidentissime asserisce, innanzi al Duca di Urbino, di <lb/>aver concluso questo medesimo, cent'anni prima che venisse a concluderlo <lb/>Galileo col suo discorso dimostrativo. </s>

<s>&ldquo; Oltre di questo, Signor generosis&shy;<lb/>simo, con ragioni evidentissime conobbi qualmente un pezzo de artiglieria <lb/>posseva, per due diverse vie, over ellevationi percottere in un medemo lnoco: <lb/>etiam trovai il modo di mandar tal cosa accadendo a essecutione: cose non <lb/>pi&ugrave; audite, Signor Preclarissimo, ne d'alcun altro antico ne moderno cogi&shy;<lb/>tate &rdquo; (ivi, fol. </s>

<s>5 a tergo). </s></p><p type="main">

<s>Comunque sia, bench&egrave; s'abbiano qui due felici divinazioni del vero, le <lb/>quali, in qualunque modo si vogliano interpetrare, lasciano l'animo nostro <lb/>pieno di maraviglia; non conferivano certo a sollevare l'arte del Bombar&shy;<lb/>diere alla dignit&agrave; di scienza: e nonostante non abbiamo in tutto il hbro del <lb/>Tartaglia altro che questo, che potesse poi dalla Scienza venire assunto per <lb/>suo soggetto. </s>

<s>Le altre parti pi&ugrave; principali, che consistono nel definire la <lb/>qualit&agrave; della linea descritta dal proietto, e la quantit&agrave; dell'impeto, non hanno <lb/>altro valore che di semplici supposizioni, le quali derivano la loro falsit&agrave; <lb/>dalla viziata radice della proposizione quinta del primo libro. </s>

<s>Si suppone in&shy;<lb/>fatti in secondo luogo, a scientifico fondamento del libro secondo, che &ldquo; ogni <lb/>transito, over moto violente de corpi egualmente gravi, che sia fuora della <lb/>perpendicolare de l'orizonte, sempre sara in parte retto e in parte curvo, e la <lb/>parte curva sara parte d'una circonferentia di cerchio &rdquo; (ivi, fol. </s>

<s>19 a tergo). <lb/>E in suppor ci&ograve; consiste tutta la scienza del Tartaglia intorno alle traiettorie. </s>

<s><lb/>Per quel poi riguarda le quantit&agrave; degl'impeti si riduce ogni scienza alla gi&agrave; <lb/>citata proposizione terza del primo libro, nella quale s'insegna tanto esser <lb/>pi&ugrave; debole il moto del proietto, quanto pi&ugrave; si dilunga dal suo principio. </s></p><p type="main">

<s>Se non che manifestamente contradiceva a questa proposizione l'arte <lb/>ballistica, principal virt&ugrave; della quale &egrave; anzi quella di allungare la linea del <lb/>tiro, perch&egrave; faccia la palla maggior passata. </s>

<s>Si studi&ograve; per questo il Tarta-<pb xlink:href="020/01/2267.jpg" pagenum="510"/>glia stesso di togliere la contradizione nel secondo dialogo del primo libro, <lb/>dove, proponendosi dal Duca di Urbino, interlocutore, il caso di avere a <lb/>battere una fortezza o con un cannone, che posto in monte tiri da vicino <lb/>di punto in bianco, o con un altro cannone, che tiri in direzione inclinata, <lb/>posto in pianura e alla stessa Fortezza pi&ugrave; di lontano; si domanda quale <lb/>de'due strumenti sia per fare maggiore effetto. </s></p><p type="main">

<s>Il Duca, secondo i supposti principii, e secondo ci&ograve; che appariva per <lb/>ragion naturale, non penava a credere ch'essendo l'artiglieria sul monte pi&ugrave; <lb/>vicina alla fortezza <emph type="italics"/>la balla doveria far maggiore effetto in lei<emph.end type="italics"/> ma Niccol&ograve; <lb/><figure id="id.020.01.2267.1.jpg" xlink:href="020/01/2267/1.jpg"/></s></p><p type="caption">

<s>Figura 274<lb/>risponde esser tutto il contrario, come <lb/>troppo ben sanno gli stessi Bombar&shy;<lb/>dieri: sembrava per&ograve; strano a credere <lb/>al Duca che una medesima palla sia, <lb/>con la medesima carica, spinta pi&ugrave; vi&shy;<lb/>gorosamente in alto e lontano, che in <lb/>piano e vicino, per cui Niccol&ograve; cerca di <lb/>soddisfarlo, ricorrendo alla Scienza dei <lb/>pesi, per la quale si vede che, stando <lb/>una Libbra a livello, si abbassa molto <lb/>pi&ugrave; in ugual declinazione ch'essendo <lb/>elevata. </s>

<s>Cos&igrave; per esempio, declinando <lb/>la libbra AB (fig. </s>

<s>274) dalla posizione <lb/>orizzontale AB per l'angolo AOC, si <lb/>abbassa della quantit&agrave; OE, mentre declinando dalla posizione verticale FI, <lb/>per un angolo FOG, uguale ad AOC, si abbassa solo quanto FH, molto <lb/>minore di OE. </s></p><p type="main">

<s>&ldquo; Voglio inferir per questo (risponde Niccol&ograve; al Duca, che non vedeva <lb/>dove fosse per riuscire il discorso) che ogni artegliaria essendo alivellata, la <lb/>se intende esser nel sito della equalit&agrave;, e la balla, tirata da quella in tal <lb/>sito, usce del pezzo pi&ugrave; grave, che in qualunque altro modo ellevata, over <lb/>separata da quel sito della equalit&agrave;, per le ragioni di sopra adutte, e per&ograve; <lb/>in tal sito la balla va con pi&ugrave; difficolt&agrave;, e molto pi&ugrave; presto comincia a de&shy;<lb/>clinar al basso, cio&egrave; verso terra, et in maggior quantit&agrave; lei va declinando, <lb/>che in qualunque modo ellevata, cio&egrave; che lei va, come fra bombardieri si <lb/>dice, molto manco per linea retta, che in qualunque altro modo ellevata, e <lb/>per&ograve; li effetti di tiri fatti in tal sito saranno men vigorosi, over di meno ef&shy;<lb/>fetto che in qualunque altro verso &rdquo; (Quesiti et inventioni cit., fol. </s>

<s>9 a tergo). </s></p><p type="main">

<s>Si puo dalle cose fin qui esposte argomentar che poco o nulla promosse <lb/>il Tartaglia la Scienza dei proietti, lasciata quasi intatta ai suoi successori, <lb/>alle speculazioni dei quali egli propriamente il primo veniva a proporre una <lb/><emph type="italics"/>Scientia nuova.<emph.end type="italics"/> Ma per investigare con la speranza di qualche buona riu&shy;<lb/>scita le propriet&agrave; del moto violento si comprendeva come bisognasse prima <lb/>definirne la natura, intorno a che esso Tartaglia, non avendo insegnato nulla <lb/>di nuovo, lasciava con gli errori di Aristotile a combatter gl'ingegni. </s></p><pb xlink:href="020/01/2268.jpg" pagenum="511"/><p type="main">

<s>Fu de'primi il Cardano a mostrar con ragioni, che non superavano la <lb/>capacit&agrave; del senso comune, quanto fosse falso quel che insegna il Filosofo <lb/>della freccia che o lungi o presso alla corda si move al moto dell'aria che <lb/>la circonda, e approvando per verissimo detto che <emph type="italics"/>omne quod movetur ab <lb/>aliquo movetur,<emph.end type="italics"/> soggiunge: &ldquo; sed illud quod movet est impetus acquisi&shy;<lb/>tus, sicut calor in aqua, qui est ibi praeter naturam ab igne inductus, et <lb/>tamen, igne sublato, manum tangentis exurit, et ideo et accidens violenter <lb/>adhaerens vim suam retinet &rdquo; (De subtilitate, Lugduni 1580, pag. </s>

<s>93). </s></p><p type="main">

<s>Giulio Cesare Scaligero, entrato col Cardano in gara di sottilizzare d'in&shy;<lb/>gegno, diceva che, a mostrar la futilit&agrave; delle ragioni di Aristotile, non era <lb/>argomento migliore di un'esperienza da lui stesso cos&igrave; descritta: Abbiasi <lb/><figure id="id.020.01.2268.1.jpg" xlink:href="020/01/2268/1.jpg"/></s></p><p type="caption">

<s>Figura 275<lb/>una levigatissima tavola, nella quale <lb/>s'incida col tornio una ruzzola, a cui <lb/>si dian le mosse per via di un ma&shy;<lb/>nubrio che, sostenuto esso stesso da <lb/>due forcelle, la sostenga: vedrai ma&shy;<lb/>nifestamente essa ruzzola seguitare a <lb/>moversi in giro, bench&egrave; non mossa <lb/>dall'aria. </s>

<s>&ldquo; A tabula (fig. </s>

<s>275) B or&shy;<lb/>bis, C, C vectis, D manubrium, F, F <lb/>furcellae. </s>

<s>Non enim tunc in motu cir&shy;<lb/>culari locus erit aeri impellenti. </s>

<s>Jam <lb/>ipse aer inter orbem ac tabulam adeo exiguus, ut nullas vires ad fictum <lb/>illum motum sit habiturus. </s>

<s>Et ipsius orbis politisima levitas neutiquam a <lb/>circumstante aere agitationis instigationem recipere poterit &rdquo; (Adversus Car&shy;<lb/>danum, Exercitationes, Francofurti 1592, pag. </s>

<s>130). </s></p><p type="main">

<s>Ma pi&ugrave; efficaci di tutti, a restaurare il vero sopra i demoliti errori ari&shy;<lb/>stotelici, furono gl'insegnamenti del Benedetti, sentenziosamente raccolti in <lb/>queste parole scritte in una di quelle Epistole, che sulla fine del secolo XVI <lb/>erano il pi&ugrave; gradito pascolo de'matematici studiosi: &ldquo; Omne corpus grave, <lb/>aut sui natura aut vi motum, in se recipit impressionem aut impetum mo&shy;<lb/>tus, ita ut, separatum a virtute movente per aliquod temporis spatium, ex <lb/>seipso moveatur &rdquo; (Speculat., lib. </s>

<s>cit., pag. </s>

<s>286, 87). Cosicch&egrave; Galileo, che <lb/>ne'suoi Dialoghi e negli scritti minori spende, a dimostrare <emph type="italics"/>a quo movean&shy;<lb/>tur proiecta,<emph.end type="italics"/> cos&igrave; lunghi discorsi, niente altro fa che confermar le dottrine, <lb/>ripetendo bene spesso gl&igrave; argomenti medesimi de'suoi predecessori. </s></p><p type="main">

<s>Aperta cos&igrave; alla Scienza la prima entrata al vero, col definir la natura <lb/>del moto violento, fu possibile al Cardano e al Benedetti farvi anche qual&shy;<lb/>che progresso, di cui vanno principalmente debitori i due valent'uomini al&shy;<lb/>l'avere scoperta la gran fallacia, che ascondevasi nella proposizione quinta <lb/>del primo libro della <emph type="italics"/>Scientia nuova,<emph.end type="italics"/> dove afferma l'Autore non poter al&shy;<lb/>cun grave andare per alcun tempo di moto misto tutt'insieme di naturale <lb/>e di violento. </s>

<s>N&egrave; per vero dire ad avvedersi della falsit&agrave; di una tale propo&shy;<lb/>sta ci bisognava troppo grande sagacia, contradicendosi manifestamente que-<pb xlink:href="020/01/2269.jpg" pagenum="512"/>sta con ci&ograve; che supponesi nel secondo libro, dove si dice: &ldquo; Niun transito, <lb/>over moto violente d'un corpo egualmente grave, che sia fuor della per&shy;<lb/>pendicolare del orizonte, mai puol havere alcuna parte, che sia perfetta&shy;<lb/>mente retta, per causa della gravit&agrave; che se ritruova in quel tal corpo, la <lb/>quale continuamente lo va stimulando e tirando verso il centro del mondo &rdquo; <lb/>(fol. </s>

<s>19 a tergo). Se dunque la gravit&agrave; non abbandona mai il proietto, con&shy;<lb/>tinuamente tirandolo verso il centro del mondo, e se in ci&ograve; consiste il moto <lb/>suo naturale, mal si dichiara dal Tartaglia esser, nel principio della traiet&shy;<lb/>toria <emph type="italics"/>insensibilmente curva,<emph.end type="italics"/> quel moto violento puro. </s>

<s>&ldquo; Sed si dixisset ipse, <lb/>soggiungo il Benedetti, illum motum esse purum naturalem, hoc esset fal&shy;<lb/>sum, eo quod purus naturalis motus alicuius corporis non impediti, extra <lb/>locum suum, sit per lineam rectam et non per curvam &rdquo; (Specul., lib. </s>

<s>cit., <lb/>pag. </s>

<s>365). </s></p><p type="main">

<s>Il Cardano si salv&ograve; provvidamente dall'errore, professando le dottrine <lb/>aristoteliche dei moti misti, dai quali insieme, secondo lui, resulta la parte <lb/>curva della traiettoria, che non &egrave; circolare, come volle dire il Tartaglia, ma <lb/><figure id="id.020.01.2269.1.jpg" xlink:href="020/01/2269/1.jpg"/></s></p><p type="caption">

<s>Figura 276<lb/>s&igrave; piuttosto somigliantissima alla Parabola. </s>

<s>&ldquo; Cum <lb/>vero pila ad supremam rectam pervenerit, non per <lb/>circulum, nec recta rursum illic descendit, sed <lb/>media quasi linea, quae Parabolae ferme imitatur <lb/>circumambientem lineam, ut BC (fig. </s>

<s>276) est. </s>

<s>De&shy;<lb/>mum, ex C in D, motu gravis recti ad unguem. </s>

<s><lb/>Quae igitur proiiciuntur tribus ex motibus con&shy;<lb/>stant: primo, violento, ultimo exquisite naturali, <lb/>et medio ex utroque mixto. </s>

<s>Propter tam multipli&shy;<lb/>cem motus rationem metiri ad unguem talia plane est impossibile &rdquo; (De su&shy;<lb/>btil. </s>

<s>cit., pag. </s>

<s>96). </s></p><p type="main">

<s>E veramente impossibile era la cosa a que'tempi, in cui del moto na&shy;<lb/>turale e del violento s'ignoravano le leggi, per cui, nel ravvisare ad occhio <lb/>una somiglianza tra la linea descritta dai proietti e la parabola, s'arrestava. </s>

<s><lb/>per quanto nuovo e inaspettato apparisse, di queste cardaniche speculazioni <lb/>ogni progresso. </s>

<s>Per quella medesima difficolt&agrave; di misurare <emph type="italics"/>ad unguem<emph.end type="italics"/> le <lb/>traiettorie, riusciva pure impossibile di determinarne nei vari punti le quan&shy;<lb/>tit&agrave; degl'impeti respettivi, ond'&egrave; che non seppe il Cardano far altro che <lb/>ripetere l'opinion di Aristotile, &ldquo; qui dixit motum naturalem in fine, vio&shy;<lb/>lentum in principio, proiectorum in medio fieri velociorem &rdquo; (De subtil. </s>

<s>cit., <lb/>pag. </s>

<s>94). </s></p><p type="main">

<s>Il Benedetti stesso, bench&egrave; riconoscesse falsa l'applicazione de'princi&shy;<lb/>pii statici della Libbra, fatta dal Tartaglia nel suo secondo Quesito, non <lb/>seppe per&ograve; sostituirvi un'altra dottrina, che sentisse meglio del vero. </s>

<s>Era <lb/>facile avvedersi ch'essendo la libbra G, nella nostra figura 274 qui poco <lb/>addietro, nelle condizioni della libbra L, ne seguirebbe che ugualmente va&shy;<lb/>lido fosse il colpo della bombarda elevata o depressa sotto l'orizzonte per <lb/>angoli uguali: <emph type="italics"/>id quod non ita se habet.<emph.end type="italics"/> Ma la vera causa per cui la bom-<pb xlink:href="020/01/2270.jpg" pagenum="513"/>barda elevata fa pi&ugrave; valido il colpo, soggiunge tosto il Benedetti, si riduce <lb/>principalmente a ci&ograve; che, con tanto maggior forza si muove un corpo, quanto <lb/>pi&ugrave; ne raccoglie in s&egrave; resistendo per pi&ugrave; lungo tempo alla virt&ugrave; movente. <lb/></s>

<s>&ldquo; Atque hoc supradictis ictibus elevatis accidit, quia gravitas pilae ea est, <lb/>quae resistens virtuti moventi dat ei commoditatem colligendi, dictam vir&shy;<lb/>tutem, multo magis quam esset ea, quae ad depressiorem elevationem eam <lb/>impelleret &rdquo; (Speculat., lib. </s>

<s>cit., pag. </s>

<s>258). </s></p><p type="main">

<s>Non rivolse il Benedetti sopr'altre parti dell'argomento le sue specu&shy;<lb/>lazioni, ma pure egli aveva col Cardano recato non piccolo giovamento alla <lb/>Scienza, liberandola dai pi&ugrave; dannosi errori del Tartaglia. </s>

<s>Ma come per lo <lb/>pi&ugrave; avviene che i primi abiti si dismettono, almeno in parte, pi&ugrave; difficil&shy;<lb/>mente; cos&igrave; avvenne degl'insegnamenti di quella, che appariva propriamente <lb/>agl'ingegni una <emph type="italics"/>Scientia nuova.<emph.end type="italics"/> Il pi&ugrave; notabile esempio di ci&ograve; n'&egrave; offerto <lb/>da Galileo, sul giovanile ingegno del quale non valse l'autorit&agrave; del Bene&shy;<lb/>detti a rimoverlo dall'opinione, che non v'abbia nella traiettoria mistione <lb/>alcuna di moto, per cui sia vero che va il proietto sempre pi&ugrave; tardo, quanto <lb/>pi&ugrave; si dilunga dal suo principio. </s>

<s>Una delle cose infatti che proponevasi di <lb/>dimostrar nel dialogo <emph type="italics"/>De motu gravium<emph.end type="italics"/> &egrave;: &ldquo; undenam accidat quod motus <lb/>naturalis velocior in fine quam in medio vel in principio; violentus vero ve&shy;<lb/>locior in principio quam in medio, et hic quam in fine existat &rdquo; (Alb. </s>

<s>XI, 11). </s></p><p type="main">

<s>Professando poi, come il Tartaglia, che la traiettoria si compone di moto <lb/>puro violento, di moto circolare e di moto naturale, par che voglia Galileo <lb/>rispondere al Benedetti col dire che nel moto circolare non &egrave; vero che siano <lb/>misti insieme due moti, ma &egrave; un moto puro distinto, che non &egrave; n&egrave; natu&shy;<lb/>rale n&egrave; violento. </s>

<s>Supposto che la circolazione, come de'proietti avviene, si <lb/>faccia intorno al centro della Terra, ch'egli immagina esser centro di una <lb/>sfera che gira, cos&igrave; Galileo stesso dimostra non essere n&egrave; violento n&egrave; natu&shy;<lb/>rale il moto di tale sfera: &ldquo; Motus itaque naturalis est dum mobilia ince&shy;<lb/>dendo ad loca propria accedunt; violentus vero est dum mobilia, quae mo&shy;<lb/>ventur, a proprio loco recedunt. </s>

<s>Haec, cum ita se habeant, manifestum est <lb/>sphaeram supra centrum mundi circumvolutam neque naturali, neque vio&shy;<lb/>lento motu moveri &rdquo; (ibid., pag. </s>

<s>65). </s></p><p type="main">

<s>Vedremo come questa giovanile opinione della linea circolare, che de&shy;<lb/>scrivono i proietti, venisse per Galileo a trovare una conferma e quasi una <lb/>dimostrazione di fatto nel moto circolare della Terra, ma giova intanto sa&shy;<lb/>pere come risolvesse l'altro quesito proposto nello stesso luogo del Dialogo <lb/>dianzi citato, &ldquo; cur tormenta tum muralia tum manualia longius per rectam <lb/>lineam plumbeas sphaeras iaciunt, si eas per lineas inclinatas orizonti proii&shy;<lb/>ciant, quam si per lineam eidem orizonti parallelam. </s>

<s>&rdquo; </s></p><p type="main">

<s>La soluzione, dalla quale doveva dipendere ogni scienza dell'arte balli&shy;<lb/>stica, si legge nell'altro trattato giovanile <emph type="italics"/>De motu,<emph.end type="italics"/> e si riduce insomma <lb/>in attribuire il fatto a due cause. </s>

<s>La prima &egrave; quella, che vedemmo essere <lb/>stata assegnata gi&agrave; dal Benedetti, in risolvere il problema del Tartaglia <emph type="italics"/>De <lb/>ictu bombardae,<emph.end type="italics"/> e che si conclude anche per Galileo da quel principio che <pb xlink:href="020/01/2271.jpg" pagenum="514"/>dice &ldquo; virtutem impellentem acrius longe imprimi in eo quod magis resi&shy;<lb/>stit &rdquo; (Edizion nazionale, T. I, 1890, pag. </s>

<s>337). L'altra causa per&ograve; &egrave; d'in&shy;<lb/>venzione propria, e balenandovi dentro un concetto nuovo merita di essere <lb/>attentamente considerata. </s></p><p type="main">

<s>Si getti il mobile A (fig. </s>

<s>277) ora per la verticale AB, ora per le obli&shy;<lb/>que AC, AD, AE: la causa per cui in AB la rettitudine &egrave; maggiore che in <lb/>AC, in AC maggiore che in AD, e in AD maggiore che in AE, dice Gali&shy;<lb/><figure id="id.020.01.2271.1.jpg" xlink:href="020/01/2271/1.jpg"/></s></p><p type="caption">

<s>Figura 277<lb/>leo, &egrave; questa: che nella direzion verticale il mobile non pu&ograve; <lb/>tornare indietro, al termine da cui si part&igrave;, che per la me&shy;<lb/>desima rettitudine dell'ascesa, per cui &egrave; costretto di sfogare <lb/>tutto il suo impeto per quella via. </s>

<s>Ma nelle direzioni obli&shy;<lb/>que pu&ograve; tornare indietro per una via diversa, deflettendosi <lb/>prima di esaurir tutto per linea retta il primo impeto con&shy;<lb/>ceputo. </s>

<s>E perch&egrave; questa facilit&agrave; di defletter dal primo corso <lb/>&egrave; tanto pi&ugrave; grande, quanto l'angolo fatto dalla direzione del <lb/>tiro con l'orizzonte &egrave; pi&ugrave; acuto; s'intende perch&egrave;, gettato <lb/>il mobile ora per AC, ora per AD, ora per AE, vada in <lb/>dirittura per tratti via via sempre minori. </s>

<s>&ldquo; Verum, si fer&shy;<lb/>tur per lineam perpendicularem AB, ab ea nullo modo mobile declinare po&shy;<lb/>test, nisi super eadem recedendo, ad terminum a quo recessit, accedat; hoc <lb/>autem, dum vivet, nunquam patietur virtus impellens. </s>

<s>Cum autem mobile <lb/>per lineam AC fertur, quia adhuc inclinatio, ad terminum a quo, tendit, nisi <lb/>valde debilitata, eam non sinet virtus motiva. </s>

<s>Cum autem fertur per AE hori&shy;<lb/>zonti fere aequidistantem, potest quantumlibet cito inclinari incipere mobile; <lb/>inclinatio enim haec recessum a termino non impedit &rdquo; (ibid., pag. </s>

<s>339, 40). </s></p><p type="main">

<s>Si diceva che da queste galileiane speculazioni si vede balenare in volto <lb/>alla Scienza de'proietti un concetto nuovo, il quale sarebbe poi per pigliare <lb/>essenza di vero, quando l'impeto verticale, che ora s'esaurisce nella retti&shy;<lb/>tudine e nella deflessione del moto, s'intender&agrave; compartito fra lo spingere <lb/>in alto il mobile, e il mandarlo al largo per l'orizzonte, in quelle che si <lb/>chiameranno <emph type="italics"/>altezza,<emph.end type="italics"/> e <emph type="italics"/>amplitudine<emph.end type="italics"/> della Parabola. </s>

<s>Prima per&ograve; che questo <lb/>essenzial vero gli si facesse noto, persist&egrave; Galileo per quarant'anni nell'er&shy;<lb/>rore, da cui venne non per propria ma per altrui virt&ugrave; finalmente salvato. </s>

<s><lb/>Come questo avvenisse &egrave; ci&ograve; che ci resta a narrar di pi&ugrave; nuovo, e anche <lb/>di pi&ugrave; curioso, perch&egrave; fu Galileo stesso che, scoperte le leggi dei moti na&shy;<lb/>turali, dava altrui il modo di dimostrar le leggi dei moti violenti. </s>

<s>Il primo <lb/>esempio del non aver saputo adoperar l'argomento colui, che industriosa&shy;<lb/>mente l'avea fabbricato, risale a quegli anni, ne'quali, dall'aver supposto <lb/>le velocit&agrave; proporzionali ai tempi riusc&igrave; a concluder che gl'incrementi degli <lb/>spazi nel moto accelerato stanno come la serie de'numeri impari, e che <emph type="italics"/>la <lb/>velocit&agrave; nel moto violento va decrescendo con la medesima proporzione, <lb/>con la quale nella medesima linea retta cresce nel moto naturale.<emph.end type="italics"/></s></p><p type="main">

<s>Che occorressero a farsi queste scoperte verso il 1604 si prov&ograve; altrove, <lb/>e si conferma qui da una lettera, scritta il d&igrave; 9 d'Ottobre di quell'anno, e <pb xlink:href="020/01/2272.jpg" pagenum="515"/>nella quale il Sarpi cos&igrave; comincia, per esporre e avere da Galileo la solu&shy;<lb/>zione di un dubbio: &ldquo; Gi&agrave; abbiamo concluso che nessun grave pu&ograve; essere <lb/>tirato all'istesso termine in su, se non con una forza, e per consequente <lb/>con una velocit&agrave;. </s>

<s>Siamo passati, cos&igrave; V. S. ultimamente afferm&ograve; ed invent&ograve;, <lb/>che per li stessi termini torner&agrave; in gi&ugrave; pei quali and&ograve; in s&ugrave; &rdquo; (Alb. </s>

<s>VIII, 29). </s></p><p type="main">

<s>Le medesime cose che al Sarpi furono nel tempo stesso partecipate da <lb/><figure id="id.020.01.2272.1.jpg" xlink:href="020/01/2272/1.jpg"/></s></p><p type="caption">

<s>Figura 278<lb/>chi le afferm&ograve; e invent&ograve; a Guidubaldo del Monte, il quale, ri&shy;<lb/>meditando il fatto che, spinto il mobile da A in B (fig. </s>

<s>278) <lb/>torna da B in A, avendo in C, D, E e in tutti gli altri punti <lb/>intermedi acquistata nello scender la medesima velocit&agrave;, che <lb/>ivi ebbe nel risalire; dovette concluderne che, leggermente <lb/>inclinata la direzione del tiro tanto da distinguere le due vie, <lb/>quella FG per cui cala &egrave; simile alla AF per cui il mobile <lb/>monta. </s>

<s>N&egrave; si vedeva perch&egrave; la medesima conclusione non si <lb/>potesse applicare al caso, in cui declinando anche di pi&ugrave; la <lb/>direzione del tiro, il proietto va, come per ACE (fig. </s>

<s>279), <lb/>per una via pi&ugrave; aperta. </s></p><p type="main">

<s>Imbevuto Guidubaldo delle pi&ugrave; sane dottrine del Benedetti fu da lui <lb/>persuaso che, non potendo per il tratto AB la gravit&agrave; abbandonare il pro&shy;<lb/><figure id="id.020.01.2272.2.jpg" xlink:href="020/01/2272/2.jpg"/></s></p><p type="caption">

<s>Figura 279<lb/>ietto, n&egrave; per il tratto DE la gravit&agrave; stessa essere abban&shy;<lb/>donata dal primo impeto impresso, che non pu&ograve; tutto <lb/>essersi esaurito; quelle linee son ambedue curve gene&shy;<lb/>rate da moto misto: ond'essendo di moto misto resul&shy;<lb/>tante tutta intera la traiettoria, ebbe a concluderne, <lb/>dietro gli avvertimenti del Cardano, che non per sola la <lb/>parte inflessa BCD, ma che per tutta la lunghezza ACE <lb/>la linea del moto si compone in modo, da rassembrare <lb/>una parabola. </s>

<s>E perch&egrave; il mobile per l'aria non lascia di s&egrave; vestigio, Gui&shy;<lb/>dubaldo stesso ricorse all'ingegnoso partito di tirar sopra un piano una palla <lb/>tinta d'inchiostro, la via disegnata dalla quale, arrovesciata e tenuta pen&shy;<lb/>dula, gli pareva, con que'punti interrotti pel saltellar che andando faceva la <lb/>palla stessa, rassomigliarsi alla sacca di una catena lentamente sospesa. </s>

<s>Gli <lb/>venne allora in pensiero che anche la sacca della catena risulti da un moto <lb/>naturale consistente nel peso degli anelli, misto al moto violento di chi la <lb/>tira ai due capi, &egrave; fu il primo a rassomigliare a vista la catenaria e la tra&shy;<lb/>iettoria fra loro, e ambedue alla parabola. </s></p><p type="main">

<s>Questi pensieri venutisi, sul principio del secolo XVII, a svolgere dalle <lb/>precedenti tradizioni, e dalle nuove dottrine galileiane, segnano nella Scienza <lb/>de'proietti un tal progresso, da non restar altro al perfezionamento di lei, <lb/>se non che la Geometria v'apponesse il suggello del vero. </s>

<s>Dalla natura e <lb/>dalla qualit&agrave; della curva riconosciuta veniva sicuro il modo di misurare gli <lb/>effetti del colpo, e nelle varie elevazioni le ragioni del tiro: ond'&egrave; che ve&shy;<lb/>ramente i teoremi dimostrati trent'anni dopo nel terzo dialogo delle due <lb/>Scienze nuove si contengono, come in germe, in queste parole di Guidu-<pb xlink:href="020/01/2273.jpg" pagenum="516"/>baldo, che si leggono sulla fine del manoscritto di lui, pubblicato fra le Note <lb/>all'ultimo tomo della <emph type="italics"/>Storia<emph.end type="italics"/> del Libri: </s></p><p type="main">

<s>&ldquo; Se si tira una palla o con una balestra o con artiglieria o con la mano <lb/>o con altro instrumento sopra la linea del horizonte, il medesimo viaggio <lb/>fa nel callar che nel montare, e la figura &egrave; quella che, rivoltata sotto la <lb/>linea horizontale, fa una corda che non stia tirata, essendo l'un e l'altro <lb/>composto di naturale e di violento, et &egrave; una linea in vista simile alla pa&shy;<lb/>rabola.... La esperienza di questo moto si po far pigliando una palla tinta <lb/>d'inchiostro, e tirandola sopra un piano di una tavola, il qual stia quasi <lb/>perpendicolare al horizonte: che se ben la palla va saltando, va per&ograve; fa&shy;<lb/>cendo li punti, dalli quali si vede chiaro che, siccome ella ascende, cos&igrave; anco <lb/>descende, et &egrave; cos&igrave; ragionevole, perch&egrave; la violentia, ch'ella ha acquistata <lb/>nel andare in su, fa che nel callar vadi medesimamente superando il moto <lb/>naturale nel venire in gi&ugrave;: che la violentia, che super&ograve; dal B (nell'ultima <lb/>figura) al C, conservandosi, fa che dal C al D sia uguale a CB, e descen&shy;<lb/>dendo, di mano in mano perdendosi la violentia, fa che dal D al E sia uguale <lb/>a BA, essendo che non ci &egrave; ragione che dal C verso DE mostri che si perda <lb/>a fatto la violentia; che se ben va continuamente perdendo verso E, non&shy;<lb/>dimeno sempre se ne resta, che &egrave; causa che verso E il peso non va mai <lb/>per linea retta &rdquo; (A Paris 1844, pag. </s>

<s>397, 98). </s></p><p type="main">

<s>Furono senza dubbio queste speculazioni risapute da Galileo, ma non <lb/>ci &egrave; riuscito ancora di sapere in che modo. </s>

<s>Disse una volta Muzio Oddi al <lb/>Cavalieri che esso Galileo e Guidubaldo avevano con le artiglierie fatto in&shy;<lb/>sieme esperienze intorno ai proietti, ci&ograve; che deve esser dunque avvenuto <lb/>prima del 1607, anno in cui mori Guidubaldo. </s>

<s>Di queste pubbliche espe&shy;<lb/>rienze per&ograve; non abbiamo n&egrave; documento certo, n&egrave; parole che ne facciano <lb/>qualche cenno, e dall'altra parte l'esperienza riferita nella sopra addotta <lb/>scrittura era cos&igrave; semplice e cos&igrave; naturale, da non aver bisogno d'altro aiuto <lb/>o testimonio. </s>

<s>Noi perci&ograve; crediamo che il manoscritto ritrovato dal Libri, o <lb/>nell'originale o in copia, fosse, poco dopo il 1607, capitato alle mani di Ga&shy;<lb/>lileo, e perch&egrave; vi s&igrave; ritrovavan dottrine di acustica, di resistenze e di moti, <lb/>che egli intendeva appropriarsi, non potendo, per la ragion che ne avreb&shy;<lb/>bero potuto richieder coloro, i quali avesser veduto o sentito dire del Ma&shy;<lb/>noscritto, tutto defraudare a Guidubaldo; per dir com'egli ci entrasse di <lb/>mezzo dette voce che avevano sperimentato, specialmente con le artiglierie, <lb/>quelle cose tutt'e due insieme. </s></p><p type="main">

<s>Comunque sia per&ograve; delle esperienze, che sian propriamente dell'Autore <lb/>del manoscritto le speculazioni ammirate, si prova dal fatto, che Galileo ri&shy;<lb/>fiut&ograve; di esse la parte migliore, rimanendo tuttavia in dubbio intorno alla <lb/>qualit&agrave; della linea descritta dal proietto, e inclinando molto verso la prima <lb/>concepita opinione che cio&egrave;, cos&igrave; la traiettoria come la catenaria partecipas&shy;<lb/>sero la loro curvit&agrave; non dalla parabola, ma s&igrave; piuttosto dal cerchio. </s>

<s>Come <lb/>avvenisse la subitanea conversione, e come quel Salviati, gi&agrave; disposto fin <lb/>da principio ad accogliere il risoluto problema della corda non tocca che <pb xlink:href="020/01/2274.jpg" pagenum="517"/>risona all'unisono di un'altra vibrata, e la ragion della resistenza de'canapi <lb/>uguale in tutta la loro lunghezza; si risolvesse all'ultimo di derivare altres&igrave; <lb/>ne'suoi dialoghi, dal manoscritto di Guidubaldo, il modo di descriver mec&shy;<lb/>canicamente la parabola, e di applicare ai proietti quella mistione di moto <lb/>naturale e di violento, che ritrovasi nella catena; lo vedremo nella seguente <lb/>parte del nostro discorso, dop'esserci trattenuti a veder quali fossero i pro&shy;<lb/>gressi, che fece Galileo speculando sopra le pi&ugrave; approvate speculazioni dello <lb/>stesso Guidubaldo. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Dovea fra le approvate speculazioni senza dubbio esser quella dell'ugual <lb/>viaggio, che il proietto fa nel salire e nello scendere, e della ugual velocit&agrave;, <lb/>che si trova ne'due punti, ne'quali son dalla medesima orizzontale interse&shy;<lb/>cati i due rami della via, essendo tuttoci&ograve; consequente come avvertimmo, <lb/><figure id="id.020.01.2274.1.jpg" xlink:href="020/01/2274/1.jpg"/></s></p><p type="caption">

<s>Figura 280<lb/>dallo stesso principio galileiano, <lb/>&ldquo; che il cadente naturale ed il <lb/>proietto violento passano per la <lb/>medesima proporzione di velo&shy;<lb/>cit&agrave; &rdquo; (Alb. </s>

<s>VI, 25). Cos&igrave; non in <lb/>sola la traiettoria ABC (fig. </s>

<s>280), <lb/>ma in tutte le altre EBF, GBH, <lb/>aventi la medesima altezza BO, <lb/>si avverer&agrave; che il cadente naturale in M e in O dovr&agrave; avere la medesima <lb/>proporzione di velocit&agrave; che il proietto violento in N e in P, in C e in H. </s></p><p type="main">

<s>Ma qui occorse alla mente di Galileo un dubbio, che gli ragionava non <lb/>parer verosimile che in N e in P abbia il grave la medesima velocit&agrave;, o <lb/>partitosi da B con moto iniziale, o partitosi dalla quiete: per gli stabiliti <lb/>principii dinamici infatti il cadente naturale da B, per i piani convessi BN, <lb/>BP, ha acquistato i medesimi gradi di velocit&agrave;, che in M, come si dice avere <lb/>acquistato il proietto violento. </s>

<s>Quella velocit&agrave; per&ograve;, proseguiva a ragionar <lb/>Galileo, non l'ha il grave acquistata, se non col tempo, il quale &egrave; propor&shy;<lb/>zionato alle lunghezze dei piani BN, BP, ond'ei sarebbe ragionevole il du&shy;<lb/>bitar dell'ugualit&agrave; degl'impeti, quando anche i tempi del proietto fossero <lb/>via via tanto pi&ugrave; lunghi, quanto son pi&ugrave; lunghi i descritti viaggi. </s></p><p type="main">

<s>Veniva cos&igrave; dunque a proporsi una nuova questione importante, che pa&shy;<lb/>reva risolversi dal considerar che forse &egrave; l'impeto impresso, il quale opera <lb/>nel proietto violento quel che nel cadente naturale opera il tempo, cosicch&egrave; <lb/>mentre qui gl'impeti naturali in M, in N e in P son ragguagliati dai di&shy;<lb/>versi tempi spesi nelle cadute, sien l&agrave; invece ragguagliati dagl'impeti vio&shy;<lb/>lenti, che una forza straniera partecipa al mobile, rimanendosi per qualun&shy;<lb/>que lunghezza di via i tempi sempre fra loro uguali. </s>

<s>Pareva insomma a <pb xlink:href="020/01/2275.jpg" pagenum="518"/>Galileo assai verosimile che, se fosse in B la bocca di un cannone livellato, <lb/>i tempi spesi a descrivere i getti BH, BF, BC dovessero essere tutti fra loro <lb/>uguali, e al tempo in cui la palla sarebbe giunta dallo stesso punto B in O, <lb/>per semplice via naturale. </s></p><p type="main">

<s>Il discorso richiedeva dalla esperienza qualche conforto, e perch&egrave; non <lb/>poteva una persona privata avere a sua disposizione artiglierie militari, e <lb/>dall'altra parte non eran queste sempre n&egrave; di pronta n&egrave; di comoda osser&shy;<lb/>vazione a un Filosofo, pens&ograve; di servirsi dei getti d'acqua, il maggiore o <lb/>minore impeto dei quali s'attemperava assai facilmente col crescere o col <lb/>diminuire l'altezza del liquido nel vaso. </s>

<s>Ebbe per Galileo di qui occasione <lb/>una Scienza nuova, gli oscuri natalizi della quale si celebrarono nella pro&shy;<lb/>posizione che i getti dell'acqua, essendo il cannone livellato, giungono a terra <lb/>nel medesimo tempo delle gocciole naturalmente cadenti, tiratesi sotto dallo <lb/>stesso cannone, e che gli zampilli, da qualunque forza sian fatti, purch&egrave; <lb/>giungano alla medesima altezza, si spediscono tutti in tempi uguali. </s>

<s>E perch&egrave; <lb/>non erano questi effetti dipendenti che dalla sola gravit&agrave;, non dubit&ograve; Gali&shy;<lb/>leo di applicarli ai tiri delle artiglierie, compiacendosi cos&igrave; di avere, tra il <lb/>finir del 1608 e il cominciar dell'anno seguente, progredito nell'acquisto <lb/>della Scienza de'proietti, e di averne fatta la prima felice applicazione alla <lb/>materia delle acque. </s>

<s>Tali erano infatti l'espressioni della sua compiacenza, <lb/>quali si leggono in una lettera scritta da Padova a un Principe di casa Me&shy;<lb/>dici, il d&igrave; 11 Febbraio 1609: </s></p><p type="main">

<s>&ldquo; Sono adesso intorno ad alcune questioni che mi restano intorno al <lb/>moto dei proietti, tra le quali molte appartengono ai tiri delle artiglierie, e <lb/>pure ultimamente ho ritrovata questa: che, ponendo il pezzo sopra qualche <lb/>luogo elevato dal piano della campagna, e appuntandolo livellato giusto, la <lb/>palla uscita dal pezzo, sia spinta da molta o da pochissima polvere, o anco <lb/>da quanto basti solamente a farla uscire dal pezzo, viene sempre declinando <lb/>ed abbassandosi verso terra con la medesima velocit&agrave;, sicch&egrave; nello stesso <lb/>tempo, in tutti i tiri livellati, la palla arriva in terra e siano i tiri lontanis&shy;<lb/>simi o brevissimi, oppure anco esca la palla dal pezzo solamente, e caschi <lb/>a piombo nel piano della campagna. </s>

<s>E l'istesso occorre nei tiri elevati, li <lb/>quali si spediscono tutti nell'istesso tempo, tuttavolta che si alzino alla me&shy;<lb/>desima altezza perpendicolare.... Nella materia delle acque e degli altri <lb/>fluidi, parte ancor lei intatta, ho parimente scoperte grandissime propriet&agrave; <lb/>della Natura &rdquo; (Alb. </s>

<s>VI, 69, 70). </s></p><p type="main">

<s>Le grandissime propriet&agrave; nella natura de'fluidi scoperte si riducevano <lb/>insomma alla sopra riferita proposizione, ma il tema delle Artiglierie si pre&shy;<lb/>sentava bene assai pi&ugrave; vasto e pi&ugrave; importante, derivando una sua tale im&shy;<lb/>portanza, non da solo avere avvertito l'isocronismo delle traiettorie, ma dal&shy;<lb/>l'avere riconosciuta l'egualit&agrave; degli impeti ne'due punti del loro viaggio <lb/>intersecato dalla medesima orizzontale. </s>

<s>Cos&igrave; veniva l'antica arte ballistica ad <lb/>essere radicalmente riformata, perch&egrave;, l&agrave; dove il Tartaglia aveva insegnato <lb/>che tanto &egrave; pi&ugrave; debole il colpo, quanto la palla &egrave; pi&ugrave; lontana dalla bocca <pb xlink:href="020/01/2276.jpg" pagenum="519"/>del cannone, e il Cardano che il maggior impeto del proietto &egrave; nel mezzo; <lb/>la nuova Scienza, come cosa inaspettata e quasi incredibile, rivelava che il <lb/>medesimo effetto fa la palla alla bocca del cannone elevato, e nel luogo pi&ugrave; <lb/>lontano, dov'ella batte per terra. </s></p><p type="main">

<s>Erano queste verit&agrave; intravedute come in ombra o indicate per assai <lb/>verosimili dall'esperienza, ma non dimostrate dalla Geometria o da discorso, <lb/>che potesse servire di fondamento alla Geometria, e nonostante lusingarono <lb/>tanto Galileo, da proporsi di stendere delle Artiglierie, con le quali ei pure <lb/>confessa di non aver mai fatto esperienza (Alb. </s>

<s>II, 100), un intero trattato, <lb/>i sommi capi del quale si trovano cos&igrave; intitolati e ordinatamente scritti di <lb/>propria mano di lui, in un foglio che ci &egrave; rimasto: </s></p><p type="main">

<s>&ldquo; I. </s>

<s>Particolari privilegi dell'Artiglieria sopra gli altri strumenti mec&shy;<lb/>canici. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; II. </s>

<s>Della sua forza, ed onde proceda. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; III. </s>

<s>Se operi con maggior forza in una certa distanza, o da vicino. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; IV. </s>

<s>Se la palla vadia per linea retta, non sendo tirata a perpendicolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; V. </s>

<s>Che linea descriva la palla nel suo moto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; VI. </s>

<s>La causa ed il tempo dello stornare il pezzo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; VII. </s>

<s>Impedimenti che rendono il pezzo difettoso ed il tiro incerto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; VIII. </s>

<s>Del metterle a cavallo e scavalcarle. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; IX. </s>

<s>Della fabbrica del calibro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; X. Dell'esamine circa la bont&agrave; e giustezza del pezzo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; XI. </s>

<s>Se quanto &egrave; pi&ugrave; lungo il pezzo tiri pi&ugrave; lontano, e perch&egrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; XII. </s>

<s>A quale elevazione tiri pi&ugrave; lontano, e perch&egrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; XIII Che nel termine la palla in gi&ugrave;, nel perpendicolo, torna con la <lb/>medes&igrave;ma forza e velocit&agrave; che andando in su. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; XIV. </s>

<s>Diverse palle artifiziate e lanterne e loro uso. </s>

<s>&rdquo; (MSS. Gal., <lb/>P. V, T. II, fol. </s>

<s>193). </s></p><p type="main">

<s>Molti de'proposti soggetti della trattazione concernono, come si vede, <lb/>la parte fisica o tecnica dell'Arte militare, ma quei che principalmente s'ap&shy;<lb/>partengono alla Scienza meccanica son fra'primi che s'incontrano in que&shy;<lb/>sto elenco il terzo, il quarto e il quinto, i quali ultimi due, insieme col XII, <lb/>venivano da Galileo risoluti con le ragioni medesime del Tartaglia. </s>

<s>Rispetto <lb/>al quarto infatti l'osservazione scritta nella seconda supposizione del secondo <lb/>libro della <emph type="italics"/>Scientia nuova<emph.end type="italics"/> vedesi tradotta in queste parole, con le quali <lb/>Simplicio, domandato quanto stia il proietto appena uscito di mano al proi&shy;<lb/>ciente a declinare in basso, risponde: &ldquo; Credo che cominci subito, perch&egrave;, <lb/>non avendo chi lo sostenti, non pu&ograve; esser che la propria gravit&agrave; non operi &rdquo; <lb/>(Alb. </s>

<s>I, 215). In piena conformit&agrave; coi quali principii Galileo pure scioglie il <lb/>quinto dei proposti quesiti, dicendo che la linea descritta dalla palla nel suo <lb/>moto &egrave; in parte tale da potersi avere per retta, e in parte manifestamente <lb/>curva, e la parte curva <emph type="italics"/>sar&agrave; parte di una circonferentia di cerchio,<emph.end type="italics"/> come <lb/>si legge nel detto libro della <emph type="italics"/>Scientia nuova.<emph.end type="italics"/> All'altro quesito XII non po&shy;<lb/>teva Galileo stesso risponder di meglio di quel che, non con ragioni geome-<pb xlink:href="020/01/2277.jpg" pagenum="520"/>triche ma sperimentali, avea gi&agrave; risposto il Tartaglia, che cio&egrave; l'elevazione, <lb/>alla quale tira l'obice pi&ugrave; di lontano, &egrave; nel sesto punto della Squadra. </s>

<s>Il <lb/>problema poi, scritto nel sopra addotto elenco in undecimo luogo, ritenevasi <lb/>come risoluto di fatto per il Cardano, il quale annovera fra le cause che <lb/>rendono o pi&ugrave; tardo o pi&ugrave; veloce il moto violento &ldquo; quod per magnum spa&shy;<lb/>tium: ideo machinae bellicae quo longiores eo procul magis eiaculantur &rdquo; <lb/>(De subtil. </s>

<s>cit., pag. </s>

<s>93). E probabilmente al fatto, che si credeva confer&shy;<lb/>mato dall'esperienza, si riducevano anche le ragioni di Galileo. </s></p><p type="main">

<s>I galileiani quesiti dunque, da risolversi coi principii nuovi, non si ri&shy;<lb/>ducevano che al III e al XIII, ne'quali volevasi dimostrare, contro le co&shy;<lb/>muni opinioni, e contro le dottrine a que'tempi insegnate, che la palla pu&ograve; <lb/>avere, cos&igrave; da vicino come a distanza, la medesima forza, essendo questa <lb/>tanta nel salire quant'&egrave; nello scendere, e spedendosi in egual tempo i due <lb/>viaggi contrarii. </s>

<s>Furono tali le conclusioni, che principalmente incorarono, <lb/>verso il 1609, la speranza di farsi maestro al mondo dell'arte bellica nel&shy;<lb/>l'animo di Galileo, ma ripensando poi che queste nuove erano bene assai <lb/>piccola parte delle dottrine antiche, e che non trovavano ancora nella Geo&shy;<lb/>metria nessun solido fondamento; non solo ei depose il pensiero di trattar <lb/>delle Artiglierie, ma non fece per allora altro conto dello scoperto isocro&shy;<lb/>nismo dei tiri, fatti con qualunque forza di punto in bianco, aspettando che <lb/>gli occorresse, a confermare il vero, discorso pi&ugrave; dimostrativo di quello, che <lb/>si fondava nel comparare gl'impeti del proietto per le vie aeree, e del ca&shy;<lb/>dente naturale lungo i piani convessi. </s></p><p type="main">

<s>Non poteva la desiderata dimostrazione aspettarsi da altro, che dal prin&shy;<lb/>cipio dei moti composti, perch&egrave; dall'ammetter che il viaggio del proietto <lb/>resulti da un moto verticale e da un altro orizzontale, come avvien per esem&shy;<lb/>pio nel considerar la palla di artiglieria scender lungo l'albero maestro, <lb/>mentre la nave si muove; era manifesto che la perpendicolar caduta natu&shy;<lb/>rale e la trasversale violenta, descritta dalla palla stessa, si spediscono nel <lb/>medesimo tempo. </s></p><p type="main">

<s>Una tal composizione di forza per&ograve;, ne'moti violenti, era stata aperta&shy;<lb/>mente negata dal Tartaglia, e bench&egrave; il Benedetti avesse lasciato scritto che <lb/><figure id="id.020.01.2277.1.jpg" xlink:href="020/01/2277/1.jpg"/></s></p><p type="caption">

<s>Figura 281<lb/>era ci&ograve; un grande errore, e avesse il Cardano dimo&shy;<lb/>strate le propriet&agrave;, che egli chiama ammirande, dei moti <lb/>misti, la XLIX proposizion nonostante pareva scritta <lb/>apposta da lui nell'<emph type="italics"/>Opus novum,<emph.end type="italics"/> per concluder tut&shy;<lb/>t'altrimenti di quel sincronismo, che era nuovamente <lb/>venuto a concludersi da Galileo. </s></p><p type="main">

<s>La detta cardanica proposizione &egrave; cos&igrave; espressa: <lb/>&ldquo; Omne mobile motum duobus motibus non ad idem <lb/>tendentibus, utrumque seorsum tardius moveretur si&shy;<lb/>mili motu &rdquo; (Operum, T. IV, Lugduni 1663, pag. </s>

<s>490). <lb/>Sia A (fig. </s>

<s>281) il mobile, mosso per ABC, con moto <lb/>misto di naturale e di violento, e sia D il termine dell'uno, E il termine <pb xlink:href="020/01/2278.jpg" pagenum="521"/>dell'altro: dice il Cardano che pi&ugrave; tardi giunger&agrave; in C, che in D, e in E. </s>

<s><lb/>Quanto ad E, la cosa &egrave; chiara: prima, perch&egrave; manca ad AE, per aggua&shy;<lb/>gliarsi ad AC, la parte AD, e poi, perch&egrave;, per la definizione della linea retta, <lb/>AC &egrave; pi&ugrave; lunga di AE &ldquo; quare tardius mobile perveniet ad C quam ad E <lb/>duplici ratione. </s>

<s>Dico etiam quod tardius ad C quam D. </s>

<s>Quia enim vis, quae <lb/>fert ad D, repugnat ei quae fert ad E, et vis quae fert ad E repugnat ei, <lb/>quae fert ad D: Igitur tardius perveniet ad C, quam D &rdquo; (ibid.). </s></p><p type="main">

<s>Galileo invece aveva scoperto che giunge in C e in E il mobile nel me&shy;<lb/>desimo tempo, e fu per questa contradizione che sempre pi&ugrave; diffid&ograve; di quei <lb/>moti misti, introdotti dal Cardano nella Scienza dei proietti. </s>

<s>Ma perch&egrave; in <lb/>ogni modo non potevasi aver quel ch'esso Galileo cercava di dimostrare, se <lb/>non che facendo uso del principio che, imbevuto oramai delle viete dottrine <lb/>del Tartaglia, egli avea ripudiato; sarebbe alle speculazioni, cos&igrave; felicemente <lb/>incominciate, venuto ad arrestarsi ogni progresso, se non gli fosse avven&shy;<lb/>turosamente occorso di scoprire che non in s&egrave;, ma nel modo, era fallace <lb/>l'argomento, di cui s'era servito il Cardano. </s></p><p type="main">

<s>Venne quell'avventurosa occasione alquanti anni dopo, quando a lui, <lb/>dichiaratosi Copernicano, opponevano i Peripatetici che, se la Terra vera&shy;<lb/>mente girasse in ventiquattr'ore in s&egrave; stessa, i corpi gravi, lasciati andar <lb/>dall'alto di una torre, non verrebber a batterle al piede. </s>

<s>Confermavano il <lb/>loro discorso con l'esempio di una nave, nella quale se, mentre sta ferma <lb/>in porto, si lascia dalla sommit&agrave; dell'albero cadere liberamente una pietra, <lb/>quella batte a pi&egrave; dell'albero stesso a piombo sotto il luogo, dove si lasci&ograve; <lb/>cadere; il quale effetto, soggiungevano, non avviene, quando va il naviglio <lb/>innanzi con corso veloce, perch&egrave;, nel tempo che il grave scende nel per <lb/>pendicolo, egli &egrave; gi&agrave; trascorso per linea orizzontale, e perci&ograve; il termine della <lb/>caduta non &egrave; pi&ugrave;, come dianzi, a pi&egrave; dell'albero, ma verso la poppa. </s></p><p type="main">

<s>Dicevano cos&igrave; costoro, non perch&egrave; avessero osservato i fatti, ma perch&egrave;, <lb/>secondo il loro vizioso istituto, dovevano i fatti accomodarsi e rispondere <lb/>alle ragioni, le quali si leggevano a nome di Aristotile scritte nella detta <lb/>proposizion XLIX del Cardano. </s>

<s>Ivi erasi concluso che in C il moto &egrave; pi&ugrave; <lb/>tardo che in E, per cui se AE rappresenta l'albero della nave, e ABC la <lb/>linea del viaggio fatto dal cader della pietra, essendo per questa linea, ch'&egrave; <lb/>della perpendicolare pi&ugrave; lunga, il moto pi&ugrave; tardo, deve la pietra stessa, cor&shy;<lb/>rendo innanzi la nave, necessariamente restare in dietro. </s></p><p type="main">

<s>L'istituto di Galileo era a questo peripatetico tutt'affatto contrario, ond'&egrave; <lb/>che saviamente secondandolo, giunse per la via regia della esperienza a sco&shy;<lb/>prir la fallacia di un tal discorso fattogli allora, insieme con altri anche pi&ugrave; <lb/>scipiti, da un tal Francesco Ingoli, casuidico di Ravenna. </s>

<s>A lui e a'peripa&shy;<lb/>tetici colleghi suoi rispondeva Galileo stesso nella primavera del 1624, ri&shy;<lb/>trovandosi a Roma, rimproverandoli del produrre esperienze come fatte e <lb/>rispondenti al bisogno, senz'averle mai fatte n&egrave; osservate &ldquo; ed una di tali <lb/>esperienze, poi soggiunge, &egrave; appunto questa del sasso cadente dalla som&shy;<lb/>mit&agrave; dell'albero nella nave, al pi&egrave; della quale va sempre a terminare e fe-<pb xlink:href="020/01/2279.jpg" pagenum="522"/>rire, tanto quando la nave &egrave; in quiete, quanto mentre ella velocemente cam&shy;<lb/>mina, e non va, com'essi credevano, scorrendo via la nave, mentre la pietra <lb/>per aria viene a basso, a ferir lontano dal piede verso la poppa. </s>

<s>Nella quale <lb/>occasione io sono stato doppiamente miglior filosofo di loro, perch&egrave; eglino <lb/>al dir quello che &egrave; contrario in effetto hanno anco aggiunta la bugia, di&shy;<lb/>cendo d'aver ci&ograve; veduto dall'esperienza, ed io ne ho fatto l'esperienza, <lb/>avanti la quale il natural discorso mi avea molto fermamente persuaso che <lb/>l'effetto doveva succedere come appunto succede &rdquo; (Alb. </s>

<s>II, 99). </s></p><p type="main">

<s>Ritrovato cos&igrave; che i fatti confermavano il discorso naturale, Galileo <lb/>cred&egrave; che la fallacia dell'argomento del Cardano consistesse nell'ammetter <lb/>che l'uno dei moti fosse d'impedimento all'altro. </s>

<s>Ond'essendo il vero che <lb/>l'impeto, con cui va la nave, resta indelebilmente impresso nella pietra, <lb/>dop'essersi separata dall'albero, e che questo moto non reca impedimento <lb/>o ritardamento al moto all'ingi&ugrave;; in quest'amica composizione di forze, che <lb/>egli aveva prima tante volte repudiata, vide chiara Galileo stesso la ragione, <lb/>che da tanto tempo cercava, del sincronismo nel perpendicolo e nella tra&shy;<lb/>sversale, o sia il grave, mentre cade naturalmente, trasportato dalla nave, <lb/>o da altro con cui si muova, o dall'impeto nella medesima direzione impres&shy;<lb/>sagli dal proiciente. </s></p><p type="main">

<s>&ldquo; Quando sia vero (cos&igrave; nel secondo dialogo dei Massimi Sistemi &egrave; messo <lb/>in bocca al Sagredo) che l'impeto, col quale si muove la nave resti im&shy;<lb/>presso indelebilmente nella pietra, dopo che s'&egrave; separata dall'albero, e sia <lb/>in oltre vero che questo moto non arrechi impedimento o ritardamento al <lb/>moto retto all'ingi&ugrave; naturale della pietra, &egrave; forza che ne segua un effetto <lb/>meraviglioso in natura. </s>

<s>Stia la nave ferma e sia il tempo della caduta d'un <lb/>sasso dalla cima dell'albero due battute di polso: muovasi poi la nave, e <lb/>lascisi andar dal medesimo luogo l'istesso sasso, il quale, per le cose dette, <lb/>metter&agrave; pure il tempo di due battute ad arrivare a basso, nel qual tempo <lb/>la nave avr&agrave; v. </s>

<s>g. </s>

<s>scorso venti braccia, talch&egrave; il vero moto della pietra sar&agrave; <lb/>stato una linea trasversale assai pi&ugrave; lunga della prima retta e perpendico&shy;<lb/>lare, che &egrave; la sola lunghezza dell'albero; tuttavia la palla l'avr&agrave; passata nel <lb/>medesimo tempo. </s>

<s>Intendasi di nuovo il moto della nave accelerato assai pi&ugrave;, <lb/>sicch&egrave; la pietra nel cadere dovr&agrave; passare una trasversale ancor pi&ugrave; lunga <lb/>dell'altra, e insomma, crescendosi la velocit&agrave; della nave quanto si voglia, il <lb/>sasso cadente descriver&agrave; le sue trasversali sempre pi&ugrave; e pi&ugrave; lunghe, e pur <lb/>tutte le passer&agrave; nelle medesime due battute di polso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; A questa similitudine, quando in cima di una torre fosse una colu&shy;<lb/>brina livellata, e con essa si tirassero tiri di punto bianco, cio&egrave; paralleli al&shy;<lb/>l'orizzonte, per poca o molta carica che si desse al pezzo, sicch&egrave; la palla <lb/>andasse a cadere ora lontana mille braccia, or quattro mila, or sei mila, or <lb/>dieci mila ecc. </s>

<s>tutti questi tiri si spedirebbero in tempi uguali tra di loro, <lb/>e ciascheduno eguale al tempo, che la palla consumerebbe a venire dalla <lb/>bocca del pezzo sino in terra, lasciata senz'altro impulso cadere semplice&shy;<lb/>mente gi&ugrave; a perpendicolo. </s>

<s>&rdquo; (Alb. </s>

<s>I, 171, 72). </s></p><pb xlink:href="020/01/2280.jpg" pagenum="523"/><p type="main">

<s>A questa medesima conclusione, quando non s'erano ancora le dispute <lb/>co'Peripatetici anticopernicani fatte cos&igrave; fervorose, era, come vedemmo, gi&agrave; <lb/>venuto Galileo nel 1609, per discorso per&ograve;, a cui mancava la fermezza del <lb/>fondamento, la quale, ritrovata ora nel principio dei moti misti, fece deli&shy;<lb/>berarlo di divulgar la scoperta come cosa nuova fra i discepoli e gli amici <lb/>curiosi. </s>

<s>Il Castelli la insegnava pubblicamente, illustrandola con l'esperienza <lb/>de'getti di acqua e degli zampilli a'suoi scolari di Pisa, fra'quali sapremo <lb/>tra poco con certezza essere &igrave;l Cavalieri. </s>

<s>Mario Guiducci la leggeva nel 1626 <lb/>in una solenne adunanza agli Accademici fiorentini, applicandola ad illu&shy;<lb/>strare un luogo di Omero. </s>

<s>Nel canto XXI dell'Odissea dice il Poeta che Pe&shy;<lb/>nelope, per far cimento del valore dei Proci, present&ograve; a loro innanzi il for&shy;<lb/>tissimo arco di Ulisse, offerendo in premio per sposa s&egrave; stessa a chi di loro <lb/>avesse avuto forza di caricarlo, e di far passar libera la scoccata saetta per <lb/>gli anelli di dodici accette, orizzontalmente disposte in fila. </s></p><p type="main">

<s>Vuole il Guiducci far rilevar l'acutezza del concetto omerico, osservando <lb/>che quel gioco presupponeva le propriet&agrave; delle curve descritte dai proietti, <lb/>le quali vanno sempre piegandosi verso terra, ma quel piegamento &egrave; tanto <lb/>meno sensibile in una breve distanza, quanto il proietto &egrave; gettato con mag&shy;<lb/>gior forza. </s>

<s>Cos&igrave;, poniamo che sia il primo anello collocato in AB (fig. </s>

<s>282), <lb/>e l'ultimo in BC, stando gli altri dieci fra mezzo. </s>

<s>Tirando la freccia in modo, <lb/><figure id="id.020.01.2280.1.jpg" xlink:href="020/01/2280/1.jpg"/></s></p><p type="caption">

<s>Figura 282<lb/>ch'ella imbocchi sotto <lb/>il punto A il primo <lb/>anello, proseguendo il <lb/>suo impeto descriver&agrave; <lb/>una curva, la quale po&shy;<lb/>trebb'essere cos&igrave; AD, <lb/>come AE, secondo che <lb/>l'arco era pi&ugrave; o meno <lb/>teso. </s>

<s>Che se ebbe tal tensione, da poter rilasciato sospinger la saetta per <lb/>la via AE, gli anelli saranno tutti passati fuor fuori, ma se fosse stata in&shy;<lb/>vece AD quella via, per pi&ugrave; debole impulso dato alla corda, non sarebbero <lb/>stati passati se non che quegli anelli soli, i quali fossero stati fra'punti B <lb/>e D collocati nel mezzo. </s></p><p type="main">

<s>Il gioco dunque ingegnosamente proposto da Penelope era bene atto a <lb/>misurare la forza della tirata dell'arco, ed era fondato sopra una nozione, <lb/>che facilmente s'aveva dalla volgare esperienza. </s>

<s>Ma il Guiducci vuol ridurre <lb/>a un principio scientifico quello strattagemma; principio, ch'egli dice essere <lb/>stato nuovamente da Galileo cos&igrave; proposto: &ldquo; I proietti scacciati con vio&shy;<lb/>lenza dal proiciente, il quale non sia elevato n&egrave; inclinato, ma parallelo al&shy;<lb/>l'orizzonte, arrivano nel tempo medesimo al piano sottopostoli della terra, <lb/>come se vi fossero dalla medesima altezza lasciati cadere perpendicolari &rdquo; <lb/>(Prefazione alle rime di M. A. Bonarroti, Firenze 1863, pag. </s>

<s>CXXXII). E <lb/>dop'aver fatto osservare che un uomo, sdrucciolando dall'albero di una barca, <lb/>giunge al piede nel medesimo tempo o la barca stessa stia ferma o si muova, <pb xlink:href="020/01/2281.jpg" pagenum="524"/>bench&egrave; in questo caso descriva una trasversale tanto pi&ugrave; lunga; &ldquo; nella <lb/>stessa guisa, soggiunge, avvien per l'appunto ai proietti, il cui moto, es&shy;<lb/>sendo composto di due moti, procedenti da due virt&ugrave; diversamente motrici, <lb/>cio&egrave; una naturale per linea tendente al centro, l'altra violenta per linea <lb/>orizzontale; non pu&ograve; questa impedire n&egrave; ritardare l'altra naturale e al cen&shy;<lb/>tro, sicch&egrave; il proietto non termini nell'istesso tempo il suo moto, nel quale <lb/>lo finirebbe, se progressivamente non si movesse &rdquo; (ivi). </s></p><p type="main">

<s>Agli Accademici fiorentini veniva cos&igrave; dunque anticipata da sei anni la <lb/>lettura di quella pagina, che vedrebbe il pubblico impressa nel secondo dia&shy;<lb/>logo dei Massimi Sistemi, ne'quali il Sagredo, a quel che dianzi udimmo, <lb/>discorre nella sostanza e nella forma come il Guiducci. </s>

<s>Se non che questi, <lb/>prima di descrivere l'esperienza della nave, avverte esservi di ci&ograve; la <emph type="italics"/>dimo&shy;<lb/>strazione geometrica,<emph.end type="italics"/> la quale egli per&ograve; non dice, e non accenna, perch&egrave; <lb/>forse da Galileo gli era stata solamente promessa. </s>

<s>Ne'citati Dialoghi infatti <lb/>la proposizion de'proietti non piglia altro valore dimostrativo che dalla espe&shy;<lb/>rienza, se forse nella composizion dei moti, che non s'impediscono, non si <lb/>volesse far consistere tutta la promessa Geometria. </s></p><p type="main">

<s>Del non esservi poi, n&egrave; in questo n&egrave; negli altri pi&ugrave; lunghi discorsi, che <lb/>ne'Dialoghi si fanno intorno ai proietti, nulla di geometrico; &egrave; manifesto <lb/>argomento il non decidersi la qualit&agrave; della linea, che descrive la pietra con <lb/>moto naturale misto al moto violento, o della barca, che con lei si muove, <lb/>o della forza a lei impressa dal proiciente. </s>

<s>Quella linea &egrave; sempre da Gali&shy;<lb/>leo vagamente chiamata col nome di <emph type="italics"/>trasversale,<emph.end type="italics"/> n&egrave; si decide mai se sia <lb/>retta o curva, o essendo curva a quale specie di linee curve appartenga. </s>

<s>A <lb/>pag. </s>

<s>169 della prima edizione, fatta nel 1632 in Firenze sotto gli occhi del&shy;<lb/>l'Autore, quella trasversale &egrave; disegnata come retta, essendo in apparenza <lb/>tale, perch&egrave; il grande impeto del cannone, che ivi si rappresenta, non rende <lb/>in s&igrave; breve tratto sensibile l'effetto della gravit&agrave; in inclinare a basso la palla. </s>

<s><lb/>Che sia per&ograve; quella linea realmente curva, non potendo il proietto essere <lb/>abbandonato mai dalla gravit&agrave; sua naturale, Galileo lo teneva per cosa certa, <lb/>come aveva insegnato il Tartaglia, di cui si crederebbe per&ograve; avesse ripu&shy;<lb/>diato l'errore delle curvit&agrave; circolari nella traiettoria, ora che alla singolar <lb/>propriet&agrave; de'proietti, scoperta nel 1609, si diceva d'aver ritrovata la geo&shy;<lb/>metrica dimostrazione. </s>

<s>&Egrave; un fatto ch'egli non ha pi&ugrave; allo stesso Tartaglia <lb/>quella prima fede, che gli fece risolutamente negare le similitudini parabo&shy;<lb/>liche, quando Guidubaldo gliele mostrava nelle vestigie lasciate impresse <lb/>sulla tavola levigata dalla palla intinta nell'inchiostro, ma vacilla. </s>

<s>Cos&igrave; va&shy;<lb/>cillando per&ograve; inclina tuttavia a credere che la curva del proietto, o appa&shy;<lb/>risca come tale o no, sia in ogni modo parte di un cerchio descritto con un <lb/>raggio o pi&ugrave; lungo o pi&ugrave; corto. </s></p><p type="main">

<s>Nella Risposta all'Ingoli sopra citata cos&igrave; concludesi l'esperienza della <lb/>pietra, lasciata liberamente cader gi&ugrave; dall'albero della nave: &ldquo; Dicovi per&shy;<lb/>tanto, signor Ingoli, che, mentre la nave &egrave; in corso, con altrettanto impeto <lb/>si muove ancor quella pietra, il qual impeto non si perde perch&egrave; quello che <pb xlink:href="020/01/2282.jpg" pagenum="525"/>la teneva apra la mano e la lasci in libert&agrave;; anzi indelebilmente si conserva <lb/>in lei, sicch&egrave; mediante quello ell'&egrave; bastante a seguitar la nave, e per la <lb/>propria gravit&agrave;, non impedita da colui, se ne discende al basso componendo <lb/>di ambedue un sol moto <emph type="italics"/>e forse anco circolare,<emph.end type="italics"/> trasversale, e inclinato verso <lb/>dove cammina la nave &rdquo; (Alb. </s>

<s>II, 100). La sostanza delle dottrine esposte <lb/>in questa Lettera copernicana venne poco di poi dialogizzata nei Massimi <lb/>Sistemi, dove si dice vedersi il sasso uscito dalla fionda <emph type="italics"/>descrivere un arco<emph.end type="italics"/><lb/>(Alb. </s>

<s>I, 212), e distendersi <emph type="italics"/>non rettamente ma in arco<emph.end type="italics"/> (ivi, pag. </s>

<s>254) si <lb/>dice, vibrando il pendolo, la catena, che, secondo Guidubaldo, s'incurva a <lb/>somiglianza di un ramo della parabola. </s></p><p type="main">

<s>Che devasi in questi passi intendere <emph type="italics"/>arco di cerchio,<emph.end type="italics"/> secondo l'opi&shy;<lb/>nione rimasta per quarant'anni di studio intorno alle propriet&agrave; dei proietti <lb/>nella mente di Galileo sempre tenace; si conferma da ci&ograve;, che dice in que&shy;<lb/>sta stessa Giornata, dove parla della fionda e della catena del pendolo, per <lb/>determinar la specie della linea, che descrive una pietra, cadendo da un'alta <lb/>torre di moto naturale composto col moto vertiginoso della Terra. </s>

<s>Sia B <lb/>(fig. </s>

<s>283) la base, e C la sommit&agrave; della torre, i quali due punti, rivolgen&shy;<lb/><figure id="id.020.01.2282.1.jpg" xlink:href="020/01/2282/1.jpg"/></s></p><p type="caption">

<s>Figura 283<lb/>dosi intorno ad A centro terrestre, descrivano <lb/>i due archi BI, CD: &ldquo; divisa poi la linea CA in <lb/>mezzo in E, col centro E, intervallo EC, de&shy;<lb/>scrivo, dice Galileo, il mezzo cerchio CIA, per <lb/>il quale dico ora che assai probabilmente si pu&ograve; <lb/>credere che una pietra, cadendo dalla sommit&agrave; <lb/>della torre C, venga, movendosi del moto compo&shy;<lb/>sto del comune circolare e del suo proprio retto &rdquo; <lb/>(Alb. </s>

<s>I, 18<gap/>). &Egrave; manifesto perci&ograve; che la cercata <lb/>linea, descritta nel cader la pietra dalla sommit&agrave; <lb/>al pi&egrave; della torre, &egrave; la CI, arco del semicer&shy;<lb/>chio AIC. </s>

<s>E perch&egrave; a questa similitudine va la <lb/>cosa, quando si supponga in C un cannone li&shy;<lb/>vellato, che avesse potenza di spinger la palla <lb/>da C in D, nello stesso tempo che quello spazio percorresi dalla Terra, il <lb/>proietto dunque, secondo Galileo, descriverebbe la medesima linea CI; ossia <lb/>il medesimo arco di cerchio. </s>

<s>Di qui nella lettera all'Ingoli vien con tutta la <lb/>precisione dichiarato il pensiero di chi la scrisse, perch&egrave; se BC rappresenta <lb/>l'albero della nave, e BI la superfice convessa dell'acqua, movendosi da B <lb/>in I essa nave, mentre dalla sommit&agrave; dell'albero cade al piede la pietra, <lb/>questa descriver&agrave; la linea CI, che &egrave; <emph type="italics"/>la trasversale, inclinata verso dove <lb/>cammina la nave e forse anche circolare,<emph.end type="italics"/> di cui, come dianzi vedemmo, <lb/>ivi scrive l'Autore. </s></p><p type="main">

<s>Se si debbon dunque intendere le parole come tutti schiettamente le <lb/>intendono a significare le idee, n&egrave; nei Dialoghi famosi, n&egrave; in nessuna delle <lb/>precedenti scritture, si dimostra da Galileo la propria specie della curva di&shy;<lb/>segnata nell'aria dal proietto, e <emph type="italics"/>forse,<emph.end type="italics"/> e <emph type="italics"/>probabilmente<emph.end type="italics"/> si dice essere un <pb xlink:href="020/01/2283.jpg" pagenum="526"/>arco di cerchio. </s>

<s>Anche il Cartesio confessava a que'tempi di non avere an&shy;<lb/>cora intorno a ci&ograve; fatto nessuno studio. </s>

<s>Credeva che una palla gettata con <lb/>pi&ugrave; o meno forza descriva due linee omogenee, &ldquo; sed cuiusmodi sint istae <lb/>lineae nunquam examinavi &rdquo; (Epist., P. II cit., pag. </s>

<s>312). Di qualunque spe&shy;<lb/>cie per&ograve; esse linee si fossero in questo si trovavano i Matematici concordi, in <lb/>escluderle cio&egrave; dal rappresentare curvit&agrave; circolari. </s>

<s>Quando il movimento retto <lb/>verso il centro della Terra fosse uniforme, dice il Salviati galileiano, essendo <lb/>anco uniforme il circolare verso oriente, si verrebbe a comporre di ambe&shy;<lb/>due un moto per una linea spirale di quelle definite da Archimede. </s>

<s>Ma per&shy;<lb/>ch&egrave; il moto retto del grave cadente &egrave; continuamente accelerato, &egrave; forza che <lb/>la linea del composto dei due movimenti sia un mezzo cerchio (Alb. </s>

<s>I, 182, 83). </s></p><p type="main">

<s>La fallacia di questo discorso, preveduta infino da Leonardo da Vinci, <lb/>ebbe facilmente a notarsi dai lettori del Dialogo, concordi nell'ammettere <lb/>che non potesse la linea del cadente al centro dall'alto della torre esser di <lb/>diverso genere dalla spirale, bench&egrave; confessassero assai facilmente dover pro&shy;<lb/>cedere con altro passo dall'archimedea. </s>

<s>Di ci&ograve; faceva il Fermat in Francia <lb/>argomento alle sue censure, e il Cabeo fra'Nostri diceva, pi&ugrave; giudiziosamente <lb/>delle altre volte, che nell'esempio della pietra cadente dall'albero, mentre <lb/>la nave scorre sopra la liquida circolar superfice del globo, la trasversale CI <lb/>generata con duplice moto s'incurva in arco no di circolo ma di spirale <lb/>&ldquo; quae composita est cum consurgat ex duplici motu descensionis et pro&shy;<lb/>gressionis, quorum alter rectus est, alter circularis supra centrum Terrae, <lb/>sicut ex duplici motu generatur spira &rdquo; (Comment. </s>

<s>meteor., T. </s>

<s>I cit., pag. </s>

<s>89). </s></p><p type="main">

<s>Era fra quei lettori del Dialogo di Galileo Bonaventura Cavalieri, il quale, <lb/>avuto nel carnevale del 1632 il libro in dono da un suo scolare in Bologna, <lb/>scriveva il d&igrave; 22 di Marzo all'Autore di averlo, in que'giorni di comune al&shy;<lb/>legrezza, allegrissimamente veduto &ldquo; anzi divorato con gli occhi, raccogliendo <lb/>con somma avidit&agrave; i fiori di s&igrave; vago giardino &rdquo; (Alb. </s>

<s>IX, 264). Ma poi, en&shy;<lb/>trato pi&ugrave; addentro ai riposti orti di Accademo, e ivi quietamente sedutosi <lb/>all'ombra per saggiarne i frutti, ebbe a trovarli agresti in alcune parti, e <lb/>principalmente in quella che riguarda la linea descritta dai proietti. </s>

<s>Non si <lb/>poteva dar pace che dalla composizion di due moti, l'uno equabile orizzon&shy;<lb/><figure id="id.020.01.2283.1.jpg" xlink:href="020/01/2283/1.jpg"/></s></p><p type="caption">

<s>Figura 284<lb/>tale, e l'altro accelerato in modo da crescer <lb/>gli spazii, secondo la serie dei numeri im&shy;<lb/>pari, come ivi s'insegna, se ne avesse a con&shy;<lb/>cludere in quel medesimo libro che la re&shy;<lb/>sultante &egrave; per un arco di cerchio. </s></p><p type="main">

<s>Sia A (fig. </s>

<s>284), ragionava cos&igrave; presso <lb/>a poco il Cavalieri, un proietto spinto da <lb/>qualunque forza per la orizzontale AC, sulla <lb/>quale seguiterebbe a moversi equabilmente, <lb/>se non lo inclinasse a basso la sua propria <lb/>gravit&agrave;, in direzione perpendicolare parallela alla AF. </s>

<s>Supponiamo che, mentre <lb/>il moto violento farebbe passare il mobile da A in B, la naturale sua forza <pb xlink:href="020/01/2284.jpg" pagenum="527"/>di gravit&agrave; l'avesse fatto scendere in D per la linea BD, e mentre passerebbe <lb/>in C, nel tempo AC, l'abbia quella stessa forza di gravit&agrave; fatto scendere in E, <lb/>per la linea CE. </s>

<s>Si possono riferire i punti D, E agli assi ortogonali AC, AF, <lb/>e cos&igrave; vedere a quale speccie di curva appartengano. </s>

<s>Rappresentando infatti, <lb/>come s'&egrave; detto le AB, AC uguali alle applicate GD, FE i tempi, e le ascisse <lb/>AG, AF uguali alle BD, CE gli spazii, i quali per la legge galileiana stanno <lb/>come i quadrati di quegli stessi tempi; sar&agrave; per conseguenza AG:AF= <lb/>GD2:FE2. </s>

<s>I punti D, E dunque e gli altri infiniti, per cui passa il proietto, <lb/>son disposti lungo una linea parabolica, ed &egrave; questa, pensava il Cavalieri, <lb/>conclusione verissima in Geometria, mentre che si rimanga sulla superficie <lb/>terrestre, dentro i quai limiti le linee BD, CE son parallele, e verissima <lb/>pure sarebbe anche in Natura, se si potesse toglier di mezzo l'impedimento <lb/>dell'aria. </s></p><p type="main">

<s>Teneva lo stesso Cavalieri da qualche tempo fra'suoi fogli un tratta&shy;<lb/>tello degli specchi parabolici, iperbolici ed ellittici, e ricondotto nel 1632 alla <lb/>cattedra di matematiche nello studio di Bologna, con aumento di cento scudi, <lb/>fece proposito, come significava in una sua lettera a Galileo (Alb. </s>

<s>IX, 269), <lb/>di stampare finalmente il libretto, e di dedicarlo per ringraziamento alla Reg&shy;<lb/>genza. </s>

<s>Mentre ivi insegnavasi con metodi nuovi a descriver le sezioni co&shy;<lb/>niche, si dimostravano alcuni loro mirabili effetti intorno al suono, al calore <lb/>e alla luce, per cui parve convenirsi al libro il titolo di <emph type="italics"/>Specchio ustorio.<emph.end type="italics"/><lb/>La legge della diffusione sferica, per cui crescono le superficie ondose lu&shy;<lb/>cide, calorifiche e sonore come i quadrati de'raggi, sugger&igrave; al Cavalieri, dopo <lb/>la lettura del Dialogo galileiano, quella bella dimostrazione delle proporzioni <lb/>del moto nei liberi cadenti, attissima a rivelar che gl'imponderabili stessi <lb/>non si sottraggono alla legge universale dei gravi, e che tutto cospira quag&shy;<lb/>gi&ugrave; in un'armonica unione di forze. </s></p><p type="main">

<s>Dal venir cos&igrave; confermati i principii dottrinali del moto, posti da Gali&shy;<lb/>leo, prese occasione il Cavalieri di mostrarne le conseguenze, per ci&ograve; che <lb/>s'appartiene ai proietti, e l'una e l'altra parte pens&ograve; d'inserir nel trattato <lb/>delle sezioni coniche, dove si vedrebbe a una nuova e mirabile dignit&agrave; esal&shy;<lb/>tata la Parabola. </s>

<s>Introdottosi perci&ograve; ne'capitoli XL e XLI alla <emph type="italics"/>Cognizione <lb/>del moto,<emph.end type="italics"/> e dal diffondersi concentrico di un punto in circoli ondosi, con&shy;<lb/>fermata, per la Geometria degl'indivisibili, la legge degli spazii proporzio&shy;<lb/>nali ai quadrati dei tempi; passa nel XLII a proporsi il quesito <emph type="italics"/>Qual sorta <lb/>di linea descrivano i gravi nel loro moto, spiccati che siano dal proiciente,<emph.end type="italics"/><lb/>e lo risolve dicendo: &ldquo; che i gravi, spinti dal proiciente a qualsivoglia banda <lb/>fuorch&egrave; per la perpendicolare all'orizzonte, separati che siano da quello, ed <lb/>escluso l'impedimento dell'ambiente, descrivono una linea curva insensibil&shy;<lb/>mente differente dalla Parabola &rdquo; (Specchio Ust., ediz. 2a, Bologna 1650, <lb/>pag. </s>

<s>99). </s></p><p type="main">

<s>La dimostrazione &egrave; conclusa dal principio dei moti misti, a quel modo <lb/>che dicemmo di sopra, ma era appena scritta e ordinata per le stampe che, <lb/>rileggendola il Cavalieri, pensava a quel che nel vederla vorrebbe dir Ga-<pb xlink:href="020/01/2285.jpg" pagenum="528"/>lileo. </s>

<s>Dubitava non dovesse incontrare a questi proietti terrestri la medesima <lb/>sorte che ai celesti: e com'esso Galileo persisteva tuttavia in approvar le <lb/>orbite circolari, bench&egrave; ellittiche le avesse dimostrate il Keplero; cos&igrave; s'aspet&shy;<lb/>tava che volesse mantener circolari le traiettorie anc'ora, che dagli stessi <lb/>principii di lui si concludevano paraboliche con facile discorso. </s>

<s>Par che, nel&shy;<lb/>l'atto stesso di venire scacciati dall'animo, scappino que'dubbi dalla punta <lb/>della penna, mentr'&egrave; menata a scrivere cos&igrave; in fine della detta dimostra&shy;<lb/>zione: &ldquo; Ci contenteremo di questo poco, per intender le varie condizioni e <lb/>nobilt&agrave; delle Sezioni coniche, avendole anco il Keplero in supremo grado <lb/>nobilitate, mentre ci ha fatto vedere con manifeste ragioni, ne'Commentari <lb/>di Marte e nell'Epitome copernicana, che le circolazion&igrave; de'Pianeti intorno <lb/>al Sole non sono altrimenti circolari, ma ellittiche &rdquo; (iv&igrave;, pag. </s>

<s>101, 2). </s></p><p type="main">

<s>Poi, quasi impaurito il Cavalieri al pensiero di diventare anch'egli og&shy;<lb/>getto al disprezzo e all'ira di Galileo, come per somiglianti motivi era di&shy;<lb/>ventato il Keplero, cerc&ograve; le vie di placarlo e di comprimerne i moti del ter&shy;<lb/>ribile sdegno. </s>

<s>Rileggendo a questo intento quella infelice opinione messa in <lb/>bocca al Salviati, e che illustravasi dalla figura rappresentata da noi nella 283 <lb/>qui poco addietro, ebbe a notar che la linea CI, secondo la quale anderebbe <lb/>in aria la palla esplosa dal cannone livellato, e posto in C con la bocca; &egrave; <lb/>una minima particella del grandissimo circolo AIC, che ha nella descrizione <lb/>di Galileo per diametro il semidiametro della Terra: onde, avendo nel co&shy;<lb/>rollario al cap. </s>

<s>LVI del medesimo Specchio ustorio dimostrato, in prepara&shy;<lb/>zione alla teoria de'circoli osculatori, che uno specchio sferico pochissimo <lb/>cavo, o una lente sferica pochissimo colma, pochissimo differiscono dalla Pa&shy;<lb/>rabola e dall'Iperbola nella curvatura; per salvare in qualche modo l'errore <lb/>di Galileo, e per farlo apparire meno strano dal vero, volle soggiungere ivi <lb/>queste parole: &ldquo; Potr&agrave; insieme ancora la dottrina di questo corollario dar <lb/>sodisfazione a coloro, che stimassero la strada disegnata dal proietto esser <lb/>circolare, poich&egrave;, essendo quel cerchio notabilmente grande, ed il viaggio del <lb/>grave poca parte dell'intera circonferenza, pu&ograve; esser che talora riesca pure <lb/>pochissimo differente dalla Parabola &rdquo; (ivi). </s></p><p type="main">

<s>Nell'Agosto del medesimo anno 1632 lo Specchio ustorio era gi&agrave; stam&shy;<lb/>pato, e l'Autore n&egrave; dava cos&igrave; avviso a Galileo in una lettera scritta l'ul&shy;<lb/>timo di quel mese da Bologna: &ldquo; Non mancher&ograve; di fargli avere uno de'miei <lb/>libretti ora stampati, quale ho intitolato <emph type="italics"/>Specchio ustorio,<emph.end type="italics"/> nel quale vedr&agrave; <lb/>un mio pensiero intorno lo Specchio d'Archimede, dove tratto universal&shy;<lb/>mente delle Sezioni coniche, considerando alcuni effetti di natura, ne'quali <lb/>hanno che fare. </s>

<s>Ho toccato qualche cosetta del moto de'proietti, mostrando <lb/>che dovria essere per una Parabola, escluso l'impedimento dell'ambiente, <lb/>supposto il suo principio del movimento dei gravi che si velociti secondo <lb/>l'incremento de'numeri dispari continuati dall'unit&agrave;, attestando per&ograve; d'aver <lb/>imparato in gran parte da lei ci&ograve; ch'io tocco in questa materia, adducendo <lb/>insieme anch'io una ragione per quel principio &rdquo; (Alb. </s>

<s>IX, 286). </s></p><p type="main">

<s>Era nella ragione di quel principio, che definiva gli spazi proporzionali <pb xlink:href="020/01/2286.jpg" pagenum="529"/>ai quadrati dei tempi, scolpita cos&igrave; a vivo l'effigie della Parabola, che Ga&shy;<lb/>lileo ebbe a stupire di non averla riconosciuta se non ora, che veniva ad <lb/>aprirgliene gli occhi la lettera del Cavalieri. </s>

<s>Avrebbe sentito dispetto di s&egrave;, <lb/>invidia della sorte altrui, se non fossero tali due sentimenti rimasti concul&shy;<lb/>cati dal baldanzoso insorgere di quell'ardor di rapina, che spira dalle se&shy;<lb/>guenti parole scritte in una lettera al signor Cesare Marsili, cittadino di Bo&shy;<lb/>logna, e protettore dello stesso Cavalieri: </s></p><p type="main">

<s>&ldquo; Tengo lettera del padre fra Bonaventura con avviso come S. P. ha <lb/>nuovamente stampato un trattato dello Specchio ustorio, nel quale, con certa <lb/>occasione, dice avervi inserito la proposizione e dimostrazione della linea de&shy;<lb/>scritta dai proietti, provando com'&egrave; una linea parabolica. </s>

<s>Io non posso na&shy;<lb/>scondere a V. S. I. tale avviso essermi stato di poco gusto, nel vedere come, <lb/>di un mio studio di pi&ugrave; di quarant'anni, conferitone buona parte con larga <lb/>confidenza al detto Padre, mi deva ora esser levato la primizia, e sfiorata <lb/>quella gloria, che tanto avidamente desideravo, e mi promettevo da s&igrave; lun&shy;<lb/>ghe mie fatiche: perch&egrave; veramente il primo intendimento che mi mosse a <lb/>specular sopra il moto, fu il ritrovar tal linea, la quale, se ben ritrovata, &egrave; <lb/>poi di non molto difficile dimostrazione, tuttavia io che l'ho provata so quanta <lb/>fatica ho avuto in ritrovar tal conclusione. </s>

<s>E se il padre fra Bonaventura <lb/>mi avesse innanzi la pubblicazione significato il suo pensiero, come forse la <lb/>civil creanza richiedea, io l'avrei tanto pregato, che mi avrebbe permesso <lb/>che io avessi prima stampato il mio libro, dopo il quale poteva egli poi sog&shy;<lb/>giunger quanti trovati gli fosse piaciuto. </s>

<s>Star&ograve; attendendo di veder ci&ograve; che <lb/>ei produce, ma gran cosa certo ci vorrebbe a temperare il mio disgusto, e di <lb/>quanti miei amici hanno ci&ograve; inteso, dai quali, per mia maggior mortificazione, <lb/>mi vien buttato in occhio il mio troppo confidare: porta la mia stella che <lb/>io abbia a combattere, e anco con p&egrave;rdita, la roba mia &rdquo; (Alb. </s>

<s>VII, 5, 6). </s></p><p type="main">

<s>La mattina del 19 Settembre 1632, otto giorni dopo la data di questa <lb/>lettera da Firenze, va il Marsili a picchiare alla cella di fra Bonaventura, il <lb/>quale ebbe a legger negli occhi di lui l'afflizione, prima che nel foglio aper&shy;<lb/>togli innanzi. </s>

<s>S'aspettava piuttosto che, per aver nello Specchio ustorio con&shy;<lb/>cluso diversamente da quel ch'era scritto nel Dialogo, se ne volesse risen&shy;<lb/>tir Galileo, n&egrave; sapeva intendere com'a veder dimostrata la Parabola dei <lb/>proietti si dovesse aspettar la stampa di un nuovo libro, quando in quello <lb/>dei due Massimi Sistemi, allora allora stampato, s'escludeva la parabola, per <lb/>ammettervi il cerchio. </s>

<s>Non avrebbe mai creduto il buon Frate che l'Uomo <lb/>tanto riverito e amato, per non confessare di non aver saputo vedere nei <lb/>suoi propri principii una conseguenza cos&igrave; manifestamente immediata, si fosse <lb/>messo a profferire altrettante menzogne, quante nella lettera al Marsili erano <lb/>le sentenze, per cui ingenuamente credendo a quei quarant'anni, a cui leg&shy;<lb/>geva risalire un tale studio, e a questa fede associando le notizie avute dal&shy;<lb/>l'Oddi, pens&ograve; che delle traiettorie paraboliche si trattasse infin da quelle <lb/>prime esperienze, che si diceva essere state fatte dallo stesso Galileo insieme <lb/>con Guidubaldo Del Monte. </s>

<s>&mdash; E dall'altra parte, discorreva fra s&egrave; il Ca-<pb xlink:href="020/01/2287.jpg" pagenum="530"/>valieri, ho io veduto tutto quel che, da'Dialoghi in fuori, si discorre da quel <lb/>grand'Uomo intorno ai moti violenti? </s>

<s>A me pareva per verit&agrave;, essendo sco&shy;<lb/>lare in Pisa, che il padre don Benedetto non pronunziasse mai esser para&shy;<lb/>bolici i getti dell'acqua, e che si limitasse a far notar l'ugual tempo, in cui <lb/>il liquido cade o naturalmente o per l'impeto ricevuto dall'altezza del suo <lb/>livello nel vaso: ma forse io non intesi bene tutta intiera la dottrina di Ga&shy;<lb/>lileo, che il Castelli ci dimostrava con s&igrave; bella esperienza. </s>

<s>&mdash; </s></p><p type="main">

<s>Cos&igrave; discorrendo, si disponeva il buon uomo a lasciarsi docilmente spo&shy;<lb/>gliare del suo: e giacch&egrave; nessuna naturale estrinseca forza par che possa <lb/>usar sull'animo violenza, convien dire che avesse qualche cosa del demo&shy;<lb/>niaco o del mago colui, che us&ograve; nel rubare tant'arte, da movere il legit&shy;<lb/>timo possessore della roba a portargliela infino a casa, confessandosi sincera&shy;<lb/>mente convinto d'avergliela rubata, come fece insomma il Cavalier&igrave; in questa <lb/>lettera a Galileo: </s></p><p type="main">

<s>&ldquo; Il cordoglio, ch'ella mostra d'aver sentito, come l'illustrissimo signor <lb/>Cesare Marsili mi ha significato, per avere io toccato non so che della linea <lb/>parabolica descritta dai proietti nel mio Specchio ustorio, non &egrave; al sicuro <lb/>stato tale e tanto, quanto il mio, per avere io inteso ch'ella abbia ricevuto <lb/>offesa da quello, che io sono trascorso a fare, piuttosto per eccesso di reve&shy;<lb/>renza, che per altro. </s>

<s>Quello che ho detto del moto, l'ho detto come suo <lb/>discepolo e del padre don Benedetto, avendone visto fare esperienze da lui <lb/>con altri scolari, da'quali pure ho sentito l'istessa conclusione, e ch'ella <lb/>n'era l'autore, sicch&egrave; non pu&ograve; cader dubbio alcuno ch'io me la potessi <lb/>arrogare come cosa mia.... Aggiungo di pi&ugrave; ch'io veramente pensai che <lb/>in qualche luogo ella ne avesse trattato, non avendo io potuto aver fortuna <lb/>di vedere tutte le opere sue, e questo molto me l'ha fatto credere il sen&shy;<lb/>tirla fatta tanto pubblica, e per tanto tempo, che l'Oddi mi disse, dieci anni <lb/>sono, ch'ella ne aveva fatto qualche esperienza col signor Guidubaldo Del <lb/>Monte &rdquo; (Alb. </s>

<s>IX, 291, 92). </s></p><p type="main">

<s>Un altr'animo franco da quella suggezione avrebbe potuto rispondere <lb/>a Galileo: ma se tanto vi stava a cuore la gloria di raccogliere il frutto <lb/>delle vostre fatiche di quarant'anni, e tanto trepidaste che non venissero <lb/>gli altri a sfiorarvela, perch&egrave;, invece di confidare a loro privatamente la cosa, <lb/>non ve ne assicuraste la propriet&agrave; nella pubblicazione del Dialogo famoso, <lb/>come pur faceste di tutte le altre conclusioni da voi ritrovate intorno alla <lb/>scienza del moto? </s>

<s>O che strana cosa &egrave; mai questa, che voi dite di aver con&shy;<lb/>ferito con larga confidenza a fra Bonaventura la proposizione che dal moto <lb/>retto del cadente, mescolato con l'equabile per l'orizzonte, resulta una pa&shy;<lb/>rabola, e poi, con pubblica solennit&agrave;, scrivete che probabilmente dalla mi&shy;<lb/>stura di que'due moti si compone un arco della circonferenza? </s></p><p type="main">

<s>La domanda nasceva dalle pretensioni di Galileo tanto spontanea, che <lb/>egli stesso, sentendone la molestia, aveva pensato di spacciarsene col ri&shy;<lb/>spondere che era detto a quel modo per celia, e per parlare, non gi&agrave; da <lb/>scienziato, ma da poeta. </s>

<s>&ldquo; Nel Dialogo, sebbene vien detto poter essere che, <pb xlink:href="020/01/2288.jpg" pagenum="531"/>mescolato il retto del cadente con l'equabile circolare del moto diurno, si <lb/>componesse una semicirconferenza, che andasse a terminare nel centro della <lb/>Terra; ci&ograve; fu detto per scherzo, come assai manifestamente apparisce, men&shy;<lb/>tre vien chiamato un capriccio e una bizzarria, cio&egrave; <emph type="italics"/>iocularis quaedam au&shy;<lb/>dacia.<emph.end type="italics"/> Desidero pertanto in questa parte esser dispensato, e massime tiran&shy;<lb/>dosi dietro questa dir&ograve; poetica finzione quelle tre inaspettate conseguenze, <lb/>cio&egrave; che il moto del mobile sarebbe sempre circolare, secondariamente sempre <lb/>equabile, terzo, che in questo apparente moto <emph type="italics"/>deorsum<emph.end type="italics"/> niente si mova di <lb/>pi&ugrave; di quello, che si faceva mentre era in quiete &rdquo; (Alb. </s>

<s>VII, 155). </s></p><p type="main">

<s>Il Salviati per verit&agrave; si mostra persuaso del suo discorso, non meno <lb/>qui che l&agrave;, nella lettera all'Ingoli, e il Sagredo gliel'approva dicendo di non <lb/>poter credere che la linea del moto composto, secondo la quale va per aria <lb/>il proietto, sia diversa dalla circolare (Alb. </s>

<s>I, 183). &mdash; Ma giacch&egrave; voi, signor <lb/>Galileo, avete voluto mettere la dignit&agrave; de'vostri attori in commedia, e in&shy;<lb/>torno a cosa di tanta importanza, e che tanto premeva di sapere ai Prin&shy;<lb/>cipi e ai Capitani conduttori degli eserciti in guerra, vi compiacete di averne <lb/>nella massima Opera vostra discorso in burla, diteci in qual altra vostra, o <lb/>dissertazione, o lettera, o nota, in quarant'anni di studii fatti intorno ai <lb/>proietti, avete scritto delle loro vie paraboliche sul serio. </s>

<s>Nel 1592 vi troviamo <lb/>a specular la ragione, per cui il proietto va tanto pi&ugrave; lungamente in linea <lb/>retta, quanto l'angolo fatto dalla direzione del tiro con l'orizzonte &egrave; pi&ugrave; <lb/>acuto: nel 1604 Guidubaldo Del Monte vi fece ravveduto di questo errore, <lb/>ma nel concedergli che la traiettoria non pu&ograve; non esser curva in ogni sua <lb/>parte, gli negaste le somiglianze con la Parabola, alla quale preferiste una <lb/>linea, che si componesse d'archi di cerchio con vario raggio di curvatura. </s>

<s><lb/>Scopriste nel 1609 l'isocronismo dei getti di qualunque ampiezza, purch&egrave; <lb/>ugualmente alti, per semplice congettura, di che poi nel 1624 diceste di <lb/>aver trovato la dimostrazione, non gi&agrave; nella teoria del moto parabolico, ma <lb/>nell'esperienza della pietra, che cade dalla sommit&agrave; a pi&egrave; dell'albero sem&shy;<lb/>pre, o stia ferma la nave o velocemente si muova. </s>

<s>S'arrestarono a questo <lb/>punto i vostri progressi, che infino al 1632 rimasero stazionari, intanto che, <lb/>se voi non producete documento anteriore al mese di Settembre di quel&shy;<lb/>l'anno, noi non vi leveremo l'accusa di avere, in modo indegno di un Fi&shy;<lb/>losofo e di un animo onesto, usurpata al Cavalieri la tanto ambita scoperta. </s></p><p type="main">

<s>Galileo present&igrave; pur troppo nella colpevole sua coscienza i terrori di <lb/>questa minaccia, i quali ei s'argoment&ograve; d'illudere, mettendo in mano al <lb/>Salviati certi foglietti, perch&egrave;, sopr'essi scritti in latino, leggesse agl'inter&shy;<lb/>locutori i teoremi <emph type="italics"/>De motu proiectorum,<emph.end type="italics"/> come seconda parte di quel trat&shy;<lb/>tato pi&ugrave; antico <emph type="italics"/>De motu loculi,<emph.end type="italics"/> in modo da fare apparir che tutto avesse <lb/>l'Accademico dimostrato nel medesimo tempo. </s>

<s>I documenti per&ograve; attestano <lb/>che, mentre le prime proposizioni latine dei moti accelerati risalgono al 1604, <lb/>quelle de'proietti son, per la massima parte, scritte nel 1636 e 37. Nel Gen&shy;<lb/>naio di quest'anno, come si rileva da una lettera di Dino Peri, l'Elzevirio <lb/>in Leida aveva sotto i torchi i Dialoghi delle Resistenze e del Moto, ma no <pb xlink:href="020/01/2289.jpg" pagenum="532"/>quello de'proietti, perch&egrave; l'Autore v'andava tuttavia lavorando (Alb. </s>

<s>X, 184): <lb/>e che vi lavorasse nel Febbraio seguente e nel Marzo, Galileo stesso lo scri&shy;<lb/>veva al Micanzio (ivi, pag. </s>

<s>188) e al Magiotti, che rispondeva godere della <lb/>notizia in estremo (MSS. Gal., P. VI, T. XIII, fol. </s>

<s>14). De'faticosi calcoli <lb/>aritmetici, fatti per costruire la <emph type="italics"/>Tabula altitudinum semiparabolarum ad <lb/>singulos gradus elevationis,<emph.end type="italics"/> &egrave; tutto pieno il tergo di una lettera di Ales&shy;<lb/>sandro Ninci, scritta da Campoli nel Marzo del 1636 (ivi, P. V, T. II, fol. </s>

<s>125). </s></p><p type="main">

<s>Del non essere i foglietti, che il Salviati legge nel terzo Dialogo, con&shy;<lb/>temporanei a quelli letti nel quarto, par che possa esser non lieve argomento <lb/>il non aver l'Accademico avvertito ch'essendo gli spazi come i quadrati dei <lb/>tempi, le relazioni, che passan fra loro, son rappresentate dalle ascisse e dalle <lb/>ordinate di una semiparabola, ci&ograve; che, dalla contemplazione de'moti natu&shy;<lb/>ralmente accelerati, avrebbe per diretta via potuto condurre a riconoscer le <lb/>propriet&agrave; della parabola ne'proietti; <emph type="italics"/>quod non scripsit Galilaeus<emph.end type="italics"/> osserv&ograve; il <lb/>Torricelli (Op. </s>

<s>geom., P. l cit., pag. </s>

<s>110), il quale fu primo a dimostrare in <lb/>pubblico che nella Parabola stessa convengono mirabilmente le due specie <lb/>di moti. </s></p><p type="main">

<s>Per confermar poi il nostro discorso che cio&egrave;, a rivelar l'ingegno della <lb/>Natura <emph type="italics"/>circa parabolicam lineam ludentis,<emph.end type="italics"/> Galileo convertito non attese che <lb/>negli ultimi anni della sua vita, si avvertir&agrave; che non abbiamo dell'avvenuta <lb/>conversione documento anteriore al d&igrave; 5 Giugno 1637, in quella lettera scritta <lb/>a Pietro Carcavy di Parigi, e nella quale, riducendo gli scherzi del Dialogo <lb/>al serio, si legge che &ldquo; sebbene dalla composizione del moto equabile col <lb/>retto perpendicolarmente discendente, con l'accelerazione fatta nella propor&shy;<lb/>zione da me assegnata, si descriverebbe una linea che, andando a terminare <lb/>nel centro, sarebbe spirale; nientedimeno, sinche noi ci trattenghiamo sopra <lb/>la superfice del globo terrestre, io non mi pento d'assegnare a tale compo&shy;<lb/>sizione una linea parabolica &rdquo; (Alb. </s>

<s>VII, 155). </s></p><p type="main">

<s>Convien dir che da scherzo intendesse pure di parlare il Salviati anche <lb/>col&agrave;, dove nel Dialogo copernicano afferma incurvarsi in arco la catena on&shy;<lb/>deggiante col grave fatto pender da lei, ond'&egrave; che, discorrendone sul serio <lb/>la prima volta in quarant'anni nel nuovo Dialogo meccanico, non solo ivi <lb/>si dice che quella medesima catena s'incurva in figura di parabola, ma, <lb/>dop'avere insegnato il modo di descriverla com'insegna Guidubaldo, acco&shy;<lb/>gliendo ora amichevolmente quel che sempre erasi rifiutato; s'aggiunge <lb/>l'altra maniera di servirsi, per quella medesima descrizione, direttamente <lb/>della catena, <emph type="italics"/>punteggiandone sopra un muro la strada<emph.end type="italics"/> (Alb. </s>

<s>XIII, 144). </s></p><p type="main">

<s>Mentre avrebbe dovuto il Salviati ripensar che il primo modo di de&shy;<lb/>scriver con maravigliosa facilit&agrave; quante parabole uno vuole, col tirare una <lb/>palla inumidita sopra la superfice di uno specchio inclinato, non era inven&shy;<lb/>zion dell'Amico; piglia occasione di soggiungere che s'ha di li esperienza il <lb/>moto de'proietti farsi per linee paraboliche: &ldquo; effetto non osservato, prima che <lb/>dal nostro Amico, il quale ne arreca anco la dimostrazione &rdquo; (Alb. </s>

<s>XIII, 144). <lb/>Nella prefazioncella latina alla Giornata terza intorno i movimenti locali, os-<pb xlink:href="020/01/2290.jpg" pagenum="533"/>serva lo stesso Amico del Salviati che, gettato un grave per aria, descrive <lb/>una certa linea curva, &ldquo; verumtamen eam esse Parabolam nemo prodidit &rdquo; <lb/>(ibid., pag. </s>

<s>148). Se fosse Galileo potuto starsi sicuro che si tenessero per <lb/>anticamente scritte nella realt&agrave; queste parole, come si volevano fare appa&shy;<lb/>rire nella forma, bastava avere ingerita ne'lettori una tale persuasione, per&shy;<lb/>ch&egrave; non dovessero mettersi a ricercar d'altro. </s>

<s>Ma pure compariva quell'an&shy;<lb/>nunzio di novit&agrave; alla luce nel 1638, che vuol dire sei anni dopo che l'aveva <lb/>gi&agrave; prodotto l'Autore dello Specchio ustorio, per cui gli avversari o i poco <lb/>facili a credere a coloro, che vogliono in ogni cosa apparire i primi, avreb&shy;<lb/>bero potuto notar l'Autore della detta prefazioncella o di avere ignorate le <lb/>tradizioni della Scienza, o di aver profferito una menzogna manifesta. </s></p><p type="main">

<s>La sagacit&agrave; di Galileo aveva prevedute anche le punte di questa saetta. </s>

<s><lb/>Atterrito dalle parole scritte al Marsili, concludeva il Cavalieri cos&igrave; le sue <lb/>difese: &ldquo; Insomma, s'ella pur vuole che sia errore, non &egrave; di malizia al si&shy;<lb/>curo. </s>

<s>Vegga pur quello vuole che io faccia per darle sodisfazione, che io son <lb/>prontissimo a farlo. </s>

<s>Ne ho dato fuori solo alcune copie qu&agrave; in Bologna: <lb/>frattanto io non ne lascer&ograve; uscire altre, sino a che sia aggiustato il negozio, <lb/>se si pu&ograve;, in modo che ella vi abbia sodisfazione. </s>

<s>Perch&egrave; o io differir&ograve; a <lb/>darne fuori pi&ugrave;, sinch'ella non abbia stampato il suo libro Del moto, o ch'ella <lb/>potr&agrave; stamparlo con l'antidata ... o che finalmente abbrucer&ograve; tutte le copie, <lb/>perch&egrave; si distrugga con quelle la ragione d'aver dato disgusto al mio signor <lb/>Galileo &rdquo; (Alb. </s>

<s>IX, 263). Galileo, bench&egrave; facesse altra vista, fu inteso pia&shy;<lb/>cergli meglio di aver sodisfazione in quest'ultimo modo, e cos&igrave;, com'era il <lb/>suo piacere, fu fatto. </s>

<s>Le copie dello Specchio ustorio nel 1638 erano dive&shy;<lb/>nute s&igrave; rare, che ne sarebbe andata perduta per sempre ogni memoria, se <lb/>Urbano Davisi, discepolo e ascritto al medesimo ordine religioso dell'Autore, <lb/>non avesse fatto ristampare il libro nel 1650 in Bologna. </s></p><p type="main">

<s>I tiranni, con esempio non infrequente nelle Storie civili, hanno lavato <lb/>le loro colpe col sangue, generosamente versato a pro della patria: Galileo, <lb/>che s'&egrave; presentato a noi sotto l'aspetto di un tiranno, lav&ograve; pure le colpe <lb/>co'sudori della sua fronte, sparsi a pro della Scienza, la quale videsi entrare <lb/>per lui, da quel varco apertole dal Cavalieri, al possesso di una provincia <lb/>nuova. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Posta, nella Giornata quarta, dove si seguita il discorso Dei movimenti <lb/>locali, per principio fondamentale la proposizione che il proietto <emph type="italics"/>dum fer&shy;<lb/>tur motu composito ex horizontali aequabili, et ex naturaliter accelerato <lb/>deorsum, lineam semiparabolicam describit in sua latione;<emph.end type="italics"/> conclude Ga&shy;<lb/>lileo da essa ordinatamente le principali propriet&agrave; dei moti violenti. </s>

<s>Queste <lb/>propriet&agrave; erano dall'altra parte oramai note, per le belle esperienze di Gui-<pb xlink:href="020/01/2291.jpg" pagenum="534"/>dubaldo Del Monte, e per le ammirabili congetture del Tartaglia, intantoch&egrave; <lb/>si proponeva al Promotor dei due Autori a dimostrare per scienza, e per <lb/>ragion conseguente dal moto parabolico, che massima &egrave; l'ampiezza del tiro <lb/>elevato a mezza sqadra: ed essendo gl'impeti nell'ascesa e nella discesa <lb/>uguali, si lasciava a lui il prefinirne la giusta quantit&agrave; in ciascun punto della <lb/>traiettoria. </s></p><p type="main">

<s>Ma non poteva il moto parabolico non ridursi, e non rientrare in quelle <lb/>leggi universali, dimostrate da Galileo nella precedente Giornata, rimanendo <lb/>in ogni modo gl'impeti proporzionali ai tempi, e variando solo la linea della <lb/>caduta, che non &egrave; retta ma curva. </s>

<s>Che poi il moto curvo circolare non si <lb/>acquisti mai naturalmente, senza il moto retto che lo precede, fu specula&shy;<lb/>zione antica dello stesso Galileo, il quale, applicandola alla Cosmografia, im&shy;<lb/>magin&ograve; che il Creatore, collocato nel Sole immobile il centro, avesse fabbri&shy;<lb/>cato tutti i pianeti nel medesimo luogo, &ldquo; e di l&igrave; datali inclinazione di moversi, <lb/>discendendo verso esso centro, sin che acquistassero quei gradi velocit&agrave;, che <lb/>pareva alla Mente Divina: li quali acquistati, fossero volti in giro ciasche&shy;<lb/>duno nel suo cerchio, mantenendo la gi&agrave; concepita velocit&agrave; &rdquo; (Alb. </s>

<s>I, 34, 35). <lb/><figure id="id.020.01.2291.1.jpg" xlink:href="020/01/2291/1.jpg"/></s></p><p type="caption">

<s>Figura 285</s></p><p type="main">

<s>Quale efficacia dovessero avere questi pensieri in confermar, nella <lb/>mente di chi gli avea concepiti, l'opinione delle traiettorie, circolari <lb/>esse pure, come le orbite celesti; si comprende assai facilmente. </s>

<s><lb/>Ma, riformatasi poi quell'opinione, il concetto della genesi del <lb/>moto curvo parabolico dal moto retto precedente rimase, e <lb/>immaginando che si riducesse quel moto retto d'acce&shy;<lb/>lerato in equabile, col rivolgersi per l'orizzontale, si <lb/>dispose Galileo a riconoscer per vero che, mentre, <lb/>rimanendosi il detto moto equabile, circolerebbe <lb/>intorno al centro; mescolato col moto naturale, <lb/>che non abbandona il mobile nemmeno per <lb/>la scesa curvilinea, compone quella stessa <lb/>linea, che sarebbe stata per s&egrave; circo&shy;<lb/>lare, in parabolica. </s></p><p type="main">

<s>S'immagini essere in C <lb/>(fig. </s>

<s>285) un grave spinto con <lb/>un dato impeto nella dire&shy;<lb/>zione orizzontale CO: <lb/>descriver&agrave; per l'aria <lb/>la semiparabola CD, <lb/>conl'impeto retto <lb/>precedente, <lb/>dovuto alla <lb/>caduta, <lb/>che sia <lb/>per <pb xlink:href="020/01/2292.jpg" pagenum="535"/>esempio tale qual'&egrave; da A in C, volto a sfogarsi orizzontalmente per la linea CO; <lb/>e con l'impeto naturale, che seguita ad accompagnare il mobile in descri&shy;<lb/>vere la semiparabola, il quale impeto &egrave; tanto, quanto ne acquisterebbe il ca&shy;<lb/>dente in G, per la libera scesa CG. </s></p><p type="main">

<s>Sopravvenga in C un impeto doppio, qual si produrrebbe, quando il <lb/>moto retto precedente fosse fatto per l'altezza BC, quadrupla di AC: per <lb/>quest'impeto cos&igrave; concepito si passerebbe orizzontalmente dal mobile uno <lb/>spazio EG, doppio del primo DG, e per una simile ragione si passerebbe lo <lb/>spazio FG, doppio di EG, quando il moto retto precedente in C fosse per <lb/>un'altezza quadrupla alla BC. </s></p><p type="main">

<s>Dietro un ragionamento, dalle gi&agrave; dimostrate leggi dei moti naturali in <lb/>simil guisa iniziato, sperava Galileo di poter determinare in D, in E e in F <lb/>le quantit&agrave; degl'impeti respettivi. </s>

<s>Sia, diceva, in C l'impeto del cadente da A <lb/>uguale a 100, e poniamo CG uguale ad AC. </s>

<s>Essendo cos&igrave; dunque in D com&shy;<lb/>posti insieme due impeti, ciascun de'quali &egrave; come 100, sar&agrave; il totale 200. <lb/>In B, l'impeto retto precedente, dovuto alla caduta in C dall'altezza BC, &egrave; <lb/>doppio del cadente da A, e perci&ograve; &egrave; come 200; onde, aggiuntosi l'impeto <lb/>acquistato dal venir per la parabola CE, o per l'altezza CG, ch'&egrave; pur 100; <lb/>tutto intero l'impeto in E torner&agrave; 300. Per queste medesime ragioni si ve&shy;<lb/>dr&agrave; che in F la somma de'due impeti &egrave; 400 pi&ugrave; 100, che vuol dir 500. <lb/>L'impeto in F, pareva di poter concludere a Galileo, sta dunque all'impeto <lb/>in E, come 5 a 3, e l'impeto in E, all'impeto in D, come 3 a 2, cio&egrave;, se&shy;<lb/>condo dicevasi allora, in sesquialtera proporzione. </s></p><p type="main">

<s>&ldquo; Cadens ex A in C, conversus, describit parabolam CD. </s>

<s>Si vero mo&shy;<lb/>mentum velocitatis in C duplum foret, describeret parabolam CE, cuius EG <lb/>dupla esset ad GD: impetus enim duplus in C permeat in orizontem du&shy;<lb/>plicem spacium tempore eodem. </s>

<s>Sed, ut acquiratur in C momentum duplum, <lb/>necesse est casum fieri ex quadrupla altitudine, nempe ex CB. Pariter, ex <lb/>altitudine quadrupla ad CB, describetur parabola CF, cuius amplitudo GF <lb/>dupla est ad GE. &rdquo; </s></p><p type="main">

<s>&ldquo; Verum mobile in D videtur supra impetum in C addere impetum <lb/>acquisitum per parabolam CD, quod respondet altitudini CG. </s>

<s>Mobile vero <lb/>in E idem momentum addit supra impetum quam habuit in C, qui erat <lb/>duplus ad impetum alterius mobilis; ergo impetus mobilis in E videtur esse <lb/>sexquialterus ad impetum mobilis in D. </s>

<s>Similiter invenietur impetum in F, <lb/>ad impetum in E, esse ut 5 ad 3. &rdquo; </s></p><p type="main">

<s>&ldquo; In elevatione igitur EA, si proiectum habuerit impetum sexquialte&shy;<lb/>rum ad impetum in D, proiecti secundum elevationem DA proiicientur se&shy;<lb/>cundum parabolas EC, DC, intra easdem parallelas, sed distantia EG dupla <lb/>erit ad DG. &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>90). </s></p><p type="main">

<s>Incominciano di qui ad apparire in queste prime speculazioni galileiane <lb/>due supposti, i quali son di non lieve importanza nella Storia dei proietti. </s>

<s><lb/>Il primo &egrave; che la stessa semiparabola venga a descriversi o dall'esplosione <lb/>in C, con tiro di punto in bianco, o dall'esplosione in D, secondo l'eleva-<pb xlink:href="020/01/2293.jpg" pagenum="536"/>zione DA. Ora, essendo DA tangente alla parabola in D, si suppone in se&shy;<lb/>condo luogo che, cessando il moto parabolico di accelerarsi nel punto D, pro&shy;<lb/>seguirebbe indefinitamente il suo moto per la direzione di essa tangente. </s>

<s>Era <lb/>anche questa per&ograve; dottrina antica di Galileo, il quale aveva nella Giornata <lb/>seconda dei Massimi Sistemi fatto sentenziare al Salviati &ldquo; che il proietto <lb/>acquista impeto di moversi per la tangente dell'arco, descritto dal moto del <lb/>proiciente nel punto della separazione di esso proietto dal proiciente &rdquo; <lb/>(Alb. </s>

<s>I, 213). </s></p><p type="main">

<s>Ritenuto dunque per vero che la direzione del tiro in D, per la quale <lb/>si ritesse dal mobile la semiparabola DC, sia secondo la tangente DA, es&shy;<lb/>sendosi fatto AG uguale a GD, l'angolo ADG torner&agrave; semiretto, e Galileo <lb/>preparavasi questa costruzione, col fine di dimostrar ci&ograve; che il Tartaglia avea <lb/>congetturato sugli avvisi dell'esperienza. </s>

<s>Facciasi GH doppia di AG: essendo <lb/>EG pure doppia di DG, ossia di AG, congiunti i punti E, H l'angolo HEG <lb/>sar&agrave; a mezza squadra, e il medesimo proietto dal medesimo punto E secondo <lb/>le direzioni EH, EA, descriver&agrave; le due semiparabole EA, EC, le quali avranno <lb/>la medesima ampiezza. </s></p><p type="main">

<s>Ora, applicando Galileo i teoremi gi&agrave; dimostrati rispetto agl'impeti pro&shy;<lb/>porzionali ai tempi, i quali stanno come le radici degli spazi, calcola le quan&shy;<lb/>tit&agrave; dell'impeto necessario al proietto in E perch&egrave; possa descrivere la semi&shy;<lb/>parabola EA: quantit&agrave; che, dovendo resultare dall'impeto del cadente in A <lb/>da H, ritrovato 141 (essendo AC sempre cento), e dall'impeto in G da A, <lb/>che &egrave; pur 141, sar&agrave; uguale a 282. Ma l'impeto necessario in E perch&egrave; possa <lb/>il proietto disegnare la via EC fu ritrovato dianzi 300, dunque, nell'eleva&shy;<lb/>zion semiretta, si passa il medesimo spazio che in elevazion minore, con tanto <lb/>minor forza, quanto 282 &egrave; minor di 300, e perci&ograve; con forza d'impeto uguale, <lb/>nel tiro a mezza squadra, si passer&agrave; secondo tal proporzione uno spazio mag&shy;<lb/>giore. </s>

<s>Soggiunge Galileo un altro simile esempio di ci&ograve;, duplicando in GX <lb/>la GH, e comparando l'impeto necessario a descriver la semiparabola FH, <lb/>secondo l'elevazion semiretta FX, con l'impeto necessario a descriver la se&shy;<lb/>miparabola FC, e trova quello tanto esser minore di questo, quanto 400 &egrave; <lb/>minore di 500. </s></p><p type="main">

<s>Restava a comparar l'impeto, nella elevazion semiretta, con l'impeto a <lb/>una elevazione maggiore, e dal calcolo result&ograve; ancora a Galileo che l'uno <lb/>riusciva sempre maggiore dell'altro. </s>

<s>Presa perci&ograve; CG uguale a RG, consi&shy;<lb/>derava la semiparabola RC generata dal moto retto antecedente, l'impeto <lb/>del quale in C, da S, trov&ograve; esser come 50, e dal moto conseguente per CG, <lb/>l'impeto del quale in G da C fu posto come 100; cosicch&egrave; l'impeto totale <lb/>in R, nella elevazione maggiore della semiretta, per la quale si suppone <lb/>esser descritta la R C, tornerebbe uguale a 150. Divisa poi la CG in mezzo <lb/>in T, passava Galileo a calcolar l'impeto che, dal medesimo punto R, fa&shy;<lb/>rebbe descrivere al proietto la via RT, secondo la elevazion semiretta RC, <lb/>e trovato al calcolo essere in T l'impeto del veniente da C 70 1/2, ne con&shy;<lb/>cluse che l'impeto della elevazion semiretta in R era 141, minore di 150. </s></p><pb xlink:href="020/01/2294.jpg" pagenum="537"/><p type="main">

<s>Incollato sotto il foglio, da cui fu trascritto il modo di misurare gl'impeti <lb/>ne'punti F, E, D, delle semiparabole aventi la medesima altezza CG, si trova <lb/>un pezzetto di carta, in un angolo della quale, dalla medesima mano di Gali&shy;<lb/>leo, &egrave; scritta in tre linee la tavoletta: &ldquo; Impetus in C, cadentis ex A, sit 100; <lb/>&mdash; cadentis ex B erit 200; &mdash; impetus in E erit 300. &rdquo; Di contro, e sotto, <lb/>seguita questa Nota, nella quale si contempla il caso della elevazion maggiore <lb/>della semiretta, che vuol aver maggior forza, per fare la medesima volata: </s></p><p type="main">

<s>&ldquo; Cadentis in A ex H impetus in E erit 141: cadentis vero per para&shy;<lb/>bolam AE impetus in E erit duplicatus, nempe 282. Constat igitur maiorem <lb/>esse impetum venientis per parabolam CE in E, quam venientis per para&shy;<lb/>bolam AE. </s>

<s>Et si proiectum ex E, secundum elevationem EH, habet impe&shy;<lb/>tum ut 282, conficiet parabolam EA: secundum elevationem vero EA, confi&shy;<lb/>ciet proiectum parabolam EC, si habuerit impetum ut 300. Ergo, in elevatione <lb/>semirecti EH, ab eadem vi, longius eiaculatur, quam in elevatione ea, quae <lb/>minor est semirecti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cadentis in H ex X impetus in H erit 200: cadentis vero per para&shy;<lb/>bolam HF impetus in F erit duplicatus, nempe 400. Impetus in F est 500 <lb/>venientis per parabolam CF: venientis vero per parabolam HF impetus in F <lb/>est 400. Ex quo patet etiam longius eiaculari ab eadem vi per elevationem <lb/>semirecti, quam per minorem &ldquo; (ibid.). </s></p><p type="main">

<s>&Egrave; sotto a questa scritta dalla penna di Galileo l'altra Nota relativa ai <lb/>calcoli comparativi fra l'impeto della elevazion semiretta e un'altra che di <lb/>lei sia comunque maggiore, e di contro alla tavoletta che dice, scritta in <lb/>due linee, &ldquo; Impetus in C ex S erit 50; &mdash; in R erit 150 &rdquo; si leggono que&shy;<lb/>ste parole: &ldquo; Impetus vero in T ex C est fere 70 1/2; conversi per para&shy;<lb/>bolam TR in R erit 141: minor nempe quam venientis ex S per C in R, <lb/>qui fuit 150. Unde constat quod in elevatione semirecti RT ab eadem vi <lb/>longior fit proiectio, quam per elevationem RC &rdquo; (ibid.). </s></p><p type="main">

<s>Queste non erano propriamente dimostrazioni, ma una buona promessa <lb/>e una lieta speranza che, dalle generali propriet&agrave; dei moti naturali, si sa&shy;<lb/>rebbero potute ritrovare, alle propriet&agrave; dei moti proiettizi, le mate natiche <lb/>dimostrazioni, le quali, svolte da principii proprii e ordinate, aggiungessero <lb/>una parte nuova e desideratissima al trattato Dei movimenti locali. </s>

<s>Essendo <lb/>que'principii premonstrati nella parabola, dovevano alcuni necessariamente <lb/>ridursi alle propriet&agrave; geometriche di lei, dipendenti dalla principalissima che <lb/>dice essere le ascisse proporzionali ai quadrati delle ordinate, d'onde il Ca&shy;<lb/>valieri, e poi Galileo, ne conclusero le fondamentali propriet&agrave; meccaniche <lb/>della curva, facendo alle ascisse rappresentare gli spazi e alle ordinate i <lb/>tempi. </s>

<s>Il supposto, applicato ne'calcoli precedenti, che cio&egrave; l'elevazione del <lb/>tiro sia designata dalla tangente, faceva alla Meccanica invocare quell'altra <lb/>propriet&agrave; geometrica della Parabola, che dice essere la suttangente dupla <lb/>all'ascissa; propriet&agrave; che Galileo, com'Apollonio, dimostra dagli assurdi, dopo <lb/>aver premessa l'equazion della curva, che il Torricelli dice &ldquo; Apollonii qui&shy;<lb/>dem, sed marte proprio a Galileo demonstratam &rdquo; (Op. </s>

<s>geom. </s>

<s>cit, pag. </s>

<s>110). </s></p><pb xlink:href="020/01/2295.jpg" pagenum="538"/><p type="main">

<s>Ma i principali elementi delle traiettorie dovevano necessariamente co&shy;<lb/>stituirsi infino da quelle prime speculazioni galileiane intorno alla misura <lb/>degl'impeti, che contenevano in germe la scienza de'proietti, dalle quali <lb/>speculazioni apparisce ridursi quegli elementi a tre: alla linea del moto retto <lb/>antecedente, alla linea del moto retto conseguente, e alla linea della distesa <lb/>orizzontale, i quali tre elementi della Scienza nuova, perch&egrave; volevano essere <lb/>designati con nomi propri, chiam&ograve; Galileo <emph type="italics"/>sublimit&agrave;<emph.end type="italics"/> la prima delle dette <lb/>linee, <emph type="italics"/>altezza<emph.end type="italics"/> la seconda, e <emph type="italics"/>amplitudine<emph.end type="italics"/> la terza. </s>

<s>&ldquo; Advertatur semiparabo&shy;<lb/>lae CD (nella precedente figura) <emph type="italics"/>amplitudinem<emph.end type="italics"/> a me vocari horizontalem <lb/>GD; <emph type="italics"/>altitudinem<emph.end type="italics"/> CG, nempe eiusdem parabolae axem: lineam vero AC, <lb/>ex cuius descensu determinatur impetus horizontalis, <emph type="italics"/>sublimitatem<emph.end type="italics"/> appelllo &rdquo; <lb/>(Alb. </s>

<s>XIII, 237). </s></p><p type="main">

<s>Perch&egrave; dalla sublimit&agrave; dipende il moto proiettizio per l'orizzonte, in <lb/>che consiste la violenza del tiro, e il fine per cui si mettono in esercizio le <lb/>macchine ballistiche, si comprende com'uno de'primi e de'pi&ugrave; importanti <lb/>problemi, che si proponesse a risolvere Galileo, fosse quello di trovare il <lb/>punto sublime, da cui dovrebbe cader il grave per descrivere una data Pa&shy;<lb/>rabola. </s>

<s>Son della soluzione rimaste ne'manoscritti le prime prove, le quali <lb/>si vedon movere dalla considerazione del caso pi&ugrave; semplice, in cui cio&egrave; l'am&shy;<lb/>piezza &egrave; doppia dell'altezza, perch'&egrave; allora la tangente stessa, che decide, <lb/>nell'incontrare l'asse prolungato, il punto della sublimit&agrave; che si cercava. </s>

<s><lb/>Passa da questo Galileo al caso, in cui l'ampiezza abbia all'altezza qualun&shy;<lb/>que proporzione; e perch&egrave; in ogni modo la Parabola &egrave; la medesima, e me&shy;<lb/>desimo &egrave; il punto sublime, dimostra essere un tal punto nel prolungamento <lb/>dell'asse, a una distanza dal vertice, che sia terza proporzionale tra l'altezza <lb/>e la met&agrave; della base. </s></p><p type="main">

<s>&ldquo; Sit parabola ABC (fig. </s>

<s>286), cuius amplitudo CD dupla sit altitudi&shy;<lb/><figure id="id.020.01.2295.1.jpg" xlink:href="020/01/2295/1.jpg"/></s></p><p type="caption">

<s>Figura 286<lb/>nis DA, et illa tangat EC in pun&shy;<lb/>cto C: erit AE aequalis AD, et cadens <lb/>ex E, conversum in A, describit pa&shy;<lb/>rabolam ABC. &rdquo; </s></p><p type="main">

<s>&ldquo; Sumatur in parabola quodli&shy;<lb/>bet punctum B: contemplandum est <lb/>quomodo, pro describenda parabola <lb/>AB, requiratur idem impetus caden&shy;<lb/>tis ex E usque ad A. </s>

<s>Ex A reperia&shy;<lb/>tur punctum E, ex quo decidat pro&shy;<lb/>iectum. </s>

<s>Tangat BGF ipsam in B, et <lb/>ducatur horizontalis BH: erit AH ae&shy;<lb/>qualis AF. </s>

<s>Dico modo punctum E re&shy;<lb/>periri, quia ut AF ad AG, ita est GA <lb/>ad AE, quod sic probatur. </s>

<s>Ut DA ad AG, ita dupla DA ad duplam AG, nempe <lb/>DC ad HB: et ut quadratus DA ad quadratum AG, ita quadratus DC ad qua&shy;<lb/>dratum HB, et ita est linea DA ad AH, seu EA ad AF &rdquo; (MSS. Gal. </s>

<s>ibid., fol. </s>

<s>115). </s></p><pb xlink:href="020/01/2296.jpg" pagenum="539"/><p type="main">

<s>La conclusione, che nel manoscritto galileiano segue immediata, dipende <lb/>dalle cose dimostrate, ed espresse dalla serie di queste equazioni: DA2:AG2= <lb/>DE2:HB2=AD:AH=EA:AF, le due estreme ragioni delle quali danno <lb/>EA.AF=AG2 ossia AF:AG=AG:EA. &ldquo; Constat igitur quod, si datae <lb/>parabolae AB inveniendus sit punctus sublimis E, ex quo cadens conficiat <lb/>parabolam AB, posita AF aequali AH, et ducta FGB, quae parabolam tan&shy;<lb/>gat in B, sumpta tertia proportionalis ipsarum FA, AG, dabit AE, ex qua <lb/>cadens etc. </s>

<s>quod erat faciendum &rdquo; (ibid.). </s></p><p type="main">

<s>Seguono sotto a queste, nel medesimo foglio, altre linee, in principio <lb/>delle quali si legge <emph type="italics"/>Melius,<emph.end type="italics"/> e in margine &egrave; notato <emph type="italics"/>Scritta,<emph.end type="italics"/> e vuol dire che <lb/>la medesima dimostrazione fatta meglio era stata inserita nel Dialogo, dove <lb/>propriamente si legge sotto la proposizione quinta <emph type="italics"/>De motu proiectorum.<emph.end type="italics"/><lb/>Nel trascriverla per&ograve; di qui Galileo fa alcune leggere variazioni, come in <lb/>tutte le altre, nelle quali si nota che furono scritte. </s>

<s>E perch&egrave; possano di tali <lb/>variazioni i Lettori avere un'idea, trascriveremo dal citato foglio il secondo <lb/>modo di trovar meglio la sublimit&agrave;, data che sia la parabola. </s></p><p type="main">

<s>&ldquo; Melius: Sit parabola AB (nella passata figura) cuius amplitudo BH, <lb/>et axis perpendicularis HE, in quo invenienda sit altitudo, ex qua cadens <lb/>parabolam describat. </s>

<s>Ponatur AF aequalis AH, et connectatur FB secans <lb/>horizontalem AG in G, et tangentem parabolam in B. </s>

<s>Sitque ipsarum FA, <lb/>AG tertia proportionalis AE. </s>

<s>Dico E esse punctum quaesitum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si enim intelligatur EA esse mensura temporis casus ex E in A, et <lb/>impetus acquisiti in A, erit AG (media nempe inter EA, AF) tempus et im&shy;<lb/>petus venientis ex F in A, seu ex A in H. </s>

<s>Sed impetus in A cadentis ex E, <lb/>tempore E A, cum impetu acquisito in A, conficit in horizontali motu ae&shy;<lb/>quabili duplam EA; ergo etiam eodem impetu, in tempore AG, conficiet <lb/>duplam GA, nempe BH, et in perpendiculari motu ex quiete, eodem tem&shy;<lb/>pore GA, conficit AH. </s>

<s>Ergo eodem tempore conficiuntur amplitudo et alti&shy;<lb/>tudo AH. </s>

<s>Describitur ergo Parabola AB ex casu F, quod quaerebatur &rdquo; (ibid.). </s></p><p type="main">

<s>Ne deduce di qui Galileo il corollario, che la met&agrave; della base &egrave; media <lb/>proporzionale tra la sublimit&agrave; e l'altezza della semiparabola, ci&ograve; che dava <lb/>occasione al Viviani di scioglier cos&igrave; in un modo assai pi&ugrave; spedito quel me&shy;<lb/>desimo problema: &ldquo; Quaeratur sublimitas parabolae AB, cuius axis AH (nella <lb/>medesima ultima figura) basis HB. </s>

<s>Ducatur tangens BF, ac tangens AG, et <lb/>iuncta HG, ipsi ad G perdendicularis, erigatur GE axi occurrens in E. </s>

<s>Nam <lb/>AE erit sublimitas quaesita. </s>

<s>Est enim AG dimidium basis HB, media pro&shy;<lb/>portionalis inter altitudinem et sublimitatem, per corollarium huius. </s>

<s>Ergo AE <lb/>erit sublimitas quaesita &rdquo; (MSS. Cal., P. V, T. IX. <emph type="italics"/>Postille del V. all'edi&shy;<lb/>zione di Leida<emph.end type="italics"/>). </s></p><p type="main">

<s>Il quesito dicemmo essere stato uno dei primi, a cui si propose di ri&shy;<lb/>spondere Galileo nel dimostrare le meccaniche propriet&agrave; dei proietti, il trat&shy;<lb/>tato delle quali, nell'intenzione che s'era formata allora, si limitava alla <lb/>misura degl'impeti, e alle ragioni dei tiri elevati a mezza squadra. </s>

<s>Diremo <lb/>com'egli aggiungesse poi a queste due una terza parte, nella quale appli-<pb xlink:href="020/01/2297.jpg" pagenum="540"/>cava agli esercizi militari le teorie, insegnando a calcolare e a disporre in <lb/>Tavole digradate i tiri del cannone. </s>

<s>Ma &egrave; da vedere intanto quanto sudasse <lb/>il grand'Uomo, e quanto s'affannassero dietro lui il Torricelli e il Viviani <lb/>per determinar l'impeto in ciascun punto della parabola, ch'&egrave; problema di <lb/>s&igrave; facile soluzione a chiunque non rifiuti di far uso del parallelogrammo o <lb/>del rettangolo delle forze. </s>

<s>Per avere infatti le relazioni tra l'impeto totale <lb/>e gl'impeti parziali nel punto C della parabola ABC, nella precedente fig. </s>

<s>286, <lb/>non occorre far altro che prendere della tangente CE una porzione a pia&shy;<lb/>cere qual sarebbe CM, e sopr'essa come diagonale costruire il rettangolo ON, <lb/>di cui il lato MN rappresenter&agrave; l'impeto perpendicolare, e l'altro CN l'im&shy;<lb/>peto orizzontale. </s>

<s>E perch&egrave; il triangolo CMN &egrave; simile al triangolo CED, s'hanno <lb/>le cercate proporzionalit&agrave; rappresentate dagli stessi elementi della Parabola, <lb/>nella quale la tangente CE &egrave; tanta parte della suttangente ED e dell'ordi&shy;<lb/>nata DC, quanta parte l'impeto totale &egrave; del diretto nel perpendicolo, e per <lb/>l'orizzonte. </s></p><p type="main">

<s>A un tal termine conducevano insomma le tortuose erte vie, proseguite <lb/>da Galileo e dai due sopra commemorati Promotori di lui, n&egrave; si crederebbe <lb/>che il veder riuscire quelle due vie s&igrave; diverse a un termine, non valesse a <lb/>persuader cos&igrave; grandi e liberi ingegni che dovevano ambedue essere ugual&shy;<lb/>mente buone, e ch'era una follia lasciar, per mettersi agli erti e lunghi, i <lb/>pi&ugrave; brevi e piani sentieri. </s>

<s>Dev'essere stato dunque motivo a cos&igrave; strano <lb/>modo di procedere qualche fallacia, l'origine della quale facilmente si sco&shy;<lb/>pre nelle cose poco addietro narrate. </s></p><p type="main">

<s>Si rammemoreranno i Lettori come il Cardano considerando che i due <lb/>moti composti AD, AE (fig. </s>

<s>287) s'impediscono a vicenda, ne aveva con&shy;<lb/>cluso che il proietto in C arriva pi&ugrave; tardi di quel che non avrebbe fatto <lb/><figure id="id.020.01.2297.1.jpg" xlink:href="020/01/2297/1.jpg"/></s></p><p type="caption">

<s>(Figura 287)<lb/>liberamente cadendo per AE: Galileo aveva invece sco&shy;<lb/>perto, per ragione e per esperienza, che tanto la linea <lb/>trasversale AC, quanto la diretta AE, son passate dal <lb/>mobile scendente in A dalla quiete nel medesimo tempo, <lb/>ond'&egrave; che, trascorrendo in una fallacia simile a quella <lb/>del Cardano, dal non essere il moto resultante per AC <lb/>indugiato, ne aveva concluso che i due componenti <lb/>per AD e per AE non s'impediscono, e che la somma <lb/>delle parti doveva esattamente essere uguale all'intero. </s>

<s><lb/>Secondo una tal conclusione vedemmo essere stati, nella <lb/>figura 284, computati gl'impeti in F, in E e in D re&shy;<lb/>sultanti dalla somma esatta del moto retto antecedente, e del conseguente <lb/>nella Parabola. </s></p><p type="main">

<s>Se non che dal pensar che il moto retto antecedente volgesi per l'orizzon&shy;<lb/>tale GD; che il retto conseguente prosegue per il perpendicolo AG, e che <lb/>il composto d'ambedue &egrave; diretto secondo la tangente AD, incominci&ograve; a na&shy;<lb/>scere nella mente di Galileo il dubbio che si venisse una linea retta a fare <lb/>uguale alla spezzata: dubbio ch'ei si studiava di quietare dicendo non si <pb xlink:href="020/01/2298.jpg" pagenum="541"/>trattar di linee geometriche circoscriventi uno spazio, ma di linee dinami&shy;<lb/>che rappresentanti una forza o una potenza, sicch'essendo l'angolo AGD <lb/>retto &egrave; verissimo che la potenza o il quadrato di AB &egrave; uguale alla somma <lb/>delle potenze, o dei quadrati di DG e di AG. </s></p><p type="main">

<s>Prende da un tale equivoco tutto il suo valore dimostrativo la propo&shy;<lb/>sizione II del quarto Dialogo galileiano, dalla quale dipendendo la teoria degli <lb/>impeti riesce questa, nell'intenzion dell'Autore, per tutto falsa, e avventu&shy;<lb/>rosamente si corregge e riducesi al vero, con l'intender che gl'impeti non <lb/>siano proporzionali alle potenze, ma alle semplici linee, cosicch&egrave; la somma <lb/>delle componenti di tanto ecceda la resultante del moto, di quanto i due <lb/>lati del rettangolo distesi in dirittura eccedono la lunghezza della diagonale. </s>

<s><lb/>Si pu&ograve; ora di qui intendere perch&egrave; Galileo e i seguaci di lui scegliessero <lb/>le vie aspre e tortuose, e come, per essere i due impeti nella Parabola or&shy;<lb/>togonali, si rendano avventurosamente veri i loro teoremi, dando altro si&shy;<lb/>gnificato alle loro espressioni, che son bene spesso quelle medesime di chi <lb/>fa libero uso del parallelogrammo delle forze. </s>

<s>Cos&igrave; non infrequentemente <lb/>leggesi nelle dimostrazioni di Galileo comporsi i due moti nella <emph type="italics"/>diagonale,<emph.end type="italics"/><lb/>invece di dir nell'<emph type="italics"/>ipotenusa,<emph.end type="italics"/> secondo il linguaggio proprio alle professate <lb/>dottrine. </s>

<s>Ma i discorsi s'intenderanno meglio dal passar che faremo all'esame <lb/>dei fatti. </s></p><p type="main">

<s>Le proposizioni terza e quarta, nella quarta Giornata delle due Nuove <lb/>Scienze, e tutta l'interlocuzione che le commenta, non sono altro per cos&igrave; <lb/><figure id="id.020.01.2298.1.jpg" xlink:href="020/01/2298/1.jpg"/></s></p><p type="caption">

<s>Figura 288<lb/>dire che una soluzione assai lunga, e spesso <lb/>spesso noiosa, della seguente Nota mano&shy;<lb/>scritta, nella quale la concisione aggiunge <lb/>al pensiero mirabile chiarezza: &ldquo; In motu <lb/>ex quiete eadem ratione intenditur velocita&shy;<lb/>tis momentum et tempus ipsius motus. </s>

<s>Fiat <lb/>enim motus per AB (fig. </s>

<s>288), ex quiete <lb/>in A, et accipiatur quodlibet punctum C, et <lb/>ponatur AC esse tempus casus per AC, et <lb/>momentum celeritatis in C acquisitum esse <lb/>pariter ut AC. </s>

<s>Sumaturque rursus quodlibet punctum B: <emph type="italics"/>Dico tempus ca&shy;<lb/>sus per AB, ad tempus per AC, esse ut momentum velocitatis in B, ad <lb/>momentum in C. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sumatur AS media inter BA, AC, et cum positum sit tempus casus <lb/>per AC esse AC, erit AS tempus per AB. </s>

<s>Demonstrandum igitur est mo&shy;<lb/>mentum celeritatis in C, ad momentum celeritatis in B, esse ut AC ad AS. &rdquo; </s></p><p type="main">

<s>&ldquo; Sumantur horizontales CD dupla ad CA, BE vero dupla ad BA. </s>

<s>Con&shy;<lb/>stat ex demonstratis cadens per AC, conversum in horizontem CD, confi&shy;<lb/>cere CD motu aequabili, aequali tempore atque ipsam AC confecit motu <lb/>accelerato naturaliter: et similiter BE confici eodcm tempore atque AB. </s>

<s>Sed <lb/>tempus ipsius AB est AS, ergo horizontalis BE conficitur tempore AS. &rdquo; </s></p><p type="main">

<s>&ldquo; Fiat ut tempus SA ad tempus AC, ita EB ad BL. </s>

<s>Cumque motus <pb xlink:href="020/01/2299.jpg" pagenum="542"/>per BE sit aequabilis, erit spacium BL peractum tempore AC, secundum <lb/>momentum celeritatis in B. </s>

<s>Sed secundum momentum celeritatis in C, eo&shy;<lb/>dem tempore AC, conficitur spacium CD: momenta autem celeritatis sunt <lb/>inter se ut spacia, quae iuxta ipsa momenta eodem conficiuntur tempore; <lb/>ergo momentum celeritatis in C, ad momentum celeritatis in B, est ut DC <lb/>ad BL. &rdquo; </s></p><p type="main">

<s>&ldquo; Quia vero ut DC ad BE, ita ipsarum dimidia, nempe CA ad AB; ut <lb/>aulem EB ad BL, ita BA ad AS, ergo, ex aequali, ut DC ad BL, ita CA <lb/>ad AS: hoc est, ut momentum celeritatis in C, ad momentum celeritatis <lb/>in B, ita CA ad AS: hoc est, tempus per CA, ad tempus per AB, quod erat <lb/>demonstrandum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Determinatur ergo impetus in singulis punctis parabolae ABC (fig. </s>

<s>289) <lb/>ex potentia momenti acquisiti per descensum EA, quod semper servatur <lb/><figure id="id.020.01.2299.1.jpg" xlink:href="020/01/2299/1.jpg"/></s></p><p type="caption">

<s>Figura 289<lb/>idem, et determinatur impetum ori&shy;<lb/>zontalem BH ex potentia alterius <lb/>momenti acquisiti in descensu per&shy;<lb/>pendiculari. </s>

<s>Ut v. </s>

<s>g, in B, erit im&shy;<lb/>petus determinatus a linea poten&shy;<lb/>tiae EA, et mediam inter AD, AH, <lb/>quae sit AI. &rdquo; (MSS. cit., P. V, T. <lb/>H, fol. </s>

<s>91 a tergo). </s></p><p type="main">

<s>Poche parole bastano a espli&shy;<lb/>care il concetto, da Galileo esplicato <lb/>nel Dialogo con si prolisso discorso, <lb/>osservando che s'insegna ivi il modo <lb/>di determinar l'impeto, in qualun&shy;<lb/>que punto delia Parabola, dall'im&shy;<lb/>peto misurato in quel particolar punto di lei, che ci vien riferito dall'ordinata <lb/>doppia all'ascissa, e perci&ograve; uguale alla suttangente, qual sarebbe il punto C <lb/>nella precedente figura. </s>

<s>Essendo in questo caso EA, uguale ad AD, i due im&shy;<lb/>peti orizzontale e perpendicolare sono uguali, ond'&egrave; che la potenza resultante <lb/>dalle due dette potenze componenti s'avr&agrave;, secondo Galileo, costruendo un <lb/>triangolo co'cateti uguali ad AE, dall'ipotenusa del quale avremo rappre&shy;<lb/>sentato l'impeto che si cerca. </s>

<s>Or perch&egrave; in questa medesima figura che ab&shy;<lb/>biamo sott'occhio AL &egrave; uguale ad AE, il triangolo EAL con l'ipotenusa <lb/>EL, ci porge la desiderata dinamica costruzione gi&agrave; fatta. </s></p><p type="main">

<s>Di qui passa Galileo, come si diceva, a determinar l'impeto in qualun&shy;<lb/>que altro punto della Parabola, come sarebbe in B, in cui l'impeto oriz&shy;<lb/>zontale rimanendo il medesimo sar&agrave; come dianzi rappresentato da AE. </s>

<s>Non <lb/>riman dunque che a determinar la lunghezza dell'altro cateto, rappresen&shy;<lb/>tante l'impeto perpendicolare, il qual impeto &egrave; tanto, quant'&egrave; del cadente <lb/>da A in H, ed ha perci&ograve; per misura AI, media tra AD, AH, essendo presa <lb/>AD qual misura del tempo e del'impeto per AD. Cosicch&egrave;, se la orizzon&shy;<lb/>tale AL si risega in G in modo, che sia AG uguale ad AI, sar&agrave; essa AG il <pb xlink:href="020/01/2300.jpg" pagenum="543"/>cateto che mancava a costruire il triangolo dinamico, e l'impeto in C star&agrave; <lb/>all'impeto in B, nella medesima Parabola, come la potenza dell'ipotenusa EL <lb/>sia alla potenza dell'ipotenusa EG. </s></p><p type="main">

<s>&Egrave; un fatto dunque che il primo modo, insegnato da Galileo per misu&shy;<lb/>rare gl'impeti ne'vari punti della traiettoria, anco corretto dalla falsit&agrave; sua <lb/>radicale, &egrave; indiretto, e perci&ograve; faticoso. </s>

<s>Gl'immediati Promotor&igrave; di lui che, <lb/>non accettando pure la regola del parallelogrammo, non poterono nemmen <lb/>essi mettersi per le vie pi&ugrave; dirette, si dovettero contentare di rendere i me&shy;<lb/>todi medes&igrave;mi del Maestro o pi&ugrave; facili o pi&ugrave; eleganti. </s>

<s>La Storia non ha fin <lb/>qui conosciuto fra que'Promotori che il Torricelli, ma noi ora gli aggiun&shy;<lb/>giamo collega il Viviani, il quale, nella postilla manoscritta alla citata copia <lb/>di Leida, osservava, nella presignata figura, ch'essendo BF tangente e AG, <lb/>uguale ad AI, media tra AD, cio&egrave; AE, e AH; congiunta la GH, il triangolo <lb/>EGH torna rettangolo in G, ond'&egrave; che, circoscrittogli col diametro EH un <lb/>mezzo cerchio, la cercata misura dell'impeto in B &egrave; data dalla sottesa EG, <lb/>che si potr&agrave; dunque definir colla semplice riga e col compasso. </s></p><p type="main">

<s>&ldquo; Quum, in superiori constructione, sit AI, vel AG, media proportio&shy;<lb/>nalis inter AD, AH, vel inter AE, AH, si iungatur GH erit angulus EGH <lb/>rectus, ac ideo EG media proportionalis inter EH, AE. </s>

<s>Impetus ergo in B <lb/>facilius reperitur describendo semicirculum super EH, cuius circumferentia, <lb/>secans AL in G, dabit chordam EG pro mensura impetus in B &rdquo; (MSS. Gal., <lb/>P. V, T. IX, pag. </s>

<s>256). </s></p><p type="main">

<s>&ldquo; Vel sic expeditius: Sumatur AG aequalis dimidio ordinatae HB; nam, <lb/>iuncta EG, erit mensura impetus in B. </s>

<s>Vel ducta ex B contingente BF, se&shy;<lb/>cante AL in G, erit EG mensura impetus in B, quae est quoque mensura <lb/>impetus in H, post casum EH, quod EG sit media proportionalis inter <lb/>AE, EH &rdquo; (ibid., pag. </s>

<s>257). </s></p><p type="main">

<s>Come corollario al teorema di Galileo, ridotto cos&igrave; alle pi&ugrave; semplici con&shy;<lb/>clusioni, credeva il Viviani d&igrave; poter dire che, essendo in ogni semiparabola, <lb/>come per esempio in ABC, nella solita figura, gl'impeti verticali, ne'vari <lb/>punti della discesa come in B, C, proporzionali alle AG, AL, e l'impeto oriz&shy;<lb/>zontale il medesimo AE; che questo sempre sta a quelli come la linea su&shy;<lb/>blime sta alla met&agrave; delle semibasi. </s>

<s>&ldquo; Essendo AE misura dell'impeto orizzon&shy;<lb/>tale, e AG misura del perpendicolare in B, e AL misura del perpendicolare <lb/>in C, avr&agrave; sempre l'orizzontale al perpendicolare, in qualunque dato punto <lb/>della parabola come in C, la medesima proporzione dell'AE, sublimit&agrave; della <lb/>parabola, alla AL, met&agrave; della semibase CD &rdquo; (ivi, pag. </s>

<s>262). </s></p><p type="main">

<s>Galileo stesso per&ograve; aveva pensato di far del corollario soggiunto poi <lb/>dal Viviani un bel teorema da potersi vantaggiosamente sostituire alla pro&shy;<lb/>posizione quarta del Dialogo: teorema, ch'ebbe a rimanersi escluso dal trat&shy;<lb/>tato, quando il problema di ritrovar la sublimit&agrave; della parabola e il corol&shy;<lb/>lario di lui, che cio&egrave; l'ampiezza &egrave; media fra l'altezza e la sublimit&agrave;, furono <lb/>posposti alla detta quarta proposizione, la quale dicemmo dover essere stata <lb/>dimostrata e rassegnata in ordine delle prime. </s>

<s>Quel galileiano teorema, in <pb xlink:href="020/01/2301.jpg" pagenum="544"/>cui, con s&igrave; spedito modo elegante, dimostravasi che, essendo l'impeto oriz&shy;<lb/>zontale rappresentato dalla linea sublime, il verticale per ogni punto della <lb/>parabola veniva rappresentato dalla met&agrave; della semibase, &egrave; quale qui noi <lb/>dall'autografo lo trascriviamo, e che, se fosse stato noto al Viviani, gli ri&shy;<lb/>sparmiava la sollecitudine della riferita postilla: </s></p><p type="main">

<s>&ldquo; Parabola BD (fig. </s>

<s>290), describitur ab elevatione AB, cum altitudine <lb/>BC. </s>

<s>Ponatur AB esse tempus et impetum casus AB, sitque DE tangens pa&shy;<lb/><figure id="id.020.01.2301.1.jpg" xlink:href="020/01/2301/1.jpg"/></s></p><p type="caption">

<s>Figura 290<lb/>rabolam: erit EB aequalis BC. </s>

<s>Cumque BF sit su&shy;<lb/>bdupla amplitudinis CD, erit quoque media inter su&shy;<lb/>blimitatem AB, et altitudinem BC, eritque tempus <lb/>casus et impetus per BC in C. </s>

<s>Iuncta igitur AF erit <lb/>mensura impetus in D cadentis per ABD &rdquo; (MSS. <lb/>Gal., P. V, T. II, fol. </s>

<s>83). </s></p><p type="main">

<s>Sfugg&igrave; per&ograve; in tal proposito a Galileo stesso e <lb/>al Viviani una considerazione importante, per la <lb/>quale si sarebbero facilmente condotti a quella tanto <lb/>desiderata, e non mai conseguita semplicit&agrave; di co&shy;<lb/>struzione, che ne suggerisce l'uso del parallelo&shy;<lb/>grammo delle forze. </s>

<s>Si tiene infatti nel superior <lb/>teorema per dimostrato dal corollario alla quinta <lb/>proposizione del Dialogo, essere FB2=AB.BE, la <lb/>quale equazion duplicata d&agrave; 2FB.FB=AB.2BE, ossia DC.FB=AB.EC, <lb/>d'onde AB:FB=DC:EC, proporzione, da cui si conclude che, essendo AB <lb/>misura dell'impeto orizzontale, e FB del verticale, se DC si far&agrave; misura del&shy;<lb/>l'orizzontale, sar&agrave; EC invece misura del verticale, come del resto s'avrebbe <lb/>avuto, applicandovi la semplicissima regola del parallelogrammo. </s></p><p type="main">

<s>&Egrave; notabile che il Viviani giunse a questa medesima conclusione, a di&shy;<lb/>mostrar cio&egrave; che l'impeto orizzontale e il verticale son proporzionali alla <lb/>semibase e alla suttangente, e che perci&ograve; l'impeto totale vien rappresentato <lb/>dalla diagonale del rettangolo costruito sopra i due detti elementi della Pa&shy;<lb/>rabola. </s>

<s>Ma &egrave; bene assai pi&ugrave; notabile ch'ei concluda dall'errore una verit&agrave;, <lb/>verso la quale mostravasi tanto ritroso. </s></p><p type="main">

<s>Riduciamoci nuovamente sott'occhio la figura 286. Dice il Viviani di <lb/>aver provato che la tangente al punto C passa per L, dove arriva la LE <lb/>misura dell'impeto composto in C, e che, essendo AL media fra AD.AH, <lb/>ossia fra AE, AF, dalla proporzione AF:AL=AL:AE si conclude che <lb/>gl'impeti orizzontale e verticale possono essere cos&igrave; bene rappresentati da <lb/>AF, AL, come da AL, AE, ossia da CD semibase e da DE suttangente. </s>

<s>Ma <lb/>o fosse causa la fretta dello scrivere, o il lubrico della dottrina galileiana, <lb/>sopra la quale credeva nonostante di poter fermare il piede, scivol&ograve; in quel&shy;<lb/>l'errore che i nostri Lettori avranno di gi&agrave; notato, non essendo altrimenti <lb/>AL media fra AD, AH, ma fra AD, AE, le quali due linee, per essersi EC <lb/>condotta tangente in C, ed E costituito punto sublime, sono tra loro uguali. </s>

<s><lb/>Dall'equazione EA:AL=AL:AD, essendo AB=AE concludesi legitti-<pb xlink:href="020/01/2302.jpg" pagenum="545"/>mamente che l'impeto orizzontale e il verticale possono essere cos&igrave; rappre&shy;<lb/>sentati da EA, AL, come da AL, AE, ossia dalla semibase CD, e dalla sut&shy;<lb/>tangente DE, la quale suttangente &egrave; in questa particolar costruzione la somma <lb/>dell'altezza, e della sublimit&agrave; della parabola. </s></p><p type="main">

<s>&ldquo; Avendo io provato nella IX precedente (scrive il Viviani in quella sua <lb/>postilla al dialogismo, che segue alla quarta proposizione galileiana) che la <lb/>tangente in C passa per L, dove arriva la EL misura dell'impeto composto <lb/>in C, ed essendo AL media proporzionale fra le AD, AH, sar&agrave; AL media <lb/>ancora fra le AE, AF; onde AF:AL=AL:AE. </s>

<s>Ma quando AF &egrave; misura <lb/>dell'impeto orizzontale, la AL &egrave; misura dell'impeto perpendicolare; adun&shy;<lb/>que, se AL sar&agrave; misura dell'orizzontale, sar&agrave; AE misura del perpendicolare, <lb/>ovvero CD dell'orizzontale e DE del perpendicolare, e cos&igrave; seguir&agrave; in ogni <lb/>altro punto della parabola fuori di C. &rdquo; </s></p><p type="main">

<s>&ldquo; Di qui &egrave; manifesto che, se il cadente, giunto in C, restasse di pi&ugrave; <lb/>accelerarsi col moto perpendicelare, conservando poi in s&egrave; l'uno o l'altro <lb/>impeto, co'quali si trova quivi; continuerebbe a moversi per la tangente EC, <lb/>prodotta in infinito sotto C, perch&egrave; per quella sola direzione segue che il <lb/>mobile passa sempre di perpendicolo e di orizzonte parti proporzionali sem&shy;<lb/>pre agl'impeti perpendicolare ed orizzontale gi&agrave; concepiti nel punto C &rdquo; (MSS. <lb/>Gal., P. V, T. IX, pag. </s>

<s>262). </s></p><p type="main">

<s>Accennammo alla lubricit&agrave; della dottrina galileiana, nel dar regola di <lb/>misurare gl'impeti nella parabola, come a una delle occasioni date all'error <lb/>del Viviani, a cui non si pu&ograve; credere che non entrasse di ci&ograve; qualche so&shy;<lb/>spetto, come siam certi ch'entr&ograve; nell'animo dello stesso Galileo, quando, <lb/>per accertarsi se veramente l'impeto totale resulta uguale in potenza alle <lb/>potenze parziali, ricorse a farne la riprova coi numeri. </s>

<s>Nell'angolo sinistro <lb/>e inferiore del foglio, dov'&egrave; il Teorema galileiano ultimamente trascritto, <lb/>leggesi la seguente Nota illustrata dalla nostra figura 290: &ldquo; Attende num&shy;<lb/>quid tempus et impetus per AB, cum parabola BD, est idem cum tempore <lb/>et impetu per inclinationem AD &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>84). La ri&shy;<lb/>prova particolare di ci&ograve; consegue dalle fatte riprove delle m sure degl'im&shy;<lb/>peti, generalmente dimostrate e concluse in quel medesimo Teorema, dando <lb/>alle linee, prese a rappresentare il moto retto antecedente e il moto retto <lb/>conseguente, particolari valori numerici, e contentandosi dell'approssima&shy;<lb/>zione dei resultati, com'apparisce da questa Nota, che si trascrive: </s></p><p type="main">

<s>&ldquo; Tutta AC 140; e tanto sia il tempo e l'impeto in C, il quale impeto <lb/>&egrave; di passare 280 nel tempo 140. &rdquo; </s></p><p type="main">

<s>&ldquo; AB 80: sar&agrave; il suo tempo la media tra AC, AB, cio&egrave; tra 140 e 80, <lb/>che &egrave; 105, e per&ograve; nell'orizzontale BG la velocit&agrave; sar&agrave; di passare, nel tempo <lb/>105 di AB, 160, che &egrave; il doppio di AB. </s>

<s>Ma il tempo di BC, dalla quiete <lb/>in B, &egrave; la media tra AC 140 e BC 60, che &egrave; 91; adunque diremo: in que&shy;<lb/>sto tempo 91, quanto si passer&agrave; di BG, della quale nel tempo di AB, che <lb/>&egrave; 105, se ne passa 160? &mdash; Per la regola se ne passer&agrave; 138, e torna bene, <lb/>cha tanto &egrave; CD. &rdquo; </s></p><pb xlink:href="020/01/2303.jpg" pagenum="546"/><p type="main">

<s>&ldquo; Sia AB 80, tempo ed impeto in B, che nella BG, in tempo 80, pas&shy;<lb/>ser&agrave; 160. Il tempo di BC sar&agrave; la media tra BC 60, e AB 80, che sar&agrave; 69. <lb/>In questo tempo 69, quanto si passer&agrave; &icirc;n BG, dove in 80 di tempo si <lb/>passa 160? &mdash; Si passa 138 e torna bene. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; AB 60, tempo et impeto; BC 30. Sar&agrave; suo tempo et impeto la media <lb/>tra 60 e 30, che &egrave; 42 1/3; adunque tutto il tempo di ABD &egrave; 102 1/3. L'am&shy;<lb/>piezza CD &egrave; doppia della media tra AB, BC: &egrave; dunque 84 2/3. Ma tutta AC <lb/>&egrave; 90, e CD 84 2/3; adunque AD sar&agrave; 123, ed il tempo di tutta AD sar&agrave; <lb/>quanto la media tra DA e AG, che torna 100 e pi&ugrave;, e mostra star bene &rdquo; <lb/>(ivi, a tergo del foglio 86). </s></p><p type="main">

<s>Assicurato cos&igrave; da queste riprove, confid&ograve; Galileo che fossero vere le <lb/>regole da lui dimostrate per la misura degl'impeti. </s>

<s>Abbiamo detto in che <lb/>modo si studiasse il Viviani di confermarle, e come, in volerle render pi&ugrave; <lb/>semplici, s'incontrasse finalmente dopo lunghi raggiri nella regola stessa del <lb/>parallelogrammo. </s>

<s>Ora &egrave; da vedere come a tal conclusione riuscissero pure le <lb/>vie segnate dal Torricelli, bench&egrave; siano rifiorite cos&igrave; di eleganza nuova, da <lb/>ingannar la fatica e il tedio della lunghezza. </s>

<s>&Egrave; dall'insigne Promotore con&shy;<lb/>seguito un tale effetto principalmente, con introdur la parabola per la scala <lb/><figure id="id.020.01.2303.1.jpg" xlink:href="020/01/2303/1.jpg"/></s></p><p type="caption">

<s>Figura 291<lb/>degl'impeti e dei tempi nelle libere cadute <lb/>naturali. </s>

<s>Ridottaci nuovamente sotto gli oc&shy;<lb/>chi la figura, sopra la quale vedemmo dianzi <lb/>come Galileo condusse la dimostrazion sua <lb/>laboriosa, il Torricelli cos&igrave; ragionava: Dati <lb/>gli spazi AC, AB (fig. </s>

<s>291), se AC &egrave; la <lb/>misura del tempo e dell'impeto per AC, la <lb/>misura del tempo e dell'impeto per AB <lb/>sar&agrave; la media fra AC, e AB: che se l'im&shy;<lb/>peto in C si rappresenta con la orizzontale <lb/>DC, e l'impeto in B con la orizzontale BE, avremo dunque CD:BE= <lb/>AC:&radic;AC.AB=&radic;AC:&radic;AB, ossia CE2:DB2=AC:AB; equazione di una <lb/>parabola. </s>

<s>&ldquo; Hinc manifestum est, ne conclude perci&ograve; il Torricelli, impetus <lb/>gravium in fine portionum diametri parabolae esse inter se ut lineae, quae <lb/>ordinatim applicantur ad extrema ipsarum portionum puncta &rdquo; (Op. </s>

<s>geom. </s>

<s><lb/>cit., pag. </s>

<s>113). </s></p><p type="main">

<s>Vedendosi di qui aprire un campo nuovo, erasi poco prima compia&shy;<lb/>ciuto il Promotore che, di quel che egli veniva ora ad annunziare nel suo <lb/>corollario, <emph type="italics"/>non scripsit Galilaeus<emph.end type="italics"/> (ibid., pag. </s>

<s>110). Ed &egrave; ci&ograve; verissimo, giu&shy;<lb/>dicando dai Dialoghi e dalle altre opere pubblicamente note, ma fra'Mano&shy;<lb/>scritti &egrave; rimasta autografa una proposizione, la quale fa mirabile riscontro <lb/>con la X torricelliana del primo libro. </s>

<s>La proposizione di Galileo, tirata fuori <lb/>da quel prunaio dove l'abbiamo trovata, &egrave; dunque tale. </s></p><p type="main">

<s>Siano AB, AC (fig. </s>

<s>292) due spazi, e AD medio fra loro. </s>

<s>Se AB rap&shy;<lb/>presenta il tempo per AB, AD rappresenter&agrave; <gap/>l tempo per AC. </s>

<s>Sia poi BE <lb/>la velocit&agrave; e l'impeto in B, e si faccia BA:AD=BE:CF; sar&agrave; CF l'im-<pb xlink:href="020/01/2304.jpg" pagenum="547"/>peto in C, presa AC per misura dello spazio. </s>

<s>Ma se, condotta la AE, si <lb/>prolunghi infino a che ella non s'incontri con DQ in Q, sar&agrave; DQ=FC <lb/>misura dell'impeto in D, presa AD per misura del tempo. </s>

<s>Ora, dal dato <lb/>AD2=CA.AB avendosi CA:AD=AD:AB=QD:EB=CF:EB, qua&shy;<lb/><figure id="id.020.01.2304.1.jpg" xlink:href="020/01/2304/1.jpg"/></s></p><p type="caption">

<s>Figura 292<lb/>drando, si concluder&agrave; CA2:AD2=CF2:EB2. </s>

<s>Dal me&shy;<lb/>desimo dato, e dall'identica AC2=AC2 si concluder&agrave; <lb/>pure AC2:AD2=AC2:AC.AB, onde avremo dalle due <lb/>conclusioni AC:AB=CF2:BE2. </s>

<s>Ma trascriviamo le <lb/>precise parole di Galileo: </s></p><p type="main">

<s>&ldquo; Sit ut BA ad AD, ita DA ad AC, et sit BE gra&shy;<lb/>dus velocitatis in B, et ut BA ad AD ita sit BE ad CF: <lb/>erit CF gradus velocitatis in C. </s>

<s>Cum itaque sit ut CA <lb/>ad AD, ita CF ad BE, erit et ut quadratus CA ad qua&shy;<lb/>dratum AD, ita quadratus CF ad quadratum BE. </s>

<s>Ut <lb/>autem quadratus CA ad quadratum AD, ita CA ad AB: <lb/>ut igitur CA ad AB, ita quadratus CF ad quadratum BE. </s>

<s><lb/>Sunt ergo puncta E, F in parabola &rdquo; (MSS. Gal., P. V, <lb/>T. II, fol. </s>

<s>152). Or perch&egrave;, sceso naturalmente il grave <lb/>dal vertice A della parabola in B e in C, gli corrispon&shy;<lb/>dono gl'impeti EB, FC, che son le ordinate delle por&shy;<lb/>zioni del diametro AB, AC; <emph type="italics"/>hinc<emph.end type="italics"/> manifestum est, si pu&ograve; soggiunger per <lb/>corollario anche a questa galileiana, <emph type="italics"/>impetus gravium, in fine portionum <lb/>diametri parabolae, esse inter se ut lineae, quae ordinatim applicantur <lb/>ad extrema ipsarum portionum puncta.<emph.end type="italics"/></s></p><p type="main">

<s>Rimase per&ograve; per Galil&egrave;o questa proposizione infruttuosa, ma il Torri&shy;<lb/>celli, invocando altre propriet&agrave; geometriche della parabola, le applic&ograve; a pro&shy;<lb/>movere mirabilmente la scienza del moto, e a determinare la misura degli <lb/>impeti, per una via tutta nuova. </s>

<s>Fra quelle geometriche propriet&agrave; notabile <lb/>&egrave; questa, che cio&egrave; sempre nella parabola terza proporzionale, dopo un'ascissa <lb/>qualunque e la corrispondente ordinata, &egrave; una linea, alla quale gli antichi <lb/>davano il nome di <emph type="italics"/>Lato retto,<emph.end type="italics"/> corrispondente a quel che ora i moderni chia&shy;<lb/><figure id="id.020.01.2304.2.jpg" xlink:href="020/01/2304/2.jpg"/></s></p><p type="caption">

<s>Figura 293<lb/>man <emph type="italics"/>Parametro.<emph.end type="italics"/> Per applicare ai moti parabolici questo <lb/>puro elemento geometrico, incomincia il Torricelli a di&shy;<lb/>mostrare, cos&igrave; presso a poco, nella VII proposizion del <lb/>primo libro, che la sublimit&agrave; della parabola &egrave; la quarta <lb/>parte del Lato retto. </s></p><p type="main">

<s>Sia CA (fig. </s>

<s>293) la parabola, AD la sua ampiezza, <lb/>e CS la sublimit&agrave;. </s>

<s>Chiamato P il parametro, abbiamo, <lb/>per la data definizione di questo elemento, P=AD2/CD: <lb/>ed essendo MD=AD/2, sar&agrave; P=4.MD2/CD. </s>

<s>Per il corolla&shy;<lb/>rio poi alla V proposizione di Galileo (Alb. </s>

<s>XIII, 248) &egrave; MD2=CD.CS, <lb/>e perci&ograve; P=4.CD.CS/CD=4.CS, ossia CS=P/4. &ldquo; Quando (dice il Tor-<pb xlink:href="020/01/2305.jpg" pagenum="548"/>ricelli) sumitur in axe parabolae, ut in praecedenti figura, ex vertice linea <lb/>CF, quae aequalis sit quartae parti lateris recti, tunc punctum F vocatur <lb/><emph type="italics"/>focus<emph.end type="italics"/> parabolae. </s>

<s>Manifestum ergo est punctum sublime S et focum F ae&shy;<lb/>qualiter distare a vertice parabolae; nempe tantum utrinque, quanta est <lb/>quarta pars Lateris recti &rdquo; (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>112). </s></p><p type="main">

<s>Soggiunge poi il Torricelli stesso che l'ordinata condotta dal foco &egrave; <lb/>doppia della sublimit&agrave;, o della porzione dell'asse intercetta al vertice, ci&ograve; <lb/>che si pu&ograve; cos&igrave;, sopra la solita figura, con facilit&agrave; dimostrare: Sia FG quel&shy;<lb/>l'ordinata:avremo CF:CD=GF2:AD2=GF2:4MD2.Ma MD2=CD.CS, <lb/>dunque CF:CD=GF2:4.CD.CS; d'onde GF2=4CF.CS=4.CF2, e <lb/>perci&ograve; GF=2.CF=2CS. </s></p><p type="main">

<s>Ora, passando ad applicare queste propriet&agrave; geometriche della parabola <lb/>ai moti proiettizi, osserva il Torricelli che GF, misura del tempo equabile <lb/>dopo l'accelerato per CF o per SC, &egrave; altresi la misura dell'impeto orizzon&shy;<lb/>tale in ciascun punto della curva, come per esempio in A, in cui l'impeto <lb/>verticale fu dimostrato aver per misura l'ordinata AD. </s>

<s>Dato dunque il foco, <lb/>non richiedevasi altro, per potersi determinare le componenti dell'impeto, in <lb/>qual si voglia punto della parabola. </s>

<s>La resultante poi sarebbe secondo Ga&shy;<lb/>lileo data dall'ipotenusa, costruita nel triangolo rettangolo avente AD, GF <lb/>per cateti, e il Torricelli mostra di professare anch'egli, specialmente nel <lb/>suo secondo libro, le false dottrine insegnate nella proposizione seconda del <lb/>quarto dialogo galileiano. </s>

<s>Ma &egrave; notabile ch'egli dimostri, e autorevolmente <lb/>sanzioni, la regola del parallelogrammo, dalla quale infatti conclude che <lb/>l'impeto composto in A &egrave; misurato dalla diagonale del rettangolo costruito <lb/>sopra i lati AD, GF, o sopra le linee ED, AD, che sono ad essi lati pro&shy;<lb/>porzionali. </s></p><p type="main">

<s>Del modo come, nella XVIII di questo primo libro torricelliano, si di&shy;<lb/>mostra quella regola del parallelogrammo, avremo in quest'altra parte della <lb/>nostra Storia della Meccanica importantissima occasion di discorso: ora &egrave; da <lb/>vedere come per il Torricelli stesso sia vero che, condotta la tangente AE, <lb/>le linee AD, GF, dalle quali verrebbero immediatamente misurati gli im&shy;<lb/>peti in A, sian proporzionali alla suttangente ED, e alla semibase AD della <lb/>parabola, d'onde ne risulti l'impeto totale esibito dalla stessa tangente AE, <lb/>riguardata come la diagonale del rettangolo, che avesse AD per base, e <lb/>DE per altezza. </s>

<s>La dimostrazione del resto &egrave; facilissima perch&egrave; dalla es&shy;<lb/>senza del Parametro, che seguiteremo a chiamar P, abbiamo l'equazione <lb/>AD:P=DC:AD, la quale, sostituitovi P=4.CF=2GF, si trasforma <lb/>nell'altra AD:2GF=DC:AD; ossia AD:GF=ED:AD. </s></p><p type="main">

<s>Potrebbesi domandare perch&egrave; dunque non applic&ograve; il Torricelli la re&shy;<lb/>gola del parallelogrammo immediata? </s>

<s>Ma essendo la risposta non breve, e <lb/>aspettando altro luogo nella nostra Storia, basti ripeter per ora quel che <lb/>poco fa s'accennava, che cio&egrave; non seppe nemmen egli scotere il prepotente <lb/>giogo galileiano, contento d'aver trasformati i rigidi legami, con i quali tutti <lb/>gli altri vi si tenevano avvinti, in lentissime trecce di fiori. </s></p><pb xlink:href="020/01/2306.jpg" pagenum="549"/><p type="main">

<s>Dei fiori di eleganza matematica, sparsi nel primo libro torricelliano, e <lb/>fra'quali s'allega il frutto di quelle proposizioni, ordinate ad illustrare il <lb/>modo di misurare gl'impeti, nella semiparabola descritta dai tiri di punto <lb/>in bianco; debbono, dai brevi saggi dati, i Lettori averne sentito il gusto: <lb/>ora &egrave; da dire come il Torricelli stesso illustri l'altro modo, che Galileo pro&shy;<lb/>pone per misurare gl'impeti, quando l'obice elevato descrive la parabola <lb/>intera. </s></p><p type="main">

<s>Sia l'elevazione seconda AH (fig. </s>

<s>294), e con essa descrivasi la para&shy;<lb/>bola ABC: condotta la orizzontale AC, domandava la nuova scienza a Ga&shy;<lb/>lileo qual misura d'impeto si dovesse assegnare al proietto in A, perch&egrave; si <lb/>venisse a disegnare la detta parabola. </s>

<s>Per rispondere a ci&ograve;, partiva dalla <lb/><figure id="id.020.01.2306.1.jpg" xlink:href="020/01/2306/1.jpg"/></s></p><p type="caption">

<s>Figura 294<lb/>considerazione del tiro eretto nel perpendicolo, in cui l'impeto necessario a <lb/>sollevare il proietto, per esempio in F, &egrave; tanto, quanto sarebbe del cadente <lb/>naturale da F in A. </s>

<s>Ma nel tiro elevato una parte dell'impeto naturale si <lb/>consuma nello spingere il proietto per l'orizzonte, cosicch&egrave; non rimane di <lb/>lui che la parte BD, ossia EA, la quale corrispondendo all'altezza lascia al&shy;<lb/>l'altra EF rappresentare la sublimit&agrave; della parabola. </s>

<s>Sarebbe dunque ben <lb/>dimostrato, argomentava Galileo, che l'impeto in A &egrave; uguale a quello del <lb/>cadente da F, quando si dimostrasse che la potenza di AF &egrave; uguale alle <lb/>potenze dell'altezza e della sublimit&agrave; sommate insieme. </s>

<s>La dimostrazione &egrave; <lb/>fatta nel VII teorema (Alb. </s>

<s>XIII, 253), dove si dice che la potenza di AE, <lb/>ossia dell'altezza, &egrave; data dalla media fra AF, e AE, e che la potenza della <lb/>sublimit&agrave; EF &egrave; data dalla media fra AF, FE. Ora, che la somma di tali due <lb/>potenze o quadrati sia uguale al quadrato di AF, lo deduce Galileo in forza <lb/>di un lemma gi&agrave; premesso al teorema, nel qual lemma, costruito sopra AF <lb/>il semicerchio AGF, apparisce manifesto, dal triangolo rettangolo AGF, che <lb/>essendo le due medie FG, AG, i quadrati di queste sommati insieme sono <lb/>uguali al quadrato di AF. </s></p><p type="main">

<s>Il Torricelli ridusse il lemma galileiano a proposizion principale, che &egrave; <lb/>la XXI del secondo suo libro (pag. </s>

<s>174), e il semicerchio si congiunse mi-<pb xlink:href="020/01/2307.jpg" pagenum="550"/>rabilmente per lui con la parabola a mostrar circa il moto l'ingegno e i <lb/>lusi della Natura. </s>

<s>&ldquo; Sit AE altitudo, et FE sublimitas parabolae: ergo, im&shy;<lb/>petus cadentis per FE sublimitatem parabolae erit ut linea FG media pro&shy;<lb/>portionalis inter AF, EF. </s>

<s>At iste impetus cadentis ex F in E est ille purus <lb/>horizontalis, qui lationi inest in quolibet puncto parabolae, et est invariabi&shy;<lb/>lis: Quare in unoquoque puncto parabolae impetus horizontalis erit ut li&shy;<lb/>nea FG. &rdquo; </s></p><p type="main">

<s>&ldquo; Perpendicularis vero impetus, qui est in primo lationis puncto, sic <lb/>determinabitur: manente semper unica suppositione, impetum scilicet casus <lb/>per FA esse ipsam FA; impetus perpendicularis, in fine parabolae C, est <lb/>tamquam naturaliter cadentis ex B in D, vel ex E in A. </s>

<s>Est ergo media <lb/>proportionalis AG &rdquo; (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>174). Di qui ne conclude esser la <lb/>somma delle potenze AG, FG uguale alla potenza AF, come si conclude per <lb/>Galileo, alle dottrine del quale dunque ancora il Torricelli ritorna, lasciata <lb/>la sicura e semplicissima regola del parallelogrammo. </s>

<s>Eppure era facile av&shy;<lb/>vedersi che, avendosi, per la similitudine dei triangoli, AF:AG:FG= <lb/>AH:HD:AD, ci&ograve; che dimostra corrispondersi la tangente col diametro, e <lb/>la semibase e la suttangente della parabola con le due suttese agli archi; la <lb/>costruzione del semicerchio non si riduceva a pi&ugrave; che a una lussuriosa bel&shy;<lb/>lezza della scienza. </s></p><p type="main">

<s>Primo a ritornare, fra'seguaci di Galileo, a quella semplicit&agrave; di costru&shy;<lb/>zione, che non si dilunga dalla regola del parallelogrammo, fu il Borelli <lb/>nella proposizione LV <emph type="italics"/>De vi percussionis.<emph.end type="italics"/> Ivi egli osserva che il proietto <lb/>esploso in B, nella precedente figura, giunge in A con impeto composto del&shy;<lb/>l'orizzontale equabile per AD, e del verticale accelerato per BD, il quale <lb/>pure pu&ograve; trasformarsi in equabile, raddoppiandone lo spazio nella suttan&shy;<lb/>gente DH. &ldquo; Et proinde erit AH tangens parabolam, quae inclinationem in&shy;<lb/>cidentiae designabit, atque hypothenusa AH ostendet impetum eiusdem cor&shy;<lb/>poris in actu incidentiae &rdquo; (Bononiae 1667, pag. </s>

<s>105). </s></p><p type="main">

<s>Non solamente per&ograve; si riducono in questa stessa proposizione alla de&shy;<lb/>siderata semplicit&agrave; le costruzioni di Galileo, ma se ne promove altres&igrave; la <lb/>scienza degl'impeti, perch&egrave;, mentre, nel quarto Dialogo delle Scienze nuove, <lb/>sempre si considera l'impeto quant'&egrave; in s&egrave; medesimo, cio&egrave; rispetto a quel <lb/>piano, in cui perpendicolarmente egli percote; il Borelli lo considera quanto <lb/>egli &egrave; rispetto al piano resistente, variato solamente dalla diversit&agrave; degl'an&shy;<lb/>goli dell'incidenza, a proporzion del seno dei quali dimostra farsi nel per&shy;<lb/>pendicolo la percossa. </s>

<s>Cosicch&egrave;, nel tiro di punto in bianco da B, la palla <lb/>del cannone giunge in A con un impeto verticale misurato da HD, ch'&egrave; il <lb/>seno dell'angolo dell'incidenza HAD: d'onde ci &egrave; dato intendere il para&shy;<lb/>dosso come la medesima bomba, che varrebbe a rovesciare il muro di una <lb/>saldissima torre, riesca impotente a passare il velo di un'acqua ghiacciata. </s></p><p type="main">

<s>&Egrave; da notar per&ograve; che XXIII anni prima era stata, cos&igrave;, promossa la <lb/>scienza galileiana dal Torricelli, il quale dice di aver trovato <emph type="italics"/>intatto<emph.end type="italics"/> il pro&shy;<lb/>blema a'suoi tempi (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>239), ne'quali erano sconosciuti <pb xlink:href="020/01/2308.jpg" pagenum="551"/>i manoscritti di Leonardo da Vinci. </s>

<s>Il Torricelli medesimo, avendo, nel co&shy;<lb/>rollario alla proposizion XXI del suo secondo libro, osservato che gl'impeti <lb/>perpendicolari non crescono secondo l'altezza della parabola, ma secondo la <lb/>corda del semicerchio, &ldquo; hinc animadvertere licet, immediatamente sog&shy;<lb/>giunge, futurum fore ut idem globus ferreus, eodem tormento explosus, <lb/>dum ad horizontem redit, aliquando tecta fornicesque domorum traiiciat, <lb/>quandoque vero, neque glaciem alicuius lacunae laedere poas&icirc;t &rdquo; (ibid., <lb/>pag. </s>

<s>174). La quarta torricelliana di questo medesimo libro secondo, inse&shy;<lb/>gna pure il modo di determinare gl'impeti in ciascuna parte della para&shy;<lb/>bola, in un modo assai pi&ugrave; semplice, e non meno dimostrativo di quello del <lb/>Borelli, prendendo le porzioni delle tangenti &ldquo; inter duas parallelas diame&shy;<lb/>tro interceptae &rdquo; (ibid., pag. </s>

<s>161); e nella quinta seguente dimostra quel <lb/>che Galileo parve avere dimenticato dopo tant'anni, da che aveva assistito <lb/>all'esperienze di Guidubaldo, che cio&egrave; gl'impeti &ldquo; in punctis parabolae ae&shy;<lb/>qualiter utrinque a vertice distantibus, aequales sunt inter se licet alter ascen&shy;<lb/>dat, alter vere descendat &rdquo; (ibid., pag. </s>

<s>162). </s></p><p type="main">

<s>Si direbbe che queste torricelliane sottigliezze fossero meglio atte di <lb/>tutte le altre a penetrare addentro a ogni parte del profondo soggetto, so&shy;<lb/>lamente toccato da Galileo, un sottil pensiero del quale vedesi mirabilmente <lb/>illustrato dalla quarta sopra citata proposizione, che mostra come nel ver&shy;<lb/>tice della parabola, bench&egrave; siavi spento ogn'impeto verticale, non &egrave; per&ograve; la <lb/>quiete assoluta. </s>

<s>&ldquo; Il mobile (leggesi cos&igrave; espresso in una Nota quel pen&shy;<lb/>siero galileiano) nel descrivere la parabola, bench&egrave; angustissima, non passa <lb/>per la quiete nel termine ultimo, ma s&igrave; bene nel moversi per la perpendi&shy;<lb/>colare, cio&egrave; ritornando per la medesima retta in gi&ugrave;: e se Aristotile avesse <lb/>detto che nel moto riflesso si passa per la quiete, avrebbe detto bene &rdquo; (MSS. <lb/>Gal., P. V, T. IV, fol. </s>

<s>15 a tergo). </s></p><p type="main">

<s>Nella medesima quarta torricelliana immediatamente, e non in alcuno <lb/>de'teoremi di Galileo trova pure quest'altra nota del Viviani il suo pi&ugrave; <lb/>chiaro commento: &ldquo; Sia l'AC (fig. </s>

<s>295) parallela all'orizzonte, e la para&shy;<lb/>bola ABC, per la quale venga spinto o cacciato il mobile S: &egrave; manifesto <lb/><figure id="id.020.01.2308.1.jpg" xlink:href="020/01/2308/1.jpg"/></s></p><p type="caption">

<s>Figura 295<lb/>per Galileo che, fin che dura la salita, <lb/>l'impeto del proietto S va diminuen&shy;<lb/>dosi, cio&egrave; fino al punto B. </s>

<s>Inclinando <lb/>poi per la BC al basso, l'impeto si do&shy;<lb/>ver&agrave; augumentare, onde ne segue che <lb/>il moto sia tardissimo in B, cio&egrave; nel <lb/>mezzo del suo viaggio ABC, e ci&ograve; si <lb/>potr&agrave; esperimentare con frecce o bolzoni. </s>

<s>Adunque, domandandosi a uno: <lb/>dovendo tu esser ferito da una freccia, tirata secondo la linea ABC, dove <lb/>vorresti stare? </s>

<s>Egli direbbe in C, ma la minore offesa sarebbe in B &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>14 a t.). </s></p><pb xlink:href="020/01/2309.jpg" pagenum="552"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Tali, quali sono stati fin qui discorsi, furono i principii e i progressi <lb/>delle speculazioni di Galileo, e de'suoi primi Promotori, per determinare, <lb/>in ciascun punto della parabola, la forza del colpo, che farebbe il proietto <lb/>sopra un piano contrappostogli nel suo libero viaggio. </s>

<s>Dopo questo, dicemmo <lb/>essere l'altro argomento, che si proponeva a trattare alla Scienza nuova, <lb/>quello di dimostrar dalla teoria del moto parabolico le verit&agrave; sperimentali <lb/>pronunziate gi&agrave; dal Tarlaglia intorno alla maggiore ampiezza del tiro semi&shy;<lb/>retto, e alla ugual distanza orizzontale, a cui giungono i proietti con eleva&shy;<lb/>zioni, che manchino ugualmente o eccedano da quella stessa semiretta per <lb/>angoli uguali. </s>

<s>I primi processi dimostrativi, che ci si rivelarono in quella <lb/>Nota manoscritta, illustrata dalla figura 285, furono quelli stessi, che poi <lb/>tenne Galileo nelle proposizioni inserite nel Dialogo, e delle quali si com&shy;<lb/>pone, come si disse, la seconda parte del suo nuovo trattato. </s></p><p type="main">

<s>Che il tiro dunque, messo l'obice a mezza squadra, dia veramente la <lb/>massima volata, anche qui, ci&ograve; nel Dialogo IV, come l&agrave;, nella detta Nota, <lb/>si conclude per corollario dalla VII proposizione, che dice: &ldquo; In proiectis, <lb/>a quibus semiparabolae eiusdem amplitudinis describuntur, minor requiri&shy;<lb/>tur impetus in eo, quod describit illam, cuius amphtudo suae altitudinis sit <lb/>dupla, quam in quolibet alio &rdquo; (Alb. </s>

<s>XIII, 249). </s></p><p type="main">

<s>Sia l'ampiezza DC (fig. </s>

<s>296) della parabola BD doppia all'altezza BC, <lb/>e si conduca l'AD tangente in D, secondo la quale sar&agrave; d&igrave;retto il tiro, con <lb/><figure id="id.020.01.2309.1.jpg" xlink:href="020/01/2309/1.jpg"/></s></p><p type="caption">

<s>Figura 296<lb/>l'inclinazione ADC semiretta. </s>

<s>L'impeto composto in D <lb/>&egrave; per le cose gi&agrave; dimostrate, dice Galileo, rappresen&shy;<lb/>tato dall'ipotenusa AE. </s></p><p type="main">

<s>Con la medesima ampiezza DC, ma con maggiore <lb/>altezza CG, abbiasi l'altra parabola GD, a descriver <lb/>la quale l'impeto necessario in D, composto del moto <lb/>retto antecedente per la sublimit&agrave;, e del conseguente <lb/>per l'altezza CG della parabola, &egrave; stato detto come <lb/>debbasi misurarlo. </s>

<s>Se GL &egrave; terza proporzionale dopo <lb/>KG, GH, sappiamo costituirsi in L il punto sublime, <lb/>da cui cadendo in G il grave d&agrave; la misura dell'im&shy;<lb/>peto retto antecedente. </s>

<s>Ora, essendosi dianzi implici&shy;<lb/>tamente supposto che sia AB la misura del tempo e <lb/>dell'impeto per AB, la misura dell'impeto, dovuto al moto del cadente per <lb/>LG, sar&agrave; una media fra AB, LG, la quale sia per esempio GM. </s></p><p type="main">

<s>Parimente, essendo NG media fra AB, GC, verr&agrave; per lei rappresentato <lb/>l'impeto, dovuto al moto retto conseguente per l'altezza GC. </s>

<s>Sar&agrave; dunque <lb/>l'ipotenusa NM la misura dell'impeto composto, necessario in D a descriver <pb xlink:href="020/01/2310.jpg" pagenum="553"/>la semiparabola GD, e si conclude perci&ograve; il proposto assunto col dimostrar <lb/>che NM &egrave; maggiore di AE. </s>

<s>In qual modo poi si faccia la dimostrazione lo <lb/>vedremo or ora, per dire intanto che, nella precitata VII proposizione, non <lb/>contempla Galileo che il caso, in cui la direzione del tiro eccede la semi&shy;<lb/>retta. </s>

<s>L'altra proposizione, in cui supponesi il caso, che l'angolo dell'in&shy;<lb/>clinazione manchi dal semiretto, &egrave; rimasta ancora fra'manoscritti, e bench&egrave; <lb/>la somiglianza de'processi dimostrativi possa aver dispensato l'Autore dal&shy;<lb/>l'inserirla nel Dialogo, noi crediamo per molte ragioni che sia bene met&shy;<lb/>terla alla notizia de'nostri Lettori. </s></p><p type="main">

<s>&ldquo; Sit CE (fig. </s>

<s>297) dupla ad EA, et FC tangat parabolam AC. </s>

<s>Sit adhuc <lb/>HD aequalis CE, et maior quam dupla ad DG, et HK tangat parabolam GH, <lb/><figure id="id.020.01.2310.1.jpg" xlink:href="020/01/2310/1.jpg"/></s></p><p type="caption">

<s>Figura 297<lb/>et ut KG ad GI, ita sint IG ad GL: <lb/>erit L punctum casus per parabo&shy;<lb/>lam. </s>

<s>Et sit GX media inter AE, GD; <lb/>GS vero media inter IG (eguale ad <lb/>AB che &egrave; eguale ad AE) GL: de&shy;<lb/>monstrandum est SX maiorem esse <lb/>quam FB. &rdquo; </s></p><p type="main">

<s>&ldquo; Quadratus FB aequatur qua&shy;<lb/>dratis FA, AB; hoc est duplum qua&shy;<lb/>drati GI: et quadratus SX aequatur <lb/>quadratis SG, GX: ostende ergo qua&shy;<lb/>drata SG, GX, vel quadratum SX, esse plus quam dupla quadrati IG. &rdquo; </s></p><p type="main">

<s>&ldquo; Quadratum GX aequatur reclangulo IGD: ut DG ad GX, ita GX ad <lb/>GI; ergo, ut DG ad GI, ita quadratum DG ad quadratum GX. </s>

<s>Ut autem DG, <lb/>seu KG, ad GI, ita IG ad GL. Quia, ut quadratum XG ad quadratum GI, <lb/>ita IG ad GL; ut autem IG ad GL, ita quadratum IG, ad quadratum me&shy;<lb/>diae inter IG, GL, quae sit GS: ergo ut quadratum XG ad quadratum GI, <lb/>ita quadratus GI ad quadratum GS: est autem XG minor quam GI, quia <lb/>et DG minor est quam GI; ergo quadratum IG minor est quadrato me&shy;<lb/>diae &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>111). </s></p><p type="main">

<s>Sin qui tutto va bene, correttosi da noi nel copiare lo sbaglio fatto per <lb/>inavvertenza da Galileo, il quale, essendosi proposto di dimostrare che SX <lb/>&egrave; maggiore di FB, scrisse <emph type="italics"/>ostende ergo quadrata LG, GX,<emph.end type="italics"/> invece di <emph type="italics"/>qua&shy;<lb/>drata SG, GX, esse plus quam dupla quadrati IG.<emph.end type="italics"/> N&egrave; accortosi dello sba&shy;<lb/>glio alla fine della dimostrazione, dop'aver concluso l'assunto, che cio&egrave; la <lb/>somma de'quadrati GX, GS &egrave; pi&ugrave; che doppia del quadrato di GI, soggiunge: <lb/><emph type="italics"/>ergo multo plus quam dupla erunt quadrata XG, GL,<emph.end type="italics"/> essendo, nel par&shy;<lb/>ticolar caso contemplatosi della direzione del tiro minore della semiretta, GL <lb/>maggiore di GS. </s>

<s>La final conclusione dunque, che soggiungesi nel Mano&shy;<lb/>scritto galileiano, dop'aver dimostrato che il quadrato di IG &egrave; minore del <lb/>quadrato della media, &egrave; come segue: &ldquo; Sed cum tria quadrata XG, GI et <lb/>mediae sint proportionalia, erunt extrema plusquam dupla quadrati GI. </s>

<s>Ergo <lb/>multo plus quam dupla erunt quadrata XG, GL &rdquo; (ibid.). </s></p><pb xlink:href="020/01/2311.jpg" pagenum="554"/><p type="main">

<s>Nella VII proposizione del Dialogo, dall'essersi in simil guisa dimo&shy;<lb/>strato che i tre quadrati NG2, KG2, GM2 sono in proporzione continua, si <lb/>conclude che la somma de'due estremi NG2+GM2=NM2 &egrave; maggiore di <lb/>2KG2=AE2. </s>

<s>&ldquo; Ergo linea MN maior linea EA, quod erat domonstran&shy;<lb/>dum &rdquo; (Alb. </s>

<s>XIII, 250). Dimostratosi cos&igrave;, in questa stampata, che maggior <lb/>impeto si richiede a fare il tiro elevato sopra il semiretto, e nella mano&shy;<lb/>scritta che maggior impeto pur si richiede a fare il tiro sotto il semiretto, <lb/>posto che debbano i mobili descriver parabole di ampiezza uguale a quella, <lb/>che si descriverebbe nella stessa elevazion semiretta; ne deduce Galileo per <lb/>corollario che, se dunque si daranno impeti uguali, &ldquo; maxima proiectio, seu <lb/>amplitudo semiparabolae, sive integrae parabolae, erit ea, quae consequitur <lb/>ad elevationem anguli semirecti &rdquo; (ibid.). </s></p><p type="main">

<s>Veniva cos&igrave;, per la prima volta, matematicamente dimostrato quel che <lb/>il Tartaglia aveva asserito un secolo prima per vero, confermatovi dalle espe&shy;<lb/>rienze dei bombardieri di Urbino. </s>

<s>Ma un'altra cosa, anche pi&ugrave; pellegrina, <lb/>aveva come accennammo prenunziato lo stesso Tartaglia, che cio&egrave; <emph type="italics"/>un pezzo <lb/>de artiglieria posseva, per due diverse vie, over elevationi, percotere in <lb/>un medemo loco,<emph.end type="italics"/> gli angoli delle quali elevazioni fossero quelli, che ecce&shy;<lb/>dono e mancano ugualmente dal semiretto. </s>

<s>Anche questo, che pure aveva <lb/>aspetto di vero, e sembrava riscontrare con l'esperienze, dovevasi dimostrar <lb/>dalla nuova Scienza, concludendolo dai principii del moto parabolico, e Ga&shy;<lb/>lileo incominci&ograve; a tentare se, cos&igrave; ragionando, gli riusciva di conseguire <lb/>l'intento. </s></p><p type="main">

<s>Sia il triangolo rettangolo ABC (fig. </s>

<s>298) semiretto in B, e si facciano <lb/>sotto e sopr'esso gli angoli ABE, ABD uguali. </s>

<s>Divisa EC in F nel mezzo, <lb/><figure id="id.020.01.2311.1.jpg" xlink:href="020/01/2311/1.jpg"/></s></p><p type="caption">

<s>Figura 298<lb/>conducasi parallela a BC la GF, la quale sia media <lb/>tra EF, FL. </s>

<s>Immaginando che passi per F, B una <lb/>semiparabola, sarebbe questa precisamente quella, <lb/>che si descriverebbe dal tiro in B, con l'eleva&shy;<lb/>zione BE, e che avrebbe per altezza FC=EF, per <lb/>sublimit&agrave; FL, e GF per met&agrave; dell'ampiezza. </s>

<s>In si&shy;<lb/>mil guisa, sia H il punto di mezzo della DC, e con&shy;<lb/>ducasi la HI parallela a BC: le semiparabola, che <lb/>s'immagini passar per B, H, sar&agrave; quella che ver&shy;<lb/>rebbe descritta dal tiro in B, con l'elevazione BD, <lb/>e che vorrebbesi dimostrare avere ampiezza uguale <lb/>a quella della semiparabola FB, descritta di sotto. </s>

<s><lb/>Or perch&egrave; si sarebbe felicemente conseguito l'in&shy;<lb/>tento, quando si fosse dimostrato che IH &egrave; media <lb/>fra HD, HL, confer&igrave; Galileo intorno a ci&ograve; il suo <lb/>primo studio, com'apparisce dalla seguente bozza di manoscritto: </s></p><p type="main">

<s>&ldquo; Sit triangulum rectangulum ABC (nella medesima figura), latera <lb/>habens aequalia AC, CB. </s>

<s>Fiant anguli aequales DBA, ABE, et divisa EC <lb/>bifariam in F, et ducta FG, parallela ad BC, fiat ut EF ad FG, ita FG ad <pb xlink:href="020/01/2312.jpg" pagenum="555"/>FL: dico quod, si tota DC bifariam secetur in H, ducta HI, parallela BC, <lb/>erit ut DH ad HI, ita IH ad HL. &rdquo; </s></p><p type="main">

<s>&ldquo; Quia enim angulus CAB aequatur angulo CBA, et DBA angulo ABE, <lb/>et angulus CEB duobus EAB, ABE est aequalis, ergo CEB ipsi CBD aequa&shy;<lb/>bitur, et triangulus ECB triangulo DCB erit similis, et illis quoque et inter <lb/>se similes sunt EGF, DIH. </s>

<s>Sed quia est ut EF ad FG, ita GF ad FL, erit <lb/>triangulus AGF ipsi EGF similis, et ipsi quoque DIH..... &rdquo; (MSS. Gal., <lb/>P. V, T. II, fol. </s>

<s>111 a tergo). </s></p><p type="main">

<s>A questo punto rimase la scrittura interrotta, perch&egrave; Galileo s'accorse <lb/>di avere sbagliato. </s>

<s>Dalla proporzione infatti EF:FG=GF:FL si con&shy;<lb/>clude, non gi&agrave; la similitudine fra i triangoli EGF, AGF, ma fra EGF e LGF, <lb/>il qual triangolo LGF conveniva dimostrar simile al triangolo ILH che pure <lb/>&egrave; simile al triangolo IDH, a voler conseguire direttamente l'intento. </s>

<s>Ma per&shy;<lb/>ch&egrave; gli sarebbe la dimostrazione riuscita contorta, non volle proseguire pi&ugrave; <lb/>oltre, e a tutto quel che aveva scritto dette di frego. </s></p><p type="main">

<s>Rinunziato a questo primo processo, si volse a pensarne un altro, di <lb/>cui ci lasci&ograve; in una nota manoscritta il disegno. </s>

<s>Supposto non aver bisogno <lb/>il Lettore che gli sia detto n&egrave; dimostrato com'avendo il triangolo ABC (nella <lb/>medesima figura 298) i due cateti BC, AC uguali, se prolungato AC e con&shy;<lb/>dotta la BD si far&agrave; l'angolo EBC uguale all'angolo BDC, i due angoli DBA, <lb/>ABE sono uguali, e i due triangoli DBC, EBC fra loro simili; ecco qual'&egrave; <lb/>la via che, per condursi alla desiderata conclusione, Galileo preparavasi in <lb/>questa Nota, riferendosi sempre alla medesima precedente figura: </s></p><p type="main">

<s>&ldquo; In triangulo rectangulo BCD fiat angulo D aequalis CBE, et iunga&shy;<lb/>tur BE. </s>

<s>Erunt ergo duo triangula DCB, EBC similia. </s>

<s>Dividatur tota DC bi&shy;<lb/>fariam in H, et parallela HI sit ipsi CB. </s>

<s>Dividatur EC bifariam in F, et <lb/>ducatur FG parallela BC, et fiat ut DH ad HI, ita IH ad HL, et iungatur <lb/>LI. </s>

<s>Erit triangulus LIH simile triangulo DHI, et ob id simile quoque ipsi <lb/>EFG. </s>

<s>Sed HI est aequalis GF, utriusque enim dupla est BC, ergo reliqua <lb/>latera HL, FE aequalia erunt: quare tertia proportionalis ipsarum LH, HI, <lb/>nempe HD, erit aequalis tertiae proportionali ipsarum EF, FG. </s>

<s>Sed HD, ter&shy;<lb/>tia proportionalis ipsarum LH, HI, est HC, dimidia nempe totius DC; ergo <lb/>tertia proportionalis ipsarum EF, FG aequabitur dimidiae CD, nempe ipsi DH. </s>

<s><lb/>Sed CH est aequalis FL, cum EF sit aequalis HL, et EH communis, ergo <lb/>tertia proportionalis ipsarum EF, FG erit FL, terminata in puncto L, ubi <lb/>terminatur tertia proportionalis ipsarum DH, HI &rdquo; (MSS. Gal., P. V, T. II, <lb/>fol. </s>

<s>80). </s></p><p type="main">

<s>Soggiunge immediatamente Galileo sotto questa dimostrazione, che do&shy;<lb/>veva far l'ufficio di lemma: &ldquo; Ex hoc demonstrabitur proiectorum, quorum <lb/>elevationes a semirecta, supra et infra per angulos aequales factorum, am&shy;<lb/>plitudines parabolarum esse aequales &rdquo; (ibid.). Immaginando infatti che per <lb/>F, B, e per H, B passino due semiparabole, saranno queste quelle mede&shy;<lb/>sime, che verrebbero disegnate in aria dal tiro in B, secondo le direzioni <lb/>BE, BD, facenti angoli uguali sopra e sotto all'angolo a mezza squadra. </s>

<s>Che <pb xlink:href="020/01/2313.jpg" pagenum="556"/>debbano poi tali due parabole avere uguale ampiezza, consegue immediata&shy;<lb/>mente dal sopra scritto Lemma, in cui, poste IH, GF uguali, fu dimostrato <lb/>essere da queste due linee misurata la met&agrave; dell'ampiezza della semipara&shy;<lb/>bola respettiva. </s></p><p type="main">

<s>Dietro il disegno cos&igrave; preparato, esegu&igrave; Galileo la proposizione VIII del <lb/>Dialogo, la quale prometteva di riuscire, se si fosse mantenuta quella prima <lb/>semplicit&agrave;, pi&ugrave; spedita e pi&ugrave; chiara. </s>

<s>Rimase anche per un lato in difetto <lb/>capitalissimo, non apparendovi la condizione che i proietti sono <emph type="italics"/>eodem im&shy;<lb/>petu explosi,<emph.end type="italics"/> ci&ograve; che dall'altra parte sarebbe tornato facilissimo dimostrare, <lb/>osservando che, per essere FL+FC=AH+HC, hanno ambedue le se&shy;<lb/>miparabole per misura dell'impeto quello del cadente per la medesima al&shy;<lb/>tezza LC. </s>

<s>La proposizione X per&ograve;, nella quale Galileo dice che l'impeto in <lb/>ciascuna semiparabola &ldquo; aequatur momento naturaliter cadentis in perpen&shy;<lb/>diculari ad horizontem, quae tanta sit, quanta est composita ex sublimitate <lb/>cum altitudine semiparabolae &rdquo; (Alb. </s>

<s>XIII, 253), non era stata ancora di&shy;<lb/>mostrata, e il Viviani perci&ograve; pens&ograve; di supplir egli al notato difetto (ivi, <lb/>pag. </s>

<s>252) applicandovi il metodo di misurare gl'impeti insegnato da Gali&shy;<lb/>leo nella proposizione sua quarta. </s>

<s>Resulta da tali insegnamenti che, essendo <lb/>LH, HI le misure dell'impeto orizzontale e del verticale nella semiparabola <lb/>HB, nell'altra FB sono invece FG, FE, cosicch&egrave;, avendosi per le cose dimo&shy;<lb/>strate LH=EF, IH=GF, e le ipotenuse IL, GE altres&igrave; uguali, saranno <lb/>perci&ograve; uguali gl'impeti composti in B, solo permutata la rappresentazion <lb/>delle componenti. </s></p><p type="main">

<s>Non lasci&ograve; pure il Torricelli di promovere anche questa parte della <lb/>Scienza galileiana, a cui dette maggior opera del Viviani, e la ridusse a una <lb/>elegante facilit&agrave; maravigliosa. </s>

<s>Nella IX del libro secondo si propone di scio&shy;<lb/>gliere il seguente problema: Dato l'impeto FA (fig. </s>

<s>299), e data la dire&shy;<lb/><figure id="id.020.01.2313.1.jpg" xlink:href="020/01/2313/1.jpg"/></s></p><p type="caption">

<s>Figura 299<lb/>zione AH del tiro, ritrovare l'ampiezza, l'altezza e tutta la parabola di que&shy;<lb/>sta proiezione. </s>

<s>Si descriva intorno al diametro FA un semicerchio, a cui sieno <lb/>le AD, FL tangenti, e condotta da E una perpendicolare, che incontri in G <pb xlink:href="020/01/2314.jpg" pagenum="557"/>il semicerchio, si prolunghi di altrettanto in B, per il qual punto passi la <lb/>DL parallela ad AF, e compiasi il rettangolo FD. </s>

<s>La parabola che pass <lb/>per A, B, dice il Torricelli, sar&agrave; la cercata, ed essendo EG media fra EF <lb/>ossia BL, e AE, ossia BD, ne saranno EG, o la sua uguale GB, la semiam&shy;<lb/>piezza, BD l'altezza, e BL la sublimit&agrave; che si voleva. </s></p><p type="main">

<s>&Egrave; di qui manifesto, soggiunge il Torricelli stesso per corollario, che <lb/>avendosi una macchina, la quale esplode con impeti uguali al cadente da <lb/>E in A (fig. </s>

<s>300), per la linea EA, diametro di un semicerchio, e con di&shy;<lb/><figure id="id.020.01.2314.1.jpg" xlink:href="020/01/2314/1.jpg"/></s></p><p type="caption">

<s>Figura 300<lb/>rezioni secondo le corde AC, AD, AB; verranno per i <lb/>seni FC, HD, GB rappresentate le semiampiezze delle <lb/>parabole, via via descritte da questi tiri, ond'&egrave; che, se <lb/>l'angolo HAD &egrave; semiretto, HD sar&agrave; il seno totale, e <lb/>perci&ograve; il massimo di tutti. </s>

<s>Ed essendo gli archi CD, <lb/>DB, che misurano gli angoli sottesi uguali, i seni FC, <lb/>GB, ossia le semiampiezze delle parabole descritte con <lb/>elevazioni dalla semiretta ugualmente distanti, saranno <lb/>pure tra loro uguali. </s>

<s>&ldquo; Corollarium ergo erit, conclude <lb/>tutto compiacente di ci&ograve; il Torricelli, quod Galileo theo&shy;<lb/>rema satis arduum fuerat &rdquo; (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Il teorema pur troppo era arduo, come i fatti ce <lb/>l'hanno mostrato, in questa nuova Scienza de'proietti &igrave;stituita da Galileo <lb/>ma pure eravi riuscito senza trasgredire in nulla i termini meccanici, co&shy;<lb/>sicch&egrave; si seppero finalmente quelle vere ragioni <emph type="italics"/>naturale et geometrice,<emph.end type="italics"/> che <lb/>il Tartaglia si lusingava di aver riconoseiute per s&egrave; <emph type="italics"/>evidentissime.<emph.end type="italics"/> Con que&shy;<lb/>sta seconda parte pens&ograve; Galileo stesso da principio di aver reso il suo nuov<gap/><lb/>trattato assoluto, ridotto cos&igrave; a quelle sole XII proposizioni, delle quali si legge <lb/>nella seguente nota autografa nitidamente scritto il sommario: </s></p><p type="main">

<s>&ldquo; Prima proposizione: Che il proietto descrive la Parabola. </s>

<s>&mdash; II. </s>

<s>Prova <lb/>il moto composto de'due equabili, orizzontale e perpendicolare, essere in <lb/>potenza uguale ad ambedue. </s>

<s>&mdash; III. </s>

<s>Considera il moto composto di due: <lb/>orizzontale equabile, e perpendicolare accelerato. </s>

<s>&mdash; IV. </s>

<s>Mostra come si debba <lb/>determinare l'impeto del proietto in tutti i punti della Parabola. </s>

<s>&mdash; V. </s>

<s>Tro&shy;<lb/>vare nell'asse prolungato della data Paradola il punto sublime, dal quale i<gap/><lb/>cadente descrive la Parabola. </s>

<s>Segue il corollario che la met&agrave; dell'ampiezza <lb/>&egrave; media tra l'altezza e la sublimit&agrave; della Parabola. </s>

<s>S'aggiunge l'altro co&shy;<lb/>rollario, che &egrave;: le amplitudini delle Parabole essere uguali, quando le loro <lb/>elevazioni e sublimit&agrave; alternativamente sono uguali. </s>

<s>&mdash; VI. </s>

<s>Data la subli&shy;<lb/>mit&agrave; e l'altezza, trovare l'ampiezza della Parabola. </s>

<s>&mdash; VII. </s>

<s>Nel descriver <lb/>parabole di ampiezze uguali, minor impeto si ricerca in quella, la cui am&shy;<lb/>piezza &egrave; doppia dell'altezza, che in qualsivoglia altra. </s>

<s>Segue il corollario <lb/>Nelle parabole descritte dal medesimo impeto, l'amplitudine massima esse<gap/><lb/>di quella, che nasce dall'elevazione dell'angolo semiretto. </s>

<s>&mdash; VIII. </s>

<s>Le am&shy;<lb/>piezze dei tiri, cacciati con l'istesso impeto e per angoli ugualmente man&shy;<lb/>canti o escedenti l'angolo semiretto, sono uguali. </s>

<s>&mdash; IX. </s>

<s>Le ampieze sono <pb xlink:href="020/01/2315.jpg" pagenum="558"/>uguali delle parabole, le altezze e sublimit&agrave; delle quali si rispondono con&shy;<lb/>trariamente. </s>

<s>&mdash; X. </s>

<s>I momenti delle parabole d'eguali ampiezze son fra loro <lb/>come i momenti delle altezze perpendicolari, dalle quali si generano esse <lb/>parabole. </s>

<s>&mdash; XI. </s>

<s>Il momento di qualsivoglia semiparabola &egrave; uguale al mo&shy;<lb/>mento del cadente per la perpendicolare, composta dell'altezza e sublimit&agrave; <lb/>della Parabola. </s>

<s>&mdash; XII. </s>

<s>Dato l'impeto e l'ampiezza, trovar l'altezza della <lb/>Parabola &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>106 a tergo). </s></p><p type="main">

<s>Corrispondono esattamente, nell'ordine e negli argomenti di questo Som&shy;<lb/>mario, le proposizioni stampate nel Dialogo quarto, se non che manca il <lb/>secondo corollario, annunziato dopo la V, per essere stato fatto soggetto di <lb/>dimostrazion propria nella IX, e manca pure la X, la quale, non sembrando <lb/>a noi formulata con chiarezza, non si saprebbe perci&ograve; nemmeno decidere se <lb/>Galileo pens&ograve; di lasciarla, per averla trovata inutile o falsa. </s>

<s>Vale in ogni <lb/>modo questo Sommario per documento certissimo che veramente, secondo <lb/>la prima intenzione di Galileo, si doveva il libro de'proietti comporre di sole <lb/>due parti, nelle quali si tratterebbe della misura degl'impeti, e delle ra&shy;<lb/>gioni de'teoremi annunziati dal Tartaglia. </s>

<s>Come poi si deliberasse l'Autore <lb/>di aggiungere una terza parte, per applicare i teoremi ai militari esercizi, <lb/>non &egrave; difficile intendere ripensando che i calcoli, dai quali il Tartaglia stesso <lb/>diceva di aver ricavato <emph type="italics"/>la proportion dil crescer e calar che fa ogni pezzo <lb/>de artiglieria, alzandolo aver arbassandolo sopra il pian del orizonte,<emph.end type="italics"/> non <lb/>erano altro che belle promesse: n&egrave; &egrave; difficile pure accorgersi che non ve&shy;<lb/>niva questa terza aggiunta preparata dall'ordine e dal modo puramente teo&shy;<lb/>rico della trattazion precedente. </s>

<s>&Egrave; da tener nonostante per una calunnia <lb/>quella del Cartesio, il quale disse che il quarto dialogo delle Nuove scienze <lb/>non con altro consiglio sembrava scritto &ldquo; quam ut tormentorum bellico&shy;<lb/>rum, secundum diversas elevationes explosorum, vim explicaret. </s>

<s>Praeterea <lb/>observandum est quod, quum hypotheses has proponeret, quo facilius admit&shy;<lb/>terentur, tormenta bellica exceperit, et tamen sub finem conclusiones suas <lb/>ad tormenta bellica potissimum applicat: hoc est uno verbo omnia aeri su&shy;<lb/>perstruxit &rdquo; (Epist., P. II cit., pag. </s>

<s>244). Quel che pu&ograve; essere in Galileo di <lb/>aereo apparir&agrave; da quest'altra parte del nostro capitolo: ora &egrave; da vedere in <lb/>che modo egli applicasse ai tiri delle artiglierie le sue conclusioni. </s></p><p type="main">

<s>Posto che sia trovato per esperienza quanto getta un cannone per l'oriz&shy;<lb/>zontale la palla, nella elevazione a mezza squadra, Galileo insegna il modo <lb/>di calcolare, e calcola in effetto, quanto quel medesimo cannone, con la me&shy;<lb/>desima carica, getterebbe la medesima palla in distanza orizzontale, elevato <lb/>o depresso, grado per grado, intorno a quella stessa direzion semiretta, la <lb/>quale, dando come si sa, la massima volata, si prende perci&ograve; per termine <lb/>di confronto. </s>

<s>Il problema &egrave; annunziato cos&igrave; nella XII proposizione del Dia&shy;<lb/>logo, secondo il linguaggio proprio della scienza: &ldquo; Semiparabolarum omnium <lb/>amplitudines calculo colligere, atque in tabulas exigere, quae a proiectis, <lb/>codem impetu explosis, describuntur &rdquo; (Alb. </s>

<s>XIII, 255). </s></p><p type="main">

<s>Per condurre i calcoli per&ograve; bisognava, direbbero i Matematici moderni, <pb xlink:href="020/01/2316.jpg" pagenum="559"/>prepararsi la formula, ci&ograve; che Galileo fa nella detta proposizione XII, ma <lb/>che noi vogliam presentare ai nostri Lettori in quell'amabile semplicit&agrave; di <lb/>abito, con cui ella usc&igrave; dalla mente dell'Autore, senza que'posticci belletti, <lb/>che le furono messi attorno, per farla comparir fra l'altre sulla pubblica <lb/>scena. </s>

<s>Chi ha dimestichezza oramai con queste cose, non ha bisogno gli si <lb/>dica che, dovendo le parabole secondo il supposto tutte avere il medesimo <lb/>impeto che nella elevazion semiretta, alla somma, che hanno in questa, <lb/>debbono in ciascuna di quelle equivaler le somme della sublimit&agrave; e della <lb/>altezza. </s></p><p type="main">

<s>&ldquo; Sia l'angolo ADC (fig. </s>

<s>301) gradi 45: &egrave; manifesto che dalla subli&shy;<lb/>mit&agrave; AB nascer&agrave; la parabola, la cui altezza BC. </s>

<s>Posto l'angolo EDC gradi 55, <lb/>si cerca la parabola alla elevazione di gradi 55, la cui sublimit&agrave; e altezza <lb/>siano uguali alla AC. &rdquo; <lb/><figure id="id.020.01.2316.1.jpg" xlink:href="020/01/2316/1.jpg"/></s></p><p type="caption">

<s>Figura 301</s></p><p type="main">

<s>&ldquo; Con falsa posizione cerca se di tal parabola <lb/>fosse l'asse nella EC, e la tangente ED, e poi, di&shy;<lb/>videndo la EC in mezzo in F, fa che l'altezza di tal <lb/>parabola sia FC, e la sublimit&agrave; FA, il che allora <lb/>sarebbe, quando la met&agrave; dell'ampiezza CD si tro&shy;<lb/>vasse esser media proporzionale tra la CF e la FA. </s>

<s><lb/>Ma tra EF, cio&egrave; FC, ed FA media una minore della <lb/>met&agrave; di CD, essendo che la met&agrave; di CD &egrave; media <lb/>tra CB e BA; cerca dunque qual'&egrave; la sublimit&agrave;, tra <lb/>la quale e la FE sia media la met&agrave; dell'ampiezza CD, <lb/>cio&egrave; la CB, e trovata che sia, pongasegli uguale la <lb/>FO, ed averassi la sublimit&agrave; OF descrivere la para&shy;<lb/>bola, la cui altezza sia FC, ed ampiezza CD. &rdquo; </s></p><p type="main">

<s>&ldquo; &Egrave; dunque tal parabola maggiore della cercata, secondo che la OC &egrave; <lb/>maggiore della AC, ma bene gli &egrave; simile, sendo toccata dalla ED. </s>

<s>Convien <lb/>dunque descriverne altra simile, diminuendo la sua sublimit&agrave; e ampiezza <lb/>secondo la proporzione di CA a CO. </s>

<s>Facciasi dunque come OC a CA, cos&igrave; <lb/>CD a DN, ed avremo l'ampiezza cercata, cio&egrave; della parabola, la cui subli&shy;<lb/>mit&agrave; e altezza sono uguali alla AC, e per conseguenza nasceranno da im&shy;<lb/>peti eguali de'proietti cacciati dal punto D &rdquo; (MSS. Gal., P. V, T. II, <lb/>fol. </s>

<s>122 a tergo). </s></p><p type="main">

<s>La formula dunque, che resulta da questa dimostrazione, e sopra la <lb/>quale si possono calcolare le ampiezze di tutte le parabole, descritte dal me&shy;<lb/>desimo cannone, che tiri in D elevato grado per grado, sopra e sotto la <lb/>elevazion semiretta AD; &egrave; DN=CA.CD/OC, dove DN rappresenta l'ampiezza <lb/>che si cerca. </s>

<s>Il prodotto CA.CD &egrave; sempre un quadrato, avendosi DC, am&shy;<lb/>piezza della parabola con elevazion semiretta, uguale ad AC, tangente del&shy;<lb/>l'angolo di 45 gradi, la qual tangente sappiamo essere uguale al raggio del <lb/>circolo, che &egrave; CD, e che ponesi uguale a diecimila. </s>

<s>&ldquo; Eligimus autem, dice <lb/>Galileo, numerum 10,000, quia utimur in calculis tabula tangentium, cuius <pb xlink:href="020/01/2317.jpg" pagenum="560"/>hic numerus congruit cum tangente gr. </s>

<s>45 &rdquo; (Alb. </s>

<s>XIII, 255, 56). Il divi&shy;<lb/>dendo della formula &egrave; perci&ograve; sempre uguale al quadrato di diecimila, ma <lb/>il divisore ad ogni calcolo varia, essendo dato in funzione della tangente <lb/>dell'angolo della elevazione. </s>

<s>Dato dunque l'angolo EDC, le Tavole daranno <lb/>la tangente EC, o la met&agrave; di lei FC, alla quale aggiunta la FO, che sap&shy;<lb/>piamo esser terza proporzionale dopo la stessa FC, e la met&agrave; di DC, e perci&ograve; <lb/>nota; sar&agrave; pur nota la CO della formula, e con essa infine la DN, ch'era <lb/>l'incognita del problema. </s>

<s>A questo modo, con moltiplicazioni e con divisioni <lb/>numeriche laboriosissime, fu calcolata da Galileo la prima Tavola, che s'in&shy;<lb/>titola: &ldquo; Amplitudines semiparabolarum ab eodem impetu descriptarum &rdquo; <lb/>(ibid., pag. </s>

<s>259). </s></p><p type="main">

<s>Per le varie elevazioni del cannone sapere la volata del tiro era, negli <lb/>eser<emph type="italics"/>c<emph.end type="italics"/>izi delle artiglierie, la cosa pi&ugrave; importante, dopo la quale veniva la no&shy;<lb/>tizia dell'altezza perpendicolare, a cui giunge la palla nel descriver le am&shy;<lb/>piezze via via calcolate. </s>

<s>Aggiunge perci&ograve; Galileo, alla prima Tavola costruita, <lb/>una seconda, per calcolar la quale bisognava pure prepararsi la formula op&shy;<lb/>portuna. </s>

<s>Come facesse ci&ograve; nella XIII proposizione del Dialogo &egrave; pubblicamente <lb/>noto, ma noi, sempre desiderosi di conoscere addentro l'Uomo famoso, an&shy;<lb/>deremo a trovarlo anche questa volta, prima ch'egli esca fuori in toga acca&shy;<lb/>demica, nella libera quiete della sua stanza di studio. </s>

<s>Ivi l'udiremo cos&igrave;, <lb/>presso a poco, ragionare fra s&egrave;, e poi scrivere: </s></p><p type="main">

<s>L'altezza della parabola con elevazion semiretta &egrave; nota, essendo ella la <lb/>met&agrave; della tangente, ossia di diecimila, ond'&egrave; che si riduce tutto il presente <lb/>problema a trovar quanta sia la distanza del vertice delle altre parabole dal <lb/>vertice di quella stessa parabola semiretta. </s>

<s>E perch&egrave; posson que'vertici ora <lb/>rimaner sotto, ora sopra a questo, secondo che gli angoli della direzion dei <lb/>tiri son minori o maggiori di 45 gradi, avr&agrave; dunque il problema a contem&shy;<lb/>plare due cas&igrave;. </s></p><p type="main">

<s>S'incominci, par che voglia dir Galileo, a calcolare le altezze al di sotto <lb/>della met&agrave; del quadrante, e sien gl'impeti, da cui nascon le altre parabole, <lb/><figure id="id.020.01.2317.1.jpg" xlink:href="020/01/2317/1.jpg"/></s></p><p type="caption">

<s>Figura 302<lb/>tutti uguali all'impeto della semiretta, rappresentato dalla <lb/>linea BD (fig. </s>

<s>302), cosicch&egrave; torner&agrave; il vertice di essa <lb/>parabola semiretta in E, dove la DB stessa &egrave; tagliata nel <lb/>mezzo. </s>

<s>Sia il vertice di un'altra parabola in A: si vuol <lb/>costruire la formula, dietro la quale possa calcolarsi <lb/>quanto A, che &egrave; uno degl'infiniti punti della linea EB, <lb/>sia distante da A, termine fisso. </s>

<s>I pensieri di Galileo <lb/>sipossono cos&igrave; brevemente significare, con queste equa&shy;<lb/>zioni: AB.AD=(BE&mdash;AE)(DE+AE)=(BE&mdash;AE) <lb/>(BE+AE)=BE2&mdash;AE2. </s>

<s>E perch&egrave; AB.AD &egrave; il pro&shy;<lb/>dotto dell'altezza per la sublimit&agrave; della parabola AC, <lb/>che sappiamo dover essere uguale al quadrato della <lb/>met&agrave; dell'ampiezza FB, sar&agrave; dunque AE2=BE2&mdash;FB2, con la quale equa&shy;<lb/>zione, essendo BE costantemente la met&agrave; dell'impeto, ossia 5000, ed FB <pb xlink:href="020/01/2318.jpg" pagenum="561"/>essendo data dalla Tavola precedente; si potr&agrave; avere il valore di AE, che <lb/>misura la distanza del vertice della parabola CA dal vertice della parabola <lb/>con elevazion semiretta. </s>

<s>Dopo ci&ograve;, per mezzo dell'equazione AB=EB&mdash;AE, <lb/>si verr&agrave; ad aver la diretta, e final soluzione del proposto problema. </s></p><p type="main">

<s>Nell'altro caso, che l'angolo della elevazione sia maggiore di 45 gradi, <lb/>e che perci&ograve; il punto A riesca superiore ad E, si potr&agrave; calcolare AE come <lb/>sopra: la quantit&agrave; per&ograve;, che dal calcolo ne resulta, si dovrebbe ora aggiun&shy;<lb/>gere ad EB, mentre dianzi si sottraeva; cosicch&egrave; la formula tornerebbe cos&igrave; <lb/>leggermente trasformata: AB=EB+AE. </s>

<s>Ma ascoltiamo come Galileo si&shy;<lb/>gnifichi questi stessi pensieri, nella sua propria maniera, e quali la prima <lb/>volta gli caddero gi&ugrave; dalla penna. </s></p><p type="main">

<s>&ldquo; Sit impetus datus semper idem, nempe BD (nella medesima fig. </s>

<s>302), <lb/>ex altitudine et sublimitate composita linea DB 10,000. Et quia dimidia am&shy;<lb/>plitudo, nempe BF, mediat inter altitudinem et sublimitatem, intelligatur DB <lb/>divisa ut rectangulum partium, quae sint v. </s>

<s>g. </s>

<s>DA, AB, sit aequale qua&shy;<lb/>drato FB. </s>

<s>Quod si DB divisa sit bifariam in E, erit quadratum BE aequale <lb/>rectangulo partium ipsius DB, et quadrato AE. </s>

<s>Si ergo a quadrato BE de&shy;<lb/>matur quadratum FB, seu dicas rectangulum illi aequale a partibus con&shy;<lb/>tentum, remanebit quadratum AE, cuius radix, dempta ex EB, relinquet BA <lb/>altitudinem quaesitam. </s>

<s>Amplitudo autem BC iam calculata est ad singulos <lb/>gradus elevationis &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>103 a tergo). </s></p><p type="main">

<s>Ne deduce di qui Galileo stesso la seguente regola pratica <emph type="italics"/>&ldquo; Per tro&shy;<lb/>vare l'altezza della parabola.<emph.end type="italics"/> Dal quadrato della met&agrave; dell'impeto, che &egrave; <lb/>l'altezza colla sublimit&agrave; della parabola, cava il quadrato della met&agrave; dell'am&shy;<lb/>piezza della semiparabola, e la radice del rimanente, aggiunta alla met&agrave; del&shy;<lb/>l'impeto, dar&agrave; l'altezza cercata, quando l'elevazione &egrave; pi&ugrave; di gradi 45. Per <lb/>la presente tavola, che si fabbrica, la met&agrave; dell'impeto &egrave; sempre 5000, e il <lb/>suo quadrato 25,000,000. Ma se l'elevazione sar&agrave; meno di gradi 45, la detta <lb/>radice del rimanente si dee sottrarre dalla met&agrave; dell'impeto, ed il restante <lb/>&egrave; l'altezza cercata &rdquo; (ivi, fol. </s>

<s>110). Sotto sono scritti alla rinfusa i calcoli, <lb/>fatti sempre per via di moltiplicazioni, di divisioni e di somme di numeri, <lb/>il primo esempio de'quali, per la costruzion della Tavola, incomincia dalla <lb/>elevazione di gradi 50. </s></p><p type="main">

<s>Calcolate cos&igrave; le Tavole delle ampiezze e delle altezze delle parabole, <lb/>descritte dal medesimo impeto, rimaneva, secondo le teorie, a considerare <lb/>il terzo elemento, che &egrave; delle sublimit&agrave;, per calcolar le quali porgeva faci&shy;<lb/>lissima e immediata la formula il corollario della proposizione quinta. </s>

<s>Chia&shy;<lb/>mata M infatti la semibase della semiparabola, S la sublimit&agrave;, e A l'altezza, <lb/>abbiamo per il detto corollario M2=S.A, d'onde S=M2/A. Fra'problemi <lb/>perci&ograve;, che risoluti dovevano servire alla costruzione delle Tavole ballistiche, <lb/>Galileo aveva preparato anche questo: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Data amplitudine et altitudine semiparabolae, sublimitatem re&shy;<lb/>perire. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><pb xlink:href="020/01/2319.jpg" pagenum="562"/><p type="main">

<s>&ldquo; Id statim colligitur ex eo quod dimidia amplitudo mediat inter alti&shy;<lb/>tudinem et sublimitatem: ergo, diviso quadrato dimidiae amplitudinis per <lb/>altitudinem, habemus sublimitatem quaesitam &rdquo; (ibid., fol. </s>

<s>118 a tergo). </s></p><p type="main">

<s>Ma rimase questo problema tra'fogli di Galileo, il quale, dopo qualche <lb/>esempio, lasci&ograve; di farne l'applicazione a costruir le Tavole delle sublimit&agrave;, <lb/>forse perch&egrave; riconosceva che sarebbero tornate inutili agli artiglieri, in ser&shy;<lb/>vigio de'quali aveva fabbricato le prime due. </s>

<s>Dall'altra parte erano le pre&shy;<lb/>cedenti dottrine di facile guida a chi avesse voluto, per sua propria curio&shy;<lb/>sit&agrave;, sapere da quale altezza dovrebbe naturalmente scender la palla, per <lb/>acquistar quella violenza d'impeto orizzontale impressale dalla forza del <lb/>cannone. </s></p><p type="main">

<s>Pi&ugrave; utile di ci&ograve; pensava Galileo che tornerebbe agli artiglieri il sapere <lb/>quanta debba esser la carica, perch&egrave;, secondo i gradi delle elevazioni via via <lb/>crescenti da uno a novanta, possa il cannone sempre cacciar la palla alla <lb/>medesima distanza orizzontale. </s>

<s>Misura alla detta carica &egrave; quel che, in que&shy;<lb/>sta nuova Scienza galileiana, chiamasi impeto, il quale si compone dell'al&shy;<lb/>tezza e della sublimit&agrave; della parabola. </s>

<s>La formula dunque, per questi cal&shy;<lb/>coli nuovi, consisteva nella soluzione di quest'altro problema: <emph type="italics"/>Trovar l'al&shy;<lb/>tezza e la sublimit&agrave; delle parabole, aventi la medesima ampiezza.<emph.end type="italics"/></s></p><p type="main">

<s>Quanto all'altezza &egrave; cosa di facilissima invenzione, perch&egrave;, avendosi i <lb/>tiri per esempio diretti secondo DM, DA, DE, nella poco addietro fig. </s>

<s>301, <lb/>le respettive altezze delle parabole s'avranno misurate dalle linee QC, BC, <lb/>FC, met&agrave; delle MC, AC. EC, che son le tangenti degli angoli MDC, ADC, <lb/>EDC nel circolo descritto col raggio DC, fatto anche per questa terza Ta&shy;<lb/>vola da Galileo diecimila: cosicch&egrave; cinquemila &egrave; l'altezza BC della parabola, <lb/>che vien descritta dal tiro diretto a mezza squadra. </s>

<s>Saranno dunque date in <lb/>generale, dalle mezze tangenti degli angoli delle elevazioni, le altitudini delle <lb/>parabole via via richieste. </s>

<s>Le sublimit&agrave; poi si possono facilmente calcolar <lb/>con la formula S=M2/A, in cui M &egrave; data, e A s'&egrave; detto ora come trovarla. </s>

<s><lb/>Ma il detto &egrave; propriamente di Galileo, nella XIV proposizione del Dialogo, <lb/>raffazzonata sopra questa semplice Nota manoscritta: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Altitudines semiparabolarum, quarum eadem sit amplitudo, re&shy;<lb/>perire. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Id autem absolvitur, per dimidiam tangentem arcum elevationis da&shy;<lb/>tae semiparabolae. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Inventa ex dictis altitudine, sublimitatem singularum semiparabola&shy;<lb/>rum, quarum eadem sit amplitudo, facilem reperies. </s>

<s>Nam, cum dimidia am&shy;<lb/>plitudo mediet inter altitudinem et sublimitatem, diviso quadrato mediae <lb/>amplitudinis per altitudinem, habebimus sublimitatem, quae postea, addita <lb/>altitudine, exhibet impetum. </s>

<s>Fabricemus ergo Tabulas sublimitatum, sitque <lb/>semper dimidia amplitudo semiparabolae 5000, cuius quadratum semper <lb/>idem 25,000,000 &rdquo; (ibid., fol. </s>

<s>125 a tergo). </s></p><p type="main">

<s>Sotto &egrave; gremito il foglio tutto di numeri, disposti in ordine, com'usava <pb xlink:href="020/01/2320.jpg" pagenum="563"/>allora, per estrarne le radici, e per farne le divisioni. </s>

<s>Si disse altrove come <lb/>sopra la faccia retta di questo medesimo foglio sia distesa una lettera di <lb/>Alessandro Ninci, scritta da Campoli nel Marzo del 1636, dopo il qual tempo <lb/>dev'essere stata dunque fabbricata questa Tavola terza, e molto ragionevol&shy;<lb/>mente anche le altre due, de'calcoli serviti per le quali &egrave; una fitta selva <lb/>in parecchi fogli del codice da noi citato. </s>

<s>Non si pu&ograve; da quella pagine le&shy;<lb/>vare gli occhi, senza ripensare alla pazienza invitta, e all'improba fatica del <lb/>calcolatore, specialmente a quei tempi, in cui la vista indebolita, non invi&shy;<lb/>gilandone i moti, poteva facilmente far trascorrere la penna in non colpe&shy;<lb/>voli errori. </s>

<s>Cosicch&egrave;, verrebbe fatto anche a noi di esclamare col Torricelli: <lb/>&ldquo; Cuius enim industriae tanta solertia est, ut per innumeras multiplicatio&shy;<lb/>num, divisionum et radicum ambages ad eosdem pene numeros appellere <lb/>potuerit, quos ex Tabula desumere nobis concessum fuit? </s>

<s>&rdquo; (Op. </s>

<s>geom. </s>

<s>cit., <lb/>pag. </s>

<s>104). </s></p><p type="main">

<s>Se non che si direbbe follia, piuttosto che industriosa solerzia, quella <lb/>di Galileo, che potendo, come poi fece il Torricelli stesso per le sue Tavole, <lb/>delle quali diremo altrove; trascrivere i calcoli <emph type="italics"/>ex ipsa Tabula sinuum, ac <lb/>tangentium, facili brevique negatio,<emph.end type="italics"/> si volesse nulladimeno sottoporre a s&igrave; <lb/>lunghe e laboriose vigilie. </s>

<s>Ma n&egrave; da industria soverchiamente solerte, n&egrave; da <lb/>follia dipende la stranezza del fatto: diremo piuttosto che dipende dagli <lb/>studii, e dall'indole dell'ingegno di Galileo, arretratosi alla vista di quella <lb/>mostruosa macchina trigonometrica, dalla gola della quale faceva. </s>

<s>Enrico <lb/>Bryggs vomitar le sue Tavole de'seni e delle tangenti. </s>

<s>Pi&ugrave; tardi, il Cava&shy;<lb/>lieri attendeva in Italia a perfezionare quelle medesime Tavole, con pi&ugrave; co&shy;<lb/>moda applicazione dei Logarimmi, la materia de'quali sent&igrave; ancora Galileo <lb/>di difficile intelligenza. </s>

<s>N&egrave; a fargliene, nei calcoli numerici, riconoscer l'uti&shy;<lb/>lit&agrave; dell'uso, valsero le persuasioni dello stesso Cavalieri, il quale scriveva <lb/>in una sua lettera non stimare i suoi <emph type="italics"/>Logarimmi<emph.end type="italics"/> materia s&igrave; difficile, che <lb/>un Galileo, <emph type="italics"/>con non molta applicazione, non l'intendesse.<emph.end type="italics"/> (Campori, Car&shy;<lb/>teggio gal., Modena 1881, pag. </s>

<s>330). </s></p><p type="main">

<s>Comunque sia, mancherebbe a queste atlantiche fatiche, durate nel ri&shy;<lb/>tessere i calcoli per le tre Tavole ballistiche, ogni ragion di scusa e di me&shy;<lb/>rito, se fosse vero ch'elle non fosser altro che castelli in aria, com'andava <lb/>dicendo fra gli amici il Cartesio. </s>

<s>L'accusa del Filosofo famoso, per quanto <lb/>possa essere stata suggerita o dall'emulazione o dall'invidia, d&agrave; indizio del <lb/>dover esservi altre difficolt&agrave; promosse da uomini d'altro animo e d'altro <lb/>ingegno, delle quali difficolt&agrave;, e della loro efficacia in confermar sempre me&shy;<lb/>glio la Scienza de'proietti, novamente istituita da Galileo, faremo ora sog&shy;<lb/>getto questa ultima parte del nostro discorso. </s></p><pb xlink:href="020/01/2321.jpg" pagenum="564"/><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>L'istituzione di quella nuova Scienza galileiana essendo tutta fondata <lb/>sul moto parabolico, sarebbe stata dunque per i contradittori rovesciata dalle <lb/>sue fondamenta, quando fossero state false le ipotesi, dalle quali consegui&shy;<lb/>van legittimamente le ragioni di una tal direzione dei moti proiettizi. </s>

<s>&ldquo; Fal&shy;<lb/>sam aliam hypothesin prioribus adiicit (soggiunge il Cartesio stesso nella <lb/>citata Epistzla al Mersenno, dove censura tante altre dottrine di Galileo) <lb/>nempe corpora in aerem proiecta aequali velocitate ferri secundum horizon&shy;<lb/>tem, descendendo vero illorum velocitatem in ratione spatii duplicata augeri. </s>

<s><lb/>Hoc autem posito, facillimum est concludere motum proiectorum sequi li&shy;<lb/>neam parabolicam, sed, cum eius hypotheses sint falsae, conclusio etiam a <lb/>vero valde remota esse potest &rdquo; (pag. </s>

<s>244). </s></p><p type="main">

<s>Perch&egrave; falsa debba tenersi l'ipotesi, che il proietto venga equabilmente <lb/>promosso per linea orizzontale, discendendo nel perpendicolo con velocit&agrave; <lb/>crescenti in duplicata proporzion degli spazi, il Cartesio non dice, ma lo <lb/>dicon bene gli altri, a cui i dubbi facevano nella mente le medesime ten&shy;<lb/>zoni. </s>

<s>Dicevan dunque che il moto nell'orizzonte, tutt'altro ch'essere equa&shy;<lb/>bile, &egrave; pi&ugrave; accelerato nel principio, e pi&ugrave; tardo verso la fine, e che una <lb/>tanta violenza d'impeto impedisce cos&igrave; la libera discesa del grave, che non <lb/>pu&ograve; accelerarsi secondo la natural sua proporzione. </s></p><p type="main">

<s>I dubbi cartesiani si vedono passar per la mente degli stessi discepoli <lb/>di Galileo, con ombre di s&igrave; ugual tinta e figura, da escludere in sollevarle <lb/>qualunque mala disposizion dell'animo nel geloso rivale. </s>

<s>Ascoltiamo Anto&shy;<lb/>nio Nardi, che cos&igrave; prosegue, nella veduta XLII della scena VI, dop'aver <lb/>censurate le dottrine del suo proprio Maestro, circa alla proporzione del&shy;<lb/>l'accelerarsi i gravi nei loro liberi moti. </s>

<s>E prima di tutto &egrave; a notare un'opi&shy;<lb/>nione di lui, dimostrata falsa dalle cose discorse ne'precedenti capitoli di <lb/>questa Storia, che cio&egrave; dalla scoperta della parabola dei proietti prendesse <lb/>Galileo occasione d'assegnare ai cadenti naturali le medesime leggi. </s>

<s>Contro <lb/>dunque quel che not&ograve; il Torricelli <emph type="italics"/>de linea parabolica pro motibus natu&shy;<lb/>raliter cadentium, quod non scripsit Galileus,<emph.end type="italics"/> cos&igrave; il Nardi incomincia la <lb/>seconda parte delle sue censure. </s></p><p type="main">

<s>&ldquo; Quanto poi all'essere il moto de'proietti apparentemente parabola, <lb/>concordo col Galilei, che forse quindi congettur&ograve; i gravi affrettarsi con la <lb/>medesima ragione, ma osservisi che diverse strade conducono al medesimo <lb/>termine. </s>

<s>Dunque &egrave; vero che il moto orizzontale &egrave; uguale, ma ci&ograve; s'intende, <lb/>mentre un mobile sia sostenuto e mosso per qualche orizzontal superfice, <lb/>sicch&egrave; compensato vengane il suo momento. </s>

<s>Ma un proietto per l'aria muo&shy;<lb/>vesi, perch&egrave; non viene compensato il momento suo, di due moti, quali in&shy;<lb/>sieme rimescolati non si mantengono ciascuno di essi sinceri, ma scambie-<pb xlink:href="020/01/2322.jpg" pagenum="565"/>volmente si alterano, e par necessario che il violento sia pi&ugrave; veloce nell'uscire <lb/>dal proiciente, che allontanatone, com'anco nel natural moto avviene, e per&ograve; <lb/>non passer&agrave; di sua natura spazi uguali in tempi uguali, come in tal punto <lb/>dubit&ograve; il Galilei. </s>

<s>Anzi che alcuni Meccanici si persuasero che nell'uscir la <lb/>palla dall'artiglieria andasse per qualche spazio rettamente, il che, sebbene <lb/>vero non &egrave;, perch&egrave; non s'annulla l'azione della gravit&agrave;, con tutto ci&ograve; par <lb/>vero che il moto orizzontale sostenga da principio il proietto, sicch&egrave; non di&shy;<lb/>scenda con la ragione, con la quale discenderebbe per la sola gravit&agrave;, ma <lb/>nel progresso &egrave; necessario che la gravit&agrave; vinca l'impeto straniero, acci&ograve; si <lb/>riconduca il proietto al centro, e cos&igrave; anche appare necessario che la forza, <lb/>quale prima mosse un proietto dallo stato di quiete, non cos&igrave; muover lo <lb/>possa, dopo l'acquisto e accrescimento di moto verso il centro. </s>

<s>Ora, dal&shy;<lb/>l'intrecciamento di questi moti, momenti e tempi, componsi una linea molto <lb/>vicino alla parabolica, ma difficilissimo da me si reputa il dimostrarla tale, <lb/>per i suoi immediati principii. </s>

<s>E tanto, per modo di semplice dubitazione, <lb/>basti aver apportato intorno a varii pensieri del mio Maestro &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. XL, pag. </s>

<s>973, 74). </s></p><p type="main">

<s>Andando a ricercar per&ograve; la profonda radice di questi dubbi, cos&igrave; libe&shy;<lb/>ramente esposti dal Nardi, si troverebbe in quel principio della composizione <lb/>dei moti, da cui risulta la parabola dei proietti; principio, che quale &egrave; espo&shy;<lb/>sto nella II proposizione di Galileo, giova ripeterlo ancora dopo tante volte, <lb/>&egrave; manifestamente falso. </s>

<s>Anche, senza il Mersenno, dovevasi a quel vivo <lb/>lampo di luce, riflesso dallo scolio alla proposizione XVIII del primo libro <lb/>del Torricelli, riconoscer impossibile, che non si elidano due forze ango&shy;<lb/>lari, onde al sentor di falso, che veniva dalla dottrina galileiana, trascorre&shy;<lb/>vasi nell'apposto errore insegnato dal Cardano. </s></p><p type="main">

<s>Ci porge un notabile esempio di ci&ograve; il Baliani, il quale dice, nel suo <lb/>breve proemio al terzo libro <emph type="italics"/>De motu naturali,<emph.end type="italics"/> che sarebbe quello il luogo <lb/>di trattar de'proietti, &ldquo; ni via, quam eorum motu conficiunt, me adhuc la&shy;<lb/>teret, quamvis non ignorem viris oculatissimis visam esse parabolicam &rdquo; <lb/>(Gennae 1646, pag. </s>

<s>80). Tale per&ograve; a me non sembra, soggiunge lo stesso <lb/>Baliani, perch&egrave;, contro ci&ograve; che da que'chiarissimi uomini si suppone, &ldquo; ap&shy;<lb/>paret proiectum descendere minori celeritate, quam si a sola ducatur gra&shy;<lb/>vitate, et libere demissum celerius solum attingere, quam horizontaliter la&shy;<lb/>tum &rdquo; (ibid., pag. </s>

<s>81). La ragione di ci&ograve; &egrave;, secondo l'Autore, quella medesima <lb/>gi&agrave; detta dal Cardano, e ripetuta dal Nardi, come dianzi udimmo, dovendo <lb/>la forza, che trasporta il grave per linea orizzontale, repugnare all'altra, che <lb/>lo farebbe scendere nel perpendicolo. </s></p><p type="main">

<s>Per altre due ragioni credeva il Baliani di non poter consentire col Ca&shy;<lb/>valieri, col Galileo e col Torricelli, che la via de'proietti sia parabolica. </s>

<s><lb/>Prima, perch&egrave;, se il mobile passa successivamente nella traiettoria spazi sem&shy;<lb/>pre pi&ugrave; lunghi, &ldquo; motus est successive velocior, quippe maius spatium aequo <lb/>tempore permeat, unde si, vis proiicientis provenit a maiori velocitate, ic&shy;<lb/>tus eo est validior, quo missile longius a proiiciente distat, contra id quod <pb xlink:href="020/01/2323.jpg" pagenum="566"/>quotidie experimur &rdquo; (idid.). Ma qui evidentemente si confonde il tiro ele&shy;<lb/>vato con quello di punto in bianco, nel qual caso concorrono la teoria e <lb/>l'esperienza a dimostrare che il colpo &egrave; veramente tanto pi&ugrave; valido, <emph type="italics"/>quo <lb/>missile longius a proiiciente distat.<emph.end type="italics"/> N&egrave; punto pi&ugrave; ragionevole di questa &egrave; <lb/>l'altra difficolt&agrave;, ivi in terzo luogo promossa dal medesimo Autore, da cui <lb/>si crede che, supponendo essere il proietto abbandonato a un tratto dal&shy;<lb/>l'impeto della propria gravit&agrave;, proseguirebbe secondo la direzion tangen&shy;<lb/>ziale, non avvedendosi che piegare il mobile verso il centro dei gravi, e sup&shy;<lb/>porlo senza gravit&agrave;, &egrave; una manifesta contradizione. </s></p><p type="main">

<s>I secondi dubbi, esposti cos&igrave; dal Baliani, nascevano dunque da incon&shy;<lb/>sideratezza delle teorie galileiane, ma del primo erano queste medesime <lb/>teorie che, cos&igrave; in lui come nel Nardi e nel Cartesio, ne avevano data pre&shy;<lb/>sentissima occasione. </s>

<s>Gli osservatori zelanti delle dottrine di Galileo avevano <lb/>un bel dire che il moto trasversale non impedisce il naturale <emph type="italics"/>deorsum,<emph.end type="italics"/> per <lb/>le ragioni e per i fatti accennati nella seguente nota del Viviani: &ldquo; Si trans&shy;<lb/>versalis motus deorsum naturalem impediret, lapis transversim proiectus <lb/>numquam descenderet, nisi assumpto transversali motu, quoniam naturalis <lb/>deorsum adeo lente in principio procedit, ut quicumque transversalis motus <lb/>ipsum naturalem impediet. </s>

<s>Sed transversalis impetus nunquam cessat, ergo <lb/>lapis nunquam descenderet, quod est contra Naturae leges, et contra quo&shy;<lb/>tidiana experimenta &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>19). Ma non pote&shy;<lb/>vano aver queste ragioni nessuna efficacia sulla mente dei dubitanti, i quali, <lb/>ben riconoscendo non essere le potenze dinamiche, introdotte da Galileo <lb/>nella sua proposizione seconda, altro che linee, vedevano concludersi da <lb/>quella medesima proposizione l'assurdo che l'ipotenusa sia uguale alla somma <lb/>dei cateti. </s>

<s>Non furono i dubbi perci&ograve;, da questa parte, soluti, se non che <lb/>quando ebbero i Matematici, con universale consentimento, approvata la re&shy;<lb/>gola del parallelogrammo, dalla quale appar&igrave; chiaro come i moti si elidano <lb/>nel compor la parabola, in modo per&ograve;, che rimangano uguali i tempi im&shy;<lb/>piegati a passar ora divisamente i lati, ora compostamente la diagonale. </s></p><p type="main">

<s>Altri dubbi, che potessero passar per la mente ai lettori, erano stati <lb/>prevenuti gi&agrave; dal Cavalieri e da Galileo, i quali condussero le loro propo&shy;<lb/>sizioni, astraendo dagl'impedimenti del mezzo, de'quali pure essendo sgom&shy;<lb/>bri i proietti disse il Cavalieri che descrivono una linea curva <emph type="italics"/>insensibil&shy;<lb/>mente differente dalla parabola.<emph.end type="italics"/> Accenna perci&ograve;, nella sua precisione, il <lb/>Matematico che non sarebbe perfettamente parabolica, nemmen la curva de&shy;<lb/>scritta nel vuoto, non essendo propriamente parallele le direzioni delle forze <lb/>di gravit&agrave;, ma concorrenti. </s>

<s>Galileo volle esplicitamente avvertire che la pro&shy;<lb/>posizione sua prima era solamente vera nel supposto medesimo fatto da Ar&shy;<lb/>chimede, &ldquo; il quale, nelle sue Meccaniche, e nella prima quadratura della <lb/>parabola, piglia come principio vero l'ago della bilancia o stadera essere <lb/>una linea retta in ogni suo punto ugualmente distante dal centro comune <lb/>dei gravi, e le corde alle quali sono appesi i gravi esser tra di loro paral&shy;<lb/>lele &rdquo; (Alb. </s>

<s>XIII, 228): ond'&egrave; che parabolica pu&ograve; esser la via de'proietti <pb xlink:href="020/01/2324.jpg" pagenum="567"/>nelle sole brevi distanze, a cui posson giungere l'esplosioni dei nostri stru&shy;<lb/>menti. </s>

<s>Con ragione dunque dimostrava Domenico Guglielmini nella VI pro&shy;<lb/>posizione della sua <emph type="italics"/>Epitropeia,<emph.end type="italics"/> che a 1600 miglia, quanto si suppone da un <lb/>suo contradittore farsi un getto, questo esorbiterebbe grandemente dalla pa&shy;<lb/>rabola <emph type="italics"/>&ldquo; etiam in doctrina Galilei &rdquo;<emph.end type="italics"/> (Bononiae 1676, pag. </s>

<s>19). Nella grande <lb/>ampiezza infatti della semiparabola BI (fig. </s>

<s>303), le direzioni della gravit&agrave; <lb/>del proietto ne'punti G, F, E essendo GX, FX, EX, se con raggi appun&shy;<lb/><figure id="id.020.01.2324.1.jpg" xlink:href="020/01/2324/1.jpg"/></s></p><p type="caption">

<s>Figura 303<lb/>tati in X si descrivono cerchi, che <lb/>seghino la parabola ne'punti D, H, I, <lb/>si vedr&agrave; manifesto che le linee obli&shy;<lb/>que GK, FN, EB son minori delle re&shy;<lb/>spettive perpendicolari GD, FH, EI, <lb/>ond'&egrave; che ne'tempi BG, BF, BE non <lb/>sarebbe il proietto sceso in D, H, I, <lb/>lungo la parabola, ma sotto i punti <lb/>K, N, B, dentro la parabola, &ldquo; quare <lb/>linea, per ea puncta descensuum de&shy;<lb/>scripta, non erit parabola &rdquo; (ibid., <lb/>pag. </s>

<s>21, 22). </s></p><p type="main">

<s>Il Guglielmini dunque conferma&shy;<lb/>va, piuttosto che impugnare le dot&shy;<lb/>trine di Galileo, le quali venivano <lb/>nonostante assalite da altre parti. </s>

<s>Le <lb/>teorie degli impeti e le loro applica&shy;<lb/>zioni si fanno, nel quarto dialogo delle <lb/>Nuove Scienze, dipendere da due sup&shy;<lb/>posti: il primo de'quali &egrave; che la direzione del moto si fa secondo la tan&shy;<lb/>gente alla curva, nel punto della separazione, e il secondo, che la parabola <lb/>CA (fig. </s>

<s>304), descritta dall'esplosione in C con tiro livellato, &egrave; la mede&shy;<lb/>sima che la parabola AC, descritta dall'esplosione in A con tiro inclinato. <lb/><figure id="id.020.01.2324.2.jpg" xlink:href="020/01/2324/2.jpg"/></s></p><p type="caption">

<s>Figura 304<lb/>Il primo era stato supposto anche dal Tartaglia, nel se&shy;<lb/>condo libro della <emph type="italics"/>Nova scientia,<emph.end type="italics"/> ove dice: &ldquo; Ogni corpo <lb/>egualmente grave in fine de ogni moto violente, che sia <lb/>fuora della perpendicolare di l'orizonte, si mover&agrave; di <lb/>moto naturale il qual sar&agrave; contingente con la parte curva <lb/>del moto violente &rdquo; (fol. </s>

<s>19 a tergo). Ma Galileo aveva, <lb/>come dicemmo, esplicato assai minutamente, ne'dialoghi <lb/>dei Massimi sistemi, queste dottrine, contro le quali nul&shy;<lb/>ladimeno cos&igrave; volle argomentare l'Aggiunti. </s></p><p type="main">

<s>&ldquo; Acciocch&egrave; un mobile acquisti da virt&ugrave; estrinseca <lb/>impeto di muoversi per una tal direzione, bisogna che <lb/>il motore l'abbia movendo accompagnato per qualche <lb/>spazio in essa dirittura. </s>

<s>Gli esempi sono di questo la balestra, che, accom&shy;<lb/>pagnando poco la palla, la move anche pochissimo. </s>

<s>Il maglio, scorrendo <pb xlink:href="020/01/2325.jpg" pagenum="568"/>e non accompagnando, non muove, e piegandosi nel manico, perch&egrave; allora <lb/>all'accompagnatura del braccio v'aggiunge quella del ritorno del manico pie&shy;<lb/>gato, fa maggior colpo. </s>

<s>La racchetta per questo manda pi&ugrave; la palla lon&shy;<lb/>tana, che la mestola. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto insomma minore sar&agrave; questa accompagnatura, <emph type="italics"/>caeteris pari&shy;<lb/>bus,<emph.end type="italics"/> minore sar&agrave; l'acquisto dell'impeto, sicch&egrave;, se un motore movesse un <lb/>mobile in un poligono di moltissimi lati e brevissimi, onde le accompagna&shy;<lb/>ture sarebbero ancor esse brevissime, questo mobile non acquisterebbe nota&shy;<lb/>bile impeto di moversi per alcuna di queste linee. </s>

<s>Adunque perch&egrave; il mobile, <lb/>mosso dai motori in un cerchio, cio&egrave; in un poligono d'infiniti lati, e per&shy;<lb/>ci&ograve; di niuna longitudine, variano ad ogni momento direzione di moto; le <lb/>accompagnature in ciascuna direzione sarebbero istantanee, e per&ograve; di niuno <lb/>o minimo momento. </s>

<s>E per questo l'acquisto d'impeto di moversi in alouna <lb/>di esse sarebbe nullo o minimo, laonde sar&agrave; falso che dalla vertigine di <lb/>una ruota si conferisca alla sua parte impeto di moversi per la tangente, <lb/>come asserisce l'eccellentissimo signor Galileo &rdquo; (MSS. Gal. </s>

<s>Disc., T. XVIII, <lb/>fol. </s>

<s>59). </s></p><p type="main">

<s>Non potrebbe dunque nemmeno il proietto aver valido impulso di mo&shy;<lb/>versi lungo la tangente della parabola, se fosse vera la conclusion dell'Ag&shy;<lb/>giunti, la quale parte dal principio delle accompagnature, male applicato <lb/>agli effetti dei citati strumenti, e manifestamente falso in s&egrave; stesso, perch&egrave; <lb/>la forza si comunica in istante, e non con tempo. </s>

<s>D'altro momento &egrave; perci&ograve; <lb/>l'opposizione fatta al secondo supposto, la quale non sfuggi alla censura del <lb/>Cartesio. </s>

<s>&ldquo; Conversam propositionis suae assumit, egli dice nella citata epi&shy;<lb/>stola al Mersenno, neque demonstratam, neque explicatam; nimirum quod, <lb/>si globus, secundum horizontem explosus a C (nella precedente figura) ver&shy;<lb/>sus O, sequatur parabolam CA, globus etiam, sursum explosus secundum <lb/>lineam AO, debeat eamdem parabolam AC sequi, quod quidem ex eius hypo&shy;<lb/>thesibus recte sequitur, sed haec explicare non videtur ausus, ne eorum fal&shy;<lb/>sitas nimis aperte pareret &rdquo; (pag. </s>

<s>244). </s></p><p type="main">

<s>Il Torricelli, che riseppe forse le calunniose cartesiane censure dallo <lb/>stesso Mersenno, pens&ograve; di ovviarle e di rispondere con quella elaboratissima <lb/>proposizione III del secondo suo libro, nella quale dimostra che la linea <lb/>curva &ldquo; quae describitur a mobili, secundum quamlibet elevationem proiecto, <lb/>parabola est, et prorsus eadem, quam describeret mobile, si cum horizon&shy;<lb/>tali impetu proiceretur a vertice eiusdem lineae curvae &rdquo; (pag. </s>

<s>157). Ma &egrave; <lb/>notabile che Galileo stesso, appena dimostrate le proposizioni attenenti alle <lb/>prime due parti del suo trattato, avesse gi&agrave; presentite quelle medesime dif&shy;<lb/>ficolt&agrave;, e quasi, per ridursene alla memoria la risposta, da inserirsi poi nel <lb/>venire a stendere il Dialogo quarto; ne lesciava scritto di sua propria mano, <lb/>sotto il sommario delle proposizioni, questo cos&igrave; compendioso commento: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Simplicio.<emph.end type="italics"/> &mdash; Che la palla, ricacciata in su, descriva la medesima SX <lb/>(fig. </s>

<s>305) mi par duro. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Sagredo.<emph.end type="italics"/> &mdash; Ma se non vi par duro che, descrivendo la parabola in-<pb xlink:href="020/01/2326.jpg" pagenum="569"/>tera YXS, possa ridescrivere la SXY, non vedete che di necessit&agrave; fa la SX? &rdquo; <lb/>(MSS. Gal., P. V, T. II, a tergo del fol. </s>

<s>106). </s></p><p type="main">

<s>Poi and&ograve; il proposito in dimenticanza, della quale dolendosi Galileo col <lb/>Viviani, gli veniva dettando il frammento del Dialogo, da aggiungere dopo <lb/>la VII proposizion de'proietti, quando delle Due nuove scienze si fosse per <lb/><figure id="id.020.01.2326.1.jpg" xlink:href="020/01/2326/1.jpg"/></s></p><p type="caption">

<s>Figura 305<lb/>fare una ristampa. </s>

<s>Avremo occasione di tornare so&shy;<lb/>pra ci&ograve; in discorso in quest'altra parte della nostra <lb/>Storia, e per ora vediamo com'esso Viviani, appro&shy;<lb/>priandoselo, esplicasse quel pensiero di Galileo: </s></p><p type="main">

<s>&ldquo; Nella dottrina de'moti de'proietti, e partico&shy;<lb/>larmente alla VII proposizione, a c. </s>

<s>270, si suppone <lb/>dal Galileo come indubitato che, venuto il proietto <lb/>da alto al basso, con descrivere la semiparabola, cac&shy;<lb/>ciato poi per lo contrario da basso ad alto, e'debba <lb/>tornare per la medesima linea parabolica, ricalcando precisamente le mede&shy;<lb/>sime vestigia. </s>

<s>Ma non avendo per ci&ograve; fare il detto proietto altro regolatore <lb/>che la direzione della semplice linea retta, toccante la gi&agrave; disegnata semi&shy;<lb/>parabola, per la cui declinazione fatta dall'alto al basso l'impeto transver&shy;<lb/>sale orizontale ed equabile ci quieta ad ammettere la molta curvazione nella <lb/>sommit&agrave;. </s>

<s>Cercasi d'intendere come l'impulso fatto da basso ad alto, per una <lb/>retta tangente, possa restituire un tal impeto trasversale, e che sia atto a re&shy;<lb/>golare la medesima curvit&agrave; nel viaggio di detto proietto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Qui per risposta potrassi dire che, nel nominare la retta tangente, si <lb/>lascia una sua condizione, che &egrave; l'esser tangente e inclinata, la quale in&shy;<lb/>clinazione &egrave; bastante a far che il proietto, in tempi eguali, si accosti oriz&shy;<lb/>zontalmente per spazi uguali all'asse della parabola. </s>

<s>Inoltre, se la linea de&shy;<lb/>scritta da un proietto da basso ad alto, secondo qualche inclinazione, &egrave; ve&shy;<lb/>ramente una intera linea parabolica, e se niente importa che la proiezione <lb/>si faccia da levante verso ponente, o per l'opposito, quando per&ograve; l'eleva&shy;<lb/>zione sia l'istessa, ed istessa la forza proiciente, fatto che si sia il tiro da <lb/>qualsivoglia parte; che cosa ha da mettere in dubbio che la semiparabola <lb/>da basso ad alto del secondo tiro, che si faccia in contrario del primo, non <lb/>sia la medesima che la seconda semiparabola del primo tiro, sicch&egrave; il pro&shy;<lb/>ietto ritorni per la medesima strada? </s>

<s>Che quando ci&ograve; non fosse, manco la <lb/>parabola intera del secondo tiro sarebbe uguale a quella del primo &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>16). </s></p><p type="main">

<s>La risposta, che faceva cos&igrave; il Viviani in quella sua <emph type="italics"/>Raccolta di espe&shy;<lb/>rienze e di pensieri,<emph.end type="italics"/> che diceva essergli sovvenuti in mente intorno a ma&shy;<lb/>terie meccaniche e fisiche, &egrave;, come si vede, uno svolgimento del pensiero <lb/>medesimo gi&agrave; sovvenuto in mente allo stesso Galileo, a prevenire le cen&shy;<lb/>sure fatte poi dal Cartesio intorno a cose puramente speculative. </s>

<s>Ma la spe&shy;<lb/>culazione stessa aveva in mano degli oppositori, per via dell'esperienza, un <lb/>criterio ben assai pi&ugrave; certo, per decidere in proposito del vero e del falso. </s></p><p type="main">

<s>Che si potessero propriamente le galileiane teorie de'proietti illustrare <pb xlink:href="020/01/2327.jpg" pagenum="570"/>con l'esperienze, sembra essere stato uno de'primi pensieri sovvenuti agli <lb/>Accademici fiorentini, come pu&ograve; congetturarsi dalla seguente Nota, lascia&shy;<lb/>taci manoscritta dal Viviani: &ldquo; Quod mobile sursum proiectum, per directio&shy;<lb/>nem non perpendicularem, in suo descensu numquam per spacium perpen&shy;<lb/>diculare moveatur, experiemur si proiectiones fiant sagittis vel virgulis ferro <lb/>cuspidatis, quae, dum solum pertingent; ad aequales angulos eum perfora&shy;<lb/>bunt, ac omnino pares iis, secundum quos factae sunt proiectiones &rdquo; (ibid., <lb/>fol. </s>

<s>14). </s></p><p type="main">

<s>La bella esperienza sar&agrave; stata forse felicemente eseguita, ma non si trova <lb/>fatto di essa, almeno nel libro dei <emph type="italics"/>Saggi,<emph.end type="italics"/> alcuna memoria, perch&egrave; dovevasi <lb/>lasciar luogo alla descrizione di altre esperienze, credute ben assai pi&ugrave; de&shy;<lb/>cisive della verit&agrave; o della falsit&agrave; delle nuove dottrine galileiane. </s>

<s>Fondamento <lb/>a cos&igrave; fatte dottrine apparisce dalla Storia essere stato l'isocronismo delle <lb/>curve de'proietti, aventi la medesima altezza, intorno a che i Matematici <lb/>sent<gap/>rono diversamente. </s>

<s>In Francia tenevasi cos&igrave; per certo spedirsi la ca&shy;<lb/>duta perpendicolare e la parabolica nel medesimo tempo, che dalla sensi&shy;<lb/>bile differenza osservata si credeva di potere argomentarne quanto fosse l'im&shy;<lb/>pedimento dell'aria. </s>

<s>Il Mersenno, nel III tomo delle sue Nuove osservazioni <lb/>fisiche matematiche, proponeva a Lodovico principe di Vales di fare espe&shy;<lb/>rienze in una fortezza, posta a mare, dalla quale si facesse con vario im&shy;<lb/>peto esplodere un cannone, con tiro semiretto. </s>

<s>S'ha dalla teoria, in questo <lb/>caso, che il tempo impiegato a descrivere l'intera parabola &egrave; doppio di quel <lb/>che ci vorrebbe a scender per l'altezza di lei, ossia uguale a quello del <lb/>veniente per una linea perpendicolare, quadrupla dell'altezza della parabola, <lb/>ond'&egrave; che misurando con un pendolo a secondi il tempo speso dalla palla <lb/>in passare queste vie diverse, se vi si nota alcuna differenza &egrave; da attribuire <lb/>all'impedimento dell'aria, che cos&igrave; dunque sapremo quanto egli sia. </s>

<s>&ldquo; Porro <lb/>Tauroentum eligi potest, a cuius portu nobili iactum semirectum in mari <lb/>mediterraneo, ad unum vel alterum milliare situm, dimetientur observato&shy;<lb/>res, vel in ipso castello, vel secus illud in statione positi, cum horologiis, <lb/>quibus tam verticalis, quam semirecti et horizontalis iactuum durationes <lb/>explorent &rdquo; (Parisiis 1647, pag. </s>

<s>III). </s></p><p type="main">

<s>Se fossero propriamente fatte, in quella fortezza o altrove, in Francia, <lb/>le difficili esperienze, non &egrave; certo, com'&egrave; certo che furon fatte in Italia, <lb/>dove le imbevute dottrine cardaniche avevano dato ai giudiz&igrave; de'matematici <lb/>altra forma. </s>

<s>Vedemmo come il Baliani tenesse esser la scesa per la curva pi&ugrave; <lb/>diuturna che per il perpendicolo, a cagione dell'impedirsi i due moti com&shy;<lb/>ponenti a vicenda, e dall'altra parte troppo aveva seducente apparenza di <lb/>vero il dir che pi<gap/> tempo bisogna a far la via pi&ugrave; lunga, che la pi&ugrave; corta. </s>

<s><lb/>De'pi&ugrave; facilmente sedotti fra costoro fu il Cabeo che, mostrandosi anche <lb/>questa volta censore di Galileo assai poco giudizioso, dop'aver riferito le <lb/>dottrine di lui circa all'isocronismo tra la scesa retta e la parabolica, sog&shy;<lb/>giunge: &ldquo; Hoc ego non admitto, donec experimentis credam, quod experi&shy;<lb/>mentum hactenus facere non potui. </s>

<s>Fiet autem facile, si in litore supra mare <pb xlink:href="020/01/2328.jpg" pagenum="571"/>quietum, aut lacum, constituas bombardam horizontaliter collocatam, et su&shy;<lb/>pra bombardam constituas globum, et explodas: dum enim explodis, ex illo <lb/>motu decidit globus &rdquo; (Metereol. </s>

<s>comm., lib. </s>

<s>I, Romae 1646, pag. </s>

<s>95). </s></p><p type="main">

<s>L'esperienza, che dice il Cabeo di non aver potuta fare, e le contro&shy;<lb/>versie insorte fra'Matematici in questo proposito, invogliarono gli Accede&shy;<lb/>mici del Cimento, in un Diario manoscritto dei quali leggesi, fra le tante <lb/>altre, &ldquo; L'esperienza CCLXXXVIII per molti, che dicevano per i loro scritti, <lb/><figure id="id.020.01.2328.1.jpg" xlink:href="020/01/2328/1.jpg"/></s></p><p type="caption">

<s>Figura 306<lb/>ed altri affermavano che, dato un tiro di una ar&shy;<lb/>tiglieria sopra una elevazione es. </s>

<s>gr. </s>

<s>A (fig. </s>

<s>306), <lb/>ove fosse la bocca del pezzo, con una palla di egual <lb/>peso di quella che dentro al pezzo era stata messa, <lb/>e quella alla bocca di detto era attaccata con un <lb/>filo, calando per l'appunto sotto l'orlo del pezzo; <lb/>che, mentre usciva la palla di dentro, faceva ca&shy;<lb/>dere ad un tratto quella di fuori: ed affermavano <lb/>che sarebbe caduta la palla, che usciva portata dal <lb/>fuoco nel punto B, nell'istesso tempo che l'altra, <lb/>a perpendicolo cadendo, arrivava nel punto C, piano <lb/>stesso di BD, e ci&ograve; fu provato a Livorno, facendosi <lb/>tirare il pezzo dalla torre della fortezza verso il <lb/>mare, con un cannone da quattordici. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Parve a molti che cadessero tutte ad un tempo, ma, con uno da venti, <lb/>fu osservato prima dare nel piano quella, che cadeva a perpendicolo, che <lb/>l'altra che cadeva nella distanza, e tanto tempo dette che, vistola cadere <lb/>in C, dette tempo di rivoltare il viso a vedere cadere l'altra in B. &rdquo; </s></p><p type="main">

<s>&ldquo; Ci fu chi appell&ograve;, bench&egrave; si riprovasse pi&ugrave; volte, che poteva venire <lb/>dalla pi&ugrave; quantit&agrave; del solito della polvere, e non di tanta squisitezza; ma <lb/>con pi&ugrave; meglio (sic) ragione, dicevano ancora che ci era differenza quanto <lb/>dalla bocca del pezzo alla fine per di sotto dell'orlo, e perci&ograve; cadeva pi&ugrave; <lb/>presto: di pi&ugrave;, che la Torre, non bagnando con il piede per l'appunto nel <lb/>mare, ma ci poteva esser differenza di pi&ugrave; alto da un braccio; che l'una e <lb/>l'altra differenza poteva far che prima quella a perpendicolo nel piano BD <lb/>arrivasse, perch&egrave; la vera ragione voleva tutt'e due in uno stesso tempo ca&shy;<lb/>dessero. </s>

<s>Ma si tennero tutti supposti, per trovare appello ancora a quel che <lb/>sensibilmente s'era visto. </s>

<s>Nulladimeno si lasci&ograve; la proposizione in pendente, <lb/>senza deciderla &rdquo; (MSS. Cim., T. III, fol. </s>

<s>66). </s></p><p type="main">

<s>La dicitura, tanto lontana dall'eleganza dei <emph type="italics"/>Saggi,<emph.end type="italics"/> &egrave; del Rinaldini, che <lb/>faceva allora l'ufficio di segretario dell'Accademia, prima del Magalotti, il <lb/>qual Rinaldini torn&ograve;, per decidere la questione, a ripetere, nel Genna io <lb/>del 1658, da quella medesima fortezza di Livorno, l'esperienze rimaste cos&igrave; <lb/>incerte. </s>

<s>&ldquo; Inoltre, scriveva il d&igrave; primo di Febbraio al Viviani, ho fatto l'espe&shy;<lb/>rienza del tiro del pezzo, osservando se la palla, nel medesimo tempo, cade <lb/>perpendicolarmente dalla bocca, e la spinta dalla polvere arriva al mede&shy;<lb/>simo piano, e dopo molte riprove abbiamo ritrovato che ambe le palle ca-<pb xlink:href="020/01/2329.jpg" pagenum="572"/>dono in un tempo stesso, onde in un medesimo tempo l'una e l'altra giunge <lb/>al piano dell'orizonte, del che ne ho avuto sommo gusto &rdquo; (ivi, T. XXXVII, <lb/>fol. </s>

<s>39). </s></p><p type="main">

<s>Tre giorni dopo, nell'occasione di dar conto allo stesso Viviani di altre <lb/>esperienze, il Rinaldini gli ripeteva: &ldquo; Di gi&agrave; le ho dato avviso dell'espe&shy;<lb/>rienza fatta a Livorno del pezzo, come nel medesimo tempo &egrave; caduta la palla <lb/>dalla bocca, e giunta all'orizonte, che quella spinta dalla polvere, e sebbene, <lb/>in un pezzo pi&ugrave; grosso, pare abbi fatto qualche poco di differenza, nulladi&shy;<lb/>meno credo assolutamente che ci&ograve; sia proceduto dal non essere ben livel&shy;<lb/>lato il pezzo, sicch&egrave; si puol concludere che cadono nel tempo medesimo &rdquo; <lb/>(ivi, fol. </s>

<s>41). </s></p><p type="main">

<s>La conclusione del Rinaldini era senza dubbio fallace, e meglio si con&shy;<lb/>formavano col vero le prime esperienze sopra descritte, perch&egrave;, se l'aria, <lb/>nel viaggio pi&ugrave; lungo, anche impedisce pi&ugrave; a proporzione la velocit&agrave; del <lb/>moto; era impossibile vedere esattamente i fatti corrispondere con le teorie, <lb/>che astraggono da ogni sorta d'impedimenti. </s>

<s>Ma quegli sperimentatori non <lb/>sembra che pensassero punto a queste cose, e le ragioni che, come udimmo, <lb/>dissero pro e contro nelle loro dispute, non rivelano degli Accademici del <lb/>Cimento il consueto senno ed acume, la misura del quale &egrave; data partico&shy;<lb/>larmente in questo fatto dalla mente propria del Rinaldini. </s>

<s>Ora, sanno bene <lb/>i nostri Lettori chi fosse quell'uomo, il quale vestiva la stola dell'Accade&shy;<lb/>mia sopra la toga peripatetica. </s>

<s>Con quale intelligenza poi egli dirigesse le <lb/>delicate esperienze si pu&ograve; argomentare dal fatto, ch'ei non s'era ancora <lb/>studiato d'intenderne il fine. </s>

<s>Aveva sentito dire essere questo fine quello <lb/>di verificare un'opinione di Galileo, ma come e dove fosse una tale opinione <lb/>esposta ei non sapeva, per cui, quasi un mese dopo aver fatta l'esperienza <lb/>a Livorno, si rivolgeva al Viviani, pregandolo a volerlo avvisare &ldquo; dove il <lb/>Galileo tratta precisamente del tiro del pezzo, e della palla cadente dalla <lb/>bocca. </s>

<s>V. S. ne puol domandare al signor Cosimo (Galilei), il quale mi pro&shy;<lb/>mise di avvisarmelo &rdquo; (ivi, fol. </s>

<s>43). </s></p><p type="main">

<s>Una tale ignoranza in un Accademico del Cimento non era scusabile, <lb/>essendo il luogo ch'ei cercava assai cospicuo nel secondo dialogo dei Mas&shy;<lb/>simi Sistemi, dove, a pag. </s>

<s>148, 49 dell'edizione originale, avrebbe potuto <lb/>leggere: &ldquo; e quando non ci fusse l'impedimento accidentario dell'aria, io <lb/>tengo per fermo che se, nell'uscir la palla dal pezzo si lasciasse cadere un'al&shy;<lb/>tra dalla medesima altezza gi&ugrave; a piombo, amendue arriverebbero in terra <lb/>nel medesimo istante. </s>

<s>&rdquo; </s></p><p type="main">

<s>N&egrave; sembra che gli altri disputanti col Rinaldini, sotto la fortezza di Li&shy;<lb/>vorno, fossero punto pi&ugrave; pratici delle materie scritte nel Dialogo famoso, <lb/>ci&ograve; che prova esservi anc'allora ammiratori fanatici del grand'Uomo, senza <lb/>averne mai meditati i libri. </s>

<s>Perch&egrave;, se avessero nel citato luogo letto ed in&shy;<lb/>teso che si verificherebbe nella caduta delle due palle l'isocronismo, <emph type="italics"/>quando <lb/>non vi fosse l'impedimento dell'aria,<emph.end type="italics"/> quella prima esperienza, che mo&shy;<lb/>strava come, vista l'una delle dette palle cadere nel perpendicolo, dette <pb xlink:href="020/01/2330.jpg" pagenum="573"/>tempo di rivoltare il viso a veder l'altra, che veniva per la parabola, do&shy;<lb/>vevasi ritener senz'altro per decisiva. </s></p><p type="main">

<s>Lasciata invece la proposizione in dipendenza, e risoluta poi dal Rinal&shy;<lb/>dini in quel modo che s'&egrave; veduto; al venire il Viviani a farne, per comando <lb/>del principe Leopoldo, esame pi&ugrave; diligente, non pot&egrave; non riconoscerne la <lb/>leggerezza. </s>

<s>E dall'altra parte troppo importava sapere e descrivere il fine <lb/>della cosa, per l'amore del vero, per l'onore di Galileo e della nobile Ac&shy;<lb/>cademia. </s>

<s>Di qui &egrave; che il Viviani stesso pens&ograve; di andare in persona a diri&shy;<lb/>gere l'esperienze a Livorno, le quali si rendevano molto pi&ugrave; precise di <lb/>quelle dirette dal Rinaldini, col misurare il tempo spesso nel cader della <lb/>palla, ora naturalmente dal medesimo punto, ora per la spinta violenta del <lb/>cannone. </s>

<s>Il delicato misuratore era il pendolo, con la palla di oro di otto <lb/>millimetri e mezzo di raggio, sospesa a un filo di seta, lungo 52 millime&shy;<lb/>tri; cosicch&egrave;, con pendolo semplice di lunghezza uguale a 0m.0605, si cre&shy;<lb/>deva aver le vibrazioni composte, esattamente corrispondenti ai mezzi se&shy;<lb/>condi. </s>

<s>L'importante notizia leggesi in una Nota autografa del Viviani, in <lb/>margine alla quale &egrave; segnata la figura del pendolo, da cui si son ricavate <lb/>le riferite misure; Nota, che il Magalotti compendi&ograve; nel descriver la prima <lb/>delle <emph type="italics"/>Esperienze intorno ai proietti,<emph.end type="italics"/> quali si leggono nel libro dei <emph type="italics"/>Saggi,<emph.end type="italics"/><lb/>ma che noi vogliamo trascrivere qui ai lettori, nella loro integrit&agrave; originale: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; A'di 2 Aprile 1662 in Livorno.<emph.end type="italics"/> Sulla torre della Fortezza vecchia, <lb/>di braccia 50 di altezza, con falconetto da 7 1/3 di palla, lungo bocche 13 1/2, <lb/>con tiri di punto in bianco, le palle fasciate arrivarono all'acqua in vibra&shy;<lb/>zioni 4 1/2, con libbre quattro di polvere fina. </s>

<s>Con la colubrinetta da 14, <lb/>con libbre dieci di polvere, la palla fasciata arriv&ograve; in cinque vibrazioni: non <lb/>fasciata, in cinque e mezzo, poco pi&ugrave;, e tanto pi&ugrave; lontano. </s>

<s>La caduta delle <lb/>due palle perpendicolarmente fu in vibrazioni quattro, e le vibrazioni erano <lb/>intere di andata e tornata, con lunghezza di filo, qual'&egrave; segnata in mar&shy;<lb/>gine, con la palla di oro, delle quali vibrazioni ne va 120 a minuto primo, <lb/>che sono mezzi minuti secondi &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXIX, fol. </s>

<s>24). </s></p><p type="main">

<s>Cos&igrave; il Viviani, come il Segretario dell'Accademia fiorentina, si stettero <lb/>contenti alla semplice descrizione del fatto, da cui resultava non trovarsi in <lb/>piena conformit&agrave; insieme la teoria e la pratica. </s>

<s>&Egrave; da credere che attribuis&shy;<lb/>sero la causa di ci&ograve; agl'impedimenti dell'aria, ma i calcoli delle Tavole bal&shy;<lb/>listiche, riscontrati ne'militari esercizi, avevano fatto troppo ben conoscere <lb/>dover essere assai pi&ugrave; complicate le cause, per le quali si vedono l'espe&shy;<lb/>rienze aberrare cos&igrave; dai teoremi. </s>

<s>Si volle prendere motivo di qui a infir&shy;<lb/>mare la virt&ugrave; di cos&igrave; fatti teoremi, a che Galileo stesso pensava di rispon&shy;<lb/>dere, dettando a Marco Ambrogetti un frammento di Dialogo, da inserirsi <lb/>nella ristampa delle <emph type="italics"/>Due nuove Scienze.<emph.end type="italics"/> E perch&egrave; avremo altrove occasione di <lb/>richiamar quei frammento, per confermare certe indagini storiche, importan&shy;<lb/>tissime alla storia della letteratura galileiana, lo trascriveremo allora, per pas&shy;<lb/>sare a far qui in ultimo un cenno di alcuni fatti, i quali si credeva che contra&shy;<lb/>dicessero, non a sole le dimostrate teorie, ma alle pi&ugrave; ovvie ragioni naturali. </s></p><pb xlink:href="020/01/2331.jpg" pagenum="574"/><p type="main">

<s>Quando le Tavole ballistiche del Torricelli erano venute a dar tanta <lb/>importanza ai calcoli di Galileo, che in quasi tutte le fortezze d'Italia si <lb/>facevano dai militari esperienze, con quelle Tavole in mano, limitandosi per <lb/>lo pi&ugrave; a riscontrare le ampiezze calcolate, con quelle date dal tiro; ai Fio&shy;<lb/>rentini, pi&ugrave; degli altri operosi, venne in mente di osservare di pi&ugrave; come si <lb/>corrispondessero gl'impeti, creduti da loro proporzionali al numero dei gra&shy;<lb/>nelli tutti uguali della medesima polvere, con la quale si caricava il can&shy;<lb/>none. </s>

<s>Dicevano che se, per esempio, con quattro grani di polvere si pas&shy;<lb/>savano sei braccia, con cinque grani se ne dovrebbero passare sette e mezzo, <lb/>avendo, a tal numero, sei quella proporzione, che cinque ha a quattro. </s>

<s>Tro&shy;<lb/>vavano invece, venendo ai fatti, esser non sette braccia e mezzo, ma qual&shy;<lb/>che cosa di pi&ugrave; di diciannove quella passata. </s></p><p type="main">

<s>Parve il caso aver qualche cosa di straordinario, e di tanto curioso, da <lb/>richiamar l'attenzione del granduca Ferdinando, il quale si compiaceva di <lb/>sodisfare a quella sua curiosit&agrave;, interrogando coloro, che avevano promosse <lb/>ed eseguite pi&ugrave; volte, e in pi&ugrave; modi, le nuove esperienze. </s>

<s>Alcuni de'pi&ugrave; <lb/>leggeri risposero l&igrave; per l&igrave; cose spropositate: altri di pi&ugrave; senno vollero tempo <lb/>a pensarvi, e intanto esponevano in scritto i loro pensieri. </s>

<s>Il Granduca per&ograve; <lb/>non sperava, e non confidava di avere da que'signori la vera soluzion del <lb/>problema, ma volle metterli alla prova, per veder quel che sapessero dire <lb/>appetto al suo gran matematico Vincenzio Viviani, a cui fece proporre il <lb/>quesito, coll'ordine di darne la risposta. </s>

<s>Non credeva il Viviani che la cosa <lb/>avesse levato tanto romore in palazzo, n&egrave; che tanti vi s'affaccendassero in&shy;<lb/>torno a stillarvi il cervello, per cui prese la penna, e scrisse cos&igrave; al Segre&shy;<lb/>tario del Granduca, sicuro che avrebbe in qualunque modo sodisfatto al <lb/>comando, il principal merito del quale sapeva che facevasi per lo pi&ugrave; con&shy;<lb/>sistere nell'esser pronto: </s></p><p type="main">

<s>&ldquo; Il problema, che V. S. mi propone di comandamento del Padron <lb/>Serenissimo, &egrave; veramente curiosissimo, e a prima faccia tiene in s&egrave; dello <lb/>stravagante, poich&egrave; l'evento si dimostra molto diverso da quello, che si pro&shy;<lb/>metterebbe il comun giudizio, pochi essendo quelli, che non credessero che, <lb/>mantenuta la medesima elevazione di canna, gli spazi passati orizzontali, che <lb/>vengono scorsi con moto equabile, non avessero a mantenere tra di loro la <lb/>medesima proporzione delle velocit&agrave; o delle forze impellenti, in tal maniera <lb/>che, se con quattro grani di polvere o con quattro gradi di forza, si passano <lb/>braccia sei, con cinque grani o cinque gradi di forza si avessero a passare <lb/>solamente braccia sette e mezzo, e non braccia 19, come mi avvisa V. S.; <lb/>che tal proporzione ha quattro a cinque, che sei a sette e mezzo: ovvero <lb/>dovrebbero dare le lunghezze 6 e 19, che son quelle che V. S. mi dice <lb/>esser passate da quattro e da cinque grani di polvere. </s>

<s>E supposto che la <lb/>prima sia scorsa dalla palla, cacciata con quattro gradi d'impeto, bisogne&shy;<lb/>rebbe che la seconda fosse stata scacciata da gradi dodici e due terzi, poi&shy;<lb/>ch&egrave; tal proporzione ha 6 a 19, che 4 a 12 2/3. &rdquo; </s></p><p type="main">

<s>&ldquo; Ma se, con la scorta della Geometria e con la dottrina de'moti del <pb xlink:href="020/01/2332.jpg" pagenum="575"/>Galileo, c'interneremo oltre alla scorza di questo effetto, vedrass&igrave; che, nel <lb/>caso di che si tratta, non pu&ograve; mai conservarsi tal proporzione, e che que&shy;<lb/>sta, rimossi gl'impedimenti, s'osserva solo dalla Natura in quei moti equa&shy;<lb/>bili, che son fatti dentro un medesimo tempo. </s>

<s>Ma perch&egrave; qui i moti son <lb/>fatti sotto tempi disuguali, &egrave; necessario tenerne conto, e ricorrere ad esa&shy;<lb/>mine pi&ugrave; accurata, per la quale si trover&agrave; mitigata alquanto la stravaganza, <lb/>poich&egrave; si avr&agrave; che la seconda proiezione dovrebb'esser, non braccia sette <lb/>e mezzo, ma bens&igrave; braccia 9 3/8, che tanto si deduce dalla Scienza de'pro&shy;<lb/>ietti, dalla quale ancora si ha che, stanti ferme le date lunghezze di brac&shy;<lb/>oia 6 e 19, supposto che la prima di sei sia fatta da un impeto di quattro <lb/>grani di polvere, o di gradi quattro di forza; la seconda di braccia 19 do&shy;<lb/>vrebbe essere scorsa da un impeto di grani 7 1/8 di polvere, e non di grani <lb/>cinque, come segue infatto, nemmeno di grani 12 2/3, come vedemmo di <lb/>sopra che dava la regola, fatta senz'altro esame. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma giacch&egrave; l'esperienza cos&igrave; dimostra, e le misure delle braccia 6 <lb/>e 19 son reali, n&egrave; vi pu&ograve; essere equivoco, mentre s&igrave; ammettano per veri <lb/>i principii supposti dal Galileo nelle dottrine dei moti, applicati ai nostri <lb/>gravi, considerati per&ograve; esenti e liberi da ogni accidentario impedimento; <lb/>converr&agrave; dire che l'equivoco sia nella considerazione degl'impeti, e che que&shy;<lb/>sti della polvere particolarmente non mantenghino la medesima proporzione <lb/>delle moli e de'pesi di essa polvere: cio&egrave; che, se quattro grani operano e <lb/>spingono, per esempio, con forza di quattro gradi; cinque grani poi non <lb/>spinghino con forza di cinque gradi, ma operino per pi&ugrave;, com'&egrave; di 7 1/8. <lb/>Qual poi sia la cagione di tal, per cos&igrave; dire, sproporzione di forza sopra la <lb/>comune stimativa, io veramente, per esimermi dal pericolo di censure in <lb/>addurla, dovrei dire col Galileo che questa ancora &egrave; una delle cose che io <lb/>non so.... &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLII, fol. </s>

<s>95). </s></p><p type="main">

<s>Mancando a questo punto del citato codice i fogli, sopra i quali si pro&shy;<lb/>seguiva, nella presente e in una lettera successiva, a dir, della cosa che si <lb/>confessava ignorare, qualche probabile opinione; non sappiamo perci&ograve; quale <lb/>ella fosse, ma in ogni modo siam certi che il Granduca aspett&ograve; a leggerla <lb/>perch&egrave; voleva sentir prima quel che ne saprebbero dire gli altri interrogati. </s>

<s><lb/>Dette il Segretario avviso di questa intenzione al Viviani, il quale intese <lb/>anche insieme che il Granduca ci premeva molto, e che molti ci stavano as&shy;<lb/>sottigliando l'ingegno. </s>

<s>Allora si pent&igrave; di aver fatto sull'argomento poco accu&shy;<lb/>rata riflessione, e conobbe che le cose scritte nelle due lettere potevano, a <lb/>rigor di scienza, andar soggette a censure. </s>

<s>Secondo quella scienza infatti <lb/>non si poteva ragionevolmente decider nulla intorno alla quantit&agrave; della vo&shy;<lb/>lata, a proporzion della carica, senza sapere il grado della elevazion del can&shy;<lb/>none. </s>

<s>Aveva imprudentemente sentenziato il Viviani, non curante di que&shy;<lb/>ste notizie, che non pu&ograve; mai, nel proposto caso, conservarsi tra gl'impeti e <lb/>le ampiezze delle parabole una tal proporzione, la quale anzi osservasi nel <lb/>tiro semiretto, essendo allora gl'impeti, uguali al doppio delle altezze delle <lb/>semiparabole, proporzionali alle semibasi. </s>

<s>Nelle altre elevazioni, superiori o <pb xlink:href="020/01/2333.jpg" pagenum="576"/>inferiori alla semiretta, essendo gl'impeti uguali alla somma della sublimit&agrave; <lb/>con l'altezza, s'intende perci&ograve; come non si possano puntualmente determi&shy;<lb/>nare, senza conoscer prima il preciso grado della detta elevazione. </s></p><p type="main">

<s>Riconosciutosi ci&ograve; dal Viviani, e saputo che le sue lettere non erano <lb/>state ancora aperte dal Granduca, pregava il Segretario, s'era permesso, a <lb/>volergliele rimandar per correggerle, e a dirgli insieme a qual preciso punto <lb/>della squadra corrispondeva nelle varie esperienze la direzione del tiro: pre&shy;<lb/>gavalo inoltre a volergli dare altre pi&ugrave; particolari notizie, come qui si leg&shy;<lb/>gon richieste, in una lettera del d&igrave; 27 Febbraio 1664, che da noi si tra&shy;<lb/>scrive: </s></p><p type="main">

<s>&ldquo; Intendo in che grado &egrave; il negozio, e giacch&egrave; si vede che S. A. ci <lb/>preme, e che altri soggetti maggiori infinitamente di me ci stanno specu&shy;<lb/>lando, per scrivere, sarebbe pur bene che io ci facessi ancora io pi&ugrave; accu&shy;<lb/>rata riflessione, oltre a quella fattavi subito improvvisamente, per mostrar <lb/>la prontezza nell'obbedire: e se V. S. mi avesse fatto onore di avvisarmi <lb/>prima che S. A. non ha voluto sentire le lettere, col fine di aspettare quel <lb/>che altri dica sopra di ci&ograve;, io l'avrei pregata a rimandarmele, per aggiu&shy;<lb/>starle meno male di quel che stanno. </s>

<s>Pure, io la prego adesso, se ella pensa <lb/>che io sia a tempo, a volermi prontamente rimandare indietro tutt'e due <lb/>le mie lettere, che parlano di ci&ograve;, perch&egrave; gli prometto di rimandargliele su&shy;<lb/>bito subito, per la prima occasione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di grazia, non manchi di favorirmi, siccome di dirmi insieme a che <lb/>elevazione si trovasse il pezzetto, quando si fecero quelle prove del caso <lb/>propostomi di grani quattro di polvere, a braccia sei di distanza, e poi di <lb/>grani cinque, a braccia diciannove in venti: cio&egrave;, se a mezzo angolo retto, <lb/>oppur sopra, oppur sotto il detto angolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Inoltre, quando la palla &egrave; dentro, vorrei sapere quanto resta lontana <lb/>dalla bocca del pezzo, e quanto &egrave; lunga la camera, che ci&ograve; facilmente V. S. <lb/>lo pu&ograve; vedere da s&egrave;, senza metterla in negozio con nessuno, bastando toc&shy;<lb/>car da s&egrave; il pezzetto, e con un fuscello misurare quanto &egrave; dalla bocca al <lb/>fondo della camera, e poi metter la palla, e misurar sul medesimo quanto <lb/>&egrave; dalla bocca alla palla, e sul medesimo fuscello metter la misura del dia&shy;<lb/>metro della medesima palla, e questa misura poi trasportarla sopra un fo&shy;<lb/>glio, insieme con la lunghezza della detta camera, perch&egrave; quella della canna <lb/>la caver&ograve; da me dalla palla. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Vorrei sapere ancora la storia degli altri tiri, oltre a que'soli due, <lb/>che V. S. mi ha scritto, cio&egrave; la lunghezza de'tiri fatti con uno, con due, <lb/>con tre grani, e poi con sei, con sette, e con quanti se n'&egrave; fati e potuti <lb/>fare. </s>

<s>Insomma vorrei pi&ugrave; di due tiri, oltre a que'fatti con quattro grani, e <lb/>con cinque di polvere. </s>

<s>Di pi&ugrave;, se &egrave; possibile, vorrei sapere se pel focone <lb/>svapora gran fiamma, e se ci hanno rimediato che non ne esca, con met&shy;<lb/>tere uno stoppino nel focone o in altro modo, e se di questo accidente di <lb/>svaporare se ne fa caso; se il pezzetto era fisso, che non potesse rinculare <lb/>n&egrave; alzarsi di bocca. </s>

<s>Finalmente, pi&ugrave; notizie che lei mi dar&agrave; sopra questo, pi&ugrave; <pb xlink:href="020/01/2334.jpg" pagenum="577"/>l'avr&ograve; caro, acciocch&egrave; io me ne possa valere, nel raggiustare le lettere, che lei <lb/>mi rimander&agrave;, le quali subito le accomoder&ograve; in miglior forma &rdquo; (ivi, fol. </s>

<s>97, 98). </s></p><p type="main">

<s>Il fine del ricercar notizie intorno alla elevazione del pezzo &egrave; manife&shy;<lb/>sto, per le cose gi&agrave; dette, ma perch&egrave; i teoremi galileiani, dietro quelle stesse <lb/>notizie applicati si vedevan pure in ogni modo cos&igrave; aberrare dai fatti; non <lb/>rimaneva altro di certo al Viviani, in mezzo a questi dubbi, che la conclu&shy;<lb/>sione scritta nella prima lettera al Segretario del Granduca, che cio&egrave; gl'im&shy;<lb/>peti della polvere non mantengono la proporzione delle moli e dei pesi. </s>

<s>La <lb/>desiderata soluzion del problema perci&ograve; usciva fuori del campo della Mate&shy;<lb/>matica astratta, per entrare in quello della Fisica, all'esperienze della quale <lb/>era necessario ricorrere, per saper quanto, sopra la proporzion della mole <lb/>e del peso, cresca, nella polvere accesa, la violenza dell'impeto. </s>

<s>A ci&ograve; ten&shy;<lb/>devano le domande fatte dal Viviani intorno alla capacit&agrave; della camera, allo <lb/>sfiatar del focone, e al rinculare del pezzo, ma pure erano troppo pochi tutti <lb/>questi dati a determinar le incognite del complicato problema. </s></p><p type="main">

<s>La difficolt&agrave; del conseguire l'intento non ne spense per&ograve; nel Viviani, <lb/>nemmeno per lunghezza di tempo, il desiderio. </s>

<s>Vent'anni dopo passava per <lb/>Firenze, sul finir della primavera, il generale Luigi Ferdinando Marsili, che <lb/>volle visitare il celebre Matematico, in cui vedevasi continuare la vita stessa <lb/>di Galileo. </s>

<s>I colloqui fra due uomini di quell'indole, e di quella professione, <lb/>era naturale che cadessero sopra le Matematiche applicate all'arte militare, <lb/>con la quale occasione raccontava il Viviani l'esperienze fatte e gli studii, <lb/>per rispondere ai quesiti, che gli erano stati proposti infin da'tempi del <lb/>granduca Ferdinando. </s>

<s>Rispose allora il Marsili che l'arte da lui esercitata, <lb/>e l'amor alla scienza, lo avevano invogliato di simili studii sperimentali, dei <lb/>quali, tornato a Bol<gap/>gna, riferiva allo stesso Viviani un saggio in questa <lb/>lettera, scritta il di 18 Giugno 1684: </s></p><p type="main">

<s>&ldquo; &Egrave; obbligo di chiunque esercita un'arte l'intendere non solo gli ef&shy;<lb/>fetti, ma anco i mezzi, con i quali la medesima s'esercita, e perci&ograve;, com'&egrave; <lb/>noto a V. S. Ill.ma, ho intrapreso d'impiegarmi in quella delle armi, che <lb/>ne'tempi d'oggi si rendono strepitose per l'industria animata della forza <lb/>della polvere, che esaminandola in pi&ugrave; occasioni non ho volsuto tralasciare <lb/>di avvertire la di lei forza, con pi&ugrave; esperimenti, che, col benefizio dell'ozio <lb/>in una pace o in un quartiere d'inverno, non mancher&ograve; pi&ugrave; fondatamente <lb/>digerire, affine di potere tutto in una esatta serie dimostrare a V. S. Ill.ma, <lb/>secondo gli ho promesso nel mio passaggio per Firenze, non solo per con&shy;<lb/>trassegno di rispetto alla di lei persona, ma anche per poterne ricavare van&shy;<lb/>taggio da quei riflessi saranno fatti dalla di lei virt&ugrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cominciando in ora a dimostrargliene uno circa l'accension della me&shy;<lb/>desima, che a me pare possi essere fondamento non solo di conoscere la <lb/>forza della stessa, ma anche di bene appropriarla a benefizio della mia arte, <lb/>dico che, per conoscere adunque verso qual parte faccia maggior impeto la <lb/>polvere di schioppo, nell'accendersi ch'ella fa, ho praticata la seguente <lb/>esperienza: &rdquo; </s></p><pb xlink:href="020/01/2335.jpg" pagenum="578"/><p type="main">

<s>&ldquo; Descritto un circoletto piccolo sopra un cartone assai grande, situato <lb/>parallelo all'orizzonte, dentro di esso disposi egualmente una certa quan&shy;<lb/>tit&agrave; di polvere, talch&egrave; da essa veniva ad essere riempita tutta la area del <lb/>detto circolo. </s>

<s>Di poi li posi nella circonferenza, distanti l'una dall'altra no&shy;<lb/>vanta gradi, quattro palline di sughero di ugual grossezza, e consequente&shy;<lb/>mente di ugual peso, e bene rotonde. </s>

<s>Accesa la polvere in una parte della <lb/>circonferenza del circolo, vicino alla pallina A (fig. </s>

<s>307) furono levate dal <lb/>suo sito dall'impeto della polvere tutt'e quattro le palline, ma disugual&shy;<lb/><figure id="id.020.01.2335.1.jpg" xlink:href="020/01/2335/1.jpg"/></s></p><p type="caption">

<s>Figura 307<lb/>mente, in maniera che la pallina A, ch'era vi&shy;<lb/>cina al luogo dell'accensione, fu spinta all'in&shy;<lb/>dietro per tanto spazio, quanto importavano <lb/>quattro diametri della stessa pallina, ma la op&shy;<lb/>posta B fu cacciata all'innanzi 36 delli stessi <lb/>diametri, ma le laterali D, C furono spinte la&shy;<lb/>teralmente 12 diametri, in maniera che, se i <lb/>spazi percorsi e gl'impeti fossero proporzio&shy;<lb/>nali, pare si potesse concludere da questa espe&shy;<lb/>rienza che l'impeto della polvere fosse nove <lb/>volte maggiore verso la parte opposta al luogo <lb/>dell'accensione, e che l'impeto laterale fosse <lb/>tre volte maggiore che nel luogo dell'accensione, e parimente tre volte mi&shy;<lb/>nore di quello sia nella parte opposta al luogo dell'accensione, supponendo <lb/>per&ograve; che l'esperienza, fatta pi&ugrave; volte con quantit&agrave; maggiore o minore di <lb/>polvere, e in altra figura, resti sempre la medesima. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Disposta la polvere nell'istesso circolo, nel modo predetto, e datogli <lb/>il fuoco nel centro, fece egual impeto per ogni verso, spingendo tutt'e quat&shy;<lb/>tro le palline per eguali spazi. </s>

<s>Senza le palline si pu&ograve;, ma non cos&igrave; esat&shy;<lb/>tamente, conoscere l'impulso dalle strisce, che lasciano segnate di nero i <lb/>grani della polvere nel cartone, le quali sempre sono maggiori dalla parte <lb/>opposta al luogo dell'accensione, in maniera che, dall'una e dall'altra espe&shy;<lb/>rienza, si viene a concludere lo stesso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Attender&ograve; con somma impazienza le di lei erudite e fondate consi&shy;<lb/>derazioni, per poter procedere nell'incominciato studio della polvere, raffer&shy;<lb/>mandomi al solito Aff.mo Obbligmo <emph type="italics"/>Luigi Ferdinando Marsili. </s>

<s>&rdquo;<emph.end type="italics"/> (MSS. Gal. </s>

<s><lb/>Disc., T. CXLVI, fol. </s>

<s>268). </s></p><p type="main">

<s>I documenti, ricercati con diligenza ne'commerci letterari de'due va&shy;<lb/>lorosi uomini, rivelerebbero forse in tale argomento conclusioni ben assai <lb/>pi&ugrave; curiose e pi&ugrave; importanti, che noi per&ograve; dobbiam lasciare allo studio di <lb/>chi scriver&agrave; la <emph type="italics"/>Storia delle artiglierie in Italia.<emph.end type="italics"/></s></p><pb xlink:href="020/01/2336.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO X.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Conclusione di questa prima Parte<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. De'principali cultori della Meccanica contemporanei di Galileo. </s>

<s>&mdash; II. De'Dialoghi de'due Massimi <lb/>Sistemi, e come s'incominciassero a diffondere di li i semi della nuova Scienza del moto. </s>

<s>&mdash; <lb/>III. </s>

<s>Del primo dialogo delle due Nuove Scienze, e della pubblicazione di lui, insieme con gli <lb/>altri tre, fatta dagli Elzeviri in Olanda. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Dop'essersi fin qui la nostra Storia aggirata per le volte e rivolte del <lb/>filo di tante sottili speculazioni, intorno ai principali argomenti della Scienza <lb/>del moto, riusciti com'a termine fisso all'anno 1638, in cui per i Dialoghi <lb/>galileiani ebbe quella stessa Scienza il suo nuovo istituto; giova trattenere <lb/>alquanto il passo, come fa il pellegrino che, riposando per pigliar lena a <lb/>proseguire, volge a pi&egrave; del grand'albero, sotto cui siede, tutt'intorno desi&shy;<lb/>deroso lo sguardo. </s>

<s>S'&egrave; per molti immaginato e descritto il termine, a cui <lb/>siamo giunti, come un campo arido e desolato, in mezzo a cui solo l'al&shy;<lb/>bero che s'&egrave; detto grandeggia, e rallegra il viandante col verde e coll'om&shy;<lb/>bra. </s>

<s>Che sia questo per&ograve; un immaginar falso, e un falso descriver le cose <lb/>lo persuade con facilit&agrave; l'osservazion naturale, che mai non &egrave; quercia soli&shy;<lb/>taria in selva, ma la circondano umili virgulti e pi&ugrave; elevati arboscelli, o <lb/>nati di straniero seme, o dalle stesse ghiande cadute dalla chioma di lei. </s>

<s><lb/>Dall'altra parte lo straordinario rigoglio della madre pianta attesta la ben <lb/>disposta qualit&agrave; del terreno, e il benigno volgere della stagion, che favori&shy;<lb/>scono, con general provvidenza, il germogliare e il crescere degli altri semi. </s>

<s><lb/>E perch&egrave; sempre nel mondo fisico vedonsi il morale e l'intellettuale sim&shy;<lb/>boleggiati, sorgono intorno al grande Galileo altri minori, nel campo della <lb/>Scienza meccanica largamente dispersi, dovunque intelligenze umane aprano <pb xlink:href="020/01/2337.jpg" pagenum="580"/>a ricever lo spirito fecondatore del vero. </s>

<s>Giunge l'aura divina attraverso a <lb/>mari in Olanda a Simeone Stevino; attraverso a monti, in Germania, a Paolo <lb/>Guldino e a Giovan Marco Marci, mentre fra noi Guidubaldo del Monte, <lb/>Girolamo Fabricio d'Acquapendente e Giovan Batista Baliani sembra che ne <lb/>risentan gl'influssi pi&ugrave; prossimi e pi&ugrave; efficaci. </s></p><p type="main">

<s>Tutti coloro i quali, contro il senso comune, contro la legge naturale <lb/>e contro i fatti, si ostinano in voler riconoscere Galileo nella Scienza mec&shy;<lb/>canica primo e unico Maestro al mondo, s'immaginano che da lui abbiano, <lb/>in qualunque modo, i commemorati Autori contemporanei imparato tutto <lb/>quel che nei loro libri hanno scritto delle ragioni del moto. </s>

<s>L'assunto per <lb/>verit&agrave; &egrave; di difficile dimostrazione, la quale anzi si direbbe impossibile, spe&shy;<lb/>cialmente riguardo allo Stevino, in cui riconoscemmo gi&agrave; il sapiente e ze&shy;<lb/>lante banditore di quella, che due secoli dopo s'intitol&ograve; Meccanica nuova. </s>

<s><lb/>Che poi le tradizioni osservate dal Matematico olandese fossero tutt'affatto <lb/>diverse dalle galileiane lo dimostrano i fatti, narrati in questo stesso Tomo <lb/>a varie occasioni, d'ond'&egrave; manifesto in quali gravissimi errori e a quali <lb/>false conseguenze si trovasse condotto Galileo, sempre che gli occorra a ra&shy;<lb/>gionare della composizion delle forze. </s></p><p type="main">

<s>Come dalle pi&ugrave; antiche fonti aristoteliche, sapientemente derivate dal <lb/>Nemorario, sorgesse l'ubert&agrave; della Statica steviniana, fu da noi mostrato a <lb/>suo luogo, n&egrave; qui importa ripetere il gi&agrave; detto, per sodisfar piuttosto alla <lb/>curiosit&agrave; di coloro, i quali hanno ora sentito annoverar fra i Meccanici <lb/>l'Acquapendente. </s>

<s>Medico e anatomico famosissimo si trov&ograve; tirato nel campo <lb/>della Meccanica quando, nella terza parte della sua Miologia, pubblicata <lb/>nel 1614, ebbe a dimostrare secondo qual ragione s'esercitano le forze mu&shy;<lb/>scolari. </s>

<s>Amico a Galileo, e collega nel medesimo Studio padovano, chi non <lb/>direbbe che l'Anatomico si fosse, in una questione difficilissima, rivolto a <lb/>consultare il Matematico, tutto allora in studio di dare alla <emph type="italics"/>Scienza mecca&shy;<lb/>nica<emph.end type="italics"/> ordine e perfezion di trattato? </s>

<s>Eppure &egrave; tanto certo non avere avuto <lb/>l'Acquapendente intorno a ci&ograve; alcun consulto che, quand'anco si fosse di&shy;<lb/>sposto a richiederlo, non avrebbe Galileo saputo ritrovar nella sua Scienza <lb/>meccanica di che sodisfarlo. </s>

<s>La questione miologica infatti risolvevasi essen&shy;<lb/>zialmente co'principii statici della Leva, ritrovati gi&agrave; da Aristotile e dal Ne&shy;<lb/>morario, co'quali due autorevolissimi Maestri anche il Fabricio, dop'aver <lb/>descritti gli effetti della macchina, dice: &ldquo; Porro haec omnia ex natura cir&shy;<lb/>culi petuntur. </s>

<s>Nimirum, quo longior a centro linea est, eo celerius fertur, <lb/>ac proinde facilius attollit breviorem, quae ultra centrum producta est li&shy;<lb/>neam &rdquo; (Opera omnia, Lugd. </s>

<s>Batav. </s>

<s>1738, pag. </s>

<s>419). </s></p><p type="main">

<s>Non era dunque bisogno consultar la moderna Scienza galileiana, per <lb/>saper da quali principii matematici derivino le propriet&agrave; generali del Vette. </s>

<s><lb/>Quanto poi ai particolari, consistenti nel miglior modo di applicar la potenza, <lb/>a che insomma si riduceva la difficolt&agrave; della questione; Galileo non poteva <lb/>nulla giovare ai progressi della Miologia, per i quali richiedevasi un argo&shy;<lb/>mento, sconosciuto affatto in quella sua nuova meccanica officina. </s>

<s>Riduce-<pb xlink:href="020/01/2338.jpg" pagenum="581"/>vasi un tale argomento infatti al principio della composizion delle forze, che <lb/>l'Acquapendente trovava preparato cos&igrave; nella Scienza antica, da poter facil&shy;<lb/>mente con esso risolvere il problema: &ldquo; Cur musculi longiores, non solum <lb/>longiores, sed etiam robustiores dant motus &rdquo; (ibid., pag. </s>

<s>420). </s></p><p type="main">

<s>Si fa la desiderata risoluzione dipendere, come da Lemma, dal seguente <lb/>Teorema, che i nostri Lettori conosceranno facilmente informato dalle pi&ugrave; <lb/>sane dottrine dei moti composti, bench&egrave; non s'applichi immediatamente la <lb/>descrizione del parallelogrammo: &ldquo; Sit vectis AB (fig. </s>

<s>308) et in ipso C <lb/>pondus, B fulcimentum; chorda vero perpendicularis DF, aliae vero obli&shy;<lb/>quae DG, DE. </s>

<s>Dico facilius attolli pondus chorda DF, quam chorda DE, <lb/>vel DG. &rdquo; <lb/><figure id="id.020.01.2338.1.jpg" xlink:href="020/01/2338/1.jpg"/></s></p><p type="caption">

<s>Figura 308</s></p><p type="main">

<s>&ldquo; Cum enim vis in E consti&shy;<lb/>tuta attrahit secundum lineam ED, <lb/>cum vectis AB attrahatur versus <lb/>fulcimentum B, pars virium absu&shy;<lb/>mitur contra fulcimentum: tractus <lb/>enim obliquus ED videtur potius <lb/>esse ad impellendum fulcimentum, <lb/>quam ad pondus attollendum. </s>

<s>Pa&shy;<lb/>riter etiam trahens chorda GD ni&shy;<lb/>titur potius ut avellat Vectem ex fulcimento, quam ut pondus attollat: <lb/>absumitur ergo vis magna ex parte in fulcimento B expellendo. </s>

<s>Quod si <lb/>attrahatur chorda perpendiculo in FD, nulla pars virium suam non exercet <lb/>facultatem in pondere elevando: imo tota ad ipsum attollendum converti&shy;<lb/>tur &rdquo; (ibid.). </s></p><p type="main">

<s>Seguono al Teorema due corollarii: &ldquo; Ex quo colligitur, quo punta E, G <lb/>elatiora fuerint, eo facilius moveri vectem, et pondus attolli &rdquo; (ibid). Non <lb/>gi&agrave; che l'Acquapendente creda, come i pi&ugrave; credevano allora, che le corde <lb/>pi&ugrave; lunghe siano a proporzione pi&ugrave; forti, ma la maggior lunghezza fa men <lb/>rapidamente diminuire l'angolo dell'inclinazione, da cui solo dipende il va&shy;<lb/>riar della forza. </s>

<s>L'altro corollario poi, da cui traluce il concetto che l'in&shy;<lb/>forma, &egrave; cos&igrave; espresso: &ldquo; Patet etiam quod, si vectis et chorda in eadem <lb/>essent linea constituta, nullo pacto motus fierent, ut patet per lineas DH, DL. </s>

<s><lb/>Posita enim vis in H, vel in L, utraque omni ex parte applicabitur ad mo&shy;<lb/>vendum fulcimentum B, non autem ad attollendum Vectem &rdquo; (ibid.). </s></p><p type="main">

<s>Quanto siano cos&igrave; fatte dottrine aliene dalle tradizioni galileiane pos&shy;<lb/>sono giudicarlo da s&egrave; i Lettori, cavandone i criterii dalle storie passate; cri&shy;<lb/>terii, che valgono altres&igrave; per Guidubaldo del Monte, nella Statica maestro a <lb/>Galileo, e nell'Acustica e nella Ballistica premostratore. </s>

<s>Il Guldin, amico <lb/>dello stesso Galileo ch'ei conobbe in Roma, e a cui mand&ograve; per mezzo di <lb/>Giovanni Pieroni il libro <emph type="italics"/>De centro gravitatis partium circuli,<emph.end type="italics"/> si faceva con <lb/>esso primo cultore di una delle pi&ugrave; belle e delle pi&ugrave; ammirate parti della <lb/>Meccanica, qual &egrave; la Centrobrarica, le tradizioni della quale risalgono, come <lb/>a suo luogo narrammo, alla Scuola alessandrina. </s>

<s>Or chi sa quanti altri Au-<pb xlink:href="020/01/2339.jpg" pagenum="582"/>tori, sconosciuti al pubblico e a noi, avranno promossa, ne'principii del se&shy;<lb/>colo XVII, la Scienza, della quale non sapevano ancora ci&ograve; che s'era nova&shy;<lb/>mente insegnato dalla cattedra di Padova, e dalla solitudine di Arcetr&igrave;? </s></p><p type="main">

<s>Si dir&agrave; che le notate promozioni appartengono tutte alla Statica, della <lb/>quale principalmente Archimede aveva preparati i progressi: ma come si <lb/>potrebbe provare che non sia la Dinamica tutt'opera di Galileo, da cui si <lb/>ebbero matematicamente dimostrate le leggi, scoperte prima per l'esperienza? </s>

<s><lb/>Le prove, rispondiamo, si ritrovano pure nella storia da noi addietro inve&shy;<lb/>stigata nei fatti, la somma dei quali si riduce a dire che, contemporanea&shy;<lb/>mente con i Dialoghi delle due Nuove Scienze, apparvero alla luce in Italia <lb/>e in Germania due altri libri di Dinamica nuova, insigni al giudizio di tutti <lb/>gl'imparziali. </s></p><p type="main">

<s>Giovan Marco Marci di Crownland, prima medico e poi gesuita, pub&shy;<lb/>blicava in Praga nel 1639, con i tipi di Giovanni Bilina, un libro intitolato <lb/><emph type="italics"/>De proportione motus,<emph.end type="italics"/> perch&egrave;, dalla legge che gl'incrementi delle velocit&agrave; <lb/><emph type="italics"/>rationem habent quam temporum quadrata,<emph.end type="italics"/> si dimostrano le propriet&agrave; dei <lb/>cadenti nel perpendicolo, per le linee oblique, e per gli archi dei cerchi. </s>

<s><lb/>L'assunto dunque &egrave; qui proprio il medesimo, che nel terzo dialogo delle <lb/>Nuove Scienze, con l'Autor del quale non si vede che relazione potess e <lb/>avere un uomo, cos&igrave; distante di patria, di educazione e di studii, e tale che, <lb/>ancora oggid&igrave; che tanto e per tutto si fruga, vien passato di vista agli eru&shy;<lb/>diti. </s>

<s>Potrebbe forse nascere il sospetto ch'essendo il manoscritto de'Dialo&shy;<lb/>ghi galileiani capitato in Praga, alle mani del Pieroni, per farlo ivi stam&shy;<lb/>pare, fosse stato veduto o riferito agli studiosi, ma la poca probabilit&agrave; del <lb/>fatto conduce a negarlo poi con certezza chiunque si metta a confrontare <lb/>insieme i due diversi trattati. </s></p><p type="main">

<s>Nel Matematico tedesco &egrave; manifesto il fine delle dinamiche proposizioni, <lb/>che &egrave; quello di applicarle alla <emph type="italics"/>Regola sfigmica;<emph.end type="italics"/> intendimento, che fallisce <lb/>affatto nel dialogo del Nostro, il quale, essendosi proposto di dimostrare <lb/>quella lunga serie di teoremi in grazia delle propriet&agrave; de'pendoli, non fa <lb/>poi de'pendoli, e fuor di proposito, che un leggerissimo motto. </s>

<s>Le leggi <lb/>delle oscillazioni dei gravi, pendenti da varie lunghezze di fili, son per Ga&shy;<lb/>lileo semplici fatti sperimentali, che matematicamente Giovan Marco riduce <lb/>ai loro propri principii, per applicarli poi alla soluzione dell'importantissimo <lb/>problema della lunghezza del pendolo a secondi. </s></p><p type="main">

<s>Se da questa sola parte si volesse considerare, basterebbe per dire che <lb/>il trattato stampato in Praga supera notabilmente quello stampato in Leid a, <lb/>ma ben altre ragioni ci sono di quella superiorit&agrave;, per prezzar debitamente <lb/>le quali giova ridurci a memoria che, a levare i voli pi&ugrave; sublimi, ebbe la <lb/>Meccanica per sue ali il Calcolo differenziale e la Regola del parallelogrammo. </s>

<s><lb/>Ora &egrave; a notare che Galileo, recidendo, come dalla Storia apparisce, i due <lb/>strumenti, ne impediva cos&igrave; que'liberi voli, che tutta la Scienza del moto, <lb/>com'egli forse avrebbe desiderato, si sarebbe anche a'nostri giorni rima&shy;<lb/>sta nella breve cerchia de'suoi teoremi. </s>

<s>Giovan Marco invece preparava al <pb xlink:href="020/01/2340.jpg" pagenum="583"/>Newton, da un secolo e mezzo, quella che, dalle mani del Varignon, gli ve&shy;<lb/>niva porta come Meccanica nuova, dimostrando che il moto perfettamente <lb/>misto &ldquo; fit per diametrum parallelogrammi, cuius latera constituit motus <lb/>simplex &rdquo; (fol. </s>

<s>38 ad t.). E quasi avesse presentiti i gravissimi danni, che <lb/>sarebbero per derivare alla Scienza dalla seconda proposizion galileiana Dei <lb/>proietti, pronunziava contro la falsit&agrave; di lei quella gran verit&agrave;, intesa allora <lb/>da pochi: &ldquo; Metus mixtus est necessario minor diametro quadrati, aut pa&shy;<lb/>rallelogrammi &rdquo; (fol. </s>

<s>40). </s></p><p type="main">

<s>Bench&egrave; grande sia, senza dubbio, il merito dell'avere imbandita cos&igrave; <lb/>la mensa di cibi salutari a gente, che gli credeva veleni: &egrave; nonostante in <lb/>qualche piccola parte minorato dal non avere le proposizioni dei moti mi&shy;<lb/>sti tutta quella originalit&agrave;, che hanno le altre nel libro di Giovan Marco, <lb/>dove ei dimostra le leggi degli urti. </s>

<s>A che si riducano tutti i discorsi, te&shy;<lb/>nuti per quarant'anni da Galileo intorno alla forza della percossa, lo ve&shy;<lb/>dranno coloro, i quali avranno la pazienza di leggere il cap. </s>

<s>III della seconda <lb/>parte di questa Storia della Meccanica. </s></p><p type="main">

<s>La nuova Scienza insomma delle proporzioni del moto, insegnata in <lb/>Germania, era per questa parte superiore a quella nel medesimo tempo inse&shy;<lb/>gnata in Italia, bench&egrave; da un altro lato gli rimanga inferiore, non trattando <lb/>Giovan Marco delle resistenze dei solidi allo spezzarsi, e de'proietti ripe&shy;<lb/>tendo gli antichi errori. </s>

<s>&ldquo; Quae autem motu violento moventur, cuiusmodi <lb/>proiecta seu manu, seu machina, a principio quidem velocissime, inde mi&shy;<lb/>nus velociter moventur, impulsu veluti senescente &rdquo; (fol. </s>

<s>18 ad t.). Or chi <lb/>non si persuaderebbe, dietro queste osservazioni, che l'Autore <emph type="italics"/>De propor&shy;<lb/>tione motus<emph.end type="italics"/> aveva speculazioni sue proprie, e indipendenti da quelle di Ga&shy;<lb/>lileo, che non si poteva dunqne vantare di avere istituita la Dinamica egli <lb/>il primo ed il solo? </s></p><p type="main">

<s>Un altro competitore egli ebbe nel Baliani, levatogli di mezzo da molti, <lb/>com'una molesta festuca dagli occhi, co'soffi del disprezzo. </s>

<s>Noi abbiamo <lb/>avuto occasione pi&ugrave; volte di esaminare le speculazioni e le scoperte del Ma&shy;<lb/>tematico genovese, e le abbiamo trovate di fatto o precedere, o esser con&shy;<lb/>temporanee, e perci&ograve; indipendenti da quelle di Galileo, che per verit&agrave; non <lb/>si mostra, come i suoi zelatori, punto maravigliato dell'esser due, che vanno <lb/>per la medesima strada, giunti insieme al termine stesso. </s>

<s>&ldquo; Il signor Fi&shy;<lb/>lippo Salviati, scriveva esso Galileo al Baliani, al quale ho conferito buona <lb/>parte delle mie immaginazioni filosofiche, mi scrive aver trovata grande con&shy;<lb/>formit&agrave; tra le sue speculazioni e le mie, di che io non mi sono punto ma&shy;<lb/>ravigliato, poich&egrave; studiamo sopra il medesimo libro e con i medesimi fon&shy;<lb/>damenti &rdquo; (Lettere di Galileo, pel suo Trecentesimo, Pisa 1864, pag. </s>

<s>16). </s></p><p type="main">

<s>Quando poi, venute queste speculazioni nel 1638 alla luce, si pot&egrave; tra <lb/>le stampate in Leida e le stampate in Genova istituire il confronto, ecco <lb/>come Galileo stesso, pi&ugrave; imparziale de'suoi fanatici esaltatori, ne scrisse al <lb/>suo proprio rivale il giudizio: &ldquo; La gratissima lettera di V. S. Ill.ma mi fu <lb/>resa ieri, insieme col suo libro <emph type="italics"/>Del moto,<emph.end type="italics"/> dal molto rev. </s>

<s>padre don Cle-<pb xlink:href="020/01/2341.jpg" pagenum="584"/>mente di S. Carlo.... Io ho trattato la medesima materia, ma alquanto pi&ugrave; <lb/>diffusamente, e con aggressioni diverse, imperocch&egrave; io non suppongo cosa <lb/>nessuna, se non la definizione del moto, del quale io voglio trattare e di&shy;<lb/>mostrare gli effetti, imitando in questo Archimede nelle sue spirali. </s>

<s>Non pre&shy;<lb/>mettendo altra cosa nessuna, vengo alla prima dimostrazione, nella quale <lb/>provo gli spazi passati da cotal mobile essere in duplicata proporzione dei <lb/>tempi, e seguito poi a dimostrare buon numero di altri accidenti, de'quali <lb/>ella ne tocca alcuni, ma io molti pi&ugrave; ve ne aggiungo, e per avventura pi&ugrave; <lb/>pellegrini &rdquo; (ivi, pag. </s>

<s>35-37). Ed &egrave; ci&ograve; verissimo, ma l'ordine del trattato <lb/>&egrave; tanto pi&ugrave; matematico, &egrave; il processo delle dimostrazioni tanto pi&ugrave; semplice <lb/>e chiaro, che chi avesse a imparar la Scienza nelle sue fonti preferirebbe <lb/>l'opuscolo del Baliani al Dialogo di Galileo. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Se ci &egrave; lecito rivolgerci ancora indietro a ripigliar l'immagine, per sim&shy;<lb/>bolegniare il nostro concetto, diremmo che gli Autori, fin qui da noi com&shy;<lb/>memorati, si rassomigliano, nel campo della Scienza del moto, a quegli al&shy;<lb/>beri cresciuti, per l'ubert&agrave; del suolo e per la benignit&agrave; del cielo, d'estraneo <lb/>seme, intorno a quel maggior albero, che ci raffigura la scienza di Gelileo. </s>

<s><lb/>Ma come vedesi nella selva verdeggiare a preferenza una specie d&igrave; piante, <lb/>disseminate o fatte scoppiare a pi&egrave; della maggiore; cos&igrave; avvenne delle dot&shy;<lb/>trine galileiane, incominciatesi a disseminar dai Dialoghi dei due Massimi <lb/>Sistemi. </s>

<s>Le ali della fama e i venti della discordia furono i principali mi&shy;<lb/>nistri di quella disseminazione, che si fece, attraverso a monti e a mari, per <lb/>tutte le regioni d'Europa. </s>

<s>Noi facciamo spesso le maraviglie, e confessiamo <lb/>la nostra propria ignoranza intorno all'origine di certe pianticelle, nate e <lb/>cresciute sotto i nostri occhi d'invisibile seme, ma lo stesso si dovrebbe dir <lb/>delle idee, le quali, apparite ne'libri di tanti scrittori stranieri quasi spon&shy;<lb/>tanee, derivarono dalla notizia dei Dialoghi famosi il germe latente. </s>

<s>Son per <lb/>que'Dialoghi infatti annunziate le conclusioni di tutte le verit&agrave; meccaniche <lb/>scoperte, e dimostrate da Galileo in trent'anni. </s></p><p type="main">

<s>Il fondamento statico, ritrovato nelle velocit&agrave; virtuali, si dimostra pro&shy;<lb/>lissamente dagl'Interlocutori nella seconda Giornata, a proposito della gra&shy;<lb/>vit&agrave;, che nella Leva di braccia disuguali lavora con altra resistenza e con <lb/>altra forza. </s>

<s>Cosicch&egrave;, propostasi per esempio la stadera, con la quale si vo&shy;<lb/>lesse pesare una balla di lana o di seta, concludesi dal Sagredo, che &ldquo; il <lb/>moversi per lo spazio di cento dita il romano, nel tempo che la balla si <lb/>muove per un sol dito, &egrave; l'istesso che il dire esser la velocit&agrave; del moto del <lb/>romano cento volte maggiore della velocit&agrave; del moto della balla &rdquo; per cui <lb/>fermasi come principio vero e notorio, &ldquo; che la resistenza, che viene dalla <pb xlink:href="020/01/2342.jpg" pagenum="585"/>velocit&agrave; del moto, compensa quella, che dipende dalla gravit&agrave; di un altro <lb/>mobile &rdquo; (Alb. </s>

<s>I, 237). </s></p><p type="main">

<s>Di maggiore importanza, e di maggior merito, erano i fondamenti della <lb/>Dinamica, i problemi appartenenti alla quale credeva Galileo non essere stati <lb/>saputi fin allora da Filosofo, n&egrave; da Matematico alcuno (ivi, pag. </s>

<s>181). Con&shy;<lb/>futato Aristotile, con ragioni cos&igrave; chiare e naturali da persuadere gli stessi <lb/>Simplicii, conclude che i corpi cadono dalla medesima altezza a terra, pi&ugrave; <lb/>o meno pesi, nel medesimo tempo; verit&agrave; che non era nuova, ma che pur <lb/>giovava trattenervi attorno eloquentemente il discorso per confermarla. </s></p><p type="main">

<s>Bench&egrave; da tutti per&ograve; si sapesse per volgare esperienza che, partendosi <lb/>i gravi dalla quiete, si vanno continuamente accelerando, la proporzione di <lb/>un tale acceleramento nulladimeno, dice il Salviati, &ldquo; &egrave; stata sino ai tempi <lb/>nostri ignota a tutti i filosofi, e primieramente ritrovata e dimostrata dal&shy;<lb/>l'Accademico, nostro comune amico, il quale, in alcuni suoi scritti non ancor <lb/>pubblicati, ma in confidenza mostrati a me e ad alcuni altri amici suoi, di&shy;<lb/>mostra come l'accelerazione del moto retto dei gravi si fa secondo i numeri <lb/>impari <emph type="italics"/>ab unitate:<emph.end type="italics"/> cio&egrave; che, segnati qual&igrave; e quanti si vogliano tempi eguali, <lb/>se nel primo tempo, partendosi il mobile dalle quiete, aver&agrave; passato un tale <lb/>spazio, come per esempio una canna, nel secondo tempo passer&agrave; tre canne, <lb/>nel terzo cinque, nel quarto sette, e cos&igrave; conseguentemente secondo i suc&shy;<lb/>cedenti numeri caffi; che insomma &egrave; l'istesso che il dire che gli spazi pas&shy;<lb/>sati dal mobile, partendosi dalla quiete, hanno tra di loro proporzione du&shy;<lb/>plicata di quella, che hanno i tempi, ne'quali tali spazi son misurati; o <lb/>vogliam dire che gli spazi passati son tra di loro come i quadrati dei tempi &rdquo; <lb/>(ivi, pag. </s>

<s>244). </s></p><p type="main">

<s>La dimostrazione promette il Salviati di darla, <emph type="italics"/>quando tratteremo la <lb/>materia de'moti separatamente,<emph.end type="italics"/> ossia nei dialoghi delle Nuove Scienze, ma <lb/>intanto si porge qui l'argomento principale della dimostrazione nel teorema <lb/>che, cessando il grave di accelerarsi, e proseguendo con gli uniformi gradi <lb/>della velocit&agrave; ultimamente acquistata, &ldquo; passa con moto equabile, nel me&shy;<lb/>desimo tempo, spazio doppio al passato dal moto accelerato &rdquo; (ivi, pag. </s>

<s>253). </s></p><p type="main">

<s>La massima proposizion dinamica, che si dimostra per mezzo di que&shy;<lb/>sto teorema, si svolge nel terzo dialogo delle Scienze nuove in quella lunga <lb/>e varia serie di teoremi, che muove dall'avere il tempo per l'obliqua e per <lb/>la perpendicolare, terminate al medesimo orizzonte, la stessa proporzione che <lb/>la lunghezza dell'obliqua ha alla lunghezza della perpendicolare; ci&ograve; che si <lb/>dimostra ne'principii della prima giornata dei Massimi Sistemi col suppo&shy;<lb/>sto famoso delle velocit&agrave; uguali nei punti ugualmente cadenti (ivi, pag. </s>

<s>30-32). <lb/>E per dar delle nuove dottrine intera notizia, insiem con ci&ograve;, che costitui&shy;<lb/>sce il principio del trattato Dei moti locali, s'annunzia l'ultima &ldquo; conclu&shy;<lb/>sione d'un problema bellissimo, che &egrave;: che, data una quarta di cerchio eretta <lb/>all'orizzonte, sicch&egrave; insista sul piano toccandolo in un punto, e fatto un arco <lb/>con una tavola ben pulita e liscia dalla parte concava, piegandola secondo <lb/>la curvit&agrave; della circonferenza, sicch&egrave; una palla ben rotonda e tersa vi possa <pb xlink:href="020/01/2343.jpg" pagenum="586"/>liberamente scorrer dentro; dico che, posta la palla in qualsivoglia luogo, o <lb/>vicino o lontano dall'infimo termine, e lasciata in libert&agrave;, in tempi eguali, <lb/>o insensibilmente differenti, arriver&agrave; al termine, partendosi da qualsivoglia <lb/>luogo; accidente veramente maraviglioso. </s>

<s>Aggiungete un altro accidente, non <lb/>meno bello di questo, che &egrave; che, anco per tutte le corde tirate dal punto <lb/>infimo a qualunque punto della circonferenza, il mobile stesso scender&agrave; in <lb/>tempi assolutamente uguali. </s>

<s>Aggiungete l'altra maraviglia, qual'&egrave; che i moti <lb/>dei cadenti, fatti per gli archi della quarta, si fanno in tempi pi&ugrave; brevi, che <lb/>quelli, che si fanno per le corde dei medesimi archi &rdquo; (ivi, pag. </s>

<s>488). </s></p><p type="main">

<s>I Matematici esperti avrebbero avuto in queste notizie i dati necessari <lb/>per costruire, sei anni prima della pubblicazione, con le loro proprie mani <lb/>l'edifizio dinamico co'materiali gi&agrave; preparati da Galileo, n&egrave; mancarono al&shy;<lb/>cuni che, frugati dalla curiosit&agrave; e dall'amor della Scienza, v'esercitarono <lb/>l'ingegno. </s>

<s>Possiamo de'nostri annoverar fra costoro principali, lasciando il <lb/>Cavalieri, di cui, in dimostrare le propriet&agrave; del moto appena pubblicate <lb/>nel 1632, son note le promozioni; il Magiotti e il Torricelli, che conveni&shy;<lb/>vano in Roma desiderosi ad ascoltare i commenti, fatti a loro sulla lettura <lb/>dei dialoghi dei Massimi Sistemi, da Benedetto Castelli, il quale scriveva <lb/>allo stesso Galileo queste parole: &ldquo; Io godo spesso la conversazione di un <lb/>signor Raffaele Magiotti da Montevarchi, e di un signor Evangelista Torri&shy;<lb/>ricelli da Imola, ambedue eruditissimi di Geometria ed Astronomia, gi&agrave; messi <lb/>da me per la buona strada. </s>

<s>Questi bene spesso mi vengono a ritrovare, e <lb/>si leggono i Dialeghi con tanto applauso della dottrina, dei concetti, della <lb/>lingua e della spiegazione, che, se bene meritano molto pi&ugrave;, so che V. S. <lb/>non lo potrebbe desiderar maggiore &rdquo; (Alb. </s>

<s>IX, 273). </s></p><p type="main">

<s>Degli studii del Magiotti non pot&egrave; il pubblico gustare i frutti, soprab&shy;<lb/>bondantemente ricompensato dal Torricelli, che ampli&ograve; le galileiane dottrine <lb/>del moto con aggressioni diverse, e con maravigliosa facilit&agrave; ed eleganza. </s>

<s><lb/>Avrebbe, insieme co'due discepoli del Castelli, dovuto formare il triunvi&shy;<lb/>rato glorioso Niccol&ograve; Aggiunti, se fosse stato a tempo di veder pubblicate, <lb/>per ispirarsi alla loro lettura, le due Nuove Scienze. </s>

<s>Ma egli &egrave; pure l'esem&shy;<lb/>pio pi&ugrave; perfetto di ci&ograve; che, a metter gl'ingegni sul diritto sentiero, confe&shy;<lb/>rissero i dialoghi de'due Massimi Sistemi. </s>

<s>Di quegli studii nemmen egli <lb/>pot&egrave; dare pubblico saggio, ma pure, a giudicar de'progressi gi&agrave; fatti e a <lb/>presagir di quelli, che avrebbe potuto fare, se cos&igrave; giovane non l'avesse <lb/>colto la morte; basta quel che fu pietosamente raccolto, e trasmesso in ere&shy;<lb/>dit&agrave; della scienza dalle pagine di lui manoscritte. </s>

<s>Le speculazioni, che ivi <lb/>si leggono intorno alla tensione delle corde, meccanicamente e acusticamente <lb/>considerata; intorno alla teoria delle taglie, e all'inerzia dei pendoli, insiem <lb/>con altri pensieri pi&ugrave; o men lucidamente riflettenti il vero, ma pur sem&shy;<lb/>pre ingegnosi e nuovi; son per le varie pagine della nostra Storia occorse <lb/>gi&agrave; alla notizia dei nostri Lettori. </s>

<s>Ma il generoso desiderio e il giovanile ar&shy;<lb/>dimento di tentar cose nuove non apparisce meglio, che dalla dimostrazione <lb/>di un fatto, intorno a cui pareva impossibile che si potesse dare scienza. </s></p><pb xlink:href="020/01/2344.jpg" pagenum="587"/><p type="main">

<s>Sia posata sul piano, per esempio di un tavolino, una catena di ferro, <lb/>e una parte di lei resti pendula: questa, nei casi ordinari, non si strasci&shy;<lb/>cher&agrave; l'altra che giace, facendola tutta cadere a terra, so non che quando <lb/>ia la stessa parte pendula tanto pesa, da vincere l'attrito degli anelli con&shy;<lb/>tro la superfice del piano. </s>

<s>Che se facciasi astrazione da questo attrito, e si <lb/>supponga quello stesso piano perfettamente livellato, dimostra l'Aggiunti che <lb/>un mezzo anello solo non sostenuto sar&agrave; bastante a tirarsi dietro tutti gli <lb/>altri, e a far tutta cader con s&egrave; la catena quant'ella &egrave; lunga. </s>

<s>La dimostra&shy;<lb/>zione perci&ograve; dipende, e come da suo proprio principio si conclude dal se&shy;<lb/>guente Lemma: </s></p><p type="main">

<s>&ldquo; Quel mobile, che non ha inclinazione a moversi verso alcun termine, <lb/>star&agrave; fermo, ma sar&agrave; indifferente a qualsivoglia moto; e da qualunque mi&shy;<lb/>nima forza sar&agrave; mosso verso qualsivoglia parte. </s>

<s>Star&agrave; fermo, perch&egrave;, s'egli <lb/>si movesse verso qualche parte, averebbe verso quella qualche inclinazione, <lb/>contro il supposto. </s>

<s>Star&agrave; ancora fermo un mobile lasciato in un mezzo li&shy;<lb/>bero, se ar&agrave; verso qualsivoglia termine eguale inclinazione al moversi. </s>

<s>Im&shy;<lb/>perocch&egrave;, essendo le inclinazioni a tutte le parti uguali, saranno ancora le <lb/>resistenze alle parti opposte uguali. </s>

<s>Ma queste resistenze si ritrovano in detto <lb/>mobile, perch&egrave;, essendo egli inclinato ugualmente, si mover&agrave; verso qualun&shy;<lb/>que parte: adunque sar&agrave; ugualmente inclinato a moversi verso i termini <lb/>opposti, cio&egrave; al moto verso qualsivoglia parte aver&agrave; altrettanta resistenza. </s>

<s><lb/>Ma egli per il supposto inclina ugualmente al moto per tutti i versi; adun&shy;<lb/>que egli stesso resiste al moto ugualmente per tutti i versi. </s>

<s>Sicch&egrave; tanto &egrave; <lb/>a dire un mobile inclinato ugualmente a moversi verso qualunque parte, <lb/>quanto dire un mobile, che resiste a moversi ugualmente per tutti i versi. </s>

<s><lb/>Ma se tale &egrave;, dunque non si mover&agrave;, lasciato in un mezzo libero, ma s&igrave; bene <lb/>ogni minima forza lo mover&agrave; a qualunque parte, perch&egrave; ogni minima forza, <lb/>aggiunta all'inclinazione verso qualche parte, fa che la resistenza opposta <lb/>resti minore, che di prima era uguale. </s>

<s>Ma quando l'inclinazione &egrave; mag&shy;<lb/>giore della resistenza il mobile si muove; adunque, con qualsivoglia minima <lb/>forza aggiunta, detto mobile si mover&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di qui si raccoglie che tanto &egrave; un mobile che resista o inclini egual&shy;<lb/>mente a moversi verso qualunque termine, quanto quel mobile, che non in&shy;<lb/>clina a moversi verso parte alcuna; perch&egrave; tanto quello come questo da ogni <lb/>minima forza &egrave; mosso a qualunque parte &rdquo; (MSS. Gal. </s>

<s>Disc., T. XVIII, <lb/>fol. </s>

<s>97). </s></p><p type="main">

<s>Posti questi principii, si preparava l'Aggiunti alla soluzione del suo <lb/>problema, prima considerando il corpo, che s'immagina posato in parte sul <lb/>piano e in parte fuori, come rigido, e tutt'insieme connesso. </s>

<s>In questo caso <lb/>le condizioni dell'equilibrio si riducono facilmente a quelle della stessa Leva. </s></p><p type="main">

<s>&ldquo; Nel piano orizzontale HF (fig. </s>

<s>309) sia posto il solido grave GF, con <lb/>la parte DE posata sopra detto piano, e col rimanente DF fuori. </s>

<s>Se il solido <lb/>sar&agrave; composto di parti fisse, dure e saldamente l'una con l'altra connesse, <lb/>non potr&agrave; abbassarsi la parte DF senza sollevar l'altra DE. &rdquo; </s></p><pb xlink:href="020/01/2345.jpg" pagenum="588"/><p type="main">

<s>&ldquo; Da'centri di gravit&agrave; della parte DE, e della DF, siano tirate le per&shy;<lb/>pendicolari al piano orizzontale HF, le quali sono tra lor parallele, e per&ograve; <lb/>nel medesimo piano. </s>

<s>Producasi dunque per esse un piano, il quale seghi <lb/>l'orizzontale HF, dilatato quanto bisogna, e la comune sezione sia la retta <lb/><figure id="id.020.01.2345.1.jpg" xlink:href="020/01/2345/1.jpg"/></s></p><p type="caption">

<s>Figura 309<lb/>AB, quale seghi la linea LM <lb/>nel punto C. </s>

<s>Sar&agrave; dunque la <lb/>linea AB una bilancia, ovvero <lb/>leva, il cui sostegno in C, ed <lb/>i pesi DF, DE pendono dalli <lb/>punti A, B. </s>

<s>Quando dunque il <lb/>peso DF, al peso DE, aver&agrave; mag&shy;<lb/>gior proporzione che la distanza <lb/>AC alla distanza CB, allora il <lb/>solido DF alzer&agrave; il solido DE. &rdquo; </s></p><p type="main">

<s>&ldquo; Ma se nel medesimo piano HF sia posto, parte in esso e parte fuori, <lb/>il solido KNO (fig. </s>

<s>310) composto, non di parti duramente affisse, ma fra <lb/>di s&egrave; lente e flessibili agevolmente, come una corda, catenella, serpe o an&shy;<lb/>guilla etc.; allora dico che, qualunque parte di esso penda fuori del piano <lb/>HF, detto solido sdruccioler&agrave; e cascher&agrave; dal piano &rdquo; (ivi). </s></p><p type="main">

<s>La dimostrazione si conduce dai principii di una Scienza nuova, della <lb/>quale Galileo ne'suoi dialoghi Del mondo non fa il minimo cenno, bench&egrave; <lb/>egli dica di avere infin dal principio del 1609 <emph type="italics"/>finito di ritrovarne tutte le <lb/>conclusioni<emph.end type="italics"/> (Alb. </s>

<s>VI, 69). Nel 1633 attendeva a dare a quelle conclusioni <lb/><figure id="id.020.01.2345.2.jpg" xlink:href="020/01/2345/2.jpg"/></s></p><p type="caption">

<s>Figura 310<lb/>ordine di trattato, con <lb/>intenzione di pubbli&shy;<lb/>carlo nei nuovi dialo&shy;<lb/>ghi Del moto, e in tale <lb/>occasione com'&egrave; certo <lb/>che fu eccitatato a stu&shy;<lb/>diar le leggi delle re&shy;<lb/>sistenze Andrea Arri&shy;<lb/>ghetti, di cui son pub&shy;<lb/>blicamente noti alcuni <lb/>teoremi (Alb. </s>

<s>VII, 34-37) dallo stesso Galileo giudicati nel loro procedere <lb/><emph type="italics"/>maestosi<emph.end type="italics"/> (ivi, pag. </s>

<s>38); cos&igrave; non ebbe a rimanersi indietro l'Aggiunti, <lb/>come pu&ograve; giudicarsi dal modo di dimostrar l'annunziata proposizione, che <lb/>&egrave; tale: </s></p><p type="main">

<s>&ldquo; Sia nell'orizzonte HF (come nella precedente figura) un cilindro di <lb/>materia omogenea, uniforme, e perci&ograve; in ogni sua parte da egual forza egual&shy;<lb/>mente flessibile, e la parte KN sia posata nel piano, NO avanzi fuori. </s>

<s>La re&shy;<lb/>sistenza all'essere inflesso detto cilindro sar&agrave; una forza posta nella leva NP, <lb/>col centro del suo momento posto in N, e il fulcimento in P. </s>

<s>La parte poi <lb/>del cilindro NO sar&agrave; come un peso attaccato nella leva PZ, il cui sostegno <lb/>&egrave; in P, e detta leva sar&agrave; congiunta con l'altra leva PN in P. </s>

<s>Sia dunque <pb xlink:href="020/01/2346.jpg" pagenum="589"/>tale il peso di NO, che superi la resistenza, che hanno le parti del cilin&shy;<lb/>dro all'esser distratte: dunque si distrarranno. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Distraggansi le parti dunque successivamente, sicch&egrave; la parte NO del <lb/>cilindro discenda in PX. </s>

<s>Di nuovo sar&agrave; nella leva PZ, che ha il fulcimento <lb/>in P, attaccato il peso del solido ZX, e nella leva PZ saranno, l'una dopo <lb/>l'altra, susseguentemente attaccate, nel punto Z, le potenze; e le resistenze <lb/>alla distrazione R, S, T saranno come pendenti dal punto N, perch&egrave; la forza, <lb/>che fa la parte del cilindro RN per stare attaccata con l'altra RS, vien mas&shy;<lb/>simamente e validissimamente fatta per la linea RN, nella quale sono i cen&shy;<lb/>tri di esse resistenze alla distrazione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Posto dunque che il peso XZ, pendente dalla leva ZP, sia tale che <lb/>possa col suo momento superar la forza, con che resistono le parti del ci&shy;<lb/>lindro all'essere distratte; perch&egrave; nel torcere un solido maggiore e mag&shy;<lb/>gior forza ci vuole di mano in mano a voler far pi&ugrave; e pi&ugrave; distratte le me&shy;<lb/>desime parti del solido, sicch&egrave; minima &egrave; quella forza, che si richiede per dar <lb/>principio alla distrazione; di qui &egrave; che il peso XZ, che per i filamenti P <lb/>e Z, con la leva PZ, fa forza di tirare il solido KN, piuttosto che maggior&shy;<lb/>mente distrarre li detti filamenti o fibre POZ, il che &egrave; pi&ugrave; difficile, prin&shy;<lb/>cipier&agrave; piuttosto, sendo questo pi&ugrave; facile, a distrarre le susseguenti prossime <lb/>parti, e in tal distrazione le minime particole indistraibili componenti il ci&shy;<lb/>lindro verranno verso PZ, e maggiormente caricando il solido ZX lo ren&shy;<lb/>deranno sempre pi&ugrave; potente a distrarre le parti che succedono. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma perch&egrave; il solido XZ, facendo forza di distrarre il solido KN, pigne <lb/>a basso, e l'istesso fanno le parti, che distratte cadono sopr'esso; perci&ograve; il <lb/>solido KN verr&agrave; nel medesimo tempo tirato orizzontalmente secondo la linea <lb/>ZP, al qual movimento, non avendo alcun grave resistenza alcuna, egli an&shy;<lb/>cora obbedir&agrave;. </s>

<s>Se dunque porremo che il cilindro sia flessibile in ogni sua <lb/>parte da ogni forza, &egrave; manifesto che qualunque parte di esso sia fuori del <lb/>piano lo far&agrave; sdrucciolare, e cader tutto &rdquo; (MSS. Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>98). </s></p><p type="main">

<s>Di qui si passa a considerare il corpo, che &egrave; posato sul piano, non come <lb/>tutto ugualmente rigido, n&egrave; come tutto in s&egrave; flessibile e lento, ma come <lb/><figure id="id.020.01.2346.1.jpg" xlink:href="020/01/2346/1.jpg"/></s></p><p type="caption">

<s>Figura 311<lb/>partecipante d'ambedue le <lb/>qualit&agrave; insieme, qual sareb&shy;<lb/>be, aggiunta con anelli ugua&shy;<lb/>li, una catena di ferro. </s>

<s>Sia <lb/>questa catena AB (fig. </s>

<s>311) <lb/>tirata dall'anello BC pendulo <lb/>o da qualunque altro minimo <lb/>peso, che la condurr&agrave; con s&egrave; <lb/>irresistibilmente a terra, fa&shy;<lb/>cendo passar ciascuno anello <lb/>di lei per varie fasi di moto. </s>

<s>Attendiamo all'anello DB, mentr'egli tutto si <lb/>giace ancora sul piano: il peso BC diffonde la sua azione per tutta la lun&shy;<lb/>ghezza della catena, sopra la quale opera a modo di cuneo, qual sarebbe <pb xlink:href="020/01/2347.jpg" pagenum="590"/>per esempio TSX, che, insinuandosi nel mezzo fra le giunture di questo e <lb/>di quello anello, sospinge ciascuno innanzi per la dirittura SP. </s>

<s>Verr&agrave; cos&igrave; <lb/>l'anello DB portato fuori del piano per la porzione FB del suo diame&shy;<lb/>tro (fig. </s>

<s>312) e ivi si rimarr&agrave;, infintantoch&egrave; il braccio della sua leva FB, <lb/>crescendo, non operi con tale momento, da prevalere sull'altro braccio FD, <lb/><figure id="id.020.01.2347.1.jpg" xlink:href="020/01/2347/1.jpg"/></s></p><p type="caption">

<s>Figura 312<lb/>facendo rivoltar l'asse dell'anello <lb/>stesso intorno ad F suo punto <lb/>d'appoggio. </s>

<s>L'estremit&agrave; D della <lb/>leva si alzer&agrave;, e alzer&agrave; con s&egrave; <lb/>insieme anche l'asse dell'anello <lb/>ED (fig. </s>

<s>313) il centro di gra&shy;<lb/>vit&agrave; del quale, tendendo ad ac&shy;<lb/>costarsi al pi&egrave; della perpendi&shy;<lb/>colare ID, far&agrave; che finalmente l'anello DB cada tutto dal piano, tornando <lb/>egli che stavagli dietro a giacervi sopra, come vi giaceva dianzi lo stesso <lb/>anello DB, di cui subir&agrave; le medesime vicende, come le subiranno tutti gli <lb/>altri anelli via via, infin tanto che non sia la catena scorsa gi&ugrave; per tutta <lb/>la sua lunghezza. </s>

<s>Il caso &egrave; descritto cos&igrave; dall'Aggiunti, con finezza di ma&shy;<lb/>tematico, e con bellezza di artista: </s></p><p type="main">

<s>&ldquo; Ma se sar&agrave; nell'orizonte HO la catena AB, della quale la parte AB <lb/>sia distesa nel piano, e il resto BC penda fuori del piano dal punto B, <lb/><figure id="id.020.01.2347.2.jpg" xlink:href="020/01/2347/2.jpg"/></s></p><p type="caption">

<s>Figura 313<lb/>ogni volta che la parte sospesa dal <lb/>punto B sar&agrave; tale, che il suo peso <lb/>possa, mediante la leva DFB, che <lb/>ha il suo sostegno in F, alzare <lb/>quella parte dell'anello DB, che <lb/>&egrave; nel piano, e gravita nella parte <lb/>DF della leva DFB; dico che al&shy;<lb/>lora la catena AB scorrer&agrave; verso B, <lb/>sin a tanto che ella vada in terra. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Perch&egrave;, nel sollevarsi l'anello DB, l'altro anello DE, il quale &egrave; con&shy;<lb/>vertibile intorno alla parrte D dell'anello DB, ed intorno alla parte E del&shy;<lb/>l'altro anello EG, non si alzer&agrave; in dirittura con l'anello DB, ma solamente <lb/>verr&agrave; sollevato dalla parte D, e con l'altra parte toccher&agrave; il piano. </s>

<s>Perch&egrave; <lb/>poi se uno anello sar&agrave; sostenuto da due forze, poste nell'estremit&agrave; di un <lb/>suo diametro parallelo all'orizonte, allora ciascuna forza sostiene la met&agrave; di <lb/>tutto il peso dell'anello; perci&ograve; solamente, quando l'anello fusse posato <lb/>orizontale, la forza, che, posta in uno estremo de'suoi diametri si serve del <lb/>diametro per leva, e del punto del toccamento per sostegno, vuole alzarlo; <lb/>deve essere sul principio eguale alla met&agrave; del peso di detto anello, ma dopo <lb/>successivamente pu&ograve; essere sempre minore, perch&egrave; sempre si diminuisce <lb/>il peso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, nel nostro caso, quando l'anello DE sar&agrave; orizontale, e perci&ograve; <lb/>l'anello DB eretto al piano orizontale, volutandosi l'anello DB nell'orizonte, <pb xlink:href="020/01/2348.jpg" pagenum="591"/>il seguente anello ED non viene alzato, non ci essendo chi gli faccia forza <lb/>all'ins&ugrave;, ed avendo egli sempre il suo medesimo peso, ma ne vien ben <lb/>tirato orizontalmente, perch&egrave;, siccome se noi volessimo cacciare il conio STX <lb/>(fig. </s>

<s>309 poco addietro) nell'anello SP, col moverlo verso S, secondo la <lb/>linea TS, &egrave; manifesto che l'anello SP, per dar luogo di mano in mano alle <lb/>parti pi&ugrave; larghe del conio, sarebbe mosso verso SP; cos&igrave;, nel subentrare <lb/>nell'anello ED, le parti dell'anello DB, che son sempre pi&ugrave; prossime al <lb/>punto B, &egrave; necessario che l'anello ED, e in conseguenza tutta la catena, <lb/>venga tirata verso B. </s></p><p type="main">

<s>&ldquo; N&egrave; a tal movimento, come orizontale, ella non ha resistenza; dun&shy;<lb/>que sar&agrave; mossa da ogni minimo peso pendente dal primo anello DB. </s>

<s>Dico <lb/>da ogni minimo peso, perch&egrave;, essendo il primo anello eretto al piano, le <lb/>parti anteriori equipondereranno alle posteriori: dunque ogni minimo peso <lb/>aggiunto a questa alzer&agrave; quella, e tirer&agrave; tutte le altre. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia dunque il primo anello caduto dal piano, dopo la caduta del <lb/>quale rester&agrave; per primo anello nell'orizonte l'anello, che diremo pure DB, <lb/>non pi&ugrave; parallelo, ma inclinato all'orizonte. </s>

<s>Se dunque il peso pendente dal <lb/>punto B sar&agrave; (come s'&egrave; rappresentato nella 311 figura) tale che alzi FD, e <lb/>di pi&ugrave; un peso eguale al predetto anello DE, il qual peso s'intendesse at&shy;<lb/>taccato nel punto D della leva DFB; allora tutta la catena scorrer&agrave;, per&shy;<lb/>ch&egrave;, alzandosi con la leva DB il punto D dell'anello DB, sar&agrave; l'anello DE <lb/>come un peso pendulo dal suo centro della gravit&agrave; nella linea, che si tira <lb/>dal punto di sospensione perpendicolare all'orizonte. </s>

<s>Dunque l'anello DE <lb/>cercher&agrave; di accomodare il suo diametro DE nella linea DI perpendicolare <lb/>all'orizonte. </s>

<s>Ma il diametro DB cio&egrave; il diametro DE, essendo gli anelli <lb/>uguali, &egrave; maggiore della linea DI, adunque, alzisi quanto si voglia il punto <lb/>D, sempre l'anello DE, con le parti verso E, inciamper&agrave; nell'orizonte, men&shy;<lb/>tre fa forza di andare in DI. </s>

<s>Perch&egrave; poi il punto D nell'alzarsi si accosta <lb/>verso B, dunque anche l'altra estremit&agrave; E del diametro ED si sar&agrave; acco&shy;<lb/>stata verso B. </s>

<s>Ma all'estremit&agrave; E vien concatenato l'altro anello EG ori&shy;<lb/>zontale, dunque, movendosi detto punto E verso B, anche l'anello EG bi&shy;<lb/>sogna che si muova. </s>

<s>Di modo che l'anello DE, nell'andar verso B, tira a <lb/>quella volta la catena EA. </s>

<s>Ma a tal tiramento, perch'&egrave; orizontale, ella non <lb/>resiste; adunque scorrer&agrave; verso, fin tanto che DB sia col centro di gravit&agrave; <lb/>fuor del piano, dal qual cadendo divenga pendulo dall'anello che gli suc&shy;<lb/>cede. </s>

<s>E cos&igrave; rinnovandosi dal peso pendulo fuori del piano, che tuttavia cre&shy;<lb/>sce, i medesimi movimenti come sopra, la catena finalmente cadr&agrave; tutta fuori <lb/>del piano &rdquo; (ivi, fol. </s>

<s>98, 99). </s></p><pb xlink:href="020/01/2349.jpg" pagenum="592"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Bench&egrave; l'Aggiunti s'educasse l'ingegno a specular cos&igrave; sottili, e cos&igrave; <lb/>nuove ragioni del moto alla lettura dei dialoghi dei due massimi Sistemi <lb/>del mondo, egli nonostante, morto tre anni prima che vedessero la pubblica <lb/>luce in Leida, attinse, delle dottrine insegnate ne'nuovi dialoghi Del moto, <lb/>qualche cosa da'familiari colloqui intrattenuti con l'Autore nelle ville di <lb/>Bellosguardo e di Arcetri. </s>

<s>Dello strumento per esempio, immaginato e de&shy;<lb/>scritto nel primo dialogo, per misurare la forza del vacuo, vedemmo come <lb/>ne facesse l'Aggiunti un'applicazione ingegnosa, per ridurre a teorema quel <lb/>che Galileo semplicemente asseriva delle corde e delle verghe ugualmente <lb/>resistenti in tutta la loro lunghezza. </s>

<s>Tra il 1632 e il 1635 infatti esso Ga&shy;<lb/>lileo attendeva a scrivere il detto dialogo primo, che doveva servir come di <lb/>prefazione ai due trattati Delle resistenze dei solidi, e Dei moti locali. </s>

<s>E <lb/>bench&egrave; nel rileggerlo sempre gli cascassero in mente nuove materie, e la <lb/>maniera dello scrivere in dialogo gli porgesse assai conveniente attacco d'in&shy;<lb/>serirle (Alb. </s>

<s>VII, 56), si potrebbe asserir nonostante che, quale diceva nel <lb/>Marzo del 1635 di averlo ridotto al netto e trascritto l'Autore, tale siaci ri&shy;<lb/>masto quello stesso primo dialogo nelle stampe. </s></p><p type="main">

<s>L'asserto da una parte conferma e dall'altra &egrave; confermato dal fatto, <lb/>che la seconda Scienza nuova, alla quale allora pensava Galileo, versava solo <lb/>intorno ai moti equabili e agli accelerati, non essendoglisi mostrata ancora <lb/>la proposizione del Cavalieri intorno ai moti parabolici feconda di tutte <lb/>quelle dottrine de'proietti, che sarebbero venute ad aggiungere un'altra no&shy;<lb/>bilissima parte al trattato Dei moti locali. </s>

<s>L'ordine storico perci&ograve;, che per <lb/>esser compiuto, dopo l'esame dei tre ultimi dialoghi non vuol che si tra&shy;<lb/>scuri il primo, e il desiderio di confermare le conclusioni del capitolo pre&shy;<lb/>cedente, in coloro che ne fossero tuttavia rimasti dubitosi, ci consigliano di <lb/>trattener qui brevemente il discorso intorno al dialogo sopraddetto, per ve&shy;<lb/>der com'egli veramente preluda al trattato Delle resistenze e dei moti na&shy;<lb/>turali, senza preparare il pensiero o fare il minimo cenno dei moti violenti. </s></p><p type="main">

<s>A proposito dell'arsenal di Venezia introduce il Salviati il suo discorso <lb/>intorno alla costruzione delle macchine navali, annunziando a coloro, che <lb/>dalla robustezza delle piccole argomentavano a quella delle grandi, la con&shy;<lb/>clusione, che nella prima Scienza nuova si vedr&agrave; dimostrata, come cio&egrave; nel <lb/>crescersi la quantit&agrave; della materia non si moltiplichino con lo stesso rag&shy;<lb/>guaglio la robustezza e la gagliardia (Alb. </s>

<s>XIII, 10). La virt&ugrave; del resistere <lb/>i corpi duri alla rottura dipende dalla tenacit&agrave; e coerenza delle loro parti, <lb/>che si riducono, specialmente ne'legni, a fibre o a filamenti, come nei ca&shy;<lb/>napi, intorno ai quali si discorrono le ragioni del loro essere in sostener <lb/>cos&igrave; validi. </s></p><pb xlink:href="020/01/2350.jpg" pagenum="593"/><p type="main">

<s>Ma considerar la testura sola non basta, dovendo essere nelle stesse <lb/>minime fibre qualche cosa, che le colleghi insieme e le tenga; ci&ograve; che dal&shy;<lb/>l'altra parte &egrave; manifesto nelle pietre e nei metalli, la coerenza ne'quali dee <lb/>dipender da altro glutine, che da filamenti. </s>

<s>Di qui si passa a cercare qual <lb/>sia questo glutine, e dove ei risegga, per risolvere la qual questione s'in&shy;<lb/>comincia ad esaminare &ldquo; quella decantata repugnanza, che ha la Natura ad <lb/>ammettere il vacuo &rdquo; (ivi, pag. </s>

<s>15). Le favolose dottrine dei peripatetici si <lb/>vedono finalmente cenfutate dai fatti sperimentali, qui per la prima volta <lb/>descritti, d'onde resulta esser la virt&ugrave; attribuita al vacuo assai limitata e <lb/>insufficiente all'effetto, essendo ella una sola delle cinque parti di quella <lb/>forza, che sarebbe necessaria per vincer l'aderenza delle superficie di due <lb/>corpi levigati (ivi, pag. </s>

<s>19). Convien dunque di una tal maggioranza di forza <lb/>ritrovar la causa, la quale, dovend'essere una sola potissima e vera, &ldquo; men&shy;<lb/>tr'io non trovo, dice il Salviati, altro glutine, perch&egrave; non debbo tentar di <lb/>vedere se questo del vacuo che si trova pu&ograve; bastarci? </s>

<s>&rdquo; (ivi, pag. </s>

<s>23). </s></p><p type="main">

<s>Come altrove notammo aveva Galileo, nelle sue prime speculazioni, at&shy;<lb/>tribuita la coerenza dei corpi a un'attrazione quasi magnetica fra le loro <lb/>particelle, prelucendo a quella, che universalmente &egrave; approvata oggid&igrave; sotto <lb/>il nome di <emph type="italics"/>attrazione molecolare.<emph.end type="italics"/> Ma i nuovi fatti osservati, e ne'quali si <lb/>lusingava di aver ritrovata la ragione del non si poter sostenere un cilindro <lb/>d'acqua, ne'tubi delle trombe aspiranti, pi&ugrave; su delle diciotto braccia; lo <lb/>consigliarono a bandir dalla sua mente ogni virt&ugrave; magnetica, per ridur tutto <lb/>a quella repugnanza del vacuo, ch'egli aveva a principio derisa, e della <lb/>quale le presenti esperienze gli avevano dimostrato l'insufficienza. </s>

<s>L'accusa <lb/>non gli &egrave; risparmiata dal suo libero Simplicio, per difendersi dalla quale <lb/>egli, al gran vacuo insufficiente a produr l'effetto, sostituendo i minimi <lb/>spazi fra particelle e particelle innumerevolmente disseminate, risponde &ldquo; che, <lb/>se bene tali vacui sarebber piccolissimi, ed in conseguenza ciascuno facile <lb/>ad esser superato, tuttavia l'innumerabile moltitudine, innumerabilmente, <lb/>per cos&igrave; dire, moltiplica le resistenze &rdquo; (ivi, pag. </s>

<s>24). </s></p><p type="main">

<s>&Egrave; da questa innumerabilit&agrave; che si coglie l'occasione d'entrare a trat&shy;<lb/>tar degl'infiniti e degli indivisibili con discorsi, che si sollevan per le ne&shy;<lb/>bulose regioni, colla principale intenzione di suscitarvi dagli elementi discordi <lb/>una tempesta contro le nuove dottrine del Cavalieri. </s>

<s>Rasserenata poi la <lb/>mente nel dire quel ch'ei si compiace altrove (Alb. </s>

<s>VII, 55) di chiamar suo <lb/>pensiero <emph type="italics"/>ammirando e assai peregrino,<emph.end type="italics"/> intorno alla rarefazione, alla con&shy;<lb/>densazione e alla penetrazione dei corpi; si termina, con una questione geo&shy;<lb/>metrica degl'isoperimetri, questa prima parte del dialogo, che prolude al <lb/>trattato delle Resistenze. </s></p><p type="main">

<s>L'altro trattato, in cui si doveva presentare al pubblico la seconda <lb/>Scienza nuova, era quello dei moti naturali, a discorrer dei quali in forma <lb/>di proemio si prende attacco dal vacuo, creduto da Aristotile impossibile, <lb/>perch&egrave; il moto si dovrebbe in esso far nell'istante. </s>

<s>La conclusion del Fi&shy;<lb/>losofo scendeva dal falso principio &ldquo; che le velocit&agrave; del medesimo mobile, <pb xlink:href="020/01/2351.jpg" pagenum="594"/>in diversi mezzi, ritengono tra di loro la proporzione contraria di quella, <lb/>che hanno le grossezze e densit&agrave; di essi mezzi &rdquo; (pag. </s>

<s>64): falsit&agrave; che con <lb/>facile discorso &egrave; scoperta qui dal Salviati, insiem con l'altra, pur dal Filo&shy;<lb/>sofo medesimo insegnata, e contro la quale si dimostra per prova &ldquo; che <lb/>una palla di artiglieria, che pesi cento, dugento ed anco pi&ugrave; libbre, non <lb/>anticiper&agrave; di un palmo solamente l'arrivo in terra della palla di un mo&shy;<lb/>schetto, che ne pesi una mezza, venendo anco dall'altezza di dugento brac&shy;<lb/>cia &rdquo; (ivi). </s></p><p type="main">

<s>La sentenza nuova, contrapposta cos&igrave; all'aristotelica antica, voleva es&shy;<lb/>sere ben dichiarata col mettere in considerazione l'operazion dell'aria, che <lb/>impedisce la velocit&agrave; naturale pi&ugrave; o meno, secondo che varia la gravit&agrave; spe&shy;<lb/>cifica e l'assoluta dei corpi cadenti. </s>

<s>Si divaga di qui il discorso intorno al <lb/>modo di misurar la gravit&agrave; in specie de'liquidi, per via degli areometri <lb/>(pag. </s>

<s>71, 72); intorno alla tenacit&agrave; dell'acqua, e alla resistenza del mezzo, <lb/>che riduce finalmente all'equabilit&agrave; ogni moto accelerato (pag. </s>

<s>77, 95, 96), <lb/>e intorno al peso e alla compressione dell'aria, ritornando all'argomento del <lb/>moto colla descrizione dei pendoli che, o gravi o leggeri, vanno oscillando <lb/>sotto i medesimi tempi, se non che anch'essi risentono l'operazione del <lb/>mezzo (pag. </s>

<s>87). </s></p><p type="main">

<s>Lo strumento non &egrave; per&ograve; solamente dimostrativo delle leggi della ca&shy;<lb/>duta dei gravi: altri quesiti ci sono attenenti a questa materia, che <emph type="italics"/>a molti <lb/>parrebbe assai arida<emph.end type="italics"/> (pag. </s>

<s>97), ma che il Salviati non vuol disprezzare, fa&shy;<lb/>cendone intanto rilevare il pregio col dar sodisfazione ad alcune difficolt&agrave; <lb/>del Sagredo intorno alle dissonanze musicali, e all'intendere il perch&egrave; tese <lb/>due corde all'unisono, sonando l'una, anche l'altra si move. </s>

<s>Il fatto, e il <lb/>modo di sperimentarlo &egrave; antichissimo, e in una Nota di Leonardo da Vinci <lb/>si legge cos&igrave; descritto: &ldquo; Il colpo dato nella campana risponder&agrave; e mover&agrave; <lb/>alquanto un'altra campana simile a s&egrave;, e la corda sonata di un liuto ri&shy;<lb/>sponder&agrave; e mover&agrave; un'altra simile corda di simile boce in un altro liuto, <lb/>e questo vedrai col porre una paglia sopra una corda simile alla sonata &rdquo; <lb/>(Les Manus., Manus A, Paris 1881, fol. </s>

<s>32). </s></p><p type="main">

<s>Guidubaldo del Monte non aveva solo descritto il fatto, ma aveva dato <lb/>di pi&ugrave; la ragione del fatto delle due corde unisone, e delle loro dissonanze, <lb/>cos&igrave; scrivendo: &ldquo; Due corde in unisono vanno bene insieme e non si per&shy;<lb/>cotono fra loro, mentre sonano; che nasce perch&egrave; hanno il medesimo moto <lb/>nell'andare e tornare: che se se ne scorda e move una, non sonano bene <lb/>insieme, ma si percotono.... Di qui ancora si pu&ograve; render ragione perch&egrave; <lb/>causa, se saranno due strumenti vicini ed abbiano pi&ugrave; corde, e posta una <lb/>paglia sopra le corde di uno, e poi con l'altro si tocchi una corda, si sente <lb/>che quella corda dell'altro strumento, che sar&agrave; unisono a quella che si tocca, <lb/>suona ancor lei, e le altre non suonano: e questo potrebbe nascer da que&shy;<lb/>sto che l'aere della corda ch'&egrave; sonata, per la sua agitazione, muove tutte <lb/>le altre corde. </s>

<s>Ma perch&egrave; quelle, che non sono in unisono, non possono ri&shy;<lb/>cevere il medesimo moto di quella ch'&egrave; sonata, e quella che &egrave; in unisono <pb xlink:href="020/01/2352.jpg" pagenum="595"/>lo pu&ograve; ricevere; per&ograve; ancor ella suona, e le altre non suonano &rdquo; (Libri, <lb/><emph type="italics"/>Histoire<emph.end type="italics"/> cit., Note al T. IV, pag. </s>

<s>395, 96). </s></p><p type="main">

<s>Galileo ebbe sott'occhio questa e le altre Note manoscritte di Guidu&shy;<lb/>baldo, e rese visibile il vibrar delle corde sonore sotto i medesimi tempi <lb/>per via dei pendoli di ugual sospensura, ai quali assegn&ograve; per legge l'iso&shy;<lb/>cronismo assoluto delle vibrazioni, e per via dei pendoli di sospensure dif&shy;<lb/>ferenti, ch'egli aveva osservato come cosa nuova, bench&egrave; non riconosciuta <lb/>conseguente dalle leggi generali del moto, far le loro vibrazioni in tempi, <lb/>che hanno suddupla proporzione delle lunghezze dei fili. </s>

<s>Tanto arida dun&shy;<lb/>que sent&igrave; Galileo questa materia, che se ne spacci&ograve; in poche parole alla fin <lb/>del proemio a quel trattato, che doveva, attraverso ai pi&ugrave; varii teoremi, con&shy;<lb/>durre a concluder le leggi dei cadenti, non per gli archi dei pendoli, ma <lb/>per le casse dei vagli. </s></p><p type="main">

<s>Bench&egrave; arido insomma, pur si fa di questi moti per gli archi dei cer&shy;<lb/>chi qualche cenno di prolusione, ma de'proietti, e del ricorrere il loro trat&shy;<lb/>tato nei Dialoghi seguenti, non si fa dall'Autore nemmeno un motto, tanto <lb/>gli premeva la gloria, e tanto era vero in lui il desiderio d'assicurarsi il <lb/>frutto di uno studio di quarant'anni. </s>

<s>E s&igrave; che non gli sarebbe mancata l'oc&shy;<lb/>casione d'entrar nel geloso argomento, specialmente l&agrave; dove, posto per teo&shy;<lb/>ria il principio che il proietto in su nel perpendicolo e il cadente natural&shy;<lb/>mente in gi&ugrave; fanno il medesimo viaggio, nel dover passare dalle specula&shy;<lb/>zioni all'esperienza, credeva il Salviati &ldquo; che la velocit&agrave;, che ha la palla <lb/>vicino all'uscita del pezzo, sarebbe di quelle che l'impedimento dell'aria <lb/>non gli lascerebbe conseguire giammai, mentre con moto naturale scen&shy;<lb/>desse, partendosi dalla quiete da qualsivoglia grande altezza &rdquo; (ivi, pag. </s>

<s>97). <lb/>Ora, perch&egrave; l'impeto della palla alla bocca del cannone si pone nel IV dia&shy;<lb/>logo uguale a quello, che la palla stessa acquisterebbe venendo per l'al&shy;<lb/>tezza, e per la sublimit&agrave; della parabola; si comprende quanto fosse questa <lb/>osservazione opportuna a prevenire le difficolt&agrave; di coloro, i quali sarebbero <lb/>per negar fede alle ragioni, non vedendole in tutto esattamente rispondere <lb/>ai fatti. </s></p><p type="main">

<s>Il moto naturale, preso per misura del violento, avrebbe potuto sugge&shy;<lb/>rire allo stesso Galileo questo pensiero, che sovvenne al Viviani come per <lb/>corollario alla X proposizione nel dialogo dei proietti. </s>

<s>&ldquo; Di qui &egrave; manifesto <lb/>che le percosse de'proietti, nei punti della sua parabola, ricevute da piani <lb/>che siano perpendicolari alle tangenti i punti di essa parabola, le quali per&shy;<lb/>cosse sono le massime; sono necessariamente uguali a quelle, che farebbe <lb/>il medesimo grave, quando cadesse per una perpendicolare composta della <lb/>sublimit&agrave; e dell'altezza della parabola. </s>

<s>Dal che si cava che la Natura non <lb/>si pu&ograve; per tal via superare, e che il proietto non scapita e non acquista di <lb/>forza, ma si conserva sempre con quella, che gli d&agrave; il discenso retto per&shy;<lb/>pendicolare &rdquo; (MSS. Gal., P. V, T. IX, pag. </s>

<s>273). Anche le ballistiche dun&shy;<lb/>que seguon la natura di tutte le altre macchine, e il beneficio, che si riceve <lb/>particolarmente da quelle, consiste nel potere imprimere immediatamente <pb xlink:href="020/01/2353.jpg" pagenum="596"/>nel proietto quella forza, che pure gli s'imprimerebbe sollevandolo con gran <lb/>disagio, e con gran perdita di tempo, alla convenevole altezza perpendi&shy;<lb/>colare. </s></p><p type="main">

<s>Ritornando ora all'intenzione del nostro discorso, chiaramente ci sem&shy;<lb/>bra dimostrato che, quando Galileo scriveva il primo Dialogo di proemio, <lb/>le due nuove Scienze, ch'egli intendeva insegnare, si riducevano alle Resi&shy;<lb/>stenze dei solidi, e ai Moti naturali. </s>

<s>Sulla fine del 1634 erano gi&agrave; stati messi <lb/>in ordine di trattato i teoremi, e quanto ai moti accelerati in particolare an&shy;<lb/>nunzia il d&igrave; 19 Novembre di quell'anno, con queste parole al Micanzio, la <lb/>final risoluzione presa di fondare il nuovo meccanico edifizio sul principio <lb/>supposto delle velocit&agrave; uguali ne'cadenti per varie linee della medesima al&shy;<lb/>tezza, dopo quelle lunghe tenzoni, che ci si rivelarono nel cap. </s>

<s>VI, confron&shy;<lb/>tando i primi libri manoscritti <emph type="italics"/>De motu<emph.end type="italics"/> con quello, che fu poi dato alle <lb/>stampe: &ldquo; Il trattato del moto, tutto nuovo, sta all'ordine, ma il mio cer&shy;<lb/>vello inquieto non pu&ograve; restar d'andar mulinando, e con gran dispendio di <lb/>tempo, perch&egrave; quel pensiero, che ultimo mi sovvenne circa qualche novit&agrave;, <lb/>mi fa buttare a monte tutti i trovati precedenti &rdquo; (Alb. </s>

<s>VII, 56). </s></p><p type="main">

<s>Stabilito dunque l'ordine e il fondamento, da sottoporre a quel trat&shy;<lb/>tato del moto, e da parecchi anni preparato gi&agrave; l'altro delle Resistenze, <lb/>attendeva Galileo, nella quieta solitudine di Arcetri, a ridurre al netto e a <lb/>trascrivere quel primo dialogo di prefazione, com'egli stesso scriveva in una <lb/>lettera del di 15 Marzo 1635 a Elia Diodati (ivi). Si diffuse la tanto desi&shy;<lb/>derata notizia fra gli amici e i discepoli, a uno de'quali, a Giovanni Pie&shy;<lb/>roni, giunse la notizia infino in Vienna, dov'era stato chiamato da Firenze <lb/>a servire l'Imperatore in qualit&agrave; d'ingegnere. </s>

<s>Non bastava per&ograve; a saziare <lb/>i desiderii di costoro il saper che l'opera si scriveva: volevano esser certi <lb/>che sarebbe stampata, ma prevedevano certe difficolt&agrave;, che ne sfioravano la <lb/>bella speranza. </s></p><p type="main">

<s>Sanno oramai troppo bene i nostri Lettori che la causa della condanna <lb/>dei dialoghi dei due Massimi Sistemi furono i Gesuiti, gelosi di mantenere <lb/>il principato in ogni ordine di scienza: e come allora contesero per rima&shy;<lb/>ner primi nell'Astronomia, cos&igrave; era da aspettarsi che volessero contender <lb/>ora, per seguitar a primeggiar nella Meccanica. </s>

<s>Pare impossibile che la cri&shy;<lb/>tica non abbia col suo senno avuto tanto di autorit&agrave;, da reprimer le voci <lb/>degl'insipienti declamatori, ai quali fu dato ad intendere che si trattasse di <lb/>mettere in contradizione un sistema scientifico co'principii religiosi. </s>

<s>Nei <lb/>nuovi dialoghi le questioni erano puramente scientifiche, eppure ebbero <lb/>anch'essi a patir le medesime contradizioni dei primi. </s>

<s>Tanto son poi leg&shy;<lb/>geri i giudizi degli scrittori volgari che anzi, andando a ricercare il vero <lb/>della cosa, si trova che coloro, i quali essi incolpano pi&ugrave; volentieri, furono <lb/>con la mente e con l'animo favorevoli a Galileo, e solo forse colpevoli in <lb/>questo: nel non aver saputo prevaler, n&egrave; resistere a una potenza, che il <lb/>Micanzio chiamava infernale. </s>

<s>Ma perch&egrave; alcuno non abbia a mettere fra i <lb/>declamatori anche noi, passiamo serenamente a raccontare la storia. </s></p><pb xlink:href="020/01/2354.jpg" pagenum="597"/><p type="main">

<s>Il Pieroni dunque, scrivendo d'Austria il di 4 Gennaio 1635, dop'aver <lb/>detto a Galileo che tutti erano in gran desiderio di veder palesato al mondo <lb/>il libro del moto, soggiungeva: &ldquo; E perch&egrave; m'&egrave; venuto pensiero che V. S. <lb/>in pubblicarlo poss'avere qualche difficolt&agrave; o rispetto, ho risoluto di signi&shy;<lb/>ficarle che, se le paresse bene e a proposito che si stampasse qu&agrave; in qual&shy;<lb/>che citt&agrave;, potrebbe questo venirle fatto molto facilmente, se ella volesse <lb/>fidarsi a mandarlo a me, perch&egrave; io lo farei stampare in buoni caratteri, con <lb/>le figure ch'ella m'imponesse, puntualissimamente &rdquo; (ivi, X, 66, 67). </s></p><p type="main">

<s>Galileo, per ragioni facili a intendersi, avrebbe voluto pi&ugrave; volentieri <lb/>stampare il libro in Italia: nonostante, mandando il primo dialogo mano&shy;<lb/>scritto a fra Fulgenzio Micanzio a Venezia, gli annunziava quel mezzo, che <lb/>gli veniva proposto di Vienna. </s>

<s>Non spiaceva al Micanzio il partito, ma in&shy;<lb/>tanto volle tastar l'animo dell'Inquisitore, mostrandogli il desiderio di far <lb/>ristampare il discorso Delle galleggianti. </s>

<s>Rispose di avere espressa commis&shy;<lb/>sione da Roma in contrario. </s>

<s>&mdash; Forse di non ristampare il Sistema coper&shy;<lb/>nicano? </s>

<s>&mdash; domand&ograve; il Micanzio &mdash; e l'altro replicava: &mdash; No, no, &egrave; di&shy;<lb/>vieto generale <emph type="italics"/>de editis et edendis.<emph.end type="italics"/> &mdash; Ma se vorr&agrave; stampare il <emph type="italics"/>Credo<emph.end type="italics"/> e il <lb/><emph type="italics"/>Pater noster?<emph.end type="italics"/> &mdash; a cui, per troncare il discorso, concludeva l'Inquisitore <lb/>che gli avrebbe fatto avere una copia della commissione in proposito venu&shy;<lb/>tagli da Roma. </s></p><p type="main">

<s>Nel riferire a Galileo questo colloquio, lo stesso Micanzio soggiungeva <lb/>che, anche facendo stampare i nuovi Dialoghi in Austria, conveniva andar <lb/>molto cauti, &ldquo; nel che pensiamo, sono sue proprie parole, se possa servire <lb/>che io, favorito di questo tesoro per mia curiosit&agrave;, ne abbia fatto copia, e <lb/>voluto cercare e procurare la stampa, che non mi curo che gridi chi vuole. </s>

<s><lb/>V. S. E. discorre singolarmente che non conviene ricevere negativa, n&egrave; an&shy;<lb/>cora io qui la voglio a modo veruno. </s>

<s>Ma se vedr&ograve; l'ordine quale di sopra, <lb/>o superer&ograve; la difficolt&agrave; o trover&ograve; modo fuori: stampati li voglio di certo &rdquo; <lb/>(ivi, pag. </s>

<s>76). Egli per&ograve; che aveva presa cos&igrave; ferma risoluzione contro la <lb/>tirannia (pag. </s>

<s>75); che giurava non perirebbero cose tali se ci si mettesse <lb/>tutto l'inferno (pag. </s>

<s>77), ritornato all'Inquisitore &ldquo; e veduto l'ordine rigo&shy;<lb/>rosissimo de'stampati e da stamparsi, a me, diceva a Galileo, non d&agrave; fasti&shy;<lb/>dio, ma non si deve creare a V. S. persecuzioni. </s>

<s>Ho pensato, se ella lo con&shy;<lb/>sente, far fare una bella copia di tutto, e collocarla nella pubblica libreria <lb/>di S. </s>

<s>Marco &rdquo; (ivi, pag. </s>

<s>81). </s></p><p type="main">

<s>Il Pieroni per&ograve; sperava che sarebbero in ogni modo stampati, almeno <lb/>i dialoghi delle Scienze nuove, in Austria, dove gli rec&ograve; il principe don Ma&shy;<lb/>tias de'Medici, che partiva da Firenze il d&igrave; 9 Giugno 1635 ambasciatore in <lb/>Alemagna (ivi, VII, 57). Un viaggio in Ungheria fece s&igrave; che le carte non <lb/>recapitassero alle mani del Pieroni, prima del d&igrave; 11 Agosto, ricevute le quali <lb/>se ne rallegr&ograve;, e pensava a dispor le cose in modo, che non s'avesse Ga&shy;<lb/>lileo a pentire di aver finalmente accettato quel partito. </s>

<s>Avrebbe voluto <lb/>stampare in Austria, mettendo il libro sotto la protezione dell'Imperatore, <lb/>ma poi consider&ograve; che i Gesuiti erano ivi onnipotenti, &ldquo; e che avrebbero <pb xlink:href="020/01/2355.jpg" pagenum="598"/>preso materia di suggerire scrupoli a quella delicatissima coscienza di Sua <lb/>Maest&agrave;, e derivarne o proibizione, o almeno non gradimento..... Il Re di <lb/>Polonia, soggiungeva significando questi pensieri allo stesso Galileo, &egrave; di <lb/>ottimo gusto, massime di simili cose, e non &egrave; soverchiamente n&egrave; scrupoloso, <lb/>n&egrave; ai Gesuiti affetto, ed in riguardo suo solo non sarebbe, credo certo, abor&shy;<lb/>rita a Roma n&egrave; avuta a male cosa posta sotto la sua protezione &rdquo; (ivi). </s></p><p type="main">

<s>Vedendo per&ograve; del negozio dall'una e dall'altra parte lunghissima la <lb/>spedizione, si volse il Pieroni per altre strade, ch'egli giudicava, da'temuti <lb/>assalti degl'inimici, assai pi&ugrave; sicure. </s>

<s>Il cardinale Dictristain aveva a sue pro&shy;<lb/>prie spese in Olmutz fondata una tipografia molto bella, e un'altra pure ne <lb/>aveva in propio il cardinale di Harach in Praga. </s>

<s>Ma perch&egrave;, pi&ugrave; che in Boe&shy;<lb/>mia, tornava comodo al Pieroni dirigere la stampa in Moravia, ne dava, per <lb/>lettera del 1&deg; Marzo 1636, a Galileo questo avviso: &ldquo; Della seguente setti&shy;<lb/>mana sar&ograve; col divino aiuto in Moravia a dar principio alla stampa del libro <lb/>di V. S., non avendo potuto prima distrigare tutti gl'intoppi che ho incon&shy;<lb/>trati, e credami V. S. che non ho riposo alla mia mente, in sino che io non <lb/>mi veda di adempire quanto devo in servirla. </s>

<s>Le figure sono intagliate quasi <lb/>tutte, e le provate riescono, pare a me, ragionevolmente &rdquo; (ivi, pag. </s>

<s>141). </s></p><p type="main">

<s>Ma di dar principio alla stampa, gi&agrave; passato tutto il mese di Marzo non <lb/>si vedeva risoluzione, perch&egrave; tardava ancora di venir la licenza. </s>

<s>S'aggiun&shy;<lb/>geva che al cardinale Dictristain, bench&egrave; avesse tutte le buone intenzioni, <lb/>mancavano le persone, che sapessero maneggiare i tipi della nuova officina: <lb/>le cose andavano in lungo, e il Pieroni era sollecitato di ritornare in patria. </s>

<s><lb/>In questo mentre si facevano premure per stampare i Dialoghi in Francia, <lb/>dove i Gesuiti eran deboli, o in Olanda d'onde erano esclusi, di che Gali&shy;<lb/>leo stesso dava questo avviso al Micanzio, curioso di sapere come in Ale&shy;<lb/>magna procedesse il negozio: &ldquo; In Alemagna s'attraversano vari impedi&shy;<lb/>menti, tra i quali uno &egrave; che quello, che si aveva preso l'assunto, sta in <lb/>proc&igrave;nto di tornarsene qui alla patria. </s>

<s>Io gli domando che mi rimandi quanto <lb/>prima la copia, la quale mi vien domandata per mandarla in luce in Lione, <lb/>o in Parigi, o in Olanda &rdquo; (ivi, VII, 61). </s></p><p type="main">

<s>Il Micanzio non dubitava di preferire alla Francia l'Olanda, nella quale <lb/>sarebbe stata piena libert&agrave; di stampare il libro, e gli parve che la fortuna <lb/>secondasse l'effetto, facendo capitare in quel tempo a Venezia Lodovico El&shy;<lb/>zevirio. </s>

<s>Scrisse, perch&egrave; fosse il manoscritto messo in ordine per le stampe, <lb/>a Galileo, il quale rispondeva, ne'principii del Luglio di quel medesimo <lb/>anno 1636, che aveva fatto gi&agrave;, per mandarle, copiare <emph type="italics"/>le due opere Del moto <lb/>e Delle resistenze<emph.end type="italics"/> (ivi, pag. </s>

<s>67), e verso la fin del mese prometteva che <lb/>avrebbe, fra una quindicina di giorni, mandato de'nuovi dialoghi il resto <lb/>(ivi, pag. </s>

<s>71). </s></p><p type="main">

<s>Don Benedetto Castelli era informato di tutto, e dolendogli che s'avesse <lb/>il libro a stampare fuori d'Italia, in paese di protestanti, faceva ogni sforzo <lb/>per veder di ricorrere alla legittima protest&agrave; contro le passionate ingerenze <lb/>dei Gesuiti. </s>

<s>Favorito dal conte di Noailles, ambasciatore di Francia, pregava <pb xlink:href="020/01/2356.jpg" pagenum="599"/>quel signore a voler trattare della licenza di questa stampa direttamente col <lb/>Papa, il quale rispose che avrebbe volentieri proposta la cosa in Congrega&shy;<lb/>zione. </s>

<s>Risaputosi ci&ograve; dal cardinale Antonio Barberini, tutt'ardente di zelo <lb/>per la causa di Galileo, disse al Conte queste parole: <emph type="italics"/>Buono, buono ed io <lb/>far&ograve; ufficio con tutti li cardinali<emph.end type="italics"/> (ivi, X, 164). La benignit&agrave; di questi per&ograve; <lb/>non valse a vincere la malignit&agrave; di quegli altri, i quali, avendo trionfato <lb/>della volont&agrave; del Papa e dei Cardinali, non pensavano che sarebbe bastato <lb/>un semplice operaio di Leida, per mandare all'aria tutti i loro trionfi. </s></p><p type="main">

<s>L'Elzevirio infatti, avuti dal Micanzio i dialoghi manoscritti, gli recava <lb/>seco in Olanda per dar principio, con tutta la libert&agrave;, alla stampa, ed il d&igrave; <lb/>16 Marzo 1637 dava avviso allo stesso Micanzio che aveva fatto gi&agrave; inta&shy;<lb/>gliar le figure, mandandone intanto quattro per prova (ivi, pag. </s>

<s>202). Nel <lb/>Novembre era l'edizione gi&agrave; condotta pi&ugrave; che a mezzo, e alla fine del Gen&shy;<lb/>naio dell'anno appresso non rimaneva ad aggiungere al volume, che la de&shy;<lb/>dica e il frontespizio (ivi, pag. </s>

<s>260). </s></p><p type="main">

<s>Si discusse lungamente, fra Galileo e gli amici pi&ugrave; confidenti, se si do&shy;<lb/>vesse in quel frontespizio scrivere il nome proprio dell'Autore, e sotto la <lb/>protezione di chi metterlo, per riparo dalle ire nemiche. </s>

<s>Fu pensato al conte <lb/>di Noailles, nella lettera dedicatoria al quale si fingeva che, essendo andate <lb/>attorno pi&ugrave; copie manoscritte, capitatane una per caso in Olanda all'Elze&shy;<lb/>virio, egli di suo proprio moto ne intraprendesse la stampa. </s>

<s>Nell'Agosto, <lb/>avutane commissione dallo stesso Galileo, Elia Diodati presentava al Conte <lb/>in Parigi una copia del libro a lui dedicato (ivi. </s>

<s>VII, 217). </s></p><p type="main">

<s>Come l'aria respirando si diffonde tanto pi&ugrave; al largo, quanto pi&ugrave; era <lb/>stata compressa; cos&igrave; avvenne a questo stesso libro, contro l'intenzione e <lb/>l'opera de'suoi propri nemici. </s>

<s>I trattati del Baliani e di Giovan Marco, an&shy;<lb/>dati in dimenticanza, rimase a questi soli dialoghi di Galileo il pi&ugrave; autore&shy;<lb/>vole magistero della nuova Scienza del moto. </s>

<s>Di qui comincia per la Mec&shy;<lb/>canica un'era novella, i fasti della quale si narreranno in quest'altra parte <lb/>della nostra Storia. <pb xlink:href="020/01/2357.jpg"/></s></p><pb xlink:href="020/01/2358.jpg"/><p type="main">

<s><emph type="center"/>INDICI<emph.end type="center"/><pb xlink:href="020/01/2359.jpg"/></s></p><pb xlink:href="020/01/2360.jpg"/><p type="main">

<s><emph type="center"/>INDICE DEI CAPITOLI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>CAPITOLO I.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Della Scienza del moto nel secolo XVI.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle prime istituzioni statiche, nella Scuola peripatetica, e nella alessandrina <emph type="italics"/>Pag.<emph.end type="italics"/> 7 </s></p><p type="main">

<s>II Dei principii statici di Giordano Nemorario: de'manoscritti di Leonardo da Vinci, e <lb/>delle fonti, dalle quali deriv&ograve; in essi la scienza del moto &rdquo; 20 </s></p><p type="main">

<s>III Delle dottrine statiche degli Antichi promosse nelle Note manoscritte di Leonardo da <lb/>Vinci &rdquo; 34 </s></p><p type="main">

<s>IV Di alcuni pi&ugrave; notabili teoremi e problemi di Meccanica dimostrati, e risoluti da Leo&shy;<lb/>nardo da Vinci &rdquo; 49 </s></p><p type="main">

<s>V Dei principii dinamici professati da Leonardo da Vinci intorno alle leggi della caduta <lb/>dei gravi, e della teoria de'proietti &rdquo; 69 </s></p><p type="main">

<s>VI Degli altri principali Autori, che promossero la Meccanica, dopo la prima met&agrave; del se&shy;<lb/>colo XVI &rdquo; 84 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO II.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dei Baricentri.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della invenzione del centro di gravit&agrave; nei solidi <emph type="italics"/>Pag.<emph.end type="italics"/> 101 </s></p><p type="main">

<s>II Dei quattro libri centrobrarici di Paolo Guldino, e della Geometria degl'Indivisibili di <lb/>Bonaventura Cavalieri &rdquo; 112 </s></p><p type="main">

<s>III Delle risposte del Cavalieri alle opposizioni fattegli dal Guldino, e come la Regola cen&shy;<lb/>trobrarica avesse dal Metodo degl'indivisibili la sua prima matematica dimostrazione &rdquo; 127 </s></p><p type="main">

<s>IV Delle nuove dimostrazioni della Regola centrobrarica, che primi vennero a dare alle <lb/>Scienze matematiche in Italia Antonio Nardi, e Vincenzio Viviani &rdquo; 138 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO III.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Degli Equiponderanti.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della legge delle Equiponderanze dimostrata col principio delle Velocit&agrave; virtuali <emph type="italics"/>Pag.<emph.end type="italics"/> 156 </s></p><p type="main">

<s>II Della legge delle Equiponderanze dimostrata coi principii archimedei &rdquo; 168 </s></p><p type="main">

<s>III Della teoria dei momenti applicata a dimostrar la legge degli Equiponderanti &rdquo; 180 </s></p><p type="main">

<s>IV Delle Bilance di braccia uguali, e delle condizioni del loro equilibrio, nel caso delle forze <lb/>o parallele o convergenti al centro terrestre &rdquo; 190 </s></p><pb xlink:href="020/01/2361.jpg" pagenum="604"/><p type="main">

<s><emph type="center"/>CAPITOLO IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Delle Macchine.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della natura delle Macchine, e del modo di operar del Vette, dell'Asse nella ruota, e <lb/>delle Taglie; del Cuneo e della Vite <emph type="italics"/>Pag.<emph.end type="italics"/> 213 </s></p><p type="main">

<s>II Delle proporzioni tra la resistenza e la potenza necessarie a sollevare i gravi per via <lb/>dei piani inclinati &rdquo; 230 </s></p><p type="main">

<s>III Delle censure di Alessandro Marchetti sopra i teoremi di Galileo e del Torricelli del mo&shy;<lb/>mento dei gravi sopra i piani inclinati: della eterodossia meccanica di Giovan Fran&shy;<lb/>cesco Vanni, e delle difficolt&agrave; che trovarono in confutarla i Galileiani &rdquo; 245 </s></p><p type="main">

<s>IV Delle confutazioni speculate dai Matematici stranieri, e della questione intorno alla com&shy;<lb/>posizion dei momenti proposta in Boma per rispondere ai sofismi del Vanni: degli <lb/>errori di Luc'Antonio Porzio confutati dal Grandi &rdquo; 256 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO V.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Delle libere cadute dei gravi.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della legge di Aristotile che le velocit&agrave; dei cadenti son proporzionali ai pesi, e come <lb/>prima si trovasse quella legge contraria alle esperienze, e poi si dimostrasse contra&shy;<lb/>ria alla ragione, e si verificasse finalmente che tutti i corpi nel vuoto scendono ugual&shy;<lb/>mente veloci <emph type="italics"/>Pag.<emph.end type="italics"/> 266 </s></p><p type="main">

<s>II Delle cause acceleratrici del moto, e come Galileo fosse il primo a concluder la legge <lb/>matematica di un tale acceleramento dai principii del Benedetti &rdquo; 289 </s></p><p type="main">

<s>III Della forza d'inerzia applicata ai moti naturali, e delle leggi dei moti accelerati geome&shy;<lb/>tricamente dimostrate da Galileo, e dal Baliani &rdquo; 302 </s></p><p type="main">

<s>IV Dei pretendenti e dei contradittori di Galileo, e come si confermassero, per l'esperienze <lb/>del Riccioli e per i teoremi dell'Huyghens, le leggi galileiane dei gravi cadenti &rdquo; 314 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Delle scese dei gravi lungo i piani inclinati.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Dei principii fondamentali, da cui si dimostra la Scienza dei moti inclinati, e di una <lb/>supposizione fatta in proposito da Galileo <emph type="italics"/>Pag.<emph.end type="italics"/> 328 </s></p><p type="main">

<s>II Ordinamento e pubblicazione del primo libro galileiano <emph type="italics"/>De motu,<emph.end type="italics"/> contenente i teoremi <lb/>dimostrati infino al 1602 &rdquo; 342 </s></p><p type="main">

<s>III Ordinamento e pubblicazione del secondo libro galileiano <emph type="italics"/>De motu,<emph.end type="italics"/> incominciato nel 1604, <lb/>e nel 1609 rimasto interrotto, per le ragioni che qui si diranno &rdquo; 350 </s></p><p type="main">

<s>IV Ordinamento delle proposizioni lasciate manoscritte da Galileo, per condurre in una <lb/>terza maniera il suo trattato <emph type="italics"/>De motu &rdquo;<emph.end type="italics"/> 357 </s></p><p type="main">

<s>V Dei teoremi concernenti i Moti locali ordinati da Galileo per la stampa, e delle critiche <lb/>fatte dal Cartesio contr'essi &rdquo; 367 </s></p><p type="main">

<s>VI Di ci&ograve; che pu&ograve; dirsi nuovo nel trattato di Galileo, che qui paragonasi con quello del <lb/>Baliani; e dell'opera data da altri Autori stranieri, come dal Mariotte e dall'Huy&shy;<lb/>ghens, intorno al medesimo soggetto del moto dei gravi per i piani inclinati &rdquo; 373 </s></p><pb xlink:href="020/01/2362.jpg" pagenum="605"/><p type="main">

<s><emph type="center"/>CAPITOLO VII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Delle scese dei gravi per gli archi dei cerchi.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle varie esperienze, e delle teorie, che persuasero essere i tempi delle scorse dei <lb/>gravi, nelle concavit&agrave; dei cerchi e nei pendoli, per qualunque ampiezza di arco, <lb/>uguali <emph type="italics"/>Pag.<emph.end type="italics"/> 382 </s></p><p type="main">

<s>II Delle nuove esperienze, e delle teorie, che dimostarono non essere i tempi delle corse <lb/>e delle ricorse dei cadenti per le concavit&agrave; dei cerchi, e nei pendoli, esattamente <lb/>uguali &rdquo; 393 </s></p><p type="main">

<s>III Delle leggi delle cadute dei gravi per archi di cerchio simili, e delle loro applicazioni <lb/>al problema del pendolo a secondi &rdquo; 405 </s></p><p type="main">

<s>IV Di ci&ograve; che operarono i discepoli di Galileo, e segnatamente il Viviani, per dare scienza <lb/>delle supposte propriet&agrave; dei pendoli disuguali &rdquo; 421 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Delle resistenze dei solidi.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Delle proposizioni dimostrate da Galileo nel secondo dialogo delle due Scienze nuove <emph type="italics"/>Pag.<emph.end type="italics"/> 436 </s></p><p type="main">

<s>II Dei trattati di Francesco Blondel, di Vincenzio Viviani e di Alessandro Marchetti &rdquo; 453 </s></p><p type="main">

<s>III Delle controversie insorte fra Alessandro Marchetti e Guido Grandi &rdquo; 462 </s></p><p type="main">

<s>IV Dell'applicazione della teoria dei momenti &rdquo; 482 </s></p><p type="main">

<s>V Delle osservazioni dei fatti, e delle esperienze concorse a promovere la nuova scienza di <lb/>Galileo &rdquo; 497 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO IX.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>De'proietti.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Di ci&ograve; che specularono il Tartaglia, il Cardano e il Benedetti, e come fossero, sui prin&shy;<lb/>cipii del secolo XVII, promosse da Guidubaldo del Monte quelle speculazioni <emph type="italics"/>Pag.<emph.end type="italics"/> 506 </s></p><p type="main">

<s>II De'progressi fatti da Galileo: com'ei credesse la linea descritta dai proietti esser, nella <lb/>sua parte curva, circolare e come primo il Cavalieri la dimostrasse parabolica &rdquo; 517 </s></p><p type="main">

<s>III Della prima parte del quarto Dialogo galileiano; ossia della misura degl'impeti in cia&shy;<lb/>scun punto della Parabola &rdquo; 533 </s></p><p type="main">

<s>IV Della seconda e terza parte del Trattato galileiano; ossia della massima ampiezza dei <lb/>tiri a mezza squadra, e della costruzione delle Tavole ballistiche &rdquo; 552 </s></p><p type="main">

<s>V Delle difficolt&agrave; mosse contro la teoria del moto parabolico, e di alcune esperienze isti&shy;<lb/>tuite per confrontarle co'teoremi di questa nuova Scienza &rdquo; 564 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO X.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Conclusione di questa prima parte.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I De'principali cultori della Meccanica contemporanei di Galileo <emph type="italics"/>Pag.<emph.end type="italics"/> 579 </s></p><p type="main">

<s>II De'dialoghi dei due Massimi Sistemi, e come s'incominciassero a diffondere di <gap/> i semi <lb/>della nuova Scienza del moto &rdquo; 584 </s></p><p type="main">

<s>III Del primo dialogo delle due nuove Scienze e della pubblicazione di lui, insieme con gli <lb/>altri tre, fatta dagli Elzeviri in Olanda &rdquo; 592 </s></p><pb xlink:href="020/01/2363.jpg"/><p type="main">

<s><emph type="center"/>INDICE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>DEI DOCUMENTI ESTRATTI DAI MANOSCRITTI GALILEIANI <lb/>E NOTATI SECONDO L'ORDINE DEI CAPITOLI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo I.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Antonio Nardi riconosce maestro a Galileo il Benedetti, pag. </s>

<s>37. </s></p><p type="main">

<s>Teorema del Torricelli appartenente al trattato <emph type="italics"/>De motu ac momentis<emph.end type="italics"/> 52. </s></p><p type="main">

<s>Teorema delle funi gravate da pesi, propostosi a risolvere dal Viviani 59. </s></p><p type="main">

<s>Il Torricelli proponesi di trovar la ragione di un effetto meccanico, che dice non essere stato ancora <lb/>avvertito 64, 65. </s></p><p type="main">

<s>Si studia di trovar quella ragione per simili vie anche il Viviani 65, 66. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo II.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Lemma preniesso da Galileo al suo trattato Dei centri di gravit&agrave; dimostrato altrimenti dal Vi&shy;<lb/>viani, pag. </s>

<s>111. </s></p><p type="main">

<s>Passi estratti da una Epistola di Stefano Gradi intorno a un paradosso di Galileo 125. </s></p><p type="main">

<s>Lettera di Bonaventura Cavalieri al Torricelli, relativa alle difficolt&agrave; promosse dal Guldino contro la <lb/>Geometria degl'Indivisibili 128-31. </s></p><p type="main">

<s>Frammento di lettera, dove il Cavalieri espone al Torricelli la sua intenzione di rispondere al Gul&shy;<lb/>dino in forma di dialogo 131. </s></p><p type="main">

<s>Altro frammento di lettera, con la quale il Cavalieri accompagna il suo primo dialogo manoscritto <lb/>in risposta al Guldino 132. </s></p><p type="main">

<s>Una difficolt&agrave; <gap/>ntro la Geometria degli Indivisibili sciolta dallo stesso Cavalieri 132, 33. </s></p><p type="main">

<s>Pocho parole estratte da una lettera del Cavalieri, il quale ringrazia il Torricelli per aver promosse <lb/>il Metodo degl'Indivisibili 134. </s></p><p type="main">

<s>Antonio Nardi par che non approvi il Metodo degl'Indivisibili 138, parole, nelle quali accenna a un <lb/>suo metodo di ritrovare il centro di gravit&agrave; delle superfice curve 139, dimostra un suo Teorema <lb/>generale meccanico, che contiene un trattato compiuto di Geometria centrobrarica 140-43, applica <lb/>il medesimo teorema alla superflce rivoltata intorno ad un assse 144-46, per rendere geometrico <lb/>il Metodo centrobrarico sostituisce al Centro di gravit&agrave; il Centro della potenza 146, 47. </s></p><p type="main">

<s>Estratto di lettera del Cavalieri al Torricelli, dove si accenna alle difficolt&agrave; di trovare venali in Ita&shy;<lb/>lia i Libri centrobrarici del Guldino 148. </s></p><p type="main">

<s>Interpetrazione, che dette il Viviani del passo centrobrarico di Pappo Alessandrino 150. </s></p><p type="main">

<s>Poscritto di Vincenzio Viviani a Erasmo Bartholin relativo alla Centrol rarica 151. </s></p><p type="main">

<s>Teoremi centrobrarici dimostrati dal Viviani 153, 54. </s></p><p type="main">

<s>Estratto di una lettera del Viviani, dove l'Autore tratta di alcune sue opere matematiche da stam&shy;<lb/>parsi 155. </s></p><pb xlink:href="020/01/2364.jpg" pagenum="607"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo III.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Passso estratto dalle Scene accademiche, dove il Nardi dichiara irragionevole il principio galileiano <lb/>delle velocit&agrave; virtuali, pag. </s>

<s>161, 62. </s></p><p type="main">

<s>Due noterelle scritte dal Viviani <emph type="italics"/>ad mentem Galilei<emph.end type="italics"/> 164. </s></p><p type="main">

<s>Scrittura, nella quale il Viviani propone, per applicarsi alla Statica, un principio diverso da quello <lb/>delle velocit&agrave; virtuali 165, 66. </s></p><p type="main">

<s>Luogo estratto dalla VI Scena di Antonio Nardi, dove si dimostrano le condizioni dell'equilibrio della <lb/>Bilancia considerate le forze sollecitanti come dirette al centro della Terra 176-78. </s></p><p type="main">

<s>Teorema del Torricelli della Libbra di braccia disuguali, e con le direzioni dei pesi convergenti al <lb/>centro terrestre 178, 79. </s></p><p type="main">

<s>Pensieri di Antonio Nardi intorno alla natura delle forze, e dei momenti 185. </s></p><p type="main">

<s>Proposizioni relative alle leggi dei momenti dimostrate da Niccol&ograve; Aggiunti 187-89. </s></p><p type="main">

<s>Parole, con le quali Antonio Nardi risolve brevemente la famosa questione delle Bilance di braccia <lb/>eguali, rimosse dalla loro posizione orizzontale 199. </s></p><p type="main">

<s>Due proposizioni del Torricelli concernenti le leggi dell'equilibrio nelle Bilance di braccia uguali, e <lb/>sollecitate da forze convergenti 203-5. </s></p><p type="main">

<s>Nota, nella quale il Viviani spiega il segreto delle figurine ondeggianti 211. </s></p><p type="main">

<s>Da una lettera di Giuseppe Ferroni, il quale domanda al Viviani spiegazione delle figurine ondeg&shy;<lb/>gianti 211. </s></p><p type="main">

<s>Da altra lettera dello stesso Ferroni, scritta pure al Viviani per ringraziarlo dello svelato segreto <lb/>delle figurine ondeggianti 211, 12. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo IV.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Teoremi, nei quali dimostra Niccol&ograve; Aggiunti le proposizioni delle Taglie, considerando la tension <lb/>delle funi e.no i sostegni, pag. </s>

<s>222, 23. </s></p><p type="main">

<s>Proposizione IX del libro VIII di Pappo compendiata da Cosimo Noferi 231. </s></p><p type="main">

<s>Teorema, con cui il Viviani dimostra, in un modo suo proprio, le proporzioni tra la gravit&agrave; assoluta <lb/>e la relativa nei piani inclinati 241. </s></p><p type="main">

<s>Proposizioni V di Vincenzio Viviani dimostrative delle proporzioni, che passano tra il momento to&shy;<lb/>tale di un grave, e il discensivo e il gravitativo di lui sopra un piano inclinato 243-45. </s></p><p type="main">

<s>Lettera al Magliabechi, dove Antonio Monfort d&agrave; il suo giudizio intorno all'argomento scritto nello <lb/><emph type="italics"/>Specimen<emph.end type="italics"/> di G. </s>

<s>Francesco Vanni 252, 53. </s></p><p type="main">

<s>Lettera, con la quale Girolamo Pollini accompagna al Viviani due foglietti, cio&egrave; lo <emph type="italics"/>Specimen<emph.end type="italics"/> del <lb/>Vanni, e la risposta di Francesco Spoleti alle opposizioni di lui 253. </s></p><p type="main">

<s>Lettera di Giuseppe Ferroni al Viviani, colla quale si accompagna un teorema, per confermare le <lb/>dottrine di Galileo contro i sofismi del Vanni 254, 55. </s></p><p type="main">

<s>Teorema del Viviani, in cui si dimostra come si comportano le pressioni di un grave appoggiato <lb/>sopra due piani 255, 56. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo V.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Nota, nella quale brevemente Galileo dimostra contro Aristotile che le velocit&agrave; dei gravi cadenti non <lb/>possono essere proporzionali ai pesi, pag. </s>

<s>268. </s></p><p type="main">

<s>Un giudizio di Galileo intorno alla scienza naturale di Benedetto Varchi 270. </s></p><p type="main">

<s>Frammento di Dialogo di Giuseppe Moleto, in cui si dimostra contro Aristotile che le velocit&agrave; dei <lb/>gravi cadenti non sono proporzionali ai pesi 271-74. </s></p><p type="main">

<s>Teorema di Galileo delle proporzioni che serbano le solidit&agrave;, rispetto alle superficie, nelle divisioni <lb/>dei corpi 285, 86. </s></p><p type="main">

<s>Altro frammento del Dialogo del Moleto relativo alle cause del velocitarsi i gravi cadenti 290-92. </s></p><p type="main">

<s>Nota di Galileo relativa alle cause del velocitarsi i corpi gravi cadenti 292. </s></p><p type="main">

<s>Note di Galileo, che efficacemente illustrano il concetto della forza d'inerzia 303. </s></p><pb xlink:href="020/01/2365.jpg" pagenum="608"/><p type="main">

<s>Passo, in cui Niccol&ograve; Aggiunti dimostra che un mobile dura a moversi con la prima velocit&agrave; im&shy;<lb/>pressa 304. </s></p><p type="main">

<s>Scrittura, nella quale Galileo, con la Geometria degli indivisibili, dimostra le relazioni, che passano <lb/>fra gli spazi e i tempi, nelle libere cadute dei gravi 307, 8. </s></p><p type="main">

<s>Passi estratti da una Scrittura, dove Stefano Gradi si propone di dimostrare <emph type="italics"/>a priori<emph.end type="italics"/> l'egualit&agrave; del <lb/>moto rappresentata per determinati intervalli nel triangolo denticulato 310. </s></p><p type="main">

<s>Discorso dettato da Galileo al Viviani <emph type="italics"/>Sopra i principii del Baliani<emph.end type="italics"/> relativi alle propriet&agrave; dei pen&shy;<lb/>doli 313, 14. </s></p><p type="main">

<s>Da uno scritto, in cui il Fermat contradice alle proporzioni assegnate da Galileo ai moti naturali 318. </s></p><p type="main">

<s>Dalla veduta XLII della seconda Scena del Nardi, dove, al triangolo preso da Galileo per la scala <lb/>delle velocit&agrave; dei cadenti, si sostituisce la semiparabola 321. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo VI.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s><gap/>na osservazione di Galileo intorno alla velocit&agrave; del moto nella direzion perpendicolare, e nella in&shy;<lb/>clinata, pag. </s>

<s>332. </s></p><p type="main">

<s>Passo di una lettera, nella quale il Mersenno censura il principio fondamentale posto alla sua Mec&shy;<lb/>canica da Galileo 335. </s></p><p type="main">

<s>Teorema, in cui il Viviani dimostra che i momenti dei gravi sopra piani di lunghezza eguale, ma <lb/>variamento inclinati, stanno come i seni degli angoli delle inclinazioni 336. </s></p><p type="main">

<s>Proposizioni X, delle quali si componeva il primo trattato galileiano <emph type="italics"/>De motu,<emph.end type="italics"/> raccolte e ordi&shy;<lb/>nate 342-49. </s></p><p type="main">

<s>Proposizioni VIII, nelle quali Galileo aveva incominciato, co'principii dinamici, a riformare il su <gap/><lb/>primo trattato <emph type="italics"/>De motu<emph.end type="italics"/> 351-54. </s></p><p type="main">

<s>Contro il principio che, essendo le moli uguali, le velocit&agrave; son proporzionali ai momenti: obiezioni <lb/>del Mersenno e risposte del Torricelli 359. </s></p><p type="main">

<s>Proposizioni XIV preparate da Galileo, per condurre il suo libro <emph type="italics"/>De motu<emph.end type="italics"/> sopra il supposto principio <lb/>delle velocit&agrave; uguali nella perpendicolare e nell'obliqua di altezze uguali 358-66. </s></p><p type="main">

<s>Note di Galileo, e Teoremi relativi al trattato <emph type="italics"/>De motu<emph.end type="italics"/> 368, 369, 379. </s></p><p type="main">

<s>Teoremi tre di Geometria, occorsi a dimostrare a Galileo in mezzo alle speculazioni dei moti 371, 372. </s></p><p type="main">

<s>Teorema aritmetico di Galileo 372. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo VII.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Notizie di V. </s>

<s>Viviani intorno ai primi usi, che Galileo <gap/> del pendolo, pag. </s>

<s>384. </s></p><p type="main">

<s>Da una lettera di Francesco Lana agli Accademici del Cimento, dove si descrivono le esperienze isti&shy;<lb/>tuite per certificarsi che le vibrazioni maggiori e le minori del pendolo non sono uguali 402, 3. </s></p><p type="main">

<s>Strumento diseguato dal Viviani, per sperimentar se le vibrazioni del pendolo son tutte isocrone nel <lb/>vuoto 404. </s></p><p type="main">

<s>Il Viviani nota un errore di calcolo, in cui trascorse Galileo nell'asseg<gap/>are il numero delle vibra&shy;<lb/>zioni, e i tempi, in pendoli variamente lunghi 411. </s></p><p type="main">

<s>Proposizione del Torricelli applicabile, ma non applicata da lui al moto dei pendeli 421. </s></p><p type="main">

<s>Nota, che contiene i primi tentativi del Viviani intorno alla decomposizione del moto nei pendoli <lb/>oscillanti 422. </s></p><p type="main">

<s>Teorema nuovo di M. A. Ricci, che si riscontra con un antico di L. da Vinci 424. </s></p><p type="main">

<s>Il Viviani accenna a un modo di dimostrar le relazioni, che passano fra le varie lunghezze dei pen&shy;<lb/>doli, e i tempi delle loro vibrazioni 425: propone l'uso della parabola, per trovar le varie lun&shy;<lb/>ghezze dei fili, per i tempi cercati 426. </s></p><p type="main">

<s>Lemmi, Teoremi e descrizioni di Vincenzio Viviani appartenenti al trattatello di lui <emph type="italics"/>Dei pendoli di <lb/>lunghezze disuguali<emph.end type="italics"/> 427-32. </s></p><p type="main">

<s>Note del Viviani e del Borelli, nelle quali si descrivono varie lunghezze di pendoli corrispondenti <lb/>a minimi tempi 433, 34. </s></p><pb xlink:href="020/01/2366.jpg" pagenum="609"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo VIII.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Discorso, in cui il Viviani applica le proposizioni galileiane delle resistenze dei solidi alle ossa degli <lb/>animali, pag. </s>

<s>441. </s></p><p type="main">

<s>Discorso del Torricelli, per dimostrare che una corda tirata soffre ugual tensione in ogni sua <lb/>parte 444, 45. </s></p><p type="main">

<s>Alcuni casi curiosi di rottura di corde, descritti dal Viviani 445. </s></p><p type="main">

<s>Postilla del Viviani, nella quale si studia di difendere Galileo accusato di aver mal dimostrata una <lb/>proposizione intorno alla leva, applicata a sollevare un masso da terra 447. </s></p><p type="main">

<s>Dimostrazione che Galileo d&agrave; della Leva, applicata a sollevare un masso da terra 448. </s></p><p type="main">

<s>Dimostrazione originale data da Galileo della quadratura della parabola 450, 51. </s></p><p type="main">

<s>Estratto da una lettera di Alessandro Marchetti al principe Leopoldo dei Medici, relativa all'argo&shy;<lb/>mento delle resistenze dei solidi 456, 57. </s></p><p type="main">

<s>Il Viviani, impugnando lo sbaglio di Galileo, dimostra, in modo simile a quel Marchetti, che il solido <lb/>parabolico per avere ugual resistenza in ogni parte, dev'esser considerato come impondera&shy;<lb/>bile 458-60. </s></p><p type="main">

<s>Il Viviani, correggendo lo sbaglio di Galileo, dimostra, in modo simile a quel del Marchetti, che nel <lb/>solido parabolico, i momenti dei pesi hanno dupla ragion sesquialtera dei momenti delle resi&shy;<lb/>stenze 460, 61. </s></p><p type="main">

<s>Informazione del p. </s>

<s>Guido Grandi alla Corte medicea intorno ai dissensi, nati fra lui e il Mar&shy;<lb/>chetti 462, 63. </s></p><p type="main">

<s>Passi estratti da una lettera del Leibniz relativi alle controversie insorte fra il Viviani e il Mar&shy;<lb/>chetti 466, 480, 497. </s></p><p type="main">

<s>Il Panzanini annunzia al Grandi di aver ritrovato, fra le carte del suo zio V. Viviani, il trattato Delle <lb/>resistenzo dei solidi 467. Annunzia allo <gap/>tesso di aver consegnato il manoscritto a Benedetto Bre&shy;<lb/>sciani, <emph type="italics"/>ivi.<emph.end type="italics"/></s></p><p type="main">

<s>Teoremi annunziati dal Viviani, e sperimenti disegnati, relativi alle resistenze dei solidi 468. </s></p><p type="main">

<s>Il Viviani coregge la proposizione XIV di Galileo nel trattato delle resistenze 470, 71. </s></p><p type="main">

<s><emph type="italics"/>Lemmata universalia pro resistentiis<emph.end type="italics"/> dimostrati dal Viviani 472-74. </s></p><p type="main">

<s>Il Viviani sentenza che non si pu&ograve; salvare la sesta proposizione galileiana delle resistenze dalla nota <lb/>di falsit&agrave;, nemmeno altrimenti interpetrata 476. </s></p><p type="main">

<s>Nota del Viviani relativa alla resistenza di un cilindro intero e appoggiato nel mezzo, o diviso in <lb/>due appoggiati agli estremi 478. </s></p><p type="main">

<s>Dimostrazione fatta da Galileo del famoso teorema che i momenti stanno in ragion composta delle <lb/>distanze e dei pesi: soggiunge altre proposizioni per corollarii 484, 85. </s></p><p type="main">

<s>Due teoremi dei momenti, erroneamente dimostrati dal Torricelli, e corretti dal Viviani 486-88. </s></p><p type="main">

<s>Teorema, in cui dal Torricelli si dimostra che i momenti dei pesi uguali prementi un'asta, soste&shy;<lb/>nuta agli estremi in vari punti della sua lunghezza, son direttamente proporzionali ai rettangoli <lb/>descritti con le distanze dai due sostegni 489, 90. </s></p><p type="main">

<s>Michelangiolo Ricci applica la parabola a sciogliere il problema proposto de Galileo nella XIII delle <lb/>resistenze 491. </s></p><p type="main">

<s>Nota, nella quale il Torricelli conclude la dimostrazione che la catenaria &egrave; una parabola 492. </s></p><p type="main">

<s>La proposizne XII delle resistenze di Galileo, resa pi&ugrave; generale dal Viviani in un Teorema, ch'egli <lb/>credeva <emph type="italics"/>a nullo demonstratum<emph.end type="italics"/> 492, 93. </s></p><p type="main">

<s>Note autografe di Galileo, nelle quali si trovano formulati, non solo il Teorema, che il Viviani cre&shy;<lb/>deva <emph type="italics"/>a nulla demonstratum,<emph.end type="italics"/> ma l'altro altresi, che dimostra la catenaria essere una para&shy;<lb/>bola 494, 95. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo IX.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Sommi capi di un trattato delle Artiglierie, che Galileo si proponeva di scrivere verso il 1609, pag.519. </s></p><p type="main">

<s>Proposizioni, e osservazioni varie di Galileo relative al moto dei proietti 535, 537, 538, 539, 541, 544, <lb/>545, 547, 551, 553, 554, 555, 557, 559, 561, 562, 598. </s></p><p type="main">

<s>Nota, nella quale il Viviani, pi&ugrave; brevemente di Galileo, risolve il problema: data una parabola, tro&shy;<lb/>vare la sublimit&agrave;, dalla quale cadendo un proietto la descriverebbe 539, e insegna un modo pi&ugrave; <lb/>facile di quello dello stesso Galileo, per determinar l'impeto nella parabola 543. Si nota per&ograve; uno <pb xlink:href="020/01/2367.jpg" pagenum="610"/>sbaglio del Postillatore di Galileo nel medesimo proposito di determinare gl'impeti 545. Nota <lb/>nella quale si propone dallo stesso Viviani un'esperienza, per dimostrare in qual punto della <lb/>parabola sia maggiore l'impeto del proietto 551. </s></p><p type="main">

<s>Obiezioni di Antonio Nardi contro il moto parabolico dimostrato da Galileo ne'proietti, 564. </s></p><p type="main">

<s>Osservazioni del Viviani, per dimostrare che il moto trasversale non impedisce il naturale de'pro&shy;<lb/>ietti 566. </s></p><p type="main">

<s>Obiezioni di Niccol&ograve; Aggiunti contro la dottrina di Galileo che la vertigine di una ruota conferisca <lb/>impeto di moversi per la tangente 568. </s></p><p type="main">

<s>Come il Viviani esplichi un pensiero di Galileo, per dimostrar che la medesima parabola &egrave; descritta <lb/>dal tiro di punto in bianco, e dal tiro elevato 569, e quale esperienza proponga per dimostrar che <lb/>il proietto non va mai per spazio perpendicolare 570. </s></p><p type="main">

<s>Esperienze fatte dagli Accademici del Cimento, per verificare l'opinione di Galileo, che il proietto, <lb/>nella semiparabola e nella orizzontale, cade nel medesimo tempo 571, 572, 573. </s></p><p type="main">

<s>Come il Viviani si studiasse di conciliar l'esperienze con le teorie, nella misura degl'impeti, parte&shy;<lb/>cipati dalla polvere pirica ai proietti 574, 75: come correggesse e perfezionasse quo'suoi primi <lb/>studi 576. </s></p><p type="main">

<s>Ferdinando Marsill riferisce al Viviani le sue esperienze, fatte intorno alla polvere pirica, in deter&shy;<lb/>minare i vari impeti dei proietti 577. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo X.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Lemmi e proposizioni di Niccol&ograve; Aggiunti, per dimostrare le condizioni d'equilibrio e di moto in <lb/>una catena, posata sopra un piano, e tirata tutta in terra dal primo anello pendulo, pag. </s>

<s>587-91. </s></p><p type="main">

<s>Corollario, che il Viviani voleva aggiungere alla X proposizione galileiana dei proietti 595. </s></p><pb xlink:href="020/01/2368.jpg"/><p type="main">

<s><emph type="center"/>INDICE ALFABETICO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>DEGLI AUTORI E DELLE COSE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Co'numeri s'accenna alle pagine.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="bold"/>Accademici del Cimento<emph.end type="bold"/> fanno esperienze del cadente, che risale all'altezza medesima d'onde <lb/>scese 333, sperimentano le corse e le nicorse di una palla dentro un canal circolare 394, ritro&shy;<lb/>vano che le oscillazioni strette dei pendoli non sono isocrone con le pi&ugrave; larghe 399, come ritro&shy;<lb/>vassero, e quanta la lunghezza del pendolo a secondi, per applicarla al loro Cronometro 433-35. </s></p><p type="main">

<s><emph type="bold"/>Acquapendente (d') Girolamo Fabricio<emph.end type="bold"/> applica i teoremi degli antichi alla Meccanica animale 581. </s></p><p type="main">

<s><emph type="bold"/>Aggiunti Niccol&ograve;<emph.end type="bold"/> promove una proposizione galileiana intorno al moto dei pendoli 422. </s></p><p type="main">

<s><emph type="bold"/>Alessandrina (scuola),<emph.end type="bold"/> qual sia l'indole sua propria negl'insegnamenti della Meccanica 14. </s></p><p type="main">

<s><emph type="bold"/>Arabi,<emph.end type="bold"/> loro cultura della Scienza meccanica 21. </s></p><p type="main">

<s><emph type="bold"/>Archimede,<emph.end type="bold"/> suoi primi libri meccanici 16, insegna primo la regola di comporre le forze parallele 17, <lb/>dimostra la legge dei moti equabili <emph type="italics"/>ivi,<emph.end type="italics"/> deduce la genesi delle spirali dal principio della com&shy;<lb/>posizione dei moti 18. </s></p><p type="main">

<s><emph type="bold"/>Aria<emph.end type="bold"/> nell'aria non &egrave; grave 71, impedisce le velocit&agrave; nei cadenti 283, d&agrave; impulso, secondo gli anti&shy;<lb/>chi, e occasione di velocitarsi ai cadenti 290. </s></p><p type="main">

<s><emph type="bold"/>Aristotile<emph.end type="bold"/> primo a dimostrar che le forze si compongono nella diagonale del parallelogrammo 10, <lb/>riduce tutte le macchine al vette 13, accenna alla legge dei moti equabili 17, due false leggi asse&shy;<lb/>gnate da lui alla caduta dei gravi 267, suoi quesiti intorno alle resistenze dei solidi 436, 37. </s></p><p type="main">

<s><emph type="bold"/>Attriti,<emph.end type="bold"/> come indugino le velocit&agrave; dei cadenti lungo i piani inclinati, secondo l'esperienze del Ric&shy;<lb/>cioli 301. </s></p><p type="main">

<s><emph type="bold"/>Ballani Giovan Batista<emph.end type="bold"/> scopre, contemporaneamente con Galileo, la ragione perch&egrave; i gravi di qua&shy;<lb/>lunqne mole cadendo vanno ugualmente veloci 278, come, contemporaneamente con Galileo, di&shy;<lb/>mostri le leggi dei liberi cadenti 311, 12, vuol rivendicare a s&egrave; il primato delle scoperte leggi <lb/>dei moti accelerati 315, confessa che Galileo l'aveva prevenuto 317, dimostra che gl'incrementi <lb/>delle velocit&agrave; nelle libere cadute dei gravi son come la serie dei numeri naturali 319, si con&shy;<lb/>frontano i teoremi di lui con quelli pubblicati nello stesso tempo da Galileo 375-77, chiede a <lb/>Galileo quanta debba essere la lunghezza del pendolo, che misura i secondi 407, sue obiezioni <lb/>contro il moto parabolico dei proietti 565, giusto giudizio de'meriti di lui nella Scienza, dato <lb/>dallo stesso Galileo 583, 84. </s></p><p type="main">

<s><emph type="bold"/>Bar<gap/>centro,<emph.end type="bold"/> sua definizione e descrizione 102, come si riscontri la sua teoria con quella della com&shy;<lb/>posizione delle forze parallele 175. </s></p><p type="main">

<s><emph type="bold"/>Benedetti Giovan Batista<emph.end type="bold"/> instauratore della Scienza del moto 97, suoi principali teoremi dimostrati <lb/>nel libro <emph type="italics"/>De mechanicis<emph.end type="italics"/> 98, conferma la verit&agrave; della regola osservata da Leonardo e dal Car&shy;<lb/>dano, per computare i momenti 183, insegna a misurar quanta parte si elida delle forze nel ti&shy;<lb/>rare obliquamente 184, corregge gli errori aristotelici nella questione relativa all'equilibrio delle <lb/>bilancie 193, sue proposizioni intorno ai gravi cadenti 274, primo a conoscere la vera causa acce&shy;<lb/>leratrice dei moti 293. </s></p><pb xlink:href="020/01/2369.jpg" pagenum="612"/><p type="main">

<s><emph type="bold"/>Beriguardi Claudio,<emph.end type="bold"/> suoi teoremi di Meccanica 33, concorre con Galileo nello stabilire i fondamenti <lb/>della Dinamica 375. </s></p><p type="main">

<s><emph type="bold"/>Bernoulli Giacomo<emph.end type="bold"/> primo a scoprire il sofisma del Vanni intorno alle pressioni di un grave sopra <lb/>due piani inclinati 259, 60, sua ipotesi delle resistenze de'solidi allo spezzarsi 503, 4. </s></p><p type="main">

<s><emph type="bold"/>Beugrand Giovanni,<emph.end type="bold"/> sua dimostrazione del variar peso i gravi, nell'avvicinarsi o nel dilungarsi dal <lb/>centro terrestre 176. </s></p><p type="main">

<s><emph type="bold"/>Bilancia,<emph.end type="bold"/> questione intorno all'equilibrio di lei promossa da Aristotile 190, 91, come fosse finalmente <lb/>risoluta 208. </s></p><p type="main">

<s><emph type="bold"/>Bilancia idrostatica<emph.end type="bold"/> come servisse a Leonardo da Vinci, per trovar la legge dei momenti dei gravi <lb/>sopra i piani inclinati 40. </s></p><p type="main">

<s><emph type="bold"/>Borelli Gian Alfonso,<emph.end type="bold"/> suo teorema concernente la forza necessaria a sollevare un braccio di leva <lb/>inclinato in sito orizontale 61. </s></p><p type="main">

<s><emph type="bold"/>Blondel Francesco<emph.end type="bold"/> medita di scrivere un libro <emph type="italics"/>De resistentia solidorum<emph.end type="italics"/> 454. </s></p><p type="main">

<s><emph type="bold"/>Cabeo Niccol&ograve;,<emph.end type="bold"/> suoi errori intorno ai gravi cadenti come fossero notati dal Riccioli 281, sue ingiuste <lb/>censure delle dottrine galileiane intorno ai gravi cadenti 317, manda al Baliani la misura del <lb/>pendolo a secondi 413, conosce falsa la IX proposizione dell'ottavo libro di Pappo, ma non rie&shy;<lb/>sce a sostituirvi la vera 238. </s></p><p type="main">

<s><emph type="bold"/>Cardano Girolamo,<emph.end type="bold"/> sua Scienza del moto 94, 95, non risolve propriamente la questione aristotelica <lb/>della Bilancia di braccia uguali 197, suo falso teorema del piano mclinato 232, sue osservazioni <lb/>intorno al moto dei pendoli 386, suo falso teorema che il moto composto sia pi&ugrave; tardo dei com&shy;<lb/>ponenti 520. </s></p><p type="main">

<s><emph type="bold"/>Cartesio Renato,<emph.end type="bold"/> suo principio statico riscontra con quello di Giordano Nemorario 24, per quali ra&shy;<lb/>gioni lo creda da preferire a quello di Galileo 159, 60, dimostra, a modo del Torricelli, il propor&shy;<lb/>zionato variar dei pesi, secondo la loro relativa positura rispetto al centro terrestre 205, esperienze <lb/>da lui citate per confermar che i corpi, dilungandosi dal centro della Terra, divengono pi&ugrave; leg&shy;<lb/>geri 207, accusa Guidubaldo, per aver ridotta la troclea al vette 222, segue, nella meccanica del <lb/>cuneo, gl'insegnamenti di Guidubaldo 229, dimostra falsa la proposizione di Galileo che final&shy;<lb/>mente i gravi cadenti si riducano all'equabilit&agrave; del moto 287, dice di aver egli prima scoperte <lb/>le leggi dei gravi cadenti 315, 16, indovina l'intenzione, ch'ebbe Galileo nello scrivere il trattato <lb/>dei moti locali 383. </s></p><p type="main">

<s><emph type="bold"/>Casati Paolo<emph.end type="bold"/> risolve il problema dei pesi pendenti da funi 258, propone e interpetra la regola del <lb/>parallelogrammo delle forze 262. </s></p><p type="main">

<s><emph type="bold"/>Cavalieri Bonaventura,<emph.end type="bold"/> sua Geometria degl'indivisibili com'avesse origine dalla stereometria del <lb/>Keplero 119, manda, nel 1622, a Galileo le sue prime proposizioni geometriche dimostrate col <lb/>metodo degli indivisibili 120, lungamente ne attende l'autorevole giudizio 121, nel 1627 ha com&shy;<lb/>piuto, nella Geometria degl'indivisibili, un intero trattato diviso in sette libri <emph type="italics"/>ivi,<emph.end type="italics"/> risponde a un <lb/>argomento, col quale Galileo pretendeva di dimostrare che il metodo degl'indivisibili conduce <lb/>all'assurdo 123, scrive al Torricelli di alcune difficolt&agrave; fatte contro la Geometria degl'indivisi&shy;<lb/>bili 128, lo invita a rispondere, piuttosto che con le parole, coi fatti 129 e pensa al miglior modo <lb/>di rispondere egli stesso 130, quale avesse occasion di scrivere le sue <emph type="italics"/>Esercitazioni geometri&shy;<lb/>che<emph.end type="italics"/> 134, avvisa Galileo di aver ritrovate le proporzioni stereometriche tra il fuso parabolico e il <lb/>cilindro circoscritto 136, conclude la dimostrazione della regola centrobrarica da un teorema di <lb/>Giann'Antonio Rocca 137, dimostra gl'incrementi del moto nei liberi cadenti con gl'incrementi <lb/>delle cinconferenze, che si diffondono equabilmente dal centro 308, d&agrave; la prima pubblica dimo&shy;<lb/>strazione che i momenti nella bilancia stanno in ragion composta dei pesi e delle distanze 488, <lb/>come dimostri esser parabolica la linea descritta dai proietti 426, come inserisse nello <emph type="italics"/>Specchio <lb/>ustorio<emph.end type="italics"/> la nuova proposizione 527, come si studiasse di scusar Galileo, che diceva essere la linea <lb/>de'proietti, non parabolica ma circolare 528, com'essendo usurpato da Galileo, se ne confessasse <lb/>egli stesso l'usurpatore 530, e come chieda di far del fallo, a richiesta dell'offensore, la peni&shy;<lb/>tenza 533. </s></p><p type="main">

<s><emph type="bold"/>Centrobrarica,<emph.end type="bold"/> in che modo se ne rinfrescasse la notizia in Italia 148. </s></p><p type="main">

<s><emph type="bold"/>Centro di gravit&agrave;,<emph.end type="bold"/> difficolt&agrave; del determinarlo in una sfera, avuto riguardo alla distanza di lei dal <lb/>centro terrestre 198. </s></p><p type="main">

<s><emph type="bold"/>Circolo,<emph.end type="bold"/> sua dignit&agrave; meccanica, secondo Aristotile 9, si genera, secondo il Filosofo, dalla composizione <lb/>di due moti 11. </s></p><p type="main">

<s><emph type="bold"/>Coesiene (forxa di)<emph.end type="bold"/> definita da Galileo 438. </s></p><p type="main">

<s><emph type="bold"/>Commsadine Federige,<emph.end type="bold"/> qual fosse l'occasione e il fine del suo trattato <emph type="italics"/>De centro gravitatis<emph.end type="italics"/> 108, sua <lb/>vera teorica dei momenti 181. </s></p><p type="main">

<s><emph type="bold"/>Corda<emph.end type="bold"/> impossibile a esser tesa in linea retta orizontale da qualunque peso la tiri, secondo la dimo&shy;<lb/>strazione di Galileo 63. </s></p><pb xlink:href="020/01/2370.jpg" pagenum="613"/><p type="main">

<s><emph type="bold"/>Corpi,<emph.end type="bold"/> se pi&ugrave; pesino avvicinati o dilungati dal centro terrestre 207, varie opinioni dei Matematici <lb/>intorno a questo punto 208. </s></p><p type="main">

<s><emph type="bold"/>Cuneo,<emph.end type="bold"/> proposizioni meccaniche di lui come dimostrate da Aristotile, da Guidubaldo e dal Bene&shy;<lb/>detti 228, 29. </s></p><p type="main">

<s><emph type="bold"/>Dialoghi<emph.end type="bold"/> delle due Scienze nuove: storia della loro pubblicazione 596. </s></p><p type="main">

<s><emph type="bold"/>Dialogo<emph.end type="bold"/> primo delle Scienze nuove serve come di larga prefazione ai trattati delle resistenze, e dei <lb/>moti accelerati 592-96. </s></p><p type="main">

<s><emph type="bold"/>Equiponderanze,<emph.end type="bold"/> loro principio come dimostrato dallo Stevino 168, come, a imitazione di lui, dimo&shy;<lb/>strato da Galileo 170, come dall'Huyghens 171, 72, come dal Newton 172, 73, come a quella di&shy;<lb/>mostrazione s'applicassero i moti composti 173. </s></p><p type="main">

<s><emph type="bold"/>Esperienza,<emph.end type="bold"/> sentenza di Leonardo da Vinci intorno alle verit&agrave; rivelate da lei 31. </s></p><p type="main">

<s><emph type="bold"/>Euclide,<emph.end type="bold"/> suo trattato <emph type="italics"/>De panderibus<emph.end type="italics"/> 13. </s></p><p type="main">

<s><emph type="bold"/>Fontana Mariano<emph.end type="bold"/> difende la verit&agrave; della XI proposizion galileiana delle resistenze contro le accuse <lb/>del De-la-Hire e del Grandi 481. </s></p><p type="main">

<s><emph type="bold"/>Forze parallele,<emph.end type="bold"/> loro composizione 17. </s></p><p type="main">

<s><emph type="bold"/>Frisi Paolo<emph.end type="bold"/> dice non esser conforme al vero l'asserto degli Accademici del Cimento che cio&egrave; Galileo <lb/>avvertisse le vibrazioni maggiori del pendolo essere pi&ugrave; diuturne delle minori 400. </s></p><p type="main">

<s><emph type="bold"/><gap/> Galileo<emph.end type="bold"/> attende giovanissimo a trattare dei centri di gravit&agrave;, per supplire ai difetti del Com&shy;<lb/>mandino 109, difficolt&agrave; trovate dai primi esaminatori di questo trattato 110, si propone di trattare <lb/>degli indivisibili 121, oppone difficolt&agrave; alle dottrine degli indivisibili del Cavalieri, prendendo ar&shy;<lb/>gomento dal teorema cos&igrave; detto della <emph type="italics"/>Scodella<emph.end type="italics"/> 122, diventa nemico degli indivisibili 124, suo teo&shy;<lb/>rema de'momenti dei gravi sopra i piani inclinati, concluso dai principii statici della Libbra 238 <lb/>osservazioni intorno a ci&ograve; che si dice da lui dei gravi cadenti da grandi altezze 276, come scopre <lb/>e dimostra la legge che ogni particella materiale ha una velocit&agrave; propria, determinata dalla Na&shy;<lb/>tura 277, prima partecip&ograve; de'comuni errori, poi trov&ograve; la vera legge dei moti accelerati, appli&shy;<lb/>cando ai teoremi di Archimede i principii del Benedetti 295, come dimostrasse matematicamente <lb/>la detta legge 305, com'applicasse gl'indivisibili a questa dimostrazione 306, crede a principio <lb/>che i tempi delle vibrazioni dei pendoli fossero come le semplici lunghezze dei fili 408, come e <lb/>quando scoprisse che i tempi stanno come le radici delle dette lunghezze 409, descrive al Ba&shy;<lb/>liani il suo misuratore del tempo 411, sue prime proposizioni delle resistenze dei solidi 438, cu&shy;<lb/>riose applicazioni fatte da lui de'teoremi delle resistenze dei solidi 440, come spieghi perch&egrave; vanno <lb/>tanto pi&ugrave; in linea retta i proietti, quanto son meno oblique le direzioni dei tiri 514, scopre, spe&shy;<lb/>rimentando coi getti di acqua, che i tiri livellati, con qualunque impeto sian fatti, giungono al <lb/>piano dell'orizzonte nel medesimo tempo 518, sperimenta, per farne l'applicazione ai proietti, che <lb/>una pietra, lasciata cader lungo l'albero di una nave, gli batte al piede, o la nave stessa si <lb/>muova o stiasi in quiete 521, come credesse a principio vera l'opinion dei Tartaglia, che cio&egrave; la <lb/>parte curva della via dei proietti sia circolare 524, scrive una lettera a Cesare Marsili, per la&shy;<lb/>mentarsi che il Cavalieri avesse pubblicata la dimostrazione della linca parabolica descritta dai <lb/>proietti 529, si scusa di un suo errore intorno ai proietti, dicendo di aver inteso di parlare da <lb/>scherzo 531. </s></p><p type="main">

<s><emph type="bold"/>Gassendo Pietro,<emph.end type="bold"/> sue esperienze istituite per confermare le leggi galileiane dei moti accelerati 323. </s></p><p type="main">

<s><emph type="bold"/>Gerli Carlo Giuseppe<emph.end type="bold"/> pubblica i disegni a tocco in penna di Leonardo da Vinci 27. </s></p><p type="main">

<s><emph type="bold"/>Giordano Vitale,<emph.end type="bold"/> suo principio dei momenti composti 262. </s></p><p type="main">

<s><emph type="bold"/>Gradi Stefano<emph.end type="bold"/> confessa che nel ragionamento fatto da Galileo, per dimostrar che una circonferenza <lb/>&egrave; uguale a un punto, si conterrebbe un paralogismo, se Galileo stesso non intendesse di parlar <lb/>da poeta 126. </s></p><p type="main">

<s><emph type="bold"/>Grandi Guido,<emph.end type="bold"/> dimostra contro L. A. </s>

<s>Porzio che la direzione del fulcro, su cui si appoggia un grave <lb/>in un piano inclinato, s'ha da prendere nella direzione del perpendicolo, condotto dal centro di <lb/>gravit&agrave; del peso sopra lo stesso piano 265, accusa il Marchetti di essersi appropriata la dimo&shy;<lb/>strazione, che i momenti hanno ragion composta delle distanze e dei pesi 485. </s></p><p type="main">

<s><emph type="bold"/>Gravi cadenti,<emph.end type="bold"/> loro uguali velocit&agrave; nel vuoto sperimentate dal Desaguliers, dal S'Gravesande e dal <lb/>Wolf 288. </s></p><p type="main">

<s><emph type="bold"/>Gravit&agrave;<emph.end type="bold"/> contrasta ne'proietti con la virt&ugrave; impressa 162. </s></p><p type="main">

<s><emph type="bold"/><gap/> Mario<emph.end type="bold"/> riferisce una proposizione di Galileo relativa ai proietti 523. </s></p><p type="main">

<s><emph type="bold"/>G<gap/> P<gap/>lo,<emph.end type="bold"/> processo della sua invenzione centrobrarica 117. </s></p><pb xlink:href="020/01/2371.jpg" pagenum="614"/><p type="main">

<s><emph type="bold"/>Herigonio Pietro,<emph.end type="bold"/> dimostrando la legge dei momenti dei gravi ne'piani inclinati, vi comprende in&shy;<lb/>sieme il teorema del Tartaglia, e la esperienza dello Stevino 236. </s></p><p type="main">

<s><emph type="bold"/>Hire (de la) Filippo<emph.end type="bold"/> censura una proposizione di Galileo, relativa alle resistenze, e il Grandi ne ap&shy;<lb/>prova le censure 478. </s></p><p type="main">

<s><emph type="bold"/>Host&eacute; Paolo,<emph.end type="bold"/> sua proposizione della resistenza dei solidi male invocata dal Grandi, per confermare <lb/>la falsit&agrave; della XI galileiana 480. </s></p><p type="main">

<s><emph type="bold"/>Huyghens Cristiano<emph.end type="bold"/> applica i moti composti a dimostrar la legge galileiana dell'acceleramento dei <lb/>gravi 326, dimostra, altrimenti da Galileo, i teoremi fondamentali dei moti accelerati <emph type="italics"/>ivi,<emph.end type="italics"/> dimo&shy;<lb/>stra matematicamente che le vibrazioni del pendolo circolare non possono essere isocrone 405, <lb/>credeva parabolica la curva catenaria, per ragioni similissime a quelle di Galileo 496. </s></p><p type="main">

<s><emph type="bold"/>Inerzia (forza d'),<emph.end type="bold"/> sua denominazione, e suo concetto definito da Galileo, dall'Aggiunti e dal Carte&shy;<lb/>sio 302-4, bench&egrave; fosse ben chiaro ai matematici del secolo XVI <emph type="italics"/>ivi,<emph.end type="italics"/> come ne facessero l'applica&shy;<lb/>zione alla Meccanica il Cardano, lo Scaligero e il Benedetti 511. </s></p><p type="main">

<s><emph type="bold"/>Isocronismo<emph.end type="bold"/> dei pendoli dimostrato da Giovan Marco Marci 390, sperimentato dal Riccioli 391, cre&shy;<lb/>duto assolutamente tale dai Fisici nella prima met&agrave; del XVII secolo 392, scoperto non vero dal <lb/>Wendelin e dal Cabeo 395. </s></p><p type="main">

<s><emph type="bold"/>Kepler Giovanni,<emph.end type="bold"/> sua stereometria nuova 115. </s></p><p type="main">

<s><emph type="bold"/>Leibniz Gotifredo Guglielmo,<emph.end type="bold"/> suo errore nel determinar le pressioni di un grave sopra due piani <lb/>inclinati 257, sua regola <emph type="italics"/>degli alternativi<emph.end type="italics"/> applicata alla Meccanica 259, dimostra che la resistenza <lb/>respettiva dei solidi allo spezzarsi non &egrave; la met&agrave;, come diceva Galileo, ma la terza parte del&shy;<lb/>l'assoluta 501. </s></p><p type="main">

<s><emph type="bold"/>Leva,<emph.end type="bold"/> esemplare, a cui s'informano le altre macchine 215, vari generi di questo strumento 217. </s></p><p type="main">

<s><emph type="bold"/>Libbra,<emph.end type="bold"/> suo fondamento meccanico, secondo Aristotile 11, e secondo Archimede 15. </s></p><p type="main">

<s><emph type="bold"/>Libramenti<emph.end type="bold"/> dei liquidi ne'sifoni sperimentati dagli Accademici del Cimento 399. </s></p><p type="main">

<s><emph type="bold"/>Libri Guglielmo<emph.end type="bold"/> si propone di pubblicare i manoscritti di Leonardo da Vinci 30, d&agrave; occasione a una <lb/>questione storica relativa al modo di ritrovare il centro della gravit&agrave; nella piramide 104. </s></p><p type="main">

<s><emph type="bold"/>Logaritmi,<emph.end type="bold"/> come Galileo confessasse al Cavalieri di non intenderli 563. </s></p><p type="main">

<s><emph type="bold"/>Macchine,<emph.end type="bold"/> loro efficacia nel sostegno 213, in che propriamente consista la loro potenza 216. </s></p><p type="main">

<s><emph type="bold"/>Magalotti Lorenzo<emph.end type="bold"/> risolve un problema delle resistenze dei solidi, applicandovi un teorema annun&shy;<lb/>ziato dal Viviani 465. </s></p><p type="main">

<s><emph type="bold"/>Manoscritti<emph.end type="bold"/> di Leonardo da Vinci: storia delle loro vicende 26. </s></p><p type="main">

<s><emph type="bold"/>Marchetti Alessandro<emph.end type="bold"/> crede di essere stato il primo a dimostrar che i momenti stanno in ragion <lb/>composta delle distanze e dei pesi 246, suo trattato dei Fondamenti della Scienza universale del <lb/>moto 247, occasione ch'egli ebbe di scrivere il trattato <emph type="italics"/>De reristentia solidorum<emph.end type="italics"/> 454, &egrave; pregato <lb/>dal Viviani a dilazionar la pubblicazione del manoscritto dello stesso trattato 456, dimostra l'ugual <lb/>resistenza del solido parabolico, considerato senza peso, pi&ugrave; speditamente di Galileo 458, risponde <lb/>alle accuse mossegli contro da Guido Grandi 464, si decide esser vera la proposizione di lui, e <lb/>falsa la VI galileiana delle resistenze 475. </s></p><p type="main">

<s><emph type="bold"/>Marci Giovan Marco<emph.end type="bold"/> dimostra le leggi delle cadute de'gravi contemporaneamente con Galileo 311, <lb/>risolve il problema del pendolo a secondi 417, istituisce la scienza del moto nel medesimo tempo, <lb/>e indipendentemente da Galileo 582. </s></p><p type="main">

<s><emph type="bold"/>Mariotte Edmondo,<emph.end type="bold"/> suo principio di statica generale sostituito a quello di Archimede e di Galileo 171, <lb/>dimostra, altrimenti da Galileo, il brachistocronismo degli archi rispetto alle corde 379, propone, <lb/>tra le resistenze assolute e le respettive, una proporzione diversa da quella di Galileo 498. </s></p><p type="main">

<s><emph type="bold"/>Martello,<emph.end type="bold"/> qual'effetto faccia la maggiore o minor lunghezza del manico 57. </s></p><p type="main">

<s><emph type="bold"/>Maurolico Francesco,<emph.end type="bold"/> storia del suo trattato manoscritto intitolato <emph type="italics"/>Monumenta Archimedis<emph.end type="italics"/> 87. </s></p><p type="main">

<s><emph type="bold"/>Mazzoni Jacopo<emph.end type="bold"/> inizia Galileo alla Scienza del moto 275. </s></p><p type="main">

<s><emph type="bold"/>Meccanica,<emph.end type="bold"/> come Aristotile la definisce 9. </s></p><p type="main">

<s><emph type="bold"/>Mechaniques (les),<emph.end type="bold"/> trattatello del Cartesio, che il Viviani ricopi&ograve; dall'originale francese 200. </s></p><p type="main">

<s><emph type="bold"/>Monte (del) Guidubaldo,<emph.end type="bold"/> come nel suo <emph type="italics"/>Mechanicorum liber<emph.end type="italics"/> promovesse la scienza 96, come dimo&shy;<lb/>stri il modo di computare i momenti contro il Cardano 182, come corregge l'errore aristotelico <lb/>rispetto all'equilibrio instabile delle Bilance 291, come dimostri che, nello scendere, il braccio <lb/>della Bilancia si aggrava 202, sua fallacia nel determinare le condizioni dell'equilibrio della <lb/>leva 218, suoi modi di descrivere le parabole, e altre novit&agrave; di lui appropriatesi da Galileo 444, <lb/>sue esperienze intorno alle traiettorie paraboliche 515, descrive e rende la ragion della corda, <lb/>che tocca fa moverne un'altra quieta ma tesa all'unisono 594. </s></p><pb xlink:href="020/01/2372.jpg" pagenum="615"/><p type="main">

<s><emph type="bold"/>Momenti<emph.end type="bold"/> stanno, secondo la dimostrazion del Maurolico, in ragion composta dei pesi e degli spazi 86, <lb/>loro teorica nel Maurolico difettosa 180, come definiti da Galileo, e da lui stesso applicati alla <lb/>Statica 184. </s></p><p type="main">

<s><emph type="bold"/>Momento<emph.end type="bold"/> come definito dal Maurolico 86. </s></p><p type="main">

<s><emph type="bold"/>Montanari Gemiuiano,<emph.end type="bold"/> sua teoria dell'equilibrio delle Bilance di braccia uguali 208, come risponda <lb/>in proposito alle contradizioni di Donato Rossetti 210. </s></p><p type="main">

<s><emph type="bold"/>Moti misti<emph.end type="bold"/> non usati da Galileo, n&egrave; dai promotori di lui, per determinar gl'impeti nelle parabole dei <lb/>proietti 540. </s></p><p type="main">

<s><emph type="bold"/>Moto<emph.end type="bold"/> circolare non &egrave;, secondo Galileo, n&egrave; naturale n&egrave; violento 513. </s></p><p type="main">

<s><emph type="bold"/>Musschenbroeck Pietro,<emph.end type="bold"/> sue esperienze e conclusioni intorno alla proporzione fra le resistenze asso&shy;<lb/>lute e respettive dei solidi 504. </s></p><p type="main">

<s><emph type="bold"/>Nardi Antonio,<emph.end type="bold"/> sue Ricercate geometriche 128, suo fecondo principio della trasformazione delle <lb/>figure 139. </s></p><p type="main">

<s><emph type="bold"/>Nemorario Giordano,<emph.end type="bold"/> sue XIII proposizioni <emph type="italics"/>De ponderibus<emph.end type="italics"/> 21, suo principio statico 22, suoi postu&shy;<lb/>lati 23, come si concluda da essi postulati la legge statica del Vette 24, come promove un teo&shy;<lb/>rema statico di Euclide 25, propone, prima del Tartaglia, una questione sulle Bilance, preter&shy;<lb/>messa da Aristotile 195 </s></p><p type="main">

<s><emph type="bold"/>Newton Isacco,<emph.end type="bold"/> sue esperienze sulle cadute dei gravi 287. </s></p><p type="main">

<s><emph type="bold"/>Pappo Alessandrino,<emph.end type="bold"/> principio meccanico da lui professato 19, suo teorema annunziato nella prefazione <lb/>al libro VII delle <emph type="italics"/>Matematiche collezioni<emph.end type="italics"/> 113, come si possa interpetrare l'oscuro significato 114. </s></p><p type="main">

<s><emph type="bold"/>Parabola<emph.end type="bold"/> descritta dai proietti, secendo il Cardano 512. </s></p><p type="main">

<s><emph type="bold"/>Parabolico (solido)<emph.end type="bold"/> dimostrato da Galileo essere di ugual resistenza in ogni sua parte 442. </s></p><p type="main">

<s><emph type="bold"/>Parallele (forze),<emph.end type="bold"/> invenzione del loro centro applicata a dimostrar la legge delle equiponderanze 174. </s></p><p type="main">

<s><emph type="bold"/>Pendoli<emph.end type="bold"/> usati da Galileo, dal Baliani e dal Newton a dimostrare che le velocit&agrave; sono uguali in qua&shy;<lb/>lunque specie di corpi cadenti 284, obiezioni di Guidubaldo contro il loro isocronismo 387, Gali&shy;<lb/>leo applica agli archi l'isocronismo dimostrato per le sole corde 389, di ugual lunghezza e diffe&shy;<lb/>rente peso, il pi&ugrave; grave fa maggior numero di vibrazioni nel medesimo tempo 396, ragione delle <lb/>loro simpatie nel vibrare, data dal Viviani, dietro le dottrine di Galileo 398, misurator dei se&shy;<lb/>condi quanto il Cabeo lo trovasse lungo 415, quanto il Castelli e il Mersenno 417, quanto il Ric&shy;<lb/>cioli 420. </s></p><p type="main">

<s><emph type="bold"/>Percossa,<emph.end type="bold"/> proporzione degli effetti di lei nelle varie direzioni 54, opera secondo la lunghezza del <lb/>percuziente 56. </s></p><p type="main">

<s><emph type="bold"/>Peritrochio (asse in),<emph.end type="bold"/> condizioni dell'equilibrio in questa macchina dimostrate da Guidubaldo e da <lb/>Galileo 219. </s></p><p type="main">

<s><emph type="bold"/>Plano inclinato<emph.end type="bold"/> esemplare, a cui s'informano le altre macchine 215, usato da Galileo a sperimentar <lb/>l'accelerazione del moto nei gravi cadenti 297. </s></p><p type="main">

<s><emph type="bold"/>Piramide,<emph.end type="bold"/> differenza tra il metodo antico e il moderno in ricercarne il centro di gravit&agrave; 105, come <lb/>insegni il Maurolico a ritrovare esso centro 107. </s></p><p type="main">

<s><emph type="bold"/>Poleni Giovanni,<emph.end type="bold"/> sue esperienze sulla resistenza dei solidi 504. </s></p><p type="main">

<s><emph type="bold"/>Porzio Luc'Antonio,<emph.end type="bold"/> sue opposizioni contro la comune teoria dei piani inclinati 263. </s></p><p type="main">

<s><emph type="bold"/>Proietti,<emph.end type="bold"/> errori detti dal Tartaglia intorno ad essi 507, come il Cardano e lo Scaligero fossero i primi <lb/>a insegnar che proseguono il loro moto, per la virt&ugrave; rimastavi impressa 511, vanno, secondo il Car&shy;<lb/>dano, per un moto impresso, che in principio &egrave; violento, in fine naturale, e nel mezzo compo&shy;<lb/>sto dell'uno e dell'altro 512. </s></p><p type="main">

<s><emph type="bold"/>Proposizioni<emph.end type="bold"/> comprendenti il trattato galileiano delle resistenze ordinatamente disposte e formn&shy;<lb/>late 452. </s></p><p type="main">

<s><emph type="bold"/>Renieri Vincenzo<emph.end type="bold"/> scopre, per esperienze fatte sul campanile di Pisa, alcuni errori detti da N. </s>

<s>Cabeo <lb/>intorno alle cadute dei gravi 279. </s></p><p type="main">

<s><emph type="bold"/>Riccioli Giovan Ratista<emph.end type="bold"/> sperimenta non esser vero che due corpi, di ugual materia e forma, ma <lb/>differenti di peso, scendano da uguali altezze nel medesimo tempo 282, ripensa alle leggi gali&shy;<lb/>leiane dei moti accelerati 298, &egrave; il primo che confermi sperimentalmente la detta legge 324, suoi <lb/>studi per trovar la precisa lunghezza del pendolo a secondi 418. </s></p><p type="main">

<s><emph type="bold"/>Rocca Giovann'Antonio,<emph.end type="bold"/> suo Lemma meccanico pubblicato dal Torricelli 136, dimostra le ragioni <lb/>stereometriche del fuso parabolico al cilindro circoscritto, per via degl'indivisibili 137. </s></p><p type="main">

<s><emph type="bold"/>Rossetti Donato,<emph.end type="bold"/> come dimostri le ragioni dell'equilibrio nelle Bilance di braccia uguali 209. </s></p><p type="main">

<s><emph type="bold"/>Sfera<emph.end type="bold"/> si muove nel piano orizontale senza sforzo 38. </s></p><p type="main">

<s><emph type="bold"/>Squadra dei bombardieri<emph.end type="bold"/> descritta dal Tartaglia 507. </s></p><pb xlink:href="020/01/2373.jpg" pagenum="616"/><p type="main">

<s><emph type="bold"/>Stevino Simeone,<emph.end type="bold"/> sua <emph type="italics"/>Spartostatica<emph.end type="italics"/> e sua <emph type="italics"/>Trocheologia<emph.end type="italics"/> trattate col principio della composizion delle <lb/>forze 226, conferma con una bella esperienza il Teorema del Tartaglia dei momenti dei gravi <lb/>sopra i piani inclinati 235. </s></p><p type="main">

<s><emph type="bold"/>Supposto<emph.end type="bold"/> principio, su cui aveva fondata la sua Meccanica Galileo 335. </s></p><p type="main">

<s><emph type="bold"/>Tardit&agrave;,<emph.end type="bold"/> come il mobile, partendosi dalla quiete, passi per tutti i gradi di lei 160. </s></p><p type="main">

<s><emph type="bold"/>Tariffe,<emph.end type="bold"/> secondo il Viviani, corrispondono coi coefficienti sperimentali da introdursi nelle formule <lb/>astratte 498. </s></p><p type="main">

<s><emph type="bold"/>Tartaglia Niccol&ograve;,<emph.end type="bold"/> suo opuscolo postumo <emph type="italics"/>De pouderositate<emph.end type="italics"/> 87, principii fondamentali della Statica <lb/>da lui dimostrati 88, narra a quali occasioni gli occorresse di applicare i principii della scienza <lb/>all'arte dei bombardieri 91, propone un quesito sopra le Bilance, lasciato indietro da Aristo&shy;<lb/>tile 194, come risolva un tal quesito coi principii del Nemorario 196, primo a dimostrar che i <lb/>pesi, proporzionali alle discese oblique de'lati di un triangolo, si fanno insieme equilibrio 233, <lb/>sue proposizioni dimostrative delle cruse e delle leggi, secondo le quali si velocitano i gravi ca&shy;<lb/>denti 294, come avesse scoperto, e creduto dimostrare che i tiri a mezza squadra son quelli della <lb/>massima volata 507, come scoprisse, prima di Galileo, che due tiri hanno la medesima ampiezza, <lb/>quando superano o mancano ugualmente della inelinazion semiretta 509, come spieghi perch&egrave; il <lb/>tiro faccia maggior colpo in direzione inclinata, che di punto in bianco 510. </s></p><p type="main">

<s><emph type="bold"/>Tempo<emph.end type="bold"/> speso da un grave nello scender per cento braccia perpendicolari, come e quanto ritrovato da <lb/>Galileo 299. </s></p><p type="main">

<s><emph type="bold"/>Torricelli Evangelista,<emph.end type="bold"/> come non si curasse a principio d'entrar nella questione della Bilancia di <lb/>braccia uguali, rimossa dalla posizione orizzontale 200, a qual proposito entrasse in cos&igrave; fatta <lb/>questione <emph type="italics"/>ivi,<emph.end type="italics"/> come si accorgesse che a trattar le questioni meccaniche, supposte le forze conver&shy;<lb/>genti al centro terrestre, fosse primo, non il Beaugrand o il Cartesio, ma Guidubaldo del Monte 201, <lb/>come risolvesse la questione della Bilancia di braccia uguali, avuto riguardo che le forze son <lb/>convergenti 203, sue singolari idee intorno alla natura dei gravi 207, sostituisce un altro princi&shy;<lb/>cipio diverso da quello delle velocit&agrave; virtuali 240, suo teorema, da cui facile concludevansi le pro&shy;<lb/>porzioni, secondo le quali si comparte un peso sopra un piano inclinato 242, come dimostri che, <lb/>nella perpendicolare e nell'obliqua, i tempi stanno come le respettive lunghezze 338, suo nuovo <lb/>modo di misurare gl'impeti nella semiparabola 548, e nella parabola intera 549, come dimostri <lb/>matematicamente, e per pi&ugrave; facile via di Galileo, le conclusioni sperimentali del Tartaglia in&shy;<lb/>torno ai tiri delle artiglierie 557, risponde a un'obiezione fatta dal Cartesio contro le dottrine ga&shy;<lb/>lileiane dei proietti 568. </s></p><p type="main">

<s><emph type="bold"/>Tradixio<gap/><emph.end type="bold"/> della Scienza, comuni a Leonardo da Vinci e al Cardano 93. </s></p><p type="main">

<s><emph type="bold"/>Triangolo,<emph.end type="bold"/> suo centro di gravit&agrave; come dimostrato dal Maurolico 106. </s></p><p type="main">

<s><emph type="bold"/>Tro<gap/>lea,<emph.end type="bold"/> errori di Aristotile intorno ad essa 12, condizioni dell'equilibrio in questa macchina dimo&shy;<lb/>strate da Guidubaldo del Monte e da Galileo 220. </s></p><p type="main">

<s><emph type="bold"/>Valerio Luca,<emph.end type="bold"/> suo trattato <emph type="italics"/>De centro gravitatis solidorum<emph.end type="italics"/> 109, come risponde, interrogato da Gali&shy;<lb/>leo intorno a due supposti principii meccanici 355, 357. </s></p><p type="main">

<s><emph type="bold"/>Vanni Gian Francesco,<emph.end type="bold"/> suo dilemma intorno al teorema del momento dei gravi sopra i piani incli&shy;<lb/>nati 250, ne propone la soluzione ai seguaci delle dottrine di Galileo 251. </s></p><p type="main">

<s><emph type="bold"/>Vanni Giuseppe<emph.end type="bold"/> dimostra l'impropriet&agrave; di un teorema del Torricelli, relativo al momento dei grael <lb/>sopra i piani inclinati 248. </s></p><p type="main">

<s><emph type="bold"/>Varchi Benedetto,<emph.end type="bold"/> suo gusto nelle scienze sperimentali 279. </s></p><p type="main">

<s><emph type="bold"/>Velocit&agrave; virtuali,<emph.end type="bold"/> loro principio applicato da Galileo alle macchine semplici 158, come, dietro il La&shy;<lb/>grange, definite dai moderni 163, principio diverso sostituito in luogo di esse dal Torricelli 164. </s></p><p type="main">

<s><emph type="bold"/>Venturi Giovan Batista<emph.end type="bold"/> pubblica un saggio dei manoscritti di Leonardo da Vinci 28, difetti di que&shy;<lb/>sta pubblicazione 29. </s></p><p type="main">

<s><emph type="bold"/>Vetro<emph.end type="bold"/> non si rompe a un tratto ma cede prima alla pressione, come dimostrarono gli Accademici <lb/>del Cimento 498. </s></p><p type="main">

<s><emph type="bold"/>Vinci (da) Leouardo,<emph.end type="bold"/> meriti scientifici di lui esagerati 31, primo a far uso delle lettere alfabetiche <lb/>in algebra, e della linea orizzontale e della crocellina, per significare le quantit&agrave; negative e vi <lb/>positive 32, de'primi a introdur nelle questioni meccaniche il principio della composizion delle <lb/>forze 33, prende a sua maestra l'esperienza 34, come descrive il concetto, e definisce la natura <lb/>della forza 34, scioglie, prima del Maurolico e del Tartaglia, il problema della pietra, che s'im&shy;<lb/>magina giungere al centro della Terra 35, suoi pensieri intorno alle forze centrali, e alle trasfor&shy;<lb/>mazioni della superficie terrestre 36, dimostra un teorema meccanico supposto da Galileo 40, <lb/>dimostra il teorema del tempo per la perpendicolare e per l'obliqua, in che si riscontra con le <lb/>proposizioni di Galileo 41, suo principio della intera restituzione del moto 42, suo teorema in <lb/>proposito della scesa di un grave per un arco di cerchio 43, suoi vari esempi d'equilibrio sta-<pb xlink:href="020/01/2374.jpg" pagenum="617"/>bile 44, vari casi da lui proposti dell'equilibrio dei pesi nella Bilancia 45, sua dimostrazione della <lb/>statica del Vette 47 e delle Taglie 48, applica il principio della composizion delle forze alla Leva <lb/>angolare 50, sua dimostrazione dei momenti dei gravi sopra i piani inclinati 52, sperimenta che <lb/>nella forza della percossa ha grande efficacia la lunghezza del percuziente 56, dimostra gli effetti <lb/>della lunghezza del manico del martello 57, scioglie il problema della tension delle funi 59 e della <lb/>corda, impossibile a ridursi in dirittura orizzontale 61, scioglie l'altro problema delle pressioni <lb/>fatte da un'asta contro il pavimento e il muro, a cui si appoggia 66, determina il punto, in cui <lb/>tocca il piano orizzontale una fune, o liberamente sostenuta ne'due capi a varie altezze, o stirata <lb/>da qualche peso che vi s'infili 68, formula le leggi dei moti equabili 71, curiosi effetti della re&shy;<lb/>sistenza dell'aria, da lui bene osservati 72, strumento da lui inventato, per conoscer la varia <lb/>densit&agrave; dell'aria atmosferica, e che riducesi a un Baroscopio 73, resultati delle sue esperienze <lb/>intorno alle velocit&agrave; dei gravi cadenti 74, sua falsa legge dei moti accelerati come pensi di di&shy;<lb/>mostrarla 76, sua esperienza del moto dell'immobile sopra sito mobile 77, dimostra che la linea <lb/>dei cadenti al centro della Terra &egrave; un'elice 78, suoi errori intorno alle traiettorie 81, suoi espe&shy;<lb/>rimenti e problemi intorno alla resistenza dei solidi a spezzarsi, e delle funi a rompersi 82, sue <lb/>leggi sperimentali degli attriti 83, determina il centro di gravit&agrave; della piramide 104, suoi prin&shy;<lb/>cipii statici contro il Pelacane 157, sua vera teorica dei momenti 181, corregge gli errori aristo&shy;<lb/>telici, relativi alle questioni delle Bilance 193, sua <emph type="italics"/>sperentia delle bilance<emph.end type="italics"/> 195, dimostra le con&shy;<lb/>dizioni dell'equilibrio nella leva di secondo genere 217, sua teoria delle taglie 224, sua bellissima <lb/>proposizione sperimentale applicata al trar delle funi nelle Taglie 227, decompone, come il Vi&shy;<lb/>viani, il momento totale dei gravi sopra i piani inclinati 243, sua bella esperienza intorno ai pen&shy;<lb/>doli 423, sua esperienza per dimostrar che, tocca una corda sonora, ne fa movere un'altra in <lb/>quiete, ma tesa all'unisono 594. </s></p><p type="main">

<s><emph type="bold"/>Vite,<emph.end type="bold"/> strumento meccanico ridotto da Guidubaldo al piano inclinato 230. </s></p><p type="main">

<s><emph type="bold"/>Viviani Vincenzio<emph.end type="bold"/> dimostra un teorema, e fa osservazioni importanti intorno al metodo degl'indivi&shy;<lb/>sibili 146, chiamato dal cardinale Leopoldo dei Medici a decidere intorno alla questione delle Bi&shy;<lb/>lance, insorta fra il Montanari e il Rossetti 210. </s></p><p type="main">

<s><emph type="bold"/>Wallis Giovanni,<emph.end type="bold"/> come stabilisse la statica sulla legge dei momenti 189, conferma il teorema del <lb/>Tartaglia della gravit&agrave; de'pesi nelle varie declivit&agrave; dei piani 237. </s></p><p type="main">

<s><emph type="bold"/>Wrz Paolo<emph.end type="bold"/> primo a riscontrare con l'esperienza i teoremi galileiani della resistenza dei solidi 497. <pb xlink:href="020/01/2375.jpg"/></s></p><pb xlink:href="020/01/2376.jpg"/><p type="main">

<s>Finito di stampare in Bologna presso la <lb/>Libreria Editrice Forni nel Marzo 1970 </s></p><pb xlink:href="020/01/2377.jpg"/></chap><chap><p type="main">

<s>350478 Storia Del Metodo Sperimentale Italia </s></p><p type="main">

<s><emph type="center"/>THE SOURCES OF SCIENCE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Editor-in-Chief: Harry Woolf<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Willis K. </s>

<s>Shepard Professor of the History of <lb/>Science, The Johns Hopkins University<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="020/01/2378.jpg"/><p type="main">

<s><emph type="center"/><emph type="bold"/><emph type="italics"/>Storia del Metodo <lb/>Sperimentale in Italia<emph.end type="italics"/><emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>by RAFFAELLO CAVERNI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>in Six Volumes<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Volume V<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>THE SOURCES OF SCIENCE, NO. 134<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT CORPORATION<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>NEW YORK LONDON 1972<emph.end type="center"/></s></p><pb xlink:href="020/01/2379.jpg"/><p type="main">

<s><emph type="center"/>Reproduced here is the Florence edition of 1891-1900.<emph.end type="center"/></s></p><figure id="id.020.01.2379.1.jpg" xlink:href="020/01/2379/1.jpg"/><p type="main">

<s><emph type="center"/>Copyright &copy; 1972 by Johnson Reprint Corporation All rights reserved <lb/>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT CORPORATION<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>111 Fifth Avenue, New York, N.Y. 10003, U.S.A.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT COMPANY LTD.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Shipton Group House, 24/28 Oval Road, London, NW17DD, England<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Printed in Italy<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="020/01/2380.jpg"/><p type="main">

<s><emph type="center"/>DEL METODO SPERIMENTALE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>APPLICATO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>ALLA SCIENZA DEL MOTO DEI GRAVI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>PARTE SECONDA<emph.end type="center"/><pb xlink:href="020/01/2381.jpg"/></s></p><pb xlink:href="020/01/2382.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO I.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle correzioni e delle riforme <lb/>ne'Dialoghi delle due Scienze nuove<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Del supposto principio delle velocit&agrave; uguali, dopo cadute uguali, e come sortisse a Galileo, al Mi&shy;<lb/>chelini e al Baliani finalmento di dimostrarlo. </s>

<s>&mdash; II. </s>

<s>Del supposto galileiano confermato per le <lb/>dimostrazioni del Torricelli, del Baliani, dell'Huyghens e del Marchetti. </s>

<s>&mdash; III. </s>

<s>Di alcune ag&shy;<lb/>giunte da farsi ai Dialoghi, dettate da Galileo al Viviani suo ospite in Arcetri. </s>

<s>&mdash; IV. Dell'opera <lb/>di ampliar le dottrine esposto no'dialoghi Del moto, proseguita dal Viviani, dopo la morte di <lb/>Galileo. </s>

<s>&mdash; V. </s>

<s>Delle correzioni di aleuni falsi teoremi di Galileo, che fecero finalmente risolvere <lb/>il Viviani d'illustrare e di promovere in un'opera a parte le dottrine del suo Maestro. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>I quattro dialoghi delle Scienze nuove apparirono in Leyda come in mezzo <lb/>all'oceano la luce di un faro, a cui tutti rivolgevano gli occhi o invidi o de&shy;<lb/>siderosi degl'insoliti splendori: I desiderii per&ograve; nei pi&ugrave; ardenti non erano pie&shy;<lb/>namente sodisfatti, promettendosi sulla fine del libro di trattare certi argo&shy;<lb/>menti, e non vedendo all'Autore poi mantenere le solenni promesse. </s>

<s>E perch&egrave; <lb/>non si vedono pure mantenute oggid&igrave;, che dicono gli editori di averci date <lb/>le opere galileiane complete, giova esaminare il fatto e scoprirne la ragione. </s></p><p type="main">

<s>Sulla sera di questa quarta Giornata promette il Salviati ai conversevoli <lb/>amici che <emph type="italics"/>appresso<emph.end type="italics"/> avrebbe detto a loro delle utilit&agrave; non piccole, alle quali <lb/>servirebbero le catenuzze, oltre a quella di descriver le linee paraboliche; a <lb/>mantenere la qual promessa &egrave; sollecitato poi da Simplicio, che s'aspettava <lb/>inoltre d'intendere le speculazioni fatte dall'Accademico intorno alla forza della <lb/>percossa (Alb. </s>

<s>XIII, 266). Ma il Salviati risponde che l'ora era troppo tarda, <lb/>e che perci&ograve; ad altro tempo pi&ugrave; opportuno si differirebbe il congresso (ivi). </s></p><p type="main">

<s>S'avvisavano cos&igrave; dunque gli spettatori che non era finito il dramma, <pb xlink:href="020/01/2383.jpg" pagenum="8"/>a cui doveva succedere una quinta scena, la quale Galileo speraya di poter <lb/>fare rappresentare in quella medesima veglia, ma per varie difficolt&agrave; attra&shy;<lb/>versatesi venute meno cos&igrave; belle speranze, si lasci&ograve; lo spettacolo senza con&shy;<lb/>gedo. </s>

<s>L'Elzevirio infatti, avendo gi&agrave; condotto a termine il dialogo quarto, <lb/>aspettava il manoscritto del rimanente, e avuto avviso dall'Autore che non <lb/>l'aveva in ordine, e ch'era costretto di lasciar la stampa a quel punto, ri&shy;<lb/>spondeva d'Amsterdam, il d&igrave; 4 Gennaio 1638: &ldquo; In quanto al trattato Della <lb/>percossa e Dell'uso della catenella, se V. S. non lo pu&ograve; condurre a perfe&shy;<lb/>zione, far&ograve; il compimento secondo il suo ordine &rdquo; (Alb. </s>

<s>X, 252). Tornava <lb/>pochi giorni appresso pur d'Amsterdam a ripetere le medesime cose a Ga&shy;<lb/>lileo, soggiungendogli che, dovendosi cos&igrave; lasciar l'opera incompleta, gli man&shy;<lb/>dasse a dire in che modo ei dovesse significarlo ai lettori, dopo l'appendice <lb/>Dei centri di gravit&agrave;, &ldquo; acciocch&egrave; non si commettano errori &rdquo; (ivi, pag. </s>

<s>260). <lb/>Ma l'Elzevirio non ebbe a ci&ograve; risposta, e gli attori taciti, come si diceva, e <lb/>senza congedo, si lasciarono sparire dietro la scena. </s></p><p type="main">

<s>Aveva Galileo per&ograve; la speranza che vi si dovessero ricondur presto, per <lb/>cui non cur&ograve; il mormorio che si farebbe tra gli uditori, curiosi di vedere il <lb/>fine dell'opera, cos&igrave; disgustosamente rimasta a mezzo. </s>

<s>Per ridurla infatti a <lb/>quel fine desiderato, non bisognando altro all'Autore che d'aggiungervi i di&shy;<lb/>scorsi delle catenuzze e della percossa, i materiali gi&agrave; preparati non richie&shy;<lb/>devano che il tempo necessario a ricever ordine conveniente, e vaghezza di <lb/>forma. </s>

<s>La speranza dunque di tornar presto in scena, e con l'occasione del <lb/>compierla correggere e perfezionare quella parte dell'opera gi&agrave; pubblicata, <lb/>non sarebbe nell'animo di Galileo stata illusoria, se non fosse venuta a in&shy;<lb/>firmarla prima, e poi a dissiparla affatto una grande sventura. </s>

<s>Il di 2 Gen&shy;<lb/>naio 1638 faceva, piangendo, scrivere da Arcetri a Elia Diodati: &ldquo; Ahim&egrave;, <lb/>signor mio, il Galileo vostro caro amico e servitore, da un mese in qua &egrave; fatto <lb/>irreparabilmente del tutto cieco &rdquo; (Alb. </s>

<s>VII, 207). </s></p><p type="main">

<s>Il sacerdote fiorentino Marco Ambrogetti, chiamato in casa pochi mesi <lb/>prima, perch&egrave; traducesse in latino l'opere, che l'Elzevirio aveva promesso di <lb/>stampar tutte insieme; serviva al povero cieco di amanuense, ma, non avendo <lb/>uso delle Matematiche, non valeva d'alcuno aiuto l&agrave; dove si trattasse di tor&shy;<lb/>nar sopra una dimostrazione, illustrata da qualche figura complessa, e perci&ograve; <lb/>difficile a ritenersi nell'immaginazione ferma, e come innanzi agli occhi pre&shy;<lb/>sente. </s>

<s>Don Clemente Settimii, che spesso, dal collegio di S. Carlo, saliva ad <lb/>Arcetri, poco poteva trattenervisi, occupato nel fare scuola, e legato alle disci&shy;<lb/>pline dell'ordine religioso; intanto che Galileo si stava nelle tenebre ad incu&shy;<lb/>bare lo svolgimento de'suoi luminosi pensieri, aspettando qualche provvida <lb/>mano, per mezzo della quale, guidata dall'intelligenza, potesse significarli: <lb/>n&egrave; la provvidenza indugi&ograve; molto a venire. </s></p><p type="main">

<s>Frequentava le scuole di S. Carlo, dove il Settimii era maestro, un gio&shy;<lb/>vane sui diciott'anni, a cui era bastato spiegare le prime proposizioni di geo&shy;<lb/>metria, perch&egrave; si mettesse da s&egrave;, senz'altra guida, a dimostrar le rimanenti, <lb/>che si leggono nei libri di Euclide. </s>

<s>Quel giovanotto si chiamava Vincenzio <pb xlink:href="020/01/2384.jpg" pagenum="9"/>Viviani, che, invaghito ogni giorno pi&ugrave; di cos&igrave; nobile studio, impaziente di <lb/>vederne l'applicazione alla Scienza dei moti naturali, si dette a leggere i Dia&shy;<lb/>loghi, allora allora venuti alla luce. </s>

<s>Desideroso di conoscere un Autore di <lb/>tanta fama, il Settimii un giorno lo condusse seco ad Arcetri, dov'ebbe da <lb/>Galileo tale accoglienza, che diventarono di l&igrave; in poi le visite quasi quoti&shy;<lb/>diane. </s>

<s>Proseguendo in tanto l'incominciata lettura; arrivato a quel princi&shy;<lb/>pal supposto che le velocit&agrave; dei mobili, naturalmente discendenti per declivii <lb/>d'una medesima elevazione, siano uguali fra loro, dubit&ograve; il Viviani, non gi&agrave; <lb/>della verit&agrave; dell'assunto, ma dell'evidenza di poterlo suppor come noto, ond'ei <lb/>richiese a voce lo stesso. </s>

<s>Galileo di qualche pi&ugrave; chiara confermazione di quel <lb/>principio (Scienza universale delle proporz., Firenze 1674, pag. </s>

<s>99). </s></p><p type="main">

<s>La domanda trov&ograve; la mente del Vecchio solitario, a cui si rendeva dif&shy;<lb/>ficile l'internarsi in pi&ugrave; profondi pensieri, tutta occupata nelle tenebre not&shy;<lb/>turne, com'egli stesso scrisse un giorno al Baliani, intorno alle prime e pi&ugrave; <lb/>semplici proposizioni dei moti naturali, riordinandole e disponendole in mi&shy;<lb/>glior forma ed evidenza (Lettere per il trecentes, natal., Pisa 1864, pag. </s>

<s>45): <lb/>sicch&egrave; in queste disposizioni s'abbatt&egrave; facile Galileo a dimostrar quello, che <lb/>il Viviani desiderava. </s>

<s>Di ci&ograve; occorrerebbe ora a dire, ma crediam bene di <lb/>dover prima risalire alle origini, ed accennar le vicende, che precedettero alla <lb/>tanto festeggiata dimostrazione. </s></p><p type="main">

<s>Che l'assunto, posto da Galileo per fondamento alla Dinamica nuova, <lb/>fosse quello medesimo, di che si veniva a informare la Statica antica, lo ab&shy;<lb/>biamo fatto gi&agrave; notare altra volta: e come il Nemorario e il Tartaglia dice&shy;<lb/>vano esser l'impeto uguale nell'ugual rettitudine del discenso; cos&igrave; in egual <lb/>forma sentenziava il Salviati che &ldquo; due mobili uguali, ancorch&egrave; scendenti per <lb/>diverse linee, senza veruno impedimento, fanno acquisto d'impeti uguali, tut&shy;<lb/>tavolta che l'avvicinamento al centro sia uguale &rdquo; (Alb. </s>

<s>I, 28). L'evidenza <lb/>dunque del principio era universalmente riconosciuta, e i semplici esempi <lb/><figure id="id.020.01.2384.1.jpg" xlink:href="020/01/2384/1.jpg"/></s></p><p type="caption">

<s>Figura 1.<lb/>de'pendoli, e dei liquidi ne'si&shy;<lb/>foni, bastavano per confermarla. </s>

<s><lb/>In mezzo a questo pacifico con&shy;<lb/>senso dei Matematici sent&igrave; piut&shy;<lb/>tosto Galileo il bisogno di ri&shy;<lb/>spondere ai peripatetici, sottil&shy;<lb/>mente scoprendo la fallacia delle <lb/>lorp ragioni. </s>

<s>Dicevano essi, co&shy;<lb/>me poi il Cabeo e il Cazr, cos&igrave; valorosamente con&shy;<lb/>futato dal Gassendo, non esser possibile che, ve&shy;<lb/>nendo da C (fig. </s>

<s>1) per la CA lentamente, e per la CB <lb/><figure id="id.020.01.2384.2.jpg" xlink:href="020/01/2384/2.jpg"/></s></p><p type="caption">

<s>Figura 2.<lb/>a precipizio, abbia il mobile <lb/>guadagnato in A e in B i me&shy;<lb/>desimi gradi di forza. </s>

<s>Quanto <lb/>poi al particolare esempio del <lb/>pendolo diceva il Cabeo che l'impeto di risalire da B in I (fig. </s>

<s>2) doveva <pb xlink:href="020/01/2385.jpg" pagenum="10"/>esser maggiore dell'impeto di risalir dal medesimo punto in G, &ldquo; cum acqui&shy;<lb/>rat idem mobile impetum ascendendi breviori tempore, et per lineam magis <lb/>erectam &rdquo; (Comment. </s>

<s>metheor., T. I, Romae 1646, pag. </s>

<s>93). </s></p><p type="main">

<s>Queste sono, nel primo dialogo dei Massimi Sistemi, le medesime diffi&shy;<lb/>colt&agrave;, che promove Simplicio, a cui il Salviati domanda quand'egli creda di <lb/>poter dire che due mobili sono ugualmente veloci. </s>

<s>E rispondendo Simplicio: <lb/>quando passano spazi uguali in tempi uguali, gli vien fatto osservare che, a <lb/>render la definizione universale, conveniva aggiunger di pi&ugrave; che le velocit&agrave; <lb/>sono uguali &ldquo; quando gli spazi passati hanno la medesima proporzione dei <lb/>tempi, ne'quali son passati &rdquo; (Alb. </s>

<s>I, 30). </s></p><p type="main">

<s>In fallacie simili a quelle dell'immaginario Simplicio incorreva in realt&agrave; <lb/>l'ingegner Bartolotti, ammettendo che in due alvei d'ugual caduta, ma di <lb/>varia lunghezza, vadan l'acque nel pi&ugrave; lungo con moto molto pi&ugrave; lento. </s>

<s>Ga&shy;<lb/>lileo affermava invece che i due moti erano uguali, per dichiarar la qual pro&shy;<lb/>posizione, che aveva l'apparenza di un paradosso, &ldquo; non credo, scriveva a <lb/>Raffaello Staccoli, auditore del tribunale delle acque in Toscana, che dall'in&shy;<lb/>gegner Bartolotti n&egrave; da altri mi sar&agrave; negato verissimo essere il pronunziato <lb/>di colui, che dir&agrave; le velocit&agrave; di due mobili potersi chiamare eguali, non so&shy;<lb/>lamente quando essi mobili passano spazi eguali in tempi eguali, ma quando <lb/>ancora li spazi passati in tempi diseguali avessero tra di loro la proporzione <lb/>dei tempi de'loro passaggi. </s>

<s>Cos&igrave; per esempio quello, che in quattr'ore an&shy;<lb/>dasse da Firenze a Pistoia, non si pu&ograve; chiamare pi&ugrave; pigro d'un altro, che <lb/>in due ore andassse da Firenze a Prato, tuttavolta che Pistoia fosse lon&shy;<lb/>tana venti miglia, e Prato solamente dieci, perch&egrave; a ciascheduno tocca sot&shy;<lb/>tosopra ad aver fatto cinque miglia per ora, cio&egrave; avere in tempi eguali pas&shy;<lb/>sati spazi eguali. </s>

<s>E per&ograve;, qualunque volta due mobili scendano per due canali <lb/>disuguali, se passassero in tempi, che avessero la medesima proporzione che <lb/>le lunghezze degli stessi canali, si potranno veramente chiamare essere ugual&shy;<lb/>mente veloci. </s>

<s>Ora bisogna che quelli, ai quali sin qui &egrave; stato ignoto, sap&shy;<lb/>piano che due canali, quanto si voglia disuguali in lunghezza, purch&egrave; le to&shy;<lb/>tali pendenze loro siano uguali, vengono dall'istesso mobile passati in tempi <lb/>proporzionali alle loro lunghezze &rdquo; (Alb. </s>

<s>VI, 354). </s></p><p type="main">

<s>Si riduce a questa medesima conclusione il discorso nel dialogo dianzi <lb/>citato, dove la risoluzion del dubbio si fa dipendere dal teorema, che il tempo <lb/>della scesa per CA, nella prima figura qui poco addietro, al tempo della ca&shy;<lb/>duta per CB, ha la medesima proporzione che la linea CA alla CB &ldquo; ma la di&shy;<lb/>mostrazione, dice il Salviati agli amici, aspettatela un'altra volta &rdquo; (Alb. </s>

<s>I, 32). </s></p><p type="main">

<s>Di qui traspariscono chiari i pensieri di Galileo, e s'intende perch'egli <lb/>allora non si desse nessuna sollecitudine di dimostrar matematicamente un <lb/>principio, che scendeva per corollario immediato dalla proposizione VI in cia&shy;<lb/>scuno de'due primi trattati manoscritti intorno ai moti locali. </s>

<s>Dimostrato <lb/>infatti, come ivi si fa, che i tempi stanno come gli spazi, ne conseguiva ne&shy;<lb/>cessariamente che le velocit&agrave; fossero uguali. </s>

<s>Come unica intenzione perci&ograve; <lb/>rimaneva quella, che poco fa si diceva, e che si pone in bocca al Salviati, <pb xlink:href="020/01/2386.jpg" pagenum="11"/>di rimover cio&egrave; l'incredulit&agrave; dalla mente dei peripatetici (ivi, pag. </s>

<s>32), ar&shy;<lb/>gomentandosi di raggiunger l'intento in vari modi. </s>

<s>Uno di questi modi, e dei <lb/>non meno efficaci, ha grandissima somiglianza con quello tenuto gi&agrave; con Gui&shy;<lb/>dubaldo del Monte, per persuadergli come possa esser vero che una palla <lb/>pendula scenda, o per l'arco di un grado o per tutto un quadrante, nel me&shy;<lb/>desimo tempo: perch&egrave;, come qui le maggiori velocit&agrave; ragguagliano i tempi, <lb/>cos&igrave; l&agrave; il maggior tempo riduce le velocit&agrave; ad essere uguali. </s>

<s>Le due propo&shy;<lb/>sizioni, soggiungeva lo stesso Galileo &ldquo; non hanno seco per avventura pi&ugrave; <lb/><figure id="id.020.01.2386.1.jpg" xlink:href="020/01/2386/1.jpg"/></s></p><p type="caption">

<s>Figura 3.<lb/>inverosimilitudine di quello che si abbia <lb/>che i triangoli tra le medesime parallele <lb/>e le basi uguali sieno sempre uguali, po&shy;<lb/>tendone fare un brevissimo, e l'altro <lb/>lungo mille miglia &rdquo; (Alb. </s>

<s>VI, 22). Come <lb/>infatti &egrave; verissimo ch'essendo le basi HI, <lb/>CH (fig. </s>

<s>3) uguali, i triangoli IAH, HAC <lb/>sono uguali; cos&igrave; &egrave; vero che in D e in F, <lb/>in C e in I le velocit&agrave; sono uguali, ben&shy;<lb/>ch&egrave; i piani AI, AC siano cos&igrave; differenti, che l'uno possa essere anche mille <lb/>miglia pi&ugrave; lungo dell'altro. </s></p><p type="main">

<s>Vien confermato insomma, per queste considerazioni, che, ne'primi or&shy;<lb/>dinamenti della Dinamica galileiana, si teneva avere i cadenti da uguali al&shy;<lb/>tezze uguali velocit&agrave; come principio tanto secondario, da <lb/>sottintendersi <lb/>qual ovvia e natural conseguenza della VI proposizione nel primo, e nel secondo <lb/>trattato manoscritto dei moti locali. </s>

<s>Come poi fosse quello stesso principio <lb/>posto per fondamento all'edifizio dinamico, si disse nel precedente tomo della <lb/>nostra Storia, al capitolo VI. </s>

<s>Bandito il Teorema meccanico, da cui si con&shy;<lb/>cludeva che nelle scese da uguale altezza i tempi son proporzionali agli spazi, <lb/>quel che lasciavasi sottintender per corollario, che cio&egrave;, dove sono i tempi <lb/>proporzionali agli spazi convien che le velocit&agrave; vadano uguali, s'esalt&ograve; al grado <lb/>di proposizion principale, senza pensar di nobilitarla dalla prima sua nativa <lb/>umilt&agrave;, o di renderla cos&igrave; cospicua, che potesse sostener la nuova dignit&agrave;, a <lb/>cui veniva assunta. </s>

<s>Il proposito era stato gi&agrave; fatto, quando Galileo scrisse in <lb/>margine a quel suo foglio 88, raccolto nel secondo tomo della quinta parte <lb/>de'suoi Manoscritti: <emph type="italics"/>credo utile, si non necessarium, demonstrasse mobile <lb/>in B<emph.end type="italics"/> (nella precedente figura) <emph type="italics"/>esse eiusdem momenti quod in C.<emph.end type="italics"/> Ma o fosse <lb/>per dimenticanza, o per qualche difficolt&agrave; trovata nella dimostrazione, il prin&shy;<lb/>cipio, da cui scende nel terzo dialogo galileiano tutta la scienza del moto, si <lb/>rimase nelle umili condizioni di un semplice postulato. </s></p><p type="main">

<s>Quando venne dunque a farsi al solitario Vecchio di Arcetri la domanda <lb/>del Viviani, dov&egrave; risovvenirsi del proposito scritto, e o sentir pentimento della <lb/>dimenticanza, o mortificazione delle difficolt&agrave; incontrate nel mandarlo ad ef&shy;<lb/>fetto. </s>

<s>In qualunque modo, se l'aveva prima creduta utile, doveva ora parergli <lb/>necessaria quella dimostrazione, nella quale felicemente s'incontr&ograve; una notte <lb/>dell'Ottobre 1638, mentre dolorando vegliava in mezzo a quelle sue tenebre <pb xlink:href="020/01/2387.jpg" pagenum="12"/>luminose. </s>

<s>Ritenuto per dimostrato nel suo primo trattato <emph type="italics"/>Della scienza mec&shy;<lb/>canica<emph.end type="italics"/> il teorema del Tartaglia, e nelle prime proposizioni del suo dialogo <lb/>terzo la legge dei moti accelerati, un semplice triangolo, che si poteva senza <lb/>gran difficolt&agrave; tenere innanzi rappresentato in immagine, bast&ograve; a Galileo per <lb/>condurre cos&igrave; il discorso alla desiderata conclusione. </s></p><p type="main">

<s>Sia ABC (fig. </s>

<s>4) quel triangolo, c CB rappresenti il perpendicolo della <lb/>caduta, AC la scesa obliqua di un medesimo grave. </s>

<s>D&agrave; il Teorema mecca&shy;<lb/><figure id="id.020.01.2387.1.jpg" xlink:href="020/01/2387/1.jpg"/></s></p><p type="caption">

<s>Figura 4.<lb/>nico che il momento per CB sta al momento per AC re&shy;<lb/>ciprocamente, come AC a CB, e omologamente come CB <lb/>sta a CD, presa questa linea terza proporzionale dopo AC <lb/>e CB. </s>

<s>Ma essere i due momenti omologamente come CB <lb/>a CD non vuol dir altro se non che, presa la CB per la <lb/>misura dell'impeto in B, la misura dell'impeto in D &egrave; <lb/>CD: ci&ograve; che ci viene signifieato per l'equazione B:D= <lb/>BC:CD, chiamati B, D gl'impeti respettivi o i momenti. </s>

<s><lb/>Ma essendo per la legge dei cadenti naturali (chiamati A, D gl'impeti in A <lb/>e in D) A:D=&radic;AC:&radic;CD=&radic;AC.DC:DC, ed avendosi &radic;AC.DC=BC <lb/>per costruzione, sar&agrave; dunque A:D=BC:CD, che, confrontata con la pro&shy;<lb/>porzion precedente, d&agrave; B=A, come dovevasi dimostrare. </s></p><p type="main">

<s>Era la dimostrazione riuscita di cos&igrave; insolita facilit&agrave;, da rimanerne lo <lb/>stesso Galileo compiacentemente stupito, ma ebbero la compiacenza e lo stu&shy;<lb/>pore a crescere molto pi&ugrave;, quando, in contemplar la nuova luce apparita, la <lb/>vide intorno intorno soavemente irradiarsi di quelle verit&agrave; principali, ch'egli <lb/>era andato prima cercando per s&igrave; lunghe vie faticose. </s>

<s>Se per CB e CD, rap&shy;<lb/>presentandoci sempre innanzi l'ultima figura, gl'impeti stanno come gli spazi, <lb/>dunque i tempi sono uguali: e perch&egrave;, congiuntisi i punti B, D, la BD scende <lb/>sopr'AC perpendicolare, vien cos&igrave; dunque risoluto il problema: trovare nel <lb/>perpendicolo e nell'obliqua gli spazi, che sarebbero in tempi uguali passati <lb/>da due mobili uguali, nel medesimo punto partitisi dalla quiete. </s>

<s>Potendosi <lb/>poi sempre intorno al triangolo rettangolo CBD circoscrivere un semicerchio, <lb/>che abbia la met&agrave; dell'ipotenusa BC per raggio, dunque la corda DC &egrave; iso&shy;<lb/>crona al diametro. </s>

<s>Questo mirabile isocronismo, con si inaspettata facilit&agrave; con&shy;<lb/>cluso, veniva di pi&ugrave; a farsi ala per condurre agile la proposizione III del <lb/>III dialogo, che, portata gi&agrave; come grave pietra fondamentale dell'edifizio, era <lb/>costata a Galileo tante ambagi e tanti sudori. </s>

<s>&Egrave;, per la legge dei moti acce&shy;<lb/>lerati, To.AC:To.DC=&radic;AC:&radic;DC=AC:&radic;AC.DC. </s>

<s>Ma &radic;AC.DC= <lb/>BC e To.DC=To.BC, resta dunque concluso To.AC:To.BC=AC:BC, <lb/>come per legittima conseguenza dell'essere, nel cadente e nell'obliqua, le ve&shy;<lb/>locit&agrave; sempre uguali. </s></p><p type="main">

<s>Se fossero state cos&igrave; riformate tutte le proposizioni, il trattato Dei moti <lb/>locali nel terzo dialogo galileiano vinceva di facilit&agrave; e d'eleganza quel ma&shy;<lb/>raviglioso inarrivabile trattato del Torricelli, ma essendo Galileo costretto dalla <lb/>vecchiezza e dalla cecit&agrave; a rimanersi intorno a ci&ograve; in sterili desiderii con&shy;<lb/>templativi, ebbe a chiamarsi contento di aver finalmente potuto mettere ad <pb xlink:href="020/01/2388.jpg" pagenum="13"/>effetto un proposito antico, e di aver sodisfatto al Viviani, e a tutti gli altri, <lb/>che fossero studiando venuti ne'medesimi dubbi di lui. </s></p><p type="main">

<s>Un altro giovane era allora in Firenze, che, se cedeva al Viviani nel&shy;<lb/>l'acutezza matematica dell'ingegno e nell'ardor degli studii, lo superava di <lb/>gran lunga per lo splendor dei natali. </s>

<s>Il principe Leopoldo dei Medici veniva <lb/>istruito nelle Matematiche, e in particolare nell'Algebra, secondo che Galileo <lb/>diceva quasi scherzando (Alb. </s>

<s>VII, 212), dall'aulico don Famiano Michelini, <lb/>il quale, appena sparsasi la nuova della ritrovata dimostrazione, cos&igrave; da Siena <lb/>scriveva il di 6 Novembre 1638, in una sua lettera indirizzata ad Arcetri: </s></p><p type="main">

<s>&ldquo; Il serenissimo signor principe Leopoldo mio signore mi ha comandato <lb/>scrivere a V. S. che S. A. S. desidera la dimostrazione nuovamente da lei <lb/>ritrovata, che, dei gravi sopra diversi piani inclinati, mentre abbino la me&shy;<lb/>desima elevazione sopra il piano orizontale, le velocit&agrave; acquistate siano uguali <lb/>sopra il detto piano orizontale: poich&egrave; S. A. ha difficolt&agrave; in ammetter per <lb/>noto l'assunto, che ella suppone nel bellissimo suo libro del moto. </s>

<s>Il Sere&shy;<lb/>nissimo ha di gi&agrave; visti i sei libri di Euclide, e di presente vede l'undecimo, <lb/>e il detto libro Del moto, col pensiero di veder prima le opere di V. S. Ecc.ma, <lb/>e poi il resto dei Matematici..... Il latore della presente &egrave; un vetturale di <lb/>palazzo, al quale S. A. desidera che V. S. dia la dimostrazione suddetta, perch&egrave; <lb/>senz'essa le pare di andare al buio, ancorch&egrave; quelle esperienze ch'ella pone nel <lb/>libro sieno poco meno che dimostrazione &rdquo; (MSS. Gal., P. VI, T. XIII, fol. </s>

<s>112). </s></p><p type="main">

<s>Ventitre giorni dopo lo stesso Michelini ringraziava Galileo, per essersi <lb/>compiaciuto d'inviargli la dimostrazione &ldquo; circa l'uguaglianza delle velocit&agrave; <lb/>dei mobili di uguale elevazione, quando siano arrivati per qualunque incli&shy;<lb/>nazione al piano orizontale &rdquo; (Alb. </s>

<s>X, 316, 17), soggiungendo che si trovava <lb/>allora, per un fiero dolor di testa, cos&igrave; ottuso l'ingegno, da disperar di sco&shy;<lb/>prire la verit&agrave; o la falsit&agrave; delle cose dimostrate. </s>

<s>Forse la difficolt&agrave; dipendeva <lb/>in gran parte dall'aver dovuto Galileo dettare a qualcuno poco pratico di <lb/>quelle materie, e compendiare con qualche scapito della chiarezza quel suo <lb/>sottile discorso, che poi disse il Michelini di avere inteso, e di averlo trovato <lb/>concludere il vero. </s>

<s>&ldquo; La difficolt&agrave;, soggiungeva, tornando a scrivere il di 11 di <lb/>Dicembre al medesimo Galileo, proveniva dal mio poco giudizio, e dallo stare <lb/>pi&ugrave; applicato al ritrovamento della mia, che al penetrar la sua bellissima di&shy;<lb/>mostrazione &rdquo; (ivi, pag. </s>

<s>321). </s></p><p type="main">

<s>Il Michelini dunque attendeva a ritrovar del supposto galileiano una dimo&shy;<lb/>strazione sua propria, ingegnandosi, com'egli dice, di persuadere altrui &ldquo; che in <lb/>tempi uguali li spazi passati dal moto accelerato stiano come gl'impeti &rdquo; (ivi). <lb/>E bench'egli stesso soggiunga esser questa una bagattella, che ogni bambino <lb/>la saprebbe dimostrare, e confessi che il discorso tornava a quel medesimo <lb/>di Galileo, poco avendoci del suo; nonostante &egrave; notabile la variet&agrave; del pro&shy;<lb/>cesso. </s>

<s>Anch'egli, il Michelini, poneva il Teorema meccanico per principio, ma <lb/>nel servirsi del mezzo differiva dai modi tenuti da Galileo, perch&egrave;, mentre <lb/>questi direttamente dimostrava che gl'impeti in B e in D, secondo l'ultima <lb/>figura, stanno come le linee CB, CD, egli invece s'ingegnava di persuadere <pb xlink:href="020/01/2389.jpg" pagenum="14"/>il medesimo dall'esser per quelle stesse linee i tempi uguali. </s>

<s>Quali per&ograve; si <lb/>fossero di una tale persuasion le ragioni non si rileva chiaro dalla citata let&shy;<lb/>tera del Michelini. </s>

<s>Ma dicendovi essere unico suo assunto &ldquo; che gl'impeti <lb/>stieno in reciproca proporzione degli spazi, nei diversi piani inclinati &rdquo; (ivi, <lb/>pag. </s>

<s>321) si pu&ograve; credere che ragionasse cos&igrave;, come, indipendentemente dai <lb/>teoremi dimostrati nelle nuove Scienze, dice di aver fatto gi&agrave; il Beriguardo. </s>

<s><lb/>Supposto che nel solito triangolo il lato AC sia triplo di CB, &ldquo; quando glo&shy;<lb/>bus (si legge nel VI dei <emph type="italics"/>Circoli pisani,<emph.end type="italics"/> parte III) saliens ex C pervenerit <lb/>ad D, aut aliud punctum lateris inclinati praedicti utlibet, si quis velit assi&shy;<lb/>gnare punctum in latere BC, producto similiter, ad quod aequali tempore <lb/>perveniret idem globus, aut alter aequalis, si demittatur simul ex puncto C <lb/>per latus CB; si quis inquam hoc velit, sumatur in latere CB punctum tri&shy;<lb/>plo magis distans a puncto C, quam punctum D distet ab ipso C, sitque <lb/>puntum illud B: nam quando globus ex C pervenerit ad D, idem aut ae&shy;<lb/>qualis ex C perveniet ad B aequali tempore &rdquo; (Patavii 1660, pag. </s>

<s>310). </s></p><p type="main">

<s>Il modo poi facile di ritrovar il punto B prosegue a dire esser quello <lb/>d'alzar sopra AC in D una perpendicolare, la quale venga a descrivere il <lb/>triangolo DCB, ch'essendo simile ad ACB dar&agrave;, per la somiglianza, che BC <lb/>&egrave; media fra le AC e DC. </s>

<s>Dimostratosi dunque anche dal Michelini, al modo <lb/>sopra detto o in altro simile, che i tempi per CB e per CD sono uguali, ne <lb/>concludeva che gl'impeti in B e in D stanno come gli spazi, e dietro l'ap&shy;<lb/>plicazion della legge dei moti accelerati, e l'invenzione della DC, terza pro&shy;<lb/>porzionale dopo AC, CB, riusciva a dimostrar finalmente, con i medesimi <lb/>processi di Galileo, che anche gl'impeti in A e in B sono uguali. </s></p><p type="main">

<s>Sembra che la dimostrazione fosse dal padre Settimii letta a Galileo, il <lb/>quale la lod&ograve; molto (Alb. </s>

<s>X, 327), specialmente per quel suo modo tenuto <lb/>in dimostrare che la CD e la CB erano passate dal mobile nel medesimo <lb/>tempo. </s>

<s>Salendo pochi giorni dopo quel medesimo Settimii ad Arcetri, portava <lb/>seco, da consegnarsi a Galileo, un libro, e una lettera del Baliani. </s>

<s>Era quella <lb/>lettera scritta da Genova il di 17 Dicembre 1638, per accompagnare il detto <lb/>libro, ch'era quello <emph type="italics"/>De motu naturali,<emph.end type="italics"/> pregando lui, a cui veniva presen&shy;<lb/>tato, a leggerlo per favore, e a volergliene dire il suo parere. </s>

<s>Se sar&agrave; Galileo <lb/>stato ad ascoltare quella lettura, specialmente alla VII proposizione, si sar&agrave; <lb/>dovuto maravigliare che l'Autor di lei e il Michelini si fossero cos&igrave; incon&shy;<lb/>trati nel medesimo modo di dimostrar che la linea, condotto da un punto <lb/>della verticale perpendicolarmente sull'inclinata, prefinisce qui come l&agrave; due <lb/>spazii, che son passati dal mobile nei medesimi tempi. </s></p><p type="main">

<s>Comunque sia, Galileo mandava per contraccambio a Genova i suoi dia&shy;<lb/>loghi Del moto, accompagnandoli con lettera del di 20 Giugno 1639 al Ba&shy;<lb/>liani, il quale rispondeva il d&igrave; primo Luglio appresso, dicendo che, sebbene <lb/>non avesse avuto per leggere e per intender le cose scritte nel libro n&egrave; il <lb/>tempo necessario, n&egrave; l'ozio, nonostante, mentr'egli in generale ammirava la <lb/>bell<gap/>zza e la bont&agrave; delle dottrine, avrebbe pure avuto a notarvi qualche cosa, <lb/>particolarmente quanto ai supposti fatti al fol. </s>

<s>166, i quali, consentendo in <pb xlink:href="020/01/2390.jpg" pagenum="15"/>ci&ograve; col Viviani e col Michelini, scriveva &ldquo; io li tengo verissimi, ma dubito <lb/>che vi sia tanta evidenza, quanto par che sia necessario nei principii &rdquo; (ivi, <lb/>pag. </s>

<s>354). A sodisfare ai quali dubbi vennero presto le seguenti parole, scritte <lb/>in una lettera del di primo Agosto da Arcetri: </s></p><p type="main">

<s>&ldquo; Che poi il principio che io suppongo, come V. S. nota, a facce 166, <lb/>non le paia di quella evidenza che si ricercherebbe nei principii da supporsi <lb/>come noti, glielo voglio concedere per ora, ancorch&egrave; Ella medesima faccia la <lb/>stessa supposizione, cio&egrave; che i gradi di velocit&agrave;, acquistati sopra l'orizzonte <lb/>da mobili discendenti per diversi piani della medesima altezza, siano uguali. </s>

<s><lb/>Ora sappia V. S. Ill.ma che, dopo aver perso la vista, e per conseguenza la <lb/>facolt&agrave; di potere andare internando in pi&ugrave; profonde proposizioni e dimostra&shy;<lb/>zioni, mi sono andato nelle tenebre notturne occupando intorno alle prime <lb/>e pi&ugrave; semplici proposizioni, riordinandole e disponendole in miglior forma ed <lb/>evidenza, tra le quali mi &egrave; occorso di dimostrare il sopraddetto principio, nel <lb/>modo che a suo tempo Ella vedr&agrave;, se mi succeder&agrave; di avere tanto di forza, <lb/>che io possa migliorare ed ampliare lo scritto e pubblicato da me sin qui in&shy;<lb/>torno al moto, con aggiungervi altre speculazioncelle, ed in particolare quelle <lb/>attinenti alla forza della percossa, nell'investigazion della quale ho consumato <lb/>molte centinaia e migliaia di ore, e finalmente ridottala ad assai facile espli&shy;<lb/>cazione, sicch&egrave; altri, in manco di mezz'ora di tempo, pu&ograve; restarne capace &rdquo; <lb/>(Lettere pel trecent. </s>

<s>natal. </s>

<s>cit., pag. </s>

<s>45, 46). </s></p><p type="main">

<s>Ricevuta cos&igrave; la notizia della dimostrazion del principio, che Galileo aveva <lb/>prima semplicemente supposto come vero, il Baliani, inclinatissimo a specu&shy;<lb/>lare intorno alla verit&agrave; delle cose (Alb. </s>

<s>X, 369), piuttosto che aspettar l'al&shy;<lb/>trui, am&ograve; meglio di tentare la propria fortuna, la quale pareva arridergli gi&agrave;, <lb/>avendolo fatto incontrare in quella settima proposizione, dalla quale Galileo <lb/>e il Michelini avevano cos&igrave; facilmente concluse le loro dimostrazioni. </s>

<s>Quella VII <lb/><emph type="italics"/>De motu naturali<emph.end type="italics"/> era ivi infatti messa in questa forma, com'a pag. </s>

<s>34 dello <lb/>stesso trattato, che pi&ugrave; ampiamente l'Autore condusse nel 1646: &ldquo; Data linea <lb/>perpendiculari, per quam grave descendat, cui annectatur linea, seu planum <lb/>declinans; in declinante reperire punctum, quo grave perveniat eo tempore, <lb/>quo pertransiverit perpendicularem. </s>

<s>&rdquo; </s></p><p type="main">

<s>Rappresentando BC quella perpendicolare e AC l'inclinata, come nella <lb/>figura ultimamente qui addietro posta, si risolve il problema, conducendo la <lb/>BD normale ad AC, d'onde, come da Galileo si conclude che le velocit&agrave; in B <lb/>e in D son proporzionali agli spazi, e, come dal Michelini, che le CB, CD <lb/>son passate dal mobile nei medesimi tempi. </s>

<s>Ma aveva il Baliani prevenuto <lb/>altres&igrave; Galileo in una cosa ben'assai pi&ugrave; importante, in servirsi cio&egrave; del co&shy;<lb/>rollario che le CB, CD sono isocrone insieme per lemma, a dimostrar la pro&shy;<lb/>posizione sua XV, ivi a pag. </s>

<s>36 cos&igrave; formulata: &ldquo; Si duo gravia descendunt, <lb/>alterum quidem perpendiculariter, alterum vero super plano declinante, per&shy;<lb/>veniunt ad idem planum orizontale tali ratione, ut sit eadem proportio inter <lb/>diuturnitates eorum, quae inter perpendicularem et declinantem. </s>

<s>&rdquo; Ha la <lb/>dimostrazione aria di novit&agrave;, e tutt'insieme di eleganza, perch&egrave;, essendo <pb xlink:href="020/01/2391.jpg" pagenum="16"/>per la legge dei moti accelerati, ritenuta la medesima figura, DC:AC= <lb/>To.DC2:To.AC2=To.BC2:To.AC2, in virt&ugrave; del precedente Lemma, e <lb/>per la similitudine de'triangoli ABC, CDB essendo CD:AC=CB2:AC2, <lb/>immediatamente se ne conclude CB2:AC2=To.CB2:To.AC2, e per&ograve; an&shy;<lb/>che i semplici spazi staranno, secondo il proposito, come i semplici tempi. </s></p><p type="main">

<s>Ripensando Galileo fra s&egrave;, in farsi leggere il trattatello del Baliani, a <lb/>queste conclusioni, avr&agrave; dovuto maravigliarsi di trovar che altri avevan gi&agrave; <lb/>penetrato quel che solitario era ito speculando in mezzo alle tenebre. </s>

<s>Non <lb/>si vedeva per&ograve; in quelle dimostrazioni concluso l'intento principale, perch&egrave; <lb/>il Baliani relegava in settimo luogo tra i postulati anche questo: &ldquo; ductis pla&shy;<lb/>nis inclinatis et linea perpendiculari inter lineas parallelas orizontales, gravia <lb/>super illis mota, ubi perveniunt ad parallelam inferiorem, habent aequales <lb/>velocitatis gradus, et proinde, si ab inde infra sortiantur parem inclinationem, <lb/>aequivelociter moventur. </s>

<s>&rdquo; Ei riteneva come Galileo la cosa probabile, s&igrave; per <lb/>l'esperienza dei pendoli, <emph type="italics"/>quae quamtumvis longiora aut breviora, et proinde <lb/>circa finem magis aut minus inclinata, pariter ascendunt si pariter de&shy;<lb/>scendant;<emph.end type="italics"/> e s&igrave; per l'esempio dell'acqua, la quale, essendo per sifoni retti o <lb/>inclinati in qualunque modo condotta, <emph type="italics"/>videmus pariter ascendere, si pariter <lb/>descendat.<emph.end type="italics"/> Ma pi&ugrave; che in questi fatti fisici s'affidava il Baliani della verit&agrave; <lb/>del suo postulato in veder ch'egli aveva una dipendenza immediata dalla pro&shy;<lb/>posizione sua XV, <emph type="italics"/>quia, si diuturnitates sunt longitudinibus proportionales, <lb/>credibile est motus in fine esse aequales.<emph.end type="italics"/></s></p><p type="main">

<s>Si vede bene insomma che, a raggiunger l'intento principale, mancava <lb/>a fare al Baliani un passo solo, tentando, per non avere a invidiare quella <lb/>di Galileo, la sua propria fortuna, che felicemente gli riusc&igrave; in questo modo. </s>

<s><lb/>Riferendosi sempre all'ultima impressa figura, &egrave; dimostrato T.oCB:T.oAC= <lb/>CB:AC. </s>

<s>Ma per la legge dei moti accelerati gli spazi stanno come i quadrati <lb/>dei tempi, o come i rettangoli delle velocit&agrave; e dei tempi; dunque, significandosi <lb/>con V.a la velocit&agrave;, come con T.o si significa il tempo, sar&agrave; T.oCB:T.oAC= <lb/>T.oCB.V.aCB:T.oAC.V.aAC, e perci&ograve; V.aCB=V.aAC. </s></p><p type="main">

<s>Quel ch'era dunque prima supposto nell'operetta <emph type="italics"/>De motu naturali,<emph.end type="italics"/> o <lb/>come sempliccmente probabile ritenuto, ottenne in tal guisa la sua matematica <lb/>dimostrazione, la quale il Baliani, occorrendogli di far ristampare un foglio per <lb/>un errore trascorso, fece inserir nel volume, revocando quelle poche copie gi&agrave; <lb/>uscite, e non approvando che le altre cos&igrave; corrette. </s>

<s>Volle una di queste mandar <lb/>subito a Galileo, accompagnandogliela con una lettera del d&igrave; 16 Settembre 1639, <lb/>nella quale, dop'altre in proposito, soggiungeva queste parole: &ldquo; Ho avuto <lb/>per bene di mandarle una copia di detta mia operetta cos&igrave; racconcia, pre&shy;<lb/>gandola che la faccia degna di star in un canto della sua libreria, con strac&shy;<lb/>ciar l'altra che le mandai prima, che non vorrei che ci stesse in alcun modo. </s>

<s><lb/>Io credo che sia buona dimostrazione, supposto per principio che la propor&shy;<lb/>zione degli spazi si compone della proporzione dei tempi e delle velocit&agrave;, e ne <lb/>ho fatta una giunta alla dimostrazione del settimo postulato &rdquo; (Alb. </s>

<s>X, 369). </s></p><p type="main">

<s>Cos&igrave;, infin dal Settembre del 1639, dava il Baliani al pubblico la sua <pb xlink:href="020/01/2392.jpg" pagenum="17"/>Dinamica confermata gi&agrave; sul suo pi&ugrave; stabile fondamento, mentre Galileo, con <lb/>speranza assai pi&ugrave; lunga di quel che l'infermit&agrave; e la vecchiezza gli avreb&shy;<lb/>bero dato per misura, aspettava il tempo e l'occasione di una ristampa dei <lb/>Dialoghi, ch'egli attendeva a correggere e ampliare. </s>

<s>Intanto, essendogli il <lb/>Viviani di frequente visitatore divenuto ospite permanente, volle facesse il <lb/>disteso della dimostrazione, che finalmente gli sort&igrave; d'incontrare, di che <lb/>mand&ograve; subito copia al Castelli, accompagnandola con una lettera del d&igrave; 3 Di&shy;<lb/>cembre 1639, nella quale, dop'essersi compiaciuto dell'invenzione cos&igrave; sog&shy;<lb/>giungeva: &ldquo; &Egrave; scritta in dialogo, come sovvenuta al Salviati, acci&ograve; si possa, <lb/>quando mai si stampassero di nuovo i miei Discorsi e dimostrazioni, inse&shy;<lb/>rirla immediatamente dopo lo scolio della seconda proposizione del suddetto <lb/>trattato, come teorema essenzialissimo allo stabilimento delle Scienze del moto <lb/>da me promosse &rdquo; (Alb. </s>

<s>VII, 238, 39). </s></p><p type="main">

<s>I Dialoghi si stamparono insieme con le altre opere in Bologna, dove il <lb/>disteso, da diciassett'anni gi&agrave; preparato, apparve postumo, facendosi il Vi&shy;<lb/>viani geloso esecutore testamentario delle ultime volont&agrave; del suo Maestro. </s>

<s><lb/>L'edizion bolognese era diretta da Carlo Rinaldini, e si faceva stampando a <lb/>parte via via i trattati, ch'erano prima venuti a mano, e raccogliendoli poi <lb/>insieme in due volumi. </s>

<s>Il primo era nel 1655 gi&agrave; pronto, e l'anno dopo si <lb/>mand&ograve; fuori il secondo, dove in ultimo si raccoglievano i Discorsi e le dimo&shy;<lb/>strazioni intorno alle due nuove Scienze del moto. </s>

<s>Il Viviani stesso in pro&shy;<lb/>posito di scrivere in una sua lettera al Rinaldini, <emph type="italics"/>della nuova impressione <lb/>delle dette Opere, promossa ed ultimata per mezzo solo di V. S. E.,<emph.end type="italics"/> sog&shy;<lb/>giungeva: &ldquo; Vi &egrave; ancora quella dimostrazione del principio supposto, che pone <lb/>il signor Galileo avanti alla Scienza del moto accelerato, ed a quella maniera <lb/>che fu distesa da me di suo ordine, in tempo ch'io mi trovavo appresso di <lb/>lui, che fu poco dopo ch'ei la ritrov&ograve;, quando gi&agrave; era composto il suddetto <lb/>libro Del moto, ed &egrave; l'istessa che si mand&ograve; fuori a diversi amici dal mede&shy;<lb/>simo signor Galileo &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXLII, fol. </s>

<s>3). </s></p><p type="main">

<s>Che veramente dopo il Castelli fosse stata mandata la dimostrazione a <lb/>diversi amici in Italia e fuori ci vien confermato dai documenti, ed era il <lb/>medesimo Viviani che ricopiava e spediva, sotto gli ordini di Galileo, questa <lb/>specie di circolari. </s>

<s>Erano per&ograve;, per maggior brevit&agrave; e per essere inutili allo <lb/>scopo, tralasciate le parti, che dovevano servir per le attaccature e per le <lb/>articolazioni del dialogo, rimanendo la nuda dimostrazione in discorso disteso. </s>

<s><lb/>L'original forma di cos&igrave; fatta scrittura circolare s'ha da carte 11-13 del <lb/>tomo IV, parte V, dei Manoscritti di Galileo, non con molta propriet&agrave; dal Vi&shy;<lb/>viani stesso intitolata <emph type="italics"/>Dimostrazione trovata dal gran Galileo l'anno 1639,<emph.end type="italics"/><lb/>perch&egrave;, sebben fosse messa in forma in quest'anno, l'invenzion nonostante, <lb/>com'apparisce dalle cose narrate, risale all'anno precedente. </s>

<s>Sembrerebbe <lb/>fosse questo il luogo opportuno di rendere alla notizia dei nostri Lettori nella <lb/>sua propria forma questo discorso, ma ei ce la esibir&agrave; fra poco in fedel copia <lb/>uno di coloro, a cui fu mandato, collega e amico a quel Torricelli, ch'&egrave; per <lb/>aver gran parte in questo episodio della storia della Meccanica. </s></p><pb xlink:href="020/01/2393.jpg" pagenum="18"/><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Mentre Galileo, come albero annoso, rimaneva sopra il colle di Arcetri <lb/>solitario, un rampollo di lui, Benedetto Castelli, spandeva in Roma i rami <lb/>rigogliosi, sotto l'ombra de'quali si raccoglievano a filosofare Evangelista <lb/>Torricelli, Raffaello Magiotti, Antonio Nardi e Michelangiolo Ricci. </s>

<s>Prediletto <lb/>argomento a quei filosofici discorsi si porgeva dalla lettura dei nuovi dialo&shy;<lb/>ghi Del moto, e incontr&ograve; specialmente al Torricelli quel ch'era in Firenze <lb/>incontrato al Viviani, di mettere cio&egrave; dubbio intorno alla evidenza dell'as&shy;<lb/>sunto di Galileo. </s>

<s>Entrato pi&ugrave; addentro alle dimostrazioni di lui, gli parve che <lb/>l'andare i mobili per varie obliquit&agrave; di scesa ugualmente veloci, dopo cadute <lb/>uguali, fosse una verit&agrave; da non doversi semplicemente supporre, ma da po&shy;<lb/>tersi con facilit&agrave; dimostrare. </s>

<s>Del modo poi volle farne alcun cenno al Ricci, <lb/>a cui bast&ograve; per condurre una dimostrazione ch'ei confer&igrave; col Magiotti, ral&shy;<lb/>legrandosi di vederla tale quale specchiata nelle Opere stampate dello stesso <lb/>Torricelli, a cui, sulla fin del Settembre 1644, scriveva queste parole: &ldquo; Mi <lb/>son rallegrato di trovarvi sopra sette o otto proposizioni, con le sue dimo&shy;<lb/>strazioni per l'appunto, come le avevo pensate io, ed in particolare la prova <lb/>di quella supposizione fatta dal Galileo ne'libri Del moto la conferii al signor <lb/>Magiotti due o tre anni sono, avendola rintracciata con quel lume, che ebbi <lb/>da V. S. &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>52). </s></p><p type="main">

<s>Posto cos&igrave; dunque il fondamento, vi and&ograve; il Torricelli sopra edificando, <lb/>e riusc&igrave; a dimostrare molte proposizioni <emph type="italics"/>De motu<emph.end type="italics"/> in diverso modo, pi&ugrave; fa&shy;<lb/>cile e pi&ugrave; elegante di quello stesso tenuto da Galileo, componendone un nuovo <lb/>trattato. </s>

<s>Il Castelli in leggerlo n'ebbe a stupire, e scrivendo da Roma il di <lb/>2 Marzo 1641 ad Arcetri avvisava il suo vecchio Maestro che, venendo pre&shy;<lb/>sto a Firenze per riverirlo, gli avrebbe portato un libro fatto da un suo di&shy;<lb/>scepolo, il quale, avendo avuti i primi principii di geometria dieci anni fa <lb/>alla sua scuola, aveva poi fatto tal progresso da mostrar quanto fossero fe&shy;<lb/>condi i germi, nei nuovi Dialoghi seminati in materia del moto (Alb. </s>

<s>X, 408). <lb/>Dopo tredici giorni infatti, salito una mattina il Castelli ad Arcetri, entrava <lb/>nella camera, dove giacevasi Galileo, presentandogli un volume manoscritto, <lb/>con una lettera che l'accompagnava. </s>

<s>Scusavasi quivi l'Autore di avere scritti <lb/>que'fogli <emph type="italics"/>De motu gravium naturaliter descendentium et proiectorum<emph.end type="italics"/> &ldquo; non <lb/>per bisogno che io giudicassi averne le sue dottrine, ma per necessit&agrave; che aveva <lb/>io di formar questo memoriale di erudizione alla mia poca intelligenza, e pel <lb/>desiderio che teneva di mostrare al mio Maestro lontano come, anco in as&shy;<lb/>senza, aveva propagato con qualche studio mio la sua disciplina &rdquo; (ivi, pag. </s>

<s>412). </s></p><p type="main">

<s>Nell'ascoltare il processo tenuto dal Torricelli nelle prime cinque propo&shy;<lb/>posizioni del primo libro, per concluder quello, che due anni fa era andato <lb/>fra le tenebre cos&igrave; affannosamente cercando; Galileo non ebbe a stupir meno <pb xlink:href="020/01/2394.jpg" pagenum="19"/>degli altri. </s>

<s>Di questi suoi sensi fatte scrivere le espressioni in una letttera <lb/>andata smarrita, tornava il d&igrave; 27 Settembre di quel medesimo anno 1641 a <lb/>dire al Torricelli la grande stima, che faceva de'suoi trovati e delle sue con&shy;<lb/>clusioni, riserbandosi a trattarne poi seco a bocca i particolari. </s>

<s>&ldquo; Mando que&shy;<lb/>sta, cos&igrave; terminava la lettera, sotto una del signor Nardi, dal quale ella la <lb/>ricever&agrave;, insieme colla dimostrazione di quello che io supponeva nell'ultimo <lb/>mio dialogo come principio conceduto. </s>

<s>Vedanla insieme e l'emendino, comu&shy;<lb/>nicandola anche al terzo mio riverito padrone il signor Magiotti, ed a tutto <lb/>il triumvirato con reverente affetto bacio le mani &rdquo; (Alb. </s>

<s>VII, 367). </s></p><p type="main">

<s>Il Nardi ci conserv&ograve; la scrittura avuta da Galileo, inserendola nella <lb/>IX veduta della seconda scena col titolo: <emph type="italics"/>D'un principio meccanico del Ga&shy;<lb/>lileo,<emph.end type="italics"/> e con questo motto per semplice introduzione: &ldquo; Cos&igrave; scrivevami sopra <lb/>tal materia il mio maestro Galilei: &rdquo; </s></p><p type="main">

<s>&ldquo; I gravi scendenti dalla medesima sublimit&agrave; sopra l'orizonte avere <lb/>acquistati uguali gradi di velocit&agrave; (proposizione da me sin qui supposta, e <lb/>solo con esperienze e probabili discorsi confermata) potremo nel seguente <lb/>modo dimostrativamente provare, pigliando com'effetto notissimo le velocit&agrave; <lb/>dello stesso mobile esser diverse sopra diverse inclinazioni, e la massima <lb/>essere per la linea perpendicolarmente sopra l'orizonte elevata, e per le altre <lb/>inclinate diminuirsi tal velocit&agrave;, secondo che pi&ugrave; dal perpendicolo si disco&shy;<lb/>stano, cio&egrave; pi&ugrave; obliquamente s'inclinano, dal che si scorge che l'impeto, il <lb/>momento, l'energia, o vogliam dire il talento del discendere, viene determi&shy;<lb/>nato nel mobile dal suggetto piano, sopra il quale s'appoggia e discende. </s>

<s>&rdquo; <lb/><figure id="id.020.01.2394.1.jpg" xlink:href="020/01/2394/1.jpg"/></s></p><p type="caption">

<s>Figura 5.</s></p><p type="main">

<s>&ldquo; E per meglio dichiararmi, <lb/>intendasi AB (fig. </s>

<s>5) perpendicolar&shy;<lb/>mente eretta sopra l'orizonte AC: <lb/>pongasi poi la medesima in diverse <lb/>inclinazioni verso l'orizonte, pie&shy;<lb/>gata come in AD, AE, AF, ecc., <lb/>dico che l'impeto massimo e totale <lb/>del grave per discendere &egrave; nella <lb/>perpendicolare BA, minore nella <lb/>AD, minore ancora nella EA, e <lb/>successivamente andarsi diminuendo nella FA, e finalmente esser del tutto <lb/>estinto nella orizontale CA, dove il mobile non ha per s&egrave; stesso inclinazione <lb/>alcuna, n&egrave; in conseguenza resistenza all'esservi mosso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Appresa questa mutazione d'impeto, mi fa mestieri ritrovare e dimo&shy;<lb/>strare con qual proporzione ella si faccia, come per esempio nel piano incli&shy;<lb/>nato AF. </s>

<s>Tirisi la sua elevazione sopra l'orizonte AC, cio&egrave; la linea FC, per <lb/>la quale l'impeto ed il momento del discendere &egrave; il massimo: cercasi qual <lb/>proporzione abbia ad esso l'impeto per l'inclinata FA. &Egrave; manifesto tanto <lb/>essere questo impeto e talento del discendere quanta &egrave; la resistenza o forza <lb/>minima, che basta per proibirlo e fermarlo. </s>

<s>Per tal forza e resistenza e sua <lb/>misura mi voglio servire della gravit&agrave; di un altro mobile grave. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2395.jpg" pagenum="20"/><p type="main">

<s>&ldquo; Intendasi sopra il piano FA posare il mobile G, il quale venga rite&shy;<lb/>nuto col filo che, cavalcando sopra FC, pendendo a perpendicolo, abbia at&shy;<lb/>taccato un peso H, il quale, gravando a perpendicolo, proibisca al G lo scen&shy;<lb/>dere per la inclinata FA. </s>

<s>Riducendosi a memoria quello che si dimostra in <lb/>tutti i casi dei movimenti meccanici, che cio&egrave; la velocit&agrave; del moto d'un mo&shy;<lb/>bile men grave compensa con reciproca proporzione della gravit&agrave; la minor <lb/>velocit&agrave; dell'altro mobile pi&ugrave; grave, che &egrave; quanto a dire che gli spazi pas&shy;<lb/>sati nell'istesso tempo abbiano reciproca proporzione della gravit&agrave;; conside&shy;<lb/>riamo che lo spazio della scesa a perpendicolo del grave H &egrave; bene uguale a <lb/>tutta la salita del mobile G per l'inclinata AF, ma non gi&agrave; per la salita a <lb/>perpendicolo, nella quale esso G esercita la sua resistenza, il che &egrave; manife&shy;<lb/>sto, imperocch&egrave;, considerando nel triangolo AFC il moto da A in F esser <lb/>composto del trasversale orizontale AC, e del perpendicolare CF, ed essendo <lb/>che, quanto all'orizontale, nessuna &egrave; la resistenza del mobile, resta la resi&shy;<lb/>stenza esser solamente rispetto alla perpendicolare CF. </s>

<s>Mentre che dunque <lb/>il mobile G, movendosi da A in F, resiste solo nel salire lo spazio perpen&shy;<lb/>dicolare CF, ma che l'altro grave scende a perpendicolo quanto &egrave; tutto lo <lb/>spazio FH, possiamo molto ragionevolmente af<gap/>ermare le velocit&agrave; o gli spazi <lb/>passati nel medesimo tempo da tali mobili dover rispondere reciprocamente <lb/>alle loro gravit&agrave;, e baster&agrave; per impedire la scesa del G che l'H sia tanto <lb/>men grave di quello, quanto lo spazio CF &egrave; minore della inclinata FA. </s>

<s>E per&shy;<lb/>ch&egrave; siamo convenuti che tanto sia l'impeto, l'energia, il momento ed il ta&shy;<lb/>lento del mobile al moto, quanta &egrave; la forza e resistenza che basta a fermarlo, <lb/>concludiamo dunque, come si &egrave; detto, l'impeto per l'inclinata, all'impeto <lb/>massimo per la perpendicolare, stare com'essa perpendicolare, cio&egrave; l'eleva&shy;<lb/>zione della inclinata, alla medesima inclinata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Stabilito ci&ograve;, e posto che il mobile grave, partendosi dalla quiete e <lb/>naturalmente scendendo, vada con eguali giunte accrescendo la sua velocit&agrave;, <lb/>onde, come quindi dimostro, gli spazi passati sono in duplicata proporzione <lb/>dei tempi, ed in conseguenza dei gradi di velocit&agrave;, la quale, come abbiamo <lb/>detto, cresce con la proporzione del tempo; dimostreremo la nostra conclu&shy;<lb/>sione, cio&egrave; i gradi di velocit&agrave; nell'orizonte essere eguali: quelli cio&egrave; acqui&shy;<lb/>stati dal mobile, che dalla quiete si parta da qualsivoglia altezza, e per quali <lb/>si siano inclinazioni pervenga all'orizonte. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E qui devesi avvertire che, stabilito che in qualsivogliano inclinazioni <lb/>il mobile dalla partita dalla quiete vada crescendo la velocit&agrave; con la propor&shy;<lb/><figure id="id.020.01.2395.1.jpg" xlink:href="020/01/2395/1.jpg"/></s></p><p type="caption">

<s>Figura 6.<lb/>zione del tempo, sia qualsivoglia l'inclinazione e in con&shy;<lb/>seguenza la quantit&agrave; dell'impeto; quali furono gl'impeti <lb/>nella prima mossa, tali saranno i gradi della velocit&agrave; gua&shy;<lb/>dagnata nello stesso tempo, poich&egrave; e questi e quelli cre&shy;<lb/>scono con la medesima proporzione, che cresce il tempo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora sia il piano inclinato AC (fig. </s>

<s>6) elevato sopra <lb/>l'orizonte, la perpendicalare CB e la orizontale AB. </s>

<s>E <lb/>poich&egrave; l'impeto per la perpendicolare CB, all'impeto per <pb xlink:href="020/01/2396.jpg" pagenum="21"/>l'inclinata AC, sta come CB ad AC, prendasi nella AC la CD, terza propor&shy;<lb/>zionale della AC, CB: l'impeto dunque per CB, all'impeto per AC, sta come <lb/>la CB alla CD. </s>

<s>Il mobile dunque, nello stesso tempo che passasse uno spazio <lb/>uguale alla CB nella perpendicolare CB, passerebbe uno spazio uguale alla <lb/>CD nell'inclinata AC, ed il grado della velocit&agrave; in B, al grado di velocit&agrave; <lb/>in D, avrebbe la medesima proporzione della CB alla CD. </s>

<s>Ma il grado di ve&shy;<lb/>locit&agrave; in A, al grado in D, ha la medesima proporzione che la media tra AC, <lb/>CD, e la media tra la AC, CD &egrave; la CB; adunque i gradi in A e in B, al <lb/>grado in D, hanno la medesima proporzione, e per&ograve; sono uguali, che &egrave; quello <lb/>che bisognava dimostrare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di qui possiamo immediatamente dimostrare un'altra proposizione: <lb/>cio&egrave; il tempo per l'inclinata, al tempo per la perpendicolare, aver la mede&shy;<lb/>sima proporzione di essa inclinata e perpendicolare. </s>

<s>Imperocch&egrave; diciamo che, <lb/>quando CA (nella solita ultima figura) sia il tempo per CA, il tempo per DC <lb/>sar&agrave; la media tra esse CA, DC, cio&egrave; sar&agrave; BC. </s>

<s>Ma quando il tempo per CD <lb/>sia CB, &egrave; anco il tempo per CB; dunque, quando AC sia il tempo per AC, <lb/>CB sar&agrave; il tempo per CB. Dunque, come AC a CB, cos&igrave; il tempo per AC al <lb/>tempo per CB. &rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>277-83). </s></p><p type="main">

<s>Il triumvirato della matematica Repubblica romana avr&agrave; con gran de&shy;<lb/>siderio letta questa dimostrazione, la quale si faceva dipendere, com'era na&shy;<lb/>turale, dal Teorema meccanico, venutosi ora a restaurare dopo quella total <lb/>demolizione, di cui nel cap. </s>

<s>VI del Tomo precedente si narrarono le origini <lb/>e le vicende. </s>

<s>&Egrave; a notar per&ograve; che, nel suo primo libro manoscritto, Galileo <lb/>rimandava per quel Teorema alla <emph type="italics"/>Scienza meccanica,<emph.end type="italics"/> dove il processo dimo&shy;<lb/>strativo &egrave; diverso, e sono altres&igrave; diversi i principii, che in questa decrepita <lb/>scrittura conservataci dal Nardi appariscono in abito nuovo, e con un rigo&shy;<lb/>glio giovanile di vita. </s>

<s>Attendendo bene infatti &egrave; tutto il vigore impartito al <lb/>Teorema dal principio dei moti misti, risolvendosi la forza AF, nella quinta <lb/>figura qui addietro, in altre due, delle quali la sola FC rimane attiva. </s>

<s>Ora <lb/>essendo misurata la forza dalla quantit&agrave; della materia o dal peso, moltipli&shy;<lb/>cato per la velocit&agrave; o per lo spazio, saran dunque nel presente caso G. FC, <lb/>H.FA le due forze, che si fanno insieme equilibrio, d'onde G:H=FA:FC <lb/>che &egrave; la conclusione, da Galileo condotta e raggirata per troppo lungo di&shy;<lb/>scorso. </s>

<s>D'onde ancora sarebbe venuta a rendersi manifesta l'intenzion prin&shy;<lb/>cipale, perch&egrave; tutti gl'impeti diretti per le oblique che, movendo da F, vanno <lb/>a raggiungere in AC l'orizonte, sono uguali ciascuno all'impeto per FC, e <lb/>perci&ograve; necessariamente uguali fra loro, che &egrave; insomma, in dimostrar la ve&shy;<lb/>rit&agrave; del supposto galileiano, il ragionamento che prima di tutti avea fatto <lb/>Luca Valerio. </s></p><p type="main">

<s>Quello per&ograve;, che da noi s'&egrave; chiamato vigor giovanile, mal giudicato dal <lb/>Nardi, non era reputato troppo sincero, come non sincero stimavalo forse il <lb/>Torricelli, il quale, tenendosi perci&ograve; affezionato pi&ugrave; che mai ai modi suoi <lb/>proprii, nel dover mandare alla luce il libro, che tre anni prima il Castelli <lb/>aveva presentato a Galileo manoscritto, vi premetteva fra le altre queste pa-<pb xlink:href="020/01/2397.jpg" pagenum="22"/>role: &ldquo; Scio Galileum, ultimis vitae suae annis, suppositionem illam demon&shy;<lb/>strare conatum, sed quia ipsius argumentatio cum libro De motu edita non <lb/>est, pauca haec de momentis gravium libello nostro praefigenda duximus, ut <lb/>appareat quod Galilei suppositio demonstrari potest &rdquo; (Opera geom., P. I, <lb/>Florentiae 1644, pag. </s>

<s>98). </s></p><p type="main">

<s>La torricelliana dimostrazione del supposto galileiano muove dal Teo&shy;<lb/>rema meccanico, condotto per&ograve; da un principio, che nella Storia della scienza <lb/><figure id="id.020.01.2397.1.jpg" xlink:href="020/01/2397/1.jpg"/></s></p><p type="caption">

<s>Figura 7.<lb/>apparisce del tutto nuovo. </s>

<s>&Egrave; quel principio che due <lb/>corpi rimangono nella posizione, in cui sono equi&shy;<lb/>librati, quando il loro comun centro di gravit&agrave;, es&shy;<lb/>sendogli impossibile scendere, si trova sempre nella <lb/>medesima linea orizontale. </s>

<s>Il Viviani lo illustrava mi&shy;<lb/>rabilmente cos&igrave;, riducendolo in forma del seguente <lb/>teorema: </s></p><p type="main">

<s>&ldquo; Se i due pesi eguali A, B (fig. </s>

<s>7) sono legati <lb/>ad un filo, passato sopra una carrucola o altro soste&shy;<lb/>gno, che possano scorrere; questi staranno in equili&shy;<lb/>brio, dovunque si saranno situati. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Perch&egrave;, se si movessero, tanto acquisterebbe <lb/>l'uno che scendesse, quanto perderebbe l'altro che <lb/>salisse, essendo i loro moti eguali, e per linee per&shy;<lb/><figure id="id.020.01.2397.2.jpg" xlink:href="020/01/2397/2.jpg"/></s></p><p type="caption">

<s>Figura 8.<lb/>pendicolari. </s>

<s>E se &egrave; possibile si muovano dal sito A, <lb/>B nel sito C, D: &egrave; manifesto che, giunti li centri di <lb/>gravit&agrave; in linea retta, il centro comune di A, B verr&agrave; <lb/>in mezzo, cio&egrave; in E, ed il centro comune di C, D verr&agrave; <lb/>in mezzo, cio&egrave; in E: perch'essendo le CA, BD uguali <lb/>tra loro e parallele, congiunte CD, AB si segano nella <lb/>medesima proporzione e nel mezzo, onde il centro <lb/>comune non si sar&agrave; mosso, e non avr&agrave; acquistato <lb/>niente, sicch&egrave; i gravi A, B non si moveranno dal loro <lb/>sito, in che furono posti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma se il peso B (fig. </s>

<s>8) sar&agrave; maggiore del <lb/>peso A, quello scender&agrave;, perch&egrave; il centro comune <lb/>loro &egrave; fuori del mezzo della BA, come in E, pi&ugrave; vi&shy;<lb/>cino al centro B, ed &egrave; in luogo che pu&ograve; scendere <lb/>sempre per la linea perpendicolare EG. &rdquo; (MSS. Gal., <lb/>P. V, T. VII, fol. </s>

<s>72 a tergo). </s></p><p type="main">

<s>Posto dunque questo principio, che il Viviani ci ha cos&igrave; ben dichiarato, <lb/>ecco come il Torricelli dimostra la sua prima proposizione, che cio&egrave; &ldquo; si in <lb/>planis inaequaliter inclinatis, eamdem tamen elevationem habentibus, duo <lb/>gravia constituantur, quae inter se eamdem homologe rationem habeant, <lb/>quam habent longitudines planorum; gravia aequale momentum habebunt &rdquo; <lb/>(Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>99). </s></p><p type="main">

<s>Siano AC, CD (fig. </s>

<s>9) i due piani inclinati, sopra i quali posino i due <pb xlink:href="020/01/2398.jpg" pagenum="23"/>gravi A, B con i loro pesi nelle dette proporzioni. </s>

<s>Avranno ugual momento <lb/>se, congiuntj insieme dal filo ACB, scendendo l'uno in D, e risalendo l'al&shy;<lb/><figure id="id.020.01.2398.1.jpg" xlink:href="020/01/2398/1.jpg"/></s></p><p type="caption">

<s>Figura 9.<lb/>tro in E, il loro comun centro di gravit&agrave; <lb/>rimanga sempre in un punto della orizon&shy;<lb/>tale AB, ci&ograve; che, chiamati E, D i due <lb/>gravi, e da E condotta la EF parallela a <lb/>CD, l'Autore dimostra con un discorso, <lb/>da noi pi&ugrave; brevemente significato per que&shy;<lb/>ste equazioni. </s>

<s>E:D=AC:CB=AE:EF <lb/>=BD:EF=GD:EG. </s>

<s>G dunque &egrave; il co&shy;<lb/>mun centro di gravit&agrave; de'pesi, n&egrave; s'&egrave; <lb/>nulla rimosso dall'AB orizontale. </s></p><p type="main">

<s>Si passa di qui a proporre, in secondo luogo, che, posandosi sopra AB, <lb/>BC (fig. </s>

<s>10), piani diversamente lunghi ma ugualmente elevati, due pesi <lb/>uguali A, C, i loro momenti <emph type="italics"/>sunt in reciproca ratione cum longitudinibus<emph.end type="italics"/><lb/><figure id="id.020.01.2398.2.jpg" xlink:href="020/01/2398/2.jpg"/></s></p><p type="caption">

<s>Figura 10.<lb/><emph type="italics"/>planorum<emph.end type="italics"/> (ibid., pag. </s>

<s>100): ci&ograve; <lb/>che, presa D quarta proporzio&shy;<lb/>nale dopo AB, BC, A, per cui i <lb/>momenti di A e di D sono uguali <lb/>per la precedente, ed osservando <lb/>ch'essendo C, D posati sul me&shy;<lb/>desimo declivio hanno i momenti <lb/>proporzionali alle moli, riman di&shy;<lb/>mostrato dalle seguenti equazioni M.oC:M.oD=C:D=A:D=AB:BC. </s>

<s><lb/>Donde si conclude il Teorema meccanico nella sua propria forma: &ldquo; Mo&shy;<lb/>mentum totale gravis, ad momentum quod habet in plano inclinato, est ut <lb/>longitudo ipsius plani inclinati ad perpendiculum &rdquo; (ibid., pag. </s>

<s>101). </s></p><p type="main">

<s>La terza proposizione che, dopo un corollario e uno scolio elegantissimi <lb/>relativi alla precedente, in questo libro del Torricelli, ricorre, non ha propria&shy;<lb/><figure id="id.020.01.2398.3.jpg" xlink:href="020/01/2398/3.jpg"/></s></p><p type="caption">

<s>Figura 11.<lb/>mente alcuna importanza, come princi&shy;<lb/>pio di mezzo a concluder la verit&agrave; del <lb/>supposto galileiano, e solamente si scrive <lb/>per supplir, come l'Autore credeva, al <lb/>difetto di Galileo. </s>

<s>Il difetto &egrave; per&ograve; di <lb/>chi non vide la cosa nel secondo modo <lb/>come si dimostra la VI proposizione del <lb/>Dialogo terzo, bench&egrave; con processo di&shy;<lb/>verso da questo qui, che &egrave; tale: s'ab&shy;<lb/>biano i piani AC, AB (fig. </s>

<s>11) di ugual lunghezza, ma variamente elevati in <lb/>C e in B: che i momenti dei gravi, posti sopra questi piani, stiano come <lb/>CE, BD, seni degli angoli delle elevazioni, &egrave; concluso dalle uguaglianze M.o<lb/>AB:M.oBF=FB:AB=FB:AC=BD:CE, osservando che M.o BF <lb/>=M.oAC, per essere AC, BF ugualmente inclinate. </s></p><p type="main">

<s>Il corollario, lo scolio, e il lemma, per servire a una nuova dimostra-<pb xlink:href="020/01/2399.jpg" pagenum="24"/>zione della Sesta galileiana, sono di una grande importanza, ma per la via <lb/>di concluder ci&ograve;, che ora a noi pi&ugrave; preme, si rientra nella quarta proposizione, <lb/>la quale, com'&egrave; presentata nel suo primo modo, non differisce per verit&agrave; che <lb/>di pochissimo dalle dimostrazioni di Galileo, del Michelini e del Baliani. </s>

<s>Im&shy;<lb/>perocch&egrave;, a provare che il tempo per BA, nella precedente figura, sta al <lb/>tempo per BF come BA sta a BF, presa BH terza proporzionale dopo AB, BF, <lb/>osserva che BF e BH sono isocrone, ond'&egrave; che, dall'aversi per la legge dei <lb/>moti accelerati T.oAB:T.oBH=&radic;AB:&radic;BH=AB:BF, ne concludeva an&shy;<lb/>che il Torricelli, come i sopra commemorati Autori, il suo intento. </s></p><p type="main">

<s>Al Teorema meccanico, e a questa quarta bastava supplir la prima di <lb/>Galileo (Alb. </s>

<s>XIII, 166), per avere i mezzi necessari a dimostrar finalmente: <lb/>&ldquo; Gradus velocitatis ciusdem mobilis, super diversas planorum inclinationes <lb/>acquisiti, tunc aequales sunt, cum corumdem planorum elevationes aequales <lb/>sunt &rdquo; (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>108). Siano, sempre riferendosi all'ultima figura, <lb/>AB, FB i piani aventi la medesima elevazione BD. </s>

<s>Sar&agrave; per la precedente <lb/>T.oAB:T.oFB=AB:FB.. Ora, qualunque ella siasi, si chiami V la velo&shy;<lb/>cit&agrave;, che acquista il grave giunto in A, e si chiami V&prime; la velocit&agrave;, qualun&shy;<lb/>que ella pure si sia, acquistata dal grave giunto in F. Avremo, per la ci&shy;<lb/>tata prima di Galileo, T.oAB=AB/V:2, T.oBF=BF/V&prime;:2, ossia V/2:V&prime;/2= <lb/>AB/(T.oAB):BF/(T.oBF). Ma i termini di questa seconda ragione sono uguali, dunque <lb/>uguali sono anche i primi, e perci&ograve; V=V&prime; come doveva dimostrarsi. </s></p><p type="main">

<s>Ora si domanda: fu egli veramente conseguito il fine, per cui il Torri&shy;<lb/>celli si dette a claborare e, intanto che si rimaneva nelle lettere private quella <lb/>di Galileo, divulgare in pubblico quest'altra sua dimostrazione? </s>

<s>Si saranno <lb/>eglino, i Matematici, persuasi che il supposto principio si veniva a rendere <lb/>nel suo libro, per geometriche ragioni, evidente? </s>

<s>Ma se fossero bastate le <lb/>ragioni, il Baliani, da cinque anni, avrebbe dovuto fare l'effetto, non essendo <lb/>la sua dimostrazione n&egrave; men bella di questa torricelliana, n&egrave; men conclu&shy;<lb/>dente. </s>

<s>Nel rifiutar dunque che si faceva da tanti, prima le probabilit&agrave; degli <lb/>sperimenti, e poi le ragioni della geometria, doveva esserci molta caparbict&agrave;, <lb/>della quale il Torricelli stesso ebbe a fare esperienza. </s></p><p type="main">

<s>Il Mersenno, dop'aver letta la prima parte del trattato <emph type="italics"/>De motu gra&shy;<lb/>vium naturaliter descendentium,<emph.end type="italics"/> prendeva la penna in mano per dire in <lb/>una sua lettera all'Autore: &ldquo; Expectamus abs te postulati rationem, ab expe&shy;<lb/>rientia, si fieri potest, independentem &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLI, fol. </s>

<s>69). <lb/>&mdash; Ma non siete, padre, domandava il Torricelli maravigliato, giunto ancora <lb/>alla quinta proposizione del mio primo libro? </s>

<s>&mdash; E si sentiva rispondere: <lb/>&mdash; Io ho per nulla quella dimostrazione, condotta dal supporre i momenti <lb/>proporzionali alle velocit&agrave;, che per me &egrave; un paralogismo vostro e di Galileo. </s>

<s>&mdash; <lb/>Alle quali accuse si rispondeva con l'eloquenza di queste ragioni: </s></p><p type="main">

<s>&ldquo; Quod ego suppono pag. </s>

<s>104 cum Galileo adeo manifestum mihi vide&shy;<lb/>tur, ut sine ulla dubitatione loco principii admitti et concedi posse videatur. <pb xlink:href="020/01/2400.jpg" pagenum="25"/>Ratio physica est: si fuerint a diversis planis duae sphaerae, ex. </s>

<s>gr. </s>

<s>vitreae <lb/>et aequales, postquam ostendero momentum unius, ad momentum alterins, <lb/>esse duplum, quis non concedat et velocitatem ad velocitatem esse duplam? </s>

<s><lb/>Dupla enim causa duplum effectum parere debet in eodem subiecto. </s>

<s>Moles <lb/>supponuntur aequales eiusdemque materiae, virtus vero, quae impellit alle&shy;<lb/>ram molem, dupla demonstratur virtutis alterius: ergo, si dupla virtus est, <lb/>duplam procul dubio velocitatem efficiet &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>76). </s></p><p type="main">

<s>&mdash; Se cos&igrave; &egrave;, insisteva a questo punto del ragionamento il Mersenno, il <lb/>momento di C (nella figura X qui poco addietro) dovrebbe esser tanto mag&shy;<lb/>giore del momento di D, quanto la mole &egrave; maggior della mole: e nonostante <lb/>voi, nella vostra proposizione seconda, dite che que'due momenti sono uguali. <lb/></s>

<s>&mdash; Ma non badava, cos&igrave; dicendo, che i due gravi eran posati sul medesimo <lb/>declivio, per cui il Torricelli, a rimuovere l'obiezione inconsiderata, prose&shy;<lb/>guiva in tal guisa il suo discorso: </s></p><p type="main">

<s>&ldquo; Neque obstat quod obiici potest de gravibus in eodem plano consti&shy;<lb/>tutis, quae, sive sint eiusdem molis, sive non, aequali tamen velocitate fe&shy;<lb/>runtur. </s>

<s>Nam omnia gravia, cuiuscumque molis, ponderis et figurae sint, li&shy;<lb/>bere demissa a loco absque impedimentis eadem velocitate feruntur deorsum, <lb/>nempe tam sphaera aurea quam lapidea, ac etiam lignea, immo et ex materia <lb/>laevissima eadem velocitate ex se descenderent. </s>

<s>Si vero pusillum quoddam <lb/>spatium graviores materiae videntur antecedere non procedit hoc ab inae&shy;<lb/>qualitate virtutum moventium, quae ulla est, sed ab inaequalitate impedimen&shy;<lb/>torum. </s>

<s>Tantum enim est in unoquolibet corpore virtutis moventis, quantum <lb/>est materiae. </s>

<s>Exempli gratia in uncia auri, atque in uncia cerae, tantumdem <lb/>est et materiae et virtutis moventis, licet caera appareat multum maiorem <lb/>locum occupare. </s>

<s>Propterea, dum quiescunt, pariter gravitant, et manifeste <lb/>aequalitatem virtutum indicant. </s>

<s>Quando vero moventur, aurum praecedit, sed <lb/>longe minus quam pro ratione specierum gravitatis, ipsam caeram, quod qui&shy;<lb/>dem accidit quia, cum virtutes aequales sint in utraque materia, si altera <lb/>cum maiori mole ambientis medii, altera cum minori luctari debet. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quando vero consideremus duas sphaeras ciusdem materiae, sed alte&shy;<lb/>ram unius unciae, alteram vero decem librarum, aequaliter hae descendunt <lb/>in eodem plano, quia in utraque sphaera virtutes illae arcanae, licet inac&shy;<lb/>quales sint inter se, eamdem habent rationem quam resistentiae, hoc est cor&shy;<lb/>pora ipsa movendo. </s>

<s>Vel si mavis, hoc modo: virtus minor, ad minus pon&shy;<lb/>dus a se movendum, eamdem habet rationem quam virtus maior, ad maius <lb/>pondus a se movendum. </s>

<s>Exiguum illud quod videtur aliquando praecedere <lb/>gravius, quando maxima fuerit inter pondera proportio, oritur, non a prin&shy;<lb/>cipiis intrinsecis, sed ab externis impedimentis, nempe a densitate medii, quae, <lb/>ut optime docet Galileus, magis impedit minores moles quam maiores, quan&shy;<lb/>doquidem minores, cum maiorem superficem habeant, a maiori quantitate <lb/>medii retardantur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Mirum ergo non sit si metalla, lapides, ligna etc. </s>

<s>tam in descensu <lb/>libero, quam in eodem plano collocata, <gap/> eadem velocitate descendere, cum <pb xlink:href="020/01/2401.jpg" pagenum="26"/>omnia gravia aequalem sibi ipsis virtutem moventem habeant. </s>

<s>At in planis <lb/>inaequaliter inclinatis, ubi ego ostendero duas sphaeras aequales et aeque <lb/>graves inaequalia momenta habere, quid ni inferre possim illam, quae maius <lb/>habet momentum, maiori velocitate delabi pro ratione momentorum? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sed ego nimis fortasse provectus sum in hac causa, quae tanto pa&shy;<lb/>trocinio mihi non videbatur indigere. </s>

<s>Satis enim erat inter pondus et mo&shy;<lb/>mentum distinguere &rdquo; (ibid., fol. </s>

<s>76, 77). </s></p><p type="main">

<s>Se avesse avuto il Mersenno la mente libera da pregiudizi e l'animo da <lb/>passioni, si sarebbe dovuto persuadere della verit&agrave; delle cose, che tanto chia&shy;<lb/>ramente veniva in questo discorso esponendogli il Torricelli, ma egli persi&shy;<lb/>steva caparbiamente in. </s>

<s>dire che, nonostante la quinta proposizione dimostrata <lb/>da lui, il supposto galileiano aveva tuttavia bisogno di prove. </s>

<s>Soggiungeva <lb/>un'altra difficolt&agrave;, ed era non si poter, dall'essere i tempi proporzionali agli <lb/>spazi, concludere che le velocit&agrave; sono uguali, altro che nei moti equabili; e <lb/>che avrebbero dovuto perci&ograve; Galileo e il Torricelli dimostrar che gli spazi <lb/>passati equabilmente dal mobile son proporzionali a quelli, che passerebbe <lb/>nel medesimo tempo con moto accelerato. </s>

<s>Sembrerebbe la cosa incredibile a <lb/>chi sa e ripensa che s'incomincia a dimostrar ci&ograve; per l'appunto infino dal <lb/>primo aprire, nel terzo dialogo delle Nuove scienze, il trattato del moto, ma <lb/>Michelangiolo Ricci ce ne assicura con queste parole, scritte da lui in una <lb/>lettera allo stesso Torricelli: </s></p><p type="main">

<s>&ldquo; Le opposizioni fatte al trattato del moto dal padre Mersenno si ridu&shy;<lb/>cono a pochi capi<gap/> Oppone primieramente, e se ne reputa assai l'Autore, a <lb/>quella riprova della volgare definizione data al moto accelerato, che si trova <lb/>a carte 164, cio&egrave; che la velocit&agrave; cresce secondo lo spazio. </s>

<s>Dice esser vero <lb/>nel moto equabile, che, sendo le velocit&agrave; in proporzione delli spazi, sono que&shy;<lb/>sti passati in egual tempo, ma bisogna che il Galileo provi, il che non fa, <lb/>che posta la definizione volgare ne segue che la velocit&agrave;, con la quale un <lb/>mobile passa v. </s>

<s>g. </s>

<s>BC, sia uguale ad un moto equabile, e la velocit&agrave;, con <lb/>la quale &egrave; passato lo spazio BA dallo stesso mobile, sia uguale ad un moto <lb/>equabile, e poi questi due moti equabili abbiano la proporzione di BC a BA. </s>

<s><lb/>Oppone nel secondo luogo che l'assunto primo fatto dal Galileo, ma da V. S. <lb/>dimostrato, sia bisognoso di prova, e perci&ograve; o probabile o improbabile, ed in <lb/>conseguenza le proposizioni sei seguenti asserisce esser tanto lontane dal&shy;<lb/>l'evidenza geometrica, quanto &egrave; impossibile aver certezza d'una conclusione <lb/>dedotta da verosimile assunto. </s>

<s>Finalmente dice esser difficilissimo il certifi&shy;<lb/>carsi dell'esattezza dell'esperienza fatta da Galileo, e riferita a carte 175 (mi&shy;<lb/>surando gli spazi in un regolo inclinato, lungo la incavatura del quale si faceva <lb/>scendere una palla di bronzo, e i tempi nelle clessidre, con pesar, durante la <lb/>scesa, l'acqua stillata) ed egli ne adduce in contrario una fallacissima, come <lb/>l'avr&agrave; letta nella lettera del padre Mersenno. </s>

<s>Con questi fondamenti presume <lb/>il Gesuita d'alzar rocca inespugnabile ai danni del Galileo e della sua Scuola, e <lb/>con mille vanti di s&egrave; medesimo e scherno del Galileo si dimostra non men leg&shy;<lb/>gero ne'costumi, che sia nella dottrina &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>116). </s></p><pb xlink:href="020/01/2402.jpg" pagenum="27"/><p type="main">

<s>Chiamasi qui dal Ricci il Mersenno gesuita, non perch&egrave; fosse propria&shy;<lb/>mente tale nell'abito esteriore, o nella profession religiosa, ma perch&egrave; con&shy;<lb/>sentiva e cooperava con i gesuiti in fare ogni sforzo per non veder altri prima <lb/>di loro sorgere a instituire la nuova scienza del moto. </s>

<s>L'ufficio per&ograve; d'alzar <lb/>rocca inespugnabile ai danni di Galileo non si stettero costoro in affidarlo <lb/>allo zelante Frate minimo, estraneo al loro collegio, ma se l'assunsero per <lb/>s&egrave; medesimi, deputandone particolarmente Pietro Cazr e Niccol&ograve; Cabeo. </s>

<s>Il <lb/>Gesuita italiano colse l'occasione d'infirmare i fondamenti della Scienza ga&shy;<lb/>lileiana nelle <emph type="italics"/>Questioni<emph.end type="italics"/> intorno ai quattro libri della meteorologia di Aristo&shy;<lb/>tile, percorrendo agile e leggero, cos&igrave; portato com'era dal vento dell'ambi&shy;<lb/>zione, il campo universale della Scienza. </s>

<s>Ma il Francese vi si dedic&ograve; di <lb/>proposito, scrivendo una dissertazione, ai paralogismi della quale non si pot&egrave; <lb/>tener di rispondere il Gassendo, per salvar, nel difendere il vero, pi&ugrave; l'onore <lb/>della sua propria nazione, che quello di Galileo. </s></p><p type="main">

<s>Era un giorno il Filosofo parigino nella sua stanza di studio, col liber&shy;<lb/>colo del Cazreo aperto innanzi agli occhi, alla pagina, dov'ei diceva non es&shy;<lb/>sere il postulato galileiano sufficientemente confermato dall'esperienza, <emph type="italics"/>cum <lb/>rationes etiam non desint, quibus oppositum probabilius reddatur,<emph.end type="italics"/> e aveva <lb/>preso in mano la penna per seguitare a scrivere il &sect; XIII della sua prima <lb/>epistola <emph type="italics"/>De proportione qua gravia decidentia accelerantur,<emph.end type="italics"/> affine di con&shy;<lb/>futar la temeraria sentenza; quando entra a visitarlo Pietro Carcavy, nobi&shy;<lb/>lissimo senatore e delle Matematiche studiosissimo, che, riconosciuta quella <lb/>cazreana dissertazione, e compresa l'intenzion del Gassendo, gli annunziava <lb/>esser gi&agrave; comparita in Parigi una copia del trattato <emph type="italics"/>De motu<emph.end type="italics"/> del Torricelli, <lb/>dove, di quello stesso cos&igrave; disputato assunto galileiano, si dava la dimostra&shy;<lb/>zione pi&ugrave; vera e pi&ugrave; concludente, che da un Geometra si potesse desiderare. <lb/></s>

<s>&ldquo; Praetereo autem, soggiunge esso Gassendo, ut, copia illius videndi statim <lb/>impetrata, deprehenderim rem confectam quinque propositionibus &rdquo; (Pari&shy;<lb/>siis 1646, pag. </s>

<s>23), di ciascuna delle quali cinque torricelliane proposizioni <lb/>prosegue ordinatamente a trascrivere l'enunciato. </s></p><p type="main">

<s>Il fatto cos&igrave; da esso Gassendo narrato, in tuono di solennit&agrave; e d'impor&shy;<lb/>tanza, dice di per s&egrave; medesimo in quanta stima s'avesse il Torricelli in <lb/>Francia, e quanto si credesse autorevole a persuadere i ritrosi con la ele&shy;<lb/>gante eloquenza delle sue dimostrazioni. </s>

<s>Del Baliani non si fa motto, quasi <lb/>non avess'egli, prima dello stesso Torricelli, dimostrato il medesimo. </s>

<s>Anzi &egrave; <lb/>notabile che, occorrendo al Gassendi nella citata epistola contro il Cazreo di <lb/>commemorare il trattato del Matematico genovese, edito in quell'anno, che <lb/>si pubblicarono i Dialoghi di Galileo; si limiti a dir ivi che anche il Ba&shy;<lb/>liani confermava essere ne'declivii di uguale altezza uguali le velocit&agrave;, <emph type="italics"/>ar&shy;<lb/>gumento sumpto ab ipsis pendulorum vibrationibus.<emph.end type="italics"/> Potrebb'esser che il <lb/>Matematico parigino avesse letto il trattatello del Nostro in una di quelle <lb/>prime copie, edite nel 1638, nella quale mancava la carta, fatta ristampar <lb/>nel Settembre dell'anno dopo, aggiuntavi la dimostrazione del supposto ga&shy;<lb/>lileiano, ma in ogni modo colui, che si voleva far passare per emulo invi-<pb xlink:href="020/01/2403.jpg" pagenum="28"/>dioso, dov&egrave; rimanersi indietro, nella fama e nella stima universale, a quel&shy;<lb/>l'altro, da per tutto acclamato come discepolo e promotore esimio di Galileo. </s></p><p type="main">

<s>L'ingiustizia del pubblico giudizio, riconosciuta ora spassionatamente da <lb/>noi, doveva esser tanto pi&ugrave; vivamente sentita da chi n'era allora fatto segno, <lb/>onde, attribuendo forse il Baliani alla esiguit&agrave; del volume, al negletto abito <lb/>esteriore, e alla trascuratezza della forma del libro l'essere cos&igrave; passata inos&shy;<lb/>servata ai Matematici la sua propria dimostrazione; volle tornare ancora a <lb/>tentare la sua fortuna, ampiando il trattato, e studiandosi di adornarlo con <lb/>qualche fior di eloquenza. </s>

<s>Lo distribu&igrave; in tre libri, in materia del moto dei <lb/>solidi, aprendosi nelle respettive prefazioni largo campo di speculare: e ve ne <lb/>aggiunse altri tre, in materia del moto dei liquidi, affinch&egrave; non avesse, nem&shy;<lb/>meno da questa parte, a rimanersi l'opera sua indietro a quella del Torri&shy;<lb/>celli, che il pubblico ammirava gi&agrave; da due anni. </s></p><p type="main">

<s>Si sente alitar da ogni pagina, per non dire da ogni parola, quello spi&shy;<lb/>rito di emulazione, che teneva agitato l'animo dell'Autore, ma perch&egrave; la <lb/>sostanza era insomma la medesima, l'esser tornato a diffonderla, con tanta <lb/>larghezza, par che faccia l'effetto de'liquori a<gap/>acquati, i quali tanto gua&shy;<lb/>dagnano nel volume, quanto scapitano nel sapore e nella fragranza. </s>

<s>Si pu&ograve; <lb/>veder l'esempio di ci&ograve;, senz'uscire dall'argomento del nostro discorso, parago&shy;<lb/>nando la dimostrazione del supposto galileiano, data nel trattatello del 1638, <lb/>con quella che si volle ampliare nel 1646, derivandola da pi&ugrave; alti principii, <lb/>e conducendola per una serie pi&ugrave; lunga di proposizioni. </s></p><p type="main">

<s>Pregevoli in ogni modo son nell'opera del Baliani, sopra le altre, due <lb/>parti, che, se non si fossero trascurate dal Torricelli, gli risparmiavano le <lb/>opposizioni e le censure vanitosamente moleste del Merseuno. </s>

<s>Sanno i nostri <lb/>Lettori che la principale di quelle opposizioni nasceva dal non sapere inten&shy;<lb/>dere qual relazione avessero con le velocit&agrave; gl'impeti o i momenti; a che il <lb/>Baliani fu sollecito di rispondere: &ldquo; Impetus differens est solum fortasse a <lb/>velocitate, quia impetus sit velocitas in actu primo, ita ut aliquo pacto im&shy;<lb/>petus sit causa velocitatis &rdquo; (De motu natur., Genuae 1646, pag. </s>

<s>70). </s></p><p type="main">

<s>L'altra censura del Mersenno consisteva nel dire che avrebbe dovnto il <lb/>Torricelli dimostrar che i moti accelerati si riducono a proporzion degli equa&shy;<lb/>bili, ci&ograve; che il Baliani fa, dimostrando, in pi&ugrave; semplice ed efficace modo di <lb/>Galileo, la seguente proposizione, scaturita dai pi&ugrave; intimi seni del principio <lb/><figure id="id.020.01.2403.1.jpg" xlink:href="020/01/2403/1.jpg"/></s></p><p type="caption">

<s>Figura 12.<lb/>d'inerzia: &ldquo; Grave in motu naturali, sive perpendiculari <lb/>sive inclinato, fertur sine ope gravitatis aequabili tempore <lb/>per duplum spatii praecedentis &rdquo; (ibid., pag. </s>

<s>58). </s></p><p type="main">

<s>Premesso ci&ograve;, e avendosi in secondo luogo per dimo&shy;<lb/>strato, nell'oramai noto triangolo ACB (fig. </s>

<s>12), che la nor&shy;<lb/>male BD precide in D lo spazio CD isocrono con CB, si fa <lb/>via il Baliani a concludere la verit&agrave; dell'assunto galileiano, <lb/>con questa proposizione: &ldquo; Si linea perpendicularis et incli&shy;<lb/>nata, ab codem puneto digressae, per quas idem grave naturaliter ducatur, se&shy;<lb/>centur a recta normali ad inelinatam; impetus in punctis sectionis sunt ut <pb xlink:href="020/01/2404.jpg" pagenum="29"/>portiones linearum infra sectiones &rdquo; (ibid., pag. </s>

<s>72). Vuol dire, ritenuti i soliti <lb/>simboli, essere V.aB:V.aD=CB:CD, ci&ograve; che immediatamente consegue <lb/>dalle due premesse proposizioni, essendo per quellla V.aB=2CB/(T.oCB), V.aD= <lb/>2CD/(T.oCD), e per questa T.oCB=T.oCD; d'onde V.aB:V.aD=CB:CD, <lb/>come si voleva provare, e anche V.aB:V.aD=CA:CB, per la similitu&shy;<lb/>dine de'triangoli ACB, DCB. </s></p><p type="main">

<s>Passa di qui il Baliani a dimostrare, in un'altra proposizione, che <lb/>V.aA:V.aD=CA:CB, invocando per far ci&ograve; la legge dei moti accelerati, <lb/>che d&agrave; AC:CD=V.aA2:V.aD2; e osserva che, avendo i triangoli simili <lb/>ABC, CBD la medesima altezza BD, le basi AC, DC stanno come i quadrati <lb/>de'lati omologhi AC, CB, onde V.aa2:V.aD2=AC2:CB2, ossia V.aA:V.aD= <lb/>CA:CB, come volevasi dimostrare. </s></p><p type="main">

<s>Per concludere poi la verit&agrave; dell'assunto galileiano mette il Baliani in <lb/>ordine un'altra proposizione distinta, la quale &egrave; per&ograve; superflua, avendosi <lb/>l'intento per corollario immediato dalle due precedenti: perch&egrave;, se questa <lb/>d&agrave; V.aA:V.aD=CA:CB, e quella d&agrave; V.aB:V.aD=CA:CB; dunque <lb/>V.aA=V.aB, senza bisogno d'altri discorsi. </s></p><p type="main">

<s>Dopo dieci anni, da che il Baliani veniva cos&igrave; pi&ugrave; solennemente a con&shy;<lb/>fermar la dimostrazione del Torricelli, usciva postuma in Bologna, inserita <lb/>nel terzo dialogo delle Nuove scienze, che per la prima volta si ristampava; <lb/>quella di Galileo, aspettata da tutti con tanto desiderio. </s>

<s>Sembrava perci&ograve; che <lb/>dovesse fra'Matematici finalmente cessare ogni mormorio, e che dovessero <lb/>nella dimostrata verit&agrave; quietar l'intelletto, quando, in un libro venuto d'Olanda, <lb/>e in cui l'Autore, per sopredificarvi suntuosamente, veniva ricercando i fon&shy;<lb/>damenti della scienza galileiana; dop'esservisi dimostrato che lo spazio per&shy;<lb/>corso equabilmente dal mobile, col massimo grado della velocit&agrave; acquistata, <lb/>&egrave; doppio di quello che aveva prima passato acceleratamente, s'ebbe a leg&shy;<lb/>gervi con gran maraviglia soggiunte queste parole: &ldquo; Hinc vero non difficile <lb/>iam erit demonstrare propositionem sequentem, quam concedi sibi ut quodam&shy;<lb/>modo per se manifestam Galileus postulavit. </s>

<s>Nam demonstratio illa, quam <lb/>postea adferre conatus est, quaeque in posteriori operum eius editione extat, <lb/>parum firma meo quidem iudicio videtur. </s>

<s>&rdquo; </s></p><p type="main">

<s>Si leggono queste parole a pag. </s>

<s>62 del primo tomo delle Opere di Cri&shy;<lb/>stiano Huyghens, stampate nel 1724 in Leida, e il nome dell'Autore, e il <lb/>saper che dal primo libro dell'<emph type="italics"/>Horologium oscillatorium<emph.end type="italics"/> sono state trascritte, <lb/>fruga vivamente la curiosit&agrave; di veder com'altrimenti e meglio di Galileo abbia <lb/>il celebre uomo, nella proposizione sua sesta, dimostrato: &ldquo; Celeritates gra&shy;<lb/>vium, super diversis planorum inclinationibus descendendo acquisitae, aequa&shy;<lb/>les sunt, si planorum elevationes fuerint aequales &rdquo; (ibid.). </s></p><p type="main">

<s>Siano, dice l'Huyghens, AB, CB (fig. </s>

<s>13) i due piani inclinati, e AE, CD <lb/>le loro elevazioni uguali: se un mobile si faccia scendere ora da A, ora da C, <lb/>giunger&agrave; in B col medesimo grado di velocit&agrave;, bench&egrave; sia l'una scesa, co-<pb xlink:href="020/01/2405.jpg" pagenum="30"/>munque vogliasi, pi&ugrave; precipitosa dell'altra. </s>

<s>Il ragionamento che in tal forma <lb/>procede, secondo le parole proprie dell'Autore, piglia valore dalla proposi&shy;<lb/>zione IV, nella quale era gi&agrave; dimostrato che risalirebbe in su il mobile da B <lb/><figure id="id.020.01.2405.1.jpg" xlink:href="020/01/2405/1.jpg"/></s></p><p type="caption">

<s>Figura 13.<lb/>nello stesso tempo, e passando per <lb/>i medesimi gradi di velocit&agrave;, coi <lb/>quali era prima sceso da C: &ldquo; Si <lb/>enim per CB cadens minorem ve&shy;<lb/>locitatem acquirere dicitur, quam <lb/>cadens per AB, habeat ergo per <lb/>CB cadens eam dumtaxat, quam <lb/>per FB acquireret, posita nimirum <lb/>FB minore quam AB. </s>

<s>Acquiret au&shy;<lb/>tem per CB cadens eam velocitatem, qua rursus por totam BC possit ascen&shy;<lb/>dere. </s>

<s>Ergo, et per FB, acquiret eam velocitatem, qua possit ascendere per <lb/>totam BC. </s>

<s>Ideoque cadens ex F in B, si continuet motum per BC, quod re&shy;<lb/>percussu ad superficiem obliquam fieri potest, ascendet usque in C, hoc est <lb/>altius quam unde decidit, quod est absurdum &rdquo; (ibid., pag. </s>

<s>63). </s></p><p type="main">

<s>Suppone dunque l'Huyghens che, sceso il mobile da F in B, nel riflet&shy;<lb/>tersi per BC o per qualunque altra inclinazione diversa, debba risalir giusto <lb/>a tanta altezza, quanta fu la caduta: ma questo insomma era quello che do&shy;<lb/>vevasi dimostrare, e intorno a che s'era sottilmente aggirato il discorso di <lb/>Galileo. </s>

<s>L'Huyghens tiene il medesimo filo, e lo conosce e lo confessa, di&shy;<lb/>cendo di voler nella sua quinta proposizione dimostrar di nuovo quel che aveva <lb/>gi&agrave; dimostrato nella seconda <emph type="italics"/>Galilei methodum sequendo.<emph.end type="italics"/> Quella quinta in&shy;<lb/>fatti dell'Orologio oscillatorio corrisponde con lo scolio alla proposizione XXIII <lb/>del Dialogo terzo, dove graficamente si dimostra che, se lo spazio passato <lb/>nello scendere acceleratamente si rappresenta dal triangolo, lo spazio passato <lb/>con moto equabile nel medesimo tempo, e con l'ultimo grado di velocit&agrave; <lb/>acquistato nella discesa, vien rappresentato dal rettangolo ossia dal doppio. </s></p><p type="main">

<s>Si fanno da ci&ograve; via ambedue gli Autori a considerare gli effetti del moto <lb/>incidente e del riflesso, cos&igrave; Galileo concludendo il suo sottile discorso: &ldquo; Ex <lb/>his igitur rationabiliter asserere possumus quod, si per aliquod planum in&shy;<lb/>clinatum fiat descensus, post quem sequatur reflexio per planum elevatum, <lb/>mobile per impetum conceptum ascendet usque ad eandem altitudinem, seu <lb/>elevationem ab horizonte. </s>

<s>Ut si fiat descensus per CB (nella precedente <lb/>figura) feretur mobile, per planum reflexum BG, usque ad horizontalem CG &rdquo; <lb/>(Alb. </s>

<s>XIII, 202). Questo si fa conseguire dai principii gi&agrave; dimostrati, quando <lb/>per&ograve; gli angoli dell'incidenza e della riflessione siano uguali, ma Galileo sog&shy;<lb/>giunge che il teorema &egrave; vero &ldquo; non tantum si inclinationes planorum sint <lb/>aequales, verum etiam si inaequales sint, qualis est plani AB &ldquo; (ibid.) e per <lb/>dimostrarlo invoca il principio, che nella prima edizione s'aveva per suppo&shy;<lb/>sto, ma che nella seconda postuma si concludeva con matematico ragiona&shy;<lb/>mento. </s>

<s>Non dando pure a questa conclusione, come vuol l'Huyghens, nessun <lb/>assoluto valore, &egrave; un fatto che nel <emph type="italics"/>Dialogo,<emph.end type="italics"/> come fu stampato nel 1638 in <pb xlink:href="020/01/2406.jpg" pagenum="31"/>Leyda, s'ha disteso il medesimo discorso, che nell'<emph type="italics"/>Orologio<emph.end type="italics"/> stampato nel 1673 <lb/>a Parigi, se non che, mentre l&agrave; si supponeva un principio per la dimostra&shy;<lb/>zione, qui supponesi invece quel medesimo, ch'era proposto di dimostrare. </s></p><p type="main">

<s>Cos&igrave; essendo, sembra a noi che fosse lodevolissima l'intenzione di Ales&shy;<lb/>sandro Marchetti, di richiamar cio&egrave; alla memoria dei Matematici, i quali die&shy;<lb/>tro la grande autorit&agrave; dell'Olandese avrebbero potuto deviare, le pi&ugrave; schiette <lb/>e severe tradizioni della scuola italiana. </s>

<s>Dell'essere esso Marchetti riuscito a <lb/>dare a quelle tradizioni, cos&igrave; variamente maneggiate, una forma nuova, con <lb/>troppa vanit&agrave; si compiacque, e ci&ograve; dette a'suoi nemici occasione di claun&shy;<lb/>niarlo, e con livore impotente di strascicarlo nel fango. </s>

<s>Il Nelli, in cui aveva <lb/>il Grandi insufflato l'odio ma non la scienza, concludeva cos&igrave; una sua que&shy;<lb/>stione storica: &ldquo; Adunque &egrave; evidente ed innegabile che il signor Alessandro <lb/>Marchetti non &egrave; l'autore dell'opera <emph type="italics"/>De resistentia solidorum &rdquo;<emph.end type="italics"/> (Saggio di <lb/>storia letter., Lucca 1759, pag. </s>

<s>53). Il principio e i termini di mezzo per <lb/>questa conclusione sono assai bene strani, fondandosi sul giudizio poco favo&shy;<lb/>revole fatto dai Matematici contemporanei intorno a varii opuscoli geometrici <lb/>dello stesso Marchetti. </s>

<s>Ma se fosse logica buona concludere da alcune pro&shy;<lb/>posizioni false o men perfettamente dimostrate l'inettitudine di un autore a <lb/>condur da s&egrave; solo un'Opera, si dovrebbe dal recente esempio argomentare <lb/>che non &egrave; l'Huyghens l'autore dell'Orologio oscillatorio, e a pi&ugrave; forte ra&shy;<lb/>gione dedurre, dai tanti falli notati e notabili, non esser di Galileo i libri dei <lb/>moti locali e dei proietti. </s></p><p type="main">

<s>Faceva dunque propriamente al Nelli pi&ugrave; difetto il senso comune che <lb/>la logica, e che mancasse a lui la scienza necessaria per scriverne la storia <lb/>&egrave; notissimo a chi ha letto que'suoi loquaci volumi; ma a cui fosse venuta <lb/>meno la pazienza, pu&ograve; servire il sapere quel ch'egli dice a sfregiar le pro&shy;<lb/>posizioni dal Marchetti ordinate, per concludere in ultimo la verit&agrave; dell'as&shy;<lb/>sunto galileiano. </s>

<s>La seconda di quelle proposizioni, che dall'Autore si mette <lb/>per <emph type="italics"/>Fondamento alla scienza universale del moto,<emph.end type="italics"/> &egrave; cos&igrave; formulata: &ldquo; Mo&shy;<lb/>menta eiusdem ponderis, supra diversas planorum inclinationes, eam inter se <lb/>habent rationem, quam perpendiculares orizonti demissae a sublimibus eo&shy;<lb/>rumdem planorum punctis, aequalesque ex ipsis longitudines abscindenti&shy;<lb/>bus &rdquo; (Pisis 1674, pag. </s>

<s>9). &ldquo; Questa, dice il Nelli, la propose e dimostr&ograve; <lb/>prima di ogni altro a me noto il Galileo nella <emph type="italics"/>Scienza meccanica,<emph.end type="italics"/> dopo di <lb/>cui la dimostr&ograve; ancora il Torricelli nella sua III proposizione, in tempo che <lb/>questi, per quanto io argomento dal suo schietto parlare, non aveva ancora <lb/>notizia del detto trattato di Galileo &rdquo; (Saggio cit., pag. </s>

<s>24, 25). Chi scrisse <lb/>cos&igrave; non doveva aver letta mai la <emph type="italics"/>Scienza meccanica,<emph.end type="italics"/> perch&egrave; Galileo sup&shy;<lb/>pone ivi solamente la verit&agrave; del Teorema, che poi incidentalmente dimostr&ograve; <lb/>nella sesta proposizione del Dialogo terzo, dove non avendo il Torricelli sa&shy;<lb/>puto riconoscere il gi&agrave; fatto, si lusing&ograve; d'esser egli stato il primo. </s>

<s>Come <lb/>non lesse il Nelli quel trattato meccanico, cos&igrave; pu&ograve; credersi che non leggesse <lb/>e non intendesse gli altri di Galileo, a quel modo che non gli leggono e non <lb/>gl'intendono tanti altri al pari di lui elogiatori del divino Uomo; ond'es-<pb xlink:href="020/01/2407.jpg" pagenum="32"/>sendo la sentenza loro senza giudizio &egrave; meglio proceder oltre per vedere, <lb/>giacch'&egrave; un'occhiata sola, qual sia quella nuova forma, che si diceva aver <lb/>data il Marchetti alla sua seconda proposizione sopra annunziata, e dalla <lb/>quale si facevano dipendere le altre tre concludenti la verit&agrave; fondamentale <lb/>della scienza universale del moto. </s></p><p type="main">

<s>Scendano (tale &egrave; la dimostrazione a cui l'analisi ha reciso le lussuria <lb/><figure id="id.020.01.2407.1.jpg" xlink:href="020/01/2407/1.jpg"/></s></p><p type="caption">

<s>Figura 14.<lb/>delle parole) dallo stesso perpen&shy;<lb/>dicolo BC (fig. </s>

<s>14) le vie oblique <lb/>AB, BD, e perch&egrave; quella &egrave; neces&shy;<lb/>sariamente pi&ugrave; lunga di questa, <lb/>sia dunque AF l'uguale,e si con&shy;<lb/>duca il perpendicolo FG: il Teo&shy;<lb/>rema meccanico gi&agrave; nella prima <lb/>proposizion dimostrato, e i trian&shy;<lb/>goli simili ABC, AFG danno M.oDB:M.oAB=AB:BD=AB:AF= <lb/>BC:FG, d'onde, osservando che M.oAB=M.oAF, &egrave; conseguito il proposito. </s></p><p type="main">

<s>La terza, nella quale si dimostra che i tempi per i piani ugualmente <lb/>clevati son proporzionali agli spazi, e la quinta che, dall'aversi i tempi pro&shy;<lb/>porzionali agli spazi, conclude dover essere le velocit&agrave; uguali, troppo risen&shy;<lb/>tono l'imitazione delle dimostrazioni date dagli Autori precedenti, perch&egrave;, <lb/>presa BF (nella figura 14) terza proporzionale dopo AB, BD, anche il Mar&shy;<lb/>chetti dimostra che, avendo il grado della velocit&agrave; in F la medesima pro&shy;<lb/>porzione tanto alla velocit&agrave; in A, quanto alla velocit&agrave; in D, queste debbono <lb/>essere tra loro uguali. </s>

<s>&ldquo; Ergo gradus velocitatis in puncto F eamdem habe&shy;<lb/>bit proportionem, ad gradum velocitatis in puncto A, quam ad gradum ve&shy;<lb/>locitatis in puncto D: ideoque gradus velocitatis acquisiti in A et D aequales <lb/>sunt &rdquo; (Fundamenta cit., pag. </s>

<s>21). &Egrave; vero dunque che la novit&agrave; non s'in&shy;<lb/>trodusse dal Marchetti, altro che nella sua seconda proposizione, ma l'utile <lb/>che conseguiva, o che poteva conseguire alla scienza da questo dispregiato <lb/>opuscolo del professore pisano, era quello di ridurla sui sentieri prima aperti <lb/>in Italia, e segnati da Galileo, dal Torricelli e dal Baliani. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Tale, quale s'&egrave; da noi fin qui narrata, &egrave; la storia delle sollecite cure, <lb/>che si dettero i Matematici, da Galileo infino all'Huyghens e al Marchetti, <lb/>per confermar la verit&agrave; del fondamento meccanico nelle menti comhattute dal <lb/>dubbio. </s>

<s>L'importanza dell'argomento ci ha tirato fuori di quella via, alla <lb/>quale intendiamo ora di ritornare, per salir dietr'essa nuovamente ad Ar&shy;<lb/>cetri, dove lasciammo Galileo che, perduta la vista e perci&ograve; la facolt&agrave; di po&shy;<lb/>tersi andare internando in pi&ugrave; profonde speculazioni, s'occupava nelle tene&shy;<lb/>bre notturne intorno ai primi e principali teoremi di Meccanica, per ordinarli <pb xlink:href="020/01/2408.jpg" pagenum="33"/>e disporli in miglior forma ed evidenza. </s>

<s>Cos&igrave; dicendo egli stesso al Baliani, <lb/>gli soggiungeva di aver la speranza di poter migliorare e ampliare lo scritto, <lb/>fin allora da s&egrave; pubblicato intorno alle nuove scoperte propriet&agrave; del moto. </s></p><p type="main">

<s>Uno de'primi frutti di quelle occupazioni fu il frammento dettato al Vi&shy;<lb/>viani, perch&egrave; alla prima occasione di una ristampa s'inserisse, dopo lo sco&shy;<lb/>lio alla proposizione seconda, nel terzo dialogo delle Scienze nuove. </s>

<s>Non fu <lb/>quella ristampa cos&igrave; sollecita come si credeva, e non ebbe perci&ograve; l'Autore <lb/>il tempo di veder l'opera sua ampliata e migliorata, secondo gli studii fat&shy;<lb/>tivi attorno, e secondo la conceputa speranza. </s>

<s>Anzi, quando fosse pure vis&shy;<lb/>suto infino al 1656, avrebbe dovuto sentir s&egrave;, e rimandare i lettori non so&shy;<lb/>disfatti, in trovar che i perfezionamenti ai Dialoghi, gi&agrave; tanto ammirati, si <lb/>riducevano alla sola dimostrazione inserita dopo il detto scolio dal nuovo edi&shy;<lb/>tore di Bologna. </s>

<s>In ripensare al fatto si sentono certi dubbi nascere nella <lb/>mente che ci ragiona: o non son vere quelle occupazioni notturne, delle <lb/>quali Galileo scriveva al Baliani, o de'frutti loro non si lasci&ograve; scritta o se <lb/>ne smarri la memoria. </s>

<s>E dall'altra parte, dovendo quelle scritture esser ri&shy;<lb/>maste in mano al Viviani, a cui furono dettate, com'era possibile che il di&shy;<lb/>scepolo zelantissimo volesse defraudare invidioso alla gloria o reluttar sacri&shy;<lb/>lego alle ultime volont&agrave; del Maestro, ritenendosi que'fogli, invece di mandargli <lb/>a Bologna al Rinaldini, che ne arricchisse la nuova edizione? </s>

<s>N&egrave; quelle ag&shy;<lb/>giunte ai Dialoghi dovevano aver minore importanza o dar minore sodisfa&shy;<lb/>zione ai lettori delle lettere al Castelli e all'Antonini, che dalle mani del <lb/>dottissimo signor Viviani, discepolo di s&igrave; gran maestro, diceva nella sua pre&shy;<lb/>fazione d'aver ricevute il bolognese tipografo Carlo Manolessi. </s></p><p type="main">

<s>Dietro queste considerazioni, ci si rendeva probabile che le speranze di <lb/>correggere e di ampliare gli scritti intorno al moto fossero, per l'impotente <lb/>vecchiezza dell'Autore, tornate vane: nonostante ci mettemmo a cercar per <lb/>i manoscritti galileiani con pi&ugrave; diligenza che mai, e fu particolarmente trat&shy;<lb/>tenuta la nostra attenzione sul Tomo quarto della Parte quinta. </s>

<s>Ivi ritrovansi <lb/>veramente di mano del Viviani scritti vari frammenti di dialogo, relativi alle <lb/>Nuove scienze, e la ben distinta calligrafia giovanile ci volle far credere da <lb/>principio che fossero in que'frammenti, dettati al suo giovane ospite, rac&shy;<lb/>colti da Galileo i frutti delle sue vigilie. </s>

<s>Essendo poi per la maggior parte <lb/>quegli argomenti riconosciuti da noi di grande importanza, e confermandoci <lb/>in credere impossibile che, se Galileo gli avesse dettati a quel modo coll'in&shy;<lb/>tenzione d'inserirli nella prima nuova edizione, non avrebbe il Viviani in <lb/>nessun modo mancato di adempire al suo sacrosanto dovere; ci volgemmo a <lb/>pensare che non dettatura altrui ma esercizio proprio di chi gli scrisse fos&shy;<lb/>sero quegli elaboratissimi dialogismi. </s>

<s>La probabilit&agrave; poi parve ci si riducesse <lb/>a certezza occorrendoci a notar nelle nostre ricerche quel che ora diremo. </s></p><p type="main">

<s>Nel citato manoscritto, volume quarto, ci abbattemmo a leggere, auto&shy;<lb/>grafo del Viviani, un colloquio, dove il Sagredo propone di dimostrar l'equi&shy;<lb/>librio nella bilancia di braccia disuguali, scansando quel comun principio dei <lb/>Meccanici reputato vizioso, perch&egrave; s'introduceva la causa, invece dell'effetto <pb xlink:href="020/01/2409.jpg" pagenum="34"/>presente. </s>

<s>Il Salviati approva come ragionevole il dubbio, e confessa di non <lb/>essere nemmen egli sodisfatto di concludere da un moto in potenza le ragioni <lb/>del moto attuale. </s></p><p type="main">

<s>L'argomento, come ben si vede, &egrave; di grande importanza, trattandosi di <lb/>decidere intorno alla verit&agrave; o alla falsit&agrave; del famoso principio delle velocit&agrave; <lb/>virtuali: che se il Salviati di questo frammento rappresentasse davvero il <lb/>Salviati del Dialogo, avremmo di qui il documento pi&ugrave; certo che Galileo, negli <lb/>ultimi anni della sua vita, repudi&ograve; quel principio, di cui il Lagrange gli attri&shy;<lb/>buiva la gloria dell'invenzione. </s>

<s>Ma come assicurarsi dell'identit&agrave; della per&shy;<lb/>sona, che qui e nelle Nuove scienze conversa? </s>

<s>Il leggervi scritto di mano <lb/>del Viviani <emph type="italics"/>di questo ho l'originale<emph.end type="italics"/> non ci quieta, potendogli noi doman&shy;<lb/>dare: a che dunque supplirvi con la copia? </s>

<s>o di quale originale si tratta, <lb/>essendo tolta all'Autore la facolt&agrave; di scrivere da s&egrave; medesimo? </s>

<s>Ma la riso&shy;<lb/>luzione di ogni dubbio ci avvenne, quando svolgendo noi, fra i manoscritti <lb/>dei Discepoli di Galileo, il tomo CXXXV intitolato <emph type="italics"/>Raccolta di esperienze <lb/>senz'ordine e di pensieri diversi di me Vincenzio Viviani, in diversi pro&shy;<lb/>positi sovvenutimi intorno a materie meccaniche, fisiche, astronomiche, filo&shy;<lb/>sofiche e altro;<emph.end type="italics"/> ci abbattemmo a leggere nei fogli 8, 9 quella scrittura da <lb/>noi pubblicata a pag. </s>

<s>165-67 del Tomo precedente, dove la sostanza del fram&shy;<lb/>mento dialogizzato s'espone in discorso disteso come pensiero proprio, sov&shy;<lb/>venuto allo stesso Viviani, che chiama testimone di ci&ograve; Cosimo Galilei. </s></p><p type="main">

<s>Proseguendo per&ograve; nei nostri studii, che potrebbero parere di arida eru&shy;<lb/>dizione, ma che servono a noi di scandaglio per misurare le profondit&agrave; del <lb/>pensiero, e di filo per aggirarci negl'intricati laberinti del cuore dell'uomo, <lb/>ci dovremmo persuadere, contro la nostra opinione, che l'aver fatti il Vi&shy;<lb/>viani suoi certi pensieri non vuol dire che non fossero stati prima di Gali&shy;<lb/>leo. </s>

<s>Fu deliberato atto di usurpazione o incoscienza del tempo e del modo <lb/>come gli erano sovvenuti i medesimi pensieri? </s>

<s>La risposta sarebbe lunga, e <lb/>senza alcuna probabilit&agrave; di cogliere il vero, e perci&ograve; basti a noi porre i fatti, <lb/>senza volerne penetrar le intenzioni, che forse traspariranno da ci&ograve;, che sa&shy;<lb/>remo per dire, prima che finisca il presente discorso. </s></p><p type="main">

<s>Raccolti fra'<emph type="italics"/>Pensieri varii<emph.end type="italics"/> del Viviani si trovano, nel citato manoscritto, <lb/>anche alcuni in materia de'proietti, ed &egrave; notabile fra questi quello, che noi <lb/>pubblicammo a pag. </s>

<s>569 del Tomo precedente. </s>

<s>Ora anche si osserva che alle <lb/>cose messe qui in discorso disteso si d&agrave; nel IV tomo della parte V forma e <lb/>andamento di dialogo, con manifesta intenzione d'inserirlo a pag. </s>

<s>270 del&shy;<lb/>l'edizione di Leida, dopo la VII proposizione della quarta Giornata. </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Di grazia, prima di passar pi&ugrave; avanti, fatemi restar ca&shy;<lb/>pace in qual modo si verifichi quel concetto, che l'Autore suppone come <lb/>chiaro ed indubitabile: dico che, venendo il proietto da alto a basso descri&shy;<lb/>vendo la semiparabola, cacciato per il converso da basso ad alto si debba ri&shy;<lb/>tornare per la medesima linea, ricalcando precisamente le medesime vestigia, <lb/>non avendo per ci&ograve; fare altro regolatore, che la direzione della semplice linea <lb/>retta toccante la gi&agrave; disegnata semiparabola: nella cui declinazione fatta dal-<pb xlink:href="020/01/2410.jpg" pagenum="35"/>l'alto al basso l'impeto trasversale orizontale mi quieta, nello ammettere la <lb/>molta curvazione nella sommit&agrave;, ma non so intendere n&egrave; discernere come <lb/>l'impulso fatto da basso, per una retta tangente, possa restituire un impeto <lb/>transversale, atto a regolare quella medesima curvit&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Voi, signor Simplicio, nel nominare la retta tangente, <lb/>lasciate una condizione, cio&egrave; tangente ed inclinata, la quale inclinazione &egrave; <lb/>bastante a fare che il proietto, in tempi eguali, si accosti orizontalmente per <lb/>spazi eguali all'asse della parabola, come forse pi&ugrave; a basso intenderemo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Ma intanto, per ora, ditemi, signor Simplicio, credete voi <lb/>che la linea descritta da un proietto da basso ad alto, secondo qualche incli&shy;<lb/>nazione, sia veramente un'intera linea parabolica, e che niente importi che <lb/>la proiezione si faccia da levante verso ponente o per l'opposito? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Credolo, purch&egrave; la elevazione sia la medesima, e che la <lb/>forza del proiciente sia la stessa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Come voi ammettete questo, fatto che si sia un tiro da <lb/>qualsivoglia parte, che cosa v'ha mettere in dubbio che la semiparabola da <lb/>basso ad alto del secondo tiro, che si faccia in contrario del primo, non sia <lb/>la medesima, che la seconda semiparabola del primo tiro, sicch&egrave; il proietto <lb/>ritorni per la medesima strada? </s>

<s>Quando ci&ograve; non fosse, n&egrave; anco la parabola <lb/>intera del secondo tiro sarebbe simile a quella del primo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Gi&agrave; intendo, e mi quieta, per&ograve; seguitiamo .... &rdquo; (MSS. <lb/>Gal., P. V, T. IV, fol. </s>

<s>4). </s></p><p type="main">

<s>Ora &egrave; manifesto essere un tal colloquio l'esplicazione di quest'altro, che <lb/>Galileo scriveva in semplice motto, di sua propria mano, a tergo del fol. </s>

<s>106, <lb/>nel secondo volume della parte quinta de'suoi Manoscritti. </s>

<s>Noi trascrivemmo <lb/>quel motto a pag. </s>

<s>568 del Tomo precedente, ma &egrave; bene ridurlo qui sotto gli <lb/>occhi dei nostri lettori, perch&egrave; si persuadano meglio di ci&ograve;, che ha da par&shy;<lb/>tecipar valore al nostro argomento. <lb/><figure id="id.020.01.2410.1.jpg" xlink:href="020/01/2410/1.jpg"/></s></p><p type="caption">

<s>Figura 15.</s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Che la palla ricacciata in su <lb/>descriva la medesima SX (fig. </s>

<s>15) mi par duro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Ma se non vi par duro che, <lb/>descrivendo la parabola intera YXS, possa ridescri&shy;<lb/>vere la SXY, non vedete che di necessit&agrave; fa la SX? &rdquo; </s></p><p type="main">

<s>Dicemmo aver fatto allora di ci&ograve; Galileo questo <lb/>semplice motto, quasi per un memoriale, quando <lb/>fosse venuto a distendere il Dialogo quarto. </s>

<s>Ma, <lb/>comunque sia, rimastosi il pensiero indietro, se ne sentiva pi&ugrave; che mai l'im&shy;<lb/>portanza, ora che andavano attorno, nella lettera al Mersennno, le invidiose <lb/>critiche del Cartesio. </s>

<s>Fu perci&ograve; sollecito Galileo di supplire alla sua dimen&shy;<lb/>ticanza, dettando al suo giovane ospite il dialogo da noi sopra trascritto, e <lb/>designandone il luogo, dove ei doveva inserirlo. </s>

<s>In mezzo a quelle sollecitu&shy;<lb/>dini accennava anzi all'intenzione di voler fare di pi&ugrave;, per confermar sem&shy;<lb/>pre meglio le sue dottrine contro gli oppositori, dimostrando che in tempi <lb/>uguali il proietto s'accosta orizontalmente per spazi uguali. </s>

<s>L'intenzione <pb xlink:href="020/01/2411.jpg" pagenum="36"/>per&ograve; non s'&egrave; trovato che fosse mandata ad effetto, e nemmeno il Torricelli <lb/><figure id="id.020.01.2411.1.jpg" xlink:href="020/01/2411/1.jpg"/></s></p><p type="caption">

<s>Figura 16.<lb/>vi s'applic&ograve; di proposito, bench&egrave; <lb/>si concluda lo stesso dalla quarta <lb/>proposizione del suo libro secondo; <lb/>imperocch&egrave;, avendosi ivi dimostrato <lb/>che gli spazi DE, FG, IH (fig. </s>

<s>16) <lb/>son passati ne'medesimi tempi, dal&shy;<lb/>l'essere le DI, EH parallele si con&shy;<lb/>clude che il proietto s'accosta o si <lb/>discosta orizontalmente per spazi <lb/>uguali. </s></p><p type="main">

<s>Ma non volendoci dilungar di <lb/>troppo dal proposito nostro, dicia&shy;<lb/>mo esser dunque un fatto certis&shy;<lb/>simo che il pensiero di dimostrar <lb/>come sia medesima la semipara&shy;<lb/>bola, o tirando di punto in bianco <lb/>o con direzione elevata, accolto dal Viviani fra'suoi, era prima albergato nel <lb/>cervello di Galileo. </s>

<s>E perch&egrave; la cosa &egrave; bene assai singolare, vogliamo aggiun&shy;<lb/>gere un altro esempio, pure in materia de'proietti, intorno ai quali mette <lb/>il Viviani per sue le considerazioni, da noi pubblicate nell'altro Tomo di <lb/>questa Storia della Meccanica. </s>

<s>Noi possiamo per&ograve; assicurare i lettori che <lb/>quelle medesime considerazioni erano state fatte gi&agrave; da Galileo, dettandole <lb/>cos&igrave; come noi le trascriviamo a Marco Ambrogetti, in quel tempo che si <lb/>pensava a far ristampare in latino, insieme con le altre opere, anche i Dia&shy;<lb/>loghi del moto. </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Summa quidem perspicuitate, atque ingenio plena sunt <lb/>vestra haec inventa, et si eo prorsus modo, quo mente percipiuntur, ita exe&shy;<lb/>qui liceret; utilitas, et praesertim in re militari, non mediocris esset existi&shy;<lb/>manda. </s>

<s>Sed ea quae extrinsecus accidentia in ipsa tractatione operis exitum <lb/>perturbare possunt, ita multa atque talia existunt, ut propterea fructus, qui <lb/>esset inde percipiendus, imminui valde videatur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Non ideo deserendae artes vel negligendae sunt, quia <lb/>speratum non semper sortiantur eventum, neque enim Medicina ars ab usu <lb/>est abligenda, quia non omnes languores curet, vel eos ipsos quos curat non <lb/>tam brevi temporis spatio, et ea medicaminum quam vellemus lenitate am&shy;<lb/>bigit et expellit &rdquo; (MSS. Gal., P. V, T. IV, fol. </s>

<s>13). </s></p><p type="main">

<s>Come dunque &egrave; certo che son di Galileo questi pensieri, cos&igrave; teniamo <lb/>per certo che fosse da lui stesso dettato il dialogo dell'equilibrio della bilan&shy;<lb/>cia di braccia disuguali, bench&egrave; anche questo discorso, insieme con gli altri <lb/>due relativi ai proietti si trovi, come s'&egrave; detto, nella <emph type="italics"/>Raccolta<emph.end type="italics"/> del Viviani. </s>

<s><lb/>E perch&egrave; vedasi che, sebben sotto forme accidentalmente diverse, medesime <lb/>son qua e l&agrave; le idee non solo, ma la maggior parte delle parole, e perci&ograve; uno <lb/>solo e medesimo l'Autore: ecco il dialogo dettato da Galileo, perch&egrave; lo con-<pb xlink:href="020/01/2412.jpg" pagenum="37"/>fronti chi vuole col discorso, appropriatosi dall'amanuense, e da noi pubbli&shy;<lb/>cato a pag. </s>

<s>165 del quarto Tomo. </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Sia sostenuta nel punto C (fig. </s>

<s>17) la Libbra di braccia <lb/>disuguali, AC maggiore, CB minore. </s>

<s>Cercasi la ragione onde avvenga che, <lb/>posti nell'estremit&agrave; due pesi uguali A, B, la Libbra non resti in quiete ed <lb/><figure id="id.020.01.2412.1.jpg" xlink:href="020/01/2412/1.jpg"/></s></p><p type="caption">

<s>Figura 17.<lb/>equilibrio, ma inclini dalla parte del brac&shy;<lb/>cio maggiore, trasferendosi come in EF. </s>

<s><lb/>La ragione, che comunemente se ne as&shy;<lb/>segna, &egrave; perch&egrave; la velocit&agrave; del peso A, <lb/>nello scendere, sarebbe maggiore della <lb/>velocit&agrave; del peso B, per essere la distanza <lb/>CA maggiore della CB, onde il mobile A, <lb/>quanto al peso uguale al B, lo supera <lb/>quanto al momento della velocit&agrave;, e per&ograve; <lb/>gli prevale e scende sollevando l'altro. </s>

<s>Dubitasi circa il valore di tal ragione, <lb/>la quale pare che non abbi forza di concludere, perch&egrave; &egrave; ben vero che il <lb/>momento di un grave si accresce congiunto con velocit&agrave; sopra il momento <lb/>di un grave, che sia costituito in quiete, ma che, posti ambedue in quiete, <lb/>cio&egrave; dove non sia pur moto, non che velocit&agrave; maggiore di un'altra, quella <lb/>maggioranza, che non &egrave; ma ancora ha da essere, possa produrre un effetto <lb/>presente, ha qualche durezza nel potersi apprendere, ed io specialmente ci <lb/>sento difficolt&agrave; notabile. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; V. S. ha molto ben ragione di dubitare, ed io ancora, <lb/>non restando ben sodisfatto di simile discorso, trovai da quietarmi per un <lb/>altro verso molto semplice e speditivo, senza suppor niente, altro che la prima <lb/>e comunissima nozione, cio&egrave; che le cose gravi vanno all'ingi&ugrave; in tutte le <lb/>maniere che gli viene permesso. </s>

<s>Quando nella Libbra AB voi ponete due pesi <lb/>eguali, se voi la lascerete andare liberamente, ella se ne caler&agrave; al centro <lb/>delle cose gravi, mantenendo sempre il centro della sua gravit&agrave;, che &egrave; il <lb/>punto di mezzo D, nella retta che da esso va al centro universale. </s>

<s>Ma se voi <lb/>a cotal moto opporrete un intoppo sotto il centro D, il moto si fermer&agrave;, re&shy;<lb/>stando la Libbra con i suoi due pesi in equilibrio. </s>

<s>Ma se l'intoppo si met&shy;<lb/>ter&agrave; fuori del centro D, come tassello in C, tale intoppo non fermer&agrave; la Bi&shy;<lb/>lancia, ma devier&agrave; il centro D dalla perpendicolare, per la quale camminava, <lb/>e lo far&agrave; scendere per l'arco DO. Insomma, la Libbra con i due pesi &egrave; un <lb/>corpo ed un grave solo, il cui centro della gravit&agrave; &egrave; il punto D, e questo <lb/>solo corpo grave scender&agrave; quanto potr&agrave;, e la sua scesa &egrave; regolata dal cen&shy;<lb/>tro di gravit&agrave; O: e cos&igrave; quel che scende &egrave; tutto il corpo o aggregato e com&shy;<lb/>posto della Libbra e suoi pesi. </s>

<s>La risposta dunque propria alla interrogazione <lb/><emph type="italics"/>Perch&egrave; inclini la Libbra ecc.<emph.end type="italics"/> &egrave; perch&egrave;, come quella che &egrave; una mole sola, <lb/>scende e si avvicina quanto pu&ograve; al centro comune di tutti i gravi &rdquo; (MSS. <lb/>Gal., P. V, T. IV, fol. </s>

<s>41 a t.). </s></p><p type="main">

<s>Qual si fosse per&ograve; il luogo, assegnato per la pi&ugrave; opportuna inserzione <lb/>di questo frammento, non apparisce da nessuna parte del manoscritto, e noi <pb xlink:href="020/01/2413.jpg" pagenum="38"/>troviamo gran difficolt&agrave; nell'indovinarlo. </s>

<s>Delle leggi delle equiponderanze, <lb/>nelle Libbre di braccia disuguali, si tratta a principio del secondo Dialogo, <lb/>dove si pongono quelle leggi per fondamento alla dottrina delle resistenze <lb/>dei solidi: e perch&egrave; la dimostrazione procede sull'esempio di Archimede, <lb/>senza invocare quel principio delle velocit&agrave; virtuali professato gi&agrave; negli avver&shy;<lb/>timenti della <emph type="italics"/>Scienza meccanica;<emph.end type="italics"/> si direbbe che fosse il sopra scritto fram&shy;<lb/>mento dettato con l'intenzione d'inserirlo l&agrave; nel detto Dialogo, quasi per <lb/>render ragione dell'aver tenuto altro metodo da quel primo che, concludendo <lb/>dalla potenza all'atto, s'incominciava ora da molti a tener per dubbioso. </s>

<s>Ma <lb/>se fossero veramente stati scelti dal Salviati i modi archimedei, per qualche <lb/>scrupolo natogli infin da quel tempo intorno al principio delle velocit&agrave; vir&shy;<lb/>tuali, perch&egrave; tornare, sul terminar della quarta Giornata, ad applicarlo alla <lb/>soluzion del problema dell'equilibrio tra i gran pesi attaccati all'estremit&agrave; <lb/>di una corda orizontalmente distesa, e il piccolo peso che la tira nel mezzo? </s></p><p type="main">

<s>Un altro pensiero per&ograve; insorge a complicare le difficolt&agrave; nella nostra <lb/>mente, perch&egrave;, mentre nella Scienza meccanica si dimostra il teorema delle <lb/>proporzioni tra il momento del grave nel perpendicolo, e il momento nel <lb/>piano inclinato, con aggressione diversa da Pappo, ma concludendolo dalla <lb/>teoria della leva angolare; ora, nel dimostrare il supposto antico e nel det&shy;<lb/>tare al Viviani il discorso in proposito, torna a invocare il principio delle <lb/>velocit&agrave; virtuali. </s>

<s>Quello &egrave; anzi il luogo, in cui si fa del detto principio la <lb/>professione pi&ugrave; aperta e l'applicazione pi&ugrave; esatta, e ivi principalmente lo ri&shy;<lb/>conobbe e lo addit&ograve; il Lagrange, quando, a superesaltare la gloria di Gali&shy;<lb/>leo, ne volle attribuire a lui l'invenzione. </s></p><p type="main">

<s>Come dunque, nelle aggiunte da farsi per migliorare i Dialoghi del moto, <lb/>potevano stare insieme il discorso, in cui si dimostrava il Teorema meccanico <lb/>col principio delle velocit&agrave; virtuali, e questo frammento, che dee esser pure <lb/>stato dettato dal medesimo Galileo, in cui al Sagredo, che trovava difficolt&agrave; ad <lb/>apprendere come quella causa che non &egrave; ma ha da essere possa produrre un <lb/>effetto presente, il Salviati risponde ch'egli aveva molto ben ragione di dubitare? </s></p><p type="main">

<s>Sembra a noi non si poter risolvere la questione altrimenti che, osser&shy;<lb/>vando come il mormorio contro il principio delle velocit&agrave; virtuali, principio <lb/>antichissimo nella Scienza meccanica, incominci&ograve; in Roma fra i discepoli del <lb/>Castelli, e le ragioni del Nardi convinsero il Torricelli, da cui facilmente si <lb/>insinuarono nel Viviani, il quale inger&igrave; lo scrupolo nello stesso Galileo, poco <lb/>dopo ch'egli aveva dettato quel suo discorso, per dimostrar ci&ograve; che prima <lb/>aveva supposto. </s>

<s>Forse l'intenzione di mettere il dialogo ultimamente da noi <lb/>trascritto non era quella di bandire addirittura dalla scienza del moto le ve&shy;<lb/>locit&agrave; in potenza, ma di suggerire a chi ci avesse trovato difficolt&agrave; un'altra <lb/>maniera di dimostrar le medesime cose. </s>

<s>Si sar&agrave; questa intenzione aspettato <lb/>a renderla espressa, quando si fosse sul punto di pubblicar le aggiunte ai <lb/>colloqui, in modo da stare l&igrave; insieme senza contradirsi, ma perch&egrave; a quel <lb/>punto Galileo mai non giunse, rimasero que'solitari pensieri, per le carte <lb/>disordinate, alle nostre disputazioni. </s></p><pb xlink:href="020/01/2414.jpg" pagenum="39"/><p type="main">

<s>Di un altro frammento, di cui il Viviani, che l'aveva attinto dall'oracolo <lb/>di Galileo, ci lasci&ograve; la copia; la destinazione, dietro le seguenti considerazioni <lb/>si presenta pi&ugrave; manifesta. </s>

<s>Nel primo Dialogo, a proposito del mezzo, che im&shy;<lb/>pedisce il naturale acceleramento dei gravi, era stato affermato dal Salviati <lb/>&ldquo; che finalmente la velocit&agrave; perviene a tal segno, e la resistenza del mezzo <lb/>a tal grandezza che, bilanciandosi fra loro, levano il pi&ugrave; accelerarsi e ridu&shy;<lb/>cono il mobile in un moto equabile ed uniforme, nel quale egli continua poi <lb/>di mantenersi sempre &rdquo; (Alb. </s>

<s>XIII, 77). Ora il Cartesio, leggendo tali cose, <lb/>ebbe a notarle di errore, perch&egrave; con calcolo matematico dimostrava essere <lb/>impossibile che il cadente giunga mai mai a tal punto della sua discesa, da <lb/>cui, per ragguagliarsi l'accelerazione della velocit&agrave; con l'impedimento del <lb/>mezzo, cominciasse il moto, d'accelerato ch'era prima, a diventare uniforme. </s>

<s><lb/>Vennero alle orecchie di Galileo queste censure, prima che si divulgassero <lb/>nell'Epistola al Mersenno, e perch&egrave; l'origine dell'errore la faceva il Censore <lb/>principalmente dipendere dal non essersi ben definita dall'Autor de'dialoghi <lb/>nuovi la natura della forza di gravit&agrave;, che &egrave; intrinseca al mobile e no stra&shy;<lb/>niera, sovvenne a Galileo l'arguto pensiero di confermare l'asserita unifor&shy;<lb/>mit&agrave; del moto, concludendola da quello stesso pi&ugrave; recondito principio, di cui <lb/>s'era servito per investigar la causa dell'accelerazion naturale. </s>

<s>Ma senten&shy;<lb/>dosi contrapporre la certezza del calcolo, non poteva sperare la prevalenza <lb/>del suo pensiero, ch'egli perci&ograve; modestamente mette in bocca a Simplicio. </s></p><p type="main">

<s>In quella prefazione dunque al trattato <emph type="italics"/>De motu naturaliter accelerato,<emph.end type="italics"/><lb/>con la quale incomincia la seconda parte del dialogo terzo, il Sagredo fa di&shy;<lb/>pender l'acceleramento del mobile, che cade in basso, dal prevaler che fa <lb/>via via sempre pi&ugrave; la gravit&agrave; al moto proiettizio in alto; a che oppone Sim&shy;<lb/>plicio non potersi applicare il discorso &ldquo; se non a quei moti naturali, ai quali <lb/>sia preceduto un moto violento &rdquo; (ivi, pag. </s>

<s>159). Il Sagredo stesso per&ograve; rispon&shy;<lb/>deva all'opposizione &ldquo; che il precedere alla caduta del sasso una quiete lunga <lb/>o breve o momentanea non fa differenza alcuna, sicch&egrave; il sasso non parta <lb/>sempre affetto da tanta virt&ugrave; contraria alla sua gravit&agrave;, quanta appunto bastava <lb/>a tenerlo in quiete &rdquo; (ivi, pag. </s>

<s>160). Dopo le quali parole Simplicio doveva <lb/>soggiunger cos&igrave;, secondo che Galileo stesso era venuto dettando al Viviani: </s></p><p type="main">

<s>&ldquo; Voi dite, signor Sagredo, che l'accelerazione di quel sasso dipende <lb/>dal continuo vantaggio della sua medesima gravit&agrave; sopra quella virt&ugrave; con&shy;<lb/>traria impressagli, che era di proibirgli lo scendere. </s>

<s>Adunque ogni volta che <lb/>mancasse questo vantaggio o superiorit&agrave; al cadente resterebbe di pi&ugrave; acce&shy;<lb/>lerarsi: sicch&egrave; a quel grave che, partendosi dalla quiete, v&agrave; con la sua gra&shy;<lb/>vit&agrave; superando continuamente quella virt&ugrave; contraria prima datagli, e in conse&shy;<lb/>guenza maggiormente prevalendosi della sua medesima gravit&agrave;, e non essendo <lb/>quell'impeto straniero infinito; dopo che si sar&agrave; consumato, non gli rester&agrave; <lb/>altro che la propria gravit&agrave;. </s>

<s>Con l'impeto dunque di quella sola seguitando <lb/>di moversi, non si accelerer&agrave;, ma equabile si rimarr&agrave; &rdquo; (MSS. Gal., P. V, <lb/>T. IV, fol. </s>

<s>29). Il Salviati per&ograve;, per troncare il discorso, ch'ei molto ben <lb/>conosceva non poter competere con la matematica del Cartesio, entra di mezzo <pb xlink:href="020/01/2415.jpg" pagenum="40"/>a dire, come nella prima edizione di Leida e in tutte le altre, <emph type="italics"/>Non mi pare <lb/>opportuno di entrare al presente ....<emph.end type="italics"/> (Alb. </s>

<s>XIII, 160). </s></p><p type="main">

<s>Forse il desiderio di confermare il discorso con pi&ugrave; esplicite ragioni ma&shy;<lb/>tematiche, per dar migliore sodisfazione agli emuli Geometri valorosi di Fran&shy;<lb/>cia, sugger&igrave; a Galileo un'altra aggiunta, che si trova fra le copiate e distese <lb/>dal Viviani. </s>

<s>Nel primo Dialogo, verso la fine, vuole il Salviati persuadere a <lb/>Simplicio che i corpi scendono tanto pi&ugrave; lentamente in un mezzo, quanto <lb/>sono pi&ugrave; sminuzzati, perch&egrave; le superfice crescendo in maggior proporzione <lb/>delle moli, crescono anche secondo quella maggior proporzione, sopra la gra&shy;<lb/>vit&agrave;, gl'impedimenti: e riducendo la cosa all'esattezza geometrica afferma: <lb/>&ldquo; che in tutti i solidi simili le moli sono in sesquialtera proporzione delle <lb/>loro superfice &rdquo; (Alb. </s>

<s>XIII, 93). La proposizione s'appoggia a certi calcoli <lb/>intorno ai cubi, ma perch&egrave; non pareva sicuro affidare una conclusion gene&shy;<lb/>rale sopra due o tre esempi numerici, Galileo pens&ograve; che, dopo le parole dette <lb/>dal Salviati, <emph type="italics"/>E intanto notate, signor Simplicio, che io non equivocai, quando <lb/>poco fa dissi la superfice de'solidi minori esser grande in comparazione <lb/>di quella dei maggiori<emph.end type="italics"/> (Alb. </s>

<s>XIII, 93), dovesse il Sagredo soggiungere cos&igrave;, <lb/>invece di quella intramessa, nella quale esso Simplicio si chiamava intera&shy;<lb/>mente appagato di un teorema geometrico, confessando di non saper nulla di <lb/>Geometria: </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Notizia veramente bella, n&egrave; priva di utilit&agrave;, per quanto <lb/>io penso, e bench&egrave;, nel caso di che si tratta, non si assesti puntualmente <lb/>come sarebbe in un sasso irregolare rotto in minutissime particelle irregola&shy;<lb/>rissime, e perci&ograve; incognite; tuttavia l'aver dimostrato il grande accrescimento, <lb/>che si fa di superfice, nella continuazione di spezzamento di qualsivoglia so&shy;<lb/>lido, mentre si risolva in minime particelle fra di loro simili ed eguali; ci <lb/>assicura il somigliante dovere accadere in tutti gli altri stritolamenti. </s>

<s>Ma mi <lb/>par di notare un altro modo di potere, in una sola e semplice operazione, <lb/>ritrovare l'eccesso delle superfice di molti solidi, tra di loro simili ed eguali, <lb/>sopra la superfice di un solo pur simile, ma uguale a tutti quelli. </s>

<s>Questo mi <lb/>par che ci venga dato dalla radice cuba del numero de'piccoli solidi, come <lb/>per esempio: la superfice di mille palline quanto &egrave; maggiore della palla sola <lb/>uguale e simile a tutte quelle eguali e simili tra di loro? </s>

<s>Diremo esser mag&shy;<lb/>giore dieci volte, per esser dieci la radice cuba di mille e dieci volte il dia&shy;<lb/>metro della grande conterr&agrave; il diametro della piccola. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Questa &egrave; la vera, e vedesi finalmente che le superfice <lb/>sopra dette, a due lati omologhi, uno del gran solido ed uno del piccolo, si <lb/>rispondono contrariamente. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Ho avuto gusto grande di questo discorso .... &rdquo; (MSS. <lb/>Gal., P. V, T. IV, fol. </s>

<s>38). </s></p><p type="main">

<s>Sono in questi colloqui fra il Sagredo e il Salviati annunziati teoremi <lb/>verissimi, come si pu&ograve; riscontrare con facili dimostrazioni. </s>

<s>Chiamate infatti <lb/>M, M&prime; le moli di due solidi simili, S, S&prime; le loro superficie, e L, L&prime;due lati <lb/>omologhi, abbiamo per gli elementi della Geometria M:M&prime;=L3:L&prime;3; S:S&prime;= <pb xlink:href="020/01/2416.jpg" pagenum="41"/>L2:L&prime;2 e perci&ograve; M2:M&prime;2=S3:S&prime;2 ossia M:M&prime;=S3/2:S&prime;3/2, che conferma <lb/>la verit&agrave; del teorema annunziato dal Salviati <emph type="italics"/>esser ne'solidi simili le moli <lb/>in sesquialtera proporzione delle loro superfice.<emph.end type="italics"/></s></p><p type="main">

<s>Chiamato inoltre A il lato di un solido, B una delle N parti, in cui &egrave; <lb/>stato diviso, cosicch&egrave; abbiasi A=N.B, troveremo con facile discorso inter&shy;<lb/>cedere fra la superfice S del solido grande, e la somma S&prime; delle superfice <lb/>de'piccoli solidi uguali e simili, in cui fu diviso, la proporzione S:S&prime;= <lb/>1:N=B:A, che conferma la verit&agrave; dell'altro Teorema formulato dal Sal&shy;<lb/>viati: <emph type="italics"/>le superficie, a due lati omologhi, uno del gran solido ed uno del <lb/>piccolo, si rispondono contrariamente.<emph.end type="italics"/> Essendo poi le moli M, M&prime; come i <lb/>cubi dei lati omologhi, ossia M&prime;:M=B3:A3=1:N3, avremo N=3&radic;M/M&prime;, <lb/>e perci&ograve; S&prime;=S.3&radic;M/M&prime;. </s>

<s>Nell'esempio addotto dianzi dal Sagredo, essendosi <lb/>della palla grande fatto mille palline, avremo dunque M&prime;=1, M=1000: <lb/>onde S&prime;=S.3&radic;1000=10.S, ci&ograve; che fa esatto riscontro con quel che il <lb/>Sagredo stesso dianzi diceva <emph type="italics"/>essere la superficie di mille palline dieci volte <lb/>maggiore di quella della palla sola, uguale e simile a tutte quelle uguali <lb/>e simili tra loro.<emph.end type="italics"/></s></p><p type="main">

<s>Anche questi teoremi per&ograve; venivano da Galileo dimostrati per via di esempi <lb/>numerici, com'avremo occasione di veder meglio altrove, ond'&egrave; che il Viviani, <lb/>ripensando al Cartesio e agli altri matematici di Francia, i quali usandovi <lb/>l'algebra gli rendevano generali, diceva a Galileo che, per dar sodisfazione <lb/>agli emuli, sarebbe stato bene far, di quegli annunziati teoremi intorno ai <lb/>solidi simili e alle loro minutissime divisioni, una dimostrazione pi&ugrave; univer&shy;<lb/>sale. </s>

<s>Approvava il buon Vecchio il pensiero, ma riconoscendosi in quelle sue <lb/>miserabili condizioni impotente a mandarlo ad effetto, se ne affliggeva, ci&ograve; <lb/>che fece risolvere il Viviani stesso d'esercitarvisi attorno. </s>

<s>Una mattina entra <lb/>con un foglio in mano, dov'era scritta la dimostrazione, nella camera di Ga&shy;<lb/>lileo, il quale se ne rallegr&ograve;, compiacendosi inoltre che fosse messa in dia&shy;<lb/>logo, per inserirla al suo proprio luogo, invece del frammento che avevano <lb/>insieme, pochi giorni fa, preparato. </s>

<s>Abbiamo il documento di ci&ograve; in una <lb/>carta, sopra la quale il Viviani, di sua propria mano, cos&igrave; scriveva: &ldquo; Fac&shy;<lb/>cia 91, verso 12 (dell'edizione di Leida, e faccia 93, verso 35 dell'Alb&egrave;ri). <lb/>Dopo quelle parole di Simplicio, che dicono <emph type="italics"/>fuor che quello che concluden&shy;<lb/>temente dimostrano,<emph.end type="italics"/> si potr&agrave; aggiungere quanto appresso io dimostro cos&igrave;, <lb/>contentandosene il medesimo signor Galileo: &rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; La verit&agrave; della conclusione nei particolari si vede per <lb/>esperienza assai manifesta, ma io desidererei avere una dimostrazione, la <lb/>quale universalmente m'insegnasse che, non solamente nel risolvere il solido <lb/>in molti simili si accresce la superficie, ma ancora secondo qual proporzione <lb/>ella venga moltiplicata. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2417.jpg" pagenum="42"/><p type="main">

<s>&ldquo; SALVIATI. &mdash; Bellissima &egrave; la proposizione, ma non men bella la dimo&shy;<lb/>strazione. </s>

<s>Dico pertanto che diviso il lato di un solido in quante si vogliano <lb/>parti uguali, e risoluto tal solido in solidi tra di loro uguali e simili al tutto, <lb/>dei quali i lati omologhi siano uguali a una parte del lato omologo del tutto; <lb/>la superfice di tutti questi piccoli presi insieme, alla superficie del grande e <lb/>intero, hanno la medesima proporzione che il lato omologo del grande diviso, <lb/>al lato omologo di uno dei piccoli; cio&egrave; a una parte della divisione del gran <lb/>lato omologo: per il che dimostrare propongo questo Lemma: &rdquo; </s></p><p type="main">

<s>&ldquo; Se saranno quattro numeri continui proporzionali, il primo dei quali <lb/>sia l'unit&agrave;, il quarto di necessit&agrave; sar&agrave; numero cubo, il terzo sar&agrave; quadrato, <lb/>il secondo sar&agrave; radice, di ambedue, il che si dimostra cos&igrave;: &rdquo; </s></p><p type="main">

<s>&ldquo; Essendo li tre primi proporzionali, il prodotto del primo nel terzo &egrave; <lb/>uguale al quadrato del secondo. </s>

<s>Ma il prodotto del primo nel terzo &egrave; l'istesso <lb/>terzo, perch&egrave; il primo &egrave; l'unit&agrave;; adunque il terzo &egrave; il quadrato del secondo, <lb/>e questo &egrave; la sua radice. </s>

<s>E perch&egrave; il prodotto del primo nel quarto &egrave; uguale <lb/>al prodotto del secondo nel terzo, e il prodotto del primo nel quarto &egrave; lo <lb/>stesso quarto; adunque il prodotto del secondo nel terzo &egrave; uguale al quarto. </s>

<s><lb/>Ma il terzo &egrave; quadrato, la cui radice &egrave; il secondo, ed il prodotto del qua&shy;<lb/>drato nella sua radice fa cubo; adunque il quarto &egrave; cubo, il che si doveva <lb/>dimostrare. </s>

<s>&rdquo; (MSS. Gal., P. V., T. IX, fol. </s>

<s>92). </s></p><p type="main">

<s>Il discorso si rende per segni algebrici molto pi&ugrave; chiaro, chiamando A, <lb/>B, C, D i quattro numeri continuamente proporzionali. </s>

<s>Perch&egrave; basta scrivere <lb/>la proporzione A:B=B:C=C:D, per vedere a colpo d'occhio che, se <lb/>A=1, sar&agrave; B2=C, D=C.B=B3, perci&ograve; B=&radic;C=3&radic;D. </s>

<s>Ma ascoltiamo <lb/>dopo questo lemma la dimostrazione, che Galileo si contentava fosse messa <lb/>in bocca al suo Salviati: </s></p><p type="main">

<s>&ldquo; Dichiarato questo, verremo alla dimostrazione dell'altra principal con&shy;<lb/>clusione, la quale esemplificheremo per maggior chiarezza nei solidi cubi. </s>

<s><lb/>Intendasi la linea B esser lato di un dado, o di un cubo vogliam dir, solido, <lb/>diviso in quante si vogliano parti uguali, ad una delle quali sia uguale la A, <lb/>e di essa e del numero delle parti di B sia terzo proporzionale il numero C, <lb/>e quarto il D: &egrave; manifesto, per il lemma di sopra, il numero D esser cubo, <lb/>ed il C numero quadrato, ed il numero B lor radice. </s>

<s>E perch&egrave; li quattro <lb/>numeri A, B, C, D sono continui proporzionali, il numero D al numero A <lb/>aver&agrave; tripla proporzione di quella, che gli ha il numero B. </s>

<s>Ma il solido cubo <lb/>del lato B, al cubo di A, ha tripla proporzione di quella del lato B ad A, <lb/>cio&egrave; del medesimo numero B ad A; adunque la medesima proporzione ha il <lb/>numero D al numero A, che il cubo solido del lato B, al cubo solido del <lb/>lato A. </s>

<s>Adunque tanti cubi solidi del lato A, quante sono le unit&agrave; del nu&shy;<lb/>mero D, saranno uguali al cubo solido del lato B. Inoltre, per essere l&igrave; tre <lb/>numeri A, B, C proporzionali, la proporzione del numero C all'A &egrave; doppia <lb/>di quella del numero B all'A. </s>

<s>Ma la proporzione del quadrato della linea B, <lb/>al quadrato della linea A, &egrave; doppia parimente della proporzione della mede-<pb xlink:href="020/01/2418.jpg" pagenum="43"/>sima B ad A, cio&egrave; del numero B ad A; adunque il numero C all'A, unit&agrave;, <lb/>ha l'istessa proporzione del quadrato B al quadrato A. </s>

<s>Tanti quadrati dun&shy;<lb/>que del lato A, quante sono le unit&agrave; del numero C, sono uguali ad un solo <lb/>quadrato di B, ed il sescuplo al sescuplo, cio&egrave; la superfice di tanti cubi del&shy;<lb/>l'A, quante unit&agrave; ha il numero C, sono, prese insieme, uguali alla superficie <lb/>del solo cubo di B. </s>

<s>Adunque le superficie di tanti cubetti di A quant'&egrave; il <lb/>numero C.... &rdquo; (ivi). </s></p><p type="main">

<s>Il discorso rimane a questo punto interrotto, venendo meno, dopo l'ul&shy;<lb/>tima riga, lo spazio, e mancando nel volume la carta, nella quale dovevano <lb/>essere state scritte dal Viviani le poche rimanenti parole di conclusione. </s>

<s>Si <lb/>suppliscono queste per&ograve; assai facilmente, ragionando in conseguenza de'due <lb/>principii gi&agrave; dimostrati, e la verit&agrave; de'quali immediatamente dipende dalle <lb/>proporzionalit&agrave; poste nel lemma. </s>

<s>Da esse infatti deriva D:A=B3:1= <lb/>B3:13=B3:A3, e di qui D.A3=AB3=B3; che vuol dire: <emph type="italics"/>tanti cubi <lb/>solidi del lato A, quante sono le unit&agrave; del numero D, sono uguali al cubo <lb/>solido del lato B.<emph.end type="italics"/> Deriva pure da quelle stesse proporzionalit&agrave; del Lemma <lb/>C:A=B2:12=B2:A2, e da ci&ograve; C.A2=B2: <emph type="italics"/>tanti quadrati dunque <lb/>del lato A, quante sono le unit&agrave; del numero C, sono uguali ad un solo <lb/>quadrato di B.<emph.end type="italics"/></s></p><p type="main">

<s>Chi fosse nel 1639, penetrato nella villa di Arcetri, avrebbe sentito echeg&shy;<lb/>giare le solitarie stanze in questi colloqui tra il Maestro e il discepolo, il <lb/>quale prendeva talvolta in mano, e sollevava la face a illuminar le tenebre <lb/>dello stesso Maestro. </s>

<s>Il fine principale di quei colloqui sapienti, quale pu&ograve; <lb/>riconoscersi ne'varii esempi da noi fin qui notati, era quello che Galileo di&shy;<lb/>chiarava nella sua lettera al Baliani, di ampliare cio&egrave; e di migliorare le cose <lb/>fin allora scritte intorno alla scienza del moto. </s>

<s>Ma presto s'ebbe a fare espe&shy;<lb/>rienza che non era, con quell'opera sola, il fine perfettamente conseguito, <lb/>perch&egrave;, dopo i benevoli che, desiderosi d'impossessarsi la mente di quelle <lb/>nuove dottrine, amavano di vederle in certe parti rese pi&ugrave; chiare, e in certe <lb/>altre meglio compiute; ci erano gli emuli e gl'invidiosi, dai quali null'altro <lb/>pi&ugrave; ardentemente si desiderava, che di cogliere que'galileiani documenti in <lb/>difetto, e, da una piaga sola facendo tutto intero il corpo apparire morboso, <lb/>proclamare al mondo che tutta la Scienza nuova si fondava sul falso. </s>

<s>Era uno <lb/>di cotesti emuli il Cartesio, ma le censure di lui si temevano forse meno di <lb/>certe altre, tanto pi&ugrave; mordaci, perch&egrave; pi&ugrave; dissennate. </s>

<s>Il Filosofo bretone in <lb/>fine, se gareggiava con Galileo nel conquistare il principato della Scienza, <lb/>non mancava di quel valore, di che erano privi i Gesuiti, i quali con le fra&shy;<lb/>gili canne peripatetiche in mano uscivano ambiziosamente in campo, a met&shy;<lb/>tersi fra i nuovi conquistatori. </s></p><p type="main">

<s>Anche contro costoro bisognava difendersi, se non appuntando la spada, <lb/>come si farebbe con gli orsi o coi leoni, menando almeno in tresca le mani, <lb/>come si fa per cacciarsi le mosche, e a ci&ograve; giusto pensava Galileo nelle sue <lb/>tenebre, specialmente quando s'incominci&ograve; a veder qualche effetto delle pre&shy;<lb/>sentite molestie. </s>

<s>In un bocconcello di carta, scritta senza dubbio dal Viviani <pb xlink:href="020/01/2419.jpg" pagenum="44"/>sul tavolino posto a pi&egrave; del letto di Galileo, o nella camera accanto dove si <lb/>giaceva il vecchio Maestro, sotto il titolo <emph type="italics"/>Domandar del Blancano<emph.end type="italics"/> si legge <lb/>cos&igrave; notato, con una certa mossa alla fiorentina: </s></p><p type="main">

<s>&ldquo; I. </s>

<s>La mi dichiari meglio, signor Galileo, come il mezzo detragga dal <lb/>grave; perch&egrave; la figura sferica sia contenuta sotto la minima superficie, come <lb/>si legge a carte 92 (della prima edizione di Leida). &rdquo; </s></p><p type="main">

<s>&ldquo; II. </s>

<s>A carte 93, l'aria reprime la velocit&agrave; del mobile, poich&egrave;, scari&shy;<lb/>cando un archibuso da grande altezza in gi&ugrave;, fa minor botta, che da una <lb/>minore: ed in altri luoghi dice che acquista pi&ugrave; velocit&agrave;, ed in conseguenza <lb/>avrebbe a far maggior colpo da grande altezza, che da piccola. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; III. </s>

<s>Par che stia come la circonferenza alla circonferenza, cos&igrave; la su&shy;<lb/>perficie alla superficie de'cilindri ugualmente alti. </s>

<s>Carte 55: par che stia <lb/>come il diametro C, al diametro A, cos&igrave; le loro circonferenze. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; IV. </s>

<s>Signor Galileo, i momenti dei cilindri ugualmente grossi, ma di&shy;<lb/>sugualmente lunghi, hanno eglino doppia proporzione delle loro resistenze <lb/>prese reciprocamente? </s>

<s>perch&egrave; pare che nella V proposizione la resistenza del <lb/>solido DG, a quella di DF, stia come DF a DG. &rdquo; </s></p><p type="main">

<s>&ldquo; V. </s>

<s>La settima proposizione non intendo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; VI. </s>

<s>A carte 134, la considerazione di que'due cilindri non la intendo. </s>

<s>&rdquo; <lb/>(MSS. Gal., P. V, T. IV, fol. </s>

<s>14). </s></p><p type="main">

<s>Il padre Giuseppe Biancani, interpetre di Aristotile profondo, e nel va&shy;<lb/>lor del quale i Gesuiti si confidavano molto, fu da loro mandato uno dei <lb/>primi perch&egrave; minasse l'edifizio galileiano, sicuri che lo manderebbe all'aria <lb/>con questi suoi domandari. </s>

<s>I quali che non fossero disprezzati par che sia <lb/>segno l'averne scritto un tal memoriale, ma quel vivace ingegno giovanile <lb/>del Viviani volle scherzarci un poco, come se ne avvedrebbe meglio colui, a <lb/>chi si potesse metter sott'occhio quel bocconcello di carta manoscritto, che, <lb/>a svolgere il volume, in luogo della <gap/>accia presenta il tergo. </s></p><p type="main">

<s>In ogni modo, &egrave; certo che si pensava a dar sodisfazione anche al nuovo <lb/>censore, ma a poco and&ograve; che il Viviani ebbe a perdere il suo tempo pi&ugrave; in <lb/>consolare e in curare i languori del Vecchio infermo, che in raccoglierne i <lb/>parti dell'ingegno. </s>

<s>Poco di poi dov&egrave; cedere il geloso ufficio al Torricelli, che <lb/>parve esser venuto ad Arcetri per assistere ai funerali, celebratisi infatti dopo <lb/>soli tre mesi. </s></p><p type="main">

<s>Anche morto per&ograve; Galileo, il Viviani persist&egrave; nella generosa intenzione <lb/>di attendere a migliorare i dialoghi delle Nuove scienze, e se mancando l'Au&shy;<lb/>tore veniva a mancar chi gli darebbe legittima autorit&agrave; di ampliarli, si sen&shy;<lb/>tiva maggiore la libert&agrave; in emendarne, senza passione, i pi&ugrave; notabili errori. </s>

<s><lb/>Procedeva dall'altra parte il Viviani sicuro del fatto suo, perch&egrave; sapeva che <lb/>le aggiunte ei le veniva facendo secondo la mente di Galileo, e le correzioni <lb/>secondo le leggi del calcolo e della retta ragione. </s>

<s>Che poi fosse veramente <lb/>cos&igrave;, lo vedranno i Lettori in queste altre due parti, che rimangono al pre&shy;<lb/>sente discorso. </s></p><pb xlink:href="020/01/2420.jpg" pagenum="45"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Tutto dunque in sollecitudine il Viviani di proseguir da s&egrave; solo l'opera <lb/>incominciata insieme con Galileo, svolgeva attentamente il libro delle Nuove <lb/>scienze, per notarvi i punti, dove le de trine de'Dialoghi qua volevano es&shy;<lb/>sere dichiarate meglio, e l&agrave; svolte nella bellezza e nella verit&agrave; di nuove con&shy;<lb/>seguenze. </s>

<s>Ei ne prendeva allora per suo uso, e ne lasciava per documento <lb/>alla storia il seguente memoriale: </s></p><p type="main">

<s>&ldquo; I. </s>

<s>Carte 6. SALV. &mdash; Dite pure ottuplo .... &rdquo; </s></p><p type="main">

<s>&ldquo; II. </s>

<s>Carte 11. SALV. &mdash; Ingegnosa veramente invenzione, e per intiera <lb/>esplicazione della sua natura mi par di scorgere, cos&igrave; per ombra, che qualche <lb/>altra speculazione si possa aggiungere .... &rdquo; </s></p><p type="main">

<s>&ldquo; III. </s>

<s>Carte 56. La dimostrazione del Torricelli dei cilindri. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; IV. </s>

<s>Carte 60. La dimostrazione che il poligono &egrave; medio tra due cer&shy;<lb/>chi, uno inscritto e l'altro isoperimetro, e la dimostrazione che qualunque <lb/>poligono circoscrittibile al cerchio &egrave; medio tra due qualsivogliano poligoni <lb/>simili, uno circoscrittibile al medesimo cerchio, e l'altro isoperimetro al detto <lb/>poligono. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; V. </s>

<s>Carte 70. Nel discorso del Salviati potrebbesi aggiungere la fabbrica <lb/>delle due palline, e con questa occasione accennare come lo strumento per <lb/>conoscere le mutazioni del caldo e del freddo nell'aria &egrave; invenzione del <lb/>Galileo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; VI. </s>

<s>Carte 81. Nel secondo modo di pesar l'aria si ha non solo il peso <lb/>di essa nel vacuo, ma dell'acqua ancora nel medesimo: cosa non avvertita <lb/>dal Galileo, per&ograve; notisi. </s>

<s>Perch&egrave;, aggiungendo al peso dell'acqua il peso di <lb/>quell'aria uscita, che &egrave; quanto l'acqua, si avr&agrave; il peso dell'acqua nel vacuo. </s>

<s><lb/>Ma perch&egrave; il lor peso nel vacuo ci vien dato da materia posta in aria, che <lb/>&egrave; l'arena, per&ograve; detto peso non sar&agrave; totalmente preciso. </s>

<s>Si aver&agrave; bene da tale <lb/>esperienza la proporzione del peso dell'acqua nel vacuo, al peso dell'aria nel <lb/>medesimo, che sar&agrave; come il contrappeso dell'acqua, con quel dell'aria, a <lb/>quel dell'aria. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; VII. </s>

<s>Carte 91. Dimostrazione da me trovata circa la moltiplicazione <lb/>delle superficie de'solidi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; VIII. </s>

<s>Carte 94. Dopo il discorso del Salviati circa il tiro del moschetto <lb/>in un corsaletto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; IX. </s>

<s>Carte 254. Il pensiero di Platone, e far quel calcolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; X. </s>

<s>Carte 284. Vedi l'ultimo verso che <emph type="italics"/>utilit&agrave;<emph.end type="italics"/> volesse dire il Galileo, <lb/>se della misura della linea parabolica, ovvero del modo di trovare le propo&shy;<lb/>sizioni dei moti de'proietti. </s>

<s>&rdquo; (MSS. Gal., P. V, T. IV, fol. </s>

<s>33). </s></p><p type="main">

<s>A questi dieci si riducevano i luoghi, nelle quattro giornate delle Nuove <pb xlink:href="020/01/2421.jpg" pagenum="46"/>scienze, presi in considerazion dal Viviani, e intorno ai quali ei si proponeva <lb/>di esercitare l'ingegno per migliorarli, avendogli Galileo stesso detto di averci <lb/>riconosciuta qualche imperfezione. </s>

<s>Non sempre si &egrave; trovato per&ograve; il proposito <lb/>messo ad effetto, o perch&egrave; cos&igrave; realmente avvenisse, o perch&egrave; siano andate <lb/>smarrite, o siano sfuggite alla nostra attenzione le schede relative. </s>

<s>Di quel <lb/>che abbiamo trovato renderemo ordinatamente conto qui ai nostri Lettori. </s></p><p type="main">

<s>Al proposito espresso nella nota prima sodisfaceva il Viviani, scrivendo <lb/>in margine alla pag. </s>

<s>6 di Leida quella postilla in lapis, che poi l'Alb&egrave;ri in&shy;<lb/>ser&igrave; a pag. </s>

<s>10 nel tomo XIII della sua edizione completa. </s>

<s>Ma all'ordigno <lb/>inventato da quel giovane parente del Sagredo, per poter con una corda ca&shy;<lb/>larsi da una finestra, senza crudelmente scorticarsi le palme delle mani, non <lb/>par che sapesse il Viviani trovar nessuna di quelle speculazioni, che credeva <lb/>di poter aggiungervi cos&igrave; facilmente il Salviati. </s></p><p type="main">

<s>Di bene altra importanza di questo ordigno, inventato da un giovane si&shy;<lb/>gnore, per rendere innocua la fuga ai giovani entrati nelle altrui case fur&shy;<lb/>tivi, erano que'teoremi geometrici intorno ai cilindri, a proposito de'quali il <lb/>Viviani accennava alla dimostrazione del Torricelli. </s>

<s>Ma perch&egrave;, da quel cenno <lb/>cos&igrave; frettoloso e solitario, non &egrave; facile intendere come, trattandosi di Galileo, <lb/>possa entrare di mezzo il Torricelli, che par si chiami a fargli da maestro; <lb/>convien ravviare il discorso, perch&egrave; dietro lui si rischiarino i nostri dubbi, <lb/>e si manifestino meglio le altrui intenzioni. </s></p><p type="main">

<s>A proposito di dimostrar la sottigliezza estrema, a cui riducesi l'oro, <lb/>quando si rivestano delle foglie di lui le verghe di argento, da tirarsi poi in <lb/>sottilissimi fili attraverso ai fori della filiera; a pag. </s>

<s>56, come nota il Viviani <lb/>nella edizione di Leida, si propone questo teorema: &ldquo; Le superficie dei cilin&shy;<lb/>dri eguali, trattone le basi, son tra di loro in sudduplicata proporzione delle <lb/>loro lunghezze, ovvero in reciproca proporzione dei diametri delle basi &rdquo; <lb/>(Alb. </s>

<s>XIII, 56). Piacque cos&igrave; al Sagredo la dimostrazion del Salviati, che <lb/>venne a questi voglia di soggiungerne all'amico un'altra compagna, dimo&shy;<lb/>strando quel che avvenga ai cilindri uguali di superficie, ma disuguali di al&shy;<lb/>tezza, in questo cos&igrave; proposto secondo teorema: &ldquo; I cilindri retti, le super&shy;<lb/>ficie dei quali, trattone le basi, sieno uguali, hanno fra di loro la medesima <lb/>proporzione, che le loro altezze contrariamente prese: ovvero in omologa pro&shy;<lb/>porzione dei diametri delle basi &rdquo; (ivi, pag. </s>

<s>58). D'onde si deduce per co&shy;<lb/>rollario la ragione di un accidente curioso, &ldquo; ed &egrave;: come possa essere che <lb/>il medesimo pezzo di tela, pi&ugrave; lungo per un verso che per l'altro, se se ne fa&shy;<lb/>cesse un sacco da tenervi dentro del grano, come costumano fare con un fondo <lb/>di tavola, terr&agrave; pi&ugrave;, servendoci per l'altezza del sacco della minor misura <lb/>della tela, e con l'altra circondando la tavola del fondo, che facendo per l'op&shy;<lb/>posito &rdquo; (ivi, pag. </s>

<s>59). </s></p><p type="main">

<s>I due teoremi geometrici, oltre al parere al gusto del Sagredo belli, si <lb/>trovano, ci&ograve; ch'&egrave; pi&ugrave;, al giudizio dei Matematici veri; imperocch&egrave; siano <lb/>AC, DF (fig. </s>

<s>18) i due cilindri uguali; S, S&prime; le loro superficie; C, C&prime; le so&shy;<lb/>lidit&agrave; respettive: avremo S=<foreign lang="greek">p</foreign>.BC.AB, S&prime;=<foreign lang="greek">p</foreign>.EF.DE, onde S:S&prime;= <pb xlink:href="020/01/2422.jpg" pagenum="47"/>BC.AB:EF.DE(*). Sar&agrave; inoltre C=<foreign lang="greek">p</foreign>.BC2/4.AB, C&prime;=<foreign lang="greek">p</foreign>.EF2/4.DE, le <lb/>quali due quantit&agrave; debbon essere per supposto uguali, ossia BC2.AB= <lb/>EF2.DE. </s>

<s>Dunque S2:S&prime;2=BC2.AB2:EF2.DE2=AB:DE, e perci&ograve; S:S&prime;= <lb/><figure id="id.020.01.2422.1.jpg" xlink:href="020/01/2422/1.jpg"/></s></p><p type="caption">

<s>Figura 18.<lb/>&radic;AB:&radic;DE. </s>

<s>E anche moltiplicando la seconda <lb/>ragione della (*) per BC.EF, avremo S:S&prime;= <lb/>BC2.AB.EF:EF2.BC.DE=EF:BC, ci&ograve; <lb/>che, sotto ambedue gli aspetti, verifica la pri&shy;<lb/>ma proposta del Salviati. </s>

<s>N&egrave; men vera appari&shy;<lb/>sce di qui la seconda, perch&egrave;, avendosi come <lb/>si &egrave; ora veduto, C:C&prime;=BC2.AB:EF2:DE, <lb/>per essere le superfice de'cilindri uguali, ne <lb/>verr&agrave; BC.AB=EE.DE, e perci&ograve; C:C&prime;= <lb/>BC:EF=DE:AB. </s></p><p type="main">

<s>I teoremi dunque di Galileo erano senza alcun dubbio veri, ma non pa&shy;<lb/>revano al Biancani troppo chiare le dimostrazioni, e il Viviani stesso ebbe a <lb/>riconoscer pur troppo che si rimanevano inferiori a quella elegante facilit&agrave;, <lb/>con la quale aveva poco fa il Torricelli condotte altre simili dimostrazioni <lb/>intorno alle propriet&agrave; dei cilindri, nel suo primo libro <emph type="italics"/>Dei solidi sferali.<emph.end type="italics"/> Nella <lb/>sesta proposizione si dimostra che le superficie cilindriche stanno come i ret&shy;<lb/>tangoli delle sezioni, ci&ograve; che immediatamente resultaya dalla equazione da <lb/>noi sopra segnata con asterisco. </s>

<s>Ma il Torricelli la concludeva da altre pro&shy;<lb/>posizioni, precedentemente dimostrate con quel metodo che, sebben sia ridotto <lb/>alla maggior facilit&agrave; ed eleganza, non per questo cessa di apparir lungo a chi <lb/>in poche parole ora sa di riuscir a dire lo stesso. </s>

<s>La terza proposizione infatti, <lb/>per dimostrar la quale il Torricelli impiega una pagina e mezzo del suo <lb/>volume, va speditamente a concluder che, avendosi il cilindro AC, nella pre&shy;<lb/>cedente figura, l'altezza AB del quale sia la quarta parte del diametro della <lb/>sua base, la superficie cilindrica S &egrave; uguale al circolo su cui risiede; osser&shy;<lb/>vando che, se AB=BC/3, la superficie S, che verrebbe espressa da <foreign lang="greek">p</foreign>.BC.AC, <lb/>si riduce a <foreign lang="greek">p</foreign>.BC2/4, che &egrave; l'area del circolo, sopra cui posa il cilindro. </s>

<s>Qua&shy;<lb/>lunque siasi poi la proporzione che passa tra la superficie S&prime; di questo circolo <lb/>base, e la superficie cilindrica S, avendosi S:S&prime;=<foreign lang="greek">p</foreign>.BC.AB:<foreign lang="greek">p</foreign>.BC2/4= <lb/>AB:BC/4, resta dimostrato <emph type="italics"/>Cylindri recti superficies, ad circulum suae ba&shy;<lb/>sis, est ut latus cylindri ad quartam partem diametri eiusdem basis,<emph.end type="italics"/> che <lb/>&egrave; la IV torricelliana <emph type="italics"/>De sphaera et solidis sphaeralibus.<emph.end type="italics"/> (Op. </s>

<s>geom., P. </s>

<s>I cit., <lb/>pag. </s>

<s>14). La V &egrave; di non men facile e spedita conclusione, perch&egrave;, a dimo&shy;<lb/>strar che la superficie di un cilindro retto sta a un circolo qualunque come <lb/>il rettangolo della sezione sta al quadrato del raggio; chiamato questo rag&shy;<lb/>gio R, sar&agrave; S&prime;=<foreign lang="greek">p</foreign>R2 la superficie del cerchio, e dall'equazione S:S&prime;= <pb xlink:href="020/01/2423.jpg" pagenum="48"/>AB.BC:R2, che di qui e dalla espressione della superficie cilindrica S ne <lb/>nasce, abbiamo gi&agrave; conseguito l'intento. </s></p><p type="main">

<s>Dovevano queste tre proposizioni servire di lemma alla VI, dimostrata <lb/>la quale era additato il pi&ugrave; spedito processo di riuscire a dimostrare i teo&shy;<lb/>remi di Galileo. </s>

<s>Perci&ograve; il Viviani accennava alla dimostrazione del Torricelli, <lb/>sull'esempio della quale intendeva di ridur cos&igrave;, come poi fece, a pi&ugrave; facile <lb/>semplicit&agrave; i prolissi e involti discorsi del Salviati. </s></p><p type="main">

<s>&ldquo; Prendasi la linea G nella stessa figura 18, terza proporzionale dopo i <lb/>diametri BC, EF dei cerchi basi de'dati cilindri. </s>

<s>E perch&egrave; questi hanno le <lb/>superticie curve eguali, sar&agrave; l'altezza AB alla DE come il diametro EF al <lb/>diametro BC, o come la linea G al diametro EF. </s>

<s>Ma il cilindro AC al DF <lb/>ha proporzione composta del diametro BC alla terza G, e dell'altezza AB <lb/>all'altezza DE, cio&egrave; della terza G al diametro EF; adunque il cilindro AC <lb/>al DF sta come il diametro BC al diametro DF, omologamente presi, o come <lb/>le altezze DE, AB prese cos&igrave; reciprocamente &rdquo; (MSS. Gal., P. V, T. IX, <lb/>pag. </s>

<s>56). </s></p><p type="main">

<s>Questa dimostrazione, da sostituirsi col presunto permesso di Galileo a <lb/>quella gi&agrave; nel primo dialogo stampata in Leida, l'aveva scritta il Viviani a <lb/>pi&egrave; della citata pagina 56, ma in un pezzetto di carta, interfogliato tra essa <lb/>pagina e la seguente, ne aveva prima distesa un'altra, che, poniamo fosse <lb/>meglio ordinata, non riusciva punto meno prolissa della stessa galileiana. </s>

<s>Per <lb/>dimostrar che i cilindri di superficie curve uguali son fra loro come i diame&shy;<lb/>tri delle basi omologamente, o come le altezze reciprocamente prese, premet&shy;<lb/>teva il Viviani un lemma, che resulta a noi dimostrato da solo moltiplicar <lb/>per A.B una delle ragioni dell'identica A:B=A:B. </s>

<s>Quel lemma infatti <lb/>cos&igrave; proponesi, e poi si dimostra: </s></p><p type="main">

<s>&ldquo; La proporzione di due linee &egrave; composta della proporzione omologa <lb/>de'loro quadrati, e della proporzion reciproca di loro medesime. </s>

<s>&mdash; Le date <lb/>linee siano A, B: dico che la ragione di A a B &egrave; composta della ragione del <lb/>quadrato A, al quadrato B, e della ragione della linea B alla A. </s>

<s>Prendasi C <lb/>terza proporzionale dopo le A, B: aver&agrave; dunque A a B ragion composta della <lb/>ragione di A alla terza C, cio&egrave; del quadrato A at quadrato della media B, <lb/>e della ragione della C alla B, cio&egrave; della B alla A, il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s>Dietro ci&ograve;, propone e dimostra il Viviani il teorema: &ldquo; I cilindri retti <lb/>AC, CD (sempre rappresentati dalla 18a figura) de'quali le superticie curve <lb/>sieno uguali, son fra loro in omologa proporzione de'diametri BC, EF delle <lb/>loro basi, ed anche in proporzione reciproca delle loro altezze DE, AB. &rdquo; </s></p><p type="main">

<s>&ldquo; La curva superficie del cilindro AC &egrave; uguale al rettangolo sul lato <lb/>uguale alla circonferenza della base, e all'altezza AB, s&igrave; come la curva del <lb/>DF &egrave; uguale al rettangolo sul lato uguale alla circonferenza del cerchio, che <lb/>ha per diametro EF, e all'altezza ED. </s>

<s>Ma tali superficie curve son date uguali, <lb/>adunque anche questi rettangoli sono uguali, e per&ograve; la circonferenza, che ha <lb/>per diametro BC, alla circonferenza che ha per diametro EF, cio&egrave; il diame&shy;<lb/>tro BC al diametro EF sta come l'altezza DE all'altezza AB. </s>

<s>Ma il cilindro <pb xlink:href="020/01/2424.jpg" pagenum="49"/>AC al DF ha ragione composta del cerchio, che ha per diametro BC, al cer&shy;<lb/>chio che ha per diametro EF, cio&egrave; del quadrato BC al quadrato EF, e del&shy;<lb/>l'altezza AB alla DE, cio&egrave; del diametro EF al BC: ed anche il diametro BC <lb/>all'EF, pel passato lemma, ha ragion composta delle medesime proporzioni, <lb/>cio&egrave; del quadrato BC al quadrato EF, e del diametro EF al BC; adunque il <lb/>cilindro AC al DF sta come il diametro BC al diametro EF, ovvero come <lb/>l'altezza DE all'altezza AB, il che dovevasi dimostrare. </s>

<s>Che vuol dire che <lb/>i sacchi, fatti con eguali quantit&agrave; di panno, quanto pi&ugrave; son bassi, tanto pi&ugrave; <lb/>tengono, e quanto sono pi&ugrave; grossi, tanto pi&ugrave; tengono &rdquo; (ivi). </s></p><p type="main">

<s>Gli altri teoremi, che si proponeva il Viviani di aggiungere secondo il <lb/>notato in quarto luogo da lui, non abbiamo trovato come fossero dimostrati, <lb/>ci&ograve; ch'egli avr&agrave; fatto in qualche parte de'suoi voluminosi manoscritti mate&shy;<lb/>matici. </s>

<s>Ma dalla Geometria trapassando alla Fisica, &egrave; notabile ch'egli volesse <lb/>dar solenne pubblicit&agrave; ne'Dialoghi all'invenzion del Termometro, per supplire <lb/>a quella, ch'egli credeva trascuratezza o dimenticanza di Galileo, ma che non <lb/>era forse altro che la coscienza di avere avuto in quella invenzione, che si <lb/>voleva attribuirgli, un'assai piccola parte del merito. </s>

<s>Avrebbe dovuto ripen&shy;<lb/>sare il Viviani che avvenne dello strumento da misurare il caldo e il freddo <lb/>quel che avvenne dell'altro modo di trovare il peso di un corpo nel vuoto, <lb/>non pesandolo realmente altro che in mezzo all'aria; cosa non avvertita da <lb/>Galileo e che perci&ograve; sugger&igrave; allo stesso Viviani quell'aggiunta interfogliata <lb/>tra le pag. </s>

<s>82, 83 di Leida, e che poi l'Alb&egrave;ri inser&igrave; a pag. </s>

<s>85 della sua <lb/>prima edizione completa. </s></p><p type="main">

<s>La settima nota del Viviani non &egrave; scritta per altro, che per assegnare <lb/>il proprio luogo ne'Dialoghi a quella sua dimostrazione circa la moltiplica&shy;<lb/>zione delle superficie de'solidi, che letta a Galileo, come sopra dicemmo, era <lb/>stata approvata da lui: ma l'ottava accenna a una questione di Meccanica <lb/>importantissima, e intorno alla quale vuol perci&ograve; trattenersi la nostra Storia <lb/>con particolar diligenza. </s></p><p type="main">

<s>Il principio fondamentale, posto alla Dinamica galileiana, &egrave; che il mo&shy;<lb/>bile scendendo naturalmente passi per tutti i gradi di velocit&agrave;, per cui era <lb/>prima passato spinto violentemente alla medesima altezza. </s>

<s>Conferito questo <lb/>pensiero col Sarpi, trov&ograve; subito una gran difficolt&agrave; ad essere ammesso per <lb/>vero, sembrando repugnante all'esperienza, come il Sarpi stesso scriveva il <lb/>d&igrave; 9 ottobre 1604 in una sua lettera a Galileo, nella quale cos&igrave; cominciava: <lb/>&ldquo; Con occasione d'inviarli l'allegata, mi &egrave; venuto pensiero di proporli un <lb/>argomento da risolvere, e un problema che mi tiene ambiguo. </s>

<s>Gi&agrave; abbiamo <lb/>concluso che nessun grave pu&ograve; essere tirato all'istesso termine in su, se non <lb/>con una forza, e per conseguente, con una velocit&agrave;. </s>

<s>Siamo passati, cos&igrave; V. S. <lb/>ultimamente afferm&ograve; e invent&ograve; ella, che per gli stessi termini torner&agrave; in gi&ugrave;, <lb/>per i quali and&ograve; in su. </s>

<s>Fa non so che obiezione la palla dell'archibugio: il <lb/>fuoco qui intorbida la forza dell'istanza. </s>

<s>Ma diciamo: un buon braccio, che <lb/>tira una freccia con un arco turchesco, passa via totalmente una tavola, e se <lb/>la freccia discender&agrave; da quella altezza, dove il braccio con l'arco la pu&ograve; <pb xlink:href="020/01/2425.jpg" pagenum="50"/>trarre, far&agrave; pochisssima passata. </s>

<s>Credo che l'istanza sii forse leggera, ma <lb/>non so che ci dire &rdquo; (Lettere raccolte da F. Polidori, Vol. </s>

<s>I, Firenze 1863, <lb/>pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Non sappiamo se questa istanza del Sarpi giungesse a Galileo nuova, <lb/>ma ei non poteva in nessun modo reputarla leggera, bench&egrave; vi rispondesse <lb/>poi indirettamente nel primo, e nel quarto dialogo delle Nuove scienze, attri&shy;<lb/>buendo la diversit&agrave; dell'effetto all'impedimento dell'aria, risentito s&igrave; nella <lb/>scesa naturale, ma sopravvinto dall'eccessiva furia della forza di proiezione. </s>

<s><lb/>Galileo anzi si serve di quella istanza del Sarpi, per confortare con qualche <lb/>argomento sperimentale una sua falsa opinione, che cio&egrave; l'impedimento del <lb/>mezzo finalmente riduca il mobile all'egualit&agrave;, nella quale poi sempre si man&shy;<lb/>tenga (Alb. </s>

<s>XIII, 96). Nel Dialogo quarto, a proposito de'proietti, si ripete <lb/>lo stesso, e si ammette per vero il fatto affermato dal Sarpi, che cio&egrave; una <lb/>palla o una freccia, scendendo dall'altezza, a cui fosse stata spinta dalla forza <lb/>del fuoco o di una molla; farebbe assai minor passata, che presso alla bocca <lb/>del moschetto o alla corda della balestra; bench&egrave; Galileo confessi di non aver <lb/>fatto una tale esperienza (ivi, pag. </s>

<s>233). </s></p><p type="main">

<s>Il Baliani, leggendo queste cose nei Dialoghi ammirati, tornava trenta&shy;<lb/>cinque anni dopo a ripetere l'istanza del Sarpi, aggiungendo di pi&ugrave; che l'ef&shy;<lb/>fetto non credeva si potesse attribuire all'impedimento del mezzo, come si <lb/>diceva da Galileo, a cui in una lettera da Genova del 1&deg; Luglio 1739 scri&shy;<lb/>veva, fra le altre considerazioni, anche questa: &ldquo; Da ci&ograve; che discorre, a fol. </s>

<s>94 <lb/>e a fol. </s>

<s>164, par che sparandosi in alto un'archibugiata dovrebbe la palla <lb/>far l'istessa passata, v. </s>

<s>g. </s>

<s>di dieci palmi, dall'archibugio, tanto nello scen&shy;<lb/>dere quanto nel salire, il che n&egrave; credo che riuscirebbe in fatto, n&egrave; pare che <lb/>si possa sciorre per la condensazione dell'aria, perciocch&egrave; non &egrave; questa per <lb/>mio avviso tale altezza, che nello scendere il grave non osservasse la regola <lb/>della duplicata proporzione dei tempi uguali &rdquo; (Alb. </s>

<s>X, 334). </s></p><p type="main">

<s>Facendo riflessione sopra queste parole, ebbe a riconoscere Galileo che <lb/>davvero, con l'introdurre l'impedimento del mezzo, la difficolt&agrave; non veniva <lb/>sciolta: rimaneva nonostante sicuro della verit&agrave; del suo principio, crollando <lb/>il quale, sarebbe venuto a minacciar rovina tutto intero l'edifizio dei moti <lb/>accelerati. </s>

<s>Perci&ograve;, nella fiducia di aver pure a trovare del dubbio la risolu&shy;<lb/>zion vera, e in altre pi&ugrave; sottili osservazioni alle impugnate dottrine una con&shy;<lb/>ferma, cos&igrave; al libero impugnatore di Genova, dopo un mese preciso, rispon&shy;<lb/>deva: &ldquo; Che la palla discendente dall'altezza, dove dalla forza del fuoco fu <lb/>cacciata, non riacquisti tornando indietro, giunta le dieci braccia vicina all'ar&shy;<lb/>chibugio, quell'impeto, che ella ebbe quando da principio fu scaricata, da <lb/>me &egrave; tenuto per effetto verissimo. </s>

<s>Ma questo non altera punto la mia pro&shy;<lb/>posizione, nella quale io dico che il grave discendendo da alto riacquista nei <lb/>medesimi luoghi della scesa quella forza, che era bastante a risospingerlo in <lb/>su, quando nei medesimi luoghi si ritrov&ograve; salendo, e forse, da quello che gi&agrave; <lb/>si legge nei luoghi da lei citati, raccogliere si potrebbe. </s>

<s>Ma &egrave; vero che, senza <lb/>aggiungere io alcune nuove osservazioni, forse non potrebbe agevolmente esser <pb xlink:href="020/01/2426.jpg" pagenum="51"/>compreso, ma il produrlo ricerca un poco pi&ugrave; di ozio e di quiete di mente, <lb/>di quella che di presente io posseggo: lo far&ograve; altra volta, quando ella pure <lb/>me lo richiegga &rdquo; (Lettere per il trecentesimo natalizio, Pisa 1864, pag. </s>

<s>45). </s></p><p type="main">

<s>Il Baliani non richiese altro, dicendo di esser sodisfatto di ci&ograve;, ch'era <lb/>detto in questa lettera e nei Dialoghi, i quali egli era perci&ograve; tornato a leg&shy;<lb/>gere di nuovo: soggiungeva solamente un suo pensiero, che cio&egrave;, perdendo <lb/>il mobile della propria naturale velocit&agrave;, per l'impedimento dell'aria inter&shy;<lb/>posta, &ldquo; poi camminando avanti possa essere che la racquisti &rdquo; (Alb. </s>

<s>X, 361). <lb/>Galileo rispondeva che questo veramente sarebbe stato per lui duro a conce&shy;<lb/>dere, quando non avesse esperienze e dimostrazioni in contrario (Lettere cit., <lb/>pag. </s>

<s>51), ma lasciando addietro questa, che era una questione incidente, ri&shy;<lb/>pensava alla principale, e come ci&ograve;, che non s'era curato di richiedere il <lb/>Baliani, poteva esser richiesto dai lettori dei Dialoghi, arretrando a que'due <lb/>passi da noi sopra citati. </s>

<s>Conferiva queste cose col Viviani, che incorava <lb/>una giovanile speranza di dover finalmente sciogliere i dubbi, aiutandosi di <lb/>esperienze pi&ugrave; diligenti. </s>

<s>Pareva anche a lui vero quel che vero era creduto <lb/>e affermato dal Sarpi, da Galileo e dallo stesso Baliani, ma non se ne poteva <lb/>aver certezza come di un fatto osservato. </s>

<s>Le osservazioni per&ograve; voleva che si <lb/>facessero nelle ammaccature, non del percuziente, ma del percosso, cosicch&egrave;, <lb/>invece di sparar l'archibugio contro una pietra, come il Salviati proponeva, <lb/>si sparasse contro un petto a botta, o contro un corsaletto o che altro, atto <lb/>a ricevere e a ritenere in s&egrave; impresse le vestigia, da congetturare del mag&shy;<lb/>giore o del minor impeto della palla. </s></p><p type="main">

<s>Piacque a Galileo l'esperienza, in questo nuovo modo proposta, e dietro <lb/>la quale si sperava di trovar la vera ragione perch&egrave; nelle cadute naturali, <lb/>anche da non grandi altezze, e nelle quali perci&ograve; pareva che di poco effetto <lb/>dovess'essere l'impedimento dell'aria; il mobile non acquisti mai impeto <lb/>uguale a quello della sua proiezione. </s>

<s>Questa ragione si doveva sostituire a <lb/>quella messa in bocca al Salviati, ed essendo la cosa di tanta importanza, <lb/>perch&egrave; non dovesse rimanere indietro, in mezzo alle presenti sollecitudini di <lb/>migliorare e ampliare i dialoghi delle Nuove scienze, Galileo stesso ne det&shy;<lb/>tava al Viviani un tal memoriale: &ldquo; Cercar di assegnar la ragione onde av&shy;<lb/>venga che la palla tirata in su col moschetto, incontrando dieci o dodici brac&shy;<lb/>cia lontano un pett'a botta lo sfonda, sopra il quale, cadendo ella dall'altezza <lb/>dove il moschetto la caccerebbe, percotendo nel ritorno in gi&ugrave; sopra il me&shy;<lb/>desimo petto, assai minore effetto vi farebbe, e forse appena l'ammacche&shy;<lb/>rebbe un poco &rdquo; (MSS. Gal., P. V, T. IV, fol. </s>

<s>19). </s></p><p type="main">

<s>Se fosse stata veramente da Galileo e dal Viviani trovata quella ra&shy;<lb/>gione, che si cercava, non potremmo noi asserire di certo, mancandoci intorno <lb/>a ci&ograve; il documento. </s>

<s>Anzi, come apparir&agrave; dal passo, che tra poco trascrive&shy;<lb/>remo, sembra che non avessero gli Accademici fiorentini trovato da dir nulla <lb/>di meglio di quel che, nel primo e nel quarto dialogo delle due Scienze <lb/>nuove, era stato insegnato dal Salviati, nonostante l'antica instanza del Ba&shy;<lb/>liani, che cio&egrave;, in s&igrave; poca altezza quant'&egrave; un trar d'archibugio, non possa <pb xlink:href="020/01/2427.jpg" pagenum="52"/>l'aria impedire alla palla il velocitarsi, secondo la legge degli spazi propor&shy;<lb/>zionali ai quadrati dei tempi. </s></p><p type="main">

<s>Certo &egrave; per&ograve; che il Viviani istitui l'esperienze a quel modo che, vivente <lb/>Galileo, le aveva a lui stesso proposte, e come appartenenti all'Accademia <lb/>del Cimento furon raccolte fra quelle, che si descrivono intorno ai proietti <lb/>nell'appendice al libro dei <emph type="italics"/>Saggi.<emph.end type="italics"/> Ivi si ripetono dal Segretario le precise <lb/>parole, che si leggono nel dialogo quarto a pag. </s>

<s>164 dell'edizione di Leida, <lb/>e a pag. </s>

<s>233 di quella dell'Alb&egrave;ri, nelle quali parole, senz'averlo ancora spe&shy;<lb/>rimentato, s'afferma per vero il fatto della percossa della palla dell'archibu&shy;<lb/>gio, presso alla bocca, maggiore di quella che la medesima palla farebbe <lb/>contro una pietra, tornando in gi&ugrave; dall'altezza, a cui l'archibugio stesso <lb/>l'avrebbe verticalmente gettata, e poi nel detto libro cos&igrave; subito si soggiunge: </s></p><p type="main">

<s>&ldquo; Noi abbiamo fatto questa prova con un archibugio rigato, non gi&agrave; spa&shy;<lb/>randolo contro una pietra, per osservar l'ammaccatura della palla, ma bens&igrave; <lb/>contro un pettabbotta di ferro. </s>

<s>In esso adunque abbiamo veduto che i tiri <lb/>fatti da minore altezza v'imprimevano forma assai pi&ugrave; profonda di quelli, che <lb/>da maggiore venivano fatti: imperocch&egrave; dicevano alcuni, seguitando in ci&ograve; <lb/>il parere del Galileo, nel pi&ugrave; lungo viaggio che fa la palla, fendendo l'aria, <lb/>si va di continuo smorzando in essa quell'impeto e forza soprannaturale im&shy;<lb/>pressale dalla violenza del fuoco &rdquo; (Firenze 1841, pag. </s>

<s>163). </s></p><p type="main">

<s>Il parere di Galileo &egrave; notabile che fosse seguito dagli Accademici fio&shy;<lb/>rentini, dopo quasi vent'anni di discussione contro le istanze del Baliani o, <lb/>per pi&ugrave; vero dire, contro le esperienze comuni. </s>

<s>Aveva tutta l'apparenza del <lb/>vero che la palla del moschetto non torni in gi&ugrave; da tale altezza, che le debba <lb/>l'aria togliere tanto di velocit&agrave;, e nonostante non vedevano a quale altra <lb/>causa, fuor che all'impedimento dell'aria, si potesse attribuire lo stravagante <lb/>effetto. </s>

<s>Implicitamente dunque ammettevano costoro, insieme col Maestro, che <lb/>solo nel vuoto acquisterebbe il mobile, scendendo naturalmente, tutto intero <lb/>il primo impeto della sua proiezione, ed esplicitamente professava cos&igrave; il Bo&shy;<lb/>relli nel suo trattato <emph type="italics"/>De vi percuss&igrave;onis.<emph.end type="italics"/> &ldquo; Si postea removeatur omnino <lb/>aeris impedimentum .... spatia ascensus atque descensus, aequalibus tempo&shy;<lb/>ribus, aequalia essent &rdquo; (Bononiae 1667, pag. </s>

<s>258). </s></p><p type="main">

<s>Scriveva cos&igrave; l'Autore nella proposizione CXIV, dop'aver descritta l'espe&shy;<lb/>rienza della palla verticalmente gettata con la saetta, l'ascesa violenta della <lb/>qual palla dice essere stata doppia della discesa naturale nel medesimo tempo. </s>

<s><lb/>Ma le esperienze, che dovevano meglio persuadere, e confermare le menti <lb/>nella verit&agrave; delle dottrine galileiane, non apparirono che sui principii del se&shy;<lb/>colo XVIII, quando il Gunther faceva, innanzi all'imperiale Accademia di <lb/>Pietroburgo, sparar con tiro verticale i cannoni, misurando il tempo e os&shy;<lb/>servando l'altezza, a cui faceva l'impeto risalire i proietti. </s>

<s>S'ebbe da una <lb/>di coteste esperienze l'altezza di 7819 piedi inglesi, mentre, secondo i cal&shy;<lb/>coli di Daniele Bernoulli, da lui stesso descritti nella dissertazione <emph type="italics"/>De actione <lb/>fluidorum in corpora solida<emph.end type="italics"/> (Comment. </s>

<s>petroburg., T. II); sarebbero nel <lb/>vuoto dovuti essere 58,750 piedi. </s>

<s>Aveva dunque la palla trovato tanto con-<pb xlink:href="020/01/2428.jpg" pagenum="53"/>trasto nell'aria, da ridurre a un ottavo la sua libera salita, d'onde mostrasi <lb/>la fallacia dell'istanza del Baliani contro la dottrina di Galileo, e si risolve <lb/>il problema del Sarpi. </s>

<s>Perch&egrave; l'impeto di proiezione non si dovrebbe com&shy;<lb/>parar con l'impeto della caduta naturale della palla o della freccia da quel&shy;<lb/>l'altezza, a cui l'avevano cacciata il moschetto o la balestra, ma da un'al&shy;<lb/>tezza tanto maggiore, quanta si pu&ograve; congetturare dietro i calcoli del Bernoulli, <lb/>e l'esperienze di Pietroburgo. </s></p><p type="main">

<s>Mancava agli Accademici fiorentini tanta perizia di calcolo, e tanta pre&shy;<lb/>cisione degli strumenti, e dall'altra parte l'esperienze da loro istituite, die&shy;<lb/>tro il suggerimento e la direzion del Viviani, e quelle stesse accennate nella <lb/>detta proposizione CXIV del Borelli, non avevano, per mancanza di preci&shy;<lb/>sione, l'efficacia che si richiedeva per rispondere alle fatte instanze, e per <lb/>risolvere i proposti quesiti, onde a poco si pu&ograve; dire che si riduca tutto quel <lb/>che a carte 94 si proponeva di aggiunger nel primo dialogo il Viviani, <emph type="italics"/>dopo <lb/>il discorso del Salviati circa il tiro del moschetto in un corsaletto:<emph.end type="italics"/> ma <lb/>l'altro proposito che segue, d'illustrare cio&egrave; <emph type="italics"/>il pensiero di Platone, e far <lb/>quel calcolo,<emph.end type="italics"/> ebbe a rimanersi anche in maggior difetto. </s>

<s>Nel dialogo quarto, <lb/>dop'avere il Salviati definita la <emph type="italics"/>sublimit&agrave;,<emph.end type="italics"/> dall'impeto acquistato nella quale, <lb/>volto orizontalmente e cougiunto col moto naturale e accelerato della gravit&agrave;, <lb/>il proietto descrive la semiparabola; viene in mente al Sagredo di applicar <lb/>quel concetto, che si confessa derivar dai placiti di Platone, alle orbite pla&shy;<lb/>netarie, il moto equabile delle quali si potrebbe immaginar preceduto da un <lb/>moto retto accelerato, incominciatosi a far da punti pi&ugrave; o meno sublimi, se&shy;<lb/>condo la maggiore o minor velocit&agrave;, che voleva il Creatore fosse impressa <lb/>ne'pianeti. </s>

<s>Dice esso Sagredo che aveva Galileo avuto talvolta il pensiero di <lb/>calcolare quelle sublimit&agrave;, per veder se si trovassero corrispondere alle gran&shy;<lb/>dezze degli orbi e ai tempi delle rivoluzioni: a cui soggiunge il Salviati che <lb/>non solo aveva Galileo avuto il pensiero, ma che aveva fatto gi&agrave; quel com&shy;<lb/>puto, &ldquo; ed anco trovatolo assai acconciamente rispondere alle osservazioni: <lb/>ma non averne voluto parlare, giudicando che le troppe novit&agrave; da lui sco&shy;<lb/>perte, che lo sdegno di molti gli hanno provocato, non accendessero nuove <lb/>scintille &rdquo; (Alb. </s>

<s>XIII, 238). </s></p><p type="main">

<s>Ora che era cenere, non poteva aver pi&ugrave; nessuna paura di quell'incen&shy;<lb/>dio, e perci&ograve; pensava il Viviani ch'era il tempo di far quel calcolo, per ador&shy;<lb/>nare il concetto platonico, e anche il dialogo galileiano. </s>

<s>Non possono i Let&shy;<lb/>tori astronomi non sentirsi a questo punto frugati da una grande curiosit&agrave; di <lb/>sapere in qual modo quel calcolo fosse fatto, perch&egrave; dalla risposta scende&shy;<lb/>rebbe un corollario importante alla nostra Storia dell'Astronomia. </s>

<s>Quel con&shy;<lb/>cetto platonico e copernicano infatti, dalla scoperta delle orbite ellittiche ve&shy;<lb/>niva dimostrato falso, e poniamo che non si vedesse ancora di li conseguir <lb/>chiaro, come poi apparve al Newton, il sistema delle forze centrali, non si <lb/>poteva pi&ugrave; pensare all'equabilit&agrave; del moto orbitale, succeduto al retto acce&shy;<lb/>lerato, ora che si osserva di fatto andar nel perigeo il pianeta alquanto pi&ugrave; <lb/>veloce che nell'apogeo. </s>

<s>Galileo non volle mai credere a queste osservazioni, <pb xlink:href="020/01/2429.jpg" pagenum="54"/>n&egrave; il corollario storico che si diceva &egrave; questo, ma un altro anche pi&ugrave; nota&shy;<lb/>bile, perch&egrave; l'essersi proposto il Viviani di far que'calcoli platonici, per in&shy;<lb/>serirli nel quarto dialogo delle Nuove scienze, sarebbe documento che, anche <lb/>dopo qualche anno la morte di Galileo, si persisteva nella scuola di lui a <lb/>repudiare le leggi scoperte dal Keplero. </s>

<s>Dell'esser poi messo o no quel pro&shy;<lb/>posito ad effetto &egrave; inutile domandare, perch&egrave;, se quei calcoli astronomici fos&shy;<lb/>sero stati fatti bene secondo le dottrine platoniche e copernicane, era impos&shy;<lb/>sibile che fossero <emph type="italics"/>trovati assai acconciamente rispondere alle osservazioni,<emph.end type="italics"/><lb/>per cui non par che possa andare assoluto dalla nota d'inverosimile il detto <lb/>del Salviati. </s></p><p type="main">

<s>A terminar questo esame dei modi come il Viviani color&igrave; que'suoi pen&shy;<lb/>sieri d'ampliare e d'illustrare le dottrine, esposte da Galileo nella prima edi&shy;<lb/>zione delle Scienze nuove, in certi punti particolari; non rimane ora a dir <lb/>che del proposito di rispondere a una domanda, messa dallo stesso Viviani <lb/>in quella forma, che si lesse nella X nota del suo memoriale. </s>

<s>Accennasi quivi <lb/>all'uso delle catenelle, di trattar delle quali si promette sulla fine del Dia&shy;<lb/>logo quarto, e poi si rimanda il discorso all'ultimo congresso, che sarebbe <lb/>in materia della forza della percossa. </s>

<s>Ma perch&egrave; dovremo di quest'ultimo <lb/>congresso far speciale soggetto la nostra Storia, vedremo allora come rispon&shy;<lb/>desse il Viviani, e com'abbiamo, dietro i documenti, a rispondere noi a chi <lb/>fosse curioso di saper se le dette catenelle dovevano secondo Galileo sola&shy;<lb/>mente servire ai Geometri, per descrivere le parabole, o anche ai militari per <lb/>dirigere i tiri delle artiglierie. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Due scienze, che al mondo matematico s'istituivano come nuove da un <lb/>uomo, dotato d'ingegno straordinario senza dubbio, ma non divino, come <lb/>tanti fanatici se lo vanno immaginando, non era possibile che, rimanendosi <lb/>per la naturale insufficienza da una parte in difetto, non trascorressero dal&shy;<lb/>l'altra in qualche errore. </s>

<s>Come fossero da Galileo stesso riconosciuti que'di&shy;<lb/>fetti, e come, con l'aiuto del Viviani ei pensasse, in mezzo alle tenebre, di <lb/>supplirvi, ce l'hanno fatto veder di sopra i documenti. </s>

<s>Ma quanto a cono&shy;<lb/>scere e a confessare gli errori, se repugna all'amor proprio di tutti gli uo&shy;<lb/>mini, doveva parer cosa contro natura a colui, che sentiva quanto fosse neces&shy;<lb/>sario confermare i discepoli in quella loro opinione, che avesse cio&egrave; impressa <lb/>quasi una certa nota d'infallibilit&agrave; nel suo magistero. </s></p><p type="main">

<s>Fu il giovane Viviani uno dei primi a creder con religioso ossequio a <lb/>una tale infallibilit&agrave; del Maestro, e trasparisce viva, senza cercar altro, la sua <lb/>fede dal modo, com'egli accolse e not&ograve; le censure del Blancano. </s>

<s>Vedemmo <lb/>come fossero le pi&ugrave; pungenti di cos&igrave; fatte censure in materia delle resistenze <pb xlink:href="020/01/2430.jpg" pagenum="55"/>dei solidi, nella quinta proposizione del qual trattato si notavano dal Gesuita <lb/><figure id="id.020.01.2430.1.jpg" xlink:href="020/01/2430/1.jpg"/></s></p><p type="caption">

<s>Figura 19.<lb/>certe conclusioni, che parevano contradire alle <lb/>precedenti. </s>

<s>Si legge infatti in quella quinta di&shy;<lb/>mostrazione che la resistenza R del cilindro <lb/>GD (fig. </s>

<s>19) sta alla resistenza R&prime; del cilindro <lb/>DF, come la lunghezza FE sta alla EG (Alb. </s>

<s>XIII, <lb/>123), per cui, moltiplicandosi le lunghezze per <lb/>le basi uguali, avremo R:R&prime;=DF:DG, mentre la terza precedente d&agrave; la <lb/>proporzione omologa R:R&prime;=EG2:FE2. </s></p><p type="main">

<s>Vivente Galileo furono anche dal Viviani queste censure, come se le <lb/>avesse suggerite l'invidia, avute in disprezzo, ma poi, quando col progredir <lb/>della scienza venne a rendersi dall'altrui suggezione pi&ugrave; libero l'ingegno, <lb/>conobbe che almeno in parte erano giuste, cosicch&egrave;, lasciando quella prima <lb/>cieca fede che aveva ai detti del Maestro, e richiamandoli a esame pi&ugrave; sottile e <lb/>pi&ugrave; giudizioso, ebbe a scoprir altre incredibili fallacie nell'oracolo venerato. </s>

<s><lb/>Di qui, morto il Maestro, incomincia per il Discepolo un'opera nuova, qual'&egrave; <lb/>quella di emendare i dialoghi delle Nuove scienze dai pi&ugrave; notabili errori. </s></p><p type="main">

<s>Ebbe quest'opera principio dall'esame delle proposizioni intorno alle <lb/>resistenze, d'onde glie n'era venuta l'occasione, e dalla Va, censurata dal <lb/>Biancani, passando alla VIa, la trov&ograve; addirittura falsa, per cui, postillando <lb/>nella solita edizione di Leida, si proponeva di ridurla a verit&agrave; pi&ugrave; generale <lb/>nella seguente maniera: &ldquo; Proposizione VI del Galileo generalmente e di&shy;<lb/>versamente enunciata per esser quella non vera. <emph type="italics"/>Dei cilindri e prismi, anzi <lb/>dei solidi regolari simili, il rispetto tra i momenti gravanti &egrave; sesquiterzo <lb/>del rispetto tra i momenti resistenti delle loro sezioni.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Siano i due solidi regolari simili AB, CD (fig. </s>

<s>20) dico ecc. </s>

<s>Prese <lb/><figure id="id.020.01.2430.2.jpg" xlink:href="020/01/2430/2.jpg"/></s></p><p type="caption">

<s>Figura 20.<lb/>dopo le linee A, C, uguali ai diametri <lb/>delle sezioni A, C, le E, F, G continue <lb/>proporzionali, il momento gravante del <lb/>solido AB, al gravante di CD, sta come <lb/>il quadrato della lunghezza AB, al qua&shy;<lb/>drato della CD: cio&egrave;, come il quadrato <lb/>della linea A, al quadrato della E, per <lb/>esser queste proporzionali alle AB, CD, <lb/>stante la similitudine dei solidi, cio&egrave; <lb/>come la prima linea A alla quinta G. </s>

<s><lb/>Ed il momento resistente della sezione A, <lb/>al resistente della C, sta come il cubo della linea A, al cubo della C, per <lb/>la IVa di Galileo, cio&egrave; come la prima A alla quarta F. </s>

<s>Perch&egrave; tra A e G <lb/>sono quattro rispetti della prima e seconda, e tra A ed F sono tre rispetti <lb/>della medesima prima e seconda; adunque anco il rispetto tra il momento <lb/>gravante di AB, al gravante di CD, sar&agrave; sesquiterzo del rispetto tra il resi&shy;<lb/>stente di A, e il resistente di C, e non &egrave; sesquialtero, come pronunzi&ograve; ed <lb/>intese di dimostrare il Galileo &rdquo; (MSS. Gal., P. V, T. IX). </s></p><pb xlink:href="020/01/2431.jpg" pagenum="56"/><p type="main">

<s>Il linguaggio, pi&ugrave; che mai insolito alle orecchie dei Matematici odierni, <lb/>si traduce nella seguente guisa, per confermare la verit&agrave; della conclusione. </s>

<s><lb/>Siano date le proporzionali continue A:C=C:E=E:F=F:G, dalle <lb/>quali &egrave; facile ottenere A2:E2=A:G=A4:C4. </s>

<s>Chiamati dunque M, M&prime; i <lb/>momenti, avremo M:M&prime;=A2:E2=A:G=A4:C4, e per la IVa di Ga&shy;<lb/>lileo R:R&prime;=A3:C3, rappresentando R, R&prime; le resistenze dei solidi contem&shy;<lb/>plati. </s>

<s>Inalzata ora questa alla quarta potenza, e quella a cubo, daranno <lb/>R4:R&prime;4=A12:C12, M3:M&prime;3=A12:C12, e perci&ograve; M3:M&prime;3=R4:R&prime;4; ossia <lb/>M:M&prime;=R4/3:R&prime;4/3, che vuol dire i momenti delle potenze aver, secondo <lb/>l'espression del Viviani, ragione sesquiterza delle resistenze. </s></p><p type="main">

<s>Aggiunge il Viviani stesso a questa sua proposizione un corollario, per <lb/>mostrar come in quella, resa cos&igrave; pi&ugrave; generale, si comprenda il caso parti&shy;<lb/>colare contemplato da Galileo, che pur viene a concludere una falsit&agrave;, da <lb/>non si poter salvare, come alcuni credevano, nemmeno profferendone l'enun&shy;<lb/>ziazione in modo diverso. </s></p><p type="main">

<s>&ldquo; COROLLARIO. &mdash; Se dunque la linea A rappresenter&agrave; il momento gra&shy;<lb/>vante del solido AB, ed anche il resistente della sua base A, che sar&agrave; quando <lb/>esso solido sia il minimo che rompa, la linea G rappresenter&agrave; il gravante <lb/>del solido CD, e la F il resistente della sua base C; sicch&egrave; il gravante CD <lb/>&egrave; tanto minore del suo resistente, quanto la G &egrave; minore di F, o, a propor&shy;<lb/>zione, quanto &egrave; minore C di A, ovvero CD di AB. </s>

<s>Sicch&egrave; il piccolo tanto pi&ugrave; <lb/>&egrave; resistente, quanto a proporzione &egrave; pi&ugrave; corto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E per chi dubitasse che l'enunziazione del Galileo si dovesse inten&shy;<lb/>dere cos&igrave;: cio&egrave; che i momenti gravanti de'cilindri simili hanno proporzione <lb/>sesquialtera di quella, che hanno le resistenze (assolute per&ograve; e non i mo&shy;<lb/>menti loro resistenti), pur si prova che, volendo paragonare il rispetto dei <lb/>momenti gravanti con quello delle resistenze assolute, l'enunziazione sia prof&shy;<lb/>ferita diversamente cos&igrave;, cio&egrave;: <emph type="italics"/>I momenti gravanti de'solidi simili sono fra <lb/>loro in doppia proporzione delle resistenze assolute delle basi.<emph.end type="italics"/> Perch&egrave;, es&shy;<lb/>sendosi provato il rispetto tra il gravante e il gravante essere come la A <lb/>alla G, ed essendo il rispetto tra la resistenza assoluta di A, all'assoluta di <lb/>C, come il quadrato della linea A, al quadrato della linea C, cio&egrave; come la <lb/>linea A alla terza E; ed avendo A a G duplo rispetto di A ad E, che &egrave; media <lb/>proporzionale tra A e G, sar&agrave; manifesto quanto si propose &rdquo; (ivi). </s></p><p type="main">

<s>E anche pi&ugrave; manifesto potrebbe rendersi, traducendo cos&igrave; nelle forme <lb/>moderne il linguaggio del Viviani: &Egrave; stato gi&agrave; dimostrato M:M&prime;=A2:E2; <lb/>R:R&prime;=A2:C2, e dalla data serie delle continue proporzionali s'ha A2:C2= <lb/>A:E. </s>

<s>Dunque M:M&prime;=R2:R&prime;2, che vuol dire: i momenti hanno doppia pro&shy;<lb/>porzione delle resistenze, ossia stanno come i quadranti delle resistenze, di&shy;<lb/>versamente da quello, che aveva preteso di dimostrar Galileo. </s></p><p type="main">

<s>Incominciatosi cos&igrave; a persuadere, con matematiche ragioni, che non era <lb/>da confidarsi in una verit&agrave;, perch&egrave; il grande Maestro della Scienza del moto <lb/>l'aveva messa, il Viviani pass&ograve; da questa proposizione, con pi&ugrave; libero esame, <lb/>a vedere anche le altre, intorno alle quali, quasi avesse creduto di offendere <pb xlink:href="020/01/2432.jpg" pagenum="57"/>l'adorabilit&agrave; di un Nume, aveva sempre cacciati i dubbi dalla sua mente. </s>

<s><lb/>Venne cos&igrave; facilmente a scoprire le tante altre fallacie, nelle quali era tra&shy;<lb/>scorso Galileo, trattando delle resistenze, e aveva avvertito gi&agrave; lo sbaglio in <lb/>assegnare la figura parabolica al solido, che per tutto resiste ugualmente alla <lb/>pressione, qualche anno prima del Blondel e del Marchetti. </s>

<s>Tanto anzi il Vi&shy;<lb/>viani stesso riconobbe il secondo dialogo delle Nuove scienze difettoso, che <lb/>s'era proposto di riformarlo nella massima parte. </s>

<s>Di quest'opera, data dallo <lb/>zelante discepolo, fu discorso da noi nel cap. </s>

<s>VIII dell'altro tomo, per le <lb/>sparse pagine del quale ricorrono varie altre notizie concernenti ci&ograve; che quel <lb/>geloso e amorevole, ma pur libero censore, aveva scritto contro molte errate <lb/>dottrine de'Dialoghi del moto. </s>

<s>Poco sembrerebbe perci&ograve; che rimanesse a dire <lb/>nel presente argomento, alla pi&ugrave; compiuta trattazione del quale, manca nono&shy;<lb/>stante un esempio, intorno a cui vogliamo trattenere i lettori, come intorno <lb/>a uno de'pi&ugrave; notabili fatti, da mostrar quanto fosse facile, anche ai pi&ugrave; <lb/>grandi ingegni, che non presero in mano il filo di Arianna, lo smarrirsi mi&shy;<lb/>seramente in questi meccanici labirinti. </s></p><p type="main">

<s>Sulla sera della quarta giornata, nella quale si tratt&ograve; de'proietti, e pro&shy;<lb/>prio nell'atto di congedarsi gl'interlocutori, il Sagredo si proponeva di dimo&shy;<lb/>strare un accidente simile a quel che si osserva nella palla di un cannone, <lb/>la quale, tirata di punto in bianco, a cagion della gravit&agrave;, che mai l'abban&shy;<lb/><figure id="id.020.01.2432.1.jpg" xlink:href="020/01/2432/1.jpg"/></s></p><p type="caption">

<s>Figura 21.<lb/>dona, &egrave; impossibile che <lb/>vada per linea retta orizon&shy;<lb/>tale; dicendo esser per so&shy;<lb/>migliante ragione &ldquo; impos&shy;<lb/>sibile distendere una corda, <lb/>sicch&egrave; resti tesa dirittta&shy;<lb/>mente e parallela all'oriz&shy;<lb/>zonte, ma sempre fa sacca <lb/>e si piega, n&egrave; vi &egrave; forza che <lb/>basti a tenderla rettamen&shy;<lb/>te &rdquo; (Alb. </s>

<s>XIII, 262). Con&shy;<lb/>cludeva ci&ograve; come corollario <lb/>da un teorema di Mecca&shy;<lb/>nica nuova, immaginando <lb/>cavalcare sopra i punti sta&shy;<lb/>bili A, B (fig. </s>

<s>21) un filo <lb/>imponderabile, teso nella <lb/>dirittura orizzontale AB da due grandi pesi uguali C, C, e soggiungeva che, se <lb/>dal mezzo E si sospendesse qualsivoglia piccolo peso, come per esempio H, <lb/>la linea AB allungandosi cederebbe in qualunque modo, e costringerebbe <lb/>perci&ograve; i ponderosi corpi C, C a salire in alto. </s></p><p type="main">

<s>Voleva il Sagredo, per provare il suo detto, che, fattosi centro in A e <lb/>in B, co'raggi uguali AE, BE si descrivessero due quadranti, e immaginando <lb/>essersi il peso H da E abbassato in F, congiunte le FA, FB, faceva osser-<pb xlink:href="020/01/2433.jpg" pagenum="58"/>vare che, mentre la scesa del peso piccolo veniva misurata dalla tangente EF, <lb/>la salita de'grandi era uguale alle porzioni esterne LF delle secanti AF, FB. </s>

<s><lb/>Tutto si riduceva dunque a provare che il momento di H &egrave;, o pu&ograve; almeno <lb/>essere maggiore della somma de'momenti C, C, richiamando perci&ograve; alla me&shy;<lb/>moria di Simplicio la nota legge aristotelica delle equiponderanze, secondo <lb/>la quale si diceva allora avere due gravi i momenti uguali, quando sono <lb/>uguali i prodotti delle velocit&agrave; per le moli. </s>

<s>Applicando ora il Sagredo al <lb/>fatto suo questa legge, voleva persuadere allo stesso Simplicio che si sarebbe <lb/>felicemente conseguito l'intento, quando si fosse dimostrato che il prodotto <lb/>di H per la linea EF, dalla quale si misura la velocit&agrave; della scesa, fosse o <lb/>potess'essere maggiore del prodotto di 2 C per LF, che nello stesso tempo <lb/>misura la velocit&agrave; della salita. </s>

<s>La dimostrazione procede in sostanza cos&igrave;, come <lb/>noi la riduciamo in pi&ugrave; semplice forma. </s></p><p type="main">

<s>Facciasi 2 C ad H come la linea BO a un'altra, che sia C, e, presa D <lb/>linea minore della C, dividasi in E la BO in modo, che sia OB:D=D:BE. </s>

<s><lb/>Menato poi il quadrante, descritto dianzi col raggio AE, per tutto il suo giro, <lb/>costituiscasi F a tal distanza da E che, tirata la FAG, debb'aversi OE:EB= <lb/>GL:LF, la quale componendo dar&agrave; OB:EB=GF:LF. </s>

<s>Posto poi nella <lb/>prima ragione di questa BE=D2/OB, e moltiplicati per LF ambedue i termini <lb/>della ragione seconda, verr&agrave; OB2:D2=GF.LF:LF2. </s>

<s>Ma il prodotto della <lb/>secante GF, per la sua porzione esterna, &egrave; uguale al quadrato della tan&shy;<lb/>gente EF; dunque, sostituendo ed estraendo le radici, avremo OB:D= <lb/>EF:LF. </s>

<s>Ma OB:D &egrave; maggiore di OB:C, ossia di 2C:H, dunque H.EF <lb/>&egrave; maggiore di 2C.LF: ci&ograve; vuol dire che, prevalendo il momento del pic&shy;<lb/>colo peso al momento de'due grandi, questi, come dovevasi dimostrare, sa&shy;<lb/>ranno in qualunque modo fatti salire da lui. </s>

<s>&ldquo; E quel che avviene alla retta <lb/>AB priva di gravit&agrave;, conclude il Sagredo, mentre si attacchi in E qualsivo&shy;<lb/>glia minimo peso H, avviene all'istessa corda AB, intesa di materia pesante, <lb/>senza l'aggiunta di alcun altro grave, poich&egrave; vi si sospende il peso stesso <lb/>della materia componente essa corda AB &rdquo; (ivi, pag. </s>

<s>265). </s></p><p type="main">

<s>Dicemmo esser questo un teorema di Meccanica nuova, per Galileo per&ograve;, <lb/>perch&egrave; Leonardo da Vinci l'aveva dimostrato quasi due secoli prima, come <lb/>si rammemoreranno coloro, che hanno letto il capitolo primo dell'altra parte <lb/>di questa Storia. </s>

<s>L'aggressione &egrave; nonostante ne'due Autori molto diversa, e <lb/>non sar&agrave; perci&ograve; inutile il trattenersi alquanto per farne insieme il confronto. </s>

<s><lb/>Proponendosi a risolvere il problema del piccolissimo, che muove il grandis&shy;<lb/>simo, pensava Leonardo non si potere far meglio che imitando Archimede, <lb/>con ricorrere alla leva, per mezzo della quale, dato il punto di appoggio, si <lb/>vantava che avrebbe con le sue proprie mani mosso il cielo e la terra. </s>

<s>N&egrave; <lb/>a conseguir ci&ograve;, bisognava fa altro, se non dare alla leva una tale lunghezza, <lb/>da stare alla lunghezza della contralleva reciprocamente come il peso del&shy;<lb/>l'universo sta al peso di un uomo senza il cappello, perch&egrave;, a solo aggiun&shy;<lb/>gervi il peso di questo, prevalendo il momento, si verrebber di fatto a com-<pb xlink:href="020/01/2434.jpg" pagenum="59"/>movere le fondamenta del mondo. </s>

<s>Essendo ora AE, nella precedente figura, <lb/>il braccio della leva, che si pone imponderabile, come ponevasi dianzi impon&shy;<lb/>derabile il filo, e potendosi a qual si voglia distanza dal punto fisso A ter&shy;<lb/>minare la contralleva, si comprende benissimo, diceva Leonardo, come possa <lb/>un capo di spillo in E sollevare in C una gran macina. </s></p><p type="main">

<s>Il discorso di Leonardo &egrave; vero, se son veri i teoremi di Archimede nel <lb/>libro Degli equiponderanti, ma non si pu&ograve; dir cos&igrave; di quell'altro discorso, <lb/>che Galileo poneva in bocca al Sagredo. </s>

<s>Basta infatti questa prima conside&shy;<lb/>razione, per metterci in sospetto che dee esser l&igrave; dentro una grande falla&shy;<lb/>cia: La mole di H, che libera pende dal punto F, non par che possa equi&shy;<lb/>ponderare alla mole di C, con la quale &egrave; congiunta per mezzo del funicolo <lb/>FAC, se non a patto che i due pesi, nelle dette moli, siano uguali, precisa&shy;<lb/>mente com'avverrebbe se fosse in F un altro punto stabile e fisso. </s>

<s>Il cal&shy;<lb/>colo conferma meglio che in questa sola uguaglianza de'contrappesi sussi&shy;<lb/>stono le condizioni dell'equilibrio, nel caso contemplato da Galileo, per cui <lb/>gli riusci tutt'al contrario della sua intenzione, ch'era quella di dimostrar <lb/>come mai un piccolissimo possa movere un grandissimo corpo. </s></p><p type="main">

<s>Un'altra considerazione sovviene a confermare il sospetto di qualche fal&shy;<lb/>lacia nel discorso di Galileo, ed &egrave; che male sembra essere applicato al caso <lb/>di questi pesi penduli dalle funi il principio delle velocit&agrave; virtuali, come nella <lb/>leva, sull'estremit&agrave; dalla quale esercitano i pesi perpendicolarmente tutto il <lb/>loro momento: perch&egrave; il peso H nello schema galileiano non &egrave; libero d'eser&shy;<lb/>citare il momento della sua gravit&agrave; per contrappesar C, C, essendo manife&shy;<lb/>stamente impedito dal funicolo FB che lo frena. </s>

<s>Intanto s'incomincia ora a <lb/>veder chiaro dove s'asconde l'errore di Galileo, il quale computava l'effetto <lb/>di H come se operasse con tutta la naturale sua gravit&agrave;, mentre invece la <lb/>gravit&agrave; totale alla parziale con cui fa da contrappeso al doppio di C, sta come <lb/>AF ad FE. </s>

<s>Tale &egrave; appunto la ragione che passa tra il momento del grave <lb/>nel perpendicolo, e nel piano inclinato: che se Galileo se l'avesse in tal pro&shy;<lb/>posito richiamata alla memoria, si sarebbe facilmente avveduto del suo fallo, <lb/>e avrebbe indirizzato a miglior fine il teorema della corda tesa, specialmente <lb/>applicandovi &igrave;l metodo di decomporre una forza in due, come poi fece in di&shy;<lb/>mostrare uguale la velocit&agrave; de'cadenti per varie vie oblique, ma della me&shy;<lb/>desima altezza. </s>

<s>Forse, quando scriveva e licenziava quella fine del quarto <lb/>Dialogo per la stampa, non aveva ancora pensato a questo nuovo modo di <lb/>condurre la dimostrazione del Teorema meccanico, e fa perci&ograve; pi&ugrave; gran ma&shy;<lb/>raviglia che l'analogia fra questa macchina funicolare e il piano inclinato <lb/>non fosse avvertita poi dal Viviani, il quale, accortosi finalmente della falla&shy;<lb/>cia del suo Maestro, prendendo la penna in mano per scrivergli contro, non <lb/>seppe nemmen egli liberarsi dal trascorrere in altra simile fallacia, ammet&shy;<lb/>tendo con Galileo che per la tangente EF perpendicolare, e per la secante AF <lb/>obliqua eserciti il peso il suo momento totale. </s>

<s>Anzi di questo non si corresse <lb/>mai, n&egrave; avrebbe ai veri termini meccanici ridotte mai le altrui trasgressioni, <lb/>se non gli fosse provvidamente occorso a fare alcune esperienze, le quali, <pb xlink:href="020/01/2435.jpg" pagenum="60"/>per parer tanto aliene dalla scienza del moto, non vogliamo ancora nemmen <lb/>pronunziare. </s>

<s>Riconosciute dai fatti sperimentati le ragioni geometriche, e dalla <lb/>Fisica tornando il Viviani alla Meccanica, per sodisfare ai curiosi di sapere <lb/>in che modo, di promotore ch'egli era della meccanica funicolare di Galileo, <lb/>si convertisse in contradittore; valgano le seguenti notizie, che dalle sparse <lb/>e informi carte manoscritte di lui passiamo a intessere nella nostra Storia. </s></p><p type="main">

<s>La prima e pi&ugrave; ovvia promozione, che occorresse al Viviani di fare del <lb/>teorema di Galileo, fu quella di ridurlo a problema, perch&egrave;, data la propor&shy;<lb/>zione tra il peso attaccato nel mezzo e gli altri due eguali, dai due capi della <lb/>fune liberamente pendenti, si determinassero le condizioni dell'equilibrio. </s>

<s>Quel <lb/>problema veniva dal Viviani stesso cos&igrave; proposto: &ldquo; Sia la corda AB, nella <lb/>precedente figura, senza peso, orizontalmente tesa sopra le due girelle A, B <lb/>dal mezzo delle quali in E penda un piccol peso I, e dalla estremit&agrave; di essa <lb/>i pesi C, C uguali tra loro, e quanto si voglia maggiori del peso I. </s>

<s>Gi&agrave; &egrave; ma&shy;<lb/>nifesto per il Galileo che il piccolo caler&agrave;, e sar&agrave; bastante a sollevare i pesi C. </s>

<s><lb/>Cali per esempio in I, e sia dato un altro peso F, maggiore di I, e minore <lb/>di ciascuno de'due pesi C, il quale si sospenda in luogo del peso I. &Egrave; certo <lb/>che questo caler&agrave; ancora pi&ugrave; a basso. </s>

<s>Cercasi fino a qual punto della per&shy;<lb/>pendicolare EI sia per fermarsi il peso F, sollevando i pesi C &rdquo; (MSS. Gal., <lb/>T. CXIII, fol. </s>

<s>14). </s></p><p type="main">

<s>Il problema &egrave; risoluto cos&igrave;, accomodandovi opportunamente il Viviani il <lb/>discorso e i modi di Galileo: Facciasi F:I=C:D, rappresentando C una <lb/>linea; e rappresentando 2C i pesi, si faccia ancora I:2C=D:OB:avremo <lb/>2C:F=OB:C. </s>

<s>Prendasi OE terza proporzionale dopo OB, C, e si acco&shy;<lb/>modi dentro l'angolo AEF la linea AF di tal lunghezza da aversi GL:LF= <lb/>EB:OE. </s>

<s>Sar&agrave; F il punto cercato perch&egrave; ivi il momento F.EF del peso che <lb/>scende s'uguaglia al momento 2C.FL dei pesi, che nello stesso tempo son <lb/>fatti salire. </s>

<s>Composta, l'ultima scritta proporzione dar&agrave; GF:LF=OB:OE, <lb/>e moltiplicati per LF i termini della prima ragione, e per OB i termini della <lb/>seconda, GF.LF:LF2=OB2:OE.OB.Ma GF.LF=FE2, OE.OB=C2, <lb/>dunque FE2:LF2=OB2:C2. </s>

<s>Estraendo le radici, e ponendo OB:C=2C:F, <lb/>avremo F.FE=2C.LF, che mostra come veramente in F, tra il peso che <lb/>scende e i due che salgono, s'equilibrino i momenti. </s>

<s>Ma ascoltiamo il Viviani: </s></p><p type="main">

<s>&ldquo; Facciasi come il peso F all'I cos&igrave; la linea C alla D, e come il peso I <lb/>ai pesi C cos&igrave; la linea D alla OB: sar&agrave; <emph type="italics"/>ex aequali<emph.end type="italics"/> il peso F ai pesi C, come <lb/>C ad OB, e permutando i pesi C al peso F come OB a C. </s>

<s>Inoltre delle due <lb/>OB, C sia terza proporzionale la OE, e si faccia come la EB ad OE, cos&igrave; il <lb/>diametro del cerchio, il cui radio AE, cio&egrave; cos&igrave; GL ad LF, prodotta in di&shy;<lb/>ritto: che adattando la AF all'angolo AEF sar&agrave; F il punto cercato. </s>

<s>Poich&egrave;, <lb/>essendo fatto GL ad LF come EB ad OE, sar&agrave; componendo GF ad FL, cio&egrave; <lb/>il quadrato di EF ad LF, come OB ad OE, cio&egrave; come il quadrato di OB a C, <lb/>e per&ograve; la linea EF ad FL, cio&egrave; la scesa del peso F alla salita dei pesi C, <lb/>come la linea OB a C: cio&egrave; come i pesi C al peso F reciprocamente, e per&ograve; <lb/>il dato peso caler&agrave; in F, e quivi si far&agrave; l'equilibrio &rdquo; (ivi). </s></p><pb xlink:href="020/01/2436.jpg" pagenum="61"/><p type="main">

<s>Risoluto cos&igrave; il meccanico problema, soggiunge il Viviani un corollario, <lb/>per farne l'applicazione a costruire quella nuova specie d'Igrometri, de'quali <lb/>parlammo a pag. </s>

<s>521 del nostro primo Tomo. </s>

<s>&ldquo; Se invece de'pesi C, egli <lb/>dice, da sollevarsi col piccolo peso I, ci figureremo la AB essere una stri&shy;<lb/>scia di carta, che priva di umido resti ben tesa e attaccata nelle estremit&agrave; <lb/>A, B, e nel mezzo E si appenda il medesimo peso I; questo far&agrave; alquanto <lb/>allungare detta striscia, e cavandola dalla rettitudine, gli far&agrave; fare un tale an&shy;<lb/>golo AIB, calando da E in I, e tale effetto sar&agrave; simile anzi lo stesso.... &rdquo; (ivi). </s></p><p type="main">

<s>Rimase a questo punto la scrittura interrotta, perch&egrave;, ripensando il Vi&shy;<lb/>viani a un fatto poco prima osservato, incominci&ograve; ad entrargli nella mente <lb/>il dubbio se, nel funicolo di Galileo e nel nuovo Igrometro, l'effetto fosse <lb/>veramente simile, anzi lo stesso. </s>

<s>Aveva fin allora con ferma fede creduto che, <lb/>nel detto funicolo, le scese del peso di mezzo si serbassero sempre propor&shy;<lb/>zionali alle salite dei pesi dalle due parti, ci&ograve; che trov&ograve; non avverarsi nello <lb/>strumento, quand'ebbe a compararlo con altri strumenti simili, per appli&shy;<lb/>carvi la scala delle proporzioni. </s>

<s>Poniamo che sia stato segnato in I, nella <lb/>precedente figura, il primo grado: credeva il Viviani che, doppia umi&shy;<lb/>dit&agrave; facendo allungare la carta il doppio, si dovesse il secondo grado segnare <lb/>in F, a una distanza da E doppia del primo. </s>

<s>Gli resultava invece dalle isti&shy;<lb/>tuite comparazioni che &ldquo; si ricerca pi&ugrave; umido ad abbassare dal secondo al <lb/>terzo grado, che dal primo al secondo, e maggiore dal terzo al quarto, che <lb/>dal secondo al terzo, supposti i gradi uguali &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXIV, <lb/>fol. </s>

<s>49). Cominci&ograve; allora il Viviani seco medesimo a pensare e a dire: o non <lb/>&egrave; vero quel che ho creduto fin qui in Fisica, che cio&egrave; la carta imbevuta di <lb/>doppia umidit&agrave; s'allunghi il doppio, o non &egrave; vero quel che m'aveva Galileo <lb/>fatto credere in Geometria, che cio&egrave;, nella macchina funicolare descritta dal <lb/>Sagredo, gli allungamenti delle tangenti serbino sempre proporzione esatta <lb/>con gli allungamenti delle secanti. </s>

<s>E perch&egrave; questa inquisizione seconda era <lb/><figure id="id.020.01.2436.1.jpg" xlink:href="020/01/2436/1.jpg"/></s></p><p type="caption">

<s>Figura 22.<lb/>assai pi&ugrave; comoda, e pi&ugrave; concludente della <lb/>prima, vi s'applic&ograve; con sollecita diligenza, <lb/>e gli riusc&igrave; facile a dimostrare che la tan&shy;<lb/>gente EI, alla parte esterna IM della se&shy;<lb/>cante, ha maggior proporzione della tan&shy;<lb/>gente EF, alla secante FL, e cos&igrave; rico&shy;<lb/>nobbe con sua gran compiacenza, per ra&shy;<lb/>gione geometrica in perfetta conformit&agrave; <lb/>con l'esperienze, che per fare scendere <lb/>al peso uno spazio doppio conveniva che <lb/>l'umidit&agrave; avesse fatto allungare la carta <lb/>qualche cosa pi&ugrave; del doppio, ond'&egrave; che, <lb/>presignatasi la figura 22, la costruzione <lb/>della quale &egrave; facile intendere, annun&shy;<lb/>ziava e dimostrava cos&igrave; il nuovo teorema: <lb/>&ldquo; Dico descensum EA ponderis H ad <pb xlink:href="020/01/2437.jpg" pagenum="62"/>ascensum AB ponderis L, minorem rationem habere, quam descensum FD, <lb/>ad ascensum DC. &rdquo; </s></p><p type="main">

<s>&ldquo; Nam, ducta AD, et producta usque ad G, et iuncta GB, et ex D ducta <lb/>parallela DH, erit EA ad FD ut AG ad GD, vel AB ad DH. Et, permutando, <lb/>EA ad AB, ut FD ad DH. </s>

<s>Sed DC, quae ad centrum M pertransit, minor <lb/>est DH, ut patet, ergo EA ad AB minorem habet rationem, quam FD ad DC. <lb/>Ergo, si pondus L ad pondus H fuerit ut EA ad AB, pondus H descendet <lb/>usque ad A, neque amplius descendet, cum ratio linearum FD, DC supra <lb/>punctum A sit semper maior, et infra A semper sit minor. </s>

<s>&rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. CXIII, fol. </s>

<s>12). </s></p><p type="main">

<s>Poi il Viviani stesso pens&ograve; che si potevano con pi&ugrave; facile brevit&agrave; dimo&shy;<lb/>strare le medesime cose in quest'altra maniera: &ldquo; Se si far&agrave; come i due <lb/><figure id="id.020.01.2437.1.jpg" xlink:href="020/01/2437/1.jpg"/></s></p><p type="caption">

<s>Figura 23.<lb/>pesi eguali L, M (fig. </s>

<s>23), <lb/>al peso N, cos&igrave; la tan&shy;<lb/>gente CF alla secante FG, <lb/>dico che il peso N arri&shy;<lb/>ver&agrave; a scendere fino in <lb/>F, e non passer&agrave; pi&ugrave; ol&shy;<lb/>tre a basso, perch&egrave; tutte <lb/>le tangenti maggiori di <lb/>CF, alle loro secanti, cio&egrave; <lb/>le scese del peso N, alle <lb/>salite de'pesi L, M, hanno <lb/>minor proporzione che <lb/>la scesa CF alla salita <lb/>FC, e tutte le tangenti <lb/>minori di CF, a tutte le <lb/>loro secanti, hanno sem&shy;<lb/>pre maggior proporzione <lb/>di detta CF alla FG. Poi&shy;<lb/>ch&egrave;, tirata la CG, e la DI parallela alla GF, sar&agrave; CF a FG come CC a DH. </s>

<s><lb/>Ma DB &egrave; minore di CH; dunque CD a BD ha maggior proporzione di CF a <lb/>FG. </s>

<s>Cos&igrave; si prova che CF a FG ha maggior proporzione di altra maggior <lb/>tangente CQ alla secante PQ &rdquo; (ivi). </s></p><p type="main">

<s>Lieto il Viviani di essersi incontrato in cos&igrave; bella, e nuova propriet&agrave; <lb/>geometrica, l'applicava da una parte, per divisar giusti i gradi dell'Igro&shy;<lb/>metro, e dall'altra per esplicar meglio e adornare il concetto galileiano. </s>

<s>Per <lb/>secondare una sua tale intenzione cos&igrave; scriveva in un foglio, in capo al quale <lb/>si legge: <emph type="italics"/>&ldquo; Per la proposizione del Galileo, a facce 286 nel trattato dei <lb/>proietti. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Se l'AB, nella medesima passata figura, sar&agrave; divisa per mezzo in C, <lb/>e co'centri A, B, ed intervalli AC, BC, siano descritti i quadranti, ai quali <lb/>sia tangente comune la CDF, e siano due qualsivogliano seganti AED, AGF, <lb/>dico che la CD alla DE ha maggior proporzione della CE alla FG. Poich&egrave;, <pb xlink:href="020/01/2438.jpg" pagenum="63"/>congiunta la CG, e tirata la DH parallela alla FG, che seghi la circonferenza <lb/>in I, sar&agrave; DE, che &egrave; la minima, minore di DI, e molto minore di DH, e <lb/>per&ograve; CD a DE aver&agrave; minor proporzione di CD a DH, cio&egrave; di CF ad FG, <lb/>come era da dimostrare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che se i pesi L, M, insieme presi, al peso N averanno la medesima <lb/>proporzione di CF a FG, potr&agrave; il peso N calare da C sino ad F, perch&egrave; sem&shy;<lb/>pre la sua scesa, avanti che ci arrivi, alla salita de'pesi aver&agrave; maggior pro&shy;<lb/>porzione de'due pesi L, M, al peso N. </s>

<s>E nota che ogni peso N, che sia <lb/>punto punto maggiore de'due pesi L, M, aver&agrave; il suo luogo nella tangente, <lb/>dove fermarsi ed equilibrarsi coi detti pesi, supposto per&ograve; che le attaccature <lb/>de'fili AL, BM siano tanto lunghe, che al calar del peso N possano sempre <lb/>salire i pesi L, M, perch&egrave; non si d&agrave; proporzione cos&igrave; grande tra il peso N, <lb/>bench&egrave; appena minor de'due L, M, ed i pesi L, M, che maggiore non si <lb/>possa dare tra una tangente CF alla sua intercetta segante FG. </s>

<s>Ma ben &egrave; <lb/>vero che, subito che si dia il peso N uguale alli due insieme L, M, quello <lb/>non rester&agrave; di scendere per CN, finch&egrave; non aver&agrave; fatto salire i pesi L, M <lb/>fino in A, B, e siano i fili lunghi pure quanto si voglia. </s>

<s>E questo perch&egrave; in <lb/>tal caso, tra la detta tangente e la porzione di segante, cio&egrave; tra la scesa del <lb/>peso D, e la totalit&agrave; de'pesi L, M, non si d&agrave; mai proporzione di egualit&agrave;, <lb/>ma sempre di maggioranza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che poi il peso N, equilibrando in F i due L, M, non possa scendere <lb/>oltre la tangente CF, cos&igrave; si prova nella seguente figura 24. Poich&egrave; dato per <lb/><figure id="id.020.01.2438.1.jpg" xlink:href="020/01/2438/1.jpg"/></s></p><p type="caption">

<s>Figura 24.<lb/>possibile che egli scenda ancora da F ad O, <lb/>col centro A, intervallo AF, fatto l'arco FP, <lb/>si prova in adesso che la nuova scesa FO, <lb/>alla nuova salita PO ha sempre minor propor&shy;<lb/>zione della tangente CF, alla porzione della <lb/>secante FG; cio&egrave; che i pesi L, M al peso N, <lb/>onde sar&agrave; sempre impossibile che il peso N <lb/>cali pi&ugrave; a basso di F. Imperocch&egrave;, congiunta <lb/>la corda PF, e la QG prodotta sino alla se&shy;<lb/>gante in R, sar&agrave; questa parallela alla PF, e <lb/>per&ograve; il triangolo RFG sar&agrave; simile al triangolo <lb/>FOP, onde, come RF ad FG, cos&igrave; FO ad OP. </s>

<s><lb/>Ma RF ad FG ha minor proporzione, che CF <lb/>ad FG; cio&egrave; minor proporzione de'pesi L, M <lb/>al peso N, che &egrave; qu&aacute;nto rimaneva a dimostrare &rdquo; (ivi, fol. </s>

<s>12, 13). </s></p><p type="main">

<s>Aveva appena cominciato il Viviani a gustare le gioie del veder con s&igrave; <lb/>belle geometriche invenzioni promosso il teorema di Galileo, che gli si apri&shy;<lb/>rono da quelle stesse invenzioni gli occhi, per veder invece la profonda fossa <lb/>dell'errore, in cui, come cieco ch'&egrave; menato da un altro cieco, era misera&shy;<lb/>mente caduto. </s>

<s>Supponiamo, diceva tenendo fisso lo sguardo sopra l'ultima <lb/>disegnata figura, che io da C conduca equabilmente a mano il peso infino <lb/>a farlo scendere in O: non per questo il peso L salir&agrave;, per la ritrovata ra-<pb xlink:href="020/01/2439.jpg" pagenum="64"/>gione, verso A con moto equabile, ma con moto sempre pi&ugrave; accelerato. </s>

<s>Or <lb/>come si pu&ograve; il momento di N, che si misura dal prodotto della mole per lo <lb/>spazio CO, comparar convenientemente col momento di L, che pur si misura <lb/>dal prodotto della mole per lo spazio OQ, passato nel medesimo tempo, se <lb/>il moto della salita dell'uno &egrave; diverso dal moto della scesa dell'altro? ... <gap/><lb/>quanto pi&ugrave; ci pensava, e pi&ugrave; si doleva che il suo Galileo l'avesse cos&igrave; in&shy;<lb/>gannato. </s>

<s>Attribuendo tutta la colpa di ci&ograve; al mal uso che delle velocit&agrave; vir&shy;<lb/>tuali aveva fatto il suo Maestro, volle tentare il Viviani se riusciva senza fal&shy;<lb/>lacia a dimostrare le condizioni dell'equilibrio nel funicolo teso, lasciando la <lb/>perigliosa via tenuta da Galileo, per mettersi a quell'altra, che credevasi pi&ugrave; <lb/>sicura, e ch'era allora, allora stata aperta ai Matematici dall'ingegno del Tor&shy;<lb/>ricelli. </s>

<s>Sembra che, per rendersi que'torricelliani principii pi&ugrave; familiari, e <lb/>per volgerli a secondar meglio le sue intenzioni, s'esercitasse cos&igrave; il Nostro <lb/>a confermare la verit&agrave; dei due seguenti teoremi: </s></p><p type="main">

<s>&ldquo; Li pesi eguali A, B (fig. </s>

<s>25), appesi ad un filo ACDB, cavalcabile <lb/>sopra due girelle C, D, fermate s&igrave;, che la CD sia orizontale o inclinata, non <lb/><figure id="id.020.01.2439.1.jpg" xlink:href="020/01/2439/1.jpg"/></s></p><p type="caption">

<s>Figura 25.<lb/>si moveranno giammai dal sito, in che <lb/>vennero poste. </s>

<s>Poich&egrave;, se fosse possibile <lb/>che venissero nel sito EF, congiunta la <lb/>EF, sarebbe <emph type="italics"/>ob parallelas EA, BF,<emph.end type="italics"/> come <lb/>EA a BF, cos&igrave; AG a GB, e cos&igrave; EG a <lb/>GF. </s>

<s>Ma le AE, BF sono uguali, adunque <lb/>anco le AG, GB e le EG, GF saranno <lb/>uguali. </s>

<s>Ma ancora i pesi A, B sono uguali, <lb/>adunque il punto G &egrave; centro di gravit&agrave; <lb/>de'pesi, tanto nel sito A, B, che nel sito <lb/>E, F, e per&ograve; tal centro comune, non acquistando niente verso il centro della <lb/><figure id="id.020.01.2439.2.jpg" xlink:href="020/01/2439/2.jpg"/></s></p><p type="caption">

<s>Figura 26.<lb/>Terra, anzi, non mutando luogo, i dati pesi <lb/>non si moveranno, ma si far&agrave; tra essi l'equi&shy;<lb/>librio o la quiete, in qualunque luogo verranno <lb/>lasciati. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma se i pesi A, B (fig. </s>

<s>26) saranno di&shy;<lb/>suguali, il peso maggiore A scender&agrave; sempre, <lb/>finch&egrave; B non arriver&agrave; in D. </s>

<s>Perch&egrave; il centro <lb/>di gravit&agrave; di essi gravi, quando venissero nel <lb/>sito E, F, tornerebbe in G, pi&ugrave; vicino ad E <lb/>che ad F, ma pi&ugrave; alto che H, centro de'medesimi nel sito AB, il che sa&shy;<lb/>rebbe un salire contro natura. </s>

<s>Ma bens&igrave; andranno verso il sito L, M, perch&egrave; <lb/>il centro comune I &egrave; sotto H, e sempre si trover&agrave; nella perpendicolare GHI, <lb/>discendendo da H verso I &rdquo; (ivi, fol. </s>

<s>21). </s></p><p type="main">

<s>Or venendo a fare il Viviani al funicolo galileiano l'applicazion di que&shy;<lb/>sti principii, ebbe a scoprir nel discorso del Sagredo un'altra fallacia, per&shy;<lb/>ch&egrave;, nello scendere il peso di mezzo, e nel salire i laterali, il centro di gra&shy;<lb/>vit&agrave; non vien nulla acquistando verso il centro terrestre. </s>

<s>Avrebbe dovuto <pb xlink:href="020/01/2440.jpg" pagenum="65"/>perci&ograve; considerare che qui s'opera dalla gravit&agrave;, come nell'esempio de'pesi <lb/>uguali rappresentati dalla figura XXV, e gli sarebbe dovuta bastar questa <lb/>considerazione, per avvedersi che la radice dell'errore consisteva nel suppor <lb/>che il peso di mezzo nel funicolo eserciti il suo momento totale per equili&shy;<lb/>brar gli altri due, come s'ei dipendesse da un punto stabile, e non dall'an&shy;<lb/>golo mobile delle due corde. </s>

<s>Persuaso in ogni modo che, per la debita appli&shy;<lb/>cazion del principio torricelliano, si dovesse dar finalmente al problema la <lb/>desiderata risoluzione, vi s'applic&ograve; con tutto il suo studio, e pentendosi di <lb/>aver perduto il tempo a promovere una fallacia del suo Maestro, prese la <lb/>penna in mano, per scrivere cos&igrave; <emph type="italics"/>Contro la dimostrazione del quarto dia&shy;<lb/>logo delle due Nuove scienze:<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia il peso A (fig. </s>

<s>27) men che doppio del peso C, sicch&egrave; la met&agrave; del <lb/>peso A sia minore del peso C, e questo ad A abbia la proporzione della tan&shy;<lb/><figure id="id.020.01.2440.1.jpg" xlink:href="020/01/2440/1.jpg"/></s></p><p type="caption">

<s>Figura 27.<lb/>gente AD alla secante DE, eccesso <lb/>della secante BD sopra il seno toto <lb/>BA, e preso CF uguale a DE si <lb/>giungano le AC, DF, segantisi in <lb/>K, e per K tirisi la ML, parallela <lb/>alle BC, AD, per cui dico che il <lb/>punto K &egrave; centro comune di gra&shy;<lb/>vit&agrave;, tanto della met&agrave; del peso in <lb/>A e del peso in C, quanto della <lb/>met&agrave; del medesimo A in D, e del <lb/>peso C in F. Perch&egrave;, come AD a <lb/>DE, ovvero a CF, cos&igrave; sta AK a <lb/>KC, e cos&igrave; DK a KF; ed AD a DE, <lb/>cio&egrave; a CF, sta per supposizione co&shy;<lb/>me il peso C alla met&agrave; di A, e <lb/>come il peso F alla met&agrave; di D. Sic&shy;<lb/>ch&egrave;, quando i pesi erano in A, C, <lb/>il loro centro comune era in K, <lb/>dove pure egli &egrave;, quando i pesi si <lb/>trovano in D, F: onde, a scendere A <lb/>fino in D, e salir C fino in F, il centro comune loro non avrebbe acquistato <lb/>nulla verso il centro della terra; eppure il Galileo, per mezzo di quel suo <lb/>principio di considerare la scesa dell'uno e la salita dell'altro, conclude che <lb/>A scender&agrave; in D, e C salir&agrave; in F. &rdquo; </s></p><p type="main">

<s>&ldquo; Ma qui, dico io, perch&egrave; seguir moto di questo composto di gravi, se <lb/>poi e'si devon fermare dove il loro centro comune torna nel medesimo luogo <lb/>dov'era prima? </s>

<s>Anzi io dimostro che prima che arrivare il peso A in D, <lb/>come per esempio A in G, e C in I, il centro comune, che &egrave; sempre nella <lb/>linea ML, si trover&agrave; sempre pi&ugrave; basso che il punto K, com'&egrave; in L; e quando <lb/>A &egrave; in Q, e C in P, il centro loro comune, che pure &egrave; nella ML, come in S, <lb/>con tutto che qui sia pi&ugrave; alto di L, &egrave; sempre sotto K, perch&egrave; io ho provato <pb xlink:href="020/01/2441.jpg" pagenum="66"/>altrove che AG a GH, cio&egrave; a CI, ha maggior proporzione che AD a DE, e <lb/>che per&ograve;, se la GI sega ML sotto K, per la medesima ragione la QP sega <lb/>ML sotto K. </s>

<s>Onde ne seguirebbe che se i pesi A, C potessero naturalmente <lb/>muoversi, e venire in D, F, come pretende il Galileo col suo principio, il lor <lb/>centro comune di gravit&agrave; K sarebbe prima sceso per la MK, e poi tornato <lb/>a salire, e fermatosi nel sito pi&ugrave; alto di quello, dove una volta ei si sia tro&shy;<lb/>vato: il che par che repugni alla natura delle cose gravi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E per&ograve; si esamini se si proceda con pi&ugrave; sicurezza in questa specula&shy;<lb/>zione, con quest'altro principio meccanico, cio&egrave; che <emph type="italics"/>il composto di pi&ugrave; gravi <lb/>si muover&agrave;, sempre che il loro comune centro di gravit&agrave;, nel loro moto, <lb/>acquisti vicinanza al centro comune delle cose gravi,<emph.end type="italics"/> perch&egrave; allora la met&agrave; <lb/>del peso A tirer&agrave; su, scendendo per AD, tutto il peso C, finch&egrave; amendue si <lb/>trovino in quel luogo, dove il centro comune loro, che sempre cammina per <lb/>la linea ML, si trovi nel punto pi&ugrave; basso verso il centro della terra, e che <lb/>per&ograve; non arriveranno mai nel sito DF, come conclude il Galileo con quel&shy;<lb/>l'altra maniera di considerare le scese e le salite, cio&egrave; le velocit&agrave; della met&agrave; <lb/>del grave A e di tutto il grave C, ma bens&igrave; scender&agrave; A e salir&agrave; C, finch&egrave; <lb/>il loro centro comune occupi il sito pi&ugrave; basso sotto K, che &egrave; il centro di gra&shy;<lb/>vit&agrave; di quand'erano in A ed in C, e di quand'ei fossero in D e in F. &rdquo; </s></p><p type="main">

<s>&ldquo; Cercasi dunque qual sia il primo sito tra A e D, e quale tra C ed F, <lb/>come per esempio in G ed I, sicch&egrave;, giunta la diagonale GI, questa dia il <lb/>segamento nella MK, pi&ugrave; infimo di K, che qualunque altra diagonale: cio&egrave; <lb/>trovare fin dove pu&ograve; scendere A e salir C, che il loro centro comune sem&shy;<lb/>pre abbia sceso sotto K a segno, che se A scendesse pi&ugrave;, e C salisse per&shy;<lb/>pendicolarmente ancor pi&ugrave; di prima, il loro centro comune cominciasse a <lb/>salire per LM, accostandosi al punto K. </s>

<s>Avvertasi che sempre ho inteso di <lb/>paragonare col peso C la met&agrave; dello A, perch&egrave; l'altra met&agrave; s'impiega con&shy;<lb/>tro l'altro peso uguale al C, pendente dall'altra parte della corda, mentre <lb/>per&ograve; A s'intenda posto in mezzo della corda orizzontale...... &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. CIX, fol. </s>

<s>3). </s></p><p type="main">

<s>Non prosegu&igrave; oltre il Viviani a ricercare la massima distanza da M, o <lb/>il minimo abbassamento sotto K del centro di gravit&agrave; dei pesi, perch&egrave; inco&shy;<lb/>minci&ograve; a dubitar se la nuova via presa era la diretta. </s>

<s>E bench&egrave; non fosse <lb/>difficile a lui, Autore del trattato <emph type="italics"/>De maximis et minimis,<emph.end type="italics"/> una tale ricerca, <lb/>non voleva nulladimeno, com'aveva fatto per lo avanti in questo argomento, <lb/>perdere inutilmente il tempo e la fatica. </s>

<s>Scrisse perci&ograve; a Roma a Michelan&shy;<lb/>giolo Ricci quella lettera del d&igrave; 21 Maggio 1675, pubblicata dal Nelli, nella <lb/>quale, esposte contro Galileo le difficolt&agrave; ch'ei ci trovava, s&igrave; applicando alla <lb/>dimostrazione di lui il principio delle velocit&agrave; virtuali, che quello dei centri <lb/>gravitativi; concludeva dicendo: &ldquo; In che consista l'errore del mio discorso <lb/>io non penetro ancora, ma ogni poco di riflessione, che vi far&agrave; V. S. Illu&shy;<lb/>strissima, sar&agrave; bastante a mostrarmelo &rdquo; (Saggio di storia letter, fiiorentina, <lb/>Lucca 1759, pag. </s>

<s>42). </s></p><p type="main">

<s>Il Ricci infatti rispondevagli nove giorni dopo, con sicura franchezza, <pb xlink:href="020/01/2442.jpg" pagenum="67"/>che l'errore, riferendosi alla disegnata figura, consisteva nel considerare i <lb/>pesi D, F; Q, P; G, I come gravati in ambedue l'estremit&agrave; della bilancia <lb/>da forze perpendicolari, mentre in D, in Q e in G le forze del peso che di&shy;<lb/>scende sono obliquamente dirette secondo le secanti BD, BQ, BG: voleva al&shy;<lb/>trimenti dire che in D, in Q e in G il peso A non esercita il suo momento <lb/>totale, per fare equilibrio al peso C in F, in P, in I, e non correndo perci&ograve; <lb/>qui la regola del centro di gravit&agrave;, come nella bilancia libera, &egrave; falso che <lb/>si trovino in R, in S e in L, lungo la medesima linea ML, quegli stessi centri <lb/>gravitativi: ond'&egrave; che male applicato al caso torna l'assunto del Torricelli. <lb/></s>

<s>&ldquo; Si compiaccia esaminare il mio pensiero, concludeva il Ricci, che forse lo <lb/>trover&agrave; sussistente e vero, e che sodisfa pienamente alle difficolt&agrave; proposte <lb/>da V. S. illustrissima &rdquo; (ivi, pag. </s>

<s>43). </s></p><p type="main">

<s>Quel perfetto giudizio non si era punto ingannato, e la verit&agrave; rivelata <lb/>da lui poteva confermarsi considerando la salita del peso C, nel perpendicolo <lb/>BF, comparata con la scesa del peso D nel piano inclinato BD, a quel modo <lb/>che aveva insegnato a fare Galileo stesso nella dimostrazione, che del famoso <lb/>supposto dettava al Viviani. </s>

<s>Ma &egrave; da notare che presero giusto da cotesta <lb/>dimostrazione motivo di dubitar del principio delle velocit&agrave; virtuali, il Nardi <lb/>e il Torricelli, ai quali s'aggiunse l'altra grande autorit&agrave; del Cavalieri. </s>

<s>Que&shy;<lb/>st'ultimo, in una sua lettera, nella quale mirabilmente si compendiano le <lb/>controversie promosse poi dal Marchetti e dal Vanni intorno al modo di com&shy;<lb/>putare i momenti di una sfera cadente lungo un piano inclinato; scriveva <lb/>cos&igrave;, dopo aver risposto alle difficolt&agrave;, che a lui faceva Gian Antonio Rocca, <lb/>come i due detti le facevano al Torricelli: </s></p><p type="main">

<s>&ldquo; S'ella avesse comodit&agrave; di fare l'esperienza quanto peso ci voglia a <lb/>sostenere una palla in un piano inclinato 22&deg;, 27&prime;, che &egrave; il gi&agrave; considerato, <lb/>mi saria assai caro, per vedere pure appresso a poco quanto gravita in sul <lb/>piano detta palla. </s>

<s>La ragione del signor Galileo e delli altri, che trattano que&shy;<lb/>sto teorema, credo sia perch&egrave;, salendo per esempio una sfera sopra un piano <lb/>acclive, collegata con un'altra discendente perpendicolare all'orizzonte, es&shy;<lb/>sendo tanta la salita sopra l'acclive, quanta la scesa per la detta perpendi&shy;<lb/>colare, l'altezza della salita, all'altezza della scesa, &egrave; come la perpendicolare <lb/>alla inclinata. </s>

<s>Veda ora se li pare che questi alzamenti e abbassamenti per&shy;<lb/>pendicolari siano sussistenti o no a determinare giustamente i loro momenti, <lb/>il che, come che appaia evidentissimo nella Libra, qui per&ograve; non mi pare che <lb/>cammini con pari evidenza &rdquo; (Lettere d'illustri del secolo XVII a G. A. Rocca, <lb/>Modena 1785, pag. </s>

<s>205, 6). </s></p><p type="main">

<s>Le medesime opinioni e i medesimi dubbi avendo intorno a ci&ograve; anche <lb/>il Viviani, e mancandogli in conseguenza questo efficacissimo modo di riscon&shy;<lb/>trare il vero annunziatogli dal Ricci, si dette a consultar l'esperienze, per <lb/>veder se la direzione obliqua delle forze che tirano alteri ne'pesi equilibrati <lb/>il momento. </s>

<s>Fra certe <emph type="italics"/>Esperienze fatte, e riuscite,<emph.end type="italics"/> &egrave; descritta dal Viviani <lb/>stesso anche questa, che porta notato in fronte <emph type="italics"/>provata.<emph.end type="italics"/> &ldquo; Se il peso D ed E <lb/>(fig. </s>

<s>28) sono uguali, ed F ed E uguali, sopra le girelle A, B, C le corde CB, <pb xlink:href="020/01/2443.jpg" pagenum="68"/>AB saranno tirate con uguali forze, bench&egrave; CB sia pi&ugrave; inclinata di AB, per&shy;<lb/>ch&egrave;... &rdquo; (MSS. Gal. </s>

<s>Disc., T. CIX, fol. </s>

<s>8). <lb/><figure id="id.020.01.2443.1.jpg" xlink:href="020/01/2443/1.jpg"/></s></p><p type="caption">

<s>Figura 28.</s></p><p type="main">

<s>Il perch&egrave; per&ograve; manca: che se lo avesse <lb/>il Viviani trovato, non bisognava altro per <lb/>cavarlo di quell'errore, nel quale tuttavia <lb/>si rimase, ingannato da varie vane appa&shy;<lb/>renze. </s>

<s>Prima di tutto si osserva che para&shy;<lb/>gonare l'obliquit&agrave; della forza CB, in questa <lb/>figura, con l'obliquit&agrave; della forza BD nella <lb/>figura precedente, suppone in D un punto <lb/>fisso, da rassomigliarsi alle pulegge C, A, <lb/>nel qual caso &egrave; manifesto che non potrebbe <lb/>sussistere l'equilibrio, se non a patto che il <lb/>peso D sia uguale, e non minore di C, <lb/>come suppone il Viviani. </s></p><p type="main">

<s>Ma la fallacia nell'esperienza delle funi, che cavalcando pi&ugrave; o meno obli&shy;<lb/>que sulle girelle equilibrano pesi uguali, era ben assai pi&ugrave; sottile, perch&egrave;, a <lb/>veder rimanere il peso F, come il peso D, in equilibrio, si crederebbe che <lb/>F e D facciano sopra E la medesima forza, ma non si pensa che l'equili&shy;<lb/>brio pu&ograve; tuttavia rimanere, quando la forza che perde il peso F, nel tirare <lb/>il peso E in direzione obliqua, sia uguale alla diminuita resistenza, che lo <lb/>stesso peso E fa all'esser tirato nella medesima direzione. </s>

<s>Il pensiero non <lb/>poteva esser suggerito da altro, che dall'uso del parallelogrammo delle forze, <lb/>di cui mancava la Scienza meccanica di Galileo e del Viviani, per cui si ri&shy;<lb/>mase cos&igrave; in difetto nella statica delle pulegge semplici, mentre si dia il caso <lb/>che la potenza non tiri in direzione parallela a quella della resistenza. </s>

<s>Fra <lb/>F ed E infatti permane l'equilibrio, che tra D ed E era dianzi, perch&egrave;, ti&shy;<lb/>rando la potenza F nella direzione obliqua BC, piuttosto che nella perpen&shy;<lb/>dicolare BH, tanto perde della sua forza, quanto la linea BH perde, rispetto <lb/>a BC, della sua lunghezza, e il peso E dall'altra parte tanto men resiste <lb/>all'esser tirato per l'obliqua BC, che per la perpendicolare BH, nella mede&shy;<lb/>sima proporzione. </s></p><p type="main">

<s>Applicando queste considerazioni alla Macchina funicolare, rappresentata <lb/>nella figura XXVII, si vede bene che, tirando il peso D obliquamente per la <lb/>linea DB, piuttosto che perpendicolarmente per una linea parallela a BF, tanto <lb/>perde del suo momento, quanto la BF perde di lunghezza rispetto a BD: il <lb/>centro di gravit&agrave; perci&ograve; non pu&ograve; essere in K, ma in un altro punto pi&ugrave; vi&shy;<lb/>cino ad F, come argutamente avvertiva il Ricci. </s>

<s>Il Viviani per&ograve; non gli pre&shy;<lb/>st&ograve; fede, ingannato dalle sue esperienze, non bene intese in s&egrave;, n&egrave; bene ap&shy;<lb/>plicate, per cui, vinto dalle difficolt&agrave;, lasci&ograve; ai Matematici, che ne avrebbero <lb/>avuto notizia, l'esame e il giudizio di quelle sue fallite speculazioni. </s>

<s>Vor&shy;<lb/>remmo procedere addiritto a dire del resultato di quegli esami, e della forma <lb/>di quei giudizi, ma un incidente arresta il passo frettoloso della nostra Storia. </s></p><p type="main">

<s>Sparsasi per Firenze la voce che il Viviani aveva dimostrato aver le <pb xlink:href="020/01/2444.jpg" pagenum="69"/>tangenti alle secanti nel cerchio tanto maggior proporzione, quanto son di <lb/>lunghezza minori, al qual teorema, per le relazioni che si diceva avere con <lb/>le cose dimostrate da Galileo, si dava una grande importanza; Alessandro <lb/>Marchetti, che aveva sciolti i <emph type="italics"/>Problemata sex,<emph.end type="italics"/> proposti ai Matematici di Ger&shy;<lb/>mania e d'Italia da Cristoforo Sadlero, vi aggiunse, nel pubblicar quelle solu&shy;<lb/>zioni, due teoremi geometrici, il secondo de'quali era cos&igrave; formulato: &ldquo; Rectae <lb/>circulum tangentes eo maiorem rationem habent, ad rectarum secantium por&shy;<lb/>tiones extra circulum, ab earumdem tangentium terminis diremptas, quo tan&shy;<lb/>gentes ipsae minores sunt &rdquo; (Pisis 1675, pag. </s>

<s>45). </s></p><p type="main">

<s>Disegnata la figura, come noi la reppresentiamo nella nostra 29a, faceva <lb/>osservare il Marchetti ch'essendo l'angolo AGB, nel semicerchio, acuto, e <lb/><figure id="id.020.01.2444.1.jpg" xlink:href="020/01/2444/1.jpg"/></s></p><p type="caption">

<s>Figura 29.<lb/>perci&ograve; acuto essendo anche l'angolo EIG, il lato EG del triangolo IEG deve <lb/>necessariamente esser minore del lato EI, il quale, essendo stato condotto <lb/>parallelo a CF, d&agrave; motivo all'equazione BE/EI=BF/FH, d'onde se ne conclude <lb/>che BE/EG deve esser maggiore di BF/FH, e con tanto pi&ugrave; ragione maggiore di <lb/>BF/FC, come pure si conclude dall'Autore, con pi&ugrave; lungo per&ograve; e avviluppato <lb/>discorso. </s></p><p type="main">

<s>Aveva inoltre sentito dire il Marchetti che il Viviani aveva mandato al <lb/>Ricci questo teorema, nel proporgli a risolvere una certa difficolt&agrave; natagli <lb/>intorno all'ultima dimostrazione, posta da Galileo nel quarto dialogo delle <lb/>due Nuove scienze: ond'&egrave; che, a prevenire anche in ci&ograve;, e a correre con <lb/>l'emulo suo anche questo stadio della palestra, soggiungeva il Marchetti <lb/>stesso al dimostrato teorema delle secanti nel cerchio il seguente <emph type="italics"/>Monito,<emph.end type="italics"/><lb/>stampato in lettere che, appetto alle altre del testo, si potrebbero dir cubi&shy;<lb/>tali: &ldquo; Scias velim, amicissime Lector geometra, hoc theoremate praemisso <lb/>tolli prorsus difficultatem, quae a rem saltem minus attente consideranti <lb/>apponi posset uni, ex alioquin admirandis ac propemodum divinis proposi&shy;<lb/>tionibus celeberrimi ac nunquam satis laudati Galilei, ut ipsemet, si Deus <lb/>faxit, commodiore occasione planum faciam &rdquo; (ibid., pag. </s>

<s>48). </s></p><pb xlink:href="020/01/2445.jpg" pagenum="70"/><p type="main">

<s>Il Viviani che, leggendo queste parole, sentiva dare il titolo di divina a <lb/>una proposizione dovuta riconoscer per falsa; che sentiva dire il teorema <lb/>delle secanti e delle tangenti aver tolte le difficolt&agrave;, ch'egli anzi avea pro&shy;<lb/>vocate, non pot&egrave; tenersi, scrivendo al conte Benedetto Porro, dal dirgli che <lb/>la dimostrazion del Marchetti procedeva con <emph type="italics"/>molto impaccio,<emph.end type="italics"/> e che pi&ugrave; sem&shy;<lb/>plice era la sua mandata al Ricci, e divulgatasi fra i Matematici qualche <lb/>mese prima della stampata nell'appendice ai <emph type="italics"/>Sei problemi,<emph.end type="italics"/> attenente senza <lb/>dubbio a una proposizione di Galileo, ch'era per&ograve; fra tutte le altre la men <lb/>divina e ammiranda, e concludeva: &ldquo; io mi do a credere che il medesimo <lb/>signor Marchetti erri in Meccanica con troppa confidenza &rdquo; (Nelli, Saggi cit., <lb/>pag. </s>

<s>38). </s></p><p type="main">

<s>Che la detta proposizione proceda con molto impaccio &egrave; vero, e si po&shy;<lb/>trebbe anche ammettere che l'altra del Viviani abbia meno costruzione e <lb/>sia pi&ugrave; breve, quando per&ograve; nessuno scrupoloso chiedesse che gli fosse dimo&shy;<lb/>strato quel che il Viviani stesso teneva per evidente, che cio&egrave;, di tutte le <lb/>linee condotte da un punto esterno alla circonferenza, la minima sia quella, <lb/>che prolungata passerebbe per il centro. </s>

<s>Il Marchetti per&ograve;, che di tutto vo&shy;<lb/>leva render ragione, ebbe a spender costruzioni e parole di pi&ugrave;, per dimo&shy;<lb/>strare che la EG nella sua figura &egrave; minore di EI, dalla minoranza degli an&shy;<lb/>goli nel triangolo argomentando alla minoranza dei lati opposti. </s>

<s>Volendo esser <lb/>giusti insomma convien dire che, se quella dimostrazion del Marchetti cede <lb/>per una parte, supera dall'altra la dimostrazion del Viviani, ond'&egrave; che, la&shy;<lb/>sciando intorno a ci&ograve; in pace i due gelosi rivali, vorremmo saper piuttosto <lb/>com'intendesse esso Marchetti di spianar col suo teorema quelle difficolt&agrave;, <lb/>ch'egli diceva incontrarsi da chi poco attentamente considera la divina e am&shy;<lb/>miranda proposizione di Galileo. </s>

<s>E per rendere questi nostri desiderii anche <lb/>pi&ugrave; modesti, vorremmo sapere in che modo s'applicasse un teorema di Geo&shy;<lb/>metria pura a un teorema di Meccanica nuova. </s></p><p type="main">

<s>Bisognerebbe, per rispondere prudentemente alla domanda, esser certi <lb/>se venne al Marchetti quella pi&ugrave; comoda occasione, che, si <emph type="italics"/>Deus faxit,<emph.end type="italics"/> si <lb/>riprometteva: di che per&ograve; confessiamo non avere altro documento da esibire <lb/>ai Lettori, che una nostra congettura, la notizia della quale non riuscir&agrave; in <lb/>ogni modo inutile in questa Storia. </s>

<s>Venne di questi ultimi giorni ad arric&shy;<lb/>chire, nella R. </s>

<s>Biblioteca nazionale di Firenze, la preziosa raccolta dei Ma&shy;<lb/>noscritti galileiani, un volume che, per aver ne'suoi primi quaderni, trascritta <lb/>la lettera intorno alla <emph type="italics"/>Renitenza certissima dell'acqua alla compressione,<emph.end type="italics"/><lb/>si cred&egrave; che fosse del medesimo Autore, cio&egrave; di Raffaello Magiotti, anche il <lb/>rimanente. </s>

<s>Chi svolge per&ograve; quelle pagine, con qualche attenzione, giudica <lb/>tutto altrimenti il libro, dentro cui si leggono di Galileo e de'principali di&shy;<lb/>scepoli di lui varii pensieri, non raccolti da libri stampati, ma da private <lb/>scritture, o dalle pi&ugrave; approvate tradizioni orali. </s>

<s>Tale &egrave; l'indole e il pregio <lb/>dell'opera, che perci&ograve; avremo occasione di citare pi&ugrave; volte, e non sapendo <lb/>per ora come designarne meglio il manoscritto, anche noi lo chiameremo il <lb/><emph type="italics"/>Magiotti.<emph.end type="italics"/></s></p><pb xlink:href="020/01/2446.jpg" pagenum="71"/><p type="main">

<s>A tergo dunque del foglio 218 si vedono disegnate in margine le due <lb/>figure, che noi riproduciamo, lasciate alcune superfluit&agrave; di linee, nella 30 e 31, <lb/>proposte a&gacute;li studiosi lettori per illustrare il seguente teorema: &ldquo; Se alla <lb/>fune SBCR siano appli&shy;<lb/><figure id="id.020.01.2446.1.jpg" xlink:href="020/01/2446/1.jpg"/></s></p><p type="caption">

<s>Figura 30.<lb/>cati i pesi S, R, e sia <lb/>messa la forza in D, e <lb/>ne'luoghi B, C ruote; dico <lb/>che, quanto pi&ugrave; essi pesi <lb/>si alzeranno, ci vorr&agrave; <lb/>sempre pi&ugrave; forza ad al&shy;<lb/>zargli, ed essi pi&ugrave; facil&shy;<lb/>mente si alzeranno, che <lb/>appesi alla fune ANR, <lb/>con una ruota in N, e la <lb/>forza in A. &rdquo; </s></p><p type="main">

<s>&ldquo; Dimostra il Galileo <lb/>che, se un capello, al qua&shy;<lb/>le fosser sospesi ne'luo&shy;<lb/>ghi S. </s>

<s>R i globi lunare <lb/><figure id="id.020.01.2446.2.jpg" xlink:href="020/01/2446/2.jpg"/></s></p><p type="caption">

<s>Figura 31.<lb/>e terrestre, ed esso avesse resistenza per reggerli, la sua piccola <lb/>gravit&agrave; gravitando su D, alzerebbe detti globi, ed esso capello <lb/>calerebbe in modo, che mai sarebbe parallelo all'orizonte, sic&shy;<lb/>ch&egrave; ogni poco di forza nel luogo D alzerebbe qualche poco i detti <lb/>pesi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se si tirer&agrave; una linea retta dal punto D al punto O, ed <lb/>essa prolungata segher&agrave; la linea BV di sotto al punto E (perch&egrave;, <lb/>se passasse per il punto L, non passerebbe per il punto O, poi&shy;<lb/>ch&egrave; se si pigli nella circonferenza di un cerchio due punti, la <lb/>linea retta che gli congiunge casca tutta dentro al cerchio) pro&shy;<lb/>lunghisi e seghila in M, e da detto segamento tirisi una paral&shy;<lb/>lela alla BL, quale segher&agrave; la linea VD. </s>

<s>Poich&egrave; la linea BV nel punto B <lb/>concorre, come sta la DL alla LO, cos&igrave; sta DI alla IM. F, perch&egrave; l'angolo <lb/>esteriore BLI &egrave; maggiore che retto, ed a lui &egrave; uguale l'angolo MIV, ed al <lb/>maggior angolo si oppone il maggior lato; sar&agrave; MV maggiore di MI. </s>

<s>E se <lb/>aggiungeremo ME, DL a LO avr&agrave; maggior proporzione che DV a VE, il che <lb/>si doveva dimostrare. </s>

<s>&rdquo; </s></p><p type="main">

<s>Ora, domandiamo: raccolse il compilator del <emph type="italics"/>Magiotti<emph.end type="italics"/> in questa scrit&shy;<lb/>tura un teorema del Marchetti? </s>

<s>La dimostrazione, come si vede, procede <lb/>proprio nel modo tenuto da lui, bench&egrave; con tanto minor impaccio, da emu&shy;<lb/>lar non solo, ma da superare per ogni lato di pregio quell'altra dimostra&shy;<lb/>zione, di che tanto si pregiava il Viviani. </s>

<s>Potrebb'essere il miglioramento <lb/>introdotto nel processo dimostrativo dallo stesso compilatore, ma chiunque <lb/>sia, che abbia dato opera ad applicar cos&igrave; le astratte linee geometriche alle <lb/>corde materiali tirate da pesi, convien dire che non poteva farlo con maggior <pb xlink:href="020/01/2447.jpg" pagenum="72"/>verit&agrave; di questa, confermata da quell'altra verit&agrave;, certissima per le pi&ugrave; ov&shy;<lb/>vie esperienze, che cio&egrave; tanto ci vuol pi&ugrave; di forza a tirare un carro, quanto <lb/>la strada &egrave; pi&ugrave; erta, come, nell'esempio del funicolo, &egrave; tirato in V il peso <lb/>pi&ugrave; all'erta nella direzione VB, che in L, nella direzione LB. </s>

<s>Avrebbe ci&ograve; <lb/>al Viviani, nel correre il periglioso mare pi&ugrave; al largo, potuto servir di splen&shy;<lb/>dido faro, senza il quale rimasto nelle tenebre ebbe a fare invece miseramente <lb/>naufragio. </s>

<s>Le reliquie del qual naufragio, insieme con la navicella di soccorso <lb/>ammannita dal Ricci, erano venute intanto alle mani di Giovan Batista Nelli, <lb/>il quale, apparecchiandosi nel 1759 a darne pubblica notizia, e non sapendo <lb/>per s&egrave; medesimo giudicare il caso da quel che si leggeva ne'documenti ri&shy;<lb/>masti, ne volle aver consiglio con un valoroso matematico amico suo, pro&shy;<lb/>fessore nella universit&agrave; di Pisa. </s></p><p type="main">

<s>Tommaso Perelli, al giudizio del quale fu sottoposta la lettera del Vi&shy;<lb/>viani, indirizzata il d&igrave; 21 Maggio 1675 a Michelangiolo Ricci, rispose che il <lb/>dubbio ivi proposto faceva molto onore all'Autore, bench&egrave; si maravigliasse <lb/>che un Geometra cos&igrave; profondo non proseguisse la speculazione, ricercando <lb/>il massimo abbassamento del peso di mezzo nel funicolo, per costituirsi con <lb/>gli altri due estremi in equilibrio. </s>

<s>Questa maraviglia inopportuna incomincia <lb/>a ingerirci il sospetto che il professore di Pisa esaminasse la cosa con troppa <lb/>leggerezza, dicendo apertamente il Viviani, nell'atto di congedarsi dal Ricci, <lb/>che <emph type="italics"/>non aveva gi&agrave; per difficile il ritrovare quel sito de'gravi mossi, che dia <lb/>il massimo abbassamento del loro comun centro sotto il primo sito,<emph.end type="italics"/> ma <lb/>che non volle mettersi a cercare pi&ugrave; oltre, <emph type="italics"/>perch&egrave; sarebbe stato superfluo, <lb/>quando fossc riconosciuto falso il suo raziocinio.<emph.end type="italics"/> (Nelli, Saggio cit., pag. </s>

<s>42). </s></p><p type="main">

<s>Ora, non doveva far altro il Perelli che esaminare se, della verit&agrave; o fal&shy;<lb/>sit&agrave; di quel raziocinio, era giusto il giudizio del Ricci, e quand'anche non <lb/>avesse ancora veduta la lettera di lui, far da buon matematico com'aveva <lb/>fatto lo stesso Ricci, scoprir cio&egrave; che tutta la fallacia consisteva nello stabi&shy;<lb/>lire il comun centro di gravit&agrave; di uno de'pesi estremi, e di quello pendente <lb/><figure id="id.020.01.2447.1.jpg" xlink:href="020/01/2447/1.jpg"/></s></p><p type="caption">

<s>Figura 32.<lb/>in mezzo alla fune, come se que&shy;<lb/>sto gravasse con tutta la libert&agrave; <lb/>del suo momento. </s>

<s>Diversamente <lb/>per&ograve; da questo, che il Perelli stesso <lb/>avrebbe dovuto fare, lo vediamo <lb/>confidente far col dubitoso Viviani <lb/>consorzio di errore, e, secondando <lb/>inconsideratamente il procedere di <lb/>lui, supporre <emph type="italics"/>due pesi qualsivo&shy;<lb/>glia P, Q<emph.end type="italics"/> (fig. </s>

<s>32) <emph type="italics"/>legati all'estre&shy;<lb/>mit&agrave; di una corda p A q, che passi <lb/>sempre per un dato punto A, i <lb/>quali pesi scorrano liberamente <lb/>per due rette date di posizione, <lb/>normali all'orizonte ApL, CqK<emph.end type="italics"/> (ivi, pag. </s>

<s>132). </s></p><pb xlink:href="020/01/2448.jpg" pagenum="73"/><p type="main">

<s>Che debba il peso Q star sollevato, contro la gravit&agrave; sua naturale, e <emph type="italics"/>libe&shy;<lb/>ramente<emph.end type="italics"/> scorrere lungo la verticale CK, &egrave; supposizione che non la farebbe <lb/>nessun nomo da senno: eppure il Perelli ci sopredifica la sua dimostrazione, <lb/>dicendo che, congiunti i due pesi con la linea <emph type="italics"/>pq,<emph.end type="italics"/> il punto G, dov'&egrave; questa <lb/>linea di congiunzione segata reciprocamente alle due gravit&agrave;, &egrave; il loro cen&shy;<lb/>tro comune. </s>

<s>Pi&ugrave; incredibile poi &egrave; quel che soggiunge, concludendo la sna ri&shy;<lb/>cerea per mezzo dell'iperbola equilatera di Apollonio, che cio&egrave; il peso Q si <lb/>costituisce con P in equilibrio, quando il suo abbassamento &egrave; tale, da dar la <lb/>proporzione P:Q=A<emph type="italics"/>q<emph.end type="italics"/>:C<emph type="italics"/>q,<emph.end type="italics"/> quasi che per abbassarsi l'un grave, e per <lb/>alzarsi l'altro mutino proporzione i segmenti fatti, nella linea di congiun&shy;<lb/>zione, dalla perpendicolare BG. </s>

<s>Che se sempre si serbano i detti segmenti <lb/>proporzionali, non si comprende come un matematico del valor del Perelli <lb/>potesse ammettere che due forze da equilibrarsi, le quali secondo lui riman&shy;<lb/>gon le stesse, debbano una volta aver la proporzione di <emph type="italics"/>q<emph.end type="italics"/>G a G<emph type="italics"/>p,<emph.end type="italics"/> ossia di <lb/><emph type="italics"/>q<emph.end type="italics"/>F ad AF, e un'altra di A<emph type="italics"/>q<emph.end type="italics"/> a <emph type="italics"/>q<emph.end type="italics"/>C, <emph type="italics"/>come d'altronde &egrave; noto per la dottrina <lb/>della composizion delle forze<emph.end type="italics"/> (ivi, pag. </s>

<s>123). </s></p><p type="main">

<s>Che se invece di accennarla cos&igrave; semplicemente, avesse posta quella dot&shy;<lb/>trina a fondamento della sua dimostrazione, si sarebbe il Perelli incontrato <lb/>nel medesimo pensiero del Ricci, e la speculazion del Viviani, sgombrata cosi <lb/>dall'errore, si sarebbe condotta a ritrovare il massimo abbassamento del peso <lb/>nel punto dell'equilibrio, con un metodo, che avrebbe veramente fatto onore <lb/>ad ambedue i Matematici, perch&egrave; insomma era quello tenuto poi, nella sua <lb/>Meccanica analitica, dal celebre Lagrange. </s>

<s>L'uso del parallelogrammo delle <lb/>forze infatti fu che decise appresso gli Stranieri la controversia insorta in <lb/>Italia, bench&egrave; sia cosa notabilissima che il Borelli, a cui parve fallace quel&shy;<lb/>l'uso, riuscisse, come vedremo in altro proposito, alle medesime conclu&shy;<lb/>sioni. </s></p><p type="main">

<s>Possiamo di cotesti stranieri citar primo Tommaso Simpson, il quale, <lb/>nella sezione XVIII del suo libro, intitolata <emph type="italics"/>The application of Algebra to<emph.end type="italics"/><lb/><figure id="id.020.01.2448.1.jpg" xlink:href="020/01/2448/1.jpg"/></s></p><p type="caption">

<s>Figura 33.<lb/><emph type="italics"/>the solution of geometrical <lb/>problems,<emph.end type="italics"/> proponeva cos&igrave; il <lb/>XXXVIII di quegli stessi <lb/>problemi: &ldquo; Let A and B <lb/>(fig. </s>

<s>33) be two equal wei&shy;<lb/>ghts, made fast to the ends <lb/>of a thread, or perfectly fle&shy;<lb/>xible line <emph type="italics"/>p<emph.end type="italics"/> P <emph type="italics"/>n<emph.end type="italics"/> Q <emph type="italics"/>q,<emph.end type="italics"/> sup&shy;<lb/>ported by two pins, or tacks <lb/>P, Q in the same horizontal <lb/>plane; over which pins the <lb/>line can freely slide either <lb/>way; and let C be another <lb/>weight, fastened to the thread, in te middle, between P and Q: now the <lb/>question is to find the position of the weight C, or it's distance below the <pb xlink:href="020/01/2449.jpg" pagenum="74"/>horizontal line PQ, to retain the other two weights A and B in equilibrio &rdquo; <lb/>(A treatise of algebre, London 1767, pag. </s>

<s>310). </s></p><p type="main">

<s>La soluzion del problema, che aveva dato a Galileo e al Viviani tanta <lb/>faccenda, da non valer nonostante a salvarli dall'errore, mediante l'uso del <lb/>parallelogrammo delle forze e l'analisi algebrica occorre al Simpson spedi&shy;<lb/>tamente sicura. </s>

<s>Chiamata <emph type="italics"/>x<emph.end type="italics"/> infatti la quantit&agrave; incognita dell'abbassamento <lb/>del peso C da R, punto di mezzo della corda PQ, in <emph type="italics"/>n,<emph.end type="italics"/> dove si suppone che <lb/>stabiliscasi in equilibrio, e fatta PR=<emph type="italics"/>a,<emph.end type="italics"/> l'ipotenusa P<emph type="italics"/>n<emph.end type="italics"/> sar&agrave; uguale alla <lb/>&radic;<emph type="italics"/>(a2+x2)<emph.end type="italics"/>. </s>

<s>Or se essa P<emph type="italics"/>n<emph.end type="italics"/> rappresenta la forza totale del peso A, la qual <lb/>forza si decomponga nelle due PR, R<emph type="italics"/>n,<emph.end type="italics"/> la met&agrave; del peso C non dee resistere <lb/>che a questa sola, essendo rintuzzata l'altra dalla fermezza del punto P. </s>

<s>Sar&agrave; <lb/>dunque A:C/2=P<emph type="italics"/>n<emph.end type="italics"/>:R<emph type="italics"/>n<emph.end type="italics"/>=&radic;<emph type="italics"/>(a2+x2)<emph.end type="italics"/>:<emph type="italics"/>x,<emph.end type="italics"/> ossia 2A<emph type="italics"/>x<emph.end type="italics"/>=C.&radic;<emph type="italics"/>(a2+x2)<emph.end type="italics"/>: <lb/>equazione che risoluta d&agrave; <emph type="italics"/>x=a<emph.end type="italics"/>C/&radic;(4A2&mdash;C2). Galileo poneva invece la rela&shy;<lb/>zione A:C/2=EF:LF, nella nostra XXI figura qui poco addietro, ingan&shy;<lb/>nato dal creder che i moti per la tangente e per la secante, nel medesimo <lb/>tempo, fossero equabili, e che il peso di mezzo equilibrasse i due estremi <lb/>col suo momento totale. </s>

<s>Il Viviani scopr&igrave; il primo inganno, ma, bench&egrave; ne <lb/>fosse avvertito dal Ricci, non riusc&igrave; a scoprire il secondo, per cui fa gran <lb/>maraviglia che il Frisl, accennando, in una nota all'<emph type="italics"/>Elogio del Galileo,<emph.end type="italics"/> al <lb/>problema della corda tesa in fine al quarto dialogo delle due Scienze nuove, <lb/>scrivesse che <emph type="italics"/>non sussiste il dubbio cavato dall'inequalit&agrave; del moto de'due <lb/>pesi<emph.end type="italics"/> (Livorno 1775, pag. </s>

<s>83), dando cos&igrave; intorno al fatto, che ci ha traviato <lb/>forse per troppo lungo cammino, giudizio non men leggero di quello dato <lb/>gi&agrave; dal Perelli. </s></p><p type="main">

<s>Ma non vogliamo, per quanto lunga, terminar la presente digressione, <lb/>senza osservar che Paolo Casati, informato dal suo confratello Giuseppe Fer&shy;<lb/>roni dei pi&ugrave; notabili fatti, che accadevano o erano accaduti intorno alla vita <lb/>scientifica del Viviani; prese parte nella questione dell'equilibrio dei pesi at&shy;<lb/>taccati all'estremit&agrave; e nel mezzo di una fune. </s>

<s>Egli che cred&egrave; vera la regola <lb/>del parallelogrammo, e la rese contro i sofismi sicura, come si vedr&agrave; meglio <lb/>a suo luogo, avrebbe potuto, prima del Simpson, rettamente risolvere il pro&shy;<lb/>blema, e nonostante sembra rimanesse cos&igrave; sedotto dagli esempi del Viviani, <lb/>che pens&ograve; non potersi per altra via giungere alla desiderata soluzione, che <lb/>comparando la tardit&agrave; dei pesi estremi che salgono con la velocit&agrave; del peso <lb/>di mezzo che scende. </s>

<s>&ldquo; Hanc vero, poi soggiunge, unius tarditatem cum al&shy;<lb/>terius velocitate comparari non posse, nisi ex longitudine spatiorum, quae <lb/>utrumque eodem temporis intervallo percurreret. </s>

<s>Ex quo manifesta consecu&shy;<lb/>tione conficitur satis esse si spatiorum inaequalitas aut aequalitas ostendatur, <lb/>ut praeponderatio aut aequilibritas innotescat. </s>

<s>Ac propterea satis est secan&shy;<lb/>tium excessus cum tangente comparare: haec enim ponderis intermedii, illi <lb/>ponderum extremorum motum definiunt &rdquo; (Mechanic. </s>

<s>libri, Lugduni 1684, <pb xlink:href="020/01/2450.jpg" pagenum="75"/>pag. </s>

<s>349). A far la qual geometrica comparazione aveva nel cap. </s>

<s>precedente <lb/>ordinate X proposizioni, la IV delle quali, che &egrave; il fondamento a tutto que&shy;<lb/>sto lemmatico apparecchio, si riscontra con quella, che il Marchetti ripeteva <lb/>pubblicamente, dop'aver saputo ch'era stata dimostrata in privato dal Vi&shy;<lb/>viani: &ldquo; Differentia inter tangentes duorum quorumlibet angulorum maior <lb/>est quam differentia inter eorum secantes &rdquo; (ibid., pag. </s>

<s>340). </s></p><p type="main">

<s>Riducendoci ora dunque in via, e rammemorando ai nostri Lettori che, <lb/>fatto accorto dalle critiche del Biancano, ritrov&ograve; il Viviani da correggere, spe&shy;<lb/>cialmente nel secondo e nel quarto dialogo di Galileo, le tante altre cose, da <lb/>noi notate nell'ottavo e nel nono capitolo del Tomo precedente; concludiamo <lb/>il nostro discorso intorno all'opera data dallo zelante Discepolo per restituire <lb/>alla sua verit&agrave; la nuova Scienza del moto, e per provvedere alla gloria del <lb/>venerato Maestro. </s>

<s>A questa per&ograve;, che fu l'ultima in tal soggetto, eran pre&shy;<lb/>cedute altre fatiche, intraprese con intenzione alquanto diversa, le quali giova <lb/>a noi riepilogar qui, per la final conclusione del nostro argomento. </s></p><p type="main">

<s>Ne'suoi primi principii, lo studio di migliorare e di ampliare i dialo&shy;<lb/>ghi delle due Scienze nuove non si ridusse, per parte del Viviani, che a pren&shy;<lb/>der nota delle cose dettategli da Galileo, suggerendo nonostante qua e l&agrave; <lb/>qualche pensiero di suo, che il buon Vecchio approvava, e permetteva s'in&shy;<lb/>serisse ne'Dialoghi alla prima occasione di una ristampa. </s>

<s>Anche morto il <lb/>Maestro, l'amorevole Discepolo, ch'era penetrato oramai nelle intenzioni di <lb/>lui, prosegu&igrave; quel primo importantissimo studio, frutto del quale si pu&ograve; cre&shy;<lb/>dere che fossero le cinque proposizioni intorno al momento totale, decompo&shy;<lb/>sto nel descensivo e nel gravitativo di una sfera cadente lungo un piano in&shy;<lb/>clinato; i teoremi relativi ai pendoli di varia lunghezza, e parecchie altre cose, <lb/>che sono state qua e l&agrave; notate da noi nella prima parte di questa Storia. </s></p><p type="main">

<s>La qualit&agrave; e la natura di cos&igrave; fatte speculazioni, esplicitamente uscite <lb/>dalla bocca e approvate dallo stesso Autore dei Dialoghi nuovi, o implicita&shy;<lb/>mente da lui consentite, non disdiceva che s'inserissero postume nella prima <lb/>nuova edizione, che se ne farebbe, e lo studio del Viviani fin qui procedeva <lb/>giusto con questa intenzione. </s>

<s>Ma, quando si venne a notar gli errori, e le <lb/>correzioni si trovarono superar di mole e d'importanza le aggiunte, da passar <lb/>per inverosimile o turpe l'introdurre il medesimo personaggio in scena a dir <lb/>poi in diverso modo, e spesso a contradire quel che, con tanta sicurezza e <lb/>solennit&agrave;, aveva affermato prima; allora il Viviani ebbe a mutar pensiero, e <lb/>lasciando star le cose, come l'Elzevirio l'aveva stampate, o facendo nella <lb/>nuova edizione sola aggiunta delle cose volute e consentite da Galileo, il ri&shy;<lb/>manente, che riguardava le proposizioni non vere, e le dimostrazioni sba&shy;<lb/>gliate, o che promoveva dottrine, al di l&agrave; di quel che avrebbe potuto pen&shy;<lb/>sar l'Autore, raccogliere e stampare a nome proprio in un volume a parte. </s>

<s><lb/>Manifestava da s&egrave; medesimo il Viviani a un amico queste sue intenzioni, con <lb/>parole, da noi trascritte anche altrove (T. I, pag. </s>

<s>183) dicendo che <emph type="italics"/>delle sue <lb/>fatiche di Matematica, fatte dal 1639 al 1644, ei pensava di scegliere e <lb/>di pubblicar quelle, che consistevano nell'illustrazione e promozione delle<emph.end type="italics"/><pb xlink:href="020/01/2451.jpg" pagenum="76"/><emph type="italics"/>opere di Galileo, suo maestro, da accoppiarsi con la descrizione della <lb/>sua rita.<emph.end type="italics"/></s></p><p type="main">

<s>Secondo questo proposito pochissimo cooper&ograve; il Viviani al perfeziona&shy;<lb/>mento de'dialoghi, quando prima occorse di ripubblicarli in Bologna, lascian&shy;<lb/>done la cura a chi egli doveva sapere esser men abile di tutti gli altri, a <lb/>Carlo Rinaldini. </s>

<s>N&egrave; senza dubbio s'intenderebbe come le promesse giurate <lb/>al venerato Maestro si lasciassero sodisfare all'editor bolognese in cos&igrave; inde&shy;<lb/>bito modo, quando non avesse il Viviani avuto il pensiero d'illustrarne in un <lb/>libro a parte o di promoverne le dottrine. </s>

<s>Com'egli attendesse alacremente <lb/>all'opera, per dedicarla a Luigi XIV, e per erigere in mezzo all'aula acca&shy;<lb/>demica di Parigi un monumento di gloria alla Scienza italiana, e come fosse, <lb/>per le rivalit&agrave; del Marehetti, distolto dal mandare il generoso proposito ad <lb/>effetto; &egrave; stato altrove da noi stessi narrato: cosicch&egrave;, delle tante sollecitu&shy;<lb/>dini, e dei tanto amorosi studii dati dall'Autore e dal suo allievo, per mi&shy;<lb/>gliorare i dialoghi delle due Scienze nuove (da alcune in fuori delle meno <lb/>importanti postille a una copia dell'edizione di Leida, inserite in carattere <lb/>corsivo dall'Alb&egrave;ri) ha ora il pubblico, dopo pi&ugrave; di due secoli e mezzo, in <lb/>queste nostre pagine la prima notizia. </s></p><pb xlink:href="020/01/2452.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO II.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Del quinto dialogo aggiunto alle due Scienze nuove <lb/>ossia <lb/>Della Scienza delle proporzioni<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Di ci&ograve; che a riformare il quinto libro di Euclide scrisse Giovan Batista Benedetti, e pens&ograve; Antonio <lb/>Nardi. </s>

<s>&mdash; II. </s>

<s>Come Gian Antonio Rocca porgesse occasione al Cavalieri di restaurare il princi&shy;<lb/>plo alla Scienza delle proporzioni, che poi Galileo fece mettere in dialogo. </s>

<s>&mdash; III. </s>

<s>Del disteso <lb/>fatto dal Torricelli del quinto dialogo galileiano aggiunto alle due Scienze nuove. </s>

<s>&mdash; IV. </s>

<s>Del <lb/>trattato torricelliano <emph type="italics"/>De proportionibus,<emph.end type="italics"/> inedito, e della Scienza universale delle proporzioni <lb/>spiegate da V. Viviani. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>La domanda, che sovverr&agrave; naturalmente a chiunque legge l'intitolazione <lb/>del presente capitolo, com'entri cio&egrave; un argomento di Geometria pura a far <lb/>parte della storia della Meccanica; &egrave; quella medesima, che si saranno dovuti <lb/>fare coloro, i quali ebbero prima a leggere nel libro del Viviani, dove si tratta <lb/>della <emph type="italics"/>Scienza universale delle proporzioni.<emph.end type="italics"/> &ldquo; Principio della quinta Giornata <lb/>del Galileo, da aggiungersi alle altre quattro dei Discorsi e dimostrazioni ma&shy;<lb/>tematiche intorno alle due nuove Scienze, appartenenti alla Meccanica e ai <lb/>movimenti locali &rdquo; (Firenze 1674, pag. </s>

<s>61). N&egrave; la risposta era difficile a darsi, <lb/>anche senz'altre dichiarazioni, ripensando che del moto non si pu&ograve; avere <lb/>scienza assoluta per noi, che ignoriamo le cause, dalle quali &egrave; prodotto: ond'&egrave; <lb/>che tutto quel che possiamo sapere di lui si riduce a compararne insieme gli <lb/>effetti. </s>

<s>E perch&egrave; tali effetti ci si rivelan principalmente dal mutar luogo, che <lb/>fanno i corpi, secondo certe direzioni, dalla proporzione degli spazi passati <lb/>nei medesimi tempi ne argomentiamo la maggiore o minore quantit&agrave; degli <pb xlink:href="020/01/2453.jpg" pagenum="78"/>impulsi. </s>

<s>La nuova scienza perci&ograve; del Galileo non si sarebbe dovuta intitolare <lb/><emph type="italics"/>De motu,<emph.end type="italics"/> ma <emph type="italics"/>De proportione motus,<emph.end type="italics"/> come, con filosofica propriet&agrave;, la inti&shy;<lb/>tolava Giovan Marco: tutti i loro teoremi infatti non si conducono alla con&shy;<lb/>clusione per altro matematico argomento, che per quello delle linee e delle <lb/>quantit&agrave; proporzionali. </s></p><p type="main">

<s>Riconosciutosi dunque che la verit&agrave; o la falsit&agrave; di quelle meccaniche con&shy;<lb/>clusioni dipende in tutto dalla savia applicazione, e dal retto uso delle pro&shy;<lb/>priet&agrave; geometriche, insegnate nel suo quinto libro da Euclide, era naturale <lb/>che, pur non dubitando della verit&agrave; delle cose annunziate da lui, restasse <lb/>nei nuovi Matematici qualche cosa da desiderare intorno al modo di condurre <lb/>le dimostrazioni, e all'ordine, secondo il quale si sarebbero dovute nel libro <lb/>altrimenti disporre le parti. </s>

<s>Dir quali si fossero cotesti desiderii, e ci&ograve; che <lb/>s'operasse per sodisfarli, &egrave; tanta parte della storia della Meccanica, da non <lb/>si dover trascurare da noi. </s></p><p type="main">

<s>&Egrave; oramai noto che uno dei primi e pi&ugrave; autorevoli che, nel rinascimento <lb/>della Scienza, dimostrassero alcune delle principali propriet&agrave; del moto, di cui <lb/>Aristotile o non aveva insegnate le proporzioni, o l'avea date false, fu Giovan <lb/>Batisia Benedetti, il quale fu perci&ograve; anche il primo che, in grazia della Mec&shy;<lb/>canica, attendesse a esaminar sottilmente il quinto libro di Euclide. <emph type="italics"/>In quin&shy;<lb/>tum Euclidis librum<emph.end type="italics"/> infatti &egrave; il titolo di una, forse delle pi&ugrave; brevi, ma non <lb/>delle meno importanti scritture raccolte dal Matematico veneziano nel suo <lb/>libro <emph type="italics"/>Delle speculazioni.<emph.end type="italics"/> Premette a cotesta scrittura l'Autore una prefazion&shy;<lb/>cella, nella quale egli dice che, sebben verissime siano tutte le cose ivi in&shy;<lb/>segnate dall'antico Maestro della Geometria, non possono molti nonostante <lb/>non trovar difficilissime le dimostrazioni, specialmente per l'astrusit&agrave; della <lb/>quinta e della sesta definizione premesse al quinto Libro, dalle quali dipende <lb/>l'intelligenza della massima parte dei teoremi. </s>

<s>Non fa perci&ograve; maraviglia se <lb/>tutti coloro, non eccettuato Galileo, i quali attesero poi alla riforma eucli&shy;<lb/>diana, si trattennero principalmente intorno alle due dette definizioni, eser&shy;<lb/>citandovisi per&ograve; in vario modo e coll'esaltarle alla dignit&agrave; di teoremi, e col <lb/>sostituire a loro altre note meglio atte a definir la natura delle quantit&agrave; pro&shy;<lb/>porzionali. </s>

<s>Piacque al Benedetti di tenere altra via, non contento a riformare <lb/>il libro in radice, ma nelle sue varie parti, dimostrando come molte delle <lb/>proposizioni di Euclide si riducono all'evidenza di semplici postulati. </s>

<s>&ldquo; Quan&shy;<lb/>doquidem iis nostris postulatis admissis, sequentia theoremata perfacillima <lb/>reddentur &rdquo; (Speculat, lib., Venetiis 1599, pag. </s>

<s>198). </s></p><p type="main">

<s>Per aver tenuta questa via pi&ugrave; larga, e assai diversa da quella de'suoi <lb/>successori, fu il Benedetti, come vedremo, censurato da un giudice argut&ograve;: <lb/>nessun per&ograve; ha potuto negare che i XII postulati di lui non dimostrino come <lb/>Euclide avesse, per pi&ugrave; che altrettante dimostrazioni, inutilmente affaticato <lb/>s&egrave;, e abusato della pazienza de'suoi studiosi. </s>

<s>La XXIIa, per esempio, &egrave; pro&shy;<lb/>posta cos&igrave;, secondo la versione del Commandino: &ldquo; Se siano quante gran&shy;<lb/>dezze si vogliano, e siano altre grandezze, di numero uguali a quelle, che si <lb/>piglino a due a due nella medesima proporzione; saranno ancora per la pro-<pb xlink:href="020/01/2454.jpg" pagenum="79"/>porzione uguale, nella medesima proporzione &rdquo; (Urbino 1575 a tergo del <lb/>fol. </s>

<s>73). E seguita dopo ci&ograve; la dimostrazione, non bastando la quale v'ag&shy;<lb/>giunge il traduttore anche il suo proprio commento, mentre &egrave; tutto, dice il <lb/>Benedetti, evidentissimo per s&egrave; nell'assioma: &ldquo; Quod tota, composita ex ae&shy;<lb/>quali numero partium aequalium, sunt invicem aequalia &rdquo; (Specul. </s>

<s>lib. </s>

<s>cit., <lb/>pag. </s>

<s>198). Or chi non riconosce, soggiunge lo stesso Benedetti, in queste pa&shy;<lb/>role <emph type="italics"/>Le grandezze uguali alla medesima hanno la medesima proporzione, <lb/>e la medesima alle eguali,<emph.end type="italics"/> le note distintissime dell'evidenza, senz'altro bi&shy;<lb/>sogno di dimostrazione, come fa Euclide nel suo VII teorema? </s></p><p type="main">

<s>L'VIIIa &egrave; dal traduttore proposta in questa forma: &ldquo; Delle grandezze <lb/>disuguali la maggiore alla medesima ha maggior proporzione che la minore: <lb/>e la medesima alla minore ha maggior proporzione che alla maggiore &rdquo; (Elem. </s>

<s><lb/>Eucl. </s>

<s>cit., fol. </s>

<s>68). Anche questo teorema si vuol dal Benedetti ridurre al&shy;<lb/>l'evidenza del seguente postulato: &ldquo; Quoties plures erunt termini, quorum <lb/>unus fuerit maior altero, si comparentur alicui tertio eiusdem generis, pro&shy;<lb/>portio maioris ad tertium illum maior erit ea, quae est minoris ad praedictum <lb/>tertium: et proportio illius tertii, ad maiorem, minor erit ea, quae eiusdem <lb/>tertii ad minorem terminum comparati &rdquo; (Specul. </s>

<s>lib. </s>

<s>cit., pag. </s>

<s>199). Potrebbe <lb/>per&ograve; ad alcuno sembrare altrimenti, e dire che quella VIIIa euclidea &egrave; biso&shy;<lb/>gnosa, o almeno suscettibile di dimostrazione. </s>

<s>Se siano infatti proposte le due <lb/>ragioni A/C, B/C, nelle quali A sia maggiore di B, dell'esser la prima di esse <lb/>ragioni maggiore della seconda si pu&ograve; dare dimostrazione, e dire il perch&egrave;, <lb/>col farsi osservare che, essendo la medesima quantit&agrave; divisa in egual numero <lb/>di parti, di queste in quella prima ragione se ne son prese di pi&ugrave;, che nella <lb/>seconda. </s>

<s>Date similmente le C/A, C/B, e rimanendo il supposto di A maggiore <lb/>di B, si pu&ograve; dimostrar che la prima ragione &egrave; minore della seconda, perch&egrave;, <lb/>in quella, l'unit&agrave; &egrave; stata divisa in maggior numero di parti che in questa, <lb/>e di tali parti s'&egrave; preso qua e l&agrave; un numero uguale. </s>

<s>Risponderebbe per&ograve; il <lb/>Benedetti all'istanza che non contengono questi discorsi una vera e propria <lb/>dimostrazione, e non fann'altro se non che dichiarare come quelle due pro&shy;<lb/>poste verit&agrave; si riducono a un principio noto per s&egrave;, senza altro mezzo. </s>

<s>&ldquo; Cum <lb/>enim hae propositiones sint ita conspicuae ipsi intellectui, ut absque dubio <lb/>inter obiecta ipsius intellectus connumerari possint, nullus sanae mentis eas <lb/>negabit &rdquo; (Specul. </s>

<s>lib. </s>

<s>cit., pag. </s>

<s>200). </s></p><p type="main">

<s>Premessi i dodici postulati, passa il riformatore di Euclide a esaminare <lb/>a uno a uno i teoremi del quinto libro, e una parte gli riduce ad assiomi, <lb/>come s'&egrave; veduto di sopra in alcuni esempi, una parte gli approva come ben <lb/>condotti, e rimanda al testo, perch&egrave; possano da s&egrave; consultarli gli studiosi: <lb/>di parecchi altri poi, per restituirgli a miglior ordine logico, e a maggior <lb/>chiarezza, suggerisce nuove dimostrazioni. </s></p><p type="main">

<s>Chi ripensa a quei tempi, ne'quali gl'ingegni, viziati dagli istituti ari&shy;<lb/>stotelici, di tutto volevano dare dimostrazione, perch&egrave; la scienza apparisse, <pb xlink:href="020/01/2455.jpg" pagenum="80"/>come il Filosofo voleva, creata dalla mente dell'uomo; comprender&agrave; l'utilit&agrave; <lb/>e l'efficacia di queste speculazioni del Benedetti, agl'insegnamenti del quale <lb/>educatosi Galileo sentenziava: &ldquo; che la pi&ugrave; ammirabile e pi&ugrave; da stimarsi con&shy;<lb/>dizione delle scienze dimostrative &egrave; lo scaturire e pullulare da principii no&shy;<lb/>tissimi &rdquo; (Alb. </s>

<s>XIII, 90). Avrebbero nonostante desiderato alcuni che, met&shy;<lb/>tendosi il grande Matematico veneziano a riformare il quinto libro di Euclide, <lb/>avesse riconosciuto che il vizio lo tiravano la maggior parte delle proposi&shy;<lb/>zioni dalla definizione quinta, come da maleficiata radice, senza risanar la <lb/>quale reputavano che non si potesse condur l'opera alla desiderata perfezione. </s></p><p type="main">

<s>Uno di cotesti censori del Benedetti era quell'Antonio Nardi, le mate&shy;<lb/>matiche speculazioni del quale, tanto ammirate dal Torricelli e dal Cavalieri, <lb/>son rimaste per la Scienza italiana sventuratamente tesori nascosti. </s>

<s>Il Nardi <lb/>dunque, ingegno veramente geometrico, aveva dovuto qua e l&agrave; notare alcuni <lb/>difetti nello studiar l'unico libro, che s'avesse allora da mettere innanzi a <lb/>chi voleva imparare i primi elementi della Geometria, e di quelle note di <lb/>lui s'&egrave; potuto aver notizia, perch&egrave; inserite, fra le <emph type="italics"/>Varie osservazioni geo&shy;<lb/>metriche,<emph.end type="italics"/> nella veduta ottava della sesta <emph type="italics"/>Scena.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nel primo degli Element&igrave; euclidiani, ivi si legge, pongonsi imperita&shy;<lb/>mente tra le domande pratiche due comuni notizie speculative, il che &egrave; er&shy;<lb/>rore. </s>

<s>Anche nel VI libro trovasi, sotto il numero V, una definizione, quale &egrave; <lb/>dimostrabile, e devesi cos&igrave; apportare: <emph type="italics"/>La ragione di due grandezze resul&shy;<lb/>tar dicesi di tante ragioni, di quante tra quelle grandezze ne stanno.<emph.end type="italics"/> Tal <lb/>definizione poi risponde alla decima del Vo, ove tal definizione non sta ben <lb/>posta, ma va nel VI<gap/>. </s>

<s>Servesi anche Euclide alcune volte del nome di <emph type="italics"/>pira&shy;<lb/>mide,<emph.end type="italics"/> in cambio di quello di <emph type="italics"/>tetraedo,<emph.end type="italics"/> il che par cosa licenziosa in uno <emph type="italics"/>Ele&shy;<lb/>mentario. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Se riceviamo doversi dir parte una grandezza di grandezza omogenea, <lb/>riceveremo anche che, se la prima della seconda, o questa di quella, sia sol <lb/>parte, che la terza della quarta o questa di quella; sar&agrave; la prima alla se&shy;<lb/>conda, nella disegual proporzione, come la terza alla quarta; ma nella eguale <lb/>bisogna che la prima s'agguagli alla seconda, e la terza alla quarta. </s>

<s>Incam&shy;<lb/>minandoci per tale strada, potremo adoprarci in diversa maniera intorno alla <lb/>economia del Vo di Euclide, ma per esser ci&ograve; opera lunga, ci basti l'averne <lb/>posti i principii. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Euclide restrinse il nome di parti alla quota: noi prendiamo general&shy;<lb/>mente, col nome di parte, la quota, le quote e l'incommensurabile al tutto, <lb/>da che forse schivasi l'oscurit&agrave; di qualche definizione del quinto suddetto, <lb/>bench&egrave; altre difficolt&agrave; qui s'incontrino. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Non si accorse il dottissimo Commandino che una comune notizia, <lb/>della quale Euclide si serve nella prima del Xo, anche nella ottava del Vo aveva <lb/>per prima avuto luogo, e cos&igrave; non la not&ograve; detto Interpetre, come doveva, <lb/>dopo la definizione del Vo, ma dopo quella del Xo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Osservo che il dottissimo Commandino s'addorment&ograve; nella decima pro&shy;<lb/>posizione del IVo euclidiano, perch&egrave;, dovendo da Teone tradurre le parole <pb xlink:href="020/01/2456.jpg" pagenum="81"/>greche <emph type="italics"/>quae non est maior,<emph.end type="italics"/> traduce <emph type="italics"/>quae non sit maior,<emph.end type="italics"/> e cos&igrave; port&ograve; una <lb/>condizione ridicola, non che superflua alla costruzione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; All'ottava definizione dell'XIo di Euclide suppliscasi, di mente del&shy;<lb/>l'Autore, <emph type="italics"/>prodotto per ogni banda.<emph.end type="italics"/> La IXa, la Xa e XIa dello stesso libro <lb/>non patiranno difficolt&agrave;, se il subietto prendasi come predicato, il che como&shy;<lb/>damente far puossi, anzi devesi, per la propriet&agrave; della lingua greca, n&egrave; hanno <lb/>ci&ograve; avvertito gl'Interpetri. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Osservo che le quattro grandezze proporzionali, definite nel Vo con la <lb/>moltiplicazione, si possono anche, con la divisione, definire, e l'un metodo, <lb/>nell'operazione, riscontrasi con l'altro &rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>844, 45). </s></p><p type="main">

<s>Questi, come si vede, eran pensieri che il Nardi frettolosamente scriveva <lb/>in distinte note, via via che gli sovvenivano alla mente, e che poi volle rac&shy;<lb/>cogliere insieme nella citata Scena. </s>

<s>Da quei frettolosi pensieri per&ograve; balena <lb/>chiaro il concetto della particolar riforma del quinto libro euclideo, il quale <lb/>si risonosce radicalmente viziato dall'essere, in quinto luogo, mal definite <lb/>dall'Autore le condizioni, che fanno consister fra loro quattro quantit&agrave; omo&shy;<lb/>genee proporzionali. </s>

<s>Quella quinta definizione infatti &egrave; tale, secondo le parole <lb/>che il traduttore premette al quinto libro: &ldquo; Le grandezze si dicono essere <lb/>nella medesima proporzione, la prima alla seconda e la terza alla quarta, <lb/>quando le ugualmente moltiplici della prima e della terza, ovvero insieme <lb/>avanzano le ugualmente moltiplici della seconda e della quarta, secondo qual&shy;<lb/>sivoglia moltiplicazione; ovvero insieme le pareggiano; ovvero insieme sono <lb/>avanzate da loro &rdquo; (Elem. </s>

<s>Eucl. </s>

<s>cit., fol. </s>

<s>63). </s></p><p type="main">

<s>Esaminando bene questo discorso &egrave; facile trovare che si riduce alla forma <lb/>seguente: Siano date le due relazioni A/B, C/D: si vuol assegnare uno dei pi&ugrave; <lb/>facili, e de'pi&ugrave; distinti caratterismi, che ce le faccia riconoscere, quando sono <lb/>fra loro uguali. </s>

<s>Euclide in sostanza risponde: quando, moltiplicate per la me&shy;<lb/>desima quantit&agrave;, la quale sia per esempio N/M; si mantengono uguali. </s>

<s>Ma per&shy;<lb/>ch&egrave; in dir cos&igrave; troppo manifesto apparirebbe il paralogismo, consistente nel <lb/>dare il segno da riconoscere un'eguaglianza, mentre implicitamente suppo&shy;<lb/>nevasi gi&agrave; nota; si raggirano in altre parole le medesime cose, dicendo che <lb/>quattro quantit&agrave; sono allora proporzionali, quando i prodotti A.N, C.N, ossia <lb/>gli equimolteplici delle due antecedenti s'accordano sempre in superare, egua&shy;<lb/>gliare e mancare co'prodotti B.M, D.M, ossia con gli equimolteplici delle <lb/>due conseguenti. </s></p><p type="main">

<s>Ora il Nardi scopriva il paralogismo anche sotto questo discorso, cos&igrave; <lb/>artificiosamente condotto, vedendo chiaro che, per moltiplicare in qualunque <lb/>modo, e secondo qualunque moltiplicazione, i termini, non verrebbero per&ograve; <lb/>le due relazioni ad acquistare quella uguaglianza, che non avessero avuto <lb/>prima: intanto che ne concludeva non dover esser quella euclidea definizione <lb/>legittima, perch&egrave; applicabile indifferentemente anche alle quantit&agrave; non pro&shy;<lb/>porzionali. </s>

<s>Soggiungeva di pi&ugrave; non sembrargli quella stessa definizione nem-<pb xlink:href="020/01/2457.jpg" pagenum="82"/>meno universale, perch&egrave;: supponiamo di avere l'angolo retto, che chiame&shy;<lb/>remo A, misurato dal quadrante Q del cerchio, di cui R sia il raggio: le <lb/>ragioni A:Q e 2:R<foreign lang="greek">p</foreign> sono senza dubbio uguali, ma bench&egrave; gli equimolte&shy;<lb/>plici degli antecedenti si possano accordare facilmente insieme nel mancare <lb/>e nell'eccedere i conseguenti, non si accorderanno in eterno nell'eguagliarsi, <lb/>essendo la circonferenza e il raggio incommensurabili. </s>

<s>Simile dicasi del lato <lb/>del quadrato e della diagonale, perch&egrave;, chiamata questa D, e quello L, che <lb/>supponesi essere uguale a 5, D:L, e &radic;50:&radic;25 stanno insieme in vera e <lb/>propria proporzione, bench&egrave; il carattere della loro proporzionalit&agrave; non si possa, <lb/>per la dottrina degl'incommensurabili, desumer dalla regola degli equimol&shy;<lb/>teplici euclidei. </s></p><p type="main">

<s>Sembravano al Nardi queste cose tanto evidenti, che si maravigliava come <lb/>non l'avessero avvertite que'cos&igrave; grandi Matematici dell'antichit&agrave;, quali erano <lb/>Archimede, Pappo e simili altri. </s>

<s>Ben per&ograve; pi&ugrave; si maravigliava che, nel dar <lb/>mano cos&igrave; valida a restaurare la scienza, non le avesse avvertite il Benedetti, <lb/>per cui soggiungeva ai sopra scritti pensieri anche il seguente, ch'egli poi <lb/>raccoglieva fra gli altri nella medesima Scena: </s></p><p type="main">

<s>&ldquo; Il Benedetti, geometra insigne, non si accorse che, volendo riformare <lb/>il quinto libro di Euclide, trascur&ograve; le definizioni delle uguali e diseguali ra&shy;<lb/>gioni, quale principio &egrave; il fondamento dell'opera. </s>

<s>Stupiscomi certo di tanta <lb/>inavvertenza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Mentre io sento dirmisi che siano quattro quantit&agrave; proporzionali, le <lb/>estreme siano maggiori delle mezzane, resto sospeso fino a che non ne fac&shy;<lb/>cia il conto nei numeri noti, ed allora ragionevolmente desidero d'intenderne <lb/>la dimostrazione, perch&egrave; l'induzione, e meno l'esempio, non appagano l'in&shy;<lb/>telletto contemplativo. </s>

<s>Che se mi si proponga due quantit&agrave; uguali aver la <lb/>stessa proporzione ad una terza, non solo l'intendo, ma vedo esser difficile <lb/>l'insegnar, con mezzi pi&ugrave; facili ed evidenti di quello che sia la proposta, tal <lb/>verit&agrave;. </s>

<s>Euclide per insegnarmela assume la definizione quinta nel Vo, qual'&egrave; <lb/>molto pi&ugrave; difficile ad intendersi che non &egrave; la proposta: onde tal definizione <lb/>rende oscure tutte le prove, nelle quali direttamente s'adopra. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ci&ograve; nondimeno poco m'importerebbe, ma trovo qualche difficolt&agrave; per <lb/>mantenerla legittima. </s>

<s>Dico dunque parermi che quella definizione convenga <lb/>ancora alle quantit&agrave; non proporzionali, il che sarebbe difetto importantissimo. </s>

<s><lb/>Sia qualsivoglia numero A il primo termine, e qualsivoglia numero B, mi&shy;<lb/>nore, il secondo: il terzo sia l'angolo retto, e il quarto l'angolo nel mezzo <lb/>cerchio. </s>

<s>Certo che questi due angoli moltiplicati si possono superare scam&shy;<lb/>bievolmente, onde hanno proporzione insieme, conforme anche ricerca Eu&shy;<lb/>clide nella quarta definizione. </s>

<s>Ora dico che, presi gli equimolteplici del primo <lb/>e del terzo termine, in qualsivoglia modo, e cos&igrave; anche del secondo e del <lb/>quarto, avverr&agrave; che, se uno antecedente superio o manchi dal suo conseg&ugrave;ente, <lb/>anche l'altro superer&agrave; o mancher&agrave; dal suo, secondo qual si voglia moltipli&shy;<lb/>cazione, nello stesso modo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che se per il primo termine prendessimo Rce 50, per il secondo Rce 25, <pb xlink:href="020/01/2458.jpg" pagenum="83"/>per il terzo la diagonale del quadrato, per il quarto il lato dello stesso; in <lb/>questo caso, posti gli equimolteplici del primo e del terzo e del secondo e del <lb/>quarto, avverr&agrave; che se uno antecedente superi o manchi dal suo conseguente, <lb/>anche l'altro superi o manchi dal suo. </s>

<s>&Egrave; ben vero che, quantunque sian pro&shy;<lb/>porzionali la diagonale e il lato, come Rce 50 e Rce 25, non per&ograve; giammai av&shy;<lb/>verr&agrave; che i molteplici degli antecedenti uguaglino i molteplici dei conseguenti, <lb/>com'&egrave; noto per la dottrina degli incommensurabili: e lo stesso avviene, nel <lb/>caso dell'angolo retto e del mezzo cerchio, e dei loro molteplici e corrispon&shy;<lb/>denti. </s>

<s>Non &egrave; dunque necessario, secondo la definizione di Euclide, che le cose <lb/>proporzionali si possano sempre, mediante la moltiplicazione, agguagliare, al&shy;<lb/>trimenti non sarebbe universale a tutte le proporzionali detta definizione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Avvezzati, o mio Lettore, a bene esaminare i detti, bench&egrave; comune&shy;<lb/>mente ricevuti per veri, dei grandi uomini, e frattanto, in difesa di Euclide, <lb/>dico ch'egli aveva bisogno di definire le quattro proporzionali con qualche <lb/>caratterismo, per poterle, nelle operazioni geometriche, riconoscere dalle non <lb/>tali: onde il definirle generalmente esser quelle, che hanno lo stesso rispetto, <lb/>secondo la quantit&agrave;, non bastava al suo proposito. </s>

<s>Ci&ograve; supposto, piacemi che <lb/>alla definizione da esso data basti solo, negli scolii, aggiungere di mente sua <lb/>che gli eccessi o difetti della prima verso la seconda, e della terza verso la <lb/>quarta, sieno capaci di proporzione: cio&egrave; che moltiplicati possano superare <lb/>la seconda e la quarta, come vedesi volere Euclide nella ottava proposizione <lb/>del Vo, dove dichiara il senso di questa definizione, e cos&igrave; togliesi ogni dif&shy;<lb/>ficolt&agrave;. </s>

<s>Vediamo ancora che Euclide propone lo scambiamento di ragione, <lb/>come indistintamente valido, nella X proposizione: eppure di mente sua bi&shy;<lb/>sognava supplire che i termini, che si scambiano, siano di proporzione capaci, <lb/>altrimenti egli c'insegnerebbe il falso &rdquo; (MSS. Gal., T. XX, pag. </s>

<s>846-48). </s></p><p type="main">

<s>L'apparire ora queste cos&igrave; savie osservazioni del Nardi, dopo pi&ugrave; che <lb/>due secoli e mezzo, alla luce, conferisce a farci meglio conoscere l'indole di <lb/>quell'ingegno, in mezzo ai tanti altri che, pur non essendo meno acuti di <lb/>lui, s'eran resi per&ograve; meno franchi dall'altrui suggezione. </s>

<s>Il Benedetti, che <lb/>senti primo alitarsi in petto questo nuovo spirito di libert&agrave;, mostr&ograve; nel pre&shy;<lb/>sente esempio d'esser rimasto avvinto in qualche parte a quel giogo, per cui <lb/>non sospett&ograve; che potesse il grande Euclide essere scorso in un paralogismo, <lb/>di che mostrava non essersi accorto nemmeno il grandissimo Archimede. </s>

<s><lb/>Galileo pure pass&ograve; inconsideratamente, com'apparir&agrave; dal processo di questa <lb/>Storia, sopra quelle medesime fallacie, attraverso alle quali lo avevano con&shy;<lb/>fidentemente menato i suoi antichi Maestri, ond'ebbe il Nardi il merito di <lb/>averle egli avvertite e scansate il primo, come prezioso frutto di quel che <lb/>avendo gi&agrave; sapientemente deliberato per s&egrave; medesimo, dava poi agli altri <lb/>qua!'utile consiglio: <emph type="italics"/>Avvezzati, o mio Lettore, a bene esaminare i detti, <lb/>bench&egrave; comunemente ricevuti per veri, dei grandi uomini.<emph.end type="italics"/></s></p><p type="main">

<s>Che veramente poi le frettolose osservazioni, raccolte dal Matematico are&shy;<lb/>tino nella sua Scena, contengano, per la riforma del quinto libro di Euclide, <lb/>i necessari principii, che ivi dice l'Autore di non si voler mettere a svol-<pb xlink:href="020/01/2459.jpg" pagenum="84"/>gere, <emph type="italics"/>per esser ci&ograve; opera lunga;<emph.end type="italics"/> apparir&agrave; manifesto da quel che saremo per <lb/>dire di quella medesima opera, eseguitasi nel medesimo tempo dal Cavalieri, <lb/>e pubblicatasi poi da Galileo, nella prima parte di quel quinto dialogo ag&shy;<lb/>giunto alle due Scienze nuove, dove si pongono dal Salviati i primi fonda&shy;<lb/>menti della detta riforma, null'altro pi&ugrave; facendo, n&egrave; potendosi per verit&agrave; fare <lb/>secondo il retto giudizio, che svolgere la fondamental proposizione accennata <lb/>dal Nardi. </s></p><p type="main">

<s>Consisteva questa proposizione nello stabilir di fatto le condizioni di <lb/>quelle uguaglianze, che. </s>

<s>Euclide dava il segno di riconoscer per tali a chi <lb/>egli supponeva gi&agrave; che fossero note, dicendo, tutt'altrimenti dal venerato idolo <lb/>antico, essere allora quattro termini proporzionali, quando il primo sia tanta <lb/>parte del secondo, quanta il terzo &egrave; del quarto. </s>

<s>Cos&igrave; venivansi ai molteplici <lb/>opportunamente a sostituire i divisori, e sopra cos&igrave; ben posto fondamento fa&shy;<lb/>ceva osservare lo stesso Nardi come quel che suppone Euclide potevasi dimo&shy;<lb/>strare, trasformandosi la sua quinta definizione in teorema. </s>

<s>Se A infatti sta <lb/>a B, come C a D, anche A.N star&agrave; a B, come C.N a D; e ancora star&agrave; <lb/>A.N a B.M come C.N a D.M: ci&ograve; che conclude come, essendo gli equi&shy;<lb/>molteplici proporzionali, sono altresi in proporzione i semplici termini re&shy;<lb/>spettivi. </s></p><p type="main">

<s>Coloro, i quali non sono avvezzi come noi, dietro i savi consigli del <lb/>Nardi, a bene esaminare i detti, bench&egrave; comunemente ricevuti per veri, dei <lb/>grandi uomini; e che anzi, fedel copia vivente dei peripatetici antichi, ten&shy;<lb/>gono che una matematica proposizione sia vera, perch&egrave; &egrave; scritta nei libri di <lb/>Galileo, e vogliono sopra pi&ugrave; non esserci verit&agrave;, che sui principii del se&shy;<lb/>colo XVII non avesse il divino uomo scoperta, e annunziata agli altri uomini, <lb/>giacentisi nelle tenebre universali dell'ignoranza; si vedrebbero aver gi&agrave; le&shy;<lb/>vate sospettosi le orecchie, in parer che s'incammini a provare il nostro di&shy;<lb/>scorso che quei, ch'essi venerano qual secondo Maestro di coloro che sanno, <lb/>sia stato prevenuto nello stabilire la nuova Scienza delle proporzioni. </s>

<s>Noi <lb/>confermiamo che fu veramente cos&igrave;, com'&egrave; intanto provato rispetto al Nardi, <lb/>che doveva verso il 1635 avere scritte le sue osservazioni, all'esempio del <lb/>quale resta a soggiungere come s'incontrasse in quel tempo nel medesimo <lb/>pensiero anche il Cavalieri, andato perci&ograve; poi soggetto a un'altra usurpazione, <lb/>dalla quale vogliamo che vengano ora finalmente a rivendicarlo, per solo amor <lb/>di giustizia, il sincero giudizio, e la libera coscienza della Storia. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Noto principalmente per la solenne pubblicazione, che il Torricelli fa&shy;<lb/>ceva, a pag. </s>

<s>77 della seconda parte delle Opere geometriche, di un teorema <lb/>di lui; Gian Antonio Rocca, gentiluomo di Reggio, fu uno dei pi&ugrave; valorosi <lb/>discepoli del Cavalieri. </s>

<s>Dalla lettura dei dialoghi dei due Massimi sistemi, <pb xlink:href="020/01/2460.jpg" pagenum="85"/>quando non erano venuti ancora alla luce gli altri delle due Scienze nuove, <lb/>apprese i primi principii della Meccanica, e lo Specchio Ustorio del suo pro&shy;<lb/>prio maestro gli porgeva gli esempi del modo, come si potessero, con la Geo&shy;<lb/>metria nuova, illustrare e promovere quegli stessi principii galileiani. </s>

<s>Non <lb/>trovando, fra le altre conclusioni annunziate nel detto dialogo Del mondo, <lb/>nulla che si riferisse ai moti equabili, dai quali dipendono, e con i quali si <lb/>paragonano le altre specie di moti, volle egli medesimo applicarvisi, incerto <lb/>s'egli fosse per supplire al difetto, o per prevenire l'apparizione di ci&ograve;, che <lb/>nel suo nuovo trattato sarebbe per dimostrare lo stesso Galileo. </s>

<s>Comunque <lb/>sia, erano gi&agrave; da Archimede, nella prima proposizione Delle spirali, posti <lb/>alla nuova Scienza, che s'intendeva di instaurare, i principii, e non restava <lb/>a far altro al Rocca, se non che a svolgerli, perch&egrave; gli venissero di l&igrave; ritro&shy;<lb/>vate le conseguenti propriet&agrave; dei moti uniformi. </s></p><p type="main">

<s>In quella prima proposizione dunque Archimede vuol dimostrare il teo&shy;<lb/>rema fondamentale, che cio&egrave;, essendo le velocit&agrave; uguali, gli spazi stanno come <lb/>i tempi. </s>

<s>Per far ci&ograve; suppone che il mobile P (fig. </s>

<s>34) inceda equiveloce nella <lb/><figure id="id.020.01.2460.1.jpg" xlink:href="020/01/2460/1.jpg"/></s></p><p type="caption">

<s>Figura 34.<lb/>direzione AB, e dato che lo spazio CD sia passato nel tempo FG, e lo spa&shy;<lb/>zio DE nel tempo GH, conclude il suo intento col provar che CD, DE e FG, <lb/>GH son quattro termini proporzionali. </s>

<s>Il mezzo per la dimostrazione doveva <lb/>esser perci&ograve; suggerito dalla Geometria pura, al maestro della quale rivolgen&shy;<lb/>dosi Archimede, e trovando essere da lui insegnato che quattro termini sono <lb/>allora proporzionali, quando gli equimolteplici degli antecedenti s'accordano <lb/>sempre in mancare o in uguagliare o in superare gli equimolteplici dei con&shy;<lb/>seguenti, non cred&egrave; il grande Siracusano che restasse a lui da far altro, se <lb/>non che a dimostrare come presi IC, LF equimolteplici di CD, FG, ed EK, <lb/>HM equimolteplici di DE e di GH, si verificassero esattamente nel suo caso <lb/>le condizioni, per le proporzionalit&agrave;, richieste da Euclide &ldquo; Quoniam FG, cos&igrave; <lb/>David Rivault ne traduceva dal greco le parole, tempus est quo P cucurrit <lb/>CD, et quoties est CD in IC, toties est FG in LF, sequitur, quia motus puncti P <lb/>est uniformis, esse LF tempus, quo eadem celeritate punctus P decurrerit IC. </s>

<s><lb/>Eadem ratione est HM tempus, quo inambulaverit idem P spatium EK. <lb/>Proinde, si IC superaverit EK, similiter LF superabit HM. </s>

<s>Et si IC defecerit <lb/>ab EK, deficiet quoque LF ab HM. </s>

<s>Demum si aequalis fuerit IC alteri multi&shy;<lb/>plici EK, etiam LF aequabitur tempori HM. </s>

<s>Est propterea CD ad DE ut FG ad <lb/>GH, ut proponebatur &rdquo; (Parisiis 1615, pag. </s>

<s>353). </s></p><p type="main">

<s>Archimede procede oltre a proporre in secondo luogo che, essendo i <pb xlink:href="020/01/2461.jpg" pagenum="86"/>tempi uguali, le varie velocit&agrave;, con le quali incedono due mobili diversi, <lb/>stanno come gli spazi, e supposto che N per esempio (fig. </s>

<s>35) passi nella <lb/>direzione AB gli spazi AE, EG, mentre O nella direzione CD passa gli spazi <lb/>CF, FH; conclude il proposito col dimostrare che AE sta ad EG, come CF <lb/>a FH. </s>

<s>Per far ci&ograve;, essendo, egli dice, per supposizione AE, CF ed EG, FH <lb/>scorsi nei medesimi tempi, siano questi stessi tempi rappresentati da IK, KM: <lb/>avremo dunque, per la proposizion precedente, AE:BG=IK:KM. &ldquo; Atqui <lb/><figure id="id.020.01.2461.1.jpg" xlink:href="020/01/2461/1.jpg"/></s></p><p type="caption">

<s>Figura 35.<lb/>etiam CF est <lb/>ad FH, ut IK <lb/>ad KM; ergo <lb/>ut AE ad EG. <lb/>sic CF ad FH, <lb/>quod fuit <lb/>probandum &rdquo; <lb/>(ibid.). </s></p><p type="main">

<s>S'arresta a questo punto il progresso archimedeo Dei moti equabili, <lb/>perch'era sufficiente all'Autore il premettere questi due soli teoremi, come <lb/>lemmi, per dimostrare, ci&ograve; ch'era allora la sua principale intenzione, le mi&shy;<lb/>rabili propriet&agrave; delle spirali. </s>

<s>Volle il Rocca proseguir l'opera del Siracusano, <lb/>e dall'aver sull'esempio di lui dimostrata la prima legge fondamentale, che <lb/>governa i moti uniformi, ne concludeva, non solo che, essendo i tempi uguali, <lb/>le velocit&agrave; stanno come gli spazi, ma di pi&ugrave; che, essendo gli spazi uguali, si <lb/>rispondono contrariamente le velocit&agrave; con i tempi; che, essendo le velocit&agrave; <lb/>e i tempi differenti, in ragion composta di loro stanno gli spazi passati; che, <lb/>se sono le velocit&agrave; e gli spazi disuguali, nella contraria ragion del loro com&shy;<lb/>posto si rispondono i tempi: con altre simili propriet&agrave;, che l'esperto Mate&shy;<lb/>matico vedeva conseguire dai medesimi principii. </s></p><p type="main">

<s>Aveva il Rocca disposti in ordine di trattato questi teoremi, della legit&shy;<lb/>tima dimostrazion dei quali non dubitava, quando fosse stato certo della <lb/>buona dimostrazione del primo, che procedeva, come s'&egrave; detto, per l'appli&shy;<lb/>cazione degli equimolteplici a dimostrar le proporzionalit&agrave;, secondo gl'insegna&shy;<lb/>menti di Euclide, e sopra gli esempi dello stesso Archimede. </s>

<s>Intorno a quegli <lb/>equimolteplici per&ograve;, e non in altro, incominciarono i dubbi a tenzonar forte <lb/>nella solitaria mente del Rocca, perch&egrave; da una parte gli pareva chiaro, per <lb/>la sua propria ragione, che non fossero n&egrave; ben definite, n&egrave; ben dimostrate <lb/>le quantit&agrave; proporzionali a quel modo; e dall'altra lo atterrivano le grandi <lb/>autorit&agrave; dei Matematici antichi, i quali concordemente lo avevano approvato. </s>

<s><lb/>Per quietar la sua penosa agitazione ebbe ricorso al Cavalieri, a cui, man&shy;<lb/>dando il trattatello <emph type="italics"/>Dei moti equabili,<emph.end type="italics"/> gli esponeva anche insieme le ragioni, <lb/>che lo avevano fatto cos&igrave; dubitare e della quinta definizione euclidea premessa <lb/>al quinto libro degli Elementi, e dell'applicazione, che ne aveva fatta Archi&shy;<lb/>mede nella prima Delle spirali. </s></p><p type="main">

<s>Il Cavalieri, attentamente esaminando nei citati libri le cose, non solo <lb/>ebbe a convenire col Rocca, ma, persuaso di pi&ugrave; che il trattato Dei moti <pb xlink:href="020/01/2462.jpg" pagenum="87"/>equabili si rimaneva a quel modo senza il suo legittimo fondamento, comin&shy;<lb/>ci&ograve; a pensare, in grazia del suo discepolo e avutane occasione da lui, secondo <lb/>qual pi&ugrave; vero e pi&ugrave; noto carattere si potessero definire le ragioni proporzio&shy;<lb/>nali. </s>

<s>Cos&igrave; di pensiero in pensiero procedendo, gli venne fatto di trovare il <lb/>modo, com'egli avrebbe creduto si dovesse emendare il quinto libro di Eu&shy;<lb/>clide, specialmente in quelle proposizioni, che rimanessero viziate dalla quinta <lb/>definizione. </s>

<s>N&egrave;, essendo la verit&agrave; una sola, far&agrave; punto maraviglia ch'ei si <lb/>fosse incontrato col Nardi, cos&igrave; in definire l'uguaglianza di due ragioni dalla <lb/>eguaglianza dei loro quozienti, come in ridurre la detta quinta definizione a <lb/>teorema da dimostrarsi. </s></p><p type="main">

<s>La novit&agrave; e l'importanza della pensata riforma euclidea allettavano cos&igrave; <lb/>l'animo del Cavalieri, che, essendo in sul punto di terminar la stampa della <lb/>Geometria degl'indivisibili, deliberava fra s&egrave; di coglier quell'occasione, che <lb/>gli si porgeva cos&igrave; comoda e pronta di pubblicare que'suoi pensieri intorno <lb/>alle proporzioni, come cosa anch'essa geometrica, in appendice ai sette libri <lb/>della detta Geometria. </s>

<s>L'argomento per&ograve; e l'indole dell'aggiunta troppo es&shy;<lb/>sendo diversi dal subietto, aveva pensato di dar a quella anche abito diverso, <lb/>mettendola in dialogo fra uno che insegna, e l'altro che ascolta. </s>

<s>Il pensiero <lb/>d'imitar Galileo, anche nell'estrinseca forma del discorso, s'appresent&ograve; forse <lb/>la prima volta alla mente del Cavalieri a quella occasione, bench&egrave; comin&shy;<lb/>ciasse ad effettuarlo solo alquanti anni dopo, e in altro proposito, quando a <lb/>Benedetto Castelli e a Cesare Marsili, che nel dialogo della riforma di Eu&shy;<lb/>clide avrebbero rappresentato il Salviati galileiano e il Sagredo, v'aggiunse <lb/>terzo un Simplicio, applicando la goffa maschera di lui, per vendetta, sulla <lb/>faccia al Guldino. </s></p><p type="main">

<s>Non volle per&ograve; mettersi il Cavalieri a colorir quella scena, senz'averne <lb/>prima consulto con Galileo, da cui, prima di tutto, voleva sapere se la quinta <lb/>definizione di Euclide stava a rigor di logica, e se, avendo bisogno di corre&shy;<lb/>zione, poteva farsi a quel modo, che si proponeva: poi voleva saper di pi&ugrave; <lb/>se convenisse pubblicar la scrittura sopra tale argomento in appendice alla <lb/>nuova Geometria. </s>

<s>Distese perci&ograve; que'suoi pensieri senz'alcuno ornamento, e <lb/>solo, per render poi pi&ugrave; docile la materia a improntarsi del dialogo, quando <lb/>fosse deciso di pubblicare il suo discorso; distinse i punti delle proposte e <lb/>delle obiezioni, delle domande e delle risposte. </s>

<s>Dettava poi le cose, scritte <lb/>cos&igrave; alla buona a un amanuense, il quale, trascrivendo com'egli stesso e il <lb/>dettator pronunziavano, venne a farne una copia da spedirsi a Galileo, la <lb/>quale, per la sola ortografia, anche senz'altri indizi, tradiva l'origine propria. </s></p><p type="main">

<s>Fu fatta la spedizione <emph type="italics"/>da Bologna alli 19 Dicembre 1634,<emph.end type="italics"/> accompa&shy;<lb/>gnando il Cavalieri il plico con una lettera, la quale cos&igrave; finiva: &ldquo; Di grazia <lb/>mi favorisca dirmi qualche cosa della mia Geometria, e se resta sodisfatto <lb/>o no liberamente delle mie risposte. </s>

<s>Scrivo con fretta, perci&ograve; mi scusi della <lb/>negligenza nello scrivere, e ci&ograve;, per avere io voluto trascrivere un pensiero <lb/>intorno alla definizione Va del quinto di Euclide, quale le mando per sen&shy;<lb/>tirne il suo parere. </s>

<s>&Egrave; cosa fatta a richiesta di un giovane studioso. </s>

<s>Se le pa-<pb xlink:href="020/01/2463.jpg" pagenum="88"/>resse cosa buona, avrei pensiero di metterla nel fine della mia Geometria, ma <lb/>desidero sentir prima il suo parere &rdquo; (Campori, Carteggio galil., Modena 1881, <lb/>pag. </s>

<s>423). </s></p><p type="main">

<s>La nostra curiosit&agrave; fu eccitata dalla lettura di queste parole a ricercar <lb/>lo scritto mandato a Galileo, di cui il Cavalieri qui fa motto, e sembrandoci <lb/>di averlo trovato, almeno in parte, lo trascriviamo, assoggettando noi e i no&shy;<lb/>stri lettori al tedio di serbare i solecismi, e la scorretta grafia dell'originale: </s></p><p type="main">

<s>&ldquo; Nella dimostrazione di un certo Autore apportando nella prima pro&shy;<lb/>posizione <emph type="italics"/>del moto equabile<emph.end type="italics"/> l'operatione delli <emph type="italics"/>egualmente moltiplici.<emph.end type="italics"/> que&shy;<lb/>sto a data occasione dessaminar la 5a e 7a definizione di Euclide. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Hora per espianar la strada quanto serra possibile alla introductione <lb/>delle <emph type="italics"/>proporzionalit&agrave;.<emph.end type="italics"/> suppongasi primieramente (come suppose anche Eu&shy;<lb/>clide mentre le defini) che le grandezze proporzionale se trovino, cio&egrave; che <lb/>date in qualunque modo 3 grandezze quella proportione o quel rispetto o <lb/>quella relazione di quantit&agrave; che ha la 1a verso la 2a l'istessa possa haver <lb/>la 3a verso una 4a. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Hora per averne una definitione vera bisogna prendere una delle lor <lb/>passioni, ma la pi&ugrave; facile de tutte del quale se puol poi cavar le pi&ugrave; recon&shy;<lb/>dite. </s>

<s>Perch&egrave; la diffinitione gi&agrave; ditta d'Euclide in questa maniera &egrave; troppo <lb/>imbrolliato: Allora 4 grandezze sono proporzionali quando gl'egualmente <lb/>moltiplici della 1a e della 3a presi secondo qualunque moltiplicit&agrave; si accor&shy;<lb/>dano sempre nel superare mancare o paregiare gl'egualmente moltiplici della <lb/>2a e della 4a *. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Obs.<emph.end type="italics"/> &mdash; (Chi habbia certezza che allora quando 4 grandezze sono pro&shy;<lb/>porzionali gl'egualmente moltiplici non si accordino sempre? </s>

<s>Overo chi me <lb/>assicur&agrave; che quelli egualmente moltiplici non si accordino sempre e che nul&shy;<lb/>ladimeno le grandezze non siano proporzionale? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Gi&agrave; Euclide nella precedente deffinitione haveva deliberato la propor&shy;<lb/>zione tra due grandezze essere un tal rispetto o relazione tra di loro per <lb/>quanto appartiene alla quantit&agrave;. </s>

<s>Hora avendo il lettore concepito gi&agrave; nel in&shy;<lb/>telletto che cosa sia la proporzione fra due grandezze sar&agrave; difficile cosa che <lb/>egli possa intendere che quel rispetto o relatione che &egrave; fra la 1a e la 2a gran&shy;<lb/>dezza allora sia simile al rispetto e relatione che si trova fra la 3a e 4a gran&shy;<lb/>dezza, quando quelli egualmente moltiplici della 1a e della 3a si accordano <lb/>sempre nella maniera predetta con glegualmente moltiplici della 2a e della 4a. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E perch&egrave; questo di Euclide &egrave; piuttosto theorema da dimostrare che una <lb/>definitione da premettersi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; * Diremo noi allora 4 grandezze esser fra loro proporzionale, cio&egrave; haver <lb/>la 1a alla 2a la stessa proportione che la 3a alla 4a quando la prima sar&agrave; <lb/>eguale alla 2a e la 3a alla 4a. </s>

<s>Overo quando la 1a sar&agrave; tante volte moltiplice <lb/>della 2a quante volte precisamente la 3a &egrave; moltiplice della 4a. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Similemente sono le grandezze proporzionale quando la 1a contenga <lb/>3 volte 1/2 per essempio la 2a et anco la 3a contenga 3 volte 1/2 la 4a, e final&shy;<lb/>mente in qualsivoglia altra denominatione mentre le grandezze siano propor-<pb xlink:href="020/01/2464.jpg" pagenum="89"/>zionale, e perci&ograve; diremo con maggiore universalit&agrave; tutto gi&agrave; stabilito, cio&egrave; allora <lb/>intendiamo 4 grandezze esser fra loro proporzionale quando l'eccesso della 1a<lb/>sopra la 2a (qualunque egli sia) sia simile all'eccesso della 3a sopra la 4a. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Questo s'intende quando gli antecedente sono maggiore delle lor con&shy;<lb/>seguente ma in caso che la 1a sia minore della 2a e la 3a della 4a alhora <lb/>sar&agrave; la 2a maggiore della 1a e la 4a della 3a. </s>

<s>Per&ograve; consideri con quest'ordine <lb/>inverso e simagini che la 2a sia 1a e la 4a sia 3a. </s>

<s>Cos&igrave; haver&agrave; sempre le an&shy;<lb/>tecedente sempre maggiore delle conseguente e laccennata diffinitione basta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Hora considerando le antecedenti maggior delle lor conseguenti di&shy;<lb/>remo 1&deg; per diffinitione in che maniera s'intende le 4 grandezze esser fra <lb/>loro proporzionali et &egrave; questa. </s>

<s>Quando la 1a per avere alla 2a la medesima <lb/>proportione che la 3a alla 4a non &egrave; punto n&egrave; maggior n&egrave; minore di quello <lb/>che ella dovrebbe essere. </s>

<s>allora s'intende aver la 1a alla seconda la mede&shy;<lb/>sima proporzione che ha la 3a alla 4a. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Con questa occasione definirei con modo assai simile la proportione <lb/>maggiore e direi cos&igrave;. </s>

<s>Ma quando la 1a grandezza sar&agrave; alquanto pi&ugrave; grande <lb/>di quel che ella dovrebbe essere per avere alla 2a la medesima proportione <lb/>che ha la 3a alla 4a. </s>

<s>allora voglio che convenghiamo di dire che la 2a hab&shy;<lb/>bia maggior proportione alla 2a che non ha la 3a alla 4a. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma in caso che la 1a sia minor di quel che si ricercherebbe per avere <lb/>alla 2a quella medesima proportione che ha la 3a alla 4a sar&agrave; segno evi&shy;<lb/>dente che la 3a &egrave; maggior del dovere per havere alla 4a quella tal propor&shy;<lb/>tione che ha la 1a alla 2a. </s>

<s>Per&ograve; in questo caso ancora V. S. si contenti di <lb/>concepir l'ordine in altro modo e simmagini che quelle grandezze che erano <lb/>3a e 4a diventino 1a e 2a. </s>

<s>e quell'altre che erano 1a e 2a V. S. le riponga <lb/>nei luoghi della 3a e della 4a. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Obs.<emph.end type="italics"/> &mdash; Bene adunque dimostrate con questi suoi principi tutto il 5&deg; di <lb/>Euclide. </s>

<s>overo di dedurre da queste due diffinitione poste da V. S. quelle <lb/>altre due che Euclide mette per 5a e per 7a che sustengano il machina del <lb/>5&deg; libro. </s>

<s>hora dimostrate queste come conclusioni. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Sol.<emph.end type="italics"/> &mdash; Quando le 4 grandezze sono proporzionali glegualmente molti&shy;<lb/>plici della 1a e della 3a eternamente concordino etc. </s>

<s>se poter&agrave; entrar senza <lb/>scorta al 5&deg; libro a intendere i theoremi delle grandezze proportionali. </s>

<s>E cos&igrave; <lb/>posta la definizione della proportione maggiore dimostrar&ograve; che in qualche <lb/>caso presi glegualmente moltiplici della 1a e della 3a et anco della 2a e della <lb/>4a quel della 1a ecceda quel della 2a ma quel della 3a non ecceda quel <lb/>della 4a. </s>

<s>Cos&igrave; questa conclusione serra la definitione della quale come prin&shy;<lb/>cipio si serve Euclide. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; D.a<emph.end type="italics"/> &mdash; Quando io restassi persuaso di queste dua passioni deglegual&shy;<lb/>mente moltiplici cio&egrave; che quando le 4 grandezze son proportionali quelli eter&shy;<lb/>namente si accordano nel paregiare eccedere e mancare. </s>

<s>e che quando le <lb/>4 grandezze non son proportionali quelli in qualche caso discordano io per <lb/>me non ricercherei altra luce per intendere con chiarezza tutto il 5&deg; degli <lb/>Elementi geometrici. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2465.jpg" pagenum="90"/><p type="main">

<s><emph type="italics"/>&ldquo; Ris.<emph.end type="italics"/> &mdash; Supponiamo che le 4 grandezze A, B, C, D siano proportio&shy;<lb/>nali cio&egrave; che la 1a A alla 2a habbi l'istessa proportione che la 3a C ha <lb/>verso la 4a D. credete che anco due della 1a verso la 2a averanno la mede&shy;<lb/>sima proportione che due della 3a verso la 4a? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Adunque intender&agrave; anco con questo che 4 o 10 o 100 delle 1m<gap/> ad <lb/>una 2a averanno listessa proportione che hanno 4 o 10 o 100 della 3a ad <lb/>una 4a. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Adunque &egrave; necessario che il moltiplice della 1a abbia listessa propor&shy;<lb/>tione alla 2a che ha legualmente molteplice della 3a alla 4a cio&egrave; che la <lb/>1a moltiplicata quante volte si pare abbia alla 2a quella proportione istessa <lb/>che ha la 3a moltiplicata altrettante volte verso la 4a. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Questo &egrave; per le antecedenti. </s>

<s>ma per le conseguenti credete voi che <lb/>date 4 grandezze proporzionali che la 1a a due della seconda abbia propor&shy;<lb/>zione diversa da quella che ha la 3a a due della 1a overo a 4 o a 10? &rdquo; </s></p><p type="main">

<s>&ldquo; Ammettendo dunque voi questo confessate di restare appagato e din&shy;<lb/>tendere con facilit&agrave; che date 4 grandezze proporzionale A, B, C, D moltipli&shy;<lb/>cate egualmente la 1a e la 3a quella proportione che ha il molteplice E della <lb/>1a A alla 2a B listessa ancora habbia precisamente la egualmente moltiplice <lb/>F della 3a C alla D. &rdquo; <lb/>&ldquo; E &mdash; A<emph type="sub"/>1<emph.end type="sub"/> B<emph type="sub"/>2<emph.end type="sub"/> &mdash; G <lb/>F &mdash; C<emph type="sub"/>3<emph.end type="sub"/> D<emph type="sub"/>4<emph.end type="sub"/> &mdash; H &rdquo;</s></p><p type="main">

<s>&ldquo; Immaginatevi dunque che queste siano le nostre 4 grandezze propor&shy;<lb/>zionali E, B, F, D cio&egrave; il molteplice F della 3a sia 3a e la 4a D sia 4a V. S. <lb/>me ha anco detto di capire che moltiplicandosi egualmente le conseguenti <lb/>B, D cio&egrave; la 2a e 4a senza alterar punto le antecedenti la medesima propor&shy;<lb/>tione aver&agrave; la 1a al moltiplicato della 2a che ha la 3a al moltiplicato della 4a. </s>

<s><lb/>Ma queste 4 grandezze saranno per appunto F, F egualmente molteplice della <lb/>1a e della 3a e G, H egualmente molteplice della 2a e della 4a. </s>

<s>&rdquo; (MSS. Gal., <lb/>P. V, T. V, fol. </s>

<s>81-83). </s></p><p type="main">

<s>Attentamente rimeditate queste cose, e cos&igrave; com'erano Galileo ritrova&shy;<lb/>tele vere, a predispor l'animo dei nostri Lettori, curiosi gi&agrave; di sapere qual <lb/>risposta si facesse al Cavalieri, giova osservar come doveva aver l'argomento <lb/>una particolare importanza per lui, il quale, bench&egrave; non avesse ancora pub&shy;<lb/>blicato il terzo dialogo delle Scienze nuove, teneva pure fra i manoscritti di&shy;<lb/>steso, parecchi anni prima del Rocca, il trattatello dei moti uniformi. </s>

<s>Il primo <lb/>principio della scrittura venutagli da Bologna gli aveva fatto rivolgere il pen&shy;<lb/>siero a quel suo trattatello, per la buona dimostrazione, se non per la verit&agrave; <lb/>del quale, ebbe allora a sentire una gran trepidazione, quando s'abbatt&egrave; ivi <lb/>a leggere le parole: <emph type="italics"/>chi mi assicura che quelli egualmente moltiplici non <lb/>si accordino sempre e che nulladimeno le grandezze non siano propor&shy;<lb/>zionali?<emph.end type="italics"/></s></p><p type="main">

<s>A ben comprendere i sentimenti di Galileo convien osservare che i due <pb xlink:href="020/01/2466.jpg" pagenum="91"/>primi teoremi <emph type="italics"/>De motu aequabili,<emph.end type="italics"/> fedelissima imitazione delle due prime pro&shy;<lb/>posizioni archimedee delle Spirali, concludono la proporzionalit&agrave; fra gli spazi <lb/>e i tempi, essendo le velocit&agrave; eguali, e la proporzionalit&agrave; fra le velocit&agrave; e gli <lb/>spazi, essendo uguali i tempi, per l'applicazione degli equimolteplici. </s>

<s>&ldquo; Sunt <lb/>itaque quatuor magnitudines.... ac demonstratum est aeque multiplicia pri&shy;<lb/>mae et tertiae vel una aequari vel una deficere, vel una excedere aeque mul&shy;<lb/>tiplicia secundae et quartae. </s>

<s>Ergo prima ad secundam eamdem habet ratio&shy;<lb/>nem quam tertia ad quartam &rdquo; (Alb. </s>

<s>XIII, 151). Or era venuto il Cavalieri, <lb/>in quelle sue carte, a far osservare che si posson bene gli equimoltiplici con&shy;<lb/>tenere fra loro a quel modo, e pure non esser vero che <emph type="italics"/>spatium ad spatium <lb/>eamdem habeat rationem, quam tempus ad tempus.<emph.end type="italics"/> Non essendo vero que&shy;<lb/>sto, o non ben dimostrato, non si poteva esser certi della verit&agrave; del primo <lb/>teorema, in cui i moti accelerati si riducono agli uniformi, d'onde verreb&shy;<lb/>besi altresi a diffondere l'incertezza sul teorema secondo, in cui, quasi per <lb/>un corollario del precedente, si stabilisce la legge degli spazi proporzionali <lb/>ai quadrati dei tempi. </s></p><p type="main">

<s>Tali sentiva Galileo dovere o poter essere le conseguenze dannose alla <lb/>nuova scienza del moto, com'ei l'aveva gi&agrave; nei suoi libri istituita, e che ora <lb/>s'apparecchiava di mettere in dialogo, per palesarla finalmente al mondo: <lb/>ond'avendo gi&agrave; deliberato di non lasciare in mano altrui un'arme cos&igrave; pe&shy;<lb/>ricolosa, qual vedeva spuntare dal pensiero del Cavalieri, non potendola get&shy;<lb/>tare o nascondere, voleva maneggiarla egli da s&egrave; medesimo destramente a <lb/>suo modo. </s>

<s>Meditava fra s&egrave; in silenzio come si potesse conseguir meglio la <lb/>desiderata intenzione, e intanto il Rocca, il quale aveva avuto copia della <lb/>scrittura sulla riforma euclidea, intorno a che dicevasi di voler consultar Ga&shy;<lb/>lileo, e dopo quasi pi&ugrave; che un mese e mezzo non aveva ancora saputo altro; <lb/>sollecitava curioso il Cavalieri che rispondeva cos&igrave; da Bologna il d&igrave; 4 Gen&shy;<lb/>naio: &ldquo; Scrissi gi&agrave; al sig. </s>

<s>Galileo e li mandai una copia della dimostrazione <lb/>intorno alla definizione quinta del Quinto di Euclide, da V. S. promossa, per <lb/>intenderne il parer suo, ed aspettone risposta: avendo cosa nuova glie ne <lb/>dar&ograve; avviso &rdquo; (Lettere a G. A. </s>

<s>Rocca etc., Modena 1725, pag. </s>

<s>21). </s></p><p type="main">

<s>Indugi&ograve; a venire parecchi altri giorni ancora l'aspettata risposta, dei <lb/>propri termini della quale non abbiamo precisa notizia, ma si congetturano <lb/>facilmente dai sentimenti, che si dovettero suscitar nell'animo di Galileo, e <lb/>dal riscontro delle seguenti parole scrittegli dal Cavalieri in una sua lettera <lb/>del d&igrave; 6 Febbraio di quel medesimo anno 1635. &ldquo; Quanto all'appendice in&shy;<lb/>torno alla definizione V del Quinto, conforme che mi pare che inclini il suo <lb/>parere, la lascer&ograve; stare, non avendo veramente alcuna connessione con l'opera, <lb/>e differir&ograve; a pi&ugrave; opportuna occasione il pubblicarla. </s>

<s>Bene avevo gusto inse&shy;<lb/>rirla nella Geometria come cosa geometrica, e maggiormente che non so se <lb/>pi&ugrave; stamper&ograve; di simili materie, che da molti sono aborrite, da pochi viste, e <lb/>da pochissimi apprezzate &rdquo; (Campori, Carteggio gal. </s>

<s>cit., pag. </s>

<s>429). Il Cava&shy;<lb/>lieri per&ograve;, in quella sua ingenuit&agrave;, non aveva ben comprese le segrete inten&shy;<lb/>zioni n&egrave; penetrato addentro al cupo animo di Galileo, il quale poi si fece <pb xlink:href="020/01/2467.jpg" pagenum="92"/>intendere meglio, che di quella dimostrazione del definito da Euclide non <lb/>doveva far l'Autore oramai pi&ugrave; conto come di cosa sua, n&egrave; perci&ograve; pensare <lb/>di pubblicarla a nome suo nella Geometria nuova, n&egrave; altrove. </s>

<s>L'artificio e <lb/>il modo cran molto diversi, ma nell'effetto si rassomigliavano a quelli dei <lb/><emph type="italics"/>bravi<emph.end type="italics"/> di que'tempi, i quali, dop'avere usata contro un pi&ugrave; debole qualche <lb/>prepotenza, lo lasciavano, sicuri d'essere bene intesi, col ficcargli in viso gli <lb/>occhi minacciosi, e con l'appuntarsi il dito su dal mento al naso. </s></p><p type="main">

<s>Divenuto Galileo con quest'arti, delle quali noi ci siam fatti al mondo <lb/>aborriti delatori, sicuro dell'usurpato possesso, resta a dire qual'ei pensasse <lb/>llora di farne, e quale veramente ne facesse poi uso. </s>

<s>Il vederlo attendere <lb/>in quel tempo a trascrivere le due prime proposizioni <emph type="italics"/>De motu aequabili,<emph.end type="italics"/><lb/>cos&igrave; com'erano state gi&agrave; dimostrate per l'applicazione degli equimolteplici, <lb/>parrebbe segno ch'ei non avesse riconosciuto ancora la verit&agrave; dei dubbi, o <lb/>l'importanza delle critiche del Cavalieri. </s>

<s>Ma furono certe difficolt&agrave;, le quali <lb/>si comprenderanno meglio fra poco, che fecero lasciare a Galileo senza ri&shy;<lb/>forma i detti teoremi, di cui poteva dall'altra parte riversare ogni responsa&shy;<lb/>bilit&agrave; sopr'Archimede, loro primo e legittimo Autore. </s>

<s>Credeva allora che do&shy;<lb/>vess'essere sufficiente a salvarlo dalle contradizioni quella grande autorit&agrave;, <lb/>invocata anche altrove, quando, nella dimostrazion delle traiettorie parabo&shy;<lb/>liche si supponevano parallele le forze sollecitanti il proietto (Alb. </s>

<s>XIII, 228), <lb/>o quando si voleva da alcuni francesi mettere in dubbio se la nuova Mecca&shy;<lb/>nica fosse una scienza reale o un romanzo, francamente rispondendo agli <lb/>oppositori, Galileo, che, pur non verificandosi le dimostrate leggi in natura, <lb/>non per questo perderebbero le sue dimostrazioni di forza e di concludenza, <lb/>&ldquo; siccome niente progiudica alle conclusioni, dimostrate da Archimede circa <lb/>la spirale, il non ritrovarsi in natura mobile, che in quella maniera spiral&shy;<lb/>mente si muova &rdquo; (Alb. </s>

<s>VII, 157). </s></p><p type="main">

<s>Appena pubblicatisi per&ograve; i Dialoghi, la critica inesorabile non volle ri&shy;<lb/>conoscere autorit&agrave;, e mentre da una parte s'assaliva a visiera scoperta il nuovo <lb/>edifizio, diceudo ch'era tutto fondato sopra un supposto; si sentiva dall'altra <lb/>i minacciosi rumori di chi soggiungeva che, non solo quel meccanico fonda&shy;<lb/>mento era ipotetico, ma che mancava affatto di fondamento, non essendo di&shy;<lb/>mostrative delle proporzionalit&agrave; fra gli spazi e i tempi le ragioni suggerite da <lb/>Euclide. </s>

<s>Avvenne perci&ograve; che, in mezzo all'opera di perfezionare i discorsi <lb/>del moto stampati in Leida, una delle sollecitudini, che si dette immediata&shy;<lb/>mente l'Autore, dopo aver ritrovata la dimostrazione del principio supposto, <lb/>fu quella d'assegnare altre note distintive e altre condizioni delle quantit&agrave; <lb/>proporzionali. </s>

<s>La notizia si raccoglie certa da ci&ograve;, che soggiunge il Viviani, <lb/>dop aver detto come volesse Galileo che gli facesse il disteso della dimostra&shy;<lb/>zion del teorema ammesso gi&agrave; come noto, intorno a che nel capitolo prece&shy;<lb/>dente s'&egrave; da noi lungamente discorso. </s></p><p type="main">

<s>&ldquo; Per una simile occasione di dubitare intorno alla quinta ed alla set&shy;<lb/>tima definizione del quinto d'Euclide, dice esso Viviani, mi aveva per avanti <lb/>conferito il Galileo la dimostrazione di quelle definizioni del quinto Libro, <pb xlink:href="020/01/2468.jpg" pagenum="93"/>senza per&ograve; applicarla a figure, che, fermatomi poi in Arcetri, egli mi dett&ograve; <lb/>in dialogo, assai prima della venuta quivi del Torricelli, quando ancora il <lb/>Galileo non aveva risoluto di porla nella quinta Giornata, ma pensava tut&shy;<lb/>tavia d'aggiungerla alla quarta <emph type="italics"/>(cos&igrave;: ma voleva dire alla terza)<emph.end type="italics"/> a facce 153 <lb/>dell'impressione di Leida, dopo la prima proposizione Dei moti equabili, nel <lb/>caso del ristamparsi, con le altre opere sue, quell'ultima delle due nuove <lb/>Scienze. </s>

<s>Questa tal dettatura diede poi qualche facilit&agrave; al medesimo Galileo <lb/>ed al Torricelli, per fare quel pi&ugrave; ampio disteso in dialogo, che si &egrave; veduto, <lb/>e la medesima come inutile rimase a me, ed ancora la conservo &rdquo; (Scienza <lb/>univ. </s>

<s>delle proporz. </s>

<s>cit., pag. </s>

<s>100). </s></p><p type="main">

<s>Tra i frammenti di dialogo per&ograve;, dettati da Galileo e notati da noi nel&shy;<lb/>l'altro capitolo, non s'&egrave; potuto trovar questo delle proporzioni, di cui qui <lb/>parla il Viviani. </s>

<s>Sar&agrave; forse andato smarrito, o rimasto ai nostri occhi co&shy;<lb/>perto dalla fitta selva dei fogli di que'numerosi volumi, e di ci&ograve; senza dub&shy;<lb/>bio ci duole, ma dalle segnate postille non &egrave; difficile ricostruire l'effigie. </s>

<s>Di&shy;<lb/>cendosi ivi che le cose dettate al Viviani era risoluto l'Autore d'inserirle dopo <lb/>la prima proposizione Dei moti equabili, e che dettero qualche facilit&agrave; al pi&ugrave; <lb/>ampio disteso in dialogo dal Torricelli, par si possa argomentare che quel <lb/>primo frammento si limitasse a definire le quantit&agrave; proporzionali, a che si <lb/>riduce propriamente la prima delle tre parti, nelle quali, come si vedr&agrave; me&shy;<lb/>glio, &egrave; distinto il dialogo torricelliano. </s>

<s>Che se alcuno desiderasse di sapere <lb/>il motivo, per cui Galileo si mut&ograve; dal primo proposito, d'una semplice ag&shy;<lb/>giunta ordinandone un dialogo distinto, potrebbe rimaner sodisfatto dalle se&shy;<lb/>guenti considerazioni, che diffonderanno forse la loro luce anche sopr'altre <lb/>parti di questa Storia. </s></p><p type="main">

<s>Ritessendo noi dunque con la mente le fila al discorso, che doverva es&shy;<lb/>sere inserito nel terzo dialogo, dopo che il Salviati ebbe letta agli amici la <lb/>dimostrazione del primo teorema dei moti equabili, sappiamo che l'argomento <lb/>si concludeva nell'osservar come la regola degli equimolteplici euclidei non <lb/>si poteva prendere per criterio certo delle proporzionalit&agrave; fra quattro termini <lb/>dati: ond'&egrave; che si sarebbe cos&igrave; venuti a confessare non essere ben dimo&shy;<lb/>strato quello stesso teorema dall'Autore. </s>

<s>Il commento insomma che si vo&shy;<lb/>leva far soggiungere agli interlocutori, non potendo non condannare o non <lb/>contraddire al testo, si vedeva da Galileo e dal Viviani la necessit&agrave; di dimo&shy;<lb/>strar che i tempi son proporzionali agli spazi, con altro mezzo e in altra <lb/>maniera. </s></p><p type="main">

<s>Ma qui stava la difficolt&agrave;, per ben comprender la quale giova ripensare <lb/>all'invenzion di quel pi&ugrave; vero principio, che i matematici posteriori a Galileo <lb/>sostituirono all'antico paralogismo di Archimede. </s>

<s>Quel principio, che doveva <lb/>essere per s&egrave; noto, consisteva nel dire che due mobili sono allora ugualmente <lb/>veloci, quando passano spazi uguali in ugual tempo, d'onde concludesi per <lb/>corollario immediato esser l'uno pi&ugrave; veloce dell'altro, che passa in pi&ugrave; pic&shy;<lb/>col tempo il medesimo spazio. </s>

<s>La folla del popolo, spettatrice curiosa delle <lb/>forse dei cavalli in un prato, si serve per giudicare della vittoria di questo <pb xlink:href="020/01/2469.jpg" pagenum="94"/>criterio, che dunque &egrave; una verit&agrave; di senso comune, espressa nella sua gene&shy;<lb/>ralit&agrave; dall'assioma: le velocit&agrave; de'mobili son tanto maggiori, quant'&egrave; pi&ugrave; <lb/>breve il tempo e lo spazio pi&ugrave; lungo. </s></p><p type="main">

<s>Gli elementi dunque compositori dei moti uniformi venivano cos&igrave; facil&shy;<lb/>mente a tradursi in una formula matematica di natura frazionaria, in cui <lb/>sarebbero le velocit&agrave; rappresentate dal quoziente, che ne resulta, dividendo <lb/>lo spazio per il tempo, e il simbolo algebrico della quale sarebbe V=S/T&prime;, <lb/>intendendosi per V la velocit&agrave;, e per S e per T gli altri due nominati ele&shy;<lb/>menti. </s>

<s>Con le lettere iniziali V&prime;, S&prime;, T&prime; denominati altri elementi simili, ma <lb/>in quantit&agrave; diversi, si compone allo stesso modo l'altro simbolo V=S&prime;/T&prime;. </s>

<s>E <lb/>perch&egrave; &egrave; chiaro che tanto &egrave; pi&ugrave; o meno grande la velocit&agrave; quanto sono pi&ugrave; <lb/>o meno grandi i corrispondenti spazi, relativamente ai tempi corrispondenti, <lb/>sar&agrave; dnnque V:V&prime;=S/T:S&prime;/T&prime;, d'onde si concludono, con somma facilit&agrave; e <lb/>con retto metodo dimostrativo, i teoremi ordinati nel suo primo libro <emph type="italics"/>De <lb/>motu<emph.end type="italics"/> da Galileo. </s></p><p type="main">

<s>Questa radicale riforma, ripetiamo, non era facile introdurla allora, che <lb/>prevalevano i metodi antichi, proseguendo i quali, come si faceva dalla Scuola <lb/>galileiana, non era possibile dilungarsi un passo dagli esempi di Archimede. </s>

<s><lb/>Costretto Galileo stesso perci&ograve; a lasciar le due proposizioni dei moti equabili <lb/>cos&igrave; com'erano state scritte nel libro, non volle mettervi a riscontro un di&shy;<lb/>scorso, che tendeva a scoprirne la fallacia del metodo dimostrativo. </s>

<s>E non <lb/>volendo pure che si rimanesse inutile il pensiero del Cavalieri, si consigli&ograve; <lb/>di trattar della nuova Scienza delle proporzioni in disparte, e in modo, che <lb/>non apparisse l'applicazione degli equimolteplici alla proporzionalit&agrave; dei moti <lb/>equabili o falsa o inconcludente, ma oscura, intantoch&egrave; colui, il quale non <lb/>fosse rimasto sodisfatto nel leggere que'suoi primi teoremi <emph type="italics"/>De motu,<emph.end type="italics"/> pen&shy;<lb/>sasse di riformar col suo proprio ingegno, e secondo le nuove avvertenze, le <lb/>dimostrazioni condotte dietro l'antica definizione di Euclide. </s>

<s>Che se l'ar&shy;<lb/>gomento delle proporzioni rimaneva scarso, per consumare il tempo di una <lb/>intera Giornata, in altri simili soggetti di Fisica e di Matematica troverebbe <lb/>il Salviati da intrattenere gli amici, perch&egrave; non oziosamente si potessero con&shy;<lb/>durre a sera. </s></p><p type="main">

<s>In questo che cos&igrave; Galileo seco medesimo proponeva, e conferiva col gio&shy;<lb/>vane Viviani, si facevano col Torricelli le trattative della sua venuta a Firenze, <lb/>che di fatti successe, come sappiamo, in que'primi giorni di ottobre 1641. <lb/>Il fine, per cui fu fatto a lui mutare il soggiorno di Roma nell'ospizio di <lb/>Arcetri, era quello di aiutare la fisica impotenza dell'ospite a ripulir certe <lb/>sue reliquie di pensieri fisici e matematici, affinch&egrave; si potessero lasciar ve&shy;<lb/>dere insieme con le altre cose meno imperfette (Alb. </s>

<s>VII, 367). Era fra quei <lb/>pensieri, principale senza dubbio per l'argomento, e urgente per le solenni <lb/>promesse fatte al pubblico, quello attenente all'uso delle catenelle e alla forza <pb xlink:href="020/01/2470.jpg" pagenum="95"/>della percossa, ond'&egrave; che ognuno si sarebbe aspettato di veder in tal con&shy;<lb/>giuntura ridotti alla loro tanto desiderata perfezione i dialoghi del moto. </s>

<s>Si <lb/>seppe invece dagli amici, e trentadue anni dopo se n'ebbe pubblica testimo&shy;<lb/>nianza, che il Salviati, dopo cos&igrave; lungo intermedio, era nuovamente tornato <lb/>in scena, e tutt'altro che scusarsi con gli spettatori, innanzi ai quali rifinire <lb/>il primo interrotto discorso, divagarsi indebitamente in soggetto straniero. </s></p><p type="main">

<s>Tale &egrave; il sentimento e il giudizio degli studiosi, i quali, giunti al ter&shy;<lb/>mine del dialogo quarto, sentono dire agl'interlocutori che nel seguente si <lb/>ricercherebbero le speculazioni fatte dall'Accademico intorno alla forza della <lb/>percossa (Alb. </s>

<s>XIII, 266), e poi svolgendo la carta trovano invece che nel <lb/>quinto dialogo non si tratta punto di Meccanica, ma di Geometria, e parti&shy;<lb/>colarmente delle proporzioni. </s>

<s>Eppure quel titolo di <emph type="italics"/>Principio della quinta <lb/>Giornata<emph.end type="italics"/> fu stampato dal Viviani, a cui fu dato a copiare sull'autografo del <lb/>Torricelli, il quale si dice che avesse scritto cos&igrave; in fronte al dialogo, per <lb/>espressa volont&agrave; di Galileo. </s>

<s>Che se fosse veramente stato cos&igrave;, bisognerebbe <lb/>dire che Galileo stesso, non curando gl'impegni solennemente contratti col <lb/>pubblico avesse dismesso il pensiero di far succedere alla quarta immedia&shy;<lb/>tamente un'altra Giornata, dove si discorrerebbe, e si dimostrerebbero i ma&shy;<lb/>ravigliosi effetti della percossa. </s>

<s>Fu anche da noi creduto un tempo cos&igrave;, e <lb/>significammo ai Lettori questa nostra opinione, ma, esaminate poi meglio le <lb/>cose, ci siam dovuti persuader finalmente che il titolo di <emph type="italics"/>Giornata quinta<emph.end type="italics"/><lb/>fu, non ben secondando le rimaste chiuse intenzioni di Galileo, posto dal <lb/>Torricelli, come apparir&agrave; dalla seguente storia del disteso fatto da lui. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Intorno a una cosa, ch'&egrave; di grande importanza per l'accennata storia, <lb/>convien prima di tutto intenderci: ed &egrave; intorno al modo, come si crede che <lb/>il Torricelli facesse quel suo disteso. </s>

<s>Il Viviani, che gli fu convivale in Ar&shy;<lb/>cetri e collega, e perci&ograve; presente all'azione e testimone del fatto, dicendo che <lb/>Galileo <emph type="italics"/>andava dettando<emph.end type="italics"/> (Scienza univ. </s>

<s>cit., pag. </s>

<s>60), non si dichiara bene <lb/>se la dettatura era anche della forma del discorso, o del solo semplice pen&shy;<lb/>siero, come par voglia insinuarci il Serenai che, copiando, metteva questo <lb/>titolo: <emph type="italics"/>Trattato del Galileo sopra la definizione delle proporzioni di Eu&shy;<lb/>clide: &mdash; Giornata quinta, da aggiungersi al,libro delle Nuove scienze, <lb/>distesa e spiegata dal Torricelli, vivente esso Galileo ceco, e per lui.<emph.end type="italics"/> Chi <lb/>per&ograve; ripensa alle qualit&agrave; dello scrivente, eletto fra i primi matematici del&shy;<lb/>l'Italia, l'opera del quale non poteva perci&ograve; limitarsi a solo il meccanico <lb/>esercizio delle mani e degli occhi; ha gi&agrave; fra s&egrave; risoluta la questione. </s>

<s>e ha <lb/>pensato che doveva la cosa essere andata cos&igrave;: Galileo significava i suoi pen&shy;<lb/>sieri, che poi il Torricelli distendeva a modo suo, e leggeva lo scritto da s&egrave;, <lb/>perch&egrave; venisse approvato. </s>

<s>Chi dall'altra parte sa giudicar dello stile, sente <pb xlink:href="020/01/2471.jpg" pagenum="96"/>la diversit&agrave; che passa tra la elegante snellezza del quinto dialogo, e la ma&shy;<lb/>gnifica posa dei precedenti: ma, fuor d'ogni meditata congettura e d'ogni <lb/>sottilit&agrave; di giudizio, si rende quel che si vuol conoscere per s&egrave; manifesto a <lb/>solo esaminar la bozza autografa, che felicemente s'&egrave; conservata. </s></p><p type="main">

<s>A chi svolge il tomo quinto della quinta parte dei manoscritti di Gali&shy;<lb/>leo occorre per prima cosa un quinternetto, in sesto pi&ugrave; piccolo dei rima&shy;<lb/>nenti, a cui par che manchi il principio, perch&egrave; fu per inavvertenza antepo&shy;<lb/>sto all'altro quinterno di maggior sesto, e della medesima calligrafia, sulla <lb/>prima faccia del quale comincia la scrittura del Dialogo, com'usci dalla stessa <lb/>mano del Torricelli di primo getto. </s>

<s>Son frequentissime perci&ograve; le cassature, <lb/>le postille in margine e in calce, e le correzioni delle parole, consistenti bene <lb/>spesso nei solecismi, ne'quali suol trascorrere colui, che non ha uso della <lb/>pronunzia e della ortografia toscana. </s>

<s>Dove, per esempio, era scritto <emph type="italics"/>pones&shy;<lb/>simo, renovatomi, arenato,<emph.end type="italics"/> &egrave; corretto <emph type="italics"/>ponemmo, rinnovatomi, arrenato;<emph.end type="italics"/><lb/>ci&ograve; che solo basterebbe a provar, con materiale certezza, che l'espressioni <lb/>avevano propria e particolar forma dallo scrivente, bench&egrave; altrui ne fosse il <lb/>concetto. </s>

<s>Intorno a ci&ograve;, com'a cosa di maggiore importanza, convien tratte&shy;<lb/>nere il nostro ragionamento, prima di tutto osservando che nel Dialogo tor&shy;<lb/>ricelliano si distingue in tre parti quello stesso unico concetto della Scienza <lb/>universale delle proporzioni: nella prima si considerano le <emph type="italics"/>proporzioni scm&shy;<lb/>plici,<emph.end type="italics"/> nella seconda le <emph type="italics"/>sproporzioni,<emph.end type="italics"/> e nella terza le <emph type="italics"/>proporzioni composte.<emph.end type="italics"/></s></p><p type="main">

<s>In che modo Galileo comunicasse al Torricelli i pensieri, per ci&ograve; che <lb/>s'appartiene a quella prima parte del discorso, &egrave; a chiunque manifesto che, <lb/>anche frettolosamente, confronta il disteso di questo stesso discorso con la <lb/>scrittura, che da Bologua mand&ograve; il Cavalicri. </s>

<s>Il prologo infatti lo svolge il <lb/>Salviati da quel che s'accenna in principio della detta scrittura, che l'occa&shy;<lb/>sione cio&egrave; di trattar delle proporzioni fu data dall'esame della prima propo&shy;<lb/>sizione del moto equabile, dimostrata da un certo Autore per l'applicazione <lb/>degli ugualmente molteplici di Euclide. </s>

<s>Il Cavalieri per quell'Autore inten&shy;<lb/>deva il Rocca, e il protagonista del dialogo introduceva sulla scena, invece <lb/>di un personaggio oscuro, il famosissimo Galileo. </s></p><p type="main">

<s>Terminato il prologo, in cui anche il Salviati accenna allo studio delle <lb/>maravigliose spirali di Archimede, da cui ebbe lo stesso Bocca a serivere <lb/>quel suo trattatello il principio e l'impulso; s'entra nell'argomento del quinto <lb/>libro di Euclide con queste parole, trascritte tali e quali si lessero nel foglio <lb/>del Cavalieri: &ldquo; Suppongasi primieramente (come le suppose anche Euclide, <lb/>mentre le defini) che le grandezze proporzionali si trovino... &rdquo; (Alb. </s>

<s>XIII, 290). <lb/>Questa medesima fedelt&agrave; di trascrizione, corretta dagli errori di ortografia e <lb/>dai solecismi, si riscontra anche nel progresso dell'interloquio, non facendo <lb/>per lo pi&ugrave; il Torricelli altro che scrivere a nome di Simplicio, del Sagredo <lb/>e del Salviati quelle obiezioni, quelle domande e quelle risposte, accennate <lb/>in margine al foglio dal bolognese amanuense. </s></p><p type="main">

<s>&Egrave; dunque manifesto che il modo, come Galileo comunic&ograve; al Torricelli <lb/>i pensieri, espressi nella prima parte del Dialogo, fu con mettergli innanzi <pb xlink:href="020/01/2472.jpg" pagenum="97"/>la scrittura del Cavalieri, nella quale, come per le cose anzi dette &egrave; noto, si <lb/>stabilisce per caratterismo delle proporzionalit&agrave; l'uguaglianza del quoziente <lb/>nelle due ragioni: d'onde poi si dimostra la definizione euclidea, che cio&egrave;, <lb/>essendo i quattro termini in una data proporzione, sono i loro equimolte&shy;<lb/>plici altresi proporzionali. </s>

<s>Si veniva qui come l&agrave; a concludere insomma che <lb/>la quinta delinizione di Euclide non era un principio, che si potesse ritener <lb/>per s&egrave; come noto, ma di un principio da preporsi come noto era piuttosto <lb/>la dimostrabile conseguenza. </s></p><p type="main">

<s>Per quel che poi riguarda le altre due parti del trattato delle proporzioni, <lb/>rimane a noi incerto il modo come Galileo comunic&ograve; al Torricelli il suo pen&shy;<lb/>siero: cio&egrave; a dire se a voce o in scritto, non progredendo il discorso del Ca&shy;<lb/>valieri oltre al termine, dove noi, ricopiando, l'abbiamo lasciato. </s>

<s>Potrebb'es&shy;<lb/>ser quel termine reale, e potrebbero i fogli successivi esser venuti meno a <lb/>chi ebbe la cura di raccoglierli nel detto volume: cosicch&egrave;, mentre resta <lb/>incerto se quel che si prosegue a trattar nel dialogo delle sproporzioni e delle <lb/>proporzioni composte sia scritto secondo la mente del Cavalieri o di Galileo; <lb/>sembra sia da concluder come cosa certissima che non appartiene a Galileo, <lb/>n&egrave; per il concetto n&egrave; per le parole, il primo fondamento della Scienza uni&shy;<lb/>versale delle proporzioni, posto nella prima parte del quinto dialogo aggiunto <lb/>alle due Scienze nuove. </s></p><p type="main">

<s>Comunque sia, la bozza del Torricelli termina col moffo <emph type="italics"/>Laus Deo,<emph.end type="italics"/> se&shy;<lb/>gno che il discorso delle proporzioni, quale ivi leggesi manoscritto, era, se&shy;<lb/>condo l'intenzione dei due collaboratori, compiuto. </s>

<s>Essendo per&ograve; appena ba&shy;<lb/>stato l'argomento per trattener la conversazione infin presso a mezzogiorno, <lb/>aveva Galileo pensato, per condurla a sera, di mettere in mano al Salviati, <lb/>da leggersi innanzi agli amiei, vari fogli, dove fossero dimostrati teoremi di <lb/>Geometria, e risoluti problemi di Fisica; ma fu impedito dalla malattia, che <lb/>aggravandosi sempre pi&ugrave;, poco tempo di poi lo condusse alla morte. </s></p><p type="main">

<s>Scarsi perei&ograve;, per la brevit&agrave; del tempo che si ridusse a soli tre mesi, <lb/>s'aspett&agrave;va che fossero i frutti raccolti ne'filosofici colloqui con Galileo dal <lb/>Torricelli, ma, per la straordinaria eccellenza dei due uomini convenuti in&shy;<lb/>sieme, tutti si ripromettevan que'frutti preziosi. </s>

<s>Di qui &egrave; che, per goderne <lb/>o per saziarne almeno la vista, si misero attorno allo stesso Torricelli, appena <lb/>sceso gi&ugrave; dalla collina di Arcetri, gli ammiratori e gli amici, il pi&ugrave; deside&shy;<lb/>roso fra'quali era il principe Leopoldo dei Medici. </s></p><p type="main">

<s>Giova in tale occasione rammemorare ch'essendo esso Principe entrato <lb/>in gran curiosit&agrave; di saper se il dialogo dell'uso delle catenuzze, e della forza <lb/>della percossa, solennemente promesso e inutilmente atteso dall'Elzevirio, si <lb/>preparava; ne fece, per mezzo del maestro suo don Famiano Michelini, in&shy;<lb/>terrogare in proposito Galileo, il quale mand&ograve; a rispondere a Sua Altezza <lb/>ch'egli aveva ben ritrovata la proporzione della forza della percossa, ma che, <lb/>per la vecchiaia e per altri accidenti, non sperava di poterla dar fuori. </s>

<s>Il <lb/>Principe allora, a rendere pi&ugrave; efficaci le premure che faceva il Castelli ag&shy;<lb/>giungendo il suo proprio invito, condusse il Torricelli a Firenze per questo <pb xlink:href="020/01/2473.jpg" pagenum="98"/>fine principalmente, perch&egrave; aiutasse Galileo a stendere il Dialogo della per&shy;<lb/>cossa. </s>

<s>Desideroso ora dunque di saper qual effetto avessero avuto le sue sol&shy;<lb/>lecitudini n'ebbe dal Torricelli stesso per risposta che, in argomento della <lb/>percossa, aveva s&igrave; udito pronunziare al suo ospite alcune conclusioni impor&shy;<lb/>tanti, ma di metterle in dialogo non se n'era discorso, n&egrave; aveva sentito dire <lb/>da lui che ne avesse ridotto a perfezione il trattato. </s></p><p type="main">

<s>Abbiamo di cos&igrave; fatte notizie il documento in una lettera autografa del <lb/>principe Leopoldo, il quale rispondeva cos&igrave; il 9 Maggio 1665 a Michelangiolo <lb/>Ricci, curioso di saper se era vero che il Borelli si preparava a scrivere un <lb/>libro sopra la forza della percossa: &ldquo; Deve sapere che le speculazioni fatte <lb/>dal medesimo Borelli sopra questa esperienza della polvere credo lo abbiano <lb/>portato a lavorare, e speculare sopra la forza e proporzione della percossa, <lb/>che la buona memoria del nostro Galileo disse a me pi&ugrave; volte aver ritro&shy;<lb/>vata, ma non pot&egrave;, per l'et&agrave; o per qualsivoglia altro accidente che ne fosse <lb/>cagione, darla fuori, com'io le feci ben cento volte istanza, ed al qual fine <lb/>condussi qua il Torricelli di suo consenso, perch&egrave; potesse servire in mettere <lb/>in carta i suoi pensieri, ma tutto fu invano &rdquo; (MSS. Cim., T. XXIII, fol. </s>

<s>113). </s></p><p type="main">

<s>Persuaso dunque il Principe che, quanto a procurare il Dialogo della <lb/>percossa, le sue proprie sollecitudini fossero tornate vane, domandava curioso <lb/>in che altro dunque si fosse, in quella dimora d'Arcetri, divagato il pensiero, <lb/>e il Torricelli rispondeva che in distendere in dialogo una nuova scienza <lb/>delle proporzioni. </s>

<s>Di veder questo Dialogo mostr&ograve; allora esso Principe vivis&shy;<lb/>simo desiderio, e il Torricelli riprese in mano la bozza, con quelle corre&shy;<lb/>zioni che ci aveva fatte nel leggerla, per averne l'approvazione, a Galileo, <lb/>il quale, sperando di poter proseguir l'opera, aspettava all'ultimo a desi&shy;<lb/>gnar del disteso il titolo e la collocazione. </s>

<s>Non si poteva per&ograve; farne per il <lb/>Principe la copia a pulito, senza nulla scrivervi in fronte, per cui, ben sa&shy;<lb/>pendo il Torricelli che il discorso intorno al quinto libro di Euclide era com&shy;<lb/>piuto, e ch'era fatto per aggiungersi agli altri dialoghi delle due Scienze <lb/>nuove, l'ultimo de'quali era il quarto, n&egrave; del Dialogo della percossa, che <lb/>sarebbe dovuto immediatamente succedere, avendo sentito mai farne motto; <lb/>non dubit&ograve; che, anche secondo la mente dello stesso Galileo, non fosse il <lb/>titolo questo: <emph type="italics"/>Trattato del Galileo sopra la definizione delle proporzioni di <lb/>Euclide &mdash; Giornata quinta da aggiungersi nel libro delle Nuove scienze.<emph.end type="italics"/><lb/>E cos&igrave; fu scritto in fronte alla copia, che di sua propria mano il Torricelli <lb/>condusse, per consegnarla al principe Leopoldo. </s></p><p type="main">

<s>Cos&igrave; essendo, non pu&ograve; dunque da quel titolo argomentarsi che Galileo <lb/>avesse dismesso il pensiero di aggiungere, dopo i primi quattro del moto, il <lb/>dialogo della percossa, il quale era gi&agrave; preparato in parte: che se avesse <lb/>l'Autore avuto il tempo di renderlo compiuto, e il Torricelli se ne fosse tro&shy;<lb/>vato in mano il disteso, non avrebbe dubitato, secondo che necessariamente <lb/>portava l'ordine logico, d'anteporlo al trattato delle proporzioni, al quale <lb/>avrebbe perci&ograve; scritto in fronte <emph type="italics"/>Giornata sesta del Galileo.<emph.end type="italics"/> Il fine e la ne&shy;<lb/>cessit&agrave; di queste osservazioni, che potrebbero qui ai lettori sembrar fuor di <pb xlink:href="020/01/2474.jpg" pagenum="99"/>proposito, si comprender&agrave; meglio, quando in quest'altro capitolo si prover&agrave; <lb/>di fatto che quel dialogo della percossa, di cui il Torricelli diceva di non saper <lb/>niente, era gi&agrave; cominciato, e quasi condotto a mezzo, prima ch'egli venisse <lb/>ospite in Arcetri; e quando diremo come tra i manoscritti galileiani fosse <lb/>ritrovato esso Dialogo, e fosse aggiunto dagli editori delle opere agli altri <lb/>cinque delle due Scienze nuove. </s>

<s>Intanto riprendiamo il filo di questa storia. </s></p><p type="main">

<s>La copia, che il Torricelli consegn&ograve; al principe Leopoldo, rimase ma&shy;<lb/>noscritta infino al 1674, quando il Viviani pens&ograve; di pubblicarla dopo quel <lb/>trattato, che ne volle scrivere per i <emph type="italics"/>nobili geometri principianti<emph.end type="italics"/> col titolo: <lb/><emph type="italics"/>Quinto libro degli Elementi di Euclide, ovvero Scienza universale delle <lb/>proporzioni.<emph.end type="italics"/> Ivi dice come venticinque anni fa, col permesso di Sua Altezza, <lb/>ne avesse dal detto autografo preso copia, e come nell'atto del darla alle <lb/>stampe l'avesse voluta diligentemente riscontrar sopra la bozza originale che, <lb/>insiem con gli altri manoscritti torricelliani, si trovava allora nelle mani di <lb/>Lodovico Serenai. </s>

<s>&ldquo; Ed avendola, soggiunge il Viviani stesso, ritrovata verso <lb/>il fine con qualche cosa di pi&ugrave;, aggiuntavi com'io credo dal Torricelli, non <lb/>ho voluto mancare di unirla a questa quinta Giornata, come si vedr&agrave;, in ca&shy;<lb/>rattere corsivo, e quale, dopo un diligente riscontro del rimanente, mi ha <lb/>dettato il medesimo signor Lodovico &rdquo; (Ediz. </s>

<s>cit., pag. </s>

<s>60). Il Serenai infatti <lb/>che, non contento di ritrar quella prima bozza, per dir cos&igrave;, in <emph type="italics"/>fac simile,<emph.end type="italics"/><lb/>aveva preso altres&igrave;, col permesso del principe Leopoldo, copia del dialogo dal <lb/>Torricelli stesso messo a pulito; notava cos&igrave; sopra la prima carta, dop'avervi <lb/>scritto il titolo: &ldquo; Ma in questa copia, oltre all'esser diversa dal manoscritto <lb/>di esso Torricelli in molte parole di poco momento, ci mancano verso il fine, <lb/>a c. </s>

<s>20, circa due facce, che si leggono in detto manoscritto, e nell'altra <lb/>copia, che ne ho fatta io &rdquo; (MSS. Gal., P. V, T. V, fol. </s>

<s>39). </s></p><p type="main">

<s>Che manchino le due facce, supplite dal Viviani e dagli altri editori in <lb/>carattere corsivo, &egrave; un fatto: ma non si rende chiara la ragione di tal man&shy;<lb/>canza da ci&ograve;, che diceva dianzi lo stesso Viviani essere state aggiunte quelle <lb/>cose dal Torricelli. </s>

<s>Nella bozza originale &egrave; tutto scritto andantemente. </s>

<s>senza <lb/>segno alcuno di un'aggiunta posteriore, e si vedono, anche per queste pagine, <lb/>ricorrere le solite correzioni, fatte alla presenza di Galileo, che dunque ebbe <lb/>approvato qui come nel resto. </s></p><p type="main">

<s>Ci&ograve; per&ograve; non vorrebbe dire che non fosse propria del Torricelli l'inven&shy;<lb/>zione di que'teoremi, con i quali concorreva a sublimare l'umile scienza ga&shy;<lb/>lileiana delle proporzioni. </s>

<s>I teoremi si riducono a due e noi gli vogliamo <lb/>ordinatamente proporre alla considerazione dei nostri Lettori, perch&egrave;, ricono&shy;<lb/>scendone da loro medesimi la superiorit&agrave;, confrontati con gli altri tutti ele&shy;<lb/>mentarissimi nei discorsi del Sagredo e del Salviati, si venga a confermare <lb/>e a dichiarar meglio quel che il Viviani credeva: essere cio&egrave; quegli stessi <lb/>teoremi aggiunti dal Torricelli, bench&egrave; Galileo, sentendoseli leggere in mezzo <lb/>agli altri, si chiamasse contento e beato di lasciarli uscir fuori sotto il suo nome. </s></p><p type="main">

<s>TEOREMA I. &mdash; &ldquo; Se fra queste grandezze A e B s'immaginer&agrave; che sia <lb/>frapposta, non una grandezza sola, ma pi&ugrave; d'una, come si vede in questi <pb xlink:href="020/01/2475.jpg" pagenum="100"/>segni A, C, D, B; s'intender&agrave; pure la proporzione della A alla B esser com&shy;<lb/>posta di tutte le proporzioni, le quali sono intermedie fra di esse: cio&egrave; delle <lb/>proporzioni, che hanno la A alla C, la C alla D, e la D alla B. </s>

<s>E cos&igrave;, se <lb/>pi&ugrave; fossero le grandezze, sempre la prima all'ultima ha proporzion compo&shy;<lb/>sta di tutte quelle proporzioni, le quali mediano fra di esse &rdquo; (Viviani, Scienza <lb/>delle prop. </s>

<s>cit., pag. </s>

<s>75). </s></p><p type="main">

<s>Il teorema &egrave; reso generale per l'induzione dai casi particolari, come si <lb/>faceva allora in Italia, dove non s'era introdotta l'Aigebra cartesiana. </s>

<s>Aven&shy;<lb/>dosi infatti A:C=C:B, avremo anche A:B=A.C:B.C, che resulta dal <lb/>moltiplicare per C la seconda ragione dell'identica A:B=A:B. </s>

<s>Come pure, <lb/>avendosi A:C=C:D=D:B, avremo altres&igrave; A:B=A.C.D:H.C.D <lb/>resultante dal moltiplicar per C. </s>

<s>D la seconda ragione della detta identica <lb/>A:B=A:B. </s>

<s>La costanza della regola, in tutti gli altri esempi per qua&shy;<lb/>lunque numero di quantit&agrave; intermedie, dava logico diritto al Matematico di <lb/>creder la proposizione, come fa qui il Torricelli, e di pronunziarla vera in <lb/>universale. </s></p><p type="main">

<s>TEOREMA II. &mdash; &ldquo; Quando le proporzioni componenti sieno uguali fra di <lb/>loro, o per dir meglio sieno le stesse; allora la prima all'ultima avr&agrave;, come <lb/>di sopra abbiamo detto, una tal proporzione composta di tutte le proporzioni <lb/>intermedie. </s>

<s>Ma perch&egrave; quelle proporzioni intermedie sono tutte uguali, po&shy;<lb/>tremo esprimere il medesimo nostro senso con dire che la proporzione della <lb/>prima all'ultima ha una proporzione tanto molteplice della proporzione, che <lb/>ha la prima alla seconda, quante per appunto saranno le proporzioni, che si <lb/>frappongono fra la prima e l'ultima &rdquo; (ivi). </s></p><p type="main">

<s>Anche questo bel teorema, nuovo affatto, come l'altro da cui deriva, <lb/>nella scienza delle proporzioni, si concludeva per induzione dai vari casi par&shy;<lb/>ticolari. </s>

<s>&ldquo; Cos&igrave; per esempio, soggiunge, per dar ragione dimostrativa della <lb/>pronunziata verit&agrave;, il Torricelli, se fossero tre termini, e che la medesima <lb/>proporzione fosse fra la prima e la seconda, che &egrave; fra la seconda e la terza; <lb/>allora sarebbe vero che la prima alla terza avrebbe proporzione composta <lb/>delle due proporzioni, le quali sono fra la prima e la seconda, e fra la se&shy;<lb/>conda e la terza. </s>

<s>Ma perch&egrave; queste due proporzioni si suppongono uguali, <lb/>cio&egrave; le stesse, potr&agrave; dirsi che la proporzione della prima alla terza &egrave; dupli&shy;<lb/>cata della proporzione, che ha la prima alla seconda &rdquo; (ivi). </s></p><p type="main">

<s>Data essendo infatti A:B=B:C, se si moltiplica per A la seconda <lb/>ragione dell'identica A:C=A:C, avremo A:C=A2:AC. </s>

<s>Ma A. C, per <lb/>la data, &egrave; uguale a B2; dunque A:C=A2:B2. </s>

<s>Similmente, essendo quat&shy;<lb/>tro i termini nelle proporzioni continue A:B=B:C=C:D, se per A2 si <lb/>moltiplicher&agrave; la seconda ragione dell'identica A:D=A:D, avremo A:D= <lb/>A3:A2.D. </s>

<s>Ma per la data A.D=B.C, ossia A2.D=A.B.C, e per <lb/>essere A.C=B2 &egrave; A.C.B=B3; dunque A:D=A3:B3, per cui si po&shy;<lb/>trebbe dire col Torricelli &ldquo; che la proporzione della prima alla quarta &egrave; com&shy;<lb/>posta di quelle tre proporzioni intermedie, ed ancora che &egrave; triplicata della <lb/>proporzione della prima alla seconda &rdquo; (ivi, pag. </s>

<s>75, 76). </s></p><pb xlink:href="020/01/2476.jpg" pagenum="101"/><p type="main">

<s>Or essendo, dall'esame di questi teoremi, confermata anche meglio l'opi&shy;<lb/>nion del Viviani, che cio&egrave; si fossero aggiunti, nello stender le bozze del Dia&shy;<lb/>logo, dal Torricelli, per arricchirne la Scienza galileiana delle proporzioni; <lb/>consideriamo quel che dovette naturalmente avvenire nel ridurre, dopo la <lb/>morte di Galileo, quella stessa bozza a pulito, per consegnarla nelle mani del <lb/>principe Leopoldo. </s>

<s>Chiunque trascrive trova sempre qualche cosa da correg&shy;<lb/>gere, nella scelta delle parole e nel disporle, per maggior chiarezza e armo&shy;<lb/>nia, con qualche variet&agrave; negl'incisi, di che il periodo s'intesse. </s>

<s>Di qui nacquero <lb/>quelle diversit&agrave; in molte parole, che diceva di aver notate il Serenai nel ri&shy;<lb/>scontrar la copia con la bozza originale, soggiungendo per&ograve; ch'eran cose di <lb/>poco momento. </s>

<s>Venuto poi il Torricelli stesso al punto, dove nella terza parte <lb/>del Dialogo si tratta delle proporzioni composte, e dov'egli aveva aggiunto <lb/>que'suoi due teoremi, ripensando forse che Galileo era tanto ricco, da non <lb/>aver bisogno della roba altrni, deliber&ograve; di ritenerseli per s&egrave;, saltando nel co&shy;<lb/>piare quel che prima con tanta liberalit&agrave; ci aveva messo. </s>

<s>Ed ecco rivelata la <lb/>causa del mancar verso il fine, nella copia a pulito fatta per il principe Leo&shy;<lb/>poldo, quelle due facce, che il Serenai e il Viviani avevano riscontrate nel&shy;<lb/>l'originale torricelliano. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>La deliberazione di serbar per s&egrave; i teoremi aggiunti nel dialogo, dovette <lb/>esser presa dal Torricelli, quand'ebbe a ripensare che Galileo, con tutto quel <lb/>suo discorso, non aveva fatt'altro che dimostrare come il quinto libro, e <lb/>molte altre parti degli Elementi di Euclide, avevano bisogno di una riforma. </s>

<s><lb/>La riforma per&ograve; non era fatta, perch&egrave; non bastava l'avere osservato che la <lb/>regola degli egualmente moltiplici era insufficiente ad assicurarci della pro&shy;<lb/>porzionalit&agrave;, che passa fra quattro grandezze, ma conveniva di pi&ugrave; insegnare <lb/>per quale altra via si potesse il Geometra condurre a quelle medesime con&shy;<lb/>clusioni. </s>

<s>Perciocch&egrave; nessuno dubitava della verit&agrave; dei Teoremi euclidei, ma <lb/>de'termini di mezzo che s'invocavano dall'Autore per dimostrarli. </s></p><p type="main">

<s>Quand'anche, ripensava tra s&egrave; il Torricelli, si pubblicasse questo dia&shy;<lb/>logo, ch'io ho qui disteso in aggiunta agli altri delle due Scienze nuove, <lb/>quale utilit&agrave; ne potrebbero ricavare i giovani studenti della Geometria e della <lb/>Meccanica? </s>

<s>Null'altra, dalla certezza in fuori che le prime proposizioni dei <lb/>moti equabili, nel terzo dialogo galileiano, e tutte le proporzionalit&agrave;, che in&shy;<lb/>tercedono fra linee e linee, fra superfice e linee, fra angoli e archi sottesi, <lb/>nei vari libri euclidei, son verit&agrave; che tuttavia rimangono a dimostrarsi. </s>

<s>&Egrave; <lb/>dunque incominciata un'opera da Galileo che, per benetizio universale della <lb/>Scienza matematica, vuol essere compiuta: d'onde, cos&igrave; discorrendo, venne <lb/>a formarsi nell'animo dello stesso Torricelli il proposito di scrivere un trat&shy;<lb/>tato delle proporzioni, in cui forse troverebbero luogo i due teoremi inseriti <pb xlink:href="020/01/2477.jpg" pagenum="102"/>nel quinto Dialogo galileiano, e in ogni modo s'insegnerebbe come dimo&shy;<lb/>strare altrimenti, senza gli equimolteplici, le proporzionalit&agrave; geometriche, e <lb/>le meccaniche concernenti i moti uniformi. </s></p><p type="main">

<s>Fu il proposito mandato ad effetto in un opuscolo latino, che corse lungo <lb/>tempo per le mani degli amici, col titolo <emph type="italics"/>De proportionibus,<emph.end type="italics"/> e che serv&igrave; di <lb/>testo nelle scuole di Geometria, per supplire al quinto, e al sesto libro degli <lb/>Elementi di Euclide. </s>

<s>&ldquo; L'appendice al mio libretto delle proporzioni, scri&shy;<lb/>veva il Torricelli il d&igrave; 24 Agosto 1647 al Ricci, &egrave; gi&agrave; messo al pulito. </s>

<s>Il <lb/>proemio mi riesce lunghissimo, particolarmente in riguardo all'opera, ma &egrave; <lb/>pur necessario diffondersi per mostrare l'insufficienza e difetto del V libro <lb/>di Euclide &rdquo; (MSS. Gal. </s>

<s>Disc., T. XV, fol. </s>

<s>115). Non fu mai stampato quel&shy;<lb/>l'opuscolo vivente l'Autore, e bench&egrave; il Serenai sollecitasse tante volte e in <lb/>vari modi il Viviani, perch&egrave; lo pubblicasse insieme con le altre opere postume <lb/>del comune Amico; si rimase nella sua bozza, e nella sua copia a pulito au&shy;<lb/>tografa, e si riman tuttavia nel tomo XXVI dei Discepoli di Galileo. </s>

<s>Ivi pu&ograve; <lb/>ritrovarlo intero chi vuole, o ne'detti originali o nella nitid<gap/>sima e diligen&shy;<lb/>tissima copia, che ne fece il medesimo Serenai: e perch&egrave; &egrave; documento im&shy;<lb/>portantissimo, non solo della Storia della Geometria, ma e della Meccanica, <lb/>ritrovandovisi la prima vera logica dimostrazione della proporzionalit&agrave; fra gli <lb/>spazi e i tempi nei moti uniformi, che in realt&agrave; manca negli antichi teoremi <lb/>di Archimede, e ne'nuovi che Galileo ritrasse da lui; non dispiacer&agrave; ai no&shy;<lb/>stri Lettori di veder qui in poche parole il riassunto della torricelliana ri&shy;<lb/>forma della Scienza delle proporzioni, e delle applicazioni di lei alla Meccanica. </s></p><p type="main">

<s>Il trattato <emph type="italics"/>De proportionibus<emph.end type="italics"/> si divide in due parti, la prima delle quali <lb/>&egrave; un proemio, dove si trattien l'Autore in assai lungo discorso col lettore <lb/>amico intorno alle geometriche definizioni. </s>

<s>Ragionando come il Nardi, e come <lb/>il Cavalieri, osserva la fallacia, che s'asconde nel definito in quinto luogo, <lb/>innanzi al suo quinto libro, da Euclide, e con queste parole termina la prima <lb/>parte del suo discorso: &ldquo; Tandem, ut ad conclusionem accedam, pari facili&shy;<lb/>tate dubitabo magnitudines non esse proportionales, licet earum aequimulti&shy;<lb/>plicia imperatam concordiam constantissime servent; et esse proportionales, <lb/>licet ab eadem concordia aliquando recedant &rdquo; (fol. </s>

<s>56 ad t.). </s></p><p type="main">

<s>Notate le difficolt&agrave;, che s'incontrano nell'intendere le definizioni di Eu&shy;<lb/>clide, prevede che qualche cosa di simile potrebbe alcuno ritrovar nelle sue, <lb/>da che s'espedisce con l'osservare la gran differenza che &egrave; tra l'altrui me&shy;<lb/>todo antico o il suo proprio nuovo. </s>

<s>&ldquo; Euclides, suppositis difficillimis prin&shy;<lb/>cipiis, faciliora quaeque demonstravit: ego contra, praemissis facilioribus, no&shy;<lb/>tioribusque principiis, difficillima quaeque demonstrare conatus sum &rdquo; (ibid.). </s></p><p type="main">

<s>Se l'effetto l'abbia poi conseguito lo lasci&ograve; il Torricelli giudicare ai <lb/>Lettori, passando all'altra parte del trattato, o, per pi&ugrave; propriamente dire, al <lb/>trattato delle proporzionali, a cui si premettono otto definizioni, e sei tra <lb/>supposizioni e assiomi. </s>

<s>Le prime proposizioni poi, che ricorrono a dimostrarsi, <lb/>son le cinque seguenti, delle quali ci content&egrave;remo di trascrivere il semplice <lb/>enunciato: </s></p><pb xlink:href="020/01/2478.jpg" pagenum="103"/><p type="main">

<s>&ldquo; PROPOSITIO I. &mdash; Propositis duabus magnitudinibus, inaequalibus et <lb/>eiusdem generis, quarum una sit maior, altera vero minor; si ex maiore au&shy;<lb/>feratur dimidium, et rursus ab ea quae remanet dimidium detrahatur, atque <lb/>iterum ex reliqua dimidium, et hoc fiat semper; relinquetur tandem quae&shy;<lb/>dam magnitudo, quae minor erit proposita minori magnitudine. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO II. &mdash; Si fuerit quodcumque triangulum, cuius basis secta <lb/>sit in quotcumque partes inter se aequales, et ex vertice trianguli ad puncta <lb/>singula divisionum basis ducantur rectae lineae; erit totum triangulum di&shy;<lb/>visum in triangula inter se aequalia, quod constat ex propos. </s>

<s>XXXVIII primi <lb/>libri: dico quamlibet summam horum triangulorum, ad reliquam, esse ut <lb/>basis ad basim. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO III. &mdash; Triangula eiusdem altitudinis eamdem habent ra&shy;<lb/>tionem quam bases. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO IV. &mdash; Si in quocumque triangulo fuerit quaedam recta <lb/>parallela ad unum latus, haec parallela proportionaliter secabit ipsius trian&shy;<lb/>guli latera. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO V. &mdash; Si in quocumque triangulo ABC (fig. </s>

<s>36) angulus <lb/>quilibet ABC bifariam secetur a recta BD, dico etiam basim AC in ratione <lb/><figure id="id.020.01.2478.1.jpg" xlink:href="020/01/2478/1.jpg"/></s></p><p type="caption">

<s>Figura 36.<lb/>laterum sectam esse: hoc est segmentum AD, ad <lb/>segmentum DC, eamdem habere rationem, quam <lb/>habet latus AB ad BC &rdquo; (ibid., fol. </s>

<s>61-65). </s></p><p type="main">

<s>Le altre cinque proposizioni, che si soggiungono, <lb/>attendono a dimostrare col medesimo metodo, indi&shy;<lb/>pendentemente cio&egrave; dagli equimolteplici, che, essendo <lb/>date quattro linee in proporzione, convertendo, com&shy;<lb/>ponendo, dividendo e permutando, rimangono pro&shy;<lb/>porzionali: e finalmente che di due uguaglianze i <lb/>membri, comunque composti, presi nel medesimo <lb/>ordine, stanno fra loro in una medesima proporzione. </s></p><p type="main">

<s>&ldquo; PROPOSITIO VI. &mdash; Si quatuor magnitudines proportionales fuerint, et <lb/>convertendo proportionales erunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO VII. &mdash; Si divisae magnitudines proportionales fuerint, et <lb/>componendo proportionales erunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO VIII. &mdash; Si compositae magnitudines proportionales fuerint, <lb/>et dividendo proportionales erunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO IX. &mdash; Si quatuor magnitudines proportionales fuerint, et <lb/>permutando proportionales erunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO X. &mdash; Si fuerint quotcumque magnitudines, et aliae ipsis <lb/>aequales numero, quae binae in eadem ratione sumantur, et ex aequo in <lb/>eadem ratione erunt &rdquo; (ibid., fol. </s>

<s>61-68). </s></p><p type="main">

<s>Bench&egrave; siano le cinque precedenti proposizioni annunziate generalmente, <lb/>non si dimostrano dall'Autore per&ograve; che secondo un determinato genere di <lb/>quantit&agrave;, fra le quali i metodi antichi portavano a sceglier le linee. </s>

<s>Cos&igrave; <lb/>per&ograve;, bench&egrave; fossero esse linee assai meno determinabili dei numeri, non si <pb xlink:href="020/01/2479.jpg" pagenum="104"/>veniva a dare alle proposizioni quella generalit&agrave;, che ricevono in s&egrave; col far <lb/>uso dei simboli algebrici, per cui fu costretto il Torricelli a soggiungere, alle <lb/>dimostrate, nuove proposizioni <emph type="italics"/>ut eas demonstremus universaliter veras esse, <lb/>etiam in omni genere quantitatis.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; PROPOSITIO XI. &mdash; Si fuerint tres magnitudines, aliaeque ipsis acqua&shy;<lb/>les numero, quae binae in eadem ratione sumantur, fuerit autem perturbata <lb/>earum proportio ex aequalitate, in eadem ratione erunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO XII. &mdash; Si compositae magnitudines proportionales fuerint, <lb/>et per conversionem rationis proportionales erunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO XIII. &mdash; Si fuerint ut totum ad totum, ita ablatum ad <lb/>ablatum, et reliqum ad reliqum erit ut erat totum ad totum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO XIV. &mdash; Partes cum pariter multiplicibus in eadem sunt <lb/>ratione, si, prout sibi mutuo respondent, ita sumantur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO XV. &mdash; Si sint magnitudines quotcumque proportionales, <lb/>quemadmodum se habuerit una antecedentium ad unam consequentium; ita <lb/>se habebunt omnes simul antecedentes ad omnes consequentes simul. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO XVI. &mdash; Eadem, ad minorem, maiorem habent rationem, <lb/>quam ad maiorem. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO XVII. &mdash; Si prima ad secundam eamdem habeat rationem <lb/>quam tertia ad quartam, habuerit autem et quinta ad secundam eamdem <lb/>rationem, quam sexta ad quintam; etiam composita prima cum secunda, ad <lb/>secundam, eamdem habebit rationem, quam tertia cum sexta ad quartam. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO XVIII. &mdash; Si quatuor magnitudines eiusdem generis pro&shy;<lb/>portionales fuerint, maxima et minima reliquis duabus maiores erunt &rdquo; (ibid., <lb/>fol. </s>

<s>69-76). </s></p><p type="main">

<s>Qui, scrive il Torricelli dop'aver dimostrata quest'ultima proposizione, <lb/>faremo fine al trattatello delle proporzioni, in cui troveranno gli studiosi rac&shy;<lb/>colto tutto quel che Euclide insegna nel suo quinto libro. </s>

<s>Bench&egrave; il numero <lb/>delle proposizioni euclidec ascenda a XXXIII o XXXIV, &egrave; per&ograve; da osservare <lb/>che non son tutte quelle propriamente dell'antico Autore, ma ve ne furono <lb/>parecchie aggiunte da chi lo comment&ograve; e lo tradusse, e perci&ograve; si possono <lb/>tralasciare, com'abbiam fatto noi, che scriviamo per i giovani principianti. </s>

<s><lb/>Nonostante, prosegue a dire il Torricelli, perch&egrave; abbiamo introdotto gli stu&shy;<lb/>diosi all'intelligenza di alcune parti delle primc proposizioni del sesto libro, <lb/>vogliamo compir l'opra, dimostrandole, col solito nostro metodo, intere &ldquo; ut <lb/>is, qui saltem libare contendit Geometriam, a sexto ipso Euclidis se citius <lb/>queat expediri, omissis videlicet omnino tribus primis propositionibus, iam sibi <lb/>notis. </s>

<s>&rdquo; </s></p><p type="main">

<s>Nella prima infatti di quelle proposizioni dice Euclide che i triangoli e <lb/>i parallelogrammi, aventi la medesima altezza, stanno fra loro come le basi, <lb/>mentre nella terza torricelliana non si dimostra questa propriet&agrave; che rispetto <lb/>ai triangoli. </s>

<s>L'Autore greco, per provare la detta proporzionalit&agrave; nell'une e <lb/>nelle altre figure, si serve degli ugualmente molteplici, e il Nostro, come <lb/>aveva senz'essi gi&agrave; conclusa l'annunziata propriet&agrave; nei triangoli. </s>

<s>cos&igrave; lo fa <pb xlink:href="020/01/2480.jpg" pagenum="105"/>nel seguente modo nei parrallelogrammi, applicandovi la proposizione XIV: <lb/>che cio&egrave; le semplici parti stanno in proporzione co'multipli, i quali secondo <lb/>le loro mutue corrispondenze sian presi. </s></p><p type="main">

<s>Abbiansi i due parallelogrammi AC, DF (figure 37, 38) con le altezze <lb/>uguali: essi staranno come le basi. </s>

<s>La dimostrazione, che s'avvolge in Eu&shy;<lb/><figure id="id.020.01.2480.1.jpg" xlink:href="020/01/2480/1.jpg"/></s></p><p type="caption">

<s>Figura 37.<lb/><figure id="id.020.01.2480.2.jpg" xlink:href="020/01/2480/2.jpg"/></s></p><p type="caption">

<s>Figura 38.<lb/>clide per discorso lun&shy;<lb/>go e inconcludente, &egrave; <lb/>dal Torricelli ridotta <lb/>alla sua massima fa&shy;<lb/>cilit&agrave; e speditezza. </s>

<s>Im&shy;<lb/>perocch&egrave;, tirate le dia&shy;<lb/>gonali GB, HE, i ret&shy;<lb/>tangoli son doppi dei triangoli inscritti, e perci&ograve;, per la XIV, proporzionali. </s>

<s>Ma <lb/>i triangoli, per la III, stanno come le basi; dunque anche i rettangoli. </s>

<s>&ldquo; Sint <lb/>parallogramma AC, DF in eadem altitudine: dico esse parallelogrammum AC <lb/>ad DF ut basis AB, ad basim DE. </s>

<s>Ductis enim diametris BG, EH, dividen&shy;<lb/>tur ab ipsis bifariam utraque parallelogramma, eruntque triangula AGB, DHE <lb/>pariter multiplicia, cum sint dupla. </s>

<s>Et erit, per XIV huius, parallelogrammum <lb/>AC ad triangulum AGB, ut parallelogrammum DF ad triangulum DHE. </s>

<s>Et <lb/>permutando parallelogrammum AC, ad parallelogrammum DF, ut triangu&shy;<lb/>lum AGB ad triangulum DHE. </s>

<s>Sed basis AB, ad basim DE, est per IIlam<lb/>huius ut triangulum AGB ad triangulum DHE; ergo etc. </s>

<s>&rdquo; (ibid., fol. </s>

<s>149). </s></p><p type="main">

<s>La seconda degli antichi Elementi &egrave; nella sua totalit&agrave; dimostrata dalla <lb/>quinta del nuovo trattato, ma la terza di l&agrave; non &egrave; nella quinta di qui dimo&shy;<lb/>strata altro che per la sua prima parte, rimanendo tuttavia a dimostrarsi, <lb/>per renderla secondo Euclide compiuta, che se le parti della base abbiano la <lb/>medesima proporzione che gli altri lati del triangolo, la linea retta, che dalla <lb/>cima si tira sino al segamento della base, segher&agrave; l'angolo per mezzo. </s>

<s>Ci&ograve; <lb/>si soggiunge appunto dal Torricelli nel suo trattato, scansando gli equimol&shy;<lb/>teplici, come pure, scansando gli equimolteplici, si dimostra l'ultima posta <lb/>da Euclide in questo sesto libro, che cio&egrave; gli angoli inscritti nel medesimo <lb/>cerchio son proporzionali agli archi compresi. </s></p><p type="main">

<s>Cos&igrave; veniva finalmente operata, negli antichi insegnamenti geometrici, <lb/>quella riforma, non troppo felicemente iniziata dal Benedetti, e solamente <lb/>proposta dal Nardi e da Galileo, o come converrebbe per giustizia dire <lb/>dal Cavalieri. </s>

<s>Ma l'intenzione del Torricelli non era quella sola, come av&shy;<lb/>vertimmo, di emendare la Geometria, ma altres&igrave; la Meccanica, i primi e <lb/>principali teoremi della quale, bench&egrave; verissimi, si rimanevano nel libro <lb/>delle Spirali e nel terzo dialogo delle Scienze nuove indimostrati. </s>

<s>La prima <lb/>legittima dimostrazione dunque che se ne avesse, &egrave; quale ora noi la diamo <lb/>alla pubbiica luce, come importantissimo documento nella storia della Scienza <lb/>del moto: </s></p><p type="main">

<s>&ldquo; Si punctum aliquod, aequabili semper velocitate, super aliqua recta <lb/>linea AB (fig. </s>

<s>39) feratur, duasque ipsius portiones AC, CB permeaverit; dico <pb xlink:href="020/01/2481.jpg" pagenum="106"/>portionem AC ad CB eamdem habere rationem, quam habent tempora ipsa, <lb/>quibus punctum portiones permeavit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ponantur DE, EF tempora, quibus punctum permeavit rectas AC, CB: <lb/><figure id="id.020.01.2481.1.jpg" xlink:href="020/01/2481/1.jpg"/></s></p><p type="caption">

<s>Figura 39.<lb/>nempe DE supponatur tempus rectae <lb/>AC: ipsum vero EF tempus rectae <lb/>CB. </s>

<s>Ostendendum est rectam AC, <lb/>ad rectam CB, esse ut tempus DE <lb/>ad tempus EF. &rdquo; </s></p><p type="main">

<s>&ldquo; Nisi enim sit ita, coucipia&shy;<lb/>mus, si possibile est, ut tempus DE ad EF, ita esse aliquam aliam lineam <lb/>IC ad eamdem CB: et erit omnino ipsa IC vel minor vel maior quam AC. &rdquo; </s></p><p type="main">

<s>&ldquo; Sit primum IC minor quam AC. </s>

<s>Secetur CB bifariam, atque iterum <lb/>bifariam, et hoc fiat sempen, donec remaneat quaedam CG minor quam AI: <lb/>dividaturque tota CB in partes aequales ipsi CG, quae quidem tota absume&shy;<lb/>tur praecise. </s>

<s>Item distribuatur et ipsa CA in partes aequales eidem CG, ini&shy;<lb/>tio facto ex C, et continuata divisione quousque fieri poterit. </s>

<s>Certum est ali&shy;<lb/>quam divisionem casuram esse inter puncta A et I, quandoquidem recta CG <lb/>metiens minor facta est quam AI. </s>

<s>Cadat itaque inter A et I divisio L, et <lb/>quoniam rectae AC tempus est ipsum DE, erit rectae LC, quae minor est, <lb/>tempus minus quam DE. </s>

<s>Esto igitur rectae LC tempus OE: tunc secetur <lb/>tempus OE in totidem partes aequales, in quot aequales partes divisa est <lb/>recta CB, eruntque singulae partes temporis OE tempora singularum partium <lb/>aequalium rectae LC. </s>

<s>Idemque dictum sit de partibus temporis EF, et rectae <lb/>CB. </s>

<s>Cum autem omnes partes rectarum LC, CB omnifariam sumptae inter <lb/>se aequales sint, per constructionem, erunt etiam omnes partes temporum <lb/>OE, EF, inter se aequales, ob suppositionem, aequalis semper velocitatis, sive <lb/>motus aequabilis. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Jam recta LC ad CB non est ut recta minor IC ad eamdem CB, sed <lb/>ipsa LC maior est, quam esse oporteret. </s>

<s>Ut autem recta LC ad CB, ita tem&shy;<lb/>pus OE ad EF, quod infertur ex prima et sexta suppositione huius. </s>

<s>Ergo <lb/>etiam tempus OE maior est, quam esse oporteret. </s>

<s>Quamobrem tempus DE <lb/>multo maius est quam esse deberot ut ad EF eamdem habeat rationem, quam <lb/>habet recta IC ad CB, quod est contra suppositum &rdquo; (ibid., fol. </s>

<s>116-17). </s></p><p type="main">

<s>Che se IC si dica dover esser maggiore di AC, e allora dimostra il <lb/>Torricelli, con un ragionamento simile al precedente, che CB &egrave; troppo pi&ugrave; <lb/>grande di quel che non dovrebb'essere, perch'ella possa aver con l'antece&shy;<lb/>dente stessa IC la ragion medesima, che ha il tempo DE al tempo EF, ci&ograve; <lb/>che pure &egrave; contrario alla fatta supposizione. </s>

<s>&ldquo; Patet ergo quod recta AC ad <lb/>CB est ut tempus DE ad EF, quandoquidem demonstravimus quam rationem <lb/>habet tempus DE ad EF, eamdem nullam aliam lineam, praeter AC, posse <lb/>habere ad CB, quod erat propositum &rdquo; (ibid.). </s></p><p type="main">

<s>La dimostrazione, lo riconosce ben da s&egrave; il Torricelli e lo confessa, non <lb/>&egrave; di quella facilit&agrave; n&egrave; di quella eleganza, che si sarebbe desiderata, ma non <lb/>si poteva aspettar di meglio in chi intendeva di trattar la scienza co'metodi <pb xlink:href="020/01/2482.jpg" pagenum="107"/>antichi, tanto alieni dalla semplicit&agrave; dei principii accennati di sopra, e dai <lb/>quali hanno derivato i moderni le medesime conclusioni. </s>

<s>La riforma in ogni <lb/>modo, dal Torricelli stesso introdotta nel dimostrar le ragioni proporzionali, <lb/>era di tanta importanza, da desiderarsi che fosse allora maggiormente dif&shy;<lb/>fusa: eppure &egrave; un fatto che la conobbero solo quei pochi, i quali erano in&shy;<lb/>tervenuti alle pubbliche lezioni dell'Autore, o avevano potuto prender copia <lb/>del manoscritto di lui. </s>

<s>Il Viviani non si risolveva di pubblicarlo, come il Se&shy;<lb/>renai glie ne faceva istanza, o fosse perch'egli aspettava di dare alle stampe <lb/>tutte insieme le opere postume dell'Amico, o fosse perch'egli stesso atten&shy;<lb/>deva a scrivere delle proporzioni un nuovo trattato. </s>

<s>Il fine, ch'ebbe di so&shy;<lb/>stituire questo stesso trattato al torricelliano, non par si possa attribuire ad <lb/>altro, che al desiderio di esaltare il suo proprio Maestro, vedendo che il Tor&shy;<lb/>ricelli non faceva li nemmeno un motto del Galileo, suo precursore, e che <lb/>solamente lo rammemorava, a fin di dire com'avesse, per seguitar gli esempi <lb/>di Archimede, lasciati i primi due teoremi dei moti uniformi senza logica <lb/>conclusione. </s></p><p type="main">

<s>Voleva dunque il Viviani fare apparire al mondo schiettamente galileiana <lb/>la nuova scienza geometrica, da sostituirsi al quinto libro di Euclide, e non <lb/>poteva dall'altra parte negare che, se l'impulso era venuto da Galileo, l'ese&shy;<lb/>cuzion dell'opera era tutto merito del Torricelli. </s>

<s>Credette perci&ograve; di potersene <lb/>sdebitare con l'inserire nel suo trattato alcune delle proposizioni di lui, e <lb/>perch&egrave; il manoscritto era affidato alla custodia del Serenai, a lui ne chiese <lb/>prima il permesso a voce, e poi nel seguente scritto, ch'egli intendeva di <lb/>premettere alla stampa del libro: </s></p><p type="main">

<s>&ldquo; Rappresentai ier mattina a V. S. che, nell'andare disponendo con qual&shy;<lb/>che nuovo ordine il trattato delle proporzioni, spiegato co'principii dimo&shy;<lb/>strati dal gran Galileo mio maestro, con animo di stamparlo ora prontamente, <lb/>s&igrave; per meglio servirne un gentilissimo cavaliere mio padrone, che mi richiese <lb/>copia di quello, come per renderlo comune ancora ai giovani, che in questo <lb/>pubblico studio si vanno introducendo nella Geometria; trovavo che mi sa&shy;<lb/>rebbe tornato molto in acconcio il valermi di due di quelle dimostrazioni, <lb/>che il nostro caro amico signor Evangelista Torricelli, d'immortal nome e me&shy;<lb/>moria, soleva spiegare nel medesimo Studio, tra le altre di quel suo libretto <lb/>delle proporzioni, che con le altre sue cose si stamper&agrave;, le quali sono la pro&shy;<lb/>posizione X e XI di quell'ordine. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Soggiunsile che in fine di questo trattatello averei voluto anco aggiun&shy;<lb/>gere due problemi, che sono l'ottavo e il nono del sesto libro di Euclide, <lb/>risoluti dal medesimo Torricelli con una sola costruzione e dimostrazione, <lb/>con brevit&agrave; maestosa, e propria di quel grand'Uomo. </s>

<s>E con tutto che que&shy;<lb/>sta proposizione, e le altre due sopraddette, siano ormai note a molti, s&igrave; per <lb/>mezzo dello stesso Autore, che and&ograve; insegnandole col detto suo libro delle <lb/>proporzioni, del quale si valeva in luogo del quinto di Euclide, dandone e <lb/>lasciandone pigliar copia liberamente; come ancora per mezzo mio, che spesso <lb/>come cose del signor Torricelli l'ho conferite a chi m'&egrave; paruto opportuno; <pb xlink:href="020/01/2483.jpg" pagenum="108"/>lo dissi che nondimeno io mi conoscevo in obbligo di non porle alle stampe, <lb/>senza la precedente licenza di V. S., la quale sola tra gli altri, a titolo di <lb/>vero amico e di fedelt&agrave; incomparabile, nell'ultima malattia del Torricelli era <lb/>stata scelta da esso alla custodia, non solamente di queste, che di tutte le <lb/>altre scritture matematiche e geometriche rimastegli da pubblicare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto fino a qui le significai in voce, tanto ho pensato poi, per mi&shy;<lb/>glior governo di questo fatto, di replicarle nel presente foglio, che io le invio, <lb/>affinch&egrave; V. S. ancora in pi&egrave; di questo si contenti, come particolarmente ne la <lb/>prego per mia maggior quiete e sodisfazione, di confermarmi di proprio scritto <lb/>quella medesima cortese facolt&agrave;, che subito ella si compiacque di darmi sopra <lb/>di ci&ograve;, assicurandola che, oltre al far noto come devo l'Autore di tali tre <lb/>proposizioni, insieme con questa permissione di V. S. mi s'aggiunger&agrave; que&shy;<lb/>sto al gran numero dei favori, de'quali ormai sono trent'anni che io mi <lb/><gap/>rovo in possesso, ed intanto io mi ra<gap/>co al solito etc. </s>

<s>&rdquo; (MSS. Gal, Disc., <lb/>T. LXVIII, fol. </s>

<s>12). </s></p><p type="main">

<s>Nel foglio, che segue in ordine a questo nel volume ora citato, il Vi&shy;<lb/>viani stesso scrisse cos&igrave; di sua propria mano, mettendo a suo piacere in forma <lb/>la risposta o l'approvazione del Serenai: &ldquo; Per quelle medesime ragioni, che <lb/>mi mossero ier mattina a darvi subito libera facolt&agrave; in voce di poter pub&shy;<lb/>blicare ogni volta queste poche cose del nostro Amico: per le medesime torno <lb/>volentierissimo a concedervele, ancora adesso in scritto, come desiderate, di&shy;<lb/>chiarandomi con questa che, non solo mi contento che nel disporre il trat&shy;<lb/>tato delle proporzioni spiegate co'principii dimostrati dal Galileo, e che vo&shy;<lb/>lete pubblicare prontamente, voi inseriate quelle due proposizioni X e XI del <lb/>signor Evangelista Torricelli, che si trovano nel suo trattato latino manoscritto <lb/><emph type="italics"/>De proportionibus,<emph.end type="italics"/> con quell'altre due unite in una proposizione, che io ho <lb/>poi trovata nel foglio originale da me segnato di sotto col n.&degree; 13; ma vi <lb/>prego inoltre con istanza particolare a non tralasciare questa opportuna oc&shy;<lb/>easione, perch&egrave;, volendo voi gi&agrave; darle fuori per di chi elle sono, venite a <lb/>cooperare all'onore del comune Amico, gli ponete anticipatamente in sicuro <lb/>quello, che per essere ormai noto a tanti potrebbe trovare chi vi s'affezio&shy;<lb/>nasse come a cosa propria, ed insieme beneficate il prossimo, senza scapito <lb/>d'aleuna delle Opere postume del medesimo Autore, che a Dio piacendo si <lb/>sono tra poco per veder fuori, nelle quali non sar&agrave; poi errore nessuno che <lb/>queste tre dimostrazioni si riveggano stampate di nuovo ai luoghi loro. </s>

<s>Di <lb/>tanto vi prego approvando, e contentandomi, e sottoscrivendomi di propria <lb/>mano.... &rdquo; (ivi, fol. </s>

<s>13). </s></p><p type="main">

<s>Invece di questa risposta per&ograve;, messagli in bocca dal Viviani, il Sere&shy;<lb/>nai scrisse di suo proprio sentimento quell'altra lettera lunga, inserita da <lb/>pag. </s>

<s>117-21 nella prima edizione della Scienza universale delle proporzioni; <lb/>pregevole lettera, per le notizie che vi si leggono relative alla storia dei ma&shy;<lb/>noscritti torricelliani. </s>

<s>Questa nuova forma di concessione sostituita a quella <lb/>ultimamente trascritta, non si trovava oramai pi&ugrave; in corrispondenza con la <lb/>formale domanda che la precedeva, per cui, come cosa fuor di luogo sop-<pb xlink:href="020/01/2484.jpg" pagenum="109"/>pressa, pens&ograve; il Viviani di supplirvi con quelle avvertenze, stampate in ca&shy;<lb/>rattere corsivo a pag. </s>

<s>114, 116 della citata edizione. </s>

<s>Del resto, beneh&egrave; due, <lb/>la X e l'XI, fossero le proposizioni, che voleva traspor nel suo dal trattato <lb/>torricelliano, si content&ograve; poi di una sola, notando in margine a pag. </s>

<s>47 che <lb/>quella sua XIX era senza gli equimolteplici dimostrata <emph type="italics"/>secondo la proposi&shy;<lb/>zione XI del trattato delle proporzioni del Torricelli.<emph.end type="italics"/> Non sapremmo poi <lb/>dire dove, e per quale occasione fosse scritta la seguente avvertenza al Let&shy;<lb/>tore, che apparisce autografa nell'estremo lembo dell'ultimo foglio del citato <lb/>volume manoscritto: </s></p><p type="main">

<s>&ldquo; Fin dall'anno 1674, e di nuovo nel 1690, fu stampato in Firenze il <lb/>quinto libro degli Elementi di Euclide con questo titolo: <emph type="italics"/>Scienza uni<gap/>crsale <lb/>delle proporzioni, spiegata con la dottrina del Galilco, con nuoro ordine <lb/>distesa dall'ultimo suo discepolo, e dedicata all'A. S.ma e R.ma del principe <lb/>cardinale Leopoldo de'Medici, beneficientissimo mecenate dci Letterati.<emph.end type="italics"/> In <lb/>questo libro, in cui esso Discepolo, nel dare ordine alle proposizioni procura <lb/>di allontanarsi men che possibile fosse da quello del proprio autore Euclide, <lb/>seguitato e citato come primo maestro da que'Ceometri, che scrissero dopo <lb/>di lui; fu in pi&ugrave; luoghi allegato in margine un trattato simile delle propor&shy;<lb/>zioni, composto, pochi anni avanti la sua morte, dal celebratissimo Evange&shy;<lb/>lista Torricelli, che ne aveva lasciato prender copia a molti suoi uditori. </s>

<s>&rdquo; </s></p><p type="main">

<s>Cos&igrave; fatte notizie per&ograve; riguardano pi&ugrave; presto la storia del libro, che <lb/>quella della scienza, dalla quale non si veniva per verit&agrave; ad accreseer di molto <lb/>i meriti dell'Autore, confessando egli stesso di avervi atteso in un tempo, in <lb/>cui si ritrovava, per gravi indisposizioni di testa, inabile a pi&ugrave; ardue con&shy;<lb/>templazioni. (Scienza delle proporz. </s>

<s>cit., pag. </s>

<s>VII). L'opera &egrave; assai pi&ugrave; ri&shy;<lb/>stretta e pi&ugrave; elementare di quella del Torricelli, alla quale, come si disse, fu <lb/>nonostante sostituita, per avere una nuova occasione di esaltare il nome di <lb/>Galileo. </s>

<s>Secondo quel che infatti egli insegna nel suo quinto Dialogo, s'in&shy;<lb/>comincia dal Viviani a dimostrare la quinta definizione di Euclide, dalla quale <lb/>si svolgono poi le altre proposizioni che, ordinate in un trattato nuovo, com&shy;<lb/>ponevano quella, che portava gi&agrave; il titolo di <emph type="italics"/>Scienza universale delle pro&shy;<lb/>porzioni.<emph.end type="italics"/></s></p><p type="main">

<s>Che fosse l'opera del Viviani pi&ugrave; ristretta di quella del Torricelli, si <lb/>dimostra dall'essersi la detta scienza delle proporzioni trascurato ivi di appli&shy;<lb/>carla alla Meccanica, che fu la prima e principale intenzione, per cui si fece <lb/>la riforma cuclidea. </s>

<s>Forse esso Viviani cans&ograve; di entrare nel geloso argomento, <lb/>perch&egrave; la legittima dimostrazione del primo teorema galileiano dei moti uni&shy;<lb/>formi, che mancava affatto ai tempi del Torricelli, era stata ora ritrovata e <lb/>messa in pubblico nella proposizione LXXV <emph type="italics"/>De vi percussionis.<emph.end type="italics"/> lvi infatti il <lb/>Borelli, con metodi nuovi e che nulla affatto partecipavano di quelle difficolt&agrave;, <lb/>per espedirsi dalle quali tanto ebbe a faticare lo stesso Autore <emph type="italics"/>De propor&shy;<lb/>tionibus;<emph.end type="italics"/> dimostra insomma cos&igrave; in poche parole che due corpi uguali, mo&shy;<lb/>ventisi con uguali impulsi, passano uniformemente spazi proporzionali ai tempi. </s></p><p type="main">

<s>Siano nelle figure 37 e 38, qui noco addietro disegnate, que'due corni <pb xlink:href="020/01/2485.jpg" pagenum="110"/>uguali A, D, che, con l'eguaglianza degl'impulsi ricevuti, passano per tutti <lb/>i punti delle linee AB, DE in istanti di tempo rappresentati dalle infinite <lb/>linee, fra s&egrave; tutte eguali, condotte da ciascuno di que'punti parallele alle <lb/>AG, DH. </s>

<s>Dalla somma di cos&igrave; fatti istanti resulta il tempo del moto, il qual <lb/>tempo dunque &egrave; rappresentato dalla superficie dei due rettangoli GB, HE <emph type="italics"/>ex <lb/>methodo indivisibilium Cavalerii.<emph.end type="italics"/> Ma i rettangoli, aventi per supposizione <lb/>altezze uguali, stanno come le basi AB, DE, che son gli spazi passati dai <lb/>due mobili ne'due vari tempi; dunque anche essi tempi stanno come gli <lb/>spazi. </s>

<s>Cos&igrave; il Borelli, promovendo la scienza, che il Lettore desiderava nel <lb/>suo primo entrare al terzo dialogo delle due Scienze nuove, tacitamente ve&shy;<lb/>niva a insinuare che il pi&ugrave; risoluto metodo di trattar le pi&ugrave; sottili questioni <lb/>meccaniche non era quello antico di Galileo, bench&egrave; riformato, ma l'altro <lb/>nuovo proposto dal Cavalieri. </s></p><pb xlink:href="020/01/2486.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO III.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Del sesto dialogo aggiunto alle due Scienze nuove <lb/>ossia <lb/>Della forza della percossa<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Dei principii, da cui dipende la forza della percossa, proposti da Aristotile, dal Cardano e da Ga&shy;<lb/>lileo; e come fossero dimostrati falsi. </s>

<s>&mdash; II. </s>

<s>Del ritrovamento e della pubblicazione del Sesto <lb/>dialogo galileiano; se ne esaminano brevemente le materie, e si conclude essere snch'egli in&shy;<lb/>formato dai medesimi falsi principii professati in giovent&ugrave; dall'Autore. </s>

<s>&mdash; III. </s>

<s>Della reintegra&shy;<lb/>zione del Dialogo galileiano pubblicato dal Bonaventuri. </s>

<s>&mdash; IV. </s>

<s>Degli strumenti immaginati e <lb/>descritti per misurare la forza della percossa. </s>

<s>&mdash; V. </s>

<s>Della nnova scienza della percossa istituita, <lb/>prima da Giovan Marco Marci fra gli stranieri, e poi dal Borelli nella Scuola galileiana, e di <lb/>ci&ograve; che conferirono a promover la detta scienza gli Accademici di Londra e di Parigi. </s>

<s>&mdash; VI. </s>

<s>Delle <lb/>relazioni fra gli angoli dell'incidenza e della riflessione, e fra i momenti delle percosse dirette <lb/>e delle oblique </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Il dialogo delle proporzioni and&ograve; separato dalle altre scritture sue so&shy;<lb/>relle, dal 1674 al 1718, anno in cui si fece in Firenze la nuova edizione <lb/>delle opere di Galileo, diretta da Tommaso Bonaventuri. </s>

<s>Alle prime quattro <lb/>giornate delle due Scienze nuove si vide anzi allora, non solo aggiuntavi <lb/>questa Quinta, trasposta dal trattato del Viviani, ma una Sesta altres&igrave;, la <lb/>quale non poteva non metter negli animi lo stupore, che si proverebbe a ve&shy;<lb/>dere improvviso comparire in piazza una persona, che da tanto tempo cre&shy;<lb/>devasi morta. </s>

<s>Quella sesta Giornata infatti s'intitolava <emph type="italics"/>Della percossa,<emph.end type="italics"/> scrit&shy;<lb/>tura che tutti lamentavano, o per non avere avuto Galileo il tempo di con&shy;<lb/>durla alla sua perfezione, o per essere andata smarrita fra le carte di lui: <lb/>lamenti universali ultimamente raccolti insieme dal Borelli come fascicolo di <pb xlink:href="020/01/2487.jpg" pagenum="112"/>mirra, ch'egli affisse alla soglia del suo libro <emph type="italics"/>De vi percussionis.<emph.end type="italics"/> La curio&shy;<lb/>sit&agrave; perci&ograve; della strana apparizione, e l'importanza dell'argomento, che ci <lb/>promette di venire a svelarci uno dei pi&ugrave; astrusi misteri, in che siasi tenuta <lb/>chiusa la scienza del moto; concorrono ad indirizzare lungo questi sentieri <lb/>il discorso, che, per correre al suo termine pi&ugrave; diretto e spedito, vuol rimon&shy;<lb/>tare in su dove la Storia ha il principio. </s></p><p type="main">

<s>Non riuscir&agrave; cosa nuova, n&egrave; inaspettata a&igrave; nostri Lettori, se diciamo che <lb/>il priucipio di questa, come dell'altra scienza del moto, &egrave; nelle Questioni <lb/>meccaniche di Aristotile, nella XIX delle quali si domanda perch&egrave; una scure <lb/>gravata da un gran peso e leggermente posata su un legno, lo incide ap&shy;<lb/>pena, e lo spacca cos&igrave; facilmente a sollevare, e a percoter con la stessa sem&shy;<lb/>plice scure, bench&egrave; ora posi tanto meno di dianzi, che quel gran carico la <lb/>premeva? </s>

<s>&ldquo; An quia, risponde, omnia cum motu tiunt, el grave ipsum gra&shy;<lb/>vitatis magis assumit, motu dum movetur, quam dum quiescit? </s>

<s>&rdquo; (Operum, <lb/>Tomus XI, Venetiis 1560, fol. </s>

<s>34). </s></p><p type="main">

<s>S'introduce dunque dal Filosofo nella Meccanica il principio, che la ve&shy;<lb/>locit&agrave; nel mobile aumenta il peso: principio, che alcuni poi giudicarono falso, <lb/>specialmente argomentando dal fatto che la percossa producesi dal martello, <lb/>anche menato di sotto in su contro la gravit&agrave; sua naturale. </s>

<s>Ci&ograve; per&ograve; non <lb/>sembra che possa con buone ragioni contradire a Aristotile, il quesito del <lb/>quale non &egrave; intorno a ogni genere di percossa, ma a quella fatta particolar&shy;<lb/>mente dalla scure, menata dai boscaioli contro un legno, che le soggiaccia <lb/>posato sul suolo. </s>

<s>Che se per gravit&agrave; si voglia intender la mole, ossia la somma <lb/>delle particelle materiali, da cui si misura il peso di un corpo sulle braccia <lb/>di una bilancia; il discorso di Aristotile si riduce all'espressioue di quell'al&shy;<lb/><gap/> pi&ugrave; vero e pi&ugrave; generale principio, che cio&egrave; la forza della percossa &egrave; il <lb/>prodotto della velocit&agrave; per la massa. </s>

<s>La dottrina insomma, dal Filosofo pro&shy;<lb/>fessata nelle Questioni meccaniche, piuttosto che falsa, si potrebbe dire non <lb/>bene e non chiaramente espressa, ci&ograve; che a fare si lasciava ai futuri com&shy;<lb/>mentatori del testo. </s>

<s>I commenti per&ograve; si videro apparire assai tardi, e intanto <lb/>i Matematici, timidi di non smarrirsi, tornarono a calcar le ristrette orme <lb/>seguate a loro innanzi dai passi del Maestro. </s></p><p type="main">

<s>Girolamo Cardano fu il primo, che os&ograve; levarsi da una tal suggezione, <lb/>per secondar piuttosto i deliri della sua propria fantasia. </s>

<s>Egli ebbe, come ad <lb/>altre occasioni fu da noi notato, fra i fisici contemporanei e i posteriori il <lb/>pi&ugrave; chiaro e pi&ugrave; distinto concetto della compressione, e della elasticit&agrave; del&shy;<lb/>l'aria: e avendo osservato che tra la pressione e la percossa &egrave; una tal no&shy;<lb/>tabile differenza, che in quella il corpo premuto rimane in quiete, e in que&shy;<lb/>sta risalta bene spesso in frautumi: pens&ograve; che non potesse quella forza di <lb/>risalto attribuirsi ad altro, che alla ekisticit&agrave; dell'aria, ond'&egrave; perci&ograve; che si <lb/>ridusse a dire non operarsi altrimenti la percossa, che per insinuarsi a modo <lb/>di cuneo ne'pori del percosso l'aria stessa, sospintavi dal perenziente con <lb/>gran violenza. </s></p><p type="main">

<s>Giulio Cesare Scaligero se ne rise, nella sua CCCXXXI Esercitazione. <pb xlink:href="020/01/2488.jpg" pagenum="113"/>Quel Genovese dunque, diceva, che, interrogato in giudizio chi avesse am&shy;<lb/>mazzato l'uomo, rispondeva: le punte del forcone; avrebbe dovuto dir piut&shy;<lb/>tosto, te giudice o Cardano, che invece fu l'aria, e i retori dovrebbero oramai <lb/>lasciar di ripetere quelle loro figure, non pi&ugrave; dicendo che fu la giovent&ugrave;, la <lb/>notte, venere e il vino, ma l'aria che commise il delitto. </s>

<s>&ldquo; Equidem didice&shy;<lb/>ram, poi soggiunge, motum sicut pulsum addere ponderi. </s>

<s>Nam et absquc <lb/>ictu sola impressione plus affertur momenti, quam quantum eius pondus effi&shy;<lb/>cere valeat. </s>

<s>Quippe rapum manus cum cultro imposita non scindet, at com&shy;<lb/>pressione secabit. </s>

<s>Hoc ex nisu fit, ita etiam in ictu. </s>

<s>Aristotiles, in XIX pro&shy;<lb/>positione Mechanicorum, ait: impositam securim non secare, quia pondus <lb/>solum habet: motum vero movere &rdquo; (Francofurti 1592, pag. </s>

<s>1060). </s></p><p type="main">

<s>Coglie di qui lo Scaligero l'occasione di dire che il suo maestro Gio&shy;<lb/>vanni del Giocondo, architetto nobilissimo, che solo seppe intendere ed ese&shy;<lb/>guire i disegni postumi di Bramante, sciolse un giorno all'imperatore Massi&shy;<lb/>miliano questo problema: &ldquo; Quot pondo proportionem haberet pugnus hominis <lb/>ferientis, cum seipso non feriente comparatus &rdquo; (ibid., pag. </s>

<s>1061). E perch&egrave;, <lb/>poi soggiunge, questa, insieme con altre simili invenzioni, <emph type="italics"/>fortunae saevitia <lb/>periere,<emph.end type="italics"/> si volle studiar di recuperarle in un suo libro un Autore fran&shy;<lb/>cese, le speculazioni del quale non dovevano essere tenute in poco pregio, se <lb/>il Viviani le tradusse di sua propria mano, e le serb&ograve; fra le sue carte come <lb/>memoriale di scienza. </s>

<s>Fra i Manoscritti galileiani infatti, al foglio 162 del <lb/>tomo 138 dei Discepoli, sotto questa avvertenza <emph type="italics"/>Da un libretto intitolato<emph.end type="italics"/><lb/>Ricreazioni scientifiche <emph type="italics"/>in francese,<emph.end type="italics"/> si legge: &ldquo; Problema III. </s>

<s>Dire quanto <lb/>pesi un colpo d'un pugno, d'un martello o di un'ascie, in riguardo di quel <lb/>che peserebbe s'egli stesse in riposo e senza battere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Giulio Scaligero, nella sua Esercitazione CCCXXXI contro il Cardano, <lb/>narra che un matematico di Massimiliano imperatore propose un giorno que&shy;<lb/>sta questione, e prometteva di darne la soluzione. </s>

<s>Ma lo Scaligero non la <lb/>diede altrimenti, e io la risolvo in questa maniera: &rdquo; </s></p><p type="main">

<s>&ldquo; Prendete una bilancia e lasciatevi posare un pugno, un martello o <lb/>un'asce sopra uno de'gusci, o sopra un braccio della bilancia, e mettete <lb/>dentro l'altro guscio tanto peso, quanto basta per contrappesarlo. </s>

<s>Dopo, ca&shy;<lb/>ricando continuamente il guscio, e percotendo dall'altra estremit&agrave; col pugno, <lb/>martello o altro; si potr&agrave; sperimentare quanto di peso possa far sollevare <lb/>ciascun colpo, e conseguentemente quanto egli valga. </s>

<s>Perch&egrave;, come dice Ari&shy;<lb/>stotile, il moto che si fa nel battere aggiunge gran peso, e ci&ograve; perch'egli &egrave; <lb/>pi&ugrave; veloce. </s>

<s>E in effetto chi mettesse mille martelli o il peso di mille libbre <lb/>sopra una pietra, e la stringesse con forza di vite, di leva o di altra mac&shy;<lb/>china; non gli farebbe niente, in riguardo di colui che la percotesse. </s>

<s>Non <lb/>si ved'egli che un coltello sopra il burro, o un'asce posata sopra una carta, <lb/>senza percossa, non l'intacca niente? </s>

<s>Battasi un poco sopra un legno, e si <lb/>vedr&agrave; che effetto ne segue. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il problema era dunque risoluto dall'Autore francese, comparando i mo&shy;<lb/>menti della gravit&agrave; con quelli della percossa. </s>

<s>e riducendone le leggi delle <pb xlink:href="020/01/2489.jpg" pagenum="114"/>proporzioni a quelle dei pesi sulla bilancia. </s>

<s>Galileo, in quel medesimo tempo <lb/>o poco prima, era venuto nello stesso concetto, se non che, invece di rico&shy;<lb/>noscerne l'inspirazione dalle dottrine aristoteliche, come fa lo scrittore delle <lb/>sopra citate parole tradotte dal Viviani, incomincia, in quel suo discorso ag&shy;<lb/>giunto alla <emph type="italics"/>Scienza meccanica,<emph.end type="italics"/> a trattare della percossa, ridendosi di Aristo&shy;<lb/>tile che, alla lunghezza del manico nel martello, ne avesse attribuita l'essen&shy;<lb/>ziale efficacia. </s>

<s>Non cita per&ograve; nelle Opere il luogo, dove dal Filosofo si dice <lb/>questo, che pure i Matematici, incominciando da Leonardo da Vinci, avevano <lb/>per verissimo, e qual legittima conseguenza del principio, che &ldquo; ab eadem <lb/>vi plus transfertur id extremum, quod longior a centro distat &rdquo; (ibid., fol. </s>

<s>34), <lb/>come giusto si verifica nel martello col manico pi&ugrave; lungo. </s>

<s>Sembrava che <lb/>piuttosto avesse dovuto Galileo citar la XIX delle Questioni meccaniche, che <lb/>serv&igrave; di documento allo Scaligero, per ridur la scienza traviata dal Cardano <lb/>sul suo retto sentiero, e che il Borelli stesso, bench&egrave; censore non troppo <lb/>indulgente, ebbe, nel proemio al suo libro Della percossa, a lodare <emph type="italics"/>pro sua <lb/>sagacitate.<emph.end type="italics"/></s></p><p type="main">

<s>Comunque sia, cos&igrave; Galileo avverso, come il francese Autore seguace di <lb/>Aristotile, riducono la forza della percossa agli effetti della stadera, e delle <lb/>altre macchine, nelle quali si vede &ldquo; potersi muovere qualunque gran resi&shy;<lb/>stenza da ogni data piccola forza, purch&egrave; lo spazio, per lo quale si mover&agrave; <lb/>la resistenza, abbia quella proporzione medesima, che tra essa gran resistenza <lb/>e la piccola forza si trova &ldquo; (Alb. </s>

<s>XI, 124). Cos&igrave;, per esempio, soggiunge, <lb/>un martello &ldquo; il quale, avendo quattro di resistenza, vien mosso da forza <lb/>tale che, liberandosi da essa in quel termine dove fa la percossa, anderia <lb/>lontano, non trovando l'intoppo, dieci passi, e viene in detto termine oppo&shy;<lb/>sto un gran trave, la cui resistenza al moto &egrave; come quattromila, cio&egrave; mille <lb/>volte maggiore di quella del martello; fatta in esso la percossa, sar&agrave; bene <lb/>spinto avanti, ma per la millesima parte delli dieci passi, nei quali si sar&agrave; <lb/>mosso il martello &rdquo; (ivi, pag. </s>

<s>125). </s></p><p type="main">

<s>Furon queste le dottrine, che si professarono dai Matematici, fatte poche <lb/>eccezioni, intorno alla forza della percossa, infino a che non venne alla luce, <lb/>nel 1667, il trattato del Borelli. </s>

<s>Il Torricelli e il Viviani intanto esplicavano <lb/>quelle galileiane dottrine, illustrandole con alcuni pensieri, che dicevano di <lb/>avere inteso profferire dalla bocca dello stesso Galileo nei congressi di Ar&shy;<lb/>cetri, e il Nardi compendiava cos&igrave; il Discorso aggiunto infine alla <emph type="italics"/>Scienza <lb/>meccanica,<emph.end type="italics"/> confermando la proporzione ivi assegnata tra la forza del percu&shy;<lb/>ziente, e la resistenza che il percosso gli contrappone. </s></p><p type="main">

<s>&ldquo; Certo che la percossa, egli dice nella veduta XXII della Scena III, <lb/>tal moltiplicazione fa di forza, che quasi mirabil sembra, attesoch&egrave; vediamo, <lb/>con un piccolo martello percotendo un chiodo, penetrarsi un legno durissimo, <lb/>bench&egrave;, se noi sopra il chiodo ponessimo un peso dieci e cento volte pi&ugrave; <lb/>grave dello stesso martello, nulla quasi di segno c'impriremmo. </s>

<s>Che diremo <lb/>poi se l'esperienza ne dimostri che, con un piccol martello, potremo anco <lb/>una grandissima mole di luogo movere, se di percoterla lungo tempo du-<pb xlink:href="020/01/2490.jpg" pagenum="115"/>riamo? </s>

<s>Di qui veramente apparisce che gli effetti insensibili di ciascun colpo <lb/>moltiplicati divengono alla fine sensibili, massime nell'ondeggiamento di qual&shy;<lb/>che mobile, o nelle sue particelle conservato: apparisce ancora che nessuno, <lb/>bench&egrave; minimo atto, manca in natura di effetto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, per trovare la cagione della forza, che la percossa dimostra, bi&shy;<lb/>sogna considerar prima il peso del martello, e quanta in esso la resistenza <lb/>all'esser mosso si trovi. </s>

<s>Secondo, per quanto spazio si moverebbe cacciato <lb/>dalla forza, se intoppo non trovasse. </s>

<s>Terzo, quanta sia la resistenza al mo&shy;<lb/>vimento di quel peso, ov'ei percote. </s>

<s>Quarto ed ultimo, per quanto spazio si <lb/>muova il corpo, che la percossa riceve. </s>

<s>Quindi tal proporzione dalla Natura <lb/>mantenersi il Galileo osserva che, quanto la resistenza del percosso &egrave; mag&shy;<lb/>giore della resistenza del percotente, tanto minore spazio il percosso passer&agrave; <lb/>di quello, che trascorso il percotente si avrebbe. </s>

<s>Sia, per esempio, la resi&shy;<lb/>stenza del martello 10, quella del percosso 100, e pongasi che spinto il mar&shy;<lb/>tello fosse per andare innanzi 100 braccia, non trovando intoppo: avverr&agrave; <lb/>che, intoppando nella resistenza suddetta, la spinger&agrave; avanti un solo braccio, <lb/>perch&egrave;, siccome la resistenza del percotente &egrave; cento volte minore di quella <lb/>del percosso, cos&igrave; lo spazio, per il quale mosso lo stesso percotente sareb&shy;<lb/>besi, &egrave; cento volte maggiore dello spazio, per cui il percosso muovesi, tal&shy;<lb/>mente che, conchiudendo, diremo la forza della percossa da tal principio <lb/>dipendere: che quella forza, che muover pu&ograve; uno di resistenza per cento di <lb/>spazio, mover&agrave; cento di resistenza per uno di spazio &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. XX, pag. </s>

<s>435, 36). </s></p><p type="main">

<s>Fra gli stranieri, a que'tempi, il Mersenno, non sodisfatto di queste <lb/>dottrine, che si professavano nella Scuola galileiana; rinnovell&ograve; la strana <lb/>ipotesi del Cardano, attribuendo all'aria annidata dentro i pori del corpo <lb/>percosso i maravigliosi effetti, che non produrrebbe il percuziente, o natu&shy;<lb/>ralmente gravitando, o compresso per via di un torchio. </s>

<s>&ldquo; Quae valde con&shy;<lb/>formia iis quae de cylindro ferreo deprimendo, vel depresso, in nostris <emph type="italics"/>Me&shy;<lb/>chanicis<emph.end type="italics"/> dicta sunt: nempe motum, quo aer interiicitur, aliquid habere, quod <lb/>non possit a pondere, imo nec a praelis suppleri. </s>

<s>Aer siquidem interceptus <lb/>subiecti corporis poros ingreditur, illiusque partes ea velocitate comprimit et <lb/>deprimit, vel cogit, ut subsiliant, quam nullum pondus, nullave pressio sup&shy;<lb/>plere potest &rdquo; (Novar. </s>

<s>Observat., T. III, Parisiis 1644, pag. </s>

<s>203). </s></p><p type="main">

<s>Ad eccezione di pochi, ai quali piaceva, come al Mersenno, di ammet&shy;<lb/>tere la fantasia dove trovavan difficile il penetrare con la ragione, i pi&ugrave;, an&shy;<lb/>che fuori d'Italia, professavano il principio galileiano, da cui diceva il Nardi <lb/>che dipende la forza della percossa. </s>

<s>Giova tra quegli stranieri annoverare <lb/>Isacco Vossio, il quale, scrivendo, in appendice al suo libro <emph type="italics"/>De Nili origine,<emph.end type="italics"/><lb/>una dissertazione intitolata <emph type="italics"/>De potentiis quibusdam mechanicis,<emph.end type="italics"/> rassegna fra <lb/>quelle meccaniche potenze anche la percossa, e dice esser verissimo il gi&agrave; <lb/>noto principio galileiano, ch'egli anzi mette in forma di proposizione, per <lb/>passare con matematici argomenti a dimostrarla, ma poi soggiunge che, n&egrave; <lb/>da Galileo stesso, n&egrave; da nessun altro de'suoi seguaci fu fatta una osserva-<pb xlink:href="020/01/2491.jpg" pagenum="116"/>zione importante, senza la quale non &egrave; possibile, trattandosi delle varie per&shy;<lb/>cosse fatte dai corpi, ritrovar la precisa misura dei loro momenti. </s>

<s>&ldquo; De vi&shy;<lb/>ribus percussionis habet nonnulla Galilaeus, vir magnae sagacitatis, qui, licet <lb/>propius veritatem attigerit, totam tamen difficultatem non sustulit. </s>

<s>Percus&shy;<lb/>sionum efficaciam refert ille ad velocitatem et pondus corporis percutientis, <lb/>neglecto pondere ad ictum perpendiculari, absque quo tamen percussionum <lb/>momenta mensurari nequeunt &rdquo; (Hagae Comitis 1666, pag. </s>

<s>170). </s></p><p type="main">

<s>Cred&egrave; insomma il Vossio di essere stato egli il primo ad osservare il <lb/>fatto, e a formulare la legge che <emph type="italics"/>omnis pressio fit a perpendiculari pon&shy;<lb/>dere,<emph.end type="italics"/> bench&egrave; Leonardo da Vinci avesse descritti in una sua nota corpi di <lb/>vario peso che, pur essendo della stessa materia e avendo altezze perpendi&shy;<lb/>colari uguali, si profondano ugualmente nel tenero fango: e il Torricelli, <lb/>nella quarta delle sue Lezioni accademiche, ripensando al grande effetto del&shy;<lb/>l'asta infilata nel ferro della picca, che pareva peso superfluo e che dovesse <lb/>perci&ograve; riuscire al colpo d'impedimento, piuttosto che di aiuto; proponeva a <lb/>risolvere il problema: &ldquo; Se quel legno della picca, essendo egualmente ve&shy;<lb/>locitato, facesse il medesimo effetto, mentre si adopra disteso in asta, e men&shy;<lb/>tre si adoprasse raccolto in una palla. </s>

<s>Cos&igrave; anco se una trave egualmente <lb/>velocitata fosse per dare il medesimo urto, percotendo una volta per lo lungo, <lb/>ed un'altra per traverso &rdquo; (Milano 1823, pag. </s>

<s>107). </s></p><p type="main">

<s>Ebbe il Vossio per risoluti i problemi, dicendo che la picca in asta e <lb/>la trave per lo lungo fanno maggior effetto, perch'&egrave; dall'altezza perpendi&shy;<lb/>colare, che si misura la forza dell'urto, ma questa era piuttosto l'afferma&shy;<lb/>zione di un fatto, che la conclusione di una verit&agrave; dal suo proprio principio, <lb/>rimanendo tuttavia a sapersi il perch&egrave; e in che modo l'altezza perpendico&shy;<lb/>lare del percuziente conferisca a render pi&ugrave; valido il colpo. </s>

<s>Che poi vera&shy;<lb/>mente non prelucessero alle speculazioni di esso Vossio i principii necessarii <lb/>a promovere utilmente la scienza, apparisce dalla soluzione di quel problema, <lb/>agitato allora fra i curiosi dell'arte cavalleresca: in qual parte cio&egrave; la spada <lb/>menata in giro faccia maggiore la ferita. </s>

<s>Rispondevano alcuni nella punta, <lb/>perch&egrave; ivi il moto &egrave; maggiormente veloce; soggiungevano altri nel centro <lb/>della gravit&agrave;, perch&egrave; ivi raccogliesi tutta insieme la potenza della materia. <lb/></s>

<s>&ldquo; Sed profecto, entra a dire in mezzo ai disputanti il Vossio, omnia haec <lb/>sunt inania: non celeritatis tantum, sed et latitudinis et ponderis perpendi&shy;<lb/>cularis singularum ensis partium habenda est ratio &rdquo; (ibid., pag. </s>

<s>166). </s></p><p type="main">

<s>Le ferite dunque, fatte nei varii punti del taglio della spada, stanno in <lb/>ragion composta della velocit&agrave; del moto, e della larghezza della lama, cosic&shy;<lb/>ch&egrave;, in un bastone o in una verga in cui le sezioni fossero tutte uguali, la <lb/>minor percossa si farebbe presso il manico, e la maggiore verso la punta. </s>

<s><lb/>Cos&igrave; pure aveva concluso Leonardo da Vinci, e gli altri matematici, dietro <lb/>il principio del Filosofo che <emph type="italics"/>ab eadem vi plus transfertur id extremum, <lb/>quod longior a centro distat;<emph.end type="italics"/> ond'&egrave; che il Vossio non fece di nulla essen&shy;<lb/>zialmente progredire la scienza della percossa, la quale si rimase perci&ograve; tra <lb/>l'ipotesi fisica del Cardano, e la teoria meccanica di Galileo. </s>

<s>E perciocch&egrave; <pb xlink:href="020/01/2492.jpg" pagenum="117"/>questa non era meno falsa di quella, non s'aveva alcuna speranza di pro&shy;<lb/>gresso, se non dallo sgombrarsi che farebbero le vie della verit&agrave; dall'uno <lb/>errore e dall'altro. </s></p><p type="main">

<s>L'ipotesi del Cardano pareva impossibile che avesse seguaci in uomini <lb/>di senno: eppure non mancarono alcuni, i quali si misero volentieri dietro <lb/>al Mersenno, principalmente sedotti dal sembrar loro che, per l'intermedio <lb/>dell'aria, si spiegassero quelle compressioni e quelle espansioni dei corpi per&shy;<lb/>cossi, che non si comprendeva come potess'esser l'effetto della sola forza <lb/>immediata nei percuzienti. </s>

<s>Benemeriti perci&ograve; dell'avere sgombrato dall'er&shy;<lb/>rore cardanico i sentieri della scienza son da dire coloro, i quali dimostra&shy;<lb/>rono in che modo agisca la forza della percossa in schiacciare e allargare i <lb/>cedevoli corpi sotto la forza del maglio. </s>

<s>Noi non possiamo citare il nome <lb/>proprio dell'Autore di cos&igrave; fatta dimostrazione, essendo di ci&ograve; solamente certi <lb/>che appartenne alla Scuola galileiana, trovandosi raccolte nel citato mano&shy;<lb/>scritto attribuito al Magiotti, insieme con le tante altre, anche le speculazioni <lb/>di lui. </s>

<s>La questione &egrave; trattata nella sua generalit&agrave;, s&igrave; rispetto ai vari generi <lb/>di corpi, s&igrave; rispetto al vario modo di agir la forza sopr'essi; e solo, per <lb/>maggiore semplicit&agrave; e per pi&ugrave; matematica esattezza, si suppongono sferiche <lb/>le particelle integranti. </s></p><p type="main">

<s>&ldquo; L'acqua, si legge, cadendo da alto, si slarga per tutti i versi, ed una <lb/>palla di terra fresca o di altra cosa tenera si schiaccia e allarga, ed ancora <lb/>un ferro o altro si lascia traforare ed aprire, se con qualche cosa dura sar&agrave; <lb/>percosso, e si distende e dilata all'incudine, perch&egrave; i componenti di quella <lb/>tal materia (quali o siano tondi o di altra figura non importa, poich&egrave; il me&shy;<lb/>desimo segue essendo dal colpo spinti) si allargano per altro verso, come <lb/>qui sotto si vede, e siano per adesso di figura sferica. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Siano i cerchi EAG e CDB (fig. </s>

<s>40), che fra loro si tocchino, e tirisi <lb/><figure id="id.020.01.2492.1.jpg" xlink:href="020/01/2492/1.jpg"/></s></p><p type="caption">

<s>Figura 40.<lb/>la CG: dico che passer&agrave; ancora per <lb/>il toccamento. </s>

<s>Se essa non passer&agrave; per <lb/>il toccamento, o passer&agrave; di sopra o <lb/>passer&agrave; di sotto. </s>

<s>Passi prima di sotto, <lb/>e sia GRC. Tirisi, dal punto G al toc&shy;<lb/>camento N, una linea retta, e dal me&shy;<lb/>desimo toccamento al punto C un'al&shy;<lb/>tra linea retta. </s>

<s>Perch&egrave; la GL all'LN <lb/>sta come la CI alla IN, e gli angoli <lb/>contenuti dai lati proporzionali sono <lb/>retti; sar&agrave; il triangolo GLN simile al triangolo GIN. </s>

<s>E perch&egrave; sopra la linea <lb/>retta AB vi cade una linea retta CN, far&agrave; gli angoli conseguenti uguali a due <lb/>retti. </s>

<s>Ma in cambio dell'angolo CNI piglisi GNL, che a lui &egrave; uguale: sar&agrave; <lb/>la GC una linea retta, quale passer&agrave; per il toccamento. </s>

<s>Adunque due linee <lb/>rette, partendosi dai medesimi termini G, C, conterrebbero spazio, che &egrave; im&shy;<lb/>possibile, quale si dovea dimostrare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Adunque, spingendosi per linea retta, niuno dei detti cerchi muter&agrave; <pb xlink:href="020/01/2493.jpg" pagenum="118"/>sito, ma &egrave; impossibile che gl'infiniti componenti di un corpo tutti nel sopra <lb/>detto modo si urtino. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se siano aggravati due cerchi, che si tocchino per di fuori, dai punti <lb/>dove si aggravano e spingono tirata una linea retta, quale non passi per i <lb/>centri, quale ancora non passer&agrave; per il toccamento; dico che si rivolgeranno <lb/>l'uno sopra l'altro verso dove i punti presi sono fuori della linea, e pi&ugrave; fa&shy;<lb/>cilmente, quanto pi&ugrave; ad essa linea saranno lontani. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Mentre si spingano i sopraddetti cerchi per il punto M e H (nella pre&shy;<lb/>cedente figura) la linea, la quale li congiunge, non passi per il toccamento: <lb/>mentre il cerchio MNG sia aggravato in M, girer&agrave; sopra il cerchio HND, ed <lb/>egli sopra MNG si rivolger&agrave;. </s>

<s>Il medesimo faranno i componenti di qualsivo&shy;<lb/>glia cosa, mentre saranno percossi: e mentre che tutti, che &egrave; impossibile, <lb/>non si urtino per quella linea che passa per i loro centri, si allargheranno <lb/>e scorreranno per diverso dove &rdquo; (fol. </s>

<s>220, 21). </s></p><p type="main">

<s>Potevano i seguaci del Cardano, per queste ragioni, persuadersi che si <lb/>ammaccano i corpi per effetto della forza della percossa, e non per l'espan&shy;<lb/>sione dell'aria dentro i loro pori rinchiusa; ond'&egrave; facile congetturare che <lb/>nessuno o pochi rimanessero, oltrepassata la met&agrave; del secolo XVII, i lusin&shy;<lb/>gati dall'esempio, o i soggiogati dall'autorit&agrave; del Mersenno. </s>

<s>Ebbe perci&ograve; ad <lb/>acquistare allora maggior prevalenza il principio galileiano, il quale a poco <lb/>and&ograve; che fu anch'esso convinto di falso. </s>

<s>Ma cos&igrave; sottili essendo gli agguati, <lb/>non fu possibile eluderli, se non da poi che la Scienza si rese esperta in <lb/>ragionare intorno alle varie proporzioni della forza, che si comunica ai corpi <lb/>pi&ugrave; o meno, secondo la quantit&agrave; della loro materia. </s>

<s>Galileo, senza dubbio, <lb/>non avrebbe potuto contro i Peripatetici concludere l'uguale velocit&agrave; dei ca&shy;<lb/>denti di qualunque peso, senza implicitamente ammettere che gl'impulsi della <lb/>gravit&agrave; son proporzionali alle masse, ma non seppe applicar n&egrave; estendere <lb/>questa legge a qualunque potenza. </s>

<s>Nel 1604 il Sarpi gli proponeva la solu&shy;<lb/>zione del seguente problema: Si hanno due palle, una di oro che pesa 20 lib&shy;<lb/>bre, e l'altra di argento di libbre 19. Supponiamo che siano ambedue mosse <lb/>da forza uguale a 12: anderanno i mobili ugualmente veloci? </s>

<s>Parrebbe di <lb/>s&igrave;, risponde il Sarpi, applicandovi le dottrine stabilite insieme con Galileo <lb/>intorno al moto naturale dei gravi. </s>

<s>Ma poi conclude con approvare colui che <lb/>dicesse non dover essere uguali le velocit&agrave; de'due mobili di differente peso, <lb/>bench&egrave; abbia ricevuto ciascuno in s&egrave; impressione uguale di forza. </s></p><p type="main">

<s>&ldquo; Se saranno due mobili di disuguale specie, e una virt&ugrave; minore di <lb/>quello, che sia capace ricevere qual si voglia di loro; si domanda se, comu&shy;<lb/>nicandosi la virt&ugrave; ad ambedue, ne riceveranno ugualmente: come se l'oro <lb/>fosse atto di ricevere dalla somma virt&ugrave; 20, e non pi&ugrave;, e l'altro 19 e non <lb/>pi&ugrave;; se saranno mossi da virt&ugrave; 12, se ambedue riceveranno 12. Par di s&igrave;, <lb/>perch&egrave; la virt&ugrave; si comunica tutta; il mobile &egrave; capace: adunque l'effetto &egrave; <lb/>lo stesso. </s>

<s>Par di no, perch&egrave; allora due mobili di specie diversa, da ugual <lb/>forza spinti, anderanno allo stessso termine con la stessa velocit&agrave;. </s>

<s>Se uno <lb/>dicesse: la forza 12 mover&agrave; l'argento e l'oro allo stesso termine, non con <pb xlink:href="020/01/2494.jpg" pagenum="119"/>la stessa velocit&agrave;?.... Perch&egrave; non, se ambedue sono capaci anco di mag&shy;<lb/>giore, che quella qual 12 li pu&ograve; comunicare? </s>

<s>&rdquo; (Lettere, Firenze 1863, Vol. </s>

<s>I, <lb/>pag. </s>

<s>14). </s></p><p type="main">

<s>Avviava cos&igrave; il Sarpi le questioni meccaniche in un campo nuovo e l'in&shy;<lb/>certezza del risolverle dipendeva come si disse dal non essersi ancora stabi&shy;<lb/>lite le leggi della comunicazione dei moti, formulate gi&agrave; in una scienza pi&ugrave; <lb/>antica. </s>

<s>Leonardo da Vinci, per esempio, dall'aver posto che ogni potenza &egrave; <lb/>il prodotto della velocit&agrave; per la quantit&agrave; di materia, ne aveva concluso che, <lb/>essendo le potenze uguali, le velocit&agrave; stanno in reciproca ragione delle masse <lb/>dei corpi. </s>

<s>&ldquo; Se una potenza, diceva, mover&agrave; un corpo, in alquanto tempo, <lb/>un alquanto spazio; la massima potenza mover&agrave; la met&agrave; di quel corpo, nel <lb/>medesimo tempo, due volte quello spazio: ovvero la medesima virt&ugrave; mover&agrave; <lb/>la met&agrave; di quel corpo, per tutto quello spazio, nella met&agrave; di quel tempo &rdquo; <lb/>(Les Manuscrits, Man. </s>

<s>F, Paris 1389, fol. </s>

<s>26). Se fosse dunque Leonardo ri&shy;<lb/>sorto, ed entrato in mezzo alle dispute insorte fra il Sarpi e Galileo, non <lb/>solo avrebbe confermato con certezza di scienza che due mobili l'uno peso <lb/>come venti, e l'altro come diciannove, sarebbero stati da ugual forza diver&shy;<lb/>samente velocilati, ma avrebbe determinate le proporzioni di quelle diversit&agrave;, <lb/>dicendo che la palla di argento si sarebbe mossa venti diciannovesimi pi&ugrave; <lb/>veloce di quella dell'oro. </s></p><p type="main">

<s>Nella risorta scienza del moto fu Niccol&ograve; Aggiunti che prese a dimo&shy;<lb/>strare le prime leggi della comunicazion delle forze, per applicarla alla per&shy;<lb/>cossa, <emph type="italics"/>la quale opera,<emph.end type="italics"/> egli dice, <emph type="italics"/>con la velocit&agrave; e con la copia della ma&shy;<lb/>teria.<emph.end type="italics"/> Non fu dunque il Borelli, se non che in pubblico, il primo a dire e <lb/>a dimostrare che la potenza percussiva, essendo le velocit&agrave; uguali, dipende <lb/>dalla mole corporea, risovvenendosi i nostri Lettori di aver sentito dimostrar, <lb/>nel precedente Tomo di questa Storia, a pag. </s>

<s>188, 89, allo stesso Aggiunti <lb/>che <emph type="italics"/>La medesima velocit&agrave;, nelle maggiori e minori quantit&agrave; di materia, <lb/>opera pi&ugrave; o meno potentemente, secondo la proporzione di essa materia: <lb/>e che, se saranno due mobili di uguale velocit&agrave;, fatti della stessa mate&shy;<lb/>ria, ma di quantit&agrave; disuguale di essa, il momento dell'uno, al momento <lb/>dell'altro, sta come la quantit&agrave; della materia dell'uno alla quantit&agrave; della <lb/>materia dell'altro.<emph.end type="italics"/></s></p><p type="main">

<s>Ebbe altrove il Borelli a notare che l'errore di tutti i suoi antecessori <lb/>nella scienza della percossa dipendeva dal creder con Aristotile che gli effetti <lb/>del colpo fossero prodotti dal peso naturale, che nel cadere si moltiplica via via: <lb/>contro il quale errore poneva nel trattato <emph type="italics"/>De vi percussionis<emph.end type="italics"/> il cap. </s>

<s>XXXIV, <lb/>in cui concludeva la proposizione CXXXIV col dire essere impossibile &ldquo; ut <lb/>vis impetus augeat vim ponderis eiusdem corporis, et hoc profecto contingit <lb/>cum pila gravis sursum proiicitur perpendiculariter ad horizontem, cum e <lb/>contra nisus gravitatis fiat deorsum &rdquo; (Bononiae 1667, pag. </s>

<s>293). Da quegli <lb/>erranti antecessori per&ograve; del Borelli era da escluder l'Aggiunti, il quale, in <lb/>una Nota da noi trascritta e pubblicata nella pagina precedente alle due so&shy;<lb/>pra citate, aggiungeva alla <emph type="italics"/>percossa naturale,<emph.end type="italics"/> di che solo s'occuparono Ari-<pb xlink:href="020/01/2495.jpg" pagenum="120"/>stotile e Galileo, la <emph type="italics"/>percossa violenta,<emph.end type="italics"/> fatta dal corpo mosso di sotto in su, <lb/>e la <emph type="italics"/>media,<emph.end type="italics"/> che dice esser quella del corpo grave che, movendosi orizontal&shy;<lb/>mente, percote. </s>

<s>Confermava questa sua terza definizione, proponendosi di <lb/>dimostrare che <emph type="italics"/>Anco la sola velocit&agrave;, senza il peso, opera ed ha momento:<emph.end type="italics"/><lb/>proposizione che apparisce falsa, come noi la giudicammo, se per peso ivi <lb/>intendesi la materia. </s>

<s>Ma se intenderemo, secondo che deve aver inteso l'Ag&shy;<lb/>giunti, la materia, che non esercita il suo peso, o perch&egrave; contrariato, come <lb/>nel moto proiettizio all'in su, o perch&egrave; equilibrato, come nel moto orizon&shy;<lb/>tale; la proposizione &egrave; verissima, e le ragioni, che la dimostran tale, son pi&ugrave; <lb/>semplici e pi&ugrave; efficaci di quelle stesse addotte nel citato cap. </s>

<s>XXXIV <emph type="italics"/>De vi <lb/>percussionis.<emph.end type="italics"/></s></p><p type="main">

<s>La morte arrest&ograve; nelle Note manoscritte dell'Aggiunti i progressi di que&shy;<lb/>ste speculazioni intorno alla nuova Scienza della percossa, a proseguir la <lb/>quale dette, pi&ugrave; di trent'anni dopo, opera il Borelli. </s>

<s>Egli incomincia dall'os&shy;<lb/>servare che la virt&ugrave; partecipata al proietto dal proiciente &egrave; diffusiva di s&egrave; <lb/>in tutte e singole le particelle del corpo, per le quali si distribuisce ugual&shy;<lb/>mente: d'onde avviene che, quanto maggiore &egrave; il numero di esse particelle <lb/>integranti, altrettanto sia divisa la virt&ugrave; motrice, e perci&ograve; minore la velocit&agrave;, <lb/>la qual dunque sar&agrave; tale, da crescere col crescer della forza impulsiva, e col <lb/>diminuire della quantit&agrave; di materia o della massa. </s>

<s>Le pi&ugrave; volgari esperienze <lb/>confermano questa conclusione, perch&egrave; agitando in mano, per esempio, un <lb/>corpo diviso in frantumi di varia grandezza, e, gittandoli tutti insieme, si ve&shy;<lb/>dono i pi&ugrave; piccoli andar pi&ugrave; lontano degli altri. </s></p><p type="main">

<s>Chiamate F, F&prime; le forze impresse in due vari corpi, de'quali M, M&prime; sian <lb/>le respettive moli o masse, il discorso del Borelli si traduce analiticamente <lb/>nelle formule V=F:M, V&prime;=F&prime;:M&prime;, dalle quali conseguono prima di <lb/>tutto le proposizioni XII e XIII, poste dall'Autore per fondamento al suo <lb/>trattato <emph type="italics"/>De vi percussionis;<emph.end type="italics"/> quella che dice: &ldquo; Si duo corpora eadem velo&shy;<lb/>citate moveantur, vis motiva ad vim motivam eamdem proportionem habet, <lb/>quam unum corpus ad aliud &rdquo; (pag. </s>

<s>36) e questa: &ldquo; Si duo corpora aequa&shy;<lb/>lia inaequalibus velocitatibus moveantur, eorum virtutes motivae eamdem pro&shy;<lb/>portionem habebunt, quam velocitates &rdquo; (pag. </s>

<s>38). Conseguiva altres&igrave; dal <lb/>sopra posto principio un'altra proposizione importante, che ricorre in ordine <lb/>la XV, e nella quale il Borelli dimostra che, essendo le forze impulsive uguali, <lb/>stanno le velocit&agrave; reciprocamente come le moli. </s>

<s>&ldquo; Igitur si fuerint duo cor&shy;<lb/>pora inaequalia, quae impellantur ab aequalibus viribus motivis, erunt eorum <lb/><figure id="id.020.01.2495.1.jpg" xlink:href="020/01/2495/1.jpg"/></s></p><p type="caption">

<s>Figura 41.<lb/>velocitates reciproce proportionales magnitudinibus <lb/>corporum impulsorum &rdquo; (pag. </s>

<s>40). </s></p><p type="main">

<s>Questa proposizione nel manoscritto attribuito <lb/>al Magiotti &egrave; confermata da una bella esperienza, <lb/>la quale &egrave; cos&igrave; un poco troppo forse frettolosa&shy;<lb/>mente descritta: &ldquo; Se appenderemo due palle A, <lb/>B (fig. </s>

<s>41) di qualsivoglia materia, una il doppio <lb/>pi&ugrave; grave dell'altra, e quella pi&ugrave; leggera rimo-<pb xlink:href="020/01/2496.jpg" pagenum="121"/>veremo lontano dal perpendicolo il doppio della pi&ugrave; grave, le quali lasciate <lb/>in libert&agrave;, acci&ograve; si urtino; una non spinger&agrave; indietro l'altra, perocch&egrave; tanto <lb/>quanto &egrave; di lei pi&ugrave; grave, tanto l'altra &egrave; pi&ugrave; veloce &rdquo; (fol. </s>

<s>205). </s></p><p type="main">

<s>La fretta nel descrivere, che si accennava, trasparisce dall'apparente <lb/>impropriet&agrave; dell'espressione, per ridur la quale alla matematica esattezza si <lb/>potr&agrave; osservar che l'Autore riferisce le distanze all'infimo punto D del per&shy;<lb/>pendicolo, a partir dal quale si deve misurar l'altezza della caduta, doppia <lb/>in potenza, ossia il quadrato. </s>

<s>Cos&igrave;, se intendasi la palla A esser sollevata per <lb/>tutto il quadrante, e perci&ograve; scendere perpendicolamente per l'altezza CD; <lb/>affinch&egrave; l'altra palla B produca in D la met&agrave; dell'urto, convien sollevarla <lb/>per un arco, di cui il seno verso DE sia la quarta parte di tutta DC, come <lb/>era per la legge galileiana notissimo all'Autore, e com'aveva proposto il Bo&shy;<lb/>relli nel descriver una simile esperienza, la quale egli diceva esser benissimo <lb/>accomodata all'intento, perch&egrave; i pendoli &ldquo; efficiunt transitus per arcum AC <lb/>(nella precedente figura) et arcum DB acquitemporaneos, et ideo, si in eo&shy;<lb/>dem instanti demittantur a terminis A, B, efficientur quoque percussiones <lb/>in D in unico quoque instanti &rdquo; (pag. </s>

<s>202). Il Mariotte poi descrisse, dietro <lb/>tali esempi, in principio del suo trattato <emph type="italics"/>De la percussion,<emph.end type="italics"/> quella Macchina <lb/>di precisione, con la quale si potevano verificar questa, e altre leggi. </s></p><p type="main">

<s>Qualche cosa di simile doveva avere inventato Leonardo da Vinci, nelle <lb/>Note del quale vedemmo essere stata annunziata gi&agrave; la proposizione XV, che <lb/>il Borelli dava al pubblico per cosa nuova, e dall'essersi ignorata la quale <lb/>nacquero le incertezze e i dubbi di Galileo e del Sarpi intorno alle quan&shy;<lb/>tit&agrave; dei moti comunicati, e nacque altres&igrave; l'errore dello stesso Galileo in asse&shy;<lb/>gnar le proporzioni delle velocit&agrave; fra il percuziente e il percosso. </s>

<s>Diceva, <lb/>come gi&agrave; sappiamo, essere queste velocit&agrave; reciproche tra la potenza del mar&shy;<lb/>tello, e la resistenza del chiodo, come son reciproche ne'pesi equilibrati nella <lb/>bilancia, o sul declivio di un piano. <emph type="italics"/>Sed negotium percussionis longe di&shy;<lb/>versa ratione procedit,<emph.end type="italics"/> ebbe a rispondere al suo gran Maestro il Borelli, <lb/>giustamente osservando che, nell'atto in cui si produce l'effetto, il martello <lb/>va con velocit&agrave; uguale a quella del chiodo, assai diversa dalla prima, che <lb/>aveva nello scender liberamente per dare il colpo. </s>

<s>E riducendo alle gi&agrave; di&shy;<lb/>mostrate leggi nuove queste sue osservazioni, trovava che la velocit&agrave; del per&shy;<lb/>cuziente a quella del percosso non sta nella proporzione della semplice mole <lb/>di questo alla mole di quello, ma in una proporzione molto maggiore. </s>

<s>&ldquo; Si <lb/>igitur potentia percussiva non est facultas motus, nec vis ponderis, reliquum <lb/>est ut sit moles corporea, quod licet videatur incredibile, vel saltem sit igno&shy;<lb/>tum, ostendetur tamen in progressu huius operis, in percussione, moles corpo&shy;<lb/>reas suis velocitatibus reciproce non respondere. </s>

<s>Nam malleus, licet vehemen&shy;<lb/>tissime moveatur, antequam percussionem inferat, et antequam ad contactum <lb/>percussi corporis perducatur, et resistentiam quiescentis corporis superet; <lb/>tamen, in actu percussionis, non potest malleus pristinam velocitatem reti&shy;<lb/>nere. </s>

<s>Cogitur enim moveri eadem velocitate simul cum corpore percusso, <lb/>quandoquidem concipi nequeunt duo corpora se tangentia, et simul agitata, <pb xlink:href="020/01/2497.jpg" pagenum="122"/>quorum subsequens et propellens celerius moveatur, quam antecedens impul&shy;<lb/>sum. </s>

<s>Itaque, si comparetur velocitas mallei, antequam percussionem inferat, <lb/>cum velocitate acquisita a corpore percusso, et tunc illa ad hanc velocitatem <lb/>maiorem proportionem habebit, quam moles percussi corporis ad molem per&shy;<lb/>cutientis: habent enim eamdem proportionem quam summa corporum percussi <lb/>et percutientis ad corpus percutiens &rdquo; (pag. </s>

<s>IX, X). </s></p><p type="main">

<s>Dimostrava ci&ograve; il Borelli nella proposizione XIX, supponendo che un <lb/>corpo indifferente al moto, come sarebbe una perfetta sfera posata sopra un <lb/>piano perfettamente orizontale, ceda a qualunque pi&ugrave; leggero impulso, a cui <lb/>nulladimeno non diminuisce la virt&ugrave; motiva. </s>

<s>Sia un corpo qualunque A che, <lb/>movendosi con la quantit&agrave; di moto A. V, ne incontri direttamente un altro B, <lb/>nello stato della detta indifferenza: ambedue procederanno insieme congiunti, <lb/>e cos&igrave; congiunti serberanno pure la medesima quantit&agrave; di moto, la quale <lb/>dovr&agrave; necessariamente risultar d'imminuita velocit&agrave;, essendo da A in A+B <lb/>cresciuta la mole corporea. </s>

<s>Qualunque siasi per&ograve; quella velocit&agrave;, che chia&shy;<lb/>meremo V&prime;, la quantit&agrave; di moto sar&agrave; espressa da (A+B)V&prime;=A.V, e <lb/>perci&ograve; V/V&prime;=(A+B)/A, che &egrave; maggior proporzione di B/A, assegnata da Ga&shy;<lb/>lileo <emph type="italics"/>per sufficientiam iuvenilis eius ratiocinii,<emph.end type="italics"/> come disse il Borelli, il quale <lb/>stim&ograve; che poi vecchio si fosse ricreduto, quand'ebbe a pronunziar che la <lb/>forza della percossa era infinita, e in un altro dialogo prometteva come tale <lb/>di dimostrarla. </s></p><p type="main">

<s>Quel dialogo per&ograve; non ebbe la fortuna di vederlo appresso all'Autore <lb/>vivente nessuno degli amici e dei familiari, non eccettuato lo stesso Torri&shy;<lb/>celli chiamato come si sa dal principe Leopoldo, per questo effetto, nell'ospi&shy;<lb/>zio di Arcetri. </s>

<s>Anzi gli eredi stessi di Galileo, soggiunge il Borelli, <emph type="italics"/>mihi <lb/>retulerunt nec inter schedulas reperta est pagella, quae hoc titulo insi&shy;<lb/>gniretur,<emph.end type="italics"/> cosicch&egrave; tutti coloro, i quali erano intervenuti nell'Accademia della <lb/>Crusca ad ascoltar le torricelliane lezioni, con tanta applaudita eloquenza re&shy;<lb/>citate intorno alla forza della percossa, <emph type="italics"/>hanc scientiam una cum Galileo <lb/>defunctam esse perpetuo questi sunt.<emph.end type="italics"/></s></p><p type="main">

<s>Per ristorar dunque la scienza di tanta iattura, rivolgendo spesso in <lb/>mente i detti di Galileo, n&egrave; potendo credere che quel grand'Uomo si fosse <lb/>allucinato, pens&ograve; il Borelli di scrivere un libro a parte sull'argomento del <lb/>Dialogo perduto. </s>

<s>&ldquo; At tandem, post diuturnas mentis agitationes, Dei bene&shy;<lb/>ficio, hanc physicae et mathematicae partem ex integro proprio marte me <lb/>reperisse puto, et veram et intimam naturam energiae percussionis, eiusque <lb/>causas, proprietates et effectus in hoc libro luculenter demonstrasse mihi <lb/>videor, quae, saltem ob novitatem et materiae praestantiam, non iniucunda <lb/>fore censeo &rdquo; (pag. </s>

<s>XII). </s></p><p type="main">

<s>La Scienza nuova, che s'istituiva nel libro <emph type="italics"/>De vi percussionis,<emph.end type="italics"/> credeva <lb/>dunque l'Autore fosse quella in sostanzn, che s'avrebbe avuta direttamente <lb/>dal grande Maestro, se si fosse potuto, dopo la morte di lui, <emph type="italics"/>in armario <lb/>secretiori, inter alia scripta, hanc dissertationem, calamo exaratam, sal-<emph.end type="italics"/><pb xlink:href="020/01/2498.jpg" pagenum="123"/><emph type="italics"/>tem non omnino completam, reperiri.<emph.end type="italics"/> E ora che la scoperta &egrave; fatta, e che <lb/>da quasi due secoli &egrave; stata esposta al pubblico dagli armadi segreti, possiamo <lb/>noi, fatti giudici con cognizione di causa, sentenziar che il Borelli s'era in&shy;<lb/>gannato a creder che la sua nuova Scienza della percossa fosse quella me&shy;<lb/>desima di Galileo, il quale avesse nel Dialogo riparato all'insufficienza del <lb/>suo primo giovanile giudizio. </s>

<s>Galileo invece non aveva fatto altro da vecchio <lb/>che confermare l'errore antico, assottigliando l'ingegno in speculazioni e in <lb/>esperienze, per dimostrar l'analogia che passa fra i momenti della gravit&agrave; <lb/>nelle macchine, e i momenti delle forze nella percossa, della quale sempre <lb/>ignor&ograve; le vere leggi ritrovate poi <emph type="italics"/>proprio marte<emph.end type="italics"/> dal Borelli: cosicch&egrave; insomma <lb/>il sesto dialogo aggiunto alle due Scienze nuove, che cost&ograve; tante lacrime al <lb/>mondo, niente altro &egrave; che uno splendido tessuto di paralogismi. </s>

<s>Cos&igrave; resulta <lb/>dal libero esame, che noi sottoporremo al giudizio dei nostri liberi Lettori, <lb/>dop'aver sodisfatta in loro la curiosit&agrave; di saper come mai avvenisse la felice <lb/>invenzione di ci&ograve;, che quelli stessi, i quali dovevano averlo in mano, cre&shy;<lb/>dettero e dissero irreparabilmente perduto: ond'&egrave; che dal suo principio al <lb/>termine, con pi&ugrave; spedito passo che sia possibile, ci studieremo di condurre <lb/>la nostra Storia. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Terminava Galileo il suo giovanile discorso <emph type="italics"/>Della forza della percossa<emph.end type="italics"/><lb/>con questa avvertenza: &ldquo; So che qui nasceranno ad alcuni delle difficolt&agrave; e <lb/>delle istanze, le quali per&ograve; con poca fatica si torranno di mezzo, e noi le <lb/>rimetteremo volontariamente tra i problemi meccanici, che in fine di que&shy;<lb/>sto discorso si aggiungeranno &rdquo; (Alb. </s>

<s>XI, 125). Fra i problemi meccanici <lb/>infatti, de'quali per&ograve; Galileo non lasci&ograve; che la semplice proposta, e qualche <lb/>frettoloso accenno alle loro soluzioni, se ne trovano alcuni relativi alla forza <lb/>della percossa, come i seguenti: &ldquo; Perch&egrave; le aste lunghe lanciate fanno mag&shy;<lb/>gior colpo. </s>

<s>&mdash; Perch&egrave; per far diversi effetti si cerchino diverse grandezze di <lb/>martello e lunghezza di manichi. </s>

<s>&mdash; Quando si voglia ficcar l'asta nel ma&shy;<lb/>glio, meglio succeder&agrave; percuotendo l'asta in terra, lasciando il maglio libero, <lb/>che se altri brancasse il maglio con la mano e percotesse con l'asta in terra &rdquo; <lb/>(Alb. </s>

<s>XIV, 321). </s></p><p type="main">

<s>Che siano veramente questi quei Problemi meccanici, accennati sulla fine <lb/>del citato <emph type="italics"/>Discorso,<emph.end type="italics"/> vien confermato dal veder che a risolverli s'invocano dal&shy;<lb/>l'Autore i medesimi principii. </s>

<s>&ldquo; Se quello, scriveva, sopra il quale si vuol <lb/>percotere, ceder&agrave; al percuziente con pari velocit&agrave; della sua, la percossa sar&agrave; <lb/>nulla. </s>

<s>&mdash; La forza dunque della percossa vien misurata dalla velocit&agrave; del per&shy;<lb/>cuziente sopra la cedenza del percosso &rdquo; (ivi): n&egrave; ci&ograve; vuol dir altro, se non <lb/>che la potenza e la resistenza stanno reciprocamente come le loro velocit&agrave;, <pb xlink:href="020/01/2499.jpg" pagenum="124"/>secondo che sempre accade in tutti gli altri meccanici strumenti. </s>

<s>Non si vede <lb/>per&ograve; come qui vengano a togliersi di mezzo le difficolt&agrave; e l&agrave; le istanze, che <lb/>potessero sovvenire alla mente di coloro, ne'quali si volevano persuadere cos&igrave; <lb/>fatti principii, e ci&ograve; s'intende essere avvenuto perch&egrave; rimasero que'mecca&shy;<lb/>nici Problemi un semplice proposito, abbandonato affatto da Galileo insieme <lb/>con le giovanili speculazioni della forza della percossa, le quali, quando tor&shy;<lb/>narono ad agitargli la mente, pens&ograve; anche a esporre il gi&agrave; maturo concetto <lb/>sotto pi&ugrave; nobile e splendida veste. </s></p><p type="main">

<s>L'occasione, che fece Galileo gi&agrave; vecchio ritornar sulle abbandonate gio&shy;<lb/>vanili speculazioni della percossa, apparisce manifesta da ci&ograve;, che si legge <lb/>nel IV dialogo, dove al Salviati, che terminava il suo lungo discorso col far <lb/>osservare i vari casi, e le varie condizioni di moto e di posizion del percosso, <lb/>che conferiscono a produrre pi&ugrave; o men gagliardo il colpo del proietto; il <lb/>Sagredo soggiunge: &ldquo; Il ricordar V. S. questi colpi e queste percosse mi ha <lb/>risvegliato nella mente un problema, o vogliam dire questione meccanica, <lb/>della quale non ho trovato appresso Autore alcuno la soluzione, n&egrave; cosa che <lb/>mi scemi la maraviglia, o almeno in parte mi quieti l'intelletto. </s>

<s>E il dub&shy;<lb/>bio e lo stupor mio consiste nel non restar capace onde possa derivare, e <lb/>da qual principio possa dipendere l'energia e la forza immensa, che si vede <lb/>consistere nella percossa, mentre col semplice colpo di un martello, che non <lb/>abbia peso maggiore di otto o dicci libbre, veggiamo superarsi resistenze tali, <lb/>le quali non cederanno al peso di un grave, che senza percossa vi faccia im&shy;<lb/>peto solamente calcando e premendo, bench&egrave; la gravit&agrave; di quello passi molte <lb/>centinaia di libbre &rdquo; (Alb. </s>

<s>XIII, 247). Che se fosse alcuno curioso di saper <lb/>con certezza il tempo, in cui le teorie dei proietti ricondussero Galileo alla <lb/>contemplazione degli effetti della percossa, potremmo sodisfarlo dicendo che fu <lb/>verso il 1634, nel Gennaio del qual anno aveva gi&agrave; concluso che <emph type="italics"/>qualun&shy;<lb/>que lieve percossa aveva forza infinita:<emph.end type="italics"/> conclusione che, annunziata all'Ag&shy;<lb/>giunti, rispondeva essere <emph type="italics"/>veramente mirabilissima &rdquo;<emph.end type="italics"/> (Alb. </s>

<s>X, 13). </s></p><p type="main">

<s>L'intenzione poi di proporre in dialogo, in quegli stessi discorsi intorno <lb/>alle due Scienze nuove, quel che aveva quarant'anni prima pensato di ri&shy;<lb/>durre fra i Problemi meccanici, &egrave; apertamente espressa dallo stesso Salviati, <lb/>il quale cos&igrave; rispondeva al Sagredo, mostratosi desiderosissimo di sapere quel <lb/>che intorno alla forza immensa della percossa avesse Galileo speculato di <lb/>nuovo: &ldquo; E perch&egrave; omai so che la curiosit&agrave; di V. S. volentieri sentirebbe <lb/>quei pensieri, che si allontanano dall'opinabile, non aspetter&ograve; la sua richie&shy;<lb/>sta, ma le d&ograve; parola che, spedita che averemo la lettura di questo trattato <lb/>dei proietti, gli spiegher&ograve; tutte quelle fantasie, o vogliam dire stravaganze, che <lb/>dai discorsi dell'Accademico mi son rimaste nella memoria &rdquo; (Alb. </s>

<s>XIII, 247). </s></p><p type="main">

<s>Sembrerebbe di qui che il primo pensiero fosse stato quello di soggiun&shy;<lb/>gere il trattato della percossa in questo stesso dialogo quarto, dopo quello <lb/>dei proietti, al quale si voleva aggiungere, come complemento dei moti pa&shy;<lb/>rabolici e dell'arte di dirigere i tiri, il discorso dell'uso delle catenuzze. </s>

<s>Ma <lb/>perch&egrave; la giornata, bench&egrave; protratta a sera, non poteva a tanto colloquio non <pb xlink:href="020/01/2500.jpg" pagenum="125"/>riuscire scarsa, a Simplicio, che chiedeva fosse mantenuta la data promessa <lb/>d'esplicare qual sia l'utilit&agrave;, che dalle catenuzze si pu&ograve; ritrarre, e dopo que&shy;<lb/>sto arrecare le speculazioni che si diceva essere state fatte dall'Accademico <lb/>intorno alla forza della percossa; il Salviati cos&igrave; rispondeva: &ldquo; Assai per <lb/>questo giorno ci siamo occupati nelle contemplazioni passate: l'ora, che non <lb/>poco &egrave; tarda, non ci basterebbe a gran segno per disbrigarci dalle nominate <lb/>materie: per&ograve; differiremo il congresso ad altro tempo pi&ugrave; opportuno &rdquo; (ivi, <lb/>pag. </s>

<s>266). </s></p><p type="main">

<s>Ci&ograve; significava che in un altro-Dialogo a parte si sarebbe trattato della <lb/>forza della percossa, e dell'utilit&agrave; delle catenuzze negli usi ballistici, di che <lb/>era incominciato a farsi il disteso, quando gi&agrave; l'Elzevirio aveva finito di stam&shy;<lb/>pare tutto quel che riguardava i proietti. </s>

<s>Ma perch&egrave;, alle difficolt&agrave; dell'ar&shy;<lb/>gomento aggiungendosi quelle della vista, che ogni giorno pi&ugrave; si affievoliva, <lb/>Galileo conosceva che troppo penoso, a voler dare l'opera compiuta, sarebbe <lb/>stato per s&egrave; e per gli editori l'indugio; prese risoluzione di pubblicare in&shy;<lb/>tanto i quattro dialoghi, aspettando per aggiungervi l'altro l'occasione, che <lb/>si credeva prossima, di una ristampa. </s>

<s>La difficolt&agrave; dell'argomento si studiava <lb/>di superarla con la meditazione pi&ugrave; intensa e, servendosi della mano di Marco <lb/>Ambrogetti, suppliva in parte all'insufficienza della sua propria vista, Cos&igrave;, <lb/>il Dialogo, verso la fine dell'Ottobre del 1638, era stato condotto infino a <lb/>quel punto, in cui il Salviati termina il suo discorso intorno all'effetto, che <lb/>nasce, quando negli strettoi, allo spingere senza percossa, s'aggiunge una <lb/>percossa, facendo un composto d'ambedue (Alb. </s>

<s>XIII, 329). La proposta del <lb/>Viviani intorno alla dimostrazione del principio supposto divag&ograve; Galileo dal&shy;<lb/>l'intrapreso argomento, ma che avesse intenzione di ritornarci sopra, per ri&shy;<lb/>durlo ad effetto, apparisce da ci&ograve; che scriveva il d&igrave; primo Agosto 1639 al <lb/>Baliani del migliorare e ampliare lo scritto e pubblicato da s&egrave;, infino a quel <lb/>tempo, intorno al moto &ldquo; con aggiungervi, altre speculazioncelle, ed in par&shy;<lb/>ticolare quella attinente alla forza della percossa, nell'investigazione della <lb/>quale ho consumate molte centinaia e migliaia di ore, e finalmente ridottala <lb/>ad assai facile esplicazione, sicch&egrave; altri, in manco di mezz'ora di tempo, potr&agrave; <lb/>restarne capace. </s>

<s>E qui voglio tornare a dirgli che non ho memoria alcuna <lb/>di quelle scritture, che Ella dice essergli state mandate gi&agrave; come pensieri <lb/>del Victa, da me affermatogli essere miei: epper&ograve; desidererei di rinfrescarmi <lb/>col suo favore la memoria, ed in particolare dello scritto intorno alla per&shy;<lb/>cossa, il quale non pu&ograve; essere se non imperfetto, essendoch&egrave; quello, nel quale <lb/>io mi quieto, non &egrave; stato da me ritrovato salvo che da pochi anni in qua, <lb/>n&egrave; so io di averne dato fuori intera notizia &rdquo; (Lettere pel trecent. </s>

<s>natalizio <lb/>cit., pag. </s>

<s>46). </s></p><p type="main">

<s>Galileo dunque aveva dimenticato affatto quel suo <emph type="italics"/>Discorso primo ed <lb/>antico,<emph.end type="italics"/> ch'ei volle rivendicare dal Vieta, a cui si attribuiva, bench&egrave; lo te&shy;<lb/>nesse per cosa imperfetta, e da non farne perci&ograve; nessun conto. </s>

<s>Dicendo poi <lb/>che non s'acquietava in altro, che nelle cose ritrovate da pochi anni in qua, <lb/>mostrava di compiacersi del nuovo dialogo, di cui diceva di non averne dato <pb xlink:href="020/01/2501.jpg" pagenum="126"/>fuori a nessuno notizia, e incorava una dolce speranza d'aver presto a darlo <lb/>compiuto, premettendolo, perch&egrave; pi&ugrave; gli premeva, e contro le prime inten&shy;<lb/>zioni, al trattato delle catenuzze, bench&egrave; pi&ugrave; immediatamente questo si rife&shy;<lb/>risse ai proietti. </s>

<s>Col Viviani per&ograve;, com'apparisce dal primo di questi capitoli, <lb/>s'intrattenne in migliorare e in correggere le parti gi&agrave; stampate, piuttostoch&egrave; <lb/>in aggiungervene delle nuove, e, venuto il Torricelli, si sa bene che in tut&shy;<lb/>t'altro fu impiegato il tempo, che in speculare e scrivere sulla forza della <lb/>percossa. </s></p><p type="main">

<s>Certo una gran curiosit&agrave; ci frugherebbe di sapere il fine, perch&egrave; Gali&shy;<lb/>leo tenesse cos&igrave; gelosamente occulta la notizia di que'fogli scritti intorno alla <lb/>detta forza, non a solo il Viviani, ma allo stesso Torricelli, il quale, mentre <lb/>da tutti si credeva esser venuto a dispensare i tesori raccolti in Arcetri, si <lb/>ud&igrave; con grande meraviglia introdursi nell'Accademia, con queste parole, a <lb/>leggere intorno alle propriet&agrave; e agli effetti delle percosse e degli urti: &ldquo; Se <lb/>la fortuna non avesse invidiata la gloria di questo scoprimento al nostro se&shy;<lb/>colo, gi&agrave; era certo che il famosissimo Galilei lavorava questa gioia, per arric&shy;<lb/>chirne il monile della toscana Filosofia. </s>

<s>Molte cose nondimeno da'suoi scritti <lb/>e da'suoi ragionamenti familiari si raccoglievano intorno alla percossa, e due <lb/>fra le altre: cio&egrave; una, l'esperienza di certi archi, con cui s'ingegnava di <lb/>dimostrare l'immensit&agrave; di detta forza: l'altra erano epiteti iperbolici, coi <lb/>quali dava manifestamente a divedere ch'egli avesse fermo concetto nell'animo <lb/>che la forza della percossa fosse infinita &rdquo; (Lez. </s>

<s>accad. </s>

<s>cit., pag. </s>

<s>68): e sog&shy;<lb/>giungeva esser venuto per rintracciare col proprio ingegno le vestigia di quelle <lb/>notizie, raccolte a voce e lette in alcuni frammenti rimasti degli scritti di <lb/>Galileo, i quali frammenti, come si confermer&agrave; dalle cose che saremo per <lb/>dire, si riducevano a quelli, che si leggono dalla linea 29, a pag. </s>

<s>330, infino <lb/>alla fine del VI dialogo stampato nella edizione completa dell'Alb&egrave;ri. </s></p><p type="main">

<s>Del Dialogo incominciato, disteso con l'aiuto manuale dell'Ambrogetti, <lb/>e condotto al punto che dicemmo di sopra, non ebbe dunque notizia dal suo <lb/>ospitatore nemmeno il Torricelli, intorno al qual fatto rimane insodisfatta la <lb/>nostra curiosit&agrave; di sapere per qual fine, invece di proseguire addiritto, diver&shy;<lb/>tisse Galileo il valido aiuto del suo ospitato intorno a un altro argomento, che, <lb/>se non era estraneo, non si riferiva per&ograve;, se non che accidentalmente, al sog&shy;<lb/>getto dei discorsi e delle dimostrazioni del moto. </s>

<s>Forse si riprometteva il <lb/>buon Vecchio pi&ugrave; lunga vita, la quale venutagli inaspettatamente meno, fece <lb/>s&igrave; che, fra gli altri scritti postumi, rimanesse anche quello, al quale aveva <lb/>dato mano, inconsapevole di ci&ograve; che scriveva, l'Ambrogetti. </s></p><p type="main">

<s>Colui che, avendone intelligenza, ebbe primo a veder quegli scritti, fu <lb/>il figliolo ed erede dell'Autore Vincenzio, il quale, dettandogliene, fece pren&shy;<lb/>derne copia al Viviani, ed egli sulla stessa copia scrisse poi questo titolo, e <lb/>questa nota: &ldquo; Ultimo congresso del signor Galileo intorno alla forza della <lb/>percossa, datomi a copiare dal signor Vincenzio Galilei, dopo la morte del <lb/>Padre. </s>

<s>Questo non &egrave; stampato, ma l'originale si trova appresso gli eredi di <lb/>detto Vincenzio, e non mi sovviene se sia di mano del medesimo signor Ga-<pb xlink:href="020/01/2502.jpg" pagenum="127"/>lileo, oppure di Marco Ambrogetti, come piuttosto io mi credo, o se fosse in <lb/>foglio o in quarto. </s>

<s>Ne lasciai di questo pigliar copia al padre Francesco delle <lb/>Scuole pie, cio&egrave; a don Famiano Michelini, in tempo che egli abitava al por&shy;<lb/>tone di Annalena, ed egli poi mi disse averne dato altre copie &rdquo; (Nelli, <lb/>Filoa IX, fol. </s>

<s>54). </s></p><p type="main">

<s>Sembra per&ograve; che fossero queste copie poco diffuse, e che quelli stessi, <lb/>i quali le presero, le tenessero fra le loro carte dimenticate, intantoch&egrave;, <lb/>nel 1665, nessuno in Toscana, non eccettuato lo stesso principe Leopoldo, <lb/>sapeva nulla di quest'ultimo congresso intorno alla percossa, ritrovato fra gli <lb/>scritti postumi di Galileo. </s>

<s>Il Borelli perci&ograve;, per rintracciare anch'egli col pro&shy;<lb/>prio ingegno le vestigia di quelle cognizioni, che si lamentavano da tutti con <lb/>grave danno perdute, aveva seco stesso proposto di scrivere il trattato <emph type="italics"/>De vi per&shy;<lb/>cussionis,<emph.end type="italics"/> del qual proposito dava cos&igrave; avviso, per lettera del d&igrave; 6 Aprile 1665 <lb/>da Pisa, al principe Leopoldo: &ldquo; Sono entrato a speculare la natura e la pro&shy;<lb/>priet&agrave; della forza della percossa, soggetto intorno al quale il gran Galileo vi <lb/>specul&ograve; gran tempo, ma non ci lasci&ograve; nulla in scritto, se non che tal forza <lb/>foss&egrave; infinita. </s>

<s>Ora, se la passione non m'inganna, mi pare d'aver trovato il <lb/>capo di questo bandolo molto intrigato, e procurato di perfezionare e poi <lb/>scrivere questi concetti, se pure mi riuscir&agrave; cosa buona &rdquo; (MSS. Cim., T. XVIII, <lb/>fol. </s>

<s>152). </s></p><p type="main">

<s>Il Principe mandava, per lettera autografa del d&igrave; 9 Maggio appresso, la <lb/>bella notizia a Roma a Michelangiolo Ricci, rallegrandosi nella speranza che <lb/>s'avesse a ristorare la toscana Filosofia della impotenza di Galileo a disten&shy;<lb/>dere i suoi concetti, al qual fine soggiungeva di aver inutilmente condotto a <lb/>Firenze il Torricelli (ivi, T. XXIII, fol. </s>

<s>113): e il Ricci rispondeva cos&igrave; due <lb/>settimane dopo, consolandosi anch'egli che al danno irreparabile s'appre&shy;<lb/>stasse qualche ristoro: &ldquo; Si fece gran perdita con la morte del signor Ga&shy;<lb/>lileo, e specialmente della dimostrazione, tanto stimata da lui e da tutti gli <lb/>intendenti, della forza della percossa: materia egualmente ardua e curiosa, <lb/>per la quale ha ingegno molto proporzionato il signor Borelli &rdquo; (ivi, T. XVIII, <lb/>fol. </s>

<s>188). </s></p><p type="main">

<s>Il Viviani, che si sentiva continuo venire intorno agli orecchi il mormo&shy;<lb/>rio di questi lamenti, reprimeva i desideri, e mortificava la piet&agrave;, che lo <lb/>avrebbe consigliato d'uscire in pubblico a consolarli: e poi, dopo aver ritratto <lb/>lo sguardo da quella copia, che aveva presa a dettatura dal signor Vincen&shy;<lb/>zio, sogghignava, leggendo cos&igrave; nel proemio al libro <emph type="italics"/>De vi percussionis:<emph.end type="italics"/><lb/>&ldquo; Cum autem hoc Galileus postremis suae vitae annis scripsisset, speraba&shy;<lb/>tur post eius mortem in armario secretiori, inter alia scripta, hanc disserta&shy;<lb/>tionem calamo exaratam, saltem non omnino completam reperiri debere: sed, <lb/>non sine amicorum tristitia, nec inter schedulas reperta est pagella, quae hoc <lb/>titulo insigneretur, ut Galilei haeredes mihi retulerunt, Idipsum testatus est <lb/>clarissimus Torricellius qui, ut audio, conatus est vesligia aliqua huius co&shy;<lb/>gnitionis inquirere, in suis lectionibus calamo exaratis,.... et post eius mor&shy;<lb/>tem stetit Florentiae de hac re altum silentium &rdquo; (pag. </s>

<s>IX, X). </s></p><pb xlink:href="020/01/2503.jpg" pagenum="128"/><p type="main">

<s>Le ragioni di quest'alto silenzio non erano di defraudare la scienza, n&egrave; <lb/>d'invidiare alla gloria di Galileo, cose tanto aliene dall'animo del Viviani, <lb/>ch'ebbe a farsi una gran violenza di tenere occulta la preziosa notizia, la <lb/>quale voleva concorresse fra le altre come pietra monumentale all'edifizio, <lb/>che meditava di erigere al suo grande Maestro, affinch&egrave; fosse meglio cono&shy;<lb/>sciuto dagli invidiosi Francesi, dedicando l'opera al loro re Luigi XIV. </s>

<s>Il <lb/>timore di essere prevenuto, come gli avvenne di fatto riguardo al trattato <lb/>delle resistenze, lo consigli&ograve; a tenere quell'alto silenzio anche con lo stesso <lb/>principe Leopoldo, e intanto, per illustrare il Dialogo che, comparendo nella <lb/>vita e nelle opere di Galileo inaspettato, avrebbe con sorpresa grande d&igrave; tutto <lb/>il mondo tolto via le lunghe e antiche querele; il Viviani pensava di dimo&shy;<lb/>strare pi&ugrave; chiaramente certe cose, e inventava e descriveva strumenti nuovi, <lb/>per meglio confermar quelle, che credeva ammirabili verit&agrave;, insegnate intorno <lb/>al modo e alle ragioni della percossa in persona del Salviati. </s>

<s>E perch&egrave; insieme <lb/>coi laboriosi commenti avessero i Lettori sott'occhio pi&ugrave; fedele e completo il <lb/>testo, essendo gi&agrave; di Vincenzio Galilei rimasto erede il figlio Cosimo, appresso <lb/>al quale si ritrovavano le carte manoscritte dell'avo, si rivolse a esso Cosimo <lb/>per collazionar la copia con l'originale, e per esaminar meglio, ci&ograve; che non <lb/>aveva potuto fare, quando alla presenza del detto signor Vincenzio, che te&shy;<lb/>neva quell'originale in mano, scriveva a dettatura; se altre carte ci fossero, <lb/>in cui si leggessero della percossa pensieri sparsi o interlocuzioni staccate. </s></p><p type="main">

<s>Trov&ograve;, cos&igrave; diligentemente collazionando, essere la sua copia mancante <lb/>di un passo, che il dettatore dovette aver saltato per inavvertenza: e per ram&shy;<lb/>memorarsi il luogo e il discorso, che voleva essere aggiunto, scriveva cos&igrave; in <lb/>una sua nota, che si legge a tergo del fol. </s>

<s>16, P. V, T. IV, de'MSS di Ga&shy;<lb/>lileo: &ldquo; Nel congresso ultimo mio manoscritto, a c. </s>

<s>8, dopo il nono verso, <lb/>deve seguitare cos&igrave;, secondo l'originale del Galileo, alle parole che dicono: <lb/><emph type="italics"/>computandovi il primo braccio, che questo scese libero e solo<emph.end type="italics"/> &mdash; SAGR. </s>

<s>Io <lb/>veramente inclino a credere questo stesso, etc. </s>

<s>&rdquo; (Alb. </s>

<s>XIII, dalla lin. </s>

<s>22-37 <lb/>della pag. </s>

<s>321). Trov&ograve; altres&igrave;, come s'aspettava, alcuni pensieri sparsi, il <lb/>prinmo de'quali trascriveva nel Tomo, e sopra la prima faccia del foglio sopra <lb/>citato, premettendovi questa avvertenza: <emph type="italics"/>&ldquo; Da un foglio originale del signor <lb/>Galilco, di sua mano, tra le cose della percossa.<emph.end type="italics"/> In ogni mobile, che deva <lb/>esser mosso violentemente, pare che siano due spezie di resistenza, etc. </s>

<s>&rdquo; <lb/>(Alb. </s>

<s>XIII, dalla linea 33-37 della pag. </s>

<s>329, e dalla 1-23 della pag. </s>

<s>seguente). <lb/>Altri simili pensieri trov&ograve; pure sparsi in alcune carte slegate, ch'egli dili&shy;<lb/>gentemente trascrisse a c. </s>

<s>37-41 del T. III, P. VI, de'citati MSS. galileiani, <lb/>forse con quell'ordine, che aveva dato prima a loro il Torricelli, e con que&shy;<lb/>sta avvertenza in principio: <emph type="italics"/>&ldquo; Roba copiata da un esemplare del Galileo, <lb/>che si trovava in mano del &sgrave;ignor Vincenzio suo figliolo, di mano di que&shy;<lb/>sto, e tutto appresso del signor Cosimo.<emph.end type="italics"/> Il momento del grave nell'alto della <lb/>percossa, etc. </s>

<s>&rdquo; (Alb. </s>

<s>XIII, dalla linea 29-37 della pag. </s>

<s>330, infino alla fine). </s></p><p type="main">

<s>Questi pensieri sparsi gli aggiunse il Viviani in fine alla copia del Dia&shy;<lb/>logo, che gli aveva dettato il signor Vincenzio, e ch'era quello incominciato <pb xlink:href="020/01/2504.jpg" pagenum="129"/>dallo stesso Galileo a distendere con l'aiuto dell'Ambrogetti, il termine del <lb/>qual Dialogo, lasciato a mezzo, &egrave; nell'interlocuzion del Salviati, che termina <lb/>alla linea 32 della pag. </s>

<s>329 nella citata edizione completa dell'Alb&egrave;ri. </s>

<s>Cos&igrave;, <lb/>sull'originale completata la copia e corretta, la custodiva gelosamente il Vi&shy;<lb/>viani per pubblicarla a suo tempo fra le opere postume di Galileo, dopo il <lb/>trattato delle Resistenze. </s>

<s>Andata l'intenzione fallita, per le avventure da noi <lb/>narrate nel cap. </s>

<s>VIII del Tomo precedente, rimase, fra le altre carte scritte <lb/>in simile soggetto dal Viviani, abbandonato anche il Dialogo della percossa. </s>

<s><lb/>Avrebbe potuto cogliere nel 1674 l'occasione di pubblicarlo nel dare, dopo <lb/>la <emph type="italics"/>Scienza delle proporzioni,<emph.end type="italics"/> quel suo <emph type="italics"/>Ragguaglio delle ultime opere del <lb/>Galileo,<emph.end type="italics"/> ma erano a quel tempo usciti alla luce, non il libro solo del Bo&shy;<lb/>relli, ma il trattato del Wallis, dai quali manifestamente si concludeva la fal&shy;<lb/>sit&agrave; del concetto galileiano intorno alla natura della forza della percossa. </s>

<s>Per <lb/>non volgere perci&ograve; in biasimo le lodi, che dava al suo Maestro il mondo, imma&shy;<lb/>ginandosi ch'egli avesse speculate le verit&agrave; recondite e maravigliose, ch'egli <lb/>stesso diceva; fu contento il Viviani a fare un semplice cenno del ritrovarsi ap&shy;<lb/>presso di lui quel che da tutti si rimpiangeva, con irreparabile danno, perduto. </s></p><p type="main">

<s>Narra come, rimasto erede di Galileo il figliolo di lui Vincenzio, col quale <lb/>seguit&ograve; a intrattenere l'antica familiare amicizia; gli dettasse, perch&egrave; ne pi&shy;<lb/>gliasse copia, tre diverse scritture, ritrovate inedite fra le altre carte di suo <lb/>padre. </s>

<s>La prima conteneva il disteso di sei Operazioni astronomiche, e la <lb/>seconda consisteva in dodici Problemi e Questioni spezzate. </s>

<s>&ldquo; La terza scrit&shy;<lb/>tura dettatami, prosegue cos&igrave; a narrare lo stesso Viviani, &egrave; un altro princi&shy;<lb/>pio di nuovo congresso intitolato <emph type="italics"/>ultimo,<emph.end type="italics"/> forse cos&igrave; detto dal Galileo, avanti <lb/>che gli venisse concetto di ridurre anche le postille a'suoi oppositori in forma <lb/>di dialogo. </s>

<s>In questo congresso il Galileo introduce al solito per interlocutori <lb/>il Salviati ed il Sagredo, escludendo Simplicio, e ponendo per terzo il signor <lb/>Paolo Aproino, stato gi&agrave; suo uditore delle Matematiche in Padova. </s>

<s>Tal prin&shy;<lb/>cipio &egrave; disteso in dialogo, in sei fogli in cirea, dove si spiegano alcune spe&shy;<lb/>rienze fatte dal Galileo fin ne'tempi ch'egli era col&agrave; lettore, allora che an&shy;<lb/>dava investigando la misura della forza della percossa, che in ultimo egli <lb/>consider&ograve; come infinita, e questa materia, dopo spiegata l'esperienza, voleva <lb/>il Galileo trattar matematicamente in tutto il restante del Congresso, come <lb/>terza Scienza, dopo le due gi&agrave; promosse da lui medesimo, e con questa finir <lb/>di pubblicare il rimanente delle sue pi&ugrave; elaborate fatiche, quale sarebbe stata <lb/>questa, intorno alla quale egli medesimo disse aver consumato molte migliaia <lb/>di ore speculando e filosofando, ed averne in fine conseguito cognizioni lon&shy;<lb/>tane da'nostri primi concetti, e per&ograve; nuove e per la loro novit&agrave; ammirande &rdquo; <lb/>(Scienza univ. </s>

<s>delle proporz. </s>

<s>cit., pag. </s>

<s>103). </s></p><p type="main">

<s>Divagato il Viviani di qui un poco il discorso in deplorare la perdita immensa <lb/>delle preziose speculazioni, rimaste entro s&igrave; ricca miniera d'un tanto Filosofo <lb/>e Matematico, e consolatosi che fosse venuto a ristorare il danno, per ci&ograve; che <lb/>s'appartiene alla percossa, il celebratissimo Gian Alfonso Borelli, che egre&shy;<lb/>giamente tratt&ograve; il subietto nella nuova opera sua; &ldquo; ma tornando, poi sog-<pb xlink:href="020/01/2505.jpg" pagenum="130"/>giunge, alla copia ch'io mi ritrovo della scrittura intitolata <emph type="italics"/>Ultimo congresso,<emph.end type="italics"/><lb/>questa, in alcuni luoghi dov'io aveva qualche difficolt&agrave;, mi fu in aiuto a ri&shy;<lb/>scontrarla col proprio suo originale il molto reverendo signor Cosimo, figliolo <lb/>del suddetto signor Vincenzio, e degno nipote del Galileo &rdquo; (ivi, pag. </s>

<s>104). </s></p><p type="main">

<s>Coloro, ch'ebbero a leggere cos&igrave; fatte notizie, pensarono che quest'ul&shy;<lb/>timo congresso, di cui qui parla il Viviani, doveva ritrovarsi postumo fra i <lb/>manoscritti, de'quali sapevano essere stato legittimo erede il nepote di lui <lb/>Jacopo Panzanini. </s>

<s>Tommaso Bonaventuri perci&ograve;, che del Panzanini era amico, <lb/>lo richese del detto manoscritto, per aggiungerlo, insieme con quell'altro <lb/>delle proporzioni, ai quattro dialoghi delle due Scienze nuove, nella edizione, <lb/>che nel 1718 stava preparando delle opere di Galileo. </s>

<s>La pubblicazione per&ograve; <lb/>non fu fatta col criterio, che sarebbesi desiderato superiore a quello della <lb/>maggior parte degli editori toccati in sorte al grand'Uomo. </s>

<s>Superficialmente <lb/>leggendo <emph type="italics"/>Principio della quinta Giornata,<emph.end type="italics"/> scritto in capo al dialogo delle <lb/>proporzioni, e <emph type="italics"/>Ultimo congresso<emph.end type="italics"/> intitolato quello della percossa, non dubit&ograve; <lb/>il Bonaventuri di posporre in ordine questo a quello, non badando all'ana&shy;<lb/>cronismo, in che avrebbero offeso i Lettori pi&ugrave; attenti. </s>

<s>Bastava del resto aver <lb/>portata questa attenzione sopra le linee di stampa, con le quali incominciano <lb/>le due scritture, per avvedersi che il dialogo della percossa si rappresenta <lb/><emph type="italics"/>quindici giorni<emph.end type="italics"/> dopo il colloquio tenuto intorno ai proietti (Alb. </s>

<s>XIII, 306), <lb/>e quello delle proporzioni con l'<emph type="italics"/>interposizione di qualche anno<emph.end type="italics"/> (ivi, pag. </s>

<s>288). </s></p><p type="main">

<s>La rappresentanza del dramma apparisce dunque nella prima edizione <lb/>fiorentina turpemente deformata, per sola colpa dell'editore, il quale avrebbe <lb/>dovuto pensare, qualunque si fosse l'autorit&agrave; del titolo, che la prima auto&shy;<lb/>rit&agrave; era quella della ragione, la quale avrebbegli suggerito che l'avvenimento <lb/>dopo quindici giorni precede a quello dopo qualche anno. </s>

<s>Vero &egrave; bene che <lb/>non era il nodo estricabile, se non a colui, che avesse avuto le necessarie <lb/>notizie storiche; intorno a che non sappiamo se il Bonaventuri, che poteva <lb/>avere a mano, come noi i documenti da rintracciarle, sia in tutto meritevole <lb/>di scusa: imperocch&egrave; il titolo di <emph type="italics"/>Giornata quinta<emph.end type="italics"/> fu posto al Dialogo delle <lb/>proporzioni, come si fece osservare altrove, quando ancora il Torricelli non <lb/>sapeva che Galileo avesse incominciato a stendere il Dialogo della percossa: <lb/>e il titolo di <emph type="italics"/>Congresso ultimo<emph.end type="italics"/> fu messo a questo stesso Dialogo della per&shy;<lb/>cossa, quando Galileo non pensava ancora di lasciarlo a mezzo, per saltare <lb/>a scriverne, con l'aiuto del Torricelli, un altro d'argomento molto diverso. </s></p><p type="main">

<s>Avrebbero queste ragioni, non solo dato la licenza o il diritto, ma im&shy;<lb/>posto il dovere all'editore di mettere, in luogo della Giornata quinta, il trat&shy;<lb/>tato della percossa, e quello delle proporzioni in ultimo luogo, non ostante <lb/>il titolo scritto dal Torricelli e da Galileo. </s>

<s>Ma perch&egrave;, come spesso segue, <lb/>l'altrui autorit&agrave; prevalse al proprio giudizio, s'incorse in quella deformit&agrave;, <lb/>la quale tuttavia resta, e rester&agrave; nelle opere galileiane indelebilmente impressa, <lb/>come le deformit&agrave; del corpo, che si contraggono dalla natura. </s></p><p type="main">

<s>Tale &egrave; la storia della pubblicazione del Dialogo della percossa, che il Vi&shy;<lb/>viani riguardava come una terza Scienza nuova. </s>

<s>E tale pure aspettavasi che <pb xlink:href="020/01/2506.jpg" pagenum="131"/>gli dovesse riuscire al giudizio anche il Borelli, il quale congetturava che, <lb/>non avendo trovato riscontrar le leggi della comunicazione dei moti con i <lb/>gi&agrave; ammessi giovanili principii, <emph type="italics"/>ab hisce difficultatibus excitatus<emph.end type="italics"/> si fosse <lb/>volto Galileo da vecchio a professar della natura della percossa pi&ugrave; sane dot&shy;<lb/>trine. </s>

<s>Non era questa per&ograve; che una dolce lusinga, perch&egrave; della promessa <lb/>nuova Scienza della percossa annunziava il Sagredo cos&igrave; la conclusione, a <lb/>mezzo alla quarta Giornata: &ldquo; Io vorrei pur trovar modo di misurar la forza <lb/>di questa percossa, la quale non penso per&ograve; che sia infinita; anzi stimo <lb/>ch'ell'abbia il suo termine, da potersi pareggiare, e finalmente regolare con <lb/>altre forze di gravit&agrave; prementi o di leve o di viti o di altri strumenti mec&shy;<lb/>canici, dei quali io a sodisfazione resto capace della moltiplicazione della forza <lb/>loro &rdquo; (Alb. </s>

<s>XIII, 247). </s></p><p type="main">

<s>Poteva di qui argomentare il Borelli che Galileo da vecchio non aveva <lb/>trovata nessuna difficolt&agrave; a professare le antiche dottrine, seguitando a com&shy;<lb/>parare il moto del martello che percote coi pesi morti sostenuti sul declivio <lb/>dei piani, o sui bracci delle leve. </s>

<s>Vero &egrave; bene che ivi il Salviati annunzia <lb/>tre proposizioni, che furono poi dimostrate nel libro del Borelli, ma essendo <lb/>di natural senso comune, e di semplice fatto, i principii dai quali si conclu&shy;<lb/>dono quelle stesse proposizioni; non si poteva congetturare di l&igrave; che Galileo <lb/>si fosse almeno introdotto alla scoperta delle vere leggi, dalle quali si regola <lb/>la forza della percossa. </s></p><p type="main">

<s>Le tre dette proposizioni corrispondono alla XXX, XXXI e XXXIV <emph type="italics"/>De <lb/>vi percussionis,<emph.end type="italics"/> ma Galileo le pronunzia com'evidenti per s&egrave; medesime. </s>

<s>Chi <lb/>potrebbe infatti metter dubbio intorno alla prima, che dice: &ldquo; Colui che corre <lb/>per ferir con una lancia il suo nemico, se nel sopraggiungerlo accader&agrave; che <lb/>quello si muova, fuggendo con pari velocit&agrave;, non far&agrave; colpo, e l'azione sar&agrave; <lb/>un semplice toccar senza offendere &rdquo; (Alb. </s>

<s>XIII, 245): o cercar dimostrazione <lb/>della seconda, che immediatamente cos&igrave; si soggiunge: &ldquo; Ma se la percossa <lb/>verr&agrave; ricevuta in un soggetto, che non in tutto ceda al percuziente, ma so&shy;<lb/>lamente in parte; la percossa dannegger&agrave;, ma non con tutto l'impeto, ma <lb/>solo con l'eccesso della velocit&agrave; di esso percuziente sopra la velocit&agrave; della <lb/>ritirata e cedenza del percosso? </s>

<s>&rdquo; (ivi, pag. </s>

<s>246). </s></p><p type="main">

<s>La terza proposizione che da Galileo s'annunzia: &ldquo; Quando il percosso <lb/>si movesse con moto contrario verso il percuziente, il colpo e l'incontro si <lb/>farebbe tanto pi&ugrave; gagliardo, quanto le due velocit&agrave; contrarie unite son mag&shy;<lb/>giori, che la sola del percuziente &rdquo; (ivi); sembra che avesse bisogno d'esser <lb/><figure id="id.020.01.2506.1.jpg" xlink:href="020/01/2506/1.jpg"/></s></p><p type="caption">

<s>Figura 42.<lb/>dichiarata con qualche discorso, come il <lb/>Borelli fa nella detta sua XXXIV: ma <lb/>basta fare una semplice riflessione per <lb/>riconoscerla vera. </s>

<s>Suppongansi per esem&shy;<lb/>pio due corpi A e B (fig. </s>

<s>42) che, venen&shy;<lb/>dosi incontro, si urtano in D con le ve&shy;<lb/>locit&agrave; CD, DF: &egrave; chiaro che l'urto ricevuto dal corpo B in D, per essergli <lb/>il corpo A venuto incontro da C, &egrave; quel medesimo che riceverebbe, se fosse <pb xlink:href="020/01/2507.jpg" pagenum="132"/>an dato a percotere nel medesimo corpo A, rimasto immobile in C, con la <lb/>e locit&agrave; FC. </s></p><p type="main">

<s>Da queste verit&agrave; non era dunque promossa la scienza, e tanto meno era <lb/>promossa da ci&ograve;, che ivi appresso il Salviati soggiunge della percossa obli&shy;<lb/>qua, la quale si dice dover esser pi&ugrave; debole della diretta, <emph type="italics"/>e pi&ugrave; e pi&ugrave; se&shy;<lb/>condo la maggiore obliquit&agrave;<emph.end type="italics"/> (Alb. </s>

<s>XIII, 246), ossia secondo gli angoli del&shy;<lb/>l'incidenza. </s>

<s>Da nessuna parte insomma aveva intorno a ci&ograve; progredito il <lb/>Salviati dei Dialoghi nuovi, applicando all'urto dei corpi ponderosi quel falso <lb/>teorema, ne'primi dialoghi pronunziato intorno alla luce, dalla quale vengono <lb/>le superficie illuminate pi&ugrave; o meno, <emph type="italics"/>secondo che i raggi illuminanti vi ca&shy;<lb/>scano sopra pi&ugrave; o meno obliquamente<emph.end type="italics"/> (Alb. </s>

<s>I, 91). Se lo sviscerato osse&shy;<lb/>quio perci&ograve;, e il desiderio di magnificar tutto ci&ograve; che si riferiva al Maestro <lb/>non avessero fatto passare il Borelli sopra questi, che dalle cose dimostrate <lb/>nel suo proprio libro apparivano errori manifesti, non sarebbesi lusingato <lb/>d'aver dovuto vedere, se la sorte non l'invidiava, aggiunta alle altre due <lb/>nuove la terza scienza della percossa. </s>

<s>Ma le lusinghe non hanno oramai pi&ugrave; <lb/>potere sopra di noi, fatti certi de'pensieri di Galileo, sopra i quali vogliamo <lb/>dare una breve scorsa, per confermare quel che si diceva: non essere cio&egrave; <lb/>per altro scritto il Dialogo, che per rimovere le difficolt&agrave; e le istanze nate <lb/>in chi, nella <emph type="italics"/>Scienza meccanica,<emph.end type="italics"/> avesse letto il primo giovanile. </s>

<s>Discorso. </s></p><p type="main">

<s>Incomincia infatti l'Aproino a rivelare le speculazioni dell'Accademico, <lb/>le quali tendevano a questo principalmente: a dimostrare cio&egrave; che, come <lb/>nelle altre macchine, cos&igrave; nell'operazione della percossa interviene il movi&shy;<lb/>mento del percuziente congiunto con la sua velocit&agrave; contro il movimento del <lb/>resistente, ed il suo poco o molto dovere esser mosso; ond'essendo simili i <lb/>modi dell'operare, simili anco saranno del percotere e del sollevar pesi le <lb/>ragioni delle misure. </s>

<s>Fu dall'intenzione di dimostrar ci&ograve; che si condusse, per <lb/>prima cosa, a immaginar l'esperienza della stadera, che da una parte risente <lb/>l'urto fatto da un filo d'acqua cadente gi&ugrave; da una secchia sul fondo di un'al&shy;<lb/>tra simile secchia a lei sottoposta, e dall'altra sostiene un peso morto, per <lb/>misurar con esso la forza della percossa. </s>

<s>Ma perch&egrave;, ignorandosi le leggi <lb/>idrauliche scoperte poi dal Castelli e dal Torricelli, non si sapeva misurare <lb/>il peso dell'acqua, rimasta in aria fra le due secchie, e non si poteva perci&ograve; <lb/>dedurne la quantit&agrave; precisa dell'urto contro il fondo della secchia inferiore, <lb/>dov&egrave; Galileo rivolgersi ad altre esperienze. </s></p><p type="main">

<s>Fra queste scelse quella del palo confitto dalla berta, della quale si po&shy;<lb/>teva misurar la caduta, come si poteva del palo misurare a ogni colpo la <lb/>quantit&agrave; della trafitta. </s>

<s>Supponeva che, essendo la berta cento libbre, cadendo <lb/>dall'altezza di quattro braccia conficcasse il palo per quattro dita, la qual <lb/>fitta fosse parimente operata da un peso morto di mille libbre. </s>

<s>Tornando a <lb/>ripetere il colpo, il palo ander&agrave; ancora pi&ugrave; gi&ugrave;: per minore spazio per&ograve; di <lb/>prima, il quale supponiamo che sia ridotto a due dita. </s>

<s>Se come si &egrave; fatto, <lb/>serbando il medesimo peso e la medesima altezza del cadente, si tornasse a <lb/>soprapporre il medesimo peso morto delle mille libbre, non se ne vedrebbe <pb xlink:href="020/01/2508.jpg" pagenum="133"/>l'effetto, se non a condizione che fosse un tal premente molto maggiore. </s>

<s>Tanto <lb/>poi maggiore dovrebb'essere pi&ugrave; e pi&ugrave;, per far le fitte uguali a quelle del <lb/>terzo, del quarto, del quinto colpo della berta: cosicch&egrave; ritrarre si pu&ograve;, con&shy;<lb/>clude il Salviati, <emph type="italics"/>la forza della percossa essere infinita, o vogliam dire inde&shy;<lb/>terminata, e indeterminabile<emph.end type="italics"/> (Alb. </s>

<s>XIII, 314). </s></p><p type="main">

<s>Qui per&ograve;, al principale intento del dimostratore, s'attraversa negli ascol&shy;<lb/>tanti una difficolt&agrave;, sembrando che negli ordigni meccanici non si verifichi <lb/>questa infinit&agrave; di forza, che s'attribuisce alla percossa. </s>

<s>Ma il Salviati risponde <lb/>ch'ei perci&ograve; non cred&egrave; doversi, nel percotere e nel sollevar pesi, procedere <lb/>dalla Natura con mezzi diversi, e conferma particolarmente il suo detto con <lb/>l'esempio della stadera, nella quale, egli dice, &ldquo; &egrave; manifesto che un picco&shy;<lb/>lissimo peso di una libbra, scendendo, alzer&agrave; un peso di cento, e di mille e <lb/>pi&ugrave; quante ne piace, se noi lo costituiremo nell'ago cento o mille volte e pi&ugrave; <lb/>lontano dal centro, che l'altro peso massimo: cio&egrave; se noi faremo che lo spa&shy;<lb/>zio, per lo quale scender&agrave; quello, sia cento e mille e pi&ugrave; volte maggiore <lb/>dello spazio della salita dell'altro: cio&egrave; se la velocit&agrave; di quello sia cento e <lb/>mille volte maggiore della velocit&agrave; di questo &rdquo; (ivi, 317). </s></p><p type="main">

<s>Credendo di aver cos&igrave; rimossa ogni difficolt&agrave;, e gl'interlocutori confes&shy;<lb/>sando di esserne rimasti sodisfatti, procede innanzi il Salviati col suo di&shy;<lb/>scorso a considerare gli effetti della berta, che ficca il palo, i quali effetti, <lb/>essendo ogni volta diversi, domanda quale di questi si dovr&agrave; prendere per <lb/>ferma e certa misura della forza del colpo, che pure, quanto a s&egrave;, &egrave; sempre <lb/>il medesimo. </s>

<s>La nuova difficolt&agrave; si trova dal promotore stesso insuperabile, <lb/>per cui si consiglia di tentare altre esperienze e altri modi di riuscire ad <lb/>avere una misura costante di quegli effetti. </s>

<s>Immagina perci&ograve; di avere sopra <lb/>un sostegno posato un gran peso, a cui, per mezzo di una fune che passi <lb/>per la gola di una carrucola fissa, sia congiunto, liberamente pendulo, un <lb/>altro peso minore. </s>

<s>Questo &egrave; certo che stando quieto non mover&agrave; l'altro, ma <lb/>sollevandolo, e poi lasciatolo di l&igrave; cader liberamente, dar&agrave;, per l'impeto con&shy;<lb/>ceputo nella discesa, alla corda una tale strappata, che sar&agrave; al gran peso <lb/>come un colpo, che lo voglia cacciare in su. </s>

<s>Supponendo ora che la gravit&agrave; <lb/>del gran solido posto in quiete sia per esempio cento volte maggiore della <lb/>gravit&agrave; del piccolo peso, cadente dall'altezza di un braccio, sar&agrave;, dice il Sal&shy;<lb/>viati, dimostrato che si osserva nella percossa la medesima regola, che negli <lb/><figure id="id.020.01.2508.1.jpg" xlink:href="020/01/2508/1.jpg"/></s></p><p type="caption">

<s>Figura 43.<lb/>altri strumenti meccanici, se si trover&agrave; che il gran <lb/>peso sia, per la strappata del minore, sollevato per <lb/>un solo centesimo di braccio. </s></p><p type="main">

<s>Per giungere alla promessa conclusione, invo&shy;<lb/>cando il teorema primo dimostrato nella terza gior&shy;<lb/>nata, riduce il Salviati a equabili i moti accelerati <lb/>della caduta del piccolo peso e del balzo del grande, <lb/>cosicch&egrave; gli si viene lo strumento delle esperienze <lb/>a trasformare in un piano inclinato, sopra il quale il peso A (fig. </s>

<s>43) sia <lb/>sostenuto dal peso B, pendente dalla carrucola all'altra estremit&agrave; della corda: <pb xlink:href="020/01/2509.jpg" pagenum="134"/>dov'&egrave; manifesto, egli dice, la resistenza del grande esser sempre ed in tutti <lb/>i luoghi la medesima, il che non accade nella resistenza del chiodo e del <lb/>palo, ne'quali ella va sempre crescendo, con proporzione ignotissima, nel <lb/>dover penetrare il muro o il terreno. </s></p><p type="main">

<s>Suppongasi ora che CD sia cento misure o CE dieci: il piccolo grave B <lb/>di dieci pesi far&agrave;, secondo le note leggi meccaniche, equilibrio al grande A <lb/>di cento, e ogni minima aggiunta a quello baster&agrave; per muovere questo. </s>

<s>Sia <lb/>mosso per esempio da M in N: per altrettanto spazio sar&agrave; sceso il peso B <lb/>nella perpendicolare. </s>

<s>E perch&egrave; questo rappresenta il percuziente e quello il <lb/>peso morto, che equivale alla percossa, se ne dovranno comparare insieme le <lb/>velocit&agrave; o gli spazi passati nelle medesime direzioni perpendicolari. </s>

<s>Condotte <lb/>perci&ograve; le MO, NO parallele alle DE, CE, sar&agrave; NO la misura dell'ascesa perpen&shy;<lb/>dicolare del corpo grave A, la quale facilmente si determina, rispetto alla ca&shy;<lb/>duta perpendicolare di B, uguale a MN, dalle equazioni MN:NO=DC:CE= <lb/>100:10, d'onde NO=MN/10. &ldquo; Adunque &egrave; manifesto, conclude il Salvlati, che <lb/>la caduta del peso di dieci libbre, fatta nella perpendicolare, &egrave; bastante a <lb/>sollevare il peso di cento libbre, pur nella perpendicolare, ma solo per lo <lb/>spazio della decima parte della scesa del cadente di dieci libbre. </s>

<s>Ma quella <lb/>forza, che pu&ograve; alzare un peso di cento libbre, &egrave; eguale alla forza, con la <lb/>quale il medesimo peso delle cento libbre calca in gi&ugrave;, e questa era la po&shy;<lb/>tente a cacciare il palo postavi sopra e premendo; ecco dunque esplicato come <lb/>la caduta di dieci libbre di peso &egrave; potente a cacciare una resistenza equiva&shy;<lb/>lente a quella, che ha il peso di cento libbre, per essere sollevato, ma la <lb/>cacciata non sar&agrave; pi&ugrave; che per la decima parte della scesa del percuziente. </s>

<s><lb/>E se noi porremo la resistenza del palo essere raddoppiata e triplicata, sic&shy;<lb/>ch&egrave; vi bisogni per superarla la pressura di dugento o trecento libbre di peso <lb/>morto, replicando simil discorso, troveremo l'impeto delle dieci libbre cadenti <lb/>a perpendicolo esser potente a cacciare, s&igrave; come la prima, la seconda e la <lb/>terza volta il palo: e come nella prima la decima parte della sua scesa, cos&igrave; <lb/>nella seconda volta la ventesima, e nella terza la trentesima parte della sua <lb/>scesa. </s>

<s>E cos&igrave;, moltiplicando la resistenza in infinito, sempre la medesima per&shy;<lb/>cossa la potr&agrave; superare, ma col cacciare il resistente sempre per minore e <lb/>minore spazio, con alterna proporzione &rdquo; (ivi, pag. </s>

<s>327, 28). </s></p><p type="main">

<s>Ecco in somma qual'&egrave; il processo del ragionamento, tenuto da Galileo <lb/>nel VI dialogo, e quale ne &egrave; la conclusione: ci&ograve; che, se avesse potuto leg&shy;<lb/>gere il Borelli, avrebbe dovuto confessare di essere rimasto illuso nel suo <lb/>giudizio, vigendo tuttavia contro le ultime speculazioni del suo Maestro la <lb/>sentenza pronunziata contro le dottrine, ch'egli aveva insegnate nel suo <lb/>primo giovanile Discorso. </s>

<s>Imperocch&egrave; la proporzione, che passa tra le ve&shy;<lb/>locit&agrave; e i corpi A, B, mentre l'uno scende nel perpendicolo, e l'altro sale <lb/>sul piano; &egrave; tutt'affatto diversa da quella, che nel libro <emph type="italics"/>De vi percussio&shy;<lb/>nis<emph.end type="italics"/> si dimostra dover passare fra quegli stessi termini, mentre che si con&shy;<lb/>siderino i due corpi venir tra loro a conflitto. </s>

<s>Essendo dunque la conclusione <pb xlink:href="020/01/2510.jpg" pagenum="135"/>di Galileo manifestamente falsa non dovrebbe far maraviglia che tutto in&shy;<lb/>tero il detto. </s>

<s>Dialogo niente altro sia che un bel tessuto di paralogismi, come <lb/>si diceva. </s></p><p type="main">

<s>Di mezzo per&ograve; a quei paralogismi risalta una verit&agrave; nuova, nella quale <lb/>consiste tutto il merito, e in cui si raccoglie il frutto unico di quelle migliaia <lb/>di ore, che Galileo stesso diceva di avere spese intorno al penetrare i mara&shy;<lb/>vigliosi effetti della percossa. </s>

<s>Ma per prepararci a dire in che consista una <lb/>tal novit&agrave;, ritorniamo indietro sulle ragioni, che il Salviati adduce per con&shy;<lb/>cluder che la Natura, nel moltiplicare la forza sopra il piano inclinato e nella <lb/>percossa, procede nella medesima maniera. </s></p><p type="main">

<s>&Egrave; chiaro che fra gli altri ordigni meccanici si sceglie il piano, perch&egrave; <lb/>meglio atto a rappresentare col peso pendulo il percuziente, e, con l'altro <lb/>appoggiato, il peso morto che preme. </s>

<s>Avrebbe del resto il discorso condotto <lb/>a concludere pi&ugrave; semplicemente il medesimo dai principii immediati della <lb/>leva, secondo i quali &egrave; manifesto che una piccolissima potenza vale a pa&shy;<lb/>reggiare una grandissima resistenza, purch&egrave; si osservi l'ordine delle di&shy;<lb/>stanze, contrariamente prese dal punto di appoggio. </s>

<s>E qui torna a propo&shy;<lb/>sito il famosissimo detto di Archimede: <emph type="italics"/>Da mihi ubi sistam, et terram <lb/>coelumque movebo,<emph.end type="italics"/> che Galileo applicava alla percossa, ripetendo anch'egli <lb/>enfaticamente per somiglianza: <emph type="italics"/>Mettimi fuori della Terra, anzi dell'uni&shy;<lb/>verso riunito insieme in un globo, e lo commover&ograve; percotendolo col mio <lb/>martello.<emph.end type="italics"/></s></p><p type="main">

<s>Ecco la maravigliosa sentenza che l'Archimede novello era venuto a pro&shy;<lb/>nunziare, concludendo in forma di general proposizione, &ldquo; come qualsivoglia <lb/>piccolissimo peso, scendendo, faccia salire qualsivoglia immensa e gravissima <lb/>mole &rdquo; (ivi, pag. </s>

<s>316). La proposizione fu poi come verissima dimostrata <lb/>anche dall'Huyghens, nella terza del suo trattato <emph type="italics"/>De motu corporum ex vi <lb/>percussionis,<emph.end type="italics"/> dove cos&igrave; l'Autore l'annunzia: &ldquo; Corpus quamlibet magnum <lb/>a quamlibet exiguo corpore, et qualicumque celeritate impacto, movetur &rdquo; <lb/>(Opuscula postuma, Lugd. </s>

<s>Batav. </s>

<s>1703, pag. </s>

<s>373). Conferm&ograve; pure lo stesso <lb/>il Mariotte nella VIII della seconda parte del suo libro <emph type="italics"/>De la percussion,<emph.end type="italics"/><lb/>esagerando anch'egli come il Nostro l'effetto del piccolissimo verso qualun&shy;<lb/>que grandissimo col chiamarlo <emph type="italics"/>infinito.<emph.end type="italics"/> &ldquo; La force du choc horisontal est <lb/>infinie: c'est-a-dire, que si un corps tres-petit en choque directement un autre <lb/>tres-pesant en repos par un mouvement horisontal, si lent, qu'il puisse &egrave;tre; <lb/>il le mettra en mouvement &rdquo; (Oeuvres, T. I, A la Haye 1740, pag. </s>

<s>72). Ma <lb/>n&egrave; l'esempio del gran naviglio, che in acqua quieta e in aria calma pu&ograve; <lb/>esser tirato a riva <emph type="italics"/>avec un tres-petit fil de soie, sans que le fil se rompe,<emph.end type="italics"/><lb/>n&egrave; l'altro dell'Huyghens, da somiglianti immagini desunto, hanno a che ri&shy;<lb/>veder nulla con la bella dimostrazione meccanica di Galileo, ricavata dal fatto <lb/>della grandissima sfera pendula, il centro di gravit&agrave; della quale &egrave; necessa&shy;<lb/>riamente spostato dal solo toccarla, non che dal percoterla che faccia un <lb/>chicco di panico: dimostrazione illustrata cos&igrave; dal Viviani con molta sempli&shy;<lb/>cit&agrave; ed evidenza. </s></p><pb xlink:href="020/01/2511.jpg" pagenum="136"/><p type="main">

<s>&ldquo; Il grandissimo peso A (fig. </s>

<s>44), pendente dal perpendicolo RA, sar&agrave; <lb/>sollevato dal piccolissimo peso B, pendente dal medesimo punto R al filo RB. <lb/><figure id="id.020.01.2511.1.jpg" xlink:href="020/01/2511/1.jpg"/></s></p><p type="caption">

<s>Figura 44.<lb/>Perch&egrave;, congiunti i centri di gravit&agrave; di <lb/>essi gravi, cio&egrave; quello di A, che si sup&shy;<lb/>pone essere condotto nell'infimo punto <lb/>del suo moto possibile, e quello di B colla <lb/>retta BA, il loro centro comune sar&agrave; in <lb/>essa BA, come in C, fuori del pendulo RA, <lb/>il qual centro C, passando per l'arco del <lb/>suo moto fatto dal semidiametro RC, ca&shy;<lb/>ler&agrave; fino che esso si ritrovi nel detto <lb/>piombo, e per&ograve; il gran peso A verr&agrave; ne&shy;<lb/>cessariamente sollevato &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. CXIII, fol. </s>

<s>6 a tergo). </s></p><p type="main">

<s>N&egrave; l'Huyghens n&egrave; il Mariotte pote&shy;<lb/>vano aver notizia di questa proposizione, <lb/>che il Viviani cos&igrave; bene illustra sopra il <lb/>testo galileiano, della copia del quale egli <lb/>era gi&agrave; venuto in possesso: e pure &egrave; <lb/>certo che non ne aveva ancora avuto no&shy;<lb/>tizia il Borelli, quando scriveva la XVI <lb/>e la XVII <emph type="italics"/>De vi percussionis.<emph.end type="italics"/> Bench&egrave; <lb/>dunque si trovassero, in dimostrare la medesima verit&agrave;, tanti insigni ma&shy;<lb/>tematici concordi, volle Onorato Fabry apporre la nota di falsit&agrave; alle due <lb/>dette proposizioni borelliane, l'Autor delle quali, per confermare l'assunto <lb/>che, rimanendosi tuttavia inedito il Dialogo galileiano compariva nella Scienza <lb/>meccanica come nuovo; s'incontr&ograve; in una dimostrazione, che concludeva dai <lb/>principii medesimi di Galileo, e si rassomigliava perci&ograve; moltissimo a quella <lb/>del Viviani. </s></p><p type="main">

<s>Sia GF (fig. </s>

<s>45) una libbra senza peso sostenuta nel suo mezzo A, da <lb/>cui penda per un filo, pur senza peso, un vastissimo globo, che movendosi <lb/><figure id="id.020.01.2511.2.jpg" xlink:href="020/01/2511/2.jpg"/></s></p><p type="caption">

<s>Figura 45.<lb/>qua e l&agrave; descriverebbe col suo centro B il <lb/>semicerchio GBF. </s>

<s>Lasciato per&ograve; in libera posa <lb/>si costituir&agrave; nel suo luogo pi&ugrave; basso, e la lib&shy;<lb/>bra FG si disporr&agrave; in perfetta linea orizon&shy;<lb/>tale. </s>

<s>Aggiungasi ora in G un altro piccolo <lb/>corpo: il centro del sistema dovr&agrave; da B risalir <lb/>verso G, per la linea di congiunzione GB, infino <lb/>a un punto, per esempio O, che sia da G, B <lb/>distante per lunghezze reciproche ai pesi. </s>

<s>Ivi <lb/>per&ograve; non potr&agrave; stabilirsi, ma scender&agrave;, infintantoch&egrave; la linea AO non si di&shy;<lb/>sponga perpendicolare in AB, ci&ograve; che non pu&ograve; farsi, senza che il punto B <lb/>non risalga alquanto su per l'arco BF. &ldquo; Ergo, ne conclude il Borelli, non <lb/>obstante illa resistentia positiva, corpus B elevabitur sursum in arcu BF. <pb xlink:href="020/01/2512.jpg" pagenum="137"/>Praeterea, quia perinde est si loco corpusculi G ponderosi applicetur quae&shy;<lb/>libet vis motiva, sive animata, sive proiectitia, quae aequalem energiam habeat <lb/>quam pondus G, et illa ubicumque applicata, sive in G ant in B idem praestat <lb/>ac pondus G; proindeque vastum corpus pensile B a quacumque vi motiva <lb/>tantulum impelli sursum poterit &rdquo; (Historia incendii aetnaei, Reg. </s>

<s>Julio 1670, <lb/>pag. </s>

<s>149). </s></p><p type="main">

<s>Il Borelli dunque, l'Huyghens e il Mariotte, a cui potremo altres&igrave; ag&shy;<lb/>giungere il Wallis, non fecero altro che confermare una verit&agrave;, la quale non <lb/>sapevano che fosse stata rivelata da Galileo, per bocca di quel suo Salviati, <lb/>a cui primo faceva pronunziare e dimostrare che qualunque grandissimo peso <lb/>pu&ograve;, in certe condizioni, esser mosso da qualunque minima forza. </s>

<s>Dal con&shy;<lb/>siderar poi che il medesimo effetto ne segue, o tocchi il piccolo corpo il gran&shy;<lb/>dissimo o lo percuota, s'inger&igrave; nello stesso Galileo il concetto che, a quel <lb/>modo che opera la Natura in moltiplicar la forza nelle macchine e negli urti <lb/>violenti, quando son le proporzioni infinite o incommensurabili; a quel me&shy;<lb/>desimo modo ella operi anche nelle proporzioni definite. </s>

<s>Sarebbe come a voler <lb/>dire che le propriet&agrave; convenienti alla somma delle infinite linee indivisibili, <lb/>contessenti una superficie, convenissero a ciascuna linea particolare, commet&shy;<lb/>tendo un paralogismo, che facilmente si scoprirebbe con l'osservare che si <lb/>paragonano insieme due cose di un genere diverso. </s></p><p type="main">

<s>Dalle astratte speculazioni venivasi quel medesimo paralogismo a tradurre <lb/>nei fatti, quando s'immaginavan da Galileo e da'suoi seguaci quegli stru&shy;<lb/>menti, e si eseguivano quelle esperienze ordinate a misurare la forza della <lb/>percossa fatta sopra uno de'piatti, a proporzione del peso morto posto sul&shy;<lb/>l'altro piatto della bilancia. </s>

<s>&Egrave; dovuto al Borelli anche il merito di aver fu&shy;<lb/>gato dalla Scienza questo errore pernicioso, predominante nella Scuola alla <lb/>quale egli stesso apparteneva, ed &egrave; argomento degno di storia. </s>

<s>Ma prima di <lb/>passar oltre a trattarlo, vogliamo ripigliare il filo del nostro primo discorso <lb/>intorno al sesto dialogo galileiano, che vedemmo esser rimasto incompleto, <lb/>s&igrave; per quel che riguarda la forza della percossa, e s&igrave; per non trovarvisi fatto <lb/>alcun motto di quell'altro promesso trattatello dell'uso delle catenuzze nella <lb/>ballistica. </s>

<s>&Egrave; come una statua di Fidia, collocata sul piedestallo in una pub&shy;<lb/>blica piazza da un archeologo, a quel modo ch'ei la ritrov&ograve;, sotto le mace&shy;<lb/>rie, mutilata, e che noi veniamo ora a reintegrare, almeno nelle principali <lb/>e pi&ugrave; distinte sue membra. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Dicemmo che Galileo, distratto da altre cure suggeritegli dal Viviani e <lb/>dal Torricelli, lasci&ograve; il dialogo della percossa interrotto al punto, dop'aver <lb/>dimostrato, per la somiglianza di ci&ograve; che avviene de'gravi sul declivio di un <lb/>piano e nel perpendicolo, che i momenti del percuziente e del percosso stanno <pb xlink:href="020/01/2513.jpg" pagenum="138"/>reciprocamente come la velocit&agrave; di questo alla velocit&agrave; di quello. </s>

<s>Confermava <lb/>da cos&igrave; fatte relazioni il primario e principale suo assunto, che cio&egrave; la forza, <lb/>cos&igrave; nelle macchine che muovono, come in quelle che percotono, sia infinita. </s>

<s><lb/>Dicemmo altres&igrave; che, per rendere di ci&ograve; l'intrapresa trattazione compiuta, <lb/>non aveva l'Autore lasciato altro che alcune frettolose note manoscritte, ri&shy;<lb/>trovate fra le carte del Viviani sotto il titolo di <emph type="italics"/>Roba copiata da un esem&shy;<lb/>plare del Galileo.<emph.end type="italics"/> Apparisce da coteste note che voleva al Salviati far pro&shy;<lb/>seguire il discorso, per confermare l'infinit&agrave; della potenza del colpo in ogni <lb/>corpo grave cadente, desumendone le ragioni dalla natura del moto accele&shy;<lb/>rato. </s>

<s>E perch&egrave; si vedeva di li nascere facilmente alcune difficolt&agrave; contro l'as&shy;<lb/>sunto, doveva intrattenersi il Salviati stesso a rimoverle dalle dubbiose menti <lb/>degl'interlocutori. </s></p><p type="main">

<s>I ragionamenti per&ograve;, fino a questo punto tenuti fra gli amici, non ave&shy;<lb/>vano avuto per subietto altro che le percosse fatte nelle cadute naturali; <lb/>ond'&egrave; che, a voler esaurire il tema, rimaneva a dir tuttavia delle percosse <lb/>artificiali: di quelle cio&egrave; prodotte da qualunque forza di proiezione, o comun&shy;<lb/>que sia dirette per l'orizzonte o all'ins&ugrave;, come nei martelli fabbrili, e che <lb/>Galileo par avesse intenzione di distinguere, comprendendone sotto il nome <lb/>di <emph type="italics"/>urti<emph.end type="italics"/> le variet&agrave; degli effetti. </s>

<s>Col dimostrar dunque che anche gli urti son <lb/>soggetti alle medesime leggi delle percosse naturali, e che son perci&ograve; anch'essi <lb/>di potenza infinita, si doveva terminar l'argomento, preso dai conversanti a <lb/>trattare in questa prima parte della giornata. </s></p><p type="main">

<s>La <emph type="italics"/>roba<emph.end type="italics"/> scritta, nella quale s'accennava a questo proposito di proseguire <lb/>e di dar perfezione al trattato della percossa; prima che dal Viviani, come <lb/>dicemmo, era stata, vivente Galileo, copiata dal Torricelli, a cui non era, di <lb/>ci&ograve; che aveva speculato il suo ospite in tal soggetto, da qualche enfatica <lb/>espressione in fuori attinta ai familiari colloqui, pervenuta altra notizia. </s>

<s>Il <lb/>principe Leopoldo, che non si poteva dar pace di vedere, con s&igrave; grave danno <lb/>della Filosofia toscana e della Scienza universale, fallite le sue intenzioni, non <lb/>lasciava mai occasione d'entrare intorno a ci&ograve; in discorso con lo stesso Tor&shy;<lb/>ricelli, il quale ebbe finalmente un giorno a mostrare a Sua Altezza, in que'fo&shy;<lb/>glietti copiati, ci&ograve; che avesse Galileo lasciato scritto della percossa. </s>

<s>Gli volle <lb/>il Principe leggere attentamente, e trovando che contenevano pensieri, i quali <lb/>s'accennava che sarebbero svolti, o proposizioni, che si prometteva verreb&shy;<lb/>bero dimostrate, espresse il suo desiderio, per non dire il comando, che adem&shy;<lb/>pisse il discepolo quel che s'era proposto di fare il Maestro. </s>

<s>Si discuteva <lb/>intorno alla forma, e se dovessero mettersi quelle cose in dialogo: ma seni&shy;<lb/>brando ci&ograve; troppo arbitrio, e vedendo tuttavia lontana l'occasion di stam&shy;<lb/>parlo, parve pi&ugrave; conveniente il leggere a qualche pubblica udienza. </s>

<s>Fece perci&ograve; <lb/>esso Principe ammettere il Torricelli fra gli Accademici della Crusea, la quale, <lb/>proponendosi allora di definir le parole con la notizia delle cose, accoglieva <lb/>in s&egrave; quegli egregi Toscani, che sapevano scrivere elegante, perch&egrave; avevano <lb/>prima imparato a pensare profondo. </s>

<s>Erano quasi tutti perci&ograve; discepoli e se&shy;<lb/>guaci di Galileo, per cui fu una tale adunanza creduta la pi&ugrave; opportuna per <pb xlink:href="020/01/2514.jpg" pagenum="139"/>divulgarvi gli oracoli ultimamente pronunziati in Arcetri, ci&ograve; che significava <lb/>il banditore dicendo &ldquo; che anco l'istesso Galileo s'appagherebbe piuttosto di <lb/>questa sola udienza, che di pubblicare i frammenti de'rimasti suoi scritti &rdquo; <lb/>(Lez. </s>

<s>accad. </s>

<s>cit., pag. </s>

<s>69). Giova a noi credere che fossero cos&igrave; fatte espres&shy;<lb/>sioni sincere, bench&egrave; alcuni si maravigliassero che si venisse a mescolare la <lb/>crusca ne'sacchi del Torricelli, tutti pieni di fior di farina. </s>

<s>Il Cavalieri, ap&shy;<lb/>pena avuta la notizia della nuova elezione accademica, scriveva cos&igrave; all'eletto, <lb/>il di 14 Luglio 1642, in una lettera da Bologna: &ldquo; Gli Accademici della Cru&shy;<lb/>sca hanno fatto un grande acquisto con l'aggregazione di V. S., che gli por&shy;<lb/>ter&agrave; fior di roba. </s>

<s>Se non che vogliono cose piuttosto fisiche che matematiche, <lb/>e forse con ragione, poich&egrave; quelle assomiglierei io piuttosto alla crusca, e <lb/>queste al fior di farina, vero cibo e nutrimento dell'intelletto. </s>

<s>Nondimeno <lb/>conviene accomodarsi al loro genio, anzi al genio universale &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. XLI, fol. </s>

<s>126). E accomodandosi a questo genio universale anche il <lb/>Torricelli, incominci&ograve; a leggere dalla bugnola i suoi fisici argomenti. </s></p><p type="main">

<s>Letto appena il primo discorso, per ringraziare il Principe e gli Acca&shy;<lb/>demici che lo avevano ammesso, entr&ograve; subito in argomento della percossa, <lb/>dimostrando ch'ell'&egrave; infinita, perch&egrave; infiniti son gl'istanti di tempo, nei <lb/>quali, cadendo il corpo che ha da percotere, si moltiplica la gravit&agrave; di lui, <lb/>che &ldquo; nei corpi naturali &egrave; come fontana, dalla quale continuamente scatu&shy;<lb/>riscono momenti di peso &rdquo; (ivi, pag. </s>

<s>73): n&egrave; la dimostrazione consiste in <lb/>altro che nell'esplicare il concetto di Galileo: &ldquo; Il momento di un grave, <lb/>nell'atto della percossa, altro non &egrave; che un composto ed aggregato d'infiniti <lb/>momenti, ciascuno di essi eguale al solo momento o interno e naturale di <lb/>s&egrave; medesimo, o estrinseco e violento, qual'&egrave; quello della forza movente. </s>

<s>Tali <lb/>momenti, nel tempo della mossa del grave, si vanno accumulando in istante, <lb/>con eguale additamento, e conservando in esso, nel modo appunto che si va <lb/>accrescendo la velocit&agrave; di un grave cadente.... &rdquo; (Alb. </s>

<s>XIII, 330, 31). </s></p><p type="main">

<s>Nasceva per&ograve; contro queste dottrine un dubbio, che non si vedeva come <lb/>risolverlo facilmente, perch&egrave; se il momento di un grave, nell'atto della per&shy;<lb/>cossa, non &egrave; altro che un aggregato degl'infiniti momenti acquistati negli <lb/>infiniti istanti del tempo della caduta, sembrava che la stessa percossa che <lb/>ne segue dovess'essere in qualunque caso infinita: ci&ograve; che contradice all'os&shy;<lb/>servazione dei fatti, potendo anche un grande grave cadente produrre un pic&shy;<lb/>colo colpo. </s>

<s>All'istanza gi&agrave; preveduta accennava di voler rispondere Galileo, <lb/>cos&igrave; scrivendo fra le altre note del suo foglio: &ldquo; La forza della percossa &egrave; <lb/>d'infinito momento, tuttavolta che ella si applichi, in un momento ed in un <lb/>istante, dal grave percuziente sopra materia non cedente, come si dimo&shy;<lb/>strer&agrave; &rdquo; (ivi, pag. </s>

<s>331). </s></p><p type="main">

<s>La dimostrazione che manca fu supplita dal Torricelli, il quale, osser&shy;<lb/>vando che l'impeto conceputo da un grave nello scendere in gi&ugrave; &egrave; total&shy;<lb/>mente estinto nel ritornare in su per altrettanto spazio, ne concluse la se&shy;<lb/>guente risposta, che si conforma col pensiero di Galileo: &ldquo; Allora seguirebbe <lb/>l'effetto infinito, ad ogni bench&egrave; piccola percossa, quando la percossa fosse <pb xlink:href="020/01/2515.jpg" pagenum="140"/>momentanea: cio&egrave; quando il percuziente applicasse tutto quel cumulo di mo&shy;<lb/>menti, che egli ha dentro di s&egrave; aggregati insieme, che sono veramente in&shy;<lb/>finiti, e gli conferisse tutti al suo resistente in un solo istante di tempo. </s>

<s>Ma <lb/>se nell'applicargli gli applica con qualche spazio di tempo non &egrave; pi&ugrave; neces&shy;<lb/>sario che l'effetto segua infinito, anzi pu&ograve; esser minimo, ma per&ograve; nullo non <lb/>mai &rdquo; (Lez. </s>

<s>accad. </s>

<s>cit., pag. </s>

<s>76). </s></p><p type="main">

<s>Che nullo veramente non sia manifesto si scorge, scriveva Galileo, <lb/>dall'esperienza, &ldquo; poich&egrave; se con un ben piccolo martello si ander&agrave; con per&shy;<lb/>cosse uniformi incontrando la testa di una grandissima trave, che sia a <lb/>giacere in terra, dopo molte e molte percosse si vedr&agrave; finalmente essersi <lb/>mossa la trave per qualche spazio percettibile: segno evidentissimo che ogni <lb/>percossa oper&ograve; separatamente per la sua parte nello spingere la trave: poi&shy;<lb/>ch&egrave;, se la prima percossa non fosse a parte di tale effetto, tutte le altre sus&shy;<lb/>seguenti, come in luogo di prime, niente affatto opererebbero &rdquo; (Alb. </s>

<s>XIII, <lb/>331, 32). Il Torricelli conferma questo stesso pensiero, asseverando niuna <lb/>sorta di percossa esser tanto debole, che non faccia effetto in qualunque ga&shy;<lb/>gliardissima resistenza, e adduce a dimostrarlo esperienze simili, e simili ra&shy;<lb/>gioni espresse talvolta con le medesime parole, che aveva lette nel manoscritto <lb/>galileiano. </s>

<s>&ldquo; Imperocch&egrave; se il primo colpo, egli dice, non avesse operato cosa <lb/>alcuna, adunque il secondo colpo si potrebbe chiamare e considerare per <lb/>primo. </s>

<s>Essendo poi il secondo eguale di forza al primo, e ritrovando il resi&shy;<lb/>stente nella medesima disposizion per appunto, n&egrave; esso ancora operer&agrave; cosa <lb/>alcuna. </s>

<s>Cos&igrave; proveremo che n&egrave; il millesimo n&egrave; il milionesimo potrebbero <lb/>giammai operare, se non avesse operato anche il primo. </s>

<s>Che poi li molti <lb/>operino, parlino questa volta per me le porte di Agrippa e le statue del Va&shy;<lb/>ti<gap/>ano: si vedono pure, bench&egrave; di bronzo durissimo, consumate dal solo acco&shy;<lb/>stamento delle mani del popolo curioso e devoto &rdquo; (Lez. </s>

<s>accad. </s>

<s>cit., pag. </s>

<s>94, 95). </s></p><p type="main">

<s>Altre obiezioni prevedeva il Torricelli contro la dottrina galileiana della <lb/>percossa infinita, e prometteva agli Accademici sarebbe venuto a ribatterle <lb/>in un'altra tornata. </s>

<s>Consisteva la principale di quelle obiezioni nel dire che, <lb/>se un grave cadente avesse dentro di s&egrave; momento infinito, dovrebbe aver <lb/>anche velocit&agrave; infinita. </s>

<s>N&egrave; il Torricelli nega che non sia veramente cos&igrave;, pur&shy;<lb/>ch&egrave; per&ograve; s'intenda di una velocit&agrave; assoluta, e non paragonata con altra mi&shy;<lb/>nore, perch&egrave; quando il grave nella quiete avesse per esempio il momento di <lb/>una libbra. </s>

<s>&ldquo; allora di velocit&agrave; non aveva cosa alcuna: avendo poi dopo la <lb/>caduta acquistato qualche velocit&agrave;, questo mi pare che si possa chiamare <lb/>accrescimento intinito. </s>

<s>Il passaggio dall'esser nulla all'essere qualche cosa <lb/>suol giudicarsi mutazione infinita &rdquo; (ivi, pag. </s>

<s>87, 88). </s></p><p type="main">

<s>Ma per ridur l'argomento contro l'avversario anche pi&ugrave; stringente, os&shy;<lb/>serva il Torricelli che i momenti intrinsechi sono un che precedente, e sono <lb/>la vera e l'unica causa della maggiore o minore velocit&agrave;, per cui &ldquo; possono <lb/>stare e sussistere da s&egrave; stessi, senza l'aiuto e la compagnia di velocit&agrave; al&shy;<lb/>cuna &rdquo; (ivi, pag. </s>

<s>100). Si richiama per confermar ci&ograve; ai principii meccanici, <lb/>da s&egrave; pubblicamente professati nel trattato <emph type="italics"/>De motu,<emph.end type="italics"/> rispetto a ci&ograve; che av-<pb xlink:href="020/01/2516.jpg" pagenum="141"/>viene de'gravi applicati all'estremit&agrave; della libbra, in distanze diverse, o po&shy;<lb/>sati sopra piani con diverse inclinazioni &ldquo; dove hanno, egli dice, i diversi <lb/>momenti in atto, ma le diverse velocit&agrave; solo in potenza. </s>

<s>Ma la velocit&agrave; per <lb/>s&egrave; stessa non pu&ograve; gi&agrave; sussistere senza i momenti esterni &rdquo; (ivi). Qui per <lb/>verit&agrave; non sembra che si sodisfaccia pienamente all'istanza, che cio&egrave; una po&shy;<lb/>tenza infinita, venendo all'atto, non debba produrre effetto infinito: si toccava <lb/>delle velocit&agrave; virtuali la gelosa questione, la quale era solamente risolubile <lb/>da principii tutt'affatto diversi dai torricelliani, considerando la quiete non <lb/>come la privazione assoluta del moto, ma come il primo principio e il ter&shy;<lb/>mine ultimo del moto. </s></p><p type="main">

<s>Comunque sia, aveva il Torricelli nelle due dette Lezioni esplicato il <lb/>pensiero galileiano per quel che riguarda la percossa naturale, ma torn&ograve; a <lb/>leggere agli Accademici anche la terza volta, per trattare dell'urto, <emph type="italics"/>fratello <lb/>della percossa, e padre di molte speculazioni<emph.end type="italics"/> (ivi, pag. </s>

<s>106). Queste specu&shy;<lb/>lazioni per&ograve;, nel foglio manoscritto di Galileo, che serviva per distendere le <lb/>Lezioni accademiche di testo; si limitavano nell'accennare ad alcune espe&shy;<lb/>rienze, per le quali si mostrava &ldquo; come s'imprima ne'mobili, e pi&ugrave; ne'pi&ugrave; <lb/>gravi, ed in essi si moltiplichi e conservi la forza, che con qualche tempo <lb/>gli si va comunicando &rdquo; (Alb. </s>

<s>XIII. 332). </s></p><p type="main">

<s>Da cos&igrave; fatte esperienze dello scaccino, che serra le porte di bronzo di <lb/>S. Giovanni, e del sagrestano, che, a furia di dare strappate alla fune, rie&shy;<lb/>sce finalmente a far sonare una grossa campana, variate dal Torricelli negli <lb/>esempi del gran vascello, e della tavola di abeto che, tirati l'una e l'altro <lb/>per un cavo dalle braccia di un uomo, si fanno arrivare a percotere con va&shy;<lb/>ria velocit&agrave;, e con vario effetto; si deduce la teoria galileiana dell'urto, che <lb/>dallo stesso Torricelli si riassume in queste parole: &ldquo; Abbiamo detto che la <lb/>forza dell'urto non dipende altrimenti dalla quantit&agrave; della materia, poich&egrave; se <lb/>ci&ograve; fosse converrebbe che la medesima palla di sessanta libbre di ferro fa&shy;<lb/>cesse sempre la medesima operazione, lanciata una volta da un uomo, e una <lb/>volta avventata da un cannone. </s>

<s>Non dipende ne anche assolutamente dalla <lb/>velocit&agrave;, perch&egrave; con maggior velocit&agrave; urter&agrave; una tavola d'abeto, tirata per <lb/>l'acqua quiescente, che un vastissimo galeone: eppure il meno veloce far&agrave; <lb/>maggior violenza nell'urtare &rdquo; (Lez. </s>

<s>accad. </s>

<s>cit., pag. </s>

<s>118). </s></p><p type="main">

<s>Sembra che da questi cos&igrave; premessi e verissimi principii ne dovesse con&shy;<lb/>cludere il valent'uomo che n&egrave; da sola la quantit&agrave; di materia, n&egrave; da sola la <lb/>velocit&agrave;, ma dal composto d'ambedue insieme ne resulta la forza dell'urto, <lb/>come pochi anni prima aveva concluso l'Aggiunti, e scritto nei dimenticati <lb/>suoi fogli: eppure non sa far altro che adombrare il concetto galileiano, in&shy;<lb/>vocando la renitenza della materia all'esser mossa. </s>

<s>&ldquo; Ella altro non &egrave;, di&shy;<lb/>ceva, che un vaso di Circe incantato, il quale serve per ricettacolo delle forze <lb/>e de'momenti dell'impeto. </s>

<s>La forza poi e gl'impeti sono astratti tanto sot&shy;<lb/>tili, son quintessenze tanto spiritose, che in altre ampolle non si posson rac&shy;<lb/>chiudere, che nell'intima corpulenza dei solidi naturali &rdquo; (ivi, pag. </s>

<s>110). E <lb/>come le ampolle tanto pi&ugrave; ricevono di liquore, quanto pi&ugrave; ne sono capaci, <pb xlink:href="020/01/2517.jpg" pagenum="142"/>cos&igrave; son atti a far maggiore conserva di forza i solidi pi&ugrave; corpulenti; e non <lb/>fa perci&ograve; maraviglia che il vascello, il quale porta seco i momenti accumu&shy;<lb/>lati per lo spazio di un'ora dal tirar delle braccia di quell'uomo, faccia mag&shy;<lb/>gior effetto della tavola di abeto, la quale non portava seco altro che la forza <lb/>e i momenti accumulati in quaranta battute di polso. </s></p><p type="main">

<s>Soggiunge immediatamente d'inclinar forse a credere &ldquo; che se fosse <lb/>possibile di racchiudere e restringere dentro a un vilissimo emisfero di noce, <lb/>ma infrangibile, tutta quella forza e fatica, che nello spazio di mezz'ora &egrave; <lb/>stata prodotta dal traente del nostro immaginato vascello; crederei, dico, che <lb/>forse quel leggerisssimo guscio facesse nell'atto dell'urtare la medesima ope&shy;<lb/>razione, che faceva l'immensa mole del naviglio &rdquo; (ivi, pag. </s>

<s>111, 12). Si con&shy;<lb/>ferma di qui che non era nella mente del Torricelli ben definito il concetto <lb/>di forza, o di quantit&agrave; di moto, che sappiamo risultar dal prodotto della ve&shy;<lb/>locit&agrave; per la massa: che se si fossero nel discorso ora trascritto disposti gli <lb/>elementi secondo l'ordine proprio, avrebbe dovuto dir chi lo fece che se <lb/>fosse impressa al guscio della noce tanta velocit&agrave;, da compensare con essa <lb/>al difetto della mole, avrebbe, nell'essere spinto a riva, prodotto la mede&shy;<lb/>sima percossa del gran naviglio. </s>

<s>L'incerta opinione si sarebbe trasformata <lb/>cos&igrave; in quelle leggi matematiche, della scoperta delle quali lasciarono Gali&shy;<lb/>leo e il Torricelli il merito a un loro discepolo. </s></p><p type="main">

<s>Le lezioni del Torricelli fatte recitare dal principe Leopoldo, affinch&egrave; si <lb/>divulgassero, nel pi&ugrave; sollecito ed efficace modo, fra i letterati e gli scienziati <lb/>toscani convenuti insieme &ngrave;ell'Accademia della Crusca, i pensieri postumi di <lb/>Galileo; rimasero sconosciute al pubblico infino al 1715, quando pens&ograve; a <lb/>stamparle insieme in un volume in Firenze quel Tommaso Bonaventuri che, <lb/>raccogliendo tre anni dopo le opere galileiane, aggiunse agli altri delle due <lb/>Scienze nuove il dialogo sesto. </s>

<s>A lui dunque aveva dato in mano la sorte <lb/>quelle scritture, dalle quali riunite insieme resultavan compiute le specula&shy;<lb/>zioni di Galileo intorno alla forza della percossa, non facendo altro il Torri&shy;<lb/>celli che proseguire l'opera del Salviati, rimasta interrotta nel manoscritto <lb/>copiato dal Viviani. </s>

<s>L'editore fiorentino per&ograve; non seppe vedere queste rela&shy;<lb/>zioni, che passavano fra le Lezioni accademiche del Discepolo, e il Dialogo <lb/>incominciato dal Maestro, perch&egrave; altrimenti non avrebbe dubitato di unire <lb/>insieme le due scritture, che, sebbene apparissero sotto forme diverse, com&shy;<lb/>prendevano in un solo pensiero la mente dell'Autore intera e perfetta. </s>

<s>Se <lb/>noi dovessimo perci&ograve;, com'editori che si assumono l'ufficio di dar le opere <lb/>galileiane complete, ristampare i dialoghi delle due Scienze nuove, aggiun&shy;<lb/>geremmo al sesto, dove fu lasciato interrotto dal Bonaventuri, le tre Lezioni <lb/>accademiche sulla forza della percossa. </s>

<s>Il disteso, &egrave; vero, &egrave; del Torricelli, ma <lb/>i pensieri sono di Galileo, com'apparisce dalla scrittura, che servi ad esse <lb/>Lezioni di testo, ond'&egrave; che la ragione d'inserirle fra le altre opere galile&shy;<lb/>iane sarebbe quella medesima, che consigli&ograve; ad inserire il quinto dialogo <lb/>sulla riforma di Euclide. </s>

<s>Cos&igrave; sarebbe riserbato a noi, condannati come rei <lb/>tante volte di avere infranto l'idolo antico, il merito di averlo invece restau-<pb xlink:href="020/01/2518.jpg" pagenum="143"/>rato in uno almeno degli angoli dell'altare, e di esser venuti, noi unici al <lb/>mondo, a tergere le lacrime al popolo devoto. </s></p><p type="main">

<s>Questo merito nonostante noi lo reputiam quasi nulla verso un altro, <lb/>che ci ripromettiamo di acquistare appresso agli offesi Galileiani, ai quasi si <lb/>annunzia che, dopo aver riconosciute e riordinate le divise scritture inte&shy;<lb/>granti il VI dialogo, per quel che riguarda il trattato della percossa; abbiam <lb/>trovato da reintegrarlo altres&igrave; per quel che riguarda l'uso delle catenelle, a <lb/>dar regola, senza ricorrere ai calcoli laboriosi, di dirigere i tiri delle arti&shy;<lb/>glierie. </s></p><p type="main">

<s>Sulla fine della quarta Giornata il Salviati, dop'aver detto che le cate&shy;<lb/>nelle, lentamente sospese per le loro estremit&agrave;, s'incurvano in una certa sacca, <lb/>che moltissimo si rassomiglia alla parabola; accenna a qualche non piccola <lb/>utilit&agrave;, alla quale potrebber cos&igrave; fatte catenelle servire, di che promette agli <lb/>interlocutori che ne avrebbe trattato appresso. </s>

<s>Speditosi poi dalla dimostra&shy;<lb/>zione della corda tesa, per la quale aveva divagato il discorso, Simplicio lo <lb/>richiama alla fatta promessa d'esplicar cio&egrave; &ldquo; qual sia l'utilit&agrave;, che da si&shy;<lb/>mili catenelle si pu&ograve; ritrarre, e dopo questo arrecare quelle speculazioni, che <lb/>dal nostro Accademico sono state fatte intorno alla forza della percossa &rdquo; <lb/>(Alb. </s>

<s>XIII, 266). Ma l'ora essendo cos&igrave; tarda, da non bastare a disbrigar le <lb/>nominate materie, si consiglia il Salviati <emph type="italics"/>di differire il congresso ad altro <lb/>tempo pi&ugrave; opportuno.<emph.end type="italics"/></s></p><p type="main">

<s>Era in quel congresso dunque proposto di trattar prima delle catenelle, <lb/>e poi della percossa, ma fu il proposito riformato, premettendo questo a quello <lb/>argomento, qualunque se ne fosse la ragione, la quale non dispensava per&ograve; <lb/>esso Salviati dal mantenere intere le sue promesse. </s>

<s>E che veramente avesse <lb/>intenzione di mantenerle, apparisce dall'avere al colloquio cos&igrave; ben misurato <lb/>il tempo che, esaurito il primo trattato, intorno al quale anche compresa la <lb/>teoria degli urti si sarebbe la conversazione intrattenuta appena infino a ora <lb/>di nona; rimanesse tanto di sera, da passare a sodisfare i desiderosi d'in&shy;<lb/>tendere a quale uso mai si adoprerebbero le catenelle. </s>

<s>Ci&ograve; nonostante que'de&shy;<lb/>siderii, dopo pi&ugrave; che un secolo e mezzo, si rimangono insodisfatti, n&egrave; par <lb/>che se ne dolesse o se ne dolga alcuno de'Galileiani pi&ugrave; infervorati. </s>

<s>Noi dun&shy;<lb/>que siamo stati fra costoro i primi ed i soli, che ci siamo industriosamente <lb/>messi a cercare, e finalmente abbiamo trovato quella seconda parte del dia&shy;<lb/>logo galileiano, la quale, soggiungendosi alla prima della percossa, dava al <lb/>buon Salviati materia da filosofar con gli amici infino a sera. </s>

<s>Come ci oc&shy;<lb/>corresse a fare la scoperta, in mezzo a certi farraginosi manoscritti datici a <lb/>esaminare da un nostro amico, ci dispenseremo dal narrarlo ai nostri Let&shy;<lb/>tori, i quali noi crediamo desiderosi piuttosto di veder senza indugio quel <lb/>che di l&agrave; fu da noi ricopiato, ed &egrave; quanto appresso: </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; I vostri ragionamenti, sig. </s>

<s>Salviati, mi hanno d'ogni <lb/>parte cos&igrave; persuaso le forze delle percosse naturali e degli urti essere infi&shy;<lb/>nite, che potete oramai risparmiarvi di trattenere intorno a ci&ograve; altri discorsi. </s>

<s><lb/>Potete dunque passar liberamente per me a mantenere l'altra vostra pro-<pb xlink:href="020/01/2519.jpg" pagenum="144"/>messa, quale era di dirci l'utilit&agrave;, che sperava di ricavare il nostro Accademico <lb/>dalle catenuzze, applicate a punteggiare molte linee paraboliche sopra una <lb/>piana superficie. </s>

<s>Ma vedo qui il sig. </s>

<s>Aproino in atto di una certa maraviglia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Voi mi avete inteso, sig. </s>

<s>Sagredo, perch&egrave; questa vostra <lb/>proposta mi riesce affatto nuova. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Avete ragione: io non ho pensato che non era la S. V. <lb/>presente, quando, prima di congedarci la sera del passato nostro congresso, <lb/>il sig. </s>

<s>Salviati fece intendere a me e al sig. </s>

<s>Simplicio che appresso alla di&shy;<lb/>mostrazione della forza della percossa avrebbe soggiunta la notizia delle ca&shy;<lb/>tenuzze appese dalle estremit&agrave; loro, le quali con la loro sacca diceva che <lb/>naturalmente s'accomodano alla curvatura di linee paraboliche. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; A una prima maraviglia voi non fate cos&igrave; che aggiun&shy;<lb/>germene un'altra molto maggiore, per la quale sono entrato in grandissima <lb/>curiosit&agrave; di vedere il fine di una cosa, ch'era sempre rimasta senz'alcuno <lb/>significato a'miei, come a tutti gli occhi volgari. </s>

<s>Mi rivolgo perci&ograve; a fare <lb/>istanza insieme con voi al sig. </s>

<s>Salviati, perch&egrave; voglia senz'altro indugio en&shy;<lb/>trare in questo nuovo ragionamento. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Il sig. </s>

<s>Aproino, che troppo tardi &egrave; venuto a pigliar parte <lb/>nella nostra conversazione, non sapr&agrave; forse che nell'altro nostro congresso si <lb/>lessero le dimostrazioni dell'Accademico intorno alla nuova Scienza dei pro&shy;<lb/>ietti, per fondamento della quale si poneva che, fatta astrazione dagl'impe&shy;<lb/>dimenti dell'aria, e da qualsivoglia altro estrinseco accidente, descrivono essi <lb/>proietti in aria una linea curva, non punto differente dalla parabola. </s>

<s>Di qui <lb/>venivano inaspettatamente suggerite certissime norme all'arte dei bombar&shy;<lb/>dieri, nel dirigere i loro tiri, cosicch&egrave;, fatto prima esperienza dell'impeto, <lb/>ossia della forza che ha di cacciare in su nel perpendicolo, con una data mi&shy;<lb/>sura di polvere, lo strumento, il sapere a qual distanza avrebbe gettata la <lb/><figure id="id.020.01.2519.1.jpg" xlink:href="020/01/2519/1.jpg"/></s></p><p type="caption">

<s>Figura 46.<lb/>medesima palla, nella tale o nella tal'altra in&shy;<lb/>clinazion della squadra, si riduceva a calcoli <lb/>matematici disposti dall'Autore in tavole esat&shy;<lb/>tissime per servigio dei militari. </s>

<s>Ma perch&egrave; l'uso <lb/>di coteste tavole richiedeva pure qualche noti&shy;<lb/>zia delle dottrine, e in ogni modo bisognava <lb/>ricorrere alle pagine di un libro, e a trattar <lb/>gli strumenti dell'uomo letterato, di che non <lb/>pu&ograve; sempre aversi comodit&agrave; in un accampa&shy;<lb/>mento; dall'avere osservato che la sacca delle <lb/>catenelle &egrave; una parabola, venne in mente allo <lb/>stesso Accademico di ridurre a un semplice <lb/>esercizio manuale quel che il Filosofo aveva <lb/>scritto ne'suoi libri. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Supponga, sig. </s>

<s>Aproino, di avere sopra <lb/>una superficie piana, come sarebbe una tavoletta di legno o un cartoncino <lb/>assai duro, appuntati in A e in B (fig. </s>

<s>46), all'estremit&agrave; di una linea ori-<pb xlink:href="020/01/2520.jpg" pagenum="145"/>zontale, due spilli, dai quali si faccia pendere una sottilissima calena, che <lb/>lenteggiando s'incurver&agrave; secondo la linea ACB in figura di una parabola, <lb/>l'altezza della quale sar&agrave; CD e AB l'ampiezza. </s>

<s>S'ella vorr&agrave; mantenere quella <lb/>medesima ampiezza, ma descrivere parabole pi&ugrave; o meno alte, che passino <lb/>per un dato scopo v. </s>

<s>g. </s>

<s>per E, ella non dovrebbe far altro che ritirare la <lb/>catenella per uno dei suoi capi. </s>

<s>S'immagini ora che coteste curve rappre&shy;<lb/>sentino le vie disegnate per aria da un proietto in B: ella intender&agrave; facil&shy;<lb/>mente come si possa, conducendo le tangenti BF, BG, misurare gli angoli <lb/>DBF, DBG, e cos&igrave; sapere l'elevazione del pezzo, a cui corrispondono le ri&shy;<lb/>chieste ampiezze e altezze del tiro. </s>

<s>Un quadrante perci&ograve; giustamente diviso <lb/>e applicato alla tavoletta, col centro in B, servirebbe a risolvere cos&igrave; questo, <lb/>come altri simili problemi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Intendo benissimo come sarebbe un tale strumento assai <lb/>comodo per i militari, ai quali presterebbe non punto minor servigio del <lb/>Compasso di proporzione, che lo stesso Inventore descrisse e pubblic&ograve;, per <lb/>facilitare le operazioni geometriche e aritmetiche a quelle persone, le quali, <lb/>essendo in tanti altri maneggi occupate e distratte, non possono avere la pa&shy;<lb/>zienza assidua, che ci vuole per seguir le regole insegnate dai libri. </s>

<s>Ma a <lb/>condurre le divisate operazioni ad effetto mi si presentano alcune difficolt&agrave;, <lb/>la prima delle quali &egrave; intorno al modo come possa la catenuzza lasciar, sulla <lb/>superficie da lei toccata, il vestigio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Il modo pi&ugrave; facile, e che pure non aberra di troppo dalla <lb/>richiesta precisione, &egrave; quello di punteggiare o con uno stile o con una penna; <lb/>ma volendo avere un disegno e serbarlo, per servirsene come di stampa, <lb/>usava il nostro Accademico di traforare con uno spillo il cartone lungo le <lb/>tracce della catena, e poi con lo spolvero ne riproduceva altrove, e quante <lb/>volte gli fosse piaciuto, il medesimo disegno. </s>

<s>Questo, che voi vedete cos&igrave; tra&shy;<lb/>forato e cos&igrave; annerito lungo queste tre linee, sopra le quali pass&ograve; il piumac&shy;<lb/>cino pieno di polvere di brace; era preparato per ritrovare i gradi delle ele&shy;<lb/>vazioni nelle parabole di varia altezza, e di tutte le quali fosse 465 l'am&shy;<lb/>piezza totale. </s>

<s>Chiesi questo cartoncino all'Autore, appresso al quale era ri&shy;<lb/>masto inutile, per averne fatto un altro simile e pi&ugrave; preciso, un giorno che <lb/>lo trovai nel suo studio, tutto intento a questi esercizi, e, bench&egrave; vile agli <lb/>occhi del volgo, la Filosofia nonostante e l'amicizia me lo fanno tenere in <lb/>grandissimo pregio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Io non me ne pregerei punto meno di voi, sig. </s>

<s>Salviati, <lb/>quanto all'amicizia, ma quanto alla Filosofia io per me non troverci d'acquie&shy;<lb/>tarmi nell'a<gap/>irare il pregio dell'invenzione, se non allora, che mi venisse <lb/>dimostrato essere veramente parabolica la linea, secondo la quale s'incurva <lb/>una catena. </s>

<s>E perch&egrave;, asseverandolo voi con tanta fiducia, non posso credere <lb/>che non ne abbiate qualche ragione dimostrativa, vi prego a dirmela, per&shy;<lb/>ch&egrave; io abbia insieme con voi a tenere da qui innanzi in quel pregio che si <lb/>merita, e ch'io desidero, la invenzione del nostro comune amico. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; La dimostrazione, che voi richiedete, si riduce all'evi-<pb xlink:href="020/01/2521.jpg" pagenum="146"/>denza di un fatto, perch&egrave;, se voi descriverete, con gli strumenti suggeritivi, <lb/>e con le regole insegnate dai Geometri, le parabole ACB, AEB, come nella <lb/>figura precedente, o quante altre pi&ugrave; ve ne piacesse, e poi vi adatterete una <lb/>catenella; troverete che ella cammina <emph type="italics"/>ad unguem<emph.end type="italics"/> sopra ognuna delle para&shy;<lb/>bole geometriche da voi descritte. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Io ho pi&ugrave; volte fatta questa esperienza, ed ho trovato <lb/>che si verifica, specialmente nelle parabole con elevazione sotto ai 45 gradi. </s>

<s><lb/>Vi confesso per&ograve;, sig. </s>

<s>Salviati, che questo modo di descrivere meccanicamente <lb/>le curve non ha ottenuto mai nella mia mente l'assenso, che avrei dato a <lb/>una vera e propria dimostrazion matematica, e quale mi sembra si richie&shy;<lb/>derebbe, per far di queste catenuzze uno strumento militare, che esattamente <lb/>risponda alle operazioni della Ballistica, come risponde il compasso alle ope&shy;<lb/>razioni dell'Aritmetica e della Geometria. </s>

<s>Sento perci&ograve; anch'io di parteci&shy;<lb/>pare con le difficolt&agrave; del signor Aproino. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Buon per me che io mi trovo in grado di poter dare <lb/>ampia sodisfazione ad ambedue, avendo io avuto dal nostro Accademico que&shy;<lb/>sta matematica dimostrazione, che voi desiderate. </s>

<s>Vi dir&ograve; anzi, per vostra <lb/>consolazione, ch'egli medesimo mi ha confessato pi&ugrave; volte di non essersi <lb/>acquietato di affidare conclusione cos&igrave; importante alla semplice vista, nella <lb/>quale, e nel non risponder sempre la materia alle intenzioni dell'arte, po&shy;<lb/>teva sospettarsi qualche fallacia. </s>

<s>Di qui &egrave; che solo allora propose l'uso del <lb/>suo nuovo strumento militare quando riusc&igrave; a dimostrar che la linea, nella <lb/>quale si dispongono gli anelli di una catena, &egrave; quella medesima, che segnano i <lb/>proietti per l'aria: n&egrave; io v'avrei promesso di darvi questo trattato, quando <lb/>non ne avessi avuto certezza di scienza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; M'immagino che non possa questa certezza dipendere da <lb/>altro, che dalle dottrine gi&agrave; dimostrate intorno alla nuova Scienza del moto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Non poteva non esser cos&igrave;, come voi dite, e son parti&shy;<lb/>colarmente cos&igrave; fatte dottrine derivate da una di quelle proposizioni, che voi <lb/>vi rammenterete di avere udita leggere da me, nel trattato delle resistenze <lb/>dei solidi allo spezzarsi. </s>

<s>Immaginate infatti che siano tutti gli anelli compo&shy;<lb/>nenti la catena infilati in un'asta orizzontale sostenuta a'due estremi, la <lb/>quale, a un tratto, nei punti dov'&egrave; gravata, si fiacchi, rimanendo esse sole <lb/>l'estremit&agrave; immobili: tutti gli altri anelli, che stavano nel mezzo, abbando&shy;<lb/>nati, cadranno, e cadendo non potranno accomodarsi in quel nuovo stato di <lb/>equilibrio, se non a condizion che ciascuno sia sceso quanto comportava il <lb/>suo proprio momento. </s>

<s>E perch&egrave; l'ordine di quelle scese, incominciando dal <lb/>secondo anello infino a quello di mezzo, &egrave; che decide della figura, secondo <lb/>la quale viene a incurvarsi la met&agrave; della catena, che necessariamente sar&agrave; <lb/>simile all'altra; voi intendete che tutto si riduce a sapere con qual mo&shy;<lb/>mento gravitino gli anelli, che si suppongono simili e uguali, sopra tutta <lb/>la lunghezza dell'asta, secondo le distanze varie di qua e di l&agrave; dai so&shy;<lb/>stegni. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Permettete, sig. </s>

<s>Salviati, che io aiuti la mia debole in-<pb xlink:href="020/01/2522.jpg" pagenum="147"/>telligenza con un poco di figura: Sia CD (fig. </s>

<s>47) l'asta appoggiata nelle sue <lb/>estremit&agrave;: supposto che i pesi di due anelli, uno in B, l'altro in A, siano <lb/><figure id="id.020.01.2522.1.jpg" xlink:href="020/01/2522/1.jpg"/></s></p><p type="caption">

<s>Figura 47.<lb/>rappresentati dai gravi H, F, fra loro <lb/>uguali e pendenti nell'asta da que'me&shy;<lb/>desimi punti B, A; voi proponete di <lb/>risolvere il problema qual sia il mo&shy;<lb/>mento del peso H in B verso il mo&shy;<lb/>mento del medesimo peso, o del suo <lb/>eguale F, in A. Io, nella scienza ma&shy;<lb/>tematica, che ho potuto fin qui impa&shy;<lb/>rare dai maestri e dai libri, non ritrovo chiari i principii per risolvere la que&shy;<lb/>stione, ma in ogni modo non mi sembrano alieni dalle speculazioni meccaniche <lb/>intorno alla Libbra, per cui non vederei come c'entrassero le proposizioni <lb/>delle resistenze dei solidi allo spezzarsi, anco quando avessi avuto la sorte <lb/>d'intervenire, come il sig. </s>

<s>Sagredo, ai passati vostri congressi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Ma la nuova Scienza delle resistenze voi dovete sapere <lb/>che da nessun'altra dipende, che da quella antica di Archimede intorno alla <lb/>Libbra, purch&egrave; la linea geometrica, all'estremit&agrave; della quale s'aggiungono i <lb/>pesi, si consideri come una verga solida, che debba spezzarsi. </s>

<s>Se sia la lib&shy;<lb/>bra AB (fig. </s>

<s>48) col sostegno in C, voi dite, per la dottrina degli equipon&shy;<lb/><figure id="id.020.01.2522.2.jpg" xlink:href="020/01/2522/2.jpg"/></s></p><p type="caption">

<s>Figura 48.<lb/>deranti, che sar&agrave; in equilibrio, <lb/>quando, alla potenza del peso A in <lb/>alzare, giustamente resista il peso <lb/>B all'essere alzato. </s>

<s>Ma le mede&shy;<lb/>sime ragioni di potenza e di resi&shy;<lb/>stenza si possono applicare allo <lb/>strumento, considerando la linea <lb/>AB come una verga solida, la <lb/>quale consister&agrave; in equilibrio, tutte <lb/>le volte che la potenza di A allo spezzare equivalga alla resistenza B all'essere <lb/>spezzato. </s>

<s>Che se quelle due opposte virt&ugrave; di operare e di resistere fossero le <lb/>massime in produrre il relativo effetto, qualunque minima aggiunta all'una o <lb/>detrazione all'altra baster&agrave; per turbar l'equilibrio, ossia per fiaccare la verga, fa&shy;<lb/>cendola abbassare e rivolgere intorno al centro C, come nella semplice Libbra. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Voi ora, sig. </s>

<s>Salviati, mi fate congetturare che la pro&shy;<lb/>posizione, nel trattato delle resistenze da voi stesso poco sopra accennata, <lb/>possa essere la dodicesima, la quale, se ben mi ricordo, pronunziaste in que&shy;<lb/>sta maniera: <emph type="italics"/>Se nella lunghezza di un cilindro si noteranno due luoghi, <lb/>sopra i quali si voglia far la frazione di esso cilindro, le resistenze di <lb/>detti due luoghi hanno fra di loro la medesima proporzione, che i ret&shy;<lb/>tangoli fatti dalle distanze di essi luoghi contrariamente presi.<emph.end type="italics"/> Se non che <lb/>io vi confesso che mi trovo combattuto da due parti circa a questa propo&shy;<lb/>sizione: il primo assalto mi viene dal considerarla in s&egrave; stessa, e il secondo <lb/>dal passare a farne l'applicazione ai momenti del medesimo peso collocato <pb xlink:href="020/01/2523.jpg" pagenum="148"/>a varie distanze dal mezzo dell'asta. </s>

<s>Io non ho infatti dubitato mai della ve&shy;<lb/>rit&agrave; della detta proposizione, ma del modo come da voi stesso veniva dimo&shy;<lb/>strata, fondandovi sopra un supposto, secondo me dubitabile, perch&egrave; forse da <lb/>me non bene inteso, che cio&egrave; i momenti dei gravi appesi in una bilancia <lb/>hanno tra loro la proporzione composta delle distanze dal sostegno e delle <lb/>moli. </s>

<s>Questo quanto alla proposizione in s&egrave; stessa: quanto poi all'applica&shy;<lb/>zione, che si accennava di farne ai momenti dei pesi, nella Libbra appog&shy;<lb/>giata alle estremit&agrave; della sua lunghezza, mi teneva in dubbio il pensare che, <lb/>nella detta XII, il cilindro, sopra cui proponevasi di far la frazione, si con&shy;<lb/>siderava invece da voi con gli appoggi nei punti di mezzo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Non dubitate, sig. </s>

<s>Sagredo, che io trover&ograve; modo di quie&shy;<lb/>tare la vostra mente intorno all'uno e all'altro dubbio. </s>

<s>E incominciando dal <lb/>primo, io non vi negher&ograve; che la proporzion dei momenti, come trasparisce <lb/>dalla XII proposizione del trattato delle resistenze, non lasciasse qualche cosa <lb/>a desiderare. </s>

<s>Si poteva per&ograve; non difficilmente supplire al difetto richiaman&shy;<lb/>dosi alla definizione, che dei momenti danno gli Autori della Scienza mec&shy;<lb/>canica, e alle note leggi degli equiponderanti nella Libbra. </s>

<s>Resultando in&shy;<lb/>fatti da quelle leggi che permane allora la macchina in equilibrio, quando, <lb/>come nella precedente figura, il peso A, moltiplicato per la distanza AC dal <lb/>sostegno, &egrave; uguale al peso B moltiplicato per la distanza BC; se voi date <lb/>alla propensione o all'impeto di andare in basso, composto di gravit&agrave; e di <lb/>posizione, il nome di <emph type="italics"/>momento,<emph.end type="italics"/> averete gi&agrave; concluso che i momenti nella bi&shy;<lb/>lancia hanno la ragion composta delle distanze e dei pesi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Dietro queste considerazioni non stim&ograve; necessario l'Autore del trat&shy;<lb/>tato delle resistenze che si dimostrasse una cosa, di s&igrave; facile conclusione dagli <lb/>antichi teoremi di Archimede. </s>

<s>Ma nell'ordinare le proposizioni ultimamente <lb/>da lui dimostrate, per servire di fondamento al nuovo trattatello dell'uso <lb/>delle catenuzze, incominciandosi dall'invocare i momenti, secondo la propor&shy;<lb/>zion dei quali scendono pi&ugrave; o meno gli anelli, cred&egrave; bene l'Accademico di <lb/>dover mettere espressa la proposizione, ch'io vi legger&ograve; sopra questo foglio, <lb/>nella forma originale, nella quale fu scritta, e che anche per noi sar&agrave; in or&shy;<lb/>dine la prima di quelle, che ricorreranno via via nel nostro ragionamento. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO I. &mdash; Ponderum in Libra suspensorum momenta habent ra&shy;<lb/>tionem compositam ex ratione ipsorum ponderum, et ex ratione distantiarum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pendeant pondera DE, et F (fig. </s>

<s>49) ex distantiis AB, BC: dico mo&shy;<lb/><figure id="id.020.01.2523.1.jpg" xlink:href="020/01/2523/1.jpg"/></s></p><p type="caption">

<s>Figura 49.<lb/>mentum ponderis DE, ad mo&shy;<lb/>mentum ponderis F, habere <lb/>rationem compositam ex ra&shy;<lb/>tionibus ponderis DE, ad pon&shy;<lb/>dus F, et distantiae AB ad di&shy;<lb/>stantiam BC. </s>

<s>Ut enim AB ad <lb/>BC, ita fiat pondus F ad pon&shy;<lb/>dus DO: cum ergo pondera F et DO habeant rationem distantiarum AB, BC <lb/>permutatam, erit momentum ponderis F aequale momento ponderis DE. </s>

<s>Cum <pb xlink:href="020/01/2524.jpg" pagenum="149"/>igitur sint tria pondera utcumque ED, F, et DO, erit ratio ponderis ED ad <lb/>DO composita ex rationibus ED ad F, et F ad DO. </s>

<s>Ut autem pondus ED, ad <lb/>pon dus DO, ita momentum ED ad momentum DO; pendent enim ex eodem <lb/>puncto: igitur, cum momentum DO sit aequale momento F, ratio momenti <lb/>ED ad momentum F erit composita ex ratione ponderis ED ad pondus F, <lb/>et ponderis F ad pondus DO. </s>

<s>Factum est autem pondus F ad pondus DO ut <lb/>distantia AB ad distantiam BC; ergo patet momentum ponderis ED, ad mo&shy;<lb/>mentum ponderis F, habere rationem compositam ex rationibus ponderum <lb/>ED, F, et distantiarum AB, BC. &rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Io ringrazio voi, sig. </s>

<s>Salviati, e benedico anche insieme <lb/>i dubbi del sig. </s>

<s>Sagredo, che hanno dato occasione di metter fuori un teo&shy;<lb/>rema, nel quale non ho memoria di essermi incontrato mai, leggendo ci&ograve; che <lb/>in simile materia &egrave; stato scritto dagli altri autori. </s>

<s>La conclusione io la vedo <lb/>poi scendere da cos&igrave; chiari principii, che mi fanno intravedere non poche <lb/>altre conseguenze utili alla dottrina dei moti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; L'utilit&agrave; che voi sagacemente avete appresa, la vedrete <lb/>presto, sig. </s>

<s>Aproino, ricavarsi dalle applicazioni che ne faremo, ma intanto &egrave; <lb/>bene che passiamo a risolvere l'altro dubbio del sig. </s>

<s>Sagredo, nel sereno volto <lb/>del quale mi par di leggere la soddisfazione, che gi&agrave; ha avuto del primo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Non dite solo sodisfazione, ma compiacenza, per essere <lb/>anche a me, come al sig. </s>

<s>Aproino, giunta quella dimostrazione della propor&shy;<lb/>zion dei momenti cosa del tutto nuova. </s>

<s>E bench&egrave; io forse potessi anche da <lb/>me riuscire a intendere le ragioni del trapasso, dal cilindro sostenuto nel <lb/>mezzo, al cilindro appoggiato negli estremi, essendo l&igrave; l&igrave; per fiaccarsi, aggra&shy;<lb/>vato nell'uno e nell'altro modo dai medesimi pesi; aspetto che voi me ne <lb/>alleviate la fatica, e rendiate me, pi&ugrave; che da me medesimo, sicuro di aver <lb/>veduto il vero. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Io lascerei volentieri intera a voi la compiacenza di <lb/>ritrovare come sia vero che s'hanno le medesime condizioni d'equilibrio <lb/>nella libbra geometrica, e nella verga rigida che vuole spezzarsi, o siano i <lb/>sostegni nel mezzo o negli estremi, essendo dall'altra parte la cosa facilis&shy;<lb/>sima a dimostrarsi. </s>

<s>Ma perch&egrave; voi volete che io sovvenga ad alleggerirvi la <lb/>fatica, richiamer&ograve; la vostra considerazione sopra la libbra AB, poco fa dise&shy;<lb/>gnata nella figura 48, la quale voi ben sapete consistere in equilibrio intorno <lb/>al punto C, quando sta il peso A al peso B reciprocamente, come la distanza <lb/>BC alla AC. Componendo, troveremo il peso A col peso B, al semplice peso A <lb/>o al semplice peso B, essere come BC con AC, ossia AB, a BC o ad AC: <lb/>ond'&egrave; manifesto che rimane la bilancia in equilibrio, tanto col sostegno in C <lb/>e i pesi in A, B, quanto col mettere in A e in B i sostegni, e in C la somma <lb/>di quegli stessi due pesi. </s>

<s>Dalla libbra geometrica facendo poi il trapasso al <lb/>cilindro solido, intenderete che, se A, B sono i massimi sforzi, ai quali quello <lb/>stesso cilindro resiste senza spezzarsi, sostenuto in C; sostenuto invece in A <lb/>e in B, la somma dei due pesi in C misurer&agrave; la massima forza, a cui pu&ograve; <lb/>resistere il solido all'esser rotto in quel medesimo punto. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2525.jpg" pagenum="150"/><p type="main">

<s>&ldquo; Riduciamoci ora alla memoria la proposizione XII delle resistenze: <lb/>fu in quella da noi dimostrato che, se le forze A, B son minime per rom&shy;<lb/>pere in C, e le E, F parimente minime per rompere in D, le forze A, B, <lb/>alle E, F hanno reciprocamente la medesima proporzione, che il rettangolo <lb/>ADB al rettangolo ACB. </s>

<s>Ma per quel che s'&egrave; detto e convenuto, tant'&egrave; a <lb/>mantenere i sostegni in D, C, e i pesi in A, B, e in E, F, quanto a traspor&shy;<lb/>tare i sostegni in A, B, e i pesi A, B, riuniti insieme, in C, e gli altri E, F <lb/>riuniti in D; diremo dunque, e sia questa la seconda proposizione, che, aven&shy;<lb/>dosi un cilindro sostenuto nelle sue estremit&agrave; A, B, il peso che pu&ograve; rompere <lb/>in C, al peso che pu&ograve; rompere in D, ossia la resistenza in C, alla resistenza <lb/>in D, sta come il rettangolo ADB, al rettangolo ACB. </s>

<s>La dimostrazione perci&ograve; <lb/>sarebbe ora quella medesima, che fu allora, e solo si potrebbe ripetere in <lb/>grazia del sig. </s>

<s>Aproino, che non era presente. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Voi mi avete cos&igrave; bene, sig. </s>

<s>Salviati, preparate le vie <lb/>co'vostri dotti ragionamenti, che non diffido di riuscire da me medesimo a <lb/>rintracciare quella dimostrazione. </s>

<s>In ogni modo, per non indugiar di troppo <lb/>a venire a concludere il rimanente che &egrave; il desiderato fine del nostro collo&shy;<lb/>quio, supporr&ograve; come vera la proposizione, che voi avete messa in ordine la <lb/>seconda. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Se cos&igrave; &egrave;, non rimane a fare che un passo solo, per riu&shy;<lb/>scire all'intento nostro principale, qual era quello di saper con quali varii <lb/>momenti pesino gli anelli sopra l'asta, nella quale s'immaginava che fossero <lb/>infilati, e di li dedurne le proporzioni delle scese, per concludere all'ultimo <lb/>qual sia la linea, nella quale s'incurva la catena. </s>

<s>Vi annunzio intanto, rife&shy;<lb/>rendoci alla figura, per quel primo proposito disegnata, questa terza propo&shy;<lb/>sizione, che dice: il momento del peso F in A, al momento del medesimo <lb/>peso, o di un peso uguale H in B, sta omologamente come il rettangolo CAD, <lb/>al rettangolo CBD. &rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Cosicch&egrave; i momenti stanno contrariamente alle resistenze, <lb/>e l'anello della catena in B aver&agrave; meno impeto di scendere, che non ha <lb/>l'anello in A, perch&egrave; quello trova, nell'asta che pi&ugrave; gli resiste, maggiore <lb/>l'impedimento. </s>

<s>Cos&igrave; pure intendo perch&egrave; la catena, dal primo anello a quello <lb/>di mezzo, si dilunghi sempre pi&ugrave; dalla disposizione orizontale, che aveva es&shy;<lb/>sendo infilata nell'asta, trovandosi poi al suo proprio peso abbandonata. </s>

<s>Mi <lb/>sembra anche di veder distinto l'albore di quel lume di verit&agrave;, che voi sa&shy;<lb/>rete presto per rivelare alle nostre desiderose pupille: e perch&egrave; l'indugio ne <lb/>riesce penoso, proseguite, sig. </s>

<s>Salviati, a dimostrare che i momenti dei pesi <lb/>F, H hanno tra di loro la medesima proporzione, che i rettangoli fatti dalle <lb/>distanze di essi luoghi omologamente presi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; La dimostrazione, dietro quel che &egrave; stato detto fin qui, <lb/>e consentito da voi insieme col sig. </s>

<s>Aproino, &egrave; facile e spedita. </s>

<s>Imperocch&egrave;, <lb/>mantenuta sott'occhio la medesima rappresentazione, supponiamo che sia il <lb/>peso F la misura della resistenza in A, e che la misura della resistenza in B <lb/>sia il peso H aggrandito in E. Sar&agrave;, per la seconda proposizione, la resistenza <pb xlink:href="020/01/2526.jpg" pagenum="151"/>in A, alla resistenza in B; ossia il peso F al peso E, come il rettangolo CBD <lb/>al rettangolo CAD. </s>

<s>Ma essendo i pesi H, E attaccati al medesimo punto della <lb/>Libbra, hanno la proporzion medesima dei loro momenti, cio&egrave; il momento <lb/>di H al momento di E (che &egrave; uguale al momento di F, per avere la mede&shy;<lb/>sima virt&ugrave; di rompere l'asta) sta come il peso F al peso E; dunque il mo&shy;<lb/>mento di H, al momento di F, sta come il rettangolo CBD al rettangolo CAD, <lb/>secondo quel che mi proposi di dimostrare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ci siamo ora finalmente condotti, per questa ordinata serie di propo&shy;<lb/>sizioni, a ritrovare quel che s'andava cercando in fino dal principio del no&shy;<lb/>stro ragionamento, e a che si diceva ridursi la somma delle cose: a sapere <lb/>cio&egrave; con qual momento facciano i vari anelli della catena impeto di scen&shy;<lb/>dere, abbandonati dall'asta che gli sosteneva. </s>

<s>Sia l'asta rappresentata dalla <lb/>linea orizontale HD (fig. </s>

<s>50) e per l'impeto o il momento, che ha l'anello <lb/>in F, supponiamo che possa scendere in fino in E, quant'&egrave; la linea perpen&shy;<lb/><figure id="id.020.01.2526.1.jpg" xlink:href="020/01/2526/1.jpg"/></s></p><p type="caption">

<s>Figura 50.<lb/>dicolare FE, e parimente l'anello in N possa scen&shy;<lb/>dere quanto la linea MN. </s>

<s>Perch&egrave; le scese debbono <lb/>essere proporzionali ai loro momenti, sar&agrave; dunque, <lb/>per le cose gi&agrave; dimostrate, FE ad NM come il ret&shy;<lb/>tangolo HFD al rettangolo HND. </s>

<s>Ora che altro ci ri&shy;<lb/>mane per concludere che i punti E, M, e tutti gli altri <lb/>rispondenti agli anelli di una catena, sono veramente <lb/>in una parabola, se non che invocare un teorema, che <lb/>non troverete scritto da nessuno Autore o antico o <lb/>moderno, ma che il nostro Accademico dimostr&ograve; in <lb/>grazia del suo trattato delle resistenze? </s>

<s>Io vi voglio ora proporre quel teorema <lb/>che &egrave; tale: Le parallele al diametro della parabola di cui seghino perpendico&shy;<lb/>larmente la base, hanno la proporzione medesima dei rettangoli fatti dai se&shy;<lb/>gamenti; e cos&igrave; v. </s>

<s>g. </s>

<s>le NM, FE, parallele al diametro AC nella disegnata <lb/>figura, staranno fra loro come i rettangoli HND, HFD. &rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Il padre Fra Bonaventura Cavalieri, quando fui poco tempo <lb/>fa a visitarlo a Bologna, e a proposito del mio strumento da rinforzare l'udito <lb/>essendo entrato con lui in ragionamento dei Conici, mi disse cotesto stesso teo&shy;<lb/>rema, ma non intesi bene, se come sua propria invenzione o del sig. </s>

<s>Galileo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Potrebb'esser benissimo che anche il padre Bonaventura, <lb/>a cui il nostro Amico &egrave; solito dare il nome di Archimede del nostro tempo, <lb/>si fosse incontrato in cotesta medesima passione della parabola, utilissima per <lb/>molte dimostrazioni di Meccanica e di Geometria: ma io posso assicurarvi <lb/>di avere avuto, ne'colloqui coll'Accademico, una tale notizia molti anni prima <lb/>che fosse l'ingegno del Cavalieri maturo a produrre di simili frutti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Voi mi fate ora risovvenire di avere udito questo mede&shy;<lb/>simo in Padova, quando il nostro Matematico insegnava nel nostro pubblico <lb/>studio. </s>

<s>E perch&egrave; la verit&agrave; non fa caro di s&egrave; a nessuno, che desiderosamente, <lb/>e per le medesime vie rette la cerca, consolateci, sig. </s>

<s>Salviati, col mostrarla <lb/>di nuovo ai nostri occhi svelata. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2527.jpg" pagenum="152"/><p type="main">

<s>&ldquo; SALVIATI. &mdash; Mi gode l'animo di poter darvi piena sodisfazione, anche <lb/>questa volta, non ricercandosi veramente in voi altra precognizione da quella in <lb/>fuori, che aveste allora, quando dalla semplice generazione della parabola imme&shy;<lb/>diatamente vi conclusi che le diametrali stanno come i quadrati delle applicate. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Io ho bene a memoria la dimostrazione, che ne d&agrave; nei <lb/>suoi Conici Apollonio, e perci&ograve; tengo anch'io come cosa gi&agrave; nota che la li&shy;<lb/>nea AC sta alla AB, come il quadrato di CD sta al quadrato di BE. &rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. </s>

<s>Cos&igrave; veramente essendo, dividiamo, e averemo AC meno AB, <lb/>ossia BC, ossia l'uguale EF, sta ad AC, come il quadrato di CD, meno il <lb/>quadrato di BE, sta al quadrato di CD. </s>

<s>Ma la differenza di due quadrati es&shy;<lb/>sendo uguale al rettangolo fatto dalla somma e dalla differenza delle radici, <lb/>secondo che facilmente si deduce dalla IVa del secondo di Euclide, sar&agrave; il <lb/>quadrato di CD, meno il quadrato di BE, uguale alla linea CD pi&ugrave; BE, ossia <lb/>HF moltiplicata per la linea CD meno BE, ossia FD, o altrimenti la diffe&shy;<lb/>renza dei due detti quadrati sar&agrave; uguale al rettangolo HFD: onde EF ad AC <lb/>avr&agrave; la proporzion medesima che il rettangolo HFD al quadrato di CD. </s>

<s>In <lb/>pari modo dimostreremo che NM ad AC ha la proporzione che il rettangolo <lb/>HND al quadrato di CD: onde avendo le due proporzioni i conseguenti uguali, <lb/>e dovendo esser perci&ograve; gli antecedenti proporzionali, si conclude che FE, MN <lb/>stanno insieme come i rettangoli HFD, HND, secondo ci&ograve; che io v'ebbi pro&shy;<lb/>messo, per satisfare al vostro desiderio. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il Dialogo rimane a questo punto interrotto, ma il trattato dell'uso delle <lb/>catenuzze in ogni modo &egrave; compiuto, e ci&ograve; che si sente dovervi mancare <lb/>non poteva esser altro che il congedo fra gl'interlocutori pi&ugrave; o meno ceri&shy;<lb/>monioso. </s>

<s>Nel consentir nonostante i nostri Lettori che si comprenda nelle <lb/>trascritte parole intero l'argomento, potrebbero domandare a noi le ragioni, <lb/>che ci hanno fatto attribuire quella scrittura a Galileo. </s>

<s>Intorno a che &egrave; da <lb/>distinguere tra la forma e la materia, la quale che sia schiettamente gali&shy;<lb/>leiana basterebbe a provarlo con certezza il fatto, che autografo dell'Accade&shy;<lb/>mico, nel codice e nel foglio da noi citati nel Tomo precedente all'articolo IV <lb/>del Cap. </s>

<s>VIII, &egrave; il teorema letto dal Salviati intorno ai momenti composti <lb/>delle distanze e delle moli; che pure &egrave; autografa la proposizione, da noi pa&shy;<lb/>rimente ivi citata, dei pesi uguali che, nell'asta sostenuta all'estremit&agrave;, ope&shy;<lb/>rano con momenti omologamente proporzionali ai rettangoli fatti sulle di&shy;<lb/>stanze dai sostegni; che autografo in fine &egrave; il disegno da noi nel citato Tomo <lb/>e capitolo rappresentato, in cui accennava Galileo di voler applicare la pro&shy;<lb/>posizione ultimamente detta agli anelli della catena, con manifesta intenzione <lb/>di concluderne la curvit&agrave; di lei parabolica. </s></p><p type="main">

<s>N&egrave; vogliamo proseguire oltre il nostro discorso, senza fare osservare che <lb/>la scoperta del Dialogo delle catenuzze, a noi felicemente in questi ultimi <lb/>giorni occorsa, ci ha tolti alcuni dubbi, e ka dichiarati certi fatti rimasti a <lb/>noi oscuri, quando nel detto Cap. </s>

<s>VIII si esponeva la nostra storia, nella quale <lb/>si diceva di non sapere intendere come si rimanessero fra le altre carte inu&shy;<lb/>tili gli autografi dianzi commemorati; e, potendo con la materia di essi l'Au-<pb xlink:href="020/01/2528.jpg" pagenum="153"/>tore illustrare il suo trattato delle resistenze, lo volesse nulladimeno lasciare <lb/>in questo difetto, perch&egrave; poi, a sovvenire ai bisogni della Scienza, vi supplis&shy;<lb/>sero a gara il Cavalieri, il Torricelli e il Viviani. </s>

<s>Ora abbiamo inteso che le <lb/>proposizioni rimaste manoscritte erano ordinate a un trattato alquanto diverso <lb/>da quello proprio delle resistenze, e che, tutt'altro ch'esser dimostrate per <lb/>esser poi rifiutate, come ci parve ritrovandole cos&igrave; neglette, dovevano anzi ser&shy;<lb/>vire di ricca trama, sopra la quale si ordirebbe il rimanente colloquio, per <lb/>condurre a sera con esso la giornata incominciatasi col discorso della percossa. </s></p><p type="main">

<s>Tornando ora a dire delle ragioni, per le quali si provi che l'altro di&shy;<lb/>scorso dell'uso delle catenuzze da noi trascritto era informato ai concetti di <lb/>Galileo, si pu&ograve; aggiungere che il cartoncino traforato lungo il filo delle linee <lb/>paraboliche con uno spillo, per riprodurre con lo spolvero il medesimo di&shy;<lb/>segno, con quelle macchie nere lasciatevi sopra dal piumaccino, e in quello <lb/>stato proprio che apparisce dalle parole del Salviati, si conserva tuttavia cu&shy;<lb/>cito, in luogo del foglio 41, nel II Tomo della Parte V dei Manoscritti di <lb/>Galileo, dove ripetutamente negli angoli opposti si legge autografo <emph type="italics"/>amplitudo <lb/>tota 465.<emph.end type="italics"/> Ma la pi&ugrave; autorevole conferma di ci&ograve;, che s'intende provare, si ha <lb/>dalla testimonianza del Viviani, a cui crediamo di dovere attribuire il disteso <lb/>del dialogo, o del frammento di dialogo da noi ritrovato, in una copia, che <lb/>deve essere di quel tempo. </s></p><p type="main">

<s>In margine alla pag. </s>

<s>284 dell'edizione di Leida, dove al Sagredo, che <lb/>proponeva potersi con una catenuzza punteggiare molte linee paraboliche, il <lb/>Salviati rispondeva <emph type="italics"/>potersi ct ancora con qualche utilit&agrave; non piccola come <lb/>appresso vi dir&ograve;;<emph.end type="italics"/> il Viviani apponeva una tale postilla: &ldquo; Per mezzo di que&shy;<lb/>sta catenella trovava forse il Galileo le elevazioni, per andare a ferire nello <lb/>scopo dato &rdquo; (MSS. Gal., P. V, T. IX). Poi, in una di quelle note, scritta <lb/>dal medesimo al fol. </s>

<s>23 del Tomo IV di quella stessa Parte V della colle&shy;<lb/>zione, esprimeva un simile dubbio in quest'altra forma: &ldquo; Vedi a carte 384 <lb/>l'ultimo verso, che utilit&agrave; volesse dire il Galileo, se della misura della linea <lb/>parabolica, ovvero del modo di trovare le proposizioni de'moti de'proietti. </s>

<s>&rdquo; </s></p><p type="main">

<s>Vennero nella mente a risolversi intorno a ci&ograve; tutti i dubbi, quando i <lb/>foglietti autografi, ne'quali erano scritte le proposizioni dei momenti fatti da <lb/>pesi uguali sopra la libbra sostenuta alle sue estremit&agrave;, d'onde si conclude&shy;<lb/>vano le virt&ugrave; degl'impeti e le quantit&agrave; della scesa in ciascuno anello della <lb/>catena; capitarono sotto gli occhi del Viviani. </s>

<s>Allora, ordinando coteste di&shy;<lb/>sperse proposizioni, e risovvenendosi di ci&ograve; che aveva udito dire al Maestro <lb/>nell'ospizio di Arcetri, ricompose il Viviani stesso quel trattatello dell'uso <lb/>delle catenuzze, di cui non avevasi altra notizia, da quegli accenni in fuori <lb/>fatti dal Salviati in sulla sera della quarta giornata. </s>

<s>Cos&igrave; il congresso ultimo <lb/>sarebbe venuto a compiersi, secondo le date promesse, nelle sue due parti; <lb/>ond'&egrave; perci&ograve; naturale che, ritenendo il Viviani copia della prima trattante <lb/>della percossa, all'intenzion ch'egli aveva di pubblicarla fra le opere postume, <lb/>dopo la vita di Galileo, da dedicarsi al re di Francia, s'aggiungesse l'altra <lb/>di ridurre il Dialogo intero, distendendo coi documenti gi&agrave; ritrovati quel che <pb xlink:href="020/01/2529.jpg" pagenum="154"/>rimaneva a dirsi dell'uso delle catenuzze nell'arte militare. </s>

<s>Fallite poi le spe&shy;<lb/>ranze di raccogliere in un libro le opere, che per ultimo meditava di scri&shy;<lb/>vere il suo Maestro, il Viviani si content&ograve;, in quel <emph type="italics"/>Ragguaglio<emph.end type="italics"/> che aggiunse <lb/>dopo la <emph type="italics"/>Scienza universale delle proporzioni,<emph.end type="italics"/> di sodisfare al pubblico, anche <lb/>in tal proposito, con queste notizie: </s></p><p type="main">

<s>&ldquo; Restami ora a dir quant'io so intorno all'uso delle catenuzze, pro&shy;<lb/>messo dal Galileo nel fine della quarta Giornata, riferendolo quale egli me <lb/>l'accenn&ograve; quando, presente lui, io stava studiando la sua Scienza de'proietti. </s>

<s><lb/>Parmi dunque che egli intendesse di valersi di simili catene sottilissime pen&shy;<lb/>denti dall'estremit&agrave; loro sopra un piano, per cavar dalle diverse tensioni di <lb/>esse la regola e la pratica di tirar coll'artiglieria ad un dato scopo. </s>

<s>Ma di <lb/>questo a sufficienza e ingegnosamente scrisse il nostro Torricelli nel fine del <lb/>suo trattato de'proietti, onde tal perdita rimane risarcita. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che poi la sacca naturale di simili catenuzze s'adatti sempre alla cur&shy;<lb/>vatura di linee paraboliche, lo deduceva egli, se mal non mi sovviene, da un <lb/>simile discorso: Dovendo i gravi scender naturalmente colla proporzione del <lb/>momento, che essi hanno da'luoghi dove e'son appesi, ed avendo i momenti <lb/>de'gravi uguali, attaccati ai punti di una libbra sostenuta nell'estremit&agrave;, la <lb/>medesima proporzion de'rettangoli delle parti di essa libbra, come il Galileo <lb/>stesso dimostr&ograve; nel trattato Delle resistenze, e questa proporzione essendo la <lb/>medesima che quella tra le linee rette, che dai punti di tal libbra, come <lb/>base d'una parabola, si tirano parallele al diametro di tal parabola, per la <lb/>dottrina de'Conici; tutti gli anelli della catenuzza, che son come tanti pesi <lb/>uguali pendenti da'punti di quella linea retta, che congiugne l'estremit&agrave; dove <lb/>essa catena &egrave; attaccata, e che serve di base della parabola, dovendo in fine <lb/>scendere quant'&egrave; loro permesso dai loro momenti e quivi fermarsi, fermar <lb/>si dovranno in que'punti, dove le scese loro son proporzionali a'propri mo&shy;<lb/>menti da'luoghi di dove pendono essi anelli nell'ultimo stante del moto, che <lb/>poi son que'punti, che s'adattano ad una curva parabolica lunga quanto la <lb/>catena, ed il di cui diametro, che si parte dal mezzo di detta base, sia per&shy;<lb/>pendicolare all'orizonte &rdquo; (Ediz. </s>

<s>cit., pag. </s>

<s>105, 6). </s></p><p type="main">

<s>&Egrave; facile vedere in queste parole compendiato il dialogo da noi trascritto, <lb/>la perdita del quale credeva il Viviani rimanesse risarcita dal Torricelli. </s>

<s>Ma <lb/>il Torricelli in verit&agrave; descrive ingegnosamente, in fine al suo trattato de'pro&shy;<lb/>ietti, un nuovo genere di Squadra, della quale potessero praticamente valersi <lb/>i Bombardieri: non fa motto per&ograve; dello strumento ideato da Galileo, n&egrave; del&shy;<lb/>l'ordine delle proposizioni, che dovevano partecipare a lui maggior certezza <lb/>di scienza meccanica, che non agli strumenti immaginati e descritti per mi&shy;<lb/>surare la forza della percossa. </s>

<s>Il dialogo perci&ograve;, quale fu pubblicato dal Bo&shy;<lb/>naventuri, si rimane in difetto della sua parte migliore, la quale non si sarebbe <lb/>aspettato mai il popolo devoto gli dovess'essere restituita da noi, sacrileghi <lb/>offensori del Nume. </s>

<s>Ma cos&igrave; &egrave;, si vede, nella religione della scienza, come in <lb/>tutte le cose di questo mondo, delle quali lasciando ad altri il pensiero, noi <lb/>ci ridurremo sul filo del nostro primo ragionamento. </s></p><pb xlink:href="020/01/2530.jpg" pagenum="155"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Fu lasciata addietro la nostra Storia dei progressi fatti intorno alla <lb/>scienza della percossa nell'esame del Dialogo di Galileo, il quale concludeva <lb/>le sue dottrine cos&igrave; nella seguente proposizione: &ldquo; Se l'effetto che fa una <lb/>percossa del medesimo peso, e cadente dalla medesima altezza, caccer&agrave; un <lb/>resistente di resistenza sempre uguale per qualche spazio, e che per fare un <lb/>simile effetto ci bisogni una determinata quantit&agrave; di peso morto, che senza <lb/>percossa prema; dico che, quando il medesimo percuziente sopra un altro <lb/>resistente maggiore con tal percossa lo caccer&agrave; v. </s>

<s>g. </s>

<s>per la met&agrave; dello spa&shy;<lb/>zio, che fu cacciato l'altro, per far questa seconda cacciata non basta la <lb/>pressura del detto peso morto, ma ve ne vuole altro il doppio pi&ugrave; grave: e <lb/>cos&igrave; in tutte le altre proporzioni, quanto una cacciata fatta dal medesimo per&shy;<lb/>cuziente &egrave; pi&ugrave; breve, tanto per l'opposto, con proporzione contraria, vi si ri&shy;<lb/>cerca, per far l'istesso, gravit&agrave; maggiore di peso morto premente &rdquo; (Alb. </s>

<s>XIII, <lb/>326, 27). Dicemmo allora come, riscontrata questa galileiana proposizione con <lb/>le nuove verit&agrave; dimostrate dal Borelli, si scoprisse manifestamente falsa, e <lb/>ora soggiungiamo che la falsit&agrave; della conclusione dipendeva dalla falsit&agrave; del <lb/>principio, consistente nel paragonare insieme due cose di genere diverso, quali <lb/>sono il peso morto e il grave, che cadendo percuote. </s>

<s>E perch&egrave; la pi&ugrave; dan&shy;<lb/>nosa applicazione di questo falso principio si faceva a quei vari strumenti im&shy;<lb/>maginati per misurare la forza della percossa, e per concluderne di l&igrave; com'ella <lb/>fosse infinita; giova trattenersi a descrivere i lusi dell'ingegno, e a dire come <lb/>finalmente se ne scoprisse la fallacia. </s></p><p type="main">

<s>Quando il congresso tra il Salviati, il Sagredo e l'Aproino non era a <lb/>nessun altro noto che al Viviani, il quale teneva di quella scrittura appresso <lb/>a s&egrave; copia segreta; correva largamente attorno la fama che Galileo avesse <lb/>inventato due insigni esperimenti, per dimostrare come la forza della per&shy;<lb/>cossa si potesse veramente dire infinita. </s>

<s>Il Torricelli si fece, nella seconda <lb/>delle sue lezioni, organo diffusivo di quella fama, descrivendo cos&igrave; le inven&shy;<lb/>zioni del famosissimo Vecchio ai suoi colleghi accademici della Crusca: </s></p><p type="main">

<s>&ldquo; Egli, mentre viveva, in Padova fece far di molti archi, tutti per&ograve; di <lb/>diversa gagliardezza. </s>

<s>Prendeva poi il pi&ugrave; debole di tutti, ed al mezzo della <lb/>corda di esso sospendeva una palla di piombo, di due oncie in circa, attac&shy;<lb/>cata con un filo lungo per esempio un braccio: fermato l'arco in una morsa, <lb/>alzava quella palla, e lasciandola ricadere osservava, per via d'un vaso so&shy;<lb/>noro sottoposto, per quanto spazio l'impeto della palla incurvasse e si tirasse <lb/>dietro la corda dell'arco: noi supporremo che fosse intorno a quattro dita. </s>

<s><lb/>Attaccava poi alla corda del medesimo arco un peso quiescente, tanto grande <lb/>che incurvasse e tirasse gi&ugrave; la corda dell'arco per lo medesimo spazio di <lb/>quattro dita, e osservava che tal peso voleva essere circa dieci libbre. </s>

<s>Fatto <pb xlink:href="020/01/2531.jpg" pagenum="156"/>questo, prendeva un altro arco pi&ugrave; gagliardo del primo, alla corda di esso <lb/>sospendeva la medesima palla di piomho col medesimo filo, e, facendola ca&shy;<lb/>dere dalla medesima altezza, notava per quanto spazio ella attraesse la corda. </s>

<s><lb/>Attaccava poi del piombo quiescente, tanto che facesse il medesimo effetto, e <lb/>trovava che non bastavano pi&ugrave; quelle dieci libbre, che bastavano prima, ma <lb/>volevano essere pi&ugrave; di venti. </s>

<s>Pigliando poi di mano in mano archi sempre <lb/>pi&ugrave; robusti, trovava che, per agguagliar la forza di quella medesima palla <lb/>di piombo e di quella medesima caduta, sempre vi voleva maggiore e mag&shy;<lb/>gior peso, conforme che l'esperienza si fosse fatta con archi pi&ugrave; e pi&ugrave; ga&shy;<lb/>gliardi. </s>

<s>Adunque, diceva egli, s'io piglier&ograve; un arco gagliardissimo, quella <lb/>palla di piombo, che non passa due once, far&agrave; effetto equivalente a mille lib&shy;<lb/>bre di piombo. </s>

<s>Pigliandosi poi un arco mille volte pi&ugrave; gagliardo di quel ga&shy;<lb/>gliardissimo, quella medesima pallina far&agrave; effetto equivalente a un milione di <lb/>libbre di piombo: segno evidentissimo che la forza di quel poco peso, e di <lb/>quel braccio di caduta &egrave; infinita &rdquo; (Ediz. </s>

<s>cit., pag. </s>

<s>100-2). </s></p><p type="main">

<s>Appresso a questo soggiunge il Torricelli l'altro galileiano esperimento, di <lb/>simile conseguenza del primo, consistente nell'aver due palle uguali di piombo, <lb/>e messa l'una sopra l'incudine, per ammaccarla con la forza di un martello <lb/>caduto dall'altezza di un braccio, far sull'altra uguale ammaccatura, posan&shy;<lb/>dovi sopra un peso morto, che voglia essere per esempio dieci libbre. </s>

<s>&ldquo; Ora <lb/>alcuno crederebbe, prosegue a leggere il nostro Accademico, che la forza di <lb/>quella percossa fosse equivalente al momento di quelle dieci libbre di peso <lb/>quiescente. </s>

<s>Ma pensutelo voi: prendasi i due medesimi pezzi di piombo egual&shy;<lb/>mente ammaccati come stanno; se sopra uno di essi io poser&ograve; dieci libbre <lb/>di peso quiescente, certa cosa &egrave; che non si spianer&agrave; pi&ugrave; di quello che sia, <lb/>avendo egli gi&agrave; un'altra volta sostenuto il medesimo peso di dieci libbre. </s>

<s>Ma <lb/>se vi far&ograve; cadere il martello dalla medesima altezza come prima, far&agrave; ben <lb/>nuova ammaccatura, e per agguagliar questa bisogner&agrave; posare sopra l'altro <lb/>pezzo di piombo molto maggior peso, che quel di prima, e questo succeder&agrave; <lb/>sempre con progresso sino in infinito &rdquo; (ivi. </s>

<s>pag. </s>

<s>103). </s></p><p type="main">

<s>Venivano queste notizie oralmente divulgate in Firenze nel 1642, poco <lb/>dopo la morte di Galileo, e passate per le orecchie degli uditori si sarebbero <lb/>rimaste dimenticate ne'manoscritti torricelliani, se non che le teneva fra noi <lb/>vive la fama, e appresso agli stranieri la commemorazione, che ne faceva <lb/>quattro anni dopo pubblicamente il Mersenno. </s>

<s>Egli dice, nel terzo tomo delle <lb/>sue <emph type="italics"/>Nuove osservazioni,<emph.end type="italics"/> che <emph type="italics"/>quae Galileus circa vim percussionis in ar&shy;<lb/>cubus consideravit<emph.end type="italics"/> gliele aveva comunicate in Roma Michelangiolo Ricci. <lb/></s>

<s>&ldquo; Vir clariss. </s>

<s>M. A. Riccius, ad analysim natus, mecum observationem Pisis <lb/>a Galileo factam comunicavit, quae sic habet &rdquo; (Parisiis 1647, pag. </s>

<s>202): e <lb/>prosegue a descrivere l'esperienza degli archi, precisamente a quel modo che <lb/>l'aveva descritta il Torricelli, concludendo per&ograve; la descrizione con queste pa&shy;<lb/>role: &ldquo; Sed de illis arcus experimentis mihi dubitare liceat, donec ipse vi&shy;<lb/>dero, cum aliae sint observationes, quae contrarium suadere videantur &rdquo; <lb/>(ibid.). Soggiunge poi l'altra esperienza galileiana delle palle di piombo, am-<pb xlink:href="020/01/2532.jpg" pagenum="157"/>maccate ora per via della percossa, ora per via della semplice pressione, in <lb/>piena conformit&agrave; con la notizia, che pochi anni prima ne avevano avuto gli <lb/>Accademici della Crusca. </s></p><p type="main">

<s>Convalidavano anche i Nostri la fama con questo pubblico documento <lb/>del Matematico parigino, e il Borelli, richiamando l'attenzione di coloro, che <lb/>avrebbero letto il suo libro <emph type="italics"/>De vi percussionis,<emph.end type="italics"/> sopra que'due preclari espe&shy;<lb/>rimenti di Galileo; gli descrive in quel modo, che gli trov&ograve; riferiti <emph type="italics"/>a Mer&shy;<lb/>senno Reflexionum physico-mathematicarum cap. </s>

<s>XXIII.<emph.end type="italics"/> Tutto insomma <lb/>quel che s'andava dicendo e scrivendo di ci&ograve; in Italia e fuori era portato <lb/>dalle sole ali della fama, degl'incerti voli della quale, come suol sempre av&shy;<lb/>venire, sarebbe segno il dirsi dal Torricelli che le magnificate esperienze fu&shy;<lb/>rono fatte in Padova, mentre il Ricci al Mersenno, e il Viviani al Ferroni, <lb/>come tra poco vedremo, dicevano invece che erano state fatte in Pisa. </s>

<s>N&egrave; <lb/>in questo caso &egrave; l'incertezza del luogo di poca importanza, perch&egrave; chi chia&shy;<lb/>mava il fatto pisano doveva riferirlo alle speculazioni giovanili di Galileo, <lb/>quando si sa che ancora non aveva concluso la forza della percossa dover <lb/>essere infinita. </s>

<s>E perch&egrave; &egrave; certo che non venne l'Autore a una tal conclu&shy;<lb/>sione, se non che verso il 1635, sembra certo altresi che n&egrave; in Pisa n&egrave; in <lb/>Padova fece egli fabbricare, per il nuovo uso filosofico, quegli archi pi&ugrave; o <lb/>meno gagliardi, ma piuttosto in una delle suburbane ville di Firenze. </s></p><p type="main">

<s>Noi per&ograve; che, invece di ascoltare la fama, abbiamo sott'occhio da con&shy;<lb/>sultare i fatti, possiamo esser certi che Galileo non fa, nel suo dialogo pub&shy;<lb/>blicato dal Bonaventuri, nessun motto di quegli archi, dagli ammiratori <lb/>chiamati insigni nella scienza e preclari. </s>

<s>Anche l'altra esperienza delle palle <lb/>di piombo ammaccate, con la sua conclusione, non si trova nel Dialogo, <lb/>se non che trasformata nell'esempio del palo e della berta, i reiterati colpi <lb/>della quale si dice che non pareggiano mai il medesimo peso morto, il quale <lb/>anzi deve sempre esser maggiore e maggiore, <emph type="italics"/>d'onde pare ritrar si possa <lb/>la forza della percossa essere infinita<emph.end type="italics"/> (Alb. </s>

<s>XIII, 314). </s></p><p type="main">

<s>N&egrave; in Pisa dunque, n&egrave; in Padova, n&egrave; altrove, sembra che avesse Gali&shy;<lb/>leo pensato di fare l'esperienza degli archi della balestra: invece della quale <lb/>ne aveva immaginata e descritta un'altra, da dirsi pi&ugrave; veramente preclara, <lb/>bench&egrave; dal Viviani in fuori nessun altro o pochissimi, anche de'pi&ugrave; fami&shy;<lb/>liari all'Autore, ne avessero a que'tempi notizia. </s>

<s>L'esperienza alla quale ac&shy;<lb/>cenniamo &egrave; quella della troscia di acqua che, dalla secchia di sopra cadendo, <lb/>percuote nella secchia di sotto, ambedue equilibrate da un peso morto al&shy;<lb/>l'estremit&agrave; di una bilancia. </s>

<s>Da cos&igrave; fatta esperienza il Viviani stesso, non <lb/>curando gli archi tesi delle balestre, o le palle di piombo ammaccate, inco&shy;<lb/>minci&ograve; a promovere l'uso di quegli strumenti da misurare con qual mo&shy;<lb/>mento, paragonato a un peso morto, naturalmente cadendo, percotano i gravi. </s>

<s><lb/>Ci son di queste speculazioni rimasti nei manoscritti non pochi documenti, <lb/>dei quali noi riferiremo intanto i pi&ugrave; importanti, incominciando da ci&ograve; che <lb/>fu suggerito al Viviani stesso dalla lettura del Dialogo galileiano, dove l'Aproino <lb/>introduce il discorso col descrivere la prima delle esperienze &ldquo; che mossero <pb xlink:href="020/01/2533.jpg" pagenum="158"/>l'Amico ad internarsi nella contemplazione dell'ammirabile problema della <lb/>percossa &rdquo; (Alb. </s>

<s>XIII, 308). </s></p><p type="main">

<s>&ldquo; Sia la libbra o stadera AB (fig. </s>

<s>51), sostenuta in C, e dall'estremit&agrave; B <lb/><figure id="id.020.01.2533.1.jpg" xlink:href="020/01/2533/1.jpg"/></s></p><p type="caption">

<s>Figura 51.<lb/>pendano due vasi E, F da fu&shy;<lb/>nicelle, de'quali quello di so&shy;<lb/>pra sia pieno d'acqua, ed <lb/>amendue si equilibrino col&shy;<lb/>l'altro D pendente dall'altra <lb/>estremit&agrave; A. </s>

<s>Si osservi poi <lb/>se, aperto il foro PQ del vaso <lb/>di sopra, nel tempo del ca&shy;<lb/>dere dell'acqua nel vaso di <lb/>sotto, si alteri l'equilibrio: <lb/>perch&egrave;, se non si guasta, &egrave; <lb/>segno che il momento acqui&shy;<lb/>stato nel moto dell'acqua ca&shy;<lb/>dente, e che percuote nel vaso di sotto, equivale a quella parte di acqua, che <lb/>&egrave; fra'due vasi. </s>

<s>Ma, se la preponderazione seguisse dalle facce del vaso, sa&shy;<lb/>rebbe segno che il momento acquistato per la percossa sar&agrave; maggiore del <lb/>momento, che si perde per il mancamento della porzione di acqua PMQN. &rdquo; <lb/><figure id="id.020.01.2533.2.jpg" xlink:href="020/01/2533/2.jpg"/></s></p><p type="caption">

<s>Figura 52.</s></p><p type="main">

<s>&ldquo; Ho fatto l'esperienza, e trovato che l'equilibrio <lb/>non si varia, ma tuttavia si mantiene in pari. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E se la tavola EF (fig. </s>

<s>52), col peso B in D, <lb/>s'equilibra col peso G in A intorno C, nel tagliare <lb/>il filo sostenente il peso B, mentr'ei sar&agrave; per aria, <lb/>preponderer&agrave; il peso G, ma la percossa di B sulla <lb/>tavola EF restituir&agrave; l'equilibrio senza passare a fare <lb/>inclinar pi&ugrave; gi&ugrave; la stadera. </s>

<s>Ma queste esperienze <lb/>vanno replicate e ben considerate &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXII, fol. </s>

<s>64). </s></p><p type="main">

<s>Replicate per&ograve; e ben considerate, non sembra che il Viviani rimanesse <lb/><figure id="id.020.01.2533.3.jpg" xlink:href="020/01/2533/3.jpg"/></s></p><p type="caption">

<s>Figura 53<lb/>sodisfatto n&egrave; della invenzione di Galileo, n&egrave; del <lb/>modo assai pi&ugrave; semplice com'ei l'avrebbe ri&shy;<lb/>dotta, per cui si volse a immaginare un'altro <lb/>strumento, premettendo queste parole alla nota, <lb/>nella quale ce lo lasciava descritto: &ldquo; Vedi se, <lb/>per misurare la forza della percossa possa essere <lb/>atto uno strumento simile a questo: &rdquo; </s></p><p type="main">

<s>&ldquo; Siano due regoli uguali AB, CD (fig. </s>

<s>53), <lb/>fermati saldamente s<gap/>tto e sopra, e tra loro pa&shy;<lb/>ralleli, anzi perpendicolari all'orizzonte, per i <lb/>quali cammini il trasversale EI, ma per&ograve; dura&shy;<lb/>mente, in virt&ugrave; d&igrave; due molle accomodate nelle <lb/>incastrature E, I. </s>

<s>Al medesimo trasversale siano <lb/>affissi pur due regoli minori SV, TR, all'estre-<pb xlink:href="020/01/2534.jpg" pagenum="159"/>mit&acirc; de'quali V, R sia saldamente fermata la tavoletta X, sulla quale per&shy;<lb/>cuota il peso N, ovvero l'O da diverse altezze: i quali percotendo in X fa&shy;<lb/>ranno scorrere in gi&ugrave; il trasversale EI pi&ugrave; o meno, secondo che la botta verr&agrave; <lb/>pi&ugrave; o meno da alto, o secondo che il peso N sar&agrave; pi&ugrave; o meno grave, lasciato <lb/>cadere dalla medesima altezza &rdquo; (ivi, fol. </s>

<s>63). </s></p><p type="main">

<s>Non apparisce da nessuna parte del manoscritto o notizia o indizio che <lb/>il Viviani mettesse in pratica cos&igrave; fatto strumento, invece del quale trov&ograve; <lb/>forse pi&ugrave; comodo valersi delle spire metalliche, dalla loro maggiore o minore <lb/>distrazione argomentando al maggiore o minor momento di un peso, ora <lb/>semplicemente posato sopra la spira, ora lasciato naturalmente cadere da un <lb/>filo attaccato all'estremo inferiore anello di essa. </s>

<s>Ne raccolse alcune conclu&shy;<lb/>sioni, alle quali se non altro la novit&agrave; conferisce importanza, e si riducono <lb/>alle seguenti: </s></p><p type="main">

<s>&ldquo; I. </s>

<s>Pesi disuguali, dalla medesima altezza, distraggono spazi nella me&shy;<lb/>desima spira, che hanno la proporzione di essi pesi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; II. </s>

<s>Il medesimo peso cadente da diverse altezze nella medesima spira <lb/>fa distrazioni disuguali, le quali hanno fra loro la medesima proporzione che <lb/>i momenti acquistati nelle cadute disuguali, i quali momenti sono in pro&shy;<lb/>porzione sudduplicata della proporzione di dette altezze: cio&egrave; sono come le <lb/>radici di dette altezze. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; III. </s>

<s>Pesi disuguali, compensati da momento di velocit&agrave;, non fanno di&shy;<lb/>strazioni uguali. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; IV. </s>

<s>Il medesimo peso cadente dalla medesima altezza in spire di re&shy;<lb/>sistenze disuguali, nella pi&ugrave; debole fa maggior distrazione, ma non secondo <lb/>la proporzione delle distrazioni, che vi fa un medesimo peso morto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; V. </s>

<s>Pesi morti disuguali, nella medesima spira, fanno distrazioni, che <lb/>hanno la proporzione di essi pesi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; VI. </s>

<s>Il medesimo peso in spire disuguali fa distrazioni disuguali, e nelle <lb/>medesime proporzioni di esse spire: cio&egrave;, se una spira &egrave; di dodici anelli, e <lb/>l'altra di otto, in quella distrarr&agrave; dodici punti, in questa otto &rdquo; (ivi, fol. </s>

<s>57). </s></p><p type="main">

<s>Da cos&igrave; fatte conclusioni sperimentali tenta il Viviani <lb/><figure id="id.020.01.2534.1.jpg" xlink:href="020/01/2534/1.jpg"/></s></p><p type="caption">

<s>Figura 54.<lb/>di sollevarsi all'altezza, e alla dignit&agrave; di qualche teorema: <lb/>e considerando che il momento del peso lasciato libera&shy;<lb/>mente cadere dal filo, che lo teneva legato all'ultimo e <lb/>inferiore anello della spira, cresce il suo momento se&shy;<lb/>condo le ordinate nella parabola, e che la spira stessa lo <lb/>impedisce sempre pi&ugrave; nello scendere, cio&egrave; proporzional&shy;<lb/>mente alle ordinate nel triangolo; ne conclude che dun&shy;<lb/>que la resultante dell'impeto &egrave; sempre la differenza fra <lb/>quelle stesse ordinate. </s>

<s>&ldquo; Se il peso B (fig. </s>

<s>54) distrae con <lb/>la sua gravit&agrave; per lo spazio AB, lasciato cadere da A, <lb/>distrae AC, doppia di AB. </s>

<s>Nel venire da A in B, rispetto <lb/>all'impeto acquistato nel cadere, cresce il suo momento come le linee nella <lb/>parabola, ma il ritardamento della spira glielo scema secondo le linee del trian-<pb xlink:href="020/01/2535.jpg" pagenum="160"/>golo; onde il suo momento va secondo le linee, che sono fra la parabola e <lb/>il triangolo &rdquo; (ivi, fol. </s>

<s>58). </s></p><p type="main">

<s>Dagl'impeti nelle cadute naturali, misuraii per via della parabola, pass&ograve; <lb/>quella feconda e instancabile mente speculativa a proporre, per misurare essi <lb/>impeti ne'moti proiettizi, un modo che per la sua facilit&agrave; era assai lusin&shy;<lb/>ghiero. </s>

<s>&ldquo; Si faccia, cos&igrave; lasci&ograve; scritto in un'altra sua nota, la proiezione della <lb/>palla A (fig. </s>

<s>55) gi&ugrave; per il piano inclinato AB, sicch&egrave; poi si volti a far la <lb/>parabola BCDE, segnata in muro o sopra una tavola verticale, e si ricevano <lb/><figure id="id.020.01.2535.1.jpg" xlink:href="020/01/2535/1.jpg"/></s></p><p type="caption">

<s>Figura 55.<lb/>le percosse di quella ad angoli retti sopra diversi <lb/>pezzi piani, o lastre di sapone, C, D, E, e si osservi <lb/>il crescere della percossa. </s>

<s>Ma, per aggiustar me&shy;<lb/>glio il tutto, si possono prima disegnare diverse <lb/>parabole nel muro &rdquo; (ivi, fol. </s>

<s>60). </s></p><p type="main">

<s>Tutte queste per&ograve;, dal Viviani immaginate, <lb/>non erano altro che assai belle proposte, le quali <lb/>non si sapeva dall'altra parte se fossero per con&shy;<lb/>durre all'effetto desiderato di ricavar l'equivalente <lb/>della percossa dalla maggiore o minore penetra&shy;<lb/>zione del percuziente in un corpo molle, o dalla <lb/>equiponderanza di esso percuziente con un peso <lb/>morto. </s>

<s>Mentr'egli intanto pensava a qualche altro strumento, e a qualche <lb/>altra maniera pi&ugrave; decisiva, si trov&ograve; prevenuto da Carlo Rinaldini, suo col&shy;<lb/>lega nella prima istituzione dell'Accademia del Cimento, il qual Rinaldini, <lb/>forse inconsapevolmente inspirato alle pi&ugrave; antiche tradizioni della scienza, che <lb/>risalivano a quel Giovanni del Giocondo commemorato dallo Scaligero; pens&ograve; <lb/>auch'egli poter essere la stadera che, ricevendo da una parte il colpo, ne mi&shy;<lb/>surasse dall'altra l'effetto, secondo la maggiore o minor distanza del romano <lb/>dal centro dell'equilibrio. </s></p><p type="main">

<s>Propose dunque il Rinaldini, in una sua scrittura ai Colleghi, il modo <lb/>di misurare la forza della percossa, valendosi della detta stadera, dal pi&ugrave; pic&shy;<lb/>colo lato della quale pendesse per un filo una palla di piombo, che nello <lb/>stato di quiete rimanesse in pari col romano, e poi, sollevata la palla e la&shy;<lb/>sciatala liberamente cadere per tutta la lunghezza del filo, per una lunghezza <lb/>doppia, tripla, ecc., fare scorrere lo stesso romano, infin tanto che, come se <lb/>si trattasse di pesare una merce, non equiponderasse ora all'una, ora all'al&shy;<lb/>tra maggiore strappata. </s>

<s>&ldquo; Questa esperienza, concludeva il proponente, quanto <lb/>sia facile e puntuale, e di quanto grande importanza, per investigare la co&shy;<lb/>gnizione di quell'ammirabil problema, non occorre esagerare a cotesta inge&shy;<lb/>gnosissima e virtuosa Accademia: per&ograve; prego a fare tale esperienza con la <lb/>maggiore esattezza che ricerca &rdquo; (Targioni, Notizie degli aggrandimenti ecc., <lb/>T. II, P. II, Firenze 1780, pag. </s>

<s>713). </s></p><p type="main">

<s>L'esperienza fu fatta a'di 19 Dicembre 1657, e giova credere con tutta <lb/>l'esattezza richiesta, ma quel che se ne pot&egrave; raccogliere si ridusse al sem&shy;<lb/>plice fatto che qualunque strappata della corda, bench&egrave; rispondente a una <pb xlink:href="020/01/2536.jpg" pagenum="161"/>discesa piccolissima della palla, &ldquo; aveva facolt&agrave; di sollevare il romano, ben&shy;<lb/>ch&egrave; allontanato dal punto dell'equilibrio, per molte libbre &rdquo; (ivi, pag. </s>

<s>668). </s></p><p type="main">

<s>Il Viviani, che dirigeva l'esperienza, e che aveva forse sentito in cuore <lb/>il rammarico del non essergli sovvenuto un tal pensiero, di s&igrave; facile esecu&shy;<lb/>zione e puntuale, come il Rinaldini diceva, e come tutti avevano creduto; <lb/>ebbe a restar maravigliato del vedersi innanzi fallite cos&igrave; belle speranze: e <lb/>mentre andava con gran sottigliezza, e pure inutilmente, investigando di ci&ograve; <lb/>la misteriosa ragione, occorsegli avventurosamente a leggere una scrittura <lb/>(MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>57, 58) che Lodovico Serenai aveva diligente&shy;<lb/>mente copiata dall'autografo del Torricelli. </s>

<s>Era una lettera indirizzata al Mer&shy;<lb/>senno, nella quale si svelavano le fallacie di un'esperienza fatta allora a Pa&shy;<lb/>rigi, per convincere di falsit&agrave; la legge galileiana dei moti accelerati. </s>

<s>E perch&egrave; <lb/>dagl'impeti di un percuziente nella bilancia determinava quel Fisico francese <lb/>le relazioni fra gli spazi e i tempi, prendeva il Torricelli occasione di descri&shy;<lb/>ver cose ed esporre pensieri, che corrispondevano con quelli passati allora <lb/>allora per la mente al Viviani, il quale fece perci&ograve; della detta lettera torri&shy;<lb/>celliana, di sua propria mano, un estratto, che ci &egrave; tuttavia rimasto sotto il <lb/>titolo <emph type="italics"/>Excerptum ex quadam epistola Torricelli ad Mersennum.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; ...... Certissimum est globum unius librae, si in alteram lancium <lb/>alicuius librae cadat a qualibet altitudine etiam minima, non solum aequalem <lb/>sibi globum, sed etiam centuplo maiorem ex altera bilancis parte elevaturum <lb/>esse. </s>

<s>Libra vero, non utcumque, sed huiusmodi esse debet, ut ipsius fila <lb/>nihil distrahantur, neque brachia curventur, neque materia, sive globi ca&shy;<lb/>dentis sive subiectae lancis, contundantur: haec enim singula effectum impe&shy;<lb/>diunt. </s>

<s>Gravitas etiam lancium et brachiorum librae experimentum minus <lb/>exactum reddere possunt, dum haec singula impetum seu momentum caden&shy;<lb/>tis globi minuere certum est: quae omnia, si penitus vitentur, sive quoad <lb/>fieri poterit minuantur, procul dubio quilibet parvi globuli casus in altera <lb/>lancium ingens pondus ab alia parte elevabit, sed per spatium exiguum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto libra AB (fig. </s>

<s>56) cuius fulcrum in medio C: ex una parte pon&shy;<lb/>dus centum librarum, ex alia unius tantum librae, cadatque pondus minus <lb/><figure id="id.020.01.2536.1.jpg" xlink:href="020/01/2536/1.jpg"/></s></p><p type="caption">

<s>Figura 56.<lb/>ex altitudine decem diametro&shy;<lb/>rum suarum. </s>

<s>Quaeritur an ele&shy;<lb/>vari possit pondus decem libra&shy;<lb/>rum? </s>

<s>Hoc quidem nescio, sed <lb/>facto experimento clavum fer&shy;<lb/>reum D, tenaci ligno infixum, <lb/>subiici lanci A, visumque est <lb/>pondus centum librarum non impellere ulterius clavum. </s>

<s>Globus vero ferreus <lb/>unius librae, cadens ab altitudine decem diametrorum, impellebat eumdem, <lb/>nam repetitis saepius ictibus totus clavus in ligno fixus tandem est. </s>

<s>Ergo <lb/>maius momentum est ictus globi minoris, quam gravitatis maioris, propterea <lb/>ictus minoris gravitatem maioris superare debet, quamquam, cum proportio <lb/>gravium maxima fuerit, spatium prae exiguitate oculis percipi nequeat, sive <pb xlink:href="020/01/2537.jpg" pagenum="162"/>etiam ob inflexionem librae nullum effectum facere videatur &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. XXVI, fol. </s>

<s>21). </s></p><p type="main">

<s>Le osservazioni fatte dal Torricelli intorno alle qualit&agrave;, che si ricercano <lb/>nella bilancia, perch&egrave; non debba impedire la buona riuscita dell'esperimento, <lb/>fece mirabilmente accorto il Viviani dei difetti, che si trovavano nella sta&shy;<lb/>dera proposta dal Rinaldini, al distrarsi della corda nella quale, per le strap&shy;<lb/>pate della palla, attribuiva principalmente il non essersi potuta ricavare alcuna <lb/>notizia certa, per le pi&ugrave; esatte misure della percossa. </s>

<s>Fatta perci&ograve; costruire <lb/>una libbra, come il Torricelli la prescriveva, e posata sopra la lancia A una <lb/>palla di cinque once, trov&ograve; che veniva sollevata per un dito, facendo dall'al&shy;<lb/>tezza di un braccio cadere sull'altra lancia B una palla di legno del peso di <lb/>un'oncia e mezzo. </s>

<s>Tornando poi a far cadere la medesima palla per un'al&shy;<lb/>tezza quadrupla, e poi nonupla, e poi sesdecupla, in modo che gl'impeti delle <lb/>percosse crescessero via via come due, tre, e quattro, trov&ograve; che i pesi morti, <lb/>i quali potevano essere sollevati a quella stessa altezza di un dito, volevano <lb/>essere 20, 45 e 80 once, n&egrave; pi&ugrave; n&egrave; meno, con tal legge sperimentata sem&shy;<lb/>pre costante. </s>

<s>Ne esult&ograve; come di una scoperta, e n'esultarono, chiamati te&shy;<lb/>stimonii del fatto, i colleghi suoi accademici del Cimento, e specialmente il <lb/>principe Leopoldo, a cui sembr&ograve; che finalmente si fosse venuti a raccogliere <lb/>il frutto delle lunghe e penose speculazioni di Galileo. </s></p><p type="main">

<s>Si dimostr&ograve; l'esperienza dal Viviani nell'Accademia il d&igrave; 23 Dicem&shy;<lb/>bre 1657; poi vennero le Feste natalizie e del capo d'anno, celebratesi le <lb/>quali in Firenze, and&ograve; il Principe alle cacce di Pisa, dove si tratteneva pro&shy;<lb/>fessore dell'Universit&agrave; il Borelli. </s>

<s>Alla prima occasione ch'ebbe esso Principe <lb/>di vederlo, fra i diporti e i negozi, disse per prima cosa di avere a dargli <lb/>una bella notizia, qual era che il Viviani, valendosi di una bilancia, secondo <lb/>che per quell'uso era stata fatta costruire dal Torricelli, aveva trovato che <lb/>i momenti delle percosse, fatte sopr'una delle lancie, stavano come i qua&shy;<lb/>drati de'pesi morti posati sull'altra. </s>

<s>Anche il Borelli prese allora parte al&shy;<lb/>l'esultanza de'suoi colleghi, dai quali era dovuto stare assente in que'giorni, <lb/>e il di 7 Gennaio appresso scriveva cos&igrave; in una lettera indirizzata a Firenze <lb/>allo stesso Viviani: &ldquo; Al serenissimo principe Leopoldo non ho parlato fuor <lb/>che una volta sola, perch&egrave; le cacce e le faccende finora l'han tenuto davvan&shy;<lb/>taggio occupato. </s>

<s>Mi accenn&ograve; in ogni modo alcune belle invenzioni di V. S., <lb/>e in particolare quell'ammirabile effetto ed inaspettato della forza della per&shy;<lb/>cossa nella stadera, ed io avrei gran curiosit&agrave; di sapere se, nella lettera che <lb/>V. S. tiene della buona memoria del Torricelli, vi &egrave; particolarmente questa <lb/>osservazione, oppure &egrave; un semplice suo discorso in confermazione del con&shy;<lb/>cetto del signor Galileo &rdquo; (MSS. Cim., T. XXIV, fol. </s>

<s>31). </s></p><p type="main">

<s>Il Viviani, per sodisfare alla filosofica curiosit&agrave; di lui, che gli era allora <lb/>affezionatissimo amico, gli mand&ograve;, insieme con le relazioni delle sue espe&shy;<lb/>rienze, esatta copia della lettera torricelliana, della quale il Borelli non fece <lb/>che una lettura superficiale. </s>

<s>Ma poi, quando si dette a specular di proposito <lb/>intorno all'energia della percossa, per penetrarne la vera e intima natura, <pb xlink:href="020/01/2538.jpg" pagenum="163"/>torn&ograve; a meditar su quell'estratto di lettera al Mersenno, e ci trov&ograve; dentro <lb/>formulata una proposizione verissima, la quale poi trasfuse in quella sua XC, <lb/>in cui, dietro i principii e gli sperimenti dello stesso Torricelli, intendeva di <lb/>dimostrare: &ldquo; Vis et energia cuiuslibet percussionis maior est quacumque <lb/>potentia finita, quae, absque motu locali, solummodo virtute gravitatis pre&shy;<lb/>mat &rdquo; (De vi percuss. </s>

<s>cit., pag. </s>

<s>203). Quanto poi ad applicare alla misura <lb/>della percossa i dimostrati principii, e il descritto strumento, ebbe a notare <lb/>il Borelli una certa esitanza, che non poteva in tant'uomo, qual era il Tor&shy;<lb/>ricelli, non esser sentita senza un giusto motivo, e quel <emph type="italics"/>nescio<emph.end type="italics"/> che leggeva <lb/>seguitare alla domanda <emph type="italics"/>an, si cadat pondus minus ex altitudine decem <lb/>diametrorum suarum, elevari possit pondus decem librarum,<emph.end type="italics"/> gli parve <lb/>fare un singolar contrapposto con la nuova baldanza del Viviani. </s></p><p type="main">

<s>Mentre gli passavano per la mente cos&igrave; fatti pensieri, capitarono al Bo&shy;<lb/>relli fra mano le epistole del Gassendo <emph type="italics"/>De proportione qua gravia deciden&shy;<lb/>tia accelerantur,<emph.end type="italics"/> nella prima delle quali lesse intitolarsi un capitolo <emph type="italics"/>De expe&shy;<lb/>rimento in Bilance facto ac aliud revera probante quam velocitates esse <lb/>sicut spatia.<emph.end type="italics"/> Dalla curiosit&agrave; e dall'importanza dell'argomento invitato a pro&shy;<lb/>seguir la lettura, trov&ograve; riferirsi, nelle sue testuali parole, da un discorso del <lb/>gesuita Pietro Cazr, la seguente conclusione sperimentale: &ldquo; Ut globus qui&shy;<lb/>libet cuiuscumque materiae ex unius diametri altitudine cadens duplum sui <lb/>ponderis: hoc est, praeter pondus quod sine impetu in aequilibrio retineret, <lb/>aliud sibi aequale attollat; et ex altitudine duarum diametrorum, triplum; <lb/>ex tribus diametris, quadruplum, et ita deinceps &rdquo; (Parisiis 1646, pag. </s>

<s>42). <lb/>Soggiungeva l'Autore delle dette Epistole altri passi, ne'quali, dop'avere il <lb/>Gesuita magnificata la novit&agrave; della stupenda legge da s&egrave; scoperta, conclu&shy;<lb/>deva dalle esperienze, contro i teoremi di Galileo, che gl'incrementi delle <lb/>velocit&agrave; hanno la proporzion medesima degli spazi passati nelle scese dei gravi. </s></p><p type="main">

<s>La curiosit&agrave; di veder l'esito di questo negozio frugava sempre pi&ugrave; l'animo <lb/>del Borelli, il quale, pi&ugrave; avidamente applicatosi a succhiare il senso di quelle <lb/>pagine, leggeva ci&ograve; che, per verificare col medesimo strumento della Bilan&shy;<lb/>cia, per quest'uso speciale fabbricata co'piatti sostenuti da robuste catene, <lb/>le vantate esperienze del Casreo; diceva di essere andato apparecchiando il <lb/>Gassendo, col far cadere i globi per altezze via via crescent&igrave; come i loro <lb/>quadrati, e concludendo cos&igrave; il ragionamento, che, tutto al contrario delle <lb/>opposizioni del Gesuita, confermava mirabilmente la legge di Galileo: &ldquo; Prae&shy;<lb/>tereo autem quemadmodum ut globus extulit dumtaxat duplum, ex diame&shy;<lb/>tris quatuor, sic etiam deinceps extulerit solummodo triplum, ex diametris <lb/>novem, et quadruplum ex sexdecim &rdquo; (ibid., pag. </s>

<s>48). </s></p><p type="main">

<s>A leggere questa conclusione, dalla quale appariva che gl'impeti della <lb/>percossa stavano come i pesi morti, ebbe a maravigliarsi il Borelli come mai <lb/>avesse il Viviani, con somiglianti processi sperimentali trovato che stavano <lb/>invece come i quadrati dei pesi morti: ed essendo la verit&agrave; una sola, e gli <lb/>sperimentatori ambedue di tal qualit&agrave;, da non credere che si fossero cos&igrave; <lb/>facilmente ingannati, andava fra s&egrave; ricercando la causa delle due opposte <pb xlink:href="020/01/2539.jpg" pagenum="164"/>osservazioni. </s>

<s>N&egrave; gli fu difficile ritrovarla, tornando a meditare sopra la let&shy;<lb/>tera del Torricelli, dalla quale si concludeva che ogni piccolo impeto, in qua&shy;<lb/>lunque pi&ugrave; piccolo corpo, bastava per superare qualsivoglia energia di gravit&agrave; <lb/>quiescente. </s>

<s>Vedeva inoltre essere ci&ograve; confermato dalle stesse esperienze, fatte <lb/>con la stadera del Rinaldini nell'Accademia del Cimento, dalle quali espe&shy;<lb/>rienze resultava che la palla, da qualunque minima altezza caduta, era ba&shy;<lb/>stante a sollevare il romano per molte libbre di pi&ugrave;, che non pesava in s&egrave; <lb/>stessa. </s>

<s>Di qui saviamente argomentava il Borelli che fra il grave in moto e <lb/>il grave in quiete non si poteva dar proporzione, per cui non faceva mara&shy;<lb/>viglia se il Gassendo e il Viviani, partitisi ambedue da un falso principio, <lb/>riuscissero a conclusioni fra loro opposte. </s>

<s>&ldquo; Quoniam quilibet impetus, in <lb/>quolibet corpusculo inexistens, superat energiam gravitatis quiescentis, et im&shy;<lb/>petu omnino privati, propterea quod ipsum impellere et elevare potest, ut <lb/>ostensum est; igitur, quantumvis augeatur multipliceturque simplex gravitas, <lb/>absque motu locali, nunquam superabit, imo nec aequabit vim impetus, et <lb/>ideo simplex gravitas et impetus non erunt quantitates eiusdem generis, et <lb/>propterea comparatio inter eas institui non potest, nec ullam proportionem <lb/>inter se habere possunt. </s>

<s>Sed nulla quantitas potest esse mensura quantitatis <lb/>alterius generis, sicut linea esse non potest mensura soni aut ponderis; igi&shy;<lb/>tur pondus simplex elevatum non potest esse mensura impetus percutientis &rdquo; <lb/>(De vi percuss. </s>

<s>cit., pag. </s>

<s>252). </s></p><p type="main">

<s>Veniva dunque di qui data sentenza contro tutti quegli strumenti che, <lb/>per ridurre la forza della percossa alla misura della gravit&agrave;, aveva immagi&shy;<lb/>nati il Viviani, sull'andare di quegli proposti da Galileo, fra quali quel degli <lb/>archi della balestra era famoso. </s>

<s>E anche contro questa famosa invenzione <lb/>s'estendeva la sentenza dello stesso Borelli, il quale dunque era venuto a <lb/>dimostrare la falsit&agrave; delle dottrine di Galileo intorno alla forza della percossa, <lb/>non tanto rispetto ai principii, quant'altres&igrave; rispetto alle loro applicazioni spe&shy;<lb/>rimentali. </s>

<s>N&egrave; la verit&agrave; di cos&igrave; fatta sentenza fu potuta mettere in dubbio da <lb/>quegli stessi, i quali avevano prima magnificate le invenzioni del famosis&shy;<lb/>simo Vecchio, intorno alle quali Giuseppe Ferroni promoveva alcuni dubbi <lb/>in una lettera indirizzata al suo maestro Viviani, facendogli osservare che, <lb/>nel restituir l'equilibrio tra le forze delle trazioni degli archi, e le semplici <lb/>gravit&agrave; delle palle di piombo prementi, si venivano a paragonare due cose <lb/>eterogenee fra loro. </s>

<s>&Egrave; notabile per&ograve; che dicesse essergli entrati nella mente <lb/>que'dubbi, per non esser rimasto sodisfatto di ci&ograve;, che aveva letto nel libro <lb/>del Borelli, il quale anzi, nella proposizione CXXXV aveva suggerite quelle <lb/>medesime osservazioni, dalle quali diceva di aver preso motivo di dubitare <lb/>il discepolo del Viviani. </s></p><p type="main">

<s>Nella citata proposizione infatti descrive l'Autore un'esperienza, ch'ei <lb/>diceva di avere istituita, <emph type="italics"/>quando, communi errore detentus, impetum per&shy;<lb/>cussivum ab aliquo pondere mensurari posse censebam<emph.end type="italics"/> (De vi percuss. </s>

<s>cit., <lb/>pag. </s>

<s>296). Consisteva nel far cadere dalla medesima altezza un'accettina di <lb/><gap/>erro di tre once, ora sopra una focaccia di cera pura, ora sopra un'altra <pb xlink:href="020/01/2540.jpg" pagenum="165"/>simile focaccia, ma pi&ugrave; morbida, perch&egrave; composta di cera mescolata con sego. </s>

<s><lb/>Le ferite poi fatte sopra le due focacce, cos&igrave; per via della percossa, procu&shy;<lb/>rava di ripeterle uguali, per via della pressione di un peso morto posato sopra <lb/>l'accetta: e perch&egrave; trov&ograve; che undici oncie bastavano per far l'incisione nella <lb/>focaccia pi&ugrave; molle, e 36 nella pi&ugrave; dura: ne concludeva, aggiungendovi il peso <lb/>dello strumento, che le percosse stavano come i pesi morti, ossia come 14 a 39. <lb/>Poi riconobbe che queste operazioni diverse dipendevano da tutt'altre cause <lb/>che dalle pressioni, e osservava inoltre &ldquo; quod, quotiescumque applicantur cor&shy;<lb/>pora ponderosa, imponunturque corporibus mollibus atque cedentibus, esse <lb/>omnino impossibile ut haec ab illis comprimantur absque motu locali, dum <lb/>corpora mollia cedunt ac stringuntur, eo tempore quo urgentur ab incum&shy;<lb/>bentibus ponderibus: comprimentur ergo corpora mollia et cedentia, non a <lb/>ponderibus quiescentibus, sed motu locali agitatis. </s>

<s>Verum concipi non potest <lb/>motus localis absque velocitate, seu impetu, nec corpus grave, impetu affectum, <lb/>subiectum corpus comprimere potest absque percussione. </s>

<s>Igitur revera cor&shy;<lb/>pora mollia quodammodo percutiuntur ab incumbentibus ponderibus, non <lb/>autem solummodo stringuntur, comprimunturque a vi gravitatis quiescentis &rdquo; <lb/>(ibid., pag. </s>

<s>297, 98). </s></p><p type="main">

<s>N&egrave; questa osservazione giustissima del Borelli &egrave; punto diversa da quel&shy;<lb/>l'altra, che condusse il Ferroni a spiegare i maravigliosi effetti degli archi <lb/>di Galileo, <emph type="italics"/>senza che ne segua questo disordine, che la stessa percossa possa <lb/>dirsi infinita, ed equivalente a pesi sempre maggiori,<emph.end type="italics"/> che &egrave; il paralogismo, <lb/>in cui per tutto il dialogo s'avvolgono le dimostrazioni e i discorsi del Sal&shy;<lb/>viati. </s>

<s>E perch&egrave; dalla proposta del discepolo &egrave; facile argomentare alla rispo&shy;<lb/>sta del Maestro, e sono ambedue documento importantissimo di questa sto&shy;<lb/>ria, bench&egrave;, avendo comunicato il Ferroni i suoi pensieri al Casati, questi <lb/>gli pubblicasse nel cap. </s>

<s>VI del suo VII libro <emph type="italics"/>Mechanicorum,<emph.end type="italics"/> (Lugduni 1684, <lb/>pag. </s>

<s>677-81); trascriveremo qui dal suo originale la lettera scritta il d&igrave; <lb/>13 Aprile 1675 da Bologna, nella quale il Ferroni stesso, dopo avere annun&shy;<lb/>ziata al Viviani la ricevuta del libro della Scienza universale delle propor&shy;<lb/>zioni, cos&igrave; soggiunge e prosegue in sino alla fine: </s></p><p type="main">

<s>&ldquo; Speravo di ritrovare nel suo libro la soluzione di quella famosa espe&shy;<lb/>rienza, fatta in Pisa, della palla di piombo cadente dagli archi, ne'quali par <lb/>che si provi la forza della percossa essere infinita, mentre pu&ograve; equivalere a <lb/>pesi e pesi sempre maggiori: esperienza confermata poi dal Borelli coll'ac&shy;<lb/>cettina cadente sulla cera e sul sego, ove lo stesso piombo, posto in testa <lb/>dell'accettina, non fece poi le medesime spaccature col premere, che fatte <lb/>furono dalla percossa cadente. </s>

<s>Or non avendo trovata la soluzione, le devo <lb/>dire una mia semplicit&agrave;, come scolare ad un mio riverito maestro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Mi pare che, nella sperienza di Galileo fatta in Pisa, male si paragoni <lb/>l'impeto della palla cadente dal filo attaccato alle corde degli archi, uno ri&shy;<lb/>gido l'altro molle, con il peso di piombo premente e sostenente le corde <lb/>degli archi ai segni delle discese cagionate dalla palla cadente, poich&egrave; <emph type="italics"/>ethe&shy;<lb/>rogenea etherogeneis non comparantur, sed homogenea homogeneis.<emph.end type="italics"/> Or <pb xlink:href="020/01/2541.jpg" pagenum="166"/>l'impeto della cadente palla, e del piombo premente col peso, sono cose ete&shy;<lb/>rogenee. </s>

<s>Devesi dunque far la comparazione delle cose omogenee, come sono <lb/>impeto ed impeto. </s>

<s>Per tanto io paragono l'impeto della palla cadente dal me&shy;<lb/>desimo filo in due archi un duro l'altro dolce, con l'impeto, che in s&egrave; pro&shy;<lb/>duce il medesimo peso di piombo attaccato alle corde dei medesimi archi, in <lb/>quella poca discesa, che fa con la sua pressione, per tirar gli archi ai segni <lb/>delle discese primarie. </s>

<s>Tra questi due impeti si trova questo divario: che la <lb/>palla, cadente sempre dal filo di una stessa lunghezza produce sempre in s&egrave; <lb/>stessa il medesimo impeto per l'uguaglianza della caduta, e giunta alla re&shy;<lb/>sistenza degli archi opera con tutto l'impeto anticipatamente preconcetto nella <lb/>caduta dal filo per l'aria libera, il qual impeto a poco a poco dalle resistenze <lb/>degli archi si va distruggendo e si annienta. </s>

<s>Ma il piombo premente attac&shy;<lb/>cato agli archi opera diversamente: poich&egrave; non opera con impeto antecipa&shy;<lb/>tamente preconcetto, ma incomincia nella sua piccolissima scesa a produrre <lb/>impeto in s&egrave;, con cui vince la forza di molla negli archi, e questo impeto <lb/>non si distrugge, anzi va sempre crescendo, sin che si giunge all'equilibrio <lb/>e consistenza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Posti questi preambuli, concludo cos&igrave;: La palla cadente, che &egrave; la me&shy;<lb/>desima e sempre cade dalla medesima altezza, opera sempre con il medesimo <lb/>impeto, anticipatamente preconcetto nella caduta, tanto dall'arco rigido, quanto <lb/>dall'arco pieghevole. </s>

<s>Ma le medesime, per esempio dieci once di piombo, <lb/>nella lor poca discesa fatta con la pressione, non operano nell'uno e nell'al&shy;<lb/>tro caso, col medesimo impeto, ma con impeti molto diversi: poich&egrave;, attac&shy;<lb/>cate le dieci once di piombo all'arco duro, trovando gagliarda resistenza, co&shy;<lb/>mincia ad operare con impeto debolissimo, il quale, crescendo sino all'equi&shy;<lb/>librio in proporzione sudduplicata del suo brevissimo spazio, poco cresce. </s>

<s>Ma <lb/>le medesime dieci once di piombo attaccate all'arco molle, trovando resistenza <lb/>minore, incominciano a premere, e a scendere con grado ed impeto assai <lb/>maggiore di quel primo prodotto nell'arco duro, e crescendo con la solita <lb/>proporzione, sino all'equilibrio, l'impeto cresce di molto. </s>

<s>Sicch&egrave; le medesime <lb/>dieci once di piombo premente producono pi&ugrave; impeto nell'arco dolce e soave, <lb/>che nell'arco gagliardo, onde maraviglia non &egrave; se, per tener l'arco duro a <lb/>quel segno ove lo trasse la percossa della palla cadente, vi vogliano forse <lb/>venti e pi&ugrave; once di peso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sicch&egrave;, paragonando impeti con impeti, mi pare di rendere la ragione <lb/>di questo maraviglioso fenomeno, perch&egrave; il medesimo peso con la pressione <lb/>non tenga le due corde degli archi a quei medesimi segni, ai quali furono <lb/>tratti dalla percossa della palla cadente, senza che ne segua questo disordine <lb/>che la stessa percossa possa dirsi infinita, ed equivalente a pesi sempre mag&shy;<lb/>giori. </s>

<s>Vi vuol pi&ugrave; peso nell'arco duro, perch&egrave; il peso primiero, che produsse <lb/>nell'arco molle impeto uguale alla percossa cadente, e perci&ograve; lo trasse e trat&shy;<lb/>tenne al medesimo segno; attaccato poi all'arco duro, non produce nella <lb/>pressione impeto uguale a quello della cadente palla, ma assai minore, e <lb/>questo per la maggior resistenza: e queste sono le mie semplicit&agrave;. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2542.jpg" pagenum="167"/><p type="main">

<s>&ldquo; Io averei in pensiero di far recitare da un mio scolare un poco di pro&shy;<lb/>blema sopra questa bellissima esperienza pisana del Galileo, ma, non avendo <lb/>trovato nel Borelli soluzione a mio gusto, e che mi oppaghi, ho speculata <lb/>questa bassezza, che gli ho proposto. </s>

<s>La prego a degnarsi correggermela, e <lb/>dirmi dintorno a detta esperienza la sua ragione, del che io la scongiuro per <lb/>tal uomo, che so che ella negare non mel potr&agrave;: dico per il nome glorioso <lb/>del nostro comune maestro, e splendore della nostra Toscana, il Galileo &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. CXLVI, fol. </s>

<s>36, 37). </s></p><p type="main">

<s>Avrebbe, se cos&igrave; propriamente non rispose, potuto pure rispondere il <lb/>Viviani non averci nessun documento certo, per provar che il notato disor&shy;<lb/>dine nell'esperienza degli archi si dovesse attribuire al Galileo, a cui, per <lb/>misurare la forza della percossa, era sovvenuta una molto diversa invenzione <lb/>e assai pi&ugrave; bella, dallo stesso Viviani letta in sul cominciar del Dialogo, <lb/>dov'&egrave; messa in bocca all'Aproino, il quale, dop'aver descritte le due sec&shy;<lb/>chie bilanciate a quel modo, che rappresentammo addietro nella figura LI, <lb/>cos&igrave; soggiunge: &ldquo; La riuscita, siccome agli altri fu inopinata, cos&igrave; fu mara&shy;<lb/>vigliosa, imperocch&egrave;, subito aperto il foro e incominciato ad uscirne l'acqua, <lb/>la bilancia inclin&ograve; dall'altra parte del contrappeso, ma non tantosto arriv&ograve; <lb/>l'acqua percotendo nel fondo dell'inferior secchia, che, restando di pi&ugrave; in&shy;<lb/>clinarsi il contrappeso, cominci&ograve; a sollevarsi, e con un moto placidissimo, <lb/>mentre l'acqua precipitava, si ricondusse all'equilibrio, e quivi, senza pas&shy;<lb/>sarlo pur di un capello, si libr&ograve; e fermossi perpetuamente &rdquo; (Alb. </s>

<s>XIII, 309, 10). </s></p><p type="main">

<s>Poteva, dicevasi, rispondere il Viviani al Ferroni che la prima esperienza <lb/>e l'unica, della quale s'abbia certezza, &egrave; questa immaginata da Galileo, per <lb/>misurare la forza della percossa, la quale si concludeva dover essere equiva&shy;<lb/>lente al momento, e al peso di quella quantit&agrave; d'acqua cadente, che si trova <lb/>in aria sospesa tra le due secchie. </s>

<s>Ma il disordine nonostante rimaneva lo <lb/>stesso, comparandosi <emph type="italics"/>etkerogenea etherogeneis,<emph.end type="italics"/> quali sono la troscia d'acqua <lb/>in moto, da una parte della bilancia, e il contrappeso dall'altra del grave <lb/>quiescente. </s></p><p type="main">

<s>Forse n&egrave; il Viviani stesso, n&egrave; il Ferroni, riconobbero nella esperienza <lb/>idraulica questo disordine, come non sembra lo riconoscesse un illustre Ma&shy;<lb/>tematico recente, il quale, in alcune sue lezioni di Fisica matematica, si giov&ograve; <lb/>dei progressi fatti dalla scienza, per misurare la quantit&agrave; dell'acqua cadente, <lb/>e per concluderne di l&igrave;, ci&ograve; che non aveva saputo fare il Salviati, la precisa <lb/>misura dell'urto fatto dall'acqua sul fondo della secchia. </s>

<s>Fu il Newton, il <lb/>quale venne a togliere nello stesso Salviati quell'ambiguit&agrave;, per cui dovette <lb/>abbandonar come inutile il bello esperimento descrittogli dall'Aproino: il <lb/>qual Newton, immaginando che la troscia sospesa in aria sia PN (fig. </s>

<s>57), e <lb/>la sua altezza KI, concludeva, nel secondo corollario della proposizione XXXVI <lb/>dimostrata nel secondo libro dei Principii di naturale Filosofia: &ldquo; Vis, qua <lb/>totus aquae exilientis motus generari petest, aequalis est ponderi cylindricae <lb/>colummae aquae, cuius basis est foramen MN, et altitudo 2 IK. </s>

<s>Nam aqua <lb/>exiliens, quo tempore hanc columnam aequat, pondere suo, ab altitudine <pb xlink:href="020/01/2543.jpg" pagenum="168"/>KI cadendo, velocitatem suam qua exilit acquirere potest &rdquo; (Genevae 1711, <lb/>pag. </s>

<s>291), come resulta, soggiungiamo noi per l'Autore, dalla prima pro&shy;<lb/><figure id="id.020.01.2543.1.jpg" xlink:href="020/01/2543/1.jpg"/></s></p><p type="caption">

<s>Figura 57.<lb/>posizione dei moti natural&shy;<lb/>mente accelerati, dimostrata <lb/>nel terzo dialogo di Galileo. </s></p><p type="main">

<s>Ma la nuova Filosofia <lb/>neutoniana suggeriva un ac&shy;<lb/>corgimento di pi&ugrave;, per la pi&ugrave; <lb/>esatta risoluzion del proble&shy;<lb/>ma. </s>

<s>Galileo e il Viviani li&shy;<lb/>mitavano alla sola scesa at&shy;<lb/>tuale, nella troscia PN, la <lb/>quantit&agrave; dell'acqua, la quale <lb/>non gravita sulla bilancia, <lb/>perch&egrave;, come si mostra per <lb/>la bella esperienza di Leonardo da Vinci, da noi riferita a pag. </s>

<s>227 del Tomo <lb/>precedente, <emph type="italics"/>il peso grave, che libero discende, non d&agrave; di s&egrave; peso ad al&shy;<lb/>cuno sostentacolo:<emph.end type="italics"/> secondo il Newton per&ograve; devesi aggiungere la quantit&agrave; <lb/>dell'acqua, compresa dentro la cateratta RQ, la quale, bench&egrave; non muovasi <lb/>in atto, opera in potenza nello spinger l'acqua dal foro MN con tal impeto, <lb/>come se fosse naturalmente caduta dall'altezza OK, per il noto teorema del <lb/>Torricelli. </s></p><p type="main">

<s>L'acqua dunque, che non gravita sulla bilancia, &egrave; secondo i principii <lb/>neutoniani uguale ad un cilindro liquido, di cui il volume &egrave; 2OI.<foreign lang="greek">p</foreign>MI2:e <lb/>chiamata D la densit&agrave;, e <emph type="italics"/>g<emph.end type="italics"/> l'intensione della gravit&agrave;, 2OI.<foreign lang="greek">p</foreign>MI2.D<emph type="italics"/>g<emph.end type="italics"/> &egrave; la <lb/>misura del peso. </s>

<s>Che se facciasi <foreign lang="greek">p</foreign>MI2, area del foro MN, uguale ad A, e <lb/>invece dell'altezza 2OI, chiamata <emph type="italics"/>v<emph.end type="italics"/> la velocit&agrave; corrispondente, si sostituisca <lb/><emph type="italics"/>v2<emph.end type="italics"/>/2<emph type="italics"/>g,<emph.end type="italics"/> sar&agrave; il peso dell'acqua, che non gravita sulla bilancia, espresso dalla <lb/>formula A.D. <emph type="italics"/>v2,<emph.end type="italics"/> &ldquo; la quale, scrisse Fabrizio Mossotti nella sua XVI lezione <lb/>di Fisica matematica, ci dice che l'urto di una vena fluida &egrave; in generale mi&shy;<lb/>surato dal prodotto della densit&agrave;, dell'area della sezione urtante, e del qua&shy;<lb/>drato della velocit&agrave; &rdquo; (Firenze 1843, T. I, pag. </s>

<s>147). Se avesse dunque, come <lb/>sembra, il valoroso professore di Pisa creduto potere equivalere una tale mi&shy;<lb/>sura di forza viva al peso morto, che fa equilibrio alle secchie nella Bilancia <lb/>gelileiana, sarebbe anch'egli incorso nel disordine del comparare insieme due <lb/>cose eterogenee, contro i precetti della logica, saviamente revocati dal Fer&shy;<lb/>roni, e prima di lui dal Borelli, il quale &egrave; notabile che, prendendo a scri&shy;<lb/>vere il suo libro coll'intenzione di esplicare i concetti di Galileo, riuscisse <lb/>invece a dimostrare la falsit&agrave; delle leggi, da lui assegnate alle forze della <lb/>percossa, e la fallacia degli strumenti da lui stesso proposti per misurarla. </s></p><pb xlink:href="020/01/2544.jpg" pagenum="169"/><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>L'esame dei fatti, indipendente e libero dalla suggezione delle prevalse <lb/>opinioni, pu&ograve; aver persuaso chiunque pi&ugrave; ritroso che la nuova Scienza del <lb/>moto, per quel che riguarda l'energia della percossa, &egrave; inutile andare a cer&shy;<lb/>carla l&agrave;, dove tutti si credevano d'averla infallibilmente a ritrovare: nei di&shy;<lb/>scorsi cio&egrave; e nel Dialogo postumo di Galileo. </s>

<s>Rimasta la sua prima Scuola <lb/>dagli errori e dalle fallacie sterilita, il Borelli poi <emph type="italics"/>proprio marte<emph.end type="italics"/> diceva di <lb/>averla recuperata, e la proponeva, nel suo trattato <emph type="italics"/>De vi percussionis,<emph.end type="italics"/> al <lb/>pubblico, a cui sperava che <emph type="italics"/>ob novitatem et materiae praestantiam,<emph.end type="italics"/> sarebbe <lb/>per riuscire non ingioconda. </s>

<s>&Egrave; da osservare per&ograve; che, nella cultura della <lb/>Scienza meccanica di quei tempi, avvenne ci&ograve; che spesso avviene nella cul&shy;<lb/>tura degli orti, che, vedendo uno nel suo mancare qualche albero pellegrino, <lb/>ve lo inserisce con la sua propria industria, mentre, per le aiuole di un altro, <lb/>si vedeva gi&agrave; da gran tempo frondeggiare, e menar fiori e frutti, propag&shy;<lb/>ginatovi o scoppiato di sottoterra spontaneo dall'ubert&agrave; delle preesistenti <lb/>radici. </s></p><p type="main">

<s>Chi crede che uno solo fosse il campo della Scienza meccanica, e quello <lb/>segnatamente piantato e coltivato, com'oasi nel deserto, in Toscana, facil&shy;<lb/>mente s'inganna, avendoci oramai rivelato a tante occasioni la storia esservi <lb/>qua e l&agrave; altre oasi sparse, alle quali erano approdati i semi e gl'impostimi <lb/>da un primo istituito paradiso terrestre. </s>

<s>N&egrave; a cotesto paradiso, alla custodia <lb/>del quale avevano i Filosofi antichi proposto Aristotile, mancarono i cultori, <lb/>il pi&ugrave; benemerito fra i quali, sorto ne'tempi nuovi, &egrave; Giordano Nemorario. </s>

<s><lb/>Si diffusero da lui quelle benefiche tradizioni, che passarono in Italia a fe&shy;<lb/>condare gl'ingegni nei contemporanei di Leonardo da Vinci, ma pi&ugrave; uber&shy;<lb/>tosamente rimasero ad allignare nella patria Alemagna, per mezzo alla quale, <lb/>essendo lungamente andate occulte e disperse, s'incominciarono a raccogliere <lb/>e a pubblicare per gli studi solerti e la diligenza insigne di Giovan Marco <lb/>Marci. </s></p><p type="main">

<s>Che veramente le tradizioni, rimaste nella Scienza galileiana intercise, <lb/>vigessero tuttavia nel campo della scienza universale, alcuni secoli prima che <lb/>venisse a resuscitarle fra noi il Borelli; s'argomenta dalle Note di Leonardo <lb/>da Vinci, in una delle quali osservammo gi&agrave; come si trovassero espresse le <lb/>quantit&agrave; del moto dal prodotto della velocit&agrave; per la mole, cosicch&egrave;, avendosi <lb/>due di quelle quantit&agrave; uguali, staranno in esse le velocit&agrave; in contraria ra&shy;<lb/>gion delle moli. </s>

<s>Conseguiva di qui che, se le velocit&agrave; sono uguali, le forze <lb/>delle percosse stanno direttamente come i pesi. </s>

<s>Confermava Leonardo que&shy;<lb/>sta proposizione con l'esperienze, per introdursi alle quali domandava &ldquo; Se <lb/>dieci colpi d'una libbra per colpo, caduti sopra uno loco, cadendo un brac&shy;<lb/>cio da alto, ficcheranno tanto uno chiodo d'uno braccio, quanto farebbe un <pb xlink:href="020/01/2545.jpg" pagenum="170"/>peso unito di dieci libbre. </s>

<s>&rdquo; Alla qual domanda faceva seguitare la facile ri&shy;<lb/>sposta: &ldquo; Questo mostra di no, imperocch&egrave;, se tu volessi ficcare uno chiodo <lb/>col peso d'un altro simile chiodo, questo sarebbe impossibile, imperocch&egrave;, se <lb/>tu vi battessi sopra esso diecimila simili colpi, tutti sarebbono niente. </s>

<s>E se <lb/>tu torrai venti tanti di peso, fia il colpo a proporzione del chiodo che voi <lb/>ficcare &rdquo; (Les Manuscrits etc., Manus. </s>

<s>A, Paris 1881, fol. </s>

<s>23). </s></p><p type="main">

<s>Soggiunge poi Leonardo un'esperienza pi&ugrave; diretta a confermare la ve&shy;<lb/>rit&agrave; dell'annunziata proposizione, osservando quanto maggior trafitta si fac&shy;<lb/>cia sopra una lamina di piombo da un martello di una libbra, e da un'altro <lb/>di cento, bench&egrave; scendano ugualmente veloci, perch&egrave; lasciati ambedue an&shy;<lb/>dare dalla medesima altezza. </s>

<s>&ldquo; Se tu lascerai cadere uno martello di una <lb/>libbra cento volte l'altezza di uno braccio sopra una verga di piombo, e poi <lb/>tolli uno martello o altro peso, che sia della grosseza del martello, e sia tanto <lb/>lungo, che pesi cento libbre, e fallo medesimamente cadere l'altezza di uno <lb/>braccio sopra una verga di piombo simile alla prima: e vederai quanto la <lb/>verga del colpo unito fia pi&ugrave; trafitta che la prima &rdquo; (ivi, fol. </s>

<s>4). </s></p><p type="main">

<s>Che le altre varie propriet&agrave; della forza della percossa fossero, per legit&shy;<lb/>tima conclusione immediata da queste proposizioni fondamentali, conosciute <lb/>da'contemporanei seguaci di quella Scuola, alla quale apparteneva Leonardo; <lb/>non sembrer&agrave; a nessuno incredibile o maraviglioso. </s>

<s>Che se anzi si ripensa <lb/>come fossero quegli sconosciuti Matematici, secondo noi vissuti in un secolo <lb/>d'ignoranza e di barbarie universale, esperti in comporre e in decomporre <lb/>le forze, ci potremmo aspettare di ritrovar, ne'loro libri o ne'loro manoscritti, <lb/>risoluti, anche della forza della percossa, problemi, intorno ai quali si sareb&shy;<lb/>bero sgomentati di mettersi a cimento Galileo, e i discepoli di lui pi&ugrave; valo&shy;<lb/>rosi. </s>

<s>Ma che ci hann'elleno luogo le espettazioni, se ne'libri di Giovan Marco <lb/>abbiamo, di quello che si congetturava, l'attestato vivo e presente? </s>

<s>Egli con&shy;<lb/>fessa che, siccome di ogni altra forza, cos&igrave; di quella della percossa la noti&shy;<lb/>zia &egrave; molto oscura, e perci&ograve; soggiunge: &ldquo; Ut in hac obscuritate aliquam lu&shy;<lb/>cem consequamur, quae non nisi ex natura impulsus prius cognita clucescit, <lb/>de qua in libro <emph type="italics"/>De arcu coelesti<emph.end type="italics"/> latius disseremus, notandum hic breviter.... &rdquo; </s></p><p type="main">

<s>Cos&igrave; fatte parole premetteva Giovan Marco, nella proposizione XXXVII <lb/><emph type="italics"/>De proportione motus,<emph.end type="italics"/> alla recensione ordinata di quei principii fondamen&shy;<lb/>tali, da'quali poi, in varii corollari o porismi, si dimostrerebbero le propriet&agrave; <lb/>dei gravi, che percotono o si urtano insieme. </s>

<s>Gli otto <emph type="italics"/>Porismi<emph.end type="italics"/> per&ograve;, che se&shy;<lb/>guitano alla detta proposizione, ci avverte l'Autore non essere altro che un <lb/>compendio di ci&ograve;, che pi&ugrave; diffusamente egli stesso avrebbe trattato nel libro <lb/>Dell'arco celeste. </s>

<s>Sembrerebbe a prima vista l'argomento alieno dal presente <lb/>soggetto, ma ripensando poi che la luce era per gli antichi composta di tanti <lb/>minimi globuli, emessi dal corpo lucente, s'intende come le riflessioni otti&shy;<lb/>che, per esempio, si facessero cadere sotto la legge meccanica universale della <lb/>riflessione dei corpi duri. </s>

<s>Meccaniche infatti son parecchie proposizioni di <lb/>Vitellione, per condur le quali si compone e si decompone un raggio di luce, <lb/>come si compongono e si decompongono nel parallelogrammo le linee, prese <pb xlink:href="020/01/2546.jpg" pagenum="171"/>a rappresentare le forze. </s>

<s>La XL proposizione meccanica perci&ograve;, nella quale <lb/>Giovan Marco dimostra che l'angolo dell'incidenza &egrave; uguale all'angolo della <lb/>riflessione, si comprende come non dovesse differire dalla proposizione ottica, <lb/>ch'egli avr&agrave; in modo simile annunziata e dimostrata nel libro dell'Arco ce&shy;<lb/>leste, solamente intendendo applicato il moto, invece che a un globo duro <lb/>di ponderosa materia, a un sottile atomo di luce. </s>

<s>Parimente, in quel capi&shy;<lb/>tolo, ch'egli intitola <emph type="italics"/>De motu reflexo lapillorum ex aqua,<emph.end type="italics"/> non &egrave; difficile <lb/>indovinare l'applicazione dei moti reflessi di una sfera, dentro le cave pareti <lb/>di un vaso, alle molteplici riflessioni di un raggio di luce, dentro una goc&shy;<lb/>ciola rorida, per venir indi a spiegare, come talvolta si osserva, la pluralit&agrave; <lb/>degli Archi celesti. </s></p><p type="main">

<s>Ci siamo espressi cos&igrave; per modo di congettura, perch&egrave;, sebbene sia un <lb/>fatto che Giovan Marco mantenne le sue promesse, chi ha mai veduto quel <lb/>suo libro <emph type="italics"/>De arcu coelesti?<emph.end type="italics"/> Quegli stessi pochi, che l'hanno commemorato, <lb/>hanno dovuto confessare di non esser riusciti a consultarlo nelle sue fonti, <lb/>rimettendosene a quello che ne portava la pubblica fama, o se n'era detto <lb/>dai discepoli dell'Autore, o dagli ascritti al medesimo sodalizio di lui. </s>

<s>Anche <lb/>il libro <emph type="italics"/>De proportione motus<emph.end type="italics"/> &egrave;, specialmente fra noi, cos&igrave; raro, da doverci <lb/>chiamare veramente felici d'averlo potuto avere ad esaminare sott'occhio. </s>

<s><lb/>N&egrave; qui possiamo tacere la maraviglia che proviamo, nel ripensare a quei <lb/>dotti Alemanni dei tempi passati e dei presenti, i quali, potendosi giusta&shy;<lb/>mente gloriare di avere avuto nella loro nazione il maestro, non delle sole <lb/>scienze del moto e della luce insegnate nel medesimo tempo e un secolo dopo <lb/>da Galileo e dal Newton, ma di parecchie altre mirabili verit&agrave; ignorate da <lb/>loro; lasciano liberamente scrivere alla Storia, bench&egrave;, riproducendo e diffon&shy;<lb/>dendo le opere di Giovan Marco, la potessero convincer di menzogna, come <lb/>venisse d'Italia e d'Inghilterra la luce a illuminar le tenebre del loro set&shy;<lb/>tentrione. </s></p><p type="main">

<s>Comunque sia, giacch&egrave; ci &egrave; stata favorevole la fortuna, proseguendo a <lb/>svolgere le preziose pagine del Matematico di Praga, per le quali trovammo <lb/>gi&agrave; dimostrate le propriet&agrave; dei moti accelerati, insieme con le leggi dei pen&shy;<lb/>doli di lunghezza varia di fili, e risoluto il problema della lunghezza del pen&shy;<lb/>dolo che misura i secondi; soggiungeremo quest'altro insigne esempio di <lb/>meccaniche dottrine recateci dallo straniero, non per supplire ai difetti, ma <lb/>per emendare gli errori di Galileo, nell'istituir che fa quegli il primo, per <lb/>via della detta proposizione XXXVII, la vera nuova Scienza della percossa. </s></p><p type="main">

<s>Le cose, che voleva ivi brevemente notar l'Autore, perch&egrave; si potesse, in <lb/>tale e tanta oscurit&agrave;, conseguir qualche luce, si riducono a cinque capi, l'es&shy;<lb/>senza dei quali si condensa in quell'ultima osservazione provocata dal dub&shy;<lb/>bio se una palla di legno, che lentamente si muova, possa ribattere un'altra <lb/>palla di ferro, che a lei venga incontro con qualunque violenza. </s>

<s>&ldquo; Ad ple&shy;<lb/>niorem huius atque aliarum obiectionum solutionem, risponde Giovan Marco, <lb/>notandum primo: Ut mobile moveatur non sufficere quamlibet impulsum, sed <lb/>proportionatum illi mobili. </s>

<s>Impulsus enim, quo globus ligneus ad motum con-<pb xlink:href="020/01/2547.jpg" pagenum="172"/>citatur, haudquaquam loco movebit pilam ferream eiusdem molis aut maio&shy;<lb/>rem: at vero, si huius impulsu moveatur globus ligneus, motu agitabitur <lb/>multo velociore. </s>

<s>Secundo: hanc proportionem motus et impulsus non a mole <lb/>sed a gravitate illorum corporum determinari &rdquo; (De proport. </s>

<s>motus, Pra&shy;<lb/>gae 1639, fol. </s>

<s>44, 45). </s></p><p type="main">

<s>La palla dunque di legno, mossa dalla medesima forza, va secondo i po&shy;<lb/>sti principii tanto pi&ugrave; veloce della palla di ferro, non a proporzion del volume, <lb/>ma della quantit&agrave; di materia o della massa: cosicch&egrave;, chiamando questa M, <lb/>F la forza, V velocit&agrave; che ne resulta, il fondamento posto da Giovan Marco alla <lb/>nuova Scienza della percossa, si potrebbe esprimere dalla formula V=F:M, <lb/>d'onde ne segue che, essendo le forze e le masse uguali o fra loro propor&shy;<lb/>zionali, le velocit&agrave; pure dovranno resultare uguali. </s>

<s>&ldquo; Itaque globus ligneus <lb/>maior et glans plumbea minor, si aequiponderant, ab impulsu aequali aequali <lb/>velocitate moventur. </s>

<s>Simili modo, si eamdem rationem habeant impulsus quam <lb/>habent pondera, erit velocitas motus aequalis &rdquo; (ibid., fol. </s>

<s>45). </s></p><p type="main">

<s>Un'altra osservazione, che Giovan Marco in terzo luogo soggiunge, &egrave; che <lb/>la percossa non si produce per il solo contatto, &ldquo; sed ex irruptione violenta, <lb/>qua veluti penetrat percutiens percussum &rdquo; (ibid.), cosicch&egrave;, movendosi un <lb/>globo contro un altro globo uguale e omogeneo, questo ch'era in quiete, per <lb/>la nuova forza in s&egrave; trapassata, si mover&agrave;, e l'altro ch'era in moto diven&shy;<lb/>ter&agrave; quiescente. </s>

<s>L'effetto, di cui chi gioca alle palle fa continua esperienza, <lb/>e descritto nel Porisma primo: &ldquo; Si globus alium globum percutiat qiescen&shy;<lb/>tem et aequalem, illo expulso quiescit &rdquo; (ibid., fol. </s>

<s>45 ad t.) &egrave; illustrato poi <lb/>nel primo Problema che, proponendosi &ldquo; Globum in plano quiescentem per&shy;<lb/>cutere alio globo quacumque violentia, neque tamen loco movere &rdquo; (fol. </s>

<s>47); <lb/>si scioglie col porre allato al globo, che ha da rimanere, un'altro globo uguale <lb/>e omogeneo, in cui venga per cos&igrave; dire travasato l'impulso, rimanendone <lb/>l'altro vuoto. </s></p><p type="main">

<s>In quasi tutti i trattati di Fisica si descrive la bella esperienza dei globi <lb/>di avorio, tutti uguali e disposti in serie a contatto, che percosso il primo <lb/>l'ultimo solo si risente al moto, e par che si sciolga dal rimanente monile: <lb/>n&egrave; ci&ograve; per altro avviene, che per secondarsi da que'globi le leggi degli urti, <lb/>dimostrate da Giovan Marco ne'suoi Porismi, dopo il quarto dei quali, ri&shy;<lb/>soluto il detto problema, adducendo per ragione <emph type="italics"/>quia enim globus, codem<emph.end type="italics"/><lb/><figure id="id.020.01.2547.1.jpg" xlink:href="020/01/2547/1.jpg"/></s></p><p type="caption">

<s>Figura 58.<lb/><emph type="italics"/>momento quo percutitur, percutit globum sibi aequalem, inducet illa per&shy;<lb/>cussione plagam perfectam ac proinde ex percussione quiescet<emph.end type="italics"/> (fol. </s>

<s>47 ad t.), <lb/>immediatamente soggiunge: &ldquo; Quod si plures globi aequales se contingant <lb/>in linea motus centri ut F, G, H, I (fig. </s>

<s>58), percusso F primo ab aequali E, <pb xlink:href="020/01/2548.jpg" pagenum="173"/>ultimus I movetur, reliquis F, G, H immotis, propterea quod, per Porisma I, <lb/>posterior prioris exhaurit plagam. </s>

<s>At vero si unus aequalium post se habeat <lb/>minores quotcumque, ut O, P, Q, percusso a K aequali L, omnes cum L <lb/>moto moventur ut constat per Porisma II. </s>

<s>Quod si demum percussio inci&shy;<lb/>piat a minori Q v. </s>

<s>g., omnibus immotis aut reflexis, ultimus movetur per <lb/>Porisma III, aut, si minor est implsus gravitate, quiescit per Porisma IV &rdquo; <lb/>(ibid., fol. </s>

<s>48). </s></p><p type="main">

<s>Questi Porismi, e gli altri quattro che si soggiungono, non son altro <lb/>che conseguenze di quella prima e principal proposizione, nella quale si de&shy;<lb/>finiva che le velocit&agrave; son tanto pi&ugrave; grandi, quant'&egrave; maggiore l'impulso dato <lb/>al grave e minore il suo peso. </s>

<s>La qual proposizione applica Giovan Marco a <lb/>ogni specie di forza, e principalmente a quella della gravit&agrave; naturale, dimo&shy;<lb/>strando quanto fossero in inganno Aristotile e i suoi seguaci nell'affermare <lb/>che le velocit&agrave; nei gravi cadenti son proporzionali alle quantit&agrave; della mate&shy;<lb/>ria. </s>

<s>&ldquo; At vero cum inferunt libras duas v. </s>

<s>g. </s>

<s>plumbi in dupla ferri celeri&shy;<lb/>tate ad libram unam, falluntur, propterea quod illa gravitas in alio fit su&shy;<lb/>biecto, cuius partes omnes aequali gravitate moventur. </s>

<s>Sicut enim pars extra <lb/>totum, v. </s>

<s>g. </s>

<s>libra una a sua gravitate movetur cum tanta velocitate; ita par&shy;<lb/>tes librarum decem aut centum in toto unitae eadem velocitate moventur a <lb/>sua cuique propria gravitate &rdquo; (ibid., fol. </s>

<s>58 ad t.). </s></p><p type="main">

<s>Galileo per confutar ne'suoi Dialoghi, e in tante altre scritture, l'errore <lb/>dei Peripatetici, spese molte parole, che non hanno per&ograve; l'efficacia dello <lb/>stringente argomento di Giovan Marco, il quale, dal suo dimostrato principio <lb/>espresso dalla formula V=F:M, e dalla sua simile V&prime;=F&prime;:M&prime;, se le <lb/>forze di gravit&agrave; son proporzionali ai pesi, come le stadere lo dimostrano nelle <lb/>pi&ugrave; volgari esperienze in ogni sorta di merci, ne traeva la matematica con&shy;<lb/>seguenza che le velocit&agrave; V, V&prime; di due cadenti, quanto si voglia diversi di <lb/>peso, si mantengono fra loro uguali. </s></p><p type="main">

<s>Passando dunque fra F ed M ed F&prime;, M&prime;, nelle dette formule, per le gra&shy;<lb/>vit&agrave; naturali, una relazione sempre costante, &ldquo; nisi gravitas, dice l'Autore, <lb/>magis sit intensa, nihil proficiet ad velocitatem augendam illorum &rdquo; (ibid., <lb/>fol. </s>

<s>59). Che se si tratti d'altra qualit&agrave; di forze, come son quelle per esem&shy;<lb/>pio che da noi s'imprimono ne'proietti, partecipandone una egual quantit&agrave; <lb/>a due globi di mole diversa, nemmeno in questo caso si trover&agrave; verificato il <lb/>peripatetico asserto, essendo le velocit&agrave; non direttamente ma reciprocamente <lb/>proporzionali alle grandezze. </s>

<s>&ldquo; Atque inde fit quod globus minor, accepta a <lb/>maiori plaga, praecurrat. </s>

<s>Quod si enim globos quotcumque ea serie dispo&shy;<lb/>nas, ut continuo maiorem minor sequatur, percusso primo, videbis quasi uno <lb/>impetu-omnes ad motum concitari, verum celeritate, pro ratione magnitudi&shy;<lb/>nis, inaequali &rdquo; (ibid.). </s></p><p type="main">

<s>S'immagini che, invece di tanti globi a contatto, s'abbiano tanti dischi <lb/>decrescenti nel medesimo ordine, e congiunti insieme per la coesion natu&shy;<lb/>rale, come per esempio in un chiodo conico, che si percota nel suo cappello. </s>

<s><lb/>La forza, secondo Giovan Marco, va diffondendosi verso la punta come un <pb xlink:href="020/01/2549.jpg" pagenum="174"/>fluido, di cui giusto ella osserva le leggi, andando con velocit&agrave; reciproche <lb/>delle sezioni. </s>

<s>Tale &egrave; la famosa legge dimostrata nell'Idraulica dal Castelli, <lb/>e tanto prima di lui da Leonardo da Vinci, che pure, riguardando la forza <lb/>come un flusso che si propaga per le particelle della materia, determinava <lb/>secondo quella medesima legge la proporzione della velocit&agrave;, con la quale va <lb/>ficcandosi la punta del chiodo, rispetto alla velocit&agrave;, con la quale penetre&shy;<lb/>rebbe la testa del martello. </s>

<s>&ldquo; Tanto quanto, egli dice, la punta del chiodo <lb/>entra nella testa del martello che lo batte, tanto si ficcher&agrave; pi&ugrave; nell'asse, <lb/>che non si ficcherebbe il martello di pari movimento e forza &rdquo; (Manus. </s>

<s>A cit., <lb/>fol. </s>

<s>53 a tergo). </s></p><p type="main">

<s>Lasciando d'osservare, come si potrebbero queste dottrine applicare util&shy;<lb/>mente alla meccanica del cuneo, appresso agli Autori cos&igrave; oscura, diremo, <lb/>per non divagar di troppo dal nostro argomento, delle loro applicazioni a un <lb/>problema, rimasto irresoluto anche dai pi&ugrave; grandi maestri della scienza. </s>

<s>Ga&shy;<lb/>lileo s'era proposto di rendere la ragione &ldquo; Perch&egrave; le aste lunghe lanciate <lb/>fanno maggior colpo &rdquo; (Alb. </s>

<s>XIV, 321), ma il proposito in lui venne meno, <lb/>come venne meno nel Torricelli, il quale par che facesse, con gli Accade&shy;<lb/>mici della Crusca, come colui che mostra un pomo al fanciullo, e poi glielo <lb/>nasconde. </s>

<s>&ldquo; Sarebbe forse, diceva, curioso problema l'investigare se quel legno <lb/>della picca, essendo egualmente velocitato, facesse il medesimo effetto, men&shy;<lb/>tre si adopra disteso in asta, e mentre si adoperasse raccolto in una palla: <lb/>cos&igrave; anco se una trave, egualmente velocitata, fosse per dare il medesimo <lb/>urto, percotendo una volta per lo lungo, ed un'altra per traverso &rdquo; (Lez. </s>

<s><lb/>accad. </s>

<s>cit., pag. </s>

<s>107). </s></p><p type="main">

<s>Presunse il Vossio di aver fatto una grande scoperta, e di avere emen&shy;<lb/>dato un grande errore di Galileo, il quale attribuiva a sola la velocit&agrave; l'ef&shy;<lb/>ficacia della percossa, <emph type="italics"/>neglecto pondere ad ictum perpendiculari.<emph.end type="italics"/> Era per&ograve; <lb/>un fatto ovvio a tutti, nelle esperienze citate dallo stesso Galileo e dal Tor&shy;<lb/>ricelli, che la trave ABCD (fig. </s>

<s>59), arietando contro il muro MN, produce <lb/>molto maggior colpo, che se percotesselo per traverso: cosicch&egrave; il Vossio, se <lb/><figure id="id.020.01.2549.1.jpg" xlink:href="020/01/2549/1.jpg"/></s></p><p type="caption">

<s>Figura 59.<lb/>voleva arrogarsi il merito di aver <lb/>promossa la scienza, doveva ad&shy;<lb/>durre non il semplice fatto gi&agrave; <lb/>benissimo noto, ma, ci&ograve; che nem&shy;<lb/>men egli fa, le ragioni del fatto, <lb/>le quali facilmente si trovano nelle <lb/>dottrine professate da Leonardo, e <lb/>da Giovan Marco. </s>

<s>La trave AD <lb/>infatti, il centro di gravit&agrave; della <lb/>quale sia O, percuote con momento uguale al suo peso, che chiameremo <lb/>P, moltiplicato per OE: mentre, nella posizione QN, percote con momento <lb/>uguale al medesimo peso P moltiplicato per ST, Le differenze dunque di <lb/>que'momenti stanno come P.OE a P.ST, o come OE a ST, o anche come <lb/>AC a QP o come PN a CD, che vuol dire in ragion reciproca delle se-<pb xlink:href="020/01/2550.jpg" pagenum="175"/>zioni, o delle aree percosse dal medesimo percuziente nella variet&agrave; delle sue <lb/>giaciture. </s></p><p type="main">

<s>Altri problemi, anche pi&ugrave; curiosi di questo, e pur rimasti difficili a molti <lb/>Fisici e Matematici, si risolvono con facilit&agrave; professando le dottrine di Giovan <lb/>Marco, che cio&egrave;, propagandosi la forza come un fluido che irrompa violen&shy;<lb/>temente e penetri attraverso alla materia, non opera in istante ma in tempo, <lb/>come si osserva nella diffusione del suono. </s>

<s>&ldquo; Notandum tertio percussionem, <lb/>et quae hanc sequitur plagam, non uno instanti, sed in aliquo tempore, quan&shy;<lb/>tumvis imperceptibili, perfici. </s>

<s>Cum enim plaga proveniat non ex solo contactu, <lb/>sed ex irruptione violenta, qua veluti penetrat percutiens percussum, non esse <lb/>potest absque motu. </s>

<s>Cum ergo percutiens tangit, necdum est plaga sed fit, <lb/>cuius signum fragor a percussione non nisi in tempore proveniens &rdquo; (De <lb/>proport. </s>

<s>motus cit., fol. </s>

<s>45). Di qui avviene che, nel menare talvolta un mar&shy;<lb/>tello, il quale lasciato andare sopra una pietra la ridurrebbe in frantumi, ri&shy;<lb/>tirato subito in su, la faccia commovere appena, e co'grandi magli a vapore, <lb/>che domano sull'incudine le pi&ugrave; dure moli del ferro, si pu&ograve;, non dandovi il <lb/>tempo, temperar l'impeto in modo, che valgano appena a infrangere il gu&shy;<lb/>scio di un pinocchio. </s></p><p type="main">

<s>Valorosi Matematici del secolo passato, come il Lambert, il Prony, e Gre&shy;<lb/>gorio Fontana fra i nostri, vollero mettersi a supplire a un difetto, che no&shy;<lb/>tarono nella Meccanica animale del Borelli, rendendo la ragione del perch&egrave;, <lb/>velocissimamente correndo, il corridore divenga pi&ugrave; leggero. </s>

<s>Crederono co&shy;<lb/>storo che l'Autor <emph type="italics"/>De motu animalium<emph.end type="italics"/> avesse lasciato indietro quella cu&shy;<lb/>riosa conclusione, per mancargli i principii necessari, i quali parve a loro di <lb/>ritrovare ne'nuovi dimostrati teoremi ugeniani, per le forze centrifughe, che <lb/>si svolgono dalla punta de'piedi verso gli archi successivamente descritti dalle <lb/>anche di chi muove il passo veloce. </s>

<s>Nelle dottrine di Giovan Marco per&ograve; <lb/>avrebbero potuto ritrovar que'medesimi principii assai prima, e cos&igrave; semplici, <lb/>da ricavarne una soluzione pi&ugrave; generale al problema, essendo un fatto che <lb/>una tal leggerezza si osserva, non ne'soli corridori, ma in qualunque corpo, <lb/>che orizontalmente si muova. </s></p><p type="main">

<s>Sembrerebbe si potesse dar sodisfazione col dire che la forza di gravit&agrave; <lb/>diretta verticalmente nel mobile, componendosi con la forza orizontale del <lb/>corso, d&agrave; per resultante un moto, che &egrave; tanto meno obliquo, quanto la ve&shy;<lb/>locit&agrave; &egrave; maggiore, a che insomma si ridurrebbe la soluzione, che il Bene&shy;<lb/>detti dava di questo problema, come si riferir&agrave; da noi in altro proposito, ma <lb/>ad alcuni Matematici del secolo XVII piacque meglio risolvere il problema, <lb/>invocando il principio che dice <emph type="italics"/>non in uno instanti, sed in aliquo tempore <lb/>perfici,<emph.end type="italics"/> cos&igrave; le percosse, come le pressioni. </s>

<s>Stefano degli Angeli, matematico <lb/>di Padova e discepolo del Cavalieri, distinguendo in un grave, che scenda <lb/>lungo un piano inclinato, il moto attuale da quello di energia, scriveva cos&igrave; <lb/>in una sua nota, che ci occorrer&agrave; di trascrivere integralmente in altra occa&shy;<lb/>sione di maggiore importanza. </s>

<s>&ldquo; Pu&ograve; accadere che il moto attuale sia ca&shy;<lb/>gione che. </s>

<s>l'energia sia men sentita dal piano. </s>

<s>Poich&egrave;, essendo vero che <pb xlink:href="020/01/2551.jpg" pagenum="176"/><emph type="italics"/>omnis actio fit in tempore,<emph.end type="italics"/> il moto attuale &egrave; cagione che l'energia non sia <lb/>esercitata sopra un luogo determinato del piano, che per un momento, ed <lb/>in scorrere. </s>

<s>Cos&igrave; &egrave; successo che, passando la ruota d'una carrozza veloce&shy;<lb/>mente mossa sopra un uomo, gli ha fatto poco male, ed una volta ho ve&shy;<lb/>duto passar con gran prestezza una carrozza sopra un ponte debolissimo, che, <lb/>se questa si fosse fermata sopra l'uno o sopra l'altro, con la energia sua <lb/>avrebbe fatto gran male e fracassato ogni cosa &rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXIX, <lb/>fol. </s>

<s>17). </s></p><p type="main">

<s>Le dottrine di Giovan Marco, cos&igrave; riguardanti la forza della percossa e <lb/>i varii problemi dipendenti da lei, come le tante altre questioni di Mecca&shy;<lb/>nica e di Ottica, che si trovano risolute ne'suoi varii libri; rimasero sta&shy;<lb/>gnanti come in ampio lago profondo, a pi&egrave; di una chiusa valle, sotto un'alpe <lb/>solitaria. </s>

<s>Il fiume della Scienza, che pure derivava da una medesima sorgente, <lb/>aveva preso altro corso attraverso a campi ubertosi e a popolose citt&agrave;, che <lb/>acclamavano dalle sponde e auguravano felici i progressi ai naviganti. </s>

<s>Quelle <lb/>acque, scese per conveniente declivio, e battute da tanti validi remi, anda&shy;<lb/>vano velocemente correnti, ma in alcuni seni men late e meno profonde di <lb/>quell'altre, rimaste morte e in disparte, cos&igrave; che sulla loro trauquilla super&shy;<lb/>ficie, da quella del Sole in fuori, non era entrata a specchiarsi mai pu&shy;<lb/>pilla viva. </s></p><p type="main">

<s>Riducendo alla realt&agrave; le immagini, la Scienza galileiana, come in altre <lb/>parti principalissime, cos&igrave; rimase in difetto, comparata con ci&ograve; che Giovan <lb/>Marco aveva dimestrato nella sua XXXVII proposizione <emph type="italics"/>De proportione mo&shy;<lb/>tus:<emph.end type="italics"/> del qual difetto, se voglia eccettuarsi l'Aggiunti, non par che si accor&shy;<lb/>gessero i primi e pi&ugrave; immediati discepoli dello stesso Galileo. </s>

<s>Quanto al Tor&shy;<lb/>ricelli, ne fanno pubblica testimonianza le sue <emph type="italics"/>Lezioni,<emph.end type="italics"/> e quanto al Viviani <lb/>le note sparse per i suoi Manoscritti, fra le quali basti a noi citar le se&shy;<lb/>guenti, a provar com'anch'egli secondasse l'errore del Maestro in ammettere <lb/>che i momenti del percuziente e del percosso siano reciprocamente propor&shy;<lb/>zionali alle velocit&agrave;, e in commettere il disordine del chiamare la percossa <lb/>infinita, piuttosto che incommensurabile col peso morto, bench&egrave; avvertisse che <lb/>il resistente non pu&ograve; moversi con lui che per uguale spazio. </s>

<s>&ldquo; Il peso morto <lb/>non pu&ograve; muover la resistenza, se non per tanto spazio, quanto &egrave; il suo: ma <lb/>nella percossa il moto del percuziente &egrave; maggiore del moto del percosso, e <lb/>forse tanto, quanto il momento del percuziente &egrave; minore del momento del <lb/>resistente &rdquo; (MSS. Gal., T. CXXXII, fol. </s>

<s>61). &mdash; &ldquo; La campana non risuona, <lb/>se non quando trema: non trema, n&egrave; pu&ograve; tremare, senza piegarsi, e risuona <lb/>ad ogni minima percossa. </s>

<s>Adunque ogni minima percossa riflette il grossis&shy;<lb/>simo metallo, e perci&ograve; la sua azione &egrave; come infinita &rdquo; (ivi, fol. </s>

<s>54). </s></p><p type="main">

<s>La nuova Scienza della percossa era dunque rilasciata intatta nella Scuola <lb/>galileiana al Borelli, il quale la ridusse alle sue ultime e pi&ugrave; vere conclu&shy;<lb/>sioni, movendo dal principio, altre volte accennato, e ritrovato gi&agrave; in Giovan <lb/>Marco espresso dalla formula, che in due corpi le velocit&agrave; sono uguali alle <lb/>forze d'impulso divise per la quantit&agrave; della materia, e per la massa. </s>

<s>Dal-<pb xlink:href="020/01/2552.jpg" pagenum="177"/>l'essere perci&ograve; V=F:M, V&prime;=F&prime;:M&prime;, se ne conclude F:F&prime;=V.M:V&prime;.M&prime;, <lb/>che corrisponde con la XXXVII proposizione <emph type="italics"/>De vi percussionis,<emph.end type="italics"/> dal Borelli <lb/>cos&igrave; formulata: &ldquo; Si duo corpora inaequalia velocitatibus inaequalibus inci&shy;<lb/>dant perpendiculariter super eiusdem corporis omnino quiescentis superficiem, <lb/>sintque praedicta corpora dura et inflexibilia; vires eorum percussionum pro&shy;<lb/>portionem compositam habebunt ex rationibus magnitudinum et velocita&shy;<lb/>tum &rdquo; (pag. </s>

<s>66). </s></p><p type="main">

<s>Si conclude altres&igrave; dalle formule stabilite, essendo le velocit&agrave; uguali, <lb/>F:F&prime;=M:M&prime;, ed essendo le masse uguali, F:F&prime;=V:V&prime;, che riscon&shy;<lb/>trano con le XXV e XXVI del citato libro, dall'Autore stesso ivi proposte <lb/>in questa forma: &ldquo; Si duo corpora, aequali velocitate traslata, perpendicu&shy;<lb/>lariter incidant in superficiem eiusdem corporis omnino immobilis, duri et <lb/>inflexibilis; eorum percussiones eamdem proportionem habebunt, quam moles <lb/>corporeae eorumdem incidentium corporum habent. </s>

<s>&mdash; Si duo corpora inter <lb/>se aequalia perpendiculariter incidant super alterius corporis omnino stabilis <lb/>superficiem, fuerintque omnia corpora dura et inflexibilia; vires percussio&shy;<lb/>num proportionales erunt velocitatibus eorumdem incidentium corporum &rdquo; <lb/>(pag. </s>

<s>64, 65). </s></p><p type="main">

<s>Il Borelli istituisce la sua Scienza nuova sul fondamento di queste pro&shy;<lb/>posizioni, n&egrave; tratta l'argomento solamente in s&egrave;, ma digredisce spesso qua <lb/>e l&agrave;, cogliendo l'occasione di dimostrare le principali propriet&agrave; dei moti, che <lb/>in qualche modo dipendono, o che si riferiscono a quello della percossa. </s>

<s>Non <lb/>sempre per&ograve; procedono le sue proposizioni con rigor matematico: vi s'im&shy;<lb/>mischia talvolta una fisica, la quale &egrave; piuttosto il parto della fantasia del&shy;<lb/>l'Autore, che un effetto della Natura, e fu questo forse il principale motivo, <lb/>per cui, non avendo avuto applauso fra gli studiosi, parve che non fossero <lb/>approvate le verit&agrave; delle nuove dottrine. </s></p><p type="main">

<s>L'Accademia di Londra propose a'suoi soci di speculare intorno al me&shy;<lb/>desimo soggetto, e vi concorsero il Wren e l'Huyghens, che nel 1663 les&shy;<lb/>sero in quelle dotte adunanze le loro dissertazioni, e vi concorse altres&igrave; il <lb/>Wallis che, pubblicando nel 1671 la terza parte del suo trattato <emph type="italics"/>De motu,<emph.end type="italics"/><lb/>v'aggiunse il capitolo <emph type="italics"/>De percussione.<emph.end type="italics"/> Bene esaminando le cose per&ograve;, non <lb/>possono i giusti estimatori non concludere il loro giudizio con dire che i tre <lb/>illustri Matematici stranieri non hanno fatto altro, che confermare, e in qual&shy;<lb/>che parte promovere i teoremi, da tre anni conosciuti in Italia, e di l&igrave; lar&shy;<lb/>gamente divulgati nel libro <emph type="italics"/>De vi percussionis.<emph.end type="italics"/></s></p><p type="main">

<s>La dissertazione accademica dell'Huyghens fu raccolta fra gli Opuscoli <lb/>postumi dell'Autore col titolo <emph type="italics"/>De motu corporum ex percussione,<emph.end type="italics"/> e risulta <lb/>di sole XIII proposizioni, le prime delle quali non differiscono forse dalle <lb/>borelliane che nella forma: vi se ne aggiunge per&ograve; due insigni, e perci&ograve; me&shy;<lb/>ritevoli che siano notate dalla Storia. </s>

<s>La prima &egrave; la XI che dice: &ldquo; Duobus <lb/>corporibus, sibi mutuo occurrentibus, id quod efficitur ducendo singulorum <lb/>magnitudines in velocitatum suarum quadrata, simul additum, ante et post <lb/>occursum corporum aequale invenitur &rdquo; (Opusc. </s>

<s>posth., Lugd. </s>

<s>Batav. </s>

<s>1703, <pb xlink:href="020/01/2553.jpg" pagenum="178"/>pag. </s>

<s>389). Si diceva questa ugeniana proposizione insigne, non tanto per la <lb/>novit&agrave;, quanto per aver dato occasione alle questioni famose intorno al do&shy;<lb/>versi le quantit&agrave; di moto misurare dal prodotto della massa per la semplice <lb/>velocit&agrave;, o per il quadrato della velocit&agrave;: queste chiamandosi forze vive e <lb/>quelle morte. </s></p><p type="main">

<s>L'altra proposizione, alla quale la sola inaspettata novit&agrave; conferisce im&shy;<lb/>portanza, &egrave; la XII, dall'Autore stesso cos&igrave; formulata: &ldquo; Si quod corpus maiori <lb/>vel minori quiescenti obviam pergat, maiorem ei celeritatem dabit per inter&shy;<lb/>positum corpus mediae magnitudinis, itidem quiescens, quam si nullo interme&shy;<lb/>dio ipsi impingatur &rdquo; (ibid., pag. </s>

<s>393). Alcuni Autori si studiarono di render <lb/>pi&ugrave; facile e pi&ugrave; breve la dimostrazione della bellissima novit&agrave; cos&igrave; annun&shy;<lb/>ziata, premettendo per lemma il teorema che <emph type="italics"/>percotendo un corpo un altro <lb/>quiescente, la velocit&agrave; di quello, alla velocit&agrave; impressa in questo, sta come <lb/>la somma d'ambedue i corpi insieme a quel primo, cio&egrave; al percuziente.<emph.end type="italics"/><lb/>Che ci&ograve; sia il vero, non &egrave; difficile riconoscerlo, ammettendo che la forza d'im&shy;<lb/>pulso sia uguale a quella della resistenza, e, d'ambedue insieme resultan&shy;<lb/>done il colpo, concludere che questo equivale al doppio del momento del <lb/>percuziente, come, dietro un cos&igrave; semplice discorso, ebbe a concluderne il <lb/>Wallis nella sua VI proposizione. </s>

<s>Ora, muovasi contro B fermo il globo A, <lb/>con momento espresso da V.A: il colpo dato a B, chiamata V&prime; la velocit&agrave; <lb/>che ne consegue, avr&agrave; per misura la quantit&agrave; di moto, della quale &egrave; l'ef&shy;<lb/>fetto; misura espressa da V&prime;(A+B), che &egrave; uguale a 2 V.A, per la VIa del <lb/>Wallis, e perci&ograve; V:V&prime;=A+B:2A. </s></p><p type="main">

<s>Premesso il qual lemma, facciansi i globi A.B (fig. </s>

<s>60) proporzionali <lb/>alle linee AC, CB, e presa AD a rappresentare la velocit&agrave;, con la quale A <lb/><figure id="id.020.01.2553.1.jpg" xlink:href="020/01/2553/1.jpg"/></s></p><p type="caption">

<s>Figura 60.<lb/>si muove contro B in quiete, si prolunghi l'AC <lb/>in E talmente, che sia CE uguale ad AC. </s>

<s>Da <lb/>E poi condotta la EL parallela ad AD, si de&shy;<lb/>scriva fra EA, EL, come fra asintoti, l'iperbola <lb/>SDV: &egrave; facile dimostrare che, essendo AD la <lb/>velocit&agrave;, come s'&egrave; detto, del globo A percu&shy;<lb/>ziente, sar&agrave; BS la velocit&agrave;, che riceve il globo <lb/>B dopo la percossa. </s></p><p type="main">

<s>Abbiamo infatti, per le note propriet&agrave; della <lb/>curva, AD:BS=BE:AE=AC+CB:2AC, <lb/>sostituita invece delle linee intere BE, AE, la <lb/>somma delle loro parti. </s>

<s>Ma per supposizione &egrave; <lb/>A:B=AC:CB, ossia, componendo e dupli&shy;<lb/>cando i conseguenti, A+B:2A=AC+CB: <lb/>2AC; dunque AD:BS=A+B:2A, ossia, per il premesso lemma, <lb/>AD:BS=V:V&prime;, e ci&ograve; vuol dire appunto che, essendo dalla AD rappre&shy;<lb/>sentata la velocit&agrave; del percuziente, sar&agrave; dalla BS rappresentata la velocit&agrave;, <lb/>che imprimesi nel percosso. </s></p><p type="main">

<s>Ci&ograve; premesso, la laboriosa conclusione dell'Huyghens non dipende che <pb xlink:href="020/01/2554.jpg" pagenum="179"/>da una semplice avvertenza sopra le cose gi&agrave; dette. </s>

<s>Siano i tre globi A, N, B <lb/>(fig. </s>

<s>61) crescenti in grandezza, secondo l'ordine che gli abbiamo nominati: <lb/>&egrave; facile vedere che il globo A, percotendo immediatamente B, gl'imprime <lb/><figure id="id.020.01.2554.1.jpg" xlink:href="020/01/2554/1.jpg"/></s></p><p type="caption">

<s>Figura 61.<lb/>una velocit&agrave; minore di quella che gl'imprime&shy;<lb/>rebbe percotendolo per l'intermedio del globo <lb/>N. Imperocch&egrave;, essendo nel primo caso rappre&shy;<lb/>sentata la velocit&agrave; del percuziente dalla linea AD, <lb/>costruita l'iperbola DVS fra gli asintoti EL, EN, <lb/>sar&agrave; da BS rappresentata la velocit&agrave; del per&shy;<lb/>cosso: mentre nell'altro caso, che cio&egrave; il per&shy;<lb/>cuziente sia il globo intermedio N, presa CH <lb/>uguale a CN, sar&agrave; il nuovo asintoto HG; fra il <lb/>quale e HN descritta l'altra iperbola IVF, la ve&shy;<lb/>locit&agrave; impressa nel globo B verr&agrave; rappresen&shy;<lb/>tata da BF, maggiore di BS, pienamente con&shy;<lb/>fermando il discorso la verit&agrave; della proposizione <lb/>ugeniana. </s></p><p type="main">

<s>Seguono da una tal proposizione due co&shy;<lb/>rollarii, il primo de'quali &egrave; che la massima velocit&agrave; verr&agrave; allora impressa, <lb/>quando N globo interposto sia esattamente medio proporzionale fra i due <lb/>estremi A, B; e l'altro, che l'Huyghens stesso si proponeva in ultimo luogo <lb/>a dimostrar sotto questa forma: &ldquo; Quo plura corpora interponentur inter <lb/>duo inaequalia, quorum alterum quiescat, alterum moveatur; eo maior mo&shy;<lb/>tus quiescenti conciliari poterit. </s>

<s>Maximus autem per unamquamque interpo&shy;<lb/>sitorum multitudinem ita conferetur, si interposita cum extremis continuam <lb/>proportionalium seriem constituant &rdquo; (Opusc. </s>

<s>cit., pag. </s>

<s>397). Se per esempio <lb/>siano cento corpi, soggiunge l'Autore, le moli de'quali crescano successiva&shy;<lb/>mente come i quadrati della serie dei numeri naturali, e il moto incominci <lb/>dal massimo, <emph type="italics"/>subducto calculo ad praeceptum regulae,<emph.end type="italics"/> si trover&agrave; la velo&shy;<lb/>cit&agrave; del minimo stare a quella del massimo prossimamente come 14,760 mi&shy;<lb/>lioni ad uno. </s>

<s>Chi poi volesse applicare a qualche effetto della natura la mi&shy;<lb/>rabile conclusione, ripensi che le rocce son tanto pi&ugrave; frantumate, quanto dal <lb/>nucleo terrestre s'ascende verso la superficie, ond'&egrave; perci&ograve; dato in qualche <lb/>modo ad intendere com'anche un leggero urto, che muova dall'interno, <lb/>possa propagandosi all'esterno del nostro globo moltiplicarsi in quelle posse <lb/>immense, che ci si manifestano per esempio nelle eruzioni sotterranee, e nei <lb/>terremoti. </s></p><p type="main">

<s>Giovanni Wallis, altro celebre accademico londinese, si tenne anche pi&ugrave; <lb/>strettamente dell'Huyghens a compendiar le dottrine del Borelli. </s>

<s>Le XV pro&shy;<lb/>posizioni infatti, ch'egli stende nel suo capitolo <emph type="italics"/>De percussione,<emph.end type="italics"/> si svolgono <lb/>essenzialmente tutte dalla seconda, che l'Autore annunzia in questa maniera: <lb/>&ldquo; Si grave motum gravi quiescenti directe impingat, sed ita constituto, ut <lb/>aliunde ne moveatur non impediatur, utrumque iunctim movebitur quam cal&shy;<lb/>culus, ponderum ratione et pristina celeritate rite computatis, indicabit &rdquo; (De <pb xlink:href="020/01/2555.jpg" pagenum="180"/>motu, cap. </s>

<s>XI, Londini 1671, pag. </s>

<s>662). L'indicazione per&ograve; direttamente sov&shy;<lb/>viene dalla XIX borelliana, la verit&agrave; della quale, chiamato A il grave in moto <lb/>con la velocit&agrave; V, da cui s'imprime la forza F nell'altro grave B in quiete, <lb/>e vien con la velocit&agrave; X trasportato nella medesima direzione; &egrave;, come al&shy;<lb/>trove dicemmo, espressa dalla formula F=A.V=X(A+B) d'onde <lb/>calcola il Wallis X=A.V/(A+B), &ldquo; nempe si momentum, ex moti gravis pon&shy;<lb/>dere et celeritate compositum, per utriusque simul pondus dividatur, habe&shy;<lb/>bitur futura celeritas &rdquo; (ibid.). </s></p><p type="main">

<s>Gli Accademici parigini non volendo, nel partecipare al merito di aver <lb/>coltivata la nuova Scienza, rimanere indietro a quelli di Londra, deputarono <lb/>il Mariotte, il quale scrisse il suo <emph type="italics"/>Trait&egrave; de la percussion, ou choc des corps,<emph.end type="italics"/><lb/>di cui nel 1679 era gi&agrave; stata fatta in Parigi la terza edizione. </s>

<s>Il nuovo Ma&shy;<lb/>tematico si dilung&ograve; anche meno degli altri dai primi instituti borelliani, de&shy;<lb/>rivando dalle fisiche esperienze le dimostrazioni dei principali teoremi. </s>

<s>Ma <lb/>imitando il nostro Italiano non sembra ne sapesse cansar que'difetti, che gli <lb/>furono spesso ingiustamente imputati, specialmente dagli stranieri, imperoc&shy;<lb/>ch&egrave;, descritta esso Mariotte quella macchina di precisione, la quale era stata <lb/>proposta gi&agrave; dal Borelli nel capitolo XXIX del suo libro, come altrove osser&shy;<lb/>vammo, suppone che siano esattamente isocrone le maggiori e le minori di&shy;<lb/>scese dei globi penduli, nel computar ch'egli fa i momenti delle loro per&shy;<lb/>cosse, ora per dimostrarne direttamente, ora per verificarne le leggi. </s>

<s>&ldquo; Les <lb/>petits battemens d'un pendule se font en des tems sensiblement &eacute;gaux, quoi <lb/>que son plomb d&eacute;crive des arcs in&eacute;gaux; mais pour la facilit&eacute; des demonstra&shy;<lb/>tions, on suppose ici que ces tems sont precisement &eacute;gaux &rdquo; (Oeuvres, T. </s>

<s>I <lb/>cit., pag. </s>

<s>5). </s></p><p type="main">

<s>Bench&egrave; il trattato del Mariotte, che si divide in due parti, sia molto pi&ugrave; <lb/>esteso della dissertazione dell'Huyghens, e del capitolo del Wallis, lascia <lb/>nulladimeno intatte alcune delle principali proposizioni, che strettamente si <lb/>riferiscono all'argomento, come son quelle delle relazioni che passano fra <lb/>l'angolo dell'incidenza e l'angolo della riflessione, e fra i varii momenti della <lb/>percossa, secondo che la direzione del moto &egrave; perpendicolare o &egrave; obliqua. </s>

<s><lb/>L'Huyghens pure non sembra che sapesse trovar luogo a queste fra le altre <lb/>sue minori, bench&egrave; elaboratissime, proposizioni, e il Borelli stesso, di queste <lb/>verit&agrave; conosciute al mondo, checch&egrave; se ne pensassero gli stranieri, primo <lb/>maestro; se ne passa con tal leggerezza per vero dire non conveniente alla <lb/>dignit&agrave; e all'importanza del soggetto. </s>

<s>Si direbbe che avessero dovuto tro&shy;<lb/>varci qualche difficolt&agrave; quei Matematici, i quali, bench&egrave; valorosissimi, sap&shy;<lb/>piamo nulladimeno che furono o ritrosi in ammettere i moti misti, o in maneg&shy;<lb/>giarli inesperti; ci&ograve; che doveva render difficilissimo, per non dire impossibile, <lb/>il condurre a buon termine le accennate dimostrazioni. </s>

<s>Si comprende perci&ograve; <lb/>come alla presente intrapresa storia della percossa manchi una parte, che in <lb/>quest'altro articolo del nostro discorso, con la maggior possibile brevit&agrave;, si <lb/>soggiunge. </s></p><pb xlink:href="020/01/2556.jpg" pagenum="181"/><p type="main">

<s><emph type="center"/>VI.<emph.end type="center"/></s></p><p type="main">

<s>Che l'angolo dell'incidenza sia uguale o quello della riflessione &egrave; una <lb/>propriet&agrave; dai pi&ugrave; antichi Filosofi conosciuta, e sperimentata nella luce. </s>

<s>Il <lb/>Kepler fu il primo a darne dimostrazione, applicandovi i moti misti, e il Car&shy;<lb/>tesio ne segui l'esempio, appropriando agli atomi luminosi in moto i dimo&shy;<lb/>strati effetti di una palla elastica, che rimbalza dalla resistenza di una dura <lb/>superficie. </s>

<s>Chi vuol rammemorarsi di queste cose si compiaccia di tornare indie&shy;<lb/>tro a pag. </s>

<s>14, 15 del secondo Tomo della nostra Storia, rileggendo le quali <lb/>pagine, gli parr&agrave; di vedere in qualche modo supplito a quel difetto, che si <lb/>notava nella prima istituzione della scienza della percossa dei corpi ponderosi. </s></p><p type="main">

<s>Non si pu&ograve; senza maraviglia ripensare come rimanessero le tradizioni <lb/>dell'Ottica inefficaci ai progressi della Meccanica, ma chi si risovviene di quel <lb/><emph type="italics"/>nescio quid subtile<emph.end type="italics"/> pronunziato dal Keplero, e di quel procedere incerto e <lb/>dubitoso del Cartesio, s'avvedr&agrave; che tutto dipendeva dal non avere avuto fede <lb/>il Borelli e il Mariotte, n&egrave; dimestichezza con quelle sottigliezze dei moti mi&shy;<lb/>sti. </s>

<s>Il Wallis, che fu il primo a riappiccare il filo alle prime tradizioni, ve&shy;<lb/>dremo com'avesse a patir contese con i matematici de'suoi tempi, ignari di <lb/>ci&ograve; che s'era luminosamente rivelato a Giovan Marco nella pace solitaria <lb/>de'suoi pensieri. </s>

<s>Ma per apprezzar meglio le gioie passate, e sentir pi&ugrave; vivo <lb/>il desiderio di un giorno sereno, descriveremo prima il nuvolo affannoso del <lb/>giorno dopo. </s></p><p type="main">

<s>Una via aperta, proseguendo per la quale si poteva riuscir felicemente <lb/>a dimostrare che, nei corpi elastici, il moto obliquo dopo la percossa si fa <lb/>con angolo uguale a quello prima della percossa; sembrava dovere apparire <lb/>innanzi al Borelli nella proposizione LXIII, nella quale egli dimostra che &ldquo; si <lb/>duo corpora, contrariis motibus per eamdem rectam lineam translata, reci&shy;<lb/>proce proportionalia fuerint suis velocitatibus, ac se mutuo perpendiculari et <lb/>media incidentia percutiant, sintque ambo corpora dura et inflexibilia; re&shy;<lb/>flectentur ad partes oppositas iisdem velocitatibus, quibus ante occursum fe&shy;<lb/>rebantur &rdquo; (De vi percuss. </s>

<s>cit., pag. </s>

<s>120). Questa medesima proposizione fu <lb/>poi dimostrata dall'Huyghens nella sua VIII, che dice: &ldquo; Si corpora duo sibi <lb/>ex adverso occurrant, quorum magnitudinibus celeritates contraria ratione <lb/>respondeant; utrumque eadem, qua accessit, celeritate resiliet &rdquo; (Opusc. </s>

<s>cit., <lb/>pag. </s>

<s>381), e fu altresi soggiunta dal Mariotte nella XV della prima parte del <lb/>suo Trattato, in cui, dop'aver provato coi supposti principii, poi con l'espe&shy;<lb/>rienza conferma che &ldquo; Si deux corps &agrave; ressort se choquent directement, avec <lb/>des vitesses reciproques &agrave; leur poids: chacun de ces corps retournera en <lb/>arriere avec sa premiere vitesse &rdquo; (Oeuvres cit., pag. </s>

<s>29). </s></p><p type="main">

<s>Restava cos&igrave; per conseguenza dimostrato, dal consenso dei tre insigni <lb/>Matematici, che un corpo elastico, il quale percuota in una dura superficie, <pb xlink:href="020/01/2557.jpg" pagenum="182"/>ritorna indietro con la medesima velocit&agrave;, con la quale era venuto, e ci&ograve; non <lb/>solo nella perpendicolare e media, ma in qualunque incidenza. </s>

<s>Cos&igrave; essendo, <lb/>tornava facile dimostrare che, cos&igrave; l'incidenza, come la riflessione del moto <lb/>dovevano farsi con angoli uguali, ma questa facilit&agrave; non fu ritrovata da nes&shy;<lb/>suno, fuor che dal Wallis, applicando a condurre la sua dimostrazione, come <lb/>or ora vedremo, i moti misti. </s></p><p type="main">

<s>L'Huyghens e il Mariotte tralasciarono l'impresa, cedendo agli scrupoli, <lb/>ma il Borelli sembrava che si fosse, con argomento diverso dalla composi&shy;<lb/>zion delle forze, aperta innanzi la porta gelosa. </s>

<s>Incomincia il cap. </s>

<s>XV del <lb/>suo libro con una considerazione, la quale si direbbe forse inspirata da ci&ograve; <lb/>che scrisse il Cartesio del non poter farsi nel punto di riflessione dal per&shy;<lb/>cuziente alcuna dimora, perch&egrave; altrimenti <emph type="italics"/>nulla extaret causa, qua inci&shy;<lb/>tante, vires resumere possent<emph.end type="italics"/> (Dioptr., Francof. </s>

<s>1692, pag. </s>

<s>47); se non si <lb/>sapesse esser questa l'espression del principio galileiano, dimostrato contro <lb/>Aristotile, <emph type="italics"/>in puncto reflexionis non dari quietem<emph.end type="italics"/> (Op. </s>

<s>Ediz. </s>

<s>naz., Fi&shy;<lb/>renze 1890, pag. </s>

<s>323). Comunque sia, l'occasione immediata a quella con&shy;<lb/>siderazione venne al Borelli da coloro, fra'quali Giovan Marco, i quali am&shy;<lb/>mettevano che il moto si estinguesse, e resuscitasse di nuovo nella resili&shy;<lb/>zione. </s>

<s>&ldquo; Ut obiectioni et experientiae satisfiat, dicendum a quolibet contactu <lb/>impulsum deficere et expirare, novum vero a percussione determinari, qui <lb/>motu, eidem plagae aequali, retroagit illud mobile &rdquo; (De prop. </s>

<s>motus cit., <lb/>fol. </s>

<s>44 ad t.). Ma qual &egrave; la causa, domandava il Borelli, di questa estinzione <lb/>e di questa resurrezione? </s>

<s>E non trovandone alcuna vide la necessit&agrave; di con&shy;<lb/>fessare &ldquo; quod idem impetus motus incidentiae perseverat, et tantummodo, <lb/>impedito transitu et progressu ab obice, itineris directionem aliorsum diri&shy;<lb/>git &rdquo; (De vi percuss. </s>

<s>cit., pag. </s>

<s>114). </s></p><p type="main">

<s>Ecco dunque per quali altre vie, diverse da quelle indicate nella LXIII pro&shy;<lb/>posizione, riusciva il Borelli a concludere che nella riflessione persevera la <lb/>medesima quantit&agrave; di moto che nell'incidenza. </s>

<s>Si crederebbe che avesse pre&shy;<lb/>parata una tal conclusione, per servirsene a dimostrare l'uguaglianza degli <lb/>angoli ne'moti che risultano uguali, tanto pi&ugrave; che nella LIX, bench&egrave; con <lb/>lo scrupoloso riserbo della regola galileiana, s'induce a decomporre nelle due <lb/><figure id="id.020.01.2557.1.jpg" xlink:href="020/01/2557/1.jpg"/></s></p><p type="caption">

<s>Figura 62.<lb/>dei cateti l'unica potenza dell'ipotenusa. </s>

<s><lb/>Con tali principii infatti, e con tali mezzi, <lb/>la desiderata dimostrazione sarebbe stata <lb/>paratissima. </s>

<s>Imperocch&egrave;, sia rappresentato <lb/>da AB (fig. </s>

<s>62) il moto incidente, decom&shy;<lb/>posto nel perpendicolare AC, e nell'ori&shy;<lb/>zontale CB, e sia da BE rappresentato <lb/>il moto riflesso: se &egrave; vero che questo ri&shy;<lb/>sulti uguale all'incidente nel tutto, gli resulter&agrave; uguale altres&igrave; nelle parti <lb/>componenti, cosicch&egrave;, se BD &egrave; uguale a CD, anche DE dovr&agrave; essere uguale <lb/>ad AC, e i triangoli ACB, BDE uguali, ed uguali ABC, EBD, angoli dell'in&shy;<lb/>cidenza e della riflessione. </s></p><pb xlink:href="020/01/2558.jpg" pagenum="183"/><p type="main">

<s>&Egrave; per&ograve; notabile che il Borelli divaga per tutt'altri sentieri, e quel che <lb/>diceva del perseverare il moto riflesso, con la medesima intensit&agrave; dell'inci&shy;<lb/>dente, &egrave; termine, e non mezzo di alcuna dimostrazione. </s>

<s>Ne'due capitoli ap&shy;<lb/>presso insiste nel medesimo argomento, dimostrando con molte e belle ra&shy;<lb/>gioni non esser possibile che il moto si distrugga in natura, e si generi di <lb/>nuovo, essendo la quiete stessa l'effetto di due moti tuttavia vigenti e ope&shy;<lb/>ranti, con direzioni per&ograve; uguali e contrarie, come per esempio nel sasso, che <lb/>non cade, perch&egrave; l'ostacolo lo trattiene. </s>

<s>&ldquo; Idemque dicendum, cos&igrave; termina <lb/>l'Autore il suo ragionamento, de omnibus aliis motionibus, quae in natura <lb/>fiunt, ut subinde concludere liceat motum, neque gigni de novo, neque destrui <lb/>in natura. </s>

<s>Hoc autem nec asseveranter nec ut certe creditum me protulisse <lb/>quis sibi persuadeat, sed tantummodo suspicando &rdquo; (ibid., pag. </s>

<s>136). L'opi&shy;<lb/>nione fu anzi benissimo accolta in quello, che poi si disse <emph type="italics"/>principio della <lb/>conservazion delle forze,<emph.end type="italics"/> il qual principio era la nostra intenzione di dimo&shy;<lb/>strare come fosse dal Borelli applicato ai moti riflessi. </s>

<s>Gi&agrave; dicemmo come <lb/>quello, che si credeva mezzo, era invece termine di una dimostrazione, e ora <lb/>&egrave; da soggiungere come si facesse in questa dimostrazione principalmente con&shy;<lb/>sistere, dallo stesso Borelli, il trattato <emph type="italics"/>De reflessione, quae ad corporum per&shy;<lb/>cussionem consequitur,<emph.end type="italics"/> lasciando indietro o dando le seconde parti a ci&ograve;, <lb/>che avrebbe dovuto avere le principali. </s></p><p type="main">

<s>Dop'aver professato che nel moto riflesso persevera il medesimo impeto, <lb/>che nell'incidente, soggiunge cos&igrave; il Nostro: &ldquo; Quod autem haec sit naturae <lb/>familiaris consuetudo constat ex penduli illa proprietate, quam nuper detexi &rdquo; <lb/>(ibid., pag. </s>

<s>114). Questa nuova propriet&agrave; del pendolo &egrave; descritta e dimostrata <lb/>nel cap. </s>

<s>XI del primo libro delle <emph type="italics"/>Theoricae Mediceorum,<emph.end type="italics"/> a proposito del ri&shy;<lb/>solvere la seguente questione: Se circolando un mobile intorno a un centro <lb/>fisso, come i pianeti intorno al Sole o i satelliti intorno a Giove, perseve&shy;<lb/>rando col medesimo vigore a rivolgersi in un cerchio pi&ugrave; angusto faccia, come <lb/>dicevano alcuni, il suo moto pi&ugrave; concitato. </s>

<s>La questione pareva per verit&agrave; <lb/>risoluta nel quarto dialogo dei Massimi Sistemi da Galileo, dove, a proposito <lb/>delle ineguaglianze della Luna, dice che nella congiunzione deve passar archi <lb/>maggiori dell'orbe magno. </s>

<s>&ldquo; Ora se &egrave; vero, dice ivi il Salviati, che la virt&ugrave;, <lb/>che muove la Terra e la Luna intorno al Sole, si mantenga del medesimo <lb/>vigore, e se &egrave; vero che il medesimo mobile, mosso dalla medesima virt&ugrave;, ma <lb/>in cerchi disuguali, in tempi pi&ugrave; brevi passi archi simili dei cerchi minori; <lb/>bisogna necessariamente dire che la Luna, quando &egrave; in minor distanza dal <lb/>Sole, cio&egrave; nel tempo della congiunzione, archi maggiori passi dell'orbe magno, <lb/>che quando &egrave; in maggior lontananza, cio&egrave; nell'opposizione e plenilunio &rdquo; <lb/>(Alb. </s>

<s>I, 490). Galileo per&ograve; tien per vero che la Luna, anche deviata dal suo <lb/>primo corso, prosegua con la medesima velocit&agrave; nel giro pi&ugrave; angusto, ma non <lb/>lo dimostra, ond'il Borelli annunzia una tal proposizione, per supplire al di&shy;<lb/>fetto: &ldquo; Aio verum non esse idem mobile, semper ab eadem virtute motiva <lb/>intrinseca translatum, ac modo percurrens maiorem circuli peripheriam, modo <lb/>vero minorem; per minorem circulum concitatiori motu cieri, quam per ma-<pb xlink:href="020/01/2559.jpg" pagenum="184"/>iorem: progreditur enim eadem velocitate per ambos circulos inaequales, hoc <lb/>est, temporibus aequalibus, aequalia spatia pertransit &rdquo; (Theoricae Medic., <lb/>Florentiae 1665, pag. </s>

<s>52). </s></p><p type="main">

<s>La proposizione si dimostra per mezzo di uno sperimento, <emph type="italics"/>aptissimum,<emph.end type="italics"/><lb/>dice il Borelli, <emph type="italics"/>ad hanc veritatem comprobandam,<emph.end type="italics"/> ed &egrave; tale: Sia AB un <lb/>pendolo (fig. </s>

<s>63) sospeso in A: rimosso in AC dal perpendicolo, e lasciato poi <lb/>andare, incontri in D un ostacolo, come per esempio un chiodo, cosicch&egrave;, con <lb/><figure id="id.020.01.2559.1.jpg" xlink:href="020/01/2559/1.jpg"/></s></p><p type="caption">

<s>Figura 63.<lb/>l'impeto conceputo in B, prosegua il suo moto per <lb/>l'arco GB, che verr&agrave; descritto col raggio DB raccor&shy;<lb/>ciato. </s>

<s>Dice il Borelli stesso di avere in questo fatto <lb/>scoperto una propriet&agrave; singolare, che cio&egrave; sempre, e <lb/>in qualunque caso, l'angolo GDB sta all'angolo BAC, <lb/>o al suo uguale FDB, reciprocamente come la radice <lb/>della maggior lunghezza del pendolo sta alla radice <lb/>della minore: e di qui ne conclude che, per essere il <lb/>mobile deviato, non per questo varia la prima impres&shy;<lb/>sagli velocit&agrave; del suo moto. </s>

<s>La conclusione &egrave; verissima, <lb/>come resulta dai principii matematici del seguente di&shy;<lb/>scorso. </s>

<s>Essendo gli angoli GDB, FDB proporzionali <lb/>agli archi intercetti, abbiamo per esperienza GB:FB=&radic;AB:&radic;BD, e per <lb/>Geometria FB:BC=DB:AB, essendo gli archi simili proporzionali alle <lb/>lunghezze dei raggi. </s>

<s>Moltiplicando ora insieme termine per termine queste <lb/>proporzioni, ne resulta GB:BC=&radic;DB:&radic;AB. </s>

<s>Ma per le note propriet&agrave; <lb/>de'pendoli di varia lunghezza anche il tempo per GB sta al tempo per BC <lb/>come la radice di DB sta alla radice di AB; dunque i tempi son proporzio&shy;<lb/>nali agli spazi. </s>

<s>&ldquo; Sed, cum tempora sunt proportionalia spatiis transactis, <lb/>celeritates aequales sunt inter se; ergo celeritas penduli AB aequalis est ce&shy;<lb/>leritati penduli BD &rdquo; (ibid., pag. </s>

<s>54). </s></p><p type="main">

<s>Questa propriet&agrave; dei pendoli per&ograve; non era ap&shy;<lb/><figure id="id.020.01.2559.2.jpg" xlink:href="020/01/2559/2.jpg"/></s></p><p type="caption">

<s>Figura 64.<lb/>plicabile alla Meccanica celeste, se non che nell'ipo&shy;<lb/>tesi di Galileo, ma nel sistema delle forze centrali, <lb/>come lo professava il Borelli, era fuor di luogo, non <lb/>potendo il pianeta deviar dal suo corso, senza variar <lb/>quell'impeto, che tutto dipende dalla maggior o mi&shy;<lb/>nor distanza ch'egli ha dal centro attrattivo; ond'&egrave; <lb/>che, per intrinseca necessit&agrave;, va nel perielio pi&ugrave; ve&shy;<lb/>loce che nell'afelio. </s>

<s>Con miglior senno perci&ograve; si di&shy;<lb/>rebbe applicata dall'Autore la sua scoperta, nelle <lb/>controversie ch'egli ebbe coll'Angeli, rispetto al de&shy;<lb/>finir la linea, che nel tendere al centro della terra <lb/>descrive il proietto. </s>

<s>Di lui si pu&ograve; dir benissimo che persevera con la sua <lb/>prima velocit&agrave;, deviando e variamente incurvando il suo moto, come vi per&shy;<lb/>severa il pendolo conico ABE (fig. </s>

<s>64), ritirando in G per esempio il filo, <lb/>scorrevole nella campanella B. </s>

<s>Se BG &egrave; un quarto di AB &ldquo; allora vedremo <pb xlink:href="020/01/2560.jpg" pagenum="185"/>dalla palla F descriversi il cerchio FG, in tempo minore, cio&egrave; la met&agrave; di <lb/>quello, che vi voleva a compiere il cerchio ADE; e per&ograve; la velocit&agrave; in FG <lb/>sar&agrave; la medesima, che aveva la palla A &rdquo; (Lettera a M. A. Ricci, Mes&shy;<lb/>sina 1667, pag. </s>

<s>4). </s></p><p type="main">

<s>Appropriata pure &egrave; la descritta esperienza a dimostrar che, nella rifles&shy;<lb/>sione, persevera la medesima quantit&agrave; di moto, che nell'incidenza, ond'&egrave; che <lb/>opportunamente citavasi dallo stesso Borelli, nel cap. </s>

<s>XV <emph type="italics"/>De vi percussio&shy;<lb/>nis,<emph.end type="italics"/> dopo di che egli ivi cos&igrave; soggiunge: &ldquo; Sed licet resistentia corporis duri <lb/>et quiescentis omnino non destruat impetum corporis in eum incidentis, ... <lb/>dubitari saltem potest an impetum eiusdem incidentis corporis debilitet, et <lb/>aliquo pacto imminuat &rdquo; (pag. </s>

<s>115), ci&ograve; che non possa essere attende a di&shy;<lb/>mostrarlo nella proposizione LIX, cos&igrave; annunziata: &ldquo; Vis motiva incidentis <lb/>corporis non debilitatur, neque imminuitur a resistentia corporis firmi et <lb/>duri &rdquo; (ibid.). </s></p><p type="main">

<s>La proposizione per&ograve;, dopo le cose dette, sembra per lo meno oziosa, <lb/>perch&egrave; o i corpi si suppongono perfettamente fermi e duri, e la verit&agrave; del&shy;<lb/>l'assunto dipende dalla fatta supposizione: o i corpi si considerano secondo <lb/>la loro fisica realt&agrave;, e la proposizione &egrave; falsa, perch&egrave;, non essendo in nes&shy;<lb/>suno di cos&igrave; fatti corpi la richiesta infiessibilit&agrave; e durezza assoluta, &egrave; impos&shy;<lb/>sibile che nel risaltare non perdano alquanto del primo impeto conceputo. </s>

<s><lb/>Apparir&agrave; poi la detta borelliana proposizione anche pi&ugrave; oziosa, se si ripensa <lb/>che, sopra la verit&agrave; di lei, era stato posto il fondamento a tutta la Meccanica <lb/>di Galileo, il quale, nello scolio alla proposizione XXIII del terzo dialogo delle <lb/>Scienze nuove, aveva dimostrato che il moto riflesso, dopo essere sceso lungo <lb/>un piano, non &egrave; punto diminuito dal moto incidente, avendo facolt&agrave; di ri&shy;<lb/>condurre il mobile alla medesima altezza, <emph type="italics"/>e ci&ograve; levato ogni intoppo, che pre&shy;<lb/>giudica all'esperienza<emph.end type="italics"/> (Alb. </s>

<s>XIII, 166). </s></p><p type="main">

<s>La galileiana dimostrazione equivale alla proposizione LXIII del Borelli, <lb/>e alle corrispondenti dell'Huyghens e del Mariotte, che pur sppongono esser <lb/>rimossi gli impedimenti, ammessi i quali non possono non esser false quelle <lb/>stesse loro proposizioni, com'ebbero a riscontrare i nostri Accademici fioren&shy;<lb/>tini ne'rimbalzi delle palle di corno di bufalo e di avorio, che non videro <lb/>mai raggiungere a quella precisa altezza, da cui erano scese. </s>

<s>Del resto aveva <lb/>anche Galileo pensato di dimostrare che, per cangiar direzione il mobile, il <lb/>moto di lui non si diminuisce, osservando che una debolissima forza, impos&shy;<lb/>sibile a muovere una gran mole, &egrave; pur capace, mossa che sia, di deviarla <lb/>dal suo sentiero. </s>

<s>&ldquo; Una palla molto grave, lasci&ograve; scritto in una nota, che fu <lb/>poi raccolta fra i <emph type="italics"/>Problemi varii;<emph.end type="italics"/> posata sopra un piano, e che percossa dal <lb/>vento gagliardo non gli ceda n&egrave; si muova, se la medesima sar&agrave; mossa sopra <lb/>quel piano, sicch&egrave; riceva il vento ad angolo retto, gli ceder&agrave; deflettendo verso <lb/>la parte, che il vento la caccia &rdquo; (Alb. </s>

<s>XIV, 321). Ma vediamo come si di&shy;<lb/>mostri dallo stesso Borelli la sopra accennata LIX proposizione. </s></p><p type="main">

<s>Tornando indietro sopra la figura 62, nella quale si rappresentava con <lb/>AB il moto incidente, decomposto nel perpendicolare AC e nel trasversale CB, <pb xlink:href="020/01/2561.jpg" pagenum="186"/><emph type="italics"/>quibus ille aequalis est potestate;<emph.end type="italics"/> rappresenti BE il moto riflesso, che si <lb/>vuol dimostrare non esser punto diminuito. </s>

<s>Perch&egrave;, se cos&igrave; fosse, presa del <lb/>trasversale una quantit&agrave; BD, uguale alla CB, il perpendicolare dovrebbe re&shy;<lb/>star minore di ED. </s>

<s>Sia per esempio DF: il moto riflesso diminuito sarebbe <lb/>dunque rappresentato da BF, per cui l'angolo della riflessione FBD torne&shy;<lb/>rebbe evidentemente minore dell'angolo dell'incidenza ABC. &ldquo; Hoc autem, dice <lb/>il Borelli, est falsum, et contra sensus evidentiam, quandoquidem perpetuo <lb/>huiusmodi anguli sunt aequales inter se &rdquo; (De vi percuss. </s>

<s>cit., pag. </s>

<s>117). </s></p><p type="main">

<s>Il teorema dunque nobilissimo, che ci si aspettava di veder dimostrato, <lb/>&egrave; rimesso all'evidenza del fatto, e parandosi innanzi all'Autore due vie, una <lb/>delle quali, dal suppor che il moto riflesso perseveri nel medesimo vigore <lb/>dell'incidente, conduceva a concluder l'uguaglianza degli angoli dell'obliquit&agrave; <lb/>ne'due moti, e l'altra che, dal supporre questa uguaglianza, menava a di&shy;<lb/>mostrar come nel riflettersi quello stesso moto non diminuisce; egli prose&shy;<lb/>gue a dirittura per questa, lasciando indietro quell'altra. </s>

<s>In ci&ograve; consiste quel <lb/>che si diceva avere il Borelli posposta nell'argomento la dignit&agrave; e l'impor&shy;<lb/>tanza delle parti. </s>

<s>Che le forze, per solo cangiar direzione, non illanguidi&shy;<lb/>scano il loro primo vigore, era cosa ammessa da tutti i matematici seguaci <lb/>delle dottrine meccaniche di Galileo, e perci&ograve; superflua si diceva tornare <lb/>l'opera del Borelli in voler mettersi a dimostrarla, mentre poteva per quel <lb/>mezzo cos&igrave; facilmente riuscire alla tanto desiderata dimostrazione dell'ugua&shy;<lb/>glianza degli angoli fatti nel venir e nel tornare del percuziente dalla super&shy;<lb/>ficie percossa. </s>

<s>Egli invece invoca l'evidenza del senso: ma quale evidenza, <lb/>se il senso stesso mostra al contrario che tutti i corpi ponderosi risalgono <lb/>con minore obliquit&agrave; di quella, con la quale erano scesi, come disse nelle <lb/>sue Lezioni di avere sperimentato il Torricelli, e se quella perpetuit&agrave; di legge, <lb/>affermata dal nostro Autore, potendosi osservare in un raggio, che mettesse <lb/>un tempo sensibile a venire allo specchio, non si verificherebbe forse pun&shy;<lb/>tualissimamente nemmen nella luce? </s></p><p type="main">

<s>Sembra nonostante che il Borelli, oltre a rimettersi al fatto, accennasse <lb/>a qualche dimostrazione del fatto, osservando che i corpi duri eleggono per <lb/><figure id="id.020.01.2561.1.jpg" xlink:href="020/01/2561/1.jpg"/></s></p><p type="caption">

<s>Figura 65.<lb/>necessit&agrave; nel riflettersi la via pi&ugrave; breve <lb/>di tutte. </s>

<s>&ldquo; Constat ergo ab eadem virtute <lb/>motiva impelli corpus incidens super ali&shy;<lb/>quod corpus durum, a qua postea fertur <lb/>necessitate naturae <emph type="italics"/>brevissima via re&shy;<lb/>flectendo &rdquo;<emph.end type="italics"/> (ibid. </s>

<s>pag. </s>

<s>115). Dalla qual <lb/>necessit&agrave; naturale, supposta vera, conse&shy;<lb/>gue senza dubbio che debba il mobile <lb/>ritornar con angolo uguale a quel che <lb/>venne, com'&egrave; facile dimostrare. </s>

<s>Sia per <lb/>esempio AB (fig. </s>

<s>65) il piano, che si vuol <lb/>percotere, e si supponga un corpo C che, nell'andare e nel tornare dalla <lb/>percossa, seguiti per istinto di natura la via pi&ugrave; breve. </s>

<s>Dovendogliela noi <pb xlink:href="020/01/2562.jpg" pagenum="187"/>geometricamente presignare, diremo: Dal punto C si abbassino sul piano la <lb/>perpendicolare CA, prolungata in D per ugual tratto, e la obliqua CE: con&shy;<lb/>giunta poi la DE, e prolungata in F, sar&agrave; CEF quella brevissima via, che si <lb/>voleva descritta. </s>

<s>Qualunque altra infatti se ne eleggesse, come per esempio <lb/>CGF, &egrave; facile vedere che sarebbe pi&ugrave; lunga, perch&egrave;, congiunta la GD, DGF, <lb/>ossia CG+GF &egrave; evidentemente maggior linea di FD, ossia di FE+EC. </s>

<s><lb/>E perch&egrave; CEA, FEB sono uguali, si conclude che non pu&ograve; dunque il mobile <lb/>eleggere per necessit&agrave; di natura la via brevissima, senza che sia dalla me&shy;<lb/>desima necessit&agrave; costretto a riflettersi con angolo uguale a quello dell'in&shy;<lb/>cidenza. </s></p><p type="main">

<s>Ma il Borelli, contento a porre il principio, lasci&ograve; al Leibniz il merito <lb/>della bellissima conclusione, intanto che, fra i primi promotori della scienza <lb/>della percossa, fu il Wallis il solo, che si proponesse di dimostrare: &ldquo; Si <lb/>grave motum in firmum obicem oblique impingat, sitque vel alterum vel <lb/>utrumque elasticum; resilitio eadem celeritate, et in eodem plano, ita fiet ut <lb/>angulus reflexionis sit angulo incidentiae aequalis &rdquo; (De motu cit., cap. </s>

<s>XIII, <lb/>pag. </s>

<s>692). &Egrave; questa la seconda proposizione, che ricorre nel trattato <emph type="italics"/>De ela&shy;<lb/>tere et reflexione,<emph.end type="italics"/> dop'essersi dimostrato dall'Autore, come aveva fatto prima <lb/>il Borelli nella sua LXIII, e poi l'Huyghens nella VIII, e nella XV della se&shy;<lb/>conde parte il Mariotte; che se un grave percote un resistente, e sia l'uno <lb/>e l'altro elastico, <emph type="italics"/>eadem velocitate resiliet, qua advenerat<emph.end type="italics"/> (ibid., pag. </s>

<s>687). </s></p><p type="main">

<s>Ci&ograve; premesso, ecco come succede per il Wallis la seconda detta propo&shy;<lb/>sizione. </s>

<s>Sia AB (fig. </s>

<s>66) la obliquit&agrave;, e la misura della forza, con la quale <lb/>il grave mosso percuote l'obice fermo CD, e sia quella forza decomposta nella <lb/><figure id="id.020.01.2562.1.jpg" xlink:href="020/01/2562/1.jpg"/></s></p><p type="caption">

<s>Figura 66.<lb/>orizontale AO, e nella perpendicolare OB, <lb/>la quale sola offende in B, d'onde ritorne&shy;<lb/>rebbe, per la precedente proposizione, in <lb/>O, alla medesima altezza: cosicch&egrave;, men&shy;<lb/>tre il mobile fosse passato orizontalmente <lb/>da B in D, nel medesimo tempo e per <lb/>spazio uguale a CB, sarebbe anche in&shy;<lb/>sieme risalito verticalmente in E, ad un'al&shy;<lb/>tezza DE uguale ad OB, ovvero a CA, con due moti, che si ricompongono nel&shy;<lb/>l'unico obliquo e riflesso BE, e i triangoli rettangoli ACB, BED, coi cateti <lb/>uguali, daranno ABC, angolo dell'incidenza uguale a DBE, angolo della ri&shy;<lb/>flessione. <emph type="italics"/>Quae,<emph.end type="italics"/> conclude il Wallis, <emph type="italics"/>erant demonstranda.<emph.end type="italics"/> Ma fa subito alla <lb/>conclusione seguitare uno Scolio, atto benissimo a testimoniare di quelle con&shy;<lb/>tradizioni, dalle quali si diceva essere stati l'Huyghens e il Mariotte, fra gli <lb/>altri, ritenuti dal professar liberamente la dottrina dei moti composti. </s></p><p type="main">

<s>Gli studenti, cos&igrave; scrive l'Autore nel detto Scolio, e anche alcuni, che <lb/>dovrebbero essere da qualche cosa pi&ugrave; degli studenti, mi domandano con <lb/>qual diritto io abbia decomposto un moto retto e semplicissimo in due: o <lb/>pur concedendomi il licenzioso arbitrio vorrebbero sapere come mai, fra gli <lb/>infiniti modi di decomporre un moto, io abbia per l'appunto scelto quello, <pb xlink:href="020/01/2563.jpg" pagenum="188"/>e non un altro. </s>

<s>&ldquo; Respondeo nullum ita simplicem esse motum posse, quin <lb/>in plures componentes resolvi possit. </s>

<s>Dum autem hunc prae caeteris modum <lb/>seligo, utor ego meo iure, qui, cum quamlibet possim, eam adhibeo compo&shy;<lb/>sitionem, quae praesenti negotio sit accomoda. </s>

<s>Neque probandum erit com&shy;<lb/>positionem hanc unicam esse possibilem, sed ex multis unam. </s>

<s>Liberum uti&shy;<lb/>que est, pro suo cuiusque constructoris arbitrio, ex veris innumeris ea seligere, <lb/>quae ad rem praesentem conducant &rdquo; (ibid., pag. </s>

<s>693). E soggiunge a illu&shy;<lb/>strare il fatto meccanico altri simili esempi di composizioni algebriche e geo&shy;<lb/>metriche, concludendo cos&igrave; l'apologetico suo discorso: &ldquo; Estque res haec tam <lb/>clara, ut nulla illustratione putaverim indiguisse, si non hoc ipsum serio <lb/>obiectum viderim a Viro cum tyronibus non camparando &rdquo; (ibid., pag. </s>

<s>695). </s></p><p type="main">

<s>S'intendeva compresa in quell'Uomo, da non mettersi coi principianti, <lb/>la maggior parte dei Matematici di Europa, i quali, a navigare per il peri&shy;<lb/>glioso oceano della Meccanica, avevano ripudiato il pi&ugrave; valido remo. </s>

<s>Ma con <lb/>questo in mano vedremo ora Giovan Marco entrare per i riposti seni, ad ap&shy;<lb/>prodare ai quali peneranno ancora un secolo i novelli esploratori, conducendo <lb/>snellamente la sua navicella per quelle acque solitarie, non agitate dai venti, <lb/>sotto quella remota zona di cielo, non offuscato dalle caligini: da quelle ca&shy;<lb/>ligini vogliam dire, a dissipar le quali, per tornare a vedere l'alma luce del <lb/>sole, ebbe ad affannarsi pi&ugrave; di una volta il Wallis. </s></p><p type="main">

<s>La proposizione XXXIX <emph type="italics"/>De proportione motus<emph.end type="italics"/> &egrave; dall'Autore stesso cos&igrave; <lb/>pronunziata: &ldquo; Motus reflexus fit per lineam parallelam illi lineae, quae cum <lb/>linea perpendiculari ad contactum angulum constituit in centro, cuius sinus <lb/>est aequalis intervallo inter centrum gravitatis, et lineam hypomochlii &rdquo; (fol. </s>

<s>50). <lb/>Cada il globo CDG (fig. </s>

<s>67) sul piano obliquo ADB, e lo percota in D: dal <lb/>qual punto sollevata la verticale DC, che &egrave; la linea dell'ipomoclio, si trovi <lb/><figure id="id.020.01.2563.1.jpg" xlink:href="020/01/2563/1.jpg"/></s></p><p type="caption">

<s>Figura 67.<lb/>questa lontana, per la distanza EF, dal cen&shy;<lb/>tro di gravit&agrave; E dello stesso globo. </s>

<s>Dentro <lb/>l'angolo retto KEH si costruisca un angolo <lb/>minore HEG, di cui il seno sia HG uguale <lb/>ad EF. </s>

<s>Descritto il parallelogrammo HK, e <lb/>condotta la diagonale EG, vuol dimostrar <lb/>Giovan Marco che, nel riflettersi il globo <lb/>dopo la percossa, si move, col centro, nella <lb/>direzione EG, e, col punto del contatto, nella <lb/>direzione DI, alla stessa EG parallela. </s></p><p type="main">

<s>Rappresentato con EB il momento to&shy;<lb/>tale, che vien decomposto nel DB sulla su&shy;<lb/>perficie del piano, e nel DE a lei stessa per&shy;<lb/>pendicolare; la dimostrazione procede cos&igrave;, <lb/>in modo che si rassomiglia nelle mosse a <lb/>quella del Wallis, se non che, mentre questi <lb/>fa precedere la proposizione che dice risalire da D in E il centro di gravit&agrave; <lb/>del percuziente, con la medesima velocit&agrave;, colla quale era da E in D dianzi <pb xlink:href="020/01/2564.jpg" pagenum="189"/>sceso; Giovan Marco suppone la stessa cosa come una verit&agrave; conseguente <lb/>dall'ipotesi, ch'egli tiene intorno alla natura della elasticit&agrave;, la quale essendo <lb/>perfetta restituisce al mobile tutto intero l'impeto perduto nell'urto. </s>

<s>Cos&igrave; <lb/>essendo, verr&agrave; dunque il centro E del globo dopo l'urto sollecitato da forze <lb/>rappresentate per linee uguali o proporzionali alle DB, DE, ma dirette in <lb/>parte, che non trovino impedimento. </s>

<s>E perch&egrave; EK, EH son quelle loro pro&shy;<lb/>porzionali, e hanno libero il loro esercizio, perch&egrave; son dirette alla parte av&shy;<lb/>versa, e fuori dell'ipomoclio del centro; trasporteranno dunque il globo, <lb/>com'era il proposito di dimostrare, dal centro stesso nella direzione della dia&shy;<lb/>gonale EG, e nella direzione DI, ad essa EG parallela, dal punto di con&shy;<lb/>tatto. </s>

<s>Ma &egrave; bene, a far conoscere la precisione e la chiarezza del dimo&shy;<lb/>strare, in mezzo alle verbosit&agrave; di quei tempi, trascriver le parole proprie <lb/>dell'Autore: </s></p><p type="main">

<s>&ldquo; Quia enim centrum gravitatis, dum sua mole ferit planum in puncto D, <lb/>per lineam ED seipsum veluti partitur: illa quidem pars quae hypomochlio <lb/>insistit, atque illam plagam inducit, eadem via qua impulit, et impulsu ae&shy;<lb/>quali, retro agitur; reliqua vero, quae cum centro extra hypomochlium cadit, <lb/>per lineam fertur EK parallelam lineae DB, propterea quod haec sit proxima <lb/>motui gravitatis ab hypomochlio impeditae. </s>

<s>Quia ergo motus EH, EK, qui&shy;<lb/>bus centrum gravitatis agitur, secundum quid sunt contrarii, propterea quod <lb/>angulus HEK sit minor duobus rectis; erit motus mixtus per lineam me&shy;<lb/>diam inter EH, et EK, cuius intervallum determinat sinus complementi in&shy;<lb/>clinationis, in ratione quam habent impulsus. </s>

<s>Est autem intervallum FE, hoc <lb/>est sinus DM anguli DEM, mensura gravitatis extra hypomochlio: linea vero <lb/>FD, sinus anguli reliqui, mensura illius, quae hypomochlio insistit, gravita&shy;<lb/>tis. </s>

<s>Si fiat ut FD ad EF, ita KG, sinus complementi anguli HEG, ad HG, <lb/>sinum complementi anguli KEG; erit linea EG linea motus mixti ex EH, <lb/>et EK.... Quia ergo mobile movetur ad motum sui centri, erit motus ex D <lb/>reflexus per lineam parallelam illi lineae, quae cum linea perpendiculari ad <lb/>contactum angulum constituit in centro, cuius sinus est aequalis intervallo <lb/>inter centrum gravitatis, et lineam hypomochlii &rdquo; (ibid., fol. </s>

<s>50, 51). </s></p><p type="main">

<s>Si diceva che questa dimostrazione si rassomiglia nelle mosse a quella, <lb/>che trentadue anni dopo, fra le contradizioni dei contemporanei, conquistava <lb/>faticosamente alla Scienza il Wallis, ma &egrave; pi&ugrave; generale e vien condotta da <lb/>Giovan Marco con tale analitico artificio, da poter da lei, come corollari, de&shy;<lb/>rivar facilmente le verit&agrave; pi&ugrave; importanti, di che &egrave; a notar che il Casati in <lb/>Italia, dove il Matematico di Praga era affatto sconosciuto, dette i primi <lb/>esempi (Mechanic., libri cit., pag. </s>

<s>739-32). Essendo infatti, nella precedente <lb/>figura, l'angolo ADC uguale all'angolo FED, che pure &egrave; uguale all'angolo <lb/>EGH, ed essendo l'angolo EGH uguale all'angolo IDB; apparisce manifesta <lb/>l'uguaglianza immediata e diretta fra ADC angolo dell'incidenza, e IDB an&shy;<lb/>golo della riflessione: corollario, che l'Autore mette in forma della propo&shy;<lb/>sizione XL: <emph type="italics"/>Anguli incidentiae et reflexionis sunt inter se aequales<emph.end type="italics"/> (ibid., <lb/>fol. </s>

<s>51). </s></p><pb xlink:href="020/01/2565.jpg" pagenum="190"/><p type="main">

<s>Un altro corollario matematico scende dalla proposizione XXXIX di <lb/>Giovan Marco, ad illustrare alcuni effetti fisici, che si osservano nelle per&shy;<lb/>cosse dei varii corpi: uno de'quali effetti &egrave; quello, che lo stesso Giovan Marco <lb/>cos&igrave; descrive: &ldquo; Impulsus ergo pilae, cum motus centri est perpendicularis <lb/>ad planum ubi percussit, in hypomochlio a motu conquiescit: at vero pla&shy;<lb/>num ex illa plaga in percutiente novum determinat impulsum, iuxta directio&shy;<lb/>nem plagae quam infert, a quo, eadem qua venit via, retroagitur, et si qui&shy;<lb/>dem duritie praestat, erit plaga, et qui hanc sequitur impulsus, in utroque <lb/>aequalis, ac proinde motus reflexus aequalis motui recto &rdquo; (ibid., fol. </s>

<s>44 ad t.). <lb/>A questa affermazione, nella quale Giovan Marco riconosceva la nota della <lb/>evidenza, corrispondono la proposizione prima del trattato <emph type="italics"/>De elatere<emph.end type="italics"/> del <lb/>Wallis, e la LXIII del Borelli, insieme con le altre simili dell'Huyghens e <lb/>del Mariotte, ma dalle matematiche astrazioni trapassando alle fisiche realt&agrave; <lb/>lo stesso Giovan Marco, con scienza pi&ugrave; comprensiva de'suoi celeberrimi <lb/>successori, soggiunge: &ldquo; Deficit autem motus reflexus a motu recto, si, de&shy;<lb/>fectu duritiei, minorem recipit quam dedit plagam &rdquo; (ibid.). </s></p><p type="main">

<s>Applicando l'osservazione ai moti obliqui, e riferendoci sempre alla figura <lb/>ultimamente rappresentata, EH non avr&agrave; dunque esatta proporzione con DE, <lb/>se non che nel supposto della elasticit&agrave; perfetta. </s>

<s>Ma se questa &egrave; in difetto, <lb/><emph type="italics"/>deficiet motus reflexus,<emph.end type="italics"/> per cui la proporzionale a DE sar&agrave; in questo caso <lb/>minore di EH. </s>

<s>Sia per esempio EP, rimanendo EK tuttavia del medesimo <lb/>vigore, perch&egrave; da nulla viene impedita: il nuovo parallelogrammo, descritto <lb/>sopra le due forze, sar&agrave; PK, e il moto riflesso piglier&agrave; la sua direzione se&shy;<lb/>condo la diagonale ER, o secondo la sua parallela DS, intantoch&egrave; l'angolo <lb/>della riflessione BDI sar&agrave; minore dell'angolo ADC dell'incidenza, e tanto <lb/>minore, quanto sar&agrave; maggiore il difetto del percuziente dalla supposta ela&shy;<lb/>sticit&agrave; perfetta. </s></p><p type="main">

<s>Ecco come da questo corollario di Giovan Marco venga illustrato un fatto <lb/>fisico, che il Torricelli dovette contentarsi di descriver nella sua seconda Le&shy;<lb/>zione della percossa, senza saper ridurlo ai principii di quella scienza, che <lb/>nella Scuola di Galileo tuttavia s'ignorava. </s>

<s>Citeremo del passo torricelliano, <lb/>invece della stampa, il manoscritto, dove son rimaste le Lezioni, in quella <lb/>parte che richiaman qualche figura illustrativa, nella forma ch'ebbero ori&shy;<lb/>ginalmente, prima che l'Autore stesso le correggesse, per accomodarle al&shy;<lb/>l'udienza, alla quale non si poteva dalla bugnola accademica comunicare le <lb/><figure id="id.020.01.2565.1.jpg" xlink:href="020/01/2565/1.jpg"/></s></p><p type="caption">

<s>Figura 68.<lb/>idee per via di segni visibili. </s>

<s>&ldquo; Questo sia detto, <lb/>leggesi dunque cos&igrave; nell'autografo, per le proiezioni, <lb/>che si faranno sul piano ad angoli retti verso la <lb/>detta parete opposta. </s>

<s>Ma quando si scagliasse ad <lb/>angolo obliquo, per la linea AB (fig. </s>

<s>68), vederemmo <lb/>far la riflessione, non per la linea BC che fa l'an&shy;<lb/>golo uguale a quello dell'incidenza, ma per la BED, <lb/>che o tocca o pochissimo va sopra il piano, come ho sperimentato con palle <lb/>di piombo e di creta. </s>

<s>Non &egrave; per&ograve; vero che la percossa estingua quell'im-<pb xlink:href="020/01/2566.jpg" pagenum="191"/>peto, che &egrave; nel mobile, di direzione equidistante dalla parete, ma solo smorza <lb/>quello, che vi &egrave; di perpendicolare alla parete, perch&egrave; questo nell'urtare trova <lb/>la contrariet&agrave; sua, cio&egrave; che gl'impedisce il suo viaggio, ma quell'atro no &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. XXXIX a tergo del fol. </s>

<s>16). </s></p><p type="main">

<s>Si direbbe aver questa cosa conclusa il Torricelli direttamente da una <lb/>proposizione simile a quella di Giovan Marco, piuttosto che dall'esperienza. </s>

<s><lb/>Ma che, mentre il Discepolo di Galileo affermava con tanta sicurezza smor&shy;<lb/>zarsi nell'urto obl&igrave;quo quel tanto solo, che v'&egrave; in lui di perpendicolare, non <lb/>s'attentasse d'assegnarne per scienza la proporzione; s'argomenta dall'incer&shy;<lb/>tezza, con la quale procede in risolvere altri simili problemi. </s>

<s>In fine al suo <lb/>trattato <emph type="italics"/>De'proietti<emph.end type="italics"/> proponesi di trovar la misura del colpo fatto dalla palla <lb/>del cannone contro il piano resistente, variato solo dalla diversit&agrave; degli an&shy;<lb/>goli dell'incidenza, premettendo al discorso un tale avvertimento: &ldquo; Il pro&shy;<lb/>blema, per quanto io sappia, &egrave; intatto; per&ograve;, se si produrr&agrave; qualche cosa <lb/>meno sussistente, e non pura geometrica, o si compatisca, sin che altri tratti <lb/>meglio la dottrina, o si rifiuti affatto, che poco importa &rdquo; (Op. </s>

<s>geom., P. </s>

<s>I <lb/>cit., pag. </s>

<s>239). </s></p><p type="main">

<s>Ci&ograve; premesso, suppone che gli impeti nel medesimo proietto siano pro&shy;<lb/>porzionali alle velocit&agrave;, le quali, ne'medesimi tempi, stanno come gli spazi. <lb/></s>

<s>&ldquo; Ci&ograve; supposto, egli dice, mentre una palla di cannone si avvicina al muro <lb/>opposto, la linea e dirittura del tiro o &egrave; perpendicolare al muro, o no. </s>

<s>Se &egrave; <lb/>perpendicolare, la percossa opera con una tal forza, che proveremo esser la <lb/>massima, che possa aver quel tiro: se sar&agrave; ad angoli obliqui, come la linea <lb/>AB (fig. </s>

<s>69) alla parete BC, io noto che, rispetto alla parete BC, sono nella <lb/>linea AB del proietto due moti insieme composti: uno cio&egrave; di avvicinamento <lb/><figure id="id.020.01.2566.1.jpg" xlink:href="020/01/2566/1.jpg"/></s></p><p type="caption">

<s>Figura 69.<lb/>perpendicolare alla parete, l'altro di passaggio laterale <lb/>o parallelo alla stessa. </s>

<s>Il perpendicolare ci viene e mo&shy;<lb/>strato e misurato dalla linea AC, il parallelo dalla linea <lb/>CB &rdquo; (ivi, pag. </s>

<s>240). Or perch&egrave; tanto il moto per AB, <lb/>quanto i moti per AC, CB son passati nel medesimo <lb/>tempo, staranno dunque, per le fatte supposizioni, come <lb/>gli spazi; ond'&egrave; che, considerati gli effetti secondo le <lb/>direzioni perpendicolari, ed essendo l'effetto di BC nullo, <lb/>staranno i detti moti come AB ad AC. </s>

<s>Per un'altra <lb/>incidenza DB del medesimo tiro staranno i moti come <lb/>DB a DE: da che dunque inferiremo &ldquo; che le attivit&agrave; o <lb/>momenti dei tiri diversamente inclinati sono come i seni retti degli angoli <lb/>delle incidenze &rdquo; (ivi, pag. </s>

<s>242). Che se, diretta secondo la linea AB, &ldquo; la <lb/>palla s'internasse tutta per l'appunto nel muro, adunque, per tutte le linee <lb/>pi&ugrave; elevate, non solo s'immerger&agrave; tutta nella solidit&agrave;, ma far&agrave; sempre mag&shy;<lb/>giore passata, perch&egrave; ha maggior forza. </s>

<s>Ma delle meno elevate, perch&egrave; cia&shy;<lb/>scuna aver&agrave; minor forza, niuna entrer&agrave; totalmente nella parete, ma alcune <lb/>anco risalteranno, e sfuggiranno dall'altra parte. <emph type="italics"/>Sia per&ograve; detto tutto que&shy;<lb/>sto astraendo da un certo effetto di piegamento o refrazione, che fanno i<emph.end type="italics"/><pb xlink:href="020/01/2567.jpg" pagenum="192"/><emph type="italics"/>proietti nel passar con inclinazione dal mezzo raro al mezzo pi&ugrave; denso, <lb/>incurvandosi la linea al contrario della refrazione della luce e spezie vi&shy;<lb/>sibili &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>243). </s></p><p type="main">

<s>Trae da quel suo teorema fondamentale il Torricelli alcuni altri corol&shy;<lb/>lari, come i due seguenti, che soli baster&agrave; commemorare. </s>

<s>Il primo &egrave; che <lb/>&ldquo; l'incidenza ad angolo di 30 gradi ha la met&agrave; della forza totale, essendo il <lb/>seno suo la met&agrave; del semidiametro &rdquo; (ivi, pag. </s>

<s>242): l'altro, che resulta da <lb/>alcune considerazioni, le quali noi riferiremo, per brevit&agrave;, col linguaggio e <lb/>co'segni dei matematici odierni. </s>

<s>Siano AC, BD (fig. </s>

<s>70) le misure delle forze <lb/>di proiezione contro i piani resistenti BC, ED:avremo AC/AB=1/cos.BAC= <lb/>sec.BAC; BD/BE=1/cos.EBD=sec.EBD. Cosicch&egrave;, se sia AC:BD=sec.BAC: <lb/>sec.BED, dovr&agrave; essere AB=BE. </s>

<s>Ma da queste linee son misurati gl'im&shy;<lb/>peti fatti perpendicolarmente contro i piani resistenti nelle due proiezioni, <lb/><figure id="id.020.01.2567.1.jpg" xlink:href="020/01/2567/1.jpg"/></s></p><p type="caption">

<s>Figura 70.<lb/>dunque &ldquo; allora i proietti averanno la stessa forza nel per&shy;<lb/>cuotere, quando gl'impeti saranno come le secanti degli an&shy;<lb/>goli del complemento delle incidenze &rdquo; (ivi, pag. </s>

<s>242). </s></p><p type="main">

<s>Il problema principale, da cui derivano questi e altri <lb/>corollari non meno importanti, aveva ragione il Torricelli <lb/>a dire che era intatto, non avendo Galileo, nel dialogismo <lb/>che succede alla quarta proposizione del quarto Dialogo delle <lb/>Scienze nuove, saputo far dire al suo Salviati in proposito <lb/>altro che questo: &ldquo; La qual positura, se sar&agrave; tale che il moto <lb/>del percuziente la vada a investire ad angoli retti, l'impeto del colpo sar&agrave; <lb/>il massimo: ma se il moto verr&agrave; obliquamente, o come diciam noi a scan&shy;<lb/>cio, il colpo sar&agrave; pi&ugrave; debole, e pi&ugrave; e pi&ugrave; secondo la maggiore obliquit&agrave; &rdquo; <lb/>(Alb. </s>

<s>XIII, 246). Il Maestro dunque della Scuola nuova aveva veramente la&shy;<lb/>sciato irresoluto il problema, professando l'errore che l'impeto del colpo obli&shy;<lb/>quo sia tanto pi&ugrave; debole, quanto &egrave; minore l'angolo dell'obliquit&agrave;, ma nella <lb/>Scuola antica, dal Torricelli ignorata, non era cos&igrave;: e noi trascrivemmo a <lb/>pag. </s>

<s>58 del precedente Tomo la nota, nella quale dimostrava Leonardo da <lb/>Vinci che i colpi stanno, non come gli angoli, ma come i seni degli angoli <lb/>delle inclinazioni. </s>

<s>A quella medesima scuola di Leonardo apparteneva anche <lb/>Giovan Marco, dalla riferita proposizione del quale, e sopra la disegnata <lb/>figura 67, si conclude che l'impeto diretto sta all'obliquo, come la linea EB <lb/>alla ED, ossia come il seno totale al seno dell'angolo dell'incidenza. </s>

<s>Ed &egrave; <lb/>pur notabile che, mentre i discepoli di Aristotile e del Nemorario procede&shy;<lb/>vano cos&igrave; sicuri alla conquista del vero, il discepolo di Galileo chiedesse com&shy;<lb/>patimento alle sue nuove intatte dottrine, confessando che poco gl'importava <lb/>di vederle anche affatto rifiutare. </s></p><p type="main">

<s>Pensava in dir cos&igrave; il Torricelli ai suoi propri colleghi nella Scuola ga&shy;<lb/>lileiana, contro i quali professava quelle dottrine, che lo condussero a riscon&shy;<lb/>trarsi col Roberval nel metodo di condurre alle curve le tangenti. </s>

<s>Anzi esso <pb xlink:href="020/01/2568.jpg" pagenum="193"/>Roberval, bench&egrave; in pubblico conosciuto pi&ugrave; tardi, appartiene al numero di <lb/>coloro, che tranquillamente facevano uso dei moti composti, non essendo in <lb/>Francia come in Italia sorta nessuna autorit&agrave; a metter dubbio intorno alle <lb/>antiche tradizioni. </s>

<s>Qualche anno prima del 1640 aveva il Matematico fran&shy;<lb/>cose fatto gi&agrave; quelle <emph type="italics"/>Observations sur la composition des mouvemens,<emph.end type="italics"/> che <lb/>il Bourdalois ridusse nel 1668 in forma di trattato, dove si legge la dimo&shy;<lb/>strazione dell'uguaglianza tra l'angolo dell'incidenza e della riflessione, decom&shy;<lb/>ponendo in due il moto incidente, e ragionando in modo simile al Wallis <lb/>(<emph type="italics"/>Ouvrage de M. </s>

<s>De Roberval,<emph.end type="italics"/> a la Haye 1731, pag. </s>

<s>11, 12). &Egrave; un fatto dun&shy;<lb/>que che il Roberval e il Torricelli si trovarono, intorno al principio della <lb/>composizion delle forze, concordi: l'Italiano per&ograve; procedeva incerto nell'appli&shy;<lb/>cazione di quel principio alla misura della percossa obliqua e della diretta, <lb/>rassegnandosi a veder, come abbiamo ora udito, dai seguaci delle dottrine di <lb/>Galileo rifiutate, per esser credute false, le sue conclusioni. </s></p><p type="main">

<s>Ma vennero anzi confermate, come meritavano, e fu primo a far ci&ograve; il <lb/>Borelli nella XLV, e nella L <emph type="italics"/>De vi percussionis,<emph.end type="italics"/> nella quale ultima si pro&shy;<lb/>poneva l'Autore di dimostrare che &ldquo; si superficies corporis ictum excipientis <lb/>perpendicularis fuerit ad lineam motus obliqui ipsius percutientis, erit vis <lb/>percussionis, ad eam quae efficitur in plano subiecto, ut sinus anguli inci&shy;<lb/>dentiae ad sinum totum &rdquo; (pag. </s>

<s>97). La dimostrazione, per condur la quale <lb/>s'invoca il principio dei moti composti, procede alquanto impacciata, n&egrave; ci&ograve; <lb/>fa gran maraviglia, persistendosi nella fallacia di riguardare il moto per l'ipo&shy;<lb/>tenusa uguale ai due per i cateti in potenza: ma fa pi&ugrave; gran maraviglia il <lb/>s<gap/>ir dallo stesso Borelli dire, nella citata lettera a M. A. Ricci, che di <lb/>queste cose &ldquo; per quanto io sappia, non &egrave; stato per ancora scritto da altri &rdquo; <lb/>(pag. </s>

<s>11). </s></p><p type="main">

<s>Eppure era da ventitre anni stato gi&agrave; stampato il libro <emph type="italics"/>De motu proie&shy;<lb/><gap/>orum,<emph.end type="italics"/> in fronte al quale si leggeva scritto, non il nome di un autore oscuro <lb/>e straniero, ma di quel celeberrimo Torricelli, in cui tutto il mondo ricono&shy;<lb/>sceva specchiata la mente di Galileo, come nel suo pi&ugrave; vivo e pi&ugrave; prossimo <lb/>parelio. </s>

<s>Forse lo scansar che facevasi nel teorema torricelliano, rispetto ai <lb/>moti composti, i fallaci insegnamenti di Galileo, dette a intendere che non <lb/>fosse ben dimostrato, e lusing&ograve; chi ci aveva interesse a tener che facesse quel <lb/>teorema nel libro <emph type="italics"/>De vi percussionis<emph.end type="italics"/> la sua prima comparsa, bench&egrave; insomma <lb/>nessuno de'due Nostri dicesse novit&agrave;, la notizia della quale non s'attingesse <lb/>da ci&ograve;, che alquanti anni prima era stato stampato in Praga. </s>

<s>Anzi la propo&shy;<lb/>sizione XXXIX <emph type="italics"/>De proportione motus<emph.end type="italics"/> non solo era feconda dei corollari, <lb/>de'quali si compiacevano il Torricelli e il Borelli di essere stati gli Autori, <lb/>ma della soluzione di alcuni problemi assai pi&ugrave; nuovi e pi&ugrave; curiosi, come <lb/>quello di determinare, in un globo pendulo, il punto della riflessione, venendo <lb/>da un altro simile globo pendulo percosso nel centro o fuori del centro; come <lb/>quell'altro del determinar la resultante del moto riflesso nelle piastrelle sca&shy;<lb/>gliate sulla superficie di un'acqua tranquilla, in quel giochetto conosciuto fra <lb/>noi sotto il nome di <emph type="italics"/>rimbalzello;<emph.end type="italics"/> e finalmente il problema, in cui, date tre <pb xlink:href="020/01/2569.jpg" pagenum="194"/>palle sul piano di un biliardo, non in linea retta, si proponeva l'Autore di <lb/>trovar nella seconda delle dette palle il punto, da cui riflessa la prima vada <lb/>a diritto a percotere nella terza: problemi risoluti tutti con tal sottile e destra <lb/>arte di decomporre e di ricomporre le forze, che, se fossero stampati in ca&shy;<lb/>rattere pi&ugrave; moderno e soppresso nel frontespizio del libro il nome dell'Au&shy;<lb/>tore, si direbbero opera di un Matematico, venuto a coltivar la scienza dopo <lb/>il Newton e l'Eulero. </s></p><pb xlink:href="020/01/2570.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Del settimo dialogo da aggiungersi <lb/>alle due Scienze nuove <lb/>ossia Dei problemi fisici e matematici<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Del problemi, che si dovevano aggiungere dopo la <emph type="italics"/>Scienza meccanica,<emph.end type="italics"/> e come Galileo pensasse di <lb/>ridurli in Dialogo. </s>

<s>&mdash; II. </s>

<s>Di altri problemi e speculazioni intorno a varii soggetti di Fisica. </s>

<s>&mdash; <lb/>III. </s>

<s>Delle questioni matematiche, e dei varii teoremi e problemi di Geometria raccolti dal Vi&shy;<lb/>viani. </s>

<s>&mdash; IV. </s>

<s>Del quesiti algebrici, e del misurar con la vista. </s>

<s>&mdash; V. </s>

<s>Dei teoremi di Geometria <lb/>avanzati alle dimostrazioni del moti locali. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Per sodisfare alla curiosit&agrave;, che deve naturalmente nascere nell'animo <lb/>di chi s'abbattesse a leggere l'intitolazione di questo capitolo, vogliam subito <lb/>rammemorare come il Viviani, raccogliendo le notizie delle opere, che per <lb/>ultimo meditava di scrivere Galileo, estraesse da una lettera di lui, del d&igrave; <lb/>7 Novembre 1637, a Pietro Carcavy di Parigi, le parole seguenti: &ldquo; Porgami <lb/>per sua piet&agrave; la sua mano adiutrice acciocch&egrave;, sgravato da cure che mi ten&shy;<lb/>gono oppresso, io possa tornare a distendere i miei <emph type="italics"/>Problemi spezzati fisici <lb/>matematici,<emph.end type="italics"/> che sono in buon numero e tutti nuovi &rdquo; (Scienza univ. </s>

<s>delle <lb/>proporz., Firenze 1674, pag. </s>

<s>83). In un'altra lettera poi del Gennaio appresso <lb/>accennava al medesimo Carcavy il suo concetto <emph type="italics"/>di portare quelle cose in <lb/>dialogo:<emph.end type="italics"/> il qual dialogo, raccogliendo le reliquie sparse degli argomenti trat&shy;<lb/>tati nelle prime quattro Giornate del Mondo, e specialmente nelle altre quat&shy;<lb/>tro del Moto; si sarebbe a queste aggiunto dall'Autore stesso, in settimo <lb/>luogo, dopo i trattati della percossa e delle proporzioni. </s></p><p type="main">

<s>Avendo noi dunque detto di que'trattati nei capitoli precedenti, resta, a <lb/>render compiuta la nostra Storia, l'argomento di quel settimo dialogo, in cui <pb xlink:href="020/01/2571.jpg" pagenum="196"/>si porterebbero, com'abbiamo inteso, i Problemi fisici e matematici. </s>

<s>Non ebbe <lb/>l'opera meditata dal Vecchio di 74 anni, e gi&agrave; cieco da circa due mesi prima, <lb/>la sua finale intenzione quanto alla forma, ma la materia doveva esser gi&agrave; <lb/>preparata, ond'&egrave; che l'ufficio nostro si riduce tutto in ricercarla, e in pro&shy;<lb/>porla alla notizia dei nostri lettori. </s>

<s>Non sarebbe quella ricerca per verit&agrave; n&egrave; <lb/>difficile n&egrave; laboriosa, quando fossero complete le raccolte di quei Problemi <lb/>fisici e matematici procuratesi, poco dopo la morte del Maestro, dal Viviani; <lb/>ma in ogni modo &egrave; nelle compilate pagine manoscritte del Discepolo amoroso <lb/>il principal fondamento alla nostra costruzione. </s></p><p type="main">

<s>Nel tomo III della VI parte dei manoscritti di Galileo, dal folio 28 al 35, <lb/>son di mano dello stesso Viviani, per la maggior parte, raccolti que'Problemi <lb/>fisici che si diceva, in fronte ai quali &egrave; dal compilatore scritta in lapis que&shy;<lb/>sta Nota: &ldquo; Problemi di mano del signor Vincenzio (di Galileo) distesi da <lb/>lui in pi&ugrave; fogli cuciti, in numero undici; che tre scritti, otto bianchi, e nella <lb/>coperta intitolati <emph type="italics"/>Problemi di mano del Galileo, e problemi distesi dal signor <lb/>Vincenzio per mano dell'Ambrogetti &rdquo;,<emph.end type="italics"/> d'onde viene a rendersi manifesta <lb/>l'origine e l'autenticit&agrave; della detta raccolta. </s></p><p type="main">

<s>Consegnatosene il manoscritto tanti anni dopo da Jacopo Panzanini, a cui <lb/>era pervenuto in eredit&agrave;, a Tommaso Bonaventuri, questi pubblic&ograve; nella nuova <lb/>edizione delle opere di Galileo alcuni di que'Problemi, de'quali veniva dun&shy;<lb/>que allora il pubblico ad avere la prima notizia, ma in privato il Viviani <lb/>stesso l'aveva diffusa ne'suoi discepoli, fra'quali Giuseppe Ferroni, che la <lb/>comunic&ograve; al confratello suo gesuita Paolo Casati, a cui piacque rifiorire, come <lb/>vedremo, di quelle galileiane curiosit&agrave; sconosciute i suoi libri delle Meccani&shy;<lb/>che. </s>

<s>L'Alb&egrave;ri dopo il Bonaventuri, essendo gi&agrave; le carte possedute dal Pan&shy;<lb/>zanini andate a riunirsi fra i codici della Biblioteca palatina di Firenze, fece <lb/>per la sua edizione raccolta pi&ugrave; diligente, ch'egli inser&igrave; da pag. </s>

<s>317-28 del <lb/>suo tomo XIV. All'uno e all'altro editore per&ograve; mancarono i criteri neces&shy;<lb/>sari, per dar ordine e conveniente scelta a quella specie di zibaldone, messo <lb/>insieme dal Viviani non per altro, che per servirsene come di un memo&shy;<lb/>riale a'suoi studi. </s>

<s>Supplendo dunque noi, come sapremo meglio, a que'man&shy;<lb/>cati criteri, sia, per ritrovar l'ordine desiderato, il nostro primo studio rivolto <lb/>a investigar l'occasione ch'ebbe l'Autore, e il tempo delle speculate ragioni <lb/>e de'risoluti problemi. </s></p><p type="main">

<s>Si termina il trattato della <emph type="italics"/>Scienza meccanica<emph.end type="italics"/> con queste parole: &ldquo; So <lb/>che qui nasceranno ad alcuni delle difficolt&agrave; e delle istanze, le quali per&ograve; con <lb/>poca fatica si torranno di mezzo, e noi le rimetteremo volontariamente tra <lb/>i <emph type="italics"/>Problemi meccanici,<emph.end type="italics"/> che in fine di questo discorso si aggiungeranno &rdquo; <lb/>(Alb. </s>

<s>XI, 125). Quel trattato si sa essere opera giovanile di Galileo, e come <lb/>il primo frutto raccolto dallo studio de'libri del Benedetti e di Guibubaldo. </s>

<s><lb/>Andata la scrittura attorno originalmente infino al 1649 manoscritta, si pub&shy;<lb/>blic&ograve; senza la promessa aggiunta dei Problemi meccanici, i quali dunque, se <lb/>vi fossero stati compresi, sarebbero de'pi&ugrave; antichi fra quelli che si raccol&shy;<lb/>sero dal Viviani. </s>

<s>Il criterio poi, da riconoscerli in mezzo a quella confusione <pb xlink:href="020/01/2572.jpg" pagenum="197"/>&egrave; l'esser di argomento meccanico, e il sentirli inspirati ai libri delle <emph type="italics"/>Specu&shy;<lb/>lazioni<emph.end type="italics"/> del Maestro. </s></p><p type="main">

<s>Ha giusto in que'libri il Benedetti una bella speculazione, per risolvere <lb/>il problema: onde avvenga che la trottola, girando velocissimamente, si man&shy;<lb/>tenga ritta sulla sua punta, e l'attribuisce alle forze centrifughe, dirette <lb/>orizontalmente, prevalenti cos&igrave; sopra la gravit&agrave; naturale, che il corpo grave <lb/>girante ubbidisce piuttosto a quelle, che a questa. </s>

<s>&ldquo; Ab huiusmodi inclina&shy;<lb/>tione rectitudinis motus partium alicuius corporis rotundi fit, ut per aliquod <lb/>temporis spacium trochus, cum magna celeritate seipsum circumagens, omnino <lb/>rectus quiescat super illam cuspidem ferri quam habet, non inclinans se ver&shy;<lb/>sus mundi centrum magis ad unam partem, quam ad aliam, cum quaelibet <lb/>suarum partium in huiusmodi motu non inclinet omnino versus mundi cen&shy;<lb/>trum, sed multo magis per transversum, ad angulos rectos cum linea directio&shy;<lb/>nis, aut verticalis, aut horizontis axe, ita ut necessario huiusmodi corpus <lb/>rectum stare debeat &rdquo; (Speculat. </s>

<s>liber, Venetiis 1599, pag. </s>

<s>286). </s></p><p type="main">

<s>Galileo deriv&ograve; manifestamente di qui le ragioni, per rispondere a quel <lb/>principale quesito, di cui l'Alb&egrave;ri non stamp&ograve; che la proposta: &ldquo; Qual sia <lb/>la ragione che le trottole o le ruzzole, girate, si mantengano ritte, e ferme <lb/>no, ma trabocchino &rdquo; (XIV, 321), lasciando nel manoscritto la risposta, che <lb/>&egrave; tale: &ldquo; Un mobile non pu&ograve; avere impeto verso diverse bande, e per&ograve; la <lb/>ruzzola andando velocemente si sostien ritta, ed infine, mancando la velocit&agrave; <lb/>per l'innanzi, comincia a piegare alla banda: e per&ograve; il peso nella trottola <lb/>lavora pochissimo, quando quella si muove velocemente, ma ben lavora assai <lb/>verso il fine del moto, dove egli &egrave; lento &rdquo; (MSS. Gal., P. VI, T. III, fol. </s>

<s>64). </s></p><p type="main">

<s>Da questa soluzione, che non &egrave; forse quella distesa da Galileo, ma &egrave; <lb/>una nota preparata per distenderla, nacque la curiosit&agrave; di simili altre solu&shy;<lb/>zioni di Problemi meccanici, fra'quali son da notare i seguenti: </s></p><p type="main">

<s>&ldquo; Quelli che giocano alla ruzzola, mediante il filo col quale la cingono <lb/>tre o quattro volte, fanno tiri assai pi&ugrave; lunghi, che non farebbero senza quel <lb/>filo: si domanda la causa di questo, ed appresso si cerca perch&egrave; con assai <lb/>minor velocit&agrave; vadia la ruzzola, quando &egrave; in aria, che quando tocca terra, <lb/>dove velocissimamente si muove. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cos&igrave; risolverassi il problema: Io ho una girella forata nel centro, e <lb/>infilzata in un pernio: gli do su con una mano, e la fo girare su quel per&shy;<lb/>nio velocissimamente. </s>

<s>Or, mentre che ella gira, la fo uscir dal pernio e ca&shy;<lb/>dere in terra per taglio. </s>

<s>Che far&agrave; questa girella? </s>

<s>Certo che, in virt&ugrave; del <lb/>moto che io gli diedi quand'ella era imperniata, subito che ella arriver&agrave; in <lb/>terra comincer&agrave; a camminare, sicch&egrave; quel moto, che gli diedi di girare in <lb/>s&egrave; stessa, &egrave; cagione che in terra ella giri e cammini. </s>

<s>Ora quelli che giocano <lb/>alla ruzzola la circondano tre o quattro volte con un filo, e poi la tirano, e <lb/>in quell'istante ella si svolge dal filo con somma prestezza, e per conseguenza <lb/>viene ad acquistare un moto velocissimo in s&egrave; stessa, onde, quand'ella arriva <lb/>in terra, va velocissimamente, non tanto per la forza datagli dal braccio del <lb/>tiratore, quanto in virt&ugrave; della veloce circumvoluzione, che ella ha acquistato <pb xlink:href="020/01/2573.jpg" pagenum="198"/>nello svilupparsi dal filo. </s>

<s>Ma quelli che tirano senza filo non danno alla ruz&shy;<lb/>zola il vantaggio del girarsi in s&egrave; medesima, ma la mandano solamente con <lb/>la forza del loro braccio; e per&ograve; tirano manco che se tirassero col filo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La causa poi perch&egrave; la ruzzola vadia con minor velocit&agrave;, mentre cam&shy;<lb/>mina per aria, che in terra, &egrave; perch&egrave; in aria ella va solamente con la ve&shy;<lb/>locit&agrave; datagli dalla forza del tiratore, e in terra cammina per la medesima <lb/>forza, e in virt&ugrave; della vertigine veloce in s&egrave; stessa, che ella aveva innanzi <lb/>che arrivasse in terra, la qual vertigine in aria non opera nulla, perch&egrave;, es&shy;<lb/>sendo l'aria tenue e sottile, cede facilmente al girar della ruzzola, la quale, <lb/>non trovando alla sua revoluzione intoppo alcuno, non ha occasione di scor&shy;<lb/>rere avanti con pi&ugrave; velocit&agrave; di quella, che gli d&agrave; il braccio di chi la tira. </s>

<s><lb/>Ma com'ella arriva in terra, che &egrave; ruvida e scabrosa, trova moltissimi in&shy;<lb/>toppi, ne'quali, nel girare ella urta, e si risospigne addietro; onde gli &egrave; forza <lb/>di scorrere avanti velocemente, non solo per la forza di chi la tira, ma an&shy;<lb/>cora in virt&ugrave; del suo volgersi in s&egrave; medesima. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Due altri Problemi hanno dependenza dal precedente, in uno de'quali <lb/>si cerca perch&egrave; quelli che giocano alla palla tanto difficilmente rimettino le <lb/>palle, che gli sono mandate <emph type="italics"/>trinciate:<emph.end type="italics"/> e nell'altro si domanda perch&egrave;, gio&shy;<lb/>cando alcuni alle pallottole in una strada disuguale e sassosa, piglino la palla <lb/>per di sopra con la mano, dove, giocando in un pallottolaio piano e pulito, <lb/>la piglierebbero per di sotto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il primo Problema si risolve cos&igrave;: Colui, che vuol trinciare la palla <lb/>al compagno che gioca seco, gli d&agrave; con la mestola o con la racchetta per di <lb/>sotto in tal modo che, mandandola innanzi verso il compagno, gli d&agrave; facolt&agrave; <lb/>di girare all'indietro in s&egrave; medesima, sicch&egrave;, quand'ella arriva in terra, <lb/>viene a fare, merc&egrave; di quel girare all'indietro, il balzo verso colui che l'ha <lb/>mandata, o almeno balza pochissimo verso quello, che aspetta di rimetterla, <lb/>il quale, giudicando il balzo dover esser verso di lui assai pi&ugrave; lungo, attende <lb/>la palla troppo di lontano, e resta ingannato e deluso. </s>

<s>Similmente non la ri&shy;<lb/>metter&agrave; di posta perch&egrave;, non essendo la palla affatto liscia e pulita, ma avendo <lb/>qualche risalto e scabrosit&agrave;, viene, nel girare all'indietro per aria, a pigliar <lb/>vento, onde la sua velocit&agrave; alquanto si ritarda, sicch&egrave; colui che la vuol ri&shy;<lb/>metter di posta l'aspetta prima che ella non arriva, e pensando di coglierla <lb/>gli tira, e fa il colpo vano. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La resoluzione del secondo problema &egrave; tale: Quelli, che giocano alle <lb/>pallottole per una strada sassosa, non possono, tirando la palla per terra, <lb/>aggiustar bene il colpo, per li molti intoppi che troverebbe la palla, ma son <lb/>necessitati, a guisa di quelli che fanno alle piastrelle, di procurare di avvi&shy;<lb/>cinarsi al <emph type="italics"/>lecco,<emph.end type="italics"/> tirando di posta. </s>

<s>Ma perch&egrave; la palla non fa l'effetto della <lb/>piastrella, che subito che ella arriva in terra si ferma, &egrave; necessario che quelli <lb/>che giocano trovin modo di fare che la palla si mova manco che sia possi&shy;<lb/>bile dal luogo dove la tirano. </s>

<s>Ma questo gli succede col tirare, presa la palla <lb/>per di sopra, perch&egrave; cos&igrave;, mentre che &egrave; in aria, viene a girare in s&egrave; mede&shy;<lb/>sima all'indietro, cio&egrave; verso chi la tira: e quando ella arriva, perch&egrave; la forza <pb xlink:href="020/01/2574.jpg" pagenum="199"/>di chi l'ha tirata la farebbe trascorrere innanzi troppo, e allontanarsi dal <lb/>lecco, il moto che ella aveva in s&egrave; stessa vien quasi a contrappesare la detta <lb/>forza, onde la palla o si ferma, o pochissimo trascorre innanzi. </s>

<s>Ma quando <lb/>poi si gioca ne'pallottolai ben netti e puliti, si pu&ograve; benissimo aggiustare il <lb/>colpo, tirando la palla per terra, onde non &egrave; necessario il pigliarla per di <lb/>sopra &rdquo; (ivi, fol. </s>

<s>31, 32). </s></p><p type="main">

<s>Il problema della ruzzola tirata con lo spago ebbe solenne pubblicit&agrave; dia&shy;<lb/>logizzato nella seconda giornata dei Massimi Sistemi, ma gli altri due, che <lb/>ne dipendono, &egrave; notabile che si rimangano tuttavia nel manoscritto, nel quale <lb/>gli lasciarono il Bonaventuri e l'Alb&egrave;ri. </s>

<s>Ben pi&ugrave; notabile &egrave; per&ograve; che, senza <lb/>saperlo, il pubblico ne avesse gi&agrave; da lungo tempo notizia per opera del Ca&shy;<lb/>sati, a cui fu la cosa comunicata privatamente dal Viviani, come avvertimmo, <lb/>per mezzo del Ferroni. </s>

<s>Nel cap. </s>

<s>XI infatti del libro VII <emph type="italics"/>Mechanicorum,<emph.end type="italics"/> fa&shy;<lb/>cendo esso Casati alcune osservazioni intorno al variarsi accidentalmente <lb/>gl'impulsi nei moti riflessi. </s>

<s>&ldquo; Deinde, egli dice, quando reticulis luditur, non <lb/>raro reticulum movetur in plano aliquo horizontali, aut valde inclinato (nos <lb/>Itali dicimus <emph type="italics"/>tagliare o trinciare una palla<emph.end type="italics"/>) ita ut, dum pilam recta expel&shy;<lb/>lit, illi etiam motum quemdam imprimat, quo ipsa circa suum centrum mo&shy;<lb/>vetur: unde fit ut, nisi pilam excipias repellasque ante quam pavimentum <lb/>attingat, frustra deinde saltum illius expectes iuxta regulas reflexionis, quia <lb/>nimirum pila terram tangens, dum pergit moveri circa suum centrum motu <lb/>orbiculari, nequit a plano impediente recipere directionem illam, cuius esset <lb/>capax, si solum simplici motu centri mota fuisset: motus enim peripheriae <lb/>globi contrarius est motui centri. </s>

<s>Idem accidit, quando pila leviore astrictu <lb/>funem perstringit, tunc scilicet concipit motum circularem adeoque saltus <lb/>fallit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quantum autem in motu valeat directiones commiscere, alteram cen&shy;<lb/>tri rectam, alteram peripheriae circularem sed oppositam, satis norunt qui, <lb/>minoribus orbiculis ludentes, globum quasi pendentem in manu tenent, dum&shy;<lb/>que illum proiiciunt manu ei motum circularem communicant, unde oritur <lb/>quod, ubi terram globus attigerit, vel sistit se, si directio peripheriae ad mo&shy;<lb/>tum circularem est aequalis directioni centri ad motum rectum, vel tardius <lb/>promovetur quam si solam centri directionem haberet, prout directio centri <lb/>maior est directione peripheriae, quae, cum primum terram attingit, apta <lb/>est sua conversione retrahere centrum versus proiicientem &rdquo; (Lugduni 1684, <lb/>pag. </s>

<s>734, 35). </s></p><p type="main">

<s>L'esempio del Casati, che cos&igrave; di nascosto raccoglieva le miche cadute <lb/>dalla lauta mensa di Galileo, ci fanno ripensare al gusto, che dovevano sen&shy;<lb/>tir di cos&igrave; fatti Problemi que'primi discepoli, per le mani dei quali correva <lb/>manoscritto il trattato della Scienza meccanica. </s>

<s>La forma stessa invitava i <lb/>curiosi a comparare le nuove scritture con le antiche Questioni aristoteliche, <lb/>le quali si volevano fare apparire tanto pi&ugrave; insulse, quanto pi&ugrave; si credeva di <lb/>dar quelle stesse novit&agrave; risolute da'pi&ugrave; veri dimostrati principii. </s>

<s>Questa anzi, <lb/>di contradire alle dottrine meccaniche di Aristotile, era la principale inten-<pb xlink:href="020/01/2575.jpg" pagenum="200"/>zione di Galileo, a cui perci&ograve; l'argomento del discorso era spesso suggerito <lb/>dagli argomenti medesimi del Filosofo, come quello per esempio che versa <lb/>intorno alle navi mosse dalle vele o dai remi. </s></p><p type="main">

<s>Se sempre i principii, dai quali si facevano dipendere le risposte a cos&igrave; <lb/>fatti quesiti, fossero, come Galileo stesso presumeva, ben dimostrati, si po&shy;<lb/>trebbe per verit&agrave; dubitarne, particolarmente per quel che riguarda l'uso del <lb/>timone, e la proporzion degl'impulsi, che riceve il naviglio o dalla ciurma <lb/>che voga, o dal vento ch'enfia la vela; perch&egrave;, trattandosi di moti misti, era <lb/>meglio parato nelle mani del Filosofo antico che del novello il sottile argo&shy;<lb/>mento, da risolvere cos&igrave; difficili questioni. </s>

<s>Comunque sia avrebbe dovuto Ga&shy;<lb/>lileo attutire quella sua giovanile baldanza, e temperare il disprezzo con la <lb/>riverenza, ripensando che non avrebbe esultato dello splendor di quella nuova <lb/>fiamma viva, se sotto le avvilite ceneri non avesse Aristotile gelosamente cu&shy;<lb/>stoditavi la scintilla. </s></p><p type="main">

<s>L'esempio cade bene a proposito rispetto alle resistenze dei solidi, la <lb/>Scienza nuova delle quali dipendeva dall'antica, che si compendiava nei mi&shy;<lb/>rabili effetti della leva. </s>

<s>Cos&igrave; veniva ovvia a rappresentarsi alla mente di Ga&shy;<lb/>lileo la distinzione fra le resistenze assolute e le respettive, della qual di&shy;<lb/>stinzione furono quasi primaticci frutti due problemi, ambedue, bench&egrave; per <lb/>contrarie ragioni, nella storia della Scienza memorabili. </s>

<s>Una verga di me&shy;<lb/>tallo, tirata fortemente per lo lungo, resiste molto pi&ugrave; che piegata per tra&shy;<lb/>verso, perch&egrave; l&agrave; opera con tutta la resistenza assoluta, e qua con quella che <lb/>&egrave; relativa al modo di operar con la leva. </s>

<s>Eppure, anco la resistenza assoluta <lb/>pu&ograve; da proporzionato peso esser vinta: che se, invece di un peso posticcio, <lb/>si prolunghi essa stessa nella sua propria materia, si dovr&agrave; giungere a un <lb/>termine, ripensava Galileo, che quel solo aver di tanto allungata la verga <lb/>basti per strapparla. </s>

<s>Dunque concludeva essere alla lunghezza di qualunque <lb/>solido prefinito dalla Natura un limite, oltre il quale, nemmen con tutta la <lb/>sua forza assoluta, mai reggerebbe. </s>

<s>Dai solidi cred&egrave; di poter fare libero pas&shy;<lb/>saggio ai liquidi, ed ebbero da ci&ograve; occasione la proposta e la risposta al se&shy;<lb/>guente Problema, leggendo il quale coloro, a cui &egrave; oramai da tanto tempo <lb/>nota la scoperta del Torricelli, intenderanno perch&egrave; si dicesse memorabile <lb/>nella Storia: </s></p><p type="main">

<s>&ldquo; Si domanda la cagione perch&egrave; le trombe, che si adoprano per cavar <lb/>acqua dai pozzi, non alzino l'acqua, se non insino ad una certa e determi&shy;<lb/>nata altezza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La cagione di tal effetto dipende da questo: Io piglio un pezzo di ca&shy;<lb/>tena di ferro, un capo della quale fermo gagliardamente a una trave, ed <lb/>all'altro incomincio ad attaccare del peso. </s>

<s>Chiara cosa &egrave; che quella catena, <lb/>non essendo possente di reggere un peso infinito, finalmente, se io seguiter&ograve; <lb/>a caricarla, si strapper&agrave;. </s>

<s>Diciamo dunque che un peso v. </s>

<s>g. </s>

<s>di mille libbre <lb/>appunto la facci strappare. </s>

<s>Ora, se, in cambio di attaccare alla catena un <lb/>peso di mille libbre, io la far&ograve; tanto pi&ugrave; lunga, che quel pezzo che io ci ag&shy;<lb/>giungo pesi le mille libbre; certo &egrave; che quella catena si strapper&agrave;, n&egrave; pi&ugrave; <pb xlink:href="020/01/2576.jpg" pagenum="201"/>n&egrave; meno che si strappasse prima con le cento libbre di peso: sicch&egrave; il pro&shy;<lb/>prio peso della catena &egrave; abile a farla strappare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora l'acqua che si tira su per le trombe si regge in s&egrave; stessa sino <lb/>ad una tale altezza, siccome si reggerebbe la catena, alla quale io aggiun&shy;<lb/>gessi un pezzo, che pesasse novecento novantanove libbre. </s>

<s>Ma se io vorr&ograve; <lb/>far passare all'acqua quell'altezza, cio&egrave; s'io vorr&ograve; allungar pi&ugrave; la sua mole, <lb/>a guisa della catena, alla quale io aggiugnessi un pezzo di mille libbre; si <lb/>strapper&agrave; per il suo proprio peso, e non potr&agrave; passare altrimenti la detta <lb/>altezza &rdquo; (MSS. Gal., P. VI, T. III, fol. </s>

<s>33). </s></p><p type="main">

<s>Galileo si compiacque molto di questa speculazione, occorsagli dal con&shy;<lb/>siderare le resistenze assolute, e non era punto temeraria una tal compia&shy;<lb/>cenza a que'tempi, nei quali, non sapendosi far altro che invocare l'orrore <lb/>al vacuo, si trovavano costretti i Filosofi a dire che non sentisse questo orror <lb/>la Natura, che infino a un certo punto. </s>

<s>Pi&ugrave; ragionevolmente per&ograve; poteva com&shy;<lb/>piacersi di quell'altro, che gli occorse al pensiero dal considerar le resistenze <lb/>respettive, le quali debbon esser tanto maggiori, quanto pi&ugrave; lungo &egrave; il brac&shy;<lb/>cio della contralleva. </s>

<s>Non &egrave; dunque il principale efficiente della resistenza di <lb/>un solido la quantit&agrave; della sua propria materia, ma s&igrave; piuttosto il venir que&shy;<lb/>sta in maggior ampiezza distribuita: ci&ograve; che facilmente ottenendosi col rare&shy;<lb/>farla, e col lasciar qualche vacuo nel mezzo, veniva a rivelar la nuova verit&agrave; <lb/>di un fatto, non ovvio ancora per la sola esperienza, che cio&egrave;, avendosi due <lb/>lance del medesimo peso, la vuota &egrave; tanto pi&ugrave; resistente della piena, quanto <lb/>maggiore &egrave; il diametro di quella che di questa. </s>

<s>Fu anche il nuovo pensiero <lb/>disteso in forma di Problema, e possono i Lettori vederlo nel IV fra i rac&shy;<lb/>colti dall'Alb&egrave;ri (XIV, 326). </s></p><p type="main">

<s>Al medesimo ordine di quei Problemi, che dovevano aggiungersi dopo <lb/>il trattato della Scienza meccanica, appartengono alcuni altri, de'quali trovasi <lb/>fatto un cenno nel citato manoscritto del Viviani in questo modo: &ldquo; Rom&shy;<lb/>pesi una corda attaccata ad una gran pietra pendente da una simile corda &rdquo; <lb/>(MSS. cit., fol. </s>

<s>63): problema di cui il Viviani stesso dava, secondo la mente <lb/>di Galileo, la soluzione in quella nota, da noi trascritta a pag. </s>

<s>445 del Tomo <lb/>precedente. </s>

<s>Altro Problema, da mettersi in questa collezione, era quello del <lb/>maggior tiro, che si credeva ottenere dagli archibusi, quanto fossero pi&ugrave; lun&shy;<lb/>ghi di canna: se non che alle ragioni antiche del Cardano e del Benedetti <lb/>s'aggiungeva da Galileo valore, introducendo il principio delle veloci&agrave; pro&shy;<lb/>porzionali ai tempi. </s>

<s>&ldquo; Perch&egrave; la velocit&agrave; cresce secondo il tempo, gli archi <lb/>grandi e le cerbottane e le canne di archibuso tirano con pi&ugrave; forza, avendo <lb/>tempo di accompagnare il proietto per pi&ugrave; spazio &rdquo; (ivi, fol. </s>

<s>62). </s></p><p type="main">

<s>Di tal qualit&agrave;, secondo i riferiti esempi, erano quei Problemi, i quali, <lb/>mostrando come si potessero applicare le leggi del moto delle macchine a <lb/>certi fatti naturali pi&ugrave; ovvii e pi&ugrave; curiosi, dovevano aggiungersi alla <emph type="italics"/>Scienza <lb/>meccanica,<emph.end type="italics"/> per dilettevole utilit&agrave; dei lettori. </s>

<s>Ma Galileo accennava nel <lb/>passo da noi sopra trascritto particolarmente ad alcuni di quegli stessi Pro&shy;<lb/>blemi, nei quali si toglierebbero di mezzo le difficolt&agrave;, e si risponderebbe <pb xlink:href="020/01/2577.jpg" pagenum="202"/>alle istanze, che potrebbero nascere intorno alla forza della percossa; ond'&egrave; <lb/>che, fatti certi per questa testimonianza dell'avere atteso l'Autore a risolvere <lb/>quest'altro nuovo genere di questioni, siamo stati solleciti di ricercarle nei <lb/>manoscritti. </s>

<s>Forse l'essere stato distratto Galileo dal proseguire in quella <lb/>speculazione, per le ragioni accennate da noi nel capitolo precedente, fu la <lb/>causa per cui le cose scritte da giovane a spiegar meglio la forza della per&shy;<lb/>cossa si siano in mezzo alle altre ritrovate cos&igrave; scarse: nonostante riferiscesi <lb/>all'argomento la seguente nota, che &egrave; l'espression di un concetto, da cui do&shy;<lb/>veva svolgersi pi&ugrave; largamente il discorso: &ldquo; Il colpo in materia cedente opera <lb/>meno tanto, quant'&egrave; la ritirata del cedente &rdquo; (ivi, fol. </s>

<s>62). </s></p><p type="main">

<s>Quest'altra nota, che ivi pure il Viviani ha raccolta, &egrave; di bene assai <lb/>maggiore importanza per la storia delle galileiane speculazioni intorno alla <lb/>forza della percossa, e intorno alle ragioni ch'ebbe lo speculatore per di&shy;<lb/>chiararla immensa: &ldquo; Se a un peso massimo, pendente da una corda, si ag&shy;<lb/>giunger&agrave; per fianco qualsivoglia altro minimo peso, questo alzer&agrave; il massimo, <lb/>essendoch&egrave; il piccolo scende per un arco verso il contatto, ed il massimo <lb/>ascende per la circonferenza: dal che ne seguir&agrave; che la sua salita sia, se&shy;<lb/>condo qualsivoglia proporzione, minore della scesa del piccolo peso &rdquo; (ivi, <lb/>a t. </s>

<s>del fol. </s>

<s>63). </s></p><p type="main">

<s>La bellissima proposizione, quale usc&igrave; dalla mente di Galileo che fu primo <lb/>a pensarla, rimase ignota al pubblico infino al 1718, anno in cui il Bona&shy;<lb/>venturi veniva ad aggiunger nelle Opere galileiane il sesto Dialogo agli altri <lb/>cinque delle Scienze nuove. </s>

<s>Come, tanto tempo prima della sua pubblica&shy;<lb/>zione, potesse avere avuto il Viviani notizia di quel meccanico teorema, ch'egli <lb/>illustr&ograve;, concorrendovi nell'opera il Borelli; &egrave; facile intendere, essendo ne'due <lb/>Discepoli quell'annunzio di scienza nuova venuto per la via ordinaria delle <lb/>tradizioni orali e manoscritte del loro grande Maestro: ma fa maraviglia che <lb/>il Wallis s'incontrasse in quel medesimo concetto, e, rappresentandosi nel <lb/>globo di Galileo pendolo da una fune il grande Globo terrestre librato in mezzo <lb/>allo spazio, ne concludeva, per le medesime meccaniche ragioni, che anche <lb/>il salto di una pulce lo avrebbe commosso. </s>

<s>&ldquo; Dato enim quod tota Telluris <lb/>moles, fluido aethere suspensa, cum saltu pulicis percussa sit; dicenda esset <lb/>loco suo tantillum dimoveri &rdquo; (De motu cit., pag. </s>

<s>663). </s></p><p type="main">

<s>Le questioni spezzate, che furono risolute da Galileo nel lungo corso <lb/>della sua vita scientifica, non tutte, com'&egrave; da credere, erano di argomento <lb/>meccanico: perci&ograve; &egrave; facile intendere come rivolgendo, quasi Maestro nell'offi&shy;<lb/>cina, lo sguardo sui materiali rimasti indietro nella costruzione dei due grandi <lb/>edifizi dei Massimi Sistemi e delle Scienze nuove, ve ne dovesse rtrovar degli <lb/>appartenenti a ogni ordine di Scienze fisiche e matematiche. </s>

<s>E tali sono ap&shy;<lb/>punto le questioni spezzate e le note sparse, che nei citati manoscritti, e in <lb/>altre carte galileiane, si vedono confusamente raccolte insiem con quelle, che <lb/>di puro argomento meccanico sono state da noi fin qui recensite. </s>

<s>Richiede&shy;<lb/>rebbe forse il filo del ragionamento che si proseguisse a dar notizia ai Let&shy;<lb/>tori di questa variet&agrave; di pensieri, come materiali sparsi e mezzo sepolti nel <pb xlink:href="020/01/2578.jpg" pagenum="203"/>terreno, che circonda i due detti grandi edifizi, ma perch&egrave; il primo e prin&shy;<lb/>cipale nostro proposito fu quello di rappresentarci l'Artefice, che medita di <lb/>dare anche a quelle sparse reliquie qualche decoro di forma; studiamoci, <lb/>prima di aumentar la congerie, di veder com'ei lo facesse nei materiali gi&agrave; <lb/>radunati. </s></p><p type="main">

<s>Gi&agrave; si sa come fosse, nel citato capitolo di lettera, significata al Carcavy <lb/>una tale intenzione, qual'era di mettere in dialogo quei pensieri, come fiori <lb/>in ghirlanda. </s>

<s>Ma perch&egrave; non ne segu&igrave; il meditato effetto, per gl'impedi&shy;<lb/>menti della cecit&agrave; e della vecchiezza, se non s'&egrave; avuto dunque l'opera com&shy;<lb/>piuta, si pu&ograve; domandare almeno se fu cominciata. </s>

<s>La risposta si restringe <lb/>intanto per noi ai Problemi meccanici, alcuni de'quali avevano gi&agrave; trovato <lb/>stabile assetto nei primi e nei secondi Dialoghi gi&agrave; stampati. </s>

<s>Cos&igrave;, per esem&shy;<lb/>pio il problema della ruzzola tirata col filo, e della palla tirata soprammano, <lb/>avevano trovato da accomodarsi nella seconda giornata dei Massimi Sistemi <lb/>(Alb. </s>

<s>I, 175-79) e nella prima e nella seconda delle Scienze nuove i pro&shy;<lb/>blemi dell'acqua nelle trombe, e nelle lance vuote pi&ugrave; resistenti delle piene <lb/>(XIII, 21, 145). Tutte le altre questioni di meccanico argomento erano ri&shy;<lb/>maste indietro, e s'aspettava a queste di venire a intessersi ne'Dialoghi no&shy;<lb/>vissimi: intorno a che, stando ai soli manoscritti esistenti nella Biblioteca <lb/>fiorentina, non avremmo da sodisfare ai Lettori, se non col dar dell'opera <lb/>incominciata da Galileo un segno, piuttosto che un saggio. </s></p><p type="main">

<s>S'introduce nella Scienza meccanica il discorso dimostrando l'utilit&agrave;, <lb/>che si pu&ograve; ricavar dalle macchine: e disingannati quegli artefici, che cre&shy;<lb/>devano di potere con poca forza movere e alzare pesi grandissimi, conclude <lb/>l'Autore col dire che la principale delle dette utilit&agrave; consiste nel poter solle&shy;<lb/>vare tutta insieme, per via dello strumento, una gran mole, che pure si sol&shy;<lb/>leverebbe, col medesimo impiego di forza, dalle semplici braccia di un uomo, <lb/>purch&egrave; si potesse ridurre quella tal mole trattabile col dividerla in pezzi. </s>

<s>Si <lb/>voleva da Galileo porgere questa stessa meccanica dottrina quasi sotto le <lb/>graziose forme di un apologo, nel dialogismo seguente: </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; In proposito di quello, che &egrave; tanto semplice, che vuole <lb/>per via di trombe alzar tant'acqua, che nel cadere poi faccia andare un mu&shy;<lb/>lino, il quale non poteva andare in virt&ugrave; della forza, che egli applica nel&shy;<lb/>l'alzare l'acqua: &egrave; egli possibile che si creda di poter riavere dall'acqua pi&ugrave; <lb/>forza di quella, che tu gli hai prestata? </s>

<s>&Egrave; possibile che tu non intenda che <lb/>quella forza, che bast&ograve; a alzar l'acqua, baster&agrave; per mover la macina? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Signor no: perch'io ho bisogno di avere per manteni&shy;<lb/>mento della mia casa uno staio di farina la settimana, ed un mio ragazzino, <lb/>in sei giorni, con una secchiolina mi conduce in una conserva tant'acqua <lb/>all'altezza di quattro braccia, che lasciandola poi cader sul ritrecine mi ma&shy;<lb/>cina in un'ora uno staio di grano &rdquo; (MSS. Gal., P. V, T. IV, fol. </s>

<s>15). </s></p><p type="main">

<s>Dicemmo ch'era questo l'unico esempio della forma del dialogo data da <lb/>Galileo alle sue Questioni meccaniche, stando ai Manoscritti palatini di Fi&shy;<lb/>renze. </s>

<s>Ma noi, pi&ugrave; attentamente rivolgendo le carte, nelle quali ritrovammo <pb xlink:href="020/01/2579.jpg" pagenum="204"/>il trattato dell'uso delle catenuzze, ci abbattemmo a leggere un colloquio, <lb/>dove il Salviati e il Sagredo dimostravano a Simplicio quant'avesse errato <lb/>il suo Aristotile, dicendo che la vela tanto pi&ugrave; velocemente spinge la nave, <lb/>quanto &egrave; sollevata pi&ugrave; in alto; e ci&ograve; per gli effetti meccanici della leva. </s>

<s>Ci <lb/>risovvenne allora ch'era questo uno degli argomenti propostisi dallo stesso <lb/>Galileo a trattare nella <emph type="italics"/>Selva di problemi vari,<emph.end type="italics"/> dove la proposizione, rima&shy;<lb/>sta come tutte le altre irresoluta, si legge cos&igrave; scritta: &ldquo; Se sia vero quello <lb/>che dice Aristotile, cio&egrave; che pi&ugrave; gagliardamente spinga la vela, quanto &egrave; pi&ugrave; <lb/>alta; e se ci&ograve; avviene per la ragione addotta da esso, presa dalla leva &rdquo; <lb/>(Alb. </s>

<s>XIV, 320). </s></p><p type="main">

<s>Ci sembrava venisse confermato da questo nuovo esempio che anche gli <lb/>altri frammenti di dialogo, ritrovati nel detto manoscritto, erano stati distesi <lb/>dal Viviani, a cui Galileo aveva significato i suoi propri concetti, di che ri&shy;<lb/>mase la testimonianza ne'libri delle Meccaniche del Casati. </s>

<s>Il confratello e <lb/>collega di Giuseppe Ferroni, discepolo di esso Viviani, ha, nel IV di quei <lb/>libri, intitolato il capitolo XVI <emph type="italics"/>An malus in motu navis habeat rationem <lb/>vectis<emph.end type="italics"/> (ediz. </s>

<s>cit., pag. </s>

<s>470), e confuta Aristotile con quelle medesime ragioni, <lb/>che il Salviati e il Sagredo confutano Simplicio, nel Dialogo che qui trascri&shy;<lb/>viamo: </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; &Egrave; il nostro Accademico, e non il vostro Aristotile, signor <lb/>Simplicio, che ha istituita la nuova Scienza meccanica. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Ma pure ha anch'egli imparato dal Filosofo che tutti <lb/>quanti gli effetti delle macchine si riducono finalmente a quello della leva, <lb/>e secondo ci&ograve; vedete nelle <emph type="italics"/>Questioni<emph.end type="italics"/> come si risolva una variet&agrave; di problemi <lb/>bellissimi e curiosi. </s>

<s>In quei giorni che mi trattenni ospite vostro nella vostra <lb/>amenissima villa delle Selve, scesi tutto solo una sera sulla riva dell'Arno, <lb/>e mentre sedevo all'ombra, guardando le acque che, per le piogge recenti, <lb/>scendevano gi&ugrave; per il fiume pi&ugrave; del solito copiose; ecco vedo risalire i na&shy;<lb/>vicelli di Signa a vele spiegate. </s>

<s>Erano cos&igrave; carichi, da rimanerne quasi tutti <lb/>inghiottiti, eppure con tanta facilit&agrave;, e direi quasi snellezza, solcavano le <lb/>acque cos&igrave; fonde e con moto contrario, che io non potei non ripensare allora <lb/>quanto veramente mirabile dev'essere la potenza della leva. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Ma, ditemi, come c'entra la leva nel moto della nave <lb/>a vela? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; C'entra benissimo, come potete vedere in Aristotile, <lb/>nella sua sesta Questione, dove dice che l'albero &egrave; un vette, che il luogo <lb/>dov'egli &egrave; fisso &egrave; l'ipomoclio, che il peso da movere &egrave; la stessa nave, e che <lb/>il vento &egrave; la forza movente. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Anch'io resto maravigliato di ci&ograve;, non meno del signor <lb/>Salviati, e non par credibile che un tanto filosofo abbia pronunziato cos&igrave; fran&shy;<lb/>camente sentenza, della quale nessun'altra mi sembra che sia pi&ugrave; aliena dal <lb/>vero. </s>

<s>Come si potrebbe infatti riconoscer l'opera della leva, dove il peso e <lb/>l'ipomoclio hanno il moto medesimo della virt&ugrave; motrice? </s>

<s>Non &egrave; ella, signor <lb/>Simplicio, dottrina di Aristotile verissima, e confermata dall'esperienza, che <pb xlink:href="020/01/2580.jpg" pagenum="205"/>la leva opera tanto pi&ugrave; validamente, quanto la virt&agrave; che muove ha maggior <lb/>velocit&agrave;, rispetto al peso che deve esser mosso? </s>

<s>Che se fossero uguali le ve&shy;<lb/>locit&agrave; del mosso e del movente, a nulla si ridurrebbe l'efficacia dello stru&shy;<lb/>mento. </s>

<s>Voi vedete dunque che, movendosi la vela e la nave con pari moto, <lb/>secondo le medesime dottrine del vostro Maestro, la leva, quando pure ci <lb/>fosse, non farebbe sulla nave nessuno effetto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Soggiungete, signor Sagredo, che, quando ci fosse opera <lb/>di leva, non solo questa riuscirebbe inutile al moto della nave, ma gli sarebbe <lb/>anzi contraria. </s>

<s>Supponete infatti che il pi&egrave; dell'albero sia fermato vicino alla <lb/>prora: ivi sar&agrave; l'ipomoclio, e intorno ad esso tender&agrave; la vela a far girare il <lb/>vascello, affondando di pi&ugrave; essa prora, che verr&agrave; perci&ograve; a ricevere maggiore <lb/>impedimento dall'acqua, e facendo capolievare la poppa. </s>

<s>I pericoli, che cor&shy;<lb/>rerebbe la navigazione per questa mobilit&agrave; di equilibrio, si comprendono assai <lb/>facilmente, ed &egrave; perci&ograve; che i nocchieri non a caso dispongono l'albero, che <lb/>ha da portare in alto la vela, ma s&igrave; che sempre la carena si mantenga ori&shy;<lb/>zontale. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Io mi sono trattenuto pi&ugrave; volte nei nostri porti di Ve&shy;<lb/>nezia a osservare le grandi navi approdatevi d'Inghilterra e d'Olanda, le <lb/>quali hanno, specialmente il maggior albero della vela maestra, disposto in <lb/>modo, che riman sempre il suo piede sulla carena, fuori del comun centro <lb/>di gravit&agrave;, e ci&ograve; col consiglio, mi credo io, che non faccia esso albero l'ufficio <lb/>di vette, e non metta la poppa con la prora in gioco pericoloso di altalena. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Vedete dunque, signor Simplicio, come sia ben confer&shy;<lb/>mato da questo esempio che, tutt'altrimenti dal ricercarsi l'utilit&agrave; del vette <lb/>in sospingere pi&ugrave; gagliardamente la nave, se n'evita con ogni studio, da chi <lb/>sa l'arte, l'ingerenza nociva. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Io non so che rispondere alle vostre ragioni, ma pur <lb/>mi sembra che potesse rispondere per me, in favor di Aristotile, un modo, <lb/>che io ho veduto praticar da coloro, i quali, mancando il vento, tirano con&shy;<lb/>tro il corso del fiume le navi a forza d'uomini o di cavalli. </s>

<s>Ho sentito que&shy;<lb/>sto chiamarsi da'navicellai di Signa <emph type="italics"/>tirar l'alzaio,<emph.end type="italics"/> il quale alzaio intesi es&shy;<lb/>sere quella fune, che da un capo &egrave; legata all'albero della nave, e dall'altra <lb/>vi sono aggiunte certe brachette, che o s'avvolgono intorno alle spalle degli <lb/>uomini, o ricingono il petto dei cavalli. </s>

<s>Ora, abbattutomi pi&ugrave; volte a vedere <lb/>questa fatica, ho sempre osservato che l'alzaio si lega pi&ugrave; su che sia pos&shy;<lb/>sibile all'albero, di che interrogata quella buona gente, che lo tirava, mi <lb/>sentivo rispondere che, quanto si tien pi&ugrave; alta la fune, tanto si muove la <lb/>nave con maggiore facilit&agrave;, e con minore fatica. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; N&egrave; foste punto ingannato, signor Simplicio, nella rispo&shy;<lb/>sta: l'inganno per&ograve; &egrave; tutto vostro in credere che la maggior distanza della <lb/>fune dal pi&egrave; dell'albero, come da suo ipomoclio, sia giusto procurata da <lb/>quella gente, per ottenere maggior favore di leva. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; O per qual altro fine dunque lo fanno, o qual ne pos&shy;<lb/>sono sperare vantaggio diverso? </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2581.jpg" pagenum="206"/><p type="main">

<s>&ldquo; SALVIATI. &mdash; Prima che io risponda a voi, rispondete voi a me, men&shy;<lb/>tre vi domando se pi&ugrave; facilmente si tira una fune libera che una impedita. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Voi volete il gioco del fatto mio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Se dunque si tira pi&ugrave; facilmente una fune libera, che <lb/>una impedita, e se tanto meglio si scansano gl'impedimenti dell'acqua cor&shy;<lb/>rente, dei sassi, dell'alveo, dei bronchi e degli sterpi delle rive, quanto la <lb/>fune &egrave; pi&ugrave; in aria, intenderete che si pratica a quel modo dai tiratori d'al&shy;<lb/>zaio, per ragioni molto pi&ugrave; semplici di quelle, che voi credete essere state <lb/>suggerite a loro dalla Filosofia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Sia pur cos&igrave;, come voi volete, ma io per me non in&shy;<lb/>tendo in che modo si possano coteste vostre ragioni applicare alla vela, che <lb/>fu il primo e principale proposito del nostro discorso: la qual vela non si <lb/>vede come venga a ricevere minor impedimento dallo stare spiegata sull'an&shy;<lb/>tenna pi&ugrave; in alto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; L'impedimento, signor Simplicio, non &egrave; da riguardar <lb/>nella vela propriamente, ma nello spirito che la muove. </s>

<s>Non vedete voi che <lb/>il vento spira pi&ugrave; gagliardo sulle alte torri, dove ha libero il moto, che in <lb/>piana terra, dove, dai tanti oggetti ch'egli v'incontra, ad ogni passo viene <lb/>impedito? </s>

<s>Non vedete voi le banderuole moversi sui campanili, anche quando <lb/>voi in piazza non sentite alito che vi rinfreschi? </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Volete dire insomma che la vela spinge tanto pi&ugrave; ga&shy;<lb/>gliardamente la nave, quanto &egrave; pi&ugrave; alta, perch&egrave; in alto il vento spira sem&shy;<lb/>pre pi&ugrave; gagliardo? </s>

<s>Ma questa &egrave; ragion troppo semplice, e non meritevole <lb/>che v'esercitasse attorno Aristotile il suo grande ingegno. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Voi credete dunque, signor Simplicio, che la Natura di&shy;<lb/>sponga le sue operazioni, per dar faccenda ai Filosofi? </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Insieme coi problemi di meccanico soggetto, dei quali abbiamo discorso <lb/>fin qui, Galileo se n'era proposti a risolvere altri di vario argomento, i quali <lb/>pure, facendo parte del materiale da portarsi in dialogo, vogliono esser se&shy;<lb/>condo il proposito nostro raccolti, perch&egrave; possan meglio riconoscersi dai no&shy;<lb/>stri Lettori. </s>

<s>Non a tutto era data la forma problematica, ma molti dei pen&shy;<lb/>sieri, che si volevano dialogizzare, erano espressi in note frettolose, e in sen&shy;<lb/>tenze disperse, delle quali anche daremo un saggio, come delle ultime foglie <lb/>e de'fiori pi&ugrave; minuti, a cui il giardiniere sa trovar qualche luogo nella gi&agrave; <lb/>imposta ghirlanda. </s></p><p type="main">

<s>Incominciando da quelle scritture di fisico argomento, le quali avevano <lb/>avuta gi&agrave; la forma determinata di problemi, per contrapporli ai <emph type="italics"/>Problemi<emph.end type="italics"/> di <lb/>Aristotile, studiati allora da tutti e da tutti creduti veri; trascriveremo i due <lb/>seguenti, rimasti tuttavia manoscritti, nella raccolta fattane dal Viviani. </s>

<s>Nel <pb xlink:href="020/01/2582.jpg" pagenum="207"/>primo &ldquo; si domanda onde avvenga che un uovo rinchiuso tra le mani per <lb/>punta, e stretto con grandissima forza, non si possa schiacciare &rdquo; (MSS. Gal., <lb/>P. VI, T. III, fol. </s>

<s>34). Alla proposta si dircbbe che anche questo problema <lb/>appartiene ai meccanici, ma troppo ardua cosa essendo alla scienza di allora <lb/>la teoria dell'equilibrio delle v&ocirc;lte e degli archi gravati da pesi, Galileo si <lb/>studi&ograve; di ridurre alla fisica la questione, si potrebbe dire ingegnosamente, <lb/>bench&egrave; costretto a invocar con Aristotile il falso principio che la Natura abor&shy;<lb/>risce il vuoto. </s></p><p type="main">

<s>&ldquo; Il presente problema facilmente si risolver&agrave;, premettendo come prin&shy;<lb/>cipii alcune vere proposizioni: La prima &egrave; che, siccome delle figure piane, <lb/>e che abbiano il medesimo ambito, la maggiore &egrave; il cerchio; cos&igrave; anco delle <lb/>figure solide isoperimetre la sfera &egrave; la maggiore, e la pi&ugrave; capace delle altre. </s>

<s><lb/>La seconda proposizione &egrave; che la Natura grandemente aborrisce il vacuo, <lb/>onde in essa ei non si d&agrave;, se non con somma violenza. </s>

<s>La terza &egrave; che l'aria <lb/>si distrae e raref&agrave;, cosa che non pu&ograve; far l'acqua, n&egrave; altri umori. </s>

<s>La quarta <lb/>&egrave; che prima s'arrende un poco il guscio di un uovo, e poi si rompe. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora da questi principii caveremo la resoluzion del problema, impe&shy;<lb/>rocch&egrave;, mentre che si preme l'uovo per lo lungo, e si stringono le sue punte <lb/>o estremit&agrave; l'una contro l'altra, il suo guscio cede alquanto, e si arrende, <lb/>sicch&egrave; l'uovo, che &egrave; di figura oblonga, viene ad acquistar dello sferico, e per <lb/>conseguenza si fa pi&ugrave; capace, perch&egrave;, come aviamo detto delle figure solide <lb/>isoperimetre, la sfera &egrave; la pi&ugrave; capace. </s>

<s>Ma perch&egrave; la roba, che &egrave; dentro del&shy;<lb/>l'uovo, non &egrave; cosa che si rarefaccia e distenda, per poter mantener pieno <lb/>l'uovo, sarebbe necessario che il luogo, che acquista l'uovo nel ridursi alla <lb/>figura sferica, rimanessi vuoto. </s>

<s>Ma la Natura, che grandemente aborrisce il <lb/>vacuo, repugna gagliardamente e resiste, per far che l'uovo non si avvicini <lb/>alla figura sferica, acci&ograve; col diventar egli pi&ugrave; capace, e per non aver dentro <lb/>cosa che lo possa riempiere, e per esser necessario che il suo guscio s'ar&shy;<lb/>renda alquanto, prima ch'e'si rompa; non si venga a dare il vacuo: quindi <lb/>&egrave; che l'uovo non si pu&ograve; schiacciare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per confermazione e chiarezza di questo pensiero, piglisi un uovo assai <lb/>scemo, sicch&egrave; dentro vi sia di molt'aria, e stringasi per lo lungo: che al <lb/>sicuro si schiaccer&agrave;, perch&egrave; l'aria che &egrave; dentro seguiter&agrave; tanto a rarefarsi, <lb/>e a distendersi per mantener pieno l'uovo, mentre con l'avvicinarsi allo sfe&shy;<lb/>rico divien pi&ugrave; capace, che il guscio, per non potere arrendersi pi&ugrave;, si verr&agrave; <lb/>a rompere, ed il medesimo seguir&agrave;, se faremo nel guscio ogni piccolo foro, <lb/>sicch&egrave; l'aria per quello possa entrare nell'uovo &rdquo; (ivi, fol. </s>

<s>34 a tergo). </s></p><p type="main">

<s>All'altro problema d'argomento fisico, che noi qui aggiungiamo, il Vi&shy;<lb/>viani apponeva la nota <emph type="italics"/>stampato,<emph.end type="italics"/> come quello che veramente era stato rac&shy;<lb/>colto dal Rinaldini fra le Opere galileiane, nel 1655, in Bologna, col titolo <lb/><emph type="italics"/>Risposta ad un problema, proposto dall'illustrissimo signor Piero Bardi <lb/>dei conti di Vernio, intorno all'apparente diversit&agrave; della temperie del&shy;<lb/>l'acqua.<emph.end type="italics"/> Nonostante &egrave; bene conoscerlo nella sua prima forma originale, non <lb/>per sola curiosit&agrave; erudita, ma perch&egrave; serva di documento a dimostrar come <pb xlink:href="020/01/2583.jpg" pagenum="208"/>Galileo, n&egrave; prima n&egrave; poi si valse del Termometro, per risolvere una questione <lb/>relativa ai gradi della temperatura assoluta dell'aria, e dell'acqua. </s></p><p type="main">

<s>&ldquo; Uno va per bagnarsi in Arno: si spoglia, e si mette a sedere all'om&shy;<lb/>bra. </s>

<s>Stando cos&igrave;, sente un fresco comportabile e temperato. </s>

<s>Entra poi nel&shy;<lb/>l'acqua, e gli par di sentirla assai fredda. </s>

<s>Statovi un pezzo ne esce, torna <lb/>all'ombra, e sente un freddo estremo. </s>

<s>Di nuovo si tuffa nell'acqua e, dove <lb/>la prima volta gli parve molto fredda, la seconda gli apparisce piuttosto tem&shy;<lb/>perata e calda. </s>

<s>Si domanda adesso la cagione di tal diversit&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il Problema si risolve cos&igrave;: Noi abbiamo in una stanza una tinozza <lb/>pi<gap/>a di acqua, e ci &egrave; stato v. </s>

<s>g. </s>

<s>quindici di freddura. </s>

<s>Viene uno, si spoglia <lb/>e entra nella tinozza. </s>

<s>Chiara cosa &egrave; ch'ei sentir&agrave; assai pi&ugrave; freddo in quel&shy;<lb/>l'acqua, ch'ei non sentiva, innanzi ch'ei v'entrasse, dal che si pu&ograve; conclu&shy;<lb/>dere che, stando l'aria e l'acqua in un medesimo luogo, cio&egrave; ad un istesso <lb/>caldo o ad un istesso freddo, sempre l'acqua apparir&agrave; assai pi&ugrave; fredda del&shy;<lb/>l'aria. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Diciamo dunque che dei gradi di freddezza, dei quali l'aria ne ha per <lb/>esempio due, l'acqua ne abbia dieci. </s>

<s>Dunque un'altr'acqua, che ne abbia <lb/>sei, apparir&agrave; fredda, in comparazione dell'aria, che ne ha due, ma ben calda <lb/>in relazione all'acqua, che ne ha dieci. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, stante questo, colui che si va a bagnare in Arno, mentre sta <lb/>ignudo all'ombra, gode il fresco temperato dell'aria, che ha due soli gradi <lb/>di freddezza, ma, quando entra nell'acqua d'Arno, sente la freddezza sua, <lb/>che &egrave; di sei gradi (di sei dico e non di dieci, perch&egrave; il sole ardente, che <lb/>l'ha percossa per lo spazio di molte miglia, glie ne viene ad aver levati quat&shy;<lb/>tro), e per&ograve;, in rispetto dell'aria, che ne ha due soli, gli pare assai fredda. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esce poi costui d'Arno, e torna all'ombra bagnato e coperto da un <lb/>sottilissimo velo d'acqua, la quale, per esser pochissima, non si tosto &egrave; con&shy;<lb/>dotta sotto l'albero all'ombra, che viene ad acquistare i quattro gradi di fred&shy;<lb/>dezza toltigli dal Sole, onde di sei, ch'ella ne aveva innanzi, si riduce ad <lb/>un tratto ad averne dieci, sicch&egrave; colui che si bagua non sente pi&ugrave; sei gradi <lb/>di freddezza, ma dieci. </s>

<s>E per&ograve;, mentre sta sotto l'albero bagnato, sente freddo <lb/>estremo, ma se ritorna poi a tuffarsi entro nell'acqua, che ha sei gradi soli <lb/>di freddezza, onde, perdendo quattro gradi di freddo, gli pare di essere en&shy;<lb/>trato in un bagno temperato &rdquo; (ivi, fol. </s>

<s>29). </s></p><p type="main">

<s>Anche questi due Problemi dovevano esser materia del Dialogo, e ma&shy;<lb/>teria del Dialogo doveva essere altresi un argomento d'assai maggiore im&shy;<lb/>portanza, intorno al quale le poche risolute questioni avevano ingerito nel&shy;<lb/>l'animo di Galileo la speranza di averne a comporre un intero trattato. </s>

<s>Di <lb/>questo trattato faceva Galileo stesso menzione in una lettera a Giuliano de'Me&shy;<lb/>dici, a cui, dicendo di avere diversi opuscoli di soggetti naturali, ne annovera <lb/>in ultimo uno <emph type="italics"/>De animalium motu<emph.end type="italics"/> (Alb. </s>

<s>VI, 98). Sembra che allora, men&shy;<lb/>tre era in Padova, emulasse l'altro celebre collega suo Girolamo Fabricio <lb/>d'Acquapendente, a cui si debbono in realt&agrave; quei trattati <emph type="italics"/>De sono et voce,<emph.end type="italics"/><lb/>e <emph type="italics"/>De visu et coloribus,<emph.end type="italics"/> nella sopra citata lettera a don Giuliano commemo-<pb xlink:href="020/01/2584.jpg" pagenum="209"/>rati. </s>

<s>Di quella emulazione si vedr&agrave;, nelle cose che saremo per dire, qualche <lb/>prova rispetto ai moti animali, intorno a che non rimase a Galileo, come <lb/>s'accennava dianzi, se non che alcune questioni relative particolarmente al <lb/>passo dell'uomo e del cavallo: questioni, il proposito di raccoglier le quali <lb/>e di portarle in dialogo, era stato espresso a Raffaello Magiotti, com'ap&shy;<lb/>parisce dalle congratulazioni di lui scritte in una lettera da Roma il di <lb/>21 Marzo 1637 (MSS. Gal., P. VI, T. XIII, fol. </s>

<s>14). </s></p><p type="main">

<s>Del passo del cavallo &egrave; gi&agrave; da qualche tempo pubblicamente nota una <lb/>scrittura galileiana, nella quale l'Autore confuta le dottrine di Aristotile, e <lb/>in che modo lo faccia lo dicemmo nel cap. </s>

<s>X del terzo tomo della nostra <lb/>Storia, e particolarmente a pag. </s>

<s>397, 98. Son forse meno note alcune altre <lb/>osservazioni, che Galileo stesso faceva intorno al passo dell'uomo, contro ci&ograve; <lb/>che Platone e Aristotile avevano insegnato nei loro libri. </s>

<s>Dicevano que'due <lb/>grandi Filosofi che, passeggiando l'uomo, la sua altezza verticale ora cresce <lb/>ora diminuisce, secondo che ora la persona si solleva sull'un piede, per poi <lb/>scendere a riposarsi sull'altro, sicch&egrave; la linea del moto non &egrave; retta, ma on&shy;<lb/>deggiante. </s>

<s>Cos&igrave; fatto ondeggiamento, dicevano, si pu&ograve; facilmente osservare, <lb/>riferendo la visuale sopr'una parete, parallelamente alla quale si guardi da <lb/>una certa distanza la testa di un che passeggia. </s></p><p type="main">

<s>La ragione, che prescriveva alla Natura questo modo indecente di ope&shy;<lb/>rare, consisteva nel credere ch'ella non avesse saputo, con tutto il suo sa&shy;<lb/>piente magistero, far s&igrave; che le gambe si potessero allungar secondo il biso&shy;<lb/><figure id="id.020.01.2584.1.jpg" xlink:href="020/01/2584/1.jpg"/></s></p><p type="caption">

<s>Figura 71.<lb/>gno, ma che sempre si dovessero mantenere <lb/>uguali. </s>

<s>Rappresenti AB (fig. </s>

<s>71) la colonna <lb/>ossea, sopra la quale si sostien l'uomo, nella <lb/>sua stazion verticale, sul suolo CD. </s>

<s>Per mo&shy;<lb/>versi innanzi fa rotare l'AB intorno al cen&shy;<lb/>tro A, nella posizione AB&prime;, ond'&egrave; che, per <lb/>andare a ritrovare e appoggiarsi sul pavi&shy;<lb/>mento in G, il punto A convien che si <lb/>abbassi, e che poi nuovamente si rialzi, per tornar nella posizion verticale <lb/>parallela all'AB, e cos&igrave; la persona non va mai di pari passo ma ondeggia. </s></p><p type="main">

<s>Galileo diceva che la Natura aveva suggerita instintivamente una bellis&shy;<lb/>sima industria, sfuggita alle considerazioni di quei Filosofi, aggiungendo la <lb/>parte B&prime; G, che manca alla gamba, per andare a toccare e fermarsi nell'ap&shy;<lb/>poggio, col sollevare in B&prime; il calcagno, e col distendere e appuntare in E il <lb/>piede, cosicch&egrave; il punto A riman sempre alla medesima altezza, e il passo <lb/>dell'uomo, come si conveniva alla sua dignit&agrave;, si serba sempre uniforme. </s>

<s><lb/>Ritrovasi notato infatti fra i pensieri di Galileo &ldquo; come il camminar di noi <lb/>bipedi non sia a onde, ancorch&egrave; le gambe siano uguali, e che si trovino di&shy;<lb/>versamente inclinate sopra l'orizonte, dove par che Aristotile e Platone ab&shy;<lb/>biano equivocato &rdquo; (MSS. Gal., P. VI, T. III, fol. </s>

<s>62): pensiero che vien <lb/>confermato dalla testimonianza, e illustrato dalle seguenti parole del Viviani: </s></p><p type="main">

<s>&ldquo; Sovviemmi aver sentito dire dal Galileo che Platone e Aristotile er-<pb xlink:href="020/01/2585.jpg" pagenum="210"/>rarono in dire che il moto dell'uomo veniva fatto a onde, cio&egrave; che, nel mo&shy;<lb/>versi e passeggiar parallelo ad una parete, osservando la testa del moventesi, <lb/>con riferirla con l'occhio sulla muraglia, appariva che essa testa descrivesse <lb/>un'onda ora alta ora bassa: perch&egrave; essi si credettero che le gambe fossero <lb/>talmente uguali, che elle non potessero mai essere disuguali. </s>

<s>Ma sono, per&shy;<lb/>ch&egrave;, nel posare il calcagno del piede precedente, si allunga l'altra gamba, <lb/>alzando il suo calcagno, e levandosi in punta di piedi &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. CXXXV, a tergo del fol. </s>

<s>29). </s></p><p type="main">

<s>Il Borelli, esaminando, nella proposizione CLVI della prima parte <emph type="italics"/>De <lb/>motu animalium,<emph.end type="italics"/> in che modo si muova l'uomo, sembra che volesse anche <lb/>egli indirettamente confermare le osservazioni di Galileo, contro le inconsi&shy;<lb/>deratezze dei Filosofi antichi, dicendo che, sebbene possa a prima vista pa&shy;<lb/>rer che le nostre gambe si rassomiglino nel moversi a quelle di un compasso, <lb/>&egrave; nonostante da confessar che un tale incesso ondeggiante <emph type="italics"/>deformis et in&shy;<lb/>commodus esset<emph.end type="italics"/> (Romae 1680, pag. </s>

<s>252), ond'ei ne conclude che la Natura <lb/><emph type="italics"/>faciliori et elegantiori motu machinam humani corporis promovet,<emph.end type="italics"/> e in <lb/>descrivere questa promozione principalmente nota, come Galileo, che ogni <lb/>incomodit&agrave; di ondeggiamento si toglie, <emph type="italics"/>quia longitudo totius cruris et coxae <lb/>elongatur, additione longitudinis pedis<emph.end type="italics"/> (ibid., pag. </s>

<s>253). </s></p><p type="main">

<s>Nella seguente proposizione per&ograve; il Borelli stesso osserva che l'ondeg&shy;<lb/>giamento, inevitabile al passo dell'uomo, si fa propriamente a quel modo che <lb/>dicevano Platone e Aristotile, ma nel piano orizontale, descrittovi sopra dal <lb/>centro di gravit&agrave;, e no nel verticale descrittovi dalla testa. </s>

<s>Che sia propria&shy;<lb/>mente cos&igrave;, che cio&egrave; le nostre gambe non conducano l'umbilico precisamente <lb/>nella linea retta della direzione del passo, ma che lo facciano ondeggiare ora <lb/>a destra ora a sinistra, il Borelli suggerisce un modo di sperimentarlo, che <lb/>potrebbe a chi l'eseguisse riuscire, oltre che di ammaestramento di questa <lb/><figure id="id.020.01.2585.1.jpg" xlink:href="020/01/2585/1.jpg"/></s></p><p type="caption">

<s>Figura 72.<lb/>verit&agrave;, di spettacolo curioso e giocondo. </s>

<s><lb/>Sia per esempio AG (fig. </s>

<s>72) la linea <lb/>lungo la quale, movendo da A, uno si <lb/>proponga di camminare, e in G sia eretta <lb/>la verga GH di color bianco, e in FI <lb/>un'altra simile verga, ma di color nero, <lb/>cosicch&egrave; all'occhio dell'uomo, che sta <lb/>fermo in A, la bianca resti totalmente coperta dalla nera. </s>

<s>Movasi, e vedr&agrave; ad <lb/>ogni passo la verga bianca ora uscir fuori dalla sinistra mano ora dalla <lb/>destra, con continua spettacolosa vicenda, e per evidentissimo segno che, ri&shy;<lb/>ferito il centro di gravit&agrave; sul pavimento, vi descriverebbe la linea ondeggiante <lb/>ABEM, le onde o i seni della quale si vedrebbero, come BC, DE, farsi molto <lb/>pi&ugrave; ampi negli uomini obesi, e nelle donne pregnanti. </s>

<s>&ldquo; Quod est argumen&shy;<lb/>tum evidentissimum, cos&igrave; propriamente conclude il Borelli la sua proposizione, <lb/>dop'aver descritta la curiosa esperienza; incessus hominum non fieri per <lb/>lineam rectam: ergo linea propensionis tortuoso et serpentino itinere tran&shy;<lb/>sfertur hinc inde, ab una ad alteram parallelarum, et proinde per unicam <pb xlink:href="020/01/2586.jpg" pagenum="211"/>simplicem rectam lineam machina humani corporis motum progressuum in&shy;<lb/>cessus efficere non potest &rdquo; (ibid., pag. </s>

<s>255). </s></p><p type="main">

<s>In proposito di cos&igrave; fatte questioni di Meccanica animale cade oppor&shy;<lb/>tuno quel confronto, dal quale si voleva far apparire come Galileo emulasse <lb/>l'Acquapendente. </s>

<s>Nel trattato <emph type="italics"/>De musculi utilitatibus<emph.end type="italics"/> &egrave; premessa dall'Ana&shy;<lb/>tomico nello Studio padovano la questione &ldquo; Cur musculi longiores, non so&shy;<lb/>lum longiores, sed robustiores dant motus &rdquo; (Opera omnia, Lugd. </s>

<s>Batav. </s>

<s>1738, <lb/>pag. </s>

<s>420); e il Matematico nel medesimo Studio si proponeva pure di dimo&shy;<lb/>strare &ldquo; che i tendini dei muscoli fanno maggior forza i lunghi che i brevi &rdquo; <lb/>(MSS. Gal., P. VI, T. III, a tergo del fol. </s>

<s>61). Ora, essendo questa propo&shy;<lb/>sizione principalissima fra quelle, che dovevano comporre il trattato <emph type="italics"/>De ani&shy;<lb/>malium motu,<emph.end type="italics"/> di cui nella storia della letteratura galileiana non &egrave; rimasto <lb/>che il titolo; &egrave; il tempo di dire a coloro, che ne hanno lamentata la per&shy;<lb/>dita, come Galileo non progredi forse oltre in quest'ordine di speculazioni, <lb/>perch&egrave; si trov&ograve; vinto dall'emulo suo, l'anatomia del quale, destramente ac&shy;<lb/>coppiata con la matematica, superava i vantaggi della matematica sola, ch'era <lb/>pur mancante dei necessari argomenti. </s></p><p type="main">

<s>Come nell'Acquapendente s'accoppiassero quelle due scienze, e come la <lb/>matematica che aveva lo fornisse dell'argomento opportuno, consistente nel <lb/>modo di decomporre le forze, secondo gl'insegnamenti di Aristotile, s'accen&shy;<lb/>nava in principio dell'ultimo capitolo della prima parte di questa Storia della <lb/>Meccanica, ma vogliamo ora meglio, nella presente occasione, dichiarare le <lb/>cose gi&agrave; dette intorno al modo di risolver, nel trattato <emph type="italics"/>De musculi utilita&shy;<lb/>tibus,<emph.end type="italics"/> la proposta questione, per concluder poi che mancavano a Galileo ve&shy;<lb/>ramente, come si diceva, gli argomenti necessari, per riuscire a quella me&shy;<lb/>desima soluzione. </s></p><p type="main">

<s>La soluzione dell'Acquapendente si fa dipendere, come da lemma, da <lb/>una proposizione meccanica cos&igrave; formulata: &ldquo; Quo corda super vecte ela&shy;<lb/>tior fuerit, idest maiorem angulum continebit, eo facilius pondus attolletur &rdquo; <lb/><figure id="id.020.01.2586.1.jpg" xlink:href="020/01/2586/1.jpg"/></s></p><p type="caption">

<s>Figura 73.<lb/>(Opera cit., pag. </s>

<s>420). Sia il vette AB <lb/>(fig. </s>

<s>73), col peso in A e col sostegno <lb/>in B, e per sostenerlo o sollevarlo <lb/>intendasi applicata in D una corda di <lb/>qualunque lunghezza. </s>

<s>Se inclinasi in <lb/>DE, in modo che l'angolo EDB sia <lb/>minore di FDB, dice l'Acquapendente <lb/>che anche sar&agrave; minore la forza fatta <lb/>dalla medesima corda, perch&egrave; allora <emph type="italics"/>pars virium absumitur contra fulci&shy;<lb/>mentum.<emph.end type="italics"/> Costruito infatti sulla DE il rettangolo HG, la forza totale si de&shy;<lb/>compone nelle due HD, DG, ed &egrave; evidente che questa <emph type="italics"/>absumitur contra ful&shy;<lb/>cimentum,<emph.end type="italics"/> non restando attiva che l'HD, minore della DF o della DE. </s>

<s>Che <lb/>se anche s'inclini di pi&ugrave; la corda, come in DI, &egrave; manifesto che, crescendosi <lb/>da una parte la forza DM, inutilmente diretta contro il fulcro, la forza utile <lb/>LD, che dall'altra parte ne resta, &egrave; anche pi&ugrave; che dianzi diminuita. </s>

<s>&Egrave; chiaro <pb xlink:href="020/01/2587.jpg" pagenum="212"/>dunque che, mentre nella direzion perpendicolare non &egrave; parte alcuna della <lb/>forza, che non si eserciti in sollevare il peso; inclinandosi la corda sempre <lb/>pi&ugrave;, anche sempre pi&ugrave; diminuisce quella sua forza, intanto che, venendo final&shy;<lb/>mente a costituirsi nella stessa linea del vette, si riduce a nulla. </s>

<s>&ldquo; Absumi&shy;<lb/>tur ergo vis magna ex parte in fulcimento B expellendo: quod, si attraha&shy;<lb/>tur chorda perpendicula in FD, nulla pars virium suam non exercet facultatem <lb/>in pondere elevando. </s>

<s>Patet etiam quod, si vectis et chorda in eadem essent <lb/>linea constituta, nullo pacto motus fieret &rdquo; (ibid.). </s></p><p type="main">

<s>Dimostrato ci&ograve;, per avvicinarsi pi&ugrave; d'appresso ad applicar le teorie mec&shy;<lb/>caniche al caso dei muscoli che, quanto son pi&ugrave; lunghi, tanto pi&ugrave; facilmente <lb/>muovon le membra, a cui son legati; soggiunge l'Acquapendente l'altra pro&shy;<lb/>posizione, che dice come, dovendosi un peso attaccato all'estremit&agrave; di un vette <lb/>semplicemente sostener da una corda, tanto fa l'esser questa o pi&ugrave; lunga o <lb/>pi&ugrave; corta: ma se debba il peso stesso poi venir sollevato, &ldquo; dico minori vi <lb/>opus esse, adhibita corda longiori, quam breviori &rdquo; (ibid.). </s></p><p type="main">

<s>Per dichiarar meglio il concetto dell'Autore, poniamolo sotto quest'altra <lb/>forma: Se il peso A (fig. </s>

<s>74) debba semplicemente sostenersi, tant'opera la <lb/><figure id="id.020.01.2587.1.jpg" xlink:href="020/01/2587/1.jpg"/></s></p><p type="caption">

<s>Figura 74.<lb/>corda AC, che la AD; ma se debba inoltre solle&shy;<lb/>varsi, infino a toccar per esempio la orizontale SX, <lb/>pi&ugrave; facilmente vi si porter&agrave;, e vi si manterr&agrave; dalla <lb/>corda pi&ugrave; lunga, che dalla pi&ugrave; corta. </s>

<s>La corda CA <lb/>infatti, girando intorno al punto C come a suo <lb/>centro, porter&agrave; il peso in R, e DA, girando intorno <lb/>a D, lo porter&agrave; in S. Ora, per concluder dietro il <lb/>lemma precedente che in S il peso vien sollevato pi&ugrave; <lb/>facilmente che in R, basta dimostrar che l'angolo <lb/>DSX, fatto dalla corda colla direzione del vette, &egrave; maggiore di CRX, ci&ograve; che <lb/>&egrave; facile a farsi conducendo le AR, AS, dai triangoli isosceli ACR, ADS de&shy;<lb/>scritti dalle quali resulta essere ADS minore di ACR, d'onde per necessit&agrave; <lb/>DSX maggiore di CRX. </s>

<s>Dietro ci&ograve;, se per AC, AD intendansi due muscoli, <lb/>e per A il peso dell'arto, a cui per moverlo son legati; il proposito &egrave; per <lb/>s&egrave; manifesto. </s></p><p type="main">

<s>Cos&igrave; risolvevasi dall'Acquapendente una delle principali questioni di Mec&shy;<lb/>canica animale, ritrovando nella regola di decomporre le forze, insegnatagli <lb/>da Aristotile, l'argomento necessario per una tal soluzione. </s>

<s>Dicemmo che a <lb/>Galileo venne a mancare cos&igrave; fatto argomento, per cui dovette necessaria&shy;<lb/>mente rimanere inferiore all'emulo suo, ma &egrave; ora il tempo di confermare <lb/>quel nostro detto. </s>

<s>La somma delle cose &egrave; chiaro che si riduce alla mecca&shy;<lb/>nica dei pesi sostenuti da funi, la pi&ugrave; propizia occasione di trattar de'quali <lb/>sarebbesi porta a Galileo, in proposito dei pendoli, ricercando in essi, quando <lb/>sian rimossi pi&ugrave; o meno dal perpendicolo, la proporzion del variare i loro <lb/>momenti. </s></p><p type="main">

<s>Sia per esempio il pendolo BC (fig. </s>

<s>75) rimosso in BA: quanto varia <lb/>la forza del peso in tirare il filo nelle due posizioni? </s>

<s>Che ci dovesse essere <pb xlink:href="020/01/2588.jpg" pagenum="213"/>una tal variet&agrave; Galileo incominci&ograve;, come Leonardo da Vinci, ad apprenderlo <lb/>per esperienza, se non che, mentre all'uno si rivelava il fatto dai globi ven&shy;<lb/><figure id="id.020.01.2588.1.jpg" xlink:href="020/01/2588/1.jpg"/></s></p><p type="caption">

<s>Figura 75.<lb/>tilati all'estremit&agrave; di una bilancia, serviva <lb/>all'altro di criterio il tatto delle proprie dita, <lb/>alle quali, ventilando il grave, teneva avvolto <lb/>o legato il filo. </s>

<s>Quel criterio poi era con <lb/>l'esercizio divenuto s&igrave; giusto che, volendo <lb/>per via delle numerate vibrazioni misurare <lb/>il tempo, diceva di saperlo far senza errore <lb/>a mente, anche senza veder l'andare e il <lb/>ritornare dello strumento. </s>

<s>&ldquo; Col misuratore <lb/>del tempo, troviamo scritto in una sua nota, <lb/>si possono numerare le vibrazioni, tenendo <lb/>il filo in mano, come se fosse legato a un <lb/>luogo stabile, e preso il tempo con la mente <lb/>si numereranno senza errrore, bench&egrave; non <lb/>si vegghino, le vibrazioni &rdquo; (MSS. Gal., P. <lb/>VI, T. III, fol. </s>

<s>63 a t.). </s></p><p type="main">

<s>Il fatto per&ograve; era per s&egrave; solo cognizione di poco acquisto, senza che la <lb/>matematica venisse a definire le proporzioni, secondo le quali via via suc&shy;<lb/>cede: proporzioni che noi crediamo non essere state da Galileo mai dimo&shy;<lb/>strate. </s>

<s>L'opinione si fonda sulla certezza che abbiamo non essere stato l'ar&shy;<lb/>gomento in proposito toccato, n&egrave; nei libri n&egrave; a viva voce, dal Maestro, al <lb/>pi&ugrave; studioso Discepolo del quale, promotore di questa nuova scienza, doman&shy;<lb/>dandosi quanta sia la violenza che patisce il filo AB, nella precedente figura, <lb/>rispetto a quella che patisce il filo BC, rispondeva: &ldquo; La violenza che pati&shy;<lb/>sce il filo AB, essendo stirato dal grave A, credo che sia tale, quale &egrave; il <lb/>momento del medesimo grave, movendosi per il piano BA: cio&egrave; che la forza <lb/>fatta dal grave al filo, nel luogo AB, alla forza fatta al filo nel luogo BC, <lb/>che &egrave; la forza totale, sia come il momento del medesimo grave sopra un <lb/>piano inclinato quanto BA, al momento totale per la perpendicolare BC &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. CXIII, fol. </s>

<s>30). </s></p><p type="main">

<s>Ma il Viviani, credendo cos&igrave;, credeva manifestamente il falso, com'avrebbe <lb/>saputo dimostrare a lui e al suo proprio Maestro l'Acquapendente, applican&shy;<lb/>dovi, a quel modo che dianzi il rettangolo aristotelico, cos&igrave; in questo caso, <lb/>e per le medesime ragioni, il parallelogrammo. </s>

<s>Facendo infatti rappresentare <lb/>alla AE la forza totale, che aveva il peso in C, questa in A decomposta nelle <lb/>due AD, AG, non si ridurrebbe che alla sola AG, essendo che l'altra AD <lb/><emph type="italics"/>absumitur contra fulcimentum.<emph.end type="italics"/> Dunque il momento totale del peso in C, <lb/>al parziale in A, sta come AE ad AG, o, prolungata l'AG infino a incon&shy;<lb/>trare in F l'orizontale EF, per i triangoli simili AEG, AEF; come AF ad <lb/>AE, per cui la forza fatta dal peso in C, alla forza fatta in A, non sta come il <lb/>momento dello stesso grave nel perpendicolo, al momento lungo un piano <lb/>inclinato quanto AD, secondo che falsamente credeva il Viviani, ma al mo-<pb xlink:href="020/01/2589.jpg" pagenum="214"/>mento lungo un piano inclinato quanto AF, no nella direzione stessa del filo, <lb/>ma in quella a lui perpendicolare. </s></p><p type="main">

<s>L'incertezza e il fallo, in cui incorse lo stesso Viviani, avevano la ra&shy;<lb/>dice nella falsit&agrave; del secondo teorema scritto nel IV dialogo delle Scienze <lb/>nuove, da cui resultava come, tutt'altro che consumarsi la forza AD in ti&shy;<lb/>rare inutilmente il sostegno, si faceva anzi cos&igrave; attiva, da rimaner per re&shy;<lb/>gola della resultante del moto. </s>

<s>Ond'essendo propriamente tali le fallacie del <lb/>Discepolo e del Maestro, abbiamo tutte le ragioni di credere che mancassero <lb/>all'uno e all'altro i principii diretti, per riuscire a dimostrar come pi&ugrave; va&shy;<lb/>lidamente operino, in movere le membra, i tendini pi&ugrave; lunghi. </s>

<s>Dicemmo che <lb/>mancavano i principii diretti, perch&egrave; non &egrave; impossibile che si risolvesse la <lb/>questione in altri modi, secondo i quali Galileo forse intendeva di portarla <lb/>in dialogo, per salvar dall'oblio questa reliquia delle sue speculazioni intorno <lb/>ai moti animali. </s></p><p type="main">

<s>Altre speculazioni intorno ai pi&ugrave; varii soggetti della Fisica aveva da rac&shy;<lb/>cogliere lo stesso Galileo, per inserirle nel suo Dialogo e salvarle anch'esse <lb/>dall'oblio, fra le quali ci sembra sia da notar fra le prime quella, che ora <lb/>diremo, relativa alle galleggianti. </s>

<s>Nel celebre discorso pubblicato nel 1612 in&shy;<lb/>torno a questo argomento, confutava quel suo avversario Francesco Buona&shy;<lb/>mico, il quale voleva confermare le sue false dottrine dal fatto, che un legno <lb/>inzuppato d'acqua finalmente va al fondo, contrapponendo Galileo le seguenti <lb/>osservazioni alle fallacie del peripatetico discorso: &ldquo; Ci&ograve; accade d'alcuni le&shy;<lb/>gni porosi, li quali, mentre hanno le porosit&agrave; ripiene di aria, o d'altra ma&shy;<lb/>teria men grave dell'acqua, sono moli in specie manco gravi di essa acqua, <lb/>ma quando, partendosi tal materia leggera, succede nelle dette porosit&agrave; o <lb/>cavernosit&agrave; l'acqua, pu&ograve; benissimo essere che allora tal composto resti pi&ugrave; <lb/>grave dell'acqua.... Cos&igrave; quel che resta del legno, partendosi l'aria dalle sue <lb/>concavit&agrave;, se sar&agrave; pi&ugrave; grave in specie dell'acqua, ripiene che saranno le sue <lb/>porosit&agrave; d'acqua, si avr&agrave; un composto d'acqua e di legno, pi&ugrave; grave del&shy;<lb/>l'acqua, e andr&agrave;, conforme alla dottrina d'Archimede, al fondo &rdquo; (Alb. </s>

<s>XII, 32). </s></p><p type="main">

<s>In questo discorso Galileo concedeva al suo avversario la possibilit&agrave; che <lb/>i legni inzuppati d'acqua si sommergano: ci&ograve; che sarebbe senza dubbio avve&shy;<lb/>nuto, quando la materia di loro che resta, partitasi l'aria, fosse pi&ugrave; grave <lb/>in specie dell'acqua stessa. </s>

<s>Nulla per&ograve; decide in proposito, non avendone <lb/>fatte esperienze, n&egrave; curandosi per allora di farle. </s>

<s>Ma negli ultimi anni della <lb/>sua vita, ritornando col pensiero sopra le cose passate, sent&igrave; nascersi una <lb/>viva curiosit&agrave; di saper come il fatto passava, e ragionando un giorno di ci&ograve; <lb/>col Viviani gli soggiungeva che, se la materia legnosa fra poro e poro &egrave; spe&shy;<lb/>cificamente pi&ugrave; grave dell'acqua, dell'andare al fondo il legno inzuppato <lb/>sarebbe argomento certo il vedervene andare la segatura. </s></p><p type="main">

<s>Il desiderio di sodisfare a una tale curiosit&agrave; s'accendeva alla fiamma di <lb/>un desiderio pi&ugrave; vivo, qual era quello di confermar che i liquidi non resi&shy;<lb/>stono colla loro viscosit&agrave; all'esser penetrati dai corpi immersivi: perniciosa <lb/>dottrina, che il Salviati ripeteva nel primo Dialogo delle Scienze nuove (Alb. <pb xlink:href="020/01/2590.jpg" pagenum="215"/>XIII, 72), con la medesima persuasione da vecchio, che l'aveva da giovane <lb/>professata nel sopra citato discorso idrostatico, le prolisse parole scritte nel <lb/>quale si possono leggere compendiate in questa nota: &ldquo; Mentre un metallo <lb/>&egrave; freddo, ed in conseguenza le sue parti continuate ed aderenti insieme, &egrave; <lb/>necessario, per dividerlo, usare strumenti gagliardi e gran forza. </s>

<s>Dopo che <lb/>il fuoco l'ha liquefatto, restano le sue parti divise, ed un solido che si ponga <lb/>dentro non l'ha pi&ugrave; a dividere, ma solamente a movere. </s>

<s>Perch&egrave; irragione&shy;<lb/>vol cosa sarebbe a dire che una verga di ferro o altro corpo solido dividesse <lb/>quello, che non ha diviso il fuoco. </s>

<s>Nel penetrar dunque i liquidi e fluidi, <lb/>non solamente non vi &egrave; resistenza alla divisione, ma non si ha a divider cosa <lb/>alcuna, ma solamente a muovere &rdquo; (MSS. Gal., P. III, T. X, fol. </s>

<s>72). </s></p><p type="main">

<s>Nel primo dialogo delle Scienze nuove, al luogo sopra citato, credeva il <lb/>Salviati di poter confermare queste dottrine, per via degl'idrostammi, ai <lb/>quali &egrave; sufficiente una leggerissima variazione di temperatura nel liquido, <lb/>perch&egrave; vi scendano o salgano prontamente: e ora nel dialogo novissimo in&shy;<lb/>tendeva di confermare quella sua antica opinione con l'esempio di ci&ograve;, che <lb/>sarebbesi osservato nei legni massicci e nella loro limatura. </s>

<s>L'esperienza non <lb/>sembra si facesse in tempo, e il Viviani indugi&ograve; ad eseguirla nell'Accademia <lb/>del Cimento, contentandosi intanto di scriver per suo memoriale in questa <lb/>nota il pensiero comunicatogli da Galileo: &ldquo; Credo che delle cose che scen&shy;<lb/>dono nell'acqua, quanto pi&ugrave; piccole sono, pi&ugrave; stieno a scendere, ma che di <lb/>quelle, che mal volentieri vi scendono, siano pi&ugrave; facili a scender le piccolis&shy;<lb/>sime che le grandi, come per esempio il legno, che non vi scende, sminuz&shy;<lb/>zato in sottil polvere vi scenda &rdquo; (MSS. Gal., P. V, T. IV, fol. </s>

<s>37). </s></p><p type="main">

<s>Dicemmo che questa opinion del Maestro aspett&ograve; il Viviani di verificarla <lb/>nell'Accademia del Cimento, e ci&ograve; fu a proposito delle controversie insorte <lb/>fra lui e il Borelli, il quale, contro il suo collega e contro lo stesso Galileo, <lb/>adduceva esperienze dimostrative di un glutine, che, come quello degli altri <lb/>corpi, tenga insieme le particelle dell'acqua. </s>

<s>Avremo intorno a questa con&shy;<lb/>troversia occasion di discorso altrove: per ora qui basti dir che il Viviani, <lb/>propugnatore delle dottrine insegnate nel discorso delle Galleggianti, propo&shy;<lb/>neva nell'Accademia di &ldquo; fare una piastra tonda di cera, che salga lenta&shy;<lb/>mente per taglio: posta poi per piano, si vede che la figura non &egrave; impo&shy;<lb/>tente a fendere l'acqua, e che in essa non ci &egrave; minima coesione e viscosit&agrave; &rdquo; <lb/>(MSS. Cim., T. X, fol. </s>

<s>27). </s></p><p type="main">

<s>Che aggiungesse a questa il Viviani l'esperienze suggeritegli da Galileo <lb/>resulta dal trovarsi, fra le altre rivendicazioni, scritta anche questa: <emph type="italics"/>Mia <lb/>l'osservazione che tutti i legni vanno al fondo nell'acqua<emph.end type="italics"/> (ivi, fol. </s>

<s>259): <lb/>e che non in loro stesse terminassero cos&igrave; fatte proposte, ma che avessero <lb/>il fine di dimostrare come sian continue, e non aderenti le particelle del&shy;<lb/>l'acqua, apparisce da un <emph type="italics"/>Registro di osservazioni ed esperienze varie, da <lb/>farsi nell'Accademia in considerando l'acqua come mezzo de'corpi mo&shy;<lb/>bili per essa<emph.end type="italics"/> (ivi, fol. </s>

<s>26). Fra quelle osservazioni &egrave; messa anche questa: <lb/>&ldquo; Se le materie, stimate pi&ugrave; leggere dell'acqua dal vederle galleggiare, ri-<pb xlink:href="020/01/2591.jpg" pagenum="216"/>dotte poi in sottilissima polvere, vi discendano: esaminar per mezzo dei corpi <lb/>discendenti se nel continuo dell'acqua sia necessario introdurre alcun glu&shy;<lb/>tine &rdquo; (ivi). Il Viviani aveva scritto a pulito questo registro da una bozza <lb/>pure autografa, nella quale alla medesima proposta era data quest'altra forma: <lb/>&ldquo; Se la sottilissima limatura delle materie, stimate pi&ugrave; leggere dell'acqua <lb/>dal galleggiare, vi discenda, come fa il sughero e la canna, per mezzo di <lb/>materie discendenti: esaminare se nella continuit&agrave; dell'acqua sia alcun glu&shy;<lb/>tine o viscosit&agrave;, come alcuni hanno creduto &rdquo; (ivi, fol. </s>

<s>28). </s></p><p type="main">

<s>La materia, che avrebbero fornito al Dialogo queste esperienze, si com&shy;<lb/>prende quanto fosse per riuscire importante, dall'importanza stessa che poi <lb/>ebbe nell'Accademia, la quale, sulla proposta del Viviani esamin&ograve; altresi la <lb/>questione dell'origine delle fonti, che Galileo aveva promossa nell'occasione <lb/>di confutar le false dottrine idrostatiche del Bonamici. </s>

<s>Diceva il Peripatetico <lb/>che le acque ascendono infino alle pi&ugrave; alte cime dei monti, spintevi dalla <lb/>gran pressione del mare comunicante con esse per sotterranei canali. </s>

<s>Gali&shy;<lb/>leo rispondeva che nei vasi comunicanti, sia l'un grandissimo e l'altro pic&shy;<lb/>colissimo, il liquido si fa equilibrio, giunto che sia qua e l&agrave; al medesimo <lb/>livello, e si richiamava, per confermare una tal verit&agrave;, alle cose, ch'egli aveva <lb/>gi&agrave; dimostrate nel suo Discorso intorno alle galleggianti. </s>

<s>Della questione, cos&igrave; <lb/>tra i Fisici controversa anche ai tempi del Guglielmini, e che doveva pure <lb/>porger materia al dialogo, come Galileo ne aveva data al Viviani intenzione, <lb/><figure id="id.020.01.2591.1.jpg" xlink:href="020/01/2591/1.jpg"/></s></p><p type="caption">

<s>Figura 76.<lb/>ci &egrave; rimasta per documento questa nota che dice: &ldquo; Aqua <lb/>DF (fig. </s>

<s>76) non plus premit quam BE, quod facile de&shy;<lb/>monstrari potest quod consonat cum eo, quod a me scri&shy;<lb/>ptum est in tractatu <emph type="italics"/>De insidentibus aqua,<emph.end type="italics"/> quod scilicet <lb/>magnum pondus ab exigua aqua sustinetur. </s>

<s>Attamen Bo&shy;<lb/>namicus, pag. </s>

<s>476, contrarium opinatur: credit nam aquam <lb/>maris comprimendo attollere ad montium cacumina aquas, per angustas venas <lb/>subterraneas, ad fontes et flumina producenda &rdquo; (MSS. Gal., P. III, T. X, <lb/>fol. </s>

<s>71). </s></p><p type="main">

<s>Le questioni di fisica, delle quali abbiamo dato fin qui gli esempi, o <lb/>erano rimaste indietro, o sovvennero poi a Galileo, nel ripensare al suo di&shy;<lb/>scorso <emph type="italics"/>Delle cose che stanno in sull'acqua,<emph.end type="italics"/> ma il <emph type="italics"/>Saggiatore,<emph.end type="italics"/> che si pu&ograve; <lb/>riguardar come un trattato della Fisica generale di que'tempi, offeriva pi&ugrave; <lb/>largo campo a cos&igrave; fatte fisiche questioni, molte delle quali si trovano accen&shy;<lb/>nate nei manoscritti, o rimaste pur esse in dietro, o sovvenute all'Autore <lb/>dop'avere scritto e pubblicato il suo libro. </s>

<s>Tale sarebbe la seguente relativa <lb/>all'origine delle piogge e delle rugiade: </s></p><p type="main">

<s>&ldquo; Essendo che dalla terra si sollevano continuamente esalazioni sottili, <lb/>tenui, ascendenti, e intanto portano seco vapori pi&ugrave; grossi ed acquei; arri&shy;<lb/>vati a una certa altezza, ch'&egrave; il termine dell'etere nostro ambiente, e l'aria <lb/>purissima, si dilatano e si distendono, e si trattengono o calano abbasso, <lb/>doppo essersi fatta una costipazione e spissitudine di questi vapori, e cos&igrave; si <lb/>fanno le piogge. </s>

<s>Ma non so in che maniera, quand'&egrave; un tempo serenissimo, <pb xlink:href="020/01/2592.jpg" pagenum="217"/>chiaro, e'si abbia subitamente a rannuvolare ogni cosa, farsi grande oscu&shy;<lb/>rit&agrave;, e venir milioni di botti d'acqua a basso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che continuamente si sollevino vapori si fa manifesto in pi&ugrave; maniere <lb/>poich&egrave;, gettando in terra un po'd'acqua e guardando con l'Occhiale, si ved<gap/><lb/>salir con prestezza un fumo, un vapore, e si fa manifesto nella fiamma, che <lb/>continuamente e con gran velocit&agrave; si vede salire ad alto: e cos&igrave; nei carboni <lb/>accesi quel calore va ad alto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Le rugiade non sono altro che vapori, della medesima sorte, e cascan<gap/><lb/>la notte come abbandonati dal Sole &rdquo; (MSS. Gal., P. V, T. IV, fol. </s>

<s>28 a t.) </s></p><p type="main">

<s>Altra questione, relativa a quella trattata nel <emph type="italics"/>Saggiatore,<emph.end type="italics"/> &egrave; la seguente <lb/>intorno al rendere la ragione dell'apparire gli astri di grandezza varia sul&shy;<lb/>l'orizonte. </s>

<s>Narrammo, nel Cap. </s>

<s>X del secondo nostro Tomo (pag. </s>

<s>397), l<gap/><lb/>controversie insorte sopra ci&ograve; tra i Filosofi, e come il Castelli si riducesse <lb/>ad attribuire il fenomeno alla nostra stimativa, che &egrave; varia, secondo che la <lb/>vista &egrave; libera, o s'interpongono tra lei e l'astro corpi, de'quali ci sia nota <lb/>la grandezza e la distanza. </s>

<s>Ora &egrave; da osservar che cos&igrave; insomma risolvevasi <lb/>da Galileo la questione, come apparisce dalla nota cos&igrave; manoscritta: &ldquo; Non <lb/>si pu&ograve; dir che il Sole o la Luna mi appariscon grandi quanto una frittata <lb/>o quanto una torta, o quella cometa mi si rappresenta alla grandezza di un <lb/>uomo, poich&egrave; queste cose possono rappresentarsi anco alla grandezza del fond<gap/><lb/>di un tino o di un quattrino, secondo come si terranno questi lontani dal&shy;<lb/>l'occhio, tra esso e altri oggetti &rdquo; (ivi, fol. </s>

<s>29). </s></p><p type="main">

<s>L'incontro fra il pensiero di Galileo e del Castelli gioverebbe ricerca<gap/><lb/>se fu inconsapevole e fortuito o, essendoselo insieme comunicato, a chi prim<gap/><lb/>di loro fosse sovvenuto, non sempre verificandosi il detto che il maestro sta <lb/>sopra al discepolo, come, per non rammemorare altri esempi, si vede essere <lb/>avvenuto rispetto al &ldquo; problema, perch&egrave; l'acqua, nel zampillare all'in su, s<gap/><lb/>separa nelle parti alte, dove il moto e<gap/> pi&ugrave; lento &rdquo; (MSS. Gal., P. VI, T. II. <lb/>fol. </s>

<s>13). La soluzione &egrave; data nel primo libro <emph type="italics"/>Della misura delle acque cor&shy;<lb/>renti<emph.end type="italics"/> (Bologna 1660, pag. </s>

<s>29), come corollario della proposizione ivi dimo&shy;<lb/>strata, che cio&egrave; le sezioni stanno in ragion reciproca delle velocit&agrave;. </s>

<s>E bench&egrave; <lb/>nel citato luogo autografo, Galileo non risponda a parole, sembra a noi che <lb/>rispondano i numeri, lungo la linea sottosignati, i quali numeri sono scritti <lb/>a mostrare i decrementi della velocit&agrave; dello zampillo quanto giunge pi&ugrave; alto<gap/><lb/>e il reciproco accrescimento delle sezioni, per cui si separano dalla parte di <lb/>sopra le particelle dell'acqua, che di sotto andavano unite. </s>

<s>Sarebbe questa <lb/>nota, scritta cos&igrave; frettolosamente, documento importantissimo per coloro, i <lb/>quali pretendono che il principio, a cui s'informa il trattato del Castelli, fosse <lb/>dovuto a Galileo: ma perch&egrave; di ci&ograve; avremo nella nostra Storia dell'Idraulica <lb/>occasione a pi&ugrave; lungo discorso, ritorniamo a quei materiali sparsi, che si ri&shy;<lb/>feriscono alle cose trattate nel <emph type="italics"/>Saggiatore,<emph.end type="italics"/> fra le quali alcune riguardan la <lb/>luce in s&egrave; stessa, e ne'suoi effetti. </s></p><p type="main">

<s>Meritevole di esser meditata, come quella che specchia lucidamente il <lb/>pensiero di Galileo intorno all'essenza della luce, &egrave; la nota seguente, nella <pb xlink:href="020/01/2593.jpg" pagenum="218"/>quale s'applicano al proposito i concetti metafisici, espressi intorno agl'in&shy;<lb/>divisibili infiniti nel primo dialogo delle Scienze nuove. </s>

<s>&ldquo; Che la luce sia <lb/>incorporea ed istantanea si potrebbe dire, poich&egrave;, avendo un pugnello di pol&shy;<lb/>vere e dandogli fuoco, ella si spande in immenso, e si pu&ograve; vedere com'&egrave; <lb/>ch'ella sia ridotta a'suoi infiniti indivisibili componenti, e fatta senza intro&shy;<lb/>duzione di corpi o di posizione di vacui quanti, ma bene d'infiniti indivisi&shy;<lb/>bili vacui, e cos&igrave; non occupa luogo, e non ricerca tempo d'andare da un <lb/>luogo a un altro &rdquo; (ivi, P. V, T. IV, fol. </s>

<s>28). </s></p><p type="main">

<s>Gli effetti della luce o son considerati nello strumento naturale che &egrave; <lb/>l'occhio, o nell'artificiale che &egrave; il Telescopio, e sovvengono opportune le note <lb/>sparse, relative a questo soggetto, per confermare ora gli crrori, ora il buon <lb/>senso, piuttosto che la scienza di Galileo. </s>

<s>Errava, quando, nelle postille alla <lb/><emph type="italics"/>Libra astronomica,<emph.end type="italics"/> si proponeva di dimostrar contro il Sarsi &ldquo; che altri&shy;<lb/>menti vede l'occhio di quel che i vetri portano le specie &rdquo; (MSS. Cal., P. III, <lb/>T. XIII, fol. </s>

<s>14). Il buon senso poi, piuttosto che la scienza delle rifrazioni, <lb/>gli facevan cogliere il vero, quando al Peripatetico, che diceva mostrare il <lb/>Canocchiale gli oggetti pi&ugrave; grandi, col renderli pi&ugrave; luminosi, contrapponeva <lb/>che &ldquo; se il medesimo oggetto ha da esser veduto sotto maggior angolo, bi&shy;<lb/>sogna che il suo lume e raggi si disperghino &rdquo; (ivi). Che, se nel discorso <lb/>del Sarsi fosse stato verit&agrave;, soggiungeva Galileo, &ldquo; gli oggetti, veduti con tra&shy;<lb/>guardi di mano in mano pi&ugrave; acuti, siccome appariscon maggiori, cos&igrave; dove&shy;<lb/>riano apparir pi&ugrave; lucidi, ma accade tutto l'opposito &rdquo; (ivi). </s></p><p type="main">

<s>Si riferisce a questo argomento un'altra nota autografa, nella quale Ga&shy;<lb/>lileo proponevasi di dimostrar contro il medesimo Sarsi &ldquo; che i raggi visivi <lb/>camminano sempre per linee rette, e non mai per curve, dal qual principio <lb/>immediatamente si conclude gli oggetti visivi, in tutte le distanze quanto si <lb/>voglia diseguali, essere dal medesimo Telescopio sempre, secondo la mede&shy;<lb/>sima proporzione, moltiplicati. </s>

<s>&ldquo; Imperocch&egrave; intendansi due raggi visivi pro&shy;<lb/><figure id="id.020.01.2593.1.jpg" xlink:href="020/01/2593/1.jpg"/></s></p><p type="caption">

<s>Figura 77.<lb/>cedenti dall'occhio libero, secondo le rette linee AG, <lb/>BH (fig. </s>

<s>77), tra le quali in diverse distanze siano <lb/>gli oggetti visivi AB, CD, EF, GII, li quali all'occhio <lb/>appariranno in grandezza uguali, essendo veduti sotto <lb/>il medesimo angolo. </s>

<s>Intendasi poi per mezzo di un <lb/>Telescopio aggrandito l'oggetto AB sino alla gran&shy;<lb/>dezza IK, e i raggi, che vengono dal Telescopio ai <lb/>termini JK, s'intendino prolungati secondo le linee <lb/>rette IP, KQ, sino alle quali si prolunghino le CD, <lb/>EF, GII, terminandole ne'punti LM, NO, PQ, ne'quali <lb/>punti veramente verrebbero a terminare, quando dal <lb/>Telescopio fossero ingrandite tutte secondo la me&shy;<lb/>desima proporzione. </s>

<s>Ma, quando gli oggetti pi&ugrave; remoti <lb/>fossero di mano in mano ingranditi meno, i termini delle medesime linee <lb/>ingranditi caderebbero dentro alle linee IP, KQ, conforme ai punti R, S; <lb/>T, U; X, Y &rdquo; (MSS. Gal., P. III, T. XI, fol. </s>

<s>21). </s></p><pb xlink:href="020/01/2594.jpg" pagenum="219"/><p type="main">

<s>Si conferma da questa proposizione, condotta sui principii della Geome&shy;<lb/>tria elementare, piuttosto che su quelli propri alle rifrazioni; come Galileo, <lb/>nemmen negli ultimi anni della sua vita, conobbe le teorie diottriche del Ca&shy;<lb/>nocchiale, cosicch&egrave; non rimane a lui altro merito, in ordine allo strumento, <lb/>che di averlo applicato a veder distintamente gli oggetti grandi lontani, e i <lb/>piccoli sotto gli occhi. </s>

<s>Quest'uso fatto del Microscopio, ma pi&ugrave; specialmente <lb/>del Telescopio, &egrave; tanto noto, che il volgo stesso ne sa la storia, ma non sanno <lb/>forse, nemmeno i pi&ugrave; informati declamatori del grand'Uomo, quel che noi <lb/>altrove accennammo, e che verrebbe ad accrescergli non poco questa parte <lb/>del merito, che cio&egrave; egli applic&ograve; il Canocchiale anche agli usi della fotome&shy;<lb/>tria. </s>

<s>Nella Lettera sul candore lunare apparisce una tale applicazion manife&shy;<lb/>sta, ma in quegli ultimi anni della sua vita descriveva Galileo stesso al Vi&shy;<lb/>viani la composizione del Fotometro pi&ugrave; squisito, il primo concetto del quale <lb/>pu&ograve; vedersi espresso in questa nota: &ldquo; Drizzando due cannoni, uno verso la <lb/>Luna quasi piena, e l'altro verso l'occidente, subito dopo il tramontar del <lb/>Sole, e ricevendo sopra due carte il lume della Luna, e quello dell'aria pros&shy;<lb/>sima al corpo solare, si potr&agrave; vedere quanto il lume dell'aria si mostri pi&ugrave; <lb/>chiaro di quel della Luna, e, secondo che il Sole si andr&agrave; abbassando, s'in&shy;<lb/>contreranno due lumi, della Luna e del crepuscolo, egualmente chiari &rdquo; <lb/>(MSS. Gal., P. III, T. X, fol. </s>

<s>75). </s></p><p type="main">

<s>Non sempre per&ograve; le questioni, che si agitavano per la mente di Gali&shy;<lb/>leo, erano intorno alle cose discorse ne'suoi propri libri, ma talvolta entra&shy;<lb/>vano nel campo altrui, come per esempio in quello del Gilberto, il pensier <lb/>del quale, fecondo della scienza del secolo XIX, e secondo il quale le attra&shy;<lb/>zioni elettriche e le magnetiche si riducevano al medesimo principio, sem&shy;<lb/>brava una stoltezza al giudizio dello stesso Galileo. </s>

<s>&ldquo; Dicere quod attractio <lb/>magnetis et electri sint principio simili, est idem ac dicere pinnam, dum a <lb/>vento agitur, ab eodem moveri principio ac avis, dum proprio nisu volat &rdquo; <lb/>(ivi, P. V, T. IV, fol. </s>

<s>15). </s></p><p type="main">

<s>Altre volte le proposte questioni non son risolute, cosicch&egrave; si rimangono <lb/>allo stato di una semplice descrizione sperimentale, e Galileo perci&ograve; si con&shy;<lb/>tenta di osservare il semplice fatto, senza dirne le cause, perch'egli ancora <lb/>non le comprende. </s>

<s>Tali sarebbero per esempio quelle relative alla pressione <lb/>ammosferica, e al vacuo lasciato dietro a s&egrave; nel muoversi i corpi velocissi&shy;<lb/>mamente in mezzo all'aria, nella notizia delle quali cause era riposta la <lb/><figure id="id.020.01.2594.1.jpg" xlink:href="020/01/2594/1.jpg"/></s></p><p type="caption">

<s>Figura 78.<lb/>scienza dei fatti seguenti: &ldquo; Accostando un dito o <lb/>mano alla fiamma o lume di candela o lucerna la&shy;<lb/>teralmente, e distaccandola con velocit&agrave;, la fiamma <lb/>ancora con gran velocit&agrave; ti vien dietro lambendo <lb/>la mano &rdquo; (ivi, fol. </s>

<s>28). Sia AB (fig. </s>

<s>78) sifone, e <lb/>dalla bocca A mettasi tanta acqua, che empia la <lb/>parte AC: poi, turando con un dito la bocca A, l'acqua AC non scorrer&agrave; <lb/>mai nell'altra parte CB, in qualsivoglia modo io tenga il sifone, finch&egrave; io non <lb/>levo il dito &rdquo; (ivi, fol. </s>

<s>29). </s></p><pb xlink:href="020/01/2595.jpg" pagenum="220"/><p type="main">

<s>Tali essendo, nella loro pi&ugrave; variata variet&agrave; le materie da inserirsi nei <lb/>Dialoghi nuovissimi, potrebbe sembrar difficile il comporle insieme in unit&agrave;, <lb/>ma era stata giusto da Galileo scelta una tale forma di colloquio, non solo <lb/>per una imitazion platonica come si dice, ma principalmente perch&egrave;, come <lb/>egli stesso scriveva in una lettera al Carcavy (Viviani, Scienza delle propor&shy;<lb/>zioni cit., pag. </s>

<s>80), quella maniera dello scrivere in dialogo gli porgeva assai <lb/>conveniente attacco, per inserirvi i pensieri, che via via gli cascavano in <lb/>mente. </s>

<s>L'artificio usato in tessere quella ghirlanda cos&igrave; varia, che &egrave; il primo <lb/>dialogo delle Scienze nuove, de'fiori rinascenti via via, era quello stesso che <lb/>doveva usarsi, in tessere questi ultimi dialoghi de'fiori rimasti sparsi per <lb/>terra, cadutivi dal troppo colmo canestro. </s>

<s>&Egrave; anzi da osservar che son nate <lb/>a questo modo quasi tutte le scritture di Galileo, le quali possono perci&ograve; dirsi <lb/>una rapsodia de'pensieri, scritti sul primo foglio che capitavagli a mano, <lb/>prima che altro occorresse ad attutarne quel subitaneo fervore. </s>

<s>Di que'fogli <lb/>sparsi si compongono infatti, per la massima parte, i manoscritti, che ci son <lb/>rimasti di lui, da'quali ricopiava e puliva, e metteva in ordine i libri da <lb/>stamparsi. </s></p><p type="main">

<s>Che poi fosse questo modo di fare un abito contratto apparisce dal ve&shy;<lb/>derlo praticato a qualunque occasione, si trattasse di scienza o di rettorica; <lb/>delle speculazioni della mente o delle deliberazioni dell'animo; della pelle&shy;<lb/>grinit&agrave; del concetto o della eleganza della forma. </s>

<s>Occorrendogli, nelle con&shy;<lb/>tinue controversie, di dover descrivere l'indole dei Peripatetici, aveva lavo&shy;<lb/>rato a parte, e teneva in serbo questa specie di apologo: &ldquo; Sembrano i <lb/>Peripatetici, verso Aristotile, quel vetturale, il quale, vedendo pendere la soma <lb/>delle mercanzie mal compartite da una banda, corre a librarla con una grave <lb/>pietra aggiunta dall'altra, quindi di poco, cominciando a declinare dal lato <lb/>dove aggiunse il sasso, il qual di nuovo eccedendo in gravit&agrave;, fa por nuove <lb/>pietre all'incontro: n&egrave; trovando il poco giudizio del mulattiere il giusto equi&shy;<lb/>librio, finalmente, con l'aggiunger molti pesi sopra pesi, fa che il povero <lb/>animale si fiacca le gambe, e resta sotto l'inegual soma oppresso. </s>

<s>Meglio <lb/>da principio cominciare a levar via della roba soverchia &rdquo; (MSS. Gal., P. III, <lb/>T. X, fol. </s>

<s>72). </s></p><p type="main">

<s>Que'Teologi, i quali inopportunamente s'ingerivano della scienza umana, <lb/>pensava Galileo che si potevano pungere con questo discorso: &ldquo; Ancorch&egrave; i <lb/>sacri Teologi siano quelli, che intendono meglio come camminano i moti del <lb/>Sole e delle altre stelle, che non lo sanno gli Astronomi; tuttavia, per rego&shy;<lb/>lare i tempi della Pasqua e delle altre feste mobili, ricorrono, anzi si rimet&shy;<lb/>tono agli Astronomi. </s>

<s>Ma perch&egrave; non regolarsi con la loro sopraeminente <lb/>intelligenza? </s>

<s>&rdquo; (ivi, P. V, T. IV, fol. </s>

<s>15). Altri di cos&igrave; fatti aculei teneva <lb/>preparati, in ripensare alle irragionevolezze degli aristotelici, e alle loro con&shy;<lb/>tradizioni. </s>

<s>&ldquo; Gli avversari tassano me, per avere scritto contro ad autore non <lb/>inteso da me: eppure essi medesimi cascano in questo medesimo errore, men&shy;<lb/>tre contradicono a me, e tanto pi&ugrave; gravemente, quanto &egrave; dubbio se sia vero <lb/>che io non abbia inteso Aristotile. </s>

<s>E non so, se lui fosse vivo, se ei mi ne-<pb xlink:href="020/01/2596.jpg" pagenum="221"/>gasse le mie interpetrazioni. </s>

<s>Ma io che vivo dico bene di non essere stato <lb/>inteso. </s>

<s>Se poi per mia colpa o di loro, questo non determiner&ograve; io. </s>

<s>Potriano <lb/>forse dire non mi avere inteso, perch&egrave; non metteva conto a porre studio <lb/>nelle cose mie, ed affaticarvisi come in quelle di Aristotile, ma io gli rispon&shy;<lb/>der&ograve; che, se non metteva conto lo studiare le cose mie, meno metteva conto <lb/>l'impugnarle &rdquo; (ivi, P. III, T. X, fol. </s>

<s>75). </s></p><p type="main">

<s>All'ufficio poi di diffondere le verit&agrave; della scienza, senza curarsi de'suoi <lb/>contradittori, si sentiva Galileo generosamente eccitato da questo pensiero: <lb/>&ldquo; Se io dover&ograve; leggere in Studio, piccolo frutto si caver&agrave; dalle mie fatiche, <lb/>occupandomi con pochi in cose minime. </s>

<s>Ma se io scriver&ograve; al mondo tutto, <lb/>maggior gloria a me, et utilit&agrave; a quello arrecher&ograve; &rdquo; (ivi, P. III, T. III, fol. </s>

<s>35). <lb/>E mentre il Carcavy era per metter mano alla stampa di tutte le opere sue <lb/>(Viviani, Scienza delle proporz. </s>

<s>cit., pag. </s>

<s>81), voleva s'imprimesse sul fron&shy;<lb/>tespizio queste parole, bench&egrave; nessun altro poi de'successivi editori leggesse <lb/>o intendesse, o comunque sia mettesse in esecuzione il testamento: <emph type="italics"/>&ldquo; Da <lb/>porsi nel titolo del libro di tutte le Opere:<emph.end type="italics"/> Di qui si comprender&agrave; in infi&shy;<lb/>niti esempi qual sia l'utilit&agrave; delle Matematiche in concludere circa alle pro&shy;<lb/>posizioni naturali, e quanto sia impossibile il poter bene filosofare, senza la <lb/>scorta della Geometria, conforme al vero pronunciato di Platone &rdquo; (ivi, P. III, <lb/>T. III, fol. </s>

<s>63 a tergo). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Oltre ai Problemi fisici, scriveva Galileo al Carcavy di averne a portare <lb/>in dialogo dei matematici. </s>

<s>Ora, a questo annunzio, furono le nostre diligenze <lb/>rivolte a cercar quali fossero, e dove potessero ritrovarsi i nuovi materiali <lb/>dispersi, e rimasti fuori di luogo nelle altre costruzioni. </s>

<s>In mezzo a tali sol&shy;<lb/>lecitudini ci venne fatto di fermar l'attenzione sul quarto tomo della parte V <lb/>dei manoscritti galileiani, dove ricorrono qua e l&agrave;, interpolati da note di ar&shy;<lb/>gomento diverso, teoremi e problemi di Geometria, i quali, bench&egrave; tutti ele&shy;<lb/>mentarissimi, ci parve nulladimeno che dalla novit&agrave;, e pi&ugrave; che altro dalla <lb/>fama dell'Autore, partecipassero qualche importanza. </s>

<s>Non son pi&ugrave; che quin&shy;<lb/>dici o sedici, ed essendo scritti dal Viviani, in quella sua ben distinta calli&shy;<lb/>grafia giovanile, possiamo ragionevolmente credere che gli fossero dettati da <lb/>Galileo, quando cieco era costretto di rappresentarsi nella mobilit&agrave; delle im&shy;<lb/>magini le figure illustrative. </s>

<s>Sarebbero di ci&ograve; indizio le dimostrazioni spesso <lb/>spesso confuse e qualche volta sbagliate, che ci occorreranno a notare, ma in&shy;<lb/>tanto si pensava fra noi che di simili teoremi ne doveva essere rimasti addie&shy;<lb/>tro parecchi altri, e forse di maggiore importanza, occorsi allo stesso Galileo, <lb/>mentre cercava i lemmi geometrici alle sue laboriose dimostrazioni delle re&shy;<lb/>ristenze dei solidi, e dei moti locali. </s>

<s>Qualche esempio, in cui ci abbattemmo <lb/>nell'ordinare i libri dei moti accelerati, avvalorava quelle nostre congetture, <pb xlink:href="020/01/2597.jpg" pagenum="222"/>dalle quali poi ne consegu&igrave; la raccolta de'teoremi di Algebra e di Geome&shy;<lb/>tria, che daremo, come parte principalissima di quelle cose matematiche, che <lb/>Galileo intendeva di ridurre in dialogo, affinch&egrave; non si dovessero, con detri&shy;<lb/>mento della sua gloria e della utilit&agrave; degli studiosi, rimaner nell'oblio. </s></p><p type="main">

<s>Essendo le nuove questioni per&ograve; molto pi&ugrave; spezzate delle fisiche e delle <lb/>meccaniche, pareva assai pi&ugrave; difficile a ridurle in unit&agrave; di composizione: e <lb/>mentre si pensava fra noi che, a superare la difficolt&agrave; avrebbe Galileo forse <lb/>usato il medesimo artifizio, che nella seconda, nella terza e nella quarta <lb/>giornata delle Scienze nuove, introducendo cio&egrave; il Salviati, che sopra alcuni <lb/>fogli dell'Accademico legge al Sagredo e a Simplicio le varie proposizioni, <lb/>attenenti a que'matematici soggetti; vedemmo l'opinione ridursi quasi a cer&shy;<lb/>tezza da un frammento di scrittura, ritrovata da noi in certe carte tanto <lb/>informi e disordinate, ne'margini e addentro cos&igrave; corrose e macere dalla <lb/>muffa, che il Bonaventuri non seppe cavarci alcun costrutto, bench&egrave; il Pan&shy;<lb/>zanini l'assicurasse esser quelle tutte robe galileiane, scritte da suo zio Vin&shy;<lb/>cenzio Viviani. </s>

<s>Sopr'una di quelle pagine, dove si pu&ograve; in qualche modo in&shy;<lb/>cominciare a leggerla, o diciam meglio a intenderne il significato, &egrave; scritto: </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Io non ho altra notizia di Geometria, da quella in fuori <lb/>che imparai essendo giovane studente sopra i libri degli Elementi di Euclide, <lb/>per cui temo che le cose scritte in cotesto libriccino dell'Accademico, e che <lb/>voi, signor Salviati, volete leggerei, mi siano per riuscire di troppo difficile <lb/>intelligenza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Non dubitate, signor Simplicio, di averei a trovare mag&shy;<lb/>giore oscurit&agrave;, che nelle dimostrazioni e discorsi intorno ai moti locali: e se <lb/>voi avete bene a mente Euclide vi basta, perch&egrave; possiate gustare il dolce di <lb/>queste vivande rimaste indietro alla mensa, come l'Accademico stesso si <lb/>esprimeva, imbandita dai Matematici antichi nei loro trattati. </s>

<s>Se qualche cosa <lb/>de'principii elementari vi fosse caduta col tempo dalla memoria, non man&shy;<lb/>cher&agrave; di ridurvela la destrezza del signor Sagredo, che, per grande desiderio <lb/>di penetrare addentro ai teoremi dimostrati dal nostro Amico, s'&egrave; reso fa&shy;<lb/>miliari i libri, non d'Euclide solo, ma di Archimede, di Apollonio e di <lb/>Pappo. </s>

<s>&rdquo; </s></p><p type="main">

<s>La nostra Storia fa riflettere cos&igrave; la sua luce sopra questo frammento, <lb/>da non si dubitare ch'egli propriamente non appartenesse a quel dialogo, in <lb/>cui Galileo intendeva di ridurre i Problemi matematici, e si pu&ograve; intendere, <lb/>da quel che ivi si dice, che nella raccolta matematica fatta dal Viviani a det&shy;<lb/>tatura in Arcetri, ora mancano le dimostrazioni e le soluzioni, e ora vi sono <lb/>semplicemente accennate, perch&egrave; il Sagredo v'avrebbe poi supplito, nell'atto <lb/>di farne a Simplicio la spiegazione. </s>

<s>A noi per&ograve; non riman dell'opera che i <lb/>materiali sparsi, ma preparati dall'Autore stesso per costruirla: ond'&egrave; che, <lb/>non potendo consolar d'altro i Lettori, porremo sotto ai loro occhi que'ma&shy;<lb/>teriali stessi, de'quali faremo primi i teoremi di Geometria raccolti dal Vi&shy;<lb/>viani. </s>

<s>Essendo nel manoscritto sopra indicato messi alla rinfusa, per non aver <lb/>gli uni dipendenza alcuna dagli altri, non si potrebbero annoverar con altr'or-<pb xlink:href="020/01/2598.jpg" pagenum="223"/>dine, da quello assiomatico in fuori, cominciando cio&egrave; dalle linee, per pas&shy;<lb/>sare alle superficie, e di l&igrave; ai solidi. </s>

<s>Cos&igrave; dunque faremo, non dimenticando <lb/>che l'ufficio nostro &egrave; di storici, no di editori, e le dimostrazioni si aggiun&shy;<lb/>gono, o si dichiarano in forma di note, non perch&egrave; crediamo che, in cose <lb/>tanto elementari, i Lettori ne abbiano bisogno, ma per dar qualche idea della <lb/>parte che, rappresentandosi il Dramma, Galileo avrebbe affidata al Sagredo. </s></p><p type="main">

<s>&ldquo; PROPOSITIO I, THEOREMA I. &mdash; <emph type="italics"/>In linea AF<emph.end type="italics"/> (fig. </s>

<s>79) <emph type="italics"/>moveantur duo<emph.end type="italics"/><lb/><figure id="id.020.01.2598.1.jpg" xlink:href="020/01/2598/1.jpg"/></s></p><p type="caption">

<s>Figura 79.<lb/><emph type="italics"/>mobilia A, B, unumquodque ubique <lb/>velociter: A vero moveatur velocius <lb/>quam B, et quam rationem habet <lb/>velocitas A, ad velocitatem B, hanc <lb/>habeat AC linea ad CB. </s>

<s>Dico codem <lb/>tempore puncta A, B, si moveantur versus C, punctum C conseculura <lb/>esse. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nisi enim A, B non convenerint in C, convenient primo, si potest fieri, <lb/>infra, in E. </s>

<s>Et quia velocitates sunt inter se ut spatia, per quae eodem tem&shy;<lb/>poris intervallo moventur mobilia; ergo velocitas A, ad velocitatem B, erit <lb/>ut spatium AE ad spatium BE. </s>

<s>Erat autem et ut AC ad CB, quod est im&shy;<lb/>possibile. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Similiter ostendetur quod neque supra numquam convenient. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sed melius: Si quando A pervenerit in C, B non eo pervenit, aut <lb/>supra aut infra perveniet, ut in E, aut F. </s>

<s>Eodem ergo tempore, quo A tran&shy;<lb/>sivit spatium AC, B transivit BE, aut BF: ergo velocitates.... ergo A, B <lb/>convenient in C &rdquo; (MSS. Gal., P. V, T. IV, fol. </s>

<s>22). </s></p><p type="main">

<s>Nel luogo, corrispondente a quello da noi punteggiato, il margine &egrave; cor&shy;<lb/>roso, ma non &egrave; difficile il supplire alle parole ivi scritte, che dovevano esser <lb/>queste o simili: <emph type="italics"/>erunt ut AC ad BE, vel BF, contra propositum,<emph.end type="italics"/> cosicch&egrave; <lb/>nella sua integrit&agrave; la conclusione sarebbe tale: &ldquo; ergo velocitates erunt ut <lb/>AC ad BE, vel BF, contra propositum: ergo A, B convenient in C. &rdquo; </s></p><p type="main">

<s>Il teorema si potrebbe dire un corollario, o forse meglio una trasforma&shy;<lb/>zione del IIo Dei moti equabili (Alb. </s>

<s>XIII, 151), sicch&egrave; partecipa del mecca&shy;<lb/>nico, come ne partecipa il seguente, a cui si riferiscono queste notizie: In <lb/>una lettera del d&igrave; 6 Febbraio 1635 cos&igrave; il Cavalieri mandava a dire a Ga&shy;<lb/>lileo da Bologna: &ldquo; Io scrissi gi&agrave; in una mia a V. S. E. un quesito mec&shy;<lb/>canico, ma perch&egrave; non me ne dice cosa alcuna, temo che la lettera non si <lb/>sia smarrita. </s>

<s>Il quesito era questo: Data una ruota volubile intorno al suo <lb/>asse, trovar modo di moverla con un'altra ruota, pur volubile intorno al <lb/>proprio asse, in tal maniera che, perseverando la medesima velocit&agrave; della <lb/>ruota movente, la ruota mossa vada sempre crescendo di velocit&agrave;. </s>

<s>Io pensai <lb/>che ci&ograve; non potesse farsi con le ruote solite dentate, n&egrave; con le funi avvol&shy;<lb/>tele intorno, camminando ambedue con pari velocit&agrave;, ed anco con pari cir&shy;<lb/>colazioni, quando sono di diametro uguale: ovvero con pari velocit&agrave; e con <lb/>dispari circolazioni, cio&egrave; conforme alla reciproca proporzione de'diametri, <lb/>quando questi sono diseguali. </s>

<s>E perci&ograve; venni in questo parere che bisognasse <pb xlink:href="020/01/2599.jpg" pagenum="224"/>fare una cosa tale, quale fanno qua a Bologna in particolare questi, che tra&shy;<lb/>filano l'argento falso &rdquo; (Campori, Carteggio gal., Modena 1881, pag. </s>

<s>430). </s></p><p type="main">

<s>Galileo, per rispondere al quesito, prepar&ograve; una serie di proposizioni re&shy;<lb/>lative al moto delle ruote, mosse da altre ruote, e delle quali non ci &egrave; ri&shy;<lb/>masto memoria che della seguente, annunziata gi&agrave; dallo stesso Cavalieri: </s></p><p type="main">

<s>&ldquo; PROPOSITIO II, THEOREMA II. &mdash; <emph type="italics"/>Le circonferenze di due ruote disu&shy;<lb/>guali, che girino, vanno con la medesima velocit&agrave;, quando le circolazioni <lb/>hanno reciproca proporzione dei diametri &rdquo;<emph.end type="italics"/> (MSS. Gal., P. V, T. IV, <lb/>fol. </s>

<s>29. </s></p><p type="main">

<s>Il teorema, a cui manca la dimostrazione, pu&ograve; formularsi pi&ugrave; chiara&shy;<lb/>mente cos&igrave;: <emph type="italics"/>Due ruote di differente raggio vanno ugualmente veloci, quando <lb/>i numeri dei giri, fatti dall'una e dall'altra nel medesimo tempo, son <lb/>reciprocamente proporzionali alle lunghezze dei raggi.<emph.end type="italics"/> Le velocit&agrave; saranno <lb/>uguali, quando ne'medesimi tempi gli spazi sono uguali. </s>

<s>Ora, chiamati R, <emph type="italics"/>r<emph.end type="italics"/><lb/>i raggi della ruota maggiore e della minore, gli spazi percorsi nelle loro cir&shy;<lb/>colazioni sono 2<foreign lang="greek">p</foreign>R, 2<foreign lang="greek">p</foreign><emph type="italics"/>r.<emph.end type="italics"/> Sia N il numero, per cui, moltiplicato 2<foreign lang="greek">p</foreign><emph type="italics"/>r,<emph.end type="italics"/> si <lb/>rende uguale a 2<foreign lang="greek">p</foreign>R: avremo 1:N=<emph type="italics"/>r<emph.end type="italics"/>:R. </s>

<s>Ma se uno &egrave; il numero dei <lb/>giri della ruota maggiore, N rappresenta il numero de'giri della minore, dun&shy;<lb/>que &egrave; vero il teorema. </s></p><p type="main">

<s>La prima proposizione d&igrave; Geometria pura, da ordinarsi fra quelle rac&shy;<lb/>colte dal Viviani, &egrave; tale: Sia il triangolo BAC (fig. </s>

<s>80), la base BC del <lb/><figure id="id.020.01.2599.1.jpg" xlink:href="020/01/2599/1.jpg"/></s></p><p type="caption">

<s>Figura 80.<lb/>quale intendasi prolungata indefini&shy;<lb/>tivamente verso K. </s>

<s>Si tirino dal ver&shy;<lb/>tice A le linee AF, AK, in modo che, <lb/>de'triangoli, i quali vengono esse a <lb/>formare col lato AC, e con le inter&shy;<lb/>sezioni del prolungamento della base <lb/>BC, il primo sia uguale, il secondo <lb/>doppio, il terzo triplo ecc. </s>

<s>del trian&shy;<lb/>golo BAC. </s>

<s>Se dal mezzo di BC, qual <lb/>sia D, si conduce una parallela all'AB e si prolunga, prima fino a incontrare <lb/>il lato AF in G, poi il lato AK in H, e via via gli altri nei punti conseguenti <lb/>O, P, ecc.; dimostra Galileo che DE:EG=2:1; DE:EH=3:2; DE:EO <lb/>=4:3; DE:EP=5:4, e cos&igrave; sempre: ossia, secondo il linguaggio antico, <lb/>che DE ad EG, ad HE, ad EO, ad EP, ecc., sta in ragion dupla, sesquialtera, <lb/>sesquiterza, sesquiquarta, ecc. </s></p><p type="main">

<s>&ldquo; PROPOSITIO III, THEOREMA III. &mdash; <emph type="italics"/>Sit triangulum ABC, cuius latus <lb/>BC infinite extensum ad K: sectaque BC bifariam in puncto D, ducatur <lb/>DH aequidistans BA, et constituatur FAC triangulum aequale CAB, cu&shy;<lb/>ius latus AF secet DH in G. </s>

<s>Dico lineam DE duplam esse lineae EG. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ducatur EL aequidistans BF: et quia DE aequidistat BA, estque BD <lb/>aequalis DC; erit CE aequalis EA. </s>

<s>Sed aequidistat EL ipsi BF, ergo FL ae&shy;<lb/>quatur LA, estque triangulum ALE simile triangulo AFC. </s>

<s>Ergo AEL est <lb/>quarta pars ipsius ACF et eamdem ob causam EDC erit quarta pars BAC, <pb xlink:href="020/01/2600.jpg" pagenum="225"/>et positum est BCA aequale ACF. </s>

<s>Ergo AEL aequatur DEC. </s>

<s>Et quia est ut <lb/>FB ad BD ita FA ad AG; erit AG quarta pars ipsius AF et LA dupla AG. </s>

<s><lb/>Quare triangulum LAE hoc est DEC, duplum trianguli AEG. </s>

<s>Et est CD linea <lb/>aequalis BD; ergo DE est dupla EG. &rdquo; </s></p><p type="main">

<s>&ldquo; Sed, si constituamus triangulum KAC duplum trianguli BAC, dico <lb/>lineam DE sesquialteram esse ipsius EH, quod simili modo ostendetur. </s>

<s>Pro&shy;<lb/>ducta enim EM aequidistans BK, quia AEM est quarta pars KAC, et EDC <lb/>quarta pars CAB, estque ACK duplum BCA; erit MEA duplum DCE, et tri&shy;<lb/>plum AEH, cum sit AH sexta pars ipsius AK, et tertia dimidiae AM. </s>

<s>Ergo <lb/>DCE, cum sit dimidium triplae AEH, erit ipsius AEH sesquialter: hoc est DE <lb/>sesquialtera EH. &rdquo; </s></p><p type="main">

<s>&ldquo; Similiter, si ponamus triangulum triplum BAC, erit DE sesquitertia <lb/>lineae consequentis: et, si quadruplum, sesquiquarta: et, si quintuplum, <lb/>sesquiquinta, et sic in infinitum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Oppositum huius theorematis facile, per reductionem ad impossibile, <lb/>ostendetur &rdquo; (ibid., fol. </s>

<s>21). </s></p><p type="main">

<s>&ldquo; PROPOSITIO IV, THEOREMA IV. &mdash; <emph type="italics"/>Dato il triangolo ABC<emph.end type="italics"/> (fig. </s>

<s>81), <lb/><figure id="id.020.01.2600.1.jpg" xlink:href="020/01/2600/1.jpg"/></s></p><p type="caption">

<s>Figura 81.<lb/><emph type="italics"/>siano divisi i due lati AB, AC per mezzo, <lb/>nei punti E, D: e dagli angoli C, B tirinsi <lb/>le linee CE, BD, e dal punto A la linea <lb/>AGF. </s>

<s>Dico che la BC &egrave; dirisa per mezzo, e <lb/>che le parti GF, GE, GD, ciascuna di loro, <lb/>sono la met&agrave; dei loro rimanenti pezzi &rdquo;<emph.end type="italics"/><lb/>(ivi, fol. </s>

<s>28). </s></p><p type="main">

<s>Questa proposizione &egrave; lacile veder come <lb/>sia quella stessa, comunemente applicata dai <lb/>Matematici, per dimostrare dove stia il centro della gravit&agrave; nel triangolo, e <lb/>Galileo la rende puramente geometrica, e cos&igrave; dimostra le relazioni, che pas&shy;<lb/>sano fra le linee e fra le superficie, astraendo dal peso. </s>

<s>La dimostrazione <lb/>per&ograve; non &egrave; bella, come quasi sempre riescon quelle condotte dagli assurdi, <lb/>ed &egrave; a notare, per renderla pi&ugrave; chiara, come s'usa le prime due volte la <lb/>parola <emph type="italics"/>trapezio,<emph.end type="italics"/> per indicar quello, che propriamente &egrave; un <emph type="italics"/>quadrilatero.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Della linea divisa in mezzo, cos&igrave; si dimostra: Poich&egrave;, se non &egrave; divisa <lb/>pel mezzo, dividasi nel punto H, e giungasi AH. </s>

<s>E perch&egrave; il triangolo BDA <lb/>&egrave; la met&agrave; di tutto, ed ancora il triangolo CEA &egrave; la met&agrave; di tutto; lascisi il <lb/>comun trapezio EGDA: rimarranno i due triangoli EGB, CDG uguali tra <lb/>loro, ed uguali saranno tutt'a quattro i triangoli EGB, DGC, AGE, DGA, e <lb/>i triangoli AGC, AGB uguali. </s>

<s>Giungasi GH: il trapezio AGHC &egrave; uguale al <lb/>trapezio ABHG, cio&egrave; la met&agrave; di tutto il triangolo. </s>

<s>Ma ancora il triangolo AHC <lb/>&egrave; la met&agrave; di tutto, adunque il maggiore al minore sar&agrave; uguale. </s>

<s>&Egrave; dunque <lb/>la BC divisa in mezzo nel punto F, e per&ograve; il triangolo BGC eguale a cia&shy;<lb/>scuno dei triangoli BGA. CGA, e le loro met&agrave; uguali ancora tra di loro, e <lb/>due di loro met&agrave; doppie di una: cio&egrave; il triangolo AGB doppio del triangolo <lb/>GBF: cio&egrave; la linea AG doppia della GF &rdquo; (ivi). </s></p><pb xlink:href="020/01/2601.jpg" pagenum="226"/><p type="main">

<s>&ldquo; PROPOSITIO V, PROBLEMA I. &mdash; <emph type="italics"/>Proponitur linea AB<emph.end type="italics"/> (fig. </s>

<s>82), <emph type="italics"/>in C <lb/>secta, cui perpendicularis est DB: circulum possumus describere transeun&shy;<lb/>tem per signa A, C, et ipsam DB tangentem. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Dividatur AC bifariam in E, a quo erecta perpendicularis EF, media <lb/><figure id="id.020.01.2601.1.jpg" xlink:href="020/01/2601/1.jpg"/></s></p><p type="caption">

<s>Figura 82.<lb/>proportionalis inter AB, BC, et ab F super DB perpen&shy;<lb/>dicularis FG ducatur. </s>

<s>Dico, facto centro F, intervallo FG, <lb/>esse petitum &rdquo; (ivi, fol. </s>

<s>25). </s></p><p type="main">

<s>La proposta soluzione sar&agrave; vera, quando prima di <lb/>tutto s'avr&agrave; dimostrato che AF, FC, FG sono uguali, e <lb/>poi che alla BG competono le propriet&agrave; delle tangenti al <lb/>cerchio. </s>

<s>Quanto alla prima parte, la verit&agrave; resulta dalla <lb/>seguente serie di equazioni: FC2=EF2+EC2=EF2+ <lb/>(EB&mdash;CB)2=EF2+EB2&mdash;2EB.CB+CB2=AB.BC+EB2&mdash; <lb/>2EB.CB+CB2=BC(AB+CB&mdash;2EB)+EB2. </s>

<s>Ma le quantit&agrave; dentro <lb/>parentesi sono zero, dunque FC2=EB2, e perci&ograve; FC=EB=FG. </s>

<s>La verit&agrave; <lb/>della seconda parte della soluzion del problema galileiano si rende manifesta <lb/>dall'essere GB uguale alla FE, la quale per supposizione &egrave; media fra la se&shy;<lb/>cante AB, e la sua parte esterna CB, e perci&ograve;, per la XXXVI del terzo di <lb/>Euclide, competono alla BG le propriet&agrave; delle tangenti il cerchio. <lb/><figure id="id.020.01.2601.2.jpg" xlink:href="020/01/2601/2.jpg"/></s></p><p type="caption">

<s>Figura 83.</s></p><p type="main">

<s>&ldquo; PROPOSITIO VI, THEOREMA V. &mdash; <emph type="italics"/>Sit sector ABDC<emph.end type="italics"/><lb/>(fig. </s>

<s>83) <emph type="italics"/>bifariam sectus in D: iunctis AD, BC constat <lb/>sectorem aequari rectangulo contento sub AD et arcu <lb/>BD; triangulum vero ABC aequatur rectangulo BEA. <lb/>Ergo, si ponatur arcus BF aequalis rectae BE, circuli <lb/>portio BDC aequabitur contento sub AE, DF, et con&shy;<lb/>tento sub BD, ED &rdquo;<emph.end type="italics"/> (ibid., fol. </s>

<s>25). </s></p><p type="main">

<s>Abbiamo infatti BDC=AB.BD&mdash;BE.AE=(AE+ED)BD&mdash; <lb/>BE.AE=AE.BD+ED.BD&mdash;BE.AE=AE(BD&mdash;BE)+ED.BD. <lb/>Ond'&egrave; che, posto BE=BF, ed essendo BD&mdash;BF=DF, si trova esser <lb/>vero che BDC &egrave; uguale ad AE.DF+ED.BD. </s></p><p type="main">

<s>Accennammo che queste proposizioni geometriche furono dimostrate da <lb/>Galileo all'occasione o di studiare nei matematici antichi, o di dimostrare i <lb/>varii lemmi per la sua Meccanica, di che abbiamo intanto un esempio nel <lb/>seguente problema, nato in mezzo alle ricerche del primo lemma, preparato <lb/><figure id="id.020.01.2601.3.jpg" xlink:href="020/01/2601/3.jpg"/></s></p><p type="caption">

<s>Figura 84.<lb/>in servigio della XXXVI proposizione, scritta nel <lb/>terzo Dialogo delle Scienze Nuove. </s></p><p type="main">

<s>&ldquo; PROPOSITIO VII, PROBLEMA II. &mdash; <emph type="italics"/>Appli&shy;<lb/>care dalla cima B<emph.end type="italics"/> (fig. </s>

<s>84) <emph type="italics"/>del semicircolo ABC <lb/>una linea, come BHG, sicch&egrave; la HG sia uguale <lb/>alla data LE. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Perch&egrave;, giunta KC, sar&agrave; BC lato del qua&shy;<lb/>drato inscritto nel cerchio, applichisi alla linea <lb/>LE un rettangolo eguale al quadrato BC, che ecceda d'una figura quadrata, <lb/>e sia questo EML. </s>

<s>E perch&egrave; il rettangolo EML &egrave; uguale al quadrato BC, <pb xlink:href="020/01/2602.jpg" pagenum="227"/>sar&agrave; ML minore di BC. </s>

<s>Si tiri dal punto B la BH eguale alla ML, e pro&shy;<lb/>lunghisi insino in G: dico, ecc. </s>

<s>&rdquo; (ivi). </s></p><p type="main">

<s>&Egrave; stato fatto EM.ML=BC2, e per il detto lemma alla proposi&shy;<lb/>zione XXXVI (Alb. </s>

<s>XIII, 214) anche BG.BH=BC2. </s>

<s>Dunque EM.ML= <lb/>BG.BH. </s>

<s>Ed essendo BH=ML per costruzione, sar&agrave; EM=BG e perci&ograve; <lb/>HG=LE. </s></p><p type="main">

<s>&ldquo; PROPOSITIO VIII, THEOREMA VI. &mdash; <emph type="italics"/>Exagonus circumscriptus exagoni <lb/>inscripti est sesquitertius. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Trigonus circulo circumscriptus duplus est exagoni inscripti: circum&shy;<lb/>scripti vero est sesquialterus; quare exagonus circumscriptus exagoni inscripti <lb/>est sesquitertius &rdquo; (ibid., fol. </s>

<s>25). </s></p><p type="main">

<s>Chiamato C l'esagono circoscritto, I l'inscritto, e T il trigono, le due <lb/>equazioni T=2I, T=(1+1/2) C danno C:I=4:3. </s></p><p type="main">

<s>&ldquo; PROPOSITIO IX, THEOREMA VII. &mdash; <emph type="italics"/>Quodratum circulo circumscri&shy;<lb/>ptum, ad circulum, minorem habet rationem quam circulus ad quadra&shy;<lb/>tum inscriptum. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Patet, nam circumscriptum latus ad latus inscripti est, ut latus in&shy;<lb/>scripti ad semidiametrum. </s>

<s>Sed quarta pars circumferentiae est maior latere <lb/>quadrati inscripti, ergo latus circumscripti, ad quartam partem peripheriae, <lb/>minorem habet proportionem quam quarta pars circumferentiae, ad latus <lb/>inscripti. </s>

<s>Est autem ut latus circumscripti, ad quartam partem peripheriae, <lb/>ita circumscriptum quadratum ad circulum. </s>

<s>Ut autem quarta pars periphe&shy;<lb/>riae, ad latus inscripti, ita circulus ad inscriptum, ergo circumscriptum, ad <lb/>circulum, minorem habet rationem, quam circulus ad inscriptum &rdquo; (ibid., <lb/>fol. </s>

<s>28). <lb/><figure id="id.020.01.2602.1.jpg" xlink:href="020/01/2602/1.jpg"/></s></p><p type="caption">

<s>Figura 85.</s></p><p type="main">

<s>Essendo il quadrato circoscritto doppio all'inscritto, <lb/>ossia (fig. </s>

<s>85) CD2=2AB2, avremo CD2:AB2=2:1= <lb/>2AO2:AO2=AB2:AO2; onde CD/AB=AB/AO. </s>

<s>Chiamata <lb/>Ca.AB l'arco, sar&agrave; questa maggiore dell'AB corda e
<lb/>perci&ograve; CD/(Ca.AB) &lt;AB/AO. </s>

<s>Di qui si potrebbe concluderne <lb/>CD/Ca.AB&lt;Ca.AB/AO, ma non si vede la ragione di quell'altra disuguaglianza <lb/>conclusa da Galileo CD/Ca.AB&lt;Ca.AB/AB, e ch'egli stesso mette sotto questa <lb/>forma: <emph type="italics"/>Ergo latus circumscripti, ad quartam partem periferiae, mi&shy;<lb/>norem habet proportionem quam quarta pars circumferentiae, ad latus <lb/>inscripti.<emph.end type="italics"/></s></p><p type="main">

<s>Essendo inoltre CD:<foreign lang="greek">p</foreign>.AO/2=CD2:<foreign lang="greek">p</foreign>.AO.CD/2=CD2:<foreign lang="greek">p</foreign>.AO2, &egrave; <lb/>perci&ograve; verissimo che <emph type="italics"/>ut latus circumscripti ad quartam partem periferiae, <lb/>ita circumscriptum quadratum ad circulum,<emph.end type="italics"/> ma che poi <emph type="italics"/>ut quarta pars <lb/>periferiae, ad latus inscripti, ita circulus ad inscriptum,<emph.end type="italics"/> non ci &egrave; riu-<pb xlink:href="020/01/2603.jpg" pagenum="228"/>scito dimostrarlo: non ci &egrave; riuscito di dimostrare cio&egrave; come <foreign lang="greek">p</foreign>.AO/2:AB= <lb/><foreign lang="greek">p</foreign>.AO2:AB2, perch&egrave; essendo <foreign lang="greek">p</foreign>.AO/2:AB=<foreign lang="greek">p</foreign>.AO.AB/2:AB2 bisognerebbe <lb/>che fosse AB/2=AO. </s></p><p type="main">

<s>Qualcuno, accecato nella mente da quel bagliore di luce, di che la fama <lb/>ha circondato il nome di Galileo, o, come altrimenti si potrebbe dire, per&shy;<lb/>duto il senno, non avr&agrave; forse difficolt&agrave; ad ammettere, persuaso dell'infalli&shy;<lb/>bile magistero dell'Uomo divino, che la met&agrave; del lato del quadrato inscritto <lb/>nel circolo sia uguale al raggio. </s>

<s>Ma noi che siamo avvezzi oramai a farci <lb/>colle mani il solecchio, e che possiamo perci&ograve; vedere distintamente nella spera <lb/>luminosa ogni macchia, crediamo che una di queste fra le pi&ugrave; nere consi&shy;<lb/>sta nell'essersi per isbaglio attribuito alle linee quel ch'&egrave; proprio dei soli <lb/>quadrati, essendo veramente il quadrato del raggio uguale alla met&agrave; del qua&shy;<lb/>drato inscritto. </s></p><p type="main">

<s>Che Galileo abbia veramente commessi sbagli, nelle pi&ugrave; sottili questioni <lb/>della Meccanica, &egrave; stato, nella nuova Storia, dimostrato con tanti esempi, da <lb/>doverne rimanere oramai persuaso ognuno, che non abbia ereditata la ca&shy;<lb/>parbiet&agrave;, o, per pi&ugrave; vero dire, la dissennatezza dei peripatetici antichi. </s>

<s>Ma <lb/>che il grand'Uomo abbia sbagliato, anche in cose riguardanti la Geometria <lb/>pi&ugrave; elementare, viene ora l'occasione di mostrarlo a coloro, i quali fossero <lb/>rimasti o irritati o incerti intorno al giudizio, che del Nostro pronunziava il <lb/>Cartesio. </s>

<s>A noi non riesce d'attribuir la sentenza del Filosofo francese, che <lb/>diceva esser Galileo poco versato nella Geometria, a rivalit&agrave; o ad invidia, <lb/>dietro i fatti, che abbiamo a rivelare. </s></p><p type="main">

<s>Troviamo che talvolta lo sbaglio &egrave; subito riconosciuto, come per esem&shy;<lb/>pio in questa proposizione, la quale, non appena Galileo ha pronunziata, che <lb/><figure id="id.020.01.2603.1.jpg" xlink:href="020/01/2603/1.jpg"/></s></p><p type="caption">

<s>Figura 86.<lb/>subito la condanna di falsa. </s>

<s>&ldquo; Sit <lb/>triangulum rectangulum ABC (figu&shy;<lb/>ra 86), et AB sit aequalis BC, et se&shy;<lb/>cetur bifariam AC in D, et conne&shy;<lb/>ctatur BD, sitque AI ipsi CB parallela, <lb/>positaque AE, ipsi AB aequalis, erunt <lb/>CA, AE, AD continue proportionales. </s>

<s><lb/>Secetur CB bifariam in F, et conne&shy;<lb/>ctatur EF. </s>

<s>Dico quod, si protrahatur <lb/>quaelibet linea, ex puncto C ad lineam AI, ut puta CGHI, esse proportionales <lb/>CI, IG, IH. &rdquo; Ma subito la stessa mano di Galileo, che aveva scritto, sog&shy;<lb/>giunge: <emph type="italics"/>falsa est.<emph.end type="italics"/> (MSS. Gal., P. V, T. II, fol. </s>

<s>176). </s></p><p type="main">

<s>Talvolta per&ograve; si trova che, caduto Galileo in errori ancora pi&ugrave; pa&shy;<lb/>tenti di questo, vi persiste lungamente, senza poter risorgere a proseguire <lb/>il cammino. </s>

<s>Riuscirebbe la cosa incredibile a noi stessi, se non ne aves&shy;<lb/>simo il documento certissimo nelle carte, non dettate al Viviani, all'Am-<pb xlink:href="020/01/2604.jpg" pagenum="229"/>brogetti o ad altri, ma scritte dalla propria mano dell'Autore, con caratteri <lb/>cos&igrave; scolpiti, da non valer per scusa il non essersi potuto aiutare dei segni <lb/>figurativi. </s></p><p type="main">

<s>Nel quarto teorema degli Elementi Euclide si propone di dimostrare che, <lb/>se una linea retta sia comunque segata in due, il quadrato di tutta sar&agrave; <lb/>uguale ai quadrati delle parti, e al rettangolo contenuto due volte dalle dette <lb/>parti. </s>

<s>Galileo, volendo per suo studio confrontare questa proposizione coi nu&shy;<lb/>meri, ne traeva un corollario tanto falso, che della falsit&agrave; si avvedrebbe qua&shy;<lb/>lunque scolaretto, a cui si dicesse che la somma de'quadrati delle parti &egrave; <lb/>uguale al doppio del rettangolo contenuto sopra esse parti. </s>

<s>La cosa, ripetiamo, <lb/>ci sembrerebbe incredibile, se non avessimo sotto gli occhi il foglio, sopra <lb/>il quale la stessa mano propria di Galileo scrisse queste parole: </s></p><p type="main">

<s>&ldquo; Quando si domanda che proportione habbia il minor numero col mag&shy;<lb/>giore, si dice un <emph type="italics"/>sub,<emph.end type="italics"/> come 7 a 3, <emph type="italics"/>dupla sesquitertia.<emph.end type="italics"/> Domandato di 3 a 7, <lb/>si chiamer&agrave; <emph type="italics"/>subdupla sesquiterlia. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Per confrontar con i numeri le proportioni del 2&deg; Libro, come della <lb/>quarta, si fa a questo modo. </s>

<s>Sia una linea retta, 8 palmi per es., segata in <lb/>qualsivoglia modo: v. </s>

<s>g. </s>

<s>che una parte sia 5, e l'altra sia 3. I quadrati della <lb/>linea che &egrave; 5, e di quella che &egrave; 3 sono uguali alli rettangoli contenuti due <lb/>volte dalle dette linee, cio&egrave; da 5 e 3, e si fa in questa maniera: si raddop&shy;<lb/>piano i numeri di questi quadrati in s&egrave; stessi, come 5 via 5 fa 25, e 3 via 3 <lb/>nove: 25 e 9 fa 34. Cos&igrave; ha da tornare raddoppiandonelo &rdquo; (MSS. Gal., P. V, <lb/>T. IV, fol. </s>

<s>27). </s></p><p type="main">

<s>Chi crederebbe che Galileo fosse stato capace di scrivere e d'insegnare <lb/>sul serio che, raddoppiando il cinque via tre deve tornar trentaquattro, come <lb/><figure id="id.020.01.2604.1.jpg" xlink:href="020/01/2604/1.jpg"/></s></p><p type="caption">

<s>Figura 87.<lb/>conferma del nuovo corollario da soggiun&shy;<lb/>gersi dopo la IV del secondo di Euclide <lb/>in questa maniera: La somma dei quadrati <lb/>delle due parti, in cui sia segata una linea, <lb/>o diviso un numero, &egrave; uguale al doppio del <lb/>rettangolo contenuto, o del prodotto formato <lb/>dalle dette parti? </s>

<s>Che il non tornare il conto <lb/>del cinque via tre pi&ugrave; cinque via tre uguale <lb/>a 34, non fosse bastante a persuadere quella <lb/>mente divina, che il corollario era falso, <lb/>resulta dal vederlo applicato, come una <lb/>verit&agrave; approvatissima in Geometria, a un frammento di proposizione, scritto <lb/>in quel carattere cos&igrave; scolpito, che rivela lo stato della pi&ugrave; valida virilit&agrave; di <lb/>Galileo. </s></p><p type="main">

<s>Riferendosi alla nostra figura 87, quel frammento &egrave; tale: &ldquo; &rect; <emph type="italics"/>bg<emph.end type="italics"/> ae&shy;<lb/>quatur &rect;is <emph type="italics"/>bf.fg<emph.end type="italics"/> et 2 &rect; <emph type="italics"/>bfg.<emph.end type="italics"/>pro &rect; <emph type="italics"/>bf<emph.end type="italics"/> sumatur &rect; <emph type="italics"/>hfg,<emph.end type="italics"/> erit &rect; <emph type="italics"/>bg<emph.end type="italics"/><lb/>aequale duobus &rect; <emph type="italics"/>bfg,<emph.end type="italics"/> &rect;o <emph type="italics"/>bf<emph.end type="italics"/> idest &rect;o <emph type="italics"/>hfg<emph.end type="italics"/> cum &rect; <emph type="italics"/>fg,<emph.end type="italics"/> id autem idem <lb/>est ae si dicas &rect; <emph type="italics"/>bg<emph.end type="italics"/> esse aequale 2 &rect; <emph type="italics"/>bfg,<emph.end type="italics"/> 2 &rect; <emph type="italics"/>egf<emph.end type="italics"/> et 2 &rect; <emph type="italics"/>fg. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><pb xlink:href="020/01/2605.jpg" pagenum="230"/><p type="main">

<s>&ldquo; ex &rect;o <emph type="italics"/>bg<emph.end type="italics"/> demitur 2 &rect; <emph type="italics"/>bfg<emph.end type="italics"/> et 1 &rect; <emph type="italics"/>gf,<emph.end type="italics"/> remanet &rect; <emph type="italics"/>bf<emph.end type="italics"/> aequale <lb/>2 &rect; <emph type="italics"/>egf<emph.end type="italics"/> minus 1 &rect; <emph type="italics"/>gf,<emph.end type="italics"/> quod est &rect; <emph type="italics"/>hfg<emph.end type="italics"/> aequale &rect;o <emph type="italics"/>bf .... &rdquo;<emph.end type="italics"/> (MSS. <lb/>Gal., P. V, T. II, a tergo del fol. </s>

<s>54). </s></p><p type="main">

<s>Essendosi dunque concluso BG2=2BFG+2EGF+2FG2, fatta la <lb/>indicata sottrazione, avremo BG2&mdash;2BFG&mdash;FG2=2EGF+FG2, ossia <lb/>BF2=2EGF+FG2. </s>

<s>Dunque &ldquo; quadratum BF aequale est duobus rectan&shy;<lb/>gulis EGF <emph type="italics"/>plus,<emph.end type="italics"/> et non <emph type="italics"/>minus<emph.end type="italics"/> uno quadrato GF &rdquo; come dice rimaner dalla <lb/>fatta sottrazione Galileo. </s>

<s>Dall'altra parte, procedendo per le vie pi&ugrave; spedite, <lb/>se BF2=HFG, come si suppone, e se HF=HG+FG=2GE+FG, <lb/>abbiamo immediatamente BF2=(2GE+FG)FG, ossia BF2=2EGF+GF2, <lb/>e non 2EGF&mdash;GF2. </s>

<s>La radice del quale errore consiste nel persistere in <lb/>ritener per vero che il quadrato di una delle parti sia uguale al doppio del <lb/>rettangolo contenuto da ambedue, meno il quadrato dell'altra parte. </s>

<s>Ci&ograve; poi <lb/>rende credibile che, nella proposizione ultimamente trascritta, avendo Gali&shy;<lb/>leo sotto gli occhi un triangolo rettangolo isoscele, e preoccupato da quel <lb/>che solamente &egrave; vero nel Teorema pitagorico, mettesse che l'ipotenusa &egrave; <lb/>doppia o dell'uno o dell'altro uguale cateto. </s>

<s>Fatta la qual digressione, per <lb/>secondare il genio di coloro, che amano di giudicare gli uomini, non dal&shy;<lb/>l'esteriore apparenza, ma dai loro pi&ugrave; intimi affetti e pensieri; liberi di noi <lb/>stessi, riduciamoci in via. </s></p><p type="main">

<s>&ldquo; PROPOSITIO X, THEOREMA VIII. &mdash; <emph type="italics"/>Si tres lineae fuerint proportio&shy;<lb/>nales, quadratum primae, ad circulum secundae, est ut periferia quadrati <lb/>primae, ad periferiam circuli tertiae &rdquo;<emph.end type="italics"/> (MSS., Gal., P. V, T. IV, a tergo <lb/>del fol. </s>

<s>23). </s></p><p type="main">

<s>Siano le tre linee A, B, C: essendo per supposizione continue propor&shy;<lb/>zionali abbiamo B2=A.C, o anche AB2=A2C, d'onde A2:B2=A:C, <lb/>ossia A2:<foreign lang="greek">p</foreign>B2/4=4A:<foreign lang="greek">p</foreign>C, Ma<foreign lang="greek">p</foreign>B2/4 esprime il circolo che ha per diame&shy;<lb/><figure id="id.020.01.2605.1.jpg" xlink:href="020/01/2605/1.jpg"/></s></p><p type="caption">

<s>Figura 88.<lb/>tro B, 4A il perimetro del quadrato A, <foreign lang="greek">p</foreign>C <lb/>la periferia del circolo, che ha per dia&shy;<lb/>metro C, <emph type="italics"/>unde patet propositum.<emph.end type="italics"/></s></p><p type="main">

<s>In mezzo allo studio della mirabile <lb/>generazione delle spirali occorse a Galileo <lb/>un nuovo teorema di Geometria, di cui <lb/>ora diremo la qualit&agrave; e il modo dell'in&shy;<lb/>venzione. </s>

<s>Sia il quadrante ABCD (fig. </s>

<s>88), <lb/>e tirata la CF parallela ad AD, fatto cen&shy;<lb/>tro in C, e col raggio AC, descrivasi il <lb/>settore ACF, che &egrave; facile vedere come sia <lb/>uguale allo stesso quadrante, essendo questo misurato da <foreign lang="greek">p</foreign>AD2/4, e quello da <lb/><foreign lang="greek">p</foreign>AC2/8 e AC2=2AD2. </s>

<s>Condotta poi la secante CB, e prolungata infino a <lb/>incontrare in E l'arco del settore AF, si serve Pappo alessandrino di questa <pb xlink:href="020/01/2606.jpg" pagenum="231"/>costruzione, nel problema VII del IV libro delle sue <emph type="italics"/>Collezioni,<emph.end type="italics"/> per dimostrare <lb/>la proporzionalit&agrave;, che passa fra la quarta parte del circolo massimo della <lb/>sfera, e la porzion di spirale in essa sfera descrittta. </s>

<s>Studiando ora Galileo <lb/>nel libro del Matematico antico, coi commenti del Commandino, ebbe a fare <lb/>un'osservazione, sfuggita a quello stesso eruditissimo commentatore, qual'&egrave; <lb/>che il quadrante sta all'arco del settore come la porzione BC di quello, in&shy;<lb/>tersecata, sta alla porzione FE di questo, terminata dal prolungamento in E <lb/>della stessa linea BC intersecante. </s></p><p type="main">

<s>Abbiamo infatti, condotta la DB, e intendendo dire degli angoli, ADC= <lb/>ADB+BDC, FCA=ECA+ECF: e pure 2FCA=2ECA+2ECF. </s>

<s>Ma <lb/>ADC=2DAC=2FCA, per essere il triangolo ADC isoscele, ed FC pa&shy;<lb/>rallela ad AD; dunque ADB+BDC=2ECA+2ECF. </s>

<s>Ma ADB=2ECA, <lb/>per la XXa del terzo di Euclide, dunque BDC=2ECF. </s>

<s>Le due equazioni perci&ograve; <lb/>danno ADC:BDC=FCA:ECF, e permutando ADC:FCA=BDC:ECF. </s>

<s><lb/>E perch&egrave; gli angoli stanno come gli archi compresi, ABC:AEF=BC:EF, <lb/>come conclude Galileo dal suo proprio discorso in questo modo: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XI, THEOREMA IX. &mdash; <emph type="italics"/>Sit quadrans ACD ipsi vero DC <lb/>perpendicularis CF, et centro C, spatio CA, describatur circumferentia <lb/>AEF, et ducatur contingenter recta EC. </s>

<s>Dico quam rationem habet AF <lb/>ad FE, hanc habere ABC ad BC. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Jungatur BD: et quia angulus ADC duplus est anguli ACF, angulus <lb/>vero ADB duplus est anguli ACB; erit reliquus BDC reliquo ECF itidem <lb/>duplus. </s>

<s>Quare ADC angulus, ad angulum ACF, erit ut BDC angulus ad an&shy;<lb/>gulum ECF. </s>

<s>Et permutando ut angulus ADC, ad angulum BDC, hoc est, ut <lb/>periferia ABC ad CB periferiam; ita angulus ACF ad angulum ECF: hoc <lb/>est periferia AEF ad periferiam EF. </s>

<s>Hanc demonstrationem non novit Coman&shy;<lb/>dinus in XXXa quarti Pappi &rdquo; (MSS. Gal., P. V, T. IV, a tergo del fol. </s>

<s>25). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XII, THEOREMA X. &mdash; <emph type="italics"/>Venduntur quaedam cartae cosmo&shy;<lb/>graficae ex pluribus triangulis, quibus abscissis, possunt ipsae sphaeris <lb/>adaptari. </s>

<s>Trianguli vero abscissi, ad id quod reliquum est, eam habent <lb/>proportionem, quam habet sphaerae diameter ad excessum, quo dimidia <lb/>circumferentia circuli maximi excedit dictam diametrum. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nam cylindri circa sphaeram superficies, exceptis basibus, aequatur <lb/>superficiei sphaerae. </s>

<s>Dicta autem carta est superficies cylindri, circa sphae&shy;<lb/>ram, habentis altitudinem aequalem dimidio sphaerae circumferentiae. </s>

<s>Quod, <lb/>si haberet altitudinem aequalem sphaerae diametro, aequaretur illius super&shy;<lb/>ficiei. </s>

<s>Ex quo patet quod dicta carta excedit sphaerae superficiem secundum <lb/><figure id="id.020.01.2606.1.jpg" xlink:href="020/01/2606/1.jpg"/></s></p><p type="caption">

<s>Figura 89.<lb/>proportionem, quam habet dimidia circumfe&shy;<lb/>rentia ad diametrum &rdquo; (ibid., fol. </s>

<s>24). </s></p><p type="main">

<s>Sia ACB (fig. </s>

<s>89) la mezza circonferenza, <lb/>DF uguale al diametro, e GF uguale in retti&shy;<lb/>tudine alla stessa mezza circonferenza. </s>

<s>Rivol&shy;<lb/>gendosi la figura tutt'intorno all'asse HI, il <lb/>mezzo cerchio descriver&agrave; una sfera, il rettangolo DB un cilindro, l'esterna <pb xlink:href="020/01/2607.jpg" pagenum="232"/>superficie S del quale uguaglier&agrave; quella della sfera, o dei triangoli ascissi. </s>

<s>Il <lb/>rettangolo GI poi generer&agrave; un cilindro, la superficie esterna del quale, che <lb/>chiameremo S&prime;, sar&agrave; uguale alla superficie della carta, e avremo S&prime;= <lb/>2<foreign lang="greek">p</foreign>.EB.GF, S=2<foreign lang="greek">p</foreign>EB.AB, d'onde S&prime;/S=GF/AB, che vuol dire appunto <lb/>che la carta eccede la superficie della sfera secondo la proporzione della <lb/>mezza circonferenza al diametro. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XIII, THEOREMA XI. &mdash; <emph type="italics"/>Cuiuscumque cylindri superficies, <lb/>exceptis basibus, sive cum basibus, minor est quam dupla superficici coni <lb/>in ipso descripti, excepta, sive cum basc. </s>

<s>E contra vero quorumdam co-<emph.end type="italics"/><lb/><figure id="id.020.01.2607.1.jpg" xlink:href="020/01/2607/1.jpg"/></s></p><p type="caption">

<s>Figura 90.<lb/><emph type="italics"/>norum in cylindris inscriptorum superficies, excepta base, <lb/>maior est quam dupla superficiei cylindri, exceptis ba&shy;<lb/>sibus &rdquo;<emph.end type="italics"/> (ibid.). </s></p><p type="main">

<s>La prima parte della proposizione si dimostra facil&shy;<lb/>mente vera dal considerare il cilindro generato dal ret&shy;<lb/>tangolo KI (fig. </s>

<s>90), e il cono dal triangolo BIH, mentre <lb/>ambedue le figure si rivolgono attorno al loro comune <lb/>asse HI. Imperocch&egrave;, chiamata S l'esterna superficie di quel solido, S&prime; l'esterna <lb/>superficie di questo, non comprese le basi, abbiamo S=2<foreign lang="greek">p</foreign>BI.KB, S&prime;= <lb/><foreign lang="greek">p</foreign>BI.BH, d'onde S/S&prime;=2KB/BH, che, per essere KB/BH un rotto proprio, <lb/>sar&agrave; necessariamente minore di due. </s>

<s>Comprese poi le basi, sar&agrave; S= <lb/>2<foreign lang="greek">p</foreign>BI.KB+2<foreign lang="greek">p</foreign>BI2=2<foreign lang="greek">p</foreign>BI(KB+BI); S&prime;=<foreign lang="greek">p</foreign>BI.BH+<foreign lang="greek">p</foreign>BI2= <lb/><foreign lang="greek">p</foreign>BI(HB+BI), onde S/S&prime;,=2(KB+BI)/(HB+BI), che &egrave; pure minore di due, per la <lb/>medesima ragione di dianzi, per essere cio&egrave; il due moltiplicato per un rotto <lb/>proprio. </s></p><p type="main">

<s>Anche nell'altra sua parte apparisce vero il proposto teorema, perch&egrave; <lb/>essendo S&prime;/S=BH/2KB, se BH=2KB, le superficie sono uguali. </s>

<s>Se BH= <lb/>4KB, la superficie del cono &egrave; doppia di quella del cilindro: se poi BH &egrave; <lb/>maggiore di 4KB, i coni inscritti hanno tutti superficie maggior del doppio <lb/>di quelle dei cilindri circoscritti. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XIV, THEOREMA XII. &mdash; <emph type="italics"/>A data sphaera, segmento plano <lb/>secto, ita ut segmentum ad conum basim habentem eamdem cum segmento <lb/>et aequalem altitudinem, datam rationem habeat; dico datam illam ra&shy;<lb/>tionem debere esse necessario sesquialtera maiorem. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Cos&igrave; Galileo intendeva di riformare la VII archimedea, problema VI del <lb/>secondo libro <emph type="italics"/>De sphaera et cylindro,<emph.end type="italics"/> secondo ci&ograve; che leggesi nella seguente <lb/>nota manoscritta: &ldquo; Ex resolutione VI problematis secundi Archimedis <emph type="italics"/>De <lb/>sphaera et cylindro,<emph.end type="italics"/> patet quamlibet sphaerae portionem maiorem esse quam <lb/>sesquialteram coni in ipsa descripti &rdquo; (ibid., fol. </s>

<s>24). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XV, PROBLEMA III. &mdash; <emph type="italics"/>Ex cylindro recto, ex altera parte <lb/>indeterminato, possumus partem sic abscindere, ut illius superficies, exceptis<emph.end type="italics"/><pb xlink:href="020/01/2608.jpg" pagenum="233"/><emph type="italics"/>basibus, ad superficiem coni in ipso descripti, excepta base, datam habeat <lb/>proportionem: oportet autem datam proportionem minorem esse quam <lb/>duplam. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sit cylindrus interminatus ABCD (fig. </s>

<s>91), axis EF; data proportio K <lb/>ad HG, minor quam dupla. </s>

<s>Ponatur HI aequalis HG, et ex puncto A duca&shy;<lb/><figure id="id.020.01.2608.1.jpg" xlink:href="020/01/2608/1.jpg"/></s></p><p type="caption">

<s>Figura 91.<lb/>tur AF, secans axem in F, et abscindens partem FE, ad <lb/>quam habeat proportionem eamdem, quam GI ad K, et <lb/>per F aequidistans ducatur FOT. </s>

<s>Dico cylindrum AOTB <lb/>esse petitum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quod enim fit ex AO in AB, et id quod fit ex <lb/>dimidio FA in AB, est ut OA ad dimidium FA. </s>

<s>Verum <lb/>quod fit ex dimidia FA in AB aequatur ei, quod fit ex <lb/>tota FA iu dimidia AB: hoc est in AE. </s>

<s>Contenta ergo <lb/>sub OA, AB, ad contentum sub FA, AE, est ut OA ad <lb/>dimidiam AF: hoc est ut K ad GH. Verum, ut contentum <lb/>sub OA, AB, ad contentum sub FA, AE, sic est superficies cylindri ad sn&shy;<lb/>perficiem coni; ergo etc. </s>

<s>&rdquo; (ibid., fol. </s>

<s>23). </s></p><p type="main">

<s>&Egrave; dato, secondo il discorso di Galileo, AO:FA/2=K:GH, ossia AO.AB: <lb/>FA.AB/2=K:GH, che, moltiplicata la prima ragione per <foreign lang="greek">p</foreign> e posta AB= <lb/>2AE, si riduce ad AO.2<foreign lang="greek">p</foreign>AE:FA.<foreign lang="greek">p</foreign>AE=K:GH. </s>

<s>Ma nella prima ra&shy;<lb/>gione il primo termine misura la superficie del cilindro, il secondo la su&shy;<lb/>perficie del cono, dunque ecc. </s>

<s>Bisogna poi, com'&egrave; stato avvertito nella pro&shy;<lb/>posta, che sia
2AO/AF=K/GH &lt; 2, perch&egrave;, se fosse uguale, sarebbe OA=AF, <lb/>e gli apotemi del cilindro e del cono si confonderebbero insieme, per cui non <lb/>sarebbe possibile la richiesta costruzione. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XVI, PROBLEMA IV. &mdash; <emph type="italics"/>Dato cylindro recto, in altera <lb/>parte indeterminato, possumus ab ipso portionem abscindere, ita ut illius <lb/>superficies, exceptis basibus, aequetur superficiei coni recti in ipso descripti, <lb/>excepta base coni. </s>

<s>&rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.2608.2.jpg" xlink:href="020/01/2608/2.jpg"/></s></p><p type="caption">

<s>Figura 92.</s></p><p type="main">

<s>&ldquo; Sit itaque cylindrus rectus indeterminatus, et <lb/>planum ductum per axem faciat sectionem ABCD <lb/>(fig. </s>

<s>92), sitque BE dupla EC, et centro C, intervallo <lb/>CB, describatur circuli circumferentia, quae secet CD <lb/>in F, et ducatur BF, quae bifariam dividatur in H, et <lb/>per H ducatur, BC aequidirtans, GHK. Dico, si con&shy;<lb/>volvantur rectangulum KGCB, et triangulum BHC, <lb/>effici quod petitur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quia enim quadratum BC triplum est quadrati <lb/>CF, erit BF quadratum quadruplum FC, hoc est HB <lb/>quadratum quadruplum quadrati BK, et linea HB dupla BK. Quare, si BC <lb/>bifariam dividatur in puncto I, erit ut HB ad BK, ita CB ad BI. </s>

<s>Quod ergo <pb xlink:href="020/01/2609.jpg" pagenum="234"/>fit ex KB in BC aequatur ei quod fit ex HB in BI. </s>

<s>Igitur mediae inter HB, <lb/>BI, et inter KB, BC; hoc est circuli, quorum dictae mediae sint semidiame&shy;<lb/>tri, sunt aequales. </s>

<s>Ergo etc. </s>

<s>&rdquo; (ibid., fol. </s>

<s>22). </s></p><p type="main">

<s>La superficie del cono, generato dalla rivoluzione del triangalo BHI in&shy;<lb/>torno all'asse HI, &egrave;, senza la base, <foreign lang="greek">p</foreign>BI.BH, e la superficie del cilindro, <lb/>generato dal rettangolo KI nel rivolgersi intorno al medesimo asse, &egrave;, senza <lb/>le hasi, <foreign lang="greek">p</foreign>BC.KB, per cui, se i rettangoli BI.BH, BC.KB fossero uguali, <lb/>sarebbe dimostrato che le due superficie sono uguali. </s>

<s>L'eguaglianza poi dei <lb/>detti rettangoli la conclude Galileo dal supporre BC2=3CF2, dal quale sup&shy;<lb/>posto ne consegue veramente BF2=3CF2+CF2=4CF2, ossia (2BH)2= <lb/>4(2KB)2, e in ultima riduzione BH=2BK. </s>

<s>Ma &egrave; strano il fare <emph type="italics"/>quadra&shy;<lb/>tum BC triplum quadrati FC,<emph.end type="italics"/> perch'essendo per costruzione BC, FC raggi <lb/>di un medesimo circolo, non possono i loro quadrati non essere uguali. </s>

<s>La <lb/>cosa anzi ci parve tanto strana che, dubitando di non aver bene interpetrato <lb/>il manoscritto, si voleva escludere questo dagli altri teoremi. </s>

<s>Essendosi per&ograve; <lb/>ritrovato per cosa certa ch'era stato propriamente messo cos&igrave;, come noi ri&shy;<lb/>copiammo, lo adduciamo come documento storico di quei falli, nei quali ebbe <lb/>pi&ugrave; volte a incorrere Galileo, principalmente per la privazion della vista, e <lb/>del potere adoperare la penna, &ldquo; infelicit&agrave;, diceva da s&egrave; stesso, che mi accade <lb/>anco nel poter discorrere sopra linee, che passino oltre un triangolo, sicch&egrave; <lb/>n&egrave; pure posso intendere una delle mie medesime proposizioni e dimostra&shy;<lb/>zioni &rdquo; (Alb. </s>

<s>VII, 236). </s></p><p type="main">

<s>Ma quest'altra proposizion che scriviamo, era tanto facile, da potersi <lb/>contemplar con la sola mente, alla quale bastava rappresentar come il qua&shy;<lb/>drato del raggio, ch'entra a misurar la base di un cilindro, &egrave; uguale a esso <lb/>raggio moltiplicato in s&egrave; stesso. </s>

<s>Essendo infatti C, C&prime; due cilindri con le basi <lb/>di raggio R, R&prime;, e con le altezze A, A&prime;, avranno fra loro la proporzione <lb/>C:C&prime;=A<foreign lang="greek">p</foreign>R2:A&prime;<foreign lang="greek">p</foreign>R&prime;2=2<foreign lang="greek">p</foreign>R..A.2R:2<foreign lang="greek">p</foreign>R&prime;.A&prime;.2R&prime;, che vuol <lb/>dire appunto quel che Galileo proponesi di dimostrare in questo modo: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XVII, THEOREMA XIII. &mdash; <emph type="italics"/>Cylindri proportionem habent <lb/>compositam ex proportione superficierum curvarum, et ex proportione <lb/>diametrorum basium. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nam habent proportionem compositam ex proportione altitudinum, et <lb/>ex proportione basium. </s>

<s>Bases autem habent proportionem compositam ex <lb/>circumferentiis, et ex proportione diametrorum. </s>

<s>Quare cylindrus ad cylindrum <lb/>habet proportionem compositam ex tribus proportionibus: nempe altitudinum. </s>

<s><lb/>circumferentiarum et diametrorum, quarum duae primae componunt pro&shy;<lb/>portionem superficierum curvarum. </s>

<s>Quare patet propos. </s>

<s>&rdquo; (ibid., fol. </s>

<s>25). </s></p><p type="main">

<s>I raccoglitori dei manoscritti attribuirono a Galileo un'altra proposizione <lb/>geometrica, che poi il Viviani pubblic&ograve; per sua, e nel dedicarla, con la data <lb/>del 1668 al padre Adamo Adamando, gl&igrave; diceva di averla ritrovata trent'anni <lb/>fa, nello studiare il teorema di Pitagora, <emph type="italics"/>vix Geometriae limin&igrave; appulsus.<emph.end type="italics"/><lb/>Poi soggiungeva essere stato condotto all'invenzione da cos&igrave; fatto pensiero: <lb/>&ldquo; Quum primum enim, nullo explicantis praeceptoris praesidio, ad illius <pb xlink:href="020/01/2610.jpg" pagenum="235"/>pithagorici inventi demonstrationent perveni, ignorans adhuc universalem <lb/>propositionem trigesimam primam, de similibus figuris ab Euclide in sexto <lb/>Elementorum allatam; excogitari coepi num, quod de figura quadrata, verum <lb/>quoque esset de prima ac simplicissima rectilinearum figurarum aequalium <lb/>pariter laterum et angulorum; nimirum de triangulo aequilatero &rdquo; (Viviani <lb/>Scienza delle proporz. </s>

<s>cit., pag. </s>

<s>126) </s></p><p type="main">

<s>Non si vuol da noi negar fede a queste asserzioni, perch&egrave; i frutti ren&shy;<lb/>don credibile la precoce eccellenza dei fiori, sullo sbocciar dei quali avendo <lb/>nonostante avuto Galileo quella parte, che ha la luce e il tiepore del sole, <lb/>non par che aberri dal vero chi attribuisce a lui i portati primaverili della <lb/>giovane pianticella. </s>

<s>Se dall'altra parte il modo, come fu distesa quella pro&shy;<lb/>posizione nella sua prima forma originale, attesta l'inesperienza del giovane <lb/>dimostratore, &egrave; anche indizio delle difficolt&agrave; dello stesso Galileo nel doversela <lb/>rappresentare in mezzo alle tenebre. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XVIII, THEOREMA XIV. &mdash; <emph type="italics"/>Sia il triangolo rettangolo <lb/>ABC<emph.end type="italics"/> (fig. </s>

<s>93), <emph type="italics"/>il di cui angolo retto ABC. </s>

<s>Dico il triangolo equilatero<emph.end type="italics"/><lb/><figure id="id.020.01.2610.1.jpg" xlink:href="020/01/2610/1.jpg"/></s></p><p type="caption">

<s>Figura 93.<lb/><emph type="italics"/>ADC, fatto sopra il lato AC opposto all'an&shy;<lb/>golo retto, essere uguale ai triangoli equi&shy;<lb/>lateri AEB, CFB, fatti dai lati AB, BC, che <lb/>l'angolo retto contengono. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Per provar questo, tirisi la linea retta <lb/>BD, e poi dal punto E tirisi la EG perpendi&shy;<lb/>colare sopra la AB. </s>

<s>Tirisi inoltre la linea retta <lb/>GC, e finalmente tirisi un'altra linea retta EC. </s>

<s><lb/>Considero ora i due triangoli EAC, BAD, i quali <lb/>hanno i lati EA, AC eguali ai due lati BA, AD, <lb/>l'uno all'altro, essendo lati di triangoli equi&shy;<lb/>lateri. </s>

<s>Inoltre l'angolo DAC &egrave; uguale all'an&shy;<lb/>golo EAB, per essere ambedue in un trian&shy;<lb/>golo equilatero: aggiunto comune CAB sar&agrave; <lb/>tutto l'angolo DAB eguale a tutto EAC, sicch&egrave; i triangoli EAC, BAD, avendo <lb/>due lati uguali a due lati, e l'angolo compreso uguale all'angolo com&shy;<lb/>preso, sar&agrave; tutto il triangolo uguale a tutto il triangolo. </s>

<s>Ma il triangolo EAC <lb/>&egrave; composto dei tre triangoli EAG, EGC, AGC, i quali fra tutti e tre fanno <lb/>tutto il triangolo AEB equilatero, e mezzo il triangolo ABC rettangolo: <lb/>perch&egrave;, essendo la EG perpendicolare sopra la AB, sar&agrave; l'angolo EGA eguale <lb/>all'angolo EGB, essendo ambedue retti. </s>

<s>L'angolo ancora EAG &egrave; uguale al&shy;<lb/>l'angolo EBG, per essere del triangolo equilatero. </s>

<s>Sicch&egrave; dunque i due <lb/>triangoli AEG, GEB saranno uguali, essendo come s'&egrave; detto l'angolo AGE <lb/>eguale all'angolo EGB, e l'angolo EAG eguale all'angolo EBG: un lato <lb/>uguale a un lato del comune EG, e il lato EA uguale al lato EB, per essere <lb/>ambedue del triangolo equilatero. </s>

<s>Sar&agrave; dunque il triangolo EAG eguale al <lb/>triangolo EGB, cio&egrave; il triangolo EGB la met&agrave; di tutto l'equilatero EAB. </s>

<s>Inol&shy;<lb/>tre essendo ancora, per la medesima ragione, il lato AG eguale al lato GB, <pb xlink:href="020/01/2611.jpg" pagenum="236"/>saranno i triangoli AGC, BGC sopra basi uguali, ed hanno la medesima al&shy;<lb/>tezza in C: sicch&egrave; saranno uguali fra di loro. </s>

<s>Per&ograve; il triangolo AGC sar&agrave; <lb/>la met&agrave; di tutto il triangolo rettangolo ABC. </s>

<s>Inoltre poi, essendo l'angolo <lb/>EGA retto, e l'angolo GBC pur retto, saranno fra loro uguali. </s>

<s>Per&ograve; le linee <lb/>EG, BC saranno parallele: per&ograve; i triangoli EGC, EGB saranno fra loro uguali, <lb/>essendo sopra la medesima base e fra le stesse parallele. </s>

<s>Ma il triangolo EGB <lb/>&egrave; la met&agrave; del triangolo equilatero AEB, adunque anche il triangolo EGC sar&agrave; <lb/>la met&agrave; di detto triangolo equilatero. </s>

<s>Sicch&egrave; dunque i due triangoli AEG, EGC <lb/>sono uguali a tutto il triangolo equilatero AEB, ed il terzo triangolo AGC &egrave; <lb/>la met&agrave; del rettangolo ABC, e fra tutt'e tre s'&egrave; detto che compongono il <lb/>solo grande EAC. </s>

<s>Adunque il triangolo EAC &egrave; uguale al triangolo equila&shy;<lb/>tero EAB, e alla met&agrave; del rettangolo ABC. </s>

<s>Ma il triangolo BAD si &egrave; provato <lb/>uguale al triangolo EAC, adunque anche il triangolo BAD sar&agrave; uguale al <lb/>triangolo equilatero EAB, e alla met&agrave; del rettangolo ABC. &rdquo; </s></p><p type="main">

<s>&ldquo; Per le medesime ragioni, e con la medesima costruzione appunto, si <lb/>prover&agrave; il triangolo BDC eguale all'equilatero BFC, con la met&agrave; del trian&shy;<lb/>golo ABC. </s>

<s>Adunque tutto il triangolo equilatero ADC, con tutto il triangolo <lb/>rettangolo, &egrave; uguale ai due triangoli equilateri EAB, BCF, con due met&agrave; del <lb/>triangolo equilatero: cio&egrave; con tutto il medesimo triangolo equilatero. </s>

<s>Ma se, <lb/>tanto dal solo triangolo equilatero, che dagli altri due, ne leveremo il co&shy;<lb/>mune triangolo rettangolo; rester&agrave; il triangolo equilatero ADC solo eguale <lb/>ai due triangoli equilateri EAB, BCF. </s>

<s>Ma il triangolo ADC &egrave; il triangolo fatto <lb/>dalla AC, lato opposto all'angolo retto del triangolo rettangolo ABC, e i trian&shy;<lb/>goli EAB, BCF i triangoli fatti dai lati, che l'angolo retto contengono del <lb/>medesimo triangolo; sicch&egrave; dunque del triangolo rettangolo il triangolo equi&shy;<lb/>latero, fatto sopra il lato opposto all'angolo retto, &egrave; uguale ai due triangoli <lb/>equilateri, fatti dai lati che l'angolo retto contengono, il che si doveva pro&shy;<lb/>vare &rdquo; (MSS. Gal., P. VI, T. III, fol. </s>

<s>11 a tergo e fol. </s>

<s>12). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XIX, THEOREMA XV. &mdash; <emph type="italics"/>Ma volendosi sapere qual parte <lb/>del triangolo equilatero, fatta dal lato opposto all'angolo retto, &egrave; uguale <lb/>a uno degli altri triangoli, e qual parte &egrave; uguale all'altro, si operer&agrave; cos&igrave;: &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia il detto triangolo rettangolo ABC, come nella precedente figura, e <lb/>fatti i triangoli voglio provare quanto di sopra. </s>

<s>Per provar questo, tirisi dal <lb/>punto B la BH perpendicolare sopra la AC: congiungasi HD. </s>

<s>Dico il trian&shy;<lb/>golo ADH essere eguale all'equilatero AEB, l'uno all'altro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Tirisi la retta BD: poi tirisi la DL perpendicolare sopra AC, e con&shy;<lb/>giungasi LB. </s>

<s>Tirisi inoltre la perpendicolare EG sopra la AB, e congiungasi <lb/>GC, e finalmente tirisi la linea retta EC. Gi&agrave;, per la di sopra, sappiamo il <lb/>triangolo AEC essere uguale al triangolo ABD, e l'uno e l'altro eguale al&shy;<lb/>l'equilatero AEB. </s>

<s>Ma essendo l'angolo DEC retto uguale all'altro retto AHB, <lb/>saranno le linee DL, BH parallele. </s>

<s>Pi&ugrave; il triangolo DLH sar&agrave; uguale al trian&shy;<lb/>golo DLB, essendo sopra la medesima base DL, e fra le stesse parallele. </s>

<s>Per&ograve;, <lb/>pigliando in cambio di BLD il triangolo DLH, sar&agrave; tutto il triangolo DAH, <lb/>con ALB, eguale al triangolo AEB, con la met&agrave; del triangolo rettangolo ACB. <pb xlink:href="020/01/2612.jpg" pagenum="237"/>Adunque anche il triangolo ADH, con il triangolo ALB, sar&agrave; uguale al trian&shy;<lb/>golo equilatero AEB, e alla met&agrave; del triangolo rettangolo ABC. </s>

<s>Ma il trian&shy;<lb/>golo ALB ancora &egrave; la met&agrave; del triangolo rettangolo, per essere sopra basi <lb/>eguali AL, LC, avendo la medesima altezza in B. </s>

<s>Ma se tanto dal triangolo <lb/>equilatero AEB, che dal triangolo ADH, si tolgano le parti uguali alla met&agrave; <lb/>del triangolo rettangolo ABC, rester&agrave; il triangolo equilatero AEB eguale al <lb/>triangolo ADH, che si doveva provare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Con la medesima costruzione si prover&agrave; l'altro triangolo CHD eguale <lb/>all'altro equilatero BCF. </s>

<s>Adunque tutto ADC sar&agrave; uguale ai due &rdquo; (ivi, fol. </s>

<s>12). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Tali essendo, quali gli abbiamo ordinati ed esposti fin qui, i problemi <lb/>e i teoremi di Galileo raccolti dal Viviani, passiamo a ordinare quegli altri, <lb/>che si sono raccolti da noi, per la massima parte dagli autografi, ne'quali, <lb/>per non aver potuto l'Autore mandare ad effetto la sua intenzione, son da <lb/>due secoli e mezzo rimasti abbandonati. </s>

<s>Dicemmo esservene alcuni concer&shy;<lb/>nenti l'Algebra, per la quale intendiamo quella parte della Matematica, che <lb/>dimostra le relazioni esistenti fra certe date quantit&agrave;, come loio propriet&agrave; <lb/>universali, comunque siano quelle stesse quantit&agrave; definite. </s>

<s>Il modo di dimo&shy;<lb/>strare cos&igrave; fatti teoremi consiste per lo pi&ugrave;, appresso agli antichi, nel con&shy;<lb/>cludere per induzione una regola generale da pochi fatti particolari, cosicch&egrave; <lb/>la fiducia, che s'aveva della verit&agrave; di queste soluzioni, si faceva unicamente <lb/>dipendere dal principio, che la Natura opera in modo sempre costante. </s>

<s>Come <lb/>il principio sia talvolta sicuro, e come non di rado riesca pericoloso, appa&shy;<lb/>risce dagli esempi dei Matematici antichi, i quali, non sapendo dar forma <lb/>ai concetti universali, per poi vedervi in essi compresi i particolari, da que&shy;<lb/>sti, risaliti per pochi gradi, distendono a quelli il volo ardito, soggiacendo bene <lb/>spesso alle sorti d'Icaro, di che ebbe talvolta a fare esperienza anche Galileo. </s></p><p type="main">

<s>PROPOSITIO XX, THEOREMA XVI. &mdash; <emph type="italics"/>Abbiasi una progressione aritme&shy;<lb/>tica che, cominciando da un numero pari, proceda costantemente per diffe&shy;<lb/>renze uguali al primo termine<emph.end type="italics"/> a, <emph type="italics"/>alla met&agrave; del quale s'agguagli il numero <lb/>degli stessi termini in progressione. </s>

<s>Si ponga poi una nuova progressione <lb/>decrescente con differenze costantemente uguali a due, e il maggior nu&shy;<lb/>mero della quale sia il primo della progressione crescente, diminuito di <lb/>un'unit&agrave;, e si proceda infin tanto che, per essere quel maggior numero <lb/>impari, non si esaurisca nell'uno. </s>

<s>Poste queste cose, si dimostra primo: <lb/>che il numero dei termini della progressione decrescente sar&agrave; uguale al <lb/>numero dei termini della crescente. </s>

<s>Secondo: che il doppio della somma <lb/>della stessa decrescente &egrave; uguale al primo termine della crescente, mol&shy;<lb/>tiplicato per il numero dei termini in progressione.<emph.end type="italics"/></s></p><pb xlink:href="020/01/2613.jpg" pagenum="238"/><p type="main">

<s>Chiamato infatti <foreign lang="greek">w</foreign> il maggior termine della progressione decrescente, e <lb/><emph type="italics"/>d<emph.end type="italics"/> la differenza, la formula <emph type="italics"/>n<emph.end type="italics"/>=1+(<foreign lang="greek">w</foreign>&mdash;<emph type="italics"/>a<emph.end type="italics"/>)/<emph type="italics"/>d<emph.end type="italics"/> dataci dai trattati di Algebra <lb/>si riduce ad <emph type="italics"/>n=a<emph.end type="italics"/>/2. Dunque il numero dei termini &egrave; veramente, come si <lb/>diceva, nelle due progressioni uguale. </s></p><p type="main">

<s>La formula poi <foreign lang="greek">w</foreign>=<emph type="italics"/>a+d(n&mdash;1)<emph.end type="italics"/> d&agrave; per la crescente <foreign lang="greek">w</foreign>= <lb/><emph type="italics"/>a+a(n&mdash;1)=an<emph.end type="italics"/>: mentre per la decrescente la somma <emph type="italics"/>s<emph.end type="italics"/> &egrave; data dalla <lb/>formola <emph type="italics"/>s=n<emph.end type="italics"/>/2(<emph type="italics"/>a<emph.end type="italics"/>+<foreign lang="greek">w</foreign>) che nel presente nostro caso si riduce a 2<emph type="italics"/>s<emph.end type="italics"/>= <lb/><emph type="italics"/>n<emph.end type="italics"/>(1+<emph type="italics"/>a<emph.end type="italics"/>&mdash;1)=<emph type="italics"/>an.<emph.end type="italics"/> Dunque <foreign lang="greek">w</foreign>=2<emph type="italics"/>s,<emph.end type="italics"/> come si doveva dimostrare. </s></p><p type="main">

<s>PROPOSITIO XXI, THEOREMA XVII. &mdash; <emph type="italics"/>Abbiansi le medesime cose come <lb/>sopra, ma il minor termine della crescente, la quale abbia tanti termini <lb/>in progressione, quant'&egrave; la met&agrave; di a+1, sia impari, e sia perci&ograve; pari il <lb/>maggior della decrescente. </s>

<s>Si dimostra, cos&igrave; posto, che il numero dei ter&shy;<lb/>mini della decrescente &egrave; sempre minore di uno del numero dei termini della <lb/>crescente; e che il doppio della somma di quella &egrave; uguale al numero dei <lb/>termini di questa moltiplicato per il suo primo termine diminuito di uno.<emph.end type="italics"/></s></p><p type="main">

<s>La formula infatti <emph type="italics"/>n<emph.end type="italics"/>=1+(<foreign lang="greek">w</foreign>&mdash;<emph type="italics"/>a<emph.end type="italics"/>)/<emph type="italics"/>d,<emph.end type="italics"/> dianzi proposta, si riduce a <emph type="italics"/>n<emph.end type="italics"/>= <lb/>1+(<emph type="italics"/>a<emph.end type="italics"/>&mdash;1&mdash;2)/2=(<emph type="italics"/>a<emph.end type="italics"/>&mdash;1)/2, ci&ograve; che dimostra la verit&agrave; della prima parte <lb/>del teorema. </s>

<s>Quanto alla seconda, l'altra formula generale, che dava la <lb/>somma dei termini in progression decrescente, torna a 2<emph type="italics"/>s(n&mdash;1)(a+1)= <lb/>an&mdash;a+n&mdash;1=an+n&mdash;(a+1).<emph.end type="italics"/> Ma <emph type="italics"/>a+1=2n,<emph.end type="italics"/> dunque <lb/>2<emph type="italics"/>s=an&mdash;n=n(a&mdash;1),<emph.end type="italics"/> come dovevasi dimostrare. </s></p><p type="main">

<s>Galileo concludeva il primo dei riferiti teoremi dal veder procedere se&shy;<lb/>condo la medesima regola le progressioni contrassegnate nel manoscritto con <lb/>le lettere D, F, E, B, A. <lb/>&divide;8:4 <lb/>D &lcub; <lb/>&divide;3:1 <lb/>&divide;6:12:18 <lb/>F &lcub; <lb/>&divide;5:3:1 <lb/>&divide;8:16:24:32 <lb/>E &lcub; <lb/>&divide;7:5:3:1 <lb/>&divide;10:20:30:40:50 <lb/>B &lcub; <lb/>&divide;9:7:5:3:1 <lb/>&divide;20:40:60:80:100:120:140:160:180:200 <lb/>A &lcub; <lb/>&divide;19:17:15:13:11:9:7:5:3:1 </s></p><pb xlink:href="020/01/2614.jpg" pagenum="239"/><p type="main">

<s>L'altro teorema era pure concluso per induzione dai particolari esempi, <lb/>offerti e considerati nelle progressioni G, H, I, L. <lb/>&divide;5:10:15 <lb/>G &lcub; <lb/>&divide;4:2 <lb/>&divide;7:14:21:28 <lb/>H &lcub; <lb/>&divide;6:4:2 <lb/>&divide;9:18:27:36:45 <lb/>I &lcub; <lb/>&divide;8:6:4:2 <lb/>&divide;25:50:75:100:125:150:175:200:225:250:275:300:325 <lb/>L &lcub; <lb/>&divide;24:22:20:18:16:14:12:10:8:6:4:2 </s></p><p type="main">

<s>L'uno e l'altro poi dei detti teoremi veniva da Galileo applicato a illu&shy;<lb/>strare la meccanica dei moti naturali, comparati con i violenti, com'appari&shy;<lb/>sce dalla seguente nota autografa, della quale &egrave; questa la fedel copia che se <lb/>n'&egrave; presa: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Notabile per i proietti nel determinare quanto detragga la propen&shy;<lb/>sione naturale in gi&ugrave; al moto preternaturale della proiezione.<emph.end type="italics"/> &mdash; Si im&shy;<lb/>petus violentus disponatur secundum numeros pares, descensus naturalis demit <lb/>dimidium, ut constat in exemplis D, F, E, B, A. Verum, si dispositio sit se&shy;<lb/>cundum numeros impares, naturalis descensus demit minus quam dimidium, <lb/>iuxta numerum partium dispositarum, ut patet in exemplis G, H, I, L. </s>

<s>In G <lb/>enim partes dispositae iuxta impetum violentum non retardatum sunt tres, <lb/>nempe 5, 10, 15, ex quibus in prima demitur 1, et relinquitur 4. Dempto <lb/>ex secunda 4, relinquitur 6. Dempto ex tertia, nempe ex 15, 9, relinquitur <lb/>idem numerus 6, quod deficit a dimidio 15 per 3, qui est numerus partium <lb/>5, 10, 15. In exemplo H numerus partium est 4: subtractiones motus na&shy;<lb/>turalis sunt 6, 4, 2, quae conficiunt 12, cuius duplum deficit a 28 per 4. In <lb/>exemplo I subtractiones 8, 6, 4, 2 exhibent 20, cuius duplus deficit a 45 per 5, <lb/>quod est numerus partium. </s>

<s>In L pariter apparet subtractiones, nempe 156, <lb/>duplicatim deficere per 13, quod est numerus partium motus violenti, a 325 &rdquo; <lb/>(MSS. Gal., P. V, T. II, fol. </s>

<s>182). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXII, THEOREMA XVIII. &mdash; <emph type="italics"/>In numeris, ab unitate con&shy;<lb/>sequentibus, summa cuiuslibet multitudinis, ad aliam summam alterius <lb/>multitudinis, si ab utraque dimidium maximi numeri auferatur, est ut <lb/>quadratum multitudinis unius, ad quadratum alterius multitudinis &rdquo;<emph.end type="italics"/> (ibid., <lb/>fol. </s>

<s>68). </s></p><p type="main">

<s>Anche di questo teorema, concluso da Galileo per induzione da pochi <lb/>esempi particolari, &egrave; manifesta la verit&agrave; generale, applicandovi la formula al&shy;<lb/>gebrica <emph type="italics"/>s=n<emph.end type="italics"/>/2(<emph type="italics"/>a<emph.end type="italics"/>+<foreign lang="greek">w</foreign>), che si trasforma in <emph type="italics"/>s<emph.end type="italics"/>&mdash;<foreign lang="greek">w</foreign>/2=<emph type="italics"/>n<emph.end type="italics"/>(<emph type="italics"/>a<emph.end type="italics"/>+<foreign lang="greek">w</foreign>)/2&mdash;<foreign lang="greek">w</foreign>/2= <pb xlink:href="020/01/2615.jpg" pagenum="240"/>(<emph type="italics"/>n<emph.end type="italics"/>(1+<foreign lang="greek">w</foreign>)&mdash;<foreign lang="greek">w</foreign>)/2, intendendosi per <emph type="italics"/>s<emph.end type="italics"/> la somma che si cerca, per <emph type="italics"/>a,<emph.end type="italics"/> <foreign lang="greek">w</foreign> il primo <lb/>e l'ultmo termine, e per <emph type="italics"/>n<emph.end type="italics"/> il numero dei termini in progressione. </s>

<s>Ora es&shy;<lb/>sendo <emph type="italics"/>a<emph.end type="italics"/>=t, e nella progressione dei numeri naturali conseguenti dall'unit&agrave; <lb/><emph type="italics"/>n<emph.end type="italics"/>=<foreign lang="greek">w</foreign>, avremo <emph type="italics"/>s<emph.end type="italics"/>&mdash;<foreign lang="greek">w</foreign>/2=<foreign lang="greek">w</foreign>2/2. Per la somma <emph type="italics"/>s<emph.end type="italics"/>&prime; di un'altra progressione, <lb/>l'ultimo termine della quale sia <foreign lang="greek">w</foreign>&prime;, essendo <emph type="italics"/>s<emph.end type="italics"/>&prime;&mdash;<foreign lang="greek">w</foreign>&prime;/2=<foreign lang="greek">w</foreign>&prime;2/2, avremo dun&shy;<lb/>que <emph type="italics"/>s<emph.end type="italics"/>&mdash;<foreign lang="greek">w</foreign>/2:<emph type="italics"/>s<emph.end type="italics"/>&prime;&mdash;<foreign lang="greek">w</foreign>&prime;/2=<foreign lang="greek">w</foreign>2:<foreign lang="greek">w</foreign>&prime;2, ci&ograve; ch'esprime la verit&agrave; che volevasi con&shy;<lb/>fermare. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXIII, THEOREMA XIX. &mdash; <emph type="italics"/>Si fuerint quatuor lineae, <lb/>quarum prima et secunda simul sumptae sint aequales tertiae et quar&shy;<lb/>tae simul sumptis, sint antem prima et secunda minus inter se differentes <lb/>quam tertia et quarta: rectangulum primae el secundae superat rectan&shy;<lb/>gulum tertiae et quartae rectangulo contento ab excessu tertiae supra pri&shy;<lb/>mam in excessu primae supra quartam &rdquo;<emph.end type="italics"/> (ibid., fol. </s>

<s>62 ad terg.). </s></p><p type="main">

<s>Galileo non dimostra direttamente il teorema, ma si contenta d'accen&shy;<lb/>nar come si veritichi nell'esempio di quattro linee, la prima e la seconda <lb/>delle quali siano 10, 8, e la terza e la quarta 12 e 6. In questo caso &egrave; <lb/>veramente 10X8&mdash;12X6=2X4. &Egrave; per&ograve; verissima la cosa in ge&shy;<lb/>nerale. </s>

<s>perch&edot; chiamate <emph type="italics"/>a, b, c, d<emph.end type="italics"/> le quattro linee o i quattro numeri, se me&shy;<lb/>glio piace, essendo per le poste condizioni <emph type="italics"/>a+b=c+d,<emph.end type="italics"/> &egrave; facile dimo&shy;<lb/>strare che <emph type="italics"/>ab&mdash;cd=(c&mdash;a)(a&mdash;d).<emph.end type="italics"/> Sostituito infatti il valore di <lb/><emph type="italics"/>b,<emph.end type="italics"/> sar&agrave; <emph type="italics"/>ab&mdash;cd=a(c+d&mdash;a)&mdash;cd=ac+ad&mdash;a2&mdash;cd= <lb/>a(c&mdash;a)+d(a&mdash;c)=a(c&mdash;a)&mdash;d(c&mdash;a)=(c&mdash;a)(a&mdash;d),<emph.end type="italics"/><lb/>che conferma la verit&agrave; dell'annunziata proposizione. </s></p><p type="main">

<s>Seguono altri teoremi, i quali pullularono fecondi nella mente di Galileo, <lb/>mentre si proponeva di dimostrare con qual proporzione crescano le super&shy;<lb/>ficie ne'solidi sminuzzati, per concluderne poi il maggiore impedimento, che <lb/>ricevon questi nello scendere per varii mezzi, rispetto all'impedimento, che <lb/>riceverebbe il solido tutto intero. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXIV, THEOREMA XX. &mdash; <emph type="italics"/>Dato un cubo, diviso in tre <lb/>parti uguali uno de'suoi lati, come uno sta a tre, cosi la superficie del <lb/>grande alla superficie di tutti que'piccoli &rdquo;<emph.end type="italics"/> (MSS. Gal., P. V, T. IV, fol. </s>

<s>37). </s></p><p type="main">

<s>Chiamato BD il lato del cubo grande, e BE il suo terzo, le superficie <lb/>S, <foreign lang="greek">s</foreign> son date da S=6.BD2, <foreign lang="greek">s</foreign>=6.BE2, onde S:<gap/>=BD2:BE2. </s>

<s>La <lb/>somma poi di tutti i cubetti, che chiameremo <foreign lang="greek">*s</foreign>, sar&agrave; 33.6.BE2, ossia <lb/>27.6.BE2, e perci&ograve; <foreign lang="greek">*s</foreign>:<foreign lang="greek">s</foreign>=27BE2:BE2, onde S:<foreign lang="greek">*s</foreign>=BD2:27.BE2. </s>

<s><lb/>E perch&egrave; BD=3BE, S:<foreign lang="greek">*s</foreign>=9:27=1:3. La qual medesima conclu&shy;<lb/>sione &egrave; dimostrata da Galileo cos&igrave;, con altra forma di discorso: </s></p><p type="main">

<s>&ldquo; Come la supertice del gran cubo alla superfice di un piccolo solo, cosi <lb/>la base del grande alla base del piccolo: e come la superfice del piccolo alla <lb/>sunerfice di tutti con esso, cio&egrave; a 27; cosi la sua base a 27 basi come la <pb xlink:href="020/01/2616.jpg" pagenum="241"/>sua. </s>

<s>Adunque <emph type="italics"/>ex aequali<emph.end type="italics"/> come la superfice del grande alla superfice di tutti <lb/>i piccoli, cos&igrave; la sua base grande a 27 di quelle basi piccole. </s>

<s>Ma questa ne <lb/>contiene nove di quelle piccole, dunque come 9 a 27, cio&egrave; come uno a tre, <lb/>cos&igrave; la superfice del grande, alla superfice di tutti que'piccoli &rdquo; (ivi). </s></p><p type="main">

<s>Potevasi il teorema dimostrar facilmente nella sua generalit&agrave;, chiamando <lb/>C il numero qualunque delle parti, nelle quali s'intenda essere stato diviso <lb/>il lato del maggior cubo, perch&egrave;, ragionando come sopra e ritenendo le si&shy;<lb/>gnificazioni di sopra, se ne concluderebbe S:<foreign lang="greek">*s</foreign>=BD2:C3.BE2. </s>

<s>E per es&shy;<lb/>sere BD=C.BE, S:<foreign lang="greek">*s</foreign>=C2.BE2:C3.BE2=1:C=BE:BD, che <lb/>vuol dire: <emph type="italics"/>la superfice grande sta alla somma delle piccole, reciprocamente <lb/>come un lato di uno de'piccoli cubi sta al lato del grande.<emph.end type="italics"/> La dimostra&shy;<lb/>zione di questo generale teorema fu data dallo stesso Galileo, facendo uso <lb/>della cos&igrave; detta <emph type="italics"/>Algebra speciosa,<emph.end type="italics"/> com'apparisce dal seguente frammento, in <lb/>cui, dietro le cose gi&agrave; esposte, non &egrave; difficile supplire al significato delle pa&shy;<lb/>role, che mancano sul principio del manoscritto: </s></p><p type="main">

<s>&ldquo; ...... alla superfice di tanti cubetti quanto &egrave; il numero B, &egrave; la <lb/>medesima che quella del cubo B alla medesima dei tanti cubetti quanto &egrave; <lb/>il numero B. </s>

<s>Ma la superfice di tanti cubetti quanto &egrave; il numero C, a quella <lb/>di tanti quanto &egrave; il numero D, sta come i cubetti del numero C ai cubetti <lb/>del numero D, cio&egrave; come il numero C al numero D, cio&egrave; il numero A al B, <lb/>cio&egrave; la linea A alla linea B; adunque la superfice di tanti cubetti quanto &egrave; <lb/>il numero C, cio&egrave; la superfice del cubo B, alla superfice dei cubetti quanto <lb/>&egrave; il numero D, cio&egrave; alla superfice di tanti cubetti, che fanno il cubo mede&shy;<lb/>simo B, sta come la A alla B, cio&egrave; come il lato di uno de'cubetti, uguali <lb/>e simili al tutto, al lato del tutto, ohe &egrave; quello che si doveva dimostrare. </s>

<s>Il <lb/>che si deve intendere esser vero in ogni solido risoluto in solidi simili, es&shy;<lb/>sendo tra di loro come i cubi de'lati omologhi &rdquo; (ivi, fol. </s>

<s>38). </s></p><p type="main">

<s>Dall'essere poi S:<foreign lang="greek">*s</foreign>=1:C, secondo i simboli da noi applicati di sopra <lb/>a questa conclusione di Galileo, ne segue <emph type="italics"/>per conversionem rationis<emph.end type="italics"/> <foreign lang="greek">*s</foreign>:S= <lb/>C:1, corollario del precedente, o nuovo teorema dallo stesso Galileo cosi <lb/>proposto e illustrato col discorso, che per noi si ricopia dal manoscritto. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXV, THEOREMA XXI. &mdash; <emph type="italics"/>Tutte le superfice dei piccoli <lb/>cubi risoluti prese insieme, alla superfice del cubo grande risoluto, hanno <lb/>la medesima proporzione, che il numero delle parti del lato che si sega <lb/>all'uno. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Il numero de'cubi, nei quali uno si risolve, &egrave; il numero cubo delle <lb/>parti, che son nel lato del cubo, che si risolve: come per esempio, diviso il <lb/>lato del cubo in tre o quattro parti, i cubi, che da esse parti si faranno, <lb/>saranno 27 o 64. Ed avendo ogni cubo sei quadrati in superfice, moltipli&shy;<lb/>cando 27 per 6, e 64 pur per 6, averemo i numeri dei quadrati, che son <lb/>superfice dei detti cubi. </s>

<s>Di qui facilmente ne consegue quel che si diceva. </s>

<s><lb/>che cio&egrave; tutte le superfice dei piccoli cubi risoluti prese insieme, alla super&shy;<lb/>fice del cubo grande risoluto, hanno la medesima proporzione che il numero <lb/>delle parti del lato che si sega all'uno. </s>

<s>E cos&igrave; tutte le superfice dei 27 cubi, <pb xlink:href="020/01/2617.jpg" pagenum="242"/>alla superfice del primo massimo cubo, saranno triple, e tutte le superfice <lb/>delli 64 cubetti prese insieme saranno quadruple della superfice dell'intero <lb/>gran cubo, essendo che il lato di questo fu diviso in tre parti, per cavarne <lb/>li 27 cubi, ed in quattro, per cavarne li cubi 64 &rdquo; (ivi, fol. </s>

<s>19). </s></p><p type="main">

<s>Osservava in simile proposito Galileo che, se il lato del quadrato &egrave; di&shy;<lb/>viso in tre parti uguali, uno solo &egrave; il quadratino, che riman rinchiuso in <lb/>mezzo a tutti gli altri. </s>

<s>Se poi la divisione sia fatta in quattro, o in cinque <lb/>parti uguali, i quadratini rinchiusi saranno quattro o nove. </s>

<s>Di qui ne con&shy;<lb/>cludeva per regola generale che, chiamato D il numero delle divisioni, il nu&shy;<lb/>mero N de'quadratini interni &egrave; (D&mdash;2)2, d'onde ne conseguiva (D&mdash;2)3, <lb/>per il numero dei cubetti rimasti dentro al gran cubo sepolti. </s>

<s>Intorno a che <lb/>formulava Galileo stesso, riscontrata sopra alcuni esempi numerici, la se&shy;<lb/>guente: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXVI, THEOREMA XXII. &mdash; <emph type="italics"/>Il numero dei cubi, che re&shy;<lb/>stano sepolti nel gran cubo, si trova essere il numero cubo delle parti, <lb/>nelle quali si divide il lato del gran cubo, trattone due. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Onde, nascendo li 27 cubi dalla divisione in tre, tratto da questo nu&shy;<lb/>mero tre, due, resta uno, ed uno solo sar&agrave; il cubo, che rimane incluso e se&shy;<lb/>polto tra li 27. Otto saranno i cubi sepolti tra li 64, nascenti dalla divisione <lb/>del primo gran lato in quattro, imperocch&egrave;, tratto dal quattro due, resta due, <lb/>il cui cubo &egrave; otto. </s>

<s>E cos&igrave; di tutti gli altri &rdquo; (ivi). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXVII, PROBLEMA V. &mdash; <emph type="italics"/>Di due palle, quanto una &egrave; mag&shy;<lb/>giore di un'altra? </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Una palla di quattro &egrave; maggiore di una di tre, ed ha la medesima <lb/>proporzione che 64 a 27, facendo i cubi loro, perch&egrave; le figure simili sono <lb/>in tripla proporzione dei lati, cio&egrave; di 4 a 3. Di qui intenderai perch&egrave; le su&shy;<lb/>perficie dei solidi simili no nell'istessa proporzione, ma in minore, cio&egrave; in <lb/>subsesquialtera di quella di essi solidi crescono e calano &rdquo; (ivi, fol. </s>

<s>31). </s></p><p type="main">

<s>Chiamati infatti S, <emph type="italics"/>s<emph.end type="italics"/> i solidi, <foreign lang="greek">*s</foreign>, <foreign lang="greek">s</foreign> le superficie, R, <emph type="italics"/>r<emph.end type="italics"/> i raggi: sar&agrave; S:<emph type="italics"/>s<emph.end type="italics"/>= <lb/>R3:<emph type="italics"/>r3,<emph.end type="italics"/> <foreign lang="greek">*s</foreign>:<gap/>=R2:<emph type="italics"/>r2,<emph.end type="italics"/> e perci&ograve; <foreign lang="greek">*s</foreign>3:<foreign lang="greek">s</foreign>3=S2:<emph type="italics"/>s<emph.end type="italics"/>2, ossia <foreign lang="greek">*s</foreign>:<foreign lang="greek">s</foreign>=S2/3:<emph type="italics"/>s<emph.end type="italics"/>2/3. </s></p><p type="main">

<s>Nel giugno del 1639 riceveva Galileo quel trattatello in forma di let&shy;<lb/>tera, nella quale il Castelli, descrivendo il Pluviometro, diceva di essersi ser&shy;<lb/>vito del nuovo inventato strumento per misurare dall'altezza di lui l'altezza, <lb/>a cui sarebbe cresciuta in tempo di pioggia la superfice del lago Trasimeno. </s>

<s><lb/>Era per caso allora esso Galileo tutto in pensiero de'teoremi aritmetici rife&shy;<lb/>riti di sopra, per ordinarli nel Dialogo, a cui parvegli si sarebbe potuta ag&shy;<lb/>giungere in simile argomento un'altra bellissima speculazione, qual era di <lb/>ritrovare il numero delle gocciole cadute sulla superfice di quello stesso lago. </s>

<s><lb/>E risoluto il problema, dettava intanto al Viviani cos&igrave;, perch&egrave; non se ne <lb/>avesse a perdere la memoria: </s></p><p type="main">

<s>&ldquo; In proposito del p. </s>

<s>ab. </s>

<s>don Benedetto, nel trattato del lago Trasimeno, <lb/>&egrave; cosa degna di esser notata quante sarebbero le gocciole dell'acqua piovente <lb/>sopra la superfice del lago, data la distanza tra gocciola e gocciola, mante&shy;<lb/>nuta sempre eguale tra ciascheduna di quelle, e dato quanto sarebbe il se-<pb xlink:href="020/01/2618.jpg" pagenum="243"/>midiametro uguale alla superfice del lago, cio&egrave; quante di tali distanze ne <lb/>conterrebbe. </s>

<s>Imperocch&egrave;, fatti due cubi, uno del numero di tutte le date di&shy;<lb/>stanze con uno pi&ugrave;, e l'altro di un numero uno manco di tutto quello, e <lb/>sottratto questo minor numero cubo dall'altro, la loro differenza &egrave; il numero <lb/>delle gocciole sopra il dato cerchio cadenti. </s>

<s>Per esempio la distanza tra goc&shy;<lb/>ciola e gocciola sia un soldo: il semidiametro del cerchio sia soldi novan&shy;<lb/>tanove. </s>

<s>Facciasi il cubo di cento, che &egrave; uno pi&ugrave; di novantanove, che &egrave; un <lb/>milione, dal quale si tragga il numero cubo di novantanove, che &egrave; 970,299. <lb/>Tratto questo da un milione, resta 29,701 e tanto sar&agrave; il numero delle goc&shy;<lb/>ciole cadenti sopra il dato cerchio &rdquo; (ivi). </s></p><p type="main">

<s>Nello stesso tempo dettava Galileo al Viviani una lettera, nella quale <lb/><emph type="italics"/>s<emph.end type="italics"/>'avvisava il Castelli che il suo discorso sul lago Trasimeno aveva provocata <lb/>la seguente </s></p><p type="main">

<s>PROPOSITIO XXVIII, PROBLEMA VI. &mdash; <emph type="italics"/>Dato un cerchio, e il numero <lb/>delle distanze fra le gocciole nel suo raggio comprese, trovare il numero <lb/>di tutte le gocciole, sopra quella circolar superfice cadenti.<emph.end type="italics"/> E chiamato N <lb/>questo numero, e D le date distanze, diceva Galileo essere risoluto il pro&shy;<lb/>hlema, in modo corrispondente alla formula N=(D+1)3&mdash;D3. </s></p><p type="main">

<s>Il Castelli fece intorno a questa soluzione qualche difficolt&agrave;, alla quale <lb/>Galileo cos&igrave; rispondeva: &ldquo; Quanto a quello, che ella tocca nella sua, in pro&shy;<lb/>posito delle gocciole cadenti, che si debbano prendere non gl'intervalli tra <lb/>gocciola e gocciola, ma i numeri di esse gocciole, &egrave; verissimo, n&egrave; io poteva <lb/>venire in cognizione di quanto scrissi, se non servendomi del numero delle <lb/>gocciole, ponendo il primo come centro, e gli altri sei come gli angoli del&shy;<lb/>l'esagono inscritto nel primo cerchio, e cos&igrave; i contenuti sono sette. </s>

<s>Presi poi <lb/>due punti, e fattone il cubo, che &egrave; otto, e trattone il primo cubo, che &egrave; uno, <lb/>restano pure sette. </s>

<s>Aggiunto il secondo cerchio, doppio in circonferenza del <lb/>primo e perci&ograve; contenente dodici gocciole nella circonferenza, e fatto il cubo <lb/>di tre punti, cio&egrave; 27, e trattone il cubo di due, che &egrave; otto, restano 19, che <lb/>&egrave; la somma stessa delli 12, delli sei, e dell'uno del centro. </s>

<s>E seguitando con <lb/>quest'ordine, aggiugnendo il terzo cerchio, e li 18 punti contenuti nella sua <lb/>circonferenza, sommandogli con gli antidetti dodici, e gli altri sei precedenti <lb/>a quello del centro, si fanno 37 gocciole, e tale &egrave; il numero che resta, ca&shy;<lb/>vando il cubo di 3 dal cubo 4, cio&egrave; 27 da 64. E cos&igrave; continuando vidi la <lb/>continuazione della regola, ma poco potei andare innanzi, vietandomelo la <lb/>privazione della vista e del potere adoperar la penna: infelicit&agrave; che mi accade <lb/>anco nel poter discorrere sopra linee, che passino oltre un triangolo, sicch&egrave; <lb/>neppure posso intendere una delle mie medesime proposizioni e dimostra&shy;<lb/>zioni, ma tutte mi giungono come ignote e inintelligibili &rdquo; (Alb. </s>

<s>VII, 235, 36). </s></p><p type="main">

<s>I riferiti esempi, bench&egrave; pochi, possono nulladimeno bastare, per dare <lb/>un'idea de'teoremi dimostrati, e de'problemi risoluti da Galileo, relativa&shy;<lb/>mente a quelle propriet&agrave;, che universalmente intercedono fra certe date quan&shy;<lb/>tit&agrave; numeriche e lineari, e che oggid&igrave; pi&ugrave; francamente e pi&ugrave; generalmente <lb/>si dimostrerebbero per via di simboli algebrici, e con la regola nota delle <pb xlink:href="020/01/2619.jpg" pagenum="244"/>loro operazioni. </s>

<s>Rimarrebbe, a condurre il nostro primo proposito ad effetto, <lb/>di raccogliere quegli altri teoremi di Geometria, i quali occorsero alla mente <lb/>di Galileo, nell'atto di dimostrare le proposizioni attinenti alle varie propriet&agrave; <lb/>dei moti: proposizioni, che, rimaste indietro nei manoscritti e fuor di luogo <lb/>nell'opera dei dialoghi stampati, si volevano dall'Autore stesso ridurre tutte <lb/>insieme in questo dialogo novissimo, incominciato, in mezzo alle tenebre este&shy;<lb/>riori, a dettare al Viviani. </s></p><p type="main">

<s>Sembrerebbe si potesse congetturare dai fatti, in questa nostra Storia <lb/>pi&ugrave; volte notati, che non fu una tal dettatura n&egrave; ordinata n&egrave; continua: ma <lb/>si dialogizzava uno o altro soggetto a parte, come ne veniva l'occasione e il <lb/>tempo, con intenzione d'intessere tutte insieme quelle parti nel tutto, rima&shy;<lb/>nendo solo a farne le facili attaccature. </s>

<s>Per conferma di che soggiungeremo <lb/>qui, prima di passare a raccogliere i promessi teoremi geometrici, una delle <lb/>dette parti dialogizzate, nelle quali, in modo che, rispetto agl'insegnamenti <lb/>degli altri Autori e del medesimo Galileo nelle opere stampate, si direbbe <lb/>nuovo; s'applica la Geometria elementare ad alcune curiose insieme, e utili <lb/>operazioni della Geodesia: </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Ha il nostro Accademico in questi fogli insegnato anche <lb/>il modo di misurar con la vista. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Ma cotesto stesso l'avevano insegnato, ne'loro libri, <lb/>tanti altri Matematici, prima di lui. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Voi dite il vero, signor Simplicio: e bench'io vi debba <lb/>concedere che il nostro Amico non abbia intorno a ci&ograve; insegnato nulla di <lb/>nuovo nella sostanza, ha nonostante il merito della novit&agrave;, quanto ai modi, <lb/>i quali, se son pi&ugrave; facili e pi&ugrave; spediti degli altri, sono anche insieme di mi&shy;<lb/>nore spesa, e di minore incomodo nel praticarli. </s>

<s>Ditemi: basta forse la sem&shy;<lb/>plice vista, per questa maniera di operazioni? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; No, ma vi si richiedono i necessari strumenti, come <lb/>sarebbero quadranti e diottre e traguardi, i quali vogliono esser fatti con <lb/>gran precisione dalle mani degli artefici pi&ugrave; periti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Ora io vi dico che il nuovo modo dispensa l'operatore <lb/>da tutto questo: basta che egli abbia un quadrato o un rettangolo, fatto di <lb/>qualunque materia, con i lati ben diritti e puliti, e con gli angoli ben pie&shy;<lb/>gati in perfetta squadra. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Ci&ograve; potr&agrave; forse bastare per l'operazione in s&egrave; stessa, ma <lb/>ella richiede pure il fondamento di altre operazioni, come sarebbe quella di <lb/>tirare la linea del perpendicolo e l'equidistante alla orizzontale, per far che <lb/>non vedo come possa bastare in tutto un semplice rettangolo o un quadrato, <lb/>e sia pure, negli angoli e ne'lati, quanto vogliate, perfetto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Voi, signor Sagredo, avete accortamente distinto il fon&shy;<lb/>damento preparatorio dalla stessa propria operazione, della quale sola s'in&shy;<lb/>tendeva parlare: e bench&egrave;, qualunque peso pendulo da un filo sia strumento <lb/>paratissimo a tutti, per una delle dette operazioni; per l'altra nonostante, <lb/>cio&egrave; per livellare, si ricerca strumento assai pi&ugrave; artificioso. </s>

<s>Tale sarebbe un <pb xlink:href="020/01/2620.jpg" pagenum="245"/>sifone pieno di liquido, per la maggior precisione del quale si vorrebbe prin&shy;<lb/>cipalmente che fosse assai lungo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Io dai pratici ho sentito dire che i due rami del si&shy;<lb/>fone, che si ripiegano in su, e nei quali trasparisce l'acqua, debbono es&shy;<lb/>sere, pi&ugrave; che sia possibile, uguali, e che la differenza del calibro, special&shy;<lb/>mente andando a restringersi i tubi, pu&ograve; rendere assai fallace la linea della <lb/>mira, ma non intendo in qual fallacia potesse indurre l'esser pi&ugrave; o meno <lb/>lungo il tubo disteso in piano, l'acqua rinchiusa del quale non apparisce <lb/>al di fuori e non si guarda. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; E io, molto diversamente da quel che voi signor Sim&shy;<lb/>plicio, credete, vi annunzio come cosa verissima che, quanto sar&agrave; pi&ugrave; lungo <lb/>lo strumento da livellare tanto sar&agrave; minore l'errore, che si potesse fare nella <lb/>linea di mira. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Che sia verissimo quel che il signor Salviati pronunzia <lb/>me lo persuade un pensiero, che m'&egrave; sovvenuto pure ora alla mente, e che <lb/>io voglio esplicare al signor Simplicio con questo discorso: Supponete di <lb/>avere lo strumento prima lungo quanto AC (fig. </s>

<s>94), poi ridotto alla lun&shy;<lb/>ghezza AF, e che, per essere il ramo del tubo in C pi&ugrave; stretto del ramo <lb/><figure id="id.020.01.2620.1.jpg" xlink:href="020/01/2620/1.jpg"/></s></p><p type="caption">

<s>Figura 94.<lb/>in A, o per qualsivoglia altro motivo, erri la <lb/>linea di mira quanto DC. </s>

<s>Facendosi il me&shy;<lb/>desimo errore anche in F, l'effetto non &egrave; <lb/>per&ograve; il medesimo, quanto al riferir la mira <lb/>per esempio sulla lunghezza della pertica BH, <lb/>messa innanzi per scopo. </s>

<s>&Egrave; facile vedere che <lb/>si dilungher&agrave; dal vero punto della orizzon&shy;<lb/>tale pi&ugrave; in questo caso che in quello, ma si <lb/>pu&ograve; anche assai facilmente dimostrare se&shy;<lb/>condo qual precisa proporzione si faccia l'er&shy;<lb/>rore, nell'un caso e nell'altro. </s>

<s>Perch&egrave;, presa <lb/>FE uguale a DC, e tirate le visuali AG, AH, le quali terminino sullo scopo <lb/>contrapposto in G e in H, i triangoli simili ACD, ABG danno che AB sta <lb/>a BG come AC a CD. Parimente, dai triangoli simili ABH, AFE, s'ha che <lb/>AB sta a BH, come AF ad FE. </s>

<s>Se ne conclude perci&ograve; che AC verso AF ha <lb/>la proporzion medesima di BH verso BG, cosicch&egrave; se voi, signor Simplicio, <lb/>supponete che lo strumento pi&ugrave; lungo sia per esempio sei braccia e il pi&ugrave; <lb/>corto tre, quando quello facesse errore di quattro, questo invece farebbe er&shy;<lb/>rore di otto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Trattandosi di ragioni geometriche, dimostrate da Eu&shy;<lb/>clide ne'suoi libri degli Elementi, sarei da dire troppo stolto o troppo ca&shy;<lb/>parbio, se non confessassi che il signor Sagredo mi ha persuaso col suo di&shy;<lb/>scorso. </s>

<s>Passate perci&ograve; senz'altro, voi signor Salviati, a levarmi la curiosit&agrave; <lb/>di sapere come si possano misurar le distanze con la vista, non avendo altro <lb/>strumento a mano, che un rettangolo o un quadrato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Vogliasi misurare un'altezza, la cui radice non si ve-<pb xlink:href="020/01/2621.jpg" pagenum="246"/>desse, come saria l'altezza del monte EF (fig. </s>

<s>95). Tirato il piano dell'oriz&shy;<lb/>zonte DF, pongasegli aderente per uno de'suoi lati il quadrato o rettangolo <lb/>DC, e traguardando dall'angolo D la sommit&agrave; E segnisi la traccia della linea <lb/><figure id="id.020.01.2621.1.jpg" xlink:href="020/01/2621/1.jpg"/></s></p><p type="caption">

<s>Figura 95.<lb/>DC, ponendo in C uno scopo fisso, <lb/>come sarebbe per esempio uno <lb/>spillo. </s>

<s>Dipoi, accostiamoci verso il <lb/>monte, facendo strisciare il qua&shy;<lb/>drato sul medesimo piano oriz&shy;<lb/>zontale in modo, che l'angolo, <lb/>che prima era in D, torni in A, e <lb/>si tenga conto della misura precisa <lb/>dell'accostamento. </s>

<s>Si traguardi <lb/>nuovamente, e si trovi essere B <lb/>il punto, dove vuole esser posto <lb/>l'occhio, perch&egrave; lo spillo e la sommit&agrave; E si trovino disposti lungo la mede&shy;<lb/>sima linea visuale. </s>

<s>Traccisi, allo stesso modo che dianzi, la CB sopra la su&shy;<lb/>perficie del quadrato, e nessun'altra operazione si richiede, fuor che misu&shy;<lb/>rare le porzioni AB, CI sopra i lati dello stesso quadrato, per sapere quant'&egrave; <lb/>l'altezza FE, la quale dunque troverete con questa semplicissima regola: Par&shy;<lb/>tite il fatto da CI in BD per AB, e l'avvenimento sar&agrave; l'altezza cercata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Cotesta regola deve necessariamente conseguire dalla <lb/>proporzione AB sta a CI, come BD ad EF, ci&ograve; che poi pare a me molto fa&shy;<lb/>cile a dimostrarsi, osservando che, per essere AC parallela a DE, i triangoli <lb/>simili ABC, DBE danno che come AB ad AC, cos&igrave; &egrave; BD a DE. Parimente, <lb/>essendo IC equidistante da FE, per li triangoli simili ACI, DEF, AC sta a <lb/>CI come DE ad EF, d'onde viene ad aversi direttamente la proporzione, <lb/>sopra la quale il signor Salviati ha concluso la regola di misurare l'altezza <lb/>del monte. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Per misurare poi una profondit&agrave;, della quale non si ve&shy;<lb/><figure id="id.020.01.2621.2.jpg" xlink:href="020/01/2621/2.jpg"/></s></p><p type="caption">

<s>Figura 96.<lb/>desse la radice, come se fossimo <lb/>sopra il monte BD (fig. </s>

<s>96), e <lb/>volessimo misurare la sua al&shy;<lb/>tezza sopra il piano della cam&shy;<lb/>pagna, non avendo noi altro stru&shy;<lb/>mento che il detto quadrato, ope&shy;<lb/>reremo con pari facilit&agrave; in questo <lb/>modo: Poniamoci in C, appi&egrave; di <lb/>qualche casa, torre o albero, e <lb/>preso il quadrato in mano, dal&shy;<lb/>l'angolo superiore del quale sia <lb/>fatto pendere un filo, tirato da <lb/>un sassolino o da altro peso, <lb/>traguardiamo lungo la costola CI qualche segno, posto nel piano della cam&shy;<lb/>pagna, come si vede nel punto A. </s>

<s>Segnata poi sulla superficie dello strumento <pb xlink:href="020/01/2622.jpg" pagenum="247"/>la traccia, lungo la direzione del filo, ascendiamo alle finestre della casa, <lb/>della torre, o sui rami dell'albero in D, misurando la quantit&agrave; dell'ascesa <lb/>CD, e di lass&ugrave; traguardando come dianzi il medesimo punto A si segni la <lb/>nuova direzione, che ha preso il filo, la quale sia per esempio FD. </s>

<s>Misurate <lb/>sopra la costola del quadrato le parti FE, EH, partite EH per AF, e l'av&shy;<lb/>venimento, moltiplicato per la misura dell'ascesa DC, vi dar&agrave; senz'altro la <lb/>profondit&agrave; del monte che si voleva. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Intendo bene che la regola &egrave; stabilita sopra la propor&shy;<lb/>zione FE ad EH, come DC a CB: ma non vedo chiari questa volta i prin&shy;<lb/>cipii, dai quali, voi signor Salviati, fate conseguire la verit&agrave; annunziata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Dal punto A, a cui tendono le linee delle mire CA, DA, <lb/>conducete la AB equidistante dalla orizontale: essendo ABC angolo retto, <lb/>saranno, per la XXXII del primo degli Elementi, GAB, ACB insieme uguali <lb/>ad un retto, e perci&ograve; CAB uguale a un retto meno ACB. </s>

<s>Ma anche ECG &egrave; <lb/>uguale a un retto (tale essendo l'angolo del quadrato) meno ACB, dunque <lb/>BAG, ECG, che &egrave; il medesimo di EDH, sono uguali, e perci&ograve; i triangoli EDH, <lb/>BAC rettangoli saranno anche insieme equiangoli, e per la Va del VIo fra <lb/>loro simili. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Passiamo ora a dimostrare, dietro le due citate proposizioni di Eu&shy;<lb/>clide, che equiangoli pure e perci&ograve; simili sono i triangoli FED, CAD. </s>

<s>La ra&shy;<lb/>gione, perch&egrave; si diceva dianzi che ECG &egrave; angolo uguale a CAB, &egrave; quella <lb/>medesima, per cui ora si dice che FDH &egrave; uguale a DAB, ond'&egrave; che facil&shy;<lb/>mente vedrete, signor Sagredo, com'essendo FDE, CAD ciascuno la differenza <lb/>di due angoli uguali, debbon essere tra loro uguali. </s>

<s>L'angolo esterno DEF <lb/>&egrave; uguale a un retto, con l'angolo EDH, ossia CAB: ma anche l'angolo <lb/>esterno ACD &egrave; uguale a un retto, col medesimo angolo CAB; dunque i due <lb/>detti esterni sono anch'essi fra loro angoli uguali. </s>

<s>Il terzo angolo DFE, do&shy;<lb/>vendo essere necessariamente uguale al terzo angolo ADC, non ci vuol altro <lb/>perch&egrave; riteniate per dimostrata l'uguaglianza tra gli angoli, e la similitudine <lb/>tra due triangoli proposti, nei quali dunque, dovendo intercedere la pro&shy;<lb/>porzionalit&agrave; dei lati contrapposti agli angoli uguali, sar&agrave; EF ad EH, come DC <lb/>a CB, che &egrave; il fondamento della regola insegnata. </s>

<s>&rdquo; </s></p><p type="main">

<s>Questa parte di Dialogo &egrave; stata da noi ritrovata fra le carte, che il Pan&shy;<lb/>zanini consegn&ograve; al Bonaventuri, il quale non seppe ricavarne alcun utile per <lb/>la sua edizione, sgomentato dall'apparirgli quelle stesse carte illeggibili, per <lb/>le macchie sparse e per i margini troppo addentro corrosi. </s>

<s>Fu tale anche la <lb/>nostra apprensione in principio, ma poi, trovando che le lacune eran tali da <lb/>potersi non difficilmente riempir con parole, se non identiche, equivalenti, non <lb/>ci siam fatti scrupolo di rassettare cos&igrave; l'oggetto prezioso, piuttosto che get&shy;<lb/>tarlo di nuovo. </s>

<s>Che sia opera di Galileo nella dettatura e nell'andamento del <lb/>discorso ci si rende certo dalla certezza, che abbiamo essere opera del me&shy;<lb/>desimo quanto alla sostanza, avendosi la proposizione degli errori negli stru&shy;<lb/>menti da livellare, e le altre del misurar l'altezza e la profondit&agrave; colla vista, <lb/>autografe, in quel modo che ora trascriveremo, e ne'luoghi che si citeranno, <pb xlink:href="020/01/2623.jpg" pagenum="248"/>quasi fretttolosi appunti e materia buona gi&agrave; preparata dallo stesso Galileo <lb/>a ricevere a suo tempo la bellezza della forma. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXIX, THEOREMA XXII. &mdash; <emph type="italics"/>Quanto sar&agrave; pi&ugrave; lungo lo <lb/>strumento da livellare, tanto minore sar&agrave; l'er&racute;ore, che si potesse fare. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia la linea AC (nella figura 94 sopra segnata) quella del vero li&shy;<lb/>vello, e dato che, con lo strumento lungo quanto AC, la linea visuale s'alzi <lb/>sopra l'estremit&agrave; C quanto &egrave; la CD, con errore dal giusto livello quanto &egrave; <lb/>la linea BG; dico che, se si adoprer&agrave; lo strumento pi&ugrave; corto, come AF, e <lb/>faccia nell'estremo F l'errore FE, uguale al CD, che l'errore BH, fatto dalla <lb/>linea visuale ABH, rar&agrave; tanto maggiore del primo BG, quanto lo strumento <lb/>AC &egrave; pi&ugrave; lungo dello strumento AF. Sicch&egrave;, se il primo strumento pi&ugrave; lungo <lb/>sar&agrave; sei braccia, ed il primo errore sia di quattro braccia, e che il pi&ugrave; corto <lb/>strumento sia tre braccia, l'errore di questo sar&agrave; otto braccia. </s>

<s>Onde, tanto <lb/>quanto sar&agrave; pi&ugrave; lungo lo strumento da livellare, tanto minore sar&agrave; l'errore <lb/>che si potesse fare &rdquo; (MSS. Gal.., P. VI, T. II, fol. </s>

<s>13). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXX, PROBLEMA VII. &mdash; <emph type="italics"/>Per mezzo del quadrato misu&shy;<lb/>rare l'altezza inaccessibile FE, sopra il piano dell'orizonte DE. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ut BA ad AC (riducendoci nuovamente sott'occhio la figura 95, che <lb/>tien luogo delle molte parole non scritte da Galileo) ita BD ad DE. </s>

<s>Ut autem <lb/>AC ad CI, ita DE ad EF: ergo ut BA ad CI, ita BD ad EF &rdquo; (MSS. Gal., <lb/>P. V, T. II, fol. </s>

<s>136). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXXI, PROBLEMA VIII. &mdash; <emph type="italics"/>Col medesimo strumento mi&shy;<lb/>surare la profondit&agrave; CB, stando in C, e poi risalendo in D. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Proponendoci la figura 96, i principali tratti della soluzion del problema <lb/>son segnati da Galileo con queste parole: &ldquo; FE ad ED est ut DC ad CA. </s>

<s>Ut <lb/>autem ED ad EH, ita AC ad CB. </s>

<s>Ergo ex aequali ut FE ad EH, ita DC <lb/>ad CB. &rdquo; </s></p><p type="main">

<s>&ldquo; Parti EH per EF, e tante volte quant'&egrave; l'avvenimento entra DC <lb/>in CB &rdquo; (ivi, fol. </s>

<s>137). </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>I teoremi geometrici, rimasti fuor di luogo, nel condurre le dimostra&shy;<lb/>zioni gi&agrave; pubblicate nel terzo e nel quarto dialogo delle due Scienze nuove, <lb/>e i quali pensava Galileo negli ultimi anni della sua vita di salvar dall'oblio; <lb/>si trovano autografi nel secondo tomo della parte quinta dei Manoscritti, dove <lb/>son raccolte le bozze, e d'onde son ridotte a pulito per la stampa le prin&shy;<lb/>cipali proposizioni dei moti accelerati e dei proietti. </s>

<s>Quanto ci abbiano gio&shy;<lb/>vato coteste carte, per ritrarre in storia il concetto, gli svolgimenti graduali, <lb/>e le pene stesse del parto, ignorate dal pubblico, che solamente lo conobbe <lb/>gi&agrave; esposto; lo possono sapere tutti coloro, i quali hanno letto il nostro pre-<pb xlink:href="020/01/2624.jpg" pagenum="249"/>cedente tomo, nei capitoli VI e IX, ma &egrave; da soggiungere che il presente ar&shy;<lb/>gomento porge occasione a considerar meglio, insieme col fine, l'origine e <lb/>il tempo di certi teoremi di Meccanica notati nel detto Manoscritto, i quali, <lb/>accennando a un progresso del pensiero, ci mettono in gran curiosit&agrave; di sa&shy;<lb/>pere perch&egrave; mai Galileo non gli riducesse nei loro luoghi pi&ugrave; convenienti, <lb/>per accrescer bellezza, e dar perfezione ai dialoghi da stamparsi. </s></p><p type="main">

<s>La questione, come s'intende bene, &egrave; della natura di altre gi&agrave; da noi <lb/>risolute con dire che que'pensieri non occorsero in tempo, per inserirsi nella <lb/>copia gi&agrave; consegnata nelle mani dell'Elzevirio: e come tale fu la sorte della <lb/>proposizion che i momenti stanno in ragion composta delle distanze e dei <lb/>pesi, e che la catena si dispone in una curva, non differente dalla parabola; <lb/>tale &egrave; pur da dire essere stata la sorte di altre proposizioni, che ci occor&shy;<lb/>rono a notare come un nuovo esempio dell'aver Galileo pensato gi&agrave; a pro&shy;<lb/>movere per s&egrave; stesso la sua propria scienza, nei medesimi modi, e anche <lb/>prima che vi desse opera il Torricelli. </s></p><p type="main">

<s>In un foglio del citato manoscritto, e sotto una figura, rappresentata <lb/>nella nostra 97, si legge scritta questa nota: &ldquo; Considera momentum in sin&shy;<lb/><figure id="id.020.01.2624.1.jpg" xlink:href="020/01/2624/1.jpg"/></s></p><p type="caption">

<s>Figura 97.<lb/>gulis circumferentiae quadrantis punctis im&shy;<lb/>minui, pro ratione accessus puncti perpendi&shy;<lb/>cularis. </s>

<s>ut T ad centrum &rdquo; (MSS. Gal., P. V, <lb/>T. II, fol. </s>

<s>131) e pi&ugrave; sotto espressa in forma <lb/>la proposizione seguente: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXXII, THEOREMA XXIV. &mdash; <lb/><emph type="italics"/>Momentum sub plano DC, ad totale momen&shy;<lb/>tum, est ut linea TR ad RD, ducta LB ae&shy;<lb/>quistante CD &rdquo;<emph.end type="italics"/> (ibid.). </s></p><p type="main">

<s>La considerazione &egrave; bene antica nella sto&shy;<lb/>ria della Scienza, non essendo sfuggita alla <lb/>sagacia di Leonardo da Vinci, il quale, come <lb/>forse si ricorderanno coloro, i quali hanno letto il nostro quarto tomo, a <lb/>pag. </s>

<s>51, concludeva l'annunziata proposizione galileiana dall'osservar che la <lb/>sfera tanto sta in equilibrio sostenuta da un filo, quanto posata in quella di&shy;<lb/>rezione sopra un piano inclinato. </s>

<s>La cosa era affatto nuova per&ograve; nella scienza <lb/>pubblicata da Galileo, e come nuova apparve la prima volta in pubblico, nel <lb/>lemma dopo la seconda proposizione del primo libro del Torricelli. </s></p><p type="main">

<s>Una fra le eleganze della Meccanica torricelliana consiste nell'uso del <lb/>semicerchio, per la invenzione delle medie proporzionali, di continuo maneg&shy;<lb/>gio per risolvere i problemi dei tempi relativamente agli spazi. </s>

<s>N&egrave; ci siamo <lb/>poco maravigliati che Galileo non tenesse questa via compendiosa, e di cosi <lb/>evidente eleganza: tanto pi&ugrave; ripensando essere stato lui che, nella XXXIII <lb/>del III dialogo, e nel Lemma alla X del IV, l'aveva aperta e additata allo <lb/>stesso Torricelli. </s>

<s>Dovremmo ora dire come si facesse quella maraviglia nel&shy;<lb/>l'animo nostro anche maggiore, quando prima ci abbattemmo a leggere, nel <lb/>suddetto codice manoscritto, il problema XV del III dialogo, per risolvere il <pb xlink:href="020/01/2625.jpg" pagenum="250"/>quale, invocandosi il semicerchio, a mezzo quella prolissa dimostrazione stam&shy;<lb/>pata si sostituiva la snellezza del seguente processo: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXXIII, PROBLEMA IX. &mdash; <emph type="italics"/>Quaeritur in AC<emph.end type="italics"/> (fig. </s>

<s>98) <emph type="italics"/>pars <lb/>aequalis AB, quae conficiatur tempore aequali tempori AB. &rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.2625.1.jpg" xlink:href="020/01/2625/1.jpg"/></s></p><p type="caption">

<s>Figura 98.</s></p><p type="main">

<s>&ldquo; Ponatur AD aequalis AB, et circa AC <lb/>semicirculus describatur, et ponatur AF aequa&shy;<lb/>lis dimidiae DC, et ab F demittatur perpendi&shy;<lb/>cularis FE, et EG ponatur aequalis AB. </s>

<s>Dico <lb/>EG, ex quiete in A, confici eodem tempore <lb/>ac AB. &rdquo; </s></p><p type="main">

<s>&ldquo; Media proportionalis inter CA, AG est <lb/>AI, et CI, cui aequatur EF, media inter CA, <lb/>AE.... &rdquo; (ibid., fol. </s>

<s>55). E a questo punto &egrave; <lb/>lasciata la dimostrazione interrotta, perch&egrave; do&shy;<lb/>veva procedere da qui innanzi come dalla li&shy;<lb/>nea 23 della stampata a pag. </s>

<s>218 del tomo XIII nella edizion dell'Alb&egrave;ri. </s></p><p type="main">

<s>L'uso del semicerchio rendeva facile e pronta a Galileo la soluzione di <lb/>un altro problema, simile al precedente, e di cui sarebbesi potuta arricchire <lb/>la raccolta delle proposizioni, lette nel terzo dialogo dal Salviati. <lb/><figure id="id.020.01.2625.2.jpg" xlink:href="020/01/2625/2.jpg"/></s></p><p type="caption">

<s>Figura 99.</s></p><p type="main">

<s>&ldquo; PROPOSITIO XXXIV, PROBLEMA X. &mdash; <emph type="italics"/>Quae&shy;<lb/>ritur versus C<emph.end type="italics"/> (fig. </s>

<s>99) <emph type="italics"/>pars, quae conflciatur <lb/>eodem tempore ac AD. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sit tempus per AC, AC; tempus per AD <lb/>erit AE. </s>

<s>Ponatur GF aequalis AE, et ipsarum CA, <lb/>AF tertia proportionalis sit AG. </s>

<s>Dico GC esse <lb/>quod quaeritur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Cum enim tempus per totam AC sit AC, <lb/>tempus per AG erit AF, media inter CA, AG, et <lb/>reliqua FC erit tempus per GC. </s>

<s>Est autem FC posita aequalis AE; ergo pa&shy;<lb/>tet propositum &rdquo; (ibid.). </s></p><p type="main">

<s>Un corollario per&ograve;, che immediatamente si soggiunge, par che riveli la <lb/>fretta, dalla quale era frugato Galileo perch&egrave; non dovesse dimenticarsi la bella <lb/>novit&agrave; trovata: ed &egrave; a questa fretta da attribuir forse l'inconsideratezza delle <lb/>seguenti parole, alle quali si riduce il detto corollario: &ldquo; In qualibet latione <lb/>spacium, quod conficitur versus finem eodem tempore, ac spacium versus <lb/>principium, est medium proportionale inter totum lationis spatium, et ipsum <lb/>spatium versus principium &rdquo; (ibid). Ma la media proporzionale fra tutto lo <lb/>spazio, e lo spazio verso il principio, &egrave; CF, la quale non rappresenta gi&agrave; lo <lb/>spazio verso la fine, ma s&igrave; invece rappresenta il tempo, che il mobile im&shy;<lb/>piega a percorrere lo spazio CG verso la fine. </s></p><p type="main">

<s>La sollecitudine in ogni modo dello scrivere cos&igrave;, senza tornare sopra a <lb/>considerare le cose scritte, &egrave; argomento che Galileo aspettava a farlo a mi&shy;<lb/>glior tempo, e quando si fosse al punto d'inserire i nuovi teoremi in una <lb/>prossima aspettata ristampa delle due Scienze nuove. </s>

<s>O forse pensava di rac-<pb xlink:href="020/01/2626.jpg" pagenum="251"/>coglierli nel dialogo novissimo, com'&egrave; certo che pensava di raccogliervi il <lb/>teorema dei momenti nelle varie parti della circonferenza, intorno a che tro&shy;<lb/>viamo il seguente frammento, fra le carte altre volte commemorate, e che <lb/>dovettero servire per l'edizione del Bonaventuri: </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Bellissima sopra le altre mi &egrave; sembrata la considerazione <lb/>del nostro Accademico intorno al variar dei momenti nei singoli punti del <lb/>quadrante di un circolo grande, mentre la sfera tocca il piano inclinato, sopra <lb/>il quale sia obbligata a far la sua scesa, e perci&ograve; non vi dispiaccia, signor <lb/>Salviati, di dimostrare secondo qual proporzione si succedano via via, dal <lb/>contatto verticale all'orizontale su un piano, le dette variazioni di moto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Immaginate che sia DBC (nella precedente figura 97) il <lb/>quadrante, e B il punto del contatto sopra il piano LG, di cui sia GH l'al&shy;<lb/>tezza verticale. </s>

<s>Sapete, per la Scienza meccanica posta dal nostro Amico a <lb/>fondamento di queste sue nuove dottrine del moto, che l'impeto dello scen&shy;<lb/>dere in B sta all'impeto totale, come GH sta a GL. Ora, dal punto B con&shy;<lb/>ducete il raggio RB, e la BT perpendicolare all'orizontale RD: vedrete fa&shy;<lb/>cilmente come il triangolo rettangolo RBT sia simile al triangolo rettangolo <lb/>LGH, per cui l'impeto, o il momento totale, che si diceva stare al parziale <lb/>in B come LG a GH, star&agrave; pure come RB, ossia RD, a RT sopra la mede&shy;<lb/>sima lunghezza del raggio orizontale. </s>

<s>Passiamo a considerare un altro punto <lb/>qualunque M, a contatto col piano IE, il quale sia lungo quanto LG, e alto <lb/>quanto EK. </s>

<s>Fatta la medesima costruzione, e il medesimo ragionamento che <lb/>abbiamo fatto di sopra, troveremo essere il momento totale al parziale in M <lb/>come RD a RN, e di qui si conclude che i momenti, nei punti B, M del <lb/>quadrante, stanno come le porzioni RT, RN. Ora, perch&egrave; il discorso si ap&shy;<lb/>plica a tutti e singoli i punti, compresi tra il contatto con la verticale in D, <lb/>e il contatto con la orizontale in C; pu&ograve; dunque concludersi in generale che <lb/>il momento nei singoli punti della circonferenza del quadrante diminuisce a <lb/>proporzione dell'accostamento del punto perpendicolare, come T o N, al cen&shy;<lb/>tro del circolo grande o della sfera. </s>

<s>&rdquo; </s></p><p type="main">

<s>I riferiti esempi, che vengono ora ad aggiungersi ai parecchi altri, no&shy;<lb/>tati da noi nel corso di questa storia della Meccanica, ci attestano, non solo <lb/>che Galileo si dava ogni sollecitudine di perfezionare i suoi trattati delle <lb/>Scienze nuove, ma che sarebbero que'perfezionamenti in non poche parti <lb/>riusciti tali, da rendere inutile l'opera de'suoi stessi discepoli. </s>

<s>L'attestazione <lb/>per&ograve; non ci viene altro che per incidenza, in mezzo al proposito nostro pre&shy;<lb/>sente, qual'&egrave; di raccogliere quelle preparazioni geometriche, che servirono a <lb/>Galileo, per dimostrar nelle varie parti della Meccanica i pi&ugrave; difficili teoremi. </s>

<s><lb/>E che propriamente non sian queste altro che preparazioni, lo dice il titolo <lb/>di <emph type="italics"/>lemma,<emph.end type="italics"/> scritto a molte in principio, come nella seguente, l'enunciazion <lb/><figure id="id.020.01.2626.1.jpg" xlink:href="020/01/2626/1.jpg"/></s></p><p type="caption">

<s>Figura 100.<lb/>della quale &egrave; preceduta dalle parole <emph type="italics"/>redacta <lb/>est res ad hoc lemma.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; PROPOSITIO XXXV, THEOREMA XXV. &mdash; <lb/><emph type="italics"/>Sit EB<emph.end type="italics"/> (fig. </s>

<s>100) <emph type="italics"/>utcumque secta in A, et<emph.end type="italics"/><pb xlink:href="020/01/2627.jpg" pagenum="252"/><emph type="italics"/>inter EB, BA media sit BO, et ut EB ad BA, ita sit OB ad BN. </s>

<s>Dico <lb/>EB, BO, BA, BN esse continuae proportionales. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Quia enim, ut EB ad BO, ita BO ad BA, ratio EB ad BA erit dupla <lb/>rationis OB ad BA. </s>

<s>Et quia, ut EB ad BA, ita OB ad BN (est autem ratio <lb/>BE ad BA dupla rationis OB ad BA) erit quoque ratio OB ad BN dupla ra&shy;<lb/>tionis BO ad BA. </s>

<s>Verum ipsa ratio OB ad BN componitur ex rationibus OB <lb/>ad BA, et AB ad BN; ergo ratio AB ad BN est eadem cum ratione OB ad <lb/>BA. </s>

<s>Ergo patet propositum &rdquo; (MSS. Gal., P. V, T. II, fol. </s>

<s>62). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXXVI, THEOREMA XXVI. &mdash; <emph type="italics"/>Sit linea AC<emph.end type="italics"/> (fig. </s>

<s>101) <lb/><figure id="id.020.01.2627.1.jpg" xlink:href="020/01/2627/1.jpg"/></s></p><p type="caption">

<s>Figura 101.<lb/><emph type="italics"/>maior ipsa DF, et habeat AB ad BC <lb/>maiorem rationem quam DE ad EF. </s>

<s><lb/>Dico AB ipsa DE maiorem esse. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Quia enim AB ad BC maiorem <lb/>rationem habet, quam DE ad EF; quam <lb/>rationem habet AB ad BC hane habe&shy;<lb/>bit DE ad minorem quam EF. </s>

<s>Sit EG: et quia AB ad BC est ut DE ad <lb/>EG, erit, ut CA ad AB, ita GD ad DE. </s>

<s>Est autem CA maior DG; ergo et <lb/>BA ipsa DE maior erit &rdquo; (ibid., fol. </s>

<s>185). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXXVII, THEOREMA XXVII. &mdash; <emph type="italics"/>Secta CA<emph.end type="italics"/> (fig. </s>

<s>102) <emph type="italics"/>ut&shy;<lb/>cumque in D, pars vero CD bifarium in I, dico quod, si fiat ut tota AC<emph.end type="italics"/><lb/><figure id="id.020.01.2627.2.jpg" xlink:href="020/01/2627/2.jpg"/></s></p><p type="caption">

<s>Figura 102.<lb/><emph type="italics"/>ad CI, ita ID ad DG, erit ut CA <lb/>ad AI, ita IA ad AG &rdquo;<emph.end type="italics"/> (ibid., fol. </s>

<s>84 <lb/>ad terg.). </s></p><p type="main">

<s>Galileo dimostra la proposizione <lb/>in due modi: il primo de'quali &egrave; indiretto, e consiste nel ridurre, cos&igrave;, <lb/>l'ipotesi a tesi: Sia dunque, come si vuol dimostrare, CA:AI=IA:AG: <lb/>dividendo, avremo CA&mdash;AI:AI=IA&mdash;AG:AG, ossia CI:AI=IG:AG, <lb/>e per metastasi CI:IG=AI:AG. </s>

<s>Da questa, con la prima data, si ot&shy;<lb/>tiene CA:CI=AI:IG, e perch&egrave; AI=AC&mdash;IC, IG=ID&mdash;DG, <lb/>sar&agrave; CA:CI=AC&mdash;IC:ID&mdash;DG: ossia, moltiplicando gli estremi, ed <lb/>eguagliandone il prodotto al prodotto dei medii, CA.ID&mdash;CA.DG= <lb/>CI.AC&mdash;CI2. </s>

<s>Ora, essendo CI=ID, rimane CA.DG=CI2, ossia <lb/>AC:CI=CI:DG, o, sostituendo all'antecedente CI della prima ragione il <lb/>suo uguale DI, AC:CI=DI:IG. </s>

<s>Ma cosi era fatto, dunque il fatto era vero. </s></p><p type="main">

<s>&ldquo; Si totum CA, cos&igrave; propriamente dice Galileo, ad totum AI est ut abla&shy;<lb/>tum IA, ad ablatum AG, erit reliquum CI, ad reliquum IG, idest reliquum <lb/>DI, ad reliquum IG, ut totum CA ad AI, seu IA ad AG. </s>

<s>Et per conversio&shy;<lb/>nem rationis ut AC ad CI. ita ID ad DG. </s>

<s>Sed ita factum est, ergo etc. </s>

<s>&rdquo; <lb/>(ibid.). </s></p><p type="main">

<s>In altro modo diretto cos&igrave; Galileo dimostra la medesima proposizione: <lb/>Essendo dato ID:DG=AC:CI, dividendo, avremo ID&mdash;DG:ID= <lb/>AC&mdash;CI:AC, ossia IG:ID=AI:AC, e per essere DI=IC, e con&shy;<lb/>vertendo, CA:AI=IC:IG. </s>

<s>Se poi si sostituiscono alle IC, IG le loro <lb/>uguali CA&mdash;AI, AI&mdash;AG, avremo CA:AI=CA&mdash;AI:AI&mdash;AG, <pb xlink:href="020/01/2628.jpg" pagenum="253"/>e ragguagliando il prodotto degli estremi con quello dei medii, avremo <lb/>AI.CA&mdash;AC.AG=AI.CA&mdash;AI2, d'onde, riducendo, AC.AG= <lb/>AI2, ossia CA:AI=IA:AG, ch'&egrave; quello appunto, che dovevasi dimo&shy;<lb/>strare. </s></p><p type="main">

<s>&ldquo; Quia ID ad DG, dice Galileo, est ut AC ad CI, erit per conversionem <lb/>rationis ut CA ad AI, ita DI ad IG, seu IC ad IG. </s>

<s>Cum itaque sit ut totum <lb/>CA, ad totum AI, ita ablatum CI ad ablatum IG, erit ut reliqua IA, ad re&shy;<lb/>liqua AG, ut totum CA, ad totum AI, quod erat ostendendum &rdquo; (ibid.). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXXVIII, PROBLEMA XI. &mdash; <emph type="italics"/>Faciendum ut AI ad IG<emph.end type="italics"/><lb/>(nella medesima figura 102) <emph type="italics"/>ita ID ad GD &rdquo;<emph.end type="italics"/> (ibid., fol. </s>

<s>84). </s></p><p type="main">

<s>&Egrave; dato AC:CI=ID:DG, e dividendo AC:AC&mdash;CI=ID:ID&mdash;DG. </s>

<s><lb/>Fatte le sostituzioni, e ponendo IC in luogo di ID, avremo AC:AI= <lb/>CI:GI. Prendendo, invece di tutte le AC, AI, le loro parti, sar&agrave; AC+CI: <lb/>AG+IG=CI:GI, e fatto il prodotto degli estremi e de'medii, e ridu&shy;<lb/>cendo, AI.GI=CI.AG, d'onde AI:AG=CI:GI, o, per essere CI=DI, <lb/>AI:AG=DI:GI. Dividendo, sar&agrave; in ultimo AI:AI&mdash;AG=DI:DI&mdash;GI, <lb/>e, dopo la sostituzione, AI:GI=DI:DG, come dovavasi fare. </s>

<s>Ma ascoltiamo <lb/>le parole proprie di Galileo. </s></p><p type="main">

<s>&ldquo; Ponatur IC aequalis ID, et fiat ut AC ad CI, ita ID ad DG. Erit, per <lb/>conversionem rationis, ut CA ad AI, ita DI ad IG, sen CI ad IG. </s>

<s>Et cum <lb/>totum CA, ad totum AI, ita ablatum CI ad ablatum IG; erit reliqua IA, ad <lb/>reliquum AG, ut ablatum CI, seu DI, ad IG. Et, per conversionem rationis, <lb/>ut AI ad IG, ita ID ad DG &rdquo; (ibid.). </s></p><p type="main">

<s>PROPOSITIO XXXIX, THEOREMA XXVIII. &mdash; <emph type="italics"/>Sia l'angolo retto AXC<emph.end type="italics"/><lb/>(fig. </s>

<s>103), <emph type="italics"/>comunque diviso dalla XM, alla quale si conduca da A una per-<emph.end type="italics"/><lb/><figure id="id.020.01.2628.1.jpg" xlink:href="020/01/2628/1.jpg"/></s></p><p type="caption">

<s>Figura 103.<lb/><emph type="italics"/>pendicolare, che la seghi in M, e si prolunghi infino all'incontro della XC <lb/>in C. </s>

<s>Sia poi diviso l'angolo CAX dalla AI in due parti uguali, e di qua<emph.end type="italics"/><pb xlink:href="020/01/2629.jpg" pagenum="254"/><emph type="italics"/>e di l&agrave; da essa AI si conducano linee a piacere AL, AO, AP, ecc., le quali <lb/>tutte saranno intersecate dalla XM. </s>

<s>Dico che il rettangolo sotto la linea <lb/>AI, e sotto la sua intersezione dalla parte dell'angolo A, sar&agrave; il minore <lb/>di tutti gli altri rettangoli sotto le altre linee, e le loro intersezioni dalla <lb/>medesima parte.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Rectangulum IAE esse omnium minimum LAB, OAN, PAE, etc., cum <lb/>angulus CAX bifariam sectus sit, pendet ex eo, quod angulus AEM trian&shy;<lb/>guli AEM est aequalis angulo AIX trianguli AIX, et, quod consequens est, <lb/>minor omnium ALX, AOX, etc., et maior omnium API, ACI, etc. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Probabitur ergo sic rectangulum IAE minus esse rectangulo LAB: <lb/>Cum enim angulus AME sit aequalis angulo AXI, et angulus MAE aequalis <lb/>angulo XAI (est enim angulus A bifariam sectus) ergo reliquus MEA reli&shy;<lb/>quo XIA aequabitur. </s>

<s>Sed angulus AEM maior est angulo ABE, ergo angu&shy;<lb/>lus AIL est maior angulo EBA. </s>

<s>Si igitur fiat angulus AIT angulo ABE ae&shy;<lb/>qualis, erit, ob triangulortun similitudinem, ut IA ad AT, ita BA ad AE, et <lb/>rectangulum IAE rectangulo TAB aequale. </s>

<s>Ergo rectangulum IAE est minus <lb/>rectangulo LAB. &rdquo; </s></p><p type="main">

<s>&ldquo; Similiter ostendetur esse quoque minus rectangulo PAF. </s>

<s>Cum enim <lb/>angulus AEF, idest AIL, sit maius angulo API, erit reliquus AFE minor re&shy;<lb/>liquo AIP. </s>

<s>Si igitur constituatur AIU angulo ipsi AFE aequalis, erit rectan&shy;<lb/>gulum UAF rectangulo IAE aequale, ex quo patet propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Coroll. </s>

<s>I.<emph.end type="italics"/> &mdash; Demonstrabitur etiam quod rectangula talia, quae a li&shy;<lb/>neis ex A ad lineam CX ductis, et a linea XM sectis, ea, quae fiunt a lineis <lb/>vicinioribus ipsi AEI, semper minora sunt illis, quae a remotioribus descri&shy;<lb/>buntur lineis. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Coroll. </s>

<s>II.<emph.end type="italics"/> &mdash; Constat insuper quod media inter IAE est omnium me&shy;<lb/>diarum minima, quae cadunt inter PAF, LAB, etc. </s>

<s>&rdquo; (ibid., fol. </s>

<s>30 ad tergum). </s></p><p type="main">

<s>Accenna Galildo in fine al manoscritto a un'altra dimostrazione dello <lb/>stesso teorema, che, per mezzo della descrizione di un semicerchio, e dietro <lb/>le note propriet&agrave; delle tangenti e delle recanti di lui, riesce assai pi&ugrave; breve. <lb/><figure id="id.020.01.2629.1.jpg" xlink:href="020/01/2629/1.jpg"/></s></p><p type="caption">

<s>Figura 104.</s></p><p type="main">

<s>&ldquo; Aliter brevius: Posito angulo AES aequale angulo <lb/>EAM erit linea ES parallela AM. </s>

<s>Ergo perpendicularis ad <lb/>MX: eritque aequalis SA. Quare, centro S et intervallo SE, <lb/>circulus tanget MX in E, unde patet propositum &rdquo; (ibid., <lb/>fol. </s>

<s>130 ad tergum). </s></p><p type="main">

<s>PROPOSITIO XL, PROBLEMA XII. &mdash; <emph type="italics"/>Nel triangolo OB<gap/><emph.end type="italics"/><lb/>(fig. </s>

<s>104) <emph type="italics"/>rettangolo in B, divisa l'ipotenusa CO in parti <lb/>date, e data la distanza dal punto H della divisione al <lb/>cateto BO; trovare la lunghezza di esso cateto.<emph.end type="italics"/></s></p><p type="main">

<s>Condotta dal punto H la LH, parallela a BI, ecco come <lb/>Galileo risolve il facile problema: &ldquo; Detur IH, dabitur IO. <lb/>per ablationem quadrati IH ex quadrato HO. Deinde, ablata IH ex BC, datur <lb/>LC, cuius quadratum, ablatum ex quadrato CH dato, dat quadratum LH, et <lb/>ipsam LH, idest BI. </s>

<s>Ergo dabitur tota BO (ibid., fol. </s>

<s>132 ad t.). </s></p><pb xlink:href="020/01/2630.jpg" pagenum="255"/><p type="main">

<s>PROPOSITIO XLI, THEOREMA XXIX. &mdash; <emph type="italics"/>Alle estremit&agrave; del diametro AF<emph.end type="italics"/><lb/>(fig. </s>

<s>105) <emph type="italics"/>condotte le tangenti AB, FE, e la secante BE, &ldquo; si ut EB ad <lb/>BD, ita est DB ad BC, erit ita ED ad DC: et quia EB est dupla BC, erit <lb/>quadratum ED duplum quadrati DC &rdquo;<emph.end type="italics"/> (ibid., fol. </s>

<s>158). <lb/><figure id="id.020.01.2630.1.jpg" xlink:href="020/01/2630/1.jpg"/></s></p><p type="caption">

<s>Figura 105.</s></p><p type="main">

<s>Se EB:BD=BD:BC, dividendo <lb/>avremo EB&mdash;BD:BD=BD&mdash;BC:BC, <lb/>ossia ED:BD=DC:BC, e per meta&shy;<lb/>stasi ED:DC=BD:BC, dalla quale <lb/>e dalla prima s'ha EB:BD=ED:DC. </s>

<s><lb/>Da questa, che conferma la verit&agrave; della <lb/>prima parte del teorema, inalzata a qua&shy;<lb/>drato, ed osservando che BD2=EB.BC, <lb/>se ne deduce EB2:EB.BC=ED2:DC2, <lb/>ossia EB:BC=ED2:DC2, che conferma la verit&agrave; dell'altra parte dello stesso <lb/>teorema, perch'essendo EB il doppio di BC, anche ED2 sar&agrave; il doppio di DC2. <lb/><figure id="id.020.01.2630.2.jpg" xlink:href="020/01/2630/2.jpg"/></s></p><p type="caption">

<s>Figura 106.</s></p><p type="main">

<s>PROPOSITIO XLII, THEOREMA XXX. &mdash; <emph type="italics"/>Nel semicir&shy;<lb/>colo ABC<emph.end type="italics"/> (fig. </s>

<s>106) <emph type="italics"/>sia condotta la corda AB, e dalla <lb/>estremit&agrave; di lei la BG perpendicolare al diametro: con&shy;<lb/>dotta un'altra corda qualunque, come AC, la quale tagli <lb/>in D quella stessa perpendicolare, dico che il quadrato di <lb/>AB &egrave; uguale al rettangolo di AC in AD.<emph.end type="italics"/></s></p><p type="main">

<s>Il quadrato di AB &egrave; uguale ad AH.AG. </s>

<s>Ma condotta <lb/>la corda CH i triangoli simili ACH, ADG danno AH:AD= <lb/>AC:AG, dunque AH.AG &egrave; uguale ad AD.AC, e perci&ograve; <lb/>il quadrato di AB &egrave; uguale al rettangolo di AC in AD, come <lb/>Galileo dimostra con queste brevi parole: &ldquo; AB est media <lb/>inter CA, AD: nam rectangulus CAD aequatur rectangulo <lb/>HAG. </s>

<s>Si enim ducatur HG, erit triangulus ACH simile triangulo ADG &rdquo; <lb/>(ibid., fol. </s>

<s>35). </s></p><p type="main">

<s>&ldquo; PROPOSITIO, XLIII, THEOREMA XXXI. &mdash; <emph type="italics"/>Sit IC<emph.end type="italics"/> (fig. </s>

<s>107) <emph type="italics"/>perpendi&shy;<lb/>cularis ad diametrum circuli AB, ductaque a puncto A quacumque linea,<emph.end type="italics"/><lb/><figure id="id.020.01.2630.3.jpg" xlink:href="020/01/2630/3.jpg"/></s></p><p type="caption">

<s>Figura 107<lb/><emph type="italics"/>circumferentiae et perpendiculari <lb/>CI occurrens, ut AID, AD, ADI, <lb/>dico rectangulum DAI rectangulo <lb/>BAC esse aequale &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Si enim iungatur recta DB, <lb/>erit angulus in semicirculo, ad pun&shy;<lb/>ctum D, rectus, estque angulus C <lb/>quoque rectus, communis autem an&shy;<lb/>gulus ad A. </s>

<s>Ergo triangulorum ae&shy;<lb/>quiangulorum DAB, CAI latera erunt <lb/>proportionalia, utque BA ad AD, ita <lb/>IA ad AC. </s>

<s>Ergo patet propositum &rdquo; <lb/>(ibid.). </s></p><pb xlink:href="020/01/2631.jpg" pagenum="256"/><p type="main">

<s>PROPOSITIO XLIV, THEOREMA XXXII. &mdash; <emph type="italics"/>Sit circulus, cuius diameter AB<emph.end type="italics"/><lb/>(fig. </s>

<s>108) <emph type="italics"/>et ipsi parallela tangens CE, et ex termino B quaelibet linea BO<emph.end type="italics"/><lb/><figure id="id.020.01.2631.1.jpg" xlink:href="020/01/2631/1.jpg"/></s></p><p type="caption">

<s>Figura 108.<lb/><emph type="italics"/>in circulo applicetur. </s>

<s>Dico perpendiculares, quae <lb/>a termino B et O ipsi BO accommodantur, pro&shy;<lb/>tractas, de linca CE partem diametro circuli ae&shy;<lb/>qualem semper intercipere. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Iungantur enim A, O, et extendatur ad <lb/>tangentem in F, quae ad BO erit perpendicularis, <lb/>cui ex B parallela sit BE: demonstrandum FE <lb/>diametro circuli esse aequalem. </s>

<s>Id autem constat, <lb/>quia in parallelogrammo ABEF latera AB, FE <lb/>opposita aequalia sunt, ex Elementis. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Vel dicas quod ducta, ex O, OG parallela <lb/>ipsi AB, et BG perpendiculari ad BO, abscindet <lb/>semper OG aequalis diametro circuli, quod patet <lb/>ex triangulis AOB, OBG similibus et aequalibus &rdquo; <lb/>(ibid., fol. </s>

<s>68). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XLV, THEOREMA XXXIII. &mdash; <lb/><emph type="italics"/>Est LI ad IE<emph.end type="italics"/> (fig. </s>

<s>109) <emph type="italics"/>ut IA ad AE; CF autem <lb/>ad FE, ut FD ad DE, et sunt EF, EI aequa&shy;<lb/>les: probandum est LE maiorem esse quam CE &rdquo;<emph.end type="italics"/><lb/>(ibid., fol. </s>

<s>61). </s></p><p type="main">

<s>Abbiamo IE/EA>FE/ED perch'essendo i numeratori uguali per supposizione. </s>

<s><lb/>EA &egrave; minore del denominatore ED. Componendo, sar&agrave; (IE+EA)/EA>(FE+ED)/ED, <lb/>ossia AI/EA>FD/ED. </s>

<s>Son dati IA/AE=LI/IE, FD/DE=CF/FE; dunque LI/IE>CF/FE, e com&shy;<lb/><figure id="id.020.01.2631.2.jpg" xlink:href="020/01/2631/2.jpg"/></s></p><p type="caption">

<s>Figura 109.<lb/>ponendo, LE/EI>CE/EF.Ma EI=EF, dunque LE>CE. <lb/>come dimostra Galileo con discorso simile a questo <lb/>nella sostanza, bench&egrave; alquanto differente nella <lb/>forma. </s></p><p type="main">

<s>&ldquo; Quia EA minor est ED, IE ad EA maio&shy;<lb/>rem habet rationem, quam FE ad ED. Et, com&shy;<lb/>ponendo, IA ad AE maiorem rationem habet quam <lb/>FD ad DE. Verum, ut IA ad AE, ita est LI ad IE. </s>

<s><lb/>Ut autem FD ad DE, ita CF ad FE. </s>

<s>Ergo LI ad IE <lb/>maiorem rationem habet, quam CF ad FE. Et, <lb/>componendo, LE ad EI maiorem habet rationem, <lb/>quam CE ad EF. </s>

<s>Sunt autem EF, EI aequales; <lb/>ergo LE maior est quam CE &rdquo; (ibid.). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XLVI, THEOREMA XXXIV. &mdash; <emph type="italics"/>Fiat ut BA<emph.end type="italics"/> (fig. </s>

<s>110), <emph type="italics"/>cum <lb/>dupla AC, ad AC, ita CA ad AE, et ut BA ad AC, ita EA ad AR, et<emph.end type="italics"/><pb xlink:href="020/01/2632.jpg" pagenum="257"/><emph type="italics"/>ab R ducatur perpendicularis RX. </s>

<s>Dico CR, ER, RA esse proportionales <lb/>et amplius EA, XA aequales. </s>

<s>&rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.2632.1.jpg" xlink:href="020/01/2632/1.jpg"/></s></p><p type="caption">

<s>Figura 110.</s></p><p type="main">

<s>&ldquo; Quia enim ut BA, cum dupla AC, ad AC, ita <lb/>CA ad AE, dividendo erit ut BA cum AC ad AC, ita <lb/>CE ad EA. </s>

<s>Et quia ut BA ad AC, ita EA ad AR, erit <lb/>componendo ut BA, cum AC, ad AC, ita ER ad RA. </s>

<s><lb/>Sed ut BA, cum AC, ad AC, ita CE ad EA, ergo ut <lb/>CE ad EA, ita ER ad RA, et ambo antecedentia ad <lb/>ambo consequentia, nempe CR ad RE. </s>

<s>Sunt itaque CR, <lb/>ER, RA proportionales &rdquo; (ibid., fol. </s>

<s>69). </s></p><p type="main">

<s>Dalla CE:ER=EA:RA abbiamo componendo CE+ER:ER= <lb/>EA+RA:RA, ossia CR:ER=ER:AR. </s></p><p type="main">

<s>&ldquo; Et amplius: quia ut BA ad AC, ita positum est EA ad AR, et, propter <lb/>similitudinem triangulorum, ut BA ad AC, ita XA ad AR; ergo ut EA ad <lb/>AR, ita XA ad AR. </s>

<s>Sunt itaque EA, XA aequales &rdquo; (ibid.). </s></p><p type="main">

<s>PROPOSITIO XLVII, THEOREMA XXXV. &mdash; <emph type="italics"/>Nel quadrante AEB<emph.end type="italics"/> (fig. </s>

<s>111) <lb/><emph type="italics"/>tirata la corda AB, e la secante AC, sopra la quale si costituisca il punto S,<emph.end type="italics"/><lb/><figure id="id.020.01.2632.2.jpg" xlink:href="020/01/2632/2.jpg"/></s></p><p type="caption">

<s>Figura 111.<lb/><emph type="italics"/>in modo che AS sia terza proporzionale <lb/>fra AC, AE; dico che AB ad AS &egrave; come <lb/>il cubo di BA al cubo di AE.<emph.end type="italics"/></s></p><p type="main">

<s>Si suppone da Galileo il primo <lb/>Lemma alla proposizione XXXVI del <lb/>terzo dialogo delle due Scienze nuove, in <lb/>cui si dimostra che il quadrato di AB &egrave; <lb/>uguale al rettangolo di CA in AE, d'onde <lb/>AB2:AE=AC:1, ossia AB2:AE2= <lb/>AC:AE. </s>

<s>E perch&egrave; AS &egrave; terza propor&shy;<lb/>zionale dopo AC, AE avremo AB2:AE2=AC:AE=AE:AS. </s>

<s>Ma per le <lb/>note propriet&agrave; geometriche &egrave;, chiamato D il diametro di tutto intero il cer&shy;<lb/>chio, AC2=D.AN, AE2=D.AR, dunque AB2:AE2=AE:AS= <lb/>AN:AR. </s>

<s>Moltiplicando la proporzione AB2:AE2=AE:AS per l'identica <lb/>BA:AE=BA:AE, se ne conclude all'ultimo AB3:AE3=BA.AE:AS.AE= <lb/>BA:AS, ch'&egrave; la proposta di Galileo, da lui stesso dimostrata con queste pa&shy;<lb/>role, che trascriviamo. </s></p><p type="main">

<s>&ldquo; Ut CA ad AB, ita AB ad AE. </s>

<s>Ergo ut quadratum CA, ad quadra&shy;<lb/>tum BA, vel quadratum BA, ad quadratum AE, ita CA ad AE, vel AE ad <lb/>AS. </s>

<s>Fiet autem hoc, si ipsarum CA, AE accipiatur tertia proportionalis AS. </s>

<s><lb/>At quadratum BA, ad quadratum AE, est ut rectangulum ex diametro in AN. <lb/>ad rectangulum ex diametro in AR, quibus sunt aequalia; ergo ut EA ad AS, <lb/>ita NA ad RA, idest altitudo lineae BA, ad altitudinem lineae AE. </s>

<s>Linea <lb/>ergo BA ad AS est ut cubus BA ad cubum AE &rdquo; (ibid., fol. </s>

<s>188). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XLVIII, THEOREMA XXXVI. &mdash; <emph type="italics"/>Productis lateribus AB, <lb/>AC<emph.end type="italics"/> (fig. </s>

<s>112) <emph type="italics"/>versus D, E, et erectis perpendicularibus CG, BF, ponatur <lb/>AN aequalis AC, et ut AB ad BN, ita fiat AL ad LC, et ipsi AL sece-<emph.end type="italics"/><pb xlink:href="020/01/2633.jpg" pagenum="258"/><emph type="italics"/>tur aequalis AI, ipsarumque AC, IB tertia proportionalis sit CE. </s>

<s>Et dia&shy;<lb/>metro AE semicirculus ducatur, secans CG in G, ductaque per E paral-<emph.end type="italics"/><lb/><figure id="id.020.01.2633.1.jpg" xlink:href="020/01/2633/1.jpg"/></s></p><p type="caption">

<s>Figura 112.<lb/><emph type="italics"/>lela ED, occurrenti AB protractae in D, alter <lb/>semicirculus describatur secans perpendiculum <lb/>BF in F, et iungatur FA. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Primo, constat ut AB ad BD, ita esse <lb/>AC ad CE, et mediam BF, ad mediam CG, ut <lb/>AB ad AC &rdquo; (ibid., fol. </s>

<s>55). </s></p><p type="main">

<s>Consta la prima parte dall'essere BC, DE <lb/>parallele, per cui le due linee AD, AE son ta&shy;<lb/>gliate in modo, da dare la proporzione AB:BD= <lb/>AC:CE, d'onde BD=AB.CE/AC, CE=BD.AC/AB. </s>

<s>Le due medie poi BF, CG <lb/>ne'semicerchi danno BF:CG=&radic;AB.BD:&radic;AC.CE, d'onde, sostituiti <lb/>i valori di BD, CE, consta la verit&agrave; della seconda parte dell'asserto, che cio&egrave; <lb/>BF:CG=AB:AC. </s></p><p type="main">

<s>&ldquo; Secundo, constat insuper IB esse aequale CG &rdquo; (ibid.). </s></p><p type="main">

<s>&Egrave; infatti IB2=AC.CE, per costruzione, ma anche CG2=AC.CE, <lb/>per le note propriet&agrave; del circolo, dunque IB=CG. </s></p><p type="main">

<s>&ldquo; Tertio, cumque FB maior sit CG, ponatur BS ipsi CG aequalis. </s>

<s>Et <lb/>quia ut BA ad AC, seu AN, ita FB ad CG, seu BS, erit, ut AB ad BN, hoc <lb/>est AL, ad LC, ita BF ad FS: et rectangulum sub FB, LC erit aequale rectan&shy;<lb/>gulo sub AL, FS, seu sub AI, FS &rdquo; (ibid.). </s></p><p type="main">

<s>Ci &egrave; constato in primo luogo AB:AC=FB:CG, ossia AB:AN= <lb/>FB:CG. </s>

<s>Dividendo e sostituendo, avremo AB:BN=FB:FS=AE:LC, <lb/>d'onde FB.LC=AL.FS=AI.FS, in conformit&agrave; con l'ultima conclu&shy;<lb/>sione pronunziata da Galileo. </s>

<s>Che poi fossero cos&igrave; fatte conclusioni geome&shy;<lb/>triche preparate per dimostrare la XXXIV proposizione meccanica, scritta nel <lb/><figure id="id.020.01.2633.2.jpg" xlink:href="020/01/2633/2.jpg"/></s></p><p type="caption">

<s>Figura 113.<lb/>terzo dialogo delle due Scienze nuove, <lb/>apparisce manifesto dalla lettura dello <lb/>stesso Dialogo, e vien confermato dalla <lb/>seguente nota, scritta in margine al fo&shy;<lb/>glio ultimamente citato: &ldquo; Totum opus <lb/>videtur esse tale: Secetur AN aequalis <lb/>AC, et, ut AB ad BN, ita fiat AL ad LC, <lb/>et ponatur AI aequalis AL, et, ut AC ad <lb/>IB, ita fiat IB ad CE. </s>

<s>Erit CE linea quae&shy;<lb/>sita, nempe pars superior perpendiculi, ex <lb/>qua mobile conficiet ipsam cum AB, tem&shy;<lb/>pore eodem ac solam AB. &rdquo; </s></p><p type="main">

<s>PROPOSITIO XLIX, THEOREMA XXXVII. &mdash; <emph type="italics"/>Sia il cerchio NDC<emph.end type="italics"/> (fig. </s>

<s>113) <lb/><emph type="italics"/>al diametro NC del quale sia condotto perpendicolare il raggio RD, che <lb/>prolungato venga preciso in A dalla secante CBA. </s>

<s>Dal punto D si con&shy;<lb/>duca DS parallela al detto diametro, e dal punto M, met&agrave; della stessa<emph.end type="italics"/><pb xlink:href="020/01/2634.jpg" pagenum="259"/><emph type="italics"/>DS, si alzi la perpendicolare MF, che incontrer&agrave; in F la corda CD. </s>

<s>Es&shy;<lb/>sendo l'angolo FDM semiretto, sar&agrave; DM uguale a FM, e col centro in M, <lb/>intervallo DM, si descriva la circonferenza DFS. </s>

<s>Fatto ci&ograve;, Galileo nota le <lb/>tre seguenti propriet&agrave; geometriche, che conseguono da una tal costruzione:<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; I. &mdash; Rectangulum CDF aequatur rectangulo RC, DS; rectangulum <lb/>ACB aequatur rectangul<emph type="italics"/>o<emph.end type="italics"/> RCN; ergo rectangulum CDF, ad rectangulum ACB, <lb/>est ut diameter DS ad diametrum NC &rdquo; (ibid., fol. </s>

<s>149 ad terg.). </s></p><p type="main">

<s>Infatti i triangoli simili RDC, DFS danno RC:DF=CD:DS, d'onde <lb/>DF.CD=RC.DS. </s>

<s>E condotta la NB, i triangoli simili NBC, RAC <lb/>danno AC:CN=RC:CB, d'onde AC.CB=CN.RC. </s>

<s>E perci&ograve; avremo <lb/>DF.CD:AC.CB=RC.DS:RC.CN, ossia DF.CD:AC.CB= <lb/>DS:CN, com'aveva concluso Galileo. </s></p><p type="main">

<s>&ldquo; II. &mdash; Ut autem CN ad DS ita CD ad DF, ob similitudinem portio&shy;<lb/>num DBC et DF &rdquo; (ibid.). </s></p><p type="main">

<s>Dall'essere infatti NC2=2DC2, DS2=2DF2, ne consegue CN:DS= <lb/>DC:DF. </s></p><p type="main">

<s>&ldquo; III. &mdash; Ut autem CD ad DF, ita quadratum CO ad quadratum OF &rdquo; <lb/>(ibid.). </s></p><p type="main">

<s>&Egrave; stato fatto tacitamente CD:DO=DO;DF. Dividendo, avremo <lb/>CD&mdash;DO:DO=DO&mdash;DF:DF. </s>

<s>Sostituendo e trasponendo, CO:OF= <lb/>DO:DF, la quale equazione inalzata a quadrato d&agrave; CO2:OF2=DO2:DF2. </s>

<s><lb/>Ma DO2=CD.DF, per la prima, dunque CO2:OF2=CD.DF:DF2, <lb/>ossia CO2:OF2=CD:DF, che conferma la verit&agrave; dell'ultima conclusione <lb/>di Galileo. </s></p><p type="main">

<s>PROPOSITIO L, THEOREMA XXXVIII. &mdash; <emph type="italics"/>Abbiansi nel circolo EIC<emph.end type="italics"/> (fig. </s>

<s>114) <lb/><emph type="italics"/>le tangenti ED, BC parallele, e la secante DB disposta in modo che, inal-<emph.end type="italics"/><lb/><figure id="id.020.01.2634.1.jpg" xlink:href="020/01/2634/1.jpg"/></s></p><p type="caption">

<s>Figura 114.<lb/><emph type="italics"/>zatale sopra, da A centro, una per&shy;<lb/>pendicolare, questa incontri in F la <lb/>ED prolungata, cosicch&egrave;, descritta col <lb/>raggio FA la circonferenza AOP, la <lb/>parte esterna OD torni uguale alla <lb/>ID. </s>

<s>Dico che la somma delle linee <lb/>DF, FA, alla somma delle DA, AE <lb/>sta come il quadrato di AD, o di AB, <lb/>al quadrato di ED o di BC.<emph.end type="italics"/></s></p><p type="main">

<s>Essendo, per la XXXVI del terzo <lb/>di Euclide, PD.DO=AD2, ND.DI= <lb/>ED2, avremo dunque, rammemorandoci <lb/>che DO, DI sono uguali, PD:ND= <lb/>AD2:ED2. </s>

<s>Ma PD=DF+FA, ND= <lb/>EA+AD, e AD, ED sono uguali ad AB, BC: dunque DF+FA:EA+AD= <lb/>AD2:ED2=AB2:BC2; come in modo simile Galileo stesso dimostra col se&shy;<lb/>guente discorso, che la brevit&agrave; del nostro render&agrave; forse pi&ugrave; chiaro: </s></p><p type="main">

<s>&ldquo; Si excessus OD aequatur DI, rectangulum PDO, idest quadratum DA, <pb xlink:href="020/01/2635.jpg" pagenum="260"/>ad rectangulum NDI, idest ad quadratum DE, erit ut linea PD ad DN. </s>

<s>Qua&shy;<lb/>dratum autem DA, ad quadratum DE, est ut quadratum AB, ad quadra&shy;<lb/>tum BC; ergo faciendum est ut PD ad ND sit ut quadratum AB, ad qua&shy;<lb/>dratum BC. PD autem componitur ex duobus mediis DF, FA, et ND constat <lb/><figure id="id.020.01.2635.1.jpg" xlink:href="020/01/2635/1.jpg"/></s></p><p type="caption">

<s>Figura 115.<lb/>ex duabus EA, AD, ita ut duae DF, FA, ad duas <lb/>DA, AE, sint ut quadratum AB, ad quadratum BC &rdquo; <lb/>(ibid., fol. </s>

<s>99). </s></p><p type="main">

<s>&ldquo; PROPOSITIO LI, PROBLEMA XIII. &mdash; <emph type="italics"/>Dato per&shy;<lb/>pendiculo AB<emph.end type="italics"/> (fig. </s>

<s>115) <emph type="italics"/>et inflexa EBG, cui perpen&shy;<lb/>dicularis sit BC; oportet semicirculum per E de&shy;<lb/>scribere ita ut excessus mediae inter EG, GB, quae <lb/>est GC, seu GD, una cum perpendiculo BF, secto <lb/>a perpendiculari GF, sint aequales mediae inter <lb/>EB, BG, nempe BC. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sit factum. </s>

<s>Si CB aequatur DB, BF, posita <lb/>communi BG, duae CB, BG, erunt aequales duabus DG, BF; idest CG, BF &rdquo; <lb/>(ibid., fol. </s>

<s>97 ad tergum). </s></p><p type="main">

<s>Se CB=DB+BF, aggiunta la comune BG, sar&agrave; BG+CB= <lb/>DB+BF+BG=DG+BF, d'onde CB=DG+BF&mdash;BG, e perci&ograve; <lb/>BG &egrave; l'eccesso cercato. </s></p><p type="main">

<s>PROPOSITIO LII, THEOREMA XXXIX. &mdash; <emph type="italics"/>Nel quadrante TCN<emph.end type="italics"/> (fig. </s>

<s>116) <lb/><emph type="italics"/>prendasi una porzione TCD, dall'estremit&agrave; D della quale si abbassi la DX<emph.end type="italics"/><lb/><figure id="id.020.01.2635.2.jpg" xlink:href="020/01/2635/2.jpg"/></s></p><p type="caption">

<s>Figura 116.<lb/><emph type="italics"/>perpendicolare al diametro TM, e condotta la <lb/>DF, ad esso diametro parallela, se le descriva <lb/>sopra il mezzo cerchio DCF. </s>

<s>Condotta la corda <lb/>DT, e la DC prolungata in S, infino all'incon&shy;<lb/>tro con la tangente TS, presa poi la DE media <lb/>proporzionale fra DS, DC, se si congiungano <lb/>con E i punti S, B, C, dico che EB sar&agrave; bisset&shy;<lb/>trice dell'angolo SEC.<emph.end type="italics"/></s></p><p type="main">

<s>Galileo stette a principio incerto se ci&ograve; fosse <lb/>vero, e in capo a un primo tentativo di dimostra&shy;<lb/>zione scriveva: <emph type="italics"/>Credo angulum SEC bifariam <lb/>esse sectum per EB<emph.end type="italics"/> (ibid., fol. </s>

<s>129), incominciando a ragionare, per veder <lb/>se la cosa riusciva, in questo modo: </s></p><p type="main">

<s>&ldquo; Angulus TDS duabus circumferentiis OC, CT insistit; ergo illae sunt <lb/>similes, et circumferentia DO similis est DCT. Ergo, ut linea DO ad OC, ita <lb/>DT ad TC. </s>

<s>Et quia rectangulum DSC aequatur quadrato ST, ergo, ut DS <lb/>ad ST, ita TS ad SC. </s>

<s>Ergo triangula DST, TSC similia sunt, quibus et trian&shy;<lb/>gula ODC, ICB similia sunt .... &rdquo; (ibid.). </s></p><p type="main">

<s>Trovatosi da un tal discorso aggirato, Galileo lasci&ograve; la dimostrazione in&shy;<lb/>terrotta, e poco di poi tornatoci sopra, ebbe dalle seguenti brevi considera&shy;<lb/>zioni la desiderata conferma della propria opinione. </s>

<s>Se DS:DE=DE:DC, <lb/>dunque i triangoli SDE. DEC son simili. </s>

<s>Ed essendo fatta DE=DB, da <pb xlink:href="020/01/2636.jpg" pagenum="261"/>DS:DB=DB:DC avremo, dividendo, SD&mdash;BD:SD=DB&mdash;DC:DE, <lb/>d'onde, per sostituzione e per trasposizione, SD:DE=SB:BC. Ma, per i <lb/>detti triangoli simili, SD:DE=SE:EC, dunque SE:EC=SB:BC, <lb/>ond'&egrave;, per la terza del Sesto, EB veramente bissettrice. </s></p><p type="main">

<s>&ldquo; Quia est, scrive Galileo, ut SD ad DE, ita DE ad DC, ergo triangu&shy;<lb/>lus SDE similis ert triangulo DEC, et, ut SE ad EC, ita SD ad DE, et ita <lb/>est SB ad BC: ergo angulus CES bifariam secatur a linea EB &rdquo; (ibid.). </s></p><p type="main">

<s>A queste proposizioni di Geometria elementare si pu&ograve; aggiungere la se&shy;<lb/>guente, che solamente annunziamo per essere stata gi&agrave; trascritta dall'auto&shy;<lb/>grafo galileiano, a pag. </s>

<s>450 del nostro Tomo quarto: </s></p><p type="main">

<s>&ldquo; PROPOSITIO LIII, THEOREMA XL. &mdash; <emph type="italics"/>Sit parabola parallelogrammo <lb/>inscripta: dico parallelogrammum parabolae esse sesquialter; hoc est esse <lb/>triplum reliqui spacii extra parabolam &rdquo;<emph.end type="italics"/> (ibid., fol. </s>

<s>102 ad tergum). </s></p><p type="main">

<s>D'altri teoremi di Geometria superiore non ci sono occorsi, nell'esame <lb/>dei manoscritti, gli esempi, e dall'altra parte, nella terza giornata dei Mas&shy;<lb/>simi sistemi, e nella terza Lettera solare pu&ograve; vedersi come Galileo risolva per <lb/>le lunghe i triangoli, calcolandone le funzioni trigonometriche dei lati, senza <lb/>l'uso dei logaritmi. </s>

<s>Di qui lo studio di lui di ridurre, quanto fosse possibile, <lb/>la Trigonometria alla Geometria semplice, come potrebbe mostrarsi dal com&shy;<lb/>parare il seguente incominciato esercizio manoscritto con quel che leggesi <lb/>stampato nella terza Lettera al Velsero (Alb. </s>

<s>III, pag. </s>

<s>479-83), per dimo&shy;<lb/>strare le incongruenze, che nascerebbero nelle proporzioni dei moti tra il Sole <lb/>e le sue macchie, quando queste si ponessero non aderenti alla superficie, <lb/>ma rivolgentisi in una sfera, concentrica col globo dello stesso Sole. </s></p><p type="main">

<s>Riferendoci alla figura, impressa in ordine la V, nella Tavola X alligata <lb/>infine al Tomo citato dell'Alb&egrave;ri, son disposti in una tavoletta i seguenti va&shy;<lb/>lori: IO=1000, ID=974, DO=227, DA=500, AE=2203, DL=866. <lb/>Di contro alla quale tavoletta sta scritto: </s></p><p type="main">

<s>&ldquo; Sian CA, AB, AD note: sar&agrave; nota anco DE e BF. </s>

<s>E perch&egrave; DH &egrave; <lb/>nota, sendo uguale a DE, ed essendo il triangolo HID simile al noto FBC, <lb/>sar&agrave; noto DI, ed &egrave; nota DL, che sono i sini degli archi HN, MN, li quali <lb/>per&ograve; saranno noti, e le loro proporzioni. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia il globo solare, il cui semidiametro AB, e sia l'arco BL gr. </s>

<s>30: <lb/>sar&agrave; la linea LD 866, di quali AB &egrave; 1000. Prima &egrave; manifesto che due punti <lb/>B, L, posti nella superficie, passeranno i sini LD, BA nell'istesso tempo. </s>

<s>&Egrave; <lb/>inoltre chiaro che, ponendogli nelle linee DE, AC, prolungate in infinito, i <lb/>punti E, C traverserebbono le medesime linee BA, BD in tempi proporzio&shy;<lb/>nali ad esse, sicch&egrave;, non si dando tal distanza infinita, i transiti per BA, LD <lb/>si faranno in tempi, che fra di loro haranno minor proporzione, che non ha <lb/>la linea BA alla DL. </s>

<s>E perch&egrave;, sendo DL 866, AB &egrave; 1000, et il tempo per <lb/>LD, al tempo per BA, deve essere come 7 a 8; facciasi come 7 a 8, cos&igrave; 866 <lb/>a un altro, che sia DI: sar&agrave; 947, e la rimanente IG sar&agrave; 53. Adattisi la IO <lb/>uguale a GD, e per A passi la parallela AE, che concorra con DC in E, e, <lb/>centro A, facciasi il cerchio CEF .... &rdquo; (ivi, fol. </s>

<s>133). </s></p><pb xlink:href="020/01/2637.jpg" pagenum="262"/><p type="main">

<s>Ma perch&egrave; meglio possa darsi un'idea de'processi trigonometrici di Ga&shy;<lb/>lileo, riferiremo la formula, per cos&igrave; dire, che serv&igrave; ai calcoli del trovar le <lb/>distanze assegnate, e da assegnarsi alla stella, della quale si tratta nei Mas&shy;<lb/>simi sistemi, verso il mezzo della terza giornata. </s>

<s>Il problema, per risolvere <lb/>il quale in tutti i casi si vuol trovar la regola dell'operazione, pu&ograve; rappre&shy;<lb/>sentarsi in questa forma: </s></p><p type="main">

<s>PROPOSITIO LIV, PROBLEMA XIV. &mdash; <emph type="italics"/>Essendo dati gli angoli IAC, AEC<emph.end type="italics"/><lb/>(fig. </s>

<s>117) <emph type="italics"/>ed essendo il lato AC noto, notificare il lato EC.<emph.end type="italics"/></s></p><p type="main">

<s>I canoni elementari della Trigonometria danno EC:AC=sen(180&mdash;IAC): <lb/><figure id="id.020.01.2637.1.jpg" xlink:href="020/01/2637/1.jpg"/></s></p><p type="caption">

<s>Figura 117.<lb/>sen AEC=sen IAC:sen AEC, in conformit&agrave; con quel <lb/>che conclude Galileo nel seguente manoscritto, al quale <lb/>&egrave; premessa una tale osservazione: </s></p><p type="main">

<s>&ldquo; Qui sotto son notate alcune computazioni, per le <lb/>quali si trova la lontananza della Stella dal centro, le <lb/>quali computazioni son fatte sopra la parallasse delle al&shy;<lb/>tezze meridiane minime, e sopra la distanza veduta della <lb/>Stella dal vertice. </s>

<s>Il progresso dell'operazione &egrave; tale: &rdquo; </s></p><p type="main">

<s>&ldquo; La distanza dal vertice MZ mi d&agrave; l'angolo IAC <lb/>e la parallasse data &egrave; l'angolo IEC. L'angolo A mi <lb/>d&agrave; il sino IC, nelle parti delle quali il sino tutto AC <lb/>&egrave; 100,000. E parimente l'angolo E mi d&agrave; il sino della <lb/>medesima IC, nelle parti delle quali il sino tutto CE &egrave; <lb/>100,000. Ora, per la regola aurea, diremo: Se quando IC, come sino del&shy;<lb/>l'angolo E, &egrave; tanto, la CE &egrave; 100,000; quando IC, come sino dell'angolo A, <lb/>&egrave; tanto, quanto sar&agrave; CE? </s>

<s>Moltiplica dunque il sino di A per 100,00, e parti <lb/>l'avvenimento per il sino di E, et arai la distanza CE nelle parti, delle quali <lb/>il semidiametro CA &egrave; 100,000. Onde, dividendo di nuovo il quoziente tro&shy;<lb/>vato per 100,000, avremo quanti semidiametri CA sono nella CE. </s>

<s>E per fare <lb/>l'operazione breviss&igrave;ma, senz'altre moltiplicazioni, hasta partire il sino del&shy;<lb/>l'angolo A per il sino dell'angolo E, ed il quoziente sar&agrave; il numero de'se&shy;<lb/>midiametri CA contenuti nella distanza CE. </s>

<s>Vegghiamo ora con tal regola <lb/>quanta venga l'altezza della Stella, secondo tutte le osservazioni, comincian&shy;<lb/>doci da Ticone &rdquo; (MSS. Gal., P. III, T II, fol. </s>

<s>14). </s></p><p type="main">

<s>Qui term&igrave;na dei <emph type="italics"/>Problemi matematici<emph.end type="italics"/> la promessa raccolta, l'intenzion <lb/>della quale essendo, come si disse, non quella solamente di dare un'idea <lb/>delle materie, che aveva Galileo da ridurre nel suo Dialogo novissimo, ma di <lb/>servire alla storia intima del pensiero di lui, e della Scienza; se ci siamo in <lb/>qualche parte riusciti &egrave; da attribuirlo all'aver noi per i primi, e con insolita <lb/>diligenza, consultati i preziosi manoscritti. </s>

<s>Anzi di quell'esame non abbiamo <lb/>dato altro che un saggio, per provocare la diligenza altrui, che dovrebbe riu&shy;<lb/>scire pi&ugrave; fruttuosa della nostra, e di quella di certi novelli editori, che, co&shy;<lb/>piando materialmente senza nulla curarsi d'intendere quel che leggono, ri&shy;<lb/>ducono a stupidi enimmi i responsi dell'Oracolo venerato. </s></p><pb xlink:href="020/01/2638.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO V.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Del trattato dei Centri di gravit&agrave; <lb/>di Evangelista Torricelli<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Dei primi csercizi giovanili intorno ai libri baricentrici di Archimede. </s>

<s>&mdash; II. Dell'invenzione de <lb/>centro di gravit&agrave; nelle porzioni di parabola e di cerchio. </s>

<s>&mdash; III. </s>

<s>Di alcune nuove invenzioni <lb/>baricentricho, per via degli indivisibili. </s>

<s>&mdash; IV. </s>

<s>Del centro di gravit&agrave; degli archi di cerchio. </s>

<s>e <lb/>delle fallacie del Guldin intorno ai centri delle callotte, delle zone e de'settori sferici, notate dal <lb/>Cavalieri, dietro le dimostrazioni avute dal Torricelli. </s>

<s>&mdash; V. </s>

<s>Della diversit&agrave; del metodo del <lb/>Keplero da quello del Cavalieri, e come fosse questo applicato dal Torricelli, per ritrovare in <lb/>vario modo il centro di gravit&agrave; del cono, e di altre figure. </s>

<s>&mdash; VI. </s>

<s>Del centro di gravit&agrave; dei so&shy;<lb/>lidi scavati &mdash; VII. </s>

<s>Del centro di gravit&agrave; dei solidi vasiformi. </s>

<s>&mdash; VIII. </s>

<s>Del centro di gravit&agrave; dei <lb/>solidi conoidali. </s>

<s>&mdash; IX. </s>

<s>Del centro di gravit&agrave; dei solidi cavalierani, e della cicloide. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>All'opera di ridurre alla maggior perfezione che fosse possibile i trattati <lb/>delle nuove Scienze del moto, intorno a che abbiamo veduto le sollecite cure <lb/>datesi negli ultimi anni della sua vita da Galileo, successe quel Torricelli, <lb/>che abbiamo trovato in Arcetri a pi&egrave; del letto, dove il vecchio maestro lan&shy;<lb/>guiva, quasi rigoglioso rampollo dell'albero, che &egrave; gi&agrave; per cadere. </s>

<s>L'eccel&shy;<lb/>lenza del successore si poteva fin d'allora giudicar dai due libri del moto <lb/>dei gravi e dei proietti, i quali erano gi&agrave; stati scritti, e due anni dipoi, nel <lb/>pubblicarli, si davano come una diligente respigolatura nel campo altrui. </s>

<s>In <lb/>fine al volume per&ograve; prometteva l'Autore ai lettori, ai quali non fossero quelle <lb/>cose dispiaciute, che avrebbe aggiunto un trattato dei centri di gravit&agrave; delle <lb/>superficie e dei solidi, come parti rimaste intatte nei libri del Commandino, <lb/>del Valerio e dello stesso Galileo. </s>

<s>Il Mersenno poi si profferse di far quel trat&shy;<lb/>tato stampare a Parigi, n&egrave; il Torricelli mostr&ograve; di ricusare il favore, rispon-<pb xlink:href="020/01/2639.jpg" pagenum="264"/>dendo alla liberale profferta cos&igrave; fatte parole: &ldquo; Inventa mea geometrica <lb/>mechanica, hoc est nugas illas, quas inveni, sed non digessi, circa centra gra&shy;<lb/>vitatis figurarum, Geometris, siquidem finita et in ordinem redacta habebo, <lb/>fortasse favorem et diligentiam, quam mihi tanta liberalitate offers, non re&shy;<lb/>cusabo (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>76). </s></p><p type="main">

<s>Si prometteva dunque dal Torricelli una cosa, che gli avrebbe dovuto <lb/>accrescere di molto il merito e la gloria, perch&egrave;, dall'umile condizione di <lb/>respigolatore nel capo altrui, veniva a sollevarsi all'altezza di cultore nel <lb/>campo proprio. </s>

<s>Ma pur egli confessa di andar languidamente a conquistare quel <lb/>merito e quella gloria, distratto dagli esercizi dell'arte di formare i vetri per i <lb/>Canocchiali, che venivano a lusingarlo con lodi molto pi&ugrave; ambite, e a ricom&shy;<lb/>pensarlo con premi assai pi&ugrave; grandi, <emph type="italics"/>quandoquidem serenissimi Magni Ducis <lb/>effusa et vere regia liberalitas magno auri pondere donatum me non se&shy;<lb/>mel voluit<emph.end type="italics"/> (Op. </s>

<s>geom., P. II cit., pag. </s>

<s>150). Ma non &egrave; gi&agrave; la sete dell'oro, <lb/>si piuttosto il gusto di avere a mano un ottimo Telescopio che, come del <lb/>trattato dei centri di gravit&agrave;, lo fa non curante di quell'altro delle propor&shy;<lb/>zioni, in fine al proemio del quale cos&igrave; scriveva: &ldquo; Interea praestat circa vitra <lb/>ad usum Telescopii potius laborare, quae ab omnibus Europae partibus expe&shy;<lb/>tuntur, quam circa theorematum dispositionem figurarumque accuratam de&shy;<lb/>scriptionem excruciari: peracta scilicet inventione, quae sola voluptati esse <lb/>potest &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXVI, fol. </s>

<s>59). </s></p><p type="main">

<s>L'invenzione, della quale il Torricelli qui e altrove tanto si compiace, <lb/>consiste nell'essersi, com'egli dice, incontrato nella soluzione di quell'ottico <lb/>problema <emph type="italics"/>tamdiu perquisiti, cuius videlicet figurae esse debeant superficies <lb/>vitrorum, quae ad usum Telescopii elaborantur<emph.end type="italics"/> (Op. </s>

<s>cit., pag. </s>

<s>150). Sa&shy;<lb/>rebbe la compiacenza stata pi&ugrave; giusta, se avesse scoperta e dimostrata la legge <lb/>delle rifrazioni, ci&ograve; ch'essendo rimasto a fare allo Snellio e al Cartesio, non <lb/>aveva dunque il Torricelli propriamente risoluto un problema di scienza, ma <lb/>di semplice arte vetraria, e per emulare un occhialaio di Napoli non si cur&ograve; <lb/>di disporre i suoi teoremi e di descrivere accuratamente le sue figure di Geo&shy;<lb/>metria. </s>

<s>Giacciono infatti que'teoremi confusamente scritti nelle carte disperse, <lb/>e abbandonati: le figure illustrative vi son neglette, e rimane appena nel&shy;<lb/>l'Autore una languida memoria di quelle, ch'erano vere invenzioni, e che <lb/>gli avrebbero meritata appresso i posteri una vera gloria: cosicch&egrave;, invitato <lb/>un giorno a discorrerne per lettera da Michelangiolo Ricci rispondeva in fretta <lb/>di non saperlo fare <emph type="italics"/>perch&egrave; aveva la testa piena di vetri &rdquo;<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., <lb/>T. XL, fol. </s>

<s>88). </s></p><p type="main">

<s>Quelle invenzioni, nelle quali non ebbero la fortuna d'incontrarsi n&egrave; <lb/>l'antico Archimede, n&egrave; i moderni commentatori di lui, come il Commandino, <lb/>il Valerio, il Galileo, consistevano nei centri di gravit&agrave; della callotta, del set&shy;<lb/>tore e del frusto di sfera; della cicloide, e d'innumerevoli altre superficie e <lb/>solidi, con metodi affatto nuovi: che se fosse stato tutto messo in ordine di <lb/>trattato alla pubblica luce, la Meccanica avrebbe avuto dal Torricelli un libro <lb/>non men compiuto, ma assai pi&ugrave; bello di quel del Wallis. </s>

<s>Ebbe non poca <pb xlink:href="020/01/2640.jpg" pagenum="265"/>parte a quella iattura la morte, e quando furono dati al Viviani, perch&egrave; si <lb/>volevano in ogni modo stampare, gli scritti postumi del Torricelli, non fu&shy;<lb/>rono le ultime cure rivolte ai centri di gravit&agrave;, il libro de'quali pensava il <lb/>Viviani stesso di distribuirlo nei quattro capitoli seguenti: I. De'piani, cio&egrave; <lb/>del Settore del circolo, di alcuni piani e solidi, per gl'indivisibili; del trian&shy;<lb/>golo, della parabola, dei frusti e porzioni di parabola. </s>

<s>II. </s>

<s>Delle superficie <lb/>curve, cio&egrave; della superficie conica, della callotta e della zona sferica. </s>

<s>III. </s>

<s>Dei <lb/>solidi sferali, cio&egrave; dell'emisferio, del settore e del frusto sferico. </s>

<s>IV. </s>

<s>Di vari <lb/>altri solidi, cio&egrave; del cono, del segmento conico, del frusto parabolico, del so&shy;<lb/>lido cavalieriano, dei cilindri sbucati. </s></p><p type="main">

<s>Pu&ograve; quest'ordinamento del Trattato torricelliano vedersi proposto nel <lb/>primo foglio del <emph type="italics"/>tomo XXXVI dei Discepoli,<emph.end type="italics"/> in fine al quale &egrave; fedelmente <lb/>eseguito in nitida copia sopr'altra copia men compiuta del Serenai. </s>

<s>Si dice <lb/>che quella copia pi&ugrave; moderna fosse preparata per le stampe, per le quali ne <lb/>fossero state gi&agrave; disegnate e incise le figure a parte, che perci&ograve; mancano ai <lb/>luoghi loro ne'larghi margini bianchi del manoscritto. </s>

<s>Fu bene che non <lb/>avesse esecuzione il meditato disegno, perch&egrave; sarebbe stato per riuscire tale <lb/>sconciatura, da non si credere che vi avesse avuto parte il Viviani, alla re&shy;<lb/>vision del quale non dovettero essere stati sottoposti que'fogli. </s>

<s>Com'&egrave; cre&shy;<lb/>dibile infatti ch'egli potesse dar licenza di stamparli, cos&igrave; com'erano man&shy;<lb/>canti, non solo delle aggiunte e delle illustrazioni fattevi da lui stesso con <lb/>tanta diligenza, ma di alcuni dei lemmi preparati gi&agrave; dall'Autore, e senza i <lb/>quali non era possibile che si avessero per ben dimostrate le pi&ugrave; importanti <lb/>fra quelle baricentriche proposizioni? </s></p><p type="main">

<s>I manoscritti fornirebbero il materiale necessario a chi volesse costruire <lb/>il trattato dei centri di gravit&agrave; del Torricelli, il qual trattato altr'ordine pren&shy;<lb/>derebbe alle mani di un semplice compilatore, o di un che vada raccogliendo <lb/>quegli sparsi teoremi, per servirsene come documenti di storia. </s>

<s>Tale essendo <lb/>l'ufficio e l'intendimento nostro, non per questo saranno defraudati i Let&shy;<lb/>tori di nessuna delle parti o principali o secondarie di quel trattato, in cui <lb/>troveranno solamente la differenza che, in vece di veder succedersi le pro&shy;<lb/>posizioni via via secondo l'ordine logico, le vedranno succedersi secondo l'or&shy;<lb/>dine cronologico: secondo il tempo cio&egrave; che le concep&igrave; la mente dell'Autore, <lb/>sotto l'influsso di queste e di quelle tradizioni, le prime e pi&ugrave; efficaci tra le <lb/><figure id="id.020.01.2640.1.jpg" xlink:href="020/01/2640/1.jpg"/></s></p><p type="caption">

<s>Figura 118.<lb/>quali son quelle derivate dai libri di Archimede <emph type="italics"/>De <lb/>aequiponderantibus,<emph.end type="italics"/> e <emph type="italics"/>De quadratura parabolae,<emph.end type="italics"/> che <lb/>il Torricelli studioso commentava con questi suoi primi <lb/>giovanili esercizi. </s></p><p type="main">

<s>&ldquo; SUPPOSIZIONI. &mdash; Supponghiamo che le grand&egrave;zze, <lb/>sospese da un punto libere, cio&egrave; che possano rivoltarsi e <lb/>moversi, non si fermino mai, fintanto che il centro della <lb/>gravit&agrave; di essa magnitudine non sia nell'infimo punto del <lb/>suo cerchio. </s>

<s>Altrimenti la magnitudine si sosterrebb&egrave; da s&egrave;, potendo discen&shy;<lb/>dere, il che &egrave; inverosimile. </s>

<s>Per esempio la magnitudine AB (fig. </s>

<s>118) di cui <pb xlink:href="020/01/2641.jpg" pagenum="266"/>centro della gravit&agrave; sia C, intendasi attaccata col filo ED. &Egrave; chiaro che la detta <lb/>grandezza non potr&agrave; mai fermarsi, fintanto che il centro C non sar&agrave; giunto <lb/>nel punto F, cio&egrave; nell'infimo di tutti i siti, che egli possa avere, il che sar&agrave; <lb/>quando il punto C si sar&agrave; accomodato perpendicolarmente sotto il punto E <lb/>della sospensione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Supponghiamo ancora che le linee abbiano il centro della gravit&agrave;, e <lb/>forse non sar&agrave; maggiore assurdo il considerar le linee come gravi, che il <lb/>considerar le superficie pesanti. </s>

<s>Gi&agrave; in buona Geometria non si pu&ograve; dire che <lb/>una linea sia minore di una superficie, ed io credo che tanto sia lontana <lb/>dall'esser grave una linea, quanto una superficie. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE I. &mdash; <emph type="italics"/>Il centro della gravit&agrave; ne'triangoli sta in quella <lb/>linea, che dalla met&agrave; di un lato si tira all'angolo opposto. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia il triangolo ABC (fig. </s>

<s>119), di cui il lato AC sia diviso per mezzo <lb/>in D, e tirata la BD, dico che il centro sta nella BD. </s>

<s>Se &egrave; possibile non vi <lb/><figure id="id.020.01.2641.1.jpg" xlink:href="020/01/2641/1.jpg"/></s></p><p type="caption">

<s>Figura 119.<lb/>stia, ma pongasi essere E. </s>

<s>Tirisi la linea IE paral&shy;<lb/>lela alla BD, ed attacchisi il triangolo con la linea <lb/>immaginaria IE, ed accomodisi in maniera tale, che <lb/>la IE sia perpendicolare all'orizonte. </s>

<s>Dovr&agrave; dunque <lb/>il triangolo star fermo, perch&egrave; il centro E sta nel <lb/>perpendicolo. </s>

<s>Ma producasi una linea HL parallela <lb/>ad AC, e divisa per mezzo in Q, e fatto centro in I, <lb/>ed intervallo IQ, facciasi un cerchio, del quale l'in&shy;<lb/>fimo punto sar&agrave; quello, che &egrave; nel perpendicolo IE, <lb/>e per&ograve; la HL sar&agrave; in stato violento, potendo il suo <lb/>centro discendere ancor pi&ugrave;. </s>

<s>&Egrave; cos&igrave; di tutte le altre <lb/>linee parallele alla medesima base, le quali tutte faranno forza verso il per&shy;<lb/>pendicolo, e per&ograve; il triangolo non star&agrave; fermo. </s>

<s>Adunque il punto E non &egrave; <lb/>centro. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scolio.<emph.end type="italics"/> &mdash; Nota che questa dimostrazione, come anche quelle di Ar&shy;<lb/>chimede e di altri, le quali sono indirette, non hanno forza di provare che <lb/>il centro della gravit&agrave; sia nella linea BD, ma solo provano che non &egrave; fuori <lb/>di essa. </s>

<s>Che poi il centro sia nella detta linea &egrave; petizione, ed &egrave; la petizione <lb/>che le grandezze abbiano il centro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE II. &mdash; <emph type="italics"/>Qualsivoglia figura, o sia piana o sia solida, o <lb/>regolare ovvero anche irregolare, purch&egrave; si possa segar con linee, ovvero<emph.end type="italics"/><lb/><figure id="id.020.01.2641.2.jpg" xlink:href="020/01/2641/2.jpg"/></s></p><p type="caption">

<s>Figura 120.<lb/><emph type="italics"/>piani sempre paralleli, ed i centri delle sezioni siano tutti <lb/>in linea retta; ha il centro della gravit&agrave; nel diametro, <lb/>se sia piana, o nell'asse, se sia solida. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia la figura ABC (120), che intendasi attaccata dal <lb/>punto B, ma per&ograve; liberamente, sicch&egrave; si possa movere. </s>

<s>&Egrave; <lb/>manifesto che la figura si volger&agrave;, sino a tanto che il cen&shy;<lb/>tro della gravit&agrave; sia perpendicolarmente sotto al punto della <lb/>sospensione B. </s>

<s>Intendasi dunque la figura ridotta alla quiete, <lb/>ed il perpendicolo sia la linea BE, nella quale sia il centro I. </s>

<s>Dico che la linea <pb xlink:href="020/01/2642.jpg" pagenum="267"/>BIE &egrave; diametro della figura. </s>

<s>Poich&egrave;, se non &egrave;, sia diametro la BD, e, tirata <lb/>la ordinatamente applicata NO, sar&agrave; il di lei centro M, il quale, per esser <lb/>fuori del perpendicolo, potr&agrave; discendere e condursi all'infimo punto del suo <lb/>giro, che &egrave; nel perpendicolo. </s>

<s>Cos&igrave; di tutte le ordinatamente applicate. </s>

<s>Per&ograve; <lb/>la figura non star&agrave; ferma, ma ander&agrave; da quella parte, verso la quale spin&shy;<lb/>gono tutte le applicate. </s>

<s>Perci&ograve; il punto I non sarebbe centro, che &egrave; contro <lb/>il supposto. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario.<emph.end type="italics"/> &mdash; Perci&ograve; &egrave; manifesto che il centro della gravit&agrave; del trian&shy;<lb/>golo, parallelogrammo, cerchio, ellissi, siccome della sfera, sferoide, ecc., sta <lb/>nel concorso dei diametri, cio&egrave; nel centro della figura. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE III. &mdash; <emph type="italics"/>In ogni figura solida, come prisma o paralle&shy;<lb/>lepipedo, ovvero cilindro, il centro della gravit&agrave; sta in quella linea, che <lb/>congiunge i centri delle basi opposte. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia un prisma, o parallelepipedo ovvero cilindro, ovvero altro solido <lb/>colonnare OI (fig. </s>

<s>121), e congiungansi i centri delle basi opposte con la retta <lb/>OI. </s>

<s>Se &egrave; possibile stia fuori, e facciasi la sospensione dal punto O. </s>

<s>Adunque <lb/><figure id="id.020.01.2642.1.jpg" xlink:href="020/01/2642/1.jpg"/></s></p><p type="caption">

<s>Figura 121.<lb/>il centro della gravit&agrave; si accomoder&agrave; nel perpendicolo sotto il <lb/>punto O e la figura star&agrave; ferma. </s>

<s>E per&ograve; segando la figura con <lb/>un piano AB, parallelo alle basi opposte, il centro della sezione <lb/>fatta sar&agrave; fuori del perpendicolo, e per&ograve; non sar&agrave; nell'infimo <lb/>punto del suo giro. </s>

<s>E cos&igrave; di tutte le sezioni possibili a farsi <lb/>parallele alle basi opposte, e perci&ograve; tutte le dette sezioni preme&shy;<lb/>ranno per un verso, e la figura non star&agrave; ferma, che &egrave; contro <lb/>il supposto. </s>

<s>Adunque il centro non &egrave; fuori della linea OI, la <lb/>quale congiunge i centri delle basi opposte, e di tutte le altre <lb/>sezioni. </s>

<s>Che poi il centro del solido divida per mezzo la linea OI &egrave; pi&ugrave; chiaro <lb/>di ogni prova, che se ne possa addurre. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE IV. &mdash; <emph type="italics"/>Il cono, la piramide ed ogni figura conica e <lb/>piramidale ha il centro della gravit&agrave; in quella linea, la quale va dalla <lb/>cima al centro della gravit&agrave; della base opposta. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia un cono, ovvero piramide, ed attacchisi dalla cima libero e s'in&shy;<lb/>tenda ridotto alla quiete. </s>

<s>Sar&agrave; dunque il centro nel perpendicolo sotto il <lb/>punto A (fig. </s>

<s>122). Dico che questo tal perpendicolo &egrave; la linea, che va dalla <lb/>cima al centro della base opposta. </s>

<s>Se non &egrave;, sia detta linea un'altra, come <lb/><figure id="id.020.01.2642.2.jpg" xlink:href="020/01/2642/2.jpg"/></s></p><p type="caption">

<s>Figura 122.<lb/>la AE. </s>

<s>Adunque prover&ograve; che i centri di tutte le sezioni pos&shy;<lb/>sibili parallele alla base sono nella linea AE. </s>

<s>Poich&egrave; prover&ograve;, <lb/>essendo cono, che il centro della sezione sta in AE, se &egrave; pi&shy;<lb/>ramide prover&ograve; che nel triangolo della sezione la linea AE passa <lb/>per un punto, il quale sta nella retta, che vien dall'angolo alla <lb/>met&agrave; di un lato, e la divide in proporzione dupla: e potendo <lb/>tutti discendere, la figura non star&agrave; ferma, che &egrave; contro il sup&shy;<lb/>posto &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXVI, 5-8). </s></p><p type="main">

<s>Ai giovanili esercizi intorno ai centri di gravit&agrave; appartengono quest'altre <lb/>proposizioni, per dimostrar le quali si suppone dal Torricelli <emph type="italics"/>congruentium<emph.end type="italics"/><pb xlink:href="020/01/2643.jpg" pagenum="268"/><emph type="italics"/>figurarum centra gravitatis congruere: item uniuscumque figurae unicum <lb/>esse centrum gravitatis.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; PROPOSIZIONE V. &mdash; <emph type="italics"/>Quodlibet parallelogrammum habet centrum gra&shy;<lb/>vitatis in recta, quae bifariam secat opposita latera. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto parallelogrammum ABCD (fig. </s>

<s>123): recta bisecans opposita la&shy;<lb/>tera sit EF. </s>

<s>Dico in EF esse centrum gravitatis parallelogrammi. </s>

<s>Nisi enim <lb/><figure id="id.020.01.2643.1.jpg" xlink:href="020/01/2643/1.jpg"/></s></p><p type="caption">

<s>Figura 123.<lb/>sit in EF, esto illud G, et producatur AB in H, DC <lb/>in I, FE in L. </s>

<s>Esto parallelogrammum BI aequale <lb/>ipsi AC. </s>

<s>Supposita ergo recta BC super AD, angu&shy;<lb/>loque HBC super angulo BAD, congruet parallelo&shy;<lb/>grammum BI cum parallelogrammo AC, et recta EL <lb/>cum FE, punctumque aliquod M in parallelogrammo <lb/>EI congruet cum puncto G. </s>

<s>Cumque G sit centrum <lb/>parallelogrammi AC, erit M centrum parallelogrammi congruentis BI. &rdquo; </s></p><p type="main">

<s>&ldquo; Invertatur iam parallelogrammum BI super eadem basi BC, ita ut <lb/>angulus HBC, mutato loco, sit NCB; angulus vero ICB, mutato loco, sit ipse <lb/>OBC, recta vero EL, mutata positione, sit eadem ac ipsa EP. </s>

<s>Punctum vero M <lb/>idem sit ac ipsum <expan abbr="q.">que</expan> Inclinato iam parallelogrammo BONC super paralle&shy;<lb/>logrammo BADC, ita ut latus BC commune maneat, congruent, congruentque <lb/>parallelogrammum BP ipsi BF, et punctum Q cum aliquo puncto R in pa&shy;<lb/>rallelogrammo BF. </s>

<s>Cum autem punctum Q centrum sit parallelogrammi BONC, <lb/>erit R centrum gravitatis parallelogrammi congruentis BADC. </s>

<s>Sed eiusdem <lb/>centrum gravitatis erat G, ergo etc. </s>

<s>&rdquo; (idid., fol. </s>

<s>20). </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE VI. &mdash; <emph type="italics"/>Cuiuscumque figurae, ex duobus semiparabolis <lb/>compositae, ita ut diametros aequales et in directum habeant, basim vero <lb/>communcm, centrum gravitatis est in basi. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sint duae semiparabolae ABC, CBD (fig. </s>

<s>124), quarum diametri ae&shy;<lb/>quales et in directum sint AC, CD, basis vero communis CB. </s>

<s>Dico huius&shy;<lb/><figure id="id.020.01.2643.2.jpg" xlink:href="020/01/2643/2.jpg"/></s></p><p type="caption">

<s>Figura 124.<lb/>modi figurae centrum gravitatis esse in basi communi <lb/>CB. </s>

<s>Producatur basis BC in E, ut sint aequales BC. <lb/>CE: tum utraque parabola perficiatur. </s>

<s>Eritque altera <lb/>alteri eadem parabola, et congruent n<gap/>tuo. </s>

<s>Secta <lb/>deinde BC bifariam in F, ducatur GH parallela ipsi <lb/>AD, iunctisque AB, BD erunt GM, NH diametri pa&shy;<lb/>rabolarum AGB, BHD et erunt aequales inter se. </s>

<s><lb/>Sint I, L centra gravitatis parabolarum AGB, BHD, <lb/>eruntque acquales IM, NL. </s>

<s>Sed etiam MF, FN sunt <lb/>aequales, ergo totae IF, FL aequales erunt. </s>

<s>Sunt au&shy;<lb/>tem aequales semiparabolae ABC, CBD cum utraque aequalis sit semipara&shy;<lb/>bolae EDC, ipsa enim ABC cum EDC eadem est et congruit, ipsa vero CBD <lb/>cum EDC a diametro bifariam dividitur. </s>

<s>Demptis itaque aequalibus triangulis <lb/>erunt aequales parabolae AGB, DBH, et punctum F erit earum centrum gra&shy;<lb/>vitatis. </s>

<s>Etiam trianguli ABD centrum gravitatis est in BC, ergo et totius <lb/>figurae, quod erat demonstrandum &rdquo; (ibid., fol. </s>

<s>26). </s></p><pb xlink:href="020/01/2644.jpg" pagenum="269"/><p type="main">

<s>&ldquo; PROPOSIZIONE VII. &mdash; <emph type="italics"/>Cuiuscumque semiparabolae centrum gravita&shy;<lb/>tis est in linea basi aequidistante, et per centrum totius producta. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>A questa &egrave; premesso un lemma, che fu poi scritto in ordine l'XI nel <lb/>libro <emph type="italics"/>De dimensione parabolae,<emph.end type="italics"/> dove pu&ograve; chi vuole leggerlo stampato sotto <lb/>una tal forma: &ldquo; Omnis semiparabola aequiponderat ex puncto basis, in quo <lb/>sic ea dividitur ut pars ad curvam terminatam sit ad reliquam ut quinque <lb/>ad tria &rdquo; (Op. </s>

<s>geom., P. II cit., pag. </s>

<s>33). Dietro ci&ograve; cos&igrave; procede nel ma&shy;<lb/>noscritto la dimostrazione della proposta: </s></p><p type="main">

<s>&ldquo; Esto parabola ABC (fig. </s>

<s>125), cuius diameter BD. </s>

<s>Centrum gravitatis <lb/>totius sit E, ductaque EG parallela ipsi basi DC, dico centrum gravitatis se&shy;<lb/><figure id="id.020.01.2644.1.jpg" xlink:href="020/01/2644/1.jpg"/></s></p><p type="caption">

<s>Figura 125.<lb/>miparabolae DBC esse in recta EG. </s>

<s>Sit enim si possibile <lb/>est extra, puta I, iunctaque et producta IE, transibit ipsa <lb/>IE per centrum gravitatis alterius semiparabolae, per <lb/>lemma primum VIIIae primi Aequiponderantium. </s>

<s>Esto <lb/>illud F ductisque IL, FH, diametro parallelis, erunt ae&shy;<lb/>quales DH, DL, sunt enim utraeque, per lemma praeced., <lb/>3/5 acqualium DA, DC. </s>

<s>Ideo aequales erunt etiam FE, EI, <lb/>et propterea semiparabolae aequales erunt. </s>

<s>Producatur <lb/>BD in N, ita ut sint aequales BD, DN, et per puncta <lb/>A, N, C transeat parabola circa diametrum ND, eritque <lb/>penitus eadem cum parabola ABC. </s>

<s>Nam superpositae invicem congruent. </s>

<s>Jam <lb/>producta IL, ut LM sit aequalis ipsi LI, erit M centrum semiparabolae CDN, <lb/>et ideo M congruet cum centro F, eruntque aequales FH, LM, et ideo etiam <lb/>FH, LI, eruntque parallelae HL, FI quod est impossibile &rdquo; (ibid., fol. </s>

<s>27). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Dopo Archimede la Baricentrica era stata promossa da Federigo Com&shy;<lb/>mandino e da Luca Valerio, ai trattati dei quali, se Galileo da una parte <lb/>faceva il commento, porgeva anche dall'altra, come vedremo, gli argomenti <lb/>a nuove dimostrazioni. </s>

<s>In generale per&ograve; sembrava che fosse ogni invenzione <lb/>esaurita in que'libri, e Galileo stesso confessava di aver desistito dall'opera, <lb/>perch&egrave; vedeva di non poterci far altro che ricalcar l'orme segnate gi&agrave; dal <lb/>Valerio. </s></p><p type="main">

<s>Nel 1632 un gesuita spagnolo, Giovanni Della Faille, pubblicava un libro <lb/>di teoremi <emph type="italics"/>De centro gravitatis partium circuli et ellipsis,<emph.end type="italics"/> cosa affatto nuova <lb/>nella Scienza, avendone taciuto Archimede, e il Commandino e il Valerio <lb/>contentandosi di dimostrare, ci&ograve; che dall'altra parte avrebbe ognuno consen&shy;<lb/>tito assai facilmente, che convengono nello stesso punto i centri delle due <lb/>figure. </s>

<s>Narrava il Della Faille, nel proemio ai lettori, donde gli fossero de&shy;<lb/>rivate le tradizioni alla sua invenzione, e diceva che, come Archimede, ritro&shy;<lb/>vatone il centro di gravit&agrave;, aveva facilmente conclusa la quadratura della pa-<pb xlink:href="020/01/2645.jpg" pagenum="270"/>rabola; cos&igrave; egli sperava che, ritrovato il centro di gravit&agrave; di una porzione <lb/>di cerchio, gli verrebbe fatto di quadrare quella stessa porzione, e perci&ograve; il <lb/>cerchio intero. </s>

<s>La nuova quadratura meccanica riusc&igrave;, al dir di un giudice <lb/>competente qual era Antonio Nardi, <emph type="italics"/>con arte maravigliosa,<emph.end type="italics"/> ci&ograve; ch'efficace&shy;<lb/>mente confer&igrave; a diffondere la fama e i libri del Matematico straniero in Italia. </s>

<s><lb/>Il Torricelli perci&ograve; ritrovava, nel nuovo trattato dei centri di gravit&agrave; delle <lb/>porzioni di circolo e di ellisse, un nuovo impulso, e un indirizzo nuovo ai <lb/>suoi studi, primo frutto de'quali fu l'invenzione del centro di gravit&agrave; nelle <lb/>porzioni di parabola, invenzione forse meno strepitosa di quell'altra simile <lb/>del padre Della Faille, ma non per&ograve; meno nuova. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE VIII. &mdash; <emph type="italics"/>Ostendemus centrum gravitatis portionis pa&shy;<lb/>rabolae qua sit in linea, et in quo ipsius puncto. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto portio parabolae ABCD (fig. </s>

<s>126), secta per lineam CD utcum&shy;<lb/><figure id="id.020.01.2645.1.jpg" xlink:href="020/01/2645/1.jpg"/></s></p><p type="caption">

<s>Figura 126.<lb/>que, sive sit ad diametrum paral&shy;<lb/>lela, sive non. </s>

<s>Secetur bifariam AC <lb/>in E, et, ducta diametro EB, sit F <lb/>centrum parabolae ABC, et H cen&shy;<lb/>trum trianguli ACD, iunctaque F, H, <lb/>in FH erit centrum portionis. </s>

<s>Jun&shy;<lb/>gatur BD, eritque triangulum ABC <lb/>ad triangulum ADC, in eadem basi, <lb/>ut altitudines BX, DY, sive ut BI, <lb/>ID per similitudinem triangulorum <lb/>rectangulorum BXI, IYD, et per IV <lb/>Sexti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Jam parabola ABC, ad triangulum ABC, est ut 4/3 rectae BI ad BI: <lb/>triangulum vero ABC ad ADC est ut BI ad ID, ergo ex aequo parabola ABC <lb/>ad triangulum ADC est ut 4/3 rectae BI ad ID, sive, sumptis subsesquiter&shy;<lb/>tiis, ut recta BI ad 3/4 ID. </s>

<s>Fiat igitur ut BI ad 3/4 ID, ita reciproce HO ad <lb/>OF et erit O centrum gravitatis portionis &rdquo; (ibid., fol. </s>

<s>30). <lb/><figure id="id.020.01.2645.2.jpg" xlink:href="020/01/2645/2.jpg"/></s></p><p type="caption">

<s>Figura 127.</s></p><p type="main">

<s>PROPOSIZIONE IX. &mdash; <lb/><emph type="italics"/>Dato il frusto di parabola <lb/>ABCD<emph.end type="italics"/> (fig. </s>

<s>127), <emph type="italics"/>con le sue <lb/>basi parallele AD, BC, e <lb/>con la sua altezza EF cor&shy;<lb/>rispondente all'asse della <lb/>figura; trovare sopra esso <lb/>asse dove gravita il centro.<emph.end type="italics"/></s></p><p type="main">

<s>Questo bello e impor&shy;<lb/>tante problema non &egrave; cos&igrave; <lb/>proposto, n&egrave; direttamente <lb/>risoluto nel manoscritto tor&shy;<lb/>ricelliano fatto copiar per la stampa, dove solamente si leggono due teoremi, <lb/>che apparirebbero fuor di luogo e insignificanti, quando non s'intendessero, <pb xlink:href="020/01/2646.jpg" pagenum="271"/>secondo che deve avere avuto in mente l'Autore, come lemmi preparati o <lb/>come principii gi&agrave; posti per riuscire alla desiderata soluzione. </s>

<s>Ci&ograve; sempre <lb/>pi&ugrave; conferma che dev'essere stata preparata la detta copia per le stampe <lb/>senza l'approvazion del Viviani, il quale non &egrave; credibile non avesse com&shy;<lb/>preso che i due teoremi erano stati dimostrati per ritrovare il centro di gra&shy;<lb/>vit&agrave; nel frusto della parabola, tanto pi&ugrave; che il Viviani stesso aveva gi&agrave; svolti <lb/>gli argomenti, ossia aveva fatto i calcoli per dimostrar che tornano le con&shy;<lb/>clusioni pronunziate dal Torricelli. </s></p><p type="main">

<s>E perch&egrave; sui materiali, che ci son rimasti in qualche parte finiti e i&ngrave; <lb/>qualche altra abbozzati, non &egrave; difficile, conforme al disegno che ne fece l'ar&shy;<lb/>tista, costruir l'edifizio; si congiungano i punti B, C, con A, D, e torner&agrave; <lb/>dalle linee AB, CD la superficie del frusto divisa in due segmenti parabolici <lb/>e in un trapezio. </s>

<s>Sia l'asse EF segato nel mezzo in P dalla linea RS pa&shy;<lb/>rallela alle basi, la quale, segando pure nel mezzo in H e in T le AB, CD, <lb/>saranno HL, NT, che si conducono paralleli all'asse per comodit&agrave; della di&shy;<lb/>mostrazione, i diametri delle due parabole. </s>

<s>Se dunque si prenda HV due <lb/>quinti di HL, sar&agrave; per l'VIII del secondo degli Equiponderanti, in V il cen&shy;<lb/>tro dalla parabola ARB, come in X sar&agrave; il centro della parabola CSD, per <lb/>la medesima proposizion di Archimede. </s>

<s>Congiungansi V, X, e sar&agrave; in O il <lb/>centro delle due stesse parabole. </s>

<s>Sia poi per la XV del primo degli Equi&shy;<lb/>ponderanti in K il centro di gravit&agrave; del trapezio: &egrave; manifesto che s'avr&agrave; <lb/>risoluto il problema, quando si sappia a qual punto riman dell'asse il cen&shy;<lb/>tro O, e qual sia la proporzione delle parabole al trapezio, perch&egrave;, chiamato T <lb/>questo e P quelle, se faremo come T a P cos&igrave; reciprocamente OZ a ZK, sar&agrave; <lb/>in Z il centro di gravit&agrave; del frusto. </s></p><p type="main">

<s>Le due proposizioni inserite nel manoscritto torricelliano dimostrano dove <lb/>il punto O sia da segnarsi sull'asse, e quale abbiano ragioni fra loro le dette <lb/>superficie. </s>

<s>Ma perch&egrave; colui che ordin&ograve; quelle proposizioni non ne intese il <lb/>fine, anche male le intitol&ograve; e le dispose, e, quasi fosse un tal fine principal&shy;<lb/>mente quello di determinar sull'asse il centro delle due parabole, volle a <lb/>questa dimostrazione premettere come lemma quell'altra delle proporzioni <lb/>tra il trapezio e le due parabole adiacenti. </s>

<s>Notato ci&ograve;, non per altro che per <lb/>avvertire il Lettore com'avendo cos&igrave; fallato gli altri in tanto lubriche mate&shy;<lb/>rie non ci assicuriamo di aver fallato o qui o altrove anche noi; ecco in qual <lb/>modo compendiosamente dimostri il Torricelli dove sull'asse del frusto si <lb/>trovi il centro delle due parabole, che ne fanno parte. </s></p><p type="main">

<s>Condotte le LI, BG, CQ parallele al detto asse, si premette dal Torri&shy;<lb/>celli la seguente, per servir di lemma a ci&ograve; che vuol dimostrare: &ldquo; Osten&shy;<lb/>dendum ita esse DG, ad GI ut IH ad HL. &rdquo; </s></p><p type="main">

<s>&ldquo; Recta IH ad GB &egrave;st ut IA ad AG, sive, sumpta communi altitudine, <lb/>ut rectangulum sub IA, GD ad rectangulum AGD. </s>

<s>Recta vero GB ad IL est <lb/>ut rectangulum AGD ad AID. </s>

<s>Ergo ex aequo IH ad IL erit ut rectangulum <lb/>sub IA, GD, ad rectangulum AID, nempe ut recta GD ad DI. Ergo, divi&shy;<lb/>dendo, DG ad GI erit ut IH ad HL &rdquo; (ibid., fol. </s>

<s>28). </s></p><pb xlink:href="020/01/2647.jpg" pagenum="272"/><p type="main">

<s>Ci&ograve; premesso, cos&igrave; conclude il Torricelli essere il punto O talmente si&shy;<lb/>tuato sull'asse, che EO ad OF abbia quella medesima proporzione che due <lb/>basi maggiori del frusto con tre delle minori hanno a tre basi maggiori con <lb/>due delle minori. </s></p><p type="main">

<s>&ldquo; Est centrum duarum parabolarum O. </s>

<s>Ergo PO crit duae quintae ipsius <lb/>HL, et ideo FP ad PO, sive EP ad PO, erit ut DG ad 2/5 GI, sive ut DG <lb/>ad 1/5 GA. </s>

<s>Sumptisque quintuplis, erit EP ad PO ut DG quinquies ad GA <lb/>semel. </s>

<s>Factisque argumentis, erit EO ad OF ut DG quater, cum GQ semel, <lb/>ad DG quinquies, una cum GA semel. </s>

<s>Nempe ut duae bases maiores, cum <lb/>tribus minoribus, ad tres maiores, cum duabus minoribus &rdquo; (ibid.). </s></p><p type="main">

<s>La division dell'asse nella proporzione di 4DG+GQ a 5DG+GA, <lb/>si dimostra cos&igrave; assai facilmente: In virt&ugrave; del Lemma gi&agrave; dimostrato &egrave; <lb/>IH:HL=DG:GI. </s>

<s>Ma IH=PF=EP, per costruzione, e perci&ograve;, mol&shy;<lb/>tiplicati i conseguenti per 2/5, e osservando che PO=HV=2/5HL; avremo <lb/>EP:PO=DG:2/5GI, ossia EP:PO=5DG:AG. </s>

<s>Dividendo e compo&shy;<lb/>nendo, questa si riduce alle due seguenti EP&mdash;PO:PO=5DG&mdash;AG:AG; <lb/>EP+PO:PO=5DG+AG:AG, onde EO:FO=5DG&mdash;AG:5DG+AG. </s>

<s><lb/>Ma 5DG&mdash;AG=4DG+DG&mdash;AG=4DG+DG&mdash;QD=4DG+QG, <lb/>dunque EO:FO=4DG+QG:5DG+AG. </s></p><p type="main">

<s>Resta ora a provare come 4DG+GQ sia uguale a 2AD+3QG, e <lb/>come 5DG+AG sia uguale a 3AD+2QG, ci&ograve; che faremo prima di tutto <lb/>osservando che 4GD+GQ=4GD+GQ+2GQ&mdash;2GQ=4GD&mdash; <lb/><expan abbr="2GQ+3Gq.">2GQ+3Gque</expan> Ma 4GD&mdash;2GQ=4(AD&mdash;AG)&mdash;2GQ=4AD&mdash; <lb/>4AG&mdash;2GQ=4AD&mdash;(2AG+2QD+2QG)=4AD&mdash;2AD= <lb/>2AD, dunque 4GD+GQ=2AD+3QG. L'altra parte poi vien pro&shy;<lb/>vata con facilit&agrave; dalle seguenti equazioni: 5DG+AG=3DG+2DG+ <lb/>GA+3GA&mdash;3GA=3(DG+AG)+2(DG&mdash;AG)=3AD+2QG. </s>

<s><lb/>E perci&ograve; EO:OF=2AD+3QG:3AD+2QG: &ldquo; nempe, come di&shy;<lb/>ceva il Torricelli, ut duae bases maiores, cum tribus minoribus, ad tres maio&shy;<lb/>res, cum duobus minoribus. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il Viviani illustrava la proposizione, cos&igrave; procedendo nel calcolo, in modo <lb/>poco differente dal nostro, che per l'uso dell'analisi ci siamo studiati di <lb/>render pi&ugrave; chiaro: &ldquo; Come EP a PO, cos&igrave; cinque DG ad una GA, <emph type="italics"/>ct sumptis <lb/>antecedentibus duplis,<emph.end type="italics"/> come EF a PO, cos&igrave; dieci DG ad una GA. </s>

<s>E perch&egrave; <lb/>EP a PO sta come cinque DG, ad una GA; sar&agrave;, componendo, FO ad OP <lb/>come cinque DG, con una GA, ad una GA. <emph type="italics"/>Et per conversionem rationis,<emph.end type="italics"/><lb/>sar&agrave; PO ad OF, come una GA a cinque DG, con una GA. </s>

<s>Ma stava come <lb/>EF a PO, cos&igrave; dieci DG ad una GA, ed ora sta PO ad FO, come una GA <lb/>a cinque DG, con una GA: ergo <emph type="italics"/>ex aequo<emph.end type="italics"/> EF ad FO star&agrave; come dieci DG <lb/>e cinque DG, con una GH, ovvero con una <expan abbr="Dq.">Dque</expan> E, dividendo, EO ad OF <lb/>star&agrave; come quattro DG, con una GQ, a cinque DG, con una GA. </s>

<s>Ma in que&shy;<lb/>sta DG con una GQ ci sono cinque GQ e quattro DQ, siccome in due DA, <lb/>con tre BC, vi sono cinque GQ, con quattro <expan abbr="Dq;">Dque</expan> adunque quattro DG, con <lb/>una GQ, sono uguali a due DA con tre BC. &rdquo; </s></p><pb xlink:href="020/01/2648.jpg" pagenum="273"/><p type="main">

<s>&ldquo; Inoltre, in cinque DG, con una GA, ci sono cinque GQ e sei GA: <lb/>siccome ancora, in tre DA con due BC, cio&egrave; due GQ, ci sono cinque GQ e <lb/>sei GA. </s>

<s>Adunque cinque DG, con una GA, sono uguali a tre DA, con due <lb/>BC. </s>

<s>Ma sopra abbiamo provato che EO ad OF sta come quattro DG, con <lb/>una GQ, a cinque DG, con una GA, ed ora si &egrave; dimostrato che quattro DG, <lb/>con una GQ, sono uguali a due basi maggiori DA, con tre basi minori BC, <lb/>e che cinque DG, con una GA, sono uguali a due basi minori BC, cou tre <lb/>maggiori AD; adunque BO ad OF star&agrave; come due basi maggiori, con tre <lb/>minori, a due minori, con tre maggiori &rdquo; (ivi, T. XXXV, fol. </s>

<s>138). </s></p><p type="main">

<s>Determinata e confermata, per i calcoli fatti, la posizione del punto O, <lb/>baricentro delle due parabole sopra l'asse, ed essendo in K, come si disse, <lb/>il baricentro del trapezio; non rimane a far altro che dimostrare in qual <lb/>proporzione stiano quelle stesse parti fra loro, ci&ograve; che il Torricelli fa pro&shy;<lb/>ponendo, e dimostrando il teorema seguente: &ldquo; Trapetium inscriptum, ad <lb/>reliquas parabolas frusti, ita est, ut quadratum DG, ad tertiam partem qua&shy;<lb/>drati GA. &rdquo; </s></p><p type="main">

<s>&ldquo; Producatur iam diameter HL parabolae ALB usque in M, ita ut MH <lb/>sesquitertia sit diametro HL: erit triangulum, altitudine MH, basi vero du&shy;<lb/>pla HN, aequale parabolae ALB. </s>

<s>Triangulum BAC ad parabolam ALB, sive <lb/>ad triangulum praedictum, rationem habebit compositam ex ratione altitudi&shy;<lb/>num BG ad HM, sive IH ad duas tertias HL, sive DG ad duas tertias GI; <lb/>et ex ratione basium BE ad HN, sive FG ad GI. </s>

<s>Ergo triangulum BAC. ad <lb/>parabolam ALB, erit ut rectangulum DGF, ad rectangulum sub IG, et sub <lb/>duabus tertiis IG: nempe ad duas tertias quadrati GI, praedicta enim rectan&shy;<lb/>gula ex iisdem rationibus componuntur. </s>

<s>Triangulum vero ACD ad BAC est <lb/>ut DA ad BC, vel ut DF ad FG, sive ut rectangulum FDG ad FGD. Ergo, <lb/>ex aequo, triangulum ACD, ad parabolam ALB, erit ut rectangulum FDG <lb/>ad 2/3 quadrati GI, et, per XXIV quinti, trapetium ad parabolam ut quadra&shy;<lb/>tum DG ad 2/3 quadrati GI. </s>

<s>Duplicando consequentia, erit idem trapetium, ad <lb/>duas parabolas residuas, ut quadratum DG ad 4/3 quadrati GI, sive ad 1/3 qua&shy;<lb/>drati GA, quod volebam ostendere. </s>

<s>&rdquo; (ibid.). </s></p><p type="main">

<s>Se faremo dunque, in ultima conclusion del discorso, OZ:ZK=DG2: <lb/>4/3 GI2, sar&agrave; nel punto Z il centro di gravit&agrave; del frusto parabolico, che si <lb/>cercava. </s></p><p type="main">

<s>Ripensando a queste nuove cose dimostrate e risolute, si compiaceva il <lb/>Torricelli di avere emulato il Della Faille, ma pure si trovava costretto di <lb/>confessare che le invenzioni di lui erano di maggior conseguenza delle sue <lb/>proprie. </s>

<s>Dicemmo che si riducevano quelle invenzioni al centro di gravit&agrave; di <lb/>una porzion di cerchio e di ellisse, e ora soggiungiamo pi&ugrave; particolarmente <lb/>che, dopo aver premesse XXXIII proposizioni, si veniva a concluder dall'Au&shy;<lb/>tore che il centro di gravit&agrave; di un settore di cerchio si trova sopra il rag&shy;<lb/>gio, che lo divide nel mezzo, a una distanza tale dal centro, che sia quarta <lb/>proporzionale dopo l'arco, dopo due terzi della corda, e dopo il raggio stesso. <lb/></s>

<s>&ldquo; Dato quolibet sectore circuli, e centro bifariam diviso, si fiat ut sectoris <pb xlink:href="020/01/2649.jpg" pagenum="274"/>arcus, ad duas tertias partes rectae subtendentis arcum, ita semidiameter ad <lb/>quartam quamdam lineam e centro sumendam, in ea quae sectorem bifariam <lb/>secat; eius terminus erit centrum gravitatis sectoris propositi &rdquo; (Theoremata <lb/>de centro grav., Antuerpiae 1632, pag. </s>

<s>36). </s></p><p type="main">

<s>Si veniva di qui a porger facile il modo di ritrovare il centro del segmento <lb/>circolare, che &egrave; uguale al settore diminuito del triangolo inscritto, e nell'ul&shy;<lb/>time parti del libro si dimostrava come, nella medesima proporzione che nel <lb/>cerchio, sia segato l'asse dal centro di gravit&agrave; nel segmento e nel settore di <lb/>ellisse, intorno a che pose l'Autore i due teoremi seguenti in questa forma: <lb/>&ldquo; Si duo segmenta data fuerint unum ellipsis, alterum circuli, et quam pre&shy;<lb/>portionem habet segmentum ellipsis, ad totam ellipsim, eamdem habeat <lb/>segmentum circuli, ad totum circulum; centra gravitatis in eamdem propor&shy;<lb/>tionem divident earum diametros. </s>

<s>&mdash; Si fuerint duo sectores unus ellipttcus, <lb/>alter circularis, dimidiis suis figuris minores, aequales vel maiores, et quam <lb/>proportionem habet unus sector ad suam figuram, eamdem habeat alter sector <lb/>ad suam; centrum gravitatis ipsorum in eamdem rati&ograve;nem dividet semidia&shy;<lb/>metros illas, quae sectores bifariam secant &rdquo; (ibid., pag. </s>

<s>49, 51). </s></p><p type="main">

<s>Erano anche questi due teoremi una conseguenza, e posti come un'ap&shy;<lb/>pendice del XXIX, dove il Della Faille aveva dimostrato il modo di ritro&shy;<lb/>vare il baricentro del settore di cerchio. </s>

<s>La dimostrazione procedeva secondo <lb/>il metodo antico degli inscritti, che menava necessariamente per le lunghe, <lb/>cosicch&egrave;, per preparare i principii, dai quali si potesse dedurre con rigoroso <lb/>discorso geometrico la conseguenza desiderata, si trov&ograve; costretto l'Autore a <lb/>scrivere un libro intero. </s>

<s>Il Torricelli cred&egrave; che ci dovesse essere una via pi&ugrave; <lb/>breve, e mettendosi a cercarla la trov&ograve;, e la rifior&igrave; delle sue proprie ele&shy;<lb/>ganze, ma in sostanza rimaneva la stessa gi&agrave; battuta da tutti gli altri, aiu&shy;<lb/>tandosi anch'egli di quegli inscritti e circoscritti, ai quali erano in simili <lb/>bisogni ricorsi sempre i Matematici antichi. </s>

<s>Non fu perci&ograve; possibile che la <lb/>brevit&agrave; raggiungesse quel grado, che si prometteva, e che poi si consegu&igrave; <lb/>con i metodi nuovi, come potranno giudicare i Lettori da ci&ograve; che ora siam <lb/>per trascrivere dal manoscrito torricelliano, in cui non si giunge a conclu&shy;<lb/>dere il proposito, se non che per la via di dieci lemmi. <lb/><figure id="id.020.01.2649.1.jpg" xlink:href="020/01/2649/1.jpg"/></s></p><p type="caption">

<s>Figura 128.</s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma I.<emph.end type="italics"/> &mdash; Si quadrata duorum laterum <lb/>trianguli, simul sumpta, minora sint reliqui lateris <lb/>quadrato; angulus, ab illis duobus lateribus com&shy;<lb/>prehensus, obtusus erit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto triangulum ABC (fig. </s>

<s>128), sintque qua&shy;<lb/>drata AB, BC, simul sumpta, reliquo quadrato AC <lb/>minora: dico angulum B esse obtusum. </s>

<s>Nisi enim <lb/>B sit obtusus, erit certe vel rectus vel acutus. </s>

<s><lb/>Rectus esse non potest, nam quadrata AB, BC essent, per XLVII Primi, ae&shy;<lb/>qualia quadrato AC. </s>

<s>Acutus esse non potest, quoniam quadrata AB, BC si <lb/>mul maiora essent quadrato AC, per XIII Secundi. </s>

<s>Superest igitur quod an&shy;<lb/>gulus B sit, obtusus, quod erat propositum. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2650.jpg" pagenum="275"/><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Omitte, si lubet, hoc primum Lemma, tamquam satis <lb/>notum ex XIII Secundi Elementorum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma II.<emph.end type="italics"/> &mdash; Si fuerit circuli sector quadrante minor, perpendicu&shy;<lb/>laris in triangulo, ad reliquam sagittam, magis quam dupla erit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto circuli sector ABCD (fig. </s>

<s>129), quadrante minor, cuius chorda <lb/>sit AC, et ex centro D demissa perpendicularis DE ad AC: dico DE, ad re&shy;<lb/><figure id="id.020.01.2650.1.jpg" xlink:href="020/01/2650/1.jpg"/></s></p><p type="caption">

<s>Figura 129.<lb/>liquam sagittam EB, magis quam duplam esse. </s>

<s>Dupla <lb/>enim esse non potest, quoniam, si ponatur DE dupla <lb/>reliqua EB, erit BD, sive CD. ad DE, ut 3 ad 2. Ergo <lb/>quadratum CD ad DB erit ut 9 ad 4. Quadratum <lb/>vero idem DC, per conversionem rationis, ad CE erit <lb/>ut 9 ad 6, et duo simul quadrata CD, DA, ad qua&shy;<lb/>dratum AO, erunt ut 18 ad 20. Propterea, per Lemma <lb/>praec., angulus ADC obtusus, quod est contra sup&shy;<lb/>positum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Maius quam dupla non potest esse. </s>

<s>Quoniam, si ponatur DE minus <lb/>quam dupla reliquae EB, erit composita BD, sive CD, magis quam sesqui&shy;<lb/>altera ipsius DE. </s>

<s>Qualium igitur partium CD est 3, ipsa DB est minus quam 2. <lb/>Qualium vero partium quadratum CD est 9, talium quadratum DE minus <lb/>erit quam 4, et talium CE quadratum erit magis quam 5. Qualium itaque <lb/>partium quadrata simul CD, DA sunt 18, talium quadratum AC est magis <lb/>quam 20. Ergo, per Lemma praec., angulus ADC est obtusus, quod est con&shy;<lb/>tra suppositum. </s>

<s>Superest igitur quod recta DE, ad reliquam EB, sit magis <lb/>quam dupla, quod erat propositum demonstrare. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma III.<emph.end type="italics"/> &mdash; Quilibet circuli sector, sive quaelibet figura rectilinea, <lb/>vel intra vel circa ipsum per continuam arcus bisectionem descripta, centrum <lb/>gravitatis habet in axe: hoc est in recta, quae bifariam secat angulum, qui <lb/>ad centrum est. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il lemma fa riscontro esatto con la XX del Della Faille, ma vedasi <lb/>quanto il processo dimostrativo ne sia diverso, supposto con Archimede che <lb/>delle figure congruenti i centri di gravit&agrave; convengano insieme. </s></p><p type="main">

<s>&ldquo; Esto circuli sector, vel figura plana qualis dicta fuit, ABCD (fig. </s>

<s>130), <lb/>linea vero bisecans angulum ADC sit DB: dico in recta BD esse centrum <lb/><figure id="id.020.01.2650.2.jpg" xlink:href="020/01/2650/2.jpg"/></s></p><p type="caption">

<s>Figura 130.<lb/>totius figurae. </s>

<s>Supponamus enim centra partium <lb/>esse quaelibet puncta E et F, ducaturque recta <lb/>EF. </s>

<s>Superpositis itaque invicem figurae partibus <lb/>BAD, BCD, ipsae partes congruent, ob aequali&shy;<lb/>tatem omnium angulorum, omniumque laterum. </s>

<s><lb/>Centra igitur E et F, per suppositionem prae&shy;<lb/>missam ex Archimede, congruent, quare recta <lb/>E, I congruet cum IF, aequalesque erunt EI, <lb/>IF. </s>

<s>Sunt autem et magnitudines, quarum cen&shy;<lb/>tra E et F, aequales inter se. </s>

<s>Ergo magnitudinis, ex utrisque magnitudi&shy;<lb/>nibus compositae, centrum gravitatis erit punctum I: punctum videlicet <pb xlink:href="020/01/2651.jpg" pagenum="276"/>medium librae EF. </s>

<s>Ergo centrum gravitatis est in axe BD, quod erat pro&shy;<lb/>positum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma IV.<emph.end type="italics"/> &mdash; Centrum gravitatis sectoris circuli, quadrante mino&shy;<lb/>ris, est inter centra triangulorum, quorum alterum inscriptum sit, alterum <lb/>vero ipsi sectori circumscriptum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto sector ABCD (fig. </s>

<s>131), quadrante minor, triangulum vero inscri&shy;<lb/>ptum sit ACD, circumscriptum EFD. </s>

<s>Patet quod perpendicularis DG magis <lb/><figure id="id.020.01.2651.1.jpg" xlink:href="020/01/2651/1.jpg"/></s></p><p type="caption">

<s>Figura 131.<lb/>quam dupla erit ad reliquam GB. </s>

<s>Sit ergo DI <lb/>dupla ad IB, et DO dupla ad OG, eruntque puncta <lb/>I et O centra gravitatis triangulorum EFD, ACD. </s>

<s><lb/>Dico inter puncta O et I esse centrum gravitatis <lb/>sectoris ABCD. </s>

<s>Sit enim, si esse potest, centrum <lb/>gravitatis sectoris punctum I. </s>

<s>Cum ergo I sit cen&shy;<lb/>trum totius, hoc est trianguli EFD et partis unius, <lb/>nempe sectoris ABCD; erit necessario centrum <lb/>gravitatis etiam partis alterius, nempe trilineo&shy;<lb/>rum EAB, BCF, quod est absurdum. </s>

<s>Sit, si esse <lb/>potest, O. </s>

<s>Cum ergo O sit centrum gravitatis totius magnitudinis, nempe <lb/>sectoris, partisque unius, nempe trianguli ACD; erit omnino centrum etiam <lb/>partis alterius, nempe segmenti ABC, quod est absurdum: Sit si esse potest V. </s>

<s><lb/>Cum ergo I sit centrum totius magnitudinis, hoc est trianguli EFD, V vero <lb/>centrum partis unius, nempe sectoris; erit centrum alterius partis, nempe <lb/>trilineorum EAB, BCF omnino versus D, quod est impossibile. </s>

<s>Sit denique, <lb/>si esse potest, R. </s>

<s>Cum ergo R sit centrum totius, nempe sectoris ABCD, <lb/>punctum autem O partis unius, hoc est trianguli ADC; erit centrum alterius <lb/>partis, nempe segmenti ABC, omnino ulterius versus D, quod est absurdum. </s>

<s><lb/>Superest ergo quod centrum gravitatis sectoris sit inter puncta I et O, quod <lb/>erat propositum demonstrare. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma V.<emph.end type="italics"/> &mdash; Si figura quaelibet ABCD (fig. </s>

<s>132) in duas figuras <lb/>congruentes secta fuerit a linea BD, dummodo congruentium figurarum ae&shy;<lb/><figure id="id.020.01.2651.2.jpg" xlink:href="020/01/2651/2.jpg"/></s></p><p type="caption">

<s>Figura 132.<lb/>quales anguli sint ad easdem partes, et supposito <lb/>centro gravitatis semifigurae BAD, quod sit E: si <lb/>ex E ducatur EI perpendicularis ad BD, dico I esse <lb/>centrum gravitatis totius figurae ABCD. </s>

<s>Producatur <lb/>enim EI, ita ut IO sit aequalis ipsi IE, eritque cen&shy;<lb/>trum reliquae semifigurae punctum O. Nam, super&shy;<lb/>positis figuris, puncta E et O congruent, cum rectae <lb/>IE, et OI perpendiculares sint ad BD, per constru&shy;<lb/>ctionem, et aequales inter se. </s>

<s>Propterea centrum magnitudinis, ex utrisque ma&shy;<lb/>gnitudinibus compositae, erit punctum I, quod erat propositum demonstrare. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma VI.<emph.end type="italics"/> &mdash; Si in sectore semicirculo minore figura rectilinea in&shy;<lb/>scribatur, per continuam arcuum bisectionem, et circa eumdem altera similis <lb/>figura circumscribatur; erit centrum gravitatis sectoris inter centra prae&shy;<lb/>dictarum figurarum. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2652.jpg" pagenum="277"/><p type="main">

<s>&ldquo; Esto sector circuli semicirculo minor ABCD (fig. </s>

<s>133), in quo, per <lb/>continuam arcuum bisectionem, figura rectilinea inscribatur AEBFC, et circa <lb/>eumdem altera similis figura circumscribatur GHILM. </s>

<s>Reperiantur centra <lb/><figure id="id.020.01.2652.1.jpg" xlink:href="020/01/2652/1.jpg"/></s></p><p type="caption">

<s>Figura 133.<lb/>triangulorum AED, GHD quae sint N <lb/>et O: inter puncta N, O erit omnino, <lb/>per lemma IV, centrum gravitatis secto&shy;<lb/>ris AED. </s>

<s>Esto illud P. </s>

<s>Ductisque ex <lb/>punctis N, P, O, ad rectam DE, perpen&shy;<lb/>dicularibus NQ, PS, OR, erunt puncta <lb/>Q, S, R, per lemma V, centra gravi&shy;<lb/>tatis: nempe Q trapetii AEBD, R vero <lb/>trapetii GHID, et S sectoris AEDB. </s>

<s>Est <lb/>autem S inter Q et R, alias duae pa&shy;<lb/>rallelae coinciderent, quod esse non po&shy;<lb/>test. </s>

<s>Ductis iterum ex Q, S, R ad DB perpendicularibus QT, SX, RV, erunt <lb/>puncta T, X, V (per lemma V) centra gravitatis: nempe T figurae AEBFCD, <lb/>V vero figurae alterius GHILMD, X denique sectoris ABCD. </s>

<s>Estque X inter T <lb/>et V, alias duae parallelae convenirent, quod esse non potest, propterea cen&shy;<lb/>trum gravitatis sectoris est inter centra figurarum, inscriptae scilicet et cir&shy;<lb/>cumscriptae, quod erat demonstrandum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma VII.<emph.end type="italics"/> &mdash; Si fuerit sector ABCD (fig. </s>

<s>134), minor semicirculo, <lb/>ipsique altera figura inscribatur, et altera circumscribatur, per continuam <lb/><figure id="id.020.01.2652.2.jpg" xlink:href="020/01/2652/2.jpg"/></s></p><p type="caption">

<s>Figura 134.<lb/>arcus bisectionem; dico ita esse <lb/>perimetrum unius AEBFC, ad <lb/>chordam suam AC, ut est peri&shy;<lb/>meter alterius GHILM, ad chor&shy;<lb/>dam suam GM. &rdquo; </s></p><p type="main">

<s>&ldquo; Facto enim centro D, in&shy;<lb/>tervallo DG, describi potest circu&shy;<lb/>lus, qui transibit per omnia puncta <lb/>G, H, I, L, M. </s>

<s>Ideo anguli ACE, <lb/>GMH, ad peripheriam constituti, <lb/>aequales erunt inter se, cum sint, per XX Tertii, subdupli ciusdem anguli <lb/>ad centrum ADE. </s>

<s>Eadem ratione anguli EAC, HGM aequales erunt inter se, <lb/>et triangula EAC, HGM aequiangula. </s>

<s>&rdquo; <lb/><figure id="id.020.01.2652.3.jpg" xlink:href="020/01/2652/3.jpg"/></s></p><p type="caption">

<s>Figura 135.</s></p><p type="main">

<s>&ldquo; Jam perimeter AEBFG ad AE est ut perime&shy;<lb/>ter GHILM ad GH, cum sint earumdem aequimul&shy;<lb/>tiplices. </s>

<s>AE vero ad AC, per IV Sexti, est ut GH <lb/>ad GM: ergo ex aequo perimeter AEBFC, ad chor&shy;<lb/>dam suam AC, est ut perimeter GHILM, ad chordam <lb/>suam GM, quod erat ostendendum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma VIII.<emph.end type="italics"/> &mdash; Si fuerit trapetium ABCD <lb/>(fig. </s>

<s>135), constans ex duobus triangulis isoscelibus ADB, BDC, quorum et <lb/>latera et bases AB, BC sint aequales, ductaque AC fiat ut AB ad 2/3 ipsius <pb xlink:href="020/01/2653.jpg" pagenum="278"/>AE, ita perpendicularis DF ad DI; dico I esse centrum gravitatis trape&shy;<lb/>tii ABCD. &rdquo; </s></p><p type="main">

<s>&ldquo; Ducatur ex I recta IO perpendicularis ad BD, eruntque duo triangula <lb/>orthogonia ODI, et BDF aequiangula, cum habeant communem angulum <lb/>BDF. </s>

<s>Sed eadem ratione triangula orthogonia ABE, BDF sunt aequiangula, <lb/>ergo ODI, et ABE aequiangula erunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Jam sic: BA ad 2/3 ipsius AE, per constructionem, est ut FD ad DI. </s>

<s><lb/>Sed 2/3 ipsius AE, ad 2/3 ipsius AB, per IV Sexti, est ut ID ad DO; ergo <lb/>ex aequo AB, ad 2/3 AB, est ut FD ad DO. </s>

<s>Propterea FD sesquialtera est <lb/>ipsius DO. </s>

<s>Ergo O est centrum trianguli ADB. </s>

<s>Sed recta OI perpendicularis <lb/>est ad BD, ergo I, per lemma V, est centrum ipsius trapetii, quod erat pro&shy;<lb/>positum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma IX.<emph.end type="italics"/> &mdash; Si fuerint quotcumque triangula deinceps isoscelia, <lb/>quorum et latera et bases aequales sint ABF, BCF, CDF (fig. </s>

<s>136), et reli&shy;<lb/><figure id="id.020.01.2653.1.jpg" xlink:href="020/01/2653/1.jpg"/></s></p><p type="caption">

<s>Figura 136.<lb/>qua quae sequntur, dummodo eorum <lb/>numerus sit in progressione nume&shy;<lb/>rorum duplorum ab unitate 1, 2, 4, <lb/>8, 16, etc.: fiat autem ut aggrega&shy;<lb/>tum omnium basium AEG, ad 2/3 <lb/>chordae AG, ita FS, catetus unius <lb/>trianguli, ad aliam sumendam ex <lb/>F versus E; dico terminum huius <lb/>quartae proportionalis esse centrum <lb/>gravitatis figurae universae, ex prae&shy;<lb/>dictis triangulis compositae. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto punctum L, iuxta lemma VIII, centrum trapetii ABCF, et, ducta <lb/>LM perpendiculari ad CF, erit punctum M, per lemma V, centrum figurae <lb/>ABCDEF. </s>

<s>Ducta vero MH perpendiculari ad EF, erit H, per lemma V, cen&shy;<lb/>trum totius figurae AEGF. &rdquo; </s></p><p type="main">

<s>&ldquo; In primis angulus CAO, per XX Tertii, subduplus est anguli CFE, <lb/>et ideo aequalis angulo EFM, et propterea triangula orthogona AOC, FML <lb/>sunt aequiangula. </s>

<s>Eadem ratione triangula ARE, FHM sunt aequiangula. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Jam, per lemma VIII, sive per constructionem, catetus FS ad FL est <lb/>ut BA ad 2/3 ipsius AI, sive ut AB, BC simul ad 2/3 AC. </s>

<s>Verum LF ad FM, <lb/>per IV Sexti, est ut 2/3 ipsius CA, ad 2/3 AO. </s>

<s>Ergo ex aequo catetus FS, <lb/>ad FM, est ut AB, BC simul ad 2/3 ipsius AO, nempe ut ABCDE simul <lb/>ad 2/3 ipsius AE. &rdquo; </s></p><p type="main">

<s>&ldquo; Amplius FM, per IV Sexti, ad FH, est ut 2/3 AE ad 2/3 AR: ergo <lb/>iterum, ex aequo, catetus FS, ad FH, est ut ABCDE ad 2/3 ipsius AR, <lb/>sive ut omnes simul bases AEG, ad 2/3 chordae AG, quod erat proposi&shy;<lb/>tum etc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma X.<emph.end type="italics"/> &mdash; Si fuerint tres magnitudines A, B, C, aliaeque ipsis <lb/>aequales numero D, E, F, quae binae in maiore ratione sumantur, sitque <lb/>perturbata earum proportio, nempe sit ratio A ad B maior ratione E ad F, <pb xlink:href="020/01/2654.jpg" pagenum="279"/>et B ad C maior sit ratione D ad E; dico A ad C maiorem habere ratio&shy;<lb/>nem quam D ad F. &rdquo; </s></p><p type="main">

<s>&ldquo; Ponatur ut A ad B, ita E ad H, eritque, per X Quinti, magnitudo H <lb/>minor quam F. </s>

<s>Ponatur etiam ut B ad C, ita G ad E, oritque, per eamdem, <lb/>G maior quam D. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam A ad C erit, per XXIII Quinti, ut G ad H. </s>

<s>Ergo necessario A <lb/>ad C, per VIII Quinti, maiorem rationem habebit quam D ad H: multoque <lb/>etiam maiorem quam D ad F, quod erat propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE X. &mdash; <emph type="italics"/>Sifuerit circuli sector minor semicirculo, fiatque <lb/>ut arcus sectoris, ad 2/3 chordae eiusdem, ita semidiameter, ad aliam su&shy;<lb/>mendam ex centro; terminus assumptae in axe erit centrum gravitatis <lb/>sectoris. </s>

<s>&rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.2654.1.jpg" xlink:href="020/01/2654/1.jpg"/></s></p><p type="caption">

<s>Figura 137.</s></p><p type="main">

<s>&ldquo; Esto circuli sector ABCD <lb/>(fig. </s>

<s>137), minor semicirculo, fiat&shy;<lb/>que ut arcus ABC, ad 2/3 suae <lb/>chordae AC, ita radius BD ad DE. </s>

<s><lb/>Dico E punctum esse centrum <lb/>gravitatis sectoris. </s>

<s>Si enim pos&shy;<lb/>sibile est non sit E: sit ergo cen&shy;<lb/>trum gravitatis sectoris vel su&shy;<lb/>pra, vel infra punctum E. </s>

<s>Esto <lb/>primo F, et sectori ABCD duae <lb/>figurae rectilineae, altera inscri&shy;<lb/>batur, altera vero circumscriba&shy;<lb/>tur per continuam arcus bisectionem, ita ut latus circumscriptae LM, ad <lb/>latus inscriptae OC, per IV <emph type="italics"/>De sphaera et cylindro,<emph.end type="italics"/> minorem habeat ra&shy;<lb/>tionem, quam ED ad DF: fiatque ut perimeter rectilineus ANBOC, ad 2/3 <lb/>chordae AC, ita catetus VD, ad rectam Q: dico primum Q maiorem esse <lb/>quam DF. &rdquo; </s></p><p type="main">

<s>&ldquo; Nam BD ad DE est ut arcus ABC, ad 2/3 chordae AC: ergo ratio BD <lb/>ad BE, per XIII Quinti, maior est ratione perimetri rectilinaei ANBOC ad <lb/>2/3 chordae AC, sive maior est, ob constructionem, ratione VD ad <expan abbr="q.">que</expan> Am&shy;<lb/>plius, ratio ED ad DF, per constructionem, maior est ratione LM ad OC, <lb/>sive, per IV Sexti, LD ad DO, sive ratione PD ad DV. </s>

<s>Propterea BD ad DF, <lb/>per lemma X, maiorem rationem habebit quam PD ad Q Maior ergo, per <lb/>X Quinti, est DF quam ipsa <expan abbr="q.">que</expan> &rdquo; </s></p><p type="main">

<s>&ldquo; Secetur DR aequalis ipsi Q, et erit R, per lemma IX, et ob con&shy;<lb/>structionem, centrum figurae inscriptae ANBOCD. </s>

<s>Centrum vero circum&shy;<lb/>scriptae adhuc ulterius erit versus B, et inter utrumque debet esse centrum <lb/>gravitatis sectoris. </s>

<s>Ergo centrum gravitatis sectoris non est F. &rdquo; </s></p><p type="main">

<s>&ldquo; Esto deinde centrum gravitatis sectoris, si fieri potest, infra punctum E, <lb/>sitque illud F (fig. </s>

<s>138). Inscribatur in sectore figura multilatera, atque al&shy;<lb/>tera circumscribatur, qer continuam arcuum bisectionem, ita ut GH latus, <lb/>ad latus AN, per IV <emph type="italics"/>De Sphaera et Cylindro,<emph.end type="italics"/> minorem habeat rationem <pb xlink:href="020/01/2655.jpg" pagenum="280"/>quam FD ad DE. </s>

<s>Eritque ratio arcus AN ad chordam AN multo minor ra&shy;<lb/>tione FD ad DE. &rdquo; </s></p><p type="main">

<s>&ldquo; Fiat, ut perimeter rectilineus GHILM ad 2/3 chordae GM, ita BD, ca&shy;<lb/>tetus figurae circumscriptae, ad P. </s>

<s>Dico primum P minorem esse quam DF. <lb/><figure id="id.020.01.2655.1.jpg" xlink:href="020/01/2655/1.jpg"/></s></p><p type="caption">

<s>Figura 138.<lb/>Nam arcus ABC, ad 2/3 chordae <lb/>AC, est ut BD ad DE, per suppo&shy;<lb/>sitam constructionem ab initio, <lb/>sed 2/3 chordae AC, ad perime&shy;<lb/>trum ANBOC, per lemma VII, <lb/>est ut 2/3 chordae GM, ad peri&shy;<lb/>metrum GHILM, sive ut P ad BD; <lb/>ergo, per perturbatam, erit ut ar&shy;<lb/>cus ABC, ad perimetrum ANBOC, <lb/>ita P ad DE. </s>

<s>Sed FD ad DE, ob <lb/>constructionem, maiorem habet ra&shy;<lb/>tionem quam arcus ABC ad peri&shy;<lb/>metrum ANBOC. </s>

<s>Necesse igitur est, per X Quinti, quod P maior sit quam <lb/>DF. </s>

<s>Secetur ergo DT aequalis ipsi P, eritque T, per lemma IX et ob con&shy;<lb/>structionem, centrum figurae circumscriptae GHILMD. </s>

<s>Centrum autem inscri&shy;<lb/>ptae adhuc inferius est versus D, et inter utrumque debet esse centrum <lb/>gravitatis sectoris ABCD. </s>

<s>Propterea punctum F non erit centrum gravitatis <lb/>sectoris, sed ipsum erit E, cum demonstratum sit sectoris centrum esse non <lb/>posse neque supra E, neque infra. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollarium.<emph.end type="italics"/> &mdash; In quolibet circuli sectore, etiamsi semicirculo maior <lb/>sit, si fiat ut arcus ad 2/3 chordae, ita semidiameter ad aliam sumendam in <lb/>axe ex centro circuli; terminus huius assumptae erit centrum gravitatis ipsius <lb/>sectoris. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto sector circuli ABCE (fig. </s>

<s>139) semicirculo maior, cuius chorda <lb/>AC, sectusque sit in duas partes aequales ab axe BEM. </s>

<s>Erunt ergo sectores <lb/><figure id="id.020.01.2655.2.jpg" xlink:href="020/01/2655/2.jpg"/></s></p><p type="caption">

<s>Figura 139.<lb/>ADBE, et BCE, uterque semicirculo minores. </s>

<s><lb/>Esto sectoris ADBE axis ED, fiatque ut arcus <lb/>ADB, ad 2/3 chordae AB, ita DE ad EI, eritque <lb/>I, per theorema praec., centrum gravitatis se&shy;<lb/>ctoris ADBE. </s>

<s>Ductaque IO perpendiculari ad <lb/>BE, erit O, per lemma V, centrum totius secto&shy;<lb/>ris semicirculo maioris ABCE. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam triangula orthogonia IOE, ABM sunt <lb/>aequiangula, nam angulus IEO, ad centrum con&shy;<lb/>stitutus, insistit arcui DB. </s>

<s>Angulus vero BAM <lb/>ad peripheriam insistit arcui duplo, nempe ipsi <lb/>BC. </s>

<s>Ergo anguli aequales sunt. </s>

<s>Propterea, ut <lb/>arcus ADB ad 2/3 chordae AB, ita BE ad EI, per constructionem. </s>

<s>Ut au&shy;<lb/>tem 2/3 AB, ad 2/3 AM, ita, per IV Sexti, IE ad EO. </s>

<s>Ergo ex aequo ut <lb/>arcus ADB, ad 2/3 AM, sive ut arcus ABC, ad 2/3 chordae AC, ita DE, <pb xlink:href="020/01/2656.jpg" pagenum="281"/>sive BE, ad EO, quae quidem est inter centrum gravitatis sectoris, et cen&shy;<lb/>trum circuli, quod erat demonstrandum &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXVII, <lb/>fol. </s>

<s>13-23). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>La superiorit&agrave; di questo processo dimostrativo, paragonato con quello <lb/>del padre Della Faille, non consiste in altro che in aver ridotti a maggiore <lb/>facilit&agrave; i metodi antichi, e ornatigli di eleganze nuove. </s>

<s>Del resto, bench&egrave; il <lb/>Torricelli si compiacesse col Cavalieri di aver dimostrato in meno di un foglio <lb/>quel che al Matematico gesuita era, per far lo stesso, bisognato un libro; e <lb/>bench&egrave; tenesse i suoi lemmi e le loro applicazioni per cose tanto acute, da <lb/>non credere che il Guldino ci fosse potuto arrivare; nonostante troppo ben <lb/>comprendeva che, a correre l'alto e profondo occano della Baricentrica, quelli <lb/>erano troppo deboli remi, e che poco era da dilungarsi dal lido, se non fosse <lb/>alla navicella sovvenuto altro pi&ugrave; valido argomento. </s>

<s>Alla Geometria era gi&agrave; <lb/>felicemente incontrata questa fortuna, per la nuova invenzione del metodo <lb/>degl'indivisibili, e alcuni tooremi, specialmente i primi fra quelli dimostrati <lb/>nel suo terzo libro dal Cavalieri, sembrava che si porgessero d'assai facile <lb/>applicazione alla ricerca del centro di gravit&agrave; nei cilindri scavati da una sfera <lb/>inscritta o da un cono. </s>

<s>Vedremo di quali conseguenze fossero nella mente <lb/>del Torricelli fecondi cos&igrave; fatti teoremi, ma intanto che il germe s'incubava <lb/>latente ne andava discorrendo con gli amici, fra i quali Antonio Nardi, che <lb/>s'era incontrato in que'medesimi pensieri, e che, essendo per stampare un <lb/>libro di Geometria, aveva dato intenzione di trattarvi del modo di applicare <lb/>gl'indivisibili ai baricentri. </s>

<s>Significava il Torricelli stesso queste intenzioni <lb/>dell'amico e sue al Cavalieri, il quale rispondeva da Bologna, il di 30 Ot&shy;<lb/>tobre 1641, cos&igrave;, dop'aver discorso di Giovanni Beugrand venuto di Parigi a <lb/>ridestar nuove scintille di scienza dall'ingegno dei Matematici italiani: </s></p><p type="main">

<s>&ldquo; Detto Beugrand poi, al quale molto piacque questa maniera nuova <lb/>degli indivisibili, aveva pensiero di praticarla in materia dei centri di gra&shy;<lb/>vit&agrave;, poich&egrave; mi domandava se l'avevo usata io, e me ne richiedeva qualche <lb/>esempio. </s>

<s>Onde, se il signor Nardi vuole stampare quello che dice per gli <lb/>indivisibili, avr&agrave; campo ancora, se non l'ha fatto, di aggiungere quello <lb/>dei centri di gravit&agrave;, quando ci abbia gusto &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLI, <lb/>fol. </s>

<s>114). </s></p><p type="main">

<s>Ma intanto che si facevano discorsi, volle il Torricelli venire ai fatti, il <lb/>primo dei quali si fu quello di applicare gl'indivisibili a dimostrare il centro <lb/>di gravit&agrave; della parabola, in quel modo che fu poi stampato nel libro della <lb/>sua <emph type="italics"/>Quadratura<emph.end type="italics"/> (Op. </s>

<s>geom., P. II cit., pag. </s>

<s>74, 75). La nuova applicazione <lb/>fu come saggio sottoposta al giudizio del Cavalieri, a cui si domandava an&shy;<lb/>che insieme consiglio, e nella incerta via intrapresa qualche pi&ugrave; sicuro in-<pb xlink:href="020/01/2657.jpg" pagenum="282"/>dirizzo. </s>

<s>La risposta fu data in una lettera del d&igrave; 29 Ottobre 1642, in questa <lb/>forma: </s></p><p type="main">

<s>&ldquo; Ho vista la sua maniera di trovare il centro della parabola, la quale <lb/>mi &egrave; piaciuta assaissimo, e credo non si possi migliorare. </s>

<s>Gli confesso non&shy;<lb/>dimeno ci&ograve; che mi &egrave; passato per la fantasia, dopo che io ebbi la lettera in <lb/>materia di trovare il centro di gravit&agrave; di alcune figure per gl'indivisibili, da <lb/>non compararsi per&ograve; nella facilit&agrave; alla sua. </s>

<s>E per dargli un poco di saggio <lb/>del mio pensiero apporter&ograve; per esempio il triangolo ed il conoide parabolico, <lb/>dai quali potr&agrave; intendere come questa maniera si possa anco applicare ad <lb/>altre figure. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E prima non tralascer&ograve;, per il triangolo, di dire che mi pare che gl'in&shy;<lb/>divisibili arrechino molta facilit&agrave; per ritrovare il di lui centro, poich&egrave;, essendo <lb/>il centro di gravit&agrave; d'ogni proposta linea retta, e terminata, nel mezzo di essa; <lb/>facilmente proveremo essere il centro del triangolo, per esempio ABD (fig. </s>

<s>140), <lb/><figure id="id.020.01.2657.1.jpg" xlink:href="020/01/2657/1.jpg"/></s></p><p type="caption">

<s>Figura 140.<lb/>nella AC, che divide ugualmente BD in C, poich&egrave; i centri <lb/>di tutte le linee parallele a BD, cio&egrave; il centro di tutto il <lb/>triangolo ABD, sono nella AC, il che pur anco si verificher&agrave; <lb/>di qual si voglia figura intorno al diametro, cio&egrave; che sar&agrave; <lb/>nell'istesso diametro. </s>

<s>Onde, se tireremo la BE che tagli AD <lb/>egu&agrave;lmente in E, e la AC in O, sar&agrave; O il centro, e sar&agrave; <lb/>AO doppia di OC, poich&egrave; i triangoli ABE, DBE sono uguali, <lb/>come anco AOE, DOE, e per&ograve; ABO, BOD saranno uguali, <lb/>cio&egrave; ABC sar&agrave; doppia di OBD, onde AO sar&agrave; doppia di OC. &rdquo; </s></p><p type="main">

<s>&ldquo; Ora vengo all'altro modo, e siccome si prova facilmente che i mo&shy;<lb/>menti dei gravi appesi in una bilancia hanno tra loro la proporzione com&shy;<lb/>posta delle moli, supponendoli ugualmente gravi in specie, e delle distanze <lb/>dal sostegno; cos&igrave;, invece di corpi attaccandovi linee o superficie piane sup&shy;<lb/>poste come gravi, ricever&ograve; per provato che pure i momenti delle prefate linee <lb/>avranno la detta proporzione composta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Venendo ora all'applicazione, sia il medesimo triangolo che sopra ADB, <lb/>nel quale sia divisa BD ugualmente in C, e tirata la AC, quale sia divisa <lb/>in O, sicch&egrave; AO sia doppia di OC; dico il centro essere O del triangolo ABD &rdquo; <lb/>(ivi, fol. </s>

<s>135). E tirata la LG parallela alla BD, ci&ograve; si conclude dopo aver <lb/>dimostrato che il momento di tutte le linee del trapezio LD &egrave; uguale al mo&shy;<lb/>mento di tutte le linee del triangolo LAG, cos&igrave;cch&egrave; conglobate queste insieme <lb/>in T, e quelle in P, sia il momento T.TO uguale al momento P.PO, <lb/>d'onde T:P=PO:TO, che vuol dire essere O, nella bilancia AC, il cen&shy;<lb/>tro dell'equilibrio. </s></p><p type="main">

<s>&ldquo; Intenda ora DAB, nella medesima figura, prosegue a scrivere il Ca&shy;<lb/>valieri, per l'ambito della parabola, che passa per l'asse AC del conoide <lb/>sopra il circolo DB, al quale ella supponga perpendicolare AC, e ci&ograve; per non <lb/>fare altra figura. </s>

<s>Si prover&agrave; dunque che il momento di tutti i circoli del <lb/>conoide ALG &egrave; uguale al momento di tutti i circoli del frusto LBDC, e per&shy;<lb/>ci&ograve; sar&agrave; O centro &rdquo; (ivi, fol. </s>

<s>137). </s></p><pb xlink:href="020/01/2658.jpg" pagenum="283"/><p type="main">

<s>La dimostrazione per&ograve; dell'uguaglianza dei momenti delle linee, nel <lb/>triangolo, e dei momenti de'cerchi nel conoide riusciva assai laboriosa e com&shy;<lb/>plicata, di che troppo bene accortosi il Cavalieri cos&igrave; concludeva: &ldquo; La fretta <lb/>&egrave; cagione che io non mi possi spiegare abbastanza, ma supplir&agrave; il suo va&shy;<lb/>lore al mio mancamento. </s>

<s>Mi favorisca del suo parere circa questa maniera, <lb/>veramente difficile, e per&ograve; da non farne molto capitale. </s>

<s>Vedr&agrave; almeno come <lb/>riescono ancora in questa parte gl'indivisibili assai fecondi, poich&egrave;, trasfor&shy;<lb/>mando i momenti in rettangoli o parallelepipe di o altri solidi, possiamo rin&shy;<lb/>tracciare i centri ancora, credo, d'altre figure &rdquo; (ivi, fol. </s>

<s>138). </s></p><p type="main">

<s>Coloro, che hanno letto il nostro secondo capitolo scritto nel tomo IV, <lb/>riconoscono qui facilmente il metodo usato dal Rocca per dimostrare in qual <lb/>proporzione stiano fra loro il fuso parabolico e il cilindro circoscritto. </s>

<s>Ma in <lb/>verit&agrave; il computo dei momenti rendeva difficile il processo dimostrativo, e <lb/>bench&egrave; non in modo da non farne capitale, come per modestia diceva il Ca&shy;<lb/>valieri, certo da non si dover preferire in tutti i casi agli stessi metodi an&shy;<lb/>tichi. </s>

<s>Scorto il Torricelli per&ograve; da quella sua sagacia geometrica ben conobbe <lb/>che il metodo nuovo si poteva rendere molto pi&ugrave; semplice e pi&ugrave; spedito, in&shy;<lb/>tendendo i pesi concentrati direttamente nel loro punto d'appoggio, e non a <lb/>quelle distanze che si facevano dal Cavalieri e dal Rocca entrare nel com&shy;<lb/>puto dei momenti. </s></p><p type="main">

<s>Nel conoide parabolico, per esempio, tutti i cerchi, come quelli di rag&shy;<lb/>gio AE, BF (fig. </s>

<s>141) si possono riguardar concentrati in A, B, e ivi pon&shy;<lb/>derare direttamente sull'asse OG, preso per libbra. </s>

<s>E il sapere per le dimo&shy;<lb/><figure id="id.020.01.2658.1.jpg" xlink:href="020/01/2658/1.jpg"/></s></p><p type="caption">

<s>Figura 141.<lb/>strazioni altrui che una tal libbra ha il suo centro di&shy;<lb/>stante dal vertice O per due terzi di tutto l'asse, dove <lb/>pur cascherebbe il centro del triangolo inscritto, fece al <lb/>Torricelli sovvenire un bel modo e facilissimo di di&shy;<lb/>mostrare il centro dello stesso conoide, supponendolo <lb/>ignoto. </s>

<s>La libbra OG infatti si pu&ograve; per una parte con&shy;<lb/>siderar gravata degl'infiniti cerchi del solido parabolico, <lb/>e per l'altra delle infinite linee della superficie trian&shy;<lb/>golare, nei quali due tessuti le fila hanno uguale spessore, e sono in gravit&agrave; <lb/>proporzionali, perch&egrave; il triangolo d&agrave; OA:OB=AC:BD, e la parabola <lb/>OA:OB=AE2:BF2, onde AC:BD=<foreign lang="greek">p</foreign>AE2:<foreign lang="greek">p</foreign>BF2, e cos&igrave; di tutte le altre <lb/>infinite linee del triangolo si dimostra la proporzionalit&agrave; ai corrispondenti cer&shy;<lb/>chi del conoideo. </s></p><p type="main">

<s>Veniva di qui facilmente suggerita una proposizione statica, la verit&agrave; <lb/>della quale non fu difficile a dimostrarsi in quel modo, che poi si vide stam&shy;<lb/>pato per servir di lemma alle quadrature della Parabola: lemma, che in or&shy;<lb/>dine &egrave; il XXII del libro, messo dal Torricelli stesso in questa forma: &ldquo; Si <lb/>magnitudines quotcumque ad libram appensae fuerint, ex quibuscumque <lb/>punctis, totidemque magnitudines alterius ordinis ex iisdem punctis pendeant, <lb/>pariter cum praedictis magnitudinibus proportionales; erit unum idemque li&shy;<lb/>brae punctum centrum aequilibrii utriusque ordinis magnitudinum &rdquo; (Op. <pb xlink:href="020/01/2659.jpg" pagenum="284"/>geom., P. II cit., pag. </s>

<s>61). Applicato il qual lemma, ecco in un brevissimo <lb/>tratto dal Torricelli condotta la dimostrazione del centro di gravit&agrave; del co&shy;<lb/>noide parabolico, che aveva dianzi aggirato il Cavalieri per cos&igrave; lungo e fa&shy;<lb/>ticoso viaggio. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XI. &mdash; <emph type="italics"/>Il centro del conoide parabolico sega l'asse <lb/>nella proporzione di due a uno, provato per via del triangolo inscritto. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Poich&egrave;, sia libbra orizontale OG (nella medesima figura 141). Il cir&shy;<lb/>colo di AE al circolo di BF sta come la retta AC alla BD. </s>

<s>Perci&ograve; i centri <lb/>divideranno la libbra nell'istesso luogo &rdquo; (MSS. Gal., T. XXXVI, fol. </s>

<s>56 <lb/>a tergo). </s></p><p type="main">

<s>La prova, cos&igrave; ben riuscita nel conoide parabolico, invogli&ograve; il Torricelli <lb/>a tentarla anche in quell'altro esempio addotto dal Cavalieri, cio&egrave; nel trian&shy;<lb/>golo, dentro cui, supposto che il centro di gravit&agrave; si trovi sopra qualche <lb/>punto della bissettrice, si potesse questa riguardar quale una bilancia, con&shy;<lb/>centrativi sopra i pesi delle infinite linee, di che s'intesse la detta triango&shy;<lb/>lar superficie. </s>

<s>Posto ci&ograve;, nient'altro rimaneva a sapere e a dimostrare, per <lb/>modo di lemma, se non che dove riesca il punto dell'equilibrio sopra una <lb/>bilancia gravata per tutta la sua lunghezza da pesi, che scemino ugualmente <lb/>a proporzione delle distanze uguali. </s>

<s>Ma il lemma era stato dimostrato gi&agrave; da <lb/>Galileo, e posto per la prima proposizione nel suo trattato dei centri di gra&shy;<lb/>vit&agrave;, sotto questa forma: &ldquo; Si magnitudines quotcumque sese aequaliter exce&shy;<lb/>dentes, et quarum excessus earum minimae sint aequales, ita in libra dispo&shy;<lb/>nantur, ut ex distantiis aequalibus pendeant: centrum gravitatis omnium <lb/>libram ita demonstratur dividere, ut pars versus minores reliquae sit dupla &rdquo; <lb/>(Alb. </s>

<s>XIII, 267). </s></p><p type="main">

<s>E in tali condizioni si trovano per l'appunto le infinite linee del trian&shy;<lb/>golo ACB (fig. </s>

<s>142) parallele ad AB, e pendenti pel loro mezzo dalla libbra <lb/><figure id="id.020.01.2659.1.jpg" xlink:href="020/01/2659/1.jpg"/></s></p><p type="caption">

<s>Figura 142.<lb/>CE, la quale dunque sar&agrave; segata dal centro <lb/>di gravit&agrave; D in modo, che la parte verso i <lb/>pesi minori, ossia CD, sia a DE doppia. </s></p><p type="main">

<s>A ridurre la conclusione assoluta rima&shy;<lb/>neva dunque solamente a dimostrare il suppo&shy;<lb/>sto, che cio&egrave; il centro di gravit&agrave; del triangolo <lb/>si trova sopra un punto della linea, la quale <lb/>sia da un vertice fatta scendere sul mezzo del <lb/>lato opposto, ci&ograve; che si proponeva di fare il <lb/>Torricelli, dietro lo stesso principio di Galileo, <lb/>intitolando cos&igrave; la sua proposizione: <emph type="italics"/>Centrum gravitatis trianguli, suppo&shy;<lb/>sito Galilei principio.<emph.end type="italics"/></s></p><p type="main">

<s>Nel medesimo triangolo dianzi figurato sia D il centro preso sopra la CE, <lb/>la quale si vuol dimostrare essere bissettrice. </s>

<s>Si consideri AB libbra, d'onde <lb/>pendano le infinite linee ponderose parallele a CB, le quali crescendo da B <lb/>verso A, a proporzione delle distanze, faranno che il centro I divida essa <lb/>libbra in modo, che la parte AI verso i pesi minori sia doppia della IB. </s>

<s>In <pb xlink:href="020/01/2660.jpg" pagenum="285"/>simil guisa considerando la medesima libbra come gravata dalle infinite linee <lb/>parallele ad AC, queste da A scemando col detto ordine verso B concentre&shy;<lb/>ranno i loro pesi in F, punto dallo stesso B distante il doppio che da A. </s>

<s>Con&shy;<lb/>dotta dunque da I la IH parallela a BC e da F la FG parallela ad AC, do&shy;<lb/>vendosi nella loro intersezione trovare il centro del triangolo passeranno <lb/>ambedue per D e la costruzione, che di qui nasce, d&agrave; facile modo a dimo&shy;<lb/>strare l'intento, che cio&egrave; sia in E il lato AB segato nel mezzo. </s></p><p type="main">

<s>Dall'essere infatti, per le cose ora dette, BI=2AI, AF=2FB, viene <lb/>AI:IB=FB:FA, e, componendo, AB:IB=AB:FA, dunque IB=FA. </s>

<s><lb/>La similitudine dei triangoli dall'altra parte d&agrave; AF:FE=CD:DE= <lb/>BI:IE, dunque EF=IE e perci&ograve; AE=EB, che &egrave; la conclusione desiderata, <lb/>in proporre e in dimostrar la quale cos&igrave; propriamente procede il Torricelli. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XII. &mdash; <emph type="italics"/>Esto triangulum ABC, cuius gravitatis cen&shy;<lb/>trum sit D, et ducta EDC, dico CE secare bifariam AB. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ducatur, per D, FDG parallela ad AC, et IDH parallela ad BC. </s>

<s>Quo&shy;<lb/>niam AB est libra et ad singula ipsius puncta magnitudines pendent, nempe <lb/>lineae parallelae ad latus BC, habentque ipsae magnitudines inter se, ob <lb/>IV Sexti, eamdem rationem quam distantiae ab extremo librae puncto A, et <lb/>omnium centrum per suppositionem est in IH una ipsarum: item quoniam <lb/>AB est libra, et ex singulis ipsius punctis magnitudines pendent, nempe li&shy;<lb/>neae parallelae ad latus AC, habentque magnitudines eamdem rationem quam <lb/>distantiae ab extremo librae puncto B, et omnium centrum est in FG per <lb/>suppositionem; erit libra AB secta in eadem ratione, nempe, ut AI ad IB, <lb/>ita BF ad FA. </s>

<s>Et componendo, AB ad BI ut BA ad AF. </s>

<s>Quare aequales <lb/>sunt AF, IB. </s>

<s>Quoniam vero AF ad FE est ut CD ad DE, sive ut BI ad IE, <lb/>erunt aequales etiam FE, EI. </s>

<s>Ergo aequales AE, EB quod erat demonstran&shy;<lb/>dum &rdquo; (ibid., fol. </s>

<s>21). </s></p><p type="main">

<s>Questa maniera di applicare gl'indivisibili alla ricerca del centro di gra&shy;<lb/>vit&agrave;, ne'due esempi del conoide parabolico, e del triangolo, parve al Torri&shy;<lb/>celli tanto pi&ugrave; facile e pi&ugrave; spedito, e da preferirsi anche in altri casi pi&ugrave; <lb/>complicati a quello propostogli dal Cavalieri, che non pot&egrave; tenersi dal far&shy;<lb/>gliene qualche motto: a che il Cavalieri stesso rispondeva il d&igrave; 23 Dicem&shy;<lb/>bre del detto anno 1642: &ldquo; La stima poi, che ella mostra di fare delle mie <lb/>debolezze, &egrave; da me ricevuta dall'abbondanza del suo affetto, e non dal me&shy;<lb/>rito di quelle, poich&egrave; sono di niuno momento, massime in comparazione di <lb/>qe'suoi sottilissimi trovati, come stimo deva essere il modo che mi accenna <lb/>di ritrovare il centro di gravit&agrave; per gl'indivisibili, intorno al quale non man&shy;<lb/>cher&ograve; di dire come il signor Giann'Antonio Rocca, gentiluomo reggiano, in&shy;<lb/>gegno vivacissimo e versatissimo nelle Matematiche, altre volte da me credo <lb/>nominato, mi mand&ograve; un altro modo assai facile di ritrovare i centri di gra&shy;<lb/>vit&agrave; per gl'indivisibili, q&ugrave;ale ora non ho alle mani, ma sta rivolto fra'miei <lb/>scartafacci, e forse potriano riscontrarsi insieme &rdquo; (ivi, T. XLI, fol. </s>

<s>140). </s></p><p type="main">

<s>Sarebbe per questa nuova storia delle Matematiche applicate alla scienza <lb/>del moto assai importante il sapere se il Rocca, mettendo a varie prove <pb xlink:href="020/01/2661.jpg" pagenum="286"/>quella sua maniera di misurare il gravitar delle linee e delle superficie dai <lb/>loro momenti, e trovandola complicata, s'incontrasse, per renderla pi&ugrave; sem&shy;<lb/>plice, in quell'altra maniera usata dal Torricelli, e l'eccellenza della quale <lb/>principalmente consisteva nel misurare il peso degli elementi infinetisimi as&shy;<lb/>solutamente in s&egrave; sulla lunghezza della libbra, e non moltiplicato per la di&shy;<lb/>stanza laterale dal punto d'appoggio. </s>

<s>Cos&igrave; si riducevano i rettangoli, presi <lb/>per la misura dei momenti, a semplici linee, e i parallelepipedi a quadrati, <lb/>il baricentro dei quali &egrave; manifestamente il medesimo che dei circoli inscritti <lb/>o circoscritti. </s>

<s>Sarebbe importante, ripetiamo, saper se si fosse in questo stesso <lb/>pensiero incontrato anche il Rocca, ma perch&egrave; a noi mancano i documenti, <lb/>unico o almen principale autore di questa applicazione degl'indivisibili alla <lb/>Baricentrica non possiamo non riconoscere il Torricelli, del quale, dopo i <lb/>saggi fatti sul conoide e sul triangolo, &egrave; da veder quali fossero, in cos&igrave; fatte <lb/>esercitazioni, i progressi. </s>

<s>Ebbero questi non leggero impulso dal ripensare <lb/>alle proposizioni gi&agrave; dimostrate intorno al centro di gravit&agrave; del settore di <lb/>circolo: proposizioni, le quali bench&egrave; fossero ridotte assai pi&ugrave; semplici e a <lb/>minor numero di quelle che bisognarono al Della Faille per dimostrare il <lb/>medesimo; il metodo degli indivisibili nonostante prometteva, nell'ordinarle <lb/>e nel condurle, d'alleviare e d'abbreviare anche di pi&ugrave; la faticosa lunghezza <lb/>del viaggio, perch&egrave; si potrebbe, dietro gli esempi del triangolo, riguardare <lb/>il settore intessuto degli infiniti archi concentrici decrescenti con sempre egual <lb/>proporzione, via via che si dilungano dalla maggiore circonferenza, concen&shy;<lb/>trando sopra il raggio, che tutti gli divide nel mezzo, come sopra una lib&shy;<lb/>bra, i loro pesi. </s></p><p type="main">

<s>Gettiamo uno sguardo sul settore ABCD (fig. </s>

<s>143) segato nel mezzo dal <lb/>raggio DB. </s>

<s>Se si sapesse il centro di gravit&agrave; degli archi che lo compongono, <lb/><figure id="id.020.01.2661.1.jpg" xlink:href="020/01/2661/1.jpg"/></s></p><p type="caption">

<s>Figura 143.<lb/>dal primo che sia per esempio E, infino <lb/>all'ultimo D, &egrave; manifesto che l'inven&shy;<lb/>zione del centro di esso settore cade&shy;<lb/>rebbe sotto quella del triangolo isoscele, <lb/>che avesse per sua altezza DE. </s>

<s>Tutto <lb/>dunque si riduce, per procedere in que&shy;<lb/>sta nuova via sicuri, e con buona spe&shy;<lb/>ranza di riuscita, a determinare sull'asse <lb/>il punto estremo E della libbra, o il cen&shy;<lb/>tro di gravit&agrave; dell'arco. </s>

<s>Il Torricelli, che <lb/>non aveva potuto ancora leggere la Cen&shy;<lb/>trobarica del Guldino, cred&egrave; che fosse <lb/>il problema intatto, e si dette all'opera, <lb/>la quale felicemente riusc&igrave;, ponendo la <lb/>ritrovata soluzione per lemma prepara&shy;<lb/>torio alla ricerca del centro di gravit&agrave; del settore di circolo, per via degli <lb/>indivisibili, intorno a che distese quell'altro trattatello, che qui appresso ri&shy;<lb/>copiamo dal manoscritto. </s></p><pb xlink:href="020/01/2662.jpg" pagenum="287"/><p type="main">

<s><emph type="italics"/>&ldquo; Supponimus<emph.end type="italics"/> primo: Cuiuscumque rectae lineae terminatae gravitatis <lb/>centrum esse punctum, quod ipsam bifariam dividit. </s>

<s>Secundo: Congruentium <lb/>perimetrorum centra gravitatis congruere. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma XI.<emph.end type="italics"/> &mdash; Si aliqua figura plana ABCD (fig. </s>

<s>144) in duas con&shy;<lb/>gruentes figuras BAD, BCD secta fuerit ab axe BD, dummodo aequales et <lb/><figure id="id.020.01.2662.1.jpg" xlink:href="020/01/2662/1.jpg"/></s></p><p type="caption">

<s>Figura 144.<lb/>sibi respondentes anguli ad easdem partes sint, suman&shy;<lb/>turque BA, BC aequales utrimque perimetri partes, et <lb/>supposito E centro gravitatis perimetri AB; si ex E <lb/>ducatur EO perpendicularis ad BD, dico punctum O <lb/>esse centrum gravitatis perimetri ABC. &rdquo; </s></p><p type="main">

<s>&ldquo; Producatur EO in F, ita ut OF aequalis sit ipsi <lb/>EO. </s>

<s>Supposita deinde semifigura BAD super BCD, con&shy;<lb/>gruent figurae per suppositionem, et perimeter BA con&shy;<lb/>gruet cum aequali BC, punctumque E congruet cum <lb/>puncto F. </s>

<s>Sunt enim aequales EO, OF, et angulos <lb/>rectos faciunt cum BD. </s>

<s>Sed E ponitur centrum gravitatis perimetri BA, ergo <lb/>F centrum gravitatis erit perimetri BC. </s>

<s>Cum autem BA, BC sint aequales, <lb/>erit centrum gravitatis, per secundam suppositionem, commune punctum O, <lb/>medium scilicet punctum librae EF. </s>

<s>Patet ergo quod erat propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollarium.<emph.end type="italics"/> &mdash; Hinc manifestum est cuiuscumque perimetri ABC, <lb/>sive ex curvis, sive ex rectis lineis componatur, centrum gravitatis esse in <lb/>axe eius BD, nempe in recta, quae secat ipsum perimetrum in duas partes <lb/>congruentes ad angulos aequales. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma XII.<emph.end type="italics"/> &mdash; Cuiuscumque arcus circuli centrum gravitatis est <lb/>inter centra rectarum, quarum una sit ipsius chorda, altera tangens chor&shy;<lb/>dae parallela. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Manifestum est hoc. </s>

<s>Esto enim arcus ABC (fig. </s>

<s>145), cuius circuli <lb/><figure id="id.020.01.2662.2.jpg" xlink:href="020/01/2662/2.jpg"/></s></p><p type="caption">

<s>Figura 145.<lb/>centrum D, linea vero bisecans angulum arcum&shy;<lb/>que sit Bd. </s>

<s>In ipsa BD erit, per corollarium lem&shy;<lb/>matis praecedentis, centrum gravitatis arcus ABC. </s>

<s><lb/>Esto chorda AC, tangens vero EF, parallela chor&shy;<lb/>dae AC: eritque G centrum gravitatis rectae AC, <lb/>et B erit centrum gravitatis EF. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam centrum gravitatis arcus non potest <lb/>esse neque B, neque G: suspenso enim arcu ex <lb/>B, sive ex G, aequiponderaret, quod est absur&shy;<lb/>dum, cum latus sit ad easdem partes. </s>

<s>Tanto mi&shy;<lb/>nus potest esse extra puncta B, G, ob eamdem causam. </s>

<s>Quare patet quod <lb/>fuerat propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma XIII.<emph.end type="italics"/> &mdash; Si intra arcum circuli coaptatae fuerint quotcumque <lb/>rectae lineae aequales, per continuam <gap/>rcus bisectionem, totidemque fuerint <lb/>tangentes ipsis coaptatis aequidistantes; erit centrum gravitatis arcus inter <lb/>centra omnium coaptatarum, et omnium tangentium. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto arcus ABC (fig. </s>

<s>146), cuius circuli centrum D. Coaptatae, per <pb xlink:href="020/01/2663.jpg" pagenum="288"/>continuam arcus bisectionem, sint rectae aequales AE, EB, BF, FC. </s>

<s>His vero <lb/>aequidistent totidem tangentes GH, HI, IL, LM, et producta DN ad con&shy;<lb/><figure id="id.020.01.2663.1.jpg" xlink:href="020/01/2663/1.jpg"/></s></p><p type="caption">

<s>Figura 146.<lb/>tactum N, erunt N et P, per primam <lb/>suppositionem, centra gravitatis recta&shy;<lb/>rum GH, AE. </s>

<s>Centrum vero arcus <lb/>ANE est, per lemma XII, inter pun&shy;<lb/>cta N et P. </s>

<s>Ponatur illud esse O. </s>

<s><lb/>Ductisque PQ, OR, NS perpendicu&shy;<lb/>laribus ad HD, erunt puncta Q, R, S <lb/>centra gravitatis: nempe Q rectarum <lb/>AE, EB, G tangentium GH, HI, R <lb/>vero arcus AEB. </s>

<s>Iterum productis QT, <lb/>RV, SX perpendicularibus ad ID, erit <lb/>V, centrum gravitatis totius arcus ABC, <lb/>inter puncta T et X, alias enim duae <lb/>parallelae convenirent: videlicet inter <lb/>centrum omnium coaptatarum, et omnium tangentium, quod erat propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma XIV.<emph.end type="italics"/> &mdash; Si arcui circuli ABC (fig. </s>

<s>147), per continuam eius&shy;<lb/>dem arcus bisectionem, quotcumque rectae lineae aequales coaptatae fuerint <lb/>AE, EF, FG, GB, BH, HI, IL, LC, fiatque, ut omnes coaptatae lineae ad <lb/><figure id="id.020.01.2663.2.jpg" xlink:href="020/01/2663/2.jpg"/></s></p><p type="caption">

<s>Figura 147.<lb/>chordam AC, ita <lb/>D, catetus unius <lb/>coaptatae, ad <lb/>aliam sumendam <lb/>ex centro D, in <lb/>axe BD; dico ter&shy;<lb/>minum huius <lb/>assumptae esse <lb/>centrum gravita&shy;<lb/>tis omnium prae&shy;<lb/>dictarum linea&shy;<lb/>rum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ducatur ex <lb/>M, puncto medio <lb/>rectae AE, per&shy;<lb/>pendicularis MP ad ipsam ED, eritque P, per corollarium lemmatis XI, cen&shy;<lb/>trum gravitat&igrave;s duarum rectarum AE, EF. </s>

<s>Ducta vero ex P recta PR per&shy;<lb/>pendiculariter ad FD, erit R, per corollarium lemmatis XI, centrum gra&shy;<lb/>vitatis quatuor rectarum AE, EF, FG, GB. </s>

<s>Ducta iterum ex R recta RN <lb/>perpendiculariter ad BD, erit N, per dictum corollarium, centrum gravitatis <lb/>rectarum AE, EF, FG, GB, BH, HI, IL, LC. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam aequiangula triangula sunt, per VIII Sexti, EMP, PME. </s>

<s>Item ae&shy;<lb/>quiangula FAT, PDR, nec non BAX, RDN, demonstraturque hoc ut in lem&shy;<lb/>mate IX factum est. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2664.jpg" pagenum="289"/><p type="main">

<s>&ldquo; Quoniam MD ad DP est ut EM ad MP, sive ut EA ad AQ, sive ut <lb/>FEA ad AF, sed PD, ad DR, per IV Sexti, est ut FA ad AT; erit ex aequo <lb/>MD ad DR ut FEA ad AT, sive ut BGFEA ad AB: DR denique ad DN, per <lb/>eamdem, est ut BA ad AX. </s>

<s>Ergo ex aequo omnes rectae BG, GF, FE, EA <lb/>ad AX, sive omnes AE, EF, FG, GB, BH, HI, IL, LC, ad AC, sunt ut MD <lb/>ad DN. </s>

<s>Unde patet quod propositum fuerat. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XIII. &mdash; <emph type="italics"/>Centrum gravitatis cuiuscumque arcus cir&shy;<lb/>culi est in axe eiusdem ita secto, ut integer axis, ad partem quae versus <lb/>centrum circuli est, ita sit ut arcus ad chordam. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto arcus ABC (fig. </s>

<s>148), cuius chorda AC, axis BD, fiatque, ut <lb/>arcus ABC ad chordam AC, ita axis BD ad DE: dico E esse centrum gra&shy;<lb/><figure id="id.020.01.2664.1.jpg" xlink:href="020/01/2664/1.jpg"/></s></p><p type="caption">

<s>Figura 148.<lb/>vitatis arcus ABC. </s>

<s>Nisi enim cen&shy;<lb/>trum gravitatis sit punctum E, <lb/>erit utique aliud punctum vel su&shy;<lb/>pra, vel infra punctum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto primum, si possibile <lb/>est, F, ipsique sectori duae figu&shy;<lb/>rae, per continuam arcuum bise&shy;<lb/>ctionem, altera quidem circum&shy;<lb/>scribatur, altera vero inseribatur <lb/>ea lege, per IV libr&igrave; I <emph type="italics"/>De sphaera <lb/>et cylindro,<emph.end type="italics"/> ut latus OR circum&shy;<lb/>scriptae, ad latus CG inscriptae, <lb/>minorem rationem habeat quam <lb/>ED ad DF. </s>

<s>Deinde fiat ut omnes <lb/>rectae AN, NB, BG, GC ad chordam AC, ita catetus DI ad M. </s>

<s>Ostendo pri&shy;<lb/>mum M esse maiorem quam DF. &rdquo; </s></p><p type="main">

<s>&ldquo; Nam BD ad DE est ut arcus ABC ad chordam AC, ergo BD ad DE <lb/>maiorem habet rationem, quam perimeter ANBGC ad AC: hoc est quam DI <lb/><figure id="id.020.01.2664.2.jpg" xlink:href="020/01/2664/2.jpg"/></s></p><p type="caption">

<s>Figura 149.<lb/>ad M. </s>

<s>Ipsa vero DE ad DF maiorem <lb/>habet rationem, quam PD ad M; <lb/>erit itaque M maior quam DF. </s>

<s>Po&shy;<lb/>natur DQ aequalis ipsi M, et erit <lb/>Q, per lemma XIV et per constru&shy;<lb/>ctionem, centrum gravitatis perime&shy;<lb/>tri ANBGD. </s>

<s>Centrum vero gravitatis <lb/>perimetri HKLOR adhuc ulterius est <lb/>versus L, et inter utrumque debet <lb/>esse centrum gravitatis arcus, ergo <lb/>centrum gravitatis arcus non est F. &rdquo; </s></p><p type="main">

<s>&ldquo; Esto deinde, si fieri potest, <lb/>centrum gravitatis arcus punctum S <lb/>(fig. </s>

<s>149), ipsique arcui duae figurae, per continuam arcus bisectionem, altera <lb/>quidem circumscribatur, altera vero inscribatur ea conditione, per IV libri I <pb xlink:href="020/01/2665.jpg" pagenum="290"/><emph type="italics"/>De sphaera et cylindro,<emph.end type="italics"/> ut latus circumscriptae OR, ad latus inscriptae GC, <lb/>minorem rationem habeat quam SD ad DE. </s>

<s>Tunc enim sine dubio ratio ar&shy;<lb/>cus GPC, ad rectam GC, sive arcus ABC, ad perimetrum ANBGC, multo <lb/>minor erit quam sit ratio SD ad DE. &rdquo; </s></p><p type="main">

<s>&ldquo; Fiat, ut perimeter HKLOR ad HR, ita catetus PD ad M: dico pri&shy;<lb/>mum M minorem esse quam DS. </s>

<s>Nam arcus ABC, ad AC, est ut BD ad <lb/>DE, ipsa vero AC, ad perimetrum ANBGC, per lemma VII, est ut HR ad <lb/>HKLOR, sive ut M ad DP. Ergo, per XXIII Quinti, arcus ABC, ad perime&shy;<lb/>trum ANBGC, est ut M ad DE. </s>

<s>Sed ratio SD ad DE maior est ratione pe&shy;<lb/>rimetri ANBGC ad AC; ergo ratio SD ad DE maior est ratione M ad DE. </s>

<s><lb/>Maior itaque est SD quam recta M. &rdquo; </s></p><p type="main">

<s>&ldquo; Ponatur DQ aequalis ipsi M, eritque Q, per lemma XIV et per con&shy;<lb/>structionem, centrum gravitatis perimetri HKLOR. </s>

<s>Centrum vero perimetri <lb/>ANBGC adhuc inferius est versus D, et inter utrumque est omnino centrum <lb/>gravitatis arcus. </s>

<s>Quamobrem centrum gravitatis arcus non est S. </s>

<s>Cum ita&shy;<lb/>que ostensum sit non esse neque supra neque infra E, superest quod cen&shy;<lb/>trum gravitatis arcus ABC sit punctum E, quod erat propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XIV. &mdash; <emph type="italics"/>Cenirum gravitatis sectoris circuli est in axe <lb/>eiusdem ita secto, ut totus axis, ad partem quae est versus circuli cen&shy;<lb/>trum, sit ut arcus sectoris ad 2/3 chordae eiusdem. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto sector ABCD (fig. </s>

<s>150), cuius chorda AC, axis vero BD, fiatque, <lb/><figure id="id.020.01.2665.1.jpg" xlink:href="020/01/2665/1.jpg"/></s></p><p type="caption">

<s>Figura 150.<lb/>ut arcus ABC ad AC, ita BD ad DE. </s>

<s><lb/>Et erit E, per propositionem praece&shy;<lb/>dentem, centrum gravitatis arcus ABC. </s>

<s><lb/>Sumpto iam in recta BD quolibet pun&shy;<lb/>cto F, agatur centro D, intervallo DF, <lb/>arcus GFH, et fiat, ut arcus GFH ad <lb/>GH, ita FD ad DI, eritque punctum I, <lb/>per eamdem, centrum gravitatis arcus <lb/>GFH. &rdquo; </s></p><p type="main">

<s>&ldquo; Quoniam, ut arcus ABC ad ar&shy;<lb/>cum GFH, ita semidiameter AD ad DG, <lb/>sive, per IV Sexti, AC ad GH; erit, <lb/>permutando, ut AHC ad AC, ita GFH <lb/>ad GH. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam BD ad DE est ut ABC ad <lb/>AC, sive, ut GFH ad GH, vel ut FD ad DI. </s>

<s>Permutando igitur erit BD ad <lb/>DF ut ED ad DI, et etiam ABC ad GFH erit ut ED ad DI. &rdquo; </s></p><p type="main">

<s>&ldquo; Est itaque DE libra, ex cuius punctis singulis magnitudines quaedam <lb/>appensae sunt, quarum duae sunt arcus ABC, GFH, reliquae vero sunt ar&shy;<lb/>cus praedictis concentrici, habentque magnitudines, ut demonstratum est, illam <lb/>inter se rationem, quam illarum distantiae ED, DI ab extremo puncto librae <lb/>D, quemadmodum etiam habent lineae alicuius trianguli. </s>

<s>Ergo libra CE, ad <lb/>quam applicatae sunt praedictae magnitudines, ita secabitur a centro gravi-<pb xlink:href="020/01/2666.jpg" pagenum="291"/>tatis omnium magnitudinum, ut secatur axis alicuius trianguli a centro gra&shy;<lb/>vitatis eiusdem, nempe ea conditione, ut pars, ad extremum D terminata ver&shy;<lb/>sus magnitudines decrescentes, sit, ad reliquam quae terminatur in E, centro <lb/>gravitatis maximae magnitudinis ABC, in proportione dupla. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Secetur ergo libra DE in O, ita ut DO ad OE sit dupla, et erit O <lb/>centrum gravitatis omnium simul arcuum concentricorum, nempe ipsius secto&shy;<lb/>ris. </s>

<s>Erit ergo arcus ABC, ad AC, ut BD ad DE. </s>

<s>Ipsa vero AC, ad 2/3 ipsius <lb/>AC, erit ut ED ad DO. </s>

<s>Quare ex aequo arcus ABC, ad 2/3 ipsius AC, erit <lb/>ut BD ad DO, nempe ut axis sectoris ad illam, quae interiicitur inter cen&shy;<lb/>trum circuli, et centrum gravitatis eiusdem sectoris, quod erat propositum &rdquo; <lb/>(ibid., T. XXXVII, fol. </s>

<s>25-31). </s></p><p type="main">

<s>La felice riuscita di questo nuovo metodo, applicato alla ricerca del cen&shy;<lb/>tro di gravit&agrave; nel settore di circolo, incor&ograve; nel Torricelli una dolce speranza <lb/>di dovere anche pi&ugrave; oltre promovere la Baricentrica da quel punto, a cui <lb/>l'aveva gi&agrave; condotta il padre Della Faille con tanta fatica. </s>

<s>Forse, incomin&shy;<lb/>ci&ograve; il Nostro a pensare, la medesima analogia, che nelle porzioni del cerchio, <lb/>corre nelle porzioni della sfera: e bench&egrave; sia stato dimostrato ormai il cen&shy;<lb/>tro di gravit&agrave; nel settore circolare e nell'emiciclo, nessuno sa per&ograve; ancora <lb/>dove stia sull'asse quello del settore sferico, desunto da quello del centro <lb/>dell'emisfero. </s>

<s>Sia questo emisfero BGC (fig. </s>

<s>151), e si riguardi, nella me&shy;<lb/><figure id="id.020.01.2666.1.jpg" xlink:href="020/01/2666/1.jpg"/></s></p><p type="caption">

<s>Figura 151.<lb/>desima maniera, come composto delle in&shy;<lb/>finite superficie concentriche intorno ad A: <lb/>si rappresentava alla mente del Torricelli <lb/>che, come dianzi dal centro di gravit&agrave; <lb/>degli archi era stato facilmente condotto <lb/>a risolvere un problema gi&agrave; reso noto; <lb/>cos&igrave; ora, dal centro di gravit&agrave; delle cal&shy;<lb/>lotte sarebbe, per vie simili, condotto a <lb/>risolvere quest'altro problema in una ma&shy;<lb/>niera del tutto nuova. </s></p><p type="main">

<s>Sia infatti il centro di gravit&agrave; della superficie emisferica BGC il punto <lb/>D, per il quale passi la LM perpendicolare all'asse AG. </s>

<s>Descrivasi qualun&shy;<lb/>que altra delle infinite superficie consentriche EPF, per il baricentro I della <lb/>quale si conduca la HK parallela a LM, e si compia il triangolo LMA. </s>

<s>Avremo <lb/>BGC:EPF=AL2:AH2=LD2:HI2=<foreign lang="greek">p</foreign>LD2:<foreign lang="greek">p</foreign>HI2, e cos&igrave; sempre, intan&shy;<lb/>toch&egrave; sopra la libbra AD si possono intendere applicate, ne'medesimi punti, <lb/>due vari ordini di grandezze proporzionali, e aventi ambedue perci&ograve; sopr'essa <lb/>libbra il medesimo centro: gl'infiniti circoli cio&egrave;, e le infinite callotte. </s>

<s>E per&shy;<lb/>ch&egrave; di queste si compone l'emisfero, e di quelle il cono; dal centro di gra&shy;<lb/>vit&agrave; noto nell'un solido, si render&agrave; manifesto il centro di gravit&agrave; nell'altro. </s></p><p type="main">

<s>Tutto il forte sta dunque nel sapere dove la volta emisferica, o qualun&shy;<lb/>que altra minore callotta o <emph type="italics"/>berrettino,<emph.end type="italics"/> come popolarmente il Torricelli la <lb/>chiamava, ha sull'asse il suo baricentro. </s>

<s>E perch&egrave;, ricercando ne'libri dei <lb/>Matematici antichi e dei moderni, ritrov&ograve; che nessuno ancora l'aveva inse-<pb xlink:href="020/01/2667.jpg" pagenum="292"/>gnato, si dette il Nostro, con trepidante sollecitudine, all'opera, la quale mo&shy;<lb/>strava di dover rendersi assai spedita, specialmente dop'essersi preparati al&shy;<lb/>cuni lemmi geometrici, conclusi dal teorema noto che cio&egrave;, rivolgendosi gli <lb/>archi EB, AB (fig. </s>

<s>152) intorno al diametro BD descrivono due callotte pro&shy;<lb/>porzionali ai quadrati delle suttese. </s>

<s>Stando infatti le dette callotte, che chia&shy;<lb/><figure id="id.020.01.2667.1.jpg" xlink:href="020/01/2667/1.jpg"/></s></p><p type="caption">

<s>Figura 152.<lb/>meremo C, C&prime;, in ragion composta delle altezze, <lb/>e della circonferenza di un circolo grande, o <lb/>del suo diametro, avremo C:C&prime;=BF.BD: <lb/>BG.BD=EB2:AB2. </s>

<s>Dietro ci&ograve; dimostrava il <lb/>Torricelli che &ldquo; se nella sfera ABCD siano ap&shy;<lb/>plicate <emph type="italics"/>utcumque<emph.end type="italics"/> EF, AG, sar&agrave; il berrettino <lb/>EBH, all'ABC, come BF alla BG. &rdquo; </s></p><p type="main">

<s>&ldquo; Tirinsi ED, AD, EB, AB. </s>

<s>Il quadrato EB <lb/>al BD sta come la retta BF alla BD. </s>

<s>Ma il qua&shy;<lb/>drato BD al BA sta come la retta DB alla BG; <lb/><emph type="italics"/>ergo ex aequo<emph.end type="italics"/> il quadrato EB al BA sta come <lb/>la retta BF alla BG. </s>

<s>Ma come il quadrato BE <lb/>al BA, cos&igrave; l'un berrettino all'altro. </s>

<s>Ergo etc. </s>

<s>&rdquo; (ivi, T. XXXVI, fol. </s>

<s>32). </s></p><p type="main">

<s>Di qui, cio&egrave; da ABC:EBH=BG:BF, dividendo, abbiamo ABC&mdash;EBH: <lb/>EBH=BG&mdash;BF:BF, ossia che la zona AEHC sta alla EBH come l'al&shy;<lb/>tezza FG di quella sta all'altezza FB di questa, e cos&igrave; per tutte le altre por&shy;<lb/>zioni intercette sulla sfera fra piani paralleli, le quali dunque saranno uguali, <lb/>quando siano le relative altezze fra loro uguali. </s></p><p type="main">

<s>Se ora si prendano quelle altezze infinitamente piccole, ragionava il Tor&shy;<lb/>ricelli, le zonule infinite intercette essendo uguali graviteranno ugualmente <lb/>co'loro centri sopra la libbra BG, la quale per conseguenza avr&agrave; nel mezzo <lb/>il punto dell'equilibrio, ond'&egrave; che il baricentro della callotta, per esempio <lb/>ABC, taglier&agrave; nel mezzo la BG sua saetta. </s>

<s>Cos&igrave; essendo, l'invenzione del <lb/>centro di gravit&agrave; dell'emisfero era ovvia, perch&egrave;, se nella figura 151 qui poco <lb/>addietro, D &egrave; il mezzo di AG, l'altezza del cono &egrave; DA, la quale essendo di&shy;<lb/>visa, a partir dal vertice, in quattro parti uguali; in P, dove si dica tornar <lb/>la terza divisione, sar&agrave; il centro cercato. </s>

<s>Che se anche GD similmente sia <lb/>quadripartito, &egrave; manifesto che GD conterr&agrave; cinque delle parti, delle quali PA <lb/>ne contiene tre sole. </s>

<s>Se poi BGC sia minore di una mezza circonferenza, per <lb/>avere il centro di gravit&agrave; del settore, basta divider nel mezzo, per esempio <lb/>in X, la saetta, la quale prolungata infino a incontrare in A il centro della <lb/>sfera, da A risalendo su per la AX per tre quarti della sua intera lunghezza, <lb/>ivi giunti troveremo il luogo, dove il settore stesso concentra il suo peso. </s></p><p type="main">

<s>Cos&igrave; annunziate aveva il Torricelli distese le sue proposizioni, la verit&agrave; <lb/>delle quali dipendendo tutta dalla verit&agrave; del teorema che cio&egrave; le callotte hanno <lb/>il baricentro nel mezzo della saetta, ne dava, come di cosa nuova e impor&shy;<lb/>tantissima avviso al Cavalieri. </s>

<s>Poi conferm&ograve; questi autorevolmente nella <lb/>XXXIV della sua quinta Esercitazione geometrica il teorema torricelliano, ma <lb/>intanto rispondeva non saperne per ora altro, se non che il Guldino, nella <pb xlink:href="020/01/2668.jpg" pagenum="293"/>Centrobarica, era venuto a una conclusione molto diversa, dicendo che il cen&shy;<lb/>tro di gravit&agrave; della cupola emisferica &egrave; il medesimo che quel del circolo fatto <lb/>passare attraverso all'asse di lei. </s></p><p type="main">

<s>Il Guldino s'era senza dubbio ingannato, ma l'inganno di lui, non con&shy;<lb/>fermato ancora da altre simili fallacie notate nel suo libro, aveva messo il <lb/>Torricelli in gran sospetto che non si fosse invece ingannato egli stesso, forse, <lb/>per non averci bene applicati gl'indivisibili, o per altre ragioni: tanto pi&ugrave; <lb/>che queste gli pareva venissero avvalorate dal saper che il Nardi e il Ricci <lb/>avevano trovato il centro di gravit&agrave; del settore sferico segar l'asse in altre <lb/>proporzioni, da quelle ch'egli aveva concluse. </s>

<s>Si volse allora a risolvere il <lb/>problema baricentrico delle superficie sferiche per altre vie, scansando gl'in&shy;<lb/>divisibili, e attenendosi ai metodi antichi, per star ne'quali maggiormente <lb/>sicuro imit&ograve; il processo tenuto da Archimede nello Scolio alla IX proposi&shy;<lb/>zione del primo degli Equiponderanti, per dimostrar che il centro di gravit&agrave; <lb/>del parallelogrammo sta nella linea retta, dalla quale due lati opposti sian <lb/>segati nel mezzo (Opera cit., pag. </s>

<s>172). La dimostrazion nonostante, che qui <lb/>trascriviamo, confermava la verit&agrave; di quel che aveva concluso per via degli <lb/>indivisibili, star sempre cio&egrave; il centro di gravit&agrave; della callotta sferica nel <lb/>mezzo della saetta. </s></p><p type="main">

<s>&ldquo; Suppongo in primo luogo che, se molte grandezze averanno li centri <lb/>di gravit&agrave; nella retta AB, tutti fra li punti A, B; che il centro comune di <lb/>tutte sia fra li punti A, B. </s>

<s>Suppongo in secondo luogo che, se una linea <lb/>retta sar&agrave; divisa in parti uguali, e di numero pari, ed in ciascuna parte di <lb/>essa sia il centro di gravit&agrave; di altrettante grandezze uguali; che il centro di <lb/>tutte stia in una delle linee di mezzo. </s>

<s>Suppongo, terzo, che il berrettino e <lb/>le zone sferiche abbiano il centro loro di gravit&agrave; nella saetta, e suppongo in <lb/>ultimo quel che ho gi&agrave; dimostrato che cio&egrave; i berrettini stanno come le saette, <lb/>e che perci&ograve; le zone, comprese fra piani equidistanti e paralleli, sempre sono <lb/>tra loro uguali. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XV. &mdash; <emph type="italics"/>Il centro del berrettino sferico sempre sta nel <lb/>mezzo della saetta. </s>

<s>&rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.2668.1.jpg" xlink:href="020/01/2668/1.jpg"/></s></p><p type="caption">

<s>Figura 153.</s></p><p type="main">

<s>&ldquo; Sia il berrettino sferico <lb/>ABC (fig. </s>

<s>153), e mezzo della <lb/>saetta D; dico ecc. </s>

<s>Se non &egrave; D <lb/>sia per esempio, se pu&ograve;, E, e di&shy;<lb/>visa BD bifariam in F e poi DF <lb/>bifariam in G, finch&egrave; resti DG <lb/>minore di DE, seghisi tutta BH <lb/>in parti uguali alla DG, e tirinsi <lb/>perpendicolari alla saetta. </s>

<s>Saranno <lb/>dunque i berrettini come le saette, <lb/>cio&egrave; in proporzione aritmetica <emph type="italics"/>ab unitate,<emph.end type="italics"/> e per&ograve; tutte le zone saranno uguali <lb/>al minor berrettino e fra di loro. </s>

<s>Ed avendo ciascuna il centro nel suo asse, <lb/>ed essendo tutte uguali, il centro di tutte dovr&agrave; essere fra il centro delle due <pb xlink:href="020/01/2669.jpg" pagenum="294"/>medie, cio&egrave; dovr&agrave; essere nella linea IG. </s>

<s>Ma &egrave; fuori di essa, essendo suppo&shy;<lb/>sto E, ergo etc. </s>

<s>&rdquo; (ivi, fol. </s>

<s>32). </s></p><p type="main">

<s>&Egrave; cosa veramente singolare che nemmeno questa dimostrazione valesse <lb/>ad assicurare il Torricelli, il quale avrebbe potuto dall'altra parte confer&shy;<lb/>marsi nella verit&agrave; della sua conclusione dalle proposizioni XVIII e XIX del <lb/>primo libro dei Solidi sferali. </s>

<s>Se &egrave; vero infatti, per la detta prima (Op. <lb/><figure id="id.020.01.2669.1.jpg" xlink:href="020/01/2669/1.jpg"/></s></p><p type="caption">

<s>Figura 154.<lb/>geom. </s>

<s>cit., pag. </s>

<s>28), che la superficie dell'emisfero <lb/>descritto dal quadrante ADH (fig. </s>

<s>154) &egrave; uguale <lb/>alla superficie esterna del cilindro descritto dal ret&shy;<lb/>tangolo FB, rivolgentesi intorno al medesimo asse <lb/>HB; e se &egrave; vero, per la seconda (ivi, pag. </s>

<s>30), che <lb/>le superficie della callotta HD e della zona DA <lb/>sono uguali alle curve superficie cilindriche de&shy;<lb/>scritte da FC e da EB; essendo manifesto de'ci&shy;<lb/>lindri che il loro centro sega l'asse nel mezzo, <lb/>sar&agrave; pur manifesto che son segate nel mezzo le <lb/>saette de'berrettini e le altezze delle zone. </s></p><p type="main">

<s>O che non avesse il Torricelli ancora dimostrate quelle sue proposizioni <lb/>sferali, o che non gli sovvenisse di applicarle opportunamente alla Baricen&shy;<lb/>trica, &egrave; un fatto che ne rimase il vantaggio al Wallis, il quale rendeva ge&shy;<lb/>neralissimi cos&igrave; i teoremi torricelliani: &ldquo; Si semicircumferentiae circuli, vel <lb/>arcui minori, circumponatur ex continuis rectis, quae mediis suis punctis pe&shy;<lb/>ripheriam contingant, conflata linea, quae ab hac linea composita circa istius <lb/>circuli diametrum quamvis, quae illam non secet, conversa, describitur su&shy;<lb/>perficies curva; aequatur superficiei curvae cylindri recti aeque alti, basim <lb/>habentis exposito circulo aequalem &rdquo; (De motu, P. II, Londini 1670, pag. </s>

<s>203). <lb/>Di qui si deduceva, per semplice corollar&igrave;o immediato, il centro di gravit&agrave; <lb/>delle superficie sferiche star nel mezzo dell'asse, con quella sicurezza venuta <lb/>a mancare nel Torricelli, che pur avrebbe potuto, trent'anni prima, cos&igrave; <lb/>utilmente valersi di quel medesimo argomento. </s>

<s>E che rimanesse veramente <lb/>esso Torricelli in timore di essersi ingannato, anche dopo aver ritrovato <lb/>quella cos&igrave; perfetta corrispondenza tra i resultati del metodo antico e degli <lb/>indivisibili; resulta dalla seguente lettera, scritta il d&igrave; 28 Marzo 1643 da Fi&shy;<lb/>renze al Cavalieri: </s></p><p type="main">

<s>&ldquo; ...... Le scrissi che il centro delle superficie sferiche stava nel mezzo <lb/>dell'asse corrispondente: glie ne dar&ograve; un cenno, per timore di essermi ingan&shy;<lb/>nato, senza indivisibili, mentre s'abbia a contendere con genti, che non gli <lb/>accettano. </s>

<s>Le premesse, che son pedanterie meccaniche e geometriche, son <lb/>tali: 1.&deg; Suppongo che i predetti centri sieno nell'asse. </s>

<s>2.&deg; Suppongo che, <lb/>se alquante grandezze avranno il centro di gravit&agrave; nella retta AB, il centro <lb/>comune di tutte sia fra i punti A, B estremi. </s>

<s>3.&deg; Suppongo che, se una sfera <lb/>sar&agrave; segata con piani paralleli, le superficie delle zone intercette, ed anco <lb/>de'segamenti estremi, siano fra di loro come le porzioni degli assi corrispon&shy;<lb/>denti. </s>

<s>4.&deg; Se una linea retta AB (fig. </s>

<s>155) sar&agrave; segata in quante parti un <pb xlink:href="020/01/2670.jpg" pagenum="295"/>vuole, eguali e di numero pari, e che ciascuna di esse sia il centro di gra&shy;<lb/>vit&agrave; di altrettante grandezze uguali fra di loro; suppongo che il centro co&shy;<lb/>mune di tutte sia in una delle sezioni di mezzo CE, ED, e lo provo cos&igrave;: <lb/><figure id="id.020.01.2670.1.jpg" xlink:href="020/01/2670/1.jpg"/></s></p><p type="caption">

<s>Figura 155.<lb/>Siano i centri di grandezze uguali <lb/>i punti F, G, H, I, N, M, L, O, <lb/>ciascuno dei quali sia in uno dei <lb/>segamenti della linea <emph type="italics"/>utcumque.<emph.end type="italics"/><lb/>Perch&egrave; dunque le grandezze, delle <lb/>quali esse son centri, si suppongono uguali, sar&agrave; il centro comune delle due <lb/>grandazze F, O il punto medio della retta FO. </s>

<s>Ma il punto medio della retta <lb/>FO sta nella retta CD; cos&igrave; anco il centro della coppia G, M sta nella retta <lb/>CD, ed il centro delle altre due coppie H, L ed I, N sta nella CD; adun&shy;<lb/>que il centro comune di tutte sta nella CD, per la seconda supposizione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia la superficie di un segmento o frusto sferico, di cui sia asse BH, <lb/>nella medesima figura 153 qui poco addietro rappresentata, e segata per <lb/>mezzo BH in D, dico che D sar&agrave; centro di gravit&agrave;. </s>

<s>Se non &egrave; D, sia un altro <lb/>per esempio E, e seghisi per mezzo BD in F, e di nuovo FD seghisi per <lb/>mezzo in G, e cos&igrave; sempre, fin che s'arrivi ad una sezione DG, minore della <lb/>retta DE. </s>

<s>Seghisi poi tutto l'asse in parti uguali alla DG, e per i punti dei <lb/>segamenti passino piani perpendicolari all'asse. </s>

<s>Non &egrave; dubbio che tutte le <lb/>superficie dei frusti e del segamento ultimo saranno uguali. </s>

<s>Anzi ognuna di <lb/>esse aver&agrave; il centro di gravit&agrave; in un segamento della saetta BH, divisa in <lb/>parti uguali. </s>

<s>Dunque il centro comune di tutte le grandezze sar&agrave; in una <lb/>delle due sezioni di mezzo DG, DI. </s>

<s>Dunque il centro di tutte non &egrave; M, ma <lb/>necessariamente sar&agrave; D, dimostrandosi che niun altro punto della retta BH <lb/>pu&ograve; essere centro di gravit&agrave; della predetta superficie sferica, di segamento o <lb/>di frusto che ella sia &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>127). </s></p><p type="main">

<s>Il Cavalieri non pot&egrave; non approvare il processo dimostrativo e la verit&agrave; <lb/>della conclusione, la quale fu, per essere ordinata con l'altre nel trattato dei <lb/>centri di gravit&agrave;, messa dallo stesso Torricelli in questa forma: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XVI. &mdash; <emph type="italics"/>Centrum gravitatis zonae sphaericae, sive su&shy;<lb/>perficiei curvae segmenti sphaerici, est in medio axis ipsius zonae.<emph.end type="italics"/></s></p><p type="main">

<s>La dimostrazione, che si legge manoscritta al fol. </s>

<s>33 del solito tomo XXXVI <lb/>crediamo di poterla tralasciare, non essendo differente da quella mandata per <lb/>lettera al Cavalieri, che nella forma esteriore della lingua latina. </s>

<s>E come <lb/>messe in ordine questa e la precedente, cos&igrave; messe in ordine le proposizioni, <lb/>che ne conseguivano, relative ai baricentri delle porzioni di sfera, tanto pi&ugrave; <lb/>che in sostanza ebbe a ritrovar che anche il Nardi e il Ricci concordavano <lb/>seco nell'ammettere la verit&agrave; cos&igrave; pronunziata: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XVII. &mdash; <emph type="italics"/>Centrum gravitatis hemisphaerii secat axem <lb/>ita, ut pars ad verticem sit ad reliquam sesquipartiens tertias. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Ma prima di trascriver la d&igrave;mostrazione vogliamo osservare che il Tor&shy;<lb/>ricelli suppone il seguente lemma: Se una libbra sia per tutta la sua lun&shy;<lb/>ghezza gravata da pesi, via via crescenti come i quadrati delle distanze, il <pb xlink:href="020/01/2671.jpg" pagenum="296"/>punto dell'equilibrio la segher&agrave; in modo, che la parte verso i pesi minori <lb/>sia tripla della rimanente. </s>

<s>Anzi scrive in parentesi, per modo di nota: <emph type="italics"/>que&shy;<lb/>sto bisogna premetterlo e cavarlo dal cono.<emph.end type="italics"/> In questo solido infatti gl'in&shy;<lb/>finiti circoli che lo compongono si possono riguardar ponderanti sopra l'asse <lb/>come sopra una libbra, ed essi circoli stanno come i quadrati dei raggi <lb/>FH, DE (fig. </s>

<s>156), o delle distanze AH, AE. </s>

<s>E perch&egrave; il centro dell'equili&shy;<lb/>brio si sa che &egrave; sull'asse a tre quarti di distanza dal vertice A; par che ne <lb/><figure id="id.020.01.2671.1.jpg" xlink:href="020/01/2671/1.jpg"/></s></p><p type="caption">

<s>Figura 156.<lb/>volesse di qui concludere il Torricelli che il centro di gravit&agrave; <lb/>nella libbra &egrave; come si &egrave; detto sopra nel lemma. </s>

<s>Sarebbe stato <lb/>meglio per&ograve; dimostrare direttamente il principio statico, e di <lb/>l&igrave; concluderne il centro di gravit&agrave; del cono, come dianzi dal <lb/>principio statico di Galileo aveva concluso il centro di gravit&agrave; <lb/>del triangolo, ma la dimostrazione dipendeva da pi&ugrave; alti prin&shy;<lb/>cipii, de'quali faremo cenno in altro proposito. </s>

<s>Forse nella <lb/>medesima statica galileiana sar&agrave; andato il Torricelli ricercando <lb/>qualche cosa, che facesse al presente suo particolare bisogno, <lb/>con intenzion di scrivere in fronte al teorema <emph type="italics"/>Centrum gravitatis coni, sup&shy;<lb/>posito principio Galilei,<emph.end type="italics"/> ma ebbe questo principio a trovarlo formulato molto <lb/>diversamente da quel che s'aspettava, perch&egrave;, nella sesta proposizione, scritta <lb/>nell'Appendice ai dialoghi delle Scienze nuove, supposta una libbra nelle <lb/>condizioni gi&agrave; dette, si dimostra che &ldquo; centrum aequilibrii libram dividit, ut <lb/>pars versus minores magnitudines reliquae sit maior quam tripla &rdquo; (Alb. </s>

<s><lb/>XIII, 280). Or qui bisognerebbe dire o che &egrave; falsa la proposizione di Gali&shy;<lb/>leo, o &egrave; falso il centro di gravit&agrave; del cono, come tutti l'hanno insegnato, o &egrave; <lb/>falsa l'applicazione voluta farsi degl'indivisibili in questo caso. </s>

<s>E perch&egrave; il <lb/>Torricelli prosegue pure con gl'indivisibili, e conferma il centro di gravit&agrave; <lb/>del cono segar l'asse in modo, che la parte verso il vertice sia precisamente <lb/>tripla, e non gi&agrave; pi&ugrave; che tripla della rimanente; lasciamo ai nostri decidere <lb/>in giudizio, per passare a leggere nel manoscritto la dimostrazione di ci&ograve;, che <lb/>s'&egrave; di sopra annunziato. </s></p><p type="main">

<s>&ldquo; Hemisphaerium sit ABC (fig. </s>

<s>157), cuius axis BD secetur bifariam <lb/>in E: eritque E centrum superficiei ABC. </s>

<s>Sumatur punctum quodvis F, et <lb/>dividatur bifariam FD in I, eritque I centrum superficiei GFH. &rdquo; <lb/><figure id="id.020.01.2671.2.jpg" xlink:href="020/01/2671/2.jpg"/></s></p><p type="caption">

<s>Figura 157.</s></p><p type="main">

<s>&ldquo; Superficies autem ABC, ad superficiem <lb/>GFH, est ut quadratum BD ad DF, sive, sumptis <lb/>subquadruplis, ut quadratum ED, ad DI. </s>

<s>Est ergo <lb/>ED libra, in qua sunt centra gravitatis infinita&shy;<lb/>rum magnitudinum, quarum maxima habet cen&shy;<lb/>trum in E, minima in D, suntque magnitudi&shy;<lb/>nes inter se in duplicata ratione distantiarum ab <lb/>extremo librae D. </s>

<s>Ergo centrum omnium erit O: <lb/>sumpta scilicet EO 1/4 totius ED. </s>

<s>Quare BO ad OD erit ut 5 ad 3, quod <lb/>erat demonstrandum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XVIII. &mdash; <emph type="italics"/>Esto solidus sphaerae sector ABCD<emph.end type="italics"/> (fig. </s>

<s>158), <pb xlink:href="020/01/2672.jpg" pagenum="297"/><emph type="italics"/>constans ex cono ADC, et ex segmento ABC, sectaque DF bifariam in E, <lb/>et ED in quatuor partes aequales, quarum una sit EO; dico centrum <lb/>gravitatis sectoris solidi esse O. &rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.2672.1.jpg" xlink:href="020/01/2672/1.jpg"/></s></p><p type="caption">

<s>Figura 158.</s></p><p type="main">

<s>&ldquo; Sumatur quodvis punctum in re&shy;<lb/>cta BD, puta I, et per illud agatur su&shy;<lb/>perficies sphaerica HIL, bisectaque IM <lb/>in N, erit N centrum superficiei HIL, si&shy;<lb/>cut et E est centrum superficiei ABC. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam tota BD, ad totam ID, est, <lb/>ob aequalitatem, ut AD ad DH, sive, per <lb/>IV Sexti, ut FD ablata ad ablatam DM. </s>

<s><lb/>Quare tota BD, ad totam DI, erit ut re&shy;<lb/>liqua BF ad IM, sive, sumptis subduplis, <lb/>ut BE ad IN. </s>

<s>Et permutando, et per con&shy;<lb/>versionem rationis, crit BD ad DE ut ID <lb/>ad DN. </s>

<s>Et permutando BD ad DI ut ED <lb/>ad DN. </s>

<s>Superficies vero ABC, ad super&shy;<lb/>ficiem HIL, est ut quadratum BD ad quadratum DI, sive ut quadratum ED <lb/>ad DN, et hoc modo semper. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pendent ergo ex libra ED magnitudines, quarum maxima centrum <lb/>habet E, minima vero D. </s>

<s>Suntque magnitudines inter se in duplicata ratione <lb/>distantiarum ab extremo librae puncto, nempe sunt inter se ut circuli ali&shy;<lb/>cuius coni. </s>

<s>Propterea centrum omnium dividet libram DE in eadem ratione <lb/>cum centro coni, nempe ita ut pars ad D reliquae sit tripla. </s>

<s>Est itaque cen&shy;<lb/>trum O, quod erat demonstrandum. </s>

<s>&rdquo; <lb/><figure id="id.020.01.2672.2.jpg" xlink:href="020/01/2672/2.jpg"/></s></p><p type="caption">

<s>Figura 159.</s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XIX. &mdash; <emph type="italics"/>Centram gravita&shy;<lb/>tis solidi sectoris sphaerici est in axe, distans <lb/>a centro sphaerae per 3/4 axis coni, et 3/8 sa&shy;<lb/>gittae segmenti. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto solidus sector sphaerae ABCF (fig. </s>

<s>159) <lb/>cuius axis BF, sectaque sagitta BE bifariam in D, <lb/>et reliqua DF quadrifariam in punctis I, H, L, <lb/>erit, per praecedentem, centrum sectoris I. </s>

<s>Dico <lb/>FI constare ex 3/4 rectae FE, et ex 3/8 rectae EB. </s>

<s><lb/>Quod patet: tota enim DF constat ex tota FE, et <lb/>ex dimidia BE, nempe constat ex 4/4 rectae FE, et ex 4/8 rectae EB. </s>

<s>Ergo sub&shy;<lb/>quadrupla recta FL, constabit ex 1/4 rectae FE et 1/8 rectae EB. </s>

<s>Ipsa ergo <lb/>Fl, tripla FL, composita crit ex 3/4 FE, et 3/8 rectae EB, quod erat demon&shy;<lb/>strandum &rdquo; (ibid., fol. </s>

<s>94, 95). </s></p><pb xlink:href="020/01/2673.jpg" pagenum="298"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Rivolgendo il Torricelli il pensiero sopra queste proposizioni, si com&shy;<lb/>piaceva tutto fra s&egrave; e con gli amici di Roma, di aver fatto tant'oltre pro&shy;<lb/>gredire la Baricentrica, che il libro del p. </s>

<s>Della Faille, appetto a suoi pochi <lb/>fogli scritti, pareva ben assai misera cosa. </s>

<s>Mentre infatti gli sforzi del padre <lb/>non erano riusciti che a dimostrare il centro di gravit&agrave; del settore di cir&shy;<lb/>colo, egli aveva di pi&ugrave; ritrovato il centro degli archi, delle callotte e delle <lb/>zone; de'settori sferici e dello stesso emisfero. </s>

<s>Quel che il Gesuita dall'altra <lb/>parte diceva di aver cio&egrave; determinati i centri di gravit&agrave; di molte altre figure, <lb/>ci&ograve; che nessun altro aveva fatto prima di lui, e di aspettare a pubblicar le <lb/>sue invenzioni <emph type="italics"/>tum ut explorarem quis de his speculationibus doctorum <lb/>virorum futurus sit sensus, tum quod antiquorum more librum uno su&shy;<lb/>biecto constare debere existimem, quale sunt circulus et ellipsisi eiusdem <lb/>omnino essentiae figurae;<emph.end type="italics"/> pareva al Torricelli una iattanza, la vanit&agrave; della <lb/>quale era facilmente scoperta dallo stesso strano giudizio, che s'adduceva per <lb/>ricoprirla. </s></p><p type="main">

<s>Dopo il gesuita accademico di Madrid, nel 1642, quando il Torricelli <lb/>attendeva a questi suoi studi, non si conosceva in Italia altro autore, che ne <lb/>avesse trattato: ci&ograve; che fa maraviglia, perch&egrave; il Guldin, in Austria, aveva <lb/>sette anni prima, cio&egrave; nel 1635, pubblicato il suo primo tomo della Centro&shy;<lb/>barica. </s>

<s>La maraviglia cresce anzi di pi&ugrave;, ripensando che il libro, con tanta <lb/>curiosit&agrave; ricercato, e non potuto vedere dai Discepoli di Galileo, se non che <lb/>dopo tanto penare per alcuni, e per altri mai; par che fosse nelle mani <lb/>del loro proprio maestro. </s>

<s>Giovanni Pieroni infatti, il di primo Marzo 1636 <lb/>scriveva da Vienna, dove pochi mesi prima quel primo tomo era stato pub&shy;<lb/>blicato, ad Arcetri, una lettera, che terminava con queste parole: &ldquo; Il padre <lb/>Guldini gesuita, amico di V. S., che la conobbe in Roma, e che &egrave; parziale <lb/>suo, ha composto un libro <emph type="italics"/>De centro gravitatis partium circuli,<emph.end type="italics"/> e mi ha <lb/>consegnato un esemplare, perch&egrave; io lo mandi a V. S., il che far&ograve; con pre&shy;<lb/>sta occasione &rdquo; (Alb. </s>

<s>X, 142). </s></p><p type="main">

<s>Potrebb'essere o che le promesse non fossero mantenute, o che il libro <lb/>si fosse smarrito per via, o che pure recapitato non se ne facesse alcun conto, <lb/>e si rimanesse perci&ograve; nella dimenticanza di tutti: fatto &egrave; che il Torricelli <lb/>riposava tranquillo nella sua gloria, senza che nessuno ancora venisse a tur&shy;<lb/>bargliene i sogni. </s>

<s>Ma quando nel 1641 si pubblic&ograve; della Centrobarica il tomo <lb/>secondo, dove si censurava il metodo degli indivisibili, il Cavalieri divulg&ograve; <lb/>la notizia dell'autore e dell'opera fra gli amici, dandola principalmente al <lb/>Torricelli, le prime impressioni sull'animo del quale possono giudicarsi dal <lb/>seguente estratto di lettera, scritta il d&igrave; 3 Febbraio 1642 al Michelini: </s></p><p type="main">

<s>&ldquo; ...... V. paternit&agrave; si compiacer&agrave; di ricevere una coppia di teoremi <pb xlink:href="020/01/2674.jpg" pagenum="299"/>geometrici nuovi, preconizzati dal miracoloso fra Bonaventura, sebbene uno <lb/>di essi l'ha disgustato, per essere di un suo emulo, che gli ha stampato un <lb/>libro contro. </s>

<s>Quel teorema dell'emulo di fra Bonaventura, che &egrave; un tal <lb/>p. </s>

<s>Guldini gesuita, &egrave; la massima conclusione di tutte quante quelle, che io <lb/>abbia mai sentito fino a questo giorno, ed &egrave; tale: Se qualsivoglia figura piana <lb/>sia girata intorno a qualsivoglia asse, o sia l'asse congiunto con la figura <lb/>o no, il solido rotondo descritto dalla figura sar&agrave; uguale ad un solido, la cui <lb/>base sia la stessa figura genitrice, ma l'altezza poi sia uguale alla perife&shy;<lb/>ria, che nel girare sar&agrave; stata descritta dal centro di gravit&agrave; della figura ge&shy;<lb/>nitrice. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di pi&ugrave;: la superficie curva di quel solido rotondo, ancorch&egrave; irregola&shy;<lb/>rissima, sar&agrave; sempre uguale ad un parallelogrammo rettangolo, un lato del <lb/>quale sia uguale alla linea genitrice, e l'altro sia uguale alla periferia de&shy;<lb/>scritta parimente dal centro di gravit&agrave; di essa linea genitrice nel girare. </s>

<s>Un <lb/>teorema poi cos&igrave; grande, che &egrave; verissimo, il buon padre non lo sa dimostrare: <lb/>solo va provando che concorda con le dottrine di Archimede e del XII di <lb/>Euclide. </s>

<s>Ma fra Bonaventura ne ha la dimostrazione facilissima per via degli <lb/>indivisibili .... &rdquo; (MSS. Gal., T. XXVI, fol. </s>

<s>6). </s></p><p type="main">

<s>Di qui apparisce che i primi pensieri del Torricelli furono serenamente <lb/>rivolti a favorire l'amico: ma quando quest'amico, cio&egrave; il Cavalieri, gli sog&shy;<lb/>giunse la notizia che, nel primo tomo dell'opera del Guldin, dove non en&shy;<lb/>travano per niente gl'indivisibili, perch&egrave; ancora non erano conosciuti; l'Au&shy;<lb/>tore vi trattava profusamente dell'invenzione dei centri di gravit&agrave; anche delle <lb/>porzioni del circolo e della sfera: e allora il Torricelli rivolse il pensiero a <lb/>s&egrave; medesimo, e trepidante che non fosse venuto l'incognito straniero a sfron&shy;<lb/>dargli di sulla fronte gli allori, prese, il di 21 di Febbraio 1643, la penna, <lb/>per scrivere cos&igrave; allo stesso Cavalieri: </s></p><p type="main">

<s>&ldquo; Non ho potuto ritrovare quest'ultimo libro della Centrobarica: sup&shy;<lb/>plico V. P. ad avvisarmi se vi sia alcuna delle seguenti conclusioni: &rdquo; </s></p><p type="main">

<s>&ldquo; I. </s>

<s>Il solido settore della sfera, che &egrave; composto di un cono e di un <lb/>segmento sferico, ha il centro di gravit&agrave; sull'asse tanto lontano dal centro <lb/>della sfera, quanto sono 3/4 dell'asse del cono, e 3/8 della saetta del segmento, <lb/>il che abbraccia l'emisferio ancora. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; II. </s>

<s>La superficie sferica di qualunque segmento <lb/><figure id="id.020.01.2674.1.jpg" xlink:href="020/01/2674/1.jpg"/></s></p><p type="caption">

<s>Figura 160.<lb/>di sfera ha il centro di gravit&agrave; nel mezzo della sua <lb/>saetta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; III. </s>

<s>Ogni zona di superficie sferica, tagliata con <lb/>piani paralleli, ha il centro nel mezzo del segmento <lb/>dell'asse intercetto tra i detti piani. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; IV. </s>

<s>Se nel settore del circolo sar&agrave; inscritta una <lb/>figura di molti lati uguali, mediante la continua bi&shy;<lb/>sezione dell'arco, se faremo come tutte le dette linee uguali ABC (fig. </s>

<s>160) <lb/>alla corda AC, cos&igrave; il cateto della figura DE alla EO; il punto O sar&agrave; cen&shy;<lb/>tro di tutte le linee rette uguali ABC. &rdquo; </s></p><pb xlink:href="020/01/2675.jpg" pagenum="300"/><p type="main">

<s>&ldquo; V. </s>

<s>Ma se faremo come tutte le rette ABC alli 2/3 della corda AC, cos&igrave; <lb/>il cateto DE alla EI, il punto I sar&agrave; centro della figura rettilinea ABCE. &rdquo; </s></p><p type="main">

<s>&ldquo; VI. </s>

<s>Facendosi poi come l'arco ABC alla corda AC, cos&igrave; il semidiame&shy;<lb/>tro BE alla EO, il punto O sar&agrave; centro dell'arco. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; VII. </s>

<s>E facendosi come l'arco ABC, alli 2/3 della corda AC, cos&igrave; BE <lb/>alla EI: il punto l sar&agrave; centro del settore. </s>

<s>Quest'ultima &egrave; del padre Della <lb/>Faille, dimostrata da lui con un libro di roba, ed io la dimostro con meno <lb/>di un foglio, in due modi diversi, per gl'indivisibili e senza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Temo che quell'autore della Centrobarica si sia incontrato in alcune <lb/>di queste verit&agrave;, il che mi dispiacerebbe, non tanto perch&egrave; ne resterei privo <lb/>io, quauto perch&egrave; ne resterebbe padrone uno, che non &egrave; degno. </s>

<s>Cos&igrave; mi pare <lb/>di poter dire di uno, che biasima la dottrina degl'indivisibili, che &egrave; la vena <lb/>e la miniera inesausta delle speculazioni belle, e delle dimostrazioni a priori &rdquo; <lb/>(ivi. </s>

<s>T. XL. fol. </s>

<s>121). </s></p><p type="main">

<s>Il Cavalieri rispose da Bologna, il d&igrave; 3 di Marzo, con una lettera, nella <lb/>quale, dop'aver discorso d'altre cose analoghe all'argomento, cos&igrave; soggiun&shy;<lb/>geva: &ldquo; Circa poi le conclusioni mandatemi devo dirle che il padre Guldini <lb/>le dimostra anch'esso, eccettuato che non torna il centro di gravit&agrave; n&egrave; del <lb/>solido settore della sfera, n&egrave; delle zone di essa o superficie delle porzioni. </s>

<s><lb/>Solo dice di stimar probabile che il centro di esse superficie sia l'istesso che <lb/>il centro di gravit&agrave; delle figure genitrici delle porzioni di sfera, o delle por&shy;<lb/>zioni comprese fra piani paralleli, provandolo <emph type="italics"/>a simili,<emph.end type="italics"/> poich&egrave; dice: siccome <lb/>il centro della superficie conica, eccettuata la base, &egrave; l'istesso che del trian&shy;<lb/>golo per l'asse; cos&igrave; accader&agrave; in questi. </s>

<s>Anzi cos&igrave; anco dice nelle porzioni <lb/>di supert&igrave;cie dello sferoide, e conoide parabolico: onde credo che in questo <lb/>inciampi, discordando dalle sue conclusioni, che veramente mi paiono bellis&shy;<lb/>sime, come anco l'altro modo nuovo, con il quale pure misura le porzioni <lb/>di sfera, sferoidi, conoidi, etc. </s>

<s>&rdquo; (ivi, T. XLI, fol. </s>

<s>157). </s></p><p type="main">

<s>Non appariva chiaro da queste prime parole se il Guldin, in dimostrare <lb/>il centro di gravit&agrave; dell'arco di cerchio, era proceduto a diritto o aveva an&shy;<lb/>che in esso inciampato, ci&ograve; che principalmente premeva di sapere al Torri&shy;<lb/>celli, il quale sarebbe volentieri tornato a far di ci&ograve; espressa domanda, se <lb/>non avesse sperato d'aver presto dalla stessa lettura del libro la desiderata <lb/>risposta. </s>

<s>Era una tale speranza poi tanto pi&ugrave; fondata, in quanto che fra i <lb/>desiderosi di aver quel libro era il giovane principe Leopoldo de'Medici, che <lb/>studiava allora le Matematiche sotto la direzione del Michelini, a cui vedemmo <lb/>come fosse dianzi dato la notizia della grande Regola centrobarica: da che, <lb/>aggiungendosi alla propria curiosit&agrave; l'altrui comando, fu il Torricelli stesso <lb/>mosso a scrivere cos&igrave; al Cavalieri: &ldquo; Diedi nuova al p. </s>

<s>Francesco delle Scuole <lb/>pie, matematico del principe Leopoldo, del nuovo libro del Guldini, ed egli <lb/>mi scrive che io procuri in tutti i modi di averne uno. </s>

<s>Supplico V. P. d'av&shy;<lb/>visarmi se cost&igrave; ve ne sar&agrave;, e almeno dov'&egrave; stampato, e quando la spera <lb/>d'aver fornita e pubblicata la <emph type="italics"/>Risposta &rdquo;<emph.end type="italics"/> (ivi, T. XL, fol. </s>

<s>123). </s></p><p type="main">

<s>Chi ha letto il secondo capitolo dell'altro nostro tomo, gi&agrave; sa che l'ac-<pb xlink:href="020/01/2676.jpg" pagenum="301"/>cennata Risposta era quella, incominciata a farsi in dialogo, alle censure dello <lb/>stesso Guldino, contro il quale il Torricelli sollecitava il Cavalieri a difen&shy;<lb/>dersi, mentr'egli intanto pensava colle offese d'attutir la baldanza del ne&shy;<lb/>mico. </s>

<s>Un tale animo si rivela da ci&ograve; che dice esso Torricelli in una lettera <lb/>scritta il di 7 Marzo 1643, cio&egrave; una settimana dopo la precedente. </s></p><p type="main">

<s>&ldquo; Dopo che io ebbi la lettera di V. P., dimostrai, anco senza indivisi&shy;<lb/>bili, che il centro delle armille e zone sferiche sia nel mezzo della porzione <lb/>d'asse, che gli corrisponde, e la dimostrazione &egrave; semplicissima, e quasi si&shy;<lb/>mile alla IX del primo <emph type="italics"/>Degli equiponderanti.<emph.end type="italics"/> Mi darebbe poi anche il cuore <lb/>di dimostrare che il centro della superficie del conoide parabolico non &egrave; <lb/>l'istesso che quello della parabola genitrice. </s>

<s>Quanto allo sferoide ed iperbo&shy;<lb/>lico non ne so nulla, ma vedendo che egli si &egrave; ingannato in queste, posso <lb/>credere che si sia ingannato anche in quelle. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io non vorrei esser tanto prosuntuoso che ardissi di consigliarla, ma <lb/>almeno antepongo al suo giudizio se ella stimer&agrave; bene toccargli questo punto <lb/>nella <emph type="italics"/>Risposta,<emph.end type="italics"/> con mostrargli che egli finalmente adduce delle conclusioni <lb/>false. </s>

<s>Io quanto a me creder&ograve; che i metodi del Padre siano ottimi, e che <lb/>quello degl'indivisibili di fra Bonaventura sia cattivo: so bene per&ograve; per cosa <lb/>certa che quegli ottimi deducono delle cose false, che tali si dimostrano, e <lb/>che da quel cattivo non si cava se non conclusioni vere, quando si operi <lb/>conforme alli precetti dell'arte, ed alle cose dimostrate negli Elementi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io non posso credere che quello sia grand'Uomo, mentre in cose tanto <lb/>gelose si lascia trasportare ad argomentare <emph type="italics"/>a simili.<emph.end type="italics"/> Il parallelogrammo &egrave; <lb/>doppio del triangolo: anco la porzione dell'asse alla cima &egrave; doppia di quella <lb/>alla base del triangolo. </s>

<s>Il parallelogrammo &egrave; sesquialtero della parabola: anco <lb/>la porzion dell'asse &egrave; sesquialtera. </s>

<s>Il cilindro &egrave; triplo del cono: anco la por&shy;<lb/>zione dell'asse alla cima &egrave; tripla della rimanente. </s>

<s>Il cilindro &egrave; doppio del <lb/>conoide parabolico, ed anco la porzione dell'asse alla cima &egrave; dupla della <lb/>rimanente. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io dunque, che avr&ograve; pi&ugrave; similitudini che non ha il Padre, seguiter&ograve; <lb/>ad argomentare e dir&ograve;: il cilindro &egrave; sesquialtero dell'emisfero, dunque la <lb/>porzione dell'asse dell'emisfero, che &egrave; dalla cima fino al centro della gra&shy;<lb/>vit&agrave;, sar&agrave; sesquialtera della rimanente. </s>

<s>Ma questo &egrave; falso, stando come cin&shy;<lb/>que a tre &rdquo; (ivi, fol. </s>

<s>124). </s></p><p type="main">

<s>Dismesso il primo proposito di rispondere al Guldin in dialogo, non la&shy;<lb/>sci&ograve; il Cavalieri di dare effetto al consiglio dell'amico nella fine del cap. </s>

<s>XIV <lb/>della terza Esercitazione geometrica, dove, con un esempio preso dalle inscri&shy;<lb/>zioni e circoscrizioni delle superficie coniche, mostrava quant'era falso l'ar&shy;<lb/>gomento <emph type="italics"/>a simili<emph.end type="italics"/> addotto nel cap. </s>

<s>X alla V proposizion centrobarica, che <lb/>cio&egrave; si corrispondono i centri di gravit&agrave; delle dette superficie, e dei solidi <lb/>rotondi (Ediz. </s>

<s>cit., pag. </s>

<s>235-38). Ma la curiosit&agrave;, che aveva il Torricelli di <lb/>riscontrar da s&egrave; queste cose nel libro, non fu in lui sodisfatta, cosicch&egrave;, di&shy;<lb/>stratto dalla fabbrica dei vetri per i canocchiali, in che diceva di ritrovar <lb/>tutto il suo diletto, non si cur&ograve; pi&ugrave; di decidere del primato intorno all'in-<pb xlink:href="020/01/2677.jpg" pagenum="302"/>venzione del baricentrico negli archi di cerchio. </s>

<s>Abbiam veduto quant'egli <lb/>avesse ambito prima a una tale invenzione, la quale, non solamente comu&shy;<lb/>nic&ograve; al Cavalieri, come apparisce dai documenti citati, ma a tutti i suoi amici <lb/>di Roma, per mezzo di Michelangiolo Ricci pregato apposta a voler dare al <lb/>Magiotti la nuova che &ldquo; se sar&agrave; un settore di cerchio, e facciasi, come l'arco <lb/>a tutta la corda, cos&igrave; l'asse a una quarta linea; nell'estremit&agrave; di questa sar&agrave; <lb/>il centro di gravit&agrave; dell'arco &rdquo; (ivi, fol. </s>

<s>100). </s></p><p type="main">

<s>&Egrave; rimasta fra le carte del Torricelli una scrittura, che avremo occasione <lb/>di citar pi&ugrave; volte, intitolata <emph type="italics"/>Racconto di alcune proposizioni proposte e pas&shy;<lb/>sate scambievolmente tra i matematici di Francia e me, dall'anno 1640 <lb/>in qua,<emph.end type="italics"/> nel quale anno racconta come avendo contratta col p. </s>

<s>Niceron una <lb/>stretta amicizia in Roma, mandasse a lui in un foglio alcune sue invenzioni <lb/>geometriche, accennando solo le enunciazioni, senza dimostrazione alcuna. </s>

<s>&ldquo; E <lb/>feci questo, soggiunge, acci&ograve; non solo il suddetto padre vedesse quel com&shy;<lb/>pendio de'miei studi, ma anco lo conferisse ai matematici della Francia, e <lb/>ne intendesse il loro giudizio &rdquo; (ivi, T. XXXII, fol. </s>

<s>21). </s></p><p type="main">

<s>Anche il baricentro dell'arco fu notato tra quelle invenzioni, e, come <lb/>di questa, fu per i matematici francesi favorevole il giudizio delle altre pro&shy;<lb/>posizioni torricelliane, infin tanto che nel 1646 non insorsero col Roberval <lb/>le famos&egrave; controversie intorno a chi avesse prima dimostrato il centro di <lb/>gravit&agrave;, e definita la misura dei solidi generati dalla Cicloide. </s>

<s>In mezzo a <lb/>cotesta animosit&agrave;, e per citar qualche altro esempio valevole a confermar <lb/>nell'avversario l'accusa di plagio, andava esso Roberval dicendo che, bench&egrave; <lb/>il Torricelli si fosse appropriata la'dimostrazione del centro di gravit&agrave; delle <lb/>porzioni di circonferenza, il Guldin nonostante aveva gi&agrave; scritto il medesimo, <lb/>e pubblicato nel primo libro della Centrobarica, dimostrando un'altra novit&agrave; <lb/>bellissima, che cio&egrave; la mezza circonferenza concentra il suo peso l&agrave; dove la <lb/>Quadratrice di Nicomede ha il termine del suo moto. </s></p><p type="main">

<s>A questa prima notizia, con l'animo agitato da varie passioni, forse non <lb/>comprese il Torricelli la relazion che passa fra il centro di gravit&agrave; di un <lb/><figure id="id.020.01.2677.1.jpg" xlink:href="020/01/2677/1.jpg"/></s></p><p type="caption">

<s>Figura 161.<lb/>arco, e la famosa curva meccanica del Matematico antico. </s>

<s><lb/>Ma poi, rivolgendo le <emph type="italics"/>Collezioni matematiche<emph.end type="italics"/> di Pappo, <lb/>nel libro IV, dove si tratta della curva assunta da Dino&shy;<lb/>strato e da Nicomede per la quadratura del circolo, rivolse <lb/>particolarmente la sua attenzione sul teorema XXIII cos&igrave; <lb/>formulato: &ldquo; Quadrato enim existente ABFC (fig. </s>

<s>161), et <lb/>circumferentia BC, circa centrum A, et linea quadrante BE, <lb/>facta sicuti dictum est; ostenditur, ut BC circumferentia, <lb/>ad rectam lineam AB, ita esse AB, ad ipsam AE &rdquo; (Bo&shy;<lb/>noniae 1660, pag. </s>

<s>89). D'ond'ebbe il Torricelli a conclu&shy;<lb/>dere che il punto E, dove il moto della Quadratrice ter&shy;<lb/>mina sull'asse, era veramente il centro di gravit&agrave; della <lb/>semicirconferenza BCD, com'egli stesso aveva concluso per vie tanto diverse. </s>

<s><lb/>Allora incominci&ograve; a dubitar che il Guldino avesse argomentato di qui, e che <pb xlink:href="020/01/2678.jpg" pagenum="303"/>fosse la sua invenzione una congettura o una supposizione, piuttosto che una <lb/>dimostrazione condotta dai principii della Geometria. </s>

<s>Questo gli premeva di <lb/>saper con certezza, per rispondere al Roberval, ond'&egrave; che, dopo tre anni, <lb/>cio&egrave; il d&igrave; 23 Marzo 1646, tornava a farne al Cavalieri, cos&igrave;, ma con pi&ugrave; tre&shy;<lb/>pida sollecitudine, la domanda: </s></p><p type="main">

<s>&ldquo; Supplico V. P., se per&ograve; ella se ne ricorda, a voler farmi grazia d'av&shy;<lb/>visarmi se quel padre gesuita della Centrobarica dimostri geometricamente <lb/>che, facendosi come l'arco di cerchio ABC (fig. </s>

<s>162) alla sua corda AC, cos&igrave; <lb/>il semidiametro BD alla DE, il punto E sia centro dell'arco ABC. </s>

<s>Mi pare <lb/>che V. P. mi scrivesse che egli diceva questo Teo&shy;<lb/><figure id="id.020.01.2678.1.jpg" xlink:href="020/01/2678/1.jpg"/></s></p><p type="caption">

<s>Figura 162.<lb/>rema, ma non mi ricordo se ella mi dicesse se egli <lb/>lo dimostrava, ovvero lo supponeva &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. XL, fol. </s>

<s>130). </s></p><p type="main">

<s>Rispose il Cavalieri che il Guldin dimostrava, e <lb/>non solamente supponeva il teorema, e nello stesso <lb/>tempo avvertiva l'amico di ci&ograve;, che andava dicendo <lb/>il Roberval, per quel che aveva risaputo dal Niceron <lb/>di Parigi. </s>

<s>A che il Torricelli subito replicava: </s></p><p type="main">

<s>&ldquo; Apposta domandai a V. P. se il Guldini dimostrava quella propriet&agrave; <lb/>dell'arco, per poter rispondere a mons&ugrave; Roberval. </s>

<s>Mi dispiace che il Gul&shy;<lb/>dini la dimostri, perch&egrave; ancor io aveva, gi&agrave; sono quattro anni, quella dimo&shy;<lb/>strazione. </s>

<s>Io provai che, facendosi come tutti i lati uguali AE (fig. </s>

<s>163), EF, <lb/>FG, GB, BH, HI, IL, LC, a due terzi della corda AC, cos&igrave; la retta BD <emph type="italics"/>ad <lb/>aliam sumendam ex centro,<emph.end type="italics"/> il termine della presa sarebbe centro di gra&shy;<lb/><figure id="id.020.01.2678.2.jpg" xlink:href="020/01/2678/2.jpg"/></s></p><p type="caption">

<s>Figura 163.<lb/>vit&agrave; della figura <lb/>rettilinea DABC. <lb/>Ma, facendosi <lb/>come i suddetti <lb/>lati uguali alla <lb/>corda AC, cos&igrave; la <lb/>BD <emph type="italics"/>ad aliam su&shy;<lb/>mendam ex cen&shy;<lb/>tro,<emph.end type="italics"/> il termine sa&shy;<lb/>rebbe stato centro <lb/>di tutte le rette <lb/>AE EF, ecc. </s>

<s>Dalla <lb/>prima inferivo il <lb/>centro del settore, <lb/><emph type="italics"/>more veterum:<emph.end type="italics"/><lb/>dalla seconda inferivo il centro dell'arco prima, e poi il centro del settore, <lb/>per gl'indivisibili. </s>

<s>Ma le dimostrazioni, con le quali applico il lemma, son <lb/>tanto acute, che non pensavo che il Guldini ci fosse potuto arrivare. </s>

<s>Giac&shy;<lb/>ch&egrave; V. P. ha inteso il mio mezzo termine, la supplico ad incomodarsi di <lb/>nuovo ad avvisarmi se va per questa strada &rdquo; (ivi, fol. </s>

<s>131). </s></p><pb xlink:href="020/01/2679.jpg" pagenum="304"/><p type="main">

<s>Ma il Cavalieri, quasi stanco di far risposte di questo genere, pens&ograve; di <lb/>mandare in prestito al requisitore, che ne aveva tanta passione, la sua pro&shy;<lb/>pria copia della <emph type="italics"/>Centrobarica,<emph.end type="italics"/> ed ei se ne soddisfacesse a suo piacere leg&shy;<lb/>gendo. </s>

<s>Di che fatto avvisato il Torricelli stesso rispondeva cos&igrave;, il di 28 Aprile <lb/>del detto anno 1646: &ldquo; Rendo infinite grazie a V. P. che, in cambio di darmi <lb/>solo un poco di ragguaglio intorno ai mezzi di una dimostrazione sola, si &egrave; <lb/>compiaciuta di mandarmi tutto il libro del Guldini, quale procurer&ograve; di re&shy;<lb/>cuperar quanto prima &rdquo; (ivi, fol. </s>

<s>133). E seguitando a scrivere non aveva <lb/>ancora sigillata la lettera, che i volumi eran gi&agrave; sul suo banco di studio, dove, <lb/>attendendo con curiosit&agrave; frettolosa a sfogliare il primo, provava nell'animo <lb/>quella impressione, e gli passavano per la mente que'pensieri, che noi vo&shy;<lb/>gliamo, come parte importantissima di quest'intima storia della Scienza, bre&shy;<lb/>vemente descrivere ai nostri Lettori. </s></p><p type="main">

<s>Il volume &egrave; in folio, ma pi&ugrave; della met&agrave; si spende in argomenti, che <lb/>poco potevano importare al Torricelli. </s>

<s>Nel cap. </s>

<s>XII si tratta dell'invenzion <lb/>meccanica dei centri di gravit&agrave;, esplicando un luogo dei commentari sulla <lb/>Sfera del Sacrobosco, dove il Clavio insegna a sospendere un corpo, sia pure <lb/>irregolare quanto si voglia, e notar la linea della direzione del filo: fatto ci&ograve;, <lb/>sospendeva il grave da un altro punto, e, notate le medesime cose, conclu&shy;<lb/>deva che l&agrave;, dove le due direzioni s'incontrano, sar&agrave; il centro richiesto. </s>

<s>Poi, <lb/>segue, nella Centrobarica, una <emph type="italics"/>Dissertazione fisico-matematica<emph.end type="italics"/> superiore nel <lb/>concetto alla mente di un Peripatetico, dimostrandovisi che, dovendo variare <lb/>i corpi componenti il Globo di posizione, non pu&ograve; la Terra consistere nel <lb/>medesimo punto, perch&egrave;, mutandosi il centro di gravit&agrave;, necessariamente si <lb/>muove. </s>

<s>S'aggiungono in ultimo questioni arimmetiche, e le Tavole de'qua&shy;<lb/>drati dei numeri e de'loro cubi dall'uno al diecimila. </s></p><p type="main">

<s>Lasciate dunque indietro queste cose, e, nel trattato geometrico de'centri <lb/>di gravit&agrave;, le proposizioni, che vi si citano da altri Autori gi&agrave; dimostrate; <lb/>ebbe il Torricelli a stupire vedendo che, nelle proposizioni V e VI del cap. </s>

<s>III, <lb/>il Guldino preparava i lemmi a quel modo, che aveva fatto egli stesso, ri&shy;<lb/>cercando il centro di gravit&agrave; delle linee inscritte e circoscritte all'arco di <lb/>cerchio, d'onde poi, nella seconda proposizione del cap. </s>

<s>V, concludeva: &ldquo; Fiat <lb/>igitur, ut semiperipheria ad semisubtensam, ita semidiameter ad aliam quam&shy;<lb/>piam, cui aequalis accipiatur AP, in semidiametro ex centro A; dico punctum P <lb/>centrum esse quod quaeritur &rdquo; (Centrobaricae, lib. </s>

<s>I, Viennae Austriae 1635, <lb/>pag. </s>

<s>59). </s></p><p type="main">

<s>Parve al Torricelli per&ograve; di vedere in queste guldiniane dimostrazioni una <lb/>gran confusione, e un grande stento, paragonate alla elegante facilit&agrave; delle <lb/>sue, ma pi&ugrave; che altro vedeva prelucervi la notizia della cosa da dimostrare: <lb/>notizia che, seguitando a sfogliare il volume, indovin&ograve; aver avuto origine dalla <lb/>Quadratrice, l'ultimo punto della quale, leggeva, <emph type="italics"/>ipsum tamen centrum esse <lb/>gravitatis semiperipheriae circuli nos primum mundo manifestamus<emph.end type="italics"/> (ibid., <lb/>pag. </s>

<s>67). Dimostra ci&ograve;, da Pappo, l'Autore della Centrobarica nella propo&shy;<lb/>sizione I del cap. </s>

<s>VI, ma il corollario, in cui egli fa osservare che, dato il <pb xlink:href="020/01/2680.jpg" pagenum="305"/>centro di gravit&agrave;, s'ha la quadratura, e data la quadratura s'ha il centro, <lb/>&egrave; cosa del p. </s>

<s>Della Faille, scritta ne'due primi corollari ai teoremi de'cen&shy;<lb/>tri di gravit&agrave; del circolo e dell'ellisse. </s>

<s>Dal principale teorema ivi dimostrato, <lb/>quale si &egrave; che l'arco sta a due terzi della corda, come il raggio a una quarta <lb/>linea, indicatrice sull'asse del baricentrico del settore; ne conclude esso Della <lb/>Faille che l'arco, e perci&ograve; anche tutta intera la circonferenza, poteva facil&shy;<lb/>mente quadrarsi, ci&ograve; che pens&ograve; il Guldin di concludere con simili ragioni <lb/>dal centro di gravit&agrave; dell'arco, come di fatti fece nel detto corollario. </s>

<s>Pro&shy;<lb/>postosi dunque l'altro principio che, datasi la quadratura &egrave; dato il baricen&shy;<lb/>tro, pens&ograve; di ricorrere alla Quadratrice antica, argomentando che il punto <lb/>cercato era, di quella linea da lui chiamata <emph type="italics"/>mirabile,<emph.end type="italics"/> l'ultimo punto. </s>

<s>L'ar&shy;<lb/>gomento sapeva per verit&agrave; di audacia, avendo argutamente Pappo, nel citato <lb/>libro delle <emph type="italics"/>Collezioni,<emph.end type="italics"/> al problema terzo, fatto osservare che Nicomede e Di&shy;<lb/>nostrato supponevan gi&agrave; quella proporzione tra la linea retta e la curva, che <lb/>si voleva cercare: e nonostante la cosa riusc&igrave; al Guldino con tanta felicit&agrave;, <lb/>da prevenire in questo le sottili invenzioni del Torricelli, il quale in somma <lb/>non ebbe il torto in sospettar che il suo emulo avesse a principio supposto <lb/>quel che poi si studi&ograve; di dimostrare con quelle sue maniere stentate e <lb/>confuse. </s></p><p type="main">

<s>Costretto in ogni modo lo stesso Torricelli a dover cedere l'ambita pri&shy;<lb/>mizia a chi egli diceva non esserne degno, e perduto l'argomento necessa&shy;<lb/>rio a recidere le calunnie del Roberval dalla loro radice, non gli rimaneva <lb/>altra gloria che di essere rimasto il primo inventore del centro di gravit&agrave; <lb/>delle callotte, delle zone, e de'settori sferici. </s>

<s>Seguitando con questa fiducia <lb/>compiacente, assicuratagli dal Cavalieri, a svolgere il volume centrobarico, <lb/>vi leggeva, nella V proposizione del cap. </s>

<s>X, dimostrato il centro di gravit&agrave; <lb/>delle porzioni delle superficie sferiche, sferoidee, e conoidee essere quel me&shy;<lb/>desimo che delle superficie piane generatrici, per queste ragioni: &ldquo; Nam, si&shy;<lb/>cuti conicae superficiei centrum gravitatis est idem, quod est trianguli, seu <lb/>in frusto trapezii per axem ducto; ita hic eodem modo centrum gravitatis <lb/>superficiei portionis sphaericae, sphaeroidicae et conoidicae, seu frusto, etiam <lb/>est centrum gravitatis segmenti, seu trapezii per axem ducti, basibus tamen <lb/>utrobique exceptis &rdquo; (ibid., pag. </s>

<s>127). </s></p><p type="main">

<s>Non rimaneva al Torricelli, per sodisfar pienamente quella sua gelosa <lb/>curiosit&agrave;, che di vedere in qual modo indicasse il <lb/><figure id="id.020.01.2680.1.jpg" xlink:href="020/01/2680/1.jpg"/></s></p><p type="caption">

<s>Figura 164.<lb/>Guldin il centro di gravit&agrave; del settore sferico, ci&ograve; <lb/>che gli occorse una sola pagina dopo quella gi&agrave; <lb/>letta, sotto il titolo della IX proposizione scritta <lb/>nel cap. </s>

<s>XI, dove, supposto il centro del solido <lb/>emisferico ABC (fig. </s>

<s>164), in I, sull'asse, come <lb/>ve lo designa Luca Valerio, dice che, inalzata <lb/>da I una perpendicolare, la quale incontri in H <lb/>la linea EF, che bipartisce il quadrante AB in due ottanti; sar&agrave; in esso <lb/>H il centro di gravit&agrave; del settore descritto dal rivolgersi uno dei detti ot-<pb xlink:href="020/01/2681.jpg" pagenum="306"/>tanti intorno alla linea FE come a suo asse. </s>

<s>Per dimostrare il quale as&shy;<lb/>serto cos&igrave; dice: &ldquo; Res haec ut demonstretur, cum pluribus indigeat verbis <lb/>quam rationibus, eaeque tales sint, quae unicuique qui praecedentia intellexit <lb/>obviae ac manifestae sint, plura in confirmationem addere noluimus. </s>

<s>Et sic <lb/>satisfactum esse propositioni iudicamus &rdquo; (ibid., pag. </s>

<s>132). <emph type="italics"/>Bravo!<emph.end type="italics"/> fece qui <lb/>il Torricelli chiudendo il libro, <emph type="italics"/>bravo il mi'bue!<emph.end type="italics"/> e ripresa in mano la let&shy;<lb/>tera al Cavalieri, dianzi lasciata aperta, v'aggiunse queste parole: &ldquo; Dopo <lb/>scritto fin qui, ho ricevuto il libro del Guldini, e scartabellato quasi tutto. </s>

<s><lb/>Ho veduto che adopra i medesimi mezzi, che adopro anch'io, per quei cen&shy;<lb/>tri, ma Dio sa con quanta confusione e stento. </s>

<s>In somma io gli pronunzio <lb/>che il padre Guldino, per quanto si pu&ograve; argomentare da questo libro, &egrave; stato <lb/>un bue &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>134). </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Il secondo volume della Centrobarica, che comprendeva i libri secondo, <lb/>terzo e quarto, dopo i primi saggi presi poco importava di consultare al Tor&shy;<lb/>ricelli, a cui il Cavalieri aveva fatta gi&agrave; nota la grande Regola dall'Autore <lb/>ivi insegnata come un fatto, la verit&agrave; del quale si confermava dal mostrar <lb/>che i resultati di lui concordavano con i teoremi della Geometria. </s>

<s>Aperto <lb/>nonostante il libro, sfogliando quelle undici pagine di prefazione, non pot&egrave; <lb/>non trattenersi dalla quinta alla settima a considerar quel passo che il Gul&shy;<lb/>din trascrive dal proemio del Cavalieri. </s>

<s>Vi si diceva dall'Autore dei sette <lb/>libri della Geometria nuova come fosse rimasto preso da gran maraviglia in <lb/>ripensare che le ragioni stereometriche e baricentriche tra i solidi rotondi <lb/>non son pi&ugrave; quelle delle superficie piane che gli hanno generati. </s>

<s>Cos&igrave; infatti, <lb/>mentre il rettangolo &egrave; doppio del triangolo, il cilindro generato &egrave; triplo del <lb/>cono; e mentre il centro di gravit&agrave; sega l'asse cos&igrave; che la parte verso il <lb/>vertice del triangolo &egrave; doppia di quella verso la base; nel cono invece si <lb/>trova esser tripla. </s>

<s>Di qui, prosegue lo stesso Cavalieri a dire, considerando <lb/>meglio le cose, conobbi che le linee, di che s'intessono le superficie, e i <lb/>piani, di che si compaginano i solidi, non son da prender per l'asse, ma pa&shy;<lb/>ralleli alla base, e cos&igrave; si trova che gl'infiniti circoli affaldati nel cilindro son <lb/>tripli degli infiniti circoli, che s'affaldano a comporre il volume del cono. </s></p><p type="main">

<s>Ben comprese il Torricelli la ragione perch&egrave; il Guldin si studiasse di <lb/>cogliere questi principii di Geometria nuova in difetto: perch&egrave; per essi si <lb/>scoprivano le sue fallacie, le quali giusto avevano avuto origine dal cre&shy;<lb/>dere che il centro di gravit&agrave; delle figure condotte per l'asse si mantenesse <lb/>il medesimo, che delle superficie dei solidi generati. </s>

<s>L'esempio nonostante, <lb/>ch'egli adduceva del triangolo e della superficie conica descritta dal rivolgi&shy;<lb/>mento di lui, era vero, e il Torricelli stesso volle ci&ograve; confermare per via <lb/>degli indivisibili, considerando i pesi concentrati sull'asse come sopra la lun-<pb xlink:href="020/01/2682.jpg" pagenum="307"/>ghezza di una libbra, a quel modo che aveva fatto per dimostrare il centro <lb/>di gravit&agrave; del triangolo e del conoide parabolico. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XX. &mdash; <emph type="italics"/>Centrum gravitatis superficiei<emph.end type="italics"/><lb/><figure id="id.020.01.2682.1.jpg" xlink:href="020/01/2682/1.jpg"/></s></p><p type="caption">

<s>Figura 165.<lb/><emph type="italics"/>conicae est in axe, ita ut pars ad verticem reliquae sit <lb/>dupla. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto conica superficies ABC (fig. </s>

<s>165) cuius axis BD, <lb/>sitque BE dupla ad ED. </s>

<s>Dico E esse centrum gravitatis. </s>

<s>Se&shy;<lb/>cetur enim superficies planis FG, HI ad axem erectis ubi&shy;<lb/>cumque: eritque peripheria, quae per F, ad peripheriam, <lb/>quae per H, ut FN ad HM, et hoc semper. </s>

<s>Ergo ad libram <lb/>BD pendent quaedam magnitudines, nempe peripheriae et totidem magnitu&shy;<lb/>dines ipsis ex ordine proportionales, nempe lineae rectae. </s>

<s>Ergo commune <lb/>centrum habebunt &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>31). </s></p><p type="main">

<s>Conclusa cos&igrave; la dimostrazione, sembrava al Torricelli di vedersi insor&shy;<lb/>gere contro il Guldino o qualcun altro, come lui avverso al metodo degli <lb/>indivisibili, e dire: Perch&egrave; mai, avendo il triangolo e la superficie conica co&shy;<lb/>mune il centro di gravit&agrave;, non debbono averlo per simili ragioni la semicir&shy;<lb/>conferenza e l'emisfero, la parabola e il conoideo da lei descritto? </s>

<s>Suppo&shy;<lb/>nete che l'ambito ABC nella vostra figura sia una mezza circonferenza o una <lb/>parabola intorno all'asse BD: condotti piani FG, HI, comunque, intercide&shy;<lb/>ranno sulla superficie emisferica o conoidea circonferenze, le quali staranno <lb/>come i raggi HM, FN, cosicch&egrave; anche il centro di quelle superficie dovrebbe <lb/>segar l'asse nel mezzo, ci&ograve; che, sebbene sia contro alle nostre supposizioni, <lb/>&egrave; altres&igrave; contrario ai vostri dimostrati teoremi. </s></p><p type="main">

<s>Rispond<gap/>a il Torricelli, richiamandosi alle regole insegnate dal Cavalieri, <lb/>una delle quali, e delle pi&ugrave; importanti ad osservare, per non si dover tro&shy;<lb/>vare ingannati, era di ricever sempre le somme di tutte le indivisibili figure <lb/>da paragonarsi <emph type="italics"/>sub quadam uniformi ratione, seu sub quodam determi&shy;<lb/>nato spissitudinis aut costipationis gradu<emph.end type="italics"/> (Exercit. </s>

<s>geom., Bononiae 1647, <lb/>pag. </s>

<s>15). </s></p><p type="main">

<s>Gl'infiniti componenti indivisibili l'intelletto gli concepisce in s&egrave; stessi, <lb/>ma il senso gli percepisce nelle relazioni di posizione, che gli uni hanno ri&shy;<lb/>spetto agli altri. </s>

<s>Cos&igrave; nella linea di un millimetro, come in quella di un <lb/>metro, per l'intelletto &egrave; la medesima infinit&agrave; di punti, ma per il senso &egrave; <lb/>questa molto pi&ugrave; lunga di quella, perch&egrave; le distanze o i <emph type="italics"/>transiti<emph.end type="italics"/> son molto <lb/>maggiori. </s>

<s>L'esempio di ci&ograve; lo abbiamo nelle proiezioni, come della linea AB <lb/><figure id="id.020.01.2682.2.jpg" xlink:href="020/01/2682/2.jpg"/></s></p><p type="caption">

<s>Figura 166.<lb/>(fig. </s>

<s>166) sul piano AC, in cui, dentro lo spazio AD, si <lb/>trovano necessariamente contratti i medesimi punti di <lb/>pi&ugrave; lungo transito, compresi nello spazio AB. </s>

<s>E perch&egrave;, <lb/>quando la stessa linea sia risalita perpendicolarmente sul <lb/>piano, la proiezion di lei &egrave; un punto, &egrave; verissimo dun&shy;<lb/>que sotto questo aspetto che una linea, anzi pi&ugrave; linee <lb/>concorrenti possono ridursi uguali a un punto, come par si verifichi nel cono <lb/>luminoso, che entra o esce dal fuoco di uno specchio. </s>

<s>Ci sovviene anzi che <pb xlink:href="020/01/2683.jpg" pagenum="308"/>di qui Galileo inferiva dovere esser la luce incorporea e istantanea, come <lb/>quella che &egrave; <emph type="italics"/>ridotta a'suoi infiniti indivisibili componenti, e fatta senza <lb/>introduzione di corpi o di posizione di vacui quanti, ma bene d'indivisi&shy;<lb/>bili vacui, e cos&igrave; non occupa luogo, e non ricerca tempo d'andare da un <lb/>luogo a un altro.<emph.end type="italics"/></s></p><p type="main">

<s>Un tal concetto per&ograve; della composizione dei corpi &egrave; falso, e la questione, <lb/>lungamente intorno a questo argomento agitata nel primo dialogo delle due <lb/>Scienze nuove, non si risolve nell'obietto percepito, ma nel soggetto perci&shy;<lb/>piente, che ora &egrave; l'intelletto ora il senso. </s>

<s>Per l'intelletto, che &egrave; semplice e <lb/>uno, l'infinito si riduce a un punto, ma per il senso &egrave; diviso, e la divisione <lb/>&egrave; finita, o, come con Galileo si direbbe, &egrave; quanta. </s>

<s>Ecco come sia da una <lb/>parte l'infinito innumerabile, e dall'altra soggetto ai calcoli del matematico, <lb/>e alle circoscrizioni del Geometra: ecco come si risolvono le questioni di si&shy;<lb/>mil genere, e com'essendo tutte le figure geometriche sensibili sia necessa&shy;<lb/>rio apprenderle nelle loro parti divise, computando la quantit&agrave; della divisione <lb/>o le <emph type="italics"/>spissitudini<emph.end type="italics"/> e i <emph type="italics"/>transiti,<emph.end type="italics"/> come diceva il Cavalieri, e come ripeteva nello <lb/>Scolio alla precedente proposizione il Torricelli: </s></p><p type="main">

<s>&ldquo; Nota quod non valet argumentum, quod contra fieri posset ab his, <lb/>qui methodum indivisibilium non admodum intelligunt. </s>

<s>Possent enim addu&shy;<lb/>cere argumentum de superficie sphaerae, aut semicirculi, quae non habent <lb/>commune centrum, sive de superficie conoidis parabolici et parabolae. </s>

<s>Causa <lb/>disparitatis est quod superficies conica eumdem transitum semper servat, sunt&shy;<lb/>que omnes peripheriae, ut ita dicam, eiusdem spissitudinis, ut rectac ad BD <lb/>applicatae, quod non est verum in dictis superficiebus, quarum peripheriae <lb/>maiorem semper habent densitatem, sive spissitudinem, versus verticem, re&shy;<lb/>spectu linearum applicatarum ad axem &rdquo; (ibid.). </s></p><p type="main">

<s>Il Guldin dunque e Galileo, chiamato, nella prefazione al secondo libro <lb/>centrobarico, per aggredire insieme il Cavalieri, in soccorso poderoso; repu&shy;<lb/>tavano fallace e ripudiavano perci&ograve; il metodo degl'indivisibili, perch&egrave;, secondo <lb/>il Torricelli, <emph type="italics"/>non admodum illud intelligunt.<emph.end type="italics"/> Il Torricelli stesso per&ograve; stimava <lb/>indegni di ogni bella invenzione coloro, che un tal metodo biasimavano, essendo <lb/>egli, diceva, <emph type="italics"/>la vena e la miniera inesauribile delle speculazioni belle, e <lb/>delle dimostrazioni a priori.<emph.end type="italics"/> Aveva fatto di ci&ograve; particolarmente esperienza nel <lb/>trattare dei baricentri, non solo rispetto alla variet&agrave; dei soggetti, ma rispetto <lb/>altres&igrave; alla variet&agrave; dei modi di trattare il soggetto medesimo, come per esem&shy;<lb/>pio il triangolo e il cono, l'emisferoide e l'emisfero, di che un primo saggio <lb/>ne porge quel capitolo intitolato nel manoscritto: <emph type="italics"/>Centrum gravitatis trian&shy;<lb/>guli, coni et hemisphaeri, hemisphaeroidisque a priori.<emph.end type="italics"/> Ma prima di veder <lb/>come il metodo degl'indivisibili sia applicato a dimostrar questi teoremi, con <lb/>elegante variet&agrave; da que'medesimi gi&agrave; prima dimostrati; giova rimovere dalla <lb/>mente dei nostri lettori una fal opinione insinuata non sapremmo dire se <lb/>dal poco giudizio, o dal mal an&igrave;mo del Guldino. </s></p><p type="main">

<s>Nel cap. </s>

<s>IV del IV libro della Centrobarica trascrive dalla <emph type="italics"/>Stereometria <lb/>nova<emph.end type="italics"/> l'interpetrazione che il Keplero d&agrave; della prima proposizione archime-<pb xlink:href="020/01/2684.jpg" pagenum="309"/>dea della misura del circolo. </s>

<s>Sia questo descritto col raggio AB (fig. </s>

<s>167), <lb/>all'estremit&agrave; del quale si conduca la perpendicolare BC. </s>

<s>La circonferenza, <lb/>dice il Kepler, ha tante parti quanti son punti, cio&egrave; infinite, su ciascuna delle <lb/>quali parti si considerino <lb/><figure id="id.020.01.2684.1.jpg" xlink:href="020/01/2684/1.jpg"/></s></p><p type="caption">

<s>Figura 167.<lb/>insistere, come sopra loro <lb/>base, triangoli isosceli, che <lb/>vadan tutti in A ad appun&shy;<lb/>tarsi nel centro. </s>

<s>Estendasi <lb/>poi essa circonferenza in <lb/>dirittura, e cominciando da <lb/>B termini in C: se da C, da <lb/>E, e dagli infiniti altri ponti di divisione, si conducano ad A linee rette, &egrave; <lb/>manifesto che verranno a disegnarsi triangoli, pari di numero, e di superficie <lb/>uguali ai settori del circolo, il quale dunque sar&agrave; uguale al triangolo rettan&shy;<lb/>golo ABC. <emph type="italics"/>Hoc vult,<emph.end type="italics"/> conclude il Keplero la sua arguta e bellissima interpe&shy;<lb/>trazione, <emph type="italics"/>illa archimedea ad impossibile deductio: mihi sensus hic esse <lb/>videtur.<emph.end type="italics"/></s></p><p type="main">

<s>Parve, soggiunge qui il Guldin, ma non &egrave;: questo kepleriano &egrave; modo <lb/>nuovo di dimostrare, e che, sebbene non sia da disprezzarsi, non ha per&ograve; <lb/>che a riveder nulla con quello di Archimede. </s>

<s>Poco pi&ugrave; sotto poi, citando dalla <lb/>Stereometria nuova il teorema IV, dove, dall'essersi dimostrato che un pri&shy;<lb/>sma colonnare &egrave; triplo della piramide sollevatasi a pari altezza dalla mede&shy;<lb/>sima base, ne conclude l'Autore, che pu&ograve; il medesimo appropriarsi al cilin&shy;<lb/>dro e al cono, riguardandosi quello come un prisma colonnare d'infinito <lb/>numero di facce, e questo come una piramide; insinua il Guldino stesso che <lb/>a ci&ograve; insomma si riduce il metodo del Cavalieri, concludendo il suo discorso <lb/>in queste parole: &ldquo; Hinc enim ansam arripuit et occasionem Bonaventura <lb/>Cavalerius suam Methodum indivisibilium producendi &rdquo; (Centrobarycae Gul&shy;<lb/>dini, Lib. </s>

<s>IV, Viennae Austriae 1641, pag. </s>

<s>325). </s></p><p type="main">

<s>Giova ora a noi esaminare cos&igrave; fatti giudizi, e prima di tutto, per quel <lb/>che spetta al Keplero, domanderemo se quel suo modo di riguardare il <lb/>circolo come un poligono d'infinito numero di lati sia da dir propriamente <lb/>nuovo. </s>

<s>Il Guldin, com'abbiamo inteso, lo crede, e par lo credano tutti gli <lb/>altri, che hanno trovato quello stesso metodo accomodatissimo ad abbreviare, <lb/>e a ridurre alla massima facilit&agrave; i pi&ugrave; ardui teoremi della Geometria. </s>

<s>Eppure <lb/>il Keplero stesso, invece di gloriarsi di questa cosa, come di sua propria in&shy;<lb/>venzione, l'attribuisce ad Archimede, non certamente per liberalit&agrave;, ma per <lb/>giustizia, com'onest'uomo ch'egli era, ed erudito della storia della Ciclome&shy;<lb/>tria. </s>

<s>Da Archimede stesso direttamente anzi &egrave; notabile che apprendesse il <lb/>metodo Leonardo da Vinci, il quale interpetr&ograve; quella sopra citata proposi&shy;<lb/>zione <emph type="italics"/>De circuli dimensione<emph.end type="italics"/> allo stesso modo, e tanto tempo prima del <lb/>Geometra alemanno. </s>

<s>&ldquo; Il cerchio, egli dice, &egrave; un parallelo rettangolo, fatto <lb/>del quarto del suo diametro, e di tutta la circonferenza sua: o vo'dire <lb/>della met&agrave; del diametro, e della periferia. </s>

<s>Come se il cerchio fosse immagi-<pb xlink:href="020/01/2685.jpg" pagenum="310"/>nato essere resoluto in quasi infinite piramidi (triangoli isosceli), le quali poi, <lb/>essendo distese sopra la linea retta che tocchi la lor base, e tolto la met&agrave; <lb/>dell'altezza e fattone un parallelo (un rettangolo); sar&agrave; con precisione uguale <lb/>al cerchio (MSS. K., fol. </s>

<s>80 r.). Non possiamo perci&ograve; non ci maravigliar gran&shy;<lb/>demente che non avesse penetrate queste cose il Guldino, il quale compen&shy;<lb/>dia nel cap. </s>

<s>I del suo secondo libro la lunga storia ciclometrica, e riferendo <lb/>i detti di Eutocio difende il grande Siracusano da coloro, che temerariamente <lb/>lo accusavano di aver data meno esatta la proporzione tra la circonferenza <lb/>e il diametro. </s>

<s>Dice esso Eutocio che Archimede si ferm&ograve; alla iscrizione del <lb/>poligono di 96 lati, perch&egrave; si contentava <emph type="italics"/>in suo libello proposuisse id quod <lb/>proprinquum est invenire, propter necessarios vitae usus.<emph.end type="italics"/> Che del resto la&shy;<lb/>sciava ai Matematici la fatica di spingere le divisioni infino alle parti pi&ugrave; <lb/>minute, mettendoli al punto di poter concludere, come poi fecero con Tolo&shy;<lb/>meo altri geometri antichi, e fra'recenti il Keplero, che, riducendosi il me&shy;<lb/>todo alle divisioni infinite, il circolo e il poligono inscritto si risponderebbero <lb/>esattamente, o per meglio dire si confonderebbero insieme. </s></p><p type="main">

<s>Comunque sia, consentendo pur col Guldin che, per essere stato un tal <lb/>metodo rinnovellato ed esteso dal Matematico alemanno, si possa dir <emph type="italics"/>keple&shy;<lb/>riano;<emph.end type="italics"/> gli neghiamo per&ograve; ogni somiglianza con quello elaborato dal Cava&shy;<lb/>lieri, il quale citava nel proemio alla sua nuova Geometria la Stereometria <lb/>nuova come inspiratrice del concetto degl'indivisibili, non gi&agrave; dalla parte <lb/>delle divisioni infinite, ma da quella delle sezioni parallele alla base dei so&shy;<lb/>lidi rotondi, a quel modo che nell'altra parte di questa Storia della Mecca&shy;<lb/>nica, alla pag. </s>

<s>115, fu descritto. </s>

<s>Chi volesse poi aver della variet&agrave; de'due <lb/>metodi un esempio efficacissimo non dovrebbe far altro che comparar l'in&shy;<lb/>terpetrazione della prima archimedea <emph type="italics"/>De circuli dimensione,<emph.end type="italics"/> data dal Keplero, <lb/>con quell'altra che, nel proemio al trattatello <emph type="italics"/>De solido acuto hyperbolico,<emph.end type="italics"/><lb/>ne d&agrave; il Torricelli. </s>

<s>Qui non si riguarda il circolo come risoluto in infiniti <lb/>triangoli appuntati nel centro, ma come intessuto d'infinite circonferenze con&shy;<lb/>centriche, a ciascuna delle quali si dimostra essere uguali le linee, di che <lb/>s'intesse il triangolo rettangolo avente per l'un de'cateti la circonferenza, e <lb/>per l'altro il raggio. </s></p><p type="main">

<s>&Egrave; anzi notabile che il Cavalieri e il Torricelli s'astenessero dall'usare <lb/>il metodo kepleriano, quasi lo reputassero abortivo da quel legittimo degli <lb/>indivisibili per essi professato. </s>

<s>Chi per esempio nel trattatello <emph type="italics"/>De centro gra&shy;<lb/>vitatis sectoris circuli more veterum,<emph.end type="italics"/> da noi addietro trascritto, non avrebbe <lb/>consigliato il Torricelli di cansar la fatica del lungo viaggio, col fare del <lb/>lemma IX la proposizion principale, e di l&igrave; concluder l'intento, per via di <lb/>corollario, senza far altro osservare, se non che l'arco si pu&ograve; riguardar come <lb/>composto d'infiniti latercoli rettilinei tutti uguali? </s></p><p type="main">

<s>Mirabile &egrave; la facilit&agrave;, con la quale il Wallis, pur usando il metodo del <lb/>Keplero, dimostra il centro di gravit&agrave; de'settori circolari e sferici, e dello <lb/>stesso emisfero. </s>

<s>Nella proposizione XV del suo trattato, considerando il set&shy;<lb/>tore AMBC (fig. </s>

<s>168) come composto degli infiniti triangoli isosceli appun-<pb xlink:href="020/01/2686.jpg" pagenum="311"/>tati in C, i centri de'quali si trovan disposti nell'arco DNE, presa per rag&shy;<lb/>gio DC doppia di AC, dice che il punto cercato &egrave; G, centro dell'arco, per <lb/>cui sar&agrave; DNE a DE, come CN a CG, ossia AMB ad AB come due terzi del&shy;<lb/>l'asse MC a CG, per giungere alla qual <lb/><figure id="id.020.01.2686.1.jpg" xlink:href="020/01/2686/1.jpg"/></s></p><p type="caption">

<s>Figura 168.<lb/>conclusione era bisognato al padre Della <lb/>Faille un libro, e al Torricelli stesso pi&ugrave; <lb/>di un foglio. </s></p><p type="main">

<s>Che se AMBC rappresenta un settore <lb/>sferico, il servigio reso dianzi dagli infiniti <lb/>triangoli verr&agrave; ora supplito dalle infinite <lb/>piramidi esse pure appuntate in C, le quali, <lb/>avendo i loro centri di gravit&agrave; disposti sulla <lb/>callotta DNE, descritta con un raggio CD, <lb/>che sia triplo della linea AD; faranno che <lb/>il punto G, mezzo della saetta della cal&shy;<lb/>lotta, sia il punto cercato, il quale dimo&shy;<lb/>stra il Wallis essere <emph type="italics"/>in axis sui illo puncto, quod a centro circuli distat <lb/>tribus quadrantibus radii, minus tribus octantibus altitudinis superficiei <lb/>cavae<emph.end type="italics"/> (De motu, P. II, Londini 1670, pag. </s>

<s>243). CG infatti &egrave; uguale a <lb/>CN&mdash;NG. </s>

<s>Ma CN=3/4 CM, NG=1/2 NP=3/8 <expan abbr="Mq;">Mque</expan> dunque CG= <lb/>3/4 CM&mdash;3/8 MQ, ci&ograve; che dall'altra parte &egrave; facile vedere come concordi con <lb/>la invenzione del Torricelli. </s></p><p type="main">

<s>Di qui deduce lo stesso Wallis, per via di corollario, il centro di gra&shy;<lb/>vit&agrave; dell'emisfero, il quale sar&agrave; in O, sulla met&agrave; del raggio CN, che in que&shy;<lb/>sto caso &egrave; uguale alla saetta della callotta emisferica, onde, esssendo CN= <lb/>3/4 CM, sar&agrave; CO=3/8 CM=3/8 (CO+OM) e perci&ograve; 5 CO=3 MO, e <lb/>MO:CO=5:3, che vuol dire essere il centro di gravit&agrave; dell'emisfero in&shy;<lb/>dicato da quel punto, <emph type="italics"/>in quo axis sic dividitur, ut pars ad verticem sit <lb/>ad reliquam ut quinque ad tria,<emph.end type="italics"/> secondo aveva prima di tutti dimostrato <lb/>Luca Valerio, nella proposizione XXXIII del secondo libro, e nella XXXV <lb/>del terzo, qui &egrave; l&agrave; con lunga, e laboriosa preparazione di lemmi. (De centro <lb/>grav., Romae 1604, pag. </s>

<s>56, 61). </s></p><p type="main">

<s>Chi crederebbe che non fosse sovvenuta al Torricelli simile compendiosa <lb/>dimostrazione? </s>

<s>Eppure egli la rifiut&ograve;, per attenersi allo schietto metodo ca&shy;<lb/><figure id="id.020.01.2686.2.jpg" xlink:href="020/01/2686/2.jpg"/></s></p><p type="caption">

<s>Figura 169.<lb/>valierano, e per dare una prova ai contradittori della <lb/>fecondit&agrave; e della variet&agrave; di lui, applicandolo a di&shy;<lb/>mostrar le medesime cose negli esempi, che ora <lb/>trascriveremo, incominciando dal citato capitolo, <lb/>dove si proponeva di dimostrare a priori il centro <lb/>del triangolo e del cono, dell'emisferoide e del&shy;<lb/>l'emisfero. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXI. &mdash; <emph type="italics"/>Centrum trianguli <lb/>diametrum secat in ratione 2 ad 1. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Sia un triangolo qualunque ABC (fig. </s>

<s>169), <pb xlink:href="020/01/2687.jpg" pagenum="312"/>e congiunto il vertice B con E, mezzo della base, si conducano a BE paral&shy;<lb/>lele AI, CD, e si compia il parallelogrammo, sopra i due diametri del quale <lb/>BE, PQ graviteranno le infinite linee ponderose condotte parallele ad AC, e <lb/>a BE. </s>

<s>Cos&igrave; poi le linee AI, DC, come le LO, MP, e le infinite altre, di che <lb/>s'intessono i triangoli esterni, le considera il Torricelli raccolte nei loro mezzi <lb/>gravitar, coppia per coppia, sulla bilancia BF, con quella regola, che le linee <lb/>del triangolo ABC pesano sopra tutta la BE, supponendo, perch&egrave; facile a di&shy;<lb/>mostrarsi, il seguente lemma: <emph type="italics"/>Due libbre, dalle quali pendano grandezze, <lb/>che si eccedano a proporzione delle distanze, son tagliate dal punto del&shy;<lb/>l'equilibrio in parti proporzionali.<emph.end type="italics"/> Dietro ci&ograve;, cos&igrave; il Torricelli proponeva, <lb/>e dimostrava la verit&agrave; sopra annunziata: </s></p><p type="main">

<s>&ldquo; Esto triangulum quodlibet ABC, sectoque bifariam AC in E, ducatur <lb/>BE, et compleatur figura AIDC. </s>

<s>Tum secetur bifariam BE in F, eritque F <lb/>centrum parallelogrammi AD. </s>

<s>Centrum vero trianguli ABC sit quodcumque H, <lb/>et reliquae figurae sit G. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam EB est libra, ad quam pendent infinitae numero magnitudines, <lb/>nempe rectae ipsi AC parallelae, quarum maxima centrum habet in E, et <lb/>minima in B, suntque magnitudines inter se ut longitudines, ad quas pen&shy;<lb/>dent, facto initio in B. Item, FB est libra, ad quam pendent magnitudines <lb/>numero infinitae, nempe lineae parallelae ipsi AI, in geminis triangulis AIB, <lb/>BDC, et maxima magnitudo centrum habet in F, minima vero in B, et sunt <lb/>magnitudines inter se ut iam dictae praecedentes, nam duae simul AI, CD, <lb/>ad duas OL, PM, sunt ut AI ad OL, sive ut AB ad BO, sive ut EB ad BN, <lb/>sive ut semisses earum, nempe FB ad distantiam centri duarum OL, PM a <lb/>puncto B. </s>

<s>Propterea centrum trianguli ABC, quod ponitur H, in eadem ra&shy;<lb/>tione secabit libram BE, in qua secat libram BF centrum reliquae figurae, <lb/>quod est G. </s>

<s>Erit ergo ut BH ad HE, ita BG ad GF, et, componendo permu&shy;<lb/>tandoque, EB ad BF ut EH ad FG, nempe EH erit dupla ad FG. </s>

<s>Sed HF, <lb/>FG sunt aequales, cum F sit centrum totius, et tam G quam H centra par&shy;<lb/><figure id="id.020.01.2687.1.jpg" xlink:href="020/01/2687/1.jpg"/></s></p><p type="caption">

<s>Figura 170.<lb/>tium aequalium; erit EH, sive BG, dupla rectae <lb/>GF. </s>

<s>Ergo patet BH duplam esse ipsius HE &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>97). In modo <lb/>analogo a questo si dimostra l'altra. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXII. &mdash; <emph type="italics"/>Centrum coni secat <lb/>axem in ratione 3 ad 1 &rdquo;<emph.end type="italics"/> avvertendo che, per es&shy;<lb/>sere nella fig. </s>

<s>170, rappresentatrice del cono ABC, <lb/>a cui sia circoscritto il cilindro AE, AI:LM= <lb/>AB:BM, IB:LB=AB:BM, e perci&ograve; AI.IB: <lb/>LM.LB=AB2:BM2; le superficie cilindriche de&shy;<lb/>scritte dalla conversione delle linee AI, LM intorno <lb/>al comune asse BD, che stanno come i rettangoli <lb/>delle altezze per i raggi delle basi, cio&egrave; come AI.IB <lb/>a LM.LB, staranno pure come AB2 a BM2. </s>

<s>Avvertasi inoltre che, supposto <lb/>in H il centro di gravit&agrave; del cilindro scavato, e in G quello del cono, per <pb xlink:href="020/01/2688.jpg" pagenum="313"/>esser l'uno doppio dell'altro, dovr&agrave; reciprocamente la distanza FH dal cen&shy;<lb/>tro F della libbra esser la met&agrave; della distanza FG. </s></p><p type="main">

<s>&ldquo; Esto conus ABC, cuius axis BD, cylindrus vero circumscriptus AE. </s>

<s><lb/>Centrum cylindri F, coni sit quodvis punctum G, et reliqui solidi sit H. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam BD libra est, ad quam pendent infiniti numero circuli ipsi AC <lb/>paralleli, quoruu maximus centrum habet in D, minimus in B, suntque ma&shy;<lb/>gnitudines inter se ut quadrata distantiarum, sive portionum librae initio <lb/>facto ex B. &rdquo; </s></p><p type="main">

<s>&ldquo; Item, FB est libra, ad quam pendent infinitae numero magnitudines, <lb/>hoc est superficies cylindricae circa axem BD, quarum maxima centrum <lb/>habet F, minima vero B, suntque magnitudines inter se ut iam dictae, nam <lb/>cylindrica ex AI, ad cylindricam ex ML, est ut rectangulum AIB, ad rectan&shy;<lb/>gulum MLB per axem, sive ut quadratum AB ad BM, vel DB ad BO, sive <lb/>ut quadrata semissium ipsarum DB, BO, quae sunt distantiae centri ab <lb/>extremo librae B. </s>

<s>Ergo erit, ut BG ad GD, ita BH ad HF, et componendo <lb/>permutandoque, ut BD ad DF, ita DG ad FH. </s>

<s>Propterea DG dupla erit ipsius <lb/>FH. </s>

<s>Est autem GF dupla ipsius FH, nam F est centrum, ex quo aequipon&shy;<lb/>derant magnitudines duplae, propterea DG, GF aequales erunt. </s>

<s>Patet totam <lb/>BG ad GD triplam esse &rdquo; (ibid., fog. </s>

<s>90). </s></p><p type="main">

<s>Segue alla proposizione un corollario <emph type="italics"/>pro centro gravitatis hemisphaeri <lb/>et hemisphaeroidis,<emph.end type="italics"/> il quale per&ograve; suppone due cose, che vedremo in seguito <lb/>dimostrate. </s>

<s>Prima: che, descritta intorno all'asse DB la DP quarta parte di <lb/>un ellisse, l'ellissoide generato da lei &egrave; uguale al cilindro scavato. </s>

<s>Seconda: <lb/>che l'emisfero e l'emisferoide hanno comune il centro di gravit&agrave; sull'asse <lb/>comune. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollarium.<emph.end type="italics"/> &mdash; Patet centrum hemisphaeri, sive hemisphaeroidis, <lb/>axem ita secare, ut partes sint quemadmodum 5 ad 3. Nam consideretur <lb/>solidum cylindricum AIEC, dempto cono ABC, non resolutum in superficies <lb/>cylindricas ut ante, sed in armillas circulorum parallelorum circulo IE. </s>

<s>So&shy;<lb/>lidi erit idem centrum H ut ante. </s>

<s>Sed huiusmodi armillae inter se sunt ut <lb/>circuli sphaeroidis, cuius axis sit BD, centrum B, et apex D. </s>

<s>Ergo semisphae&shy;<lb/>roidis centrum, in eadem libra BD, idem erit ac praedicti solidi, nempe erit <lb/>punctum H. </s>

<s>Patet iam BH ad HD esse ut 3 ad 5 &rdquo; (ibid., fol. </s>

<s>91). </s></p><p type="main">

<s>Il metodo degl'indivisibili non esauriva qui la sua virt&ugrave; in dimostrare <lb/>il centro di gravit&agrave; del cono, ma al Torricelli, che cos&igrave; destramente sapeva <lb/>maneggiarlo, suggeriva intanto <lb/><figure id="id.020.01.2688.1.jpg" xlink:href="020/01/2688/1.jpg"/></s></p><p type="caption">

<s>Figura 171.<lb/>due altri esempi, che ora trascri&shy;<lb/>veremo. </s>

<s>Per il primo si derivava <lb/>dalla Geometria pi&ugrave; elementare <lb/>il seguente Lemma: <emph type="italics"/>Se AB, AC, <lb/>AD<emph.end type="italics"/> (fig. </s>

<s>171) <emph type="italics"/>son proporzionali <lb/>alle AE, AF, AG, e se le differenze BC, CD sono uguali, saranno pure <lb/>uguali le differenze EF, FG.<emph.end type="italics"/></s></p><p type="main">

<s>Abbiamo per supposizione AB:AE=AC:AF. Permutando, AB:AC= <pb xlink:href="020/01/2689.jpg" pagenum="314"/>AE:AF. Dividendo, AB&mdash;AC:AC=AE&mdash;AF:AF. Sostituendo, e nuo&shy;<lb/>vamente permutando, BC:EF=AC:AF=AD:AG. </s>

<s>In simil guisa di&shy;<lb/>mostreremo CD:FG=AD:AG, onde BC:CD=EF:FG. </s>

<s>Ma per sup&shy;<lb/>posizione BC=CD, dunque EF=FG. </s>

<s>Alla qual conclusione si conduce <lb/>pure il Torricelli cos&igrave; discorrendo. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma.<emph.end type="italics"/> &mdash; Si tres rectae lineae BA, CA, DA in aritmetica ratione <lb/>fuerint; et earum partes proportionales EA, FA, GA in aritmetica propor&shy;<lb/>tione erunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto ut ponitur, nempe BA ad AE ut CA ad AF, et ut DA ad AG. </s>

<s><lb/>Cum enim BA ad AE sit ut CA ad AF, erit permutando, dividendo, et rursus <lb/>permutando, BC ad EF ut CA ad AF, sive, ob suppositionem, ut DA ad <lb/>AG. </s>

<s>Sed eodemmodo ostendetur CD ad FG esse ut DA ad AG, ergo, per <lb/>XI Quinti, erit BC ad EF ut CD ad FG. </s>

<s>Sed antecedentia sunt aequalia, <lb/>ergo, etc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Aliter.<emph.end type="italics"/> &mdash; Quoniam, per suppositionem, DA ad AE est ut CA ad AF, <lb/>erit permutando, dividendo et convertendo, AC ad CB, sive ad aequalem CD, <lb/>ut AF ad FE. Amplius, quia CA ad AF est, ob suppositionem, ut DA ad <lb/><figure id="id.020.01.2689.1.jpg" xlink:href="020/01/2689/1.jpg"/></s></p><p type="caption">

<s>Figura 172.<lb/>AG, erit permutando, et per conversionem ratio&shy;<lb/>nis, AC ad CD ut AF ad FG. Ergo, per IX Quinti, <lb/>aequales sunt GF, et FE, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (ibid., fol. </s>

<s>41). </s></p><p type="main">

<s>Dietro ci&ograve;, ecco qual'&egrave; il concetto e il modo <lb/>della nuova dimostrazione. </s>

<s>Sia il cono ABC <lb/>(fig. </s>

<s>172), e dal mezzo E dell'asse BD s'intenda <lb/>moversi equabilmente, sempre dentro lo spazio <lb/>triangolare, due linee, che si mantengano nei loro <lb/>moti contrari equidistanti fra loro, e alla AC. </s>

<s>Se <lb/>sopra tutte queste linee, quante son le infinite, <lb/>che vanno restringendosi verso il vertice del trian&shy;<lb/>golo, e allargandosi verso la base; si costruiscano <lb/>rettangoli per l'asse, verr&agrave; dalle superficie cilin&shy;<lb/>driche descritte da loro a compaginarsi il volume <lb/>del cono, il centro di gravit&agrave; del quale sar&agrave; perci&ograve; il medesimo di quelle infi&shy;<lb/>nite cilindriche superficie. </s></p><p type="main">

<s>Divisa ora ED in mezzo in O, concorreranno in quel punto i centri di <lb/>gravit&agrave; di ciascuna coppia delle dette superficie generate in ugual fase dei <lb/>moti opposti. </s>

<s>Siano per esempio IG, LH due di queste fasi, in cui IG tanto <lb/>si sia dilungato dal centro verso il vertice, quanto se n'&egrave; dilungato LH verso <lb/>la base. </s>

<s>Costruiti i rettangoli IP, LF, &egrave; facile veder che sono uguali, perch&egrave; <lb/>FD:DP=NH:MG=NB:MB=MD:ND=GP:FH, d'onde FD.FH= <lb/>DP.GP. </s>

<s>Ed essendo i rettangoli per l'asse uguali, come da questa equazion <lb/>duplicata si mostra, eguali pure saranno, per la VI torricelliana <emph type="italics"/>De solidis <lb/>sphacralibus,<emph.end type="italics"/> le cilindriche superficie (Op. </s>

<s>geom., P. </s>

<s>I cit., pag. </s>

<s>16). </s></p><p type="main">

<s>Se S dunque &egrave; il mezzo di ND, e V il mezzo di MD, in S e in V sa&shy;<lb/>ranno i centri di gravit&agrave; delle due superficie cilindriche, e sar&agrave; vero che s&igrave; <pb xlink:href="020/01/2690.jpg" pagenum="315"/>riduce in O il loro centro comune, quando siasi dimostrato che OV, OS <lb/>sono uguali. </s>

<s>Ci&ograve; che a fare &egrave; assai facile, perch'essendo DE&mdash;DN=EN, <lb/>DM&mdash;DE=EM, ed EN, EM uguali; DN, DE, DM sono in proporzione arim&shy;<lb/>metica, e in proporzione arimmetica son perci&ograve;, per il premesso lemma, an&shy;<lb/>che le loro met&agrave; DS, DO, DV; onde DO&mdash;DS=DV&mdash;DO, ossia OS=OV, <lb/>come volevasi dimostrare. </s></p><p type="main">

<s>Ci&ograve; ch'&egrave; delle linee IG, LH, verificandosi di tutte le altre infinite, prese <lb/>coppia per coppia nelle uguali fasi dei loro moti opposti; resta dunque cos&igrave; <lb/>dimostrato che in O, a tre quarti dell'&agrave;sse a partire dal vertice, concorrono <lb/>i centri delle infinite superficie cilindriche componenti il cono, e per&ograve; ivi con&shy;<lb/>corre il centro del cono stesso, come il Torricelli annunzia e poi dimostra <lb/>nella seguente. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXIII. &mdash; <emph type="italics"/>Centrum gravitatis coni secat axem ut pars <lb/>ad verticem sit ad reliqua in ratione 3 ad 1. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Supponitur cylindricas superficies esse inter se ut earumdem rectan&shy;<lb/>gula per axem, ex VI primi <emph type="italics"/>De solidis sphaeralibus. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto conus ABC, cuius axis BD, et ab omnibus punctis rectae DC in&shy;<lb/>telligantur parallelae ad axem BD, quae quidem parallelae totidem cylindri&shy;<lb/>cas superficies in revolutione describunt, quae simul omnes cylindricae su&shy;<lb/>perficies idem sunt ac ipse conus. </s>

<s>Harum superficierum, si dici hoc potest, <lb/>extremae sunt recta DB, et peripheria, cuius diameter AC, illiusque centrum <lb/>est punctum E, medium axis BD, istius vero punctum D. (<emph type="italics"/>Quae quamvis <lb/>scripserim, tamen non sunt necessaria ad demonstrationem<emph.end type="italics"/>). &rdquo; </s></p><p type="main">

<s>&ldquo; Secetur libra ED bifariam in O: dico omnes praedictas cylindricas <lb/>superficies centrum habere gravitatis in O. </s>

<s>Sumantur IG, LH aequaliter re&shy;<lb/>motae a punctis B et D, sintque ipsarum rectangula per axem PI, FL, quae <lb/>sunt aequalia, nam FD ad DP est ut PG ad FH. Ergo, per praemissam sup&shy;<lb/>positionem, aequales erunt cylindricae superficies. </s>

<s>Sint V, S puncta media <lb/>rectarum MD, DN: quoniam CF aequalis est ipsi PD, sive MG, erunt, per <lb/>IV Sexti, aequales FH, sive DN et MB. </s>

<s>Ergo DN, DE, DM in aritmetica sunt <lb/>proportione, quare etiam earum semisses DS, DO, DV. </s>

<s>Si ergo sunt aequa&shy;<lb/>les SO, OV, erit O centrum duarum cylindricarum superficierum FH, PG, <lb/>et sic semper. </s>

<s>Ergo O est centrum omnium, nempe coni, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>42). </s></p><p type="main">

<s>Per l'altro modo di dimostrare, sempre con gl'indivisibili, la medesima <lb/>proposizione, si premette dal Torricelli il seguente Lemma, per s&egrave; stesso evi&shy;<lb/>dente: &ldquo; Se saranno nella libbra attaccate molte grandezze, le quali stiano <lb/>in equilibrio, fatta la sospensione da un punto, stanno anco in equilibrio al&shy;<lb/>trettante grandezze sospese dalli medesimi punti, ciascuna delle quali sia <lb/>uguale a quella, che prima era nel suo luogo &rdquo; (ivi, fol. </s>

<s>10). </s></p><p type="main">

<s>Dietro ci&ograve;, l'argomento, in mezzo all'abbondanza nuovo, consiste in <lb/>inscrivere nel cono una piramide equivalente di base, e l'altezza della quale <lb/>sia lo stesso asse del solido rotondo, il quale asse, se prendasi per libbra, da <lb/>cui pendano ora gl'infiniti circoli del cono, ora gl'infiniti triangoli della pi-<pb xlink:href="020/01/2691.jpg" pagenum="316"/>ramide, fra loro uguali di grandezza e di numero; &egrave; manifesto, in virt&ugrave; del <lb/>premesso lemma, che in ambedue i casi il centro delle grandezze segher&agrave; la <lb/>libbra nel medes&igrave;mo punto. </s>

<s>Tutto l'ingegno dunque del nuovo argomento <lb/><figure id="id.020.01.2691.1.jpg" xlink:href="020/01/2691/1.jpg"/></s></p><p type="caption">

<s>Figura 173.<lb/>si riduceva a risolvere il seguente problema: <lb/><emph type="italics"/>Dato un circolo, disegnarvi sopra un trani&shy;<lb/>golo, che sia di superficie uguale, e in gra&shy;<lb/>vit&agrave; concentrico.<emph.end type="italics"/></s></p><p type="main">

<s>Sia il dato circolo col centro in A <lb/>(fig. </s>

<s>173), per il quale facciasi passare la <lb/>AB di tal lunghezza, che sia un terzo della <lb/>periferia, e si prolunghi in C d'altrettanto. </s>

<s><lb/>Si alzi sopra questa linea da A una per&shy;<lb/>pendicolare AD, uguale a due terzi del <lb/>raggio, e si prolunghi al di sotto in E tal&shy;<lb/>mente, che AE sia un terzo dello stesso rag&shy;<lb/>gio. </s>

<s>Poi si congiungano con D i punti B, C, <lb/>e la linea di congiunzione, prolungata, sia in F e in G precisa dalla FG, <lb/>condotta alla BC equidistante. </s>

<s>La superficie del triangolo DFG, dice il Tor&shy;<lb/>ricelli, &egrave; uguale alla superficie del circolo. </s>

<s>Infatti FE:AB=DE:DA=3:2. <lb/>Ed essendo AB uguale per costruzione a un terzo della circonferenza, sar&agrave; <lb/>FE uguale a un mezzo, e perci&ograve; FG uguale alla circonferenza intera. </s>

<s>La su&shy;<lb/>perficie dunque del triangolo, FG.DE/2, &egrave; uguale alla circonferenza moltiplicata <lb/>per la met&agrave; del raggio, ossia &egrave; uguale alla superficie del circolo, ed essendo <lb/>AE per costruzione un terzo di AD, che sieno le due figure concentriche in <lb/>gravit&agrave; &egrave; manifesto. </s></p><p type="main">

<s>Valgano queste osservazioni a commentare la frettolosa scrittura del Tor&shy;<lb/>ricelli, che nella sua concisione potente non manca di naturale chiarezza. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXIV. &mdash; <emph type="italics"/>Il cono ha il centro nell'asse e lo divide in <lb/>modo, che la parte ad verticem sia tripla dell'altra. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia il cono, il cui centro della base in A. </s>

<s>Tirisi la BAC utcumque, e <lb/>sia AB uguale ad un terzo della periferia: cos&igrave; anco la AC, e sia la AD <lb/>due terzi del semidiametro, ed AE un terzo di esso, e finiscasi il triangolo, <lb/>il quale sar&agrave; uguale al circolo, Facciasi poi una piramide, che abbia la mede&shy;<lb/>sima cima con il cono, e segandosi questa figura con piani paralleli alla base <lb/>sempre nascer&agrave; un circolo nel cono, ed un triangolo nella piramide uguali <lb/>fra di loro. </s>

<s>Per&ograve;, se le grandezze triangolari equiponderano dal punto I, fatta <lb/>libbra la AH, anco le circolari equipondereranno dall'istesso &rdquo; (ivi). </s></p><p type="main">

<s>Ora &egrave; da vedere in quale altro modo, diverso da quello gi&agrave; scritto nella <lb/>proposizione XVII qui addietro, facessero gl'indivisibili trovare al Torricelli <lb/>il centro di gravit&agrave; dell'emisfero. </s>

<s>Si fa via alla nuova invenzione con due <lb/>proposizioni, riguardanti il centro di gravit&agrave; de'prismoidi o de'<emph type="italics"/>prismali,<emph.end type="italics"/> cos&igrave; <lb/>definiti: <emph type="italics"/>Prismale solidum voco solidum illud, quod fit ex sectione obliqua <lb/>prismatis triangularis, scrvata una ex faciebus parallelogrammi<emph.end type="italics"/> (ibid., <pb xlink:href="020/01/2692.jpg" pagenum="317"/>fol. </s>

<s>17). Alla prima proposizione, riguardante il baricentro di cos&igrave; fatti pri&shy;<lb/>smali, premette il Torricelli stesso il Lemma seguente: </s></p><p type="main">

<s>&ldquo; Se sar&agrave; un prisma triangolare, di cui <lb/><figure id="id.020.01.2692.1.jpg" xlink:href="020/01/2692/1.jpg"/></s></p><p type="caption">

<s>Figura 174.<lb/>siano le basi opposte ABC, DEF (fig. </s>

<s>174) <lb/>e si prolunghi un lato DB, il quale non <lb/>sia nelle basi opposte, e preso il punto <lb/>H si faccia la piramide CABH; se questa <lb/>figura sar&agrave; segata con un piano LM pa&shy;<lb/>rallelo al parallelogrammo CE, opposto al <lb/>lato DB prolungato, sar&agrave; la sezione un pa&shy;<lb/>rallelogrammo. </s>

<s>Poich&egrave; essendo paralleli i <lb/>piani LM, AF, sar&agrave; la II parallela ad AC, <lb/>cio&egrave; alla FE, cio&egrave; alla MN. </s>

<s>Cos&igrave; anco sar&agrave; <lb/>IM parallela a CF, cio&egrave; alla AE, cio&egrave; alla LN. </s>

<s>Quare etc. </s>

<s>&rdquo; (ivi, fol. </s>

<s>13). </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXV. &mdash; <emph type="italics"/>Ogni prismale ha il centro in quella linea, <lb/>la quale parte dal centro della base parallelogramma, e va alla met&agrave; della <lb/>linea opposta. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Sia il prismale, la cui base AB (fig. </s>

<s>175) e centro della base C, e la <lb/><figure id="id.020.01.2692.2.jpg" xlink:href="020/01/2692/2.jpg"/></s></p><p type="caption">

<s>Figura 175.<lb/>DCE parallela alla FA, e si tirino dal punto <lb/>medio M le ME, MD. Poi, calato qualunque <lb/>piano GN parallelo alla base, perch&egrave; sono uguali <lb/>AE, EP saranno anco GH, HL: e perch&egrave; sono <lb/>uguali EC, CD saranno anco HI, IO. </s>

<s>Per&ograve; I <lb/>sar&agrave; centro del parallelogrammo GN e cos&igrave; di <lb/>tutti. </s>

<s>Dunque il centro del perismale sta nella <lb/>retta MC, la quale parte dal centro della base <lb/>parallelogramma e va alla met&agrave; della linea <lb/>opposta. </s>

<s>La linea MC la diremo <emph type="italics"/>asse<emph.end type="italics"/> (ivi, fol. </s>

<s>18). </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXVI. &mdash; <emph type="italics"/>Se sar&agrave; un solido, come nella passata, ma <lb/>che per&ograve; la prolungata AB<emph.end type="italics"/> (fig. </s>

<s>176) <emph type="italics"/>sia uguale alla AC, il centro di <lb/>questo solido sar&agrave; nella linea, la quale parte da A, e va al centro della <lb/>figura DE, per la precedente dimostra-<emph.end type="italics"/><lb/><figure id="id.020.01.2692.3.jpg" xlink:href="020/01/2692/3.jpg"/></s></p><p type="caption">

<s>Figura 176.<lb/><emph type="italics"/>zione, ma la divide in maniera che la <lb/>parte verso A, alla rimanente, sta come <lb/>5 a 3. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Prima di trascriver la dimostrazione <lb/>di questa, avvertiremo che ella conclude <lb/>solo in virt&ugrave; del seguente teorema geo&shy;<lb/>metrico, dal Torricelli supposto gi&agrave; di&shy;<lb/>mostrato. <emph type="italics"/>Data la linea retta AN<emph.end type="italics"/> (quella <lb/>stessa che entra nella figura) <emph type="italics"/>e divisa nelle <lb/>sue parti in modo, che sia AP=PN, <lb/>PQ=3OQ, AO=2NO; dimostrare che AQ a QN sta come cinque <lb/>a tre.<emph.end type="italics"/> Infatti QN=QO+NO=QO+AO/2=QO+(PN+PQ+OQ)/2= <pb xlink:href="020/01/2693.jpg" pagenum="318"/>(PN+PQ+3OQ)/2=(QN+2PQ+3OQ)/2=(QN+6OQ+3OQ)/2= <lb/>(QN+9OQ)/2, onde avremo di qui 2QN=QN+9OQ, ossia QN=9Oq. </s>

<s><lb/>Rispetto a quell'altra parte della linea, abbiamo AQ=AP+PQ= <lb/>PN+PQ=QN+PQ+PQ=QN+2PQ=QN+6Oq. </s>

<s>Sosti&shy;<lb/>tuitovi il valore di QN, sar&agrave; AQ=9OQ+6OQ=15OQ, e perci&ograve; in ul&shy;<lb/>timo AQ:QN=15OQ:9OQ=5:3, ci&ograve; che dimostrato, come si doveva, <lb/>ritorniamo a trascrivere il discorso del Torricelli. </s></p><p type="main">

<s>&ldquo; Seghisi MA, sicch&egrave; la AH sia doppia di HM, e tirato il piano GHF <lb/>parallelo alla faccia DG, sar&agrave; in esso il centro del prisma. </s>

<s>Segando poi MA <lb/><emph type="italics"/>bifariam<emph.end type="italics"/> in I, e tirato il piano IL parallelo al DG, saranno segate per mezzo <lb/>quattro linee della piramide, per la XVII dell'XI, ed in esso sar&agrave; il centro <lb/>della piramide. </s>

<s>Ora pongasi che il centro del prisma sia R, e della piramide <lb/>sia S, e tirisi la RS quale segher&agrave; per forza la AN, quale va da A al cen&shy;<lb/>tro della faccia DG. &rdquo; </s></p><p type="main">

<s>&ldquo; Poich&egrave;, se in NR &egrave; il centro di tutto, ed &egrave; anco in AN, per&ograve; devono <lb/>concorrere, e sar&agrave; il concorso il centro di tutto. </s>

<s>Sia dunque Q: sar&agrave; SQ alla <lb/>QR come il prisma alla piramide, cio&egrave; tripla. </s>

<s>Immaginiamoci prolungato in <lb/>infinito il piano LI, sicch&egrave; seghi AN, v. </s>

<s>g. </s>

<s>in P. </s>

<s>Sar&agrave; dunque PQ tripla di <lb/><expan abbr="Oq.">Oque</expan> Ma essendo AP, PN, siccome sono AI, IM, uguali, ed essendo AO du&shy;<lb/>pla di ON, siccome AH &egrave; dupla di HM; fatto il conto, sar&agrave; tutta la AQ, alla <lb/>QN, come 15 a 9, ovvero come 5 a 3 &rdquo; (ivi, fol. </s>

<s>186). </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXVII. &mdash; <emph type="italics"/>Il centro dell'emisfero &egrave; nell'asse in sul <lb/>luogo, che sta come cinque a tre. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia il quadrante BAC (fig. </s>

<s>177), il cui asse AC. </s>

<s>Immaginisi AD uguale <lb/>alla semiperiferia del circolo, e sia l'angolo BAD retto, e finiscasi il rettan&shy;<lb/><figure id="id.020.01.2693.1.jpg" xlink:href="020/01/2693/1.jpg"/></s></p><p type="caption">

<s>Figura 177.<lb/>golo BD, che sar&agrave; uguale al suo cerchio. </s>

<s>Poi tirisi <lb/>la BC, e sopra il triangolo BAC facciasi il prisma <lb/>BGA, con l'altezza AD, &egrave; prodotta AH eguale ad <lb/>AC tirisi la HD, sicch&egrave; seghi la CG prodotta in E, <lb/>e facciasi la piramide FDGE. Tirisi, tra l'appli&shy;<lb/>cata MN e per essa, un piano LO parallelo a <lb/>piano BD. &rdquo; </s></p><p type="main">

<s>&ldquo; Che il rettangolo HAC, al rettangolo HNC, <lb/>sia come il rettangolo BD ad LO, <emph type="italics"/>ratio est<emph.end type="italics"/> perch&egrave; <lb/>il rettangolo HAC, al rettangolo HNC, ha ragion <lb/>composta di AH ad HN, cio&egrave; AD ad NO, e di AC <lb/>a CN, ovvero AB ad NL: per&ograve; sar&agrave; il rettangolo <lb/>LO eguale al circolo MN. &rdquo; </s></p><p type="main">

<s>&ldquo; Ora il cerchio AB, al cerchio MN, sta come <lb/>il quadrato AB al quadrato MN, cio&egrave; come il rettangolo HAC al rettangolo <lb/>HNC, ovvero come il rettangolo BD ad LO. </s>

<s>Gli antecedenti sono uguali, ergo <lb/>ed i consequenti. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2694.jpg" pagenum="319"/><p type="main">

<s>&ldquo; Fatta ora libbra AC abbiamo alla libbra attaccate grandezze rettan&shy;<lb/>gole, ed altrettante circolari, ciascuna uguale a ciascuna: per&ograve; li centri sa&shy;<lb/>ranno nel medesimo perpendicolo, ovvero il perpendicolo, che passa per i <lb/>centri, divider&agrave; la libbra nello stesso punto. </s>

<s>Ma i rettangoli equiponderano, <lb/>dal punto che divide la libbra, come cinque a tre; ergo anche i circoli, che <lb/>compongono l'emisfero &rdquo; (ivi, fol. </s>

<s>15). </s></p><p type="main">

<s>Di questo modo ingegnoso, per ritrovare i baricentri delle figure note, <lb/>risolute in piani perpendicolari all'asse, volle dare il Torricelli un altro esem&shy;<lb/>pio nel conoide parabolico, adattandolo talmente al prisma triangolare, che <lb/>gl'infiniti rettangoli di questo riuscissero proporzionali agl'infiniti circoli di <lb/>quello, e ci&ograve; egli ottiene prendendo le facce DF, FG uguali (fig. </s>

<s>178), e l'AC, <lb/>che sega in mezzo i lati opposti ED, FN, per asse della parabola ALB, il pa&shy;<lb/>rametro della quale sia la DE stessa. </s>

<s>Prese le due ordinate BC, LM avremo, per <lb/>le note propriet&agrave; della curva, BC2:LM2=AC.DE:AM.DE=DF:DH= <lb/>FG:HI=<foreign lang="greek">p</foreign>BC2:<foreign lang="greek">p</foreign>LM2, e cos&igrave; essendo sempre, &egrave; <lb/><figure id="id.020.01.2694.1.jpg" xlink:href="020/01/2694/1.jpg"/></s></p><p type="caption">

<s>Figura 178.<lb/>dunque vero che i circoli del conoide pendenti dalla <lb/>libbra AC son proporzionali ai rettangoli del prisma, <lb/>e perci&ograve; hanno il centro dell'equilibrio nel mede&shy;<lb/>simo punto, per esempio in M, cosicch&egrave; AM sia a MC <lb/>doppia, come si propone il Torricelli stesso di dimo&shy;<lb/>strare concisamente in questa maniera: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXVIII. &mdash; <emph type="italics"/>Il centro del co&shy;<lb/>noide parabolico sega l'asse nella proporzione di <lb/>due a uno. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia la parabola del conoide la AB, asse AC, <lb/>lato retto DE, mezzo <emph type="italics"/>utrimque,<emph.end type="italics"/> e, fatto il rettan&shy;<lb/>golo DF, pongasi, eguale ad esso, FG, e ad angolo retto. </s>

<s>Sar&agrave; dunque il qua&shy;<lb/>drato BC eguale al rettangolo DF, ovvero al rettangolo FG, ed il quadrato <lb/>LM sar&agrave; uguale al rettangolo DH, ovvero HI, e cos&igrave; di tutti. </s>

<s>Per&ograve;, essendo <lb/>libbra AC, il centro delle une e delle altre magnitudini sar&agrave; nel medesimo <lb/><figure id="id.020.01.2694.2.jpg" xlink:href="020/01/2694/2.jpg"/></s></p><p type="caption">

<s>Figura 179.<lb/>perpendicolo. </s>

<s>Ma il centro del prisma sta nel <lb/>perpendicolo, che passa per M, quando la AM <lb/>&egrave; doppia di MC; adunque anche il centro del <lb/>conoide. </s>

<s>Ma sappiamo che anco sta nell'asse, <lb/>ergo sar&agrave; M &rdquo; (ivi, fol. </s>

<s>56). </s></p><p type="main">

<s>A simil genere di dimostrazioni, alle quali <lb/>sembra che il Torricelli avesse preso gusto, <lb/>appartiene anche la seguente, che in questa <lb/>parte del trattato da noi si soggiunge come <lb/>ultimo esempio: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXIX. &mdash; <emph type="italics"/>Ostendemus <lb/>centrum gravitatis portionis parabolae qua <lb/>sit in linea, et in quo ipsius puncto. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto portio quaelibet ABC (fig. </s>

<s>179) parabolae, abscissa per rectam <pb xlink:href="020/01/2695.jpg" pagenum="320"/>BC, diametro parallelam, ductaque AB, et divisa CA bifariam in L, ductaque <lb/>parallela LH, fiat ut HL, ad dimldiam LI, ita CO ad OL; erit in OQ cen&shy;<lb/>trum portionis &rdquo; (ibid., fol. </s>

<s>29). </s></p><p type="main">

<s>Per dimostrare che in OQ &egrave; veramente il centro della porzione ricorre <lb/>il Nostro a un terzo termine, che consiste nel riguardare AC come una lib&shy;<lb/>bra, gravata dalle infinite linee, che contessono il segmento, a ciascuna delle <lb/>quali si vuol che rispondano in proporzione gl'infiniti cerchi di una sfera o <lb/>di uno sferoide. </s>

<s>S'immagini rivolgersi intorno ad AG, come ad asse, AFG, <lb/>semicirconferenza o semiellisse che ella sia: se dentro ad essa tirisi AF, e <lb/>la HL si prolunghi in M, &egrave; facile dimostrare che da una tal costruzione &egrave; <lb/>conseguito l'intento. </s>

<s>Essendo infatti, per la parabola, HL:BC=AL.LG: <lb/>AC.CG, e per il circolo o la ellisse LM2:CF3=AL.LG:AC.CG; sar&agrave; <lb/>HL:BC=LM2:CF2. </s>

<s>Dividendo i conseguenti per 4, e osservando che <lb/>BC/4=LI/2, e CF2/4=LN2, sar&agrave; HL a LI/2, ossia CO ad OL, come LM2 a LN2, <lb/>nel qual caso, come vedremo essere dimostrato dal Torricelli in generale <lb/>per tutti i conoidei, O &egrave; il centro di gravit&agrave; della porzione sferica descritta <lb/>dall'arco AMF, e perci&ograve; in O batter&agrave; pure il perpendicolo calato dal centro <lb/>di gravit&agrave; del segmento parabolico. </s></p><p type="main">

<s>&ldquo; Fiat, dice il Torricelli, circa axem sphaerois, sive sphaera AFG, et, <lb/>productis lineis BC, HL in F, M, ducatur AF. CO ad OL est ut HL ad se&shy;<lb/>missem LI, sive HL ad 1/4 BC, sive ut quadratum ML ad 1/4 quadrati FC, <lb/>nempe ut ML quadratum ad quadratum LN. </s>

<s>Ergo O est centrum portionis <lb/>sphaeroidis, vel sphaerae FAC. &rdquo; </s></p><p type="main">

<s>&ldquo; Sed ad libram AC quaedam magnitudines pendent, quae erunt circuli <lb/>sphaeroidis, et aliae quaedam magnitudines, quae sunt lineae portionis pa&shy;<lb/>rabolicae, praedictis circulis ex ordine proportionales. </s>

<s>Ergo centra illarum <lb/>similiter divident libram. </s>

<s>Propterea parabolicae portionis centrum erit in <lb/>recta OQ &rdquo; (ibid.). </s></p><p type="main">

<s>Resta a definire il luogo, dove precisamente il punto O si trova sul&shy;<lb/>l'asse, il quale dice il Torricelli essere segato in parti tali, che AO ad AC <lb/>&ldquo; sit ut HL cum LI ad HL. Nam, per praecedentem constructionem, cum <lb/>centrum sit in secta per O, erit CO ad OL, ut HL ad semissem LI. </s>

<s>Et com&shy;<lb/>ponendo CL ad LO ut HL, cum semisse LI, ad semissem LI. </s>

<s>Et per con&shy;<lb/>versionem rationis CL ad CO, ut HL, cum semisse LI, ad HL. </s>

<s>Et duplica&shy;<lb/>tis antecedentibus AC ad CO ut bis HL, cum LI, ad HL. </s>

<s>Et dividendo AO <lb/>ad OC ut HL cum LI ad HL, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (ibid.). </s></p><p type="main">

<s>Cos&igrave; essendo, perch&egrave; il tutto si compone di due parti, l'una delle quali <lb/>&egrave; la parabola AHB, l'altra il triangolo ABC; &ldquo; iungantur, ne conclude il <lb/>Torricelli, centra parabolae AHB, et trianguli ABC, et ubi recta coniungens <lb/>concurret cum OQ, ibi erit centrum portionis &rdquo; (ibid.). </s></p><pb xlink:href="020/01/2696.jpg" pagenum="321"/><p type="main">

<s><emph type="center"/>VI.<emph.end type="center"/></s></p><p type="main">

<s>L'aver dato alla Baricentrica questa variet&agrave; di metodi nuovi non quie&shy;<lb/>tava l'animo del Torricelli, che rivolse l'operosa fecondit&agrave; dell'ingegno in&shy;<lb/>torno a immaginar solidi nuovi, quali sarebbero gli scavati e i vasiformi. </s>

<s><lb/>Vedremo come di questi gli venisse l'occasione da quel solido acuto iperbo&shy;<lb/>lico, che non cessa, dopo due secoli e mezzo, di destar la maraviglia nei Ma&shy;<lb/>tematici, ma di quelli, cio&egrave; de'solidi scavati, principio alla ricerca dei centri <lb/>di gravit&agrave; furono i centri delle porzioni di sfera, che tanto si desideravano, <lb/>dopo quello dei settori, a cui s'erano in questo argomento arrestate le inven&shy;<lb/>zioni dello stesso Torricelli. </s></p><p type="main">

<s>Luca Valerio aveva tutte esaurite le sue forze nell'emisfero, ma in quel <lb/>secondo modo d'indicarne il centro di gravit&agrave;, togliendo dal cilindro circo&shy;<lb/>scritto la scodella esterna, la quale si dimostrava uguale a un cono, vede&shy;<lb/>vasi il Torricelli aperta innanzi la via di giungere al suo proprio intento. </s>

<s>La <lb/>proposizione scritta nel terzo libro <emph type="italics"/>De centro gravitatis solidorum,<emph.end type="italics"/> ammi&shy;<lb/>rata per la sua novit&agrave;, era stata resa anche pi&ugrave; cospicua da Galileo, il quale, <lb/>come i nostri Lettori gi&agrave; sanno, la cit&ograve;, nella prima giornata delle due Scienze <lb/>nuove, per concluder da lei che il metodo degli indivisibili era un assurdo. </s>

<s><lb/>Il Torricelli invece l'andava predicando come la vena, e la miniera inesausta <lb/>delle speculazioni belle, quali giusto son queste che ora diremo, e che gli <lb/>occorsero alla mente dal ripensare in che modo si potessero ridurre alla fa&shy;<lb/>cile brevit&agrave; del metodo cavalierano i lunghi e faticosi processi del Valerio e <lb/>di Galileo. </s></p><p type="main">

<s>Ma il modo glielo suggeriva lo stesso Cavalieri, il quale, nel terzo libro <lb/>della sua Geometria nuova, dimostrava in quinto luogo questo teorema: Sia <lb/>BDHF (fig. </s>

<s>180) circolo o ellisse: BH, DF gli assi <lb/><figure id="id.020.01.2696.1.jpg" xlink:href="020/01/2696/1.jpg"/></s></p><p type="caption">

<s>Figura 180.<lb/>coniugati o i diametri, sopra l'un de'quali, per esem&shy;<lb/>pio sopra DF, come sopra base, e circa l'asse o il <lb/>diametro EB sian descritti il rettangolo AF e il trian&shy;<lb/>golo AEC. </s>

<s>Sia dovunque, per esempio in M, perpen&shy;<lb/>dicolarmente attraversato l'asse dalla RV, la quale <lb/>seghi i lati del triangolo in N, S, e gli archi del <lb/>circolo o dell'ellisse in I, T, e si rivolga tutta in&shy;<lb/>sieme la figura intorno ad EB: &ldquo; dico ergo, scrive <lb/>il Cavalleri, quadratum SN aequari reliquo quadrato <lb/>VR, dempto quadrato TI &rdquo; (Bononiae 1635, Lib. </s>

<s>III, pag. </s>

<s>11). </s></p><p type="main">

<s>Cos&igrave; essendo, ragionava il Torricelli, presi i suqquadrupli, avremo SN2/4= <lb/>((VR+TI)/2)((VR&mdash;TI)/2), ossia SM2=VI.IR. </s>

<s>Ma il quadrato di SM stando <pb xlink:href="020/01/2697.jpg" pagenum="322"/>al rettangolo sotto VI, IR come il circolo descritto dal raggio SM all'armilla <lb/>descritta da IR o da VT intorno all'asse, e cos&igrave; essendo di tutti gl'infiniti <lb/>circoli e delle armille infinite; sar&agrave; dunque il cono uguale alla scodella. </s></p><p type="main">

<s>Mentre che il Torricelli si compiaceva fra s&egrave; di esser giunto con tanta <lb/><figure id="id.020.01.2697.1.jpg" xlink:href="020/01/2697/1.jpg"/></s></p><p type="caption">

<s>Figura 181.<lb/>facilit&agrave; a dimostrare ci&ograve; che al Valerio <lb/>e a Galileo era costato tanta fatica, <lb/>prendeva animo di valersi della speri&shy;<lb/>mentata potenza di questo nuovo stru&shy;<lb/>mento, per ritrovare il centro nelle <lb/>porzioni di sfera. </s>

<s>Sia dunque AGBHC <lb/>(fig. </s>

<s>181) la proposta porzione, la quale <lb/>si risolva nel cono del triangolo ABD, <lb/>e nel solido del bilineo AGB. </s>

<s>Sarebbe <lb/>il problema risoluto, quando si sapesse <lb/>la proporzione che hanno le armille <lb/>esterne, rispetto ai circoli. </s>

<s>Intorno a che <lb/>studiando il Torricelli riusc&igrave; a un'in&shy;<lb/>venzione mirabile, inaspettata, qual'era <lb/>che il solido del bilineo si uguagliava <lb/>allo sferoide descritto da una semiellisse, avente per asse maggiore BD, e il <lb/>minore uguale alla met&agrave; di AB. </s></p><p type="main">

<s>Il mezzo poi dell'invenzione &egrave; d'incredibile facilit&agrave;, perch&egrave;, supponen&shy;<lb/>dosi essere la DFB la detta semiellisse, se il minore asse di lei FE inten&shy;<lb/>dasi prolungato in G, e si conduca qualunque altra ordinata LP, s'avranno, <lb/>per le geometriche propriet&agrave; assai ben note, le seguenti equazioni: LN.NM: <lb/>GI.IH=AN.NB:AI.IB=DP.PB:DE.EB=OP2:FE2. </s>

<s>Ma essendo <lb/>AI=IB, perch&egrave; E &egrave; il mezzo di BD, e IB=EF per costruzione, GI.IH= <lb/>FE2: dunque anche LN.NM=PO2. </s>

<s>Onde le armille LN, GI saranno uguali <lb/>ai circoli OP, FE, e, cos&igrave; essendo sempre, il solido del bilineo sar&agrave; uguale allo <lb/>sferoide, come, cos&igrave; avendo proposto il Torricelli, dimostrava con queste sue <lb/>proprie parole: </s></p><p type="main">

<s>&ldquo; Si ex segmento sphaerico ABC (nella precedente figura) dematur co&shy;<lb/>nus inscriptus, erit reliquum solidum sphaericum excavatum aequale sphae&shy;<lb/>roidi, cuius axis sit BD, diameter vero EF sit aequalis semissi rectae AB. &rdquo; </s></p><p type="main">

<s>&ldquo; Nam ducto plano quodlibet LM, ad axem erecto, erit rectangulum LNM, <lb/>ad GIH, ut ANB ad AIB, ob aequalitatem, per XXXV. Tertii, sive ut DPB <lb/>ad DEB, nam omnes ex iisdem rationibus componuntur, sive ut quadrata PO <lb/>et EF, ob ellipsim. </s>

<s>Sed conseguentia ponebantur aequalia, ob suppositionem, <lb/>ergo etiam antecedentia, nempe rectangulum LNM quadrato PO aequale est, <lb/>ideoque armilla LN circulo OP et hoc semper. </s>

<s>Ergo omnes simul armillae, <lb/>sive solidum sphaericum excavatum, omnibus simul circulis, nempe sphae&shy;<lb/>roidi, aequales sunt &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>37). </s></p><p type="main">

<s>Essendo ora in E il centro dello sferoide, e, presa BP tripla di PD, in P <lb/>il centro del cono; non resterebbe che a sapere la proporzione, che passa tra <pb xlink:href="020/01/2698.jpg" pagenum="323"/>la misura dei due solidi, per avere il centro del tutto: sembrava tendere a <lb/>ci&ograve; il corollario dallo stesso Torricelli ivi soggiunto: &ldquo; Solidum ergo exca&shy;<lb/>vatum, ad conum ABC, erit ut sphaerois praedicta ad eumdem conum, nempe <lb/>ut duo quadrata FE ad quadratum AD, sive ut duo rectangula AIB ad qua&shy;<lb/>dratum AD &rdquo; (ibid.). Ma volendosi riferire il ritrovato centro della porzione <lb/>sferica all'asse, conduceva all'intento direttamente quest'altro teorema, di&shy;<lb/>mostrato dal Cavalieri nel citato libro della Geometria nuova: &ldquo; Sit circu&shy;<lb/>lus BARC cuius axis vel diameter BR, ad quem ordinatim applicetur AC, <lb/>abscindens utcumque portionem ABC, et centrum sit <expan abbr="q.">que</expan> Dico omnia quadrata <lb/>portionis ABC ad omnia quadrata trianguli ABC esse ut composita ex dimi&shy;<lb/>dio totius BR, idest QR, et ipsa DR, ad eamdem DR &rdquo; (Editio cit., pag. </s>

<s>1). Di <lb/>qui derivava nel manoscritto torricelliano la proposizione e la pratica seguente: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXX. &mdash; <emph type="italics"/>Segmenti sphaerici ABC<emph.end type="italics"/> (sempre nella me&shy;<lb/>desima figura) <emph type="italics"/>centrum gravitatis reperire. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Seca bifariam BD in E, et PD sit 1/3 BD, et sphaerae diameter BR <lb/>bifariam secetur in <expan abbr="q.">que</expan> Deinde fac ut DR ad RQ, ita ET ad TP, et erit T <lb/>centrum quaesitum, &rdquo; verit&agrave; conseguente dai premessi principii, e confermata, <lb/>con questa nota illustrativa, dal Viviani: &ldquo; Nam, si intelligamus in segmento <lb/>conus inscriptus ABC, erit P centrum coni, et E centrum reliqui solidi, dempto <lb/>cono, cum alibi ostensum sit solidum genitum a bilineo AB aequari sphae&shy;<lb/>roidi cuidam, cuius centrum est in E. </s>

<s>Sed totum segmentum ABC, ad co&shy;<lb/>num inscriptum ABC (per Iam Tertii Geometriae Cavalerii), est ut QR cum <lb/>DR ad DR; ergo, dividendo, solidum bilineum AB, ad conum ABC, erit ut <lb/>QR ad DR. </s>

<s>Et convertendo conus ad solidum erit ut DR ad QR, vel ut ET <lb/>ad TP. </s>

<s>Ergo magnitudines distan&shy;<lb/><figure id="id.020.01.2698.1.jpg" xlink:href="020/01/2698/1.jpg"/></s></p><p type="caption">

<s>Figura 182.<lb/>tiis e contrario respondent, idcirco <lb/>T erit centrum commune magni&shy;<lb/>tudinum, nempe segmenti sphaerici <lb/>ABC, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. XXXV, fol. </s>

<s>37). </s></p><p type="main">

<s>Indicato cos&igrave; il centro di gra&shy;<lb/>vit&agrave; del segmento sferico, e mo&shy;<lb/>strate le ragioni perch&egrave; fosse que&shy;<lb/>sta indicazione da tenersi per vera, <lb/>rimaneva a cercar dove si dovesse <lb/>collocare sull'asse il centro di gra&shy;<lb/>vit&agrave; del frusto. </s>

<s>Rappresentandolo <lb/>nella figura ABCD (182) fu primo <lb/>pensiero del Torricelli di risolverlo <lb/>nel segmento EFG, la regola ba&shy;<lb/>ricentrica del quale era stata dianzi indicata, e nel solido generato dal quadri&shy;<lb/>lineo ABFE, che bisognava studiarsi di ridurre a qualche solido comunemente <lb/>noto. </s>

<s>Lo studio riusc&igrave; anche questa volta felicemente, nel modo che segue: </s></p><p type="main">

<s>&ldquo; Si ex frusto sphaerico ABCD, planis parallelis abseisso, demptum sit <pb xlink:href="020/01/2699.jpg" pagenum="324"/>segmentum sphaericum EFG concentricum et aequealtum, erit reliquum so&shy;<lb/>lidum excavatum aequale cylindro KC, super basi BC constituto, et aequealto. </s>

<s><lb/>Nam, ducto ubicumque plano LM ad axem erecto, erit circulus LM, ad QV, <lb/>ut quadratum LN ad quadratum <expan abbr="Nq.">Nque</expan> Et, dividendo, armilla cuius latitudo <lb/>LQ, ad circulum QV, erit ut rectangulum LQM ad quadratum QN. </s>

<s>Sed cir&shy;<lb/>culus QV, ad circulum BC, est ut quadratum QN ad BF; ergo ex aequo erit <lb/>armilla LQ, ad circulum BC, ut rectangulum LQM ad quadratum BF, nempe <lb/>aequalis est, et hoc semper. </s>

<s>Ergo omnes simul armillae, hoc est solidum <lb/>excavatum quale dictum est, aequales erunt omnibus simul circulis, nempe <lb/>cylindro KC &rdquo; (ibid., fol. </s>

<s>37). </s></p><p type="main">

<s>Dell'applicazione per&ograve; di questo lemma non ci &egrave; nel manoscritto torri&shy;<lb/>celliano altro che il principio nell'appresso </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXXI. &mdash; <emph type="italics"/>Frusti sphaerici ABCD centrum reperire. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Seca FX ita ut XH sit 1/2, XI 1/3 totius FX, et centrum sphaerae sit T. </s>

<s><lb/>Fac ut XY ad XT, ita HO ad OI ut supra, et hoc serva.... &rdquo; (ibid., fol. </s>

<s>214). </s></p><p type="main">

<s>Il Viviani pens&ograve; di ridurre la proposizione compiuta, facendo osservare <lb/>che intanto era indicato in O il centro di gravit&agrave; del segmento sferico, a cui <lb/>bisognava aggiungere il solido generato dal quadrilineo ABFE, che s'&egrave; di&shy;<lb/>mostrato uguale al cilindro CK. </s>

<s>Di tali due parti si compone il frusto, ma <lb/>si faceva dal Viviani stesso notare che il segmento e il solido descritto dal <lb/>trilineo ABK sono uguali, ond'&egrave; che le parti componenti si riducono al detto <lb/>trilineo, e al cilindro inscritto. </s>

<s>Di quello il centro &egrave; O, medesimo che del <lb/>segmento, di questo &egrave; in H, a mezzo l'asse FX. </s>

<s>Facendosi dunque come HS <lb/>a SO, cos&igrave; reciprocamente il solido del trilineo al cilindro inscritto; sar&agrave; in S <lb/>il centro cercato. </s></p><p type="main">

<s>&ldquo; Et erit O (soggiunge all'interrotta scrittura torricelliana il Viviani) <lb/>centrum solidi a trilineo ABK geniti, cum sit centrum portionis sphaericae <lb/>EFG, quae aequatur dicto solido. </s>

<s>Sed H est centrum cylindri inscripti KC, <lb/>ergo centrum frusti ABCD est inter H et O. </s>

<s>Si fiat ergo ut HS ad SO, ita <lb/>solidum a trilineo ABK, ad cylindrum CK, erit S centrum frusti ABCD &rdquo; <lb/>(ibid., T. XXXV, fol. </s>

<s>138). </s></p><p type="main">

<s>Del trilineo, che &egrave; uguale al segmento, e del cilindro si possono dalla Geo&shy;<lb/>metria aver le misure, alle quali son proporzionali le indicate parti dell'asse, <lb/>e il problema sarebbe perci&ograve; risoluto. </s>

<s>Ma se il Torricelli ne lasci&ograve; la solu&shy;<lb/>zione incompiuta, non dovette essere senza un motivo, che a noi giova d'in&shy;<lb/>vestigare. </s>

<s>Si potrebbe credere che fosse stato perch&egrave; la formula non gli riu&shy;<lb/>sciva della consueta semplicit&agrave; ed eleganza, e poniamo che vi concorresse <lb/>anche questa ragione, la principale nulladimeno fu quella di voler avere il <lb/>vantaggio sopra Luca Valerio. </s>

<s>Nelle due ultime proposizioni trascritte la su&shy;<lb/>periorit&agrave; del Torricelli consisteva solamente nel comprendersi insieme i due <lb/>casi, che il centro della sfera intera rimanesse cos&igrave; dentro, come fuori del&shy;<lb/>l'asse della porzione, ma si seguitava pure a distinguere il caso che la por&shy;<lb/>zione contemplata avesse una sola, o due basi, porgendo della stessa sfera ora <lb/>un semplice segmento, ora un frusto. </s></p><pb xlink:href="020/01/2700.jpg" pagenum="325"/><p type="main">

<s>Si voleva dunque da esso Torricelli anche in ci&ograve; superare il Valerio, <lb/>che, nel suo secondo libro <emph type="italics"/>De centro gravitatis,<emph.end type="italics"/> aveva distinte sei proposi&shy;<lb/>zioni, per dimostrare il centro di gravit&agrave; delle porzioni sferiche, secondo che <lb/>il centro della figura intera riman dentro o fuori dell'asse, e secondo che <lb/>esso asse tocca con ambedue le estremit&agrave; i piani secanti, o ne tocca uno <lb/>solo, perch&egrave; l'altro svanisce; comprendendo tutte queste verit&agrave; in una pro&shy;<lb/>posizione universalissima, a condur la quale riusc&igrave; esso Torricelli felicemente, <lb/>supposte le cose, per le due precedenti gi&agrave; dimo&shy;<lb/><figure id="id.020.01.2700.1.jpg" xlink:href="020/01/2700/1.jpg"/></s></p><p type="caption">

<s>Figura 183.<lb/>strate, aggiuntovi quest'altro lemma, che dice: <lb/>&ldquo; Se sar&agrave; un cilindro ed un cono intorno al me&shy;<lb/>desimo asse, il cilindro al cono sta come tre <lb/>quadrati AB (fig. </s>

<s>183) al quadrato AC. </s>

<s>Poich&egrave; il <lb/>cilindro BE al cilindro CD sta come il quadrato <lb/>AB al quadrato AC, <emph type="italics"/>sumptisque consequentium <lb/>triplis,<emph.end type="italics"/> il cilindro BE al cono sta come il quadrato AB ad un terzo di AC, <lb/>ovvero come tre quadrati AB al quadrato AC &rdquo; (ivi, T. XXXVI, fol. </s>

<s>53). </s></p><p type="main">

<s>Ecco ora come, preparate queste cose, si dia dal Torricelli, con regola <lb/>universalissima, l'invenzione del centro di gravit&agrave; delle porzioni, comunque <lb/>sian segate nella sfera: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXXII. &mdash; <emph type="italics"/>Esto frustum sphaericum planis parallelis <lb/>AD, BC<emph.end type="italics"/> (fig. </s>

<s>184) <emph type="italics"/>abscissum, axis EF. </s>

<s>Dico centrum gravitatis ita secare <lb/>EF, ut pars ad E terminata sit ad reliquam, ut quadratum BC, cum<emph.end type="italics"/><lb/><figure id="id.020.01.2700.2.jpg" xlink:href="020/01/2700/2.jpg"/></s></p><p type="caption">

<s>Figura 184.<lb/><emph type="italics"/>duobus quadratis EF, duobusque AD, ad <lb/>quadratum AD, cum duobus FE, duobus&shy;<lb/>que BC. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Fiat segmentum sphaericum GHEIL <lb/>concentricum et aeque altum cum frusto, in&shy;<lb/>scribaturque conus GEL, et, secto axe bifa&shy;<lb/>riam in M, applicetur HMI. </s>

<s>Demonstratum est <lb/>solidum sphaericum excavatum GHEBA ae&shy;<lb/>quari cylindro, cuius basis sit circulus BC, altitudo vero EF; sive cono, cuius <lb/>basis sit tripla circuli BC, altitudo vero EF. </s>

<s>Ergo solidum GHEBA, ad conum <lb/>GEL, est ut triplum quadrati EB ad quadratum FG. </s>

<s>Solidum vero excavatum, <lb/>factum a bilineo GHE, ad conum eumdem GEL, demonstratum est esse ut <lb/>duo rectangula GNE ad quadratum FG. Ergo, per XXIV Quinti, totum simul <lb/>solidum ABENG, ad conum GEL, erit ut tria quadrata BE, cum duobus <lb/>rectangulis GNE, ad quadratum GF, sive, sumptis duplis, ut sex quadrata <lb/>BE, cum quadrato GE, ad duo quadrata GF. &rdquo; </s></p><p type="main">

<s>&ldquo; Secetur FM bifariam in P: eritque P centrum coni GEL, et est idem <lb/>centrum tam solidi GHEBA, quam etiam solidi GHE, propterea M erit cen&shy;<lb/>trum totius solidi ABENG. </s>

<s>Fiat ergo ut sex quadrata BE, cum quadrato GE, <lb/>ad duo quadrata FG, ita reciproce recta PO ad OM, et erit O centrum gra&shy;<lb/>vitatis totius frusti sphaerici. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Iam argumenta sunt componendo, duplicando antecedentia, per con-<pb xlink:href="020/01/2701.jpg" pagenum="326"/>versionem rationis, duplicando antecedentia, dividendo, et postea facta re&shy;<lb/>ductione. </s>

<s>Per constructionem est recta PO ad OM ut sex quadrata BE, cum <lb/>quadrato EG, ad duplum quadrati FG. Componendo, PM ad OM erit ut sex <lb/>quadrata BE, cum quadrato EG et duplo quadrati FG, ad duplum quadrati <lb/>FG. </s>

<s>Duplicando antecedentia, FM, ad MO, erit ut 12 quadrata BE, cum <lb/>2EG+4FG, ad 2FG. </s>

<s>Per conversionem rationis, MF ad FO ut 12BE+ <lb/>2EG+4FG ad 12BE+2EG+2FG. </s>

<s>Duplicando antecedentia, EF ad <lb/>FO ut 24BE+4EG+8FG, ad 12BE+2EG+2FG. Dividendo, EO <lb/>ad OF ut 12BE+2EG+6FG ad 12BE+2EG+2FG. &rdquo; </s></p><p type="main">

<s>&ldquo; Sed quoniam rectangulum AGD quadrato BE est aequale, erit diffe&shy;<lb/>rentia quadratorum AF, BE. </s>

<s>Ergo potest fieri reductio talis, mutato prius <lb/>quadrato EG cum quadratis EF, FG. </s>

<s>Sic EO ad OF est ut 12BE+2EF+ <lb/>8FG, ad 12BE+2EF+4FG. Vel, facta reductione, EO ad OF est ut <lb/>4BE+2EF+8AF ad 8BE+2EF+4AF. Vel, facta ultima re&shy;<lb/>ductione, EO ad OF est ut quadratum BC, cum duobus EF duobusque AD, <lb/>ad 2BC+2EF+uno AD, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (ibid., fol. </s>

<s>39). </s></p><p type="main">

<s>Notabile fra tutte le altre passate &egrave; questa proposizione, non solo riguar&shy;<lb/>data in s&egrave; stessa, ma nel suo processo dimostrativo, che offre il primo esem&shy;<lb/>pio, dato dal Torricelli nella Scuola galileiana, per tentar di vincere la ritrosia <lb/>contro i metodi analitici, ritrovati tanto utili allora dai Matematici francesi. </s>

<s><lb/>Se ne compiacque il Nostro non poco, e annunziando il teorema a Miche&shy;<lb/>langiolo Ricci, il di 7 Marzo 1642, pochi giorni dopo averlo dimostrato, gli <lb/>diceva: &ldquo; Giacch&egrave; V. S. studia Luca Valerio, eccogli una proposizione, che <lb/>ne abbraccia molte di Luca Valerio. </s>

<s>Giudichi V. S. chi la porti meglio o egli <lb/>o io. </s>

<s>Se sar&agrave; un frusto di sfera ABCD (nella preced. </s>

<s>figura) tagliato co'piani <lb/>paralleli AD, BC, o passino per il centro s&igrave; o no, o l'intraprendano s&igrave; o no, <lb/>e sia l'asse del frusto EF, e centro di gravit&agrave; O; sar&agrave; la retta EO alla retta <lb/>OF come il quadrato AB, con due quadrati EF, e due quadrati DC, ad un <lb/>quadrato DC, con due quadrati EF, e due quadrati AB. </s>

<s>Se V. S. la comu&shy;<lb/>nica al sig. </s>

<s>Raffaello (Magiotti) so certo che l'avr&agrave; cara, perch&egrave; sui libri non <lb/>la trover&agrave; portata a questo modo &rdquo; (ivi, T. XL, fol. </s>

<s>100). </s></p><p type="main">

<s>Un anno dopo, dando la medesima notizia al Cavalieri si compiaceva di <lb/>fargli notare che il suo processo era molto pi&ugrave; spedito che quello di Luca Va&shy;<lb/>lerio, &ldquo; ed &egrave;, soggiungeva, universale, o sia intrapreso il centro o no. </s>

<s>Insomma <lb/>a me pare che, per via degli indivisibili, si trovino, oltre le innumerabili e <lb/>maravigliose di V. P., anco tuttavia delle conclusioni da non sprezzarsi, e <lb/>che, se io le trovassi in altri, mi parrebbero speciose. </s>

<s>Come dunque questa <lb/>dottrina non &egrave; da stimarsi? </s>

<s>Se costoro ammettessero le conclusioni per belle, <lb/>come credo che bisogni concedere, converr&agrave; pur anco approvare le dottrine: <lb/>ovvero, se lodano le conclusioni e non le dottrine, almeno doveranno mo&shy;<lb/>strare che ve ne siano delle false, ma credo che dureranno fatica &rdquo; (ivi, <lb/>fol. </s>

<s>123). </s></p><p type="main">

<s>Fra i <emph type="italics"/>Problemi proposti ai Matematici di Francia<emph.end type="italics"/> era notato anche <lb/>quello del centro di gravit&agrave; nel frusto sferico, e, dopo averlo enumerato, sog-<pb xlink:href="020/01/2702.jpg" pagenum="327"/>giungeva il Torricelli cos&igrave;, nel suo <emph type="italics"/>Racconto:<emph.end type="italics"/> &ldquo; Questa enunciazione, con po&shy;<lb/>chissime mutazioni, si riduce a comprendere anco i frusti, ed i segmenti <lb/>della sferoide. </s>

<s>Cos&igrave;, in una sola e facilissima enunciazione, si vedono ristrette <lb/>molte e difficilissime proposizioni ignote agli antichi, ma dimostrate da L. </s>

<s>Va&shy;<lb/>lerio con molte proposizioni, e con diversissime enunciazioni, non essendosi <lb/>accorto che, sotto una sola, semplicissima e universale, si potevano compren&shy;<lb/>dere tutti i casi, sopra i quali egli forma proposizioni tanto diverse &rdquo; (ivi, <lb/>T. XXXII, fol. </s>

<s>23). </s></p><p type="main">

<s>Che sia veramente la proposizione torricelliana universalissima e gene&shy;<lb/>rale si conferma dai seguenti corollari: Sia il frusto sferico a una sola base <lb/>come per esempio ABC (fig. </s>

<s>185), il quadrato dell'altra <lb/><figure id="id.020.01.2702.1.jpg" xlink:href="020/01/2702/1.jpg"/></s></p><p type="caption">

<s>Figura 185.<lb/>base &egrave; zero, e perci&ograve; sar&agrave; in questo caso BO:OD= <lb/>2(BD2+AC2):AC2+2 DB2, come fa osservare lo stesso <lb/>Torricelli: &ldquo; In segmento sphaerico superioris figurae <lb/>quadratum BC (nella figura 184) penitus evanescit. </s>

<s>Ergo <lb/>recta BO ad OD est ut duo quadrata BD+2 AC, ad <lb/>quadratum AC+2 DB &rdquo; (ibid., T. XXV, fol. </s>

<s>74). </s></p><p type="main">

<s>Che se il frusto sferico ha una base sola, e questa sia uguale a un cir&shy;<lb/>colo massimo, BO sta a OD come 5 a tre: ci&ograve; che conferma il gi&agrave; dimo&shy;<lb/>strato in altri modi, essendo allora il frusto un emisfero, e si conclude dalla <lb/>formula della proposizion generale, illustrata dalla figura 184, e cos&igrave; scritta: <lb/>EO:OF=BC2+2(EF2+AD2):2(BC2+EF2)+AD2. </s>

<s>Essendo nell'emi&shy;<lb/>sfero BC2=O, AD=2EF, la detta formula si trasformer&agrave; nella seguente: <lb/>EO:OF=2EF2+8EF2:2EF2+4EF2=10:6=5:3. <lb/><figure id="id.020.01.2702.2.jpg" xlink:href="020/01/2702/2.jpg"/></s></p><p type="caption">

<s>Figura 186.</s></p><p type="main">

<s>Che poi in quella universalit&agrave; si comprendano an&shy;<lb/>che i frusti e i segmenti dello sferoide intendeva il Tor&shy;<lb/>ricelli di dimostrarlo, con questa proposizione: &ldquo; In fru&shy;<lb/>sto sphaeroidali ABCD (fig. </s>

<s>186) centrum gravitatis O <lb/>secat EF in eadem ratione, ac si esset frustum sphae&shy;<lb/>ricum circa axem GH, et aeque altum &rdquo; (ibid., T. XXV, <lb/>fol. </s>

<s>74). Invece della dimostrazione per&ograve; si trovano nel <lb/>manoscritto le due seguenti osservazioni: &ldquo; Ci&ograve; che si <lb/>dice del cerchio si pu&ograve; trasportare all'ellisse, perch&egrave; le <lb/>linee tutte del cerchio hanno la medesima proporzione, <lb/>che quelle dell'ellisse: per&ograve; il punto dell'equilibrio sega la libbra <emph type="italics"/>in eadem <lb/>ratione.<emph.end type="italics"/> &mdash; Quello che si dice della sfera si pu&ograve; trasportare alla sferoide, <lb/>perch&egrave; tutti i circoli della sfera sono tra di loro come tutte le ellissi della sfe&shy;<lb/>roide &rdquo; (ivi, T. XXX, fol. </s>

<s>40). </s></p><p type="main">

<s>Avendosi infatti, per le note propriet&agrave; geometriche delle due figure, <lb/>LE2:MF2=BE2:AF2, ossia <foreign lang="greek">p</foreign>LE2:<foreign lang="greek">p</foreign> MF2=<foreign lang="greek">p</foreign> BE2:<foreign lang="greek">p</foreign>AF2, fatta EF lib&shy;<lb/>bra, dovr&agrave; questa, per il lemma XXII alla XIV <emph type="italics"/>De dimensione parabolae<emph.end type="italics"/><lb/>altre volte citato, avere il medesimo punto dell'equilibrio, o sia ella gravata <lb/>dal circolo LE, con tutti gli altri infiniti, che compongono il frusto sferico; <lb/>o sia gravata dal circolo BE, con tutti gli altri infiniti, che compongono il <pb xlink:href="020/01/2703.jpg" pagenum="328"/>frusto sferoideo, perch&egrave; ha un solido all'altro la medesima proporzione. </s>

<s>&ldquo; Ergo <lb/>in sphaeroide (essendo BC2=4BE2=4GEH, AD2=4AF2=4HFG) <lb/>EO ad OF est ut duo rectangula GEH+quadrato EF+4 rectangulis <lb/>HEG &rdquo; (ivi, T. XXV, fol. </s>

<s>74). </s></p><p type="main">

<s>Se la base superiore svanisce, ossia se BC, e con esso GE, si riducono <lb/>a zero, anche il rettangolo GE.EH &egrave; zero, e la formula si trasforma nella <lb/>seguente EO:OF=EF2+4GFH:EF2+2GFH. </s>

<s>Che se, mentre da una <lb/>parte svanisce la base superiore, l'inferiore diventa il circolo massimo del <lb/>fuso ellittico, ossia, se il frusto si riduce all'emisferoide, GFH=EF2, e perci&ograve; <lb/>EO:OF=EF2+4EF2:EF2+2EF2=5:3, come in seguito vedremo <lb/>dimostrarsi dall'Autore direttamente. </s></p><p type="main">

<s>Frattanto osserviamo che, mentre il Torricelli studiavasi di emulare il <lb/>Valerio, deduceva dalle proposizioni dell'emulo, e dalle sue proprie, alcuni <lb/>corollari, che l'avviavano a trattar l'argomento indicato nel nostro somma&shy;<lb/>rio. </s>

<s>Dall'aver dimostrato, rivolgendo l'occhio indietro sopra la figura 182, <lb/>che il solido descritto dal quadrilineo BE &egrave; uguale al cilindro CK di pari al&shy;<lb/>tezza, risultava che il centro del solido scavato &egrave; nella met&agrave; dell'asse, come <lb/>nello stesso cilindro. </s>

<s>&ldquo; Patet centrum gravitatis dicti solidi excavati esse idem <lb/>cum centro cylindri &rdquo; (ibid., T. XXXVI, fol. </s>

<s>37). E per essersi, nella figura 181, <lb/>dimostrato il solido generato dal bilineo AGB uguale allo sferoide, &ldquo; Patet <lb/>centrum etiam praedicti solidi sphaerici esse idem ac centrum sphaeroidis &rdquo; <lb/><figure id="id.020.01.2703.1.jpg" xlink:href="020/01/2703/1.jpg"/></s></p><p type="caption">

<s>Figura 187.<lb/>(ibid.), ossia nel mezzo dell'asse, come il Torricelli stesso con&shy;<lb/>ferm&ograve; cos&igrave;, con dimostrazione diretta, e per il caso particolare <lb/>che il segmento contemplato fosse un emisfero. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXXIII. &mdash; <emph type="italics"/>Se dall'emisfero sar&agrave; levato <lb/>il cono, dico che il centro del bicchiere che resta sta nel <lb/>mezzo dell'asse AB<emph.end type="italics"/> (fig. </s>

<s>187). &rdquo; </s></p><p type="main">

<s>&ldquo; Mettasi AB per libbra, e prendansi uguali AC, DB. </s>

<s><lb/>Saranno anco uguali OE, IB. </s>

<s>Ma l'armilla di EF, all'armilla <lb/>di IG, le quali sono grandezze, che hanno il centro nella lib&shy;<lb/>bra AB; sta come il rettango FEM, cio&egrave; OEB, <emph type="italics"/>ob rirculum <lb/>et per XXXV Tertii,<emph.end type="italics"/> cio&egrave; OIB. <emph type="italics"/>ob aequalitatem,<emph.end type="italics"/> cio&egrave; il rettangolo GIN, al <lb/>rettangolo GIN: per&ograve; sono uguali <emph type="italics"/>et sic semper. </s>

<s>Ergo<emph.end type="italics"/><lb/><figure id="id.020.01.2703.2.jpg" xlink:href="020/01/2703/2.jpg"/></s></p><p type="caption">

<s>Figura 188.<lb/><emph type="italics"/>solidum vasiforme a bilineo OBG genitum, habet cen&shy;<lb/>trum gravitatis in medio axis AB &rdquo;<emph.end type="italics"/> (ibid., T. XXXVI <lb/>fol. </s>

<s>11). </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXXIV. &mdash; <emph type="italics"/>Dimostrare il mede&shy;<lb/>simo anco nello sferoide. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Procederemo cos&igrave;: Sia la emisferoide ABC (fig. </s>

<s>188), <lb/>dalla quale leva il cono, e prendi uguali EM, IB, ed anco <lb/>EF uguale ad EM. </s>

<s>E prova genericamente, per via di <lb/>lemma, che il cerchio MH, alla sua armilla GH, sta come <lb/>il quadrato BM al rettangolo BME, preso due volte, e poi <lb/>seguita cos&igrave;.... &rdquo; (ivi, fol. </s>

<s>13). </s></p><pb xlink:href="020/01/2704.jpg" pagenum="329"/><p type="main">

<s>Prima per&ograve; di seguitare, avvertiamo che, non essendosi il promesso <lb/>lemma ritrovato nel manoscritto torricelliano, il Viviani vi suppli di suo, come <lb/>si legge in un foglio intitolato <emph type="italics"/>&ldquo; Mio lemma supposto dal Torricelli.<emph.end type="italics"/> Dico <lb/>che il quadrato MH, alla sua armilla HG, o il cerchio MH, alla armilla HG, <lb/>sta sempre come il quadrato BM a due rettangoli BME. &rdquo; </s></p><p type="main">

<s>&ldquo; Prendi EF eguale ad ME: sar&agrave; il quadrato MH, al quadrato AE, come <lb/>il quadrato BM al quadrato BE; cio&egrave; al rettangolo BED, ed il quadrato AE, <lb/>al quadrato GM, <emph type="italics"/>ob ellipsim, vel circulum,<emph.end type="italics"/> sta come il rettangolo BED al <lb/>rettangolo BMD. </s>

<s>Adunque <emph type="italics"/>ex aequo<emph.end type="italics"/> il quadrato HM, al quadrato MG, star&agrave; <lb/>come il quadrato BM al rettangolo BMD; cio&egrave;, essendo BF eguale ad MD, <lb/>al rettangolo BMF. E, dividendo, il quadrato MH, all'armilla HG, come il <lb/>quadrato BM al rettangolo BMF, cio&egrave; a due rettangoli BME &rdquo; (ivi, T. XXXV, <lb/>fol. </s>

<s>124). </s></p><p type="main">

<s>Tornando ora al Torricelli seguitiamo con lui cos&igrave;: &ldquo; L'armilla GH, al <lb/>cerchio MH, sta come il rettangolo BME, preso due volte, al quadrato MB. </s>

<s><lb/>Il cerchio poi HM, al cerchio RI, sta come il quadrato MB, al quadrato BI, <lb/>ed il cerchio RI, alla sua armilla, sta come il quadrato BI al rettangolo BIE, <lb/>preso due volte. </s>

<s>Adunque, <emph type="italics"/>ex aequo et sumptis consequentium dimidiis.<emph.end type="italics"/><lb/>l'armilla GH, alla LR, sta come il rettangolo BME al rettangolo BIE, cio&egrave; <lb/>uguali: e cos&igrave; sempre. </s>

<s>Adunque, il centro del bicchiere dell'emisferoide &egrave; <lb/>nel mezzo dell'asse EB &rdquo; (ivi, T. XXXVI, fol. </s>

<s>13). </s></p><p type="main">

<s>Di qui volle il Torricelli passare a esercitarsi intorno ai bicchieri cilin&shy;<lb/>drici, considerandoli prima di tutto scavati da un cono. </s>

<s>Ne contempl&ograve; due <lb/>casi: il primo, in cui il cilindro avesse uguale altezza, ma base diversa dal <lb/>cono; il secondo, in cui l'altezza e la base fossero uguali. </s>

<s>E, supposto il <lb/>teorema, che noi premettemmo alla XXXII qui addietro per lemma; dimo&shy;<lb/>strava, e scriveva fra'suoi fogli, per quel primo caso del cilindro scavato, la <lb/>seguente </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXXV. &mdash; <emph type="italics"/>Se sar&agrave; un cilindro<emph.end type="italics"/><lb/><figure id="id.020.01.2704.1.jpg" xlink:href="020/01/2704/1.jpg"/></s></p><p type="caption">

<s>Figura 189.<lb/><emph type="italics"/>ed un cono intorno al medesimo asse, fa'come tre <lb/>quadrati AC<emph.end type="italics"/> (fig. </s>

<s>189), <emph type="italics"/>al quadrato AB, cos&igrave; EI alla <lb/>ID<emph.end type="italics"/> (il punto 1) &egrave; mezzo di AH, ed E mezzo di AD) <lb/><emph type="italics"/>sar&agrave; il punto I centro del cilindro sbucato. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Poich&egrave; D &egrave; centro di tutto il cilindro, ma E <lb/>del cono. </s>

<s>Per&ograve; tutto il cilindro, al cono, sta come tre <lb/>quadrati AC al quadrato AB, cio&egrave;, come EI ad ID. E, dividendo, il solido <lb/><figure id="id.020.01.2704.2.jpg" xlink:href="020/01/2704/2.jpg"/></s></p><p type="caption">

<s>Figura 190.<lb/>forato, al cono, come ED alla DI. </s>

<s>Per&ograve; il punto I <lb/>&egrave; centro del cilindro forato &rdquo; (ivi. </s>

<s>T, XXXVI, <lb/>fol. </s>

<s>53). </s></p><p type="main">

<s>L'altro caso del centro di gravit&agrave; nel bic&shy;<lb/>chiere cilindrico &egrave; d'invenzione simile a quella <lb/>del primo. </s>

<s>Si chiami C il cilindro intero, <emph type="italics"/>c<emph.end type="italics"/> il <lb/>cono, CS il cilindro scavato. </s>

<s>Se A (fig. </s>

<s>190) &egrave; <lb/>il centro di gravit&agrave; del cono, e B quello del cilindro, Archimede insegna <pb xlink:href="020/01/2705.jpg" pagenum="330"/>nella VIII degli Equiponderanti (Op. </s>

<s>cit., pag. </s>

<s>170) che, se faremo BD:AB= <lb/><emph type="italics"/>c<emph.end type="italics"/>:CS, verr&agrave; in D indicato il punto richiesto. </s>

<s>Componendo sar&agrave; AD:BD= <lb/>C:<emph type="italics"/>c<emph.end type="italics"/>=3:1. Dividendo, AB:BD=2:1. Duplicando gli antecedenti, <lb/>EB:BD=4:1. Componendo, ED:BD=5:1. Dividendo quella mede&shy;<lb/>sima, che ora si &egrave; composta, FD:BD=3:1. D'onde ED:FD=5:3. </s></p><p type="main">

<s>La medesima relazione era stata conclusa poco addietro per corollario <lb/>dalla XXXII, ond'&egrave; che, volendo il Torricelli farne una proposizione distinta, <lb/>incominci&ograve; a pensare che, presa GH=FG, e sopra IG, GH disegnata una <lb/>semiellisse, rivolgendosi questa intorno alla IG descriverebbe un solido, il <lb/>centro di gravit&agrave; del quale sarebbe indicato nel medesimo modo, che nel <lb/>bicchiere cilindrico, per cui tenne per certo che esso bicchiere e l'ellissoide <lb/>fossero uguali. </s>

<s>Trovato che cos&igrave; era veramente, ne fece un lemma per questa </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXXVI. &mdash; <emph type="italics"/>Centrum gravitatis hemisphaeroidis ita <lb/>secat axem, ut pars ad verticem sit ad reliqua ut quinque ad tria. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Il detto lemma per la dimostrazione si preparava in questa maniera: <lb/>&ldquo; Esto cylindrus rectus ABCD (fig. </s>

<s>191) excavatus, cui nimirum demptus <lb/>sit conus BEC. </s>

<s>Ponatur DF aequalis ipsi DE. </s>

<s>Dico cylindrum excavatum <lb/><figure id="id.020.01.2705.1.jpg" xlink:href="020/01/2705/1.jpg"/></s></p><p type="caption">

<s>Figura 191.<lb/>ABECD aequalem esse hemisphaeroidi, quae fit <lb/>a semiellipsi DCF circa axem DC revoluta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Agatur planum GH, ad axem erectum, <lb/>producanturque BA, CE donec contingant in <lb/>N, et producatur CDO axis integer, Habebit <lb/>circulus AD, ad armillam LI, rationem compo&shy;<lb/>sitam ex ratione rectae ED, ad LI, sive DC ad <lb/>CI, et ex ratione AE ad GL, sive ex ratione <lb/>AN ad NG, sive DO ad OI. </s>

<s>Ergo circulus AD, <lb/>ad armillam LI, erit ut rectangulum CDO ad <lb/>CIO, sive, ut quadratum DF ad IH, vel, ut <lb/>circulus radio DF ad circulum ex radio IH. </s>

<s><lb/>Sed antecedentia sunt aequalia, ergo etc. </s>

<s>Et hoc semper, ergo etc. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ho passato per noto che la retta AN sia uguale alla DO, ed &egrave; chiare, <lb/>perch&egrave; la DO &egrave; uguale alla DC, <emph type="italics"/>per constructionem,<emph.end type="italics"/> ma la AN &egrave; uguale alla <lb/>AB, <emph type="italics"/>ob parallelas,<emph.end type="italics"/> essendo BC doppia alla AE. &rdquo; </s></p><p type="main">

<s>&ldquo; Ritornando al proposito, e facendo dalla Geometria trapasso alla Mec&shy;<lb/>canica, per&ograve; si prova il centro della emisforoide con facilit&agrave;, perch&egrave; stato <lb/>facile trovar quello del cilindro sbucato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto centrum totius cylindri B (nella figura 190 qui poco addietro) <lb/>coni vero ablati A. Ergo, per VIII primi Aequiponderantium, erit D centrum <lb/>solidi excavati, si fiat ut cylindrus ad conum, ita AD ad DB, nempe, ut tria <lb/>ad unum. </s>

<s>Ergo, dividendo, AB ad BD crit ut duo ad unum. </s>

<s>Et, sumptis du&shy;<lb/>plis, EB ad BD ut quatuor ad unum. </s>

<s>Ergo ED ad DF erit ut quinque ad <lb/>tria. </s>

<s>Et in eadem ratione secat axem hemisphaeroidis centrum gravitatis &rdquo; <lb/>(ibid., T. XXX, fol. </s>

<s>116). </s></p><p type="main">

<s>Le medesime cose era il Torricelli riuscito a dimostrarle per altre vie, <pb xlink:href="020/01/2706.jpg" pagenum="331"/>non meno splendide e nuove. </s>

<s>Dalla V del III del Cavalieri si concludeva es&shy;<lb/>sere la scodella esterna uguale al cono, o fosse il cilindro circoscritto alla <lb/>sfera, o alla sferoide, cosicch&egrave; in questo caso, togliendosi la scodella stessa, <lb/>rimaneva l'emisferoide ignuda, della quale potevasi, con la nota regola del&shy;<lb/>l'VIII degli Equiponderanti, ritrovare il baricentro, conoscendosi quello del <lb/>tutto e di una sua parte. </s>

<s>La proporzione stereometrica poi tra l'una e l'al&shy;<lb/>tro, cio&egrave; tra l'emisferoide e il cono inscritto, era nota per la XXIX di Ar&shy;<lb/>chimede nel libro <emph type="italics"/>De conoid. </s>

<s>et sphaer.,<emph.end type="italics"/> ma il Torricelli, per far prova della <lb/>superiorit&agrave; del metodo degl'indivisibili verso l'antico, e per mostrare con <lb/>quanto maravigliosa facilit&agrave; e speditezza si potesse giungere a quelle mede&shy;<lb/>sime conclusioni, alle quali si giungeva pure dai matematici seguaci del Si&shy;<lb/>racusano, ma per vie tanto aspre e affannose; si applic&ograve; a dimostrare, con <lb/>aggressioni nuove, che l'emisfero o l'emisferoide &egrave; doppia del cono inscritto, <lb/>premettendo tre lemmi alla proposizione. </s></p><p type="main">

<s>Il primo &egrave; compreso nella VI archimedea <emph type="italics"/>De conoid. </s>

<s>et sphaer.,<emph.end type="italics"/> nella <lb/>quale si dimostra che l'ellisse sta al circolo come il rettangolo sotto gli assi <lb/>sta al quadrato del diametro; d'onde si deriva che, se uno degli assi &egrave; uguale <lb/>al diametro, come suppone il Torricelli, l'ellisse sta al circolo come l'altro <lb/>asse al diametro, secondo che il Torricell&igrave; stesso proponevasi di dimostrare, <lb/>bench&egrave; in un modo del tutto nuovo. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma I.<emph.end type="italics"/> &mdash; Omnis ellipsis, ad circulum qui habeat diametrum ae&shy;<lb/>quale alteri axium ellipseos, eam habet proportionem, quam alter, nempe <lb/>inaequalis axis, ad circuli diametrum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto ellipsis ABC (fig. </s>

<s>192), circulus ADC, et sit axis ellipsis AC ae&shy;<lb/>qualis diametro circuli AC. </s>

<s>Sitque alter axis BH: dico <lb/><figure id="id.020.01.2706.1.jpg" xlink:href="020/01/2706/1.jpg"/></s></p><p type="caption">

<s>Figura 192.<lb/>ellipsim ad circulum esse ut BH ad HD. </s>

<s>Ducatur enim <lb/>ordinatim EF, ubicumque, et erit quadratum EF, ad qua&shy;<lb/>dratum BH, ut rectangulum AFC, ad rectangulum AHC. </s>

<s><lb/>Sed etiam quadratum IF, ad quadratum DH, est ut re&shy;<lb/>ctangulum AFC ad rectangulum AHC; ergo quadratum <lb/>EF, ad quadratum BH, est ut quadratum IF ad quadra&shy;<lb/>tum DH. </s>

<s>Ergo et lineae sunt proportionales. </s>

<s>Et, permu&shy;<lb/>tando, EF ad FI est ut BH ad HD, et hoc semper. </s>

<s>Propterea erunt omnes <lb/>antecedentes simul, ad omnes simul consequentes, ut una antecedentium ad <lb/>unam consequentium, nempe ellipsis ABC, ad circulum ADC, ut BH ad HD &rdquo; <lb/>(idid., fol. </s>

<s>172). </s></p><p type="main">

<s>Segue l'altro lemma, che, trapassando dal circolo e dall'ellisse alla sfera <lb/>e allo sferoide, procede per gl'indivisibili in modo analogo al primo. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma II.<emph.end type="italics"/> &mdash; Omnis sphaerois, ad sphaeram, quae habeat maximum <lb/>circulum aequalem maximo circulo sphaeroidis, est ut axis ad axem. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto sphaerois ABC (fig. </s>

<s>193) sphaera vero ADC quales dictae sunt: <lb/>maximus utriusque circulus sit AHCL. </s>

<s>Dico sphaeroidem ad sphaeram esse <lb/>ut axis BE ad axem ED. </s>

<s>Secetur enim utraque per centrum E, plano HBL <lb/>ad diametrum AC erecto, et iterum altero plano MFN, ipsi HBL parallelo <pb xlink:href="020/01/2707.jpg" pagenum="332"/>ubicumque. </s>

<s>Eritque, per praecedens lemma, ellipsis HBL, ad circulum HDL, <lb/><figure id="id.020.01.2707.1.jpg" xlink:href="020/01/2707/1.jpg"/></s></p><p type="caption">

<s>Figura 193.<lb/>ut BE ad ED. </s>

<s>Sed etiam ellipsis MFN est <lb/>ad circulum MIN ut FG ad GI, sive ut BE <lb/>ad ED, et sic semper. </s>

<s>Propterea erunt <lb/>omnes simul antecedentes, ad omnes con&shy;<lb/>sequentes simul, ut una ad unum, nempe <lb/>ut ellipsis HBL ad circulum HDL, sive ut <lb/>axis BE ad axem ED &rdquo; (ibid., fol. </s>

<s>173). </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma III.<emph.end type="italics"/> &mdash; Sphaeroides inter <lb/>se sunt ut solida parallelepipeda, quorum <lb/>bases sunt quadrata diametrorum, altitu&shy;<lb/>dines vero longitudines axium. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sint sphaeroides ABC, DEF (fig. </s>

<s>194) <lb/>quarum axes BG, EH, diametri vero AC, <lb/>DF. </s>

<s>Dico sphaeroidem ABC, ad sphaeroidem <lb/><figure id="id.020.01.2707.2.jpg" xlink:href="020/01/2707/2.jpg"/></s></p><p type="caption">

<s>Figura 194.<lb/>DEF, esse ut solidum parallelepipedum, basi <lb/>quadrato AC, altitudine vero BG, ad solidum <lb/>parallelepipedum, basi quadrato DF, altitudine <lb/>vero EH. </s>

<s>Concipiatur enim, in utraque sphae&shy;<lb/>roide, sphaera aequalis diametri AIC, DOF. </s>

<s>Erit&shy;<lb/>que sphaerois ABC, ad sphaeram AIC, ut recta <lb/>BG ad GI, per praecedens, sive, ut solidum <lb/>basiquadrato GI, altitudine BG, ad cubum GI. </s>

<s>Sphaera vero AIC, ad sphae&shy;<lb/>ram DOF, est ut cubus GI ad cubum HO, et denique sphaera DOF, ad <lb/>sphaeroidem DEF, est ut cubus HO ad solidum parallelepipedum, basi qua&shy;<lb/>drato HO, altitudine vero HE. </s>

<s>Ergo ex aequo patet propositum. </s>

<s>Sumptis <lb/>vero quadruplis, erit sphaerois ABC ad DEF ut solidum basi quadrato AC, <lb/>altitudine BG, ad solidnm basiquadrato DF. altitudine EH, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (ibid., <lb/>fol. </s>

<s>174). </s></p><p type="main">

<s>Con l'aiuto de'quali tre lemmi passa il Torricelli finalmente a dimo&shy;<lb/><figure id="id.020.01.2707.3.jpg" xlink:href="020/01/2707/3.jpg"/></s></p><p type="caption">

<s>Figura 195.<lb/>strar la proposizione, che dice: <emph type="italics"/>Hemisphaerium, sive <lb/>hemisphaeroides dupla est coni inscripti.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto hemisphaerum sive hemisphaeroides ABC <lb/>(fig. </s>

<s>195), cuius axis BD, et applicata ex puncto E <lb/>medio axis sit FEH, conus inscriptus ABC. </s>

<s>Jam osten&shy;<lb/>dimus solidum reliquum, dempto cono ABC, aequale <lb/>esse sphaeroidi cuidam, cuius axis sit BD, maximus <lb/>vero circulus sit aequalis armillae FG, nempe cuius <lb/>radius I medius sit inter FG, GH. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam ratio sphaeroidis ABCO, ad sphaeroidem <lb/>cuius radius est I, axis vero BD, est, per praecedens lemma, ut solidum ba&shy;<lb/>siquadrato I, altitudine BE. </s>

<s>Ergo rationem habet compositam ex ratione <lb/>quadrati AD, ad quadratum I, sive ad rectangulum FGH, nempe ut 4 ad 2, <lb/>et ex ratione altitudinis DB ad BE, nempe 2 ad 1. Ergo sphaerois ABCO, <pb xlink:href="020/01/2708.jpg" pagenum="333"/>ad sphaeroidem praedictam, sive ad reliquum solidum, dempto cono ABC, <lb/>est ut 4 ad 1. Ergo hemisphaerium, vel hemisphaeroides, ad dictum solidum, <lb/>est ut 2 ad 1, et, per conversionem rationis, ad conum inscriptum erit ut <lb/>2 ad 1, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che il quadrato AD sia sempre doppio del rettangolo patet, perch&egrave; il <lb/>quadrato FE al quadrato AD sta come il rettangolo BEO al rettangolo BDO, <lb/>cio&egrave; come 3 a 4, ed il quadrato AD, al quadrato GE, sta come 4 a 1. Ergo <lb/>ex aequo il quadrato FE, all'EG, sta come 3 a 1. E, dividendo, il rettan&shy;<lb/>golo FGH, al quadrato GE, sta come 2 a 1, ed al quadrato AD come 2 a 4, <lb/><expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (ivi, fol. </s>

<s>175). </s></p><p type="main">

<s>Sia ora CM, nella stessa figura 195, il cilindro circoscritto: se di lui si <lb/>tolga la scodella esterna, il rimanente &egrave; l'emisferoide nuda, della quale si <lb/>pu&ograve; ritrovare il centro, perch'essendo E quello del tutto, N quello della parte <lb/>tolta, che si sa essere uguale al cono MDP; avremo in Q il centro dell'emi&shy;<lb/>sferoide che si voleva, se faremo EQ a EN reciprocamente come il cono <lb/>inscritto alla stessa emisferoide, o, per le cose ora dimostrate, come uno a <lb/>due, d'onde &egrave; manifesto che BQ &egrave; cinque delle parti, delle quali QD &egrave; tre <lb/>solamente. </s></p><p type="main">

<s>Ma, per tornare all'argomento dei solidi scavati, e per mostrare la va&shy;<lb/>riet&agrave; dell'aspetto e delle forme, sotto le quali gli con&shy;<lb/><figure id="id.020.01.2708.1.jpg" xlink:href="020/01/2708/1.jpg"/></s></p><p type="caption">

<s>Figura 196.<lb/>siderava il Torricelli, trascriveremo dal manoscritto di <lb/>lui quest'altre proposizioni. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXXVII. &mdash; <emph type="italics"/>Esto portio circuli <lb/>ABC<emph.end type="italics"/> (fig. </s>

<s>196) <emph type="italics"/>sive minor, sive maior semicirculi: <lb/>duae tangentes AD, DB, axis BM, et convertatur. </s>

<s>Dico <lb/>solidum vasiforme, genitum a trilineo ADB, aequale esse cono DMO. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ducta enim EI, erit rectangulum EFI, sive FEL, aequale quadrato EA, <lb/>per penultimam Tertii, vel quadrato GH (quadratum enim EA, ad quadra&shy;<lb/>tum AD, est ut quadratum HM ad MB, sive GH ad DB, et consequentia <lb/>sunt aequalia). Quare armilla EF aequalis est circulo GH, propterea solidum <lb/>vasiforme aequalis erit cono DMO &rdquo; (ibid. </s>

<s>T. XXX, fol. </s>

<s>71). <lb/><figure id="id.020.01.2708.2.jpg" xlink:href="020/01/2708/2.jpg"/></s></p><p type="caption">

<s>Figura 197.</s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXXVIII. &mdash; <emph type="italics"/>Se la parabola <lb/>ABC<emph.end type="italics"/> (fig. </s>

<s>197), <emph type="italics"/>il cui diametro BF, aver&agrave; la tan&shy;<lb/>gente DBE per la cima, e le tangenti AD, CE alla <lb/>base, e prodotta FD si giri la figura; sar&agrave; la sco&shy;<lb/>della del triangolo ADF eguale al conoide, e lo <lb/>scodellino del trilineo DAB eguale al cono DFE, <lb/>e perci&ograve; medesimo sar&agrave; il centro di gravit&agrave; della <lb/>scodella e del conoide; dello scodellino e del cono. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Tirisi l'applicata GL: aver&agrave; il rettangolo GIL, al quadralo AF, ra&shy;<lb/>gion composta di GI ad AF, ovvero di ID a DF, ovvero di OB a BF, e di <lb/>IL a FC, e, perch&egrave; sono uguali, diremo di BF alla BF. </s>

<s>Sta dunque il ret&shy;<lb/>tangolo GIL, al quadrato AF, come la OB alla BF, ovvero come il quadrato <lb/>OR al quadrato FA, e per&ograve; sono uguali il rettangolo GIL e il quadrato RO, <pb xlink:href="020/01/2709.jpg" pagenum="334"/>ossia l'armilla descritta da GI, e il circolo descritto da GO: e cos&igrave; essendo <lb/>di tutte le applicate, la scodella del triangolo ADF sar&agrave; uguale al conoide <lb/>parabolico, c. </s>

<s>d. </s>

<s>d. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Essendosi poi provata uguale l'armilla GI al quadrato RO, <emph type="italics"/>adde com&shy;<lb/>munem<emph.end type="italics"/> l'armilla IR, e sar&agrave; l'armilla GR uguale al quadrato IO. </s>

<s>Essendo <lb/>anco provato uguale l'armilla NQ al quadrato PT, <emph type="italics"/>deme communem<emph.end type="italics"/> l'ar&shy;<lb/>milla PQ, e resteranno uguali l'armilla NP, e il circolo QT. </s>

<s>Dunque sar&agrave; <lb/>la scodellina parabolica del trilineo uguale al cono DFE &rdquo; (ivi, fol. </s>

<s>69). </s></p><p type="main">

<s>Apparterrebbero a questo medesimo argomento alcune altre proposizioni, <lb/>scritte per dimostrare il centro di gravit&agrave; nei tronchi di cono scavati da un <lb/>cono solo o da pi&ugrave; coni: ma perch&egrave; le dimostrazioni conseguono da prin&shy;<lb/>cipii pi&ugrave; alti, che si po&rdot;ranno dal Torricelli a proposito dei centri di gravit&agrave; <lb/>dei solidi conoidali, le trascriveremo allora, per passar senza indugio alla se&shy;<lb/>conda parte promessa intorno a questo argomento, che &egrave; dei centri di gra&shy;<lb/>vit&agrave; nei solidi vasiformi. </s></p><p type="main">

<s><emph type="center"/>VII.<emph.end type="center"/></s></p><p type="main">

<s>Dicemmo che l'occasione al trattato nacque dal solido acuto iperbolico, <lb/>ingerendosi la fantasia a consigliar la Matematica severa di condiscendere tal&shy;<lb/>volta ai lusi dell'ingegno. </s>

<s>A chiunque infatti posi l'occhio sulla figura geo&shy;<lb/>metrica del detto solido acuto col suo asse verticale, si rappresenta, come si <lb/>rappresent&ograve; al Torricelli, l'immagine di un piede, che quasi aspetti di so&shy;<lb/>stener la coppa di un calice o di un bicchiere. </s>

<s>E perch&egrave; <emph type="italics"/>bicchiere<emph.end type="italics"/> era il <lb/>nome uscitogli pi&ugrave; volte di bocca, per chiamare que'solidi scavati, intorno <lb/>ai quali vedemmo come si fosse il nostro Autore esercitato, per ritrovarne <lb/>il centro gravitativo; sembrava dunque che la Geometria fosse, con le sue <lb/>proprie mani, venuta a lavorar lo strumento, per apparecchiare il convito <lb/>della Scienza. </s>

<s>Cos&igrave;, il calice, che il Torricelli pensava di porgere a Minerva <lb/>per celebrare i divini misteri, aveva per piede il solido acuto iperbolico, per <lb/>nodo una sfera, e per coppa ora una, ora un'altra figura di quelle varie, che <lb/>possono immaginarsi descritte dal rivolgersi iperbole con gli asintoti, e pa&shy;<lb/>rabole, e porzioni di ellissi e di circoli intorno ai loro proprii assi. </s>

<s>Il trat&shy;<lb/>tato nuovo veniva perci&ograve; a partecipare delle festosit&agrave; del ditirambo, e delle <lb/>grazie dell'idillio, come possono sentire i lettori infin dal primo presentarlo, <lb/>che il Torricelli stesso faceva all'amico suo Raffaello Magiotti, mentre que&shy;<lb/>sti, per fuggire i calori estivi di Roma, stavasi riparato all'ombra sui colli <lb/>tusculani. </s></p><p type="main">

<s>&ldquo; Erras, amice Magiotti, si speras in tusculanum collem seductus mea&shy;<lb/>rum effugere potuisse obsidionem ineptiarum. </s>

<s>Ecce enim persequor te quo&shy;<lb/>cumque fugis, solito molestiarum genere, nugis meis. </s>

<s>Libet exemplo tuo, qui <lb/>fusum parabolicum aliquando contemplari dignatus es, de Acu hyperbolica <pb xlink:href="020/01/2710.jpg" pagenum="335"/>quaedam dicere. </s>

<s>Utinam tibi libeat audire. </s>

<s>Contemplationem leges, in qua <lb/>fortasse acumen desiderabis, non autem in solido, cuius tanta subtilitas est <lb/>ut, quamvis in infinitam longitudinem producatur, exigui tamen cylindri mo&shy;<lb/>lem non excedat. </s>

<s>I nunc et procul recede: aculeum habet Geometria lon&shy;<lb/>giorem, quam tu ab ipso evadere possis. </s>

<s>Huius ego mucrone, non minus <lb/>subtili quam longo, eruditas et vere geometricas aures tuas non expungere <lb/>hesitabo. </s>

<s>Caeterum lege libenter hoc, quicquid est, mox enim videbis huius <lb/>contemplationis materiam, quae nunc cuspis est, meliore figura refusam in <lb/>calicem tantae capacitatis, ut sitim vel giganteam extinguere possit &rdquo; (ibid., <lb/>T. XXX, fol. </s>

<s>3). </s></p><p type="main">

<s>Di qui apparisce che lo scopo &egrave; principalmente quello di trovar, delle <lb/>varie coppe da soprapporre al pi&egrave; del calice, la grandezza e no il centro, di&shy;<lb/>cendo scherzevolmente al Magiotti che nel Luglio sitibondo, in cui scriveva, <lb/>metteva pi&ugrave; conto di ritrovar del bicchiere da rinfrescarsi le misure della <lb/>capacit&agrave;, che del peso. </s>

<s>Nonostante, s'indica anche delle varie coppe descritte <lb/>il luogo del baricentro, e bench&egrave; tutte l'abbiano in mezzo all'asse, era pur <lb/>necessario dimostrarlo per vie geometriche, come il Torricelli fa in quel suo <lb/>modo, sempre facile ed elegante, cosicch&egrave; par che chi legge, sedotto dal de&shy;<lb/>siderio di cogliere le rose, non senta pi&ugrave; la mano pungersi dalle spine. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma I.<emph.end type="italics"/> &mdash; Si fuerint tres lineae in continua proportione, erit ar&shy;<lb/>milla, sive differentia circulorum, quorum alter fit ex semisse aggregati, alter <lb/>vero ex semisse differentiae extremorum; aequalis circulo, qui fit ex media <lb/>proportionalium linearum. </s>

<s>&rdquo; <lb/><figure id="id.020.01.2710.1.jpg" xlink:href="020/01/2710/1.jpg"/></s></p><p type="caption">

<s>Figura 198.</s></p><p type="main">

<s>&ldquo; Sint tres lineae in continua ratione AB, BC, <lb/>BD (fig. </s>

<s>198), et ponantur extremae in directum ABD, <lb/>ipsa vero media BC erigatur in B ad angulos rectos. </s>

<s><lb/>Secta deinde AD bifariam in E, fiat ex ED, semisse <lb/>aggregati extremarum, circulus ACD. </s>

<s>Ex ipsa vero <lb/>EB, semisse differentiae extremarum, fiat circulus <lb/>FB. </s>

<s>Dico armillam AFCD aequale esse circulo ex BC, <lb/>tamquam semidiametro descripto. </s>

<s>Juncta enim EC <lb/>erit, ex XLVII Primi, et II Duodecimi, circulus ex EC <lb/>aequalis duobus simul circulis ex EB, et ex BC, ob angulum rectum EBC. </s>

<s><lb/>Dempto ergo communi circulo ex EB, remanebit armilla AFCD aequalis cir&shy;<lb/>culo ex BC, q&ugrave;od etc. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XXXIX. &mdash; <emph type="italics"/>Si hyperbola, una cum asymptotis, circa<emph.end type="italics"/><lb/><figure id="id.020.01.2710.2.jpg" xlink:href="020/01/2710/2.jpg"/></s></p><p type="caption">

<s>Figura 199.<lb/><emph type="italics"/>axem proprium convertatur, erit solidum <lb/>vasiforme, abscissum plano ad axem erecto, <lb/>aequale cylindro, qui eamdem cum solido <lb/>basim habeat, et eamdem altitudinem. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sit hyperbola, cuius axis AB (fig. </s>

<s>199), <lb/>asymptoti vero AC, AD, ipsa vero EF contin&shy;<lb/>gat sectionem in E, et convertatur figura circa <lb/>AB. </s>

<s>Supra circulo FG intelligatur cylindrus OFGI, et secetur solidum plano <pb xlink:href="020/01/2711.jpg" pagenum="336"/>quodcumque CD, ad axem erecto. </s>

<s>Dico solidum, quod <emph type="italics"/>Vasiformem hyperbo&shy;<lb/>licum<emph.end type="italics"/> appello, descriptum a revolutione quadrilinei CFEH, aequale esse cy&shy;<lb/>lindro FI, super eadem basi FG, et sub eadem altitudine EB. </s>

<s>Quia nam, ex <lb/>X Secundi Conicorum, in continua ratione sunt CH, FE, HD, erit armilla, quae <lb/>fit ex revolutione lineae CH, aequalis circulo ex FE, hoc est ex OB, et hoc <lb/>semper. </s>

<s>Quare erunt omnes simul armillae, hoc est solidum Vasiforme hyper&shy;<lb/>bolicum, aequales simul omnibus circulis, hoc est cylindro super eadem basi, <lb/>et sub eadem altitudine, quod etc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Ex hac propositione colligeretur mensura Conoidis hyper&shy;<lb/>bolici. </s>

<s>Notus enim est conus integer circumscriptus, prout conus, et notum <lb/>solidum vasiforme ablatum aequale cylindro: quare reliquum etiam conoidis <lb/>notum esset. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Item, centrum gravitatis eiusdem conoidis hyperbolici ex hac propo&shy;<lb/>sitione educeretur. </s>

<s>Centrum enim coni integri circumscripti notum est; cen&shy;<lb/>trum etiam solidi vasiformis in medio suo axe notum est. </s>

<s>Item, centrum parvi <lb/>coni FAG, quare notum esset centrum reliqui conoidis. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sed institutum nostrum est solum poculum metiri, et reliqua magnis <lb/>Geometris renuntiare. </s>

<s>Nihil enim nostra interest, adveniente iam canicula, <lb/>quantum ponderet ipsum poculum, sed quantum capiat. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE LX. &mdash; <emph type="italics"/>Si hyperbola cum asymptoto convertatur circa <lb/>axem coniugatum, erit solidum vasiforme, abscissum plano ad axem erecto, <lb/>aequale cylindro, qui eamdem cum solido basim habeat, eamdemque alti&shy;<lb/>tudinem. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sit hyperbola AB (fig. </s>

<s>200), cuius axis coniugatus DC, asymptotus <lb/>vero CE, et convertatur figura circa CD. </s>

<s>Intelligatur super circulo AH cy&shy;<lb/><figure id="id.020.01.2711.1.jpg" xlink:href="020/01/2711/1.jpg"/></s></p><p type="caption">

<s>Figura 200.<lb/>lindrus FAHG, et secetur solidum plano BI ad <lb/>axem erecto. </s>

<s>Dico solidum vasiforme, descriptum <lb/>a quadrilineo BACE, aequale esse cylindro AG <lb/>habenti basim AH, altitudinem vero CD. </s>

<s>Erunt <lb/>enim, per XI secundi Conicorum, in continua <lb/>ratione BE, CA, EI. Quare, per Lemma I, erit <lb/>armilla, descripta a linea BE, aequalis circulo <lb/>ex CA, sive ex DF, et hoc semper. </s>

<s>Quare erunt <lb/>omnes simul armillae, hoc est solidum vasiforme, aequales omnibus simul <lb/>circulis, hoc est cylindro AG, quod erat demonstrandum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Ex hac propositione totius solidi BAHI mensura, et cen&shy;<lb/>trum gravitatis daretur. </s>

<s>Solidum enim vasiforme quantitate notum est: item <lb/>inclusus conus ECK, ergo et totum solidum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Solidi vero vasiformis centrum gravitatis est in medio suo axe: cen&shy;<lb/>trum autem intercepti coni ECK notum est; quare et totius compositi solidi <lb/>centrum gravitatis daretur. </s>

<s>Sed nihil hoc ad nos qui, sitiente Julio, solam <lb/>calicis mensuram aextimamus. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma II.<emph.end type="italics"/> &mdash; Si fuerint duae parabolae aequales circa communem <lb/>axem AB (fig. </s>

<s>201), ducanturque ordinatim CD, EF, quarum CD sit per ver-<pb xlink:href="020/01/2712.jpg" pagenum="337"/>ticem inclusae parabolae, sed EF ubicumque, dummodo utranque parabolam <lb/>secet; dico esse ut EG ad CD, ita CD ad GF. </s>

<s>Ponatur enim AH latus rectum <lb/>commune, et erit, ob parabolam, rectangulum <lb/><figure id="id.020.01.2712.1.jpg" xlink:href="020/01/2712/1.jpg"/></s></p><p type="caption">

<s>Figura 201.<lb/>HAB aequale quadrato BE. </s>

<s>Si ergo ab aequa&shy;<lb/>libus aequalia demas, nempe rectangulum sub <lb/>AH, CB, ex rectangulo HAB, et quadratum <lb/>BG ex quadrato BE, quae remanent aequalia <lb/>erunt, nempe rectangulum HAC, sive quadra&shy;<lb/>tum CD, et rectangulum EGF. </s>

<s>Quare erit ut <lb/>EG ad CD, ita CD ad GF, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XLI. &mdash; <emph type="italics"/>Si fuerint duae <lb/>parabolae aequales circa communem axem, et convertatur figura, erit <lb/>solidum vasiforme descriptum aequale cylindro, eamdem basim cum so&shy;<lb/>lido, eamdemque altitudinem habenti. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sint circa communem axem AB, uti in praeced. </s>

<s>figura, duae para&shy;<lb/>bolae aequales DE, GC hoc est quarum latera recta sint aequalia, et ductis <lb/>ordinatim CD, BE, quarum CD tangat inclusam parabolam, BE vero secet, <lb/>convertatur figura circa axem AB. </s>

<s>Dico solidum vasiforme, descriptum a <lb/>quadrilineo EDCG, aequale esse cylindro, cuius basis sit circulus circa DO, <lb/>altitudo vero CB. &rdquo; </s></p><p type="main">

<s>&ldquo; Cum enim, per lemma praecedens, in continua ratione sint EG, DC, <lb/>GF, erit, per lemma I, armilla, ex linea EG descripta, aequalis circulo ex <lb/>DC, hoc est ex BH, et hoc semper. </s>

<s>Ergo omnes simul armillae, hoc est so&shy;<lb/><figure id="id.020.01.2712.2.jpg" xlink:href="020/01/2712/2.jpg"/></s></p><p type="caption">

<s>Figura 202.<lb/>lidum vasiforme parabolicum, aequales <lb/>erunt omnibus simul circulis, hoc est cy&shy;<lb/>lindro HDOL, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma III.<emph.end type="italics"/> &mdash; Si recta linea AB <lb/>(fig. </s>

<s>202) secetur inaequaliter bis in C <lb/>et D, ponaturque BE aequalis ipsi CA; erit rectangulum ADB, partium scili&shy;<lb/>cet minus inaequalium, aequale duobus simul rectangulis, nempe ACB, par&shy;<lb/>tium magis inaequalium, et rectangulo CDE sub intermediis sectionibus. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Secetur AB bifariam in I, et erunt aequales <lb/><figure id="id.020.01.2712.3.jpg" xlink:href="020/01/2712/3.jpg"/></s></p><p type="caption">

<s>Figura 203.<lb/>ipsae etiam IC, IE. Sed, cum rectangulum ADB, si&shy;<lb/>mul cum quadrato DI, aequale sit quadrato AI; item, <lb/>rectangulum ACB, cum quadrato CI, eidem quadrato <lb/>AI aequale sit; erunt rectangulum ADB, cum qua&shy;<lb/>drato DI, aequalia rectangulo ACB cum quadrato CI. </s>

<s><lb/>Commune auferatur quadratum DI, erit reliquum <lb/>rectangulum ADB aequale reliquis duobus rectan&shy;<lb/>gulis ACB, et CDE. </s>

<s>Si enim demas, ex quadralo CI, <lb/>quadratum DI, spatium quod relinquitur est rectan&shy;<lb/>gulum CDE. </s>

<s>Ergo constat propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma IV.<emph.end type="italics"/> &mdash; Si fuerint circa communem <lb/>axem AB (fig. </s>

<s>203), et circa idem contrum C, duo <pb xlink:href="020/01/2713.jpg" pagenum="338"/>ellipses similes, nempe ut DC ad CE, ita BC ad CF; ordinatimque ducantur <lb/>FH tangens, et IL secans inclusam ellipsim; dico ita esse IM ad HF, ut HF <lb/>ad ML. &rdquo; </s></p><p type="main">

<s>&ldquo; Est enim quadratum IN, ad quadratum DC, ut rectangulum BNA, ad <lb/>rectangulum BCA: hoc est, ut quadratum BC. </s>

<s>Sed DC quadratum, ad qua&shy;<lb/>dratum CE, est ut quadratum BC ad CF, et quadratum CE, ad quadratum <lb/>MN, est ut quadratum CF ad rectangulum ONF; quare ex aequo erit qua&shy;<lb/>dratum IN, ad quadrat&ugrave;m MN, ut rectangulum BNA, ad rectangulum FNO. &rdquo; </s></p><p type="main">

<s>&ldquo; Iterum, quadratum idem IN, ad quadratum HF, est ut rectangulum <lb/>idem BNA, ad rectangulum BFA. </s>

<s>Quare erit quadratum IN, ad duo simul <lb/>quadrata MN, HF, ut rectangulum BNA, ad duo simul rectangula FNO, BFA. </s>

<s><lb/>Sed rectangulum BNA, per lemma praecedens, duobus dictis rectangulis ae&shy;<lb/>quale est; ergo et quadratum IN duobus simul quadratis MN, HF aequale <lb/>erit. </s>

<s>Si ergo ab aequalibus commune auferas quadratum MN, reliquum re&shy;<lb/>ctangulum IML aequale erit reliquo quadrato HF. </s>

<s>Propterea patet propo&shy;<lb/>situm. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XLII. &mdash; <emph type="italics"/>Si fuerint circa communem axem CB, in <lb/>eadem figura, et circa idem centrum C, duo ellipses similes, et converta&shy;<lb/>tur figura circa axem; erit solidum vasiforme, factum a revolutione qua&shy;<lb/>drilinei DHFE, aequale cylindro eamdem ipso basi, eamdemque altitudinem <lb/>habenti. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Intelligatur enim super basi HP cylindrus HQ, et planum DR ad axem <lb/>erectum. </s>

<s>Erunt itaque, per lemma praecedens, DE, HF, ER in continua ra&shy;<lb/>tione. </s>

<s>Quare, per Lemma I, erit armilla ex DE descripta aequalis circulo ex <lb/>HF, vel ex CS, et hoc semper. </s>

<s>Quare erunt omnes simul armillae aequa&shy;<lb/>les omnibus simul circulis, nempe solidum vasiforme ellipticum aequale cy&shy;<lb/>lindro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XLIII. &mdash; <emph type="italics"/>Si intra parallelogrammum rectangulum <lb/>ABCD<emph.end type="italics"/> (fig. </s>

<s>204) <emph type="italics"/>sit quadrans ellipsis DB, et convertatur figura circa al&shy;<lb/>terutrum vel AB vel AD; erit solidum vasiforme, factum a trilineo BDC,<emph.end type="italics"/><lb/><figure id="id.020.01.2713.1.jpg" xlink:href="020/01/2713/1.jpg"/></s></p><p type="caption">

<s>Figura 204.<lb/><emph type="italics"/>acquale cono CAH eamdem ipsi basim, eamdemque <lb/>altitudinem habenti. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Agatur enim planum EF ad axem erectum, <lb/>ponaturque BO axis integrae ellipsis. </s>

<s>Quadratum EI, <lb/>vel DA, ad quadratum LI, est ut quadratum BA, <lb/>ad rectangulum BIO. </s>

<s>Quadratum iterum EI, vel CB. <lb/>ad quadratum MI, est ut quadratum BA, ad qua&shy;<lb/>dratum IA. </s>

<s>Quare erit idem quadratum EI, ad duo <lb/>simul quadrata LI, MI, ut quadratum BA, ad duo <lb/>simul spatia: rectangulum scilicet BIO et quadra&shy;<lb/>tum IA. </s>

<s>Sed quadratum BA aequale est dictis duo&shy;<lb/>bus spatiis, ergo et quadratum EI aequale erit duo&shy;<lb/>bus quadratis LI, MI. </s>

<s>Dempto autem communi quadrato LI, erit reliquum <lb/>rectangulum ELF aequale quadrato MI. </s>

<s>Constat igitur, per Lemma I, armil-<pb xlink:href="020/01/2714.jpg" pagenum="339"/>lam, a linea EL dascriptam, aequalem esse circulo ex MI, et hoc semper. </s>

<s><lb/>Propterea erunt omnes simul armillae aequales omnibus simul circulis, nempe <lb/>solidum vasiforme aequale cono, quod etc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Hinc deduci posset sphaeroidem ut sphaeram circum&shy;<lb/>scripti sibi cylindri sexquialteram esse. </s>

<s>Centrum etiam gravitatis, quod in <lb/>hemisphaerio et portionibus sphaerae reperit Lucas Valerius, eodem progressu <lb/>erueretur in hemisphaeroide, eiusque portionibus. <lb/><figure id="id.020.01.2714.1.jpg" xlink:href="020/01/2714/1.jpg"/></s></p><p type="caption">

<s>Figura 205.<lb/>Sed tanti non est minuta haec omnia prosequi ut <lb/>inceptum poculum deseramus. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XLIV. &mdash; <emph type="italics"/>Si fuerit in quadrato <lb/>ABCD<emph.end type="italics"/> (fig. </s>

<s>205) <emph type="italics"/>quadrans circuli DB, et conver&shy;<lb/>tatur figura circa AB; erit solidum vasiforme, de&shy;<lb/>scriptum a trilineo BDC, aequale cono CAE eam&shy;<lb/>dem ipsi basim, eamdemque altitudinem habenti. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Agatur enim planum FH ad axem erectum, et ducatur IL parallela <lb/>ad AB. </s>

<s>Erit igitur rectangulum FIH, hoc est DLM, aequale quadrato LI, <lb/>propter circulum, sive quadrato AO, sive OP, et per Lemma I erit armilla, <lb/>a linea FI descripta, aequalis circulo ex OP, et hoc semper. </s>

<s>Propterea erunt <lb/>omnes armillae simul aequales omnibus simul circulis, nempe solidum va&shy;<lb/>siforme aequale cono praedicto, quod erat etc. </s>

<s>&rdquo; <lb/><figure id="id.020.01.2714.2.jpg" xlink:href="020/01/2714/2.jpg"/></s></p><p type="caption">

<s>Figura 206.</s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Lucas Valerius, Galileus et alii <lb/>demonstrant hanc eamdem propositionem. </s>

<s>Nos, quia <lb/>facit ad rem nostram, illam desumpsimus nostroque <lb/>modo demonstravimus. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma V.<emph.end type="italics"/> &mdash; Si fuerint circa idem centrum <lb/>A (fig. </s>

<s>206) duo circuli, et BC tangat inclusam pe&shy;<lb/>ripheriam, DE vero secet; dico esse, ut DI ad BC, <lb/>ita BC ad IE. &rdquo; </s></p><p type="main">

<s>&ldquo; Ducatur enim altera tangens ML per pun&shy;<lb/>ctum I: eruntque aequales inter se MI, IL, BC, cum <lb/>circuli sint concentrici. </s>

<s>Erit igitur rectangulum DIE aequale rectangulo MIL, <lb/>secant enim se intra circulum, hoc est quadrato MI, sive BC. </s>

<s>Quare constat <lb/>propositum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XLV. &mdash; <emph type="italics"/>Si fuerint circa idem centrum A<emph.end type="italics"/> (fig. </s>

<s>207) <lb/><emph type="italics"/>duo circuli, et ductis BC, DE parallelis, ipsa BC tangat interiorem peri&shy;<lb/>pheriam, ipsa vero DE secet, et circa CE axem<emph.end type="italics"/><lb/><figure id="id.020.01.2714.3.jpg" xlink:href="020/01/2714/3.jpg"/></s></p><p type="caption">

<s>Figura 207.<lb/><emph type="italics"/>convertatur figura; dico salidum vasiforme, quod <lb/>a quadrilineo DBCF describitur, aequale esse <lb/>cylindro eamdem ipsi basim, eamdemque alti&shy;<lb/>tudinem habenti. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Concipiatur enim cylindrus, uti dictum est, <lb/>IBHL: et quia, per Lemma praecedens, sunt in <lb/>continua ratione DF, BC, FM, erit, per Lemma I, armilla, descripta a linea <lb/>DF, aequalis circulo ex BC, sive ex EI, et hoc semper. </s>

<s>Propterea erunt <pb xlink:href="020/01/2715.jpg" pagenum="340"/>omnes simul armillae aequales omnibus simul circulis, hoc est solidum va&shy;<lb/>siforme sphaericum aequale cylindro praedicto, quod etc. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. XXX, fol. </s>

<s>18-25). </s></p><p type="main">

<s><emph type="center"/>VIII.<emph.end type="center"/></s></p><p type="main">

<s>Il trattatello elegante della stereometria e della baricentrica dei solidi <lb/>vasiformi, di cui abbiamo dal manoscritto torricelliano scelto i teoremi prin&shy;<lb/>cipali, s'incontrava in qualche parte nelle medesime cose dimostrate da al&shy;<lb/>tri, come dal Commandino, dal Valerio e dal Galileo; ma il Torricelli faceva <lb/>notare che le sue dimostrazioni procedevano in modo nuovo, e che si face&shy;<lb/>vano derivare da principii pi&ugrave; generali, comprendenti in una somma unit&agrave; <lb/>i vari casi particolari. </s>

<s>Si compiaceva di ci&ograve; molto a ragione il Nostro, perch&egrave; <lb/>il merito della novit&agrave; non consisteva semplicemente nel compendiare, o nel <lb/>ridurre a maggior facilit&agrave; le cose da trattarsi, ma nel premostrare ai Mate&shy;<lb/>matici quel vigore potente, che si verrebbe a infondere nella Scienza dal li&shy;<lb/>bero uso dell'analisi, applicata al Metodo degli indivisibili in quel che si <lb/>chiamerebbe poi Calcolo differenziale. </s>

<s>Un esempio di ci&ograve; l'aveva lo stesso <lb/>Torricelli dato a proposito del centro di gravit&agrave; nella sfera, comunque ella <lb/>venisse ridotta o in segmenti o in frusti, e lo udimmo poco fa quasi com&shy;<lb/>passionare il Valerio, per non essersi accorto che la fatica del ritessere tante <lb/>volte il viaggio potevasi risparmiare movendo a dirittura dal suo primo prin&shy;<lb/>cipio. </s>

<s>Un altro simile incomodo, di divagar nei particolari senz'aver ricono&shy;<lb/>sciuta la generalit&agrave;, nella quale potevano tutti esser compresi, ebbe a notarla <lb/>nell'argomento del centro di gravit&agrave; dei solidi conoidali, intorno a che il <lb/>Valerio e Galileo avevano sudato tanto, per dimostrare alcune proposizioni, ri&shy;<lb/>maste ne'loro libri come membra sparse e inerti, perch&egrave; non ricongiunte a <lb/>quel principio, che avrebbe dovuto in esse far refluire la vita. </s></p><p type="main">

<s>Nel numero dei Problemi, proposti e passati scambievolmente tra i ma&shy;<lb/>tematici di Francia, il Torricelli racconta di aver messo anche questo: &ldquo; Se <lb/>sar&agrave; il solido CFAHD (fig. </s>

<s>208), nato dalla rivoluzione di una sezione conica, <lb/>o sia perabola o iperbola o porzione di circolo, ovvero di ellisse, e sia tirato il <lb/><figure id="id.020.01.2715.1.jpg" xlink:href="020/01/2715/1.jpg"/></s></p><p type="caption">

<s>Figura 208.<lb/>piano FH parallelo alla base CD, e che seghi per <lb/>mezzo l'asse nel punto E; chiameremo il cerchio <lb/>FH media sezione, e intorno a ci&ograve; si dimostrarono <lb/>e si proposero i due teoremi seguenti: I. </s>

<s>Il solido <lb/>predetto, al suo cono inscritto, sar&agrave; come una sua <lb/>base, con quattro medie sezioni, e due sue basi. </s>

<s><lb/>II. </s>

<s>Ma facendosi come una base, con due medie <lb/>sezioni, a due medie sezioni, cos&igrave; la retta AO alla <lb/>OB; sar&agrave; il punto O centro di gravit&agrave; di quel tale solido. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Nella prima di queste due enunciazioni sta compendiata &ugrave;na gran <pb xlink:href="020/01/2716.jpg" pagenum="341"/>parte delle dottrine di Archimede, cio&egrave; la sostanza principale delli libri <emph type="italics"/>De <lb/>sphaera et cylindro,<emph.end type="italics"/> et <emph type="italics"/>De sphaer. </s>

<s>et conoidibus:<emph.end type="italics"/> nella seconda poi sta gran&shy;<lb/>dissima parte della dottrina di Luca Valerio, del Commandino e del Galileo, <lb/>i quali, con numero grandissimo di proposizioni, hanno cercato i centri di <lb/>gravit&agrave; nei solidi delle sezioni coniche, i quali da noi in una sola proposi&shy;<lb/>zione sono stati ristretti. </s>

<s>L'uno e l'altro dei predetti teoremi si dimostra <lb/>con una sola dimostrazione. </s>

<s>La proposta fu lodata in Francia, ma non gi&agrave; <lb/>sciolta, ed io qualche anno dopo conferii la dimostrazione con gli amici d'Ita&shy;<lb/>lia &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXII, fol. </s>

<s>25). Uno de'q&ugrave;ali amici, e de'primi, <lb/>dee essere stato il Michelini, a cui, il di 3 Febbraio 1642, annunziava, in&shy;<lb/>sieme col teorema centrobarico generale del Guldin, anche i due sopra nar&shy;<lb/>rati, chiamandoli <emph type="italics"/>nuovi preconizzati dal miracoloso fra Bonaventura:<emph.end type="italics"/> e <lb/>in che modo s'avverasse il preconio lo diranno i seguenti tratti di storia. </s></p><p type="main">

<s>Riuscito a quella inaspettata trasformazione del solido descritto dal bi&shy;<lb/>lineo (nato in un segmento di circolo, a cui sia <lb/><figure id="id.020.01.2716.1.jpg" xlink:href="020/01/2716/1.jpg"/></s></p><p type="caption">

<s>Figura 209.<lb/>stato inscritto un triangolo), in una certa sfe&shy;<lb/>roide, come si vide in principio del paragrafo VI <lb/>del presente capitolo; il Torricelli presenti che <lb/>forse le medesime cose s'avveravano qualunque <lb/>fosse la sezione conica generatrice del solido <lb/>rotondo, come infatti poi dimostr&ograve; aiutandosi <lb/>di questo lemma: &ldquo; Se in una sezione conica <lb/>qualunque linea AB (fig. </s>

<s>209), terminata da <lb/>ambe le parti nella sezione, segher&agrave; due linee <lb/>rette parallele CD, EF, terminanti parimente nella sezione; il rettangolo CGD, <lb/>al rettangolo EHF, sar&agrave; come il rettangolo AGB al rettangolo AHB &rdquo; (ivi, <lb/>T. XL, fol. </s>

<s>26). </s></p><p type="main">

<s>Per la dimostrazione si cita il libro archimedeo <emph type="italics"/>De conoid. </s>

<s>et sphaer.,<emph.end type="italics"/><lb/>dalle proposizioni XIII, XIV e XV del quale resulta che, condotta la tan&shy;<lb/>gente IL, parallela ad AB, e la ML parallela ad EF, i rettangoli CGD, EHF, <lb/><figure id="id.020.01.2716.2.jpg" xlink:href="020/01/2716/2.jpg"/></s></p><p type="caption">

<s>Figura 210.<lb/>e parimente i rettangoli AGB, AHB stanno <lb/>come i quadrati ML, LI: d'onde immedia&shy;<lb/>tamente si conclude il proposito, che cio&egrave; <lb/>quegli stessi quattro rettangoli sono in pro&shy;<lb/>porzione fra loro. </s>

<s>Dietro ci&ograve; passava cos&igrave; il <lb/>Torricelli a proporre, e a dimostrare il di&shy;<lb/>vinato teorema: </s></p><p type="main">

<s>&ldquo; Sia una sezione di cono, il cui asse <lb/>AB (fig. </s>

<s>210), triangolo inscritto CAD, e gi&shy;<lb/>risi la figura: dico che il residuo del solido, levatone il cono inscritto, sar&agrave; <lb/>uguale ad una tale sferoide, il cui asse sia AB. &rdquo; </s></p><p type="main">

<s>&ldquo; Sia il quadrato FB doppio al quadrato BC, e congiunta AF seghi la <lb/>sezione in E, ed applicata EG facciasi, per li punti A, I, B, una ellisse in&shy;<lb/>torno all'asse AB, e girisi, Intendasi poi la figura segata con un piano LP <pb xlink:href="020/01/2717.jpg" pagenum="342"/>parallelo alla base. </s>

<s>Essendo ora il quadrato FB doppio del BC, sar&agrave; EG dop&shy;<lb/>pio del GI, e per&ograve; il rettangolo EIH eguale al quadrato IG, e per&ograve; l'armilla <lb/>EI eguale al cerchio IG. </s>

<s>Ma l'armilla LM, all'armilla EI, sta come il ret&shy;<lb/>tangolo LMP al rettangolo EIH, ovvero, per il lemma precedente, come il <lb/>rettangolo CMA al rettangolo CIA, cio&egrave;, come il rettangolo BOA al rettan&shy;<lb/>golo BGA, cio&egrave; come il quadrato ON al quadrato GI. </s>

<s>Ma i conseguenti sono <lb/>uguali, per&ograve; anche gli antecedenti, cio&egrave; l'armilla LM sar&agrave; uguale al cerchio <lb/>ON, et sic semper, ergo patet propositum &rdquo; (ivi). </s></p><p type="main">

<s>Cos&igrave;, il conoide si veniva a risolvere in due figure, delle quali era nota <lb/>la stereometria, e si poteva con gran facilit&agrave;, componendo, ricavarne la pro&shy;<lb/>porzione di tutto il solido a una delle sue parti componenti, come per esem&shy;<lb/>pio al cono inscritto, intorno a che il Torricelli si proponeva di dimostrare: <lb/>&ldquo; Se sar&agrave; una porzione di sfera o sferoide, ovvero conoide parabolico, op&shy;<lb/>pure iperbolico, di cui asse sia AB (nella figura 208 qui poco addietro) e <lb/>cono inscritto CAD, e dal mezzo dell'asse sia applicata la EF; dico che tutto <lb/>il solido al cono sta come il quadrato FE, col quadrato EG, al doppio del <lb/>quadrato EG &rdquo; (ivi). </s></p><p type="main">

<s>Per la dimostrazione supponesi un lemma, taciuto dall'Autore per al&shy;<lb/>cune ragioni, che appariranno in seguito da questa intima storia svelate, ma <lb/>intanto quel lemma &egrave; tale: <emph type="italics"/>La sferoide &egrave; doppia del rombo solido inscritto,<emph.end type="italics"/><lb/>verit&agrave;, che si conclude per corollario immediato dalla XXIX archimedea <emph type="italics"/>De <lb/>conoid. </s>

<s>et sphaer.,<emph.end type="italics"/> semplicemente osservando che, se le due emisferoidi sono <lb/>uguali ciascuna al doppio del cono inscritto, sar&agrave; la sferoide intera uguale <lb/>al doppio del rombo solido, composto di quegli stessi due coni, la misura dei <lb/>quali essendo AB.<foreign lang="greek">p</foreign>GE2/3=AB.<foreign lang="greek">p</foreign>FG.GH/3, sar&agrave; perci&ograve; AB.2<foreign lang="greek">p</foreign>.FG.GH/3 <lb/>la misura della sferoide o del bilineo, che chiameremo Bo, tra il quale e <lb/>Co, che vuol dire il cono CAD inscritto e misurato da AB.<foreign lang="greek">p</foreign>CB2/3; interce&shy;<lb/>der&agrave; la proporzione Bo:Co=2FG.GH:CB2, la quale, per essere CB= <lb/>2EG, e perci&ograve; CB2=4EG, sostituendo, <emph type="italics"/>et sumptis dimidiis,<emph.end type="italics"/> si trasformer&agrave; <lb/>in quest'altra Bo:Co=FG.GH:2EG2. </s>

<s>Poi, componendo, e osservando che <lb/>il bilineo insieme col cono compongono tutto il solido So, avremo So:Co= <lb/>FG.GH+2EG2:2EG2. </s>

<s>Sostituendo in fine, in luogo del rettangolo, la diffe&shy;<lb/>renza de'quadrati espressa da FE2&mdash;EG2, avremo So:Co=FE2+EG2:2 ES2, <lb/>come concisamente viene il Torricelli a dimostrare cos&igrave;, col suo proprio di&shy;<lb/>scorso: </s></p><p type="main">

<s>&ldquo; Il solido descritto dal bilineo CFA gi&agrave; &egrave; uguale ad una sferoide, il <lb/>cui asse sia BA, ed il cui massimo cerchio sia uguale all'armilla FG, ovvero, <lb/>risolvendo la sferoide in cono, &egrave; uguale ad un cono, la cui altezza sia BA, <lb/>ed il quadrato del semidiametro della base fosse due rettangoli FG.GH, <lb/>perch&egrave; allora la base del cono sar&agrave; doppia dell'armilla FG, e per&ograve; doppia <lb/>del massimo cerchio della sferoide. </s>

<s>Dunque il solido del detto bilineo CFA, <lb/>al cono inscritto, sta come due rettangoli FG.GH al quadrato CB, cio&egrave; a <pb xlink:href="020/01/2718.jpg" pagenum="343"/>quattro quadrati EG: ovvero <emph type="italics"/>sumptis dimidiis,<emph.end type="italics"/> come il rettangolo FGH a <lb/>due quadrati GE. <emph type="italics"/>Et componendo patet propositum &rdquo;<emph.end type="italics"/> (ivi). </s></p><p type="main">

<s>Nel <emph type="italics"/>Ra&cacute;conto<emph.end type="italics"/> dei problemi proposti ai Matematici francesi udimmo dianzi <lb/>il teorema formulato dal Torricelli in altra maniera, alla quale &egrave; facile ri&shy;<lb/>durre questa, ora espressa dalla relazione So:Co=FE2+EG2:2EG2, <lb/>perch'essendo EG=CB/2, sostituendo, e moltiplicando per <foreign lang="greek">p</foreign>, avremo So:Co= <lb/><foreign lang="greek">p</foreign>FE2+<foreign lang="greek">p</foreign>CB2/4:CB2/2=<foreign lang="greek">p</foreign>CB2+4<foreign lang="greek">p</foreign>FE2:2<foreign lang="greek">p</foreign>CB2, che vuol dire appunto, <lb/>rammemorandoci che la FE sega l'asse nel mezzo, stare il solido al cono <lb/>inscritto come una sua base, con quattro medie sezioni, a due basi. </s></p><p type="main">

<s>Udimmo pure, in quel Racconto, il Torricelli compiacersi di avere in <lb/>questo suo teorema compendiata una gran parte delle dottrine di Archimede, <lb/>per conferma di che, specialmente contro i dubitanti della verit&agrave; delle con&shy;<lb/>clusioni, alle quali conduceva il metodo del Cavalieri; faceva notare come il <lb/>detto teorema universalissimo, applicato ai vari casi particolari, concordava <lb/>con le proposizioni dimostrate ne'libri <emph type="italics"/>De sphaera et cylindro,<emph.end type="italics"/> e <emph type="italics"/>De conoid. </s>

<s><lb/>et sphaeralibus.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto conoides parabolicum CFAHD (nella medesima figura 298), conus <lb/>inscriptus CAD, axis AB sectus bifariam in E, et applicata EF. </s>

<s>Dixi conoi&shy;<lb/>des ad conum esse ut duo quadrata ex EF, EG, ad duplum quadrati EG, ut <lb/>ostensum est. </s>

<s>Dico convenire cum Archimedis XXIII <emph type="italics"/>De con. </s>

<s>et spaer.<emph.end type="italics"/> Pona&shy;<lb/>tur enim quadratum EF esse ut duo: erit AD ut quatuor, et ideo EG ut <lb/>unum. </s>

<s>Quare, componendo sumptisque consequentium duplis, erit quadratum <lb/>FE, cum quadrato EG, ad duo quadrata ex EG, ut 3 ad duo. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Che la proposizione universalissima concordi con quella della Sfera, <lb/>et con la XXIX De con. </s>

<s>et spaer.:<emph.end type="italics"/> Sit hemisphaerium, vel hemisphaeroides <lb/>ABC (fig. </s>

<s>211), conus inscriptus ABC, axis BD sectus <lb/><figure id="id.020.01.2718.1.jpg" xlink:href="020/01/2718/1.jpg"/></s></p><p type="caption">

<s>Figura 211.<lb/>sit bifariam in E, et applicata EF. </s>

<s>Dixi hemisphaerium <lb/>ad conum inscriptum esse ut duo quadrata ex FE et ex <lb/>EG, ad duplum quadrati EG. </s>

<s>Probo convenire cum Ar&shy;<lb/>chimede. </s>

<s>Esto axis integer BH, ponaturque quadratum <lb/>FE esse 3. Quadratum FE, ad quadratum AD, est ut <lb/>rectangulum BFH, ad rectangulum BDH, nempe ut <lb/>3 ad 4. Quadratum vero AD ad EG est ut 4 ad 1. Ergo <lb/>ex aequo quadratum FE, ad EG, est ut 3 ad 1. Ergo, <lb/>componendo, sumptisque consequentium duplis, patet duo quadrata FE, EG, <lb/>ad duo quadrata EG, esse ut 4 ad 2 &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXX, fol. </s>

<s>184). </s></p><p type="main">

<s>Soggiunse il Torricelli a queste due un'altra Nota, per provar <emph type="italics"/>che la <lb/>dimostrazione universalissima, nel conoide iperbolico e nella porzion di <lb/>sferoide, concordi con la volgata di Archimede XXVII e XXXI De conoid. </s>

<s><lb/>et sphaer.<emph.end type="italics"/> (ivi). Rappresenti AIBC (fig. </s>

<s>212) una delle iperbole, l'asse DB <lb/>della quale sia prolungato infino a incontrare in E il vertice dell'altra iper&shy;<lb/>bola. </s>

<s>Sia L il centro, ed EO uguale ad EL, cosicch&egrave; insomma sia BO ses-<pb xlink:href="020/01/2719.jpg" pagenum="344"/>quialtera della BE, ossia quella stia a questa come tre a due. </s>

<s>Chiamato S <lb/><figure id="id.020.01.2719.1.jpg" xlink:href="020/01/2719/1.jpg"/></s></p><p type="caption">

<s>Figura 212.<lb/>il solido, C il cono inscritto, dimostra nella <lb/><figure id="id.020.01.2719.2.jpg" xlink:href="020/01/2719/2.jpg"/></s></p><p type="caption">

<s>Figura 213.<lb/>detta XXVII Archimede che So:Co= <lb/>OD:DE. </s></p><p type="main">

<s>Rappresenti in simil guisa AIBC (fi&shy;<lb/>gura 213) una porzion di sferoide, l'asse BE <lb/>della quale sia prolungato in fin tanto che, <lb/>giunto in O, la BO non sia, come dianzi, <lb/>sesquialtera della BE. </s>

<s>Dimostra Archimede, <lb/>nella XXXI del libro citato, che il solido <lb/>al cono &ldquo; hanc habet rationem, quam li&shy;<lb/>nea composita ex dimidio axe sphaeroidis, <lb/>et ex axe maioris portionis, habet ad axem <lb/>maioris portionis &rdquo; (Opera cit., pag. </s>

<s>322), ossia si dimostra So:Co= <lb/>BE/2+ED:ED. </s>

<s>Ma &egrave; facile vedere ch'essendo per supposizione OB= <lb/>3/2 BE, OD=OB&mdash;BD=OB&mdash;BE+ED=3/2 BE&mdash;BE+ED= <lb/>BE/2+ED: onde in ambedue i casi bast&ograve; al Torricelli di dimostrar che la <lb/>proporzione So:Co=OD:DE di Archimede concordava con la sua, come <lb/>egli fece cos&igrave; scrivendo: </s></p><p type="main">

<s>&ldquo; Abbiamo provato che il solido tutto, al cono inscritto, sta come i due <lb/>quadrati insieme IG, GH al doppio del quadrato GH. </s>

<s>Mostrer&ograve; ora che li due <lb/>quadrati IG, GH, al doppio del quadrato GH, sono come la OD alla DE, <lb/>presa OB sesquialtera di BE. &rdquo; </s></p><p type="main">

<s>&ldquo; Il quadrato IG, al quadrato AD, sta come il rettangolo EGB al ret&shy;<lb/>tangolo EDB, <emph type="italics"/>et sumptis consequentium subquadruplis,<emph.end type="italics"/> il quadrato IG, al <lb/>quadrato GH, sta come il rettangolo EGB al rettangolo LGB, ovvero come <lb/>la retta EG alla GL. E, componendo, il quadrato IG, con il quadrato GH, al <lb/>quadrato GH, sta come EG con GL alla GL, cio&egrave; come OD alla GL. <emph type="italics"/>Et <lb/>sumptis consequentium duplis,<emph.end type="italics"/> il quadrato IG, col quadrato GH, al doppio <lb/>del quadrato GH, sta come la retta OD alla DE, <expan abbr="q.">que</expan> e. </s>

<s>d. (ivi, fol. </s>

<s>186). </s></p><p type="main">

<s>La principale intenzione del Torricelli per&ograve; era quella di applicare cos&igrave; <lb/>fatte questioni stereometriche alla Baricentrica, ci&ograve; che, ritornando al primo <lb/>proposito e alla rappresentazione di lui nella figura 208, si conseguir&agrave; col <lb/>dire che, costituitosi sopra l'asse un punto O, in modo che sia BO:OE= <lb/>FE2:GE2, sarebbe in quello stesso punto O il centro di gravit&agrave; del tutto. <lb/>&ldquo; Iisdem positis dico, si fiat ut quadratum FE, ad quadratum EG, ita BO <lb/>ad OE; dico, inquam, O esse centrum gravitatis totius solidi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Secetur BE bifariam in I: eritque I centrum gravitatis coni inscri&shy;<lb/>pti. </s>

<s>Centrum autem reliqui solidi, dempto cono, est in medio axe, quando&shy;<lb/>quidem demonstratum est singulas eiusdem solidi armillas aequales esse sin&shy;<lb/>gulis circulis unius sphaeroidis, circa axem AB constitutae. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Jam BO ad OE est ut quadratum FE ad quadratum EG. Et, com-<pb xlink:href="020/01/2720.jpg" pagenum="345"/>ponendo, erit BE ad EO ut quadrata FE, EG, ad quadratum EG, vel ut duo <lb/>quadrata FE, cum duobus EG, ad duo quadrata EG. </s>

<s>Sumptisque anteceden&shy;<lb/>tium dimidiis, erit IE ad EO ut quadratum FE, cum quadrato EG, ad duo <lb/>quadrata EG: nempe ut totum solidum ad conum inscriptum. </s>

<s>Puncta vero <lb/>I, E sunt centra partium, ergo O erit centrum totius &rdquo; (ivi, T. XL, fol. </s>

<s>27). </s></p><p type="main">

<s>Nel Racconto de'problemi ai Francesi era questo teorema, come si ram&shy;<lb/>menteranno i Lettori, formulato altrimenti, ond'&egrave; che, a mostrarne la con&shy;<lb/>cordanza, il Torricelli stesso cos&igrave; ragionava: &ldquo; Esto BE ad OE ut quadra&shy;<lb/>tum FE ad EG. Ergo, componendo, BE ad EO erit ut quadrata FE, EG ad <lb/>quadratum EG. Convertendo, OE ad EA ut quadratum EG ad duo quadrata <lb/>FE, EG. Et, componendo, AO ad AE ut quadrata EG, FE, EG ad duo qua&shy;<lb/>drata FE, EG. </s>

<s>Sumptis vero consequentium duplis, erit OA ad AB ut qua&shy;<lb/>drata EG, EG, FE ad quadrata EG, EG; FE, FE. </s>

<s>Et convertendo erit BA <lb/>ad AO ut quadrata EG, EG; FE, FE, ad quadrata EG, EG; FE &rdquo; (ivi, <lb/>T. XXXVI, fol. </s>

<s>219), ossia, facendo uso dei segni analitici, BA:AO= <lb/>2GE2+2FE2:2EG2+FE2. </s>

<s>Dividendo, riducendo e trasponendo, AO:BO= <lb/>2EG2+FE2:FE2=4<foreign lang="greek">p</foreign>EG2+.2<foreign lang="greek">p</foreign>FE2:2<foreign lang="greek">p</foreign>FE2=<foreign lang="greek">p</foreign>CB2+2<foreign lang="greek">p</foreign>FE2:2<foreign lang="greek">p</foreign>FE. </s>

<s><lb/>Alla qual riduzione accennava cos&igrave; lo stesso Torricelli: &ldquo; Nota che AO ad OB <lb/>sta come quattro quadrati EG, con due quadrati FE, a due quadrati FE: <lb/>ovvero, come il quadrato CB, con due quadrati FE, a due quadrati FE: cio&egrave;, <lb/>ed &egrave; il mio intento, come un cerchio CD, con due FH, a due FH &rdquo; (ivi): <lb/>a seconda del quale intento aveva stabilito di formulare cos&igrave; quella che, dopo <lb/>le altre da noi scritte, era in ordine la </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XLVI. &mdash; <emph type="italics"/>Centrum gravitatis cuiuscumque conoidalis, <lb/>verticem habentis, dividit axem solidi, ita ut pars ad verticem terminata, <lb/>ad reliquam, sit ut basis solidi, cum duobus circulis qui axem bifariam <lb/>secant, ad duos circulos, qui axem bifariam secant &rdquo;<emph.end type="italics"/> (ivi, T. XXV, fol. </s>

<s>58). </s></p><p type="main">

<s>Essendo dunque AB l'asse del conoide, con l'una estremit&agrave; A al ver&shy;<lb/>tice, e con l'altra B alla base, e chiamato B il circolo di essa base, S quello <lb/>della media sezione, il punto O, dove riesce il centro di gravit&agrave; del solido, <lb/>sar&agrave; indicato dalla relazione AO/BO=(B+2S)/2S. </s>

<s>Con ci&ograve; poneva il Torricelli <lb/>il fondamento alla nuova baricentrica dei conoidei, ai progressi della quale <lb/>gli soccorreva opportuna un'altra proposizione stereometrica, suggeritagli da <lb/>Michelangiolo Ricci. </s>

<s>Gli scriveva questi da Roma una lettera, nel di 16 Gen&shy;<lb/>naio 1644, per descrivergli il modo com'aveva dimostrato che un frusto co&shy;<lb/>nico, toltine due coni appuntati insieme sull'asse, fosse uguale a un terzo <lb/>cono, che avesse per base la superficie laterale involgente il solido intero, e <lb/>per altezza la perpendicolare, condotta dal vertice comune ai due detti coni <lb/>sopra uno degli apotemi del frusto. </s>

<s>Nel processo della dimostrazione s'in&shy;<lb/>voca pi&ugrave; volte un teorema, non con altro segno indicato che di un asteri&shy;<lb/>sco, intorno al quale teorema il Ricci stesso cos&igrave; si dichiarava: &ldquo; Devo solo <lb/>avvertire V. S. che, dove vedr&agrave; questo asterisco, denota il bisogno di una <lb/>proposizione, che mi trovo aver dimostrata in tre maniere, della quale feci <pb xlink:href="020/01/2721.jpg" pagenum="346"/>a V. S. un cenno questa Pasqua passata: cio&egrave; che il frusto conico &egrave; uguale <lb/>a tre coni, che abbiano la medesima altezza del frusto, ma che due basi siano <lb/>le medesime che del frusto, e l'altra del terzo cono sia media proporzionale <lb/>tra quelle &rdquo; (ivi, T. XLII, fol. </s>

<s>3). </s></p><p type="main">

<s>In un'altra lettera, scritta pur da Roma il di 18 Giugno di quel me&shy;<lb/>desimo anno, nella quale il Ricci stesso trascriveva una sua proposizione in&shy;<lb/>torno ai frusti parabolici, iperbolici, etc., come si vedr&agrave; meglio altrove; diceva <lb/>al Torricelli di essersi valuto di quel medesimo teorema, in cui risolveva lo <lb/>stesso frusto in tre coni, ma non resulta, n&egrave; di qui, n&egrave; da altre carte ca&shy;<lb/>duteci sott'occhio, che ne comunicasse la dimostrazione all'amico, il quale <lb/>ebbe a ritrovarla da s&egrave;, senz'alcuna difficolt&agrave;, aiutandosi dei due lemmi se&shy;<lb/>guenti: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma I.<emph.end type="italics"/> &mdash; Si a circulo duo circuli demantur, ita ut duo diametri <lb/>simul demptorum circulorum totam alterius circuli diametrum exaequent; <lb/>erit reliqua perforata lunula, ad assumptum circulum quemlibet, ut semissis <lb/><figure id="id.020.01.2721.1.jpg" xlink:href="020/01/2721/1.jpg"/></s></p><p type="caption">

<s>Figura 214.<lb/>rectanguli, sub diametris dempto&shy;<lb/>rum circulorum contenti, ad qua&shy;<lb/>dratum radii assumpti circuli. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto etc. </s>

<s>et sint centra to&shy;<lb/>tius circuli C, demptorum B et E <lb/>(fig. </s>

<s>214), et intelligatur primo <lb/>demptus solum circulus AD: erit&shy;<lb/>que reliqua integra lunula aequa&shy;<lb/>lis armillae unius rectanguli FEA. </s>

<s><lb/>Erit ergo integra lunula, ad cir&shy;<lb/>culum FD, ut rectangulum FEA, <lb/>sive DEA, ad quadratum DE. Et, <lb/>dividendo, lunula perforata, ad <lb/>eumdem circulum DF, erit ut re&shy;<lb/>ctangulum EDA ad quadratum <lb/>DE. </s>

<s>Circulus vero DF, ad circu&shy;<lb/>lum OS, est ut quadratum DE ad quadratum OS: ergo ex aequo patet pro&shy;<lb/>positum. </s>

<s>Nam lunula perforata erit ad circulum OS ut rectangulum EDA, <lb/>nempe, ut semissis rectanguli FDA, sub diametris demptorum circulorum <lb/>contenti, ad quadratum OS &rdquo; (ivi, T. XXXVI, fol. </s>

<s>47). </s></p><p type="main">

<s>Per intelligenza della qual dimostrazione, al solito tirata gi&ugrave; dal Torri&shy;<lb/>celli pi&ugrave; per suo memoriale, che per esser veduta da altri in quell'abito <lb/>trasparentissimo, ma negletto, discorreremo cos&igrave;, facendo uso del linguaggio, <lb/>e dei segni dei Matematici odierni: Abbiamo per costruzione AB+DE= <lb/>AC, onde DE=AC&mdash;AB=BC. </s>

<s>Chiamata <emph type="italics"/>L<emph.end type="italics"/> la lunula, sar&agrave; <emph type="italics"/>L<emph.end type="italics"/>= <lb/><foreign lang="greek">p</foreign>AC2&mdash;<foreign lang="greek">p</foreign>AB2=<foreign lang="greek">p</foreign>(AC+AB)(AC&mdash;AB). Ma AC+AB=AB+ <lb/>BC+AB=AB+BC+BD=AB+BD+DE=AE. </s>

<s>Quanto al&shy;<lb/>l'altro coefficiente, AC&mdash;AB=DE=EF, dunque <emph type="italics"/>L<emph.end type="italics"/>=<foreign lang="greek">p</foreign>AE.EF. </s>

<s>Ma <lb/>anche l'armilla EF=<foreign lang="greek">p</foreign>CF2&mdash;<foreign lang="greek">p</foreign>CE2=<foreign lang="greek">p</foreign>(CF+CE)(CF&mdash;CE)= <pb xlink:href="020/01/2722.jpg" pagenum="347"/><foreign lang="greek">p</foreign>AE.EF; dunque <emph type="italics"/>lunula integra est aequalis armillae unius rectanguli <lb/>AEF,<emph.end type="italics"/> come l'Autore dianzi diceva. </s></p><p type="main">

<s>Chiamato C il circolo dal diametro FD, ed L al solito la lunula, <lb/>avremo dunque L:C=AE.EF:DE2. </s>

<s>Dividendo, sar&agrave; L&mdash;C:C= <lb/>AE.EF&mdash;DE2:DE2=AE.ED&mdash;DE2:DE2=ED(AE&mdash;DE):DE2= <lb/>ED.DA:DE2. </s>

<s>Chiamisi ora C&prime; un altro circulo qualunque, di raggio OS: <lb/>avremo C&prime;:C=OS2:DE2, e di qui L&mdash;C:C&prime;=ED.DA:CB2, e sostituito <lb/>DE=DF/2, L&mdash;C:C&prime;=FD.DA/2:OS2. </s>

<s>Ma L&mdash;C rappresenta la lunula <lb/>perforata dal circolo DF, e C&prime; il circolo assunto, dunque si conferma di qui <lb/>la verit&agrave; del lemma torricelliano. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma II.<emph.end type="italics"/> &mdash; Perforatae lunulae, quales ante dicebamus, sunt inter <lb/>se ut rectangula sub diametris demptorum circulorum contenta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto etc.: erit <lb/><figure id="id.020.01.2722.1.jpg" xlink:href="020/01/2722/1.jpg"/></s></p><p type="caption">

<s>Figura 215.<lb/>ergo lunula perforata <lb/>AMP (fig. </s>

<s>215), ad cir&shy;<lb/>culum FH, ut rectan&shy;<lb/>gulum ABC ad qua&shy;<lb/>dratum FI. </s>

<s>Sed circu&shy;<lb/>lus FH, ad lunulam <lb/>perforatam EOR, est ut <lb/>quadratum FI ad re&shy;<lb/>ctangulum EFI; ergo <lb/>ex aequo lunula perfo&shy;<lb/>rata AMP, ad lunulam perforatam EOR, est ut rectangulum ABC ad rectan&shy;<lb/>gulum EFI, sive, sumptis duplis, ut rectangulum ABD ad rectangulum EFH &rdquo; <lb/>(ibid.). </s></p><p type="main">

<s>Premessi i quali due lemmi, passa il Torricelli a dimostrare, in una sua <lb/>prima proposizione, che, tolti dal frusto conico i due coni designati dal Ricci, <lb/>quel che riman del solido uguaglia una sferoide, la quale dimostra, in un'al&shy;<lb/><figure id="id.020.01.2722.2.jpg" xlink:href="020/01/2722/2.jpg"/></s></p><p type="caption">

<s>Figura 216.<lb/>tra proposizione, risolversi in quel terzo <lb/>cono, dallo stesso Ricci designato per me&shy;<lb/>dio proporzionale tra gli altri due. </s></p><p type="main">

<s><emph type="italics"/>Proposizione prima.<emph.end type="italics"/> &mdash; &ldquo; Si a seg&shy;<lb/>mento conico demantur duo coni, aeque <lb/>alti cum segmento, et super utraque ipsius <lb/>basi constituti, reliquum solidum erit ae&shy;<lb/>quale sphaeroidi cuidam, eamdem cum <lb/>segmento conico altitudinem habenti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto segmentum coni ABCD (fig. </s>

<s>216), cuius axis EF, et ab ipso de&shy;<lb/>mantur duo coni ABD, BDC, etc. </s>

<s>Ponatur quadratum PH duplum quadrati <lb/>GH, et per PO intelligatur planum oppositis basibus parallelum: eritque lu&shy;<lb/>nula perforata PO, demptis circulis PH, HO, aequalis circulo, cuius radius <lb/>GH, ob constructionem, et ex demonstratis &rdquo; (ibid., fol. </s>

<s>48). </s></p><pb xlink:href="020/01/2723.jpg" pagenum="348"/><p type="main">

<s>La lunula PO infatti, perforata da circoli uguali, che hanno per diametro <lb/>ciascuno la met&agrave; di PO, ossia PH, ovvero OH, chiamata al solito L, sar&agrave; uguale <lb/>a <foreign lang="greek">p</foreign>PH2&mdash;<foreign lang="greek">p</foreign>PH2/4&mdash;<foreign lang="greek">p</foreign>OH2/4=<foreign lang="greek">p</foreign>PH2/2. Ma perch&egrave; si &egrave; fatto PH2=2GH2, <lb/>sar&agrave; dunque L=<foreign lang="greek">p</foreign>PH2/2=<foreign lang="greek">p</foreign>GH2, e perci&ograve; sar&agrave; la lunula uguale a un cir&shy;<lb/>colo, che abbia per raggio GH, come dice l'Autore. </s></p><p type="main">

<s>Ora &egrave; chiaro che, riguardando il proposto frusto conico come compagi&shy;<lb/>nato d'infiniti circoli eretti all'asse, verr&agrave; il solido dai due coni ABD, BDC <lb/>terebrato in modo, che di ciascun di que'circoli riman solo una lunula per&shy;<lb/>forata, ciascuna delle quali dimostra il Torricelli equivalere al circolo della <lb/>sferoide, descritta da una semiellisse, che passi per i punti E, G, F, e che <lb/>si rivolga intorno alla EF, come a suo proprio asse. </s></p><p type="main">

<s>Sia, fra quegli infiniti circoli, in che si assomma il frusto, considerata <lb/>la sezione LN. &Egrave; facile dimostrare che la lunula perforata &egrave; uguale al circolo <lb/>dell'ellissoide, descritto dal raggio IQ intorno all'asse. </s>

<s>Sar&agrave; infatti, per il <lb/>secondo lemma, significando la lunula col solito simbolo <emph type="italics"/>L, L<emph.end type="italics"/>.PN:<emph type="italics"/>L<emph.end type="italics"/>.PO= <lb/>LM.MN:PH.HO. Ma, per ragion delle parallele LN.PO, abbiamo le due <lb/>proporzioni LM:PH=EI:EH; MN:HO=IF:FH, le quali, moltiplicate <lb/>termine per termine, danno LM.MN:PH.HO=EI.IF:EH.HF; ond'&egrave; <lb/>che <emph type="italics"/>L<emph.end type="italics"/>.LN:<emph type="italics"/>L<emph.end type="italics"/>.PO=EI.IF:EH.HF. Ma, per la natura dell'ellisse, <lb/>EI.IF=IQ2, EH.HF=GH2; dunque <emph type="italics"/>L<emph.end type="italics"/>.LN:<emph type="italics"/>L<emph.end type="italics"/>.PO=<foreign lang="greek">p</foreign>IQ2:<foreign lang="greek">p</foreign>GH2. </s>

<s><lb/>Ora &egrave; per supposizione <emph type="italics"/>L<emph.end type="italics"/>.PO=<foreign lang="greek">p</foreign>GH2, dunque anche <emph type="italics"/>L<emph.end type="italics"/>.LN=<foreign lang="greek">p</foreign>IQ2, e <lb/>ci&ograve; a qualunque punto sia fatta la sezione LN, cosicch&egrave; sempre la lunula <lb/>perforata sar&agrave; uguale al circolo, e perci&ograve; tutte le lunule perforate compor&shy;<lb/>ranno un solido uguale all'ellissoide intera, come nel suo manoscritto il Tor&shy;<lb/>ricelli stesso dimostra con queste parole: </s></p><p type="main">

<s>&ldquo; Fiat per puncta EGF ellipsis circa axem EF, et convertatur, sectoque <lb/>segmento per planum LN, basibus parallelum, erit lunula perforata LN, ad <lb/>lunulam perforatam PO, ut rectangulum LMN ad rectangulum PHO, nempe <lb/>rationem compositam habebit ex rationibus LM ad PH, et MN ad HO, sive <lb/>ex rationibus IE ad EH, et IF ad FH, quae sunt aeedem cum praedictis. </s>

<s><lb/>Ergo perforata lunula LN, ad perforatam lunulam PO, erit ut rectangulum <lb/>FIE ad rectangulum FHE, sive, ut circulus ex IQ, ad circulum ex HG. Con&shy;<lb/><figure id="id.020.01.2723.1.jpg" xlink:href="020/01/2723/1.jpg"/></s></p><p type="caption">

<s>Figura 217.<lb/>sequentia vero ex constructione sunt aequalia, quare <lb/>et lunula perforata LN aequalis erit circulo ex IQ, <lb/>et hoc semper. </s>

<s>Quare patet propositum &rdquo; (ibid.). </s></p><p type="main">

<s><emph type="italics"/>Proposizione seconda.<emph.end type="italics"/> &mdash; &ldquo; Dico huiusmodi <lb/>sphaerois medio loco proportionalis esse inter abla&shy;<lb/>tos conos. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Secetur axis MN (fig. </s>

<s>217) bifariam in F, <lb/>ab applicata EH: eritque perforata lunula EH ae&shy;<lb/>qualis maximo circulo praedictae sphaeroidis. </s>

<s>Sit quadratum I aequale re&shy;<lb/>ctangulo EGH, eritque circulus, cuius radius I, ad lunulam perforatam HE, <pb xlink:href="020/01/2724.jpg" pagenum="349"/>ut quadratum I ad semissem rectanguli EGH, nempe duplus. </s>

<s>Propterea co&shy;<lb/>nus, cuius radius basis sit I, altitudo vero MN, aequalis erit sphaeroidi, sive <lb/>reliquo segmenti conici, demptis duobus conis &rdquo; (ibid.). </s></p><p type="main">

<s>Sia dunque, come vuole il Torricelli, I2=EG.GH. </s>

<s>Avremo per il <lb/>lemma primo, significati con <emph type="italics"/>C<emph.end type="italics"/> il circolo, e con <emph type="italics"/>L<emph.end type="italics"/> la lunula, <emph type="italics"/>C<emph.end type="italics"/>.I:<emph type="italics"/>L<emph.end type="italics"/>.EH= <lb/>I2:EG.GH/2, che vuol dire il circolo esser doppio della lunula, e perci&ograve; il <lb/>cono, la base del quale abbia per raggio I, con l'altezza MN, sar&agrave;, per fa&shy;<lb/>cile corollario dalla XXIX archimedea <emph type="italics"/>De conoid. </s>

<s>et sphaer.,<emph.end type="italics"/> uguale alla <lb/>sferoide. </s></p><p type="main">

<s>&Egrave; il presente proposito quello di dimostrare che una tale sferoide, o il <lb/>cono a lei equivalente, &egrave; medio proporzionale fra i due coni ABD, BDC, le&shy;<lb/>vati dal frusto, i quali coni, per avere altezza uguale, stanno come i qua&shy;<lb/>drati de'raggi delle basi, ossia come AN2 a BM2. </s>

<s>Ma anche il terzo cono, a <lb/>cui s'&egrave; detto uguagliarsi la sferoide, ha la medesima altezza degli altri due; <lb/>dunque tutto si riduce a dimostrare che il quadrato del raggio I, ossia il <lb/>rettangolo EG.GH &egrave; medio proporzionale tra AN2 e BM2, ci&ograve; che si pu&ograve; <lb/>fare in questa maniera: Abbiamo, per ragion delle parallele, NF:FM= <lb/>AE:EB. Componendo, NF+FM:FM=AE+EB:EB, ossia NM:FM= <lb/>AB:EB. </s>

<s>Ma NM=2FM, dunque AB=2EB, e perci&ograve; AD=2EG, ossia <lb/>AN=EG, come, per le medesime ragioni, GH=BM. </s>

<s>Ora EG:GH= <lb/>EG2:EG.GH=EG.GH:GH2, per cui, sostituendo AN2 ad EG2, se ne <lb/>concluder&agrave; il proposito, come il Torricelli stesso lo conclude con questo di&shy;<lb/>scorso: </s></p><p type="main">

<s>&ldquo; Conum autem praedictum I medium proportionalem esse inter ABD, <lb/>BDC, patet. </s>

<s>Nam, cum rectangulum EGH medium sit inter quadratum AN, <lb/>BM, etiam quadratum I medium erit inter eadem. </s>

<s>Et propterea conus I, sive <lb/>sphaerois illa media proportionalis erit inter demptos conos. </s>

<s>Erit enim, ob <lb/>parallelas, ut NF ad FM, ita AE ad EB. </s>

<s>Et componendo etc. </s>

<s>Sed NM dupla <lb/>est MF; ergo AB dupla est BE, et propterea AD dupla EG. </s>

<s>Quare AN et <lb/>EG sunt aequales, et GH, BM sunt aequales. </s>

<s>Quadratum vero EG, ad rectan&shy;<lb/>gulum EGG, est ut EG ad GH, et rectangulum EGH, ad quadratum GH, <lb/>est ut EG ad GH. </s>

<s>Quare patet propositum &rdquo; (ibid.). </s></p><p type="main">

<s>Cos&igrave; dimostrava il Torricelli, con la fecondit&agrave; del suo proprio ingegno, <lb/>in una maniera forse diversa da quelle tre usate dal Ricci, la risoluzione del <lb/>frusto conico in tre coni di altezze uguali. </s>

<s>Se non che al terzo cono di mezzo <lb/>sostituiva una sferoide, perch&egrave; l'intento suo principale era quello di trasporre <lb/>la bella proposizione, dal campo della Stereometria pura, dove lo stesso Ricci <lb/>l'aveva lasciata, in quello della Baricentrica. </s>

<s>Riducendosi infatti il centro di <lb/>gravit&agrave; di essa sferoide nel mezzo dell'asse, si venivano a render pi&ugrave; sem&shy;<lb/>plici, nella libbra gravata delle parti, nelle quali era il solido risoluto, le ra&shy;<lb/>gioni delle equiponderanze. </s></p><p type="main">

<s>Venne al nostro Autore l'occasione di far ci&ograve;, essendo intorno a esami&shy;<lb/>nare le proposizioni galileiane <emph type="italics"/>De centro gravitatis,<emph.end type="italics"/> alcuna delle quali essen-<pb xlink:href="020/01/2725.jpg" pagenum="350"/>dosi da lui sospettata per falsa, volle d'altre confermare la verit&agrave;, in chi ne <lb/>avesse dubitato, per averle forse trovate di non facile intelligenza. </s>

<s>Tale parve <lb/>la X, nella quale, premesso un lemma geometrico, Galileo dimostrava che, <lb/>nel frusto di un cono o di una piramide, il centro di gravit&agrave; sega talmente <lb/><figure id="id.020.01.2725.1.jpg" xlink:href="020/01/2725/1.jpg"/></s></p><p type="caption">

<s>Figura 218.<lb/>l'asse, che la parte verso la base minore <lb/>stia all'altra, &ldquo; ut tripla minoris basis, <lb/>cum spatio duplo medii geometrici inter <lb/>basin maiorem et minorem, una cum basi <lb/>minori; ad triplam minoris basis eum eo&shy;<lb/>dem duplo spatii medii, ac una cum basi <lb/>maiori &rdquo; (Alb. </s>

<s>XIII, 286). O altrimenti, <lb/>rappresentandosi dalla figura 218 il frusto <lb/>proposto, con l'asse EF parallelo alla lib&shy;<lb/>bra AL, e significandosi con B la maggior bas&egrave; AD, con B&prime; la minore BC, e <lb/>con B&Prime; una media proporzionale fra ambedue; vuol Galileo dimostrare che <lb/>il centro Q dell'equilibrio &egrave; indicato dalla relazione QL/AQ=(3B+B&prime;+2B&Prime;)/(B+3B&prime;+2B&Prime;). <lb/>Ora il Torricelli applicava al caso le dimostrate risoluzioni del frusto conico, <lb/>e confermava esser veramente tale nel solido la ragion dell'equiponderanza, <lb/>con la seguente illustrazione stupenda delle dottrine di Galileo: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XLVII. &mdash; <emph type="italics"/>Segmentum coni habet centrum gravitatis, <lb/>ut ait Galileus propos. </s>

<s>ultima appendicis<emph.end type="italics"/> De centro gravitatis solidorum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto frustum coni ABCD (nella precedente figura) cuius axis FE, <lb/>appensumque sit ad libram AL, ita ut circuli, qui per AD, BC ducuntur, <lb/>perpendiculares sint ad horizontem. </s>

<s>Tum, secta FE in quatuor partes aequa&shy;<lb/>les per puncta H, G, I, ducantur perpendicula OH, MG, NI, LE. </s>

<s>Trium ergo <lb/>magnitudinum ad libram appensarum centra gravitatis erunt in rectis OH, <lb/>MG, NI: nempe, coni ACD, in OH; coni BAC in NI, reliqui vero solidi in <lb/>GM, quandoquidem ostensum est singulas ipsius perforatas lunulas aequales <lb/>esse singulis circulis alicuius sphaeroidis, cuius axis erat FE. &rdquo; </s></p><p type="main">

<s>&ldquo; Centrum vero praedictarum trium magnitudinum sic habebitur: In&shy;<lb/>telligatur unaquaeque dictarum magnitudinum divisa in quatuor partes ae&shy;<lb/>quales, et concipiantur appendi ad libram, ita ut coni ACD 3/4 pendeant ex <lb/>A, reliqua vero 1/4 ex L. </s>

<s>Coni vero BAC 3/4 pendeant ex L, reliqua vero <lb/>1/4 ex A. </s>

<s>Reliqui tandem solidi 2/4 pendeant ex A. et 2/4 ex L. </s>

<s>Manifestum <lb/>est punctum aequilibrii harum trium magnitudinum sectarum idem prorsus <lb/>futurum esse, quod erat ante illarum sectionem, quandoquidem ipsarum cen&shy;<lb/>tra gravitatis, propter sectionem a nobis factam, non mutaverunt dispositionem <lb/>neque inter se, neque ad libram comparata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto illud Q, ergo, centrum gravitatis. </s>

<s>Q secabit libram AL, ita ut sit <lb/>AQ ad QL, quemadmodum est magnitudo, appensa ex L, ad magnitudinem <lb/>appensam ex A: nempe ut 3/4 coni BAC, 2/4 reliqui solidi, et 1/4 coni ACD, <lb/>ad 3/4 coni ACD, cum 2/4 reliqui solidi, et 1/4 coni BAC, sive, sumptis qua&shy;<lb/>druplis, ut tres coni BAC, cum duobus ex reliquis solidis, et uno cono ACD, <pb xlink:href="020/01/2726.jpg" pagenum="351"/>ad tres conos ACD, duos ex reliquis solidis, et unum conum BAC: sive, ut <lb/>eorum bases, quae sunt in continua proportione, quod proposuerat Galileus. </s>

<s><lb/>Ostendimus enim dictum reliquum solidum cuidam sphaeroidi aequale esse, <lb/>quae quidem sphaerois medio loco proportionalis est inter illos duos conos. </s>

<s><lb/>Ergo, si ipsa reducatur ad conum aeque altum, erit ipsius basis medio loco <lb/>proportionalis inter bases conorum, sive inter bases segmenti nostri coni &rdquo; <lb/>(ibid., T. XXXVI, fol. </s>

<s>49). </s></p><p type="main">

<s>La conclusione dunque del Torricelli &egrave; analiticamente espressa da que&shy;<lb/>sti segni, chiamando R quel che riman del frusto, toltine i coni sulle sue due <lb/>basi, QL:AQ=3/4ACD+1/4ACB+2/4R:1/4ACD+3/4ACB+2/4R. </s>

<s><lb/>Sostituiti gli elementi geometrici, considerando che le altezze de'coni ACD, <lb/>ACB sono uguali, e che perci&ograve; stanno essi coni come le basi B, B&prime;: osser&shy;<lb/>vando di pi&ugrave; che R equivale a una sferoide, o a un cono, la base del quale <lb/>B&Prime; sia media fra le altre due B, B&prime;, e l'altezza sia la medesima; sarebbe un <lb/>perdere il tempo e le parole a dire che la formula del Torricelli si riduce <lb/>a quella medesima di Galileo. </s></p><p type="main">

<s>Sul finir della giornata quarta delle due Scienze nuove diceva il Sal&shy;<lb/>viati, quasi proemiando a quell'<emph type="italics"/>Appendice,<emph.end type="italics"/> che sarebbe per leggere intorno <lb/>ai centri di gravit&agrave;, com'avesse l'Accademico intrapreso da giovane un tale <lb/>studio, per supplire a quello che si desiderava nel libro del Commandino, col <lb/>pensiero di andar seguitando la materia, anco negli altri solidi non tocchi da <lb/>lui: ma che poi, incontratosi nel trattato di Luca Valerio, non seguit&ograve; pi&ugrave; <lb/>avanti, bench&egrave; fossero le sue aggressioni per istrade molto diverse (Alb. </s>

<s><lb/>XIII, 266). Apparisce di questa diversit&agrave;, nella proposizione fin qui discorsa, <lb/>il pi&ugrave; chiaro esempio, avendo esso Valerio nella XXV del suo terzo libro gi&agrave; <lb/>dimostrato il centro di gravit&agrave; del frusto conico. </s>

<s>Sembra anzi che sia que&shy;<lb/>sta tanto pi&ugrave; facile e breve, che si direbbe superflua l'opera aggiuntavi da <lb/>Galileo, se non si ripensasse che la diversit&agrave; fra l'una e l'altra aggressione <lb/>non &egrave; puramente accidentale, o di semplice forma. </s>

<s>Mentre infatti il Valerio <lb/>chiedeva si perfezionasse il cono, per riferire a un punto preso sull'asse in&shy;<lb/>tero di lui il centro di gravit&agrave; della porzione, Galileo invece lo riferiva alle <lb/>estremit&agrave; dell'asse proprio del frusto terminato in s&egrave; stesso. </s></p><p type="main">

<s>Ora, non contento il Torricelli di avere in s&igrave; bel modo illustrato il suo <lb/>Maestro, volle di pi&ugrave; emularlo, proseguendo per quell'altre strade tanto pi&ugrave; <lb/>agevoli e spedite, ch'egli gi&agrave; per s&egrave; erasi aperte. </s>

<s>Veniva di qui condotto a <lb/>riguardare il frusto come un bicchiere scavato da un cono. </s>

<s>La speculazione <lb/>era gi&agrave; balenata anche alla mente del Valerio, nella proposizione X del ci&shy;<lb/>tato suo libro terzo, ma perch&egrave; gli mancavano gli argomenti necessari a di&shy;<lb/>mostrare il centro di gravit&agrave; nel detto solido scavato, dovettero quelle sue <lb/>speculazioni rimanersi nel campo della Geometria, limitandosi ad assegnare <lb/>la proporzione tra il frusto e il cono inscritto sulla base maggiore. </s></p><p type="main">

<s>I processi torricelliani si vedono in fin da questo punto gi&agrave; disegnati: <lb/>il bicchiere e il cono pendono come da libbra dall'asse, e non occorre far <lb/>altro che ritrovare il centro di gravit&agrave; delle parti, e le ragioni stereometri-<pb xlink:href="020/01/2727.jpg" pagenum="352"/>che intercedenti, per aver fra l'estremit&agrave; della detta libbra indicato il punto, <lb/>dove il solido tutto intero concentra il suo peso. </s>

<s>Il primo passo perci&ograve; si fa <lb/>dimostrando la seguente <lb/><figure id="id.020.01.2727.1.jpg" xlink:href="020/01/2727/1.jpg"/></s></p><p type="caption">

<s>Figura 219.</s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XLVIII. &mdash; <emph type="italics"/>Reliquum <lb/>segmenti conici, dempto cono maioris basis, <lb/>centrum habet in axe, si fiat, ut quatuor <lb/>diametri maiores cum quatuor minoribus, <lb/>ad duos maiores cum uno minori, ita axis <lb/>AB ad BC &rdquo;<emph.end type="italics"/> (fig. </s>

<s>219). </s></p><p type="main">

<s>In aiuto alla dimostrazione soccorre un <lb/>lemma, in cui si dimostra che, dato il segmento conico ABCD (fig. </s>

<s>220), <lb/>scavato dal cono AED, prolungate le AE, DC infino all'incontro in H, e da <lb/>questo punto condotta una linea parallela ad EC, che incontri il prolunga&shy;<lb/>mento dell'asse EF in G; se per G, C, F si far&agrave; passare una semiellisse, <lb/>dalla rivoluzion della quale intorno a EF si descriva una sferoide; il rima&shy;<lb/>nente del segmento conico, toltone il cono della maggior base, sar&agrave; equiva&shy;<lb/>lente a CFB, porzione della detta sferoide. </s></p><p type="main">

<s>Si dimostra ci&ograve; dal Torricelli co'soliti modi suoi proprii, che si com&shy;<lb/>pendiano ne'seguenti. </s>

<s>&Egrave; per ragion delle parallele BE:IM=AE:AM= <lb/><figure id="id.020.01.2727.2.jpg" xlink:href="020/01/2727/2.jpg"/></s></p><p type="caption">

<s>Figura 220.<lb/>EF:FL, e anche insieme BE:MO=EC:MO= <lb/>CH:HO=EG:GI. Dunque, moltiplicando termine a <lb/>termine, e per le propriet&agrave; dell'ellisse, BE3:IM.MO= <lb/>FE.EG:FL.LG=BE2:NL2, e perci&ograve; <foreign lang="greek">p</foreign>IM.MO= <lb/><foreign lang="greek">p</foreign>NL2, ossia l'armilla IM &egrave; uguale al circolo LN. </s>

<s><lb/>Cos&igrave; essendo di tutte le altre sezioni resta dimo&shy;<lb/>strata vera l'eguaglianza tra la sferoide e il bic&shy;<lb/>chiere. </s></p><p type="main">

<s>&ldquo; Reliquum segmenti conici (frettolosamente il <lb/>Torricelli scriveva) dempto cono maioris basis, est sphaerois, cuius axis in&shy;<lb/>teger habebitur si fiat, ut FD ad EC, ita FG ad GE. &rdquo; </s></p><p type="main">

<s>&ldquo; Fiat, et per CBF transeat ellipsis, ex qua fiat sphaerois. </s>

<s>Ductaque IO, <lb/>parallela ad AD, habebit quadratum BE, ad rectangulum IMO, compositam <lb/>rationem ex rationibus BE ad IM, sive EA ad AM, sive EF ad FL, et ex <lb/>ratione BE ad MO, vel EC ad MO, vel CH ad HO, vel EG ad GL. </s>

<s>Quare <lb/>quadratum BE, ad rectangulum IMO, est ut rectangulum FEG ad rectangu&shy;<lb/>lum FLG, sive ut quadratum idem BE ad quadratum NL. </s>

<s>Sunt ergo aequa&shy;<lb/>lia rectangulum IMO, et quadratum NL; quare armilla IM aequatur cir&shy;<lb/>culo NL &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>43). </s></p><p type="main">

<s>Riducendoci ora nuovamente sott'occhio la figura 219, si costruisca, <lb/>secondo la regola ora insegnata, la sferoide, alla porzione EIAF della quale <lb/>sappiamo equivalere quel che riman del tronco, tolto il cono inscritto DBG. </s>

<s><lb/>Sia C il centro della descritta porzione sferoidea, che sar&agrave; anche insieme il <lb/>centro del solido scavato: rimane a dimostrare che C sta veramente sull'asse <lb/>AB in quel punto, che il Torricelli annunziava. </s></p><pb xlink:href="020/01/2728.jpg" pagenum="353"/><p type="main">

<s>Per la proposizione XLV, qui addietro scritta, essendo BC:AC= <lb/>2IM2:2IM2+EB2, &egrave; facile dedurne BC:CM=IM2:ML2. </s>

<s>Ma, per il <lb/>precedente lemma, <foreign lang="greek">p</foreign>IM2=<foreign lang="greek">p</foreign>HI.IN; dunque IM2=HI.IN; e dall'altra <lb/>parte ML2=HI2, per essere HN parallela alla base e bissettrice dell'asse: <lb/>onde BC:CM=HI.IN:HI2=IN:HI=4IN:4IH. </s>

<s>Ma IH=EB/2= <lb/>EF/4, e perci&ograve; 4IH=EF. </s>

<s>Di pi&ugrave; essendo IN=HN&mdash;IH=(EF+DG)/2&mdash;EF/4, <lb/>sar&agrave; 4IN=2EF+2DG&mdash;EF=2DG+EF. </s>

<s>Dunque BC:CM= <lb/>2DG+EF:EF. Componendo, BC+CM:BC=2DG+2EF:2DG+EF. </s>

<s><lb/>Sostituendo a BC+CM, BM, e duplicando gli antecedenti, 2BM:BC= <lb/>4DG+4EF:2DG+EF, ossia AB:BC=4DG+4EF:2DG+EF, <lb/>come da principii frettolosamente posti conclude, nelle seguenti parole, il Tor&shy;<lb/>ricelli, ripigliando il costrutto da noi di sopra nell'annunziata proposizione <lb/>lasciato interrotto. </s></p><p type="main">

<s>&ldquo; Nam sit centrum praedictum C: erit ergo BC ad CM ut quadratum <lb/>IM ad ML, sive, ob aequalitatem, ut rectangulum HIN ad quadratum HI, <lb/>nempe ut recta NI ad IH. </s>

<s>Sumptisque quadruplis, ut duo diametri maiores <lb/>DG, cum uno minori EF, ad EF. </s>

<s>Et convertendo, componendoque, sumptisque <lb/>antecedentibus duplis, erit AB ad BC ut quatuor EF, cum quatuor DG, ad <lb/>DG bis, cum EF semel, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (ibid., fol. </s>

<s>45). </s></p><p type="main">

<s>Il secondo passo, che bisognava fare, perch&egrave;, procedendo per questa via, <lb/>potesse il Torricelli conseguire il suo intento, era quello di dimostrare qual <lb/><figure id="id.020.01.2728.1.jpg" xlink:href="020/01/2728/1.jpg"/></s></p><p type="caption">

<s>Figura 221.<lb/>ragione avesse il solido generato dal trian&shy;<lb/>golo ABE (fig. </s>

<s>221) al solido del triangolo <lb/>AEF, rivolgendosi ambedue le figure intorno <lb/>all'asse EF: ragione, ch'esso Torricelli an&shy;<lb/>nunzia essere di BC(BC+AD) a 2AD2. </s>

<s><lb/>Qui per&ograve; &egrave; uno sbaglio manifesto, occasionato <lb/>senza dubbio dalla fretta nello scrivere, per&shy;<lb/>ch&egrave; il quarto termine della relazione, secondo il calcolo rettamente condotto, <lb/>&egrave; AD2 semplicemente, e non 2AD2. </s></p><p type="main">

<s>Seguitiamo infatti l'Autore, da cui si suppone per gi&agrave; dimostrato avere <lb/>il segmento della sferoide, che significheremo con <emph type="italics"/>S<emph.end type="italics"/>.BFC, al cono BFC, la <lb/>proporzione di MG2+GN2 a GN2. </s>

<s>Duplicando i termini della seconda ra&shy;<lb/>gione, sar&agrave; <emph type="italics"/>S<emph.end type="italics"/>.BFC:BFC=2MG2+2GN2:4GN2=2MG2+2GN2:BE2. </s>

<s><lb/>Ma AED:BFC=AF2:BE2, dunque <emph type="italics"/>S<emph.end type="italics"/>.BFC:AED=2MG2+2GN2:AF2. </s>

<s><lb/>Ora MG2=HI.IL, come fu dimostrato nel lemma alla precedente, e NG2= <lb/>HI2, per essere HL bissettrice dell'asse, e perci&ograve; 2MG2+2GN2= <lb/>2HI(IL+IH)=2HI.HL. </s>

<s>Sar&agrave; dunque, sostituendo, <emph type="italics"/>S<emph.end type="italics"/>.BFC:AED= <lb/>2HI.HL:AF2. </s>

<s>Ma HI=BC/4, HL=(BC+AD)/2, per cui 2MG2+2GN2= <lb/>2.BC/4((BC+AD)/2)=BC/4(BC+AD), e in conclusione <emph type="italics"/>S<emph.end type="italics"/>.BFC:AED= <pb xlink:href="020/01/2729.jpg" pagenum="354"/>BC(BC+AD):4AF2=BC(BC+AD):AD2. </s>

<s>E perch&egrave; <emph type="italics"/>S<emph.end type="italics"/>.BFC, per il <lb/>lemma alla precedente, &egrave; uguale al solido generato dalla conversione del trian&shy;<lb/>golo ABE intorno all'asse EF; dunque questo solido, o tronco di cono sca&shy;<lb/>vato, al cono descritto dal triangolo AEF, ha la proporzione di BC(BC+AD) <lb/>a AD2, e non a 2AD2, come, per uno sbaglio di calcolo, fu condotto a con&shy;<lb/>cludere il Torricelli dalla dimostrazione, che qui trascriviamo. </s></p><p type="main">

<s>&ldquo; Secetur axis EF bifariam in G, appliceturque GH. </s>

<s>Erit segmentum <lb/>sphaeroidis BFC, ad conum BFC, ut quadrata MG, GN simul, ad duo qua&shy;<lb/>drata GN. </s>

<s>Sumptisque duplis, ut duo quadrata MG, cum duobus NG, ad <lb/>quatuor NG, sive ad quadratum BE. </s>

<s>Conus vero BFC, ad conum AED, est <lb/>ut quadratum BE ad quadratum AF. </s>

<s>Ergo ex aequo segmentum sphaeroi&shy;<lb/>dis, ad conum AED, erit ut duo quadrata MG, cum duobus quadratis NG, <lb/>sive, ut duo rectangula HIL, quae aequantur duobus quadratis MG, sive col&shy;<lb/>lectim, ut duo tantum rectangula IHL ad quadratum AF. </s>

<s>Sumptisque octu&shy;<lb/>plis, erit ut rectangulum, ex minori basi in minorem maioremque simul, ad <lb/>duplum quadrati maioris basis &rdquo; (ibid., fol. </s>

<s>44). </s></p><p type="main">

<s>Se avesse avuto l'occasione e il tempo di tornare sopra questo disteso, <lb/>si sarebbe senza dubbio dal Torricelli ritrovato e corretto lo sbaglio, tanto <lb/>pi&ugrave; che ne lo avrebbe potuto fare accorto lo stesso Luca Valerio, il quale <lb/>aveva, nella X proposizione del suo terzo libro, dimostrato che &ldquo; omne fru&shy;<lb/>stum coni, ad conum cuius basis est eadem, quae maior basis frusti et eadem <lb/>altitudo, est ut rectangulum contentum basium diametris, una cum tertia parte <lb/>quadrati differentiae eorumdem diametrorum, ad tertiam partem quadrati, ex <lb/>diametro maioris basis &rdquo; (De centro grav., Lib. </s>

<s>III, Romae 1604, pag. </s>

<s>14). </s></p><p type="main">

<s>Chiamato dunque F il frusto, C il cono, e segnato sopra AD, nella pro&shy;<lb/>posta figura, il punto O, in tal parte che AO sia uguale a BC, e perci&ograve; OD <lb/>la differenza de'diametri delle basi; sarebbe la relazione espressa da F:C= <lb/>AD.AO+DO2/3:AD2/3, ci&ograve; che, triplicati i termini della seconda ragione, <lb/>dividendo, e sostituendo BC ad AO, si riduce a F&mdash;C:C=3AD.BC+ <lb/>DO2&mdash;AD2:AD2. </s>

<s>Ma, essendo per costruzione DO=AD&mdash;BC, avremo <lb/>DO&mdash;AD=&mdash;BC, DO+AD=2AD&mdash;BC, e perci&ograve; la differenza dei <lb/>quadrati, ch'&egrave; uguale a (DO+AD)(DO&mdash;AD), sar&agrave; BC(BC&mdash;2AD). <lb/>Sostituendo, se ne concluder&agrave; dunque, per Luca Valerio, F&mdash;C:C= <lb/>3AD.BC&mdash;2AD.BC+BC2:AD2=BC2+AD.BC:AD2, che vuol <lb/>dire &ldquo; segmentum coni ABCD dempto cono maioris basis AD, ad conum AED <lb/>maioris basis, est ut quadratum diametri minoris basis, cum rectangulo sub <lb/>utraque, ad quadratum maioris &rdquo; e non <emph type="italics"/>ad duplum quadrati maioris,<emph.end type="italics"/> come <lb/>annunziava, e si credeva di aver dimostrato il Torricelli, per cui va corretta <lb/>la proposizione, che ora trascriveremo di lui, e a dimostrar la quale erano <lb/>ordinate le precedenti. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XLIX. &mdash; <emph type="italics"/>Centrum gravitatis segmenti coni BC<emph.end type="italics"/> (fig. </s>

<s>222) <lb/><emph type="italics"/>habetur in axe EF, si fiat primo, ut CD quater, cum AB quater, ad CD bis <lb/>et AB semel sumptis; ita FE ad EG; iterumque, sumpta FH 1/4 axis,<emph.end type="italics"/><pb xlink:href="020/01/2730.jpg" pagenum="355"/><emph type="italics"/>fiat, ut quadratum AB cum rectangulo AB in CD, ad duo quadrata CD, <lb/>ita HI ad IG, eritque centrum I. &rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.2730.1.jpg" xlink:href="020/01/2730/1.jpg"/></s></p><p type="caption">

<s>Figura 222.</s></p><p type="main">

<s>&ldquo; Nam, ex demonstratis, erit G centrum reliqui, <lb/>dempto cono maioris basis, H vero centrum est prae&shy;<lb/>dicti coni, demonstratumque est reliquum illud, ad di&shy;<lb/>ctum conum, esse ut quadratum AB, cum rectangulo <lb/>AB in CD, ad duo quadrata CD: nempe, ex suppo&shy;<lb/>sitione, ut HI ad IG. </s>

<s>Quare centrum erit I &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>46). </s></p><p type="main">

<s>Dal frusto del cono volle il Torricelli passare al frusto del conoide para&shy;<lb/>bolico, e bench&egrave; il Valerio, nella XLII del secondo libro, ne avesse, con una <lb/>dimostrazione assai semplice, indicato il centro; non pat&igrave; il Nostro di rima&shy;<lb/>nergli indietro, formulando la proposizion nel medesimo modo, ma dimostran&shy;<lb/>dola diversamente da'suoi proprii principii, e secondo il metodo usato. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE L. &mdash; <emph type="italics"/>Esto frustum conoidis parabolici ABCD<emph.end type="italics"/> (fig. </s>

<s>223), <lb/><emph type="italics"/>cuius axis EF, centrum O: dico EO ad OF esse ut quadratum BC, cum <lb/>duobus quadratis AD, ad quadratum AD, cum duobus BC. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Compleatur parabola AID, et fiat parabola GEH idem habens latus <lb/>rectum cum AID. </s>

<s>Concipiatur ex frusto ABCD demptum conoides paraboli&shy;<lb/>cum GEH, in quo inscriptus sit conus GEH, et, secta EF bifariam in L, appli&shy;<lb/>cetur <expan abbr="NLq.">NLque</expan> &rdquo; </s></p><p type="main">

<s>&ldquo; Jam solidum factum a quadrilineo GNEBA, per lemma II ad prop. </s>

<s>XLI, <lb/>aequalis est cylindro, cuius basis circulus BC, altitudo vero EF: sive cono, <lb/><figure id="id.020.01.2730.2.jpg" xlink:href="020/01/2730/2.jpg"/></s></p><p type="caption">

<s>Figura 223.<lb/>cuius basis sit tripla circuli BC, altitudo vero <lb/>sit ipsa FE. </s>

<s>Solidum vero factum a bilineo GNE, <lb/>ad conum GEH, est, per lemma ad propos. </s>

<s>XLV, <lb/>ut duo rectangula NPQ, ad quadratum GF. </s>

<s><lb/>Ergo simul, per XXIV Quinti, totum solidum <lb/>ABEG, ad conum GEH, est ut 3 quadrata BE, <lb/>cum duobus rectangulis NPQ, ad quadratum <lb/>GF. </s>

<s>Sed in parabola rectangulum NPQ aequale <lb/>est quadrato PL (perch&egrave; PL &egrave; il raggio del cir&shy;<lb/>colo massimo della sferoide) ergo solidum ABEG, ad conum GEH, est ut tria <lb/>quadrata BE, cum duobus quadratis PL, ad quadratum FG, sive, ut sex qua&shy;<lb/>drata BE, cum quadrato FG, ad duo quadrata FG. &rdquo; </s></p><p type="main">

<s>&ldquo; Centrum gravitatis solidi GNEBA est L, nam ostensae sunt singulae <lb/>ipsius armillae aequales singulis unius cylindri circulis: solidi vero GNE cen&shy;<lb/>trum est L, nam singulae ipsius armillae ostensae sunt aequales singulis <lb/>unius sphaeroidis circuli; ergo totius solidi GEBA centrum est L. </s>

<s>Sed coni <lb/>GEH est M, sempta FM dimidia ipsius FL; ergo, si fiat ut sex quadrata BE, <lb/>cum quadrato FG, ad duo quadrata FG, ita reciproce MO ad OL; erit O <lb/>centrum totius. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Jam quinque erunt argumenta, praeter reductionem: Per constructio&shy;<lb/>nem, MO ad OL est ut sex quadrata BE, cum quadrato FG, ad duo qua-<pb xlink:href="020/01/2731.jpg" pagenum="356"/>drata FG. Componendo, ML ad LO est ut sex quadrata BE, cum tribus qua&shy;<lb/>dratis FG, ad duo quadrata FG. </s>

<s>Duplicando antecedentia, FL ad LO ut <lb/>12 quadrata BE+6 quadratis FG, ad 2FG. </s>

<s>Per conversionem rationis, LF <lb/>ad FO ut 12 quadrata BE+6 quadratis FG, ed 12BE+4FG. </s>

<s>Dupli&shy;<lb/>cando antecedentia, EF ad FO ut 24 quadrata BE+12FG, ad 12BE+4FG. <lb/>Dividendo, EO ad OF ut 12BE+8FG ad 12BE+4FG. &rdquo; </s></p><p type="main">

<s>&ldquo; Sed quia rectangulum AGD, per lemma II ad propos. </s>

<s>XL, aequale <lb/>est quadrato BE, erit quadratum FG differentia inter quadratum AF, BE. </s>

<s><lb/>Ergo fieri poterit talis reductio: EO ad OF est ut 4BE, cum 8FA, ad 8BE <lb/><figure id="id.020.01.2731.1.jpg" xlink:href="020/01/2731/1.jpg"/></s></p><p type="caption">

<s>Figura 224.<lb/>cum 4FA: vel, ut quadratum BC, cum 2AD, ad <lb/>quadratum AD, cum 2BC, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (ibid., fol. </s>

<s>50). </s></p><p type="main">

<s>Ma, per comprendere tutte le conoidali in una <lb/>proposizione universalissima, premetteva il seguente <lb/><emph type="italics"/>Lemma:<emph.end type="italics"/> &ldquo; Se sar&agrave; un solido o conoidale o porzione <lb/>di sfera o sferoide ABC (fig. </s>

<s>224), cni asse sia BD, <lb/>cono inscritto ABC, tangenti AE, ed EB, segmento <lb/>conico AEFC; dico che il cono inscritto, il solido <lb/>intermedio e la scodella esterna sono in continua proporzione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Concepiscasi il cono EDF il quale, nella XXXVII, &egrave; stato provato <lb/>eguale alla scodella esterna, fatta dalla tangente. </s>

<s>Si &egrave; anco dimostrato, nella <lb/>proposizione seconda premessa alla XLVI come lemma, che, se dal segmento <lb/>conico leveremo li due coni ABC, EDF, il rimanente &egrave; medio proporzionale <lb/>fra essi coni. </s>

<s>Dunque, levando il cono ABC o scodella esterna, il rimanente <lb/>sar&agrave; medio proporzionale fra esso cono e la scodella &rdquo; (ivi, fol. </s>

<s>112). Ci&ograve;, <lb/>chiamato I il detto solido medio proporzionale, potr&agrave; scriversi sotto la forma <lb/>ABC:I=I:EDF. </s>

<s>Ma ABC:EDF=AD2:EB2, dunque EDF=EB2.ABC/AD2, <lb/>e perci&ograve; I2=ABC.EDF=ABC2.EB2/AD2, ossia I2:ABC2=EB2:AD2, ed <lb/>estratta la radice e trasponendo, ABC:I=AD:EB. </s></p><p type="main">

<s>Il centro di gravit&agrave; del cono ABC &egrave; in N, punto noto; del solido inter&shy;<lb/>medio I, ossia del bilineo AGB equivalente a una sferoide, &egrave; in M nel mezzo <lb/>dell'asse. </s>

<s>Se dunque si supponga in O il centro del tutto, sar&agrave; questo indi&shy;<lb/>cato dalla relazione ABC:I, ossia (<emph type="italics"/>a<emph.end type="italics"/>) AD:EB=MO:ON. </s>

<s>Moltiplicando <lb/>l'una e l'altra ragione di questa per 3/2, e componendo, avremo (<emph type="italics"/>b<emph.end type="italics"/>) 3AD+ <lb/>2EB:2EB=3MO+2NO:2NO. </s>

<s>Moltiplicando per 2 i conseguenti di (<emph type="italics"/>a<emph.end type="italics"/>), <lb/>AD:2B=MO:2NO, la quale, per composizione, dar&agrave; AD+2EB:2EB= <lb/>MO+2NO:2NO; ond'&egrave; che si trasformer&agrave; la (<emph type="italics"/>b<emph.end type="italics"/>) in 3AD+2EB:AD+ <lb/>2EB=3MO+2NO:MO+2NO. </s>

<s>Ma 3MO+2NO=3(BO&mdash;BM)+ <lb/>2(BN&mdash;BO)=3BO&mdash;3BM+2BN&mdash;2BO=BO&mdash;3BM+2BN= <lb/>BO, e dall'altra parte MO+2NO=MD&mdash;OD+2(OD&mdash;ND)=OD+ <lb/>MD&mdash;2ND=OD; dunque 3AD+2EB:2EB+AD=BO:DO, ed &egrave; <lb/>ci&ograve; che appunto intende di dimostrare il Torricelli in questa sua </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE LI. &mdash; <emph type="italics"/>Poste le medesime cose che nella precedente<emph.end type="italics"/><pb xlink:href="020/01/2732.jpg" pagenum="357"/><emph type="italics"/>figura, dico che, se si far&agrave; come tre delle AD, con due delle EB, a due <lb/>delle EB &ccedil;on una delle AD, cos&igrave; BO ad OD; che il punto O &egrave; il centro <lb/>del solido conoidale, o della porzione di sfera o di sferoide.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Perch&egrave; il cono ABC, al cono EDF, sta come il quadrato AD al qua&shy;<lb/>drato EB: per&ograve; il cono inscritto ABC, al solido intermedio, sar&agrave; come la retta <lb/>AD alla retta EB. </s>

<s>Se dunque segheremo BD in quattro parti uguali BI, IM, <lb/>MN, ND, sar&agrave; M centro del solido AGB, ed N centro del cono. </s>

<s>E se faremo, <lb/>come AD alla BE, cos&igrave; MO ad ON <emph type="italics"/>reciproce,<emph.end type="italics"/> sar&agrave; O centro di tutto. </s>

<s>Per&ograve; <lb/>sar&agrave; come tre delle AD, con due delle EB, a due delle EB, con una delle <lb/>AD; cos&igrave; BO ad OD, c. </s>

<s>d. </s>

<s>d. </s>

<s>&rdquo; (ivi, fol. </s>

<s>237). </s></p><p type="main">

<s>Soggiunge il Torricelli, dopo questa, un corollario <emph type="italics"/>pro centro gravitatis<emph.end type="italics"/><lb/><figure id="id.020.01.2732.1.jpg" xlink:href="020/01/2732/1.jpg"/></s></p><p type="caption">

<s>Figura 225.<lb/><emph type="italics"/>hyperbolici, et segmenti sphaerae, aut sphaeroidis tantum.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto conois hyperbolicum, sive sphaerae aut sphae&shy;<lb/>roidis portio ABC (fig. </s>

<s>225), cuius diameter BG, axis BD, <lb/>centrum H, tangentes AF, BF. </s>

<s>Suppono quod, si fiat ut tri&shy;<lb/>pla AD, cum dupla BF, ad duplam BF, cum AD, ita BO <lb/>ad OD; O esse centrum gravitatis, ut ostendimus in praece&shy;<lb/>denti. </s>

<s>His positis, fiat ut tripla axis BD, cum quadrupla diame&shy;<lb/>tri BG, ad duplam diametri BG cum BD, ita BO ad OE: dico <lb/>iterum O esse centrum gravitatis conoidis, sive portionis. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ducatur enim FI parallela ad BD. </s>

<s>Erit ergo AI ad ID <lb/>ut DB ad BE: nempe, ob tangentem sectionis coni AE, ut <lb/>DH ad HB. Et, componendo, erit AD ad FB ut DG ad GH: <lb/>quare, ut tripla AD, cum dupla FB, ad duplam FB, cum AD; ita tripla DG, <lb/>cum dupla GH, ad duplam GH cum GD: nempe ita tripla BD, cum quadru&shy;<lb/>pla BG, ad duplam BG, cum BD, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (ibid., fol. </s>

<s>214). </s></p><p type="main">

<s>Istituiscasi il calcolo, tenendo dietro al processo dell'Autore. </s>

<s>Abbiamo, <lb/>per la natura della tangente alla sezione conica, essendone in H segnato il <lb/>centro, DB:BE=DH:HB. </s>

<s>E condotta la FI parallela all'asse, AI:DI= <lb/>DB:BE; dunque AI:DI=DH:HB, relazione che, componendo e sosti&shy;<lb/><figure id="id.020.01.2732.2.jpg" xlink:href="020/01/2732/2.jpg"/></s></p><p type="caption">

<s>Figura 226.<lb/>tuendo gli equivalenti, si trasforma nell'altra (<emph type="italics"/>a<emph.end type="italics"/>) AD:FB= <lb/>DG:GH. </s>

<s>Triplicando in questa gli antecedenti, e duplicando <lb/>i conseguenti, avremo 3AD:3FB=3DG:2GH, dalla <lb/>quale deriver&agrave; per composizione la (<emph type="italics"/>b<emph.end type="italics"/>) 3AD+2FB:2FB= <lb/>3DG+2GH:2GH. </s>

<s>Duplicando i conseguenti della (<emph type="italics"/>a<emph.end type="italics"/>) e <lb/>componendo, avremo anche insieme AD+2FB:2FB= <lb/>DG+2GH:2GH, e da questa e dalla (<emph type="italics"/>b<emph.end type="italics"/>) ne conseguir&agrave; <lb/>3AD+2FB:AD+2FB=3DG+2GH:DG+2GH. </s>

<s><lb/>Ma 3DG+2GH=3(GB&mdash;BD)+BG=4BG&mdash;3BD, e <lb/>2GH+DG=GB+GB&mdash;BD=2GB&mdash;BD; dunque <lb/>3AD+2FB:AD+2FB=4BG&mdash;3BD:2BG&mdash;BD. </s></p><p type="main">

<s>Questa conclusione &egrave; manifestamente diversa da quella, <lb/>che abbiamo letta di sopra nel Torricelli, la quale non s'appro&shy;<lb/>pria ad altra sezione che all'iperbola. </s>

<s>In tal caso, com'apparisce dalla fig. </s>

<s>226, <pb xlink:href="020/01/2733.jpg" pagenum="358"/>in cui le indicazioni del centro, dell'asse, del diametro e di tutto il resto cor&shy;<lb/>rispondono con quelle della figura 225; DG=BG+GD. Ma, nel caso della <lb/>sferoide o della sfera, DG non &egrave; uguale alla somma delle due dette por&shy;<lb/>zioni del diametro, ma com'&egrave; evidente, alla loro differenza; e perci&ograve; la for&shy;<lb/>mula, applicabile ai tre casi contemplati dal Torricelli, si dovrebbe scrivere <lb/>BO:OE=4BG&plusmn;3BD:2BG&plusmn;BD, nella quale il segno di sopra vale <lb/>per l'iperbola, o per il conoidale iperbolico, e quel di sotto per la sferoide e <lb/>per la sfera. </s></p><p type="main">

<s><emph type="center"/>IX.<emph.end type="center"/></s></p><p type="main">

<s>I solidi conoidei, intorno ai quali aveva il Valerio fatte prove ammi&shy;<lb/>rande ai matematici de'suoi tempi, venivano, per lo studio del Torricelli, <lb/>compresi cos&igrave; in una formula universale, che se ne poteva calcolare il centro <lb/>di gravit&agrave;, fossero que'corpi descritti da qualunque sezione conica, o si ri&shy;<lb/>manessero interi o ridotti nei loro frusti. </s>

<s>La Baricentrica perci&ograve; era, per via <lb/>di queste torricelliane proposizioni, fatta notabilmente progredire sopra quella <lb/>degli antichi, e s'avviava a vestir lo splendore e l'agilit&agrave; di quell'abito nuovo, <lb/>che le avrebbero presto assettato in dosso l'analisi cartesiana e il calcolo <lb/>differenziale. </s>

<s>N&egrave; per solo il metodo &egrave; il Nostro benemerito della scienza, ma <lb/>per la variet&agrave; de'soggetti discorsi, e delle fogge dei solidi immaginati, fra'quali <lb/>si sono in questo trattato veduti apparire i bicchieri e i calici, dentro i quali <lb/>viene a infondere Minerva agl'ingegni sitibondi, con larga mano, l'ambrosia. </s></p><p type="main">

<s>Rimangon per&ograve; ancora, a condurre il presente trattato alla sua perfe&shy;<lb/>zione, altre fogge di solidi, e altre figure di superficie, non pi&ugrave; immaginate <lb/>o conosciute agli antichi, intorno ai centri di gravit&agrave; delle quati s'esercit&ograve; <lb/>con gloriosa riuscita il Torricelli. </s>

<s>Son tra que'solidi principalmente da anno&shy;<lb/>verare i cos&igrave; detti <emph type="italics"/>cavalieriani,<emph.end type="italics"/> e fra quelle superficiali figure le cicloidali, <lb/>che ci vogliono brevemente trattenere in discorso, in quest'ultima parte del <lb/>presente capitolo. </s></p><p type="main">

<s>In una lettera a Michelangiolo Ricci, della quale &egrave; rimasto solo l'estratto, <lb/><figure id="id.020.01.2733.1.jpg" xlink:href="020/01/2733/1.jpg"/></s></p><p type="caption">

<s>Figura 227.<lb/>senza alcuna data precisa, scriveva cos&igrave; il Torricelli circa <lb/>l'anno 1644: &ldquo; Il padre fra Bonaventura mi scrisse la set&shy;<lb/>timana passata, e aggiunger&ograve; qui un capitolo della sua let&shy;<lb/>tera: <emph type="italics"/>Con tale occasione dissi al p. </s>

<s>Mersenno che io ero in&shy;<lb/>torno a speculare sopra un quesito, non ancora digerito, <lb/>quale bisogn&ograve; dirgli, facendomene instanza, per conferirlo <lb/>al signor Robervallio. </s>

<s>Io dissi che non era quesito da un <lb/>par suo: tuttavia volle che io glielo dicessi, ed &egrave; tale: Sia <lb/>sopra la parabola ACB<emph.end type="italics"/> (fig. </s>

<s>227), <emph type="italics"/>come base, il corpo co&shy;<lb/>lonnare o cilindrico, come lo chiamo nella mia Geometria, <lb/>ADEBCF, sicch&egrave; DFE sia l'opposta base, ed anche essa parabola simile,<emph.end type="italics"/><pb xlink:href="020/01/2734.jpg" pagenum="359"/><emph type="italics"/>uguale e similmente posta come ACB. </s>

<s>Stendasi poi un piano per la retta <lb/>AB, e per la cima F della parabola DFE: ora io dissi che cereaco la <lb/>proporzione delli due frusti di detto corpo, fatti dal piano AFB. </s>

<s>Io poi non <lb/>l'ho pi&ugrave; pensato, ma per una certa analogia stimai che fussero fra di loro <lb/>come cinque a due.<emph.end type="italics"/> Queste sono le precise parole di fra Bonaventura. </s>

<s>Io vi <lb/>pensai subito, e trovai subito la dimostrazione, ed il medesimo giorno, che <lb/>ebbi la lettera, gli mandai la risposta. </s>

<s>Parteciper&ograve; anche a V. S. il mio pen&shy;<lb/>siero, rimettendomi a lei il parteciparlo a cotesti signori, se lo stimer&agrave; degno. <lb/><emph type="italics"/>Esto figura quaelibet ABC.... &rdquo;<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>107). </s></p><p type="main">

<s>Nel <emph type="italics"/>Racconto<emph.end type="italics"/> poi dei problemi mandati ai Matematici francesi, pi&ugrave; volte <lb/>da noi citato, dop'avere scritto il quesito, lo stesso Torricelli soggiunge: <lb/>&ldquo; Questo fu da me sciolto universalmente, e non solo risposi che il solido <lb/>a me proposto era segato in proporzion sesquialtera, e non in ragione di <lb/>5 a 3, come il Cavalieri credette per isbaglio stare il frusto maggiore al mi&shy;<lb/>nore; ma in una annunciazione, facile e universalissima, dissi a esso Cava&shy;<lb/>lieri qual proporzione abbiano le parti di tale solido, anco quando le basi <lb/>opposte siano qualunque altra sorta di figura, purch&egrave; abbiano diametro. </s>

<s>Gli <lb/>mandai la brevissima dimostrazione, come anco la mandai agli altri amici <lb/>d'Italia &rdquo; (ivi, T. XXXII, fol. </s>

<s>41). </s></p><p type="main">

<s>Sarebbe nonostante rimasta nel pubblico ignorata di ci&ograve; la notizia, se <lb/>il Cavalieri stesso, nella sua Quinta esercitazione geometrica, dop'aver dimo&shy;<lb/>strata la proposizione XVII, non avesse in uno scolio accennato al quesito, <lb/><figure id="id.020.01.2734.1.jpg" xlink:href="020/01/2734/1.jpg"/></s></p><p type="caption">

<s>Figura 228.<lb/>ch'egli aveva proposto gi&agrave; di risolvere al Tor&shy;<lb/>ricelli, e non avesse soggiunta la dimostra&shy;<lb/>zione, ehe n'ebbe da lui per risposta. </s>

<s>&ldquo; Et <lb/>quia demonstratio elegantissima est, et ad&shy;<lb/>ducta brevior, ideo hic eam subnectere libuit, <lb/>quae talis est &rdquo; (Bononiae 1647, pag. </s>

<s>365). <lb/>Tale per&ograve; crediamo che fosse la dimostrazione <lb/><emph type="italics"/>ex Torricellio<emph.end type="italics"/> quivi addotta, quanto alla so&shy;<lb/>stanza, non per&ograve; quanto alla forma, che il <lb/>Cavalieri ridusse pi&ugrave; geometricamente ordi&shy;<lb/>nata. </s>

<s>Ma perch&egrave; la dimostrazione, rimasta nel <lb/>manoscritto, &egrave; anche pi&ugrave; breve, e non meno <lb/>chiara, e dalla universalit&agrave; della figura, sopra <lb/>la quale s'erige il solido colonnare, passa in <lb/>uno scolio l'Autore a contemplare il caso par&shy;<lb/>ticolare, che la base del detto solido sia para&shy;<lb/>bolica come s'era contentato di proporgli il <lb/>Cavalieri; pensiamo di pubblicar, nella sua <lb/>propria original forma, quella medesima tor&shy;<lb/>ricelliana proposizione, che &egrave; tale: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE LII. &mdash; <emph type="italics"/>Esto figurae ABC<emph.end type="italics"/> (228) <emph type="italics"/>diameter BE, centrum <lb/>vero gravitatis sit F. </s>

<s>Dico frustum, quod sub tribus planis curvague su-<emph.end type="italics"/><pb xlink:href="020/01/2735.jpg" pagenum="360"/><emph type="italics"/>perficie continebitur, ad reliquum sub duobus planis et curva quadam <lb/>superficie contentum; esse ut recta BF ad FE. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nam producatur FH, axis totius solidi, ductaque IOL, quae bifariam <lb/>secet latera EG, BD, connectantur EL, DI. </s>

<s>Patet primo: quod centrum to&shy;<lb/>tius solidi erit punctum O, medium scilicet totius axis FH. </s>

<s>Centrum vero <lb/>frusti superioris ACBD erit in recta EL, et reliqui frusti in recta DI. </s>

<s>Facile <lb/>probatur hoc, nam, si totum solidum secetur plano, ad planum CP parallelo, <lb/>quodlibet parallelogrammum, quod nascetur in superiori frusto, centrum habe&shy;<lb/>bit in recta EL, et reliquum parallelogrammum, quod fiet in frusto inferiori, <lb/>centrum habebit in recta DI. </s>

<s>Propterea omnia simul parallelogramma supe&shy;<lb/>rioris frusti, sive ipsum superius frustum, centrum habebunt in recta EL, et <lb/>sic de reliquo inferiori. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Esto iam centrum gravitatis frusti ACBD punctum quodlibet M, in <lb/>recta EL, productaque MON, erit omnino N centrum reliqui frusti, eritque <lb/>frustum inferius, ad frustum superius, reciproce, ut MO ad ON, sive ut LO <lb/>ad OI: hoc est ut BF ad FE, quod erat propositum &rdquo; (ibid., T. XXXVI, <lb/>fol. </s>

<s>239). </s></p><p type="main">

<s>Suppongasi ora che ACB, come proponeva il Cavalieri, sia una parabola: <lb/>se con F s'indica tuttavia il centro, sar&agrave; per le notissime cose BF:FE= <lb/>3:2. Condotta poi FD, il centro di gravit&agrave; del frusto superiore si dovr&agrave; tro&shy;<lb/>vare sopra un punto di lei, e per le cose gi&egrave; dette anche insieme sopra un <lb/>punto della EL: dunque in R, dove ambedue quelle linee concorrono: cosic&shy;<lb/>ch&egrave; la parte intersecata ER stia all'altra RL, come quattro sta a tre. </s>

<s>Con&shy;<lb/>ducansi infatti le ED, BR: i triangoli EDF, FDB, appnntati in D, e pari&shy;<lb/>mente i triangoli ERF, FRB, appuntati in R, stanno come le respettive basi: <lb/>cio&egrave;, come due a tre, e stanno nella medesima proporzione i rimanenti, tolti <lb/>i triangoli col vertice in R da quegli altri col vertice in D: cio&egrave; ERD:BRD= <lb/>2:3. Dividendo per due i conseguenti, e osservando che la met&agrave; del trian&shy;<lb/>golo BRD &egrave; LRD, avremo ERD:LRD=4:3. E i triangoli con uguale al&shy;<lb/>tezza stando come le loro basi, sar&agrave; dunque, come si diceva, ER:RL= <lb/>4:3. Se infine conducasi ancora da R, attraverso a O, la linea RS, sar&agrave; in S <lb/>il centro di gravit&agrave; del frusto inferiore, il quale star&agrave; al superiore reciproca&shy;<lb/>mente come RO ad OS, o come LO ad OI, cio&egrave; come FB ad EF, in sesquial&shy;<lb/>tera proporzione, secondo che il Torricelli annunziava, correggendo lo sba&shy;<lb/>glio del Cavalieri, e secondo si conclude da questo scolio, che alla proposizion <lb/>precedente si soggiunge nel manoscritto: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Quando vero huiusmodi solidum ab aliqua parabola ortum <lb/>ducat, et oporteat centrum partium reperire; centrum gravitatis frusti ACBD <lb/>habebitur producta recta DF in communi concursu cum recta EL. Nam, si <lb/>secetur planis ad oppositas bases parallelis, sectiones omnes parabolae erunt, <lb/>omniumque et singularum centra gravitatis erunt in recta DF. </s>

<s>Ergo frusti <lb/>centrum erit in DF. </s>

<s>Sed erat etiam in EL, ergo in communi concursu R. &rdquo; </s></p><p type="main">

<s>&ldquo; Amplius dico ER ad RL esse ut 4 ad 3. Nam triangulum BDF, ad <lb/>triangulum EDF, est ut 3 ad 2. Item, ablatum BRF ad ablatum ERF: ergo <pb xlink:href="020/01/2736.jpg" pagenum="361"/>reliquum BRD, ad reliquum ERD, est ut 3 ad 2 etc. </s>

<s>Si denique ab hoc <lb/>communi concursu R producatur recta quaedam linea per O usque ad rectam <lb/>DI; habebitur centrum reliqui frusti &rdquo; (ibid., fol. </s>

<s>240). </s></p><p type="main">

<s>Dop'aver raccontat&ograve; in che modo, e a quale occasione gli proponesse il <lb/>Cavalieri il problema, risoluto cos&igrave; nella sua generalit&agrave; e ne'suoi particolari, <lb/>soggiungeva il Torricelli in tal guisa nella scrittura sopra citata: &ldquo; Il me&shy;<lb/>desimo padre fra Bonaventura mi ha fatto istanza pi&ugrave; di una volta, in diversi <lb/>tempi, acci&ograve; che io volessi trovare la dimostrazione di un altro quesito, che <lb/>neanco egli sapeva, ed &egrave; cos&igrave; definito: &rdquo; </s></p><p type="main">

<s>&ldquo; Se sar&agrave; un solido, nato e segato come il precedente, ma che le basi <lb/>opposte siano figure composte di due mezze parabole ABC, ABF (fig. </s>

<s>229), <lb/>congiunte con la base comune AB, e che le cime siano C ed F; si cerca il <lb/>centro di gravit&agrave; delle due parti del solido. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io dimostrai che, facendosi DA alla DB come 8 a 7, nel caso propo&shy;<lb/>stomi, e tirando la DE parallela alla BI, e di nuovo facendo OD alla OE <lb/><figure id="id.020.01.2736.1.jpg" xlink:href="020/01/2736/1.jpg"/></s></p><p type="caption">

<s>Figura 229.<lb/>come 8 a 7; il punto Q, cio&egrave; il mezzo della retta <lb/>OD, era centro della parte di sopra del solido se&shy;<lb/>gato. </s>

<s>Ma la mia dimostrazione essendo univer&shy;<lb/>sale, provavo che, se il solido nasceva dalla prima <lb/>parabola, che &egrave; il triangolo, la retta BD alla DA <lb/>era come 6 a 6. Se della seconda parabola, era <lb/>come 8 a 7; se della terza, come 9 a 8; se della <lb/>quarta, come 10 a 9, et sic semper. </s>

<s>La retta poi <lb/>ED va segata nella medesima proporzione che <lb/>la BA, e si trover&agrave; il punto O. </s>

<s>E segando per <lb/>mezzo la OD in Q, sar&agrave; Q centro della parte su&shy;<lb/>periore del solido segato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto al centro della parte inferiore non <lb/>soggiunger&ograve; altro, poich&egrave;, essendo dato il centro <lb/>di tutto, e di una parte, con la proporzione delle <lb/>parti, &egrave; dato ancora il centro della parte rima&shy;<lb/>nente, per la VIII del primo degli Equiponde&shy;<lb/>ranti. </s>

<s>La dimostrazione di questo &egrave; stata da me <lb/>conferita solo al medesimo fra Bonaventura, il <lb/>quale me l'ha chiesta &rdquo; (ivi, T. XXXII, fol. </s>

<s>42). <lb/>E allo stesso fra Bonaventura fu da questa sug&shy;<lb/>gerita la dimostrazione della XXI della sua quinta Esercitazione geometrica, <lb/>ma la originale proposizione torricelliana &egrave;, per quel che da noi si sappia, al <lb/>pubblico ignota, per cui ci sentiamo tanto pi&ugrave; fortemente invogliati di pub&shy;<lb/>blicarla, come corona e fastigio delle precedenti. </s>

<s>Ci&ograve; facciamo altres&igrave; perch&egrave; <lb/>quella si tira dietro queste altre due proposizioni, che le servon per lemmi, <lb/>il secondo dei quali specialmente &egrave;, per la sua universalit&agrave;, nella Baricentrica <lb/>di non lieve importanza. </s></p><p type="main">

<s>PROPOSIZIONE LIII. &mdash; <emph type="italics"/>Di due mezze parabole simili e uguali, con-<emph.end type="italics"/><pb xlink:href="020/01/2737.jpg" pagenum="362"/><emph type="italics"/>giunte con la base comune, il centro di gravit&ugrave; sega essa base con tal <lb/>proporzione, che la parte verso il vertice stia alla rimanente come cinque <lb/>sta a tre.<emph.end type="italics"/></s></p><p type="main">

<s>Deriva per corollario dal lemma XI, e dalla proposizione XXI <emph type="italics"/>De di&shy;<lb/>mensione parabolae<emph.end type="italics"/> (Op. </s>

<s>geom., P. II cit., pag. </s>

<s>33, 84), imperocch&egrave;, se siano <lb/><figure id="id.020.01.2737.1.jpg" xlink:href="020/01/2737/1.jpg"/></s></p><p type="caption">

<s>Figura 230.<lb/>le due mezze parabole AHB, AMN (fig. </s>

<s>230) con&shy;<lb/>giunte con la base comune AC, la quale sia anche <lb/>insieme asse dell'emisfero descritto dal quadrante <lb/>ARC, compiuto il semicircolo sul diametro AF, e <lb/>descritte intere le ABF, ANF, abbiamo per la para&shy;<lb/>bola IIL:BC=AL.LF:AC.CF=HM:BN, <lb/>e per il circolo LP2:CR2=AL.LF:AC.CF. </s>

<s><lb/>Dunque HM:BN=<foreign lang="greek">p</foreign>LP2:<foreign lang="greek">p</foreign>CR2, che vuol dire <lb/>essere le infinite linee, delle quali s'intessono le <lb/>due mezze parabole, proporzionali ai cerchi, di che <lb/>si compagina l'emisfero: e perci&ograve; il centro del&shy;<lb/>l'equilibrio nella superficie e nel solido segher&agrave; la <lb/>libbra AC nella medesima proporzione. </s>

<s>Ond'essendo <lb/>nell'emisfero, per le cose gi&agrave; dimostrate, nella proporzione di cinque a tre: <lb/>dunque anche nelle due mezze parabole sar&agrave; tale. </s></p><p type="main">

<s>Ma l'annunziata proposizione deriva pi&ugrave; prossimamente dalla XXIX di <lb/>questo trattato, nella quale si comprende come nella sua formula generale, <lb/>espressa da AO:OC=HL+LI:HL, sostituitivi i valori particolari, che <lb/>sono LI=BC/2, HL=3/4BC, come, osservando che BC sega nel mezzo la <lb/>AF, e HL la AC, resulta dalla proporzione CB:HL=AC.CF:AL.LF= <lb/>4:3. Fatte le sostituzioni s'ha veramente AO:OC=3/4CB+1/2CB: <lb/>3/4CB=5:3, in conferma di quel che sentiremo tra poco asserirsi dal <lb/>Torricelli, come legittima conseguenza di principii gi&agrave; dimostrati. </s></p><p type="main">

<s>PROPOSIZIONE LIV. &mdash; <emph type="italics"/>De'trilinei, formati da qualunque parabola, il <lb/>centro di gravit&agrave; sega l'asse con tal proporzione, che la parte verso il ver&shy;<lb/>tice, alla rimanente, stia come il grado della parabola, eresciuto di un'unit&agrave;, <lb/>all'unit&agrave; stessa.<emph.end type="italics"/></s></p><p type="main">

<s>Che ci&ograve; sia il vero, <emph type="italics"/>ostenditur,<emph.end type="italics"/> dice il Torricelli, <emph type="italics"/>in doctrina parabo&shy;<lb/>larum.<emph.end type="italics"/> Ma perch&egrave; a voler tener dietro all'Autore in quelle dottrine saremm<gap/><lb/>tirati troppo in lungo, e fuori del campo nostro, ci contenteremo di far osser&shy;<lb/>vare come l'annunziata verit&agrave; si confermi per induzione da alcuni esempi. </s></p><p type="main">

<s>Nel triangolo, ch'&egrave; il trilineo formato dalla parabola di primo grado, &egrave; <lb/>stato gi&agrave; da tanti e in tanti modi dimostrato che il centro di gravit&agrave; sega <lb/>l'asse cos&igrave;, che la parte verso il vertice stia a quella verso la base come uno <lb/>pi&ugrave; uno, ossia due, sta a uno. </s>

<s>Verificarsi poi nel trilineo della seconda pa&shy;<lb/>rabola l'annunziata regola generale fu primo a dimostrarlo Luca Valerio, <lb/>nella XXII del suo terzo libro, che dice esser segato dal centro dell'equili&shy;<lb/>brio il diametro della figura <emph type="italics"/>ita, ut pars quae est ad verticem sit tripla<emph.end type="italics"/><pb xlink:href="020/01/2738.jpg" pagenum="363"/><emph type="italics"/>reliquae<emph.end type="italics"/> (pag. </s>

<s>43), ossia come due, grado della parabola, pi&ugrave; uno, &egrave; ad uno. </s>

<s><lb/>Il Torricelli poi v'applic&ograve; il metodo degl'indivisibili, e riusc&igrave; alla medesima <lb/>conclusione, supponendo noto il centro di gravit&agrave; del cono. </s></p><p type="main">

<s>Sia infatti CAG (fig. </s>

<s>231) il trilineo proposto: condotta la AC, e pro&shy;<lb/>lungata in E l'ascissa NB, avremo, per la parabola da una parte, e per la <lb/>similitudine dei triangoli dall'altra, CI:BN=AI2:AN2=IC2:NE2, d'onde, <lb/>moltiplicando per 2 la prima ragione, e per <foreign lang="greek">p</foreign> la seconda, CG:BM=<foreign lang="greek">p</foreign>IC2: <lb/><figure id="id.020.01.2738.1.jpg" xlink:href="020/01/2738/1.jpg"/></s></p><p type="caption">

<s>Figura 231.<lb/><foreign lang="greek">p</foreign>NE2, che vuol dire essere le infinite li&shy;<lb/>nee del trilineo proporzionali agl'infiniti <lb/>circoli di un cono, avente sopra quello <lb/>descritto col raggio IC la base, e in A il <lb/>vertice: per cui avr&agrave; la libbra AI, nel me&shy;<lb/>desimo punto, per ambedue le figure, il <lb/>centro dell'equilibrio. </s>

<s>E perch&egrave; nel cono <lb/>quel centro sega l'asse cos&igrave;, che la parte verso il vertice &egrave; tripla della <lb/>rimanente, dunque anche nell'asse del trilineo tale &egrave; la sezione. </s></p><p type="main">

<s>Il Cavalieri divulg&ograve; questo modo, avuto privatamente dal Torricelli, nella <lb/>propos. </s>

<s>XXIX della sua quinta Esercitazione, bench&egrave; con ordine inverso, ser&shy;<lb/>vendosi del centro del trilineo per indicare quello del cono: e fu lo stesso <lb/>Cavalieri che, nella XXX appresso, rese al pubblico nota l'altra bella ma&shy;<lb/>niera di ritrovare il centro del conoide parabolico, da quello del triangolo, <lb/>come si vide fare al nostro Autore nella XI di questo trattato. </s></p><p type="main">

<s>Ma tornando al proposito, se CI:BN=AI3:AN3, e la parabola &egrave; perci&ograve; <lb/>del terzo grado, o &egrave; cubica, come si dice; il Torricelli dimostr&ograve; che la parte <lb/>dell'asse verso il vertice sta alla rimanente come 3+1, ossia 4, sta ad uno. </s>

<s><lb/>Se CI:BN=AI4:AN4, e perci&ograve; la parabola &egrave; biquadratica, le due dette <lb/>porzioni dell'asse stanno come 4+1 a uno, ossia l'una &egrave; quintupla del&shy;<lb/>l'altra, e cos&igrave; sempre con regola universale, <emph type="italics"/>ut ostenditur in doctrina pa&shy;<lb/>rabolarum.<emph.end type="italics"/></s></p><p type="main">

<s>Si consideri dunque AI come una libbra gravata da grandezze, che si <lb/>eccedono via via a proporzione delle distanze uguali, come nel triangolo, o a <lb/>proporzion de'quadrati, de'cubi, de'quadrato-quadrati, o di qualsivoglia altra <lb/>potenza, come ne'trilinei formati da parabole ordinarie, cubiche, biquadra&shy;<lb/>tiche ecc.; rester&agrave; dimostrato da queste dottrine torricelliane il medesimo <lb/>teorema generalissimo proposto di sopra, messo per&ograve; sotto quest'altra forma: <lb/><emph type="italics"/>Se si disporranno in una libbra grandezze eccedentisi l'una sopra l'altra, <lb/>a proporzione delle semplici distanze uguali, de'quadrati, de'cubi, de'bi&shy;<lb/>quadrati o di qualsivoglia altra potenza di esse distanze; sar&agrave; la detta <lb/>libbra segata dal centro dell'equilibrio con tal ragione, che la parte verso <lb/>le grandezze minori stia alla rimanente, come il grado della potenza, cre&shy;<lb/>sciuto di un'unit&agrave;, sta all'unit&agrave; stessa.<emph.end type="italics"/></s></p><p type="main">

<s>Galileo non riusc&igrave;, nella sua prima proposizione <emph type="italics"/>De centro gravitatis,<emph.end type="italics"/><lb/>a dimostrare il teorema, se non che nel caso che la potenza sia uno. </s>

<s>Per le <lb/>seconde potenze cadde in una fallacia, come apparisce in quel suo medesimo <pb xlink:href="020/01/2739.jpg" pagenum="364"/>trattato dalla proposizlone VI, ma dimostrar la regola universalissima, da va&shy;<lb/>lere per qualunque potenza, non era riserbato che alla potenza matematica <lb/>del Torricelli. </s></p><p type="main">

<s>Cos&igrave; dunque preparatesi le vie, pot&egrave; esso Torricelli riuscire a risolvere <lb/>anche il secondo problema, propostogli dal Cavalieri con questa, che nel ma&shy;<lb/>noscritto &egrave; cos&igrave; intitolata: <emph type="italics"/>Demonstratio centri gravitatis cuiusdam solidi, <lb/>a parabola geniti, cuius dimidium tantum depinximus.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; PROPOSIZIONE LV. &mdash; <emph type="italics"/>Esto parabola quaelibet ABC<emph.end type="italics"/> (fig. </s>

<s>232), <emph type="italics"/>cuius <lb/>vertex A, diameter AD, basis vero DC (nos hic, facilitatis gratia et bre&shy;<lb/>vitatis causa, parabolam ipsam quadraticam supponemus) et super hac <lb/>concipiatur cylindricum parabolicum, cuius oppositae bases sint ABCD,<emph.end type="italics"/><lb/><figure id="id.020.01.2739.1.jpg" xlink:href="020/01/2739/1.jpg"/></s></p><p type="caption">

<s>Figura 232.<lb/><emph type="italics"/>EFG: intelligaturque <lb/>sectum huiusmodi soli&shy;<lb/>dum plano ADFH, per <lb/>diametrum AD, et <lb/>extremam ipsius pa&shy;<lb/>rallelam EH, in oppo&shy;<lb/>sita base ducto. </s>

<s>Quae&shy;<lb/>ritur centrum gravita&shy;<lb/>tis alterius partis, puta <lb/>superioris ABCDF. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Circumscribatur <lb/>ipsi cylindrico parabo&shy;<lb/>lico solidum parallele&shy;<lb/>pipedum AICDGEHF. </s>

<s><lb/>Secetur solidum alio <lb/>plano HO, ubicumque <lb/>sit, dummodo plano DE <lb/>aequidistet, nasceturque <lb/>parallelogrammum BHLM in frusto solidi parabolici, et parallelogrammum <lb/>BMON in quodam solido, cuius basis est CIHF, apex vero A. </s>

<s>Huiusmodi so&shy;<lb/>lidum vocabimus <emph type="italics"/>Pyramidale,<emph.end type="italics"/> licet quatuor tantum ipsius superficies planae <lb/>sint, reliqua vero curva &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXI, fol. </s>

<s>293). </s></p><p type="main">

<s><emph type="italics"/>His suppositis,<emph.end type="italics"/> soggiunge il Torricelli, procederemo alla nostra dimo&shy;<lb/>strazione: della quale per&ograve; chi ha letto il principio non intende quanto po&shy;<lb/>tesse riuscire utile complicarla anche di pi&ugrave; con quella circoscrizione. </s>

<s>Eppure <lb/>sta tutta qui la macchina, disposta co'suoi organi in modo, che pu&ograve;, dalla <lb/>VIII del primo degli Equiponderanti, ricevere l'impulso e la regola del moto. </s>

<s><lb/>In quella archimedea proposizione infatti, dato il contro di gravit&agrave; di qua&shy;<lb/>lunque grandezza, e di una parte, in cui sia stata divisa; s'insegna a ritro&shy;<lb/>vare il centro dell'altra. </s></p><p type="main">

<s>Anche nel presente caso, per via della circoscrizione, il prisma triango&shy;<lb/>lare, che nasce dalla bisezione fatta dal piano DH nel parallelepipedo, si <lb/>compone di due solidi: del frusto parabolico e del piramidale, i quali chia-<pb xlink:href="020/01/2740.jpg" pagenum="365"/>meremo F e P, e immagineremo pendere insieme con le altre loro met&agrave; <lb/>dalla libbra DC, sopra la quale, essendo Q il centro dell'equilibrio del prisma, <lb/>in R quello della parte tolta, ossia del piramidale; il centro del rimanente, <lb/>cio&egrave; di quel che si cerca, supposto essere in S, verr&agrave; indicato dalla rela&shy;<lb/>zione (*) QS:QR=P:F. </s>

<s>Di qui si vede che sar&agrave; allora risoluto il pro&shy;<lb/>blema, quando siano i punti Q, R determinati sopra la libbra, e sia tra P, F <lb/>ritrovata la proporzione della grandezza. </s></p><p type="main">

<s>Il punto Q, da cui pendendo s'equilibra il prisma triangolare, sega la <lb/>libbra in modo, che la parte DQ sia alla QC doppia, com'&egrave; noto per le cose <lb/>gi&agrave; dimostrate, e si potrebbe concludere dalla universalit&agrave; del principio for&shy;<lb/>mulato nella precedente proposizione, dalla quale &egrave; dato pure con facilit&agrave; <lb/>ritrovare il centro, intorno a cui s'equilibra il piramidale. </s>

<s>S'osservi infatti <lb/>che CH:BO=CI.IH:BN.NO. </s>

<s>Ma CI:BN=AI2:AN2, per la parabola, <lb/>e IH:NO=AI:AN, per la similitudine dei triangoli; dunque CH:BO= <lb/>AI3:AN3, e ci&ograve; significa che i parallelogrammi del piramidale son propor&shy;<lb/>zionali alle linee di un trilineo cubico, ond'&egrave; che quelli segheranno l'asse <lb/>nella medesima proporzione di questi, in modo cio&egrave; che la parte verso il ver&shy;<lb/>tice sia quadrupla della rimanente. </s>

<s>Se perci&ograve; intendasi lo spigolo AI traspor&shy;<lb/>tato in DC, e ivi lo stesso piramidale raddoppiato; sar&agrave; il punto R cos&igrave; di&shy;<lb/>sposto sopra la libbra DC, che la parte di lei DR stia all'altra RC come <lb/>quattro sta a uno. </s></p><p type="main">

<s>S'ha dunque di qui notificato, colla formula segnata con asterisco, il <lb/>valore di QR. </s>

<s>Resta a notificarsi la proporzione tra P e F, per che fare <lb/>applicheremo le proposizioni gi&agrave; poco fa scritte: che se dalla LIII veniva <lb/>dimostrato che il centro di gravit&agrave; delle semiparabole, congiunte per la base, <lb/>&egrave; a tal distanza da C, che stia a quella da D come cinque a tre; dalla LII <lb/>si conclude che anche il frusto inferiore, o nel suo tutto o nella sua met&agrave;, <lb/>quale ora solamente viene in considerazione, sta al frusto superiore F, come <lb/>cinque sta a tre: cosicch&egrave; chiamato <emph type="italics"/>CP<emph.end type="italics"/> tutto intero il solido colonnare parabo&shy;<lb/>lico, sar&agrave; F=3/8<emph type="italics"/>CP.<emph.end type="italics"/></s></p><p type="main">

<s>Dai medesimi principii si concluder&agrave; pure che, avendo il trilineo AIC <lb/>il suo centro di gravit&agrave; a tre quarti dal vertice, il frusto superiore di lui, <lb/>chiamandosi <emph type="italics"/>CT<emph.end type="italics"/> il colonnare intero, sar&agrave; P=3/4<emph type="italics"/>CT.<emph.end type="italics"/> Consideriamo ora che <lb/>il colonnare <emph type="italics"/>CP<emph.end type="italics"/> &egrave; doppio di <emph type="italics"/>CT,<emph.end type="italics"/> perch&egrave;, avendo ambedue i solidi la mede&shy;<lb/>sima altezza, la base parabolica DAC &egrave; doppia della trilinea AIC, e perci&ograve; <lb/>F=3/8.2<emph type="italics"/>CT<emph.end type="italics"/>=3/4<emph type="italics"/>CT<emph.end type="italics"/>=P. </s>

<s>Se dunque P=F, per la sopra contrasse&shy;<lb/>gnata con asterisco, sar&agrave; anche QS=QR, e son con ci&ograve; fatte note tutte <lb/>quelle porzioni, che bisognano per riferire il punto S alle due estremit&agrave; della <lb/>libbra. </s>

<s>Abbiamo infatti DS=DQ&mdash;QR=DQ&mdash;(DR&mdash;DQ)=2DQ&mdash;DR; <lb/>SC=QC+QR=QC+QC&mdash;RC=2QC&mdash;RC. </s>

<s>Ma 2DQ&mdash;DR= <lb/>2.2/3DC&mdash;4/5DC=8/15DC; 2QC&mdash;RC=2/3DC&mdash;1/5DC=7/15DC; <lb/>dunque DS:SC=8:7. </s></p><p type="main">

<s>Cos&igrave; viene ad essere dimostrata la verit&agrave;, che il nostro Autore solamente <lb/>annunziava in quelle parole poco addietro da noi trascritte, e illustrate dalla <pb xlink:href="020/01/2741.jpg" pagenum="366"/>figura 229, nella quale sappiamo ora per certa scienza che la distanza AD <lb/>&egrave; 8/15 di tutta intera la libbra. </s>

<s>Se perci&ograve; s'immagina sospeso il frusto dal <lb/>punto D, il centro di gravit&agrave; dovr&agrave; trovarsi lungo il perpendicolo DE, e, per <lb/>le cose dette nella proposizione LII, anche lungo la linea AH, che attraversa <lb/>il centro di tutte le figure parallelogramme componenti lo stesso frusto, di <lb/>cui dunque il centro gravitativo torner&agrave; in Q, dove le due dette linee hanno <lb/>il loro concorso. </s>

<s>Di un tal concorso &egrave; poi facile indicar la posizione nel per&shy;<lb/>pendicolo DE, attraversato in O dalla AI diagonale, perch&egrave; i triangoli simili <lb/>gi&agrave; disegnati danno AD:DB=AO:OI=OD:OE=8:7, per cui &egrave; OD <lb/>8/15 di DE, e DQ, che &egrave; met&agrave; di DO, com'&egrave; BH, met&agrave; di BI, 4/15. Riferito <lb/>insomma il centro di gravit&agrave; del frusto agli assi ortogonali AD, DE, che siano <lb/>ciascuno divisi in quindici parti uguali, s'avr&agrave; l'ascissa a otto, e l'ordinata <lb/>a quattro di quelle parti. </s></p><p type="main">

<s>La medesima proposizione VIII del primo libro degli Equiponderanti, <lb/>che ne ha guidato in questa ricerca, vale per buona regola anche nell'altra: <lb/>nella ricerca cio&egrave; del centro di gravit&agrave; del solido inferiore. </s>

<s>Presa infatti BK <lb/>5/8 di AB, e condotto il perpendicolo KN, che sia attraversato dalla HP in L, <lb/>sar&agrave; L il centro di gravit&agrave; del solido colonnare. </s>

<s>Ma essendo Q quello della <lb/>parte tolta, prolungato QL cos&igrave; in fino in M, che stia LM a LQ reciproca&shy;<lb/>mente come il frusto superiore sta all'inferiore, ossia come tre sta a cinque; <lb/>sar&agrave; in M il centro di gravit&agrave; del rimanente, ossia del frusto inferiore che <lb/>si voleva. </s></p><p type="main">

<s>Le coordinate ortogonali, che indicano la situazione del punto M, sono <lb/>IT=IN+TN e TM=SE&mdash;LR. </s>

<s>Ora IN &egrave; porzione nota dell'asse IV, <lb/>ed SE &egrave; la met&agrave; del perpendicolo ED. </s>

<s>La TN poi, ossia la MR, e la LR sono <lb/>notificate dai triangoli simili LMR, QLS, i quali danno RM=ML/Lq.LS= <lb/>3/5LS; LR=ML/Lq.OQ=3/5OQ, ed LS &egrave; uguale a LH&mdash;SH; OQ= <lb/>OD&mdash;DQ tutte quantit&agrave; note. </s>

<s>Per quantit&agrave; tutte note verr&agrave; dunque a in&shy;<lb/>dicarsi dalle dette coordinate ortogonali il centro di gravit&agrave; del frusto infe&shy;<lb/>riore. </s>

<s>Valga questo nostro discorso, qualunque egli sia, a illustrare per qualche <lb/>parte, e a rendere per qualche altra compiuta la dimostrazione scritta dal <lb/>Torricelli per suo memoriale, e per parteciparla al Cavalieri, che curioso <lb/>gliela aveva chiesta, intanto che l'Autore di lei aspettava a ripulirla, e a met&shy;<lb/>terla in ordine per la stampa quell'occasione, che invidiosamente gli tolse la <lb/>morte. </s>

<s>La detta dimostrazione poi, supposte le cose gi&agrave; annunziate di sopra, <lb/>&egrave; tale: </s></p><p type="main">

<s>&ldquo; His suppositis, esto parallelepipedum 12: eritque cylindricum parabo&shy;<lb/>licum integrum, ad reliquam partem, ut basis ad basim, ob eamdem altitu&shy;<lb/>dinem: nempe ut parabola ABCD ad trilineum externum ABCI; hoc est, in <lb/>nostro casu, ut 8 ad 4. Pars inferior cylindri parabolici, ad superiorem ABCDF, <lb/>est ut 5 ad 3, ut ostendimus iam pridem. </s>

<s>Si enim intelligantur duae semipa&shy;<lb/>rabolae ad eamdem basim CD coniunctae cum suo solido atque sectione, uti <pb xlink:href="020/01/2742.jpg" pagenum="367"/>supra dictum est, erit centrum basis, hoc est duarum semiparabolarum in <lb/>recta CD, ita secta, ut pars ad C terminata sit ad reliquam ut 5 ad 3. Ergo <lb/>etiam solidum inferius ad superius erit, in eo casu, ut 5 ad 3. Quare etiam, <lb/>sumptis tantum dimidiis, erit in nostro casu pars inferior, ad superiorem <lb/>ABCDF, ut 5 ad 3. &rdquo; </s></p><p type="main">

<s>&ldquo; Remanet cylindricum trilineare, cuius oppositae bases sunt ABCI, <lb/>EPFH. </s>

<s>Pars eius inferior, ad superiorem quam Pyramidale vocamus, est ut <lb/>unum ad 3. Si enim intelligantur duo trilinea ad eamdem rectam AI com&shy;<lb/>posita, cum suo solido atque sectione, uti supra explicatum est, erit centrum <lb/>basis, hoc est duorum trilineorum, in recta AI ita secta, ut pars ad I sit ad <lb/>reliquam ut unum ad tria. </s>

<s>Ratio est quia omnes lineae in trilineo, quales <lb/>sunt IC, NB, etc., inter se erunt ut circuli alicuius coni, qui axem habeat <lb/>AI, et verticem A. </s>

<s>Quare etiam pars inferior, ad superiorem, erit in eo casu <lb/>ut unum ad tria. </s>

<s>Ergo, sumptis etiam tantum dimidiis, erit in nostro casu <lb/>pars inferior ad superiorem, sive ad nostrum pyramidale CIHFA, ut unum <lb/>ad tria. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ostensum itaque est quod, si ponatur parallelepipedum 12, pars su&shy;<lb/>perior solidi cylindrici parabolici erit 3. Itemque ipsum sibi adiacens pyrami&shy;<lb/>dale erit 3. Propterea huiusmadi solida, quando parabola quadratica fuerit, <lb/>sunt aequalia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pyramidale CIHFA centrum gravitatis habet in plano basi parallelo, <lb/>quod quidem planum secat AI rectam in ratione quadrupla: nempe ita ut <lb/>pars ad A sit ad reliquam ut 4 ad 1. Ratio est quia parallelogrammum CH, <lb/>ad BO, rationem habet compositam ex ratione rectae CI ad rectam BN, sive <lb/>ex ratione quadrati IA ad AN, ob parabolam quadraticam, et ex ratione rectae <lb/>IH ad NO, sive ex ratione rectae IA ad AN. </s>

<s>Quare parallelogrammum BO <lb/>erit ut cubus IA ad cubum AN, et hoc semper. </s>

<s>Propterea omnia simul pa&shy;<lb/>rallelogramma, sive ipsum pyramidale, centrum gravitatis habebit in eodem <lb/>plano, in quo est centrum gravitatis trilinei externae parabolae cubicae, cum <lb/>plana pyramidalis inter se sint ut lineae trilinei cubici. </s>

<s>Trilineum autem cu&shy;<lb/>bicum centrum gravitatis habet in quadam aequidistante ipsi IC, quae qui&shy;<lb/>dem secat rectam AI in ratione quadrupla, ut ostenditur in <emph type="italics"/>doctrina para&shy;<lb/>bolarum.<emph.end type="italics"/> Quare centrum gravitatis pyramidalis erit in plano, quod secat <lb/>tangentem AI in ratione ut 4 ad 1. &rdquo; </s></p><p type="main">

<s>&ldquo; Ponamus iam omnia corpora a nobis delineata duplicari etiam ex al&shy;<lb/>tera parte ad rectam DC. </s>

<s>Ponaturque rectam DC esse libram quamdam, <lb/>divisam in quindecim partes aequales. </s>

<s>Centrum aequilibrii prismatis, cuius <lb/>dimidium est AHFDIC, erit punctum Q, in quo libra dividitur in ratione <lb/>dupla. </s>

<s>Magnitudines enim appensae sunt infinita parallelogramma, quorum <lb/>unum est HO, inter se eamdem rationem servantia, quam servant lineae <lb/>trianguli DCF, quarum una est HL. </s>

<s>At centrum aequilibrii duorum pyrami&shy;<lb/>dalium, quorum unum est CIHFA, erit punctum R, in quo libra dividitur <lb/>in ratione quadrupla, uti ante explicatum est, ergo centrum aequilibrii re&shy;<lb/>liqui solidi, cuius dimidium est ABCDF, erit S, nempe, sumpta QS, quae sit <pb xlink:href="020/01/2743.jpg" pagenum="368"/>aequalis ipsi QR, cum demonstraverimus ipsum pyramidale aequale esse so&shy;<lb/>lido ABCDF in parabola quadratica. </s>

<s>Propterea centrum gravitatis solidi pro&shy;<lb/>positi erit in recta, quae ex puncto S demittitur aequidistanter ipsi CF. </s>

<s>Est <lb/>autem etiam in recta, quae ex D producitur ad punctum medium ipsius CF, <lb/>ergo in communi concursu. </s>

<s>In nostro casu punctum S secat rectam DC in <lb/>ratione 8 ad 7. &rdquo; </s></p><p type="main">

<s>&ldquo; Si quis vero desideret centrum gravitatis etiam partis inferioris, ipsam <lb/>habebit per VIII libri primi Aequiponderantium, cum datum sit centrum <lb/>totius in medio axis integri solidi, centrumque unius partis, una cum ratione <lb/>partium &rdquo; (ibid., fol. </s>

<s>294, 95). </s></p><p type="main">

<s>Rimane a dire dell'invenzione del centro di gravit&agrave; dentro lo spazio ci&shy;<lb/>cloidale, intorno a che avr&agrave; la nostra Storia, in altro proposito, occasione a <lb/>lungo e importante discorso, l'argomento del quale si vedr&agrave; intanto accen&shy;<lb/>nato dalle seguenti parole, che il Torricelli stesso scriveva nel raccontar le <lb/>vicende subite da'suoi varii problemi, proposti ai matematici di Francia: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Il centro di gravit&agrave; della cicloide sta nell'asse e lo sega in pro&shy;<lb/>porzione di sette a cinque.<emph.end type="italics"/> Avendo io avvisato la sola annunciazione di <lb/>quest'ultimo teorema in Francia, mi fu risposto dal p. </s>

<s>Mersenno, che allora <lb/>era l'interpetre tra mons&ugrave; Roberval e me, che io in questo avevo prevenuto <lb/>il loro geometra Roberval, il quale circa alla cicloide aveva dimostrata ogni <lb/>altra cosa, fuor che il centro di gravit&agrave;, e il solido intorno all'asse: e che <lb/>riconoscevano da me, come da primo inventore, questa invenzione del centro <lb/>di gravit&agrave; della cicloide, e che non credevano che geometricamente potesse <lb/>esser vera la mia proposta. <emph type="italics"/>Dubitat Robervallius noster an mechanice tan&shy;<lb/>tum centrum gravitatis inveneris, quod tamen geometrice falsum suspi&shy;<lb/>catur. </s>

<s>Docebis num demonstrationem habeas<emph.end type="italics"/> con altre confessioni simili, <lb/>come appare in lettere di propria mano del p. </s>

<s>Mersenno, le quali sono ap&shy;<lb/>presso di me. </s>

<s>In queste confessa apertamente che monsu Roberval non aveva <lb/>quel teorema, se ne chiamano debitori a me, e parlando di Roberval dice <lb/>queste parole: <emph type="italics"/>Qui cum tuas postremas literas legisset praedictum centrum <lb/>gravitatis tibi debere fatetur qui primus invenisti,<emph.end type="italics"/> e mi prega pi&ugrave; di una <lb/>volta, acci&ograve; che io voglia mandargli la dimostrazione, con promettermi che <lb/>si sarebbe messa fra quelle di mons&ugrave; Roberval, e cos&igrave; per l'appunto segu&igrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io subito gli mandai, e questo fu la state del 1644, in una lunga <lb/>scrittura, non solo la dimostrazione del centro di gravit&agrave;, ma anco la dimo&shy;<lb/>strazione del teorema seguente, poich&egrave; serviva per lemma alla dimostrazione <lb/>mia: <emph type="italics"/>Se due figure piane saranno girate intorno a due lince come assi, <lb/>gli solidi fatti dalla revoluzione averanno fra di loro la proporzione com&shy;<lb/>posta della proporzione, che hanno le figure piane genitrici, e della pro&shy;<lb/>porzione, che hanno le distanze del centro di gravit&agrave; delle medesime dal&shy;<lb/>l'asse della revoluzione.<emph.end type="italics"/> Essi hanno tardato due anni a rispondere, ed ora, <lb/>dimenticati delle lettere passate, e confidando che io, avendole sprezzate, non <lb/>le abbia pi&ugrave;, scrivono che le predette dimostrazioni, mandategli da me a loro <lb/>istanza, le avevano un pezzo fa. </s>

<s>Ora si sta controvertendo questo punto, e <pb xlink:href="020/01/2744.jpg" pagenum="369"/>se essi persisteranno in dire che, avanti a me avevano le predette due dimo&shy;<lb/>strazioni, io sono risoluto di far riconoscere le lettere, le quali sono notis&shy;<lb/>sime a molti in Italia, e stamparle, insieme con le ragioni mie, acci&ograve; il mondo <lb/>veda che furto vergognoso hanno tentato di farmi &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXII, <lb/>fol. </s>

<s>39). </s></p><p type="main">

<s>Troppo semplici bisognerebbe dire i nostri Lettori, se credessero, come <lb/>alcuni hanno fatto, che sia decisa la sentenza cos&igrave; dietro le ragioni dette a <lb/>favor suo da uno solo dei litiganti. </s>

<s>Ascolteremo altrove anche l'altra parte, <lb/>e, se non c'inganniamo, sar&agrave; allora che la Storia ci avr&agrave; dato della causa <lb/>cognizione perfetta, pronunziato finalmente il giudizio secondo giustizia. </s>

<s>In&shy;<lb/>tanto, messa la proposizione del centro di gravit&agrave; della cicloide in forma, per <lb/>aggiungersi a questo trattato, vediamo come l'Autore l'avesse dimostrata. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE LVI. &mdash; <emph type="italics"/>Centrum gravitatis cycloidis dividit axem ita, <lb/>ut pars ad verticem terminata sit ad reliqua ut 7 ad 5. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Vi &egrave; premesso un lemma simile, e di non men facile dimostrazion di <lb/>quell'altro, che in primo luogo precede al secondo teorema <emph type="italics"/>De dimensione <lb/>Cycloidis<emph.end type="italics"/> (Op. </s>

<s>geom., P. II cit., pag. </s>

<s>87): il detto lemma &egrave; tale: </s></p><p type="main">

<s>&ldquo; Si super lateribus oppositis alicuius parallelogrammi rectanguli ABCD <lb/>(fig. </s>

<s>233), duo semicirculi descripti sint, figuram mixtam AEBCFD <emph type="italics"/>arcuatum<emph.end type="italics"/><lb/><figure id="id.020.01.2744.1.jpg" xlink:href="020/01/2744/1.jpg"/></s></p><p type="caption">

<s>Figura 233.<lb/>appello, lineasque rectas AD, BC ipsius bases. </s>

<s>Quando <lb/>vero arcuatum iam dictum sectum fuerit ab aliqua <lb/>recta EF, basibus parallela, utramque figuram a se&shy;<lb/>ctione factam <emph type="italics"/>arcuatum<emph.end type="italics"/> item appello. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Unnmquodque arcuatum aequale est rectangulo <lb/>super eadem basi, et sub eadem altitudine constituto: <lb/>facile probatur hoc per subtractionem, additionemque. </s>

<s><lb/>Ergo patet quod arcuata, super aequalibus basibus <lb/>constituta, erunt inter se ut altitudines. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Denique si alicuius arcuati AEFD altitudo HD <lb/>bifariam secetur in I, suppono centrum gravitatis arcuati esse in ea linea, <lb/>quae per I ducitur aequidistanter basibus arcuati. </s>

<s>Quod quidem utraque ra&shy;<lb/>tione, nova veterique, facile probari potest: facilius tamen concedi et omitti &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. XXXIV, fol. </s>

<s>275). </s></p><p type="main">

<s>Che per semplice addizione e sottrazione sia veramente la cosa dimo&shy;<lb/>strabile, resulta, chiamando A l'arcuato, dall'equazione A=<foreign lang="greek">p</foreign>BA2/2+ <lb/>BI.IH&mdash;<foreign lang="greek">p</foreign>CD2/2=BI.IH. </s>

<s>E ci&ograve; che del tutto essendo vero altres&igrave; delle <lb/>parti corrispondenti, sar&agrave; l'arcuato CBEF uguale al rettangolo BH, e l'ar&shy;<lb/>cuato ADFE uguale al rettangolo AH: ond'&egrave; che sulla linea, condotta dal <lb/>mezzo di HD parallela alla base comune, si trover&agrave; il centro di gravit&agrave; del&shy;<lb/>l'una e dell'altra figura. </s></p><p type="main">

<s>Se ora dell'emicicloide ABCD (fig. </s>

<s>234) si divida in F, nel mezzo, la <lb/>semibase AD, e sopra il diametro FG si disegni una met&agrave; del circolo geni-<pb xlink:href="020/01/2745.jpg" pagenum="370"/>tore, e poi dal punto B, dove la circonferenza di lui sega la cicloide, si con&shy;<lb/>duca la BE parallela alla base; &egrave; manifesto che questa passer&agrave; per i centri <lb/><figure id="id.020.01.2745.1.jpg" xlink:href="020/01/2745/1.jpg"/></s></p><p type="caption">

<s>Figura 234.<lb/>L, E, e che con una tal costruzione <lb/>si verr&agrave; lo spazio cicloidale a dividere <lb/>in quattro parti, che sono: il semi&shy;<lb/>circolo CHD, l'arcuato BHDF e i due <lb/>trilinei CBH, ABF. L'arcuato, che &egrave; <lb/>per il precedente lemma uguale al ret&shy;<lb/>tangolo FE, ossia a FD quarta parte <lb/>della circonferenza moltiplicata per il <lb/>raggio ED, sar&agrave; dunque uguale a mezzo il circolo CHD: e perch&egrave; tutto lo spa&shy;<lb/>zio si compone di tre tali mezzi circoli, dunque i due trilinei insieme equi&shy;<lb/>varranno al terzo. </s></p><p type="main">

<s>Oltre alle proporzioni delle aree di due delle parti componenti, sappiamo <lb/>anche il centro di gravit&agrave; in quale ordinata egli sia, e il centro di CHD <lb/>semicircolo essere in EB, e dell'arcuato in IM. </s>

<s>E ci&ograve; tanto basta, senza che <lb/>sia determinato in quelle linee il punto preciso, perch'essendo la presente <lb/>invenzione rivolta, non alla mezza cicloide particolarmente, ma alla cicloide <lb/>intera; basta a noi sapere dove la linea, che ricongiunge i centri di gravit&agrave; <lb/>delle due parti in distanze uguali dall'asse, sega l'asse stesso: nel qual punto <lb/>della sezione ha in ogni modo a ritrovarsi il centro di gravit&agrave; del tutto. </s>

<s>Si <lb/>riduce dunque il negozio a dimostrare in quale ordinata si trovi il centro di <lb/>gravit&agrave; dei due trilinei, intorno a che tutto si affatic&ograve; il Torricelli a quel <lb/>modo, e con quella riuscita, che i Lettori qui appresso intenderanno. <lb/><figure id="id.020.01.2745.2.jpg" xlink:href="020/01/2745/2.jpg"/></s></p><p type="caption">

<s>Figura 235.</s></p><p type="main">

<s>&ldquo; Esto dimidium lineae cycloidis ABC (fig. </s>

<s>235), cuius axis CD, basis <lb/>vero sit AD, et ordinata, per punctum axis medium, sit EB. </s>

<s>Transeat autem <lb/>per B circulus genitor FBG, contingens basim in F lineamque CG in G. </s>

<s><lb/>Patet quod aequales erunt AF, FD, nam, cum arcus FB, BG quadrantis sint, <pb xlink:href="020/01/2746.jpg" pagenum="371"/>recta AF aequalis est arcui BF: recta vero GC aequalis est arcui GB, utra&shy;<lb/>que ob naturam cycloidis primariae. </s>

<s>Cum vero latera opposita arcuati FBHD <lb/>aequalia sint, nempe BH, FD erunt aequales, et rectae AF, BH. </s>

<s>Secetur ita&shy;<lb/>que utraque illarum in partes quotcumque aequales, et erunt in recta BH <lb/>partes totidem quot sunt in AF. </s>

<s>Transeat iam per unumquodque sectionum <lb/>punctum peripheria circuli genitoris, et super singulis basibus HI, IL, etc., <lb/>item super singulis basibus FM, MN, etc., concipiantur constituta arcuata <lb/>usque ad cycloidem lineam, ita ut arcuata tangant, sed non excedant lineam <lb/>cycloidalem. </s>

<s>Manifestum est quod numerus arcuatorum, quot sunt in trili&shy;<lb/>neo ABF, aequalis erit numero arcuatorum, quot sunt in trilineo BCH, nam <lb/>super singulis partibus rectae AF, excepta extrema quae terminatur ad A, <lb/>item, super singulis partibus rectae BH, excepta extrema quae terminatur <lb/>ad B, singula arcuata erecta sunt. </s>

<s>Dico universa huiusmodi arcuata centrum <lb/>commune gravitatis habere in recta BE, quae per medium axis punctum in <lb/>cycloide applicatur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sumantur enim duo quaelibet ex praedictis arcuatis MP, IO, quorum <lb/>bases NM, LI aequaliter remotae sunt a punctis A et B: tum producantur <lb/>ordinatim PQ, OR, ducaturque ST parallela ad axem, et secentur bifariam <lb/>QD in V, RE in X, ST in Y, et HT in Z. Jam, ob naturam cycloidis, arcus <lb/>OK aequalis est rectae KC, sed quadrans LK rectae GC: ergo reliquus ar&shy;<lb/>cus LO rectae GK aequalis erit, sive rectae BL, sive rectae AN, ob suppo&shy;<lb/>sitionem, bases enim sumptorum arcuatorum aequaliter distant ab A et B <lb/>punctis; sive arcui PN, ob cycloidem. </s>

<s>Ergo, cum aequales sint arcus OL, PN, <lb/>aequales erunt eorum sagittae, sive sinus versi HT, QD, quod memento. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quoniam tota HW, et tota HE est ut ablata HT ad TZ, nempe dupla, <lb/>erit reliqua TW dupla reliquae ZE. </s>

<s>Arcuatum vero MP, ad arcuatum IO, <lb/>est ut altitudo QD ad ST, sive ut HT ad TS, sive, ob circulum, ut TS ad <lb/>TW, sive, sumptis subduplis, ut TY ad ZE, sive, sumptis aequalibus, ut XE <lb/>ad EV. </s>

<s>Est autem centrum gravitatis arcuati MP in linea applicata ex V, et <lb/>centrum arcuati OI est in linea applicata ex puncto X, ostendimusque arcua&shy;<lb/>tum MP, ad IO, esse ut recta XE ad EV, reciproce. </s>

<s>Propterea commune illo&shy;<lb/>rum centrum erit in recta BE, ubicumque tamdem sit. </s>

<s>Sic ostendetur cen&shy;<lb/>trum omnium reliquorum, si bina sumantur, ea lege ut sumptorum bases <lb/>aequaliter distent a punctis A et B; ostendetur, inquam, centrum gravitatis <lb/>omnium esse in eadem recta BE. </s>

<s>Propterea et commune centrum gravitatis <lb/>universorum, simul sumptorum, erit in BE. &rdquo; </s></p><p type="main">

<s>&ldquo; Amplius, dico commune centrum gravitatis duorum trilineorum ABF, <lb/>BCH esse in eadem recta BE. </s>

<s>Si enim possibile est, ponatur extra rectam <lb/>BE, ubicumque, puta <foreign lang="greek">b. </foreign></s>

<s>Ducatur ordinatim recta <foreign lang="greek">ab. </foreign></s>

<s>Tum inscribantur intra <lb/>ipsa trilinea duae figurae, constantes ex arcuatis aeque altis, et numero ae&shy;<lb/>qualibus, utrimque, ita tamen ut trilinea ipsa, ad differentiam, quae inter <lb/>ipsa et inscriptas figuras est, maiorem habeant rationem, quam CE ad E<foreign lang="greek">a. </foreign></s>

<s><lb/>Quod autem hoc fieri possit, constat: nam, supponamus ita esse duo trilinea, <lb/>ad aliquod spatium <foreign lang="greek">*s</foreign>, uti est CE ad E<foreign lang="greek">a</foreign>: tum inscribantur intra ipsa trili-<pb xlink:href="020/01/2747.jpg" pagenum="372"/>nea duae figurae, constantes ex arcuatis aeqealtis, ita ut defectus figurarum <lb/>inscriptarum a trilineis minor sit spatio <foreign lang="greek">*s. </foreign></s>

<s>Tunc enim erit ratio trilineorum, <lb/>ad differentiam, maior ratione CE ad E<foreign lang="greek">a. </foreign></s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Factum ergo sit, supponamusque inscriptas in trilineis esse duas figu&shy;<lb/>ras, ex arcuatis compositas, uti iussum est. </s>

<s>Ex demonstratis, erit centrum <lb/>gravitatis incriptarum figurarum in recta BE. </s>

<s>Esto illud punctum quodcum&shy;<lb/>que <foreign lang="greek">g</foreign>, ducaturque recta <foreign lang="greek">gb</foreign>, et extendatur. </s>

<s>Fiat deinde ut ipsa duo trilinea <lb/>ABF, BCH, ad praedictam differentiam, ita recta quaedam <foreign lang="greek">eg</foreign> ad <foreign lang="greek">gb</foreign>: patet <lb/>quod recta <foreign lang="greek">eg</foreign> maior erit quam <foreign lang="greek">dg</foreign>, nam ratio <foreign lang="greek">eg</foreign>, ad <foreign lang="greek">gb</foreign>, eadem est ac ratio <lb/>trilineorum ad differentiam, quae quidem ratio, per constructionem, maior <lb/>est ratione CE ad E<foreign lang="greek">a</foreign>: hoc est ratione <foreign lang="greek">dg</foreign> ad <foreign lang="greek">gb. </foreign></s>

<s>Ergo recta <foreign lang="greek">eg</foreign> maior est <lb/>quam recta <foreign lang="greek">dg. </foreign></s>

<s>Dividendo itaque, erunt figurae inscriptae in arcuatis constan&shy;<lb/>tes, ad illam differentiam, ut recta <foreign lang="greek">eb</foreign> ad <foreign lang="greek">bg. </foreign></s>

<s>Sed <foreign lang="greek">b</foreign> centrum gravitatis est <lb/>totius, et <foreign lang="greek">g</foreign> figurarum inscriptarum; ergo <foreign lang="greek">e</foreign> erit centrum gravitatis differen&shy;<lb/>tiae, absurdum. </s>

<s>Non est ergo centrum gravitatis trilineorum extra rectam BE, <lb/>sed in ipsa, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; (ibid., fol. </s>

<s>275, 76). </s></p><p type="main">

<s>Essendosi cos&igrave; dunque dimostrato che il centro di gravit&agrave; d'ambedue i <lb/>trilinei &egrave; sopra l'ordinata BE (rivolgendo l'occhio indietro sulla figura 234) <lb/>in E dunque, sull'asse, saranno i centri di gravit&agrave; di questi, come degli altri <lb/>due trilinei a questi uguali, che son dentro l'altro spazio cicloidale: e in E, <lb/>centro della figura, sar&agrave; pure il centro di gravit&agrave; del circolo intero, a cui <lb/>i detti quattro trilinei, e i due arcuati col centro comune in I, sono uguali. </s>

<s><lb/>Delle tre pari grandezze dunque, delle quali si compone lo spazio cicloidale, <lb/>due pendono in E, e una in I, ond'&egrave; che, se la libbra EI si divide ugual&shy;<lb/>mente in tre parti, due delle quali ne abbia IO, e la terza EO; in O sar&agrave; <lb/>il centro di gravit&agrave; del tutto, ossia della Cicloide. </s>

<s>Se poi anche ID nello stesso <lb/>modo si tripartisca, e in sei, come riman divisa questa met&agrave;, si divida pa&shy;<lb/>rimente anche l'altra met&agrave; dell'asse; &egrave; manifesto che, delle dodici parti, CO <lb/>ne contien 7, e OD 5, come gi&agrave; il Torricelli annunziava in principio, e in <lb/>fine alla sua dimostrazione ora conclude con queste parole: </s></p><p type="main">

<s>&ldquo; Praeterea, cum arcuatum FBHD aequale sit rectangulo FLED, et se&shy;<lb/>micirculus CHD eidem rectangulo aequalis sit; aequales erunt inter se tres <lb/>figurae, nempe semicirculus CHD, arcuatum FBHD, et reliqua duo trilinea <lb/>ABF, BCH simul sumpta. </s>

<s>Secetur ED bifariam in I, et EI in tres partes <lb/>aequales EO, OP, PI: manifestum est quod centrum gravitatis arcuati FBHD <lb/>est in applicata ex puncto I, et reliquarum duarum magnitudinum, nempe <lb/>semicirculi trilineorumque, centrum gravitatis est in applicata BE, estque ar&shy;<lb/>cuatum FBHD, ad reliquas figuras, subduplum, hoc est ut EO ad OI reci&shy;<lb/>proce. </s>

<s>Ergo centrum gravitatis compositae emicicloidis erit in applicata, quae <lb/>per O ducitur. </s>

<s>Propterea centrum gravitatis integrae cicloidis erit ipsummet <lb/>punctum O. </s>

<s>Quod autem CO ad OD sit ut numerus 7 ad 5, manifestum est <lb/>ex imperata divisione &rdquo; (ibid., fol. </s>

<s>276). </s></p><pb xlink:href="020/01/2748.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Di varie altre cose di Meccanica <lb/>lasciate dal Torricelli<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Di alcune proposizioni relative al trattato <emph type="italics"/>De motu.<emph.end type="italics"/> &mdash; II. </s>

<s>Di alcune altre proposizioni relative al <lb/>trattato <emph type="italics"/>De momentis.<emph.end type="italics"/> &mdash; III. </s>

<s>Del modo meccanico di condur le tangenti, e di varii altri teo&shy;<lb/>remi di Meccanica nuova. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Se non avesse il Torricelli lasciato altro di manoscritto che le proposi&shy;<lb/>zioni dei centri di gravit&agrave;, delle quali nel precedente capitolo ci siamo stu&shy;<lb/>diati di ordinare e di esporre la storia, basterebbe questo solo per giustificare <lb/>le sollecitudini del principe Leopoldo de'Medici, il quale, persuasosi che fos&shy;<lb/>sero quelle carte non intelligibili che al loro proprio autore, e rappresenta&shy;<lb/>tive cos&igrave; informi di un disegno, che nessun altro saprebbe mettere in ese&shy;<lb/>cuzione; avrebbe voluto che nella Biblioteca laurenziana fossero custodite, <lb/>dentro un'arca fatta fabbricare con regia munificenza, le preziose reliquie. </s>

<s><lb/>Lodovico Serenai per&ograve;, bench&egrave; fossero morti il Cavalieri e il Ricci, che il <lb/>Torricelli stesso aveva designati della sua scientifica eredit&agrave; esecutori testa&shy;<lb/>mentari, non aveva perduta affatto la speranza di veder que'teoremi, in <lb/>qualche parte compiuti e in qualche altra illustrati, messi in ordine di trat&shy;<lb/>tato cos&igrave;, da supplire nel miglior modo possibile a quella perdita, che da tutti <lb/>si deplorava. </s>

<s>Aveva il verde di una tale speranza fondate le sue radici nella <lb/>perizia delle cose, e nella affezione che, come discepolo verso l'autore di loro, <lb/>tutti riconoscevano nel Viviani. </s>

<s>Da lui perci&ograve; i Matematici di Europa, i quali <lb/>avevano con tanto applauso e con tanta ammirazione accolte le Opere geo&shy;<lb/>metriche stampate nel 1644, aspettavano di veder sodisfatti i loro desiderii. <pb xlink:href="020/01/2749.jpg" pagenum="374"/>E quasi fosse divenuto intollerabile ogni pi&ugrave; lungo indugio, Erasmo Bartho&shy;<lb/>lin, che trattenendosi in Italia aveva con lo stesso Viviani contratta partico&shy;<lb/>lare amicizia, veniva da Padova con sue lettere sollecitando il fiorentino amico, <lb/>perch&egrave; gli volesse intanto trascrivere la nota degli argomenti, intorno a che <lb/>verserebbero le opere postume del Torricelli. </s>

<s>Il qual desiderio era sodisfatto <lb/>cos&igrave;, con lettera del d&igrave; 4 Settembre 1655 da Firenze: </s></p><p type="main">

<s>&ldquo; Invio a V. S. la qui inclusa nota delle opere postume originali del <lb/>signor Torricelli, che, dalla morte di esso in qua, si trovano appresso il signor <lb/>Lodovico Serenai, il quale, per ratificare in parte al desiderio e alla curio&shy;<lb/>sit&agrave; di V. S., ha trascritto dal proemio del libro <emph type="italics"/>Delle proporzioni<emph.end type="italics"/> quant'ella <lb/>vede in proposito del trattato <emph type="italics"/>De lineis novis,<emph.end type="italics"/> che il medesimo signor Tor&shy;<lb/>ricelli prometteva di dar fuori. </s>

<s>Non so gi&agrave; se l'improvvisa morte di lui gli <lb/>abbia tolto il poter colorire e perfezionare cos&igrave; peregrini e maravigliosi di&shy;<lb/>segni, quali egli va leggermente toccando in detto suo proemio, non avendo <lb/>io avuto per ancora appresso di me copia di alcun foglio di detta materia. </s>

<s><lb/>Dubito per&ograve; che, per essere i primi abbozzi ed i primi delineamenti di cos&igrave; <lb/>alte meditazioni, ci sia, oltre al disordine, ed errori e imperfezioni dell'opera <lb/>stessa, la quale forse non ha finita e dimostrata in ogni sua parte, ma solo <lb/>in molti luoghi accennata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Alle due prime necessit&agrave; procurer&ograve; di ovviare, nella maniera che ho <lb/>fatto intorno alla copia di altre cose geometriche del medesimo Autore, che <lb/>ultimamente ho avuto alle mani, avendogli dato il miglior ordine a me pos&shy;<lb/>sibile, per essersi trovate confusissime, correttele ne'luoghi difettosi, e nei <lb/>trascorsi di penna, soliti farsi per lo pi&ugrave; nelle prime bozze, tolte via quelle <lb/>che sono gi&agrave; stampate da lui medesimo o da altri, e che <emph type="italics"/>ad institutum non <lb/>faciunt,<emph.end type="italics"/> e ridotte finalmente a vero senso quelle, che per avventura propon&shy;<lb/>gono o concludono il falso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto alla terza, lascer&ograve; che venga supplito da altri, assai pi&ugrave; di me <lb/>esercitato in queste nuove speculazioni, con dimostrare e aggiungere ci&ograve; che <lb/>potesse mancarci, trovandomi da dieci anni, o piuttosto dalla morte del signor <lb/>Galileo mio maestro in qua, per varie disavventure e pessime contingenze, <lb/>nemici, domestici affari, etc., quasi affatto alienato da simili studi, che per <lb/>altro sariano proporzionatissimi al genio mio, se non alla mia inclinazione. </s>

<s><lb/>Intanto V. S., insieme con gli altri acutissimi geometri d'Europa, aspetti in <lb/>breve la pubblicazione di tali opere, e compatisca a qualche poca di dila&shy;<lb/>zione, non essendo in potest&agrave; mia il disporre delle altrui cose &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. CXLII, fol. </s>

<s>4). </s></p><p type="main">

<s>Quella dilazione per&ograve;, che si prometteva si poca, era giunta a ben ven&shy;<lb/>titre anni, dopo il qual tempo cos&igrave; scriveva il Viviani stesso in una sua let&shy;<lb/>tera del d&igrave; 7 Giugno 1678 al p. </s>

<s>Antonio Baldigiani gesuita, che attendeva <lb/>allora a scrivere gli elogi di Galileo, e de'pi&ugrave; illustri discepoli di lui: &ldquo; Ve&shy;<lb/>nendo ora all'acutissimo geometra Torricelli, il quale, bench&egrave; di nazione non <lb/>toscano, illustr&ograve; mirabilmente il posto del suo predecessore Galileo, ed in <lb/>conseguenza la nostra Toscana con le sue speculazioni; io son pur certo che <pb xlink:href="020/01/2750.jpg" pagenum="375"/>di questo ancora, essendovi assaissimo da commendare, assai ella e felicis&shy;<lb/>simamente avr&agrave; detto. </s>

<s>Di questo le Opere pubblicate sin ora son comprese <lb/>in un tomo in quarto, stampato in Firenze nel 1644, ecc. </s>

<s>&rdquo; (ivi, fol. </s>

<s>272), e <lb/>seguitando a enarrare i titoli delle Opere varie, poi cos&igrave; soggiunge: </s></p><p type="main">

<s>&ldquo; Le opere rimanenti da stamparsi ora saranno sotto questo titolo: <lb/>EVANGELISTAE TORRICELLI FAVENTINI &mdash; MATHEMATICI OLIM SERENISS. &mdash; FER&shy;<lb/>DINANDI-II. M. E. D. &mdash; OPERA POSTHUMA MATHEMATICA &mdash; QUAE EXTANT OMNIA <lb/>&mdash; IN TRES PARTES DIVISAS &mdash; QUARUM PRIMA, STYLO VETERUM CONTINET &mdash; <lb/><emph type="italics"/>Miscellanea circa magnitudines planas, curvas, ac solidas &mdash; Mechanica <lb/>quaedam &mdash; De tactionibus et de proportionibus libros cum enarratione <lb/>quorundam problematum geometricorum.<emph.end type="italics"/> &mdash; SECUNDA CONTINET, INDIVISI&shy;<lb/>BILIUM METHODO, <emph type="italics"/>Stereometria et eentrobaryca.<emph.end type="italics"/> &mdash; TERTIA, <emph type="italics"/>Tractatus de li&shy;<lb/>neis novis. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; In quarto luogo saranno alcune <emph type="italics"/>Lezioni Accademiche<emph.end type="italics"/> italiane e Let&shy;<lb/>tere familiari. </s>

<s>Ci&ograve; che io abbia faticato e contribuito a quest'Opere si cono&shy;<lb/>scer&agrave; apertamente, ma non mai tanto, quanto da chi le vedde disordinate e <lb/>imperfette &rdquo; (ivi). </s></p><p type="main">

<s>Sono ormai passati, dalla data di questa lettera al Baldigiani, dugento <lb/>e vent'anni, e delle opere postume del Torricelli, quivi annunziate e solen&shy;<lb/>nemente promesse come di prossima pubblicazione, non si son vedute che <lb/>le Lezioni accademiche, per cura di tutt'altri che del Viviani. </s>

<s>Erano forse <lb/>una menzogna le sue promesse, o era vero quel che dissero alcuni, che cio&egrave; <lb/>vi si trovasse contro sua voglia impegnato, e che per invidia e per rivalit&agrave; <lb/>col Torricelli menasse cos&igrave; la cosa in lungo, da riuscire a eludere i deside&shy;<lb/>rii del Serenai, e i comandi del principe Leopoldo? </s></p><p type="main">

<s>La calunnia si dissipa senz'altro, osservando che non fa maraviglia se <lb/>manc&ograve; al Viviani, per curare le opere altrui, quel tempo o quella comodit&agrave;, <lb/>che non seppe trovar per le proprie: bench&egrave; non si venga a togliere con ci&ograve; <lb/>qualche dubbio, che rimarrebbe intorno alla sincerit&agrave; del titolo, che tenevasi <lb/>preparato per mettersi innanzi alla stampa del libro. </s>

<s>S'avevano veramente <lb/>in ordine tutti i trattati matematici secondo le tre parti, nelle quali il dili&shy;<lb/>gente compilatore pensava di distribuire le opere postume del Torricelli? </s>

<s>Si <lb/>risponderebbe di no, se la maggior parte de'fascicoli non manca ne'raccolti <lb/>volumi manoscritti. </s>

<s>E fra quei che ci sono abbiamo avuto occasione nel pre&shy;<lb/>cedente capitolo di parlare dei centrobarici, confessando di averli trovati cos&igrave; <lb/>negligentemente condotti nelle parti loro pi&ugrave; sostanziali, da non sembrar cre&shy;<lb/>dibile che avesse permesso di stamparli a quel modo il Viviani. </s>

<s>Il medesimo <lb/>giudizio &egrave;, secondo noi, da fare di quegli altri trattatelli, per i quali si ri&shy;<lb/>chiedeva l'opera del compilatore in compiere, in ordinare e in illustrare i <lb/>varii teoremi. </s>

<s>E perch&egrave; fra questi i pi&ugrave; importanti per noi son quelli di argo&shy;<lb/>mento meccanico, intorno ad essi soli restringeremo le nostre osservazioni. </s></p><p type="main">

<s>All'argomento ora detto appartiene principalmente quel trattatello inti&shy;<lb/>tolatosi dal Viviani <emph type="italics"/>De motu ac momentis,<emph.end type="italics"/> di cui ci &egrave; rimasto un abbozzo <lb/>informe, e che, sebbene abbia ripescato per tutto il campo della scienza del <pb xlink:href="020/01/2751.jpg" pagenum="376"/>moto, de'solidi non solo, ma e de'liquidi; non giunge pi&ugrave; che a diciassette <lb/>o a diciotto proposizioni. </s>

<s>Ci sarebbe ne'manoscritti torricelliani materia da <lb/>raddoppiarne senza dubbio, e da triplicarne, non forse il numero solo ma <lb/>l'importanza, e noi avremmo anche volentieri presa a fare questa fatica, se <lb/>l'ufficio nostro di storici, e non di editori, non ci consigliasse di tener, nella <lb/>scelta e nell'ordine dei teoremi, quelle ragioni, dalle quali appariscano i pro&shy;<lb/>gressi fatti fare o preparati alla scienza meccanica dal Torricelli. </s>

<s>Quelle cose <lb/>perci&ograve;, che si riferiscono alle leggi e alle propriet&agrave; del moto in generale, <lb/>abbiamo voluto presentar separate da quell'altre, che si riferiscono partico&shy;<lb/>larmente ai momenti, e sacrificando all'ubert&agrave; della messe, che volentieri <lb/>lasciamo a chi vorr&agrave; dietro a noi tornare a respigolare nei manoscritti; ci <lb/>siamo solamente curati di fare apparir come il pensiero dell'Autore s'in&shy;<lb/>grada via via, e si estende nella variet&agrave; degli esempi. </s>

<s>Tende efficacemente <lb/>a conseguire il fine, che ci siamo proposti, la terza parte aggiunta alle due <lb/>dette dei moti e dei momenti, nella qual terza parte si metteranno i teoremi <lb/>relativi a quella, che dai Francesi, quasi un secolo dopo, si appell&ograve; col nome <lb/>di Meccanica nuova. </s></p><p type="main">

<s>I primi esempi, che da noi qui si scelgono per il trattatello <emph type="italics"/>De motu,<emph.end type="italics"/><lb/>si tenevano dall'Autore preparati per inserirsi, e per aggiungersi come co&shy;<lb/>rollari alle proposizioni del primo libro <emph type="italics"/>De motu gravium,<emph.end type="italics"/> quand'occorresse <lb/>di far dell'opera una ristampa, e perci&ograve; il risaperli non par che serva se <lb/>non a sodisfare alla curiosit&agrave; degli eruditi. </s>

<s>N&egrave;, trattandosi di un Torricelli, <lb/>si pu&ograve; cos&igrave; fatta erudizione reputare aliena dagli uffici della Storia, i quali <lb/>sarebbero in ogni modo scusati, in grazia di quegli altri uffici, ch'ella passa <lb/>a fare di maggiore importanza, mostrandoci quel che avesse speculato il Tor&shy;<lb/>ricelli stesso intorno all'impeto dei punti geometrici in descrivere il circolo <lb/>e l'iperbola, e sull'esempio loro altre curve; intorno al dimostrar che la <lb/>catena, insenandosi, s'adatta alla figura di una parabola, e intorno al crear <lb/>nuove leggi nel moto accelerato, per cui le parabole descritte dai proietti na&shy;<lb/>turali si variano in parabole di qualunque potenza, descritte da corpi appar&shy;<lb/>tenenti a mondi immaginari, ma ai quali pure la Geometria prescrive, non <lb/>men che per il presente nostro mondo reale, certezza impreteribile di leggi. </s></p><p type="main">

<s>Cominciando dunque dai primi promessi esempi ci occorre a notare nel <lb/>nostro Autore un concetto nuovo, per concluder che la forza in s&egrave; stessa &egrave; <lb/>infinita: imperocch&egrave;, diviso il subietto materiale in ch'ella si propaga, in <lb/>parti minutissime infinite, non perci&ograve; rimette nulla del suo primo vigore, ma <lb/>si mantiene in ciascuna divisione intera, e sempre uguale a s&egrave; stessa. </s>

<s>Ci&ograve; si <lb/>dimostra particolarmente avvenire nel tirare una corda, fatta per&ograve; un'ipo&shy;<lb/>tesi, la quale non si vede come possa facilmente verificarsi nella materia. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE I. &mdash; <emph type="italics"/>Che la forza sia infinita. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia il gran sasso A (fig. </s>

<s>236) e sia attaccata ad esso una lunga corda <lb/>BG. </s>

<s>Io suppongo che un uomo abbia forza di tirare la corda BG, cio&egrave; di <lb/>conferire a tutta essa corda una tal tensione, qualunque ella si sia: e questo <lb/>si vede per esperienza. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2752.jpg" pagenum="377"/><p type="main">

<s>&ldquo; Io considero qui primieramente che tutta la corda BG aver&agrave; la me&shy;<lb/>desima tensione in ogni sua parte, cio&egrave; tanto sar&agrave; tirata nel principio B, <lb/><figure id="id.020.01.2752.1.jpg" xlink:href="020/01/2752/1.jpg"/></s></p><p type="caption">

<s>Figura 236.<lb/>quanto nel mezzo D, e quanto verso <lb/>il fine C. </s>

<s>Questo &egrave; assai chiaro, <lb/>astraendo per&ograve; da qualche variet&agrave;, <lb/>che potesse fare il proprio peso <lb/>della corda, ed anco astraendo dalla <lb/>differenza, che potesse nascere dal <lb/>toccamento della corda sopra il piano a lei sottoposto, che per&ograve; la consi&shy;<lb/>dereremo in aria, e senza la gravit&agrave; propria. </s>

<s>Non di meno si pu&ograve; con questo <lb/>discorso dimostrar cos&igrave;: &rdquo; </s></p><p type="main">

<s>&ldquo; L'uomo traente conferisce al punto B tanta forza, quanta ne ha esso <lb/>uomo: il punto B tira poi con tanta forza il punto E suo congiunto, quanta <lb/>ne ha esso B, cio&egrave; quanta &egrave; la forza dell'uomo, e il punto E tira il punto <lb/>F suo congiunto con quanta ne ha esso E, cio&egrave; quanta &egrave; la forza del&shy;<lb/>l'uomo, e cos&igrave; si pu&ograve; andar discorrendo di tutti i punti, cio&egrave; di tutta <lb/>la corda BG, e concluderemo che l'ultimo punto G, e perci&ograve; il gran sasso <lb/>A, vien tirato con altrettanta forza per appunto con quanta vien tirato il <lb/>punto B, cio&egrave; con la forza dell'uomo traente, non accresciuta n&egrave; diminuita. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Stabiliremo dunque questo principio: che qualunque volta avremo una <lb/>lunghezza, cio&egrave; una estensione di punti continuati, e che il primo di essi <lb/>punti venga tirato e spinto con una tal forza, anco tutti gli altri successi&shy;<lb/>van&inodot;ente saranno tirati e spinti con la medesima forza, senz'accrescerla o <lb/>diminuirla, ma trasmettendola sino al fine. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Consideriamo poi che, se fosse possibile tagliar la corda BG in due <lb/>parti, senza guastargli quella tensione, che ella aveva avanti fosse tagliata, <lb/>e se si potesse attaccare la parte tagliata BE in F, e fosse vero che l'una <lb/>e l'altra corda, tanto BE, quanto EF, ritenesse la medesima tensione di prima; <lb/>sarebbe vero che il punto F verrebbe tirato, non pi&ugrave; da una, ma da due <lb/>forze uguali a quella dell'uomo traente. </s>

<s>Nello stesso modo, chi facesse, non <lb/>due parti della corda, ma dieci o cento, e le attaccasse tutte nel punto F, e <lb/>ciascuna parte ritenesse la medesima tensione, che aveva la corda avanti <lb/>fosse divisa in parti; certo &egrave; che il punto F sarebbe tirato con forza dieci, <lb/>e cento volte maggiore di quella, dalla quale era tirato in principio. </s>

<s>Gli altri <lb/>punti poi susseguenti tutti sarebbero tirati dalle medesime forze, che vien <lb/>tirato il punto F, e cos&igrave; per conseguenza il sasso ancora &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. XXXVII, fol. </s>

<s>123). </s></p><p type="main">

<s>A questa, che intende ad esplicare la recondita natura della forza, fa&shy;<lb/>remo succedere un'altra proposizion generale, da premettersi alle dimostra&shy;<lb/>zioni dei moti accelerati, conducendola dal principio degl'indivisibili. </s>

<s>La detta <lb/>proposizione &egrave; scritta <emph type="italics"/>pro confirmanda prima Galilei,<emph.end type="italics"/> e per mostrare a co&shy;<lb/>loro, i quali non si fidavano del metodo del Cavalieri, come anche i punti, <lb/>bench&egrave; indivisibili, hanno ragioni fra loro infinite, come tutte le altre ter&shy;<lb/>minate grandezze. </s>

<s>&ldquo; Quod puncta, et reliqua indivisibilia, cos&igrave; preavverte <pb xlink:href="020/01/2753.jpg" pagenum="378"/>l'Autore, habeant rationes inter se infinitas, sicuti habent magnitudines ter&shy;<lb/>minatae, atque divisibiles, mihi iam satis superque patet, quamquam semper <lb/>sint indivisibilia &rdquo; (ivi, T. XXXI, fol. </s>

<s>61). </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE II. &mdash; <emph type="italics"/>Esto tempus AB<emph.end type="italics"/> (fig. </s>

<s>237), <emph type="italics"/>moveaturque mobile, <lb/>et tempore AB percurrat rectas GF, OH, ted rectam GF currat motu <lb/>aequabili, cum gradu velocitatis semper eodem AV, rectam vero OH cur-<emph.end type="italics"/><lb/><figure id="id.020.01.2753.1.jpg" xlink:href="020/01/2753/1.jpg"/></s></p><p type="caption">

<s>Figura 237.<lb/><emph type="italics"/>rat motu non aequabili, cum gradibus velocitatis homo&shy;<lb/>logis ad lineas AC, sive ME; dico spatium OH, ad <lb/>GF, esse ut figura ACDB, ad figuram AVDB. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nam totidem sunt puncta in spatio GF, quot <lb/>sunt in spatio OH: nempe totidem, quot fuerunt in&shy;<lb/>stantes eiusdem temporis, sed illa puncta sunt inae&shy;<lb/>qualia. </s>

<s>Jam, sumpto quolibet instanti temporis, puta M, <lb/>sint puncta peracta hoc instanti ipsa L et N, eritque ut <lb/>recta MI ad ME, hoc est, ut impetus, ita spatium L ad <lb/>spatium N, et hoc semper. </s>

<s>Suntque antecedentes aequales, ergo, ut AVDB ad <lb/>ACDB, ita quantitas omnium punctorum GF, ad quantitatem omnium, nempe <lb/>totidem punctorum OH, sive ita GF ad OH &rdquo; (ibid.). </s></p><p type="main">

<s>Che questa propriamente, nella sua universalit&agrave;, confermi il vero della <lb/>prima proposizione galileiana <emph type="italics"/>De motu naturaliter accelerato,<emph.end type="italics"/> &egrave; manifesto, <lb/>perch&egrave;, se il moto comincia in D dalla quiete, e vanno le velocit&agrave; crescendo <lb/>a proporzione dei tempi, la DEC &egrave; una linea retta, e la figura DVC un trian&shy;<lb/>golo. </s>

<s>Se suppongasi inoltre che la linea EG, nel medesimo tempo AB, sia <lb/>corsa con moto equabile, cos&igrave; cio&egrave; che i gradi delle velocit&agrave; sian sempre <lb/>i medesimi, e tutti uguali a VC, ultimo grado della velocit&agrave; accelerata&shy;<lb/>mente acquistata; sar&agrave; la figura AD doppia della DVC, e tale anco sar&agrave; <lb/>l'uno spazio all'altro, come nella detta proposizione prima si dimostra da <lb/>Galileo. </s></p><p type="main">

<s>In tal proposizione, che si legge scritta nel terzo diologo delle due <lb/>Scienze nuove, &egrave; noto come sia costituito uno de'fondamenti alle dottrine <lb/>galileiane dei moti accelerati, ma il principale di quei fondamenti &egrave; nel Teo&shy;<lb/><figure id="id.020.01.2753.2.jpg" xlink:href="020/01/2753/2.jpg"/></s></p><p type="caption">

<s>Figura 238.<lb/>rema cos&igrave; detto <emph type="italics"/>meccanico,<emph.end type="italics"/> il quale si vo&shy;<lb/>leva dal Torricelli illustrare nel modo che <lb/>segue: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE III. &mdash; <emph type="italics"/>Qual si coglia <lb/>gran peso da qualunque piccola forza pu&ograve; <lb/>essere tirato su, per un piano clevato <lb/>utcumque. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia nel piano dato l'orizontale AB <lb/>(fig. </s>

<s>238), e ad essa la perpendicolare CE, e sia in E il peso dato, quale pon&shy;<lb/>gasi essere come EC, e la data forza sia come FH, minore di CD, perch&egrave;, se <lb/>fosse come CD, moverebbe il peso per tutta la linea del piano dato. </s>

<s>Fac&shy;<lb/>ciasi dal centro E, con l'intervallo EC, il semicircolo ACB nel piano, e si <lb/>tiri l'orizontale FI, e per la linea EI si potr&agrave; tirare il peso dalla forza FH, <pb xlink:href="020/01/2754.jpg" pagenum="379"/>ovvero IL, poich&egrave;, se il peso &egrave; come EC, ovvero EI, sar&agrave; in EI come IL, <lb/>e per&ograve; la forza IL lo agguaglier&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario I.<emph.end type="italics"/> &mdash; Di qui si ricava che le strade pi&ugrave; oblique dei monti <lb/>sono tanto pi&ugrave; agevoli, quanto la IL &egrave; minore della CD, ovvero la IM della <lb/>CE, essendo simili CED, IML. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario II.<emph.end type="italics"/> &mdash; Per&ograve;, quando l'angolo IEB sar&agrave; gradi 30, allora la <lb/>salita per EI sar&agrave; la met&agrave; pi&ugrave; agevole, che per EC, essendo il sino IM di <lb/>gradi 30 la met&agrave; del sino toto EC: ovvero inferisci che la fatica della salita <lb/>sar&agrave; come i sini degli angoli, che far&agrave; la strada con la orizontale. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario III.<emph.end type="italics"/> &mdash; I pesi dei corpi nostri, e delle cose che porteremo, <lb/>saranno per le strade EC, EI come CD, IL, ovvero, come CE, IM, che sono <lb/>i sini suddetti &rdquo; (ivi, T. XXXIII, fol. </s>

<s>87). </s></p><p type="main">

<s>Questa proposizione la dicemmo semplicemente illustrativa del Teorema <lb/>meccanico, la dimostrativa del quale &egrave; la prima del trattato stampato, la <lb/>quale si conduce dal celebre principio che due pesi stanno allora fra loro in <lb/>equilibrio, quando congiunti insieme, a rimoverli dalla loro prima stazione, <lb/>il centro di gravit&agrave; rimane sulla medesima linea orizontale. </s>

<s>Condizioni di un <lb/>tale equilibrio si dimostra esser che i pesi abbiano omologa proporzione con <lb/>le lunghezze dei piani inclinati: che, se varia l'inclinazione, i pesi stessi ne&shy;<lb/>cessariamente si muovono, e il Torricelli investiga cos&igrave; qual via si farebbe <lb/>dal comun centro di gravit&agrave; nel moto. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE IV. &mdash; <emph type="italics"/>Si plana AB, BC<emph.end type="italics"/> (fig. </s>

<s>239) <emph type="italics"/>fuerint utcumque <lb/>inclinata, et gravia A, C aequalia, aequaliterque a puncto B remota; erit <lb/>AC via centri gravitatis. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Venerint enim in D et E, et erunt aequales AD, CE: dico centrum <lb/>esse F. </s>

<s>Agatur EH parallela ipsi BD: erit, ut CB ad BA, ita CE ad EH, <lb/><figure id="id.020.01.2754.1.jpg" xlink:href="020/01/2754/1.jpg"/></s></p><p type="caption">

<s>Figura 239.<lb/>vel DA ad EH. Sed, cum CB, BA sint aequales, erunt <lb/>DA, EH aequales, et erunt parallelae. </s>

<s>Quare EF, FD <lb/>aequales erunt. </s>

<s>Ergo etc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Quando vero gravia non sint ae&shy;<lb/>qualia, aptentur gravia ita, ut sit ut grave A ad grave <lb/>C, ita AB ad BC, et erit iterum AC via centri. </s>

<s>Mo&shy;<lb/>veantur usque in D et E: eruntque DA, CE aequales. </s>

<s><lb/>At grave A, ad grave C, est ut AB ad BC, vel HE <lb/>ad EC, vel HE ad AD, vel FE ad FD reciproce; est <lb/>ergo F centrum &rdquo; (ivi, T, XXXVII, fol. </s>

<s>72). </s></p><p type="main">

<s>Vedremo, nel seguente trattato <emph type="italics"/>De momentis,<emph.end type="italics"/> an&shy;<lb/>che pi&ugrave; spiegatamente condotta questa proposizione, che <lb/>sar&agrave; premessa per lemma ad altre proposizioni, ma per ora, proseguendo il <lb/>divisato ordine nostro, raccoglieremo le poche cose seguenti, relative alle pro&shy;<lb/>porzioni che passano tra le velocit&agrave; e i tempi de'mobili nei piani inclinati, <lb/>quasi fragrante mazzolino di fiori, di che la Meccanica severa non sdegner&agrave; <lb/>ornarsene il seno. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE V. &mdash; <emph type="italics"/>Si duo circuli se se in infimo puncto tangant,<emph.end type="italics"/><pb xlink:href="020/01/2755.jpg" pagenum="380"/><emph type="italics"/>erunt tempora per AB, DC<emph.end type="italics"/> (fig. </s>

<s>240), <emph type="italics"/>aequalia. </s>

<s>Item, cum tota tempora <lb/>aequalia sint, et ablata ablatis, erunt reliqua BE, CE, etiam si non sint <lb/>ex quiete, aequalia &rdquo;<emph.end type="italics"/> (ivi, T. XXXIII, fol. </s>

<s>82). <lb/><figure id="id.020.01.2755.1.jpg" xlink:href="020/01/2755/1.jpg"/></s></p><p type="caption">

<s>Figura 240.</s></p><p type="main">

<s>Di ci&ograve; che &egrave; scritto, insieme con tant'altre cose messe <lb/>alla rinfusa in quel volume, intitolato dal Torricelli <emph type="italics"/>Campo <lb/>di tartufi:<emph.end type="italics"/> manca la dimostrazione, perch&egrave; forse troppo <lb/>facile a ritrovarsi dietro i teoremi meccanici di Galileo, e <lb/>la CVI del VII libro delle Matematiche collezioni, nella <lb/>quale Pappo dimostra (ediz. </s>

<s>cit., pag. </s>

<s>334) che le corde <lb/>AB, ED son parallele, e perci&ograve; AC:BC=AD:BE. Ma, <lb/>per le note leggi, stando i tempi come le radici degli spazi, <lb/>cio&egrave; To.AC:To.AD=&radic;AC:&radic;AD, To.BC:To.BE= <lb/>&radic;BC:&radic;BE, abbiamo To.AC:To.BC=To.AD:To.EB. </s>

<s>Dunque essendo <lb/>i tempi per AC, BC uguali, anco uguali saranno i tempi per AD, BE, come <lb/>voleva dimostrarsi. </s></p><p type="main">

<s>Che se le AC, BC intere sono isocrone, e isocrone le loro parti AD, BE; <lb/>isocrone dovranno essere per conseguenza anche le DC, EC rimanenti: non <lb/>inutile corollario, in cui la verit&agrave; dimostrata da Galileo nel caso, che il mo&shy;<lb/>bile si parta in D e in E dalla quiete, si conferma, anche quando esso mobile <lb/>abbia un moto antecedente, e quello per l'appunto, che ha il principio in <lb/>A, B, sull'altra circonfcrenza di contatto. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE VI. &mdash; <emph type="italics"/>Si duo circuli se exterius tangant, in puncto <lb/>sublimiori et infimo, erunt tempora AB, MD<emph.end type="italics"/> (fig. </s>

<s>241) <emph type="italics"/>aequalia. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>La proposizione si dimostrerebbe speditamente dalla CII del citato lib. </s>

<s>VII <lb/>di Pappo (pag. </s>

<s>334), secondo la quale, essendo la AD parallela alla MB, se <lb/><figure id="id.020.01.2755.2.jpg" xlink:href="020/01/2755/2.jpg"/></s></p><p type="caption">

<s>Figura 241.<lb/>questa si prolunghi infino a incontrare <lb/>in H la AH condotta parallela a MD; la <lb/>figura HD sar&agrave; un rettangolo, e perci&ograve; <lb/>AH=MD, e il tempo per l'una uguale <lb/>al tempo per l'altra, ond'ei non restava <lb/>al Torricelli che a invocare il lemma alla <lb/>sua XIII stampata, per concluder senz'al&shy;<lb/>tro l'intento. </s>

<s>E nonostante segu&igrave; una via <lb/>pi&ugrave; lunga e indiretta, dimostrando prima, <lb/>per modo di lemma, che, tirata la BE pa&shy;<lb/>rallela alla MD, le FE, ID erano uguali <lb/>&ldquo; nam, iunctis AD, DE, una eademque <lb/>recta erunt, alias, continuata AD, faceret <lb/>angulum rectum extra E, quod est absur&shy;<lb/>dum &rdquo; (MSS. Gal., T. XXXIII, fol. </s>

<s>82). </s></p><p type="main">

<s>Dalla dimostrata uguaglianza delle FE, ID, conclude il Torricelli il suo <lb/>proposito, lasciati sottintesi i principii di mezzo, i quali si riducono a que&shy;<lb/>sti: ch'essendo i tempi per le FE, ID, e per le FB, IM uguali, saranno pure <lb/>uguali i tempi per le intere MD, EB. </s>

<s>Ma EB nel cerchio &egrave; isocrona al diame-<pb xlink:href="020/01/2756.jpg" pagenum="381"/>tro AB, dunque isocrona allo stesso diametro sar&agrave; la MD, ci&ograve; che doveva <lb/>provarsi. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE VII. &mdash; <emph type="italics"/>Si latus exagoni sit AC<emph.end type="italics"/> (fig. </s>

<s>242), <emph type="italics"/>erit velo-<emph.end type="italics"/><lb/><figure id="id.020.01.2756.1.jpg" xlink:href="020/01/2756/1.jpg"/></s></p><p type="caption">

<s>Figura 242.<lb/><emph type="italics"/>citas, sive maximum momentum in AB, duplum momenti <lb/>in AC, qui eodem tempore duplum spatium peragit &rdquo;<emph.end type="italics"/><lb/>(ivi, T. XXXVII, fol. </s>

<s>94). </s></p><p type="main">

<s>Infatti, per essere i tempi uguali, le velocit&agrave; stanno <lb/>come gli spazi. </s>

<s>Ma lo spazio AB, diametro, &egrave; doppio dello <lb/>spazio AC, lato dell'esagono; dunque anche la velocit&agrave; per <lb/>quella via sar&agrave; doppia alla velocit&agrave; per questa. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE VIII. &mdash; <emph type="italics"/>Si angulus A<emph.end type="italics"/> (fig. </s>

<s>243) <emph type="italics"/>fuerit angulus trian&shy;<lb/>guli aequilateri, erit momentum in AC duplum momenti per AB &rdquo;<emph.end type="italics"/> (ibid.). </s></p><p type="main">

<s>Esser A angolo del triangolo equilatero non vuol dir altro che esser di <lb/>60 gradi. </s>

<s>Dunque, supponendosi AC verticale, e BC orizontale, e perci&ograve; ACB <lb/><figure id="id.020.01.2756.2.jpg" xlink:href="020/01/2756/2.jpg"/></s></p><p type="caption">

<s>Figura 243.<lb/>angolo retto; sar&agrave; ABC 30 gradi. </s>

<s>Si prolunghi AC di altret&shy;<lb/>tanto in D, e si congiunga la DB: &egrave; manifesto che ABD &egrave; il <lb/>triangolo equilatero. </s>

<s>&ldquo; Si fuerit AB dupla ipsius AC, erit an&shy;<lb/>gulus A angulus trianguli aequilateri. </s>

<s>Producatur CD aequalis <lb/>ipsi CA, et erunt aequalia latera BA, AD. Sed, per IV Primi, <lb/>etiam BD aequatur ipsi BA; ergo etc. </s>

<s>&rdquo; (ibid.). E qui s'ar&shy;<lb/>resta il discorso del Torricelli, che facilmente si compie col <lb/>seguente costrutto: Il momento o la velocit&agrave; per AC, al momento o alla ve&shy;<lb/>locit&agrave; per AB, sta come la AC alla AB. </s>

<s>Ma AB &egrave; doppia di AC, dunque <lb/>anche quella velocit&agrave; nel perpendicolo sar&agrave; doppia a questa nell'inclinata, <lb/>com'era il proposito di dimostrare. </s></p><p type="main">

<s>Queste ultime quattro proposizioni non sono altro per verit&agrave; che ele&shy;<lb/>ganze, preparate dal Torricelli per ornare il suo proprio, e il trattato di Ga&shy;<lb/>lileo, e l'Autore stesso, in certe sue note interpolate nel manoscritto, le qua&shy;<lb/>lificava per bagattelle. </s>

<s>Comunque sia, hanno ben altra importanza le proposi&shy;<lb/>zioni, che si soggiungeranno, incominciando da quelle intitolate <emph type="italics"/>Dell'impeto <lb/>de'punti.<emph.end type="italics"/> L'origine, che queste speculazioni ebbero nel nostro Torricelli e <lb/>nel Roberval comune, &egrave; manifestamente dallo studio della spirale di Archi&shy;<lb/>mede, intorno alla quale tratterremo il discorso pi&ugrave; a lungo nella terza parte <lb/>di questo capitolo, contentandoci di notar per ora che, cos&igrave; il Nostro come <lb/><figure id="id.020.01.2756.3.jpg" xlink:href="020/01/2756/3.jpg"/></s></p><p type="caption">

<s>Figura 244.<lb/>il Matematico di Francia, ammettevano, con il grande <lb/>Maestro siracusano, che la resultante de'due moti, dai <lb/>quali insieme composti viene a descriversi la curva, sia <lb/>diretta secondo la tangente al punto della curva stessa, <lb/>la quale proseguirebbe perci&ograve; indi il suo moto in li&shy;<lb/>nea retta. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE IX. &mdash; <emph type="italics"/>Si recta AB<emph.end type="italics"/> (fig. </s>

<s>244) <lb/><emph type="italics"/>super DC perpendicularis semper existat, in eodem&shy;<lb/>que plano, et moveatur motu progressivo aequabili, simulque aliquod <lb/>ipsius punctum A moveatur in recta AB, ita ut velocitas puncti A, ad<emph.end type="italics"/><pb xlink:href="020/01/2757.jpg" pagenum="382"/><emph type="italics"/>velocitatem lineac AB sit semper ut recta DB ad BA; punctum A cir&shy;<lb/>culum describet. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto enim tangens lineae curvae in A ipsa AC: et quia impetus puncti A <lb/>versus B, ad impetum lineae AB versus C, est ut DB ad BA; erit etiam, ob <lb/>leges motuum, AB ad BC ut BD ad BA: ergo angulus DAC rectus est, sed <lb/>AD tangens; ergo figura circulus est &rdquo; (ivi, T. XXXI, fol. </s>

<s>86). </s></p><p type="main">

<s>&Egrave; scritto in principio di questa, dalla mano dello stesso Torricelli: <emph type="italics"/>Porta <lb/>la conversa, perch&egrave; cos&igrave; non prova,<emph.end type="italics"/> e la conversa si potrebbe formulare, e <lb/>facilmente provare in questa maniera: <emph type="italics"/>Nel punto mobile, che descrive il <lb/>circolo, l'impeto discensivo al progressivo sta come il coseno, al seno del&shy;<lb/>l'angolo dell'inclinazione.<emph.end type="italics"/> Si consideri il punto A, nella medesima figura 244, <lb/>con l'inclinazione ADB. </s>

<s>Condotta la tangente AC, resultante del moto, le <lb/>componenti di lei saranno AB misura dell'impeto D discensivo e DB misura <lb/>dell'impeto P progressivo, onde avremo D:P=AB:BC. </s>

<s>Ma i triangoli si&shy;<lb/>mili ABC, ADB danno AB:BC=DB:AB, dunque D:P=DB:AB: e <lb/>di qui &egrave; che, sempre che si verifichi questa proporzione fra i moti descri&shy;<lb/>venti una curva, la curva stessa sar&agrave; un circolo, come il Torricelli si pro&shy;<lb/>poneva di dimostrare nella sua diretta. </s></p><p type="main">

<s>Intendono bene i Lettori come si sarebbe facilmente potuta applicare <lb/>questa proposizione ai pendoli, per risolvere il problema, in cui si domanda <lb/>secondo qual proporzione diminuisca la forza in tirare il filo, via via che il <lb/>pendolo si rimove dal suo perpendicolo. </s>

<s>Eppure non si vede balenar di ci&ograve; <lb/>nessuna idea nella mente del Torricelli, per cui si rimase il Viviani in quelle <lb/>incertezze, e poi si volse a seguitar quell'errore, da noi notato qui addietro, <lb/>nella seconda parte del capitolo quarto. </s></p><p type="main">

<s>Passa nella seguente il nostro Autore a dimostrar che gl'impeti puri, <lb/>misurati in due vari punti del medesimo circolo, stanno reciprocamente come <lb/>le loro tangenti. </s>

<s>La dimostrazione, chiamati I.oA, I.oC (fig. </s>

<s>245) gl'impeti <lb/><figure id="id.020.01.2757.1.jpg" xlink:href="020/01/2757/1.jpg"/></s></p><p type="caption">

<s>Figura 245.<lb/>puri in A e in C, e chiamato I.o AD l'impeto pro&shy;<lb/>gressivo equabile della linea AD; procede in questa <lb/>guisa: Abbiamo per la precedente I.oA:I.oAD= <lb/>BD:DA; I.oAD:I.oC=CE:EB, le quali due <lb/>proporzioni moltiplicate termine per termine, danno <lb/>I.oA:I.oC=BD.CE:DA.EB. </s>

<s>Per la similitu&shy;<lb/>dine dei triangoli BAD, BAG e BCE, ECF &egrave; altresi <lb/>BD:DA=BA:AG; CE:EB=FC:CB, dalla quale per moltiplicazione resulta <lb/>BD.CE:DA.EB=BA.FC:AG.CB=FC:AG, d'onde I.oA:I.oC= <lb/>FC:AG, come propone e dimostra il Torricelli nella seguente </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE X. &mdash; <emph type="italics"/>Impetus descendens purus in A<emph.end type="italics"/> (nella medesima <lb/>figura passata), <emph type="italics"/>ad impetum descendentem purum in C, est ut tangens <lb/>CF ad AG. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nam impetus in A ad impetum lineae AD, est ut BD ad DA: impe&shy;<lb/>tus autem lineae, qui semper idem est, ad impetum puncti C est ut CE ad <lb/>EB. </s>

<s>Ergo impetus descendens puncti A, ad impetum in C, rationem habet <pb xlink:href="020/01/2758.jpg" pagenum="383"/>compositam ex ratione BD ad DA, et ex ratione CE ad EB, sive, ex ratione <lb/>FC ad CB, et ex ratione BA ad AG. </s>

<s>Sed medii termini CB, BA sunt aequa&shy;<lb/>les, ergo patet propositum &rdquo; (ibid.). </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XI. &mdash; <emph type="italics"/>Si recta AB<emph.end type="italics"/> (fig. </s>

<s>246), <emph type="italics"/>cum eadem semper in&shy;<lb/>clinatione insistat super CD, inoveaturque motu aequabili in eodem plano,<emph.end type="italics"/><lb/><figure id="id.020.01.2758.1.jpg" xlink:href="020/01/2758/1.jpg"/></s></p><p type="caption">

<s>Figura 246.<lb/><emph type="italics"/>et punctum aliquod ipsius moveatur sur&shy;<lb/>sum vel deorsum, ita ut velocitates sint in&shy;<lb/>ter se, ut quadrata distantiarum ipsius a <lb/>recta CD; hyperbola erit &rdquo;<emph.end type="italics"/> (ibid.). </s></p><p type="main">

<s><emph type="italics"/>Porta la conversa,<emph.end type="italics"/> si legge notato in <lb/>margine nel manoscritto. </s>

<s>E infatti si dimo&shy;<lb/>stra che, supposto essere la curva un'iper&shy;<lb/>bola, i punti nel descriverla si muovono con <lb/>la legge assegnata. </s>

<s>Di qui &egrave; che ogni volta <lb/>si verifichi nei punti mobili una tal regola di <lb/>andamento, si conclude dover essere un'iperbola la linea descritta dal loro moto. </s></p><p type="main">

<s>&ldquo; Esto hyperbola AE, cuius axis CA, asymptoti CF, CH, et sit punctum <lb/>A, quod supponimus pervenisse ad E. </s>

<s>Ducantur tangentes FG, IH. </s>

<s>Erit im&shy;<lb/>petus compositus puncti E secundum lineam EH. </s>

<s>Ergo impetus progressivus <lb/>lineae, ad impetum descendentem puncti, erit ut DH ad DE (applicandovi la <lb/>regola del parallelogrammo delle forze come si vedr&agrave; meglio appresso) sive <lb/>ut CD ad DE, sunt enim aequales, ob hyperbolam, IE, EH, et CD, DH. </s>

<s>Jam <lb/>impetus descendens in A, ad progressivum in A, aequalis est, nempe ut AB <lb/>ad BC: progressivus vero, ad descendentem in E, est ut CD ad DE. </s>

<s>Ergo <lb/>ex aequo impetus descendens in A, ad descendentem in E, rationem habet <lb/>compositam ex ratione AB ad BC, et CD ad DE. </s>

<s>Ergo est ut CD ad DE, <lb/>nam termini AB, BC sunt aequales, sive ut rectangulum CDE ad quadra&shy;<lb/>tum DE, sive ut rectangulum CBA, vel quadratum BA, ad quadratum DE, <lb/>quod volebam. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Quando est hyperbola, cum praedictis iis velocitatum <lb/>legibus punctum movetur: propterea, etiam quando movetur ex se, hyper&shy;<lb/>bolam describet: alias idem punctum motum iisdem semper velocitatibus per <lb/>diversas inter se lineas curreret, quod probatur esse absurdum &rdquo; (ibid., ad. </s>

<s>t.). </s></p><p type="main">

<s>Quel detto che la Natura &egrave; geometrica non par s'illustri con altro pi&ugrave; <lb/>efficace esempio, che col descriver ch'ella fa al proietto, il quale pu&ograve; riguar&shy;<lb/>darsi come condensato in un punto, linee curve, con regole simili a quelle, <lb/>che nelle due precedenti proposizioni il Geometra ha speculato. </s>

<s>E perch&egrave; la <lb/>Natura sempre all'Arte &egrave; di nuove invenzioni maestra, immaginiamo, pen&shy;<lb/>sava il Torricelli, che le velocit&agrave; non crescano secondo la semplice propor&shy;<lb/>zione de'tempi, come Galileo dimostr&ograve; nei gravi sulla superficie di questo <lb/>nostro Globo cadenti, ma secondo la proporzion de'quadrati, dei cubi, dei <lb/>quadrato quadrati, o di qualsivoglia altra potenza: &egrave; certo che dal moto, com&shy;<lb/>posto del descensivo con tali leggi e del progressivo equabilmente per l'oriz&shy;<lb/>zonte, resulteranno descritte curve appartenenti senza dubbio alla medesima <pb xlink:href="020/01/2759.jpg" pagenum="384"/>famiglia delle parabole quadratiche o naturali. </s>

<s>Intorno a che il Torricelli <lb/>dimostr&ograve; che, se la velocit&agrave; &egrave; quadratica, la parabola che descriverebbe il <lb/>proietto &egrave; cubica: se la velocit&agrave; &egrave; cubica, la parabola &egrave; biquadratica, e in <lb/>generale, se la velocit&agrave; &egrave; di grado <emph type="italics"/>n,<emph.end type="italics"/> sar&agrave; di grado <emph type="italics"/>n+1<emph.end type="italics"/> la potenza della <lb/>parabola relativa. </s>

<s>Sebbene sia il concetto assai pellegrino, &egrave; nonostante di <lb/>molto facile dimostrazione, come apparisce dal seguente esempio, applicato al <lb/>caso della parabola cubica, premessovi questo problema per lemma: <lb/><figure id="id.020.01.2759.1.jpg" xlink:href="020/01/2759/1.jpg"/></s></p><p type="caption">

<s>Figura 247.</s></p><p type="main">

<s>&ldquo; Si mobile moveatur deorsum tempore AC <lb/>(fig. </s>

<s>247), et tempore AB, et augeatur velocitas qua&shy;<lb/>dratice, quaeritur ratio spatiorum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Dico sic: Spatia peracta habent rationem <lb/>compositam ex ratione velocitatum, et ex ratione <lb/>temporum. </s>

<s>Sint spatia peracta AB, AC, tempora <lb/>vero DE, DF. </s>

<s>Supponamus mobile in B et in C <lb/>converti horizontaliter. </s>

<s>Jam impetus in B, ad im&shy;<lb/>petum in C, erit ut quadratum temporis DE, ad <lb/>quadratum DF. </s>

<s>Ergo spatium BH, factum tempore casus AB, ad spatium CI, <lb/>factum tempore casus AC, rationem habebit compositam rectae DE ad DF, <lb/>et quadrati DE ad quadratum DF. </s>

<s>Ergo spatium BH ad CI erit ut cubus DE <lb/>ad DF. </s>

<s>Sed ut spatia BH, CI, ita sunt spatia AB, AC, ipsorum submultiplicia <lb/>aequaliter, ergo patet etc. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XII. &mdash; <emph type="italics"/>Cadat mobile aliquod horizontaliter concitatum <lb/>ex plano DA<emph.end type="italics"/> (fig. </s>

<s>248), <emph type="italics"/>ita ut duos impetus habeat, alterum aequabilem<emph.end type="italics"/><lb/><figure id="id.020.01.2759.2.jpg" xlink:href="020/01/2759/2.jpg"/></s></p><p type="caption">

<s>Figura 248.<lb/><emph type="italics"/>horizontalem versus partes EC. alterum de&shy;<lb/>scendentem acceleratum quadratice. </s>

<s>Dico pa&shy;<lb/>rabolam cubicam fieri. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Hoc ex dictis patet. </s>

<s>Nam consideretur <lb/>mobile in quibuslibet punctis B, C. </s>

<s>Cum im&shy;<lb/>petus horizontalis externus sit et aequabilis, <lb/>erunt CI, BH ut tempora casuum. </s>

<s>Sed spatia <lb/>peracta EC, FB sunt ut cubi temporum; ergo <lb/>cubi rectarum CI, BH erunt ut EC, FB, sive <lb/>ut IA ad AH &rdquo; (ibid., T. XXXI, fol. </s>

<s>341). </s></p><p type="main">

<s>Perch&egrave; dunque la proposta verit&agrave;, dato il lemma, &egrave; patente, si pu&ograve; quello <lb/>stesso lemma dimostrare nella sua universalit&agrave;, d'onde ne derivi la univer&shy;<lb/>salit&agrave; sua anche la proposizione ora scritta. </s>

<s>Chiamati S, S&prime;, V, V&prime;, T, T&prime; due <lb/>spazi, due varie velocit&agrave;, due vari tempi, abbiamo, per le note leggi del moto, <lb/>S:S&prime;=V.T:V&prime;.T&prime;. </s>

<s>Che se l'accelerazione &egrave; lineare, ossia se V:V&prime;= <lb/>T:T&prime;, sar&agrave; S:S&prime;=T2:T&prime;2; se l'accelerazione &egrave; quadratica, e perci&ograve; V:V= <lb/>T2:T&prime;2, sar&agrave; S:S&prime;=T3:T&prime;3: se poi l'accelerazione &egrave; cubica, e V:V&prime;= <lb/>T3:T&prime;3, sar&agrave; S:S&prime;=T1:T&prime;1, e in generale, se l'accelerazione &egrave; di grado <emph type="italics"/>n,<emph.end type="italics"/><lb/>sar&agrave; S:S&prime;=T<emph type="italics"/>n+1<emph.end type="italics"/>:T&prime;

<emph type="italics"/>n+1<emph.end type="italics"/>.</s> 

<s>Cosicch&egrave;, facendone l'applicazione alla para&shy;<lb/>bola, rappresentata dalla stessa ultima figura, sar&agrave; l'equazione di lei espressa <lb/>da AH:AI=HB</s>

<s><emph type="italics"/>n+1<emph.end type="italics"/>:IC<emph type="italics"/>n+1<emph.end type="italics"/>.</s></p><pb xlink:href="020/01/2760.jpg" pagenum="385"/><p type="main">

<s>Il concetto, che rifulge assai chiaro per la Geometria di Euclide, e se&shy;<lb/>condo il quale sarebbero le varie figure descritte da un punto, che con certe <lb/>determinate leggi si muove; ha nella precedente del Torricelli l'applicazione <lb/>pi&ugrave; bella, che si potesse fare alla genesi meccanica delle infinite parabole, <lb/>comprese fra il triangolo e il parallelogrammo. </s>

<s>Di qui si vede che la Geo&shy;<lb/>metria &egrave; meccanica, come la Meccanica &egrave; geometrica: anzi pu&ograve; dirsi che la <lb/>Scienza, della quale scriviamo la Storia, &egrave; una Geometria particolare, di cui <lb/>i punti mobili, che descrivono le figure, son gravi, soggetti cio&egrave; per naturale <lb/>necessit&agrave; a ubbidire a certe leggi proprie del moto, dipendenti dall'attra&shy;<lb/>zione centrale della Terra, cosicch&egrave; i proietti sulla superficie di lei, tra le <lb/>infinite parabole possibili, descrivono le quadratiche. </s></p><p type="main">

<s>Si pu&ograve; dunque riguardar la proposizione poco fa dimostrata come il prin&shy;<lb/>cipio generalissimo, a cui s'informa il quarto dialogo delle due Scienze nuove, <lb/>che, non potutosi maturare da Galileo, in quegli ultimi anni della sua vec&shy;<lb/>chiezza, fu mirabilmente illustrato e compiuto dal Torricelli. </s>

<s>Egli fu il primo <lb/>ad applicar la parabola ai moti naturali, come Galileo stesso l'aveva appli&shy;<lb/>cata ai moti violenti, e son di questi nuovi teoremi cos&igrave; pieni i due libri <emph type="italics"/>De <lb/>motu gravium<emph.end type="italics"/> fra le altre Opere geometriche di lui gi&agrave; stampati, da non <lb/>avere speranza di trovarne dei rimasti indietro nei manoscritti. </s>

<s>Non ci sem&shy;<lb/>bra nonostante che siano di leggera importanza quest'altre poche cose che <lb/>soggiungiamo, la prima delle quali appartiene a quel libretto indirizzato in <lb/>forma di lettera a Raffaello Magiotti, il qual libretto, che insieme col trat&shy;<lb/>tato <emph type="italics"/>De motu proiectorum<emph.end type="italics"/> passerebbe per proemio e per introduzione; cos&igrave; <lb/>disgiunto da lui, diceva il Torricelli stesso per modestia, non contenere che <lb/>baie. </s>

<s>Una di queste, che i Lettori ritroveranno tutt'altro che una baia, man&shy;<lb/>data a esso Magiotti nel libretto a lui dedicato, sarebbe la seguente, con le <lb/>parole, che trascriviamo premesse alla proposizione: </s></p><p type="main">

<s>&ldquo; Perch&egrave; il foco delle parabole ha che fare in alcuni teoremi dei pro&shy;<lb/>ietti pi&ugrave; che qualcuno non pensa, l'inserisco nel mio libretto, e mi pare di <lb/><figure id="id.020.01.2760.1.jpg" xlink:href="020/01/2760/1.jpg"/></s></p><p type="caption">

<s>Figura 249.<lb/>dimostrarlo assai pi&ugrave; facilmente che Vitellione, <lb/>Marin Ghetaldo e fra Bonaventura, i quali appor&shy;<lb/>tano tutti la medesima dimostrazione: per&ograve; non <lb/>vorrei arrogarmi una dimostrazione non mia. </s>

<s><lb/>Mando questa copia a V. S. acci&ograve; mi faccia gra&shy;<lb/>zia di vedere se confronta con quella di Oronzio <lb/>Fineo, se ben credo che lui ancora porter&agrave; la <lb/>comune di Vitellione, che va per via di quei quat&shy;<lb/>tro rettangoli del Secondo di Euclide. </s>

<s>Oltre a <lb/>questi quattro autori non so che altri tratti del <lb/>foco delle parabole. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Propriet&agrave; della Parabola, Lemma.<emph.end type="italics"/> &mdash; Se <lb/>sar&agrave; la parabola, il cui asse AB (fig. </s>

<s>249), e la quarta parte del lato retto <lb/>sia AC, e preso qualunque punto E si tirino due tangenti AD, ED; dico che <lb/>l'angolo HDC &egrave; retto. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2761.jpg" pagenum="386"/><p type="main">

<s>&ldquo; Tirisi l'ordinatamente applicata EB: e perch&egrave; le AB, AH sono uguali, <lb/>ed EB, AD parallele, sar&agrave; il quadrato EB quadruplo del quadrato AD. </s>

<s>Lo <lb/>stesso quadrato EB &egrave; quadruplo del rettangolo BAC, cio&egrave; HAC; adunque il <lb/>quadrato AD &egrave; uguale al rettangolo HAC: per&ograve; l'angolo HDC &egrave; retto. </s>

<s>&rdquo; </s></p><p type="main">

<s>Mostrato questo, cio&egrave; che la linea, che dal punto C va al concorso delle <lb/>due tangenti, sempre fa angoli retti con la tangente, la quale <emph type="italics"/>non est per <lb/>verticem parabolae;<emph.end type="italics"/> si mostra la propriet&agrave; del foco, per la quarta proposi&shy;<lb/>zione del primo libro di Euclide. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Proposizione.<emph.end type="italics"/> &mdash; Sia la parabola, il cui asse AB (nella medesima <lb/>figura) ed AC sia la quarta parte del lato retto. </s>

<s>Prendasi qualunque punto <lb/>E, e sia EG parallela all'asse, e tirinsi le tangenti ED, AD, e si congiun&shy;<lb/>gano CE, CD: dico che gli angoli GEF, CED sono uguali. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Poich&egrave;, tirata la ordinatamente applicata BE, perch&egrave; le BE, AD sono <lb/>parallele, e BA, AH uguali, saranno ancora ED, DH uguali fra loro, e la DC <lb/>&egrave; comune, e gli angoli in D sono retti. </s>

<s>Adunque, per la quarta del primo <lb/>di Euclide, l'angolo CED &egrave; uguale all'angolo DHC, cio&egrave; al GEF. &rdquo; </s></p><p type="main">

<s>&ldquo; In questa dimostrazione il caso &egrave; unico, ma nella comune sono tre <lb/>casi, e sempre bisogna variar la dimostrazione, poich&egrave; o la BE casca tra il <lb/>foco e la cima, ovvero alla parte opposta, ovvero sul foco stesso &rdquo; (MSS. <lb/>Gal., T. XL, fol. </s>

<s>20). </s></p><p type="main">

<s>Avuto forse in risposta dal Magiotti che il modo di dimostrare era nuovo, <lb/>e da non reputarsi perci&ograve; una baia, pens&ograve; il Torricelli di metter cos&igrave; la pro&shy;<lb/>posizione in miglior forma, per inserirla nel primo libro <emph type="italics"/>De motu gravium,<emph.end type="italics"/><lb/>innanzi alla XIX, nella quale l'invenzion del foco si suppone per ritrovar <lb/>dalla distanza di lui sull'asse della parabola le ordinatamente applicate, che <lb/>s'han da prendere per la misura degl'impeti, in ciascun punto della curva. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XIII. &mdash; <emph type="italics"/>Sit parabola AE<emph.end type="italics"/> (sempre nell'ultima figura) <lb/><emph type="italics"/>axis AB, ipsique parallela EG. </s>

<s>Ponatur AC quarta pars lateris recti, <lb/>ductisque tangentibus EH, AD, iungantur CD, EC. </s>

<s>Dico angulos GEF, <lb/>CED aequales esse. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ducatur ordinatim BE: cum enim aequales sint BA, AH, erit qua&shy;<lb/>dratum AD quarta pars quadrati BE. </s>

<s>Rectangulum etiam CAB est quarta <lb/>pars eiusdem quadrati BE. </s>

<s>Quare quadratum AD aequatur rectangulo CAB, <lb/>hoc est CAH. </s>

<s>Erit igitur angulus HDC in semicirculo, et ideo rectus. </s>

<s>Sed <lb/>cum latera DH, DC aequalia sint lateribus ED, DC, utrumque, et anguli in <lb/>D recti; erunt reliqua aequalia, per quartam Primi, nempe angulus CHD, <lb/>sive GEF, aequalis angulo DEC, quod erat demonstrandum &rdquo; (ibid. </s>

<s>ad t.). </s></p><p type="main">

<s>Dimostrato cos&igrave; che il foco &egrave; veramente sull'asse della parabola, a una <lb/>distanza dal vertice uguale alla quarta parte del parametro, si confermavano <lb/>dal Torricelli tutte quelle sue proposizioni, scritte a illustrare i teoremi letti <lb/>nel quarto Dialogo dal Salviati. </s>

<s>Ma un altro ufficio, ben assai pi&ugrave; impor&shy;<lb/>tante, erasi assunto il Discepolo valoroso, ed era quello di perfezionare l'opera <lb/>del suo proprio Maestro, lasciata di parecchie altre parti, ma principalmente <lb/>del trattato delle catenuzze ballistiche in difetto. </s>

<s>Non deve nemmen egli il <pb xlink:href="020/01/2762.jpg" pagenum="387"/>Torricelli aver saputa da quali principii meccanici, e per quali vie riuscisse <lb/>Galileo a dimostrare che quelle stesse catenuzze si dispongono in figura di <lb/>parabola: o forse volle alla non facile dimostrazione trovare da s&egrave; stesso altri <lb/>modi, se veramente concludenti, e da doversi preferire ai galileiani, lo giu&shy;<lb/>dicheranno i Lettori. </s>

<s>Si pone per fondamento al discorso un teorema statico, <lb/>a cui preluce il seguente <lb/><figure id="id.020.01.2762.1.jpg" xlink:href="020/01/2762/1.jpg"/></s></p><p type="caption">

<s>Figura 250.</s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma.<emph.end type="italics"/> &mdash; Si angulus ABC (fig. </s>

<s>250) <lb/>sectus bifariam sit a linea BD, ductaque sit quae&shy;<lb/>libet AC, et sumatur AE aequalis ipsi BC, inde <lb/>EH parallela sit ipsi BD; dico AH, DC aequa&shy;<lb/>les esse. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Est enim, per tertiam Sexti, ut AD ad DC, <lb/>ita AB ad BC, vel AB ad AE, vel AD ad AH. </s>

<s>Quare aequales sunt AH, DC. &rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XIV. &mdash; <emph type="italics"/>Sit angulus quilibet GBF<emph.end type="italics"/> (nella medesima <lb/>figura) <emph type="italics"/>et loca centrorum extrema G, F, linea bisecans angulum sit BD. <lb/>Deinde, moto loco, sit linea centrorum AC, sumaturque AH aequalis ipsi <lb/>DC: dico H esse centrum loci. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nam ut totum locum ad totum, ita dimidium AB ad dimidium BC, <lb/>vel, per tertiam Sexti, AD ad DC, vel, per praec. </s>

<s>lemma, HC ad AH reci&shy;<lb/>proce. </s>

<s>Quare H centrum est gravitatis loci sic positum &rdquo; (ibid., T. XXXVII, <lb/>fol. </s>

<s>115). </s></p><p type="main">

<s>La difficolt&agrave;, che debbono tutti i lettori trovare in intendere queste ra&shy;<lb/>gioni, dipende dal non essersi ben definito dal Torricelli il significato della <lb/>parola <emph type="italics"/>loco,<emph.end type="italics"/> n&egrave; del suo centro gravitativo, ond'&egrave; che opportunamente soc&shy;<lb/>corre in aiuto nostro il Viviani con questa nota, intitolata <emph type="italics"/>Mia raba, per <lb/>chiarezza della precedente.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia l'angolo MBN (fig. </s>

<s>251) fatto da due piani MB, NB, e sia la fune <lb/>o catena MB, ora distesa da B sino ad M, ora da B sino ad N: &egrave; chiaro che <lb/><figure id="id.020.01.2762.2.jpg" xlink:href="020/01/2762/2.jpg"/></s></p><p type="caption">

<s>Figura 251.<lb/>il pi&ugrave; lontano luogo de'centri di gravit&agrave; <lb/>della catena, posta in MB, sar&agrave; il punto <lb/>di mezzo A, ed il pi&ugrave; lontano luogo del <lb/>centro, quando la catena sia in BN, sar&agrave; <lb/>il punto di mezzo C; sicch&egrave; questi A, C <lb/>si diranno <emph type="italics"/>loca centrorum extrema.<emph.end type="italics"/> Ma, <lb/>movendo la catena in modo che pigli del&shy;<lb/>l'uno e dell'altro piano, nel sito per esem&shy;<lb/>pio OBP, il centro della parte OB sar&agrave; <lb/>nel mezzo E, e della parte BP nel mezzo <lb/>H, sicch&egrave;, giunta la EH, questa si pu&ograve; dire <lb/><emph type="italics"/>linea centrorum moti loci,<emph.end type="italics"/> perch&egrave; con&shy;<lb/>giunge i centri di gravit&agrave; delle parti della catena mossa di luogo. </s>

<s>E perch&egrave; <lb/>la EH congiunge i centri delle parti della catena, in essa EH sar&agrave; il centro <lb/>di tutto, ed in luogo, che la parte verso H, alla parte verso E, sia come la <lb/>parte OB della catena, alla parte BP, cio&egrave; come la met&agrave; EB, alla met&agrave; BH. <pb xlink:href="020/01/2763.jpg" pagenum="388"/><emph type="italics"/>Ergo,<emph.end type="italics"/> dice il Torricelli, <emph type="italics"/>ut totum locum ad totum,<emph.end type="italics"/> cio&egrave; <emph type="italics"/>ut totum OB ad <lb/>totum BP, ita dimidium EB ad dimidium BH, vel EI ad IH, vel HL <lb/>ad LE reciproce. </s>

<s>Ergo L centrum gravitatis est loci &rdquo;<emph.end type="italics"/> (ibid., fol 115). </s></p><p type="main">

<s>Queste cose premesse e dimostrate, vuole il Torricelli che le condizioni <lb/>dell'equilibrio della catena, parte disposta sul piano comunqu e inclinato MB, <lb/>e parte sul piano BN, siano quelle medesime, che se si tenesse sospesa per <lb/>i punti estremi A, e C liberamente pendula. </s>

<s>La supposizione fatta dal Disce&shy;<lb/>polo &egrave; senza dubbio non meno arbitraria di quell'altra fatta dal Maestro, ma <lb/>&egrave; certo che, come dal concedersi a Galileo che gli anelli sian discesi nella <lb/>catena insaccata, secondo la ragion de'momenti, che avrebbe ciascuno di essi <lb/>in romper l'asta, nella quale si supponessero orizontalmente infilati, resta <lb/>legittimamente dimostrato che quella tal saccaia &egrave; in figura di parabola; cos&igrave;, <lb/>dal concedere al Torricelli quella sua ipotesi gi&agrave; detta, si vien pur legittima&shy;<lb/><figure id="id.020.01.2763.1.jpg" xlink:href="020/01/2763/1.jpg"/></s></p><p type="caption">

<s>Figura 252.<lb/>mente alla medesima conclusione, premesso il <lb/>seguente <emph type="italics"/>Lemma,<emph.end type="italics"/> relativo alle propriet&agrave; di <lb/>certe linee, con premeditata intenzione tirate <lb/>intorno, e dentro alla Parabola. </s></p><p type="main">

<s>&ldquo; Sia la parabola ABC (fig. </s>

<s>252), il cui <lb/>asse BH, ed ordinatamente applicata AC, e, <lb/>presa BD uguale a BH, tirinsi AD, CD, che <lb/>saranno tangenti. </s>

<s>Preso poi qualunque punto <lb/>E, tirisi l'altra tangente FEG; dimostreremo <lb/>pi&ugrave; cose: &rdquo; </s></p><p type="main">

<s>&ldquo; Per i punti F, E, G tirinsi parallele <lb/>all'asse FM, NP, IL, e si prolunghi AD, che <lb/>concorra con LG in I, e si tiri AP parallela <lb/>a FE. </s>

<s>Perch&egrave; si &egrave; preso nella parabola un punto E, e la EP parallela al&shy;<lb/>l'asse, e la AP parallela alla tangente FE, e la AF tangente in A; saranno <lb/>uguali PE, EN, e per&ograve; saranno uguali AF, FN fra le stesse parallele. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Perch&egrave; poi l'angolo ADC &egrave; diviso bifariam dalla HD, e la GI paral&shy;<lb/>lela alla HD, saranno uguali GD, DI. &rdquo; </s></p><p type="main">

<s>&ldquo; Perch&egrave; CG ad AF ha proporzione subdupla di GL a FM, sar&agrave;, come <lb/>CG ad AF, cos&igrave; GE ad EF, ovvero IN ad NF. </s>

<s>Ma perch&egrave; i conseguenti AF, <lb/>NF sono uguali, saranno uguali gli antecedenti CG, NI. </s>

<s>Ed aggiunta la co&shy;<lb/>mune DG sar&agrave; CD, ovvero AD, uguale alle NI, DG. </s>

<s>E levata la comune ND, <lb/>sar&agrave; AN uguale alle ID, DG, e per&ograve; la met&agrave; AF uguale alla met&agrave; DG. &rdquo; <lb/><figure id="id.020.01.2763.2.jpg" xlink:href="020/01/2763/2.jpg"/></s></p><p type="caption">

<s>Figura 253.</s></p><p type="main">

<s>&ldquo; Stante questo, dico che anco FE sar&agrave; uguale <lb/>ad OG. S'&egrave; mostrato che GE a EF sta come CG <lb/>ad AF, ovvero come FD a DG, ovvero FO ad OG, <lb/><emph type="italics"/>ob angulum D bifariam sectum.<emph.end type="italics"/> Come dunque GE <lb/>ad EF, cos&igrave; FO ad OG. </s>

<s>E componendo, GF ad FE, <lb/>come FG a GO, e cos&igrave; sono uguali FE, GO. &rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XV. &mdash; <emph type="italics"/>Siano i due centri <lb/>primarii A, B<emph.end type="italics"/> (fig. </s>

<s>253) <emph type="italics"/>e sia mossa la catena,<emph.end type="italics"/><pb xlink:href="020/01/2764.jpg" pagenum="389"/><emph type="italics"/>sicch&egrave; i centri siano C, D, e sia la EF che seghi l'angolo bifariam, e <lb/>prendasi DI uguale a CF: &egrave; chiaro che I sar&agrave; il centro comune. </s>

<s>Dico <lb/>ora che I sta nella parabola. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Se non ci sta, passi la parabola sulla MIN, parallela all'asse EF in <lb/>L, e si prenda LN uguale ad LM, e si tiri la retta DLO. &Egrave; certo che, es&shy;<lb/>sendo uguali MD, DA, come ora prover&ograve;, ed uguali NL, LM, saranno paral&shy;<lb/>lele AN, DL. </s>

<s>Dunque DLO sar&agrave; la seconda tangente della parabola, e per la <lb/>proposizion precedente saranno uguali AD, EO, <emph type="italics"/>quod est absurdum<emph.end type="italics"/> perch&egrave; <lb/>AD, EC sono uguali. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Provo ora che MD, DA sono uguali fra loro. </s>

<s>Sono uguali AD ed EC <lb/><emph type="italics"/>per hypothesim,<emph.end type="italics"/> e CF, DI <emph type="italics"/>per constructionem.<emph.end type="italics"/> Ora ED a DA sta come ED <lb/>a EC, vel DF ad FC, vel FD ad DI, vel ED ad DM. </s>

<s>Per&ograve; sono uguali AD, <lb/>DM, come avevo promesso di dimostrare &rdquo; (ivi, T. XXXVII, fol. </s>

<s>122). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Abbiamo riserbato a parte il trattar de'momenti s&igrave; per essere argomento <lb/>nella nostra Storia della principale importanza, e s&igrave; per avere intorno a tali <lb/>dottrine patito il Torricelli le maggiori contradizioni. </s>

<s>Incominciarono queste, <lb/>lui vivente, in Francia, per opera del Roberval, con l'intermedio del padre <lb/>Mersenno, e le resuscit&ograve;, contro lui gi&agrave; morto, in Italia, Alessandro Mar&shy;<lb/>chetti. </s>

<s>Il Borelli ammoniva il discepolo suo prediletto che, almeno per l'av&shy;<lb/>venire, imparasse a procedere <emph type="italics"/>con pi&ugrave; cautela e modestia<emph.end type="italics"/> (Tondini, Let&shy;<lb/>tere, T. I, Macerata 1782, pag. </s>

<s>90), e Sfefano Angeli, tirato dagli stessi amici <lb/>suoi e del Marchetti a prender parte al pericoloso giudizio, inclinava a di&shy;<lb/>fendere il Torricelli (ivi, pag. </s>

<s>131). </s></p><p type="main">

<s>Ma il Torricelli stesso, che conosceva non dipendere da altro le censure, <lb/>che dall'aver lasciate in qualche parte mancanti, e in qualche altra non bene <lb/>spiegate le sue proposizioni; col ritornar sopra l'opera gi&agrave; stampata, per <lb/>perfezionarla, intendeva di difendersi, nel migliore e pi&ugrave; virtuoso modo, con&shy;<lb/>tro i Francesi. </s>

<s>Col fatto poi veniva dal silenzioso sepolcro a sbugiardare i <lb/>vanti del Marchetti, il quale erasi compiaciuto a principio di aver egli dimo&shy;<lb/>strato il primo che i momenti hanno la ragion composta delle distanze e dei <lb/>pesi: poi, fatto avvertito che la dimostrazione l'aveva data parecchi anni <lb/>prima, e in una solenne opera sua stampata il Cavalieri, si consolava che <lb/>non gli avrebbe nessuno contesa la gloria dell'avere egli veramente il primo <lb/>applicato alle dottrine del moto il teorema. </s>

<s>Ma il Serenai e il Viviani ma&shy;<lb/>neggiavano intanto quelle carte torricelliane, nelle quali leggevano fatta gi&agrave; <lb/>dall'Autore la stessa applicazione ad alcune nuove proposizioni baricentriche, <lb/>e per dimostrar dai principii geometrici la regola centrobarica del Guldino. </s>

<s><lb/>Di qui nasce la triplice partizion delle cose, che s'ordineranno in questa se-<pb xlink:href="020/01/2765.jpg" pagenum="390"/>conda parte del presente capitolo, per servire alla storia de'concetti postumi <lb/>del Torricelli, e dei loro svolgimenti fecondi. </s></p><p type="main">

<s>Incominciamo dalla prima parte, in cui ci si rappresenta il Nostro tutto <lb/>in sollecitudine di aggiungere la desiderata perfezione a quelle proposizioni <lb/><emph type="italics"/>De motu gravium naturaliter descendentium,<emph.end type="italics"/> nelle quali si dimostrano le <lb/>propriet&agrave; e le leggi de'momenti dei gravi, mentre scendono lungo i piani <lb/>inclinati. </s>

<s>Dipendono queste leggi, come da loro universale principio, dal <emph type="italics"/>Teo&shy;<lb/>rema meccanico,<emph.end type="italics"/> che dice stare allora due gravi in equilibrio, sopra due piani <lb/>ugualmente alti, quando le loro lunghezze siano alle gravit&agrave; omologamente <lb/>proporzionali. </s>

<s>Alla dimostrazione di ci&ograve;, che in primo luogo ricorre nel libro <lb/>stampato, voleva il Torricelli aggiungere un tal corollario: &ldquo; Ergo gravia <lb/>tunc habebunt aequalia momenta, quando ipsa fuerint ut secantes comple&shy;<lb/>mentorum anguli elevationis. </s>

<s>Posito enim sinu toto AB (fig. </s>

<s>254) erunt AC, <lb/>AD dictae secantes &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXIII, fol. </s>

<s>83). &Egrave; infatti AC:AB= <lb/>1:cos.CAB=sec.CAB:1; AD:AB=1:cos.BAD=sec.BAD:1. <lb/>D'onde AC:AD=sec.CAB:sec.BAD. <lb/><figure id="id.020.01.2765.1.jpg" xlink:href="020/01/2765/1.jpg"/></s></p><p type="caption">

<s>Figura 254.</s></p><p type="main">

<s>Nella seconda <emph type="italics"/>De motu gravium,<emph.end type="italics"/> avendo gi&agrave; di <lb/>mostrato l'Autore che i momenti di due gravi uguali, <lb/>sopra due piani di uguale altezza, stanno come le <lb/>loro lunghezze reciproche; poi pens&ograve; di mettere la <lb/>medesima conclusione sotto altra forma, dicendo <lb/>che que'momenti hanno la proporzione omologa <lb/>dei seni degli angoli delle elevazioni. </s>

<s>Si trova il pensiero sotto il n.o XXX <lb/>del citato <emph type="italics"/>Campo di tartufi,<emph.end type="italics"/> notato in questa forma: &ldquo; Quando vero gravia <lb/>aequalia fuerint, erunt momenta ut sinus angulorum elevationis. <emph type="italics"/>Nota che <lb/>vi &egrave; (nel libro stampato), ma la prova &egrave; pi&ugrave; bella cos&igrave;:<emph.end type="italics"/> nam, cum sint <lb/>momenta ut ED, FD (fig. </s>

<s>255), hae sunt sinus angulorum DAC, DBC &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. XXXIII, fol. </s>

<s>82). </s></p><p type="main">

<s>Come per&ograve; AD, BD, a cui contrariamente rispondono i momenti, abbian <lb/>la proporzion medesima delle loro porzioni DF, DE, segate dal mezzo cerchio, <lb/><figure id="id.020.01.2765.2.jpg" xlink:href="020/01/2765/2.jpg"/></s></p><p type="caption">

<s>Figura 255.<lb/>che sia descritto intorno a DC; non si <lb/>trova dimostrato, e non si trova pur di&shy;<lb/>mostrato come le due corde intercette <lb/>siano uguali ai seni dell'angolo dell'incli&shy;<lb/>nazione de'piani. </s>

<s>N&egrave; si pu&ograve; la prima di <lb/>queste due verit&agrave; supporre nota dall'iso&shy;<lb/>cronismo delle sottese al circolo, non di&shy;<lb/>mostrato ancora, per cui s'argomenta che <lb/>dalle propriet&agrave; geometriche, e non dalle <lb/>meccaniche, intendesse il Torricelli che fosse da concludere la proporzionalit&agrave; <lb/>reciproca tra le lunghezze de'piani AD, BD, e le loro porzioni intersecate. </s>

<s><lb/>Essendo infatti la BC tangente, la DB secante, e il triangolo BDC rettangolo <lb/>in C, abbiamo, per le notissime propriet&agrave; geometriche, BC2=BD.BF= <lb/>DB2&mdash;DC2, e perci&ograve; DC2=DB (DB&mdash;BF)=DB.FD. </s>

<s>Nel medesimo <pb xlink:href="020/01/2766.jpg" pagenum="391"/>modo si troverebbe DC2=AD.ED. Che, se dunque AD.ED=DB.FD, <lb/>AD:DB=FD:ED. </s></p><p type="main">

<s>La seconda torricelliana si sarebbe potuta perci&ograve; mettere anche sotto <lb/>quest'altra forma, dicendo che i momenti del medesimo grave, sopra i piani <lb/>AD, BD, stanno omologamente come le loro parti intersecate dal semicerchio, <lb/>d'onde il corollario bellissimo che, essendo per DF, DE gl'impeti o le velo&shy;<lb/>cit&agrave; proporzionali agli spazi, i tempi sono uguali, per venire alla qual con&shy;<lb/>clusione ebbe Galileo a prepararsi la macchina di parecchie laboriose pro&shy;<lb/>posizioni. </s></p><p type="main">

<s>Ma la presente intenzione del Nostro era, come si diceva, quella di <lb/>dimostrar che i momenti son proporzionali ai seni degli angoli delle eleva&shy;<lb/>zioni. </s>

<s>Forse la dimostrazione era la medesima o simile, che nel lemma pre&shy;<lb/>messo alla proposizione IV (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>106), ma pi&ugrave; facile e pi&ugrave; <lb/>diretta sovviene dal considerar l'uguaglianza del triangolo HID (nella fatta <lb/>costruzione) col CED, e del GMD col DFC, d'onde il lato ED viene a dimo&shy;<lb/>strarsi uguale a LH, seno dell'angolo LDH, o del suo uguale DAC, secondo <lb/>cui s'inclina il piano AD sopra l'orizontale AC; e il lato FD uguale al lato <lb/>GM, seno di MDG, o del suo uguale DBC, angolo dell'inclinazione dell'al&shy;<lb/>tro piano. </s></p><p type="main">

<s>A cos&igrave; fatte dimostrazioni, mancanti nel manoscritto, pens&ograve; di supplir <lb/>di buon'ora il Viviani, il quale ordin&ograve; cos&igrave; quella, che, fra le occorseci in <lb/>questo proposito, si contrassegna da noi per la proposizione prima. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE I. &mdash; <emph type="italics"/>Momenta gravium aequalium super plana DA, <lb/>DB<emph.end type="italics"/> (nella medesima figura), <emph type="italics"/>sunt ut sinus angulorum elevationis. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Quod, per primum, momenta gravium aequalium super plana DA, DB, <lb/>de quibus Auctor loquitur, sint inter se ut ipsorum segmenta ED, FD, in <lb/>semicirculo DEC inscripta, dum sit DC ad horizontalem AC perpendicula&shy;<lb/>ris; patet sic: Nam iunctis CE, CF, rectangula ADE, BDF inter se sunt ae&shy;<lb/>qualia, utrumque enim aequatur quadrato diametri DC. </s>

<s>Quare ut BD ad DA, <lb/>ita est ED ad DF. </s>

<s>Sed ut BD ad DA, ita est reciproce momentum gravis <lb/>super DA, ad momentum aequalis gravis super DB, per secundam proposi&shy;<lb/>tionem eiusdem libri primi <emph type="italics"/>De motu;<emph.end type="italics"/> ergo ut ED ad DF, ita est momen&shy;<lb/>tum super DA, ad momentum super DB. &rdquo; </s></p><p type="main">

<s>&ldquo; Insuper, quod ipsae DE, DF sint sinus angulorum elevationis DAC, <lb/>DBC, ita ostenditur: Descripto enim, ex centro D, ac intervallo DC, qua&shy;<lb/>drante circuli DCI, secante plana in G, H, atque ex GH ductis GM, HL, si&shy;<lb/>nubus angulorum GDI, HDI, vel sibi aequalium DBC, DAC; hi aequantur <lb/>ipsis inscriptis DF, DE, singuli singulis, quoniam, in triangulis DLH, CED, <lb/>angulus LDH, a tangente et secante constitutus, aequatur angulo in alterna <lb/>portione ECD: anguli ad M, E sunt recti, latus vero DH aequatur lateri DC, <lb/>cum utrumque sit radius quadrantis; ideoque et latus HL aequatur lateri DE. </s>

<s><lb/>Eademque ratione GM aequale ipsi DF, quod supererat, demonstratur &rdquo; (ibid., <lb/>T. XXXVII, fol. </s>

<s>93). </s></p><p type="main">

<s>Di qui si conclude, intendendo significato con Mo il momento, e riferen-<pb xlink:href="020/01/2767.jpg" pagenum="392"/>doci alla medesima figura, Mo.DB:Mo.DC=sen.DBC:sen.DCB= <lb/>DC:DB, che vuol dire il momento parziale sopra il piano inclinato stare al <lb/>totale, nel perpendicolo, contrariamente come la lunghezza di esso perpen&shy;<lb/>dicolo sta alla lunghezza del piano. </s>

<s>Che se il grave s'immagini essere una <lb/>sfera, posata sul declivio BG (fig. </s>

<s>256), e si faccia dal diametro di lei rap&shy;<lb/><figure id="id.020.01.2767.1.jpg" xlink:href="020/01/2767/1.jpg"/></s></p><p type="caption">

<s>Figura 256.<lb/>presentare il momento totale, sar&agrave; il parziale, dice il <lb/>Torricelli nel corollario alla citata proposizione (Op. </s>

<s><lb/>geom. </s>

<s>cit., pag. </s>

<s>102), rappresentato dalla corda AB, co&shy;<lb/>sicch&egrave;, intendendosi significati con Mo.T, Mo.P i due <lb/>detti momenti, avremo Mo.T:Mo.P=HB:AB. </s>

<s><lb/>Moltiplicando ora la seconda ragione per la circonfe&shy;<lb/>renza di un cerchio massimo, e osservando che essa cir&shy;<lb/>conferenza moltiplicat&agrave; per il diametro &egrave; uguale a tutta <lb/>intera la superficie sferica, e moltiplicata per la corda AB &egrave; uguale all'ar&shy;<lb/>milla descritta dall'arco AB, supposto che la rivoluzione si faccia intorno al <lb/>diametro EF; avremo dimostrata la proposizione che segue: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE II. &mdash; <emph type="italics"/>Momentum totale ad momentum in hoc situ<emph.end type="italics"/><lb/>(quale cio&egrave; vien rappresentato dalla figura) <emph type="italics"/>est ut tota sphaerae superficies <lb/>ad armillarem sphaerae superficiem, quam subtendit AB,<emph.end type="italics"/> si <emph type="italics"/>sphaera vol&shy;<lb/>vatur circa EF &rdquo;<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., T. XXX, fol. </s>

<s>79). </s></p><p type="main">

<s>Questa e la precedente, incluse come in loro principio nelle proposizioni <lb/>gi&agrave; divulgate, aggiungevano al trattato eleganza, ma quella, che ora in terzo <lb/>luogo porremo, suppliva una notizia importante, della quale anche Galileo <lb/>aveva lasciato il suo dialogo in difetto, ed &egrave;: secondo qual proporzione stiano <lb/>i momenti, quando, essendo i piani quali si sono descritti, i mobili per&ograve; sono <lb/>in mole e in gravit&agrave; differenti: per rispondere al quale quesito aveva il Tor&shy;<lb/>ricelli distesa la seguente </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE III. &mdash; <emph type="italics"/>Si AB, BC<emph.end type="italics"/> (fig. </s>

<s>257) <emph type="italics"/>duo plana fuerint inae&shy;<lb/>qualiter inclinata, et AC horizontalis, sintque in planis duo gravia quae-<emph.end type="italics"/><lb/><figure id="id.020.01.2767.2.jpg" xlink:href="020/01/2767/2.jpg"/></s></p><p type="caption">

<s>Figura 257.<lb/><emph type="italics"/>cumque D, et E; dico momentum D, ad mo&shy;<lb/>mentum E, compositam habere rationem ex <lb/>ratione molis D, ad molem E homologe, et <lb/>ex ratione longitudinis CB ad BA, reci&shy;<lb/>proce. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ponatur enim grave F aequale ipsi D, in <lb/>altero plano BC, et erit, per propositionem secundam libelli nostri <emph type="italics"/>De motu,<emph.end type="italics"/><lb/>momentum D, ad momentum F, ut est CB ad BA. </s>

<s>At momentum F, ad <lb/>momentum E, est ut molis F ad molem E; ergo momentum D, ad momen&shy;<lb/>tum E, compositam rationem habet ex ratione CB ad BA, et ex ratione mo&shy;<lb/>lis D ad E, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Sed quia CB ad BA est ut sinus anguli A, ad sinum <lb/>anguli C, dicemus etiam rationem momenti D, ad momentum E, componi <lb/>ex ratione molis D, ad molem E, et ex ratione sinus elevationis plani AB, <lb/>ad sinum elevationis plani CB &rdquo; (ibid., T. XXXVII, fol. </s>

<s>72). </s></p><pb xlink:href="020/01/2768.jpg" pagenum="393"/><p type="main">

<s>Aveva il Mersenno rimproverato, in una sua lettera, il Torricelli perch&egrave; <lb/>egli suppone nel corollario, dopo la propozione terza, una cosa, senz'altri&shy;<lb/>menti dimostrarla. </s>

<s>Di che avendo esso Torricelli giustamente riconosciuto <lb/>essere il suo trattato in difetto, pens&ograve; di supplirvi in questa maniera: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE IV. &mdash; <emph type="italics"/>Posita cadem figura, quae in libello<emph.end type="italics"/> (per noi <lb/>la 258), <emph type="italics"/>dico momentum A, ad momentum B, ita esse ut CD ad DE. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sumantur enim ID, DH aequales ipsis CD, DE, et in punctis I, H <lb/><figure id="id.020.01.2768.1.jpg" xlink:href="020/01/2768/1.jpg"/></s></p><p type="caption">

<s>Figura 258.<lb/>duae sphaerae constituantur aequales, tum inter <lb/>se, tum ipsis B, A, et connectatur recta BH, <lb/>quae tamquam libra concipiatur. </s>

<s>Patet quod <lb/>recta BH bifariam secabitur in L, per secun&shy;<lb/>dam Sexti, ergo punctum L erit centrum gra&shy;<lb/>vitatis gravium B, H, et est L in perpendiculo <lb/>per punctum suspensionis ducto: ergo gravia <lb/>sic connexa, sive colligentur recta BH, sive linea <lb/>inflexa BDH, non movebuntur, nulla enim maior <lb/>ratio est cur ad dextram descendant, potius quam ad sinistram. </s>

<s>Si manent, <lb/>ergo momentum in B aequale est momento in H. &rdquo; </s></p><p type="main">

<s>&ldquo; Idem dicendum de gravibus A, I. </s>

<s>Propterea momenta in A, B erunt <lb/>ut momenta in I, H, nempe ut distantiae ID, DH, sive ut CD, DE &rdquo; (ibid., <lb/>T. XL, fol. </s>

<s>77). </s></p><p type="main">

<s>Il Torricelli per far prova della sua fecondit&agrave; in quello stesso, che da'suoi <lb/>proprii censori si giudicava difetto, volle dimostrare cos&igrave; la medesima cosa. <lb/><figure id="id.020.01.2768.2.jpg" xlink:href="020/01/2768/2.jpg"/></s></p><p type="caption">

<s>Figura 259.<lb/>anche in un altro modo assai pi&ugrave; bello, per <lb/>via della costruzione, ch'&egrave; data assai facil&shy;<lb/>mente ad intendere dalla nostra figura 259, <lb/>senza che ci sia bisogno di altre parole: <lb/>&ldquo; Momentum partiale descensivum per DF, <lb/>ad totale per DK, est ut DK ad DF, vel ut <lb/>AK ad AD, vel AC: et totale per DK, vel EI, <lb/>ad partiale descensivum per EG, est ut EG <lb/>ad EI, vel ut AE ad AI, vel ut AC ad AI. </s>

<s>Ergo ex aequali partiale descen&shy;<lb/>sivum per DF, ad partiale descensivum per EG, est ut AK ad AI, vel ut <lb/>totale appensum in K, ad totale idem appensum in I &rdquo; (ibid., T. XXXIV, <lb/>fol. </s>

<s>134). </s></p><p type="main">

<s>Cos&igrave; gl'importanti corollari della proposizione terza venivano ad essere <lb/>anche meglio nella loro verit&agrave; confermati. </s>

<s>Ma il Torricelli pensava di ar&shy;<lb/>ricchire anche pi&ugrave; questa parte del suo trattato, aggiungendovi le seguenti, <lb/>che noi raccoglieremo qui fra le nostre proposizioni meccaniche dei mo&shy;<lb/>menti. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE V. &mdash; <emph type="italics"/>Sint duo plana utcumque AB, AC<emph.end type="italics"/> (fig. </s>

<s>260) <emph type="italics"/>et <lb/>duo gravia utcumque B, C. </s>

<s>Iungatur BC, et fiat ut grave B ad C, ita CD <lb/>ad DB. </s>

<s>Tum per D ducatur EF, ita ut secet ipsas EA, AF in ratione gra&shy;<lb/>vis B ad grave C: dico EF esse viam centri aravitatis. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><pb xlink:href="020/01/2769.jpg" pagenum="394"/><p type="main">

<s>&ldquo; Primo ostendemus BE, FC aequales esse. </s>

<s>Ducatur BI parallela ad AC: <lb/><figure id="id.020.01.2769.1.jpg" xlink:href="020/01/2769/1.jpg"/></s></p><p type="caption">

<s>Figura 260.<lb/>erit EB ad BI ut EA ad EF, hoc est <lb/>CD ad DB, hoc est FC ad BI eam&shy;<lb/>dem. </s>

<s>Quare aequales erunt EB, FC. &rdquo; </s></p><p type="main">

<s>&ldquo; Moveantur iam gravia, et sint <lb/>B in L, C in M: erunt aequales totae <lb/>EL, FM. </s>

<s>Ducatur LO parallela ad <lb/>AM, et iungatur LM. </s>

<s>Erit grave L, ad <lb/>grave M, ut EA ad AF, vel EL ad LO, <lb/>vel MF ad LO, vel MP ad PL. </s>

<s>Ergo <lb/>centrum est P &rdquo; (ibid., T. XXXVII, <lb/>fol. </s>

<s>69). </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE VI. &mdash; <emph type="italics"/>Datis ut supra, fiat ut grave A<emph.end type="italics"/> (fig. </s>

<s>261), <emph type="italics"/>ad <lb/>grave B, ita quaelibet CD ad DE: et erit planum CE tale planum, quod <lb/>si in ipso grave A sit, erit momentum gravis A in plano CE idem ac <lb/>momentum gravis A in plano CD &rdquo;<emph.end type="italics"/> (ibid.). </s></p><p type="main">

<s>La dimostrazione &egrave; taciuta, perch&egrave; forse la credeva il Torricelli ovvia <lb/>alla mente di ognuno, che vada ripensando come, per la prima <emph type="italics"/>De motu,<emph.end type="italics"/> i <lb/><figure id="id.020.01.2769.2.jpg" xlink:href="020/01/2769/2.jpg"/></s></p><p type="caption">

<s>Figura 261.<lb/>due gravi rimarrebbero allora fra loro sopra i due piani <lb/>in equilibrio, ossi asenza momento, quando la linea di <lb/>congiunzione CE tornasse in posizione orizontale. </s>

<s>E se <lb/>sopra essa orizontale s'intendesse posato il grave A o E <lb/>rimarrebbe ivi egli pure senza momento. </s>

<s>Inclinando poi <lb/>la figura, in quel modo che si &egrave; rappresentata, &egrave; ma&shy;<lb/>nifesto che l'impeto di discendere lungo il piauo DC &egrave;, per il grave A con&shy;<lb/>giunto col grave B, quel medesimo che sarebbe di scendere lungo il piano <lb/>CE, essendo A libero. </s>

<s>Che se fosse la figura piegata e volta alla parte con&shy;<lb/>traria, in modo cio&egrave; che il punto E si abbassasse, anche il grave E sarebbe <lb/>quello disposto a scendere col gi&agrave; detto momento. </s></p><p type="main">

<s>Questa, con la precedente, della quale non &egrave; che un corollario, servi&shy;<lb/>vano a preparare la proposizione che segue, la quale doveva inserirsi nel li&shy;<lb/><figure id="id.020.01.2769.3.jpg" xlink:href="020/01/2769/3.jpg"/></s></p><p type="caption">

<s>Figura 262.<lb/>bretto stampato, dopo la dimostrazione <lb/>che, passandosi le corde, nel circolo col <lb/>diametro verticalmente eretto, nel mede&shy;<lb/>simo tempo; le velocit&agrave; o i momenti son <lb/>per esse corde proporzionali agli spazi <lb/>passati. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE VII. &mdash; <emph type="italics"/>Sit planum <lb/>AB<emph.end type="italics"/> (fig. </s>

<s>262) <emph type="italics"/>utcumque inclinatum, et <lb/>grave D sit in ipso, sitque aliud plannm <lb/>BC utlibet inclinatum. </s>

<s>Fiat circulus qui&shy;<lb/>libet, cuius tamen infimum punctum sit in AB, et concipiatur momentum <lb/>gravis D esse ut AB: si ponatur grave aliud E connexum cum D, et fiat, ut <lb/>grave D ad E, ita AB ad BC, erit AH momentum gravis D connexi &rdquo;<emph.end type="italics"/> (ibid.). </s></p><pb xlink:href="020/01/2770.jpg" pagenum="395"/><p type="main">

<s>La dimostrazione, che manca nel manoscritto, si supplisce assai facil&shy;<lb/>mente dopo le cose gi&agrave; dette, imperocch&egrave; il momento di D in AB, al mo&shy;<lb/>mento di D in AH, sta come AB ad AH. </s>

<s>Ma il momento di D sopra il piano <lb/>AH &egrave;, per la V di questo, uguale al momento di D congiunto con E sopra <lb/>il piano AB; dunque il momento di D libero, al momento di D congiunto, <lb/>sta come AB ad AH, ci&ograve; che dimostra la verit&agrave; di quel che il Torricelli <lb/>dianzi annunziava. </s></p><p type="main">

<s>Le sette proposizioni intorno ai momenti, fin qui da noi raccolte dai <lb/>manoscritti del Torricelli, sono ordinate alla storia del trattato <emph type="italics"/>De motu gra&shy;<lb/>vium,<emph.end type="italics"/> secondo la prima nostra data intenzione. </s>

<s>La seconda era quella di <lb/>mostrar come avesse lo stesso Torricelli, tanto prima del Marchetti, non so&shy;<lb/>lamente saputo dedurre dai principii statici che i momenti hanno la ragion <lb/>composta delle distanze e dei pesi, ma come egli ne avesse, nel medesimo <lb/>tempo, fatta l'applicazione ad alcuni teoremi concernenti la Baricentrica e <lb/>la Centrobarica guldiniana. </s>

<s>Di che il primo documento, per quel che riguarda <lb/>i centri di gravit&agrave;, ci &egrave; offerto dalla seguente lettera, scritta da Firenze il <lb/>di 7 Aprile 1646 al Cavalieri:. </s></p><p type="main">

<s>&ldquo; Quando, nella lettera di V. P., veddi che ella trattava di quei centri <lb/>di gravit&agrave; intorno a quel suo solido, ebbi paura che ella mi avesse scoperta <lb/>una passione, che io trovai. </s>

<s>Ora perch&egrave; ella non abbia a trovarla, io la dir&ograve;: <lb/>Il centro della gravit&agrave;, in tutte le figure piane e solide, purch&egrave; abbiano l'asse <lb/>o il diametro, sega sempre l'asse, o il diametro che sia, con la medesima <lb/>regola. </s>

<s>La Natura non &egrave; cos&igrave; ricca d'invenzioni, come a noi sembra per la <lb/>nostra propria debolezza. </s>

<s>Ella non bada che la proporzione delle parti del <lb/>diametro in alcune figure sia dupla, in altre tripla, in altre sesquialtera, come <lb/>cinque a tre, come sette a cinque, e tante altre sorti di proporzioni, anco <lb/>incommensurabili. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Questi sono corollari, ma il Teorema universale non so se sia sovve&shy;<lb/>nuto ancora a nessuno: anzi credo che nessuno abbia mai pensato che ci <lb/>possa essere, eppure vi &egrave;, ed &egrave; tale: </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE VIII. &mdash; <emph type="italics"/>Centrum gravitatis in qualibet figura, sive <lb/>plana sive solida, dummodo axem habeat vel diametrum, secat axem vel <lb/>diametrum semper hac lege, ut pars versus verticem sit ad reliquam que&shy;<lb/>madmodum sunt omnes ductus applicatorum, in omnes axis vel diametri <lb/>portiones versus verticem abscissas, ad omnes ductus eorumdem applica&shy;<lb/>torum in reliquas axis vel diametri portiones. </s>

<s>Intelligimus autem, nomine <lb/>applicatorum, in figuris planis, lineas applicatas, in solidis, plana. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ella vede che quelli <emph type="italics"/>ductus<emph.end type="italics"/> in figure piane saranno rettangoli, in so&shy;<lb/>lidi poi saranno solidi. </s>

<s>Ella conoscer&agrave; subito che questo &egrave; un corollario della <lb/>dimostrazione, ch'io gli mandai intorno al solido segato per traverso in un <lb/>piano, che passi <emph type="italics"/>per extremas applicatas.<emph.end type="italics"/> Infatti, esto semifigura qualis de&shy;<lb/>finita est ABC (fig. </s>

<s>263), cuius diameter AB, vertex B, fiatque suum solidum <lb/>cylindricum cavalerianum BD, ita ut altitudo AE sit aequalis diametro AB, <lb/>seceturque plano ACG. </s>

<s>Ostensum est a nobis quod, si F sit centrum gravi-<pb xlink:href="020/01/2771.jpg" pagenum="396"/>tatis totius figurae, ita esse solidum ADEG, ad reliquum, ut BF ad FA. </s>

<s>His <lb/><figure id="id.020.01.2771.1.jpg" xlink:href="020/01/2771/1.jpg"/></s></p><p type="caption">

<s>Figura 263.<lb/>positis, omnia rectangula, quorum unum HL <lb/>(nempe sub applicata HI et sub IL, sive sub por&shy;<lb/>tione IG diametri abcissae versus verticem), ad <lb/>omnia rectangula, quorum unum LP (nempe sub <lb/>applicata OP, et OL, sive reliqua portione dia&shy;<lb/>metri OA) sunt ut solidum ADEG, ad solidum <lb/>ABCG: ergo patet ita esse BF ad FA ut omnia <lb/>praedicta rectangula. </s>

<s>Bench&egrave; dunque si potesse <lb/>dal solido cavaleriano dimostrare in questo modo <lb/>il Teorema, nulladimeno io ne ho trovata un'al&shy;<lb/>tra dimostrazione apposta, ed &egrave; tale: &rdquo; </s></p><p type="main">

<s>&ldquo; Esto figura quaelibet ABCD (fig. </s>

<s>264), sive plana sive solida, dum&shy;<lb/>modo axem vel diametrum habeat AC, sitque centrum gravitatis E: dico CE <lb/>ad EA esse ut dictum est supra. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Nam ponatur ei in directum alia similis et aequalis figura CFGH, <lb/>cuius centrum sit I, sumaturque homologa applicatae LB, MF, et intelliga&shy;<lb/><figure id="id.020.01.2771.2.jpg" xlink:href="020/01/2771/2.jpg"/></s></p><p type="caption">

<s>Figura 264.<lb/>tur suspensa libra ex C, sive aequipon&shy;<lb/>deret, sive non. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Jam, ex principiis mechanicis, <lb/>erit momentum applicati LB, ad mo&shy;<lb/>mentum applicati MF, ut ductus appli&shy;<lb/>cati LB in distantiam LC, ad ductum <lb/>applicati MF, in distantiam MC, et hoc <lb/>semper verum est, ubicumque sumpta fuerint homologa applicata. </s>

<s>Ergo mo&shy;<lb/>mentum omnium applicatorum, seu figurarum ABCD, ad momentum figurae <lb/>CFGH, erit ut omnes ductus applicatorum, quorum unum est LB, in omnes <lb/>diametri vel axis portiones versus verticem abscissas, quarum una est LC; <lb/>ad omnes ductus eorumdem applicatorum, quorum unum est MF, in reli&shy;<lb/>quas diametri portiones, quorum una est MC. </s>

<s>Sed momentum figurae ABCD, <lb/>ad momentum figurae CFGH, est ut distantia EC ad distantiam CI; ergo <lb/>EC ad CI, hoc est EC ad EA, erit ut omnes praedicti illi ductus, quorum <lb/>unum est BL in LC, ad omnes praedictos ductus, quorum unum est MF in <lb/>MC, quod erat domonstrandum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Nelle figure solide basta mutar nome all'applicato, che non &egrave; linea <lb/>ma piano, e per&ograve; anco il rettangolo si muter&agrave; in solido. </s>

<s>La stessa proposi&shy;<lb/>zione abbraccia il centro anche delle linee e delle superficie, ma, in cambio <lb/>delle porzioni del diametro, si adoprano le tangenti. </s>

<s>Supplico V. P. a non <lb/>conferire la cosa con alcuno, perch&egrave; proposi il teorema agli amici di Roma, <lb/>e forse lo proporr&ograve; in Francia, e non l'ho conferita se non a V. P. &rdquo; (ivi, <lb/>T. XL, fol. </s>

<s>132). </s></p><p type="main">

<s>Si sente da queste espressioni che il Torricelli faceva gran conto della <lb/>sua invenzione, la quale nonostante il Cavalieri diceva che sarebbe da pre&shy;<lb/>giare anche di pi&ugrave;, quando vi s'insegnasse il modo di trovare le proporzioni <pb xlink:href="020/01/2772.jpg" pagenum="397"/>fra gli uni e gli altri di que'prodotti. </s>

<s>Ma il Torricelli ingenuamente rispon&shy;<lb/>deva: &ldquo; quanto al trovar la proporzione di quelli <emph type="italics"/>omnes ductus, ad omnes <lb/>ductus,<emph.end type="italics"/> io non ci ho nulla, e non ho cercato altro, stimandola assai intri&shy;<lb/>cata materia &rdquo; (ivi, fol. </s>

<s>133). Nonostante, dando poco tempo dopo notizia al <lb/>Carcavy di questo teorema, dop'averglielo formulato cos&igrave;, soggiungeva: &ldquo; Haec <lb/>est regula, ex qua centra gravitatis exprimo, cum habeam methodum, non <lb/>adeo difficilem, pro invenienda ratione, quam habent praedicti omnes ductus, <lb/>ad omnes ductus &rdquo; (ibid., fol. </s>

<s>39). Potrebb'essere che si fosse messo a ricer&shy;<lb/>care il metodo, e che fosse riuscito a trovarlo, dop'aver tutt'altrimenti con&shy;<lb/>fessato al Cavalieri, ma non se ne conosce da noi il documento, che giustifi&shy;<lb/>chi la vantazione datasi innanzi all'illustre Senator parigino, in una sua <lb/>lettera, dove sono altre vantazioni, che appariranno dalla Storia non giuste. </s></p><p type="main">

<s>Ma, per non interrompere ora il filo del nostro discorso, diremo come <lb/>applicasse il Torricelli il teorema dei momenti a dimostrare la Regola cen&shy;<lb/>trobarica. </s>

<s>Non aveva intorno a ci&ograve; insegnato altro il Guldino, se non che ogni <lb/>solido rotondo &egrave; uguale alla figura genitrice, moltiplicata per il viaggio fatto <lb/>dal centro di gravit&agrave; di lei nella sua conversione. </s>

<s>Il Cavalieri fu il primo <lb/>a dimostrare la verit&agrave; di quella Regola universalissima, per via degl'indivi&shy;<lb/>sibili, e il Torricelli, come gi&agrave; faceva allora anche il Nardi, pens&ograve; che si po&shy;<lb/>teva concludere il medesimo dai pi&ugrave; elementari principii della Geometria e <lb/>della Meccanica, proponendosi intanto questo semplice esempio: </s></p><p type="main">

<s>Si rivolgano co'loro centri di gravit&agrave;, posti nelle distanze FE, DE (fig. </s>

<s>265) <lb/><figure id="id.020.01.2772.1.jpg" xlink:href="020/01/2772/1.jpg"/></s></p><p type="caption">

<s>Figura 265.<lb/>dall'asse comune AE, i due rettangoli AB, BC: <lb/>&egrave; manifesto che si descriver&agrave; da quello un cilin&shy;<lb/>dro solido, e da questo un anello circolare o ci&shy;<lb/>lindro forato, la misura del quale sar&agrave;, secondo <lb/>la Regola guldiniana, BC.2<foreign lang="greek">p</foreign>DE, come sar&agrave; <lb/>AB.2<foreign lang="greek">p</foreign>FE la misura delll'altro: ond'&egrave; che colui, <lb/>il quale si proponesse di voler avere i due solidi <lb/>uguali, dovrebbe fare AB a BC reciprocamente <lb/>come DE a FE. </s>

<s>Ora &egrave; appunto ci&ograve; che intende <lb/>di dimostrare il Torricelli nella seguente, per <lb/>accordare la centrobarica alla geometria. </s></p><p type="main">

<s>&ldquo; PROPOSITIONE IX. &mdash; <emph type="italics"/>Si fuerit ut rectan&shy;<lb/>gulum AB ad BC, ita reviproce recta DE ad <lb/>EF, nempe distantia centri gravitatis rectan&shy;<lb/>guli BC, ad distantiam centri gravitatis re&shy;<lb/>ctanguli AB ab axe AE, convertaturque utra&shy;<lb/>que figura circa axem AE; dico solida aequalia <lb/>circumscribi: nempe cylindrum, ex AB factum, aequalem esse solido annu&shy;<lb/>lari, sive cylindrico excavato, ex BC facto. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ponatur HL aequalis ipsi CE, et fiat ut LB ad BH, ita BH ad BI, et <lb/>compleantur figurae ut in schemate. </s>

<s>Jam spatium AB ad BC est ut recta <lb/>DE ad EF, per suppositionem, sive, in duplis, ut CE, EG, simul, ad EG: <pb xlink:href="020/01/2773.jpg" pagenum="398"/>nempe ut LB ad BH, sive ut HB ad BI, per constructionem; hoc est ut spa&shy;<lb/>tium idem AB ad NI. </s>

<s>Propterea aequalia sunt NI, BC, et eorum latera re&shy;<lb/>ciproce, nempe NB ad BG erit ut recta OB ad BI, sive, sumpta BL communi <lb/>altitudine, ut rectangulum OBL ad rectangulum IBL, hoc est, ut rectangu&shy;<lb/>lum OBL ad quadratum BH. </s>

<s>Et componendo erit NG ad GB ut quadratum <lb/>OH ad BH, sive ut circulus ex OH ad circulum ex BH. </s>

<s>Cylindrorum itaque, <lb/>factorum ex AG et HC circa axem AE, reciprocantur bases et altitudines; <lb/>quare aequales sunt. </s>

<s>Et, dempto communi cylindro facto ex HG, reliqua so&shy;<lb/>lida aequalia erunt &rdquo; (ibid., T. XXXI, fol. </s>

<s>38). </s></p><p type="main">

<s>Il discorso &egrave; chiarissimo, se non che, giunto a concludere la propor&shy;<lb/>zione NB:EG=OB.BL:BH2, dalla quale s'ha, componendo, NG:BG= <lb/>OB.BL+BH2:BH2, suppone il Torricelli che il terzo termine proporzio&shy;<lb/>nale di questa sia uguale al quadrato di OH, come cosa che dall'altra parte <lb/>cos&igrave; assai facilmente si dimostra: Abbiamo OB.BL=OB(BH+HL)= <lb/>OB.BH+OB.HL. </s>

<s>Dunque OB.BL+BH2=OB.BH+OB.HL+BH2= <lb/>BH (OB+BH)+OB.HL=BH.OH+OB.HL. </s>

<s>Ma HL=OH, dunque <lb/>OB.BL+BH2=OH (BH+OB)=OH.OH=OH2. </s></p><p type="main">

<s>In questo esempio per&ograve; le superficie genitrici son regolari, e regolari <lb/>son per conseguenza i solidi generati. </s>

<s>Ma la Regola guldiniana si diceva va&shy;<lb/>lere per qualunque figura, ci&ograve; che rimaneva al Torricelli da dimostrare, spe&shy;<lb/>cialmente allora, che si disponeva a ritrovar la misura dei solidi rotondi <lb/>descritti dagli spazi cicloidali. </s>

<s>Si conseguiva poi il laborioso intento per via <lb/><figure id="id.020.01.2773.1.jpg" xlink:href="020/01/2773/1.jpg"/></s></p><p type="caption">

<s>Figura 266.<lb/>delle tre proposizioni, che si mettono da noi l'ultime fra <lb/>le raccolte qui, per servire alla Storia, e per compilarne <lb/>insieme il promesso trattato postumo <emph type="italics"/>De momentis.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; PROPOSIZIONE X. &mdash; <emph type="italics"/>Si rectangulum aliquod AB<emph.end type="italics"/><lb/>(fig. </s>

<s>266) <emph type="italics"/>libratum, sive suspensum sit super aliqua <lb/>recta ED, lateribus parallela, erunt momenta partium <lb/>rectanguli ut quadrata laterum homologe: hoc est mo&shy;<lb/>mentum figurae AD, ad momentum figurae EB, erit <lb/>ut quadratum CD, ad quadratum DB. &rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.2773.2.jpg" xlink:href="020/01/2773/2.jpg"/></s></p><p type="caption">

<s>Figura 267.</s></p><p type="main">

<s>&ldquo; Ponantur enim centra gravitatis par&shy;<lb/>tium esse I et O, habebiturque momentum <lb/>AD, ad momentum EB, rationem composi&shy;<lb/>tam ex ratione magnitudinum, et ex ratione <lb/>distantiarum: nempe ex ratione figurae AD <lb/>ad EB, sive rectae CD ad DB, et ex ratione <lb/>rectae IH, ad HO, vel CD ad DB. </s>

<s>Ergo mo&shy;<lb/>mentum AD, ad momentum EB, erit ut qua&shy;<lb/>dratum CD, ad quadratum DB &rdquo; (ibid., <lb/>T. XXXIV, fol. </s>

<s>277). </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XI. &mdash; <emph type="italics"/>Si quaelibet <lb/>figura ABCD<emph.end type="italics"/> (fig. </s>

<s>267), <emph type="italics"/>habens perimetrum <lb/>in easdem partes cavum, super aliqua re-<emph.end type="italics"/><pb xlink:href="020/01/2774.jpg" pagenum="399"/><emph type="italics"/>cta AD aequilibretur cum rectangulo AE, hoc est aequale momentum ha&shy;<lb/>beat tam figura ACD, quam rectangulum AE; dico solida rotunda, quae <lb/>circa axem AD fiunt, tam a figura ABCD, quam a rectangulo AE, aequa&shy;<lb/>lia esse inter se. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Supponendo che siano GO, NP le distanze dei centri di gravit&agrave; delle due <lb/>figure dall'asse, avere esse figure il momento uguale non vuol dir altro che <lb/>essere ABCD.NP=AE.GO, ossia ABCD.2<foreign lang="greek">p</foreign>NP=AE.2<foreign lang="greek">p</foreign>GO, Ora, per <lb/>chi ammette la Regola centrobarica, l'uguaglianza fra'due solidi rotondi &egrave; <lb/>di qui manifesta. </s>

<s>Ma il Torricelli vuole, indipendentemente da ogni altro <lb/>principio che non sia geometrico, dimostrare l'uguaglianza dei due solidi ro&shy;<lb/>tondi, per confermare la verit&agrave; della stessa Regola centrobarica. </s></p><p type="main">

<s>&ldquo; Nisi enim (cosi egli infatti per la via obliqua procede, perch&egrave; la di&shy;<lb/>retta era evidente) aequalia sint, erit solidum figurae ABCD vel maius vel <lb/>minus cylindri rectanguli AE. Esto, si potest, primum maius, et intra ipsum <lb/>describatur figura solida constans ex cylindris aeque altis, ita ut inscripta <lb/>etiam figura solida maior sit cylindro facto ex rectangulo AE: quod hoc pos&shy;<lb/>sit fieri, et quomodo, notissimum iam est apud Geometras. </s>

<s>Tunc enim erit <lb/>cylindrus ex DL, ad cylindrum ex DI, ut quadratum LF ad FI, sive ut mo&shy;<lb/>mentum rectanguli DL, ad momentum DI, et hoc verum erit de reliquis <lb/>omnibus cylindrulis et rectangulorum momentis, excepto ultimo AM. </s>

<s>Suntque <lb/>omnes primi ordinis magnitudines, omnesque tertii aequales, propterea erunt, <lb/>per lemma XVIII libelli nostri <emph type="italics"/>De dimensione parabolac,<emph.end type="italics"/> omnes primae, hoc <lb/>est omnes cylindri ex MD simul sumpti, ad figuram solidam inscriptam ex <lb/>cylindris constantem, ut omnes simul tertiae: hoc est ut momentum collectum <lb/>omnium rectangulorum MD ad momentum figurae planae inscriptae. </s>

<s>Sed <lb/>omnes cylindri ex AE, ad omnes ex MD, sunt ut momentum omnium rectan&shy;<lb/>gulorum AE, ad momentum omnium MD; ergo ex aequo omnes cylindri ex <lb/>AE, ad figuram solidam inscriptam, sunt ut momenta figurae planae AE, ad <lb/><figure id="id.020.01.2774.1.jpg" xlink:href="020/01/2774/1.jpg"/></s></p><p type="caption">

<s>Figura 268.<lb/>momentum figurae planae intra ABCD descriptae, hoc <lb/>est maiores, quod est contra suppositum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quando vero solidum rotundum ex ABCD pona&shy;<lb/>tur minus cylindro ex AE facto, tunc circumscribenda <lb/>erit ipsi solido figura quaedam, ex cylindris aeque altis <lb/>constans, ita ut circumscripta figura minor sit eodem <lb/>cylindro ex AE facto, quod fieri potest more solito, <lb/>eademque demonstratio praecedens adhiberi poterit, <lb/>brevior tamen et facilior, siquidem numerus cylindro&shy;<lb/>rum et rectangulorum utrimque idem erit, et argu&shy;<lb/>mentum illud ex aequo evanescit. </s>

<s>Cum ergo solidum <lb/>figurae ABCD non possit esse neque maius neque <lb/>minus cylindri rectanguli AE, erit aequale, quod erat <lb/>ostendendum &rdquo; (ibid., T. XXVI, fol. </s>

<s>41, 42). </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE XII. &mdash; <emph type="italics"/>Solidum rotundum ex qualibet figura plana <lb/>ABC<emph.end type="italics"/> (fig. </s>

<s>268), <emph type="italics"/>cuius tamen perimeter sit ad easdem partes cavus, circa<emph.end type="italics"/><pb xlink:href="020/01/2775.jpg" pagenum="400"/><emph type="italics"/>axem AC factum, ad cylindrum ex rectangulo quolibet DC circa eumdem <lb/>axem factum, rationem habet compositam ex ratione figurae planae ABC, <lb/>ad rectangulum DC, et ex ratione distantiae GE ad distantiam GF: nempe <lb/>centri gravitatis E et F ab axe communi AC. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ponatur rectangulum AH, cuius centrum I, quod aequale momentum <lb/>habeat cum figura plana ABC, eritque figura ABC ad AH reciproce ut IG <lb/>ad GE, cum aequiponderent. </s>

<s>Fiat etiam ut IG ad GF, ita EG ad GO. </s>

<s>Jam <lb/>ex praeced. </s>

<s>patet quod cylindrus factus ex AH aequalis erit solido rotundo <lb/>ex figura ABC. </s>

<s>Propterea solidum ex ABC, ad cylindrum ex DC, erit ut <lb/>cylindrus ex AH, ad cylindrum ex DC: nempe ut quadratum IG, ad qua&shy;<lb/>dratum GF. </s>

<s>Ratio itaque solidi rotundi ex ABC, ad cylindrum ex DC, com&shy;<lb/>ponitur ex ratione rectae IG ad GF, bis sumpta, sive ex ratione rectae IG <lb/>ad GF semel, et ex ratione restae EG ad GO, per constructionem. </s>

<s>Ergo so&shy;<lb/>lidum ex ABC, ad cylindrum ex DC, erit ut rectangulum IGE ad rectangu&shy;<lb/>lum FGO, nempe rationem habebit compositam ex ratione laterum IG ad GO, <lb/>vel, ut infra ostendam, figurae planae ABC ad DC, et ex ratione distantiae <lb/>EG ad GF, quod erat ostendendum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quod promisimus ostendemus sic: figura plana ABC ad AH est ut <lb/>IG ad GE: sed figura AH ad DC est ut IG ad GF, vel ut EG ad GO; ergo <lb/>ex aequo erit figura plana ABC, ad DC, ut recta IG ad GO &rdquo; (ibid., fol. </s>

<s>43). </s></p><p type="main">

<s>Queste proposizioni erano, come dicemmo, state preparate dal Torricelli <lb/>per applicarle a ritrovare la proporzione che passa tra il solido rotondo, ge&shy;<lb/><figure id="id.020.01.2775.1.jpg" xlink:href="020/01/2775/1.jpg"/></s></p><p type="caption">

<s>Figura 269.<lb/>nerato dallo spazio cicloidale, <lb/>e il cilindro del rettangolo <lb/>circoscritto, rivolgendosi am&shy;<lb/>bedue le figure insieme in&shy;<lb/>torno al medesimo asse. </s>

<s>Es&shy;<lb/>sendo infatti FE (fig. </s>

<s>269) la <lb/>distanza del centro di gra&shy;<lb/>vit&agrave; del rettangolo, e GE quella del centro della Cicloide, come il Torricelli <lb/>stesso ha insegnato a ritrovarlo nella proposizione LVI da noi scritta nel ca&shy;<lb/>pitolo precedente; dalla passata resulta che il solido rotondo ha verso il cilin&shy;<lb/>dro circoscritto la ragion composta delle figure AD, ABC, e delle distanze <lb/>EF, EG de'respettivi centri dall'asse della rivoluzione. </s>

<s>Ma perch&egrave; di ci&ograve; avr&agrave; <lb/>da intrattenersi altrove la nostra Storia in discorso importante, passeremo <lb/>senz'altro a raccogliere dai Manoscritti torricelliani i promessi teoremi di <lb/>Meccanica nuova. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Quel maraviglioso argomento meccanico di comporre e decomporre le <lb/>forze fu dai Matematici francesi, sul finir del secolo XVII, creduto cosa nuova, <lb/>perch&egrave; il lungo decorrer dei secoli, e la giovanile baldanza dei progressi, <pb xlink:href="020/01/2776.jpg" pagenum="401"/>avevano fatto dimenticare e disprezzare le antiche tradizioni della Scienza. </s>

<s><lb/>Scaturivano quelle tradizioni dalle fonti aristoteliche, le quali poi vennero a <lb/>formare due rivi, sullo scoperto margine dell'un de'quali scendevano ad abbe&shy;<lb/>verarsi i Matematici, pi&ugrave; seguaci del vero che di questo o di quel Maestro. </s>

<s><lb/>L'altro rivo parve disperdersi sotto terra, e ivi dentro, quasi a mantenervi <lb/>perpetua la verdura, ricircolare invisibile nel Libro archimedeo delle Spirali. </s>

<s><lb/>La XVIII proposizione di questo, e la prima Della dimensione del circolo, <lb/>per volerne penetrare il segreto, posero, da che riapparirono al mondo, a <lb/>tortura gl'ingegni dei primi interpetri, i quali vi s'affaticarono inutilmente, <lb/>perch&egrave;, non curando i libri aristotelici, non era a loro venuta a mano la <lb/>chiave per aprir quei misteri. </s>

<s>Ond'a ripensar che fra cotesti non curanti era <lb/>anche il Torricelli, sarebbe da dir miracoloso il suo ingegno, perch'egli fu, <lb/>almeno tra noi, il primo a scoprir che il segreto della XVIII delle Spirali <lb/>dipendeva tutto dal principio dei moti composti. </s>

<s>Il miracolo per&ograve; svanisce <lb/>osservando che al difetto delle tradizioni aristoteliche supplirono le galileiane, <lb/>bench&egrave; non legittime, come pi&ugrave; qua vedremo. </s>

<s>Ma per dichiarar meglio i fatti <lb/>recenti giova risalir col discorso a quell'alta sfera, dove il contemplativo Si&shy;<lb/>racusano ha il suo cielo, se i troppo acuti raggi non c'impediranno la de&shy;<lb/>bole vista. </s></p><p type="main">

<s>Da che nacque la Geometria sino al tempo nostro (scriveva Antonio <lb/>Nardi in un suo libro rimasto manoscritto, e di cui daremo qualche notizia <lb/>in quest'altro capitolo) s'&egrave; senza successo cercata la misura precisa del cer&shy;<lb/>chio, e del suo perimetro. </s>

<s>&Egrave; fra cotesti cercatori il pi&ugrave; celebre Archimede, <lb/>gli sforzi del quale, bench&egrave; fossero senza successo in ordine al fine che di&shy;<lb/>rettamente s'era prefisso, pur lo condussero per via indiretta a quella geo&shy;<lb/>metrica invenzione stupenda, nei pi&ugrave; riposti segreti della quale osa ora di <lb/>penetrare la nostra Storia. </s></p><p type="main">

<s>Ritornando indietro per XXII secoli, troveremo il nostro Matematico <lb/>lungo il solitario lido siracusano sedersi contemplativo innanzi alla figura di <lb/>un circolo, ch'egli ha descritto sopra l'arena. </s>

<s>La cura, che al presente lo <lb/>preme, &egrave; di misurare la precisa lunghezza delle linee rette, dall'ambito delle <lb/>quali si racchiuda uno spazio uguale a quello, che dentro s&egrave; racchiude l'am&shy;<lb/>bito della curva. </s>

<s>Il primo pensiero che lo lusinga &egrave; quello d'inscrivere un <lb/>poligono regolare, a cui solo mancano, per uguagliarsi al circolo, gli spazi <lb/>rimasti presi tra i lati inscritti e gli esterni archi sottesi: spazi, che vanno <lb/>sempre pi&ugrave; ad assottigliarsi, quanto i lati del poligono son pi&ugrave; suddivisi. </s>

<s>Cos&igrave; <lb/>la circolar superficie differirebbe di poco da quella di altrettanti triangoli, <lb/>appuntati tutti nel centro, e perci&ograve; tutti aventi la medesima altezza poco dif&shy;<lb/>ferente dal raggio, quanti sono i lati del poligono, che a ciascun triangolo <lb/>servon di base. </s>

<s>E qui gli balen&ograve; alla mente che si potevano que'tanti trian&shy;<lb/>goli ridurre a uno solo, stirando in dirittura il perimetro dello stesso poli&shy;<lb/>gono inscritto. </s>

<s>Anzi, perch&egrave; non si potrebbe far ci&ograve; della medesima circon&shy;<lb/>ferenza? </s>

<s>la quale immagina Archimede essere diventata un filo flessibile, con <lb/>le due estremit&agrave; toccantisi in B (fig. </s>

<s>270), l'una delle quali tenuta in B <pb xlink:href="020/01/2777.jpg" pagenum="402"/>ferma, prende l'altra, e la svolge, e la stira nella dirittura BC in modo, che <lb/>faccia con AB un angolo retto. </s>

<s>Or che rimane altro a fare, se non che ricon&shy;<lb/><figure id="id.020.01.2777.1.jpg" xlink:href="020/01/2777/1.jpg"/></s></p><p type="caption">

<s>Figura 270.<lb/>giungere i punti A, C, per <lb/>annunziare questa verit&agrave; <lb/>al mondo maravigliato? <lb/><emph type="italics"/>Omnis circulus aequalis <lb/>est triangulo rectangulo, <lb/>cuius radius est par uni <lb/>eorum, quae sunt circa <lb/>rectum angulum; circumferentia vero basi.<emph.end type="italics"/> (Opera cit., pag. </s>

<s>128). </s></p><p type="main">

<s>Conseguiva di qui una verit&agrave;, la quale, bench&egrave; non riuscisse ai Geome&shy;<lb/>tri nuova, aveva nonostante abito nuovo, e maniera pi&ugrave; familiare, perch&egrave;, <lb/>come sapevasi che il triangolo ha per misura la base moltiplicata per la met&agrave; <lb/>dell'altezza, cos&igrave; rendevasi ora manifesto che lo spazio circolare &egrave; misurato <lb/>dal prodotto della circonferenza per la met&agrave; del raggio. </s>

<s>Il principale intento <lb/>per&ograve;, con quella meccanica stiratura violenta, non era conseguito, dovendosi, <lb/>tra la curvit&agrave; e la rettitudine, trovar piuttosto la proporzion naturale nei le&shy;<lb/>gittimi termini della Geometria. </s>

<s>Parve allora ad Archimede che l'astrusa <lb/>questione si risolverebbe, quando, invece di dare il punto C alla AC deter&shy;<lb/>minato, fosse ella stessa che lo determinasse sopra la BC, condottavi per una <lb/>certa necessit&agrave; di legge: a ricercar la qual legge, essendo ora rivolti gli studi <lb/>del Matematico, dobbiam dire come e quale ei la trovasse. </s></p><p type="main">

<s>L'avevano nell'ardua via preceduto Dinostrato e Nicomede, la quadra&shy;<lb/>trice famosa proposta dai quali porse al Nostro occasione di formulare, e di <lb/>dimostrare matematicamente le leggi dei moti uniformi. </s>

<s>Essendo una di co&shy;<lb/>teste leggi che, dove i tempi sono uguali, le velocit&agrave; stanno come gli spazi, <lb/><figure id="id.020.01.2777.2.jpg" xlink:href="020/01/2777/2.jpg"/></s></p><p type="caption">

<s>Figura 271.<lb/>ebbe, assai prima di Pappo, ad accorgersi che <lb/>nel meccanismo della Quadratrice, inventato ap&shy;<lb/>posta per uso della Ciclometria, quel che s'an&shy;<lb/>dava cercando gi&agrave; supponevasi noto. </s>

<s>Giov&ograve; nono&shy;<lb/>stante ad Archimede l'invenzione de'due Geome&shy;<lb/>tri, che gli fece rivolgere la mente sopra le curve <lb/>descritte dalla mistion di due moti. </s>

<s>Parve a tutti <lb/>fra coteste curve sopra ogni altra bellissima quella, <lb/>che a testimonianza di Pappo (Collect. </s>

<s>mathem. </s>

<s><lb/>cit., pag. </s>

<s>82) aveva gi&agrave; Conone Hamio immagi&shy;<lb/>nato descriversi da un punto, il quale, mentre, a <lb/>mover dal centro, passa equabilmente tutto intero <lb/>il raggio, nel medesimo tempo compia intorno a <lb/>esso centro il suo giro. </s></p><p type="main">

<s>Suppongasi, diceva Archimede, che sia in B <lb/>(fig. </s>

<s>271) il termine del moto composto, e che <lb/>di l&igrave; in poi sia il punto mobile lasciato in libert&agrave;: avverr&agrave; di lui quel che <lb/>avviene del sasso, nell'atto di sciogliersi dai legami della fionda, o del fango <pb xlink:href="020/01/2778.jpg" pagenum="403"/>schizzato dal carro, nel veloce rivolgersi della ruota: avverr&agrave; cio&egrave; che i detti <lb/>mobili proseguiranno col preconcetto impeto il loro viaggio in linea retta tan&shy;<lb/>gente il punto, dove si separarono dalla curva. </s>

<s>Era appunto questa tangente <lb/>la linea, che Archimede cercava, perch&egrave;, resultando per essa il moto unico <lb/>composto dei due, uno proporzionale alla lunghezza del raggio, e l'altro pro&shy;<lb/>porzionale alla circonferenza; tirata al raggio AB, o al suo uguale BC, perpen&shy;<lb/>dicolare una linea indefinita, basta condur da B una tangente al circolo, o <lb/>all'elice, perch&egrave; ella intersechi sopra quella linea lasciata indefinita una lun&shy;<lb/>ghezza precisamente uguale alla stessa circonferenza. </s>

<s>Erano dall'altra parte <lb/>ad Archimede noti i principii, per giunger direttamente a una tal conclusione, <lb/>avendo Aristotile insegnato, anzi riconosciuto come cosa per s&egrave; man&igrave;festa, <lb/><emph type="italics"/>quod id, quod secundum diametrum duobus fertur lationibus, necessario <lb/>secundum laterum proportionem fertur:<emph.end type="italics"/> onde il punto, mosso dianzi con <lb/>impeto proporzionale al raggio BC, e alla circonferenza rettificata CD, che sono <lb/>i lati del triangolo o del mezzo rettangolo; ora ch'egli &egrave; libero sar&agrave; neces&shy;<lb/>sariamente trasportato secondo il diametro BD. </s></p><p type="main">

<s>La nuova bellissima propriet&agrave; cos&igrave; scoperta s'annunziava nella XVIII pro&shy;<lb/>posizione del libro delle Spirali, ma chi legge ivi il modo com'&egrave; dimostrata <lb/>direbbe che qualche malevolo abbia sostituita alla vera quest'altra dimostra&shy;<lb/>zione, andante per vie oblique e intralciate, quasi per trarre studiosamente <lb/>in agguato l'ingenuo lettore. </s>

<s>E avvenne infatti cos&igrave;, perch&egrave; i commentatori <lb/>e gl'interpetri non riuscirono a indovinare qual si potess'essere la mente <lb/>dell'Autore. </s>

<s>Alcuni fra costoro, come il Rivault in Francia, e il nostro <lb/>Nardi, crederono che la detta proposizione XVIII fosse ordinata alla quadra&shy;<lb/>tura del circolo, non per concluderla direttamente, ma per mostrare che <lb/>ell'era possibile. </s>

<s>L'inganno sarebbesi potuto fin d'allora sospettar facilmente, <lb/>perch&egrave; da nessuna parte del libro delle Spirali trasparisce che tal si fosse <lb/>l'intenzion dell'Autore: ma si rende ora manifesto dall'investigata storia <lb/>dell'invenzione, la quale, bench&egrave; avvenisse propriamente in grazia del cir&shy;<lb/>colo, riconosciuta per lui inutile ancella, fu costituita in dignit&agrave; propria, indi&shy;<lb/>pendente e signora. </s>

<s>Rimase in ogni modo, per tanti secoli infino al Torri&shy;<lb/>celli, una tale notizia occulta, come occulta rimane tuttavia la ragione, perch&egrave; <lb/>Archimede, alle facili vie dirette, preferisse le oblique. </s></p><p type="main">

<s>Il Nardi fa in proposito un'osservazione importante, dicendo, in una <lb/>delle sue <emph type="italics"/>Ricercate geometriche,<emph.end type="italics"/> che, se le dimostrazioni indirette o all'as&shy;<lb/>surdo possono nelle menti generare certezza, non valgono nulladimeno a dare <lb/>alle verit&agrave; dimostrate evidenza. </s>

<s>&ldquo; E per&ograve;, soggiunge, io me ne asterrei sem&shy;<lb/>pre, quando potessi per altra via arrivare al proprio fine. </s>

<s>Imperocch&egrave;, pochi <lb/>penetrando la forza di tali dimostrazioni, dubitasi talvolta del loro fondamento. </s>

<s><lb/>Archimede con tutto ci&ograve; non solo non s'astenne, ma incredibilmente am&ograve; tal <lb/>maniera di dimostrare. </s>

<s>Non fu gi&agrave; il primo a servirsene, poich&egrave; dal XII degli <lb/>Elementi l'apprese, dove materie simili a quelle ch'egli tratta si trattano <lb/>nella stessa guisa, sicch&egrave; il contrario di quello che scrisse scriver doveva Luca <lb/>Valerio, mentre diverso dallo stile di Euclide giudic&ograve; quello di Archimede. <pb xlink:href="020/01/2779.jpg" pagenum="404"/>Piacque ad Archimede tal metodo, non tanto perch&egrave; in pronto non avesse <lb/>forse sempre il diretto, e pur volesse far uniforme delle sue dimostrazioni il <lb/>metodo; quanto per pi&ugrave; mirabili far le sue proposte apparire, il che non cos&igrave; <lb/>conseguito avrebbe con l'altro. </s>

<s>&rdquo; </s></p><p type="main">

<s>Non tutti forse di questo discorso resteranno sodisfatti, ma comunque <lb/>sia &egrave; tempo di venire al proposito nostro, ch'era quello di narrar come fosse <lb/>il Torricelli il primo a scoprire che, procedendo per la via de'moti compo&shy;<lb/>sti, s'incontr&ograve; Archimede in quell'ammirabile propriet&agrave; delle Spirali. </s>

<s>Qual <lb/>si fosse l'occasione della scoperta &egrave; dal Torricelli stesso detto in una lettera <lb/>a Galileo, scritta da Roma il d&igrave; 29 Giugno 1641. &ldquo; Questi giorni passati, <lb/>leggendo un manoscritto d'un amico virtuoso, notai uno sforzo ch'egli fa, <lb/>per trovar l'origine della proposizione XVIII della Spirale di Archimede. </s>

<s>Mi <lb/>parve che io ne cavassi poco frutto, onde ripensandovi dopo mi venne so&shy;<lb/>spetto che quella dottrina pendesse dalla Scienza del moto, e in particolare <lb/>da una proposizione di V. S. E., posta nel principio <emph type="italics"/>Dei proietti,<emph.end type="italics"/> la quale <lb/>facilmente le sovverr&agrave; nelle sue tenebre luminose, per essere un semplicis&shy;<lb/>simo triangolo rettangolo, e tratta di questo: che se un mobile camminer&agrave; <lb/>di due moti ecc. </s>

<s>il momento della velocit&agrave; sar&agrave; in potenza uguale a quelli <lb/>due &rdquo; (Alb. </s>

<s>X, 423, 24). E con queste parole accompagna al Maestro il Tor&shy;<lb/>riselli <emph type="italics"/>un suo discorsetto,<emph.end type="italics"/> in cui veniva applicando il detto teorema dei Pro&shy;<lb/>ietti a dimostrar la proposizione, ch'&egrave; in ordine la XVIII dell'antico libro <lb/>delle Spirali, e la prima di questo nuovo, formulata cos&igrave; nello stesso modo <lb/>archimedeo: </s></p><p type="main">

<s>&ldquo; PROPOSITIO I. &mdash; <emph type="italics"/>Si spiralem, ex prima circumvolutione ortam, recta <lb/>linea tetigerit in termino Spirae, a puncto vero, quod est in principio <lb/>spirae, quaedam ducatur ad angulos rectos ei, quae est principium revo&shy;<lb/>lutionis; ducta incidet in tangentem et ipsius, quae pars media erit inter <lb/>tangentem et principium spirae, aequalis erit periferiae primi circuli &rdquo;<emph.end type="italics"/><lb/>(Opera cit., pag. </s>

<s>377). </s></p><p type="main">

<s>&ldquo; Domandiamo che se un mobile sar&agrave; trasportato con impeto per alcuna <lb/>linea curva, liberato ch'egli sia dal legame, che lo necessitava a camminar <lb/>per la curva, seguiti il suo moto per linea retta, non avendo egli nuova oc&shy;<lb/>casione di piegare il suo viaggio da alcuna parte. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Domandiamo ancora che tal retta sia tangente della linea curva, in <lb/>quel punto d'essa, nel quale sar&agrave; stato liberato il mobile dalla precedente <lb/>curvit&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Fu la verit&agrave; di questa domanda provata gi&agrave; con acuti discorsi dal <lb/>signor Galileo, in altre sue opere. </s>

<s>Noi solamente l'esemplificheremo cos&igrave;: <lb/>Intendasi in un piano orizontale incavato un canalino, e sia di pianta cir&shy;<lb/>colare, o parabolica o spirale. </s>

<s>Se una palla di metallo perfettamente liscia <lb/>sar&agrave; da qualche impulso spinta nel canaletto, ella trascorrer&agrave; in esso, ed obbe&shy;<lb/>dir&agrave; necessariamente alla piegatura degli argini suoi, sin tanto che durer&agrave; <lb/>l'incassamento di essi. </s>

<s>Ma subito finito il canale, mentre la palla resti li&shy;<lb/>bera sopra il piano orizontale, dimenticata della strada precedente, seguiter&agrave; <pb xlink:href="020/01/2780.jpg" pagenum="405"/>con il suo impeto a correre, non pi&ugrave; per circolo o per elice, ma s&igrave; bene per <lb/>linea retta. </s>

<s>Sar&agrave; poi per appunto tal linea retta tangente alla curva del ca&shy;<lb/>naletto in quel punto, dove il mobile si sar&agrave; liberato dalla sua piegatura. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Definizione: <emph type="italics"/>Si recta linea in plano sit ducta, et, quiescente altero <lb/>eius termino, aequali velocitate circumferatur, donec restituatur in eum <lb/>locum, unde moveri coeperat, et simul cum linea circumlata punctum fe&shy;<lb/>ratur aequali velocitate ipsum sibi ipsi, et per se secundum dictam lineam <lb/>latum, incipiens a termino quiescente; punctum hoc describit in plano <lb/>lineam, quam Spiralem, sive Helicem vocamus &rdquo;<emph.end type="italics"/> (Archim. </s>

<s>ad propos. </s>

<s>XII <lb/>De lineis spiralibus). </s></p><p type="main">

<s>&ldquo; Stante questo, io dico che quel punto mobile, il quale descrive l'Elice, <lb/>aver&agrave; nel fine della prima revoluzione un momento tale d'impeto, che, se <lb/>seguitasse a camminare di moto equabile con quello, trascorrerebbe, in al&shy;<lb/>trettanto tempo quanto ne ha speso nella prima conversione, due spazi, uno <lb/>per&ograve; progressivo e l'altro laterale, ed il progressivo sarebbe uguale al semi&shy;<lb/>diametro del circolo della prima revoluzione, l'altro, cio&egrave; il laterale, sarebbe <lb/>uguale alla periferia dello stesso circolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La prova di questo sar&agrave; facile, se noi separeremo con l'astrazione i <lb/>due momenti d'impeto l'uno dall'altro. </s>

<s>Immaginiamoci dunque che nel&shy;<lb/>l'estremo della prima circolazione il punto mobile seguiti a camminare pro&shy;<lb/>gressivamente per il semidiametro, slongato fuori del circolo, ma che intanto <lb/>il semidiametro medesimo stia fermo. </s>

<s>Non &egrave; dubbio che, in altrettanto tempo <lb/>quanto il punto mobile aver&agrave; speso nella prima conversione, camminer&agrave; fuori <lb/>del circolo altrettanto spazio progressivo quanto ne aver&agrave; camminato nella <lb/>prima conversione, cio&egrave; precisamente un semidiametro del primo circolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Astragghiamo ora al contrario, ed immaginiamoci che, nella medesima <lb/>estremit&agrave; della prima conversione, il punto mobile si fermi nel semidiame&shy;<lb/>tro, e resti senza alcun moto progressivo, ma per&ograve; che il semidiametro se&shy;<lb/>guiti il suo moto conversivo. </s>

<s>&Egrave; chiaro che il punto mobile camminer&agrave; ora <lb/>per la periferia del primo circolo, e la scorrer&agrave; tutta precisamente in altret&shy;<lb/>tanto tempo, quanto egli ne aveva speso nella prima conversione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Parmi abbastanza provato che il punto mobile di Archimede, nella <lb/>estremit&agrave; della prima revoluzione, abbia un tale momento composto di due <lb/>momenti, ovvero impeti, cio&egrave; uno progressivo e dilungativo dal centro, e <lb/>l'altro laterale, sicch&egrave; questi due impeti abbiano una particolar proporzione <lb/>fra di loro, come quella del semidiametro alla periferia: cio&egrave; tale, che nello <lb/>stesso tempo, nel quale il punto mobile si avanzer&agrave; di moto progressivo, <lb/>quanto &egrave; lungo un semidiametro; in quello stesso tempo per l'appunto si <lb/>spinger&agrave; lateralmente per tanto spazio, quanto &egrave; lunga la periferia dello stesso <lb/>circolo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si proponga ora la XVIII delle Spirali. </s>

<s>Immaginiamoci che il semi&shy;<lb/>diametro AB (nella precedente figura 271), nel quale &egrave; il principio e fine <lb/>dell'Elice, sia prodotto e prolungato fuori del circolo altrettanto, quanto &egrave; <lb/>esso semidiametro, sicch&egrave; la BC sia uguale alla AB, e per l'estremo punto <pb xlink:href="020/01/2781.jpg" pagenum="406"/>della prolungata tirisi una linea CD ad angolo retto con essa, da quella <lb/>parte, verso dove camminano l'ultime parti della Spirale. </s>

<s>Supponiamo ora <lb/>che il punto mobile di Archimede, subito giunto all'estremit&agrave; della prima <lb/>rivoluzione in B, resti libero dal semidiametro suo deferente, e dalla Spirale <lb/>fin l&agrave; descritta, e seguiti a camminare con tutto l'acquistato momento delli <lb/>suoi impeti: conforme alle petizioni premesse, questo punto continuer&agrave; la <lb/>sua lazione per una linea retta, e questa linea retta sar&agrave; tangente alla Spi&shy;<lb/>rale. </s>

<s>Dico che questa tangente concorrer&agrave; con la perpendicolare da noi ti&shy;<lb/>rata CD, e che la porzione CD di detta perpendicolare, intercetta tra il con&shy;<lb/>corso della tangente e il semidiametro prolungato, sar&agrave; uguale alla periferia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quanto al primo, che la retta tangente prolungata concorre con CD, <lb/>&egrave; manifesto: poich&egrave; se non concorresse, essendo retta, averebbe dunque il <lb/>punto mobile perso l'impeto progressivo, ch'egli in B aveva verso la linea <lb/>CD, contro supposizione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Concorra dunque per esempio in D: prover&ograve; che la porzione tagliata <lb/>CD sia uguale alla periferia del primo circolo. </s>

<s>Poich&egrave;, se fosse disuguale, <lb/>averebbe il punto mobile compito <emph type="italics"/>eodem tempore<emph.end type="italics"/> per la diagonale BD tanto <lb/>di spazio progressivo, quanto &egrave; il semidiametro BC, ma non gi&agrave; tanto di la&shy;<lb/>terale, quanto la periferia. </s>

<s>E per&ograve; conseguentemente, quando il punto mo&shy;<lb/>bile rest&ograve; libero in B, non averebbe avuto in s&egrave; quel momento, che da noi <lb/>si dimostr&ograve; avere, cio&egrave; di correre <emph type="italics"/>eodem tempore<emph.end type="italics"/> due spazi, uno progres&shy;<lb/>sivo quanto il semidiametro, e l'altro laterale quanto la periferia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che poi il triangolo BCD sia lo stesso che quello di Archimede, seb&shy;<lb/>bene contrariamente posto, non ci &egrave; difficolt&agrave;. </s>

<s>Nello stesso modo si dimostra <lb/>la verit&agrave; delle due seguenti proposizioni, nel maraviglioso libro delle Spirali. </s>

<s><lb/>A noi baster&agrave; di avere accennato per qual via Archimede possa essere ve&shy;<lb/>nuto in cognizione d'una verit&agrave; tanto astrusa, e per cos&igrave; dire inopinabile, <lb/>come la suddetta. </s>

<s>Credo certo che l'Autore a bello studio volesse occultare <lb/>ed inviluppare la dimostrazione del teorema a segno tale, che non si potesse <lb/>conoscere da che origine glie n'era derivata la cognizione. </s>

<s>Per&ograve; nel corso <lb/>di tanti secoli non fu mai capita evidentemente questa passione della Spi&shy;<lb/>rale, non per altro, che per la mancanza della dottrina <emph type="italics"/>De motu,<emph.end type="italics"/> nota be&shy;<lb/>nissimo fino ne'suoi tempi all'Archimede antico, ma pubblicata solamente <lb/>ne'nostri dal Moderno. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che i mezzi, dei quali l'Autore si serve nella dimostrazione, siano <lb/>per cos&igrave; dire improprii, e che altrettanto appropriati siano quelli, che pro&shy;<lb/>cederanno con la dottrina del moto, si pu&ograve; argomentare dalla definizione <lb/>stessa, la quale altro non contiene che l'immaginazione di due movimenti, <lb/>dalla mistione dei quali resulta poi quel viaggio spirale. </s>

<s>Perci&ograve; chi con le <lb/>cose poste nella definizione, cio&egrave; con la scienza del moto, cercasse di pro&shy;<lb/>vare anco i teoremi dipendenti da quella, mi pare ch'egli si servirebbe dei <lb/>mezzi propri per arrivare alle conclusioni, e che per&ograve; produrrebbe scienza <lb/>evidente, o come dicono, <emph type="italics"/>a priori.<emph.end type="italics"/> Al contrario, dimostrandosi indirettamente <lb/>tali propriet&agrave;, con mezzi alieni dalla definizione, oltre l'oscurit&agrave; e la lun-<pb xlink:href="020/01/2782.jpg" pagenum="407"/>ghezza, nella quale s'incorrer&agrave;, si produrr&agrave; al lettore una scienza in certo <lb/>modo accidentale, di tal sorta che egli conoscer&agrave; bene di non poter contra&shy;<lb/>dire a quella proposta, ma non intender&agrave; gi&agrave; come, e per qual causa, quella <lb/>conclusione sia necessariamente vera &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXIV, fol. </s>

<s>201-5). </s></p><p type="main">

<s>Stato con grande attenzione ad ascoltare questo discorso, dett&ograve; Galileo <lb/>per risposta essergli sembrato maraviglioso il concetto, sovvenuto al Torri&shy;<lb/>celli per dimostrare, con tanta facilit&agrave; e leggiadria, quello, che Archimede, <lb/>con strada tanto inospite e travagliosa, investig&ograve; nelle sue Spirali: &ldquo; strada, <lb/>soggiungeva, la quale a me parve sempre tanto astrusa e recondita, che, dove <lb/>con lo studio per avventura di cento anni non mi sarei disperato del tutto <lb/>di trovare l'altre conclusioni del medesimo Autore, di questa sola non mi <lb/>sarei promessa l'invenzione in molti anni, n&egrave; in perpetuo. </s>

<s>Ora giudichi V. S. <lb/>quale mi sia riuscito il suo gentilissimo trovato &rdquo; (Alb. </s>

<s>VII, 366). Delle quali <lb/>parole di lode, e della lettera in cui furono scritte, tanto si compiacque il <lb/>Torricelli, che, nello scolio alla sua XVIII del primo libro <emph type="italics"/>De motu,<emph.end type="italics"/> ne volle <lb/>fare solenne commemorazione. (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>121). </s></p><p type="main">

<s>Notabilissima cosa &egrave; che in quello stesso Scolio, sottilmente esaminando, <lb/>si trova una confutazione di quelle dottrine galileiane <emph type="italics"/>De motu,<emph.end type="italics"/> dimostrate <lb/>nel Dialogo dei proietti, che il Torricelli diceva essergli servite di chiave per <lb/>aprire il segreto archimedeo delle Spirali. </s>

<s>Il teorema infatti del Maestro inse&shy;<lb/>gnava che il moto per l'ipotenusa era uguale in potenza alla somma dei <lb/>moti per i cateti, e il Discepolo, nello Scolio citato, par che voglia correg&shy;<lb/><figure id="id.020.01.2782.1.jpg" xlink:href="020/01/2782/1.jpg"/></s></p><p type="caption">

<s>Figura 272.<lb/>gere l'errore, dicendo che, non uguali in potenza, ma <lb/>proporzionali ai due lati BD, DC (fig. </s>

<s>272) di un paral&shy;<lb/>lelogrammo son le due forze resultanti nell'unica dire&shy;<lb/>zione della diagonale. </s>

<s>Ma intorno a ci&ograve;, dovendoci tratte&shy;<lb/>nere altrove, trapasseremo per ora a dire come, applicando <lb/>esso Torricelli i principii dimostrati in quel medesimo Sco&shy;<lb/>lio, risolvesse varii problemi di Meccanica nuova, incominciando da quello <lb/>delle tangenti. </s></p><p type="main">

<s>L'invenzione di condurre per via meccanica le tangenti alle curve occorse <lb/><figure id="id.020.01.2782.2.jpg" xlink:href="020/01/2782/2.jpg"/></s></p><p type="caption">

<s>Figura 273.<lb/>al Nostro, come anche al Roberval in Francia, a pro&shy;<lb/>posito della Spirale, d'onde venne facilmente il pensiero <lb/>di farne alla Parabola de'proietti l'applicazione imme&shy;<lb/>diata. </s>

<s>Sia AB (fig. </s>

<s>273) la curva descritta, al punto B <lb/>della quale si vuol condurre la tangente. </s>

<s>Sar&agrave; tale, per <lb/>le supposizioni premesse alla precedente proposizione, la <lb/>resultante unica de'due impeti, dai quali &egrave; sollecitato <lb/>il mobile in B, uno progressivo secondo BC, e l'altro <lb/>discensivo secondo AC, ond'&egrave; che torner&agrave; allora sciolto <lb/>il problema, quando sian ritrovate fra quegli stessi due <lb/>impeti le proporzioni. </s>

<s>Dovendo in ogni modo essere <lb/>ambedue proporzionali agli spazi passati, se il progressivo &egrave; rappresentato <lb/>da BC, il discensivo sar&agrave;, per il primo teorema dimostrato nel terzo dia-<pb xlink:href="020/01/2783.jpg" pagenum="408"/>logo di Galileo, rappresentato dal doppio di AC. </s>

<s>Si prolunghi perci&ograve; la CB <lb/>per altrettanto spazio in D, e si conduca BE, che sia alla AC doppia e pa&shy;<lb/>rallela: compiuto il parallelogrammo DE, e tirata la diagonale BF, se si im&shy;<lb/>magini essere il mobile in B abbandonato a un tratto dall'impeto violento, <lb/>proseguir&agrave; naturalmente nella direzione BF il suo viaggio, tangente in B la <lb/>curva, da cui s'&egrave; sciolto. </s>

<s>&Egrave; dunque la BF o la sua uguale BG la linea cer&shy;<lb/>cata, la quale poteva descriversi con pi&ugrave; facile costruzione, duplicando in G <lb/>la lunghezza AC dell'asse della parabola, e congiungendo i punti G, B, come <lb/>avrebbe insegnato di fare la Geometria. </s></p><p type="main">

<s>Cos&igrave; &egrave; sciolto dal Torricelli il problema, quando l'incremento della ve&shy;<lb/>locit&agrave; nel moto discensivo &egrave; lineare, e la parabola descritta &egrave; perci&ograve; la na&shy;<lb/>turale, ossia la quadratica. </s>

<s>Che se il detto incremento invece &egrave; quadratico, <lb/>cubico, biquadratico, ecc., e le parabole, per quel che fu dimostrato nella <lb/>XII proposizione della prima parte di questo capitolo, son cubiche, biquadra&shy;<lb/>tiche, cuboquadratiche, ecc., immaginando che sia il proietto attratto al cen&shy;<lb/>tro con qualunque fra gli assegnati gradi di accelerazione, prosegue il Tor&shy;<lb/>ricelli ad applicare il medesimo metodo per condur le tangenti anco a queste <lb/>curve paraboliche, che s'ingradano via via. </s>

<s>Qualunque poi sia questo grado, <lb/>l'impeto progressivo &egrave; sempre rappresentato da un'ordinata simile alla BC, <lb/>nella precedente figura, ond'&egrave; che tutto si riduce a sapere ne'vari casi qual <lb/>sia la proporzione, che ha la BE verso l'AC, perch&egrave; cos&igrave; anche sapremo <lb/>quali sono i lati del parallelogrammo, dal diametro del quale &egrave; designata la <lb/>tangente richiesta. </s>

<s>Per dimostrar dunque con qual varia proporzione crescon <lb/>gli spazi, passati equabilmente nel medesimo tempo che si passa lo spazio <lb/>AC, co'vari gradi di accelerazion discensiva; si premette dal Torricelli per <lb/>lemma un teorema, che, fra quelli mandati in Francia, &egrave; sotto il numero LI <lb/>formulato in questa maniera: </s></p><p type="main">

<s>&ldquo; Se sar&agrave; il parallelogrammo ABCD (fig. </s>

<s>274), col suo triangolo ACD, <lb/>tutte le infinite linee del parallelogrammo, a tutte le infinite linee del trian&shy;<lb/><figure id="id.020.01.2783.1.jpg" xlink:href="020/01/2783/1.jpg"/></s></p><p type="caption">

<s>Figura 274.<lb/>golo, sono duple: ma tutti i quadranti sono tripli di <lb/>tutti i quadrati; tutti i cubi sono quadrupli di tutti i <lb/>cubi, tutti i quadratoquadrati sono quintupli di tutti <lb/>i quadratoquadrati, ecc., in infinitum in tutte le infinite <lb/>dignit&agrave; dell'algebra &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXIII, <lb/>fol. </s>

<s>39). I matematici moderni formulerebbero cos&igrave;, <lb/>nel loro proprio linguaggio, il medesimo teorema: <emph type="italics"/>La <lb/>somma di tutte le potenze dell'ordine<emph.end type="italics"/> n <emph type="italics"/>di una quan&shy;<lb/>tit&agrave;, continuamente crescente, &egrave; alla somma di altrettante potenze simili <lb/>della quantit&agrave; massima nella proporzione medesima di<emph.end type="italics"/> 1 <emph type="italics"/>ad<emph.end type="italics"/> n+1. </s></p><p type="main">

<s>Il Frisi, nelle Operette scelte dal Silvestri di Milano (1825, pag. </s>

<s>239), <lb/>attribuisce questo teorema al Cavalieri, di cui fa l'elogio: ed &egrave; un fatto che <lb/>nella quarta Esercitazione geometrica le proposizioni XIX, XX e XXI dimo&shy;<lb/>strano verificarsi la cosa annunziata, particolarmente per le potenze lineari, <lb/>quadratiche e cubiche. </s>

<s>Nella XXII poi si propone similmente il Cavalieri di <pb xlink:href="020/01/2784.jpg" pagenum="409"/>dimostrare che &ldquo; Omnia quadratoquadrata parallelogrammi quintupla sunt <lb/>omnium quadratoquadratorum trianguli, per diametrum constituti &rdquo; (Bono&shy;<lb/>niae 1647, pag. </s>

<s>274), ma la via da lui presa non lo porta pi&ugrave; oltre, ond'&egrave; <lb/>vera l'osservazione storica dopo le parole da noi sopra trascritte, cos&igrave; dallo <lb/>stesso Torricelli soggiunta: </s></p><p type="main">

<s>&ldquo; Questo teorema fu primieramente inventato e proposto da fra Bona&shy;<lb/>ventura Cavalieri, ma per&ograve; da esso non fu ritrovata la dimostrazione uni&shy;<lb/>versale, avendo egli presa una strada che, per quanto intendo, cammina solo <lb/>infino alli cubi, ovvero alli quadratoquadrati. </s>

<s>Il primo, che abbia dimostrato <lb/>il teorema universalmente in tutte le infinite dignit&agrave; dell'algebra, &egrave; stato <lb/>mons&ugrave; Beugrand francese, che ora &egrave; morto. </s>

<s>La sua dimostrazione per&ograve; cam&shy;<lb/>mina per via di algebra. </s>

<s>Dopo questo, per quel ch'io sappia, nessuno ha <lb/>dimostrato il teorema, fuor che me, e la mia dimostrazione procede senz'al&shy;<lb/>gebra, per sola Geometria, e non solo &egrave; universalissima, come quella di mons&ugrave; <lb/>Beugrand, ma &egrave; infinite volte pi&ugrave; universale &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXII, <lb/>fol. </s>

<s>40). </s></p><p type="main">

<s>Essendo alieno dal presente nostro proposito, non ci tratterremo qui a <lb/>dire in qual modo si dimostrasse dal Torricelli, per sola Geometria, il Teo&shy;<lb/>rema, contentandoci pi&ugrave; qu&agrave; di riferire, per i quadrati particolarmente, un <lb/>esempio. </s>

<s>Tenendo perci&ograve; il detto Teorema, quale fu proposto ai Francesi, per <lb/>dimostrato, &egrave; da vedere come servisse di lemma a ritrovare quanto della AC, <lb/>rappresentata nella figura 273 qui poco addictro, debba essere in qualunque <lb/>parabola molteplice la CG, che s'ha da prendere per la misura dell'impeto <lb/>verticale, costruendosi sopr'essa, e sopra un'ordinata simile alla BC, il pa&shy;<lb/>rallelogrammo delle forze. </s>

<s>Il Torricelli conclude essere la richiesta moltipli&shy;<lb/>plicit&agrave; uguale al grado della parabola, con un discorso che brevemente ri&shy;<lb/>ducesi a questo: </s></p><p type="main">

<s>Se le velocit&agrave; crescono come i semplici tempi, lo spazio, che equabil&shy;<lb/>mente &egrave; passato dal mobile con l'ultimo grado dell'accelerazione, &egrave; doppio, <lb/>per il teorema primo di Galileo, di quello stesso passato acceleratamente nel <lb/>medesimo tempo, ossia sta come le infinite linee del parallelogrammo ulti&shy;<lb/>mamente disegnato, alle infinite linee del triangolo inscritto. </s>

<s>Ma se le velo&shy;<lb/>cit&agrave; crescono come i quadrati dei tempi, lo spazio allo spazio sta come i <lb/>quadrati ai quadrati, ossia, per il passato lemma, come tre a uno: se le ve&shy;<lb/>locit&agrave; crescono come i cubi, lo spazio sta allo spazio, come i cubi ai cubi, <lb/>ossia come quattro a uno: e in generale, se le velocit&agrave; crescono come la po&shy;<lb/>tenza <emph type="italics"/>n<emph.end type="italics"/> dei tempi, lo spazio allo spazio star&agrave; come <emph type="italics"/>n+1,<emph.end type="italics"/> ossia, per le <lb/>cose dimostrate, come l'esponente della parabola ad uno. </s>

<s>Di qui la regola <lb/>torricelliana <emph type="italics"/>Pro tangentibus infinitarum parabolarum,<emph.end type="italics"/> formulata nell'ap&shy;<lb/>presso </s></p><p type="main">

<s>&ldquo; PROPOSITIO II. &mdash; <emph type="italics"/>Esto in parabola quaelibet AB<emph.end type="italics"/> (nella passata <lb/>figura 273), <emph type="italics"/>cuius diameter AC, applicata CB: fiat ut esponens ad uni&shy;<lb/>tatem, ita CG ad AC. </s>

<s>Dico ductam BG esse tangentem. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nam, quaecumque sit parabola, velocitas puncti mobilis crescit secun-<pb xlink:href="020/01/2785.jpg" pagenum="410"/>dum rationem dignitatis parabolae: hoc est, in quadratica, velocitas crescit <lb/>in ratione duplicata temporum; in cubica vero crescit in triplicata etc. </s>

<s>Ergo, <lb/>per iam dicta, si mobile B, dum est in B, per tangentem procedat, et re&shy;<lb/>currat motu aequabili, debet, quo tempore recurrit BC, hoc est tempore ca&shy;<lb/>sus, duplam, triplam, quadruplam, ipsius AC recurrere, secundum rationem <lb/>dignitatis parabolae. </s>

<s>Ergo tangens pertinet ad G &rdquo; (MSS. </s>

<s>Gal Disc., T. XXXI, <lb/>fol. </s>

<s>342). </s></p><p type="main">

<s>Il processo di questa dimostrazione si trova ordinatamente disposto nel <lb/>manoscritto esemplificato nelle tangenti la parabola cubica, per dimostrar la <lb/>via da seguirsi in qualunque altro caso proposto. </s>

<s>Mostreremo ora qual sia <lb/>quel processo nelle sue varie parti, cominciando dal seguente lemma, pre&shy;<lb/>parato apposta dal Torricelli per dimostrar che gl'infiniti quadrati delle linee, <lb/>che compongono il parallelogrammo, son tripli degli infiniti quadrati, fatti <lb/>sulle linee del triangolo inscritto. </s></p><p type="main">

<s>Abbiasi un parallelepipedo, quale si rappresenta nella figura 275, e sopra <lb/>la medesima base DL si inscriva una piramide appuntata in B, il lato AB <lb/>della quale far&agrave; nel parallelogrammo CD da diametro. </s>

<s>Siano ambedue i so&shy;<lb/><figure id="id.020.01.2785.1.jpg" xlink:href="020/01/2785/1.jpg"/></s></p><p type="caption">

<s>Figura 275.<lb/>lidi, a qualsivoglia punto della loro altezza, <lb/>attraversati da un medesimo piano, che faccia <lb/>nel parallelepipedo la sezione FH, e la FI <lb/>nella piramide. </s>

<s>&Egrave; facile dimostrare che il <lb/>quadrato della linea EF, la quale &egrave; una delle <lb/>infinite del parallelogrammo CD, sta al qua&shy;<lb/>drato della GF, una delle infinite linee com&shy;<lb/>ponenti il triangolo ADB, come la sezione FH <lb/>sta alla sezione FI. </s>

<s>Chiamate infatti S, S&prime; le due <lb/>dette sezioni, sar&agrave; S:S&prime;=EF.EH:GF.GI. <lb/>Ma, per la similitudine de'triangoli, abbiamo <lb/>AL:GI=AB:BG=AD:GF, e AL= <lb/>EH, AD=EF; dunque EH:GI=EF:GF, e perci&ograve; S:S&prime;=EF2:GF2, <lb/>come si doveva dimostrare. </s>

<s>Cos&igrave; poi sempre essendo, per qualunque sezione, <lb/>si potr&agrave; concluderne che gl'infiniti quadrati del parallelogrammo stanno agli <lb/>infiniti quadrati del triangolo, come gl'infiniti piani tutti uguali a FH, com&shy;<lb/>ponenti il parallelepipedo, stanno agl'infiniti piani simili ad FI, componenti <lb/>la Piramide, ossia come tre sta a uno. </s></p><p type="main">

<s>&ldquo; Posta la figura come qui (cos&igrave;, attraverso alle parole che trascriviamo, <lb/>come attraverso a interrotti globi metallici fa il Torricelli passar la folgore <lb/>del suo pensiero) dico che tutti i quadrati del parallelogrammo AB son tri&shy;<lb/>pli di tutti quelli del triangolo ADB. Perch&egrave;, tirata la EF a caso, dirai: Il <lb/>quadrato EF all'FG sta come il piano FH ad FI, et hoc semper, e gli an&shy;<lb/>tecedenti sono uguali sempre, dunque etc. </s>

<s>Come il parallelepipedo alla pi&shy;<lb/>ramide, cos&igrave; tutti i quadrati del parallelogrammo a tutti i quadrati del trian&shy;<lb/>golo, quod etc. </s>

<s>&rdquo; (ivi, T. XXXV, fol. </s>

<s>13). </s></p><p type="main">

<s>&ldquo; PROPOSITIO III. &mdash; <emph type="italics"/>Gravia descendunt ita ut temporibus aequalibus<emph.end type="italics"/><pb xlink:href="020/01/2786.jpg" pagenum="411"/><emph type="italics"/>aequaliter crescant velocitates, ut optime docet Galileus. </s>

<s>Supponamus iam <lb/>mobile aliquod descendere ita ut velocitates crescant ut quadrata tempo&shy;<lb/>rum. </s>

<s>Ex. </s>

<s>gr. </s>

<s>esto CD<emph.end type="italics"/> (nella passata figura 274), <emph type="italics"/>tempus descensionis, et sit <lb/>quadratum AD velocitas, quam habet mobile in fine descensionis. </s>

<s>Peracto <lb/>tempore CE, debebit eius velocitas esse ut quadratum EF, nam quadratum <lb/>AD et EF sunt ut quadrata temporum CD, CE. </s>

<s>Esto GH spatium peracto <lb/>tempore CD, quaeritur: si grave in fine descensionis convertatur horizon&shy;<lb/>taliter, cum impetu AD, quodnam spatium conficiet tempore aequali tem&shy;<lb/>pori descensus? </s>

<s>Dico triplum. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nam, quando mobile, tempore CD, adhibet tot tantasque velocitates, <lb/>quot quantaque sunt omnia quadrata trianguli ACD, peragit spatium GH. </s>

<s><lb/>Sed quando eodem tempore adhibet tot tantasque velocitates, quot quantasque <lb/>sunt omnia quadrata parallelogrammi BD, triplum spatium conficere debe&shy;<lb/>bit, nam, per praecedentem demonstrationem, quadrata quadratorum sunt tri&shy;<lb/>pla. </s>

<s>Idem dicas de reliquis algebrae dignitatibus &rdquo; (ibid., T. XXXI, fol. </s>

<s>341). </s></p><p type="main">

<s>&ldquo; PROPOSITIO IV. &mdash; <emph type="italics"/>Esto parabola quaelibet ex. </s>

<s>gr. </s>

<s>cubica AB<emph.end type="italics"/> (nella <lb/>figura 273), <emph type="italics"/>cuius ad punctum B quaero tangentem. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sumatur CG multiplex ipsius AC iuxta dignitatem parabolae; hoc est <lb/>in casu nostro tripla, et, iuncta GB, tangens erit. </s>

<s>Nam punctum mobile B, <lb/>quod parabolam describit, in loco B duos impetus habet, alterum horizonta&shy;<lb/>lem secundum AH, tangentem, alterum perpendicularem secundum diame&shy;<lb/>trum AC, quorum rationem inquiro hoc modo: Impetus horizontalis, tempore <lb/>casus, peragit spatium CB: impetus vero perpendicularis, per iam dicta, si <lb/>aequabilis conservetur, tempore casus, curreret triplum ipsius casus AC spa&shy;<lb/>tium. </s>

<s>Ergo motus, sive directio puncti B, quae componitur ex duobus velo&shy;<lb/>citatibus, quae sunt ut BC ad CG, erit iuxta lineam BG. </s>

<s>Propterea BG non <lb/>secat curvam, sed tangit. </s>

<s>Quae vero, brevitatis causa, exemplivificavimus in <lb/>cubica, dici posset de quacumque parabola &rdquo; (ibid., fol. </s>

<s>341). </s></p><p type="main">

<s><emph type="italics"/>Haec demonstratio peculiaris est pro parabola<emph.end type="italics"/> poteva qui ripetere il <lb/>Torricelli, com'aveva scritto nello Scolio alla XVIII proposizione del primo <lb/>libro <emph type="italics"/>De motu gravium<emph.end type="italics"/> (Op. </s>

<s>geom., P. I, pag. </s>

<s>121), dove, dopo la detta <lb/>osservazione, soggiunge ch'egli aveva altres&igrave; un metodo di condur le tan&shy;<lb/>genti universale per tutte le sezioni coniche, per la Spirale archimedea, e <lb/>per simili altre curve; fra le quali anche la Cicloide. </s>

<s>Riguardo alla Spirale <lb/>il metodo &egrave; stato esposto nella prima proposizione di questa terza parte: ri&shy;<lb/>guardo al circolo e all'iperbola, fra le sezioni coniche, nella IX, X e XI della <lb/>prima parte del presente capitolo, e tra poco ne vedremo fatta l'applicazione <lb/>alla Cicloide. </s>

<s>Ma perch&egrave; cos&igrave; fatte invenzioni matematiche del Torricelli com&shy;<lb/>pariscono ora, dopo due secoli e mezzo, nella nostra Storia, alla luce; e il <lb/>metodo del Roberval, infino dal 1668, era stato in Francia dal Bourdelois <lb/>fatto noto; invece di disputare a quale de'due Matematici si convenga il pri&shy;<lb/>mato, giova per ora osservare com'ambedue, partiti dai medesimi principii, <lb/>procedessero indipendenti per vie diverse, ma che pure s'incontrano spesso <lb/>spesso, come quelle che tendevano al medesimo fine. </s></p><pb xlink:href="020/01/2787.jpg" pagenum="412"/><p type="main">

<s>Il principio comune al Roberval e al Torricelli &egrave; il parallelogrammo <lb/>delle forze, proposto e dimostrato cos&igrave; nel sopra citato scolio <emph type="italics"/>De motu gra&shy;<lb/>vium,<emph.end type="italics"/> che il latino di lui sembra essere una traduzione del teorema primo <lb/><emph type="italics"/>Des mouvemens composez:<emph.end type="italics"/> &ldquo; Si un mobile est port&eacute; par deux divers mou&shy;<lb/>vemens, chacun droit et uniforme, le mouvement compos&eacute; de ces deux sera <lb/>un mouvement droit et uniforme diff&egrave;rent de chacun d'eux, mais toutefois <lb/>en mesme plan, en sorte que la ligne droite que d&eacute;crira le mobile sera le <lb/>diam&egrave;tre d'un parallelogramme, les costez duquel seront entre eux comme <lb/>les vitesses de ces deux mouvemens, et la vitesse du compos&eacute; sera &agrave; cha&shy;<lb/>cun des composans comme le diam&egrave;tre a chacun des costez &rdquo; (Roberval, <lb/>Ouvrages a la Haye, 1731). </s></p><p type="main">

<s>Cos&igrave; l'Accademico di Parigi, come quel di Firenze, considerando che le <lb/>curvit&agrave; delle linee geometriche risultano di due moti misti, si proposero di <lb/>sceverarli ne'due lati opposti di un parallelogrammo, per aver dalla diago&shy;<lb/>nale di lui la direzione delle tangenti. </s>

<s>Sono i detti moti per le curve in ge&shy;<lb/>nerale ambedue uniformi, cosicch&egrave; i punti mobili, che le descrivono nel me&shy;<lb/>desimo tempo, vanno con velocit&agrave; proporzionali agli spazi. </s>

<s>Ma nella parabola <lb/>in particolare, riguardando il punto mobile come un proietto, uno di que'moti <lb/>&egrave; accelerato, cosicch&egrave;, partecipando la linea alle propriet&agrave; della Meccanica <lb/>naturale, sembrava che ad esser trattata col metodo nuovo, dovesse esser la <lb/>prima. </s>

<s>Cos&igrave; fu veramente per il Torricelli, il quale anzi ne deriv&ograve; un metodo <lb/>generalissimo per le infinite parabole, da vincere di gran lunga il Roberval, <lb/>che, facendone anch'egli la prima applicazione alla parabola ordinaria, non <lb/>la consider&ograve; come descritta dalla Natura, ma dall'arte, a quel modo che nella <lb/>proposizione XXV del suo secondo libro insegnava il Mydorgio. </s></p><p type="main">

<s>Per le altre curve la differenza fra'due Autori consiste nella variet&agrave; degli <lb/>esempi, in cui il Francese ha il vantaggio, avendogli estesi a tutte le sezioni <lb/>coniche, alla coclea, alla spirale, alla cissoide, alla concoide, alla quadratrice, <lb/>alla parabola cartesiana: e consiste nella facilit&agrave;, nella quale insuperabile &egrave; <lb/>il Nostro, bench&egrave; sia in ambedue simile il processo dimostrativo, specialmente <lb/>trattandosi di curve della pi&ugrave; facile composizione, qual sarebbe la Cicloide, per <lb/>condurre le tangenti alla quale la regola del Torricelli, come ora vedremo, &egrave; <lb/>conclusa dal Roberval in queste parole: &ldquo; Pour trouver la tangente de la Rou&shy;<lb/>lette en un point donn&eacute;, je tire du dit point une touchante au cercle, qui pas&shy;<lb/><figure id="id.020.01.2787.1.jpg" xlink:href="020/01/2787/1.jpg"/></s></p><p type="caption">

<s>Figura 276.<lb/>seroit par le dit point, car chaque point <lb/>de cercle se meut selon la touchante de <lb/>ce cercle. </s>

<s>Je considere ensuite le mouve&shy;<lb/>ment, que nous avons donn&eacute; a nostre <lb/>point, emport&eacute; par le diam&eacute;tre marchant <lb/>parallelement a soy mesme. </s>

<s>Tirant du <lb/>mesme point la ligne de ce mouvement, si <lb/>je paracheve le parallelogramme, qui doit <lb/>toujours avoir les quatre costez &eacute;gaux, <lb/>lors que le chemin du point F (fig. </s>

<s>276) <pb xlink:href="020/01/2788.jpg" pagenum="413"/>par la circonf&eacute;rence est &eacute;gal au chemin du diam&eacute;tre FB par la ligne AF, et <lb/>si du mesme point je tire la diagonale, j'ay la touchante de la figure, qui a <lb/>e&ugrave; ces deux mouvemens pour sa composition, scavoir le circolaire et le di&shy;<lb/>rect &rdquo; (Ouvrages cit., pag. </s>

<s>211). </s></p><p type="main">

<s>La regola &egrave; nel <emph type="italics"/>Trait&eacute; des indivisibles<emph.end type="italics"/> cos&igrave; semplicemente descritta, per&shy;<lb/>ch&egrave; dipende dai principii gi&agrave; dimostrati nelle <emph type="italics"/>Observations sur la composi&shy;<lb/>tion des mouvemens:<emph.end type="italics"/> principii per applicare i quali al caso presente si <lb/>suppone questo facilissimo lemma: <emph type="italics"/>Se abbiasi un cerchio col diametro per&shy;<lb/>pendicalarmente eretto all'orizonte, tutte le corde, condotte dalla sommit&agrave; <lb/>di esso diametro a un punto della circonferenza, dividono nel mezzo l'an&shy;<lb/>golo fatto dalla tangente e dalla orizontale in quel punto.<emph.end type="italics"/> Sia IEL, nella <lb/>medesima figura, il cerchio come s'&egrave; detto, E il punto, da cui vengon ti&shy;<lb/>rate la orizontale EM, la tangente EN, e la corda EI: &egrave; manifesto che gli <lb/>angoli NEI, IEM hanno per misura ciascuno la met&agrave; dell'arco IE, o del suo <lb/>uguale, e che perci&ograve; l'angolo NEM &egrave; dalla IE diviso nel mezzo. </s></p><p type="main">

<s>Considerando ora il punto E moventesi nella Cicloide, le EN, EM se&shy;<lb/>gnano la direzione dei moti componenti, i quali sono fra loro uguali, avendo <lb/>il circolo nel progredire per la FA quel medesimo impeto, che nel rivolgersi <lb/>intorno al suo centro. </s>

<s>E di qui &egrave; che, presa EM uguale ad EN, e costruito <lb/>il parallelogrammo, la diagonale ED, diretta secondo EI, sar&agrave; la resultante <lb/>del moto, e la tangente richiesta nel dato punto. </s></p><p type="main">

<s>Il metodo meccanico fa esatto riscontro col geometrico, il quale dimo&shy;<lb/>stra che la tangente alla Cicloide nel punto E &egrave; parallela alla corda GH del <lb/>circolo genitore descritto intorno all'asse. <emph type="italics"/>Quae Cycloidem contingit recta <lb/>est correspondenti circuli genitoris circa Cycloidis axem positi chordae ad <lb/>verticem terminatae, parallela.<emph.end type="italics"/> Il teorema cos&igrave; proposto fu dimostrato, dopo <lb/>il Cartesio e il Fermat, dal Wallis, nella prima parte della XXII <emph type="italics"/>De centro <lb/>gravitatis<emph.end type="italics"/> (Mechanica, P. II, Londini 1670, pag. </s>

<s>424 e 23), ma il Viviani, <lb/>tuttavia giovanetto, aveva in Italia preceduto tutti costoro. </s>

<s>Fece di ci&ograve; so&shy;<lb/>lenne testimonianza il Torricelli, il quale, in una lettera scritta sul finir del&shy;<lb/>l'Ottobre 1643 al Roberval, gli diceva: &ldquo; Tangentem Cycloidi iam ostende&shy;<lb/>rat mihi Vincentius Vivianus Vivianus florentinus, clarissimi Galilaei alumnus, etiam <lb/>nunc adolescens &rdquo; (Roberval, ouvrages cit., pag. </s>

<s>360). Alla dimostrazione geo&shy;<lb/>metrica del Viviani aggiunse poi il Torricelli la sua meccanica, della quale <lb/>non pubblic&ograve; che l'enunciato in questa forma: </s></p><p type="main">

<s>&ldquo; PROPOSITIO V. &mdash; <emph type="italics"/>Tangens ad datum quodlibet punctum primariae <lb/>Cycloidis ducitur ex puncto sublimiori genitoris circuli, per ipsum datum <lb/>punctum transeuntis &rdquo;<emph.end type="italics"/> (Op. </s>

<s>geom. </s>

<s>cit., P. II, pag. </s>

<s>92). </s></p><p type="main">

<s>La dimostrazione per&ograve; &egrave; rimasta fin qui sconosciuta in una lettera, scritta <lb/>da Firenze il di 27 Febbraio 1643 a Michelangiolo Ricci. </s>

<s>Ivi anzi &egrave; annun&shy;<lb/>ziato un altro teorema, del quale non fece il Torricelli allora nessun conto, <lb/>bench&egrave; ne avrebbe indi potuto dedur per corollario immediato il tautocro&shy;<lb/>nismo della Cicloide. </s>

<s>Cos&igrave;, prevenendo l'Huyghens in una scoperta di tanta <lb/>importanza, si sarebbe meritata molto maggiore, e pi&ugrave; sincera gloria, di <pb xlink:href="020/01/2789.jpg" pagenum="414"/>quella che s'aspettava dall'invenzion del modo di ripulire per i Telescopi le <lb/>superficie de'vetri, de'quali diceva al Ricci di aver piena la testa. </s>

<s>Quella <lb/>torricelliana proposizione poi &egrave; tale: </s></p><p type="main">

<s>&ldquo; PROPOSITIO VI. &mdash; <emph type="italics"/>Se una ruota si rivolger&agrave; sopra un piano, le ve&shy;<lb/>locit&agrave; degl'infiniti punti di lei sono come le corde, che da quei punti vanno <lb/>al contatto. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Sia della ruota DBC (fig. </s>

<s>277) il contatto col piano il punto C, da cui, <lb/>come da centro, e con gl'intervalli DC, AC, BC, si descrivano archi infini&shy;<lb/>tesimi sulla periferia della ruota: la proposizione &egrave; manifesta, considerando <lb/><figure id="id.020.01.2789.1.jpg" xlink:href="020/01/2789/1.jpg"/></s></p><p type="caption">

<s>Figura 277.<lb/>che i punti D, A, B si movono nel medesimo istante come <lb/>sopra le circonferenze di tre ruote concentriche, le velocit&agrave; <lb/>delle quali, essendo il moto comune, hanno la medesima pro&shy;<lb/>porzione dei raggi. </s></p><p type="main">

<s>Passando ora ad applicare la proposizione alla ruota, che <lb/>descrive la Cicloide nella figura 276, qui poco addietro gi&agrave; <lb/>disegnata; la velocit&agrave; dunque del punto G sta alla velocit&agrave; del <lb/>punto E, come GA ad EL, o come GHA ad EKL, ossia come AF a FL: <lb/>ond'essendo le velocit&agrave; come gli spazi, debbono i tempi necessariamente <lb/>essere uguali, e perci&ograve; la curva cicloidale FEG &egrave; <emph type="italics"/>tautocrona.<emph.end type="italics"/> Il documento <lb/>di questa, e della precedente proposizione torricelliana, &egrave; nella detta lettera <lb/>al Ricci, che ora diamo alla luce, lasciate indietro le cose, che non appar&shy;<lb/>tengono al soggetto presente: </s></p><p type="main">

<s>&ldquo; Dir&ograve; a V. S. due bagattelle: Se una ruota si volger&agrave; sopra un piano, <lb/>come quella delle carrozze, ovvero la ruzzola, le velocit&agrave; degl'infiniti punti <lb/>della ruota sono come le corde, che da quei punti vanno al contatto: cio&egrave; <lb/>la velocit&agrave; di A (nella figura 277) a quella di B, sta come AC alla CB. </s>

<s>Ma <lb/>la dirittura dell'impeto &egrave; comune a tutti gl'infiniti punti della ruota, poich&egrave; <lb/>tutti sono diretti verso il punto D. </s>

<s>La ruota per&ograve; va considerata come una <lb/>semplice periferia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di qui nasce che la tangente EI della Cicloide, nella figura 276, passa <lb/>sempre per il punto sublime I del cerchio, che passa per il contatto E. </s>

<s>Di&shy;<lb/>scorro cos&igrave;: il punto E <emph type="italics"/>duplici latione fertur, nempe directa aequidistan&shy;<lb/>ter rectae FL, per rectam EM, et circulariter per periferiam, hoc est per <lb/>tangentem EN, suntque impetus huiusmodi lationum, sive ipsae lationes, <lb/>aequales. </s>

<s>Ergo neutri illarum obediet, sed aequaliter feretur inter utram-<emph.end type="italics"/><lb/><figure id="id.020.01.2789.2.jpg" xlink:href="020/01/2789/2.jpg"/></s></p><p type="caption">

<s>Figura 278.<lb/><emph type="italics"/>que directionem, nempe per lineam EI, quae bifa&shy;<lb/>riam secat angulum NEM.<emph.end type="italics"/> Mi scusi per grazia, perch&egrave; <lb/>ho la testa piena di vetri &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, <lb/>fol. </s>

<s>88). </s></p><p type="main">

<s>&ldquo; PROPOSITIO VII. &mdash; <emph type="italics"/>Sia AB<emph.end type="italics"/> (fig. </s>

<s>278) <emph type="italics"/>un muro <lb/>eretto al piano dell'orizonte BC, e sia AC una trave <lb/>appoggiata al muro: cercasi la proporzione del mo&shy;<lb/>mento, che averanno queste due forze, e dico che la forza A, alla C, sar&agrave; <lb/>come la linea CB alla BA, permutatamente prese.<emph.end type="italics"/></s></p><pb xlink:href="020/01/2790.jpg" pagenum="415"/><p type="main">

<s>Questa medesima proposizione fu da noi trascritta nel Tomo quarto a <lb/>pag. </s>

<s>64, dove la dimostrazione, rimasta nel manoscritto torricelliano inter&shy;<lb/>rotta, si vede supplita dal Viviani, dietro que'cenni, che il Torricelli stesso, <lb/>in una lettera del d&igrave; 20 Gennaio 1643, soggiungeva cos&igrave; a M. A. Ricci, dopo <lb/>avergli annunziata la scoperta: &ldquo; La dimostrazione non l'ho scritta, ma pende <lb/>dalla velocit&agrave;, poich&egrave; movendosi la stanga AC radente le due linee dell'an&shy;<lb/>golo retto ABC, la velocit&agrave;, nella quale sta costituito il punto A, alla velo&shy;<lb/>cit&agrave;, nella quale sta costituito il punto C, sta come BC alla BA &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>82). </s></p><p type="main">

<s>Bench&egrave; dunque sia certo che il Torricelli intendeva di dimostrare dai <lb/>principii statici la verit&agrave; sopra annunziata, abbiamo voluto nonostante racco&shy;<lb/>gliere la proposizione fra le altre di Meccanica nuova, perch&egrave; dette ai Mate&shy;<lb/>matici, sul cominciare di questo secolo, occasione d'applicarvi il principio <lb/>delle forze composte. </s>

<s>L'applicazione per&ograve;, secondo i varii Autori, fu varia, e <lb/>il problema, proposto gi&agrave; da Leonardo da Vinci, e rinnovellato dal discepolo <lb/>di Galileo, ebbe, per le complicanze del nodo, maggiori di quel che non par&shy;<lb/>rebbe, soluzioni diverse. </s>

<s>Sembra nonostante a noi la pi&ugrave; razionale quella, <lb/>che ne dette Giuseppe Venturoli, desumendola dalle leggi di un sistema ri&shy;<lb/>gido in equilibrio, sollecitato da forze parallele. (Elementi di Meccanica, Na&shy;<lb/>poli 1852, pag. </s>

<s>40). </s></p><p type="main">

<s>Rappresentino la verticale AC (fig. </s>

<s>279) e la orizzontale CB il profilo <lb/>del muro, e del pavimento, a cui s'appoggia una trave con le sue testate <lb/><figure id="id.020.01.2790.1.jpg" xlink:href="020/01/2790/1.jpg"/></s></p><p type="caption">

<s>Figura 279.<lb/>A, B. </s>

<s>Sia in G raccolto il peso P di <lb/>essa trave e, fatta per G passare la ver&shy;<lb/>ticale TP, limitata in P dalla orizontale <lb/>MP, intendasi in P trasportato il peso, di <lb/>cui la forza PQ sia decomposta nelle due <lb/>EP, PD, applicate in AM, BN ai due <lb/>punti d'appoggio. </s>

<s>Si vuol sapere in qual <lb/>proporzione debbano stare queste forze <lb/>tra loro, e rispetto al peso, perch&egrave; la <lb/>trave rimanga in equilibrio. </s></p><p type="main">

<s>Si decomponga nuovamente la BN <lb/>nelle due BX, BZ, e rimossi gli ap&shy;<lb/>poggi sieno le forze applicate in direzioni contrarie, cos&igrave; cio&egrave; che AM tiri <lb/>da sinistra a destra, BX da destra a sinistra, e BZ di sotto in su. </s>

<s>Le solle&shy;<lb/>citanti al moto orizontalmente il sistema sono le AM, BX, mentre le P, BZ <lb/>lo spingono verticalmente. </s>

<s>A farlo poi rotare intorno al centro C, prese le <lb/>AC, CB per gli assi, tendono da sinistra a destra le forze AM, P, con mo&shy;<lb/>menti uguali a AM.CA, P.CT: e a farla rotare da destra a sinistra tende <lb/>la forza BZ con momento uguale a BZ.BC. </s></p><p type="main">

<s>Perch&egrave; dunque tutto rimanga in equilibrio, dovranno aversi le tre se&shy;<lb/>guenti equazioni: 1.a AM&mdash;BX=O; 2.a P&mdash;BZ=O; 3.a P.CT+ <lb/>AM.CA&mdash;BZ.BC=O. </s>

<s>Dalla prima delle quali si apprende che s'ugua-<pb xlink:href="020/01/2791.jpg" pagenum="416"/>gliano le due contrarie spinte fatte orizontalmente: e dalla seconda, che il <lb/>peso della trave preme con tutto s&egrave; il pavimento. </s>

<s>Dalla terza poi, sostitui&shy;<lb/>tovi P in luogo di BZ, e risoluta rispetto ad AM, avremo AM=BX= <lb/>P.BT/CA.E perch&egrave;, chiamato <foreign lang="greek">f</foreign> l'angolo BAC, BT=BG sen <foreign lang="greek">f</foreign>, AC=AB cos <foreign lang="greek">f</foreign>; <lb/>sar&agrave; AM=BX=P.BG/AB tang <foreign lang="greek">f</foreign>, e ci&ograve; vuol dire che la spinta orizontale <lb/>sta al peso della trave, come la distanza del centro di gravit&agrave; di lei dal pa&shy;<lb/>vimento, moltiplicata per la tangente dell'angolo dell'inclinazione sul muro, <lb/>sta alla total lunghezza della stessa trave. </s></p><p type="main">

<s>Il Torricelli nonostante, avendo a modo suo risoluto il problema, inten&shy;<lb/>deva d'applicarlo a simili altri problemi di Meccanica nuova, e principal&shy;<lb/>mente a quella, che qui segue in ordine: </s></p><p type="main">

<s>&ldquo; PROPOSITIO VIII. &mdash; <emph type="italics"/>Si cerca per che causa un piccol cerchio di ferro, <lb/>che fascia una colonna fessa, come nel cortile del palazzo de'Medici, e<emph.end type="italics"/><lb/><figure id="id.020.01.2791.1.jpg" xlink:href="020/01/2791/1.jpg"/></s></p><p type="caption">

<s>Figura 280.<lb/><emph type="italics"/>sotto le logge degli Ufizi, sia bastante a tenere quella co&shy;<lb/>lonna che non s'apra, e per conseguenza a reggere quella <lb/>macchina, acci&ograve; non rovini. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia la colonna fessa AB (fig. </s>

<s>280) quale si consideri in <lb/>quattro parti divisa. </s>

<s>Certo &egrave; che, premendo il peso della fab&shy;<lb/>brica soprapposta in AC, la colonna procurer&agrave; di slargarsi in <lb/>EF, non potendo AC discendere, se nelle parti di mezzo la <lb/>fessura della colonna non si slarga. </s>

<s>Ora io dico che, ovviandosi <lb/>presto al disordine, ogni minima forza baster&agrave; per fermarla, <lb/>e che, lasciando fare l'apertura grande, ci vorr&agrave; una volta forza eguale al <lb/>peso, e pu&ograve; anche essere che una volta vi si ricerchi forza mille volte mag&shy;<lb/>giore del peso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia la fessura ABCD (fig. </s>

<s>281), l'apertura o larghezza della quale sia <lb/>BD, e linea perpendicolare sia AC. </s>

<s>Per le cose dimostrate nella precedente <lb/><figure id="id.020.01.2791.2.jpg" xlink:href="020/01/2791/2.jpg"/></s></p><p type="caption">

<s>Figura 281.<lb/>ponendo un peso in A, ed una potenza uguale in D, il <lb/>momento della potenza, a quello del peso, sta come la <lb/>AO alla OD. </s>

<s>Per far dunque che i momenti siano uguali, <lb/>pongasi una potenza, che al peso sia come DO ad AO. </s>

<s><lb/>Cos&igrave; poi diremo in questo modo: la potenza piccola alla <lb/>grande sta come DO ad AO, ma la grande al peso stava <lb/>come AO a DO; ergo ex aequo la potenza piccola &egrave; uguale <lb/>al peso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si cava dunque che, per tenere unite le colonne, <lb/>che non s'aprano maggiormente, ci vuole una forza, la quale al peso abbia <lb/>la proporzione, che ha il diametro della figura BD, alla perpendicolare AC &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. XXXVII, fol. </s>

<s>78). </s></p><p type="main">

<s>Sembra che la proposizione sia confermata, anche applicandovi diretta&shy;<lb/>mente la regola del parallelogrammo, dalla diagonale AC del quale sia rappre&shy;<lb/>sentato il peso. </s>

<s>Nella figura ABCD, per far l'equilibrio, ci vogliono due forze <pb xlink:href="020/01/2792.jpg" pagenum="417"/>uguali a DA, AB, o ad AB, BC; ma, se la fessura s'allarga in AECF, le <lb/>forze necessarie a resistere son cresciute come AE, AF, o come AE, EC, e <lb/>quelle prime stanno a queste, come la diagonale ED sta ad EF. </s>

<s>Tali insomma, <lb/>quali noi gli abbiamo nel fertile campo dissepolti, sono i germi di Mecca&shy;<lb/>nica nuova che, spuntati appena nella mente del Torricelli, risecchirono mi&shy;<lb/>seramente sotto il gelo della morte. </s></p><pb xlink:href="020/01/2793.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Di altri Discepoli di Galileo <lb/>promotori della Scienza del moto<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. &mdash; Di Antonio Nardi, e particolarmente delle sue <emph type="italics"/>Ricercate geometriche:<emph.end type="italics"/> di Michelangiolo Ricci. </s>

<s><lb/>II. </s>

<s>Digressione intorno alla Cicloide: delle propriet&agrave; di le&igrave; scoperte dal Roberval, e da altri <lb/>Matematici francesi. </s>

<s>&mdash; III. </s>

<s>Di ci&ograve; che dimostrarono intorno alla Cicloide il Nardi, il Torricelli <lb/>e il Ricci. </s>

<s>&mdash; IV. </s>

<s>Delle controversie insorte fra il Robervai e il Torricelli, prima intorno alla <lb/>quadratura, poi intorno al baricentro della Cicloide. </s>

<s>&mdash; V. </s>

<s>Di ci&ograve; che a illustrare, a compiere <lb/>e a divulgare le dottrine galileiane del moto operarono il Cavalieri, il Borelli e il Viviani. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>A solo sentirsi annunziare il soggetto del presente discorso non pu&ograve;, <lb/>chiunque legge, non precorrere con la mente a pensare ai nomi del Cava&shy;<lb/>lieri, del Viviani e del Borelli, che son, per le opere e per la fama, i pi&ugrave; <lb/>conosciuti dopo il Torricelli fra i discepoli di Galileo. </s>

<s>La cosa &egrave; per s&egrave; tanto <lb/>naturale, che null'altro s'indovinerebbe con maggiore certezza, ma bench&egrave; <lb/>sia un fatto che debbono i tre ora commemorati entrare nell'argomento, non <lb/>si faranno per&ograve; i primi, essendo la notizia di essi men desiderata di quella <lb/>di altri loro colleghi, non punto men valorosi, e rimasti al pubblico scono&shy;<lb/>sciuti. </s></p><p type="main">

<s>Di Antonio Nardi aretino non &egrave; stato fin qui oscuro fra i Matematici il <lb/>nome, per essersi scolpito in fronte ai libri torricelliani Dei solidi sferali, ma <lb/>chi ivi legge, con riconoscenza di discepolo, commemorato l'acutissimo scru&shy;<lb/>tatore dei libri di Archimede non pu&ograve; non sentirsi nascere il desiderio di <lb/>conoscere, o di avere almeno un saggio delle opere matematiche di colui, <lb/>che ispir&ograve; e dette impulso alla maggiore opera matematica del Torricelli. </s>

<s>A <pb xlink:href="020/01/2794.jpg" pagenum="419"/>sodisfare al qual desiderio ha conferito in parte la nostra Storia a varie occa&shy;<lb/>sioni, e particolarmente discorrendo dei Baricentri, dove si ordinarono dai <lb/>manoscritti le proposizioni dimostrate dal Nardi, per confermare geometrica&shy;<lb/>mente la verit&agrave; della regola meccanica del Guldino. </s>

<s>Altra occasione, per so&shy;<lb/>disfare ai desiderosi di conoscere un tale uomo, ci si porgeva ora, che tro&shy;<lb/>vavasi esso Nardi aver precorso, e in ogni modo concorso col Torricelli nel&shy;<lb/>l'invenzione dei centri di gravit&agrave; di alcune figure, o rimasti ai Matematici <lb/>fin allora ignoti, o dimostrati con troppo lunghi e faticosi processi. </s>

<s>Vorremmo <lb/>senza indugio dar opera a raccogliere e ordinare cos&igrave; fatti teoremi baricen&shy;<lb/>trici, se non si credesse opportuno il premettere alcune notizie intorno ai <lb/>manoscritti, da cui sono stati raccolti. </s></p><p type="main">

<s>Questi manoscritti son le <emph type="italics"/>Scene accademiche,<emph.end type="italics"/> penseranno i Lettori, se <lb/>pur ce ne sono, che dal nostro Discorso preliminare fin qui ci hanno tenuto <lb/>dietro, e ai quali &egrave; noto essere quelle Scene, negli argomenti i pi&ugrave; varii, <lb/>cos&igrave; disordinate, da parere un caos filosofico, piuttosto che un libro. </s>

<s>Per tale <lb/>anzi si riconobbe, e con tal nome si chiam&ograve; l'opera dal suo proprio Autore, <lb/>il quale cos&igrave; ripensava fra s&egrave;, e notava in una pagina, giunto a scrivere <lb/>mezzo il grosso volume: </s></p><p type="main">

<s>&ldquo; Oh quanto confuse sono queste accademiche Scene! Parrebbero l'idea <lb/>della confusione, se idea la confusione avesse. </s>

<s>Ma se ordinate fossino non <lb/>sarebbero formate da un confuso. </s>

<s>Io per me stimo che siano un caos filo&shy;<lb/>sofico, il quale facilmente ordinar si possa, purch&egrave; la mente gli soprarrivi. </s>

<s><lb/>Certo che mi sono abbattuto in un luogo loro, d'onde non affatto senz'or&shy;<lb/>dine sembravano. </s>

<s>Sovviemmi che, quand'era giovanetto, soleva per ischerzo <lb/>fingere alcuni disegni che a caso delineati, fuorch&egrave; da un sol punto, sem&shy;<lb/>bravano. </s>

<s>Lo stesso quasi parmi che in questi componimenti accada, di cui <lb/>la forma un filosofico quasi e tetracordo sistema mi rappresenta. </s>

<s>La prima <lb/>corda &egrave; matematica, sopra la quale ricercansi teorie spettanti al numero, mi&shy;<lb/>sura, momento, movimento ed apparenza delle cose: qual punto della Filosofia <lb/>con nome di Arismetrica, Geometria, Meccanica, Astronomia e con altri an&shy;<lb/>cora si addita. </s>

<s>Quindi la seconda corda segue, che pi&ugrave; al concreto ed all'in&shy;<lb/>timo delle cose corporee pertiene, nella quale ricercasi la natura dei veraci <lb/>corpi, e i loro principii e passioni. </s>

<s>Nella stessa maniera si arriva alle parti&shy;<lb/>colari nature, incominciando dalle pi&ugrave; comuni e men degne, insino all'anima <lb/>ragionevole si giunge. </s>

<s>Qui s'attacca la corda metafisica, ove dell'ente gene&shy;<lb/>ralmente e de'suoi principii, e del supremo di ogni Ente, con gli aiuti della <lb/>Natura e della Grazia, discorresi. </s>

<s>L'ultima corda aggiunta &egrave; varia di criti&shy;<lb/>che, per lo pi&ugrave;, e morali materie &rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>745). </s></p><p type="main">

<s>Di qui si comprende come non fossero le Scene scritte per stamparsi a <lb/>quel modo, ma per raccogliervi i materiali, da ordinarsi in un libro, dove <lb/>si ricercherebbero cose di matematica, di fisica, di metafisica e di morale, <lb/>quasi riducendo la verit&agrave; n&egrave;ll'armonia di un tetracordo. </s>

<s>A raccogliere e a <lb/>far copiare, tra cos&igrave; fatte <emph type="italics"/>Ricercate,<emph.end type="italics"/> le matematiche, per darsi alle stampe, <lb/>attendeva il Nardi nel 1641, come si rileva dalle seguenti parole scritte dal <pb xlink:href="020/01/2795.jpg" pagenum="420"/>Cavalieri in una lettera del d&igrave; primo Novembre di quell'anno a Giann'An&shy;<lb/>tonio Rocca: &ldquo; Gli d&ograve; poi nuova che mi scrive il Torricelli trovarsi di stanza <lb/>dal sig. </s>

<s>Galileo, ed aspettare in Firenze il sig. </s>

<s>Antonio Nardi, credo genti&shy;<lb/>luomo aretino, che ha da stampare un libro di Geometria, nel quale pre&shy;<lb/>tende con modi nuovi di mostrare tutte le cose di Archimede, per via degli <lb/>indivisibili, quale dice avere fatto una grandissima pratica sopra la mia Geo&shy;<lb/>metria &rdquo; (Lettere a G. A. Rocca, Modena 1785, pag. </s>

<s>268). </s></p><p type="main">

<s>Il proposito di venire a Firenze, per aver consiglio col Torricelli, e di&shy;<lb/>videre con lui le cure della stampa, non sembra fosse dal Nardi mandato ad <lb/>effetto. </s>

<s>Un anno e mezzo dopo era tuttavia in Arezzo, dove, scriveva il Tor&shy;<lb/>ricelli stesso al Cavalieri, attendeva &ldquo; a far copiare il suo libro geometrico per <lb/>mandarlo qua a me, acci&ograve; io lo faccia pervenire anco in mano di V. P. per <lb/>sentire una parola del suo purgatissimo giudizio &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, <lb/>fol. </s>

<s>127). A mezzo l'anno 1645, avendo gi&agrave; il Nardi messo in ordine la parte <lb/>metafisica del suo libro, attendeva alla fisica, ma gli rimaneva tuttavia da tor&shy;<lb/>nare sopra alla matematica, come si raccoglie da queste parole, che M. A. </s>

<s>Ricci <lb/>scriveva al Torricelli: &ldquo; Il sig. </s>

<s>Antonio Nardi fatica intorno l'opera sua. </s>

<s>Ha <lb/>dato perfezione alla parte metafisica, ora &egrave; d'intorno alla fisica, e poi rive&shy;<lb/>dr&agrave; la matematica, il che non potr&agrave; seguir prima di dieci mesi, ovvero un <lb/>anno. </s>

<s>E mi duole che tardi tanto ad uscire in luce Opera, che si spera debba <lb/>essere doviziosa di tutte le speculazioni, cio&egrave; pasto per ogni sorta di profes&shy;<lb/>sori di Scienza &rdquo; (ivi, T. XLII, fol. </s>

<s>121). </s></p><p type="main">

<s>Bench&egrave; fossero le Ricercate matematiche state a copiarsi le prime, dice <lb/>nonostante il Ricci che volle tornar l'Autore in dietro a rivederle, perch&egrave; ci <lb/>aveva certe cose da aggiungere, alcune delle quali, come vedremo, importan&shy;<lb/>tissime. </s>

<s>Passarono del resto i dieci mesi e l'anno, e le durate fatiche, qua&shy;<lb/>lunque se ne fosse la ragione, riuscirono infruttuose. </s>

<s>La copia delle Ricer&shy;<lb/>cate geometriche, con correzioni e postille autografe, rimase per due secoli <lb/>e mezzo dimenticata in Arezzo, dove si ritrovarono in questi ultimi giorni <lb/>alcuni pochi fascicoli mutilati e dispersi, de'quali (non sapremmo con qual <lb/>consiglio, se non fu quello di mantenere fra le sventurate carte la dispersione) <lb/>parte fu donato da un Aretino alla Biblioteca nazionale di Firenze, e parte a <lb/>quella di Roma. </s>

<s>N&egrave; ha perci&ograve; l'una citt&agrave; nulla da invidiare o da reclamare <lb/>all'altra, la quale possiede, nella raccolta de'manoscritti galileiani, le Scene <lb/>intere, inclusevi le Ricercate, no nei loro materiali solamente, ma nell'or&shy;<lb/>dine, secondo il quale volevano essere disposti dallo stesso Autore. </s>

<s>&Egrave; dunque <lb/>poco da lamentar la perdita, e meno da esultar per l'acquisto, bench&egrave; l'aver <lb/>noi potuto consultare e collazionar con le Scene i manoscritti, donati alle due <lb/>dette Biblioteche, abbia conferito a darci alcuni utilissimi documenti di sto&shy;<lb/>ria, come sarebbe per esempio quel che riguarda gli studi fatti dal Nardi <lb/>intorno alla Cicloide. </s>

<s>Cos&igrave;, dall'aver letto nella prima copia delle Ricercate <lb/>geometriche essersi ritrovata la misura dello spazio cicloidale, per sola mec&shy;<lb/>canica esperienza; abbiamo potuto ragionevolmente argomentare che, dopo <lb/>il 1641, attese il Nardi a dimostrare geometricamente le propriet&agrave; della curva. </s></p><pb xlink:href="020/01/2796.jpg" pagenum="421"/><p type="main">

<s>Vedremo pi&ugrave; qua l'importanza di una tale notizia: ora &egrave; da tornar sopra <lb/>quello, che si diceva, dell'ordine delle materie da trattarsi nelle Ricercate, il <lb/>quale ordine resulta dagl'indici particolari, scritti dal Nardi stesso per cia&shy;<lb/>scun sistema del suo Tetracordo. </s>

<s>Quel che a noi nel presente proposito pi&ugrave; <lb/>importa &egrave; l'indice delle Ricercate matematiche, le quali sono otto: le prime <lb/>tre ordinate a riformare le dimostrazioni di Euclide, le quattro seguenti a <lb/>dimostrar le ragioni del curvo e del retto, con altro metodo da quello ar&shy;<lb/>chimedeo, e l'ultima intorno alla dottrina meccanica dei momenti e dei mo&shy;<lb/>vimenti, alla quale propriamente si riferisce il soggetto del nostro discorso. </s></p><p type="main">

<s>Di questa ottava Ricercata matematica l'indice delle materie &egrave; cos&igrave; scritto: <lb/><emph type="italics"/>I. </s>

<s>Divisione delle Meccaniche. </s>

<s>&mdash; II. </s>

<s>Se Archimede supponga un falso mec&shy;<lb/>canico nella quadratura parabolica. </s>

<s>&mdash; III. </s>

<s>Centro di gravit&agrave; di alcuni <lb/>rettilinei, mostrati diversamente dal metodo di Archimede. </s>

<s>&mdash; IV. </s>

<s>Centro <lb/>di gravit&agrave; dei triangoli e dei coni. </s>

<s>&mdash; V. </s>

<s>Centro di gravit&agrave; d'un frusto <lb/>parabolico. </s>

<s>&mdash; VI. </s>

<s>Centro di gravit&agrave; del settore di cerchio. </s>

<s>&mdash; VII. </s>

<s>Cen&shy;<lb/>tro di gravit&agrave; d'un settore di sfera. </s>

<s>&mdash; VIII. </s>

<s>Centro della potenza, o di <lb/>gravit&agrave;, della Cicloide nostra. </s>

<s>&mdash; IX. </s>

<s>Teorema generale meccanico. </s>

<s>&mdash; <lb/>X. </s>

<s>Forza della percossa. </s>

<s>&mdash; XI. </s>

<s>Di un principio meccanico di Galileo. </s>

<s>&mdash; <lb/>XII. </s>

<s>Varie osservazioni meccaniche. </s>

<s>&mdash; XIII. </s>

<s>Della scienza esatta del moto. <lb/></s>

<s>&mdash; XIV. </s>

<s>Parere del Galilei intorno al moto dei grari cadenti.<emph.end type="italics"/> (MSS. Gal. </s>

<s><lb/>Disc., T. XX, pag. </s>

<s>745). </s></p><p type="main">

<s>Intorno a varie, fra queste cos&igrave; indicate proposizioni, abbiamo avuto pi&ugrave; <lb/>qua e pi&ugrave; l&agrave; occasione di riferire i pensieri del Nardi, cosicch&egrave; non ci ri&shy;<lb/>mane altro a dire, che del metodo come furono mostrati dal Nostro i cen&shy;<lb/>tri di gravit&agrave; delle varie figure, diversamente da Archimede fra gli antichi, <lb/>e dal Torricelli fra i matematici moderni. </s>

<s>Sar&agrave; il trattatello da noi distinto <lb/>in due parti, secondo che l'invenzione del baricentrico ha per soggetto le <lb/>figure ordinarie, o quella particolarmente inventata dal Nardi, e che perci&ograve; <lb/>designeremo col nome di <emph type="italics"/>Cicloide nardiana.<emph.end type="italics"/> La prima di queste parti si <lb/><figure id="id.020.01.2796.1.jpg" xlink:href="020/01/2796/1.jpg"/></s></p><p type="caption">

<s>Figura 282.<lb/>compone dei seguenti XII teoremi, da noi rac&shy;<lb/>colti, e qui appresso ordinati: </s></p><p type="main">

<s>&ldquo; TEOREMA I. &mdash; <emph type="italics"/>Nel triangolo VCQ<emph.end type="italics"/><lb/>(fig. </s>

<s>282) <emph type="italics"/>dalla cima C cada CO nella base <lb/>VQ, dividendola ugualmente: dico che il <lb/>centro d&igrave; gravit&agrave; di esso triangolo &egrave; nel <lb/>punto X, il quale divide CO in modo, che CX <lb/>&egrave; doppio di XO. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Dividansi ugualmente CV, CQ nei punti <lb/>F, G, e tirate OFI, OGR, s'eguaglino all'al&shy;<lb/>tezza C, sicch&egrave; la retta IR passi per C, e sia <lb/>parallela alla base <expan abbr="Vq.">Vque</expan> Tirisi anche FG, che <lb/>in H divida CO. </s>

<s>I triangoli dunque IFC, CGR <lb/>sono simili, uguali e similmente posti in riguardo di CH; onde egualmente <lb/>gravano in CH. </s>

<s>Nello stesso modo avviene degli altri VFO, OGQ, che egual-<pb xlink:href="020/01/2797.jpg" pagenum="422"/>mente gravano in HO, e ancora il trapezio FVGQ eguale, simile e contrap&shy;<lb/>posto all'altro FIRG, e cos&igrave; graveranno ugualmente in FG, come parimente <lb/>i triangoli FCG, FOG, o veramente OFC, OGC. </s>

<s>Il punto H dunque &egrave; centro <lb/>della figura, e perch&egrave; X &egrave; centro del triangolo VCQ, il quale &egrave; simile a CGR, <lb/>ed agli altri collaterali e opposti, sar&agrave; in essi il centro similmente posto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia D il eentro di CGR, e intendasi tirata da D una retta al centro <lb/>del triangolo IFC, la quale seghi HC in T, e sar&agrave; HT uguale a GD. </s>

<s>E per&shy;<lb/>ch&egrave; la retta CX &egrave; doppia di XO, anche GD o HT sar&agrave; doppia di DS o TC: <lb/>T poi &egrave; il centro della gravit&agrave; composta dei due triangoli IFC, CGR. </s>

<s>Dun&shy;<lb/>que tolti questi, scorrer&agrave; il centro H in X, sicch&egrave; HX ad HT sar&agrave; come i <lb/>due triangoli al triangolo <expan abbr="VCq.">VCque</expan> Ma HT &egrave; dupla di HX, adunque il triangolo <lb/>VCQ sar&agrave; duplo degli altri due, il che &egrave; vero, perch&egrave; &egrave; vero che il trian&shy;<lb/>golo VCQ &egrave; doppio degli altri due &rdquo; (ivi, pag. </s>

<s>49). </s></p><p type="main">

<s>La conclusione, forse dal Nardi non troppo chiaramente scritta, dipende <lb/>da un principio assai per s&egrave; noto, qual'&egrave; che due grandezze uguali e simil&shy;<lb/>mente poste gravano ugualmente sopra la libbra, e si pu&ograve; ridurre al seguente <lb/>discorso: Dalla libbra XT col centro in H pendono, dalla parte di T, due <lb/>sole grandezze uguali, che sono i triangoli IFC, CGR, e dalla parte di X ne <lb/>pendono quattro di cos&igrave; fatte grandezze, tutte eguali fra loro e alle altre due, <lb/>che sono i triangoli VFO, FOC, e OGQ, COG. </s>

<s>Dunque TH=2XH, e perci&ograve; <lb/>XH=TC, CX=CT+TH+XH=4XH, XO=CT+TH&mdash;HX= <lb/>2XH, d'onde CX:XO=4:2=2:1, come dal Nardi intendevasi di dimo&shy;<lb/>strare. </s></p><p type="main">

<s>Dipendono da questo primo altri due teoremi, i quali, bench&egrave; risalgano <lb/>a un tratto a figure assai pi&ugrave; composte, pur crediamo di doverli ordinar qui, <lb/>perch&egrave; strettamente si ritengono con quello, per modo o di corollari o di <lb/>scolii. </s></p><p type="main">

<s>TEOREMA II. &mdash; <emph type="italics"/>Del trapezio, segato da un triangolo per una linea <lb/>che ne divide nel mezzo i lati, il centro di gravit&agrave; cos&igrave; sega l'asse, che la <lb/>parte verso la maggior base stia a quella verso la minore come quattro <lb/>sta a cinque.<emph.end type="italics"/></s></p><p type="main">

<s>Nella precedente figura &egrave; GV il trapezio, quale viene proposto, di cui si <lb/>supponga essere in Z il centro. </s>

<s>La libbra ZT, sospesa in X, &egrave; dalla parte <lb/>T gravata del solo triangolo FCG, e dalla parte Z dei tre triangoli VFO, <lb/>FOG, OGQ, tutti uguali insieme, e con quel primo. </s>

<s>Avremo perci&ograve; ZX:XT= <lb/>1:3, ossia ZX=XT/3=2/3 XH. Ora, essendo ZH=ZX+HX= <lb/>2/3 HX+3/3 HX=5/3 XH; ZO=HO&mdash;ZH=3XH&mdash;5/3 XH=4/3 XH; <lb/>se ne concluder&agrave; l'intento cio&egrave; OZ:HZ=4:5. </s></p><p type="main">

<s>La medesima conclusione si sarebbe, osserva il Nardi, ottenuta dalla <lb/>XV archimedea del primo libro degli Equiponderanti, applicandovi la for&shy;<lb/>mula generale quivi proposta ZO:HZ=2FG+VQ:2VQ+FG, impe&shy;<lb/>rocch&egrave;, fatto VQ=4, e perci&ograve; FG=2, sar&agrave; ZO:HZ=4+4:8+2= <lb/>8:10=4:5. </s></p><pb xlink:href="020/01/2798.jpg" pagenum="423"/><p type="main">

<s>TEOREMA III. &mdash; <emph type="italics"/>Del frusto che riman del cono, segato per un piano <lb/>erettamente condotto sulla met&agrave; dell'asse, il centro di gravit&agrave; divide la <lb/>porzion di esso asse in modo, che la parte verso la base minore sia a quella <lb/>verso la base maggiore, come 17 a 11.<emph.end type="italics"/></s></p><p type="main">

<s>Rappresentando, sempre nella medesima figura, VCQ il cono, di cui il <lb/>centro di gravit&agrave; X sia, per le note regole, gi&agrave; determinato; apparir&agrave; in FQ <lb/>il tronco proposto, sull'asse HO del quale vuole ora indicarsi il luogo Z del <lb/>centro. </s>

<s>Essendo CVQ=<foreign lang="greek">p</foreign>VQ2.OC/3=4<foreign lang="greek">p</foreign>FH2.2CH/3; CFG=<foreign lang="greek">p</foreign>FH2.CH/3, <lb/>avremo CVQ:CFG=8:1. E, dividendo, CVQ&mdash;CFG:CFG=7:1, co&shy;<lb/>sicch&egrave; il frusto applicato in Z essendo settuplo del cono applicato in T, verr&agrave; <lb/>la libbra TZ, col sostegno in Z, a esser divisa talmente, da aversi ZX:XT= <lb/>1:7; ossia ZX=XT/7. Suppongasi ora diviso tutto l'asse CO in 56 parti <lb/>uguali: sar&agrave; HO=CH=28; XH=14; HT=7; XT=21; XZ=3. <lb/>Dunque HZ=HX+ZX=14+3=17; ZO=HO&mdash;HZ=28&mdash;17= <lb/>11, e perci&ograve; HZ:OZ=17:11, com'era proposto. </s></p><p type="main">

<s>Vuole omologamente il Nardi far osservare che &ecaron; incluso anche questo <lb/>caso nella generalit&agrave;, proposta in ultimo luogo da Galileo nell'Appendice dei <lb/>centri di gravit&agrave; (Alb. </s>

<s>XIII, 286), sotto la forma <lb/>HZ:ZO=2<foreign lang="greek">p</foreign>VO2+<foreign lang="greek">p</foreign>FH2+2<foreign lang="greek">p</foreign>VO.FH:3<foreign lang="greek">p</foreign>FH2+<foreign lang="greek">p</foreign>VO2+<foreign lang="greek">p</foreign>VO.FH. </s>

<s><lb/>Dividendo infatti la seconda ragione per <foreign lang="greek">p</foreign>, fatto VO=2, e sostituiti i valori, <lb/>avremo HZ:ZO=12+1+4:3+4+4=17:11. Ma &egrave; bene prose&shy;<lb/>guire di l&agrave;, dove fu da noi lasciato interrotto, a trascrivere il manoscritto, <lb/>per vedervi i due teoremi dimostrati nelle loro forme originali. </s></p><p type="main">

<s>&ldquo; Per trovare il centro del cono, soggiunge il Nardi, altri si potr&agrave; incam&shy;<lb/>minare con proporzional metodo: e qui solo noter&ograve; che, nel trapezio FGQV, <lb/>il centro di gravit&agrave;, posto per ora Z, divide HO con tal ragione, che ZH ad <lb/>OZ sia come il doppio di VQ con FG al doppio di EG con <expan abbr="Vq.">Vque</expan> Imperocch&egrave;, <lb/>tolto dal triangolo CVQ l'altro FCG, sar&agrave; XZ all'aggregato di XH, HT, posto <lb/>T centro del triangolo FCG, come il triangolo FCG al trapezio <expan abbr="VFGq;">VFGque</expan> cio&egrave; <lb/>come uno a tre. </s>

<s>E cos&igrave; OZ ad HZ sar&agrave; come quattro a cinque, cosicch&egrave;, <lb/>posto HT tre, XH tre, sar&agrave; l'aggregato sei, e ZX due. </s>

<s>Ma posto VQ quat&shy;<lb/>tro, sar&agrave; il suo doppio otto. </s>

<s>Ed aggiuntoli FG due, sar&agrave; dieci. </s>

<s>Qual somma, <lb/>al doppio di FG, cio&egrave; a quattro e a VQ quattro ha la ragione di cinque a <lb/>quattro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Anche raccorrassi che del frusto solido VFGQ il centro Z divide HO <lb/>in modo, che ZH a ZO sia come il triplo del cerchio, di cui diametro VQ, <lb/>col cerchio, di cui diametro FG, e con due proporzionali di mezzo, al triplo <lb/>del cerchio di FG, col cerchio di VQ, e con due di mezzo, qual proporzione <lb/>&egrave; di 17 a 11, come qui si vede: &rdquo; </s></p><p type="main">

<s>&ldquo; Posto VQ quattro, sar&agrave; FG due, e i loro quadrati saranno come otto <lb/>a due. </s>

<s>Dunque il triplo di otto, con due e con otto, cio&egrave; 34, al triplo di due <pb xlink:href="020/01/2799.jpg" pagenum="424"/>con otto due volte, cio&egrave; 22, sono come 51 a 33, o come 17 a 11. Ma tal <lb/>corollario suppone essere il cono VCQ ottuplo dell'altro FCG, e che, essendo X <lb/>il centro del cono VCQ, sia CX triplo di XO, di che altrove. </s>

<s>E frattanto <lb/>avvertiremo come dalle pi&ugrave; semplici e regolari figure l'intelletto nostro saglia <lb/>alle pi&ugrave; irregolari e composte, per poi generalmente le stesse propriet&agrave; nelle <lb/>une e nelle altre dimostrare &rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>50). </s></p><p type="main">

<s>TEOREMA IV. &mdash; <emph type="italics"/>Cuiuscumque parallelogrammi centrum gravitatis est <lb/>in recta linca coniungente opposita parallelogrammi latera, bifariam secta.<emph.end type="italics"/></s></p><p type="main">

<s>Abbiamo annunziato il teorema nelle forme proprie, e con le medesime <lb/>parole di Archimede, perch'era l'intenzione del Nardi di rendere assai pi&ugrave; <lb/>semplice la proposizione IX del primo libro <emph type="italics"/>De aequiponderantibus,<emph.end type="italics"/> conclu&shy;<lb/>dendola da un principio evidente, a cui poi riducesi la petizione X dal Si&shy;<lb/>racusano premessa al detto libro primo, che cio&egrave; due grandezze eguali s'equi&shy;<lb/>librano sull'asse, intorno a cui siano similmente disposte, e sopra esso asse, <lb/>come sopra loro libra, hanno il centro comune. </s></p><p type="main">

<s>Sia il parallelogrammo AD (fig. </s>

<s>283) segato nelle due uguali grandezze <lb/>AB, CD dall'asse CB, che prolungato seghi allo stesso modo il parallelo&shy;<lb/><figure id="id.020.01.2799.1.jpg" xlink:href="020/01/2799/1.jpg"/></s></p><p type="caption">

<s>Figura 283.<lb/>grammo EH, uguale in tutto e <lb/>per tutto all'AD. </s>

<s>Preso nel mezzo <lb/>di CF il punto O, sar&agrave; ivi il cen&shy;<lb/>tro comune, che si rimarr&agrave; tale <lb/>avvicinandosi con egual moto i <lb/>due parallelogrammi, infintanto&shy;<lb/>ch&egrave; i loro lati non giungano a toccarsi e a confondersi nell'unico ED della <lb/>figura AH, della quale rimane pur in O il centro, ond'&egrave; manifesto che que&shy;<lb/>sto segher&agrave;, come dovevasi dimostrare, la linea ED nel mezzo. </s></p><p type="main">

<s>&ldquo; Siano, cos&igrave; dice propriamente il Nardi, due simili ed uguali paralle&shy;<lb/>logrammi AD, EH, i quali abbiano paralleli i lati omologhi. </s>

<s>Dunque, sospesi <lb/>dai centri della loro gravit&agrave; in una retta, di cui il mezzo sia O, peseranno <lb/>ugualmente da O. </s>

<s>Intendasi ora avvicinarsi egualmente l'uno all'altro, senza <lb/>mutare inclinazione: adunque avverr&agrave; che resti sempre l'equilibrio, sino a <lb/>che il lato D si faccia uno con l'omologo E, e cos&igrave; di due si former&agrave; un <lb/>solo lato ED, e un parallelogrammo solo AH &rdquo; (ivi, pag. </s>

<s>1282). </s></p><p type="main">

<s>TEOREMA V. &mdash; <emph type="italics"/>Il centro di gravit&agrave; di una superficie emisferica &egrave; nel <lb/>mezzo dell'asse.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Essere il centro di gravit&agrave; di una superficie emisferica nel mezzo del&shy;<lb/>l'asse, in che sbagliossi il Guldino, provasi da me facilmente con dividere <lb/>detto asse in particelle eguali, e ciascuna minore della distanza, che l'avver&shy;<lb/>sario vuole dal mezzo. </s>

<s>Quindi, tirati piani paralleli alla base, per dette divi&shy;<lb/>sioni si tagliano parti uguali di superficie, quali, per essere uniformemente <lb/>gravi, peseranno ugualmente, ed aver&agrave; ciascuna il centro dentro i termini <lb/>della sua particella di asse, e quindi dedurrassi brevemente l'assurdo &rdquo; (ivi, <lb/>pag. </s>

<s>1360). </s></p><p type="main">

<s>Era dunque la dimostrazione del Nardi quella medesima, che il Torri-<pb xlink:href="020/01/2800.jpg" pagenum="425"/>celli diceva di avere imitata da Archimede, ma nell'osservazione aggiunta <lb/>e che dice <emph type="italics"/>trovarsi anche facilmente il centro delle superficie coniche e <lb/>cilindriche,<emph.end type="italics"/> &egrave; intesa la dimostrazione a priori, ossia per via degli indivisi&shy;<lb/>bili, secondo la quale, considerandosi le due dette superficie rotonde come <lb/>composte delle infinite circonferenze proporzionali ai raggi, il centro della <lb/>superficie conica si riduce a quello di un triangolo, e della superficie cilin&shy;<lb/>drica a quello di un parallelogrammo. </s></p><p type="main">

<s>Un'altra osservazione anche vi si soggiunge di maggiore importanza, ed <lb/>&egrave; che col <emph type="italics"/>Teorema generale meccanico,<emph.end type="italics"/> ossia con la regola centrobarica del <lb/>Guldino si poteva con facilit&agrave; inaspettata, dimostrare il seguente </s></p><p type="main">

<s>TEOREMA VI. &mdash; <emph type="italics"/>Il centro di gravit&agrave; della mezza circonferenza DAF<emph.end type="italics"/><lb/><figure id="id.020.01.2800.1.jpg" xlink:href="020/01/2800/1.jpg"/></s></p><p type="caption">

<s>Figura 284.<lb/>(fig. </s>

<s>284), <emph type="italics"/>divisa nel mezzo in A, &egrave; in X, punto cos&igrave; <lb/>collocato, che sia CX quarta proporzionale, dopo essa <lb/>mezza circonferenza, il diametro e il raggio.<emph.end type="italics"/></s></p><p type="main">

<s>Valgano per una dimostrazione di ci&ograve; le parole: <lb/><emph type="italics"/>ed in questa ossservasi la medesima analogia, chi ben <lb/>l'intende, che nella superficie emisferica<emph.end type="italics"/> (ivi). Chia&shy;<lb/>mata infatti S questa superficie, la Geometria d&agrave; S= <lb/>DF.<foreign lang="greek">p</foreign>AC, e la Centrobarica S=DAF.<foreign lang="greek">p</foreign>CX, d'onde DAF:DF=AC:CX. </s></p><p type="main">

<s>Si diceva essere questa invenzione di maggiore importanza delle altre, <lb/>non solamente perch&egrave; nuova, ma perch&egrave; vi si faceva uso di un argomento <lb/>nuovo, non avvertito n&egrave; dallo stesso Guldino, n&egrave; ancora dal Torricelli, n&egrave; da <lb/>nessun altro prima del Wallis, preceduto di tanto tempo dal Nardi, il quale <lb/>avvertiva, nel citato luogo, altres&igrave; che, <emph type="italics"/>con l'aiuto di questa centrobarica, <lb/>si discende alle pi&ugrave; particolari proposte intorno alla stessa materia.<emph.end type="italics"/> Ve&shy;<lb/>dremo di cos&igrave; fatte proposte un esempio insigne applicato alla misura dei <lb/>solidi rotondi generati dalla Cicloide, ma intanto &egrave; da proseguire nel nostro <lb/>proposito, qual'era di mostrare come il Nardi concorresse col Torricelli in <lb/>facilitare e in promovere la Scienza dei precursori. </s>

<s>E quanto alla facilit&agrave;, <lb/>abbiamo ora da proporre l'esempio del baricentrico nel frusto di parabola, <lb/><figure id="id.020.01.2800.2.jpg" xlink:href="020/01/2800/2.jpg"/></s></p><p type="caption">

<s>Figura 285.<lb/>e nel settore di circolo, <lb/>da preferirsi alle lunghe <lb/>e stentate dimostrazioni di <lb/>Archimede, e del Della <lb/>Faille. </s></p><p type="main">

<s>TEOREMA VII. &mdash; <emph type="italics"/>Nel <lb/>frusto parabolico ARBCD<emph.end type="italics"/><lb/>(fig. </s>

<s>285) <emph type="italics"/>siano inscritte <lb/>le parabole ARB, CSD <lb/>col centro comune in O, <lb/>e il trapezio ABCD col <lb/>centro in K: se, come il <lb/>trapezio alle parabole, cos&igrave; faremo reciprocamente OZ a ZK, dico che in Z <lb/>sar&agrave; il centro di gravit&agrave; del frusto.<emph.end type="italics"/></s></p><pb xlink:href="020/01/2801.jpg" pagenum="426"/><p type="main">

<s>Il teorema s'&egrave; veduto gi&agrave; dimostrato dal Torricelli nella IX proposizione <lb/>da noi raccolta nel capitolo V, e il Nardi accennava con queste parole al <lb/>medesimo processo dimostrativo: &ldquo; Difficilissime di gran lunga, fra tutte le <lb/>altre di Archimede, sono le due ultime del secondo libro dei superficiali equi&shy;<lb/>libri (cos&igrave; traduce l'Autore il titolo, a cui comunemente corrisponde quello <lb/><emph type="italics"/>De aequiponderantibus<emph.end type="italics"/>) delle quali la prima serve per lemma della seguente, <lb/>ove s'investiga il centro d'un frusto parabolico, potendosi in altro modo pro&shy;<lb/>porre, e facilissimamente trovare lo stesso quesito, con dire per esempio <lb/>cos&igrave;: D'ogni frusto parabolico il centro di gravit&agrave; sta nell'asse suo collocato <lb/>tra il centro del trapezio in esso descritto, e tra quello delle due parabole <lb/>collaterali in modo, che la distanza del centro del frusto a quella delle pa&shy;<lb/>rabole, alla distanza del centro del frusto a quella del trapezio, sia come il <lb/>trapezio alle parabole. </s>

<s>Il tutto s'intende e si dimostra con ridursi un tratto <lb/><figure id="id.020.01.2801.1.jpg" xlink:href="020/01/2801/1.jpg"/></s></p><p type="caption">

<s>Figura 286.<lb/>alla VIa del primo <emph type="italics"/>Dei superficiali equili&shy;<lb/>brii,<emph.end type="italics"/> come alla fine fa Archimede, e cos&igrave; <lb/>risparmiamo cento sillogismi &rdquo; (ivi, p. </s>

<s>935). </s></p><p type="main">

<s>Passeremo ora al <emph type="italics"/>Centro di gravit&agrave; <lb/>del settore di cerchio,<emph.end type="italics"/> dopo il qual titolo il <lb/>Nardi cos&igrave; soggiunge: <emph type="italics"/>Dell'invenzione mia <lb/>del mezzo per provare tal teorema nel modo <lb/>che segue; Il lettore conoscer&agrave; quanto ab&shy;<lb/>breviato siasi il progresso del p. </s>

<s>Faille.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; TEOREMA VIII. &mdash; <emph type="italics"/>Nel settore AECD<emph.end type="italics"/><lb/>(fig. </s>

<s>286), <emph type="italics"/>o maggiore o minore di un <lb/>niezzo cerchio, sia inscritto il quadrila <lb/>tero ABCD, ed essendo AB, BC lati uguali, <lb/>intendansi dal centro D tirate a que'lati le perpendicolari DF, DG, e si <lb/>congiunga DB. </s>

<s>I centri di gravit&agrave; dei triangoli ABD, BDC siano K, P, i <lb/>quali si connettano con la KP segante BD in L, che sar&agrave; centro del&shy;<lb/><figure id="id.020.01.2801.2.jpg" xlink:href="020/01/2801/2.jpg"/></s></p><p type="caption">

<s>Figura 287.<lb/>l'inscritto quadrilatero. </s>

<s>Dico che <lb/>FD a DL sar&agrave; come AB+BC a <lb/>2/3 AC, sottesa dell'arco ABC. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Perch&egrave; ne'triangoli rettan&shy;<lb/>goli ABE, KDL l'angolo al centro <lb/>KDL &egrave; uguale all'angolo CAB, <lb/>alla periferia insistente sopra dop&shy;<lb/>pio arco. </s>

<s>Dunque KD a DL, come <lb/>AB ad AE; FD a KD, come AE a <lb/>2/3 AE; dunque, per l'ugualit&agrave; per&shy;<lb/>turbata, FD a DL, come AB a 2/3 <lb/>AE, ovvero AB+BC a 2/3 AC. &rdquo; </s></p><p type="main">

<s>&ldquo; TEOREMA IX &mdash; <emph type="italics"/>Stando la <lb/>medesima costruzione, immagi&shy;<lb/>niamoci ne'settori AGBD, BHCD<emph.end type="italics"/> (fig. </s>

<s>287) <emph type="italics"/>i quadrilateri segnati con le<emph.end type="italics"/><pb xlink:href="020/01/2802.jpg" pagenum="427"/><emph type="italics"/>medesime lettere, de'quali siano i centri di gravit&agrave; L, R e si connetta <lb/>LSR, che seghi BD in S, il quale S sar&agrave; centro di gravit&agrave; di tutto il po&shy;<lb/>ligono equilatero inscritto nell'ABCD. </s>

<s>Ad un lato AG sia tirata dal cen&shy;<lb/>tro perpendicolarmente DI. </s>

<s>Dico che DI a DS, &egrave; come l'aggregato de'lati <lb/>del poligono a 2/3 AC. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Imperocch&egrave; AG+GB a 2/3 AB &egrave; come ID a DL, per l'antecedente. </s>

<s><lb/>LD a DS come 2/3 AB a 2/3 AE, per la similitudine dei triangoli ABE, SLD, <lb/>essendo LDS al centro insistente alla met&agrave; dell'arco AB, ovvero BC; e gli <lb/>angoli ad E, S retti. </s>

<s>Adunque, per l'ugualit&agrave; di ragione, ID a DS, come <lb/>AG+GB a 2/3 AE, ovvero AG+GB+BH+HC a 2/3 AC, che sono i <lb/>doppi, ond'&egrave; chiaro etc. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Volendo continuare la inscrizione faremo un quadrilatero nel settore <lb/>AMGD, un altro nel GNBD, ove ne resulter&agrave; un poligono di doppi lati, uno <lb/>de'quali pongasi AM. </s>

<s>Per le cose ora dimostrate sar&agrave; la perpendicolare dal <lb/>centro D nel lato AM, alla DLT, supposto che T sia centro del poligono <lb/>inscritto ultimamente in AGBD, come tutti i lati di esso poligono a 2/3 AB. </s>

<s><lb/>Tirando poi da T la TV perpendicolare alla BD, si costituiranno, come sopra, <lb/>i triangoli rettangoli simili ABE, TDV, dal che segue di nuovo TD a DV <lb/>come 2/3 AB a 2/3 AE, o per l'ugualit&agrave; la perpendicolare nel lato AM, alla <lb/>DV, come tutti i lati del detto poligono a 2/3 di AE. E, presi i doppi, come <lb/>tutti i lati del poligono inscritto in ABCD, uno de'quali AM, a 2/3 AC. </s>

<s>E cos&igrave; <lb/>continueremo l'inscrizione in infinito, essendo sempre vero che il perimetro <lb/>del poligono, inscritto nel settore nel modo suddetto, a due terzi della sut&shy;<lb/>tesa AC, sia come la perpendicolare del centro di un lato alla distanza dal <lb/>centro di gravit&agrave; del poligono dal centro del cerchio. </s>

<s>Il che etc. </s>

<s>Ma ad ogni <lb/>poligono regolare simile ai suddetti si puote circoscrivere un settore di cer&shy;<lb/>chio; adunque sar&agrave; generalmente conchiuso in ogni poligono, e quindi si passa <lb/>al settore. </s>

<s>Avvertisco poi come la mia invenzione di tal mezzo si faciliti nelle <lb/>prove dal p. </s>

<s>Ricci &rdquo; (ivi, pag. </s>

<s>1003-5). </s></p><p type="main">

<s>A dimostrare il centro di gravit&agrave; del settore, ch'era l'intento princi&shy;<lb/>pale, si passa dunque secondo il Nardi per corollario dai teoremi precedenti, <lb/>e specialmente dall'ultimo, perch&egrave;, continuata l'inscrizione all'infinito, i lati <lb/>del poligono si confondono con l'arco, e il cateto uguaglia il raggio, con cui <lb/>l'arco stesso &egrave; stato descritto. </s>

<s>Di qui &egrave; che il centro di gravit&agrave; viene in que&shy;<lb/>sto caso indicato dall'estremo punto di una linea, che muova dal centro del <lb/>circolo, e che sia quarta proporzionale dopo l'arco, i due terzi della corda <lb/>che lo sottende, e il'raggio. </s></p><p type="main">

<s>Se il Ricci facilit&ograve; anche di pi&ugrave; la prova del mezzo usato dal Nardi, <lb/>s'intende quanto si rimanessero i due amici superiori al Torricelli, il quale <lb/>non riusc&igrave; ad abbreviare il Della Faille, se non che anch'egli scrivendo, per <lb/>il baricentrico del settor circolare, quasi un libro. </s>

<s>N&egrave; punto inferiori si ri&shy;<lb/>masero i due detti al valoroso emulo loro, quando vennero insieme con lui <lb/>al cimento di ritrovare il centro di gravit&agrave; del settore sferico. </s></p><p type="main">

<s>&ldquo; Nell'aver fatto trascrivere le opere mie (tale avvertenza premette il <pb xlink:href="020/01/2803.jpg" pagenum="428"/>Nardi alla sua dimostrazione) occorse che ultimamente si perdesse un qua&shy;<lb/>derno di molta importanza, in riguardo di esse, imperocch&egrave; contenevasi in <lb/>quello il meglio delle mie geometriche contemplazioni, delle quali nemmeno, <lb/>il che importa, copia ritenuto m'avea. </s>

<s>La memoria per alquanto m'&egrave; ser&shy;<lb/>vita, ma non il tempo, sicch&egrave;, per ristorarne i danni, mi &egrave; stato di sommo <lb/>aiuto il signor M. A. Bicci, gentiluomo mio amicissimo, e col quale comu&shy;<lb/>nico da alquanto tempo in qua, cio&egrave; da che conosco un giovane di cos&igrave; alto <lb/>intelletto, le debolezze de'miei discorsi. </s>

<s>Egli non solo ha supplito al bisogno <lb/>mio, ma anche, pi&ugrave; sottilmente e copiosamente di quel che fatto avevomi, <lb/>ha ristorato ogni perdita, e da vantaggio altre sue nobilissime contemplazioni <lb/>ha aggiunto alla mia selva, di che a luogo per luogo faccio menzione. </s>

<s>Fuor <lb/>di modo poi me li conosco obbligato, per la dimostrazione rinvenuta di que&shy;<lb/>sto mio, forse non volgare, teorema. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Definizioni.<emph.end type="italics"/> &mdash; I. </s>

<s>Sotto il nome di <emph type="italics"/>cilindrico<emph.end type="italics"/> e di <emph type="italics"/>conico<emph.end type="italics"/> intendo di <lb/>comprendervi il cilindro e la porzione cilindrica, il cono e la porzione conica. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; II. </s>

<s>Segandosi una sfera o sferoide con piano eretto all'asse, l'una e <lb/>l'altra delle due parti fatte io chiamo assolutamente <emph type="italics"/>segamento,<emph.end type="italics"/> di cui sar&agrave; <lb/>base un cerchio o un ellisse. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; III. </s>

<s>Per <emph type="italics"/>solido settore<emph.end type="italics"/> intendo un segamento maggiore o minore del&shy;<lb/>l'emisfero o emisferoide, insieme con un conico, ovvero toltone un conico, <lb/>quando il segamento &egrave; maggiore, la cui cima sia nel centro di essa sfera o <lb/>sferoide, e la base sia quella stessa del segamento, e questo segamento si <lb/>dir&agrave; segamento del settore. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma geometrico.<emph.end type="italics"/> &mdash; Espongasi un solido settore HABCKD (fig. </s>

<s>288), <lb/>ossia il suo segamento minore o maggiore di una mezza sfera, intorno l'asse <lb/><figure id="id.020.01.2803.1.jpg" xlink:href="020/01/2803/1.jpg"/></s></p><p type="caption">

<s>Figura 288.<lb/>BF, ovvero BDF, il quale asse, prodotto <lb/>nel primo caso fino al centro della sfera <lb/>o sferoide in D, sia segato in F dalla base <lb/>del detto segamento: Dico che il settor so&shy;<lb/>lido, al residuo AHDKC, sar&agrave; in ragione <lb/>di BF ad FD. &rdquo; </s></p><p type="main">

<s>&ldquo; Intendasi descritto il cilindro AE <lb/>intorno il segamento ABC, ed intorno il <lb/>segamento del settore il cilindrico GE, con <lb/>simile ed egual base, ed intorno il mede&shy;<lb/>simo asse con l'AE. </s>

<s>Immaginiamoci in&shy;<lb/>torno DF come asse tre conici, col vertice <lb/>D e la base nel piano GFI. </s>

<s>Il cerchio o <lb/>ellisse base del primo abbia per diametro GI, il secondo HK, il terzo una <lb/>retta che pareggi di quadrato l'eccesso del quadrato GI sopra il quadrato <lb/>HK. </s>

<s>In riguardo per&ograve; dell'ellisse bisogner&agrave; che i diametri siano omologhi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, dei tre conici suddetti, il secondo e il terzo insieme presi s'ag&shy;<lb/>guagliano al primo, per l'egualit&agrave; delle basi e delle altezze; ma il terzo <lb/>conico &egrave; uguale al cilindrico AI, senza la porzione AHFKC, per la XIVa del <pb xlink:href="020/01/2804.jpg" pagenum="429"/>terzo di Luca Valerio. </s>

<s>Adunque il cilindrico AI, senza la detta porzione, preso <lb/>insieme col secondo conico HDK, &egrave; uguale al primo conico, e conseguente&shy;<lb/>mente un terzo del cilindrico AI intero, del quale sar&agrave; due terzi la residua <lb/>porzione AHDKC e questa residua porzione sar&agrave; doppia del primo conico. </s>

<s><lb/>Adunque, essendo il cilindrico AE, al segamento ABC, come il cilindrico AI, <lb/>alla residua porzione AHDKC, cio&egrave; in ragion sesquialtera; segue, per la XIX <lb/>del Quinto, nel primo caso, e per la XII nel secondo caso, che nella mede&shy;<lb/>sima ragione sia il cilindrico GE al solido settore, cio&egrave; in ragion sesquial&shy;<lb/>tera. </s>

<s>E finalmente, permutando e convertendo, il cilindrico GE, al cilindrico <lb/>AI, cio&egrave; l'asse BF all'asse FD, come il solido settore alla residua porzione <lb/>AHDKC. </s>

<s>Il che etc. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; TEOREMA X. &mdash; Nella medesima figura dividasi DF nel mezzo in L, <lb/>ed LF nel mezzo in O, che DO sia tripla di OF. </s>

<s>Sar&agrave; L centro di gravit&agrave; <lb/>del cilindrico AI, ed O del secondo conico HDK, ed anco del cilindrico AI, <lb/>senza la porzione AHKC, secondo che dimostra Luca Valerio nel libro citato, <lb/>alla proposizion XXVII. </s>

<s>Facciasi LN, che sia met&agrave; di LO. </s>

<s>Siccome il secondo <lb/>conico, insieme col cilindrico AI senza la porzione AHKC, &egrave; met&agrave; della re&shy;<lb/>sidua porzione AHDKC, per le cose dimostrate nell'antecedente lemma; sar&agrave;, <lb/>per la ragion reciproca dei pesi con le distanze LN, LO, N centro di gra&shy;<lb/>vit&agrave; della suddetta porzion residua AHDKC. </s>

<s>E supponendo DF esser otto, <lb/>sar&agrave; LO due, LN uno, FN cinque, ed ND tre. </s>

<s>Per la qual cosa N divide <lb/>l'asse DF in ragione di cinque a tre. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; TEOREMA XI. &mdash; Espongasi il sopra detto settore HBKD, e tutto il <lb/>resto della figura, lasciando per&ograve; i cilindrici e le divisioni fatte in L ed O. </s>

<s><lb/>Prendasi PD tre ottavi della BD, e saranno P ed N i centri di gravit&agrave; del <lb/>segamento ABC, e della residua porzione AHDKC. </s>

<s>Nel primo caso facciasi <lb/>NP a PQ come BF a FD, cio&egrave; come il solido settore alla detta residua por&shy;<lb/>zione, reciprocamente, e sar&agrave; Q centro di gravit&agrave; del settore. </s>

<s>Nel secondo <lb/>caso, dividasi PN in Q, che NQ a PQ sia come BD a FB, ovvero, come il <lb/>segamento ABC alla residua porzione AHDKC, e similmente Q sar&agrave; centro <lb/>di gravit&agrave; del settore, com'&egrave; manifesto. </s>

<s>Dico che, prendendosi tre ottavi del <lb/>semidiametro BD, e tre ottavi della parte FD, l'aggregato loro nel primo <lb/>caso, o la differenza nel secondo caso, sar&agrave; uguale alla distanza DQ, cio&egrave; del <lb/>centro di gravit&agrave; del settore dal centro della sfera o sferoide. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Imperocch&egrave;, essendo PB le medesime parti di BD, che DN di DF, <lb/>sar&agrave; permutando BD a DF, come PB a DN. </s>

<s>E dividendo nel primo caso, <lb/>componendo nel secondo, BF a FD, ovvero NP a PQ, come la medesima NP <lb/>a ND. </s>

<s>Adunque PQ &egrave; uguale a ND, e per&ograve; DQ sar&agrave; uguale nel primo caso <lb/>a DP+DN, cio&egrave; a 3/8 di BD+3/8 di FD, e nel secondo caso a DP&mdash;DN, <lb/>cio&egrave; a 3/8 di BD&mdash;3/8 di FD, il che etc. </s>

<s>Quindi verremo alla dimostrazione <lb/>del proposto &rdquo; </s></p><p type="main">

<s>&ldquo; TEOREMA XII. &mdash; Sia nella medesima figura il settor di sfera HBKD, <lb/>il cui centro di gravit&agrave; il punto Q, il centro della sfera D, l'asse BE, la su&shy;<lb/>perficie sferica del settore HBK. </s>

<s>Tirisi la retta HB, e sar&agrave; il quadrato di HB, <pb xlink:href="020/01/2805.jpg" pagenum="430"/>al quadrato di HF, o il rettangolo EBF al rettangolo EFB, o la base EB alla <lb/>base EF, per esser comune BF, come la superficie sferica HBK, al cerchio <lb/>del semidiametro HF. </s>

<s>Ma questo cerchio, a tre suoi quarti, &egrave; come EF a tre <lb/>quarti dello stesso EF; adunque, per la eguale, la superficie sferica ABK, a <lb/>tre quarti del cerchio descritto con la distanza HF, &egrave; come la retta EB a tre <lb/>quarti di essa EF. E, presa la met&agrave;, come BD a tre ottavi della stessa FE, <lb/>poich&egrave; un ottavo &egrave; la met&agrave; di un quarto, e tre ottavi la met&agrave; di tre quarti, <lb/>ovvero, nel primo caso, 3/8 di ED+DF, cio&egrave; 3/8 di ED+3/8 di EF; e nel <lb/>secondo caso, 3/8 di ED&mdash;DF, ovvero 3/8 di ED&mdash;3/8 di DF. </s>

<s>Ma tale an&shy;<lb/>cora &egrave; BQ, per le cose dette, adunque la superficie sferica HBK, a tre quarti <lb/>del cerchio descritto dal semidiametro HF, sar&agrave; come BD a DQ, il che etc. </s>

<s>&rdquo; <lb/>(ivi, pag. </s>

<s>372-76). </s></p><p type="main">

<s>Della conclusione, appena ritrovatasi, dette il Nardi notizia al Torricelli, <lb/>il quale cos&igrave; scriveva in un poscritto di lettera indirizzata il d&igrave; 7 Marzo 1640 <lb/>al Cavalieri: &ldquo; Il signor Antonio Nardi mi avvisa di aver dimostrato il cen&shy;<lb/>tro di gravit&agrave; del settore solido di sfera, con conclusione pi&ugrave; bella della mia, <lb/>ed &egrave; questa: <emph type="italics"/>Facciasi come la superficie sferica del settore alli tre quarti <lb/>del cerchio sua base, cos&igrave; il semidiametro ad un'altra da prendersi dal <lb/>centro della sfera, che quel punto sar&agrave; centro,<emph.end type="italics"/> ed &egrave; verissima e concorda <lb/>con la mia &rdquo; (MSS. Gal. </s>

<s>Dis., T. XL, fol. </s>

<s>125). </s></p><p type="main">

<s>Smarritesi poi le carte, dove il Nardi aveva disteso quel suo teorema, e <lb/>volendo anche questo, come uno de'pi&ugrave; importanti, inserire nelle <emph type="italics"/>Ricercate <lb/>geometriche,<emph.end type="italics"/> vi suppli il Ricci, che, mettendosi a ricercare i centri di gra&shy;<lb/>vit&agrave; nel settor circolare e nello sferico, era con grandissima facilit&agrave; riuscito <lb/>alle medesime conclusioni. </s>

<s>Sulla fine del 1645, nel mandare esso Ricci, per&shy;<lb/>ch&egrave; fossero stampati nelle dette Ricercate, i suoi teoremi baricentrici; ne <lb/>dava compiacentesi avviso al Torricelli, che rispondeva cos&igrave; da Firenze, il d&igrave; <lb/>due di dicembre: </s></p><p type="main">

<s>&ldquo; Mi rallegro che con tanta facilit&agrave; abbia trovato i centri di gravit&agrave; delle <lb/>parti del cerchio e della sfera: taccio l'ellissi e la sferoide, perch&egrave; vanno <lb/>sotto la medesima invenzione. </s>

<s>Non so se ella vedesse certi fogliacci, che io, <lb/>gi&agrave; sono due anni, mandai al signor Raffaello (Magiotti). Dimostravo il cen&shy;<lb/>tro di gravit&agrave; nel settore del cerchio in due modi, e brevemente, cio&egrave; <emph type="italics"/>more <lb/>veterum,<emph.end type="italics"/> e per gl'indivisibili. </s>

<s>Quanto al centro di gravit&agrave; del settore di sfera, <lb/>mi scrisse il signor Antonio Nardi di Arezzo di averlo mostrato, e annun&shy;<lb/>ziato come fa V. S. </s>

<s>Io gli risposi di averlo mostrato e annunziato in un altro <lb/>modo, cio&egrave; che sia nell'asse del settore lontano dal centro della sfera per tre <lb/>quarti dell'asse del cono, e tre ottavi della saetta del segmento. </s>

<s>V. S. intende <lb/>gi&agrave; che il settore &egrave; composto di un cono, e di un segmento. </s>

<s>La medesima <lb/>enunciazione credo che mi paresse adattarla anco alla sferoide, ma ora ho <lb/>la testa lontanissima da simili cose. </s>

<s>Dimostrai la concordanza tra la propo&shy;<lb/>sizione del signor Nardi e la mia, e devo averla in scritto &rdquo; (ivi, fol. </s>

<s>101). </s></p><p type="main">

<s>Noi infatti abbiamo ritrovato cotesto scritto, in cui le due apparentemente <lb/>diverse indicazioni del centro di gravit&agrave; del settore sferico si conciliano fa-<pb xlink:href="020/01/2806.jpg" pagenum="431"/>cilmente insieme, con questo discorso, riducendoci la figura 289 sott'occhio. </s>

<s><lb/>Posto che sia il centro di gravit&agrave; del settore ABCD collocato in F, mezzo <lb/>della saetta BE, a una distanza X dal centro della figura, il Torricelli d&agrave; <lb/>X=3/4 DF, e il Nardi X=3<foreign lang="greek">p</foreign>AE2.BD/4.ABC, ond'&egrave; che la ragion della con&shy;<lb/>cordanza si riduce a dimostrare che <foreign lang="greek">p</foreign>AE2.BD/ABC &egrave; uguale a DF. </s>

<s>La dimo&shy;<lb/>strazione poi &egrave; assai facile, perch&egrave; BD:DF=2BD:2DF=BG:GE= <lb/><figure id="id.020.01.2806.1.jpg" xlink:href="020/01/2806/1.jpg"/></s></p><p type="caption">

<s>Figura 289.<lb/><foreign lang="greek">p</foreign>BG.BE:<foreign lang="greek">p</foreign>GE.BE. </s>

<s>Ma il primo termine di <lb/>quest'ultima ragione &egrave; uguale alla callotta ABC, e il <lb/>secondo al circolo di raggio AE; dunque BD:DF= <lb/>ABC:<foreign lang="greek">p</foreign>AE2, d'onde DF=<foreign lang="greek">p</foreign>AE2.BD/ABC, come in <lb/>sostanza scrisse cos&igrave; di aver ritrovato il Torricelli <lb/>stesso, bench&egrave; con altre parole: </s></p><p type="main">

<s>&ldquo; Sia il settore ABCD, e divisa BE bifariam <lb/>in F, sar&agrave; il centro di gravit&agrave; nelli tre quarti di <lb/>DF (ait Torricellius). &rdquo; </s></p><p type="main">

<s>&ldquo; Facciasi come la superficie ABC, alli tre <lb/>quarti del cerchio AC, cos&igrave; BD ad un'altra, da <lb/>pigliarsi dal centro: il termine di questa sar&agrave; centro (ait Nardius). &rdquo; </s></p><p type="main">

<s>&ldquo; Congiungansi AB, AG. </s>

<s>E perch&egrave; tutta GB, a tutta BD, sta come la <lb/>levata EB, alla levata BF; sar&agrave; la rimanente GE, alla rimanente DF, come <lb/>tutta a tutta, cio&egrave; doppia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Jam BD ad DF est ut, sumptis duplis, BG ad GE, sive, ut quadra&shy;<lb/>tum BG ad GA, sive ut quadratum BA ad AE, sive, ut superficies ABC ad <lb/>circulum AC. </s>

<s>Sumptis vero consequentium subsesquitertiis, erit ut BD ad <lb/>rectam Torricellii, ita superficies ABC ad 3/4 circuli AC. </s>

<s>Eadem ergo est recta <lb/>Torricellii cum recta Nardii &rdquo; (MSS. Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>96). </s></p><p type="main">

<s>Apparisce dalle cose fin qui esposte che, mentre si credeva di dare i <lb/>teoremi baricentrici del Nardi, abbiamo dati anche insieme quelli del Ricci, <lb/>quasi in una mente sola, come in un sol cuore, si fossero trasfusi i due <lb/>amici. </s>

<s>Essi perci&ograve; fra i promotori della Scienza meccanica non vogliono es&shy;<lb/>sere separati fra loro, come non vogliono essere separati dal Torricelli, in&shy;<lb/>sieme col quale compongono quel triumvirato glorioso, che la nostra Storia <lb/>ha collocato nel suo proprio seggio. </s>

<s>Intorno al Ricci sono state le notizie pi&ugrave; <lb/>scarse che intorno agli altri due, perch&egrave;, non essendo suo fine di stampare, <lb/>protestava <emph type="italics"/>di disprezzare le sue speculazioni come in s&egrave; stesse di nulla <lb/>estimazione, e di non scriverne se non che qualcuna, per mantenere il. </s>

<s><lb/>commercio col Torricelli.<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>60). </s></p><p type="main">

<s>Son fra queste speculazioni notabili, per il presente nostro argomento, <lb/>le considerazioni intorno i frusti conoidali segati con due piani paralleli, com&shy;<lb/>prendendosi dal Ricci, sotto una sola universalissima, varie proposizioni dello <lb/>stesso Torricelli. </s>

<s>Sia richiesto il centro di gravit&agrave; del frusto AKBCD (fig. </s>

<s>290) <pb xlink:href="020/01/2807.jpg" pagenum="432"/>intero, o scavato dal cono AHD. </s>

<s>Per risolvere il problema, il metodo era <lb/>quello di dimostrare qual proporzione abbia il tutto verso la parte, ossia il <lb/><figure id="id.020.01.2807.1.jpg" xlink:href="020/01/2807/1.jpg"/></s></p><p type="caption">

<s>Figura 290.<lb/>frusto verso il cono inscritto: proporzione, <lb/>che il Ricci annunziava in questa forma: <lb/>&ldquo; In detto frusto intendasi il frusto conico, <lb/>ovvero di porzione conica ABCD, il cui asse <lb/>HE sia diviso nel mezzo dall'applicata KL, <lb/>e la MI sia differenza delle rette AE, GI. </s>

<s><lb/>Dico il frusto AKBCD, al suo cono inscritto <lb/>AHD, essere in proporzione di due quadrati KI ed un quadrato GI col qua&shy;<lb/>drato MI, al quadrato AE &rdquo; (ivi, T. XLII, fol. </s>

<s>29). </s></p><p type="main">

<s>Suppone il Ricci, per dimostrare che il suo teorema &egrave; veramente con&shy;<lb/>cluso nella formula esposta, due proposizioni, la prima delle quali &egrave; che il <lb/>residuo del frusto AKBCD, toltone il frusto conico, sia verso il cono AHD <lb/>come due rettangoli KGL al quadrato di AE: e la seconda, che il frusto <lb/>ABCD, al cono AHD, stia come i quadrati di AE, BH con un medio tra loro, <lb/>al quadrato di AE. </s>

<s>Riconosce della prima proposizione autore il Torricelli, <lb/>se non che, invece di ridurre il solido annulare, descritto dal bilineo AKB <lb/>intorno all'asse, a uno sferoide, ci&ograve; che suppone la notizia de'solidi sferali, <lb/>per non uscir dalle dottrine dei Conici, pens&ograve; il Ricci di ridurre il detto so&shy;<lb/>lido annulare a un cilindro come RQ (fig. </s>

<s>291), il quale, avendo pari altezza <lb/><figure id="id.020.01.2807.2.jpg" xlink:href="020/01/2807/2.jpg"/></s></p><p type="caption">

<s>Figura 291.<lb/>a quella del frusto, e per base un circolo di raggio RE, o TI <lb/>a mezzo l'asse, il quadrato del quale uguagli il rettangolo <lb/>KGL; fosse scavato dai due coni PIQ, RIS. </s>

<s>La proporzione <lb/>del resto fra il solido annulare e il cono AHD riman tut&shy;<lb/>tavia quella del doppio rettangolo KGL, al quadrato di AE, <lb/>data dal Torricelli, perch&egrave;, chiamato S quel solido, e C il <lb/>cono, essendo S=<foreign lang="greek">p</foreign>TI2.EH&mdash;<foreign lang="greek">p</foreign>TI2.EH/3=2/3<foreign lang="greek">p</foreign>XGL.EH, <lb/>e C=<foreign lang="greek">p</foreign>AE2.EH/3, abbiamo S:C=2KGL:AE2. </s></p><p type="main">

<s>L'altra proposizione poi, che risolve il frusto conico in tre coni, rite&shy;<lb/>neva, com'era giusto, il Ricci per sua, sapendo di averla egli il primo co&shy;<lb/>municata al Torricelli, bench&egrave; questi poi la dimostrasse di sua propria indu&shy;<lb/>stria, riducendo ad uno sferoide il terzo cono proporzionale, come si vide <lb/>nell'ordinare la proposizione XLVI, qui addietro, nel capitolo quinto. </s>

<s>Cos&igrave; <lb/>essendo, premettiamo per maggiore intelligenza gli argomenti analitici alla <lb/>fedel trascrizione del proposto teorema universale dei conoidali. </s></p><p type="main">

<s>Son date le due equazioni AKBCD&mdash;ABCD:AHD=2KGL:AE2; <lb/>ABCD:AHD=AE2+F2+BH2:AE2, intendendosi per F2 il medio <lb/>proporzionale fra AE2, BH2. </s>

<s>Conseguono da queste due le tre seguenti: </s></p><p type="main">

<s><emph type="center"/>AKBCD&mdash;ABCD:ABCD=2KGL:AE2+F2+BH2; <lb/>AKBCD:ABCD=2KGL+AE2+F2+BH2:AE2+F2+BH2; <lb/>AKBCD:AHD=2KGL+AE2+F2+BH2:AE2.<emph.end type="center"/></s></p><pb xlink:href="020/01/2808.jpg" pagenum="433"/><p type="main">

<s>Facciansi NE, OE uguali alle rette GI, BH. </s>

<s>Avremo AE+BH=2GI= <lb/>2NE, d'onde AE=2NE&mdash;BH=2NE&mdash;OE, ossia AE&mdash;NE=NE&mdash;OE, <lb/>e in conclusione AN=NO. </s></p><p type="main">

<s>AE2=(AN+NE)2=AN2+2ANE+NE2; OE2=(NE&mdash;NO)2= <lb/>NE2&mdash;2ENO+NO2. </s>

<s>Sommando queste due equazioni, e sostituendo AN <lb/>a NO, avremo AE2+OE2=2NE2+2AN2=AE2+BH2. </s></p><p type="main">

<s>F2=AE.BH=AEO, e perci&ograve; F2+AN2=AEO+AN2=NE2. </s>

<s><lb/>Dunque AE2+BH2+F2=3NE2+AN2+AN2+F2=3NE2+AN2= <lb/>3NE+MI2. </s></p><p type="main">

<s>E in ultimo, 2KGL+AE2+BH2+F2=2KGL+3NE2+MI2= <lb/>2(KI2&mdash;IG2)+3IG2+MI2=2KI2+IG2+MI2. </s></p><p type="main">

<s>&ldquo; Sia il quadrato di F (per dar la dimostrazione con le parole proprie <lb/>del Ricci) medio proporzionale tra li quadrati AE, BH. </s>

<s>E perch&egrave; il frusto <lb/>AKBCD, toltone il frusto ABCD, al cono AHD sta come due rettangoli KGL, <lb/>al quadrato AE, e il frusto ABCD, al cono medesimo, come li tre quadrati <lb/>AE, F, BH al medesimo quadrato AE; dunque tutto il frusto AKBCD, al <lb/>cono AHD, &egrave; come due rettangoli KGL, con li quadrati AE, F, BH, al qua&shy;<lb/>drato AE. &rdquo; </s></p><p type="main">

<s>&ldquo; Ora, per ridurli alli termini detti nella proposizione, facciansi NE, OE <lb/>uguali alle rette GI, BH. </s>

<s>Saranno gli eccessi AN, NO uguali, e perci&ograve; li qua&shy;<lb/>drati AE, OE, insieme, uguali a due quadrati NE e due quadrati NA, per <lb/>la X del Secondo. </s>

<s>Inoltre, essendo li quadrati AE, F, RH proporzionali, sa&shy;<lb/>ranno anche i lati, e il quadrato della media F, uguale al rettangolo AEO, <lb/>giuntovi uno de'quadrati NA, ovvero NO, doventer&agrave; uguale al quadrato NE. </s>

<s><lb/>Sicch&egrave; ridotti sono li tre quadrati AE, F, BH a tre quadrati NE ed uno AN, <lb/>ovvero MI. </s>

<s>E congiunti con li due rettangoli KGL, averemo due quadrati KI, <lb/>un quadrato GI, ed uno MI (in luogo di due rettangoli KGL, e dei tre qua&shy;<lb/>drati AB, F, BH) al quadrato AE, in proporzione medesima che il frusto <lb/>AKBCD al cono AHD, <emph type="italics"/>quod proponebatur. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Che il residuo del frusto AKBCD, toltone il frusto conico, sia verso <lb/>il cono AHD come due rettangoli KGL al quadrato AE, suppongo dimostrato <lb/>da V. S. (cio&egrave; dal Torricelli a cui si rivolge il discorso) molto egregiamente, <lb/>e la maniera mia poco varia, avendolo io dimostrato uguale al qui descritto <lb/>cilindro intorno l'asse stesso del frusto, e che il suo quadrato TI sia uguale <lb/>al rettangolo KGL; al cilindro dico, toltine li coni PIQ, RIS, e mi vaglio <lb/>della medesima proposizione presa dai Conici. </s>

<s>Che poi il frusto ABCD, al <lb/>cono AHD, stia come que'tre quadrati al quadrato AE, il raccolgo da una <lb/>proposizione mia altre volte accennata a V. S., che un tal frusto sia uguale <lb/>a tre coni, con l'altezza HE, e sopra i cerchi descritti dagl'intervalli AE, <lb/>F, BH &rdquo; (ivi, fol. </s>

<s>30, 31). </s></p><p type="main">

<s>Queste ultime parole destarono nell'animo del Torricelli un sentimento, <lb/>che si direbbe di gelosia, non quale per&ograve; &egrave; generata dall'impotenza, ma dalla <lb/>prepotenza. </s>

<s>Contenne per allora in silenzio i primi moti della sua passione, <lb/>ma quando il Ricci impaziente torn&ograve; una settimana dopo a scrivere in una <pb xlink:href="020/01/2809.jpg" pagenum="434"/>lettera queste parole: <emph type="italics"/>un'altra volta la pregher&ograve; a voler vedere una mia <lb/>proposizione intorno li frusti parabolici, iperbolici, sferici, compresi sotto <lb/>una sola proposizione<emph.end type="italics"/> (ivi, fol. </s>

<s>27); il Torricelli risoluto rispose che anzi <lb/>quella universale proposizione era sua, e non poteva patire che nessun altro <lb/>se la fosse appropriata. </s>

<s>S'&egrave; veduto quanto equamente avesse nella prima let&shy;<lb/>tera il Ricci distribuite le parti del merito, e perch&egrave; di esse non ne toccava al&shy;<lb/>trui che le secondarie, rimanendo le principali per s&egrave;; con buon diritto po&shy;<lb/>teva chiamar sua la proposizione delle conoidali. </s>

<s>Facile nonostante a cedere, <lb/>e disposto a riversare nel pingue erario del Torricelli anche questa moneta <lb/>ingiusta, presa occasione da altre cose, che aveva a dire, cos&igrave; soggiungeva: </s></p><p type="main">

<s>&ldquo; Passo all'altra lettera, per la quale pare che V. S. mi accenni di so&shy;<lb/>spettare un poco che io voglia attribuirmi l'invenzione di cotesta sua pro&shy;<lb/>posizione dei solidi conoidali. </s>

<s>Non piaccia a Dio che io faccia mai simile <lb/>azione. </s>

<s>Si ricordi pure V. S. di una lettera, che io le scrissi molte setti&shy;<lb/>mane sono, dove le dicevo di aver considerato che il modo usato da V. S. <lb/>per li frusti sferici poteva portarsi in modo pi&ugrave; generale: intendo quanto alla <lb/>sfera scavata dal cono e dal cilindro. </s>

<s>Secondariamente dissi a V. S. che, <lb/>dovendo un tal solido escavato essere uguale ad una tale sferoide, non po&shy;<lb/>teva servire alla proposizion generale, nella quale si cercasse la proporzione <lb/>di sfera, sferoide, conoide etc. </s>

<s>al cono inscritto, poich&egrave; bisognava supporre <lb/>come noto la sferoide essere doppia del rombo inscrittole. </s>

<s>Ed a questo pre&shy;<lb/>tesi poi di ovviare io con dimostrare que'solidi uguali ad un cilindro, con <lb/>le determinazioni gi&agrave; avvisatele nell'ultima mia. </s>

<s>Si tolga dunque dall'animo <lb/>tali pensieri. </s>

<s>Che se mai avessi neppur ombra che V. S. mi tenesse in con&shy;<lb/>cetto di arrogarmi nemmeno un ette d'altrui, vorrei imporre alli miei stu&shy;<lb/>dii perpetuo silenzio, poich&egrave; con essi &egrave; solo il mio fine di spassarmi, e di <lb/>continuare il commercio con V. S., a me senza modo dilettevole..... Roma, <lb/>16 Luglio 1644 &rdquo; (ivi, fol. </s>

<s>36). </s></p><p type="main">

<s>Non abbiamo voluto lasciar l'occasione di rivelar verso i pi&ugrave; cari amici <lb/>quell'animo, il mal abito del quale vedremo esser portato dal Torricelli an&shy;<lb/>che in pubblico, nelle contese ch'egli ebbe con gli stranieri. </s>

<s>Dopo ci&ograve;, ritor&shy;<lb/>nando sopra il nostro sentiero, si dovrebbe per le fatte promesse aggiungere <lb/>la seconda parte di quel trattato dei centri di gravit&agrave;, a cui dette opera il <lb/>Nardi, dicendo com'egli investigasse il centro delle potenze nella sua propria <lb/>Cicloide. </s>

<s>L'ordine cronologico per&ograve;, secondo il quale ha da svolgersi questa <lb/>nobilissima parte della Storia, ci consiglia a non introdurci ancora dietro il <lb/>Nostro nel campo, senza prima riconoscere la cultura, e saggiare i frutti rac&shy;<lb/>coltivi da uno straniero, facendo invece una breve sosta fuor della chiusa <lb/>siepe, in faccia al callare, per osservar gli strumenti che lo dettero aperto. </s></p><p type="main">

<s>Principalissimi fra questi sono il Teorema meccanico universale, ossia la <lb/>Regola centrobarica, e il metodo degl'indivisibili. </s>

<s>Nell'altro Tomo e nel pre&shy;<lb/>sente abbiam veduto come prendesse il Nardi quel primo strumento dalla <lb/>officina guldiniana, e com'ei lo temprasse e affinasse alla fucina della Geo&shy;<lb/>metria, facendo le prime prove delle virt&ugrave; di lui nel baricentro della mezza <pb xlink:href="020/01/2810.jpg" pagenum="435"/>circonferenza. </s>

<s>Quanto al metodo degli indivisibili si lusingava il buon Cava&shy;<lb/>lieri di essere egli stato il primo a insegnarlo, ma il Nardi riconosce di cos&igrave; <lb/>fatte dottrine, che apparvero nuove, pi&ugrave; antichi e autorevoli maestri. </s>

<s>La cosa, <lb/>come s'intende, &egrave; di tale e tanta importanza, da non doversene passare con <lb/>sentenza s&igrave; asciutta. </s></p><p type="main">

<s>La seconda Ricercata geometrica, qual si legge nel manoscritto donato <lb/>alla Biblioteca di Roma, conclude le risposte alle obiezioni contro Archimede <lb/>col pronunziare che queste son nulle, o per lo pi&ugrave; leggere. </s>

<s>Si direbbe no&shy;<lb/>nostante, soggiunge l'Autore, essersi il Siracusano messo a inchieste ardue <lb/>e lubriche, se non si pensasse agl'impulsi ch'egli ebbe, nello speculare e <lb/>nell'inventare, dalle precedenti tradizioni, e al molto aiuto che gli venne <lb/>dall'usare il metodo degli indivisibili, e dal praticar l'esperienze. </s>

<s>A queste, <lb/>risolvendo le questioni accennate da noi nel secondo capitolo della prima <lb/>parte di questa Storia, attribuisce l'invenzione del centro di gravit&agrave; nella <lb/>rettangola conoidale, supposto noto nella IIa del secondo libro <emph type="italics"/>De insiden&shy;<lb/>tibus humido:<emph.end type="italics"/> e a quello, cio&egrave; al metodo degl'indivisibili, il segreto di tante <lb/>geometriche verit&agrave;, da parer quasi rivelazioni di un Nume. </s></p><p type="main">

<s>Da Archimede confessa dunque il Nardi di avere appresa la dottrina del&shy;<lb/>l'infinito, riducendo per essa le quantit&agrave; lineari a tal piccolezza da trasfor&shy;<lb/>mare il curvo nel retto. </s>

<s>Ma delle particolari applicazioni del metodo gli sparse <lb/>nella mente i primi semi una pellegrina dimostrazione di Pappo, chi ripensi <lb/>alla quale sentesi compreso da uno stupore, com'a vedere sotto il sol me&shy;<lb/>ridiano scintillare una stella in mezzo al cielo profondo. </s>

<s>&Egrave; data quella dimo&shy;<lb/>strazione dal Matematico alessandrino nel teorema XXI del quarto libro delle <lb/><emph type="italics"/>Collezioni,<emph.end type="italics"/> per concluderne che lo spazio, compreso tra la spirale e la linea <lb/><figure id="id.020.01.2810.1.jpg" xlink:href="020/01/2810/1.jpg"/></s></p><p type="caption">

<s>Figura 292.<lb/>condotta al centro dal princi&shy;<lb/>pio della circolazione, &egrave; la ter&shy;<lb/>za parte della superficie del <lb/>cerchio. </s></p><p type="main">

<s>Sia lo spazio da misurare <lb/>BEFAB, nella figura 292. Di&shy;<lb/>visa tutta la circonferenza in <lb/>parti uguali, sian due di que&shy;<lb/>ste AC, CD, dalle quali e dalle <lb/>loro concentriche FG, EH sian <lb/>chiusi quattro settori. </s>

<s>Espon&shy;<lb/>gasi anche insieme un rettangolo KL, di cui i lati KP, KN sian divisi in tante <lb/>parti uguali, in quante fu divisa la stessa circonferenza, ed essendo due di <lb/>queste parti KR, RQ sopra l'un lato, KM, MS sopra l'altro; si conducano <lb/>RT, QV parallele a KN, e MZ, SO parallele a KP. </s></p><p type="main">

<s>Per la genesi della spirale archimedea, per supposizione e per costru&shy;<lb/>zione, sar&agrave;, chiamata C la circonferenza, BC:CF=C:CA=KP:KR= <lb/>KL:KZ=RT:RZ. </s>

<s>Dividendo la prima e l'ultima ragione e de'loro ter&shy;<lb/>mini facendo il quadrato, BC2:BF2=RT2:TZ2. </s>

<s>Con simile ragione dimo-<pb xlink:href="020/01/2811.jpg" pagenum="436"/>streremo DB2:BE2=QV2:VO2, e cos&igrave; sar&agrave; vero passando a ricercare le <lb/>altre parti. </s>

<s>Ora essendo ai quadrati de'raggi de'circoli proporzionali i set&shy;<lb/>tori, e ai quadrati de'raggi delle basi proporzionali i cilindri ugualmente alti, <lb/>si potr&agrave; concluderne che ciascun settore circoscritto sta al corrispondente, <lb/>inscritto nella spirale, come ciascun cilindro circoscritto sta all'inscritto nel <lb/>triangolo KNL, rivolgendosi i rettangoli genitori intorno all'asse NL. </s>

<s>E perch&egrave; <lb/>in tutte le proporzionali cos&igrave; dimostrate i primi e i terzi termini sono uguali, <lb/>staranno dunque le somme dei settori ai settori come le somme dei cilindri <lb/>ai cilindri, ossia la superficie del circolo, alla somma dei settori inscritti nella <lb/>spirale, come il cilindro del rettangolo NP, alla somma de'cilindri, de'quali <lb/>si costruisce il conoide gradinato. </s>

<s>Supponendo poi Pappo che sian prese cos&igrave; <lb/>minime le divisioni, da sparire i trilinei FGA, EHF .... e le addentellature <lb/>KMZ, ZXO .... riduce in ultimo la proporzione a dire: <emph type="italics"/>circulum, ad eam <lb/>figuram, quae inter lineam spiralem et rectam AB intercipitur, ita esse <lb/>ut cylindrus ad conum<emph.end type="italics"/> (editio cit., pag. </s>

<s>84) cio&egrave; come tre a uno. </s>

<s>Nella qual <lb/>supposizione vide il Nardi il metodo degl'indivisibili nascosto come in un nido, <lb/>da cui, incubato sotto le ali del suo proprio ingegno, vide con lieta maravi&shy;<lb/>glia uscirne un modo nuovo di quadrar la parabola. </s></p><p type="main">

<s>Sia la mezza figura 293 intorno al diametro AO, e sopra la base OX, <lb/>con la quale e col centro in O sia descritto il quadrante OCX, a cui e alla <lb/>semiparabola circoscrivansi i rettangoli OL, OM. </s>

<s>Presa una minima parte <lb/>AD, si conduca da D una parallela ad AO, e si prolunghi in I. </s>

<s>Dai punti <lb/>poi E, H, ne'quali la detta linea incontra le due curve, si conducano ordinata&shy;<lb/>mente FE, GH. </s>

<s>Avremo OD:OE=DR:RE=AO:RE=OX2:OX.RX= <lb/>OC2:RH2=<foreign lang="greek">p</foreign>OC2:<foreign lang="greek">p</foreign>RH2. </s>

<s>E perci&ograve; OD:OE=<foreign lang="greek">p</foreign>OC2.OR:<foreign lang="greek">p</foreign>RH2.OR. <lb/><figure id="id.020.01.2811.1.jpg" xlink:href="020/01/2811/1.jpg"/></s></p><p type="caption">

<s>Figura 293.<lb/>E cos&igrave; per tutte le altre infinite divisioni saranno simili <lb/>proporzionalit&agrave; fra i rettangoli della figura superiore e i <lb/>cilindri della inferiore, supponendo questa rivolgersi intorno <lb/>alla linea OX come a suo proprio asse. </s>

<s>Ora, osservando <lb/>che in ognuna delle dette proporzionalit&agrave; i primi e i terzi <lb/>termini sono uguali, avremo la somma di tutti i rettangoli, <lb/>ai rettangoli, come la somma di tutti i cilindri ai cilindri; <lb/>ossia il r&egrave;ttangolo OM, alla semiparabola, come il cilindro <lb/>all'emisfero, che vuol dire, come tre a due. </s>

<s>Ma ascoltiamo <lb/>il Nardi, che non solamente discorre cos&igrave;, ma aggiunge altre <lb/>importanti notizie al suo discorso. </s></p><p type="main">

<s>&ldquo; Una pellegrina dimostrazione di Pappo, ove egli, con <lb/>l'aiuto dei solidi e col ridurli occultamente agl'indivisibili, <lb/>prova la ragione del cerchio allo spazio elico, mi diede oc&shy;<lb/>casione, per la conformit&agrave; dei soggetti, di pensar con lo <lb/>stesso metodo alla ragione di un rettilineo alla parabola, il che felicemente <lb/>successemi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia una mezza parabola AXO, di cui il diametro AO, e la mezza base <lb/>OX sia semidiametro d'un cerchio, di cui un quadrante OCB, centro O, e <pb xlink:href="020/01/2812.jpg" pagenum="437"/>il rettangolo OL sia circoscritto ad esso quadrante. </s>

<s>Dividasi ora tanto la retta <lb/>AM, quanto la uguale CL, in parti minime, sicch&egrave;, essendo una di loro AD, <lb/>manchi DM da AM meno di ogni proponibile distanza, e lo stesso avvenga <lb/>di LI rispetto ad LC. &rdquo; </s></p><p type="main">

<s>&ldquo; Ci&ograve; supposto, tirisi DR parallela ad AO, e seghi la curva parabolica <lb/>in E, e sia FE applicata alla mezza parabola. </s>

<s>Lo stesso accada nel rettan&shy;<lb/>golo OL, dove, tirata IR parallela al semidiametro, seghi la periferia nel <lb/>punto H, e quindi nel semidiametro cada la perpendicolare HG. &Egrave; poi vero <lb/>che il parallelogrammo OD, all'altro OE, &egrave; come DR ad RE, o come il qua&shy;<lb/>drato OC al quadrato HR, o come il cilindro CR all'altro HO. Adunque, <lb/>come tutti i minimi rettangoli circoscritti o inscritti nella mezza parabola, ad <lb/>essa mezza parabola; cos&igrave; tutti i minimi cilindri circoscritti o inscritti nel <lb/>quadrante di sfera, ad esso quadrante. </s>

<s>Onde di nuovo sar&agrave; il parallelogrammo <lb/>OM, alla mezza parabola, come il cilindro OL al quadrante di sfera. </s>

<s>&Egrave; poi il <lb/>cilindro sesquialtero del quadrante di sfera; adunque il parallelogrammo sar&agrave; <lb/>sesquialtero della mezza parabola. </s>

<s>E per&ograve;, essendo il triangolo inscritto nella <lb/>mezza parabola tre di quelle parti, delle quali il parallelogrammo OM &egrave; sei, <lb/>e la mezza parabola quattro; sar&agrave; questa sesquiterza del triangolo inscritto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E qui ultimamente ho osservato aver avuto l'occhio il dottissimo Tor&shy;<lb/>ricelli, nel X e XIII modo di quadrar la parabola. </s>

<s>Ma, tornando alla dimo&shy;<lb/>strazione di Pappo, confesso che quella fra le antiche fu la prima, che spar&shy;<lb/>semi nella mente i semi della retta maniera di dimostrare le ragioni del <lb/>curvo e del retto, e della dottrina degl'indivisibili, quale poi da'moderni, e <lb/>in particolare dall'ingegnosissimo p. </s>

<s>Cavalieri, ho veduta coltivata lauta&shy;<lb/>mente &rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>141). </s></p><p type="main">

<s>Avremmo voluto rendere questo documento sopra gli altri anche pi&ugrave; <lb/>cospicuo, a ritirare il dubbio da noi altrove, per insufficiente esame, emesso, <lb/>che cio&egrave; fosse il Nardi non troppo favorevole al metodo cavalierano, mentre <lb/>&egrave; un fatto ch'egli ne aveva prevenuta gi&agrave; l'invenzione. </s>

<s>Non fa perci&ograve; ma&shy;<lb/>raviglia se con tale argomento in mano, aggiuntavi la Regola centrobarica, <lb/>fosse il Nostro in Italia de'primi a penetrare i segreti della Cicloide, aperti <lb/>con argomenti uguali o simili qualche anno prima in Francia. </s>

<s>Ma la sen&shy;<lb/>tenza, che da noi s'anticipa, intorno a una questione delle pi&ugrave; vivamente <lb/>agitate fra i Matematici, dopo la prima met&agrave; del secolo XVII, e che non ha <lb/>avuto fin qui altra regola delle preconcette opinioni in fuori, e dell'amor <lb/>nazionale; vuol essere confermata dai fatti, che sinceramente passeremo a <lb/>narrare dai loro principii. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Le prime dispute insorsero intorno all'inventore della Cicloide, dicen&shy;<lb/>dosi comunemente in Italia essere stato costui Galileo. </s>

<s>E veramente sembre&shy;<lb/>rebbe favorire una tale opinione un documento prezioso, ritrovato da noi in <pb xlink:href="020/01/2813.jpg" pagenum="438"/>alcuni manoscritti, derivati senza dubbio dalla libreria del p. </s>

<s>ab. </s>

<s>Guido Grandi, <lb/>col titolo: <emph type="italics"/>Roba del gran Galileo, in parte copiata dagli originali, e in <lb/>parte dettata da lui cieco a me Vincenzio Viviani, mentre dimoravo nella <lb/>sua casa di Arcetri.<emph.end type="italics"/> Quel documento, che si diceva, &egrave; dettato e scritto in <lb/>dialogo, per inserirsi nella prima giornata delle due Scienze nuove &ldquo; a facce 25 <lb/>(dell'edizione di Leida) dopo le parole che dice il Sagredo <emph type="italics"/>Il negozio &egrave; vera&shy;<lb/>mente molto intrigato .... per&ograve; diteci quel che ne conviene. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Prima per&ograve; di dirvi una mia opinione, non voglio la&shy;<lb/>sciare indietro di proporvi un fatto, che mi occorse a notare, speculando io <lb/>intorno al modo di risolvere, forse pi&ugrave; ragionevolmente di quel che non avesse <lb/>fatto Aristotile, questo problema della ruota veramente ammirando. </s>

<s>Per ri&shy;<lb/>durmi la cosa pi&ugrave; sotto i sensi, e per aiutare la mia immaginazione, feci <lb/>quell'esagono, che vi ho detto, di cartone ben sodo, mettendomi a ruzzolarlo <lb/>lungo una riga, tenuta ferma applicata contro un foglio, sopra il quale due <lb/>punte di spillo, una infissa nel centro del poligono esterno, l'altra nel sog&shy;<lb/>giacente angolo del poligono interno e concentrico, mi avrebbero lasciate <lb/>impresse le vestigie degli archi continui e de'saltuari, dei quali ho discorso. </s>

<s><lb/>Trasformando poi i due esagoni in due cerchi, pur col medesimo centro, per <lb/>ridurmi pi&ugrave; d'appresso alla contemplazione della ruota di Aristotile, mi ven&shy;<lb/>nero messi i due spilli in C e in B (fig. </s>

<s>294), e facendo rivolgere la ruota <lb/><figure id="id.020.01.2813.1.jpg" xlink:href="020/01/2813/1.jpg"/></s></p><p type="caption">

<s>Figura 294.<lb/>sopra la riga BF per una intera circolazione, trovai con una certa maravi&shy;<lb/>glia tracciate sopra il foglio le due curve linee BIF, CHE, quali vedete rap&shy;<lb/>presentate in questa figura. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Elegantissime curve in vero, le quali, insistendo sopra <lb/>due corde di uguale lunghezza, e soprastando ad esse con differente altezza; <lb/>sembra che possano adattarsi alla costruzione dei ponti, ai quali, mantenendo <lb/>la medesima luce, si volesse dare o maggiore o minore il rigoglio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Cos&igrave; parve anche a me, e a proposito del disegno del <lb/>nuovo ponte di Pisa, che si voleva fare di un arco solo, avrei volentieri sug&shy;<lb/>gerito all'architetto una centina di quella figura, che mi aveva tanto bel <lb/>garbo. </s>

<s>Ma le mie speranze erano principalmente rivolte a promovere la scienza, <lb/>ch'era mia professione, perch&egrave; forse, dallo spazio compreso fra l'arco della <pb xlink:href="020/01/2814.jpg" pagenum="439"/>curva e la base, ne sarebbe potuta derivare qualche utile notizia per la tanto <lb/>desiderata misura dello spazio circolare. </s>

<s>Vero &egrave; bene che, partecipando na&shy;<lb/>turalmente ciascun generato delle qualit&agrave; dei generanti, dubitai non fossero <lb/>tra loro le due quantit&agrave; incommensurabili, e fu per questa ragione che, prima <lb/>di applicarmi agl'incerti e faticosi argomenti della Geometria, volli averne <lb/>qualche consiglio con l'esperienza. </s>

<s>Scelsi dunque un cartone, della pi&ugrave; uni&shy;<lb/>forme solidit&agrave; e superficie che mi fosse possibile ritrovare, e di una parte <lb/>di esso incisi, come seppi far meglio, una perfettissima ruota. </s>

<s>Sopra il ri&shy;<lb/>manente poi con esquisito macchinamento, disegnai la curva, a fil della quale <lb/>e della linea, ch'era lungo la sottoposta riga servita di base, diligentemente <lb/>tagliai il cartone. </s>

<s>Avuta in fine una bilancetta da orafi, delle pi&ugrave; esatte e <lb/>gelose, pesai, pi&ugrave; accuratamente che se fossero stati oro o margarite preziose, <lb/>i due incisi cartoni, e poco manc&ograve; che l'uno non fosse il triplo dell'altro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Se fossi stato chiamato io a consulto, quando si posero <lb/>l'origini delle cose, vi confesso, signor Salviati, la mia temerit&agrave;, che avrei <lb/>consigliato la Geometria a fare una tal proporzione esattamente tripla, attem&shy;<lb/>perando all'armonia universale anco questa corda, fin qui rimasta non tocca. </s>

<s><lb/>Ma ditemi, non si potrebbe attribuire la differenza a qualche inesattezza nello <lb/>sperimentare, o non potrebbe dipendere dal non avere scelta conveniente <lb/>materia? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Io usai d'incidere le figure anche sopra lamine di me&shy;<lb/>tallo, ma sempre l'un peso mi riusc&igrave; qualche poco men che triplo dell'altro. </s>

<s><lb/>Se la differenza avesse avuto origine dall'imperfezione della materia, o dal <lb/>poco esatto strumento, o dalla mia propria imperizia nel maneggiarlo, non <lb/>sembra anche a voi che, conseguendo da cos&igrave; fatti inevitabili difetti il dar <lb/>talvolta di meno, non si fosse tal altra dovuto aver qualche cosa pi&ugrave; del <lb/>giusto? </s>

<s>Or perch&egrave; accordarsi perpetuamente in andar nel medesimo eccesso, <lb/>se non per intrinseca natura della cosa, e perch&egrave; insomma le due proposte <lb/>grandezze non hanno fra loro nessuna misura comune? </s>

<s>E cos&igrave;, parendomi <lb/>esser certo, abbandonai l'impresa, che mi s'era prima presentata con spe&shy;<lb/>ranza cos&igrave; lusinghiera. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Se da questa speculazione non pu&ograve; ricavarsi alcun utile <lb/>per la Geometria, come voi dite, la lascieremo anche noi volentieri, per tor&shy;<lb/>nare a pregarvi, signor Salviati, ci diciate quel che convenga a noi di pen&shy;<lb/>sare intorno alla ragione dello scorrere il cerchio minore una linea tanto <lb/>maggiore della sua circonferenza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Io ricorrerei alla considerazione dei poligoni sopra con&shy;<lb/>siderati etc. </s>

<s>&rdquo; </s></p><p type="main">

<s>Quanto &egrave; certo che fu dettato e disteso questo frammento di dialogo sui <lb/>principii dell'anno 1639, altrettanto &egrave; dubbio quando occorresse a osservare <lb/>la Cicloide primaria e la secondaria, tracciate sul foglio dal moto dello stru&shy;<lb/>mento descritto dal Salviati. </s>

<s>Quel che fu detto, essere cio&egrave; stata fatta l'os&shy;<lb/>servazione infino dal 1600, &egrave; una congettura, una reminiscenza, una giacu&shy;<lb/>latoria de pi&ugrave; devoti discepoli di Galileo. </s>

<s>&Egrave; certo altres&igrave; che, sotto il nome <pb xlink:href="020/01/2815.jpg" pagenum="440"/>volgare di <emph type="italics"/>Roulette,<emph.end type="italics"/> si trattava della nuova curva in Parigi, infino dal 1628, <lb/>e il Roberval attesta averne udito ivi parlare al Mersenno come di cosa in&shy;<lb/>torno alla quale, bench&egrave; inutilmente, s'erano da molti anni travagliati gl'in&shy;<lb/>gegni. </s>

<s>Hanno alcuni voluto confermare, dietro questa notizia, l'antichit&agrave; e <lb/>il primato dell'invenzione galileiana, ma come, essendo fra noi rimasta di&shy;<lb/>menticata, pellegrinasse a que'tempi in Francia, e ritrovasse fra gli stranieri <lb/>quell'accoglienza, che non ebbe fra'suoi; secondo l'ordine naturale delle <lb/>cose, non si comprende. </s></p><p type="main">

<s>Ben assai pi&ugrave; conforme a quest'ordine &egrave; il pensare che il caso occorso <lb/>al Salviati fosse occorso tante volte prima a quei Matematici, i quali, non <lb/>avendo altro maestro che Aristotile, e da'libri di lui attingendo i principii <lb/>da risolvere le pi&ugrave; ardue questioni, pensavano di risolvere anche quella della <lb/>quadratura del circolo dallo speculare intorno alla Ruota famosa, e alla linea <lb/>descritta, nel rivolgersi, da un punto fisso della sua circonferenza. </s>

<s>Inutili co&shy;<lb/>nati &egrave; vero, ma da'quali si pu&ograve; argomentare come dovesse ai contemporanei <lb/>di Leonardo da Vinci, del Cardano e del Vieta appresentarsi spontanea, nel <lb/>meditare sopra la XXIV questione meccanica del Filosofo, la curva gentile. <lb/></s>

<s>&Egrave; da ripensare anzi alle occasioni forse pi&ugrave; efficaci e immediate d'incontrarsi <lb/>nella Cicloide, studiando quella meccanica quadratura del circolo, che i Ma&shy;<lb/>tematici infin dal secolo XIV leggevano con tanto gusto in Archimede, quando <lb/>s'incominci&ograve; a divulgare la prima collezione delle opere di lui. </s>

<s>&ldquo; Dal moto <lb/>del carro, scriveva in una sua Nota Leonardo, ci &egrave; sempre stato dimostro <lb/>dirizzare la circonferenza de'cerchi. </s>

<s>La mezza circonferenza della rota, della <lb/>quale la grossezza sia uguale al suo semidiametro, lascia di s&egrave; vestigio eguale <lb/>alla quadratura del suo cerchio &rdquo; (MSS. E, fol. </s>

<s>25 v.). </s></p><p type="main">

<s>Comunque sia, da Galileo in Firenze, e dal Mersenno in Parigi ha i suoi <lb/>principii storici la Cicloide, che per&ograve; non va, n&egrave; all'un celebre uomo n&egrave; <lb/>all'altro, debitrice de'suoi progressi. </s>

<s>Il Francese nonostante, a cui non ne <lb/>venne mai meno la speranza, fu di cos&igrave; fatti progressi assai pi&ugrave; benemerito <lb/>dell'Italiano, che distolse dall'applicarvisi gl'ingegni, reputando la quadra&shy;<lb/>tura della Cicloide problema non men disperato di quell'altro della quadra&shy;<lb/>tura del circolo genitore. </s>

<s>Di qui &egrave; che fu causa l'inganno di Galileo del&shy;<lb/>l'essersi indugiato fra noi a riconoscere il vero una diecina di anni dopo i <lb/>Francesi, come si vedr&agrave; resultare dai fatti, che passiamo a narrare imparziali. </s></p><p type="main">

<s>Egidio Roberval era assai giovane, quando il Mersenno gli propose di <lb/>studiare intorno alle propriet&agrave; della curva, descritta dal rivolgersi della Ruota <lb/>aristotelica, e perci&ograve; difficilissima apparvegli allora la proposta. </s>

<s>Seguitando <lb/>intanto gli amati esercizi, apprese dal divino Archimede quella dottrina del&shy;<lb/>l'infinito, che poi il Cavalieri chiam&ograve; degl'indivisibili, col retto metodo dei <lb/>quali sciolse alcuni de'pi&ugrave; ardui problemi geometrici, qual'era quello di mi&shy;<lb/>surare la superficie conica di uno scaleno. </s>

<s>Erano in questo passati sei anni, <lb/>e il Mersenno torn&ograve; a battere sulla Trochoide, rimproverando il giovane amico <lb/>ch'egli avesse lasciato indietro un cos&igrave; nobile studio, quasi si confessasse <lb/>dalle difficolt&agrave; esser vilmente rimasto atterrito. </s>

<s>&ldquo; Ego sic castigatus, coepi <pb xlink:href="020/01/2816.jpg" pagenum="441"/>sedulo ipsam (trochoidem) inspicere, ac tunc quidem, quae absque indivisi&shy;<lb/>bilibus difficillima visa erat, ipsis opitulantibus nullo negotio patuit &rdquo; (<emph type="italics"/>Ro&shy;<lb/>bervallii epist. </s>

<s>ad Torricellium,<emph.end type="italics"/> Oouvrages cit., pag. </s>

<s>369). </s></p><p type="main">

<s>Le proposizioni, che con l'aiuto degli indivisibili il Roberval dimostr&ograve; <lb/>intorno alla Trocoide, furono lette privatamente in scuola, e comunicate agli <lb/>amici, n&egrave; si resero di pubblica ragione, se non che molto tardi, qua e l&agrave; <lb/>disperse per le Opere, raccolte poi fra le memorie dell'Accademia di Parigi. </s>

<s><lb/>Noi ordineremo quelle proposizioni, con i lemmi, da cui alcune son prece&shy;<lb/>dute, e di molto abbrevieremo il discorso, usando il metodo analitico, e in&shy;<lb/>troducendo il segno &int; nel calcolo delle quantit&agrave; indivisibili, perch&egrave;, non es&shy;<lb/><figure id="id.020.01.2816.1.jpg" xlink:href="020/01/2816/1.jpg"/></s></p><p type="caption">

<s>Figura 295.<lb/>sendo altro esse quantit&agrave; che i <lb/>differenziali dei Matematici mo&shy;<lb/>derni, la loro somma dunque <lb/>corrisponde a una vera e pro&shy;<lb/>pria integrazione. </s></p><p type="main">

<s>&ldquo; PROPOSITIO I. &mdash; <emph type="italics"/>Semi&shy;<lb/>trochoides AFD<emph.end type="italics"/> (fig. </s>

<s>295) <emph type="italics"/>sinus <lb/>versi IL est quadrupla, seu <lb/>diametri IH dupla &rdquo;<emph.end type="italics"/> (De tro&shy;<lb/>choide, Ouvrages cit., pag. </s>

<s>342). </s></p><p type="main">

<s>Conclude il Roberval il suo <lb/>assunto col dimostrar che, presa <lb/>qualsivoglia porzione AF della <lb/>curva, alla quale corrisponda l'arco circolare IMF, essa porzione &egrave; uguale al <lb/>quadruplo del seno verso IQ della met&agrave; IM dell'arco. </s>

<s>Son mezzi della di&shy;<lb/>mostrazione tre principii, il primo geometrico, il secondo meccanico, e il terzo, <lb/>che partecipa dell'uno e dell'altro modo. </s></p><p type="main">

<s>Il primo principio, di cui fa l'Autore frequenti applicazioni, si trova fa&shy;<lb/>cilmente dimostrato nel <emph type="italics"/>Trait&eacute; des indivisibles,<emph.end type="italics"/> ed &egrave; tale: Sia del semicer&shy;<lb/>chio ADB (fig. </s>

<s>296) presa qualunque parte, come per es. </s>

<s>CD o AC: diviso <lb/>l'arco AC ugualmente in E, F, G .... e da ciascun punto della divisione <lb/>abbassati i seni EL, FM, GN .... &ldquo; je dis que la ligne AH est &agrave; la circon&shy;<lb/>ference AC comme tous les sinus ensemble sont &agrave; autant des sinus totaux, <lb/>ou demidiam&egrave;tres &rdquo; (pag. </s>

<s>212). </s></p><p type="main">

<s>Il secondo principio dipende dal metodo di condur le tangenti, applican&shy;<lb/>dovi la regola del parallelogrammo delle forze, a quel modo che vedemmo <lb/><figure id="id.020.01.2816.2.jpg" xlink:href="020/01/2816/2.jpg"/></s></p><p type="caption">

<s>Figura 296.<lb/>nella proposizione V della Meccanica nuova <lb/>del Torricelli. </s>

<s>Secondo questa dottrina si <lb/>trovano in F, nella figura 295, raccolte le <lb/>velocit&agrave; degl'infiniti punti dell'arco IF, e <lb/>della porzion di cicloide AF: velocit&agrave;, che <lb/>resultano delle infinite respettive tangenti. </s>

<s><lb/>E perch&egrave; nei moti equabili le velocit&agrave; son <lb/>proporzionali agli spazi AF, FMI, passati nel <pb xlink:href="020/01/2817.jpg" pagenum="442"/>medesimo tempo &ldquo; ut ergo omnes tangentes curvae AF ad omnes tangentes <lb/>arcus IMF, sic ipsa curva AF ad ipsum arcum IMF (pag. </s>

<s>341). </s></p><p type="main">

<s>A instituire i terzo principio, essendo FG tangente al circolo nel punto <lb/>F, FH tangente alla curva, e perci&ograve; resultante del moto, si conducano il rag&shy;<lb/>gio FL, e la corda FI. </s>

<s>I triangoli simili FGH, FLI danno FH ad FG, come <lb/>IF ad FL. </s>

<s>Se ora intendansi fatte nell'arco IMF, e nella porzione di curva <lb/>AF, le medesime infinite divisioni, e, condotte le medesime infinite tangenti, <lb/>se ne prenda le somme; ne concluderemo, con l'Autore, per terzo principio, <lb/>&ldquo; chordas illas omnes simul sumptas, ad radium FL toties sumptum, sic se <lb/>habere, ut omnes tangentes curvae AF simul, ad omnes tangentes arcus IMF <lb/>simul, hoc est, per secundum notatum, ut curva ipsa AF, ad arcum ipsum <lb/>IMF &rdquo; (pag. </s>

<s>341). </s></p><p type="main">

<s>Premonstrati i quali principii, cos&igrave; facilmente si conduce il Roberval alla <lb/>desiderata conclusione. </s>

<s>Dagli infiniti punti di divisione dell'arco IM, met&agrave; di <lb/>IMF, si conducano sul raggio LI gl'infiniti seni retti corrispondenti, ciascun <lb/>de'quali essendo la met&agrave; della corda, la met&agrave; pure sar&agrave; quella di questa loro <lb/>somma. </s>

<s>Se perci&ograve; si chiamino <emph type="italics"/>s.r<emph.end type="italics"/> i seni retti, <emph type="italics"/>e<emph.end type="italics"/> le corde, e con &int; si signi&shy;<lb/>fichi la loro somma, avremo 2&int;<emph type="italics"/>s.r<emph.end type="italics"/>=&int;c. </s>

<s>E se con &int;<emph type="italics"/>r<emph.end type="italics"/> si rappresenti la <lb/>somma dei raggi, sar&agrave;, per il terzo premesso principio, &int;<emph type="italics"/>c<emph.end type="italics"/>:&int;<emph type="italics"/>r<emph.end type="italics"/>=AF:IMF= <lb/>2&int;<emph type="italics"/>s.r<emph.end type="italics"/>:&int;<emph type="italics"/>r.<emph.end type="italics"/> E perch&egrave;, per il primo degli stessi premessi principii, &int;<emph type="italics"/>s.r<emph.end type="italics"/>:&int;<emph type="italics"/>r<emph.end type="italics"/>= <lb/>IQ:IM, ossia 2&int;<emph type="italics"/>s.r<emph.end type="italics"/>:&int;<emph type="italics"/>r<emph.end type="italics"/>=2IQ:IM; dunque AF:IMF=2IQ:IM= <lb/>4IQ:2IM=4IQ:IMF, ond'&egrave; veramente AF=4Iq. </s></p><p type="main">

<s>Potendosi ora una tale dimostrazione applicare a qualunque punto della <lb/>mezza Cicloide, comunque sia dall'origine A distante, supponiamo che il dato <lb/>punto sia D. </s>

<s>Troveremo ancora, col medesimo processo, AFD=4IL=2IH, <lb/>ci&ograve; che vuol dire essere, cos&igrave; com'era il proposito di dimostrare, la mezza <lb/>Cicloide doppia al diametro del circolo genitore. </s></p><p type="main">

<s><emph type="italics"/>Corollario.<emph.end type="italics"/> &mdash; Diviso l'arco IR nel mezzo in P, come nel mezzo M &egrave; <lb/>stato diviso l'arco IF, e condotte le due corde FP, RM, &egrave; facile vedere che <lb/>queste s'intersecheranno fra loro e col diametro HI nel punto T, in modo <lb/>che sia HF=HT=HI&mdash;IT=HI&mdash;2IQ, d'onde 2HF+4IQ=2HI= <lb/>AFD, essendo la semicicloide, per le cose gi&agrave; dimostrate, uguale al doppio del <lb/>diametro. </s>

<s>E perch'&egrave; stato altres&igrave; dimostrato che la porzione AF &egrave; uguale al <lb/>quadruplo del seno verso IQ, dunque 2HF=AFD&mdash;AF=DF, ci&ograve; che <lb/>vuol dire essere ogni porzione, presa dal vertice, uguale al doppio della tan&shy;<lb/>gente. </s>

<s>Cos&igrave; il Wallis, quell'<emph type="italics"/>Anglus vir doctissimus, qui et praelo per se, <lb/>vel per amicos suo nomine vulgavit<emph.end type="italics"/> (pag. </s>

<s>344), formul&ograve; la seconda parte <lb/>della proposiz. </s>

<s>XXII, nel cap. </s>

<s>V della sua <emph type="italics"/>Mechanica:<emph.end type="italics"/> &ldquo; Curvae semicycloi&shy;<lb/>dis portio quaevis, ad verticem terminata, est dupla subtensae corresponden&shy;<lb/>tis arcus circuli genitoris &rdquo; (Londini 1741, pag. </s>

<s>424). </s></p><p type="main">

<s>&ldquo; PROPOSITIO II. &mdash; <emph type="italics"/>In rota simplici spatium trochoidis triplum est <lb/>eiusdem rotae &rdquo;<emph.end type="italics"/> (Ouvr. </s>

<s>cit., pag. </s>

<s>310). </s></p><p type="main">

<s>La facilit&agrave; della dimostrazione dipende dall'invenzion di quella curva, <lb/>che il Roberval chiamava la <emph type="italics"/>Compagne de la roulette,<emph.end type="italics"/> e noi la <emph type="italics"/>Comite<emph.end type="italics"/> della <pb xlink:href="020/01/2818.jpg" pagenum="443"/>Cicloide. </s>

<s>&ldquo; Pour d&eacute;crire cette ligne, dice l'Autore, ayant tir&eacute; des point de la <lb/>Roulette des lignes paralleles &agrave; AC (fig. </s>

<s>297), si dans chacune de ces lignes, <lb/>a commencer aux points de la Roulette, l'on prend une ligne &eacute;gale &agrave; la por&shy;<lb/>tion de la mesme ligne comprise entre la demi-circonference du cercle et <lb/>son axe, l'on avra les points par lesquels cette ligne est d&eacute;crite. </s>

<s>Ainsi tirant <lb/>comme nous avons dit la ligne GHI, si dans la mesme ligne vous prenez GN <lb/><figure id="id.020.01.2818.1.jpg" xlink:href="020/01/2818/1.jpg"/></s></p><p type="caption">

<s>Figura 297.<lb/>&eacute;gale a HI, vous avrez le point N, par lequel passe la compagne de la Tro&shy;<lb/>choide. </s>

<s>De mesme prenant dans KLM la ligne KO &eacute;gale &agrave; LM, vous avrez <lb/>un autre point O de la mesme ligne. </s>

<s>Et si par le centre E vous tirez EF <lb/>perpendiculaire a BD, et si vous la prolongez en P, jusqu'&agrave; la Roulette, <lb/>ayant pris de P vers F la ligne PQ &eacute;gale &agrave; EF, dans la mesme ligne PF <lb/>vous avrez le point Q, qui est le milieu de cette ligne-cy, et auquel elle <lb/>change de courbure &rdquo; (pag. </s>

<s>64). </s></p><p type="main">

<s>Apparisce in primo luogo da una tal descrizione che lo spazio rinchiuso <lb/>fra la cicloide e la comite &egrave; diviso dalla linea PQ in due parti uguali, come <lb/>quelle che sono intessute de'seni retti di due quadranti del medesimo cir&shy;<lb/>colo, con transiti, non equabili, ma simili qua e l&agrave; nelle due figure, ond'&egrave; <lb/>che tutto il detto spazio &egrave; uguale a quello dello stesso mezzo cerchio. </s>

<s>2.o Dai <lb/>punti N, O, Q abbassando perpendicolari sulla base AD, saranno queste linee <lb/>i seni versi corrispondenti ai seni retti gi&agrave; presi. </s>

<s>3.o La parte superiore QB <lb/>della comite sar&agrave; uguale all'inferiore ANQ, perch&egrave; tutte le linee condotte <lb/>parallelamente alla base son tagliate in parti contrariamente uguali, e di qui <lb/>&egrave; ch'essa comite divide il rettangolo nel mezzo, come l'AB diagonale. </s>

<s>Con&shy;<lb/>segue in ultimo dalla fatta costruzione che i due bilinei ANQA, QBQ sono <lb/>uguali, e che perci&ograve; uguale spazio rinchiudono dentro l'angolo retto ADB la <lb/>comite e la diagonale. </s></p><p type="main">

<s>La superficie dunque, che si propone a quadrare, &egrave; composta di quella <lb/>compresa tra la cicloide e la comite, e dell'altra occupata dal triangolo mi&shy;<lb/>stilineo AQBD, uguale al rettilineo ABD, che ha per misura AD.BD/2= <lb/><foreign lang="greek">p</foreign>DB/2.DB/2=<foreign lang="greek">p</foreign>DB2/4, ossia uguale al circolo di diametro BD. </s>

<s>Aggiunta a <lb/>questa l'altra superficie, compresa tra la linea cicloidale e la comite, e che <pb xlink:href="020/01/2819.jpg" pagenum="444"/>vedemmo essere uguale al mezzo cerchio, &ldquo; toute la figure de la Cycloide <lb/>vaudra trois fois le cercle &rdquo; (ivi, pag. </s>

<s>211). </s></p><p type="main">

<s><emph type="italics"/>Corollario.<emph.end type="italics"/> &mdash; Di qui &egrave; patente che i quattro spazi compresi tra l'asse e il <lb/>semicircolo, tra il semicircolo e la comite, tra la comite e la cicloide, tra la ci&shy;<lb/>cloide e il rettangolo circoscritto; sono uguali, e che perci&ograve; il detto rettangolo <lb/>contiene quattro di quelle parti, delle quali la cicloide ne contiene tre sole. </s></p><p type="main">

<s>Ecco come veramente il Roberval avesse <emph type="italics"/>nullo negotio<emph.end type="italics"/> risoluto il pro&shy;<lb/>blema della quadratura della Cicloide, che Galileo aveva abbandonato come <lb/>impresa, non solo difficilissima, ma disperata. </s>

<s>La stereometria per&ograve; de'solidi, <lb/>generati dal rivolgersi la figura col suo rettangolo circoscritto intorno alla <lb/>base, intorno a una tangente al vertice, intorno all'asse; era altro negozio, <lb/>a trattare il quale, non bastando le forze naturali, bisognava, come a rimo&shy;<lb/>vere un corpo troppo ponderoso, ricorrere all'aiuto dei macchinamenti. </s>

<s>Il <lb/>Torricelli, come vedremo, ritrov&ograve; questi validissimi aiuti nella Regola cen&shy;<lb/>trobarica, ma il Roberval, o che non avesse ancora veduti i libri del Gul&shy;<lb/>dino, o che sdegnasse di ricorrere agli stranieri soccorsi della Meccanica, <lb/>volle tutto ricavare dagl'intimi seni della Geometria pura, dimostrando la <lb/>seguente proposizione, da servire, alla stereometria de'cicloidali, di primo e <lb/>principalissimo lemma: </s></p><p type="main">

<s>&ldquo; Si on decrit alentour d'une figure un parallelogramme (nous avons <lb/>pris un cercle en cet exemple) et qu'on fasse tourner le tout sur un des <lb/>costez du parallelogramme; le solide fait par ce parallelogramme est au so&shy;<lb/>lide fait par la figure, comme le plan du parallelogramme est au plan de la <lb/>figure &rdquo; (pag. </s>

<s>222). </s></p><p type="main">

<s>Essendo un circolo, col quadrato a lui circoscritto, come nella fig. </s>

<s>298, <lb/>e HF l'asse della rivoluzione, &egrave; manifesto che saranno i solidi generati un <lb/><figure id="id.020.01.2819.1.jpg" xlink:href="020/01/2819/1.jpg"/></s></p><p type="caption">

<s>Figura 298.<lb/>anello stretto e un cilindro, la pro&shy;<lb/>porzion tra i quali e le figure ge&shy;<lb/>nitrici si dimostra in questo caso <lb/>assai facilmente. </s>

<s>L'anello infatti si <lb/>compone delle infinite armille QM, <lb/>VN .... come il cilindro dei corri&shy;<lb/>spondenti circoli SO, TP .... Inten&shy;<lb/>dendosi ora con <emph type="italics"/>a<emph.end type="italics"/> significata l'armilla <lb/>abbiamo <emph type="italics"/>a<emph.end type="italics"/> QM=<foreign lang="greek">p</foreign>SQ2&mdash;<foreign lang="greek">p</foreign>MS2= <lb/><foreign lang="greek">p</foreign>(SQ+MS)(SQ&mdash;MS)= <lb/><foreign lang="greek">p</foreign>SO.QM. </s>

<s>Troveremo allo stesso <lb/>modo <emph type="italics"/>a<emph.end type="italics"/> VN=<foreign lang="greek">p</foreign>TP.VN, e cos&igrave; di <lb/>tutte le altre. </s>

<s>La somma dunque di <lb/>tutte queste infinite armille, delle <lb/>quali si compone l'anello A, sar&agrave;, osservando che TP=SO, A= <lb/>SO(QM+VN...). </s></p><p type="main">

<s>Il circolo poi descritto da SO &egrave; uguale a <foreign lang="greek">p</foreign>SO2 come il circolo di TP <lb/>a <foreign lang="greek">p</foreign>TP2. </s>

<s>Della somma di tutti questi circoli componendosi il cilindro C, sar&agrave; <pb xlink:href="020/01/2820.jpg" pagenum="445"/>dunque C=<foreign lang="greek">p</foreign>SO(SO+TP...) e perci&ograve; A:C=QM+VN...:SO+TP... <lb/>Ma di questa seconda ragione il primo termine &egrave; la somma di tutte le linee, <lb/>che intessono il circolo, e il secondo &egrave; la somma di tutte le linee, che intes&shy;<lb/>sono il quadrato; dunque i solidi rotondi stanno come le figure. </s></p><p type="main">

<s>Tale dimostrazione per&ograve; non s'adatta che al circolo, o a figure segate <lb/>dall'AB in due parti, non solamente uguali, ma simmetriche intorno all'asse. </s>

<s><lb/>Per&ograve; volendo il Roberval dare dimostrazione pi&ugrave; generale, applicabile a qua&shy;<lb/>lunque figura divisa in due parti uguali, o simmetriche o no intorno all'asse, <lb/>procede in quest'altra maniera, considerando l'armilla QM composta delle due <lb/>parti IM, IQ, quella uguale a <foreign lang="greek">p</foreign>IS2&mdash;<foreign lang="greek">p</foreign>SM2, questa uguale a <foreign lang="greek">p</foreign>SQ2&mdash;<foreign lang="greek">p</foreign>SI2. </s>

<s><lb/>Si tratta ora di riunire insieme queste due armille, al quale intento si giunge <lb/>cos&igrave;, abbreviando la via tenuta dall'Autore: </s></p><p type="main">

<s>IS2&mdash;SM2=MI2+2IM.MS=MI(MI+MS)+IM.MS= <lb/>MI.IS+IM.MS, onde (*) IS2&mdash;SM2+IQ2=MI.IS+IM.MS+IQ2= <lb/>MI.IS+MI.MS+MI2=MI.IS+MI(MS+MI)=MI.IS+MI.IS= <lb/>2MI.IS. </s>

<s>Abbiamo inoltre SQ2&mdash;SI2&mdash;IQ2=2SI.IQ=2SI.IM, la quale, <lb/>sommata con quella notata sopra con asterisco, dar&agrave; IS2&mdash;SM2+SQ2&mdash;SI2= <lb/>4SI.IM. </s>

<s>Troveremo nello stesso modo TK2&mdash;TN2+TV2&mdash;TK2=4TK.NK <lb/>e cos&igrave; di tutte le altre infinite armille, che sommate insieme comporranno l'anello <lb/>A=<foreign lang="greek">p</foreign>SI(IM+KN...)=2<foreign lang="greek">p</foreign>SI2(IM+KN...)=<foreign lang="greek">p</foreign>SO(MQ+NV...). </s></p><p type="main">

<s>Venendo ai circoli, quello descritto da SO sar&agrave; <foreign lang="greek">p</foreign>SO2; quello descritto <lb/>da TP=<foreign lang="greek">p</foreign>TP2, e cos&igrave; di tutti gli altri infiniti, i quali sommati insieme <lb/>comporranno il cilindro C=<foreign lang="greek">p</foreign>SO(SO+TP...), onde </s></p><p type="main">

<s><emph type="center"/>A:C=MQ+NV...:SO+TP...<emph.end type="center"/><lb/>Ma nel secondo membro di questa equazione il primo termine &egrave; la somma <lb/>di tutte le infinite linee tessenti il circolo, il secondo la somma di tutte le <lb/>infinite linee tessenti il rettangolo; dunque l'anello sta al cilindro, come il <lb/>circolo al rettangolo circoscritto. </s></p><p type="main">

<s><emph type="italics"/>Corollario I.<emph.end type="italics"/> &mdash; Qualunque sia la figura inscritta nel rettangolo, purch&egrave; <lb/>venga dalla linea AB, parallela all'asse di rotazione, segata in due parti <lb/>uguali, com'esso rettangolo; i solidi rotondi saranno sempre proporzionali <lb/>ai piani da cui son generati. </s></p><p type="main">

<s><emph type="italics"/>Scolio.<emph.end type="italics"/> &mdash; &ldquo; Nous trouverons la mesme chose en faisant tourner toute <lb/>la figure sur la ligne YZ &rdquo; (pag. </s>

<s>224) e tirate le sezioni come dianzi, per <lb/>esempio la UO, si dimostra dall'Autore in simile modo che &ldquo; le quadruple <lb/>du rectangle UIO sera au quarr&eacute; de EY comme le cylindre, ou plutost le <lb/>rouleau GEFH, est au cylindre total EGZY &rdquo; (ivi, pag. </s>

<s>225). </s></p><p type="main">

<s>Se dunque son vere le cose dimostrate, anche quando l'asse della rivo&shy;<lb/>luzione sia una parallela a HF, come per esempio ZY, chiamato Ro il rotondo, <lb/>che descrive il parallelogrammo Po, e Ao l'anello descritto dal circolo Co; <lb/>avremo Ro:Ao=Po:Co. </s>

<s>Moltiplicando la seconda ragione per 2<foreign lang="greek">p</foreign>LP, <lb/>ossia per la circonferenza descritta dal raggio LR, sar&agrave; </s></p><p type="main">

<s><emph type="center"/>Ro:Ao=Po.2<foreign lang="greek">p</foreign>LR:Co.2<foreign lang="greek">p</foreign>LR.<emph.end type="center"/><pb xlink:href="020/01/2821.jpg" pagenum="446"/>Ora il Roberval dimosta che, essendo Ro=Po.2<foreign lang="greek">p</foreign>LR, &egrave; anche in conse&shy;<lb/>guenza Ao=Co.2<foreign lang="greek">p</foreign>LR, ci&ograve; che d&agrave; luogo a formulare la proposizione: <lb/>&ldquo; Je dis que la roule GF est egal au solide qui a pour base le parallelo&shy;<lb/>gramme GF, et pour hauteur la circonference d'un cercle, qui a pour demi&shy;<lb/>diametre la ligne LR &rdquo; (pag. </s>

<s>228). </s></p><p type="main">

<s>Concludesi dall'Autore l'uguaglianza tra EFGH.2<foreign lang="greek">p</foreign>LR e Ro.EFGH <lb/>(ossia il rotondo descritto dal rettangolo EH) dimostrando che ambedue si <lb/>uguagliano a un terzo solido Co.GY, che vuol dire al cilindro descritto dal <lb/>rettangolo GY. </s>

<s>La dimostrazione procede facilmente per questa via: </s></p><p type="main">

<s><emph type="center"/>Co.GY=<foreign lang="greek">p</foreign>GZ.GZ.HF; EFGH.2<foreign lang="greek">p</foreign>LR=HF.GH.2<foreign lang="greek">p</foreign>LR,<emph.end type="center"/><lb/>onde EFGH.2<foreign lang="greek">p</foreign>LR:Co.GY=GH.2LR:GZ2=4GB.BZ:GZ2. </s>

<s><lb/>Ma per lo Scolio precedente 4GB.BZ sta a GZ2 come il rotondo di EGFH <lb/>sta a Co.GY; dunque questo rotondo &egrave; uguale al solido, che ha per base <lb/>EFGH, e per altezza 2<foreign lang="greek">p</foreign>LR. </s>

<s>E perci&ograve; dall'essersi cos&igrave; dimostrato Ro= <lb/>Po.2<foreign lang="greek">p</foreign>LR, ne consegue Ao=Co.2<foreign lang="greek">p</foreign>LR, che vuol dire insomma equiva&shy;<lb/>lere i due solidi a due prismi di pari altezza, uguale alla circonferenza de&shy;<lb/>scritta dal raggio LR distesa in dirittura, ma l'un dei quali avesse per base <lb/>il rettangolo, e l'altro il circolo, dal rivolgimento de'quali furono quelli stessi <lb/>solidi generati. </s></p><p type="main">

<s>Questo teorema, che il Roberval intitola <emph type="italics"/>Des anneaux,<emph.end type="italics"/> apparir&agrave; a chiun&shy;<lb/>que vi ripensi notabilissimo, avuto riguardo alla Regola centrobarica, o non <lb/>conosciuta allora in Francia, o trasposta cos&igrave; di proposito, dal campo della <lb/>Meccanica, in quello della Geometria, qualche tempo prima che, a confortar <lb/><figure id="id.020.01.2821.1.jpg" xlink:href="020/01/2821/1.jpg"/></s></p><p type="caption">

<s>Figura 299.<lb/>di matematiche ragioni le proposte del Gul&shy;<lb/>dino, si pensasse in Italia. </s>

<s>Ma lasciando stare <lb/>le applicazioni feconde, che di questo teorema <lb/>robervalliano della trasformazion de'solidi annu&shy;<lb/>lari in prismi si poteva fare alla Stereometria; <lb/>il principale intento, per cui lo troviamo rac&shy;<lb/>colto fra queste proposizioni, &egrave; quello di ser&shy;<lb/>vire di lemma principale alla misura dei solidi <lb/>cicloidali. </s>

<s>Altri due lemmi per&ograve;, per agevolar <lb/>l'ardua via, e da nessune altre orme segnata, <lb/>erano necessari, e il Roberval cos&igrave; se gli pro&shy;<lb/>poneva a dimostrar facilmente, aiutandosi degli <lb/>indivisibili. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma II.<emph.end type="italics"/> &mdash; Les quarrez des sinus sont <lb/>au quarre du diametre pris autant de fois comme <lb/>1 &agrave; 8 &rdquo; (pag. </s>

<s>251). </s></p><p type="main">

<s>Sia il quadrante FLN (fig. </s>

<s>299) diviso in un numero infinito di parti <lb/>uguali. </s>

<s>Noi considereremo le tre divisioni fatte in M, L, K, dalle quali si <pb xlink:href="020/01/2822.jpg" pagenum="447"/>conducano i seni retti GM, HL, IK, e i seni retti KQ, LP, MO dei loro com&shy;<lb/>plementi. </s>

<s>Avremo </s></p><p type="main">

<s><emph type="center"/>DM2=GM2+GD2<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>DL2=HL2+HD2<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>DK2=KI2+ID2<emph.end type="center"/><lb/>&hellip; <lb/>Sommando queste equazioni, e osservando che tutti i loro primi membri sono <lb/>uguali al raggio R, avremo &int;R2=GM2+HL2+KI2...+GD2+HD2+ID2... <lb/>Ma nel secondo rispetto la prima somma &egrave; quella de'quadrati de'seni retti, <lb/>che potr&agrave; significarsi con &int;<emph type="italics"/>s.r2,<emph.end type="italics"/> la seconda &egrave; quella dei complementi de'seni <lb/>retti, ed &egrave; manifestamente in numero e in quantit&agrave; uguale all'altra; e perci&ograve; <lb/>&int;R2=2&int;<emph type="italics"/>sr2.<emph.end type="italics"/> Ora, intendendosi per D il diametro, R2 &egrave; uguale a D2/4: <lb/>dunque &int;D2/4=2&int;<emph type="italics"/>sr2,<emph.end type="italics"/> ossia &int;<emph type="italics"/>sr2:<emph.end type="italics"/>&int;D2=1:8. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma III.<emph.end type="italics"/> &mdash; Le quarr&eacute; du diametre pris autant de fois est aux <lb/>quarrez des sinus verses comm&egrave; 8 &agrave; 3 &rdquo; (pag. </s>

<s>252). </s></p><p type="main">

<s>Osservando che FE2=(FI+IE)2=FI2+IE2+2FI.IE, e che <lb/>FI.IE=IK2, e cos&igrave; di tutte le altre infinite sezioni del diametro EF; <lb/>avremo </s></p><p type="main">

<s><emph type="center"/>EF2=FI2+IE2+2IK2<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>EF1=FH2+HE2+2HL2<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>EF2=FG2+GE2+2GM2<emph.end type="center"/><lb/>&hellip; <lb/>Sommando e osservando che FI2+FH2+FG2.... &egrave; la somma di tutti i <lb/>quadrati dei seni versi, che significheremo con &int;<emph type="italics"/>s.v2;<emph.end type="italics"/> e IE2+HE2+GE2.... <lb/>la somma de'loro complementi, e che perci&ograve; tutti questi sono uguali a tutti <lb/>quelli; avremo &int;EF2=2&int;<emph type="italics"/>s.v2<emph.end type="italics"/>+2(IK2+KL2+GM2....). Ma la <lb/>somma dentro parentesi &egrave;, per il lemma precedente, uguale 1/8 &int;EF2, dun&shy;<lb/>que &int;EF2&mdash;1/4 &int;EF2=2&int;<emph type="italics"/>s.v2,<emph.end type="italics"/> d'onde 3&int;EG2=8&int;<emph type="italics"/>s.v2,<emph.end type="italics"/> ossia <lb/>&int;EF2:&int;<emph type="italics"/>s.v2<emph.end type="italics"/>=8:3. </s></p><p type="main">

<s>Premessi i quali tre lemmi, le proporzioni, che passano tra i solidi e i <lb/>cilindri circoscritti, rivolgendosi le figure intorno alla base, e intorno alle <lb/>tangenti o al vertice o all'origine della Cicloide; tornarono al Roberval cos&igrave;, <lb/>come noi le compendieremo con discorso analitico, d'assai facile invenzione. <lb/><figure id="id.020.01.2822.1.jpg" xlink:href="020/01/2822/1.jpg"/></s></p><p type="caption">

<s>Figura 300.</s></p><p type="main">

<s>&ldquo; PROPOSITIO III. &mdash; <emph type="italics"/>La <lb/>raison de 5 &agrave; 8 est celle du <lb/>solide, que fait la roulette <lb/>AIB<emph.end type="italics"/> (fig. </s>

<s>300) <emph type="italics"/>au cylindre <lb/>AM, le tout tournant sur <lb/>ACB &rdquo;<emph.end type="italics"/> (pag. </s>

<s>267). </s></p><p type="main">

<s>Considera l'Autore il so&shy;<lb/>lido proposto resultar di due parti: di quella descritta dallo spazio AFIRA, <pb xlink:href="020/01/2823.jpg" pagenum="448"/>compreso tra la cicloide e la comite, e dell'altra, che vien descritta dal tri&shy;<lb/>lineo AFIC. </s>

<s>Ora la prima detta figura &egrave;, per il corollario della seconda pro&shy;<lb/>posizione, un quarto del rettangolo AI, ed ha, come il detto rettangolo, il <lb/>centro sopra la GD, che sega in due parti uguali ambedue le figure, ed &egrave; <lb/>parallela all'asse AB della revoluzione. </s>

<s>Dunque i solidi rotondi, per il co&shy;<lb/>rollario primo del primo lemma, stanno come le figure piane, e perci&ograve; il solido, <lb/>che chiameremo S, al cilindro C, come uno a quattro, o come due a otto. </s></p><p type="main">

<s>La figura poi AFIC &egrave; per costruzione intessuta delle infinite linee pa&shy;<lb/>rallele a IC, ossia degli infiniti seni versi del mezzo circolo IEC, ed &egrave; nel <lb/>terzo lemma stato dimostrato che la somma de'quadrati di tutti questi seni <lb/>versi, o de'circoli da essi descritti, sta alla somma de'quadrati del diame&shy;<lb/>tro IC, o de'circoli da lui descritti e presi altrettante volte, come 3 a 8. Ora, <lb/>essendo manifesto che la somma de'primi circoli costituisce il solido T del <lb/>trilineo, e la somma dei secondi il solido C del cilindro; avremo T:C=3:8. <lb/>Ma &egrave; altres&igrave; S:C=2:8, dunque S:T=2:3. Componendo S+T:T= <lb/>5:3, d'onde S+T:C<gap/>5:8. </s></p><p type="main">

<s>Di qui manifestamente resultando </s></p><p type="main">

<s><emph type="center"/><foreign lang="greek">p</foreign>KV2+<foreign lang="greek">p</foreign>ON2+<foreign lang="greek">p</foreign>RQ2...:<foreign lang="greek">p</foreign>ZV2+<foreign lang="greek">p</foreign>PN2+<foreign lang="greek">p</foreign>SQ2=5:8,<emph.end type="center"/><lb/>avremo, dividendo per <foreign lang="greek">p</foreign>, KV2+ON2...:ZV2+PN2...=5:8. </s></p><p type="main">

<s>&ldquo; PROPOSITIO IV. &mdash; <emph type="italics"/>Maintenant il faut voir quelle raison il y avra <lb/>entre le solide de la mesme roulette a son cylindre, lors qu'elle tourne <lb/>sur LM<emph.end type="italics"/> (uella medesima figura) <emph type="italics"/>parallele &agrave; AB, qui est celle de 7 &agrave; 8 &rdquo;<emph.end type="italics"/><lb/>(pag. </s>

<s>268). </s></p><p type="main">

<s>Considera l'Autore che il solido descritto dallo spazio cicloidale, in que&shy;<lb/>sto caso, uguaglia il cilindro, toltone il solido generato dai trilinci ALI, IMB, <lb/>a trovar la misura del quale si riduce il presente negozio. </s>

<s>E perch&egrave; resulta <lb/>la detta misura dalla somma degl'infiniti circoli, come sarebbro quelli de&shy;<lb/>scritti da ZK, PO, SR, ecc., convien prima dunque con le seguenti equa&shy;<lb/>zioni predisporre per ciascuno i valori </s></p><p type="main">

<s><emph type="center"/>ZK2=ZV2+KV2&mdash;2VZ.VK<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>PO2=PN2+ON2&mdash;2PN.ON<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SR2=SQ2+RQ2&mdash;2Sq.RQ<emph.end type="center"/><lb/>&hellip; <lb/>Sommando tutte queste equazioni, e osservando che <expan abbr="ZV+PN+Sq.">ZV+PN+Sque</expan>..= <lb/>&int;IC, avremo </s></p><p type="main">

<s><emph type="center"/>ZK2+PO2+SR2=&int;IC2+KV2+ON2...&mdash;2&int;IC(VK+ON...).<emph.end type="center"/><lb/>Ma, per il corollario della precedente, KV2+ON2...=5/8 &int;IC2, e, per il <lb/>corollario della seconda, VK+ON...=3/4 &int;IC; dunque </s></p><p type="main">

<s><emph type="center"/>ZK2+PO2...=8/8 &int;IC2+5/8 &int;IC2&mdash;12/8 &int;IC2=1/8 &int;IC2.<emph.end type="center"/><lb/>Moltiplicando per <foreign lang="greek">p</foreign>, <foreign lang="greek">p</foreign>KZ2+<foreign lang="greek">p</foreign>PO2...=1/8<foreign lang="greek">p</foreign>&int;IC2. </s>

<s>Ond'&egrave; che, compo-<pb xlink:href="020/01/2824.jpg" pagenum="449"/>nendosi degl'infiniti circoli di raggio KZ, PO, ecc., come si disse, il solido T <lb/>descritto dal trilineo ALI, e degl'infiniti circoli, tutti di raggio uguale a IC, <lb/>il cilindro C; avremo C:T=8:1. Dividendo, C&mdash;T:T=7:1, d'onde <lb/>C&mdash;T:C=7:8. </s></p><p type="main">

<s>&ldquo; PROPOSITIO V. &mdash; <emph type="italics"/>Il faut maintenant considerer les solides, qui se <lb/>font quand la figure tourne sur LA. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; O&ugrave; on remarquera que la ligne IC, parallele &agrave; la dite LA, coupe le <lb/>parallelogramme AM et la figure AIB en deux egalement, et partant les so&shy;<lb/>lides sont entr'eux comme les plans, et ainsi le solide fait par AIB sera au <lb/>cylindre, form&eacute; par le parallelogramme AM, comme le plan de l'un est au <lb/>plan de l'autre. </s>

<s>Mais les plans sont entr'eux comme 4 &agrave; 3, partant le cylin&shy;<lb/>dre sera au solide de la roulette comme 4 &agrave; 3 &rdquo; (pag. </s>

<s>269). </s></p><p type="main">

<s>&ldquo; Haec et multa alia, conclude il Roberval, circa annos 1635 et 1640, <lb/>vigente animi vigore, detexi &rdquo; (pag. </s>

<s>342). Tent&ograve; altres&igrave; la misura del solido <lb/>generato dalla mezza cicloide e dal cilindro circoscritto, facendosi la rivolu&shy;<lb/>zione intorno all'asse, ma lasci&ograve; allora l'impresa per disperata, sembrandogli <lb/>essere i due solidi fra loro incommensurabili. </s>

<s>Vi torn&ograve; poi sopra, quando il <lb/>Torricelli annunzi&ograve; di aver avuta in proporzioni definite quella misura, di <lb/>che diremo altrove, prima di por termine a questa digressione. </s></p><p type="main">

<s>Intanto lo stesso Roberval e il Mersenno andavano tutti compiacenti <lb/>diffondendo fra i Matematici la notizia di queste scoperte, e principalmente <lb/>della quadratura della Cicloide, facendosi intendere com'ella fosse stata di&shy;<lb/>mostrata precisamente tripla del circolo genitore. </s>

<s>Ne sentirono allegrezza gli <lb/>amici, e livore gli emuli e gl'invidiosi, sfogandosi col dire che la cosa era <lb/>poi tanto facile, da non meritar che se ne facesse tutto quel gran rumore, <lb/>non ripensando costoro che una tale facilit&agrave; dipendeva dall'essersi per il Ro&shy;<lb/>berval l'ipotesi ridotta a tesi, che ciascuno era certo di poter dimostrare. <lb/><figure id="id.020.01.2824.1.jpg" xlink:href="020/01/2824/1.jpg"/></s></p><p type="caption">

<s>Figura 301.</s></p><p type="main">

<s>Essendo infatti due le vie, che na&shy;<lb/>turalmente si paravano innanzi, l'una <lb/>delle quali consisteva nel decomporre <lb/>lo spazio cicloidale DGABD (fig. </s>

<s>301), <lb/>nel triangolo rettilineo DAB; e nel bi&shy;<lb/>lineo DGAD; e l'altra nel decomporre <lb/>quel medesimo spazio nel mezzo cerchio <lb/>DHA, e nel trilineo DGAHB; &egrave; ma&shy;<lb/>nifesto che, dovendo essere il t&ugrave;tto uguale a tre mezzi cerchi, de'quali il <lb/>triangolo, che ha per base la mezza circonferenza e per altezza il diametro, <lb/>&egrave; due; tutto si riduceva a trovar modo di dimostrare come li bilineo fosse <lb/>uguale a uno, e il trilineo a due di quei mezzi cerchi. </s>

<s>Tenne questa via il <lb/>Fermat, e quella il Cartesio, il quale, in comunicarne la dimostrazione al <lb/>Mersenno, cos&igrave; gli scriveva: &ldquo; Inchoasti per inventionem d. </s>

<s>De Roberval de <lb/>spatio comprehenso in linea curva, quam describit punctum aliquod circum&shy;<lb/>ferentiae circuli, qui concipitur rotari aut currere super plano quodam, quam <lb/>mihi fateor nunquam in mentem venisse, et eius annotationem perelegantem <pb xlink:href="020/01/2825.jpg" pagenum="450"/>esse. </s>

<s>Caeterum non video rem tanti esse, quae buccina vulgetur, cum sit in&shy;<lb/>ventu facilis, quamque vel mediocriter in Geometria versatus certo invenire <lb/>potest, si eam quaerit &rdquo; (<emph type="italics"/>Epistolae,<emph.end type="italics"/> P. III, Amstelod. </s>

<s>1683, pag. </s>

<s>240). </s></p><p type="main">

<s>Chiunque infatti pu&ograve; facilmente dimostrare che tutte le infinite linee <lb/>come GH, EI (nella medesima figura) equidistanti alla FC, che parallela&shy;<lb/>mente alla base attraversa il centro; son coppia a coppia uguali alla corda, <lb/>come KL, condotta parallelamente al diametro, a una distanza MC, che si <lb/>uguagli alla NC. </s>

<s>Or perch&egrave; di quelle infinite linee accoppiate si compone il <lb/>bilineo, e delle infinite corde, corrispondenti a ciascuna di quelle coppie, il <lb/>semicerchio; dunque le due superficie sono uguali. </s></p><p type="main">

<s>Riduce ingegnosamente il Cartesio a maggior facilit&agrave; la cosa, disponendo <lb/>le coppie GH, EI, e tutte le altre infinite in continuit&agrave; lungo una medesima <lb/>direzione, col trasportar lo spazio DFO, che nella figura 301 riman di sotto, <lb/>invece allato, come ACD nella figura 302. Resulta da una tale disposizione <lb/><figure id="id.020.01.2825.1.jpg" xlink:href="020/01/2825/1.jpg"/></s></p><p type="caption">

<s>Figura 302.<lb/>che la linea FD, divisa nel mezzo in B, uguaglia EH diametro del semicir&shy;<lb/>colo EIH, da cui &egrave; generata la cicloide, e che tutte le corde, come KL, sono <lb/>uguali alle infinite linee, una delle quali &egrave; GC essendo queste tanto distanti <lb/>da FD, quanto dal centro O sono distanti quelle. </s>

<s>Ci&ograve; che evidentemente prova, <lb/>dice il Cartesio, essere le due superficie uguali a chi non ignora che due <lb/>figure, aventi la medesima base e la medesima altezza, e tutte le linee rette <lb/>parallele, inscritte nell'una, uguali alle infinite inscritte nell'altra; si disten&shy;<lb/>dono nello spazio ugualmente. </s>

<s>&ldquo; Verum, poi soggiunge, cum fortasse sint qui <lb/>theoremati isti non applaudant, pergendum duxi hoc modo (ibid., pag. </s>

<s>228). <lb/>Il modo consiste nel comune e antico degl'inscritti, facendo osservare che <lb/>sono uguali qua e l&agrave; i triangoli EIH, FAD, insistenti con pari altezza sopra <lb/>basi uguali: e uguali i triangoli SAP, QAC insieme, ai triangoli KIM, INL <lb/>insieme, e anche il triangolo FGP+QCD uguale al triangolo EKM+NLH, <lb/>per le medesime assai patenti ragioni. </s>

<s>Cos&igrave; essendo vero di tutti i triangoli, <lb/>che resultano dal moltiplicare all'infinito le iscrizioni, resta provato che lo <lb/>spazio FGAD, da cui si rappresenta il bilineo della Cicloide, &egrave; uguale a mezzo <lb/>il circolo genitore. </s></p><p type="main">

<s>Non vogliamo proseguire il discorso, senza arrestarci un poco a ripen&shy;<lb/>sare come il Cartesio &egrave; il terzo, dopo il Roberval e il Nardi, a far uso degli <lb/>indivisibili, prima che se ne istituisse il metodo nella <emph type="italics"/>Geometria nuova.<emph.end type="italics"/> I <lb/>primi due commemorati, bench&egrave; confessassero di aver non da altri che <pb xlink:href="020/01/2826.jpg" pagenum="451"/>da Archimede e da Pappo derivata la dottrina dell'infinito, pur non de&shy;<lb/>trassero poi nulla alla gloria del Cavalieri, la Geometria del quale parve <lb/>al Nardi <emph type="italics"/>o&pacute;era gigantea, cos&igrave; oscure verit&agrave; discopre e in s&igrave; nobile maniera<emph.end type="italics"/><lb/>(MSS. Gal., T. XX, pag. </s>

<s>1895), e il Roberval, che pure avrebbe potuto chia&shy;<lb/>marsi a parte col Cavalieri nel merito dell'invenzione, cos&igrave; generosamente <lb/>si protestava in pubblico con queste parole: &ldquo; Ego tanto viro, tantae ac tam <lb/>sublimis doctrinae inventionem non eripiam, nec possum, nec si possim fa&shy;<lb/>ciam. </s>

<s>Ille prius vulgavit, ille hoc iure suam fecit: ille hoc iure habeat, atque <lb/>possideat, ille tandem hoc iure inventoris nomine gaudeat &rdquo; (Ouvrages cit., <lb/>pag. </s>

<s>367). </s></p><p type="main">

<s>Il Cartesio per&ograve;, n&egrave; fra gli antichi n&egrave; fra i moderni, non conosce mae&shy;<lb/>stro: il metodo degli indivisibili &egrave; parto del suo proprio cervello, per cui si <lb/>ride e sente compassione di questo povero Cavalieri. </s>

<s>Nell'Aprile del 1646, <lb/>essendo in Leida, gli si fa incontro il professore Schoten, il giuniore, per <lb/>dirgli ch'era recapitata quivi d'Italia la <emph type="italics"/>Geometria nuova.<emph.end type="italics"/> Prende il Car&shy;<lb/>tesio fra le mani il libro, e lo svolge non pi&ugrave; che per un quarto d'ora, <emph type="italics"/>qua&shy;<lb/>drantis horae spatio,<emph.end type="italics"/> eppure ci&ograve; gli basta per formarsi il giudizio che non <lb/>si faceva l&igrave; dall'Autore altro che ripetere cose viete, dimostrandole in quel <lb/>modo, con cui aveva egli stesso dimostrata la quadratura della Cicloide. </s>

<s>Poi <lb/>si mette a dire che alla chiave di questo Cavalieri mancavano per aprire gli <lb/><figure id="id.020.01.2826.1.jpg" xlink:href="020/01/2826/1.jpg"/></s></p><p type="caption">

<s>Figura 303.<lb/>ingegni. </s>

<s>&ldquo; Ego enim multa plura novi maio&shy;<lb/>ris ponderis, quorum vim magnam in meam <lb/>Geometriam contuli: ille autem ea non facile <lb/>inveniet, neque intelliget unum ex illis, nisi <lb/>prolixo volumine explicatum &rdquo; (Epistol., P. III <lb/>cit., pag. </s>

<s>343). Ma vediamo come il Fermat <lb/>dimostrasse, non men facilmente del Cartesio, <lb/>che il trilineo ABFD (fig. </s>

<s>303) nella mezza ci&shy;<lb/>cloide &egrave; in superficie uguale al circolo genitore. </s></p><p type="main">

<s>Essenziale propriet&agrave; della curva &egrave; che, a partire dal vertice B, dove in&shy;<lb/>tendasi fermato il diametro BD del circolo genitore con la sua semicircon&shy;<lb/>ferenza DLFD; tutte le ordinate, come IL, EF, sono uguali agli archi inter&shy;<lb/>cetti LB, BLF: ond'&egrave; che se le due dette ordinate sono ugualmente distanti <lb/>dal centro C, sommate insieme, saranno uguali alla stessa semicirconferenza, <lb/>e cos&igrave; sar&agrave; vero delle infinite simili coppie. </s>

<s>Qui il metodo degl'indivisibili <lb/>avrebbe somministrato al Fermat una dimostrazione, da non si paragonare, <lb/>nella brevit&agrave; e nella eleganza, n&egrave; a quella del Cartesio, n&egrave; del Torricelli <lb/>stesso o di qualunque altro avesse voluto concorrere nell'argomento. </s>

<s>Impe&shy;<lb/>rocch&egrave;, soprammesse tutte quelle mezze circonferenze, comporrebbero la mezza <lb/>superficie convessa di un cilindro, descritto da un quadrato, di cui fosse il <lb/>lato uguale al raggio CD del circolo genitore, la qual superficie convessa es&shy;<lb/>sendo uguale a uno de'circoli, che fanno da base al medesimo cilindro, an&shy;<lb/>che il trilineo AIBFD sar&agrave; dunque uguale a quel circolo. </s></p><p type="main">

<s>Ma, o che il Fermat non conoscesse questo metodo, o che non l'appro-<pb xlink:href="020/01/2827.jpg" pagenum="452"/>vasse, ricorse a un altro espediente, molto allora in voga per gli esempi <lb/>datine dal Keplero, qual era quello di pigliar delle curve cos&igrave; minime parti, <lb/>da poterle riguardar come rette. </s>

<s>Cos&igrave; dunque divisi i raggi CD, CB nel me&shy;<lb/>desimo numero di particelle, tutte fra loro uguali, e da ciascun punto di divi&shy;<lb/>sione, sotto e sopra, a ugual distanza dal centro C, condotti seni come FG, LH, <lb/>prodotti nelle ordinate FE, LI; la figura ED si potr&agrave; riguardar come un tra&shy;<lb/>pezio, e tale pure, cio&egrave; come un trapezio, la minor base del quale sia ridotta <lb/>a zero, si potr&agrave; riguardare il triangolo ILB, e cos&igrave; dicasi delle altre infinite <lb/>simili figure intercette. </s>

<s>Chiamati ora T, <emph type="italics"/>t,<emph.end type="italics"/> que'trapezi ED, ILB, con le al&shy;<lb/>tezze GD, BH uguali, e ugualmente distanti dal mezzo C; sommati insieme <lb/>daranno T+<emph type="italics"/>t<emph.end type="italics"/>=GD/2(AD+EF+IL)=GD.<foreign lang="greek">p</foreign>CD. </s>

<s>Suppongasi ora <lb/>essere <emph type="italics"/>n<emph.end type="italics"/> il numero delle divisioni, corrispondente al numero delle coppie dei <lb/>trapezi descritti nel trilineo AIBFD, e per questo numero <emph type="italics"/>n<emph.end type="italics"/> si moltiplichi la <lb/>trovata equazione. </s>

<s>Verr&agrave; <emph type="italics"/>n<emph.end type="italics"/>(T+<emph type="italics"/>t<emph.end type="italics"/>)=<emph type="italics"/>n<emph.end type="italics"/>GD<foreign lang="greek">p</foreign>CD. </s>

<s>Ma <emph type="italics"/>n<emph.end type="italics"/>(T+<emph type="italics"/>t<emph.end type="italics"/>) &egrave; mani&shy;<lb/>festamente uguale alla superficie S del detto trilineo, e <emph type="italics"/>n<emph.end type="italics"/> GD=CD; dun&shy;<lb/>que S=<foreign lang="greek">p</foreign>CD2. </s></p><p type="main">

<s>Tale facilit&agrave; di via apr&igrave; il Roberval ai matematici di Francia, i quali <lb/>avevano gi&agrave; nel 1641, infino al punto che abbiam veduto, promossa la scienza <lb/>della Cicloide. </s>

<s>Ma fra noi si rimaneva in quel tempo tuttavia stagnante, im&shy;<lb/>peditone il libero corso da quell'argine contrappostole da Galileo, e descritto <lb/>dal Salviati nel frammento di dialogo sopra trascritto, il quale argine ora &egrave; <lb/>a narrare quando, da chi e con quali conati fosse superato, d'onde scesero <lb/>le acque di sopra a irrigar largamente anche i nostri campi. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Il d&igrave; 14 Febbraio 1640 scriveva il Cavalieri in una lettera, indirizzata a <lb/>Galileo da Bologna, queste parole rimasteci come certissimo documento della <lb/>prima occasione, che il Roberval, aiutato dalle ingerenze del Mersenno, dette <lb/>ai nostri Matematici di risolvere i problemi intorno alla linea, allo spazio e <lb/>ai solidi generati dalla Cicloide: &ldquo; Mi sono stati mandati da Parigi due que&shy;<lb/>siti da quei Matematici, circa de'quali temo di farmi poco onore, perch&egrave; mi <lb/>paiono cure disperate. </s>

<s>L'uno &egrave; la misura della superficie del cono scaleno, <lb/>l'altro la misura di quella linea curva, simile alla curvatura di un ponte, <lb/>descritta dalla rivoluzione di un cerchio, sino che scorra con tutta la sua cir&shy;<lb/>conferenza una linea retta, e dello spazio piano compreso da quella, e del <lb/>corpo generato per la rivoluzione intorno all'asse e alla base: il che mi ri&shy;<lb/>cordo che una volta mi domand&ograve; lei, ma che infruttuosamente mi vi affati&shy;<lb/>cai. </s>

<s>Di grazia mi dica se sa che queste due cose sieno state dimostrate da <lb/>nessuno, perch&egrave;, per quello che io vedo, mi paiono difficilissime. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2828.jpg" pagenum="453"/><p type="main">

<s>&ldquo; L'occasione &egrave; stata che, passando un padre di S. </s>

<s>Francesco di Paola <lb/>(<emph type="italics"/>il padre Niceron<emph.end type="italics"/>) qua da Bologna, che &egrave; di Parigi, e molto intendente delle <lb/>matematiche, nel discorrere seco di diverse cose gli venni a dire che avevo <lb/>trovata la misura del corpo parabolico nato dalla rivoluzione della parabola <lb/>intorno alla base, e che avevo trovato che il cilindro, generato dal paralle&shy;<lb/>logrammo circoscritto alla parabola, era al detto corpo come 15 a 8, sebbene <lb/>uno dei principali gesuiti matematici mi aveva gi&agrave; un pezzo fa scritto che <lb/>era doppio. </s>

<s>Ora il detto Padre disse: Lasci di grazia che io lo scriva a quei <lb/>matematici di Parigi, per vedere se rincontrano questa verit&agrave;, e cos&igrave; l'hanno, <lb/>dice, trovata come 15 a 8. E questa &egrave; stata l'occasione di propormi questi <lb/>altri problemi, da me reputati di difficilissima risoluzione, per quel poco che <lb/>io vedo &rdquo; (Alb. </s>

<s>X, 379, 80). </s></p><p type="main">

<s>Galileo rispose, dopo dieci giorni, parere anche a lui i problemi man&shy;<lb/>dati di Francia difficilissimi, n&egrave; sapere che ancora fossero sciolti, e soggiun&shy;<lb/>geva: &ldquo; Quella linea arcuata sono pi&ugrave; di cinquant'anni che mi venne in <lb/>mente il descriverla, e l'ammirai per una curvit&agrave; graziosissima, per adat&shy;<lb/>tarla agli archi d'un ponte. </s>

<s>Feci sopra di essa, e sopra lo spazio da lei e <lb/>dalla sua corda compreso, diversi tentativi per dimostrarne qualche passione, <lb/>e parvemi da principio che tale spazio potesse esser triplo del cerchio che <lb/>lo descrive, ma non fu cos&igrave;, bench&egrave; la differenza non sia molta. </s>

<s>Tocca all'in&shy;<lb/>gegno del p. </s>

<s>Cavalieri e non d'altro il ritrovarne il tutto, e mettere tutti li <lb/>speculativi in disperazione di poter venire a capo di questa contemplazione &rdquo; <lb/>(Dati, <emph type="italics"/>Lettera ai Filaleti,<emph.end type="italics"/> Firenze 1663, pag. </s>

<s>4, 5). </s></p><p type="main">

<s>Invece il Cavalieri aveva, dietro queste parole, messo s&egrave; medesimo in pi&ugrave; <lb/>disperazione che mai. </s>

<s>Chi avrebbe creduto ci&ograve; dell'Autore degli indivisibili? </s>

<s><lb/>Fosse allora venuto uno a mostrargli con quanta facilit&agrave; conduceva il me&shy;<lb/>todo da lui stesso iusegnato a riconoscere, com'aveva fatto il Cartesio, che <lb/>il bilineo compreso fra la diagonale del rettangolo circoscritto e la mezza ci&shy;<lb/>cloide uguaglia il semicircolo che la descrive; o che il trilineo compreso fra <lb/>le due mezze curve &egrave; uguale alla met&agrave; della superficie convessa di un cilin&shy;<lb/>dro, descritto dal rivolgersi di un quadrato costruitosi sul raggio del circolo <lb/>genitore! Ma il saper che in tale esercizio s'era per cinquant'anni inutil&shy;<lb/>mente straccato Galileo, e il credere con lui che le proposizioni venute di <lb/>Parigi fossero problemi da risolversi, e non teoremi gi&agrave; dimostrati, fu causa <lb/>che il Cavalieri adombrasse puerilmente cos&igrave;, da ritrarsi dalla nobile impresa. </s></p><p type="main">

<s>La vilt&agrave; del capitano impaur&igrave; anche gli altri militi, fra quali il Nardi, <lb/>ch'era pure uno dei pi&ugrave; coraggiosi, n&egrave; manc&ograve; di giovare quel poco di co&shy;<lb/>raggio, di che egli dava gli esempi. </s>

<s>Discepolo fedelissimo di Archimede, che <lb/>aveva secondo lui ritrovato il centro di gravit&agrave; nel conoide, e in altre strane <lb/>figure per via di meccaniche esperienze, torn&ograve; il Nardi a tentare le prove, <lb/>che a Galileo non erano mai riuscite. </s>

<s>Se non che pens&ograve; di paragonare il <lb/>peso della cicloide con quello del rettangolo circoscritto, piuttosto che del cir&shy;<lb/>colo genitore. </s>

<s>Cos&igrave; le rasure, dalle quali si temeva che principalmente dipen&shy;<lb/>dessero le fallacie, riuscivano molto minori di quelle fatte da Galileo, e d'av-<pb xlink:href="020/01/2829.jpg" pagenum="454"/>vantaggio s'avevano due riscontri: prima col rettangolo intero, e poi co'due <lb/>triangoli aventi un lato curvilineo opposto all'angolo retto, e rimasti dal re&shy;<lb/>cider la cicloide dal rettangolo stesso. </s>

<s>Fatta dunque l'operazione, trov&ograve; il <lb/>Nardi che il peso del rettangolo era a quello della cicloide come quattro a <lb/>tre, d'onde credeva se ne potesse concludere esser essa cicloide esattamente <lb/>tripla del circolo, che movendosi la descrive. </s>

<s>Ma rimanendo tuttavia incerto <lb/>se dicesse il vero la sua o la bilancetta di Galileo, lasci&ograve; anch'egli ai geo&shy;<lb/>metri il dar sentenza finale. </s></p><p type="main">

<s>L'invenzione meccanica della quadratura della Cicloide occorse al Nardi <lb/>nel 1641, quando faceva copiare la seconda Ricercata geometrica, nella quale <lb/>era scritto: &ldquo; Osservo, per le meccaniche esperienze, che un rettangolo di <lb/>ugual base e altezza con la cicloide sia sesquiterzo di essa, da che, quando <lb/>vero sia, vero anche sar&agrave; che la cicloide sia tripla di quel cerchio da cui <lb/>descrivesi. </s>

<s>&rdquo; E si termina dall'Autore questo discorso della Cicloide con le <lb/>seguenti parole: &ldquo; Finalmente non stimo gettarsi il tempo che s'impieghi <lb/>nel coltivare tal campo della Geometria, in grazia d'agguagliare il cerchio <lb/>ad un rettilineo. </s>

<s>Ma chiunque per questa strada arriver&agrave; a tal segno sapr&agrave; <lb/>forse anche trovare la proporzione della linea cicloide verso la base sua, come <lb/>anche quella del solido e superficie prodotti mentre intorno alla base o al&shy;<lb/>l'asse si rivolga lo spazio clcloidale. </s>

<s>Lasciamo dunque tali contemplazioni agli <lb/>altri, e ripigliamo il nostro discorso. </s>

<s>&rdquo; </s></p><p type="main">

<s>L'esperienza meccanica, dalla quale resultava essere la cicloide esatta&shy;<lb/>mente tripla del circolo che l'ha descritta, fu dal Nardi annunziata al Tor&shy;<lb/>ricelli, il quale incominci&ograve; allora a dubitare che Galileo si fosse ingannato. </s>

<s><lb/>Da ci&ograve; prese animo di posporre l'autorit&agrave; di lui alla legittima della Geome&shy;<lb/>tria, dalla quale, interrogata, ebbe il responso di quel teorema, che, in pi&ugrave; <lb/>maniere, e tutte concludentissime, confermava la verit&agrave; dell'esperienza. </s>

<s>Ben&shy;<lb/>ch&egrave; la dimostrazione riuscisse, per via degli indivisibili, assai facile, com'ap&shy;<lb/>parisce dall'appendice <emph type="italics"/>De dimensione Cycloidis,<emph.end type="italics"/> nella seconda parte delle <lb/>Opere geometriche, pur il Torricelli, ch'era cos&igrave; felicemente riuscito in un'im&shy;<lb/>presa da'suoi grandi maestri creduta disperata, esult&ograve; della scoperta, annun&shy;<lb/>ziandola senza indugio, sulla fine del Marzo 1643, agli amici e agli stranieri. </s>

<s><lb/>Ci&ograve; che rispondessero questi, ossia i Francesi, ai quali non riusciva la cosa <lb/>punto nuova, si dir&agrave; altrove, per trattenerci ora a narrare qual effetto pro&shy;<lb/>ducesse nell'animo, e nella mente dei nostri Italiani. </s></p><p type="main">

<s>Il Cavalieri si rimase passivo da uno stupore molto simile a quello di <lb/>colui, che, avendo intorno a un segreto ritrovato scarso ogni sforzo delle mani <lb/>e delle braccia, veda entrare un altro ad aprirlo col dito, a un legger tocco <lb/>di molla. </s>

<s>Trasparisce un tal sentimento da ci&ograve;, che il d&igrave; 23 Aprile 1643 cos&igrave; <lb/>rispondeva all'annunzio: &ldquo; Finalmente ho sentito nell'ultima sua la misura <lb/>dello spazio cicloidale, con molta mia maraviglia, essendo stato sempre sti&shy;<lb/>mato problema di molta difficolt&agrave;, che stracc&ograve; gi&agrave; il Galileo: siccome io pure, <lb/>parendomi assai difficile, lo lasciai andare, ond'ella ne aver&agrave; non poca lode <lb/>di questo, oltre le tante sue maravigliose invenzioni, che gli daranno eterna <pb xlink:href="020/01/2830.jpg" pagenum="455"/>fama. </s>

<s>Non rester&ograve; poi di dirle intorno a questo che il signor Galileo mi <lb/>scrisse una volta di avervi applicato quarant'anni fa, e che non aveva po&shy;<lb/>tuto trovar niente, e che s'era persuaso che il detto spazio fosse triplo del <lb/>circolo suo genitore, ma che poi gli pareva che non fosse precisamente, se <lb/>mal non mi ricordo, poich&egrave;, per quanto abbi cercato nelle mie scritture, non <lb/>ho mai potuto tal lettera ritrovare. </s>

<s>Sicch&egrave;, se sta, come mi pare di ricor&shy;<lb/>darmi, bisogna che esso molto s'ingannasse a credere che fosse altrimenti <lb/>che triplo &rdquo; (MSS. Gal. </s>

<s>Disc., XLI, fol. </s>

<s>171). </s></p><p type="main">

<s>Ma il Nardi si pent&igrave; di avere a cos&igrave; bella e facile contemplazione la&shy;<lb/>sciato altrui correre il campo, in cui, trovandosi ora a dover fare da respi&shy;<lb/>golatore, si studi&ograve; di portarvisi da par suo. </s>

<s>E come il Roberval alla deside&shy;<lb/>rata quadratura s'agevol&ograve; la via con la invenzion della comite, cos&igrave; il Nostro <lb/>invent&ograve; al medesimo effetto una cicloide nuova, in tale artificioso modo de&shy;<lb/><figure id="id.020.01.2830.1.jpg" xlink:href="020/01/2830/1.jpg"/></s></p><p type="caption">

<s>Figura 304.<lb/>scritta, che l'eccesso CFHAGC di <lb/>lei (fig. </s>

<s>304), sopra il triangolo CAD, <lb/>fosse uguale al semicircolo genitore. </s>

<s><lb/>Di qui essendo manifesto che tanto <lb/>questa curva, quanto la volgare <lb/>CFEA, circoscrivono uguale spazio, <lb/>bench&egrave; con andamento diverso, e <lb/>dall'altra parte sapendosi con cer&shy;<lb/>tezza che il triangolo al semicircolo <lb/>&egrave; doppio; immediatamente si con&shy;<lb/>clude il tutto dover esserne triplo. </s>

<s><lb/>N&egrave; qui, per confermare altri esempi, &egrave; da passare inosservato l'incontro, <lb/>senza dubbio fortuito, del Matematico francese col Nostro, il quale notava <lb/>come i seni del semicircolo applicati sopra la diagonale AC terminano di <lb/>fuori nella cicloide nuova, ma, applicati sulla cicloide volgare, terminano di <lb/>dentro in una curva, simile a un &int; inclinata, che evidentemente &egrave; la comite <lb/>robervalliana. </s></p><p type="main">

<s>Furono le inclinazioni del Nardi, come negli altri studi geometrici cos&igrave; <lb/>in questo, secondate dal Ricci, il quale dette anzi alla linea, vagheggiata fin <lb/>qui solitaria, una nobile famiglia di curve, che gli piacque chiamar <emph type="italics"/>cicloi&shy;<lb/>dali.<emph.end type="italics"/> Nel Settembre del 1645 conferiva col Torricelli queste sue nuove spe&shy;<lb/>culazioni, dicendogli che rimaneva in dubbio da qual principio far ad esse <lb/>curve dipendere la <emph type="italics"/>limitazion<emph.end type="italics"/> necessaria. </s>

<s>Che del resto, &ldquo; quanto a quel che <lb/>ella dice, scriveva all'amico e al maestro, che la lor quadratura &egrave; troppo re&shy;<lb/>condita, pare a me che sia teorema non dispregevole il dire che in tutte le <lb/>suddette figure l'eccesso della cicloidale, sopra il triangolo, sia uguale alla <lb/>figura genitrice. </s>

<s>E V. S. non si maravigli se queste figure non osservano le <lb/>leggi delle cicloidali considerate da lei, perch&egrave; a quelle son come genere alla <lb/>sua specie, e sarebbe strano allora che le osservassero, ovvero che le cicloi&shy;<lb/>dali di V. S. non avessero le condizioni generali delle figure da me consi&shy;<lb/>derate. </s>

<s>La facilit&agrave;, o diciamo la sincerit&agrave; della mia <emph type="italics"/>definizione,<emph.end type="italics"/> che scopre a <pb xlink:href="020/01/2831.jpg" pagenum="456"/>prima vista tutto il segreto, sappia V. S. che &egrave; stata procurata da me, pia&shy;<lb/>cendomi assai pi&ugrave; di rendere facilissime le cose, dove gli altri hanno affet&shy;<lb/>tato l'oscurit&agrave;, o che non hanno saputo ritrovare il suo natural principio; <lb/>che di renderle oscure, perch&egrave; altri ammiri in questa oscurit&agrave; quel che non <lb/>ci si trova &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>138). </s></p><p type="main">

<s>Quel principio generale poi, o quella limitazion necessaria, che il Ricci <lb/>fra il dubbio ricercava, pens&ograve; di stabilirla, definendo le relazioni fra la figura <lb/><figure id="id.020.01.2831.1.jpg" xlink:href="020/01/2831/1.jpg"/></s></p><p type="caption">

<s>Figura 305.<lb/>genitrice ECDB <lb/>(fig. </s>

<s>305) e la <lb/>generata AXC <lb/>in modo, che <lb/>tutto il perime&shy;<lb/>tro CDB, alla <lb/>sua parte EC o <lb/>CD, avesse la <lb/>proporzion me&shy;<lb/>desima che la <lb/>AB, alla EG o alla DF, questa e quella supposte parallele alla base. </s>

<s>Se dunque si <lb/>costruisce sopra i lati AB, BC il rettangolo MB, e sopra la AM la figura MHIA, <lb/>uguale e simile alla CEDB, e le due ordinate GE, FD sian condotte equidi&shy;<lb/>stanti dal centro O; avremo, per la fatta supposizione, AB:EG=BEC:EC= <lb/>HE:EG. Dividendo, HE:HG=BEC:EDB=BEC:CED=AB:FD. </s>

<s>Ma <lb/>HE=AB, dunque HG=FD, d'onde GE=IF. </s></p><p type="main">

<s>Con queste medesime ragioni dimostrandosi che tutte le altre infinite <lb/>ordinate, prese a coppia a coppia a ugual distanza dal centro O, son tagliate <lb/>dalla cicloidale in parti contrariamente uguali; se ne concluder&agrave; l'uguaglianza <lb/>de'trilinei CMIAC, CFABEC, ciascun de'quali sar&agrave; perci&ograve; la met&agrave; del qua&shy;<lb/>drilineo CMIABEC. </s>

<s>Ma questo quadrilineo &egrave; manifestamente uguale al ret&shy;<lb/>tangolo MB, di cui &egrave; met&agrave; il triangolo ABC; dunque un tal triangolo e il <lb/>trilineo corrispondente sono uguali, e perci&ograve; l'eccesso dello spazio cicloidale, <lb/>sopra il detto triangolo rettilineo, uguaglier&agrave; lo spazio della figura genitrice. </s></p><p type="main">

<s>Suppongasi ora che questa figura sia un mezzo cerchio, la semicircon&shy;<lb/>ferenza del quale sia stesa nella dirittura AB. </s>

<s>La curva AXC sar&agrave; allora una <lb/>cicloide primaria, essenzial propriet&agrave; della quale &egrave;, non solamente l'ugua&shy;<lb/>glianza tra AB e BEC, ma tra GE ed EC, da cui vien ordinata la propor&shy;<lb/>zione AB:GE=BEC:EC. </s>

<s>Dunque anche la cicloide primaria &egrave; generata <lb/>al modo delle altre curve, secondo la data definizione, e dovendo necessaria&shy;<lb/>mente esser proprio di lei quel che delle altre sue congeneri s'&egrave; dimostrato; <lb/>l'eccesso. </s>

<s>dunque dello spazio cicloidale, sopra il triangolo ACB uguaglier&agrave; il <lb/>semicircolo, e tutto intero esso spazio cicloidale a quel medesimo semicir&shy;<lb/>colo sar&agrave; triplo. </s></p><p type="main">

<s>Una tale uguaglianza tra la base e il perimetro del circolo genitore, e <lb/>tra qualunque ordinata e l'arco intercetto, a partire dal vertice, passa anche <lb/>in tutte le cicloidi secondarie, allungate che siano o contratte, e perci&ograve; di esse <pb xlink:href="020/01/2832.jpg" pagenum="457"/>pure, come appartenenti alla famiglia delle curve descritte, sar&agrave; vero che <lb/>l'eccesso dello spazio sopra il triangolo uguaglia la superficie del semi&shy;<lb/>cerchio. </s></p><p type="main">

<s>&Egrave; da notare per&ograve; che il Ricci non segue queste vie dirette, ma le obli&shy;<lb/>que, riducendo le sue dimostrazioni agli assurdi, e ci&ograve; forse con l'intenzione <lb/>di supplire al difetto, in cui aveva il Torricelli lasciata la scienza delle ci&shy;<lb/>cloidi secondarie, confermandone la verit&agrave; dei principii e delle conseguenze <lb/>anche nella mente di coloro, che non avessero accettata la dottrina degl'in&shy;<lb/>divisibili. </s>

<s>Nello scolio infatti all'appendice <emph type="italics"/>De dimensione cycloidis<emph.end type="italics"/> s'annun&shy;<lb/>ziano tre teoremi, ne'quali si suppone che lo spazio di qualunque cicloide <lb/>si componga d'un triangolo e d'un bilineo, ambedue i quali presi insieme <lb/>pareggino il triplo del semicerchio. </s>

<s>Chiamati T il triangolo, B la sua base, <lb/>R il raggio del circolo genitore, S lo spazio cicloidale, resulta dalle proposizioni <lb/>del Ricci T=B.R, S=B.R+<foreign lang="greek">p</foreign>R2, onde S:T=B.R+<foreign lang="greek">p</foreign>R2:B.R= <lb/>B+<foreign lang="greek">p</foreign>R:B=2B+2<foreign lang="greek">p</foreign>R:2B, che conferma la verit&agrave; del primo teorema <lb/>torricelliano, annunziato a pag. </s>

<s>92 della seconda parte delle Opere geome&shy;<lb/>triche. </s>

<s>Il secondo, chiamato C il circolo, trova espressa la sua verit&agrave; dalla <lb/>seguente equazione: S:C=B.R+<foreign lang="greek">p</foreign>R2:<foreign lang="greek">p</foreign>R2=2B+2<foreign lang="greek">p</foreign>R:2<foreign lang="greek">p</foreign>R. </s>

<s><lb/>Il terzo finalmente, ritenute le denominazioni di sopra, e per S&prime;, B&prime;, R&prime; in&shy;<lb/>tendendosi il secondo spazio cicloidale, la sua base e il raggio del circolo <lb/>genitore; si conclude facilmente cos&igrave;, dai principii dimostrati dal Ricci, S= <lb/>B.R+<foreign lang="greek">p</foreign>R2, S&prime;=B&prime;.R&prime;+<foreign lang="greek">p</foreign>R&prime;2, onde </s></p><p type="main">

<s><emph type="center"/>S:S&prime;=R(B+<foreign lang="greek">p</foreign>R):R&prime;(B&prime;+<foreign lang="greek">p</foreign>R&prime;)= <lb/>2R(2B+2<foreign lang="greek">p</foreign>R):2R&prime;(2B&prime;+2<foreign lang="greek">p</foreign>R&prime;).<emph.end type="center"/><lb/>&Egrave; perch&egrave; 2R, 2R&prime; son de'due spazi le respettive altezze, &egrave; patente che <lb/><emph type="italics"/>cuiuscumque cycloidalis spatii, ad quodlibet spatium cycloidale, ratio com&shy;<lb/>ponitur ex ratione altitudinis ad altitudinem, et ex ratione dupli basis <lb/>cum periphaeria genitrice, ad duplum basis cum periphaeria genitrice,<emph.end type="italics"/><lb/>come annunziava il Torricelli, tacendone la dimostrazione, perch&egrave;, essendosi <lb/>messo per vie tanto pi&ugrave; lunghe di quelle del Ricci, diceva che l'appendice <lb/>gli si sarebbe trasformata in un libro. </s></p><p type="main">

<s>Comuni essendo del Matematico di Arezzo e di quel di Roma gli studi, <lb/>nemmeno in pubblico volevano andar separati, e perci&ograve; il Nardi, riformando <lb/>nella seconda Ricercata geometrica il discorso intorno alla Cicloide, e facen&shy;<lb/>dolo copiare per darlo alle stampe; soggiungeva dopo le sue le speculazioni <lb/>del Ricci, che trascriviamo qui con fedelt&agrave; e con amore, riducendole nella <lb/>nostra Storia come gemme preziose, che la Scienza italiana viene ora per noi <lb/>ad aggiungere al suo ricco monile. </s></p><p type="main">

<s>&ldquo; Del rettangolo BD (nella figura 304 qui poco addietro) sia un lato <lb/>CD uguale alla circonferenza del mezzo cerchio AID, di cui il diametro sia <lb/>l'altro lato AD del rettangolo. </s>

<s>In questo intendasi la mezza cicloide COEA, <lb/>qual viene disegnata dal punto A, mentre il mezzo cerchio si ruzzola una <lb/>volta sopra il piano CD. </s>

<s>Quando dunque il mezzo cerchio abbia trascorso la <pb xlink:href="020/01/2833.jpg" pagenum="458"/>met&agrave; di DC, si trover&agrave; il punto A in F, il qual punto F tanto pi&ugrave; oltre <lb/>della met&agrave; trovasi di DC, ovvero della uguale KL, quanto &egrave; il semidiametro <lb/>IK: da che raccogliesi essere KF uguale alla retta IK, ed alla quarta parte <lb/>di periferia cio&egrave; a ID. </s>

<s>Con lo stesso metodo bisogna investigare gli altri siti <lb/>in altre date distanze. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; &Egrave; poi stato da altri insegnato che lo spazio della cicloide CEAD &egrave; tri&shy;<lb/>plo del mezzo cerchio AID, da cui descrivesi, e per dimostrar tal conclu&shy;<lb/>sione serve ancora una nuova, e forse piu naturale cicloide da noi inventata, <lb/>la cui origine &egrave; questa: Del mezzo cerchio AID sia diametro AD, e dagli <lb/>estremi di esso diametro si partano le tangenti AB, DC, delle quali ciascuna <lb/>si agguagli alla periferia AID. </s>

<s>Intendasi poi la retta AD moversi, senza mu&shy;<lb/>tare inclinazione, sino a che arrivi in BC, onde descrivasi il rettangolo BD, <lb/>e nello stesso tempo A trascorra con moto eguale la retta AD, dall'accop&shy;<lb/>piamento de'quali due moti si descriva la retta AC, e finalmente da ogni <lb/>punto di AC si continui verso BC una retta posta in dirittura con la sua <lb/>corrispondente ed eguale nel mezzo cerchio. </s>

<s>E cos&igrave; per esempio la retta FG <lb/>sia a dirittura con la sua corrispondente ed eguale IK. </s>

<s>Dunque tutte le or&shy;<lb/>dinate nel mezzo cerchio s'agguagheranno a tutte le ordinate nella figura <lb/>CFHAG, e l'altezza &egrave; uguale; adunque il mezzo cerchio s'agguaglier&agrave; alla <lb/>figura suddetta, ed in quella trasformerassi. </s>

<s>Il triangolo poi ADC &egrave; duplo <lb/>dello stesso mezzo cerchio, come nella misura del cerchio insegnammo, e ora <lb/>piacemi anche in quest'altro modo provare, acci&ograve; si osservi la variet&agrave; delle <lb/>invenzioni. </s>

<s>Intendasi ad un cerchio circoscritto qualsivoglia regolar poligono, <lb/>e siano il cerchio e il poligono basi co'loro perimetri di una superficie di <lb/>cilindro e di prisma retti, quali abbiano per altezza il semidiametro del cer&shy;<lb/>chio. </s>

<s>Adunque sar&agrave; la superficie del prisma il doppio del poligono, e ci&ograve; &egrave; <lb/>vero in infinito, sino al trasformarsi il poligono in cerchio, e la superficie <lb/>del prisma in cilindrica. </s>

<s>Adunque di nuovo, per le cose mostrate la super&shy;<lb/>ficie cilindrica sar&agrave; anch'essa doppia del cerchio. </s>

<s>Questa superficie poi s'ag&shy;<lb/>guaglia, come altrove provammo, ad un rettangolo, di cui un lato sia il se&shy;<lb/>midiametro, l'altro lato il perimetro del suddetto cerchio, e del medesimo <lb/>rettangolo &egrave; met&agrave; un triangolo rettangolo, che abbia seco comuni i lati com&shy;<lb/>prendenti l'angolo retto. </s>

<s>Adunque tal triangolo o il suo uguale ACD s'ag&shy;<lb/>guaglier&agrave; al cerchio predetto, ossia a due mezzi cerchi AID. </s>

<s>Adunque tutta <lb/>la mezza cicloide sar&agrave; tripla dello stesso mezzo cerchio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Qui considerisi come, dal rivolgersi una volta il perimetro del qua&shy;<lb/>drato sopra di una linea retta, descriverassi una figura composta di due trian&shy;<lb/>goli, e di tre quarte di cerchio. </s>

<s>Di queste le due estreme hanno per semidia&shy;<lb/>metro il lato del quadrato, e la di mezzo ha il diametro dello stesso. </s>

<s>Appellisi <lb/>tal figura <emph type="italics"/>Cicloide falsa.<emph.end type="italics"/> Negli altri regolari poligoni il simile proporzional&shy;<lb/>mente avviene, ed osservisi che dagli isoperimetri al cerchio descrivesi mag&shy;<lb/>giormente la linea curva, e tanto pi&ugrave; quanto meno numero di lati ottengono. </s>

<s><lb/>Ma quanto pi&ugrave; s'avvicinano alla condizione del circolo i poligoni, col numero <lb/>e con la parit&agrave; de'lati, pi&ugrave; regolare la formano. </s>

<s>Ma i contrari a questi la <pb xlink:href="020/01/2834.jpg" pagenum="459"/>formano pi&ugrave; sregolata, sebbene tutti la formano di porzioni circolari, una <lb/>meno di numero dei lati del descrivente poligono. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Or non &egrave; cosa mirabile che gli estremi dei cateti o semidiametri dei <lb/>poligoni descrivano porzioni di cerchi e di periferia, e che gli estremi pro&shy;<lb/>porzionali del cerchio descrivano altre linee e figure! Notisi di pi&ugrave; che nelle <lb/>cicloidi, descritte da poligoni di numero pari di lati, le porzioni di cerchio <lb/>sono impari, e la maggiore altezza &egrave; nel mezzo delle basi, e s'agguaglia al <lb/>diametro del poligono. </s>

<s>Ma negli impari poligoni le porzioni sono pari di nu&shy;<lb/>mero, e l'altezza maggiore non &egrave; nel mezzo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di nuovo, nella figura 304, la curva AHFC rappresenti la linea della <lb/>cicloide regolare e la curva AEFOC rappresenti la linea della volgare. </s>

<s>La <lb/>differenza consiste perch&egrave;, tirata FG parallela a BA, lato del rettangolo com&shy;<lb/>prendente la mezza cicloide, sicch&egrave; seghi, prodotta, il diametro AC ugual&shy;<lb/>mente; la volgare racchiude tra BAFG la regolare, e tra FGCD &egrave; racchiusa <lb/>dalla stessa. </s>

<s>Parimente la linea simile ad uno &int; inclinato significa co'suoi <lb/>punti i termini delle applicate nella volgare, ma i termini delle applicate nella <lb/>regolare sono nella AC. </s>

<s>La cagione poi di tal differenza scorgesi, per tro&shy;<lb/>varsi nella volgare il diametro del cerchio descrivente essa cicloide (qual <lb/>diametro si supponga parallelo ad AD) avanti CA, verso DC, mentre egli <lb/>trascorra tra il punto G e il lato AD, ma tra il punto G e il lato BC &egrave; posto <lb/>dopo, e solo nel punto G conviene l'uno e l'altro diametro. </s>

<s>Quindi le appli&shy;<lb/>cate s'avanzano in una parte e si ritirano nell'altra, con la stessa propor&shy;<lb/>zione, e dando in un luogo quanto tolgono nell'altro, mediante la condizione <lb/>del cerchio, s'agguagliano tutte le applicate nella suddetta parte della vol&shy;<lb/>gare a tutte le applicate nella parte della nostra cicloide. </s>

<s>E si osservi come <lb/>anche sopra basi circolari si possono formare altre cicloidi, di che esempi <lb/>non mancano nei moti annui e diurni dei mondani corpi. </s>

<s>A queste conside&shy;<lb/>razioni, per ultimo, aggiungeremo quest'altra del signor M. A. Ricci. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma I.<emph.end type="italics"/> &mdash; Sia CPB (nella passata 305) una figura intorno all'asse <lb/>PO, la quale manchi verso la parte P, e l'ordinatamente applicata COB le <lb/>serva di base, in cui sian prese due porzioni uguali CK, LB, dagli estremi <lb/>di essa C, B. S'alzino dai punti K, L le perpendicolari KE, LD, che seghino <lb/>del perimetro EC, DB. </s>

<s>Dico che EC, DB sono uguali, come si prova facil&shy;<lb/>mente con la sopraposizione. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Definizione.<emph.end type="italics"/> &mdash; Sia BDC una figura intorno l'asse, che manchi verso <lb/>la parte P, col cavo indentro, il convesso di fuori, e BC sia una delle ordi&shy;<lb/>natamente applicate. </s>

<s>Pongasi BA perpendicolare alla BC, e di che lunghezza <lb/>si vuole, e nel perimetro della figura sia preso qualsivoglia altro punto E, <lb/>e supponendo che tutto il perimetro BDC, alla parte CE ovvero CD, stia <lb/>come AB all'EG, e siano GE, DF equidistanti alla BA; si former&agrave; in tal ma&shy;<lb/>niera una figura AFGCEDB, la quale chiamo triangolo curvilineo; AB sua <lb/>base, e la figura BPC figura genitrice. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma II.<emph.end type="italics"/> &mdash; Sia dunque il suddetto triangolo curvilineo, con la sua <lb/>genitrice BDC, ed al punto A della base AB sia eretta la AM, base della <pb xlink:href="020/01/2835.jpg" pagenum="460"/>figura MHA, simile ed uguale alla medesima genitrice. </s>

<s>Si prendano nella BC <lb/>le parti KC, BL, e si passino le HK, LI parallele alla BA, le quali seghino <lb/>il triangolo in E, G; D, F, e la MHA ne'punti H ed I. </s>

<s>Dico che FD sar&agrave; <lb/>uguale a GH, e GE ad FI. </s>

<s>Imperocch&egrave; DL, KE segano, per il primo Lemma, <lb/>le parti BD, EC uguali: dunque BEC ad EC come AB ad EG, cio&egrave; HE ad EG. </s>

<s><lb/>E per conversion di ragione, HE ad HG come BEC a BE, ovvero il suo <lb/>uguale DC: e cos&igrave; AB a DF. </s>

<s>Dunque HE ad HG come AB a DF. </s>

<s>Ma BA, <lb/>HE sono uguali, dunque ancora HG, DF, e conseguentemente i loro residui <lb/>GE, FI, il che etc. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE. &mdash; <emph type="italics"/>Supposte le medesime cose, dico che il triangolo <lb/>curvilineo ACB sar&agrave; uguale all'altro ACM. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Perch&egrave; altrimenti sar&agrave; maggiore o minore. </s>

<s>Pongasi prima eccedente <lb/>della quantit&agrave; Y, e si divida con rette parallele alla BA il curvilineo parallelo&shy;<lb/>grammo AHMCEB, finch&egrave; troviamo il parallelogrammo IADB minore della Y. </s>

<s><lb/>Poi s'inscriva nei triangoli una figura composta di parallelogrammi curvili&shy;<lb/>nei, egualmente con l'IADB alt&igrave;, intendendo che per F passi la figura ge&shy;<lb/>nitrice con la applicata perpendicolare alla BA, della qual figura, per il primo <lb/>lemma, LDF ne segher&agrave; le parti uguali e congruenti FN, DB, che forme&shy;<lb/>ranno un parallelogrammo curvilineo inscritto: e similmente formeranno gli <lb/>altri inscritti, come MHGS, facendo passar la genitrice figura per il puuto G. </s>

<s><lb/>Ma questi curvilinei hanno le altezze uguali BL, KC, e le basi FD, GH pur <lb/>uguali; dunque saranno uguali. </s>

<s>Il simile proveremo delli altri parallelogrammi <lb/>inscritti, egualmente lontani dalle basi AB ed MC. </s>

<s>Dunque le inscritte figure <lb/>ne'triangoli sono uguali e minori de'triangoli, ne'quali s'inscrivono. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Inoltre, il parallelogrammo curvilineo FX &egrave; uguale all'FR, per l'ugua&shy;<lb/>lit&agrave; delle bas&igrave; e delle altezze: XG al ZR, CG al ZB. </s>

<s>Dunque l'eccesso della <lb/>figura circoscritta al trilineo ACB, sopra l'inscritto nel medesimo, &egrave; uguale <lb/>ad IADB, e minore di Y. </s>

<s>Sar&agrave; dunque molto minore di Y l'eccesso del&shy;<lb/>l'ACB sopra la sua inscritta, e per&ograve; detta inscritta ancora eccedente l'altro <lb/>triangolo, il che &egrave; impossibile, poich&egrave; si &egrave; provata minore del triangolo. </s>

<s>Dun&shy;<lb/>que ACB triangolo non &egrave; maggiore dell'altro ACM. L'istesso progresso ci <lb/>varr&agrave; per dimostrare che ACM non sia maggiore di ACB, dunque sono uguali, <lb/>il che etc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario I.<emph.end type="italics"/> &mdash; Essendo che facilmente si dimostra il curvilineo AMCB <lb/>essere uguale al rettilineo parallelogrammo MB, segue che MB sia doppio <lb/>del triangolo ACB curvilineo, e per&ograve; uguale al rettilineo triangolo ABC, <lb/>quando si giunga la retta AC. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario II.<emph.end type="italics"/> &mdash; Perch&egrave; la figura AGCKB &egrave; uguale al triangolo cur&shy;<lb/>vilineo ACB, insieme con la figura genitrice, e il triangolo detto &egrave; uguale al <lb/>triangolo rettilineo ABC; dunque l'eccesso della figura AGCKB, sopra il trian&shy;<lb/>golo rettilineo ABC, sar&agrave; uguale alla figura genitrice. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Or noto che, ponendosi BDC essere un semicerchio, e la base AB <lb/>uguale alla sua periferia; la AGCKB sar&agrave; una primaria semicicloide. </s>

<s>Perch&egrave; <lb/>allora sar&agrave; AB, a tutta la periferia BEC, come FD alla DEC, e per&ograve; la parte <pb xlink:href="020/01/2836.jpg" pagenum="461"/>residua FI, ovvero AN, sar&agrave; uguale alla parte residua BD, ovvero FN, se&shy;<lb/>condo la passione della Cicloide primaria. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Immaginiamoci poi sopra l'AB rivolgersi il semicerchio OHN (fig. </s>

<s>306), <lb/>per descrivere col punto H una semicicloide primaria AHCB, ed il mezzo <lb/><figure id="id.020.01.2836.1.jpg" xlink:href="020/01/2836/1.jpg"/></s></p><p type="caption">

<s>Figura 306.<lb/>cerchio concentrico KGL, in <lb/>quel moto, descriva, con uno <lb/>de'suoi punti G, la semicicloide <lb/>secondaria, di cui sia base DE, <lb/>uguale all'AB. </s>

<s>Mentre OH avr&agrave; <lb/>calcata la parte AO, il punto <lb/>concentrico avr&agrave; calcata la parte <lb/>DL, con la sua parte GL, la quale <lb/>&egrave; simile alla OH, per l'angolo <lb/>GIL al centro comune. </s>

<s>Dunque <lb/>LGK a GK, ovvero OHN all'arco <lb/>HN &egrave; come AB, ovvero DE, <lb/>all'HR o al suo uguale OB, ovvero GF. </s>

<s>Dunque EFS ad FS come DE a GF, <lb/>ed &egrave; il punto S vertice della secondaria cicloide, DE sua base. </s>

<s>Adunque tanto <lb/>la cicloide primaria quanto la secondaria sono specie della figura da noi pro&shy;<lb/>posta nel principio, e per conseguenza l'eccesso della semicicloide, o prima&shy;<lb/>ria o secondaria, sopra il triangolo rettilineo, i lati del quale sono la base e <lb/>l'altezza di detta semicicloide; &egrave; uguale al semicircolo genitore, il che etc. </s>

<s>&rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>951-59). </s></p><p type="main">

<s>In queste geometriche speculazioni del Ricci, il merito e l'importanza <lb/>delle quali si conosceranno facilmente dai nostri Lettori, termina la storia <lb/>de'progressi fatti in Italia intorno alla quadratura della Cicloide. </s>

<s>Non si te&shy;<lb/>neva per&ograve; ancora per assoluta la scienza di lei, tuttavia rimanendo a defi&shy;<lb/>nire le proporzioni, che passano tra i solidi rotondi generati dallo spazio ci&shy;<lb/>cloidale, e i cilindri a lui circoscritti. </s>

<s>Ora &egrave; notabile questo passaggio dalla <lb/>Geometria pura alla Stereometria, a che non pensarono punto da principio <lb/>n&egrave; Galileo n&egrave; il Mersenno; ond'&egrave; a ricercar l'occasione, per cui dalle sem&shy;<lb/>plici superficie si venne, col proporre i solidi, a complicare il problema. </s></p><p type="main">

<s>Quell'occasione dai recati documenti &egrave; manifesta: ella risale al teo&shy;<lb/>rema dal Niceron proposto a dimostrarsi ai Matematici suoi francesi, avutene <lb/>in Bologna le conclusioni dal Cavalieri. </s>

<s>Al Roberval dunque, tutto allora in&shy;<lb/>torno alla Cicloide, cadde facilmente in pensiero che si potesse circoscrivere <lb/>a lei un rettangolo, come intorno alla parabola, e il bel teorema nuovo ve&shy;<lb/>nuto d'Italia, delle proporzioni che passano tra il fuso parabolico e il cilin&shy;<lb/>dro circoscritto, dette all'ingegnoso Parigino motivo di dimostrare intorno al <lb/>solido cicloidale un altro simile, e non men bello e nuovo teorema. </s>

<s>Anzi il <lb/>giovanile ardor della mente lo port&ograve; a considerare che poteva farsi il rivol&shy;<lb/>gimento non solo intorno alla base, ma intorno agli altri lati del rettangolo <lb/>circoscritto, d'onde venissero a nascer solidi di varia forma e misura, tra'quali <lb/>egli ebbe pure a trovare le proporzioni. </s></p><pb xlink:href="020/01/2837.jpg" pagenum="462"/><p type="main">

<s>Di qui avvenne che, scambiatesi tra il Cavalieri e il Roberval le pro&shy;<lb/>poste, quegli le partecipasse non a Galileo solo, ma ai discepoli e agli amici <lb/>compiute nel numero e nell'ordine dei quesiti, sempre confermando gli altri <lb/>nella propria opinione, che cio&egrave; fossero cos&igrave; fatte proposte francesi problemi <lb/>da risolversi in Italia, e non teoremi gi&agrave; dimostrati. </s>

<s>Con questo falso con&shy;<lb/>cetto nella mente, da cui ebbero poi precipua causa i litigi che diremo, s'era <lb/>il Torricelli messo all'impresa, nella quale aveva appena fatto il primo passo, <lb/>che ne volle dare al Roberval l'annunzio, dicendogli com'avesse in cinque <lb/>varie maniere dimostrata la misura dello spazio cicloidale. </s>

<s>Ma del resto, sog&shy;<lb/>giungeva il di primo ottobre 1643, <emph type="italics"/>quoad solida nihil habeo,<emph.end type="italics"/> ond'&egrave; a nar&shy;<lb/>rare come e quando gli occorresse l'ambita invenzione, con la quale in mano <lb/>lo vedremo tornare innanzi allo stesso Roberval, compiacendosi d'aver della <lb/>Cicloide ritrovata tutta intera la scienza da lui proposta. </s></p><p type="main">

<s>Venne anche questa volta la prima occasione dal Nardi, il quale, come <lb/>si rammemoreranno coloro, che nel Cap. </s>

<s>II del precedente nostro Tomo hanno <lb/>letto il paragrafo IV; aveva dimostrato in che facile modo si potesse, con la <lb/>regola centrobarica, ritrovar la misura del fuso parabolico rispetto al cilin&shy;<lb/>dro circoscritto. </s>

<s>I problemi perci&ograve; dei solidi cicloidali, quali venivano propo&shy;<lb/>sti dai Francesi, vide bene esso Nardi che s&igrave; sarebbero potuti risolvere con <lb/>la medesima facilit&agrave;, quando per&ograve; si sapesse, come della parabola, il centro <lb/>di gravit&agrave; della Cicloide. </s>

<s>Si poteva dentro lo spazio inscrivere un triangolo <lb/>di pari base e altezza della curva, ma rimaneva tuttavia incerto il centro <lb/>de'bilinei laterali, essendo la Cicloide volgare. </s>

<s>Nella regolare per&ograve;, novamente <lb/>inventata, era quel centro manifestamente il medesimo che del circolo geni&shy;<lb/>tore descritto intorno all'asse, sopra il quale asse il centro di gravit&agrave; del <lb/>tutto, per i noti teoremi archimedei, necessariamente consegue da quello delle <lb/>parti, Propostasi dunque questa sua Cicloide non ebbe il Nardi alcuna diffi&shy;<lb/>colt&agrave; in ritrovar la stereometria dei solidi rotondi, con quel metodo centro&shy;<lb/><figure id="id.020.01.2837.1.jpg" xlink:href="020/01/2837/1.jpg"/></s></p><p type="caption">

<s>Figura 307.<lb/>barico, di cui fu egli il primo <lb/>a farne, in cos&igrave; fatti quesiti, <lb/>l'applicazione, sia diretta&shy;<lb/>mente dal centro di gravit&agrave; <lb/>desumendo i solidi e le su&shy;<lb/>perficie dei rivolgimenti, sia <lb/>conversamente da'solidi e <lb/>dalle superficie revolute de&shy;<lb/>sumendone i centri. </s></p><p type="main">

<s>Abbiasi la Cicloide nardiana DHEF, (fig. </s>

<s>307) col vertice in E, e con la <lb/>base DF, dal mezzo L della quale s'alzi perpendicolarmente LE, asse della <lb/>figura e diametro del circolo genitore, di cui il centro A sar&agrave;, per la natural <lb/>costruzione della curva, centro di gravit&agrave; de'bilinei laterali, i quali ugua&shy;<lb/>gliano, per le cose gi&agrave; dimostrate, la superficie dello stesso circolo genitore. </s>

<s><lb/>Se CE &egrave; doppia di CL, avverr&agrave; in C il centro di gravit&agrave; del triangolo DEF, <lb/>onde il centro di tutto lo spazio cicloidale sar&agrave; in B, talmente situato, che <pb xlink:href="020/01/2838.jpg" pagenum="463"/>AB abbia a BC la proporzione di due a uno, come reciprocamente ha tal <lb/>proporzione il triangolo ai due bilinei insieme, o al circolo solo. </s>

<s>Che se di&shy;<lb/>vidasi LE in 36 parti uguali, AL sar&agrave; di queste parti 18, LB 14, e BE 22. </s></p><p type="main">

<s>Sia circoscritto ora alla cicloide il rettangolo GF, e si rivolgano ambedue <lb/>le figure intorno alla DF loro base comune. </s>

<s>Verr&agrave; da cos&igrave; fatto rivolgimento <lb/>generato un solido rotondo, che chiameremo S, e che, secondo la regola <lb/>guldiniana dallo stesso Nardi confermata con le ragioni della Geometria, &egrave; <lb/>uguale a un prisma avente per base il piano cicloidale, e per altezza la cir&shy;<lb/>conferenza ridotta in dirittura, e quale si descriverebbe dal raggio LB, di&shy;<lb/>stanza del centro di gravit&agrave; di esso piano dall'asse della revoluzione. </s>

<s>Sar&agrave; <lb/>nello stesso tempo generato un cilindro C, uguale per le medesime ragioni a <lb/>un parallelepipedo avente per base il rettangolo GF, e per altezza la circonfe&shy;<lb/>renza descritta dal raggio AL, cosicch&egrave;, dietro le equazioni S=DHEIF.2<foreign lang="greek">p</foreign>BI., <lb/>e C=GF.2<foreign lang="greek">p</foreign>AL, potr&agrave; scriversi la proporzione S:C=DHEIF.BL:GF.AL, <lb/>la quale, essendo lo spazio cicloidale al rettangolo circoscritto come 3 a 4, e <lb/>BL=14, AL=18; si riduce alla proporzione definita in numeri S:C= <lb/>3.14:4.18=7:12. </s></p><p type="main">

<s>Se il rivolgimento si facesse intorno alla GK, tangente il vertice, &egrave; ma&shy;<lb/>nifesto che rimarrebbero le cose come di sopra, eccettuato che il prisma, a <lb/>cui s'uguaglia il solido cicloidale, invece di aver per altezza la circonferenza <lb/>di LB, avr&agrave; quella descritta da EB, e la proporzione si trasformer&agrave; nella se&shy;<lb/>guente S:C=DHEIF.EB:GF.AE=3.22:4.18=11:12. Che se in&shy;<lb/>vece si supponga rivolgersi le figure intorno alla GD, parallela all'asse, i <lb/>solidi rotondi che indi nascono uguaglieranno due prismi aventi la medesima <lb/>altezza, perch&egrave; le distanze de'centri di gravit&agrave; dall'asse tornano uguali: ond'&egrave; <lb/>ch'essi rotondi staranno come le rispettive basi prismali, cio&egrave; come 3 a 4. </s></p><p type="main">

<s>Di conseguire con un tal metodo la proporzione de'solidi intorno l'asse <lb/>non era speranza, bisognandovi il centro di gravit&agrave; della mezza cicloide, <lb/>ignoto al Nardi, cos&igrave; nella sua, come nella volgare. </s>

<s>Ond'&egrave; che soli questi <lb/>tre problemi fece, cos&igrave; come noi gli trascriviamo, mettere nelle <emph type="italics"/>Scene,<emph.end type="italics"/> per <lb/>poi ridurli ai loro luoghi insieme, con le altre matematiche invenzioni, e <lb/>pubblicarli nelle sue Ricercate: </s></p><p type="main">

<s>&ldquo; Sia la Cicloide nostra, che <emph type="italics"/>regolare<emph.end type="italics"/> nominiamo, DHEIF, nella mede&shy;<lb/>sima figura, di cui la base DF, la sommit&agrave; E, l'asse EL, ed in essa descri&shy;<lb/>vasi il triangolo DEF, e intorno alla stessa il rettangolo GF. Ora, posto es&shy;<lb/>sere EL 18, sar&agrave; la met&agrave; sua AE 9, ed il punto A sar&agrave; centro delle due <lb/>porzioni DHE, FIE, come per le cose altrove dimostrate, si pu&ograve; intendere. </s>

<s><lb/>Ma posta EC 12, sar&agrave; il punto C centro del triangolo DEF. </s>

<s>E perch&egrave; questo, <lb/>alle due porzioni, ha la ragione di due a uno; sar&agrave; EB, posta 11, centro <lb/>della Cicloide. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Dunque il cilindro, nato dalla revoluzione del rettangolo intorno a DF, <lb/>al solido, nato dalla revoluzione della Cicloide intorno alla stessa DF, sar&agrave; <lb/>come 12 a 7. Ma intorno a GE sar&agrave; come 12 a 11, e intorno a GD come <lb/>4 a 3. &ldquo; (Mss. </s>

<s>Gal. </s>

<s>Disc. </s>

<s>T. XX, pag. </s>

<s>149). </s></p><pb xlink:href="020/01/2839.jpg" pagenum="464"/><p type="main">

<s>Fu la nuova invenzione del Nardi prima, che a ogni altro, comunicata al <lb/>suo carissimo Ricci, il quale facevagli osservare che l'ultimo dei tre teoremi <lb/>si verifica anche nella Cicloide volgare, essendo il solido, nato di lei mentre <lb/>ch'ella si rivolge intorno al lato del rettangolo parallelo all'asse, al cilindro <lb/>circoscritto, come l'una all'altra figura genitrice, cio&egrave; come tre a quattro, <lb/>ossia, secondo che egli diceva, in ragione subsesquiterza. </s>

<s>Di qui avvenne che <lb/>il Nardi, ai tre teoremi relativi alla sua cicloide nuova, v'aggiungesse il <lb/>quarto relativo alla cicloide antica, nell'annunziargli che fece al Torricelli, <lb/>il quale, credendo che fosse quell'osservazione sovvenuta allo stesso Nardi, <lb/>gliene volle rendere pubblica testimonianza, quasi in segno di gratitudine <lb/>verso colui, che avevagli aperta e dimostrata la via, da giungere al termine <lb/>desiderato. </s>

<s>Che altro infatti gli rimaneva, per risolvere i problemi venuti di <lb/>Francia, se non che a ritrovare il centro di gravit&agrave; della cicloide, coraggio&shy;<lb/>samente affrontando quelle difficolt&agrave;, innanzi alle quali s'erano arretrati, o <lb/>l'avevano tentate solamente di traverso, gli amici suoi pur cos&igrave; valorosi? </s>

<s><lb/>Come riportasse il Torricelli di ci&ograve; lieta vittoria fu veduto nella proposi&shy;<lb/>zione LVI, scritta da noi nel capitolo V qui addietro, nella qual proposizione <lb/>l'Autor dimostrava che il centro di gravit&agrave; della Cicloide cos&igrave; divide l'asse, <lb/>che la parte al vertice stia a quella verso la base, come sette sta a cinque. </s></p><p type="main">

<s>Or s'intenda nella solita figura 307, disegnata in DHEIF la cicloide <lb/>volgare, col suo baricentro in B. </s>

<s>Essendo EB=7, BL=5, e AL=6, non <lb/>rimane a far altro che a sostituire questi numeri nelle formule gi&agrave; poste dal <lb/>Nardi, le quali, per i solidi intorno alla base si riducono a S:C=3.5:4.6= <lb/>5:8, e per i solidi intorno al lato opposto alla base a S:C=3.7:4.6= <lb/>7:8. Il primo de'quali teoremi, tralasciando l'altro perch&egrave; facilissimo con <lb/>somiglianti metodi a dimostrarsi, si legge manoscritto cos&igrave;, in fine al trat&shy;<lb/>tatello torricelliano della Cicloide: </s></p><p type="main">

<s>&ldquo; Solidum cycloidale circa basim revolutum ad cylindrum circumscriptum <lb/>est ut 5 ad 8. &ldquo; </s></p><p type="main">

<s>&ldquo; Esto cycloidale spatium DHEIF, cuius axis EL, centrum gravitatis B, <lb/>rectangulum vero circumscriptum sit GF, ipsiusque centrum gravitatis sit A. </s>

<s><lb/>Demonstratum iam est NL ad BL esse ut 6 ad 5, et spatium GF, ad spa&shy;<lb/>tium DHEIF, esse ut 4 ad 3. (Hoc in appendice ad libellum <emph type="italics"/>De dimensione <lb/>parabolae.<emph.end type="italics"/>) &rdquo; </s></p><p type="main">

<s>&ldquo; Convertatur iam utraque figura circa basim DF, habebitque solidum <lb/>ex DHEIF, ad cylindrum ex GF, rationem compositam ex ratione figurae <lb/>planae DHEIF ad rectangulum GF, nempe ex ratione numeri 15 ad 20, et <lb/>ex ratione distantiarum BL ad AL, nempe ex ratione 20 ad 24. Ergo soli&shy;<lb/>dum cycloidale circa basim, ad cylindrum sibi circumscriptum, erit ut 15 <lb/>ad 24, sive in minimis ut 5 ad 8, quod ostendere volebam. </s>

<s>&rdquo; (ibid., T. XXXIV, <lb/>fol. </s>

<s>278). </s></p><p type="main">

<s>De'solidi intorno alla GK parallela alla base dicemmo come il Torri&shy;<lb/>celli ne lasciasse a concludere facilmente la proporzione di 7 a 8, richiaman&shy;<lb/>dosi al teorema del Nardi, per i solidi nati dal rivolgersi le due figure in-<pb xlink:href="020/01/2840.jpg" pagenum="465"/>torno al lato GD del rettangolo circoscritto. </s>

<s>Rimaneva, per aver questo <lb/>trattatello cicloidale compiuto, a ritrovar la proporzione che passa tra il so&shy;<lb/>lido e il cilindro generati ambedue dalla rivoluzione intorno all'asse, ci&ograve; che <lb/>non potevasi con l'intrapreso metodo conseguire, senz'aver prima determinato <lb/>il punto, in cui la mezza cicloide concentra il suo peso. </s>

<s>Da B condotta una <lb/>parallela alla base, era certissimo che doveva sopra questa linea cadere quel <lb/>punto, ma a qual distanza precisamente dall'asse pareva difficilissimo, per non <lb/>dire impossibile, a dimostrare. </s>

<s>E nonostante volle il Torricelli far credere <lb/>di avere anche di ci&ograve; certissima matematica dimostrazione, dalla quale, per <lb/>l'applicazione della Regola guldiniana, conseguiva essere il solido della mezza <lb/>cicloide, al cilindro circoscritto, nella proporzion medesima di 11 a 18. Tro&shy;<lb/>viamo una tal presunzione espressa in pubblico nel documento che citeremo <lb/>e in un estratto di lettera privata a Raffaello Magiotti, a cui il Torricelli <lb/>stesso cos&igrave; diceva: </s></p><p type="main">

<s>&ldquo; Il solido della Cicloide rivolta intorno all'asse, al cilindro circoscritto, <lb/>&egrave; come 11 a 18, dimostrazione difficilissima. </s>

<s>Il solido <emph type="italics"/>circa basim,<emph.end type="italics"/> al suo <lb/>cilindro &egrave; come 5 a 8 &egrave; pi&ugrave; facile. </s>

<s>Pur l'una e l'altra si trova per via di <lb/>meccanica, trovato prima il centro di gravit&agrave; della figura genitrice, in che <lb/>linea stia, or parallela alla base, che &egrave; difficilissimo, ed or parallela all'asse, <lb/>che &egrave; peggiore. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Trovato questo centro, ho poi la dimostrazione dei solidi. </s>

<s>La proposi&shy;<lb/>zione &egrave; questa: <emph type="italics"/>Date due figure piane<emph.end type="italics"/> DK, (nella ultima figura 307) <emph type="italics"/>di cui <lb/>sia centro A, e DETF, di cui sia centro M, e si rivolgano intorno al&shy;<lb/>l'asse DF; il solido di DK, al solido di DEIF, avr&agrave; proporzione composta <lb/>della figura DK alla DEIF, e della distanza AL alla distanza MN.<emph.end type="italics"/> Per&ograve;, <lb/>supposta questa proposizione che da me si dimostra, (come si vede nella pro&shy;<lb/>posizione XII <emph type="italics"/>De momentis,<emph.end type="italics"/> da noi ordinata nel capitolo precedente) o per <lb/>dirla &egrave; piuttosto invenzione d'altri che mia, e trovato i centri della cicloide <lb/>e semicicloide, sapendosi gi&agrave; la proporzione delle figure piane e la propor&shy;<lb/>zione delle distanze dall'asse; si trova la proporzione composta, che &egrave; quella <lb/>dei solidi. </s>

<s>La dimostrazione del solido <emph type="italics"/>circa basim<emph.end type="italics"/> l'ebbe il signor Nardi e <lb/>il signor Ricci dal 1644. &rdquo; (ivi T. XL, fol. </s>

<s>23). </s></p><p type="main">

<s>Erano di una tal dimostrazione in gran desiderio i due amici, special&shy;<lb/>mente dietro quel che avevano letto fra le varie Opere geometriche, nello <lb/>Scolio alla proposizione XVIII del primo libro <emph type="italics"/>De motu gravium,<emph.end type="italics"/> in fine al <lb/>quale Scolio, dop'aver detto il Torricelli che ometteva la dimostrazione delle <lb/>tangenti, de'solidi e de'centri di gravit&agrave; degli spazi cicloidali, <emph type="italics"/>ad evitandam <lb/>molem,<emph.end type="italics"/> soggiungeva in tal guisa: &ldquo; Satis sit interea lectorem hic admo&shy;<lb/>nuisse quod, si Cycloidis spatium circa basim convertatur, erit solidum ad <lb/>cylindrum circumscriptum ut 5 ad 8: si vero circa tangentem basi paralle&shy;<lb/>lam ut 7 ad 8. Centrum Cycloidis axem secat, ita ut partes sint ut 7 ad 5. <lb/>Demonstratur etiam ratio solidi circa axem, ad cylindrum circumscriptum: <lb/>item in qua linea axi parallela sit centrum semicycloidis. </s>

<s>Clar. </s>

<s>vir Antonius <lb/>Nardi ostendit quod, si cyclois circa tangentem axi parallelam convertatur, <pb xlink:href="020/01/2841.jpg" pagenum="466"/>solidum ad suum cylindrum erit subsesquitertium. </s>

<s>&rdquo; (pag. </s>

<s>121, 22). Le quali <lb/>parole leggendo il Ricci nel settembre del 1644 ringraziava l'Autore dell'aver&shy;<lb/>gli donato il libro, in cui trovava tutte quelle proposizioni ammirabili, fa&shy;<lb/>cendogli questa osservazione. </s>

<s>&ldquo; Ho poi veduto citare una proposizione tale: <lb/><emph type="italics"/>Il solido nato dalla Cicloide, girata intorno una tangente all'asse paral&shy;<lb/>lela, del suo cilindro &egrave; subsesquiterza:<emph.end type="italics"/> cosa dimostrata da me fin da prin&shy;<lb/>cipio che sentii nominar la Cicloide, e, per la facilit&agrave; con che si dimostra, <lb/>non ne ho mai fatta stima veruna. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Tom. </s>

<s>XLII, fol. </s>

<s>50). </s></p><p type="main">

<s>Non deve averne fatta grande stima nemmeno il Nardi, per cui non <lb/>pens&ograve; di avvertire il Torricelli che il teorema del solido intorno alla tangente <lb/>parallela all'asse era del Ricci. </s>

<s>Il sentirsi ora attribuire cosa di s&igrave; poco mo&shy;<lb/>mento, senza far motto del metodo ch'era proprio suo, avuto il quale, il <lb/>merito del Torricelli non riusciva che secondario; deve essere dispiaciuto al <lb/>Nardi, il quale per&ograve; non fece, che da noi si sappia, di ci&ograve; lagnanza con nes&shy;<lb/>suno. </s>

<s>Rimase perci&ograve; nell'animo dello stesso Torricelli dell'ambita invenzione <lb/>la compiacenza intera, la quale venne nonostante a diminuirsegli da un'altra <lb/>parte, quando il Mersenno, a proposito della quadratura, gli soggiungeva in <lb/>una lettera del d&igrave; 13 giugno 1644, aver il Roberval da qualche anno dimo&shy;<lb/>strato che il solido cicloidale intorno alla base sta al cilindro circoscritto <lb/>come 5 a 8. </s></p><p type="main">

<s>Se fosse stata dal Matematico parigino ritrovata la proporzione anche <lb/>fra gli altri solidi il Torricelli era incerto, ma pure si lusingava che no, <lb/>fermamente credendo che il centro di gravit&agrave; della Cicloide, e l'applicazione <lb/>della regola centrobarica, non fosser cose note che a lui. </s>

<s>Di qui &egrave; che al&shy;<lb/>l'unico teorema annunziatogli dal Mersenno aggiungeva la nota dei parecchi <lb/>altri da s&egrave; dimostrati intorno alle propriet&agrave; della cicloide, nella qual nota <lb/>mandata in Francia parve al Roberval di sentire alitarvi uno spirito di ar&shy;<lb/>roganza. </s>

<s>Altre occas&igrave;oni s'aggiunser poi ad irritare sempre pi&ugrave; gli animi <lb/>de'due matematici, che finirono per accusarsi obbrobriosamente a vicenda <lb/>d'usurpazione e di plagio. </s>

<s>&mdash; Ora imparo a credere, scriveva il Torricelli del <lb/>Roberval, ch'ei non avesse la quadratura della Cicloide, <emph type="italics"/>ma la prendesse <lb/>dalla mia.<emph.end type="italics"/> &mdash; E dop'aver minutamente raccontato come passassero le cose <lb/>fra lui, e quei signori francesi, concludeva, invocando a suo giudice il mondo <lb/>scientifico: <emph type="italics"/>vedete che furto vergognoso hanno tentato di farmi!<emph.end type="italics"/></s></p><p type="main">

<s>Il Roherval di rincontro, descritte l'arti degli invidiosi e degli emuli, da <lb/>lui rassomigliati ai fuchi, che non sapendo elaborare il dolce miele, inva&shy;<lb/>dono i favi delle api: &ldquo; his artibus, soggiungeva, ipsa trochoides, eiusque <lb/>tangentes, et plana, sed et solida ferme omnia mihi erepta sunt. </s>

<s>&rdquo; (<emph type="italics"/>DeTro&shy;<lb/>choide.<emph.end type="italics"/> Ouvr. </s>

<s>cit. </s>

<s>p. </s>

<s>343). E perch&egrave; non apparisse dubbio essere contro il <lb/>Torricelli propriamente diretta l'accusa di furto diceva di serbare ancora le <lb/>lettere di lui: di lui, <emph type="italics"/>qui prae caeteris sapere videri volebat,<emph.end type="italics"/> ed ebbesi al <lb/>contrario, rispetto al solido intorno l'asse, scoperta la propria ignoranza, d'onde <lb/>gli nacque nell'animo quella indignazione e quella rabbia! (ivi.) </s></p><p type="main">

<s>S'ingerirono nella lite avvocati, difensori naturalmente delle ragioni dei <pb xlink:href="020/01/2842.jpg" pagenum="467"/>loro clienti, e prima usc&igrave; in francese un libretto intitolato <emph type="italics"/>Histoire de la <lb/>Roulette,<emph.end type="italics"/> che per dargli anche maggior diffusione, fu tradotto in latino. </s>

<s>Si <lb/>voleva dimostrare in esso che aveva la Cicloide avuto in Parigi la nascita e <lb/>l'educazione, e che perci&ograve; il Torricelli bugiardamente diceva esser sua figlia <lb/>naturale quella, che in verit&agrave; non era che adottiva. </s>

<s>Carlo Dati, nella sua <lb/><emph type="italics"/>Lettera a'Filaleti,<emph.end type="italics"/> stampata in Firenze nel 1663 sotto il nome di <emph type="italics"/>Timauro <lb/>Antiate,<emph.end type="italics"/> rispose alle accuse dello storico francese, che sentenziava senza re&shy;<lb/>car documenti, con i quali in mano concludeva esso Dati col dire che, non <lb/>dubitando punto della verit&agrave; delle invenzioni robervelliane e del loro pri&shy;<lb/>mato, si negava per&ograve; che il Torricelli fosse giunto a ritrovar le medesime <lb/>cose, dietro la notizia di quel che era stato fatto dagli altri. </s></p><p type="main">

<s>L'apologia del Dati &egrave; pienamente confermata dalla nostra Storia, la quale <lb/>ha gi&agrave; contato passo per passo i progressi fatti dalla scienza della Cicloide, <lb/>prima in Parigi e poi in Firenze, dove le prime mosse furon date da Ga&shy;<lb/>lileo. </s>

<s>L'incertezze e le fallacie dell'esperienza meccanica essendo state tolte <lb/>dal Nardi, venne da ci&ograve; a incorarsi la speranza della quadratura nel Torri&shy;<lb/>celli, che riusc&igrave; a dimostrarla con feconda facilit&agrave;, e con geometrica accura&shy;<lb/>tezza. </s>

<s>Persuasi da questo fatto i dubitosi Galileiani che il problema era so&shy;<lb/>lubile per ragioni di Geometria, il Nardi stesso vi s'applic&ograve;, immaginando <lb/>la Cicloide regolare, la quale, per la facile invenzione del suo centro di gravit&agrave;, <lb/>dette modo al suo Autore di ritrovar con la regola centrobarica le propor&shy;<lb/>zioni tra i solidi, e i cilindri circoscritti, rivolgendosi le figure ora intorno <lb/>alla base, e ora intorno alla tangente all'origine e alla cima. </s>

<s>Da ci&ograve; prese <lb/>l'esempio il Torricelli di trattar col medesimo metodo la Cicloide volgare, e <lb/>datosi a ricercare il centro di gravit&agrave; di lei, e ritrovatolo esattamente, gli <lb/>vennero con facilit&agrave; conclusi per questa figura i tre teoremi de'solidi, che <lb/>analogamente il Nardi aveva conclusi per la sua. </s></p><p type="main">

<s>In Parigi l'ufficio di ostetricante fu fatto dal Mersenno, ma il parto lo <lb/>dette alla luce il Roberval da s&egrave; solo, avuta da Archimede la dottrina degli <lb/>indivisibili, e col teorema geometrico <emph type="italics"/>Degli anelli<emph.end type="italics"/> supplendo al servigio reso <lb/>in Italia dal teorema del Guldino. </s>

<s>Bench&egrave; dunque vari fossero gl'inlzi, e vari <lb/>gli istrumenti, &egrave; un fatto ormai dimostrato dalla Storia che si condussero <lb/>i due Matematici a scoprire le medesime verit&agrave;, senza che l'uno sapesse <lb/>nulla dell'altro. </s>

<s>E perci&ograve; si diceva che l'apologia del Dati era giusta, in quanto <lb/>l'Autore difendeva il suo proprio amico e maestro dall'accusa d'aver rubato <lb/>nulla allo straniero. </s>

<s>Ma i Lettori imparziali sentono gi&agrave; nella loro propria <lb/>coscienza che la giustizia non pu&ograve; dirsi intera, infintantoche non sia anche <lb/>lo Straniero purgato dall'accusa di furto mossagli dal Nostro. </s></p><p type="main">

<s>Il Dati manca di far ci&ograve;, e anzi conferma le ragioni, con le quali pre&shy;<lb/>tendeva il Torricelli che il Roberval si fosse appropriato il centro di gravit&agrave; <lb/>della Cicloide, e l'applicazione di lui al metodo di ritrovare i solidi rotondi. </s>

<s><lb/>L'affezione doveva senza dubbio aver fatto velo al giudizio, ma &egrave; da aggiun&shy;<lb/>gere di pi&ugrave; che il Dati non pot&egrave; ascoltare, o non avrebbe forse avuta tanta <lb/>sincerit&agrave; di mente, da apprezzar le ragioni, che l'irritato Francese adduceva <pb xlink:href="020/01/2843.jpg" pagenum="468"/>per dimostrar ch'era suo il metodo inverso di concluder dai dati solidi il <lb/>baricentro, e altre cose che si possono ora legger da noi fra le Opere rober&shy;<lb/>valliane; nell'ultima epistola stampata <emph type="italics"/>ad Torricellium.<emph.end type="italics"/> Di questa epistola <lb/>sappiamo aver esso Dati fatto ricerca appresso il Ricci, a cui scriveva: &ldquo; Mi <lb/>par di sentire che m. </s>

<s>Roberval gi&agrave; minacciasse di rispondere con una pie&shy;<lb/>nissima lettera a quella che scrisse il Torricelli sotto il d&igrave; 7 Luglio 1646, <lb/>risentendosi dell'usurpato centro di gravit&agrave; della Cicloide, la quale per&ograve; non <lb/>so se mai comparisse, nulla trovando fra le scritture di esso Torricelli, n&egrave; <lb/>incontrando chi l'abbia veduta o sentita nominare. </s>

<s>Onde supplico V.S.I. a <lb/>compiacersi, per l'amore della reputazione dell'amico e della verit&agrave;, a darmi <lb/>non solamente notizia di questa lettera di m. </s>

<s>Roberval, se per&ograve; &egrave; nel mondo, <lb/>ma avendola a farmene fare una copia. </s>

<s>&rdquo; (MSS. Palatini, Raccolta Baldovi&shy;<lb/>netti n.&degree; 258, fasc. </s>

<s>2&degree;.) Ma n&egrave; il Ricci sapendone nulla, non pot&egrave; il Dati <lb/>esaminar le ragioni dell'imputato, le quali imparzialmente s'esamineranno <lb/>ora da noi, facendo da'suoi principii derivare il processo di questa lite famosa. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Racconta il Torricelli come, ritrovandosi in Roma nel 1640, avesse occa&shy;<lb/>sione di conoscere il padre Giovan Francesco Niceron, de'frati Minimi, va&shy;<lb/>lentissimo matematico francese e pittore, con cui, anche trasferito che si fu <lb/>a Parigi, mantenendo esso Torricelli qualche commercio di virtuosa amicizia, <lb/>ci&ograve; dette opportunit&agrave; di mandare al detto padre la nota di alcune sue inven&shy;<lb/>zioni geometriche, proponendole semplicemente senz'alcuna dimostrazione. </s>

<s><lb/>Erano fra quelle proposizioni, ridotte al numero di venti, incluse anche quelle <lb/>del Solido acuto iperbolico, e della quadratura della Cicloide, che richiama&shy;<lb/>rono particolarmente l'attenzione del Roberval, all'esame del quale le aveva <lb/>il Niceron sottoposte, per mezzo del coufrate suo Marino Mersenno. </s></p><p type="main">

<s>Nella ferma persuasione che non fosse la Cicloide nota altro che in Fran&shy;<lb/>cia, ebbe il Roberval a maravigliarsi, ripensando in che modo fosse potuta <lb/>pellegrinare in Italia, e, non trovando in che altro sodisfare la sua curiosit&agrave;, <lb/>sospett&ograve; che il Beaugrand, ne'suoi viaggi, ne avesse comunicata la notizia <lb/>o a Galileo o al Castelli o al Cavalieri. </s>

<s>In ogni modo la XIV delle dette <lb/>proposizioni, cio&egrave; quella del solido iperbolico, gli parve tanto elegante, che <lb/>volle applicarvisi a dimostrarla, in che felicemente essendo riuscito, si volse <lb/>con lieto animo a ringraziare il Mersenno, che gli avesse fatto conoscere un <lb/>tant'Uomo, da non posporsi, diceva, allo stesso Archimede, e degno di esser <lb/>fatto conoscere al Fermat, e al Cartesio. </s>

<s>Con queste enfatiche espressioni <lb/>terminava una lettera latina indirizzata allo stesso Mersenno, il quale non <lb/>indugi&ograve; a mandarne fedel copia a Firenze, rallegrandosi col Torricelli che <lb/>fosse da que'dottissimi Matematici tanto applaudito. </s>

<s>Il Torricelli corrispose <lb/>con non minore ardore dell'animo, andando direttamente a ritrovare il Ro-<pb xlink:href="020/01/2844.jpg" pagenum="469"/>berval, e contraccambiandogli il titolo di Apollo dei Geometri. </s>

<s>Con tali sen&shy;<lb/>timenti scriveva a Parigi in una lettera latina, sottoscritta da Firenze il di <lb/>primo Ottobre 1643, ma fra gli amici si lagnava che si fosse il Roberval <lb/>arrogato il primato della quadratura della Cicloide, e dicesse che il Beaugrand <lb/>ne aveva recata la notizia in Italia: lagnanze, che il Cavalieri veniva a con&shy;<lb/>solare nell'animo dell'amico con queste parole: </s></p><p type="main">

<s>&ldquo; Mi &egrave; giunto nuovo il nome del Robervallio, tuttavia non lo stimo io <lb/>manco, mentre ella lo giudica soggetto eminente, il che non pu&ograve; essere di <lb/>meno, avendogli dimostrate le cose che dice, e massime le sue maravigliose <lb/>proposizioni.... Mi rallegro poi-seco che la fama delle sue ammirabili pro&shy;<lb/>posizioni sia arrivata in Francia, sebbene mi dispiace che il detto Roberval&shy;<lb/>lio si arroghi il primato circa la Cicloide, o almeno che da esso sia venuta <lb/>a notizia di V. S., e immeritatamente incolpa in questo il Beaugrand, quale <lb/>non parl&ograve; di tal cosa n&egrave; a me, n&egrave; credo neanco al Galileo o al padre don <lb/>Benedetto, quando venne in Italia, o scrisse mai, che io sappia, di tal cosa, <lb/>poich&egrave; ne averei pure avuto qualche sentore. </s>

<s>Fu bene il Nicerone, che pro&shy;<lb/>pose a me tal quesito, al quale per&ograve; non applicai, spaventato dalla lettera <lb/>del Galileo, quale mi avvisava d'avervi pensato indarno molto e molto tempo, <lb/>come credo che altra volta gli scrivessi. </s>

<s>Se poi fosse il primo il Galileo a <lb/>pensare a un tal quesito, o gli fosse proposto da altri, veramente non lo so.... <lb/>&Egrave; ben vero che, scrivendo ultimamente al p. </s>

<s>Nicerone, gli dissi come V. S. <lb/>aveva dimostrato la misura dello spazio cicloidale in tre modi, ma non ac&shy;<lb/>cennai gi&agrave; qual fosse la proporzion ritrovata, n&egrave; altro mi ricordo di avere <lb/>scritto col&agrave;, parendomi che da questo solo, come <emph type="italics"/>ex ungue leonem,<emph.end type="italics"/> potes&shy;<lb/>sero essere ragguagliati di qual sorta d'ingegni produca l'Italia, e che pro&shy;<lb/>gressi farebbono, se qua vi fosse il fervore in questa scienza, che tra quei <lb/>virtuosi e studiosi di Parigi &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLI, fol. </s>

<s>177-81). </s></p><p type="main">

<s>La causa tra'due competitori, nella quale, a favore del Torricelli, en&shy;<lb/>trava, cos&igrave;, testimone di mezzo il Cavalieri; s'agit&ograve; da principio sommessa&shy;<lb/>mente, o come si direbbe dietro le spalle: in faccia il Roberval non si fece <lb/>altro uscire dalla bocca, che queste parole: &ldquo; In cycloide Torricellii agnosco <lb/>nostram trochoidem, nec recte percipio quomodo ipsa ad Italos pervenerit, <lb/>nobis nescientibus &rdquo; (Epist. </s>

<s>Rob. </s>

<s>ad Mersennum. </s>

<s>Ouvrages cit., pag. </s>

<s>350): <lb/>a che il Torricelli stesso rispondeva che una tal linea cos&igrave; <emph type="italics"/>natura familia&shy;<lb/>ris erat<emph.end type="italics"/> (ivi, pag. </s>

<s>360), da non far maraviglia ch'ella fosse pubblicamente <lb/>nota, senza che nessuno l'avesse mostrata, e voleva con ci&ograve; insinuare che <lb/>le tradizioni erano ben pi&ugrave; antiche e pi&ugrave; universali di quelle, che correvano <lb/>allora tra i Francesi. </s></p><p type="main">

<s>Dicemmo che cos&igrave; passarono tra il Roberval e il Torricelli le cose sul <lb/>principio, ma poi tornarono a rinfacciarsi acerbamente le accuse di plagio, <lb/>quando ne'solidi e nel centro di gravit&agrave; della Cicloide venne ad aggropparsi <lb/>la lite, che ora a noi resta a enodare. </s></p><p type="main">

<s>Ricevuta il Roberval la lettera da Firenze del d&igrave; primo Ottobre 1643, <lb/>da noi sopra commemorata, ne sent&igrave; gran piacere, esprimendo questi suoi <pb xlink:href="020/01/2845.jpg" pagenum="470"/>sensi al Mersenno, il quale, dop'avergli significati al Torricelli in una let&shy;<lb/>tera da Parigi del d&igrave; 13 Gennaio 1644, cos&igrave; soggiungeva: &ldquo; Trochoidis vero <lb/>naturam, vel ut vis Cycloidis, ita penetravit Robervallius noster nihil ut ele&shy;<lb/>gantius, vel profundius videris: eiusque solidum cum super base convertitur, <lb/>ad cylindrum eiusdem altitudinis, demonstravit esse ut 5 ad 8 &rdquo; (Lett. </s>

<s>a'Fi&shy;<lb/>laleti, pag. </s>

<s>11). </s></p><p type="main">

<s>Il Torricelli che pochi mesi fa, ritrovato il baricentro della Cicloide, aveva <lb/>col metodo del Nardi dimostrato non solamente la proporzione tra il solido <lb/>e il cilindro circa la base, ma circa le tangenti all'origine e alla cima, e <lb/>anche, come si lusingava di far credere, intorno all'asse; per contrapporre <lb/>a quella, che appariva aridit&agrave; nel Francese, la sua vena feconda, prese, il d&igrave; <lb/>primo del Maggio 1644, in mano la penna. </s>

<s>per annunziare al Mersenno, e <lb/>mediante lui al Roberval la serie di questi teoremi, dal primo in fuori com&shy;<lb/>piacendosi che tutti gli altri fossero sue proprie invenzioni. </s></p><p type="main">

<s>&ldquo; Solidum, quod fit a spatio cycloidali circa tangentem axi aequidistan&shy;<lb/>tem revoluto, ad cylindrum eiusdem altitudinis eiusdemque diametri, est sub&shy;<lb/>sesquitertium. </s>

<s>Demonstratio non est mea, sed inventum demonstratumque <lb/>fuit hoc ab Antonio Nardio, patritio aretino, olim Galilei amicissimo. </s>

<s>Reli&shy;<lb/>qua mea sunt. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Solidum, quod fit a spatio cycloidali circa tangentem basi parallelam re&shy;<lb/>voluto, est ad cylindrum eiusdem altitudinis et diametri, subsesquiseptimum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Solidum, quod fit a spatio cycloidali circa axem revoluto, ad cylindrum <lb/>eiusdem axis et diametri, est ut 11 ad 18. Solidum idem circa axem, ad so&shy;<lb/>lidum circa basim, est ut circulus aliquis ad quadratum sibi circumscriptum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Hinc est solidum etiam circa basim, ad cylindrum eiusdem axis et <lb/>diametri, ut 5 ad 8. &rdquo; </s></p><p type="main">

<s>&ldquo; Centrum gravitatis spatii cycloidalis axem ita dividit, ut pars, quae <lb/>ad verticem, sit ad reliquam ut 7 ad 5 &rdquo; (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>42 <lb/>ad tergum). </s></p><p type="main">

<s>Presentata questa nota di teoremi al Roberval, i nostri Lettori, che hanno <lb/>gi&agrave; vedute le cinque proposizioni, dimostrate da lui infino dal 1640 in que&shy;<lb/>sto medesimo soggetto, indipendentemente dalla Regola centrobarica, allora <lb/>a lui forse ignota; possono indovinar facilmente che nulla gli dovesse appa&shy;<lb/>rire, fra quelle cose, nuovo, fuor che il centro di gravit&agrave; della Cicloide, e il <lb/>solido circa l'asse. </s>

<s>Il teorema degli anelli dispensandolo dal pensiero di quello, <lb/>e intorno a questo abbandonato ogni studio, per parergli la proporzione <lb/>incommensurabile, confess&ograve; ingenuamente, e secondo il giudizio che poteva <lb/>farne allora dietro quelle semplici enunciazioni, che il Torricelli l'aveva pre&shy;<lb/>venuto nelle due dette cose, nel dimostrar cio&egrave; il centro cicloidale, e il so&shy;<lb/>lido circa l'asse, delle quali due dimostrazioni perci&ograve; ei generosamente lo <lb/>riconosceva primo e prestantissimo autore. </s>

<s>E cos&igrave;, come disse al Mersenno, <lb/>cos&igrave; il Mersenno scrisse al Torricelli con queste parole: &ldquo; qui, cum tuas <lb/>postremas legisset, praedictum solidum, et centrum gravitatis tibi debere fa&shy;<lb/>tetur, qui primus invenisti &rdquo; (Lett. </s>

<s>a'Filaleti, pag. </s>

<s>12). </s></p><pb xlink:href="020/01/2846.jpg" pagenum="471"/><p type="main">

<s>Ma si sent&igrave; il Roberval, ripensando a que'teoremi torricelliani, frugato <lb/>da una gran curiosit&agrave; di sapere com'entrasse il centro di gravit&agrave; della Ci&shy;<lb/>cloide nelle proposizioni de'solidi generati da lei, per cui, non sapendo se <lb/>l'invenzione apparteneva come l'altre alla Geometria, o resultava da qualche <lb/>meccanica esperienza, il Mersenno, che anch'egli era incerto della risposta, <lb/>interrog&ograve; in proposito il Torricelli, cos&igrave; soggiungendo dopo le riferite parole: <lb/>&ldquo; Dubitat noster Robervallius an mechanice tantum centra gravitatis Cycloi&shy;<lb/>dis inveneris, quae geometrice falsa suspicantur: docebis num ipsius rei de&shy;<lb/>monstrationem habeas? </s>

<s>&rdquo; (ibid.). Che si debbano intendere queste dure frasi <lb/>mersenniane come noi abbiam detto, non &egrave; dubbio, cos&igrave; avendole intese da <lb/>principio anche lo stesso Torricelli, ma poi, perch&egrave; faceva gioco alla sua <lb/>causa, le interpetr&ograve; troppo materialmente, facendo dire a'due francesi la stra&shy;<lb/>nezza che possa essere una cosa meccanicamente vera, e geometricamente <lb/>falsa, quasich&egrave; la quadratura della cicloide, ritrovata meccanicamente dal <lb/>Nardi, non fosse anche vera in Geometria, e quella di Galileo, errata nel&shy;<lb/>l'esperienza, anche alla Geometria non riuscisse ugualmente falsa. </s></p><p type="main">

<s>Ma non interrompendo il filo della storia, vediamo come rispondesse il <lb/>Torricelli interrogato se aveva esatta dimostrazione geometrica de'baricentri <lb/>cicloidali, e del solido circa l'asse. </s>

<s>Quanto ai primi fu largo, ordinando le <lb/>proposizioni, insieme con la dimostrazione dei solidi rotondi, i quali stanno <lb/>in ragion composta delle figure genitrici e delle distanze de'loro centri di <lb/>gravit&agrave; dall'asse della rotazione, tutto premettendo per lemmi al teorema del <lb/>solido circa la base: e cos&igrave; disposto il trattatelo, quale si legge fra i mano&shy;<lb/>scritti appartenenti ai discepoli di Galileo, nell'autografo e nelle copie del <lb/>Viviani e del Serenai; lo mand&ograve; a Parigi al Mersenno, accompagnando la <lb/>scrittura con una lettera, nella quale diceva: &ldquo; Heri (24 Luglio 1644) ad me <lb/>delatae fuerunt literae tuae, Vir clarissime, ideoque inter paucas horas pro&shy;<lb/>positiunculas, quas nunc mitto, composui conscripsique. </s>

<s>Constitueram propo&shy;<lb/>sitiones de centro grav. </s>

<s>cycloidis, semicicloidisque, quas in mente tantum <lb/>tenebam, nulli per aliquot menses communes facere. </s>

<s>Attamen victus alteram <lb/>earum mitto, nempe Cycloidis. </s>

<s>Sileo alteram, cum ex ea pendeat demonstra&shy;<lb/>tionem solidi circa axem, victus autem fui, quando in illa verba incidi: Du&shy;<lb/>bitat Robervallius noster geometrica ne, an aliqua mechanica ratione, de&shy;<lb/>monstrationem habeas de centro gravitatis &rdquo; (Lett. </s>

<s>a'Fil., pag. </s>

<s>12). </s></p><p type="main">

<s>Soprabbondando dunque nel rispondere alla prima parte della domanda, <lb/>tacque il Torricelli affatto rispetto alla seconda, n&egrave; s'intenderebbe il perch&egrave;, <lb/>se non si cominciasse fin d'ora a sospettare che il centro di gravit&agrave; della <lb/>semicicloide lo doveva aver davvero, non in altro che nella mente, non po&shy;<lb/>tend'essere nella realt&agrave; delle cose. </s>

<s>Bast&ograve; nulladimeno al Roberval l'accenno, <lb/>che dal detto centro della semicicloide dipendeva la dimostrazione del solido <lb/>circa l'asse, come gli bast&ograve; la lettura delle rimanenti proposizioni, per inten&shy;<lb/>dere quale ingerenza avesse negli altri solidi il centro di gravit&agrave; della Ci&shy;<lb/>cloide intera, d'onde vennegli giusto motivo di riformare, intorno all'Autore <lb/>dei due detti teoremi, quel primo fatto giudizio: cosa che poi tanto dispiacque <pb xlink:href="020/01/2847.jpg" pagenum="472"/>a chi ci aveva interesse, qualificandola per una contradizione indegna, e per <lb/>una meditata rapina. </s></p><p type="main">

<s>Il Torricelli, come in questa apparisce e in molte altre parti della Sto&shy;<lb/>ria, era troppo geloso, sospettoso e prepotente in rivendicare a s&egrave; quel che <lb/>non aveva sempre ragione di chiamar suo, e nonostante avrebbe forse rico&shy;<lb/>nosciuto giusto o scusato almeno quel rivoltar giubba, siaci permesso il detto, <lb/>se il Roberval gli avesse mandate a esaminare le sue cinque proposizioni, <lb/>come l'altro aveva a Parigi mandato le sue. </s>

<s>Tardi riconobbe da s&egrave; stesso il <lb/>Roberval che sarebbe stato bene di far cos&igrave;, per evitare i litigi, e per assi&shy;<lb/>curarsi la propriet&agrave; delle invenzioni, e pubblicamente ne disse sua colpa. <lb/></s>

<s>&ldquo; Negligentia mea, quod nihil praelo committerem, factum est ut quidam <lb/>extranei nationis nostrae aemuli, vel potius eidem invidi,... multa mea mibi <lb/>eripere conarentur, eaque sibi tribuere &rdquo; (<emph type="italics"/>De Trochoide,<emph.end type="italics"/> Ouvrages cit., p. </s>

<s>343). <lb/>E non solamente si sarebbe assicurato dai furti, ma avrebbe meglio provve&shy;<lb/>duto ai progressi e agl'incrementi della Scienza, la quale perci&ograve; professa <lb/>maggior gratitudine al Geometra nostro, che a lui. </s>

<s>Eppure anche il Torri&shy;<lb/>celli, temendo di andar troppo per le lunghe, non fece della maggior parte <lb/>delle cose da s&egrave; dimostrate intorno alla Cicloide altro che un motto, il quale <lb/>nulladimeno bast&ograve; a produrre il suo effetto, largamente diffondendosi da due <lb/>centri impulsivi: in Italia dall'appendice <emph type="italics"/>De cycloide,<emph.end type="italics"/> in fine alla seconda <lb/>parte delle Opere geometriche torricelliane; e in Francia dai <emph type="italics"/>Cogitata phi&shy;<lb/>sico mathematica,<emph.end type="italics"/> dov'&egrave; notabile che il Mersenno, a proposito dei solidi ci&shy;<lb/>cloidali, citi non il suo Matematico ma il nostro, forse perch&egrave; questi aveva <lb/>aggiunto agli altri teoremi e dimostrato &ldquo; solidum factum a spatio cycloidali <lb/>circa axem revoluto esse ad cylindrum ut 11 ad 18, atque ideo rationem <lb/>ineffabilem habere ad solidum circa basim, quippe quae componatur ex ra&shy;<lb/>tione 44 ad 45, et rationem circuli alicuius ad quadratum circumscriptum &rdquo; <lb/>(Mechan., Parisiis 1644, pag. </s>

<s>24). </s></p><p type="main">

<s>Due anni dopo, nel 1646, era in tutto da que'Francesi mutata sentenza. </s>

<s><lb/>Il Mersenno, scrivendo le <emph type="italics"/>Riflessioni fisico-matematiche,<emph.end type="italics"/> che l'anno appresso <lb/>comparirebbero in Parigi alla luce, cantava la palinodia, sostituendo al sot&shy;<lb/>tilissimo Torricelli il chiarissimo Roberval, che si proclamava primo e solo <lb/>autore della Trocoide, della quadratura, e de'solidi di lei, particolarmente di <lb/>quello circa l'asse, che non sta altrimenti al cilindro circoscritto come 11 <lb/>a 18, ma come tre quarti del quadrato della mezza base &ldquo; si dematur ter&shy;<lb/>tia pars quadrati altitudinis, ad ipsum dimidiae basis quadratum &rdquo; (Pari&shy;<lb/>siis 1647, pag. </s>

<s>71). Il Roberval scriveva dall'altra parte, privatamente allo <lb/>stesso Torricelli, essere dal Beaugrand pervenuta la notizia della quadratura <lb/>della Cicloide in Italia; aver da gran tempo, per la ricerca de'centri di gra&shy;<lb/>vit&agrave;, dati i solidi o le figure piane, il metodo universalissimo, e finalmente <lb/>essersi scoperto che la proporzione di 11 a 18 era minor della vera, che si <lb/>dava formulata dal Roberval in questa lettera nei medesimi termini, pub&shy;<lb/>blicati poco di poi dal Mersenno nel detto libro delle Riflessioni. </s></p><p type="main">

<s>Il sospetto, nato nel 1643, che si fosse dal Beaugrand recata la notizia <pb xlink:href="020/01/2848.jpg" pagenum="473"/>della Cicloide in Italia, torna ora pel Roberval, sotto l'aspetto di una cer&shy;<lb/>tezza, aggiuntevi le particolari circostanze del fatto. </s>

<s>Il Du-Verdus di Roma <lb/>aveva ad esso Beaugrand mandati i tre modi di quadrar la Cicloide, quali si <lb/>leggono stampati nell'appendice alla seconda parte delle Opere geometriche <lb/>del Torricelli: e perch&egrave; il primo di que'modi aveva una certa somiglianza <lb/>con quello seguito dal Cartesio, e che a'nostri Lettori &egrave; ben noto, ci&ograve; bast&ograve; <lb/>al Roberval per dire che il Beaugrand aveva consegnato in mano di Gali&shy;<lb/>leo, e da questi era venuta nel Torricelli, quella dimostrazion cartesiana. </s>

<s>Ma <lb/>rispondeva a ci&ograve; il Torricelli con tali ragioni, che il Roberval stesso s'ebbe <lb/>facilmente a persuadere non avere il suo sospetto e i suoi commenti nessuna <lb/>corrispondenza col vero. </s>

<s>Rispondeva: se la quadratura della Cicloide Galileo <lb/>l'ebbe in mano dimostrata, come mai persist&egrave; in fino alla morte in dire che <lb/>non la sapeva? </s>

<s>Maggiore insistenza faceva il Nostro contro quel che il Fran&shy;<lb/>cese diceva ora del baricentro cicloidale, contrapponendogli quel che aveva <lb/>detto prima al Mersenno, e confessando di non sapere intendere come po&shy;<lb/>tesse il Roberval sospettar falsa geometricamente l'indicazione del detto ba&shy;<lb/>ricentro, se era vero ch'ei ne avesse avuto certezza. </s></p><p type="main">

<s>Notabile in questa lettera, pubblicata da Timauro Antiate a pag. </s>

<s>15, che <lb/>il Torricelli non fa cenno di risposta a ci&ograve; che gli si rinfacciava aver egli <lb/>data la proporzione tra il solido circa l'asse, e il cilindro circoscritto, non <lb/>esatta. </s>

<s>Sembra anzi gli si rintuzzasse da ci&ograve; cos&igrave; l'animo, da diffondere anche <lb/>sopra gli altri punti della difesa un avvilimento, e una fiacchezza, simile a <lb/>quella di un che sia rimasto stordito da un gran colpo, bench&egrave; minore ne <lb/>dovesse sentir la ferita, per averlo previsto. </s>

<s>Il Ricci, sotto il d&igrave; 23 Giu&shy;<lb/>gno 1645, fra le altre cose, gli scriveva: &ldquo; Ho poi lettere del p. </s>

<s>Mersenno, <lb/>che saluta caramente V. S., e l'avvertisce come mons&ugrave; de Roberval ha dimo&shy;<lb/>strato che il solido, fatto dalla rivoluzione di una Cicloide intorno l'asse, non <lb/>osservi la ragione di 11 a 18 verso il cilindro circoscrittogli, ma, posto che <lb/>sia questo 11, il cilindro sar&agrave; pi&ugrave; che 18 &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, <lb/>fol. </s>

<s>155). La robervalliana dimostrazione di ci&ograve; &egrave; tanta parte di questa Sto&shy;<lb/>ria, che dobbiam trattenerci ad avvolgere intorno a lei il filo del nostro <lb/>discorso. </s></p><p type="main">

<s>Entriamo nella segreta stanza, dove il Matematico parigino &egrave; con grande <lb/>attenzione a leggere il manoscritto <emph type="italics"/>Della cicloide,<emph.end type="italics"/> venuto da Firenze, e in&shy;<lb/>doviniamo i pensieri, che gli passano per la mente. </s>

<s>La curiosit&agrave; vuol prima <lb/>di tutto sodisfarla rispetto al centro di gravit&agrave; dello spazio cicloidale, e ora <lb/>finalmente intende il perch&egrave; di un tal centro, e quale principale importanza <lb/>egli abbia nella dimostrazione dei solidi rotondi. </s>

<s>Ora &egrave; che si leva da quella <lb/>lettura, per ricercar notizie, e per erudirsi intorno alla Regola centrobarica, <lb/>con lieta maraviglia ripensando ai riscontri, ch'ella ha col suo proprio teo&shy;<lb/>rema degli Anelli. </s>

<s>Al diritto, che da ci&ograve; glie ne consegue, non ha il tempo <lb/>di pensar ora, che si vede messo sulla via d'intender quello che pi&ugrave; gli pre&shy;<lb/>meva, come procedesse cio&egrave; il Torricelli a dimostrare il solido circa l'asse. </s></p><p type="main">

<s>Ritorniamo anche noi indietro con l'occhio sopra la figura 307, dise-<pb xlink:href="020/01/2849.jpg" pagenum="474"/>gnata nel manoscritto torricelliano, e nella quale il punto B sull'asse indica <lb/>il centro di gravit&agrave; della Cicloide. </s>

<s>Ha inteso il Roberval, e per la sua faci&shy;<lb/>lit&agrave; anche ammirato il metodo ivi tenuto, per giunger dalla proporzione com&shy;<lb/>posta delle distanze BL, AL, e delle figure piane, a quella dei solidi, facen&shy;<lb/>dosi il rivolgimento intorno alla base. </s>

<s>Volendosi per la medesima via riuscire <lb/>a dimostrare i solidi circa l'asse, ben comprese come doveva il Torricelli <lb/>attendere a ritrovare il centro di gravit&agrave; della semicicloide, in che linea stia, <lb/>ora parallela alla base, e ora parallela all'asse. </s>

<s>Quanto alla prima, resultava <lb/>dalle cose, gi&agrave; dimostrate per la Cicloide intera, dover essere la BP, ma la <lb/>difficolt&agrave; stava nella seconda linea, da tirarsi parallela all'asse, la quale no&shy;<lb/>nostante voleva far credere il Torricelli di averla trovata, bench&egrave; a tutti e <lb/>sempre ne tacesse il modo e la ragione. </s>

<s>Ma sia pure qual si voglia OQ Ia <lb/>detta linea, ella dee necessariamente, per sodisfare alle posizioni, esser tale, <lb/>da incontrare la BP in R, a una distanza RB dall'asse, che stia alla SA, <lb/>come 22 a 27. Chiamati infatti S, C il solido e il cilindro circoscritto, gene&shy;<lb/>rati dal rivolgersi la semicicloide DHEL e il rettangolo GL intorno ad EL, <lb/>e stando i detti solidi in ragion composta delle figure piane, ossia di 3 a 4, <lb/>e delle distanze BR, AS; &egrave; manifesto che, per aver la proporzione S:C= <lb/>11:18, dev'essere RB=22, e AS=27. Se ora la proporzione RB:AS= <lb/>22:27 dal Torricelli si d&agrave; per esatta, e tale ei la pretende, essendo AS la <lb/>quarta parte della circonferenza, anche la circonferenza intera torner&agrave; dun&shy;<lb/>que esattamente per lui rettificata. </s>

<s>Laonde ebbe qui il Roberval a dire: o <lb/>questo Torricelli ha trovato l'impossibile, o vuol dare a credere ai Matema&shy;<lb/>tici cose non vere. </s>

<s>Il dilemma era solubile assai facilmente, ma colui, che <lb/>se l'era proposto, volle con ragioni geometriche assicurarsi della fallacia, di&shy;<lb/>mostrando come la proporzione di 11 a 18 non si concilia con quest'altro <lb/>teorema, annunziato cos&igrave; dallo stesso Torricelli, nella nota scritta al Mer&shy;<lb/>senno: <emph type="italics"/>&ldquo; Solidum, quod fit a spatio cycloidali circa axem revoluto, ad <lb/>solidum circa basim, est ut circulus aliquis ad quadratum sibi circum&shy;<lb/>scriptum.<emph.end type="italics"/></s></p><p type="main">

<s>Ma una tal proporzione l'hanno anche i respettivi cilindri circoscritti. </s>

<s><lb/>Chiamato infatti C quello generato dal rivolgersi il rettangolo GL intorno <lb/>ad EL, abbiamo C=<foreign lang="greek">p</foreign>DL2.EL, e chiamato C&prime; l'altro cilindro, fatto dal <lb/>rettangolo GF intorno a DF, avremo C&prime;=<foreign lang="greek">p</foreign>EL2.2DL, donde C:C&prime;= <lb/>DL2.EL:EL2.2DL=DL:2EL=DL.EL/2:EL2=2DL.EL/4:EL2, ossia <lb/>come il circolo che ha generata la Cicloide, al quadrato del diametro. </s>

<s>Se <lb/>dunque intendansi con S.A, S.B significati i solidi circa l'asse, e circa la <lb/>base avremo S.A:S.B=C:C&prime;. </s></p><p type="main">

<s>Ritengansi ora per vere le date posizioni torricelliane S.A=11/18.C, <lb/>S.B=5/8.C&prime;:verr&agrave; da ci&ograve; ordinata la proporzione </s></p><p type="main">

<s><emph type="center"/>S.A:S.B=11/18C;5/8C&prime;=44/72C=45/72C&prime;,<emph.end type="center"/><lb/>giunto alla quale, il Roberval cos&igrave; ragionava: o non son veri i teoremi, che <pb xlink:href="020/01/2850.jpg" pagenum="475"/>il solido circa l'asse al solido circa la base sta come un circolo al quadrato <lb/>del suo diametro, e che il solido circa la base &egrave; 45/72 del cilindro circoscritto; <lb/>o &egrave; falso che il solido circa l'asse sia 44/72 del respettivo cilindro. </s>

<s>Ma perch&egrave; <lb/>i due primi teoremi son verissimi, dunque &egrave; falso il terzo, dando egli minor <lb/>proporzione della vera, la quale dovrebbe essere non 44, ma 45/72, com'&egrave; <lb/>manifesto. </s></p><p type="main">

<s>Cosi essendo, proseguiva addirittura il Roberval nel suo ragionamento, <lb/>non &egrave; possibile che il Torricelli abbia avuto, come per la cicloide intera, <lb/>l'indicazione esatta del centro di gravit&agrave; della semicicloide dal legittimo ma&shy;<lb/>gistero della Geometria, ma egli deve averla ricavata per approssimazione <lb/>dall'esperienza; e credendo non si poter da nessuno dimostrare la ragione <lb/>esatta, si confid&ograve; che nessuno avrebbe saputo scoprire che la sua era falsa. </s>

<s><lb/>Cos&igrave;, come seco medesimo pensava, disse al Mersenno, e rifer&igrave; al Torricelli, <lb/>con queste precise parole, quello che aveva detto: &ldquo; Quid ergo, iniquit Mer&shy;<lb/>sennus, dices de clarissimo Torricellio? </s>

<s>nonne insignium adeo theorematum <lb/>cognitionem ipsi te debere fateberis? </s>

<s>&mdash; Faterer, respondi, si vera essent, at <lb/>talia non esse certus sum. </s>

<s>Miror sane quod vir talis falsum pro vero nobis <lb/>velit obtrudere, nec aliud suspicari possum nisi quod ille mechanica quadam <lb/>ratione, per approximationem, huiusmodi rationem, a vero non admodum <lb/>longe aberrantem, invenerit, existimaveritque veram rationem non posse de&shy;<lb/>tegi, ac proinde suam haud veram esse a nemine posse demonstrari. </s>

<s>&rdquo; (Ou&shy;<lb/>vrages cit. </s>

<s>pag. </s>

<s>377-78). </s></p><p type="main">

<s>Il sospetto era fondato sopra buone ragioni, n&egrave; qualunque sia tra i pi&ugrave; <lb/>gelosi della fama del Torricelli saprebbe secondo noi rispondere all'accusa: <lb/>chi avrebbe creduto mai un cos&igrave; nobile geometra, <emph type="italics"/>aliquid pure geometricum <lb/>sine demonstatione affirmare voluisse?<emph.end type="italics"/> (ibid. </s>

<s>p. </s>

<s>394). </s></p><p type="main">

<s>La dimostrazione del centro di gravit&agrave; della semicicloide non l'abbiamo <lb/>potuta trovare, per quanto abbiamo frugato, in nessuna parte dei manoscritti <lb/>da noi consultati, eppure il Torricelli faceva conto di averla fra le sue carte, <lb/>bench&egrave; a nessuno, o familiare o estraneo, riuscisse mai di vederla, e richie&shy;<lb/>stone l'Autore ne sapeva uscir sempre con qualche scusa. </s>

<s>Ma pi&ugrave; che una <lb/>scusa (ce lo perdoni il grand'Uomo) trasparisce l'arte di un furbo, per non <lb/>dire la stizza di un imputato dal seguente poscritto, taciuto, per non esser <lb/>forse conveniente a un apologista, da <emph type="italics"/>Timauro Antiate,<emph.end type="italics"/> nel trascrivere dalla <lb/>bozza originale, e nel pubblicar la lettera intera: &ldquo; Lecta iterum epistola <lb/>cl. </s>

<s>Robervallii et obsignata iam mea ad ipsum data, animadverto me nihil <lb/>respondisse de solido cycloidis circa axem, sed neque responsum quodpiam <lb/>dari necesse existimo. </s>

<s>Tunc enim quisquam iure arguere poterit me, quando <lb/>in paralogismos meos incidet. </s>

<s>Habemus apud Archimedem, propos. </s>

<s>II, <emph type="italics"/>De <lb/>circuli dimensione,<emph.end type="italics"/> circulum ad quadratum diametri esse ut 11 ad 14: quaero <lb/>ab ipso unde nam putet me habuisse rationem, quam ad numeros 11 et 18 <lb/>reducebam? </s>

<s>Si vero eo dicit, ut ego demonstrationes iterum ultro mittam, <lb/>fallitur. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XL, fol. </s>

<s>44). </s></p><p type="main">

<s>E noi credemmo che si fosse rimasto il Torricelli di rispondere all'ac-<pb xlink:href="020/01/2851.jpg" pagenum="476"/><gap/>usa dell'errore intorno al solido circa l'asse, perch&egrave; lo avesse riconosciuto, <lb/>ora che da altri si vedeva scoperto. </s>

<s>Abbiamo invece da lui stesso ora inteso <lb/>che tuttavia persiste in far credere di aver la dimostrazione del centro di <lb/>gravit&agrave; della semicicloide, e del teorema stereometrico che ne consegue; che <lb/>se non lo manda al Roberval, ne abbiamo ud&igrave;ta la ragione, la quale, diceva <lb/>il sagace Francese sentir <emph type="italics"/>redolere totius epistolae acerbitatem.<emph.end type="italics"/> Ma perch&egrave; in <lb/>ogni modo non era possibile levar le accuse, senza mandar quella dimostra&shy;<lb/>zione, e il Torricelli non la mand&ograve; mai, perch&egrave; non l'aveva, pens&ograve; che i suoi <lb/>diritti si potrebbero ridurre almeno al centro di gravit&agrave; della Cicloide, di <lb/>che, lasciato il resto, si content&ograve; di rivendicarsi il primato dell'invenzione. </s>

<s><lb/>In tal proposito cos&igrave; scriveva il d&igrave; 14 luglio 1646 da Firenze, in una lettera <lb/>al Cavalieri: </s></p><p type="main">

<s>&ldquo; Faccio sapere a V.P. come in questi giorni mi trovo due liti, una col <lb/>Robervallio di Francia, il quale sfacciatissimamente e vergognosissimamente <lb/>scrive aver avuto il centro di gravit&agrave; della Cicloide, avanti che io gli man&shy;<lb/>dassi la dimostrazione, e non solo il centro predetto della gravit&agrave; della Ci&shy;<lb/>cloide, ma dice che anco aveva quel metodo, da me dimostrato e mandato <lb/>da me in mano sua, dove io mostravo che, dato il centro di gravit&agrave; e qua&shy;<lb/>dratura di un piano, si d&agrave; il solido. </s>

<s>Esso l'ha rivoltata, e dice che aveva il <lb/>metodo di trovare il centro di gravit&agrave;, data la quadratura e il solido. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quando avvisai in Francia la sola enunciazione di quel centro, dicendo <lb/>che sta nell'asse segato come 7 a 5, il p. </s>

<s>Mersenno mi scrisse una lettera <lb/>piena d'iperbole di lodi, confessando che io ho prevenuto in questo il loro <lb/>geometra Robervallio: mi prega a mandar la dimostrazione: mi dice che <lb/>Robervallio ha dimostrato ogni cosa fuor che questa, mi dice che i suoi Geo&shy;<lb/>metri non credono queste cose si siano trovate, e parlando di Robervallio <lb/>dice: <emph type="italics"/>qui cum tuas postremas legisset, praedictum solidum et centrum gra&shy;<lb/>vitatis tibi fatetur debere, qui primus invenisti. </s>

<s>Rogamus tamen an cen&shy;<lb/>trum gravitatis etc.<emph.end type="italics"/> Ed in ultimo della lettera lunghissima scrive: <emph type="italics"/>Dubitat <lb/>noster Robervallius an mechanice tantum centra gravitatis Cycloidis, et <lb/>semicicloidis inveneris, quae geometrice falsa suspicantur. </s>

<s>Docebis num <lb/>istius rei demonstrationem habeas.<emph.end type="italics"/> E molte altre simili confessioni, le quali <lb/>sono in una lunghissima lettera, che io ho stimato da quaresima in qua per <lb/>persa. </s>

<s>Finalmente, dopo moltissime diligenze l'ho trovata, ed ho scritto le <lb/>mie ragioni in Francia, con copia delle lettere loro, e la testimonianza delle <lb/>recognizioni, e quando occorrer&agrave; le far&ograve; riconoscere da otto o dieci letterati, <lb/>e le stamper&ograve; con le ragioni mie. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; L'altra lite l'ho col signor M. A. </s>

<s>Ricci di Roma. </s>

<s>Al suddetto signore <lb/>mandai la dimostrazione da me adattata alle figure infinitamente lunghe di <lb/>Robervallio, fin di marzo passato. </s>

<s>Alla settimana passata io mandai al me&shy;<lb/>desimo la stessa dimostrazione, applicata alla quadratura delle infinite para&shy;<lb/>bole, in due modi. </s>

<s>Quando aspetto che mi ringrazi, trovo che egli dice avere <lb/>adattata ancor lui quella mia dimostrazione alla quadratura delle parabole, ed <lb/>ora vi pretende il medesimo gius che ci ho io. </s>

<s>Primieramente, la dimostra-<pb xlink:href="020/01/2852.jpg" pagenum="477"/>zione fondamentale &egrave; mia, senza controversia, ed egli lo confessa. </s>

<s>Avanti <lb/>ch'egli me ne dia motivi gli mando l'applicazione alle parabole, ed ora nella <lb/>risposta mi dice che quella applicazione l'aveva e quel che pi&ugrave; mi duole mi <lb/>dice che gi&agrave; era accordato di stampar questa sua cosa nel libro, che uscir&agrave; <lb/>presto del sig. </s>

<s>Antonio Nardi. </s>

<s>Dico il fatto mio all'uno e all'altro, cio&egrave; al <lb/>Roberval e al Ricci. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XL, fol. </s>

<s>138, 39). </s></p><p type="main">

<s>L'essersela il Torricelli presa col Ricci, di cui si conoscono i generosi <lb/>atti, e i nobili portamenti, quando prima cadde in sospetto di volersi appro&shy;<lb/>priare i teoremi de'solidi conoidali, predispone i nostri lettori a credere che, <lb/>come esso Torricelli ebbe il torto a risentirsi contro l'amico, cos&igrave; lo dovesse <lb/>avere anche risentendosi contro lo straniero. </s>

<s>Si faceva in questa seconda lite <lb/>forte di due ragioni: prima, perch&egrave; il Roberval aveva indugiato due anni a <lb/>rispondere; poi perch&egrave; avuto il metodo di dimostrare i solidi, dati i centri <lb/>di gravit&agrave; e le quadrature; pretendeva d'appropriarsi il metodo inverso di <lb/>dimostrare il centro di gravit&agrave;, dati i solidi e le figure piane, da cui sono <lb/>essi solidi generati. </s></p><p type="main">

<s>Ma il Roberval credeva di aver data sufficiente ragione di quell'indugio, <lb/>attribuendolo alle difficolt&agrave; incontrate nel ritrovar la vera proporzione geo&shy;<lb/>metrica tra il solido circa l'asse, e il cilindro circoscritto. </s>

<s>&ldquo; Ne vero mireris <lb/>quod tantum temporis in unico problemate solvendo consumpserimus, illud <lb/>enim ex iis est, quae et longa inquisitione indigent, et acrem pertinacis geo&shy;<lb/>metrae requirunt operam, nec memini me aliuid unquam demonstrasse, quod <lb/>cum eo conferri posset. </s>

<s>&rdquo; (Lettera a'Filaleti, p. </s>

<s>13). Il Torricelli invece at&shy;<lb/>tribuiva quell'indugio a ci&ograve;, che il Roberval si confidava dover essere andata <lb/>in tanto tempo smarrita la lettera, mandata a Firenze dal Mersenno, per cui <lb/>non si potessero contestare le contradizioni. </s>

<s>Giustizia ora vuole che si tolga <lb/>dal Francese una tale ingiuria, dimostrando ch'ebbe di fatto a penar cos&igrave; <lb/>lungamente, com'egli dice, prima d'assicurarsi di aver propriamente ridotta <lb/>all'esattezza geometrica la poco accurata proporzione torricelliana. </s></p><p type="main">

<s>Alla dimostrazione, che si promette, porgono i documenti necessari le <lb/>Opere robervelliane, per le quali troviamo in tre modi, e in termini sempre <lb/>diversi assegnate le proporzioni tra il solido cicloidale e il cilindro circoscrit&shy;<lb/>togli intorno all'asse. </s>

<s>La cosa pare strana in s&egrave;, e tanto pi&ugrave; rispetto alla ve&shy;<lb/>rit&agrave; geometrica, la quale non pu&ograve; essere che una sola, ma si comprende come <lb/>ci&ograve; accadesse, ripensando che furono raccolti insieme dagli Editori parigini i <lb/>trattati, rimasti inediti, e scritti dal loro Accademico in vari tempi, nella suc&shy;<lb/>cessione de'quali, esaminate meglio le cose, giunse finalmente a conquistare <lb/>la verit&agrave;, ravvedendosi dei primi errori. </s>

<s>Di qui &egrave; che abbiamo, nei vari trat&shy;<lb/>tati robervalliani della Cicloide, segnate cos&igrave; l'orme dei passi, da creder fa&shy;<lb/>cilmente lungo dover essere stato il tempo, che, per giungere al termine <lb/>faticoso, venne a spender l'Autore. </s></p><p type="main">

<s>Nel trattato <emph type="italics"/>De trochoide<emph.end type="italics"/> aveva detto il solido stare al cilindro <emph type="italics"/>ut differentia <lb/>inter quadratum quadrantis et<emph.end type="italics"/> 4/3 <emph type="italics"/>quadrati radii, ad quadratum ipsius se&shy;<lb/>micircumferentiae<emph.end type="italics"/> (Ouvrages cit. </s>

<s>pag. </s>

<s>319): cosicch&egrave;, chiamati S il detto solido, <pb xlink:href="020/01/2853.jpg" pagenum="478"/>C il cilindro, e riferendoci alla figura 308, nella quale AC s'uguaglia alla mezza <lb/>circonferenza, e CI &egrave; il raggio della ruota; sarebbe quella ragione espressa da <lb/>S:C=AC2/4&mdash;4/3CI2:AC2. </s>

<s>Quest&igrave; termini per&ograve; non riscontrano con quegli <lb/>altri, che si deducono col calcolo, componendo insieme le proporzioni, che hanno <lb/>i solidi generati dagli spazi compresi tra la cicloide e la comite, e tra la co&shy;<lb/>mite e l'asse, verso il cilindro circoscritto, che per ambedue manifestamente <lb/>&egrave; lo stesso. </s>

<s>Quanto a quel primo solido, che chiameremo S&prime; &ldquo; patet itaque <lb/>(cos&igrave; conclude il Roberval la sua dimostrazione) continere portionem, quae <lb/>ad ipsum totum cylindrum eam habet rationem, quam 2/3 quadrati semidia&shy;<lb/>metri, ad quadratum semicircumferentiae &rdquo; (ibid. </s>

<s>pag. </s>

<s>322): conclusione, che <lb/>scritta per simboli &egrave; tale S&prime;:C=2/3CI2:AC2. </s>

<s>Dell'altro solido S&Prime; descritto <lb/>dalla comite nel rivolgersi intorno all'asse, dallo stesso Roberval si dimostra <lb/>&ldquo; ad cylindrum cui inscribitur eamdem rationem habere, quam dimidium <lb/>quadrati semicircumferentiae rotae, dempto dimidio quadrati diametri, ad <lb/>integrum quadratum semircumferentiae &rdquo; (ibid. </s>

<s>p. </s>

<s>332) ossia S&Prime;:C= <lb/>AC2/2&mdash;CF2/2:AC2. </s>

<s>Or da questa e dalla precedente omologa proporzione, in <lb/>cui i secondi e quarti termini sono uguali, s'ha S&prime;:S&Prime;=2/3CI2:AC2/2&mdash;CF2/2, <lb/>e componendo, S&prime;+S&Prime;:S&prime;=2/3CI2&mdash;CF2/2+AC2/2:2/3CI2. </s>

<s>E per&ograve; <lb/>S&prime;+S&Prime;:C=2/3CI2&mdash;CF2/2+AC2/2:AC2=AC2/2+2/3CI2&mdash;2CI2:AC2= <lb/>AC2/2&mdash;4/3CI2:AC2. </s></p><p type="main">

<s>Essendo S=S&prime;+S&Prime;, si vede bene che la discordanza, tra questa e la <lb/>proporzion precedente, non cade in altro, che nel terzo termine, il quale, se <lb/>non &egrave; vero in quella, non si pu&ograve; credere per&ograve; che sia venuto a correggersi <lb/>in questa, conclusa dal Roberval dietro un principio, ch'esaminato bene si <lb/>scopre falso. </s>

<s>Dice l'Autore che la somma degli infiniti quadrati KM, BH, <lb/><expan abbr="Tq.">Tque</expan>... al quadrato di CA preso altrettante volte, ossia a &int;AC2, <emph type="italics"/>rationem <lb/>habet, quam sphaera rotae ad totum cylindrum<emph.end type="italics"/> (ibid. </s>

<s>pag. </s>

<s>321). Ora, es&shy;<lb/>sendo la sfera uguale alla terza parte del raggio moltiplicata per la super&shy;<lb/>ficie, che &egrave; quadrupla di un circolo grande, sar&agrave; la solidit&agrave; di essa sfera <lb/>espressa da 4/3<foreign lang="greek">p</foreign>CI2, e quella del cilindro da 2<foreign lang="greek">p</foreign>AC2. </s>

<s>CI per cui i due so&shy;<lb/>lidi staranno fra loro come 2/3 CI2 ad AC2. </s>

<s>E perch&egrave;, dice esso Roberval, tale <lb/>esser pure la ragione del solido S&prime; al medesimo cilindro C, avremo dunque <lb/>KM2+BH2....:&int;AC2=2/3CI:AC2=S&prime;:C=S&prime;:<foreign lang="greek">p</foreign>&int;AC2.D'onde S&prime;= <lb/><foreign lang="greek">p</foreign>(KM2+BH2....) ci&ograve; che non sembra esser vero, dimostrandosi il solido S&prime; <lb/>uguale alla somma degli infiniti circoli descritti dai raggi KM, BM .... in&shy;<lb/>torno alla comite, aggiuntavi la quarta parte del cilindro totale, anche se&shy;<lb/>condo lo stesso calcolo robervalliano. </s></p><p type="main">

<s>Il solido infatti, che si descrive dallo spazio, compreso tra la cicloide e <pb xlink:href="020/01/2854.jpg" pagenum="479"/>la comite nel rivolgersi intorno all'asse, &egrave; composto delle infinite armille KM, <lb/>BH, TQ .... il valor delle quali, chiamate A, A&prime;, A&Prime;, si trover&agrave; cos&igrave; assai <lb/>facilmente: A=<foreign lang="greek">p</foreign>EK2&mdash;<foreign lang="greek">p</foreign>EM2=<foreign lang="greek">p</foreign>(KM2+ME2+2KME&mdash;ME2)= <lb/><foreign lang="greek">p</foreign>KM2+2<foreign lang="greek">p</foreign>KME. </s>

<s>Troveremo con simile discorso A&prime;=<foreign lang="greek">p</foreign>BH2+2<foreign lang="greek">p</foreign>BHI, <lb/>A&Prime;=<foreign lang="greek">p</foreign>TQ2+2<foreign lang="greek">p</foreign>TQS .... Sommate ora insieme tutte queste armille, il <lb/>solido delle quali si compone sar&agrave; </s></p><p type="main">

<s><emph type="center"/>S&prime;=<foreign lang="greek">p</foreign>(KM2+BH2+QT2....)+2<foreign lang="greek">p</foreign>(KME+BHI+TQS....)<emph.end type="center"/></s></p><p type="main">

<s>Giunti a questo punto, rispetto alla somma degl'infiniti rettangoli, com&shy;<lb/>presi fra parentesi, ascoltiamo come il Roberval ne ragioni: &ldquo; At dupla illa <lb/>rectangula aequivalent semel omnibus rectangulis sub EL, sive CA et KM; <lb/>sub IG, sive CA et HB; sub SN, sive CA et QT .... propterea quod omnes <lb/>rectae EM, IH, SQ .... bis sumptae aequivalent omnibus rectis EL, IG, <lb/>SN .... semel sumptis; hoc est rectae BA toties sumptae: et haec rectan&shy;<lb/>gula constituunt quartam partem quadrati CA toties sumpti. </s>

<s>&rdquo; (ibid. </s>

<s>pag. </s>

<s>321). <lb/>Stabilisce dunque il Roberval questa equazione: 2(KME+BHI+TQS....)= <lb/>2(ME+HI+QS....) (<expan abbr="KM+BH+Tq.">KM+BH+Tque</expan>...) dietro la quale, supponen&shy;<lb/>dola vera, in tal guisa prosegue il suo discorso: Della somma delle infinite <lb/>linee ME, HI, QS .... s'intesse la superficie del trilineo AFC, che sappiamo <lb/>essere uguale all'altro trilineo AFD, e perci&ograve; quella somma, presa due volte, <lb/>equivarr&agrave; allo spazio circoscritto dal rettangolo DC, ossia a &int;AC. </s>

<s>Della <lb/>somma poi delle linee infinite KM, BH, TQ s'intesse la figura disegnata <lb/>dalla cicloide e dalla sua comite, la qual figura, essendo, come si sa, la quarta <lb/>parte del rettangolo intero, equivarr&agrave; dunque a &int;AC/4, d'onde verr&agrave; ad essere <lb/>trasformata cos&igrave; l'equazione lasciata di sopra: </s></p><p type="main">

<s><emph type="center"/>S&prime;=<foreign lang="greek">p</foreign>(KM2+BH2+QT2....)+<foreign lang="greek">p</foreign>&int;AC2/4.<emph.end type="center"/></s></p><p type="main">

<s>Se il calcolo robervalliano sia condotto secondo le buone regole alge&shy;<lb/>briche sel vedono i Matematici lettori, ma in ogni modo si deve l'Autore <lb/>stesso essere accorto, dalla fallacia dei mezzi, dell'inesattezza dei resultati, <lb/>ridotti finalmente alla ragione S:C=3/4AC2&mdash;CF2/3:AC2, che &egrave; quella <lb/>creduta, sopra le altre due precedenti, per vera, e che sotto questa formula <lb/>fu definitivamente annunziata nella lettera al Torricelli. </s>

<s>Non fu dunque per <lb/>quel malizioso fine, che ingiuriosamente al Roberval s'imputava, l'indugio di <lb/>quasi due anni a far la risposta, ma per la difficolt&agrave; della ricerca, che ri&shy;<lb/>chiese veramente dal pertinace Geometra, com'ei diceva, opera cosi lunga e <lb/>faticosa. </s></p><p type="main">

<s>La causa per&ograve; s'agitava principalmente, e con grande ardore degli animi, <lb/>circa al centro di gravit&agrave; della Cicloide, che il Torricelli difendeva come sua <lb/>propria invenzione, contro le usurpazioni del Roberval, a cui, diceva quegli, <lb/>non pass&ograve; tal cosa mai per la mente. </s>

<s>A questo capo di accusa cos&igrave; giungeva <lb/>solenne da Parigi a Firenze la risposta. </s></p><pb xlink:href="020/01/2855.jpg" pagenum="480"/><p type="main">

<s>&ldquo; Dum ais me nunquam ne verbum quidem fecisse de centro gravitatis <lb/>Trochoidis, cum interea tantopere, et quidem merito, gloriarer de omnibus <lb/>aliis, quadratura, tangentibus, solidis etc., nec verisimile esse, cum reliqua <lb/>omnia proponerem, de unico centro gravitatis siluisse, si illud tantum spe&shy;<lb/>ravissem, quod quidem problema, tuo iudicio nulli reliquorum posthabendum <lb/>videtur; dum haec ais, inquam, Vir clarissime, ex tuo genio loqueris: nos, <lb/>dum scripsimus, ex nostro etiam genio scripsimus. </s>

<s>Tu, cum magnifaceres <lb/>centra, quia ex iis solida deducere posse confidebas, solida autem praecipue <lb/>intendebas, ideo centrorum inventionem magnifice extulisti, nec caeteris post&shy;<lb/>habendam, immo praehabendam iudicasti. </s>

<s>Ego contra, quia sine centris solida <lb/>et quaesivi et via geometrica inveni, datis autem solidis, statim et absque la&shy;<lb/>bore centra sequebantur. </s>

<s>Ideo centra ne respexi quidem, neque ad ea un&shy;<lb/>quam animum applicui, certus omnino, ex praemissa nostra methodo, dato <lb/>plano quod dudum habebam, sola solida mihi quaerenda superesse, centra <lb/>autem simul cum plano et solidis haberi. </s>

<s>&rdquo; (ibid. </s>

<s>pag. </s>

<s>376). </s></p><p type="main">

<s>Ora, che cosa potrebbesi trovare in questa risposta, che non riscontri <lb/>con la verit&agrave; dei fatti? </s>

<s>Era ad ambedue i Matematici data la Regola cen&shy;<lb/>trobarica, dalla quale si deduceva per corollario immediato che i solidi ro&shy;<lb/>tondi stanno in ragion composta delle figure piane, e delle distanze dei loro <lb/>centri di gravit&agrave; dall'asse della rivoluzione. </s>

<s>Se sia data dunque la quadratura, <lb/>o se in altre parole sia detto secondo qual proporzione stanno fra loro le <lb/>superficie genitrici, il teorema universalissimo del Guldino non solo porgeva <lb/>facile il modo di risolvere direttamente il problema: dati i centri di gravit&agrave; <lb/>trovare i solidi; ma conversamente di risolver l'altro: dati i solidi trovare i <lb/>centri. </s>

<s>E come il Torricelli pretendeva essere sua propria quella soluzione <lb/>diretta, cos&igrave; sua propria diceva il Roberval essere questa conversa, la quale, <lb/>se ci avesse pensato, o sentitone il bisogno, lo conduceva, assai prima del suo <lb/>rivale, a dimostrare il centro di gravit&agrave; della Cicloide <emph type="italics"/>statim et absque la&shy;<lb/>bore.<emph.end type="italics"/> Riducendoci infatti sott'occhio la figura 307, se con S, C si rappresen&shy;<lb/>tano il solido e il cilindro circa la base, che nella terza proposizione rober&shy;<lb/>valliana erano stati gi&agrave; ritrovati stare come 5 a 8, e se con T, R si significhino <lb/>la trochoide e il rettangolo, che, nel corollario della proposizione precedente <lb/>alla citata, si trovarono aver tra loro la proporzione di 3 a 4; subito vera&shy;<lb/>mente e senza alcuna fatica s'ha indicato il punto B sull'asse dalla propor&shy;<lb/>zione BL.T:AL.R=3BL:4AL=S:C=5:8, la quale si riduce a <lb/>BL:AL=5:6, secondo che, per altra via laboriosissima, era giunto pure <lb/>a concludere il Torricelli. </s>

<s>Con quanta coscienza poi potesse questi affermare <lb/>nella citata lettera al Mersenno: <emph type="italics"/>Misi etiam demonstrationem meam et vere <lb/>meam, pro methodo, quae inservit ad inveniendum centrum gravitatis ex <lb/>dato solido, sive solidum ex dato centro;<emph.end type="italics"/> lo lasciamo giudicare ai nostri <lb/>Lettori, i quali sanno oramai troppo bene che quel medodo era invece del <lb/>Nardi. </s></p><p type="main">

<s>N&egrave; il Roberval, dall'altra parte, era meno illuso, quando dal suo teo&shy;<lb/>rema <emph type="italics"/>Des anneaux<emph.end type="italics"/> credeva potersi, per la ricerca de'centri di gravit&agrave;, dati <pb xlink:href="020/01/2856.jpg" pagenum="481"/>i solidi, derivare il metodo universalissimo. </s>

<s>Quel teorema invece, supponendo <lb/>le superficie piane concentriche, non suppliva se non che parzialmente alla <lb/>Regola centrobarica, nel solo caso cio&egrave; che i centri di gravit&agrave; delle figure <lb/>fossero ugualmente distanti dall'asse della rivoluzione. </s>

<s>Di qui nacquero senza <lb/>dubbio alcuni errori di lui, come sarebbe quello, che &egrave; a notar nel calcolo del <lb/>solido generato dallo spazio intercetto tra la Cicloide e la comite, nel rivol&shy;<lb/>gersi intorno all'asse, del qual solido dice; <emph type="italics"/>patet continere quartam partem <lb/>totius cylindri<emph.end type="italics"/> (Ouvrag. </s>

<s>cit. </s>

<s>pag. </s>

<s>322). </s></p><p type="main">

<s>Sarebbe la cosa patente, quando le due superficie piane, rappresentateci <lb/>dal rettangolo DC e dal bilineo AMFT, nella figura 308, avessero &igrave; loro centri <lb/><figure id="id.020.01.2856.1.jpg" xlink:href="020/01/2856/1.jpg"/></s></p><p type="caption">

<s>Figura 308.<lb/>di gravit&agrave; a ugual distanza dalla FC, <lb/>perch&egrave; allora, stando i solidi com'esse <lb/>superficie semplicemente, starebbero <lb/>anche insieme come uno a quattro. </s>

<s><lb/>Ma chi sa in qual punto della BH cade <lb/>il centro del detto bilineo, o qual <lb/>fiducia pu&ograve; aversi che coincida col <lb/>punto di mezzo della GI, dove il ret&shy;<lb/>tangolo DC concentra il suo peso? </s>

<s><lb/>Non avvert&igrave; il Roberval essere la cosa <lb/>molto diversa, quando il rivolgimento si fa intorno alla base, perch&egrave; allora <lb/>il bilineo e il rettangolo, raddoppiati dall'altra parte dell'asse, riescono con&shy;<lb/>centrici in I, e il metodo, solamente applicabile in questo caso, lo cred&egrave; <lb/>universale. </s></p><p type="main">

<s>Cos&igrave; sembra a noi venga dato imparziale giudizio intorno al torto e al <lb/>diritto di questa lite, la quale non si sarebbe forse agitata cos&igrave; diuturna e <lb/>fervente, se ambedue i grandi Uomini non avessero falsamente creduto al&shy;<lb/>l'impossibilit&agrave; del riscontrarsi, per vie diverse, nella medesima invenzione <lb/>due ingegni, senza che all'uno fossero in qualunque modo noti i progressi <lb/>dell'altro. </s>

<s>Fu da un tal dannoso pregiudizio mosso principalmente il Torri&shy;<lb/>celli, quando, posate appena le armi contro il Roberval, le riprese subito in <lb/>mano, per usarle contro il Ricci, da cui intendeva di rivendicarsi il primato <lb/>e la propriet&agrave; del metodo per la quadratura delle infinite parabole. </s>

<s>Ma il <lb/>Ricci, con coscienza non men sincera e dignitosa del Roberval, rispondeva <lb/>cos&igrave; francamente alle pretensioni: </s></p><p type="main">

<s>&ldquo; Passo dunque al punto principale, cio&egrave; che la quadratura delle infi&shy;<lb/>nite parabole io deva totalmente riconoscerla come sua, bench&egrave; io scriva di <lb/>averla molto prima, che ella mi scrivesse la sua, che quasi &egrave; la medesima, <lb/>e bench&egrave; io l'abbia ritrovata prima di lei, per quel che posso congetturare <lb/>da una sua lettera, che mi scrisse il marzo passato, dove disprezzava l'in&shy;<lb/>venzione del Robervallio. </s>

<s>E fu allora che io le risposi che io non potevo non <lb/>estimarla assai come fecondo principio di bellissime conseguenze, alludendo <lb/>alla quadratura suddetta, di che avevo preso motivo da quella invenzione, e <lb/>alla invenzione de'centri di gravit&agrave; della stessa parabola, con altri misteri, <pb xlink:href="020/01/2857.jpg" pagenum="482"/>ai quali scorgevo aperta la strada. </s>

<s>Questa ultima per&ograve; dei centri di gravit&agrave; <lb/>non la perfezionai, stante l'indisposizione, che allora mi travagliava. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Le ragioni di V. S. son due: la prima, che sar&agrave; giudicato impossi&shy;<lb/>bile che ci siamo incontrati ambedue nel medesimo metodo cos&igrave; precisamente, <lb/>senza che uno di noi abbia veduto il progresso dell'altro, e di poco l'abbia <lb/>alterato, essendo troppo fuori dell'usato quel modo di provare. </s>

<s>La seconda <lb/>vuole che io non possa avere quella quadratura generalmente, perch&egrave; vi si <lb/>richiederebbe il teorema delle tangenti, a questo il teorema de'massimi, il <lb/>quale io confesso di non aver generalmente trovato per ancora. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Io dico a V. S. che la proposta di Robervallio mi fu comunicata dal <lb/>sig. </s>

<s>Raffaello Magiotti, per ordine di lei, e ne ammirai la dimostrazione, che <lb/>ella subitamente vi fece, come a V. S. ne scrissi in quel tempo. </s>

<s>Da questo <lb/>io presi occasione di mostrare la quadratura delle infinite parabole, non lo <lb/>metto in dubbio. </s>

<s>Se poi si giustificher&agrave; impossibile (cosa che V. S. non disse <lb/>mai) il dedurre questa quadratura, io avr&ograve; fatto l'impossibile, e il sig. </s>

<s>An&shy;<lb/>tonio Nardi me ne far&agrave; fede. </s>

<s>Ma perch&egrave; V. S. non dir&agrave; che sia difficile, ma <lb/>facilissimo il dedurla dalla proposizione di Robervallio, anzi una cosa mede&shy;<lb/>sima, io replico che ci&ograve; non sar&agrave; agevolmente ammesso da chi sapr&agrave; che <lb/>Robervallio, avendo dimostrata la proposizione, stim&ograve; ardua impresa il ca&shy;<lb/>varne la quadratura della sola parabola vulgata, come V. S. mi signific&ograve; nella <lb/>sua de'28 di Maggio prossimo. </s>

<s>Ed aggiungo quel che di sopra dicevo, che <lb/>ella avrebbe fatto stima grandissima di quella proposta, quando ne avesse <lb/>dedotta la detta quadratura, che, sebbene ora mostra di prezzar poco, allora <lb/>era uno dei massimi teoremi, che fossero in volta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Circa poi all'essere una cosa medesima la proposta di Robervallio e <lb/>la quadratura, onde seguirebbe che la dimostrazione di questa io non potessi <lb/>appropriarmi, quando avessi con poca alterazione da quella proposta preso <lb/>fondamento alla mia dimostrazione; le ridurr&ograve; solamente a memoria il suo <lb/>senso, avvisatomi nella lettera poco dianzi mentovata. </s>

<s>Ella mi comunica due <lb/>maniere per dimostrare le infinite quadrature, l'una delle quali ha il me&shy;<lb/>desimo progresso con la mia maniera, e piglia per fondamento una dimo&shy;<lb/>strazione, da quella della proposta di Robervallio poco differente, come V. S. <lb/>asserisce. </s>

<s>L'altra si serve espressamente della proposta di Robervallio, con <lb/>la dimostrazione fattale da V. S., e conclude la lettera: <emph type="italics"/>Noi da quelle sue <lb/>figure,<emph.end type="italics"/> cio&egrave; di Robervallio, <emph type="italics"/>caviamo la quadratura di tutte le parabole, <lb/>come apparve in quest'ultima: ed in modo poco differente con invenzione <lb/>propria affatto, senza nulla d'altri come la precedente, dimostriamo un'al&shy;<lb/>tra volta il medesimo.<emph.end type="italics"/> Ecco dunque che, variandosi un poco la dimostra&shy;<lb/>zione adattata alla proposta di Robervallio, e da questa derivandosi la qua&shy;<lb/>dratura delle infinite parabole (ed io poi non solo vario il poco di V. S. ma <lb/>forse assai pi&ugrave;) si pu&ograve;, per detto di lei, chiamare invenzione senza nulla <lb/>d'altri. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma non &egrave; da tacere che nella dimostrazione di V. S. fanno gioco prin&shy;<lb/>cipale le tangenti, delle quali, non solamente io posso dirmi il primo, per la <pb xlink:href="020/01/2858.jpg" pagenum="483"/>verit&agrave; che generalmente le partecipai; ma per il metodo generale ancora, <lb/>dal quale confessa ella d'aver avuto motivo per la dimostrazione fattane dopo <lb/>per via del moto. </s>

<s>Ella scrive, sotto li 26 di Febbraio dell'anno passato, in <lb/>questo tenore, rispondendo alla lettera, con la quale avvisavo l'invenzione <lb/>delle suddette tangenti: <emph type="italics"/>Ho bene io imparato dalle sue lettere cose, che <lb/>forse non avrei avvertite mai, perch&egrave;, tornando iersera con le lettere di <lb/>V. S. in mano, mi entr&ograve; in testa che quelle tangenti non potesssero essere. </s>

<s><lb/>Ci&ograve; fu causa che feci non so che figure, e trovai poi ch'era verissimo, e <lb/>ne scrissi la dimostrazione universale, per via del moto.<emph.end type="italics"/> Se dunque io non <lb/>posso per l'un rispetto attribuirmi questa quadratura, ella pare a me che <lb/>non vorr&agrave; attribuirsela, avendo riguardo a quest'altro rispetto. </s>

<s>Sicch&egrave; re&shy;<lb/>ster&agrave; come effetto di mutua causalit&agrave;, per favellar con le scuole, e non si <lb/>dir&agrave; n&egrave; suo n&egrave; mio parto proprio e totale, essendo ella primo in un genere <lb/>ed io primo in un altro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Alla seconda ragione rispondo che io facevo due conti, in caso che <lb/>mi fosse succeduto di provare quel lemma generalmente: cio&egrave; di supplicar <lb/>V. S. che me ne favorisse, conforme all'intenzione che me ne diede l'anno <lb/>passato, quando mi mand&ograve; il medesimo lemma dimostrato, ma in casi par&shy;<lb/>ticolari; ovvero di proporre il metodo e darne come un esempio in que'casi <lb/>che posso, avvertendo che, riducendo qual si voglia caso all'invenzione dei <lb/>massimi, si trova generalmente la ragione di tutto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Mando a V. S. parte della mia dimostrazione nel proposito nostro, <lb/>stimandola sufficiente per questo che si pretende, cio&egrave; di scoprire la conve&shy;<lb/>nienza de'metodi, e giuro a V. S. che questa &egrave; la medesima dimostrazione, <lb/>che io scrissi nel marzo passato: solo qualche paroluccia ho mutato nel tra&shy;<lb/>scrivere.... Ella si ricorder&agrave;, due mesi sono, che mi avvis&ograve; una sua pro&shy;<lb/>posizione dimostrata da lei in modo recondito, eppure io l'indovinai..... <lb/>Roma, 7 Luglio 1646. &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>162-66). </s></p><p type="main">

<s>Da queste ragioni giova a noi credere che rimanesse persuaso il Tor&shy;<lb/>ricelli, nel quale &egrave; certo che torn&ograve; presto la consueta serenit&agrave; verso il Ricci, <lb/>come pure giova similmente credere che facesse col Roberval accettando <lb/>l'amicizia da lui generosamente proffertagli, <emph type="italics"/>litibus valere iussis<emph.end type="italics"/> (Ouvrages, <lb/>pag. </s>

<s>398) dalla naturale bont&agrave; dell'animo, e dal presentimento della morte <lb/>vicina. </s></p><p type="main">

<s>Chi potrebbe in ogni modo negare ai due grandi Matematici l'aver <lb/>concorso con pari merito, l'uno a istituire, l'altro a diffondere quella scienza <lb/>della Cicloide, che avrebbe poco di poi, per il Pascal, pel Wallis e per l'Huy&shy;<lb/>ghens progredito tant'oltre? </s>

<s>Che se l'ultimo commemorato, nello scolio al&shy;<lb/>l'ottava proposizione della terza parte dell'<emph type="italics"/>Orologio oscillatorio,<emph.end type="italics"/> compen&shy;<lb/>diando questa Storia non ricorda del Torricelli nemmeno il nome, l'altro, <lb/>il Wallis, nella prefazione al suo <emph type="italics"/>Trattato della Cicloide<emph.end type="italics"/> confessa di averne <lb/>da solo il Torricelli imparata la quadratura, non pensando nemmen per sogno <lb/>che il Roberval, nulla avendo dato ancora alla luce, si fosse esercitato nel <lb/>medesimo soggetto. </s></p><pb xlink:href="020/01/2859.jpg" pagenum="484"/><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>La storia della Cicloide, perch&egrave; troppo importante in s&egrave; stessa, e per&shy;<lb/>ch&egrave; troppo bisognosa di essere illustrata nelle sue origini, rimaste fin qui <lb/>occulte nei manoscritti; &egrave; stata in questo capitolo una assai lunga digressione <lb/>da quella via, sopra la quale siam solleciti ora di ritornare, per accennar <lb/>frettolosamente all'opera, data dai colleghi e dai discepoli del Torricelli in <lb/>promovere la Meccanica galileiana. </s>

<s>Si disse gi&agrave;, infin dal principio del pre&shy;<lb/>sente discorso, ch'erano principalmente da annoverare fra cotesti promotori <lb/>il Cavalieri, il Borelli e il Viviani, i quali tre insigni personaggi sono oramai <lb/>tante volte compariti sopra la scena, come principali attori del dramma, e i <lb/>nostri Lettori perci&ograve; gli debbono conoscere cos&igrave; bene, che alla tela, sopra la <lb/>quale &egrave; disegnata la loro effige, manca solamente l'essere circoscritta, e ter&shy;<lb/>minata dalla sua propria cornice. </s></p><p type="main">

<s>Il Cavalieri, avutone l'impulso dalla lettura dei dialoghi dei Due mas&shy;<lb/>simi sistemi, esord&igrave; i suoi studi con lo <emph type="italics"/>Specchio ustorio,<emph.end type="italics"/> dimostando che, <lb/>nelle naturali scese dei gravi, gli spazi crescono come i quadrati dei tempi, <lb/>in un modo nuovo e affatto geometrico, come pure ei fu il primo a dimo&shy;<lb/>strar, nella parabola de'proietti, i ludi geometrici della Natura. </s>

<s>Galileo, o <lb/>fossero le sue espressioni sincere, o tinte della gelosa paura di un potente <lb/>rivale; designava per suo successore nella Scienza del moto lo stesso Cava&shy;<lb/>lieri, che rispondeva nel Giugno del 1635 in questi termini, interpetrando <lb/>meglio il suo proprio genio, che le intenzioni degli altrui onorevoli inviti: <lb/><emph type="italics"/>Quanto alla qualit&agrave; degli studi, ai quali sia ora per applicarmi, se io <lb/>riguardo al mio gusto, mi saria piaciuto applicarmi io ancora alla dot&shy;<lb/>trina del moto, parendomi cosa di gran momento, ed il compendio della <lb/>vera Filosofia:<emph.end type="italics"/> ma soggiunge che, per badare alla sodisfazione del luogo, <lb/>ossia della cattedra bolognese, nella quale era stato il Magini suo anteces&shy;<lb/>sore tanto onorato, gli sarebbe convenuto piuttosto attendere a calcolare le <lb/>Effemeridi per gli anni prossimi futuri (Campori, Carteggio gal., Modena 1881). <lb/>Da un'altra lettera, scritta allo stesso Galileo pochi giorni appresso, traspa&shy;<lb/>risce pi&ugrave; chiaramente essere una delle principali ragioni, che lo ritengono <lb/>dal coltivare gli studi della Meccanica, quella di non far nascere nuove om&shy;<lb/>bre di gelosia nel mal disposto animo del suo Maestro, scusandosi con lui, <lb/>un'altra volta fra le tante, del disgusto, che gli potesse ignorantemente aver <lb/>dato con l'occasione dello <emph type="italics"/>Specchio ustorio<emph.end type="italics"/> &ldquo; nel quale, prosegue a dire, ve&shy;<lb/>nendomi cos&igrave; bene a taglio la linea descritta dal proietto per le sezioni co&shy;<lb/>niche, pensando che ella non ne facesse conto pi&ugrave; che tanto, mi presi licenza <lb/>d'inserirla in quel libro, credendo che le proposte mie, fatte in quello, che <lb/>era cosa imparata da lei, dovessero piuttosto cagionarle piacere che dispia&shy;<lb/>cere &rdquo; (ivi, pag. </s>

<s>442). </s></p><pb xlink:href="020/01/2860.jpg" pagenum="485"/><p type="main">

<s>Non &egrave; il tempo n&egrave; il bisogno di tornare indietro sopra la storia odiosa <lb/>di quella incredibile usurpazione, dalla quale si deriv&ograve; grave danno ai pro&shy;<lb/>gressi della Scienza del moto, abbandonata dal Cavalieri afflitto e sbigottito. </s>

<s><lb/>Non abbiamo infatti su quel soggetto, dopo quel che ne tocc&ograve; l'Autore nello <lb/>Specchio ustorio, altro che la Quinta esercitazione geometrica, nella quale <lb/>pure s'intravede una trepida sollecitudine di non mettere il pie'nel campo <lb/>galileiano, limitandosi a percorrerne, nella statica dei momenti e dei centri <lb/>di gravit&agrave;, le estreme prode. </s>

<s>Notabile, a proposito dell'invenzione di questi <lb/>centri, che fosse il Cavalieri il primo e l'unico a riguardare i corpi in gra&shy;<lb/>vit&agrave; come <emph type="italics"/>uniformemente disformi,<emph.end type="italics"/> ci&ograve; che si meriterebbe il nome, scritto <lb/>nel titolo, di una pura esercitazione geometrica, se in qualche caso, da con&shy;<lb/>siderarsi forse meglio dai Fisici, non se ne vedesse possibile l'applicazione, <lb/>come per esempio nella ricerca de'centri di gravit&agrave; delle grandi moli solle&shy;<lb/>vate dalle forze endogene della Terra, supponendo che la densit&agrave; degli strati <lb/>sia proporzionale alle pressioni o alle attrazioni, le quali crescano reciproca&shy;<lb/>mente alle distanze dal centro. </s></p><p type="main">

<s>Altra cosa notabile &egrave; che, delle tante invenzioni comunicategli dal Tor&shy;<lb/>ricelli intorno ai centri di gravit&agrave; delle varie figure, non faccia il Cavalieri <lb/>motto che del solido colonnare insignito del suo proprio nome; e, nella pro&shy;<lb/>posizione XVII, del centro di gravit&agrave; della callotta sferica, <emph type="italics"/>quod novissime <lb/>probavit Torricellius,<emph.end type="italics"/> e, nella XXXIV, del centro di gravit&agrave; dell'emisfero, <lb/>dimostrato per via degl'indivisibili con eleganze, che poco paion diverse dalle <lb/>torricelliane. </s>

<s>La ragione scusabilissima di questo silenzio sar&agrave; stata, perch&egrave; <lb/>sperava che avrebbe il Torricelli stesso presto dato ordine e pubblicit&agrave; al <lb/>suo libro <emph type="italics"/>De centro gravitatis,<emph.end type="italics"/> il quale, rimastosi invece per due secoli e <lb/>mezzo ne'suoi materiali disordinato e disperso, oggi finalmente ha preso qui <lb/>addietro nella nostra Storia, men per noi che per i pregi suoi propri, bel&shy;<lb/>lezza nuova di forma. </s></p><p type="main">

<s>Il Borelli, fra i discepoli di Galileo, attese allo studio della Meccanica <lb/>sopra tutti gli altri, dando in quell'argomento alla luce quattro opere insi&shy;<lb/>gni, quali sono <emph type="italics"/>De vi percussionis, De motionibus naturalibus a gravitate <lb/>pendentibus, Theoricae Mediceorum<emph.end type="italics"/> e <emph type="italics"/>De motu animalium.<emph.end type="italics"/> Nelle prime <lb/>due l'intento dell'Autore non &egrave; che di promovere le dottrine del suo Mae&shy;<lb/>stro, ma nelle altre due rimanenti apre campi nuovi alla Scienza, e dai pic&shy;<lb/>coli gravi terrestri risale arditamente alle grandi moli de'pianeti, e da'moti <lb/>apperenti nella materia bruta deriva leggi, che rivelano gli occulti misteri <lb/>della vita. </s></p><p type="main">

<s>Del trattato della percossa e degli urti, e come il Borelli, prima del Wal&shy;<lb/>lis, del Mariotte e dell'Huyghens ne dimostrasse le leggi, fu detto qui addie&shy;<lb/>tro nel capitolo III quanto ne pare a sufficienza per la storia dell'invenzione, <lb/>se non del libro, che, sospingendone la via, lasciamo alle cure degli eruditi. </s></p><p type="main">

<s>N&egrave; solamente rispetto alla forza della percossa lasciava da desiderare la <lb/>Scienza galileiana, ma rispetto ancora ad altre dottrine pi&ugrave; fondamentali, che <lb/>il Borelli si studi&ograve; di confermare, e di esplicare nel libro <emph type="italics"/>De motionibus na-<emph.end type="italics"/><pb xlink:href="020/01/2861.jpg" pagenum="486"/><emph type="italics"/>turalibus.<emph.end type="italics"/> Gli errori di Aristotile intorno alle cadute naturali dei gravi erano <lb/>stati scoperti liberamente da Galileo, il quale fu il primo ad annunziare <lb/>quella proposizione, apparita a tutti ammirabile, che cio&egrave; nel vuoto i corpi, <lb/>di qualunque mole e di qualunque figura, scenderebbero nel medesimo tempo <lb/>spazi uguali. </s>

<s>&ldquo; Eam tamen propositionem, soggiunge il Borelli, Galileus non <lb/>demonstravit, sed coniecturis et probabilibus tantummodo rationibus confir&shy;<lb/>mare conatus est. </s>

<s>Quia vero huiusmodi propositio usum habet in hac phy&shy;<lb/>sicee parte, quam praemanibus habemus, propterea operae pretium duxi fir&shy;<lb/>mis demonstrationibus eam confirmare &rdquo; (Regio Julio 1670, pag. </s>

<s>439, 40). </s></p><p type="main">

<s>Le dimostrazioni per&ograve; dell'Autore, come si pu&ograve; facilmente indovinare, <lb/>erano di ragion pura e non sperimentali, mancando anche a lui, come a <lb/>Galileo, della Macchina pneumatica l'invenzione e l'uso. </s>

<s>Nulladimeno saga&shy;<lb/>cemente avvertiva che del fatto, solamente operantesi nel vuoto, si poteva <lb/>aver qualche indizio certo o almeno probabile anche nel pieno, quando le <lb/>cadute si osservino in distanze talmente piccole, che poco sia l'impedimento <lb/>opposto dalla consistenza o viscosit&agrave; del mezzo. </s>

<s>Di qui apparisce, soggiunge <lb/>il Borelli, l'imperizia di coloro, da'quali non &egrave; escluso lo stesso Galileo, che, <lb/>volendo investigare se i corpi inegualmente gravi discendono inegualmente, <lb/>pensan&ograve; doversi sperimentare facendo cadere i gravi dalle altissime torri <lb/>&ldquo; ubi velocitates plumbi et argillae valde differunt inter se, cum tamen in <lb/>brevioribus altitudinibus nullo sensu distingui possint eorum inaequalitates, <lb/>cum ambo eodem tempore ferri videantur &rdquo; (ibid., pag. </s>

<s>500). </s></p><p type="main">

<s>Non sempre per&ograve; il Borelli si contenta di confermare, come fa qui, le <lb/>dottrine del suo Maestro, ma altrove anche le compie, annunziando e dimo&shy;<lb/>strando proposizioni nuove, qual sarebbe per esempio la seguente: &ldquo; Si fue&shy;<lb/>rint duo cylindri homogenei aqua demersi, aequalium basium et inaequalium <lb/>altitudinum, semperque eorum latera perpendicularia sint ad horizontem; <lb/>tempora, quibus aequalia spatia ascendendo vel descendendo percurrunt, eam&shy;<lb/>dem proportionem reciprocam habebunt, quam subduplicata ratio altitudinum <lb/>fuerit &rdquo; (ibid., pag. </s>

<s>470). La proposizione &egrave; contro Antonio Oliva, il quale <lb/>aveva proposto nell'Accademia del Cimento alcune esperienze, per confer&shy;<lb/>mare una sua opinione, che cio&egrave; le velocit&agrave; de'corpi, o discendenti o ascen&shy;<lb/>denti nell'acqua, osservino la proporzion diretta delle loro altezze. </s></p><p type="main">

<s>Erano altri, n&egrave; sappiamo se fosse tra costoro lo stesso Oliva, che nega&shy;<lb/>vano l'accelerarsi i corpi nell'andare al fondo, o nel risalir pur per l'acqua. </s>

<s><lb/>L'errore aveva avuto occasione e veniva confermato da quell'altro errore di <lb/>Galileo, che insegnava giungere nelle prolisse cadute il grave a ricevere dal <lb/>mezzo tale impedimento, da vietargli di pi&ugrave; accelerarsi, cosicch&egrave; il moto pro&shy;<lb/>cede di l&igrave; in poi sempre uniforme. </s>

<s>Credettero que'Fisici che impedimento di <lb/>tal qualit&agrave; e potenza fosse al mobile l'acqua, e il Borelli non volle lasciar <lb/>l'occasione di scoprire con due belle esperienze quella loro fallacia, dimo&shy;<lb/>strata gi&agrave; dai calcoli del Cartesio. </s>

<s>A un vaso aveva spalmato il fondo di cera, <lb/>e riempiutolo del liquido, vi faceva da varie altezze cadere una palla di <lb/>piombo, infissovi sotto un ago. </s>

<s>Osserv&ograve; che la punta era entrata nella cera <pb xlink:href="020/01/2862.jpg" pagenum="487"/>tanto pi&ugrave; addentro, quanto la palla era venuta pi&ugrave; d'alto. </s>

<s>A far poi espe&shy;<lb/>rienza del medesimo, nel risalire, affondava, per via di un bastoncello, un <lb/>cannellino, a cui era zavorra un globetto di piombo, che lasciato libero si <lb/>vedeva risaltar pi&ugrave; o meno sull'acqua, secondo ch'era stato pi&ugrave; o meno som&shy;<lb/>merso. </s>

<s>&ldquo; Unde patet, ne conclude il Borelli, quod saltus altior produci de&shy;<lb/>buit a vehementiori velocitate eiusdem calami, acquisita in eius ascensu pro&shy;<lb/>lixiori &rdquo; (ibid., pag. </s>

<s>501). </s></p><p type="main">

<s>Le due opere di Meccanica pura, esaminate o per pi&ugrave; vero dire ridotte <lb/>alla memoria dei nostri Lettori, erano nell'intendimento dell'Autore una <lb/>preparazione, e dovevano quasi servir di proemio alla grande opera dei moti <lb/>animali. </s>

<s>La celebrit&agrave; di lei dispensa la nostra Storia dall'entrare ne'pi&ugrave; mi&shy;<lb/>nuti particolari, e da un altro lato, nel Tomo III, sono inseriti in gran nu&shy;<lb/>mero documenti, che mostrano quali progressi venisse a fare la Fisiologia, <lb/>per le speculazioni e per l'esperienze del Borelli. </s>

<s>De'tanti lemmi premess <lb/>alle varie proposizioni, per preparar dalle forze che tendon le funi il pas&shy;<lb/>saggio alle forze che contraggono i tendini e i muscoli, abbiamo avuto oc&shy;<lb/>casione di toccare in vario proposito, e cose anche di maggiore importanza <lb/>ci occorreranno a dire pi&ugrave; qua nel capitolo IX: ond'&egrave; che sole le <emph type="italics"/>Theori&shy;<lb/>cae Mediceorum<emph.end type="italics"/> ci rimangono a ridurre dentro la cornice del quadro. </s></p><p type="main">

<s>Non si possono l'importanza e il fine di quest'Opera nuova di Mecca&shy;<lb/>nica celeste pienamente comprendere, senza risalire, e intrattener la mente <lb/>nella grande riforma astronomica del Keplero. </s>

<s>L'orbita ellittica, dimostrata <lb/>da lui nella stella di Marte come cosa di fatto, apr&igrave; gli occhi via via agli <lb/>osservatori del Cielo, i quali presto ebbero a persuadersi che in simil modo <lb/>ricircolano intorno al Sole tutti gli altri pianeti, e i satelliti stessi intorno a <lb/>Giove. </s>

<s>Venivano cos&igrave; a dissiparsi de'costruttori dei mondani sistemi le mac&shy;<lb/>chine incantate, ma restava a spiegarsi come mai le circolanti moli s'appres&shy;<lb/>sassero e si dilungassero, con vicenda incessante, dai loro centri. </s>

<s>Il Keplero <lb/>s'era immaginato che una faccia del Pianeta fosse amica al Sole, e l'altra <lb/>nemica, d'onde ora avvenisse un'attrazione, ora una repulsione, a somi&shy;<lb/>glianza di quel che il magnete, dagli opposti poli, fa verso il ferro: e com'era <lb/>una strana immaginazione, cos&igrave; a buon diritto si repudi&ograve; dagli Astronomi. </s></p><p type="main">

<s>Con nessun diritto per&ograve; s'ostinarono altri a negare l'esistenza del fatto, <lb/>perch&egrave; non ne intendevano le ragioni, di che Galileo dette al mondo, ne'dia&shy;<lb/>loghi dei Due massimi sistemi, esempio cos&igrave; famoso. </s>

<s>Si condannarono cote&shy;<lb/>sti Dialoghi dalla Curia, instigata dai professori del Collegio romano, ma gli <lb/>aveva prima con pi&ugrave; legittima autorit&agrave; condannati la Scienza, la quale, per <lb/>le prove del moto della Terra, prolissamente ridotte all'intelligenza dei Sim&shy;<lb/>plicii, non seppe perdonare le inverosimiglianze e le irragionevolezze del si&shy;<lb/>stema copernicano, per vedersi liberata dalle quali aveva fatto dianzi cos&igrave; <lb/>gran plauso al Keplero. </s>

<s>Di qui &egrave; che gli Astronomi, i quali, bench&egrave; per ra&shy;<lb/>gioni diverse, si trovarono esser concorsi nella medesima sentenza col Santo <lb/>Uffizio, non fecero que'reclami, di che poi assordarono il mondo tanti scrit&shy;<lb/>tori, quando nell'argomento veniva a porgersi alla loro rettorica un s&igrave; favo-<pb xlink:href="020/01/2863.jpg" pagenum="488"/>rito esercizio. </s>

<s>N&egrave; furono quegli astronomi solamente i Roberval e i Cartesii, o <lb/>altri stranieri indifferenti o plaudenti agl'immolatori della vittima del loro ri&shy;<lb/>vale, ma gli stessi discepoli di Galileo pi&ugrave; assennati e pi&ugrave; liberi, fra'quali, <lb/>da che s'&egrave; imparato a conoscerlo in questa Storia, &egrave; de'primi Antonio Nardi. </s></p><p type="main">

<s>Pi&ugrave; forse del libro <emph type="italics"/>De revolutionibus<emph.end type="italics"/> del Copernico confer&igrave; a persuadere <lb/>che, non la Terra ma il Sole, sia centro de'moti planetari l'Arenario di Ar&shy;<lb/>chimede, intorno al quale il Nardi, nella sua <emph type="italics"/>Ricercata seconda,<emph.end type="italics"/> sotto il ti&shy;<lb/>tolo: &ldquo; Del sistema del mondo sopra quelle parole di Archimede nell'Are&shy;<lb/>nario <emph type="italics"/>Supponit Aristarchus inerrantia sidera et Solem non moveri, Terram <lb/>vero ferri in gyrum circa Solem, qui in medio stadio iaceat;<emph.end type="italics"/> scriveva la <lb/>seguente osservazione, compendiando una delle pagine pi&ugrave; importanti della <lb/>Storia filosofica dell'Astronomia: </s></p><p type="main">

<s>&ldquo; Molto rozzo, e molto nell'apparenza dalla verisimilitudine repugnante, <lb/>parmi il sistema del Mondo, che per vero al tempo di Archimede da molti <lb/>si riceveva, poich&egrave; credevasi con Anassimandro il mondo essere una sfera, <lb/>di cui il centro fosse quello della Terra, e il semidiametro quella linea, che <lb/>dalla Terra andasse al Sole. </s>

<s>Platone con tutto ci&ograve; ed altri avevano creduto <lb/>diversamente, a'quali, dopo Archimede, accostossi Ipparco Rodio, a cui To&shy;<lb/>lomeo, e a Tolomeo gli altri tutti, sino all'et&agrave; de'nostri avi, si sottoscris&shy;<lb/>sero. </s>

<s>Ma Filolao da Crotone e Iceta Siracusano erano stati avanti Platone <lb/>inventori in parte di un paradosso sistema, il quale da Aristarco Samio fu <lb/>molto coltivato e perfezionato, di tal maniera che Archimede ad Aristarco il <lb/>parto di tal sistema attribuisce. </s>

<s>Ma tal parto mor&igrave; quasi in fasce, se non che <lb/>Niccol&ograve; Copernico, dopo il giro dintorno a diciotto secoli, lo cav&ograve; dal sepol&shy;<lb/>cro, e all'et&agrave; nostra, per le osservazioni del Telescopio, si &egrave; grandemente <lb/>avanzato nella credenza di molti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; &Egrave; ben vero che alla Santa Romana Chiesa tal sistema &egrave; per gravis&shy;<lb/>sime cagioni sospetto, di che per ora ragionare non &egrave; mio proposito, e solo <lb/>avvertir&ograve; come, anche col semplice lume naturale discorrendo, parmi che il <lb/>sistema del Copernico in molte cose sia difettoso. </s>

<s>Egli in prima asserisce il <lb/>Sole e le fisse Stelle essere in tutto immobili, e per il contrario di&egrave; tante e <lb/>cos&igrave; strane maniere di movimenti alla Terra, senz'addurne almeno qualche <lb/>ingegnosa, se non vera cagione, che sembra l'opinion sua una fantasia troppo <lb/>fantastica, e pareva molto meglio il dare a ciascun corpo il suo moto, poich&egrave; <lb/>de'corpi &egrave; comune accidente il moversi, che ad alcuni in tutto levandolo, e <lb/>troppi ad altri assegnandone, disturbare il mondano concerto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Impossibili dunque paiono quelle copernicane posizioni intorno a tanti <lb/>e s&igrave; diversi commovimenti, che come propri attribuisce alla Terra. </s>

<s>Quindi <lb/>ancora non l&egrave; librazioni sole e l'inclinazioni, quali esso le finge, stimeran&shy;<lb/>nosi da molti cose adulterine, ma ancora molto pi&ugrave; quel forzato discorri&shy;<lb/>mento, che per diritta linea in gi&ugrave; e in s&ugrave; fa Mercurio. </s>

<s>S'aggiunga ancora <lb/>che, essendo cose immaginarie, i centri degli Orbi descrivono con tutto ci&ograve; <lb/>appo il Copernico altri cerchi, e seco ne rapiscono gli orbi loro, il che &egrave; <lb/>inverosimile grande. </s>

<s>Lascio che in tal caso, mentre saglie e discende l'Orbe, <pb xlink:href="020/01/2864.jpg" pagenum="489"/>che egli dice inconsideratamente Magno; offender&agrave; il maggiore di Marte, e <lb/>quello di Venere, se per&ograve; non voglia che fra l'uno orbe e l'altro ci sia molto <lb/>spazio vano, il che lo sproposito accresce: come anco a volere che insieme <lb/>si confondessero o si condensassero o rarefacessero. </s>

<s>Il vedersi ancora alcuni <lb/>mondani movimenti avere i loro periodi ubbidienti ai movimenti di altri corpi, <lb/>come per esempio il trovarsi Venere e Mercurio prossimi o lontani da un <lb/>certo punto, mentre la Terra in una tal linea si trovi; d&agrave; di chimerica po&shy;<lb/>sizione indizio, sicch&egrave; almeno bisogna scansare, se non torre in tutto questo <lb/>inverosimile. </s>

<s>Ma supera tutti gl'inverosimili l'immensa distanza eterea fra <lb/>le fisse e i pianeti, poich&egrave; la sola ragione delle rifrazioni orizontali poteva <lb/>rimediare a molte apparenze, senza per cos&igrave; dire disgiungere il mondo da <lb/>s&egrave; medesimo, acci&ograve; di notte non si veda meno che mezzo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Tolomeo, dall'altra banda, molto seccamente s'invent&ograve; e abbracci&ograve; <lb/>quei cerchi, che irregolarmente sopra il suo, e regolarmente sopra gli altri <lb/>centri si muovono. </s>

<s>Pare ancora che nulla di naturale artifizio abbiano gli <lb/>orbi vuoti e di grossezza disuguale, per dove gli eccentri scorrano: oltrech&egrave; <lb/>troppo il rendere ragione &egrave; difficile come, gli uni combaciandosi con gli altri, <lb/>possano o congiunti o separati movimenti ottenere. </s>

<s>&Egrave; anche strano a inten&shy;<lb/>dersi come l'ottavo cielo, contiguo a Saturno, comunichi a Saturno il suo <lb/>moto, ma Saturno non comunichi il suo a Giove, massime che la Luna co&shy;<lb/>munica il suo al fuoco, se ci sia, e all'aria, nature dalla quinta essenza to&shy;<lb/>lemaica dissimili e fra s&egrave; ancora, e che, di pi&ugrave;, propria origine di movi&shy;<lb/>mento, e diverso dal circolare, ottengono in tale ipotesi. </s>

<s>Moversi ancora <lb/>l'ottavo Orbe di movimento si tard&ograve;, e il settimo contiguo s&igrave; veloce, e di <lb/>velocissimo il nono; moversi ancora il secondo, il terzo e il quarto di eguale, <lb/>non ha del probabile in modo alcuno, come nemmeno che la Luna sia, nella <lb/>quarta, nell'imo apside dell'eccentro, e non riluca quattro volte pi&ugrave; di quello <lb/>che fa, e ancora che si muova nell'epiciclo, e che mostri l'istessa faccia a <lb/>noi. </s>

<s>Certo che Tolomeo, purch&egrave; in qualche maniera alle apparenze dei moti <lb/>(questo &egrave; suo fine) sodisfaccia, poco della mondana armonia e convenienza <lb/>gli cale. </s>

<s>Quindi anco vediamo che poco la mal proporzionata proporzione <lb/>degli epicicli di Marte e di Venere gli prema, e cos&igrave; anche, ora gli eccentri <lb/>e gli epicicli, ora l'epiciclo dell'epiciclo e l'eccentro epiciclo ei prenda nella <lb/>gran composizione, senza di tal differenza briga prendersi, in che, come in <lb/>altri inconvenienti, ha Tolomeo compagno il Copernico, e massime nel far <lb/>movere i pianeti intorno a centri immaginari. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Meglio fece Aristotile a voler che i pianeti si movessero intorno alla <lb/>Terra come intorno a proprio centro, ma in tal caso bisogna render qualche <lb/>ragione dell'avvicinarsi e discostarsi i Pianeti da esso centro, il che ha ten&shy;<lb/>tato di fare in altra ipotesi il Keplero. </s>

<s>Delle cagioni poi di cotesti moti non <lb/>si trova parola appo Tolomeo e il Copernico, ma lasciano di ci&ograve; la briga ai <lb/>Fisici, i quali per lo pi&ugrave; ricorrono alle macchine. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In ultimo, merc&egrave; di tante apparenze nuovamente manifestateci, e per <lb/>essersi nuovi corpi mondani, e nuovi movimenti scoperti, o meglio i vecchi <pb xlink:href="020/01/2865.jpg" pagenum="490"/>osservati; bisogna non solo poco probabili stimare molte supposizioni degli <lb/>antichi, ma ancora in molte parti false. </s>

<s>Ticone di due sistemi ha fatto una <lb/>mal digerita confusione. </s>

<s>Non voglio esaminare tal suo parto, perch&egrave;, dal solo <lb/>aspetto, mostruoso apparisce. </s>

<s>Marte solo, rompendo col suo un altro giro, <lb/>impaurisce chiunque abbracciar dette posizioni volesse. </s>

<s>Ma di queste materie <lb/>nel mio sistema pi&ugrave; accuratamente trattasi. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il sistema planetario, immaginato dal Nardi, metteva, come quel di Ari&shy;<lb/>starco, nel Sole il centro dei moti, ma scansava gl'inconvenienti del Coper&shy;<lb/>nico, non considerati da Galileo, pi&ugrave; filosoficamente del quale sentiva il Di&shy;<lb/>scepolo come giovasse al progredir dell'Astronomia investigar le ragioni <lb/>del discendere e del risalire i pianeti dal Sole, senza introdurre gli epicicli <lb/>e gli equanti. </s>

<s>Vero &egrave; bene che parve anche a lui cosa dura ammettere le <lb/>orbite kepleriane schiettamente ellittiche, ma per non mostrarsi, in rifiutar <lb/>ci&ograve; che si proponeva come cosa di fatto, o dissennato o caparbio, pens&ograve; che <lb/>di ellittico non avessero esse orbite che l'apparenza o la similitudine, essendo <lb/>in realt&agrave; una trasformazione da certe figure elicali, che sarebbero secondo <lb/>lui le vere orbite descritte dai pianeti. </s>

<s>Troviamo questa opinione accennata <lb/>cos&igrave; per incidenza, trattandosi dall'Autore <emph type="italics"/>Delle spirali o elici di Archimede:<emph.end type="italics"/><lb/>&ldquo; E chi sa che ancora i Pianeti non descrivano, intorno al Sole loro centro, <lb/>porzioni di elice, mentre ora da quello meno tirati discendono, ora, in virt&ugrave; <lb/>dell'attrazione e del consenso con gli altri membri del mondo, risagliono con <lb/>reciproche vibrazioni? </s>

<s>Certo che tal mio parere &egrave; forse non meno verosi&shy;<lb/>mile che l'introdurre gli epicicli e gli equanti, o il dare il moto ai punti <lb/>immaginari del centro, o finalmente inventare i moti ellittici. </s>

<s>&rdquo; </s></p><p type="main">

<s>Ma perch&egrave;, in dimostrare la verosomiglianza di questo parere, si ridu&shy;<lb/>ceva, del Sistema astronomico del Nardi, la maggiore importanza e il me&shy;<lb/>rito principale; attese a farlo di proposito in una veduta delle sue <emph type="italics"/>Scene,<emph.end type="italics"/><lb/>introducendovi il principio delle forze centrali, immaginate spirar dal Sole a <lb/>guisa di un vento perpetuo, che meni in giro una nave. <lb/><figure id="id.020.01.2865.1.jpg" xlink:href="020/01/2865/1.jpg"/></s></p><p type="caption">

<s>Figura 309.</s></p><p type="main">

<s>&ldquo; Sia, egli dice, il cerchio ABC (fig. </s>

<s>309) di cui <lb/>centro F, diametro AB. </s>

<s>Intendasi il centro esser occu&shy;<lb/>pato dal Sole ed un pianeta A, per esempio Giove, <lb/>il suo centro abbia nella periferia. </s>

<s>Giove, per la pro&shy;<lb/>pria forma, moversi in s&egrave; stesso circolarmente pon&shy;<lb/>gasi, ed anco intorno al Sole. </s>

<s>D'avvantaggio pongasi <lb/>che il Sole e la sua forma, essendo quasi cuore ed <lb/>anima del mondo planetario, muovano in qualche <lb/>modo e formino i moti degli altri membri, e in con&shy;<lb/>seguenza pi&ugrave; veloci moveranno i pi&ugrave; vicini. </s>

<s>Il loro muovere non sar&agrave; im&shy;<lb/>pulso esterno, ma una informazione interna o vitale, mediante la virt&ugrave; pro&shy;<lb/>pria e solare, che muove equabilmente, ed in conseguenza perpetuamente. </s>

<s><lb/>Vento, che stabile. </s>

<s>gonfi ed animi una vela per un tranquillo orizonte, <lb/>cagioner&agrave;, nel movere egualmente in giro una nave, certa somiglianza dello <lb/>effetto solare nei circostanti corpi. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/2866.jpg" pagenum="491"/><p type="main">

<s>&ldquo; Ma perch&egrave; Giove aspira, nel suo condursi in giro per la periferia ABC, <lb/>all'accostamento verso il suo centro, quindi &egrave; che nel circolare sopraggiunge <lb/>il retto moto, il quale &egrave; congiunto dello accoppiarsi delle virt&ugrave; gioviale e <lb/>solare, e cos&igrave; ancora avviene nel grave cadente, il quale, dalla propria forma <lb/>e dal consenso delle sottoposte cose, &egrave; rapito al centro, e sempre con impeto <lb/>pi&ugrave; accelerato s'avanza. </s>

<s>Lo stesso forse fa Giove, se non che l'impeto suo <lb/>non si accelera evidentemente nell'accostarsi al Sole, perch&egrave; la lontananza <lb/>e grandezza sua fanno diversa ragione di accelerarsi, che non fa la piccolezza di <lb/>un sasso cadente, e la vicinanza alle altre parti congeneri che l'attraggono. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il moto dunque composto di circolare e diretto non par altro che una <lb/>spira, e questa tanto s'avvicina al centro, quanto mirando la causa finale <lb/>comporta la convenienza e il bisogno di Giove in riguardo del Sole, onde, <lb/>arrivato al termine, ritorna alla medesima altezza. </s>

<s>Ma perch&egrave; verso la stessa <lb/>parte concorrono i moti del Sole e di Giove in s&egrave; stessi, e di pi&ugrave; quello di <lb/>Giove &egrave; messo in giro diverso; avvien forse che la spira del punto A non <lb/>termini in un punto del diametro AB, ma trascorra alquanto pi&ugrave; in l&agrave;, come <lb/>in E, onde, restituendosi il periodo della risalita, anch'egli alquanto mag&shy;<lb/>giore di quello della scesa, trascorrer&agrave; anche A, punto dell'auge, secondo <lb/>l'ordine de'segni in D, e segherassi ne'punti A, D la prima spira dalla se&shy;<lb/>conda. </s>

<s>Vento che, uniforme spirando, spieghi la chioma di qualche albero <lb/>sino a certo segno, onde quella per s&egrave; stessa ritorni in altrettanta inclina&shy;<lb/>zione verso della contraria parte, e che di nuovo alternando si lasci dal vento <lb/>spiegare; somiglia al meglio che pu&ograve; tra le cose nostre l'ordine e la ragione <lb/>delle celesti spire. </s>

<s>Tal maniera poi di spira, poich&egrave; le spire sono d'infinite <lb/>sorti, riscontrasi, almeno prossimamente, con una ellisse, in uno dei cui fochi <lb/>sia il Sole. </s>

<s>E tanto secondo questi principi apportato sia, poich&egrave; anche in <lb/>questa via si trovano intoppi &rdquo; (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>291-94). </s></p><p type="main">

<s>Gl'intoppi erano per questa via inevitabili, come a colui che si trovava <lb/>costretto ad ammettere una conseguenza di fatto, senza conoscerne i prin&shy;<lb/>cipii. </s>

<s>Di qui &egrave; che lo studio del Nardi si ridusse a dimostrare in qualche <lb/>modo come le orbite ellittiche fossero una trasformazione dalle circolari. </s>

<s>Il <lb/>Boulliaud non seppe tenere altra via diversa da questa, immaginando quel <lb/>suo aereo cono scaleno, per dare ad intendere come dai circoli, descritti in&shy;<lb/>torno all'asse di lui dal pianeta, che dal vertice equabilmente discende verso <lb/>la base; venga a disegnarsi sulla superficie di esso cono un'ellisse, che in <lb/>uno de'suoi fochi abbia il Sole. </s></p><p type="main">

<s>Di non lieve importanza apparir&agrave; perci&ograve; il passo, che fece fare il Bo&shy;<lb/>relli alla Scienza, ammettendo che l'eccentricit&agrave; sia all'orbite congenita, e <lb/>non avventizia. </s>

<s>Di qui &egrave; che il problema si poteva proporre ne'suoi veri ter&shy;<lb/>mini, avviandolo a ricercare d'onde resultin le forze che, sollecitando i sa&shy;<lb/>telliti e i pianeti, gli fanno rivolgere non pi&ugrave; in circoli ma in ellissi. </s>

<s>Alla <lb/>ricerca per&ograve; non consegu&igrave; per il Nostro la desiderata invenzione, perch&egrave;, seb&shy;<lb/>bene egli avesse felicemente sottoposti i moti celesti all'azione delle forze <lb/>centrifughe e delle centripete, ignor&ograve; le loro vere leggi, credendo che queste <pb xlink:href="020/01/2867.jpg" pagenum="492"/>attraessero secondo la ragion semplice reciproca delle distanze, e quelle non <lb/>sapendo risolvere nelle loro direzioni tangenziali, d'onde il moto iniziale si <lb/>veniva a ridurre a una certa proiezione. </s>

<s>Cosi ebbe anch'egli a giocare di <lb/>fantasia come il Nardi, ripetendo con lui che il Sole volge in giro intorno a <lb/>s&egrave; il pianeta, spirandogli la forza, <emph type="italics"/>ad instar venti alicuius perpetui.<emph.end type="italics"/> (Flo&shy;<lb/>rentiae 1665, pag. </s>

<s>61). </s></p><p type="main">

<s>Ignorata la ragione del moto proiettizio ne'suoi principii, da'quali re&shy;<lb/>sultava che un mobile attratto a un centro, con forze reciprocamente pro&shy;<lb/>porzionali ai quadrati delle distanze, descrive intorno a esso centro una curva, <lb/>che dal circolo via via si trasformerebbe in ellisse, in parabola, in iperbola, <lb/>secondo che sempre maggiore si facesse la proiezione iniziale; il Borelli si <lb/>trov&ograve; anche un'altra volta a dover imitare le immaginazioni del Nardi. </s>

<s>E <lb/>come questi avea fatto ricorso all'azion del Sole, che interrottamente spi&shy;<lb/>rando i suoi effluvi fa ondeggiare il pianeta, come il vento la chioma di un <lb/>albero; cos&igrave; il Borelli rassomigli&ograve; esso pianeta galleggiante nell'etere a un <lb/>cilindro galleggiante nell'acqua, che, sommerso una volta pi&ugrave; gi&ugrave; di quel che <lb/>non importi alla sua gravit&agrave; in specie, ritorna in su reciprocando le sue vi&shy;<lb/>brazioni di andare e di venire con vicenda, che sarebbe perpetua, se non tro&shy;<lb/>vasse impedimento nel peso e nella viscosit&agrave; del liquido, come, secondo che <lb/>credevasi allora, non ne trovano nel sottilissimo etere i vaganti corpi celesti. </s>

<s><lb/>Di qui &egrave; a concludere che le <emph type="italics"/>Theoricae Mediceorum<emph.end type="italics"/> preparano quelle vie al <lb/>Newton, che esse stesse trovarono dal Nardi gi&agrave; preparate, e cos&igrave; la luce <lb/>venuta a illuminare le tenebre del mondo, apparita in Germania, non si di&shy;<lb/>resse verso l'Inghilterra fortunata, se non che dopo essersi, come da spec&shy;<lb/>chio, riflessa dall'Italia. </s></p><p type="main">

<s>Del Viviani sembrerebbe che poco rimanesse a dire, non essendosi in <lb/>questa lunga Storia della Meccanica toccato quasi argomento, in cui egli non <lb/>sia entrato, e non v'abbia preso gran parte. </s>

<s>Un intento unico per&ograve;, quasi <lb/>meta de'suoi desideri, abbiamo fin qui scorto nell'opera di lui, qual &egrave; di <lb/>esplicare, di correggere e di promovere i teoremi (non sempre dimostrati, <lb/>ma talvolta solamente proposti da Galileo) in commentari, da sottoscriversi <lb/>in note, e in appendici ai dialoghi delle Due Scienze nuove. </s>

<s>Prelude&shy;<lb/>vano a questi, chi ben considera, gli altri dialoghi del Mondo, in cui le <lb/>leggi pi&ugrave; generali del moto, richiamate destramente dai conversanti a pro&shy;<lb/>posito del moto della Terra, si dimostravano con discorsi accomodati all'in&shy;<lb/>telligenza delle menti volgari. </s>

<s>Ma se queste ne ritraevano utilit&agrave; con diletto, <lb/>ai Filosofi frettolosi di passar dai principii alla conclusione riuscivano quelle <lb/>lunghe digressioni di tedio, e divagatrici del pensiero: incomode poi torna&shy;<lb/>vano agli studiosi, i quali avrebbero voluto meglio apprendere cos&igrave; fatte dot&shy;<lb/>trine da un libro, scritto con la brevit&agrave; e con l'ordine di un trattato. </s></p><p type="main">

<s>A tale ufficio desideratissimo attese dunque il Viviani, e con tale inten&shy;<lb/>zione fu incominciata da lui quella scrittura, che nel Tomo VII, Parte V <lb/>de'Manoscritti di Galileo, si legge dal foglio 89 al 95, sotto il titolo <emph type="italics"/>Varie <lb/>propriet&agrave; del moto dei gravi naturale e violento.<emph.end type="italics"/> Raccoglie quivi e d&agrave; or-<pb xlink:href="020/01/2868.jpg" pagenum="493"/>dine l'Autore alle principali proposte, che ricorrono nella terza giornata delle <lb/>Due nuove Scienze, e riducendo il trattatello a un semplice memoriale, con <lb/>mettere solamente e dichiararne le tesi, apre ai lettori la via di ritrovarne <lb/>per s&egrave; medesimi le dimostrazioni. </s>

<s>Nel Tomo XXXIV de'Manoscritti del Ci&shy;<lb/>mento, dal foglio 54 al 113, si trovan raccolti i materiali, per trattare <emph type="italics"/>Delle <lb/>gravit&agrave; specifiche e assolute,<emph.end type="italics"/> e ivi pure, dal foglio 114 al 145, e dal foglio <lb/>204 al 208, si trova il principio posto a due altri libri, il primo de'quali <lb/>s'intitolava <emph type="italics"/>Del moto dei gravi,<emph.end type="italics"/> e il secondo <emph type="italics"/>De momentis gravium in ge&shy;<lb/>nere.<emph.end type="italics"/> Per chi poi volesse avere un saggio della lucida brevit&agrave;, con la quale <lb/>il Viviani esponeva le dottrine meccaniche del suo Maestro, sceglieremo da <lb/>varie Note le due seguenti, perch&egrave; si possano confrontare con que'lunghi <lb/>discorsi tenuti da Galileo ne'Dialoghi, e in varie altre scritture minori, per <lb/>confutar gli errori, che intorno alle cadute naturali dei gravi erano stati detti <lb/>gi&agrave; da Aristotile, e che tuttavia si ripetevano dai seguaci di lui: </s></p><p type="main">

<s>&ldquo; I. </s>

<s>Si domanda ai signori Peripatetici se, lasciando cadere a basso mille <lb/>particole di legno, come per esempio una giumella di segatura, ei credano <lb/>che tutte scendessero con pari velocit&agrave;. </s>

<s>Credo sian per rispondere di si. </s>

<s>Se <lb/>dunque queste particole si accosteranno insieme, e si attaccassero in modo, <lb/>che tra loro non restasse aria (che &egrave; il mezzo nel quale si pone che si muo&shy;<lb/>vano) domandisegli se credono che queste continuassero il moto con la me&shy;<lb/>desima velocit&agrave; di prima, poich&egrave; non potendo altri, anche per detto loro, <lb/>conferir pi&ugrave; di quello che esso ha, non mi pare che assegnar si possa quali <lb/>fossero quelle particole, che augumentassero la velocit&agrave; alle altre loro simi&shy;<lb/>lissime e ugualissime. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Diranno forse che, quando altro acquisto non ci fosse, vi sarebbe la <lb/>diminuzione della superficie, la maggior parte della quale si occulta nelle <lb/>attaccature. </s>

<s>E concedendo che la confricazione del mezzo con la superficie <lb/>del mobile ritarda la di lui velocit&agrave;, soggiungeranno che perci&ograve; quelle molte <lb/>particole, ridotte in un sol corpo di superficie grandemente minore, acqui&shy;<lb/>steranno velocit&agrave; nel moto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se tale sar&agrave; la risposta loro, diranno benissimo, perch&egrave; basta che <lb/>eglino concedano e sian capaci che, non per accrescimento di velocit&agrave;, ma <lb/>per diminuzione di superficie, cio&egrave;, per diminuzione dell'impedimento del <lb/>mezzo, si cresce la velocit&agrave;. </s>

<s>E se di ci&ograve; volessero anche pi&ugrave; chiara esperienza <lb/>considerino come una foglia d'oro battuto, che sotto cos&igrave; gran superficie <lb/>discende per aria lentissimamente, ridotta poi in un piccolo globetto scende <lb/>cento volte pi&ugrave; veloce, bench&egrave; il peso sia lo stesso. </s>

<s>Ma quanto importi l'im&shy;<lb/>pedimento del mezzo si ha manifesto da una palla, che venga cacciata dalla <lb/>artiglieria, alla quale l'impedimento di non molte braccia di acqua, che ella <lb/>incontri dopo il moto per l'aria, talmente ritarda la sua velocit&agrave;, che la sua <lb/>percossa ne resta fiacchissima. </s>

<s>Eppure l'acqua, come priva in tutto di tena&shy;<lb/>cit&agrave;, non resiste con altro che col doversi movere lateralmente, come a lungo <lb/>dimostr&ograve; il Galileo nel suo trattato delle Galleggianti &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. CXXXV, fol. </s>

<s>15). </s></p><pb xlink:href="020/01/2869.jpg" pagenum="494"/><p type="main">

<s>&ldquo; II. </s>

<s>Dicunt aliqui gravia, quae deorsum feruntur, magis semper intendi <lb/>in motu, quia pauciores partes aeris sibi scindendae restant, quod quidem <lb/>falsu m videtur. </s>

<s>Nam, si tunc grave velocius fertur, quando pauciores partes <lb/>aeris sunt scindendae; ergo, si aliquod grave ab altissimo loco demittatur, <lb/>ut ab aliqua turri, cuius altitudo sit 100, idem autem demittatur ab alio <lb/>loco, cuius altitudo sit 10; celerius movebitur in fine huius altitudinis, quae <lb/>est 10, quam in medio altioris altitudinis, puta ut 50, quod absurdum vi&shy;<lb/>detur &rdquo; (ibid., fol. </s>

<s>25). </s></p><p type="main">

<s>Da queste e da simili altre Note, dai titoli de'trattati dianzi trascritti, <lb/>dai teoremi dimostrati intorno ai pendoli, ai momenti de'gravi lungo i piani <lb/>inclinati, alle resistenze de'solidi, per tacere di tante altre cose; si conferma <lb/>esser quale si disse la principale intenzione di questi studi intorno alla <lb/>Scienza meccanica fatti dal Viviani. </s>

<s>Ma venivano spesso spesso a stimolarlo <lb/>gli esempi degli altri Colleghi suoi, ritrovatori di verit&agrave; nuove, in campi non <lb/>punto meno fertili di quegli stessi coltivati da Galileo, com'era per esempio <lb/>la Centrobarica, che apparita maravigliosa in s&egrave; stessa prometteva di aprir <lb/>la via a cento altre non meno mirabili invenzioni. </s>

<s>Ci&ograve; fu che mosse il Vi&shy;<lb/>viani a comporre quel trattatello <emph type="italics"/>Dei centri di gravit&agrave;,<emph.end type="italics"/> e a distendere quelle <lb/>proposizioni spicciolate, che s'hanno raccolte ne'tomi LXXI, XCII della ci&shy;<lb/>tata collezion manoscritta dei Discepoli di Galileo. </s>

<s>E per chi credesse non <lb/>esser nulla rimasto a chi, dopo il Torricelli e il Nardi, il Cavalieri e il Ricci, <lb/>s'assideva al medesimo convivio; sceglieremo dal detto manoscritto le sei pro&shy;<lb/><figure id="id.020.01.2869.1.jpg" xlink:href="020/01/2869/1.jpg"/></s></p><p type="caption">

<s>Figura 310.<lb/>posizioni seguenti, dalle quali apparir&agrave; <lb/>come ben sapesse l'Autore una eser&shy;<lb/>citazione gi&agrave; fatta trattare con metodi <lb/>nuovi, o promoverla oltre a quel che <lb/>non aveva ancora pensato nessuno dei <lb/>predecessori: e le relazioni date da <lb/>loro in funzioni algebriche, per alcune <lb/>figure circoscritte da qualche arco di <lb/>cerchio, riducesse a numeri, quanto <lb/>pi&ugrave; prossimamente era possibile, de&shy;<lb/>terminati. </s></p><p type="main">

<s>&ldquo; PROPOSITIO I. &mdash; <emph type="italics"/>Centrum gra&shy;<lb/>vitatis curvae superficiei coni recti <lb/>ABC<emph.end type="italics"/> (fig. </s>

<s>310), <emph type="italics"/>cuius axis BD, hanc <lb/>dividit in E, ita ut BE sit dupla ED, adeo ut idem sit centrum gravitatis <lb/>curvae, et centrum gravitatis trianguli per axem coni. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Producta axe BD, sumatur ipsi aequalis DG, ac DF aequalis DE, et <lb/>quaevis DM aequalis DI: sumptaque DH aequali circumferentiae circuli AC, <lb/>basis coni, iungatur GH, et in triangulis ABC, GDH sint per I, E, et per <lb/>F, M ductae OP, QR, FL, MN parallelae ipsi AC:BG vero concipiatur tam&shy;<lb/>quam libra horizontalis appensa ex D. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam, cum sit DE tertia pars DB, et DF erit pars tertia DG, ac ideo <pb xlink:href="020/01/2870.jpg" pagenum="495"/>centrum gravitatis trianguli rectanguli GDH sui momentum exercet per li&shy;<lb/>neam FL. </s>

<s>Et cum sit DH ad FL ut DG ad GF, vel, ob aequalitatem, ut DB <lb/>ad BE; vel, ob homologorum laterum in similibus triangulis ADB, QEB pro&shy;<lb/>portione laterum, ut DA, radius basis coni, ad EQ, radium circuli in cono <lb/>per E ducti, vel ut periferia AC in conica superficie ad superficiem QR in <lb/>cadem conica utcumque sit secta, DH aequalis periferiae ADC, ex constru&shy;<lb/>ctione; erit quoque recta FL aequalis periferiae QR. </s>

<s>Sed illa gravitat in F, <lb/>haec vero in E, suntque distantiae DF, DE inter se aequales, prout sunt ma&shy;<lb/>gnitudines; ergo in D inter se aequiponderant. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Eadem penitus ratione ostendetur recta MN aequalis esse, et aequi&shy;<lb/>ponderare in D cum periferia OP, ex aequalibus distantiis DI, DM, et hoc <lb/>semper. </s>

<s>Ergo omnes simul rectae in triangulo GDH, sive ipsum triangulum, <lb/>aequale est ac aequale momentum habet circa D cum omnibus simul peri&shy;<lb/>feriis, hoc est cum conica superficie curva ABC. </s>

<s>Quare ipsarum superficie&shy;<lb/>rum centra gravitatis aeque distant a D. </s>

<s>Sed centrum trianguli gravitat in F, <lb/>ergo centrum curvae conicae est in E, prout ostendere propositum fuit. </s>

<s>&rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. LXVI, fol. </s>

<s>99). </s></p><p type="main">

<s>Il Torricelli in tre modi dimostr&ograve; questa medesima proposizione, e il Viviani <lb/>volle far vedere che non perci&ograve; la fecondit&agrave; era esaurita. </s>

<s>Ma cos&igrave; esso Torricelli, <lb/>come tutti gli altri, si limitarono alla ricerca del centro di gravit&agrave; della sola <lb/>superficie conica convessa, e il Nostro pens&ograve; che si poteva anche oltre pro&shy;<lb/>moverla, comprendendovi il circolo base. </s>

<s>Cos&igrave;, del centro della universale su&shy;<lb/>perficie del solido, riusc&igrave; a dare elegantemente questa nuova indicazione. </s></p><p type="main">

<s>&ldquo; PROPOSITIO II. &mdash; <emph type="italics"/>Centrum gravitatis universae superficiei coni recti <lb/>sic dividit axem, ut pars ad verticem coni sit ad reliquam ad basim ut <lb/>tres radii basis, cum duplo lateris coni, ad latus idem coni. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto ABC (fig. </s>

<s>311) triangulum per axem BD, quo secto in E, ut DE <lb/>sit pars tertia totius BD, constat in E esse centrum gravitatis curvae coni&shy;<lb/><figure id="id.020.01.2870.1.jpg" xlink:href="020/01/2870/1.jpg"/></s></p><p type="caption">

<s>Figura 311.<lb/>cae ABC, et in D centrum gravitatis circuli suae basis. </s>

<s><lb/>Sed curva conica ad basim est ut latus BA ad AD, ergo, <lb/>si DE secetur in F, ita ut DF ad FE sit ut BA ad AD, <lb/>erit F centrum gravitatis utriusque superficiei. </s>

<s>Sed BF <lb/>constat ex duabus DF, et ex tribus FE; FD vero ex <lb/>unica FD: duo autem DF exhibent duo latera AB, et <lb/>tres FE exhibent tres AD, ac unica DF unicam AB, <lb/>quod sit DF ad FE ut BA ad AD. </s>

<s>Quare BF ad FD <lb/>est ut duo DF, cum tribus FE, ad ipsum FD, vel ut duo <lb/>latera AB, cum tribus radiis AD, ad idem latus AB, quod etc. </s>

<s>&rdquo; (ibid., fol. </s>

<s>102). </s></p><p type="main">

<s>Abbiamo infatti BF=BE+EF=2DE+EF=2(DF+EF)+EF= <lb/>2DF+3EF, e di qui la proporzione BF:DF=2DF+3EF:DF. </s>

<s>Ma <lb/>essendo per la legge delle equiponderanze DF:EE=AB:AD, sar&agrave; anche <lb/>insieme 2DF:3FE=2AB:3AD. Componendo, 2DF+3FE:2DF= <lb/>2AB+3AD:2AB. </s>

<s>Dividendo i conseguenti per due, se ne conclude imme&shy;<lb/>diatamente la relazione BF:DF=2AB+2AD:AB. </s></p><pb xlink:href="020/01/2871.jpg" pagenum="496"/><p type="main">

<s>Anche il centro di gravit&agrave; della callotta sferica era stato ritrovato dal <lb/>Torricelli per la sola parte curva della figura, escluso il circolo base, ma il <lb/>Viviani pass&ograve; oltre a indicarne cos&igrave; il punto sull'asse, dove gravita la su&shy;<lb/>perficie universale. </s></p><p type="main">

<s>&ldquo; PROPOSITIO III. &mdash; <emph type="italics"/>Centrum gravitatis universae superficiei portionis <lb/>sphaericae sic dividit axem, ut pars ad polum terminata sit ad reliquam, <lb/>ut axis portionis reliquae, cum semiaxe sphaerae, ad ipsum semiaxem:<emph.end type="italics"/><lb/><figure id="id.020.01.2871.1.jpg" xlink:href="020/01/2871/1.jpg"/></s></p><p type="caption">

<s>Figura 312.<lb/><emph type="italics"/>vel, ut duplum basis portionis sphaericae, una cum <lb/>eius curva superficie, ad ipsam curvam. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Esto ABC (fig. </s>

<s>312) sphaerae portio, cuius <lb/>axis BD, diameter basis AC, et axis totius sphaerae <lb/>BE. </s>

<s>Jam constat quod, secto BD bifariam in F, id <lb/>est centrum gravitatis curvae superficiei ABC. </s>

<s>Sed D <lb/>est centrum circuli AC, ergo utriusque simul super&shy;<lb/>ficiei centrum gravitatis est inter F et D, ut in G. </s>

<s><lb/>Dico BG ad GD esse ut axis DE, cum dimidio axis <lb/>EB, ad ipsum dimidium. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Jungantur AB, AE. </s>

<s>Erit ergo, ob aequilibrium in G curvae ABC cum <lb/>circulo AC, FG ad GD ut circulus AC ad curvam ABC, vel ut quadratum <lb/>radii DA ad quadratum radii BA, cuius circulus aequatur ipsi curvae super&shy;<lb/>ficiei ABC, vel, ob triangulorum DAB, DEA similitudinem, ut quadratum DE <lb/>ad quadratum EA, vel ut linea DE ad tertiam proportionalem EB in semi&shy;<lb/>circulo BAE. </s>

<s>Et componendo, FD ad DG ut DE cum EB ad EB. </s>

<s>Et divi&shy;<lb/>dendo, BG ad GD ut duplum DE cum EB ad EB, vel, sumptis horum di&shy;<lb/>midiis, ut una DE cum dimidio EB, seu cum semiaxe sphaerae, ad dimidium <lb/>EB, vel ad ipsum semiaxem, quod erat primo etc. </s>

<s>&rdquo; (ibid., fol. </s>

<s>108). </s></p><p type="main">

<s>Per passare al secondo modo, o alla seconda forma, sotto la quale la <lb/>medesima verit&agrave; propone l'Autore a dimostrarsi, si osservi che fu gi&agrave; con&shy;<lb/>cluso FG:GD=DE:EB. </s>

<s>Ma AE2=EB.ED, EB2=EB2 d'onde ED:EB= <lb/>AE2:EB2=DA2:AB2=<foreign lang="greek">p</foreign>DA2:<foreign lang="greek">p</foreign>AB2, e perci&ograve; FG:GD=<foreign lang="greek">p</foreign>DA2:<foreign lang="greek">p</foreign>AB2. </s>

<s><lb/>Componendo, FD:DG=<foreign lang="greek">p</foreign>DA2+<foreign lang="greek">p</foreign>AB2:<foreign lang="greek">p</foreign>AB2. </s>

<s>Duplicando gli antecedenti, <lb/>BD:DG=2<foreign lang="greek">p</foreign>DA2+2<foreign lang="greek">p</foreign>AB2:<foreign lang="greek">p</foreign>AB2. </s>

<s>E in ultimo dividendo, BG:GD= <lb/>2<foreign lang="greek">p</foreign>DA2+<foreign lang="greek">p</foreign>AB2:<foreign lang="greek">p</foreign>AB2. </s>

<s>Ora essendo la superficie di una callotta sferica <lb/>uguale al prodotto della sua altezza per la circonferenza di un circolo grande, <lb/>ossia essendo uguale a <foreign lang="greek">p</foreign>BD.BE=<foreign lang="greek">p</foreign>AB2, e dall'altra parte rappresentan&shy;<lb/>dosi da <foreign lang="greek">p</foreign> DA2 il circolo descritto col raggio AD, sopra il quale la cupola <lb/>risiede; &egrave; manifesto che il punto G sega cos&igrave; l'asse, che la parte verso il polo <lb/>abbia alla rimanente la proporzion medesima, che la doppia base con la callotta <lb/>ha alla callotta sola, secondo che cos&igrave; il Viviani soggiunge nel suo foglio: </s></p><p type="main">

<s>&ldquo; Sed DE ad EB est ut quadratum AE ad quadratum EB, vel ut qua&shy;<lb/>dratum DA ad quadratum AB, vel ut circulus ex radio DA seu basis por&shy;<lb/>tionis ABC, ad circulum ex radio AB, vel ad curvam superficiem portionis; <lb/>ergo BG ad GD est quoque ut duae bases portionis sphaericae ABC, cum <lb/>curva eius superficie, ad ipsam curvam &rdquo; (ibid.). </s></p><pb xlink:href="020/01/2872.jpg" pagenum="497"/><p type="main">

<s>Che se BE=2BD, ossia se la callotta sia emisferica, torner&agrave; la su&shy;<lb/>perficie di lei, ch'era 2<foreign lang="greek">p</foreign>BD2, ossia <foreign lang="greek">p</foreign>AB2, espressa da 2<foreign lang="greek">p</foreign>DA2, e perci&ograve; <lb/>BG:GD=2<foreign lang="greek">p</foreign>DA2+2<foreign lang="greek">p</foreign>DA2:2<foreign lang="greek">p</foreign>DA2=2:1, come il Viviani stesso <lb/>soggiunge in questo suo <emph type="italics"/>Corollario:<emph.end type="italics"/> &ldquo; Hinc centrum gravitatis universae <lb/>superficiei haemisphaericae sic axem dividit, ut pars ad polum terminata sit <lb/>ad reliquam, ut duo ad unum: tunc enim duae bases aequantur uni curvae, <lb/>et duae bases cum curva duplae sunt unica curva, adeoque et pars ad polum <lb/>terminata reliquae ad centrum basis dupla erit &rdquo; (ibid.). </s></p><p type="main">

<s>&ldquo; PROPOSITIO IV. &mdash; <emph type="italics"/>Centrum gravitatis E<emph.end type="italics"/> (fig. </s>

<s>313), <emph type="italics"/>quadrantis cir&shy;<lb/>culi ABCD, cuius centrum D, axis DB, ita hunc secat, ut totus BA, ad<emph.end type="italics"/><lb/><figure id="id.020.01.2872.1.jpg" xlink:href="020/01/2872/1.jpg"/></s></p><p type="caption">

<s>Figura 313.<lb/><emph type="italics"/>partem DE attingentem centrum D arcus ABC, sit <lb/>quam proxime ut 5 ad 3. Circumscripto vero qua&shy;<lb/>dranti huic quadrato ADCF, centrum gravitatis G <lb/>trilinei ABCF sic dividit axem DF, ut radius DB <lb/>ad DG sit quam proxime ut 10 ad 11. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Quoad primum, diameter FD secetur bifariam <lb/>in I, atque ex G, I, E super DA ducantur perpen&shy;<lb/>diculares GL, IK, EH, et concipiatur figura converti <lb/>circa AD. &rdquo; </s></p><p type="main">

<s>&ldquo; Jam constat cylindrum a quadrato AC, ad hemisphaerium a quadrante <lb/>ABCD, esse ut 3 ad 2, sive ut 42 ad 28. Sed ipse cylindrus ad ipsum hemi&shy;<lb/>sphaerium, ex Centrobaryca, rationem habet compositam ex ratione quadrati <lb/>ad quadrantem, sive ex ratione proxime 14 ad 11, sive ex ratione 42 ad 33, <lb/>et ex ratione distantiae IK ad distantiam EH centrorum gravitatis quadrati <lb/>et quadrantis ab axe revolutionis AD, atque etiam 42 ad 28 rationem habet <lb/>compositam ex 42 ad 33, et ex ratione 33 ad 28, et ratio quadrati ad qua&shy;<lb/>drantem est ut 42 ad 33; ergo ratio distantiae IK, ad rationem EH, est ut <lb/>33 ad 28, velut ut 9 ad 7+7/11. Qualium ergo partium IK est 9, talium <lb/>EH est 7+7/11, et talium DC, quae dupla est ipsius IK, quae est 9, erit 18. &rdquo; </s></p><p type="main">

<s>&ldquo; Sed DB vel DC latus quadrati AC, ad diametrum DF, vel ad AC <lb/>chordam arcus ABC, est ut 5 ad 7+1/14, vel ut 18 ad 25+16/35; ergo tam <lb/>DF quam AC, cum sit DB partium 18, erit earumdem 25+16/35, et DI, <lb/>dimidium ipsius DF, erit 12+51/70. Sed IK 9, ad EH 7+7/11, est ut DI <lb/>12+51/70 ad DE, quae invenitur partium earumdem 10+4/5, et DB in&shy;<lb/>venta est earumdem partium 18; ergo radius BD, ad distantiam DE a cen&shy;<lb/>tro quadrantis ad eius centrum gravitatis, est ut 18 ad 10+4/5, vel at 90 <lb/>ad 54, vel ut 10 ad 6, vel ut 5 ad 3, quod erat primo demonstrandum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Cum sit arcus ABC quadrantis, ad 2/3 chordae AC, ut <lb/>BD ad DE, quod E sit centrum gravitatis quadrantis, vel ut 5 ad 3, ex modo <lb/>assertis, vel ut 10 ad 6; erit idem arcus ad totam chordam ut 10 ad 9. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollarium.<emph.end type="italics"/> &mdash; Hinc, sumptis quadruplis, perimeter circuli, ad pe&shy;<lb/>rimetrum quadrati inscripti, est proxime ut 90 ad 36, vel ut 10 ad 9 &rdquo; (ibid., <lb/>T. XCII, fol. </s>

<s>21). </s></p><p type="main">

<s>&ldquo; Quod vero ad secundum, hoc in theoremate propositum, cylindrus a <pb xlink:href="020/01/2873.jpg" pagenum="498"/>quadrato AC revoluto circa AD, ad rotundum a trilineo ABCF circa AD, est, <lb/>ex eadem Centrobaryca, in ratione composita quadrati AC ad trilineum ABCF, <lb/>hoc est in ratione 14 ad 3 proxime, vel 42 ad 9, et ex ratione distantiae IK <lb/>ad distantiam GL eorum centrorum gravitatis I, G ab axe AD. </s>

<s>Sed cylin&shy;<lb/>drus ad rotundum est ut 3 ad 1, vel ut 42 ad 14; ergo 42 ad 14 rationem <lb/>habet compositam ex ratione 42 ad 9, et ex ratione earumdem distantiarum <lb/>IK, GL. </s>

<s>Sed 42 ad 14 habet queque rationem compositam ex 42 ad 9, et <lb/>ex 9 ad 14, et ex his prima ratio est ea, quae inter quadratum et trilineum; <lb/>ergo secunda ratio inter 9 et 14 erit ratio distantiarum IK, GL. </s>

<s>Sed IK in&shy;<lb/>venta est partium 9, qualium DB erit 18; ergo GL est earumdem 14. Sed <lb/>IK ad GL est ut DI ad DG, ergo etiam DI ad DG est ut 9 ad 14. Sed DI <lb/>inventa est earumdem partium 12+51/70, si fiat ergo ut 9 ad 14, ita 12+51/70 <lb/>ad aliam, quae est 19+4/5 totidem partium, erit ipsa DG, ad quam radius <lb/>DB erit ut 18 ad 19+4/5, vel ut 90 ad 99, vel ut 10 ad 11, quod erat se&shy;<lb/>cundo ostendendum &rdquo; (ibid., fol. </s>

<s>18). </s></p><p type="main">

<s>&ldquo; PROPOSITIO V. &mdash; <emph type="italics"/>Centrum gravitatis G, in eadem figura, trilinei <lb/>ABCF sic dividit rectam FD iungentem eius verticem F, et centrum D <lb/>sui arcus ABC, ut tota FD ad DG sit quam proxime ut 9 ad 7. &mdash; In&shy;<lb/>super ipsum centrum gravitatis G trilinei AGCF sic dividit eius axem <lb/>FD, ut pars FG ad F, ad partem GB ad B, sit quam proxime ut 22 <lb/>ad 7, vel ut circuli periferia ad diametrum. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Et primo, cum sit IK 9 et GL 14, sitque DI 12+51/70, cumque ut <lb/>IK ad GL ita sit DI ad DG; erit DG 19+28/35. Sed tota DF est 25+16/35, <lb/>ergo DF ad DG erit ut 25+16/35 ad 19+28/35, vel ut 891 ad 693, vel ut <lb/>99 ad 77, vel ut 9 ad 7. Et convertendo, DG, ad DF ut 7 ad 9, quocirca <lb/>centrum gravitatis trilinei ABCF distat a centro D sui ipsius per distantiam <lb/>DG, ad quam tota diameter FD quadrati circumscripti proprio quadranti sit <lb/>quam proxime ut 9 ad 7. &rdquo; </s></p><p type="main">

<s>&ldquo; Secundo, cumque DB ad DG sit quam proxime ut 10 ad 11, et DG <lb/>ad DF, ex nuper ostensis, quam proxime ut 7 ad 9, vel ut 11 ad 14+1/7; <lb/>tres DB, DG, DF erunt ut 10, 11, 14+1/7, vel ut 70, 77, 99. Quare ipsa&shy;<lb/>rum differentiae BG, GF erunt ut hi numeri 7, 22, adeoque centrum gra&shy;<lb/>vitatis G trilinei ABCF secat sic eius axem FB, ut pars ad F, ad partem <lb/>ad B, sit quam proxime ut 22 ad 7, vel ut circuli periferia ad suam dia&shy;<lb/>metrum. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Propterea cum qualium partium DB ponitur 10, ta&shy;<lb/>lium DE sit quam proxime 6, et DI 7+1/14, et DB 10, et DG 11, et DF <lb/>14+2/14; ipsae DE, DI, DB, DG, DF erunt ut hi numeri 84, 99, 140, <lb/>154, 198. Et, cum DE, DB, DG sint ut 84, 140, 154, in minimis terminis <lb/>essent ut 6, 10, 11 &rdquo; (ibid., fol. </s>

<s>19). </s></p><p type="main">

<s>Termineremo questo breve ordine di proposizioni baricentriche con una <lb/>relativa alla Cicloide, e che senza dubbio &egrave; posteriore al trattato wallisiano <lb/><emph type="italics"/>De centro gravitatis,<emph.end type="italics"/> supponendovisi la rettificazion della curva, pubblicata <lb/>quivi dal Matematico inglese nella seconda parte della proposizione XXII, <pb xlink:href="020/01/2874.jpg" pagenum="499"/>bench&egrave; il Roberval, come si vide, l'avesse dimostrata assai prima. </s>

<s>Vi si sup&shy;<lb/>pone altres&igrave; noto il centro di gravit&agrave; della linea semicicloidale: ma n&egrave; lo <lb/>stesso Pascal sdegnerebbe di vedere aggiunto alla sua ricca e pellegrina co&shy;<lb/>rona di teoremi questo fiore elegante, colto nella medesima aiola dal nostro <lb/>Viviani. </s></p><p type="main">

<s>&ldquo; PROPOSITIO VI. &mdash; <emph type="italics"/>Esto ABC<emph.end type="italics"/> (fig. </s>

<s>314) <emph type="italics"/>Cyclois primaria, cuius dia&shy;<lb/>meter BD, sitque rectangulum BDAE, et curvae AIB sit centrum G, a <lb/>quo demittatur GF perpendicularis super BD, sumaturque HF aequalis<emph.end type="italics"/><lb/><figure id="id.020.01.2874.1.jpg" xlink:href="020/01/2874/1.jpg"/></s></p><p type="caption">

<s>Figura 314.<lb/><emph type="italics"/>dimidio AD, et fiat revo&shy;<lb/>lutio circa BD: cylindrica <lb/>superficies ab AE, ad ro&shy;<lb/>tundam semicycloidis AIB, <lb/>est ut FH ad FG distan&shy;<lb/>tia centri gravitatis arcus <lb/>AIB ab axe BD. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Nam, sumpta rotunda <lb/>a recta AE, ad rotundam AIB, esse in ratione composita rectae AE ad cur&shy;<lb/>vam AIB, sive 1 ad 2, sive FH ad AD, et ex distantia AD centri gravitatis <lb/>AE a BD, ad FG distantiam centri gravitatis curvae AIB: hae rationes con&shy;<lb/>ficiunt rationem rectae FH ad FG, quod erat demonstrandum &rdquo; (ibid., fol. </s>

<s>32). </s></p><p type="main">

<s>N&egrave; a queste sole eleganze s'arrestano le ricerche intorno ai centri di <lb/>gravit&agrave;, fatte dal Viviani, le quali si estesero all'emiperboloide, alla lunula, <lb/>e ad altre figure, rimaste inscritte ne'cerchi; come furono altres&igrave; frutto degli <lb/>infaticabili studii di lui que'teoremi, che si dimostrano intorno a questo <lb/>stesso argomento in varii fogli, rilegati insieme nel volume manoscritto, che <lb/>&egrave; il CIX dei Discepoli di Galileo. </s>

<s>Anzi in tutti gli altri nove, che vanno sotto <lb/>il titolo di <emph type="italics"/>Meccanica dei solidi,<emph.end type="italics"/> sarebbero da raccogliere documenti di non <lb/>poca importanza. </s>

<s>Nel CVI, per esempio, varii assiomi, con proposizioni e co&shy;<lb/>rollari, intorno alle forze de'pesi sostenuti da corde; nel CVIII, un tratta&shy;<lb/>tello intorno all'arte dei pesi nella stadera; e per tutti i volumi sparsi teo&shy;<lb/>remi, dimostrativi delle proporzioni, secondo le quali si velocitano i gravi <lb/>discendenti per i piani inclinati, ordinati per verit&agrave; a illustrare, piuttosto che <lb/>a promovere la scienza di Galileo o del Torricelli. </s>

<s>E tra per questa ragione, <lb/>e per essere condotte le dimostrazioni per le solite vie oblique, senza far uso <lb/>cio&egrave; del principio della composizion delle forze, abbiamo creduto dover ba&shy;<lb/>stare questo cenno, affinch&egrave; possano dalla Storia i nostri Lettori far pi&ugrave; giu&shy;<lb/>sto giudizio dell'opera, data, in coltivar la Meccanica, dal Viviani. </s></p><pb xlink:href="020/01/2875.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dei Matematici stranieri <lb/>principali promotori della Scienza del moto<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Degli otto libri della Statica del Roberval, e come il Wallis e il Mariotte confermarono la Dina&shy;<lb/>mica galileiana, che l'Huyghens coron&ograve; di nuovi teoremi. </s>

<s>&mdash; IL Delle propriet&agrave; meccaniche della <lb/>Cicloide. </s>

<s>&mdash; III. </s>

<s>De centri delle percosse e delle oscillazioni. </s>

<s>&mdash; IV. </s>

<s>Delle forze centrifughe. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>S'&egrave; narrato fin qui quale e quanta si fosse la cultura della Scienza del <lb/>moto in Italia, dove Galileo, con l'insegnamento orale e co'libri, s'era fatto <lb/>maestro. </s>

<s>Ne giunse la fama anche appresso gli stranieri, ne'quali parve na&shy;<lb/>scere allora un gran fervore di applicarsi a quei medesimi studii, particolar&shy;<lb/>mente in Francia, dove fiorivano pi&ugrave; che altrove gl'ingegni. </s>

<s>Le dottrine ga&shy;<lb/>lileiane, raccomandate l&agrave; dal Peiresc, dal Carcavy, e dal Beaugrand, in tutti e <lb/>tre i quali, dalla probit&agrave; della vita, e dalla dignit&agrave; del grado si rendeva pi&ugrave; <lb/>autorevole la Scienza; furono accolte in modi e con effetti s&igrave; varii, che vo&shy;<lb/>gliono essere principalmente notati. </s></p><p type="main">

<s>Per alcuni, e furono de'primi, rassomigliasi l'accoglienza a quella di un <lb/>ospite illustre, a cui non s'attende che a fare onore, e si vuol che tutti gli <lb/>altri di casa facciano il somigliante, aspramente garrendo coloro, che osas&shy;<lb/>sero di contradire. </s>

<s>Tale immagine sembra a noi rendersi dal Gassendo, la <lb/>Meccanica del quale &egrave; unicamente istituita a confermare le dottrine galile&shy;<lb/>iane, sia co'ragionamenti, sia con l'esperienze. </s>

<s>Abbiamo avuto pi&ugrave; volte oc&shy;<lb/>casione di citar di lui l'epistole contro Pietro Cazr <emph type="italics"/>De proportione, qua<emph.end type="italics"/><pb xlink:href="020/01/2876.jpg" pagenum="501"/><emph type="italics"/>gravia decidentia accelerantur,<emph.end type="italics"/> scritte per confermar che quella proporzione, <lb/>con cui crescono gli spazi, &egrave; veramente secondo i quadrati, come Galileo di&shy;<lb/>ceva, e non secondo i semplici tempi, come presumevasi dal Gesuita. </s></p><p type="main">

<s>Il contradittore, che voleva il Gassendo cos&igrave; confutare, insorse da poi <lb/>che la legge, annunziata ne'primi dialoghi del Mondo, venne a esplicarsi e <lb/>a dimostrarsi matematicamente ne'secondi dialoghi del Moto, ma intanto che <lb/>aspettavasi la pubblicazione di questo libro s'apprendevano dall'altro, che <lb/>l'aveva preceduto, le principali nozioni di Dinamica nuova. </s>

<s>Le verit&agrave; per&ograve; <lb/>si proponevan quivi semplicemente senza dimostrazione: erano conclusioni <lb/>delle quali i principii, per lo pi&ugrave;, rimanevano occulti, e invogliavano gli stu&shy;<lb/>diosi a mettersi per s&egrave; stessi a ritrovarli. </s>

<s>Quanto giovasse una tale palestra, <lb/>in esercitare gl'ingegni, si pu&ograve; facilmente immaginare, anche senza i fatti <lb/>narrati: poi, venendosi a leggere in pubblico le Due Scienze nuove, parve <lb/>facesse Galileo quel che fa il Maestro, quando mette a cimento col proporre <lb/>una tesi agli scolari, i quali, riscontrando le proprie con le dimostrazioni di <lb/>lui, son lieti o d'aver colto nel vero, o di vedersi aperti gli occhi a ricono&shy;<lb/>scere il falso. </s></p><p type="main">

<s>Una particolar dottrina per&ograve; avvert&igrave; il Gassendo che rimaneva nei nuovi <lb/>Dialoghi dimenticata cos&igrave;, da desiderarsi di udire ancora il Salviati dispu&shy;<lb/>tare intorno al farsi tutti i nostri moti, sul veicolo in cui sediamo, sempre <lb/>allo stesso modo, o egli corra velocissimamente, o stia fermo. </s>

<s>Cos&igrave; fatta di&shy;<lb/>menticanza, comunque sia, non fu volontaria, ma suggerita dal giudizio, non <lb/>potendosi quel che si dice nella seconda Giornata dei Due massimi sistemi <lb/>intorno ai proietti conferire con i teoremi, nel quarto dialogo delle nuove <lb/>Scienze poi dimostrati. </s>

<s>Nella detta Giornata infatti si discorre a lungo del <lb/>moto impresso dal motore, concludendovisi che la palla, tirata con direzione <lb/>perpendicolare, torna in gi&ugrave; alla bocca del cannone, o stia egli fermo o sia <lb/>con qualunque velocit&agrave; tirato sopra una carretta. </s>

<s>Il fatto era in s&egrave; notissimo <lb/>anche ai fanciulli, i quali, correndo per via, si gettan sulla testa un pomo, <lb/>che ritorna a loro in gi&ugrave; nella mano: ma la scienza del fatto dipendeva dalla <lb/>composizion di due moti, dai quali non seppe Galileo altro dedurre se non <lb/>che il pomo non rimane indietro, correndo il fanciullo, perch&egrave;, sebbene sem&shy;<lb/>bri che esso pomo vada e venga nel perpendicolo, ei propriamente descrive <lb/>in aria una linea <emph type="italics"/>trasversale.<emph.end type="italics"/> Forse il Gassendo non penetr&ograve; pi&ugrave; addentro, <lb/>e quella linea trasversale benignamente interpetr&ograve; per una parabola. </s>

<s>Ma che <lb/>parabola fosse restava a dimostrarsi, ed &egrave; ci&ograve; ch'egli intese di fare in quelle <lb/>sue epistole <emph type="italics"/>De motu impresso a motore translato.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ipse recensui obiter (scriveva l'Autore nell'Epistola prima, dopo po&shy;<lb/>che parole d'introduzione) tum observata propria, tum quae Galileus con&shy;<lb/>gessit adstruendo illi theoremati: <emph type="italics"/>Si id corpus, cui insistimus, transferatur; <lb/>omnes nostros motus, rerumque a nobis mobilium, perinde fieri appare&shy;<lb/>reque, ac si illud quiesceret.....<emph.end type="italics"/> Experimentum vero facillimum est ut dum <lb/>deambulabis pilam lusoriam, aliumve globum manu tenens, remque explo&shy;<lb/>res &rdquo; (Opusc. </s>

<s>philos., Florentiae 1727, pag. </s>

<s>436). Pi&ugrave; mirabile e pi&ugrave; diffi-<pb xlink:href="020/01/2877.jpg" pagenum="502"/>cile a intendere ti sembrer&agrave;, soggiunge a Pietro Puteano, ci&ograve; che avviene, <lb/>quando tu, correndo velocemente sopra un cavallo, apri la mano, in cui te&shy;<lb/>nevi una palla, la quale tu vedi cadere a perpendicolo sotto la sella, bench&egrave; <lb/>avesse cominciato a moversi in gi&ugrave; tanto di pi&ugrave; lontano. </s>

<s>Ella dunque t'ha <lb/>seguito in tutto il cammino, inflettendosi per una linea che, se avesse la&shy;<lb/>sciata di s&egrave; visibile traccia per l'aria, troveresti essere la trasversale non <lb/>retta ma curva. </s>

<s>&ldquo; Causa vero cur motus pilae a rectitudine deflectatur, et <lb/>curvam sequatur describatque lineam, illius compositio est, quatenus ex du&shy;<lb/>plici vi motrice originem habet &rdquo; (ibid., pag. </s>

<s>438), e da questa duplice virt&ugrave; <lb/>motrice dimostra resultarne una semiparabola. </s></p><p type="main">

<s>Per l'amore, con cui il Gassendo accolse, comment&ograve; e diffuse le dot&shy;<lb/>trine di Galileo, si merit&ograve; la riconoscenza dei Discepoli, i quali pi&ugrave; volte <lb/>commemorarono solennemente il Filosofo francese nella loro Accademia fio&shy;<lb/>rentina. </s>

<s>E quasi, per far eco alle applaudite epistole <emph type="italics"/>De motu impresso,<emph.end type="italics"/><lb/>instituirono e descrissero nel loro libro dei <emph type="italics"/>Saggi<emph.end type="italics"/> quelle esperienze, in con&shy;<lb/>fermazione di quel che asserisce in pi&ugrave; luoghi il medesimo Galileo &ldquo; che la <lb/>virt&ugrave; impressa ne'proietti, per novella direzione di moto, non si distrugge &rdquo; <lb/>(Firenze 1841, pag. </s>

<s>163). </s></p><p type="main">

<s>Ci furono per&ograve; in Francia, insieme col Gassendo, altri, che delle dot&shy;<lb/>trine, insegnate ne'dialoghi dei due Massimi sistemi intorno alle propriet&agrave; <lb/>del moto, si fecero acuti e liberi censori. </s>

<s>A un geometra cos&igrave; profondo, come <lb/>era il Fermat, non sfugg&igrave; quello, in cui era trascorso Galileo, quando asse&shy;<lb/>gn&ograve; l'orbita circolare al sasso cadente dall'alto di una torre, movendosi in <lb/>giro la Terra, e dette al Carcavy, perch&egrave; la mandasse a leggere allo stesso <lb/>Galileo, la dimostrazione che la detta orbita, nel medesimo supposto, doveva <lb/>rassomigliarsi invece a una spirale. </s>

<s>Consapevole di tutto ci&ograve; era il Mersenno, <lb/>quel buon padre, disse il Dati, atto meglio a raccogliere e a promovere le <lb/>altrui invenzioni, che a mettere in luce le proprie &ldquo; facendo come quei mer&shy;<lb/>catanti che, per iscarsezza di loro avere, malamente potendo far negozi, sfo&shy;<lb/>gano il genio loro guadagnando pure assai nel contrattare, e mettere in ven&shy;<lb/>dita le merci altrui &rdquo; (Lettera a'Filaleti cit., pag. </s>

<s>6). Si potrebbe anche bene <lb/>rassomigliare a quell'aure instabili, o a quegl'insetti faccendieri, che traspor&shy;<lb/>tano il polline per fecondarne qua e l&agrave; gli aperti fiori; il qual ufficio e il <lb/>qual genio mostr&ograve; il Padre di averlo veramente esercitato e portato in tutti <lb/>i libri che scrisse, incominciando dai primi, ch'egli fuse poi in quel volu&shy;<lb/>mone in foglio, intitolato <emph type="italics"/>De la nature des sons, des mouvemens, et de <lb/>leurs proprietez,<emph.end type="italics"/> stampato a Parigi nel 1635. Fu qui che, negoziando la <lb/>scrittura fatta dal Fermat sopra la linea, che descrive il cadente, cavando la <lb/>dimostrazione dallo scrigno privato, per metterla in pubblico corso; esamin&ograve; <lb/>prima il Mersenno, nella III proposizione del secondo suo libro, quel che <lb/>Galileo dice del peso, che scendendo dall'alto di una torre giungerebbe a <lb/>toccare il centro terrestre, passando per una mezza circonferenza, e poi sog&shy;<lb/>giunse immediatamente una proposizione cos&igrave; formulata: &ldquo; Monstrer qu'il <lb/>est impossible que les corps pesans, descendans iusques au centre de la <pb xlink:href="020/01/2878.jpg" pagenum="503"/>Terre, descrivent le demicercle precedant, et donner la ligne, par la quelle <lb/>ils descendroient si la Terre tournoit en 24 heures auteur de son assieu &rdquo; <lb/>(pag. </s>

<s>96). </s></p><p type="main">

<s>Ma la linea descritta dai cadenti si riduceva a una speculazione geome&shy;<lb/>trica, che aveva il suo fondamento nella composizione dei moti, per cui non <lb/>fa maraviglia che avesse intorno ad essa fallato quel Galileo, dal quale erasi <lb/>data la sentenza non si poter comporre di due moti retti un moto circolare <lb/>(Alb. </s>

<s>I, 446). Le nuove cose di Meccanica per&ograve;, che si proponevano ne'dia&shy;<lb/>loghi dei Due massimi sistemi, non tutte erano di questa natura: vi si de&shy;<lb/>finiva per esempio il tempo, che impiega un grave a passare lo spazio di <lb/>cento braccia; la proporzion dei momenti de'mobili lungo i piani pi&ugrave; o meno <lb/>inclinati; l'equidiuturnit&agrave; de'pendoli di varia mole, per qualunque ampiezza <lb/>d'arco oscillanti, e simili altre cose, la verit&agrave; delle quali si pretendeva, non <lb/>senza ragione, che dovess'essere confermata dall'esperienza. </s>

<s>Ora parve a quei <lb/>censori Parigini che troppo confidentemente avesse Galileo asserite le sue <lb/>proposizioni, le quali perci&ograve; messero in dubbio, avendole trovate, non sola&shy;<lb/>mente non riscontrare, ma spesso contradire ai fatti osservati. </s>

<s>Il Mersenno, <lb/>alla proposizione VII del secondo libro citato, scritta per dimostrare il mo&shy;<lb/>mento dei pesi lungo i piani inclinati, e per determinare se il cadente passa, <lb/>come diceva Galileo, per tutti gl'infiniti gradi di tardit&agrave;; aggiunse un tal <lb/>corollario: </s></p><p type="main">

<s>&ldquo; Je doute que le sieur Galilee ayt fait les experiences des cheutes sur <lb/>le plan, puis qu'il n'en parle nullement, et que la proportion qui donne con&shy;<lb/>tradit souvent l'experience: et desire que plusieurs esprouvent la mesme <lb/>chose sur des plans differens avec toutes les precautions, dont ils pourront <lb/>s'aviser, afin qu'ils voyent si leurs experiences respondront aux nostres, et <lb/>si l'on en pourra tirer assez de lumiere pour faire un theorema en faveur <lb/>de la vitesse de ces cheutes obliques, dont les vitesses pourroient estre me&shy;<lb/>surees par les differens effets du poids, qui frappera dautant plus fort que <lb/>le plan sera moins inclin&eacute; sur l'horizon, et qu'il approchera davantage de la <lb/>ligne perpendiculaire &rdquo; (ivi, pag. </s>

<s>112). </s></p><p type="main">

<s>Le censure del Mersenno potevano approvarsi per quel che riguarda il <lb/>tempo speso dal cadente a passare le cento braccia, o l'isocronismo dei pen&shy;<lb/>doli, qualunque fosse l'ampiezza dell'arco descritto dalle loro vibrazioni. </s>

<s>Ma <lb/>rispetto alla proporzion dei momenti, con cui scendono i gravi lungo i piani <lb/>inclinati, non potevano l'esperienze infirmare la verit&agrave; dei teoremi galileiani, <lb/>avendo supposto l'Autore che venisse dal mobile rimosso tutto ci&ograve; che, per <lb/>via dell'attrito dell'aria, o di qualsivoglia altro accidente ne impedisce la li&shy;<lb/>bera caduta. </s>

<s>Di qui &egrave; che, sembrando impossibile sperimentare nel vuoto, e <lb/>senza che dal grave si tocchi, almeno in alcuni punti, il piano soggetto, si <lb/>vede la necessit&agrave; del non corrispondere esattamente alle leggi inatematiche <lb/>i fatti osservati. </s>

<s>Presto per tal rispetto cessarono i dubbi, ma intanto le li&shy;<lb/>bere censure del Mersenno, dop'aver tolta agl'insegnamenti di Galileo quella <lb/>fedelt&agrave; di ossequio, con cui gli aveva accolti il Gassendo, suscitarono nel-<pb xlink:href="020/01/2879.jpg" pagenum="504"/>l'animo dei Matematici parigini un baldanzoso spirito di emulazione. </s>

<s>Non <lb/>sappiamo per verit&agrave; con qual coscienza il Cartesio potesse dir sua la sco&shy;<lb/>perta delle leggi, con cui si accelerano i gravi, e suoi, nella Dinamica nuo&shy;<lb/>vamente instituita in Italia, tanti altri teoremi: ma, mentre tutto il mondo <lb/>applaudiva all'opera del nostro Italiano, consentendogli volentieri che le due <lb/>Scienze ivi istituite fossero propriamente nuove; non si pu&ograve; non ascoltare <lb/>con maraviglia il Roberval vantarsi di queste cose col Torricelli: &ldquo; At Me&shy;<lb/>chanicam a fundamentis ad fastigium novam extruximus, reiectis omnibus, <lb/>praeter paucos admodum, antiquis lapidibus, quibus illa constahat &rdquo; (Ouvr. </s>

<s>cit., <lb/>pag. </s>

<s>396). E soggiunge di non ammettere nessun nuovo postulato, come fa <lb/>Galileo, e come fai tu. </s>

<s>&ldquo; Vir clarissime, qui propositione prima libri primi <lb/><emph type="italics"/>De motu gravium descendentium<emph.end type="italics"/> ad id demonstrandum novo postulato usus <lb/>es, quod quivis non facile concesserit, quia pondera, quae proponis, non libra <lb/>rigida et recta, ut fieri solet, sed fune molli ac perfecte plicabili invicem alli&shy;<lb/>gantur. </s>

<s>Nos autem ad hoc libra utimur modo usitato disposita, cuius bene&shy;<lb/>ficio propositionem illam non aliter demonstramus, quam aut vectem aut <lb/>axem in peritrochio. </s>

<s>Eam autem iam ante quindecim annos invenimus, atque <lb/>anno 1636, tamquam Mechanicae nostrae prodromum, praelo commisimus <lb/>atque vulgavimus, sed gallico idiomate &rdquo; (ibid., pag. </s>

<s>397). La notizia &egrave; tale, <lb/>da non si passar per noi senza un breve esame questa nuova Meccanica ro&shy;<lb/>bervalliana condotta come si dice dai fondamenti al suo pi&ugrave; alto fastigio, <lb/>senza che da Galileo o da nessun altro degli antichi sia stato preso per l'edi&shy;<lb/>fizio altro che qualche pietra. </s></p><p type="main">

<s>&Egrave; divisa l'opera in otto libri, in ciascuno de'quali dice il Roberval esser <lb/>questi i soggetti via via trattati: I. </s>

<s>Se si dia un centro delle virt&ugrave; potenziali <lb/>in universale. </s>

<s>II. </s>

<s>Della Libbra, e degli Equiponderanti. </s>

<s>III. </s>

<s>Dei centri di gra&shy;<lb/>vit&agrave; dell&egrave; varie figure. </s>

<s>IV. </s>

<s>Di alcune mirabili propriet&agrave; delle forze applicate <lb/>alle funi. </s>

<s>V. </s>

<s>Delle macchine, e degli strumenti. </s>

<s>VI. </s>

<s>Delle potenze, che agi&shy;<lb/>scono in vari mezzi. </s>

<s>VII. </s>

<s>Dei moti composti. </s>

<s>VIII. </s>

<s>Dei centri delle percosse. </s></p><p type="main">

<s>Per dar di queste cose al Torricelli qualche saggio, sceglieva il Rober&shy;<lb/>val dal quarto libro alcuni teoremi, fra'quali quello della fune tesa, che gra&shy;<lb/>vata nel mezzo da un peso anche piccolissimo o s'inflette o si rompe, senza <lb/>che sia possibile a qualunque gran forza ridurla mai in dirittura. </s>

<s>N&egrave; temeva <lb/>gli rinfacciasse il Torricelli che la questione era gi&agrave; trattata da Galileo, <lb/>avendo pronta la risposta col dire ch'essendo il problema, infine al quarto <lb/>dialogo delle nuove Scienze, mal risoluto, egli era propriamente il primo, che <lb/>ne avesse data la risoluzion vera, applicandovi il principio dei moti compo&shy;<lb/>sti. </s>

<s>Ma due altri teoremi soggiungeva lo stesso Roberval, per confermare che <lb/>veramente maravigliosa era questa nuova meccanica delle funi. </s>

<s>Il primo si <lb/>annunziava in questa maniera: &ldquo; Si tres potentiae, totidem funibus, ad com&shy;<lb/>munem nodum religatis, agentes (nodus est quodvis punctum in fune) aequi&shy;<lb/>librium constituant; tunc describi poterit triangulum, cuius centrum gravitatis <lb/>sit nodus ipse, tres autem anguli ad tria funium puncta alicubi terminentur <lb/>(infinita quidem describerentur triangula sed omnia similia): erunt autem <pb xlink:href="020/01/2880.jpg" pagenum="505"/>tunc tres potentiae in eadem ratione cum tribus rectis a centro trianguli ad <lb/>tres angulos terminatis, ita ut quaelibet potentia homologa sit ei rectae, quae <lb/>in fune ipsius existit &rdquo; (ibid). </s></p><p type="main">

<s>L'elegantissimo teorema si pu&ograve;, pi&ugrave; semplicemente, proporre sotto quest'al&shy;<lb/>tra forma: Sia nel triangolo ABC (fig. </s>

<s>315) il centro di gravit&agrave; F, da cui si <lb/><figure id="id.020.01.2880.1.jpg" xlink:href="020/01/2880/1.jpg"/></s></p><p type="caption">

<s>Figura 315.<lb/>conducano le AF, FC, FB ai tre vertici. </s>

<s>Se queste tre <lb/>linee rappresentano tre funi annodate in F, e si supponga <lb/>che vengano ciascuna tirate da forze proporzionali alle <lb/>lunghezze, il nodo rimarr&agrave; in equilibrio. </s>

<s>Costruito infatti <lb/>il parallelogrammo BFCD, la diagonale di lui FD &egrave; la <lb/>resultante delle forze BF, FC, che tirano in gi&ugrave;, ed &egrave; <lb/>manifestamente essa diagonale in dirittura, contrapposta, <lb/>e uguale alla AF, essendo ambedue doppie della EF. </s>

<s>Se <lb/>ai lati AB, AC, CB si conducano esternamente o inter&shy;<lb/>namente, a qual si voglia distanza, e quanti pi&ugrave; piaccia <lb/>lati paralleli; gl'infiniti triangoli, che ne nascono, son tutti simili, e perci&ograve; le <lb/>distanze dal comun centro di gravit&agrave; ai respettivi vertici tutte proporzionali. </s></p><p type="main">

<s>L'altro teorema analogo cos&igrave; dal Roberval si proponeva: &ldquo; Si quatuor <lb/>potentiae, non existentes in eodem plano, totidem funibus ad communem <lb/><figure id="id.020.01.2880.2.jpg" xlink:href="020/01/2880/2.jpg"/></s></p><p type="caption">

<s>Figura 316.<lb/>nodum religatis agentes, aequilibrium consti&shy;<lb/>tuant; tunc quod supra de triangulo dictum est de <lb/>quadam pyramide tetragona verum erit &rdquo; (ibid.). </s></p><p type="main">

<s>Sia ABCD (fig. </s>

<s>316) la piramide tetragona, <lb/>col vertice in A, e avente per base il triangolo <lb/>BDC, col centro di gravit&agrave; in E. </s>

<s>Congiunta la <lb/>AE, la quale sia segata in F talmente, che AF <lb/>riesca tripla di FE, sar&agrave; in F il centro di gra&shy;<lb/>vit&agrave; della piramide. </s>

<s>Se ora, come ad A la AF, <lb/>si conducano dal medesimo punto F agli altri <lb/>tre vertici in basso le FD, FB, FC, e s'intenda <lb/>esser queste altrettante funi applicate a tirare <lb/>il nodo F, con forze proporzionali alle rispettive <lb/>lunghezze; dice il Roberval che le forze traenti <lb/>in basso equivalgono a quell'unica AF, che tira <lb/>in alto, per cui il nodo F star&agrave; fermo. </s></p><p type="main">

<s>Che sia vera l'asserita uguaglianza tra le <lb/>forze opposte, si dimostra assai facilmente, com&shy;<lb/>ponendo le BF, FC nella FG, e questa con la <lb/>DF nella FH, costruendo il parallelogrammo DG, <lb/>di cui essa FH sar&agrave; diagonale, che proceder&agrave; <lb/>nella medesima dirittura con la AF, e sar&agrave; la resultante unica delle tre <lb/>forze inferiori. </s>

<s>Che poi questa resultante sia uguale ad AF, per cui le due <lb/>forze, tirando contrariamente, deve il nodo F permanere nell'equilibrio, <lb/>consegue dalla similitudine dei triangoli DEH, FEI i quali danno la pro-<pb xlink:href="020/01/2881.jpg" pagenum="506"/>porzione DE:EI=EH:EF. </s>

<s>Ma DE &egrave; doppia di EI, dunque anche EH &egrave; <lb/>doppia di EF, della quale essendo FH e AF ambedue triple, saranno dunque <lb/>queste due linee, o le due forze che rappresentano, fra loro uguali. </s></p><p type="main">

<s>Tali erano le eleganze, che il Roberval dava al Torricelli, per saggio del <lb/>IV libro della sua Meccanica. </s>

<s>Dal V poi sceglieva la dimostrazione di un tal <lb/>paradosso: se un corpo A (fig. </s>

<s>317) sia dal piano BC premuto con quanta <lb/><figure id="id.020.01.2881.1.jpg" xlink:href="020/01/2881/1.jpg"/></s></p><p type="caption">

<s>Figura 317.<lb/>forza si voglia sul piano inclinato DE, e i due piani si <lb/>suppongano perfettamente rigidi e fra s&egrave; paralleli, il <lb/>detto corpo interposto scender&agrave; in ogni modo lungo il <lb/>declivio DE, se da qualche forza straniera non vi sia <lb/>ritenuto. </s>

<s>Altra cosa di minor curiosit&agrave;, ma di maggiore <lb/>importanza, faceva il Roberval notare in questo suo <lb/>libro, ed era che, nel trattar de'gravi scendenti lungo <lb/>i piani inclinati, &ldquo; non tantum casum consideravimus, <lb/>qui solus ab omnibus attenditur, cum scilicet potentia pondus in plano in&shy;<lb/>clinato positum retinens, agit per lineam directionis ipsi plano parallelam, <lb/>sed et dum eadem linea directionis aliam quamcumque positionem obtinue&shy;<lb/>rit, quo pacto ratio ponderis ad potentiam infinite mutatur &rdquo; (Ouvrag. </s>

<s>cit., <lb/>pag. </s>

<s>397). </s></p><p type="main">

<s>Sia sul piano inclinato AC (fig. </s>

<s>318) posto il peso D; tutti i Matema&shy;<lb/>tici, dice il Roberval, dimostrano che questo sta al suo contrappeso come <lb/><figure id="id.020.01.2881.2.jpg" xlink:href="020/01/2881/2.jpg"/></s></p><p type="caption">

<s>Figura 318.<lb/>AC, lunghezza dello stesso piano, <lb/>sta all'AB sua elevazione, tacita&shy;<lb/>mente supponendo che le forze <lb/>agiscano in direzioni parallele alle <lb/>due dette linee. </s>

<s>Supponiamo invece <lb/>che il peso venga sostenuto, con <lb/>direzione diversa, dalla fune DE, la <lb/>quale sia presa lunga quanto AC: <lb/>non sar&agrave; mica vero che si possa <lb/>come dianzi con questa lunghezza <lb/>misurare la forza, ma sar&agrave; tanto <lb/>diversa, soggiungeva lo stesso Ro&shy;<lb/>berval, quanto ED diagonale del <lb/>parallelogrammo &egrave; diversa da DG <lb/>lato di lui, condotto parallelamente <lb/>all'inclinazione del piano. </s></p><p type="main">

<s>Con simil ragione, proseguiva a dire l'Autore di questa meccanica nuova, <lb/>diversifica la cosa se il contrappeso F, invece di tirare verticalmente in di&shy;<lb/>rezione parallela ad AB, come tutti suppongono, tiri obliquamente secondo <lb/>IH, perch'essendo in quel primo caso rappresentata la forza da IK uguale <lb/>ad AB, dovr&agrave; &egrave;sser nell'altro rappresentata da una linea tanto maggiore, <lb/>quanto la diagonale IH &egrave; maggiore del lato IK del parallelogrammo, con le <lb/>solite regole costruito. </s></p><pb xlink:href="020/01/2882.jpg" pagenum="507"/><p type="main">

<s>Se avesse il Roberval ragione di credersi primo autore di questa novit&agrave; <lb/>introdotta nella Statica del piano inclinato, lo vedremo nel capitolo appresso. </s>

<s><lb/>Ma di fatto egli riaccendeva la face di quella tradizione, che parve essersi <lb/><figure id="id.020.01.2882.1.jpg" xlink:href="020/01/2882/1.jpg"/></s></p><p type="caption">

<s>Figura 319.<lb/>spenta nella memoria de'suoi contemporanei, e de'loro <lb/>discepoli pi&ugrave; immediati. </s>

<s>Nel qual proposito ci oc&shy;<lb/>corre a notare la proposizione LXIII della prima <lb/>parte <emph type="italics"/>De motu animalium,<emph.end type="italics"/> dove, considerandosi dal <lb/>Borelli le condizioni dell'equilibrio tra le potenze <lb/>T ed R (fig. </s>

<s>319), tendenti obliquamente la fune <lb/>DE, ne conclude dover essere le due dette potenze <lb/>uguali. </s>

<s>Ma non aveva pronunziata la conclusione, <lb/>che soggiunge un lungo scolio, per avvertire i lettori <lb/>che il suo teorema non contradice all'altro <emph type="italics"/>ab <lb/>omnibus receptum<emph.end type="italics"/> (Romae 1880, pag. </s>

<s>120), e se&shy;<lb/>condo il quale si dice che il peso R sta al contrappeso T come la lun&shy;<lb/>ghezza AC del piano sta all'altezza BC, essendo questo da quell'altro con&shy;<lb/>templato caso molto diverso. </s></p><p type="main">

<s>Poteva, con efficace brevit&agrave;, far osservare l'Autore che il peso R opera <lb/>nel medesimo modo che se pendesse in E da una puleggia sola con direzion <lb/>verticale, parallela alla CB, il qual caso &egrave; assai diverso dall'altro, quando la <lb/>direzione fosse obliqua come ED, perch&egrave; allora, costruito il parallelogrammo <lb/>FH, il contrappeso R dovrebbe esser tanto maggiore del peso T, quanto la <lb/>ED diagonale &egrave; maggiore del lato EF del descritto parallelogrammo, ci&ograve; che <lb/>torna come se il detto peso esercitasse no il suo momento totale, ma quale <lb/>gli converrebbe posato che fosse sul declivio AC del piano. </s>

<s>Cos&igrave;, ripetiamo, <lb/>poteva il Borelli, come avrebbe fatto il Roberval in simile occorrenza, discor&shy;<lb/>rere nel suo scolio, e invece si conduce per vie lunghe e oblique a dimo&shy;<lb/>strare il suo intento, riducendo i due casi alle varie condizioni dell'equili&shy;<lb/>brio, che si osservano nella leva diritta e nella angolare. </s></p><p type="main">

<s>Nel suo ottavo libro diceva il Roberval trattarsi dei centri delle percosse, <lb/>e come saggio annunziava intanto al Torricelli un teorema dimostrativo del <lb/>punto, da cui, percotendo, si fa il massimo colpo in un settore di cerchio <lb/>ondeggiante intorno al centro della figura intera alla quale egli appartiene, <lb/>dicendo che si troverebbe quel punto col fare &ldquo; ut chorda arcus sectoris, ad <lb/>ipsum arcum, ita tres quadrantes semidiametri circuli ad rectam inter ipsius <lb/>circuli centrum et centrum percussionis sectoris interceptam &rdquo; (ibid., pag. </s>

<s>398). <lb/>Di ci&ograve; avremo occasione di dir altrove pi&ugrave; di proposito, ma per ora &egrave; da <lb/>ripensare a questa Meccanica robervalliana, che non a torto il suo autore <lb/>chiamava nuova, ritrovandosi veramente tale per la massima parte, se si pa&shy;<lb/>ragona con ci&ograve; che delle macchine e delle altre statiche questioni scrissero <lb/>Galileo, e i Matematici contemporanei nei loro libri. </s>

<s>Vero &egrave; che la Sparto&shy;<lb/>statica era stata precedentemente istituita dallo Stevino, ma il Roberval di&shy;<lb/>mostr&ograve; la regola del parallelogrammo delle forze da'suoi veri principii, e <lb/>l'applic&ograve; a risolvere nuovi mirabili problemi intorno all'equilibrio de'pesi o <pb xlink:href="020/01/2883.jpg" pagenum="508"/>tirati o sostenuti da funi. </s>

<s>Come fosse poi rispetto a ci&ograve; difettosa la Scienza <lb/>galileiana, lo sanno oramai troppo bene coloro, che hanno letto addietro la <lb/>nostra Storia. </s>

<s>La teoria del piano inclinato, da cui le altre macchine dove&shy;<lb/>vano prender la legge, vedemmo come fosse stata dimostrata gi&agrave; dal Tarta&shy;<lb/>glia, a cui Galileo stesso e il Cartesio e il Torricelli non aggiunsero in so&shy;<lb/>stanza nulla di nuovo, prima che il Roberval venisse a considerare il caso, <lb/>in cui le potenze sostenenti il peso hanno qualunque direzione diversa da <lb/>quella del perpendicolo, e del piano o del suo declivio. </s>

<s>Ma de'centri delle <lb/>percosse le questioni erano affatto intatte, specialmente appresso i seguaci <lb/>della Scuola galileiana, per non avere intorno a ci&ograve; il loro Maestro proposto <lb/>se non che principii falsi, e alla nuova inquisizione in qualunque modo insuf&shy;<lb/>ficienti. </s></p><p type="main">

<s>Molto pi&ugrave; dunque sarebbe da confessare aver progredito la Meccanica <lb/>in Francia che in Italia, ma que'progressi riguardavano solamente la Sta&shy;<lb/>tica, mentre la Dinamica si rimaneva tutta intera nelle mani di Galileo, come <lb/>conseguenza feconda del principio da lui professato che cio&egrave;, nelle libere ca&shy;<lb/>dute, le velocit&agrave; de'gravi crescono come i tempi. </s>

<s>Il Cartesio fece a quel prin&shy;<lb/>cipio, verissimo in s&egrave; e nella sua forma, alcune cavillose osservazioni, ma il <lb/>Roberval sembra che lo negasse affatto, come trasparisce da queste parole <lb/>scritte dal Ricci, nel chiudere una sua lettera indirizzata da Roma al Tor&shy;<lb/>ricelli: &ldquo; In ultimo prego V. S. che voglia rispondere alle lettere di quel <lb/>gesuita (cio&egrave; del Mersenno, cos&igrave; spesso chiamato dal Ricci, poi cardinale, non <lb/>perch&egrave; il Padre professasse de'gesuiti la religione, ma perch&egrave;, secondo lui, <lb/>ne imitava l'ipocrisia) che impugna le dottrine del moto, conforme gi&agrave; ne <lb/>ragguagliai V. S., e soggiunge alcuni pensieri di Robervallio in questa parte, <lb/>con caratteri poi cos&igrave; sconci, che finora non ho potuto trovare persona, che <lb/>ne possa dar chiara interpetrazione. </s>

<s>E per me vado considerando che Ro&shy;<lb/>bervallio sia contrario alle posizioni del Galileo in materia dell'augumento <lb/>di velocit&agrave; nei gravi cadenti, e contrario in modo, che neghi ogni posizione <lb/>del Galileo. </s>

<s>Ma di questo ha promesso di scriverne il suo parere, ed allora, <lb/>per mezzo del Mersenno, intenderemo il tutto &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, <lb/>fol. </s>

<s>156). </s></p><p type="main">

<s>Rimase per queste ragioni nel Roberval la Dinamica cos&igrave; sterilita, che <lb/>non fa maraviglia se non s&igrave; vide menare i frutti aspettati, per raccogliere i <lb/>quali, essendo stato necessario tornare a Galileo, da ci&ograve; si segna il terzo passo, <lb/>che, poco dopo la met&agrave; del secolo XVII, fecero gl'insegnamenti di lui appresso <lb/>gli stranieri. </s>

<s>Si videro allora sorgere principali il Wallis in Inghitterra, il <lb/>Mariotte in Francia e l'Huyghens nell'Olanda, al quale ultimo va massima&shy;<lb/>mente debitrice la Scienza del moto dell'avere in provincie nuove esteso il <lb/>suo antico dominio. </s>

<s>Ma a preparare l'opera di lui giovarono grandemente <lb/>quelle degli altri due commemorati, e in special modo del Wallis, che, trat&shy;<lb/>tandone con regole di calcolo pi&ugrave; precise i teoremi, conferm&ograve;, contro gli oppo&shy;<lb/>sitori e i dubitanti, la Scienza galileiana nella geometrica verit&agrave; de'suoi <lb/>principii. </s></p><pb xlink:href="020/01/2884.jpg" pagenum="509"/><p type="main">

<s>I capitoli perci&ograve;, dove il celebre Professor saviliano tratta del moto in <lb/>generale, della discesa dei gravi, e della libbra, se son per matematica po&shy;<lb/>tenza notabili, non hanno per&ograve; altra ragione che di commenti a verit&agrave; pre&shy;<lb/>cedentemente gi&agrave; dimostrate; come pure col&agrave;, dove tratta delle percosse e <lb/>degli urti, non sembra facesse altro il Wallis che dar miglior ordine e chia&shy;<lb/>rezza, e forma pi&ugrave; rigorosamente matematica alle proposizioni del nostro <lb/>Borelli. </s>

<s>Ma il trattato <emph type="italics"/>De centro gravitatis,<emph.end type="italics"/> che comprende esso solo due <lb/>terzi della intera Meccanica wallisiana, dovette apparire al mondo opera nuova, <lb/>rimanendosi allora, e per pi&ugrave; di due secoli appresso, sconosciuto e seppel&shy;<lb/>lito ne'manoscritti ci&ograve; che dai nostri Matematici erasi scritto in quel mede&shy;<lb/>simo soggetto. </s>

<s>Che se le invenzioni del Torricelli, del Nardi e del Ricci fos&shy;<lb/>sero state raccolte e pubblicate in un libro dai loro propri autori, s'intende <lb/>come l'Italia avrebbe avuto della Baricentrica un trattato compiuto, venti <lb/>anni prima dell'Inghilterra. </s>

<s>Anche al Wallis, come agli Italiani che l'ave&shy;<lb/>vano preceduto, serve di strumento, per domar la durezza del campo da <lb/>dissodarsi, la dottrina degli indivisibili, ch'egli, con i pi&ugrave; celebri matematici <lb/>stranieri, approva, e l'ha dal suo proprio inventore per ben dimostrata. <lb/></s>

<s>&ldquo; Atque hanc <emph type="italics"/>De indivisibilibus<emph.end type="italics"/> doctrinam, nunc passim receptam atque <lb/>post Cavallerium a celeberrimis Mathematicis approbatam, pro veterum con&shy;<lb/>tinua figurarum adscriptione substituire visum est &rdquo; (Mechan., P. II, Lon&shy;<lb/>dini 1670, pag. </s>

<s>112). </s></p><p type="main">

<s>Il Mariotte men predilesse i calcoli sottili, che le fisiche esperienze, ma <lb/>l'Huyghens parve comprendere in s&egrave; le virt&ugrave; de'suoi predecessori, non ri&shy;<lb/>manendosi inferiore al Wallis nella Matematica, e dall'altra parte applicando <lb/>i teoremi di lei a dar fermezza di leggi ai fuggevoli fatti osservati. </s>

<s>Nel terzo <lb/>dialogo delle due Nuove Scienze, come altrove osservammo, si proponeva una <lb/>lunga serie di principii, da'quali poi non si vedeva conseguir la finale inten&shy;<lb/>zione dell'Autore, ch'era quella di dimostrare l'isocronismo dei pendoli per <lb/>qualunque ampiezza delle loro vibrazioni. </s>

<s>Tutta quella gran mole di teoremi, <lb/>congesta nel detto dialogo, non era per altro servita, che per dimostrare <lb/>quello stesso isocronismo nelle corde, d'onde Galileo lasciava a concluderne <lb/>l'isocronismo per gli archi circolari sottesi. </s>

<s>Ma la conclusione, non essendo <lb/>logica, riusciva perci&ograve; tutt'insieme anche falsa, e fu l'Huyghens che ridusse <lb/>nella via retta, e dette perfezione alla Scienza galileiana, dimostrando che <lb/>dall'esser le suttese tautocrone conseguiva, secondo le buone regole ragionando, <lb/>il tautocronismo, non per gli archi dei circoli, ma per quelli della cicloide. </s></p><p type="main">

<s>Si riform&ograve; per la nuova scoperta la costruzione degli Orologi, che dal&shy;<lb/>l'umile arte fabbrile si sollevarono alle pi&ugrave; alte dignit&agrave; della Geometria. </s>

<s>Se&shy;<lb/>condo qual pi&ugrave; giusta regola si dovesse prefinire la lunghezza del pendolo, <lb/>sanno bene i nostri Lettori come fosse questione antica, avendola allo stesso <lb/>Galileo proposta il Pieroni, quando prima pens&ograve; di valersi di quel semplice <lb/>strumento, per le osservazioni celesti: e gli stessi Accademici fiorentini, qua&shy;<lb/>rant'anni dipoi, essendo tuttavia nella incertezza, si studiavano d'assicurarsi <lb/>prudentemente dalle fallacie, col far sottilissimo il filo, e col ridurre sotto <pb xlink:href="020/01/2885.jpg" pagenum="510"/>la minor mole possibile la gravit&agrave; del peso ondeggiante. </s>

<s>Bench&egrave; alcuni Ma&shy;<lb/>tematici stranieri facessero derivar quella regola dai centri delle percosse, fu <lb/>nonostante l'Huyghens il primo che, all'occasion di descrivere il suo nuovo <lb/>Orologio oscillatorio, ne dette dimostrazione propria e diretta. </s>

<s>&ldquo; Occasio vero <lb/>ad haec denuo tentanda ex pendulorum automati nostri temperandorum ra&shy;<lb/>tione oblata est, dum pondus mobile, praeter id quod in imo est, illis ap&shy;<lb/>plico &rdquo; (Opera varia, T. I, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>118). </s></p><p type="main">

<s>Altra occasione, da questo stesso Orologio, venne all'Huyghens di spe&shy;<lb/>cular cose di Meccanica nuova, dall'osservar che il pendolo, menando qua e <lb/>l&agrave; per l'ambito di un circolo il peso, gl'imprime una forza, <emph type="italics"/>quam centri&shy;<lb/>fugam vocare libet,<emph.end type="italics"/> e che sopravvien nel mobile ad alterargli in qualche <lb/>modo la gravit&agrave; naturale. </s>

<s>&ldquo; Unde aliud quoque Horologii commentum de&shy;<lb/>duximus &rdquo; (ibid., pag. </s>

<s>185), formulando intanto <emph type="italics"/>De vi centrifuga ex motu <lb/>circulari<emph.end type="italics"/> tredici teoremi, ai quali poi negli Opuscoli postumi ebbe la Geo&shy;<lb/>metria meccanica a rallegrarsi di veder fatte le dimostrazioni. </s>

<s>Con questi <lb/>teoremi e con quegli altri relativi ai centri delle oscillazioni, e alle propriet&agrave; <lb/>meccaniche della Cicloide, aggiungeva il Matematico olandese, a quelle isti&shy;<lb/>tuite gi&agrave; da Galileo, tre nuove Scienze, intorno alle quali ha da trattenersi <lb/>ora particolarmente la nostra Storia con breve discorso. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Il tautocronismo della Cicloide vedemmo come derivasse per corollario <lb/>dalla proposizione XI torricelliana di <emph type="italics"/>Meccan&igrave;ca nuova,<emph.end type="italics"/> scritta qui addietro <lb/><figure id="id.020.01.2885.1.jpg" xlink:href="020/01/2885/1.jpg"/></s></p><p type="caption">

<s>Figura 320.<lb/>nel &sect; 3&deg; del <lb/>capitolo se&shy;<lb/>sto. </s>

<s>Ma con&shy;<lb/>segue anche <lb/>immediatamente <lb/>dai teoremi gali&shy;<lb/>leiani dei moti ac&shy;<lb/>celerati, dietro le <lb/>propriet&agrave; geome&shy;<lb/>triche della curva dimo&shy;<lb/>strate dal Roberval, una <lb/>delle quali propriet&agrave; &egrave; <lb/>che qualunque porzione <lb/>di essa curva, presa dal ver&shy;<lb/>tice, &egrave; uguale al doppio della <lb/>tangente. </s>

<s>Gl'impeti infatti <lb/>acquistati dal medesimo mobile, nello scendere da B (fig. </s>

<s>320) in I e in <lb/>A sul piano orizontale AI, sono uguali, o sia fatta la scesa per l'arco <pb xlink:href="020/01/2886.jpg" pagenum="511"/>cicloidale AB, o per la tangente BI: e proseguirebbe esso mobile equabil&shy;<lb/>mente passando, nel medesimo tempo impiegato a venire da B in I, uno <lb/>spazio doppio di BI, ossia uguale all'arco AB. </s>

<s>Lo stesso dicasi di qualunque <lb/>altro punto, da cui partendosi il grave acquisterebbe, giunto in A per la <lb/>concavit&agrave; cicloidale, tal impeto, da passare equabilmente uno spazio uguale <lb/>a quello del cammin curvo, acceleratamente descritto in quel medesimo tempo, <lb/>che sarebbe venuto gi&ugrave; per la tangente: onde essendo gl'impeti o le velo&shy;<lb/>cit&agrave;, in qualunque caso, proporzionali agli spazi, i tempi necessariamente sono <lb/>uguali. </s></p><p type="main">

<s>E per dire come dal tautocronismo delle scese per le corde dei cerchi <lb/>si potesse concludere a quello per gli archi della cicloide, e non degli stessi <lb/>cerchi, come fece Galileo; si osservi essere le cadute dai vari punti della <lb/>curva CA quelle medesime, che per le loro tangenti o per le corde, nel cir&shy;<lb/>colo DVA condotte a loro uguali e parallele, come la AV per esempio alla <lb/>BI: ond'essendo, per i teoremi galileiani, esse corde tautocrone, tautocrona <lb/>sar&agrave; dunque anche la Cicloide. </s></p><p type="main">

<s>Si pu&ograve; veder di qui quale stretta dipendenza avesse con la precedente <lb/>la Meccanica ugeniana, ma l'Autore aveva dimostrato della curva altre pro&shy;<lb/>priet&agrave; meccaniche pi&ugrave; generali, dalle quali faceva come per corollario deri&shy;<lb/>vare non solamente il tautocronismo, ma anche insieme altre verit&agrave; non men <lb/>nuove e maravigliose. </s>

<s>Quella generale proposizione &egrave; la XXV della seconda <lb/>parte dell'<emph type="italics"/>Orologio oscillatorio,<emph.end type="italics"/> in cui dimostrasi dall'Autore che, disposta <lb/>la Cicloide con la base orizontale, come la rappresenta la passata figura, il <lb/>tempo della scesa di un grave, da qualunque punto della concavit&agrave; all'imo <lb/>vertice, sta al tempo della scesa per l'asse come la semicirconferenza sta al <lb/>suo diametro. </s>

<s>Servono per lemma a questa le due proposizioni precedenti, <lb/>la prima delle quali &egrave; cos&igrave; annunziata: </s></p><p type="main">

<s>&ldquo; Sit cyclois ABC (nella medesima figura) cuius vertex A deorsum con&shy;<lb/>versus sit, axe AD ad perpendiculum erecto: sumptoque in ea quolibet puncto <lb/>B, ducatur inde deorsum recta BI, quae cycloidem tangat, termineturque <lb/>recta horizontali AI, recta vero BF ad axem perpendicularis agatur, et, di&shy;<lb/>visa bifariam FA in X, super ea describatur semicirculus FHA. </s>

<s>Ducta deinde <lb/>per punctum quodlibet G, in curva BA sumptum, recta <foreign lang="greek">*s</foreign>G, parallela BF, <lb/>quae circumferentiae FHA occurrat in H, axi AD in <foreign lang="greek">*s</foreign>; intelligantur per pun&shy;<lb/>cta G et H rectae tangentes utriusque curvae, earumque tangentium partes, <lb/>iisdem duabus horizontalibus MS, NT interceptae, sint MN, ST. </s>

<s>Iisdemque <lb/>rectis MS, NT includantur tangentis BI pars OP, et axis DA pars QR. </s>

<s>Qui&shy;<lb/>bus ita se habentibus, dico tempus quo grave percurret rectam MN, celeri&shy;<lb/>tate aequabili quanta acquiritur descendendo per arcum cycloidis BG, fore <lb/>ad tempus quo percurretur recta OP, celeritate aequabili dimidia eius, quae <lb/>acquiritur descendendo per totam tangentem BI; sicut est tangens ST ad <lb/>partem axis QR &rdquo; (ibid., pag. </s>

<s>79, 80). </s></p><p type="main">

<s>Si compia la costruzione descrivendo intorno al diametro AD il semicir&shy;<lb/>colo AVD, che incontrer&agrave; le parallele <foreign lang="greek">*s</foreign>G, BF ne'punti <emph type="italics"/>f,<emph.end type="italics"/> V, e si congiunga <pb xlink:href="020/01/2887.jpg" pagenum="512"/>A con V per una linea, la quale intersecher&agrave; nel suo passaggio le PR, G<foreign lang="greek">*s</foreign>, <lb/>OQ in K, L, E. </s>

<s>Si congiungano poi con H i punti F, A, X, e il punto A <lb/>con <emph type="italics"/>f<emph.end type="italics"/> per una linea, che attraverser&agrave; la PR in <emph type="italics"/>p,<emph.end type="italics"/> e prolungata raggiunger&agrave; <lb/>la OQ in <emph type="italics"/>d.<emph.end type="italics"/></s></p><p type="main">

<s>Ci&ograve; fatto, sappiamo per i teoremi galileiani che il tempo equabilmente <lb/>passato per la MN, al tempo per la OP, passato con la mezza celerit&agrave; detta, <lb/>ha la ragion composta diretta degli spazi, e reciproca delle velocit&agrave;: cosicch&egrave;, <lb/>chiamati To.MN, To.OP quegli stessi tempi e, Va.MN, Va.OP/2 le velocit&agrave; <lb/>corrispondenti; avremo To.MN:To.OP=MN.Va.OP/2:OP.Va.MN. </s>

<s>Ma <lb/>perch&egrave; tutta intera la velocit&agrave; equabile per OP &egrave; quella conveniente alla ca&shy;<lb/>duta da B in I, e la velocit&agrave; per MN &egrave; quella dovuta al cadente, con moto <lb/>accelerato da B in G, o da F in <foreign lang="greek">*s</foreign>; dunque, essendo per le note leggi della <lb/>Dinamica le velocit&agrave; proporzionali alle radici degli spazi, avremo </s></p><p type="main">

<s><emph type="center"/>Va.OP:Va.MN=&radic;AF:&radic;F<foreign lang="greek">*s</foreign>=AF:&radic;AF.F<foreign lang="greek">*s</foreign>=AF:FH.<emph.end type="center"/><lb/>Dividendo gli antecedenti per due, e facendo le sostituzioni, la ritrovata re&shy;<lb/>lazion de'tempi si trasformer&agrave; nell'altra </s></p><p type="main">

<s><emph type="center"/>To.MN:To.OP=MN.FX:OP.FH.<emph.end type="center"/></s></p><p type="main">

<s>Ora essendo, per le parallele e i parallelogrammi da esse circoscritti, <lb/>MN=<emph type="italics"/>dp,<emph.end type="italics"/> OP=EK, abbiamo MN:OP=<emph type="italics"/>dp<emph.end type="italics"/>:EK=<emph type="italics"/>d<emph.end type="italics"/>A:EA=<emph type="italics"/>f<emph.end type="italics"/>A:LA. </s>

<s><lb/>E perch&egrave; congiunti V, <emph type="italics"/>f,<emph.end type="italics"/> il triangolo AV<emph type="italics"/>f<emph.end type="italics"/> che ne nasce essendo simile al <lb/>triangolo AL<emph type="italics"/>f,<emph.end type="italics"/> d&agrave; la proporzione AV:A<emph type="italics"/>f<emph.end type="italics"/>=A<emph type="italics"/>f<emph.end type="italics"/>:AL; sar&agrave; dunque MN:OP= <lb/>AV:A<emph type="italics"/>f,<emph.end type="italics"/> la qual seconda ragione facilmente si dimostra esser quella mede&shy;<lb/>sima di FA ad AH. </s>

<s>Imperocch&egrave; AV2=DA.AF e A<emph type="italics"/>f<emph.end type="italics"/>2=DA.A<foreign lang="greek">*s</foreign>, d'onde <lb/>AV2:A<emph type="italics"/>f<emph.end type="italics"/>2=AF:A<foreign lang="greek">*s</foreign>=AF2:AF.A<foreign lang="greek">*s</foreign>=AF2:AH2, e perci&ograve; AV:A<emph type="italics"/>f<emph.end type="italics"/>= <lb/>AF:AH. </s>

<s>Essendo poi, per la similitudine dei triangoli FAH, FH<foreign lang="greek">*s</foreign>, la ragione <lb/>di AF ad AH uguale a quella di FH a H<foreign lang="greek">*s</foreign>; questa sar&agrave; dunque anche la <lb/>ragione di MN a OP, che, sostituita nella relazione de'tempi ultimamente <lb/>scritta, la trasformer&agrave; nell'altra To.MN:To.OP=FX.FH:H<foreign lang="greek">*s</foreign>.FH= <lb/>FX:H<foreign lang="greek">*s</foreign>=HX:H<foreign lang="greek">*s</foreign>, la quale, osservando che, condotta la T<emph type="italics"/>b<emph.end type="italics"/> perpendico&shy;<lb/>lare sopra SQ, i triangoli simili ST<emph type="italics"/>b,<emph.end type="italics"/> TH<foreign lang="greek">*s</foreign> danno HX:H<foreign lang="greek">*s</foreign>=ST:T<emph type="italics"/>b<emph.end type="italics"/>= <lb/>ST:QR; si riduce finalmente a To.MN:T.OP=ST:QR, d'onde appa&shy;<lb/>risce vera la conclusione dall'Huyghens stesso espressa in questa forma: <lb/>&ldquo; Igitur tempus motus qualem diximus per MN, ad tempus per OP, constat <lb/>esse sicut ST ad QR, quod erat demonstrandum &rdquo; (ibid., pag. </s>

<s>81). </s></p><p type="main">

<s>Se la porzione QR fosse stata presa infinitesima, gli archi del semicir&shy;<lb/>colo e della semicicloide, intercetti fra le parallele OQ, PR, si sarebbero <lb/>confusi con le tangenti ST, MN, ond'&egrave; che la medesima conclusione uge&shy;<lb/>niana poteva mettersi in altra forma, dicendo che il tempo della scesa per <lb/>l'arco cicloidale MN sta al tempo della scesa per la porzione di tangente OP, <lb/>come l'arco ST del circolo sta alla porzione QR dell'asse. </s>

<s>E perch&egrave;, divi-<pb xlink:href="020/01/2888.jpg" pagenum="513"/>dendo tutto intero il diametro AF in parti infinitamente piccole, e tutte uguali <lb/>a QR, la dimostrazione fatta per questa particolar divisione &egrave; applicabile a <lb/>ciascuna delle altre infinite, &egrave; manifesto che verrebbero da ci&ograve; ordinate al&shy;<lb/>trettante proporzioni, in cui i secondi termini, che sono i tempi impiegati a <lb/>passare equabilmente spazi tutti uguali ad OP, ed i quarti termini, ossia le <lb/>porzioni dell'asse AF, sono tutti fra loro uguali. </s>

<s>Ora, non sarebbe bisognato <lb/>all'Huyghens che d'invocare il <emph type="italics"/>Teorema integrale,<emph.end type="italics"/> per conseguir dalle cose <lb/>gi&agrave; dimostrate la sua principale intenzione. </s></p><p type="main">

<s>Che se giungesse a qualcuno oscura la nuova denominazione, sappia che <lb/>da noi si chiama Teorema integrale quello, che fu gi&agrave; proposto in questa <lb/>forma: &ldquo; Si fuerit ut prima magnitudo ad secundam, ita tertia ad quartam, <lb/>et hoc quotiescumque libuerit, fuerintque omnes primae inter se, item omnes <lb/>tertiae magnitudines inter se aequales; erunt omnes primae simul, ad omnes <lb/>secundas, ut sunt omnes tertiae simul, ad omnes quartas magnitudines &rdquo; <lb/>(Torricelli, Op. </s>

<s>geom. </s>

<s>cit., P. II, pag. </s>

<s>50). Il Roberval suppose ci&ograve; come <lb/>dimostrato, per facile corollario, da due proposizioni del quinto libro Degli <lb/>elementi, e il Torricelli ne fece una dimostrazione particolare, da lui stesso <lb/>inserita nel luogo sopra citato, come XVIII lemma <emph type="italics"/>De dimensione parabolae.<emph.end type="italics"/></s></p><p type="main">

<s>Che poi convenga al detto teorema il titolo d'integrale, adempiendo agli <lb/>uffici del calcolo, che per le posteriori istituzioni prese quel nome, &egrave; mani&shy;<lb/>festo dall'uso, che ne fecero i due stessi promotori insigni del metodo degli <lb/>indivisibili ora commemorati, e segnatamente il Torricelli, nelle varie occor&shy;<lb/>renze di ricercare i centri di gravit&agrave; delle varie figure, e le dimensioni delle <lb/>parabole. </s>

<s>Prendasi per esempio, da questo Libro torricelliano, quella propo&shy;<lb/>sizione XIII, il modo di dimostrar la quale disse il Nardi di averlo qualche <lb/>tempo prima imparato da Pappo. </s>

<s>Essendo ABC <lb/><figure id="id.020.01.2888.1.jpg" xlink:href="020/01/2888/1.jpg"/></s></p><p type="caption">

<s>Figura 321.<lb/>(fig. </s>

<s>321) una parabola, intorno alla base AC della <lb/>quale sia descritto il semicircolo ANC, e AD, AE <lb/>rettangoli circoscritti alle due figure, si dimostra <lb/>dall'Autore che FG:GI=<foreign lang="greek">p</foreign>GL2:<foreign lang="greek">p</foreign>GM2, e cos&igrave; <lb/>sempre, qualunque siano, fra le infinite linee <lb/>uguali equidistanti dal diametro BN, quelle che <lb/>incontrano la parabola, la base di lei, e il circolo <lb/>ne'punti dei loro passaggi. </s>

<s>Ora essendo, secondo <lb/>il metodo cavalierano, risolute nelle infinite linee costanti come FG, e nelle <lb/>infinite variabili come GI le superficie del rettangolo e della parabola, e si&shy;<lb/>milmente negli infiniti circoli di costante raggio GL, e di variabile GM, essendo <lb/>risoluti i solidi rotondi generati dal rivolgersi intorno ad AC il semicircolo e il <lb/>rettangolo a lui circoscritto; &egrave; manifesto che i termini FG, GI; <foreign lang="greek">p</foreign>GL2, <foreign lang="greek">p</foreign>GM2<lb/>sono altrettante quantit&agrave; differenziali, che si scriverebbero, seeondo i sim&shy;<lb/>boli usati dai matematici moderni, <emph type="italics"/>da:dx=db:dy,<emph.end type="italics"/> rappresentando <emph type="italics"/>a<emph.end type="italics"/> e <emph type="italics"/>x<emph.end type="italics"/><lb/>il rettangolo e la parabola, <emph type="italics"/>b<emph.end type="italics"/> e <emph type="italics"/>y<emph.end type="italics"/> il cilindro e la sfera. </s>

<s>Dall'analisi differen&shy;<lb/>ziale della funzione si risale alla sintesi integrale, per via della somma, in <lb/>virt&ugrave; del Teorema sopra accennato, da cui resulta che la somma delle infi-<pb xlink:href="020/01/2889.jpg" pagenum="514"/>nite quantit&agrave;, tutte uguali a <emph type="italics"/>da, db,<emph.end type="italics"/> uguaglia <emph type="italics"/>a, b:<emph.end type="italics"/> e la somma delle infinite <lb/>flussioni di <emph type="italics"/>x<emph.end type="italics"/> e di <emph type="italics"/>y<emph.end type="italics"/> uguaglia agli stessi <emph type="italics"/>x, y,<emph.end type="italics"/> precisamente come nel cal&shy;<lb/>colo recente &int; <emph type="italics"/>da,<emph.end type="italics"/> &int; <emph type="italics"/>dx,<emph.end type="italics"/> &int; <emph type="italics"/>db,<emph.end type="italics"/> &int; <emph type="italics"/>dy<emph.end type="italics"/> sono uguali ad <emph type="italics"/>a, x, b, y,<emph.end type="italics"/> non te&shy;<lb/>nuto conto delle costanti. </s></p><p type="main">

<s>Ritornando ora indietro sopra l'ultima conclusione dell'Huyghens, nel <lb/>supposto che fossero le due parallele OQ, PR condotte infinitamente poco <lb/>distanti fra loro, e quantit&agrave; infinitamente piccole perci&ograve; riuscissero cos&igrave; gli <lb/>archi ST, MN del semicircolo e della semicicloide, come le porzioni QR, OP <lb/>dell'asse e della tangente; si sarebbero potute istituire infinite equazioni diffe&shy;<lb/>renziali, che s'integrerebbero assai facilmente applicandovi il Teorema del <lb/>Torricelli, da cui per via diretta resulterebbe che il tempo speso a passare <lb/>per gl'infiniti tratti della curva AB, ossia per tutto l'arco cicloidale AB, sta <lb/>al tempo per le infinite parti della tangente IB, ossia per tutta intera la tan&shy;<lb/>gente IB, come la somma di tutte le infinite porzioni degli archi circolari, <lb/>ossia tutto il semicerchio AHF, sta alla somma di tutte le porzioni, ossia <lb/>a tutto il diametro AF. </s></p><p type="main">

<s>Essendo poi il tempo speso a passare equabilmente la BI, con la mezza <lb/>velocit&agrave; che si sarebbe acquistata dal mobile dopo la caduta naturale per la <lb/>stessa BI, uguale al tempo speso a passare equabilmente uno spazio doppio, <lb/>con la velocit&agrave; intera; &egrave; chiaro esser medesimo il tempo di passare equabil&shy;<lb/>mente la BI con velocit&agrave; dimidiata, e il tempo di passarla con moto acce&shy;<lb/>lerato, partendosi il mobile dalla quiete. </s>

<s>Ma il tempo della caduta accelerata <lb/>per BI, ossia per AV, &egrave;, per i noti teoremi galileiani, uguale al tempo per <lb/>l'asse AD; dunque rimarrebbe, senz'altro discorso, dimostrata la verit&agrave;, cos&igrave; <lb/>dall'Huyghens stesso in XXV luogo, nel citato libro, proposta: &ldquo; In cycloide, <lb/>cuius axis ad perpendiculum erectus est, vertice deorsum spectante, tempora <lb/>descensus, quibus mobile a quocumque in ea puncto dimissum ad punctum <lb/>imum verticis pervenit, sunt inter se aequalia, habentque ad tempus casus <lb/>perpendicularis per totum axem cycloidis eam rationem, quam semicircum&shy;<lb/>ferentia circuli ad diametrum &rdquo; (Op. </s>

<s>et Tom. </s>

<s>cit., pag. </s>

<s>87). </s></p><p type="main">

<s>Ma l'Huyghens non procede per le vie da noi disegnate, e che a quei <lb/>tempi apparivano nuove: calcando invece le orme dei Matematici antichi, <lb/>egli si attiene piuttosto alle circoscrizioni, affaticandosi di giungere al suo <lb/>intento, col far uso di quel metodo obliquo, e perci&ograve; lungo, con cui si vede <lb/>esser penosamente condotta da lui la XXIV proposizione. </s>

<s>La cosa &egrave; veramente <lb/>notabile, dopo gli esempi pubblicamente dati dal Roberval, dal Torricelli, dal <lb/>Wallis e da altri insigni promotori degl'indivisibili, ma &egrave; dall'altra parte un <lb/>segno manifesto della poca fede, che s'aveva nella sincerit&agrave; di quel metodo, <lb/>pochi anni prima del Leibniz e del Newton: e anche l'Huyghens se ne <lb/>astenne, si perch&egrave; voleva non cadesse ombra di dubbio sopra la verit&agrave; dei <lb/>suoi teoremi, e si per dar prova del suo proprio valore, nel riuscire a dimo&shy;<lb/>strar cose tanto nuove e tanto difficili, non valendosi d'altro, che de'vecchi <lb/>rugginosi strumenti. </s></p><p type="main">

<s>La novit&agrave; per&ograve; delle invenzioni ugeniane non apparisce, da quel che se <pb xlink:href="020/01/2890.jpg" pagenum="515"/>n'&egrave; detto fin qui, che per una parte sola, in quanto cio&egrave;, dall'avere il tempo <lb/>della scesa da qualunque punto della Cicloide al tempo della caduta per <lb/>l'asse, una proporzione sempre costante, qual'&egrave; quella della circonferenza al <lb/>diametro; se ne concludeva per corollario il tautocronismo della stessa Ci&shy;<lb/>cloide: ma ben altre verit&agrave; pi&ugrave; importanti faceva l'Autor conseguire dalle <lb/>verit&agrave; dimostrate, in ordine al cadere i gravi ora liberamente, ora vibrando <lb/>sospes&igrave; dai fili dei pendoli. </s></p><p type="main">

<s>S'accenn&ograve; di sopra che, dall'essere isocrone le cadute per le corde dei <lb/>circoli, male a ragione inferiva Galileo l'isocronismo per gli archi sottesi, <lb/>non essendo l'illazione logicamente valida, se non che rispetto agli archi ci&shy;<lb/>cloidali: ci&ograve; che, rimastosi nella stessa Meccanica galileiana latente, fu primo <lb/>l'Huyghens a produrre alla luce. </s>

<s>Sarebbe per&ograve; da stimarsi la scoperta non <lb/>pi&ugrave; che per una bella speculazione, quando non si fosse potuta applicare alla <lb/>misura dei minimi tempi, n&egrave; si vedeva possibile dall'altra parte la deside&shy;<lb/>rata applicazione, se non col trovare il modo di far descrivere ai pendoli <lb/>archi, non pi&ugrave; di cerchio, ma di cicloide. </s>

<s>L'invenzione, che avrebbe tratte&shy;<lb/>tenuto intorno a un semplice fatto fisico un ingegno volgare, apr&igrave; all'Huy&shy;<lb/>ghens quel campo nuovo nella Geometria, ch'egli chiam&ograve; <emph type="italics"/>Delle evolute,<emph.end type="italics"/> per&shy;<lb/>ch&egrave;, data una curva, sulla convessit&agrave; della quale s'intendesse applicato un <lb/>filo di ugual lunghezza, si proponeva l'Autore di mostrar la linea, che de&shy;<lb/>scriverebbe il capo di esso filo, svolgendosi in modo, che sempre la lunghezza <lb/>svolta si serbasse tangente. </s>

<s>Il particolar teorema poi di questo trattato, dal&shy;<lb/>l'applicazione del quale dipendeva la trasformazione degli archi circolari dei <lb/>pendoli in archi cicloidali, si trova cos&igrave; proposto nella citata terza parte del&shy;<lb/><figure id="id.020.01.2890.1.jpg" xlink:href="020/01/2890/1.jpg"/></s></p><p type="caption">

<s>Figura 322.<lb/>l'Orologio oscil&shy;<lb/>latorio: &ldquo; Semi&shy;<lb/>cycloidis evolu&shy;<lb/>tione, a vertice <lb/>coepta, alia se&shy;<lb/>micyclois de&shy;<lb/>scribitur, evolu&shy;<lb/>tae aequalis et <lb/>similis, cuius <lb/>basis est in ea <lb/>recta, quae cy&shy;<lb/>cloidem evolu&shy;<lb/>tam in vertice <lb/>contingit &rdquo; (pa&shy;<lb/>gina 96). </s></p><p type="main">

<s>Sia ABC <lb/>(fig. </s>

<s>322) semi&shy;<lb/>cicloide, asse <lb/>AD, base DC, AHD semicircolo genitore, a cui in A giunga la GA tangente. </s>

<s><lb/>Sia sulla convessit&agrave; della curva applicato il filo ABC, di cui il capo A, svolto <pb xlink:href="020/01/2891.jpg" pagenum="516"/>intorno a C, si vuol dimostrare che descrive, nella sua evoluzion progressiva, <lb/>una linea AEF eguale e simile all'evolvente, cio&egrave; un'altra semicicloide. </s></p><p type="main">

<s>Si consideri giunta l'evoluzione a un punto qualunque, per esempio E, <lb/>cosicch&egrave; la lunghezza del filo svolto sia BE, intersecante in K l'AG. </s>

<s>Dai <lb/>punti K, E s'alzino alle AG, EK le perpendicolari KM, EM, le quali s'in&shy;<lb/>contrino in M, disegnando il triangolo EMK. </s>

<s>Da B poi si conduca una pa&shy;<lb/>rallela alla base, e raggiunga il semicircolo in H, d'onde si tiri la corda HD. </s>

<s><lb/>Il triangolo rettangolo AHD, che ne nasce, e il triangolo EMK sono uguali, <lb/>essendo in primo luogo equiangoli perch&egrave; per le note propriet&agrave; della Cicloide, <lb/>la tangente EB &egrave; parallela alla corda AH, e perci&ograve; EM, DH lati paralleli, e <lb/>paralleli KM, AD: in secondo luogo poi EK &egrave; uguale ad AH, perch&egrave; EB <lb/>uguaglia per supposizione la porzion di curva AB, la quale, per il corollario <lb/>alla Prima robervalliana, nel capitolo precedente ordinata, &egrave; doppia di KB, e <lb/>perci&ograve; EK &egrave; uguale a BK, ossia ad AH. </s>

<s>Se son dunque veramente, come si <lb/>diceva, i due triangoli rettangoli MEK, AHD uguali, uguali pure saranno i <lb/>semicircoli ad essi circoscritti, onde, a concluder l'intento, riman solo a dimo&shy;<lb/>strare come E sia un punto nella semicicloide generata dallo stesso MEK, ci&ograve; <lb/>che poi &egrave; in conseguenza dell'essere l'arco EK uguale alla porzion di base <lb/>AK, com'&egrave; di fatto, essendo esso arco uguale all'arco AH, a cui, per quel <lb/>che hanno inteso i Lettori dalle dimostrazioni del Ricci e del Nardi, s'ugua&shy;<lb/>glia l'ordinata HB, ossia la AK. Cos&igrave;, comprendendo le proposizioni uge&shy;<lb/>niane IV, V e VI, nella terza parte dell'Opera citata, si dimostrerebbe che <lb/>qualunque altro punto della evoluta AEF &egrave; in una semicicloide generata dal <lb/>ruzzolarsi la ruota HEM su per la via AG, e perci&ograve; &egrave; una curva uguale e <lb/>simile alla ABC semicicloide evolvente. </s></p><p type="main">

<s>Dicemmo che da questa dimostrata propriet&agrave; dipendeva la trasformazione <lb/>degli archi circolari nei cicloidali, descritti dai pendoli oscillatorii. </s>

<s>Immagi&shy;<lb/>nando infatti di aver la disegnata figura capovolta, e intorno a C, punto di <lb/>sospensione del pendolo CF, applicate le due lamine cicloidali CB, CO, conse&shy;<lb/>gue dalle cose fin qui discorse e dimostrate che, svolgendosi e avvolgendosi <lb/>il filo nel vibrare, descrive archi di cicloide uguali e simili a BC, OC, e sem&shy;<lb/>pre fra loro isocroni, qualunque sia l'ampiezza della vibrazione. </s>

<s>Cos&igrave;, com'&egrave; <lb/>noto, prescriveva di fare l'Huyghens stesso ai costruttori degli Orologi della <lb/>nuova invenzione, e cos&igrave; i teoremi astratti della Meccanica venivano applicati <lb/>agli strumenti, da misurare con la massima esattezza i pi&ugrave; piccoli tempi. </s></p><p type="main">

<s>Un'altra importantissima applicazione si soggiungeva avere avuto i me&shy;<lb/>desimi teoremi ugeniani, a determinare cio&egrave;, si direbbe quasi, l'istante, in <lb/>cui cade un grave da un'altezza osservabile. </s>

<s>I predecessori dell'Huyghens <lb/>furono tutti costretti a ricorrere alle esperienze, le quali quanto fossero pe&shy;<lb/>nose e fallaci s'&egrave; veduto nell'altro Tomo di questa Storia della Meccanica, <lb/>per gli esempi di Galileo e del Riccioli. </s>

<s>Ma ora, che &egrave; stato dimostrato avere <lb/>il tempo di qualunque vibrazione intera del pendolo cicloidale, al tempo della <lb/>scesa naturale per l'asse della curva, la proporzione medesima che ha la <lb/>circonferenza al diametro; non occorre di saper altro, per risolvere esatta-<pb xlink:href="020/01/2892.jpg" pagenum="517"/>mente il geloso problema, se non che quanto vada lungo il pendolo dei se&shy;<lb/>condi. </s>

<s>Sia questa lunghezza, nella medesima figura, la CF, la met&agrave; GC della <lb/>quale uguaglier&agrave; l'asse, che secondo l'Huyghens torna precisamente 18 once <lb/>del piede orario. </s>

<s>Si potr&agrave; senz'altro avere il tempo X, impiegato da un grave <lb/>a scendere dall'altezza perpendicolare di quelle 18 once, dalla formula T:X= <lb/>C:D, intendendosi per T il tempo di un secondo, ossia di 60&tprime;, e per C, D <lb/>la circonferenza e il suo diametro, la ragion tra'quali &egrave; presa di 355 a 113. <lb/>Dunque X=T.D/C=19&tprime;+1/10=19&tprime;, 1, molto prossimamente. </s>

<s>Di qui, <lb/>essendo per i noti Teoremi galileiani, gli spazi proporzionali ai quadrati dei <lb/>tempi, si pu&ograve; facilmente rispondere a chi volesse sapere da quanta altezza <lb/>sia sceso nel perpendicolo un grave, in un minuto secondo. </s>

<s>Perch&egrave;, come il <lb/>quadrato di 19, 1, a quello di 60, ossia di 191 a 600, che sono i quadrati <lb/>dei tempi; cos&igrave; lo spazio delle 18 once, a quello che si cerca, e che dovendo <lb/>essere quarto proporzionale dopo 36481, 360000 e 18, si troverebbe di 14 piedi, <lb/>9 once e 6 linee del piede orario, ossia di 15 piedi e un oncia prossimamente, <lb/>fatta la riduzione al piede parigino. </s></p><p type="main">

<s>&ldquo; Quia igitur (per riferir con le parole proprie dell'Autore la nuova mi&shy;<lb/>rabile invenzione) penduli ad secunda scrupula longitudinem diximus esse <lb/>pedum horariorum 3, tempus autem unius oscillationis minimae est ad tem&shy;<lb/>pus descensus perpendicularis ex dimidia penduli altitudine ut circumferentia <lb/>circuli ad diametrum, hoc est ut 355 ad 113; si fiat ut numerus horum prior <lb/>ad alterum, ita tempus unius secundi scrupuli, sive sexaginta tertiorum, ad <lb/>aliud, fiet 19&tprime;+1/10 tempus descensus per dimidiam penduli altitudinem, <lb/>quae nempe est pedis unciarum 18. Sicut autem quadrata temporum ita sunt <lb/>spatia illis temporibus peracta, ergo, si fiat ut quadratum ex 19+1/10, ad <lb/>quadratum ex 60, hoc est ut 36481 ad 360000, ita 18 unciae ad aliud; fient <lb/>ped. </s>

<s>14, unc. </s>

<s>9, lin. </s>

<s>6 altitudo descensus perpendicularis tempore unius se&shy;<lb/>cundi. </s>

<s>Cum autem pes horarius sit ad parisiensem ut 881 ad 864, erit eadem <lb/>altitudo, ad hanc mensuram reducta, proxime pedum 15, et unciae unius &rdquo; <lb/>(ibid., pag. </s>

<s>282, 83). </s></p><p type="main">

<s>In un tempo, in cui si seguitava tuttavia da alcuni Matematici a dubitar <lb/>se le leggi dimostrate da Galileo fossero ipotetiche o realmente corrispon&shy;<lb/>denti con i fatti osservati, si comprende quale efficace modo porgesse l'in&shy;<lb/>venzione ugeniana di verificare le dette leggi. </s>

<s>Ma non si sarebbe potuto recare <lb/>alla Scienza questo benefizio, se prima non si rimovevano dagli sperimenti <lb/>le occasioni delle fallacie, le quali principalmente consistevano nell'incertezza <lb/>di definire, a giudizio dell'occhio, il preciso punto del tempo, in cui il grave <lb/>termina la sua caduta. </s>

<s>Si volse perci&ograve; l'Huyghens a disporre le cose con <lb/>tale ingegno, che il pendolo stesso, nell'atto del suo moto, fosse tutto insieme <lb/>misuratore del tempo, e dello spazio. </s></p><p type="main">

<s>Sia AB (fig. </s>

<s>323) il profilo di una parete o di un'asse di legno, per&shy;<lb/>pendicolarmente eretta, a cui in A sia raccomandato il capo del pendolo ci&shy;<lb/>cloidale AC che, con la sua mezza oscillazione CD, ha da misurare il tempo <pb xlink:href="020/01/2893.jpg" pagenum="518"/>della caduta del grave, tenuto fermo in D, come il pendolo in C, da un te&shy;<lb/>nuissimo filo, che gli congiunge ambedue. </s>

<s>Al cadente poi nel perpendicolo <lb/>&egrave; legato un secondo filo, l'altro capo del quale &egrave; raccomandato a una stri&shy;<lb/><figure id="id.020.01.2893.1.jpg" xlink:href="020/01/2893/1.jpg"/></s></p><p type="caption">

<s>Figura 323.<lb/>sciola di carta, col suo lembo inferiore toccante il punto D, <lb/>e applicata alla parete in modo, da cedere facilmente al ti&shy;<lb/>rare del filo stesso, non preso cos&igrave; lungo, che nel secondar <lb/>la caduta sia tutto scorso, quando da C il pendolo &egrave; ve&shy;<lb/>nuto in D, compiuta la sua mezza vibrazione. </s>

<s>Dunque esso <lb/>pendolo batte sulla striscia di carta, e vi lascia impresso <lb/>il vestigio, perch&egrave; la palla C era stata poco prima tinta di <lb/>filiggine o d'atramento. </s>

<s>Di qui &egrave; manifesto potersi, anche <lb/>finito il caso, osservare lo spazio passato nel tempo della <lb/>mezza scorsa del pendolo, il quale spazio sar&agrave; giusto quant'&egrave; <lb/>la lunghezza del filo tirato, aggiuntavi la lunghezza della <lb/>striscia di carta sotto il segno. </s>

<s>E perch&egrave; importa massi&shy;<lb/>mamente alla precisione dell'esperienza che la scesa del <lb/>pendolo e la caduta naturale del grave incomincino nel <lb/>medesimo istante, ci&ograve; otteneva l'Huyghens abbruciando, <lb/>con accostarvi la fiamma di un cerino, il sopra detto te&shy;<lb/>nuissimo filo di congiunzione. </s>

<s>Cos&igrave; pot&egrave; l'Huyghens stesso <lb/>riscontrar le cose, e dire che le teorie <emph type="italics"/>cum accuratissimis <lb/>experimentis nostris prorsus conveniunt &rdquo;<emph.end type="italics"/> (ibid., pag. </s>

<s>183). </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Dei centri delle oscillazioni, che subito si dissero essere una medesima <lb/>cosa con i centri delle percosse, la Meccanica anch'ebbe dall'Huyghens la <lb/>teoria generale. </s>

<s>Vi s'erano nulladimeno esercitati i Matematici molto prima, <lb/>per rispondere alle domande importune de'gladiatori e dei duellanti, curiosi <lb/>di sapere a qual punto dovessero appioppare il bastone sulle spalle dell'av&shy;<lb/>versario, perch&egrave; ne dovesse maggiore sentir la percossa. </s>

<s>Quei che nelle Mec&shy;<lb/>caniche di Aristotile cercavano i principii, per risolvere il problema, dice&shy;<lb/>vano, come Leonardo da Vinci, che quel punto era verso la cima, perch&egrave; <lb/>ivi il moto &egrave; pi&ugrave; veloce. </s>

<s>Poi pi&ugrave; tardi lo ritirarono verso il centro di gravit&agrave;, <lb/>sapendo che quivi concorre d'ogni parte all'effetto la materia del legno. </s>

<s>Ve&shy;<lb/>nivano per&ograve; l'esperienze a mettere in dubbio ambedue le soluzioni, e spe&shy;<lb/>cialmente la seconda, essendo facile accorgersi dall'altra parte che vi si con&shy;<lb/>siderava, piuttosto la semplice gravit&agrave; del bastone, che la gravit&agrave; di lui, <lb/>congiunta con l'impeto del braccio che lo mena. </s></p><p type="main">

<s>Il principio professato dal Filosofo, che cio&egrave; il moto accresce peso al <lb/>grave mosso, rettamente interpetrato, fu primo ad aprire le vie all'ingegno <lb/>speculativo, il quale ebbe a ripensare che, movendosi nella lunghezza del <pb xlink:href="020/01/2894.jpg" pagenum="519"/>bastone le sezioni materiali via via dalla mano alla cima sempre pi&ugrave; veloci, <lb/>era come se diventassero via via sempre pi&ugrave; gravi. </s>

<s>Conseguiva di qui dover <lb/>essere il centro delle forze che si cercava, nel legno mosso, diverso dal cen&shy;<lb/>tro di gravit&agrave; del legno fermo, e s'intese come non si potrebbe avere altri&shy;<lb/>menti la ragione di questa diversit&agrave;, che ritrovando le proporzioni, secondo <lb/>le quali, nell'agitarsi la verga, crescono i pesi o i momenti alle particelle <lb/>distribuite in tutta la sua lunghezza. </s></p><p type="main">

<s>Si prevede bene, dietro queste considerazioni, come la soluzion del pro&shy;<lb/>blema del centro della percossa nella clava dovesse occorrere a quei soli Ma&shy;<lb/>tematici, che avessero chiara notizia della statica dei momenti, misurati dal <lb/>prodotto dei pesi nelle respettive distanze dai loro punti d'appoggio, d'onde <lb/>ne conseguiva la misura delle forze, o degli impeti, da quegli stessi pesi, <lb/>moltiplicatisi per le velocit&agrave; o per gli spazi passati. </s>

<s>Ma si doveva, anche dopo <lb/>una tale notizia, trovar non poca difficolt&agrave; nell'applicarla, essendo la clava <lb/>tutto un corpo solo: n&egrave; giovava riguardare la sua gravit&agrave; dispersa adunata <lb/>in un centro, richiedendovisi, per riuscir nell'intenzione, la pi&ugrave; giusta mi&shy;<lb/>sura degl'incrementi proporzionali di moto nelle singole particelle, le quali <lb/>essendo infinite non promettevano di darsi resolute, se non a colui, che avesse <lb/>avuta la dottrina matematica degl'infiniti. </s>

<s>La scienza necessaria perci&ograve;, a <lb/>dimostrare il centro della percossa, non sarebbe mancata n&egrave; al Cavalieri, n&egrave; <lb/>al Nardi, n&egrave; al Torricelli: eppure &egrave; notabile, nella storia della Meccanica, <lb/>che lasciassero que'tre grandi nostri Matematici, per s&egrave; e per i loro succes&shy;<lb/>sori, la questione intatta, della quale perci&ograve; rimase tutto il merito agli stra&shy;<lb/>nieri. </s>

<s>Sappiamo che il Roberval diceva di aver trattato, nell'ottavo libro della <lb/>sua Meccanica riformata, <emph type="italics"/>De centro percussionis potentiarum mobilium,<emph.end type="italics"/> e <lb/>ora &egrave; il tempo per noi di narrare i principii e i progressi fatti dal Mate&shy;<lb/>matico francese nell'istituire, e nell'aggiungere alla Scienza della percossa <lb/>questa nuova e nobilissima parte, di che il Borelli stesso trentatre anni di <lb/>poi la lascerebbe in difetto. </s></p><p type="main">

<s>Per risponder dunque con geometrici argomenti alla proposta, che aveva <lb/>dato occasione a queste speculazioni, riguardava il Roberval il bastone cilin&shy;<lb/><figure id="id.020.01.2894.1.jpg" xlink:href="020/01/2894/1.jpg"/></s></p><p type="caption">

<s>Figura 324.<lb/>drico ridotto a una linea materiale, <lb/>che, affissa in una delle sue estremit&agrave;, <lb/>ondeggi liberamente dall'altra. </s>

<s>Sia <lb/>AC (fig. </s>

<s>324) la detta linea, che ri&shy;<lb/>mossa dal suo perpendicolo in AB <lb/>incontri, nello scendere e nel ridursi <lb/>alla sua prima stazione, un ostacolo, <lb/>contro cui si vuol sapere in qual punto <lb/>concentra le forze della percossa. </s>

<s>Qui <lb/>il metodo degl'indivisibili suggeriva <lb/>di riguardare la linea oscillante riso&shy;<lb/>luta in infiniti uguali punti ponderosi, come G, E, B, i momenti dei quali <lb/>vanno via via crescendo a proporzion degli spazi passati nel medesimo tempo, <pb xlink:href="020/01/2895.jpg" pagenum="520"/>ossia degli archi GNK, ELH, BCD, cosicch&egrave;, riducendo a pesi questi stessi <lb/>momenti, mentre nella quiete erano tutti uguali, ora nell'agitazione son cre&shy;<lb/>sciuti nelle dette proporzioni, e perci&ograve; il centro dell'equilibrio, che dianzi <lb/>era nel mezzo, si deve ora esser mutato, e rimane a sapere dove sia sceso. </s></p><p type="main">

<s>A ci&ograve; invocava il Roberval questo teorema, d'assai facile conclusione dai <lb/>principii archimedei: <emph type="italics"/>Due libbre caricate d'ugual numero di pesi, di gran&shy;<lb/>dezze proporzionali, e disposti in distanze proporzionali, son segate dal <lb/>centro dell'equilibrio in parti proporzionali.<emph.end type="italics"/> Ora essendo gli archi GNK, <lb/>ELH, BCD proporzionali alle loro corde GK, EH, BD, e queste e quelli di&shy;<lb/>sposti dal centro A in distanze proporzionali; &egrave; manifesto che la libbra AB <lb/>gravata di tutti i suoi infiniti momenti oscillatorii e la libbra AP gravata <lb/>delle linee BD, EH, GK, e di tutte le altre infinite, che contessono il trian&shy;<lb/>golo ABD, son segate dai loro centri dell'equilibrio o delle gravit&agrave; in parti <lb/>proporzionali. </s>

<s>&ldquo; Centrum autem gravitatis trianguli ABD (conclude il Ro&shy;<lb/>berval il suo ragionamento) dividit AP in Q, adeo ut AQ duplum sit <expan abbr="Pq.">Pque</expan> <lb/>uti demonstravit Lucas Valerius in tractatu suo <emph type="italics"/>De centro gravitatis,<emph.end type="italics"/> itaque <lb/>et O centrum agitationis rectae AB dividit AB in O, adeo ut AO duplum <lb/>sit BO, atque ita inventum est centrum percussionis rectae AB, quod erat <lb/>demonstrandum &rdquo; (Epist. </s>

<s>cartes., P. III, Amstelodami 1683, pag. </s>

<s>330). </s></p><p type="main">

<s>La bella dimostrazione fu inserita nel luogo citato col titolo soprascrit&shy;<lb/>tovi: <emph type="italics"/>Centrum percussionis lineae rectae AB, circulariter rotatum circa <lb/>punctum fixum A, per D. </s>

<s>Roberval anno 1646,<emph.end type="italics"/> nel qual tempo l'ebbe il <lb/>Cartesio, ma ell'era stata ritrovata gi&agrave; da qualche anno, e certamente prima <lb/>del 1644, perch&egrave;, mostrata al Mersenno, questi se ne rallegr&ograve;, e prese ne'suoi <lb/><emph type="italics"/>Cogitata physico-mathem.,<emph.end type="italics"/> a proposito della Meccanica, occasione d'inserir <lb/>la notizia per decidere la questione, che vivamente s'agitava intorno al cen&shy;<lb/>tro della percossa nel bastone o nella spada, pronunziando risolutamente <lb/>questa sentenza: &ldquo; Ensis, cuius percussio maxima est, neque est in illius <lb/>centro gravitatis, neque in mucrone, sed versus ensis dodrantem, a cuspide <lb/>incipiente &rdquo; (Parisiis 1644, pag. </s>

<s>84). </s></p><p type="main">

<s>Ma il Roberval, ritornando sopra a considerare le oscillazioni di quella <lb/>sua linea, vedeva aprirsi la via a speculazioni di ben altra importanza, e <lb/>d'altra nobilt&agrave;, rappresentandoglisi nel moto di lei l'oscillare di un pendolo. </s>

<s><lb/>Riconobbe allora che il centro della percossa di quella era una medesima <lb/>cosa col centro di agitazione di questo, riguardate le forze sotto vario aspetto: <lb/>o in quanto cio&egrave; si concentrano nella linea o nella verga cilindrica, per perco&shy;<lb/>tere con la massima energia in un ostacolo, che le sia contrapposto; o in <lb/>quanto si concentrano nel pendolo, a dare e a mantenere l'impulso di reci&shy;<lb/>procare le sue vibrazioni. </s>

<s>Resultava intanto alla mente del Roberval che le <lb/>vibrazioni del cilindro AB sono isocrone a quelle di un pendolo semplice, <lb/>lungo quanto AO, avendo ambedue in A il centro della sospensione. </s></p><p type="main">

<s>Era, in questa nuova e inaspettata notizia, come la prima e pi&ugrave; lusin&shy;<lb/>ghiera promessa di aver finalmente a risolvere un problema desideratissimo <lb/>dalla Cronometria, e il Roberval, <emph type="italics"/>vigente animi ardore,<emph.end type="italics"/> prosegu&igrave; con l'in-<pb xlink:href="020/01/2896.jpg" pagenum="521"/>trapreso metodo a ricercare i centri dell'agitazione nelle superficie e ne'so&shy;<lb/>lidi, scegliendo, per non trovarsi impedito o arretrato ne'primi passi, le <lb/>figure pi&ugrave; semplici e pi&ugrave; regolari, come i triangoli isosceli, le piramidi o <lb/>i coni. </s></p><p type="main">

<s>Sia il triangolo ABD, nella medesima figura, che oscilli avanti e indie&shy;<lb/>tro intorno al vertice A: risoluto nelle sue linee infinite, tre delle quali siano <lb/>GK, FH, BD, i momenti ridotti a pesi, e de'quali intendasi esser gravata la <lb/>libbra AP, stanno come le porzioni di superficie cilindriche descritte nel&shy;<lb/>l'oscillazione dalle dette linee, ossia come i rettangoli GK.AR, FH.AQ, <lb/>BD.AP, o come i quadrati di AR, AQ, AP, o finalmente come le ordinate <lb/>ER, IN, LM nel trilineo parabolico acuto AML, il centro di gravit&agrave; del quale <lb/>essendo in una ordinata, che sega in Q l'asse, talmente che sia AQ tre quarti <lb/>della AP, come Luca Valerio dimostra nella XXII proposizione del III libro <lb/><emph type="italics"/>De centro gravitatis;<emph.end type="italics"/> dunque in Q sar&agrave; pure il centro della percossa, nel <lb/>triangolo agitato. </s></p><p type="main">

<s>Se BAD rappresenta una piramide o un cono, le sezioni de'piani o dei <lb/>circoli aventi per diametri GK,.FH, BD stanno come i quadrati delle distanze <lb/>AR, AQ, AP dal vertice, e perci&ograve; i loro momenti avranno la ragion com&shy;<lb/>posta di essi quadrati e delle loro radici, ossia staranno come i cubi delle <lb/>distanze AR, AQ, AP, ossia come le ordinate ER, IN, ML nel trilineo AML, <lb/>supposto che la semiparabola AIM sia cubicale. </s>

<s>Di qui &egrave; che il centro della <lb/>percossa del solido sar&agrave; in Q, dove cade sulla libbra AP quell'ordinata, che <lb/>passa per il centro di gravit&agrave; del trilineo acuto. </s></p><p type="main">

<s>A indicar la posizione di questo centro sull'asse occorreva opportuna la <lb/>proposizione LIV del trattato <emph type="italics"/>Dei centri di gravit&agrave;<emph.end type="italics"/> del Torricelli, pubblicato <lb/>da noi qui addietro nel capitolo V: proposizione che l'Autore diceva di aver <lb/>a quel modo generalmente conclusa <emph type="italics"/>ex doctrina parabolarum.<emph.end type="italics"/> Fosse nota <lb/>o no al Roberval questa generalissima dottrina, &egrave; un fatto che, nel caso par&shy;<lb/>ticolare della parabola cubica, sapeva benissimo il Matematico parigino che <lb/>il centro di gravit&agrave; del trilineo circoscritto da tale curva sega l'asse cos&igrave;, <lb/>che la parte al vertice stia alla rimanente come quattro sta a uno: e tale <lb/>concludeva essere l'indicazione del centro della percossa nella piramide o nel <lb/>cono. </s>

<s>Per la teoria de'pendoli poi derivava il Roberval stesso dalle sue pro&shy;<lb/>posizioni il seguente corollario: <emph type="italics"/>I pendoli semplici, isocroni ai composti della <lb/>figura ABD, che ora sia triangolo, ora piramide o cono, vanno lunghi nel <lb/>primo caso per tre quarti dell'altezza del triangolo, e nel secondo per quat&shy;<lb/>tro quinti dell'altezza del cono.<emph.end type="italics"/> Nel caso per&ograve; che la sospensione fosse fatta <lb/>dal mezzo P della base, il Roberval forse non ritrov&ograve; il centro della percossa <lb/>altro che per il triangolo, dicendo che divide l'asse in due parti uguali, a <lb/>una delle quali perci&ograve; corrisponderebbe la lunghezza del pendolo, che fa nel <lb/>medesimo tempo il medesimo numero di vibrazioni. </s></p><p type="main">

<s>Dicemmo che forse fu cos&igrave;, perch&egrave; la regola fin qui seguita veniva, nelle <lb/>dette figure sospese per la base, a complicarsi di troppo: ond'ebbe il Ro&shy;<lb/>berval a cercare altre vie, quando volle proporsi figure di diversa indole dalle <pb xlink:href="020/01/2897.jpg" pagenum="522"/>precedenti, come per esempio il settor di cilindro, che, essendo un solido co&shy;<lb/>lonnare ogni sezion del quale &egrave; un settore di circolo va sotto la medesima <lb/>invenzione di esso settor circolare. </s></p><p type="main">

<s>Se sia, nella medesima figura, AFLH il detto settore, col raggio per&shy;<lb/>pendicolare AL sospeso dal punto A, intorno al quale si supponga oscillare <lb/>avanti e indietro dal piano, sopra cui s'&egrave; disegnato; ritrov&ograve; il Roberval che <lb/>il centro della percossa nella figura cade in P, a una distanza da A, che sia <lb/>quarta proporzionale dopo la corda, l'arco sotteso, e tre quarti del raggio; <lb/>cosicch&egrave;, fatto AQ=3/4 AL, sarebbe quel centro indicato dalla relazione <lb/>FH:FLH=AQ:AP. </s>

<s>Di qui resulta: I.o Che, essendo l'arco di grandezza <lb/>finita, e perci&ograve; sempre maggiore della sua corda, il punto P riman sempre <lb/>al di sotto di <expan abbr="q.">que</expan> II.o Che, quando fosse FLH=4/3 FH, tornerebbe AP=AL, <lb/>ossia il centro della percossa sarebbe sceso nell'infimo punto del settore. </s>

<s><lb/>III.o Finalmente che, quando la proporzione dell'arco alla sua corda fosse <lb/>maggiore di quattro a tre, AP allora sarebbe maggiore di AL, e ci&ograve; vorrebbe <lb/>dire che il centro della percossa &egrave; passato fuori del settore, con esempio non <lb/>raro, ma pur notabile nella risoluzione di cos&igrave; fatti problemi, che, applicati <lb/>ai pendoli propri, dicono che il pendolo semplice isocrono pu&ograve; talvolta andar <lb/>pi&ugrave; lungo di quello composto. </s></p><p type="main">

<s>Se avesse il Roberval, in questo soggetto, dimostrato altri teoremi non <lb/>&egrave; ora a investigarsi da noi, lasciandone la cura ai dotti Francesi, che, am&shy;<lb/>biziosi di primeggiare sopra le altre nazioni, reintegrando, cos&igrave; per ci&ograve; che <lb/>riguarda i centri delle percosse, come per le altre sue sette parti, la Mecca&shy;<lb/>nica robervalliana, darebbero un esempio ammirabile al mondo di quell'alto <lb/>fastigio, a cui diceva il loro connazionale, contemporaneo a Galileo, di avere <lb/>eretta dai fondamenti la Scienza nuova del moto. </s>

<s>A noi basti di aver rac&shy;<lb/>colti questi pochi materiali, preparati per soprapporsi come pietre angolari <lb/>nel superbo edifizio, ma rimasti, a quel che sembra, senza forma e dispersi <lb/>nella gelosa officina, alla quale non fu lasciato entrare che al solo Marino <lb/>Mersenno. </s>

<s>Egli, secondando quel suo genio, che per altre parti di questa <lb/>Storia &egrave; oramai ben conosciuto, proponeva a risolvere i problemi de'centri <lb/>delle oscillazioni o delle percosse a quanti matematici incontrava, non per&shy;<lb/>donando, per esempio, a Onorato Fabry, bench&egrave; sapesse il capo strambo <lb/>ch'egli era, n&egrave; a Cristiano Huyghens, bench&egrave; lo vedesse ancora cos&igrave; giova&shy;<lb/>netto. </s>

<s>Ma il Roberval, che sotto sotto stimolava il Frate, ardeva di un gran&shy;<lb/>dissimo desiderio ch'entrasse nell'agone, per cimentarne le forze, il Carte&shy;<lb/>sio, allora e sempre odiosissimo suo rivale, e il Cartesio rispondeva all'invito <lb/>in una lettera sottoscritta il di 2 Marzo 1646, stabilendo al Mersenno, che <lb/>glie ne aveva fatto richiesta pochi giorni prima, per l'invenzion de'centri <lb/>delle percosse, le tre regole seguenti: </s></p><p type="main">

<s>I. </s>

<s>Se il corpo ha una sola dimensione sensibile, quale si pu&ograve; supporre <lb/>avere un cilindro, che sia pochissimo gresso, &ldquo; centrum eius agitationis est <lb/>in illo loco huius corporis, quod transit per centrum gravitatis trianguli ABCD <lb/>(nella medesima figura) cum describit triangulum illum per motum suum, <pb xlink:href="020/01/2898.jpg" pagenum="523"/>nimirum in puncto P, quod relinquit trientem longitudinis AC versus basin &rdquo; <lb/>(Epist., P. III cit., pag. </s>

<s>317). &mdash; II. </s>

<s>Se il corpo ha due dimensioni sensibili, <lb/>come la superficie del triangolo isoscele ABD, &ldquo; tum centrum agitationis illius <lb/>est in puncto lineae AP perpendicularis basi BD, quod transit per centrum <lb/>gravitatis pyramidis, quam describit triangulum, tum cum se movet circa <lb/>punctum A, nimirum in puncto Q, adeo ut QP sit quadrans lineae AP &rdquo; (ibid.). </s></p><p type="main">

<s>Passa il Cartesio a dare la terza regola, quando cio&egrave; il corpo abbia tre <lb/>dimensioni sensibili: regola, che poi spieg&ograve; meglio, quando il Mersenno, met&shy;<lb/>tendosi a riscontrare le cose lette, le trov&ograve; discordare dalla esperienza. </s>

<s>Di ci&ograve; <lb/>sparse voce fra gli amici, nel numero de'quali era il signore di Cavendisck, <lb/>gentiluomo inglese, che si trovava allora a Parigi, e il Cavendisck si rivolse <lb/>direttamente allo stesso Cartesio, che il di 30 Marzo di quello stesso anno 1646 <lb/>gli rispondeva in questa sentenza: Non deve far maraviglia se le mie regole <lb/>non rispondono ai fatti, concorrendo ad alterarle gl'impedimenti, che il corpo <lb/>oscillante ha dal sostegno, e principalmente dal mezzo dell'aria. </s>

<s>Del resto <lb/>il mio modo di ragionare &egrave; geometrico, e non pu&ograve; indurre in fallacie. </s>

<s>Se sia <lb/>un corpo solido, comunque irregolare, ABCD (fig. </s>

<s>325) sospeso in A, e avente <lb/><figure id="id.020.01.2898.1.jpg" xlink:href="020/01/2898/1.jpg"/></s></p><p type="caption">

<s>Figura 325.<lb/>nel perpendicolo AO il centro della sua gravit&agrave; <lb/>naturale, io lo considero diviso in infinite sezioni <lb/>parallele all'orizonte, le quali nell'agitarsi descri&shy;<lb/>vono porzioni di superficie cilindriche, ch'io riduco <lb/>a piramidi tutte appuntate in A, e che, stando in <lb/>ragion composta delle basi e delle altezze, mi danno <lb/>la proporzione dei loro momenti. </s>

<s>&ldquo; Vis enim agita&shy;<lb/>tionis earum, non saltem ex modo celeritatis earum <lb/>aextimatur, cuius differentia repraesentatur per di&shy;<lb/>versas altitudines horum solidorum; verum etiam per diversam quantitatem <lb/>materiae ipsarum, quae per diversas magnitudines basium repraesentatur &rdquo; <lb/>(ibid., pag. </s>

<s>322). Poi da ciascuno degli infiniti punti dell'asse AO immagin&ograve; che <lb/>sian segate nel mezzo, condotte perpendicolarmente a lui, altrettante linee <lb/>tutte proporzionali alle piramidi che iusiston sopr'esse, come per esempio <lb/>sarebbero le linee FG, HI, e dice che nel centro di gravit&agrave; della figura <lb/>piana AFHOIG, tessuta delle dette linee infinite, sta il centro dell'agitazione <lb/>che si cercava. </s></p><p type="main">

<s>Questa, e l'altra epistola cartesiana, che 28 giorni prima aveva diretta&shy;<lb/>mente ricevuta, il Mersenno mostr&ograve; al Roberval, il quale not&ograve; che le prime <lb/>due regole in conseguenza riscontravano con le sue: Voleva per&ograve; esaminarne <lb/>pi&ugrave; sottilmente le ragioni, e intanto, non sazio ancora di tentare intorno a <lb/>ci&ograve; le forze dell'ingegno matematico del Cartesio, &mdash; domandategli, padre, <lb/>diceva a esso Mersenno, se sa dirvi dove stia il centro della percossa nel <lb/>triangolo isoscele, quando sia sospeso dal mezzo della base, o quanta sia la <lb/>lunghezza del pendolo, che va sotto il medesimo tempo di un cono sospeso <lb/>per la cima. </s>

<s>&mdash; </s></p><p type="main">

<s>Il Mersenno, qualunque poi ne fosse la ragione, fece a nome suo far la <pb xlink:href="020/01/2899.jpg" pagenum="524"/>richiesta a una terza persona, alla quale il Cartesio francamente rispondeva <lb/>che, quanto al triangolo, il centro della percossa divide l'asse in due parti <lb/>uguali. </s>

<s>&ldquo; Nam sumptis ad libitum in perpendiculari CD (fig. </s>

<s>326) punctis <lb/>E, H a medio E aequaliter distantibus, tum, ductis lineis FG, HI parallelis <lb/>basi, rectangulum CFG, semper aequale est rectangulo CHI, et consequenter <lb/><figure id="id.020.01.2899.1.jpg" xlink:href="020/01/2899/1.jpg"/></s></p><p type="caption">

<s>Figura 326.<lb/>figura, cuius centra gravitatis quaerenda essent, ex prae&shy;<lb/>scripto regulae meae ad habendum centrum agitationis <lb/>huius trianguli, foret quadrangularis, et haberet centrum <lb/>suum gravitatis in puncto E &rdquo; (ibid., pag. </s>

<s>336). Quanto al <lb/>pendolo isocrono al cono, soggiungeva il Cartesio, a che <lb/>me ne richiede il Mersenno? </s>

<s>Non aveva egli quella lun&shy;<lb/>ghezza dalla mia terza regola, con faeile calcolo, di che <lb/>perci&ograve; a lui, e al signore di Roberval ne lasciavo la cura? </s>

<s><lb/>Ma se vogliono risparmiarsi questa fatica, dir&ograve; a loro <lb/>la cosa, ch'&egrave; tale: &ldquo; nimirum, tum cum pyramis aut conus per apicem su&shy;<lb/>spensus est, altitudo eius debet esse, secundum longitudinem funependuli, <lb/>veluti quinque ad quatuor &rdquo; (ibid.). </s></p><p type="main">

<s>Esaminatesi dal Roberval le tre regole cartesiane, con quell'animosit&agrave; <lb/>che gl'intorbidava il giudizio, sentenzi&ograve; che i principii, dietro i quali erano <lb/>state condotte, non potevano approvarsi, perch&egrave;, venendo a farne l'applica&shy;<lb/>zione ai centri della percossa ne'settori di cilindro o di cerchio, conducevano <lb/>a conseguenze false. </s>

<s>Ritornando infatti alla figura 324, che ha in AFLH di&shy;<lb/>segnato un settor circolare, la superficie, dal centro di gravit&agrave; della quale <lb/>sarebbe, secondo la regola cartesiana, indicato nel detto settore il centro della <lb/>percossa, &egrave; il trilineo parabolico AML, per cui tornerebbe esso centro in Q, <lb/>distante da A per tre quarti di AL. </s>

<s>Ma io ho dimostrato, diceva il Rober&shy;<lb/>val, che il punto richiesto deve essere di Q sempre pi&ugrave; basso, qual sarebbe <lb/>per esempio P, n&egrave; pu&ograve; questo concorrere mai con quello, se non a patto <lb/>che l'arco del settore sia uguale alla corda, ossia quando l'angolo FAH fosse <lb/>minimo cos&igrave;, da poter aversi la figura per un triangolo isoscele, in cui vera&shy;<lb/>mente il centro della percossa cade sull'asse a tre quarti di distanza dal <lb/>punto di sospensione. </s>

<s>Ma per il settore di grandezza finita, che naturalmente <lb/>&egrave; quello sopra cui pu&ograve; cader l'invenzione, il metodo cartesiano, sentenzio&shy;<lb/>samente concludeva il Roberval, &egrave; manifestamente falso. </s></p><p type="main">

<s>Pervenute a notizia del Cartesio queste censure, diceva per risposta che <lb/>sarebbero allora convinte di falsit&agrave; le sue conclusioni, quando quelle dell'av&shy;<lb/>versario si dovessero aver per indubitate. </s>

<s>Ma perch&egrave; ci&ograve; non apparisce dal <lb/>suo discorso, &ldquo; nihil me iudice aliud probat quam quod praetendat ut plus <lb/>authoritati eius, quam meis rationibus tribuam &rdquo; (ibid., pag. </s>

<s>331). Nella epi&shy;<lb/>stola infatti, nella quale si facevano al Cavendisck notare gli errori del Car&shy;<lb/>tesio, lasci&ograve; il Roberval di dimostrare la proposizione del centro della per&shy;<lb/>cossa nei settori, <emph type="italics"/>quia aequo longior esset<emph.end type="italics"/> (ibid., pag. </s>

<s>326), ma egli era <lb/>sicuro della verit&agrave; di lei, confermata poi da tutti i Matematici, e principal&shy;<lb/>mente dall'Huyghens, nella propos. </s>

<s>XXI della quarta parte dell'Orologio oscil-<pb xlink:href="020/01/2900.jpg" pagenum="525"/>latorio, dove dice che il pendolo isocrono al settore di circolo ha lunghezza <lb/><emph type="italics"/>trium quartarum rectae, quae sit ad radium ut arcus ad subtensam<emph.end type="italics"/><lb/>(pag. </s>

<s>159). N&egrave; l'Huyghens per&ograve; n&egrave; nessun altro di que'matematici avrebbero <lb/>cos&igrave; assolutamente sentenziato contro il Cartesio, come fece il Roberval, esa&shy;<lb/>minando la questione con pi&ugrave; sincero giudizio di lui. </s></p><p type="main">

<s>La prima regola per verit&agrave;, scritta nella Lettera al Mersenno, appresso <lb/>un rigido Geometra non troverebbe scusa, perch&egrave; quel che si chiama trian&shy;<lb/>golo &egrave; un settore di cerchio, e si sa bene quanto sia diverso il centro di <lb/>gravit&agrave; nelle due figure, quando siano, come sempre si suppone in questi <lb/>esempi, di grandezze finite. </s>

<s>Anche la seconda non si pu&ograve; dlre esattamente <lb/>descritta, ma la colpa maggiore &egrave; della terza, lusingatrice come chi prometta <lb/>di torre uno di difficolt&agrave;, mettendolo in un'altra maggiore; quasi che il tro&shy;<lb/>var il centro di gravit&agrave; nelle superfice piane fosse pi&ugrave; facile, che trovar nel <lb/>solido direttamente il centro della percossa. </s></p><p type="main">

<s>Nel caso per&ograve; che il solido fosse di figura regolare, e fosse di pi&ugrave; de&shy;<lb/>terminato il modo della sua sospensione, come nel cono pendulo dalla cima, <lb/>il metodo era per s&egrave; sufficiente, e aveva infatti condotto il Cartesio a una <lb/>conclusione, confermata da tutti per vera. </s>

<s>N&egrave; differiva questo metodo carte&shy;<lb/>siano in sostanza da quello del Roberval, come non ne differiva l'altro, con <lb/>cui si ricercava il centro della percossa nel triangolo isoscele pendulo dalla <lb/>base, applicandosi qui alla libbra i pesi proporzionali alle piramidi, o alle <lb/>linee rette nella figura piana, mentre l&agrave; le si applicavano que'medesimi pesi <lb/>ridotti all'egualit&agrave; dinamica dei momenti. </s>

<s>Ma la virt&ugrave; di concludere derivava <lb/>in ambedue gli autori dall'essere i rettangoli, fatti delle equidistanti dal mezzo <lb/>dell'asse e dalle rispettive distanze dai punti di sospensione, uguali, come, <lb/>prese per esempio nella medesima figura 326 le due FG, HI, o le loro duple <lb/>GM, IN, si vede conseguire dall'equazione GM:IN=DF:DH=CH:CF. </s>

<s><lb/>Il Roberval considerava la libbra CD gravata de'momenti <foreign lang="greek">p</foreign>GM.CF, <foreign lang="greek">p</foreign>IN.CH, <lb/>i quali eguagliandosi insieme essi stessi, come pure s'uguagliano gli altri loro <lb/>simili infiniti, debbono avere nel mezzo di essa CD il centro del loro equi&shy;<lb/>librio. </s>

<s>Il Cartesio trasformava i momenti in piramidi, le basi delle quali rap&shy;<lb/>presentassero la quantit&agrave; di materia, e le altezze la velocit&agrave;: e trovate que&shy;<lb/>ste piramidi uguali, le linee, secondo la regola prese ad esse proporzionali, <lb/>intessono il rettangolo PQ, e gravitando tutte ugualmente sopra la libbra CD, <lb/>s'equilibrano perci&ograve; intorno al centro della figura. </s></p><p type="main">

<s>Dunque il Roberval, condannando senza discrezione il Cartesio, condan&shy;<lb/>nava insieme anche s&egrave; stesso: che se voleva esser pi&ugrave; giusto doveva dire <lb/>piuttosto che la terza regola cartesiana non era cos&igrave; generale come l'Autore <lb/>la spacciava, ma solamente applicabile in alcuni esempi pi&ugrave; semplici di figure <lb/>regolari, e cos&igrave; confessare che n&egrave; egli n&egrave; il suo emulo, guali che si fossero <lb/>i progressi fatti, non avevano per&ograve; ancora trovato il metodo universale di ri&shy;<lb/>solvere questo nuovo genere di problemi. </s></p><p type="main">

<s>Que'progressi nonostante non giovarono alla Scienza, perch&egrave; ne rimase <lb/>per qualche tempo ne'soli privati commerci epistolari la notizia: e avendo <pb xlink:href="020/01/2901.jpg" pagenum="526"/>il Mersenno nel 1644 annunziato, senza dir le ragioni, che il centro della <lb/>percossa nella spada o nella verga cade in parte, distante dalla punta il dop&shy;<lb/>pio che dalla impugnatura; Isacco Vossio nel 1666, come aveva condannate <lb/>tutte le altre opinioni, cos&igrave; non risparmiava quella di coloro &ldquo; qui maximam <lb/>statuunt percussionem provenientem ab ea parte ensis, quae dodrante abest <lb/>a mucrone &rdquo; (<emph type="italics"/>De Nili orig.,<emph.end type="italics"/> Hagae Com. </s>

<s>1666, pag. </s>

<s>165-66). </s></p><p type="main">

<s>Poco prima che si pubblicasse l'Orologio oscillatorio, e in quel tempo <lb/>che il Wallis attendeva a dar perfezione alla terza parte della sua Mecca&shy;<lb/>nica, si divulgarono le epistole al Mersenno e al Cavendisck, dove il Car&shy;<lb/>tesio e il Roberval stabilivano le regole, e annunziavano le conclusioni dei <lb/>loro teoremi. </s>

<s>O si fosse inspirato a coteste letture, o fosse il frutto di spe&shy;<lb/>culazioni sue proprie, &egrave; un fatto ch'esso Wallis, aggiungendo in fine al suo <lb/>trattato <emph type="italics"/>De percussione<emph.end type="italics"/> la proposizione XV, nella quale si sottoponevano al <lb/>calcolo le forze, che si concentrano in un punto a dare la massima percossa; <lb/>non fa altro se non che ordinare i teoremi cartesiani o robervalliani, dimo&shy;<lb/>strandoli col medesimo metodo e ripetendone talvolta gli errori, come per <lb/>esempio intorno al centro dell'oscillazione della piramide o del cono, indi&shy;<lb/>cato al medesimo modo che dal Cartesio e dal Roberval, ma tanto diversa&shy;<lb/>mente da quel che poi trov&ograve; l'Huyghens, nella XXII proposizione della P.IV <lb/>dell'<emph type="italics"/>Orologio oscillatorio<emph.end type="italics"/> (ediz. </s>

<s>cit., pag. </s>

<s>166, 67), che Giacomo Bernoulli <lb/>ebbe ad accusar pubblicamente il Wallis di avere sbagliato: &ldquo; Wallisius in <lb/>cono ex. </s>

<s>gr. </s>

<s>aliud percussionis, Hugenius aliud oscillationis centrum assignat. </s>

<s><lb/>Fallitur enim Wallisius in eo quod integrae basi coni, circulisque basi pa&shy;<lb/>rallelis, non maiorem distantiam ab axe rotationis, celeritatemque tribuit, ea <lb/>quam ipsa horum circulorum centra obtinent &rdquo; (<emph type="italics"/>Opera,<emph.end type="italics"/> T. I, Genevae 1744, <lb/>pag. </s>

<s>464). Il Wallis infatti (chiamato <emph type="italics"/>a<emph.end type="italics"/> l'asse, <emph type="italics"/>b<emph.end type="italics"/> il raggio della base del <lb/>cono) aveva indicata la distanza D del centro dell'oscillazione dal vertice con <lb/>l'equazione D=4/5<emph type="italics"/>a,<emph.end type="italics"/> mentre &egrave; veramente D=4/5<emph type="italics"/>a<emph.end type="italics"/>+<emph type="italics"/>b2<emph.end type="italics"/>/5<emph type="italics"/>a,<emph.end type="italics"/> per cui l'in&shy;<lb/>dicazion wallisiana &egrave; in difetto dalla vera dimostrata dall'Huyghens del quinto <lb/>della terza proporzionale, dopo l'altezza del cono, e il raggio della base. <lb/><figure id="id.020.01.2901.1.jpg" xlink:href="020/01/2901/1.jpg"/></s></p><p type="caption">

<s>Figura 327.</s></p><p type="main">

<s>Si propone anche il Wallis in primo luogo <lb/>il centro della percossa nella linea materiale o <lb/>nella sottilissima verga cilindrica AB (fig. </s>

<s>327), <lb/>la quale egli immagina rotarsi intorno al <lb/>punto A, per cadere liberamente sul piano AC. </s>

<s><lb/>Divide essa verga in infinite sezioni uguali, <lb/>che crescono via via i loro momenti a propor&shy;<lb/>zione delle distanze, come le linee del trian&shy;<lb/>golo ACD: e ne conclude che, essendo AC <lb/>libbra sopra la quale s'intendano gravare, a <lb/>proporzione di esse linee, i momenti; il ri&shy;<lb/>chiesto centro della percossa, nella detta verga, risponde in E, dove cade <lb/>la linea, che passa per il centro di gravit&agrave; del piano triangolare. </s></p><pb xlink:href="020/01/2902.jpg" pagenum="527"/><p type="main">

<s>Se il percuziente &egrave; un triangolo isoscele, appuntato in A con l'apice, le <lb/>sezioni e le velocit&agrave; crescono come le distanze, e perci&ograve; i momenti come i <lb/>quadrati di esse distanze, o come le ordinate del trilineo parabolico ACD <lb/>(fig. </s>

<s>328), ond'&egrave; che se FE &egrave; tra queste ordinate quella, che passa per il <lb/>baricentro di esso trilineo, in E cader&agrave; il centro della percossa. </s>

<s>Se poi <lb/>suppongasi il triangolo AB trasformato in un cono, <lb/><figure id="id.020.01.2902.1.jpg" xlink:href="020/01/2902/1.jpg"/></s></p><p type="caption">

<s>Figura 328.<lb/>crescendo le sezioni di lui come i quadrati delle di&shy;<lb/>stanze, e le velocit&agrave; come le semplici distanze dal <lb/>centro della rotazione, i momenti progrediranno <lb/>come i cubi delle distanze medesime, e dal punto <lb/>E pure, da cui s'intenda pendere nella libbra l'or&shy;<lb/>dinata, che passa per il centro di gravit&agrave; del trilineo <lb/>parabolico cubico ACD; verr&agrave; indicato il luogo, dove <lb/>il cono percote con la massima energia. </s></p><p type="main">

<s>Mirabile &egrave; in verit&agrave; la legge dinamica di questi <lb/>progressi: un punto, come sarebbe F nella fig. </s>

<s>327, <lb/>acquista movendosi per percotere la potenza della <lb/>linea GH, ossia della parabola di grado zero; la linea <lb/>acquista la potenza di un triangolo, ossia della pa&shy;<lb/>rabola di grado uno; il triangolo quella di una parabola di grado due, e <lb/>il cono o la piramide di una parabola di grado tre. </s>

<s>Il centro poi della per&shy;<lb/>cossa, nell'ingradarsi cos&igrave; il percuziente dal punto alla linea, dalla linea <lb/>alla superficie, dalla superficie al solido; sega cos&igrave; la libbra, che la parte al <lb/>vertice stia alla rimanente come uno a due, come due a tre, come tre a <lb/>quattro, come quattro a cinque: intanto che, lusingato il Wallis dal mirabile <lb/>ordinamento di questa serie, cred&egrave; che seguitasse anche al di l&agrave; de'pochi, <lb/>e cos&igrave; semplici esempi considerati. </s>

<s>&ldquo; Atque ad eamdem formam, mutatis <lb/>mutandis, procedendum erit, quaecumque fuerit figura corporis moti, sive <lb/>ordinata sive utcumque inordinata, et ubicumque ponatur centrum rotationis <lb/>&ldquo; (Londini 1871, pag. </s>

<s>679). Ma avrebbe il Roberval anche a lui ripetute le <lb/>obiezioni fatte al Cartesio, e noi concluderemo che nessuno dei tre grandi <lb/>Matematici s'era ancora incontrato in quella regola universale, che si desi&shy;<lb/>derava, e dalla quale solamente si deciderebbe con autorit&agrave; di scienza se <lb/>sian sempre e in tutti i casi una medesima cosa i centri dell'oscillazione, <lb/>e della percossa. </s></p><p type="main">

<s>Intanto quel giovanetto, a cui aveva il Mersenno proposto a risolvere i <lb/>problemi robervalliani, era divenuto l'autore dell'<emph type="italics"/>Orologio oscillatorio,<emph.end type="italics"/> nella <lb/>introduzione alla quarta parte della quale opera narrava come, arretratosi da <lb/>principio alle difficolt&agrave; nel primo aggresso incontrate, poi le superasse feli&shy;<lb/>cemente, all'occasione di cercare una regola matematica, per temperare i pesi <lb/>al pendolo del suo nuovo automato, deducendo quella stessa regola da prin&shy;<lb/>cipii pi&ugrave; certi, e pi&ugrave; generali di quel che non avessero fatto i suoi prede&shy;<lb/>cessori. </s>

<s>Erano cotali principii illustrati dall'Huyghens per definizioni, e sta&shy;<lb/>biliti sopra ipotesi nuove, d'onde venivasi a concluder l'intento nella quinta <pb xlink:href="020/01/2903.jpg" pagenum="528"/>proposizione dell'opera e della parte citata, apparecchiatesi gi&agrave; le quattro <lb/>precedenti per lemmi. </s></p><p type="main">

<s>Siano i due pesi A, B (fig. </s>

<s>329) sulla leva AC: tenderanno a scendere <lb/>intorno al centro C, con momenti misurati da A.AC+B.BC. </s>

<s>Ma se nei <lb/>punti A&prime;, B&prime; si sospenderanno due <lb/><figure id="id.020.01.2903.1.jpg" xlink:href="020/01/2903/1.jpg"/></s></p><p type="caption">

<s>Figura 329.<lb/>altri pesi A&prime;, B&prime;, uguali ai primi <lb/>e a distanze uguali dal centro, si <lb/>far&agrave; l'equilibrio. </s>

<s>Ora, essendo in D <lb/>il centro di gravit&agrave; dei detti pesi <lb/>A, B, &egrave; manifesto che rimarr&agrave; pure <lb/>fra questi l'equilibrio, ridotti che <lb/>siano in esso centro, e perci&ograve; i <lb/>momenti di A&prime; e di B&prime;, ossia di A <lb/>e di B, equivarranno al momento <lb/>unico di A e di B concentrati in <lb/>D insieme, e sar&agrave; insomma A.AC+B.BC=(A+B)DC, come per <lb/>altre vie pi&ugrave; oblique dimostra l'Huyghens, nella sua prima proposta, in que&shy;<lb/>sta forma: <emph type="italics"/>Ponderibus quotlibet, ad eamdem partem plani existentibus, si <lb/>a singulorum centris gravitatis agantur in planum illud perpendiculares; <lb/>hae singulae in sua pondera ductae tantundem simul efficient, ac perpen&shy;<lb/>dicularis, a centro gravitatis ponderum omnium in planum idem cadens, <lb/>ducta in pondera omnia<emph.end type="italics"/> (pag. </s>

<s>123). </s></p><p type="main">

<s>Che se A, B sono uguali, dalle cose dimostrate torner&agrave; AC+BC= <lb/>2 DC, per facile corollario, di cui nonostante fece l'Huyghens soggetto alla <lb/>sua proposizione seconda: <emph type="italics"/>Positis quae prius, si pondera omnia sint aequa&shy;<lb/>lia, dico summam omnium perpendicularium aequari perpendiculari a cen&shy;<lb/>tro gravitatis ductae, secundum ponderum numerum<emph.end type="italics"/> (pag. </s>

<s>125). </s></p><p type="main">

<s>Rimossi A&prime;, B&prime; contrappesi della leva, i pesi A, B insieme col punto D <lb/>scenderanno per gli archi AF, BE, DH dalle altezze perpendicolari CF, CE, CH, <lb/>uguali alle distanze AC, BC, DC: e perci&ograve;, sostituite queste distanze nell'equa&shy;<lb/>zione data dalla prima, riman senz'altro dimostrata la terza proposizione <lb/>ugeniana: <emph type="italics"/>Si magnitudines quaedam descendant omnes vel ascendant, licet <lb/>inaequalibus intervallis; altitudines descensus vel ascensus cuiusque, in <lb/>ipsam magnitudinem ductae, efficient summam productorum aequalem ei, <lb/>quae fit ex altitudine descensus vel ascensus centri gravitatis omnium ma&shy;<lb/>gnitudinum, ducta in omnes magnitudines<emph.end type="italics"/> (ibid.). </s></p><p type="main">

<s>Di qui, e dal principio fondamentale dinamico, che cio&egrave; un grave, scen&shy;<lb/>dendo e riflettendo in alto il suo moto, giunge alla precisa altezza perpen&shy;<lb/>dicolare da cui fu sceso, e non pi&ugrave; in alto, perch&egrave; la forza non pu&ograve; dar pi&ugrave; <lb/>di quel ch'ella ha, e non pi&ugrave; in basso dando essa forza di meno, perch&egrave; si <lb/>suppone che di lei nulla si perda, e che produca tutto il suo effetto; l'Huy&shy;<lb/>ghens conclude la sua quarta proposizione, che &egrave; tale: Siano i tre corpi <lb/>A, B, C (fig. </s>

<s>330) connessi colla verga senza peso DC, nell'atto di girare <lb/>intorno al centro D, per sceudere a quietarsi nel perpendicolo DF: e giunti <pb xlink:href="020/01/2904.jpg" pagenum="529"/>i detti corpi in G, H, K, supponiamo che incontrino un ostacolo, in cui ur&shy;<lb/>tando si sciolgano dai loro legami, e risaltino A in L, B in M, C in N, dove <lb/>essendo, risponda in P il loro comun centro di gravit&agrave;, mentre trovavasi <lb/><figure id="id.020.01.2904.1.jpg" xlink:href="020/01/2904/1.jpg"/></s></p><p type="caption">

<s>Figura 330.<lb/>dianzi in E, quand'erano connessi con la verga: &egrave; <lb/>manifesto, dalle cose dimostrate e supposte, che non <lb/>pu&ograve; il punto P essere risalito n&egrave; a maggiore, n&egrave; a <lb/>minore altezza perpendicolare del punto E. </s></p><p type="main">

<s>Premesse le quali cose, abbiasi il pendolo com&shy;<lb/>posto dei tre pesi A, B, C (fig. </s>

<s>331): il pendolo <lb/>semplice corrispondente, dice l'Huyghens, avr&agrave; tale <lb/>precisa lunghezza quale resulta dal dividere la somma <lb/>de'prodotti de'pesi ne'quadrati delle distanze dal&shy;<lb/>l'asse dell'oscillazione, per il prodotto della somma <lb/>dei detti pesi nella distanza del loro centro di gra&shy;<lb/>vit&agrave; dal medesimo asse, cosicch&egrave;, posta essere DL la <lb/>richiesta lunghezza, sia <lb/>DL=(A.AD2+B.BD2+C.CD2)/DE(A+B+C). </s></p><p type="main">

<s>Dimostrar ci&ograve;, dice l'Autore, vale quanto dimostrare che, presa FG <lb/>nella figura 332 uguale a DL, e fatto l'angolo GFH uguale ad LDK, in tutti <lb/><figure id="id.020.01.2904.2.jpg" xlink:href="020/01/2904/2.jpg"/></s></p><p type="caption">

<s>Figura 331.<lb/>i punti, come P, O, similmente situati negli <lb/>archi LN, GM, le velocit&agrave; sono uguali: cosic&shy;<lb/>ch&egrave;, giunto G in O, abbia concepito tale im&shy;<lb/>peto, da sollevarsi all'altezza perpendicolare <lb/>OY, uguale alla PS. </s></p><p type="main">

<s>Se ci&ograve; che si asserisce non &egrave; vero, pro&shy;<lb/>segue cos&igrave; l'Huyghens a ragionare, ammettasi <lb/>dunque che la velocit&agrave; in P sia diversa da <lb/>quella in O, e in primo luogo si supponga <lb/>maggiore, cosicch&egrave; l'altezza, a cui pu&ograve; solle&shy;<lb/>varsi il mobile, scioltosi dal suo vincolo, sia <lb/>maggiore della PS. </s>

<s>Presi AT, EQ, BV, CX <lb/>archi tutti simili a LP, chiamate Va.P, <lb/>Va.T le velocit&agrave; in P e in T, e invocata <lb/>la nota legge de'quadrati delle velocit&agrave; proporzionali agli spazi, avremo <lb/>Va.P:Va.T=DL:AD, e insieme Va.P2:Va.T2=DL2:AD2= <lb/>SP:TZ. </s>

<s>Ma perch&egrave; si vuole che il mobile nello scendere abbia, giunto <lb/>ch'egli sia in P, acquistato tal impeto, da sollevarsi ad altezza maggiore di PS; <lb/>sar&agrave; dunque TZ>SP.AD2/DL2, e anche, per simili ragioni, VZ&prime;>SP.BD2/DL2, <lb/>e XZ&Prime;>SP.CD2/DL2, d'onde </s></p><p type="main">

<s><emph type="center"/>A.TZ+B.VZ&prime;+CXZ&Prime;>SP(A.AD2+B.BD2+C.CD2)/DL2.<emph.end type="center"/><pb xlink:href="020/01/2905.jpg" pagenum="530"/>Or, essendosi posto DL=(A.AD2+B.BD2+C.CD2)/DE(A+B+C), dal moltiplicarsi <lb/>questa stessa equazione per SP s'ottiene </s></p><p type="main">

<s><emph type="center"/>SP(A.AD2+B.BD2+C.CD2)/DL2=SP.DE(A+B+C)/DL,<emph.end type="center"/><lb/>e in conseguenza A.TZ+B.VZ&prime;+CXZ&Prime;>SP.DE(A+B+C)/DL. </s>

<s><lb/>Posto poi in R&prime; il centro di gravit&agrave; de'pesi risaliti in Z, Z&prime;, Z&Prime;, sar&agrave; <lb/>A.TZ+B.VZ&prime;+CXZ&Prime;=QR&prime;(A+B+C) e dall'essere LD:ED= <lb/>SP:QR s'ha QR=SP.ED/LD, e perci&ograve; QR&prime;(A+B+C)>QR(A+B+C). <lb/>E perch&egrave; il primo termine della disuguaglianza esprime la quantit&agrave; di moto <lb/>nell'ascesa del sistema, e il secondo la quantit&agrave; di moto nella discesa; ne <lb/>verrebbe per conseguenza l'assurdo che questo sia maggiore di quello. </s>

<s>A un <lb/>simile assurdo condurrebbe il supposto che la velocit&agrave; in P, nel percorrere <lb/>l'arco LN, sia minore della velocit&agrave; in O, nel percorrere l'arco GM; dun&shy;<lb/>que riman da ci&ograve; dimostrata la celebre proposizione quinta ugeniana: <emph type="italics"/>Dato <lb/>pendulo ex ponderibus quotlibet composito, si singula ducantur in qua&shy;<lb/>drata distantiarum suarum ab axe oscillationis, et summa productorum <lb/>dividatur per id quod fit, ducendo ponderum summam in distantiam cen&shy;<lb/>tri gravitatis communis omnium ab eodem axe oscillationis; orietur lon&shy;<lb/>gitudo penduli simplicis composito isochroni, sive distantia inter axem et <lb/>centrum oscillationis ipsius penduli compositi<emph.end type="italics"/> (pag. </s>

<s>127, 28). </s></p><p type="main">

<s>Di qui &egrave; che se i pesi, qualunque sia il loro numero N, son tutti uguali, <lb/>rappresentati da P; se le distanze di ciascuno dal punto di sospensione del <lb/>sistema si chiamino A, B, C...., e sia D la distanza del comun centro di <lb/>gravit&agrave; di essi pesi dal detto punto di sospensione; la lunghezza X del <lb/>pendolo semplice, isocrono al composto, sar&agrave; data dalla formula X= <lb/>P(A2+B2+C2....)/N.P.D=(A2+B2+C2....)/N.D, secondo quel che s'annun&shy;<lb/>ziava dall'Huyghens stesso nella sua VI proposizione: <emph type="italics"/>Dato pendulo, ex <lb/>quotcumque ponderibus aequalibus composito, si summa quadratorum facto&shy;<lb/>rum a distantiis, quibus unumquodque pondus abest ab axe oscillationis, <lb/>applicetur ad distantiam centri gravitatis communis ab eodem oscillatio&shy;<lb/>nis axe, multiplicem secundum ipsorum ponderum numerum; orietur lon&shy;<lb/>gitudo penduli simplicis composito isochroni<emph.end type="italics"/> (pag. </s>

<s>131). </s></p><p type="main">

<s>Si disse la quinta di queste recondite proposizioni ugeniane celebre, non <lb/>tanto per l'importanza ch'ell'ebbe ne'progressi della Scienza del moto, <lb/>quanto per le contradizioni da varie parti subite, e dalle quali finalmente <lb/>riusc&igrave; vittoriosa. </s>

<s>Il padre Deschales, dop'aver nel trattato VIII del suo <emph type="italics"/>Mun&shy;<lb/>dus mathematicus<emph.end type="italics"/> proposti vari teoremi, attinenti al centro delle percosse, <lb/>ne'quali per verit&agrave; non s'aggiungeva nulla di nuovo a ci&ograve;, che avevano dimo&shy;<lb/>strato il Roberval e il Cartesio, e che oramai per l'opera del Wallis era <lb/>stato fatto pubblicamente noto; soggiungeva, nel seguente trattato IX, al-<pb xlink:href="020/01/2906.jpg" pagenum="531"/>cune cose concernenti i centri delle oscillazioni, proponendosene principal&shy;<lb/>mente l'invenzione in un pendolo composto di due globi uguali. </s></p><p type="main">

<s>Se questi globi, quali s'intendono rappresentati per B, C (fig. </s>

<s>332), fos&shy;<lb/>sero in quiete, il centro del moto sarebbe nel mezzo di BC. </s>

<s>Ma perch&egrave; C &egrave; <lb/>pi&ugrave; lontano dal punto A di sospen&shy;<lb/><figure id="id.020.01.2906.1.jpg" xlink:href="020/01/2906/1.jpg"/></s></p><p type="caption">

<s>Figura 332.<lb/>sione, intorno a cui si move pi&ugrave; <lb/>veloce, &egrave; come se fosse pi&ugrave; peso di <lb/>B, secondo la ragion dei momenti, <lb/>i quali sono C.AC, B.AB, e per&shy;<lb/>ci&ograve; il centro del moto divider&agrave; la <lb/>linea BC in D talmente, che deb&shy;<lb/>ba aversi la proporzion reciproca <lb/>B.AB:C.AC=CD:DB, ossia, <lb/>nel presente supposto, AB:AC= <lb/>CD:DB, dalla quale s'avr&agrave; indi&shy;<lb/>cato il punto D, in cui termina la <lb/>lunghezza del pendolo semplice iso&shy;<lb/>crono al composto. </s></p><p type="main">

<s>Maggior difficolt&agrave;, prosegue il <lb/>Deschales a dire, s'incontra, met&shy;<lb/>tendosi a ricercare il centro dell'o&shy;<lb/>scillazione in un triangolo isoscele <lb/>o in un cono, sospesi ora per l'apice, <lb/>ora per la base: ma difficilissima &egrave; <lb/>questa medesima invenzione, quan&shy;<lb/>do tutto intero il triangolo o il cono <lb/>si facciano oscillare pendenti da un <lb/>filo, &ldquo; quae tantum innuere volui ut is cui licebit per otium examinet, haec <lb/>autem non sunt ita constituta, ut iis acquiescam. </s>

<s>Profert regulam aliquam <lb/>D. Eughens, nempe ut multiplicetur pondus quodlibet per quadratum suae <lb/>distantiae, fiatque summa productorum: haec summa dividatur per sum&shy;<lb/><gap/>am momentorum &rdquo; (Lugduni, editio alt. </s>

<s>1690, T. II, pag. </s>

<s>322): regola <lb/>che il Deschales confessa aver esatto riscontro con la sua data di sopra, <lb/>a proposito del pendolo composto di due pesi uguali. </s>

<s>Se sia infatti AB= <lb/>2, AC=8, B=C=4, e per conseguenza BC=6, sostituiti que&shy;<lb/>sti valori numerici nell'equazione AB:AC=CD:DB, o nella compo&shy;<lb/>sta da lei AB+AC:AB=CD+DB:CD, avremo CD=2.6/10=1+1/5, <lb/>e perci&ograve; AD=AC&mdash;CD=8&mdash;1&mdash;1/5=6+4/5, precisamente come <lb/>s'ha dalla regola ugeniana, secondo la quale condotto il calcolo s'ha pure <lb/>AD=(4+64)/10=6+4/5. </s></p><p type="main">

<s>Ma potevasi il riscontro fra le due regole dimostrare pi&ugrave; generalmente, <lb/>concludendo il valore di AD dall'equazione AB:AC=CD:DB, la quale <pb xlink:href="020/01/2907.jpg" pagenum="532"/>d&agrave; per composizione AB+AC:AB=CD+DB:CD=BC:CD= <lb/>AC&mdash;AB:CD, d'onde CD=AB(AC&mdash;AB)/(AC+AB), e perci&ograve; AC&mdash;CD=AD= <lb/>AC&mdash;AB(AC&mdash;AB)/(AC+AB)=(AC2+AB2)/(AC+AB), che &egrave; la formula stessa stabilita dal&shy;<lb/>l'Huyghens nella sua VI proposizione. </s></p><p type="main">

<s>Non per questo cred&egrave; il Deschales di dover revocare contro lo stesso <lb/>Huyghens la sua sentenza, ma anzi, considerando il pendolo composto, nel <lb/>caso che i due globi uguali comprendessero nel mezzo il centro dell'oscilla&shy;<lb/>zione, concluse da parecchie esperienze, istituite col variare ai pesi grandezze <lb/>e distanze, <emph type="italics"/>in omnibus regulam D. </s>

<s>Eughens non ad amussim experien&shy;<lb/>tiis respondere<emph.end type="italics"/> (ibid., pag. </s>

<s>323) a cui il signor Huyghens contrapponeva che <lb/>la non rispondenza fra la teoria e la pratica, notata dal Padre, dipendeva da <lb/>ci&ograve; che, ne'suoi computi, <emph type="italics"/>rationem non habuit, ut debebat, ponderis ba&shy;<lb/>culi cui pondera erant appensa<emph.end type="italics"/> (Op. </s>

<s>et T. cit., pag. </s>

<s>225). N&egrave; l'inconsi&shy;<lb/>deratezza del. </s>

<s>Deschales fu sola, ma ebbe anche altri matematici seguaci, <lb/>da'quali non si pu&ograve; escludere il Mariotte, che, nella seconda parte del suo <lb/>trattato <emph type="italics"/>De la percussion,<emph.end type="italics"/> proponendosi di trovare <emph type="italics"/>le centre d'agitation d'une <lb/>partie d'une ligne, qui se meut a l'entour d'un de ses points extremes, et <lb/>le centre de percussion d'un pendule compost<emph.end type="italics"/> (Oeuvres, T. I, a l'Haye, <lb/>pag. </s>

<s>89, 91); si limitava ai pochi e pi&ugrave; facili esempi toccati dallo stesso <lb/>Deschales, e fedelmente ne imitava i processi dimostrativi. </s></p><p type="main">

<s>Ma sorsero altri in mezzo alla controversia, per dire che la teorica uge&shy;<lb/>niana non corrisponde con l'esperienza, perch'&egrave; falsa, essendo il modo del&shy;<lb/>l'agire la gravit&agrave; nei pesi congiunti diverso dal modo dell'agire nei sepa&shy;<lb/>rati. </s>

<s>Primo a movere questa difficolt&agrave; fu l'abate Catelani, d'onde nacque tra <lb/>lui e l'Huyghens un'altra controversia, agitata pi&ugrave; assai della prima, e nella <lb/>quale prese gran parte Giacomo Bernoulli. </s>

<s>Esaminando egli bene la propo&shy;<lb/>sta questione, dimostr&ograve; che veramente due corpi, ponderando a varie distanze <lb/>dal centro sul braccio di una libbra, percorrono, abbandonati a s&egrave; stessi, nel <lb/>medesimo tempo, uguali spazi, o cadendo liberamente o rimanendo con essa <lb/>libbra congiunti. (<emph type="italics"/>Controversia de hugen. </s>

<s>centri oscill. </s>

<s>determinatione,<emph.end type="italics"/><lb/>Op. </s>

<s>et T. cit., pag. </s>

<s>240). E come da questa parte favoriva l'Huyghens, cos&igrave; <lb/>dall'altra confermava le opposizioni del Catelani, concludendo dalla detta di&shy;<lb/>mostrazione che la somma delle altezze, alle quali risalgono i gravi separa&shy;<lb/>tamente componenti il pendolo, &egrave; minore della somma delle altezze, dalle <lb/>quali erano quegli stessi gravi congiuntamente discesi (ivi, pag. </s>

<s>241). Il mar&shy;<lb/>chese De l'H&ograve;pital ebbe a maravigliarsi, vedendo che dai medesimi princi&shy;<lb/>pii ugeniani si traevano inaspettatamente conclusioni, che contradicevano alle <lb/>verit&agrave; de'teoremi dimostrati da lui; ond'&egrave; che, esaminate meglio le cose, <lb/>ritrov&ograve; nascondersi nel discorso del Bernoulli una fallacia, consistente nel <lb/>considerare le velocit&agrave; acquistate, piuttosto che le virtuali, come si fa in di&shy;<lb/>mostrare le ragioni dell'equilibrio nel vette, quando i pesi non sono uguali <lb/>(ivi, pag. </s>

<s>245). Usciva l'Huyghens da questa controversia dicendo che solo <pb xlink:href="020/01/2908.jpg" pagenum="533"/>il De l'H&ograve;pital s'era pi&ugrave; di tutti avvicinato alla vera soluzion del problema: <lb/>reputar del resto difficilissimo il risolverlo con altro metodo diverso dal suo, <lb/>com'avevano tentato di fare il Wallis, il Deschales e il Mariotte, i quali <lb/>&ldquo; quaesiverunt tantum centrum percussionis, nec potuerunt demonstrare idem <lb/>esse cum centro oscillationis, licet id revera se habeat &rdquo; (ibid., pag. </s>

<s>246). </s></p><p type="main">

<s>La sentenza per&ograve; dell'Huyghens &egrave; pronunziata in forma troppo assoluta: <lb/>essere il centro della percossa una medesima cosa col centro dell'oscillazione <lb/>resultava dalla definizione del Roberval e del Cartesio assai manifesto, senz'aver <lb/>bisogno di essere dimostrato, bench&egrave; non valessero cos&igrave; fatte definizioni, se <lb/>non che in certi esempi particolari. </s>

<s>Cos&igrave;, anche il Wallis scriveva nello Scolio <lb/>alla proposizione citata: &ldquo; Atque hinc ad funependula aextimanda via patet: <lb/>nempe cuiuscumque figurae sit suspensum solidum, vibrationem quod spectat, <lb/>tantae longitudinis reputandum esse, quanta est distantia a suspensionis puncto <lb/>ad centrum &rdquo; (pag. </s>

<s>681) e il Mariotte s'era limitato a dimostrare, nel luogo <lb/>sopra citato, che &ldquo; Les centres de vibration, agitation et percussion sont un <lb/>m&egrave;me point dans un triangle, qui se meut sur sa base &rdquo; (pag. </s>

<s>93). </s></p><p type="main">

<s>Restava a confermare la verit&agrave;, non per il triangolo solo o per le altre <lb/>figure contemplate gi&agrave; dal Roberval, dal Cartesio, dal Deschales e dal Wal&shy;<lb/>lis, ma per ogni sistema di pesi in generale, ci&ograve; che pretendeva di aver fatto <lb/>l'Huyghens, bench&egrave; le ragioni di lui si riconoscessero pi&ugrave; tardi, quando sul <lb/>principio del secolo XVIII si resero i Matematici nel calcolare pi&ugrave; esperti. </s>

<s><lb/>Allora fu che, ricercandosi in un sistema di corpi, solidamente attaccati a <lb/>distanze invariabili sopra un piano materiale, supposto senza peso e senza <lb/>inerzia, il punto dove tutte si concentrano le forze per operare contro un re&shy;<lb/>sistente con la massima energia; si riusc&igrave; a dimostrare che quel punto &egrave; a <lb/>una distanza dall'asse, precisamente uguale a quella data dalla formula uge&shy;<lb/>niana per il centro dell'oscillazione. </s></p><p type="main">

<s>Col calcolo infinitesimale poi riusc&igrave; facile a dimostrare che la regola, <lb/><figure id="id.020.01.2908.1.jpg" xlink:href="020/01/2908/1.jpg"/></s></p><p type="caption">

<s>Figura 333.<lb/>insegnata nella V proposizione della parte quarta dell'Oro&shy;<lb/>logio oscillatorio, riscontra esattamente con la verit&agrave; dei <lb/>teoremi robervalliani. </s>

<s>Era il primo di questi teoremi in&shy;<lb/>torno al centro di una linea come AB (fig. </s>

<s>333), che si <lb/>far&agrave; per comodo uguale ad <emph type="italics"/>a,<emph.end type="italics"/> agitata mentr'&egrave; sospesa dalla <lb/>sua estremit&agrave; superiore. </s>

<s>Preso di AP, uguale ad <emph type="italics"/>x,<emph.end type="italics"/> un <lb/>elemento infinitesimale <emph type="italics"/>dx,<emph.end type="italics"/> moltiplicato questo per il qua&shy;<lb/>drato della distanza dal punto A, sar&agrave; il prodotto <emph type="italics"/>x2 dx,<emph.end type="italics"/><lb/>e sar&agrave; la somma di tutti gli altri infiniti prodotti simili &int; <emph type="italics"/>x2 dx,<emph.end type="italics"/> che, in&shy;<lb/>tegrato ed esteso l'integrale a tutta la linea, ossia fatto <emph type="italics"/>x=a;<emph.end type="italics"/> d&agrave; <lb/><emph type="italics"/>a2<emph.end type="italics"/>/3, e cos&igrave; abbiamo il dividendo della formula ugeniana. </s>

<s>Il divisore poi sar&agrave; <lb/>dato dalla somma degl'infiniti punti ponderosi componenti la linea, molti&shy;<lb/>plicati per la distanza del loro centro comune di gravit&agrave;, ossia sar&agrave; dato dal <lb/>prodotto <emph type="italics"/>a.a<emph.end type="italics"/>/2=<emph type="italics"/>a2<emph.end type="italics"/>/2, ond'&egrave; che per il quoziente, da cui viene indicato il <pb xlink:href="020/01/2909.jpg" pagenum="534"/>centro richiesto, troveremo <emph type="italics"/>a3<emph.end type="italics"/>/3:<emph type="italics"/>a2<emph.end type="italics"/>/2=2/3.a, com'aveva ritrovato per altra <lb/>via il Roberval, e dopo lui tutti gli Autori. </s></p><p type="main">

<s>Rispetto al secondo teorema robervalliano, che considera il triangolo ABC, <lb/>nella medesima figura, agitato intorno al vertice A, fatta AH=<emph type="italics"/>a,<emph.end type="italics"/> BC=<emph type="italics"/>b,<emph.end type="italics"/><lb/>AP=<emph type="italics"/>x,<emph.end type="italics"/> e condotte le due DE, GF parallele alla base, e distanti fra loro <lb/>della quantit&agrave; infinitesimale PQ=<emph type="italics"/>dx;<emph.end type="italics"/> essendo DE=<emph type="italics"/>bx/a,<emph.end type="italics"/> sar&agrave; l'elemento <lb/>superficiale DG del triangolo uguale a <emph type="italics"/>bx dx/a,<emph.end type="italics"/> e il prodotto di lui nel qua&shy;<lb/>drato della sua distanza dal punto A, <emph type="italics"/>bx3 dx/a:<emph.end type="italics"/> cosicch&egrave; &int; <emph type="italics"/>bx3 dx/a<emph.end type="italics"/> sar&agrave; la somma <lb/>di tutti gl'infiniti prodotti simili, che integrata, ed esteso l'integrale a tutto <lb/>il triangolo, ossia fatto <emph type="italics"/>x=a,<emph.end type="italics"/> sar&agrave; <emph type="italics"/>ba3/4.<emph.end type="italics"/> Dovendosi ora questa quantit&agrave;, se&shy;<lb/>condo la regola ugeniana, dividere per <emph type="italics"/>ab<emph.end type="italics"/>/2.<emph type="italics"/>2a<emph.end type="italics"/>/3, che &egrave; la somma degli infi&shy;<lb/>niti elementi ponderosi del triangolo, moltiplicati per la distanza del loro centro <lb/>di gravit&agrave; dal punto di sospensione; avremo per quoziente <emph type="italics"/>ba3<emph.end type="italics"/>/4:<emph type="italics"/>ba2<emph.end type="italics"/>/3=3/4<emph type="italics"/>a,<emph.end type="italics"/><lb/>non altrimenti da quel che tanti anni prima aveva lo stesso Roberval dimo&shy;<lb/>strato al Mersenno. </s></p><p type="main">

<s>Non potevano questi, e altri simili riscontri, che, secondo il medesimo <lb/>ordine erano facili a farsi, non avere una grande efficacia in persuadere i <lb/>dissidenti, ma s'agitava allora vivamente la questione delle forze vive, dal <lb/>principio della conservazion delle quali era condotta la dimostrazione del Teo&shy;<lb/>rema ugeniano. </s>

<s>Pensarono perci&ograve; i Matematici di valersi d'altri principii, che <lb/>non fossero controversi, e Giov. </s>

<s>Bernoulli, applicando le leggi che muovono <lb/>il vette a quello stesso Teorema, giungeva a una formula, dopo scritta la <lb/>quale cos&igrave; notava: &ldquo; Id quod omnino conforme est Regulae hugenianae, quam&shy;<lb/>vis elicitae ex principio indirecto, fundato in aequalitate descensus et ascen&shy;<lb/>sus communis centri gravitatis, quod redit ad suppositionem <emph type="italics"/>Conservationis <lb/>virum vivarum &rdquo;<emph.end type="italics"/> (Opera omnia, Lausannae 1742, pag. </s>

<s>261). Il D'Alembert <lb/>poi rese la dimostrazion del Bernoulli anche pi&ugrave; semplice, facendola deri&shy;<lb/>vare dalla soluzion del seguente problema: &ldquo; Trouver la vitesse d'une verge <lb/>fixe, et charg&eacute;e de tant de corps, qu'on voudra, en supposant que ces corps, <lb/>si la verge ne les en empechoit, decrivissent dans des tems egaux les lignes <lb/>infiniment petites perpendiculaires a la verge &rdquo; (<emph type="italics"/>Trait&egrave; de Dinamique,<emph.end type="italics"/> a <lb/>Paris 1758, pag. 96). </s></p><p type="main">

<s>In cotesto tempo, da certe iattanze degl'Inglesi, presero i Matematici oc&shy;<lb/>casione di definir nei loro precisi termini le relazioni, che passano tra il cen&shy;<lb/>tro dell'oscillazione e quello della percossa. </s>

<s>L'Huyghens, come udimmo, aveva <lb/>detto che n&egrave; il Wallis, n&egrave; nessun altro de'suoi predecessori, era riuscito a <lb/>dimostrar l'identit&agrave;, bench&egrave; fosse verissima, dei due detti centri, ma lo Stone, <pb xlink:href="020/01/2910.jpg" pagenum="535"/>accademico reale di Londra, citando quel documento, che noi pure trascri&shy;<lb/>vemmo dallo Scolio alla XV proposizion wallisiana <emph type="italics"/>De percussione,<emph.end type="italics"/> preten&shy;<lb/>deva che, per avere esso Wallis riconosciuta quella identit&agrave;, avesse ragione <lb/>di precedenza sull'Huyghens intorno alla teoria de'centri oscillatorii. </s>

<s>Soste&shy;<lb/>neva queste sue pretensioni in un libro, stampato nel 1735 in Parigi, col <lb/>titolo di <emph type="italics"/>Analyse des infinimens petits,<emph.end type="italics"/> e scritto con la principale intenzione <lb/>di rivendicare al Newton il primato dell'invenzione del Calcolo infinitesimale. </s>

<s><lb/>A quel libro facendo Giov. </s>

<s>Bernoulli alcune argute postille, mentre mostrava <lb/>da una parte l'opera, che avevano dato seco il Leibniz, l'H&ograve;pital e altri non <lb/>Inglesi a istituir l'analisi degl'infinitamente piccoli, toglieva dall'altra al Wal&shy;<lb/>lis, quanto all'invenzion dei centri d'oscillazione, ogni diritto di precedenza, <lb/>col negar che sia, come leggermente si credeva da tutti, tra esso centro e <lb/>quello della percossa alcuna connession necessaria: a persuadersi di che egli <lb/>dice &ldquo; il n'y a qu'a consid&eacute;rer ces deux choses: 1.&deg; La nature du centre <lb/>d'oscillation d&eacute;pend enti&eacute;rement de la nature et de l'action de la pesanteur, <lb/>au lieu que, dans la theorie du centre de percussion, la pesanteur n'entre <lb/>aucunement en consideration, mais seulement la matiere et la vitesse, quoi&shy;<lb/>que uniforme, de ses parties. </s>

<s>De-l&agrave; il arrive qu'un pendule compose de plu&shy;<lb/>sieurs corps de differentes densit&eacute;s, agit&eacute; dans l'air, a son centre d'oscillation <lb/>different de celui qu'il avroit, s'il etoit agit&eacute; dans une liqueur, par &eacute;xemple <lb/>dans l'eau. </s>

<s>Mais le centre de p&eacute;rcussion sera le m&ecirc;me dans l'air et dans <lb/>l'eau. </s>

<s>2.&deg; Au contraire, si les corps se meuvent dans un m&ecirc;me milieu, le <lb/>centre d'oscillation est quelque chose d'absolu et independant de toute rela&shy;<lb/>tion, au lieu que le centre de percussion varie selon la diversit&eacute; de situa&shy;<lb/>tion du corps choqu&eacute;, ensorte qu'il y a une mutuelle d&eacute;pendance entre les <lb/>corps choquans et choqu&eacute;s &rdquo; (Opera cit., pag. 180). </s></p><p type="main">

<s>A ridur ne'precisi termini la questione accennava anche il D'Alembert, <lb/>dop'aver risoluto il problema, da cui si disse ch'egli faceva dipendere l'in&shy;<lb/>venzione dei centri oscillatorii. </s>

<s>&ldquo; Il est a remarquer qu'on ne s'exprimeroit <lb/>pas exactement en disant, avec quelques auteurs, que la distance du centre <lb/>d'oscillation est toujours la m&ecirc;me, soit que le milieu resiste, soit qu'il ne <lb/>resiste pas. </s>

<s>&rdquo; E ci&ograve; perch&egrave; nella formula ritrovata entrano quantit&agrave; &ldquo; qui, <lb/>dependent de la pesanteur, ne sont pas les m&ecirc;mes que dans le vuide, par&shy;<lb/>ceque la pesanteur de chaque corps est diminu&eacute;e par celle du fluide, et <lb/>qu'elle l'est differentment a raison de la densit&eacute;, du volume et de la figure <lb/>de chaque corps &rdquo; (<emph type="italics"/>Trait&eacute; de Dinamique<emph.end type="italics"/> cit., pag. </s>

<s>100). </s></p><p type="main">

<s>Ma a far queste considerazioni erano predisposte le menti dalle dottrine <lb/>dell'Herman, il quale, dopo aver notato che, se il pendolo &egrave; composto di <lb/>corpi di differente gravit&agrave; specifica, il centro dell'oscillazione varia nella varia <lb/>densit&agrave; dei mezzi, per cui rimprovera coloro, che inconsideratamente con&shy;<lb/>fondono questo col centro della percossa; passa a dimostrare nel 1.&deg; libro <lb/>della <emph type="italics"/>Foronomia<emph.end type="italics"/> la proposizione XXXVI, che dice: non verificarsi l'identit&agrave; <lb/>del centro dell'oscillazione col centro della percossa, se non nel caso partico&shy;<lb/>lare, che i pesi componenti il pendolo siano proporzionali alle masse. </s>

<s>&ldquo; Iden-<pb xlink:href="020/01/2911.jpg" pagenum="536"/>titas centri oscillationis et percussionis eo casu, quo singularum penduli com&shy;<lb/>positi partium pondera massis eorumdem proportionalia sunt &rdquo; (Amstelo&shy;<lb/>dami 1716, pag. </s>

<s>108). E cosi pu&ograve; dirsi che, per opera e studio de'Matematici <lb/>stranieri, giungesse al suo ultimo perfezionamento l'invenzione ugeniana. </s></p><p type="main">

<s>In Italia, dove Galileo aveva insegnate intorno alla forza della percossa <lb/>dottrine false, e insufficienti, ad emendare e a restaurar le quali aveva tutte <lb/>esaurite le sue forze il Borelli; rimasero intatte queste importantissime que&shy;<lb/>stioni, cosicch&egrave; il Torricelli ebbe e restarsi muto a certe domande, che in <lb/>una lettera del d&igrave; 6 Novembre 1646 gli faceva da Parigi il Mersenno: &ldquo; Ab <lb/>hinc anno plurimum laboravimus in regulis inveniendis, quibus agnoscitur <lb/>et determinatur centrum percussionis cuiuslibet corporis alicui clavo ita ap&shy;<lb/>pensi, ut libere hinc inde instar funependuli moveri possit... punctum seu <lb/>centrum percussionis seu virtutis, hoc est in quo vehementissime percutiat <lb/>vel, quod eodem recidit, putamus quantae longitudinis debet esse funependu&shy;<lb/>lum ut moveatur seu vibretur aequali tempore ac praedictum triangulum. </s>

<s><lb/>Vide ut mihi significes an Galileus ea de re cogitavit et si regulam invene&shy;<lb/>rit &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLI, f. </s>

<s>28). </s></p><p type="main">

<s>N&egrave; solamente non aveva trovata la regola Galileo, ma non l'avevano <lb/>trovata nemmeno gli Accademici del Cimento, quando gi&agrave; potevano aver no&shy;<lb/>tizia delle invenzioni del Roberval e del Cartesio, le quali &egrave; certo che fu&shy;<lb/>rono comunicate, nell'Agosto del 1646, al Torricelli per lettera scrittagli di <lb/>Parigi dal Mersenno: &ldquo; Sit baculus sive quadratus, sive rotundus: dico fu&shy;<lb/>nependulum longitudine subsesquialtera longitudini baculi suas habere vibra&shy;<lb/>tiones aequales tempore. </s>

<s>Itaque dividatur cylindrus sive baculus in tres par&shy;<lb/>tes: funependulum duorum erit partium. </s>

<s>Regula generalis, quam nobis <lb/>D. </s>

<s>Cartesius a nobis rogatus misit, haec est: omnia corpora, praeter cen&shy;<lb/>trum gravitatis, aliud centrum percussionis, sive agitationis habere &rdquo; (ibid., <lb/>fol. </s>

<s>59). Nonostante i nostri Accademici fiorentini non sapevano ancora dire <lb/>con certezza di scienza quanta parte dell'asse della pallina d'oro dovesse <lb/>aggiungersi al filo di seta, per aver la lunghezza esatta del loro pendolo pre&shy;<lb/>diletto. </s>

<s>Abbiamo di ci&ograve; il documento in una nota autografa del Viviani, scritta <lb/>per insegnare il modo di <emph type="italics"/>trovare qual punto del pendolo sia quello, dal <lb/>quale si regola il moto.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Prendi egli dice, una palla di piombo come A (fig. </s>

<s>334) e sospendila <lb/>ad un filo di qualunque lunghezza come BC. </s>

<s>Con questa fa vibrare il pen&shy;<lb/>dolo, e numera le vibrazioni, che esso fa in un tal tempo, v. </s>

<s>g. </s>

<s>in cento vi&shy;<lb/>brazioni di un altro qualsiasi pendolo esploratore, che siano v. </s>

<s>g. </s>

<s>60, con il <lb/>filo AH e palla A. </s>

<s>Prova poi ad accorciare il filo quanto DC, in modo che <lb/>le vibrazioni del medesimo peso A col filo DC siano la met&agrave; meno, cio&egrave; 30, <lb/>nel tempo che l'esploratore ne faceva pur cento. </s>

<s>Dividi poi il residuo del <lb/>filo BD in tre parti uguali, ed una divisione dal punto D gettala verso A: <lb/>ch&egrave;, dove il punto A termina, questo sar&agrave; il regolatore del moto del detto <lb/>pendolo, e si trover&agrave; che detta misura della terza parte di BD arriva ad A, <lb/>centro di gravit&agrave; della palla, quando essa sar&agrave; omogenea, e il filo sia sotti-<pb xlink:href="020/01/2912.jpg" pagenum="537"/>lissimo. </s>

<s>Ma quando anche non arrivi al centro, ma termini sopra A, ovvero <lb/>sotto A, tal punto sar&agrave; nondimeno quello, che d&agrave; regola alle vibrazioni del <lb/>detto pendolo &rdquo; (MSS. Cim., T. X, fol. </s>

<s>48). <lb/><figure id="id.020.01.2912.1.jpg" xlink:href="020/01/2912/1.jpg"/></s></p><p type="caption">

<s>Figura 334.</s></p><p type="main">

<s>Da quali principii concludesse il Viviani questa sua regola <lb/>non ci &egrave; noto, ma &egrave; certissimo in ogni modo che il punto <lb/>regolatore delle vibrazioni del pendolo deve necessariamente <lb/>esser pi&ugrave; basso di A. Perch&egrave;, intendendosi divisa la palla in <lb/>due emisferi soprapposti, quel di sotto, nell'agitazione, acqui&shy;<lb/>sta maggiore momento. </s>

<s>Che se siano dei due detti emisferi i <lb/>centri di gravit&agrave; in E, F, la regola semplicissima di ritrovare <lb/>in G il punto, da cui si regola il moto, &egrave; data, com'insegnava <lb/>il Deschales, dalla proporzione GE:GF=BF:BE. </s></p><p type="main">

<s>Dopo gli Accademici del Cimento, fu forse, nel 1684, il <lb/>primo in Italia a trattare de'centri delle oscillazioni e delle <lb/>percosse Paolo Casati. </s>

<s>In qual modo per&ograve; ci&ograve; facesse pu&ograve; giu&shy;<lb/>dicarlo chi legge il capitolo IX del VII libro della sua Mec&shy;<lb/>canica. </s>

<s>Proponendosi egli l'invenzione del centro della percossa <lb/>in un cilindro sottilissimo, o in una verga girevole intorno ad <lb/>una sua estremit&agrave;, considerava che i momenti andavano cre&shy;<lb/>scendo a proporzion de'seni degli archi concentrici, ma non <lb/>sapendo applicarvi, come il Roberval, il Cartesio e il Wallis il <lb/>metodo degli indivisibili, non riusc&igrave; a determinare il punto della <lb/>maggiore energia delle forze, che dentro certi limiti, usandovi <lb/>un metodo di falsa posizione. </s>

<s>E pi&ugrave; da fisico che da matematico raccoglie il fiore <lb/>delle sue dottrine nell'insegnar che il centro della percossa di un sistema, <lb/>per esempio di una clava, &egrave; a tanta distanza dall'asse della sospensione, quant'&egrave; <lb/>la lunghezza di un pendolo isocrono, composto di un sottilissimo filo di rame, <lb/>e di un piccolo globo, avvertendo che &ldquo; si una perpendiculi vibratio diutur&shy;<lb/>nior sit quam una clavae vibratio, decurtandum est filum, si brevior, produ&shy;<lb/>cendum usque eo, dum perpendiculi vibrationes singulae singulis clavae vi&shy;<lb/>brationibus isochronae fuerint &rdquo; (Mechanic. </s>

<s>libri, Lugduni 1684, pag. </s>

<s>716). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Rimane a dire, secondo l'ordine propostoci, delle Forze centrifughe, a <lb/>dimostrar la natura e le propriet&agrave; delle quali anche venne all'Huyghens <lb/>l'occasione dall'Orologio oscillatorio. </s>

<s>I teoremi nuovi relativi a questo argo&shy;<lb/>mento, e solamente pubblicati dall'Autore per dar perfezione di scienza al <lb/>nuovo automato, sparsero nelle menti dell'Hook, del Newton, c di altri Ma&shy;<lb/>tematici inglesi i germi fecondi della Meccanica celeste, d'onde &egrave; facile ar&shy;<lb/>gomentare all'importanza della presente parte della nostra Storia, la quale, <lb/>aprendosi a un tratto, poco dopo la met&agrave; del secolo XVII, com'alveo a rice&shy;<lb/>vere un gran fiume, ebbe pure da lontani e sottilissimi rivoli la sua sorgente. </s></p><pb xlink:href="020/01/2913.jpg" pagenum="538"/><p type="main">

<s>Quella forza, a cui piacque all'Huyghens di dare il nome di <emph type="italics"/>centrifuga,<emph.end type="italics"/><lb/>si rimase per lunghissimo tempo implicata cos&igrave; ne'moti di rotazione, che <lb/>l'ufficio nostro si riduce ora a narrar come e quando riuscissero finalmente <lb/>i Matematici a distinguerla, e a misurare la proporzione ch'ell'ha all'altra <lb/>sua componente. </s>

<s>Le prime speculazioni perci&ograve; versarono intorno a que'moti <lb/>violenti, de'quali Aristotile, nella sua XII questione meccanica, era venuto a <lb/>porgere i primi esempi. </s>

<s>Si propone quivi il Filosofo di rendere la ragione <lb/>perch&egrave; un proietto vada con tanto maggior impeto, girato nella fionda, che se <lb/>fosse gettato dalla semplice mano: e dice che ci&ograve; forse avviene, perch&egrave; quel <lb/>che si getta, nella mano, si parte dalla quiete, e nella fionda con velocit&agrave; <lb/>precedente: <emph type="italics"/>omnia autem, cum in motu sunt, quam cum quiescunt, faci&shy;<lb/>lius moventur<emph.end type="italics"/> (Operum, T. XI, Venetiis 1560, fol. </s>

<s>32 ad t.). Ma un'altra <lb/>ragione soggiunge a questa il Filosofo, ed &egrave; che la mano fa da centro del <lb/>moto, e la fionda si dilunga dal centro: <emph type="italics"/>quanto autem productius fuerit id <lb/>quod a centro est, tanto citius movetur<emph.end type="italics"/> (ibid.). </s></p><p type="main">

<s>Il principio aristotelico era l'unico, che senz'altra dichiarazione s'appli&shy;<lb/>casse, in simili questioni meccaniche, dai Matematici, fra quali basti citare <lb/>il Cardano, che, nel capitolo LVI dell'XI libro <emph type="italics"/>De rerum varietate,<emph.end type="italics"/> lo for&shy;<lb/>mulava con queste parole: &ldquo; Omne quod movetur violenter eo velocius mo&shy;<lb/>vetur, quo celerius et per longius spatium ab eo a quo movetur &rdquo; (Op. </s>

<s>omnia, <lb/>T. III, Lugduni 1663, pag. </s>

<s>214). </s></p><p type="main">

<s>Anche Giovan Batista Benedetti ripet&egrave; poi che <emph type="italics"/>quanto maior est ali&shy;<lb/>qua rota tanto maiorem quoque impetum, et impressionem motus eius cir&shy;<lb/>cumferentiae partes recipiunt<emph.end type="italics"/> (Speculationum liber, Venetiis 1599, pag. </s>

<s>159), <lb/>ma egli ha il merito di avere speculato un principio pi&ugrave; prossimo e pi&ugrave; im&shy;<lb/>mediato, da concluder la proposta verit&agrave; del teorema. </s>

<s>Cred&egrave; di aver egli ri&shy;<lb/>trovato quel principio in un fatto, <emph type="italics"/>quod a nemine adhuc, quod sciam, in <lb/>trocho est observatum,<emph.end type="italics"/> ed &egrave; che, immaginando essa trottola, mentre gira <lb/>velocissimamente sul suo punzone, esser ridotta in minute schegge, queste <lb/>non cadono a perpendicolo, ma vanno per linea retta orizontale, e tangente <lb/>a quel punto del giro, da cui furono scisse: ci&ograve; che dall'altra parte si vede <lb/>avvenire ordinariamente nelle ruote de'carri, e in qualunque altro corpo, <lb/>che sia da estrinseco moto violentemente circondotto. </s>

<s>Intorno ai quali moti <lb/>rotatorii il Matematico veneziano stabilisce le dottrine seguenti: &ldquo; Quaelibet <lb/>pars corporea, quae a se movetur, impetu eidem a qualibet extrinseca vir&shy;<lb/>tute movente impresso, habet naturalem inclinationem ad rectum iter, non <lb/>autem curvum. </s>

<s>Unde, si a dicta rota particula aliqua suae circumferentiae <lb/>disiungeretur, absque dubio per aliquod temporis spatio pars separata recto <lb/>itinere ferretur per aerem, ut exemplo a fundis, quibus iaciuntur lapides, <lb/>sumpto, cognoscere possumus. </s>

<s>In quibus impetus motus impressus naturali <lb/>quadam propensione rectum iter peragit, cum evibratus lapis per lineam re&shy;<lb/>ctam contiguam giro, quem primo faciebat, in puncto in quo dimissus fuit, <lb/>rectum iter instituit &rdquo; (ibid.). </s></p><p type="main">

<s>Posto cos&igrave; il principio che il mobile, per inclinazion sua naturale, &egrave; di-<pb xlink:href="020/01/2914.jpg" pagenum="539"/>sposto d'andare in linea retta, tangente al punto del giro, da cui si scioglie, <lb/>ed essendo facil cosa a concedere che tanto sia maggiore il moto, quanto &egrave; <lb/>pi&ugrave; secondato dalla sua propria natura; conclude il Benedetti dovere essere <lb/>nella ruota maggiore, maggiore altres&igrave; l'impeto della proiezione, perch&egrave; la <lb/>sua curvatura, pi&ugrave; che nella ruota minore, s'accosta alla linea retta. </s>

<s>&ldquo; Quia, <lb/>quanto maior est diameter unius circuli, tanto minus curva est eiusdem cir&shy;<lb/>cumferentia, et tanto propius accedit ad rectitudinem linearem. </s>

<s>Unde earum&shy;<lb/>dem partium dictae circumferentiae motus ad inclinationem sibi a natura <lb/>tribulam, quae est incedendi per lineam rectam, magis accedit &rdquo; (ibid.). </s></p><p type="main">

<s>In questi moti giratorii per&ograve;, come per esempio in quello volgare della <lb/>fionda, s'osserva, dice il Benedetti, un certo effetto <emph type="italics"/>notatu dignus,<emph.end type="italics"/> ed &egrave; che, <lb/>quanto pi&ugrave; cresce l'impeto del corpo girato, tanto pi&ugrave; &egrave; necessario che, me&shy;<lb/>diante la fune, si senta a lui tirare la mano. </s>

<s>Ecco dunque proporsi alla <lb/>mente dello speculatore la question della forza centrifuga propriamente detta, <lb/>che par nascere dall'impeto di proiezione, ma egli non sa far altro intorno <lb/>a ci&ograve; che applicare il professato principio, dicendo essere di quel notabile <lb/>effetto la ragione &ldquo; quia, quanto maior impetus impressus, tanto magis cor&shy;<lb/>pus ad rectum iter peragendum inclinatur: unde, ut recta incedat, tanto <lb/>maiore vi trahit &rdquo; (ibid., pag. </s>

<s>161). </s></p><p type="main">

<s>Di qui si vede che il Benedetti aveva fatto un notabilissimo progresso, <lb/>riducendo l'impeto del mobile alla forza della sua proiezione per la tan&shy;<lb/>gente, ma non perci&ograve; era entrato addentro al mistero di queste forze, non <lb/>penetrabile se non a colui, che avesse saputo decomporre quell'unico moto <lb/>proiettizio in due: uno che mena il mobile in giro, e l'altro che nello stesso <lb/>tempo lo farebbe rifuggire dal centro, se un'arcana forza di attrazione non <lb/>lo tenesse a s&egrave; immobile e fisso. </s>

<s>Questa forza, che poi si disse <emph type="italics"/>centripeta,<emph.end type="italics"/><lb/>e che &egrave; una delle componenti il moto tangenziale, fu primo a riconoscerla <lb/>Galileo, che ne'dialoghi dei due Massimi Sistemi, fra i promotori di questa <lb/>scienza, immediatamente succede all'Autor del libro delle Speculazioni. </s>

<s>Nella <lb/>seconda Giornata, in proposito di rispondere all'obiezione, che, quando la <lb/>Terra girasse in s&egrave; stessa, il moto della superficie, verso il circolo massimo, <lb/>come incomparabilmente pi&ugrave; veloce dei paralleli, dovrebbe estrudere ogni <lb/>cosa verso il cielo; proponeva e dimostrava poi agl'interlocutori il seguente </s></p><p type="main">

<s>TEOREMA. &mdash; <emph type="italics"/>&ldquo; Quanto pi&ugrave; si cresce la ruota, tanto si scema la causa <lb/>della proiezione. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Siano due ruote diseguali intorno al centro A (fig. </s>

<s>335), e della mi&shy;<lb/>nore sia la circonferenza BG, e della maggiore CE, e il semidiametro ABC <lb/>sia eretto all'orizonte, e per i punti B, C segniamo le rette linee tangenti <lb/>BF, CD, e negli archi BG, CE sieno prese due parti eguali BG, CE, e in&shy;<lb/>tendasi le due ruote esser girate sopra i loro centri con eguali velocit&agrave;, sic&shy;<lb/>ch&egrave; i due mobili, quali sariano v. </s>

<s>g. </s>

<s>due pietre poste ne'punti B e C, ven&shy;<lb/>gano portate per le circonferenze BG, CE con eguali velocit&agrave;, talch&egrave;, nel&shy;<lb/>l'istesso tempo che la pietra B scorrerebbe per l'arco BG, la pietra C <lb/>passerebbe l'arco CE: dico adesso che la vertigine della minor ruota &egrave; molto <pb xlink:href="020/01/2915.jpg" pagenum="540"/>pi&ugrave; potente a far la proiezione della pietra B, che non &egrave; la vertigine della <lb/>maggior ruota della pietra C. &rdquo; </s></p><p type="main">

<s>&ldquo; Imperocch&egrave; dovendosi, come gi&agrave; si &egrave; dichiarato, far la proiezione per <lb/><figure id="id.020.01.2915.1.jpg" xlink:href="020/01/2915/1.jpg"/></s></p><p type="caption">

<s>Figura 335.<lb/>la tangente, quando le pietre B, C dovessero sepa&shy;<lb/>rarsi dalle lor ruote, e cominciare il moto della proie&shy;<lb/>zione dai punti B, C, verrebbero dall'impeto conce&shy;<lb/>pito dalla vertigine scagliate per le tangenti BF, CD. </s>

<s><lb/>Per le tangenti dunque BF, CD hanno le due pietre <lb/>eguali impeti di scorrere, e vi scorrerebbero, se da <lb/>qualche altra forza non ne fossero deviate, la qual <lb/>forza non pu&ograve; essere che la propria gravit&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora considerate che, per deviar la pietra della <lb/>minor ruota dal moto della proiezione, che ella fa&shy;<lb/>rebbe per la tangente BF, e ritenerla attaccata alla <lb/>ruota; bisogna che la propria gravit&agrave; la ritiri per quanto &egrave; lunga la se&shy;<lb/>gante FG, ovvero la perpendicolare tirata dal punto G sopra la linea BF, <lb/>dovecch&egrave;, nella ruota maggiore, il ritiramento non ha da essere pi&ugrave; che si <lb/>sia la segante DE, ovvero la perpendicolare tirata dal punto E sopra la tan&shy;<lb/>gente DC, minor assai della FG, e sempre minore e minore, secondo che la <lb/>ruota si facesse maggiore. </s>

<s>E perch&egrave; questi ritiramenti si hanno a fare in <lb/>tempi eguali, cio&egrave; mentre che si passano li due archi uguali BG, CE, quello <lb/>della pietra B, cio&egrave; il ritiramento FG, dovr&agrave; esser pi&ugrave; veloce dell'altro DE, <lb/>e per&ograve; molto maggior forza si ricercher&agrave;, per tener la pietra B congiunta <lb/>alla sua piccola ruota, che la pietra C alla sua grande: che &egrave; il medesimo <lb/>che dire che tal poca cosa impedir&agrave; lo scagliamento nella ruota grande, che <lb/>non lo proibir&agrave; nella piccola. </s>

<s>&Egrave; manifesto dunque ecc. </s>

<s>&rdquo; (Alb. </s>

<s>I, 238, 39). </s></p><p type="main">

<s>Trattandosi di ruote artificiali, non si potrebbe dire esser la gravit&agrave; la <lb/>forza, che tira la ruota al centro, nemmen quando, come qui si vuole, i se&shy;<lb/>midiametri AB, AC fossero eretti all'orizonte. </s>

<s>Ma, essendo la principale inten&shy;<lb/>zione di questo teorema quella di applicarlo al moto rotatorio intorno all'asse <lb/>della Terra, della quale A fosse il centro, e intorno a lui i due archi dise&shy;<lb/>gnati; il concetto di Galileo riscontra mirabilmente con le dottrine neuto&shy;<lb/>niane, secondo le quali propriamente la forza centripeta della pietra, in un <lb/>circolo concentrico con la Terra, non &egrave; che la gravit&agrave; sua naturale. </s>

<s>Torna <lb/>in ogni modo benissimo, a conferire il discorso di Galileo co'teoremi del <lb/>Newton, che i ritiramenti al centro, o le forze centripete, s&ograve;n proporzionali <lb/>alle parti esterne FG, DE delle secanti, o alle perpendicolari GH, EL, o ai <lb/>seni versi BN, MC: cosicch&egrave; non rimaneva a far altro ne'dialoghi del Mondo, <lb/>per prevenire la conclusione annunziata nel V corollario della IV proposi&shy;<lb/>zione, scritta nel Tomo primo dei Principii di Filosofia naturale, che dimo&shy;<lb/>strar la ragione delle linee GH, EL, o delle loro uguali. </s></p><p type="main">

<s>Nemmeno il Mersenno, inserendo nella XVIII proposizione del suo libro <lb/><emph type="italics"/>Du mouvement des corps,<emph.end type="italics"/> pubblicato in Parigi nel 1635, questa medesima <lb/>argomentazione contro chi, per gli effetti della proiezion superficiale, negava <pb xlink:href="020/01/2916.jpg" pagenum="541"/>la diurna vergine terrestre; promoveva di un passo le dottrine galileiane <lb/>verso la teoria delle forze centrali, limitandosi a tradurre fedelmente in fran&shy;<lb/>cese l'interlocuzion del Salviati. </s></p><p type="main">

<s>Forse opponeva qualche difficolt&agrave; a questa promozione la Geometria ele&shy;<lb/>mentare, mentre quella degli indivisibili, se avesse incontrato il favore di <lb/>Galileo, gli avrebbe di un intuito rivelato che la proporzione tra BN e CM <lb/>&egrave; quella reciproca dei raggi. </s>

<s>Se BG, CE infatti son archi cos&igrave; minimi, da <lb/>confondersi con le loro sottese, BG2 &egrave; uguale a 2AB.BN, e CE2=2AC.CM; <lb/>ond'essendo per supposizione BG=CE, ne consegue senz'altro BN:CM= <lb/>AC:AB. </s></p><p type="main">

<s>A chi poi fosse curioso di sapere se fu veramente qualche difficolt&agrave;, <lb/>incontrata nella dimostrazione, o il pensiero di non divagar dal soggetto del <lb/>discorso, che fece a Galileo lasciar l'occasione di concluder nel luogo citato <lb/>la verit&agrave; del nuovo e bellissimo teorema; inclineremmo a dire essere stato <lb/>piuttosto quel motivo che questo. </s>

<s>Perch&egrave; vinte, nel caso de'ritiramenti al <lb/>centro sulle ruote di varia grandezza, ma ugualmente veloci, le difficolt&agrave; geo&shy;<lb/>metriche, che si paravano nel dimostrar l'altro caso; troviamo, tra i copiati <lb/>dal Viviani, il teorema di Galileo, che i ritiramenti o le forze centripete, o <lb/>le centrifughe a loro uguali e contrarie, stanno direttamente come i semi&shy;<lb/>diametri delle ruote. </s></p><p type="main">

<s>&ldquo; Siano le due circonferenze AB, DE (fig. </s>

<s>336), sopra le quali s'inten&shy;<lb/>dano in B e in E posati due gravi, quali sariano due pietre, e rivolgendosi <lb/>intorno al centro O le due ruote, vengano le dette pietre per la vertigine <lb/><figure id="id.020.01.2916.1.jpg" xlink:href="020/01/2916/1.jpg"/></s></p><p type="caption">

<s>Figura 336.<lb/>estruse secondo le direzioni delle tangenti BH, <lb/>EL. </s>

<s>Dico che il ritiramento AH, al ritiramento <lb/>LD, o la perpendicolare AM, uguale alla BC, alla <lb/>perpendicolare DN, uguale alla EF, ha la propor&shy;<lb/>zion medesima che il semidiametro OB, al semi&shy;<lb/>diametro OE. &rdquo; </s></p><p type="main">

<s>&ldquo; Imperocch&egrave;, tirate le suttese AB, ED, i <lb/>triangoli simili danno che AB a DE &egrave; come OB <lb/>ad OE, ed anche, che il quadrato di AB, al qua&shy;<lb/>drato di DE, &egrave; come il quadrato di OB al qua&shy;<lb/>drato di OE. Dall'altra parte il quadrato di AB <lb/>&egrave; uguale al doppio di BO moltiplicato per BC, e <lb/>il quadrato di ED &egrave; uguale al doppio di EO mol&shy;<lb/>tiplicato per EF. </s>

<s>Dunque diremo che il quadrato di AB sta al quadrato di <lb/>ED, come il rettangolo di BO e di BC sta al rettangolo di EC e di EF, ossia <lb/>come il-quadrato di BO sta al quadrato di EO. </s>

<s>E di qui &egrave; manifesto che BC <lb/>ad EF ha egual proporzione che BO ad EO, com'era il proposito di dimo&shy;<lb/>strare. </s>

<s>&rdquo; <emph type="italics"/>(Roba del gran Galileo, in parte copiata dagli originali, e in <lb/>parte dettata da lui cieco a me Vincenzio Viviani, mentre dimoravo nella <lb/>sua casa d'Arcetri).<emph.end type="italics"/></s></p><p type="main">

<s>Rimasto questo teorema dimenticato ne'manoscritti, e l'altro della se-<pb xlink:href="020/01/2917.jpg" pagenum="542"/>conda giornata dei Massimi Sistemi chiuso nel suo germe, e perci&ograve; non appa&shy;<lb/>rente, si pu&ograve; dir che non dette Galileo nessuno impulso a far progredire la <lb/>Scienza delle forze centrali, che intanto dalle umili fionde, e dalle ruote dei <lb/>carri, il Borelli sublimava alle ruote celesti. </s>

<s>A coloro che opponevano non <lb/>poter la Terra moversi dal suo proprio luogo, perch&egrave;, non avendo chi la <lb/>sostenti, cadrebbe; si rispondeva, come da Galileo stesso a quel peripatetico <lb/>cappuccino veronese, essere una tale opposizione ridicola, &ldquo; quasi che il moto <lb/>velocissimo per l'opposto non sia quello, che vieta il cadere agli uccelli vo&shy;<lb/>lanti, a'sassi scagliati, alle trottole dei fanclulli. </s>

<s>Ma non dicono i Filosofi <lb/>che la Luna e le altre stelle non cadono, perch&egrave; la velocit&agrave; del loro moto <lb/>le trattiene? </s>

<s>&rdquo; (Alb. </s>

<s>VII, 61). </s></p><p type="main">

<s>Questa vera Filosofia per&ograve; non fu prima insegnata che dal libro <emph type="italics"/>Theo&shy;<lb/>ricae Mediceorum,<emph.end type="italics"/> dicendovisi che la Luna non cade sulla Terra, n&egrave; i sa&shy;<lb/>telliti su Giove, n&egrave; i pianeti sul Sole, perch&egrave; la forza magnetica dell'attra&shy;<lb/>zione, sola causa efficiente di quelle cadute, viene equilibrata dalla contra&shy;<lb/>ria forza centrifuga, che svolgesi nel girare. </s>

<s>Ma il Borelli pretendeva di pi&ugrave; <lb/>che, dalla composizione di queste forze contrarie, dipendesse la maggiore <lb/>o minore velocit&agrave; del pianeta nel perielio e nell'afelio: &ldquo; Ex compositione <lb/>dictorum motuum efficitur vis quaedam et impetus compositus, ex quo pen&shy;<lb/>det periodus celeritatis acquisitae a planeta, quae a remotissimo termino, <lb/>usque ad proprinquissimum, augetur ca proportione, quo distantiae decre&shy;<lb/>scunt &rdquo; (Florentiae 1665, pag. </s>

<s>77). E in ci&ograve; il valent'uomo aberrava, per&shy;<lb/>ch&egrave; dalla composizione di quelle due forze opposte, quando l'una fosse stata <lb/>maggiore dell'altra, non poteva nascere un moto progressivo nell'orbita, ma <lb/>solo un avvicinarsi o un dilungarsi del pianeta dal centro. </s>

<s>Da che &egrave; mani&shy;<lb/>festo che l'Autore, nonostante che la lettura del secondo dialogo dei Mas&shy;<lb/>simi Sistemi l'avesse potuto avviare alla scoperta del vero, confondeva la <lb/>forza centrifuga con quella di proiezione. </s></p><p type="main">

<s>Duravano dunque ancora nel 1665 le tenebre, che involgevano il cielo <lb/>aristotelico, non rischiarato che da'lampi del Benedetti e di Galileo, quando <lb/>apparve alla luce l'Orologio oscillatorio, nelle ultime pagine del quale l'Huy&shy;<lb/>ghens, dopo avere accennato a un'altra costruzione dell'automato con pen&shy;<lb/>dolo circolare, cos&igrave; soggiungeva: &ldquo; Et constitueram quidem descriptionem <lb/>horum cum iis demum edere, quae ad motum circularem et <emph type="italics"/>Vim centrifu&shy;<lb/>gam,<emph.end type="italics"/> ita enim eam vocare libet, attinent, de quo argumento plura dicenda <lb/>habeo, quam quae hoc tempore exequi vacet. </s>

<s>Sed ut nova nec inutili spe&shy;<lb/>culatione maturius fruantur harum rerum studiosi, Theoremata traduntur ad <lb/>vim centrifugam pertinentia, demonstratione ipsorum in aliud tempus di&shy;<lb/>lata &rdquo; (Op., T. cit., pag. </s>

<s>185, 86): i quali teoremi, cos&igrave; solamente annun&shy;<lb/>ziati, son di numero tredici, i primi cinque relativi alle forze centrifughe, <lb/>quando i raggi vettori son sul piano di rotazione, come nei cerchi, e gli altri <lb/>otto, quasi tutti, quando essi raggi son fuori del piano della rotazione, come <lb/>nei pendoli conici. </s></p><p type="main">

<s>Era per l'Huyghens quasi un tentar le forze dei Matematici in ritro-<pb xlink:href="020/01/2918.jpg" pagenum="543"/>vare la dimostrazione di quei teoremi, i quali parvero anche di maggiore <lb/>importanza, dappoich&egrave; aveva il Borelli additato che dipendevano da essi prin&shy;<lb/>cipalmente le leggi dei moti celesti. </s>

<s>A scoprir cos&igrave; fatte leggi attendevano <lb/>allora intensamente i matematici inglesi Wren, Hook, Halley, i quali perci&ograve;, <lb/>rimeditando le conclusioni dei teoremi ugeniani, ne raccolsero per primo <lb/>frutto la notizia distinta delle forze centrifughe, per cui si avvidero facil&shy;<lb/>mente della fallacia, in ch'era incorso lo stesso Borelli. </s>

<s>Dall'uso della fionda, <lb/>pensavano, s'impara due essere le forze: una che mena in giro la pietra, <lb/><figure id="id.020.01.2918.1.jpg" xlink:href="020/01/2918/1.jpg"/></s></p><p type="caption">

<s>Figura 337.<lb/>e l'altra che tira la mano, le quali due forze, percioc&shy;<lb/>ch&egrave; si riducono in una, quando il mob&igrave;le esce fuori del&shy;<lb/>l'orbita, in direzion tangenziale; non pu&ograve; dunque esser <lb/>altra quest'unica forza cos&igrave; diretta, che la resultante <lb/>dalla composizione di quelle stesse due. </s>

<s>E applicandovi <lb/>la regola dei moti composti, era tale il discorso: Sia <lb/>AB (fig. </s>

<s>337) la forza tangenziale, e l'arco AE si prenda <lb/>cos&igrave; piccolo, da riguardarsi come una linea retta: co&shy;<lb/>struito il parallelogrammo DE, vien da AE rappresen&shy;<lb/>tata la forza di circolazione, e da AD la centrifuga, co&shy;<lb/>sicch&egrave;, soiogliendosi il grave da'suoi legami, la stessa <lb/>forza tangenziale AB &egrave; quella che resulta dal comporsi <lb/>insieme le due AE, AD. </s>

<s>Il Borelli dunque, e tutti i se&shy;<lb/>guaci di Aristotile, s'ingannavano in questo: che cre&shy;<lb/>devan esser le forze centrifughe una delle cause del <lb/>moto nell'orbita, mentre in verit&agrave; non ne son che l'effetto. </s></p><p type="main">

<s>Conseguiva per facile calcolo, dall'altra parte, dai teoremi annunziati <lb/>dall'Huyghens, della verit&agrave; de'quali si poteva aver fede, anche senza le di&shy;<lb/>mostrazioni; che le forze centrifughe di due pianeti stanno direttamente <lb/>come i prodotti delle masse e de'raggi delle orbite, e reciprocamente come <lb/>i quadrati dei tempi periodici, cosicch&egrave;, chiamate F, <emph type="italics"/>f;<emph.end type="italics"/> M, <emph type="italics"/>m;<emph.end type="italics"/> R, <emph type="italics"/>r;<emph.end type="italics"/> T, <emph type="italics"/>t<emph.end type="italics"/><lb/>le dette forze, le masse, i raggi e i tempi; la legge di queste stesse forze &egrave; <lb/>scritta da F:<emph type="italics"/>f<emph.end type="italics"/>=M.R/T2:<emph type="italics"/>m.r/t2.<emph.end type="italics"/> Se dunque i quadrati dei tempi, seguitava <lb/>l'Hook a ragionare, stanno, secondo la terza legge kepleriana, come i cubi <lb/>dei raggi, sar&agrave; F:<emph type="italics"/>f<emph.end type="italics"/>=M<emph type="italics"/>r2<emph.end type="italics"/>:MR2, ond'&egrave; che, per un medesimo pianeta, le <lb/>forze centripete o di attrazione stanno in reciproca ragione de'quadrati delle <lb/>distanze. </s></p><p type="main">

<s>Se ora si risovvengano i Lettori delle cose da noi narrate, nel cap. </s>

<s>XIV <lb/>del secondo tomo, intorno alle proporzioni del diffondersi la luce, la virt&ugrave; <lb/>magnetica e le forze cosmiche, allo stesso modo irradianti, e che, nonostante <lb/>la certezza geometrica del crescer le superficie sferiche come i quadrati dei <lb/>raggi, si credeva che le forze radianti da un centro diminuissero d'intensit&agrave; <lb/>col semplice crescer dei raggi, per cui, non tornando il calcolo del cader della <lb/>Luna, aveva abbandonato il Newton le sue sublimi speculazioni; si possono <lb/>immaginare quale efficace impulso a ritornar sulla sua via ricevesse lo stesso <pb xlink:href="020/01/2919.jpg" pagenum="544"/>Newton per la notizia partecipatagli dall'Hook, che cio&egrave;, ammesse le sco&shy;<lb/>perte del Kepler, conseguiva da'nuovi canoni ugeniani crescer le forze, che <lb/>farebbero cader la Luna, non secondo i semplici avvicinamenti, ma secondo <lb/>i quadrati degli avvicinamenti di lei alla Terra. </s></p><p type="main">

<s>Germogliarono di qui i Principii matematici di Filosofia naturale, per <lb/>fondamento de'quali si prevede, dal filo delle idee, come dovesse l'Autore <lb/>porre la dimostrazione dei teoremi dell'Huyghens, e delle leggi dei moti, da <lb/>cui, come da principii generali, scendessero i fatti dal Keplero osservati, e <lb/>come tali da lui stesso descritti. </s>

<s>Il Newton non solamente s'accorse, come <lb/>l'Hook e i suoi connazionali, che le forze centrifughe conseguono com'effetto <lb/>necessario dal moto circolatorio, ma che di pi&ugrave; quell'effetto nasce sempre e <lb/>per la medesima necessit&agrave;, quando il moto, dalla retta direzione passa alla <lb/>curva, qualunque poi siasi una tale curvit&agrave; o di circolo o di ellisse o d'altra <lb/>linea anche pi&ugrave; irregolare. </s>

<s>N&egrave; il caratterismo di un tale effetto gli parve si <lb/>trovasse espresso meglio, che dalla seconda legge kepleriana delle aree pro&shy;<lb/>porzionali ai tempi impiegati a descriverle dai raggi vettori. </s>

<s>Il primo teorema <lb/>infatti dimostrato dal Newton &egrave; tale: &ldquo; Areas, quas corpora, in gyros acta radiis <lb/>ad immobile centrum virium, describunt, et in planis immobilibus consistere, <lb/>et esse temporibus proportionales &rdquo; (Genevae 1739, pag. </s>

<s>89). Conversamente <lb/>poi dimostr&ograve; nel secondo: &ldquo; Corpus omne, quod movetur in linea aliqua curva, <lb/>in plano descripta, et radio ducto ad punctum vel immobile vel motu rectilineo <lb/>uniformiter progrediens, describit areas circa punctum illud temporibus propor&shy;<lb/>tionales; urgetur a vi centripeta tendente ad idem punctum &rdquo; (ibid., pag. </s>

<s>92). </s></p><p type="main">

<s>Sia ora il circolo intorno a cui si fa il moto: &egrave; dunque gi&agrave; dimostrato <lb/>che il grave corpo circolante &egrave; ritirato al centro, con una certa forza, della <lb/>quale il Newton, che sempre vuol risalire alla universalit&agrave; dei principii, at&shy;<lb/>tende a ritrovar la misura. </s>

<s>Sarebbe stata l'impresa di difficile, anzi d'im&shy;<lb/>possibile esecuzione, mentre che si durava a confondere le forze centrifughe <lb/>con le tangenziali. </s>

<s>Ma pure era a Galileo riuscita bene la misura delle forze <lb/>dei ritiramenti dagli spazi passati ne'medesimi tempi. </s>

<s>Il prodotto della massa <lb/>per la velocit&agrave;, che vale per la misura dei moti equabili e retti, non basta <lb/>trattandosi dei curvi, i quali variano per altre ragioni, non difficili a sco&shy;<lb/>prirsi nelle rappresentazioni, esibiteci dalle figure 337 e 335. Se la velocit&agrave; <lb/>&egrave; come AE, la forza centrifuga &egrave; come AD. </s>

<s>Ma se la velocit&agrave; diminuisce, <lb/>riducendosi per esempio ad AL, anche la forza centrifuga diminuisce, ridu&shy;<lb/>cendosi ad AF, ond'&egrave; che esse forze, nel medesimo circolo, dipendono dalle <lb/>varie velocit&agrave;, a cui sono direttamente proporzionali. </s>

<s>Se poi s'eguagliano le <lb/>velocit&agrave;, e differiscono i circoli, come nella figura 335, le forze centrifughe <lb/>variano anche per un'altra ragione, che &egrave; quella reciproca dei raggi. </s>

<s>Ond'&egrave; <lb/>a concludere che, per aver la misura dell'intensit&agrave; delle dette forze, non <lb/>basta il prodotto della massa e della velocit&agrave;, ma bisogna aggiungervi per <lb/>fattore il quoziente della velocit&agrave; divisa per il raggio, cosicch&egrave; resulti tutto <lb/>insieme quel che si cerca espresso dalla massa moltiplicata per il quadrato <lb/>della velocit&agrave;, e divisa per lo stesso raggio. </s></p><pb xlink:href="020/01/2920.jpg" pagenum="545"/><p type="main">

<s>Il Newton per&ograve; sostituiva a questo un ragionamento non men semplice, <lb/>e non men concludente. </s>

<s>Diceva che ne'moti diretti le forze son proporzio&shy;<lb/>nali ai prodotti delle masse e delle velocit&agrave;, ma ne'curvi la proporzione deve <lb/>essere anche pi&ugrave; composta, riguardando la curvit&agrave; come linee poligonari in&shy;<lb/>finilatere, per gli angoli delle quali, dovendo entrare e uscire continuamente <lb/>nel suo viaggio, il mobile ha bisogno di esser sospinto al moto da un im&shy;<lb/>pulso maggiore. </s>

<s>Or perch&egrave; cotesti angoli son tanti pi&ugrave; di numero, quanto <lb/>l'arco &egrave; pi&ugrave; grande, e son tanto meno incavati quant'&egrave; maggiore la curva&shy;<lb/>tura, o il raggio che la descrive; la maggioranza dunque dell'impulso richie&shy;<lb/>sto dovr&agrave; essere proporzionale direttamente alle velocit&agrave;, e reciprocamente ai <lb/>raggi, per cui le forze, che osservavano nel moto retto la semplice ragion <lb/>composta delle masse e delle velocit&agrave;, sopravvenendo il curvo, si compon&shy;<lb/>gono anche di pi&ugrave; della ragione delle velocit&agrave; divise per i raggi: ossia sar&agrave; <lb/>la loro proporzion definita quella delle masse e de'quadrati delle velocit&agrave;, <lb/>divisi per essi raggi. </s>

<s>&ldquo; Haec est vis centrifuga, qua corpus urget circulum, <lb/>et huic aequalis est vis contraria, qua circulus continuo repellit corpus cen&shy;<lb/>trum versus &rdquo; (Principia mathem. </s>

<s>cit., pag. </s>

<s>104). </s></p><p type="main">

<s>Ma volendosi aver di ci&ograve; una dimostrazion matematica, il Newton sodi&shy;<lb/>sfa i Lettori nel suo IV teorema, con facile ragionamento, che si pu&ograve; ridurre <lb/>alla seguente forma, ritornando indietro sopra la figura 336. Essendo le forze <lb/>centrifughe, ne'gravi uguali, misurate da'seni versi EF, BC, non rimane <lb/>altro a fare, che a determinare i loro valori in funzione degli elementi dei <lb/>circoli, e ci&ograve; si consegue immediatamente dai canoni della Geometria pi&ugrave; <lb/>elementare, riducendo gli archi ED, AB a una piccolezza infinitesima, o come <lb/>diceva il Newton alla <emph type="italics"/>evanescenza,<emph.end type="italics"/> cosicch&egrave;, confondendosi essi archi con le <lb/>loro suttese, avremo EF=DE2/2EO, BC=AB2/2BO. </s>

<s>E perch&egrave;, essendo uguali i <lb/>tempi, come qui suppone, le velocit&agrave; V, <emph type="italics"/>v<emph.end type="italics"/> son proporzionali agli spazi, e son <lb/>proporzionali agli spazi, ossia alle circonferenze o ai loro raggi divisi per i <lb/>tempi T, <emph type="italics"/>t,<emph.end type="italics"/> essendo essi tempi diversi; ritenute del resto le solite denomi&shy;<lb/>nazioni, sar&agrave; la legge delle forze centrifughe espressa dalla formula generale <lb/>F:<emph type="italics"/>f<emph.end type="italics"/>=V2/R:<emph type="italics"/>v2/r<emph.end type="italics"/>=R/T2:<emph type="italics"/>r/t2.<emph.end type="italics"/></s></p><p type="main">

<s>Di qui deduce il Newton in forma di corollarii, e conferma la verit&agrave; dei <lb/>primi cinque teoremi, annunziati in fine all'Orologio oscillatorio. </s>

<s>Se i tempi <lb/>sono uguali, F:<emph type="italics"/>f<emph.end type="italics"/>=R:<emph type="italics"/>r,<emph.end type="italics"/> cio&egrave;: <emph type="italics"/>Si mobilie duo aequalia, aequaiibus tem&shy;<lb/>poribus circumferentias inaequales percurrant, erit vis centrifuga in ma&shy;<lb/>iori circumferentia, ad eam quae in minori, sicut ipsae inter se circum&shy;<lb/>ferentiae vel eorum diametri.<emph.end type="italics"/> Se le velocit&agrave; sono uguali, F:<emph type="italics"/>f<emph.end type="italics"/>=<emph type="italics"/>r:<emph.end type="italics"/>R, <lb/>secondo che l'Huyghens aveva pronunziato cos&igrave; &igrave;n secondo luogo: <emph type="italics"/>Si duo <lb/>mobilia aequalia, aequali celeritate ferantur in circumferentiis inaequali&shy;<lb/>bus; erunt eorum vires centrifugae in ratione contraria diametrorum.<emph.end type="italics"/> Se <lb/>i raggi sono uguali, F:<emph type="italics"/>f<emph.end type="italics"/>=V2:<emph type="italics"/>v2,<emph.end type="italics"/> e se le forze centrifughe sono uguali, <lb/>T2:<emph type="italics"/>t2<emph.end type="italics"/>=R:<emph type="italics"/>r,<emph.end type="italics"/> ossia T:<emph type="italics"/>t<emph.end type="italics"/>=&radic;R:&radic;<emph type="italics"/>r,<emph.end type="italics"/> ci&ograve; che perfettamente corrisponde <pb xlink:href="020/01/2921.jpg" pagenum="546"/>col III e col IV ugeniano: <emph type="italics"/>Si duo mobilia aequalia in circumferentiis ae&shy;<lb/>qualibus ferantur, celeritate inaequali, sed utraque motu aequabili, qua&shy;<lb/>lem in his omnibus intelligi volumus; erit vis centrifuga velocioris, ad <lb/>vim tardioris, in ratione duplicata celeritatum. </s>

<s>&mdash; Si mobilia duo aequa&shy;<lb/>lia, in circumferentiis inaequalibus circumlata, vim centrifugam aequalem <lb/>habuerint; erit tempus circuitus in maiori circumferentia, ad tempus <lb/>circuitus in minori, in subdupla ratione diametrorum.<emph.end type="italics"/> (Opera, T. cit., <lb/>pag. </s>

<s>188, 89). </s></p><p type="main">

<s>Il teorema V aveva pel Newton una singolare importanza, direttamente <lb/>entrando nell'ordine delle sue speculazioni, per cui ne volle, nello scolio alla <lb/>citata proposizione IV de'suoi <emph type="italics"/>Principii,<emph.end type="italics"/> far solenne commemorazione con <lb/>queste parole: &ldquo; Datur autem ex descensu gravium et tempus revolutionis <lb/>unius, et arcus, dato quovis tempore descriptus, per huius corollarium IX. </s>

<s><lb/>Ex huiusmodi propositionibus Hugenius, in eximio suo tractatu <emph type="italics"/>De horolo&shy;<lb/>gio oscillatorio,<emph.end type="italics"/> vim gravitatis cum revolventium viribus centrifugis contu&shy;<lb/>lit &rdquo; (pag. </s>

<s>103). </s></p><p type="main">

<s>Il corollario IX, che qui si cita, e per mezzo del quale si poteva, come <lb/>aveva fatto l'Huyghens, conferire la gravit&agrave; con la forza centrifuga, &egrave; scritto <lb/>dall'Autore in questa forma: <emph type="italics"/>Ex eadem demonstratione consequitur etiam <lb/>quod arcus, quem corpus in circulo, data vi centripeta, uniformiter re&shy;<lb/>volvendo tempore quovis describit; medius est proportionalis inter diame&shy;<lb/>trum circuli, et descensum corporis, eadem data vi, eodemque tempore <lb/>cadendo confectum &rdquo;<emph.end type="italics"/> (ibid., pag. </s>

<s>101, 2). </s></p><p type="main">

<s>Sia ABG (fig. </s>

<s>338) il circolo, e la forza centripeta, che urge il mobile <lb/><figure id="id.020.01.2921.1.jpg" xlink:href="020/01/2921/1.jpg"/></s></p><p type="caption">

<s>Figura 338.<lb/>in esso, sia pari a quella che ne sollecita la discesa <lb/>lungo il diametro AG, come lo solleciterebbe la gravit&agrave; <lb/>naturale, della quale dunque subir&agrave; il detto mobile le <lb/>medesime leggi, rispetto ai tempi e agli spazi passati. </s>

<s><lb/>Sia descritto l'arco AF, nel tempo della discesa AL: <lb/>consegue, dice il Newton, dalla mia dimostrazione che <lb/>AF2 &egrave; uguale ad AL.AG. </s>

<s>Preso infatti un arco mini&shy;<lb/>mo AB, in cui la forza centrifuga sappiamo essere mi&shy;<lb/>surata dal seno verso AC, per le note leggi dinamiche <lb/>gli spazi AC, AL stanno come i quadrati dei tempi, o <lb/>delle velocit&agrave;, o degli spazi percorsi nel circolo, essendo <lb/>per supposizione in esso i moti uniformi. </s>

<s>Cosicch&egrave;, divisi ambedue i termini della <lb/>seconda ragione per AG, avremo AC:AL=AB2/AG:AF2/AG. </s>

<s>E perch&egrave;, essendo <lb/>l'arco AB evanescente, uguaglia la sua sottesa, d'onde AB2=AC.AG, ossia <lb/>AC=AB2/AG; dunque anche AL=AF2/AG, e AL:AF=AF:AG, secondo quel <lb/>che veramente il Newton diceva conseguire dalla sua dimostrazione. </s></p><p type="main">

<s>Se la forza, che urge il mobile per farlo scendere lungo il diametro del <lb/>circolo, &egrave; quella della sua gravit&agrave; naturale, si giunge per facile via, dalla <pb xlink:href="020/01/2922.jpg" pagenum="547"/>stessa dimostrazion newtoniana, a concludere che la forza centripeta del mo&shy;<lb/>bile, a quella del suo peso, sta come la met&agrave; del raggio del circolo, allo spa&shy;<lb/>zio percorse nel tempo, che esso mobile, sollecitato dalla forza centripeta, <lb/>passerebbe quel medesimo mezzo raggio. </s>

<s>Cosicch&egrave;, chiamato S questo stesso <lb/>spazio, F la forza centripeta, G la gravit&agrave; del mobile o il peso, e finalmente <lb/>R il raggio, avremo F:G=R/2:S. </s>

<s>Che se S=R/2, F e G pure sono <lb/>uguali, secondo il detto quinto teorema, che l'Autore dell'Orologio oscillato&shy;<lb/>rio aveva proposto a dimostrare ai Matematici in questa forma: <emph type="italics"/>Si mobile <lb/>in circumferentia circuli feratur, ea celeritate, quam acquirit cadendo ex <lb/>altitudine, quae sit quartae parti diametri aequalis; habebit vim centrifu&shy;<lb/>gam suae gravitati aequalem: hoc est eadem vi funem, quo in centro de&shy;<lb/>tinetur, intendit, atque cum ex co suspensum est<emph.end type="italics"/> (pag. </s>

<s>189). </s></p><p type="main">

<s>Nel 1701 il marchese De l'H&ograve;pital aveva dimostrati questi medesimi <lb/>teoremi innanzi all'Accademia di Parigi, quando gi&agrave; l'Huyghens era morto <lb/>da sei anni. </s>

<s>Ma bene era vivo nel 1687, quando il Newton pubblic&ograve; per la <lb/>prima volta la sua sublime Filosofia naturale, cosicch&egrave; vedendovi esso Huy&shy;<lb/>ghens la sua scienza delle forze centrifughe, non solamente conclusa da prin&shy;<lb/>cipii pi&ugrave; generali, ma cos&igrave; altamente promossa alla Meccanica celeste, stim&ograve; <lb/>inutile oramai il suo trattatello, che perci&ograve; Burchero De Volder e Bernardo <lb/>Fullen, a'quali fu commessa la cura di pubblicarlo, insieme con gli altri <lb/>opuscoli postumi dell'Autore, dissero di aver trovato <emph type="italics"/>nequaquam convenienti <lb/>ordine dispositum.<emph.end type="italics"/> Nonostante hanno un carattere loro proprio, che li rende <lb/>degni di storia, i teoremi delle forze centrifughe ne'pendoli conici, che l'Huy&shy;<lb/>ghens fa dipendere principalmente da alcuni teoremi, la verit&agrave; de'quali, egli <lb/>dice, <emph type="italics"/>constat ex Mechanicis.<emph.end type="italics"/></s></p><p type="main">

<s>Sia il corpo C (fig. </s>

<s>339) posato sul declivio AB, e la forza che ve lo <lb/>trattiene tiri secondo la direzione orizontale CE: la proporzione di questa <lb/>forza, a quella della gravit&agrave; assoluta del detto corpo, s'avr&agrave; decomponendo <lb/>la CD, condotta perpendicolare al piano AB, nella CF, diretta secondo l'azione <lb/>della gravit&agrave;, e nella CG, diretta secondo l'azione della potenza. </s>

<s>Dalla qual <lb/><figure id="id.020.01.2922.1.jpg" xlink:href="020/01/2922/1.jpg"/></s></p><p type="caption">

<s>Figura 339.<lb/>decomposizione resulta, osservando che CG=FD, e <lb/>chiamando <emph type="italics"/>a<emph.end type="italics"/> l'angolo CDF, G la gravit&agrave;, e P la po&shy;<lb/>tenza; G:P=FC:FD=sen <emph type="italics"/>a<emph.end type="italics"/>:cos <emph type="italics"/>a<emph.end type="italics"/>=tang <emph type="italics"/>a<emph.end type="italics"/>:1, <lb/>d'onde &egrave; manifesto che, se l'inclinazione del piano <lb/>AB sull'orizonte &egrave; ad angolo semiretto, ossia se <emph type="italics"/>a<emph.end type="italics"/>= <lb/>45&deg;, G=P, e ci&ograve; vuol dire che sono uguali in quel <lb/>caso la gravit&agrave; del corpo, e la forza necessaria a te&shy;<lb/>nerlo sul declivio. </s>

<s>Per un'altra inclinazione qualun&shy;<lb/>que <emph type="italics"/>a&prime;<emph.end type="italics"/> si troverebbe, fra la gravit&agrave; e la nuova po&shy;<lb/>tenza, la proporzione G:P&prime;=tang <emph type="italics"/>a&prime;<emph.end type="italics"/>:1, d'onde si <lb/>conclude che le potenze debbono essere proporzio&shy;<lb/>nali alle tangenti degli angoli delle inclinazioni. </s>

<s>Se invece che dal piano in&shy;<lb/>clinato s'immagini poi il grave sorretto dal filo HC, come nel pendolo, fatta <pb xlink:href="020/01/2923.jpg" pagenum="548"/>rappresentare da HC la forza della trazione, questa si risolverebbe nella ver&shy;<lb/>ticale KC, e nella orizontale HK, in proporzion delle quali starebbe la gravit&agrave; <lb/>del pendolo stesso rispetto alla forza che lo sostiene in C, rimosso dalla sta&shy;<lb/>zion sua naturale. </s></p><p type="main">

<s>Premessi i quali principii meccanici, passa l'Huyghens a dimostrare: <lb/><emph type="italics"/>In curva superficie Conoidis parabolici, quod axem ad perpendiculum <lb/>erectum habeat, circuitus omnes mobilis circumferentias horizonti paral&shy;<lb/>lelas percurrentis, sive parvae, sive magnae fuerint, aequalibus temporibus <lb/>peraguntur, quae tempora singula aequantur binis oscillationibus penduli, <lb/>cuius longitudo sit dimidium lateris recti parabolae genitricis<emph.end type="italics"/> (Opuscula <lb/>posthuma, Lugd. </s>

<s>Batav. </s>

<s>1703, pag. </s>

<s>416). Questa &egrave; la VII proposizione <emph type="italics"/>De <lb/>vi centrifuga,<emph.end type="italics"/> rispondente alla VI dell'Orologio oscillatorio, la dimostrazion <lb/>della quale leggendo innanzi all'Accademia parigina, il marchese De l'H&ocirc;&shy;<lb/>pital, osservava che mancavano nella proposta dell'Autore due condizioni, <lb/>senza le quali si rimaneva indeterminata: <emph type="italics"/>prima, ut filum semper sit <lb/>superficiei Conoidis perpendiculare, altera, ut semper fiat gyratio ad per&shy;<lb/>pendicularem altitudinem dimidii lateris recti.<emph.end type="italics"/> Il De Volder rispondeva <lb/>che, se mai, la condizione mancante &egrave; una sola, riducendosi manifestamente <lb/>la seconda alla prima; ma che in effetto la proposizione ugeniana non &egrave; li&shy;<lb/>mitata da condizioni, essendo ella universalissima, come <emph type="italics"/>patet ex demonstra&shy;<lb/>tione, quam hic libellus exhibet.<emph.end type="italics"/> In sostanza il De Volder aveva ragione, <lb/>ma riuscirebbe ai Lettori del libretto la cosa anche pi&ugrave; patente, quando alla <lb/>dimostrazione, per non aver tenuto l'Autore le vie pi&ugrave; semplici, non fosse <lb/>venuta a mancare quella chiarezza, che sarebbesi potuta secondo noi conse&shy;<lb/>guire, dimostrando indipendentemente l'una dall'altra le due parti, nelle <lb/>quali &egrave; distinto il teorema. </s></p><p type="main">

<s>Quanto alla prima, essendo nella semiparabola HDB (fig. </s>

<s>340) rappre&shy;<lb/>sentata la sezion del Conoide, sul quale s'appoggi in H il corpo, condotta <lb/><figure id="id.020.01.2923.1.jpg" xlink:href="020/01/2923/1.jpg"/></s></p><p type="caption">

<s>Figura 340.<lb/>la tangente HF, e la perpendicolare HG, consegue dai <lb/>principii meccanici gi&agrave; dimostrati che la potenza, o la <lb/>forza centrifuga F che l'eguaglia, e che &egrave; necessaria a <lb/>sostenere il detto corpo in H, sta alla gravit&agrave; naturale <lb/>di lui come HG a GF: o, riguardato pendulo dal filo <lb/>HL, come l'ordinata HK alla sunnormale LK. </s>

<s>In un'al&shy;<lb/>tra posizione, per esempio M, la proporzione tra la forza <lb/>centrifuga F&prime;, e la gravit&agrave;, sarebbe quella dell'ordinata <lb/>MN, alla sunnormale NO: e perch&egrave;, per la propriet&agrave; <lb/>della curva, le sunnormali s'eguaglian tutte fra loro, <lb/>sar&agrave; dunque F:F&prime;=HK:MN. Ond'essendo le forze <lb/>centrifughe, in queste e in tutte le altre posizioni sulla <lb/>concavit&agrave; del Conoide, proporzionali ai raggi delle ro&shy;<lb/>tazioni, saranno, per la conversa della prima <emph type="italics"/>De vi cen&shy;<lb/>trifuga,<emph.end type="italics"/> i tempi periodici uguali. </s></p><p type="main">

<s>Di qui, osservando che i pendoli H, M, e tutti gli altri, descrivono coni <pb xlink:href="020/01/2924.jpg" pagenum="549"/>tutti aventi la medesima altezza uguale alla sunnormale, o alla met&agrave; del pa&shy;<lb/>rametro della parabola; veniva per corollario, senza trattenervi come fa l'Huy&shy;<lb/>ghens altro discorso, dimostrata la seguente proposizione VIII: <emph type="italics"/>Si mobilia <lb/>duo ex filis inaequalibus suspensa gyrentur, ita ut circumferentias hori&shy;<lb/>zonti parallelas percurrant, capite altero fili manente immoto, fuerint au&shy;<lb/>tem conorum, quorum superficiem fila hoc motu describunt, axes sive al&shy;<lb/>titudines aequales; tempora quoque, quibus utrumque mobile circulum <lb/>suum percurrit, aequalia erunt &rdquo;<emph.end type="italics"/> (ibid., pag. </s>

<s>418). Conversamente poi, dimo&shy;<lb/>strata questa, si sarebbe potuta per corollario dimostrar la VII, quanto alla <lb/>sua prima parte, osservando che i pendoli H, M descrivono, rotando intorno <lb/>all'asse del Conoide parabolico, coni tutti di pari altezza. </s></p><p type="main">

<s>Venendo alla seconda parte della proposizione VII, supposto essere in A <lb/>il foco della parabola, per le propriet&agrave; di lei, particolarmente dimostrate dal <lb/>Torricelli, nella VII e VIII del primo libro <emph type="italics"/>De motu gravium,<emph.end type="italics"/> sappiamo che <lb/>l'ascissa AB &egrave; uguale a un quarto, e l'ordinata AD alla met&agrave; del lato retto, <lb/>ossia del parametro, e, prolungato l'asse in E, cosicch&egrave; AB e HE siano <lb/>uguali, sappiamo pure che la linea condotta fra D ed E &egrave; tangente alla curva, <lb/>e che, il triangolo BAE essendo isoscele, l'angolo ADE &egrave; semiretto, per cui <lb/>la forza centrifuga in D, e la gravit&agrave; naturale del corpo che ivi riposa, per <lb/>i lemmi meccanici poco fa commemorati, sono uguali. </s>

<s>Di qui &egrave; che, per la <lb/>conversa della quinta di questo libretto, e dell'Orologio oscillatorio, il tempo, <lb/>in cui il corpo D compie il suo giro, sta al tempo della discesa naturale di <lb/>lui da pari altezza alla met&agrave; del raggio DA, come la circonferenza sta a quel <lb/>suo medesimo raggio: cosicch&egrave;, chiamati To.P, To.AD/2 i detti tempi, avremo <lb/>To.P:To.AD/2=2<foreign lang="greek">p</foreign>AD:AD. </s>

<s>Riguardato poi D come un pendolo, che <lb/>faccia le sue minime oscillazioni in archi di circoli osculatori alla Cicloide, <lb/>dalla XXV della seconda parte dell'Orologio oscillatorio sappiamo che il tempo <lb/>di una di queste minime oscillazioni, al tempo della scesa perpendicolare per <lb/>la met&agrave; della lunghezza del pendolo, ha la proporzione della circonferenza <lb/>al diametro: cosicch&egrave; chiamato To.O il tempo della detta minima oscilla&shy;<lb/>zione, avremo To.O:To.AD/2=2<foreign lang="greek">p</foreign>AD:2AD, ossia To.2O:To.AD/2= <lb/>2<foreign lang="greek">p</foreign>AD:AD, dalla quale, paragonata con la precedente, resulta To.P= <lb/>To.2O.E perch&egrave; il tempo periodico del corpo in D &egrave; uguale al tempo del <lb/>medesimo corpo in M, in H, o in qual si voglia altro punto della concavit&agrave; <lb/>del Conoide; si conclude generalmente cos&igrave; la proposizione, con le parole <lb/>stesse dell'Huyghens: &ldquo; Tempus ergo gyrationis in Conoide parabolico ae&shy;<lb/>quatur tempori, quo binae peraguntur oscillationes penduli, cuius longitudo <lb/>sit DA, dimidium lateris recti parabolae genitricis &rdquo; (ibid., pag. </s>

<s>417). </s></p><p type="main">

<s>Le osservazioni dunque del De l'H&ograve;pital non hanno pi&ugrave; luogo, data cos&igrave; <lb/>altra forma pi&ugrave; semplice e pi&ugrave; chiara alla VII proposizione <emph type="italics"/>De vi centrifuga.<emph.end type="italics"/><lb/>Ma fa gran maraviglia che a quegli acuti censori parigini passasse inosser-<pb xlink:href="020/01/2925.jpg" pagenum="550"/>vata la proposizione XVI di questo stesso libretto, corrispondente con la XIII <lb/>e ultima dell'Orologio oscillatorio, che un nostro Matematico, trent'anni e <lb/>pi&ugrave; dopo, sent&igrave; subodorare di falsa, cos&igrave; come l'Autore la pronunziava: <emph type="italics"/>Si <lb/>pendulum simplex oscillatione laterali maxima agitetur, hoc est, si per to&shy;<lb/>tum circuli quadrantem descendat, ubi ad punctum imum circumferen&shy;<lb/>tiae pervenerit, triplo maiori vi filum suum trahet, quam si ex illo sim&shy;<lb/>pliciter suspensum foret<emph.end type="italics"/> (ibid., pag. </s>

<s>425). </s></p><p type="main">

<s>L'occasione di sospettare che in questo teorema ugeniano s'ascondesse <lb/>una fallacia venne al Grandi, quando il Bonaventuri, esaminando varie pic&shy;<lb/>cole carte, nelle quali aveva il Viviani scritte certe cose di Meccanica, che <lb/>dovevano aggiungersi per illustrare le materie in simile argomento trattate <lb/>dal suo Maestro; ebbe a notarvi, a proposito del pendolo, quel che ivi dice <lb/>l'Autore del manoscritto, che cio&egrave; la forza, che fa esso pendolo tirando il <lb/>filo, quando sta perpendicolare all'orizonte, &ldquo; alla forza ch'egli fa tirandolo, <lb/>se si pone il filo obliquo, rimovendolo dal perpendicolo, sta come il momento <lb/>totale al momento discensivo, che avrebbe nel piano inclinato secondo l'obli&shy;<lb/>quit&agrave; del medesimo filo. </s>

<s>Il che per&ograve; non si trova esser vero, se non quando <lb/>il filo obliquamente posto si tien fermo, ma non gi&agrave; quando vibrando si <lb/>muove, perch&egrave; allora la forza centrifuga fa stirare viepi&ugrave; il filo, bench&egrave; sia <lb/>obliquo, di quando &egrave; semplicemente nella sua quiete nel perpendicolo &rdquo; <lb/>(Alb. </s>

<s>XI, 132, 33). </s></p><p type="main">

<s>Noi trattammo gi&agrave;, nella prima parte del cap. </s>

<s>IV di questo Tomo, la <lb/>presente questione, alla quale non rimane ora da aggiungere se non che, <lb/>conferite il Bonaventuri le sue osservazioni col Grandi, questi prese motivo <lb/>di correggere, e di perfezionare il teorema propostosi dal Viviani, dimostrando <lb/>che le forze centrifughe, ne'pendoli variamente inclinati all'orizonte, stanno <lb/>come i seni degli angoli delle inclinazioni. </s>

<s>Poco esperto esso Grandi nel ma&shy;<lb/>neggio dei moti misti, di che in altre parti di questa Storia vedremo gli <lb/>esempi, si condusse a ritrovare il vero per certe vie oblique, le quali nondi&shy;<lb/>meno tornano alle dirette, perch&egrave;, rimosso il pendolo AB (fig. </s>

<s>341), dalla <lb/>sua stazione perpendicolare, in C, col filo AC inclinato all'orizzonte per l'an&shy;<lb/><figure id="id.020.01.2925.1.jpg" xlink:href="020/01/2925/1.jpg"/></s></p><p type="caption">

<s>Figura 341.<lb/>golo CAD, che chiameremo <emph type="italics"/>a<emph.end type="italics"/>; decomposta <lb/>la gravit&agrave; CE, espressa con G, nella CF, <lb/>secondo la direzione del filo, e perci&ograve; mi&shy;<lb/>suratrice della forza centrifuga F, e nell'al&shy;<lb/>tra CG, ad esso filo perpendicolare; avremo <lb/>F:G=CF:CE=CH:AC=sen <emph type="italics"/>a<emph.end type="italics"/>:1. <lb/>Per un altro angolo d'inclinazione <emph type="italics"/>a&prime;<emph.end type="italics"/> si <lb/>trova allo stesso modo, tra la nuova forza <lb/>centrifuga F e la gravit&agrave; naturale, la pro&shy;<lb/>porzione F&prime;:G=sen <emph type="italics"/>a&prime;<emph.end type="italics"/>:1, e perci&ograve; F:F=sen <emph type="italics"/>a<emph.end type="italics"/>:sen <emph type="italics"/>a&prime;<emph.end type="italics"/>. </s></p><p type="main">

<s>Con questo teorema il Grandi, cos&igrave; studioso dell'Huyghens, ebbe a con&shy;<lb/>ferire la detta proposizione XVI <emph type="italics"/>De vi centrifuga,<emph.end type="italics"/> e avendo trovato che il <lb/>pendolo in B, dop'essere sceso da D, ha una forza centrifuga proporzionale <pb xlink:href="020/01/2926.jpg" pagenum="551"/>ad AB, alla quale &egrave; pure proporzionale la gravit&agrave; del peso fermo; <emph type="italics"/>parmi,<emph.end type="italics"/><lb/>ne concluse, <emph type="italics"/>che caduto il globo per tutto il quadrante DCB, dovr&agrave; tirare <lb/>il centro A doppiamente di quando gli era attaccato fermo.<emph.end type="italics"/> (Instituz. </s>

<s>mec&shy;<lb/>caniche, Firenze 1739, pag. </s>

<s>128). E cos&igrave;, per verit&agrave;, pare anche a noi, ra&shy;<lb/>gionando pure al modo dell'Huyghens, bench'egli dica che tripla, piuttosto <lb/>che doppia essere la ritirata del centro <emph type="italics"/>ad amussim experientiae consentit,<emph.end type="italics"/><lb/>perch&egrave;, immaginando esser la forza del peso fermo in B quella, che lo fa&shy;<lb/>rebbe passare equabilmente lo spazio BK, uguale ad AB, nel tempo della <lb/>discesa naturale per la stessa AB; venendo il medesimo peso da D per l'arco, <lb/>o da A per il perpendicolo, passerebbe equabilmente con l'impeto concepito, <lb/>secondo le note leggi dinamiche, spazio doppio di BK, e non triplo. </s></p><p type="main">

<s>Gli altri teoremi de'pendoli conici, che si dimostrano nel trattatello uge&shy;<lb/>niano, dipendono pi&ugrave; o meno da questi, e avendo le loro particolari appli&shy;<lb/>cazioni alla fabbrica degli Orologi, cedono d'importanza a que'primi, sopra <lb/>il metro de'quali, trasferitosi in cielo, temperava il Newton le danze degli Dei. </s></p><pb xlink:href="020/01/2927.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO IX.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Della proposta di una Meccanica nuova <lb/>e della composizione dei moti<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della <emph type="italics"/>Nouvelle Macanique<emph.end type="italics"/> di Pietro Varignon: degli errori del Cartesio e di Galileo intorno alle <lb/>propriet&agrave; dei moti composti, dimostrate da Giovan Marco Marci. </s>

<s>&mdash; II.<gap/>i ci&ograve; che operarono <lb/>i Matematici stranieri, per confutare il Cartesio, e per dimostrar come debba usarsi, e come <lb/>sia vera la regola del parallelogrammo. </s>

<s>&mdash; III. </s>

<s>Come le fallacie di Galileo seducessero il Tor&shy;<lb/>ricelli e il Viviani, e come fossero solennemente dal Borelli confermate co'suoi paralogismi. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Le promozioni date alla Scienza meccanica dagli Stranieri, nella seconda <lb/>met&agrave; del secolo XVII, parvero esser giunte al loro pi&ugrave; alto fastigio, quando <lb/>Pietro Varignon, avendo prima inserita nella sua <emph type="italics"/>Histoire de la Repubbli&shy;<lb/>que des Lettres<emph.end type="italics"/> una dissertazione, dove le condizioni dell'equilibrio nelle pu&shy;<lb/>legge si dimostravano col principio dei moti composti; leggeva poco dipoi, <lb/>innanzi all'Accademia parigina, la proposta di trattar tutte le macchine col <lb/>medesimo principio: proposta, che venne postuma alla luce nel 1725, col <lb/>titolo di <emph type="italics"/>Nouvelle Mechanique.<emph.end type="italics"/> Gli editori fecero preceder l'Opera, che si <lb/>raccolse in due grossi volumi, da un discorso, in cui diceva l'Autore come, <lb/>ripensando al metodo tenuto da Archimede, dal Cartesio e dal Wallis, nello <lb/>stabilire le leggi dell'equilibrio nelle macchine semplici, gli parve che quegli <lb/>insigni Matematici s'arrestassero piuttosto a provar la necessit&agrave; di esso equi&shy;<lb/>librio, che il modo com'egli avviene: d'onde si sent&igrave; nascere il desiderio <lb/>d'investigar le cose pi&ugrave; addentro, mettendosi dietro a nuove speculazioni, <lb/>delle quali passa a narrare il progresso. </s></p><p type="main">

<s>Dice che <emph type="italics"/>le premier obiet qui me vint &agrave; l'esprit ce fut un poids qu'une <lb/>puissance so&ucirc;tient sur un plan inclin&eacute;,<emph.end type="italics"/> intorno a che vennegli considerato <pb xlink:href="020/01/2928.jpg" pagenum="553"/>che l'impressione, fatta dal grave sul piano, &egrave; misurata dalla diagonale del <lb/>parallelogrammo, di cui siano i lati presi proporzionali al peso, e alla forza <lb/>che lo sostiene, d'onde vide aprirsi la mente a <emph type="italics"/>choses toutes nouvelles.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Apres avoir ainsi trouv&eacute;, prosegue a dire, la maniere dont l'equilibre <lb/>se fait sur des plans inclinez, je cherche, par le m&ecirc;me chemin, comment des <lb/>poids so&ugrave; tenus avec des cordes soulement, ou appliquez &agrave; des poulies, ou <lb/>bien &agrave; des leviers, font &eacute;quilibre entr'eux, au avec les puissances qui les <lb/>so&ucirc;tiennent, et j'apper&ccedil;&ucirc;s de m&ecirc;me que tout cela se faisent encore par la <lb/>voye des mouvemens composez, et avec tant d'uniformit&egrave;, que je ne pus <lb/>m'emp&ecirc;cher de croire que cette voye ne f&ugrave;t veritablement celle, que fait la <lb/>nature dans le concours d'action de deux poids, ou de deux puissances, en <lb/>faisent que leurs impressions particulieres, quelque proportions qu'elles ayent, <lb/>se confondent en une soule, qui se d&eacute;charge toute entiere sur se point, ou <lb/>se fait cet equilibre: de sorte que la raison physique des effets, qu'on admire <lb/>le plus dans les machines, me paruit &ecirc;tre justement celle des mouvemens <lb/>composez. </s>

<s>&rdquo; </s></p><p type="main">

<s>Chi legge per&ograve; queste cose dubita se siano veramente, come vuole il <lb/>Varignon, le sue speculazioni <emph type="italics"/>toutes nouvelles,<emph.end type="italics"/> e ripensa al Roberval, che <lb/>aveva anch'egli, un mezzo secolo prima, dimostrate le proporzioni dei gravi <lb/>sopra i piani inclinati, con questi stessi principii di Meccanica nuova: e ri&shy;<lb/>pensa all'Huyghens che, ne'lemmi alla VII, e nella XV proposizione <emph type="italics"/>De vi <lb/>centrifuga,<emph.end type="italics"/> dava, come cosa nota appresso i Meccanici, la regola di misurare <lb/>l'impressione di un corpo sopra un piano inclinato dalla diagonale del pa&shy;<lb/>rallelogrammo, descritto sopra due linee, l'una delle quali fosse proporzio&shy;<lb/>nale al peso, e l'altra alla forza necessaria a tenerlo sul declivio. </s>

<s>Che se si <lb/>volesse dire non essere ancora, nel 1685, quando fece il Varignon la sua <lb/>prima proposta, queste cose del Roberval e dell'Huyghens pubblicamente <lb/>note, si potrebbe rispondere che nota era senza dubbio la <emph type="italics"/>Spartostatica<emph.end type="italics"/> dello <lb/>Stevino, e notissimo il Corso matematico dell'Herigonio. </s>

<s>Ma n&egrave; perci&ograve;, fa&shy;<lb/>rebbero tuttavia istanza alcuni, sarebbe a diminuire il pregio della novit&agrave; <lb/>nella proposta dell'Accademico di Parigi, non avendo lo Stevino applicato il <lb/>principio della composizione delle forze a tutte le macchine, n&egrave; essendosi di&shy;<lb/>mostrati dall'Herigonio i principii, da'quali consegue la verit&agrave; del suo teorema. </s></p><p type="main">

<s>Comunque sia, la disputa, che troppo andrebbe in lungo, vien final&shy;<lb/>mente decisa dalla Storia, la quale si propone in questo capitolo a narrare <lb/>come la regola del parallelogrammo delle forze fosse antichissima, e come, <lb/>avendo pacificamente per tanti secoli regnato nel campo della Meccanica, <lb/>giunto a un terzo del suo corso il secolo XVII, due potentissimi nemici le <lb/>movessero guerra. </s>

<s>Contro la quale essendo andate per alcun tempo deboli <lb/>le difese, perch&egrave; soggiogate dalla prepotenza e disperse dal timore, insorsero <lb/>poi pi&ugrave; animose e tutte insieme raccolte nel Varignon, il quale, bench&egrave; non <lb/>fosse propriamente altro che il restauratore, pure ebbe il nome, e s'acqui&shy;<lb/>st&ograve; appresso i pi&ugrave; il merito di novello instauratore dei moti composti, e delle <lb/>loro pi&ugrave; ammirabili applicazioni. </s></p><pb xlink:href="020/01/2929.jpg" pagenum="554"/><p type="main">

<s>Che fosse veramente antichissima la regola del parallelogrammo si ram&shy;<lb/>memor&ograve; da noi stessi ai Lettori, infin dai principii di questa Storia della <lb/>Meccanica, dove, nella prima parte del capitolo primo dell'altro tomo, si ci&shy;<lb/>tava dalle Meccaniche di Aristotile la questione, risolutasi dal Filosofo con <lb/>dire che, se un corpo &egrave; spinto nel medesimo tempo da due forze proporzio&shy;<lb/>nali ai lati di un parallelogrammo, il moto unico che ne resulta &egrave; diretto <lb/>secondo la diagonale. </s>

<s>Che veramente poi si tenessero dai Matematici queste <lb/>dottrine per certe, e che s'applicassero a risolvere i pi&ugrave; difficili problemi <lb/>della Scienza, si mostr&ograve; per gli esempi di Leonardo da Vinci e di Vitellione, <lb/>i quali, come cosa notissima ai Meccanici; e perci&ograve; da loro universalmente <lb/>accettata, senza prendersi altra cura di dimostrarla; decomponevano le forze <lb/>dei pesi, e le velocit&agrave; dei raggi di luce, fatte rappresentare alla diagonale di <lb/>un parallelogrammo, in due altre forze o velocit&agrave; o moti, che avessero ad <lb/>essa diagonale la proporzione dei lati. </s></p><p type="main">

<s>Cos&igrave; operando, non credevano n&egrave; Leonardo n&egrave; Vitellione d'ingannarsi, <lb/>sembrando a loro le ragioni del Filosofo dimostrative, come per dimostrative <lb/>l'ebbe pure, un secolo e pi&ugrave; dopo lo Stevino, &igrave;l quale instituiva la sua nuova <lb/>Spartostatica confermando la verit&agrave; dell'aristotelico teorema. </s>

<s>Ma i dubbi erano <lb/>incominciati qualche tempo prima, quando si vollero sottilizzar col discorso <lb/>quelle prime apprensioni di verit&agrave;, cos&igrave; ben rispondenti al senso comune, e <lb/>confermate dalle esperienze. </s>

<s>Girolamo Cardano, nel libro IX dei <emph type="italics"/>Paralipo&shy;<lb/>meni,<emph.end type="italics"/> ha il capitolo X intitolato <emph type="italics"/>De motibus mirabilibus,<emph.end type="italics"/> fra le quali ma&shy;<lb/>raviglie scriveva anche questa: </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Si duobus motibus rectis idem feratur eodem modo altero ad alte&shy;<lb/>rum, ad rectum stante, movebitur secundum reclam per rectangulum, iuxta <lb/>proportionem dimetientis. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sit A (fig. </s>

<s>342) motum ad B, et eodemmodo, idest aequaliter, in <lb/>aequalibus temporibus, et regula, in qua est A, quae est AB, moveatur ver&shy;<lb/>sus CD ita, quod sit aliqua proportio inter AB et AC et ducatur AD dime&shy;<lb/>tiens: dico quod A feretur perpetuo his duobus motibus per AGD. </s>

<s>Feratur <lb/><figure id="id.020.01.2929.1.jpg" xlink:href="020/01/2929/1.jpg"/></s></p><p type="caption">

<s>Figura 342.<lb/>enim in E: igitur si regula feratur in F erit ex sup&shy;<lb/>posito AC ad AF ut AB ad AE. </s>

<s>Cumque commu&shy;<lb/>nicent rectangula in A recto, erunt similia, igitur <lb/>circa eamdem dimetientem. </s>

<s>Igitur punctum G cadet <lb/>in recta AD. </s>

<s>Quod si A moveretur aequaliter in AB, <lb/>ut AB regula versus CD, manifestum esset quod A <lb/>ferretur per dimetientem quadrati, et superficies <lb/>ABCD esset quadrata &rdquo; (<emph type="italics"/>Opera omnia,<emph.end type="italics"/> T. X, Lugduni 1663, pag. </s>

<s>516). </s></p><p type="main">

<s>La dimostrazion del Cardano, come di tutti gli Autori infino al Newton, <lb/>e lo vedremo, somiglia quella di Aristotile. </s>

<s>Ma mentre il Filosofo insegnava <lb/>andar sotto la medesima regola la composizione dei moti, qualunque si fosse <lb/>l'angolo del loro concorso, il Cardano soggiungeva quest'altro teorema: &ldquo; Si <lb/>vero eodemmodo idem punctum moveatur, sed motibus non ad rectum an&shy;<lb/>gulum constitutis, efficiet punctum istud lineam obliquam &rdquo; (ibid., pag. </s>

<s>517). <pb xlink:href="020/01/2930.jpg" pagenum="555"/>E dai paralogismi di questa cardanica dimostrazione ebbero origine que'dubbi, <lb/>i quali parve non lasciassero la mente quieta nemmeno al Keplero, quando, <lb/>introducendo nell'Ottica il metodo usato da Vitellione, di decomporre il rag&shy;<lb/>gio incidente in due, l'uno perpendicolare e l'altro parallelo alla superficie <lb/>dello specchio; chiamava con una certa espressione, che non sfugge all'at&shy;<lb/>tenzion dei Lettori, quello stesso metodo una finzione, <emph type="italics"/>commentum.<emph.end type="italics"/> Ma nei <lb/>primi quarant'anni del secolo XVII i dubbi, avutane gi&agrave; la spinta dal Car&shy;<lb/>dano, rovinarono in tali errori, che, insiem con gli sforzi per ritirarli in sul <lb/>retto sentiero, formano in questa Storia un quadro notabile, di cui con brevi <lb/>tocchi daremo il disegno. </s></p><p type="main">

<s>Quando il Cartesio volle, nel suo celebre discorso <emph type="italics"/>Del metodo,<emph.end type="italics"/> restaurar <lb/>l'Ottica, pens&ograve; di applicare alle sue dimostrazioni, sull'esempio di Vitellione, <lb/>rinnovellato poco fa dal Keplero, il principio dei moti composti. </s>

<s>Ma per poca <lb/>considerazione intorno ai teoremi gi&agrave; dimostrati dai suoi predecessori, ch'egli <lb/>al solito disprezzava, cred&egrave; che il moto resultante per esempio secondo la <lb/>diagonale del quadrato AB (fig. </s>

<s>343) dovesse equivalere alla somma dei moti <lb/>componenti fatti per AH, AC, cosicch&egrave;, supposto avere questi due moti cia&shy;<lb/>scuno un grado di velocit&agrave;, il mobile ne avesse in B acquistati due. </s>

<s>Simil&shy;<lb/>mente, facendosi il moto per AH con un grado di velocit&agrave;, e per l'AD con <lb/>due, credeva che per la diagonale AG andasse il mobile con velocit&agrave; di <lb/>tre gradi. </s></p><p type="main">

<s>Secondo questa opinione le due diagonali dunque starebbero fra loro <lb/>come due a tre, ci&ograve; che contradice apertamente ai canoni della Geometria, <lb/>perch&egrave; AB2=2AH2, e AG2=5AH2, d'onde AB:AG=&radic;4:&radic;10= <lb/>2:&radic;10. Avrebbe dovuto di qui avvedersi il Filosofo che, non potendo non <lb/>dire il vero la Geometria, quella sua opinione doveva esser falsa, ma, non <lb/>permettendogli ci&ograve; il filosofico orgoglio, ricorse allo strattagemma di riguar&shy;<lb/><figure id="id.020.01.2930.1.jpg" xlink:href="020/01/2930/1.jpg"/></s></p><p type="caption">

<s>Figura 343.<lb/>dar le linee come quelle che determinano la via, e no che <lb/>misurano la quantit&agrave; del moto. </s>

<s>Ma perch&egrave; il metodo ch'egli <lb/>seguiva supponeva le dette linee proporzionali alle quantit&agrave;, <lb/>non bast&ograve; al Cartesio l'aver sostituito i nomi alle cose, per <lb/>ricoprire il paralogismo del suo discorso, nel quale, ammet&shy;<lb/>tendosi la coesistenza delle due equazioni AB:AG=2:3, <lb/>e AB:AG=2:&radic;10, veniva a dirsi che tre &egrave; uguale alla <lb/>radice di dieci. </s>

<s>Che poi di fatto ammettesse paralogizzando il <lb/>Cartesio una tale coesistenza, si ricava dalle sue proprie pa&shy;<lb/>role, scritte in una epistola al Mersenno, per rispondere a <lb/>un suo censore, che lo aveva accusato di poca chiarezza nel chiamar <emph type="italics"/>de&shy;<lb/>terminazione al moto<emph.end type="italics"/> quel che si sarebbe dovuto piuttosto dire <emph type="italics"/>moto deter&shy;<lb/>minato.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; In primis ait me clarius locuturum fuisse, si pro determinatione mo&shy;<lb/>tum determinatum dixissem, qua in re ipsi non assentior. </s>

<s>Etsi enim dici <lb/>possit velocitatem pilae ab A ad B componi ex duabus aliis, scilicet ab A <lb/>ad H, et ab A ad C; abstinendum tamen esse putavi ab isto modo loquendi, <pb xlink:href="020/01/2931.jpg" pagenum="556"/>ne forte ita intelligeretur, ut istarum velocitatum, in motu sic composito, <lb/>quantitas et unius ad alteram proportio remaneret, quod nullo modo est ve&shy;<lb/>rum. </s>

<s>Nam si, exempli causa, ponamns pilam ab A ferri dextrorsum uno <lb/>gradu celeritatis, et deorsum uno etiam gradu, perveniet ad B cum duobus <lb/>gradibus celeritatis, eodem tempore quo alia, quae ferretur etiam ab A <lb/>dextrorsum uno gradu celeritatis, et deorsum duobus, perveniet ad G cum <lb/>tribus gradibus celeritatis: unde sequeretur lineam AB esse ad AG ut 2 <lb/>ad 3, quae tamen est ut 2 ad &radic;10 &rdquo; (<emph type="italics"/>Epist. </s>

<s>cartes.,<emph.end type="italics"/> P. III, Amstelodami 1683, <lb/>pag. </s>

<s>69). </s></p><p type="main">

<s>L'error del Cartesio in credere che, facendosi separatamente il moto per <lb/>la AH con un grado, e per l'AD con due, fosse nel composto per l'AG con <lb/>tre gradi di velocit&agrave;, esattamente serbando la somma dei due componenti; <lb/>fu comune, affinch&egrave; imparino i Lettori a credere alla divinit&agrave; dell'ingegno <lb/>degli uomini, anche a Galileo, a cui il Lagrange attribuiva l'invenzione dei <lb/>moti composti, e poi soggiungeva: <emph type="italics"/>mais il paro&icirc;t en m&ecirc;me tems que Ga&shy;<lb/>lilee n'a pas connu toute l'importance de ce theor&ecirc;me dans la theorie de <lb/>l'equilibre,<emph.end type="italics"/> e ci&ograve; dice perch&egrave;, dimostrando esso Galileo le proporzioni dei pesi <lb/>nel perpendicolo e sopra il piano inclinato, lo vede ricorrere ai principii sta&shy;<lb/>tici della leva, piuttosto che alla regola del parallelogrammo (<emph type="italics"/>Mechanique <lb/>anal.,<emph.end type="italics"/> Paris 1788, pag. </s>

<s>8). Ma non deve il celebre Matematico torinese aver <lb/>bene considerato quel teorema II, ch'egli cita dal IV dialogo delle Scienze <lb/>nuove, perch&egrave; altrimenti l'ammirazion dell'invenzione si sarebbe convertita <lb/>nella compassione del paralogismo che l'informa: paralogismo tanto men per&shy;<lb/>donabile che al Cartesio, ripensando alle tradizioni pi&ugrave; prossime, che Gali&shy;<lb/>leo ebbe di quelle dottrine. </s></p><p type="main">

<s>Accenna a cos&igrave; fatte tradizioni l'interloquio, che succede al detto teo&shy;<lb/>rema, e in cui fa a Simplicio difficolt&agrave; l'ammetter che l'impeto composto <lb/>in B (nell'ultima figura) sia maggiore del semplice in C, mentre altrove era <lb/>stato detto, e poi dimostrato, che dovevano essere que'due impeti uguali. </s>

<s><lb/>Alla quale difficolt&agrave; risponde il Salviati essersi dimostrata una tale ugua&shy;<lb/>glianza, no nel caso che il grave si muova equabilmente di moto composto, <lb/>ma quando, partendosi in A dalla quiete, scende acceleratamente lungo l'AB <lb/>inclinata sull'orizonte: intorno a che si sovverranno i Lettori come Galileo <lb/>interpellasse Luca Valerio, il quale, in una lettera scritta da Roma il di 18 Lu&shy;<lb/>glio 1609, confermava, dimostrandola cos&igrave; col principio dei moti composti, <lb/>la verit&agrave; dell'assunto: </s></p><p type="main">

<s>&ldquo; Essendo il moto del corpo grave D (fig. </s>

<s>344), mosso per l'AC al&shy;<lb/>l'orizonte BC, mobile verso la BC, e l'altro per una perpendicolare all'ori&shy;<lb/>zonte, essa ancor mobile; cosa chiara &egrave; che, quando D sar&agrave; in C, avr&agrave; acqui&shy;<lb/>stato tanto impeto, o inclinazione a velocemente moversi, che &egrave; la quantit&agrave; <lb/>dell'effetto (in quanto effetto, dico, di quella parte del moto composto, che si <lb/>fa per la perpendicolare mobile eguale alla stabile AB) quanto avrebbe acqui&shy;<lb/>stato, se D si fosse mosso per la sola perpendicolare AB &rdquo; (Alb. </s>

<s>VIII, 47, 48). </s></p><p type="main">

<s>Da questo discorso dunque, i principii che informano il quale dovevano <pb xlink:href="020/01/2932.jpg" pagenum="557"/>esser veri, perch&egrave; si vedevano condurre a conseguenze, che Galileo stimava <lb/>verissime; resultava che il moto composto non era uguale alla somma, ma <lb/>a uno solo dei componenti, rimanendosi l'altro senza effetto. </s>

<s>E perch&egrave;, non <lb/><figure id="id.020.01.2932.1.jpg" xlink:href="020/01/2932/1.jpg"/></s></p><p type="caption">

<s>Figura 344.<lb/>in questo caso solo, ma in tutti gli altri, dove le forze <lb/>sono angolari, qualche parte di esse necessariamente si <lb/>elide, avrebbe dovuto persuadersi Galileo che il moto mi&shy;<lb/>sto non pu&ograve; essere uguale, ma sempre minor della somma <lb/>dei moti semplici separati. </s>

<s>Tutt'altrimenti da ci&ograve;, che <lb/>avrebbe suggerito il retto discorso, leggiamo annunziato <lb/>cos&igrave; dall'Autore il teorema: <emph type="italics"/>Si aliquod mobile duplici <lb/>motu aequabili moveatur, nempe orizontali et perpen&shy;<lb/>diculari, impetus seu momentum lationis, ex utroque motu compositae, erit <lb/>potentia aequalis ambobus momentis priorum motuum.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Moveatur enim aliquod mobile aequabiliter duplici latione, et motioni <lb/>perpendiculari respondeat spatium AB (nella medesima ultima figura) lationi <lb/>vero horizontali, eodem tempore confectae, respondeat BC. </s>

<s>Cum igitur, per <lb/>motus aequabiles, conficiantur eodem tempore spatia AB, BC, erunt harum <lb/>lationum momenta inter se ut ipsae AB, BC. </s>

<s>Mobile vero, quod secundum <lb/>hasce duas moti&oacute;nes movetur, describit diagonalem AC: erit momentum suae <lb/>velocitatis ut AC &rdquo; (Alb. </s>

<s>XIII, 234). Chiamate dunque F, F&prime;, F&Prime; quelle forze, <lb/>o quei momenti di velocit&agrave;, sarebbe secondo questo discorso F:F&prime;=AB:BC, <lb/>e anche F:F&Prime;=AB:AC, d'onde F+F&prime;:F&Prime;=AB+BC:AC. </s>

<s>Cos&igrave; <lb/>(anche Galileo ripetendo i medesimi paralogismi del Cartesio) si pu&ograve; dire <lb/>che &egrave;, ma non lo permette la Geometria, perch&egrave;, dovendo le due parti F, F&prime; <lb/>tornare uguali al tutto F&Prime;, parrebbe che i cateti all'ipotenusa, o la linea <lb/>spezzata ABC dovesse tornare uguale alla AC linea retta. </s>

<s>Onde, a salvar da <lb/>una parte il suo proprio errore, e dall'altra la verit&agrave; geometrica, Galileo <lb/>ricorse a uno strattagemma, ch'&egrave; poi un equivoco non men meschino di <lb/>quello del Cartesio, dicendo che AB, BC, AC non son linee, ma potenze, e <lb/>sta bene che le potenze, o i quadrati di AB e di BC, uguaglino insieme la <lb/>potenza o il quadrato di AC diagonale. </s>

<s>&ldquo; Verum AC potentia aequatur ipsis <lb/>AB, BC: ergo momentum, compositum ex utrisque momentis AB, BC, est <lb/>potentia tantum illis simul sumptis aequale, quod erat ostendendum &rdquo; (ibid.). </s></p><p type="main">

<s>Quando Galileo accomodava cos&igrave; questa sua dimostrazione aveva sot&shy;<lb/>t'occhio il terzo tomo del <emph type="italics"/>Cursus Mathematicus<emph.end type="italics"/> di Pietro Herigon, stam&shy;<lb/>pato per la prima volta in Parigi nel 1634, e dove &egrave; inserito un trattatello <lb/>di Meccanica, la XII proposizione del quale &egrave; cos&igrave; espressa: <emph type="italics"/>Dato pondere, <lb/>duobus funibus suspenso, invenire quantum ponderis singuli funes ferant.<emph.end type="italics"/><lb/>La soluzion del problema &egrave; data, per dir cos&igrave;, alla mutola, per via di segni, <lb/>che sono una figura simile alla nostra (fig. </s>

<s>345) allato alla quale e sotto sono <lb/>scritte le equazioni: A=1000, C=800, D=600, EB:BF=A:C, <lb/>EB:BG=A:D. </s>

<s>Un corollario vi s'aggiunge, che dice: Se C=D= <lb/>A=100, il quadrilatero FG &egrave; una losanga, e perci&ograve; FBG=120&deg;. </s></p><p type="main">

<s>Galileo e qualunque altro lettore deduceva da quelle equazioni BF:BG= <pb xlink:href="020/01/2933.jpg" pagenum="558"/>C:D: e componendo, BF+BC:BF=C+D:A, d'onde, se veramente <lb/>le parti rimanendo intere dovessero tornare uguali al tutto, se cio&egrave; C+D=A, <lb/>come lo stesso Galileo credeva, ne sarebbe dal Teorema herigoniano venuto <lb/>per conseguenza BF+BC=BF+FE=EB, ci&ograve; che, conferito con l'al&shy;<lb/><figure id="id.020.01.2933.1.jpg" xlink:href="020/01/2933/1.jpg"/></s></p><p type="caption">

<s>Figura 345.<lb/>tro teorema recitato nel Dialogo dal Salviati, conduceva <lb/>necessariamente a dire o che non &egrave; incluso in questo <lb/>esso teorema herigoniano, o ch'egli &egrave; un'aperta fallacia, <lb/>perch&egrave;, non essendo l'angolo in F retto, le potenze di <lb/>BF e di EF insieme non sono uguali alla potenza di <lb/>BE sola. </s>

<s>Non si sa come la pensasse intorno a ci&ograve; Ga&shy;<lb/>lileo, ma nei discepoli di lui prevalse, come vedremo, <lb/>l'opinione che la regola seguita dall'Herigonio si do&shy;<lb/>vesse sospettare di falsa, e che perci&ograve; non fosse lecito <lb/>comporre i moti dei lati nella diagonale del parallelogrammo, altro che nel <lb/>caso delle forze ortogonali. </s></p><p type="main">

<s>Si potrebbe qui opportunamente ripetere da noi ai Lettori quel che <lb/>disse l'Hobbes al Mersenno, a proposito del Cartesio: vedete quanto sia fa&shy;<lb/>cile anche ai dottissimi uomini, per troppo confidar di s&egrave;, il cadere in pa&shy;<lb/>ralogismi. </s>

<s>Ma giova, per amor della dignit&agrave; dell'ingegno umano e della <lb/>Scienza, rammemorare un altro dottissimo uomo, che sanamente ragionava <lb/>in mezzo ai delirii incredibili del Cartesio e di Galileo. </s>

<s>A Giovan Marco <lb/>Marci, matematico di Praga, si deve il merito di aver dimostrate le leggi <lb/>della composizione dei moti con tal perfezione, da rimaner tuttavia superiore, <lb/>a nostro giudizio, agli stessi autori pi&ugrave; moderni. </s></p><p type="main">

<s>Due moti si possono, dice Giovan Marco, mescere in uno solo, e questo <lb/>novamente sceverarsi ne'due, non cos&igrave; per&ograve; che la miscela torni esattamente <lb/>alla somma delle parti, come a pesare con la stadera due corpi, ma facendo <lb/>de'componenti una terza cosa, che non &egrave; n&egrave; l'uno n&egrave; l'altro di quelli, ben&shy;<lb/>ch&egrave; ne partecipi delle qualit&agrave;, come a mescere insieme due colori. </s>

<s>E perch&egrave; <lb/>del moto quel che pu&ograve; sapersi &egrave; la direzione e l'intensit&agrave;, il proposito del&shy;<lb/>l'Autore &egrave; quello di dimostrare come sia diretta, e quanta sia la grandezza <lb/>della linea, che rappresenta il moto misto, rispetto alla direzione e alla gran&shy;<lb/>dezza delle linee, che rappresentano i moti semplici componenti. </s>

<s>I principii <lb/>della dimostrazione si desumono dai teoremi premessi intorno ai moti o alle <lb/>forze, che produce ne'corpi la gravit&agrave; naturale, con la continua e regolare <lb/>successione de'suoi impulsi. </s>

<s>Ora, supposto che un'altra forza qualunque operi <lb/>in modi simili a quello della gravit&agrave;, saranno simili anche le proporzioni dei <lb/>moti, qualunque sia la loro direzione assoluta, diversa da quella, che &egrave; al <lb/>centro della Terra. </s>

<s>Le forze poi, che hanno generalmente, nel rettangolo <lb/>della massa e della velocit&agrave; del corpo mosso, la loro misura, fa pi&ugrave; sempli&shy;<lb/>cemente Giovan Marco rappresentar dai quadrati, ossia dalle potenze delle <lb/>linee geometriche, sapientemente per&ograve; riducendo alla verit&agrave; logica i paralo&shy;<lb/>gismi di Galileo. </s></p><p type="main">

<s>Bench&egrave; sia cosa da tutti gli autori chiesta, e da tutti i lettori facilmente <pb xlink:href="020/01/2934.jpg" pagenum="559"/>concessa come assioma, pure il Matematico di Praga si propone per prima <lb/>cosa di dimostrare che <emph type="italics"/>Ab impulsu contrario et aequali nullus est motus; <lb/>ab impulsu vero contrario et inaequali motus est aequalis excessus maio&shy;<lb/>ris (De proportione motus,<emph.end type="italics"/> Pragae 1639, fol. </s>

<s>36 ad t.). Dopo la qual pro&shy;<lb/>posizione passa l'Autore, nella XXXI appresso, a stabilire per fondamento <lb/>alle sue dottrine: <emph type="italics"/>Motus secundum quid contrarii per lineam fiunt me&shy;<lb/>diam, cuius intervallum determinat sinus complementi inclinationis, in <lb/>ratione quam habent impulsus<emph.end type="italics"/> (ibid., fol. </s>

<s>37). </s></p><p type="main">

<s>Se il mobile dal medesimo punto A (fig. </s>

<s>346) si muova per le linee <lb/>AB, AF, inclinate fra loro ad angolo maggiore o minore di un retto, &ldquo; erunt <lb/>hi motus secundum quid contrarii, ac proinde, in eo quo sunt contrarii, tol&shy;<lb/>lunt aut impediunt suum contrarium. </s>

<s>Impulsus ergo in AF, ab impulsu in <lb/>AB, et hic ab impulsu in AF retractus, quia idem mobile esse non potest <lb/>in pluribus locis, ac proinde neque pluribus motibus agitari; movebitur motu <lb/>inter utrumque medio, cuiusmodi linea motus AD. </s>

<s>Dico huius lineae inter&shy;<lb/>vallum lineis extremis AB, AF esse sinum complementi angulorum FAD, <lb/><figure id="id.020.01.2934.1.jpg" xlink:href="020/01/2934/1.jpg"/></s></p><p type="caption">

<s>Figura 346.<lb/>BAD, in ratione quam habet impulsus AB ad impul<gap/>um <lb/>AF &rdquo; (ibid.). Condotte infatti dai punti F, B sopra la <lb/>AD le perpendicolari FC, BE, e chiamate AF, AB due <lb/>forze qualunque, proporzionali ai momenti della gravit&agrave; <lb/>naturale del medesimo corpo, o di due corpi uguali, <lb/>scendenti lungo i piani inclinati AF, AB; aveva Gio&shy;<lb/>van Marco dimostrato nella sua XIV, corrispondente con <lb/>la III del primo libro <emph type="italics"/>De motu gravium<emph.end type="italics"/> del Torricelli, <lb/>essere AF:AB=AC:AE=sen AFC:sen ABE=cos FAD:cos BAD. </s></p><p type="main">

<s>Siano ora i due moti fatti per AB, AE (fig. </s>

<s>347) lati del parallelo&shy;<lb/>grammo BE: ossendo AD il seno del complemento, ossia il coseno dell'an&shy;<lb/>golo dell'inclinazione DAE, e AC il coseno dell'angolo dell'inclinazione BA, <lb/>la direzion della resultante sar&agrave; dunque per l'ACD secondo la diagonale. </s>

<s>E <lb/>perch&egrave;, condotte dai punti E, B le perpendicolari ED, BC sopra la linea della <lb/>notata direzione, il moto per l'AE e per l'AD, come anche per l'AB e per <lb/>l'AC, o per la sua uguale DF, secondo la XIII di Giovan Marco, e pi&ugrave; di&shy;<lb/>rettamente secondo il lemma dopo la XII del sopra citato libro primo del <lb/><figure id="id.020.01.2934.2.jpg" xlink:href="020/01/2934/2.jpg"/></s></p><p type="caption">

<s>Figura 347.<lb/>Torricelli, si fanno in tempi eguali; &egrave; manifesto che nel tempo <lb/>che il mobile sarebbe, co'moti semplici separati, portato da <lb/>A in E, e da A in B, mescendosi insieme quegli stessi due <lb/>moti, sar&agrave; portato per AD+DF=AF, ossia per la diago&shy;<lb/>nale del parallelogrammo. </s>

<s>E perch&egrave;, essendo i tempi eguali, <lb/>gl'impeti per AB, AE, AF, che si chiameranno B, E, F, stanno <lb/>come gli spazi; sar&agrave; dunque B:F=AB:AF, E:F=AE:AF, <lb/>d'onde B:E=AB:AE. Componendo, B+E:E= <lb/>AB+AE:AE, e perci&ograve; B+E:F=AB+AE:AF. </s>

<s>Cos&igrave; dava G. </s>

<s>Marco ma&shy;<lb/>tematica dimostrazione di quel che aveva semplicemente asserito nella pro&shy;<lb/>posizione III, che cio&egrave;, uscita fuor dell'arco la saetta, &ldquo; quia a nullo deti-<pb xlink:href="020/01/2935.jpg" pagenum="560"/>netur, per lineam fit mediam inter tangentem et lineam rectam, sive per <lb/>diametrum parallelogrammi, cuius latera sunt in proportione illorum mo&shy;<lb/>tuum &rdquo; (ibid., fol. </s>

<s>12). </s></p><p type="main">

<s>Rimaneva ancora all'Autoro, nella presente dottrina dei moti misti, a <lb/>risolvere una questione importante: qual proporzione cio&egrave; abbia il moto per <lb/>i lati a quello per la diagonale. </s>

<s>Il Cartesio e Galileo avevano creduto essere <lb/>una tal proporzione di perfetta uguaglianza, ma in mezzo a loro cos&igrave; ingan&shy;<lb/>nati sorgeva G. </s>

<s>Marco ad annunziare in nome della verit&agrave;: <emph type="italics"/>Motus perfecte <lb/>mixtus fit per diametrum parallelogrammi, cuius latera constituit motus <lb/>simplex, et, ex impulsu quidem aequali, est aequalis semissi, ex inaequali <lb/>vero, maior semisse eiusdem motus<emph.end type="italics"/> (ibid., fol. </s>

<s>37 ad t.). </s></p><p type="main">

<s>Chiama moto perfettamente misto quello, che resulta di due moti sem&shy;<lb/>plici uguali e similmento contrari, come sarebbe in un mobile sollecitato da <lb/>forze proporzionali, e dirette secondo i lati di una figura quadrata. </s>

<s>Sia AD <lb/>questa figura (348) nella quale AD, BC diametri, intersecantisi in E. </s>

<s>Es&shy;<lb/>sendo AE2=AC2&mdash;CE2, dunque, bench&egrave; sia vero che per AE, AC i moti <lb/>sono eguali nel tempo, differiscono nulladimeno in grandezza, e CE2, ossia <lb/>AE2 &egrave; questa differenza. </s>

<s>Similmente, AB2 differisce da AE2 di BE2, ossia di <lb/>ED2, onde il moto per la diagonale AD &egrave; AE2+ED2=AD2/2. E perch&egrave; <lb/>AD2=AC2+CD2=AC2+AB2, dunque il moto misto nella diagonale <lb/><figure id="id.020.01.2935.1.jpg" xlink:href="020/01/2935/1.jpg"/></s></p><p type="caption">

<s>Figura 348.<lb/>&egrave; la met&agrave; de'moti semplici componenti. </s>

<s>&ldquo; Est autem (per <lb/>citar le parole proprie dell'Autore da noi commentate) mo&shy;<lb/>tus in AB et AC, duratione quidem, aequalis motui in AE, <lb/>per proposit. </s>

<s>XIII, magnitudine vero minor, cuius excessus <lb/>quadratum EB et EC, seu AE et ED. </s>

<s>At vero duo quadrata <lb/>AE, ED sunt semisses quadrati AD: hoc est motus in AB, <lb/>AC, cui aequale est quadratum AD, propterea quod AD sit <lb/>dupla AE aut ED; igitur motus aequaliter mixtus fit per diametrum paral&shy;<lb/>lelogrammi, et, ab aequali impulsu, est aequalis semissi utriusque motus <lb/>simul sumpti &rdquo; (ibid., fol. </s>

<s>38). </s></p><p type="main">

<s>Suppongasi in secondo luogo, presegue G. </s>

<s>Marco a dire, che i due moti <lb/>siano differenti, e precisamente FE (fig. </s>

<s>349) doppio di EG. </s>

<s>Condotte dai <lb/>vertici G, F le perpendicolari GO, FL alla diagonale EH, sar&agrave;, per i teo&shy;<lb/>remi della Geometria elementare, EF:FH=EL:LF=LF:LH, e anche <lb/>insieme EF2:FH2=EL2:LF2=LF2:LH2. </s>

<s>Avendosi poi, per le cose sup&shy;<lb/>poste, EF2=2EG2=2FH2, avremo anche LF2=2LH, ossia LF2+LH2= <lb/>FH2=3LH2: e, duplicando, 2FH2=6LH2. </s>

<s>Ora, perch&egrave; EH2=EF2+FH2, <lb/>ed EF2=2FH2, si trasformer&agrave; la trovata uguaglianza del quadrato di EH, <lb/>fatte le sostituzioni, in EH2=3FH2=9LH2, e perci&ograve; EH2/2=(4+1/2)LH2. </s>

<s><lb/>Dalla prima quadratica poi dianzi istituita resulta EL2=LF2.EF2/FH2: e perch&egrave;, <lb/>come si disse, EF2=2FH2, e si trov&ograve; LF2=2LH2, si trasformer&agrave; quella <pb xlink:href="020/01/2936.jpg" pagenum="561"/>eguaglianza del quadrato di EL, aggiuntovi il quadrato di LH, in EL2+LH2= <lb/>5LH2. </s>

<s>Dunque EL2+LH2>EH2/2. Ed essendo EL2+LH2 il moto nella dia&shy;<lb/>gonale, ed EH2=EG2+GH2=EG2+EF2 la somma dei moti semplici <lb/>componenti, quello sar&agrave; maggiore della met&agrave; di questi, come G. </s>

<s>Marco erasi <lb/>proposto di dimostrare. </s></p><p type="main">

<s>Concludesi questa teoria col rendere la ragione del perch&egrave; il moto re&shy;<lb/>sultante non sia n&egrave; possa essere uguale, come il Cartesio e Galileo crede&shy;<lb/>vano, ma si trovi sempre in difetto verso la somma dei componenti. </s>

<s>&ldquo; Causa <lb/>vero huius defectus, dice l'Autore, est contrarietas illorum motuum, ex an&shy;<lb/>gulis proveniens, cum quibus augetur et minuitur quousque angulus latescens <lb/>aequalis sit duobus rectis, in quo summa est contrarietas, ac proinde nullus <lb/>esse potest motus. </s>

<s>Angulo vero decrescente augetur similitudo motus, quou&shy;<lb/>sque, angulo deficiente, fiat una linea motus, in qua perfecta similitudo, <lb/>nulla autem contrarietas. </s>

<s>Itaque motus aequalis motum auget in cadem ra&shy;<lb/>tione: totus quidem totum, pars vero partem sibi aequalem &rdquo; (ibid., fol. </s>

<s>39). <lb/>Ci&ograve; che poi si rende evidente per la stessa figura, nella quale, diminuendo <lb/>l'angolo GEF, diminuiscono anche le perpendicolari GO, LF, e al contrario <lb/>crescono col crescer dell'angolo stesso. </s>

<s>Di quelle perpendicolari poi si dice <lb/>che misurano il difetto del moto: <emph type="italics"/>ductae lineae perpendiculares FL, GO <lb/><figure id="id.020.01.2936.1.jpg" xlink:href="020/01/2936/1.jpg"/></s></p><p type="caption">

<s>Figura 349.<lb/>metientur defectum motus in EII<emph.end type="italics"/> (fol. </s>

<s>38). <lb/>E infatti, osservando bene, rappresentano due <lb/>forze che si fanno insieme equilibrio, essendo <lb/>uguali e contrarie, per cui, son veramente la <lb/>misura dell'elisione, quando le forze stesse, di <lb/>concorrenti o di contrarie che erano, diventano <lb/>angolari. </s>

<s>Si rende la cosa anche pi&ugrave; manifesta, <lb/>costruendo i rettangoli LM, ON, in cui le forze <lb/>opposte EM, EN, che uguagliano le dette per&shy;<lb/>pendicolari, sono contrariamente applicate al <lb/>medesimo punto E. </s>

<s>Dalla qual costruzione si confermano altres&igrave; le cose <lb/>da G. </s>

<s>Marco gi&agrave; dimostrate, perch&egrave; EF2=EM2+MF2=EM2+EL2, <lb/>ed EG2=EN2+NG2=EN2+EO2, d'onde, sommando e osservando che <lb/>EM2+EN2 &egrave; uguale a zero, EF2+EG2=EH2=EL2+EO2=EL2+LH2. </s></p><p type="main">

<s>Tali cose insegnava il Matematico tedesco, e sarebbero le dottrine di lui <lb/>potute esser segno di stella ai naviganti nel periglioso oceano della Mecca&shy;<lb/>nica. </s>

<s>Ma, rimastosi quel solitario splendore velato dalle nebbie settentrionali, <lb/>predominarono nelle scuole gli errori del Cartesio e di Galileo, che, com&shy;<lb/>battuti dai matematici delle straniere nazioni, e dannosamente secondati in <lb/>Italia, porgono soggetto importante al seguito, e al termine del presente ca&shy;<lb/>pitolo di storia. </s></p><pb xlink:href="020/01/2937.jpg" pagenum="562"/><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Quel valoroso emulo del Cartesio, che fu il Roberval, l'abbiamo dovuto <lb/>pi&ugrave; volte ammirare per le sue invenzioni, non con altro argomento felice&shy;<lb/>mente da lui conseguite, che con quello dei moti composti, come nel metodo <lb/>di condur le tangenti alle curve, nella teoria del piano inclinato, quando la <lb/>potenza non &egrave; diretta secondo il declivio, e negli elegantissimi teoremi del <lb/>nodo delle funi, che tirato sta fermo, quando le forze son proporzionali alle <lb/>linee condotte dal centro di gravit&agrave; ai vertici del triangolo e della piramide. </s>

<s><lb/>Or, quello stesso Roberval aveva dimostrati i principii, de'quali faceva cos&igrave; <lb/>le applicazioni, in un libro <emph type="italics"/>Sur la composition des mouvemens,<emph.end type="italics"/> in cui parve <lb/>che le antiche tradizioni della scienza riprendessero, dopo il Cardano, il loro <lb/>naturale e libero corso. </s>

<s>S'aggiungeva al detto libro il <emph type="italics"/>Projet d'un livre de <lb/>Mechanique traitant des mouvemens composez,<emph.end type="italics"/> fecondo seme di specula&shy;<lb/>zioni larghe e profonde, gettato dalla frettolosa mano dell'Autore nel campo <lb/>della scienza, e destinato a crescere e a fruttificare nei secoli futuri, come <lb/>per esempio il seguente: <emph type="italics"/>La nature en g&eacute;n&eacute;ral possede les principes des <lb/>mouvemens simples, dont il s'en compose una infinit&eacute; d'autres dans les <lb/>animaux, vegetaux, mineraux etc.<emph.end type="italics"/> (Ouvrages de Mathem. </s>

<s>a la Haye 1731, <lb/>pag. </s>

<s>68). Ma lo splendore di tutti questi pensieri sparsi accendesi, come a <lb/>scintilla viva, a un tale teorema, posto per fondamento al trattato rober&shy;<lb/>valliano: </s></p><p type="main">

<s>&ldquo; Soit le mobile A (nella figura 347 qui poco addietro) port&eacute; par deux <lb/>divers mouvemens, desquels les lignes de direction soient AB, AE faisant <lb/>l'angle BAE, et que les mouvemens droits et uniformes soient tels, qu'en <lb/>mesme temps, que l'impression AB auroit port&eacute; le mobile en B, en mesme <lb/>temps l'impression AE l'eust port&eacute;e en E. </s>

<s>Je dis que le mobile, port&eacute; par <lb/>le mouvement compose de ces deux, sera port&eacute; le long du diametre AF du <lb/>parallelogramme AF, duquel les deux lignes AB, AE son les deux costez, <lb/>et que le mouvement, qu'il aura sur le diametre AF, sera uniforme. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ce que nous comprendrons, si nous imaginons que la ligne AB de&shy;<lb/>scendant to&ucirc;jours uniformement et parallelament a la ligne EF, jusqu'a ce <lb/>qu'elle ne soit qu'une mesme ligne avec la ligne EF, e la ligne AE se mou&shy;<lb/>vent vers la ligne BF en la mesme facon; nostre mobile A ne fait autre <lb/>chose que se rencontrer &agrave; tout moment en la commune section de ces deux <lb/>lignes. </s>

<s>Or il est assez clair que les points de cette commune section sont <lb/>tous dans le diam&eacute;tre AF, ce que nous d&eacute;monstrerons encore mieux par cette <lb/>consideration &rdquo; (ivi, pag. </s>

<s>6, 7): considerazione, che &egrave; poi quella stessa fattta <lb/>dal Cardano, e prima di lui da Aristotile, per condurre le loro dimostrazioni. </s></p><p type="main">

<s>Di qui si vede aprirsi, soggiungeva il Roberval, <emph type="italics"/>un champs d'une in&shy;<lb/>finit&eacute; de belles speculations,<emph.end type="italics"/> come sarebbero quelle, che riguardano le ri-<pb xlink:href="020/01/2938.jpg" pagenum="563"/>flessioni e le rifrazioni dei corpi obliquamente incidenti in una superficie, <lb/>che ne impedisca o ne debiliti il moto. </s>

<s>Sia AB (fig. </s>

<s>350) la direzione di <lb/>questo moto decomposto ne'due AH, AC: la riflessione dal punto B del <lb/>piano BCE, dice il Roberval, si far&agrave; con angolo uguale, o minore o mag&shy;<lb/>giore dell'angolo dell'incidenza ABC, secondo che il mobile in B acquista <lb/>impeto di risalire precisamente ad H, o sotto o sopra a questo punto, come <lb/>per esempio in G o in I, perch&egrave; nel primo caso la resultante del moto com&shy;<lb/>posto dell'orizontale BE e del verticale BH, &egrave; BF; nel secondo &egrave; BL, e nel <lb/>terzo BM. </s>

<s>Rispetto poi alle rifrazioni, soggiunge lo stesso Roberval, si pu&ograve; <lb/>supporre che nel punto dell'incidenza B il moto o aumenti o scemi la sua <lb/>prima energia, cosicch&egrave;, rimanendosi invariato il moto orizontale, il verticale <lb/>si riduca a BO maggiore di AC, o a BQ minore, nel qual primo caso la re&shy;<lb/>sultante del moto, o la rifrazione, sarebbe diretta secondo la linea BS, e nel&shy;<lb/>l'altro secondo la linea BR. </s></p><p type="main">

<s>Si presente con facilit&agrave; che in queste osservazioni aveva il Roberval di <lb/>mira l'Ottica del Cartesio, contro la quale infatti si sentono apertamente <lb/>pronunziare poco pi&ugrave; sotto le seguenti parole: &ldquo; Or il faut remarquer avec <lb/>soin cette facon de composer, et mesler les mouvemens, puis que nous vo&shy;<lb/><figure id="id.020.01.2938.1.jpg" xlink:href="020/01/2938/1.jpg"/></s></p><p type="caption">

<s>Figura 350.<lb/>yons que des personnes, les plus exerc&eacute;es dans la r&eacute;&shy;<lb/>cherche des veritez mathematiques, se sont tromp&eacute;es <lb/>en cet endroit. </s>

<s>Ainsi M. Des-Cartes, pour expliquer la <lb/>reflexion, d&eacute;crit un cercle du centre B, qui passe par <lb/>A, et trouve que le point de la circonf&eacute;rence, auquel le <lb/>mobile retournera en autant de temps, qu'il a mis &agrave; <lb/>aller de A vers B; doit estre F, au lieu que, d'un rai&shy;<lb/>sonnemeut semblable au nostre, il devoit en tirer comme <lb/>une cons&eacute;quence que le point F dans cette hypothese <lb/>se rencontrera dans la circonference du cercle d&eacute;crit du <lb/>centre B par A. </s>

<s>Secondement expliquant la r&eacute;fraction <lb/>de la bale dans l'eau, il a confondu les termes d'im&shy;<lb/>pression ou vistesse, et de determination, lesquels pourtant il avoit distinguez <lb/>peu auparavant, car en la pag. </s>

<s>17, ligne derniere, il dit <emph type="italics"/>et puis qu'elle ne <lb/>perd rien du tout de la determination.... &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Scriveva il Roberval queste censure in tale forma, da proporsi al giu&shy;<lb/>dizio del pubblico nel suo libro, ma privatamente si dirigevano epistole al <lb/>Mersenno, dove gli si facevano notare i.medesimi falli, perch&egrave; gli riferisse <lb/>al Cartesio. </s>

<s>L'Hobbes erasi fra tutti gli altri maravigliato del discorso poco <lb/>logico fatto dall'Autore della logica del <emph type="italics"/>Metodo,<emph.end type="italics"/> che cio&egrave; una cosa manife&shy;<lb/>stamente falsa si potesse dir vera, e dimostrava come invece la falsit&agrave; con&shy;<lb/>sistesse nel credere che la quantit&agrave; del moto composto fosse uguale alla <lb/>somma dei componenti, dovendo essere in realt&agrave; quella sempre minore di <lb/>questa, perch&egrave; nelle direzioni angolari tanto pi&ugrave; delle forze si elide, quanto <lb/>maggiore &egrave; l'angolo del concorso. </s>

<s>E per dimostrare anche meglio questa eli&shy;<lb/>sione, supposto essere le due forze proporzionali ad AB, AC (fig. </s>

<s>351), con-<pb xlink:href="020/01/2939.jpg" pagenum="564"/>correnti in A ad angolo retto, le decomponeva ciascuna in altre due AF, FB; <lb/>AE, EC, e osservava che si perdono nella resultante del moto per la BC le <lb/>due forze FB, EC, operanti in diversa, anzi opposta direzione. </s>

<s>Di qui con&shy;<lb/>cludeva che i moti composti nella figura 343 stanno come le diagonali AB, <lb/>AG, ossia, nell'esempio del Cartesio, come due alla radice di dieci, e non <lb/>come due a tre, secondo che il Cartesio stesso credeva si potesse dire, stra&shy;<lb/>namente paralogizzando. </s></p><p type="main">

<s>&ldquo; Nam et si pilam (per riferir le parole scritte dall'Hobbes di Parigi, <lb/>il di 7 Febbraio 1641 al Mersenno) ponamus ferri ab A (nella figura 343) <lb/>dextrorsum uno gradu celeritatis, et deorsum uno etiam gradu, non tamen <lb/><figure id="id.020.01.2939.1.jpg" xlink:href="020/01/2939/1.jpg"/></s></p><p type="caption">

<s>Figura 351.<lb/>perveniet ad B duobus gradibus celeritatis: similiter, si <lb/>A feratur dextrorsum uno gradu, deorsum duobus, non <lb/>tamen perveniet ad G tribus gradibus, ut D. </s>

<s>Descartes <lb/>supponit. </s>

<s>Supponamus enim duas rectas constitutas ad <lb/>angulum rectum BAC (come nella figura 351) sitque <lb/>velocitas ab A versus B in ratione, ad velocitatem ab <lb/>A versus C, quam habet ipsa AB ad ipsam AC: hae <lb/>duae velocitates componunt velocitatem, quae est a B versus C. </s>

<s>Dico veloci&shy;<lb/>tatem a B versus C esse ad velocitatem ab A versus C, vel ab A versus B, <lb/>ut recta BC ad rectam AC, vel AB. &rdquo; </s></p><p type="main">

<s>&ldquo; Ducatur ab A recta AD perpendicularis ad BC, et per A recta FAE <lb/>eidem BC parallela: item BF, CE perpendiculares ad FE. </s>

<s>Quoniam igitur <lb/>motus ab A ad B componitur ex motibus ab F ad A, et ab F ad B, non <lb/>contribuet motus compositus AB plus celeritatis ad motum a B versus C, <lb/>quam possunt contribuere componentes FA, FB. </s>

<s>Sed motus FB nihil con&shy;<lb/>tribuit motui a B versus C, motus enim ille determinatur deorsum, nec <lb/>omnino tendit a B versus C; solus igitur motus FA dat motum a B ver&shy;<lb/>sus C. &rdquo; </s></p><p type="main">

<s>&ldquo; Similiter probatur AC dare motum a D versus C, in virtute solius <lb/>AE. </s>

<s>Sed celeritas, quam participat AB ab AF, et qua operatur a B versus C, <lb/>est ad celeritatem totam AB in proportione FA, vel BD, ad AB: item cele&shy;<lb/>ritas, quam habet AC virtute AE est, ad celeritatem totam AC, ut AE vel <lb/>DC ad AC; sunt ergo ambae celeritates iunctae, quibus fit motus a B ver&shy;<lb/>sus C, ad celeritatem simpliciter sumptam in AC vel AB, ut tota BC ad AC, <lb/>vel AB. </s>

<s>Quare sumpta figura 343, erunt celeritates per AB, AG ut ipsae AB, <lb/>AG, hoc est ut &radic;2 ad &radic;5, hoc est ut &radic;4 ad &radic;10, hoc est ut 2 ad &radic;10, <lb/>et non ut 2 ad 3. Non igitur sequitur absurdum illud ab isto modo loquendi, <lb/>quod probat D. Descartes. </s>

<s>Vide, Pater, quam pronum sit, etiam doctissimis <lb/>viris, per nimiam securitatem, quandoque in paralogysmos incidere. </s>

<s>&rdquo; (<emph type="italics"/>Epist. </s>

<s><lb/>cart.,<emph.end type="italics"/> P. III cit., pag. </s>

<s>73, 74). </s></p><p type="main">

<s>La dimostrazione che, per essere cos&igrave; chiara, e perci&ograve; cos&igrave; efficace ad <lb/>aprire le menti a conoscere il vero dei moti misti, abbiamo voluto riferire <lb/>nella sua integrit&agrave;; l'applicava l'Hobbes al teorema cartesiano della rifles&shy;<lb/>sion della luce, per scoprir la fallacia del ragionamento. </s>

<s>In quel medesimo <pb xlink:href="020/01/2940.jpg" pagenum="565"/>tempo il Fermat notava simili fallacie, nelle quali il Cartesio stesso era in&shy;<lb/>corso a proposito delle rifrazioni, il teorema relativo alle quali si fondava <lb/>principalm&eacute;nte sul supposto che rimanesse la medesima velocit&agrave; nel raggio <lb/>rifratto, bench&egrave; l'angolo di lui colla perpendicolare variasse da quel primo <lb/>fatto nell'incidenza. </s>

<s>Era come a dire che le diagonali BR, BS, nella fig. </s>

<s>350, <lb/>sono uguali alla AB. </s>

<s>E perch&egrave; ben conosceva il Fermat nascere un tale er&shy;<lb/>rore, nell'Autor del discorso intorno al Metodo, per non aver compresa la <lb/>natura dei moti semplici, relativamente al loro composto; si mette a spie&shy;<lb/>garla in una epistola diretta al Mersenno, incominciando dal rammemorargli <lb/>come di una tal qualit&agrave; di moti avessero fatto uso Archimede, e altri ma&shy;<lb/>tematici antichi nel comporre le loro Elici, e poi soggiunge: &ldquo; verum quia <lb/>motus ille compositus non ita frequenter in usum cadit, oportet ut alio modo <lb/>consideretur, et ut specialis de eo meditatio fiat &rdquo; (ibid., pag. </s>

<s>97). </s></p><p type="main">

<s>La prima parte di questa meditazione &egrave; tale: Supposto che il mobile A <lb/><figure id="id.020.01.2940.1.jpg" xlink:href="020/01/2940/1.jpg"/></s></p><p type="caption">

<s>Figura 352.<lb/>(fig. </s>

<s>352) passi lo spazio AN in un minuto d'ora e <lb/>lo spazio AC nel medesimo tempo; con ragioni molto <lb/>simili a quelle del Roberval si conclude: &ldquo; Fiet ergo <lb/>motus compositus super linea AB, et possumus as&shy;<lb/>serere grave illud percursurum lineam AR in mi&shy;<lb/>nuto horae &rdquo; (ibid., pag. </s>

<s>98). Cosicch&egrave;, essendo i <lb/>moti equabili, e perci&ograve; le velocit&agrave;, supposta l'egua&shy;<lb/>glianza dei tempi, proporzionali agli spazi, il moto <lb/>per AB star&agrave; al moto per AN, o per AC, come la <lb/>stessa AB alle stesse AN, AC. </s></p><p type="main">

<s>Nella seconda parte del ragionamento considera il Fermat l'angolo CAN <lb/>variare, e diventar per esempio maggiore qual'&egrave; C&prime; AN&prime;, e da ragioni simili <lb/>a quelle dette di sopra &egrave; portato a concludere: &ldquo; quod eadem erit propor&shy;<lb/>tio velocitatis motus compositi in prima figura, ad velocitatem motus com&shy;<lb/>positi in secunda, quae est longitudinis lineae AB in prima ad longitudinem <lb/>lineae AB&prime; in secunda &rdquo; (ibid.). E perch&egrave; AB&prime; &egrave; manifestamente, e con fa&shy;<lb/>citit&agrave; potrebbe provarsi dover esser necessariamente minore di AB, riman <lb/>dunque cos&igrave; dimostrata la verit&agrave; del parallelogrammo delle forze, e scoperto <lb/>l'errore del Cartesio. </s></p><p type="main">

<s>Queste censure dell'Hobbes e del Fermat erano scritte, come si disse, <lb/>privatamente al Mersenno, al quale pure erano dirette le difese che, per la <lb/>propria causa, faceva lo stesso Cartesio, aggiuntevi quelle degli amici e dei <lb/>seguaci delle dottrine di lui, col non far altro insomma che avvolgersi dispe&shy;<lb/>ratamente in nuovi paralogismi. </s>

<s>Ma il Mersenno ebbe tanto giudizio e tanta <lb/>coscienza, da non avere nessun riguardo all'amico, per difendere contro lui <lb/>la verit&agrave;, pubblicamente annunziata agli erranti nella XXXII proposizione <lb/>della sua <emph type="italics"/>Ballistica.<emph.end type="italics"/> Ivi, a proposito dei moti composti, considerati nella <lb/>figura 343 qui poco addietro, com'era stata disegnata dall'Hobbes, veniva <lb/>cos&igrave; saviamente ripetendo le osservazioni lette e meditate nell'epistola di lui. <lb/></s>

<s>&ldquo; Ubi notandum est grave A latum vel impulsum uno gradu velocitatis <pb xlink:href="020/01/2941.jpg" pagenum="566"/>dextrorsum ad H, et uno gradu velocitatis deorsum in C, quibus pervenit <lb/>ad B, non acquisivisse duos gradus velocitatis, aut tres gradus in puncto G, <lb/>cum duobus gradibus celeritatis motum est ab A ad D, et uno ab A ad H <lb/>per rectam AG pervenit ad G, alioqui recta AB esset ad rectam AG ut 2 <lb/>ad 3, cum linea sit ad lineam ut celeritas ad celeritatem, quod verum non <lb/>est, quandoquidem est AB ad AG ut 2 ad radicem 10, vel ut radix 2 ad <lb/>radicem 5, hoc est: celeritas ab A ad B, ad celeritatem ab A ad G, non est <lb/>ut composita ex AH et HB, ad compositam ex AH et HG: sunt enim velo&shy;<lb/>citates ut subtensae AB, AG &rdquo; (Parisiis 1644, pag. </s>

<s>110). </s></p><p type="main">

<s>Utilissimi sarebbero tornati agli studiosi questi mersenniani avvertimenti, <lb/>se la prepotente autorit&agrave; del Cartesio e l'aforismo, male applicato al caso, <lb/>che cio&egrave; le parti debbono uguagliare il tutto, non avessero congiurato cos&igrave; <lb/>ai danni della Scienza, da consigliarla a provocare poco di poi per ristorar&shy;<lb/>sene l'opera poderosa di Giovanni Wallis. </s>

<s>Egli infatti intitolava <emph type="italics"/>De motibus <lb/>compositis, acceleratis, retardatis et proiectorum<emph.end type="italics"/> il capitolo X della terza <lb/>parte del suo trattato <emph type="italics"/>De motu,<emph.end type="italics"/> nel qual capitolo formulava cos&igrave; la VI pro&shy;<lb/>posizione: &ldquo; Si mobile, ob duas causas motrices, duos concipiat directos im&shy;<lb/>petus, puta secundum duas rectas positione datas angulum facientes, celeri&shy;<lb/>tatibus in se aequalibus, ad invicem vero eisdem ut parallelogrammi lateribus <lb/>longitudine datis proportionalibus; feretur mobile per parallelogrammi dia&shy;<lb/>gonium ea celeritate, quae sit ad datas ut diagonium illud ad respectiva <lb/>latera. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Adeoque tantumdem est, lationem quod spectat, sive feratur mobile <lb/>motu ex duobus composito, qui directiones habeant secundum parallelogrammi <lb/>latera, et celeritatibus ipsis proportionales, sive motu simplici secundum eius&shy;<lb/>dem diagonium et celeritate proportionali: quippe utrovis modo, eodem tem&shy;<lb/>pore, per eumdem tramitem eadem celeritate feretur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ideoque motui ex pluribus composito similiter accommodabitur, sive <lb/>directiones habeant in eodem plano omnes, sive secus, potestque idem pro&shy;<lb/>pterea motus infinitis modis componi. </s>

<s>&rdquo; (Londini 1671, pag. </s>

<s>654). </s></p><p type="main">

<s>E passa il Wallis a dimostrare la proposizione nelle sue tre distinte <lb/>parti, bench&egrave; le ultime due dipendano dalla prima condotta anch'essa, ad <lb/>imitazione de'precedenti Autori, dal considerar che a qualunque punto preso <lb/>in distanze proporzionali nelle linee de'moti semplici, diretti secondo i lati <lb/>del parallelogrammo, corrisponde il moto composto in un punto della dia&shy;<lb/>gonale. </s>

<s>Ma rende l'Autore in cos&igrave; fare l'immagine di colui, che perorando <lb/>si guarda sospettoso all'intorno, perch&egrave; sa di trovarsi in mezzo a contradit&shy;<lb/>tori ostinati, ai quali direttamente rivolge la parola nello Scolio dopo la pro&shy;<lb/>posizione seconda <emph type="italics"/>De elatere.<emph.end type="italics"/> Domandavano codesti contradittori al Wallis <lb/>chi gli avesse dato autorit&agrave; di decomporre un moto unico in due, presi a <lb/>capriccio e secondo gli tornava meglio, per accomodare il negozio: a'quali <lb/>il Matematico rispondeva avere avuto una tale autorit&agrave; da chi l'aveva data <lb/>a loro di decomporre per esempio il numero 8 nelle parti 2X4, o nelle <lb/>2X2X2, o nelle altre infinite, quali resulterebbero da fattori frazionari, <pb xlink:href="020/01/2942.jpg" pagenum="567"/>scegliendo fra queste infinite scomposizioni quella, che pi&ugrave; accomoda al cal&shy;<lb/>colo, certi che in ogni modo la libert&agrave; della scelta non offende le leggi o le <lb/>ragioni del vero. </s></p><p type="main">

<s>S'argomenta di qui che nel 1670 duravano quelle contradizioni dei Car&shy;<lb/>tesiani, delle quali ebbero a fare esperienza l'Hobbes e il Fermat trent'anni <lb/>prima, ed &egrave; anche resa di qui la ragione di un certo riserbo, notabile ne'Ma&shy;<lb/>tematici di que'tempi, di non professare apertamente la regola del paralle&shy;<lb/>logrammo, bench&egrave; intendessero e volessero essere intesi che quel loro me&shy;<lb/>todo, riconosciuto da tutti per vero, conduceva ai medesimi resultati di <lb/>quell'altro, che si diceva sbagliato. </s>

<s>Citeremo per primo esempio, tra quei <lb/>Matematici, Niccol&ograve; Witsen, il quale, nel suo libro <emph type="italics"/>Del modo di costruire <lb/>e di dirigere i bastimenti,<emph.end type="italics"/> pubblicato nel 1671, risolveva il problema <emph type="italics"/>In <lb/>qual modo pi&ugrave; profittevole si voltino le vele ai venti.<emph.end type="italics"/> Ma il Witsen era <lb/>discepolo dello Stevin, che egli cita, e dalla XIX proposizione statica del quale <lb/>aveva appreso il modo e la ragione di risolvere i moti nei due lati di un <lb/>triangolo, di cui l'altro lato fosse la diagonale del parallelogrammo doppio. </s>

<s><lb/>La detta proposizione steviniana &egrave; celebre nella storia del piano inclinato, <lb/>per esservi dimostrata la proporzion dei momenti dall'equilibrio della catena <lb/>posata su due pendenze di uguale altezza, ma ben si meriterebbero maggior <lb/>celebrit&agrave; di lei i corollari, de'quali se si fosse rammemorato il Roberval non <lb/>lo avremmo udito vantarsi di essere egli stato il primo a dimostrare qual <lb/>proporzione abbia alla resistenza la potenza, che tira in direzione non pa&shy;<lb/>rallela al declivio. </s></p><p type="main">

<s>Dop'aver concluso generalmente lo Stevino, nel terzo dei corollari ci&shy;<lb/>tati, che la resistenza assoluta del grave sta alla potenza che l'equilibra, come <lb/>la lunghezza del piano sta alla sua altezza; passa nel quarto a considerare <lb/>quello stesso grave configurato in un rettangolo, che, per dargli qualche <lb/>aspetto di materialit&agrave;, vuol s'intenda come la sezione di un cilindro o di <lb/>una colonna. </s>

<s>Sia dunque HG (fig. </s>

<s>353) l'asse di questa colonna, al centro <lb/>di gravit&agrave; della quale D venga applicata la fune DF, che impedisce al peso <lb/><figure id="id.020.01.2942.1.jpg" xlink:href="020/01/2942/1.jpg"/></s></p><p type="caption">

<s>Figura 353.<lb/>di scendere col contrappeso E: &ldquo; il appert que comme <lb/>AB &agrave; BC ainsi la colonne D au poids E &rdquo; (Oeuvres <lb/>mathem., Leyde 1634, pag. </s>

<s>449). E ci&ograve; detto, cos&igrave; <lb/>l'Autore soggiunge nel corollario V: &ldquo; Soit icy men&eacute;e <lb/>une perpendiculaire par le centre de la colonne D <lb/>comme DK, coupant le cost&eacute; d'icelle en L: alors le <lb/>triangle LDI sera semblable au triangle ABC, car les <lb/>angles ACB et LID sont droits, et LD est parallele &agrave; <lb/>BC, et DI &agrave; AB, par quoy comme AB &agrave; BC ainsi LD <lb/>&agrave; DI &rdquo; (ivi). E perch&egrave;, condotta la LQ parallela ed <lb/>uguale &agrave; DI, il parallelogrammo &egrave; compiuto; &egrave; mani&shy;<lb/>festo dunque che lo Stevin fu il primo a riconoscere quell'importanza del <lb/>teorema della composizione dei moti <emph type="italics"/>dans la theorie de l'equilibre,<emph.end type="italics"/> che il <lb/>Lagrange lamentava essere sfuggita alla considerazione di Galileo, &ldquo; qui au <pb xlink:href="020/01/2943.jpg" pagenum="568"/>lieu d'employer le principe de la composition du mouvement pour deter&shy;<lb/>miner directement la gravit&eacute; relative d'un corps sur un plan inclin&eacute;e, il <lb/>rappelle le plan inclin&eacute; au levier &rdquo; (<emph type="italics"/>Mechanique anal.<emph.end type="italics"/> cit., pag. </s>

<s>8). </s></p><p type="main">

<s>Ma lo Stevino rimaneva allo stesso Galileo superiore per un'altra ra&shy;<lb/>gione, per aver cio&egrave; dimostrate le condizioni dell'equilibrio, non solamente <lb/>quando la potenza agisce in direzion parallela, ma altres&igrave; quand'ella con&shy;<lb/>corre secondo qualunque obliquit&agrave; col declivio. </s>

<s>Sia DO (nella medesima <lb/>figura) questa direzione, e il peso M della colonna sia equilibrato dal con&shy;<lb/>trappeso P: condotto il piano BN, con l'inclinazione CBN uguale a IDO, <lb/>sar&agrave; per le cose dimostrate AB:BN=M:P. &ldquo; Aussi, dice lo Stevin, LD <lb/>&agrave; DO seront comme les pesanteurs y appartenans, c'est &agrave; dire comme M <lb/>&agrave; P &rdquo; (Oeuvr. </s>

<s>cit., pag. </s>

<s>449), a quel modo che se fosse compiuto, secondo <lb/>le regole note, il parallelogrammo OR. </s>

<s>A che, in guisa di Scolio soggiungesi <lb/>dall'Autore: &ldquo; Ce que dessus peut aussi estre entendu d'un globe sur la <lb/>ligne AB (fig. </s>

<s>354) comme icy joignant, l&agrave; o&ugrave; nous dirons comme devant: <lb/>que comme LD &agrave; DO, ainsi M &agrave; P (pourveu que CL soit en angles droits <lb/>sur AB, c'est &agrave; dire parallele &agrave; l'axe HG du globe D) et partant comme LD <lb/>&agrave; DO, ainsi la pesanteur du globe &agrave; P &rdquo; (ivi). </s></p><p type="main">

<s>Insegnavasi dunque dallo Stevino, come poi dal Roberval e dai Mate&shy;<lb/><figure id="id.020.01.2943.1.jpg" xlink:href="020/01/2943/1.jpg"/></s></p><p type="caption">

<s>Figura 354.<lb/>matici moderni, a usar la regola in questo modo: Inal&shy;<lb/>zate dal centro di gravit&agrave; la verticale DL, che rap&shy;<lb/>presenti il peso assoluto del globo, o la forza che lo <lb/>tien sollevato nel perpendicolo (<emph type="italics"/>elevant direct<emph.end type="italics"/>) e so&shy;<lb/>pr'essa DI come diagonale costruite un triangolo o <lb/>un parallelogrammo intero, con un de'lati perpendi&shy;<lb/>colare al piano inclinato, come HD, e con l'altro se&shy;<lb/>condo la direzione della potenza o della forza, che tira <lb/>obliquamente a sollevare lo stesso globo (<emph type="italics"/>elevation <lb/>oblique<emph.end type="italics"/>), come DO: e qual proporzione &egrave; tra la linea <lb/>DL e la DO, tale sar&agrave; tra il peso assoluto, e la potenza che lo tiene equi&shy;<lb/>librato sul declivio. </s></p><p type="main">

<s>A cos&igrave; fatta scuola ammaestrato il Witsen, francamente risolveva il suo <lb/>problema navale, rassomigliando la vela, e il vascello spinto da lei lungo il <lb/>solco apertogli dal timone, a un piano o a una riga come CD (fig. </s>

<s>355), <lb/>spingente il globo A contro l'ostacolo CB, che rende immagine dell'ostacolo <lb/><figure id="id.020.01.2943.2.jpg" xlink:href="020/01/2943/2.jpg"/></s></p><p type="caption">

<s>Figura 355.<lb/>opposto dall'acqua al moto laterale dello stesso va&shy;<lb/>scello. </s>

<s>Rappresentata con FE la forza, che spinge <lb/>la riga, o lo strale del vento, che d&agrave; nella vela, <lb/>decompone esso Witsen, secondo la regola steviniana, <lb/>la detta forza unica nelle due FD, ED: e perch&egrave; <lb/>quella non fa nessuno effetto nello spingere, riman <lb/>questa sola, che opera sopra la CD con tutta l'ener&shy;<lb/>gia, essendole condotta perpendicolare. </s>

<s>Una tale ener&shy;<lb/>gia poi si comunicherebbe tutta intera al globo A, se <pb xlink:href="020/01/2944.jpg" pagenum="569"/>l'ostacolo non ne rintuzzasse una parte, che il Witsen ha dal suo Maestro <lb/>imparato a misurare dalla FG, lato del triangolo FGB o del parallelogrammo <lb/>a lui doppio, fatta dalla diagonale FB rappresentare quella stessa energia <lb/>intera, cosicch&egrave; non rimane che la GB, altro lato di quel medesimo paralle&shy;<lb/>logrammo, a rappresentar l'attivit&agrave; e la direzion della forza, con cui la riga <lb/>sospinge innanzi il globo, o la vela il vascello. </s></p><p type="main">

<s>Premessi cos&igrave; fatti principii statici in generale, passa il Witsen ad ap&shy;<lb/>plicargli alla particolar soluzione del suo problema, considerando che la pi&ugrave; <lb/>favorevole disposizion della riga &egrave; quando della forza, che immediatamente <lb/>riceve, se ne perde meno, e perci&ograve; se ne partecipa pi&ugrave; che sia possibile: <lb/>ci&ograve; che comprendesi facilmente dovere avvenire quando sia EF/DE=FB/GB=CB/BF <lb/>Ma FE/DE=1/sen EFD, CB/BF=1/sen BCF; dunque EFD, ossia CFG, e BCF, ossia <lb/>GCE, debbono essere uguali, ed uguali anche perci&ograve; CG e GF, affinch&egrave; il <lb/>vento sopra la vela, e la vela sopra il vascello possano produrre il loro mag&shy;<lb/>gior possibile effetto, come con particolari esempi numerici si dimostra dal&shy;<lb/>l'Autore nella sua V proposizione. </s>

<s>Il modo, con cui questa &egrave; distesa, insieme <lb/>con le altre che la precedono, lo vedrenio apparirci tra poco domestico in <lb/>lingua italiana, nelle carte private del Viviani, e intanto possiam renderci di <lb/>qui la ragione del perch&egrave; l'Huyghens, olandese anch'egli come lo Stevino <lb/>e il Witsen, trattasse qual cosa nota e consentita dai Matematici della sua <lb/>nazione quel modo di comporre e decomporre nel parallelogrammo le forze, <lb/>che appresso altri Matematici era penosamente dubbioso, e fieramente con&shy;<lb/>troverso. </s></p><p type="main">

<s>Queste patrie tradizioni della Scienza le vedemmo invocate dallo stesso <lb/><figure id="id.020.01.2944.1.jpg" xlink:href="020/01/2944/1.jpg"/></s></p><p type="caption">

<s>Figura 356.<lb/>Huyghens, nel suo trattato <emph type="italics"/>De vi centrifuga,<emph.end type="italics"/> e nell'O&shy;<lb/>rologio oscillatorio, ma non possiam tacere un altro no&shy;<lb/>tabile esempio di ci&ograve;, offertoci dalla prima proposizione <lb/><emph type="italics"/>De potentiis fila funesve trahentibus,<emph.end type="italics"/> che s'informa al <lb/>teorema seguente di Geometria: Siano le due linee AB, <lb/>AC (fig. </s>

<s>356), concorrenti nell'angolo A, prese secondo <lb/>qualunque moltiplicit&agrave;, per esempio AF=N.AB, AG= <lb/>O.AC, e si costruisca sui lati AF, AG il parallelo&shy;<lb/>grammo, di cui AP sia la diagonale intersecata in E <lb/>dalla linea BC: dico che AP=AE(N+O). Condotte infatti le FQ, GR <lb/>parallele a BC, avremo AE:AR=1:O, AE:AQ=1:N, d'onde <lb/>AR:AQ=O:N, e componendo </s></p><p type="main">

<s><emph type="center"/>AR+AQ:AQ=O+N:N.<emph.end type="center"/><lb/>Osservando poi che, per essere i triangoli PFQ, ARG simili, PQ=AR, e <lb/>perci&ograve; AR+AQ=AP, torner&agrave; la scritta proporzione composta ad AP:AQ= <lb/>O+N:N, e da questa, AP:AE=O+N:1, d'onde AP=AE(O+N) <lb/>com'erasi detto. </s></p><pb xlink:href="020/01/2945.jpg" pagenum="570"/><p type="main">

<s>Ora l'Huyghens vuol dimostrare che, se le fila AB, AC son tirate da <lb/>forze proporzionali ad AB.N, AC.O, ossia ad AF, AG, la resultante o l'equi&shy;<lb/>valente di queste due forze insieme &egrave; quell'unica proporzionale ad AE(N+O), <lb/>ed &egrave; il mezzo della dimostrazione il citato teorema geometrico, che cio&egrave; l'AE, <lb/>presa molteplice secondo la somma di N con O, uguaglia la diagonale di quel <lb/>parallelogrammo, che, per le regole assai note, &egrave; atto, dice l'Autore, a rap&shy;<lb/>presentare le forze, ond'egli cos&igrave; ne conclude la propostasi verit&agrave; con que&shy;<lb/>ste parole: &ldquo; Cum ergo potentiae fila AB, AC trahentes sint ut AF, AG, <lb/>quibus acquipollet attractio per filum AE, a potentia quae sit ut AP, <emph type="italics"/>ex <lb/>theoremate mechanico satis noto;<emph.end type="italics"/> manifesta est proposita veritas &rdquo; (<emph type="italics"/>Opera <lb/>varia<emph.end type="italics"/> et T. </s>

<s>I cit., pag, 287). </s></p><p type="main">

<s>Non poteva nonostante l'Huyghens ignorare le contradizioni, alle quali <lb/>andava soggetto quel meccanico teorema appresso i Matematici, che igno&shy;<lb/>ravano o negavan fede agli insegnamenti dello Stevino, per cui parve inten&shy;<lb/>desse di confermare nella verit&agrave; i diffidenti, dimostrando come per altre vie <lb/>si giungesse a quella medesima conclusione, alla quale era giunto il Rober&shy;<lb/>val con applicarvi direttamente la regola del parallelogrammo. </s>

<s>&ldquo; Et hine pa&shy;<lb/>tet (conclude la sua proposizione seconda <emph type="italics"/>De potentiis fila funesve trahen&shy;<lb/>tibus<emph.end type="italics"/>) veritas theorematis robervalliani. <emph type="italics"/>Si a centro gravitatis pyramidis <lb/>fila tendantur ad quatuor angulos, quae trahantur a potentiis, quae sint <lb/>inter se ut filorum ipsorum longitudines; fieri acquilibrium, manente nodo <lb/>in dicto gravitatis centro &rdquo;<emph.end type="italics"/> (ibid., pag. </s>

<s>290). </s></p><p type="main">

<s>La medesima intenzione dell'Huyghens ebbe anche il De-la-Hire, quando, <lb/>nella proposizione XXI del suo <emph type="italics"/>Trait&eacute; de Mecanique,<emph.end type="italics"/> risolveva, dietro i prin&shy;<lb/>cipii statici precedentemente dimostrati, il problema robervalliano: &ldquo; Il faut <lb/>trouver trois puissances, qui tirant un point par trois directions donn&eacute;es, <lb/>soient en equilibre entr'elles &rdquo; (A Paris 1695, pag. </s>

<s>70). Che se siano que&shy;<lb/>ste tre potenze nel vigore proporzionali e dirette secondo le linee KC, KD, <lb/>KE (fig. </s>

<s>357), &ldquo; je dis que les trois puissances cherchees seron entr'elles <lb/><figure id="id.020.01.2945.1.jpg" xlink:href="020/01/2945/1.jpg"/></s></p><p type="caption">

<s>Figura 357.<lb/>comme les trois lignes EF ou GK son egale, EG ou KF, et EK, <lb/>qui son prises dans le meme ordre, et qui sont paralleles, ou <lb/>qui son partie des directions des puissances ausquelles elles re&shy;<lb/>spondent &rdquo; (ivi, pag. </s>

<s>70, 71): secondo dunque la medesima <lb/>regola prescritta da coloro, che applicano direttamente alla so&shy;<lb/>luzion del problema, imitando il Roberval, la costruzione del <lb/>parallelogrammo, ai due lati del quale prese proporzionali due <lb/>qualunque delle date potenze, facesse a queste insieme equilibrio la terza, <lb/>presa a proporzion della diagonale. </s></p><p type="main">

<s>Ma nella patria dell'Herigon e del Roberval altri matematici avevano <lb/>preceduto il De-la-Hire, dimostrando che dai principii statici del vette e del <lb/>piano inclinato si giungeva alle medesime conclusioni, che col far uso del <lb/>parallelogrammo. </s>

<s>Fra cotesti matematici &egrave; da annoverare principalmente Ga&shy;<lb/>stone Pardies, a cui par che accenni il Borelli l&agrave;, dove esamina il modo come <lb/>s'intendeva da'vari autori di confermare la verit&agrave; dei teoremi dello stesso <pb xlink:href="020/01/2946.jpg" pagenum="571"/>Herigonio, e dello Stevino. </s>

<s>Ci&ograve; vedremo particolarmente fra poco, osservando <lb/>intanto che il Pardies, il De-la-Hire, l'Huyghens, il Wallis, e gli altri com&shy;<lb/>memorati nel nostro discorso, preparavano e concorrevano all'opera del Va&shy;<lb/>rignon, i benefizi arrecati dalla quale alla Scienza si comprenderanno anche <lb/>meglio, quando gli vedremo diffondersi nella nostra Italia, dove, per i falsi <lb/>insegnamenti di Galileo, viziate le menti, erano pi&ugrave; che altrove ritrose a <lb/>riconoscere quella verit&agrave;, della quale l'Accademico di Parigi proclamava al <lb/>mondo la finale vittoria. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Viziata nelle sue pi&ugrave; profonde radici si pu&ograve; dire una cosa, quando n&egrave; <lb/>la pronta, n&egrave; la facile correzione le giova, come si vede essere avvenuto alle <lb/>menti dei discepoli di Galileo, in proposito delle dottrine intorno ai moti <lb/>composti. </s>

<s>Che pronte poi e facili fossero quelle correzioni agli errori, inse&shy;<lb/>gnati dal loro Maestro, si vede per l'esempio del Mersenno, il quale fu dei <lb/>primi a praticarle in s&egrave; stesso, a quel tempo e con quella occasione, che gli <lb/>aveva fatto riconoscere il medesimo error nel Cartesio. </s></p><p type="main">

<s>Nella proposizione XXII della sua Meccanica dimostrava cos&igrave; il Mersenno <lb/>che un moto semplice si pu&ograve; dir generato da due moti diversi: &ldquo; Sit enim <lb/>motus AB (fig. </s>

<s>358) simplex, quo globus vel aliud quodvis mobile feratur <lb/>aequabili motu ab A ad B: certum est motum illum posse componi sive ge&shy;<lb/>nerari ex motu A in D, et ex motu A in C. </s>

<s>Enim vero sint duo venti ae&shy;<lb/>quales, quorum unus ab A in C, alius ab A in D sufflet in mobile A, cuius <lb/>partes omnes sunt aequaliter mobiles. </s>

<s>Mobile non perveniet in C vel in D, <lb/>sed in B: cumque pervenerit ad I, erit in medio sui motns.... Quamquam <lb/>AB motus dici potest aequalis potentia duobus motibus AD, AC, ut est dia&shy;<lb/>meter duobus suis costis potentia aequalis &rdquo; (Parisiis 1644, pag. </s>

<s>79-81). </s></p><p type="main">

<s>Erano gi&agrave; stampati e approvati i fogli del volume, sopra i quali aveva <lb/><figure id="id.020.01.2946.1.jpg" xlink:href="020/01/2946/1.jpg"/></s></p><p type="caption">

<s>Figura 358.<lb/>inconsideratamente il Mersenno lasciate cader dalla penna <lb/>queste parole, quando le censure dell'Hobbes al Cartesio <lb/>lo fecero tutto insieme accorto della fallacia di Galileo, in <lb/>scoprire anche meglio la quale si aiutava cos&igrave; col suo proprio <lb/>discorso: Sottoponiamo in C un corpo alla percussion di un <lb/>martello, che ora venga equabilmente mosso per la diago&shy;<lb/>nale DC, ora per la GC uguale alla somma de'due lati AD, <lb/>AC: com'&egrave; possibile che faccia nel percotere il medesimo <lb/>effetto, con impeti tanto diversi, quanto la DC &egrave; diversa <lb/>dalla GC? </s>

<s>Non &egrave; egli manifesto che, concorrendo i due moti <lb/>in A ad angolo retto, si elidono insieme, e che l'elisione &egrave; <lb/>tanta, quant'&egrave; la differenza tra le due dette lunghezze lineari? </s></p><p type="main">

<s>Persuaso dunque il Mersenno, per queste evidentissime ragioni, della fal-<pb xlink:href="020/01/2947.jpg" pagenum="572"/>sit&agrave; di ci&ograve;, che era trascorso a scrivere nel testo della sua Meccanica, che <lb/>cio&egrave; i due moti per l'AD e per l'AC insieme equivalgono in potenza al moto <lb/>unico per l'AB; pens&ograve; di premettere alquante pagine innumerate, e stam&shy;<lb/>pate dopo il volume, nelle quali, fra le altre correzioni e ritrattazioni, a chi <lb/>fosse per leggere, scriveva anche questa: &ldquo; Rursus quod pagina 81, linea 28, <lb/>dicitur AB motum dici posse aequalem potentia duobus motibus AD et AC, <lb/>est ex mente Galilaei, pag. </s>

<s>250 Dialogorum, quod tamen minime verum esse <lb/>videtur. </s>

<s>Sit enim aliquid in puncto C percutiendum, malleusque percussu&shy;<lb/>rus a puncto D ad C, per DC diametrum, ita moveatur, ut motus per DC <lb/>componatur ex motu D in A, et D in B, seu A in C. </s>

<s>Si duo illi motus DA, <lb/>AC simul ita iungantur, ut malleus per lineam AC motus eodem tempore <lb/>percurreret lineam AC duplam, hoc est lineam GC, quo prius percurrebat <lb/>diametrum DC, certum est eo fortius a malleo per GC, quam a malleo per <lb/>DC, motum percussum iri, tantoque fortius, quanto recta GC longior est <lb/>recta DC, cum eo maior censeatur percussio, quo fit maiore velocitate, sit&shy;<lb/>que eo maior velocitas quo malleus percussurus, et uniformiter motus, spa&shy;<lb/>tium maius, eodem vel aequali tempore, percurrerit. </s>

<s>Hine fit ut ex motibus <lb/>per AD, AC, ex quibus AB motus componi supponitur, tantumdem perire <lb/>videatur quanto AB brevius est AD bis sumpta, et omnes motus, qui a suis <lb/>lineis rectis recedunt, semper aliquid amittent &rdquo; (<emph type="italics"/>Praefatio ad Mechan.<emph.end type="italics"/> cit.). </s></p><p type="main">

<s>Il fatto di queste perdite di forza, avvertito dal Mersenno, &egrave; tanto ma&shy;<lb/>nifesto, da persuadersene facilmente qualunque ingegno volgare, e non privo <lb/>effatto di senso comune. </s>

<s>Imperocch&egrave;, supponiamo che A sia un sasso, e AD <lb/>una fune soprammessa a un'altra fune, tirate ambedue da uomini ugual&shy;<lb/>mente validi, o nella medesima direzione. </s>

<s>Chi direbbe che seguitano con pari <lb/>forza a tirare quel peso le due funi, anche quando, invece di star come <lb/>dianzi soprammesse, si sian dilungate per un quadrante di cerchio, cosicch&egrave; <lb/>uno degli uomini sia in D, e l'altro in C? </s>

<s>Secondo il calcolo di Giovan <lb/>Marco questo secondo sforzo &egrave; ridotto alla met&agrave; del primo, ma anche senza <lb/>troppi calcoli insegna l'esperienza ai manuali di tirare, stando pi&ugrave; uniti che <lb/>sia possibile, perch&egrave; sanno che tanto &egrave; minore l'effetto delle funi, quanto <lb/>maggiore &egrave; l'angolo del loro concorso. </s>

<s>E il grande Galileo invece insegnava <lb/>che due uomini, posti in B all'estremit&agrave; della fune AB, hanno ugual po&shy;<lb/>tenza di tirare il masso A, che posti in D e in C all'estremit&agrave; delle funi <lb/>AD, AC. </s>

<s>Questo pare incredibile in tant'uomo, ma &egrave; pi&ugrave; incredibile che si <lb/>lasciassero cader cecamente nel medesimo errore di lui altri uomini come il <lb/>Torricelli, il Viviani e il Borelli, intorno a'quali ci duole di dover tratte&shy;<lb/>nerci a misurar quelle loro cadute, piuttosto che a contarne, come altre volte, <lb/>i progressi. </s></p><p type="main">

<s>Nello scolio alla proposizione XVIII del primo libro <emph type="italics"/>De motu gravium<emph.end type="italics"/><lb/>il Torricelli, quasi per digressione dal suo principale soggetto, metteva que&shy;<lb/>sto teorema: <emph type="italics"/>&ldquo; Si mobile aliquod A<emph.end type="italics"/> (fig. </s>

<s>359) <emph type="italics"/>ex angulo parallelogrammi <lb/>alicuius, vel ex quolibet puncto diametri, feratur aequabiliter duplici si&shy;<lb/>mul latione, nempe progressiva secundum lineam AC, et laterali secun-<emph.end type="italics"/><pb xlink:href="020/01/2948.jpg" pagenum="573"/><emph type="italics"/>dum AB, utcumque inclinatam, sitque proportio duarum vclocitatum ca&shy;<lb/>dem ac proportio laterum AC ad AB homologe; dico mobile iturum esse <lb/>secundum diametrum AD, hoc est per ipsam diametrum. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Si enim possibile est, feratur mobile extra diametrum per aliquod <lb/><figure id="id.020.01.2948.1.jpg" xlink:href="020/01/2948/1.jpg"/></s></p><p type="caption">

<s>Figura 359.<lb/>punctum E, ducaturque EG parallela ad AB. </s>

<s>Ergo quam pro&shy;<lb/>portionem habent spatia peracta a mobili, eam habebunt et <lb/>impetus: nempe, ut spatium progressivum peractum AG, ad <lb/>laterale peractum GE, ita impetus progressivus ad impetum <lb/>lateralem, ideoque, ut AG ad GE, ita AC ad AB, ob suppo&shy;<lb/>sitionem, sive AC ad CD, sive AG ad GI. </s>

<s>Essent ergo aequa&shy;<lb/>les GE et EI, totum et pars. </s>

<s>&rdquo; (Op. </s>

<s>geom., P. </s>

<s>I cit., pag. </s>

<s>120). </s></p><p type="main">

<s>Riconoscono bene i nostri Lettori esser questo del Torricelli quel me&shy;<lb/>desimo teorema, posto dal Roberval per fondamento alle sue osservazioni <lb/><emph type="italics"/>Sur la composition des mouvemens,<emph.end type="italics"/> con la differenza che il Nostro tiene <lb/>in dimostrar le vie oblique, piuttosto che le dirette, e sono altres&igrave; in am&shy;<lb/>bedue gli Autori medesime l'intenzioni d'applicar cio&egrave; la detta proposizione <lb/>meccanica al metodo di condur le tangenti alle curve. </s></p><p type="main">

<s>Da un tale Scolio. </s>

<s>col solo intermedio di un brevissimo lemma, si passa <lb/>alla XIX proposizione torricelliana, nella quale si dimostra dall'Autore che <lb/>gl'impeti, ne'varii punti della parabola, non son precisamente proporzionali <lb/>alle loro proprie ordinate, ma si ad altre ordinate pi&ugrave; distanti dal vertice, <lb/>quant'&egrave; la quarta parte del parametro della curva, e adduce per ragione di <lb/>ci&ograve; che queste seconde ordinate son sempre l'ipotenuse di triangoli, che hanno <lb/>per cateti le ordinate stesse de'punti respettivi, e l'ordinata del foco: d'onde, <lb/>invocando il teorema galileiano, che cio&egrave; la somma de'momenti per i cateti <lb/>equivale in potenza al momento per l'ipotenusa, ne conclude il suo intento. <lb/><figure id="id.020.01.2948.2.jpg" xlink:href="020/01/2948/2.jpg"/></s></p><p type="caption">

<s>Figura 360.<lb/>L'impeto insomma nel punto C (fig. </s>

<s>360), della parabola ACD, <lb/>della quale F sia il foco, e FH la sua ordinata; dice il Torri&shy;<lb/>celli esser proporzionale all'ordinata DE, presa BE uguale ad <lb/>AF. &ldquo; Impetus enim, qui simul sunt in C, sunt CB, HF. </s>

<s>Ergo <lb/>momentum impetus, ex ipsis compositum, debet esse potentia <lb/>ipsis aequale, per 2am Galilaei <emph type="italics"/>De motu accelerato.<emph.end type="italics"/> Sed et recta <lb/>DE aequatur potentia ipsis CB, HF, per lemma praecedens, ergo <lb/>momentum DE est momentum, sive impetus compositus ex duo&shy;<lb/>bus illis, qui sunt in puncto C &rdquo; (ibid.). </s></p><p type="main">

<s>Seguitando a svolgere il volume di queste Opere geometriche del Tor&shy;<lb/>ricelli, ci abbattiamo a leggere, in sul terminar della scrittura distesa in ita&shy;<lb/>liano, e aggiunta al trattato <emph type="italics"/>De motu proiectorum;<emph.end type="italics"/> quelle belle considera&shy;<lb/>razioni intorno al misurar quanto varino gl'impeti, fatti da una palla di <lb/>cannone contro un piano resistente, secondo il variar degli angoli dell'inci&shy;<lb/>denza: e supposto, per esempio, che sia AC, nella passata figura 358, una <lb/>muraglia, e AB la direzione del tiro, &ldquo; io noto, dice il Torricelli, che, ri&shy;<lb/>spetto alla parete AC, sono nella linea AB del proietto due moti insieme <lb/>composti: uno cio&egrave; di avvicinamento perpendicolare alla parete, l'altro di <pb xlink:href="020/01/2949.jpg" pagenum="574"/>passaggio laterale, o parallelo alla stessa. </s>

<s>Il perpendicolare ci viene e mo&shy;<lb/>strato e misurato dalla linea BC, il parallelo dalla linea AC, poich&egrave; nel me&shy;<lb/>desimo tempo vengono passati dalla palla ambedue gli spazi BC, AC &rdquo; (ivi, <lb/>pag. </s>

<s>240). </s></p><p type="main">

<s>E perch&egrave;, soggiungiamo noi a questo discorso, essendo anche la BA pas&shy;<lb/>sata nel medesimo tempo, l'impeto per essa &egrave; proporzionale allo spazio, ne <lb/>consegue che questo stesso impeto sta alla somma degl'impeti per BC, AC <lb/>come la linea AB sta alle due linee BC e AC, prese insieme. </s>

<s>Ma i detti im&shy;<lb/>peti sono in potenza uguali, secondo la dottrina di Galileo, fedelmente se&shy;<lb/>guita dal Torricelli, dunque AB &egrave; uguale a BC con AC: l'ipotenusa cio&egrave; alla <lb/>somma dei cateti, una linea retta alla spezzata. </s></p><p type="main">

<s>Come un s&igrave; grande Matematico non si avvedesse di un tale assurdo, a <lb/>cui precipitosamente menava il suo ragionamento, &egrave; cosa tanto da stupire, <lb/>che ne invoglia di ricercar la causa di s&igrave; incredibile paralogismo: ricerca <lb/>che si riduce a intendere come mai potesse il Torricelli conciliare insicme <lb/>il teorema del Roberval, dimostrato nello Scolio alla proposizione XVIII, con <lb/>quell'altro di Galileo citato nella proposizione seguente, senza considerar che, <lb/>se l'uno era vero, l'altro necessariamente doveva esser falso. </s>

<s>N&egrave;, avendo <lb/>esso Torricelli, nel discorso intorno alla Spirale archimedea, riconosciuto Ga&shy;<lb/>lileo qual restauratore dei moti composti, e imitatine gli esempi; si potrebbe <lb/>intendere quel che s&igrave; diceva senza ammetter che la notizia del teorema ro&shy;<lb/>verballiano fosse pervenuta al Nostro di Francia, d'onde si verrebbe a de&shy;<lb/>cidero <emph type="italics"/>a priori<emph.end type="italics"/> a favore del Roberval la lite famosa intorno a chi di loro <lb/>due fosse stato primo inventore del metodo delle tangenti. </s>

<s>Imperocch&egrave; &egrave; ma&shy;<lb/>nifesto che non poteva quel metodo essere spontaneamente sovvenuto nella <lb/>mente di uno, che professava dottrine fatte apposta per contradirlo. </s>

<s>Che se <lb/>il Torricelli, senza pur contradirlo, lo accolse, e lo applic&ograve; a risolvere que'suoi <lb/>vari problemi di <emph type="italics"/>Meccanica nuova,<emph.end type="italics"/> fu, con buona pace d&igrave; s&igrave; grand'uomo, <lb/>inconsideratezza, la quale si direbbe consigliata, per una parte, da quella <lb/>cieca fede che aveva alle dottrine di Galileo, e per l'altra da uno sfrenato <lb/>ardor di contendere e di non rimanere, o almeno di non apparire in nulla <lb/>inferiore al suo rivale. </s></p><p type="main">

<s>E cos&igrave;, come volle apparire, fu creduto il Torricelli dai discepoli e dagli <lb/>amici, fra'quali perci&ograve; s'inger&igrave; l'opinione ch'egli avesse introdotto nella <lb/>Meccanica, e applicato alla Geometria il parallelogrammo per la composizione <lb/>dei moti; e ch'egli avesse nel medesimo tempo, con la sua nuova autorit&agrave;, <lb/>confermate le dottrine insegnate da Galileo nel secondo teorema dei proietti. </s>

<s><lb/>N&egrave; dubitavano punto che l'una opinione repugnasse con l'altra, perch&egrave;, trat&shy;<lb/>tenendo la mente sulla proposizione XIX <emph type="italics"/>De motu gravium,<emph.end type="italics"/> non pensavano <lb/>a quel che aveva dimostrato l'Autore poco prima, o a quel ch'egli aveva <lb/>soggiunto di poi, tanto &egrave; vero che al Borelli, come i nostri Lettori gi&agrave; sanno, <lb/>pass&ograve; cos&igrave; inosservato quel che era stato scritto nell'appendice al libro tor&shy;<lb/>ricelliano <emph type="italics"/>De motu proiectorum,<emph.end type="italics"/> ch'egli si compiaceva di essere stato il primo <lb/>a dimostrar che, nelle direzioni oblique, gl'impeti delle percosse son pro-<pb xlink:href="020/01/2950.jpg" pagenum="575"/>porziali ai seni degli angoli delle incidenze. </s>

<s>Il Ricci, a cui furono dall'amico <lb/>e dal Maestro comunicati, insiem col metodo di condur le tangenti alla Ci&shy;<lb/>cloide, altri problemi di Meccanica nuova; fu della prima opinione, ma la <lb/>seconda s'apprese cos&igrave; tenacemente nel Viviani e nel Borelli, che serbarono <lb/>intorno a ci&ograve; pari fede agli oracoli dei loro due grandi maestri, bench&egrave; fos&shy;<lb/>sero in altre cose fieramente discordi. </s></p><p type="main">

<s>Era da queste discordie sollecitato nel Viviani il proposito di servirsi <lb/>della scienza anatomica del suo amico Stenone, per prevenir l'opera <emph type="italics"/>De motu <lb/>animalium,<emph.end type="italics"/> che il Borelli allora faticosamente ammanniva. </s>

<s>Ma lo Stenone, <lb/>educato alla scuola dello Stevino, trovava comodo e ragionevole, in calcolar <lb/>la potenza de'muscoli, rassomigliati a corde, che sostengono o che tirano <lb/>pesi; far uso del triangolo o del parallelogrammo intero, costruito sulle di&shy;<lb/>rezioni delle leve, con tal regola, che, sospettata dal Viviani fallace, fu pre&shy;<lb/>cipua causa del rimanersi que'suoi cos&igrave; ardenti propositi senza effetto. </s>

<s>Una <lb/>mattina, andato a far visita allo Stenone, lo trov&ograve; seduto nella sua solita <lb/>stanza innanzi a un banco, sopra il quale era posato un volumone in foglio, <lb/>legato in cartapecora, che tiratoselo con familiare libert&agrave; innanzi il soprav&shy;<lb/>venuto apr&igrave;, e nel frontespizio leggeva, o quasi si direbbe compitava, con&shy;<lb/>tornate da figure simboliche e da fregi, cos&igrave; fatte parole: <emph type="italics"/>Scheepsbouw en <lb/>Bestier, door Nicolaes Witsen, t'Amsterdam 1671.<emph.end type="italics"/> &mdash; Oh questo, disse il <lb/>Viviani, &egrave; per me un linguaggio molto simile a quello usato in Dante dalla <lb/>voce chioccia di Pluto. </s>

<s>&mdash; A cui sorridendo lo Stenone rispondeva: &mdash; Si <lb/>potrebbe tradurre <emph type="italics"/>De re navali veterum et hodierna commentarium Ni&shy;<lb/>colai Witsen:<emph.end type="italics"/> me l'hanno mandato, pochi giorni sono, i miei amici d'Olanda, <lb/>ed &egrave; libro di una variet&agrave; di cose dilettevolissime, ora di pellegrina erudi&shy;<lb/>zione, ora di sottilissima scienza. </s>

<s>Qui a facce 141 ho trovato sciolto un pro&shy;<lb/>blema utilissimo ai naviganti, e ne fa il Witsen dipendere la soluzione da <lb/>certi teoremi, ai quali so che voi non fareste buon viso, ma che io non posso <lb/>non approvare e, almeno matematicamente, tenerli per veri. </s>

<s>&mdash; E proseguiva <lb/>cos&igrave; a esporli sommariamente, ma con tanto calore, che il Viviani disse gli <lb/>avrebbe voluti volentieri esaminare con pace, se avesse avuto intelligenza <lb/>della lingua, nella quale erano scritti. </s>

<s>Allora lo Stonone si esib&igrave; di tradur&shy;<lb/>glieli in lingua italiana, giacch&egrave; non eran pi&ugrave; che cinque proposizioni, le <lb/>prime delle quali assai brevi, e il Viviani, presa la penna in mano, scriveva <lb/>a dettatura sopra certi fogli, che ci sono rimasti, e in fronte ai quali, tor&shy;<lb/>nato a casa, aggiungeva la nota, che ricopieremo qui fedelmente col resto, <lb/>quasi esotica pianticella trasposta ora in mezzo alle nostre aiole: </s></p><p type="main">

<s>&ldquo; Da Niccol&ograve; Witsen, a faccie 141, stampato in.... traduzion&egrave; detta&shy;<lb/>tami dal signor Niccol&ograve; Stenon&egrave;: <emph type="italics"/>In qual modo pi&ugrave; profittevole si voltino <lb/>le vele ai venti. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Per far questo facciasi che una linea retta, tirata dal di dietro della <lb/>vela parallela allo strale del vento, sino all'opposta banda del vascello; sia <lb/>lunga quanto una linea intercetta tra la vela e la prima linea: per esempio, <lb/>nella figura 361, la linea CD sia lo strale del vento, BA la vela. </s>

<s>Per fare <pb xlink:href="020/01/2951.jpg" pagenum="576"/>quel che si cerca, di presentare cio&egrave; nel miglior modo la vela al vento, dico <lb/>che DL deve essere uguale alla HL, il che si dimostra per mezzo delle se&shy;<lb/>guenti proposizioni, come si vedr&agrave; alla fine di esse. </s>

<s>Come parimente con <lb/>quello si dimostra in che modo si possa sapere, essendo cognita la forza del <lb/>vento, lo strale e il corso del vascello, quanto meno tutti i venti laterali, <lb/>secondo la loro natura, spingano meno il vascello, che se venissero a dar per&shy;<lb/>pendicolarmente sopra la vela, supposto che il vento perpendicolare dia la <lb/>massima velocit&agrave; al vascello. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE I. &mdash; <emph type="italics"/>Se un corpo sopra un piano orizontale viene <lb/>spinto da un altro piano perpendicolare ad esso orizonte, detto corpo dal <lb/>piano impellente si allontaner&agrave; secondo la linea perpendicolare. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia, nella medesima figura 361, il piano perpendicolare AB spinto se&shy;<lb/><figure id="id.020.01.2951.1.jpg" xlink:href="020/01/2951/1.jpg"/></s></p><p type="caption">

<s>Figura 361.<lb/>condo la linea CD, ed incontri in D il corpo E, e sia DF <lb/>perpendicolare ad AB; dico che il corpo E scorrer&agrave; secondo <lb/>la linea DF. </s>

<s>Imperocch&egrave; la spinta del piano AB non pu&ograve; far <lb/>forza sopra il corpo E per moverlo verso A o verso B, per&shy;<lb/>ch&egrave;, essendo egli egualmente piano per tutto, non vi &egrave; mag&shy;<lb/>gior ragione che deva il corpo moversi per altra via, che per <lb/>quella che perpendicolarmente l'allontana dal corpo, che im&shy;<lb/>mediatamente lo tocca, bench&egrave; obliquamente venga mosso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE II. &mdash; <emph type="italics"/>Se un piano sar&agrave; spinto da una linea obliqua, <lb/>la forza spingente, alla resistenza del piano spinto, sta come la detta linea <lb/>obliqua ad un'altra, tirata perpendicolarmente dall'estremit&agrave; di detta <lb/>obliqua. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia il detto piano AB (fig. </s>

<s>362), la linea obliqua CD, secondo la quale <lb/>venga spinta la AB. </s>

<s>Sia DE perpendicolare ad AB: dico che la forza, con <lb/>la quale il piano AB viene spinto per la linea DC, alla resistenza di detto <lb/>piano, sta come CD a DE. &rdquo; </s></p><p type="main">

<s>&ldquo; Per dimostrar questo, sia ABD una colonna; DB una leva obliqua, <lb/><figure id="id.020.01.2951.2.jpg" xlink:href="020/01/2951/2.jpg"/></s></p><p type="caption">

<s>Figura 362.<lb/>DC una leva diritta, e sia la forza traente per CF uguale <lb/>alla forza spingente per CD: il piano BA aver&agrave; la mede&shy;<lb/>sima resistenza alla forza traente, che alla spingente. </s>

<s>Ora <lb/>se il piano si tirer&agrave; per la linea EG talmente, che il piano <lb/>AB da questa forza traente patisca lo stesso che dalla <lb/>traente per CF, o dalla spingente per CD, cio&egrave; se la forza <lb/>traente per EG fosse dell'istesso vigore con quella di CF; <lb/>per la XIX proposizione della Statica di Stevino, la forza <lb/>traente per CF, o spingente per CD, alla forza traente per EG, o alla resi&shy;<lb/>stenza del piano, star&agrave; come CD a DE. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario.<emph.end type="italics"/> &mdash; Di qui &egrave; che in un corpo, spinto come nella I proposi&shy;<lb/>zione, la linea CD alla CG star&agrave; come la forza, che si applica per la linea <lb/>CD sopra il corpo E, al moto che riceve il medesimo corpo E. &rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE III. &mdash; <emph type="italics"/>Se un corpo E<emph.end type="italics"/> (fig. </s>

<s>363) <emph type="italics"/>sopra un piano ori&shy;<lb/>zontale si mover&agrave; verso un muro o qualche impedimento AB da un piano<emph.end type="italics"/><pb xlink:href="020/01/2952.jpg" pagenum="577"/><emph type="italics"/>ad esso corpo perpendicolare, e secondo la linea DF perpendicolare al <lb/>piano CD; la forza per DF, alla forza o resistenza del corpo E, star&agrave; <lb/>come AB ad AD, quando ADF &egrave; perpendicolare a DB. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Imperocch&egrave; sia BD come un piano obliquo, secondo la passata pro&shy;<lb/><figure id="id.020.01.2952.1.jpg" xlink:href="020/01/2952/1.jpg"/></s></p><p type="caption">

<s>Figura 363.<lb/>posizione, e sia EG parallela alla linea DF, ed <lb/>EH parallela ad AB, ed LK perpendicolare ad <lb/>AB. </s>

<s>Sia EL una leva d'una forza traente in <lb/>G, che tanto ritenga il corpo, quanto esso viene <lb/>spintogli contro dal piano CDB, il che si pu&ograve; <lb/>supporre, ed EM sia una leva d'una forza <lb/>traente in H, che parimente ritenga il corpo <lb/>E in equilibrio, con la forza spingente il me&shy;<lb/>desimo corpo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Questo cos&igrave; supposto, di nuovo, secondo la proposizione XIX della <lb/>Statica di Stevino, sar&agrave; EL ad EM come la forza in G o la spinta in FD <lb/>alla forza in H, o alla spinta del corpo E secondo la linea HME. </s>

<s>Ma per <lb/>essere EM ed EL parallele alle AB ed AD, gli angoli I ed A sono uguali, <lb/>siccome sono uguali EML, ADB per essere retti; e perci&ograve; li due triangoli <lb/>EML, ADB sono simili. </s>

<s>Onde ne segue che AB ad AD, come EL ad EM, <lb/>cio&egrave; come la forza traente in G, o la spinta in FD, alla forza traente in H, <lb/>ovvero alla forza, che spinge il corpo E. &rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE IV. &mdash; <emph type="italics"/>Trovar la forza, con la quale un corpo cam&shy;<lb/>mina sopra un piano orizontale lungo un impedimento, quando sia mosso <lb/>da un piano, che sia spinto obliquamente. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia, come di sopra, il corpo E (fig. </s>

<s>364), l'impedimento AB, il piano <lb/>spingente AC secondo la linea GH: si cerca la forza, con la quale il corpo <lb/><figure id="id.020.01.2952.2.jpg" xlink:href="020/01/2952/2.jpg"/></s></p><p type="caption">

<s>Figura 364.<lb/>E viene spinto lungo l'impedimento AB. </s>

<s><lb/>Per esempio, se in GH fosse un peso di <lb/>10 libbre, essendo GC perpendicolare ad <lb/>AC, e BDF perpendicolare alla medesima <lb/>AC, e sia trovato che HG a GC stia come <lb/>5 a 4: sar&agrave; come 5 a 4 cos&igrave; 19 libbre <lb/>ad 8, le quali in FD bisogneranno per <lb/>spingere il corpo E con una forza uguale <lb/>a 10 libbre per la linea GH, per la se&shy;<lb/>conda dimostrata proposizione. </s>

<s>Ora sia <lb/>trovato AB a BD stare come 4 a 3: star&agrave; <lb/>come 4 a 3, cos&igrave; 8 libbre in FD, a libbre 6, che &egrave; la forza cercata, cio&egrave; quella, <lb/>con la quale il corpo E viene ad essere spinto da una spinta obliqua se&shy;<lb/>condo GH di 10 libbre lungo l'impedimento AB, per la terza proposizione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE V. &mdash; <emph type="italics"/>Data una linea, per la quale un piano debba <lb/>essere spinto per far camminare un corpo lungo un dato impedimento, <lb/>trovare lo stato, il sito o inclinazione del piano spingente, per far cam&shy;<lb/>minare il detto corpo con la massima forza possibile. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><pb xlink:href="020/01/2953.jpg" pagenum="578"/><p type="main">

<s><emph type="italics"/>&ldquo; Primo caso.<emph.end type="italics"/> &mdash; Sia il corpo A (nella figura 355 poco addietro rap&shy;<lb/>presentata) l'impedimento BC, la linea, per la quale si fa la forza, EFG, po&shy;<lb/>sta perpendicolare all'impedimento CB. </s>

<s>Volendo dare una tal situazione a <lb/>CD, che faccia la maggior possibile forza contro il corpo A, si tiri la linea <lb/>CFD in modo, che CG sia uguale a GF, e quella sar&agrave; la linea desiderata, <lb/>secondo la quale si deve situare il piano, per spingere il corpo A con la <lb/>maggiore forza possibile. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Imperocch&egrave;, essendo i due lati GC, GF uguali del triangolo CGF, e <lb/>ciascuno mezzo retto, e similmente gli angoli DFE, DEF uguali fra loro nel <lb/>triangolo EDF, siccome gli angoli FCB, FBC nel triangolo FBC, per essere <lb/>questi tre triangoli simili fra loro; dico dunque che posta EF libbre 2, a <lb/>ED 1, cos&igrave; libbre 10, che &egrave; la forza per EF, alle 5 libbre; questa sar&agrave; la <lb/>forza spingente il piano. </s>

<s>Inoltre, come BC 2 a BF 1, cos&igrave; libbre 10 spingenti <lb/>il piano, a libbre 5, e questa sar&agrave; la forza, con la quale viene spinto il <lb/>corpo A. &rdquo; </s></p><p type="main">

<s>&ldquo; Ponghiamo adesso CG maggiore di GF nella proporzione, per esem&shy;<lb/>pio, di 4 a 3, ossia ponghiamo che il quadrato di CG stia al quadrato di GF <lb/>come 16 a 9: essendo il triangolo CGF rettangolo in G, il quadrato di CF <lb/>sar&agrave; 25, e CF 5, onde EF ad ED sar&agrave; come 5 a 4, per essere gli angoli <lb/>GFC, DFE uguali, e gli angoli FGC, FDE retti, e per&ograve; i triangoli simili. </s>

<s><lb/>Parimente, avendo i triangoli FGC, BCF un angolo comune C, e ciascuno <lb/>un retto FGC e BFC, saranno essi triangoli simili tra loro, onde BC a BF <lb/>sta come 5 a 3. &rdquo; </s></p><p type="main">

<s>&ldquo; Facciasi dunque come EF 5 a DE 4, cos&igrave; 10 libbre di forza ad 8 di <lb/>resistenza del piano: inoltre si faccia come BC 5 a BF 3, cos&igrave; 8 libbre di <lb/>resistenza a 4+4/5 di forza, con la quale il corpo A viene spinto, la quale <lb/>&egrave; minore delle cinque libbre trovate nel primo supposto. </s>

<s>Nel medesimo modo, <lb/>se ponghiamo GC minore di GF, troveremo 4+4/5 per la forza premente <lb/>il corpo A, posto cio&egrave; che GC a GF stia come 3 a 4, sicch&egrave;, quando GC <lb/>e GF sono uguali, la spinta per EF sar&agrave; la pi&ugrave; vantaggiosa. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Secondo caso.<emph.end type="italics"/> &mdash; Sia dato il corpo A, (fig. </s>

<s>365) la linea, per la quale si <lb/>fa la forza, FDG, l'impedimento BC non perpendicolare ad FG: per trovare <lb/><figure id="id.020.01.2953.1.jpg" xlink:href="020/01/2953/1.jpg"/></s></p><p type="caption">

<s>Figura 365.<lb/>quel che si domanda facciasi GC uguale a GD, e <lb/>giunta la linea CDE, questa sar&agrave; la desiderata <lb/>situazione del piano. </s>

<s>Imperocch&egrave; DF ad EF stia <lb/>come 5 a 3, come &egrave; lecito di supporre secondo <lb/>il caso di Stevino. </s>

<s>Facciasi dunque come 5 a 3, <lb/>cos&igrave; 10 libbre di forza in FD, a 6 libbre di re&shy;<lb/>sistenza del piano, e per essere GC, GD uguali <lb/>saranno anco uguali gli angoli GDC, GCD. </s>

<s>Ma <lb/>GDC &egrave; anco uguale all'EDF, dunque EDF &egrave; <lb/>uguale a GCD, ovvero BBD, e gli angoli BDG, <lb/>DEF son retti, onde i triangoli BDC, FED sono simili: sicch&egrave;, come CB a <lb/>BD, cos&igrave; DF ad FE, cio&egrave; come 5 a 3. Si faccia dunque come BC 5 a BD 3, <pb xlink:href="020/01/2954.jpg" pagenum="579"/>cos&igrave; libbre sei di resistenza del piano, a libbre 3 3/5, che sar&agrave; la forza, con <lb/>cui il corpo A viene spinto. </s>

<s>Ma posto GC maggiore, ovvero minore di GD, <lb/>il corpo A non verr&agrave; spinto con tanta forza, come si prova per il calcolo, <lb/>e perci&ograve; questa &egrave; la situazione pi&ugrave; vantaggiosa del piano DC. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario I.<emph.end type="italics"/> &mdash; Per la quarta proposizione si &egrave; dimostrato il modo <lb/>di trovare per mezzo del calcolo la forza, con la quale un vascello viene <lb/>spinto, quando sia data la forza del vento contro la vela, e lo strale del vento, <lb/>e la situazione della vela. </s>

<s>Imperocch&egrave; sia AB (fig. </s>

<s>366) un vascello, che per <lb/><figure id="id.020.01.2954.1.jpg" xlink:href="020/01/2954/1.jpg"/></s></p><p type="caption">

<s>Figura 366.<lb/>mezzo del timone viene forzato a cammi&shy;<lb/>nare lungo la linea AB, ovvero FG, lo <lb/>strale del vento sia CD, la vela EF, e sia <lb/>il vento di mille libbre di peso, ovvero sia <lb/>la sua forza bastante a operare come se <lb/>fosse di tanto peso, il qual vento per la <lb/>linea CD, o altra parallela ad essa, urti <lb/>nella vela, e sia dato che DC ad EC stia <lb/>come 5 a 3. Facciasi come DC 5 ad EC 3, cos&igrave; libbre mille a seicento, che <lb/>questa sar&agrave; la resistenza della vela. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di nuovo, sia per esempio che GF a GD stia come 5 a 4. Si faccia <lb/>come 5 a 4, cos&igrave; seicento libbre a quattrocento ottanta, che questa sar&agrave; la <lb/>forza spingente il vascello, il che chiaramente apparisce per la quarta pro&shy;<lb/>posizione. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario II.<emph.end type="italics"/> &mdash; Dalla quinta proposizione si cava come la vela deve <lb/>esser situata col maggiore avvantaggio, quando sia data la linea del vento. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia di nuovo, nella medesima figura, il vascello AB andante da B <lb/>in A, sia FG l'impedimento, HG la linea del vento, FE la vela, la quale si <lb/>deve situare in tal maniera, che FG sia uguale a GD, tirando la vela da F <lb/>per D ad E, il qual tiramento, per la quinta proposizione, dar&agrave; la maggior <lb/>forza per far camminare il vascello, il che &egrave; quello, che io mi sono propo&shy;<lb/>sto di dimostrare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E questo da tutti i marinari pu&ograve; essere praticato, misurando la lun&shy;<lb/>ghezza della banda dal luogo, dove vien segata dalla vela, sino al luogo, dove <lb/>la linea del vento taglia l'istessa banda, facendo quella uguale con la linea <lb/>tirata dal luogo della banda, che vien tagliata dalla linea del vento, sino al <lb/>corpo della vela. </s></p><p type="main">

<s>&ldquo; Qui non paia strano che si misuri il vento a libbre, giacch&egrave; si pu&ograve; <lb/>pesarlo, o almeno la di lui forza. </s>

<s>Ma caso che la parola di peso vi dispiac&shy;<lb/>cia, valetevi di quella de'gradi in suo luogo, e dite un vento di tanti gradi <lb/>di forza o potenza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Vero &egrave; bene che, a voler praticar ci&ograve;, non si troverebbe sempre che <lb/>tutto a capello riuscisse con quella esattezza, che qui si &egrave; scritto, il che ac&shy;<lb/>caderebbe, perch&egrave; di rado la forza del vento &egrave; uniforme per lungo tempo, e <lb/>i vascelli per alcune ragioni talvolta deviano dalla linea del loro cammino, <lb/>e per l'incostanza degli impedimenti, e per non essere la situazione della <pb xlink:href="020/01/2955.jpg" pagenum="580"/>vela simile a quella delle tavole, fermandosi queste nella situazione che si <lb/>d&agrave; loro, laddove le vele vengono stravolte da ogni minimo moto. </s>

<s>&rdquo; (MSS. <lb/>Gal., T. CLXI, fol. </s>

<s>1-6). </s></p><p type="main">

<s>Qual si fosse il giudizio riportato dal Viviani dopo la diligente lettura <lb/>di questi teoremi del Witsen, e dopo le istanze fattegliene dallo Stenone, <lb/>non si potrebbe dir con esattezza, ma noi crediamo che si rimanesse tuttavia <lb/>fedele agl'insegnamenti di Galileo, sedotto, e confermatovi forse da quelle <lb/>esperienze, che gli fecero eludere gli avvedimenti saggiamente suggeritigli <lb/>da Michelangiolo Ricci, quando si trattava di risolvere, con miglior ragione <lb/>di quella addotta nell'ultimo Dialogo dal Salviati, il problema della corda <lb/>tesa. </s>

<s>Da un tal fatto, che si narr&ograve; da noi nel capitolo I di questo Tomo, da <lb/>pag. </s>

<s>60-67, apparisce che fu esso Ricci l'unico a que'tempi, nella scuola <lb/>galilciana, che con libert&agrave; di giudizio intendesse la natura dei moti compo&shy;<lb/>sti, e che ne sentisse la grandissima utilit&agrave; delle applicazioni. </s>

<s>Ricevuta, per <lb/>mezzo del principe Leopoldo dei Medici, una di quelle scritture, nelle quali <lb/>il Borelli dava saggio de'progressi che sarebbe presto per fare nella Scienza <lb/>del moto, ringraziato esso Principe, che gli avesse fatte gustare cos&igrave; profonde <lb/>e belle speculazioni, gli soggiungeva: &ldquo; E saria forse bene che s'applicasse <lb/>il signor Borelli a dare in luce un trattato della composizione dei moti, e <lb/>dell'aumento e diminuzione loro, giacch&egrave; tant'oltre si &egrave; internato nella ma&shy;<lb/>teria, perch&egrave; quivi pescano molti che oggid&igrave; vanno speculando per le cose <lb/>geometriche, astronomiche e fisiche. </s>

<s>Vostra Altezza si ricorder&agrave; quanto ca&shy;<lb/>pitale ne faceva il Torricelli, e quanto se ne sia valso il Robervallio, ed altri <lb/>matematici famosi, e Des-Cartes in filosofia, e Keplero nell'astronomia. </s>

<s>Cos&igrave; <lb/>verrebbe egli a farsi autore di tante verit&agrave;, che s'inventeranno con l'aiuto <lb/>di quelle dottrine dei moti, che sono innumerabili &rdquo; (Fabbroni, <emph type="italics"/>Lettere di <lb/>uomini illustri,<emph.end type="italics"/> T. II, Firenze 1765, pag. </s>

<s>127). </s></p><p type="main">

<s>Le invenzioni con questi aiuti si fecero veramente e innumerevoli, come <lb/>il Ricci divinava, ma da tutti altri autori da quello, in cui egli aveva ripo&shy;<lb/>ste le sue speranze, il quale, riducendo con logica inesorabile, e pi&ugrave; incon&shy;<lb/>siderata di quella de'suoi colleghi, il teorema galileiano alle sue ultime con&shy;<lb/>seguenze, disse che i moti per i lati si possono ben comporre nel moto per <lb/>la diagonale, quando si fanno i loro concorsi ad angolo retto, come nel qua&shy;<lb/>drato o nel rettangolo, ma non gi&agrave;, quando concorrono secondo qualunque <lb/>angolo, come nella losanga o nel parallelogrammo, non verificandosi in que&shy;<lb/>ste figure, come in quelle, la ragione addotta da Galileo dell'equivalere cio&egrave; <lb/>la potenza della resultante alla somma delle due componenti. </s>

<s>N&egrave; lo disse il <lb/>Borelli in privato discorso con gli amici, ma al pubblico in quel solenne an&shy;<lb/>fiteatro della sua Scienza, che &egrave; l'Opera dei Moti animali. </s></p><p type="main">

<s>Nella proposizione LXIX della Prima Parte, si voleva dimostrar dall'Au&shy;<lb/>tore: &ldquo; Duae potentiae sustinentes, ad resistentiam, erunt ut longitudines <lb/>funium obliquae, quae proportionales sint conterminalibus potentiis, ad ea&shy;<lb/>rum sublimitates &rdquo; (Romae 1680, pag. </s>

<s>131). Cio&egrave;: essendo le due potenze <lb/>R, S (fig. </s>

<s>367), che per mezzo delle funi AC, BC sostengono il peso T, con <pb xlink:href="020/01/2956.jpg" pagenum="581"/>forze proporzionali ad AC, CM, se dai punti A, M si conducono sulla ver&shy;<lb/>ticale FC, sicch&egrave; la raggiungano in D e in O le due perpendicolari AD, MO, <lb/>chiama il Borelli le sezioni CD, CO le <emph type="italics"/>sublimit&agrave;,<emph.end type="italics"/> alle quali dice essere le <lb/>contermine potenze proporzionali, d'onde in ultimo conclude cos&igrave; il ragiona&shy;<lb/>mento: &ldquo; Ergo duae potentiae R, S simul sumptae, ad resistentiam T, eam&shy;<lb/>dem rationem habebunt quam duae AC, CM simul, ad duas DC, OC simul &rdquo; <lb/>(ibid., pag. </s>

<s>132). </s></p><p type="main">

<s>A questo punto il Lettore, che non sa nulla ancora, crederebbe avesse <lb/>voluto il Borelli trasformare cos&igrave; la sua proposizione per mostrar che la nuova <lb/>regola da lui insegnata &egrave; quella medesima, a cui avrebbe direttamente con&shy;<lb/><figure id="id.020.01.2956.1.jpg" xlink:href="020/01/2956/1.jpg"/></s></p><p type="caption">

<s>Figura 367.<lb/>dotto il parallelogrammo, costruito sui lati AC, CM. </s>

<s>Ti&shy;<lb/>rata infatti dal punto A una parallela a CM, che incontri <lb/>la verticale, e il punto F di tale incontro congiunto <lb/>con M, &egrave; facile riconoscere, nella figura AM che ne <lb/>resulta, la propriet&agrave; del parallelogrammo, essendo per <lb/>le parallele AF, MC; AD, MO gli angoli opposti uguali. </s>

<s><lb/>Uguali anche essendo DA a MO, e OC a FD, d'onde <lb/>viene DC+OC=FC, che &egrave; la diagonale del detto <lb/>parallelogrammo; la proporzionalit&agrave; dunque ultimamen&shy;<lb/>te conclusa dal Borelli si riduce a R+S:T= <lb/>AC+CM:FC, conforme a quel che avevano insegnato lo Stevino e l'He&shy;<lb/>rigonio. </s></p><p type="main">

<s>Ma mentre aveva creduto il Lettore essere l'intenzion del Borelli quella <lb/>di dimostrare una tale conformit&agrave;, con sua gran maraviglia proseguendo s'in&shy;<lb/>contra in una digressione cos&igrave; intitolata: &ldquo; Quia Stevinus et Herigonius et <lb/>alii viri doctissimi alia longe diversa via hanc eamdem propositionem se de&shy;<lb/>monstrasse putant, cogor paucis innuere rationes, quibus methodum a Viris <lb/>praeclaris servatam, non omnino tutam et legitimam censuerim &rdquo; (ibid., <lb/>pag. </s>

<s>133). </s></p><p type="main">

<s>La maraviglia cresce tanto pi&ugrave;, in quanto che il Borelli, per dimostrare <lb/>che non era legittimo il metodo dello Stevino e dell'Herigonio, incomincia <lb/>dal riferire i discorsi di quei Matematici, che ne avevano dovuta confermare <lb/>la verit&agrave;, riducendolo ai principii statici del piano inclinato e del vette. </s>

<s>Il <lb/>secondo di que'discorsi il Borelli l'attribuisce a un <emph type="italics"/>insigne Geometra neo&shy;<lb/>terico,<emph.end type="italics"/> per il quale par che debba intendersi il Pardies, nella sua <emph type="italics"/>Statique, <lb/>ou Scienc des forces mouvantes,<emph.end type="italics"/> libro stampato in Parigi nel 1673: ma il <lb/>primo l'attribuisce espressamente all'Herigonio, e si pu&ograve; facilmente conce&shy;<lb/>dere al Borelli che sia in questa sua digressione il discorso <emph type="italics"/>aliler et clarius <lb/>ostensus,<emph.end type="italics"/> perch&egrave; in esso Herigonio non apparisce di ci&ograve; nessuna esplicita <lb/>dimostrazione. </s>

<s>Si dubiterebbe anzi se l'Autor della detta digressione avesse <lb/>veduto mai il libro oggetto alle sue contradizioni, il quale forse conosceva <lb/>solamente per fama, e per le raccomandazioni, che ne faceva il Cavalieri <lb/>a'suoi discepoli, come particolarmente al Rocca, con queste parole: &ldquo; Di li&shy;<lb/>bri nuovi non ho nuova alcuna, ma non so se ella abbi visto il <emph type="italics"/>Cursus ma-<emph.end type="italics"/><pb xlink:href="020/01/2957.jpg" pagenum="582"/><emph type="italics"/>thematicus<emph.end type="italics"/> di Pietro Herigoni, matematico di Parigi, diviso in cinque tomi, <lb/>stampato a Parigi, nel quale, con maniera molto breve, professa insegnare <lb/>tutte le Matematiche, ed &egrave; degno di esser visto, ed opera nuova &rdquo; (<emph type="italics"/>Lettere <lb/>d'uomini illustri a G. A. Rocca,<emph.end type="italics"/> Modena 1785, pag. </s>

<s>153). </s></p><p type="main">

<s>In qualunque modo, ecco quali erano, secondo il Borelli, i ragionamenti, <lb/>che si facevano dai Matematici de'suoi tempi, per confermare, dai principii <lb/>statici universalmente consentiti, la verit&agrave; dell'uso di ricomporre nella diagonale <lb/>del parallelogrammo i moti, che s'intendessero fatti per i due lati. </s>

<s>Il globo T <lb/>(fig. </s>

<s>368), sorretto per il centro C dalle potenze R, S, applicate alle funi AC, <lb/>BC, starebbe egualmente in equilibrio sopra i due piani IH, IG, inclinati <lb/>nelle direzioni delle tangenti VH, OG: e le relazioni tra il peso assoluto T, <lb/>e il suo momento MoT sul piano OG, son date, secondo le note leggi, da <lb/>T:MoT=IG:IP. </s>

<s>Si disegni il parallelogrammo MN, e sul prolungamento <lb/>di DM si abbassi dal centro C la perpendicolare CL:il triangolo DLC, che <lb/>indi nasce, &egrave; simile al triangolo IPG, e perci&ograve; T:MoT=DC:CL. </s>

<s>Se ora <lb/>si conduca da O perpendicolarmente la OQ sopra VC, i triangoli MLC, COQ <lb/>danno, per la loro similitudine, LC:CM=QO:OC. </s>

<s>E considerando essere <lb/><figure id="id.020.01.2957.1.jpg" xlink:href="020/01/2957/1.jpg"/></s></p><p type="caption">

<s>Figura 368.<lb/>OC la lunghezza del vette, che appoggiandosi col so&shy;<lb/>stegno in O fa ruzzolare il globo sul piano; consi&shy;<lb/>derato inoltre che OQ &egrave; la distanza della direzione <lb/>obliqua della potenza R da esso sostegno, per cui <lb/>OC &egrave; la misura assoluta di R, e OQ &egrave; la misura <lb/>di lei, che equilibra il momento di T sul declivio, <lb/>tirando in direzione non parallela, ma convergente <lb/>con esso declivio; avremo LC:CM=QO:OC= <lb/>Mo.T:R. Ora, moltiplicata questa Mo.T:R= <lb/>LC:CM per l'altra gi&agrave; trovata T:Mo.T=DC:CL, <lb/>ne conseguir&agrave; T:R=DC:CM. </s>

<s>Con simile ragio&shy;<lb/>namento, soggiunge il Borelli, trovano pure questi <lb/>Matematici T:S=DC:CN, e perci&ograve; R:S= <lb/>CM:CN:e ancora, R+S:T=CM+CN:DC, d'onde intendono costoro <lb/>di confermare la regola insegnata dallo Stevino e dall'Herigonio, per com&shy;<lb/>porre in uno solo due moti, con qualunque angolo concorrenti. </s></p><p type="main">

<s>L'altra dimostrazione, attribuita a quell'insigne Geometra neoterico, &egrave; <lb/><figure id="id.020.01.2957.2.jpg" xlink:href="020/01/2957/2.jpg"/></s></p><p type="caption">

<s>Figura 369.<lb/>riferita dal Borelli stesso con tal discorso, che si pu&ograve; <lb/>compendiare in questo modo: Le funi AC, BC (fig. </s>

<s>369) <lb/>si riguardino come due vetti appuntati in C, e co'so&shy;<lb/>stegni in A, B, cosicch&egrave; il peso T tiri in gi&ugrave; il vette <lb/>AC, con momento, che star&agrave; al peso assoluto come <lb/>la lunghezza AC dello strumento sta alla distanza AD <lb/>della direzione obliqua dall'ipomoclio, mentre dall'al&shy;<lb/>tra parte &egrave; sostenuto esso vette, uguale in potenza ad <lb/>S, con momento, che sta alla forza assoluta, la quale tenderebbe a far girare il <lb/>peso T intorno al centro A; come la distanza AE sta al raggio AC, per cui si <pb xlink:href="020/01/2958.jpg" pagenum="583"/>avranno le equazioni T:Mo.S=CA:DA, Mo.S:S=EA:CA:e, co&shy;<lb/>struito il parallelogrammo MN, T:S=EA:DA=<emph type="italics"/>sen<emph.end type="italics"/> ACE:<emph type="italics"/>sen<emph.end type="italics"/> ACD= <lb/><emph type="italics"/>sen<emph.end type="italics"/> DNC:<emph type="italics"/>sen<emph.end type="italics"/> CDN=DC:CN. </s>

<s>Il ragionamento, per dimostrare che T sta ad <lb/>R, come DC a MC, &egrave; simile a questo, e perci&ograve; si giunge anche di qui a quel <lb/>medesimo, che i Matematici detti di sopra avevano gi&agrave; concluso per altre vie. </s></p><p type="main">

<s>Ora ognuno si aspetterebbe, dopo aver riferite cos&igrave; queste dimostrazioni, <lb/>che il Borelli avesse da scoprirci dentro qualche fallacia. </s>

<s>Ma, tutt'altrimenti <lb/><figure id="id.020.01.2958.1.jpg" xlink:href="020/01/2958/1.jpg"/></s></p><p type="caption">

<s>Figura 370.<lb/>da ci&ograve;, confessa che non &egrave; in esse nessuna fal&shy;<lb/>lace argomentazione, <emph type="italics"/>nec quicquam assumptum <lb/>est praeceptis mechanicis repugnans.<emph.end type="italics"/> &mdash; Oh <lb/>dunque, perch&egrave; non debbono valere que'discorsi <lb/>a confermar la verit&agrave; della regola herigoniana? <lb/></s>

<s>&mdash; E risponde il Borelli che cos&igrave; &egrave; per due ra&shy;<lb/>gioni: la prima delle quali &egrave; l'esperienza, invo&shy;<lb/>cata da me, egli dice, a confermare quel che al&shy;<lb/>trove ho dimostrato, &ldquo; quod duae potentiae R <lb/>et S (fig. </s>

<s>370), oblique sustinendo pondus T, <lb/>cum eodem aequilibrari possunt, licet R ad S habeat quamcumque pro&shy;<lb/>portionem, ac proinde maiorem aut minorem ea, quam CM habet ad CN, <lb/>et licet duae potentiae R et S simul sumptae, ad pondus T, habeant quam&shy;<lb/>cumque diversam proportionem ab ea, quam CM et CN simul sumptae ha&shy;<lb/>bent ad DC &rdquo; (Loco cit., pag. </s>

<s>138). </s></p><p type="main">

<s>Aggiungasi, prosegue a dire lo stesso Borelli, che, fatte le medesime <lb/>ipotesi di quei Matematici, si giunge, ragionando dai loro medesimi princi&shy;<lb/>pii, a concludere che il peso assoluto T sta alle due potenze R, S insieme, <lb/>come CO ad OP, ossia come CD a DX. &ldquo; Hoc autem nedum est evidenter <lb/>falsum, sed etiam contra eosdem praeclaros auctores, qui censent pondus T, <lb/>ad duas potentias R et S, esse ut DC ad MC, et CN simul sumptas, quae <lb/>multo maiores sunt, quam DX, ut facile ostendi potest &rdquo; (ibid., pag. </s>

<s>141). <lb/>Di qui si passa immediatamente a concludere che, se fossero legittimi i pro&shy;<lb/>gressi di quegli stessi preclarissimi Autori, si dovrebbe, fra le due potenze <lb/>e il peso che sostengono, sempre avere la medesima proporzione, e non dif&shy;<lb/>ferente. </s>

<s>Che se ci&ograve; non avviene, non pu&ograve;, dice, attribuirsi ad altro, che al&shy;<lb/>l'essere quelle fatte supposizioni n&egrave; possibili n&egrave; vere, &ldquo; quod nimirum duo <lb/>termini funium A et B, sigillatim vel coniunctim, ut centra fixa vectium <lb/>usurpari possint, et quod sola potentia R, vel sola potentia S, aequari possit <lb/>momento totius resistentiae T &rdquo; (ibid., pag. </s>

<s>142). </s></p><p type="main">

<s>Verrebbe di qui facile sulla bocca di ognuno la risposta che quei Ma&shy;<lb/>tematici non trattavano di una uguaglianza, ma di una certa proporzionalit&agrave;, <lb/>che passa tra ciascuna parzial potenza, e la resistenza totale. </s>

<s>In qualunque <lb/>modo per&ograve; s'avvedono i Lettori che debbono essere le esperienze del Bo&shy;<lb/>relli fallacie, e paralogismi i suoi ragionamenti. </s>

<s>Non mancarono Matematici, <lb/>anche tra noi, i quali ebbero questi avvedimenti, ma il pi&ugrave; libero, e il pi&ugrave; <lb/>eloquente in denunziarli, fu il Varignon, il quale scrisse, e aggiunse in fine <pb xlink:href="020/01/2959.jpg" pagenum="584"/>alla sua <emph type="italics"/>Nouvelle mecanique,<emph.end type="italics"/> un opuscolo critico, diviso in due capitoli, e <lb/>intitolato: <emph type="italics"/>Examen de l'opinion de M. </s>

<s>Borelli sur les proprietez des poids <lb/>suspendus par des cordez.<emph.end type="italics"/> Quanto all'esperienza, osserva saviamente il Va&shy;<lb/>rignon, che, in fatto d'esattezza e di precisione, &ldquo; ne prouve rien, sur tout <lb/>ici, ou la resistance, qui vient du frottement des poulies avec leurs pivons etc., <lb/>rend ces sortes d'experiences possibles en tant de manieres differentes, qu'il <lb/>n'y a presque point de sentiment, pour ou contre le quel on n'en puisse <lb/>faire &agrave; son gr&eacute; &rdquo; (A Paris, T. II, 1725, pag. </s>

<s>454). </s></p><p type="main">

<s>Quanto poi al ragionamento, in cui pretende il Borelli di dimostrare <lb/>che il peso assoluto sta alle due potenze che lo sostengono, come CO ad OP, <lb/>nella medesima figura 370, soggiunge lo stesso Varignon ch'egli &egrave; condotto <lb/>da varie supposizioni o principii, tutti manifestamente falsi. </s>

<s>Il Critico fran&shy;<lb/>cese per&ograve; non entr&ograve; addentro a ricercar la radice di queste fallacie, che perci&ograve; <lb/>non si crederebbero in un ingegno, come &egrave; quello dell'Autore dei Moti ani&shy;<lb/>mali, ma che, piuttosto ch'esser proprie di lui solo, appartennero a tutta in&shy;<lb/>tera quella Scuola dominatrice, nella quale si teneva con fermissima fede non <lb/>aver Galileo insegnato mai nulla, che non fosse vero e perfetto. </s>

<s>Di qui &egrave; che <lb/>o non si curavano, o si disprezzavano gl'insegnamenti di quell'altra Scuola, <lb/>pi&ugrave; umile e pi&ugrave; dispersa, istituita dallo Stevino, negli insegnamenti del quale <lb/>si sarebbe dovuto piuttosto, principalmente per ci&ograve; che concerne i moti com&shy;<lb/>posti, cercar quella verit&agrave; e quella perfezione, che non si trovava affatto nella <lb/>Scienza meccanica di Galileo. </s></p><p type="main">

<s>L'applicazione del parallelogrammo delle forze alla teoria del piano in&shy;<lb/>clinato non era da lamentar negletta, come sembra facesse il Lagrange, per&shy;<lb/>ch&egrave; avrebbe dato a Galileo maggior facilit&agrave; di dimostrare, ma perch&egrave; glie ne <lb/>sarebbe derivata perfezione di scienza, in distinguere le variet&agrave;, e in misu&shy;<lb/>rar le grandezze dei momenti, con cui il grave preme il piano, e lunghesso <lb/>discende: e ci&ograve; non solamente nel caso, che sia sostenuto da potenza con <lb/>direzion parallela, ma comunque convergente con la linea del declivio. </s>

<s>Nello <lb/>Stevino basta tornare in dietro sulla figura 353, per vedervi distinti que'due <lb/>momenti e le loro proporzioni, rispetto al peso assoluto della colonna, il qual <lb/>peso essendo rappresentato dalla diagonale DL, vengono dai lati QD, DI a <lb/>rappresentarsi i respettivi momenti, con cui la colonna stessa preme, o stri&shy;<lb/>scerebbe gi&ugrave; lungo il piano. </s>

<s>Che se la direzione della potenza non &egrave;, come <lb/>DF, parallela, ma, come DB, convergente con la linea AB del declivio, la <lb/>diagonale DL e il lato DO, nel parallelogrammo RO nuovamente costruito, <lb/>daranno la proporzione tra il peso assoluto del grave, e la forza bastante a <lb/>trattenerlo in quel sito: proporzione che, ridotta in forma trigonometrica, &egrave; <lb/>tale:LD:DO=<emph type="italics"/>sen<emph.end type="italics"/> LOD:<emph type="italics"/>sen<emph.end type="italics"/> DLO. </s>

<s>E perch&egrave; LOD, ossia IQD, &egrave; uguale <lb/>a 90&deg;&mdash;IDO, e DLO=BAC; dunque LD:DO=<emph type="italics"/>cos<emph.end type="italics"/> IDO:<emph type="italics"/>sen<emph.end type="italics"/> BAC, se&shy;<lb/>condo che il Dechales, infino dal 1673, annunziava nella prima edizione del <lb/>suo <emph type="italics"/>Mundus mathematicus<emph.end type="italics"/> agli studiosi della Statica steviniana: <emph type="italics"/>&ldquo; Pondus, <lb/>in plano inclinato consistens, se habet ad pondus aequalis momenti, tra&shy;<lb/>hens linea plano non parallela, ut sinus complementi anguli tractionis,<emph.end type="italics"/><pb xlink:href="020/01/2960.jpg" pagenum="585"/><emph type="italics"/>ad sinum anguli inclinationis plani &rdquo;<emph.end type="italics"/> (T. II, editio altera, Lugduni 1690, <lb/>pag. </s>

<s>204). </s></p><p type="main">

<s>&ldquo; Et de mesme seroit, per citar le parole proprie dello Stevino, si BN <lb/>estoit de l'altre coste de la perpendicolaire BC, assavoir entre AB, BC, et <lb/>sembleblament DO entre DL et DI &rdquo; (Ouvr. </s>

<s>cit., pag. </s>

<s>449), ossia, se la fune <lb/>DB, invece di convergere con B, converge con A dalla parte opposta, come <lb/>nell'esempio esibitoci dalla 354a figura, dove, essendo LOD=180&deg;&mdash;DOF= <lb/>180&deg;&mdash;(90&deg;&mdash;ODF)=90&deg;&mdash;ODF, s'ha DL:LO=<emph type="italics"/>sen<emph.end type="italics"/> LOD:<emph type="italics"/>sen<emph.end type="italics"/> DLO= <lb/><emph type="italics"/>cos<emph.end type="italics"/> ODF:<emph type="italics"/>sen<emph.end type="italics"/> BAC, ossia, come dianzi, il peso sta alla potenza che lo sostiene <lb/>come il coseno dell'angolo della trazione sta al seno dell'angolo dell'incli&shy;<lb/>nazion del piano sull'orizonte. </s></p><p type="main">

<s>Galileo invece insegnava che il peso sta alla potenza come il seno to&shy;<lb/>tale, ossia il raggio, sta al seno dell'angolo dell'inclinazione, con teorema, <lb/>che rimanendosi nello stato, in cui la Scienza lo aveva avuto gi&agrave; dal Tar&shy;<lb/>taglia, cos&igrave; assolutamente pronunziato &egrave;, a confronto di quello dello Stevino, <lb/>da dire addirittura falso, non verificandosi che nel caso dell'angolo della tra&shy;<lb/>zione uguale a zero, perch&egrave; allora il coseno di zero torna veramente alla <lb/>lunghezza del raggio. </s></p><p type="main">

<s>Dall'avere il Maestro, dietro un esempio particolare, formulato un teo&shy;<lb/>rema generalissimo, s'inger&igrave; ne'Discepoli l'opinione che si mantenesse sem&shy;<lb/>pre uguale la forza applicata a una fune secondo qualunque direzione, e il <lb/>Viviani, come vedemmo (pag. </s>

<s>67, 68 di questo Tomo) istituiva per confer&shy;<lb/>marla esperienze, e il Borelli se ne serviva come principio, da concluderne tra <lb/>la potenza e il peso una proporzione, diversa da quella che passa tra i lati <lb/>e la diagonale del parallelogrammo. </s>

<s>E dal non aver saputo Galileo decom&shy;<lb/>porre il peso assoluto del grave sopra il piano ne'suoi momenti parziali, de&shy;<lb/>riv&ograve; nel Borelli, bench&egrave; fosse per le medesime vie oblique giunto a dimo&shy;<lb/>strare i teoremi del Viviani (vedi il nostro Tomo IV, pag. </s>

<s>244, 45), quella <lb/>confusione d'idee, che trasparisce dal suo ragionamento. </s>

<s>Fra gli altri prin&shy;<lb/>cipii quivi assunti &egrave; notabile quello, che suppone la resultante divider nel <lb/>mezzo l'angolo del concorso, anco quando i moti componenti non sono uguali: <lb/>supposizione affatto gratuita, ma che &egrave; in conseguenza delle dottrine profes&shy;<lb/>sate dall'Autore, nello scolio alla proposizione LXIX di questa prima parte <lb/><emph type="italics"/>De motu animalium:<emph.end type="italics"/> &ldquo; Manifeste colligitur, ex dictis propositionibus, quod <lb/>duae quaelibet potentiae, sive aequales sive inaequales inter se fuerint, pos&shy;<lb/>sunt aequilibrari alicui resistentiae, trahendo funes obliquos, efficientes cum <lb/>directione resistentiae angulos acutos, sive aequales, sive inaequales inter se &rdquo; <lb/>(pag. </s>

<s>132). Ma tutte queste fallacie dipendevano dalla massima e principale, <lb/>introdotta da Galileo in questa Scienza dei moti composti, che cio&egrave;, dovendo <lb/>le parti essere in ogni modo uguali al tutto, le potenze sostenitrici debbono, <lb/>senz'alcuna diminuzione, equivalere al tutto. </s></p><p type="main">

<s>Il Varignon dunque, senza curarsi, come si diceva, di cercar d'onde <lb/>avessero avuto origine, notava nel <emph type="italics"/>Remarque,<emph.end type="italics"/> in fine al capitolo I del citato <lb/><emph type="italics"/>Examen<emph.end type="italics"/> queste fallacie, incominciando da ci&ograve; che il Borelli soggiunge, dopo <pb xlink:href="020/01/2961.jpg" pagenum="586"/>aver detto che, riguardandosi la corda AC (fig. </s>

<s>371) come una verga rigida, <lb/>girevole intorno al punto fisso A, e all'estremit&egrave; C della quale sia attaccato <lb/>il peso T; questo peso &egrave; da essa verga sostenuto come se riposasse sul piano <lb/><figure id="id.020.01.2961.1.jpg" xlink:href="020/01/2961/1.jpg"/></s></p><p type="caption">

<s>Figura 371.<lb/>CI perpendicolare ad AC, e con l'elevazione <lb/>IL: <emph type="italics"/>patet quod pondus T, ad vim qua idem <lb/>T innitur, et comprimit planum IC, est <lb/>ut IC ad CL<emph.end type="italics"/> (pag. </s>

<s>139). &ldquo; Cela seroit vrai, <lb/>osserva qui il Varignon, si BC etoit paral&shy;<lb/>lele a CI perpendiculaire &agrave; AC, mais non <lb/>pas, lorsqu'elle lui est oblique, comme ici, <lb/>ou le poids S aide au poids T a charger <lb/>le plan CI, qui ne le seroit qui par ce poids <lb/>T, si BC lui &eacute;toit parallele &rdquo; (<emph type="italics"/>Nouvelle mechan.,<emph.end type="italics"/> T. </s>

<s>I cit., pag. </s>

<s>461). </s></p><p type="main">

<s>&Egrave; chiaro infatti che la corda AC equilibra il momento gravitativo sul <lb/>piano, ma il discensivo viene equilibrato dall'altra corda BC: e se quello &egrave; <lb/>secondo il Borelli proporzionale a LC, questo deve necessariamente esser pro&shy;<lb/>porzionale a LI. </s>

<s>Cosicch&egrave; egli viene a dire che T sta ad S come il raggio <lb/>CI sta al seno LI dell'inclinazione, ci&ograve; che non &egrave; assolutamente vero, come <lb/>si credeva dai discepoli di Galileo s<gap/>ll'autorit&agrave; del Maestro, ma nel solo caso <lb/>particolare che CB sia parallela a CI: cosa che non si verifica in questo <lb/>esempio, in cui la proporzione tra T ed S &egrave; quella del coseno dell'angolo <lb/>della trazione ICB, e non del raggio, al seno dell'angolo dell'inclinazione <lb/>del piano, secondo il teorema generalissimo e verissimo dimostrato dallo <lb/>Stevino. </s></p><p type="main">

<s>In un'altra fallacia, simile a questa, notava il Varignon essere incorso <lb/>il Borelli, quando, dop'avere abbassata nella figura. </s>

<s>370 la CP perpendico&shy;<lb/>lare sopra la KG, soggiungeva: <emph type="italics"/>Idem pondus absolutum T, ad vim qua com&shy;<lb/>primit planum CO, eamdem rationem habebit quam CO ad OP<emph.end type="italics"/> (pag. </s>

<s>141). <lb/>&ldquo; Cela seroit vrai, si ce poids T &eacute;toit retenu sur CO par une puissance d'une <lb/>direction parallele &agrave; CO &rdquo; (ivi, pag. </s>

<s>462). Ritornando infatti sopra la fig. </s>

<s>353, <lb/>ritratta dalla Statica dello Stevino, si vede che il momento gravitativo della <lb/>colonna sul piano &egrave; proporzionale a LI, coseno dell'angolo dell'inclinazione, <lb/>nel solo caso contemplato da Galileo e dal Borelli, e da loro supposto gene&shy;<lb/>ralissimo, che la fune DF tiri con direzione parallela al declivio. </s>

<s>Ma se tira <lb/>con altra direzione, o sotto o sopra a quella, come DB, DV, il detto mo&shy;<lb/>mento gravitativo o cresce come LO, o scema come LS, seni dell'angolo fatto <lb/>dalla trazione con la linea verticale. </s></p><p type="main">

<s>&ldquo; Dans la critique, prosegue il Varignon, qu'il (M. Borelli) fait ensuite <lb/>du raisonnement d'H&eacute;rigone, de Stevin, etc., apr&egrave;s avoir regard&eacute; le poids T <lb/>(nella figura 370) so&ucirc;tenu par les cordes AC et BC, comme s'il l'&eacute;toit sur <lb/>les plans CK perpendiculaire &agrave; AC, et CG perpendiculaire &agrave; CB, inegale&shy;<lb/>ment inclinez, il dit, pag. </s>

<s>141. <emph type="italics"/>Tunc pondus T, dum moveri niteretur per <lb/>duas rectas inclinatas CK et CG, cogeretur moveri, aut nisum exercere <lb/>per diagonalem CO, secantem angulum GCK bifariam.<emph.end type="italics"/> Pour cela il fau-<pb xlink:href="020/01/2962.jpg" pagenum="587"/>droit que ces deux plans CK, CG fussent &eacute;galement inclinez, et conseguen&shy;<lb/>tement aussi les directions AC, BC, qu'on leur suppose perpendiculaires &rdquo; <lb/>(ivi, pag. </s>

<s>461, 62). </s></p><p type="main">

<s>L'ultima osservazione si fa dal Critico francese alle parole del Nostro: <lb/><emph type="italics"/>Vis, quam patitur planum CO<emph.end type="italics"/> (nella medesima figura 370) <emph type="italics"/>a compressione <lb/>ponderis T, aequalis est viribus ambarum potentiarum R et S, quae su&shy;<lb/>stinendo idem pondus in tali situ plani CO inclinati vicem supplent.<emph.end type="italics"/><lb/>&ldquo; Cela est faux. </s>

<s>La force resultante du concours des deux autres (ripete il <lb/>Varignon al Borelli quel che tanto tempo prima avevano detto l'Hobbes al <lb/>Cartesio, e il Mersenno a Galileo) est toujours moindre que leur somme, <lb/>tant que leurs directions font quelque angle entr'elles. </s>

<s>Outre que cette force <lb/>resultante le long du plan CO, &eacute;tant ainsi parallele a ce plan, ne seroit pas <lb/>celle de sa compression, qui r&eacute;sulteroit du concours de cette force parallele, <lb/>et de la pesanteur du poids so&ucirc;ttenu par elle sur ce plan &rdquo; (ivi, pag. </s>

<s>462). </s></p><p type="main">

<s>Supponiamo ora che il Borelli fosse sopravvissuto a questo esame, che <lb/>del suo ragionamento faceva cos&igrave; l'Accademico parigino. </s>

<s>Si crederebb'egli <lb/>forse che avesse riconosciuto e confessato il suo errore? </s>

<s>Noi per verit&agrave; met&shy;<lb/>tiamo la cosa in dubbio, ripensando a quei cos&igrave; tenaci pregiudizi della sua <lb/>Scuola, che tuttavia durano dopo due secoli e mezzo. </s>

<s>Dall'altra parte l'os&shy;<lb/>servazione da noi fatta di sopra, che cio&egrave; il metodo, con cui egli si studi&ograve; <lb/>di dimostrar le potenze proporzionali alle sublimit&agrave;, conduceva alla medesima <lb/>regola del parallelogrammo, non sarebbe dovuta bastar per s&egrave; sola a per&shy;<lb/>suaderlo? </s>

<s>E quell'altra sua opinione del non si poter comporre i moti per i <lb/>lati in quello per la diagonale, altro che nel caso dei concorsi ortogonali, non <lb/>gli si sarebbe potuta dissipar dalla mente come nebbia al chiaro sole di un cos&igrave; <lb/>fatto ragionamento? </s>

<s>Concorrano secondo qualunque angolo GCH (fig. </s>

<s>372) le <lb/>due potenze R, S a sostenere il peso T. Costruito, secondo qualunque pro&shy;<lb/>porzione, un parallelogrammo, come per esempio GH, lo Stevino e l'Heri&shy;<lb/>gonio dicevano che le due potenze rappresentate da GC, CH equivalgono in&shy;<lb/>sieme alla potenza unica rappresentata dalla diagonale CD, e il Borelli osti&shy;<lb/>natamente ci&ograve; negava, perch&egrave; GCH non &egrave;, come prescrivevasi da Galileo, un <lb/><figure id="id.020.01.2962.1.jpg" xlink:href="020/01/2962/1.jpg"/></s></p><p type="caption">

<s>Figura 372.<lb/>angolo retto. </s>

<s>Or bene: si abbassino dai punti G, H, perpen&shy;<lb/>dicolari sull'orizontale MN, le GM, HN, e le due forze GC, <lb/>CH equivarranno, secondo il precetto galileiano, alle quattro <lb/>GM, HN; MC, CN. </s>

<s>E perch&egrave; queste &egrave; facile veder che sono <lb/>uguali e contrarie, rimangono attive quelle sole, ossia le loro <lb/>uguali QC, PC, ossia l'intera DC, diagonale del parallelo&shy;<lb/>grammo, che dunque equivale in potenza alle potenze dei lati. </s>

<s><lb/>Notabile &egrave; poi che il Borelli non s'avvede come nel metodo, <lb/>ch'egli dice suo proprio, e che consiste nel pigliar le linee <lb/>delle potenze proporzionali alle sublimit&agrave;, si fa sempre la ri&shy;<lb/>duzione, dalle forze concorrenti con qualunque angolo, alle forze ortogonali, <lb/>e che da questa riduzione, la quale senza volerlo, anzi reluttante lo conduce <lb/>alla regola del parallelogrammo, dipende la verit&agrave; di quasi tutte le sue pro-<pb xlink:href="020/01/2963.jpg" pagenum="588"/>posizioni, e l'aver principalmente risoluto, al modo del Simpson, il problema <lb/>della corda tesa, che dette al Viviani, come si narr&ograve;, tanto travaglio. </s></p><p type="main">

<s>E qui cade opportuno riferire le belle osservazioni, fatte dal Varignon <lb/>in questo proposito, del decomporre ciascuna delle forze concorrenti in altre <lb/>due ortogonali, come nell'esempio illustrato dall'ultima figura: &ldquo; Si M. Bo&shy;<lb/>relli, egli dice, e&ugrave;t fait reflexion que les puissances R et S n'agissent pas <lb/>seulement contre le poids T, mais aussi l'une contre l'autre, et que de m&ecirc;me <lb/>qu'elles concourent ensemble pour emp&ecirc;cher que ce poids n'attire a lui le <lb/>noeud C, de m&egrave;me aussi chacune d'elles concourt avec lui pour emp&egrave;cher <lb/>que l'autre ne l'emporte; si dis-je il avoit fait cette reflexion, il avroit v&ugrave; <lb/>sans doute que chacune de ces puissances fait impression sur ce noeud, non <lb/>seulement suivant la direction du poids qu'elles soutiennent pour le tenir <lb/>to&ugrave;jours a m&egrave;me hauteur, mais aussi suivant l'horisontale MCN, pour em&shy;<lb/>p&egrave;cher qu'aucune d'elles ne l'attire ni &agrave; droit ni &agrave; gauche. </s>

<s>D'ou il avroit <lb/>infailliblement conclu que ces impressions horisontales &eacute;tant diametralement <lb/>oppos&eacute;es doivent to&ugrave;jours etre egales. </s>

<s>De-l&agrave; voyant qu'elles augmentent on <lb/>diminuent necessairement &agrave; mesure que les angles, que font les cordes de <lb/>ces puissances avec la ligne de direction du poids qu'elles soutiennent, s'ap&shy;<lb/>prochent ou s'eloignent de l'angle droit; il avroit enfin apper<gap/>&ugrave; l'impossibi&shy;<lb/>lit&eacute; de faire, si non aucun, du moins un tel changement a leurs directions, <lb/>sans en rompre l'equilibre &rdquo; (ivi, pag. </s>

<s>477). </s></p><p type="main">

<s>Avrebbe anche di pi&ugrave; conosciuto il Borelli, soggiungiamo noi, che mal<gap/><lb/>s'applicava da Galileo l'aforismo che dice dover le parti essere uguali al <lb/>tutto, e ch'&egrave; un tale aforismo solamente vero, quando le parti stesse si pren&shy;<lb/>dono tutte, e non diminuite come qui, con diminuzione misurata dalla linea <lb/>MC, o dalla CN sua eguale e contraria, la quale evidentemente riesce mag&shy;<lb/>giore o minore, secondo che maggiore o minore &egrave; l'angolo del concorso. </s>

<s><lb/>Questa osservazione, che sarebbe stata della maggiore importanza, perch&egrave; in&shy;<lb/>somma tutte le fallacie in questo argomento derivavano dalla massima delle <lb/>fallacie, contenutasi nel secondo Teorema galileiano, e intorno a che si pass&ograve; <lb/>il Varignon assai leggermente; questa osservazione, voleva dirsi, era stata <lb/>fatta assai tempo prima, che il Critico francese pubblicasse il suo opuscolo <lb/>sul Borelli, dal nostro piacentino Paolo Casati, il quale, a proposito del peso <lb/>sostenuto da due funi, pronunziava, in mezzo ai comuni errori, la salutare <lb/>sentenza, <emph type="italics"/>re autem ipsa quod ex iis componitur momentum, non ex ipso&shy;<lb/>rum momentorum additione conflatur, sed ex ipsis temperatur.<emph.end type="italics"/> (<emph type="italics"/>Mechanic. </s>

<s><lb/>libri,<emph.end type="italics"/> Lugduni 1684, pag. </s>

<s>103). Sia A (fig. </s>

<s>373) il detto peso, e AB, AC le <lb/>due funi, che lo sostengono, e che supporremo essere di lunghezze uguali. </s>

<s><lb/>Abbassate da B, C, sulla orizontale DE le BD, CE perpendicolari, osserva il <lb/>Casati che, recisa la fune AC, il pendolo AB scenderebbe con momento pro&shy;<lb/>porzionale ad AD, e similmente, con momento proporzionale ad AE scende&shy;<lb/>rebbe il pendolo AC, venendogli a mancare la fune AB, che lo tien solle&shy;<lb/>vato. </s>

<s>Si conducano le tangenti AR, AG, uguali alle DA, AE, immaginando <lb/>quelle sottoposte dall'una e dall'altra parte al globo, quasi piani inclinati <pb xlink:href="020/01/2964.jpg" pagenum="589"/>alle sue libere scese: &ldquo; ex quo fit corpus A, suspensum hac ratione, mo&shy;<lb/>menta descendendi habere in diversas partes abeuntia AR, AG. </s>

<s>Perfecto igi&shy;<lb/>tur parallelogrammo ARNG, ex duobus illis momentis temperatur momen&shy;<lb/>tum AN &rdquo; (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>Ora essendo DA, AE i seni degli angoli delle inclinazioni DBA, ACE <lb/>delle funi, i quali si suppongono noti, s'ha dalle Tavole trigonometriche AE, <lb/><figure id="id.020.01.2964.1.jpg" xlink:href="020/01/2964/1.jpg"/></s></p><p type="caption">

<s>Figura 373.<lb/>ossia AG, 81496, e DA, ossia AR, 37784; dai quali <lb/>numeri essendo rappresentati i momenti parziali, <lb/>verr&agrave; perci&ograve; la loro somma rappresentata da 119280. <lb/>Ma il triangolo ANG, in cui son noti i lati AG, <lb/>GN, e noto &egrave; altres&igrave; l'angolo G da essi compreso, <lb/>perch&egrave; conoscesi l'angolo RAG, e il suo opposto N, <lb/>che resultano ambedue dalla somma de'comple&shy;<lb/>menti degli angoli delle inclinazioni delle funi; pu&ograve; <lb/>risolversi rispetto al lato AN, diagonale del paralle&shy;<lb/>logrammo, la quale trovasi 81613. &ldquo; Ex quibus <lb/>apparet (ne conclude il Casati da questo suo cal&shy;<lb/>colo, che pare istituito apposta per dimostrar quanto fosse falso il teorema <lb/>di Galileo, e falsi i corollari che ne traeva il Borelli) descendendi momen&shy;<lb/>tum, quod componitur ex momentis in planis inctinatis, non esse 119280 ex <lb/>corum summa, sed ita temperari, ut longe minus sit, videlicet solum 81613 &rdquo; <lb/>(ibid., pag. </s>

<s>105). </s></p><p type="main">

<s>Ma il Casati che, come gesuita, non apparteneva a nessuna nazione, e <lb/>che, come peripatetico, era inviso alla nuova Scuola, non ebbe co'suoi in&shy;<lb/>segnamenti nessuna efficacia in ridurre gli erranti sulla retta via; tanto &egrave; <lb/>vero che, quando il Vanni avvent&ograve; contro Galileo quel suo <emph type="italics"/>Specimen<emph.end type="italics"/> famoso, <lb/>i Galieiani si trovarono impacciati nelle difese, le quali avrebbero potuto tro&shy;<lb/>var paratissime nel primo degli otto libri Meccanici dell'Autor piacentino. </s>

<s><lb/>Anzi noi preghiamo i nostri Lettori a voler tornare indietro sul capitolo IV <lb/>del nostro Tomo di storia, che precede a questo, dove l&agrave; troveranno, in pro&shy;<lb/>posito del rispondere al Vanni, descritto lo stato, in cui si trovava la Scienza <lb/>dei moti composti appresso i principali Matematici dell'Europa, sul finir del <lb/>secolo XVII. </s>

<s>E ripensando alle cose lette, e a quelle che poi leggeranno nella <lb/>Storia dell'Idraulica intorno ai trascorsi del Michelini, del Guglielmini e del <lb/>Grandi, in materie gravissime; comprenderanno quanto benefica riuscisse <lb/>l'opera del Varignon, a cui veramente vi deve l'aver, per la sua pi&ugrave; man&shy;<lb/>chevole parte, rinnovellata la Meccanica di Galileo. </s></p><p type="main">

<s>La Scienza, nella quale era stato per due secoli assoluto principe quel&shy;<lb/>l'Uomo, rimaneva per lui in difetto anche da due altre parti, quali erano <lb/>l'analisi algebrica, e la dottrina dell'infinito, da quella aborrendo, perch&egrave; <lb/>recideva i nervi dell'eloquenza, e da questa, a quel che ci ha rivelato la sto&shy;<lb/>ria, per non aver l'animo e la mente disposti a penetrare addentro alle pro&shy;<lb/>fonde speculazioni del Cavalieri. </s>

<s>N'ebbero di que'difetti a risentirsi natu&shy;<lb/>ralmente i Discepoli, e specialmente del primo, che si trovaron costretti a <pb xlink:href="020/01/2965.jpg" pagenum="590"/>dover confessare, e a riconoscere che di gran lunga rimanevan per quel mo&shy;<lb/>tivo superati dai loro emuli d'oltremonte. </s>

<s>Il Cavalieri, avuta dal Rocca la so&shy;<lb/>luzione algebrica di un problema, gli rispondeva: &ldquo; Mi sentii un prurito di <lb/>applicarmi per vedere se geometricamente si poteva sciogliere tal problema, <lb/>e mi ci applicai tanto pi&ugrave;, che io le confesso ingenuamente che le opera&shy;<lb/>zioni algebraiche non le ho troppo alle mani, non vi avendo fatto molto stu&shy;<lb/>dio &rdquo; (<emph type="italics"/>Lettere a C. A. Rocca<emph.end type="italics"/> cit., pag. </s>

<s>188). E Michelangiolo Ricci si rac&shy;<lb/>comandava al Marchetti, per l'onore della Scienza italiana, che sopprimess<gap/><lb/>o ritirasse la stampa di que'suoi sciagurati <emph type="italics"/>Problemata Sex,<emph.end type="italics"/> &ldquo; perch&egrave; vi &egrave; <lb/>molto che dire, e non vorrei che i Virtuosi oltramontani, dei quali assais&shy;<lb/>simi hanno emulazione grande con gl'Italiani, com'ella sa, pigliassero mo&shy;<lb/>tivo di biasimare, s&igrave; perch&egrave; nelle cose di V. S. ritroveranno che riprendere, <lb/>s&igrave; ancora in vedere che ella ne faccia tanto conto, con aver messo alle stampe <lb/>quelle soluzioni di problemi, i quali sono veramente difficili, ma essi, che <lb/>possiedono l'Algebra, in un giorno e francamente gli risolverebbero, e per&ograve; <lb/>meno gli stimano..... Frascati, 4 giugno 1675. &rdquo; (Nelli <emph type="italics"/>Saggio di storia <lb/>letter.,<emph.end type="italics"/> Lucca 1749, pag. </s>

<s>32). </s></p><p type="main">

<s>La mirabile facilit&agrave; del metodo degli indivisibili, applicato a risolvere <lb/>problemi nuovi di Geometria, da tutti reputati difficilissimi, aveva nel Tor&shy;<lb/>ricelli e nel Nardi fatte chiudere le orecchie a quelle arguzie eloquenti, con <lb/>le quali pretendeva Galileo di dimostrare che il metodo cavalierano condu&shy;<lb/>ceva all'assurdo di ragguagliare una circonferenza, grande quanto l'orbe <lb/>magno, a un semplice punto. </s>

<s>Ma si trovarono que'due Autori, e tutti gli <lb/>altri che ne avevano seguiti gli esempi, chiusa la via di progredire piu oltre, <lb/>non avendo saputo nemmen essi trattare le questioni geometriche con quel&shy;<lb/>l'analisi algebrica, senza la quale il metodo stesso non pigliava l'agilit&agrave; ne&shy;<lb/>cessaria a sublimarsi, e a spaziare per le regioni dell'infinito. </s></p><p type="main">

<s>&Egrave; un fatto che Galileo, a cui pur tanto deve la Scienza del moto, le <lb/>aveva anche insieme recisi cos&igrave; i germi, da non poter aprirsi in rami no&shy;<lb/>velli, costringendola a rimanersi perpetuamente nella statura di quell'arbo&shy;<lb/>scello, ch'egli aveva educato ne'Dialoghi delle due nuove Scienze. </s>

<s>O fosse <lb/>presunzione di voler col suo prescrivere i limiti all'ingegno umano, o per&shy;<lb/>suasione del non v'essere altri mezzi, da quelli in fuori da s&egrave; usati in far <lb/>progredire la Meccanica; questa ebbe a rinnovellarsi, oltre a ci&ograve; che con&shy;<lb/>cerne i moti composti, per altre due parti, per l'uso cio&egrave; dell'analisi alge&shy;<lb/>brica e della infinitesimale. </s>

<s>E come fu quel primo rinnovellamento fatto dal <lb/>Varignon, questi altri due pure furono opera di Matematici stranieri, i quali <lb/>perci&ograve; tolsero, sul finir del secolo XVII, il principato di questa Scienza al&shy;<lb/>l'Italia. </s>

<s>Cos&igrave; vien tolto anche insieme di mano a noi l'argomento di questa <lb/>Storia, alla quale non rimane oramai che di gettare uno sguardo sopra quella <lb/>superba mole, a cui i Nostri abbiam veduto come ponessero i fondamenti, e <lb/>per cui raccolsero la maggiore, e pi&ugrave; eletta parte dei materiali. </s></p><pb xlink:href="020/01/2966.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO X.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dei progressi fatti dalla Meccanica nuova<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Dei <emph type="italics"/>Principii matematici di Filosofia naturale<emph.end type="italics"/> del Newton. </s>

<s>&mdash; II. </s>

<s>Della <emph type="italics"/>Foronomia<emph.end type="italics"/> dell'Her&shy;<lb/>mann. </s>

<s>&mdash; III. </s>

<s>Del parallelogrammo delle forze, e del Calcolo infinitesimale nella Meccanica <lb/>nuova. </s>

<s>&mdash; IV. </s>

<s>Della Meccanica analitica dell'Euler, del D'Alembert e del Lagrange. </s>

<s>&mdash; V. </s>

<s>Brevi <lb/>parole di conclusione. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Come, quando &egrave; nato un animale o una pianta, non si pensa pi&ugrave; al&shy;<lb/>l'uovo o al seme, ma tutta la nostra ammirazione &egrave; rivolta all'apparizione <lb/>di quella nuova giovent&ugrave; di vita, che si manifesta nella variet&agrave; dei moti, e <lb/>nella sagacia degl'istinti, o nella lussuria dei rami e nella ubert&agrave; dei fiori <lb/>e de'frutti; cos&igrave;, tra lo scader del secolo XVII e il cominciar del seguente, <lb/>l'ammirazione dei Matematici si rivolse tutta alla Meccanica nuova, non sem&shy;<lb/>plicemente rinnovellata per quella agilit&agrave;, che le aveva il Varignon infuso <lb/>nelle vecchie membra, ma per nuovi organi aggiunti, quasi ali sul dorso a <lb/>chi fin allora era andato col solo passo dei piedi. </s>

<s>La palingenesi maravigliosa <lb/>apparve nei <emph type="italics"/>Principii matematici di Filosofia naturale<emph.end type="italics"/> del Newton, intorno <lb/>ai quali per&ograve; il tempo e l'intento nostro non ci permetton di fare che una <lb/>brevissima storia. </s></p><p type="main">

<s>&Egrave; noto che se ne fecero in Londra, vivente l'Autore, tre edizioni: nel 1686, <lb/>nel 1713 e nel 1725 sempre con nuove aggiunte e con nuove correzioni, infin <lb/>tanto che l'Opera non si rimase distinta in quei tre Tomi, i quali sono og&shy;<lb/>gid&igrave; per le mani degli studiosi. </s>

<s>E perch&egrave; nel secondo Tomo si tratta delle <lb/>resistenze opposte al moto dai mezzi fluidi, e delle propriet&agrave; statiche e di&shy;<lb/>namiche di essi fluidi, e nel terzo si mostra come si applichino particolar&shy;<lb/>mente al circolar dei corpi celesti i teoremi di Meccanica astratta esposti nel <pb xlink:href="020/01/2967.jpg" pagenum="592"/>Tomo primo; al solo esame di questo dunque si limita il soggetto del no&shy;<lb/>stro discorso. </s></p><p type="main">

<s>Il trattato &egrave; diviso in XIV sezioni, nelle quali tutto &egrave; nuovo. </s>

<s>La Mec&shy;<lb/>canica antica sta compendiata in poche pagine a parte: e perch&egrave; non con&shy;<lb/>tien per l'Autore se non che principii comunemente ricevuti dai Matematici, <lb/>e confermati dalle esperienze; ei la raccoglie sotto il titolo di <emph type="italics"/>Assiomi,<emph.end type="italics"/> ossia <lb/><emph type="italics"/>Leggi del moto.<emph.end type="italics"/> La prima legge &egrave; quella che, dopo il Keplero, si chiam&ograve; <lb/><emph type="italics"/>d'inerzia,<emph.end type="italics"/> e dalla quale dipende la seconda, che dice come le mutazioni son <lb/>proporzionali alle forze motrici impresse, e dirette per la linea, lungo la quale <lb/>fu fatta l'impressione. </s>

<s>Ma la terza legge, che cio&egrave;, all'azione, sempre uguale <lb/>e contraria &egrave; la reazione, &egrave; avuta dal Newton per cosa di maggiore impor&shy;<lb/>tanza, e nello Scolio scritto dopo i corollari si trattiene a far vedere come <lb/>abbia quella terza legge, non solamente l'applicazione alla teoria degli urti <lb/>e delle riflessioni, ma come altres&igrave; si riducano a lei le condizioni generali <lb/>dell'equilibro tra la potenza e la resistenza in tutte le Macchine, l'efficacia <lb/>delle quali, egli dice, non consiste in altro, che in aumentar la forza col <lb/>diminuire la velocit&agrave;. </s>

<s>&ldquo; Unde solvitur, in omni aptorum instrumentorum <lb/>genere, problema: <emph type="italics"/>Datum pondus data vi movendi, aliamve datam resisten&shy;<lb/>tiam vi data superandi.<emph.end type="italics"/> Nam si Machinae ita formentur, ut velocitates agen&shy;<lb/>tis et resistentis sint reciproce ut vires, agens resistentiam sustinebit, et ma&shy;<lb/>iori cum velocitatum disparitate eamdem vincit &rdquo; (Genevae 1739, pag. </s>

<s>59). </s></p><p type="main">

<s>Questo non era altro per&ograve; che il principio antico professato da Galileo, <lb/>e che il Newton faceva derivar da un assioma troppo volgare, e non bene <lb/>confacentesi con la Scienza nuova, all'altezza e alla dignit&agrave; della quale fu <lb/>il primo che pensasse di ridurvelo Giovanni Bernoulli. </s>

<s>Questi inviava, sot&shy;<lb/>toscritta nel d&igrave; 26 Gennaio 1717, una lettera al Varignon, nella quale inco&shy;<lb/>mincia dal proporgli un nuovo modo per misurar l'energia, valendosi di <lb/>quelle, ch'egli incominci&ograve; allora a chiamare <emph type="italics"/>velocit&agrave; virtuali.<emph.end type="italics"/> Sia P (fig. </s>

<s>374) <lb/>un punto qualunque, in un sistema di forze in equilibrio, ed F una di queste <lb/>forze, che spinga innanzi o ritiri in dietro, nella direzione FP, il detto punto. </s>

<s><lb/>Sopravvenendo un piccolissimo moto, la FP sar&agrave; trasportata in <emph type="italics"/>fp,<emph.end type="italics"/> mante&shy;<lb/>nendosi questa sempre parallela a quella, se il sistema tutto insieme si muove <lb/>parallelamente a una linea data: o, prolungate le due direzioni, concorre&shy;<lb/>ranno con un angolo infinitamente piccolo, se il moto del detto sistema si <lb/>facesse intorno ad un centro fisso. </s>

<s>&ldquo; Tirez donc (cos&igrave; propriamente scriveva <lb/>il Bernoulli al Varignon) PC perpendiculaire sur <emph type="italics"/>fp,<emph.end type="italics"/> et vous avrez C<emph type="italics"/>p<emph.end type="italics"/> pour <lb/>la <emph type="italics"/>vitesse virtuelle<emph.end type="italics"/> de la force F, en sorte que F. C<emph type="italics"/>p<emph.end type="italics"/> fait ce quoi j'appelle <lb/><emph type="italics"/>energie. </s>

<s>&rdquo;<emph.end type="italics"/> Osservate, soggiunge qui lo stesso Bernoulli, che la C<emph type="italics"/>p<emph.end type="italics"/> pu&ograve; es&shy;<lb/>sere o <emph type="italics"/>positiva<emph.end type="italics"/> o <emph type="italics"/>negativa<emph.end type="italics"/> rispetto alle altre forze: Venendo il punto P <lb/>spinto innanzi &egrave; positiva, se l'angolo FP<emph type="italics"/>p<emph.end type="italics"/> &egrave; ottuso, ed &egrave; negativa, se acuto. </s>

<s><lb/>Ma quando il punto fosse invece tirato indietro, C<emph type="italics"/>p<emph.end type="italics"/> &egrave; negativa, se l'angolo &egrave; <lb/>ottuso, ed &egrave; positiva se acuto: ci&ograve; che facilmente si comprende dal pensar <lb/>che, con quelle contrariet&agrave; di segni, si vogliono dal Bernoulli distinguere i <lb/>moti, che al punto C tendono, da quelli che ne rifuggono. </s></p><pb xlink:href="020/01/2968.jpg" pagenum="593"/><p type="main">

<s>&ldquo; Tout cela etant bien entendu, je forme, dit M. Bernoulli, cette pro&shy;<lb/>position generale: <emph type="italics"/>En tout equilibre de forces quelconque, en quelque ma&shy;<lb/>niere qu'elles soient appliqu&eacute;es, et suivant quelques directions qu'elles agis-<emph.end type="italics"/><lb/><figure id="id.020.01.2968.1.jpg" xlink:href="020/01/2968/1.jpg"/></s></p><p type="caption">

<s>Figura 374.<lb/><emph type="italics"/>sent les unes sur les autres, ou mediatement, ou immediate&shy;<lb/>ment; la somme des energies affirmatives sera egale &agrave; la <lb/>somme des energies negatives prises affirmativement &rdquo;<emph.end type="italics"/> (<emph type="italics"/>Nou&shy;<lb/>velle Mecan.,<emph.end type="italics"/> T. cit., pag. </s>

<s>176). Questa proposizione mi parve, <lb/>dice il Varignon, cos&igrave; semplice e cos&igrave; bella, che, vedendo com'ella <lb/>si poteva benissimo derivare dalla teoria dei moti composti, pen&shy;<lb/>sai d'introdurla nella mia Meccanica nuova, dimostrandola co'miei <lb/>proprii principii applicati a ritrovar le condizioni dell'equilibrio <lb/>nelle varie Macchine. </s>

<s>E cos&igrave; veramente egli fece nella Sezione IX, <lb/>soggiunta all'opera, come generale corollario delle teorie prece&shy;<lb/>denti, ed ebbe cos&igrave; la notizia del Teorema bernulliano la diffusion pi&ugrave; de&shy;<lb/>siderata, e la verit&agrave; di lui la pi&ugrave; solenne conferma. </s></p><p type="main">

<s>Ma di quella terza Legge del moto, per tornare al Newton, si fa dal&shy;<lb/>l'Autore apparir l'importanza, che si diceva, in que'sei corollari compren&shy;<lb/>denti in s&egrave; tutte le leggi scoperte dalla Meccanica antica, inclusavi la stessa <lb/>riforma varignoniana. </s>

<s>Nel primo corollario infatti si propone la Regola del <lb/>parallelogrammo delle forze, e nel secondo, dop'aver applicata quella regola <lb/>a dimostrar le condizioni dell'equilibrio nella Libbra, nel Vette, nell'Asse, e <lb/>nel Cuneo e nella Vite; ne conclude cos&igrave;, in poche parole, il fatto di quella <lb/><emph type="italics"/>Nouvelle mecanique,<emph.end type="italics"/> allora solamente proposta dall'Accademico di Parigi: <lb/>&ldquo; Usus igitur Corollarii huius latissime patet, et late patendo veritatem eius <lb/>evincit, cum pendeat ex iam dictis Mechanica tota ab Auctoribus diversi&shy;<lb/>mode domonstrata. </s>

<s>Ex hisce enim facile derivantur vires Machinarum quae, <lb/>ex rotis, tympanis, trochleis, vectibus, nervis tensis et ponderibus, directe vel <lb/>oblique ascendentibus, caeterisque potentiis mechanicis componi solent, ut et <lb/>vires tendinum ad animalium ossa movenda &rdquo; (pag. </s>

<s>30). </s></p><p type="main">

<s>Il terzo corollario, applicabile agli urti e alle riflessioni de'corpi duri, <lb/>col ridurre in una le leggi dimostrate dal Borelli; poteva anche tacersi, senza <lb/>grave scapito della Scienza, dopo i teoremi del Wallis. </s>

<s>Ma il corollario IV <lb/>che segue apparve a tutti i Matematici nuovo, e anche i censori stessi lo <lb/>trovarono elegantissimo. </s>

<s>&Egrave; dall'Autore cos&igrave; proposto: &ldquo; Commune gravitatis <lb/>centrum corporum duorum vel plurium, ab actionibus corporum inter se, <lb/><figure id="id.020.01.2968.2.jpg" xlink:href="020/01/2968/2.jpg"/></s></p><p type="caption">

<s>Figura 375.<lb/>non mutat statum suum vel motus vel <lb/>quietis, et propterea corporum omnium <lb/>in se mutuo agentium, exclusis actioni&shy;<lb/>bus et impedimentis externis, commune <lb/>centrum gravitatis vel quiescit, vel mo&shy;<lb/>vetur uniformiter in directum &rdquo; (p. </s>

<s>36). <lb/>Ci&ograve; che si pu&ograve; spiegare cos&igrave; in poche parole: Sia C (fig. </s>

<s>375) il centro di <lb/>gravit&agrave; dei corpi A, B: sostenuto il sistema in C, star&agrave; in quiete: abban&shy;<lb/>donato a s&egrave; stesso, cadr&agrave; lungo la linea CD verticale. </s>

<s>E ci&ograve; sar&agrave; vero, an-<pb xlink:href="020/01/2969.jpg" pagenum="594"/>che quando i detti corpi si attraggano o si respingano a vicenda con eguale <lb/>quantit&agrave; di moto, ossia in modo che i prodotti delle velocit&agrave; per le masse, <lb/>di qua e di l&agrave;, tornino uguali. </s>

<s>Se infatti AA&prime;XA=BB&prime;XB, &egrave; facile ve&shy;<lb/>dere che il centro C della gravit&agrave; non si muta. </s>

<s>Lo stesso dicasi, nel caso <lb/>che i corpi sian tre o pi&ugrave;, componendo i loro centri di gravit&agrave; nei so&shy;<lb/>liti modi. </s></p><p type="main">

<s>Abbiamo accennato che questo Corollario del Newton ebbe censori, <lb/>fra quali s'indovina facilmente dover essere Giovanni Bernoulli, che, pur non <lb/>mancando di riverenza verso il grande Matematico inglese, non poteva patire <lb/>che egli, e forse peggio i suoi, volessero tirare a s&egrave; tutto il merito de'pro&shy;<lb/>gressi, che veniva facendo la nuova Filosofia matematica. </s>

<s>Il Bernoulli dun&shy;<lb/>que sent&igrave; che il Corollario neutoniano non si dimostrava dal suo Autore se&shy;<lb/>condo quella generalit&agrave;, con la quale era stato proposto. </s>

<s>E infatti non sembra <lb/>avesse il Newton in mente, quando lo formul&ograve;, che di farne l'applicazione <lb/>alla proposizione LXV, e alle altre simili, delle quali intendeva poi valersi <lb/>nel Tomo terzo, per illustrare la teoria delle perturbazioni dei corpi celesti. </s>

<s><lb/>I Matematici invece si credettero a prima vista di avere avuto un Teorema <lb/>dinamico generale, e il Bernoulli ne scopr&igrave; sagacemente l'inganno, facendo <lb/>osservare che <emph type="italics"/>etsi hoc Theorema, elegantissimum quidem, in generali sensu <lb/>sit propositum, demonstratio tamen Newtoni minime est generalis.<emph.end type="italics"/> E ci&ograve; <lb/>perch&egrave;, prosegue a dire, in quel suo lungo discorso non si contempla altro <lb/>caso che quello, in cui i corpi concorrano a due a due, o due o pi&ugrave; insieme <lb/>combinati con un terzo, ma non si mette mai in considerazione il caso, che <lb/>tre o pi&ugrave; corpi si sospingano a vicenda in varie direzioni, tutti a una volta, <lb/>e nel medesimo istante, <emph type="italics"/>cuius casus neglectio, relinquit sane demonstra&shy;<lb/>tionem Newtoni longe imperfectissimam, quae vix periculum praestat eius <lb/>quod promittitur in propositione generali.<emph.end type="italics"/> Per supplire al qual difetto, sog&shy;<lb/>giunge, &egrave; da tenere altra via, la quale &egrave; quella che mi ha menato a formu&shy;<lb/>lare e a dimostrar questo, che &egrave; veramente generale Teorema, da sostituirsi <lb/><figure id="id.020.01.2969.1.jpg" xlink:href="020/01/2969/1.jpg"/></s></p><p type="caption">

<s>Figura 376.<lb/>all'altro annunziato dal Newton in quel suo Corol&shy;<lb/>lario quarto: <emph type="italics"/>Si dati corporis ABC<emph.end type="italics"/> (fig. </s>

<s>376) <emph type="italics"/>cen&shy;<lb/>trum gravitatis Q sollicitatur a pluribus potentiis, <lb/>seu viribus motricibus, quarum directiones et quan&shy;<lb/>titates designentur per rectas datas OD, OE, OF, <lb/>OG etc, sitque punctum P centrum commune gra&shy;<lb/>vitatis punctorum D, E, F, G, instar ponderum <lb/>aequalium consideratorum; dico rectam OP fore <lb/>directionem, secundum quam movebitur centrum gravitatis O corporis <lb/>ABC, et quidem motu sibi semper parallelo, sive accedendo versus P, <lb/>sive ab eodem recedendo, prout vires motrices sunt vel trahentes vel pel&shy;<lb/>lentes<emph.end type="italics"/> (Op. </s>

<s>omnia, T. cit., pag. </s>

<s>341). </s></p><p type="main">

<s>Il Leibniz poi aveva reso anche pi&ugrave; perfetto il bellissimo Teorema, sog&shy;<lb/>giungendo che la resultante del moto, non solamente &egrave; diretta lungo la OP, <lb/>ma &egrave; altres&igrave; misurata dalla OP stessa, presa molteplice secondo il numero <pb xlink:href="020/01/2970.jpg" pagenum="595"/>de'punti gravi, de'quali P sia, com'&egrave; detto, nel centro. </s>

<s>Dette esso Leibniz, <lb/>in una epistola al Wallis, l'annunzio della invenzione, senza per&ograve; dimostrarla, <lb/>ma non indugiarono molto gli studiosi ad aver la desiderata dimostrazione <lb/>dall'Hermann, il quale anzi promosse la cosa tant'oltre, da riuscire a tro&shy;<lb/>var la ragione ultima dell'uguagliarsi insieme i momenti nella Libbra ar&shy;<lb/>chimedea: n&egrave; vogliam qui tacerne ai nostri Lettori il modo, riferendosi stret&shy;<lb/>tamente alla storia del Corollario neutoniano, da cui insomma ebbero que&shy;<lb/>ste alte speculazioni il principio. </s></p><p type="main">

<s>Esposto in brevi, ma chiarissime parole, e in pochi segni il Teorema <lb/>del Leibniz, si propone l'Hermann a risolvere un tal problema: <emph type="italics"/>Invenire <lb/>mediam directionem solicitationum quarumvis AG, BG, CG, DG<emph.end type="italics"/> (fig. </s>

<s>377) <lb/><emph type="italics"/>quibus puncta A, B, C, D lineae rectae inflexilis AD urgentur<emph.end type="italics"/> (Forono&shy;<lb/><figure id="id.020.01.2970.1.jpg" xlink:href="020/01/2970/1.jpg"/></s></p><p type="caption">

<s>Figura 377.<lb/>mia cit,, pag. </s>

<s>18), e la pratica, della <lb/>quale passa poi a dimostrar la ra&shy;<lb/>gione e la verit&agrave;, &egrave; cos&igrave; comandata. </s>

<s><lb/>Prendete fuori della verga rigida un <lb/>centro qualunque O, da cui irrag&shy;<lb/>gino, passando per A, B, C, D ... <lb/>altrettante linee prefinite, ne'punti <lb/>omonomi F, dalle respettive linee <lb/>GF, condotte, dalle estremit&agrave; G delle <lb/>potenze, parallele alla direzione AD <lb/>della verga. </s>

<s>Fate gl'intervali OA&prime;, <lb/>OB&prime;, OC&prime;, OD&prime; ... uguali ad AF, <lb/>BF, CF, DF, e, de'punti A&prime;, B&prime;, C&prime;, <lb/>D&prime; ... essendo baricentro E&prime;, per <lb/>questo punto e per O fate passare <lb/>una linea, che prolungata attraversi <lb/>in E la verga stessa, d'onde la pro&shy;<lb/>lungherete ancora, in fin tanto che <lb/>non vada EM lunga quanto OE&prime;, <lb/>presa molteplice secondo il numero <lb/>de'punti A&prime;, B&prime;, C&prime;, D&prime; ... All'ul&shy;<lb/>timo, condotta la ML parallela ad <lb/>AD, e presa di tal lunghezza tanto <lb/>che valga quanto tutte insieme le FG, congiungete i punti L, E, e avrete <lb/>nella LE, non solamente la direzione, ma anche la misura della resultante <lb/>unica delle varie potenze applicate a sollecitare il sistema, di cui dunque E <lb/>sar&agrave; il centro, intorno al quale o si mover&agrave; o permarr&agrave; in equilibrio. </s></p><p type="main">

<s>Rispetto a questo centro dell'equilibrio avverte l'Herman una certa pro&shy;<lb/>priet&agrave;, per farne nel corollario secondo un'applicazione importante, ed &egrave; che, <lb/>abbassate dai punti A, B, C, D ... le AH, BH, CH. DH ... perpendicolari <lb/>sui prolungamenti delle FG, i rettangoli fatti da queste perpendicolari, e dalle <lb/>respettive distanze dal centro E da una parte, sommati insieme, sono uguali <pb xlink:href="020/01/2971.jpg" pagenum="596"/>alla somma dei rettangoli, che in modo simile si facesser dall'altra: cio&egrave; <lb/>AH.AE+BH.BE=DH.DE+CH.CE. </s></p><p type="main">

<s>L'applicazione importante che si diceva &egrave; al vette sollecitato dalle po&shy;<lb/>tenze oblique AG, BG; DG, CG (fig. </s>

<s>378), intorno al centro E dell'equili&shy;<lb/>brio, da cui conducendosi sui prolungamenti delle linee rappresentanti esse <lb/>potenze le perpendicolari EP, <expan abbr="Eq;">Eque</expan> ES, ER, i triangoli simili, che per que&shy;<lb/>sta costruzione vengono a disegnarsi, danno i rettangoli AH.AE, BH.BE, <lb/>DH.DE, CH.CE rispettivamente uguali ai rettangoli AG.EP, BG.EQ, <lb/>DG.ES, CG.ER. </s>

<s>Ma AG.EP+BG.EQ &egrave;, per le cose dimostrate, uguale <lb/>a DG.ES+CG.ER; dunque AH.AE+BH.BE=DH.DE+CH.CE, <lb/>ossia, per le condizioni dell'equilibrio, la somma dei momenti, che solleci&shy;<lb/>tano il vette da una parte, deve essere uguale alla somma dei momenti, che <lb/>lo sollecitano dall'altra. </s>

<s>E ci&ograve; concluso, soggiunge l'Herman questo che, per <lb/>la storia del quarto Corollario del Newton, &egrave; notabilissimo Scolio: &ldquo; Casus <lb/>Corollarii huius secundi obtinet non solum tunc cum linea AD est recta, cui <lb/><figure id="id.020.01.2971.1.jpg" xlink:href="020/01/2971/1.jpg"/></s></p><p type="caption">

<s>Figura 378.<lb/>potentiae obliquae AG, BG ... <lb/>applicantur, sed etiam in casu, <lb/>quo ipsa linea applicatas poten&shy;<lb/>tias habens est curva, immo e&shy;<lb/>tiam in rotis aliisque eiusmodi <lb/>organis. </s>

<s>Uno verbo <emph type="italics"/>si circa ali&shy;<lb/>quod punctum potentiae aut <lb/>solicitationes quaecumque in ae&shy;<lb/>guilibrio sunt; momenta potentiarum, quae agunt in unam partem, aequa&shy;<lb/>lia sunt momentis potentiarum, quae agunt in partem oppositam,<emph.end type="italics"/> atque <lb/>sic inopinato incidimus in demonstrationem directam et immediatam prin&shy;<lb/>cipii Archimedei de aequalitate momentorum, in casu aequilibrii potentia&shy;<lb/>rum inter se commissarum, quod varii varie demonstrare conati sunt &rdquo; (Fo&shy;<lb/>ron. </s>

<s>cit., pag. </s>

<s>21). </s></p><p type="main">

<s>Al quarto Corollario che l'Herman, il Leibniz e il Bernoulli promossero <lb/>cos&igrave; com'abbiamo veduto, ne fa seguitare il Newton altri due d'assai minore <lb/>importanza, dopo i quali riassume il suo discorso in uno Scolio, e che co&shy;<lb/>mincia: &ldquo; Hactenus principia tradidi a Mathematicis recepta et experientia <lb/>multiplici confirmata. </s>

<s>Per leges duas primas et corollaria duo prima Gali&shy;<lb/>leus invenit descensum gravium esse in duplicata ratione temporis, et mo&shy;<lb/>tum proiectorum fieri in parabola &rdquo; (pag. </s>

<s>45, 46), che sono gli argomenti <lb/>trattati nel terzo e nel quarto Dialogo delle due nuove Scienze, ritirati qui <lb/>a pi&egrave; della nuova Filosofia matematica, quasi soggetta valle disegnata nel <lb/>quadro, perch&egrave; possa l'occhio misurare la superba altura del monte. </s>

<s>E per&shy;<lb/>ch&egrave; non si pu&ograve; aver la misura giusta del fastigio, senza ricercarne il prin&shy;<lb/>cipio e la radice, premettiamo queste considerazioni. </s></p><p type="main">

<s>Due massimi problemi, su quella via per la quale s'erano messi i suoi <lb/>nuovi studi, ebbe a trovare il Newton irresoluti: il primo de'quali era per&shy;<lb/>ch&egrave; i pianeti circondassero il Sole, e i satelliti Giove, in orbite ellittiche, e <pb xlink:href="020/01/2972.jpg" pagenum="597"/>il secondo, in cui si domandava quale curvit&agrave; di linea descriverebbe un pro&shy;<lb/>ietto, che a movere dalla superficie andasse finalmente a quetar nel centro <lb/>della Terra. </s></p><p type="main">

<s>Bench&egrave; commenti indegni della Scienza gli dovessero sembrar le ragioni <lb/>del Keplero, e le opinioni del Boulliaud e del Borelli cose molto somiglianti <lb/>ai romanzi, nonostante il Newton non aveva ancora trovato nulla di meglio, <lb/>per risolvere il primo dei detti problemi, quando gli si rivel&ograve;, dalle specu&shy;<lb/>lazioni del Wren, dell'Hook e dell'Halley intorno alle forze centrali, che il <lb/>Sole attrae i pianeti e Giove i satelliti con forze, che diminuiscono, non col <lb/>crescere delle semplici distanze, ma de'quadrati delle distanze dal centro <lb/>dell'attrazione. </s>

<s>Allora, come emend&ograve;, e trov&ograve; che tornava bene il calcolo <lb/>della velocit&agrave;, con cui sarebbe caduta sulla Terra la Luna; cos&igrave; pens&ograve; che, <lb/>del non aver saputo gli Astronomi suoi precursori render la ragione geome&shy;<lb/>trica dell'eccentricit&agrave; delle orbite, fosse stata potissima causa l'ignorar la <lb/>vera legge del variar le forze centripete, rispetto al variare delle distanze. </s>

<s><lb/>Ond'&egrave; che, mettendosi a cercare in qual curva si volgerebbe un proietto, il <lb/>quale fosse continuamente ritirato verso un punto, con forze reciprocamente <lb/>proporzionali ai quadrati delle distanze; trov&ograve; con ineffabile compiacenza che <lb/>quella curva era un'ellisse, in un foco della quale risedesse il centro del&shy;<lb/>l'attrazione. </s>

<s>Contrariamente, dato che un corpo vada in giro per un'ellisse, <lb/>attratto continuamente a uno de'fochi; trov&ograve; che le forze centripete erano <lb/>reciprocamente proporzionali ai quadrati delle distanze. </s></p><p type="main">

<s>Intorno al secondo problema sopra notato i Matematici, a'tempi del <lb/>Newton, erano molto discordi. </s>

<s>Galileo, prima di aver veduto lo <emph type="italics"/>Specchio <lb/>ustorio<emph.end type="italics"/> del Cavalieri, cred&egrave; verosimile che un grave cadente dall'alto di una <lb/>torre, menata in giro dalla vertigine della Terra, giungerebbe al centro di <lb/>lei per una mezza circonferenza. </s>

<s>Poi non dubit&ograve; di asserire che, almeno per <lb/>qualche tratto, quel moto composto del retto accelerato e del circolare equa&shy;<lb/>bile si farebbe per una parabola, ma il Fermat pretese di dimostrare che, <lb/>non potendo esser parabolica una linea, la quale ritorna all'asse, da cui si <lb/>era partita; era invece una spirale, non difforme da quella di Archimede. </s>

<s><lb/>Il Borelli, nella proposizione LVII <emph type="italics"/>De vi percussionis,<emph.end type="italics"/> sentenzi&ograve; che tutte e <lb/>tre queste opinioni erano false. </s>

<s>Falsa quella prima di Galileo, perch&egrave; le scese <lb/>starebbero come i seni versi delle met&agrave; degli archi passati, e perci&ograve; in pro&shy;<lb/>porzione assai minore di quella dei quadrati dei tempi: falsa anche la se&shy;<lb/>conda dello stesso Galileo, e incompetente nella questione, non potendo evi&shy;<lb/>dentemente esser parabolica una curva, che ritorna in s&egrave; stessa. </s>

<s>Ma falsa <lb/>concludeva all'ultimo essere anche l'opinione del Fermat, il quale, egli dice, <lb/>s'ingann&ograve; a credere che, col medesimo impeto trasversale, il mobile in tempi <lb/>uguali percorra spazi sottendenti al centro angoli uguali. </s>

<s>Or perch&egrave; &egrave; un <lb/>fatto che quegli crescono successivamente, secondo che diminuiscono via via <lb/>le distanze da esso centro, <emph type="italics"/>constat curvam lineam non esse regularem.<emph.end type="italics"/> (Bo&shy;<lb/>noniae 1667, pag. </s>

<s>109). </s></p><p type="main">

<s>Il Newton senti che il Borelli da una parte aveva ragione, stando egli <pb xlink:href="020/01/2973.jpg" pagenum="598"/>nell'ipotesi comune della gravit&agrave;, che sollecita il mobile con impulso uni&shy;<lb/>forme, ma sent&igrave; dall'altra che non si decideva nulla in proposito, non es&shy;<lb/>sendo verosimile che il cadente venga attratto, come supponevasi da Galileo, <lb/>dal Fermat e dallo stesso Borelli, sempre con la medesima forza, a qualun&shy;<lb/>que distanza dal centro. </s>

<s>E perch&egrave; non aveva forse pensato ancora ad asse&shy;<lb/>gnar la legge naturale di quelle forze, per sciogliere direttamente il problema; <lb/>si limit&ograve; a darne una soluzione indiretta: <emph type="italics"/>Gyretur corpus in spirali secante <lb/>radios omnes in angulo dato: requiritur lex vis centripetae tendentis ad <lb/>centrum spiralis<emph.end type="italics"/> (pag. </s>

<s>136), e il frutto della ricerca fu che le forze centri&shy;<lb/>pete debbono esser reciprocamente proporzionali ai cubi delle distanze. </s></p><p type="main">

<s>Poi la detta legge naturale la desunse immaginando un grave, che giri <lb/>in orbite circolari o ellittiche, ora pi&ugrave; lontane, ora pi&ugrave; vicine al centro, da <lb/>cui venga attratto, e trov&ograve; che la legge dell'attrazione in questo caso era <lb/>quella diretta delle distanze. </s>

<s>Conseguiva di qui che, trasformandosi l'ellisse <lb/>in parabola, coll'andare il centro infinitamente distante dal vertice della nuova <lb/>sezione; le forze centripete, che tutte hanno verso l'infinito la medesima <lb/>proporzione, divengono uniformi, e cos&igrave; la presente questione ricade in quella <lb/>particolare di Galileo intorno ai proietti. </s>

<s>&ldquo; Si ellipsis, centro in infinitum <lb/>abeunte, vertatur in parabolam, corpus movebitur in hac parabola, et vis, ad <lb/>centrum infinite distans iam tendens, evadet aequabilis. </s>

<s>Hoc est theorema <lb/>Galilei &rdquo; (pag. </s>

<s>149). Dunque, nell'ipotesi della gravit&agrave; uniforme, la pietra <lb/>che cade dall'alta torre viene attratta a un punto, che &egrave; a una distanza infi&shy;<lb/>nita, e che perci&ograve; non pu&ograve; essere il centro della Terra: ond'&egrave; chiaro che <lb/>la detta pietra descriver&agrave; una parabola, non per un tratto solo, come pens&ograve; <lb/>Galileo, ma per tutto il suo viaggio, che dovrebbe proseguire in infinito. </s></p><p type="main">

<s>Traspariva da queste speculazioni che, nella Dinamica galileiana, si <lb/>contemplava il solo caso particolare, in cui i corpi son continuamente sol&shy;<lb/>lecitati da impulsi di gravit&agrave; sempre uguali, e sent&igrave; perci&ograve; il Newton che <lb/>la Scienza, com'ei l'aveva trovata, era tuttavia ne'suoi principii, e che ri&shy;<lb/>maneva a promoverla in assai pi&ugrave; vasto e pi&ugrave; nobile campo, dimostrando le <lb/>leggi universalissime de'moti, nel caso che gl'impulsi gravitativi, ossia le <lb/>forze centripete, variassero ora secondo le semplici distanze, ora secondo i <lb/>quadrati delle distanze, ora secondo qualsiasi proporzione. </s>

<s>Ecco l'indole della <lb/>nuova Dinamica neutoniana, della quale tutte le cose scoperte, e tutti i teo&shy;<lb/>remi dimostrati dai Matematici, che avevano preceduto l'Autore infino a Ga&shy;<lb/>lileo e all'Huyghens; non sarebbero stati pi&ugrave; che semplici corollari: ecco il <lb/>compasso da misurar giusta l'estensione e la sublimit&agrave;, a cui giunse la <lb/>Scienza del moto nei <emph type="italics"/>Principii matematici di Filosofia naturale.<emph.end type="italics"/></s></p><p type="main">

<s>Se l'uno di que'due massimi problemi, da'quali si diceva aver avuto <lb/>questa nuova Filosofia gli inizii, dette occasione al Newton di ritrovar le <lb/>leggi delle forze centripete, nel corpo che gira in una spirale, in un'ellisse, <lb/>in una parabola, d'onde si veniva a definir la linea descritta dal cadente, <lb/>che non arrestasse il moto sulla superficie terrestre; l'altro dei detti pro&shy;<lb/>blemi porgeva allo stesso Autore un argomento d'assai maggiore importanza, <pb xlink:href="020/01/2974.jpg" pagenum="599"/>qual'&egrave; il trattato del moto dei corpi nelle sezioni coniche eccentriche. </s>

<s>E fu <lb/>appunto per questa importanza che v'intrattenne intorno il Newton pi&ugrave; dif&shy;<lb/>fusamente il discorso, com'egli stesso dice, ripensando a quel sesto corolla&shy;<lb/>rio della proposizione IV, in cui era stato concluso che, essendo i tempi pe&shy;<lb/>riodici nelle ellissi proporzionali ai cubi dei grandi assi, le forze centripete <lb/>son reciprocamente proporzionali ai quadrati dei raggi vettori: &ldquo; Casus co&shy;<lb/>rollarii sexti obtinet in corporibus coelestibus, ut seorsum collegerunt etiam <lb/>nostrates Wrennus, Hockius et Hallaeus, et propterea quae spectant ad vim <lb/>centripetam decrescentem in duplicata ratione distantiarum a centris, decrevi <lb/>fusius in sequentibus exponere &rdquo; (pag. </s>

<s>103): che &egrave; l'argomento sopra accen&shy;<lb/>nato, e che s&igrave; svolge ne'teoremi della terza sezione. </s></p><p type="main">

<s>Piglia dunque motivo questo argomento dalle tre celebri leggi del Ke&shy;<lb/>plero, astraendo dalle particolari osservazioni dei corpi celesti, e considerando <lb/>il moto di un semplice punto fisico o materiale, continuamente sollecitato da <lb/>forze centripete, che diminuiscono d'intensit&agrave; col crescere dei quadrati delle <lb/>distanze. </s>

<s>Alla nuova Dinamica razionale preluceva nei fatti naturali osser&shy;<lb/>vati la notizia certa delle conclusioni, ma rimaneva al Newton a ritrovarne <lb/>i principii. </s>

<s>E perch&egrave; in que'fatti era una intima dipendenza di ragioni fra <lb/>i tempi periodici, e le linee delle orbite, e le forze attrattive, cosicch&egrave; l'una <lb/>poteva indifferentemente prendersi per principio, da cui conseguissero le <lb/>altre; pose esso Newton per fondamento al suo trattato l'osservazione fatta <lb/>dal Keplero intorno ai pianeti, che cio&egrave; le aree son proporzionali ai tempi, <lb/>riducendola a dimostrarsi matematicamente in quel teorema, che &egrave; il primo <lb/>e principale della Sezione seconda, e da cui si svolgono tutte le altre pro&shy;<lb/>posizioni relative alle forze centripete, che sollecitano i corpi, mentre girano <lb/>intorno ai centri di una spirale, e delle varie sezioni di un cono. </s></p><p type="main">

<s>La Sezione terza, come si disse, &egrave; propriamente quella, in cui si tratta <lb/>astrattamente del moto di qualunque corpo, supposto ch'egli pesi verso un <lb/>dato punto, come i pianeti verso il Sole, e i satelliti verso Giove: e dop'aver <lb/>dimostrate le proporzioni di quel peso, nel moversi ora in una, ora in un'altra <lb/>delle sezioni coniche eccentriche, passa a propor la soluzione di questo mas&shy;<lb/>simo problema: &ldquo; Posito quod vis centripeta sit reciproce proportionalis qua&shy;<lb/>drato distantiae locorum a centro, et quod vis illius quantitas absoluta sit <lb/>cognita; requiritur linea, quam corpus describit de loco dato, cum data ve&shy;<lb/>locitate, secundum datam rectam egrediens &rdquo; (pag. </s>

<s>170). </s></p><p type="main">

<s>Esca il corpo P (fig. </s>

<s>379) con la velocit&agrave; data, secondo la tangente PR, <lb/>e subito sia costretto dalla forza centripeta, diretta verso il punto S, a de&shy;<lb/>scrivere la curva PQ, che per le cose dimostrate appartien senza dubbio a <lb/>una sezione conica, avente in S uno de'fochi, e della quale si vuol determi&shy;<lb/>nare la specie. </s>

<s>Facciasi RPH complementare dell'angolo RPS a due angoli <lb/>retti: sopra un punto della PH si dovr&agrave; trovare l'altro foco della sezione, <lb/>che supponesi essere H. </s>

<s>Congiunti S e H, e dal vertice S del triangolo che <lb/>indi nasce condotta la SK, perpendicolare sul lato opposto PH, e chiamato L <lb/>il lato retto, ossia il parametro della curva, a qualunque sezion del cono ella <pb xlink:href="020/01/2975.jpg" pagenum="600"/>appartenga; riesce il Newton, calcolando, all'equazione L (SP+PH)= <lb/>PH (2SP+2KP), d'onde L:2SP+2KP=PH:SP+PH. </s>

<s>Ora pu&ograve; <lb/>darsi il caso che il corpo esca con tal impeto tangenziale da far s&igrave; che L, <lb/>ossia il parametro, manchi, uguagli o superi il doppio della somma SP+KP, <lb/>nel qual caso anche PH mancher&agrave;, uguaglier&agrave; o superer&agrave; SP+PH: cio&egrave; <lb/>la linea SP sar&agrave; o positiva o nulla o negativa, e secondo che questo o quello <lb/>o quell'altro caso avviene, la sezione conica dell'orbita sar&agrave; o un'ellisse o <lb/>una parabola o una iperbola. </s>

<s>&ldquo; Si ea sit corporis in P velocitas, ut latus <lb/>rectum L minus fuerit quam 2SP+2KP, iacebit PH ad eamdem partem <lb/><figure id="id.020.01.2975.1.jpg" xlink:href="020/01/2975/1.jpg"/></s></p><p type="caption">

<s>Figura 379.<lb/>tangentis PR cum linea PS, ideoque <lb/>figura erit ellipsis, et, ex datis umbilicis <lb/>S, H et axe principali SP+PH, da&shy;<lb/>bitur. </s>

<s>Sin tanta sit corporis velocitas, ut <lb/>latus rectum L aequale fuerit 2SP+ <lb/>2KP, longitudo PH infinita erit, et prop&shy;<lb/>terea figura erit parabola, axem habens <lb/>GH parallelum lineae PK, et inde dabi&shy;<lb/>tur. </s>

<s>Quod si corpus maiori adhuc cum <lb/>velocitate de loco suo P exeat, capienda erit longitudo PH ad alteram par&shy;<lb/>tem tangentis, ideoque, tangente inter umbilicos pergente, figura erit hyper&shy;<lb/>bola, axem habens principalem aequalem differentiae linearum SP et PH, et <lb/>inde dabitur &rdquo; (pag. </s>

<s>172, 73). </s></p><p type="main">

<s>Applicato questo Teorema alla Meccanica celeste, non solamente confer&shy;<lb/>mava la ragion geometrica della orbite ellittiche, in cui si rivolgono i satelliti <lb/>e i pianeti, ma rivelava inoltre il mistero di altri corpi celesti, come delle <lb/>Comete, le quali, avendo ricevuto il primo impulso tangenziale pi&ugrave; forte dei <lb/>satelliti detti e de'pianeti, descriverebbero parabole: ed, essendo quell'im&shy;<lb/>pulso anche pi&ugrave; forte, iperbole; cosicch&egrave; vedute una volta in cielo non appa&shy;<lb/>rirebbero mai pi&ugrave; ad occhio mortale. </s></p><p type="main">

<s>La sublimit&agrave; del pensiero dest&ograve; in tutti la maraviglia, ed in alcuni po&shy;<lb/>chi uno spirito d'emulazione, da cui furono stimolati a dire che non aveva <lb/>il Newton dimostrato bene come il corpo, uscito con quell'impeto tangen&shy;<lb/>ziale, e con quella legge d'attrazione al centro, non potesse moversi in altra <lb/>curva diversa da una sezione del cono. </s>

<s>Fu perci&ograve; che Giov. </s>

<s>Bernoulli e il <lb/>Leibniz e il Varignon vollero tentare il problema inverso, ricercando cio&egrave; in <lb/>qual curva s'avvierebbe un proietto, con un dato impulso tangenziale, e at&shy;<lb/>tratto a un centro fisso in reciproca ragione dei quadrati delle distanze. </s>

<s><lb/>L'Euler si maravigli&ograve; di queste censure, quasi non resultasse ad evidenza, <lb/>da quella XVII proposizion neutoniana, nessun altra curva, da una sezione <lb/>conica in fuori, poter sodisfare al quesito, e si compiaceva di aver nel primo <lb/>tomo della sua <emph type="italics"/>Mechanica analitice exposita<emph.end type="italics"/> data della cosa tal risoluzione, <lb/>&ldquo; qua Newtoni assertio extra dubium ponitur &rdquo; (Petropoli 1746, pag. </s>

<s>271). <lb/>Ma era quella risoluzione stata data alquanto prima dall'Herman, il quale, <lb/>proponendosi <emph type="italics"/>invenire canonem generalem determinandae gravitatis va-<emph.end type="italics"/><pb xlink:href="020/01/2976.jpg" pagenum="601"/><emph type="italics"/>riabilis seu leges solicitationum centralium pro omnibus curvis algebraicis <lb/>in infinitum, quantitatibus finitis expressum<emph.end type="italics"/> (Foron. </s>

<s>cit., pag. </s>

<s>74); osserva <lb/>poi in uno Scolio che, se la legge delle dette sollecitazioni &egrave; la reciproca dei <lb/>quadrati delle distanze, l'equazion generale della curva algebrica &egrave; propria&shy;<lb/>mente quella, che si riferisce alle Sezioni del cono, concludendo cos&igrave; il suo <lb/>discorso &ldquo; Ergo in hac hypothesi centrum virium, seu solicitationum gravi&shy;<lb/>tatis, sunt umbilici Sectionum conicarum, quod iam omnibus constat egre&shy;<lb/>gie conspirare cum iis, quae demonstrata sunt ab illustr. </s>

<s>Newtono, Leibni&shy;<lb/>tio, Varignonio ed aliis, circa vires, quas vocant centripetas, in Sectionibus <lb/>conicis methodis directis &rdquo; (ibid., pag. </s>

<s>79). </s></p><p type="main">

<s>Tre sono le ipotesi in tal proposito, alle quali rispondono i fatti che si <lb/>osservano, o che si sperimentano nella Natura: quella delle sollecitazioni <lb/>della gravit&agrave; sempre uguali ne'cadenti sulla superficie terrestre, e quella <lb/>delle sollecitazioni della gravit&agrave;, che variano in ragion diretta delle semplici <lb/>distanze, e in reciproca de'quadrati delle distanze, come s'argomenta de'corpi <lb/>tendenti al centro della Terra, sotto la sua superficie, e si osserva de'Pia&shy;<lb/>neti attratti al centro del Sole. </s>

<s>S'arresta forse qui ne'primi termini la pro&shy;<lb/>gressione, e ne'primi gradi &egrave; rotta la foga dell'ascesa: o ripensando alla <lb/>instancabile operosit&agrave;, e alla onnipotenza della somma Virt&ugrave; creativa, si cre&shy;<lb/>derebbe piuttosto che fosse il Sole anch'egli un pianeta, attratto a un centro <lb/>da forze decrescenti via via coll'aumentar de'cubi delle distanze, e che que&shy;<lb/>sto centro, a cui move il Sole, tenda a moversi anch'egli alla sua volta a <lb/>un altro centro pi&ugrave; lontano, che con tanto pi&ugrave; debole forza l'attragga, quanto <lb/>secondo i quadrato quadrati n'&egrave; cresciuta la lontananza? </s>

<s>Chi potrebbe im&shy;<lb/>por limite a questo ingradarsi sempre pi&ugrave; in alto gli ordinamenti del Cosmo, <lb/>innanzi alla pensata immensit&agrave; del quale sentendosi rintuzzare il filosofico <lb/>orgoglio dell'uomo, par che volesse prepotentemente reagire nel Newton, <lb/>quando si propose l'invenzion dell'orbite, nelle quali si rivolgerebbero i corpi <lb/>sollecitati da forze centripete, secondo qualunque ragione operanti. </s>

<s>&ldquo; Posita <lb/>cuiuscumque generis vi centripeta, et concessis figurarum curvilinearum qua&shy;<lb/>draturis, requiruntur tum traiectoriae, in quibus corpora movebuntur, tum <lb/>tempora motuum in traiectoriis inventis &rdquo; (pag. </s>

<s>318). Cos&igrave; era risalito il <lb/>Newton, con l'ala del suo proprio ingegno, a descriver le vie, che percor&shy;<lb/>rerebbero nello spazio immenso gl'incogniti mondi, usciti dalla mano del <lb/>Creatore con qualunque forza gli fosse piaciuto di sollevare, nel gettarli, il <lb/>suo braccio; mentre Galileo erasi rimasto nel suo quarto Dialogo a inse&shy;<lb/>gnare ai militari il modo di dirigere i tiri delle bombarde, per distrugger <lb/>queste povere nostre figuline! </s></p><p type="main">

<s>A pari sublime altezza promoveva il Newton la scienza del terzo dia&shy;<lb/>logo galileiano, dalle pallottole di argilla cadenti dalla cima del campanile di <lb/>Pisa sollevando il pensiero al cader della Luna sopra la Terra, della Terra <lb/>sopra il Sole, del Sole sopra il suo centro: e finalmente, lasciate libere le <lb/>ali all'ardito volo, misurare i gradi della velocit&agrave;, con cui, da qualunque <lb/>legge di gravit&agrave; sollecitati cadrebbero i rilucenti globi dal firmamento. </s>

<s>&ldquo; Po-<pb xlink:href="020/01/2977.jpg" pagenum="602"/>sita cuiuscumque generis vi centripeta, et concessis figurarum curvilinearum <lb/>quadraturis, requiritur corporis recta ascendentis vel discendentis tum velo&shy;<lb/>citas in locis singulis, tum tempus quo corpus ad locum quemvis perveniet, <lb/>et e contra &rdquo; (pag. </s>

<s>305). </s></p><p type="main">

<s>Dai due Dialoghi di Galileo sopra commemorati la Dinamica, poco dopo <lb/>la met&agrave; del secolo XVII, non avrebbe forse sperato di avanzarsi tant'oltre, <lb/>quanto fece per opera dell'Huyghens nell'<emph type="italics"/>Orologio oscillatorio.<emph.end type="italics"/> Si rimaneva <lb/>per&ograve; quivi l'Autore tuttavia a considerare i gravi sulla superficie terrestre, <lb/>come sollecitati continuamente dagl'impulsi della gravit&agrave; naturale, che si sup&shy;<lb/>ponevano, ma che di fatto non potevano essere uniformi. </s>

<s>La Cicloide poi, <lb/>ch'era la curva, sopra le propriet&agrave; meccaniche della quale, nuovamente sco&shy;<lb/>perte e dimostrate, si volevano costruire i nuovi Orologi; appariva, a consi&shy;<lb/>derarla bene, come un'opera dell'arte piuttosto che della Natura, la quale <lb/>non porge mai alla ruota genitrice una via piana, ma incurvata nell'arco di <lb/>qualche circolo massimo della Terra. </s>

<s>I teoremi ugeniani non uscivan dunque <lb/>fuori di que'limiti, dentro i quali Archimede aveva circoscritta la Scienza, <lb/>e il Newton, per volerla promovere alle sue generalit&agrave; anche da questa parte, <lb/>ricerc&ograve; la Cicloide naturale, e in lei quelle leggi de'pendoli, delle qnali le <lb/>scoperte dall'Huyghens non potevano essere che un caso particolare. </s></p><p type="main">

<s>Sia C (fig. </s>

<s>380) il centro, e CB l'intervallo, con cui &egrave; descritto l'areo <lb/>ABL del cerchio massimo di un globo, sulla convessit&agrave;, e sulla concavit&agrave; del <lb/>quale arco passeggiando una ruota, descriver&agrave; due distinte curve cicloidee, <lb/>e il nome di <emph type="italics"/>epicicloide<emph.end type="italics"/> dato dall'inventore a quella, suggerisce a noi di <lb/>chiamare <emph type="italics"/>ipocicloide<emph.end type="italics"/> quest'altra. </s>

<s>Essendosi da A partita la detta ruota, giunta <lb/>in B, abbia descritto l'arco d'epicicloide AP. </s>

<s>Prolungato il raggio CB di una <lb/>lunghezza uguale al diametro BV, e congiunti V e P, il Newton trov&ograve; essere <lb/>essenziale propriet&agrave; della nuova linea che AP a BV&mdash;VP, e 2CE a CB <lb/>hanno insieme la medesima proporzione. </s></p><p type="main">

<s>Dal centro E si abbassi sul mezzo dell'arco BGP la EG, che segher&agrave; <lb/>perpendicolarmente la corda in F, e al segamento EF torner&agrave; la VP paral&shy;<lb/>lela e doppia, essendo anche BV diametro doppio del raggio EB. Ora, perch&egrave; <lb/>FG=EG&mdash;EF=(2EB&mdash;VP)/2=(BV&mdash;VP)/2, sar&agrave; 2FG=BV&mdash;VP, <lb/>ond'&egrave; che la proporzione sopra annunziata dal Newton si potr&agrave; scrivere nella <lb/>forma AP:2FG=2CE:CB. </s>

<s>Ma 2EG &egrave; il duplo seno verso della met&agrave; <lb/>dell'arco BGP, 2CE &egrave; la somma de'diametri del globo e della ruota, e CB <lb/>&egrave; il raggio della stessa ruota; dunque &egrave; vero quel che aveva l'Autore, nella <lb/>proposizione XLVIII, annunziato, che cio&egrave; &ldquo; longitudo itineris curvilinei, quod <lb/>punctum quodvis in rotae perimetro datum, ex quo globum tetigit, confecit, <lb/>quodque <emph type="italics"/>cycloidem vel epycicloidem<emph.end type="italics"/> nominare licet; erit ad duplicatum si&shy;<lb/>num versum arcus dimidii, qui globum ex eo tempore inter eumdem teti&shy;<lb/>git, ut summa diametrorum globi et rotae, ad semidiametrum globi &rdquo; (p. </s>

<s>364). <lb/>Per l'ipocicloide ricorre una simile proporzione, se non che il terzo termine, <lb/>invece d'essere come dianzi la somma dei diametri, &egrave; la differenza. </s></p><pb xlink:href="020/01/2978.jpg" pagenum="603"/><p type="main">

<s>Il pensiero della nuova curva cos&igrave; generata era balenato in mente anche <lb/>al Nardi, quando, dop'avere accennato alle infinite cicloidi secondarie, descritte <lb/>dagli infiniti circoli concentrici alla ruota, soggiungeva: <emph type="italics"/>Osservo anche po&shy;<lb/>tersi la stessa linea cicloidale fra due periferie, ad imitazione dell'elice, <lb/>disegnare.<emph.end type="italics"/> Ma il Newton aveva ben altre intenzioni che alla Geometria pura, <lb/>bench&egrave; nella sua Cicloide nuova si comprendessero anche le propriet&agrave; geo&shy;<lb/>metriche della volgare, la quale s'intende bene come non sia altro che la <lb/>stessa Cicloide neutoniana, nel caso che il raggio BC sia infinito, e che perci&ograve; <lb/>l'arco ABL si riduca a una linea retta. </s>

<s>Se CB infatti &egrave; infinita, si rimarr&agrave; <lb/>tale anche aggiungendovi il piccolo raggio BE della ruota, e perci&ograve;, essendo <lb/>CR, CE uguali, la sopra trovata proporzione si trasforma in quest'altra: <lb/>AP:BV&mdash;VP=2:1, d'onde AP=2 (BV&mdash;VP), in cui si sa che <lb/>BV&mdash;VP &egrave; il doppio seno verso della met&agrave; dell'arco BGP. </s>

<s>Quando il punto <lb/>P, giunto in S, abbia descritta la mezza cicloide AS, allora la met&agrave; dell'arco <lb/>BGP &egrave; divenuta un quadrante, il seno verso del quale uguagliando il raggio, <lb/>far&agrave; AS=2BS, e 2AS=4BS, ossia tutta intera la curva uguale al <lb/>diametro quadruplicato della ruota; notissima propriet&agrave; della Cicloide or&shy;<lb/>dinaria. </s></p><p type="main">

<s>Le intenzioni per&ograve; del Newton, come si diceva, non erano rivolte alla <lb/><figure id="id.020.01.2978.1.jpg" xlink:href="020/01/2978/1.jpg"/></s></p><p type="caption">

<s>Figura 380.<lb/>Geometria, ma s&igrave; alla Mec&shy;<lb/>canica, per promoverla al di <lb/>l&agrave; di quel termine, dove l'a&shy;<lb/>veva lasciata l'Huyghens. </s>

<s>Si <lb/>supponeva da lui nell'<emph type="italics"/>Oro&shy;<lb/>logio oscillatorio<emph.end type="italics"/> che fosse <lb/>il pendolo sollecitato dagli <lb/>impulsi della gravit&agrave; sempre <lb/>uniformi, ci&ograve; che dunque <lb/>prescriveva allo strumento <lb/>una sola particolare e im&shy;<lb/>mutabile stazione, la quale <lb/>dall'altra parte non era pos&shy;<lb/>sibile ritrovar qui sulla su&shy;<lb/>perficie della Terra, che in <lb/>effetto non &egrave; piana, ma curva. </s>

<s><lb/>Oscilli dunque il pendolo, disse il Newton, no nella volgare cicloide ugeniana, <lb/>ma nella nostra, e le forze di gravit&agrave; che lo sollecitano siano proporzionali alle <lb/>distanze dal centro attrattivo: allora solamente io dimostrer&ograve; che quel pendolo <lb/>&egrave; isocrono. </s>

<s>&ldquo; Si vis centripeta, tendens undique ad globi centrum, sit in locis <lb/>singulis ut distantia loci cuiusque a centro, et hac sola vi agente corpus oscil&shy;<lb/>letur in perimetro Cycloidis; dico quod oscillationum utcumque inaequalium <lb/>aequalia erunt tempora &rdquo; (pag. </s>

<s>374). </s></p><p type="main">

<s>Di qui scendevano corollarii mirabili inaspettati: Decrescendo la gravit&agrave;, <lb/>dalla superficie della Terra in gi&ugrave;, in ragion semplice, e dalla superficie della <pb xlink:href="020/01/2979.jpg" pagenum="604"/>Terra in su in ragion de'quadrati delle distanze, non son dunque propria&shy;<lb/>mente isocroni altro che i pendoli ipocicloidali, oscillanti ne'fondi delle mi&shy;<lb/>niere e delle caverne: non per&ograve; gli epicicloidali sulla superficie terrestre, e <lb/>gl'ipercicloidali sulle alture de'monti, e oscillino pure nella Cicloide neuto&shy;<lb/>niana o nella volgare. </s>

<s>&ldquo; Aptantur autem propositiones a nohis demontratae <lb/>ad veram constitutionem Terrae, quatenus rotae, eundo in eius circulis maxi&shy;<lb/>mis, descrihunt motu clavorum, perimetris suis infixorum, Cycloides extra <lb/>globum, et pendula, inferius in fodinis et cavernis Terrae suspensa, in Cy&shy;<lb/>cloidibus intra globos oscillari debent ut oscillationes omnes evadant isochro&shy;<lb/>nae. </s>

<s>Nam gravitas, ut in Libro tertio docebitur, decrescit in progressu a su&shy;<lb/>perficie Terrae, sursum quidem in duplicata distantiarum a centro eius, <lb/>deorsum vero in ratione simplici &rdquo; (pag. </s>

<s>383). </s></p><p type="main">

<s>Non vogliamo, per la sua importanza, lasciar questo argomento, senza <lb/>osservare che il Newton soggiunse nel suo Libro secondo le leggi del moto <lb/>oscillatorio, anche avuto riguardo all'impedimento del mezzo, dimostrando <lb/>che il pendolo cicloidale &egrave; solamente isocrono allora, ch'esso mezzo gli re&shy;<lb/>siste in ragion semplice della velocit&agrave;. </s>

<s>Ma se le resistenze si fanno propor&shy;<lb/>zionali ai quadrati delle velocit&agrave;, e allora, &ldquo; oscillationes breviores sunt ma&shy;<lb/>gis isochronae. </s>

<s>et brevissimae iisdem temporibus peraguntur, ac in medio <lb/>non resistente, quam proxime: earum vero, quae in maioribus arcubus fiunt, <lb/>tempora sunt paulo maiora &rdquo; (pag. </s>

<s>201). Conseguiva di qui che, resistendo <lb/>l'aria, come resulta dalle esperienze, in duplicata ragione delle celerit&agrave;, nem&shy;<lb/>meno i pendoli ugeniani, secondo l'uso che se ne pu&ograve; fare da noi, sono iso&shy;<lb/>croni. </s>

<s>&ldquo; Cyclois igitur, scriveva in tal proposito l'Eulero, quae ab Hugenio <lb/>apta est demonstrata ad isochronismum pendulorum producendum, hanc pro&shy;<lb/>prietatem in medio resistente in duplicata celeritatum ratione amittit, et hanc <lb/>ob rem in aere non inservit, nisi vel oscillationes sint valde parvae, vel inter <lb/>se proxime aequales &rdquo; (Mechan., T. II, Petropoli 1736, pag. </s>

<s>291): ci&ograve; che <lb/>verificandosi pure ne'semplici pendoli circolari, ci fa intender come e perch&egrave; <lb/>andassero cos&igrave; presto in disuso i magnificati Orologi nuovi olandesi. </s></p><p type="main">

<s>L'opera dunque dell'Huyghens aveva pi&ugrave; conferito ai progressi della <lb/>Geometria e della Meccanica, che non a quelli della Fisica, alla quale eran <lb/>principalmente rivolte le intenzioni dell'Autore. </s>

<s>Ma la Meccanica stessa del&shy;<lb/>l'Huyghens, come abbiamo veduto, aveva bisogno di essere ritirata verso la <lb/>generalit&agrave; de'principii, da'quali dipendeva essa, e la Meccanica galileiana in&shy;<lb/>sieme con lei, ci&ograve; che fece il Newton in quel modo, che da noi sommaria&shy;<lb/>mente s'&egrave; esposto. </s>

<s>Non ci siamo per&ograve; curati nel nostro discorso che di dare <lb/>un saggio della materia, cosicch&egrave; la forma &egrave; rimasta solamente <gap/>isibile a co&shy;<lb/>loro, che hanno avuto per le mani e studiato il primo libro dei Principii di <lb/>Filosofia naturale. </s></p><p type="main">

<s>Quanti possano essere oggidi cos&igrave; fatti studiosi non &egrave; difficile indovinare, <lb/>bench&egrave; la scarsit&agrave; presente non sia forse punto minore di quella, che si not&ograve; <lb/>nel suo primo venire il libro alla luce: messe ne'pi&ugrave; lo stupore, e per qual&shy;<lb/>che tempo si rimase incompreso. </s>

<s>Lo stupore nasceva dalla novit&agrave; inaspettata <pb xlink:href="020/01/2980.jpg" pagenum="605"/>delle conclusioni, e il parere impossibile che potessero queste capire nella <lb/>mente di un uomo le fece giudicare incomprensibili a chi, con quelle del&shy;<lb/>l'Autore, misurava le forze del proprio ingegno. </s>

<s>Ma consistevano altre e pi&ugrave; <lb/>forti ragioni di queste difficolt&agrave; dell'intenderle, nel modo com'erano esposte <lb/>e dimostrate le nuove dottrine. </s>

<s>In Galileo rimaneva riparato l'apparente di&shy;<lb/>sordine dalla forma del dialogo, unificatrice presso a poco, come l'impasto <lb/>nel mosaico a scaglie, ma l'Huyghens, che usciva fuori nel semplice e suc&shy;<lb/>cinto abito del Matematico, distribuiva il suo <emph type="italics"/>Orologio<emph.end type="italics"/> in cinque parti di&shy;<lb/>stinte, descrivendo nella prima lo strumento, e nella seconda dimostrando <lb/>que'teoremi <emph type="italics"/>De descensu gravium,<emph.end type="italics"/> che giovarono, col loro ordine e con la <lb/>loro brevit&agrave;, a diffondere la notizia della nuova Scienza galileiana, meglio <lb/>de'prolissi ragionamenti del Salviati. </s>

<s>Dalle leggi delle scese de'gravi nelle <lb/>linee rette e nelle oblique si passa poi a dimostrare le nuove leggi della <lb/>scesa de'gravi nella Cicloide. </s>

<s>Qui dunque &egrave; tutto bene ordinato quanto al <lb/>principio, al mezzo e al fine: &egrave; una figura tutta intera dalla pianta de'piedi <lb/>ai capelli, mentre nel Newton non vedi del gran gigante altro che il torso, <lb/>e qualcuna delle membra principali contratte, per una sublime sdegnosit&agrave; <lb/>michelangiolesca, e perch&egrave; mancava il marmo a rappresentar nella sua inte&shy;<lb/>grit&agrave; la sconfinata ampiezza del concetto. </s>

<s>Il metodo poi non &egrave; n&egrave; quello <lb/>schiettamente sintetico di Galileo, n&egrave; quell'altro dell'Huyghens, qualche cosa <lb/>partecipante dell'analisi cartesiana; ma, fra questa e la nuova analisi infini&shy;<lb/>tesimale, fa sui pi&ugrave; l'effetto di una nuvola molesta innanzi agli occhi, e in <lb/>altri pochi provoca un disgusto espresso, somigliante a quello che si prove&shy;<lb/>rebbe nel mangiare una frutta di squisitissima qualit&agrave;, ma tuttavia legnosa <lb/>e acerbetta. </s></p><p type="main">

<s>Questi secondi si riducevano a que'tre o quattro Tedeschi, che vole&shy;<lb/>vano sopra gl'Inglesi rivendicare alla loro nazione l'invenzion del calcolo <lb/>infinitesimale: e di quel disgusto che si diceva abbiamo pi&ugrave; volte veduto <lb/>l'esempio in Giovanni Bernoulli, il quale, non solamente perfezion&ograve; alcuni <lb/>teoremi neutoniani, ma in qualche parte trovatili sbagliati gli emend&ograve;, come <lb/>quando, nel secondo libro <emph type="italics"/>De principii,<emph.end type="italics"/> proponendosi l'Autore di trovare la <lb/>resistenza, che farebbe liberamente movere un corpo nella periferia di un <lb/>circolo, chiamata G la forza assolutamente uniforme, R la resistenza incon&shy;<lb/>t<emph type="italics"/>v<emph.end type="italics"/>ata dal punto M mobile in un quadrante, l'ordinata ortogogona del quale <lb/>fosse QM, preso il raggio AC per asse delle ascisse, con l'origine al con&shy;<lb/>tatto della curva; assegn&ograve; tra G ed R la proporzion medesima, che &egrave; tra <lb/>AC e QM, mentre il Bernoulli dimostr&ograve; che doveva esser invece l'altra, che <lb/>&egrave; tra 2AC e 3QM, e il Newton docilmente corresse, nelle successive edi&shy;<lb/>zioni, il suo errore. </s>

<s>La moltitudine degli studiosi per&ograve; si rimaneva tuttavia <lb/>atterrita dalle difficolt&agrave;, e perch&egrave; queste dipendevano come si disse dalla <lb/>mancanza dell'ordine, e dalla qualit&agrave; del metodo, con cui il libro era scritto; <lb/>que'che avevano amore ai progressi della Scienza pensarono di ordinare in <lb/>compendio, e di trattare con pi&ugrave; facili aggressioni i teoremi del Newton, ri&shy;<lb/>ducendoli all'intelligenza della stessa giovent&ugrave;, che frequentava le scuole. </s></p><pb xlink:href="020/01/2981.jpg" pagenum="606"/><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Il merito di aver fatto cos&igrave; riprendere il corso al cavallo, che aveva <lb/>adombrato, &egrave; principalmente dovuto a Giacomo Herman. </s>

<s>Chiamato da Ba&shy;<lb/>silea sua patria a leggere le Matematiche nel nostro studio di Padova, elesse <lb/>per soggetto delle sue lezioni l'Idrostatica. </s>

<s>Trov&ograve; che aveva questa scienza <lb/>da Archimede in poi progredito molto per opera e studio di Galileo, del Tor&shy;<lb/>ricelli, del Pascal, del Boyle, e molto pi&ugrave; ancora per quel che avevano il <lb/>Castelli e il Guglielmini insegnato intorno alle acque correnti. </s>

<s>&ldquo; Sed quia, <lb/>egli dice, eximia haec inventa in variis diariis aliisque libris dispersa et ex <lb/>diversis, saepe principiis elicila sunt, gratum me iis facturum, qui hisce rebus <lb/>delectantur, existimavi, si omnia iuxta genuinum ordinem in unum collecta, <lb/>ex paucis iisque simplicibus principiis deducta et aucta publicae luci siste&shy;<lb/>rem &rdquo; (<emph type="italics"/>Phoron. </s>

<s>cit. </s>

<s>praefatio<emph.end type="italics"/>). </s></p><p type="main">

<s>Da queste parole si rivela espressamente l'indole del magistero dell'Her&shy;<lb/>man, il quale prosegue a dire che dovendo, per risalire alla desiderata gene&shy;<lb/>ralit&agrave;, richiamar molte dottrine appartenenti alla Meccanica pura, e non <lb/>volendo rimandare i giovani suoi lettori a ricercarle altrove, pens&ograve; di premet&shy;<lb/>tere quello de'solidi al trattato del moto e dell'equilibrio de'fluidi, e cos&igrave; <lb/>gli venne ripartita in due libri l'opera, alla quale impose il titolo di Legge <lb/>delle forze o di <emph type="italics"/>Phoronomia, sive de viribus et motibus corporum solidorum <lb/>et fluidorum.<emph.end type="italics"/> Essendo sua principale intenzione l'ordine, ei fu il primo a <lb/>trattar separatamente, prima dell'equilibrio e poi del moto dei corpi, dalla <lb/>qual propriet&agrave; delle cose si venne poi a introdurre nell'uso la propriet&agrave; delle <lb/>parole. </s>

<s>Ai tempi di Galileo per Meccanica s'intendeva il trattato delle mac&shy;<lb/>chine: poi si messe fuori il nome di Statica, cos&igrave; mal definito per&ograve;, come <lb/>si vede nel Deschales, e in altri scrittori. </s>

<s>Ma dopo l'Herman la parola <emph type="italics"/>Mec&shy;<lb/>canica<emph.end type="italics"/> si us&ograve; a significare in generale la Scienza del moto, la quale si di&shy;<lb/>vise nella <emph type="italics"/>Statica<emph.end type="italics"/> e nella <emph type="italics"/>Dinamica,<emph.end type="italics"/> secondo che si trattava del moto in po&shy;<lb/>tenza e impedito, o nel suo attuale e libero esercizio. </s></p><p type="main">

<s>La prima sezione dunque del primo libro della Foronomia &egrave; un trat&shy;<lb/>tato di Statica, che in sole XIV brevissime proposizioni comprende tutti i <lb/>progressi fatti dalla Scienza, da Archimede in fino a que'tempi. </s>

<s>E perch&egrave; <lb/>uno di questi pi&ugrave; notabili progressi consisteva nell'applicar i moti composti, <lb/>incominci&ograve; l'Herman dal dimostrare che la resultante di due forze angolari <lb/>&egrave; diretta e misurata dalla diagonale del parallelogrammo. </s>

<s>L'ammirata bre&shy;<lb/>vit&agrave; poi e la lucidezza nascono dalle generalit&agrave; de'principii, da cui i parti&shy;<lb/>colari teoremi scendono dimostrati con facilit&agrave;, in semplici corollari: si pu&ograve; <lb/>dir anzi che la Statica venisse per l'Herman ridotta a un unico principio <lb/>supremo, qual'&egrave; quello dell'eguaglianza de'momenti delle potenze, applicate <lb/>di qua e di l&agrave; dal centro della Libbra. </s></p><pb xlink:href="020/01/2982.jpg" pagenum="607"/><p type="main">

<s>Di ben altra comprensione e importanza &egrave; la Dinamica, trattata dal&shy;<lb/>l'Herman nella Sezione seconda. </s>

<s>I teoremi sparsi nel terzo e quarto dialogo <lb/>delle due nuove Scienze; nella seconda, terza e quarta parte dell'Orologio <lb/>oscillatorio, e nel primo libro de'Principii di Filosofia naturale; si trovan <lb/>tutti ordinati qui in queste XLIII proposizioni, che son quasi altrettante fonti <lb/>scaturite dalle alture del monte a irrigar largamento i campi della Scienza <lb/>del moto. </s>

<s>E come chi ha raggiunta la fonte riceve comodamente nella ca&shy;<lb/>vit&agrave; della mano tutta l'acqna, che ander&agrave; poi a diffrangersi fra'sassi del ru&shy;<lb/>scello; cos&igrave; avviene a chi legge il libro dell'Herman. </s></p><p type="main">

<s>Mosse la restaurata Scienza dal fondamento di due supposizioni, l'una <lb/>delle quali diceva che si raggiunge sempre uguale velocit&agrave; ne'cadenti dalla <lb/>medesima altezza, e l'altra che le velocit&agrave; son proporzionali ai tempi. </s>

<s>Come <lb/>Galileo, il Torricelli e l'Huyghens fossero stati solleciti di confermare quel <lb/>primo fondamento della Scienza con qualche ragione dimostrativa, ben se lo <lb/>sanno i nostri Lettori, ma chi pens&ograve; mai o sper&ograve; di riuscire a dimostrare <lb/>quell'altro principio fondamentale della Dinamica galileiana<emph type="italics"/>?<emph.end type="italics"/> Che sapeva o <lb/>poteva egli rispondere Galileo stesso al Baliani, quando opponeva parergli <lb/>pi&ugrave; ragionevole l'ammetter che le velocit&agrave; crescessero come gli spazi? </s>

<s>niente <lb/>altro se non che l'esperienze confermavano le sue supposizioni. </s>

<s>E cos&igrave; come <lb/>sent&igrave; l'Herman che la Scienza pativa difetto ne'suoi pi&ugrave; vitali principii; cos&igrave; <lb/>pens&ograve; d'infonderveli derivandoli dalle altissime fonti. </s></p><p type="main">

<s>Sia la linea retta AD (fig. </s>

<s>381) con qualunque curva MON, e fatto cen&shy;<lb/><figure id="id.020.01.2982.1.jpg" xlink:href="020/01/2982/1.jpg"/></s></p><p type="caption">

<s>Figura 381.<lb/>tro in D, si descrivano <lb/>gli archi di cerchio NE, <lb/>OP, MA. S'immagini <lb/>che il medesimo mobile <lb/>o due mobili uguali, <lb/>partendosi dalla quiete <lb/>in A e in M, discendano <lb/>per le due dette linee <lb/>attratti al centro D con <lb/>forze, che saranno u&shy;<lb/>guali in N, E; O, P; <lb/>M, A, per esser punti <lb/>situati respettivamente <lb/>a distanze uguali dal <lb/>centro dell'attrazione. </s>

<s><lb/>Sia la forza centripeta, <lb/>che sollecita il punto N, <lb/>rappresentata da NB, la quale si decomponga nella tangenziale NC, e nel&shy;<lb/>l'altra BC, perpendicolare a lei, e perci&ograve; non considerata in questo calcolo <lb/>come inulile a produrre il moto discensivo. </s>

<s>Da E alzata sopra la AD una <lb/>linea ad angolo retto, si prenda in essa ES=NB, e in simile modo, cer&shy;<lb/>cate le forze tangenziali in O, e in tutte le altre parti della curva, le linee <pb xlink:href="020/01/2983.jpg" pagenum="608"/>che le rappresentano si applichino in P, e negli altri punti corrispondenti: <lb/>&egrave; manifesto che la curva AS sar&agrave; la scala delle velocit&agrave; tangenziali. </s></p><p type="main">

<s>Cos&igrave; definite le cose, l'Herman si propone di dimostrare questo teorema: <lb/>&ldquo; Si mobilia M, et A ex punctis M, et A in curva MON et recta AD a quiete <lb/>cadere incipiant, celeritates ipsorum in punctis N, E; O, P etc. </s>

<s>acquisitae <lb/>erunt aequales &rdquo; (pag. </s>

<s>58). La proposizione essendo universalissima, deve <lb/>esser vera a qualunque distanza trovisi il punto D. </s>

<s>Che se questa distanza <lb/>&egrave; infinita, gli archi AM, PO, EN torneranno nelle rettitudini AM&prime;, PO&prime; EN&prime;, <lb/>e perci&ograve; le velocit&agrave; tangenziali in M&prime;, O&prime;, N&prime; saranno quelle medesime delle <lb/>discensive in A, P, E. &ldquo; Adeoque celeritates in diversis planorum et curva&shy;<lb/>rum continuam curvaturam habentium inclinationibus descensu acquisitae, <lb/>aequales sunt in omni gravitatis variabilis et uniformis hypothesi, si plano&shy;<lb/>rum vel curvarum elevationes aequales fuerint &rdquo; (ibid., pag. </s>

<s>62). </s></p><p type="main">

<s>Ecco in qual modo il famoso supposto galileiano &egrave; dimostrato vero, e <lb/>no solamente nel caso della gravit&agrave; uniforme, ma in qualunque ipotesi della <lb/>gravit&agrave; variabile; cosicch&egrave; i corpi raggiungono velocit&agrave; uguali, dopo cadute <lb/>uguali, cos&igrave; sulla superficie e nell'interno della nostra Terra, come &egrave; nei <lb/>mondi, che si governassero con altre leggi. </s>

<s>E qui vien voglia di domandare <lb/>se qualunque legge di gravit&agrave; sia possibile. </s>

<s>Chi non lo crederebbe, pensando <lb/>alla Onnipotenza del Creatore? </s>

<s>Eppure la Matematica risponde di no, per la <lb/>contrariet&agrave; che talvolta non lo consente, come non consentirebbe a nessuna <lb/>potenza di far che un circolo sia quadrato, e di qui &egrave; che essa Matematica <lb/>decise esser solamente possibile la proposta in que'casi, ne'quali il calcolo <lb/>d&agrave; un resultato reale; impossibile poi in tutti gli altri, per i quali s'hanno <lb/>resultati assurdi e immaginari. </s>

<s>Per questa via sottilmente apertasi v&agrave; l'Her&shy;<lb/>man a decidere tra la ipotesi di Galileo e quella del Baliani, e cos&igrave; nello <lb/>stesso tempo gli vien conclusa la dimostrazione, che le velocit&agrave; son propor&shy;<lb/>zionali ai tempi e non agli spazi. </s></p><p type="main">

<s>Stando infatti la velocit&agrave; <emph type="italics"/>u<emph.end type="italics"/> in ragion diretta dello spazio <emph type="italics"/>s,<emph.end type="italics"/> e reciproca <lb/>del tempo <emph type="italics"/>t,<emph.end type="italics"/> e la forza sollecitante <emph type="italics"/>g<emph.end type="italics"/> della gravit&agrave; in ragion diretta della <lb/>velocit&agrave;, e pur essa reciproca del tempo; dalle equazioni <emph type="italics"/>u=ds:dt, g= <lb/>du:dt<emph.end type="italics"/> abbiamo <emph type="italics"/>u:g=ds:du,<emph.end type="italics"/> ossia <emph type="italics"/>gds=udu.<emph.end type="italics"/> Poniamo, come vuole <lb/>il Baliani, <emph type="italics"/>u=s<emph.end type="italics"/> o <emph type="italics"/>u2=s2,<emph.end type="italics"/> d'onde viene, differenziando, <emph type="italics"/>udu=sds= <lb/>gds,<emph.end type="italics"/> e perci&ograve; <emph type="italics"/>g=s.<emph.end type="italics"/> Dunque, essendo <emph type="italics"/>s=o,<emph.end type="italics"/> sar&agrave; anche <emph type="italics"/>g=o,<emph.end type="italics"/> e ci&ograve; vuol <lb/>dire che, venendo meno nell'atto della discesa l'impulso della gravit&agrave;, il <lb/>corpo, come non potrebbe cominciare, cos&igrave; sarebbe impossibile che prose&shy;<lb/>guisse nel moto. </s>

<s>Di pi&ugrave;, nella formula <emph type="italics"/>dt=du:g<emph.end type="italics"/> posto <emph type="italics"/>g=s,<emph.end type="italics"/> avremmo <lb/>secondo l'ipotesi del Baliani <emph type="italics"/>dt=ds:s,<emph.end type="italics"/> la quale equazione integrata d&agrave; <lb/><emph type="italics"/>t=log.s,<emph.end type="italics"/> cosicch&egrave;, essendo <emph type="italics"/>s=o,<emph.end type="italics"/> e il logaritmo di zero infinito; ne con&shy;<lb/>seguirebbe che il mobile impiegasse un tempo infinito nella quiete, ossia che <lb/>assolutamente non si movesse, <emph type="italics"/>adeoque Baliani hypothesis impossibilis et <lb/>imaginaria est.<emph.end type="italics"/> (Phoron., pag. </s>

<s>65). </s></p><p type="main">

<s>Questa ipotesi fu poi sostenuta da altri, fra i quali il Cazr, il Descha&shy;<lb/>les, il Lana, tutti gesuiti: e perch&egrave; dalle cose narrate nel capitolo terzo di <pb xlink:href="020/01/2984.jpg" pagenum="609"/>questo Tomo apparisce quanto fossero insufficienti l'esperienze a decidere la <lb/>questione; si comprende come giungesse opportuno, a confermare i fonda&shy;<lb/>menti della Scienza galileiana, il calcolo dell'Herman, ripetuto poi dall'Eulero <lb/>nel primo tomo della sua Meccanica analitica, al secondo Scolio dopo la pro&shy;<lb/>posizione XV, concludendovi col dire che la legge supposta da Galileo era <lb/>necessaria, e che perci&ograve; ne escludeva ogni altra diversa. </s>

<s>&ldquo; Ex data vero pro&shy;<lb/>blematis solutione unde consequitur celeritatis incrementa fore temporibus <lb/>quibus producuntur proportionalia, intelligitur legem inventam necessariam <lb/>esse, neque ullam aliam vi principii contradictionis existere posse &rdquo; (pag. </s>

<s>54). </s></p><p type="main">

<s>L'Herman aveva particolarmente notate alcune altre di queste ipotesi, <lb/>dimostrandole in contradizion con la vera, perch&egrave;, ridotte nella formula, da&shy;<lb/>vano resultati anch'esse impossibili e immaginari, e dopo ci&ograve; cos&igrave; dice: <lb/>&ldquo; Hactenus generalia motuum acceleratorum habuimus: dispiciendum restat <lb/>quid ex una alteraque gravitatis hypotesi sequi debeat &rdquo; (pag. </s>

<s>65). Le ipo&shy;<lb/>tesi della gravit&agrave; allora ammesse si riducevano a quella del Newton per l'in&shy;<lb/>terno della Terra, dove le forze sollecitanti son proporzionali alle distanze, <lb/>e a quella di Galileo comunemente professata ne'cadenti sulla superficie della <lb/>Terra, sollecitati da impulsi di gravit&agrave; sempre uniformi. </s>

<s>Essendo manifesta&shy;<lb/>mente in quella prima ipotesi la scala delle forze in un triangolo, si propose <lb/>l'Herman di trovar la scala delle relative velocit&agrave;, ci&ograve; che gli riusc&igrave; di fa&shy;<lb/>cile invenzione, dietro il teorema XIX illustrato dalla figura 381, e in cui <lb/>si dimostrava che, essendo IHG la scala delle gravit&agrave;, i quadrati delle linee <lb/>PO&prime;, EN&prime;, e delle altre simili, che espongono le velocit&agrave;, equivalgono al dop&shy;<lb/>pio delle aree IAPH, IAEG. </s></p><p type="main">

<s>Ci&ograve; posto, e dato che sia AD (fig. </s>

<s>382) la linea della scesa d'un corpo <lb/>attratto al punto D, con forze proporzionali alle distanze, e perci&ograve; anche alle <lb/>ordinate del triangolo ADQ, dalla DQ con qualunque angolo al centro de&shy;<lb/>scritto; per concluder che la scala delle velocit&agrave; &egrave; il quadrante ASR di una <lb/>ellisse, il semiasse maggior della quale sia AD, e DR=&radic;AD.AQ semiasse <lb/>minore; non occorr<gap/> dimostrar altro se non che, segnata ordinatamente qua&shy;<lb/>lunque linea ES, il quadrato di questa uguaglia il doppio dell'area del trape&shy;<lb/>zio AC, a che facilmente conduce la costruzione del quadrante circolare AFL, <lb/>e del triangolo isoscele AGD, dal qual triangolo e dall'altro inscrittogli AQD, <lb/>prolungata la ES, in F da una parte, e in B dall'altra; avremo per le pa&shy;<lb/>rallele AG, BE, AG:BE=AQ:CE. </s>

<s>Componendo e trasponendo, sar&agrave; <lb/>AG+BE:AQ+CE=AG:AQ=2T:2<emph type="italics"/>t,<emph.end type="italics"/> intendendosi per T, <emph type="italics"/>t<emph.end type="italics"/> i <lb/>trapezii, de'quali AG+BE, AQ+CE son la somma delle basi parallele. </s>

<s>Ora <lb/>essendo, per le propriet&agrave; del circolo e dell'ellisse, EF2:ES2=DL2:DR2= <lb/>AG2:AG.AQ=AG:AQ=2T:2<emph type="italics"/>t,<emph.end type="italics"/> ed EF2=DF2&mdash;DE2=DA2&mdash;DE2= <lb/>AH&mdash;EI=AGHIBE=2T; dunque ES2=2<emph type="italics"/>t,<emph.end type="italics"/> com'era l'intenzione di di&shy;<lb/>mostrare. </s>

<s>In qual modo poi si derivi di qui, quasi per corollario, la XLVII pro&shy;<lb/>posizione del Newton (T. I, pag. </s>

<s>362) &egrave; cosa per s&egrave; tanto manifesta, che <lb/>hasti averla avvertita. </s></p><p type="main">

<s>Nella comune ipotesi della gravit&agrave; uniforme, D andando infinitamente <pb xlink:href="020/01/2985.jpg" pagenum="610"/>distante da A, le due linee AD, QD diventano parallele, e l'area AC trasfor&shy;<lb/>mandosi in un rettangolo riduce l'equazione alla forma 2Aq.AE=ES2, <lb/>che &egrave; l'equazione di una parabola, col parametro <expan abbr="2Aq.">2Aque</expan> Donde &egrave; manifesto <lb/>che la scala delle velocit&agrave;, in questa ipotesi, &egrave; nella parabola; e perch&egrave; le <lb/>ascisse rappresentan gli spazii, e le ordinate le velocit&agrave; o i tempi; questi <lb/>stanno dunque come le radici di essi spazi. </s>

<s>Cos&igrave; l'Herman, derivandola da <lb/>principii universali, confermava la verit&agrave; della X proposizione del primo libro <lb/><emph type="italics"/>De motu<emph.end type="italics"/> del Torricelli, il quale fu il primo a designar la parabola per la <lb/>scala delle velocit&agrave; de'corpi, secondo la legge di Galileo naturalmente cadenti. </s></p><p type="main">

<s>Ipotesi si possono, e anzi, a rigore di Matematica, si debbono dire le <lb/>leggi della gravit&agrave; sulla superficie e nell'interno della Terra, ma per gli <lb/>spazi planetarii il Keplero e il Newton avevano ridotte le leggi, secondo le <lb/>quali gravitano i pianeti nel Sole, a certissima tesi: di certezza fisica per le <lb/>osservazioni d&egrave;l primo de'commemorati astronomi, e di certezza matematica <lb/><figure id="id.020.01.2985.1.jpg" xlink:href="020/01/2985/1.jpg"/></s></p><p type="caption">

<s>Figura 382.<lb/>per i teoremi del se&shy;<lb/>condo, che applica al <lb/>moto iniziale dei Pia&shy;<lb/>neti le propriet&agrave; dina&shy;<lb/>miche de'proietti. </s>

<s>La <lb/>dinamica nuova neu&shy;<lb/>toniana era senza dub&shy;<lb/>bio pi&ugrave; generale di <lb/>quella insegnata da <lb/>Galileo nel suo Dialo&shy;<lb/>go quarto, dove si <lb/>suppone che il cen&shy;<lb/>tro attrattivo sia a <lb/>una distanza infinita <lb/>dal mobile, ma pure si limitava a rendere la ragione di un fatto particolare, <lb/>quale si osserva nella Natura. </s>

<s>L'Herman volle dare a questo problema della <lb/>Scienza la sua massima generalit&agrave;, proponendosi di trovare in qual curva si <lb/>volgerebbe un proietto, attratto al centro con qualunque legge di gravit&agrave; va&shy;<lb/>riabile, senza richiedere altra condizione, se non che la detta curva sia alge&shy;<lb/>brica e non trascendente. </s>

<s>Cos&igrave; i teoremi scritti nella terza sezione de'Principii <lb/>di Filosofia naturale si derivano come semplici corollarii da questa univer&shy;<lb/>salissima proposizione dell'Herman, e accennammo di sopra come in uno di <lb/>questi stessi corollarii, in cui si concludeva che, variando la gravit&agrave; recipro&shy;<lb/>camente ai quadrati delle distanze, il proietto si volgerebbe in una sezione <lb/>conica; le censurate dottrine del Newton trovarono la loro pi&ugrave; autorevole <lb/>conferma. </s></p><p type="main">

<s>Non sempre si porge all'Herman l'occasione di sublimare di pi&ugrave; queste <lb/>assai per s&egrave; stesse sublimi speculazioni neutoniane, ma sempre per&ograve; si stu&shy;<lb/>dia e giunge a renderle di pi&ugrave; facile trattato, e pi&ugrave; chiare. </s>

<s>Potremo, fra'tanti <lb/>esempi di ci&ograve;, citar le leggi delle sollecitazioni centrali nelle orbite mobili, <pb xlink:href="020/01/2986.jpg" pagenum="611"/>e del <emph type="italics"/>Moto degli apsidi.<emph.end type="italics"/> Sia ABE (fig. </s>

<s>383) qualunque orbita immobile, uguale <lb/>e simile all'orbita A&prime;B&prime;E&prime;, descritta da un proietto, che si volga in essa e <lb/>con essa, la quale si suppone che giri intorno al centro C dell'attrazione con <lb/><figure id="id.020.01.2986.1.jpg" xlink:href="020/01/2986/1.jpg"/></s></p><p type="caption">

<s>Figura 383.<lb/>tal legge, che l'angolo ACA&prime;, rotatorio dell'asse, all'an&shy;<lb/>golo A&prime;CB&prime; sotteso dall'arco A&prime;B&prime; passato dal proietto <lb/>nel medesimo tempo, che fu descritto l'angolo della <lb/>rotazione ACA&prime;; stia in qualunque ragion data, per <lb/>esempio ACA&prime;:A&prime;CB&prime;=H:F, o componendo B&prime;CA: <lb/>A&prime;CB&prime;=H+F:F=G:F, facendo per semplicit&agrave; <lb/>H+F=G. </s>

<s>Il moto dell'asse A&prime;E&prime; &egrave; un esempio di <lb/>quello che si chiama <emph type="italics"/>Moto degli apsidi,<emph.end type="italics"/> e che vien <lb/>determinato dalla ragione di F a G, per trovar la quale <lb/>il Newton ricorre al suo teorema delle serie conver&shy;<lb/>genti infinite: &ldquo; Sed quid, entra qui a dire l'Herman, <lb/>si modum facillimum aperuero, quo idem, absque ulla <lb/>serierum infinitarum auxilio, obtineri queat, imo longe <lb/>plura, quandoquidem praebet canonem generalem, quaecumque solicitationis <lb/>centripetae sit lex, rationem F ad G manifestantem? </s>

<s>&rdquo; (pag. </s>

<s>99). </s></p><p type="main">

<s>Bastano questi, senz'aver bisogno di aggiungere altri esempi, a persua&shy;<lb/>derci che la facilit&agrave;, con cui l'Herman dimostrava i teoremi di Galileo e del <lb/>Newton, oltre tanti altri, che non si trovano compresi nelle loro proposizioni, <lb/>dipendeva dall'essere risalito agli altissimi principii. </s>

<s>Dicemmo che di mezzo <lb/>a que'due grandi promotori della Scienza stava l'Huyghens, l'opera del <lb/>quale, bench&egrave; forse ristretta, parve nulladimeno insigne, per aver quietate le <lb/>affannose ambagi dei Matematici, col definir la vera natura della curva tau&shy;<lb/>tocrona. </s>

<s>Ripensando l'Herman anche sopra questa nuova ammirata inven&shy;<lb/>zione, si domandava se il tautocronismo fosse propriet&agrave; di sola la cicloide, e <lb/>a chi gli avesse risposto di s&igrave;, almeno nell'ipotesi della gravit&agrave; uniforme, <lb/>sentiva di poter citare i progressi fatti dal Newton in questa stessa specu&shy;<lb/>lazione, supposto che la gravit&agrave; sia variabile ora come le distanze, ora come <lb/>i quadrati delle distanze dal centro dell'attrazione. </s>

<s>Ma dato che si facessero <lb/>queste variabilit&agrave; in qualunque modo, qual sarebbe la curva, nella quale scen&shy;<lb/>dendo un grave per archi o maggiori o minori gli passerebbe nonostante <lb/>tutti nel medesimo tempo? </s>

<s>Ecco ci&ograve; che cercava di far l'Herman, con sol&shy;<lb/>lecitudine che si sarebbe detta un'incredibile audacia, se il fine cos&igrave; felice&shy;<lb/>mente conseguito non avesse con lo stupore soppresso ogni alito della voce. </s></p><p type="main">

<s>Circa l'asse CA (fig. </s>

<s>384) descrivasi la IKLN, che sia la scala della <lb/>gravit&agrave; variabile sollecitatrice al centro O. </s>

<s>Da A, dove si pone il loro prin&shy;<lb/>cipio, vadano le ordinate XZ, HR, GQ e le altre simili via via crescendo con <lb/>tal legge, che i loro quadrati uguaglino il doppio delle aree XN, HN, GN...: <lb/>gli estremi punti Z, R, <expan abbr="q.">que</expan>.. delle dette ordinate si troveranno in una curva <lb/>continua AZRQD, che per le cose dette &egrave; la scala delle velocit&agrave;. </s>

<s>Ora, a par&shy;<lb/>tire dal punto A, pure intorno all'asse AC, descrivasi una terza curva BEA, <lb/>di tal figura che, menati col centro in O e con gl'intervalli CO, GO, HO... <pb xlink:href="020/01/2987.jpg" pagenum="612"/>gli archi di cerchio BC, FG, EH..., i curvilinei BFEA, FEA, EYA ... alle <lb/>ordinate CD, GQ, HR stiano come un numero qualunque N all'unit&agrave;: la&shy;<lb/>sciato un grave cadere, nella concavit&agrave; disegnata, da R, da F, da Y o da <lb/>qualsivoglia altro punto, giunger&agrave; in A sempre nel medesimo tempo, e perci&ograve; <lb/>la BEA sar&agrave; la curva tautocrona, con qualunque legge la gravit&agrave; del corpo <lb/>ne vada sollecitando la discesa. </s></p><p type="main">

<s>La dimostrazione non costa all'Herman che una pagina di scritto, la <lb/>quale anche si potrebbe ridurre alla met&agrave;, introducendovi i simboli algebrici, <lb/>e gli usati segni convenzionali: eppure &egrave; in quelle pagine condensata tutta <lb/>la scienza dell'Huyghens, con le sue pi&ugrave; notabili conseguenze. </s>

<s>Infatti se la <lb/>gravit&agrave; &egrave; uniforme la linea curva ILN torna a una linea retta parallela al&shy;<lb/>l'asse, e la scala ARD delle velocit&agrave; si riduce a una parabola conica: gli <lb/>archi BC, FG, YX..., essendo O a una distanza infinita, si rettificano nelle <lb/>corde, le quali ordinatamente riferiscono all'asse AC la curva tautocrona AEB, <lb/>che dunque &egrave; una Cicloide ordinaria. </s>

<s>Di qui anche consegue che il tempo <lb/>impiegato dal mobile a passare la met&agrave; della curva, &egrave; al tempo della scesa <lb/>perpendicolare per l'asse, come la semicirconferenza al diametro. </s></p><p type="main">

<s>L'Huyhens non ebbe altra intenzione, in cercare nel tautocronismo della <lb/><figure id="id.020.01.2987.1.jpg" xlink:href="020/01/2987/1.jpg"/></s></p><p type="caption">

<s>Figura 384.<lb/>Cicloide il pendolo isocrono, che di ap&shy;<lb/>plicarlo alla misura del tempo, prin&shy;<lb/>cipale e unico ufficio commessogli da <lb/>Galileo. </s>

<s>Poi il Newton dette ingerenza <lb/>allo strumento di misurare le varia&shy;<lb/>bili distanze della superficie dal centro <lb/>della Terra, e di scandagliare, per le <lb/>segrete viscere di lei, la quantit&agrave; e qua&shy;<lb/>lit&agrave; della materia: n&egrave; ci&ograve; bastando, il <lb/>Bernoulli addit&ograve; in lui le virt&ugrave; stesse <lb/>dell'areometro, dalla gravit&agrave; assoluta <lb/>passando a rivelar la specifica dei corpi. </s>

<s><lb/>Tutte queste propriet&agrave;, sparsamente di&shy;<lb/>mostrate dai vari autori, son comprese <lb/>nel teorema generale dell'Herman, il <lb/>quale, ripensando da una parte alla <lb/>dignit&agrave; dell'argomento, e dall'altra <lb/>all'insufficienza de'principii, con cui <lb/>si era trattato; ebbe ragione di scrive&shy;<lb/>re, compiacentesi, queste parole: &ldquo; Ex <lb/>corollariis proxime antecedentibus satis elucere existimo quantae utilitatis sit <lb/>Theorema nostrum generale isochronismi corporum in curvis, assignata lege <lb/>descriptis, descendentium, cum ex ea omnia, quae ad pendulorum motus <lb/>spectant, tanta facilitate deducantur &rdquo; (<emph type="italics"/>Phoron.<emph.end type="italics"/> cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Sia infatti, nella medesima figura 384 illustrativa di quel teorema ge&shy;<lb/>nerale, T il centro del circolo osculatore alla curva nel tratto AY: se dal <pb xlink:href="020/01/2988.jpg" pagenum="613"/>raggio TA, come da filo attaccato in T o da verga, vada pendulo il globo A, <lb/>far&agrave; questo le sue vibrazioni isocrone, ond'&egrave; che tutte le minime vibrazioni <lb/>circolari si fanno nel medesimo tempo, non solamente sulla superficie terre&shy;<lb/>stre, ma dovunque le sollecitazioni della gravit&agrave; sian variabili secondo qua&shy;<lb/>lunque ragione. </s>

<s>Chiamato T il tempo di due delle dette minime vibrazioni, <lb/>M la massa del corpo A, P il suo peso, l'Herman ha per facile corollario <lb/>dal suo teorema: T=2<emph type="italics"/>r<emph.end type="italics"/><foreign lang="greek">p</foreign>&radic;M.TA.AO/P.TO, equazione, che vale per tutti <lb/>i pendoli, da qualunque variabile forza acceleratrice siano sollecitati, e dalla <lb/>quale resulta che i tempi delle oscillazioni di due pendoli varii stanno in <lb/>ragion diretta delle radici delle masse, delle lunghezze e delle minori distanze <lb/>dal centro dell'attrazione; e in ragion contraria delle radici dei pesi e delle <lb/>distanze de'punti di sospensione dal detto centro. </s>

<s>&ldquo; Haec determinatio, dice <lb/>l'Herman, probe consentit cum assertionibus paulo specialioribus Neutoni, <lb/>propos. </s>

<s>LH libri primi Phil. </s>

<s>Natur. </s>

<s>&rdquo; (ibid., pag. </s>

<s>85). Il Newton infatti non <lb/>giunge quivi a questa determinazione dalla curva isocrona universale, ma <lb/>dalle particolari propriet&agrave; dimostrate nel suo pendolo ipocicloidale, in quello <lb/>cio&egrave; che oscilla in un arco della cicloide, generata dal ruzzolarsi la ruota <lb/>nella concavit&agrave; del cerchio massimo di un globo. </s>

<s>Ed essendo V di esso globo <lb/>la forza assoluta, trova che i tempi delle oscillazioni <emph type="italics"/>&ldquo; sunt in ratione, quae <lb/>componitur ex subduplicata ratione longitudinis fili directe, et subdupli&shy;<lb/>cata ratione distantiae inter punctum suspensionis, et centrum globi in&shy;<lb/>verse, et subduplicata ratione vis absolutae globi etiam inversae &rdquo;<emph.end type="italics"/> (pag. </s>

<s>381): <lb/>ossia, come &radic;AT/OT.V Ora, avendosi <emph type="italics"/>g<emph.end type="italics"/>=AO.V, perch&egrave; la forza accelera&shy;<lb/>trice <emph type="italics"/>g<emph.end type="italics"/> cresce col crescere della distanza dal centro attrattivo, e della forza <lb/>assoluta, ed essendo <emph type="italics"/>g<emph.end type="italics"/>=P/M, verr&agrave; 1/V=AO.M/P, che sostituito riduce l'asser&shy;<lb/>zione del Newton manifestamente alla determinazione dell'Herman. </s></p><p type="main">

<s>Bellissime cose fin qui, senza dubbio, ma inutili a noi, che non abitiamo <lb/>n&egrave; sotto terra, n&egrave; nel mondo delle astrazioni. </s>

<s>Pensiamo perci&ograve; ai pendoli, <lb/>disse l'Herman, che si possono trattar con le nostre proprie mani, e per i <lb/>quali (le forze acceleratrici supposte uniformi, e AO infinita rendendosi uguale <lb/>a TO) la formula del tempo, chiamata L la lunghezza del filo, si riduce a <lb/>T=2<emph type="italics"/>r<emph.end type="italics"/><foreign lang="greek">p</foreign>&radic;M.L/P, d'onde T:T&prime;=&radic;M.L/P:&radic;M&prime;.L&prime;/P&prime;. </s>

<s>Che se le lun&shy;<lb/>ghezze dei fili sono uguali, T:T&prime;=&radic;M/P:&radic;M&prime;/P&prime;; se i pesi a quelle stesse <lb/>lunghezze son proporzionali, T:T&prime;=&radic;M:&radic;M&prime;; e se di pi&ugrave; anche le masse <lb/>ad essi pesi sono proporzionali, se cio&egrave; &radic;M.L/P=&radic;M&prime;.L&prime;/P&prime;; e i tempi <lb/>pure anderanno uguali. </s>

<s>Avremo all'ultimo, in pendoli ugualmente lunghi, <lb/>M:M&prime;=PT2:P&prime;T&prime;2. </s>

<s>&ldquo; Atque hoc ipsum est, dice l'Herman, propos. </s>

<s>XXVII <pb xlink:href="020/01/2989.jpg" pagenum="614"/>libri II Princ. </s>

<s>Phil. </s>

<s>Natur. </s>

<s>qua usus est cl. </s>

<s>Vir ad explorandum utrum pon&shy;<lb/>dera corporum ipsorum massis proportionalia sint nec ne &rdquo; (<emph type="italics"/>Phoron.,<emph.end type="italics"/> pag. </s>

<s>85): <lb/>la qual proposizione corrisponde, nelle posteriori edizioni, alla XXIV cos&igrave; for&shy;<lb/>mulata: <emph type="italics"/>&ldquo; Quantitates materiae in corporibus funependulis, quorum cen&shy;<lb/>tra oscillationum a centro suspensionis aequaliter distant, sunt in ratione <lb/>composita ex ratione ponderum, et ex ratione duplicata temporum oscil&shy;<lb/>lationum in vacuo &rdquo;<emph.end type="italics"/> (pag. </s>

<s>189). E perch&egrave;, essendo i pesi uguali, le masse <lb/>stanno direttamente come i quadrati dei tempi, ed essendo le masse uguali <lb/>i pesi stanno reciprocamente come i detti quadrati; &ldquo; hinc liquet, conclude <lb/>il Newton, ratio tum comparandi corpora inter se, quoad quantitatem mate&shy;<lb/>riae in singulis, tum comparandi pondera eiusdem corporis in diversis locis, <lb/>ad cognoscendam variationem gravitatis. </s>

<s>Factis autem experimentis quam <lb/>accuratissimis, inveni semper quantitatem materiae in corporibus singulis <lb/>eorum ponderi proportionalem esse &rdquo; (pag. </s>

<s>194). </s></p><p type="main">

<s>Perch&egrave; poi &egrave; un fatto che due diversi pendoli, quanto son pi&ugrave; lesti, <lb/>tanto fanno, nel medesimo tempo, un pi&ugrave; gran numero N, N&prime; di vibrazioni, <lb/>ossia, avendosi per esperienza N:N&prime;=T&prime;:T; sostituiti i valori di T&prime;, T, <lb/>verr&agrave; N:N&prime;=&radic;M&prime;.T&prime;/P&prime;:&radic;M.L/P, e anche, perch&egrave; M/P=1/<emph type="italics"/>g,<emph.end type="italics"/> N:N&prime;= <lb/>&radic;L&prime;/<emph type="italics"/>g&prime;<emph.end type="italics"/>:&radic;L/<emph type="italics"/>g,<emph.end type="italics"/> d'onde, in pendoli da gravit&agrave; uguali sollecitati; N:N&prime;= <lb/>&radic;L&prime;:&radic;L, e in pendoli ugualmente lunghi, N:N&prime;=&radic;<emph type="italics"/>g<emph.end type="italics"/>:&radic;<emph type="italics"/>g&prime;.<emph.end type="italics"/> &ldquo; Atque <lb/>hoc posterius (che cio&egrave; i numeri delle vibrazioni di due pendoli, con lun&shy;<lb/>ghezze uguali, stanno come le radici delle gravit&agrave; sollecitanti) ad amussim <lb/>convenit cum regula, quam Bernoullius in elegantissimo suo schediasmate, <lb/>Act. </s>

<s>Lips. </s>

<s>1713 m. </s>

<s>februario inserto, tradit paragrapho 16, ex qua deinceps <lb/>gravitates specificas eruere docet ex pendulorum experimentis, modo plane <lb/>novo nec antea cognito &rdquo; (<emph type="italics"/>Phoron.<emph.end type="italics"/> cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Il capitolo ultimo della Meccanica dell'Herman s'intitola <emph type="italics"/>De regulis <lb/>motus in collisione corporum,<emph.end type="italics"/> dove per verit&agrave;, piuttosto che promovere la <lb/>scienza de'suoi precursori, ne rende la trattazione pi&ugrave; facil&egrave; e pi&ugrave; ordinata. </s>

<s><lb/>Notabile &egrave; nonostante q'ipotesi della conservazione delle forze assolute, che <lb/>egli crede liberamente di poter professare, in mezzo alla controversie, e cita <lb/>il Leibniz e l'Huyghens, per dare autorit&agrave; alla sua opinione, bench&egrave; sarebbe <lb/>stato forse pi&ugrave; giusto citar prima di loro il Borelli, il quale aveva concluso <lb/>il cap. </s>

<s>XVII del suo libro <emph type="italics"/>De vi percussionis<emph.end type="italics"/> col dire: <emph type="italics"/>motum neque gigni <lb/>de novo, neque destrui in natura<emph.end type="italics"/> (pag. </s>

<s>136). </s></p><p type="main">

<s>Non ritorneremo sopra la formula generale data dall'Herman, per cal&shy;<lb/>colare i centri delle oscillazioni, n&egrave; sopra quel ch'egli aggiunse, per appli&shy;<lb/>carla direttamente ai pendoli, e alla teoria delle forze centrifughe, gi&agrave; sufficien&shy;<lb/>temente illustrata dall'Hopital e dal Newton, essendo oramai tempo di con&shy;<lb/>cludere il nostro discorso, col rassomigliare la Foronomia, nella vita della <lb/>Scienza, al ventricolo del cuore, in cui, scesovi dalle vene, s'&egrave; raccolto nella <lb/>diastole il sangue. </s>

<s>Nel successivo moto di sistole quel sangue gi&agrave; vivificato <pb xlink:href="020/01/2990.jpg" pagenum="615"/>si diffonder&agrave; a irrigare le membra rigogliose per la grande arteria della Mec&shy;<lb/>canica analitica, alla quale ci rimarrebbe a rivolgere uno sguardo. </s>

<s>Ma per&shy;<lb/>ch&egrave; si vuole che questi spiriti vitali vi siano suscitati, quasi come da fer&shy;<lb/>mento, dalle Regole dei moti composti e del calcolo infinitesimale; diremo <lb/>prima qualche cosa di loro, nell'ammetterle che fecero i Matematici ai ser&shy;<lb/>vigi della Meccanica nuova. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>O consapevoli o no i novelli Matematici, nel dimostrare le leggi dei moti <lb/>composti, non si dilungarono dalla semplicit&agrave; dei metodi antichi. </s>

<s>Supposto che <lb/>un corpo venga sollecitato insieme da due forze angolari, proporzionate ai <lb/>lati di un parallelogrammo, il Varignon, il Newton e l'Herman procedevano, <lb/>in concluder che la resultante &egrave; rappresentata in direzione e in grandezza <lb/>dalla diagonale, in quel modo ch'erano gi&agrave; proceduti Aristotile, il Cardano, <lb/>il Roberval, il Torricelli e il Wallis. </s>

<s>Ma il Newton sopra gli altri riduceva <lb/>la dimostrazion del teorema da lui formulato: <emph type="italics"/>Corpus viribus coniunctis <lb/>diagonalem parallelogrammi eodem tempore describere quo latera sepa&shy;<lb/>ratis<emph.end type="italics"/> (<emph type="italics"/>Principia<emph.end type="italics"/> cit., T. I, pag. </s>

<s>24) a quella cos&igrave; efficace semplicit&agrave;, che de&shy;<lb/>rivava nel suo discorso dalla precisione, e dall'evidenza de'premessi assiomi, <lb/>o com'egli stesso gli chiamava <emph type="italics"/>Leggi dei moti.<emph.end type="italics"/></s></p><p type="main">

<s>La prima legge &egrave; quella cos&igrave; detta dell'inerzia, in virt&ugrave; della quale un <lb/>corpo gi&agrave; mosso persevera uniformemente a moversi in diretto: cosicch&egrave; se <lb/>prima era per esempio in A (fig. </s>

<s>385), e poi in D, possiamo esser certi che <lb/>non &egrave; mai uscito dalla rettitudine DA del precedente viaggio. </s>

<s>La seconda <lb/>legge, dipendente dalla prima, &egrave; che la velocit&agrave; di un corpo non muta n&egrave; <lb/>grado n&egrave; direzione, per sopravvenirgli un altro impulso in direzione diversa: <lb/>cosicch&egrave;, se il punto A per esempio si move nell'AC uniformemente, con <lb/>una data velocit&agrave;; con questa seguiter&agrave; a moversi parallelamente a se stesso, <lb/>anche trasportato che sia nella direzione AB: assioma, che giov&ograve; ridurre alla <lb/>mente di coloro, i quali, tuttavia sofisticando intorno all'impedirsi che fanno <lb/>in concorrere insieme due forze, si mettevano al pericolo di errare, quando <lb/>si trattava di definir l'essere, e la ragion della resultante. </s></p><p type="main">

<s>Ci&ograve; premesso, sia, dice il Newton, in un dato tempo, per la sola forza <lb/>M, il corpo A uniformemente portato da A in B, e, per la sola forza N, da <lb/>A in C. </s>

<s>Compiuto il parallelogrammo, perciocch&egrave;, per la seconda legge, la <lb/>forza che agisce nella direzione AC non muta la velocit&agrave; di avvicinarsi alla <lb/>linea BD, dovr&agrave; in qualche punto di questa, alla fine del dato tempo, ritro&shy;<lb/>varsi il mobile A, e dovr&agrave; per le medesime ragioni trovarsi anche insieme <lb/>in qualche punto della CD; dunque nel loro concorso D: e il mobile stesso, <lb/>che a principio era in A, non pu&ograve;, in virt&ugrave; della prima legge, non esser pas&shy;<lb/>sato per la rettitudine AD, diagonale del parallelogrammo. </s></p><pb xlink:href="020/01/2991.jpg" pagenum="616"/><p type="main">

<s>Il Varignon, nei principii che premette alla <emph type="italics"/>Nouvelle mecanique,<emph.end type="italics"/> invoca, <lb/>pi&ugrave; espressamente del Newton, l'assioma che <emph type="italics"/>les espaces parcourus de vi&shy;<lb/>tesses uniformes en tems egaux par des corps quelconques sont entr'eux <lb/>comme ces memes vitesses<emph.end type="italics"/> (T. </s>

<s>I cit., pag. </s>

<s>5), e simile fa l'Herman nel teo&shy;<lb/>rema III del primo libro della Foronomia, cosicch&egrave; le loro dimostrazioni pro&shy;<lb/>cedon nel modo medesimo di quella del Newton, ma con diverso andamento, <lb/>il quale consiste nel considerare che, mentre il mobile ha passato, nella di&shy;<lb/>rezione AC, lo spazio AK, deve nella direzione AB aver passato tale altro <lb/>spazio KG, che sia AC:CD=AK:KG, cosicch&egrave; G &egrave; il punto, dove si trova <lb/>il mobile alla fine di quei due moti. </s>

<s>S'avranno allo stesso modo indicati i <lb/>punti G&prime;, G&Prime; .... dove esso mobile &egrave; giunto alla fine dei moti AK&prime;, K&prime;G&prime;; <lb/>AK&Prime;, K&Prime;G&Prime; .... ed &egrave; facile vedere come tutti questi punti sian disposti lungo <lb/>la diagonale AD del parallelogrammo, la quale dunque indica la direzione, e <lb/>misura la quantit&agrave; del moto unico, che resulta dai due componenti. </s></p><p type="main">

<s>Era il bel teorema, per tanti secoli quanti se ne contano da Aristotile <lb/>all'Herman, andato attorno in quest'abito semplice e schietto, bene accolto <lb/>da tutti e onorato, quando Giovanni Bernoulli usc&igrave; fuori con giovanile bal&shy;<lb/>danza a dire che quell'abito non era il suo, e che bisognava tagliargliene <lb/><figure id="id.020.01.2991.1.jpg" xlink:href="020/01/2991/1.jpg"/></s></p><p type="caption">

<s>Figura 385.<lb/>un'altro, che s'adattasse me&shy;<lb/>glio al suo dosso. </s>

<s>&ldquo; Peccant <lb/>qui confundunt compositio&shy;<lb/>nem virium cum compositione <lb/>motuum. </s>

<s>Vis enim vel poten&shy;<lb/>tia, utpote consistens in solo <lb/>nisu vel conatu, ad motum <lb/>generandum, nullam sane ve&shy;<lb/>locitatem actualem, ne mini&shy;<lb/>mam quidem, producit, si cor&shy;<lb/>pus in quod agit est immobile. </s>

<s>Ubi perfectum est aequilibrium, ibi nullus <lb/>adest motus. </s>

<s>Qui ergo considerari possit motus, in aequilibrii natura expli&shy;<lb/>canda, non video &rdquo; (<emph type="italics"/>De composit. </s>

<s>et resolut. </s>

<s>virium,<emph.end type="italics"/> Op. </s>

<s>omnia, T. IV cit., <lb/>pag. </s>

<s>256). </s></p><p type="main">

<s>Non vedeva ci&ograve; il Bernoulli, perch&egrave; non aveva letto, o aveva dimenti&shy;<lb/>cato quel ch'era stato scritto da alcuni Matematici insigni, essere cio&egrave; nel&shy;<lb/>l'equilibrio due moti uguali e contrari, e perci&ograve; la quiete non altro che ap&shy;<lb/>parente. </s>

<s>Il Borelli, nel cap. </s>

<s>XVII del suo libro <emph type="italics"/>De vi percussionis,<emph.end type="italics"/> pronunziava <lb/>questa, non sentenza assoluta, ma probabile opinione: &ldquo; Si vero conside&shy;<lb/>retur actio illa, quae vera destructio motus appellatur, profecto in ea nil <lb/>omnino destruitur, sed tantummodo imprimitur motus contrarius, ita ut post&shy;<lb/>modum in eodem subiecto duo impetus et motus contrarii vigentes et perse&shy;<lb/>verantes apparentiam quietis pariant, et sic videantur ambo destructi, cum <lb/>tamen utrumque vivere ac existere in natura non videatur improbabile: et <lb/>universe, quotiescumque corpus aliquod post eius motum quiescere conspi&shy;<lb/>citur, tunc dicendum est ab obstaculo vel impedimento eidem impressum <pb xlink:href="020/01/2992.jpg" pagenum="617"/>fuisse gradum impetus contrarium omnino aequalem ei quo prius fereba&shy;<lb/>tur &rdquo; (Editio cit., pag. </s>

<s>135). </s></p><p type="main">

<s>Del resto non si vede che gran peccato facessero coloro, i quali ave&shy;<lb/>vano confusa la composizione dei moti con quella delle forze. </s>

<s>Confondere le <lb/>azioni si sarebbe stato gran vizio logico, perch&egrave; le forze son le cause e i <lb/>moti l'effetto: ma qui si tratta di una passione, che sopravviene ai loro <lb/>composti, n&egrave; si vede per qual ragione s'avesse a condannar chi dicesse che <lb/>la causa e l'effetto possono, in certe loro passioni, rassomigliarsi. </s>

<s>&ldquo; Quaeri&shy;<lb/>tur enim, soggiunge ivi il Bernoulli, cur tres potentiae C, B, F (nella fig. </s>

<s>385) <lb/>commune punctum A sollicitantes, ea qua dictum est conditione (cio&egrave; che la <lb/>diagonale del parallelogrammo, descritto sopra due qualunque delle date forze, <lb/>sia uguale e direttamente contraria alla terza) perfectum inter se servent <lb/>aequilibrium? </s>

<s>Quomodo igitur introduci possit ulla velocitas, ubi perfecta <lb/>adest quies, non video. </s>

<s>&rdquo; </s></p><p type="main">

<s>Ma suppongasi che le AB, AC, AF (nella medesima figura) siano tre <lb/>funi, che mantengono il nodo A in equilibrio: recisa l'AF, l'equilibrio &egrave; <lb/>rotto, e succede il moto nella direzione AD resultante dalla composizione dei <lb/>moti per AB, AC. </s>

<s>Ecco per qual ragione i Matematici anteriori al Bernoulli <lb/>erano trapassati a introdurre le velocit&agrave;, dov'era quiete perfetta. </s>

<s>Anzi tanto <lb/>facile e naturale si presentava questo passaggio, che il Bernoulli stesso, nella <lb/>sua dimostrazione, come vedremo, non pot&egrave; astenersi dal farlo. </s>

<s>Il teorema <lb/>insomma si pu&ograve; proporre in due vari modi: nel primo, che dice restare in <lb/>quiete il punto A sollecitato dalle tre forze AB, AC, AF, se la diagonale AD <lb/>&egrave; uguale e direttamente contraria alla terza forza AF; e nel secondo modo <lb/>cos&igrave;: il punto A, che, divisamente, si moverebbe con le velocit&agrave; AB, AC, <lb/>compostamente, &egrave; diretto e va con velocit&agrave; rappresentata dalla diagonale AD <lb/>del parallelogrammo. </s>

<s>In quel primo modo proposto il teorema apparterrebbe <lb/>alla Statica, ma alla Dinamica nel secondo. </s></p><p type="main">

<s>Ora, sarebbe stato il Bernoulli assai pi&ugrave; giusto censore, se avesse detto <lb/>che il Varignon, il Newton e l'Herman confondevano la Statica con la Di&shy;<lb/>namica: o meglio, se avesse rimproverato a quegli Autori, per aver trattato <lb/>dell'equilibrio, con l'invocare le leggi del moto. </s>

<s>Il Varignon per esempio pre&shy;<lb/>mette come principio assiomatico della sua dimostrazione che, nei moti uni&shy;<lb/>formi, essendo i tempi uguali, le velocit&agrave; son proporzionali agli spazi. </s>

<s>Ma <lb/>questo non &egrave;, n&egrave; pu&ograve; citarsi come assioma, essendo un teorema da dimo&shy;<lb/>strarsi in una Scienza superiore. </s>

<s>Parimente l'Herman dimostra la regola di <lb/>comporre in uno due moti, nella prima sezione del primo libro della Foro&shy;<lb/>mia, ossia nella Statica, dove anch'egli cit&agrave; quella propriet&agrave; dei moti uni&shy;<lb/>formi, dicendola manifesta: <emph type="italics"/>manifestum est.<emph.end type="italics"/> E poniamo che tale ei la dica <lb/>per le cose gi&agrave; dimostrate infin da Archimede nel libro delle Spirali, non <lb/>potrebbe per&ograve; apparir tale alla mente de'suoi lettori, i quali si suppone che <lb/>non sappiano ancora nulla della Dinamica, di che si tratter&agrave; nella Sezione <lb/>seconda. </s>

<s>Quivi era logico ammettere per cosa nota, perch&egrave; recentemente di&shy;<lb/>mostrata da Galileo e dall'Huyghens, che <emph type="italics"/>spatiola, aequabili motu percursa,<emph.end type="italics"/><pb xlink:href="020/01/2993.jpg" pagenum="618"/><emph type="italics"/>sunt in composita ratione temporum et velocitatum<emph.end type="italics"/> (Phoron., pag. </s>

<s>55): non <lb/>logico per&ograve; sembra a noi che sia suppor la notizia di quelle leggi de'moti <lb/>equabili, nel teorema terzo degli equilibri. </s></p><p type="main">

<s>Ma come da un'altra parte trattar dei moti, senza presupporne le leggi? <lb/></s>

<s>&mdash; A che bene a proposito ci vien la risposta dal Bernoulli: &mdash; Scansate di <lb/>trattar dei moti, e attenetevi alle semplici forze. </s>

<s>&mdash; E cos&igrave;, come egli disse, <lb/>anche insegn&ograve; di fare con assai bella dimostrazione, non da altri principii <lb/>condotta che dalla statica del vette. </s>

<s>&ldquo; Archimedes, aliique ex veteribus, ad <lb/>vectis indolem recurrcrunt ut phaenomena gravitationum, se mutuo in aequi&shy;<lb/>librio vel quiete retinentium, demonstrarent. </s>

<s>Nos eorum exemplum secuti <lb/>idem fecimus, dum potentiarum compositionem ad vectis leges, utpote a longo <lb/>adeo tempore dmonstratas atque receptas, reduximus, reiecto nempe expli&shy;<lb/>candi modo recentiorum Geometrarum, ut Cartesii, Stevini, Newtoni, Vari&shy;<lb/>gnonii, Hermanni aliorumque, qui velocitatem saltem initialem in auxilium <lb/>vocarunt, ad principii elegantissimi veritatem stabiliendam; ubi tamen nulla <lb/>prorsus adest velocitas &rdquo; (Op. </s>

<s>cit., pag. </s>

<s>256). </s></p><p type="main">

<s>La dimostrazion del Bernoulli, che nella scrittura di lui forse appari&shy;<lb/>sce prolissa, si pu&ograve; rendere cos&igrave; in poche parole. </s>

<s>Siano le tre potenze A, B, D <lb/><figure id="id.020.01.2993.1.jpg" xlink:href="020/01/2993/1.jpg"/></s></p><p type="caption">

<s>Figura 386.<lb/>(fig. </s>

<s>386) rappresentate dalle linee AP, BP, DP, con&shy;<lb/>correnti a mantenere il punto P in equilibrio. </s>

<s>&Egrave; ma&shy;<lb/>nifesto che, rimossa una qualunque delle dette po&shy;<lb/>tenze, per esempio D, il punto P si mover&agrave; con <lb/>direzione, dice il Bornoulli, e con forza rappresen&shy;<lb/>tata dalla diagonale del parallelogrammo AB, co&shy;<lb/>struito sulle direzioni delle due forze rimaste. </s></p><p type="main">

<s>Esser questa veramente e non altra la direzione <lb/>resulta dall'aversi AP a BP contrariamente, come <lb/>il seno dell'angolo BPC al seno dell'angolo APC: <lb/>ci&ograve; che dall'Autore si dimostra prolungando le AP, <lb/>PB, e sopra i loro prolungamenti abbassando dal <lb/>punto C le perpendicolari CE, CF. Allora, trasferite <lb/>le potenze A, B, D in E, F, C, la ECF si pu&ograve; ri&shy;<lb/>guardar come una leva angolare coll'ipomoclio in <lb/>C, e in cui, per le note leggi, &egrave; A:B=CF:EC=BC:AC=AP:BP= <lb/>sen BPC:sen APC. </s></p><p type="main">

<s>Supponendo ora invece rimossa l'AP, il moto resultante dalle D, R sar&agrave; <lb/>dunque, per le cose gi&agrave; dimostrate, diretto secondo PG, in modo che sia <lb/>B:D=senDPG:senGPB=senAPC:senPAC=AC:PC=PB:PC. </s>

<s><lb/>E perch&egrave; PB rappresenta la potenza B, dunque PC rappresenter&agrave; la po&shy;<lb/>tenza D, e perci&ograve; veramente si far&agrave; il moto nella direzione e nella misura <lb/>che s'era detto, cio&egrave; lungo, e per tutta intera la diagonale del parallelo&shy;<lb/>grammo. </s></p><p type="main">

<s>Chi potrebbe negare che questa dimostrazione non si addica meglio alla <lb/>Statica di quell'altre del Varignon e dell'Herman? </s>

<s>Anzi, perch&egrave; cos&igrave; que-<pb xlink:href="020/01/2994.jpg" pagenum="619"/>ste, come quelle de'precedenti autori, eccettuatone Giov. </s>

<s>Marco, son tutte <lb/>uscite dal medesimo antico stampo aristotelico, &egrave; da dire che incontr&ograve; prima <lb/>al Bernoulli, non contento degli altrui processi, di dare alla dimostrazione del <lb/>bello e importantissimo teorema un processo del tutto nuovo. </s></p><p type="main">

<s>Un secondo e simile incontro ebbe poco di poi in Italia Vincenzo Ric&shy;<lb/>cati, bench&egrave; per vario, ma forse pi&ugrave; giusto e pi&ugrave; generoso motivo, quale si <lb/>fu di persuadere la verit&agrave; a quelle poche e sparse reliquie de'Galileiani, i <lb/>quali duravano ostinati a dire che nella regola del parallelogrammo non si <lb/>osserva la necessaria equivalenza tra le potenze componenti e la resultante. </s>

<s><lb/>Per dare alla sua dimostrazione la maggiore evidenza, pens&ograve; il Riccati d'in&shy;<lb/>trodurre le potenze direttamente, invece delle velocit&agrave; o delle forze, come <lb/>avevano fatto gli altri. </s>

<s>E per rendere meno astratte queste matematiche spe&shy;<lb/>culazioni, finse cotali potenze in corde elastiche, come quelle delle cetre, le <lb/>quali corde, essendo state prima stirate, poi nel contrarsi rapiscono violen&shy;<lb/>temente a s&egrave; un corpo, a cui si fossero applicate. </s>

<s>Se sia dunque A (fig. </s>

<s>387) <lb/>un punto mobile, e AS una corda, che con potenza rappresentata da AB lo <lb/>tira un istante per lo spazio infinitamente piccolo A <emph type="italics"/>p,<emph.end type="italics"/> verr&agrave; l'azione di essa <lb/>potenza rappresentata dal rettangolo AB. </s>

<s>A <emph type="italics"/>p,<emph.end type="italics"/> essendo AB, come s'&egrave; detto, <lb/>la forza, e A <emph type="italics"/>p<emph.end type="italics"/> la velocit&agrave; virtuale. </s></p><p type="main">

<s>Ci&ograve; premesso, il Riccati raggiunge il suo intento, qual'era di dimostrare <lb/><figure id="id.020.01.2994.1.jpg" xlink:href="020/01/2994/1.jpg"/></s></p><p type="caption">

<s>Figura 387.<lb/>che, qualunque sia l'angolo del concorso, il <lb/>moto per la diagonale uguaglia in potenza <lb/>il moto per i due lati del parallelogrammo, <lb/>in virt&ugrave; di due lemmatiche proposizioni, la <lb/>prima delle quali &egrave; questa: Insieme con AS <lb/>(nella medesima figura) potente come AB, <lb/>sia un'altra corda AT, potente come AC, ap&shy;<lb/>plicate ambedue al punto A, il quale sia co&shy;<lb/>stretto a moversi nella direzione AD, quasi <lb/>ritenutovi dalle sponde di un canaletto o <lb/>solco inciso sul piano BC: &ldquo; Se da'punti B, <lb/>C, nella direzione AD si menino le normali <lb/>BH, CK, e si tagli HD uguale ad AK, dico che la retta AD rappresenter&agrave; <lb/>la potenza equipollente alle due potenze AB, AC &rdquo; (<emph type="italics"/>Dialogo delle forze vive,<emph.end type="italics"/><lb/>Bologna 1749, pag. </s>

<s>221, 22). </s></p><p type="main">

<s>S'immagini che, rapito dal concorso delle due corde il punto A, in un <lb/>primo istante abbia passato lo spazio infinitamente piccolo A <emph type="italics"/>a:<emph.end type="italics"/> col centro S, <lb/>intervallo S<emph type="italics"/>a,<emph.end type="italics"/> e col centro T, intervallo T<emph type="italics"/>a,<emph.end type="italics"/> descritti gli archetti <emph type="italics"/>ap, aq,<emph.end type="italics"/> &egrave; <lb/>manifesto che gli spazioli A<emph type="italics"/>p,<emph.end type="italics"/> A<emph type="italics"/>q<emph.end type="italics"/> misurano i ritiramenti delle corde o le <lb/>loro velocit&agrave; virtuali: ond'essendo AB.A<emph type="italics"/>p,<emph.end type="italics"/> AC.A<emph type="italics"/>q<emph.end type="italics"/> le azioni delle potenze <lb/>AB, AC, e AD.A<emph type="italics"/>a<emph.end type="italics"/> l'azione della potenza AD; s'avr&agrave; conclusa la proposi&shy;<lb/>zione quando sia dimostrato AB.A<emph type="italics"/>p<emph.end type="italics"/>+AC.A<emph type="italics"/>q<emph.end type="italics"/>=AD.A<emph type="italics"/>a,<emph.end type="italics"/> ci&ograve; che poi <lb/>&egrave; d'assai facile conseguenza, imperocch&egrave; i triangoli simili ABH, A <emph type="italics"/>ap<emph.end type="italics"/> da una <lb/>parte, e AKD, A<emph type="italics"/>aq<emph.end type="italics"/> dall'altra, danno l'equazioni AB:AH=A<emph type="italics"/>a<emph.end type="italics"/>:A<emph type="italics"/>p,<emph.end type="italics"/> ossia <pb xlink:href="020/01/2995.jpg" pagenum="620"/>AH.A<emph type="italics"/>a<emph.end type="italics"/>=AB.A<emph type="italics"/>p,<emph.end type="italics"/> e AC:AK=A<emph type="italics"/>a<emph.end type="italics"/>:A<emph type="italics"/>q,<emph.end type="italics"/> ossia AK.A<emph type="italics"/>a<emph.end type="italics"/>=AC.A<emph type="italics"/>q,<emph.end type="italics"/><lb/>d'onde AB.A<emph type="italics"/>p<emph.end type="italics"/>+AC.A<emph type="italics"/>q<emph.end type="italics"/>=A<emph type="italics"/>a<emph.end type="italics"/>(AH+AK)=A<emph type="italics"/>a<emph.end type="italics"/>.AD, la quale ugua&shy;<lb/>glianza, venendo cos&igrave; a dimostrarsi vera, non significa altro, se non che <lb/>l'azione della potenza AD uguaglia le azioni delle due potenze AB, AC, e <lb/>per&ograve; quella potenza a questa verr&agrave; ad essere equipollente, come il Riccati <lb/>s'era proposto di dimostrare. </s></p><p type="main">

<s>Nell'altra proposizione, che si diceva essere stata insieme con questa da <lb/>esso Riccati preparata, per riuscire con facilit&agrave; all'intenzion principale; si <lb/>considerano gl'incitamenti, che ha il punto mobile di delirare dal solco, e <lb/>si conclude che, essendo cos&igrave; fatti incitamenti uguali e contrari, il punto pro&shy;<lb/>cederebbe liberamente nel suo viaggio. </s>

<s>La conclusione ovvia a chi riguardi <lb/>la contrariet&agrave; nelle forze poste in dirittura fra loro, e perpendicolarmente alla <lb/>linea AD, la trae il Riccati dal suo solito principio che cio&egrave; l'azione equivale <lb/>alla potenza di una corda elastica, d'ond'egli viene a sapere che il punto A <lb/>allora sar&agrave; libero di ubbidire alla sollecitazione delle potenze AB, AC, e di <lb/>dirigere e contemperare ai loro impulsi il suo moto, quando le BH, CK, prese <lb/>a rappresentare due forze contrarie perpendicolarmente dirette sulla linea AD, <lb/>sono uguali. </s>

<s>Dopo ci&ograve; un solo e breve passo rimane a farsi, per giungere <lb/>al termine desiderato. </s>

<s>Congiungansi con D i punti B, C: i triangoli BHD, <lb/>AKC rettangoli, e con i cateti uguali, sono uguali, e perci&ograve; il quadrilatero BC <lb/>&egrave; un perfetto parallelogrammo. </s>

<s>&ldquo; Questa per l'appunto, dice il Riccati, &egrave; la <lb/>legge ordinaria della composizione e risoluzion delle forze, ed essa &egrave; dedotta <lb/>dal principio dell'egualit&agrave; tra le azioni delle potenze laterali, e l'azione del&shy;<lb/>l'equipollente: cio&egrave; dal principio dell'egualit&agrave; tra la cagione e l'effetto, tanto <lb/>&egrave; falso che, nella legge della composizione e risoluzion delle forze, cotal prin&shy;<lb/>cipio non si mantenga &rdquo; (ivi, pag. </s>

<s>225). </s></p><p type="main">

<s>Qual efficacia avessero queste nuove dimostrazioni del Riccati e del Ber&shy;<lb/>noulli, in por suggello di verit&agrave;, e nel dare ordine dimostrativo al Teorema <lb/>del parallelogrammo, non si saprebbe dir da noi con certezza. </s>

<s>Ma &egrave; un fatto <lb/>che il D'Alembert, pochi anni appresso, notava queste cose che trascriviamo, <lb/>dop'avere distesa di quello stesso Teorema una dimostrazione sua nuova: <lb/>&ldquo; La dimonstration qu'on apporte d'ordinaire du Th<gap/>or&egrave;me pr&eacute;c&eacute;dent, con&shy;<lb/>siste &agrave; imaginer que le point A (nella figura 385 qui poco addietro) se meuve <lb/>uniform&eacute;ment sur une regle AB avec la vitesse qu'il a rec&ugrave;e suivant AB, et <lb/>qu'en m&egrave;me tems la ligne ou regle AB se meuve suivant AC, avec la vi&shy;<lb/>tesse que le corps A a rec&ugrave;e suivant AC. </s>

<s>On prouve tr&egrave;s-bien dans cette <lb/>supposition, que le point mobile A d&eacute;crit la diagonale AD &rdquo; (<emph type="italics"/>Trait&egrave; de Dy&shy;<lb/>namiqae,<emph.end type="italics"/> a Paris 1758, pag. </s>

<s>37). </s></p><p type="main">

<s>Si direbbe che il D'Alembert non fece conto delle censure del Bernoulli, <lb/>se non si ripensasse che, trattando esso D'Alemb&egrave;rt della Dinamica sola, <lb/>trov&ograve; le supposizioni fatte dal Varignon, dal Newton e dall'Herman non punto <lb/>fuori del suo proposito, ond'ei pot&egrave; senz'altro riguardo aver ragione di dire <lb/>che da quegli Autori si provavano a quel modo le cose <emph type="italics"/>tr&egrave;s-bien.<emph.end type="italics"/> Ma ascol&shy;<lb/>tiamo quel che ivi soggiunge: &ldquo; En g&eacute;n&eacute;ral la pl&ugrave;part des d&eacute;monstrations <pb xlink:href="020/01/2996.jpg" pagenum="621"/>communes de cette proposition sont fond&eacute;es sur ce qu'on regarde les deux <lb/>puissances suivant AB et AC (nella detta figura) comme agissant sur le <lb/>corps A, pendant tout le tems de son mouvement, ce qui n'est pas pr&eacute;cis&eacute;&shy;<lb/>ment l'etat de la question. </s>

<s>Car l'hypothese est que le corps A tend &agrave; se <lb/>mouvoir au premier instant suivant AB et AC &agrave; la fois, et l'on demande la <lb/>direction et la vitesse, qu'il doit avoir en vertu du concours d'action des <lb/>deux puissances. </s>

<s>D&egrave;s qu'il a pris une direction moyenne AD, les deux ten&shy;<lb/>dances suivant AB et AC n'existent plus: il n'y a plus de r&eacute;el que sa ten&shy;<lb/>dance suivant AD &rdquo; (pag. </s>

<s>37, 38). </s></p><p type="main">

<s>Per prevenir dunque anche questa difficolt&agrave;, ne'malcontenti e ne'ritrosi <lb/>di professare la Meccanica nuova, pens&ograve; il D'Alembert di dimostrare che il <lb/>corpo A prende, in virt&ugrave; dei moti componenti, sempre la medesima direzione, <lb/>sia che le due potenze agiscano un istante sopra lui, e poi lo abbandonino, <lb/>sia che l'accompagnino in tutto il suo viaggio. </s>

<s>Ammesse per buone le ra&shy;<lb/>gioni di coloro, che dimostravano essere nel secondo caso quella direzione <lb/>lungo la diagonale del parallelogrammo; per concluder che tale dovesse esser <lb/>pure anche nel primo, parve a principio al D'Alembert bastasse considerare <lb/>che, ricevuto il primo impulso, il mobile, anche abbandonato a s&egrave; stesso, <lb/>prosegue nella medesima dirittura, la quale, se era dunque secondo la dia&shy;<lb/>gonale nel principio, non devier&agrave; da essa nel mezzo e nella fine, o sia breve <lb/>il tempo o sia lungo. </s></p><p type="main">

<s>Poi, essendo questo un teorema cos&igrave; fondamentale della Dinamica, de&shy;<lb/>liber&ograve; il d'Alembert di darne una prova diretta, e ricercandola nel subietto, <lb/>arido per s&egrave; stesso e da altri autori sfruttato, gli venne fatto di rinvenirla <lb/>a giudizio nostro ingegnosa. </s>

<s>Era senza dubbio difficile paragonare insieme la <lb/>resultante con le componenti, se, quando quella incomincia a nascere, que&shy;<lb/>ste gi&agrave; non son pi&ugrave;, ma fu la difficolt&agrave; superata col fare in modo, che il <lb/>mobile fosse in continuo conato di moversi, eppure si rimanesse in quiete <lb/>nello spazio assoluto. </s>

<s>N&egrave; le condizioni di ci&ograve; potevano esser altre, se non che <lb/>a ogni conato se ne opponesse un altro uguale in grado e in direzione con&shy;<lb/>traria, come se per esempio il punto A (sempre nella medesima figura 385) <lb/>posato sopra un piano fosse sollecitato a moversi con la direzione, e con la <lb/>velocit&agrave; AD, e il piano stesso, con quella medesima velocit&agrave;, si movesse e <lb/>con la direzion resultante DA in contrario. </s></p><p type="main">

<s>S'immagini dunque il detto punto A sollecitato dai conati instantanei <lb/>AB, AC, e il piano ABDC, su cui s'immagina posato, moversi con l'assi&shy;<lb/>stenza continua delle forze DB, DC, uguali e parallele alle AC, AB, sicch&egrave; <lb/>il detto piano &egrave; un parallelogrammo. </s>

<s>Si rimarr&agrave; dunque A in quiete nello <lb/>spazio assoluto, ma ci&ograve; non potrebb'essere, se al suo conato al moto non si <lb/>contrapponesse, con uguale velocit&agrave; e direzione, il moto attuale del piano. </s>

<s>Ora <lb/>questa velocit&agrave; e questa direzione si tengon dal D'Alembert per benissimo <lb/>dimostrate dai Matematici, nell'ipotesi fatta da loro che sian misurate e in&shy;<lb/>dicate dalla diagonale DA; dunque tanto negli impulsi istantanei, quanto <lb/>nella continua assistenza delle forze. </s>

<s>il viaggio del punto A &egrave; il medesimo, <pb xlink:href="020/01/2997.jpg" pagenum="622"/>secondo che l'Autore, per prevenire ogni difficolt&agrave;, aveva creduto bene di <lb/>dover dimostrare. </s>

<s>&ldquo; J'ai donc cr&ugrave; devoir prevenir cette difficult&eacute;, et faire <lb/>voir que le chemin du corps A est le m&egrave;me, soit que les deux puissances <lb/>n'agissent sur lni que dans le premier instant, soit qu'elles agissent conti&shy;<lb/>nuellement toutes deux &agrave; la fois sur le corps. </s>

<s>C'est &agrave; quoi je crois &egrave;tre par&shy;<lb/>venu dans la demonstration que j'ai donn&eacute;e ci-dessus &rdquo; (pag. </s>

<s>38). </s></p><p type="main">

<s>Pi&ugrave; tardi, quando la sperimentata efficacia del Teorema in risolvere le <lb/>pi&ugrave; intricate questioni della Meccanica glie ne crebbe la dignit&agrave; e l'im&shy;<lb/>portanza, si cred&egrave; di doverlo nobilitare, assumendolo alla gloria del nuovo <lb/>calcolo infinitesimale. </s>

<s>Dopo Daniele Bernoulli, che ne dette il primo esempio, <lb/>il Teorema del parallelogrammo usc&igrave; tante volte fuori in quest'abito sun&shy;<lb/>tuoso, ch'essendo superfluo, per giudicarne la convenienza, il mostrarlo in <lb/>tutte le sue comparse, baster&agrave; vederlo in quella sola, che &egrave; la pi&ugrave; magnifica <lb/>di tutte, nella <emph type="italics"/>Mecanique celeste.<emph.end type="italics"/></s></p><p type="main">

<s>Siano, dice il Laplace, <emph type="italics"/>x<emph.end type="italics"/> e <emph type="italics"/>y<emph.end type="italics"/> (fig. </s>

<s>388) due forze ortogonali sollecitanti <lb/><figure id="id.020.01.2997.1.jpg" xlink:href="020/01/2997/1.jpg"/></s></p><p type="caption">

<s>Figura 388.<lb/>il punto M, e <emph type="italics"/>z<emph.end type="italics"/> la loro resul&shy;<lb/>tante, che faccia con <emph type="italics"/>x<emph.end type="italics"/> un an&shy;<lb/>golo <foreign lang="greek">q. </foreign></s>

<s>Dalle date <emph type="italics"/>x, y<emph.end type="italics"/> si tratta <lb/>di determinar <foreign lang="greek">q</foreign>, e con esso <emph type="italics"/>z<emph.end type="italics"/><lb/>che ne dipende. </s>

<s>Divise le due <lb/>componenti in quantit&agrave; infini&shy;<lb/>tamente piccole, cosicch&egrave; vada&shy;<lb/>no successivamente crescendo <lb/>secondo i termini delle serie <lb/><emph type="italics"/>dx,<emph.end type="italics"/> 2<emph type="italics"/>dx,<emph.end type="italics"/> 3<emph type="italics"/>dx..., dy,<emph.end type="italics"/> 2<emph type="italics"/>dy,<emph.end type="italics"/><lb/>3<emph type="italics"/>dy...,<emph.end type="italics"/> &egrave; manifesto che l'an&shy;<lb/>golo <foreign lang="greek">q</foreign> riman sempre il med&egrave;&shy;<lb/>simo, e che la resultante cre&shy;<lb/>sce nella med&egrave;sima proporzione, cio&egrave; secondo i termini della serie <emph type="italics"/>dz,<emph.end type="italics"/><lb/>2 <emph type="italics"/>dz,<emph.end type="italics"/> 3 <emph type="italics"/>dz....<emph.end type="italics"/> ed &egrave; manifesto altresi che, ne'successivi incrementi delle tre <lb/>forze, le relazioni di <emph type="italics"/>x<emph.end type="italics"/> e <emph type="italics"/>y<emph.end type="italics"/> a <emph type="italics"/>z<emph.end type="italics"/> saranno costantemente date in funzione di <foreign lang="greek">q</foreign>, <lb/>e che perci&ograve; si avranno le due equazioni <emph type="italics"/>x=z<foreign lang="greek">f</foreign>(<foreign lang="greek">q</foreign>), y=z<foreign lang="greek">f</foreign>(90&deg;&mdash;<foreign lang="greek">q</foreign>).<emph.end type="italics"/></s></p><p type="main">

<s>Riguardando poi la <emph type="italics"/>x<emph.end type="italics"/> come la resultante delle due forze ortogonali <lb/><emph type="italics"/>x&prime;, x&Prime;,<emph.end type="italics"/> perciocch&egrave; quella &egrave; sopr'essa resultante inclinata con l'angolo <foreign lang="greek">q</foreign>, e <lb/>questa con l'angolo 90&deg;&mdash;<foreign lang="greek">q</foreign>; avremo dunque di <emph type="italics"/>x&prime;,<emph.end type="italics"/> e di <emph type="italics"/>x&Prime;<emph.end type="italics"/> due altre equa&shy;<lb/>zioni simili a quelle scritte di sopra, cio&egrave; <emph type="italics"/>x&prime;=x<foreign lang="greek">f</foreign>(<foreign lang="greek">q</foreign>)=x2/z, x&Prime;= <lb/>x<foreign lang="greek">f</foreign>(90&deg;&mdash;<foreign lang="greek">q</foreign>)=xy/z.<emph.end type="italics"/> Parimente, decomposta la <emph type="italics"/>y<emph.end type="italics"/> nelle due ortogonali <emph type="italics"/>y, y&Prime;,<emph.end type="italics"/><lb/>inclinate con gli angoli 90&deg;&mdash;<foreign lang="greek">q</foreign>, e <foreign lang="greek">q</foreign>, sar&agrave; <emph type="italics"/>y&prime;=y<foreign lang="greek">f</foreign>(90&deg;&mdash;<foreign lang="greek">q</foreign>)=y2/z, y&Prime;= <lb/>y<foreign lang="greek">f</foreign>(<foreign lang="greek">q</foreign>)=xy/z.<emph.end type="italics"/> Alle due <emph type="italics"/>x, y<emph.end type="italics"/> si potranno dunque sostituire le quattro forze <lb/><emph type="italics"/>x&prime;, y&prime;; x&Prime;, y&Prime;.<emph.end type="italics"/> E perch&egrave; le due ultime, oltre a essere uguali, son diretta-<pb xlink:href="020/01/2998.jpg" pagenum="623"/>mente contrarie, e l'uguaglianza tra <emph type="italics"/>x&prime;z<emph.end type="italics"/> e <emph type="italics"/>y&prime;<emph.end type="italics"/> produce tra <emph type="italics"/>x&prime;+y&prime;,<emph.end type="italics"/> ossia tra <lb/><emph type="italics"/>(x2+y2)/z<emph.end type="italics"/>e <emph type="italics"/>z,<emph.end type="italics"/> un'altra uguaglianza; dunque <emph type="italics"/>x2+y2=z2.<emph.end type="italics"/> &ldquo; D'ou il suit, dice <lb/>il Laplace, que la resultante des deux forces <emph type="italics"/>x<emph.end type="italics"/> et <emph type="italics"/>y<emph.end type="italics"/> est represent&eacute;e pour la <lb/>quantit&eacute; par la diagonale du rectangle, dont les cotes representent ces for&shy;<lb/>ces &rdquo; (<emph type="italics"/>Trait&eacute; de Mecanique celeste,<emph.end type="italics"/> a Paris, T. I, an. </s>

<s>VII, pag. </s>

<s>5). </s></p><p type="main">

<s>Rimane a determinare l'angolo <foreign lang="greek">q</foreign>, e per far ci&ograve; immagina il Laplace <lb/>che la <emph type="italics"/>x<emph.end type="italics"/> cresca della quantit&agrave; infinitesima <emph type="italics"/>dx,<emph.end type="italics"/> rimanendosi l'altra <emph type="italics"/>y<emph.end type="italics"/> inva&shy;<lb/>riabile. </s>

<s>Per maggiore chiarezza di ci&ograve; che dice l'Autore, appongasi l'incre&shy;<lb/>mento <emph type="italics"/>dx<emph.end type="italics"/> non a <emph type="italics"/>x<emph.end type="italics"/> direttamente, ma alla sua uguale e parallela <emph type="italics"/>yz,<emph.end type="italics"/> e questo <lb/>incremento infinitesimale di forza cos&igrave; apposto decompongasi ne'due ortogo&shy;<lb/>nali <emph type="italics"/>dx&prime;, dx&Prime;.<emph.end type="italics"/> Poi <emph type="italics"/>dx&prime;<emph.end type="italics"/> si prolunghi di una quantit&agrave; uguale a <emph type="italics"/>z:<emph.end type="italics"/>&egrave; manife&shy;<lb/>sto che le forze sollecitanti il punto M sono le due <emph type="italics"/>z+dx&prime;, dx&Prime;,<emph.end type="italics"/> sopra le <lb/>quali costruito un rettangolo, la diagonale di lui <emph type="italics"/>z&prime;<emph.end type="italics"/> sar&agrave; la resultante, che <lb/>far&agrave; l'angolo <emph type="italics"/>dx&Prime;z&prime;z=d<foreign lang="greek">q</foreign>,<emph.end type="italics"/> e l'angolo <emph type="italics"/>dx&Prime;zz&prime;=90&deg;&mdash;d<foreign lang="greek">q</foreign>.<emph.end type="italics"/> Dunque per&shy;<lb/>ch&egrave;, omologamente a quel che s'&egrave; fatto di sopra, <emph type="italics"/>dx&Prime;=z&prime;<foreign lang="greek">f</foreign>(90&deg;&mdash;d<foreign lang="greek">q</foreign>= <lb/>&mdash;z&prime;kd<foreign lang="greek">q</foreign><emph.end type="italics"/> (essendo <emph type="italics"/>k<emph.end type="italics"/> una costante arbitraria, e indipendente dall'angolo <foreign lang="greek">q</foreign>) <lb/>e anche <emph type="italics"/>dx&Prime;=dx<foreign lang="greek">f</foreign>(90&deg;&mdash;<foreign lang="greek">q</foreign>)=ydx/z;<emph.end type="italics"/> avremo <emph type="italics"/>ydx/z=&mdash;z&prime;kd<foreign lang="greek">q</foreign>,<emph.end type="italics"/> d'onde, <lb/>considerando che <emph type="italics"/>z&prime;<emph.end type="italics"/> e <emph type="italics"/>z,<emph.end type="italics"/> per differire di una quantit&agrave; infinitesima sono uguali, <lb/><emph type="italics"/>d<foreign lang="greek">q</foreign>=(&mdash;ydy)/kz2.<emph.end type="italics"/> Se poi in questa si cambi <emph type="italics"/>x<emph.end type="italics"/> in <emph type="italics"/>y, y<emph.end type="italics"/> in <emph type="italics"/>x,<emph.end type="italics"/> e <foreign lang="greek">q</foreign> in 90&deg;&mdash;<foreign lang="greek">q</foreign>, <lb/>avremo per la variazione di <emph type="italics"/>y,<emph.end type="italics"/> rimanendosi <emph type="italics"/>x<emph.end type="italics"/> costante, <emph type="italics"/>d<foreign lang="greek">q</foreign>=xdy/kz2,<emph.end type="italics"/> cosicch&egrave;, <lb/>per il simultaneo variar di <emph type="italics"/>x<emph.end type="italics"/> e di <emph type="italics"/>y,<emph.end type="italics"/> la variazione totale dell'angolo <foreign lang="greek">q</foreign> sar&agrave; <lb/><emph type="italics"/>d<foreign lang="greek">q</foreign>=(xdy&mdash;ydx)/kz2.<emph.end type="italics"/></s></p><p type="main">

<s>Questa ultima integrata rende <emph type="italics"/>y/x<emph.end type="italics"/>=tang.(<emph type="italics"/>k<emph.end type="italics"/><foreign lang="greek">q</foreign>+C), ossia <emph type="italics"/>y2= <lb/>x2<emph.end type="italics"/>tang2(<emph type="italics"/>k<emph.end type="italics"/><foreign lang="greek">q</foreign>+C)=<emph type="italics"/>z2&mdash;x2,<emph.end type="italics"/> d'onde <emph type="italics"/>x=z<emph.end type="italics"/>&radic;1/tang2(<emph type="italics"/>k<foreign lang="greek">q</foreign><emph.end type="italics"/>+C)= <lb/><emph type="italics"/>z<emph.end type="italics"/>cos(<emph type="italics"/>k<emph.end type="italics"/><foreign lang="greek">q</foreign>+C), n&egrave; rimane a far altro che a determinare le due costanti. </s>

<s>Se <lb/><emph type="italics"/>y<emph.end type="italics"/> &egrave; zero, evidentemente <emph type="italics"/>z=x,<emph.end type="italics"/> e <foreign lang="greek">q</foreign>=0, nel qual caso l'equazione si ri&shy;<lb/>duce a cos C=<emph type="italics"/>x/z<emph.end type="italics"/>=1, d'onde C=360&deg;, che sostituito d&agrave; </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>x=z<emph.end type="italics"/>cos(360+<emph type="italics"/>k<foreign lang="greek">q</foreign>)=z<emph.end type="italics"/>cos<emph type="italics"/>k<emph.end type="italics"/><foreign lang="greek">q</foreign>.<emph.end type="center"/><lb/>Se invece &egrave; zero <emph type="italics"/>x,<emph.end type="italics"/> l'uguaglianza tra <emph type="italics"/>z<emph.end type="italics"/> e <emph type="italics"/>y,<emph.end type="italics"/> e tra <foreign lang="greek">q</foreign> e 90&deg; che ne resulta, <lb/>riduce cos <emph type="italics"/>k<emph.end type="italics"/><foreign lang="greek">q</foreign>=0, equazione non esistente se no nel caso che <emph type="italics"/>k<emph.end type="italics"/> sia un <lb/>numero impari (quale si suol esprimere con 2<emph type="italics"/>n<emph.end type="italics"/>+1) e <foreign lang="greek">q</foreign> sia uguale <foreign lang="greek">q</foreign><lb/>90&deg;:2<emph type="italics"/>n<emph.end type="italics"/>+1. Ma nella fatta supposizione che <emph type="italics"/>x<emph.end type="italics"/> sia nullo evidentemente a <lb/>deve essere uguale a 90&deg;; dunque, affinch&egrave; sia 90&deg;=90&deg;:2<emph type="italics"/>n<emph.end type="italics"/>+1, biso&shy;<lb/>gna che <emph type="italics"/>n<emph.end type="italics"/> sia zero, e perci&ograve; <emph type="italics"/>k<emph.end type="italics"/>=1, il quale valore sostituito riduce final&shy;<lb/>mente l'integrata equazione alla forma <emph type="italics"/>y=zcos<foreign lang="greek">q</foreign>.<emph.end type="italics"/> &ldquo; De l&agrave; il suit, ne con-<pb xlink:href="020/01/2999.jpg" pagenum="624"/>clude il Laplace, que la diagonale du rectangle construit sur les droites qui <lb/>representent les deux forces <emph type="italics"/>x<emph.end type="italics"/> et <emph type="italics"/>y,<emph.end type="italics"/> represente non seulement la quantit&eacute;, <lb/>mais encore la direction de leur resultante &rdquo; (ivi, pag. </s>

<s>6). </s></p><p type="main">

<s>Abbiamo esposta la dimostrazione non solo agli occhi, ma al giudizio <lb/>dei nostri Lettori, ai quali sembrer&agrave; forse come a noi di trovarci quel difetto <lb/>capitalissimo, rimproverato da altri al Duchayle, di supporre cio&egrave; come noto <lb/>quel che si proponeva di dimostrare. </s>

<s>L'ipotesi non &egrave; altro che la conversa <lb/>della tesi: si vuol concludere che la risultante di due forze ortogonali &egrave; la <lb/>diagonale del rettangolo, e per far ci&ograve; si suppone che le componenti siano <lb/>i lati del rettangolo stesso. </s>

<s>&Egrave; poi vero che dal caso delle forze concorrenti <lb/>insieme ad angolo retto si pu&ograve; facilmente passare agli altri casi che sia qua&shy;<lb/>lunque l'angolo del detto concorso, ma la proposizione del Laplace in ogni <lb/>modo &egrave; particolare, e volendola ridurre alla sua generalit&agrave;, il calcolo istituito <lb/>da lui riuscirebbe assai pi&ugrave; complicato. </s>

<s>Ma rimanendosi pure in quella mas&shy;<lb/>sima semplicit&agrave; di differenziali e d'integrazioni, si domanda qual maggiore <lb/>evidenza e fermezza viene a darsi al Teorema trattato a quel modo, verso <lb/>l'altra trattazione del Newton, che si spedisce in cos&igrave; poche parole, e per <lb/>intender le quali basta la notizia della Geometria pi&ugrave; elementare? </s></p><p type="main">

<s>Si direbbe che &egrave; cominciato il tempo, in cui si creder&agrave; colla potenza <lb/>del calcolo di soggiogar l'esperienza e la ragione, ma alcuni Matematici fe&shy;<lb/>cero senno, e pensarono che al Teorema del parallelogrammo era avvenuto <lb/>come agli animali domestici e alle piante, che bene spesso si ammalano per <lb/>volerle troppo curare. </s>

<s>Il Varignon, il Newton e l'Herman, che furono i primi <lb/>a riconoscere d&igrave; quel gran Teorema l'importanza, avrebbero senza dubbio <lb/>saputo darne dimostrazione pi&ugrave; elaborata, e al D'Alembert per esempio non <lb/>mancava del calcolo pi&ugrave; sublime n&egrave; l'uso n&egrave; il senso della potenza: eppure, <lb/>avvisando nella prefazione alla sua Dinamica i Lettori di aver trattato del <lb/>principio della composizion delle forze in una maniera nuova, soggiungeva <lb/>di essersi guardato in essa &ldquo; de ne pas deduire d'un grand nombre de pro&shy;<lb/>positions compliqu&eacute;es un principe qui, etant l'un des premiers de la Mecha&shy;<lb/>nique, doit n&eacute;cessairement &egrave;tre appuy&eacute; sur des preuves simples et faciles &rdquo; <lb/>(pag. </s>

<s>XIII). Di questo medesimo parere fu il Lagrange, ond'&egrave; che si ridus&shy;<lb/>sero alla primiera semplicit&agrave; molti autori, fra'quali &egrave; particolarmente da com&shy;<lb/>memorare quel Marie, tanto benemerito in Francia e fuori dell'ordinamento <lb/>delle Matematiche nelle Scuole di que'tempi. </s></p><p type="main">

<s>I savi metodi proposti alla giovent&ugrave; pigliavano autorit&agrave; dal vederli se&shy;<lb/>guiti anche dai provetti, come dal Prony, il quale, ponendo per fondamento <lb/>alla sua <emph type="italics"/>Nouvelle architecture hydrauliche<emph.end type="italics"/> la regola del parallelogrammo, <lb/>suppone di avere un corpo in quiete posato sopra un piano, che equabil&shy;<lb/>mente si muove. </s>

<s>&ldquo; Cela pos&eacute;, poi soggiunge, si on concoit qu'une force quel&shy;<lb/>conque agisse sur lui (cio&egrave; sul detto corpo mobile rappresentato da A nella <lb/>figura 385 qui poco addietro) selon la direction AC, et lui imprime una vi&shy;<lb/>tesse telle que dans une unit&eacute; de temps il puisse parcourir l'espace AC uni&shy;<lb/>formement, on ne peut douter qu'en vertu de cette premiere impression, qui <pb xlink:href="020/01/3000.jpg" pagenum="625"/>lui est proprie, il ne doive se trouver au point C, lorsque cette unit&eacute; de <lb/>temps finira. </s>

<s>Mais comme en vertu du mouvement du plan la ligne AC <lb/>s'avance d'un mouvement parallele et uniforme vers BD, et qu'elle doit reel&shy;<lb/>lement se confondre avec BD au bout d'une unit&eacute; de temps; il est clair que <lb/>le point C se confondra avec le point D &rdquo; (A Paris 1790, pag. </s>

<s>25). Cos&igrave; da <lb/>questi medesimi principii, concludendo al medesimo modo che nell'introdu&shy;<lb/>zione al primo libro della matematica Filosofia naturale, restituiva il Prony, <lb/>dopo un secolo ai meritati onori la repudiata semplicit&agrave; della dimostrazion <lb/>neutoniana. </s></p><p type="main">

<s>Nonostante pensarono alcuni che tanta faccenda dei Matematici intorno <lb/>al nobile e insigne Teorema non doveva esser riuscita senza frutto, il quale <lb/>era ben raccogliere sceverato da'bozzacchioni e dalle fronde. </s>

<s>Attendendo <lb/>da una parte a rendere il metodo semplice e facile, e dall'altra a partir da <lb/>principii evidenti, e non complicati con le idee di moto e di tempo, si chie&shy;<lb/>deva principalmente e unicamente si concedesse per vero che la resultante <lb/>divide nel preciso mezzo l'angolo fatto da due componenti uguali. </s>

<s>Chi vuol <lb/>che tutto sia dimostrato pretender&agrave; forse di aver dimostrazione anche di que&shy;<lb/>sto, ma chi pi&ugrave; saviamente ripensa che un punto di partenza &egrave; necessario <lb/>alla possibilit&agrave; logica di ogni discorso, non dubiter&agrave; di concedere il postu&shy;<lb/>lato, dipendente da quell'altro non saputosi ancora negar da nessuno, che <lb/>cio&egrave; la direzion della resultante &egrave; media fra la direzion delle due compo&shy;<lb/>nenti, le quali, se si uguagliano, par dunque evidente che la mediet&agrave; debba <lb/>esser perfetta. </s></p><p type="main">

<s>Dietro ci&ograve; &egrave; manifesto che la resultante delle due forze uguali AB, AC <lb/>(fig. </s>

<s>389) &egrave; diretta secondo la AD, diagonale del rombo CB, e nel modo che <lb/>si dir&agrave; ragionando, facilmente si dimostra che alla stessa AD deve essere <lb/><figure id="id.020.01.3000.1.jpg" xlink:href="020/01/3000/1.jpg"/></s></p><p type="caption">

<s>Figura 389.<lb/>inoltre la detta resultante uguale: Sia, se &egrave; possibile, <lb/>minore. </s>

<s>Divisa tutta la AD in parti uguali, grandi o <lb/>piccole a piacere, come le D<emph type="italics"/>a, ab, bc ....<emph.end type="italics"/> dicasi per <lb/>esempio che la resultante &egrave; A<emph type="italics"/>a.<emph.end type="italics"/> Si inscrivano nel mag&shy;<lb/>gior rombo i rombi EK, FI .... GH: come della A<emph type="italics"/>a<emph.end type="italics"/><lb/>son le componenti AB, AC, cos&igrave; della A<emph type="italics"/>b<emph.end type="italics"/> saranno AE, <lb/>AK, e su su procedendo della resultante, che s'&egrave; gi&agrave; <lb/>in A esaurita, rimarranno le componenti AG, AH, ci&ograve; <lb/>che &egrave; assurdo. </s>

<s>Se poi si dice che la resultante &egrave; mag&shy;<lb/>giore di AD, ragionando in simile modo, e sopr'ana&shy;<lb/>loga costruzione, giungeremo a un'ultima resultante <lb/>senza pi&ugrave; le componenti, altro assurdo manifesto. </s>

<s>Non <lb/>potendo esser dunque la resultante delle forze uguali AB, AC n&egrave; minore n&egrave; <lb/>maggiore di AD, sar&agrave; l'AD stessa, e avremo perci&ograve;, non solamente la dire&shy;<lb/>zione, ma la grandezza altres&igrave; di lei rappresentata dalla diagonale del rombo. </s></p><p type="main">

<s>Di qui concluderemo per la conversa che all'unica AD equivalgono le <lb/>due forze AB, AC, e si potranno all'occorrenza sostituir le une alle altre. </s></p><p type="main">

<s>Da questo corollario, e da quel lemma, vien aperta la via alla dimostra-<pb xlink:href="020/01/3001.jpg" pagenum="626"/>zione, quando le forze son di differente grandezza, e retto o acuto ne sia <lb/>l'angolo del concorso. </s>

<s>Nel primo caso infatti (fig. </s>

<s>390) che rappresenta il <lb/>rettangolo AD, in cui son tirate le diagonali AD, BC, e intorno a cui son <lb/><figure id="id.020.01.3001.1.jpg" xlink:href="020/01/3001/1.jpg"/></s></p><p type="caption">

<s>Figura 390.<lb/>disegnati i rombi EG, FG; chi cercasse la <lb/>resultante X delle due componenti date, la <lb/>troverebbe facilmente osservando che all'una <lb/>AC equivalgono le due forze AE, AG, e al&shy;<lb/>l'altra AB le due AF, AG, onde X= <lb/>AC+AB=AE+AG+AF+AG. </s>

<s><lb/>E perch&egrave; AE, AP sono uguali e contrarie, e <lb/>2AG=AD, dunque X=AD. </s></p><p type="main">

<s>Se poi l'angolo del concorso &egrave; acuto, (fig. </s>

<s>391) e allora, costruiti i ret&shy;<lb/>tangoli EF, HG, sar&agrave;, per l'applicazione del caso precedente, X=AC+AB= <lb/>AF+AE+AG+AH. </s>

<s>E perch&egrave; AE, AH sono uguali e contrarie, e AF= <lb/>GD, sar&agrave; ancora X=AD. </s></p><p type="main">

<s>Diventando l'angolo BAC ottuso si giunge anche in questo caso a con&shy;<lb/>cludere similmente, dietro una omologa costruzione, e perci&ograve; sempre, siano <lb/>le forze uguali o diverse, e con qualunque angolo concorrenti, la resultante <lb/>avr&agrave; direzione e grandezza proporzionali alla diagonale del parallelogrammo <lb/>fatto sulle due componenti. </s></p><p type="main">

<s>Cos&igrave; conducendo la dimostrazione s&igrave; soddisfaceva a coloro, che la vo&shy;<lb/><figure id="id.020.01.3001.2.jpg" xlink:href="020/01/3001/2.jpg"/></s></p><p type="caption">

<s>Figura 391.<lb/>levano indipendente da qualunque idea di <lb/>moto, e dall'altra parte era cos&igrave; semplice e <lb/>facile, da bastare per la piena intelligenza <lb/>di lei le prime nozioni della Geometria. </s>

<s>Tali <lb/>essendo le avventure del Teorema, quando, <lb/>tra il finir del secolo XVII e il cominciar <lb/>del seguente, s'inger&igrave; nella Meccanica nuo&shy;<lb/>va; non ci rimane a dir, secondo il propo&shy;<lb/>sito fatto, che del Calcolo infinitesimale, altro massimo efficiente di quel rin&shy;<lb/>novamento della Scienza. </s></p><p type="main">

<s>Come dalle tradizioni antiche di Pappo e di Archimede derivasse, nel <lb/>nostro Nardi e nel francese Roberval, la dottrina dell'infinito, non &egrave; neces&shy;<lb/>sario ripeterlo a chi ha letto i fatti da noi narrati in questo stesso Tomo. </s>

<s><lb/>Sull'esempio offertogli dalla XXI proposizione del IV libro delle Matemati&shy;<lb/>che collezioni anche il Nardi riguardava le superficie come composte d'in&shy;<lb/>finiti rettangoli, e i solidi rotondi d'infiniti cilindri: di rettangoli cio&egrave; e di <lb/>cilindri, le altezze de'quali fossero minime, o indivisibili come dicevasi al&shy;<lb/>lora. </s>

<s>&Egrave; notabile la definizione data da esso Nardi di questi indivisibili, di&shy;<lb/>cendo tali precise parole, nella sua Quadratura nuova della parabola, da noi <lb/>altrove integralmente trascritte dall'originale: <emph type="italics"/>Dividasi la retta AM in parti <lb/>minime, sicch&egrave;, essendo una di loro AD, manchi DM da AM meno di ogni <lb/>proposta distanza:<emph.end type="italics"/> notabile si diceva, perch&egrave; fa esatto riscontro con i <emph type="italics"/>dif&shy;<lb/>ferenziali<emph.end type="italics"/> leibniziani. </s></p><pb xlink:href="020/01/3002.jpg" pagenum="627"/><p type="main">

<s>L'essere delle parti indivisibili componenti le linee, le superficie e i so&shy;<lb/>lidi, era definito, a quel modo che Pappo suggeriva al Nardi, anche dal Ro&shy;<lb/>berval, il quale cos&igrave; conclude nell'introduzione al suo <emph type="italics"/>Trait&eacute; des indivisibles:<emph.end type="italics"/><lb/>&ldquo; Par tout ce discours on peut comprendre que la multitude infinie de points <lb/>se prend pour une infinit&eacute; de petites lignes, et compose la ligne intiere. </s>

<s>L'in&shy;<lb/>finit&eacute; des lignes represente l'infinit&eacute; des petites superficies qui composent la <lb/>superficie totale. </s>

<s>L'infinit&eacute; des superficies represente l'infinit&eacute; de petites so&shy;<lb/>lides, qui composent ensemble le solide total &rdquo; (<emph type="italics"/>Ouvrages de Matem.<emph.end type="italics"/> cit., <lb/>pag. </s>

<s>209), </s></p><p type="main">

<s>Bench&egrave; il Nardi e il Roberval, non riconoscendo altri Maestri che gli <lb/>antichi, si potessero compiacere di essere stati i primi a istituire il nuovo <lb/>metodo degli indivisibili, concessero nonostante generosamente ambedue le <lb/>prime parti del merito al Cavalieri, il quale si lasci&ograve; incautamente uscir di <lb/>bocca che di punti si compongon le linee, di linee le superficie, e di super&shy;<lb/>ficie i solidi. </s>

<s>Farebbe maraviglia il trovare, dopo le opposizioni di Galileo, <lb/>rimasta questa impropriet&agrave; di linguaggio nel libro della Geometria nuova, se <lb/>non si ripensasse che non avrebbe creduto mai l'Autore d'incontrarsi in let&shy;<lb/>tori tanto indiscreti, e se forse non avesse temuto, col rifare il libro, di per&shy;<lb/>dere l'opportunit&agrave; di dedicarlo a que'signori, padroni suoi di Bologna. </s>

<s>L'in&shy;<lb/>discretezza, a cui si accennava, consisteva nell'interpetrare rigidamente che <lb/>i punti, non aventi nessuna dimensione, potessero generar la linea, e la li&shy;<lb/>nea, con una dimensione sola, la superficie che ne ha due, e la superficie il <lb/>solido, che ne ha tre: del qual rigore indiscreto dava il primo esempio Ga&shy;<lb/>lileo nell'obiezione famosa, tolta dal considerar l'esaustione della scodella in <lb/>un circolo, e del cono inscritto in un punto. </s></p><p type="main">

<s>Dalle risposte fatte, come si narr&ograve; a pag. </s>

<s>123 del Tomo precedente, appa&shy;<lb/>risce chiaro che il Cavalieri negava terminarsi la scodella in un circolo, e il <lb/>cono in un punto, perch&egrave; il punto che genera la linea, e la linea che ge&shy;<lb/>nera la superficie debbono, secondo le sue definizioni, aver ciascuno una di&shy;<lb/>mensione minima, quella di lunghezza e questa di altezza, cosicch&egrave;, venendo <lb/>a mancare un tal minimo elemento da una parte e dall'altra, l'orlo della <lb/>scodella non si riduce a un circolo, n&egrave; l'apice del cono a un punto, ma am&shy;<lb/>bedue svaniscono, e anche nell'evanescenza perci&ograve; sono uguali. </s></p><p type="main">

<s>Che tale fosse veramente il concetto del Cavalieri si dichiara da quelle <lb/>parole scritte in risposta a Galileo, e sopra le quali giova ritornar col pen&shy;<lb/>siero per meditarle: &ldquo; Al suo dubbio della scodella pareami ancora si po&shy;<lb/>tesse risponder cos&igrave;: che nel concetto di tutte le linee d'una figura piana, <lb/>o di tutti i piani di un corpo, non si debbono, secondo le mie definizioni, <lb/>intendere le estreme, bench&egrave; paiano del medesimo genere, poich&egrave; chiamo <lb/>tutte le linee d'una figura piana le comuni sezioni del piano segante la figura <lb/>nel moto fatto da esso da un estremo all'altro, o da una tangente infino al&shy;<lb/>l'opposta tangente. </s>

<s>Ora poi che il principio e termine del moto non &egrave; moto, <lb/>perci&ograve; non si debbono computare le estreme tangenti fra tutte le linee, e <lb/>cos&igrave; non &egrave; maraviglia, intendendo lo stesso per i piani ne'solidi, che questi <pb xlink:href="020/01/3003.jpg" pagenum="628"/>estremi restino diseguali, come nel suo esempio della scodella &rdquo; (Campori, <lb/><emph type="italics"/>Carteggio gal.<emph.end type="italics"/> cit., pag. </s>

<s>422, 423). </s></p><p type="main">

<s>Ecco in queste parole il metodo degli indivisibili, presentato sotto il me&shy;<lb/>desimo aspetto di quello delle <emph type="italics"/>flussioni,<emph.end type="italics"/> che il Newton giusto immagin&ograve; per <lb/>evitar le censure fatte al Cavalieri. </s>

<s>E perch&egrave; l'ultimo termine della flussione <lb/>&egrave; nella evanescenza, come il Newton &egrave; sollecito d'avvertire che la infinita <lb/>piccolezza della quantit&agrave; non si considera, quando &egrave; svanita, perch&egrave; allora &egrave; <lb/>nulla, ma nell'atto della evanescenza; cos&igrave; similmente avverte il Cavalieri <lb/>che il termine del moto non &egrave; moto. </s></p><p type="main">

<s>Se il Newton, togliendosi dal numero degli indiscreti, indovinava questo <lb/>consenso, non avrebbe, per parergli troppo dura, rifiutata l'ipotesi degl'in&shy;<lb/>divisibili, come non la rifiutarono il Torricelli e il Cartesio co'loro nume&shy;<lb/>rosi e valenti seguaci, i quali non si pu&ograve; credere che fossero di cos&igrave; debole <lb/>ingegno, da non conoscere che un punto senza alcuna dimensione, non pu&ograve;, <lb/>nemmeno moltiplicandosi all'infinito, prodursi nella lunghezza di una linea. </s>

<s><lb/>Del proprio senno supponevano que'valentuomini ne partecipassero anche i <lb/>loro lettori, nella mente de'quali perci&ograve; non sospettarono il dubbio che linee <lb/>disegnate a intessere una superficie avessero la sola dimensione della lun&shy;<lb/>ghezza: bench&egrave; quella della larghezza la mettessero cos&igrave; piccola, da non sem&shy;<lb/>brar conveniente il farla apparire, e quasi che col tacerla credessero di si&shy;<lb/>gnificar meglio, e di farne meglio intendere l'incomprensibile piccolezza. </s></p><p type="main">

<s>Al Torricelli e al Cartesio si pu&ograve; aggiungere il Roberval, il quale, bench&egrave; <lb/>avesse dal canto suo scansato ogni occasione alle censure, dichiarava quelle <lb/>fatte al Cavalieri per ingiuste, e le diceva mosse dall'invidia di certi scioli, <lb/>che si metton fra'piedi a'valentuomini per indugiarne i progressi. </s>

<s>La difesa <lb/>&egrave; tanto pi&ugrave; eloquente, in quanto che esso Roberval la faceva, dop'aver detto <lb/>d'essersi gi&agrave; servito degli indivisibili, per risolver non pochi difficilissimi <lb/>problemi, cinque anni prima che il Cavalieri pubblicasse la sua nuova Geo&shy;<lb/>metria. </s>

<s>&ldquo; Illa ergo indivisibilia an ante nos clarissimus Cavalerius invenerit <lb/>nescio: certe illud scio me integro quinquennio, antequam in lucem emise&shy;<lb/>rit, ea doctrina usum fuisse in solvendis multis iisque plane arduis proposi&shy;<lb/>tionibus. </s>

<s>Attamen ergo tanto viro non eripiam, nec possum, nec si possem <lb/>faciam.... Est autem inter clarissimi Cavalerii methodum et nostra exigua <lb/>quaedam differentia. </s>

<s>Ille enim cuiusvis superficiei indivisibilia secundum in&shy;<lb/>finitas lineas, solidi autem indivisibia secundum infinitas superficies conside&shy;<lb/>rat. </s>

<s>Unde ex vulgaribus Geometris plerique, sed et quidam ex superbis illis <lb/>sciolis, qui soli docti haberi volunt, quique si nihil aliud certe hoc unum sa&shy;<lb/>tis habent ut in magnorum Virorum opera insurgant, quod a se minime <lb/>profecta esse invideant; occasionem carpendi Cavalerii arripuerunt, tamquam <lb/>si ille aut superficies ex lineis, aut solida ex superficiebus reyera constare <lb/>vellet &rdquo; (<emph type="italics"/>Epist. </s>

<s>ad Torricellium,<emph.end type="italics"/> Ouvrages cit., pag. </s>

<s>367, 68). </s></p><p type="main">

<s>Che tra que'geometri volgari e fra quegli scioli superbi intendesse il <lb/>Roberval di comprendere Galileo, noi non lo crediamo, ma &egrave; un fatto che <lb/>Galileo fu il primo a cogliere in fallacia il Cavalieri, quasi egli avesse vo-<pb xlink:href="020/01/3004.jpg" pagenum="629"/>luto dire di fatto che le linee constan di punti, come di linee le superficie, <lb/>e di superficie i solidi. </s>

<s>La zizania, sparsa ne'dialoghi delle due nuove Scienze <lb/>da quel nimico uomo del Salviati, crebbe in mezzo alla buona sementa del <lb/>Cavalieri, specialmente per opera del celebre Maclaurin, il quale scrisse con&shy;<lb/>tro la Matematica degli infiniti un libro, che il D'Alembert condann&ograve; col ti&shy;<lb/>tolo di malvagio: <emph type="italics"/>mauvais livre contr&eacute; la certitude de la Geom&eacute;trie.<emph.end type="italics"/></s></p><p type="main">

<s>Insorsero contro queste insane calunnie i Matematici, e mentre da una <lb/>parte ne rimproveravano agramente i colpevoli, si consigliarono dall'altra di <lb/>levarne ogni ooccasione, con usare una maggiore propriet&agrave; di linguaggio, e <lb/>con definire pi&ugrave; precisamente le matematiche ragioni dell'infinito. </s>

<s>Un certo <lb/>Autore, per citar qualche esempio, volle mettersi a commentare l'<emph type="italics"/>Analyse <lb/>des infiniment petits<emph.end type="italics"/> del marchese De l'Hopital, e mand&ograve; a Giovanni Ber&shy;<lb/>noulli, per averne da lui il giudizio, il suo commentario. </s>

<s>Era quell'Autore <lb/>fra il numero de'congiurati ai danni dell'Analisi infinitesimale, non per de&shy;<lb/>liberato animo, ma per ignoranza, e il Bernoulli, fattegli prima notare certe <lb/>espressioni, che suonano troppo dure a un orecchio geometrico, seguitava <lb/>cos&igrave; a dirgli liberamente: &ldquo; Elles jettent pl&ucirc;tot dans l'erreur, et dans le <lb/>prejug&eacute;, ou on est avant que d'etre Geometre, comme si le corps &eacute;toit com&shy;<lb/>pos&eacute; de surfaces, la surface compos&eacute;e de lignes, et la l&igrave;gne compos&eacute;e de <lb/>points: prejuge fort difficile &agrave; d&eacute;truire dans les jeunes gens, et qui les em&shy;<lb/>p&eacute;che de comprendre les d&eacute;monstrations sur les figures geometriques. </s>

<s>Car <lb/>qu'est-ce qui les trouble d'avantage, que quand ils ne savent pas distinguer, <lb/>par exempl&eacute;, la surface d'avec les lignes qui la terminent? </s>

<s>Il ne faudroit <lb/>donc pas se servir de ces facons de parler, qui noutrissent les prejug&eacute;s au <lb/>lieu de les d&eacute;truire &rdquo; (<emph type="italics"/>Opera omnia,<emph.end type="italics"/> T. IV cit., pag. </s>

<s>162). </s></p><p type="main">

<s>Il D'Alembert credeva che anche da un'altra parte derivassero i pre&shy;<lb/>giudizi, dal non essersi cio&egrave; ben definito il concetto delle quantit&agrave; infinita&shy;<lb/>mente piccole, le quali, egli diceva, non sono qualche cosa di reale, come <lb/>dai pi&ugrave; si crede, ma una semplice idea di relazione. </s>

<s>&ldquo; Le methode des infi&shy;<lb/>niment petits n'est autre chose que la m&eacute;thode des raisons premieres et <lb/>dernieres, c'est-a-dire des rapports des limites des quantit&eacute;s finies. </s>

<s>Quan&shy;<lb/>d'on a bien conc&ugrave; l'esprit et les principes de cette Methode, alors il est <lb/>utile de la mettre en usage pour parvenir &agrave; des solutions &eacute;l&eacute;gantes &rdquo; (<emph type="italics"/>Trait&eacute; <lb/>de Dynam.<emph.end type="italics"/> cit., pag. </s>

<s>50). </s></p><p type="main">

<s>In questo stato d'incertezze, di ostacoli e di battaglie, quale da questi <lb/>esempi ci si rappresenta, nel primo quarto e nella prima met&agrave; del secolo; <lb/>era il Calcolo infinitesimale anche nel principio, quando la Meccanica nuova <lb/>cominci&ograve; a chiamarlo in suo aiuto. </s>

<s>Il Newton, trovatoselo innanzi con l'abito <lb/>messogli addosso dal Cavalieri, giudicandolo poco decente, volle da s&egrave; rive&shy;<lb/>stirlo di un abito nuovo. </s>

<s>&ldquo; Contractiores enim redduntur demonstrationes per <lb/>methodum indivisibilium. </s>

<s>Sed quoniam durior est indivisibilium hypothesis, <lb/>et propterea methodus illa minus geometrica censetur; malui demonstratio&shy;<lb/>nes rerum sequentium ad ultimas quantitatum evanescentium summas et <lb/>rationes, primasque nascentium, idest ad limites summarum et rationum de-<pb xlink:href="020/01/3005.jpg" pagenum="630"/>ducere, et propterea limitum illorum demonstrationes, qua potui brevitate, <lb/>praemittere &rdquo; (<emph type="italics"/>Principia Philos.<emph.end type="italics"/> cit., L. I, pag. </s>

<s>80, 81). </s></p><p type="main">

<s>Il Newton dunque cred&egrave; di aver migliorato e corretto il metodo degli <lb/>indivisibili, non riguardando le quantit&agrave; crescenti per apposizione di parti, <lb/>ma per un moto continuo, o per un continuo flusso del punto nel generar <lb/>la linea, della linea nel generare la superficie, della superficie nel generare <lb/>il solido, e dell'angolo per la rotazione di un lato, dalla qual genesi mec&shy;<lb/>canica &egrave; manifesto perch&egrave; venisse al metodo il nome delle <emph type="italics"/>flussioni.<emph.end type="italics"/> Un tal <lb/>metodo per&ograve; non &egrave; in sostanza diverso da quello del Cavalieri, il quale, come <lb/>abbiamo veduto e come si potrebbe notar nel suo libro, ripete spesso i nomi <lb/>di esaustione, di esinanizione e di moto, equivalenti a quelli delle evane&shy;<lb/>scenze, de'limiti, e delle flussioni neutoniane. </s>

<s>Forse nel metodo dell'Inglese <lb/>&egrave; pi&ugrave; unit&agrave; di concetto, e pi&ugrave; matematica precisione, ma l'avere introdotto <lb/>l'elemento straniero del moto, che si fa col tempo, il quale ha la sua mi&shy;<lb/>sura dalla velocit&agrave; e dallo spazio, fece s&igrave; che i processi non si rendessero <lb/>direttamente applicabili altro che alla Geometria, a cui si limitava la istitu&shy;<lb/>zione del Cavalieri. </s>

<s>Dentro questi limiti poi veniva a trattenere e a risospin&shy;<lb/>gere il metodo riformato il principio dominatore di lui, ch'escludeva le quan&shy;<lb/>tit&agrave; assolute, per considerarne solamente la relazione, tanto &egrave; vero che il <lb/>Newton non insegn&ograve; a differenziare altro che equazioni. </s></p><p type="main">

<s>In considerar queste cose si troverebbe forse la norma ai giudizi da <lb/>farsi intorno alle pretese degli Inglesi, per l'invenzione del Calcolo infinite&shy;<lb/>simale. </s>

<s>Ma lasciando le dispute altrui, per passare ai fatti nostri, esaminiamo <lb/>qual uso facesse di quel Calcolo il Newton, e quali vantaggi ne ritraesse per <lb/>dimostrare que'suoi sublimi teoremi di Meccanica nuova: e dall'esame re&shy;<lb/>sulter&agrave; confermato che i vantaggi venuti dallo strumento rifatto erano quelli <lb/>stessi che i precedenti Matematici avevano avuto dall'originale. </s>

<s>Anzi, chi <lb/>paragoni co'trattati robervalliani della Cicloide, e con quegli altri torricel&shy;<lb/>liani delle seconde quadrature delle parabole e dei baricentri, le proposizioni <lb/>scritte nel primo libro dei Principii di Filosofia naturale, non esita a decider <lb/>che la Matematica piglia pi&ugrave; agile, pi&ugrave; largo e pi&ugrave; robusto il volo l&agrave; per <lb/>gl'indivisibili, che qua per le flussioni. </s></p><p type="main">

<s>I Tedeschi hanno senza dubbio maggior merito nell'invenzione, ma <lb/>anch'essi nel pretenderlo sembran troppo dimentichi de'benefizi ricevuti dalle <lb/>prime tradizioni. </s>

<s>Ascoltiamo il Leibniz: &ldquo; L'analyse des infinis est intiere&shy;<lb/>ment differente de la Geometrie des indivisibles de Cavalieri, et de l'Arithme&shy;<lb/>tique des infinis de M. Wallis. </s>

<s>Car cette Geometrie de Cavalieri, qui est <lb/>tres-bornie d'ailleurs, est attach&eacute;e aux figures, ou elle cherch&eacute; les sommes <lb/>des ordonn&eacute;es; et M. </s>

<s>Wallis pour faciliter cette recherche nous donn&eacute; par <lb/>induction les sommes de certains rangs de nombres; au lieu que l'analyse <lb/>nouvelle des infinis ne regarde ni les figures, ni les nombres, mais les gran&shy;<lb/>deurs en general, comme fait la spacieuse ordinaire &rdquo; (<emph type="italics"/>Opera omnia,<emph.end type="italics"/> T. III, <lb/>Genevae 1768, pag. </s>

<s>260, 61). </s></p><p type="main">

<s>Pi&ugrave; proprio &egrave; far tra la Geometria del Cavalieri e l'Analisi infinitesi-<pb xlink:href="020/01/3006.jpg" pagenum="631"/>male la differenza, che &egrave; tra la fanciullezza e la virilit&agrave;, rimanendo sempre <lb/>medesima la persona. </s>

<s>E come di questa medesimezza potrebb'essere una <lb/>prova l'abito che sta bene addosso nelle due varie et&agrave;, solamente a ridurne <lb/>le proporzioni del taglio; cos&igrave; sarebbe prova dell'identit&agrave; de'due metodi <lb/>l'adattarsi proporzionatamente agl'indivisibili le fogge stesse dei differenziali. </s>

<s><lb/>La prova fu fatta dall'Herman sul teorema centrobarico del Guldino, pre&shy;<lb/>messovi per lemma il teorema ugeniano che cio&egrave; la somma de'momenti di <lb/>pi&ugrave; corpi divisi equivale al momento unico di essi corpi insieme, dal loro <lb/>comun centro di gravit&agrave; ponderanti. </s></p><p type="main">

<s>Quanto da quel lemma derivasse facilit&agrave; nelle dimostrazioni che il Nardi, <lb/>il Cavalieri e il Torricelli dettero della Regola guldiniana, si pu&ograve; compren&shy;<lb/>dere dal confrontare que'loro lunghi e laboriosi discorsi con questo, che si <lb/>spedisce cos&igrave; in due parole: Sia AB (fig. </s>

<s>392) l'asse, intorno a cui si ri&shy;<lb/>volge la figura ACFB, per generare il solido rotondo, che s'affalda de'cir&shy;<lb/>coli descritti dai raggi DC, EF, o di tutti gli altri infiniti: cosicch&egrave;, chiamato <lb/>quel solido S; sar&agrave; S=<foreign lang="greek">p</foreign>(DC2+EF2....)=2<foreign lang="greek">p</foreign>(DC.DC/2+EF.EF/2...). <lb/>Ma le quantit&agrave; dentro parentesi son la somma de'momenti delle infinite linee <lb/>ponderose, che s'immaginano concentrate nel loro mezzo, i quali momenti <lb/>sono uguali, pel Teorema ugeniano, al momento che resulta dal moltiplicar <lb/>le dette infinite linee ponderose, ossia la figura F, per la distanza D del <lb/>suo centro di gravit&agrave; dall'asse; dunque S=2<foreign lang="greek">p</foreign>D.F, come per la regola <lb/>del Guldino. <lb/><figure id="id.020.01.3006.1.jpg" xlink:href="020/01/3006/1.jpg"/></s></p><p type="caption">

<s>Figura 392.</s></p><p type="main">

<s>Al corollario, che immediatamente deriva da questa pro&shy;<lb/>posizione, e che dice stare i solidi rotondi in ragion composta <lb/>delle figure genitrici, e delle distanze de'loro centri di gra&shy;<lb/>vit&agrave;, o delle circonferenze da esse distanze, come raggi, descritte <lb/>intorno all'asse della rotazione; si giungerebbe, per la me&shy;<lb/>desima via brevissima, dal teorema del Rocca, secondo il quale <lb/>i solidi S, S&prime; stanno come i momenti dell&egrave; figure F, F&prime; (Tor&shy;<lb/>ricelli, <emph type="italics"/>Op. </s>

<s>Geom.<emph.end type="italics"/> cit., P. II, pag. </s>

<s>76). Ma questi momenti <lb/>sono, secondo il detto Teorema ugeniano, uguali al prodotto <lb/>di quelle stesse figure, e delle distanze D, D&prime; de'loro centri <lb/>di gravit&agrave; dall'asse; dunque S:S&prime;=D.F:D&prime;.F&prime;=2<foreign lang="greek">p</foreign>D.F:2<foreign lang="greek">p</foreign>D&prime;.F&prime;. </s></p><p type="main">

<s>L'Herman sostitu&igrave;, come il Nardi e il Roberval, alle linee genitrici dei <lb/>circoli i rettangoli generatori dei cilindri, le lunghezze de'quali rettangoli <lb/>chiama <emph type="italics"/>y,<emph.end type="italics"/> e le altezze <emph type="italics"/>dx,<emph.end type="italics"/> essendo <emph type="italics"/>x<emph.end type="italics"/> l'asse, cosicch&egrave; la figura F, che re&shy;<lb/>sulta dalla somma di cotesti infiniti rettangoli, verr&agrave; data da <emph type="italics"/>&int;ydx.<emph.end type="italics"/> Essendo <lb/>poi la somma degli infiniti momenti de'rettangoli ponderosi <emph type="italics"/>&int;1/2y2 dy,<emph.end type="italics"/> dun&shy;<lb/>que, chiamata D la distanza del centro di gravit&agrave; della figura dall'asse, sar&agrave; <lb/>D.&int;<emph type="italics"/>ydx<emph.end type="italics"/>=D.F=&int;1/2<emph type="italics"/>y2dx,<emph.end type="italics"/> ossia 2<foreign lang="greek">p</foreign>D.F=&int;<foreign lang="greek">p</foreign><emph type="italics"/>y2dx.<emph.end type="italics"/> Ma questa <lb/>significa la somma degl'infiniti cilindri, che compongono il solido rotondo, <lb/>ossia lo stesso solido rotondo S; dunque S=2<foreign lang="greek">p</foreign>D.P. &ldquo; Figura genitrix <lb/>dicatur F, distantia centri eius gravitatis ab axe rotationis D, ordinata figu-<pb xlink:href="020/01/3007.jpg" pagenum="632"/>rae <emph type="italics"/>y<emph.end type="italics"/> ad axem rotationis, <emph type="italics"/>dx<emph.end type="italics"/> elementum axis, solidum, ex conversione figu&shy;<lb/>rae F circa axem <emph type="italics"/>x,<emph.end type="italics"/> dicatur S, eius elementum <emph type="italics"/>d<emph.end type="italics"/> S. </s>

<s>Quibus positis, per prae&shy;<lb/>sentem propositionem, erit D.F aequale summae momentorum elementorum <lb/>magnitudinis F=&int;1/2<emph type="italics"/>yydx,<emph.end type="italics"/> nam elementum ipsius F est <emph type="italics"/>ydx,<emph.end type="italics"/> et huius <lb/>momentum 1/2<emph type="italics"/>yydx.<emph.end type="italics"/> Sit <emph type="italics"/>p<emph.end type="italics"/> circumferentia circuli, cuius radius est I, et du&shy;<lb/>catur antecedens aequatio in <emph type="italics"/>p,<emph.end type="italics"/> ut fiat <emph type="italics"/>p<emph.end type="italics"/>D.F=&int;1/2<emph type="italics"/>pyydx.<emph.end type="italics"/> Iam <emph type="italics"/>p<emph.end type="italics"/> D est <lb/>circumferentia radii D, et <emph type="italics"/>py<emph.end type="italics"/> circumferentia radii <emph type="italics"/>y,<emph.end type="italics"/> atque adeo. </s>

<s>1/2<emph type="italics"/>pyy<emph.end type="italics"/><lb/>area circuli eiusdem radii <emph type="italics"/>y,<emph.end type="italics"/> et per cousequens 1/2<emph type="italics"/>pyydx<emph.end type="italics"/> cylindrulus so&shy;<lb/>lido S inscriptus, seu eius elementum <emph type="italics"/>d<emph.end type="italics"/> S. </s>

<s>Ergo <emph type="italics"/>p<emph.end type="italics"/>D.F=&int;<emph type="italics"/>d<emph.end type="italics"/>S=S, quod <lb/>erat ostendendum (<emph type="italics"/>Phoron.<emph.end type="italics"/> cit., pag. </s>

<s>15). </s></p><p type="main">

<s>Il libro, in cui si dava questa dimostrazione, era dedicato al Leibniz, in <lb/>quel tempo che pi&ugrave; calorosamente i connazionali di lui agitavano la questione <lb/>con i connazionali del Newton, intorno a chi si dovesse de'due grandi uo&shy;<lb/>mini dir primo inventore del Calcolo infinitesimale. </s>

<s>L'Herman volle forse <lb/>insinuare che l'invenzione era pi&ugrave; antica, e che, essendo stata gi&agrave; fatta, non <lb/>era maraviglia che per opera del Newton e del Leibniz, l'uno inconsapevole <lb/>dell'altro, avesse nel medesimo tempo presa un'educazione diversa. </s>

<s>Se non <lb/>fu questa l'intenzione dell'Herman difficilmente si spiegherebbe com'egli in&shy;<lb/>tegrasse gli elementi delle figure genitrici de'solidi rotondi, riguardando le <lb/>ordinate <emph type="italics"/>y<emph.end type="italics"/> come tutte invariabili, ci&ograve; che renderebbe dimostrativa la propo&shy;<lb/>sizione solamente nel caso che il solido generato dalla figura fosse un cilin&shy;<lb/>dro: e dall'altra parte si vedeva impossibile l'integrare le dette ordinate, <lb/>variabili senz'alcuna legge, come nelle figure irregolari. </s>

<s>Il solo pensiero di <lb/>queste variabili, che in un medesimo termine possono esser pi&ugrave; d'una, e le <lb/>regole ritrovate per differenziarle e integrarle nelle serie ordinate, bastava per <lb/>far comprendere quanto avesse progredito l'Analisi nuova sopra il Metodo <lb/>degl'indivisibili, e perci&ograve; l'Herman, nello Scolio all'XI proposizione, si con&shy;<lb/>tenta di dare un'idea della istituzion leibniziana con qualche esempio, accen&shy;<lb/>nando come quella stessa ardua istituzione dipendeva dal seguente principio <lb/>semplicissimo, e che parrebbe a primo aspetto di nessun uso: &ldquo; Si fuerint <lb/>quotcumque decrescentes magnitudines A, B, C, D, F, erunt omnium differen&shy;<lb/>tiae simul sumptae aequales excessui maximae supra minimam &rdquo; (<emph type="italics"/>Phoron.<emph.end type="italics"/> cit., <lb/>pag. </s>

<s>37). </s></p><p type="main">

<s>L'intenzione di scrivere, non per i Geometri provetti ma per i giovani <lb/>principianti, al genio de'quali pi&ugrave; che le algebriche par che s'addicano le <lb/>dimostrazioni lineari, fu cagione che l'Herman cos&igrave; sobriamente usasse il <lb/>Calcolo infinitesimale, e questo con metodi, che s'avvicinavano in qualche <lb/>modo ai geometrici del Cavalieri. </s>

<s>L'uso esteso, continuo e sicuro di quello <lb/>stesso Calcolo, che parve essere divenuto la ruota maestra del carro, inco&shy;<lb/>minci&ograve; a farsi da'successori, i progressi de'quali, che ora ci rimangono a <lb/>esaminare, si rassomigliavano al moto del sangue nelle arterie, che succede <lb/>a quel delle vene, raccolto e vivificato, come nel ventricolo del cuore, nella <lb/>Foronomia del Matematico di Basilea. </s></p><pb xlink:href="020/01/3008.jpg" pagenum="633"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Nel 1736 usciva in Pietroburgo alla luce, dalla tipografia dell'Accade&shy;<lb/>mia delle Scienze, un'Opera in due tomi, nel titolo de'quali prometteva l'Au&shy;<lb/>tore che s'esporrebbe la Meccanica in una maniera affatto nuova. <emph type="italics"/>Mechanica, <lb/>sive motus scientia, analytice exposita, auctore Leonhardo Eulero.<emph.end type="italics"/> In che <lb/>consista la novit&agrave; promessa lo scopre facilmente il Lettore, il quale non aveva <lb/>avuto fin allora tra mano che il Newton e l'Herman, a solamente svolgere <lb/>le nuove pagine, cos&igrave; magre di parole e tutte infarcite de'segni proprii al&shy;<lb/>l'analisi algebrica, ma principalmente alla infinitesimale. </s>

<s>In vent'anni s'&egrave; <lb/>fatto un gran cambiamento d'idee intorno al modo pi&ugrave; conveniente di trat&shy;<lb/>tare la Scienza. </s>

<s>L'Herman avvertiva, nella prefazione alla Foronomia, di aver <lb/>segu&igrave;to il metodo geometrico, perch&egrave; col benefizio di lui <emph type="italics"/>multa elegantius <lb/>obtinentur, quam calculis analyticis,<emph.end type="italics"/> mentre l'Eulero professava che senza <lb/>i calcoli analitici &egrave; impossibile affatto aver delle propriet&agrave; del moto chiara <lb/>cognizione e distinta. </s>

<s>Ascoltiamo le sue proprie parole, scritte nella prefa&shy;<lb/>zione, subito dop'aver commemorati l'Herman e il Newton, ne'libri de'quali <lb/>diceva non si trovar la Meccanica se non che sinteticamente trattata col me&shy;<lb/>todo degli antichi. </s>

<s>&ldquo; Sed quod omnibus scriptis, quae sine analysi sunt com&shy;<lb/>posita, id potissimum Mechanicis obtingit ut lector, etiamsi de veritate eo&shy;<lb/>rum quae proferuntur convincatur, tamen non satis claram et distinctam <lb/>eorum coguitionem assequatur, ita ut easdem quaestiones, si tantillum immu&shy;<lb/>tentur, proprio marte vix resolvere valeat, nisi ipse in analysim inquirat, <lb/>easdemque propositiones analytica methodo evolvat. </s>

<s>&rdquo; </s></p><p type="main">

<s>Per verit&agrave; l'esperienza fatta sopra noi stessi sembrerebbe che provasse <lb/>tutto il contrario. </s>

<s>Abbiamo anche noi da giovani imparato la Meccanica <emph type="italics"/>ana&shy;<lb/>lytice exposita:<emph.end type="italics"/> eppure dobbiamo ingenuamente confessare di non esserci <lb/>fatta un'idea chiara delle particolari propriet&agrave; dei moti, se non da poi che <lb/>le vedemmo dimostrate ne'libri del Torricelli, dell'Huyghens, del Newton, <lb/>dell'Herman, con i sintetici metodi antichi. </s>

<s>I moderni pedagogisti poi con&shy;<lb/>fermano che questo s'&egrave; confessato da noi avviene in tutti gli altri per legge <lb/>di natura, dietro l'osservazione, dalla quale stabiliscono per regola doversi la <lb/>mente dell'alunno dai particolari far risalire alla notizia degli universali. </s>

<s>Tale <lb/>anzi &egrave; il processo della mente umana nell'acquisto di qualunque genere di <lb/>cognizioni, come questa nostra, e ogni altra storia delle Scienze chiaramente <lb/>ci dimostra. </s></p><p type="main">

<s>Dalle sensate osservazioni, e non gi&agrave; da'sistemi de'Filosofi, si scopre <lb/>questo esser vero: che cio&egrave; nell'universale, incompreso ancora e incosciente, <lb/>vediamo i particolari, i quali poi ci fanno per riflessione risalire a compren&shy;<lb/>dere, e ad aver chiara e distinta scienza dell'universale. </s>

<s>Nello spazio etereo, <lb/>fuor d'ogni vista degli oggetti terreni, l'occhio &egrave; in mezzo ai raggi del sole, <pb xlink:href="020/01/3009.jpg" pagenum="634"/>eppure ei non se ne avvede, e non s'avvede della presenza del solo stesso, <lb/>se non che quando riflette que'suoi raggi da qualche parte, tanto pi&ugrave; facen&shy;<lb/>done la rivelazion luminosa, quanto &egrave; pi&ugrave; largo e costipato il campo delle <lb/>riflessioni. </s>

<s>I particolari perci&ograve; non formano la vera scienza, la quale consi&shy;<lb/>ste nel veder com'essi dipendano da quell'universale, che per mezzo loro <lb/>s'&egrave; saputo riconoscere, e s'&egrave; potuto contemplare. </s></p><p type="main">

<s>Par che volesse intendere ci&ograve; l'Euler, quando diceva che non si possono <lb/>risolvere le questioni meccaniche, se co'metodi analitici la mente non le <lb/>svolge. </s>

<s>La notizia de'vari teoremi spicciolati non fa il Matematico, come la <lb/>notizia de'vari individui, o animali o piante o minerali, non fa il Naturali&shy;<lb/>sta. </s>

<s>Osservano diligentemente gli studiosi della Natura in quali caratteri con&shy;<lb/>vengano pi&ugrave; individui, e ne forman le specie, i generi e le classi, in che ri&shy;<lb/>conoscono poi le particolari propriet&agrave; degl'individui stessi. </s>

<s>E come, senza <lb/>aver fatto prima questo ordinamento, al veder qualche nuovo organo acci&shy;<lb/>dentalmente sopravvenuto in una pianta, non saprebbe il Botanico pi&ugrave; qua&shy;<lb/>lificarla; cos&igrave;, dice l'Eulero, se un tantin si rimovano le condizioni a un pro&shy;<lb/>blema, la mente nel risolverlo si trova impacciata. </s></p><p type="main">

<s>Questo discorso per&ograve; non sembra che si possa giustamente applicare al <lb/>Newton e all'Herman, i quali sempre ebbero per principale intento di risa&shy;<lb/>lire alle generalit&agrave;, dalle quali le particolari questioni, trattate da Galileo e <lb/>dall'Huyghens, si facevano scendere, come semplici corollari. </s>

<s>Si direbbe che <lb/>l'Eulero facesse essenzialmente consistere il metodo analitico nel calcolo, con&shy;<lb/>fondendo l'opera con lo strumento. </s>

<s>Se sia giusta l'accusa contro un tant'uomo, <lb/>forse molti ne dubiteranno, ma &egrave; un fatto che, dopo lui, tanto s'incominci&ograve; <lb/>ad esagerare la potenza del calcolo, da farlo prevalere al raziocinio e all'espe&shy;<lb/>rienza. </s>

<s>Gli esageratori per&ograve; sempre hanno male interpetrate le parole, che <lb/>citano con grand'enfasi dallo stesso Eulero: <emph type="italics"/>quidquid autem sit, hic calculo <lb/>potius quam nostro iudicio est fidendum,<emph.end type="italics"/> e la mala interpetrazione consi&shy;<lb/>ste nel farle cos&igrave; sonare fuori del loro contesto, e contro l'intenzion dell'Au&shy;<lb/>tore. </s>

<s>Chi legge il passo intero, com'&egrave; scritto nel primo tomo della Mecca&shy;<lb/>nica analitica, al secondo Scolio dopo la XXXV proposizione, trova esser <lb/>diversa, e pi&ugrave; con la verit&agrave; conforme, la sentenza. </s>

<s>Si propone ivi l'Autore <lb/>di trovare la velocit&agrave; in ogni punto del viaggio di un corpo, attratto con <lb/>qualunque ragion di forze al suo centro, e il calcolo porta che, giunto il <lb/>mobile in esso centro con velocit&agrave; infinita, non pu&ograve; proseguire oltre nella <lb/>medesima direzione. </s>

<s>La conseguenza sembra senza dubbio, dice l'Eulero, assai <lb/>strana, ma comunque sia, poi soggiunge, <emph type="italics"/>&ldquo; hic calculo potius quam nostro <lb/>iudicio est fidendum, atque statuendum nos saltum, si sit ex infinito in <lb/>finitum, penitus non comprehendere &rdquo;<emph.end type="italics"/> (pag. </s>

<s>108). </s></p><p type="main">

<s>La sentenza dunque euleriana non &egrave; assoluta, ma da pronunziarsi so&shy;<lb/>lamente col&agrave;, dove si tratti di un trapasso dal finito all'infinito, che per noi <lb/>&egrave; incomprensibile. </s>

<s>Ma come, si dir&agrave;, &egrave; incomprensibile l'infinito matematico <lb/>all'ingegno dell'uomo, se egli &egrave; che lo crea? </s>

<s>Si risponde che non si tratta <lb/>dell'infinito in s&egrave; stesso, ma del giudizio che si fa di lui, trapassando alle <pb xlink:href="020/01/3010.jpg" pagenum="635"/>cose finite. </s>

<s>Noi non siamo avvezzi a vedere i corpi cadere, che per uno spa&shy;<lb/>zio determinato, e giunto a un termine, con una certa velocit&agrave;, non si du&shy;<lb/>bita se, non essendo impedito, proseguirebbe oltre nella medesima direzione <lb/>il suo viaggio. </s>

<s>Ci&ograve; che avverrebbe per&ograve;, quando quella velocit&agrave; fosse infinita, <lb/>non si pu&ograve;, dice l'Eulero, giudicare da noi, che non abbiamo veduto mai <lb/>andare un corpo con velocit&agrave; infinita. </s>

<s>Il mondo creato dal calcolo &egrave; molto <lb/>diverso da questo mondo reale, e si governa con altre leggi, che il calcolo <lb/>solo, avendole create, ha il diritto d'interpetrare. </s>

<s>Ecco in quali casi esso cal&shy;<lb/>colo prevale all'esperienza nostra e al nostro giudizio! onde il fallo di molti <lb/>consiste nell'aver dato all'Analisi la medesima potenza sopra le quantit&agrave; al&shy;<lb/>gebriche, e sopra le infinitesimali; e nell'aver creduto che risegga in essa <lb/>la virt&ugrave; di partecipare la verit&agrave; a tutti i nostri discorsi. </s>

<s>Se fu l'Euler che <lb/>pose il lubrico di cadere in queste fallacie, si deve dir per&ograve; che cautamente <lb/>trattenne sull'orlo il piede, bench&egrave; anch'egli s'illuse, credendo che le solu&shy;<lb/>zioni generali de'vari problemi di Meccanica, ottenute per via dell'analisi, <lb/>equivalessero alla generalit&agrave; di quei principii, che, premostrati da lui, si vol&shy;<lb/>sero a ricercare i suoi successori. </s></p><p type="main">

<s>Stava infatti da alquanti anni sollevato innanzi all'ammirazione de'Matema&shy;<lb/>tici questo grande edifizio della Meccanica euleriana, e nonostante il D'Alem&shy;<lb/>bert lamentava che si fosse pensato piuttosto a sollevare il fastigio della gran <lb/>mole, che a dare al fondamento di lei la stabilit&agrave; conveniente. </s>

<s>I principii, <lb/>ne'quali consiste un tal fondamento, sono, diceva <emph type="italics"/>&ldquo; ou obseurs par eux&shy;<lb/>memes, ou &eacute;nonc&eacute;s et d&eacute;monstr&eacute;s d'une maniere obscure &rdquo;<emph.end type="italics"/> (<emph type="italics"/>Trait&eacute; de <lb/>Dinam. </s>

<s>cit., Discours prelim.,<emph.end type="italics"/> pag. </s>

<s>IV). &Egrave; necessario perci&ograve;, soggiungeva, <lb/>stabilire la scienza sopra principii semplici e chiari. </s>

<s>Ma se ci&ograve; solo baste&shy;<lb/>rebbe a chi volesse confermare i teoremi della Meccanica, fin qui dimostrati, <lb/>non basta per&ograve; a chi attenda insieme a provvedere ai progressi di lei, e perci&ograve; <lb/>vogliono que'principii inoltre essere scelti tali, da accomodarsi ai nuovi usi, <lb/>e rifiutar quelli, che inutilmente vi si fossero introdotti. </s></p><p type="main">

<s>Ai tempi del D'Alembert, cio&egrave; verso la met&agrave; del secolo XVIII, non s'era <lb/>ancora ricomposta con pace una gran questione, incominciata fra i Matema&shy;<lb/>tici a'principii del secolo, intorno alle ragioni del misurare le forze, che di&shy;<lb/>stinguevano in <emph type="italics"/>morte<emph.end type="italics"/> e <emph type="italics"/>vive:<emph.end type="italics"/> questione, alla quale si dava grande impor&shy;<lb/>tanza, ma che lo stesso D'Alembert riponeva nel numero delle altre cose inu&shy;<lb/>tili alla Meccanica. <emph type="italics"/>&ldquo; La question de la mesure des forces est intierement <lb/>inutile &agrave; la M&eacute;chanique, et meme sans aucun obiet r&eacute;el &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>XXIV). <lb/>La sentenza in conclusione &egrave; giusta, ma perch&egrave; tale non potrebbe apparire <lb/>a chi cos&igrave; asciuttamente se l'udisse pronunziare, giova ridursi alla memoria <lb/>il commento storico, relativo alle forze vive, e alla pi&ugrave; giusta ragione del <lb/>misurarle. </s></p><p type="main">

<s>Ripensando il Leibniz alle contrariet&agrave;, alle quali era andata soggetta la <lb/>verissima teoria ugeniana del centro delle oscillazioni, scopri che dipende&shy;<lb/>vano da una fallacia de'contradittori, la quale consisteva nel misurare per <lb/>la quantit&agrave; di moto il grado e l'intensit&agrave; di qualunque forza. </s>

<s>Ma altro &egrave;, <pb xlink:href="020/01/3011.jpg" pagenum="636"/>diceva, la forza, che opera con semplice conato, come nella libbra, altro &egrave; <lb/>la forza, che produce un moto attuale, come nella percossa di un cadente da <lb/>maggiore o minore altezza. </s>

<s>Concedasi, soggiungeva il Leibniz, che in ambedue <lb/>i casi la quantit&agrave; di moto, ossia la forza, sia misurata dal prodotto della <lb/>massa per lo spazio passato, ma perch&egrave; nella libbra, dove la forza &egrave; morta, <lb/>esso spazio sta come la velocit&agrave;, e nel cadente, dove la forza &egrave; viva, sta <lb/>come il quadrato della velocit&agrave;; dunque &egrave; falso che dal prodotto della massa <lb/>per la velocit&agrave; si possa, come alcuni fanno, misurare allo stesso modo la <lb/>forza morta e la viva. </s>

<s>Il principio cartesiano perci&ograve;, che tanta forza ci vuole <lb/>a sollevare un peso di una libbra a due gradi di altezza, quanto a sollevare <lb/>a un grado solo il peso di due libbre, non vale che per le macchine in equi&shy;<lb/>librio. </s>

<s>Ma negli altri casi, diceva il Leibniz, essendo una verit&agrave; gi&agrave; dimo&shy;<lb/>strata da Galileo, e confermata dall'Huyghens, <emph type="italics"/>Corpus cadens ex certa al&shy;<lb/>titudine acquirere vim eousque rursus assurgendi, uti in pendulorum motu <lb/>evidens est;<emph.end type="italics"/> la vera regola, da sostituirsi alla cartesiana, &egrave; questa: <emph type="italics"/>Tanta <lb/>vi aptus est ad elevandum corpus A unius librae ad altitudinem quatuor <lb/>ulnarum, quanta opus est ad elevandum corpus B quatuor librarum <lb/>usque ad altitudinem unius ulnae.<emph.end type="italics"/></s></p><p type="main">

<s>Annunziava serenamente il Leibniz agli amatori della verit&agrave; queste cose, <lb/>negli atti degli Eruditi di Lipsia del mese di Marzo 1686. Ma quel Catelan, <lb/>oppositore dell'Huyghens, che vedeva cos&igrave; essere sottilmente scoperta l'ori&shy;<lb/>gine delle sue fallacie, fieramente se ne risent&igrave;, e si risent&igrave; insieme con lui <lb/>Dionigi Papin, appartenente alla setta dei Cartesiani. </s>

<s>Si conosceva bene che <lb/>in ambedue i fumi dell'orgoglio eran saliti a far velo al giudizio, e perch&egrave; <lb/>il Leibniz, vedendo scendere cos&igrave; chiara la conclusione dai premessi princi&shy;<lb/>pii. </s>

<s>non s'era dato troppa cura di confermarla con altri argomenti, vi s'ap&shy;<lb/>plic&ograve; sollecitamente Giov. </s>

<s>Bernoulli, dimostrando che se un corpo, con un <lb/>grado di velocit&agrave;, tende un elastro, con due gradi ne tende quattro, con tre <lb/>nove, e cos&igrave; di seguito, d'onde ne concludeva <emph type="italics"/>vires corporum aequalium <lb/>csse in duplicata ratione celeritatum,<emph.end type="italics"/> come comunic&ograve; per lettera al Wolf, <lb/>il quale, nel secondo tomo degli Elementi di Matematica universale, pubblico <lb/>la nuova bernulliana dimostrazione. (Genevae 1746, pag. </s>

<s>62). </s></p><p type="main">

<s>Il Leibniz intanto era entrato nell'agone a difendersi contro i suoi ne&shy;<lb/>mici, e specialmente contro il Papin, a cui raccomandava di meditar meglio <lb/>come stavan le cose. </s>

<s>Prese di questo modo di procedere tanta maraviglia il <lb/>nostro Poleni, che volle consigliare lo stesso Leibniz d'usar co'caparbi non <lb/>parole ma fatti. </s>

<s>Se i quadrati delle velocit&agrave; son la vera misura delle forze vive <lb/>debbono, diceva, mostrarcelo le esperienze, e ripensando al miglior modo di <lb/>farle, trov&ograve; questo, che poi descrisse nel suo libro <emph type="italics"/>De Castellis,<emph.end type="italics"/> pubblicato <lb/>in Padova nel 1718. Prese un vaso pieno di sego rappreso, sulla piana su&shy;<lb/>perficie del quale fece, da due fili, pender due globi di ugual volume, ma <lb/>l'uno peso il doppio dell'altro, e cos&igrave; disposti, che il pi&ugrave; leggiero rimanesse <lb/>dal sego stesso distante il doppio. </s>

<s>Tagliate le sospensure, i globi caddero, e <lb/>scavarono nella cedente materia sottoposta due callotte, che si trovarono <pb xlink:href="020/01/3012.jpg" pagenum="637"/>uguali. </s>

<s>Ripetuta l'esperienza pi&ugrave; volte, col variare i pesi e le altezze delle <lb/>cadute, dietro la costanza de'resultati ottenuti cred&egrave; il Poleni doversi con&shy;<lb/>cludere in generale: &ldquo; Tunc aequales vires corporum cadentium esse, cum <lb/>ipsorum propria pondera rationem habent reciprocam eius, quam habent <lb/>spatia ab iisdem corporibus cadendo emensa &rdquo; (pag. </s>

<s>57). Cosicch&egrave;, chiamate <lb/>F, <emph type="italics"/>f<emph.end type="italics"/> le forze, P, <emph type="italics"/>p<emph.end type="italics"/> i pesi, e A, <emph type="italics"/>a<emph.end type="italics"/> le altezze, le quali stanno come i quadrati <lb/>delle velocit&agrave; V, <emph type="italics"/>v;<emph.end type="italics"/> l'equazione F:<emph type="italics"/>f<emph.end type="italics"/>=PV2:<emph type="italics"/>pv2,<emph.end type="italics"/> che resulta dalla espe&shy;<lb/>rienza, conferma pienamente la teoria leibniziana. </s></p><p type="main">

<s>Piacque allo 's Gravesande cos&igrave; la bella e nuova esperienza del Poleni, <lb/>che costru&igrave; per ripeterla quello strumento di precisione, ch'ei descrisse nel <lb/>capitolo terzo del secondo libro de'suoi Elementi di fisica matematica, sotto <lb/>il titolo di &ldquo; Machina, qua corporum directe cadentium vires conferuntur &rdquo; <lb/>(<emph type="italics"/>Physices elem. </s>

<s>mathem.,<emph.end type="italics"/> T. I, Leidae 1748, pag. </s>

<s>235). Consisteva in una <lb/>cassetta parallelepipeda di legno, piena rasa fino all'orlo di molle argilla, <lb/>sugli angoli della quale cassetta quattro ritti formavano come due spalliere <lb/>di seggiola, sulle traverse delle quali, poste a uguali distanze, s'appoggia&shy;<lb/>vano regoli per sostenere i pesi, d'onde poi si lasciavan cadere, penetrando <lb/>nella sottoposta mollizie pi&ugrave; o meno, secondo il maggiore o minor impeto <lb/>delle cadute. </s>

<s>Que'pesi constavano di tre globi di rame d'un pollice e mezzo <lb/>di diametro ciascuno, composti di emisferi, che si ricongiungano a vite, ma <lb/>le loro diverse gravit&agrave; stanno come uno, due, e tre. </s>

<s>Eseguitasi pi&ugrave; volte <lb/>l'esperienza, da altezze diverse, result&ograve; in generale, come al Poleni, che le <lb/>cavit&agrave; non differivano, &ldquo; quando altitudines sunt inverse ut massae, in quo <lb/>casu vires sunt aequales &rdquo; (ibid., pag. </s>

<s>237). </s></p><p type="main">

<s>Vincenzo Riccati ridusse all'analisi matematica queste esperienze dello <lb/>'s Gravesande e del Poleni. </s>

<s>Si chiamino <emph type="italics"/>m,<emph.end type="italics"/> M le masse, <emph type="italics"/>c,<emph.end type="italics"/> C le celerit&agrave; ini&shy;<lb/>ziali degli scavamenti: <emph type="italics"/>r,<emph.end type="italics"/> R le resistenze della materia molle, o argila, o sego, <lb/><emph type="italics"/>n,<emph.end type="italics"/> N le profondit&agrave; delle fosse scavate. </s>

<s>Dalle note formole <emph type="italics"/>m<foreign lang="greek">f</foreign>ds=mudu,<emph.end type="italics"/><lb/>M<foreign lang="greek">f</foreign><emph type="italics"/>d<emph.end type="italics"/>S=MV<emph type="italics"/>d<emph.end type="italics"/>V, osservando che <emph type="italics"/>m<foreign lang="greek">f</foreign>=&mdash;rn,<emph.end type="italics"/> M<foreign lang="greek">f</foreign>=&mdash;R.N, per es&shy;<lb/>sere le forze delle resistenze ritardatrici, avremo <emph type="italics"/>rnds=&mdash;mudu,<emph.end type="italics"/> RN<emph type="italics"/>d<emph.end type="italics"/>S= <lb/>&mdash;MV<emph type="italics"/>d<emph.end type="italics"/>V, le quali integrate danno </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>rns<emph.end type="italics"/>=&mdash;<emph type="italics"/>m(u2<emph.end type="italics"/>/2+P), RNS=&mdash;M(V2/2+Q).<emph.end type="center"/><lb/>Per determinare le costanti P, Q osserviamo che, quando <emph type="italics"/>u,<emph.end type="italics"/> V sono uguali <lb/>a <emph type="italics"/>c,<emph.end type="italics"/> C, le quantit&agrave; <emph type="italics"/>s,<emph.end type="italics"/> S divengono zero, e perci&ograve; <emph type="italics"/>rns=(mc2&mdash;mu2<emph.end type="italics"/>)/2, RNS= <lb/>(MC2&mdash;MV2)/2. Ma quando <emph type="italics"/>u,<emph.end type="italics"/> V sono zero, <emph type="italics"/>s,<emph.end type="italics"/> S tornano uguali a uno; dunque <lb/><emph type="italics"/>rn<emph.end type="italics"/>:RN=<emph type="italics"/>mc2<emph.end type="italics"/>:MC2. </s>

<s>&ldquo; Ecco pertanto, ne conclude il Riccati, che la pro&shy;<lb/>fondit&agrave; delle fosse per la costante resistenza moltiplicata, che altro non &egrave; se <lb/>non l'effetto che si vede e che si tocca con mano, riesce proporzionale alla <lb/>massa, e al quadrato della velocit&agrave; &rdquo; (<emph type="italics"/>Dialogo delle forze vive<emph.end type="italics"/> cit., pag. </s>

<s>49). </s></p><p type="main">

<s>Tutto questo faticar dunque di speculazioni, d'esperienze e di calcoli, di <pb xlink:href="020/01/3013.jpg" pagenum="638"/>cui i citati da noi non son che pochissimi esempi, diceva il D'Alembert non <lb/>ebbe altro scopo che di risolvere una question di parole, e perci&ograve; affatto inu&shy;<lb/>tile alla Meccanica, per le seguenti ragioni: Chi misura l'intensit&agrave; di una <lb/>forza dalla velocit&agrave;, che imprime in un corpo, mette in considerazione piut&shy;<lb/>tosto l'effetto che l'intrinseca causa, essendo chiaro che quel corpo va pi&ugrave; <lb/>o meno veloce, secondo il maggiore o minor numero degli ostacoli, che in&shy;<lb/>contra nel suo viaggio. </s>

<s>Ora questi ostacoli possono essere o insuperabili <lb/>affatto, o tali che facciano la resistenza precisamente necessaria ad arrestare <lb/>per un momento il moto, come nel caso dell'equilibrio, o tali finalmente, da <lb/>impedire al mobile il corso a poco a poco, come ne'moti ritardati. </s>

<s>I primi <lb/>dei detti ostacoli &egrave; chiaro che non possono servire a misurare la forza, che <lb/>da essi stessi &egrave; distrutta, ma quanto agli altri, &ldquo; tout le monde, dice il <lb/>D'Alembert, convient qu'il y a &eacute;quilibre entre doux corps, quand les pro&shy;<lb/>duits de leurs masses par leurs vitesses virtuelles, c'est-&agrave;-dire par les vi&shy;<lb/>tesses avec lesquelles ils tendent &agrave; se mouvoir, sont &eacute;gaux de part et d'au&shy;<lb/>tre. </s>

<s>Donc dans l'&eacute;quilibre le produit de la masse par la vitesse, ou, ce qui <lb/>est la m&ecirc;me chose, la quantit&eacute; de mouvement, peut repr&eacute;senter la force. </s>

<s><lb/>Tout le mond convient aussi que dans le mouvement retard&eacute; le nombre des <lb/>obstacles vaincus est comme le quarr&eacute; de la vitesse.... d'ou les partisans <lb/>des forces vives concluent que la force des corps, qui se meuvent actuelle&shy;<lb/>ment, est en g&eacute;n&eacute;ral comme le produit de la masse par le quarr&eacute; de la vi&shy;<lb/>tesse &rdquo; (pag. </s>

<s>XX). A che disputar dunque di cose, dice il D'Alembert, di <lb/>cui tutto il mondo-conviene? </s></p><p type="main">

<s>La conclusione in sostanza &egrave; giusta, e tutti que'valentuomini, che in&shy;<lb/>torno al misurar le forze esercitarono l'ingegno e la mano, avrebbero fatto <lb/>cosa inutile davvero, quando, essendo tutti i Matematici concordi nell'ammet&shy;<lb/>tere i principii, avessero anche ugualmente concordato nella logica delle con&shy;<lb/>seguenze. </s>

<s>Ma perch&egrave; non avvenne cos&igrave;, ecco qual si fu la ragione, il merito <lb/>e l'utilit&agrave; del disputare. </s>

<s>Che del resto, ne'precisi termini del D'Alembert, <lb/>aveva alquanti anni prima ridotta la questione il Wolf, il quale, in due di&shy;<lb/>stinti teoremi, che sono il XXXVI e il XLIX degli elementi di Meccanica, <lb/>nel citato secondo tomo della Matematica universale, aveva dimostrato che <lb/>le forze morte e le vive stanno in ragion composta delle masse, e delle sem&shy;<lb/>plici velocit&agrave; quelle, ma de'quadrati delle velocit&agrave; queste, concludendo che <lb/>facevano le dimostrate verit&agrave; contro coloro &ldquo; qui promiscue vires omnes in <lb/>ratione composita massarum et velocitatum esse statuunt &rdquo; (pag. </s>

<s>61): errore, <lb/>soggiungeva, che fu primo il Leibniz a scoprire e ad emendare. </s></p><p type="main">

<s>Se poi sia vero quel che dice il D'Alembert, che cio&egrave; per questo fatto <lb/>esso Leibniz &ldquo; a cru pouvoir se faire honneur comme d'une d&eacute;couverte &rdquo; <lb/>(pag. </s>

<s>XVII) non possiamo dir niente, ma sappiamo di certissimo che la sco&shy;<lb/>perta era stata fatta da pi&ugrave; di un mezzo secolo in Italia. </s>

<s>Il primo infatti a <lb/>commettere l'errore di misurar promiscuamente, con una medesima regola, <lb/>le forze morte e le vive, fu Galileo, seguito poi dal Viviani, quando intesero <lb/>ambedue concordi d'assegnar la proporzione tra gli effetti de'pesi morti e <pb xlink:href="020/01/3014.jpg" pagenum="639"/>delle percosse: errore, che non fu scoperto n&egrave; emendato dal Leibniz, ma dal <lb/>Borelli, il quale osserv&ograve; che le semplici gravit&agrave; e gl'impeti son due cose di <lb/>genere diverso, come di genere diverso, e perci&ograve; non comparabili insieme, <lb/>sono i moti uniformi e gli accelerati (<emph type="italics"/>De vi percuss.,<emph.end type="italics"/> Cap. </s>

<s>XXXIII). Pi&ugrave; de&shy;<lb/>cisiva era stata la questione rispetto ai liquidi, le velocit&agrave; de'quali nel fluire <lb/>da'vasi erano da Galileo e dal Castelli misurate proporzionalmente alle al&shy;<lb/>tezze morte, ma il Torricelli dimostr&ograve; che dovevano essere invece propor&shy;<lb/>zionali alle radici delle altezze vive. </s>

<s>&Egrave; notabile a questo proposito un teo&shy;<lb/>rema dell'Herman, in cui stare gl'impeti de'liquidi erompenti dai fori in <lb/>ragion composta delle moli e de'quadrati delle velocit&agrave; si conclude dalla nota <lb/>proposizion del Castelli, che le quantit&agrave; son proporzionali alle velocit&agrave; mol&shy;<lb/>tiplicate per le sezioni. </s>

<s>Or perch&egrave; gl'impeti son misurati dal prodotto delle <lb/>quantit&agrave; per le velocit&agrave; respettive, &egrave; manifesto che stanno in ragion compo&shy;<lb/>sta delle sezioni, ossia delle moli liquide in esse comprese, e de'quadrati delle <lb/>velocit&agrave;. </s>

<s>Pi&ugrave; notabile poi &egrave; che di questo si serva l'Herman, per dimostrare <lb/>il principio idrodinamico del Torricelli, che cio&egrave; gl'impeti degli zampilli <lb/>stanno come le radici delle altezze vive. </s></p><p type="main">

<s>Cos&igrave; fatte questioni, che ritorneranno nella Storia dell'Idrodinamica, non <lb/>furono certamente di semplici parole, e intesero i savi che non si sarebbero <lb/>potute altrimenti risolvere, che per via delle esperienze, come intese il Po&shy;<lb/>leni di risolvere, a quello stesso modo, la question delle forze vive. </s>

<s>Ma forse <lb/>il D'Alembert prese di qui occasione a riputare inutile le dispute tra il <lb/>Leibniz e il Papin, perch&egrave; la contingenza de'principii, d'onde movevasi da <lb/>una parte e dall'altra, &ldquo; ruineroit la certitude de la M&eacute;chanique, et la re&shy;<lb/>duiroit &agrave; n'etre plus qu'une science experimentale &rdquo; (pag. </s>

<s>XII). E perch&egrave; il <lb/>principale intento dell'Autore era quello di ridur la Meccanica stessa a una <lb/>scienza puramente razionale, e perci&ograve; volle che i principii, posti a lei per <lb/>fondamento, fossero tutti di verit&agrave; necessarie, e non contingenti. </s></p><p type="main">

<s>L'Eulero aveva creduto di sollevare la Scienza a quella dignit&agrave;, fra gli <lb/>altri argomenti estrinseci, col riguardare i corpi come ridotti a punti mate&shy;<lb/>riali, e in fatti chi bene osserva le astratte propriet&agrave; meccaniche degli urti <lb/>e delle riflessioni non si verificano esattamente che ne'globuli della luce, e <lb/>gli stessi teoremi pi&ugrave; fondamentali, come quello del piano inclinato, non sono <lb/>in ogni loro parte applicabili, che ai semplici punti ponderosi. </s>

<s>Le censure e <lb/>i vaniloqu&igrave; del Marchetti, e di altri, non si sarebbero potuti evitare altri&shy;<lb/>menti, perch&egrave; il corpo che ha sensibili dimensioni o rotola o scivola, secondo <lb/>che la perpendicolare, abbassata dal suo centro di gravit&agrave;, cade dentro la <lb/>base o fuori; e ruzzolando e scivolando non serba secondo la teoria la co&shy;<lb/>stante ragione esatta del suo proprio momento. </s>

<s>Il D'Alembert dunque, che <lb/>non parve contentarsi del fatto dall'Eulero, volle rendere la Meccanica una <lb/>scienza puramente razionale, costituendola sul fondamento di tre principii, <lb/>reputati da lui semplici e di verit&agrave; necessaria, quali sarebbero la forza d'iner&shy;<lb/>zia, la composizione dei moti, e l'equilibrio che si fanno insieme due corpi, <lb/>di masse uguali, e d'uguali velocit&agrave; virtuali e contrarie. </s>

<s>&ldquo; Le principe de <pb xlink:href="020/01/3015.jpg" pagenum="640"/>l'equilibre, joint &agrave; ceux de la force d'inertie, et du mouvement compos&eacute;, <lb/>nous conduit &agrave; la solution de tous les problemes, ou l'on considere le mou&shy;<lb/>vement d'un corps &rdquo; (pag. </s>

<s>XV). </s></p><p type="main">

<s>Che, ne'principii dell'inerzia e della composizion delle forze, possa avere <lb/>i suoi fondamenti la Dinamica, si comprende con facilit&agrave;, ripensando che per <lb/>via di quello ritrov&ograve; Galileo le leggi della caduta de'gravi, e per via di que&shy;<lb/>sto ebbero i Matematici in mano il filo di Arianna, per non smarrirsi ne'mec&shy;<lb/>canici laberinti. </s>

<s>Pi&ugrave; difficile, anzi quasi impossibile sembrava l'altro assunto <lb/>del D'Alembert, di derivar cio&egrave; dalla quiete le leggi universali del moto. </s>

<s>La <lb/>difficolt&agrave; nondimeno pu&ograve; solo sulla mente di coloro, i quali riguardano nella <lb/>quiete il moto come estinto, mentre in verit&agrave; non &egrave; che contrariato. </s>

<s>Il pen&shy;<lb/>siero profondo del Borelli trov&ograve; la sua pi&ugrave; splendida applicazione nel metodo <lb/>di ritrovare il centro oscillatorio secondo Giacomo Bernoulli, il quale, consi&shy;<lb/>derando essere le parti componenti il pendolo alcune pi&ugrave; ritardate e altre <lb/>pi&ugrave; velocitate, che se oscillassero con libert&agrave; dal medesimo punto, le une in&shy;<lb/>dipendenti dalle altre; vide che il problema si riduceva alle condizioni del&shy;<lb/>l'equilibrio nella leva. </s>

<s>Il D'Alembert poi rese generale il metodo bernoul&shy;<lb/>liano, applicandolo a ritrovare la resultante del moto in pi&ugrave; corpi, che agiscono <lb/>comunque gli uni sopra gli altri, e concludendolo in una regola cos&igrave; espressa: <lb/>&ldquo; D&eacute;composes les mouvemens A, B, C..., imprim&eacute;s a chaque corps, cha&shy;<lb/>cun en deux autres <emph type="italics"/>a, a&prime;, b, b&prime;, c, c&prime;...;<emph.end type="italics"/> qui soient tels que, si l'on n'e&ugrave;t <lb/>imprim&eacute; aux corps que les mouvemens <emph type="italics"/>a, b, c...,<emph.end type="italics"/> ils eussent p&ugrave; conser&shy;<lb/>ver ces mouvemens sans se nuire reciproquement, et que, si on ne leur e&ugrave;t <lb/>imprim&egrave; que les mouv&egrave;mens <emph type="italics"/>a&prime;, b&prime;, c&prime;...,<emph.end type="italics"/> le systeme f&ugrave;t demeure en repos. </s>

<s><lb/>Il est clair que <emph type="italics"/>a, b, c...<emph.end type="italics"/> seront les mouvemens, que ces corps prendront <lb/>en vertu de leur action &rdquo; (pag. </s>

<s>74, 75). </s></p><p type="main">

<s>Cos&igrave; tutte le leggi del moto venivano a ridursi a quelle dell'equilibrio <lb/>de'corpi. </s>

<s>La Statica e la Dinamica, che parevano contenere in s&egrave; una con&shy;<lb/>tradizion naturale, si unirono per opera del D'Alembert a comporre insieme <lb/>una scienza sola, cosicch&egrave; le distinzioni, cos&igrave; utilmente introdotte dall'Her&shy;<lb/>man, non rimasero che di nome. </s></p><p type="main">

<s>Ripensando alle cose fin qui discorse concluderemo che all'analisi aveva <lb/>l'Eulero educato la Meccanica, pi&ugrave; co'calcoli che coi principii; il D'Alembert <lb/>pi&ugrave; coi principii che con i calcoli; ma il Lagrange congiunse insieme e con&shy;<lb/>temper&ograve; cos&igrave; bene le due virt&ugrave;, che la Meccanica analitica si pu&ograve; dire giun&shy;<lb/>gesse finalmente per lui alla sua perfezione. </s>

<s>Ei lo sente e se ne compiace, <lb/>infin dalle prime parole premesse all'opera, facendovi notar come cosa nuova <lb/>che il metodo proseguito da lui l'ha dispensato dall'usar le figure illustra&shy;<lb/>tive, cosicch&egrave; il trattato procede ne'ragionamenti geometrici o meccanici, so&shy;<lb/>lamente con operazioni algebriche, regolare e uniforme. </s>

<s>&ldquo; Ceux qui aiment <lb/>l'analyse, soggiunge e termina cos&igrave; quelle brevi parole, verront avec plaisir <lb/>la Mechanique en devenir une nouvelle branche, et me sauront gr&eacute; d'en avoir <lb/>&eacute;tendu ainsi le domaine &rdquo; (<emph type="italics"/>Mechan. </s>

<s>anal.,<emph.end type="italics"/> a Paris 1788, pag. </s>

<s>VI). </s></p><p type="main">

<s>Ma il metodo, pi&ugrave; che dalla forma esteriore del calcolo, prende effica-<pb xlink:href="020/01/3016.jpg" pagenum="641"/>cia dalla generalit&agrave; dei principii, che anche il Lagrange riduce sommaria&shy;<lb/>mente a tre: a quello dell'equilibrio nella leva, a quello della composizion <lb/>delle forze, e all'altro infine delle velocit&agrave; virtuali. </s>

<s>Il D'Alembert, come ve&shy;<lb/>demmo, dietro l'esempio dei predecessori, aveva ridotto questi due ultimi a <lb/>uno solo, ma il Nostro vide tanta essere l'importanza del principio delle <lb/>velocit&agrave; virtuali, che da lui, reso universale, fece principalmente dipendere <lb/>tutta la Scienza del moto. </s>

<s>Il primo uso, che se ne fece nelle questioni mec&shy;<lb/>caniche, lo ravvisa nel trattato delle macchine di Galileo, con quanta ragione <lb/>poi se lo sanno oramai bene i nostri Lettori, a'quali giova rammem&oacute;rare in <lb/>proposito i dubbi de'Discepoli, che si volsero, per dar pi&ugrave; fermo fondamento <lb/>alla Statica, a cercare e a sostituire altri principii diversi da quello delle <lb/>velocit&agrave; virtuali, creduto da loro contenere in s&egrave; una fallacia. </s>

<s>N&egrave; que'dubbi <lb/>erano irragionevoli, allora che Galileo stesso proponeva intorno alle quantit&agrave; <lb/>infinitamente piccole dottrine cos&igrave; imperfette, anzi false, e insegnava a diffi&shy;<lb/>dare della bont&agrave; de'nuovi metodi del Cavalieri. </s>

<s>Di qui &egrave; che il principio <lb/>delle velocit&agrave; virtuali, bench&egrave; verissimo in s&egrave; stesso, era ai discepoli di Ga&shy;<lb/>lileo indimostrabile, e perci&ograve; non si pot&egrave; farne sicuro uso nella Meccanica, <lb/>se non da poi che s'istitui, e si diffuse il calcolo infinitesimale. </s>

<s>Primo infatti <lb/>a proporlo in forma ben definita fu Giovanni Bernoulli, come dice il La&shy;<lb/>grange, e come si rifer&igrave; da noi in altra occasione, citando la lettera, in cui <lb/>esso Bernoulli comunicava al Varignon il suo proprio Teorema. </s>

<s>Da questa <lb/>scrittura del Matematico di Basilea s'apr&igrave; la mente al Nostro, il quale rico&shy;<lb/>nobbe che le velocit&agrave; virtuali porgevano al Matematico un principio sem&shy;<lb/>plice, e nello stesso tempo cos&igrave; preciso, da esser l'unico possibile a tradursi <lb/>in una equazion generale, in cui si comprenderebbe tutta la variet&agrave; de'teo&shy;<lb/>remi, che si potrebbero proporre intorno all'equilibrio dei gravi. </s>

<s>&ldquo; Nous al&shy;<lb/>lons exposer cette formule dans toute son &eacute;tendue; nous t&agrave;cherons m&egrave;me <lb/>de la pr&eacute;sent&eacute;r d'une maniere &egrave;ncore plus g&eacute;n&eacute;rale qu'on ne l'a fait jusqu'&agrave; <lb/>present, et d'en donner des applications nouvelles &rdquo; (pag. </s>

<s>12). Fra queste <lb/>nuove applicazioni forse &egrave; la pi&ugrave; notabile quella fatta all'equilibrio di pi&ugrave; <lb/>forze, in un sistema di punti connessi con un filo flessibile o con una verga <lb/>rigida, ma dal proposto disegno, che poi nella prima parte dell'Opera si vede <lb/>dall'Autore maestrevolmente eseguito, si possono giudicare le promozioni ve&shy;<lb/>nute alla Statica per opera del Lagrange. </s></p><p type="main">

<s>Rispetto alla Dinamica il teorema generalissimo proposto dal D'Alem&shy;<lb/>bert, e che consisteva, come si disse, nel dedurre dalle precedenti condizioni <lb/>dell'equilibrio, per via indiretta, le equazioni necessarie a risolvere qual si <lb/>voglia problema concernente il moto; era senza dubbio assai seducente, ma, <lb/>in venire a farne l'applicazione, s'ebbe pi&ugrave; volte a incontrarvi non poche <lb/>difficolt&agrave;, per determinar le forze che debbono esser distrutte, e a fare espe&shy;<lb/>rienza che la legge dell'equilibrio fra esse forze menava troppo spesso alla <lb/>conclusione per vie intralciate e penose. </s>

<s>A ridurle perci&ograve; pi&ugrave; agevoli, e pi&ugrave; <lb/>spedite, il Lagrange sper&ograve; che gioverebbero le velocit&agrave; virtuali, le quali, come <lb/>lo avevano cos&igrave; facilmente condotto a risolvere tutte le questioni della Sta-<pb xlink:href="020/01/3017.jpg" pagenum="642"/>tica; cos&igrave; lo condurrebbero similmente a risolvere le questioni della Dina&shy;<lb/>mica. </s>

<s>Se non che, mentre l&agrave; bastava quel principio solo, qui voleva esser <lb/>congiunto con un altro, dalla qual congiunzione glie ne venne a resultare <lb/>un metodo nuovo, molto simile al primo, cosicch&egrave; le due Scienze dell'equi&shy;<lb/>librio e del moto de'gravi, se naturalmente avevano abito vario, non si po&shy;<lb/>teva per&ograve; dire che l'avessero diverso. </s></p><p type="main">

<s>Volendo il Lagrange stesso, nella prima sezione della seconda parte del&shy;<lb/>l'Opera, dare una certa idea di quel metodo a'suoi Lettori, riduce alla loro <lb/>memoria che il principio delle velocit&agrave; virtuali consiste in ci&ograve; che, essendo <lb/>un sistema di punti fisici, e sollecitato da qualunque forza, in equilibrio, se <lb/>diasi al detto sistema un piccolissimo impulso, e tale da promovere ciascun <lb/>punto per uno spazio infinitesimo; la somma delle forze, moltiplicate a una <lb/>a una per il respettivo spazio percorso, deve sempre essere uguale a zero. </s>

<s><lb/>Se inoltre si suppone il sistema esser mosso, e il moto particolare, che cia&shy;<lb/>scuno dei punti componenti ha in un dato istante, si decomponga in due, <lb/>l'un de'quali sia quello che prender&agrave; il punto stesso nell'istante successivo; <lb/>si vedr&agrave; facilmente che l'altro deve esser distrutto, per l'azion reciproca dei <lb/>punti materiali, e per quella delle forze motrici, dalle quali sono attualmente <lb/>sollecitati. </s>

<s>Dovendo poi queste forze equilibrarsi con le resistenze opposte, <lb/>ne consegue che, per applicare a un sistema in moto la formula del suo pro&shy;<lb/>prio equilibrio, basta aggiungervi i termini rappresentativi di quelle stesse <lb/>forze motrici. </s></p><p type="main">

<s>&ldquo; Or si on considere, prosegue a dire il Lagrange, ainsi que nous l'avons <lb/>d&eacute;ja fait plus haut, les vitesses, que chaque corps a suivant trois directions <lb/>fixes et perpendiculaires entr'elles, les d&eacute;croissemens de ces vitesses repr&eacute;&shy;<lb/>senteront les mouvemens perdue suivant les m&egrave;m&egrave;s directions, et leurs <lb/>accroissemens seront par consequent les mouvemens perdus dans des di&shy;<lb/>rections oppos&eacute;es. </s>

<s>Donc les pressions resultantes de ces mouvemens perdus <lb/>seront exprim&eacute;es en g&eacute;n&eacute;ral par la masse multipli&eacute;e par l'&eacute;l&eacute;ment de la vi&shy;<lb/>tesse, et divis&eacute;e par l'&eacute;l&eacute;ment de tems, et auront des directions directement <lb/>contraires &agrave; celles des vitesses. </s>

<s>De cette maniere on pourra exprimer anali&shy;<lb/>tiquement les termes dont il s'agit, et l'on aura une formule generale pour <lb/>le mouvement des corps, la quelle renformera la solution de tous les pro&shy;<lb/>blemes de Dynamique, comme on le verra dans la suite de cet trait&eacute; &rdquo; <lb/>(<emph type="italics"/>Mechan. </s>

<s>anal.<emph.end type="italics"/> cit., pag. </s>

<s>181, 82). </s></p><p type="main">

<s>E quei che seguitano a leggere e a meditare il trattato non posson non <lb/>ammirar la profondit&agrave;, a cui si ridusse la Meccanica per opera dell'Autore. <lb/></s>

<s>&Egrave; una profondit&agrave; quasi direbbesi paurosa, simile a quella di una immensa <lb/>cisterna, attraverso alle limpide acque della quale scorge l'occhio ogni og&shy;<lb/>getto giacente sul fondo: sono i brividi, che mette addosso il pensiero del&shy;<lb/>l'infinito, e che fanno quasi rifuggire dal contemplarlo. </s>

<s>E come all'infinito <lb/>non si pu&ograve; aggiungere nulla di pi&ugrave;, cos&igrave; nulla di pi&ugrave; sembrava si potesse <lb/>oramai aggiungere alla Meccanica analitica del Lagrange. </s>

<s>Che se anche que&shy;<lb/>sto, come tutti gli altri discorsi, che prescrivono un limite al progredir del-<pb xlink:href="020/01/3018.jpg" pagenum="643"/>l'ingegno, sembrasse una esagerazione, si ripensi che i progressi fatti di poi <lb/>dall'analisi applicata alla Scienza del moto riguardano piuttosto la facilit&agrave; <lb/>de'calcoli, e la semplicit&agrave; de'metodi, che la universalit&agrave; de'principii in&shy;<lb/>formativi. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>L'indole della Meccanica analitica &egrave;, per le cose fin qui discorse, defi&shy;<lb/>nita in s&egrave; stessa, e si vede consistere nel ridur la Scienza del moto alla cer&shy;<lb/>tezza della verit&agrave; matematica. </s>

<s>La parte fisica o sperimentale &egrave; sparita affatto, <lb/>e si direbbe piuttosto ch'&egrave; dissipata, come a un calore intenso si dissipa un <lb/>corpo, di cui non riman che l'ultima e sottilissima essenza. </s>

<s>Ci&ograve; che ne av&shy;<lb/>verte dover essersi gi&agrave; posto il termine alla nostra Storia, la quale nulladi&shy;<lb/>meno, non contenta di esser risalita sul monte, ha voluto anche mostrar come <lb/>su quella cima fermato il piede spiccassero i Matematici il volo sublime. </s>

<s>E <lb/>ora che quel termine &egrave; giunto realmente, vogliam dare uno sguardo fuggi&shy;<lb/>tivo indietro alla via lunga e faticosa, che vi ci ha condotti. </s></p><p type="main">

<s>Della lunghezza non diciamo, ma della fatica pu&ograve; farsi un'idea chiun&shy;<lb/>que ripensi che della Meccanica mancava fin qui una Storia ordinata, e che <lb/>avesse particolar riguardo alla cultura datasi a questa Scienza in Italia. </s>

<s>Ma <lb/>mentre si meditava da noi l'ardua impresa, e si significava per le pagine <lb/>dei due Tomi, che son sotto gli occhi del pubblico, i nostri pensieri; nella <lb/>dotta Germania si leggevano dalle cattedre scritti, e si stampavano libri sullo <lb/>stesso argomento. </s>

<s>I nostri, che non si risolvono a far nulla se non venga a <lb/>loro l'esempio dagli stranieri, hanno incominciato a delibare il soggetto, non <lb/>curato fin qui, bench&egrave; le istituzioni meccaniche formino una delle glorie pi&ugrave; <lb/>insigni della Scienza italiana. </s>

<s>Come poi que'tali prendono dagli altri gli im&shy;<lb/>pulsi a fare, cos&igrave; del fare ne imitano fedelmente i modi. </s>

<s>Ora, hanno trovato <lb/>i sapienti d'oltremonti un modo di risolvere facilmente qualunque pi&ugrave; arduo <lb/>problema della Scienza, in quella, ch'essi chiamano legge dell'evoluzione, e <lb/>per la quale si d&agrave; ad intendere come una semplice cellula siasi andata in&shy;<lb/>gradando via via, da venire all'essere di una pianta e di un animale. </s>

<s>Il prin&shy;<lb/>cipio informativo e regolatore di cos&igrave; fatti progressi consiste in ci&ograve; che, degli <lb/>organi accidentalmente sopravvenuti, non rimangono se non che quelli, che <lb/>favoriscono il ben essere dell'individuo, e stringono meglio insieme le rela&shy;<lb/>zioni ch'egli ha co'suoi simili, per cui prosperano quegli organi, e prospe&shy;<lb/>rando si perfezionano; a differenza degli altri, che vanno a perdersi a poco <lb/>a poco o a ridursi nello stato di rudimenti. </s>

<s>Cos&igrave;, per questo provvido istinto <lb/>di sceglier sempre il migliore, e di repudiare il peggiore, tutti gli esseri na&shy;<lb/>turali son giunti via via dall'infimo al pi&ugrave; alto grado e perfetto. </s></p><p type="main">

<s>Chi veramente abbia infuso quell'istinto nella Natura, e da chi sia re&shy;<lb/>golato, la maggior parte de'settatori di queste nuove dottrine non lo sa e <pb xlink:href="020/01/3019.jpg" pagenum="644"/>non lo dice, per cui lasciano mancare alla loro scienza il primo fondamento. </s>

<s><lb/>Ma i pi&ugrave; savi la riconoscono da un Dio creatore, e nelle loro mani quella <lb/>stessa Scienza, per tanti altri cos&igrave; desolata, come viene ad aver fermezza di <lb/>principii, cos&igrave; ha o potrebbe avere speranza di pi&ugrave; lieti progressi. </s>

<s>A torto <lb/>perci&ograve; alcuni, per il solito vezzo di recalcitrare a ogni novit&agrave;, condannano <lb/>il sistema dell'evoluzione, per il quale &egrave; venuta a'nostri giorni a ricevere <lb/>tanto incremento la Storia naturale, e anche maggiore ne potrebbe ricevere, <lb/>se con pi&ugrave; senno si procedesse dagli uomini in questo mondo. </s>

<s>Fin qui sven&shy;<lb/>turatamente ci troviamo stare tra i due eccessi con coloro, che da una parte <lb/>rifuggono dal cos&igrave; detto darvinismo come da una empiet&agrave;, e con quegli altri <lb/>che lo vogliono con incredibile imprudenza costituire a principio supremo di <lb/>ogni ordine di cose, o sieno percettibili per gli occhi o per la mente, o si <lb/>tratti insomma di Fisica o di Psicologia. </s>

<s>Allo svolgersi del pensiero nel cer&shy;<lb/>vello di un uomo s'intende applicar le medesime leggi, che allo svolgimento <lb/>dell'ovulo in un nido, o del seme in un orto. </s></p><p type="main">

<s>Dal pensiero dell'individuo era naturale il trapasso a farne l'applica&shy;<lb/>zione al pensiero di tutto il genere nella Storia delle scienze, fra le quali &egrave; <lb/>toccato finalmente la sorte anche alla Meccanica. </s>

<s>Le minute notizie partico&shy;<lb/>lari si stimano oramai cose indegne de'novelli scrittori, l'alto ufficio de'quali <lb/>si &egrave; quello di descrivere le lotte, in cui son dovuti entrare l'un contro l'al&shy;<lb/>tro i vari principii assunti via via da'vari autori, per farne conseguire le <lb/>verit&agrave; dei loro teoremi: lotte, nelle quali, rimasero sopra gli altri vittoriosi, <lb/>fra i predetti principii, quelli, che pi&ugrave; facilmente si porgevano a risolvere le <lb/>proposte questioni. </s>

<s>Cos&igrave; spiegasi come ai tempi per esempio del Lagrange <lb/>toccasse la fortunata vittoria al principio delle velocit&agrave; virtuali. </s></p><p type="main">

<s>Noi, dietro i canoni di una Filosofia pi&ugrave; antica, e confermata anch'essa <lb/>dalle osservazioni dei fatti, abbiamo riconosciute le ragioni di quel progre&shy;<lb/>dire che ha fatto la Meccanica dall'invenzion de'principii, scelti dagli Au&shy;<lb/>tori fra i pi&ugrave; semplici e universali, ma quella scelta l'abbiamo veduta di&shy;<lb/>pendere e regolarsi con una legge tutta propria dell'intelletto, e che non ha <lb/>con la selezion darviniana altra analogia, da quella in fuori che passa tra il <lb/>mondo fisico e il mondo morale. </s>

<s>I novelli Filosofi gli confondono in un mondo <lb/>solo, e in ci&ograve; consiste quella imprudenza che si diceva. </s>

<s>Si persuadono co&shy;<lb/>storo che medesimi siano gli organi inservienti alla vita intellettiva e all'a&shy;<lb/>nimale, perch&egrave; credono che cotesti organi si riducano solamente a quelli, <lb/>che si possono dissecare col coltello anatomico, o vedere col microscopio, e <lb/>che perci&ograve; son composti di solidi e di liquidi, in mezzo a'quali se ne sco&shy;<lb/>prono altri aerei e vaporosi. </s>

<s>Ma in queste esalazioni, non difficili a racco&shy;<lb/>gliersi e a esaminarsi, termina la serie de'corpi conoscibili da noi con l'uso <lb/>dei nostri sensi, bench&egrave; si comprenda dover essere in natura altre sostanze, <lb/>pi&ugrave; sottili per dir cos&igrave; e pi&ugrave; raffinate, e delle quali, come dell'elettricit&agrave;, non <lb/>abbiamo altra notizia che dagli effetti osservabili da noi nelle materie crasse. </s>

<s><lb/>Or chi sa di quante altre varie essenze e propriet&agrave; son fluidi eterei in na&shy;<lb/>tura? </s>

<s>Eppure, dovendo essere essi gli organi immediati della vita, bisogne-<pb xlink:href="020/01/3020.jpg" pagenum="645"/>rebbe conoscerli nella loro pi&ugrave; intima essenza, per decider prudentemente, <lb/>se medesimi essendo della vita fisiologica e della psicologica gli organi e le <lb/>funzioni, si possano i loro svolgimenti assoggettare alle medesime leggi. </s>

<s>In <lb/>tanta incertezza la filosofica prudenza ci consiglia di starcene all'osservazione <lb/>de'fatti, da'quali apparisce che son diverse qua e l&agrave; le funzioni, e che per&shy;<lb/>ci&ograve; diverse, nell'uno ordine di cose e nell'altro, debbon essere le leggi degli <lb/>svolgimenti. </s></p><p type="main">

<s>Ma o si seguano intorno a ci&ograve; le pi&ugrave; sane antiche dottrine, o si corra <lb/>inconsideratamente dietro alle nuove, sembra la questione in ogni modo o <lb/>affatto estranea, o non toccar che indirettamente la Storia, ufficio della quale <lb/>&egrave; di narrare i principii, da cui mosse la Scienza, e i termini a cui giunse <lb/>finalmente vittoriosa, dopo il travaglio dei dubbi combattuti, e l'esperienza <lb/>dei patiti errori. </s>

<s>Lo storico insomma non pu&ograve; dispensarsi dal dar notizie, <lb/>rese dalle testimonianze certe, e dalla critica sincere. </s>

<s>La maggior parte degli <lb/>scrittori &egrave; vero ha male adempiuto fin qui a un tale ufficio, facendo per lo <lb/>pi&ugrave; consistere la storia nel descriver la vita civile e letteraria de'varii au&shy;<lb/>tori, senza curarsi di penetrare addentro alla vita del pensiero, o leggendola, <lb/>no negli originali, ma nelle relazioni di questo o di quello, desunte senza <lb/>giudizio da altre precedenti relazioni. </s></p><p type="main">

<s>Riconosciuta l'imperfezione del metodo, tutto rivolto a rappresentar le <lb/>cose nel solo abito esterno, o nelle loro pi&ugrave; insignificanti minuzie; s'&egrave; cre&shy;<lb/>duto di emendarlo, con risalir d'un tratto a ritrovar le supreme leggi in&shy;<lb/>formative di que'fatti particolari: e invece della Storia son venuti que'dotti <lb/>stranieri a darci una Filosofia della Storia. </s>

<s>Ma se questa Filosofia, a qua&shy;<lb/>lunque soggetto storico si riferisca, suppone com'&egrave; ragionevole la notizia dei <lb/>fatti particolari, da'quali si vuol risalire al principio universale che gl'in&shy;<lb/>forma, per dedurne la legge degli svolgimenti; &egrave; manifesto che si crede da <lb/>costoro essere cotali fatti bene accertati, perch&egrave; altrimenti sarebbero senza <lb/>fondamento le loro speculazioni. </s>

<s>Ora a noi sembra questa opinione inconsi&shy;<lb/>derata, e ci fa maraviglia che non se ne siano accorti que'valentuomini, se <lb/>fu la detta imperfezione de'metodi storici precedenti, che gli consigli&ograve; cos&igrave; <lb/>risolutamente a repudiarli. </s>

<s>E se gli avessero per ci&ograve; solo repudiati, perch&egrave; <lb/>si trattenevano in minuzie, si potrebbe dire che una certa boria filosofica fu <lb/>che ve gl'indusse, perch&egrave; avrebbero dovuto invece prima esaminare se quelle <lb/>sparse e minuziose notizie almeno erano vere, e sopra quelle riconosciute ve&shy;<lb/>rit&agrave;, come sopra stabile fondamento, edificare la nuova Storia filosofica. </s></p><p type="main">

<s>Quell'esame, dannosamente trascurato dai nostri predecessori, l'abbiamo <lb/>voluto istituir noi, non facendo alcun conto delle relazioni altrui, ma ricer&shy;<lb/>cando i pensieri e le scoperte de'varii autori nelle loro opere originali. </s>

<s>E <lb/>perch&egrave; di que'pensieri e di quelle scoperte, per ci&ograve; che particolarmente con&shy;<lb/>cerne la Scuola italiana, rimaneva tuttavia la miglior parte nei manoscritti, <lb/>abbiamo usato una special diligenza nel produrli alla luce con i loro com&shy;<lb/>menti storici, superate le difficolt&agrave;, che avevano fatto fin qui arretrar dal&shy;<lb/>l'impresa tanti altri, senza dubbio pi&ugrave; valorosi di noi, ma forse meno pazienti. </s></p><pb xlink:href="020/01/3021.jpg" pagenum="646"/><p type="main">

<s>N&egrave; del trascrivere da quelli, che volgarmente si chiamerebbero scara&shy;<lb/>bocchi, tante proposizioni, e anzi trattati interi, fu solo il nostro pensiero <lb/>quello di far note al mondo le importanti verit&agrave; dimostrate, ma di aggiun&shy;<lb/>gere esempi nuovi di ci&ograve;, che valesse alle mani di quegli antichi il calcolo <lb/>infinitesimale, sotto l'abito geometrico degl'indivisibili cavalierani. </s>

<s>I canoni <lb/>di questo metodo si desumono con facilit&agrave; da pochi teoremi degli Elementi <lb/>di Euclide, cosicch&egrave; possono speditamente maneggiarlo anehe i giovani prin&shy;<lb/>cipianti, e con esso risolvere in Geometria e in Meccanica grandissima parte <lb/>de'pi&ugrave; ardui problemi. </s>

<s>Ora, cotesti problemi non si propongono alla gio&shy;<lb/>vent&ugrave; studiosa, se non che dopo quel lungo e periglioso tirocinio, che &egrave; ne&shy;<lb/>cessario per giungere a trattar le regole de'calcoli differenziale e integrale. </s>

<s><lb/>Si sperava perci&ograve; da noi che non inutili riuscirebbero gli esempi del Rober&shy;<lb/>val, del Torricelli, del Nardi e degli altri, che ricorrono in questa Storia, se <lb/>consigliassero qualche maestro a imitarli, e a suoi giovani discepoli, che hanno <lb/>appena varcate le soglie della Geometria, facesse pregustare molte di quelle <lb/>verit&agrave;, il penetrar le quali non si crede possibile a nessuno, che non abbia <lb/>in mano le chiavi della Matematica pi&ugrave; sublime. </s>

<s>La fallacia di una tale <lb/>opinione fu primo a riconoscerla, e a mostrarla l'Herman, il quale, come si <lb/>legge nella sua prefazione alla <emph type="italics"/>Foronomia,<emph.end type="italics"/> per molteplici esperienze ammae&shy;<lb/>strato fornirsi dalla meditazione delle figure soluzioni pi&ugrave; semplici ed ele&shy;<lb/>ganti che dall'analisi speciosa; applic&ograve; gli stessi segni e simboli leibniziani <lb/>allo schietto metodo geometrico del Cavalieri. </s></p><p type="main">

<s>Per quel che riguarda poi i documenti ricavati da'libri, che sono alla <lb/>pubblica luce, non ci siam contentati d'indicar semplicemente le pagine del&shy;<lb/>l'Opere via via citate, ma ne abbiamo trascritte le parole proprie, perch&egrave; <lb/>rimeditandole possano per s&egrave; medesimi giudicare i Lettori se le abbiamo sem&shy;<lb/>pre interpetrate a dovere, o se ci fossimo anche pi&ugrave; spesso ingannati. </s>

<s>In tali <lb/>inganni, quando qualcuno ve gli scoprisse, confessiamo che consisterebbe il <lb/>maggior difetto della nostra Storia, la quale, qualunque ella si sia, presen&shy;<lb/>tiamo al pubblico perch&egrave;, o approvandola o correggendola, possa stare in <lb/>quel giusto mezzo in cui ci siamo studiati di metterla, cosicch&egrave; da una parte <lb/>supplisca alle notizie o false o insufficienti, date da chi ci ha preceduto, e <lb/>dall'altra possa fornire a chi ci succede materia di pi&ugrave; sublimi storiche spe&shy;<lb/>culazioni. </s></p><pb xlink:href="020/01/3022.jpg"/><p type="main">

<s><emph type="center"/>INDICI<emph.end type="center"/><pb xlink:href="020/01/3023.jpg"/></s></p><pb xlink:href="020/01/3024.jpg"/><p type="main">

<s><emph type="center"/>INDICE DEI CAPITOLI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>CAPITOLO I.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Delle correzioni e delle riforme ne'Dialoghi delle due Scienze nuove.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Del supposto principio delle velocit&agrave; uguali dopo cadute uguali, e come sortisse a Ga&shy;<lb/>lileo, al Michelini, al Baliani finalmente di dimostrarlo <emph type="italics"/>Pag.<emph.end type="italics"/> 7 </s></p><p type="main">

<s>II Del supposto galieiano confermato per le dimostrazioni del Torricelli, del Baliani, del&shy;<lb/>l'Huyghens e del Marchetti &rdquo; 18 </s></p><p type="main">

<s>III Di alcune aggiunte, da farsi ai Dialoghi, dettate da Galileo al Viviani suo ospite in Ar&shy;<lb/>cetri &rdquo; 32 </s></p><p type="main">

<s>IV Dell'opera di ampliare le dottrine esposte ne'Dialoghi del moto, proseguita dal Viviani, <lb/>dopo la morte di Galileo &rdquo; 45 </s></p><p type="main">

<s>V Delle correzioni di alcuni falsi teoremi di Galileo, che fecero finalmente risolvere il Vi&shy;<lb/>viani d'illustrare e di promovere, in un'Opera a parte, le dottrine del suo Maestro &rdquo; 54 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO II.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del quinto Dialogo aggiunto alle due Scienze nuove, <lb/>ossia della Scienza delle proporzioni.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Di ci&ograve; che, a riformare il quinto libro di Euclide, scrisse Giovan Batista Benedetti, e <lb/>pens&ograve; Antonio Nardi <emph type="italics"/>Pag.<emph.end type="italics"/> 77 </s></p><p type="main">

<s>II Come Giovan Antonio Rocca porgesse occasione al Cavalieri di restaurare il principio alla <lb/>Scienza delle proporzioni, che poi Galileo fece mettere in dialogo &rdquo; 84 </s></p><p type="main">

<s>I Del disteso fatto dal Torricelli del quinto dialogo galileiano, aggiunto alle due Scienze <lb/>nuove &rdquo; 95 </s></p><p type="main">

<s>IV Del trattato torricelliano <emph type="italics"/>De proportionibus,<emph.end type="italics"/> inedito, e della Scienza universale delle <lb/>proporzioni spiegata da V. </s>

<s>Viviani &rdquo; 101 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO III.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del sesto Dialogo aggiunto alle due Scienze nuove, <lb/>ossia della forza della percossa.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Dei principii, da cui dipende la forza della percossa, proposti da Aristotile, dal Cardano <lb/>e da Galileo, e come fossero dimostrati falsi <emph type="italics"/>Pag.<emph.end type="italics"/>111 </s></p><p type="main">

<s>II Del ritrovamento e della pubblicazione del sesto dialogo galileiano: se ne esaminano <lb/>brevemente le materie, e si conclude essere anch'egli informato dai medesimi falsi <lb/>principii professati in giovent&ugrave; dall'Autore &rdquo; 123 </s></p><p type="main">

<s>III Della reintegrazione del Dialogo galileiano, pubblicato dal Bonaventuri &rdquo; 137 </s></p><p type="main">

<s>IV Degli strumenti immaginati e descritti per misurare la forza della percossa &rdquo; 155 </s></p><pb xlink:href="020/01/3025.jpg" pagenum="650"/><p type="main">

<s>V Della nuova Scienza della percossa, istituita prima da Giovan Marco Marci tra gli stra&shy;<lb/>nieri, e poi dal Borelli nella Scuola galileiana, e di ci&ograve; che conferirono a promover <lb/>la detta Scienza gli Accademici di Londra e di Parigi <emph type="italics"/>Pag.<emph.end type="italics"/>169 </s></p><p type="main">

<s>VI Delle relazioni fra gli angoli dell'incidenza e della riflessione, e fra i momenti delle per&shy;<lb/>cosse dirette e delle oblique &rdquo; 181 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del settimo Dialogo da aggiungersi alle due Scienze nuove, <lb/>ossia dei Problemi fisici e matematici.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Dei problemi, che si dovevano aggiungere dopo la <emph type="italics"/>Scienza meccanica,<emph.end type="italics"/> e come Galileo <lb/>pensasse di ridurli in Dialogo <emph type="italics"/>Pag.<emph.end type="italics"/>195 </s></p><p type="main">

<s>II Di altri problemi e speculazioni intorno a varii soggetti di Fisica &rdquo; 206 </s></p><p type="main">

<s>III Delle questioni matematiche, e dei varii teoremi e problemi di Geometria raccolti dal <lb/>Viviani &rdquo; 221 </s></p><p type="main">

<s>IV Dei quesiti algebrici, e del misurar con la vista &rdquo; 237 </s></p><p type="main">

<s>V Dei Teoremi di Geometria avanzati alle dimostrazioni dei moti locali &rdquo; 248 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO V.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Del trattato dei centri di gravit&agrave; di Evangelista Torricelli.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Dei primi esercizi giovanili intorno ai libri baricentrici di Archimede <emph type="italics"/>Pag.<emph.end type="italics"/>263 </s></p><p type="main">

<s>II Dell'invenzione dei centri di gravit&agrave;, nelle porzioni di parabola e di cerchio &rdquo; 269 </s></p><p type="main">

<s>III Di alcnne nuove invenzioni haricentriche, per via degli indivisibili &rdquo; 281 </s></p><p type="main">

<s>IV Dei centro di gravit&agrave; degli archi di cerchio, e delle fallacie del Guldin intorno ai centri <lb/>delle callotte, delle zone e de'settori sferici, notate dal Cavalieri, dopo le dimostra&shy;<lb/>zioni avute dal Torricelli &rdquo; 298 </s></p><p type="main">

<s>V Della diversit&agrave; del metodo del Keplero da quello del Cavalieri, e come fosse questo ap&shy;<lb/>plicato dal Torricelli per ritrovare in vario modo il centro di gravit&agrave; del cono, e di <lb/>altre figure &rdquo; 306 </s></p><p type="main">

<s>VI Del centro di gravit&agrave; dei solidi scavati &rdquo; 321 </s></p><p type="main">

<s>VII Del centro di gravit&agrave; dei solidi vasiformi &rdquo; 334 </s></p><p type="main">

<s>VIII Del centro di gravit&agrave; dei solidi conoidali &rdquo; 340 </s></p><p type="main">

<s>IX Del centro di gravit&agrave; dei solidi cavalierani e della Cicloide &rdquo; 358 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Di varie altre cose di Meccanica lasciate dal Torricelli.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Di alcune proposizioni relative al trattato <emph type="italics"/>De motu Pag.<emph.end type="italics"/>373 </s></p><p type="main">

<s>II Di alcune altre proposizioni relative al trattato <emph type="italics"/>De momentis &rdquo;<emph.end type="italics"/> 389 </s></p><p type="main">

<s>III Del modo meccanico di condur le tangenti, e di vari altri teoremi di Meccanica nuova &rdquo; 400 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Di altri Discepoli di Galileo, promotori della Scienza del moto.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Di Antonio Nardi, e particolarmente delle sue <emph type="italics"/>Ricercate geometriche:<emph.end type="italics"/> di Michelangiolo <lb/>Ricci <emph type="italics"/>Pag.<emph.end type="italics"/>418 </s></p><p type="main">

<s>II Digressione intorno alla Cicloide: delle propriet&agrave; di lei scoperte dal Roberval, e da altri <lb/>Matematici francesi &rdquo; 437 </s></p><pb xlink:href="020/01/3026.jpg" pagenum="651"/><p type="main">

<s>III Di ci&ograve; che dimostrarono, intorno alla Cicloide, il Nardi, il Torricelli e il Ricci <emph type="italics"/>Pag.<emph.end type="italics"/>452 </s></p><p type="main">

<s>IV Delle controversie insorte fra il Roberval e il Torricelli, prima intorno alla quadratura, <lb/>poi intorno al baricentro della Cicloide &rdquo; 468 </s></p><p type="main">

<s>V Di ci&ograve; che, a illustrare, a compiere e a divulgare le dottrine galileiane del moto, opera&shy;<lb/>reno il Cavalieri, il Borelli e il Viviani &rdquo; 484 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO VIII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dei matematici stranieri principali promotori della Scienza del moto.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Degli otto libri della Statica del Roberval, e come il Wallis e il Mariotte confermarono <lb/>la Dinamica galileiana, che l'Huyghens coron&ograve; di nuovi teoremi <emph type="italics"/>Pag.<emph.end type="italics"/>500 </s></p><p type="main">

<s>II Delle propriet&agrave; meccaniche della Cicloide &rdquo; 510 </s></p><p type="main">

<s>III De'centri delle percosse e delle oscillazioni &rdquo; 518 </s></p><p type="main">

<s>IV Delle forze centrifughe &rdquo; 537 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO IX.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Della proposta di una Meccanica nuova, e della composizione dei moti.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Della <emph type="italics"/>Nouvelle mecanique<emph.end type="italics"/> di Pietro Varignon: degli errori del Cartesio e di Galileo <lb/>intorno alle propriet&agrave; dei moti composti, dimostrate da Giovan Marco Marci <emph type="italics"/>Pag.<emph.end type="italics"/>552 </s></p><p type="main">

<s>II Di ci&ograve; che operarono i Matematici stranieri per confutare il Cartesio, e per dimostrar <lb/>come debba usarsi, e come sia vera la regola del parallelogrammo &rdquo; 562 </s></p><p type="main">

<s>III Come le fallacie di Galileo seducessero il Torricelli e il Viviani, e come fossero solen&shy;<lb/>nemente dal Borelli confermate co'suoi paralogismi &rdquo; 571 </s></p><p type="main">

<s><emph type="center"/>CAPITOLO X.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Dei progressi fatti dalla Meccanica nuova.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>I Dei <emph type="italics"/>Principii matematici di Filosofla naturale<emph.end type="italics"/> del Newton <emph type="italics"/>Pag.<emph.end type="italics"/>591 </s></p><p type="main">

<s>II Della <emph type="italics"/>Foronomia<emph.end type="italics"/> dell'Herman &rdquo; 606 </s></p><p type="main">

<s>III Del parallelogrammo delle forze e del Calcolo infinitesimale nella Meccanica nuova &rdquo; 615 </s></p><p type="main">

<s>IV Della Meccanica analitica dell'Euler, del D'Alembert, e del Lagrange &rdquo; 633 </s></p><p type="main">

<s>V Brevi parole di conclusione &rdquo; 643 </s></p><pb xlink:href="020/01/3027.jpg"/><p type="main">

<s><emph type="center"/>INDICE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>DEI DOCUMENTI ESTRATTI DAI MANOSCRITTI GALILEIANI <lb/>E NOTATI SECONDO L'ORDINE DEI CAPITOLI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo I.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Da una lettera di Famiano Michelini, che chiedeva a Galileo la dimostrazione di un suo supposto <lb/>principio meccanico, pag. </s>

<s>13. </s></p><p type="main">

<s>Cenno, estratto da una lettera del Viviani al Rinaldini, relativo alla pubblicazione delle opere di Ga&shy;<lb/>lileo 17. </s></p><p type="main">

<s>Motto, dal Ricci fatto al Torricelli, intorno a una dimostrazione del supposto galileiano 18. </s></p><p type="main">

<s>Scrittura mandata da Galileo ad Antonio Nardi, e nella quale si dimostrava il principio mec&shy;<lb/>canico 19-21. </s></p><p type="main">

<s>Due teoremi del Viviani, in cui si dichiara la verit&agrave; di un nuovo principio meccanico professato dal <lb/>Torricelli 22. </s></p><p type="main">

<s>Ii Mersenno chiede al Torricelli una dimostrazione del supposto galileiano, indipendente dall'espe&shy;<lb/>rienza 24, come rispondesse il Torricelli alla richiesta 24-26. </s></p><p type="main">

<s>Da una lettera al Torricelli, dove il Ricci nota alcune censure temerariamente fatte dal Mersenno al <lb/>trattato del moto di Galileo 26. </s></p><p type="main">

<s>Frammento di dialogo, di mano del Viviani 34, 35, il quale &egrave; un'esplicazione di quell'altro autografo <lb/>accennato da Galileo 35. </s></p><p type="main">

<s>Frammento di Dialogo in latino, dettato da Galileo a Marco Ambrogetti 36. </s></p><p type="main">

<s>Dialogo galileiano, in cui, messo in dubbio il principio delle velocit&agrave; virtuali, se ne propone un'altro <lb/>diverso, per dimostrare le condizioni dell'equilibrio nelle bilance 37, 38. </s></p><p type="main">

<s>Passo da inserirsi nel primo dialogo delle Scienze nuove, e in cui Galileo intendeva di rispondere <lb/>al Cartesio 39, 40. </s></p><p type="main">

<s>Frammento da inserirsi nei detto dialogo primo, perch&egrave; Galileo voleva rendere pi&ugrave; generale un esem&shy;<lb/>pio numerico 40. </s></p><p type="main">

<s>Aggiunta di ci&ograve; che aveva dimostrato il Viviani, per inserirsi verso la fine del medesimo dialogo <lb/>primo, contentandosene il signor Galileo 42, 43. </s></p><p type="main">

<s><emph type="italics"/>Domandari del Blaneano,<emph.end type="italics"/> notati dal Viviani, in dichiarazione di alcuni dubbi contro le dottrine ga&shy;<lb/>lileiane del moto 44. </s></p><p type="main">

<s>Luoghi nelle Scienze nuove, notati dal Viviani, con l'intenzione di correggerli e di esplicarli 45. </s></p><p type="main">

<s>Dimostrazione della capacit&agrave; dei sacchi cilindrici, che il Viviani voleva sostituire a quella di Ga&shy;<lb/>lileo 48, 49. </s></p><p type="main">

<s>Memoriale di un argomento da trattarsi, scritto dal Viviani ad istanza di Galileo 51. </s></p><p type="main">

<s>Proposizione VI delle resistenze del Galileo, generalmeate e diversamente enunciata dal Viviani, per <lb/>esser quella non vera 55, e corollario di questa proposizione 56. </s></p><p type="main">

<s>Prima promozione, occorsa a far dal Viviani, del teorema galileiano della corda tesa 60. </s></p><p type="main">

<s>Note del Viviani, relative a un nuovo Igrometro 61. </s></p><pb xlink:href="020/01/3028.jpg" pagenum="653"/><p type="main">

<s>Teoremi del Viviani, relativi allo scendere di un peso attaccato in mezzo a una fune, e al salire dei <lb/>pesi pendenti dagli estremi 62, 63. </s></p><p type="main">

<s>Teoremi dimostrati dal Viviani, per confermare la verit&agrave; del principio torricelliane, da sostituirsi a <lb/>quello delle velocit&agrave; virtuali 64. </s></p><p type="main">

<s>Scrittura cominciata dal Viviani, contro la dimostrazione uitima del quarto dialogo galileiano delle due <lb/>Nuove Scienze 65, 66. </s></p><p type="main">

<s>Esperienza del Viviani, per dimostrar che due funi tirano con egual forza, nella direzione obliqua e <lb/>nella perpendicolare 67. </s></p><p type="main">

<s>Applicazione dell'ultimo tcorema dimostrato da Galileo nel quarto dialogo delle due Nuove Scienze 71. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo II.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Varie osservazioni di Antonio Nardi intorno alla Scienza delle proporzioni, pag. </s>

<s>80, 82. </s></p><p type="main">

<s>Scrittura intorno alla riforma del quinto libro di Euclide, che il Cavalieri mand&ograve; a Galileo 88-90. </s></p><p type="main">

<s>Estranto di lettera del principe Leopoldo dei Medici, dove dice di aver chiamato a Firenze il Torri&shy;<lb/>celli, perch&egrave; aiutasse Galileo, gi&agrave; vecchio e cieco, a distendere il dialogo <emph type="italics"/>Della percossa<emph.end type="italics"/> 98. </s></p><p type="main">

<s>Motto fatto dal Torricelli, in proposito del suo trattato <emph type="italics"/>De proportionibus<emph.end type="italics"/> 102. </s></p><p type="main">

<s>Compendio del trattato torricelliano <emph type="italics"/>De proportionibus<emph.end type="italics"/> 102-6. </s></p><p type="main">

<s>Licenza, richiesta al Serenai dal Viviani, d'inserire nella sua Scienza delle proporzioni alcune pro&shy;<lb/>posizioni del Torricelli 107-8, e permesso ricevutone 108. </s></p><p type="main">

<s>Accenno fatto dal Viviani al trattato torricelliano <emph type="italics"/>De propoctionibus<emph.end type="italics"/> 109. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo III.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Passo, intorno al misurar la forza della percossa, estratto da un libretto intitolato <emph type="italics"/>Ricreazioni scien&shy;<lb/>tifu he,<emph.end type="italics"/> in francese, e tradotto dal Viviani, pag. </s>

<s>113. </s></p><p type="main">

<s>Pensieri del Nardi intorno al confermare le proporzioni, assegnate da Galileo tra la forza del percu&shy;<lb/>ziente e la resistenza del percosso, 114. </s></p><p type="main">

<s>Dimostrazione dello schiaccialsi i corpi sotto i colpi delle percosse 117, 18, e ove descrivesi nel me&shy;<lb/>desimo manescritto un'esperienza, per confermare la legge dell'urto dei corpi 120. </s></p><p type="main">

<s>Titolo e osservazioni del Viviani, intorno all'ultimo congresso di Galileo 126, 27. </s></p><p type="main">

<s>Il Borelli d&aacute; notizia al principe Leopoldo dei Medici di essere entrato a speculare intorno alla na&shy;<lb/>tura, e alla propriet&agrave; della forza della percossa: notizia che, passata nel Ricci, questi se ne <lb/>rallegra 127. </s></p><p type="main">

<s>Appunti manoscritti del Viviani, relativi alla collazione fatta della copia del Dialogo della percossa, <lb/>con l'originale di Galileo 128. </s></p><p type="main">

<s>Dimostrazione data dal Viviani, che qualunque piecolissimo pu&ograve; movere qualunque altro grandissimo <lb/>corpo 136. </s></p><p type="main">

<s>Estratto di lettera del Cavalieri, il quale si congratula col Torricelli che sia stato eletto Accademico <lb/>della Crusca 139. </s></p><p type="main">

<s>Trattato delle propriet&agrave; delle catenelle, da applicarsi agli usi ballistici, disteso in dialogo, per aggiun&shy;<lb/>gersi al trattoto della percossa, finalmente ritrovato fra i manoscritti galileiani, e qui pubblicato <lb/>da pag. </s>

<s>143-52. </s></p><p type="main">

<s>Postille del Viviani, relative all'uso che Galileo intendeva fare delle catenuzze 153. </s></p><p type="main">

<s>Strumnti inventati, e sperienze fatte e descritte dal Viviani, per misurare la forza della percossa 158-60. </s></p><p type="main">

<s><emph type="italics"/>Exscerptum ex quadam epistola Torricelli ad Mersennum<emph.end type="italics"/> fatto e di sua propria mano trascritto <lb/>dal Viviani 161. </s></p><p type="main">

<s>Da una lettera, nella quale il Borelli domanda al Viviani schiarimenti intorno alla stadera del Tor&shy;<lb/>ricelli, per misurar la forza della percossa 162. </s></p><p type="main">

<s>Lettera al Viviani, dove Giuseppe Farroni espone alcuni suoi dubbi intorno all'esperienza, che si di&shy;<lb/>ceva esser fatta da Galileo, per misurare la forza della percossa 165-67. </s></p><p type="main">

<s>Passo, in cui Stefano Angeli spiega la leggerezza del correre 176. </s></p><p type="main">

<s>Due note sentenziose del Viviani intorno alla forza della percossa 176. </s></p><p type="main">

<s>Passo autografo, trascritto dalle Lezioni accademiche del Torricelli, concernente la ragion degli angoli <lb/>dell'incidenza e della riflessione 190, 91. </s></p><pb xlink:href="020/01/3029.jpg" pagenum="654"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo IV.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Problemi di mano del signor Vincenzo di Galileo, pag. </s>

<s>196: della trottola, perch&egrave; girando stia ritta 197, <lb/>delle ruzzole girate col filo, delle palle gettate in aria con la racchetta, e per i pallottolai in piana <lb/>terra 197-99: delle trombe, che sollevano l'acqua solamente infino a una certa altezza 200, 1: del <lb/>rompersi delle corde tirate da pesi, e della maggior portata degli <gap/> baano le canno <lb/>pi&ugrave; lunghe, 201: della percossa e di qualunque grandissimo peso moss<gap/> da lei 202. </s></p><p type="main">

<s><gap/> apologo meccanico dialogizzato da Galileo, 203. </s></p><p type="main">

<s>Dialogo di Galileo, dove si discute se l'albero delle navi, trasportato dalla vela, fa l'ufficio di <lb/>vette 201-6. </s></p><p type="main">

<s>Problemi di vario argomento risoluti da Galileo: dell'uovo, che premutone il guscio non si schiac&shy;<lb/>cia 207: della varia temperatura, che pare aver l'acqua d'estate nell'entrare e nell'uscire dal <lb/>bag<gap/> 208. </s></p><p type="main">

<s>Intorno al passo dell'uomo: pensioro di Galileo illustrato dal Viviani 209, 10. Proposizione intorno al <lb/>tirar dei tendini, solamente annunziate da Galileo 211. Moti del pendolo da Galileo misura<gap/> col <lb/>semplice tatto 213. </s></p><p type="main">

<s>Proposizione falsa del Viviani intorno alle forze centrifughe dei pendoli 213. </s></p><p type="main">

<s>Pensieri di Galileo, illustrati dal Viviani, intorno alla viscosit&agrave; dell'acqua, argomentata dalle scendervi <lb/>la limatura dei corpi galleggianti 215, 16. </s></p><p type="main">

<s>Nota, nella quale Galileo confuta l'opinione del Bonamici intorno all'origine delle fonti 216. </s></p><p type="main">

<s>Ragioni delle piogge e delle rugiade, notate da Galileo 216, 17, e del parer pi&ugrave; grande la luna vicino <lb/>all'orizzonte 217, e dell'ingrossare in alto i fili degli zampili <emph type="italics"/>ivi.<emph.end type="italics"/></s></p><p type="main">

<s>Note sparse di Galileo intorno all'essenza della luce, e a corte propriet&agrave; di lei, nell'occhio naturale <lb/>e nel Telescopio 218. </s></p><p type="main">

<s>Compendiosa descrizione fatta da Galileo di un Fotometro perfetto: un pensiero di lui intorno all'al&shy;<lb/>trazion del magnete, e alcune osservazioni di fatti dipendenti dalla pressione dell'aria 210. </s></p><p type="main">

<s>Detti satiri<gap/>i di Galileo contro i Peripatetici, i Teologi, i suoi oppositori: proposito di scrivere in pub&shy;<lb/>bli<gap/>, e senzenza che voleva si scrivesse nel titolo delle sue Opere, pubblicandosi tutte in&shy;<lb/>sieme 220, 21. </s></p><p type="main">

<s>Frammento appartenente al Dialogo, in cui voleva Galileo portare i Problemi matematiri 222. </s></p><p type="main">

<s>Proposizioni XIX di Geometria, che dalla bocca e dagli scritti di Galileo raccolse il Viviani 223-37. </s></p><p type="main">

<s>Una proposizione riconosciuta falsa da Galileo, e due altre falsissime da lui stesso credute per <lb/>vere 228, 29. </s></p><p type="main">

<s>Proposizioni IX di algebra, quasi tutto autograle di Galileo, con un frammento di Dialogo intorno al <lb/>misurar con la vista 237-48. </s></p><p type="main">

<s>Teoremi XXIII di Geometria, occorsi alla mente di Galileo, nell'atto di dimostrare le proposizioni <lb/>attinenti alle varie propriot&agrave; dei moti 249-62. </s></p><p type="main">

<s>Frammento di Dialogo, in cui il Salviati dimostra la varict&agrave; de'momenti di un circolo o di una sfera, <lb/>nelle scendere lungo piani variamente inclinati 251. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo V.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Passo di lettera, in cui il Torricelli ringrazia il Mersenno dolla pro<gap/>erta di fare stampare a Parigi il <lb/>trattato dei centri di gravit&agrave;, pag. </s>

<s>264. </s></p><p type="main">

<s>Eatratto dal pro<gap/>io al trattato Delle proporzioni, dove il Torricelli esprime la fatta deliberazione di <lb/>lasciare i teoremi della geometria, per attendere ai vetri del Canocchiali <emph type="italics"/>ivi.<emph.end type="italics"/></s></p><p type="main">

<s>Proposizioni VII, che si riferiscono ai primi giovanili esercizi del Torricelli intorno ai centri di gra&shy;<lb/>vit&agrave; 265-69. </s></p><p type="main">

<s>Proposizioni due del Torricelli, dimostrative del centro di gravit&agrave; nelle porzioni, e ne'frusti di pa&shy;<lb/>rabola 270-73. </s></p><p type="main">

<s>Lemmi X, con i quali si prepara il Torricelli le vie a dimostrere il centro di gravit&agrave; del settore di <lb/>circolo, proseguendo il metodo degl'inscritti e dei circoscritti: e dimostrazione di esso centro con <lb/>un unico teorema 274-81. </s></p><pb xlink:href="020/01/3030.jpg" pagenum="655"/><p type="main">

<s>Estratto di lettera al Torricelli, in cui il Cavalieri propone l'applicazione degli indivisibili alla ricerca <lb/>dei centri di gravit&agrave; 281. </s></p><p type="main">

<s>Altro estratto di lettera al medesimo, dove il Cavalieri propone il modo, come si potrebbero appl&shy;<lb/>care gl'indivisibili alla ricerca del centro di gravit&agrave; del triangolo, e del conoide parabolico 282, 83. </s></p><p type="main">

<s>Proposizione, nella quale speditamente il Torricelli dimostra il centro di gravit&agrave; del conoide parala&shy;<lb/>lico, da quello del triangolo inscritto 284. </s></p><p type="main">

<s>Altra proposizione, in cui dal medesimo si dimostra il centro di gravit&agrave; del triangolo da un teorema <lb/>s<gap/>atico di Galileo 283. </s></p><p type="main">

<s>Da una lettera dove, a proposito di Baricentrica, il Cavalieri accenna alla possibilit&agrave; del riscontrarsi <lb/>il metodo del Torricelli con quello del Rocca, 285. </s></p><p type="main">

<s>Proposizizne del Torricelli, preceduta da quattro lemmi, per dimostrare il centro di gravit&agrave; di qua&shy;<lb/>lunque arco di cerchio 287-90: dietro la qual proposizione, in altro medo dal precedente, cio&egrave;, per <lb/>via degli indivisibili, si dimostra il centro di gravit&agrave; del settore di circolo 290, 91. </s></p><p type="main">

<s>Studi del Torricelli per l'invenzione del centro di gravit&agrave; delle callotte, che poi dimostr&ograve; star nel <lb/>mezzo della sactta 291-94. </s></p><p type="main">

<s>Da una lettera del Torricelli, nella quale espone al Cavalieri le ragioni del centro di gravit&agrave; nelle <lb/>callotte, dubitando di essersi ingannato 391, 95; delle quali ragioni poi esso Torricelli si servi, per <lb/>dimostrare il centro di gravit&agrave; dell'emisfero e del settore sferico 295-97. </s></p><p type="main">

<s>Estratto di lettera, in cui il Torricelli d&agrave; al Michelini notizia del Teorema centrobarico del Gul&shy;<lb/>dino 298, 99. </s></p><p type="main">

<s>Domande del Torricelli se VII sue proposizioni baricentriche erano state dimostrate dal Guldino, e <lb/>risposte del Cavalieri 299-300, che attizzarono le rivalit&agrave; di esso Torricelli contro alcuni errori <lb/>dell'Autore della Centrobarica 301. </s></p><p type="main">

<s>Nuove istanze fatte appresso il Cavalieri dal Torricelli, per assicurarsi in che modo avesse il Guldino <lb/>desunto il centro di gravit&agrave; della semicirconferenza dalla Quadratrice di Dinostrato, e per poter <lb/>indi rispondere alle accuse del Roberval 303. </s></p><p type="main">

<s>Giudizio poco favorevole del Torricelli, dop'avere sfogliata la Centrobarica del Guldino 306. </s></p><p type="main">

<s>Centro di gravit&agrave; della superficie conica: nuova dimostrazione del Torricelli 307. </s></p><p type="main">

<s>Nuovo modo di dimostrare, per via degli indivisibili, il centro di gravit&agrave; del triangolo e del cono 311-16: <lb/>similmene, dell'emisfero e dell'emisferoide 313: e, premesso a ciascuno un lemma, due altri modi, <lb/>suggeriti dagli indivisibili al Torricelli, di dimostrare il centro di gravit&agrave; del cono 314-16. Con <lb/>simil metodo, premessa l'invenzione del centro di gravit&agrave; dei prismali, si trovano dal medesimo <lb/>Autore i centri nell'emisfero, nel conoide parabolico, e nelle porzioni di parabola 317-20. </s></p><p type="main">

<s>Torricelliane dimostrazioni del centro di gravit&agrave; de'segmenti e de'frusti sferici, con alcuni supple&shy;<lb/>menti del Viviani 322-26: della brevit&agrave; e universalit&agrave; delle quali dimostrazioni sopra quelle di <lb/>L. </s>

<s>Valerio si compiace l'Autore col Ricci, col Cavalieri e con altri 326-28, e da ci&ograve; piglia occa&shy;<lb/>sione di ritrovare il centro di gravit&agrave; ne'solidi scavati, premessovi un lemma, la dimostrazione <lb/>del quale in supplita dal Viviani 328-30. </s></p><p type="main">

<s>Dimostrazione del Torricelli, col metodo degli indivisibili, e premessivi tre lemmi geometrici, che <lb/>l'emistero e l'emisferoide son doppi del cono inscritto 331-33, dopo la qual dimostrazione si torna <lb/>dal medesimo Autore a ricercare, per via del solito metodo degl'indivisibili, il centro di gravit&agrave; <lb/>ne'solidi scavati 333, 34. </s></p><p type="main">

<s>Varie proposizioni, raccolte dal Trattato del Torricelli, <emph type="italics"/>Della misura e del centro di gravit&agrave; dei so&shy;<lb/>lidi vasiformi<emph.end type="italics"/> 335-40. </s></p><p type="main">

<s>Teorema universalissimo del Torricelli, comprendente le dottrine degli Sferici e de'Conoidali di Ar&shy;<lb/>chimede: dal qual Teorema stereometrico se ne deriva un altro, pure universalissimo, per l'in&shy;<lb/>venzione del centro di gravit&agrave; di qualunque solido conoideo 340-45: per giungere alla quale inven&shy;<lb/>zione, esso Torricelli dimostra che un frusto conico si compone di tre coni, come gli aveva <lb/>annunziato il Ricci, e applica questa dimostrazione a confermar la formul&agrave;, con la quale da Ga&shy;<lb/>lileo s'indicava il centro di gravit&agrave; di esso frusto 345-51. </s></p><p type="main">

<s>Proposizioni IV, nelle quali il medesimo Torricelli dimostra dove stia il centro di gravit&agrave; nei segmenti <lb/>conici scavati e interi, nel frusto di conoide parabolico, sferico, e iperbolideo 352-57. </s></p><p type="main">

<s>Estratto di una lettera del Torricelli a M. A. Ricci, relativa alle sezioni del solido cavalierano 358, 59. </s></p><p type="main">

<s>Teorema, in cui il Torricelli, correggendo uno sbaglio del suo inventore, dimostra in qual propor&shy;<lb/>zione sia, secondo la proposta, segato il solido cavalierano 359-61. </s></p><p type="main">

<s>Ricerca del centro di gravit&agrave; nel solido colonnare, che ha per base due mezze parabole, premessavi <lb/>l'invenzione del centro di gravit&agrave; di esse mezze parabole congiunte per la base, e del trilineo <lb/>parabolico, in tre proposizioni dimostrate dal Torricelli 361-68. </s></p><p type="main">

<s>Centro di gravit&agrave; della Cicloide, indicato per una proposizione del Torricelli 369-72. </s></p><pb xlink:href="020/01/3031.jpg" pagenum="656"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo VI.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Lettera di V. </s>

<s>Viviani a Erasmo Bartholin, relativa alle opere inedite del Torricelli, pag. </s>

<s>374. </s></p><p type="main">

<s>Da una lettera del medesimo al p. </s>

<s>Baldigiani, sopra lo stesso argomento 374, 75. </s></p><p type="main">

<s>Proposizione, in cui si dimostra dal Torricelli che la forza &egrave; infinita 376, 77. </s></p><p type="main">

<s>Proposizioni due dimostrate dal Torricelli, per render pi&ugrave; generale, e per confermare il fondamento <lb/>della Dinamica galileiana 378, 79, con un teorema, soggiunto dal medesimo, per designar la via, <lb/>che fa il centro di gravit&agrave; di due corpi congiunti per un filo, e moventisi lungo piani comunque <lb/>inclinati 379. </s></p><p type="main">

<s>Proposizioni IV, relative alle proporzioni, che passano tra le velocit&agrave; e i tempi dei mobili ne'piani <lb/>inclinati, dimostrate dal Torricelli, per aggiungerle al suo trattato <emph type="italics"/>De motu<emph.end type="italics"/> 379-31. </s></p><p type="main">

<s>Dell'impeto dei punti, nel descrivere il circolo e l'iperbola: tooremi dimostrati dal Torricelli 381-33. </s></p><p type="main">

<s>Delle infinite parabole: teoremi dimostrati dal Torricelli, per estendere a qualunque legge di accele&shy;<lb/>razione la teoria de'proietti 384, 85. </s></p><p type="main">

<s>Del feco, e di altre propriet&agrave; della parabola, nell'use de'proietti, e per applicarle alla catenaria: <lb/>lemmi e proposizioni dimostrate dal Torricelli 385-89. </s></p><p type="main">

<s>Illustrazione del Viviani al teorema torricelliano della catenaria 387, 88. </s></p><p type="main">

<s>Note intorno ai momenti de'gravi, scritte dal Torricelli, per aggiungerle e dar perfezione al suo trat&shy;<lb/>tato <emph type="italics"/>De motu gravium<emph.end type="italics"/> 389-91. </s></p><p type="main">

<s>Proposizioni VII, dimostrate dal Torricelli intorno ai momenti dei gravi sopra i piani inclinati 391-94. </s></p><p type="main">

<s>Proposizioni IV, nelle quali applica il Torricelli alla Baricentrica i teoremi de'momenti dei gravi 395-400. </s></p><p type="main">

<s>Giudizio del Nardi intorno a preferirsi da Archimede i metodi obliqui ai diretti 403, 4. </s></p><p type="main">

<s>Discorso del Torricelli, in cui, a dimostrare le propriet&agrave; della Spirale archimedea, s'applica il prin&shy;<lb/>cipio della composizione dei moti 404-7. </s></p><p type="main">

<s>Regola del Torricelli <emph type="italics"/>pro tangentibus infinitarum parabolarum<emph.end type="italics"/> 409, 10. </s></p><p type="main">

<s>Lemma premesso dal Torricelli, per poi dimostrare un teorema, riguardante lo spazio passato ori&shy;<lb/>zontalmente da un mobile, supposto che l'antecedento velocit&agrave; fosse cresciuta come i quadrati <lb/>dei tempi 410, 11. </s></p><p type="main">

<s>Modo insegnato dal Torricelli, per condurre una tangente alla parabola cubica 411. </s></p><p type="main">

<s>Proposizioni due, nelle quali il Torricelli insegna il modo di condur meccanicamente le tangenti alla <lb/>Cicloide, e pone i principii, da concluderne il tautocronismo di lei 413, 14. </s></p><p type="main">

<s>Problemi risoluti dal Torricelli: trovar lo sforzo fatto da una trave, appoggiata al muro, e la causa <lb/>perch&egrave; a una colonna fessa s'impedisca l'aprirsi di pi&ugrave; e il rovinare, con una semplice fascia&shy;<lb/>tura 414-17. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo VII.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Giudizio, che da s&egrave; d&agrave; il Nardi delle sue Scene, pag 419. </s></p><p type="main">

<s>Cenni, dal Torricelli fatti al Cavalieri, e dal Ricci al Torricelli, relativi a un libro, che voleva stam&shy;<lb/>pare il Nardi 420. </s></p><p type="main">

<s>Indice della VIII Ricercata matematica del Nardi 421. </s></p><p type="main">

<s>Tooremi XII, de'quali si compila il trattato <emph type="italics"/>Dei centri di gravit&agrave;<emph.end type="italics"/> di Antonio Nardi, con le cose <lb/>supplitevi da M. A. </s>

<s>Ricci 421-30. </s></p><p type="main">

<s>Centro di gravit&agrave; del settore di sfera, commemorato in alcune sue lettere dal Torricelli, e concor&shy;<lb/>danza della indicazione data da lui con quella del Nardi 430, 31. </s></p><p type="main">

<s>Del centro di gravit&agrave; nei frusti conoidali universalmente: teorematiche indicazioni del Ricci, che su&shy;<lb/>scitarono la gelosia nell'animo del Torricelli 431-34. </s></p><p type="main">

<s>Quadratura della parabola, col metodo degli indivisibili, che dice il Nardi di avere imparato da Pappo <lb/>Alessandrino 436, 37. </s></p><p type="main">

<s>Dialogo, intorno all'invenzione della Cicloide, dettato da Galileo al Viviani, per inserirlo nella prima <lb/>Giornata delle que nuove Scienze, nell'occasione di una ristampa 438, 39. </s></p><p type="main">

<s>Passi estratti dalle <emph type="italics"/>Ricercate,<emph.end type="italics"/> dove il Nardi accenna alla quadratura meccanica della Cicloide, da s&egrave; <lb/>ritrovata, e ai problemi intorno ai solidi cicloidali 454. </s></p><pb xlink:href="020/01/3032.jpg" pagenum="657"/><p type="main">

<s>Estratto di lettera, nella quale il Cavalieri si rallegra col Torricelli delle ritrovate misure dello spazio <lb/>cicloidale, e narra come Galileo intorno a ci&ograve; si fosse ingannato 454, 55. </s></p><p type="main">

<s>Passo di una lettera del Ricci al Torricelli, concernente le curve cicloidali 455, 56. </s></p><p type="main">

<s>Discorso del Nardi intorno alla Cicloide, e in cui si comprendono le proposizioni dimostrate dal <lb/>Ricci 457-61. </s></p><p type="main">

<s>Luogo estratto dalle <emph type="italics"/>Scene,<emph.end type="italics"/> in cui il Nardi dimostra le proporzioni, che hanno i solidi ai cilindri cir&shy;<lb/>coscritti nella sua propria cicloide 463. </s></p><p type="main">

<s>Conclusione scritta dal Torricelli, relativa alla misura, che ha il solido cicloidale circa la base, verso <lb/>il cilindro a lui circoscritto 464. </s></p><p type="main">

<s>Conclusioni, relative ai solidi cicloidali, scritte dal Torricelli al Magiotti 465. </s></p><p type="main">

<s>Osservazione del Ricci, relativa alla facilit&agrave;, con cui dice al Torricelli di aver dimostrato il solido ci&shy;<lb/>cloidale circa la tangente parallela all'asse 466. </s></p><p type="main">

<s>Da una lettera, nella quale il Dati fa premure al Ricci, per aver notizia dell'Epistola robervalliana <lb/><emph type="italics"/>ad Torricellium<emph.end type="italics"/> 468. </s></p><p type="main">

<s>Da una lettera del Cavalieri al Torricelli: notizie relative alla cicloide 469. </s></p><p type="main">

<s>Teoremi cicloidali annunziat&igrave; dal Torricelli al Mersenno 470. </s></p><p type="main">

<s>Poscritto importante, in una lettera del Torricelli, tralasciato, nel pubblicarla, dal Dati 475. </s></p><p type="main">

<s>Il Torricelli scrive com'avesse insieme due fiere liti, l'una col Roberval, l'altra col Ricci 476, 77. </s></p><p type="main">

<s>Lettera, nella quale il Ricci si difende dall'accusa datagli dal Torricelli di avergli usurpato il metodo <lb/>di quadrare le infinite parabole 481-83. </s></p><p type="main">

<s>Discorso, in cui Antonio Nardi compendia una parte importantissima della storia filosofica dell'Astro&shy;<lb/>nomia 488-90. </s></p><p type="main">

<s>Due passi estratti dalle <emph type="italics"/>Scene accademiche,<emph.end type="italics"/> rlative ai pianeti, nel primo de'quali il Nardi professa <lb/>il principio delle forze centrali, e nel secondo dimostra che le orbite sono spirali molto simili <lb/>alle ellissi 490, 91. </s></p><p type="main">

<s>Note due, nelle quali il Viviani esplica alcune proposizioni meccaniche fondamentali di Galileo 493, 94. </s></p><p type="main">

<s>Proposizioni sei, intorno ai centri di gravit&agrave;, dimostrate dal Viviani 494-99. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo VIII.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Da una lettera del Ricci, dove accenna al Torricelli che il Mersenno e il Roberval contradicevano ai <lb/>principii fondamentali della Dinamica di Galileo, pag. </s>

<s>508. </s></p><p type="main">

<s>Da una lettera, nella quale il Mersenno domanda al Torricelli se Galileo aveva trovata la regola di <lb/>ridurre al pendolo semplice un pendolo composto 536. </s></p><p type="main">

<s>Regola data dal Viviani, per trovare qual punto del pendolo sia quello, dal quale si regola il <lb/>moto 536, 37. </s></p><p type="main">

<s>Teorema, in cui Galileo aveva dimostrato che le forze centripete stanno direttamente come i raggi <lb/>delle ruote 541. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Nel Capitolo IX.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Da Niccol&ograve; Witsen: traduzione dettata da Niccol&ograve; Stenone a Vincenzo Viviani: <emph type="italics"/>In qual modo pi&ugrave; <lb/>profittevole si voltino le vele ai venti,<emph.end type="italics"/> pag. </s>

<s>375-80. </s></p><pb xlink:href="020/01/3033.jpg"/><p type="main">

<s><emph type="center"/>INDICE ALFABETICO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>DEGLI AUTORI E DELLE COSE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Co'numeri s'accenna alle pagine<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="bold"/>Accademici di Londra<emph.end type="bold"/> ripetono, intorno alla forza della percossa, in sostanza, le dottrine del Bo&shy;<lb/>relli 77. </s></p><p type="main">

<s><emph type="bold"/>Acquapendente (d') Girolamo Fabricio,<emph.end type="bold"/> teoremi di Meccanica animale da lui dimostrati 211. </s></p><p type="main">

<s><emph type="bold"/>Aggiunti Niccol&ograve;<emph.end type="bold"/> previene il Borelli nel determinar la misura dei momenti, e delle quantit&agrave; di <lb/>moto 119. </s></p><p type="main">

<s><emph type="bold"/>Alemanni<emph.end type="bold"/> non curanti del loro connazionale Giovan Marco Marci 171. </s></p><p type="main">

<s><emph type="bold"/>Alembert (d'),<emph.end type="bold"/> sua nuova dimostrazione del parallelogrammo delle forze 621. </s></p><p type="main">

<s><emph type="bold"/>Analisi algebrica,<emph.end type="bold"/> come ne difettassero i Discepoli di Galileo 590. </s></p><p type="main">

<s><emph type="bold"/>Archimede,<emph.end type="bold"/> si scopre il segreto della XVIII proposizione dimostrata da lui intoruo alle propriet&agrave; delle <lb/>Spirali 401, e qual relazione ell'abbia con la quadratura del circolo 402, perch&egrave;, in dimostrare le <lb/>propriet&agrave; delle Spirali, seguisse il metodo obliquo invece del diretto 403. </s></p><p type="main">

<s><emph type="bold"/>Aria,<emph.end type="bold"/> quanto impedisca il risalir de'proietti nei tiri verticali 53. </s></p><p type="main">

<s><emph type="bold"/>Ariete,<emph.end type="bold"/> ragione della forza della sua percossa 174. </s></p><p type="main">

<s><emph type="bold"/>Aristotile,<emph.end type="bold"/> primo a propor la questione della forza della percossa 112. </s></p><p type="main">

<s><emph type="bold"/>Atomi della luce,<emph.end type="bold"/> si applicano ad essi le leggi del moto dei corpi ponderosi 471. </s></p><p type="main">

<s><emph type="bold"/>Baliani Giovan Batista,<emph.end type="bold"/> ingiusto giudizio dei meriti di lui rivendicato 28, trova difficolt&agrave; d'attribuire <lb/>all'aria la varia passata di una palla esplosa da un moschetto, presso alla bocca di lui, e in di&shy;<lb/>stanza 50. </s></p><p type="main">

<s><emph type="bold"/>Benedetti Giovan Batista,<emph.end type="bold"/> riforma del V libro di Euclide proposta da lui 78, sue speculazioni impor&shy;<lb/>tanti intorno alle forze centrifughe 539. </s></p><p type="main">

<s><emph type="bold"/>Beriguardi Claudio<emph.end type="bold"/> come dimostrasse un teorema fondamentale della Meccanica, indipendentemente, <lb/>e prima di Galileo 14. </s></p><p type="main">

<s><emph type="bold"/>Bernoulli Giovanni<emph.end type="bold"/> censura un corollario del Newton 594, sua nuova dimostrazione del parallelo&shy;<lb/>grammo delle forze 616. </s></p><p type="main">

<s><emph type="bold"/>Bilancia<emph.end type="bold"/> delle due secchie, immaginata da Galileo per misurar la forza della percossa, ridotta alle <lb/>sue ragioni idrostatiche 168. </s></p><p type="main">

<s><emph type="bold"/>Bonaventuri Tommaso,<emph.end type="bold"/> doveva, nella pubblicazione delle opere di Galileo, premettere al Dialogo detla <lb/>percossa quello della riforma di Euclide, e perch&egrave; 130. </s></p><p type="main">

<s><emph type="bold"/>Borelli Giovann'Alfonso,<emph.end type="bold"/> come applicasse il metodo degl'indivisibili, per superare le difficolt&agrave;, in&shy;<lb/>contrate da Galileo e dal Torricelli, nel dimostrare il teorema fondamentale dei moti uniformi 110, <lb/>sue proposizioni intorno alla forza della percossa 120, 122, 163, qual fosse l'intenzione che lo <lb/>mosse a scrivere il trattato <emph type="italics"/>De vi percussionis<emph.end type="italics"/> 122, come dimostri che qualunque piccolissimo <lb/>corpo pu&ograve; movere un grandissimo 136, scopre l'origine della fallacia in alcune esperienza del <lb/>Gassendo e del Viviani 164, sue esperienze della percossa sopra focacce pi&ugrave; o meno molli 165, <lb/>esperienza proposta da lui per dimostrar l'ondeggiamento de'passi dell'uomo 210, sue due opere <lb/>di Meccanica pura, brevemente esaminate 485-87, suo libro <emph type="italics"/>Theoricae Mediceorum<emph.end type="italics"/> 487-92, come <pb xlink:href="020/01/3034.jpg" pagenum="659"/>confondesso la forza centrifuga con quella di proiezione 542, sue fallacie relative al modo di com&shy;<lb/>porre le forze, ripudiando la regola del parallelogrammo 580-88, primo a dimostrar la misura vera <lb/>delle forze vivo 639. </s></p><p type="main">

<s><emph type="bold"/>Cabeo Niccol&ograve;,<emph.end type="bold"/> sua opposizione a un principio meccanico fondamentale supposto da Galileo 9. </s></p><p type="main">

<s><emph type="bold"/>Calcolo astronomico,<emph.end type="bold"/> propostosi da Galileo e dal Viviani, per adornare un concetto platonico 54. </s></p><p type="main">

<s><emph type="bold"/>Cardano Girolamo,<emph.end type="bold"/> suoi teoremi intorno ai moti composti 554. </s></p><p type="main">

<s><emph type="bold"/>Cartesio Renato,<emph.end type="bold"/> suoi paralogismi in soggetto de'moti composti 555. </s></p><p type="main">

<s><emph type="bold"/>Casati Paolo,<emph.end type="bold"/> come risolva il problema del funicolo gravato nel mezzo 74, scioglie uno dei problemi <lb/>naturali di Galileo 199, primo a dimostrar la verit&agrave; del parallelogrammo delle forze, contro le <lb/>fallacie de'seguaci di Galileo 588. </s></p><p type="main">

<s><emph type="bold"/>Catenelle,<emph.end type="bold"/> loro usa nella Ballistica, trattato in dialogo di Galileo, ora da noi ritrovato 143. </s></p><p type="main">

<s><emph type="bold"/>Cavalieri Bonaventura<emph.end type="bold"/> intraprende, a istanza di G. A. Rocca, la riforma di Euclide 87, proposizioni <lb/>geomotriche di lui, che aprirono la via alle invenzioni baricentriche del Torricelli 321-23, pro&shy;<lb/>pone un teorema intorno alle potenze algebriche, dal Torricelli poi dimostrato universalmente 408, <lb/>riassunto di ei&ograve; ch'egli operasse intorno alla Meccanica 484, raccomanda ai suoi scolari il Corso <lb/>matematico dell'Herigonio 581, sua geometria paragonata con l'Analisi infinitesimale 631. </s></p><p type="main">

<s><emph type="bold"/>Cazr Pletro,<emph.end type="bold"/> esperienza, da cui vuol concludere esser faisa la legge galileiana dei gravi naturalmente <lb/>cadenti 163. </s></p><p type="main">

<s><emph type="bold"/>Centri<emph.end type="bold"/> dell'oscillazione e della percossa, come si dimostrasse che non sono identici 535. </s></p><p type="main">

<s><emph type="bold"/>Centrigfuhe (forze),<emph.end type="bold"/> prime osservazioni fatte intorno ad esse 538, da quali considerazioni il Newton <lb/>ne rieavasse l'equazione, e ne concludesse i principali teoremi ugeniani 545-47, loro propriet&agrave; di&shy;<lb/>mostrate dall'Huyghens ne'pendoli conici 547-49. </s></p><p type="main">

<s><emph type="bold"/>Centro della<emph.end type="bold"/> percossa nelle varie figure, primi teoremi dimostrati dal Roberval 520, regole stabilite <lb/>dal Cartesio, e loro applicazione 522, esame di queste regole 525. </s></p><p type="main">

<s><emph type="bold"/>Centrebarico (teorema)<emph.end type="bold"/> come speditamente dimostrato dall'Herman 631. </s></p><p type="main">

<s><emph type="bold"/>Cicloide,<emph.end type="bold"/> origine della sua invenzione 440, liti, accuse e difese fra il Torricelli e il Roberval intorno <lb/>al primato delle scoperte propriet&agrave; di lei 466, e particolarmente intorno al centro di gravit&agrave; della <lb/>figura, e del solido circa l'asse 469-73, come il Roberval, esaminando la proporzione del solido <lb/>circa l'asse al cilindro circoscritto, data dal Torricelli, la trovasse falsa 473-75, come il Roberval, <lb/>dopo penosi indugi, trovasse la proporzione vera 478, tautocronismo di lei dimostrato dall'Huy&shy;<lb/>ghens 510-14. </s></p><p type="main">

<s><emph type="bold"/>Cimento (Accademia del),<emph.end type="bold"/> esperienza fatta in essa con un archibugio rigato, per confermare che alla <lb/>palla, nel tornare in gi&ugrave; naturalmente, &egrave; impedito il coipo dall'aria 52. </s></p><p type="main">

<s><emph type="bold"/>Colpi<emph.end type="bold"/> obliqui e diretti, leggi delle loro forze dimostrate dal Torricelli 191. </s></p><p type="main">

<s><emph type="bold"/>Comite<emph.end type="bold"/> della Cicloide 442, a quale occasione se ne intraprendesse lo studio in Italia, 542. </s></p><p type="main">

<s><emph type="bold"/>Conservazione<emph.end type="bold"/> della forza creduta razionale dal Borelli 183. </s></p><p type="main">

<s><emph type="bold"/>Corda<emph.end type="bold"/> tesa orizontalmente, qualunque minimo peso posto nel mezzo di lei vale a sollevarne due <lb/>grandissimi pendenti dagli estremi 58. </s></p><p type="main">

<s><emph type="bold"/>Cuneo,<emph.end type="bold"/> sua ragion meccanica derivata dalle dottrine di Giovan Marco Marci, e di Leonardo da <lb/>Vinci 174. </s></p><p type="main">

<s><emph type="bold"/>Dialeghi<emph.end type="bold"/> galileiani Del moto, come nella stampa degli Elzeviri rimanessero incompiuti 8. </s></p><p type="main">

<s><emph type="bold"/>Dialege V,<emph.end type="bold"/> delle due nuove Scienze, suo titolo proprio scritto dal Torricelli in fronte a una copia, da <lb/>presentarsi al principe Leopoldo de'Medici 98. </s></p><p type="main">

<s><emph type="bold"/>Differenziali<emph.end type="bold"/> leibniziani definiti dal Nardi 626. </s></p><p type="main">

<s><emph type="bold"/>Elasticit&agrave;<emph.end type="bold"/> imperfetta, perch&egrave; renda l'angolo della riflessione minore di quello dell'incidenza 190. </s></p><p type="main">

<s><emph type="bold"/>Esperimenti<emph.end type="bold"/> insigni, per misurare la forza della percossa, inventati da Galileo e descritti dal Torri&shy;<lb/>celli 155, pubblicati dal Mersenno 156, delle due secchie, dove l'acqua cadente da quella di sopra <lb/>percote il fondo dell'altra di sotto 167. </s></p><p type="main">

<s><emph type="bold"/>Euler Leonardo,<emph.end type="bold"/> interpetrazione di un passo della Meccanica analitica di lui 634. </s></p><p type="main">

<s><emph type="bold"/>Evolute<emph.end type="bold"/> delle curve, e specialmente della Cicloide 315. </s></p><p type="main">

<s><emph type="bold"/>Faille (della) Giovannl,<emph.end type="bold"/> suo trattato de'centri di gravit&agrave; delle porzioni di circolo e di ellisse 269, primo <lb/>a indicare il centro di gravit&agrave; nei semmenti, e nei settori di circolo e di ellisse 274. </s></p><p type="main">

<s><emph type="bold"/>Flussioni,<emph.end type="bold"/> metodo del Newton, non diverso da quello del Cavalieri 631. </s></p><p type="main">

<s><emph type="bold"/>Forze<emph.end type="bold"/> centrali, come si riconoscesse che variano d'intensit&agrave; in ragion reciproca de quadrati delle <lb/>distanze, 543, Composte, applicate alla teoria del piano inclinato 584, Vive, questione intorno al <lb/>pi&ugrave; giusto modo di misurarle 635-39. </s></p><pb xlink:href="020/01/3035.jpg" pagenum="660"/><p type="main">

<s><emph type="bold"/>Frammento,<emph.end type="bold"/> da inserirsi nel III dialogo delle due nuove Scienze, dopo la prima proposizione dei <lb/>moti equabili 93. </s></p><p type="main">

<s><emph type="bold"/>Galilei Galileo,<emph.end type="bold"/> come scoprisse una fallacia dell'ingegner Bartolotti 10, come iu un caso simile per&shy;<lb/>suadesse Guidubaldo del Monte 11, con quali arti usurpasse la riforma del V libro d'Euclide al <lb/>Cavalieri 91, per qual ragione pensasse di fare un dialogo a parte intorno alla Scienza delle pro&shy;<lb/>porzioni 93, non appartiene a lui il fondamento della Scienza delle proporzioni, n&egrave; quanto al con&shy;<lb/>cetto. </s>

<s>n&egrave; quanto alla forma 97, suo errore nell'assegnare le proporzioni delle velocit&agrave; fra i corpi, <lb/>prima e dopo l'urto 122, per quale occasione, e quando riprendesse le speculazioni intorno alla <lb/>forza della percossa 124, a che punto, nell'ottobre del 1638, avesse condotto il dialogo della per&shy;<lb/>cossa 125, suo tre proposizioni intorno all'urto dei corpi 131, processo del ragionamento di lui, nel <lb/>Dialogo della percossa 132-34, suo mirabile detto, confermato dall'Huyghens e dal Mariotte 135, <lb/>suoi sbagli in cose di Matematica pi&ugrave; elementare 228, sua proposizione lemmatica dei centri di <lb/>gravit&agrave;, subodorata falsa dal Torricelli 296, relazioni di lui col Guldino 298, suo teorema relativo <lb/>alle forze centripete 539, suo teorema de'moti composti, che si riconosce falso, paragonato con <lb/>quello dell'Herigonio 557. </s></p><p type="main">

<s><emph type="bold"/>Gassendo Pietro<emph.end type="bold"/> accolse, comment&ograve; e diffuse le dottrine dinamiche di Galileo 501. </s></p><p type="main">

<s><emph type="bold"/>Guldin Paolo,<emph.end type="bold"/> sue false proposizioni baricentriche, esaminate dal Torricelli 305, quale origine avesse, <lb/>secondo lui, il metodo del Cavalieri 309. </s></p><p type="main">

<s><emph type="bold"/>Herman Giacomo<emph.end type="bold"/> dimostra generalmento un corollario neutoniano 595, esame della <emph type="italics"/>Foronomia<emph.end type="italics"/> di <lb/>lui 606-15, con gl'indivisibili del Cavalieri, e co'segni del Leibniz, usa il calcolo infinitesi&shy;<lb/>male 632. </s></p><p type="main">

<s><emph type="bold"/>Hire (de la)<emph.end type="bold"/> come risolvesse il problema robervalliano del nodo della fune, che rimane in equilibrio, <lb/>tirato da tre potenze 570. </s></p><p type="main">

<s><emph type="bold"/>Hopital (de l'),<emph.end type="bold"/> sue censure al VII teorema ugeniano <emph type="italics"/>De vi centrifuga,<emph.end type="italics"/> e loro difesa 548, suo teo&shy;<lb/>rema <emph type="italics"/>De potentiis fila funesve trahentibus<emph.end type="italics"/> dimostrato col principio della composizione delle <lb/>forze 569. </s></p><p type="main">

<s><emph type="bold"/>Huyghens Cristiano,<emph.end type="bold"/> suo trattato <emph type="italics"/>De motu corporum ex percussione<emph.end type="italics"/> 177-79, primo a risolvere, con <lb/>metodo generale, i problemi del centro delle oscillazioni e delle percosse 528, sua XVI proposf&shy;<lb/>zione <emph type="italics"/>De vi centrifuga,<emph.end type="italics"/> riconosciata falsa 450. </s></p><p type="main">

<s><emph type="bold"/>Indivisibili,<emph.end type="bold"/> metodo, secondo il Nardi, usato da Archimede e da Pappo 435, il Roberval ne riconosce <lb/>autore il Cavalieri, ma il Cartesio ne attribuisce il merito dell'invenzione a s&egrave; stesso 451, usato <lb/>dal Wallis, e dai principali Matematici d'Europa 509, definito dallo stesso Cavalieri, per rispon&shy;<lb/>dere alle critiche di Galileo 627, corrisponde alle flussioni del Newton 628, pregiudizi di alcuni <lb/>intorno ad esso 629. </s></p><p type="main">

<s><emph type="bold"/>Integrale<emph.end type="bold"/> (teorema) di cui fecero uso principalmente il Torricelli e il Roberval, per sommare le quan&shy;<lb/>tit&agrave; indivisibili 513. </s></p><p type="main">

<s><emph type="bold"/>Kepler Giovanni,<emph.end type="bold"/> come interpetri la I2 archimedea <emph type="italics"/>De dimensione circuli<emph.end type="italics"/> 309. </s></p><p type="main">

<s><emph type="bold"/>Lagrange Luigi,<emph.end type="bold"/> sua Meccanica analitica 640-42. </s></p><p type="main">

<s><emph type="bold"/>Laplace,<emph.end type="bold"/> sua nuova dimostrazione del parallelogrammo delle forze, condotta per via del calcolo infi&shy;<lb/>nitesimale 622. </s></p><p type="main">

<s><emph type="bold"/>Leggerezza<emph.end type="bold"/> del correre, dimostrata da vari principii meccanici 175. </s></p><p type="main">

<s><emph type="bold"/>Lexioni accademiche<emph.end type="bold"/> del Torricelli intorno alla forza della percossa: loro occasione e intendimento <lb/>dell'Autore 138, loro sommario 139-42, completano il dialogo della percossa, lasciato interrotto da <lb/>Galileo 142. </s></p><p type="main">

<s><emph type="bold"/>Lemiti,<emph.end type="bold"/> loro metodo applicato dal Nawton agli indivisibili 629. </s></p><p type="main">

<s><emph type="bold"/>Magiotti Eaffaelle,<emph.end type="bold"/> notizie di un manoscritto di lui aggiunto alla raccolta de'galileiani 70. </s></p><p type="main">

<s><emph type="bold"/>Magli<emph.end type="bold"/> a vapore, come si spieghino i varii effetti curiosi delle loro percosse 175. </s></p><p type="main">

<s><emph type="bold"/>Marchetti Alessandro,<emph.end type="bold"/> suo teorema delle tangeati e delle secanti nel circolo, dimostrato in concor&shy;<lb/>renza col Viviani 69. </s></p><p type="main">

<s><emph type="bold"/>Marci Giovan Marce,<emph.end type="bold"/> opere di lui poco conosciute 171, instituisce la nuova Scienza della percossa, e <lb/>della comunicazione dei moti 172, sue leggi degli urti dei corpi <emph type="italics"/>ivi,<emph.end type="italics"/> come, dalle sue formule, l'er&shy;<lb/>rore peripatetico delle velocit&agrave; proporzionali alle masse sia meglio confutato, che dai lunghi ra&shy;<lb/>gionamenti di Galileo 173, confronto di alcuni suoi teoremi con quelli del Borelli 177, come dimo&shy;<lb/>stri le ragioni dell'uguaglianza dell'angolo dell'incidenza con quello della riflessione, per via dei <lb/>moti composti 189, primo a dar la dimostrazion razionale dei moti composti 558-61. </s></p><pb xlink:href="020/01/3036.jpg" pagenum="661"/><p type="main">

<s><emph type="bold"/>Mariotte Edmondo,<emph.end type="bold"/> suo trattato della percossa 180. </s></p><p type="main">

<s><emph type="bold"/>Martello,<emph.end type="bold"/> modo e forza della percossa fatta da lui 114. </s></p><p type="main">

<s><emph type="bold"/>Mersenno Marino<emph.end type="bold"/> censura alcune proposizioni dinamiche di Galileo 502, professa con Galileo che la <lb/>resultante debba uguagliar la somma delle componenti, e poi riconosce il suo errore 571. </s></p><p type="main">

<s><emph type="bold"/>Moto<emph.end type="bold"/> non muore, n&egrave; rinvivisce, ma si conserva latente 182. </s></p><p type="main">

<s><emph type="bold"/>Nardi Antonio,<emph.end type="bold"/> suo savio avvertimento intorno al giudicare i grandi uomini 83, notizie de'mano&shy;<lb/>scritti di lui 419-21, trova per via meccanica la quadratura della Cicloide esatta 453, immagina <lb/>una Cicloide nuova, per la quadratura della volgare 455, 58. </s></p><p type="main">

<s><emph type="bold"/>Newton Isacco,<emph.end type="bold"/> storia del primo tomo de'suoi Principii matematici di Filosofia naturale 591-605. </s></p><p type="main">

<s><emph type="bold"/>Ottica<emph.end type="bold"/> cartesiana, censure relative ai moti composti, fatte dal Roberval, dall'Hobbes e dal Fer&shy;<lb/>mat 563-65. </s></p><p type="main">

<s><emph type="bold"/>Pappo Alessandrino,<emph.end type="bold"/> dimostrazione di lui condotta col metodo degli indivisibili 435. </s></p><p type="main">

<s><emph type="bold"/>Parallelogrammo<emph.end type="bold"/> delle forze, come dimostrato dal Newton 615, come dal Varignen e dall'Herman 616, <lb/>come dal Prony 624, come da altri, comprendendo le virt&ugrave; delle dimostrazioni precedenti 625. </s></p><p type="main">

<s><emph type="bold"/>Pendolo<emph.end type="bold"/> semplice, una propriet&agrave; di lui scoperta dal Borelli 183, come l'Huyghens riuscisse a fargli <lb/>descrivere arehi cicloidali 516, composto, come si riduce al semplice 528-30, regola di questa <lb/>riduzione data dall'Huyghens, che il Deschales non riconosce vera, se non in alcuni casi parti&shy;<lb/>colari 531, obiexioni fatte all'Huyghens in questo proposito da altri Matematici 532, finalmente la <lb/>verit&agrave; della Regola ugeniana vien confermata, per via del calcolo infinitesimale 533, e derivan&shy;<lb/>dola da principii diversi da quello della conservazione delle forze vive 534. </s></p><p type="main">

<s><emph type="bold"/>Percossa,<emph.end type="bold"/> forza di lei paragonata da Galileo con quella delle Macchine 114, quali false idee ne avesse <lb/>il Mersenno 115, distinta dall'Aggiunti in naturale, violenta e media 119, leggi di lei, che si lu&shy;<lb/>sing&ograve; di avere scoperte il Viviani, usando una stadera costruita sopra un disegno del Torri&shy;<lb/>celli 162. </s></p><p type="main">

<s><emph type="bold"/>Perelli Tommaso<emph.end type="bold"/> erra insieme col Viviani nel risolvere il problema della corda tesa, gravata nel <lb/>mezzo da un piccolissimo peso 72. </s></p><p type="main">

<s><emph type="bold"/>Pietroburge,<emph.end type="bold"/> esperienze ivi fatte per dimostrare il grande impedimento, che ricevon dall'aria i pro&shy;<lb/>ietti nei tiri verticali 53. </s></p><p type="main">

<s><emph type="bold"/>Platone,<emph.end type="bold"/> suo concetto voluto ridurro a calcolo da Galileo e dal Viviani 53. </s></p><p type="main">

<s><emph type="bold"/>Poleni Giovanni,<emph.end type="bold"/> sue esperienze per la misura delle forze vive 636. </s></p><p type="main">

<s><emph type="bold"/>Postulate,<emph.end type="bold"/> principio meccanico di Galileo 11, come da Galileo stesso dimostrato 12, come dal Miche&shy;<lb/>lini 14, come dal Baliani 15, come dal Torricelli, invocando un principio nuovo 23, come, in di&shy;<lb/>verso modo da quel che che aveva fatto nella prima edizione, il Baliani lo dimostrasse nella <lb/>seconda 29, come lo dimostrasse l'Huyghens che, malcontento di Galileo, cade in un paralogi&shy;<lb/>smo 29, come finalmente lo dimostrasse A. </s>

<s>Marchetti 32. </s></p><p type="main">

<s><emph type="bold"/>Problemi naturali,<emph.end type="bold"/> occasione che Galileo ebbe di scriverli 196. </s></p><p type="main">

<s><emph type="bold"/>Quadratura<emph.end type="bold"/> della Cicloide, come fosse dimostrata dal Cartesio e dal Fermat 449-52. </s></p><p type="main">

<s><emph type="bold"/>Riccati Vincenzo,<emph.end type="bold"/> come dimostrl il parallelogrammo delle forze 619, sottopone al calcolo l'esperienza <lb/>dimostrativa della vera misura delle forze vive 637. </s></p><p type="main">

<s><emph type="bold"/>Ricci Michelangiolo<emph.end type="bold"/> risolve al Viviani un dubbio meccanico, per il principio dei moti composti 67, <lb/>esorta il Borelli a trattare della composizione dei moti 580. </s></p><p type="main">

<s><emph type="bold"/>Riflessione<emph.end type="bold"/> conserva, secondo il Borelli, la stessa quantit&agrave; di moto dell'incidenza 186, segue nel suo <lb/>viaggio la via pi&ugrave; breve <emph type="italics"/>ivi.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="bold"/>Rimbalzello,<emph.end type="bold"/> sua ragione data da G. M. </s>

<s>Marci 193. </s></p><p type="main">

<s><emph type="bold"/>Rimbalzi<emph.end type="bold"/> non giungono mai alla precisa altezza, da cui scesero i corpi 185. </s></p><p type="main">

<s><emph type="bold"/>Roberval Egidio,<emph.end type="bold"/> sue proposizioni dimostrative delle propriet&agrave; della Cicloide, raccolte e ordinata&shy;<lb/>mente narrate 441, suo notabile teorema <emph type="italics"/>Des anneaux<emph.end type="italics"/> 446, lemmi premessi, per dimostrare in <lb/>tre distinte proposizioni la proporzion che passa tra i solidi cicloidali e i cilindri circoscritti 446-49, <lb/>come si difendesse dall'accuse mossegli dal Torricelli di avergli usurpata l'invenxione del cen&shy;<lb/>tro di gravit&agrave; della Cicloide 480, degli otto libri di Meccanica nuova, pubblicati da lui 504-8, suo <lb/>trattato Dei moti composti 562, riconosce il Cavalieri autore degli indivisibili 628. </s></p><p type="main">

<s><emph type="bold"/>Rocca Giovann'Antonio,<emph.end type="bold"/> suo trattato dei moti equabili 86. </s></p><p type="main">

<s><emph type="bold"/>Sarpi Paolo,<emph.end type="bold"/> sue istanze contro un principio fondamentale della Meccanica di Galileo 50, propone <lb/>a Galileo un problema relativo alle quantit&agrave; di moto 118, il qual problema era stato risoluto gi&agrave; <lb/>da Leonardo da Vinci 119. </s></p><pb xlink:href="020/01/3037.jpg" pagenum="662"/><p type="main">

<s><emph type="bold"/>Scaligero G. Cesare,<emph.end type="bold"/> qual opposizione facesse alle opinioni del Cardano intorno alla forza della per&shy;<lb/>cossa 113. </s></p><p type="main">

<s><emph type="bold"/>Secchie,<emph.end type="bold"/> per la misura della forza della percossa, esperienza di Galileo illustrata 168. </s></p><p type="main">

<s><emph type="bold"/>Simpson Tommaso<emph.end type="bold"/> applica il principio della composizion delle forze a dimostrare il teorema gali&shy;<lb/>leiano della corda tesa 73. </s></p><p type="main">

<s><emph type="bold"/>Spada,<emph.end type="bold"/> in qual parte della sua lunghezza faccia, secondo Isacco Vossio, maggiore la ferita 116. </s></p><p type="main">

<s><emph type="bold"/>Stadera<emph.end type="bold"/> per la misura della forza della percossa, proposta dal Rinaldini nell'Accademia del Ci&shy;<lb/>mento 160. </s></p><p type="main">

<s><emph type="bold"/>Stenone Niccol&ograve;,<emph.end type="bold"/> colloquio di lui col Viviani, relativo ai moti composti 575. </s></p><p type="main">

<s><emph type="bold"/>Stevino Simeone,<emph.end type="bold"/> primo a dimostrar geometricamente il teorema della scesa di un grave per un <lb/>piano inclinato, qualunque sia la direzione, che la potenza fa col declivio 567. </s></p><p type="main">

<s><emph type="bold"/>Tangenti,<emph.end type="bold"/> loro descrizione meccanica 407. </s></p><p type="main">

<s><emph type="bold"/>Teoremi<emph.end type="bold"/> due, inseriti dal Torricelli, annuente e compiacentesi Galileo, nel Dialogo delle propor&shy;<lb/>zioni 99, perch&egrave; manchino nella copia originate di detto Dialogo fatta dal Torricelli per il prin&shy;<lb/>cipe Leopoldo de'Medici 101. </s></p><p type="main">

<s><emph type="bold"/>Tempo<emph.end type="bold"/> impiegato dal grave a passare naturalmente uno spazio determinato, come misurato dall'Huy&shy;<lb/>ghens 517. </s></p><p type="main">

<s><emph type="bold"/>Termometro,<emph.end type="bold"/> come l'invenzione di lui, attribuita a Galileo, pensasse il Viviani di commemorar nei <lb/>dialoghi delle due nuove Scienze 49. </s></p><p type="main">

<s><emph type="bold"/>Torricelli Evangellsta,<emph.end type="bold"/> il libro di lui <emph type="italics"/>De motu<emph.end type="italics"/> presentato a Galileo 19, quanto fosse stimato in Fran&shy;<lb/>cia si d&agrave; a giudicar da ci&ograve;, che si narra esser passato fra il Carcary e il Gassendo 27, in che <lb/>modo distese a dettatura il dialogo delle proporzioni 95, descrizione de'pensieri, che gli passa&shy;<lb/>rono per la mente, nel leggero i libri della Centrobarica guldiniana, mandatigli dal Cavalieri, e <lb/>in cui not&ograve; vari falsi teoremi 304, suoi teoremi de'moti composti esaminati 573. </s></p><p type="main">

<s><emph type="bold"/>Trottole,<emph.end type="bold"/> perch&egrave; girando stien ritte 197. </s></p><p type="main">

<s><emph type="bold"/>Ultimo<emph.end type="bold"/> congresso di Galileo, storia relativa a lui narrata dal Viviani 129. </s></p><p type="main">

<s><emph type="bold"/>Uniforme,<emph.end type="bold"/> moto, sue principali propriet&agrave; dimostrate da Archimede 85. </s></p><p type="main">

<s><emph type="bold"/>Valerio Luca<emph.end type="bold"/> applica il principio della composizion delle forze a dimostrare il supposto meccanico <lb/>di Galileo 21, 556. </s></p><p type="main">

<s><emph type="bold"/>Varignon Pietro,<emph.end type="bold"/> sua <emph type="italics"/>Nouvelle mecanique<emph.end type="italics"/> 552, suo esame critico dell'opinion del Borelli intorno <lb/>alle proporzioni de'pesi pendenti le corde 584-87. </s></p><p type="main">

<s><emph type="bold"/>Velocit&agrave; virtuoli,<emph.end type="bold"/> dubbi intorno ad esse mossi da Galileo e dalla sua Scuola 38, e segnatamente dal <lb/>Cavalieri 67, come le definisse Giovanni Bernoulli, che cos&igrave; fu il primo a chiamarle 682. </s></p><p type="main">

<s><emph type="bold"/>Vinci (da) Leonardo,<emph.end type="bold"/> suoi teoremi relativi alle quantit&agrave; di moto e ai loro effetti 119, 170, relativi alla <lb/>forza della percossa 270, 74, aveva interpetrato allo stesso modo del Kepler la Ia archimedea <emph type="italics"/>De <lb/>circuli dimensione<emph.end type="italics"/> 309. </s></p><p type="main">

<s><emph type="bold"/>Viviani Viucenzo,<emph.end type="bold"/> come facesse ia prima conoscenza di Galileo in Arcetri, e gli proponesse alcuni <lb/>suoi dubbi 9, come s'avvedesse che i dialoghi delle due nuovo Scienze avevano bisogno d'esser <lb/>corretti 55, si rivolge a M. A. Ricci, per aver da lui la soluzione meccanica di un suo dubbio 66, <lb/>intento principale degli studii, dati da lui alla meccanica 492. </s></p><p type="main">

<s><emph type="bold"/>Vessio Isacco,<emph.end type="bold"/> come si lusingasse di aver suggerito certe considerazioni intorno al modo pi&ugrave; van&shy;<lb/>vantaggioso di disporre le parti de'corpi, che han da operar la percossa 116. </s></p><p type="main">

<s><emph type="bold"/>Wallis Giovanni,<emph.end type="bold"/> suo trattato <emph type="italics"/>De percussione<emph.end type="italics"/> 179, come dimostrasse l'uguaglianza fra l'angolo del&shy;<lb/>l'incidenza e della riflessione, e rispondesse a coloro, che chiamavano una temerit&agrave; la composi&shy;<lb/>zione e scomposizione delle forze 187, conclude come Galileo che anche il salto di una pulce <lb/>commoverebbe la Terra 202, generalizza alcuni teoremi del Torricelli, per applicarli all'inven&shy;<lb/>zione del centro di gravit&agrave; delle superficie curve 294, applica il metodo kepleriano all'invenzione <lb/>de'centri di gravit&agrave; dei settori circolari e sferici 210, rispetto al centro della percossa usa il me&shy;<lb/>todo, e conferma le conclusioni del Roberval e del Cartesio 526, suo teorema, e difesa de'moti <lb/>composti 568. </s></p><p type="main">

<s><emph type="bold"/>Witsen Niccol&ograve;,<emph.end type="bold"/> come, applicandovi i teoremi steviniani della composizion dei moti, sciogliesse il <lb/>problema del voltar, nel modo pi&ugrave; profittevole, le vele ai venti 568. <pb xlink:href="020/01/3038.jpg"/><pb xlink:href="020/01/3039.jpg"/></s></p><pb xlink:href="020/01/3040.jpg"/><p type="main">

<s>Finito di stampare in Bologna presso la <lb/>Libreria Editrice Forni nel Giugno 1970 </s></p><pb xlink:href="020/01/3041.jpg"/></chap><chap><p type="main">

<s>350478 Storia Del Metodo Sperimentale Italia </s></p><p type="main">

<s><emph type="center"/>THE SOURCES OF SCIENCE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Editor-in-Chief: Harry Woolf<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Willis K. </s>

<s>Shepard Professor of the History of <lb/>Science, The Johns Hopkins University<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="020/01/3042.jpg"/><p type="main">

<s><emph type="center"/><emph type="bold"/><emph type="italics"/>Storia del Metodo <lb/>Sperimentale in Italia<emph.end type="italics"/><emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>by RAFFAELLO CAVERNI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>in Six Volumes<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Volume VI<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>THE SOURCES OF SCIENCE, NO. 134<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT CORPORATION<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>NEW YORK LONDON 1972<emph.end type="center"/></s></p><pb xlink:href="020/01/3043.jpg"/><p type="main">

<s>Reproduced here is the Florence edition of 1891-1900. </s></p><p type="main">

<s>This sixth volume of the <emph type="italics"/>Storia del Metodo Sperimentale <lb/>in Italia<emph.end type="italics"/> was published posthumously and is incomplete. </s>

<s><lb/>It breaks off suddenly on page 464. </s></p><figure id="id.020.01.3043.1.jpg" xlink:href="020/01/3043/1.jpg"/><p type="main">

<s><emph type="center"/>Copyright &copy; 1972 by Johnson Reprint Corporation All rights reserved <lb/>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT CORPORATION<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>111 Fifth Avenue, New York, N.Y. 10003, U.S.A.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>JOHNSON REPRINT COMPANY LTD.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>Shipton Group House, 24/28 Oval Road, London, NW17DD, England<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Printed in Italy<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="020/01/3044.jpg"/><p type="main">

<s><emph type="center"/>DEL METODO SPERIMENTALE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>APPLICATO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>ALLA SCIENZA DEL MOTO DELLE ACQUE<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>PARTE PRIMA<emph.end type="center"/><pb xlink:href="020/01/3045.jpg"/></s></p><pb xlink:href="020/01/3046.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO I.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Della Scienza dell'equilibrio e del moto delle acque <lb/>da'suoi principii infino a tutto il secolo XVI<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Della partizione di questa Storia: di Archimede, e del suo primo libro delle Galleggianti. </s>

<s>&mdash; II. </s>

<s>Del <lb/>secondo libro archimedeo delle Galleggianti. </s>

<s>&mdash; III. </s>

<s>Della Scienza del moto delle acque da Sesto <lb/>Giulio Frontino a Leonardo da Vinci. </s>

<s>&mdash; IV. </s>

<s>Delle dottrine idrauliche di L. da Vinci, parago&shy;<lb/>nate con quello di Girolamo Cardano. </s>

<s>&mdash; V. De'progressi fatti dall'Idrostatica nella seconda <lb/>met&agrave; del secolo XVI. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Chiamare <emph type="italics"/>acque<emph.end type="italics"/> i liquidi, come arie i corpi gazosi, potrebbe sembrare <lb/>improprio, o almen basso, nell'artificioso linguaggio, di che fanno uso gli <lb/>scienziati moderni. </s>

<s>Ma pure, amando noi di essere anche nelle parole sem&shy;<lb/>plici e chiari, abbiam creduto di non doverci dilungare in ci&ograve; dall'esempio <lb/>di quei buoni antichi, i quali, per non coniar vocaboli strani e non intesi, <lb/>davano a tutta una specie il nome stesso di uno degli oggetti, che, fra'com&shy;<lb/>presi in essa, fosse de'pi&ugrave; comuni. </s>

<s>E qual cosa infatti &egrave; pi&ugrave; comune e pi&ugrave; <lb/>nota dell'acqua, alla quale tutti sappiamo doversi attribuire, nelle piante e <lb/>negli animali, quella che propriamente si dice freschezza di vita? </s>

<s>Aggiun&shy;<lb/>gasi che parte principalissima della Scienza, di cui siamo per narrare la Sto&shy;<lb/>ria, consiste nell'investigare le ragioni e i modi del correre le acque sull'al&shy;<lb/>veo, e dentro gli argini dei fiumi. </s></p><p type="main">

<s>Ma o siano acque o di qualunque altra natura i liquidi, per questo si <lb/>distinguono, e formano una specie a parte dagli altri trattabili corpi, perch&egrave;, <lb/>sebben rimangano quanto al volume costanti, son, quanto alla forma, conti&shy;<lb/>nuamente variabili, accomodandosi, quando sono in quiete, a prendere quella, <pb xlink:href="020/01/3047.jpg" pagenum="8"/>qualunque ella si sia, dei recipienti. </s>

<s>&Egrave; di qui manifesto che se il recipiente <lb/>ha figura regolare, come di cono o di sfera, il liquido infusovi, in quanto &egrave; <lb/>grave, tende al centro terrestre secondo la direzione, e con la intensit&agrave; di un <lb/>solido, che fosse denso ugualmente, e il centro di gravit&agrave; si troverebbe perci&ograve; <lb/>nello stesso punto, che nel cono solido o nella sfera. </s>

<s>Ma se le pareti si rom&shy;<lb/>pono, e il contenuto si versa, &egrave; impossibile a sapere oramai pi&ugrave; dove sia an&shy;<lb/>dato il centro di gravit&agrave;, s&igrave; perch&egrave; la mole liquida ha preso una figura irre&shy;<lb/>golare, e s&igrave; perch&egrave; questa stessa figura ad ogni istante si varia. </s></p><p type="main">

<s>Pu&ograve; intravedersi di qui una di quelle difficolt&agrave;, che la Scienza trova <lb/>assai maggiore in investigar le leggi del moto ne'liquidi, che ne'solidi. </s>

<s>Ma <lb/>non &egrave; la sola, imperocch&egrave; ogni particella liquida com'&egrave; premuta per la pro&shy;<lb/>pria gravit&agrave;, e per il peso delle soprastanti, cos&igrave; ripreme col medesimo im&shy;<lb/>pulso tutte le altre, che le stanno all'intorno, ond'&egrave; in tutta la mole un'in&shy;<lb/>finit&agrave; d'infinite forze intestine, fra le quali pu&ograve; turbar l'equilibrio ogni pi&ugrave; <lb/>lieve accidente. </s>

<s>Si presentano perci&ograve; allo scienziato a risolvere problemi di <lb/>un'infinita infinit&agrave; d'incognite, fortunato se pu&ograve; riuscire a determinarne qual&shy;<lb/>cuna, e pi&ugrave; fortunato che mai se la travagliata determinazion particolare &egrave; <lb/>la vera. </s></p><p type="main">

<s>Tante altre considerazioni, che si potrebbero fare in simile proposito, <lb/>predispongono i nostri Lettori ad ascoltare una storia, in cui il Metodo spe&shy;<lb/>rimentale, quando non si confesser&agrave; insufficiente a scoprire la verit&agrave; deside&shy;<lb/>rata, dar&agrave; le prove estreme della sua propria bont&agrave; e del suo valore. </s>

<s>Di qui <lb/>&egrave; che, mentre la Meccanica de'solidi era giunta alla perfezione, che si vide <lb/>ne'Dialoghi delle due nuove Scienze; quella de'liquidi si pu&ograve; dire che ri&shy;<lb/>maneva tuttavia nell'infanzia. </s>

<s>N&egrave; de'progressi fatti poco di poi si deve tutto <lb/>il merito attribuire agli sperimenti, ma pure si furon questi, che addirizza&shy;<lb/>rono il filo alle speculazioni, e che ne assicurarono della rettitudine in tanti <lb/>casi, come per esempio quando s'applic&ograve; agli efflussi dai vasi le scoperte <lb/>leggi delle cadute naturali dei gravi, e dei getti parabolici. </s>

<s>Si prese da ci&ograve; <lb/>fiducia di ridur la Scienza del moto de'liquidi a partecipar de'progressi cos&igrave; <lb/>felicemente fatti dalla Scienza del moto dei corpi duri, ma tanti dubbi assa&shy;<lb/>lirono le menti, e tante cause concorsero a rompere i ritrosi vincoli di quei <lb/>connubii, che le stesse esperienze pi&ugrave; diligenti ebbero a travagliarsi lunga&shy;<lb/>mente in stabilirgli, e no assolutamente, ma in certe date condizioni. </s></p><p type="main">

<s>In ogni modo partecipano i liquidi co'solidi una propriet&agrave; essenziale, che <lb/>consiste nell'essere ambedue le specie de'corpi similmente gravi; ond'&egrave; che, <lb/>se questa forza di gravit&agrave; &egrave; ritenuta da qualche ostacolo, come dalle pareti <lb/>di un recipiente, il liquido rimane in quiete, ma lasciato in libert&agrave; si muove, <lb/>scendendo, per la pi&ugrave; breve e diretta via, al comun centro terrestre. </s>

<s>Anche <lb/>questa Scienza perci&ograve; and&ograve; soggetta a quelle due massime distinzioni, che si <lb/>fecero della Meccanica, chiamandosi <emph type="italics"/>Idrostatica<emph.end type="italics"/> l'una parte, che tratta del&shy;<lb/>l'equilibrio, e <emph type="italics"/>Idrodinamica<emph.end type="italics"/> quell'altra, che tratta del moto. </s>

<s>Le leggi idro&shy;<lb/>statiche e idrodinamiche, dai Matematici dimostrate co'calcoli, e da'Fisici <lb/>verificate con l'esperienze, s'appropriano a ogni specie di liquidi, che si con-<pb xlink:href="020/01/3048.jpg" pagenum="9"/>tengano in piccoli vasi, da'fori aperti ne'quali fluiscano liberamente o dentro <lb/>tubi aggiunti, o in artificiosi canali. </s>

<s>Ma ci &egrave; un liquido, fra i mondani elementi <lb/>diffusissimo, e uno de'maggiori ministri deputato dalla Natura a dispensare <lb/>sul nostro globo la vita; liquido, che ha per suoi propri vasi i laghi e i <lb/>mari, sull'ampia superficie de'quali corre e ricorre senza mai posa tra invi&shy;<lb/>sibili sponde, che gli si vedono poi distinte negli argini de'fiumi e negli <lb/>alvei, da s&egrave; stesso scavatisi con provvido istinto a'suoi liberi flussi perenni. </s></p><p type="main">

<s>Sembrerebbe a prima vista che, essendo le velocit&agrave; indipendenti dalla <lb/>maggiore o minor mole della materia, e dal pi&ugrave; lungo o breve spazio per&shy;<lb/>corso, fossero con pari legge velocitate le acque, sia ch'ell'escano da piccol <lb/>vaso o da larga fonte, e s'avviino a scendere gi&ugrave; pel declivio di un tavolato <lb/>manufatto o di un alveo naturale, senz'altra differenza che degli impedi&shy;<lb/>menti nel pi&ugrave; lungo corso, e nel declivio pi&ugrave; scabroso, maggiormente ritar&shy;<lb/>datori del moto. </s>

<s>Ma ripensando poi che ne'fiumi le sezioni premono tanto <lb/>pi&ugrave; fortemente sopra s&egrave; medesime, e incalzano le sezioni seguenti, quanto <lb/>pi&ugrave; crescono le loro altezze, come si vede avvenir nelle piene, cosicch&egrave; non <lb/>si verifica la legge delle velocit&agrave; indipendenti dalle moli; si potr&agrave; da ci&ograve; solo <lb/>argomentare che tante altre cause concorrono a far differire il flusso del&shy;<lb/>l'acqua dai vasi, e il loro correr per gli alvei dei fiumi, da render neces&shy;<lb/>sario d'aggiungere alla Scienza una terza parte distinta, che &egrave; quella pro&shy;<lb/>priamente chiamata col nome di <emph type="italics"/>Idraulica.<emph.end type="italics"/> Cos&igrave; dunque, come tripartita &egrave; <lb/>la Scienza stessa, tripartiremo noi la sua propria Storia, dell'Idrostatica e <lb/>dell'Idrodinamica trattando in questo tomo, e dell'Idraulica nel seguente. </s></p><p type="main">

<s>Secondo i limiti, che ci siamo prefissi, dovrebbe la nostra narrazione <lb/>incominciare da quel risorgimento intellettuale, che sul finir del secolo XVI <lb/>si rese pi&ugrave; cospicuo e ammirato. </s>

<s>Ma come, a conoscer bene un albero, e a <lb/>giudicar del portato de'suoi frutti, &egrave; necessario andare a ricercarne le intime <lb/>radici; cos&igrave;, per conoscer meglio i portati della mente speculativa, e dell'arte <lb/>sperimentale in quel tempo, &egrave; ben risalire alle prime tradizioni. </s>

<s>Si trova, <lb/>cos&igrave; facendo, quel ch'&egrave; consueto osservarsi in tutti gli svolgimenti naturali <lb/>dal loro proprio principio, che cio&egrave;, prima d'apparire distintamente le varie <lb/>membra organiche, sono insieme confuse. </s>

<s>Ne'tempi infatti, che precederono <lb/>al risorgere della Scienza, le speculazioni intorno all'equilibrio e al moto <lb/>de'liquidi, intorno alle loro leggi del fluire dentro i tubi o dentro gli alvei <lb/>de'fiumi, bench&egrave; si distinguano ora da noi per la variet&agrave; dell'obbietto, si <lb/>comprendevano nonostante dai loro Autori in un solo esercizio, ond'&egrave; che <lb/>in questo rapido sguardo, che siam per dare indietro alla lunga via, ci verr&agrave; <lb/>tutt'insieme in considerazione quel che intorno all'Idrostatica, all'Idrodina&shy;<lb/>mica e all'Idraulica fu speculato, e sperimentato dai precursori dello Stevino <lb/>e del Castelli. </s></p><p type="main">

<s>Il pi&ugrave; antico documento che abbiamo, e che, nel decorrere di tanti secoli, <lb/>e in mezzo a tanti progressi, riman colle sue proprie note distinto, quasi ra&shy;<lb/>dice maestra, che tuttavia duri a infondere i vitali umori nell'albero della <lb/>Scienza; &egrave; fra le opere di Archimede quella, che tratta del galleggiare dei <pb xlink:href="020/01/3049.jpg" pagenum="10"/>corpi. </s>

<s>Di sottile e difficile materia dissero di averla trovata sempre tutti gli <lb/>studiosi, e coloro, che non lo confessarono con le parole, lo mostraron co'fatti <lb/>ne'loro infelici commentarii. </s>

<s>Si direbbe che tali difficolt&agrave; sono inevitabili in <lb/>uno scrittore antico, le opere del quale non ci son pervenute, che nelle copie <lb/>di amanuensi inesperti, e si soggiungerebbe che sono ai pi&ugrave; dotti critici insu&shy;<lb/>perabili, per la impossibilit&agrave; delle collazioni, se non si ripensasse che assai <lb/>leggeri sono i difficili incontri, per ragion del testo o guasto o corrotto, e <lb/>del processo delle dimostrazioni disordinato, rispetto a quelli, che si parano <lb/>innanzi alla mente dell'interpetre, per la sottigliezza dell'argomento. </s>

<s>A dif&shy;<lb/>fondere perci&ograve; su tante tenebre qualche raggio di luce poco possono giovare <lb/>le pi&ugrave; diligenti cure di rendere quant'&egrave; possibile genuina la lezione, in&shy;<lb/>torno a che par che cons&ugrave;mino tutta l'opera loro i critici e i commentatori, <lb/>ma bisogna penetrare addentro al segreto e profondo pensiero dell'Autore, <lb/>per poi ritrarne l'indole propria dell'esposizione. </s></p><p type="main">

<s>L'intenzion nostra presente non &egrave; alle cose geometriche, ma alle fisiche <lb/>e meccaniche, e pi&ugrave; particolarmente a quelle, che riguardano il galleggiare <lb/>dei corpi. </s>

<s>L'indole della trattazione archimedea intorno a un tale soggetto <lb/>si pu&ograve; conoscere in precedenza, ripensando esser egli stato fedel seguace di <lb/>quel Platone, che reputava indegno del Filosofo il trattenersi a contemplare <lb/>le vili e variabili passioni della materia. </s>

<s>Passando poi a leggere si trova con&shy;<lb/>fermata la verit&agrave; del preconcetto, imperocch&egrave; quell'ingegno ogni volta che <lb/>ripiega le ali, per scendere a posarsi sulla materia, &egrave; studioso di sceglierne <lb/>il fiore, quasi ape, che ne trasforma la nativa insipidezza in ambrosia celeste. </s>

<s><lb/>La sua trutina, per esempio, &egrave; quasi un invisibile genio, che distende per <lb/>sostenere i pesi le impalpabili braccia. </s>

<s>Le piu disperse virt&ugrave; di que'pesi si <lb/>riducono per Archimede in un punto, a cui vanno, e da cui vengono i moti <lb/>dispensati con ordine e con misura, come cuore o punto saliente, da cui <lb/>escono, e in cui rientrano gli spiriti della vita. </s>

<s>Il liquido, in che egli imma&shy;<lb/>gina galleggiare i corpi, non &egrave; acqua propriamente, n&egrave; altro di simile e par&shy;<lb/>ticolare natura, ma quasi una stillata essenza di tutte le loro propriet&agrave;, a <lb/>cui non si saprebbe, e non s'&egrave; saputo dare altro nome che di <emph type="italics"/>umido.<emph.end type="italics"/></s></p><p type="main">

<s>Ma pure una fama antica, e di riflesso in riflesso fattasi infino a noi <lb/>sempre pi&ugrave; diffusa, ci rappresenta Archimede quale uno de'pi&ugrave; affaccendati <lb/>in voler ridurre alla sua suggezione le forze pi&ugrave; ritrose della materia. </s>

<s>Egli <lb/>inventore di macchine prodigiose, da offendere i nemici, e da difendere la <lb/>sua patria dai loro assalti: egli costruttore sul mobile mare di un edifizio, <lb/>da render pi&ugrave; comodo e delizioso il soggiorno del Re, che in mezzo ai giar&shy;<lb/>dini di Siracusa. </s>

<s>Non le sentine sole de'vascelli, ma i laghi stessi si asciu&shy;<lb/>gano con la sua Coclea: le pi&ugrave; gravi moli si trasportano con facilit&agrave;, per il <lb/>felice accoppiamento ch'egli ha pensato di fare dell'elice con la ruota: e ri&shy;<lb/>salendo ardito infino a invadere i dominii del Sole, lo costringe a conden&shy;<lb/>sare il potente calore de'suoi raggi, per abbruciare in mezzo alle acque i <lb/>navigli nemici dei Romani. </s>

<s>E che pi&ugrave;? </s>

<s>ci vien dipinto ebro della sua scienza <lb/>correre per le vie ad annunziare la scoperta inaspettatamente sovvenutagli <pb xlink:href="020/01/3050.jpg" pagenum="11"/>della quantit&agrave; dell'argento, furtivamente sostituito dall'orefice all'oro, che <lb/>egli aveva avuto dal suo Re, per costruirne una corona yotiva. </s></p><p type="main">

<s>Si dir&agrave; forse che Archimede sapeva, per colmo delle sue virt&ugrave;, congiun&shy;<lb/>gere insieme la contemplazione e l'azione? </s>

<s>Ma perch&egrave; in tutti i suoi libri <lb/>serba sempre il carattere di filosofo platonico, e in mezzo a tante astratte <lb/>verit&agrave; spec&udot;late non si legge fatto mai nemmeno un cenno a qualcuna di <lb/>quelle pratiche applicazioni, che la fama gli ha attribuito? </s>

<s>Com'&egrave; possibile <lb/>non riconoscere una diversit&agrave; fra le opere endoteriche e le esoteriche, ben&shy;<lb/>ch&egrave; vadano sotto il medesimo nome di Archimede Siracusano? </s>

<s>E da un'altra <lb/>parte, perch&egrave; le notizie sparse da cos&igrave; nobili scrittori, quali sono Diodoro, <lb/>Polibio, Ateneo non possono non essere sostentate da qualche aura di vero;, <lb/>giova ricercar da qual parte sia quella sottile aura spirata. </s>

<s>N&egrave; difficile ci si <lb/>presenta la ricerca, ripensando a quelle leggi d'induzione e di deduzione, <lb/>secondando le quali il pensiero, con moto simile all'andare e al ritornar di <lb/>una spola, va intessendo la sua sottilissima tela. </s>

<s>Archimede induce per astra&shy;<lb/>zione dalle cose fisiche una propriet&agrave; geometrica, da cui potr&agrave; chi vuole de&shy;<lb/>durne la notizia dei vari fatti particolari. </s>

<s>Tra le prime sensibili apprensioni, <lb/>e questa notizia acquistata cos&igrave; per riflessione, ci &egrave; la differenza che passa <lb/>tra uno, che lavora un oggetto a mano, e un altro, che si trova gi&agrave; prepa&shy;<lb/>rata la forma. </s>

<s>E come chi ha preparato la forma si pu&ograve; giustamente dire <lb/>autore della statua, che dentro vi s'&egrave; gettata; cos&igrave; pu&ograve; dirsi Archimede au&shy;<lb/>tore di tutte le invenzioni, che gli studiosi stessi contemporanei attinsero <lb/>da'suoi libri. </s>

<s>Chi trova ragionevoli queste considerazioni si vedr&agrave; facilmente <lb/>risoluti molti problemi, e fra gli altri quello del non parer credibile che, <lb/>all'invenzione e all'esecuzione di tante maraviglie, potesse bastar la vita di <lb/>un Filosofo. </s>

<s>Quel Filosofo dunque invent&ograve;, e altri eseguirono: gli autori delle <lb/>opere endoteriche e delle esoteriche son diversi, e nonostante sta bene che <lb/>s'attribuiscano a uno solo. </s></p><p type="main">

<s>Passiamo ora a considerare particolarmente, fra quelle opere, il trattato <lb/>delle Galleggianti. </s>

<s>Che questo insigne monumento della Scienza avesse occa&shy;<lb/>sione dal sentirsi l'autore alleggerire il corpo nel bagno, e dal pensiero che <lb/>si sarebbe quella leggerezza potuta misurare per la quantit&agrave; dell'acqua river&shy;<lb/>satasi dalla tinozza; saranno anche i nostri Lettori disposti a non reputarlo <lb/>oramai pi&ugrave; che quale un apologo nella Storia. </s>

<s>Ben pi&ugrave; alti furono que'prin&shy;<lb/>cipii, e pi&ugrave; degni della Filosofia. </s>

<s>Avvezzo Archimede, infin da fanciullo, a <lb/>vedere i porti della sua Siracusa tutto intorno assiepati di navi, non era pos&shy;<lb/>sibile che non rivolgesse poi le sue speculazioni a macchine cos&igrave; suntuose, <lb/>e dalle quali principalmente dipendevano le sorti della sua terra, per l'uti&shy;<lb/>lit&agrave; de'commerci, e per la sicurezza dagli assalti nemici. </s>

<s>E quanto, e da <lb/>quante parti porgevan materia da specular quelle moli, cos&igrave; intorno alle ra&shy;<lb/>gioni del loro galleggiare sull'acque, come del mantenere sulle mobili onde <lb/>fermezza di equilibrio fra la prora e la poppa? </s></p><p type="main">

<s>Il soggetto attraeva tanto pi&ugrave; fortemente Archimede a contemplarlo, in <lb/>quanto che l'ebbe a trovare intatto, e anzi da gravissimi errori deturpato <pb xlink:href="020/01/3051.jpg" pagenum="12"/>nella scuola del Filosofo, il quale, domandandosi, nel problema secondo della <lb/>XXIII sezione, <emph type="italics"/>Cur navigia onustioria in portu, quam in altu esse viden&shy;<lb/>tur;<emph.end type="italics"/> rispondeva: &ldquo; An quia plus aquae quam minus reniti validius potest, <lb/>pauca nam oppressa onere cedit, ut demergi necesse sit: multa e contrario <lb/>repellit ac sustinet &rdquo; (<emph type="italics"/>Aristot. </s>

<s>Opera,<emph.end type="italics"/> T. IX, Venetiis 1550, fol. </s>

<s>316). Archi&shy;<lb/>mede invece veniva, co'suoi nuovi teoremi, a insegnare che del galleggiar <lb/>pi&ugrave; o meno, e dell'affondare un solido dentro un liquido non &egrave; altra ragione <lb/>dalla proporzionalit&agrave; in fuori, che passa tra la gravezza di esso solido im&shy;<lb/>merso e la gravezza del liquido, in cui quello per l'immersione occupa il <lb/>luogo, intantoch&egrave; o egli giunger&agrave; al livello del vaso o soprastar&agrave; o precipi&shy;<lb/>ter&agrave; sott'esso, secondo che sar&agrave; la detta proporzione o d'eguaglianza o di <lb/>eccesso. </s>

<s>Non dalla quantit&agrave; dunque dell'acqua, come insegnava Aristotile, ma <lb/>dalla sua sola gravit&agrave; in specie dipende il fatto, ond'&egrave; che, riducendo ne'ter&shy;<lb/>mini della verit&agrave; il problema, deve il mare, di un medesimo vascello e ugual&shy;<lb/>mente carico, inghiottir meno che un lago o un fiume, avendo maggiore gra&shy;<lb/>vit&agrave; specifica l'acqua salsa che la dolce. </s>

<s>Ma non condiscendeva a cos&igrave; fatte <lb/>minuzie il genio di Archimede, le proposizioni del quale comprendono nella <lb/>loro universalit&agrave; ogni sorta di acqua, anzi ogni liquefatta sostanza, purch&egrave; <lb/>ell'abbia le propriet&agrave; generali dell'umido, di giacersi cio&egrave; in superficie ori&shy;<lb/>zontale e di ceder le parti men premute alle pi&ugrave; compresse. </s>

<s>Del problema <lb/>proposto da Aristotile, e di altri sim&igrave;li, lasciava l'Autore ricavarne per co&shy;<lb/>rollario la soluzione agli studiosi, i quali impararono, fra le altre cose, a ri&shy;<lb/>trovare il peso specifico de'vari corpi, e la proporzione de'loro misti, d'onde <lb/>ebbe l'origine, come si spiegher&agrave; meglio altrove, il famoso apologo dell'in&shy;<lb/>venzione della quantit&agrave; dell'argento sostituito dall'oretice del re Gerone all'oro <lb/>della corona. </s></p><p type="main">

<s>&Egrave; tale, cio&egrave; del semplice galleggiamento, la prima parte del trattato ar&shy;<lb/>chimedeo. </s>

<s>Ma la seconda &egrave; d'assai pi&ugrave; sottile speculazione e di maggiore <lb/>importanza nella pratica, proponendovisi l'Autore di dimostrare le ragioni <lb/>dello stabile equilibrio dei galleggianti. </s>

<s>Ch'egli avesse anche qui di mira la <lb/>Nautica si pu&ograve; ragionevolmente argomentare dall'avere scelto, fra'solidi ro&shy;<lb/>tondi, il settore di sfera principalmente e il conoide parabolico, che son le <lb/>forme geometriche astratte, alle quali pi&ugrave; prossimamente ci pu&ograve; rassomi&shy;<lb/>gliare e ridurre la mole di una nave. </s>

<s>D'applicarne poi la teoria alle costru&shy;<lb/>zioni negli arsenali lasciava Archimede l'ufficio agl'ingegneri, i quali non <lb/>mancarono di adempirlo, come discepoli diligenti, e fu la loro ammirabile <lb/>solerzia simboleggiata in quel palazzo incantato, che essere stato costruito <lb/>dallo stesso Archimede sulle onde marine, per variar le delizie alla dimora <lb/>del re Gerone, scrive, ne'suoi <emph type="italics"/>Dinnosofisti,<emph.end type="italics"/> Diogene Laerzio. </s></p><p type="main">

<s>Ma dai simboli passando alla realt&agrave;, &egrave; un fatto che i Siracusani avevano, <lb/>sotto le discipline di Archimede, molto progredito e nella costruzione e nel <lb/>governo delle belliche navi, di che ebbe a fare esperienza pi&ugrave; volte, venendo <lb/>a cimento con loro, l'armata dei Romani. </s>

<s>Rimasti questi vittoriosi, ed eser&shy;<lb/>citando la loro prepotenza in ridurre in schiavit&ugrave; non le membra ma l'in-<pb xlink:href="020/01/3052.jpg" pagenum="13"/>gegno dei vinti, tradussero nella loro propria lingua, col titolo <emph type="italics"/>De insidenti&shy;<lb/>bus aquae,<emph.end type="italics"/> il libro, da cui tant'arte pericolosa era derivata ne'loro nemici, <lb/>non riserbandosi dell'originale, che perci&ograve; and&ograve; miseramente smarrito; altro <lb/>che le figure illustrative. </s></p><p type="main">

<s>La storia dell'Architettura navale di que'tempi ci potr&agrave; narrare qual <lb/>pro sapesse ritrarre dalle male conquistate teorie l'arte dei Romani, ma nel <lb/>campo della Filosofia naturale &egrave; pi&ugrave; facile ritrovare intorno a ci&ograve; i docu&shy;<lb/>menti, de'quali ci contenteremo citar da Seneca uno, in cui si pu&ograve; dir che <lb/>s'interpetrano, e si compendiano le proposizioni, dall'appresso Siracusano <lb/>dimostrate nella prima parte delle sue Galleggianti. </s>

<s>Voleva Seneca confer&shy;<lb/>mare quella verissima sentenza della Filosofia platonica non essere cio&egrave; una <lb/>cosa leggera o grave, secondo la nostra stima, ma in comparazione col mezzo, <lb/>e di ci&ograve; fare prende occasione nel terzo libro delle <emph type="italics"/>Questioni naturali,<emph.end type="italics"/> dove, <lb/>nel cap. </s>

<s>XXV, spieg&ograve; cos&igrave; il perch&egrave; in alcuni laghi il corpo di un uomo, <lb/>anche senza notare, e in qualche stagno i mattoni stessi rimangano a galla: <lb/>&ldquo; Huius rei palam causa est. </s>

<s>Quamcumque vis rem expende, et contra aquam <lb/>statue, dummodo utriusque par sit modus. </s>

<s>Si aqua gravior est, leviorem rem <lb/>quam ipsa est fert, et tanto supra se extollit, quanto erit levior. </s>

<s>Graviora de&shy;<lb/>scendunt. </s>

<s>At si aquae et eius rei quam contra pensabis par pondus erit, nec <lb/>pessum ibit nec extabit, sed aequabitur aquae et natabit quidem, sed pene <lb/>mersa ac nulla eminens parte. </s>

<s>Hoc est cur quaedam tigna supra aquam pene <lb/>tota efferantur, quaedam ad medium submissa sint, quaedam ad aequilibrium <lb/>aquae descendant. </s>

<s>Nam, cum utriusque pondus par est, neutra res alteri ce&shy;<lb/>dit. </s>

<s>Graviora descendunt, leviora gestantur. </s>

<s>Grave autem et leve est, non <lb/>aestimatione nostra, sed comparatione eius, quo vehi debet. </s>

<s>Itaque, ubi aqua <lb/>gravior est, hominis corpore aut saxi, non sinit id quo non vincitur mergi &rdquo; <lb/>(Venetiis 1522, fol. </s>

<s>30). </s></p><p type="main">

<s>Da Vitruvio poi, e da qualche altro autore di que'tempi, si raccoglie che <lb/>i principii archimedei, dimostrati nel primo libro <emph type="italics"/>De insidentibus aquae,<emph.end type="italics"/> si <lb/>applicavano alla invenzione delle gravit&agrave; specifiche dei varii corpi, ma il se&shy;<lb/>condo libro parve si rimanesse oscuro a quegli stessi, che s'erano confidati <lb/>di far romana la scienza di dare stabilit&agrave; d'equilibrio sul mare agli agitati <lb/>vascelli. </s>

<s>Diciamo cos&igrave; perch&egrave; si vedono qualche tempo dopo que'baldanzosi <lb/>tornare a ricercar fra le spoglie dei vinti altri trattati dello stesso Archimede, <lb/>scegliendo principalmente quelli, ne'quali si dimostrano le leggi dell'equili&shy;<lb/>brio de'gravi nell'aria, mossi dalla speranza che verrebbe luce di l&igrave; a intender <lb/>meglio le leggi dell'equilibrio ne'galleggianti sull'acqua. </s>

<s>Di qui ebbe ori&shy;<lb/>gine quella prima collezione delle Opere archimedee, che si componeva del&shy;<lb/>l'<foreign lang="greek">*e<gap/>*e*d*w*n *i*s*o*p*p*o<gap/>*w*n</foreign> tradotto, o per dir meglio interpetrato <emph type="italics"/>Liber de cen&shy;<lb/>tro gravium,<emph.end type="italics"/> del <foreign lang="greek">*t*e*t*p*a*g*w*n*i*s*m*o*s *r*l*p*a*b*o*l*e*s</foreign>, a cui rimase il titolo asso&shy;<lb/>luto di <emph type="italics"/>Tetragonismus, e De insidentibus aquae.<emph.end type="italics"/> Chiameremo questa raccolta <lb/><emph type="italics"/>Romana,<emph.end type="italics"/> per distinguerla da quell'altra, che si fece molto pi&ugrave; tardi, e alla <lb/>quale, per la legittimit&agrave; dell'origine, ci sia lecito dare il nome di <emph type="italics"/>Siracu&shy;<lb/>sana.<emph.end type="italics"/> Si comprendono in questa tutte le opere, che per la diligenza degli <pb xlink:href="020/01/3053.jpg" pagenum="14"/>eruditi, nell'epoca del Rinascimento, si poterono ritrovare, ma in quella si <lb/>scelsero, come s'&egrave; inteso, i soli trattati in materia di Meccanica, dal <foreign lang="greek">*k*u*k*l*o*u <lb/>*m*e*t*p*h*s*i*s</foreign> in fuori, che, per esser breve e di facile e maravigliosa inven&shy;<lb/>zione, s'inser&igrave; quasi parte dell'altro Tetragonismo. </s></p><p type="main">

<s>Nel tempo del decadimento, come andarono dimenticati e dispersi gli <lb/>altri documenti della Scienza antica, e della letteratura; cos&igrave; incontr&ograve; alle <lb/>Opere di Archimede, che si ricercarono poi con desiderio, nel secolo XV, <lb/>quando da Cicerone e da Plutarco, da Vitruvio e da Polibio, insieme coi <lb/>tanti altri autori latini e greci resuscitati, se ne ud&igrave; magnificare cos&igrave; l'eccel&shy;<lb/>lenza. </s>

<s>&Egrave; facile indovinare, dietro ci&ograve; che s'&egrave; detto, e secondo i naturali avve&shy;<lb/>nimenti delle cose, come dovesse esser prima a trovarsi, e a richiamare a s&egrave; <lb/>l'attenzione degli studiosi, la collezione Romana, della quale una copia si fece, <lb/>con la maggior diligenza possibile, a richiesta e a spese del vescovo di Pa&shy;<lb/>dova, quando s'incominci&ograve; a istituire q&udot;ella Biblioteca, assegnata poi al Se&shy;<lb/>minario, e che fu una delle prime e delle pi&ugrave; benemerite degli studii in Italia. </s>

<s><lb/>Si diffusero di li come da centro le altre copie, che se ne fecero via via, fra <lb/>le quali son memorabili quelle, sopra cui studiarono Leonardo da Vinci, e <lb/>Niccol&ograve; Tartaglia. </s>

<s>Superate con l'esercizio le prime difficolt&agrave;, che ebbe a in&shy;<lb/>contrare l'arte della stampa, pens&ograve; esso Tartaglia, nella povert&agrave; munifico, di <lb/>pubblicare a sue spese, per comun benefizio, come poi fece in Venezia nel 1543, <lb/>il manoscritto, intitolandolo <emph type="italics"/>Opera Archimedis Siracusani per Nicolaum <lb/>Tartaleam multis erroribus emendata.<emph.end type="italics"/> Questa non &egrave;, come si disse, altro <lb/>che la parzial Collezione romana, comprendente le sole Opere in materia di <lb/>Meccanica: anzi, perch&egrave; l'intenzion principale de'collettori fu rivolta al <emph type="italics"/>De <lb/>insidentibus aquae,<emph.end type="italics"/> a cui il libro de'Centri di gravit&agrave; e il Tetragonismo non <lb/>servivano che di preparazione; intorno al <emph type="italics"/>De insidentibus aquae<emph.end type="italics"/> vers&ograve; prin&shy;<lb/>cipalmente lo studio anche del Tartaglia, il quale vi si mostr&ograve; meno editor <lb/>diligente, che sottile e acuto commentatore. </s>

<s>Di ci&ograve; diremo pi&ugrave; qua, ma in&shy;<lb/>tanto non &egrave; da passare sotto silenzio un errore, che un nostro eloquente sto&shy;<lb/>rico delle Matematiche pu&ograve; facilmente avere insinuato ne'suoi Lettori. </s></p><p type="main">

<s>Guglielmo Libri, discorrendo nel suo secondo libro del Tartaglia, dice <lb/>che &ldquo; on lui doit le trait&eacute; <emph type="italics"/>De insidentibus<emph.end type="italics"/> d'Archimede, dont il connaissait <lb/>l'original grec, qui a &eacute;t&eacute; perdu depuis &rdquo; (<emph type="italics"/>Histoire des Sciences mathem.,<emph.end type="italics"/><lb/>T. III, a Paris, pag. </s>

<s>165). Come fosse quell'originale greco perduto assai <lb/>tempo prima fu detto da noi di sopra, e c&igrave; fa gran maraviglia non avesse <lb/>quel valent'uomo fatto attenzione che il Tartaglia stesso conferma di non <lb/>avere avuto, del testo archimedeo, notizia, in quella lettera al conte Antonio <lb/>Landriani, dedicatoria del suo primo <emph type="italics"/>Ragionamento.<emph.end type="italics"/> Dichiarasi in questo il <lb/>libro di Archimede Siracusano <emph type="italics"/>De insidentibus aquae,<emph.end type="italics"/> e perch&egrave;, essendo cos&igrave; <lb/>fatta traduzione dal greco in molte parti oscura, esso conte, per collazionarla <lb/>coll'originale, voleva mettersi a ogni costo a ricercarlo; il Tartaglia, che re&shy;<lb/>putava questa di lui fatica inutile, e opera perduta, cos&igrave;, nella detta lettera <lb/>dedicatoria, gli soggiungeva: &ldquo; Onde, per levar questa fatica a V. S. di stare <lb/>a ricercare tale original greco, qual forse pi&ugrave; oscuro ed incorretto ritrover&agrave; <pb xlink:href="020/01/3054.jpg" pagenum="15"/>della detta traduzione latina, ho dichiarata e minutamente dilucidata tal parte <lb/>in questo mio primo Ragionamento &rdquo; (Venetia 1551). </s></p><p type="main">

<s>Il Libri deve senza dubbio esser rimasto ingannato da quel che dice il <lb/>compar Riccardo, sulla fine di quel primo ragionamento in dialogo, rispetto <lb/>alla figura illustrativa della VIII proposizion di Archimede, la qual figura, <lb/>essendo mal disegnata, voleva esso Riccardo che fosse nel ricopiarla corretta, <lb/>ma a lui Niccol&ograve; rispondeva: &ldquo; Voi dite la verit&agrave;, ma perch&egrave; cos&igrave; era quella <lb/>figura nell'esempio greco, non m'&egrave; parso di contraffarla, ancorch&egrave; fosse stato <lb/>meglio &rdquo; (iv&inodot;, pag. </s>

<s>21). L'inganno dello Storico dunque stette nel credere <lb/>che con quell'<emph type="italics"/>esempio greco<emph.end type="italics"/> s'appellasse al testo, e non alle tavole unica&shy;<lb/>mente rimaste, come si disse, e com'&egrave; confermato dal Commandino, il quale, <lb/>supplendo di suo alla detta VIII del primo libro archimedeo, e alla seconda <lb/>del secondo, che per l'ingiuria de'tempi si desideravano; dice di averle re&shy;<lb/>stituite <emph type="italics"/>ad mentem Archimedis ex figuris, quae remanserunt<emph.end type="italics"/> (Archimedis, <lb/><emph type="italics"/>De his quae vehuntur in aqua,<emph.end type="italics"/> Rononiae 1565, fol. </s>

<s>7 et 11). Non vediamo <lb/>poi come possa eludere la forza di questi argomenti Carlo Thurot, il quale <lb/>supponeva che si fosse il Tartaglia fatto tradurre per suo servigio i libri <lb/>idrostatici di Archimede da qualcuno, quanto dotto della lingua greca, altret&shy;<lb/>tanto ignaro della Matematica (<emph type="italics"/>Revue archeol.,<emph.end type="italics"/> 1868, 69). </s></p><p type="main">

<s>Nelle collezioni archimedee, che via via si completarono, con l'aggiunta <lb/>delle Opere geometriche in greco, o in latino col testo a fronte, i soli due <lb/>libri <emph type="italics"/>De insidentibus aquae<emph.end type="italics"/> si rimanevano scritti in una lingua, che si pu&ograve; <lb/>dire straniera all'Autore, e fu primo tra gli editori David Rivault, che osasse <lb/>di restituirla alle imitate forme del dialetto dorico. </s>

<s>Fu lo stesso Rivault anche <lb/>il primo a movere questioni intorno al titolo, che, per relazion di Strabone, <lb/>era <foreign lang="greek">*r*e*p*i *t*w*n *o*x*o*u*m*e*n*w*n</foreign>, ma Pappo, soggiunge l'editor francese sulla fine <lb/>del suo proemio, per togliere ogni ambiguit&agrave;, e per dichiarar sopra che cosa <lb/>particolarmente farebbesi l'insidenza, v'aggiunse <foreign lang="greek">uf'udatos. </foreign></s>

<s>Io poi, conclude <lb/>il proemiatore, volentieri starei con Pappo, se non temessi di far contro allo <lb/>stesso Archimede, che non fece motto mai particolarmente dell'acqua, ma <lb/>sempre us&ograve; la parola <emph type="italics"/>umido:<emph.end type="italics"/> onde, a rendere il titolo pi&ugrave; universale, e pi&ugrave; <lb/>conforme con l'intenzion dell'Autore, direi che si dovesse piuttosto aggiun&shy;<lb/>gere <foreign lang="greek">ef'ugrwn. </foreign></s></p><p type="main">

<s>La questione, che par di semplici parole, &egrave;, come vedremo, di gran <lb/>conseguenza, per le strette relazioni, che le parole stesse hanno con le cose. </s>

<s><lb/>L'aggiunta della parola <emph type="italics"/>acqua,<emph.end type="italics"/> per denotare il subietto del galleggiante o <lb/>l'insidenza, fu fatta dal traduttore latino, forse prima che da Pappo, il quale <lb/>non sembra a noi che avesse l'intenzione, attribuitagli dal Rivault, di defi&shy;<lb/>nir cio&egrave; il titolo dell'Archimede, essendo manifesto ch'egli intende piuttosto <lb/>di dichiarare ai lettori il suo proprio discorso. </s>

<s>Nel proemio infatti all'ottavo <lb/>libro delle <emph type="italics"/>Matematiche collezioni<emph.end type="italics"/> annovera l'Autore i vari inventori delle <lb/>macchine, e il vario modo d'esercitarle: &ldquo; alii quidem per spiritus, ut Hero <lb/><foreign lang="greek">pneumatixois</foreign>, alii per nervos et funes, ut Hero ad <foreign lang="greek"><gap/>oma ois xai c giois</foreign>, alii vero <lb/>per ea quae in aqua vehuntur, ut Archimedes <foreign lang="greek">oxonmenois. </foreign></s>

<s>&rdquo; (Bononiae 1660, <pb xlink:href="020/01/3055.jpg" pagenum="16"/>pag. </s>

<s>448): onde s'intende come al Commandino stesso, che cos&igrave; traduceva, <lb/>sovvenisse di dare il titolo, ai due libri del Siracusano, <emph type="italics"/>De his quae vehun&shy;<lb/>tur in aqua.<emph.end type="italics"/></s></p><p type="main">

<s>&Egrave; notabile a questo proposito che il Nardi riprendesse esso Comman&shy;<lb/>dino, per aver seguitato cos&igrave; autorevoli esempi, invece di correggere il titolo, <lb/>posto in fronte alla stessa antichissima versione latina. </s>

<s>&ldquo; La traduzione di <lb/>Archimede <emph type="italics"/>Delle cose che stanno nell'umido<emph.end type="italics"/> mentisce il titolo, perch&egrave; dice <lb/><emph type="italics"/>nell'acqua,<emph.end type="italics"/> e non so perch&egrave; il Commandino non correggessela. </s>

<s>Non si parla <lb/>dell'acqua in detto libro, ne &egrave; vero che l'acqua sia sinceramente umida, <lb/>onde molti, non attendendo lo scopo di Archimede, hanno preteso che egli <lb/>abbia dimostrato, o voluto dimostrare, che la superficie dell'acqua sia per&shy;<lb/>fettamente sferica, il che non &egrave; vero. </s>

<s>L'Autore semplicemente suppone tro&shy;<lb/>varsi l'umido in natura, cio&egrave; una sostanza grave e scontinuata, o senza vi&shy;<lb/>scosit&agrave; di parti. </s>

<s>N&egrave; sapere gl'importa se tale squisitamente sia l'acqua, o <lb/>altro liquore, od anche il vapore o l'etere: nemmeno saper gl'importa se <lb/>tal qualit&agrave; di umido si trovi sincera o rimescolata, onde per le mescolate <lb/>ragioni della viscosit&agrave; si alterino gli effetti, bastandogli che sia in atto natu&shy;<lb/>ralmente, e che con l'intelletto si separi dalla mistione &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. XX, pag. </s>

<s>846). </s></p><p type="main">

<s>Avrebbe potuto il Commandino rispondere che non corresse il titolo, per <lb/>la ragione che non l'aveva prima di lui corretto il Tartaglia, il quale osser&shy;<lb/>vava che, verificandosi le proposizioni archimedee per ogni qualit&agrave; di umido, <lb/>si poteva questo universalmente significare col nome di acqua, <emph type="italics"/>essendo l'acqua <lb/>la principale di tutte le cose umide<emph.end type="italics"/> (Ragionam. </s>

<s>I cit., pag. </s>

<s>6). Ma il Nardi, <lb/>nell'accennare a que'molti, che non avevano inteso Archimede, aveva piu <lb/>ragione che di riprendere il Commandino, bench&edot; il titolo non corretto da <lb/>lui avesse dato motivo di riguardar l'acqua come un umido astratto, e di <lb/>negarle perci&ograve; una delle pi&ugrave; importanti sue propriet&agrave; naturali, qual'&egrave; d'es&shy;<lb/>sere tegnente nelle particelle componenti, o viscosa. </s>

<s>Vedremo di ci&ograve; notabili <lb/>fatti nel corso della nostra Storia, ma per ora &egrave; da ritornare al titolo im&shy;<lb/>presso, o da imprimersi a'due libri idrostatici del Siracusano, concludendo <lb/>che il riferitoci da Strabone dev'esser propriamente quello scritto in fronte <lb/>al codice originale. </s>

<s>Supponiamo che qualche nostro scrittore intitolasse un <lb/>suo trattato <emph type="italics"/>Delle galleggianti.<emph.end type="italics"/> Gli si potrebbe domandare: galleggianti in <lb/>che? </s>

<s>nell'acqua, nel mercurio, o piuttosto nella cera, o nella pece liquefatta? </s>

<s><lb/>Ma ei risponderebbe: sopra nessuna di queste cose in particolare; io intendo <lb/>di trattar del galleggiamento dei corpi in generale. </s>

<s>Ora, essendo precisa&shy;<lb/>mente questa l'intenzione di Archimede, &egrave; manifesto quanto fosse bene ap&shy;<lb/>propriato a significarla il titolo assoluto di <foreign lang="greek">*h*e*p*i *o*x*o*u*m*e*n*w*n</foreign>, purch&egrave; questa <lb/>voce avesse nel comune uso, oltre al general significato d'<emph type="italics"/>insidente,<emph.end type="italics"/> anche <lb/>quello, che particolarmento si d&agrave; da noi al nome di <emph type="italics"/>galleggiante.<emph.end type="italics"/> I latini <lb/>non avevano forse una parola, che rispondesse a quella di Archimede come <lb/>la nostra, e traducendola nel general significato che ha la frase <emph type="italics"/>De insiden&shy;<lb/>tibus,<emph.end type="italics"/> o <emph type="italics"/>De his quae vehuntur,<emph.end type="italics"/> furono costretti a dichiarare che l'insidenza <pb xlink:href="020/01/3056.jpg" pagenum="17"/>o il sostentamento doveva intendersi particolarmente su un liquido, a rappre&shy;<lb/>sentare il quale scelsero l'acqua, a quel modo che i nostri Autori intitolano <lb/>i loro libri <emph type="italics"/>Del moto delle acque,<emph.end type="italics"/> bench&egrave; di qualunque altro liquido si ve&shy;<lb/>rifichi quel che attendono a dimostrare. </s>

<s>Dunque &egrave; <foreign lang="greek">*h*e*p*i *o*x*o*u*m*e*n*w*n</foreign> il vero <lb/>titolo dell'Opera di Archimede, che per noi si traduce, con mirabile fedelt&agrave;, <lb/>in quello <emph type="italics"/>Delle galleggianti:<emph.end type="italics"/> e tanto bastando, per quel che riguarda la que&shy;<lb/>stione delle parole, &egrave; tempo oramai di passare a dir delle cose. </s></p><p type="main">

<s>&Egrave; diviso il trattato, come s'&egrave; accennato pi&ugrave; volte, e come tutti sanno, <lb/>in due libri, de'quali intanto esamineremo il primo, che procede con una <lb/>semplicit&agrave; e facilit&agrave;, veramente maravigliose in cos&igrave; sottile e delicato argo&shy;<lb/>mento. </s>

<s>Una tale semplicit&agrave; poi del processo, e una tale facilit&agrave; della dimo&shy;<lb/>strazione, non da altro dipendono che dall'aver saputo Archimede ridurre il <lb/>modo di pesare i corpi nell'acqua a quello ordinario di pesare i solidi nel&shy;<lb/>l'aria, per mezzo della Bilancia. </s>

<s>E come avviene in questo strumento che il <lb/>peso, posto in un de'bacini, si dice uguale, o pi&ugrave; leggero, o pi&ugrave; grave del <lb/>contrappeso nell'altro, secondo che fa rimanere uguale o sollevare o abbas&shy;<lb/>sare il giogo; cos&igrave; un corpo immerso si dice, ed &egrave; ugualmente grave, o pi&ugrave; <lb/>lieve o pi&ugrave; ponderoso del liquido stesso, secondo che ne pareggia il livello, <lb/>o lo sovrasta, o gli sottost&agrave;, seguitando a precipitare infino al fondo del vaso. </s>

<s><lb/>La somiglianza per&ograve; tra i due modi &egrave; solamente evidente rispetto a ci&ograve;, che <lb/>anche i liquidi son come i solidi gravi, e tendono perci&ograve; tutti ugualmente <lb/>al comun centro terrestre. </s>

<s>Ma non &egrave; chiaro in che si corrispondano i due <lb/>strumenti, dove cio&egrave; sia nell'umido l'ipomoclio, e cos'&egrave; che rappresenta in <lb/>esso, e fa l'ufficio del giogo, e de'bacini della Bilancia, come quando si pe&shy;<lb/>sano i corpi nell'aria. </s>

<s>In dichiarar dunque tuttoci&ograve; consiste la dottrina di <lb/>questo libro, che si compendia nella prima supposizione. </s>

<s>In essa infatti si <lb/>dice che le parti componenti ogni liquido son per loro natura continue, ed <lb/>equigiacenti, ossia si dispongono in superficie orizzontali concentriche, in cia&shy;<lb/>scuna delle quali si pu&ograve; mettere il giogo della Bilancia. </s>

<s>Il qual giogo liquido, <lb/>se sia o pi&ugrave; o meno premuto da una parte che dall'altra, necessariamente <lb/>s'abbassa o si alza. </s>

<s>E perch&egrave; anche il liquido &egrave; grave, o egli naturalmente <lb/>discenda o sia premuto da qualche forza straniera, le discese e le pressioni <lb/>non hanno in ogai modo altra direzione diversa dalla linea perpendicolare. <lb/></s>

<s>&ldquo; Ponatur humidi cam esse naturam ut, partibus ipsius aequaliter iacenti&shy;<lb/>bus et continuatis, inter sese minus pressa a magis pressa expellatur. </s>

<s>Una&shy;<lb/>quaeque auteni pars eius premitur humido supra ipsam existente ad per&shy;<lb/>pendiculum, si humidum sit descendens in aliquo, aut ab alio aliquo pres&shy;<lb/>sum &rdquo; (Archimedis, Opera, Parisiis 1615, pag. </s>

<s>491). </s></p><p type="main">

<s>Sembrerebbe che la desiderata Bilancia liquida si dovesse spontanea&shy;<lb/>mente offerire alle speculazioni di Archimede nel sifone di braccia uguali. </s>

<s><lb/>In esso infatti il liquido omogeneo si livella, o sottost&agrave; o sovrast&agrave;, se ci&ograve; che <lb/>vi s'&egrave; infuso &egrave; pi&ugrave; grave, o pi&ugrave; leggero da una parte che dall'altra, come <lb/>se per esempio si fosse riversato mereurio o olio sull'acqua. </s>

<s>Nonostante Ar&shy;<lb/>chimede scelse una via pi&ugrave; semplice, che consiste nel ridurre all'equilibrio <pb xlink:href="020/01/3057.jpg" pagenum="18"/>le braccia uguali della Bilancia, supponendo il vaso di figura regolare, e <lb/>l'umor contenutovi diviso in due parti uguali da un piano, che l'attraversi <lb/>nel mezzo. </s>

<s>La detta regolarit&agrave; si sarebbe potuta ottenere formando un vaso <lb/><figure id="id.020.01.3057.1.jpg" xlink:href="020/01/3057/1.jpg"/></s></p><p type="caption">

<s>Figura 1.<lb/>parallelepipedo, orizzontalmente posato con la sua base, <lb/>come si rappresenta nella figura 1, nella quale, essendo <lb/>CD il piano, che divide nel mezzo il liquido contenuto <lb/>nel vaso AB, con le pareti AE, FB verticali; in qua&shy;<lb/>lunque sezione liquida orizzontale, come in GH, pu&ograve; <lb/>stabilirsi il giogo immaginario della Bilancia, col soste&shy;<lb/>gno in I, intorno al quale sta in equilibrio, perch&egrave; si <lb/>suppone che il peso AI da una parte sia uguale al peso CH dall'altra. </s></p><p type="main">

<s>Ma &egrave; notabile che quell'Archimede, il quale non bad&ograve; tanto in suppor <lb/>parallele le direzioni dei pesi attaccati alle braccia della Bilancia solida, si <lb/>mostri ora nella Bilancia liquida cos&igrave; scrupoloso, in descriver sempre quelle <lb/>medesime direzioni come convergenti, cosicch&egrave; il vaso, in ch'egli intende <lb/>contenersi l'umido, non &egrave; composto sulla regola di un parallelepipedo, ma <lb/>di un cono o di una piramide, che, avendo la base sulla superficie della <lb/><figure id="id.020.01.3057.2.jpg" xlink:href="020/01/3057/2.jpg"/></s></p><p type="caption">

<s>Figura 2.<lb/>Terra, scenda precisamente infino ad appuntarsi nel cen&shy;<lb/>tro B della sfera, qui disegnata nella figura 2. In questa <lb/>la superficie AOC non &egrave; piana, ma convessa, e le braccia <lb/>DF, FE, bench&egrave; uguali, perch&egrave; la OB divide nel mezzo <lb/>la sezione ABC del vaso; non son per&ograve; in linea retta, <lb/>ma curvate in archi di cerchio. </s></p><p type="main">

<s>Qualunque si fosse l'intenzion di Archimede, che in dimostrare i suoi <lb/>teoremi volle sempre eleggere questa teorica posizione, &egrave; un fatto che in <lb/>realt&agrave; non &egrave; possibile il considerare, del gran vaso piramidale ABC, altro <lb/>che una minima parte, cosicch&egrave; la superficie dell'umido, ristretta nella por&shy;<lb/>zion tangenziale alla grande sfera terrestre, sia piana; le pareti AB, BC, in <lb/>cos&igrave; breve tratto, convergano tanto poco, da potersi avere per parallele; e <lb/>l'arco DFE, ridotto a essere quasi infinitesimo, si confonda con la rettitu&shy;<lb/>dine della sua propria tangente. </s>

<s>Ond'&egrave; che, per maggiore semplicit&agrave; ed evi&shy;<lb/>denza, riferiremo i Teoremi archimedei con le loro proprie ragioni, suppo&shy;<lb/>nendo parallelepipedo, come nella prima figura, il vaso; piana la superficie <lb/>dell'umido, e rettilineo perci&ograve; il giogo della Bilancia. </s>

<s>Le quali cose tutte <lb/>presupposte, sar&agrave; facile intendere per prima cosa come sia vero che un corpo, <lb/><figure id="id.020.01.3057.3.jpg" xlink:href="020/01/3057/3.jpg"/></s></p><p type="caption">

<s>Figura 3.<lb/>d'eguale peso specifico a quello di un liquido, si <lb/>sommerga in esso cos&igrave;, che nulla ne resti sopra, <lb/>ma senza andare pi&ugrave; al fondo. </s></p><p type="main">

<s>Sia un quadrato solido S (fig. </s>

<s>3) lasciato sulla <lb/>superficie del detto liquido, di cui si suppone essere <lb/>esso solido ugualmente grave in specie: &egrave; certo che <lb/>vi si sommerger&agrave; tutto, come si rappresenta nella <lb/>indicata figura, e quivi permarr&agrave; in equilibrio, perch&egrave;, preso un quadrato <lb/>liquido L, uguale e a ugual distanza dal punto I della bilancia CD, pesano <pb xlink:href="020/01/3058.jpg" pagenum="19"/>ugualmente le due grandezze sulle braccia di lei. </s>

<s>A ci&ograve; si riduce insomma <lb/>la ragion del Teorema, che vien terzo nell'ordinamento del libro, perch&egrave; suc&shy;<lb/>cede a due lemmi di Geometria, ma che veramente &egrave; il primo fra gl'idrosta&shy;<lb/>tici, da Archimede stesso cos&igrave; proposto: &ldquo; Solidarum magnitudinum, quae, <lb/>aequalem molem habentes, aeque graves sunt atque humidum; in humidum <lb/>demissae mergentur, ita ut ex humidi superficie nihil extet, non tamen <lb/>adhuc deorsum ferentur &rdquo; (Archim., Opera, Parisiis 1615, pag. </s>

<s>493). </s></p><p type="main">

<s>Che se S, stante la medesima figura, &egrave; pi&ugrave; leggero di L, &egrave; patente che <lb/>questo preponderando s'abbasser&agrave;, e far&agrave; sollevar quello in modo, che ne <lb/>rimanga qualche parte fuori dell'umido, secondo che, fra'teoremi idrostatici <lb/>di Archimede, si legge scritto cos&igrave; in secondo luogo: &ldquo; Solidarum magnitu&shy;<lb/>dinum quaecumque levior humido fuerit, demissa in humidum, non demer&shy;<lb/>getur tota, sed aliqua pars ipsius ex humidi superficie extabit &rdquo; (ibid., <lb/>pag. </s>

<s>496). </s></p><p type="main">

<s>Suppongasi il proposto solido esser sollevato sulla superficie dell'umido <lb/>infino in EF (fig. </s>

<s>4), e che l&igrave; giunto rimangasi in equilibrio. </s>

<s>Essendo che <lb/><figure id="id.020.01.3058.1.jpg" xlink:href="020/01/3058/1.jpg"/></s></p><p type="caption">

<s>Figura 4.<lb/>pur in equilibrio si rimarrebbe la bilancia, <lb/>quando, estrattone il solido, si riempisse del&shy;<lb/>l'umido circostante la pozzetta lasciata da lui; <lb/>&egrave; dunque vero quel che nel suo terzo teorema <lb/>idrostatico propone lo stesso Archimede: &ldquo; So&shy;<lb/>lidarum magnitudinum quaecumque levior hu&shy;<lb/>mido fuerit, demissa in humidum, usque eo demergetur, ut tanta moles <lb/>humidi, quanta est partis demersae, eamdem quam tota magnitudo gravita&shy;<lb/>tem habeat &rdquo; (ibid.). </s></p><p type="main">

<s>La forza poi dell'impeto di L, nella terza figura, per far sollevare S, &egrave; <lb/>manifesto esser tanta, quant'&egrave; l'eccesso della gravit&agrave;, che ha quella gran&shy;<lb/>dezza sopra questa, secondo che Archimede stesso pronunzi&ograve; in questa forma: <lb/>&ldquo; Solidae magnitudines humido leviores, in humidum impulsae, sursum fe&shy;<lb/>runtur tanta vi, quanto humidum, molem hadens magnitudini aequalem, gra&shy;<lb/>vius est ipsa magnitudine &rdquo; (ibid., pag. </s>

<s>497). </s></p><p type="main">

<s>Sia all'ultimo S pi&ugrave; grave di L, nella figura 3a. </s>

<s>Si immagini essere S <lb/>trasformato in umido cos&igrave;, che si debba aggiungere a lui il peso P, per egua&shy;<lb/>gliare il peso suo primo. </s>

<s>&Egrave; facile vedere come S e L equilibrandosi, la bi&shy;<lb/>lancia preponderer&agrave; in forza del solo peso P, che &egrave; la differenza tra il peso <lb/>del solido e quello di un ugual mole dell'umido, in cui egli &egrave; sommerso: <lb/>d'onde riman provata la verit&agrave; dell'ultima proposizione idrostatica di Ar&shy;<lb/>chimede, che dice: &ldquo; Solidae magnitudines humido graviores, demissae in <lb/>humidum, ferentur deorsum donec descendant, et erunt in humido tanto le&shy;<lb/>viores, quanta est gravitas humidi, molem habens solidae magnitudini aequa&shy;<lb/>lem &rdquo; (ibid., pag. </s>

<s>498). </s></p><p type="main">

<s>S'&egrave; detto che questa &egrave; l'ultima proposizione idrostatica, dimostrata da <lb/>Archimede nel suo libro primo, bench&egrave;, nella Collezione romana e in tutte <lb/>le altre edizioni, che si fecero poi su quell'esempio, se ne aggiunga un'al-<pb xlink:href="020/01/3059.jpg" pagenum="20"/>tra, che &egrave; l'ottava segnata nell'ordinamento primo di quello stesso libro. </s>

<s>Ma <lb/>chi ben attende si persuade con facilit&agrave; che la detta proposizione appartiene <lb/>all'argomento, dall'Autore stesso trattato nel libro secondo, e che ella anzi <lb/>contiene in s&egrave; il principio, da cui si svolgono, e a cui s'informa il processo <lb/>dimostrativo di tutte le altre. </s>

<s>La supposizione, premessa qui sul fine, piut&shy;<lb/>tostoch&egrave; in principio del libro, insieme e subito dopo la prima; avrebbe do&shy;<lb/>vuto far accorti gli editori e i commentatori che si preparava gi&agrave; fin di li <lb/>la trattazione di un argomento diverso, ma nessuno ebbe questa felice rive&shy;<lb/>lazione all'intelletto, per cui le dottrine archimedee nel secolo XVIII si ri&shy;<lb/>manevano tuttavia non comprese. </s>

<s>A chi poi sembrasse questa asserzion teme&shy;<lb/>raria sodisfaranno forse le considerazioni qui appresso. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>All'uno e all'altro libro dunque del trattato delle Galleggianti &egrave; premesso <lb/>un principio proprio e distinto, e a riconoscer l'importanza di ciascuno par <lb/>che nocesse non poco il titolo di <emph type="italics"/>supposizione.<emph.end type="italics"/> Tale &egrave; veramente quella <lb/>prima, nella quale si suppone un fatto, e si ricercano tali proprict&agrave; fisiche <lb/>dell'umido, concesse le quali ne conseguono necessariamente i teoremi idro&shy;<lb/>statici, di cui s'&egrave; discorso. </s></p><p type="main">

<s>Il principio per&ograve; premesso al secondo libro ha indole e significazione <lb/>molto diversa da quella, che gli si suol dare comunemente, e che, primo <lb/>fra'commentatori di Archimede, gli fu data dal Tartaglia: di principio cio&egrave; <lb/>per s&egrave; noto e indimostrabile, come son quelli &ldquo; che alcuni gli dicono pe&shy;<lb/>titioni, e gli altri chiamano dignit&agrave;, ovver supposizioni &rdquo; (Ragionamento <lb/>primo cit., pag. </s>

<s>4). Chi si persuaderebbe infatti di ricever tra i principii di <lb/>senso comune, o fra gli assiomi, questo cos&igrave; formulato, secondo la trascri&shy;<lb/>zione dello stesso Tartaglia? </s>

<s>&ldquo; Supponatur corum, quae in humido sursum <lb/>feruntur, unumquodque sursum ferri secundum perpendicularem, quae per <lb/>centrum gravitatis ipsorum producitur &rdquo; (ivi, pag. </s>

<s>18). </s></p><p type="main">

<s>Vero &egrave; bene che nemmen l'Autore di questo primo Ragionamento idro&shy;<lb/>statico sembra che se ne persuadesse, giacch&egrave; egli accenna al suo interlocu&shy;<lb/>tore, compar Riccardo, quel che Archimede stesso aveva dimostrato nell'altro <lb/>suo libro <emph type="italics"/>De centro gravitatis.<emph.end type="italics"/> Trasparisce di qui intanto che il Tartaglia <lb/>non d&agrave; al premesso principio valor proprio di assioma, ma di verit&agrave;, che, <lb/>sebbene non sia per s&egrave; nota, pur supponesi tale, perch&egrave; fu altrove gi&agrave; dimo&shy;<lb/>strata. </s>

<s>Nell'indicato libro per&ograve; non avrebbe trovato messer Riccardo da sodi&shy;<lb/>sfare la sua curiosit&agrave;, se non che circa al modo di determinare il centro gra&shy;<lb/>vitativo ne'piani, o circoscritti da linee rette, o da curve paraboliche, men&shy;<lb/>tre nella pronunziata supposizione apparisce definito esso centro come il punto <lb/>dell'applicazion di una forza unica, resultante da tutte insieme quelle che <lb/>risospingono in su un solido, tutto sommerso in un umido specificamente pi&ugrave; <pb xlink:href="020/01/3060.jpg" pagenum="21"/>grave. </s>

<s>&Egrave; certo insomma che Archimede suppone avere i suoi Lettori la no&shy;<lb/>tizia di quel che i moderni chiamano <emph type="italics"/>Centro delle pressioni,<emph.end type="italics"/> che &egrave; giusto <lb/>il punto, a cui s'applica la resultante di tutte le forze parallele, che nascono <lb/>dal riflettersi in su le pressioni idrostatiche. </s>

<s>Or trattandosi di una scienza, <lb/>la quale non refulse chiara agli intelletti, se non che a mezzo il secolo XVIII, <lb/>come apparir&agrave; dalla Storia, s'intende di quanta curiosit&agrave;, e di quanta im&shy;<lb/>portanza sia il saper come Archimede a'suoi tempi la supponesse gi&agrave; nota. </s></p><p type="main">

<s>Egli deve senza dubbio averla gi&agrave; dimostrata, e perch&egrave; ne tace qui nel <lb/><emph type="italics"/>De insidentibus aquae,<emph.end type="italics"/> e negli stessi libri <emph type="italics"/>De aequiponderantibus<emph.end type="italics"/> si sup&shy;<lb/>pongono le verit&agrave; de'medesimi o di simili altri pronunziati; si pu&ograve; doman&shy;<lb/>dare se la dimostrazione fu fatta in un libro, che sia andato smarrito, o che <lb/>Archimede avesse intenzione di scrivere, ma che poi la morte o altro caso <lb/>glielo impedisse. </s>

<s>Di questo vezzo, del supporre vera cio&egrave; una proposizione <lb/>da dimostrarsi, ne abbiamo nel nostro Autore, in altro proposito, notabili <lb/>esempi. </s>

<s>Nessuno, che da noi si sappia, potrebbe decidere con certezza quale <lb/>delle due opere, intorno agli Equiponderanti e alla Quadratura della para&shy;<lb/>bola, fosse scritta o messa in ordine per la prima. </s>

<s>Se fu tale quella degli <lb/>Equiponderanti, nel Problema premesso al secondo libro si suppone essere <lb/>il piano parabolico sesquiterzo al triangolo inscritto, che &egrave; l'ultima conclu&shy;<lb/>sione, a cui si giunge dopo quella lunga serie di proposizioni, dimostrate nel <lb/>libro della Quadratura della parabola. </s>

<s>Che se altri volesse dire invece aver <lb/>la scrittura di questo preceduto a quella del libro degli Equiponderanti, si <lb/>trova supposto l&agrave; come noto il centro di gravit&agrave; del triangolo e del trape&shy;<lb/>zio, che qua sarebbesi dimostrato. </s></p><p type="main">

<s>Ma lasciando per ora addietro la questione se Archimede pronunziasse <lb/>la verit&agrave; fondamentale, premessa al suo secondo libro delle Galleggianti, come <lb/>cosa dimostrata o da dimostrarsi; l'importante sta nell'investigare da quali <lb/>principii movesse, e per quali mezzi fosse condotta la desiderata dimostra&shy;<lb/>zione. </s>

<s>Rispetto a che giova principalmente osservare che la detta premessa <lb/>&egrave; quasi il corollario di un'altra pi&ugrave; generale, concernente le cadute naturali <lb/>dirette secondo la perpendicolare, che passa per il centro di gravit&agrave; del ca&shy;<lb/>dente. </s>

<s>Una tal direzione unica delle varie parti, che compongono il grave, si <lb/>pu&ograve; ammettere come cosa di fatto, da cui argomentar che gl'impulsi gravi&shy;<lb/>tativi distribuiti per le sparse particelle della materia si raccolgano in qualche <lb/>punto di quella stessa retta perpendicolare. </s>

<s>E perch&egrave; in un'altra simile per&shy;<lb/>pendicolare si raccoglierebbe quella medesima somma d'impulsi, variando al <lb/>corpo la posizione; sarebbe lecito concludere che dalla intersecazion delle due <lb/>linee viene indicato il punto, intorno a cui gravita tutta intera la mole. </s>

<s>L'in&shy;<lb/>venzione per&ograve; del centro di gravit&agrave; fatta in questo modo non era punto conforme <lb/>col genio di Archimede, che dalle nuvolose questioni della Fisica risale sempre <lb/>alle serene alture della Geometria. </s>

<s>E della Geometria pur valendosi nella <lb/>proposta inquisizione, non sembra aver potuto tenere altra via, da quella dei <lb/>Matematici moderni, con la differenza forse di qualche pi&ugrave; comodo veicolo, e, <lb/>per essere stati battuti per tanti secoli, con la facilit&agrave; de'pi&ugrave; appianati sentieri. </s></p><pb xlink:href="020/01/3061.jpg" pagenum="22"/><p type="main">

<s>I moderni dunque si sa che riducono la questione a trovare la resul&shy;<lb/>tante, e il centro di pi&ugrave; forze parallele, in un modo che pu&ograve; ridirsi cos&igrave; in <lb/>poche parole: Siano alla verga inflessibile AB (fig. </s>

<s>5) applicate le due forze <lb/><figure id="id.020.01.3061.1.jpg" xlink:href="020/01/3061/1.jpg"/></s></p><p type="caption">

<s>Figura 5.<lb/>parallele AP, <expan abbr="Bq.">Bque</expan> Aggiuntene due altre AM, <lb/>BN, nella stessa direzion della verga uguali ed <lb/>opposte, si possono, invece delle quattro forze, <lb/>considerare le lore resultanti AC, BD, o, pro&shy;<lb/>lungatene le direzioni concorrenti in S, le loro <lb/>uguali SE, SF, che si possono decomporre <lb/>nelle SI, SK, e nelle SG, SH, queste alla linea <lb/>AB perpendicolari, e quelle parallele. </s>

<s>Protratta <lb/>poi la SG, e dal punto O, in cui ella incontra <lb/>la verga, presa la OL=SG+SH, &egrave; manifesto <lb/>che, intesa questa applicata in O, &egrave; la resul&shy;<lb/>tante cercata delle due forze parallele, verso <lb/>esse stesse parallelamente diretta, e uguale alla <lb/>loro somma. </s>

<s>E perch&egrave; EG:AO=SG:SO, e HF:OB=SH:SO, d'onde, <lb/>essendo EG, HF uguali, consegue AO:OB=SH:SG=BQ:AP; &egrave; ma&shy;<lb/>nifesto che il punto O, a cui viene applicata la resultante, divide la verga in <lb/>due parti, che sono alle due forze componenti reciprocamente proporzionali. </s>

<s><lb/>Anche pi&ugrave; manifestamente poi ne consegue che, se le due forze componenti <lb/>sono uguali, il punto dell'applicazione della loro resultante divide la verga <lb/>AB nel mezzo. </s></p><p type="main">

<s>S'immagini ora che A, B (fig. </s>

<s>6) sian due corpi congiunti insieme, o <lb/>due distinte porzioni di un medesimo corpo, e con esse altre due porzioni <lb/><figure id="id.020.01.3061.2.jpg" xlink:href="020/01/3061/2.jpg"/></s></p><p type="caption">

<s>Figura 6.<lb/>C, D, o quante pi&ugrave; se ne voglia, sol&shy;<lb/>lecitate ciascuna dai propri impulsi <lb/>gravitativi, rappresentati dalle verti&shy;<lb/>cali AP, BQ, CR, DS. </s>

<s>Congiunto A <lb/>con B, e divisa la linea di congiun&shy;<lb/>zione in O, cosicch&egrave; OB ad AO stia <lb/>reciprocamente come AP a <expan abbr="Bq;">Bque</expan> nel&shy;<lb/>l'unica V s'assommano le potenze di <lb/>P e di Q, come nell'unica X s'as&shy;<lb/>sommano le due R, V, fatta in M, <lb/>della linea CO, secondo le medesime contrariet&agrave;, la divi&shy;<lb/>sione: e s'assommano all'ultimo nell'unica Z le quattro <lb/>forze componenti, divisa la MD in N come dianzi. </s></p><p type="main">

<s>Simile essendo il processo del ragionamento, quando <lb/>le porzioni, in cui s'intenda esser diviso il corpo, fossero <lb/>ridotte all'infinito numero delle minime particelle di lui <lb/>componenti; &egrave; manifesto, trattenendosi nella semplicit&agrave; <lb/>del proposto esempio, che N &egrave; il punto, intorno a cui si raccolgono i pesi, <lb/>ossia &egrave; il centro di gravit&agrave;, e che il tutto prende una direzione unica se-<pb xlink:href="020/01/3062.jpg" pagenum="23"/>condo NZ. </s>

<s>Di qui perci&ograve; torna geometricamente dimostrato perch&egrave; i moti in <lb/>gi&ugrave; son diretti lungo la linea perpendicolare, che passa per il centro di gra&shy;<lb/>vit&agrave; del cadente, E perch&egrave;, ne'moti in su, non &egrave; da fare altra variazione al <lb/>discorso, che di considerare le forze P, Q, R e tutte le altre, quante ce ne <lb/>fossero, in verso opposto; ecco da quali principii deriva la scienza, che si <lb/>presuppone da Archimede nel suo secondo libro delle Galleggianti: scienza, <lb/>che si riduce dunque a saper comporre in una qualunque numero, o finito <lb/>o infinito di forze parallele, e che, sebbene sia resa cos&igrave; nelle sue conclu&shy;<lb/>sioni evidente, potrebbe fare alcun dubitare se vi giunse propriamente il suo <lb/>Autore per le vie da noi disegnate: per l'una cio&egrave; del parallelogrammo delle <lb/>forze, e per l'altra della risoluzion del continuo nelle minime parti indivi&shy;<lb/>sibili. </s>

<s>Abbiamo giusta ragione di temer di que'dubbi, ripensando come pre&shy;<lb/>valga anche oggid&igrave; in molti l'idea, che il parallelogrammo sia d'invenzione <lb/>recente, e leggendo in alcuni commentatori moderni che Archimede costan&shy;<lb/>temente rifugg&igrave; da ogni speculazione, che sapesse d'infinitesimale. </s>

<s>Quanto <lb/>al primo, il libro delle Spirali, e le precedenti invenzioni di simili altre curve <lb/>meccaniche, persuadono essere antichissima la notizia de'moti composti, di <lb/>che s'addussero, nella passata Storia della Meccanica, tali documenti, da es&shy;<lb/>sere oramai soverchio spendervi attorno altri discorsi. </s>

<s>Di maggiore curiosit&agrave; <lb/>e importanza &egrave; il saper se sia vero, come si dice, che Archimede aborrisse <lb/>dall'ammettere nelle quantit&agrave; continue la possibile divisione all'infinito. </s>

<s>Per <lb/>verit&agrave; sembrerebbe invece che dovess'essere un tal genere di speculazioni <lb/>propriamente conforme col suo genio, e non mancano fatti, che da pi&ugrave; parti <lb/>sovvengono a confermarne il giudizio. </s></p><p type="main">

<s>Le tradizioni del nuovo metodo pi&ugrave; immediate vennero al Cavalieri dal <lb/>Kepler, e il Guldin argutamente notava che la quadratura Kepleriana del <lb/>circolo si concludeva per via degli indivisibili. </s>

<s>Ma perch&egrave; esso Kepler pro&shy;<lb/>testava di non aver fatto altro che commentare una proposizion di Archimede, <lb/>rimasta alquanto oscura, e variamente interpetrata; egli insomma veniva ad <lb/>attribuire allo stesso Archimede l'invenzione e l'uso del metodo cavalierano. </s></p><p type="main">

<s>Il Matematico di Praga ne deve essere stato inconsapevole, ma &egrave; un fatto <lb/>che l'avevano prevenuto i Matematici del secolo precedente nell'interpetrare, <lb/>con la dottrina degli infinitamente piccoli, la recondita ciclometria del Sira&shy;<lb/>cusano. </s>

<s>&ldquo; Il cerchio, scriveva Leonardo da Vinci, &egrave; una figura parallela, per&shy;<lb/>ch&egrave; tutte le linee rette prodotte dal centro alla circonferenza sono eguali, e <lb/>caggiono in nella lor linea circonferenziale infra angoli eguali eretti sferici. </s>

<s><lb/>Il cerchio &egrave; simile a un parallelo rettangolo, fatto del quarto del suo diame&shy;<lb/><figure id="id.020.01.3062.1.jpg" xlink:href="020/01/3062/1.jpg"/></s></p><p type="caption">

<s>Figura 7.<lb/>tro, e di tutta la circum&shy;<lb/>ferentia sua, o vo'dir e <lb/>della met&agrave; del diametro, e <lb/>della periferia. </s>

<s>Come se il <lb/>cerchio EF (fig. </s>

<s>7) fusse <lb/>immaginato essere reso&shy;<lb/>luto in quasi infinite pi-<pb xlink:href="020/01/3063.jpg" pagenum="24"/>ramidi, le quali poi essendo distese sopra la linea retta, che tocchi la loro <lb/>base BD, e tolto la met&agrave; dell'altezza, e fatto il parallelo ABCD; sar&agrave; con <lb/>precisione eguale al circolo EF &rdquo; (MSS. K, fol. </s>

<s>80 r.). </s></p><p type="main">

<s>In simile modo quadrava Leonardo il settor circolare ABC (fig. </s>

<s>8) divi&shy;<lb/>dendolo in altri settori infinitesimi. </s>

<s>Poi dirizzava l'arco, col farlo movere <lb/><figure id="id.020.01.3063.1.jpg" xlink:href="020/01/3063/1.jpg"/></s></p><p type="caption">

<s>Figura 8.<lb/>sopra la linea retta DE, per <lb/>cui veniva esso settore ad <lb/>aprirsi, e allargarsi nel ret&shy;<lb/>tangolo DF duplicando il suo <lb/>proprio spazio, cos&igrave; meccani&shy;<lb/>camente riquadrato. </s>

<s>&ldquo; E que&shy;<lb/>sta, ne concludeva, &egrave; la sola <lb/>e vera regola da dare la quadratura d'ogni porzion di cerchio, minore del <lb/>semicircolo, della quale nulla scientia vale, se non col moto predetto &rdquo; (MSS. <lb/>E, fol. </s>

<s>25 r.). </s></p><p type="main">

<s>Con la medesima regola, applicandovi cio&egrave; il metodo degl'indivisibili, <lb/>tacitamente supposto da Archimede, insegnava Leonardo a quadrare la su&shy;<lb/>perficie della sfera, come si vede in varie sue Note, e specialmente in quella, <lb/>che si legge nel MSS. E, a tergo del foglio 24. N&egrave; di altre simili applica&shy;<lb/>zioni manca, in questi preziosi documenti Vinciani della Scienza, l'esempio. </s>

<s><lb/>Nella prima faccia del foglio 73 del medesimo manoscritto &egrave; formulata que&shy;<lb/>sta proposizione: <emph type="italics"/>&ldquo; Il descenso del grave situato per qualunque obliquit&agrave; <lb/>sempre fia per diritta linea. </s>

<s>&rdquo;<emph.end type="italics"/> S'immagina l'Autore di avere la trave AB <lb/><figure id="id.020.01.3063.2.jpg" xlink:href="020/01/3063/2.jpg"/></s></p><p type="caption">

<s>Figura 9.<lb/>(fig. </s>

<s>9) di uniforme figura e peso, e perci&ograve; <lb/>col centro di gravit&agrave; nel suo mezzo. </s>

<s>Ora, a pro&shy;<lb/>vare che, sebbene si giaccia obliqua, essa trave <lb/>cader&agrave; nonostante per la rettitudine CD della <lb/>sua perpendicolare; divide il cadente in minime <lb/>particelle, di uniforme figura e peso, nella <lb/>piccolezza delle quali perci&ograve; l'obliquit&agrave; del tutto <lb/>sparisce. </s>

<s>E perch&egrave; ciascuna delle dette parti&shy;<lb/>celle &egrave; sollecitata dal proprio impulso gravita&shy;<lb/>tivo, rappresentato da altrettante linee perpen&shy;<lb/>dicolari uguali, come si vede nella figura dise&shy;<lb/>gnata nel citato foglio in margine; ne conclude <lb/>Leonardo che la resultante delle parti &egrave; la mede&shy;<lb/>sima linea perpendicolare CD, applicata al centro di gravit&agrave; della trave. </s>

<s>&ldquo; Pro&shy;<lb/>vasi per la settima di questo che dice: Li gravi d'uniforme figura e peso, che <lb/>descenderanno per mezzo eguale, saranno d'egual velocit&agrave;. </s>

<s>Adunque, se il <lb/>trave d'uniforme figura e peso sar&agrave; diviso in parti eguali, e simili per di&shy;<lb/>rezione, sar&agrave; di velocit&agrave; uguale e simile, E quel che fa la parte far&agrave; il tutto. </s>

<s>&rdquo; <lb/>Chi, penetrando addentro al significato di queste parole, non vi riconosce <lb/>schietto il principio della composizion delle forze parallele, rappresentanti la <lb/>velocit&agrave; della caduta, o il peso delle particelle, in cui &egrave; lecito immaginar di-<pb xlink:href="020/01/3064.jpg" pagenum="25"/>viso qualunque corpo? </s>

<s>E da che pu&ograve; avere appreso Leonardo una tale scienza, <lb/>se non dalla V proposizione archimedea <emph type="italics"/>De aequiponderantibus,<emph.end type="italics"/> la quale, <lb/>lasciando immaginar qualunque numero di grandezze, pendenti intorno al <lb/>centro di gravit&agrave;, nella verga che le sostiene; confermava in quella medesima <lb/>verit&agrave; gli studiosi, anche quando fosse a loro piaciuto di ridurre quelle stesse <lb/>grandezze a un numero infinito? </s></p><p type="main">

<s>A questo punto i Lettori, a cui non sia passato dalla memoria quel che <lb/>da noi stessi fu scritto a pag. </s>

<s>104, 105 del Tomo IV, troveranno da notare <lb/>una contradizione, la quale per&ograve; non &egrave; temeraria, avendoci le nuove cose <lb/>meglio considerate fatto ritrattare le prime opinioni. </s>

<s>Anche la sentenza ivi <lb/>citata dal Torricelli ci parve poi verissima, messa specialmente a riscontro <lb/>di altri documenti, che s'addurranno fra poco. </s>

<s>Ma la questione concernente <lb/>Leonardo &egrave; di tale importanza, da non lasciar l'occasione di ritornarvici <lb/>sopra. </s></p><p type="main">

<s>Il Libri not&ograve; che <emph type="italics"/>le Peintre toscan<emph.end type="italics"/> era stato il primo a indicare il cen&shy;<lb/>tro di gravit&agrave; della piramide, decomponendola in piani paralleli alla base, <lb/>come si rileva dalle figure dimostrative. </s>

<s>Ripetiamo che di qui non si rileva <lb/>propriamente altro, se non che la proposizione si voleva concludere dall'in&shy;<lb/>tersecarsi gli assi, condotti dagli opposti vertici sopra le respettive basi, a <lb/>quel modo che, nella sua XXII <emph type="italics"/>De centro gravitatis,<emph.end type="italics"/> fa il Commandino, la <lb/>figura del quale &egrave; similissima a quella dello stesso Leonardo. </s>

<s>Questa XXII <lb/>per&ograve; si faceva, come da principal lemma, dipendere dalla XIV fra le prece&shy;<lb/>denti, nella quale si dimostrava che il centro di gravit&agrave; di qualunque solido <lb/>piramidale si ritrova necessariamente in qualche punto sull'asse. </s>

<s>La dimo&shy;<lb/>strazione, che ne d&agrave; di ci&ograve; esso Commandino, procede all'assurdo, per le so&shy;<lb/>lite vie lunghe e faticose degl'inscritti e dei circoscritti, mentre Leonardo &egrave; <lb/>da credere se ne spedisse, decomponendo la piramide o il cono in infiniti <lb/>piani triangolari o circoli, i centri di ciascun de'quali essendo disposti lungo <lb/>l'asse, sull'asse stesso era necessario che cadesse pure il centro di gravit&agrave; <lb/>del tutto. </s>

<s>E perch&egrave; le medesime ragioni manifestamente valevano, da qua&shy;<lb/>lunque vertice si conducessero i detti assi sopra l'opposta base triangolare; <lb/>legittimo era concluderne che dovesse essere il richiesto punto quello della <lb/>loro comune intersezione. </s></p><p type="main">

<s>Ecco in qual modo si pu&ograve; dir che il Pittore toscano applicasse alla Ba&shy;<lb/>ricentrica stereometrica il metodo degl'indivisibili, ci&ograve; che non s'argomenta <lb/>mica dalle figure, ma dal ripensare che dovette esser venuta a Leonardo, <lb/>come poi venne al Roberval, l'inspirazione da quel loro profondo meditare <lb/>sui libri di Archimede, da cui intesero esser proposti i piani ponderosi, non <lb/>come superficie astratte, ma come solidi veri, con le loro altezze infinitesi&shy;<lb/>mali. </s>

<s>E giacch&egrave; il Libri, anzi tutti gl'interpetri dei Manoscritti vinciani, trat&shy;<lb/>tandosi di Matematiche, non possono trascurar le figure, bene spesso signifi&shy;<lb/>cative ora del concetto, ora del processo dimostrativo di qualche teorema; a <lb/>noi pare di vedere in que'segni, dalla scienza insieme e dall'arte resi cosi <lb/>eloquenti, un proposito anche pi&ugrave; ardito di quel che si sia annunziato fin qui, <pb xlink:href="020/01/3065.jpg" pagenum="26"/>ed &egrave; che il Nostro, oltre alla piramide intera, o al cono, instituiva un me&shy;<lb/>todo, da ritrovare il centro di gravit&agrave; ne'loro frusti: metodo, che non &egrave; so&shy;<lb/>lamente pi&ugrave; facile e pi&ugrave; elegante, ma anche pi&ugrave; diretto e pi&ugrave; universale di <lb/>quelli stessi usati di poi dal Commandino, dal Valerio e da Galileo. </s>

<s>Dell'esser <lb/>diretto n'&egrave; prova la derivazione immediata dalla VIII archimedea del primo <lb/>libro <emph type="italics"/>Degli Equiponderanti,<emph.end type="italics"/> e dell'essere universale l'estendersi per analo&shy;<lb/>gia dal triangolo genitore, che Leonardo chiam&ograve; <emph type="italics"/>piramide di due lati equi&shy;<lb/>distanti,<emph.end type="italics"/> al cono, da lui stesso detto <emph type="italics"/>piramide di lati piramidali.<emph.end type="italics"/></s></p><p type="main">

<s>Nel manoscritto E, a tergo del fol. </s>

<s>X, &egrave; una nota che dice: &ldquo; Sia con <lb/>un taglio diviso il triangolo equidistante alla base in due parti uguali. </s>

<s>Que&shy;<lb/>sto &egrave; provato nella sesta del 3&deg; <emph type="italics"/>De ponderibus. </s>

<s>&rdquo;<emph.end type="italics"/> Tale era il titolo che, ad <lb/>imitazione del loro pi&ugrave; prossimo maestro Giordano Nemorario, si dava ai trat&shy;<lb/>tati di Meccanica dagli Autori di que'tempi, e cos&igrave; anche Leonardo, richia&shy;<lb/>mandosi a quel suo libro, che sarebbesi potuto compilar delle sue note sparse, <lb/>mentalmente se lo rappresentava come gi&agrave; scritto, e lo intitolava <emph type="italics"/>De pon&shy;<lb/>deribus.<emph.end type="italics"/> La prova poi, o la soluzion del problema dipendeva dalla proposta <lb/><figure id="id.020.01.3065.1.jpg" xlink:href="020/01/3065/1.jpg"/></s></p><p type="caption">

<s>Figura 10.<lb/>di un problema pi&ugrave; generale, che si trova altrove <lb/>scritto cos&igrave; in una nota: <emph type="italics"/>&ldquo; Io voglio saper quante <lb/>piramide CED<emph.end type="italics"/> (fig. </s>

<s>10) <emph type="italics"/>entra nella piramide <lb/><expan abbr="CVq.">CVque</expan><emph.end type="italics"/> &mdash; Io multiplicher&ograve; la linea CV in s&egrave;, la <lb/>quale avendo la parte EV per sua parte aliquota, <lb/>troverai tal piramide grande contenere in s&egrave; <lb/>tante delle piramidi piccole, quant'&egrave; la somma, <lb/>che resulta dalle parti, in che &egrave; partita la linea <lb/>CV, che son simili alla linea CE, come dire la <lb/>linea DE eqidistante alla linea <expan abbr="Vq.">Vque</expan> E il lato CE <lb/>entra 8 volte nel lato CV. </s>

<s>Dirai dunque: 8 via <lb/>8 fa 64, e tanto fia il numero delle piramide <lb/>CED, che entrano nella piramide maggiore &rdquo; (K, fol. </s>

<s>6 r.). </s></p><p type="main">

<s><emph type="italics"/>E questo modo,<emph.end type="italics"/> soggiunge Leonardo, <emph type="italics"/>&egrave; regola generale.<emph.end type="italics"/> Condotto in&shy;<lb/>fatti l'asse CO, abbiamo CED:CVQ=CI.EI:CO.VO.E perch&egrave; tanto <lb/>CI a CO, quanto EI a VO stanno come EC a CV; dunque ECD:CVQ= <lb/>EC2:CV2.E prendendo CE per unit&agrave; di misura, CVQ=FCD.CV2, onde <lb/>essendo CV=8, come suppone Leonardo, &egrave; manifesto che, de'piccoli trian&shy;<lb/>goli isosceli CED, se ne contengono nel maggiore CVQ, 64. Se poi la figura <lb/>&egrave; un cono, si ha, per l'omologa regola generale ECD:CVQ=EC3:CV3. </s>

<s><lb/>Trasponendo e dividendo, EQ:ECD=CV3&mdash;EC3:EC3, e per il triangolo <lb/>EQ:ECD=CV2&mdash;EC2:EC2. </s>

<s>Che se EQ=ECD, sar&agrave; per l'una figura <lb/>CV=EC.3&radic;2, e per l'altra CV=EC.&radic;2, d'onde vien la regola per <lb/>sapere dove debba farsi il taglio, che divida il triangolo, equidistante alla <lb/>base, in due parti uguali, secondo il proposto problema, per la prova del <lb/>quale rimandava Leonardo al suo libro <emph type="italics"/>De ponderibus.<emph.end type="italics"/></s></p><p type="main">

<s>Ma trattandosi di un teorema puramente geometrico, qual relazione, vien <pb xlink:href="020/01/3066.jpg" pagenum="27"/>fatto di domandare, pu&ograve; aver egli con un libro di Meccanica? </s>

<s>La risposta <lb/>al quesito incomincia ad apparire da quest'altra nota: &ldquo; La piramide ha tre <lb/>centri, de'quali uno &egrave; centro della magnitudine, l'altro &egrave; centro della gra&shy;<lb/>vit&agrave; accidentale, e il terzo &egrave; centro della gravit&agrave; naturale. </s>

<s>Centro della ma&shy;<lb/>gnitudine &egrave; quello, che divide la lunghezza della piramide in due uguali <lb/>parti. </s>

<s>E centro della gravit&agrave; naturale &egrave; quello, nel quale sospendendo la pi&shy;<lb/>ramide fa che essa piramide sta nel sito dell'egualit&agrave; colli stremi della sua <lb/>linea centrale. </s>

<s>Centro della gravit&agrave; naturale &egrave; detto quello, sopra del quale, <lb/>dividendo la piramide per linea retta per qualunque verso, sempre resta di&shy;<lb/>visa in due parti d'egual peso. </s>

<s>Ma lo centro della gravit&agrave; naturale, per qua&shy;<lb/>lunque verso sar&agrave; tocco dalla linea retta, che divide la piramide; sempre <lb/>sar&agrave; di 5/9 di tutta la piramide, di verso la base, ed &egrave; posto il centro d'essa <lb/>gravit&agrave; accidentale nel terzo della lunghezza di verso la base, essendo pira&shy;<lb/>mide di due lati equidistanti, e, se ella piramide fusse di lati piramidali, il <lb/>centro della sua gravit&agrave; accidentale sar&agrave; nel quarto della sua lunghezza di <lb/>verso la base &rdquo; (K, fol. </s>

<s>89). </s></p><p type="main">

<s>La dicitura impropria e confusa non toglie nulla alla verit&agrave; del concetto, <lb/>che si conferma per corollario dal Teorema geometrico, preparato dianzi dallo <lb/>stesso Leonardo, per fondamento di questa conclusione. </s>

<s>Se nella formula in&shy;<lb/>fatti CED:CVQ=CE2:CV2, si fa CE=2/3CV (nel qual caso, essendo <lb/>CE a CV, come CI a CO, il punto I sarebbe sceso nel centro di gravit&agrave; del <lb/>triangolo) avremo CED:CVQ=4/9:1, ossia CED=4/9CVQ, e perci&ograve; <lb/>sar&agrave; la parte EQ di verso la base 5/9 di tutta la piramide, onde il trapezio <lb/>al triangolo viene a essere come 5 a 4. Che se la formula &egrave; CED:CVQ= <lb/>CE3:CV3, fatto CE=3/4CV (nel qual caso il punto I sarebbe sceso nel <lb/>centro di gravit&agrave; del cono) sar&agrave; CED:CVQ=27/64:1. E come la parte <lb/>CED &egrave; 27/64, cos&igrave; la rimanente EQ deve essere 37/64 del tutto, e perci&ograve; il fru&shy;<lb/>sto al minor cono otterrebbe la proporzione di 37 a 27. </s></p><p type="main">

<s>Ora, come avrebbe Leonardo, in proposito <emph type="italics"/>De ponderibus,<emph.end type="italics"/> cercato le <lb/>geometriche proporzioni delle parti, in cui la linea e il piano, che passano <lb/>per i centri di gravit&agrave;, segano il triangolo e il cono; se non perch&egrave;, appli&shy;<lb/>candovi la proposizione VIII del primo libro <emph type="italics"/>Degli equiponderanti,<emph.end type="italics"/> voleva <lb/>istituire una reogla generale, da ritrovare il punto, intorno a cui gravitano <lb/>il trapezio, e il frusto rimasti dal segamento delle due dette figure, che pur <lb/>s'osservano nel Manoscritto, bench&egrave; senz'altra dichiarazione? </s>

<s>La regola dal&shy;<lb/>l'altra parte riusciva di tal bellezza d'ordine e di semplicit&agrave;, da far mara&shy;<lb/>viglia che sfuggisse all'industria di que'tre valorosi, poco fa commemorati, <lb/>i quali, tra la seconda met&agrave; e il finir del secolo XVI, ripresero a trattare <lb/>l'arduo soggetto. </s></p><p type="main">

<s>Sia il triangolo isoscele VOQ (nella precedente figura) il cui centro di <lb/>gravit&agrave; X, e sia segato esso triangolo, secondo qualunque proporzione, dalla <lb/>linea FG in due parti: cio&egrave; nel triangolo CFG, col centro in T, e nel tra&shy;<lb/>pezio FQ, di cui si cerca sull'asse HO il centro Z. </s>

<s>Fatta CO=<emph type="italics"/>m,<emph.end type="italics"/> HC=<emph type="italics"/>n,<emph.end type="italics"/><lb/>abbiamo, per il Teorema geometrico di Leonardo, FCG:FQ=<emph type="italics"/>n2:m2&mdash;n2,<emph.end type="italics"/><pb xlink:href="020/01/3067.jpg" pagenum="28"/>e, per la VIII proposizione meccanica di Archimede, ZX:XT=<emph type="italics"/>n2:m2&mdash;n2,<emph.end type="italics"/><lb/>onde ZX=(<emph type="italics"/>n2<emph.end type="italics"/>XT)/(<emph type="italics"/>m2&mdash;n2<emph.end type="italics"/>). Ma perch&egrave; XH=XC&mdash;CH=<emph type="italics"/>2/3m&mdash;n,<emph.end type="italics"/> e HT= <lb/><emph type="italics"/>1/3n;<emph.end type="italics"/> dunque XT=XH+HT=<emph type="italics"/>2/3m&mdash;n+n/3=2/3(m&mdash;n),<emph.end type="italics"/> il qual <lb/>valore sostituito, d&agrave; ZX=<emph type="italics"/>2n2/(3(m+n)),<emph.end type="italics"/> onde </s></p><p type="main">

<s><emph type="center"/>ZH=ZX+HX=<emph type="italics"/>2n2/(3(m+n))+2/3m&mdash;n.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Per l'altra porzione dell'asse abbiamo </s></p><p type="main">

<s><emph type="center"/>ZO=HO&mdash;HZ=<emph type="italics"/>m&mdash;n&mdash;2n2/(3(m+n))&mdash;2/3m+n=1/3(m&mdash;2n2/(m+n))<emph.end type="italics"/><emph.end type="center"/><lb/>e di qui viene a istituirsi la proporzione </s></p><p type="main">

<s><emph type="center"/>OZ:HZ=<emph type="italics"/>1/3(m&mdash;2n2/(m+n)):2n2/(3(m+n))+2/3m&mdash;n= <lb/>(m2&mdash;2n2+mn):(2m&mdash;n2&mdash;mn).<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Volendosi avere la relazione in funzion della base maggiore, che chia&shy;<lb/>meremo <emph type="italics"/>a,<emph.end type="italics"/> e della minore, che chiameremo <emph type="italics"/>b;<emph.end type="italics"/> perch&egrave; <emph type="italics"/>a:b=m:n,<emph.end type="italics"/> avremo </s></p><p type="main">

<s><emph type="center"/>OZ:HZ=<emph type="italics"/>(a2&mdash;2b2+ab):(2a2&mdash;b2&mdash;ab)= <lb/>[(a&mdash;b)(a+b)+b(a&mdash;b)]:[(a+b)(a&mdash;b)+a(a&mdash;b)]= <lb/>(a&mdash;b)(a+2b):(a&mdash;b)(2a+b)=(a+2b):(2a+b)<emph.end type="italics"/><emph.end type="center"/><lb/>che &egrave; la formula, con la quale Archimede, e dietro lui i Meccanici sogliono <lb/>indicare il centro di gravit&agrave; del trapezio. </s></p><p type="main">

<s>Se <emph type="italics"/>m<emph.end type="italics"/>=2, e <emph type="italics"/>n<emph.end type="italics"/>=1, tanto da questa, quanto dalla formula di Leo&shy;<lb/>nardo, s'ha OZ:HZ=4:5, com'aveva trovato il Nardi. </s>

<s>Se <emph type="italics"/>m<emph.end type="italics"/>=3, e <lb/><emph type="italics"/>n<emph.end type="italics"/>=2, nel qual caso la sezione FG passa per il centro di gravit&agrave; del trian&shy;<lb/>golo grande, OZ:HZ=7:8. Se poi VQ2:FG2=OC2:HC2=2:1, ossia <lb/>OC:HC=&radic;2:1=<emph type="italics"/>m:n,<emph.end type="italics"/> per cui <emph type="italics"/>m=n&radic;2;<emph.end type="italics"/> sostituito questo valore <lb/>di <emph type="italics"/>m<emph.end type="italics"/> nella formula di Leonardo, viene OZ:HZ=&radic;2:3&mdash;&radic;2. </s></p><p type="main">

<s>Queste cose per&ograve;, che non promovevano, ma illustravano la Scienza, <lb/>erano da Leonardo preparate in grazia del centro di gravit&agrave; del frusto co&shy;<lb/>nico, l'invenzion del quale il Commandino si cred&egrave; che fosse nuova, e Ga&shy;<lb/>lileo si compiacque di averla perfezionata. </s>

<s>Per il teorema stereometrico in&shy;<lb/>fatti, che dice avere il cono maggiore, e il minore segato da lui con un piano <lb/>parallelo alla base, la proporzion de'cubi dei loro assi, il valore di ZX si <lb/>trasforma in quello di (<emph type="italics"/>n3<emph.end type="italics"/>XT)/(<emph type="italics"/>m3&mdash;n3<emph.end type="italics"/>). E perch&egrave; XT=<emph type="italics"/>3/4(m&mdash;n),<emph.end type="italics"/> e XH= <lb/><emph type="italics"/>3/4(m&mdash;n);<emph.end type="italics"/> dunque ZX=<emph type="italics"/>n3/(m3&mdash;n3).3/4(m&mdash;n)<emph.end type="italics"/> e perci&ograve; ZH=ZX+XH= <lb/><emph type="italics"/>n3/(m3&mdash;n3).3/4(m&mdash;n)+3/4m&mdash;n=(n

<gap/>+3m

<gap/>&mdash;4nm
<gap/>)/(4(m3&mdash;n3)).<emph.end type="italics"/></s></p><pb xlink:href="020/01/3068.jpg" pagenum="29"/><p type="main">

<s>Si trova poi, per l'altra porzione dell'asse, ZO&mdash;HO&mdash;ZH&mdash; <lb/><emph type="italics"/>m&mdash;n=n3/(m3&mdash;n3).3/4(m&mdash;n)&mdash;3/4m+n=(m

<gap/>+3n

<gap/>&mdash;4mn3)/(4(m3&mdash;n3)),<emph.end type="italics"/><lb/>d'ond&egrave; HZ:ZO=<emph type="italics"/>(n

<gap/>+3m

<gap/>&mdash;4nm3):(m<gap/><gap/>3n

<gap/>&mdash;4mn3).<emph.end type="italics"/> E po&shy;<lb/>tendosi agli assi <emph type="italics"/>m, n,<emph.end type="italics"/> sostituire le basi <emph type="italics"/>a, b<emph.end type="italics"/> loro proporzionali, avremo <lb/>un'analoga relazione espressa dalla formula </s></p><p type="main">

<s><emph type="center"/>HZ:ZO=<emph type="italics"/>(b<gap/>+3a<gap/>&mdash;4a3b):(a<gap/>+3b<gap/>&mdash;4ab3)<emph.end type="italics"/><emph.end type="center"/><lb/>la quale &egrave; facile vedere come si riduca a quella che Galileo d&agrave; nel suo tral&shy;<lb/>tatello (Alb. </s>

<s>XIII, 286): </s></p><p type="main">

<s><emph type="center"/>HZ:ZO=<emph type="italics"/>(3a2+b2+2ab):(3b2+a2+ab).<emph.end type="italics"/><emph.end type="center"/><lb/>Che se <emph type="italics"/>a<emph.end type="italics"/>=2, e <emph type="italics"/>b<emph.end type="italics"/>=1, tanto dalla formula di Galileo, quanto da quella <lb/>di Leonardo, s'ha il centro di gravit&agrave; del frusto conico indicato dalla rela&shy;<lb/>zione HZ:ZO=17:11. </s></p><p type="main">

<s>Chi non ha dimenticato il precedente nostro Tomo, nella prima parte <lb/>del capitolo VII, sa che questa medesima indicazione era stata data da An&shy;<lb/>tonio Nardi, e il comparare il metodo di lui con quello di Leonardo, che ha <lb/>dato luogo a questa forse lunga, ma non inutile digressione, giova a confer&shy;<lb/>mare come derivasse in ambedue una tale elegante facilit&agrave;, anche ne'me&shy;<lb/>todi ordinarii, da quello principalissimo degli indivisibili, di cui dunque esso <lb/>Leonardo conterma l'antichit&agrave; dell'origine. </s></p><p type="main">

<s>Bench&egrave; irragionevole sarebbe il pensare altrimenti, nondimeno abbiamo <lb/>la pi&ugrave; efficace, e pi&ugrave; espressa testimonianza di ci&ograve;, che intendiamo provare, <lb/>da que'due stessi, i quali nella nostra Storia appariscono del Cavalieri pre&shy;<lb/>cursori immediati, anzi nella istituzione del metodo degl'indivisibili compe&shy;<lb/>titori con lui. </s>

<s>Il Nardi, ora commemorato, in quella sua <emph type="italics"/>Ricercata seconda<emph.end type="italics"/><lb/>sopra Archimede, nella quale risponde alle obiezioni, che si fanno all'opere <lb/>di lui, dop'aver concluso che nulle per lo pi&ugrave;, o leggere almeno sono tali <lb/>obiezioni, cos&igrave; soggiunge: &ldquo; Eppure ad inchieste cos&igrave; ardue egli si pone, che <lb/>molto difficile il non mai sdrucciolare apparisce. </s>

<s>&Egrave; vero che molto dal me&shy;<lb/>todo degli indivisibili, se per&ograve; io posso ben giudicare, o veracemente mo&shy;<lb/>strare in quest'opera cosa alcuna, ed anche dagli sperimenti meccanici Ar&shy;<lb/>chimede fu in parte aiutato per l'investigazione di tante astruse verit&agrave;, il <lb/>che da pi&ugrave; capi argomento, e in particolare dai proemii delle Conoidali e <lb/>delle Spirali, ed anco dal supporre noto il centro della gravit&agrave; nella rettan&shy;<lb/>gola conoidale. </s>

<s>&rdquo; </s></p><p type="main">

<s>La testimonianza dell'altro, dopo il Nardi, a cui s'accennava di sopra, <lb/>&egrave; quella del Roberval, che, ne'documenti riferiti da noi a varie occasioni, <lb/>fu udito confessare apertamente aver dal divino Archimede appresa quella <lb/>Scienza matematica dell'infinito, la quale egli poi applic&ograve; alla soluzione dei <lb/>pi&ugrave; ardui problemi, <emph type="italics"/>integro quinquennio<emph.end type="italics"/> prima, che si pubblicasse il me&shy;<lb/>todo del Cavalieri. </s>

<s>Non cita per&ograve; il Roberval nessun libro particolare, e nes&shy;<lb/>suna proposizione, d'onde almen trasparisca aver Archimede riguardate le <lb/>superficie come composte della somma d'infinite linee, o il solido della somma <pb xlink:href="020/01/3069.jpg" pagenum="30"/>d'infinite superficie indivisibili, per cui si crederebbe un'invenzione l'asserto <lb/>del Matematico francese, che, per non parere secondo al Nostro, pens&ograve; astu&shy;<lb/>tamente di sott&ouml;porre s&egrave; e lui a un'autorit&agrave; tanto maggiore. </s>

<s>La sincerit&agrave; <lb/>nonostante e la generosit&agrave; dell'animo, che si dimostra nell'epistola al Tor&shy;<lb/>ricelli, non facendo lecito un tal giudizio, s'andava ripensando fra noi da <lb/>qual parte delle opere del Siracusano potess'esser derivata la Scienza degli <lb/>indivisibili robervalliani, e finalmente parve avere il nostro proposito risolu&shy;<lb/>zione dalla risoluzione stessa di quel famoso problema, in cui domandavasi <lb/>com'&egrave; possibile che le superficie sian gravi, secondo che sempre supponesi <lb/>da Archimede, nell'uno e nell'altro libro de'Piani equiponderanti. </s></p><p type="main">

<s>Il Nardi nella Ricercata seconda sopra citata, tocca cos&igrave; frettolosamente <lb/>la sottile questione: &ldquo; Suppone parimente egli (Archimede) nella stessa opera <lb/>della Quadratura della parabola, e nei Superficiali equilibri, che le superfice <lb/>gravi siano, il che ad alcuno parve sproposito s&igrave; grave, che per fuggirlo ne <lb/>commesse un gravissimo, col sostituire i corpi in luogo delle superficie. </s>

<s>Ma <lb/>se a chi separa le considerazioni sue dal materiale non si permette tal li&shy;<lb/>bert&agrave;, nemmeno si permetter&agrave; il far muovere una linea o una superficie.... <lb/>Ma alcuni, superficiali nella dottrina peripatetica, intendono sinistramente il <lb/>detto del loro Maestro, mentr'egli serive che il Matematico astrae dal moto, <lb/>cio&egrave; dal naturale e concreto, e non dall'astratto e immaginario, altrimenti <lb/>avverria che Euclide non saria geometra, quando l'origine di tante figure <lb/>riconosce dal moto. </s>

<s>&rdquo; </s></p><p type="main">

<s>Colui che volle correggere lo sproposito di Archimede, e a cui il Nardi <lb/>accennava, &egrave; senza dubbio David Rivault, il quale avvertiva nella sua ver&shy;<lb/>sione, e nel suo commento all'opera <emph type="italics"/>De aequiponderantibus,<emph.end type="italics"/> dopo il primo <lb/>lemma del libro primo: &ldquo; Caeterum, licet in sequentibus agatur de planis, <lb/>tamen ne planae superficies intelligerentur, quae pondus habere non cer&shy;<lb/>nuntur, figuras ut corpora adsignavimus &rdquo; (Archim., Opera illustrata, Pari&shy;<lb/>siis 1615, pag. </s>

<s>169). Sempre infatti egli embreggia le figure in modo, che <lb/>rappresentano non piani, ma prismi o prismoidi o solidi colonnari, non av&shy;<lb/>vedendosi dell'errore veramente gravissimo, in cui veniva a compromettere <lb/>il suo Archimede, perch&egrave; in queste rappresentazioni di corpi solidi, doven&shy;<lb/>dosi il centro di gravit&agrave; ridurre nel preciso mezzo dell'asse, tutte le propo&shy;<lb/>sizioni archimedee, manifestamente riuscirebbero false. </s></p><p type="main">

<s>Che se errata &egrave; la soluzion del problema, data dal Rivault, non &egrave; per <lb/>questo punto pi&ugrave; accettevole l'altra, suggerita dallo stesso Nardi, il quale <lb/>diceva esser lecito per astrazione attribuire alle superficie il peso, com'Eu&shy;<lb/>clide, e tutti i geometri, per astrazione attribuiscono a loro stesse il moto. </s>

<s><lb/>Rispetto a che giova invocare l'antica distinzion metafisica tra forma e ma&shy;<lb/>teria, e rammemorar che la forma, a cui si riferiscono le superficie, non <lb/>pesa, come, valendosi degli stessi principii idrostatici di Archimede, Galileo <lb/>dimostr&ograve; contro i Peripatetici, e come ce he persuadono l'esperienze, pesando <lb/>nel vuoto qualche plasmabile corpo, trasfigurato in qualunque maniera. </s>

<s>Se <lb/>il peso dunque &egrave; inerente e proprio alla sola materia, &egrave; irragionevole attri-<pb xlink:href="020/01/3070.jpg" pagenum="31"/>buirlo alle superficie, rese per astrazione immateriali. </s>

<s>Si pu&ograve; inoltre osser&shy;<lb/>vare che, se il peso &egrave; causa produttrice del moto, non ogni moto per&ograve;, com'&egrave; <lb/>quello della linea che genera la superficie, &egrave; l'effetto del peso. </s>

<s>Una tale ge&shy;<lb/>nerazione meccanica infatti, suggerita ai Geometri dall'esempio di un punto <lb/>discreto e luminoso, che movendosi velocissimo apparisce una continuata stri&shy;<lb/>scia di luce; ha relazione piuttosto con la forma imponderabile, che con la <lb/>gravit&agrave; essenzialmente propria della materia. </s></p><p type="main">

<s>Antonio Rocca avrebbe, secondo il Rivault, introdotto nella Baricentrica <lb/>un altro sproposito pi&ugrave; grosso di quello di Archimede, facendo, non solo le <lb/>superficie, ma le linee stesse pesanti. </s>

<s>Eppure il Torricelli non dubit&ograve; d'imi&shy;<lb/>tarne gli esempi, e chi ha letto, nel Tomo precedente, il trattato dei Centri <lb/>di gravit&agrave; di lui, si rammenter&agrave; di aver trovata anche questa, fra le altre <lb/>supposizioni: &ldquo; Supponghiamo ancora che le linee abbiano il centro di gra&shy;<lb/>vit&agrave;, e forse non sar&agrave; maggiore assurdo il considerare le linee come gravi, <lb/>che il considerar le superficie pesanti. </s>

<s>Gi&agrave; in buona Geometria non si pu&ograve; <lb/>dire che una linea sia minore di una superficie, ed io credo che tanto sia <lb/>lontano dall'esser grave una linea, quanto una superficie. </s>

<s>&rdquo; </s></p><p type="main">

<s>Il discorso dunque del Torricelli riesce a questo: non esser ragionevole <lb/>negare il peso alle linee, se si concede alle superficie. </s>

<s>E perci&ograve; sembra che, <lb/>senza troppo travagliarsene, volesse risolvere il problema col dire: Archi&shy;<lb/>mede l'ha supposto, i Matematici in generale hanno menata buona quella <lb/>sua supposizione; sia dunque anche a noi lecito ammettere che le superfi&shy;<lb/>cie, e perci&ograve; anche le linee, gravitano intorno al sostegno delle loro bilance. </s>

<s><lb/>Il ragionamento del Torricelli &egrave; quello insomma, che s'&egrave; fatto sempre, e si <lb/>fa tuttavia dagli Scrittori, i quali si propongono nei loro trattati di trovare <lb/>il centro di gravit&agrave; del triangolo, per esempio, e della parabola, come un <lb/>esercizio usato infin dagli antichissimi tempi, senza ripensare alla vanit&agrave; del&shy;<lb/>l'opera loro, quando si terminasse l'inquisizione in quelle figure, e senza <lb/>pur sospettare che le cose dimostrate da Archimede non son veramente pro&shy;<lb/>posizioni, ma lemmi. </s></p><p type="main">

<s>I reconditi sensi del Siracusano sembra a noi che fossero penetrati dal&shy;<lb/>l'acutissimo Roberval, il quale, unico forse, comprese che i piani, di cui si <lb/>tratta ne'libri degli Equiponderanti, son solidi: il triangolo, s&igrave;, un prisma, <lb/>la parabola un cilindroide, non per&ograve; con altezze definite, come le metteva il <lb/>Rivault, ma infinitamente piccole, indivisibili. </s>

<s>Par che si voglia il centro di <lb/>gravit&agrave; di piani, e l'invenzione &egrave; invece ai solidi colonnari, che si possono <lb/>costruire con soprapporre essi piani infiniti, il centro di gravit&agrave; de'quali so&shy;<lb/>lidi essere in mezzo all'asse, alla linea cio&egrave; che congiunge i centri di gra&shy;<lb/>vit&agrave; delle bas&igrave;, &egrave; pi&ugrave; chiaro, diceva il Torricelli, di ogni prova, che se ne <lb/>potesse addurre. </s>

<s>Ecco perch&egrave;, convien che il Roberval dicesse, volendo Ar&shy;<lb/>chimede indicare il centro di gravit&agrave; del prisma triangolare, o del paralle&shy;<lb/>lepipedo, o del cilindroide parabolico, si limita a trovar que'medesimi centri <lb/>nel triangolo, nel parallelogrammo, e nella parabola: perch&egrave; di li, come da <lb/>lemmi, chiunque avrebbe potuto con facilit&agrave; concluderne il fine delle pro-<pb xlink:href="020/01/3071.jpg" pagenum="32"/>posizioni. </s>

<s>Fattosi cos&igrave; pervente a esso Roberval lo spirito di Archimede, <lb/>s'intende come ammirato lo salutasse col titolo di divino. </s>

<s>A lui era debi&shy;<lb/>tore, non solamente d'aver appresa la scienza dell'infinito, e di averla insti&shy;<lb/>tuita in un metodo nuovo, ma di esser felicemente riuscito a scansar le cri&shy;<lb/>tiche, che incontr&ograve; il Cavalieri, malignamente inconsiderate, non intendendo <lb/>come lui il solido compaginato d'infinite superficie, ma d'infiniti piani con <lb/>altezze indivisibili, e quali volevano esser quelli del suo divino premonstra&shy;<lb/>tore, affinch&egrave; si potessero dire, e trattar come gravi. </s></p><p type="main">

<s>Bench&egrave; queste cose sian forse trapassate fin qui dai critici inosservate, <lb/>non sembrano a noi per&ograve; meno evidenti, e mentre la scoperta del Rober&shy;<lb/>val da una parte conferma l'origine antica del metodo degl'indivisibili, de&shy;<lb/>rivata direttamente da Archimede ne'contemporanci di Leonardo, e nel Ro&shy;<lb/>berval, e per riflesso dalle Collezioni di Pappo nel Nardi, e dalla Stereometria <lb/>o dalla Ciclometria del Kepler nel Cavalieri; dall'altra riduce a ragionevoli <lb/>termini una nuova questione, come Archimede cio&egrave; ritrovasse il centro di <lb/>gravit&agrave; nel solido parabolico. </s>

<s>Il Commandino fu primo ad avvertire la mi&shy;<lb/>rabile invenzione. </s>

<s>Pervenutogli alle mani il trattato delle Galleggianti, &ldquo; ani&shy;<lb/>madverti, egli dice nel dedicare il suo libro del centro di gravit&agrave; de'solidi <lb/>al cardinale Farnese, dubitari non posse quin Archimedes, vel de hac ma&shy;<lb/>teria scripsisset, vel aliorum mathematicorum scripta perlegisset; nam in iis <lb/>tum alia nonnulla, tum maxime illam propositionem ut evidentem, et alias <lb/>probatam assumit: centrum gravitatis in portionibus conoidis rectanguli axem <lb/>ita dividere, ut pars, quae ad verticem terminatur, alterius partis, quae ad <lb/>basim, dupla sit &rdquo;: proposizione che, sebbene non sia dall'Autore espressa&shy;<lb/>mente formulata, pur s'argomenta dall'enunziato della seconda, e dalle altre <lb/>proposizioni, che seguono nel secondo libro. </s>

<s>Il Nardi insinuava, come udimmo <lb/>poco fa, che l'invenzion del punto gravitativo nel Conoide occorresse ad Ar&shy;<lb/>chimede, per via dell'esperienza, ci&ograve; che sembra alieno dall'istituto schiet&shy;<lb/>tamente geometrico di lui, sempre avverso alla scienza somministrata dai <lb/>sensi, i quali ei reputava fallaci, e non senza ragione, per le prove che se ne <lb/>ebbe a far poi, come da Galileo, quando volle colla bilancia tentare il centro <lb/>di gravit&agrave; della cicloide. </s>

<s>Or si comprende come l'incertezza del fatto venisse <lb/>a togliersi con facilit&agrave;, per via della speculazione, ammettendo che proce&shy;<lb/>desse anche Archimede, nell'invenzion del centro di gravit&agrave; del Conoide, a <lb/>quel modo, che vedemmo gi&agrave; fare al Torricelli. </s>

<s>Il metodo degl'indivisibili <lb/>rivelava cos&igrave; patente l'analogia fra il triangolo ed essa Conoidale, da dover <lb/>concluderne con tutta la certezza geometrica essere gli assi del piano e del <lb/>solido segati dal centro di gravit&agrave;, secondo la medesima proporzione. </s></p><p type="main">

<s>Deve il Commandino, dietro quella prima avvertenza, averne fatta anche <lb/>un'altra, ed &egrave; che Archimede, nella figura illustrativa l'ottava proposizione <lb/>del primo libro, indicava il centro di gravit&agrave; del settore sferico con quella <lb/>precisione, che poi sarebbe per indicare il centre della Conoidate. </s>

<s>Al Mate&shy;<lb/>matico urbinate per&ograve; questa volta non serv&igrave;, per la difticile inquisizione, la <lb/>Geometria ordinaria, ond'ei non seppe dir altro, se non che il richiesto cen-<pb xlink:href="020/01/3072.jpg" pagenum="33"/>tro di gravit&agrave; del settore trovavasi su qualche punto dell'asse. </s>

<s>A questa vaga <lb/>indicazione si sarebbe dovuto star senza dubbio contento anche Archimede, <lb/>quando non avesse invocati i soccorsi della Geometria infinitesimale, in modo <lb/>simile a quel che fecero il Nardi, il Cavalieri, il Torricelli e il Wallis, i <lb/>quali, immaginando essere il solido composto d'infinite callotte concentriche, <lb/>vinsero del problema quella gran ritrosia, di che il Tartaglia e il Comman&shy;<lb/>dino ebbero a fare non vincibile prova. </s></p><p type="main">

<s>Che Archimede avesse penetrato, con l'acume degl'indivisibili, il centro <lb/>di gravit&agrave; del conoide parabolico e del settore di sfera, sembra che lo cre&shy;<lb/>desse anche lo stesso Torricelli, il quale anzi si persuase che gli antichi aves&shy;<lb/>sero in quel metodo, e nel principio della composizione de'moti, un segreto <lb/>efficacissimo, per aprire in Geometria i pi&ugrave; reconditi misteri. </s>

<s>Di questo me&shy;<lb/>desimo parere fu anche il Wallis, come apparisce dal commentario di lui <lb/>sopra il libro archimedeo <emph type="italics"/>De circuli dimensione,<emph.end type="italics"/> e prima dell'Inglese e del <lb/>Nostro aveva il Nunnez, nel suo trattato di algebra in lingua spagnola, sen&shy;<lb/>tenziato non doversi reputar da nessuno che le proposizioni di Euclide e di <lb/>Archimede fossero trovate per quelle medesime vie che appariscono ne'loro <lb/>libri (Antuerpiae 1567, pag. </s>

<s>114). Occultassero quest'arcano dell'arte, per <lb/>non soggiacere all'invidia, e alle contradizioni, come disse il Torricelli (Opera <lb/>geom., P. II, pag. </s>

<s>56), o per far pi&ugrave; mirabili apparire i loro trovati, come <lb/>pens&ograve; il Nardi, o per qualsivoglia altra ragione molto difficile a indovinarsi <lb/>da noi, gente tanto diversa da quella di que'tempi; sarebbe vano, secondo <lb/>le riferite opinioni, aspettare l'apparizion di que'libri, dove Archimede dimo&shy;<lb/>strerebbe la natura e le propriet&agrave; de'centri gravitativi, che si presuppongono <lb/>ai teoremi <emph type="italics"/>De aequiponderantibus,<emph.end type="italics"/> e il principio della composizion delle <lb/>forze parallele, da cui resulta che il moto in su si fa nella direzion della <lb/>perpendicolare, che passa per il centro di gravit&agrave; del galleggiante. </s>

<s>Anche in <lb/>quel trattato <foreign lang="greek">*reri cugw_n</foreign>, che tanto si desidera dai cultori di Archimede, si <lb/>troverebbe forse, quando finalmente apparisse alla luce, essersi dall'Autore <lb/>mantenuto quel segreto geloso, che ora gli studii ci hanno scoperto, e per <lb/>cui pu&ograve; svelarsi la scienza, rimasta fin qui coperta dal pellucido tessuto delle <lb/>supposizioni. </s></p><p type="main">

<s>Ammessa infatti la dottrina degli infinitesimi, e l'uso del parallelogrammo <lb/>delle forze, abbiamo potuto rintracciare le sottilissime vie, per le quali si <lb/>condusse Archimede (riguardando le infinite particelle materiali come solle&shy;<lb/>citate da forze parallele) a ritrovare il punto, dov'&egrave; applicata l'unica forza <lb/>resultante dalla somma delle componenti infinite: punto, che riferito ai pesi, <lb/>&egrave; quel centro di gravit&agrave;, che dal chiuso pensiero dell'Autore sale a un tratto, <lb/>com'acqua da nascosta vena, a irrigar largamente i campi della Statica ar&shy;<lb/>chimedea. </s>

<s>La famosa dimostrazione del vette e quella, che pi&ugrave; al vivo ri&shy;<lb/>tragga in s&egrave; l'immagine della teoria, da cui con occulto parto fu esposta, <lb/>sostituendo i pesi, moltiplicabili all'infinito, alle forze parallele, il centro delle <lb/>quali vedemmo segar la linea di congiunzione (che per la Va del primo libro <lb/><emph type="italics"/>De aequiponderantibus<emph.end type="italics"/> si trasforma nel vette) in parti reciprocamente pro-<pb xlink:href="020/01/3073.jpg" pagenum="34"/>porzionali alle stesse forze sollecitanti, s&igrave; considerate in astratto, e s&igrave; come <lb/>applicate a rappresentare le gravit&agrave; delle appese grandezze. </s></p><p type="main">

<s>Abbiasi ora, per ridursi pi&ugrave; da vicino al nostro proposito, in AB (fig. </s>

<s>11) <lb/>un corpo, che supporremo in forma di quadrato, e di tale gravit&agrave; in specie <lb/>da cader liberamente nell'aria, e siaci proposto a ritrovare la direzione e <lb/><figure id="id.020.01.3073.1.jpg" xlink:href="020/01/3073/1.jpg"/></s></p><p type="caption">

<s>Figura 11.<lb/>l'intensit&agrave; di una tale caduta. </s>

<s>Risoluto il <lb/>detto quadrato in infiniti rettangoli, nel <lb/>mezzo C della linea ED, che ricongiunge <lb/>i centri di gravit&agrave; di ciascuna grandezza, <lb/>deve, per la citata quinta proposizion di <lb/>Archimede, ritrovarsi il centro di gravit&agrave; <lb/>del tutto, e sostituite altrettante forze pa&shy;<lb/>rallele a rappresentare le sollecitazioni in <lb/>tutti gl'infiniti elementi, la resultante CM, <lb/>uguale a tutte insieme le forze parziali, e <lb/>a esse stesse parallela, misura la intensit&agrave; <lb/>e la direzione della caduta. </s></p><p type="main">

<s>S'immagini poi esser messo il corpo AB in fondo a un liquido, di cui <lb/>sia specificatamente men grave: &egrave; un fatto che il moto, dianzi discensivo, <lb/>ora si converte in ascensivo, ci&ograve; che non pu&ograve; avvenire altrimenti, se non per <lb/>essere le forze sollecitanti ciascuna particella rivolte in direzione opposta, e <lb/>per aver raggiunta proporzion maggiore verso le prime. </s>

<s>Dovendo poi l'in&shy;<lb/>cremento in ciascuna essere uguale, il centro delle nuove forze parallele potr&agrave; <lb/>essere il medesimo, e la medesima direzione, bench&egrave; con pi&ugrave; gagliardo moto, <lb/>avr&agrave; la resultante CN, la quale &egrave; alla CM direttamente opposta. </s>

<s>D'onde &egrave; <lb/>manifesto i corpi pi&ugrave; leggeri del liquido, in cui sono immersi, <emph type="italics"/>sursum ferri <lb/>secundum perpendicularem, quae per centrum gravitatis eorum ducitur,<emph.end type="italics"/><lb/>come dice Archimede, supponendo i principii, dall'investigazione de'quali <lb/>s'&egrave; veduta scaturire questa stessa conclusione. </s></p><p type="main">

<s>Giunto il corpo immerso alla sommit&agrave; del liquido, e sopra il livello di <lb/>lui sollevatosi tanto, quanto dalla Va del primo libro archimedeo delle Gal&shy;<lb/>leggianti &egrave; prescritto; ivi si rimane, ci&ograve; che non pu&ograve; essere, se non perch&egrave; <lb/>la forza, che violentemente lo sospingeva in alto, s'&egrave; fatta uguale a quella <lb/>che lo portava in basso, e qui giova trattenersi alquanto in considerare le <lb/>condizioni di un tale equilibrio. </s></p><p type="main">

<s>Sia il solido, quietandosi nel termine della sua ascesa, rimasto nella po&shy;<lb/>sizione rappresentata per la medesima figura, nella quale FO segna la linea <lb/>del livello. </s>

<s>Si potrebbe ritrovare la causa della sua stazione, immaginando <lb/>che il peso de'prismetti infinitesimi, componenti esso solido, uno de'quali <lb/>AH, sia uguale al peso degl'infiniti filetti liquidi, simili a LH, in modo per&ograve; <lb/>che questi tendano non verso M, ma verso N, centro contrapposto a quello <lb/>della Terra. </s>

<s>La speculazione sarebbe senza dubbio conforme a quel che &egrave; <lb/>stato dimostrato nella proposizione V del primo libro <emph type="italics"/>De insidentibus aquae,<emph.end type="italics"/><lb/>essendo manifesto che di quegli infiniti filetti liquidi componesi una mole di <pb xlink:href="020/01/3074.jpg" pagenum="35"/>umido uguale alla parte del solido sommersa, e che pesa quanto esso solido <lb/>intero. </s>

<s>Tale fu appunto la speculazion di Archimede, ma rimase per molti <lb/>secoli incompresa, d'onde ebbero origine le vicende, che ci porgeranno argo&shy;<lb/>mento, anzi saranno come il polo, intorno a cui s'aggira la storia dell'Idro&shy;<lb/>statica: per ora non &egrave; da interrompere il filo del discorso. </s></p><p type="main">

<s>Il quadrato o altro solido qualunque ABCD (fig. </s>

<s>12) galleggiante sul <lb/>liquido, sia tenuto per forza con l'asse BD inclinato alla superficie FO del <lb/><figure id="id.020.01.3074.1.jpg" xlink:href="020/01/3074/1.jpg"/></s></p><p type="caption">

<s>Figura 12.<lb/>livello: consegue da'premessi principii <lb/>la ragion meccanica perch&egrave;, abbando&shy;<lb/>nato a s&egrave; stesso, si dirizza naturalmente <lb/>coll'asse perpendicolare. </s>

<s>Essendo infatti <lb/>in X il centro di gravit&agrave; del tutto, e <lb/>in Z quello della parte sommersa, il <lb/>galleggiante &egrave; spinto in basso dalla <lb/>forza ZY, e in alto dalla forza a lei <lb/>uguale TU, trasportata da Z in T sopra <lb/>l'asse, e basta osservare al loro modo di agire, per concluder che non ces&shy;<lb/>seranno di far rotare il solido, da destra a sinistra, infintanto che non giun&shy;<lb/>gano a contrapporsi lungo la medesima linea, diretta al centro della Terra. </s></p><p type="main">

<s>Propriet&agrave; simili a queste si proponeva Archimede a dimostrare nel suo <lb/>secondo libro, in galleggianti scelti di tal figura, che potessero accomodarsi <lb/>all'intenzione dell'Opera. </s>

<s>Posto dunque, come principio, fondamentale, esser <lb/>portati in su i corpi nell'umido, secondo la perpendicolare, che dal loro cen&shy;<lb/>tro di gravit&agrave; si produce, &egrave; secondo la traduzion latina, edita dal Tartaglia, <lb/>formulata cos&igrave; la proposizione, che, secondo l'ordine logico, si disse dover <lb/>esser la prima: &ldquo; Si aliqua solida magnitudo habens figuram portionis sphae&shy;<lb/>rae in humidum demittatur, ita ut basis portionis non tangat humidum, figura <lb/>insidebit recta, ita ut axis portionis secundum perpendicularem sit: et si ab <lb/>aliquo trahitur figura, ita ut basis portionis tangat humidum, non manet de&shy;<lb/>clinata, secundum dimittatur, sed recta restituatur. </s>

<s>&rdquo; </s></p><p type="main">

<s>Doveva il testo ragionevolmente avere: <emph type="italics"/>sed, cum dimittitur, recta resti&shy;<lb/>tuctur,<emph.end type="italics"/> e ci&ograve; osservatosi per fare accorto chi legge de'tanti errori scorsi nella <lb/>trascrizione, da qualunque mano abbiano avuto origine, seguitiamo a leggere <lb/>nella stessa copia del Tartaglia scritto cos&igrave;, che pare incominci la dimostra&shy;<lb/>zione del proposto teorema: &ldquo; Et igitur, si figura levior existens humido de&shy;<lb/>mittatur in humidum, ita ut basis ipsius tota sit in humido; figura inside&shy;<lb/>bit recta ita, ut axis ipsius sit secundum perpendicularem. </s>

<s>Intelligatur enim <lb/>aliqua magnitudo in humidum demissa: intelligatur etiam etc. </s>

<s>&rdquo; proseguen&shy;<lb/>dovisi a dimostrare in che modo il segmento sferico, che sia messo con tutta <lb/>la base nell'umido, rimosso dal perpendicolo, vi ritorna. </s>

<s>La dimostrazion di&shy;<lb/>retta perci&ograve; della proposta &egrave; taciuta, e forse Archimede, dall'esposte ragioni <lb/>dell'equilibrio nel segmento con la base nell'umido, lasciava a'suoi studiosi <lb/>la facile applicazione al primo proposito, ch'era del segmento stesso, con la <lb/>base fuori dell'umido. </s>

<s>E perch&egrave;, primo fra quegli studiosi, fu lo stesso Tar-<pb xlink:href="020/01/3075.jpg" pagenum="36"/>taglia, non manc&ograve; di mettersi, nel Ragionamento primo sopra la sua <emph type="italics"/>Tra&shy;<lb/>vagliata invenzione,<emph.end type="italics"/> a un tale esercizio. </s>

<s>Quivi, esposto il teorema tutto in&shy;<lb/>sieme nelle due parti, incomincia dal dimostrar la seconda, proponendosi il <lb/>caso di un segmento maggiore dell'emisfero, come si rappresenta dalla no&shy;<lb/><figure id="id.020.01.3075.1.jpg" xlink:href="020/01/3075/1.jpg"/></s></p><p type="caption">

<s>Figura 13.<lb/>stra figura 13, nella quale ACD &egrave; la super&shy;<lb/>ficie sferica dell'umido, col centro in L, e <lb/>HNE il galleggiante, ora con l'asse eretto <lb/>secondo NL, ora, secondo ZT, inclinato, la <lb/>porzione emersa del qual ga&igrave;leggiante abbia <lb/>raccolto in R il suo peso, che per la RL &egrave; <lb/>diretto in L suo stesso centro. </s>

<s>&ldquo; Il restante <lb/>dunque di tal figura, dice il Tartaglia, cio&egrave; <lb/>quella parte, che &egrave; nell'umido sommersa, <lb/>aver&agrave; il centro della sua gravit&agrave;, per la sesta <lb/>proposizione del libro <emph type="italics"/>De centro gravium,<emph.end type="italics"/> nella linea CR, prodotta in diretto <lb/>dalla banda del C, tolta talmente, che la parte allungata, alla CR, abbia la me&shy;<lb/>desima proporzione, che ha la gravit&agrave; di quella parte di figura, che &egrave; di fuori <lb/>dell'umido, alla gravit&agrave; di quella parte, che &egrave; nell'umido sommersa. </s>

<s>Or po&shy;<lb/>niamo che tal centro di detta figura sia il punto O, e per il detto centro O <lb/>sia protratta la perpendicolare LO. </s>

<s>Adunque la gravit&agrave; della parte che &egrave; fuora <lb/>dell'umido premer&agrave; di suso in giuso, secondo la perpendicolare RL, e la <lb/>parte della figura, che &egrave; sommersa nell'umido, premer&agrave; di sotto in suso, <lb/>per la seconda supposizione, secondo la perpendicolare LO. </s>

<s>Adunque tal figura <lb/>non rimarr&agrave;, ma le parti della figura, che son&ograve; verso H, saranno portate in <lb/>giuso, e quelle che sono verso E saranno portate in suso, e questo sar&agrave;, per <lb/>fino a tanto che l'assis ZT sia fatto secondo la perpendicolare. </s>

<s>E questa tal <lb/>dimostrazione si verifica ancora nella mezza sfera, che stia nell'umido con <lb/>tutta la base.... e si verifica ancora nella porzion minore della mezza sfera. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Con questi medesimi argomenti si <lb/><figure id="id.020.01.3075.2.jpg" xlink:href="020/01/3075/2.jpg"/></s></p><p type="caption">

<s>Figura 14.<lb/>dimostra il medesimo, quando che queste <lb/>sopraddette figure siano lasciate nell'umido <lb/>talmente, che le base di quelle stiano in suso, <lb/>cio&egrave; che niuna di quelle tocchi l'umido, con&shy;<lb/>chiudendo quasi con parole contrarie a quelle <lb/>di sopra narrate, cio&egrave; che la parte della figu&shy;<lb/>ra, che &egrave; fuora dell'umido, premer&agrave; di suso <lb/>in giuso, secondo la perpendicolare LS (figu&shy;<lb/>ra 14) per la prima supposizione. </s>

<s>E la parte <lb/>della figura summersa premer&agrave; di sotto in <lb/>suso, secondo la perpendicolare LR, per la <lb/>seconda supposizione. </s>

<s>Adunque tal figura, secondo quest'altra posizione, non <lb/>star&agrave;: anzi le parti di tutta la figura, che sono verso E, saranno premute <lb/>di suso in giuso, e quelle che sono verso H saranno urtate e spinte di sotto <lb/>in suso, e questo perseverer&agrave; per fino a tanto che l'assis ZT sia fatta se-<pb xlink:href="020/01/3076.jpg" pagenum="37"/>condo la perpendicolare pi&ugrave; volte detta, che &egrave; il proposito vero &rdquo; (Vene&shy;<lb/>tia 1551, pag. </s>

<s>20, 21): ossia &egrave; la parte principale della proposizione. </s>

<s>Che se <lb/>il Tartaglia ne pospose l'ordine, fu per mantenersi fedele al testo, e per <lb/>tener dietro alla scorta delle figure, le quali si succedevano nella tavola, ri&shy;<lb/>masta dell'originale greco, in due gruppi, il primo de'quali rappresentava <lb/>il galleggiante ora uguale all'emisfero, poi maggiore, e all'ultimo minore, <lb/>con la base immersa nell'umido, mentre le tre analoghe figure dell'altro <lb/>gruppo rappresentavano que'medesimi segmenti sferici con la base emersa. </s>

<s><lb/>Per questo stesso amore di fedelt&agrave; s'indusse a porre l'asse ZT, non secondo <lb/>il suo debito stare, cio&egrave; nella met&agrave; dell'arco della figura, ma alquanto obli&shy;<lb/>quo, e bench&egrave; conoscesse che a quel modo <emph type="italics"/>saria pi&ugrave; naturale e pi&ugrave; chiaro,<emph.end type="italics"/><lb/>nonostante <emph type="italics"/>perch&egrave;,<emph.end type="italics"/> dice, <emph type="italics"/>cos&igrave; erano tali figure nell'esempio greco, non me <lb/>parso di contrafar quelle, anchor che fusse stato meglio<emph.end type="italics"/> (ivi, pag. </s>

<s>21). </s></p><p type="main">

<s>Il Commandino non ebbe tanti scrupoli. </s>

<s>Ridusse le figure al loro de&shy;<lb/>bito stare, come s'&egrave; fatto da noi con le linee punteggiate: ritocc&ograve; qua e l&agrave; <lb/>la forma dell'enunciato, e corresse gli sbagli della trascrizione dal codice la&shy;<lb/>tino. </s>

<s>Poi, bench&egrave; la licenza paresse oltrepassare il necessario, di una propo&shy;<lb/>sizione unica divisa in due parti, ne volle fare due distinte proposizioni, la <lb/>prima delle quali cos&igrave; diceva: &ldquo; Si aliqua magnitudo solida, levior humido, <lb/>quae figuram portionis sphaerae habeat, in humidum demittatur, ita ut ba&shy;<lb/>sis portionis non tangat humidum: figura insidebit recta, ita ut axis portio&shy;<lb/>nis sit secundum perpendicularem. </s>

<s>Et si ab aliquo inclinetur figura, ut basis <lb/>portionis humidum contingat, non manebit inclinata, si demittatur, sed recta <lb/>restituetur. </s>

<s>&rdquo; L'altra proposizione viene appresso cos&igrave; formulata: &ldquo; Quod si <lb/>figura humido levior in humidum demittatur, ut basis tota sit in humido; <lb/>insidebit recta, ita ut axis ipsius secundum perpendicularem constituatur. </s>

<s>&rdquo; <lb/>La qual verit&agrave; cos&igrave; proposta si passa a dimostrare in quel modo, che aveva <lb/>fatto Archimede: modo con tanta facilit&agrave; applicabile a dimostrar la prece&shy;<lb/>dente, che, anche quando non si fosse l'Autore curato di vedere il Ragiona&shy;<lb/>mento del Tartaglia, parrebbe una vanagloria lo scrivere in margine <emph type="italics"/>Sup&shy;<lb/>pleta a Federico Commandino,<emph.end type="italics"/> e si direbbe adulazione quella di un valoroso <lb/>Critico tedesco, il quale annotava: <emph type="italics"/>Demonstrationem de suo adiecit Com&shy;<lb/>mandinus<emph.end type="italics"/> (Heiberg. </s>

<s>Archim. </s>

<s>Op., Vol. </s>

<s>II, Lipsiae 1881, pag. </s>

<s>371). </s></p><p type="main">

<s>N&egrave; maggior ragione di compiacersi sembra avesse lo stesso Comman&shy;<lb/>dino, nell'annunziar che di suo proprio s'era pure supplito alla parte, man&shy;<lb/>cante nel primo di quei teoremi, in cui proponevasi il galleggiante in figura <lb/>di un solido conoidale. </s>

<s>Intorno a ci&ograve; &egrave; da osservare che, nel segmento sfe&shy;<lb/>rico, non s'attendeva ad altro, che a dimostrare il gioco delle forze, e come <lb/>per-il modo dell'agir di loro fosse costretto a rotare in s&egrave; stesso il galleg&shy;<lb/>giante, non quietandosi infin tanto che le dette forze non venissero a con&shy;<lb/>trapporsi lungo la medesima verticale. </s>

<s>Anche in questo caso per&ograve; potrebbe <lb/>darsi che l'equilibrio si facesse, ma che non fosse stabile, ond'&egrave; che le con&shy;<lb/>dizioni di una tale stabilit&agrave;, trascurate dianzi nel segmento sferico, si ven&shy;<lb/>gono ora a considerar particolarmente da Archimede nel solido parabolico. </s></p><pb xlink:href="020/01/3077.jpg" pagenum="38"/><p type="main">

<s>Sia il detto solido, quale, nella sua sezione AOL, ce lo rappresenta la <lb/>figura 15. Immerso nel liquido col suo vertice, vi si manterr&agrave; stabilmente <lb/>eretto, ogni volta che il suo centro di gravit&agrave; rimanga alquanto di sotto al <lb/><emph type="italics"/>centro della pressione.<emph.end type="italics"/> E perch&egrave; una condizion tale dipende, non solamente <lb/><figure id="id.020.01.3077.1.jpg" xlink:href="020/01/3077/1.jpg"/></s></p><p type="caption">

<s>Figura 15.<lb/>dalla proporzione, che ha la gravit&agrave; spe&shy;<lb/>cifica del solido al liquido, ma e dal pa&shy;<lb/>rametro della parabola genitrice, o dalla <lb/>distanza fra l'apice del cono, e il punto, <lb/>in cui cade sull'apotema il vertice della <lb/>sezione, distanza che Archimede chiama <lb/><emph type="italics"/>linea all'asse;<emph.end type="italics"/> e perch&egrave; il centro di gra&shy;<lb/>vit&agrave; del conoideo sega cos&igrave; l'asse di lui, <lb/>che il tutto sia sesquialtero della parte, <lb/>che &egrave; verso il vertice, ossia che stia a que&shy;<lb/>sta come tre sta a due; &egrave; perci&ograve; che si <lb/>dice l'annunziato fatto verificarsi, quando la porzione del conoideo rettangolo <lb/>abbia l'asse minore che <emph type="italics"/>sesquialtero<emph.end type="italics"/> (dal greco latinamente trasvestito in <emph type="italics"/>emio&shy;<lb/>lium<emph.end type="italics"/>) della linea stessa che &egrave; all'asse. <emph type="italics"/>&ldquo; Recta portio rectanguli conoida&shy;<lb/>lis,<emph.end type="italics"/> cos&igrave; &egrave; nella edizione del Tartaglia, <emph type="italics"/>quando axem habuerit non mino&shy;<lb/>rem, quam emiolium eius, quae usque ad axem, omnem proportionem <lb/>habens ad humidum in gravitate, dimissa in humido ita, ut basis ipsius <lb/>non tangat humidum, posita inclinata, non manet inclinata, sed restitue&shy;<lb/>tur recta: rectam dico consistere talem portionem, quando, quod secuit <lb/>ipsam, fuerit aequidistanter superficiei humidi. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Le parole che seguitano si crederebbe che fossero il principio della di&shy;<lb/>mostrazione, ma di questa propriamente non sono che l'<emph type="italics"/>ipotesi:<emph.end type="italics"/> non si fa <lb/>cio&egrave; altro con esse che dichiarare esser l'asse del solido veramente inclinato, <lb/>come si vuole, alla superficie del liquido, perch&egrave; non fa con essa da una <lb/>parte e dall'altra angoli uguali. </s>

<s>La dimostrazione per&ograve; manca affatto, e il <lb/>Commandino al solito nota in margine di averla supplita di suo, concludendo <lb/>che se R, nella proposta figura, &egrave; il centro di gravit&agrave; del tutto, H della parte <lb/>immersa, e G della emersa; la forza applicata in H, e che spinge in alto, <lb/>insieme con quella applicata in G, e che spinga in basso, faranno rotare il <lb/>solido, infin tanto che il suo asse ON non torni nella dirittura RT della per&shy;<lb/>pendicolare. </s></p><p type="main">

<s>A questa conclusione per&ograve; sarebbero bastati i principii, premessi per il <lb/>segmento sferico, cosicch&egrave; inutile, e tutto affatto fuor del proposito, appari&shy;<lb/>sce quel che il Commandino, dall'essere la linea RO minore di quella che <lb/>&egrave; all'asse, argomenta: che cio&egrave; l'angolo RT<foreign lang="greek">*w</foreign> &egrave; acuto, e che perci&ograve; il punto T <lb/>della perpendicolare alla superficie del livello cade tra P e <foreign lang="greek">*w. </foreign></s>

<s>Di qui &egrave; ma&shy;<lb/>nifesto che il benemerito commentatore di Urbino non comprese come quei <lb/>principii erano da Archimede premessi, e presupposte quelle condizioni, non <lb/>a dimostrar che l'effetto resultante dalle due forze contrariamente applicate <lb/>in H o in G, &egrave; quello di dirizzare il conoideo, ma che esso conoideo, venuto <pb xlink:href="020/01/3078.jpg" pagenum="39"/>a mettersi in dirittura, anche vi permarrebbe, perch&egrave; il centro H della pres&shy;<lb/>sione riman di sopra al centro R, intorno a cui s'intende gravitar tutta <lb/>la mole. </s></p><p type="main">

<s>Si pu&ograve; dietro questo giudicare qual fiducia debba aversi ai commenti, <lb/>fatti dal Commandino intorno alle seguenti parti del Trattato archimedeo, <lb/>le proposizioni del quale si vanno via via sempre pi&ugrave; complicando, da smar&shy;<lb/>rirsi ne'sottilissimi laberinti anche i matematici, a cui benevola Arianna, non <lb/>avesse dato in mano il suo filo. </s>

<s>Non poche difficolt&agrave; dipendono senza dubbio <lb/>da quella sciagurata traduzione latina, ma son queste un nulla, appetto a <lb/>quell'altre, che si sono incontrate dai commentatori, per avere smarrito il <lb/>filo, veramente arianneo, delle archimedee tradizioni: smarrimento che, av&shy;<lb/>venuto poco dopo i tempi dell'Autore, riapparve nel risorgere della Scienza <lb/>manifesto, lasciamo stare per ora Leonardo da Vinci, nei commentarii stessi <lb/>del Commandino. </s>

<s>La conclusione della proposizione ottava del primo libro, <lb/>nella quale si dice che la porzion del segmento sferico, rappresentato nella <lb/>figura 14a qui poco addietro, fuori dell'umido, sar&agrave; per la retta SL spinta <lb/><emph type="italics"/>deorsum,<emph.end type="italics"/> e l'altra porzion che &egrave; nell'umido, per la retta RL, <emph type="italics"/>sursum;<emph.end type="italics"/> &egrave; <lb/>da esso Commandino dichiarata con queste parole: &ldquo; Magnitudo enim, quae <lb/>in humido demersa est, tanta vi per lineam RL sursum fertur, quanta quae <lb/>extra humidum per lineam SL deorsum: id quod ex propositione sexta huius <lb/>libri constare potest. </s>

<s>Et quoniam feruntur per alias, atque alias lineas, neutra <lb/>alteri obsistit quominus moveatur, idque continenter fiet dum portio in rectum <lb/>fuerit constituta. </s>

<s>Tunc enim utrorumque magnitudinum gravitatis centra in <lb/>unam eamdemque perpendicularem conveniunt, videlicet in axem portionis. </s>

<s><lb/>Et quanto conatu impetuve ea quae in humido est sursum, tanto quae extra <lb/>humidum deorsum, per eamdem lineam, contendit. </s>

<s>Quare, cum altera alte&shy;<lb/>ram non superet, non amplius movebitur portio, sed consistet manebitque <lb/>in eodem semper situ, nisi forte aliqua causa extrinsecus accesserit &rdquo; (<emph type="italics"/>De <lb/>iis quae veh. </s>

<s>in aqua<emph.end type="italics"/> cit., fol. </s>

<s>7, 8). </s></p><p type="main">

<s>Ora, &egrave; notabile l'errore del Commandino, il quale fa le due forze RL, <lb/>SL eguali, e da esse sole perci&ograve; dipendere l'equilibrio. </s>

<s>Ma ben assai pi&ugrave; <lb/>notabile &egrave; quel richiamarsi alla proposizione VI, senz'avvedersi il valent'uomo <lb/>che questa, e pi&ugrave; manifestamente la quinta che la precede, scoprono anzi la <lb/>fallacia di quella sua posizione. </s>

<s>Imperocch&egrave;, se son le spinte uguali e con&shy;<lb/>trarie della porzione immersa e della emersa del galleggiante, che lo fanno <lb/>rimanere in quiete, e allora non sarebbe vera quella stessa quinta proposi&shy;<lb/>zione citata, la quale ammette l'uguaglianza in gravit&agrave;, o rispetto alle forze <lb/>de'pesi, non tra la mole dell'umido uguale alla porzione immersa, e la sola <lb/>porzione emersa, ma tra quella e la gravit&agrave; di tutta intera la mole. </s>

<s>Cosic&shy;<lb/>ch&egrave;, secondo il vero senso delle tradizioni archimedee, le due forze che si <lb/>equilibrano sono quella diretta in gi&ugrave;, secondo XL, e l'altra diretta in su, <lb/>secondo RL. </s></p><p type="main">

<s>L'origine dell'inganno consiste nel non avere il Commandino avvertito <lb/>che, essendo la XL decomposta nelle SL, RL, ambedue dirette al centro della <pb xlink:href="020/01/3079.jpg" pagenum="40"/>Terra, vengono a trovarsi lungo la medesima direzione RL, e applicate al <lb/>medesimo punto R due forze differenti e contrapposte: l'una dovuta alla <lb/>gravit&agrave; naturale della porzione BRG immersa, e l'altra dovuta alla spinta <lb/>che si farebbe dal peso riflesso in su di un egual mole di liquido, la quale <lb/>spinta il Commandino ammetteva che fosse una forza semplice, e non resul&shy;<lb/>tante dalla differenza di lei con un'altra forza opposta. </s></p><p type="main">

<s>I commentatori che successero, non solo non emendarono l'errore, ma <lb/>volsero le cose in peggio, non facendo nessun conto della pressione idrosta&shy;<lb/>tica <emph type="italics"/>sursum,<emph.end type="italics"/> da Archimede stesso richiesta come principio necessario nella <lb/>sua seconda supposizione. </s>

<s>Cosicch&egrave; le forze sollecitanti il galleggiante incli&shy;<lb/>nato si riducevano per costoro alle sole SL, RL, ambedue dirette al cen&shy;<lb/>tro L con impeti uguali. </s>

<s>La restituzione perci&ograve; del segmento sferico alla prima <lb/>sua rettitudine la facevano dipendere dalla medesima causa, che fa restituire <lb/>orizzontale una bilancia di braccia, e di momenti uguali, quando il centro <lb/>di gravit&agrave;, torna in qualche punto della linea verticale e inferiore alla so&shy;<lb/>spensura. </s>

<s>Cos&igrave;, mentre il Commandino, intendendo a mezzo Archimede, non <lb/>riconosceva lungo la direzione RL che una forza <emph type="italics"/>sursum,<emph.end type="italics"/> questi altri non <lb/>riconobbero che una sola forza <emph type="italics"/>deorsum,<emph.end type="italics"/> contro la manifesta intenzion dello <lb/>stesso Archimede, il quale, per aprirsi la via alle future e pi&ugrave; complicate <lb/>proposizioni de'galleggianti conoidei, incominciava fin d'ora a considerare, <lb/>invece della forza unica XL, applicata al centro di gravit&agrave; del tutto, le SL, <lb/>RL applicate al centro di gravit&agrave; delle parti. </s>

<s>Quando dunque l'asse TZ, <lb/>scendendo si sia abbattuto sulla NL, le forze che ve lo fanno rimanere, e <lb/>che si possono intendere applicate tutte nel punto X&prime;, son tre: due diretta&shy;<lb/>mente concorrenti e, sommate insieme, proporzionali alla gravit&agrave; di tutta la <lb/>grandezza, e una ad esse contraria, e proporzionale alla reazione del peso <lb/>di una mole di umido uguale a quella della parte sommersa. </s>

<s>E ci&ograve; fa esatto <lb/>riscontro con quel che, per altre vie molto diverse, era stato dallo stesso <lb/>Archimede dimostrato nella sua proposizione quinta, la quale si pu&ograve;, secondo <lb/>questo nuovo ordine di speculazioni, rendere pi&ugrave; evidente, immaginando che <lb/>le due dette forze concorrenti vengano assommate nella X&prime;R, e che la terza <lb/>sia rappresentata dalla X&prime;K, le quali due forze cos&igrave; ridotte, essendo uguali <lb/>e contrarie, manterranno il punto X&prime;, intorno a cui s'aduna il peso di tutta <lb/>la magnitudine, in stabilit&agrave; di equilibrio. </s>

<s>La cosa insomma, sotto questo <lb/>aspetto, torna a quel pi&ugrave; semplice caso, illustrato addietro dalla figura 12.a</s></p><p type="main">

<s>Intendasi perci&ograve; il galleggiante ABCD restituito, per l'azion delle forze <lb/>Y, U componenti una di quelle che il Poinsot chiamava <emph type="italics"/>coppie,<emph.end type="italics"/> nella retti&shy;<lb/>tudine del suo asse, e cos&igrave; stando s'immagini essere violentemente profondato <lb/>esso galleggiante sotto il livello FO del liquido pi&ugrave; grave in specie. </s>

<s>&Egrave; ma&shy;<lb/>nifesto che, rimanendo la Y sempre la medesima, la contraria forza U cre&shy;<lb/>sce via via, secondo che il corpo via via pi&ugrave; s'immerge, ond'&egrave; che lasciato <lb/>in libert&agrave; torna in su con tant'impeto, quant'&egrave; dovuto alla differenza che <lb/>passa fra'due impulsi contrarii, in piena conformit&agrave; con quel ch'era stato <lb/>detto nella proposizione sesta: <emph type="italics"/>&ldquo; Solidae magnitudines humido leviores, in<emph.end type="italics"/><pb xlink:href="020/01/3080.jpg" pagenum="41"/><emph type="italics"/>humidum impulsae, sursum feruntur tanta vi, quanto humidum, molem <lb/>habens magnitudini aequalem, gravius est ipsa magnitudine. </s>

<s>&rdquo;<emph.end type="italics"/> Come poi <lb/>si possano da questi medesimi principii concludere con facilit&agrave; tutti gli altri <lb/>teoremi, proposti nel primo libro <emph type="italics"/>De insidentibus,<emph.end type="italics"/> &egrave; cos&igrave; agevole a com&shy;<lb/>prendere, che ce ne passiamo senz'altri discorsi. </s></p><p type="main">

<s>N&egrave; son questi principii dell'antichissimo Maestro dell'Idrostatica punto <lb/>differenti da quelli professati sui principii del secolo XVIII, nel capitolo III <lb/>del secondo libro della <emph type="italics"/>Foronomia,<emph.end type="italics"/> dove l'Herman, dop'aver concluso in un <lb/>corollario della sua proposizione XIII universalissima che, per non essere le <lb/>due forze Y, U congruenti, il galleggiante &egrave; costretto a convertirsi in s&egrave; me&shy;<lb/>desimo, infin tanto che l'asse di lui non sia tornato perpendicolare alla su&shy;<lb/>perficie del liquido; soggiunge: &ldquo; Atque in hoc corollariolo fundantur ferme <lb/>omnes regulae, quas Autores circa aequilibria solidorum cum fluidis homo&shy;<lb/>geneis subinde tradunt &rdquo; (Amstelodami 1716, pag. </s>

<s>155), </s></p><p type="main">

<s>La conclusione dunque &egrave; quella medesima, a cui giungemmo dianzi dal&shy;<lb/>l'aver bene addentro esaminata la dottrina ascosta ne'teoremi archimedei: <lb/>eppure l'Herman crede esservi giunto per vie affatto nuove, e incognite ai <lb/>suoi predecessori, fra'quali nomina espressamente il Pascal, che dimostr&ograve; <lb/>le ragioni degli idrostatici equilibri col principio delle velocit&agrave; virtuali: prin&shy;<lb/>cipio, dice l'Herman, indiretto, e difficilmente applicabile ai fluidi eterogenei <lb/>(ivi, Schol. </s>

<s>II, pag. </s>

<s>157). </s></p><p type="main">

<s>La Storia conferma esser verissimo pur troppo quel che da una parte <lb/>asserisce il Matematico di Basilea, ma dall'altra gli contende la compiacenza <lb/>del credersi autore di que'principii diretti, de'quali, bench&egrave; non sapessero <lb/>far uso n&egrave; il Pascal, n&egrave; altri, si trova pure il documento nell'antichissimo <lb/>Siracusano. </s>

<s>I due libri di lui hanno indole alquanto diversa, riconoscibile, <lb/>chi sottilmente penetra il mistero, nelle due distinte supposizioni, separata&shy;<lb/>mente premesse innanzi all'un libro e all'altro. </s>

<s>Nel primo libro i galleggia&shy;<lb/>menti e le sommersioni de'corpi si riducono alle ragioni de'loro pesi, mi&shy;<lb/>surabili con la bilancia, ma nel secondo, invece de'pesi, si considerano le <lb/>forze, che le ponderose moli traggono al centro, per cui pu&ograve; dirsi che quella <lb/>prima parte dottrinale sta a questa seconda, come la Fisica sta alla Geome&shy;<lb/>tria. </s>

<s>Le geometriche sottigliezze per&ograve; si stavano cos&igrave; sotto la crassizie fisica <lb/>velate, che sino all'Herman, in tanti secoli, nessun Matematico valse a rico&shy;<lb/>noscerle. </s>

<s>Se tutti i corpi son ponderosi, e perci&ograve; tendono in basso, e se anche <lb/>ogni umido &egrave; un corpo, com'&egrave; possibile, dicevano, che contro alla comun <lb/>legge naturale debba spingere in alto? </s>

<s>La riflessione delle pressioni idro&shy;<lb/>statiche verticali rimase, anche dopo il Torricelli, per qualche tempo, dalla <lb/>maggior parte de'Fisici, incompresa, come incomprese rimasero pure per <lb/>molti le pressioni laterali: ond'&egrave; che, lusingati da quel che pareva porgere <lb/>la prima supposizion di Archimede, si cred&egrave; che il liquido non premesse altro <lb/>che il fondo del vaso. </s></p><p type="main">

<s>A questa estrema conseguenza, preparata gi&agrave; dal prevaler delle prece&shy;<lb/>denti opinioni, giunse Famiano Michelini, secondato e difeso da quel Viviani <pb xlink:href="020/01/3081.jpg" pagenum="42"/>che, nell'atto di correggersene, faceva complice dell'errore Archimede, accu&shy;<lb/>sandolo di aver trattato l'Idrostatica con principii poco universali, perch&egrave; il <lb/>progresso delle sue dimostrazioni, diceva, non vale, se non in caso che le <lb/>parti infime del fluido si trovino ugualmente poste in continuazione fra loro, <lb/>e premute dalla mole che le sovrasta perpendicolarmente. </s>

<s>Il quale esempio <lb/>ci basti per ora a provar che in sul declinare del secolo XVII, si teneva dai <lb/>pi&ugrave; insigni cultori della Scienza che unico modo di dimostrar le leggi idro&shy;<lb/>statiche fosse quello tenuto dall'antico Maestro, nel suo primo fisico libro. </s>

<s><lb/>E come il Viviani stesso, dando mano a scrivere il suo trattatello <emph type="italics"/>Degli ab&shy;<lb/>bassamenti e de'sollevamenti dei corpi ne'fluidi,<emph.end type="italics"/> non sospett&ograve; che l'opera <lb/>sua era simile a quella di chi fa riapparire una scrittura su un palinsesto; <lb/>cos&igrave; parve non ne sospettare nemmeno l'Herman. </s>

<s>Ond'&egrave; alla nostra Storia <lb/>affidato tale ufficio che, sebbene non sia affatto nuovo, ha qualche cosa di <lb/>straordinario: a noi incombe narrare i delirii lunghi e affannosi di venti <lb/>secoli, prima che l'Idrostatica si riduca nella rettitudine de'sentieri ar&shy;<lb/>chimedei. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Si direbbe che Archimede, da quella parte, nella quale insegnava essere <lb/>il galleggiante sostenuto da forze, suscitatesi nell'umido contrariamente a <lb/>quelle della gravit&agrave; naturale; fosse rimasto incompreso da quegli stessi, che <lb/>convissero con lui, o che gli successero poco di poi. </s>

<s>Scarsi e languidi, per <lb/>la lunga oblivione, ci sono i documenti, ma qualcuno che n'&egrave; rimasto, e che <lb/>non &egrave; sfuggito alla nostra scarsa erudizione, par che dia ragionevole fonda&shy;<lb/>mento al nostro giudizio. </s></p><p type="main">

<s>Herone Alessandrino, nel proemio al suo libro <emph type="italics"/>Degli spiritali,<emph.end type="italics"/> propone <lb/>un problema, che fra gl'idrostatici &egrave; uno de'pi&ugrave; famosi, e che serve quasi <lb/>di metro a misurare i progressi di questa scienza: onde avvenga che coloro, <lb/>i quali notano nel profondo del mare, avendo un peso d'acqua inestimabile <lb/>sopra le spalle, non ne vengano oppressi. </s>

<s>E l'Autore, per la soluzione della <lb/>proposta, invoca Archimede, non gi&agrave; l&agrave;, dove dimostra che le pressioni deor&shy;<lb/>sum sono equilibrate da quelle sursum, perch&egrave; eguali e contrarie, ma l&agrave; <lb/>dove, dai teoremi del primo libro, si raccoglie che l'acqua non pesa in s&egrave; <lb/>stessa, e n&egrave; perci&ograve; sopra il corpo del marangone, secondo qualunque pro&shy;<lb/>fondit&agrave; a lei soggetto. </s>

<s>N&egrave; a principii punto diversi da questi &egrave; informata, nel <lb/>capitolo I dei detti <emph type="italics"/>Spiritali,<emph.end type="italics"/> la teoria del sifone ritorto, la quale, invece che <lb/>sopra le pressioni idrostatiche, e sopra le ragioni del loro equilibrio, si fonda <lb/>inopportunamente sul principio che deve l'acqua disporsi necessariamente in <lb/>una superficie sferica, &ldquo; il centro della quale sia l'istesso con il centro della <lb/>Terra, perciocch&egrave;, se la superficie di qualche acqua &egrave; sferica, ed ha l'istesso <lb/>centro della Terra, essa si posa, ma se &egrave; possibile non posi .... &rdquo; (<emph type="italics"/>Tradu-<emph.end type="italics"/><pb xlink:href="020/01/3082.jpg" pagenum="43"/><emph type="italics"/>zione di A. Giorgi,<emph.end type="italics"/> Urbino 1592, fol. </s>

<s>14), e seguita ripetendo il senso di <lb/>Archimede, nella proposizione seconda del primo libro. </s></p><p type="main">

<s>Trapassando ad altra nazione, ad altre discipline, e ad altri tempi, da'li&shy;<lb/>bri di Seneca s'attinge un'altra prova del ridursi tutta la scienza degli idro&shy;<lb/>statici equilibrii a un fatto, non dissimile da quello, che si osserva, pesando <lb/>i corpi solidi sulla bilancia. <emph type="italics"/>Quamcumque vis rem expende, et contra aquam <lb/>statute, dummodo utriusque par sit modus.<emph.end type="italics"/> Or che altro significano cos&igrave; <lb/>fatte parole, se non quella parit&agrave; di modi, che s'otteneva da Archimede nelle <lb/>proposizioni del suo primo libro, col divider l'umido in due settori uguali, <lb/>quasi bilancia, che nel punto di mezzo sostiene il giogo, sopra cui s'intenda <lb/>da una parte posato il galleggiante, e dall'altra un'egual mole di liquido, <lb/>che lo contrappesa? </s></p><p type="main">

<s>Seneca invocava, come avvertimmo, queste dottrine, per confermare i <lb/>placiti della Filosofia platonica, nella quale s'insegnava non essere i corpi o <lb/>gravi o leggeri, secondo la nostra stima, ma per comparazione del mezzo, <lb/>da cui son portati. </s>

<s>La Filosofia per&ograve; non era la Scienza pi&ugrave; gradita a quei <lb/>tempi, ne'quali, piuttosto che alla speculazione s'andava dietro a ci&ograve;, che <lb/>potesse in qualche modo servire alle utilit&agrave;, e ai comodi della vita. </s>

<s>E spen&shy;<lb/>tasi quella face, che precorreva nelle mani di Archimede, a dimostrare i <lb/>sottili e ascosti sentieri, per i quali si sarebbe dovuta metter l'arte dell'ar&shy;<lb/>chitettura navale; non si vedeva quale altro vantaggio riceverebbero le co&shy;<lb/>munanze civili dalla Scienza delle acque, se non imparando a regolarne <lb/>equamente la dispensa, ne'domestici usi, e per la irrigazione delle campa&shy;<lb/>gne. </s>

<s>Ma n&egrave; Archimede stesso, n&egrave; nessun altro avevano ancora insegnato nulla <lb/>intorno a ci&ograve;, per cui unica regola, intorno a un fatto di cos&igrave; grande impor&shy;<lb/>tanza alla vita sociale, si rimaneva la volgare esperienza. </s></p><p type="main">

<s>I primi suggerimenti, che di qui vennero all'arte, furono quelli di re&shy;<lb/>golar le dispense secondo la maggiore o minore ampiezza delle bocche, ma <lb/>non pot&egrave; nello stesso tempo sfuggire alla considerazione de'legislatori quel <lb/>che dall'altra parte era notissimo ai villici, e a'canovai, che cio&egrave; da una me&shy;<lb/>desima cannella s'attinge in ugual tempo maggior misura di vino dalla botte <lb/>piena, che dalla scema, passando con maggior impeto il liquido in quella, che <lb/>in questa. </s>

<s>Si trova perci&ograve; che furono, infin dagli antichissimi moderatori, <lb/>avvertite alcune fra le cause principali del crescere e del diminuire la rapi&shy;<lb/>dit&agrave; del corso dell'acque, d'onde, venendosi a dare ai privati meno o pi&ugrave; del <lb/>convenuto, o farebbe ingiustizia il Principe, o ne riceverebbe danno lo Stato. </s></p><p type="main">

<s>I Romani, fra le antiche nazioni, furono, in costruire acquedotti, spe&shy;<lb/>cialmente per la loro citt&agrave;, i pi&ugrave; suntuosi, e ne eleggevano a prefetto uno <lb/>de'cittadini pi&ugrave; principali. </s>

<s>Sotto gl'imperi di Nerva e di Traiano cotesta <lb/>prefettura delle acque venne in Sesto Giulio Frontino che, zelantissimo del <lb/>commessogli ufficio, e letterato, scrisse quel Commentario <emph type="italics"/>De aquaeducti&shy;<lb/>ctibus Urbis Romae,<emph.end type="italics"/> da cui ci viene il primo documento di ci&ograve;, che sapesse <lb/>la Scienza, e praticasse l'arte, intorno al regolar le misure delle acque <lb/>correnti. </s></p><pb xlink:href="020/01/3083.jpg" pagenum="44"/><p type="main">

<s>Incomincia Frontino dal descrivere gli Acquidotti, col nome proprio a <lb/>ciascuno, e poi dice d'onde movessero, quanto corressero per giungere alla <lb/>Citt&agrave;, quanto rimanessero incavati entrando sottoterra, e quanti archi gli so&shy;<lb/>stenessero, uscendo fuori all'aperto. </s>

<s>Seguita poi a narrare quant'acqua porti <lb/>ciascun condotto, o dentro o fuori della Citt&agrave;, quante siano le piscine o i <lb/>conservatoi, quanto se ne dispensasse di l&igrave; ai laghi, quanto a nome di Ce&shy;<lb/>sare, quanto ad uso de'privati, per benefizio del Principe. </s>

<s>Venivano le di&shy;<lb/>stribuzioni regolate col crescere o col diminuire le bocche delle fistole, la pi&ugrave; <lb/>comune tra le quali era detta <emph type="italics"/>quinaria,<emph.end type="italics"/> per essere un circolo inciso in una <lb/>lamina di piombo, e d'un diametro di cinque quarte di digito del piede <lb/>romano. </s></p><p type="main">

<s>&Egrave; un fatto dunque che la regola si riduceva principalmente a moderare <lb/>le luci, ma che inoltre la maggiore o minore velocit&agrave; del corso conferisse ad <lb/>alterare le misure dell'acqua era cosa che Frontino, come insisteva, perch&egrave; <lb/>non la dimenticassero i suoi ufficiali; cos&igrave; voleva rammemorarla ai suoi let&shy;<lb/>tori: &ldquo; Meminerimus omnem aquam, quotiens ex altiore loco venit, et intra <lb/>breve spatium in castellum cadit, non tantum respondere modulo suo, sed <lb/>etiam ex superare: quotiens vero ex humiliore, idest minore pressura, lon&shy;<lb/>gius ducatur, segnitia ductus modum quoque deperdere: ideo, secundum hanc <lb/>rationem, aut onerandam esse erogationem, aut relevandam &rdquo; (<emph type="italics"/>S. I. </s>

<s>Fron&shy;<lb/>tini Comment. </s>

<s>restitutus atque explicatus op. </s>

<s>ct studio I.<emph.end type="italics"/> Poleni, Pata&shy;<lb/>vii 1722, pag. </s>

<s>100-2). </s></p><p type="main">

<s>Il Poleni, in questa riconosciuta necessit&agrave; di onerare o di relevare l'ero&shy;<lb/>gazione, ossia, com'egli interpetra, di ampliare o di restringere il modulo o <lb/>la sezion della bocca, secondo che maggiore o minore &egrave; la natural velocit&agrave; <lb/>dell'acqua che passa; argomenta non essere ignoto a Frontino il principio <lb/>delle velocit&agrave; medie, bench&egrave; non sapesse farne l'applicazione. </s>

<s>Ma comunque <lb/>sia per ora di ci&ograve;, le parole, che immediatamente seguono alle citate, con&shy;<lb/>tengono un altro avvedimento che, sebbene ora sembri a noi ovvio, doveva <lb/>nonostante allora valere per una sottigliezza, ed &egrave; che i <emph type="italics"/>calici,<emph.end type="italics"/> ossia quei <lb/>tubi, che si mettevano nel grosso della muratura de'conservatoi, e che si <lb/>facevano di bronzo, perch&egrave; gli attriti e le fraudi non ne dovessero alterar la <lb/>misura; facevano differenza nella portata, secondo la loro collocazione ri&shy;<lb/>spetto alla linea orizontale, o alla direzione dell'acqua. </s>

<s>&ldquo; Sed et calicis po&shy;<lb/>sitio habet momentum: in rectum, et ad libram collocatus, modum servat: <lb/>ad cursum aquae oppositus et devexus amplius rapit: ad latus praetereuntis <lb/>aquae conversus et supinus, nec ad haustum pronus, segniter exiguum su&shy;<lb/>mit &rdquo; (ibid., pag. </s>

<s>102, 3). </s></p><p type="main">

<s>Per un'altra variet&agrave; di collocamento, soggiunge altrove Frontino, fanno <lb/>i calici differenza nella portata, cio&egrave;, per non essere tutti disposti nella me&shy;<lb/>desima linea orizontale, ma alcuni pi&ugrave; bassi, altri pi&ugrave; alti; intorno a che <lb/>mette questa avvertenza: &ldquo; Circa collocandos quoque calices observari opor&shy;<lb/>tet, ut ad lineam ordinentur; nec alterius inferior calix, alterius superior po&shy;<lb/>natur. </s>

<s>Inferior plus trahit; superior, quia cursus aquae ab inferiore rapitur, <pb xlink:href="020/01/3084.jpg" pagenum="45"/>minus ducit &rdquo; (ibid., pag. </s>

<s>197-99). La ragione del trar pi&ugrave; l'inferiore che <lb/>il superiore, perch&egrave; in quello vien l'acqua pi&ugrave; rapidamente che in questo; <lb/>&egrave; la stessa, che dicemmo esser nota anche alla gente volgare, la quale sa <lb/>altres&igrave; molto bene, come Frontino, che del gettar pi&ugrave; lo zipolo di sotto, che <lb/>quello di sopra, &egrave; immediata causa la maggiore o minore altezza del vino, <lb/>che fa, in dargli esito, maggiore o minore la pressura. </s>

<s>Dalla collazione del <lb/>qual passo, con quello primo citato, par se ne ricavi un'interpetrazione di&shy;<lb/>versa, da quella datagli dal Poleni, cosicch&egrave; <emph type="italics"/>onerare<emph.end type="italics"/> o <emph type="italics"/>relevare<emph.end type="italics"/> l'erogazione <lb/>non significhi direttamente allargare o restringere il modane, ma aumentare <lb/>o diminuire l'altezza, e con essa la pressione e l'impulso velocitativo, infino <lb/>a ridur la cosa al suo temperamento. </s></p><p type="main">

<s>Bench&egrave; cos&igrave; chiari, e derivati dalle loro legittime fonti, ne siano i do&shy;<lb/>cumenti, s'accusava nulladimeno, da un autorevolissimo giudice, Frontino di <lb/>non aver bene considerato quanto conferiscano le velocit&agrave; in mutar le mi&shy;<lb/>sure della medesima acqua corrente. </s>

<s>Fondamento all'accusa era quel che <lb/>si legge all'articolo LXIV del citato Commentario degli acquedotti di Roma, <lb/>che qui trascriviamo: &ldquo; Persecutus ea quae de modulis dici fuit necessarium, <lb/>nunc ponam quem modum quaeque Aqua, ut Principum commentariis com&shy;<lb/>prehensum est, usque ad nostram curam habere visa sit, quantumque ero&shy;<lb/>gaverit; deinde quem ipsi scrupulosa inquisitione, praeeunte providentia optimi <lb/>diligentissimique principis Nervae, invenerimus. </s>

<s>Fuere ergo in commenta&shy;<lb/>riis in universo quinariarum XII millia DCCLVI: in erogatione XIV millia <lb/>XVIII; plus in distributione, quam in accepto, computabantur quinariae <lb/>MCCLXIII. </s>

<s>Huius rei admiratio, cum praecipuum officii opus in exploranda <lb/>fide Aquarum atque copia crederem, non mediocriter me convertit ad scru&shy;<lb/>tandum, quemadmodum amplius erogaretur, quam in patrimoni, ut ita di&shy;<lb/>cam, esset. </s>

<s>Ante omnia itaque capita ductuum metiri aggressus sum, sed <lb/>longe, idest circiter quinariis X millibus, ampliorem, quam in commentariis <lb/>modum inveni: ut per singulas demonstrabo &rdquo; (ibid., pag. </s>

<s>112-15). </s></p><p type="main">

<s>Il conto si riduce a questo, come, per ciascun acqua, si raccoglie dai <lb/>successivi articoli del Commentario: Dall'Appia, quinarie 1825; dal Teve&shy;<lb/>rone, 4398; dalla Marcia, 4690; dalla Tepula, 445: dalla Giulia, 1206; dalla <lb/>Vergine, 2504; dalla Claudia, 4607; dal Tevere, 4738: in tutto quinarie 24413. <lb/>Onde essendo nell'erogazione quinarie 14018, la trovata differenza era di <lb/>10395 quinarie, <emph type="italics"/>idest,<emph.end type="italics"/> preso il numero tondo, <emph type="italics"/>circiter quinariis X millibus,<emph.end type="italics"/><lb/>come dice Frontino, a cui venne perci&ograve; il sospetto che quel di pi&ugrave; se l'aves&shy;<lb/>sero usurpato <expan abbr="&itilde;">im</expan> ministri o i partecipanti. </s></p><p type="main">

<s>&ldquo; La qual cosa, soggiunge in tal proposito il Castelli, poteva essere in <lb/>parte, perch&egrave; pur troppo &egrave; vero che il pubblico quasi sempre &egrave; ingannato. </s>

<s><lb/>Con tutto ci&ograve; io penso ancora assolutamente che, oltre le fraudi di quelli <lb/>officiali, le velocit&agrave; dell'acqua nei luoghi, ne'quali Frontino le misur&ograve;, po&shy;<lb/>tessero essere diverse da quelle velocit&agrave;, che si ritrovavano nelli altri luoghi <lb/>misurati da altri per avanti, e perci&ograve; le misure dell'acque potevano, anzi do&shy;<lb/>vevano necessariamente essere diverse, essendosi da noi stato dimostrato che <pb xlink:href="020/01/3085.jpg" pagenum="46"/>le misure della medesima acqua fluente hanno reciproca proporzione delle <lb/>loro velocit&agrave;. </s>

<s>Il che non considerando bene Frontino, e ritrovando l'acqua <lb/><emph type="italics"/>in commentariis<emph.end type="italics"/> 12755 quinarie, <emph type="italics"/>in erogatione<emph.end type="italics"/> 14018, e nella propria mi&shy;<lb/>sura, fatta da s&egrave; medesimo <emph type="italics"/>ad capita ductuum,<emph.end type="italics"/> 22755 (<emph type="italics"/>cos&igrave; &egrave; scritto, ma <lb/>veramente &egrave; 24413, come torna alla somma de'numeri dati dallo stesso <lb/>Frontino<emph.end type="italics"/>) quinarie in circa; pens&ograve; che in tutti questi luoghi passasse diversa <lb/>quantit&agrave; d'acqua, cio&egrave; maggiore <emph type="italics"/>ad capita ductuum<emph.end type="italics"/> di quella, che era <emph type="italics"/>in <lb/>erogatione,<emph.end type="italics"/> e questa giudic&ograve; maggiore di quella, che era <emph type="italics"/>in commentariis &rdquo;<emph.end type="italics"/><lb/>(<emph type="italics"/>Della Misura delle acque correnti,<emph.end type="italics"/> Bologna 1660, pag. </s>

<s>29, 30). </s></p><p type="main">

<s>Ora, alcuni zelantissimi partigiani dell'antico Scrittore si risentirono <lb/>acerbamente contro il Castelli, e allegando i passi da noi sopra alligati ne <lb/>concludevano che l'accusa era ingiusta, e che il Console romano aveva dato <lb/>la vera regola di misurare le acque, tanti secoli prima, e pi&ugrave; esattamente <lb/>del Discepolo di Galileo. </s>

<s>A suo tempo la Storia dar&agrave; intorno alla passionata <lb/>questione definitiva sentenza, e per ora si conceda liberamente agli amici, e <lb/>agli ammiratori di Frontino, come cosa di fatto, aver egli avuto qualche no&shy;<lb/>tizia del Teorema, che dice stare le quantit&agrave; dell'acque erogate in ragion <lb/>composta delle velocit&agrave; e delle sezioni. </s>

<s>Anzi soggiungeremo per conferma di <lb/>ci&ograve; che, sebbene Frontino stesso ne faccia qualche cenno, si trova nelle leggi <lb/>degli antichi pretori di Roma espresso di quel generale teorema idrodina&shy;<lb/>mico sopra formulato una importantissima conseguenza, qual'&egrave; che, avendosi <lb/>quantit&agrave; d'acque uguali, stanno le loro velocit&agrave; reciprocamente come le se&shy;<lb/>zioni. </s>

<s>La notizia era stata data in una scrittura idraulica dal padre Guido <lb/>Grandi, le parole del quale trascriviamo qui tanto pi&ugrave; volentieri, in quanto <lb/>che sono tutt'insieme illustrative della Scienza, e interpetrative dell'antica <lb/>legge pretoria. </s></p><p type="main">

<s>&ldquo; L'acqua corrente, egli scrive, con somma facilit&agrave; si adatta a pi&ugrave; e <lb/>diverse aperture, compensando colla velocit&agrave; ci&ograve; che manca alla grandezza <lb/>della sezione, per cui &egrave; obbligata a passare. </s>

<s>Cos&igrave; il medesimo fiume passa da <lb/>un luogo pi&ugrave; largo ad uno pi&ugrave; stretto, e viceversa dal pi&ugrave; angusto al pi&ugrave; am&shy;<lb/>pio, e passa sotto gli archi de'ponti tutta quella piena, che pare non possa <lb/>capire nell'alveo inferiore pi&ugrave; dilatato, e che talvolta lo trabocca. </s>

<s>E per&ograve; <lb/>una minor sezione, o per larghezza o per altezza, o per entrambe, non &egrave; sem&shy;<lb/>pre segno di minor quantit&agrave; d'acqua, che passi per essa, ma per lo pi&ugrave;, <lb/>secondo le circostanze del caso, di cui si parla, indica solamente maggiore <lb/>velocit&agrave; della medesima quantit&agrave; di acqua. </s>

<s>E cos&igrave;, nella Legge: <emph type="italics"/>Ait prae&shy;<lb/>tor ff. </s>

<s>ne quid in flum. </s>

<s>publ.,<emph.end type="italics"/> dicesi che, senza mutare la quantit&agrave; dell'acqua <lb/>corrente, si fa innovazione nel fiume, con farla correre per sezione o pi&ugrave; <lb/>bassa o pi&ugrave; stretta, rendendola con questo pi&ugrave; rapida e pi&ugrave; veloce. <emph type="italics"/>Si mu&shy;<lb/>tetur aquae cursus, dum vel depressior vel arctior fiat aqua, ac per hoc <lb/>rapidior sit ...:<emph.end type="italics"/> non dovendosi attendere chi legge in questo luogo <emph type="italics"/>altior<emph.end type="italics"/><lb/>ovvero <emph type="italics"/>auctior,<emph.end type="italics"/> ma bens&igrave; <emph type="italics"/>arctior,<emph.end type="italics"/> come sta nelle Pandette fiorentine, il che <lb/>meglio corrisponde al sentimento di quella legge &rdquo; (<emph type="italics"/>Raccolta di Autori che <lb/>trattano del moto delle acque,<emph.end type="italics"/> ediz. 2a, Firenze 1774, T. IX, pag. 274). </s></p><pb xlink:href="020/01/3086.jpg" pagenum="47"/><p type="main">

<s>I regolamenti, che poteva suggerire la Scienza nella pubblica dispensa <lb/>dell'acque, si mantennero quali ce li porgono Frontino ne'suoi commenta&shy;<lb/>rii, e nelle loro leggi i Pretori romani, senza nessun progresso, in tutto il <lb/>tempo della decadenza. </s>

<s>E anche, ne'primi albori del Rinascimento, non si <lb/>sapeva aggiungere nulla di pi&ugrave; alle avvertenze date in proposito dagli anti&shy;<lb/>chi. </s>

<s>&ldquo; La cannella, dice Leon Batista Alberti nel X libro della sua <emph type="italics"/>Architet&shy;<lb/>tura,<emph.end type="italics"/> che sar&agrave; messa a piano e diritta, manterr&agrave; il modine, ed hanno tro&shy;<lb/>vato che detta cannella, per lo attingere, dir&ograve; cos&igrave;, si consuma &rdquo; (<emph type="italics"/>Tradu&shy;<lb/>zione di C. Bartoli,<emph.end type="italics"/> Milano 1833, pag. </s>

<s>364). E aveva poco prima lo stesso <lb/>Autore notato che &ldquo; i buchi delli sboccatoi si variano per versare le acque, <lb/>secondo il concorso deli'acqua che viene, e secondo i doccioni. </s>

<s>Perciocch&egrave; <lb/>quanto pi&ugrave; l'acqua sar&agrave; presa da un largo e veloce fiume, e quanto ella <lb/>sar&agrave; condotta per canali e vie pi&ugrave; spedite, e quanto ella sar&agrave; per esse stretta <lb/>insieme, tanto pi&ugrave; bisogner&agrave; allargare il modine da versare &rdquo; (ivi). In que&shy;<lb/>ste parole si comprendono dall'Alberti le due massime leggi, da s&igrave; lungo <lb/>tempo gi&agrave; note, che cio&egrave; le quantit&agrave; dell'acqua stanno in ragion composta <lb/>delle velocit&agrave; e delle sezioni, ond'&egrave; perci&ograve; che, avendosi quantit&agrave; uguali, esse <lb/>stesse velocit&agrave; e sezioni si corrispondono in ragion contraria. </s>

<s>Ma non era <lb/>per&ograve; questa altro che una semplice notizia sperimentale, e come non si sa&shy;<lb/>peva da quegli Autori mettere nella sua precisa forma il Teorema, cos&igrave; man&shy;<lb/>cava a loro il modo di dimostrarlo scientificamente dai suoi principii. </s></p><p type="main">

<s>Il primo tentativo di una dimostrazione geometrica sembra a noi che, <lb/>fra gli Autori pi&ugrave; noti, s'incontri ne'libri di Girolamo Cardano. </s>

<s>Mentre la <lb/>Idrostatica si teneva nel trattato di Archimede come perfetta, per cui non si <lb/>ridussero in tanti secoli le promozioni di lei, che a mettere le verit&agrave; pro&shy;<lb/>poste dal Siracusano sotto altra forma; l'Idrodinamica, verso la met&agrave; del <lb/>secolo XVI, fa la sua prima pubblica comparsa. </s>

<s>Diciamo cos&igrave;, perch&egrave; il Car&shy;<lb/>dano stesso mostra di non esser venuto a dire cose del tutto nuove; anzi <lb/>alcune delle sue proposizioni non hanno altro scopo, che di contradire a ci&ograve;, <lb/>che intorno al moto delle acque avevano insegnato i suoi predecessori. </s></p><p type="main">

<s>Or chi erano costoro, che avevano preceduto l'Autore <emph type="italics"/>De rerum varie&shy;<lb/>tate?<emph.end type="italics"/> E, nella mancanza di pubblici documenti, chi altri si penserebbe che <lb/>potessero essere, se non i discepoli di Giordano Nemorario, i quali, appli&shy;<lb/>cando ai liquidi la promossa scienza del moto, istituirono l'Idrodinamica? </s>

<s><lb/>Cos&igrave; fatte promozioni ebbero efficacissimo impulso dalla benefica resurrezione <lb/>dei libri meccanici di Archimede, ci&ograve; che, mentre vale a determinar l'epoca <lb/>in cui esso Giordano scrisse, e incominci&ograve; a fiorir la sua scuola; mostra <lb/>quanto poco probabile sia l'opinione di chi fa un tale autore molto pi&ugrave; an&shy;<lb/>tico, e dice essere il trattato di lui <emph type="italics"/>De ponderibus<emph.end type="italics"/> tradotto dal greco. </s>

<s>La sto&shy;<lb/>ria della Meccanica ci ha narrato che in cotesto libro s'insegnava a misu&shy;<lb/>rare le forze e i loro momenti dal prodotto della massa e della rettitudine <lb/>del discenso, ossia dalla massa e dalla velocit&agrave;, la quale per un medesimo <lb/>tempo &egrave; proporzionale allo spazio: n&egrave; con diversa formola, secondo quegli <lb/>insegnamenti, si misurava ci&ograve; che i Matematici odierni chiamano <emph type="italics"/>quantit&agrave;<emph.end type="italics"/><pb xlink:href="020/01/3087.jpg" pagenum="48"/><emph type="italics"/>di moto.<emph.end type="italics"/> Ora, essendo anche i liquidi corpi, soggetti come gli altri agli im&shy;<lb/>pulsi della gravit&agrave; naturale, s'intende facilmente che le loro quantit&agrave; nel&shy;<lb/>l'uscire dai vasi, o nel passar per i fiumi, corrispondevano ad altrettante <lb/>quantit&agrave; di moto, le quali perci&ograve; volevano essere misurate dalla massa (pro&shy;<lb/>porzionale alla grandezza del foro o della sezione dell'alveo) e dalla velocit&agrave;, <lb/>con cui il liquido stesso era mosso. </s>

<s>Che se il corso, invece di essere libero, <lb/>si facesse dentro il chiuso di tubi inclinati, la nuova Scienza meccanica <lb/>aveva insegnato a desumerne il grado della velocit&agrave;, non secondo la mag&shy;<lb/>giore o minor lunghezza di essi tubi, ma secondo la quantit&agrave; della discesa <lb/>verticale, cosicch&egrave; con pari impeto esca l'acqua da bocche disposte lungo <lb/>una medesima linea orizontale, qualunque sia l'obliquit&agrave; del loro scen&shy;<lb/>dere dal medesimo punto della conserva. </s>

<s>Quanto fosse questo principio fe&shy;<lb/>condo d'importantissime conseguenze, trattandosi di fiumi, che andando o <lb/>diretti o tortuosi allo sbocco, &egrave; come se corressero in un alveo pi&ugrave; o meno <lb/>obliquo; si pu&ograve; preveder facilmente anche prima, che venga la storia a dimo&shy;<lb/>strarcelo col fatto. </s></p><p type="main">

<s>Cos&igrave; ebbe le sue prime istituzioni, e fece i suoi progressi quella Scienza <lb/>idrodinamica, che il Cardano in parte volle confutare, e in parte promovere <lb/>nei suoi libri, bench&egrave; non apparisca il filo, a cui si riappiccano le sue tra&shy;<lb/>dizioni. </s>

<s>Confutando infatti, o accettando le dottrine correnti, non nomina mai, <lb/>da Frontino in fuori, nessun Autore particolare. </s>

<s>N&egrave; poteva nominarli, perch&egrave; <lb/>i Maestri si confondevano nella Scuola, gl'insegnamenti della quale erano <lb/>orali e non scritti, o, se scritti, in carte senza l'impronta pubblica della <lb/>stampa, bench&egrave; non fossero perci&ograve; tra gli studiosi di allora meno diffusi. </s>

<s>Di <lb/>qui s'intende quanto benefica, a rischiarare il buio di que'secoli, tornasse <lb/>l'apparizione dei manoscritti di Leonardo da Vinci, in cui si specchia, non <lb/>la particolare sapienza dell'uomo, ma e del tempo in cui visse, e di quello <lb/>che pi&ugrave; prossimamente l'aveva preceduto. </s></p><p type="main">

<s>Quell'apparizione, dopo tre secoli, parve che suscitasse nell'animo degli <lb/>studiosi un senso molto simile a quello che, a incontrarsi nel cappello d'oro <lb/>di un fungo, in mezzo alla borraccina e alle foglie secche del bosco, prova <lb/>la villanella, la quale stupisce lieta dell'improvvisa apparizion solitaria, per&shy;<lb/>ch&egrave; nulla aveva mai visto, e nulla saputo della sottilissima rete del micelio. </s>

<s>Gli <lb/>stupefatti lettori proclamarono allora Leonardo creatore dal nulla della Scienza <lb/>enciclopedica, e lo adorarono come un Dio pi&ugrave; vero e onnipotente di quello <lb/>descrittoci da Mos&egrave;, che dianzi avevano deriso. </s>

<s>I pi&ugrave; temperati si contenta&shy;<lb/>rono di dire che non prima d'oggidi s'&egrave; rivolto lo studio ai manoscritti di&shy;<lb/>vini, perch&egrave; a tanta altezza non era possibile risalisse l'ingegno degli stu&shy;<lb/>diosi, se non da poi che gli avessero impennate le ali Galileo e il Newton, <lb/>non inventori in realt&agrave;, ma banditori o espositori di una sapienza pi&ugrave; antica. </s>

<s><lb/>Strane opinioni, che non s'intenderebbe come potessero essere invalse in <lb/>tempi, in cui la teoria delle evoluzioni lente e progressive, dalla storia na&shy;<lb/>turale, s'&egrave; tanto audacemente estesa alla psicologia; se non si ripensasse che <lb/>i sistemi filosofici pi&ugrave; declamati sempre anche sono i meno compresi. </s></p><pb xlink:href="020/01/3088.jpg" pagenum="49"/><p type="main">

<s>Sembrerebbe dunque che fosse ora il tempo di dimostrare, come nem&shy;<lb/>meno l'ingegno di Leonardo da Vinci si sottrasse all'impero di una legge, <lb/>che &egrave; generalissima, e naturale a tutte le cose. </s>

<s>E perch&egrave;, concedendo che <lb/>sia cos&igrave;, &egrave; necessario ammettere un subietto, che venendo a perfezionarsi, in <lb/>virt&ugrave; dell'evoluzione, doveva essere prima difettivo in s&egrave; stesso; a ogni passo, <lb/>fra le ammirate scritture di Leonardo, ne ricorrono alcune, che accennano <lb/>all'imperfezione, e ai difetti proprii alle scienze, specialmente fisiche, le quali <lb/>abbiano incominciato pur ora a movere dai loro principii. </s></p><p type="main">

<s>In questi giorni Teodoro Sabachnikoff ha pubblicato, dai manoscritti <lb/>della R. biblioteca di Windsor, i primi fogli <emph type="italics"/>Dell'anatomia,<emph.end type="italics"/> e Mathias Duval <lb/>vi premette un discorso, in cui magnifica le scoperte fatte da Leonardo in&shy;<lb/>torno alla descrizione delle membra umane, e alla fisiologia delle loro fun&shy;<lb/>zioni, senz'avvedersi ch'eran piuttosto le scoperte degli anatomici e de'fisio&shy;<lb/>logi di quel tempo, de'quali, insieme con alcune verit&agrave;, Leonardo stesso <lb/>ripete i moltissimi errori. </s></p><p type="main">

<s>Tutte quelle note, che ricorrono ne'primi fogli del MSS. H, del Ra&shy;<lb/>vaisson, in soggetto di storia naturale, non sono altro che apologhi, o fatti <lb/>ingegnosamente trasportati al morale: e se possono essere un esempio, imi&shy;<lb/>tabile anche dagli scrittori d'oggidi, di stile descrittivo, non oltrepassano la <lb/>credula semplicit&agrave; delle narrazioni di Plinio. </s>

<s>In fatto di biologia, la genera&shy;<lb/>zione spontanea, e la trasformazione immediata di un essere insensitivo in <lb/>un animale, era una di quelle semplicit&agrave;, che Leonardo aveva comuni col <lb/>volgo. </s>

<s>&ldquo; La setola del bue, egli scrive, messa in acqua morta di state, pi&shy;<lb/>glia sensitivit&agrave; e moto per s&egrave; medesima, e paura e fuga, e sente dolore. </s>

<s>E <lb/>prova sia che stringendola, e si storce, e si divincola. </s>

<s>Ma riaila nell'acqua: <lb/>essa, come di sopra, ripiglia fuga, e levasi dal pericolo &rdquo; (MSS. K, fol. </s>

<s>81). </s></p><p type="main">

<s>Senza dubbio i Naturalisti moderni commettono peccato pi&ugrave; grave, e <lb/>meno scusabile di quello di Leonardo, quando, ingannati dalle medesime <lb/>apparenze, concedono l'animalit&agrave; a certi infusorii. </s>

<s>Ma lasciando star ci&ograve;, se <lb/>esso Leonardo credeva cos&igrave; facilmente alla trasformazione degli esseri vege&shy;<lb/>tanti ne'sensitivi, non fa maraviglia che secondasse la comune opinione, in&shy;<lb/>torno alla trasformazione degli elementi. </s>

<s>&ldquo; Quando l'aria, si legge altrove, <lb/>si converte in pioggia, essa farebbe vacuo, se l'altr'aria non lo proibisse col <lb/>suo soccorso, lo quale fa con impetuoso moto, e questo &egrave; quel vento, che <lb/>nasce di state insieme colle furiose piogge &rdquo; (MSS. E, in fine). </s></p><p type="main">

<s>Non &egrave; tutta di questa qualit&agrave; &egrave; vero, n&egrave; tutta consiste qui la scienza <lb/>di Leonardo, ma anche l&agrave; dove annunzia una proposizione vera, e descrive <lb/>qualche fatto osservato, non &egrave; poi cosa di tanta maraviglia, che trascenda la <lb/>virt&ugrave; naturale, e la possibile cultura dell'ingegno. </s>

<s>In materia di ottica, per <lb/>esempio, &egrave; notabile la riduzione di certi fenomeni al principio della persi&shy;<lb/>stenza delle immagini sopra la retina. </s>

<s>&ldquo; Se l'occhio, che risguarda la stella, <lb/>si volta con prestezza in contraria parte, li parr&agrave; che quella stella si com&shy;<lb/>ponga in una linea curva infocata, e questo accade perch&egrave; l'occhio riserva <lb/>per alquanto spazio la similitudine della cosa che splende. </s>

<s>E perch&egrave; tale im-<pb xlink:href="020/01/3089.jpg" pagenum="50"/>pressione dello splendore della stella &egrave; pi&ugrave; permanente nella pupilla, che non <lb/>fu il tempo del suo moto; &egrave; che tale impressione dura insieme col moto <lb/>in tutti i siti, che passano a riscontro della stella &rdquo; (MSS. K, fol. </s>

<s>120). L'in&shy;<lb/>crociamento de'raggi, che passano per un piccolo foro, e gli effetti, che ne <lb/>conseguono rispetto al modo di vedere l'oggetto, come si descrivono, fra'tanti <lb/>luoghi, nel foglio 127 del MSS. K, son delicatissime osservazioni; e i Teo&shy;<lb/>remi di prospettiva, sparsi per queste pagine, son tanto numerosi, da avan&shy;<lb/>zarne largamente alla compilazione di un libro, ma non sono altro in sostanza <lb/>che illustrazioni, o promozioni de'teoremi di Euclide, concernenti le propriet&agrave; <lb/>della sola luce riflessa. </s>

<s>Della luce rifratta per&ograve;, e delle applicazioni di lei <lb/>agli strumenti ottici, e alla visione, non se ne legge fatto negli ammirati vo&shy;<lb/>lumi il minimo cenno, ond'&egrave; a concludere che l'Autore sapesse di ottica <lb/>quanto ne potessero sapere gli altri pi&ugrave; dotti uomini di que'tempi, ignari <lb/>tuttavia come lui de'teoremi diottrici dello Snellio, e del Cartesio. </s></p><p type="main">

<s>Fra le note di Leonardo, che possono richiamar l'attenzione de'lettori <lb/>e la maraviglia, una delle principali sembra a noi che sia questa: &ldquo; La figura <lb/>del corpo luminoso, ancora che partecipassi del lungo, in lunga distantia pa&shy;<lb/>rer&agrave; di rotondo corpo. </s>

<s>Questo si prova nel lume della candela che, bench&egrave; <lb/>sia lungo pure in lunga distantia pare rotondo. </s>

<s>E questo medesimo pu&ograve; acca&shy;<lb/>dere alle stelle, che ancora che fussino come la luna cornute, la lunga di&shy;<lb/>stantia le farebbe parere rotonde &rdquo; (MSS. C, fol. </s>

<s>8). Chi tali parole rileg&shy;<lb/>gendo avrebbe il coraggio di negare a Leonardo il merito di aver prevenuto <lb/>Galileo, la principale opera di cui, in confermare la verit&agrave; della Sintassi co&shy;<lb/>pernicana, si riduce in aver dimostrato di fatto che Venere &egrave; corniculata, <lb/>bench&egrave; sempre all'occhio nudo apparisca rotonda? </s>

<s>La difficolt&agrave;, allo stesso <lb/>Copernico irresolubile, prima della invenzione del Canocchiale, dovette pa&shy;<lb/>rarsi alla mente degli Astronomi, infin da quando s'ebbe a tener per certo <lb/>che Venere e Mercurio son collocati fra la Terra e il Sole: certezza che, <lb/>insieme con Dante e con la massima parte degli uomini dotti, ebbe anche <lb/>Leonardo, nonostante che i due detti pianeti apparissero sempre rotondi, ci&ograve; <lb/>che egli attribuiva come Galileo alla irradiazione ascitizia. </s>

<s>&ldquo; Se l'occhio ri&shy;<lb/>guarda il lume di una candela lontana 400 braccia, esso lume apparir&agrave; a <lb/>esso occhio suo riguardatore cresciuto 100 volte la sua vera quantit&agrave;. </s>

<s>Ma se <lb/>li poni dinanzi un bastone (<emph type="italics"/>Galileo invece usava una cordicella<emph.end type="italics"/>) alquanto <lb/>pi&ugrave; di esso lume grosso, esso bastone occuper&agrave; quel lume, che pareva largo <lb/>due braccia. </s>

<s>Adunque questo errore viene dall'occhio, che piglia le spetie <lb/>luminose, non solamente per lo punto della luce, ma etiam con tutta essa <lb/>luce &rdquo; (MSS. C, fol. </s>

<s>60). Che se il Nostro avesse anche fatto professione di <lb/>copernicanismo perfetto, non sarebbe cosa da stupire, avendo il sistema del <lb/>Sole, posto nel centro e immoto, attirato a s&egrave; l'attenzione de'pi&ugrave; eletti in&shy;<lb/>gegni, infin da quando, fra le resuscitate opere di Archimede, s'incominci&ograve; <lb/>a leggere, e a meditar l'Arenario. </s></p><p type="main">

<s>Chi si crede d'aver ritrovato in Leonardo tutta la scienza del Coper&shy;<lb/>nico, di Galileo, e del Newton, o non ha pensato che doveva averla deri-<pb xlink:href="020/01/3090.jpg" pagenum="51"/>vata dalle precedenti tradizioni immediate, o ha fatto dire all'Autore altri&shy;<lb/>menti, da quel che egli intendeva, specialmente trattenendosi in una sen&shy;<lb/>tenza staccata dal contesto. </s>

<s>In un familiare colloquio udimmo una volta un <lb/>uomo assai dotto magnificare con grand'enfasi Leonardo da Vinci, per aver <lb/>notato ne'suoi volumi che la Terra &egrave; di figura sferoidea, pi&ugrave; sollevata sotto <lb/>il circolo equinoziale, che intorno ai poli. </s>

<s>E perch&egrave; possano i nostri Lettori <lb/>avvedersi da s&egrave; medesimi come si fosse quel buon uomo illuso, trascriveremo <lb/>dal foglio 12 del MSS. </s>

<s>E il passo, ch'egli citava, e dove, fra i sommari dei <lb/>capitoli trattanti del moto dell'acqua, mette Leonardo stesso anche quello, <lb/>in cui si direbbe &ldquo; come l'acqua delli mari equinoziali &egrave; pi&ugrave; alta che le <lb/>acque settentrionali, ed &egrave; pi&ugrave; alta sotto il corpo del Sole, che in nessuna <lb/>parte del circolo equinoziale, come si sperimenta sotto il calore dello Stizzo <lb/>infocato l'acqua, che mediante tale stizzo bolle, e l'acqua circostante al cen&shy;<lb/>tro di tal bollore sempre discende con onda circolare: e come l'acque set&shy;<lb/>tentrionale son pi&ugrave; basse, che li altri mari, e tanto pi&ugrave;, quanto esse son pi&ugrave; <lb/>fredde, in sin che si convertano in ghiaccio. </s>

<s>&rdquo; </s></p><p type="main">

<s>Ma cotesto citato libro <emph type="italics"/>Delle acque<emph.end type="italics"/> &egrave; quello, che pi&ugrave; strettamente si <lb/>riferisce al presente nostro discorso, ond'&egrave; che dovendosi da noi, come prin&shy;<lb/>cipal documento di storia, sottoporre ad esame, dobbiamo prima di tutto <lb/>osservar che l'Autore non dette esecuzione al proposito pi&ugrave; volte espresso <lb/>di metterlo in ordine, ma ne lasci&ograve; i materiali, che si trovano per le nu&shy;<lb/>merose sue carte informi e dispersi. </s></p><p type="main">

<s>Come rimanessero queste carte, dopo la morte di Leonardo, nella villa <lb/>Melzi di Vaprio dimenticate, e come poi la miglior parte di loro venisse alle <lb/>mani di Galeazzo Arconati; son cose oramati tanto note, ch'&egrave; superfluo il <lb/>ripeterle. </s>

<s>Alla famiglia degli Arconati apparteneva il padre Luigi Maria, frate <lb/>domenicano, il quale, mettendosi a esaminare e a studiare i curiosi volumi, <lb/>ebbe a restar maravigliato di trovar, fra gli scritti di un pittore, tanta copia <lb/>di quella Scienza idraulica, dell'istituzion della quale tutta la lode e il me&shy;<lb/>rito si dava allora al Castelli. </s>

<s>Con l'intenzione di mostrare a chi fossero tali <lb/>lodi e tali meriti per giustizia dovuti, il p. </s>

<s>Arconati, raccogliendo le sparse <lb/>note le ordin&ograve; in un libro, ch'egli intitolava <emph type="italics"/>Del moto e della misura delle <lb/>acque.<emph.end type="italics"/> Il manoscritto pervenne alla Biblioteca barberiniana di Roma, dove, <lb/>contro l'intenzione del laborioso compilatore, si rimase dimenticato, infin <lb/>tanto che il Venturi, andato a Parigi a ritrovare gl'involati volumi, e mosso <lb/>da'medesimi sentimenti, ebbe a ripetere, non meno maravigliato, che da Leo&shy;<lb/>nardo era stata l'Idraulica pi&ugrave; copiosamente, e pi&ugrave; perfettamente trattata che <lb/>dal Castelli. </s>

<s>Mossi da queste voci i Raccoglitori d'Autori italiani, che trattano <lb/>del moto dell'acque, pubblicarono in Bologna, nel 1828, il manoscritto, che l'Ar&shy;<lb/>conati aveva preparato 185 anni prima. </s>

<s>L'edizione, fattasi in tempi, in cui era <lb/>difficile il collazionare in Italia le trascrizioni con le note originali; &egrave; scorret&shy;<lb/>tissima, e nonostante ha giovato agli studiosi, e pu&ograve; giovare tuttavia, non <lb/>foss'altro per aver tutto insieme raccolto quel che si squaderna ne'sei volumi <lb/>in foglio del Ravaisson-Mollien, e negli altri pubblicati dopo e da pubblicarsi. </s></p><pb xlink:href="020/01/3091.jpg" pagenum="52"/><p type="main">

<s>Riducendosi ora sul filo del nostro ragionamento, cos&igrave; l'Arconati come <lb/>il Venturi, dal confronto che facevano del Castelli con Leonardo, intendevano <lb/>concluderne che questi avesse precorsi i fioritissimi tempi della scuola di Ga&shy;<lb/>lileo, e, incominciatosi cos&igrave; a dar fiato alla tuba, se ne diffuse largamente il <lb/>suono in quelle esagerazioni, che poco fa si diceva. </s>

<s>Il proposto confronto tra <lb/>i due Autori non &egrave; cosa da spedirsi in brevi parole, e noi lo rimetteremo <lb/>al giudizio, che ne proverr&agrave; dalla Storia: basti per ora confermare quel che <lb/>altra volta abbiamo accennato, che cio&egrave; Leonardo non &egrave; creatore, e nem&shy;<lb/>meno istitutore della Scienza idraulica, ma cultore e promotore di lei, quanto <lb/>ne potess'essere uno studioso di Archimede, qual maestro dell'Idrostatica, e <lb/>del Nemorario, qual premostratore della Idrodinamica. </s>

<s>Onde, essendo le scuole <lb/>pubbliche, si comprende come Leonardo dovesse avere condiscepoli, sopra i <lb/>quali non si vede che s'avvantaggiasse per tanto spazio smisurato. </s>

<s>Se nel <lb/>trattare dell'equilibrio de'liquidi ne avesse considerate le pressioni, e la loro <lb/>uguaglianza per tutti i versi; se nel trattar del moto avesse scoperta la legge <lb/>delle velocit&agrave;, e ne avesse fatta l'applicazione ai getti parabolici; avrebbe <lb/>dato qualche ragionevole motivo di ammirazione, e ne sarebbe in qualche <lb/>modo giustificato, o scusato il titolo d'ingegno creatore. </s>

<s>Ma se i Teoremi <lb/>archimedei non sa interpetrarli con altro, che con ammettere la leggerezza <lb/>positiva, e se ne fa da essa conseguire a dirittura le pi&ugrave; false dottrine pe&shy;<lb/>ripatetiche; se dagli insegnamenti del Nemorario non sa ricavarne altro, se <lb/>non che l'acqua &egrave; velocitata a proporzione del numero degli strati soprop&shy;<lb/>posti, o delle altezze; e se delle elevazioni e delle ampiezze de'getti liquidi, <lb/>fatti con varia inclinazione de'tubi, non sa dar che una regola a caso, o <lb/>come egli stesso confessa in di grosso; come dubitar se sia vero ch'egli non <lb/>oltrepass&ograve; i limiti della Scuola, alla quale s'era educato l'ingegno? </s>

<s>Ma per&shy;<lb/>ch&egrave; si potrebbe dubitare dell'esistenza di questa Scuola, noi ne osserveremo <lb/>le tradizioni riversarsi, come sotteraneo fiume che scaturisce, ne'libri del <lb/>Cardano, di cui nessuno sospetter&agrave; che avesse veduti i Manoscritti di Leo&shy;<lb/>nardo da Vinci, per attingerne le dottrine idrauliche, o per confutarle: d'onde <lb/>verr&agrave; altres&igrave; efficacemente provato che del patrimonio della Scienza, bench&egrave; <lb/>in moneta senza pubblica impronta, si faceva in fin d'allora comune e libe&shy;<lb/>rale commercio fra'dotti, e non ingiusto e sterile monopolio. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Il libro <emph type="italics"/>Del moto delle acque<emph.end type="italics"/> di Leonardo da Vinci, comunque siasi <lb/>dall'Arconati ordinato, contiene l'Idrostatica, l'Idrodinamica, e le applica&shy;<lb/>zioni di lei alla cos&igrave; detta <emph type="italics"/>misura dell'oncia,<emph.end type="italics"/> e al regolamento dei fiumi. </s>

<s><lb/>La prima parte resulta dai primi teoremi di Archimede, i quali hanno il loro <lb/>principal fondamento nella proposizione che la superficie dell'acqua &egrave; sfe&shy;<lb/>rica, e concentrica con la Terra: proposizione, che Leonardo commentava <pb xlink:href="020/01/3092.jpg" pagenum="53"/>con questo discorso: &ldquo; Dico che nessuna parte della superficie dell'acqua <lb/>per s&egrave; non si muove, se ella non discende. </s>

<s>Adunque la spera dell'acqua, non <lb/>avendo superficie in nessuna parte da potere scendere, gli &egrave; necessario che <lb/>per s&egrave; essa non si muova. </s>

<s>E se tu ben consideri ogni minima particula di <lb/>tal superficie, tu la troverai circondata da altre simili particule, le quali sono <lb/>di egual distantia in fra loro dal centro del mondo, e della medesima distan&shy;<lb/>tia da esso centro &egrave; quella particula, che da queste &egrave; circondata. </s>

<s>Adunque <lb/>tal particula dell'acqua da s&egrave; non si mover&agrave;, per essere circondata da sponde <lb/>d'uguale altezza. </s>

<s>E cos&igrave; ogni circulo di tali particule si fa vaso alla parti&shy;<lb/>cola, che dentro a tal circolo si racchiude, il qual vaso ha circuizione de'sua <lb/>labbri d'uguali altezze, e per questo tal particula, insieme con tutte le altre <lb/>simili, di che &egrave; composta la superficie della spera dell'acqua, per necessit&agrave; <lb/>sar&agrave; per s&egrave; senza moto, e per conseguenza, essendo ciascuna d'uguale al&shy;<lb/>tezza dal centro del mondo, necessit&agrave; fa essa superficie essere sferica &rdquo; <lb/>(MSS. F, fol. </s>

<s>26). </s></p><p type="main">

<s>La dimostrazione &egrave;, come s'&egrave; inteso, condotta dal principio che <emph type="italics"/>la su&shy;<lb/>perficie dell'acqua per s&egrave; non si muove, se ella non discende,<emph.end type="italics"/> e non di&shy;<lb/>scende, se non per la linea del suo moto, ossia per la perpendicolare, se&shy;<lb/>condo la prima supposizion di Archimede. </s>

<s>La cosa male interpetrata fu <lb/>occasione di gravissimi errori, qual'&egrave; quello che s'accennava del Michelini, <lb/>e da cui non in tutto and&ograve; esente Leonardo. </s>

<s>&ldquo; Il centro del fondo del vaso, <lb/>egli dice, riceve pi&ugrave; peso dell'acqua, che altro loco &rdquo; (MSS. H, fol. </s>

<s>68). No&shy;<lb/>nostante ci&ograve;, la quotidiana volgare esperienza del versare i liquidi anche dalle <lb/>pareti de'recipienti, era argomento certo del loro premere, non sul fondo <lb/>solo, ma anche lateralmente: e intorno a due figure di vasi, il primo dei <lb/>quali s'intendesse pieno d'acqua o d'altra cosa liquida, e il secondo di mi&shy;<lb/>glio, di rena o di altra cosa discontinua, nel fol. </s>

<s>62 del MSS. I, si legge: <lb/>&ldquo; Io voglio sapere quanta forza e peso faran le cose contenute dai due vasi <lb/>in tutti i lati de'vasi, cio&egrave; che differenza &egrave; del peso, che riceve il fondo, e <lb/>quanto le pareti, bench&egrave; tutto il peso si carica sul fondo. </s>

<s>&rdquo; </s></p><p type="main">

<s>Non era nemmeno sfuggito alla considerazione di Leonardo che le pres&shy;<lb/>sioni laterali crescono via via, secondo la profondit&agrave; del liquido, intorno a <lb/>che, oltre all'averne esperienza nel maggior impeto, con cui si vede uscire <lb/>il vino delle botti dal foro pi&ugrave; basso, era confermato da ci&ograve;, che veniva os&shy;<lb/>servando e speculando sui vortici o sui ritrosi. </s>

<s>Domandavasi: &ldquo; qual causa <lb/>fa l'acqua de'ritrosi stare pi&ugrave; alta, che il fondo d'esso ritroso, che in sin <lb/>li &egrave; pien d'aria? </s>

<s>&rdquo; (MSS. F, fol. </s>

<s>14). E rispondeva Leonardo esser questa <lb/>la causa medesima, per cui sta ritta la trottola, &ldquo; che, per la velocit&agrave; del <lb/>suo circonvolubile, perde la potenza, che ha l'inegualit&agrave; della sua gravezza <lb/>intorno al centro del suo circonvolubile, per causa dello impeto, che signo&shy;<lb/>reggia esso corpo &rdquo; (MSS. E, fol. </s>

<s>5). Ma nell'acqua &egrave; col moto centrifugo <lb/>congiunto un moto centripeto, dovuto alle spinte laterali. </s>

<s>E perch&egrave; l'acqua <lb/>spinge pi&ugrave; in basso che di sopra, essa restringe pi&ugrave; la vacuita al ritroso &rdquo; <lb/>(<emph type="italics"/>Compilazione dell'Arconati,<emph.end type="italics"/> Bologna 1828, pag. </s>

<s>356). </s></p><pb xlink:href="020/01/3093.jpg" pagenum="54"/><p type="main">

<s>Di qui pu&ograve; concludersi che Leonardo non negava farsi le pressioni an&shy;<lb/>che lateralmente sui vasi, ma le reputava minime, rispetto a quelle, che si <lb/>ricevon dal fondo. </s>

<s>Ond'&egrave; che la sentenza <emph type="italics"/>L'acqua non pesa manco per <lb/>traverso, che per la sua perpendicolare<emph.end type="italics"/> (MSS. H, fol. </s>

<s>68) non deve gi&agrave; in&shy;<lb/>tendersi che le due pressioni siano uguali, ma che per l'una non &egrave; da esclu&shy;<lb/>dersi l'altra, quasi la giusta interpetrazione del detto si fosse questa: L'acqua <lb/>non solamente pesa per la perpendicolare, ma anche per traverso. </s>

<s>O meglio, <lb/>si dovrebbe intendere: l'acqua pesa perpendicolarmente, con forza propor&shy;<lb/>zionale a quella, che si fa per traverso, secondo il principio idrodinamico, <lb/>professato da Leonardo stesso, come vedremo. </s></p><p type="main">

<s>Proseguendo per ora il cominciato argomento, si trovano dal nostro Au&shy;<lb/>tore formulate le seguenti proposizioni: &ldquo; Tanto peso d'acqua si fuggir&agrave; dal <lb/>suo sito, quanto &egrave; la somma del peso, che essa acqua caccia. </s>

<s>&mdash; Tanto fia <lb/>il peso, che si sostien sopra l'acqua, quanta &egrave; la somma del peso dell'acqua, <lb/>che d&agrave; luogo a esso peso &rdquo; (MSS. H, fol. </s>

<s>92). &mdash; L'acqua, che manca nel <lb/>loco che occupa la nave, pesa quanto tutto il resto del navilio che la cac&shy;<lb/>cia (ivi, fol. </s>

<s>69). Sono in queste sentenze compendiati senza dubbio i teoremi <lb/>idrostatici di Archimede, e in s&egrave; stesse considerate son vere. </s>

<s>Ma i pesi del&shy;<lb/>l'acqua nell'acqua, troppo strettamente rassomigliati ai pesi de'corpi solidi <lb/>nell'aria, fanno molto lungi dal vero aberrare Leonardo, il quale misura le <lb/>quantit&agrave; delle pressioni idrostatiche dalla quantit&agrave; del liquido circonfuso, come <lb/>dal resistere al contrappeso suol misurarsi il peso di un corpo posto sopra <lb/>l'altro bacino della bilancia. </s>

<s>Di qui &egrave; che, nel libro Del moto delle acque, <lb/>si trovano proposti e dimostrati i due seguenti falsissimi teoremi: &ldquo; I. Del&shy;<lb/>l'acque di pari profondit&agrave; quella, che sar&agrave; pi&ugrave; stretta, sosterr&agrave; meno peso <lb/>sopra di s&egrave;. </s>

<s>&mdash; II. Dell'acque di pari larghezza, quella sosterr&agrave; men peso, <lb/>che fia pi&ugrave; bassa. </s>

<s>&rdquo; (<emph type="italics"/>Compilazione<emph.end type="italics"/> cit., pag. </s>

<s>412). </s></p><p type="main">

<s>Si venivano a rinnovellare cos&igrave; le peripatetiche fallacie antiche, lusin&shy;<lb/>gando la ragione con questo discorso: &ldquo; Provasi la prima, perch&egrave;, ficcan&shy;<lb/>dosi la barca nell'acqua, per il peso da lei contenuto, s'alza l'acqua. </s>

<s>Ma <lb/>con questa differenza che, quando &egrave; l'acqua larga che s'alza v. </s>

<s>g. </s>

<s>un palmo, <lb/><figure id="id.020.01.3093.1.jpg" xlink:href="020/01/3093/1.jpg"/></s></p><p type="caption">

<s>Figura 16.<lb/>per la barca, che col suo peso si ficca <lb/>verso il fondo, anche, per tale profon&shy;<lb/>darsi della barca l'altezza di un palmo, <lb/>un palmo l'acqua si viene ad alzare, e <lb/>gran peso acquista. </s>

<s>E quanto maggior <lb/>peso acquista, tanto maggior peso sostiene. </s>

<s><lb/>Ma quando &egrave; stretta, per essere poca <lb/>somma di acqua, che nel profondarsi della <lb/>barca s'alza; ancora poco peso acquista, <lb/>e poco peso pu&ograve; sostenere. </s>

<s>E per questo <lb/>l'acqua qui da basso (fig. </s>

<s>16) del vaso <lb/>minore DH, quale con la sua acqua circonda il peso posto sopra l'aria, non pesa <lb/>sopra essa aria, quanto fa il peso, che le &egrave; posto di sopra, sopra essa acqua, <pb xlink:href="020/01/3094.jpg" pagenum="55"/>come fa l'acqua del vaso maggiore, la quale &egrave; fatta tanto alta sopra a tal aria, <lb/>che sostiene il peso, ed ha acquistato per tale altezza tanto peso, che ella <lb/>&egrave; potente a spingere l'aria in su, con il peso che le &egrave; posto di sopra, quanto <lb/>sia potente tal peso a premerla in gi&ugrave; &rdquo; (ivi). Da questi medesimi principii <lb/>si concludono le ragioni dell'altro annunziato teorema, per intender bene <lb/>le quali &egrave; da sapere che Leonardo professava, insieme con altri falsi prin&shy;<lb/>cipii peripatetici, anche questo: &ldquo; Tutti gli elementi, fuori del loro sito, de&shy;<lb/>siderano a esso sito ritornare, e massime aria e fuoco, acqua e terra &rdquo; <lb/>(MSS. C, fol. </s>

<s>26): e come in questi riconosceva una gravit&agrave; naturale; cos&igrave; <lb/>a quelli attribuiva una leggerezza positiva. </s>

<s>Di qui &egrave; che, trattandosi de'so&shy;<lb/>lidi immersi ne'liquidi, sempre attribuisce l'Autore le spinte sursum all'aria, <lb/>la quale tanto pi&ugrave; efficacemente &egrave; costretta a operare, quanto alla tendenza <lb/>sua naturale s'aggiunge l'estrusione, provocata dal peso dell'acqua che la <lb/>circonda. </s>

<s>Ed essendo il peso proporzionale alla massa, &egrave; facile intendere come <lb/>da cos&igrave; falsi principii conseguissero le falsit&agrave; de'sopraddetti due teoremi. </s></p><p type="main">

<s>Da questi medesimi principii, sostituiti a quello delle pressioni idrosta&shy;<lb/>tiche riflesse, ragionando Leonardo, spiegava come mai un corpo specifica&shy;<lb/>mente pi&ugrave; grave dell'acqua, qual'&egrave; la materia, di che si compongono le navi, <lb/>cos&igrave; facilmente galleggi, in virt&ugrave; cio&egrave;, egli diceva, della leggerezza dell'aria, <lb/>che si contrappone, e fa equilibrio alla gravit&agrave; del composto del legno duro <lb/>e del ferro, che per s&egrave; andrebbe necessariamente al fondo. </s>

<s>&ldquo; Tutto il peso <lb/>della barca, posto al livello dell'acqua, &egrave; fatto uguale ad altrettant'acqua, <lb/>computato la levit&agrave; dell'aria, che li sta di sotto, la quale la tiene in tale al&shy;<lb/>tezza. </s>

<s>Questa proposizione resta provata cos&igrave;: Imperocch&egrave;, a fare che l'aria <lb/>della barca resti a livello con l'acqua che la circonda, necessit&agrave; vuole che, <lb/>quanto l'aria della barca supera in levit&agrave; la detta acqua, che la circonda, <lb/>tanto il peso della barca venga proporzionatamente a superare il peso del&shy;<lb/>l'acqua, sicch&egrave;, tra la levit&agrave; dell'aria, e gravit&agrave; del peso nella barca, si faccia <lb/>un misto di tanta gravit&agrave;, quanto &egrave; quella dell'acqua &rdquo; (<emph type="italics"/>Compilaz.<emph.end type="italics"/> cit., pag. </s>

<s>410). </s></p><p type="main">

<s>Le obiezioni, che poi fecero gli Accademici del Cimento, per confutare <lb/>con le loro esperienze l'errore della leggerezza positiva, anche si pararono <lb/>innanzi alla mente di Leonardo. </s>

<s>Ma egli vi si trov&ograve; impacciato, e per dar&shy;<lb/>sele in qualche modo risolute, s'acquiet&ograve; finalmente in un paralogismo: <lb/>&ldquo; Egli &egrave; un pozzo, cos&igrave; scrive, il quale ha nel suo fondo un otro di tal <lb/>grandezza, e in tal modo situato, che di sotto e da lato non si trova pi&ugrave; di <lb/>un dito di grossezza d'acqua, in modo che l'acqua, che riposa sul fondo, <lb/>pesa libbre 100, e quella, che si posa sopra della baga, pesa libbre 10,000. <lb/>Se cos&igrave; &egrave;, la baga scoppier&agrave;, avendo sopra s&egrave; tanto peso. </s>

<s>E se quel peso non <lb/>la preme, che lo sostiene? </s>

<s>E se pure esso fussi sostenuto, perch&egrave; avrebbe <lb/>a passare l'otre sopra l'acqua? </s>

<s>E se pure l'acqua carica sopra il suo fondo, <lb/>perch&egrave; non patisce passione un uomo, passione di peso, stando sopra il suo <lb/>fondo? </s>

<s>Adunque, se la baga sostiene l'acqua, la baga toglie il peso di essa <lb/>acqua al fondo del pozzo &rdquo; (MSS. A, fol. </s>

<s>25). </s></p><p type="main">

<s>L'ipotesi, in un'altra nota, si riduce, e si presenta cos&igrave; sotto forma di <pb xlink:href="020/01/3095.jpg" pagenum="56"/>tesi: &ldquo; Io ti voglio mostrare in che modo l'acqua pu&ograve; essere sostenuta dal&shy;<lb/>l'aria, essendo da quella divisa e separata. </s>

<s>Certo se tu hai in te ragione, io <lb/>credo che tu non mi negherai che, essendo una baga nel fondo dell'acqua <lb/>di un pozzo, la qual baga tocchi tutti i lati del fondo d'esso pozzo, in modo <lb/>che acqua non possi passare sotto lei; questa baga, essendo piena di aria, <lb/>non far&agrave; minor forza d'andare alla superficie dell'acqua a ritrovare l'altra <lb/>aria, che si facci l'acqua a volere toccare il fondo del pozzo. </s>

<s>E se questa <lb/>baga vuole andare in alto, ella spinger&agrave; in alto l'acqua a lei soprapposta, e <lb/>levando l'acqua in alto ella scarica il fondo del pozzo, onde quasi esso pozzo, <lb/>a questa ragione, potrebbe stare senza fondo &rdquo; (MSS. C, fol. </s>

<s>26); </s></p><p type="main">

<s>La verit&agrave; si &egrave; che il fondo &egrave; gravato invece da tutt'insieme il peso della <lb/>baga, e dell'acqua che le sovrasta, ed &egrave; notabile che Leonardo non faccia <lb/>differenza dal primo esempio, in cui si supponeva che l'otre avesse l'acqua <lb/>da'lati e di sotto, a questo, in cui la baga l'ha solamente di sopra: e non <lb/>attendesse il fatto che l&agrave; si vede l'aria essere spinta alla superficie, e qua <lb/>rimanersi immobile nel fondo, sopra cui scoppierebbe necessariamente, quando, <lb/>per la grande altezza del liquido superiore, non potesse resisterne la pressione. </s></p><p type="main">

<s>Si vede che il divino uomo, l'ammirabile ingegno non sempre seppe <lb/>sollevarsi sulla volgare turba peripatetica, vizio della quale era di accomo&shy;<lb/>dar l'esperienze alle preconcette opinioni: e se si debba giudicare da'ma&shy;<lb/>noscritti di lui si direbbe che l'Idrostatica, tutt'altro ch'esservi creata o <lb/>promossa, &egrave; anzi ritirata indietro da quella dirittura, a che l'avevano avviata <lb/>i Platonici, i quali, come s'ha per l'esempio di Seneca, applicarono i teo&shy;<lb/>remi archimedei a dimostrare sperimentalmente che non si d&agrave; leggerezza <lb/>positiva, e che gravi e lievi non son le cose per s&egrave; stesse, ma che, per com&shy;<lb/>parazione col mezzo, si dicono tali. </s></p><p type="main">

<s>L'Idrodinamica dicemmo esser nata nel secolo XV, per l'applicazione <lb/>che si fece a'liquidi delle nuove dimostrate propriet&agrave; del moto dei gravi. </s>

<s><lb/>Leonardo stesso cita il libro <emph type="italics"/>De proportionibus<emph.end type="italics"/> di Alberto di Sassonia, in <lb/>cui si formulava la legge delle potenze, le quali stanno in ragion composta <lb/>delle velocit&agrave; e delle masse. </s>

<s>&ldquo; Dice Alberto di Sassonia, nel suo <emph type="italics"/>Di propor&shy;<lb/>tione,<emph.end type="italics"/> che, se una potentia move un mobile con certa velocit&agrave;, che mover&agrave; <lb/>la met&agrave; di esso mobile in duplo veloce. </s>

<s>La qual cosa a me non pare, im&shy;<lb/>perocch&egrave; lui non mette che questa tale potentia adoperi l'ultima sua vale&shy;<lb/>tudine &rdquo; (MSS. I, fol. </s>

<s>120). </s></p><p type="main">

<s>Si censura dunque dal Nostro la proposizione del Sassone, discepolo del <lb/>Nemorario, come poco precisa, e no come falsa. </s>

<s>Anzi, pur che s'intenda che <lb/>la potenza venga nel mobile tutta esaurita, riconosceva la proposizione stessa <lb/>per cos&igrave; vera, che dava per altrettante verit&agrave; i corollari immediati di lei. </s>

<s><lb/>Chiamata P la potenza, M il mobile e V la velocit&agrave;, se sostituiscasi alla ve&shy;<lb/>locit&agrave; stessa la relazione tra lo spazio S, e il tempo T, avremo quella me&shy;<lb/>desima equazione espressa sotto l'altra forma P=(M.S)/T, e perch&egrave; (M.S)/T= <lb/>M/2.2S/T=M/2.S:T/2, di qui si vede la ragione de'corollari, che da Leonardo <pb xlink:href="020/01/3096.jpg" pagenum="57"/>stesso si trovano cos&igrave; scritti: I. </s>

<s>Se una potentia move un corpo, nun quanto <lb/>tempo, la medesima potentia mover&agrave; la met&agrave; di quel corpo, nel medesimo <lb/>tempo, due volte quello spatio. </s>

<s>II. </s>

<s>Se alcuna virt&ugrave; mover&agrave; alcun mobile, per <lb/>alcuno spatio, ine qual tempo, (<emph type="italics"/>in qualche tempo<emph.end type="italics"/>) la medesima virt&ugrave; mo&shy;<lb/>ver&agrave; la met&agrave; di quel mobile, in tutto quello spatio, la met&agrave; di quel tempo &rdquo; <lb/>(MSS. F, fol. </s>

<s>51). </s></p><p type="main">

<s>Come poi l'equazione della potenza, data dal Nemorario, e applicata da <lb/>Alberto, si teneva che fosse vera per s&egrave; anche dal Nostro; cos&igrave; secondo la <lb/>verit&agrave; s'applicava da lui stesso al moto delle acque. </s>

<s>In due fiumi dunque, <lb/>o in due distinte sezioni di un medesimo fiume, le potenze motrici son mi&shy;<lb/>surate dal prodotto delle moli dell'acqua, contenuta in esse sezioni, e delle <lb/>velocit&agrave; respettive, di modo che, essendo simboleggiate da P, P&prime; le dette po&shy;<lb/>tenze, e da V, V&prime; le velocit&agrave;, secondo le quali son sollecitate le corrispon&shy;<lb/>denti sezioni S, S&prime;, abbiamo le due equazioni P=S.V, P&prime;=S&prime;.V&prime;. </s></p><p type="main">

<s>Ora, nel libro dell'Arconati che teniamo sott'occhio, si trova compilata <lb/>anche questa proposizione: &ldquo; Il moto d'ogni fiume, con egual tempo, d&agrave; in <lb/>ogni parte della sua lunghezza egual peso d'acqua. </s>

<s>E questo accade perch&egrave;, <lb/>se il fiume nello sboccamento che fa scarica un tanto peso d'acqua, in tanto <lb/>tempo, necessit&agrave; vuole che, in luogo dell'argine scaricata, succeda un altret&shy;<lb/>tanto peso di acqua, in altrettanto tempo, quale si muova dalla parte imme&shy;<lb/>diatamente antecedente, e cos&igrave; successivamente, in luogo di quest'altra acqua, <lb/>succeda un altrettanto peso, insintanto che s'arrivi alla prima parte della <lb/>lunghezza del fiume. </s>

<s>Altrimenti, se nello sboccamento si scaricasse maggior <lb/>somma di acqua, di quella che si trova al principio del fiume; seguirebbe <lb/>che nel mezzo del canale l'acqua di continuo s'andasse sminuendo. </s>

<s>E per <lb/>il contrario, se nel medesimo sboccamento passasse minor somma di acqua, <lb/>di quella che entra al suo nascimento; l'acqua di mezzo crescerebbe conti&shy;<lb/>nuamente. </s>

<s>Ma l'uno e l'altro &egrave; manifestamente falso, dunque il moto di ogni <lb/>fiume, con ugual tempo, d&agrave; in ogni parte della sua larghezza uguale peso <lb/>di acqua &rdquo; (pag. </s>

<s>427): ossia, riducendosi alla formula sopra scritta, P &egrave; <lb/>uguale a P&prime;, e perci&ograve; S:S&prime;=V&prime;:V, conseguenza che Leonardo, nel suo <lb/>proprio linguaggio, significava: &ldquo; Tanto quanto crescerai il fiume di lar&shy;<lb/>ghezza, tanto diminuirai la qualit&agrave; del suo movimento: Tanto quanto di&shy;<lb/>minuirai la larghezza del fiume, tanto crescerai la qualit&agrave; del suo movi&shy;<lb/>mento &rdquo; (ivi). </s></p><p type="main">

<s>Cos&igrave;, il teorema principalissimo, che le velocit&agrave; e le sezioni si rispon&shy;<lb/>dono contrariamente, veniva provato per ragion matematica, ma Leonardo <lb/>soggiungeva che poteva confermarsi altres&igrave; per le esperienze, o per gli esempi, <lb/>fra'quali ne sceglie uno assai efficace, tolto da un esercito costretto a pas&shy;<lb/>sare per varie ampiezze di luogo, che, a voler mantenersi unito, debbono i <lb/>soldati tanto affrettare il passo di pi&ugrave;, quanto il luogo stesso &egrave; pi&ugrave; stretto. <lb/></s>

<s>&ldquo; Se fia uno loco, che abbi tre varie larghezze, le quali si contengano in&shy;<lb/>sieme, e la prima minore di larghezza entri nella seconda quattro volte, e <lb/>la seconda entri due volte nella terza; dico che li uomini, che compieranno <pb xlink:href="020/01/3097.jpg" pagenum="58"/>colle loro persone i detti lochi, che avranno a essere in continuo cammino; <lb/>che, quando li uomini del maggiore loco faranno uno passo, che quelli della <lb/>seconda minore stantia ne faran due; e quelli del terzo loco, che &egrave; minore <lb/>il quarto che il secondo loco, in quel medesimo tempo, faranno otto pass&igrave;, <lb/>e che questa medesima proportione troverai in tutti i movimenti, che pas&shy;<lb/>sano per varie larghezze di lochi &rdquo; (MSS. A, fol, 37). Fra'quali movimenti <lb/>Leonardo non annovera solamente quelli fatti dai liquidi, <emph type="italics"/>non condensabili <lb/>n&egrave; rarefattibili<emph.end type="italics"/> (MSS. E, fol. </s>

<s>71), ma quelli stessi fatti dai fluidi elastici, <lb/>come dall'aria. </s>

<s>&ldquo; Il vento, nel passare gli stremi dei monti, si fa veloce e <lb/>denso, e quando discorre di l&agrave; dalli monti si fa raro e tardo, a similitudine <lb/>dell'acqua, che sbocca di stretto canale in largo pelago &rdquo; (ivi, fol. </s>

<s>54). </s></p><p type="main">

<s>La legge universalissima, applicata a ogni sorta di fluidi, che abbiamo <lb/>trovata scritta da Leonardo da Vinci, era comunemente nota nella Scuola, <lb/>alla quale egli apparteneva, e da essa la ricev&egrave; il Cardano, e la divulg&ograve; nel <lb/>cap. </s>

<s>VI del primo libro <emph type="italics"/>De rerum varietate<emph.end type="italics"/> dove, trattando delle acque, dice <lb/>che le ragioni de'loro moti, cos&igrave; utili a sapersi, dipendono essenzialmente da <lb/>questi due principii: &ldquo; alterum quod iuxta foraminis amplitudinem aqua de&shy;<lb/>fertur; alterum quod iuxta impetum. </s>

<s>Nam si reliqua paria sint, quae per <lb/>angustum foramen et lente exit paucior est: contra, quae per ampliora et <lb/>patentiora loca maioreque impetu. </s>

<s>Porro ratio foraminis, si ad basim refe&shy;<lb/>ratur, eamdem retinebit proportionem, atque ideo simplicissima est. </s>

<s>Ponatur <lb/><figure id="id.020.01.3097.1.jpg" xlink:href="020/01/3097/1.jpg"/></s></p><p type="caption">

<s>Figura 17.<lb/>enim quod AB (fig. </s>

<s>17), inxta altitudinem AC, qua&shy;<lb/>dratam, ita ut AB sit unum, et locus super quem <lb/>aqua transit, emittat unciam aquae: dico quod non <lb/>mutato situ si BD, DE, EF aequales sint AB, <lb/>quod iuxta eamdem altitudinem profluunt unciae <lb/>singulae. </s>

<s>Ita, quod per AD unciae duae, per AE <lb/>tria, per AF quatuor, et ita de aliis quotquot fuerint. </s>

<s>Nam seorsum per BD, <lb/>ex supposito, flueret uncia et per DF, et per EF, ubi adessent latera et al&shy;<lb/>titudo quanta est AC. </s>

<s>Sed aqua, quae fluit per AB, nec impedit nec iuvat <lb/>eam quae fluit per BD, nec, quae per BD, eam quae per DE, atque ita de <lb/>aliis. </s>

<s>Constat igitur quod ut multiplex, aut quam proportionem habebit AF <lb/>ad AB, seu AD, aut alia quaepiam; eamdem proportionem habebit aqua <lb/>fluens secundum latitudinem AF, vel AD, altitudinem autem AC ad unciam &rdquo; <lb/>(Basilaee 1581, pag. </s>

<s>61, 62). </s></p><p type="main">

<s>Questo dice il Cardano, per quel che riguarda l'ampiezza delle sezioni. </s>

<s><lb/>Per quel che poi riguarda le proporzioni degl'impeti, soggiunge che questi <lb/>sono secondo l'altezze delle discese, come si vede ne'vasi vinarii: &ldquo; Impe&shy;<lb/>tus vero aquae fit, vel ob descensus magnitudinem, vel quia protruditur. </s>

<s><lb/>Unde videmus in vinariis vasis, per siphunculos in medio et imo aequales, <lb/>celerius impleri cirneas, quam per eos, qui in suprema parte positi sunt &rdquo; <lb/>(ibid., pag. </s>

<s>62). E perch&egrave; &ldquo; quae velocius labitur maiore etiam copia exit &rdquo; <lb/>(ibid., pag. </s>

<s>63), e son le velocit&agrave; proporzionali alle altezze; saranno ad esse <lb/>altezze pure proporzionali le quantit&agrave; d'acqua uscita in pari tempo dalla me-<pb xlink:href="020/01/3098.jpg" pagenum="59"/>desima, o da uguale sezione: ci&ograve; che esattamente riscontra con la proposi&shy;<lb/>zione scritta da Leonardo: &ldquo; Dell'acqua, che non manca di una ordinata <lb/>altezza nella sua superficie, tale sar&agrave; la quantit&agrave; dell'acqua, che versa per <lb/>un dato spiracolo in un dato tempo, quale quella della data altezza di esso <lb/>spiracolo. </s>

<s>Dico che se B (fig. </s>

<s>18) versa in un tempo una quantit&agrave; d'acqua, <lb/><figure id="id.020.01.3098.1.jpg" xlink:href="020/01/3098/1.jpg"/></s></p><p type="caption">

<s>Figura 18.<lb/>che C verser&agrave; due tanti acqua, nel medesimo tempo, perch&egrave; ha <lb/>due tanti pi&ugrave; peso d'acqua sopra di s&egrave; &rdquo; (MSS. F, fol. </s>

<s>53). </s></p><p type="main">

<s>La legge delle velocit&agrave; proporzionali alle pressioni derivava <lb/>immediatamente dalla prima supposizion di Archimede. </s>

<s>E per&shy;<lb/>ch&egrave; sembrava che non si dovessero ammettere, secondo queste <lb/>dottrine, altre pressioni, che le perpendicolari sul fondo dei vasi, <lb/>e l'esperienze dimostravano manifestamente che si fanno anche <lb/>sui lati; di qui nascevano difficolt&agrave;, da mettere a dura prova <lb/>gl'ingegni speculativi. </s>

<s>Il Cardano si propone, fra gli altri, a risolvere <lb/>anche il problema: &ldquo; Cur aquae a lateribus etiam stantium paludum effu&shy;<lb/>sae, per rimas tabularum impetum secum afferant &rdquo; (<emph type="italics"/>De rerum var.<emph.end type="italics"/> cit., <lb/>pag. </s>

<s>69). E risponde che sarebbe cosa di facile spiegazione, contentandoci di <lb/>dire, come avevano detto i suoi predecessori, fra'quali abbiamo ritrovato an&shy;<lb/>che Leonardo da Vinci; che l'acqua superiore preme anche dai lati. </s>

<s>&ldquo; Ve&shy;<lb/>rum ex nodo, immediatamente soggiunge, nodus oritur, nam verisimile non <lb/>est premi a tota aqua, neque enim proportio motus servari videtur, cum <lb/>ex vase vinario tam parvo nec pleno adeo celeriter vinum effundatur, ut, si <lb/>iuxta proportionem multitudinis totius aquae id fieret, necesse esset impetum <lb/>illum esse multo maiorem, ac pene insuperabilem. </s>

<s>Si vero non a tota aqua <lb/>compressio fiet, questio manet. </s>

<s>Dicimus itaque aquam totam premi, et ut <lb/>premitur premere, sed non adeo vehementer, quia, dum premuntur partes, <lb/>et ipsae premunt, quamobrem pars illa quae exit a tota premitur, sed a re&shy;<lb/>motiore multo minus: vehementer vero a proxima, nec etiam aequaliter ab <lb/>aequaliter distantibus, sed vehementer ab ea, quae in directo est effluentis, <lb/>usque ad adversam ripam: parum vero ab ea, quae est a laterihus, et iuxta <lb/>fluminis aut rivi longitudinem posita, nec ab hac etiam aequaliter, sed ab ea <lb/>quae antecedit nullo modo. </s>

<s>Ab ea autem, quae in superiore loco, adhuc di&shy;<lb/>versa ratione, siquidem a proximiore plus, a remotiore autem minus &rdquo; (ibid.). </s></p><p type="main">

<s>Bench&egrave; il problema non sia a questo modo risoluto, pure &egrave; molto lo&shy;<lb/>devole il Cardano, per aver fatto sforzi cos&igrave; generosi, i quali avrebbero po&shy;<lb/>tuto rendergli buon frutto, se avesse saputo fermarsi in quella verit&agrave;, bale&shy;<lb/>natagli alla mente, <emph type="italics"/>aquam totam premi et ut premitur premere.<emph.end type="italics"/> Leonardo, <lb/>dall'altra parte, come fu pi&ugrave; leggero in questa contemplazione, cos&igrave;, nell'ap&shy;<lb/>plicarla alle curve descritte dai getti liquidi, parve pi&ugrave; audace. </s>

<s>Egli si fa <lb/>questa domanda: &ldquo; Se una botte ha in s&egrave; il vino alto quattro braccia, e <lb/>getta il vino lontano da s&egrave; quattro braccia; se quando il vino sar&agrave; nel ca&shy;<lb/>lare disceso all'altezza di due braccia della botte, getter&agrave; ella il vino per la <lb/>medesima cannella ancora due braccia: cio&egrave;, se il calo e l'empito del get&shy;<lb/>tare della cannella diminuisce con uguale proporzione o no; e se, essendo la <pb xlink:href="020/01/3099.jpg" pagenum="60"/>botte piena, e s'empier&agrave; per la sua cannella due boccali per ora, se dover&agrave; <lb/>a questa ragione empiere un sol boccale per ora, colla medesima cannella <lb/>che versava &rdquo; (MSS. I, fol. </s>

<s>73). </s></p><p type="main">

<s>Il problema fu risoluto affermativamente in questa nota, scritta di rin&shy;<lb/>contro a una figura simile alla nostra 19. &ldquo; &Egrave; in natura che una medesima <lb/><figure id="id.020.01.3099.1.jpg" xlink:href="020/01/3099/1.jpg"/></s></p><p type="caption">

<s>Figura 19.<lb/>canna pu&ograve; gettare lontan da s&egrave; infinita distantia, perch&egrave; infi&shy;<lb/>nita pu&ograve; essere l'altezza ingorgata dell'acqua, che carica sopra <lb/>tale uscita di acqua, come fa la canna BAC, che pu&ograve; essere <lb/>d'infinita altezza coll'immaginazione, e in ogni grado d'altezza <lb/>la canna AC acquista gradi di distantia nel gettare da lon&shy;<lb/>tano &rdquo; (ivi, fol. </s>

<s>14). </s></p><p type="main">

<s>Il teorema consegue immediatamente dal principio, che <lb/>ammette le velocit&agrave; proporzionali alle altezze, ma l'applica&shy;<lb/>zione, che se ne fa agli efflussi laterali, &egrave; arbitraria, come <lb/>arbitraria &egrave; la seguente proposizione, insieme col problema che ne dipende: <lb/><figure id="id.020.01.3099.2.jpg" xlink:href="020/01/3099/2.jpg"/></s></p><p type="caption">

<s>Figura 20.<lb/>&ldquo; Quella proporzione, che aver&agrave; BC (fig. </s>

<s>20) con AC, tale <lb/>proporzione troverai nelle due quantit&agrave; del vino, che si <lb/>trova in nel vasello, che cagione desse di versar pi&ugrave; presso <lb/>o lontano: cio&egrave; se il vino del vasello prima versava in C, <lb/>essendo pieno, e quando era quasi vuoto versava in A; sappi <lb/>che, quando e'verser&agrave; in mezzo fra A e C, nel punto B, <lb/>il vasello sar&agrave; appunto mezzo &rdquo; (MSS. C, fol. </s>

<s>5). &ldquo; Di qui <lb/>puossi conoscere quando sia tratto il vino d'un vasello pi&ugrave; <lb/>alto o pi&ugrave; basso e quanto, sapendo solamente il diametro <lb/>di esso. </s>

<s>Fa'cos&igrave;: ricevi il vino, quando &egrave; caduto fuori del vasello, e dopo che <lb/><figure id="id.020.01.3099.3.jpg" xlink:href="020/01/3099/3.jpg"/></s></p><p type="caption">

<s>Figura 21.<lb/>la sua curvazione s'&egrave; ridotta alquanto perpendicolare <lb/>linea, e ricevi in prima AN (fig. </s>

<s>21) nel luogo N, e <lb/>nota il punto N. </s>

<s>Dipoi ricevi B nel punto M, e poni <lb/>col filo piombato F a punto, dove il vino di dentro <lb/>confina dinanzi col suo vasello. </s>

<s>E tanto quanto AO <lb/>entra in OP, tanto FN entrer&agrave; a proporzione in FM <lb/><figure id="id.020.01.3099.4.jpg" xlink:href="020/01/3099/4.jpg"/></s></p><p type="caption">

<s>Figura 22.<lb/>appunto, essendo i buchi <lb/>del vasello di egual gran&shy;<lb/>dezza, e cos&igrave; il legno di <lb/>grossezza &rdquo; (ivi, fol. </s>

<s>6). </s></p><p type="main">

<s>Che poi queste propo&shy;<lb/>sizioni non avessero in s&egrave; certezza alcuna di scienza <lb/>lo riconosce pur troppo bene, e lo confessa Leo&shy;<lb/>nardo, nel provarsi a dar regola delle ampiezze, <lb/>che secondo le varie inclinazioni delle fistole descri&shy;<lb/>vono per aria gli zampilli. </s>

<s>Sotto una figura, imi&shy;<lb/>tata qui da noi nella 22, &egrave; scritto: &ldquo; Prova per fare regola di questi moti. </s>

<s><lb/>Faraila con una baga piena di acqua, con molte cannelle di pari busi, posti <lb/>per una linea. </s>

<s>Io giudico, cos&igrave; in di grosso, che quanto C si leva pi&ugrave; alto <pb xlink:href="020/01/3100.jpg" pagenum="61"/>che D, tanto il mezzo dell'arco D si ritrover&agrave; pi&ugrave; lontano sotto il suo per&shy;<lb/>pendicolare in H. Cio&egrave;: tanto, quanto D fia pi&ugrave; basso di C, tanto H fia pi&ugrave; <lb/>lontano da O che G. </s>

<s>Vero &egrave; che le cannelle, che gettano l'acqua, vogliono <lb/>tutte nascere su un piano a livello, e di medesima lunghezza, e poi piegate <lb/>a diversi siti &rdquo; (ivi, fol. </s>

<s>7). </s></p><p type="main">

<s>Il Cardano non ebbe il coraggio di entrare in cos&igrave; fatte questioni, per&shy;<lb/>ch&egrave; si sentiva mancare la scienza necessaria a risolverle, e dall'altra parte <lb/>troppo ben comprendeva che quelle ordinate non si sarebbero potute riferire <lb/>a una linea curva, e tanto meno a un arco di cerchio, secondo la curvit&agrave; <lb/>del quale si credeva inflettersi lo zampillo, come in un arco di cerchio si cre&shy;<lb/>deva insenarsi le corde lentamente sospese dai due loro estremi. </s>

<s>&ldquo; L'arco, <lb/>scrive Leonardo, che si genera dalla corda, che s'estende infra le due car&shy;<lb/>rucole, poste nel sito della egualit&agrave;; &egrave; una parte della circonferentia di un <lb/>cerchio &rdquo; (MSS. E, fol. </s>

<s>62). Il Cardano vedeva invece in quella incurvatura <lb/>l'apparenza di una parabola e atterrito dalla difficolt&agrave; di dimostrarla geome&shy;<lb/>tricamente tale, si content&ograve; di osservare che, uscendo l'acqua libera dalla <lb/>bocca di un sifone, non prosegue nella sua prima dirittura, n&egrave; cade perpen&shy;<lb/>dicolare, ma tiene una via di mezzo, descrivendo nelle prime parti del suo <lb/><figure id="id.020.01.3100.1.jpg" xlink:href="020/01/3100/1.jpg"/></s></p><p type="caption">

<s>Figura 23.<lb/>moto una linea, che si rassomiglia molto <lb/>a un arco di parabola. </s>

<s>&ldquo; Aquae, quae <lb/>per canales efferuntur, media linea effluunt <lb/>inter lineam descensus et rectam. </s>

<s>Velut <lb/>aqua per canalem delata AB (fig. </s>

<s>23) <lb/>deberet, toto impetu servato, effundi per <lb/>BC. </s>

<s>Et si nullum haberet impetum, per <lb/>BD, quod videmus in aquis, quae a late&shy;<lb/>ribus canalium, non ab ore effunduntur. </s>

<s>Igitur, iuxta rationem mediam, <lb/>feretur primum per partem BE. </s>

<s>Inde eo magis removebitur a C, quo etiam <lb/>a B, et ita ad F: infra vero F, recta, per aequidistantem BD &rdquo; (<emph type="italics"/>De rerum <lb/>var.<emph.end type="italics"/> cit., pag. </s>

<s>65). </s></p><p type="main">

<s>Se per&ograve; era tuttavia lontano colui, che avrebbe dimostrata la teoria pa&shy;<lb/>rabolica de'proietti, il'Nemorario aveva dato gi&agrave; fondamento alla futura Di&shy;<lb/>namica galileiana, ponendo il principio che i cadenti lungo piani, comunque <lb/>siansi inclinati, raggiungono in fine la medesima velocit&agrave;, come se fossero <lb/>venuti per linea perpendicolare. </s>

<s>Non bisognava per ci&ograve; far altro che ridurre <lb/>i piani inclinati a canali o a sifoni, perch&egrave;, essendo anche l'acqua un corpo <lb/>grave, fiorisse nella scuola dello stesso Nemorario questo capitalissimo teo&shy;<lb/><figure id="id.020.01.3100.2.jpg" xlink:href="020/01/3100/2.jpg"/></s></p><p type="caption">

<s>Figura 24.<lb/>rema d'Idrodinamica, da Leonardo cos&igrave; annun&shy;<lb/>ziato: &ldquo; La obliquit&agrave; del corso dell'acqua adopera <lb/>come se fussi perpendicolare: tanto fa l'obliquit&agrave; <lb/>AM (fig. </s>

<s>24), quanto il perpendicolare AN &rdquo; <lb/>(MSS. H, fol. </s>

<s>73). Il Cardano poi esplicava il con&shy;<lb/>cetto, frettolosamente qui espresso, e da'sifoni <lb/>chiusi passando ai canali aperti, mostrava che <pb xlink:href="020/01/3101.jpg" pagenum="62"/>ne'vari punti B, C, D.... (fig. </s>

<s>25) le velocit&agrave; dell'acqua son quelle con&shy;<lb/>venienti alle loro cadute, cosicch&egrave; giungono allo sbocco E con impeto, come <lb/><figure id="id.020.01.3101.1.jpg" xlink:href="020/01/3101/1.jpg"/></s></p><p type="caption">

<s>Figura 25.<lb/>se fossero da A scese in F, per altezza per&shy;<lb/>pendicolare. </s>

<s>&ldquo; Cum igitur fluxerit per lon&shy;<lb/>gius iter, lineam que eamdem rectam, quanto <lb/>magis a principio ortus distiterit, eo velo&shy;<lb/>cius movebitur. </s>

<s>Sit enim aqua, quae fluat <lb/>per ABCDE. </s>

<s>Sit FE libella, seu AG, ferme <lb/>aequidistans: dico ergo quod, cum CL sit dupla BH, et DL eidem tripla, <lb/>et GE quadrupla; quod motus etiam erit velocior, quo remotior aqua a <lb/>fonte &rdquo; (<emph type="italics"/>De rerum var.<emph.end type="italics"/> cit., pag. </s>

<s>72). </s></p><p type="main">

<s>Si sa oramai dalla storia della Meccanica che ambedue i commemorati <lb/>Autori professavano il principio, altro fondamento alla dinamica galileiana, <lb/>che un corpo sferico, posato sopra un piano perfettamente orizontale, astra&shy;<lb/>zion fatta da ogni altro impedimento, pu&ograve; esser mosso da qualunque minima <lb/>forza; e che, cos&igrave; essendo mosso, proseguirebbe sempre colla medesima ve&shy;<lb/>locit&agrave; il suo viaggio. </s>

<s>Fatta l'applicazione di questo stesso principio al corso <lb/><figure id="id.020.01.3101.2.jpg" xlink:href="020/01/3101/2.jpg"/></s></p><p type="caption">

<s>Figura 26.<lb/>dell'acqua dentro il tubo AM, perfettamente <lb/>livellato (fig. </s>

<s>26), ne'punti A, M, e in tutti <lb/>gli altri, variamente distanti dal principio del <lb/>moto R; passer&agrave; dunque l'acqua ugualmente <lb/>veloce; ond'essendo per supposizione i sifoni <lb/>AN, MO egualmente inclinati, e di uguale lunghezza, tanto sar&agrave; veloce, e <lb/>perci&ograve; in tanta copia uscir&agrave; l'acqua dalla bocca N, quanta ne esce dalla <lb/>bocca O, come in una sua nota scrive Leonardo: &ldquo; Se tu torrai l'acqua da <lb/>una altra acqua, che sia di pari livello, con uguale obliquit&agrave;, sappi che tanto <lb/>fia a torla vicino al loco R, con la caduta AN, quanto lontano in MO &rdquo; <lb/>(MSS. N, fol. </s>

<s>87). </s></p><p type="main">

<s>Altro corollario del medesimo Teorema &egrave; il seguente: Se saranno due <lb/>sifoni ugualmente inclinati, ma di varia lunghezza come, AM, AP (nella <lb/>passata figura 24) dalla bocca P del pi&ugrave; lungo uscir&agrave; l'acqua maggiormente <lb/>veloce, che dalla bocca M del pi&ugrave; corto, perch&egrave; l'altezza AQ, alla AN, ha <lb/>maggior proporzione. </s>

<s>&ldquo; L'acqua cadente da un mdesimo livello, per canali <lb/>di eguali obliquit&agrave;, quella sar&agrave; di pi&ugrave; veloce corso, che fia di maggiore lun&shy;<lb/>ghezza &rdquo; (MSS. H, fol. </s>

<s>39). </s></p><p type="main">

<s>Dietro i quali principii &egrave; facile intendere come risolvesse Leonardo al&shy;<lb/>cuni problemi, che si trovano ne'manoscritti di lui semplicemente proposti, <lb/><figure id="id.020.01.3101.3.jpg" xlink:href="020/01/3101/3.jpg"/></s></p><p type="caption">

<s>Figura 27.<lb/>quali sarebbero per esempio i due seguenti: <lb/>I. &ldquo; L'acqua AB (fig. </s>

<s>27), che discende, quanto <lb/>monter&agrave; in BC? &rdquo; (MSS. K, fol. </s>

<s>99). La ri&shy;<lb/>sposta a ci&ograve;, dietro i professati principii, &egrave; <lb/>manifestamente tale: essendo la discesa retta <lb/>AD, l'acqua salir&agrave; fino a tal punto O, che le <lb/>perpendicolari OE, AD tornino uguali. </s>

<s>&mdash; <pb xlink:href="020/01/3102.jpg" pagenum="63"/>II. &ldquo; L'acqua CN (fig. </s>

<s>28) &egrave; piana: domando quanto verser&agrave; pi&ugrave; presto essa <lb/>aqua il canale AC, che il canale BC &rdquo; (MSS. H, fol. </s>

<s>89). Un discepolo, cos&igrave; <lb/><figure id="id.020.01.3102.1.jpg" xlink:href="020/01/3102/1.jpg"/></s></p><p type="caption">

<s>Figura 28.<lb/>interrogato, darebbe questa risposta, con piena <lb/>sodisfazion del Maestro: Essendo gli spazi AC, <lb/>BC, per supposizione uguali, e perci&ograve; avendo i <lb/>tempi reciproca ragione delle velocit&agrave;, le quali <lb/>stanno come le altezze; l'acqua dunque tanto si <lb/>verser&agrave; pi&ugrave; presto dalla bocca B, che dalla bocca <lb/>A, quanto l'altezza CE &egrave; maggiore della CD. </s></p><p type="main">

<s>Ritornando sul problema primo, l'acqua giunta in O rimarr&agrave; nelle due <lb/>canne AB, BO, con congiunzione angolare, senza movimento, e ci&ograve; &ldquo; perch&egrave;, <lb/>dice Leonardo, tanto pesa l'acqua AB, quanto l'acqua BO &rdquo; (<emph type="italics"/>Arconati,<emph.end type="italics"/><lb/>pag. </s>

<s>436). E poi soggiunge nel capitoletto appresso: &ldquo; Tal movimento far&agrave; <lb/>l'acqua per la cicognola qua di sopra ABO qual'essa farebbe se corresse <lb/>per la linea AB &rdquo; (ivi). Dunque l'elemento liquido A giunto in B ha con&shy;<lb/>cepito per la discesa tant'impeto, da risalire in O alla medesima altezza, se&shy;<lb/>condo i principii, che poi si professerebbero da Galileo. </s>

<s>Dipende senza dub&shy;<lb/><figure id="id.020.01.3102.2.jpg" xlink:href="020/01/3102/2.jpg"/></s></p><p type="caption">

<s>Figura 29.<lb/>bio da tali principii il teorema noto del Torricelli, <lb/>intorno a cui anche Leonardo pensava che, ne'vasi <lb/>comunicanti rappresentati per noi dalla fig. </s>

<s>29, il <lb/>libero zampillo A, e l'acqua dentro la canna B do&shy;<lb/>vevano giungere al livello C del liquido, da cui sono <lb/>spinti. </s>

<s>Poi gli venne dubbio se la forza del getto fosse <lb/>alquanto maggiore, per non essere impedita dalle <lb/>confregazioni con le pareti del tubo, come apparisce da questa nota: &ldquo; Se <lb/>l'acqua, schizzata in A dalla canna, &egrave; mossa da maggior potentia, che da <lb/>quella della canna B &rdquo; (MSS. K, fol. </s>

<s>98): dubbio risoluto poi dalle espe&shy;<lb/>rienze del Mariotte, che confermarono essere veramente cos&igrave;, come Leonardo <lb/>stesso aveva sospettato. </s></p><p type="main">

<s>Tanto basti per avere un'idea dello stato, in cui, tra il secolo XV e <lb/>il XVI, si trovava l'Idrodinamica. </s>

<s>Ora &egrave; da dire delle applicazioni di lei, e <lb/>prima di tutto al modo di misurare le acque nel dispensarle a once, per gli <lb/>usi del pubblico e dei privati. </s></p><p type="main">

<s>Essendo stato dimostrato che le quantit&agrave; hanno la ragion composta delle <lb/>velocit&agrave; e delle sezioni, veniva per conseguenza che fossero esse quantit&agrave; alle <lb/>semplici velocit&agrave; proporzionali, passando l'acqua per la medesima bocca. </s>

<s>&ldquo; La <lb/>misura dell'once, dice Leonardo, che si danno nelle bocche dell'acqua, son <lb/>maggiori o minori, secondo le maggiori o minori velocit&agrave; dell'acqua, che per <lb/>essa bocca passa. </s>

<s>Doppia velocit&agrave; d&agrave; doppia acqua, in un medesimo tempo, <lb/>e cos&igrave; tripla velocit&agrave;, in un medesimo tempo, dar&agrave; tripla quantit&agrave; d'acqua &rdquo; <lb/>(MSS. F, fol. </s>

<s>16). </s></p><p type="main">

<s>Questa legge sarebbe assoluta, se non fossero le velocit&agrave; soggette ad al&shy;<lb/>terazioni, delle quali alcune cause furono avvertite gi&agrave; da Frontino, e dai <lb/>Pretori romani, ma assai pi&ugrave; ne pensarono i Fisici del secolo XV, alle quali <pb xlink:href="020/01/3103.jpg" pagenum="64"/>il nostro Leonardo ne aggiunse altre di suo, riducendole a uu buon numero, <lb/>che nonostante sperava di accrescere anche di pi&ugrave;, com'apparisce dalla cifra <lb/>lasciata in bianco nell'elenco, che di queste XVII intanto lasciava, cos&igrave;, in <lb/>una sua nota ordinatamente descritto: &ldquo; L'acqua, che versa per una mede&shy;<lb/>sima quantit&agrave; di bocca, si pu&ograve; variare di quantit&agrave; maggiore o minore per .... <lb/>modi, de'quali il I &egrave; da essere pi&ugrave; alta o pi&ugrave; bassa la superficie dell'acqua <lb/>sopra la bocca d'onde versa. </s>

<s>&mdash; II. </s>

<s>Da passare l'acqua con maggiore o mi&shy;<lb/>nore velocit&agrave; da quell'argine, dov'&egrave; fatta essa bocca. </s>

<s>&mdash; III. </s>

<s>Da essere pi&ugrave; <lb/>o meno obliquo il lato di sotto della grossezza della bocca, dove l'acqua <lb/>passa. </s>

<s>&mdash; IV. </s>

<s>Dalla variet&agrave; dell'obliquit&agrave; de'lati di tal bocca. </s>

<s>&mdash; V. </s>

<s>Dalla <lb/>grossezza del labbro di essa bocca. </s>

<s>&mdash; VI. </s>

<s>Per la figura della bocca: cio&egrave; <lb/>da essere tonda o quadra o rettangolare o lunga. </s>

<s>&mdash; VII. </s>

<s>Da essere posta <lb/>essa bocca in maggiore o minore obliquit&agrave; d'argine, per la sua lunghezza. <lb/></s>

<s>&mdash; VIII. </s>

<s>Per essere posta tal bocca in maggiore o minore obliquit&agrave; d'argine, <lb/>per la sua altezza. </s>

<s>&mdash; IX. </s>

<s>Da essere posta nella concavit&agrave; o convessit&agrave; del&shy;<lb/>l'argine. </s>

<s>&mdash; X. </s>

<s>Da essere posta ovvero in maggiore, o minore larghezza del <lb/>canale. </s>

<s>&mdash; XI. </s>

<s>Se l'altezza del canale ha pi&ugrave; velocit&agrave; nell'altezza della bocca, <lb/>o pi&ugrave; tardit&agrave; che altrove. </s>

<s>&mdash; XII. </s>

<s>Se il fondo ha globosit&agrave; o convessit&agrave;, a <lb/>riscontro di essa bocca o pi&ugrave; alte o pi&ugrave; basse. </s>

<s>&mdash; XIII. </s>

<s>Se l'acqua, che <lb/>passa per tal bocca, piglia vento o no. </s>

<s>&mdash; XIV. </s>

<s>Se l'acqua, che cade fuor <lb/>dalla bocca, cade in fra l'aria, ovvero rinchiusa da un lato, o da tutti, salvo <lb/>la fronte. </s>

<s>&mdash; XV. </s>

<s>Se l'acqua, che cade rinchiusa, sar&agrave; grossa nel suo peso <lb/>o sottile. </s>

<s>&mdash; XVI. </s>

<s>Se l'acqua che cade, essendo rinchiusa, sar&agrave; lunga di ca&shy;<lb/>duta o breve. </s>

<s>&mdash; XVII. </s>

<s>Se i lati del canale, d'onde discende tale acqua, <lb/>saran solli o globulosi &rdquo; (ivi, fol. </s>

<s>9). </s></p><p type="main">

<s>Il Cardano, delle cause, che fanno variar le velocit&agrave;, e perci&ograve; le misure <lb/>delle acque correnti; non ne annovera molte di pi&ugrave; di quelle, venute in <lb/>mente a Frontino, a cui volentieri concede che, tanto pi&ugrave; se ne attinga da <lb/>un fiume, quanto egli &egrave; pi&ugrave; alto e veloce. </s>

<s>Ma son notabili, fra cos&igrave; fatte cause <lb/>modificatrici delle velocit&agrave;, quelle, che egli attribuisce allo spirare de'venti, <lb/>e alla disposizione e figura dei tubi addizionali, bench&egrave; sembrino strani gli <lb/>effetti, da lui stesso attribuiti alla qualit&agrave; della materia, di che si compon&shy;<lb/>gono essi tubi. </s>

<s>&ldquo; Venti enim, si quandoque possint obesse, solent et pro&shy;<lb/>desse. </s>

<s>Constat ergo, ubi venti certi regnant, aliquos plus accipere, aliquos <lb/>minus longe quam debeant. </s>

<s>Plurimum quoque referre an aqua a latere rivi, <lb/>an ab ore sumatur. </s>

<s>Sed haee minora videntur, quandoquidem referat Fron&shy;<lb/>tinus, Nervae aetate, Romanos adeo oscitanter aquarum rationem tractasse, <lb/>ut dimidio aberrarent. </s>

<s>Plurimum quoque refert si per fistulam, quae plerum&shy;<lb/>que metallo constat, aut tubis fietilibus, aut canali ligneo, nam, non ob ma&shy;<lb/>teriam differunt, sed quia canalis haud clausus est, verum respirat. </s>

<s>Educuntur <lb/>tamen aquae plerumque tubis aut fistulis, quoniam canalis aquam effluen&shy;<lb/>tem spargit, ob id igitur privat<gap/>rum usus a fistulis et tubis, non autem ea&shy;<lb/>ualibus, sumuntur. </s>

<s>Multum quoque refert quomodo calix collo<gap/>tur, ut inquit <lb/>Frontinus. </s>

<s>Circa collocandos quoque calices observari oportet ut ad lineam <pb xlink:href="020/01/3104.jpg" pagenum="65"/>ordinentur, nec alterius inferior calix, alterum superior ponatur: inferior plus <lb/>trahit, superior minus ducit, quia cursus aquae ab inferiore rapitur. </s>

<s>Haec <lb/>ille &rdquo; (<emph type="italics"/>De r&eacute;rum var.<emph.end type="italics"/> cit., pag. </s>

<s>66). </s></p><p type="main">

<s>Altre cause ritardatrici delle velocit&agrave; riconosce il Cardano, alcune delle <lb/>quali son fra quelle annoverate da Leonardo, ma di cui quegli spesso rende <lb/>la'ragione, dedotta da principii fisici pi&ugrave; sani, e che risentono talora il leg&shy;<lb/>gero alitare di una scienza lontana. </s>

<s>C'incontreremo e c'intratterremo sopra <lb/>qualche pi&ugrave; notabile esempio di ci&ograve; nel ritornare all'elenco di esso Leonardo, <lb/>per ritrovarvi i vestigi lasciativi dalla Scienza, talvolta nelle sue cadute, ma <lb/>pi&ugrave; spesso ne'suoi progressi, primo a notar fra'quali &egrave; l'osservazione intorno <lb/>al variarsi le velocit&agrave;, per la variet&agrave; del perimetro di una sezione, pur ser&shy;<lb/>bandosi dall'area di lei la medesima ampiezza. </s>

<s>La cosa, accennata dianzi <lb/>nel sesto numero del detto elenco, &egrave; spiegata altrove cos&igrave;, nella sua ragione <lb/>geometrica: &ldquo; Fra le bocche dell'acqua, poste in altezze uguali sotto la su&shy;<lb/><figure id="id.020.01.3104.1.jpg" xlink:href="020/01/3104/1.jpg"/></s></p><p type="caption">

<s>Figura 30.<lb/>perficie dell'acqua del suo bottino, quella che ha men con&shy;<lb/>tatto con l'acqua, che per li passa, meno impedir&agrave; il tran&shy;<lb/>sito a essa acqua. </s>

<s>A e B (fig. </s>

<s>30) siano le bocche uguali, <lb/>A quadrato, e B circolo. </s>

<s>Dico che l'acqua, che passa per <lb/>la bocca circolare, ar&agrave; men contatto che l'acqua, che <lb/>passa per il quadrato, uguale a esso circolo, perch&egrave; pi&ugrave; <lb/>lunga &egrave; la linea, che circuisce il quadrato, che quella, <lb/>che circuisce il tondo &rdquo; (MSS. F, fol. </s>

<s>55). </s></p><p type="main">

<s>Da questa proposizione vedeva opportunamente Leonardo scendere un <lb/>corollario, che gli dava modo a risolvere il seguente problema: &ldquo; Che figura <lb/>ar&agrave; una medesima quantit&agrave; d'acqua, movendosi per una medesima obliquit&agrave; <lb/>di fondo, a farsi pi&ugrave; veloce che sia possibile? </s>

<s>&mdash; Fia quella che ar&agrave; minore <lb/>contatto col suo fondo, cio&egrave; mezzo cerchio &rdquo; (MSS. E, fol. </s>

<s>105). </s></p><p type="main">

<s>In questo argomento osservava il Nostro un'altra cosa importante, messa <lb/>cos&igrave; in forma di proposizione: &ldquo; Delle bocche uguali, e di uguale altezza, <lb/>quella verser&agrave; pi&ugrave; acqua, in pari tempo, che ar&agrave; maggiore somma di s&egrave;, <lb/>nella sua parte inferiore, che nella parte di sopra &rdquo; (MSS. F, fol. </s>

<s>54). La <lb/>dimostrazione di ci&ograve; &egrave; affidata tutta all'eloquenza de'segni, rappresentativi <lb/>il medesimo triangolo isoscele, ora colla base in alto, ora col vertice, come <lb/><figure id="id.020.01.3104.2.jpg" xlink:href="020/01/3104/2.jpg"/></s></p><p type="caption">

<s>Figura 31.<lb/>si vede in A, B <lb/>(fig. </s>

<s>31). Siano le <lb/>loro altezze per&shy;<lb/>pendicolaritaglia&shy;<lb/>te nel mezzo dal&shy;<lb/>la orizontale CD. </s>

<s><lb/>La EP &egrave; maggior <lb/>somma della par&shy;<lb/>te GHI, e perch&egrave; <emph type="italics"/>inferior plus rapitur,<emph.end type="italics"/> secondo lo stesso Frontino, &egrave; dun&shy;<lb/>que maggiore la quantit&agrave; dell'acqua velocitata in B, che in A, e perci&ograve; <lb/>quella, in pari tempo, verser&agrave; pi&ugrave; di questa. </s></p><pb xlink:href="020/01/3105.jpg" pagenum="66"/><p type="main">

<s>Si dispongano similmente il circolo L, e il quadrato M, in modo cio&egrave; <lb/>che le loro estremit&agrave; inferiori insistano sulla medesima linea orizontale NO. <lb/>&Egrave; manifesto che la parallela a questa, fatta passare per il centro Q del qua&shy;<lb/>drato, prolungata riman sotto al centro P del circolo, per cui, essendo la <lb/>quantit&agrave; dell'acqua RST tutta insieme men premuta della sua uguale quan&shy;<lb/>tit&agrave; UVX, quella passer&agrave; men veloce di questa, e perci&ograve; in tal caso il cir&shy;<lb/>colo, dal mezzo in gi&ugrave;, verser&agrave;, in pari tempo, alquanto men del quadrato. </s>

<s><lb/>Di qui, comparando le portate di queste due bocche con quell'altre due trian&shy;<lb/>golari gi&agrave; dette, si comprende secondo qual ragione sentenziasse Leonardo: <lb/>&ldquo; Queste quattro bocche sono in fra loro uguali, e co'loro estremi posti in <lb/>altezze uguali. </s>

<s>L versa meno, dal mezzo in gi&ugrave;, di M, e men A che B &rdquo; <lb/>(MSS. F, fol. </s>

<s>54). A che, per rendere queste sperimentali verit&agrave; pi&ugrave; com&shy;<lb/>piute, pu&ograve; aggiungersi l'altra conclusione: &ldquo; Delle bocche di ugual lar&shy;<lb/>ghezza, figura e altezza, quella verser&agrave; pi&ugrave; acqua in pari tempo, che sar&agrave; <lb/>in pi&ugrave; sottile pariete, ovvero che aver&agrave; pi&ugrave; breve contatto co'lati della sua <lb/>bocca &rdquo; (ivi, fol. </s>

<s>55). </s></p><p type="main">

<s>In simile proposito, e dietro simili considerazioni, concludeva anche il <lb/>Cardano: &ldquo; Constat igitur aquarum ductus, non ex fistularum magnitudine <lb/>consistere, sed si proportio latitudinis servetur &rdquo; <emph type="italics"/>(De rer. </s>

<s>var.<emph.end type="italics"/> cit., pag. </s>

<s>73). <lb/>Sia, ritornando indietro sulla XVII figura, CB la bocca dell'oncia, e si vo&shy;<lb/>glia quadruplicarla. </s>

<s>Geometricamente si conseguirebbe ci&ograve; tanto col quadru&shy;<lb/>plicare la semplice larghezza AB, quanto col duplicar questa, e insieme l'al&shy;<lb/>tezza AC. </s>

<s>Or bench&egrave;, per le cose dimostrate da Euclide, le due aree siano <lb/>perfettamente uguali, non si creda per&ograve;, dice il Cardano, che quattr'oncie <lb/>sian versate dall'una, ugualmente che dall'altra, ma faranno differenza no&shy;<lb/>tabile, dipendente dalla varia distanza, in cui rimangono i centri delle due <lb/>figure sotto il livello del recipiente. </s>

<s>&ldquo; Quare solum quadratas superficies <lb/>iuxta latitudinem basis commensurare licebit aquam, non secundum lineas <lb/>proportionales medias &rdquo; (ihid.). </s></p><p type="main">

<s>Ma ritornando sopra l'elenco ordinato da Leonardo, ci occorre a consi&shy;<lb/>derare quel che dice sotto il numero VIII, spiegato meglio cos&igrave;, nella com&shy;<lb/>pilazione dell'Arconati: &ldquo; Quanto l'argine, dove &egrave; posta la bocca dell'oncia <lb/>dell'acqua, fia pi&ugrave; obliqua nella sua altezza inverso la caduta della bocca <lb/>dell'acqua, tanto maggior quantit&agrave; d'acqua verser&agrave; la sua bocca. </s>

<s>Provasi, <lb/>perch&egrave; l'acqua nella bocca in tal caso caderebbe per linea pi&ugrave; obliqua, e <lb/>per la XXI del V quell'acqua &egrave; pi&ugrave; veloce, che discende per linea pi&ugrave; obli&shy;<lb/>qua, e per la XXVIII del medesimo l'acqua, che cade per linea pi&ugrave; vicina <lb/>alla perpendicolare, pi&ugrave; presto discende &rdquo; (pag. </s>

<s>426, 27). </s></p><p type="main">

<s>Le due proposizioni qui citate, e che non &egrave; possibile riscontrare, perch&egrave; <lb/>la stesura di que'due libri rimase nel pensiero; son quelle medesime, che il <lb/>Cardano riduceva cos&igrave; a postulati: &ldquo; Constat etiam quod velocissimus mo&shy;<lb/>tus est, qui fit ex maiore altitudine, in aequali spacio, aut aequali altitudine, <lb/>in minore spacio &rdquo; <emph type="italics"/>(De rer. </s>

<s>var.<emph.end type="italics"/> cit., pag. </s>

<s>63). Ma come, si domander&agrave;, sono <lb/>applicabili all'obliquit&agrave; degli argini cos&igrave; fatti principii? </s>

<s>N&egrave; si pu&ograve; dare al <pb xlink:href="020/01/3106.jpg" pagenum="67"/>quesito la sua debita risposta, senza esplicare il concetto di Leonardo, che <lb/>&egrave; tale: S'immagini l'argine con la sponda esterna AE (fig. </s>

<s>32) perpendi&shy;<lb/>colare, ma con l'interna ora pi&ugrave; obliqua, come AB, ora meno, come AC, e <lb/><figure id="id.020.01.3106.1.jpg" xlink:href="020/01/3106/1.jpg"/></s></p><p type="caption">

<s>Figura 32.<lb/>una fistola DC penetri attraverso esso argine, da cui at&shy;<lb/>tinga ora dalla bocca, B, ora dalla C l'acqua del fiume. </s>

<s><lb/>Dice il Nostro che, scendendo per la linea AB, pi&ugrave; vicina <lb/>alla perpendicolare, il liquido pi&ugrave; veloce, che per la linea <lb/>AC; anche pi&ugrave; veloce imboccher&agrave; per B, che per C. </s>

<s>La <lb/>conclusione &egrave; falsa in se, e in contradizione con le cose <lb/>precedentemente dimostrate dal medesimo Autore, secondo <lb/>le quali, essendo in B e in C l'acqua scesa dalla me&shy;<lb/>desima altezza, dovrebbe avervi anche acquistati impeti <lb/>uguali. </s>

<s>Ma non faccia maraviglia che rimanesse un Fisico <lb/>del secolo XV irretito in una fallacia, alla quale furon presi, come vedremo, <lb/>alcuni fra i pi&ugrave; eletti discepoli di Galileo. </s></p><p type="main">

<s>Fra le cause, che fanno variare le velocit&agrave; dell'acqua, annovera Leo&shy;<lb/>nardo, in IX luogo, l'esser poste le fistole in argine concavo. </s>

<s>E quivi in <lb/>verit&agrave;, come specialmente s'osserva nelle piene, la superficie dell'acqua &egrave; <lb/>pi&ugrave; alta che altrove, ma &egrave; un inganno il credere che da tale altezza si pro&shy;<lb/>duca maggior pressione, e perci&ograve; maggiore velocit&agrave; nella fistola sottoposta. </s>

<s><lb/>La velocit&agrave; straordinaria, con cui per la forza centrifuga, son dentro alla detta <lb/>concavit&agrave; spinti gli strati liquidi, gli fa essere specificamente pi&ugrave; leggeri, e <lb/>perci&ograve; debbono sollevarsi, come l'olio nel sifone, per mettersi in equilibrio <lb/>con gli strati acquei comunicanti, e pi&ugrave; gravi. </s></p><p type="main">

<s>Da questa medesima fallacia &egrave; informata l'osservazione XI, ma la XIII <lb/>&egrave; giusta, specialmente ridotta alle ragioni, che si spiegano altrove: &ldquo; L'acqua, <lb/>che cade per linea perpendicolare si fa acuta in una parte del suo descenso, <lb/>e il condotto d'onde cadea resta vacuo. </s>

<s>E qui combatte l'aria con l'acqua, <lb/>come si dir&agrave; a suo loco, ma non dimenticher&ograve; per&ograve; di dire che tal descenso <lb/>d'acqua &egrave; impedito dalla condensazione dell'aria nel condotto di essa acqua &rdquo; <lb/>(MSS. E, fol. </s>

<s>103). </s></p><p type="main">

<s>Ci&ograve; che si dice sotto i numeri XIV, XV e XVI ha maggiore importanza <lb/>storica, toccandovisi questioni, che si crede essere state solamente risolute <lb/>dagli Idraulici moderni, come quella, per esempio, che, dentro i tubi, scende <lb/>l'acqua da pari altezza pi&ugrave; veloce che fra l'aria. </s>

<s>Anche le cause modifica&shy;<lb/>trici delle velocit&agrave;, secondo la ragion della lunghezza o della grossezza delle <lb/>canne, e le variet&agrave; fatte dall'andar l'acqua per canale tutt'intorno chiuso, <lb/>o di sopra aperto; riconosciute cos&igrave; bene infin da que'tempi, son degne di <lb/>nota. </s>

<s>&ldquo; L'acqua, che per diretto discense si move, per canna di uniforme <lb/>larghezza, sar&agrave; tanto pi&ugrave; veloce, quanto tal canna fia pi&ugrave; lunga. </s>

<s>&mdash; L'acqua, <lb/>che per diretto descenso si move per canne di uguali lunghezze, fia di tanto <lb/>pi&ugrave; veloce moto, quanto tali canne fiano di maggiori larghezze. </s>

<s>E questo si <lb/>prova, perch&egrave; la linea centrale di tale acqua &egrave; pi&ugrave; remota dalla confreca&shy;<lb/>tione della canna larga, che della stretta, e per questo il suo moto &egrave; meno <pb xlink:href="020/01/3107.jpg" pagenum="68"/>impedito, e per questo si fa pi&ugrave; veloce. </s>

<s>&mdash; L'acqua, che si move per canna <lb/>equigiacente, &egrave; pi&ugrave; grossa che quella, che corre per canale scoperto, e mas&shy;<lb/>sime, quando tal canna riceve l'acqua perpendicolare, e la lascia perpendi&shy;<lb/>colare &rdquo; (ivi, fol. </s>

<s>12). </s></p><p type="main">

<s>Nella compilazione dell'Arconati s'aggiunge, per provare la verit&agrave; qui <lb/>in terzo luogo proposta: &ldquo; Questo accade per quello, che &egrave; detto nella XX <lb/>del V, perch&egrave; quella parte dell'acqua cadente, che &egrave; contigua all'aria, si <lb/>mischia con l'aria, e si fa pi&ugrave; lieve. </s>

<s>E quanto &egrave; pi&ugrave; lieve, pi&ugrave; si tarda &rdquo; <lb/>(pag. </s>

<s>431). Ma il Cardano aveva intorno a ci&ograve; idee molto pi&ugrave; sane. </s>

<s>&rdquo; Itaque, <lb/>egli dice, haud dubium est aquas, quae per fistulas et siphones deducuntur, <lb/>et impetu et continuitate agi. </s>

<s>Quae vero per canales, rivos et locos paten&shy;<lb/>tes, solo impetu. </s>

<s>Quamobrem velocius semper fertur aqua per siphones, quam <lb/>per rivos, pari ratione, paribusque auxiliis ac impedimentis constitutis &rdquo; <emph type="italics"/>(De <lb/>rer. </s>

<s>var.<emph.end type="italics"/> cit., pag. </s>

<s>63). La ragione del doversi l'acqua mantenere ne'tubi <lb/>continua, e andarvi perci&ograve; pi&ugrave; veloce che nel canale scoperto, il Cardano la <lb/>riconosce nell'aria, alla quale egli attribuisce il peso, come a tutti gli altri <lb/>corpi, mentre Leonardo la faceva positiva causa della leggerezza. </s>

<s>Nella teoria <lb/>del sifone ritorto spiega meglio esso Cardano l'azione del peso dell'aria, che <lb/>efficacemente concorre a mantenervi il flusso continuo, cos&igrave; dicendo: &ldquo; Deni&shy;<lb/>que tota haec contemplatio absolvitur hoc argumento: quod aqua, quae debet <lb/>trahere aliam aquam secum, oportet ut vase contineatur, quoniam sine illo <lb/>convelli nequit, sed ab aere iuvatur adveniente, et ut corpus continuum ad <lb/>aequilibrium perveniat &rdquo; <emph type="italics"/>(De subtilitate,<emph.end type="italics"/> Lugduni 1580, pag. </s>

<s>25). Le quali <lb/>dottrine, inspirate forse da Herone Alessandrino, aspettavano di ricevere dalla <lb/>scoperta del Torricelli la loro ultima perfezione. </s></p><p type="main">

<s>Finalmente, per esaurir questo esame intorno all'elenco di Leonardo, <lb/>osserveremo che l'ultima assegnata causa, per cui una medesima bocca di <lb/>erogazione pu&ograve; variare di quantit&agrave;, l'abbiamo trascritta: <emph type="italics"/>Se i lati del ca&shy;<lb/>nale, d'onde discende tale acqua, saran solli o globulosi.<emph.end type="italics"/> L'Arconati in&shy;<lb/>terpetr&ograve; <emph type="italics"/>sodi o globulosi<emph.end type="italics"/> (pag. </s>

<s>420), n&egrave; punto meglio sembra a noi tradu&shy;<lb/>cesse il Ravaisson-Mollien <emph type="italics"/>mous ou bossues,<emph.end type="italics"/> ma &egrave; un fatto che deve inten&shy;<lb/>dersi solli o globulosi, cio&egrave; levigati o aspri. </s></p><p type="main">

<s>Le XVII recensite cause, che fanno variare le portate, erano altrettanti <lb/>avvedimenti suggeriti ai dispensatori delle acque, e qui si arrestavano i be&shy;<lb/>nefizi della Scienza, la quale s'apparecchiava di farne altri migliori, intorno <lb/>al modo di regolare il corso dei fiumi. </s>

<s>I moderni Idraulici fecero il gran <lb/>passo, applicando a quest&igrave; le scoperte leggi degli efflussi da'vasi; e come il <lb/>Wolf, per esempio, nel corollario V dopo il XXVIII teorema della sua Idrau&shy;<lb/>lica (Elem. </s>

<s>Matheseos univ., T. II, Genevae 1746, pag. </s>

<s>374), intendeva che <lb/>la velocit&agrave; nel punto E dell'alveo (fig. </s>

<s>25 qui addietro) fosse quella mede&shy;<lb/>sima, con cui uscirebbe ivi da un foro aperto nel vaso ACE l'acqua sta&shy;<lb/>gnante; cos&igrave; la intendeva il Cardano, di cui vedemmo essere dalla medesima <lb/>figura XXV illustrato il concetto, e la intendeva pure Leonardo da Vinci, il <lb/>quale, applicando il teorema <emph type="italics"/>che in ogni grado di altezza la canna acqui-<emph.end type="italics"/><pb xlink:href="020/01/3108.jpg" pagenum="69"/><emph type="italics"/>sta gradi di distantia, nel gettar da lontano,<emph.end type="italics"/> alle acque correnti ne'fiumi; <lb/>concludeva questa sua proposizione: &ldquo; Se un sostegno d&agrave; sopra di s&egrave; il tran&shy;<lb/>sito a una data quantit&agrave; d'acqua di due once di grossezza, e vi s'aggiunge <lb/>una terza oncia, allora l'oncia di sotto raddoppia la potenza, la velocit&agrave; e la <lb/>quantit&agrave; della prima acqua. </s>

<s>Provasi per la seguente, che mostra, delle acque <lb/>correnti sopra li fondi de'fiumi d'uniforme obliquit&agrave;, tali essere le propor&shy;<lb/>zioni della velocit&agrave; del moto, quale &egrave; quella delle loro altezze. </s>

<s>Adunque, se <lb/>la prima oncia detta di sopra fia premuta da un'altra oncia, e poi da due <lb/>once, senza dubbio la potenza che preme &egrave; duplicata, e per conseguenza, come <lb/>&egrave; detto, la velocit&agrave; e la quantit&agrave; &egrave; raddoppiata &rdquo; <emph type="italics"/>(Arconati,<emph.end type="italics"/> pag. </s>

<s>422). Que&shy;<lb/>sta proposizione, come fu bene da altri osservato, fa esatto riscontro con la <lb/>II del II libro del Castelli: &ldquo; Se un fiume, movendosi con una velocit&agrave; per <lb/>un suo regolatore, aver&agrave; una data altezza viva, e poi, per nuova acqua cre&shy;<lb/>scer&agrave; il doppio; crescer&agrave; ancora il doppio la velocit&agrave; &rdquo; <emph type="italics"/>(Della misura delle <lb/>acque corr.,<emph.end type="italics"/> Bologna 1660, pag. </s>

<s>82). </s></p><p type="main">

<s>Simili applicazioni, che mettevano sulla via d'intendere la natura dei <lb/>fiumi, si fecero da'tubi agli alvei, negli uni de'quali e negli altri si ritenne <lb/>che la velocit&agrave; allo sbocco fosse quella conveniente alla discesa perpendico&shy;<lb/>lare. </s>

<s>Ma cos&igrave; questa, come l'altra proposizione rinnovellata dal Castelli, non <lb/>son vere, se non che nella loro assoluta ragione, ossia, astraendo da ogni <lb/>sorta d'impedimenti, inevitabili in ogni caso, o si confreghi la corrente con <lb/>le pareti de'tubi, o col ghiareto, e con le ripe degli alvei. </s>

<s>&ldquo; Quanto l'acqua, <lb/>dice Leonardo, sar&agrave; pi&ugrave; distante dal fondo, tanto pi&ugrave; libera sar&agrave; nel suo na&shy;<lb/>tural moto (MSS. H, fol. </s>

<s>72). L'acqua, che corre presso al fondo, tra le rive, <lb/>sar&agrave; pi&ugrave; tarda che l'altra (ivi, fol. </s>

<s>77). L'acqua di sotto obbedisce manco <lb/>al suo naturale corso, che quella di sopra, e questo accade perch&egrave; l'acqua, <lb/>che confina con l'aria, non &egrave; aggravata da alcun peso, onde semplicemente, <lb/>senz'alcuno impedimento, ubbidisce al suo natural corso: quella di sotto &egrave; <lb/>aggravata e premuta &rdquo; (ivi, fol. </s>

<s>85). E tante altre cause incomputabili rico&shy;<lb/>nosceva Leonardo stesso concorrere ad alterare le velocit&agrave; naturali, che ebbe <lb/>a uscire in questa sentenza: &ldquo; Pochissime son le parti delle acque correnti, <lb/>che si trovano in fra la superficie e il fondo suo, che corrano a un mede&shy;<lb/>simo aspetto &rdquo; (MSS. F, fol., 47). </s></p><p type="main">

<s>Tutto questo, che si diceva dal Nostro, e in che consentivano gli altri, <lb/>non era per&ograve; che il frutto della speculazione, la quale sembrava ai pi&ugrave; che <lb/>contendesse co'fatti osservati. </s>

<s>Se non corrono le parti dell'acqua tutte a un <lb/>medesimo aspetto, com'&egrave;, dicevano costoro, che si mantengono unite, e con&shy;<lb/>tinuo si vede andare al suo termine il fiume? </s>

<s>La difficolt&agrave; era tale che, per <lb/>assicurarsi della verit&agrave; di quelle speculate conclusioni, fu necessario ricor&shy;<lb/>rere alle esperienze. </s>

<s>Una delle prime, occorse fra le pensate, dee essere stata <lb/>quella descritta cos&igrave; nella compilazione dell'Arconati: &ldquo; Se vuoi vedere dove, <lb/>in alcun luogo sopra la superficie, ed in alcuno sotto la superficie sia pi&ugrave; <lb/>veloce, getta acqua tinta, insieme con olio, sopra l'acqua corrente, ed avverti <lb/>al fine del corso chi prima giunge: cio&egrave;, se giunge prima l'olio, l'acqua <pb xlink:href="020/01/3109.jpg" pagenum="70"/>corre pi&ugrave; di sopra che di sotto; se giunge prima l'acqua tinta, il fiume corre <lb/>pi&ugrave; di sotto, che di sopra &rdquo; (pag. </s>

<s>307). </s></p><p type="main">

<s>L'esperienza per&ograve; non era praticabile, che ne'piccoli canali, e quand'an&shy;<lb/>che si fosse riusciti in questi a riconoscere il vero, poteva rimaner dubbio <lb/>nel passare ad applicarlo ai grandi corsi de'fiumi, intorno ai quali s'aggi&shy;<lb/><figure id="id.020.01.3109.1.jpg" xlink:href="020/01/3109/1.jpg"/></s></p><p type="caption">

<s>Figura 33.<lb/>rava tutta l'importanza della questione. </s>

<s>Di qui ebbe origine <lb/>quel primo Idrometro, l'invenzion del quale s'attribuisce al <lb/>Cabeo, ma che, a tergo del fol. </s>

<s>42 del MSS. A, Leonardo <lb/>rappresentava con questo disegno (fig. </s>

<s>33) dichiarandone cos&igrave; <lb/>le parti &ldquo; N sughero &mdash; AQ canna: falla avanzare in AN uno <lb/>braccio, acci&ograve; che per la piega del quadrello si veda quella <lb/>di AN. &rdquo; Quanto poi all'uso di un tale strumento si trova <lb/>nell'<emph type="italics"/>Arconati<emph.end type="italics"/> cos&igrave; descritto: &ldquo; Di una bacchetta, che sia di <lb/>sopra infilata in baga, e di sotto in sasso, quella parte, che <lb/>avanza di sopra alla baga, se pender&agrave; in verso all'avvenimento <lb/>dell'acqua, correr&agrave; l'acqua pi&ugrave; in fondo che di sopra: e, se detta bacchetta <lb/>pender&agrave; inverso il fuggimento dell'acqua, correr&agrave; il fiume pi&ugrave; di sopra che <lb/>di sotto: e, se resta diritta la bacchetta, il corso sar&agrave; di pari velocit&agrave; di <lb/>sotto e di sopra &rdquo; (pag. </s>

<s>306). </s></p><p type="main">

<s>Fu in questo modo esplorato che, quando la corrente &egrave; bassa, la super&shy;<lb/>ficie e il fondo restano uguali in velocit&agrave;, ma che, vicino alle cascate, &egrave; pi&ugrave; <lb/>veloce la superficie che il fondo: fatto verissimo, a cui poi gli Idraulici det&shy;<lb/>tero il nome di <emph type="italics"/>chiamata allo sbocco,<emph.end type="italics"/> e che anco Leonardo sembra attri&shy;<lb/>buisse alla viscosit&agrave; dell'acqua. </s>

<s>&ldquo; Coll'antidetta ragione, scriveva, si dimo&shy;<lb/>stra come i fiumi d'ugual fondo e larghezza, i quali ruinano il lor fine, che <lb/>corrono pi&ugrave; di sopra che di sotto, perch&egrave; nel fine l'acqua di sopra &egrave; pi&ugrave; ve&shy;<lb/>loce nel cadere, che quella di sotto: onde l'acqua superiore, che successiva&shy;<lb/>mente s'appoggia a quella &egrave; necessario che sia di tal moto, quanto fu quello <lb/>che &egrave; detto &rdquo; (MSS, I, fol. </s>

<s>89). </s></p><p type="main">

<s>Non tutti per&ograve; erano, di queste speculazioni, e di queste conclusioni spe&shy;<lb/>rimentali sodisfatti, e, durando tuttavia le controversie, ci entr&ograve; di mezzo il <lb/>Cardano. </s>

<s>Le prime difficolt&agrave;, che avevano fatto dubitare altrui se gli strati <lb/>acquei corressero tutti, come si diceva, a vario aspetto; ei l'ebbe in ogni <lb/>modo per decisive, &ldquo; quia necesse esset ut altior et humilior appareret, quod <lb/>tamen non contingit, nisi vel, dum alveus inaequalis est, vel flante vento &rdquo; <lb/><emph type="italics"/>(De rer. </s>

<s>var.<emph.end type="italics"/> cit., pag. </s>

<s>66). E aggiuntavi l'osservazione che nelle cascate <lb/>l'acqua non prosegue per la sua prima dirittura BC (fig. </s>

<s>23 qui addietro), <lb/>n&egrave; cade perpendicolare lungo BD, ma tiene la via di mezzo BE; si confer&shy;<lb/>mava nell'opinione che tutti gli strati, dall'imo al sommo, corressero in&shy;<lb/>sieme a un medesimo aspetto, ossia con tale uniforme velocit&agrave;, che, tra la <lb/>massima e la minima delle parti, resultasse al tutto la media. </s>

<s>&ldquo; Quamobrem <lb/>dicendum est aequaliter moveri imum aquae et supremum, in alveis aequa&shy;<lb/>libus, quoniam, dum effunditur a canali, etiam videntur partes aequaliter <lb/>ferri &rdquo; (ibid.). </s></p><pb xlink:href="020/01/3110.jpg" pagenum="71"/><p type="main">

<s>Ma si citavano in contrario le esperienze idrometriche, sull'andare di <lb/>quelle, che registrava ne'suoi quaderni Leonardo, a che rispondeva il Car&shy;<lb/>dano che lo strumento non diceva il vero, e che l'esser egli pi&ugrave; violente&shy;<lb/>mente spinto in basso, che in alto, o al contrario, non era segno certo che <lb/>la corrente fosse, su e gi&ugrave;, o pi&ugrave; o meno veloce, dovendosi attribuir ci&ograve; piut&shy;<lb/>tosto a un effetto necessario, dipendente dalla natura del vette. </s>

<s>&ldquo; Moveri au&shy;<lb/>tem velocius aquam in imo quam in summo, argumentum non est quod ba&shy;<lb/><figure id="id.020.01.3110.1.jpg" xlink:href="020/01/3110/1.jpg"/></s></p><p type="caption">

<s>Figura 34.<lb/>culus in imo sentiatur vehementer agi, atque abduci, ut <lb/>in C (fig. </s>

<s>34) quam in B; nam C longius ab hypomoclio <lb/>distat, ideo aequaliter fluere videtur &rdquo; (ibid., pag. </s>

<s>67). </s></p><p type="main">

<s>Queste opposizioni del Cardano, contro le esperienze <lb/>dell'Idrometro, forse erano state fatte da altri, ma rico&shy;<lb/>nosciutesi insussistenti, si confermarono gl'Idraulici nella <lb/>verit&agrave;, che gli strati, dalla superficie al fondo, nelle varie <lb/>condizioni del fiume, corressero a vario aspetto. </s>

<s>Cos&igrave; poi <lb/>questo principio, come gli altri concernenti la teoria delle <lb/>velocit&agrave;, si applicarono a regolare il corso naturale dell'acqua. </s></p><p type="main">

<s>&Egrave; davvero notabile come potesse il Castelli lusingar s&egrave;, e tutto il mondo <lb/>scientifico, che questa a'suoi tempi fosse una scienza nuova. </s>

<s>Si poneva dal&shy;<lb/>l'Autore, per uno de'principali corollarii di lei, la considerazione dei venti, <lb/>i quali, imboccando un fiume, e spirando contro la corrente, <emph type="italics"/>ritardano il <lb/>suo corso e la sua velocit&agrave; ordinaria, per cui vengono necessariamente ad <lb/>ampliar la misura del medesimo fiume (Misura delle acque corr.,<emph.end type="italics"/> Lib. </s>

<s>I <lb/>cit., pag. </s>

<s>13): parole, nelle quali non si fa poi che rendere dilavato il con&shy;<lb/>cetto stesso di Seneca: &ldquo; Si crebrioribus ventis ostium caeditur, et rever&shy;<lb/>beratur fluctis, amnis resistit, qui crescere videtur, quia non effunditur &rdquo; <lb/><emph type="italics"/>(Quaest. </s>

<s>natur.<emph.end type="italics"/> cit. </s>

<s>fol. </s>

<s>30). </s></p><p type="main">

<s>Ma molto pi&ugrave; di vicino al Castelli il Cardano, come udimmo, aveva detto <lb/>essere una delle principali cause, che modificano le velocit&agrave;, e perci&ograve; le mi&shy;<lb/>sure dell'acqua, i venti, sia che soffino avversi, o a seconda della sua libera <lb/>corrente. </s>

<s>Che se, contro al corollario di esso Castelli, si moveranno difficolt&agrave;, <lb/>sembrando che le correnti dell'aria non possano far altro, che increspar leg&shy;<lb/>germente la superficie dell'acqua; aveva ad esse Leonardo preparata la ri&shy;<lb/>sposta due secoli prima: &ldquo; I fiumi, egli dice, che si moveranno contro ai <lb/>corsi dei venti, fieno di tanto maggiore corso di sotto, che di sopra, quanto <lb/>la sua superfitie si fa pi&ugrave; tarda, essendo sospinta da'venti, che prima. </s>

<s>La <lb/>ragione di questo si &egrave; che, essendo i fiumi d'eguale profondit&agrave; e latitudine, <lb/>di pari corso in sul fondo che in superficie, necessaria cosa &egrave; che la recal&shy;<lb/>citazione, che fa il vento contro alla corrente superficie, faccia quella tor&shy;<lb/>nare indietro, e non bastando a esse onde alquanto elevarsi in alto, che al <lb/>fine cadendo entran sotto le altre, e vanno al fondo, dove, trovando l'altra cor&shy;<lb/>rente del fondo, s'accompagna con essa. </s>

<s>E perch&egrave; l'argine non &egrave; capace di questa <lb/>multiplicazione, &egrave; necessario che esso fondale corso si raddoppi, se no l'acqua <lb/>verrebbe a elevarsi molto fuori delle argini di essi fiumi &rdquo; (MSS. C, fol. </s>

<s>25). </s></p><pb xlink:href="020/01/3111.jpg" pagenum="72"/><p type="main">

<s>In un altro corollario della nuova Scienza delle acque correnti faceva il <lb/>Castelli notare un puerile errore dell'architetto Giovanni Fontana, il quale, <lb/>a spiegar come fosse una gran piena del Tevere passata sotto il ponte di <lb/>Quattrocapi, diceva che tra quelle angustie v'era l'acqua premuta, quasi <lb/>fosse bombice o lana. </s>

<s>Ma, mentre Galileo si studiava di difendere l'Archi&shy;<lb/>tetto romano, rassomigliando lo scorso di essa acqua <emph type="italics"/>al nocciolo di ciliega, <lb/>che premuto dalle dita scappa<emph.end type="italics"/> (Alb. </s>

<s>VI, 324), e il Castelli seguitava ad <lb/>accampare quel suo principio, nella generalit&agrave; indeterminato; Leonardo asse&shy;<lb/>gnava, di quella sopravvenuta velocit&agrave; nello stretto della sezione, la causa <lb/>vera e immediata, dicendo che la piena passa liberamente per gli archi dei <lb/>ponti &ldquo; perch&egrave; l'acqua, che passa per tali archi, cresce l'impeto, per avere <lb/>gran peso di sopra &rdquo; (MSS. I, fol. </s>

<s>87). La ragion poi di un tale accresci&shy;<lb/>mento d'impeto, per il peso che sovrasta, &egrave; meglio spiegata altrove, e con&shy;<lb/>fermata dal fatto delle corrosioni degli argini e del fondo, nella proposizione, <lb/>che Leonardo stesso cos&igrave; scriveva; &ldquo; Ogni canale d'acqua, d'uguale obli&shy;<lb/>quit&agrave; e profondit&agrave; e larghezza, che sar&agrave; in alcun luogo restretto, roder&agrave; il <lb/>fondo dell'argine, dopo il transito di essa strettezza. </s>

<s>Questo accade perch&egrave;, <lb/>dove l'acqua &egrave; ristretta, ella s'alza di rietro a essa strettura, e, passando per <lb/>esso loco stretto, vi passa con furore, perch&egrave; dichina: trova l'acqua di sotto, <lb/>che non corre, e riceve impedimento, onde, seguitando la linea del suo de&shy;<lb/>scenso, vassene al fondo, e li cava, e con ritrose circulazioni si volta all'ar&shy;<lb/>gine, e quello sotto cavando lo fa ruinare &rdquo; (MSS. H, fol. </s>

<s>85). </s></p><p type="main">

<s>Quando le nuove istituzioni idrauliche del Castelli mossero Galileo a <lb/>scrivere la celebre lettera sul fiume Bisenzio, i discepoli di lui immediati e <lb/>i successori salutarono in quella scrittura le prime applicazioni, fatte all'acque, <lb/>della teoria de'gravi scendenti lungo i piani inclinati. </s>

<s>Ma questa teoria, e <lb/>quella applicazione, si sa bene oramai essere cosa molto pi&ugrave; antica, avendo <lb/>noi letto, ne'fogli manoscritti di Leonardo, e nelle pagine stampate del Car&shy;<lb/>dano, che in ugual caduta perpendicolare sbocca l'acqua dai tubi ugualmente <lb/>veloce. </s>

<s>Ci&ograve; che per&ograve; volevano quegli Autori s'intendesse delle velocit&agrave; asso&shy;<lb/>lute, e no delle relative alle resistenze, cosicch&egrave;, sebbene in teoria sia vero <lb/>che in B e in C (fig. </s>

<s>35) i due tubi AB, AC gettano con pari impeto; no&shy;<lb/><figure id="id.020.01.3111.1.jpg" xlink:href="020/01/3111/1.jpg"/></s></p><p type="caption">

<s>Figura 35.<lb/>nostante si vede in pratica uscire da C il liquido con <lb/>minor foga, rallentatagli dalla pi&ugrave; lunga confregazione <lb/>contro le pareti del tubo. </s>

<s>E perch&egrave; un medesimo fiume, <lb/>che corresse al medesimo sbocco ora diritto ora torto, <lb/>sarebbe come se ci venisse per un canale ora corto <lb/>ora lungo; di qui presero quegli Idraulici la regola di <lb/>torcere o di raddirizzare un alveo, secondo il riconosciuto bisogno di velo&shy;<lb/>citar o di raffrenare l'impeto della corrente, come si legge in un capitolo <lb/>di Leonardo, cos&igrave; intitolato: <emph type="italics"/>&ldquo; Del modo di dirizzare i fiumi, essendo con <lb/>tardi corsi.<emph.end type="italics"/> Perch&egrave;, quanto il fiume &egrave; pi&ugrave; diritto, esso si fa pi&ugrave; veloce e rode <lb/>pi&ugrave; forte e consuma l'argine e il fondo, onde a questi tali fiumi &egrave; necessario <lb/>allargarli forte, o veramente mandarli per molte torture, o dividerli in molti <pb xlink:href="020/01/3112.jpg" pagenum="73"/>rami. </s>

<s>E se il fiume, per molte torture si facesse pigro e paludoso, allora tu <lb/>lo debbi in modo dirizzare, che l'acque piglino sufficiente moto, e non che <lb/>abbia a dare ruina di ripe o di argini. </s>

<s>E quando sar&agrave; profondit&agrave; vicino ad <lb/>alcuna argine, allora si debbe tale loco riempire di gabbioni con fascine, e <lb/>giova, acci&ograve; non cavi in modo sotto l'argine, che rovinandola abbia poi il <lb/>fiume a fare un gomito nella tua possessione o villa, e raddirizzarvi suo corso &rdquo; <lb/>(MSS. I, fol. </s>

<s>82). </s></p><p type="main">

<s>Dire che, in queste brevi parole, si conclude la scienza della Lettera sul <lb/>fiume Bisenzio non &egrave; tutta, n&egrave; la miglior parte del vero: bisogna soggiun&shy;<lb/>gere che quella stessa scienza vi &egrave; corretta da'suoi errori pi&ugrave; radicali, e per&shy;<lb/>fezionata a quel modo, che poi fece il Viviani, costretto a ripudiare gl'inse&shy;<lb/>gnamenti del suo Maestro, troppo astratti dalla presente realt&agrave; delle cose. </s>

<s>E <lb/>la famosa questione della Laguna veneta, e de'benefizi o de'danni, che ri&shy;<lb/>ceverebbe dalla diversione dei fiumi, non si trova ella, pi&ugrave; magistralmente, <lb/>che da'lunghi e battaglieri discorsi del Castelli, risoluta dalla brevit&agrave; senten&shy;<lb/>ziosa di questi motti?: &ldquo; Se la superchia grandezza de'fiumi guasta e rompe <lb/>i liti marittimi, devesi tali fiumi, poich&egrave; non si possono voltare in altri lochi, <lb/>disfarli in minuti rivicelli &rdquo; (MSS. I, fol. </s>

<s>111). E altrove, anche pi&ugrave; a pro&shy;<lb/>posito, scriveva lo stesso Leonardo: &ldquo; Lo atterramento de'paduli sar&agrave; fatto, <lb/>quando in essi paduli fien condotti li fiumi torbidi. </s>

<s>Questo si prova perch&egrave;, <lb/>dove il fiume corre, di l&igrave; lieva il terreno, e dove si ritarda qui lascia la sua <lb/>turbolentia. </s>

<s>E per questo, e perch&egrave; nei fiumi mai l'acqua si ritarda, come <lb/>nei paduli, nei quali le acque son di moto insensibile; mai in essi paduli il <lb/>fiume debbe entrare per loco basso e stretto, e uscirne per ispazio largo e <lb/>di poca profondit&agrave;. </s>

<s>E questo &egrave; necessario; perch&egrave; l'acqua corrente del fiume <lb/>&egrave; pi&ugrave; grossa e terrestre di sotto che di sopra, e l'acqua tarda de'paduli an&shy;<lb/>cora &egrave; il simile, ma molto &egrave; differente la levit&agrave; superiore delli paduli, alla <lb/>gravit&agrave; sua inferiore, che non &egrave; nella corrente de'fiumi, nelli quali la levit&agrave; <lb/>superiore poco si varia dalla gravit&agrave; inferiore &rdquo; (MSS. E, fol. </s>

<s>5). </s></p><p type="main">

<s>Dietro queste cose, messe insieme con tutte le altre, che si son da noi <lb/>particolarmente discorse, intorno alla scienza idraulica di Leonardo da Vinci; <lb/>s'intende come, paragonandolo col Castelli, giustamente il Venturi, nel suo <lb/>ben noto <emph type="italics"/>Essai,<emph.end type="italics"/> concludesse: <emph type="italics"/>Le primier me par&oacute;it dans cette partie su&shy;<lb/>perieur de beaucoup &agrave; l'autre, que l'Italie cependant a regard&eacute; comme <lb/>le fondateur de l'Hydraulique.<emph.end type="italics"/> Dopo, fu un continuo ripeter l'acclamazione, <lb/>ma si esager&ograve;, non solamente in credere che fosse Leonardo inventore della <lb/>scienza, ma in attribuirgli certi meriti, che son dovuti propriamente al Ca&shy;<lb/>stelli, e i quali non consistono nell'aver egli avvertite le velocit&agrave;, ma nel&shy;<lb/>l'avere insegnato il modo pratico di misurarle. </s></p><p type="main">

<s>Quegli avvertimenti vedemmo che furono dati dagli stessi antichi Ro&shy;<lb/>mani, e s'aveva dopo tanti secoli un bel predicare: &ldquo; Tu, che compri l'acqua <lb/>a once, sappi che tu ti puoi forte ingannare. </s>

<s>Imperocch&egrave;, se tu tolli un'on&shy;<lb/>cia in acqua morta, e un'oncia in acqua corrente contro al buso della tua <lb/>oncia; un'oncia averai vicino alla superficie, un'oncia vicino al fondo, una <pb xlink:href="020/01/3113.jpg" pagenum="74"/>in traverso alla corsia &rdquo; (MSS. H, fol. </s>

<s>78). Tali erano de'patiti inganni le <lb/>remote cause generali, senza le parecchie altre, dallo zelante nostro Filosofo <lb/>riconosciute. </s>

<s>Ma quali rimedi si suggerivano da lui ai poveri ingannati? </s>

<s>Il <lb/>Castelli penetr&ograve; la causa prossima e particolare del malefizio, riducendola al <lb/>trascurar che si faceva, nel misurare un solido, la sua lunghezza: ci&ograve; che <lb/>egli dava ad intendere con l'esempio dell'oro o di altro metallo, tirato alla <lb/>trafila. </s>

<s>Ci sovviene che anche Leonardo si volse a un simile esempio, non <lb/>meno argutamente, ma in proposito molto diverso, qual'&egrave; di dimostrare, in <lb/>una maniera meccanica, che in solidi uguali stanno le altezze reciprocamente <lb/>alle basi. </s>

<s>Abbiasi, diceva, una quantit&agrave; di materia dilatabile, come cera, e <lb/>se ne formi un parallelepipedo con base quadrata. </s>

<s>Trafilando la cera per un <lb/>foro quadrato, che sia la quarta parte della detta base, ne uscir&agrave; un altro <lb/>parallelepipedo, che alla misura si trover&agrave; quattro volte pi&ugrave; lungo. </s>

<s>E rispon&shy;<lb/>dendo sempre i particolari esempi con simile ragione, concludeva da ci&ograve; in <lb/>generale: &ldquo; Il corpo uniforme, che uniformemente si restringe, tanto acqui&shy;<lb/>sta di lunghezza, quanto e'perde della sua larghezza &rdquo; (MSS. E, fol. </s>

<s>8). </s></p><p type="main">

<s>Il Castelli, in quell'allungamento del corpo duttile, quale pure &egrave; l'acqua <lb/>che si restringe, riconobbe l'espressione della velocit&agrave;, o dello spazio che lo <lb/>misura, in relazione col tempo; cosicch&egrave; la questione della pi&ugrave; giusta di&shy;<lb/>spensa dell'acqua si veniva a risolvere per lui con l'orologio alla mano. </s>

<s>Ma <lb/>Leonardo non seppe sollevarsi punto sopra alla turba volgare, la quale non <lb/>capiva come si potesse definir la lunghezza a un corpo, che mai non cessa <lb/>di scorrere. </s>

<s>E adducendo l'esempio dello schizzatoio, <emph type="italics"/>che, quando il ma&shy;<lb/>schio si move un dito, l'acqua di fuori si &egrave; allontanata due braccia;<emph.end type="italics"/> ne parla <lb/>come di cosa ipotetica, e d'impossibile esperienza <emph type="italics"/>(Arconati,<emph.end type="italics"/> pag. </s>

<s>428, 29). </s></p><p type="main">

<s>Il gelo della critica &egrave; finalmente venuto a bruciare le fronde tenerelle <lb/>della Rettorica, ma se Leonardo, da inventore della Scienza, n'&egrave; rimasto un <lb/>semplice cultore, coltivandola, la promosse forse pi&ugrave; al di l&agrave; di ogni altro <lb/>discepolo di Giordano, perch&egrave; possedeva le virt&ugrave; necessarie in grado pi&ugrave; <lb/>eccellente. </s>

<s>La prima e principale di queste virt&ugrave; noi la riconosciamo nella <lb/>grande perizia, ch'ebbe delle Matematiche. </s>

<s>&Egrave; cosa veramente notabile che, <lb/>mentre tutti si affaccendano a indicare ne'Manoscritti del Nostro specula&shy;<lb/>zioni, scoperte e invenzioni di ogni genere, e tutte ammirande; nessuno abbia <lb/>ancora avvertito la grande arte di lui, in maneggiar l'algebra e la geome&shy;<lb/>tria, da emulare, e da superare talvolta gli stessi metodi odierni, per la fa&shy;<lb/>cilit&agrave; delle dimostrazioni, e per l'eleganza. </s></p><p type="main">

<s>Un'altra virt&ugrave; consisteva in quella diligente pazienza d'osservare i vari <lb/>fatti naturali, che non gli lasciava fuggire all'occhio la minima cosa. </s>

<s>Una <lb/>buona parte del libro, compilato dall'Arconati, s'impiega a descrivere le <lb/>figure bizzarre e capricciose, alla superficie e nell'interno dell'acqua, che <lb/>movendosi incontra ostacoli al suo libero corso, e secondo il modo di questi <lb/>incontri ora si riflette, ora si rifrange, ora s'affila e intesse panneggiamenti, <lb/>ora s'avvolge e fa vortici, girandole e cirri, da importar forse meno alla <lb/>scienza, che all'arte della pittura. </s>

<s>A questa artistica curiosit&agrave; nondimeno de-<pb xlink:href="020/01/3114.jpg" pagenum="75"/>vesi l'osservazione della vena contratta, del meccanismo, che produce i ven&shy;<lb/>tri e i nodi in un fil d'acqua che cada, e di tanti altri fenomeni, osservati <lb/>da Leonardo in recipienti con pareti diafane, immersevi polveri o altri mi&shy;<lb/>nuti galleggianti colorati, per rendersi meglio visibili i complicati moti inte&shy;<lb/>stini. </s>

<s>Ond'&egrave; facile intendere come giungesse cos&igrave; a fare scoperte, l'onor delle <lb/>quali poi si distribul fra il Mariotte, il Newton e il Poleni. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Le tradizioni di quella Scienza, la quale ora desta in noi la maraviglia, <lb/>non sapremmo dire se pi&ugrave; per i grandi progressi fatti da lei, o per essere <lb/>stata dimenticata; derivarono, come da triplice fonte, da Archimede, da Fron&shy;<lb/>tino e dal Nemorario. </s>

<s>Ma la vena intima alimentatrice si pu&ograve; dire che fosse <lb/>una sola: quella cio&egrave;, che si sentiva scorrere in mezzo a'due libri <emph type="italics"/>De insi&shy;<lb/>dentibus aquae.<emph.end type="italics"/> E perch&egrave; la loro pubblicazione era naturale che venisse a <lb/>dare nuovo e validissimo impulso a questi studii, l'importanza dell'argo&shy;<lb/>mento c'invita a trattenerci attorno pi&ugrave; particolarmente il discorso. </s></p><p type="main">

<s>Si disse gi&agrave; come fosse condotta la versione latina del trattato <foreign lang="greek">peri <lb/>o\xoume/nwn</foreign>, e come questa pervenisse nella penisola insieme con le altre Opere <lb/>meccaniche di Archimede. </s>

<s>Rimasto il codice lungamente negletto, nel se&shy;<lb/>colo XIV si dette opera a copiarlo, e il copiatore premetteva, ripetendola in&shy;<lb/>nanzi a ogni libro distinto, un'avvertenza, nella quale scusavasi delle lacune, <lb/>e de'frantesi, per essere, com'egli diceva, il codice, in certi punti, cos&igrave; la&shy;<lb/>cero, da non si poter leggere in nessun modo. </s>

<s>Altre copie se ne presero, <lb/>conformi in tutto e per tutto con questa, e n'ebbe una il Vescovo di Pa&shy;<lb/>dova, d'onde si diffusero le altre, venute a mano di Leonardo da Vinc, e <lb/>un poco pi&ugrave; tardi del Tartaglia, e del cardinale Cervini, poi papa Marcello II, <lb/>che ne fece dono al Commandino. </s></p><p type="main">

<s>Sent&igrave; il Tartaglia tanto gusto della bellezza matematica di quelle dot&shy;<lb/>trine, che per comun benefizio pens&ograve; di pubblicarle. </s>

<s>Ma se la Scienza da <lb/>una parte lo confortava, veniva dall'altra a disanimarlo la Filologia, a che, <lb/>non potendo reprimere l'incredibile ardore, trov&ograve; rimedio, pubblicando le <lb/>sole cose in latino, come l'aveva trovate, e scusandosene a quel modo, che <lb/>aveva fatto il primo copiatore, l'avvertenza del quale trasfuse nella sua pre&shy;<lb/>fazione. </s>

<s>Anzi, perch&egrave; il libro secondo <emph type="italics"/>De insidentibus aquae<emph.end type="italics"/> era di cos&igrave; sot&shy;<lb/>tile e oscura materia, da non giovare a bene interpetrarlo nemmeno la <lb/>scienza; trovatosi il poco esperto editore da ambedue le parti sopraffatto e <lb/>vinto, pens&ograve; di lasciarlo indietro, non riducendo nella sua compilazione che <lb/>il primo. </s></p><p type="main">

<s>Morto nel 1557 il Tartaglia, furono i manoscritti di lui venduti a Cur&shy;<lb/>zio Troiano, tipografo-editore in Venezia, il quale, avendo tra quelle com&shy;<lb/>prate carte ritrovata la trascrizione del secondo libro <emph type="italics"/>De insidentibus hu-<emph.end type="italics"/><pb xlink:href="020/01/3115.jpg" pagenum="76"/><emph type="italics"/>mido,<emph.end type="italics"/> non esit&ograve; di darlo, nella sua propria officina, alla pubblica luce. </s>

<s>Nel <lb/>dedicare l'opuscolo a Fabrizio de Nores, dop'aver detto che si crederebbe <lb/>meritevole di riprensione, se egli, che aveva in mano le rimaste scritture del <lb/>grandissimo Tartaglia, ne avesse dinegato lo studio agli uomini letterati; cos&igrave; <lb/>soggiungeva: &ldquo; Quare, cum habeam adhuc apud me Archimedem <emph type="italics"/>De insi&shy;<lb/>dentibus aquae,<emph.end type="italics"/> ab ipso Nicolao in lucem revocatum, et quantum ab ipso <lb/>fieri potuit ab erroribus librarii emendatum, et suis lucubrationibus illustra&shy;<lb/>tum; videor fraudare omnes literatos sua possessione, ni omnia, quae huius <lb/>ingeniosissimi viri apud me restant, in lucem emisero, et omnibus ea com&shy;<lb/>municavero. </s>

<s>&rdquo; </s></p><p type="main">

<s>J. L. Heiberg, dando alla Biblioteca teubneriana di Lipsia le opere di <lb/>Archimede, da s&egrave; recensite, tradotte in latino e illustrate; al titolo <emph type="italics"/>De iis <lb/>quae in humido vchuntur<emph.end type="italics"/> sottoponeva questa nota: &ldquo; Librum I primus <lb/>edidit N. Tartalea, Venetiis 1543. Deinde ex schedis eius et primum et se&shy;<lb/>cundum librum edidit Troianus Curtius, Venetiis 1565. Hanc interpetratio&shy;<lb/>nem emendavit F. Commandinus, Bononiae 1565 &rdquo; (Vol. </s>

<s>II, 1881, pag. </s>

<s>359). </s></p><p type="main">

<s>Ma com'&egrave; possibile che il Commandino conducesse in pochi mesi quella <lb/>sua, che da ogni parte apparisce penosissima emendazione, e anzi d&igrave; pi&ugrave; ri&shy;<lb/>trovasse, in tal brevissimo tempo, quelle sue laboriosissime proposizioni dei <lb/>centri di gravit&agrave; de'solidi, l'argomento delle quali confessa essergli stato <lb/>suggerito dalla meditazione del secondo libro idrostatico di Archimede? </s>

<s>Il <lb/>Torelli, nella prefazione a tutte le Opere del Siracusano, suppose che il <lb/>Tartaglia e il Commandino s'abbattessero ne'libri <foreign lang="greek">peri oxome/nwn</foreign> quasi nel me&shy;<lb/>desimo tempo, bench&egrave; l'uno indipendentemente dall'altro. </s>

<s>&ldquo; Caeterum, egli <lb/>dice, cum Commandinus in libros, quos memoravimus, eodem fere tempore <lb/>incidisset, quo illos Tartalea invenit; egregiam in iis operam insumpsit &rdquo; <lb/>(Oxonii 1792, pag. </s>

<s>XVIII). Cosicch&egrave;, verso l'anno 1543, suppone il To&shy;<lb/>relli che i libri idrostatici di Archimede capitassero alle mani del Matema&shy;<lb/>tico di Urbino. </s>

<s>Ma in questo caso non si comprenderebbe perch&egrave; non gli <lb/>raccogliesse fra le altre opere del medesimo Autore, le quali egli stesso pub&shy;<lb/>blicava nel 1558, con tant'amorosa diligenza, in Venezia. </s>

<s>Fu da questo no&shy;<lb/>tato difetto anzi indotto &igrave;l cardinale Cervini a fare il dono al diligentissimo <lb/>editore, il quale, dicendo di averlo ricevuto non molti anni prima del 1565 <lb/>(Lettera dedic. </s>

<s>del libro <emph type="italics"/>De centro gravitatis),<emph.end type="italics"/> ne fa con certezza argomen&shy;<lb/>tare che ci&ograve; accadesse circa l'anno 1560, diciassette o diciotto anni dopo il <lb/>Tartaglia. </s></p><p type="main">

<s>Cos&igrave;, anche quei cinque anni, che precedettero la pubblicazione, essendo <lb/>tempo sufficiente a commentare i libri <emph type="italics"/>De iis quae vehuntur in aqua,<emph.end type="italics"/> e a <lb/>preparare il trattato <emph type="italics"/>De centro gravitatis solidorum,<emph.end type="italics"/> si vengono a togliere <lb/>l'inconvenienze, che nascono dalle posizioni del valoroso, e benemerito pro&shy;<lb/><gap/>essore di Copenaghen, il quale, se avesse ripensato a queste cose, si sarebbe <lb/>anche insieme deliberata la mente da que'suoi dubbi, espressi ne'Prolego&shy;<lb/>meni al Commentario di Eutocio, dove si fa maraviglia che il Commandino, <lb/>successore immediato nell'ufficio di editore al Tartaglia, non ne profferisca <pb xlink:href="020/01/3116.jpg" pagenum="77"/>mai il nome. </s>

<s>&ldquo; Is (Commandinus) in praefatione editionis librorum <foreign lang="greek">peri <lb/>oxoume/nwn,</foreign> fol. </s>

<s>2, hacc habet: <emph type="italics"/>Cum enim graecus Archimedis codex nondum <lb/>in lucem venerit, non solum is qui eum latinitate donavit multis in locis <lb/>foede lapsus est, verum etiam codex ipse, ut etiam interpres fatetur, ve&shy;<lb/>tustate corruptus et mancus est.<emph.end type="italics"/> His verbis Tartaleam et descriptionem co&shy;<lb/>dicis eius, quam ex praefatione eius supra attuli, significari adparet, et mi&shy;<lb/>ramur cur nomen eius non nominaverit &rdquo; (Archim., <emph type="italics"/>Op. </s>

<s>omnia,<emph.end type="italics"/> Vol. </s>

<s>III, <lb/>pag. </s>

<s>XXXII). Alla pagina XXIX infatti aveva l'Heiberg trascritte queste <lb/>parole, con le quali il Tartaglia cominciava la sua prefazione all'edizione <lb/>delle Opere meccaniche d'Archimede: &ldquo; Cum sorte quadam ad manus meas <lb/>pervenissent fracti, et qui vix legi poterant, quidam libri manu graeca scripti <lb/>illius celeberrimi philosophi Archimedis..... &rdquo; Ma queste medesime espres&shy;<lb/>sioni vedemmo essere nell'avvertenza del copiatore antico, la quale av&shy;<lb/>vertenza leggendo il Commandino riportata nel suo manoscritto cred&egrave; che <lb/>fosse di colui, che aveva fatta la traduzione latina, direttamente dal testo <lb/>greco. </s></p><p type="main">

<s>La maraviglia dunque dell'illustre editore tedesco dipende tutta dal&shy;<lb/>l'avere ingerita l'opinione che il Commandino avesse condotte le sue recen&shy;<lb/>sioni sopra la pubblicazion del Tartaglia, nella quale consistesse il libro do&shy;<lb/>natogli dal cardinale Cervini: opinione comunemente invalsa, e che fu tenuta <lb/>anche da noi, prima di considerare che il detto libro era il manoscritto, di <lb/>cui s'&egrave; discorso di sopra, e che il Cardinale consegnava al Matematico di <lb/>Urbino, raccomandandogliene la pubblicazione, quando quella del Tartaglia <lb/>giudicavasi troppo informe, e ritrovavasi mancante della sua seconda parte. </s>

<s><lb/>Se, nella dedica infatti del libro <emph type="italics"/>De centro grav.,<emph.end type="italics"/> quelle parole <emph type="italics"/>non multos <lb/>abhinc annos Mareellus Il Pont. </s>

<s>Max., cum abhuc cardinalis esset, mihi, <lb/>quae sua erat humanitas, libros Archimedis de iis quae vehuntur in aqua <lb/>latine redditos dono dedit,<emph.end type="italics"/> lasciano ambiguo il lettore intorno all'essere il <lb/>libro, di cui si parla, o manoscritto o stampato; dalla dedica del <emph type="italics"/>De iis quae <lb/>vehuntur in aqua<emph.end type="italics"/> chiaramente apparisce che si trattava della pubblicazione <lb/>di un codice, simile a quella, che l'Autore stesso ivi dice avere gi&agrave; fatta <lb/>degli analemmi di Tolomeo. </s>

<s>&ldquo; Quod tibi (al card. </s>

<s>Ranuccio Farnese, a cui <lb/>l'edizione si dedicava) superioribus diebus pollicitus sum, cum libellum Pto&shy;<lb/>lomaei De analemmate in lucem proferrem, brevi fore ut Archimedis etiam <lb/>libri De iis quae in aqua vehuntur et emendatiores, et fortasse opera mea <lb/>illustriores ederentur..... &rdquo; </s></p><p type="main">

<s>Essendo cos&igrave; dichiarata l'indipendenza della pubblicazione del Comman&shy;<lb/>dino, da quella del Tartaglia, si pu&ograve; giudicare quanto fuori del segno co&shy;<lb/>gliessero le congetture dell'Heiberg, per risolvere gli esposti dubbi, e altri <lb/>nuovi, che nascevano intorno alla questione, la quale quanto pi&ugrave; maneggia&shy;<lb/>vasi, per trovare il bandolo della matassa, e pi&ugrave; si arruffava. </s>

<s>&ldquo; His omnibus <lb/>rebus adductus, nunc in eam potius partem inclinaverim, ut putem Tarta&shy;<lb/>leam, ex Codice illo graeco antiquo et dilacerato, ceteros libros ipsum latine <lb/>interpetratum esse. </s>

<s>Sed librum I <emph type="italics"/>De insidentibus aquae,<emph.end type="italics"/> sicut etiam li-<pb xlink:href="020/01/3117.jpg" pagenum="78"/>brum II ei e graeco latine conversum, nescio quo modo oblatum esse &rdquo; <lb/><emph type="italics"/>(Op. </s>

<s>Archim.,<emph.end type="italics"/> Vol. </s>

<s>III cit., pag. </s>

<s>XXXII). </s></p><p type="main">

<s>La nuova risoluta questione, intorno ai due primi editori de'libri idro&shy;<lb/>statici di Archimede, giova a risolvere definitivamente anche quell'altra, che <lb/>riguarda il codice greco. </s>

<s>Quando il Tartaglia diceva, in quella sua prefa&shy;<lb/>zione, essergli per sorte pervenuti alcuni libri di Archimede, <emph type="italics"/>manu graeca <lb/>scripti,<emph.end type="italics"/> era da eccettuare il trattato <emph type="italics"/>De insidentibns aquae,<emph.end type="italics"/> di cui trov&ograve; la <lb/>sola traduzione latina, senza il testo greco a fronte, come avevano gli altri. </s>

<s><lb/>N&egrave; ci&ograve; &egrave; un induzione, ma un fatto attestato dallo stesso Tartaglia, chi ben <lb/>l'intende, nella lettera dedicatoria al conte Landriani. </s>

<s>Il medesimo fatto poi <lb/>&egrave; confermato dal Commandino, il quale, bench&egrave; credesse, come avvertimmo, <lb/>essere il codice che aveva fra mano quello, in cui si dava la version di Ar&shy;<lb/>chimede, fatta direttamente dal testo greco; il vero testo greco nonostante <lb/>dice che <emph type="italics"/>nondum in lucem venit.<emph.end type="italics"/> E come s'ha, dalle stesse parole del Tar&shy;<lb/>taglia, espressa la notizia che di quel codice nient'altro era rimasto, che le <lb/>figure illustrative; cos&igrave; &egrave; ripetuto dal Commandino, nel luogo da noi citato <lb/>dal suo Commentario. </s></p><p type="main">

<s>Ci&ograve; basti a noi aver detto, per quel che s'appartiene alla storia di una <lb/>pubblicazione, la quale tanto efficacemente sarebbe concorsa a promovere la <lb/>scienza idrostatica. </s>

<s>Son fra que'primi promotori senza dubbio da annove&shy;<lb/>rare ambedue coloro, che tanto cooperarono a diffondere la notizia, e lo stu&shy;<lb/>dio dei libri archimedei, bench&egrave; ne siano i meriti, nell'estimazione e nel <lb/>grado, molto diversi. </s>

<s>Il Commandino supera di gran lunga, nella diligenza <lb/>e nella critica necessaria a un editore, il Tartaglia, cos&igrave; rude in ogni genere <lb/>di letteratura, da far veramente maraviglia che l'Heiberg se lo immagini <lb/>tutto intento a compulsare codici greci e latini, con gli avvedimenti dell'arte, <lb/>e con la minuziosa pazienza di un moderno critico tedesco. </s>

<s>Esso Heiberg non <lb/>pot&egrave; passar senza nota l'errore lasciato trascorrere in fronte, nella prima <lb/>aperta del libro: <emph type="italics"/>Incipit liber Archimenidis de centris gravium valde pla&shy;<lb/>nis aequerepentibus,<emph.end type="italics"/> e l'attribuisce alla negligenza del tipografo. </s>

<s>Ma ripen&shy;<lb/>sando come costui era quel veneziano Venturino Ruffinelli, che tanto cor&shy;<lb/>rettamente poi stamp&ograve; i nove libri intitolati <emph type="italics"/>Quesiti et inventioni diverse,<emph.end type="italics"/><lb/>si direbbe piuttosto che la differenza nasceva dallo stampare nel materno <lb/>vernacolo lombardo, o nella lingua latina, rispetto alla quale essendo, edi&shy;<lb/>tore e tipografo, simili a un cieco, che si facesse guida a un altro cieco, non <lb/>fa maraviglia che ambedue cadessero nella medesima fossa. </s>

<s>Un tal giudizio <lb/>vien confermato da altri esempi, come da questo: <emph type="italics"/>Explicet liber Archime&shy;<lb/>dis de centrum gravitatis vel duplationis aequerepentibus (Opera Archim. </s>

<s><lb/>per N. Tartaleam,<emph.end type="italics"/> Venetiis 1543, fol. </s>

<s>19). E perch&egrave; tali erano per cos&igrave; dire <lb/>le rubriche, dall'editore aggiunte al manoscritto, si pu&ograve; di qui giudicare <lb/>quanto valesse il Tartaglia nella lingua latina, persuaso talmente essere il <lb/>vero titolo de'libri di Archimede, intorno agli Equiponderanti, qual'egli lo <lb/>faceva stampare al Ruffinelli, senz'avvedersi del bisogno che v'era di cor&shy;<lb/>reggervi <emph type="italics"/>vel de planis<emph.end type="italics"/> sulle bozze di stampa; che torna, nel Ragionamento <pb xlink:href="020/01/3118.jpg" pagenum="79"/>primo sopra la sua <emph type="italics"/>Travagliata inventione,<emph.end type="italics"/> a citare i detti libri, con la stessa <lb/>sicurt&agrave; e franchezza, <emph type="italics"/>De centro gravium valde planis aequerepentibus<emph.end type="italics"/><lb/>(pag. </s>

<s>18). E un tal uomo si vuol far credere il traduttore dal latino di un <lb/>codice greco?! Ma se il Tartaglia &egrave; inferiore al Commandino, in letteratura, <lb/>ei lo supera lungamente nella scienza, perch&egrave; mentre l'uno non &egrave; che un <lb/>semplice commentator di Archimede, e non sempre felice come vedemmo, <lb/>l'altro lo promove a tal punto, che &egrave; bene segnar con lapide, perch&egrave; sem&shy;<lb/>bra essere stato sepolto dalle sabbie portatevi sepra dai venti del deserto. </s>

<s><lb/>Intendiamo dire della tooria e della pratica di ritrovare i pesi specifici dei <lb/>varii corpi, che rimaste, per pregiudizi e per ambizione, dimenticate, riap&shy;<lb/>parvero un mezzo secolo dopo, nel Ghetaldo e nel Galileo, come nuove. </s></p><p type="main">

<s>Dalle varie scritture dello stesso Tartaglia si ricava qual si fosse l'ori&shy;<lb/>gine, e l'occasione di dimostrare la scienza, e d'insegnar l'arte da misurare <lb/>quanto un solido o un liquido fossero, rispetto all'acqua, pi&ugrave; o meno gravi. </s>

<s><lb/>Egli era a Brescia sua patria, quando giunse la notizia che una nave carica <lb/>erasi affondata presso a Malamocco, n&egrave;, per qualunque arte vi si fosse usata <lb/>attorno, era stato possibile recuperarla. </s>

<s>Un'altra nave, che similmente affond&ograve; <lb/>poco dopo, e, per l'esperienze fattesi nella prima, perduta ogni speranza di <lb/>riaverla, bench&egrave; ne rimanessero a fior d'acqua la poppa e la prora; si de&shy;<lb/>cret&ograve; di ridurla in pezzi, e sgombrarne poi il porto da'rottami. </s>

<s>&ldquo; Ond'io, <lb/>dice il Tartaglia al doge Francesco Donato, considerando di quanto danno <lb/>era il rompere un simil vaso, oltre la perdita del cargo, deliberai da inve&shy;<lb/>stigare qualche modo, over regola da sovenire a tai dannose occorrentie. </s>

<s><lb/>Onde, havendone ritrovata una generale et indubitata, me apparso per co&shy;<lb/>mun benefitio di questa magnifica Citt&agrave; da dichiarare, et figuralmente delu&shy;<lb/>cidare tal regola, nella presente operina &rdquo; che nel 1551 si dava, nella stessa <lb/>Venezia, alla luce, col titolo di <emph type="italics"/>Travagliata inventione.<emph.end type="italics"/></s></p><p type="main">

<s>&Egrave; divisa la detta operina in tre brevissimi libri, bench&egrave; l'argomento sia <lb/>quanto alla sostanza esaurito nel primo, &igrave;n cui, supponendo la media gravit&agrave; <lb/>specifica del carico della nave ridotta a quella di un solido omogeneo, come <lb/>terra cotta, marmo, ferro, piombo, rame, oro, ecc., si assegnano le minime <lb/>dimensioni al vacuo di un vaso di legno, perch&egrave;, caricatosi di un determi&shy;<lb/>nato volume del tale o del tale altro solido, potesse ivi dentro sostenersi a <lb/>galla. </s>

<s>Ma sembrando difficile l'imbragare, per via di strumenti, il solido <lb/>sommerso per sollevarlo, senza l'assistente mano dell'uomo; immagin&ograve; l'Au&shy;<lb/>tore, e poi descrisse nel secondo libro una macchina, nella quale a tutto si <lb/>provvedeva, per calarsi a lavorare gi&ugrave; sul fondo marino, fuor che alla cosa <lb/>principale, qual'era il modo di respirare in un piccolo vaso chiuso: modo, <lb/>che, conseguitosi pol senza molta difficolt&agrave;, dette l'invenzione del Tartaglia <lb/>perfezionata in quell'utilissimo strumento peschereccio, da gran tempo co&shy;<lb/>nosciuto sotto il nome di <emph type="italics"/>Campana del palombaro.<emph.end type="italics"/> Nel terzo libro final&shy;<lb/>mente si raccolgono, da varii autori e dalle tradizioni popolari, i segni delle <lb/>mutazioni dell'aria o dei tempi. </s></p><p type="main">

<s>Ma ritornando alla parte sostanziale dell'invenzione, &ldquo; acciocch&egrave;, dice il <pb xlink:href="020/01/3119.jpg" pagenum="80"/>Tartaglia, se ne habbia generale dottrina, per recuperare ogni specie di co&shy;<lb/>losso affondato, cio&egrave; de ogni specie di corpo solido, o sia di pietra, over di <lb/>ferro, over di stagno, over di rame, over di piombo, over di argento, over <lb/>di oro (come che facilmente occorrer potria di affondarlo volontariamente, <lb/>in tempo di guerra, per salvarlo, e da poi saperlo anchora con ragion recu&shy;<lb/>perare) bisogna tener questa regola: Sel solido per longo tempo affondato <lb/>fosse de pietra cotta (detta matone, over quadrello) da poi che afferrato fusse, <lb/>saria necessario a tuor tanti para di navi over navigli, barche over burchii, <lb/>che tutti li vacui de quelli in summa non fussen men che quadruppli al&shy;<lb/>l'area corporale di quel tal solido affondato. </s>

<s>E se per sorte il solido, gi&agrave; <lb/>longo tempo affondato, fusse di pietra marmorina, bisogneria che l'area cor&shy;<lb/>porale de tutti li vacui di detti legni over vasi in summa non fusseno men <lb/>che settupli all'area corporale de l'affondato solido, cio&egrave; sette volte tanto &rdquo; <lb/>(pag. </s>

<s>67). E seguita a dar similmente la regola, nel caso che il solido affon&shy;<lb/>dato fosse ferro, piombo, rame, argento, oro. </s>

<s>Una tal regola poi facilmente <lb/>si comprende come fosse fondata nell'invenzione dei pesi specifici delle dette <lb/>terre e metalli, ma, non essendo quivi il luogo di renderne le ragioni, il Tar&shy;<lb/>taglia vi suppl&igrave; con alcuni Ragionamenti, ne'quali si dava scienza di ci&ograve;, che <lb/>solo praticamente aveva prima insegnato ai marangoni. </s>

<s>E perch&egrave; tale scienza <lb/>derivava necessariamente dai principii idrostatici, per l'antico Maestro gi&agrave; <lb/>dimostrati, nel Ragionamento primo sopra le cose dette nel principio della <lb/><emph type="italics"/>Travagliata inventione<emph.end type="italics"/> &ldquo; s&egrave; dichiara volgarmente quel libro di Archimede <lb/>siracusano, detto <emph type="italics"/>De insidentibus aquae,<emph.end type="italics"/> materia di non poca speculatione <lb/>et intellettual dilettatione &rdquo; ci&ograve; che l'Autore fa risaltar dalle parafrasi e dai <lb/>commenti, a cui gli porge occasione quel suo compare Riccardo Ventvorth, <lb/>insiem col quale dialogizzando si studia di abbellire in qualche modo il di&shy;<lb/>scorso. </s></p><p type="main">

<s>Questo primo ragionamento serviva di preparazion fondamentale alle <lb/>dottrine, che si dimostrerebbero nel secondo, intorno al determinar la forza <lb/>necessaria per sollevar la nave sommersa, e distingue il caso importante che <lb/>il fondo di lei sia circondato dall'acqua, come avviene quando fosse caduto <lb/>sui sassi, o sia da essa acqua escluso, come quando riman confitto nell'arena. </s>

<s><lb/>Dicevasi questa distinzione importante, perch&egrave; si riduceva alla question della <lb/>baga di Leonardo da Vinci messa in fondo all'acqua del pozzo, dal modo di <lb/>risolver la quale si deciderebbe de'progressi che, nel riconoscere l'azione <lb/>delle pressioni <emph type="italics"/>sursum,<emph.end type="italics"/> per riflessione delle pressioni <emph type="italics"/>deorsum,<emph.end type="italics"/> avrebbe fatto <lb/>in quel tempo la Scienza, la quale si pu&ograve; dunque concludere che si rima&shy;<lb/>nesse stazionaria, perch&egrave; il Tartaglia attribuisce la maggiore o minore diffi&shy;<lb/>colt&agrave; di riaver la nave, nei due detti casi, a ragioni immaginarie, sostituite <lb/>in luogo delle vere non conosciute. </s></p><p type="main">

<s>&ldquo; Hor perch&egrave;, egli dice, sia mo tanto e tanto difficile separare il corpo <lb/>da un fondo pantanoso, over arenoso, da quello che sia da un sassoso; la <lb/>causa &egrave; questa: Che in un fondo sassoso tutto il detto affondato corpo &egrave; <lb/>abbrazato et circondato dal'acqua, accettuando quella poca parte, che tocca <pb xlink:href="020/01/3120.jpg" pagenum="81"/>il detto fondo sassoso, la qual parte ancora, quanto che &egrave; pi&ugrave; accuta, cio&egrave; <lb/>che tocca manco del detto fondo, tanto &egrave; pi&ugrave; facile a separarlo da quello, <lb/>perch&egrave; l'acqua, che ha da empire quel luoco, che lassar&agrave; il detto corpo nella <lb/>sua assensione; &egrave; ivi presente, cio&egrave; che non ha da venire da loco molto lon&shy;<lb/>tano, e per&ograve; il detto corpo, non ha tanta difficolt&agrave; a tirare da longinque <lb/>parti, come che gli occorreria, quando che fusse in gran parte sepulto nel <lb/>pantano, over sabbia, nella qual positione gli bisogneria tirare la detta acqua <lb/>dalla suprema parte di quella sua cassa pantanosa, over arenosa, per fin nella <lb/>infima parte di quella. </s>

<s>E perch&egrave; tal acqua non puol cos&igrave; immediate, over <lb/>in un istante, discorrere in tal parte infima, ma solamente in tempo, e la <lb/>Natura non permette che un loco possi restar vacuo per alcuno minimo spa&shy;<lb/>cio di tempo; e perci&ograve; &egrave; cosa molto e molto pi&ugrave; difficultosa a separare un <lb/>corpo grave da un fondo pantanoso, di quello sar&agrave; in un fondo sassoso &rdquo; <lb/>(pag. </s>

<s>27). </s></p><p type="main">

<s>Smossa che sia l'arrenata mole dal fondo, la maggiore o minor forza, <lb/>che tuttavia ve la trattiene, dipende solamente dal maggiore o minore peso <lb/>specifico, cosicch&egrave;, conosciutosi questo, s'avr&agrave; anche insieme la misura di <lb/>quella, e della contraria potenza sollevatrice. </s>

<s>Or il Tartaglia annunzia di <lb/>aver trovati i pesi specifici di varie sorta di corpi, quale annunzio dest&ograve; in <lb/>Riccardo la curiosit&agrave; di sapere com'avesse fatto a misurarli con tanta pre&shy;<lb/>cisione, che pareva s&igrave; difficile ad ottenersi co'metodi antichi. </s>

<s>Qe'metodi in&shy;<lb/>fatti, derivando dalle tradizioni archimedee, consistevano nel pesare il corpo <lb/>in aria, e poi, sommersolo in un vaso pieno, pesar l'acqua versata, non poca <lb/>parte della quale, come quella rimasta a bagnar le pareti, andando dispersa, <lb/>era potissima causa del non si corrispondere esattamente insieme i due com&shy;<lb/>parati volumi. </s>

<s>Il Tartaglia rimedi&ograve; a questo, e ad altri inconvenienti, pe&shy;<lb/>sando il medesimo corpo prima in aria, poi in acqua, e desumendone la <lb/>gravit&agrave; specifica dalla differenza de'due pesi, in virt&ugrave; della VII proposizione <lb/>archimedea. </s>

<s>Cos&igrave; egli fu il primo a inventare, e a far uso della <emph type="italics"/>Bilancetta <lb/>idrostatica,<emph.end type="italics"/> ch'egli stesso cos&igrave; deserive, per sodisfare alla sopra accennata <lb/>curiosit&agrave; del suo Riccardo: </s></p><p type="main">

<s>&ldquo; Ve dir&ograve;, compare, volendomi certificare che proportion havesse la pie&shy;<lb/>tra cotta (detta matone over quadrello) in gravit&agrave; con l'acqua. </s>

<s>Io pesai due <lb/>pietre cotte, over quadrelli, sottili, li quali trovai essere libbre 7, once 2 alla <lb/>grossa, et da poi li legai con uno spagheto longheto attacato a li ancini della <lb/>stadera, over piombino, et questo feci, acci&ograve; che li detti ancini non intras&shy;<lb/>seno nell'acqua, dove faceva conto di pesarli, et cos&igrave; con tal cautella li ri&shy;<lb/>pesai in un vaso di acqua dolce, ed in quella li trovai esser solamente lib&shy;<lb/>bre 3, once 5, onde, per la VII di Archimede, tanta acqua, quanto saria li <lb/>detti due quarelli, veneria a pesare libbre 3, once 9, cio&egrave; la differentia, che <lb/>&egrave; fra le libbre 7, once 2, che, pes&ograve; in aere, e le libbre 3, once 9, che pes&ograve; <lb/>in acqua. </s>

<s>Per la qual cosa io conclusi che la proportione della pietra cotta <lb/>all'acqua, in gravit&agrave;, fusse come da once 86 a 41, che saria pi&ugrave; che dop&shy;<lb/>pia in gravit&agrave;. </s>

<s>Ma, per certificarmi meglio, il giorno seguente ripesai li dui <pb xlink:href="020/01/3121.jpg" pagenum="82"/>medesimi quarelli, li quali trovai in aere essere libbre 7, once 9, cio&egrave; cre&shy;<lb/>scerno once 7, per essere imbeverati di acqua, et da poi li ripesai in acqua, <lb/>e li retrovai libbre 3, once 9. La differentia di questi due pesi saria libbre 4, <lb/>onde, secondo questa seconda sperientia, la proportione di tal pietra cotta <lb/>all'acqua in gravit&agrave; saria come once 93 a 48, cio&egrave; men che doppia. </s>

<s>Onde, <lb/>per esser molto il variare di tal sorta di quadrelli, e tal hor uno &egrave; pi&ugrave; grave <lb/>de l'altro per la humidit&agrave; e siccit&agrave;, pigliai il mezzo di queste due sperien&shy;<lb/>tie, cio&egrave; conclusi che la proportione della detta pietra cotta in gravit&agrave; con <lb/>l'acqua essere circa doppia &rdquo; (pag. </s>

<s>30). </s></p><p type="main">

<s>Di poi, seguita a dire il Tartaglia, pesai una palla di marmo, e la tro&shy;<lb/>vai in aria once 7, e in acqua once 5, di modo che ne conclusi stare il peso <lb/>del marmo, a quello di un ugual volume di acqua, come 7 a 2. E come 19 <lb/>a 3 trov&ograve; per il ferro, come 65 a 10 per il rame, come 30 a 3 per il piombo, <lb/>come 313 a 32 per l'argento, e finalmente come 17 a 1, per l'oro. </s>

<s>&ldquo; Ces <lb/>pesanteurs, osserva il Libri, semblent en general un peu trop flaibles, mais <lb/>il faut remarquer que non seulement Tartaglia, qui les determinait en obser&shy;<lb/>vant combien un corps perduit de son poids lorsqu'on le plongeait dans l'eau, <lb/>ne se servait pas d'eau distill&eacute;e, mais que de plus, faisant ses experiences a <lb/>Venise, dans le dessein surtout de les appliquer au sauvetage des vaisseaux <lb/>submerg&eacute;s, il employait peut-<gap/>tre l'eau de la mer pour unit&eacute; &rdquo; <emph type="italics"/>(Histoire des <lb/>sciences mathem.,<emph.end type="italics"/> T. III, a Paris 1840, pag. </s>

<s>166). </s></p><p type="main">

<s>Se l'acqua in cui immergeva i corpi il Tartaglia, non era distillata, sap&shy;<lb/>piamo per&ograve; da lui stesso che era pura; &ldquo; Sel fusse possibile a formare un <lb/>cubo di <emph type="italics"/>acqua pura,<emph.end type="italics"/> che fusse poniamo un piede per fazza, formandone poi <lb/>un altro simile, et uguale in quantit&agrave; di detta pietra cotta, dico che il detto <lb/>cubo di pietra cotta pesaria circa il doppio di quello, che pesaria quel cubo <lb/>di acqua &rdquo; (pag. </s>

<s>28). Che se lo Storico dalle Matematiche in Italia pot&egrave; so&shy;<lb/>spettar che il Tartaglia riferisse le proporzioni de'pesi all'acqua marina, <lb/>convien dire ch'ei non leggesse questa avvertenza, premessa dall'Autore alla <lb/>descrizione della Bilancietta idrostatica, e alla tavola de'pesi specifici ritro&shy;<lb/>vati con essa: &ldquo; Tutte queste proportioni delli detti corpi materiali con l'acqua <lb/>sono state da me ritrovate con l'acqua comune di pozzo, cio&egrave; dolce e non <lb/>salsa, e per&ograve;, essendo la salsa alquanto pi&ugrave; grave della dolce, varier&agrave; al&shy;<lb/>quanto, ma poco &rdquo; (pag. </s>

<s>30). Per cui, se i pesi, nella detta Tavola descritti, <lb/>non solo sembrano, ma son veramente <emph type="italics"/>un peu trop faibles;<emph.end type="italics"/> non &egrave; da at&shy;<lb/>tribuir ci&ograve; ad altro che all'impurit&agrave; de'metalli sottoposti alle esperienze: <lb/>considerazione che non poteva essere sfuggita al Tartaglia, il quale perci&ograve; <lb/>non intese dare i pesi specifici del rame, dell'argento e dell'oro puri, ma <lb/>quali ei gli trov&ograve; alligati nelle monete, che erano allora in corso nel Regno <lb/>veneto, come bagatini, mocenighi, ducati: cos&igrave;, nella proposta Tavola, qua&shy;<lb/>lificatisi, per prevenire i dubbi di chi fosse per ritrovare altre proporzioni, <lb/>in oggetti formati di metalli, che vanno sotto que'medesimi nomi. </s></p><p type="main">

<s>Fin qui non esce fuori il Tartaglia del campo della Fisica, ma egli vuol <lb/>coronare la sua invenzione di quattro Teoremi, che egli giudica degni di <pb xlink:href="020/01/3122.jpg" pagenum="83"/>essere aggiunti a quelli dello stesso Archimede. </s>

<s>&ldquo; Quattro altre ingegnose <lb/>proposizioni, compare honorando, oltre quelle dette da Archimede, vi voglio <lb/>in questo loco narrare dimostrativamente, delle quale la prima &egrave; questa: <lb/><emph type="italics"/>La proportione de ogni dui corpi gravi in grandezza, o sia de un mede&shy;<lb/>simo, overo de diversi generi, &egrave; si come la differentia del peso de luno de <lb/>quelli in aere al peso de quel medesimo in acqua, alla differentia del peso <lb/>del altro in aere al peso di quello medesimo in acqua. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia uno de dui corpi A, et sia C tanta acqua a quel eguale in gran&shy;<lb/>dezza, et il peso di tal acqua sia E. </s>

<s>Et sia simelmente B l'altro corpo, et D <lb/>sia l'acqua a quello uguale in grandezza, et F sia il peso di quella acqua. </s>

<s><lb/>Perch&egrave; adunque, compare carissimo, l'acqua C &egrave; uguale al corpo A in gran&shy;<lb/>dezza, e similmente l'acqua D &egrave; uguale al corpo B; permutatamente la pro&shy;<lb/>portione del A al B sar&agrave; siccome del C al D, e la proportione, che &egrave; dalla <lb/>acqua C alla acqua D, quella medesima sar&agrave; del suo peso E al peso F. Adun&shy;<lb/>que, per la XI del V di Euclide, la proportione del peso E al peso F sar&agrave; <lb/>si come del corpo A al corpo B in grandezza. </s>

<s>E perch&egrave; il peso E, per la VII <lb/>del nostro Archimede, viene a esser la differentia del peso del corpo A in <lb/>aere, al peso di quel medesimo in acqua, e cos&igrave; il peso F vien a esser la <lb/>differentia del peso del corpo B in aere, al peso di quel medesimo in acqua; <lb/>per il che seguita il proposito &rdquo; (pag. </s>

<s>31, 32). </s></p><p type="main">

<s>Si possono dunque scrivere, secondo questo discorso del Tartaglia, le <lb/>proporzioni A:B=C:D=E:F, nelle quali A, B sono i volumi di due <lb/>corpi, a cui corrispondono due uguali volumi di acqua C, D: ed E, F sono <lb/>le differenze de'pesi di quegli stessi corpi in aria e in acqua. </s>

<s>Chiamate <lb/>P&mdash;<emph type="italics"/>p,<emph.end type="italics"/> P&prime;&mdash;<emph type="italics"/>p&prime;<emph.end type="italics"/> queste differenze, V, <emph type="italics"/>v<emph.end type="italics"/> i volumi, avremo perci&ograve; V:<emph type="italics"/>v<emph.end type="italics"/>= <lb/>P&mdash;<emph type="italics"/>p<emph.end type="italics"/>:P&prime;&mdash;<emph type="italics"/>p&prime;.<emph.end type="italics"/> Ora, perch&egrave;, secondo la loro naturale definizione, le gra&shy;<lb/>vit&agrave; specifiche stanno come i pesi assoluti, divisi per i volumi; dunque sta&shy;<lb/>ranno anche com'essi pesi assoluti, divisi per le differenze de'pesi in aria e <lb/>in acqua, d'onde una nuova espressione della gravit&agrave; specifica. </s></p><p type="main">

<s>Da questa proposizione trae il Tartaglia un nuovo e importantissimo co&shy;<lb/>rollario: Se <emph type="italics"/>v<emph.end type="italics"/> &egrave; il volume noto di un cubo, rispetto al quale siasi, per mezzo <lb/>della Bilancetta, trovato il valore di P&prime;&mdash;<emph type="italics"/>p&prime;,<emph.end type="italics"/> e se V &egrave; il volume incognito <lb/>di qualunque forma irregolare di corpo, per cui siasi col medesimo stru&shy;<lb/>mento determinato il valore di P&mdash;<emph type="italics"/>p;<emph.end type="italics"/> &egrave; manifesto che, per la superiore <lb/>equazione, sar&agrave; noto il valore di V. </s>

<s>Per cui, specialmente ripensando che il <lb/>Mantovani e il Viviani darebbero questa come una loro novit&agrave;, s'intende <lb/>quant'avesse giusta ragione il Tartaglia di far dire all'interlocutore suo Ric&shy;<lb/>cardo: &ldquo; Compare, questa &egrave; stata certamente una bellissima e utile propo&shy;<lb/>sitione et demostratione, perch&egrave; con grandissima facilit&agrave; se pu&ograve; cognoscere <lb/>l'area corporale de ogni strania forma di corpo, il che importa assai, perch&egrave; <lb/>saria impossibile a poterla investigare, n&egrave; sapere, per i semplici termini di <lb/>Geometria &rdquo; (ivi, pag. </s>

<s>32). </s></p><p type="main">

<s>Nella sua seconda proposizione il Tartaglia insegna a trovare il peso <lb/>specifico di due liquidi, per esempio acqua e olio. </s>

<s>Presi de'due detti liquidi <pb xlink:href="020/01/3123.jpg" pagenum="84"/>volumi uguali, non &egrave; dubbio che, dalle due equazioni G=P:V, <emph type="italics"/>g=p:v,<emph.end type="italics"/><lb/>si ha le gravit&agrave; specifiche proporzionali ai pesi assoluti. </s>

<s>Ond'&egrave; che s'otter&shy;<lb/>rebbe con facilit&agrave; la desiderata invenzione, per via della Stadera ordinaria, <lb/>pesando il medesimo vaso, per esempio un fiasco, prima pieno d'acqua, e <lb/>poi di olio. </s>

<s>Ma vuole il Nostro, anche in questo caso, applicar la Bilancetta, <lb/>osservando che, per la VII del primo di Archimede, i valori, rappresentati <lb/>con P, <emph type="italics"/>p<emph.end type="italics"/> si possono avere dalle differenze che ne resultano, pesando il me&shy;<lb/>desimo oggetto, di qualunque materia egli sia, prima nell'aria, e poi nell'un <lb/>liquido e nell'altro, per cui quella sua detta proposizione seconda fu dal&shy;<lb/>l'Autore stesso cos&igrave; formulata: <emph type="italics"/>&ldquo; Se la proportione del peso de alcun corpo <lb/>in duoi diversi liquori et in aere sar&agrave; nota; la proportione della gravit&agrave; <lb/>de l'uno de quei liquori, alla gravit&agrave; de laltro secondo la specie, sar&agrave; <lb/>manifesta &rdquo;<emph.end type="italics"/> (pag. </s>

<s>32). </s></p><p type="main">

<s>Dalla stabilita proporzione poi V:<emph type="italics"/>v<emph.end type="italics"/>=P&mdash;<emph type="italics"/>p<emph.end type="italics"/>:P&prime;&mdash;<emph type="italics"/>p&prime;,<emph.end type="italics"/> e da quell'al&shy;<lb/>tra G:<emph type="italics"/>g<emph.end type="italics"/>=P/P&mdash;<emph type="italics"/>p<emph.end type="italics"/>:P&prime;/P&prime;&mdash;<emph type="italics"/>p&prime;.<emph.end type="italics"/> conclusa gi&agrave; nella prima di queste proposi&shy;<lb/>zioni, scende senz'altro dimostrata la III dello stesso Tartaglia: <emph type="italics"/>&ldquo; Se li pesi <lb/>in aere et in acqua de dui qual si voglia corpi, poniamo di oro e di ar&shy;<lb/>gento, saranno noti; le proportioni de quelli medesimi corpi, in grandezza <lb/>et secondo la specie, saranno note &rdquo;<emph.end type="italics"/> (ivi). </s></p><p type="main">

<s>Nella quarta proposizione, pur procedendo analiticamente, come nella <lb/>passata, si cerca una formula generale, che renda possibile la risoluzione di <lb/>questo problema: <emph type="italics"/>&ldquo; Ritrovare la proportione della grandezza, et la pro&shy;<lb/>portione della gravit&agrave;, secondo la specie, de dui corpi, di quali l'uno sia <lb/>di natura pi&ugrave; grave di lacqua, come &egrave; il ferro, et l'altro di natura pi&ugrave; <lb/>leggier di lacqua, come &egrave; la cera. </s>

<s>&rdquo;<emph.end type="italics"/> Risoluto il problema, cos&igrave; l'Autore <lb/>immediatamente soggiunge: &ldquo; Con la evidentia di questa propositione egli <lb/>&egrave; possibile, de un corpo misto di dui corpi differenti in gravit&agrave;, poniamo di <lb/>oro e di argento; a dichiarare quanto vi sia dentro dell'uno, e quanto del&shy;<lb/>l'altro &rdquo; (ivi, pag. </s>

<s>33, 34). </s></p><p type="main">

<s>La formula infatti, alla quale conduce il ragionamento del Tartaglia, si <lb/>traduce facilmente in quest'altra, chiamata G la gravit&agrave; specifica del misto, <lb/><emph type="italics"/>p, p&prime;<emph.end type="italics"/> i pesi assoluti dell'oro e dell'argento, <emph type="italics"/>v, v&prime;<emph.end type="italics"/> i volumi: G=<emph type="italics"/>(p+p&prime;)/(v+v&prime;).<emph.end type="italics"/><lb/>E perch&egrave;, supponendo esser P il peso assoluto del detto misto, &egrave; manifesta&shy;<lb/>mente <emph type="italics"/>p&prime;<emph.end type="italics"/>=P&mdash;<emph type="italics"/>p,<emph.end type="italics"/> e <emph type="italics"/>v=p/g, v&prime;=p&prime;/g&prime;,<emph.end type="italics"/> intendendosi per <emph type="italics"/>g, g&prime;<emph.end type="italics"/> le respettive <lb/>gravit&agrave; specifiche dell'oro e dell'argento; avremo dunque G=P:<emph type="italics"/>(p/g<emph.end type="italics"/>+(P&mdash;<emph type="italics"/>p)/g&prime;)<emph.end type="italics"/>, <lb/>d'onde <emph type="italics"/>p<emph.end type="italics"/>=P<emph type="italics"/>g (g&prime;<emph.end type="italics"/>&mdash;G)/G <emph type="italics"/>(g&prime;&mdash;g)<emph.end type="italics"/>. </s>

<s>Ora, avendosi il valore di P dalla Stadera, e dalla <lb/>Bilancetta idrostatica i valori di G, <emph type="italics"/>g, g&prime;<emph.end type="italics"/>; sar&agrave; dunque noto <emph type="italics"/>p,<emph.end type="italics"/> ossia il peso <lb/>dell'oro, e verr&agrave; per esso notificato altres&igrave; il peso dell'argento, perch&egrave; <emph type="italics"/>p&prime;<emph.end type="italics"/>= <lb/>P&mdash;<emph type="italics"/>p,<emph.end type="italics"/> &ldquo; la qual regola, giustamente ne conclude il Tartaglia, sar&agrave; molto e <pb xlink:href="020/01/3124.jpg" pagenum="85"/>molto piu certa et men fallace di quella, che nara Vitruvio et altri autori <lb/>haver trovata Archimede, per cognoscer la fraude del artefice nell'aurea co&shy;<lb/>rona di Hierone. </s>

<s>Perch&egrave; tal sua via non servir&agrave;, salvo che in una gran massa <lb/>di oro. </s>

<s>Ma con questa se potr&agrave; conoscere tal fraude pontualmente, in un du&shy;<lb/>cato, et men de un ducato doro, domente che (purch&egrave;) si sia diligenti nel <lb/>operare &rdquo; (pag. </s>

<s>34). </s></p><p type="main">

<s>La critica, fatta cos&igrave; dal Tartaglia al metodo attribuito ad Archimede, <lb/>&egrave; giusta, per le ragioni accennate di sopra, e perch&egrave;, se l'oggetto &egrave; piccolo, <lb/>pu&ograve; essere che, nell'infonderlo, o non si versi nulla dell'acqua del vaso colmo, <lb/>o che non si versi tutta, perch&egrave; la pellicola superficiale, prima di squarciarsi, <lb/>rigonfia, e non versa che dalla parte, dov'&egrave; avvenuto lo squarcio. </s>

<s>Cos&igrave; fatti <lb/>inconvenienti si evitano manifestamente con l'uso della Bilancetta, la quale, <lb/>dando in ogni modo la differenza del peso, per qualunque minimo corpo, <lb/>fa che senza difficolt&agrave;, e con tutta la precisione, se ne possa conseguire <lb/>l'intento. </s></p><p type="main">

<s>Tali erano le utilissime promozioni che dopo la prima met&agrave; del se&shy;<lb/>colo XVI, ebbe l'idrostatica di Archimede. </s>

<s>Ma perch&egrave; s'aggiungevano a que&shy;<lb/>ste tradizioni antiche quelle altre, derivate da Frontino, anche da tal parte <lb/>fu, in quel medesimo tempo, la scienza utilmente promossa. </s>

<s>Nel 1554, in&shy;<lb/>sieme con altri opuscoli geometrici di Giovanni Buteone, ne usc&igrave; in Lione <lb/>alla luce uno, che s'intitolava <emph type="italics"/>De fluentis aquae mensura.<emph.end type="italics"/> L'Autore, dopo <lb/>avervi diligentemente esaminati i Commentarii sopra gli Acquedutti romani, <lb/>conclude che cos&igrave; Frontino come tutti gli altri Scrittori, prima e dopo lui, <lb/>quant'erano stati solleciti, in avvertire alcune cause alteratrici della velocit&agrave; <lb/>delle acque correnti, e perci&ograve; della loro misura; altrettanto s'erano dimo&shy;<lb/>strati incerti, in suggerirne i rimedii. </s>

<s>&ldquo; Multa igitur, poi soggiunge, scru&shy;<lb/>pulose mihi denique cogitanti, illa tandem subiit animum cogitatio ut que&shy;<lb/>madmodum tempus ipsum aqua stillante metitur, sic et fluentis aquae <lb/>modum mensura temporis veluti mutua posse constitui &rdquo; <emph type="italics"/>(J. </s>

<s>Buteonis Qp. </s>

<s>geo&shy;<lb/>metrica, nunc primum impressa,<emph.end type="italics"/> Lugduni 1554, pag. </s>

<s>71). E il modo, che <lb/>suggerisce, consiste nel dar, nel medesimo istante, esito all'acqua della con&shy;<lb/>serva e della clessidra, cosicch&egrave; il riempimento di un vaso di nota capacit&agrave;, <lb/>per esempio di un piede cubico, corrisponda a un determinato tempo, come <lb/>sarebbe un minuto. </s>

<s>Chiamandosi la detta capacit&agrave;, per conformarsi con Fron&shy;<lb/>tino, quinaria, &egrave; certo, dice il Buteone, che, volendosi dare due, o tre o <lb/>quattro quinarie, si far&agrave; passar l'acqua dalla medesima cannella per due, o <lb/>tre o quattro minuti, e cos&igrave; verranno misurate giustamente le dispense dalla <lb/>preparata conserva, che sempre si mantenesse alla medesima altezza, misu&shy;<lb/>rando le parti proporzionali del tempo. </s>

<s>&ldquo; His itaque rationibus et exemplis, <lb/>ni fallor, et antiquorum error manifestus, et emendatio probabilis erit. </s>

<s>Et ita <lb/>ad fluentis aquae mensuram se nostrum habet inventum &rdquo; (ibid., pag. </s>

<s>72). </s></p><p type="main">

<s>Oltre a quelle, raccolte dai libri di Archimede e di Frontino, proveni&shy;<lb/>vano altre nuove tradizioni alla Scienza dagli insegnamenti del Nemorario, <lb/>la fecondit&agrave; de'quali vedemmo rigogliosamente apparire ne'Manoscritti di Leo-<pb xlink:href="020/01/3125.jpg" pagenum="86"/>nardo da Vinci, e nelle pubbliche opere del Cardano. </s>

<s>Ma, dopo la prima <lb/>met&agrave; del secolo XVI, parve che di queste ultime tradizioni, per cui si vi&shy;<lb/>dero applicate ai liquidi le velocit&agrave;, che sollecitano tutti i gravi cadenti; ne <lb/>rimanesse spenta ogni notizia. </s>

<s>Basti a provar ci&ograve; l'esempio del Benedetti, <lb/>in quella, che egli intitolava: <emph type="italics"/>Nova solutio problematis de vase pleno li&shy;<lb/>quoris. (Speculat. </s>

<s>liber. </s>

<s>Epistolae,<emph.end type="italics"/> Venetiis 1599, pag. </s>

<s>289). </s></p><p type="main">

<s>Proponevasi il caso di un tino pieno, con tre cannelle al fondo di varia <lb/>grandezza, la prima delle quali valesse a evacuarlo in un'ora, la seconda in <lb/>due, e la terza in tre: domandavasi in quanto tempo, lasciando dette can&shy;<lb/>nelle aperte tutt'e tre insieme, voterebbero quel medesimo vaso. </s>

<s>&ldquo; Ad hoc <lb/>volo, risponde il Benedetti, ut qua&egrave;ratur primo quanta pars aquae unaquae&shy;<lb/>que fistula evacuabit in aliquo dato tempore, quod facile est, ut puta prima <lb/>fistula spatio dimidiae horae evacuabit dimidium vas, eo quod spatio inte&shy;<lb/>grae horae potest totum evacuare: secunda fistula, eodem temporis spatio, <lb/>evacuabit quartam partem ipsius vasis; tertia vero fistula, eodemmet spatio <lb/>temporis dimidiae horae, evacuabit sextam partem ipsius vasis &rdquo; (ibid.). </s></p><p type="main">

<s>Pare impossibile che un tale uomo profferisse cose tanto contrarie alla <lb/>ragione e all'esperienza, e, se non avessimo questa certezza di documenti, <lb/>non si crederebbe che le proposizioni, dimostrate dal Cardano intorno al&shy;<lb/>l'acque fluenti da'vasi, o correnti lungo i canali, si rimanessero cos&igrave; total&shy;<lb/>mente sepolte nell'oblio, che le potessero il Castelli e Galileo dare per nuove <lb/>apparizioni. </s>

<s>Ma capitali, in questa nobilissima parte dello scientifico istituto, <lb/>rimanevano, prima e dopo il Cardano, i teoremi di Archimede, i quali, se <lb/>porgevano facilissimo il modo a spiegar come l'acqua s'equilibrasse in un <lb/>sifone, co'due rami di ugual calibro, lasciavano tuttavia inesplicato e ine&shy;<lb/>splicabile il fatto del serbarsi parimente l'equilibrio, anche quando l'uno dei <lb/>detti rami fosse straordinariamente pi&ugrave; capace dell'altro. </s>

<s>Questo, che ha <lb/>l'aria di un paradosso, e che giusto &egrave; andato, e va nella Scienza idrosta&shy;<lb/>tica, sotto un tal nome, famoso, richiam&ograve; a s&egrave;, tra il finir del secolo XVI e <lb/>il cominciar del seguente, l'ingegno e lo studio dei Matematici, e parve esau&shy;<lb/>rirli tutti cos&igrave;, da non lasciarli in libert&agrave; di attendere ad altre simili spe&shy;<lb/>culazioni. </s>

<s>Vedremo infatti come fosse questo l'oggetto, a cui si rivolsero, e <lb/>da cui si svolsero le nuove istituzioni idrostatiche dello Stevino e di Galileo, <lb/><figure id="id.020.01.3125.1.jpg" xlink:href="020/01/3125/1.jpg"/></s></p><p type="caption">

<s>Figura 36.<lb/>ma prima &egrave; da mostrare come fossero, all'uno e all'al&shy;<lb/>tro autore, aperte prima le vie dallo stesso Benedetti. </s></p><p type="main">

<s>In una delle sue epistole a Giovan Paolo Capra si <lb/>propone di dimostrare perch&egrave;, avendosi un largo vaso o <lb/>mortaio come AB (fig. </s>

<s>36), a cui sia annessa una gracile <lb/>fistola C, la piccola acqua contenuta in questa possa far <lb/>resistenza alla gran mole dell'altra. </s>

<s>&ldquo; Hoc autem evenit, <lb/>egli dice, ex eo quod aqua AB non impellit aquam C toto <lb/>suo pondere, propterea quod pondus dividitur proportionaliter supra basim <lb/>vasis &rdquo; <emph type="italics"/>(Specul. </s>

<s>lib.<emph.end type="italics"/> cit., pag. </s>

<s>187, 88). Come poi sia vero che il peso vien <lb/>distribuito proporzionalmente sopra il fondo del vaso si studia di provarlo <pb xlink:href="020/01/3126.jpg" pagenum="87"/>con questo discorso: Sia un tal vaso in figura di tronco di cono, come DBNM <lb/>(fig. </s>

<s>37), e il diametro BD della base maggiore sia multiplo del diametro <lb/>della base minore, poniamo triplo, cosicch&egrave; BF. FG, GD siano uguali insieme <lb/><figure id="id.020.01.3126.1.jpg" xlink:href="020/01/3126/1.jpg"/></s></p><p type="caption">

<s>Figura 37.<lb/>e con NM. </s>

<s>Dipoi si abbassino dai punti S, G, F, O <lb/>perpendicolari in R, M, N, T, per le quali s'imma&shy;<lb/>gini passare le superficie coniche, che circumcingono <lb/>il cilindro FM. </s>

<s>Ci&ograve; fatto, si consideri l'acqua com&shy;<lb/>presa tra GM, SR, il peso della quale si dispensa <lb/>sopra MR, latitudine maggiore della GS. &ldquo; Cogi&shy;<lb/>temus igitur MC, cos&igrave; soggiunge con le sue proprie parole il Benedetti, ae&shy;<lb/>qualem esse GS: manifestum erit quod MC non sustinebit totum pondus <lb/>aquae, quae inter GM et SR reperitur, eo quod omnis pars aquae ad per&shy;<lb/>pendiculum inclinat versus mundi centrum, quapropter fundus, seu basis <lb/>MN, non sustinet aliud pondus, quam aquae FM &rdquo; (ibid., pag. </s>

<s>188). </s></p><p type="main">

<s>Cos&igrave; concludesi la dimostrazione, per confermar la quale si soggiunge <lb/>la risoluzion di un dubbio, che potrebbe nascere dal supporre il fondo alleg&shy;<lb/>gerito dalle pressioni, che l'acqua laterale fa sull'interna FM. &ldquo; Sed si quis <lb/>hoc in dubium revocaret dicens quod aqua, circumscribens situm corporis <lb/>aquei FM, impellit lateraliter dictum corpus aqueum, respondendum est quod <lb/>ex aequo huius corporis FM aqua impellit etiam aquam circumstantem, eo <lb/>quod sunt corpora homogenea, cum in corporibus homogeneis aequales par&shy;<lb/>tes habeant aequales vires &rdquo; (ibid.). </s></p><p type="main">

<s>Dunque il Benedetti suppone che l'acqua laterale sia di parti uguali, e <lb/>perci&ograve; di pari forza all'interna: o se fosse maggiore o minore? </s>

<s>E anche ri&shy;<lb/>tenendo per dimostrati questi principii, e per evidente che la porzion di pa&shy;<lb/>rete MC non sostien tutta l'acqua compresa fra GM, SR, chi da ci&ograve; vede <lb/>conseguir le ragioni del paradosso idrostatico, secondo che l'Autore s'era <lb/>proposto? </s>

<s>Nasce l'oscurit&agrave; da quel combattersi, che facevano, dentro la mente <lb/>del Benedetti, le idee vecchie, cos&igrave; tenacemente radicate nella prima suppo&shy;<lb/>sizion di Archimede, con le nuove: combattimento che pi&ugrave; affannoso appa&shy;<lb/>risce ne'lettori studiosi, che nell'Autore stesso del libro delle Speculazioni. </s>

<s><lb/>Basti, tra il numero di cos&igrave; fatti studiosi, additare il Porta, il quale cos&igrave; scri&shy;<lb/>veva, nel primo libro de'suoi <emph type="italics"/>Spiritali,<emph.end type="italics"/> al cap. </s>

<s>X, per dimostrare che ogni <lb/>parte dell'umido preme s&egrave; stessa a perpendicolo: </s></p><p type="main">

<s>&ldquo; Bisogna ancora un'altro assioma, per la ragion de'principii. </s>

<s>Ogni <lb/>parte dell'umido, che sta in alcun vaso, non ognuna preme ognuna, ma cia&shy;<lb/>scuna preme quella sola parte, la quale le sta sotto a perpendicolo. </s>

<s>Noi ne <lb/>porremo un esempio assai bastevole. </s>

<s>Sia alcun vaso piramidale, di cui il cono <lb/>sia sotto, e la base di sopra, e sia la cima rotta NM (nella precedente figura) <lb/>e si tirino le linee GM, FN. </s>

<s>Dico che l'acqua, che star&agrave; in GD, in quella <lb/>parte della piramide DGM; che solo preme col suo peso l'acqua DM, perch&egrave; <lb/>le sta sotto a perpendicolo, e non preme la GF ovvero MN, n&egrave; s'intromette <lb/>ne'luoghi GF, MN, se non che, cacciata l'acqua dal suo luogo, da GD sia <lb/>forzata passare in FG, o MN. </s>

<s>Ma ne seguirebbe da questo che la parte <pb xlink:href="020/01/3127.jpg" pagenum="88"/>FGMN sarebbe premuta dall'acqua GDM di fuori del suo luogo, il che &egrave; <lb/>impossibile, per esser l'acqua corpo di una medesima specie, e le sue parti <lb/>uguali hanno forze uguali &rdquo; (Napoli 1606, pag. </s>

<s>25). Il simile, soggiunge, &egrave; <lb/>da dire di un esperimento, che egli passa a descrivere, ed &egrave; quello del mor&shy;<lb/>taio, proposto dal Benedetti, ch'esso Porta conferma e illustra in altri due <lb/>modi: col far cio&egrave; osservare che rimosso il tubo C (nella figura XXXVI) lo <lb/>zampillo risale sempre alla medesima altezza, per allargare o restringere il <lb/>vaso AB quanto si vuole; poi riducendo alla mente le frodi di taluni, i quali, <lb/>cavato vin dalla botte, la riempiono, per un sottilissimo cannello, con altret&shy;<lb/>tanta acqua, la quale ha nonostante virt&ugrave; di movere e di sostituirsi alla gran <lb/>mole, purch&egrave; sia fatta scendere da tale altezza, che superi il livello del li&shy;<lb/>quido nella stessa botte. </s></p><p type="main">

<s>Lo scioglimento e il progresso di queste dottrine non si poteva sperare, <lb/>n&egrave; aversi, che dal ridurre alla sua massima generalit&agrave; la particolare ipotesi <lb/>di Archimede, riconoscendo cio&egrave; che l'umido non preme solo a perpendi&shy;<lb/>colo, ma per tutti i versi. </s>

<s>Che se il Benedetti poneva tra i principii dimo&shy;<lb/>strativi del paradosso idrostatico le pressioni, che soffrono le pareti, erette <lb/>sopra il fondo del vaso; non faceva che mostrar la chiave da aprire il mi&shy;<lb/>stero. </s>

<s>Rimaneva per&ograve; a lavorarne l'ingegno, e ci&ograve; fece Simeone Stevino, <lb/>venuto dalla lontana Bruges a inserire mirabilmente, nel tronco della scienza, <lb/>un surculo nuovo. </s></p><pb xlink:href="020/01/3128.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO II.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dell'Idrostatica nei principii del secolo XVII<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. Dell'Idrostatica negli <emph type="italics"/>Elementi<emph.end type="italics"/> di Simeone Stevino. </s>

<s>&mdash; II. Dell'Idrostalica nei varii seritti di Ga&shy;<lb/>lileo, e particolarmente nel Discorso intorno alle galleggianti. </s>

<s>&mdash; III. Dell'Idrostatica nei com&shy;<lb/>menti di Marino Ghetaldo, di David Rivault, e di altri, sopra i libri di Arehimede. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Mentre il Benedetti, e gli studiosi delle Speculazioni di lui, ripetevano <lb/>quel che sempre s'era detto da tutti, giurandolo sull'autorit&agrave; di Archimede, <lb/>che <emph type="italics"/>omnis pars aquae ad perpendiculum inclinat:<emph.end type="italics"/> lo Stevino, migliore in&shy;<lb/>terpetre degli antichi insegnamenti, e non da altra autorit&agrave; soggiogato, che <lb/>da quella della ragione; usciva il primo a pronunziare con libera sicurt&agrave; la <lb/>sentenza nuova: &ldquo; que l'eau propos&eacute;e soit de tout cost&eacute; de pesanteur uni&shy;<lb/>forme &rdquo; <emph type="italics"/>(Oeuvres mathem.<emph.end type="italics"/> a Leyde 1634, pag, 485), e perci&ograve; che essa acqua <lb/>inclina, ed &egrave; premuta, non solo <emph type="italics"/>ad perpendiculum,<emph.end type="italics"/> ma di sotto e di sopra <lb/>ugualmente, e da'lati, e insomma per tutti i versi. </s>

<s>Da che faceva l'Autore <lb/>conseguire la proposizione, posta da lui per fondamento al trattato suo nuovo <lb/><emph type="italics"/>Des elemens hydrostatiques,<emph.end type="italics"/> sotto la forma: &ldquo; L'eau propos&eacute;e tient telle po&shy;<lb/>sition, qu'on voudra dans l'eau &rdquo; (ivi). </s></p><p type="main">

<s>Se l'acqua dunque, contenuta in un vaso, pesa per tutti i versi, pre&shy;<lb/>mer&agrave; non solamente il fondo, ma le pareti di lui laterali, ci&ograve; che, sebbene <lb/>molti riconoscessero esser vero, persuasi dalla esperienza, non ne avevano <lb/>per&ograve; certezza alcuna di scienza, la quale si riduceva a dire con qual legge <lb/>e misura si facessero quelle pressioni. </s>

<s>Lo Stevino perci&ograve; attese principal&shy;<lb/>mente a ritrovare una tale scienza, proponendosi di dimostrarla tanto rispetto, <pb xlink:href="020/01/3129.jpg" pagenum="90"/>al premere, che fa il liquido contro una parete, da lui detta <emph type="italics"/>convenant,<emph.end type="italics"/><lb/>quanto contro pareti di qualunque figura: &ldquo; Fond convenant, poi, come dal&shy;<lb/>l'Autore stesso si definisce, est celuy duquel chaque deux mottiez conve&shy;<lb/>nient: ou pourroit dire que c'est celuy, dont tous les diametres sont coupez <lb/>en deux egalement par le centre &rdquo; (ivi): e tali sarebbero i circoli, le ellissi, <lb/>i parallelogrammi, i poligoni regolari di pari numero di lati, anche mi&shy;<lb/>stilinei. </s></p><p type="main">

<s>Incominciando dal dimostrar le leggi, e le misure delle pressioni, fatte <lb/>dall'acqua sopra i detti fondi <emph type="italics"/>convenant,<emph.end type="italics"/> o simmetrici, distingue lo Stevino <lb/>due casi: il primo de'quali &egrave; che il piano del fondo laterale sia a perpen&shy;<lb/>dicolo sotto il livello del liquido sostenuto, e il secondo, che lo stesso piano <lb/>fondale sia obliquo. </s>

<s>In ogni caso per&ograve; dimostra esser vero ci&ograve; che si pro&shy;<lb/>pone, cos&igrave; dicendo: &ldquo; Sur un fond convenant, duquel le plus haut poinct <lb/>est a fleur d'eau, repose un poids egal &agrave; la demi-colomne d'eau, de la quelle <lb/>la base est pareille au dit fond, et sa hauteur egale a la perpendicle com&shy;<lb/>prise entre les niveaux, qui passent par le plus haut, et plus bas poinct du <lb/>dit fond &rdquo; (ivi, pag. </s>

<s>488). </s></p><p type="main">

<s>Sia AB (fig. </s>

<s>38) un vaso pieno, e la parete laterale AD un rettangolo, <lb/>perpendicolarmente eretto alla orizzontale, col supremo lato AC a fior d'acqua: <lb/>presa DH uguale a DC, e condotta la CH, si vuol dallo Stevino dimostrare <lb/>che la pressione contro la parete AD &egrave; quella medesima, che si farebbe dal <lb/><figure id="id.020.01.3129.1.jpg" xlink:href="020/01/3129/1.jpg"/></s></p><p type="caption">

<s>Figura 38.<lb/>prisma triangolare EACDH, se fosse <lb/>un solido di pari gravit&agrave; all'acqua, po&shy;<lb/>sato sopra lo stesso fondo AD, suppo&shy;<lb/>sto mobile, e ridotto a giacitura oriz&shy;<lb/>zontale. </s>

<s>La dimostrazione &egrave; condotta <lb/>per via degli inscritti e dei circoscritti, <lb/>secondo il metodo antico, il quale, o <lb/>si chiami de'l&igrave;miti, come oggid&igrave; si fa, <lb/>o delle esaustioni, ridotto ai suoi pi&ugrave; <lb/>semplici termini, si riscontra con quel&shy;<lb/>lo degl'indivisibili. </s>

<s>Invece infatti di di&shy;<lb/>vider la base AD prima in quattro, poi <lb/>in otto, poi in sedici parti uguali, e cos&igrave; procedere, infin tanto che i paral&shy;<lb/>lelepipedi inscritti e circoscritti, riposanti sopra quelle cos&igrave; moltiplicate sud&shy;<lb/>divisioni di basi, <emph type="italics"/>differeroyent moins qu'aucun corps donn&eacute;;<emph.end type="italics"/> si pu&ograve; diret&shy;<lb/>tamente considerare la colonna acquea, o il prisma triangolare EACDH, come <lb/>diviso in infiniti piani rettangolari, via via decrescenti, e tutti paralleli al <lb/>massimo AD: o anche, come diviso in triangoli infiniti, tutti uguali al DCH, <lb/>e a lui stesso paralleli. </s>

<s>Cos&igrave;, la proposizione viene a dimostrarsi per via assai <lb/>facile e breve, perch&egrave;, dovendo le pressioni crescere come le profondit&agrave;, la <lb/>loro scala &egrave; data dalle infinite ordinate nel triangolo CDH, parallele a DH. <lb/>Or, intessendosi esso triangolo di queste stesse ordinate infinite, &egrave; manife&shy;<lb/>sto che la pressione, fatta sul latercolo CD, &egrave; uguale al peso della colonna <pb xlink:href="020/01/3130.jpg" pagenum="91"/>acquea triangolare CDH. </s>

<s>E intessendosi dall'altra parte degli infiniti piani <lb/>triangolari, tutti uguali a CDH, la colonna acquea o il prisma EACDH, mi&shy;<lb/>surato dal prodotto della base AD, e della met&agrave; dell'altezza DH, o DC; ri&shy;<lb/>mane dimostrato senz'altro il proposito dello Stevino. </s></p><p type="main">

<s>Si pu&ograve; con pari facilit&agrave; dimostrare quanta sia la pressione, fatta su <lb/>qualche parte della parete AD, verso il fondo, pur rimanendosi come dianzi <lb/>il vaso, infino al supremo orlo AC, pieno. </s>

<s>Vogliasi per esempio sapere qual <lb/>peso d'acqua preme la porzion di parete GD. </s>

<s>Condotta la IK parallela a DH, <lb/>e la KL parallela a DC, &egrave; manifesto che il latercolo ID &egrave; premuto dal peso <lb/>del rettangolo acqueo IL, e del triangolo KLH, e per&ograve; tutta la parete GD, <lb/>che s'intesse degl'infiniti latercoli tutti uguali ad ID, verr&agrave; premuta da un <lb/>parallelepipedo acqueo, e da un prisma triangolare, ambedue risiedenti sopra <lb/>base uguale, ma quello alto quanto DL, ossia IC, e questo alto quanto LH, <lb/>ossia ID, la qual linea si supponga esser tagliata nel mezzo in M. </s>

<s>Sar&agrave; dun&shy;<lb/>que la somma dei due solidi GD.IC+GD.ID/2=GD(IC+CM), se&shy;<lb/>condo che proponevasi lo Stevino di dimostrare in questa forma: &ldquo; Estant <lb/>un fond convenant dans l'eau, ayant son extremit&eacute; superieure sous fleur <lb/>d'eau, le poids qui repose a l'encontre est egal a la pesanteur de la colomne <lb/>d'eau, ayant le dit fond pour base et pour hauteur la perpendiculaire entre <lb/>la fleur d'eau, et le plus haut poinct du fond: et d'avantage la moiti&eacute; de la <lb/><figure id="id.020.01.3130.1.jpg" xlink:href="020/01/3130/1.jpg"/></s></p><p type="caption">

<s>Figura 39.<lb/>perpendule depuis le pius haut poinct <lb/>du fond, jusques au niveau passant <lb/>par le plus bas &rdquo; (pag. </s>

<s>491). </s></p><p type="main">

<s>Come poi si verifichino le due di&shy;<lb/>mostrate proposizioni altres&igrave; nel caso, <lb/>che la parete, invece di essere perpen&shy;<lb/>dicolare al livello del liquido, gli sia <lb/>obliqua; &egrave; facile certificarsene, per&shy;<lb/>ch&egrave;, trasformata nella 39 la prece&shy;<lb/>dente figura, il triangolo DCH ha <lb/>sempre la medesima base DH, uguale <lb/>a DC, e per altezza la perpendicolare <lb/>CO, abbassata fra il livello del liquido, <lb/>e il pi&ugrave; basso fondo orizontale del vaso. </s>

<s>Come pure al rettangolo IL, e al <lb/>triangolo KLH, riman la medesima base ID, ma l'altezza, nel primo di <lb/>que'due solidi, &egrave; ridotta a PQ, e a QH nel secondo, le quali due altezze, <lb/>come resultino uguali alle CN, NO, &egrave; manifesto dalla punteggiata costru&shy;<lb/>zione della figura. </s></p><p type="main">

<s>Sia nel rettangolo AD (fig. </s>

<s>39) inscritta un'ellisse, in cui suppongasi <lb/>trasformata la parete, sopra la quale si vuol misurar la pressione. </s>

<s>&Egrave; mani&shy;<lb/>festo che questa, per un discorso simile a quello fatto dallo Stevino, &egrave; quella <lb/>che vi si produrrebbe dal peso di un cilindroide, avente per base l'ellisse <lb/>stessa, e per altezza la perpendicolare CD: cilindroide che, essendo di pari <pb xlink:href="020/01/3131.jpg" pagenum="92"/>gravit&agrave; all'acqua, fosse segato dal piano diametrale, che passa per CH. </s>

<s>Quel <lb/>che dicesi dell'ellisse &egrave; facile vedere come sia applicabile a tutte le altre <lb/>figure qualunque, purch&egrave; simmetriche intorno a un asse. </s>

<s>Ma anche per le <lb/>figure asimmetriche o <emph type="italics"/>inconvenants<emph.end type="italics"/> lo Stevino stesso insegna a misurar le <lb/>pressioni idrostatiche fatte sopr'esse, mediante la soluzione del seguente pro&shy;<lb/>blema: &ldquo; Estant dans l'eau un fond plat, de figure quelconque, trouver un <lb/>corps d'eau equiponderant au poids reposant contre le dit fond &rdquo; (ivi, <lb/>pag. </s>

<s>494). </s></p><p type="main">

<s>Premessi i quali principii, si pu&ograve; facilmente intendere perch&egrave; si faccia <lb/>l'equilibrio tra l'acqua del mortaio, e quella della fistola annessa, secondo <lb/>la proposizione del Benedetti: &ldquo; parquoy la petite eau CDE (nella figura 36) <lb/>pousse autant contre le fond HB, que la grande eau AB &rdquo; (ivi, pag. </s>

<s>499). <lb/>Abbassate infatti sulla orizontale FD, che passa per il centro E della parete <lb/>acquea HB, le perpendicolari GF, CD; la pressione fatta dalla piccola acqua <lb/>CDE, sulla detta parete, &egrave;, per le cose gi&agrave; dimostrate, HB.CD, e la pres&shy;<lb/>sione, fatta sulla medesima dalla grande acqua AB, &egrave; per le stesse ragioni <lb/>HB.GF. </s>

<s>Ma CD, GF sono uguali, dunque il velo acqueo HB, essendo pre&shy;<lb/>muto da due forze uguali e contrarie, s'intende perch&egrave; non pu&ograve; muoversi, <lb/>n&egrave; passare egli e i successivi a ingrosssre l'acqua del pi&ugrave; piccolo recipiente. </s></p><p type="main">

<s>Cos&igrave; riduceva lo Stevino a ragioni matematiche quel che il Benedetti <lb/>diceva distribuirsi il peso proporzionalmente sopra il fondo del vaso, e solo <lb/>parzialmente sopra le pareti laterali di lui. </s>

<s>Ma perch&egrave; la nuova Scienza idro&shy;<lb/>statica era universale, si poteva per essa ugualmente bene rivelare il mistero <lb/><figure id="id.020.01.3131.1.jpg" xlink:href="020/01/3131/1.jpg"/></s></p><p type="caption">

<s>Figura 40.<lb/>della Natura, anche presentandosi sotto altri varii <lb/>aspetti, come quando per esempio il vaso conico <lb/>avesse la sua maggior base in basso. </s>

<s>Suppongasi <lb/>essere un tal vaso ABCD (fig. </s>

<s>40): lo Stevino <lb/>aveva ne'suoi principii ritrovate le ragioni, per <lb/>cui il fondo CD riceve ugual pressione dalla pic&shy;<lb/>cola acqua ABCD, e dalla grande EFCD. </s></p><p type="main">

<s>Non difficilmente poteva occorrere al pensiero anche degli studiosi del <lb/>Benedetti, che come, stando la minor base del vaso in basso, il fondo era <lb/>dalle pareti alleggerito, cos&igrave; in questa nuova posizione fosse invece aggra&shy;<lb/>vato: per cui la pressione contro esso fondo l&agrave; fosse meno, &egrave; qua pi&ugrave; di <lb/>quella fatta da tutta l'acqua del recipiente. </s>

<s>Il concetto, vero in s&egrave; stesso, <lb/>voleva come tale essere dimostrato, ci&ograve; che poteva facilmente farsi cos&igrave;, ap&shy;<lb/>plicandovi le proposizioni dello stesso Stevino: Consideriamo sopra il fondo <lb/>CD un punto qualunque M, il quale sarebbe premuto da solo il peso del <lb/>filetto liquido GM, se questo fosse in stato naturale. </s>

<s>Ma egli &egrave; invece in <lb/>stato violento, tendendo a risalire in su, come si vedrebbe avvenire di fatto, <lb/>se nel punto G la parete avesse un foro. </s>

<s>Dunque essa parete ripreme il <lb/>filetto in gi&ugrave;, ed &egrave; causa, cosi facendo, d'accrescergli nuovo peso sopra il <lb/>suo proprio e naturale. </s>

<s>Or perch&egrave; la repressione &egrave; tanta, quanta &egrave; la pres&shy;<lb/>sione, la quale, essendosi l'area parietale ridotta a un punto, &egrave; per la pro-<pb xlink:href="020/01/3132.jpg" pagenum="93"/>posizione dello stesso Stevino uguale al gravitar del filetto liquido GL; tanto <lb/>sar&agrave; il peso, che aggiungesi al peso naturale del filetto GM: cosicch&egrave; il punto <lb/>M sar&agrave; premuto da tutto intero il filetto ML. </s>

<s>Col medesimo ragionamento <lb/>si dimostrerebbe che, non solo il punto N, ma tutti gli altri infiniti, com&shy;<lb/>ponenti la sezione CD del fondo, son premuti ciascuno dal peso de'respet&shy;<lb/>tivi filetti liquidi, che risalgono in fin su all'altezza del livello. </s>

<s>Ma dalla <lb/>somma di cotali filetti infiniti resulta la mole acquea EFDC; dunque &egrave; da <lb/>questa premuto il detto fondo, come da quella, bench&egrave; tanto minore, che <lb/>realmente ritiene in s&egrave; il vaso fra le sue sponde. </s></p><p type="main">

<s>Che se fosse esso vaso configurato come nella 41, &egrave; facile vedere che <lb/>al peso naturale dei filetti AB, CD, e degli altri simili infiniti, aggiungen&shy;<lb/><figure id="id.020.01.3132.1.jpg" xlink:href="020/01/3132/1.jpg"/></s></p><p type="caption">

<s>Figura 41.<lb/>dosi le repressioni fatte da'punti A, C del coperchio, le <lb/>quali equivalgono alle pressioni dei filetti AE, CF; il <lb/>fondo GH &egrave; premuto cos&igrave; dalla piccola acqua MHGNO, <lb/>come dalla grande EGHM. Cosicch&egrave;, qualunque forma <lb/>abbiasi il recipiente, e o poco o molto, mantenendo il <lb/>medesimo fondo e la medesima altezza, sia il liquido con&shy;<lb/>tenuto, si pu&ograve; con lo Stevino concludere in generale: &ldquo; Sur <lb/>le fond de l'eau, parallele a l'horizon, repose un poids <lb/>egal a la pesanteur de l'eau, qui est egal &agrave; la colomne, dont la base est le <lb/>fond susdit, et la hauteur la perpendicle sur l'horizon, entre le fond et la <lb/>fleur de l'eau &rdquo; (ivi, pag. </s>

<s>487). </s></p><p type="main">

<s>La dimostrazione dell'Autore per&ograve; procede in altra maniera, da quella <lb/>che s'&egrave; detta, e pi&ugrave; accomodata alla qualit&agrave; de'Filosofi di que'tempi, tut&shy;<lb/>tavia alieni dal professare il metodo degli indivisibili, e meglio che dalla ra&shy;<lb/>gion matematica disposti a persuadersi dalla naturale semplicit&agrave; di queste <lb/><figure id="id.020.01.3132.2.jpg" xlink:href="020/01/3132/2.jpg"/></s></p><p type="caption">

<s>Figura 42.<lb/>osservazioni: Sia il vaso ADCE (fig. </s>

<s>42): che il suo fondo <lb/>DC sia premuto dal peso di una colonna d'acqua, la <lb/>quale abbia per base DC, e per altezza la perpendicolare <lb/>AD; &egrave; cosa tanto per s&egrave; manifesta, da rendere superfluo <lb/>ogni discorso, intorno al quale perci&ograve; non trova lo <lb/>Stevino altro modo di procedere, che dall'assurdo. </s></p><p type="main">

<s>Cos&igrave; essendo, come da ogni parte apparisce il vero, <lb/>si separi nella massa del liquido la porzione GHIE, e non per questo ver&shy;<lb/>ranno alterate le prime condizioni dell'equilibrio, le quali anzi seguiteranno <lb/>a rimaner tali, anche quando, alla mole acquea GI, si sostituisca un solido <lb/>di pari gravit&agrave;, e talmente aderente e fisso alle contigue pareti, che la capa&shy;<lb/>cit&agrave; del vaso si riduca all'acqua ADCIHG. </s>

<s>Dunque sar&agrave; cos&igrave; premuto il <lb/>fondo DC da questa sola, come da tutta l'AC. </s></p><p type="main">

<s>Da una tal proposizione fa lo Stevino scendere un corollario importante, <lb/>ed &egrave; che, trovandosi il velo acqueo HI premuto dal peso della colonna GI, <lb/>e pur non movendosi in basso; &egrave; necessario che sia risospinto in alto con <lb/>forza uguale, di che si vedrebbe l'effetto manifesto, quando lo spazio GI <lb/>restasse vuoto, e il coperchio HI del vaso fosse in qualche punto forato. </s></p><pb xlink:href="020/01/3133.jpg" pagenum="94"/><p type="main">

<s>Come queste fisiche conclusioni si riscontrino con le dimostrazioni ma&shy;<lb/>tematiche dette di sopra, si comprende assai facilmente. </s>

<s>Ma la ragione s'ar&shy;<lb/>rendeva cos&igrave; malvolentieri a consentire ugual peso a un'oncia d'acqua, e a <lb/>mille libbre, e cos&igrave; pareva ritrosa ad ammetter nel liquido la spinta in su, <lb/>contro la gravit&agrave; sua naturale; che lo Stevino pens&ograve; di dover l'uno e l'al&shy;<lb/><figure id="id.020.01.3133.1.jpg" xlink:href="020/01/3133/1.jpg"/></s></p><p type="caption">

<s>Figura 43.<lb/>tro paradosso confermare con l'esperienza. </s>

<s>Che la <lb/>poca acqua della fistola contrappesi alla molta del <lb/>mortaio appariva, nello strumento del Benedetti, come <lb/>cosa di fatto. </s>

<s>Ma esso Stevino soggiunge, a questi, due <lb/>altri esempi, in cui si parrebbe operar piuttosto'dal&shy;<lb/>l'arte magica, che dalla Natura. </s></p><p type="main">

<s>Un cilindro DE (fig. </s>

<s>43), cavo e pien d'acqua, <lb/>sia contrappesato dal grave P sul braccio di una bi&shy;<lb/>lancia, sostenuta in C. </s>

<s>Si cali, per via del filo FG, <lb/>un cilindro solido, che non riempia tutta la cavit&agrave; <lb/>del vaso sottoposto, facendone versare tutta l'acqua, ma lasciandovene in&shy;<lb/><figure id="id.020.01.3133.2.jpg" xlink:href="020/01/3133/2.jpg"/></s></p><p type="caption">

<s>Figura 44.<lb/>torno alle pareti e sul fondo un velo, il quale, bench&egrave; ri&shy;<lb/>dotto a un'estrema sottigliezza, pur mostra di pesar quanto <lb/>tutta l'acqua che v'era prima, giacch&egrave; si vede che la bi&shy;<lb/>lancia non s'&egrave; mossa. </s>

<s>Siano inoltre due vasi con fondi <lb/>circolari uguali, e traforati ugualmente nel centro, ma <lb/>l'uno sia cilindrico, come AB (fig. </s>

<s>44), l'altro tubulare, <lb/>come DEF (fig. </s>

<s>45). Si coprano i fori de'<gap/>ondi con ro&shy;<lb/><figure id="id.020.01.3133.3.jpg" xlink:href="020/01/3133/3.jpg"/></s></p><p type="caption">

<s>Figura 45.<lb/>telle GH, fatte del medesimo legno, e di uguale diametro, <lb/>e s'infonda l'acqua infin che non giunga a pari altezza, <lb/>nell'un recipiente e nell'altro. </s>

<s>Dovrebbero le dette rotelle, <lb/>secondo le cose dimostrate, esser premute ugualmente, ben&shy;<lb/>ch&egrave; l'una abbia sopra s&egrave; la poca acqua del tubo, e l'altra <lb/>quella del gran cilindro: &ldquo; ce qu'on peut recognoistre par <lb/>experience, dice lo Stevino, en attachant des poids elevans <lb/>egaux T, S, equiponderans a l'eau que l'assiette GH supporte &rdquo; (ivi, pag. </s>

<s>499). </s></p><p type="main">

<s>L'altro paradosso del sospingere in su l'acqua, che pure, come tutti i <lb/>gravi tende naturalmente in basso, bench&egrave; reso dagli zampilli evidente, si <lb/>studiava lo Stevino di confermare con una esperienza cos&igrave; semplice e dimo&shy;<lb/>strativa, che dopo tre secoli si dura tuttavia a ripetere nelle Scuole. </s>

<s>Consi&shy;<lb/>steva nell'apporre a un tubo di vetro per fondo posticcio una rotella di mate&shy;<lb/>ria grave, come sarebbe di piombo, la quale rotella, mentre che il tubo sta <lb/>in aria, non gli si pu&ograve; tenere applicata, se non tirandovela per un filo, ma, <lb/>immersa con tutto il tubo nell'acqua, vi si vede esser sostenuta dalla pres&shy;<lb/>sione in su, senza altro aiuto. </s></p><p type="main">

<s>Questa pressione, che evidentemente appariva operare dal basso in alto, <lb/>notava lo Stevino non dipender punto dalla quantit&agrave; dell'acqua circumfusa, <lb/>ma dalla sola sua altezza, cosicch&egrave; un sottil filo di acqua perpendicolare <lb/>avrebbe potuto vincere quella di tutto l'oceano, com'egli stesso particolar-<pb xlink:href="020/01/3134.jpg" pagenum="95"/>mente descriveva con questo esempio: &ldquo; Soit ABCD (fig. </s>

<s>46) un vaisseau <lb/>plein d'eau, avec un pertuis EF au fond DC, sur le quel repose une assiette <lb/><figure id="id.020.01.3134.1.jpg" xlink:href="020/01/3134/1.jpg"/></s></p><p type="caption">

<s>Figura 46.<lb/>minugrave a l'eau: la mesme pressera le <lb/>fond comme il a est&eacute; dit cy dessus. </s>

<s>Soit <lb/>puis apres IKL un petit canal, dont le trou <lb/>superieur I soit de mesme hauteur que AB, <lb/>et son trou inferieur soit EF. </s>

<s>Et remplis&shy;<lb/>sant ce canal plein d'eau, ce peu d'eau <lb/>poussera autant contre l'assiette par des&shy;<lb/>sous, que la grande eau par dessus, car <lb/>alors l'assiette GH s'elevera en haut. </s>

<s>Tel&shy;<lb/>lement que 1 lb. </s>

<s>d'eau (je pose qu'autant <lb/>contienne le canal IKL) fera plus d'effort <lb/>contre l'assiette GH, que non pas 100,000 lb.: ce qu'on pourroit estimer <lb/>un mystere en la Nature, si la cause estoit incognue &rdquo; (ivi, pag. </s>

<s>500). </s></p><p type="main">

<s>Ed ecco venir di qui la soluzion vera al problema, che tanto dette tra&shy;<lb/>vaglio a Leonardo da Vinci e al Tartaglia. </s>

<s>Se DC, nella medesima figura 46, <lb/>rappresenta il fondo del pozzo, e GH la baga, &egrave; manifesto, per queste dot&shy;<lb/>trine dello Stevino, che, non comunicando con l'acqua la parte inferiore EF <lb/>di essa baga, sar&agrave; premuta sul fondo con tutto il suo proprio peso, e con <lb/>quello del liquido soprapposto. </s>

<s>Mentre invece, se vi &egrave; qualche comunicazion <lb/>da'lati e di sotto, questa fa l'effetto del tubo IKL, e la baga stessa risale <lb/>a galla per la sua propria leggerezza. </s>

<s>Pu&ograve; similmente DC rappresentare il <lb/>fondo marino, e GH la nave sommersa, secondo il problema propostosi dal <lb/>Tartaglia, e la maggiore difficolt&agrave; del riavere essa nave, quando &egrave; arrenata, <lb/>che quando semplicemente riposa sui sassi, corrisponde alle difficolt&agrave;, che si <lb/>provano nel voler ritirare in su l'assicella, tanto maggiori, quando la sua <lb/>inferiore superficie ne &egrave; esclusa, che quando comunica con l'acqua supe&shy;<lb/>riore, per via del sottilissimo tubo. </s></p><p type="main">

<s>Nel ricercare la ragione delle pressioni, che soffre l'otre pien d'aria <lb/>posto in fondo al pozzo, occorreva a Leonardo a risolvere un altro simile <lb/>problema: perch&egrave;, cio&egrave;, l'uomo, stando in luogo dell'otre, non sente pas&shy;<lb/>sione dal gran peso dell'acqua, che gli sovrasta. </s>

<s>La speculazione &egrave; di an&shy;<lb/>tica data, e si trova, come accennammo altrove, proposta da Herone Ates&shy;<lb/>sandrino, nel proemio al suo libro <emph type="italics"/>Degli spiritali,<emph.end type="italics"/> dove si legge: &ldquo; Dicono <lb/>dunque certi, a proposito del non essere oppressi i notanti nel fondo del <lb/>mare, che ci&ograve; avviene, perch&egrave; l'acqua in s&egrave; stessa &egrave; ugualmente grave. </s>

<s>Ma <lb/>questi non vengono punto ad assegnare altra ragione del fatto, la quale fa <lb/>di mestieri dimostrarla in questa guisa. </s>

<s>Immaginiamoci la parte superiore <lb/>dell'acqua dalla superficie, che tocca il corpo in essa immerso, e sopra la <lb/>quale seguita l'acqua; essere una mole o corpo egualmente grave come <lb/>l'acqua, e che abbi conforme figura al resto dell'acqua che &egrave; di sopra, ed <lb/>immaginiamoci che questa mole sia mossa nel resto dell'acqua, di modo che <lb/>la superficie sua inferiore si accosti al corpo immerso, e sia quasi come una <pb xlink:href="020/01/3135.jpg" pagenum="96"/>cosa stessa con quello, e che successivamente vi sia sopra la parte superiore <lb/>dell'acqua: &egrave; chiara cosa che questa mole immersa non sovrasta tanto o <lb/>quanto al resto dell'acqua, e meno &egrave; sommersa sotto la superficie superiore <lb/>di essa. </s>

<s>&Egrave; poi per certo stato da Archimede dimostrato, nel Libro che fa <lb/><emph type="italics"/>Delle cose che vanno per acqua,<emph.end type="italics"/> che li corpi ugualmente gravi, e l'acqua <lb/>immersa nell'altr'acqua non seprast&agrave; punto all'acqua, n&egrave; meno viene da <lb/>questa depressa. </s>

<s>Adunque non calcher&agrave; le a lei sottoposte cose, e, levatone <lb/>di sopra tutto quello che premere averia potuto, nondimeno quel corpo se <lb/>ne star&agrave; nell'istesso loco. </s>

<s>Per qual conto dunque premer&agrave; quel corpo, che <lb/>non appetisce di calare in altro pi&ugrave; basso loco? (Traduz. </s>

<s>cit., fol. </s>

<s>10, 11). </s></p><p type="main">

<s>Il ragionamento di Herone sembra a prima vista ridursi a quello dello <lb/>Stevino, messo cos&igrave; da lui in forma di sillogismo: &ldquo; Tout pressement qui <lb/>blesse le corps pousse quelque partie du corps hors de son lieu naturel. </s>

<s>Ce <lb/>pressement caus&egrave; par l'eau ne pousse aucune partie du corps hors de son <lb/>lieu naturel; Ce pressement donc caus&eacute; par l'eau ne blesse nullement le <lb/>corps. </s>

<s>La mineure est manifeste par l'experience, don la raison est que s'il <lb/>y avoit quelque chose qui soit pouss&eacute;e hors de son lieu, il faudroit que cela <lb/>rentrast en un autre lieu, mais ce lieu n'est pas dehors, a cause que l'eau <lb/>presse de tout cost&eacute; egalement (quant &agrave; la partie de dessous elle est un <lb/>peu plus press&eacute;e que celle de dessus par la XI proposition des Elemens hy&shy;<lb/>drostatiques, ce qui n'est d'aucune estime, d'autant que telle difference ne <lb/>peut pousser aucune partie hors de son lieu naturel) ce lieu n'est pas aussi <lb/>dedans le corps, car il n'y a rien de vuide non plus que dehors; d'ou il <lb/>s'ensuit que les parties s'entre poussent egalement, pource que l'eau a une <lb/>mesme raison a l'entour du corps. </s>

<s>Ce lieu-la done n'est dehors ny dedans <lb/>le corps et par consequent en nulle part, ce qui fait que nulle partie n'est <lb/>pouss&eacute;e hors de son lieu, et partant ne blesse nullement le corps &rdquo; (ivi, <lb/>pag. </s>

<s>500). </s></p><p type="main">

<s>Dicemmo che la soluzione dell'antico Autore e del moderno sembran <lb/>ridursi ai medesimi principii, ma ripensandoci bene vi si trova una sostan&shy;<lb/>ziale differenza, perch&egrave;, sebbene Herone par che voglia confutare coloro, i <lb/>quali dicevano esser l'acqua ugualmente grave in s&egrave; stessa, pur egli riesce <lb/>a dire il medesimo, dai Teoremi archimedei concludendo che l'acqua nel&shy;<lb/>l'acqua non pesa. </s>

<s>Questo principio, cos&igrave; assolutamente pronunziato, &egrave; falso, <lb/>e perci&ograve; vi si sostituisce dallo Stevino quell'altro verissimo dell'uguaglianza <lb/>delle pressioni per ogni verso. </s>

<s>Esser poi falso che l'acqua nell'acqua non <lb/>pesa, per cui non si pu&ograve; con tale supposto spiegare perch&egrave; non sia oppresso <lb/><figure id="id.020.01.3135.1.jpg" xlink:href="020/01/3135/1.jpg"/></s></p><p type="caption">

<s>Figura 47.<lb/>chi nota per un pelago profondo; si dimostrava dallo <lb/>stesso Stevino immaginando di avere un gran vaso ABCD <lb/>(fig. </s>

<s>47) campato in aria, con un foro E aperto nel fondo. </s>

<s><lb/>Turato il foro, sopra il quale si supponga giacere un <lb/>uomo, rappresentato nell'assicella F; riempiasi per tutta <lb/>la sua altezza il detto vaso. </s>

<s>Si vuole che quell'uomo non <lb/>patisca, perch&egrave; l'acqua nell'acqua non pesa. </s>

<s>Ma levis&igrave; il <pb xlink:href="020/01/3136.jpg" pagenum="97"/>turo E: riman sempre l'acqua nell'acqua, eppure ella si sentirebbe ora pesar <lb/>tanto, che il misero marangone a questo patto ne sarebbe schiacciato. </s>

<s>&ldquo; Soit <lb/>ABCD (cos&igrave; scrive propriamente lo Stevino, riferendo alla medesima figura, <lb/>per noi 47a, il discorso) une eau, ayant au fond DC un trou form&eacute; d'une <lb/>broche E, sur le quel fond gist un homme F, ayant son dos sur E. </s>

<s>Ce <lb/>qu'estant ainsi, l'eau le pressant de tout cost&eacute;, celle qui est dessus luy ne <lb/>pousse aucune partie hors de son lieu. </s>

<s>Mais si on veut voir par effect que <lb/>cecy est la cause veritable, il ne faut qu'oster la broche E. </s>

<s>Alors il n'y aura <lb/>aucun poussement contre son dos en E, comme aux autres lieux de son <lb/>corps, pourtant aussi son corps patira l&agrave; une compression voire aussi forte, <lb/>comme il a est&eacute; demonstr&eacute; au troisiesme exemple de la II proposition du <lb/>present livre: assavoir autant que pese la colomne d'eau, ayant le trou E <lb/>pour base et AD hauteur et ainsi le dessein est demonstr&eacute; apertement &rdquo; (ivi). </s></p><p type="main">

<s>Potrebbe questo solo esempio esser sufficiente a dimostrare quanto si <lb/>fosse la scienza dello Stevino avvantaggiata sopra quella di Leonardo da Vinci, <lb/>e del Tartaglia. </s>

<s>Eppure furono dalle medesime ombre oscurati cos&igrave; gli Ele&shy;<lb/>menti idrostatici dell'olandese, come i Manoscritti del Pittore toscano, e i <lb/>discorsi intorno alla Tavagliata invenzione del Matematico di Brescia. </s>

<s>Men&shy;<lb/>tre, sorti i novelli promotori di Archimede, sedevano di queste cose maestri, <lb/>e da un'elettissima scuola e numerosa s'ascoltavano come oracoli i loro in&shy;<lb/>segnamenti; il solitario di Bruges s'additava dalla lontana col suo turbante <lb/>di mago in capo, e ravvolto nella sua toga nera, men pauroso che sospetto, <lb/>per avere insegnato a far s&igrave; che un'oncia di liquido pesasse quanto cento&shy;<lb/>mila libbre sul piatto della stadera. </s>

<s>Apparve nondimeno una volta con tutto <lb/>il suo abito filosofale in Toscana. </s>

<s>E perch&egrave; vi furono approvati i suoi detti, <lb/>e vi fecero ravvedere uno de'nostri pi&ugrave; gran Savii, giova accennare all'oc&shy;<lb/>casione, e al modo di quella visita clandestina. </s></p><p type="main">

<s>Chi ha letto la terza parte del capitolo IX, scritto da noi nel Tomo che <lb/>precede a questo, sa come il Viviani venisse, per mezzo dello Stenone, ad <lb/>aver notizia e intelligenza nella sua propria lingua di alcuni teoremi di Mec&shy;<lb/>canica, da Niccol&ograve; Witsen dimostrati nel suo libro, scritto in lingua olan&shy;<lb/>dese, intorno al modo di costruire e di governare le navi. </s>

<s>Ricorrevano in <lb/>quel medesimo volume del connazionale e discepolo dello Stevino altri teo&shy;<lb/>remi d'Idrostatica, dimostrati sull'andare di quelli del suo Maestro, e anche <lb/>sopra questi volle lo Stenone richiamar l'attenzione del Viviani, il quale, <lb/>gustandovi dentro tale Scienza, che gli sembrava non solo promovere, ma <lb/>correggere in parte quella stessa, che aveva imparata da Archimede e da <lb/>Galileo; chiese all'amico gli dettasse anche di questa la traduzione italiana. </s>

<s><lb/>Di che gentilmente compiaciuto, scrisse di sua propria mano, sopra certi fogli <lb/>che ci son rimasti, ordinatamente, queste otto proposizioni: </s></p><p type="main">

<s>PROPOSIZIONE I. &mdash; <emph type="italics"/>&ldquo; Sopra un fondo parallelo alla superficie del&shy;<lb/>l'acqua riposa un peso uguale al peso di una colonna o cilindrico, la di <lb/>cui base &egrave; uguale al fondo dato, e l'altezza uguale alla perpendicolare <lb/>della superficie dell'acqu<gap/> sopra il fondo dato. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><pb xlink:href="020/01/3137.jpg" pagenum="98"/><p type="main">

<s>&ldquo; Sia, nelle figure 48 e 49, ABCD l'acqua, AB la superficie, GH il <lb/>fondo parallelo ad AB: dico che sopra GH riposa una colonna d'acqua EFGH. <lb/><figure id="id.020.01.3137.1.jpg" xlink:href="020/01/3137/1.jpg"/></s></p><p type="caption">

<s>Figura 48.<lb/>Nella figura 48 la proposizione per s&egrave; &egrave; manifesta; nella 49 cos&igrave; <lb/><figure id="id.020.01.3137.2.jpg" xlink:href="020/01/3137/2.jpg"/></s></p><p type="caption">

<s>Figura 49.<lb/>si dimostra: Sia in essa un corpo solido EFGH, <lb/>della medesima gravit&agrave; in specie dell'acqua. </s>

<s>Egli <lb/>&egrave; evidente che il corpo galleggiante nell'acqua <lb/>preme l'acqua, che &egrave; sotto GH, col peso del corpo <lb/>EFGH. </s>

<s>Bisogna dunque che l'acqua ancora prema <lb/>verso GH coll'istesso peso, altrimenti il corpo non <lb/>si quieterebbe in quel luogo. </s>

<s>Ora, se il corpo <lb/>EFGH fosse attaccato al lato AD, questo non farebbe alterazione alcuna. </s>

<s><lb/>Sicch&egrave; un peso uguale al peso d'un prisma d'acqua, grande quanto EFGH, <lb/>riposa sopra il fondo GH. </s>

<s>Il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s>PROPOSIZIONE II. &mdash; <emph type="italics"/>&ldquo; Sopra un fondo quadrato, non parallelo alla <lb/>superficie dell'acqua, il di cui lato pi&ugrave; alto &egrave; sotto la superficie dell'acqua, <lb/>riposa un peso pi&ugrave; leggiero d'una colonna d'acqua, la di cui base &egrave; uguale <lb/>al fondo prescritto, e l'altezza alla linea perpendicolare tra la superficie <lb/>dell'acqua, e del pi&ugrave; basso lato del dato fondo, e pi&ugrave; grave di una co&shy;<lb/>lonna d'acqua della stessa base, ma di altezza uguale alla perpendicolare <lb/>tra la superficie dell'acqua, e del pi&ugrave; alto lato del dato fondo. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia, nella figura 50, dato il fondo EF, e siano EG, FH uguali ad EF, <lb/>e parallele alla superficie dell'acqua AB: dico che sopra EF riposa un peso <lb/>minore che FHIA, e maggiore che EGIA &rdquo; (MSS. Gal., T. CXLI, fol. </s>

<s>7). <lb/><figure id="id.020.01.3137.3.jpg" xlink:href="020/01/3137/3.jpg"/></s></p><p type="caption">

<s>Figura 50.</s></p><p type="main">

<s>Prima di trascrivere la dimostrazione, giova osser&shy;<lb/>vare che, in questa e nelle seguenti, si procede dal&shy;<lb/>l'Autore per via degl'indivisibili, considerando della <lb/>parete uno degl'infiniti latercoli, di cui essa s'intesse, <lb/>rappresentato nel profilo EF. </s>

<s>Come pure egli intende <lb/>esser esso profilo gravato da infiniti filetti liquidi, fra <lb/>s&egrave; paralleli, e a'due estremi GE, HF. </s>

<s>Giova osservare <lb/>inoltre che la stessa dimostrazione, specialmente nella <lb/>sua seconda maniera, si conduce da un principio assai <lb/>evidente, ed &egrave; che dal mezzo di EF in su i filetti liquidi, che premono la <lb/>parete, son di numero maggiori di quelli compresi nel rettangolo EI, e dal <lb/>mezzo in gi&ugrave; minori di quelli compresi in IF. </s>

<s>Le medesime ragioni poi sono <lb/>tanto evidentemente applicabili anche al caso che il fondo laterale, invece <lb/>di essere perpendicolare alla superficie del liquido, come qui si rappresenta, <lb/>sia obliqua; che s'&egrave; creduto inutile farne avvertiti i Lettori a parole, o di&shy;<lb/>segnandone, come l'Autore fa, una figura apposta. </s></p><p type="main">

<s>&ldquo; Pongasi, cos&igrave; seguita nel Manoscritto la traduzione del Witsen, che <lb/>l'acqua EFGH non abbia peso. </s>

<s>Il che essendo, l'acqua &egrave; premuta verso EG <lb/>col peso della colonna d'acqua AIGE, e per ragioni conosciute l'acqua EFGH <lb/>preme verso EG col peso eguale, essendo che l'acqua di sotto coll'istessa <lb/>forza resiste a quella di sopra, con la quale l'acqua di sopra preme contro <pb xlink:href="020/01/3138.jpg" pagenum="99"/>di essa, mentre restano in tale stato di quiete (Veggasi la X proposizione di <lb/>Stevino nella Statica). Nondimeno, per la fluidit&agrave; dell'acqua, verr&agrave; l'istessa <lb/>pressione sopra EF ed FH, e l'acqua in EG, GH, essendo premuta, pre&shy;<lb/>mer&agrave; coll'istessa forza tuttoci&ograve; che la sostiene, considerato che l'acqua (ol&shy;<lb/>tre al suo peso, che solamente preme in gi&ugrave;, del che qui non si parla, e <lb/>che senza impedimento considerabile pu&ograve; trascurarsi nella pratica) &egrave; anco <lb/>fluida, la qual fluidit&agrave; dell'acqua, per esser premuta verso tutte le bande <lb/>con egual forza, cerca di ripremere, e per conseguenza preme con egual <lb/>forza verso i quattro lati. </s>

<s>Ma per esser l'acqua in EFGH anco grave &egrave; che <lb/>questa gravit&agrave; verso EF pi&ugrave; preme che nulla, e meno che verso FH. </s>

<s>Per <lb/>questo anco riposer&agrave; pi&ugrave; peso, verso EF, che la colonna d'acqua EGAI, e <lb/>meno che la colonna d'acqua FHIA, il che si doveva dimostrare. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>&ldquo; Altrimenti. </s>

<s>&rdquo;<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>&ldquo; Verso l'angolo E riposa tanto, quanto verso qualsivoglia altro luogo <lb/>uguale ad esso nella linea EG, imperocch&egrave; ogni punto nell'acqua, in quanto <lb/>alla sua fluidit&agrave;, viene ad essere premuto ugualmente verso tutte le bande <lb/>(Vedi Stevino sopra ci&ograve;). E verso l'angolo di qualsivoglia altra linea, tirata <lb/>parallela con la linea EG, tanto riposa, quanto verso altro luogo nell'istessa <lb/>linea. </s>

<s>E perch&egrave; riposa pi&ugrave; verso qualunque linea che verso EG, e meno che <lb/>verso FH; seguita che verso gli angoli inferiori riposa pi&ugrave; che verso l'an&shy;<lb/>golo E, e meno che verso l'angolo F, e per conseguenza verso tutti gli an&shy;<lb/>goli, cio&egrave; verso la linea EF (imperocch&egrave; tutti gli angoli o punti solidi com&shy;<lb/>pongono la linea EF) pi&ugrave; che verso EG, e meno che verso FH. &rdquo; </s></p><p type="main">

<s>PROPOSIZIONE III. &mdash; <emph type="italics"/>&ldquo; Verso un fondo quadrato, il di cui lato supe&shy;<lb/>riore &egrave; nella superficie dell'acqua, riposa un peso eguale alla met&agrave; d'una <lb/>colonna d'acqua, la cui base &egrave; uguale al fondo dato, e l'altezza uguale <lb/>alla perpendicolare tra la superficie dell'acqua, ed il lato inferiore del <lb/>fondo dato. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia nella figura 51 l'acqua ABCD, la superficie AB, il fondo AD: <lb/>dico che verso AD riposa la met&agrave; di una colonna d'acqua, il cui fondo o <lb/>base fosse AD, o DE, posta uguale ad AD; ovvero, che &egrave; l'istesso, una co&shy;<lb/>lonna trilatera d'acqua ADE. &rdquo; </s></p><p type="main">

<s>&ldquo; Per dimostrar ci&ograve;, si divida AD e DE <lb/><figure id="id.020.01.3138.1.jpg" xlink:href="020/01/3138/1.jpg"/></s></p><p type="caption">

<s>Figura 51.<lb/>in parti uguali, e da'punti delle divisioni si <lb/>tirino linee parallele ad AB, e ad AD. </s>

<s>Dalla <lb/>passata proposizione &egrave; evidente che sopra AF <lb/>riposa pi&ugrave; che niente, e meno che la co&shy;<lb/>lonna d'acqua FL. Parimente, sopra FG ri&shy;<lb/>posa pi&ugrave; che FL o GR, e meno che GL o <lb/>MN. </s>

<s>Come anche sopra GH pi&ugrave; che GL o <lb/>HS, e meno che HL o HN, e cos&igrave; sopra HI <lb/>pi&ugrave; che IT, e meno che IO. </s>

<s>Sopra IK pi&ugrave; <lb/>che KV, e meno che KP, e finalmente sopra <pb xlink:href="020/01/3139.jpg" pagenum="100"/>KD pi&ugrave; che DZ, e meno che <expan abbr="Dq.">Dque</expan> Adunque il peso, che riposa sopra AD, &egrave; <lb/>sempre pi&ugrave; che tutte queste inscritte colonne d'acqua, che toccano la linea <lb/>AE, e meno che tutte le circoscritte colonne. </s>

<s>Ma quanto sono pi&ugrave; piccole le <lb/>parti, nelle quali si divide le AD, DE, tanto sar&agrave; minore la differenza, e tanto <lb/>pi&ugrave; si accosteranno al triangolo ADE. </s>

<s>Ora si pu&ograve; dividere AD e DE in tante <lb/>parti, che all'ultimo la loro differenza sar&agrave; minore di qualunque quantit&agrave; <lb/>data, il che si riduce nella pratica quasi al niente. </s>

<s>Nondimeno, resta la co&shy;<lb/>lonna trilatera d'acqua sempre dimostrata tra il meno e il pi&ugrave;, cio&egrave; tra le <lb/>inscritte e le circoscritte, e perci&ograve; riposa verso AD un peso grave quanto la <lb/>detta colonna d'acqua ADE, o la met&agrave; di una colonna d'acqua, il di cui <lb/>fendo sia AD, e l'altezza la perpendicolare tra la superficie dell'acqua, e il <lb/>suo pi&ugrave; basso fondo, il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s>PROPOSIZIONE IV. &mdash; <emph type="italics"/>&ldquo; Verso un fondo quadrato, il di cui lato supe&shy;<lb/>riore &egrave; sotto la superficie dell'acqua, riposa il peso di una colonna di <lb/>acqua, la di cui base &egrave; uguale al fondo dato, e l'altezza alla perpendi&shy;<lb/>colare tra la superficie dell'acqua, e il mezzo del fondo dato. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia, nella figura 52, l'acqua ABCD, la sua superficie AB, il fondo <lb/>dato DE, il di cui mezzo I: dico che sopra DE riposa un peso eguale al peso <lb/><figure id="id.020.01.3139.1.jpg" xlink:href="020/01/3139/1.jpg"/></s></p><p type="caption">

<s>Figura 52.<lb/>di una colonna d'acqua, la di cui base &egrave; ED, <lb/>e l'altezza &egrave; la IK. Imperocch&egrave;, per la prece&shy;<lb/>dente, la colonna trilatera d'acqua ADH riposa <lb/>sopra AD, ed AEF riposa sopra AE. </s>

<s>Adunque <lb/>il triangolo ADH, diminuito del triangolo AEF, <lb/>riposa sopra ED, cio&egrave; la colonna d'aqua EFHD. </s>

<s><lb/>Ma questa &egrave; uguale alla colonna, la di cui base <lb/>&egrave; ED, e altezza IK. Imperocch&egrave;, tirata LN nel <lb/>mezzo di GH, parallela ad AD, e prolungata <lb/>EF in N; EDLN sar&agrave; uguale ad EFHD. </s>

<s>Tirata <lb/>poi LM perpendicolare sopra AD, o alla sua prolungata; EDLN &egrave; una co&shy;<lb/>lonna, la di cui base ED e altezza LM. </s>

<s>Se dunque IK &egrave; uguale ad LM, sar&agrave; <lb/>provata la proposizione. </s>

<s>Ci&ograve; si dimostra cos&igrave;: AE &egrave; uguale ad EF o DG, <lb/>ed AD a DH, onde ED &egrave; uguale a GH, e le loro met&agrave; anco uguali, cio&egrave; EI <lb/>a GL, ed AI a DL, e gli angoli LDM, KAI sono uguali, per essere AK e DL <lb/>parallele, e l'angolo DML all'AKI, per essere retti, ed i triangoli, e le LM, <lb/>IK uguali. </s>

<s>&rdquo; </s></p><p type="main">

<s>PROPOSIZIONE V. &mdash; <emph type="italics"/>&ldquo; Di due fondi quadrati di acqua, d'ugual lar&shy;<lb/>ghezza, ma di lunghezza ineguale, i lati de'quali pi&ugrave; alti e pi&ugrave; bassi <lb/>stiano ugualmente sotto la superficie dell'acqua; i <lb/>pesi, che riposano verso essi, hanno fra loro la pro&shy;<lb/>porzione, che tra la loro lunghezza. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Siano, nella figura 53, i dati fondi CE, DF, <lb/>la superficie dell'acqua AB: dico che CE sta a DF, <lb/>come il peso, posante sopra CE, al peso sopra DF. </s>

<s>Im&shy;<lb/>perocch&egrave; siano G, H il mezzo de'fondi dati CF, DF, <lb/><figure id="id.020.01.3139.2.jpg" xlink:href="020/01/3139/2.jpg"/></s></p><p type="caption">

<s>Figura 53.<pb xlink:href="020/01/3140.jpg" pagenum="101"/>e si tirino GI, HK perpendicolari ad AB. </s>

<s>Sar&agrave; il peso sopra CE la colonna <lb/>d'acqua, la di cui base sar&agrave; CE, e l'altezza GI: e sopra DF la colonna, la <lb/>di cui base DF, ed altezza HK, o GI, per le due passate proposizioni. </s>

<s>Ma que&shy;<lb/>ste colonne sono fra loro come CE, DF; e per conseguenza anco i pesi, che <lb/>posano sopra essi fondi, il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scolio I.<emph.end type="italics"/> &mdash; Nota che nella III proposizione, alla quale si applica que&shy;<lb/>sta stessa figura, si &egrave; parlato di una mezza colonna d'acqua, la di cui base <lb/>sia CE, ovvero DF, e l'altezza la perpendicolare tra la superficie dell'acqua <lb/>AB, e il punto E, ovvero F. </s>

<s>Ed &egrave; chiaro che queste mezze colonne sono <lb/>uguali alle colonne intere, le di cui basi sono le stesse CE e DF, e l'altezza <lb/>la met&agrave; delle dette perpendicolari, cio&egrave; le linee intere GI, e HK, e perci&ograve; <lb/>resta la dimostrazione la stessa. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scolio II.<emph.end type="italics"/> &mdash; Nota inoltre che ho indicato i fondi per mezzo di linee, <lb/>per le quali bisogna intendere quadrati, di quella lunghezza, che uno gli vuol <lb/>dare. </s>

<s>E che questo non apporti alcuna variazione, si vede per s&egrave; medesimo, <lb/>ond'&egrave; superfluo farne altra menzione &rdquo; (ivi, fol. </s>

<s>8, 9). </s></p><p type="main">

<s>Le proposizioni, dimostrate fin qui dal Witsen, corrispondono a quelle <lb/>dello Stevino, il quale per&ograve; sempre suppone che i fondi e le pareti dei re&shy;<lb/>cipienti siano superficie piane, come si conveniva alla natura del suo trat&shy;<lb/>tato, in cui s'astraeva dai casi particolari, che quegli stessi fondi ora spor&shy;<lb/>gessero, ora rientrassero con andamenti sinuosi, de'quali offrono giusto l'esem&shy;<lb/>pio i fianchi nell'interno delle navi. </s>

<s>E potendo quegli andamenti essere in <lb/>varii piani, il Witsen ne considera i principali distintamente in due propo&shy;<lb/>sizioni. </s></p><p type="main">

<s>PROPOSIZIONE VI. &mdash; <emph type="italics"/>&ldquo; Contro un fondo, il di cui lato superiore e l'in&shy;<lb/>feriore ciascuno &egrave; in un piano parallelo alla superficie dell'acqua, ma <lb/>l'uno e l'altro piegato egualmente, per&ograve; in tal modo, che tutte le linee, <lb/>da certi punti del lato superiore tirate verso altrettanti punti del lato in&shy;<lb/>feriore, siano tutte linee parallele fra loro; vi riposa tanto peso, quanto <lb/>riposerebbe contro un fondo quadrato piano d'egual lunghezza, e larghezza <lb/>e profondit&agrave; sotto l'acqua. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia, nella figura 54, l'acqua ABCD, la superficie AB, i due piani EF, <lb/>CD paralleli alla superficie AB. </s>

<s>Nel piano EF sia il lato superiore del fondo <lb/>AEGILC, e su CD il lato inferiore BFHKMD, i due estremi AB, CD. </s>

<s>Dico <lb/>che, verso questo fondo serpeggiante, riposa un peso, che riposerebbe verso <lb/><figure id="id.020.01.3140.1.jpg" xlink:href="020/01/3140/1.jpg"/></s></p><p type="caption">

<s>Figura 54.<lb/>un fondo piano, largo quanto AB o CD, e <lb/>lungo quanto AEGILC, ovvero BFHKMD. <lb/>ed ugualmente profondo nell'acqua. </s>

<s>Im&shy;<lb/>perocch&egrave; siano AC, BD divise in tante <lb/>parti uguali, che le parti tra le divisioni <lb/>diventino linee rette, come in EG, IL ecc. </s>

<s><lb/>ed FH, KM ecc., e sian tirate le EF, GH, <lb/>IK, LM ecc., di maniera che il fondo ser&shy;<lb/>peggiante sia diviso in fondi quadrati. <pb xlink:href="020/01/3141.jpg" pagenum="102"/>come sarebbe ABFE. </s>

<s>Nello stesso modo si potrebbe anco dividere i fondi <lb/>piani in altrettanti ed uguali fondi quadrati, i quali ugualmente sono pre&shy;<lb/>muti, per la IV proposizione, e conseguentemente tutti i quadrati del fondo <lb/>serpeggiante saranno premuti altrettanto, quanto tutti i quadrati del fondo <lb/>piano. </s>

<s>Il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s>PROPOSIZIONE VII. &mdash; <emph type="italics"/>&ldquo; Contro un fondo piegato, i di cui lati supe&shy;<lb/>riori ed inferiori sono paralleli alla superficie dell'acqua, e i due altri <lb/>lati paralleli fra loro, e similmente piegati; riposa un peso eguale a quello, <lb/>che riposerebbe contro un fondo piano, dell'istessa lunghezza, larghezza, <lb/>e profondit&agrave; sotto l'acqua &rdquo;<emph.end type="italics"/> (ivi, fol. </s>

<s>10, 11). </s></p><p type="main">

<s>La diversit&agrave; di questa proposizione dalla precedente consiste nel consi&shy;<lb/>derare le pieghe, con la loro longitudine orizzontale, ci&ograve; che meglio si potr&agrave; <lb/><figure id="id.020.01.3141.1.jpg" xlink:href="020/01/3141/1.jpg"/></s></p><p type="caption">

<s>Figura 55.<lb/>intendere, immaginando il fondo ondulato, che <lb/>si rappresentava in ABCD, nella passata figura, <lb/>essere eretto in modo, che i due lati estremi AB, <lb/>CD riescano paralleli al livello dell'acqua LO, <lb/>come nella figura 55. Supponiano che le linee <lb/>BD, AC spiegate, s'allunghino quanto le FH, <lb/>EG, e che le due superficie tra esse comprese, <lb/>la piana cio&egrave; e la piegata, rimangano profon&shy;<lb/>date ugualmente sotto l'acqua, come la figura 56, ne'loro profili OA, OB, <lb/>le rappresenta. </s>

<s>Rimanendo alle due prementi colonne liquide ampiezza pari <lb/>di base e pari altezza, &egrave; manifesto che saranno <lb/><figure id="id.020.01.3141.2.jpg" xlink:href="020/01/3141/2.jpg"/></s></p><p type="caption">

<s>Figura 56.<lb/>uguali, come il Witsen ha gi&agrave; proposto, e poi <lb/>cos&igrave; dimostra: </s></p><p type="main">

<s>&ldquo; Sia, nella figura 55, la superficie del&shy;<lb/>l'acqua LO, i fondi dati ABDC, ed EFHG, dei <lb/>quali AB, DC; EF, HG sono uguali fra loro, e <lb/>tutti paralleli alla superficie dell'acqua OL. </s>

<s>I <lb/>lati AB ed EF siano ugualmente profondi sotto <lb/>l'acqua, come anco i lati CD, GH. </s>

<s>Dico che contro ABDC, ed EFHG, ri&shy;<lb/>posa l'istesso peso di acqua. </s>

<s>Imperocch&egrave;, dividansi AC, BD in parti uguali, <lb/>e tirinsi le linee, e cos&igrave; sar&agrave; diviso il fondo in divers&igrave; fondi quadrilateri. </s>

<s><lb/>Dividansi parimente le EG, FH: ne segue, per le proposizioni III e IV, che, <lb/>verso i quadrati superiori di ABDC, riposa lo stesso peso, che sopra i qua&shy;<lb/>drati superiori di EFHG, e verso i susseguenti dell'uno, che verso i susse&shy;<lb/>guenti dell'altro; e per conseguenza verso tutti dell'uno, che verso tutti <lb/>dell'altro. </s>

<s>&rdquo; </s></p><p type="main">

<s>PROPOSIZIONE VIII. &mdash; <emph type="italics"/>&ldquo; In due fondi, ugualmente profondi sotto la <lb/>superficie dell'acqua, e di ugual larghezza, e de'quali uno sia piegato e <lb/>l'altro no; la lunghezza alla lunghezza cos&igrave; sta, come la pressione alla <lb/>pressione. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sian, nella figura 57, i fondi dati AB, CD, sia A a C egualmente pro&shy;<lb/>fondo sotto la superficie dell'acqua LO, come anco B a D. Dico: come la <pb xlink:href="020/01/3142.jpg" pagenum="103"/>lunghezza del fondo piegato AB, alla lunghezza del diritto CD; cos&igrave; il peso, <lb/>che riposa verso AB, al peso che riposa verso CD. Imperocch&egrave;, siano AB, <lb/>CD divisi in pi&ugrave; fondi quadrati, come nella passata, e sar&agrave;, per i fondi qua&shy;<lb/>drati superiori, AE a CF, come il peso contro AE, al <lb/><figure id="id.020.01.3142.1.jpg" xlink:href="020/01/3142/1.jpg"/></s></p><p type="caption">

<s>Figura 57.<lb/>peso contro CF, per la V proposizione. </s>

<s>E similmente <lb/>EG ad FH come il peso contro EG, al peso contro FH. </s>

<s><lb/>Onde tutti i piccoli quadrati del fondo piegato, e tutti <lb/>i quadrilateri del fondo diritto, saranno premuti con <lb/>la proporzione, che &egrave; tra la lunghezza della linea in&shy;<lb/>tera dell'uno, alla lunghezza della linea intera del&shy;<lb/>l'altro fondo. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scolio.<emph.end type="italics"/> &mdash; Di qui &egrave; che, se il fondo AB fosse piegato nel modo che <lb/>nella VI e VII proposizione, sempre si conserver&agrave; le medesime proporzioni &rdquo; <lb/>(ivi, fol. </s>

<s>12). </s></p><p type="main">

<s>Rimeditando il Viviani su questi fogli, che tornandosene dalla casa dello <lb/>Stenone recava seco manoscritti, si persuase sempre pi&ugrave; della verit&agrave; di que&shy;<lb/>ste nuove dottrine, e se prima aveva distese proposizioni, per dimostrare che <lb/>il liquido non preme niente contro le pareti laterali dei vasi, in difesa del <lb/>Michelini; ora dava mano a scrivere un trattato, in cui, per supplire ai di&shy;<lb/>fetti di Archimede, si concluderebbe, da principii meccanici pi&ugrave; certi, e con <lb/>tutto il rigore geometrico, che la mole di esso liquido preme non solo in gi&ugrave;, <lb/>ma ugualmente per ogni verso. </s>

<s>Racconteremo in seguito i fatti relativi alla <lb/>scrittura di questo trattato, per ora semplicemente osservando che il Viviani, <lb/>per non parere di detrar nulla al suo Maestro, non osserv&ograve; la debita giu&shy;<lb/>stizia verso i meriti, che si'dovevano allo Stevino. </s>

<s>N&egrave; pi&ugrave; giusti verso lui si <lb/>mostrarono i contemporanei e i successori, i quali, sotto il sol meridiano <lb/>dello stesso Galileo e del Torricelli, del Boyle e del Pascal, avevano perduto <lb/>affatto di vista quella solitaria stella lontana, de'raggi della quale s'erano <lb/>rischiarate le tenebre del mattino. </s></p><p type="main">

<s>Nonostante, pochi anni prima che terminasse il secolo XVIII, sorgeva <lb/>il Lagrange a commemorare solennemente gli <emph type="italics"/>Hypomnemata mathematica,<emph.end type="italics"/><lb/>e sarebbe potuto bastare esso solo a far perdonare all'Autore, e a rivendi&shy;<lb/>carlo della lunga ingiustizia patita. </s>

<s>Ma il Lagrange stesso ebbe a risentirsi <lb/>del malefico influsso, e, o riferisse sopra le relazioni altrui, o ricorrendo al&shy;<lb/>l'originale lo consultasse con troppa fretta; i teoremi idrostatici dello Stevino <lb/>sono esposti da lui in maniera impropria, e sotto mendaci forme si porgono <lb/>le pi&ugrave; importanti verit&agrave; dimostrate. </s>

<s>Non si crederebbe ci&ograve;, ma &egrave; un fatto, e <lb/>noi non vogliamo passarci d'esaminarlo, fra gli altri motivi, affinch&egrave; si per&shy;<lb/>suadano alcuni che, senza sufficiente criterio, s'&egrave; trattata fin qui la Storia <lb/>della Scienza, anche dagli scrittori piu celebri, e da'giudici pi&ugrave; competenti <lb/>di questa materia. </s></p><p type="main">

<s>L&agrave; dove dunque il Lagrange descrive il quadro storico, per rappresen&shy;<lb/>tare ai Lettori quel che s'era fatto nell'Idrostatica da tutti coloro, che l'ave&shy;<lb/>vano preceduto, incominciando da Archimede, e affinch&egrave; si potessero giusta-<pb xlink:href="020/01/3143.jpg" pagenum="104"/>mente apprezzare gl'impulsi, ch'egli stesso, con la sua <emph type="italics"/>Meccanica analitica<emph.end type="italics"/><lb/>nuova, avrebbe dato alla Scienza; si legge: &mdash; Dai principii di Archimede <lb/>si desumono facilmente le pressioni sui fondi, e sopra le pareti dei vasi: lo <lb/>Stevino nonostante &egrave; il primo che l'abbia fatto, e che abbia scoperto il <emph type="italics"/>Pa&shy;<lb/>radosso idrostatico.<emph.end type="italics"/> &Egrave; nel terzo tomo degli <emph type="italics"/>Hypomnemata mathematica,<emph.end type="italics"/><lb/>tradotto dall'olandese per lo Snellio, e pubblicato a Leyda nel 1608, che si <lb/>trova l'Idrostatica dello Stevino. </s>

<s>Egli immagina un vaso rettangolare pieno <lb/>d'acqua, in cui sia immerso un solido del medesimo peso, sotto un egual <lb/>volume, il quale corpo, occupando il posto dell'acqua, lascia che si faccia la <lb/>medesima pressione sul fondo, anco quando non vi resti del fluido che un <lb/>sottilissimo filo. </s>

<s>Ora esso Stevino osserva che, supponendo questo solido fer&shy;<lb/>mato al suo posto, non pu&ograve; resultarne alcuna variet&agrave; nell'azion dell'acqua <lb/>contro il fondo del vaso. </s>

<s>Dunque, ei ne conclude, la pressione sopra questo <lb/>fondo sar&agrave; sempre uguale al peso della medesima colonna d'acqua, e sia <lb/>qualunque la figura del recipiente. </s>

<s>Passa di qui l'Autore a determinare la <lb/>pressione del liquido sopra pareti verticali o inclinate, e, applicandovi il me&shy;<lb/>todo dei limiti, dimostra che la detta pressione &egrave; uguale al peso di una co&shy;<lb/>lonna d'acqua, di cui la base fosse la stessa parete, e l'altezza la met&agrave; del&shy;<lb/>l'altezza del vaso. </s></p><p type="main">

<s>Dette le quali cose il Lagrange, nel suo proprio linguaggio, cos&igrave;, dello <lb/>Stevino, soggiunge: &ldquo; Il determine ensuite la pression sur une partie quel&shy;<lb/>conque d'une paroi plane inclin&eacute;e, et il la trouve &eacute;gale au poids d'une co&shy;<lb/>lonne d'eau, qui saroit form&egrave;e en appliquant perpendiculairement a chaque <lb/>point de cette partie des droites egales a la profondeur de ce point sous <lb/>l'eau &rdquo; (<emph type="italics"/>Mechan, analit.,<emph.end type="italics"/> a Paris 1788, pag. </s>

<s>126). Lo Stevino, &egrave; vero, de&shy;<lb/>termina nel suo X teorema le pressioni, fatte sopra qualunque porzion di <lb/>parete inclinata, ma la sua dimostrazione vale altresi, quando la detta pa&shy;<lb/>rete sia perpendicolare, nel qual caso la colonna che preme &egrave; propriamente <lb/>formata degl'infiniti filetti liquidi orizzontali, aventi ciascuno lunghezza uguale <lb/>alla sua respettiva profondit&agrave; sotto la linea del livello. </s>

<s>Cos&igrave;, ritornando in&shy;<lb/>dietro sopra la figura 38, &egrave; manifesto che la colonna IDHK si compone degli <lb/>infiniti filetti liquidi, compresi fra IK, e DH, i quali due estremi, come gli <lb/>altri infiniti di mezzo, son perpendicolari al profilo parietale CD, e sono uguali <lb/>ciascuno alle respettive profondit&agrave; CI, CD. </s>

<s>Ma quando la parete &egrave; inclinata, <lb/>che &egrave; il caso particolarmente riferito dal Lagrange, gli omonimi filetti IK, <lb/>DH nella figura 39 non sono altrimenti perpendicolari, n&egrave; la loro lunghezza <lb/>uguaglia la profondit&agrave; sotto l'acqua, ma la lunghezza della parete sopra&shy;<lb/>stante, dal punto del loro contatto con essa, infin su a fior d'acqua. </s>

<s>Cos&igrave;, <lb/>IK, DH non sono uguali ai perpendicoli delle profondit&agrave; CN, CO, ma alle <lb/>oblique CI, CD, ossia ai profili delle pareti. </s></p><p type="main">

<s>&ldquo; Ce theoreme, prosegue a dire il Lagrange, &eacute;tant ainsi demontr&eacute; pour <lb/>des surfaces planes quelconques, situ&eacute;es comme l'on voudra, il est facile de <lb/>l'etendre &agrave; des surfaces courbes quelconques, et d'en conclure que la pres&shy;<lb/>sion exerc&eacute;e par un fluide pesant contre une surface quelconque, a pour me-<pb xlink:href="020/01/3144.jpg" pagenum="105"/>sure le poids d'une colonne de ce m&egrave;me fluide, la quelle auroit pour base <lb/>cette m&egrave;me surface convertie en une surface plane, s'il est necessaire, et <lb/>dont les hauteurs, r&eacute;pondantes aux diff&eacute;rens points de la base, seroient les <lb/>m&egrave;mes que les distances des points correspondens de la surface a la ligne <lb/>de niveau du fluide; ou, ce qui revient au m&egrave;me, cette pression sera mesu&shy;<lb/>r&eacute;e par le poids d'une colonne, qui auroit pour base la surface press&eacute;e, et <lb/>pour hauteur la distance verticale du centre de gravit&eacute; de cette meme sur&shy;<lb/>face, a la surface superieure de fluide &rdquo; (ivi). </s></p><p type="main">

<s>Ma il teorema dello Stevino &egrave; formulato bene altrimenti, e chi vuol per&shy;<lb/>suadersene legga quel ch'egli cos&igrave; propriamente dice, nel secondo esempio, <lb/>dopo la XII proposizione: &ldquo; Soit AB (fig. </s>

<s>58) un fond <lb/><figure id="id.020.01.3144.1.jpg" xlink:href="020/01/3144/1.jpg"/></s></p><p type="caption">

<s>Figura 58.<lb/>convenant, ayant son plus haut poinct A sous fleur d'eau C, <lb/>et AD perpendicle de A sur le niveau passant par le plus <lb/>bas poinct B, et prolong&eacute;e jusques &agrave; fleur d'eau C. </s>

<s>Soit E <lb/>au milieu de AD: Ie dis que le poids, qui repose con&shy;<lb/>tre AB, est egal a la pesanteur de la colonne, ayant le dit <lb/>fond AB pour base, et CE p&ograve;ur bauteur &rdquo; (Elemens hydr, <lb/>cit., pag. </s>

<s>494). Ora &egrave; chiaro che il punto E non &egrave; centro <lb/>di gravit&agrave; del fondo <emph type="italics"/>convenant<emph.end type="italics"/> AB, altro che per acci&shy;<lb/>dente, e non s'intende come questo stesso centro possa <lb/>entrare in questione, se la parete del vaso, sopra cui riposa l'acqua, non fa <lb/>altro ufficio che della libbra, alla quale sono attaccati i pesi o applicate le <lb/>forze. </s>

<s>N&egrave; lo Stevino dall'altra parte invoca la Baricentrica, se non col&agrave;, dove <lb/>si mette a ricercare il centro della pressione, in due proposizioni, che il La&shy;<lb/>grange, a voler dare perfezione al suo quadro storico, rappresentandovi le <lb/>cose nella loro integrit&agrave; sostanziale; non avrebbe dovuto lasciar di comme&shy;<lb/>morare. </s></p><p type="main">

<s>Volgiamo ancora indietro lo sguardo sopra la figura 38. Si pu&ograve; la CD <lb/>riguardare come una libbra, gravata di pesi via via crescenti da C verso D, <lb/>a proporzione delle distanze, perch&egrave; tali in verit&agrave; sono, e talmente operano <lb/>i filetti liquidi orizzontali, prementi contro la detta porzione indivisibile della <lb/>parete. </s>

<s>Ma si sa dalla Meccanica che il centro dell'equilibrio sega cos&igrave; la <lb/>libbra, in questo caso, che la parte verso i pesi minori sia doppia di quella <lb/>verso i pesi maggiori; dunque il centro della pressione, fatta contro CD, &egrave; <lb/>in M, se DM &egrave; la met&agrave; di CM. </s>

<s>Lo Stevino per&ograve; giunge a questa medesima <lb/>conclusione, immaginando che il triangolo CDH, trasformato in un solido di <lb/>pari gravit&agrave; all'acqua sia fatto rivolgere cos&igrave; in s&egrave; stesso, che CD base rie&shy;<lb/>sca orizzontale. </s>

<s>In questo caso &egrave; manifesto che il centro di gravit&agrave; di detto <lb/>solido batte pure in M. </s>

<s>E perch&egrave; sopra la linea MN, parallela ad AC, bat&shy;<lb/>tono per le medesime ragioni i centri di gravit&agrave; di tutti gl'infiniti piani <lb/>triangolari, componenti il prisma EACDH; nel mezzo dunque di MN batter&agrave; <lb/>il centro di esso prisma, e ivi perci&ograve; cader&agrave; il centro della pressione, che la <lb/>prismatica colonna d'acqua fa contro la parete parallelogramma, secondo che <lb/>si propone lo Stevino di dimostrare in questa forma: &ldquo; Si le fond d'une eau <pb xlink:href="020/01/3145.jpg" pagenum="106"/>n'est a niveau, estant parallelogramme, du quel le plus haut cost&eacute; soit &agrave; <lb/>fleur d'eau, et de son milieu au milieu de son cost&eacute; opposite est men&eacute;e une <lb/>ligne; le centre de gravit&eacute; (du pressement de l'eau congreg&eacute; contre le fond) <lb/>divise ceste ligne de telle sorte, que la partie haute &agrave; la basse est en rai&shy;<lb/>son double &rdquo; (ivi, pag. </s>

<s>495). </s></p><p type="main">

<s>Passa di qui lo Stevino a dimostrare in qual punto risponda il centro <lb/>della pressione, dentro la porzione ID della parete, come nella 39, qui addie&shy;<lb/>tro, &egrave; prefigurata. </s>

<s>E osservando che una tale pressione si deve al peso del <lb/>piano acqueo, composto del parallelogrammo IL, e del triangolo KLH, aventi <lb/>quello e questo i centri di gravit&agrave;, che riposano ne'punti P ed R, sul mezzo, <lb/>e ai due terzi della base ID; ne conclude che il centro della gravit&agrave; del <lb/>piano, o della pression del liquido, risponde al punto Q, fermato sulla PR <lb/>con tal ragione, che la parte QR stia alla QP, reciprocamente, come il pa&shy;<lb/>rallelogrammo sta al triangolo; ossia, per le cose gi&agrave; dimostrate, come CI <lb/>sta ad IP, o come CN a NS. </s>

<s>E perch&egrave; di tutti gl'infiniti piani, uguali e pa&shy;<lb/>ralleli a IDHK, s'affalda la colonna liquida, premente la parete parallelo&shy;<lb/>gramma, il superior lato e l'inferior della quale, suppongasi essere dalla ID <lb/>divisi nel mezzo; nello stesso punto Q, com'&egrave; stato geometricamente indi&shy;<lb/>cato, risponde il punto che si cercava, quello cio&egrave;, in cui si concentra tutto <lb/>insieme il peso della detta colonna, secondo che cos&igrave; propriamente lo Ste&shy;<lb/>vino stesso annunziava: &ldquo; Estant un fond dans l'eau, parallelogramme, non <lb/>a niveau, et son plus haut cost&eacute; sous fleur d'eau, et a niveau, du milieu du <lb/>quel cost&eacute; au milieu de son opposite on mene une ligne; en icelle ligne est <lb/>le centre de gravit&eacute; de compression congreg&eacute;e contre le fond la divisant en&shy;<lb/>tre deux certains poincts, dont celuy d'en-haut est centre du fond, l'autre <lb/>divise la ligne totale en raison double. </s>

<s>Or entre ces deux poincts le dit cen&shy;<lb/>tre se trouve diviser l'intervalle ainsi que la partie inferieure &agrave; la superieure <lb/>est comme la ligne a plomb, entre fleur d'eau et le plus haut cost&eacute; du fond, <lb/>a la moitie de la ligne a plomb (<emph type="italics"/>cos&igrave; propriamente si deve leggere e non <lb/>semplicemente<emph.end type="italics"/> &agrave; la ligne a plomb, <emph type="italics"/>com'&egrave; trascorso in questa edizione<emph.end type="italics"/>) en&shy;<lb/>tre le dit plus haut cost&eacute;, et le niveau qui passe sous son cost&eacute; opposite &rdquo; <lb/>(ivi, pag. </s>

<s>496). </s></p><p type="main">

<s>Tali erano le importanti novit&agrave;, che si venivano per lo Stevino a intro&shy;<lb/>durre nell'Idrostatica, la precipua fra le quali consisteva in aver messe nella <lb/>loro pi&ugrave; piena evidenza le pressioni in su e per ogni verso, rimaste a tutti <lb/>un'enimma dentro la seconda supposizion di Archimede. </s>

<s>D'onde &egrave; facile <lb/>persuadersi che sarebbe giunta questa Scienza, gi&agrave; fino dal cominciar del <lb/>secolo XVII, a quella perfezione, a cui la ridusse l'Hermann, se l'autorit&agrave; <lb/>del magistero non fosse tutta passata nelle mani di Galileo, l'opera posta <lb/>dal quale intorno all'Idrostatica, fin qui forse mal giudicata, apparir&agrave; quale <lb/>si fosse in effetto nella seguente Storia. </s></p><pb xlink:href="020/01/3146.jpg" pagenum="107"/><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Quale occasione avesse Galileo di applicarsi, ne'suoi anni giovanili, allo <lb/>studio dei teoremi idrostatici di Archimede, lo racconta da s&egrave; stesso in quel <lb/>dialogo latino, che fu per la prima volta pubblicato dall'Alb&egrave;ri, in cui si <lb/>gettavano dall'Autore i semi della nuova Scienza del moto. </s>

<s>Quivi dice, per <lb/>mezzo del suo interlocutore sotto il nome di Alessandro, che la ragion vera, <lb/>secondo la quale un corpo ci apparisce grave o leggero, dipende dalla pro&shy;<lb/>porzione ch'egli ha col mezzo, a quel modo che s'era studiato di dimostrare <lb/>&ldquo; cum veram rationem invenire tentassem, qua possimus, in mixto ex duo&shy;<lb/>bus metallis, singuli metalli exactissimam proportionem assignare: quorum <lb/>theorematum licet non dissimilia ab Archimede demonstrata sint, demon&shy;<lb/>strationes minus mathematicas, et magis physicas in medium afferam &rdquo; <lb/>(Alb. </s>

<s>XI, 21). L'occasione dunque di ritrovare queste prime fisiche dimo&shy;<lb/>strazioni de'medesimi teoremi archimedei venne a Galileo, mentre, circa al&shy;<lb/>l'anno 1587, attendeva all'invenzione di quella Bilancetta idrostatica, per <lb/>l'applicazion della quale si sarebbe potuto praticamente risolvere uno de'pi&ugrave; <lb/>mirabili e pi&ugrave; curiosi problemi, fra quanti se ne raccontino dallle pi&ugrave; anti&shy;<lb/>che Storie della Scienza. </s></p><p type="main">

<s>La narrazione di ci&ograve;, pi&ugrave; autorevole e pi&ugrave; diffusa, &egrave; quella fattaci da <lb/>Vitruvio, il quale, dopo aver detto come Gerone re dei Siracusani, avendo <lb/>dato una massa di oro a un orefice perch&egrave; glie ne formasse una corona vo&shy;<lb/>tiva, ed entrato poi in sospetto che fosse impiegata nell'opera una parte di <lb/>argento, ricorresse ad Archimede, affinch&egrave; gli scoprisse per via di scienza la <lb/>ragione del furto; &ldquo; tunc is, Vitruvio stesso soggiunge, cum haberet eius rei <lb/>curam, casu venit in balneum, ibique, cum in solium descenderet, animad&shy;<lb/>vertit quantum corporis sui in eo insideret tantum aquae extra solium ef&shy;<lb/>fluere. </s>

<s>Itaque, cum eius rei rationem explicationis offendisset, non est mora&shy;<lb/>tus, sed exilivit gaudio motus de solio, et nudus vadens domum versus, <lb/>significabat clara voce invenisse quod quaereret. </s>

<s>Nam currens identidem <lb/>graece clamabat <foreign lang="greek">e)urpxa, e)urpxa. </foreign></s>

<s>Tum vero ex eo inventionis ingressu duas <lb/>dicitur fecisse massas aequo pondere, quo etiam fuerat corona, unam ex auro, <lb/>alteram ex argento. </s>

<s>Cum ita fecisset, vas amplum ad summa labra imple&shy;<lb/>vit aqua, in quo demisit argenteam massam. </s>

<s>Cuius quanta magnitudo in vase <lb/>depressa est, tantum aquae effluxit. </s>

<s>Ita exempta massa quanto minus factum <lb/>fuerat refudit, sextario mensus, ut eodem modo quo prius fuerat ad labra <lb/>aequaretur. </s>

<s>Ita ex eo invenit quantum, ad certum pondus argenti, certa aquae <lb/>mensura responderet. </s>

<s>Cum id expertus esset, tum auream massam similiter <lb/>pleno vase dimisit, et ea exempta, eadem ratione mensura addita, invenit ex <lb/>aqua non tantum defluxisse, sed tantum minus quantum minus magno cor&shy;<lb/>pore eodem pondere auri massa esset quam argenti. </s>

<s>Postea vero repleto vase, <lb/>in eadem aqua ipsa corona demissa, invenit plus aquae defluxisse in coro-<pb xlink:href="020/01/3147.jpg" pagenum="108"/>nam, quam in auream eodem pondere massam, et ita, ex eo quod plus de&shy;<lb/>fluxerat aquae in corona quam in massa, ratiocinatus deprehendit argenti in <lb/>auro mixtionem, et manifestum furtum redemptoris &rdquo; (<emph type="italics"/>Architecturae,<emph.end type="italics"/> Lib. </s>

<s>IX, <lb/>Cap. </s>

<s>III). </s></p><p type="main">

<s>Il Fazello, in un passo dell'<emph type="italics"/>Istoria Siciliana,<emph.end type="italics"/> riferitoci dall'Hodierna, <lb/>aggiunge cos&igrave; al racconto alcune particolarit&agrave; degne di nota: &ldquo; Lucio Pol&shy;<lb/>lione scrive che Archimede fu inventore di questa cosa, che si dir&agrave; adesso. </s>

<s><lb/>Jerone minore, re di Siracusa, avendo fatto voto di mettere una corona d'oro <lb/>in un certo tempio, diede l'oro ad un orefice perch&egrave; la facesse. </s>

<s>Ma egli con <lb/>tanta gran maestria mise l'argento sotto l'oro, che ella pareva veramente <lb/>tutta d'oro. </s>

<s>Ma avendo il Re qualche sospetto di questo, per averlo udito <lb/>dir dalle spie, e non potendo per s&egrave; stesso <gap/> il furto, preg&ograve; Archi&shy;<lb/>mede che volesse scoprire la malignit&agrave; dell'orefice, e convincerlo. </s>

<s>Onde egli, <lb/>pigliando tal carico sopra di s&egrave;, venne a caso nel bagno .... &rdquo; (<emph type="italics"/>Archimede <lb/>redivivo,<emph.end type="italics"/> Palermo 1644, pag. </s>

<s>9) e prosegue a narrare come da ci&ograve; gli ve&shy;<lb/>nisse suggerita l'invenzione, aiutandosi delle esperienze, a quel medesimo <lb/>modo, che Vitruvio le descrive. </s></p><p type="main">

<s>Si disse esser questo nella Storia un apologo, il significato proprio del <lb/>quale si raccoglier&agrave; facilmente, ripensando a que'primi studiosi delle dottrine <lb/>idrostatiche di Archimede, le quali, nelle loro astratte generalit&agrave;, pur s&igrave; mo&shy;<lb/>stravano cos&igrave; feconde delle pi&ugrave; nuove e pi&ugrave; utili applicazioni. </s>

<s>Una di coteste <lb/>utilit&agrave; nella Fisica si riconosceva principalmente dal saper secondo qual pi&ugrave; <lb/>esatta proporzione si corrispondano le gravit&agrave; di due o pi&ugrave; corpi, sotto uguali <lb/>ampiezze di moli: ci&ograve; che vedevasi direttamente conseguire dalla Scienza ar&shy;<lb/>chimedea, nella quale dimostravasi che i solidi immersi tanto perdono della <lb/>loro propria gravit&agrave;, quant'&egrave; quella dell'umido, di cui occupano il luogo. </s>

<s>Che <lb/>se quest'umido &egrave; l'acqua, dalla sola perdita, che subisce un corpo nell'im&shy;<lb/>mersione, s'avrebbe verso un egual mole di lei, e secondo la pi&ugrave; precisa <lb/>verit&agrave;, la proporzione desiderata. </s>

<s>Non occorreva altro a farsi poi che un com&shy;<lb/>puto numerico, perch&egrave;, dato il peso di una massa, per esempio composta di <lb/>oro e di argento, si potesse da que'medesimi principii archimedei certamente <lb/>concludere quanto fosse nel misto, distintamente, il peso dell'un metallo e <lb/>dell'altro. </s>

<s>E il computo que'primi discepoli e promotori di Archimede non <lb/>penarono a farlo, di che lasciarono, com'era giusto, tutta attribuire al Mae&shy;<lb/>stro la gloria, cantatagli innanzi, sopra la lira di Bione e di Mosco, con quel&shy;<lb/>l'idillio, che in pi&ugrave; rozze note ci ha trasmesso Vitruvio. </s></p><p type="main">

<s>Dietro l'esperienza delle gravit&agrave; specifiche de'due metalli, e del loro <lb/>composto, il calcolo della quantit&agrave; dell'argento, sostituito all'oro nella corona <lb/>del re Gerone, certissimamente fu fatto, e si pu&ograve;, dietro questa certezza, ar&shy;<lb/>gomentare quanto amorosi e intensi fossero gli studii dati all'Idrostatica dai <lb/>contemporanei di Archimede, o da'successori immediati di lui, bench&egrave; quel <lb/>calcolo non dovesse poi parer tanto difficile a chi meditava e aveva intelligenza <lb/>dei libri <emph type="italics"/>Della sfera e cilindro, Dei conoidi e sferoidei.<emph.end type="italics"/> Nonostante non sap&shy;<lb/>piamo altro da Vitruvio, se non che la proporzione de'due metalli nel misto <pb xlink:href="020/01/3148.jpg" pagenum="109"/>fu ritrovata <emph type="italics"/>ratiocinando,<emph.end type="italics"/> ma nessuno aveva ancora detto in qual modo fosse <lb/>fatta, o si potesse fare questa raziocinazione o questo calcolo, prima del Tar&shy;<lb/>taglia, a cui pure venne primo in pensiero d'istituirlo sopra pi&ugrave; precisi dati <lb/>sperimentali, inventando l'uso della Bilancetta. </s></p><p type="main">

<s>Che in mezzo a tanto squisita cultura di lettere umane le rozze pagine <lb/>del Matematico di Brescia andassero dimenticate, non fa maraviglia, ma ben <lb/>fa maraviglia che le potessero cos&igrave; disprezzare coloro, i quali incominciarono <lb/>nel secolo appresso a infondere nelle parole un succo di verit&agrave; nuove, come <lb/>ristorativo sapore di frutto in mezzo al vano susurrar delle fronde. </s>

<s>Comun&shy;<lb/>que sia, bench&egrave; Galileo ostentasse il suo disprezzo, come sopra tutti gli altri <lb/>che lo avevano preceduto, cos&igrave; e sopra il Tartaglia; &egrave; un fatto che s'intro&shy;<lb/>dusse in questi studii delle gravit&agrave; specifiche con l'aggiungere qualche per&shy;<lb/>fezione a quello stesso strumento, che da quasi cinquant'anni tutti legge&shy;<lb/>vano, o potevano leggere in quel secondo ragionamento, fatto dall'Autore <lb/>intorno alla sua propria <emph type="italics"/>Travagliata invenzione.<emph.end type="italics"/></s></p><p type="main">

<s>Gi&agrave; ben sanno i nostri Lettori, a cui poco addietro si commemorava, <lb/>come fosse quello strumento idrostatico inventato dal Tartaglia, a evitar le <lb/>fallacie, inevitabili nel metodo, che, per trovare i pesi specifici de'vari corpi, <lb/>si diceva avere usato Archimede: e che tale pure si fosse il primo passo <lb/>fatto da Galileo intorno alla Bilancetta, apparisce da una sua nota, la quale, <lb/>essendo scritta in mezzo a quella salva di <emph type="italics"/>Problemi varii,<emph.end type="italics"/> che poi risoluti <lb/>si sarebbero voluti inserire nel <emph type="italics"/>Dialogo novissimo:<emph.end type="italics"/> ne fa presentir l'origine <lb/>e la ragione di quel frammento, che pi&ugrave; qua pubblicheremo. </s>

<s>In quella nota <lb/>dunque si legge: &ldquo; Esperienza di Archimede falsa intorno alla Corona di <lb/>Jerone, con l'esplicazione della Bilancia, per trovare i pesi delle diverse ma&shy;<lb/>terie &rdquo; (MSS. Gal., P. III, T. III, fol. </s>

<s>62). E appunto &egrave; questa quella Bilan&shy;<lb/>cia, che si diceva non essere di originale invenzione, ma un perfezionamento <lb/>di quell'altra del Tartaglia. </s>

<s>Un documento, ritrovato da noi nelle <emph type="italics"/>Aggiunte <lb/>ai Manoscritti galileiani, esistenti nella R. </s>

<s>Biblioteca nazionale di Firenze,<emph.end type="italics"/><lb/>e che ora siam per trascrivere, conferma il nostro asserto. </s>

<s>Prima che l'Ho&shy;<lb/>dierna pubblicasse la scrittura autografa di Galileo, non si sapeva della Bi&shy;<lb/>lancetta di lui se non ci&ograve; che, per tradizione orale, ne venivano dicendo i <lb/>Discepoli, le particolarit&agrave; de'quali detti in proposito possono raccogliersi dal <lb/>documento, inserito nelle <emph type="italics"/>Aggiunte<emph.end type="italics"/> sopra annunziate, prezioso organo di tante <lb/>altre tradizioni scientifiche, ignote, della Scuola galileiana. </s>

<s>In quel documento <lb/>manoscritto dunque si dice: </s></p><p type="main">

<s>&ldquo; Il signor Galileo trov&ograve; una invenzione per pesare le materie pi&ugrave; gravi <lb/>dell'acqua, abbiano che figura si vuole, ed &egrave; facendo una Bilancia, anzi Sta&shy;<lb/>dera, con ispazi giustissimi e minuti, <lb/><figure id="id.020.01.3148.1.jpg" xlink:href="020/01/3148/1.jpg"/></s></p><p type="caption">

<s>Figura 59.<lb/>ed i metalli o altro si pongono sopra <lb/>la Bilancia immersi dentro all'acqua, <lb/>appesi per un filo di seta cruda, ov&shy;<lb/>vero capello, e si legano alla stadera <lb/>mel punto B (fig. </s>

<s>59). E per fare li <pb xlink:href="020/01/3149.jpg" pagenum="110"/>scompartimenti giustissimi fanno l'ago BD tondo, e sopra ci avvolgono a <lb/>spira un filo di metallo, tirato alla filiera, che benissimo si accosti, quale, <lb/>per essere grosso tutto ugualmente, e tra loro toccarsi le spire, viene a fare <lb/>li scompartimenti uguali fra loro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per fare il computo della gravit&agrave; dell'argento si sospender&agrave; un pezzo <lb/>di argento C ad un capello, alla testa della stadera B, ed immerso nell'acqua <lb/>chiara, ed ivi si tiri il guscio F, che serve invece di romano, in luogo che <lb/>stia in equilibrio, e sia per esempio al decimo scompartimento (quali si con&shy;<lb/>tano toccandoli con la punta di un ago, ovvero con il taglio di un coltello) <lb/>e se non star&agrave; perfettamente in equilibrio, cavisi ovvero aggiungasi della pol&shy;<lb/>vere di piombo o altro grave, che in detto guscio si deve ponere, fino a che <lb/>ugualmente bilanci. </s>

<s>Cavisi poi detto argento fuori dell'acqua, e si lasci asciu&shy;<lb/>gare al sole o altrimenti, e si tiri tanto avanti il guscio, che serve per ro&shy;<lb/>mano, in fino a che stia in equilibrio, e sia v. </s>

<s>g. </s>

<s>a venti gradi o scompar&shy;<lb/>timenti. </s>

<s>Io dico che la gravit&agrave; dell'argento a quella dell'acqua star&agrave; come <lb/>venti a dieci, perch&egrave; infondendolo nell'acqua noi abbiamo detratto dal suo <lb/>peso totale dieci gradi di gravit&agrave;. </s>

<s>Ma l'acqua non detrae dalle materie gravi <lb/>altro che quanto peserebbe una mole di acqua per l'appunto, uguale a quella <lb/>che s'immerge, abbia che figura si vuole, perch&egrave; l'acqua nell'acqua non <lb/>pesa; adunque l'argento sar&agrave; il doppio pi&ugrave; grave dell'acqua. </s>

<s>E permutan&shy;<lb/>dosi, a volere che l'argento fosse uguale di peso all'acqua, sarebbe neces&shy;<lb/>sario che quel medesimo pezzo fussi di superficie due volte maggiore. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Dicono che la stadera, per esser comoda, vorrebbe esser lunga un <lb/>gran palmo, e di robustezza basta che possa sostenere un'oncia di peso: il <lb/>filo di ottone o di acciaio vuol essere sottilissimo, e la bilancia gelosa, che <lb/>ogni poco di grave la muova. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per fare la bilancia assai gelosa, si faccia che il fulcimento sia fuora <lb/>della traversa, e tanto quanto sar&agrave; alle braccia della bilancia o traversa lon&shy;<lb/>tano, tanto sar&agrave; piu gelosa. </s>

<s>Come per esempio nella bilancia ABC (fig. </s>

<s>60), <lb/><figure id="id.020.01.3149.1.jpg" xlink:href="020/01/3149/1.jpg"/></s></p><p type="caption">

<s>Figura 60.<lb/>se in cambio di porre il pernio del fulcimento nel <lb/>luogo B, come si usa, lo porremo lontano alle brac&shy;<lb/>cia AB, BC, e lo porremo nel luogo D, ella sar&agrave; pi&ugrave; <lb/>gelosa e mobile: tanto pi&ugrave;, quanto dal luogo B sta <lb/>lontano l'ago. </s>

<s>Allora, ogni tantino che esca la Bi&shy;<lb/>lancia dall'equilibrio, far&agrave; molto maggior mutazione, <lb/>ed &egrave; meglio, invece di fare il buco nel luogo D, ed il fulcimento o pernio <lb/>farlo nel sostegno, che detta Bilancia sostiene; farlo nel sostegno: e nel&igrave;'ago <lb/>della Bilancia in D farvi un coltello tagliente. </s>

<s>&rdquo; </s></p><p type="main">

<s>Queste ultime osservazioni sono di non lieve importanza, per la storia <lb/>della costruzione, e delle leggi statiche applicate alla Bilancia, bench&egrave; al&shy;<lb/>quanto fuori del presente proposito, qual'era di confermare che la princi&shy;<lb/>pale intenzione, per cui Galileo costru&igrave; la sua Bilancetta idrostatica, fu <emph type="italics"/>per <lb/>trovare i pesi in specie delle varie materie,<emph.end type="italics"/> non altrimenti da quel che un <lb/>mezzo secolo prima aveva pure inteso di fare il Tartaglia. </s>

<s>Quali modifica-<pb xlink:href="020/01/3150.jpg" pagenum="111"/>zioni poi all'invenzione di questo facesse l'altro, dalla precedente descrizione <lb/>&egrave; manifesto: allo <emph type="italics"/>spaghetto lunghetto<emph.end type="italics"/> si sostitu&igrave; uu filo di seta cruda, o un <lb/>capello, e alla inesattezza delle divisioni, segnate con le tacche ordinarie sul&shy;<lb/>l'ago della Stadera <emph type="italics"/>ovver piombino,<emph.end type="italics"/> si provvide ingegnosamente, riducendo <lb/>l'ago stesso quasi a vite micrometrica, co'sottili e stretti avvolgimenti di un <lb/>filo di metallo. </s></p><p type="main">

<s>Con un tale strumento, ridotto cos&igrave;, per via dei detti artificii, squ&iacute;sito, <lb/>Galileo speriment&ograve; le gravit&agrave; specifiche dei varii corpi, e, in ordine al pro&shy;<lb/>blema della corona, dava per risolverlo fondamenti assai pi&ugrave; sicuri di quelli, <lb/>che si proponevano dagli Antichi. </s>

<s>Quella completa soluzion nonostante ri&shy;<lb/>maneva tuttavia affidata a un calcolo, come nella prima istituzion di Archi&shy;<lb/>mede, e fu propriamente Galileo, che dispens&ograve; da ogni esercizio matematico, <lb/>insegnando a chi ne fosse stato curioso di ritrovare le proporzioni de'due <lb/>metalli nel misto, col semplice uso manuale del suo strumento. </s>

<s>Tutto ci&ograve;, <lb/>insieme con altri particolari, da cui si viene a illustrare la storia della Bilan&shy;<lb/>cetta galileiana, s'intender&agrave; meglio da un frammento di Dialogo, che si rende <lb/>ora per noi alla pubblica notizia dal manoscritto altre volte citato: <emph type="italics"/>Roba del <lb/>gran Galileo, in parte copiata dagli originali, e in parte dettata da lui <lb/>cieco a me Vincenzo Viviani, mentre dimoravo nella sua casa di Arcetri.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Ammiranda, sopra tutte le altre che si leggono nelle an&shy;<lb/>tiche scritture, mi &egrave; sembrata sempre l'invenzion di Archimede, per la quale <lb/>scopri il furto della corona di Jerone, e tanto pi&ugrave; mi s'accresce di ci&ograve; la <lb/>maraviglia, quanto pi&ugrave; vo fra me ripensando come il nostro Accademico ri&shy;<lb/>dusse l'operazione assai pi&ugrave; facile e pi&ugrave; precisa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Io n'ho sentito anch'io tante volte parlare, e a chi non <lb/>&egrave; noto oramai quel famoso <emph type="italics"/>eurika, eurika?<emph.end type="italics"/> Non intendo per&ograve; come a sco&shy;<lb/>prir se un oggetto &egrave; di oro puro, o mescolato con altro, ci sia bisogno di <lb/>una scienza cos&igrave; pellegrina. </s>

<s>Non era ella forse nota a que'tempi la pietra <lb/>del paragone? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Era anzi notissima sotto il nome di pietra eracl&egrave;a o lidia, <lb/>e se ne trovano descritte le maravigliose virt&ugrave; da Teofrasto, antichissimo <lb/>scrittore greco. </s>

<s>Poco o nulla per&ograve; poteva giovare il ricorrere a un tale espe&shy;<lb/>diente, trattandosi, non di scoprir la natura de'metalli, ma di sapere secondo <lb/>qual proporzione si trovassero nel composto, ci&ograve; che si desiderava principal&shy;<lb/>mente, per far la giusta ragione del furto. </s>

<s>Del qual furto gl'indizi non ve&shy;<lb/>nivano dall'aspetto esteriore, o da qualche esame che si fosse fatto intorno <lb/>alla parte sostanziale della corona, la quale, come mostrava, cos&igrave; era al di <lb/>fuori tutta aurea, e rispondeva esattamente al peso del metallo puro conse&shy;<lb/>gnato all'orefice, perch&egrave; ne conducesse il lavoro. </s>

<s>Sembra piuttosto, a quel <lb/>che si pu&ograve;, con la ragione e con la prudenza, congetturare di un fatto da <lb/>noi tanto remoto, che i cortigiani sapessero qualche cosa di certo, e che, <lb/>susurrandone in palazzo, facessero entrare nel Re il sospetto che a una buona <lb/>parte dell'oro fosse furtivamente sostituito altrettanto peso di argento, cosic&shy;<lb/>ch&egrave; la materia della corona resultasse del loro misto. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/3151.jpg" pagenum="112"/><p type="main">

<s>&ldquo; SAGREDO. &mdash; Mi sembrerebbe, essendo cos&igrave;, che dal solo colore si sa&shy;<lb/>rebbe potuto sospettar dell'inganno, perch&egrave;, mescolandosi insieme due pol&shy;<lb/>veri, l'una delle quali tirasse al giallo rossigno dell'oro, e l'altra al bianco <lb/>cenerino dell'argento; se ne vedrebbe nascere un terzo colore, che non &egrave; <lb/>bene n&egrave; questo schietto, n&egrave; quello. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Voi, signor Sagredo, mostrate di participar con l'opi&shy;<lb/>nione di molti, che la mescolanza dei due metalli nella corona fosse fatta <lb/>per fusione, e per effetto del fuoco. </s>

<s>Ma non fu propriamente cos&igrave;: anzi vi <lb/>dico che cos&igrave; non pu&ograve; essere stato, perch&egrave; altrimenti sarebbono riuscite fal&shy;<lb/>laci le liberali applicazioni della scienza, nel far le quali necessariamente si <lb/>presuppone che le densit&agrave;, da cui dipendono le moli de'due metalli, separa&shy;<lb/>tamente e nel misto, si mantengano inalterate. </s>

<s>Voi dovete sapere che sono <lb/>in tutti i corpi sparsi vacuetti, dal maggiore o minor numero de'quali, e <lb/>dalla loro maggiore o minore grandezza, dipende l'essere alcuni solidi, sotto <lb/>parit&agrave; di superficie, pi&ugrave; o meno gravi di altri. </s>

<s>&Egrave; perch&egrave; togliendo due palle <lb/>di diametro uguale, ma la prima d'oro e la seconda d'argento, si trova es&shy;<lb/>ser quella notabilmente pi&ugrave; grave di questa; convien dire che nell'argento <lb/>siano que'vacuetti in pi&ugrave; larga copia disseminati, che in mezzo all'oro. </s>

<s>Ora <lb/>accade che, fondendosi insieme i due metalli, nelle maggiori vacuit&agrave; dell'uno <lb/>penetra, assottigliata dal fuoco, la sostanza dell'altro, intanto che il misto <lb/>viene a ridursi sotto mole assai minore di quella, che avevano prima i due <lb/>metalli separati. </s>

<s>Cos&igrave; essendo, il ragionamento di Archimede, che partivasi <lb/>da falsi principii, sarebbe giunto a conseguenze false. </s>

<s>N&egrave; potendosi ci&ograve; pre&shy;<lb/>supporre in un ingegno tanto eccellente, mi fa con certezza asseverare che <lb/>fossero i due metalli insieme nella corona per semplice apponimento di parti, <lb/>e non per fusione: come a dire che l'armilla e i raggi, consolidati dentro <lb/>nella materia dell'argento, fossero tutti ricoperti di fuori, e fasciati, da una <lb/>foglia di purissimo oro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Se cos&igrave; stanno, signor Salviati, le cose, come voi dite, <lb/>non aveva bisogno Jerone di ricorrere alla sapienza del grande Archimede: <lb/>qualunque artefice, co'suoi strumenti acuti e taglienti, rimovendo la foglia <lb/>dell'oro, gli avrebbe reso visibile l'argento che v'era sotto, e senza indugio <lb/>scoperta la ragione del furto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Pensate per&ograve;, signor Simplicio, che si sarebbe cos&igrave; gua&shy;<lb/>stato il lavoro, con finissima arte e diligenza condotto, e da questa parte <lb/>giusto ne pare maravigliosa la scienza di Archimede, perch&egrave;, mentre non <lb/>rendeva men certo e men patente il fatto, che a metterlo sotto gli occhi; <lb/>lasciava, secondo il desiderio del Re, l'opera dell'artefice intatta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Il signor Simplicio, col suo stesso silenzio, mostra di es&shy;<lb/><gap/> sodisfatto. </s>

<s>Vi resta ora, signor Salviati, a dare sodisfazione anche a me <lb/>intorno a due dubbii, che mi son nati, ascoltando il vostro discorso. </s>

<s>Il primo <lb/>si &egrave; che io non posso persuadermi avere metalli cos&igrave; compatti, come sono <lb/>l'oro e l'argento, vacuetti o pori aperti in mezzo alla loro sostanza, come <lb/>si vede ne'legni o in altri corpi, che galleggiano sopra l'acqua. </s>

<s>Il secondo <pb xlink:href="020/01/3152.jpg" pagenum="113"/>&egrave; che io non intendo come, non serbando i due metalli nel misto la mede&shy;<lb/>sima proporzion di mole, che separati, fallaci, come voi dite, ne dovessero <lb/>riuscire i giudizi di Archimede, o di chiunque altro si volesse mettere a imi&shy;<lb/>tarne gli esempi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; L'esperienze del nostro Accademico vi risolveranno il <lb/>primo dubbio. </s>

<s>Il secondo ve lo troverete per voi medesimo risoluto, da poi <lb/>che io vi avr&ograve; descritto il processo della maravigliosa invenzione, che, se&shy;<lb/>condo ne riferiscono gli Scrittori, sarebbe questo: Avendo Archimede, men&shy;<lb/>tre era tutto in pensiero della proposta fattagli da Jerone, scoperto che il suo <lb/>proprio corpo, immerso nell'acqua della tinozza piena, tanto perdeva della <lb/>sua gravit&agrave; naturale, quant'era il peso dell'acqua versata; prese una massa <lb/>di oro schietto, e separatamente una massa di argento, ambedue di pari peso <lb/>a quello, che dava la corona, posta sopra una squisitissima Bilancia. </s>

<s>Poi <lb/>riemp&igrave; un vaso di acqua, e vi tuff&ograve; la massa dell'oro, la quale ne fece tra&shy;<lb/>boccar tanta, quant'era precisamente la propria mole, tenendo esattissimo <lb/>conto del peso dell'acqua versata. </s>

<s>Similmente oper&ograve; con l'argento, e con la <lb/>corona, la quale fu trovata versar meno acqua dell'argento stesso, e pi&ugrave; di <lb/>quello, che non avesse fatto l'oro solo, e da questo pi&ugrave; o meno dell'acqua, <lb/>ne'detti versamenti con diligenza raccolta, riusc&igrave; poi, per via di calcolo, Ar&shy;<lb/>chimede a saper quanto pi&ugrave; o meno dell'un metallo o dell'altro avesse im&shy;<lb/>piegato l'orefice nel suo lavoro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Or ben comprendo, signor Salviati, che, non potendosi <lb/>paragonare insieme due cose di natura diversa, male avrebbe Archimede ri&shy;<lb/>soluto il problema, se le moli ai pesi, de'due metalli separati e nel misto, <lb/>non avessero osservata la medesima proporzione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Quanto a me confesso che, dal discorso del signor Sal&shy;<lb/>viati, mi si rappresenta il furto della corona di cos&igrave; facile ritrovato, che io <lb/>non intendo com'egli abbia potuto destar nel mondo tanta ammirazione. </s>

<s><lb/>Trattandosi di versar acqua in un vaso, e di farvela traboccare col tuffarvi <lb/>dentro un oggetto, mi pare che tutto si riduca a un gioco da fanciulli, n&egrave; <lb/>so quale gloria potesse guadagnarne il nostro Accademico, a ingerirsi di que&shy;<lb/>ste bagattelle, per renderle, come voi dite, pi&ugrave; facili e pi&ugrave; precise. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Bagattelle si potrebbero forse dire in s&egrave; stesse, non con&shy;<lb/>siderata la loro intenzione finale, che se voi poteste, signor Simplicio, pene&shy;<lb/>trar col vostro cervello, vi farebbe dare di queste cose ben altro giudizio. </s>

<s>Vi <lb/>concedero; in ogni modo che sia ovvio infondere l'acqua in un vaso, e per <lb/>l'immersione di una mole straniera farla riversar fuori dal suo labbro. </s>

<s>Ma, <lb/>per la bont&agrave; dell'operazione, &egrave; necessario saper la misura esatta di quel ver&shy;<lb/>samento. </s>

<s>Ripensate ora a quel che in tale atto rimane attaccato agli orli, e <lb/>alle pareti esterne, e vi persuaderete che il liquido cos&igrave; raccolto non &egrave; pre&shy;<lb/>cisamente tutto quello, di cui la mole straniera &egrave; sottentrata a prendere il <lb/>luogo. </s>

<s>N&egrave; a punto minor pericolo di fallacie menava il metodo, che si dice <lb/>aver tenuto Archimede. </s>

<s>Egli lasciava liberamente versar l'acqua, infin tanto <lb/>che non fosse la mole tutta immersa. </s>

<s>Poi estraeva questa dal vaso, che ne-<pb xlink:href="020/01/3153.jpg" pagenum="114"/>cessariamente si rimaneva scemo, e l'acqua, che poi ci bisognava a colmarlo, <lb/>era la misura di quella dianzi versata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Questa operazione dispensava &egrave; vero da ogni cura lo sperimentatore, <lb/>per quella parte dell'acqua che si perdeva, rimanendo nel versare attaccata <lb/>agli orli, e alle pareti del vaso: ma se ne perdeva pure in altra maniera, <lb/>in quel velo cio&egrave;, di che tornavano rivestite le moli, nel tirarle fuori dal ba&shy;<lb/>gno, e specialmente la corona, con tutti que'suoi incavi e risalti, sfuggimenti <lb/>e trafori. </s>

<s>E nell'atto stesso di colmare il vaso, dopo l'estrazione, a quanti <lb/>scorsi non andava ella soggetta la mano incerta? </s>

<s>Bisognava badar bene che <lb/>l'acqua non traboccasse: eppure, se non traboccava, non si poteva esser certi <lb/>che il vaso era colmo. </s>

<s>Giunto il liquido all'orlo supremo, si poteva, colla <lb/>sestaria o con altra ampolla di misura nota, seguitare a infondere a gocciola <lb/>a gocciola, e una e due e quattro non bastano, in fin tanto che, squarcian&shy;<lb/>dosi a un tratto quella specie di pellicola, che involge, e che, quasi vi fosse <lb/>cucita in giro, trattiene il colmo; tutto va gi&ugrave; a precipizio. </s>

<s>Ond'ei non &egrave; <lb/>possibile sapere, con quella precisione che pur si richiede, quant'&egrave; l'acqua <lb/>versata dall'ampolla, a riempire lo scemo, rimasto dentro il vaso, dall'estrarne <lb/>fuori i metalli. </s>

<s>E anche, nel misurar l'acqua dell'ampolla dopo il riempi&shy;<lb/>mento, altra nuova occasione a fallacie. </s>

<s>Perch&egrave;, non valendoci le misure di <lb/>capacit&agrave;, e dovendosi ricorrere alla Stadera, ci bisognavano due pesate: una <lb/>prima, e un'altra dopo l'infusione, a fin di argomentare, dalla trovata dif&shy;<lb/>ferenza, quanto sia il peso dell'acqua, di mole uguale a quella dell'oro, del&shy;<lb/>l'argento, e della corona. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora il nostro Accademico, ripensando a ci&ograve;, e specialmente che per <lb/>l'operazione era la Stadera strumento indispensabile, si maravigli&ograve; che Ar&shy;<lb/>chimede eleggesse modi cos&igrave; complicati e fallaci, invece di quegli altri tanto <lb/>pi&ugrave; semplici, e pi&ugrave; sicuri, che pareva dover essergli suggeriti da'suoi stessi <lb/>teoremi. </s>

<s>In uno di questi infatti dimostra che un solido immerso nell'umido <lb/>perde tanto di gravit&agrave;, quant'&egrave; la gravit&agrave; dell'umido, di cui dentro il vaso <lb/>egli occupa il luogo. </s>

<s>Immaginate dunque essere BD (nella figura 59) la sta&shy;<lb/>dera, con la quale si &egrave; pesato il solido C, o oro o argento che egli sia, o un <lb/>composto di tutt'e due, e che siasi quel peso v. </s>

<s>g. </s>

<s>trovato venti libbre. </s>

<s>Non <lb/>rimovete nulla dal suo posto: se mai, allungate il filo BC, che ha da essere <lb/>sottilissimo e resistente come d'acciaio, infin tanto che il solido C, da cui <lb/>pende, non vada a tuffarsi tutto nell'acqua di un vaso, sottopostogli a que&shy;<lb/>sto effetto. </s>

<s>Perder&agrave;, cos&igrave; stante, del suo proprio peso, e quanto ne perder&agrave; <lb/>per l'appunto si potr&agrave; saperlo dal ritirare indietro il romano, il quale sup&shy;<lb/>poniamo che faccia l'equilibrio, giunto sul segno delle dieci libbre. </s>

<s>La diffe&shy;<lb/>renza &egrave; dunque dieci, e tanto &egrave; il giusto peso di una mole di acqua, uguale <lb/>alla mole C, che, per ritrovarlo, si facevano quelle penose e incerte opera&shy;<lb/>zioni da me narrate. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Io rimango veramente stupito, nel ripensare al modo delle <lb/>antiche e delle nuove esperienze. </s>

<s>In queste il solido imprime nell'umido la <lb/>sua propria stampa, intanto che la mole di questo, corrispondente alla mole <pb xlink:href="020/01/3154.jpg" pagenum="115"/>di quello, si pu&ograve; dire che sia esattamente ritrovata dalla stessa Natura, non <lb/>rimanendo all'arte altra faccenda, che di ritirare innanzi e indietro il con&shy;<lb/>trappeso della stadera. </s>

<s>Mirabilmente si viene per questa via a scansare ogni <lb/>fallacia, da quella in fuori che pu&ograve; nascer dal filo. </s>

<s>Ma pur, lasciandone tuffare <lb/>assai poco, ed essendo sottilissimo, come avete prescritto, non pu&ograve; produrre <lb/>che qualche minimo effetto. </s>

<s>Io non avrei avuto il coraggio di dire, come il <lb/>signor Simplicio, che queste erano bagattelle, ma non avrei nemmeno creduto <lb/>che fossero invenzioni cos&igrave; pellegrine e ammirande, come ora intendo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; E anch'io pronunziai quel giudizio, perch&egrave; da tanti avevo <lb/>sentito parlare di questo furto, fatto nella corona del re Jerone, ma nes&shy;<lb/>suno me ne aveva ancora spiegato cos&igrave; bene il modo, com'avete fatto voi, <lb/>signor Salviati, a cui raccomando di congratularvi di ci&ograve; con l'Accademico, <lb/>a nome mio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Aspettate a far questo di avere inteso il tutto, non essen&shy;<lb/>dosi detto fin qui da me che il principio, a movere dal quale sia fatto il <lb/>primo passo, considerando che col metodo nuovo &egrave; possibile ritrovare la pro&shy;<lb/>porzione, che, al peso di un'egual mole di acqua, ha il peso di qualunque <lb/>pi&ugrave; piccolo oggetto, come sarebbe per esempio di una margarita. </s>

<s>Se non <lb/>che si richiede al proposito una stadera assai delicata, e con la lunghezza <lb/>divisa in minime parti, le quali vogliono essere tutte puntualissimamente <lb/>uguali. </s>

<s>Una tal precisione, difficile ad aversi dall'arte fabbrile, si conseguiva <lb/>dal nostro Accademico, avvolgendo intorno al ferro tondo dell'ago un filo <lb/>sottilissimo di acciaio, passato alla filiera, e stringendone le spire l'una con&shy;<lb/>tro l'altra a esquisitissimo contatto. </s>

<s>Cos&igrave;, alle tacche ordinarie si sostituivano <lb/>i passi di una vite, i quali, per essere cos&igrave; brevi, e perci&ograve; non bene discer&shy;<lb/>nibili alla vista, abbarbagliata di pi&ugrave; dai riflessi; si contano dagli scatti della <lb/>punta di un ago o del taglio di un coltello strisciativi sopra. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Strumento gentilissimo in vero, e a quel che intendo di <lb/>uso assai pi&ugrave; universale di quello, che a prima vista non sembrerebbe. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Serve infatti a ritrovare le gravit&agrave; in specie di qualun&shy;<lb/>que corpo con tal precisione, che il nostro Accademico ebbe a notare essere <lb/>gli sperimentatori, avanti a lui, proceduti, intorno a ci&ograve; troppo in di grosso, <lb/>bench&egrave; possa anch'egli aver talvolta fallato, specialmente rispetto a certi me&shy;<lb/>talli, per non esserglisi sempre offerti purissimi, com'avrebbe voluto. </s>

<s>La pron&shy;<lb/>tezza poi e la facilit&agrave; dell'operazione &egrave; manifesta, dietro ci&ograve; che io vi ho <lb/>detto, e ritornando con l'occhio sopra questo foglio, disegnatovi dianzi, per <lb/>darvi a intendere la costruzione e il modo della Bilancia. </s>

<s>Imperocch&egrave;, se la <lb/>mole C &egrave; oro, che in aria stia col contrappeso in H, distante dal perpendi&shy;<lb/>colo E, quant'&egrave; la linea EH, e poi in acqua voglia essere ritirato in G; <lb/>dalla proporzione delle due linee EH, GH, che &egrave; quella de'numeri degli scatti <lb/>ascoltati, nel fare strisciare, ora sopra l'una lunghezza ora sopra l'altra, <lb/>l'aguto; s'aver&agrave; la proporzione della gravit&agrave; in specie dell'oro, alla gra&shy;<lb/>vit&agrave; di una egual mole di acqua, o di altro liquore. </s>

<s>E con questo &egrave; venuto <lb/>il proposito di dirvi in che modo si certificasse il nostro Accademico che, <pb xlink:href="020/01/3155.jpg" pagenum="116"/>in mezzo alla sostanza dell'oro e dell'argento, per non dire di altri metalli <lb/>meno densi, siano disseminati pori, bench&egrave; tanto piccoli, da sfuggire alla <lb/>vista pi&ugrave; acuta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia novamente C o palla o cubo di oro, che pesato, come si &egrave; detto, <lb/>prima in aria e poi in acqua, abbia data la differenza GH. </s>

<s>Prendeva poi <lb/>l'Amico nostro quel medesimo cubo, e, posatolo sopra un'incudine, gli fa&shy;<lb/>ceva dare gagliardissimi colpi con un martello di acciaio. </s>

<s>Tornando poi a <lb/>sospendere alla bilancia l'oro cos&igrave; ammaccato, e tuffandolo in acqua, trovava <lb/>che il contrappeso voleva essere ritirato alquanto pi&ugrave; distante dal perpendi&shy;<lb/>colo, che non era il punto G; segno evidentissimo che nell'ammaccatura la <lb/>mole era diminuita, e ci&ograve; non per altro, che per essere entrata la materia <lb/>a occupare gli spazi prima rimasti vacui. </s>

<s>Il rientramento poi e il ritiramento <lb/>della mole in s&egrave; stessa fu a proporzione anche maggiore nell'argento, in si&shy;<lb/>mile modo ammaccato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Bellissima e delicata esperienza, da cui si conferma che <lb/>non dovevano essere i due metalli confusi nella corona di Jerone, ma sem&shy;<lb/>plicemente congiunti. </s>

<s>Da tutto quel che avete detto per&ograve;, signor Salviati, <lb/>non vedo come ne resultino le proporzioni dell'oro all'argento, di rassegnar <lb/>le quali era il fine principalissimo di questa invenzione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Archimede ci and&ograve; per via di calcolo, tutta la precision <lb/>del quale dipendendo dalle sperimentate gravit&agrave; in specie, ci aveva il Nostro <lb/>opportunamente provveduto, valendosi di quel suo perfettissimo strumento. </s>

<s><lb/>Da principio si content&ograve; di questa semplice promozione, lasciando anch'egli <lb/>alle ragioni numeriche concludere il rimanente. </s>

<s>E perch&egrave; queste ragioni non <lb/>si sa come propriamente Archimede le istituisse, e i commentatori di lui si <lb/>erano messi per vie tanto intralciate, da non si parer confacevoli col genio <lb/>nobilissimo del Matematico antico; il comune Amico nostro ridusse tutto alla <lb/>semplicit&agrave; di quella regola, per la quale, dati essendo tre termini in pro&shy;<lb/>porzione, &egrave; possibile a ritrovar sempre il quarto termine ignoto. </s>

<s>Il primo <lb/>dunque di quei termini &egrave; l'eccesso della gravit&agrave; in specie dell'oro, sopra la <lb/>gravit&agrave; in specie, dell'argento, diviso per la gravit&agrave; in specie dell'argento: <lb/>il secondo &egrave; l'eccesso della gravit&agrave; in specie dell'oro, sopra la gravit&agrave; in <lb/>specie del composto, diviso per la gravit&agrave; in specie del composto: il terzo &egrave; <lb/>la gravit&agrave; in aria di esso composto, che per supposizione &egrave; la medesima che <lb/>la gravit&agrave; delle parti separate, e che pu&ograve; aversi dalla Bilancia ordinaria, <lb/>come pure dalla Bilancia, per trovare i pesi nell'acqua, s'avranno gli altri <lb/>due detti termini. </s>

<s>Ond'ei potranno tutti e tre sapersi, e sapersi con essi in&shy;<lb/>sieme anche il quarto, che &egrave; il peso dell'argento. </s>

<s>Il peso dell'oro ne verr&agrave; <lb/>in conseguenza, perch&egrave;, se il composto &egrave; v. </s>

<s>g. </s>

<s>sessanta libbre, e che l'ar&shy;<lb/>gento si sia trovato venti; &egrave; manifesto che l'oro sar&agrave; quaranta. </s>

<s>Ma poi pens&ograve; <lb/>che queste stesse proporzioni si potevano direttamente conoscere, mediante <lb/>lo strumento, senza far altro che contarne i segni, sopra la lunghezza del&shy;<lb/>l'ago compresi fra le varie distanze dai punti, dove, per ottener l'equilibrio, <lb/>s'erano fatti rimanere i contrappesi. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/3156.jpg" pagenum="117"/><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Questo mi piace, ed essendo cos&igrave;, l'invenzione mi rie&shy;<lb/>sce bellissima, e praticabile a tutti, che come me non sanno, o non vogliono <lb/>tornare a stillarsi il cervello sopra il quinto libro di Euclide. </s>

<s>Ditemi dun&shy;<lb/>que, signor Salviati, in che modo io potessi ritrovare, in un oggetto compo&shy;<lb/>sto di oro e di argento, la proporzione dei due metalli, senz'avere a far al&shy;<lb/>tro, che pesare alla stadera, con l'arte semplicissima di chi vende sopra le <lb/>piazze o nelle botteghe. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Nella figura (61) che io, per vostra maggiore intelligenza, <lb/>vo'disegnarvi su questo foglio, immaginate che in E stia il perpendicolo della <lb/><figure id="id.020.01.3156.1.jpg" xlink:href="020/01/3156/1.jpg"/></s></p><p type="caption">

<s>Figura 61.<lb/>stadera, e che il vostro og&shy;<lb/>getto, rappresentato con A, <lb/>e pendente in F da uno <lb/>estremo, sia dall'altro C <lb/>esattamente contrappesato <lb/>in aria dal grave B, il quale <lb/>suppongo che faccia da con&shy;<lb/>trappeso a due separate <lb/>quantit&agrave; di oro e di argento, che, remosso A, si facessero una per volta pen&shy;<lb/>dere dal punto F. </s>

<s>Sia dunque, prima, A oro puro, che tuffato in acqua faccia <lb/>ritirare il grave B da C in D, e si noti diligentemente questo punto. </s>

<s>Si levi <lb/>poi l'oro, e si metta in suo logo l'argento, che, dall'aria passando in acqua, <lb/>voglia il ritiramento nel punto G, il quale similmente si noti con diligenza. </s>

<s><lb/>Tornando all'ultimo a sospendere l'oggetto A, che si faccia anch'egli scen&shy;<lb/>dere sotto l'acqua, si pu&ograve; con assai facilit&agrave; prevedere come, essendo pi&ugrave; lieve <lb/>che se fosse oro pretto, e pi&ugrave; grave, che se fosse pretto argento; far&agrave; tal&shy;<lb/>mente ritirare il contrappeso, che tra D e G consista in qualche punto di <lb/>mezzo, quale, venendo al fatto, si trovi essere H. </s>

<s>Contate ora i passi, che fa <lb/>il filo di acciaio tra G e H, e poi tra H e D; e quant'&egrave; il numero di quelli, <lb/>rispetto al numero di questi, altrettante direte, signor Simplicio, essere le parti <lb/>dell'oro, rispetto a quelle dell'argento. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; La conclusione &egrave; semplicissima in vero, e deve il nostro <lb/>Accademico esservi giunto per via di qualche ragionamento geometrico, che, <lb/>se non supera la mia capacit&agrave;, vi prego a riferirmelo secondo il suo proprio <lb/>processo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Il ragionamento anzi &egrave; facilissimo, n&egrave; richiede altra pre&shy;<lb/>cognizione, che de'primi principii della Scienza meccanica, da cui si con&shy;<lb/>duce in poche parole. </s>

<s>Rimangano infatti le medesime supposizioni, ma in A <lb/>siano distintamente contrassegnate due parti: una I dell'oro, contrappesata <lb/>in aria dalla porzione M, e l'altra L dell'argento, contrappesata dalla por&shy;<lb/>zione N. </s>

<s>Fatto dal filo attaccato in F calare l'oggetto A nell'acqua, il riti&shy;<lb/>ramento si trov&ograve; essere in H, da cui pendono dunque congiunti insieme M <lb/>ed N. </s>

<s>Stante ci&ograve;, immaginate che venga remossa da A la parte L: l'altra <lb/>che rimane sar&agrave; contrappesata da M in D. </s>

<s>Rimovete invece la parte I, e ci&ograve; <lb/>che di A rimane sar&agrave; contrappesato da N in G. </s>

<s>Dunque il medesimo og-<pb xlink:href="020/01/3157.jpg" pagenum="118"/>getto A si trova sopra la libbra ugualmente bene in equilibrio, tanto a far <lb/>pendere collettivamente i due pesi M ed N da H, quanto a far distributiva&shy;<lb/>mente pendere M da D, ed N da G. </s>

<s>Dunque &egrave;, per la Scienza meccanica, <lb/>H il centro dell'equilibrio, dal qual punto debbono le distanze HG e DH <lb/>stare reciprocamente come il peso M, al peso N, ossia, come il peso dell'oro <lb/>al peso dell'argento, secondo che da me poco fa si diceva al signor Simpli&shy;<lb/>cio, nel descrivergli la sola arte pratica dell'operazione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Quest'arte ora, in grazia del vostro discorso dimostra&shy;<lb/>tivo, mi &egrave; tornata chiarissima, e se io fossi quell'Archimede, a cui fu pro&shy;<lb/>posto di scoprire la ragione del furto famoso, sospenderei dalla bilancia in F, <lb/>prima la corona del re Jerone, poi un pezzo di oro, poi un pezzo di argento, <lb/>che tutti e tre in aria valessero il medesimo peso B. Poi, tuffando le tre moli <lb/>una per volta nell'acqua, farei i ritiramenti in H, in D, e in G: e se, a <lb/>strisciare la punta dello stiletto da G fino in H, ne contassi 21 scatto, e da <lb/>H in D ne contassi 40; direi che la parte dell'oro puro sta alla parte del&shy;<lb/>l'argento, furtivamente sostituito dall'orafo, come 40 sta a 21. Che se, po&shy;<lb/>niamo, tutto il peso della corona fosse stato 61 libbra, direi che certissima&shy;<lb/>mente 40 libbre erano oro, e 21 argento. </s>

<s>Ma in qualunque numero fosse <lb/>dato quel peso, lo partirei per 61, e l'avvenimento in once, e in divisioni <lb/>di oncia, moltiplicato per 40, e poi per 21, mi scoprirebbe il peso dell'oro <lb/>e dell'argento in once, o in altre pi&ugrave; minute divisioni di oncia, e mi ren&shy;<lb/>derebbe la ragione esattamente matematica del furto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SIMPLICIO. &mdash; Dunque non si pu&ograve;, nemmeno operando con lo stru&shy;<lb/>mento, evitare il calcolo, come il signor Salviati ci aveva promesso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Ma &egrave; un calcolo, da non superare l'abilit&agrave; di un fan&shy;<lb/>ciullo, che abbia rivedute appena le prime pagine dell'abbaco: n&egrave; molto pi&ugrave; <lb/>difficile, a dire il vero, mi parve quell'altro, che voi diceste, signor Salviati, <lb/>essere stato ridotto dal nostro Accademico alla semplicit&agrave; della regola aurea. </s>

<s><lb/>Vorrei per&ograve; sapere da voi se si pu&ograve; essere certi, che la regola dell'arimme&shy;<lb/>tica, e la pratica operazione con lo strumento, conducono infallibilmente a <lb/>concludere il medesimo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Il riscontro che voi, signor Sagredo, desiderate, si riduce <lb/>insomma a dimostrare che la proporzione tra i pesi e le distanze, segnate <lb/>sopra la lunghezza della libbra, &egrave; la stessa che tra i pesi, e quegli eccessi <lb/>di gravit&agrave; in specie, e loro quoti, a quel modo che vi pronunziai. </s>

<s>Fu con&shy;<lb/>cluso per la Scienza meccanica che GH sta a DH, come il peso dell'oro al <lb/>peso dell'argento. </s>

<s>Componendo, averemo GH con DH, ossia DG, a DH, come <lb/>il peso dell'oro, insieme col peso dell'argento, ossia, come tutto il peso della <lb/>corona, al peso dell'argento solo. </s>

<s>Per la concordanza dunque delle due re&shy;<lb/>gole si deve dimostrare che GD, verso DH, ha la medesima proporzione, che <lb/>l'eccesso della gravit&agrave; in specie dell'oro, sopra la gravit&agrave; in specie dell'ar&shy;<lb/>gento, diviso per la gravit&agrave; in specie dell'argento; ha verso l'eccesso della <lb/>gravit&agrave; in specie dell'oro, sopra la gravit&agrave; in specie della corona, diviso per <lb/>la gravit&agrave; in specie della corona. </s>

<s>Alla dimostrazione di che ci condurr&agrave; fa-<pb xlink:href="020/01/3158.jpg" pagenum="119"/>cilmente un principio, quale io vi propongo cos&igrave; in forma di lemma: Se la <lb/>mole A, sospesa in F dalla bilancia, ora sia oro, ora sia argento del mede&shy;<lb/>simo peso B in aria, e che, successivamente tuffate le due moli in acqua, <lb/>quella faccia ritirare da C in D, e questa da C in G; dico che la gravit&agrave; in <lb/>specie dell'oro, alla gravit&agrave; in specie dell'argento, aver&agrave; tal proporzione, <lb/>quale ha GC alla CD. </s>

<s>La proposta verit&agrave; si conclude immediata da ci&ograve;, che <lb/>su tal proposito in precedenza fu detto, che cio&egrave; la gravit&agrave; in specie dell'oro, <lb/>alla gravit&agrave; in specie dell'acqua, &egrave; come la EC alla CD. </s>

<s>E similmente, la <lb/>gravit&agrave; in specie dell'acqua, alla gravit&agrave; in spece dell'argento, come la CG <lb/>alla EC: onde ex aequali, per la perturbata, la gravit&agrave; in specie dell'oro aver&agrave;, <lb/>alla gravit&agrave; in specie dell'argento, la medesima proporzione, che la CG <lb/>alla CD. E, supponendo che le moli considerate siano ugualmente gravi alla <lb/>corona di Jerone, il ritiramento della quale in acqua sia da C in D; si pro&shy;<lb/>durr&agrave; similmente che la gravit&agrave; in specie dell'oro, alla gravit&agrave; in specie della <lb/>corona, sta come la CH alla CD. Ora, dividendo queste due proporzioni, tro&shy;<lb/>verete che, come l'eccesso della gravit&agrave; in specie dell'oro, sopra la gravit&agrave; <lb/>in specie dell'argento, alla gravit&agrave; in specie dell'argento; cos&igrave; &egrave; l'eccesso <lb/>della GC sopra la CD, ossia la DG alla CD. </s>

<s>In pari modo l'eccesso della <lb/>gravit&agrave; in specie dell'oro, sopra la gravit&agrave; in specie della corona, &egrave;, alla gra&shy;<lb/>vit&agrave; in specie della corona, come l'eccesso della CH sopra la CD, ossia la <lb/>DH, sopra la DC. </s>

<s>Dunque ex aequali, per la perturbata, l'eccesso della gra&shy;<lb/>vit&agrave; in specie dell'oro, sopra la gravit&agrave; in specie dell'argento, diviso per la <lb/>gravit&agrave; in specie dell'argento, sta all'eccesso della gravit&agrave; in specie dell'oro, <lb/>sopra la gravit&agrave; in specie della corona, diviso per la gravit&agrave; in specie della <lb/>corona, come la GD, divisa per la CD, sta alla DH, divisa per la medesima <lb/>CD: ossia, come la GD sola sta alla DH sola, secondo che, per sodisfare <lb/>alla curiosit&agrave; filosofica del nostro signor Sagredo, si voleva che io dimo&shy;<lb/>strassi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Son gratissimo alla vostra cortesia. </s>

<s>Io ho tenuto cos&igrave; <lb/>dietro a tutto il vostro discorso, da cui siamo stati condotti a conclusioni tanto <lb/>belle nella Scienza, e ad applicazioni cos&igrave; curiose nella pratica; che, per non <lb/>interromperlo, mi sono tante volte astenuto di manifestarvi un mio pensiero, <lb/>sovvenutomi improvvisamente, in mezzo a quel descriver che ci faceste le <lb/>esperienze di Archimede, per ritrovar le moli dell'acqua, esattamente uguali <lb/>a quelle dei due metalli e della corona. </s>

<s>Ora quel pensiero, quell'idea lusin&shy;<lb/>gatrice, era questa: che, se il vaso fosse stato perfettamente prismatico, un <lb/>corpo, per quanto si voglia irregolare, o formato con tutt'altra regola, da <lb/>quella cos&igrave; semplice, che prescrive ne'suoi solidi la Geometria, quale sarebbe <lb/>stata giusto quella corona; averebbe trovato nello scemo dell'acqua dentro <lb/>il vaso la sua quadratura prontissima e perfetta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Il medesimo sovvenne a me, n&egrave; saprei ben definire se, <lb/>dell'esserci cos&igrave; incontrati insieme in questa speculazione, io senta maggiore <lb/>in me o la compiacenza o la maraviglia. </s>

<s>Procurai di avere un vaso, tirato <lb/>pi&ugrave; esattamente che fosse possibile in forma di cubo, e, in mezzo al vano di <pb xlink:href="020/01/3159.jpg" pagenum="120"/>lui fatto sospendere un esattissimo cilindro, colmai il detto vaso di acqua, e <lb/>poi ne estrassi il solido, che, per essere stato scelto da me di materia pi&ugrave; <lb/>grave in specie, era tutto rimasto sommerso. </s>

<s>Il vuoto, da lui lasciato in figura <lb/>di un prisma, corrispondeva dunque esattamente alla mole cilindrica, la cir&shy;<lb/>colar base della quale mi si veniva perci&ograve; a trasformare in base quadrata. </s>

<s><lb/>Entrato in questa curiosit&agrave;, passai anche pi&ugrave; oltre. </s>

<s>Feci il vaso, da ricevere <lb/>l'acqua, cilindrico, &egrave; con esso un cono e una sfera, di tali diametri il cir&shy;<lb/>colo grande di questa, e la base di quello, che entrassero esattamente a riem&shy;<lb/>pire la cavit&agrave; del cilindro, sol lasciandovi intorno quant'&egrave; grosso un capello, <lb/>per la penetrazione del sottilissimo liquido, e per la libert&agrave; del suo passarvi <lb/>attraverso. </s>

<s>Estratte le due moli, mi si venivano a trasformare in due cilin&shy;<lb/>dri vacui, i quali, potendosi comodamente da me misurare, mi fecero cu&shy;<lb/>rioso di veder come si corrispondessero questi modi meccanici con i teoremi <lb/>dimostrati dalla Geometria. </s>

<s>Sapete bene da Euclide che il cono uguaglia un <lb/>cilindro di pari base, ma con la sola terza parte dell'altezza. </s>

<s>Quanto alla <lb/>sfera poi, si ricava per corollario dalla XXXI proposizione del libro, in cui <lb/>Archimede tratt&ograve; di queste cose, essere ella uguale a un cilindro, che avesse <lb/>per base un circolo grande, e per altezza quattro terzi del semidiametro di <lb/>esso circolo grande, ossia due terzi del diametro intero. </s>

<s>Ora, venuto al mi&shy;<lb/>surare, con quella maggiore diligenza che mi fu possibile, i vacui cilindrici <lb/>lasciati, per avere estratte dall'acqua le due dette moli; trovai tale corrispon&shy;<lb/>denza con le conclusioni dei Matematici, da superare ogni mia aspettazione, <lb/>ripensando a quante fallacie potevano essere andate soggette le mie proprie <lb/>esperienze. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Son senza dubbio cos&igrave; fatti esercizi manuali soggetti a <lb/>fallacie, ma chi sa che non potessero tornare di qualche utilit&agrave; ai Geome&shy;<lb/>tri, bench&egrave; pur troppo sia vero che le imperfezioni della materia son po&shy;<lb/>tenti a contaminare le purissime dimostrazioni della Matematica? </s>

<s>Ripensando <lb/>come tante invenzioni di Archimede son cos&igrave; pellegrine da ci&ograve;, che l'inge&shy;<lb/>gno di un uomo avrebbe senza altri indizi potuto per s&egrave; solo prevedere, du&shy;<lb/>bitai che, siccome giova allo statuario, per rifinire l'opera nel marmo, l'es&shy;<lb/>sersene messo innanzi nella rozza creta l'esempio:.... &rdquo; </s></p><p type="main">

<s>Qui termina lo scritto a tergo nel foglio, a cui manca il seguente, e <lb/>perci&ograve; rimane interrotto il costrutto, non per&ograve; cos&igrave;, che non si possa facil&shy;<lb/>mente supplire, intendendo che Archimede, per l'investigazione di cos&igrave; astruse <lb/>verit&agrave; geometriche, si potesse essere in parte aiutato con l'esperienze. </s>

<s>Tale si <lb/>fu pure l'opinione del Nardi, n&egrave; &egrave; necessario ripetere le ragioni, per cui si <lb/>giudic&ograve; da noi poco probabile: ma l'invenzione di trasformare i solidi, e di <lb/>quadrarne i volumi e le superficie per via dell'acqua, &egrave; notabile, e vedremo <lb/>qual partito per s&egrave; ne sapesse trarre il Viviani. </s></p><p type="main">

<s>Altre cose, di non minore curiosit&agrave; e importanza, ricorrono in questo <lb/>Dialogo, che non si vuol lasciare senza pure notarle, e sia prima fra tutte <lb/>la negazione espressa di un supposto, che alcuni dissero implicito ne'discorsi <lb/>di Archimede e di Galileo. </s>

<s>Il Nardi, troppo inconsideratamente fuor del suo <pb xlink:href="020/01/3160.jpg" pagenum="121"/>solito, scriveva anche questa fra le altre libere censure al grande Siracu&shy;<lb/>sano: &ldquo; Anco Archimede, nell'investigare il furto della corona, non consi&shy;<lb/>der&ograve;, per quanto sappiamo, che due insieme fusi metalli occupino minor mole <lb/>che separati, poich&egrave; dal pi&ugrave; rado di essi imbevesi il pi&ugrave; denso, come l'espe&shy;<lb/>rienza insegna. </s>

<s>E veramente non devesi dal natural Filosofo trascurare tal <lb/>punto, e non dovevasi da Archimede &rdquo; (MSS. Gal., T. XX, pag. </s>

<s>879, 80). <lb/>Ma ben assai pi&ugrave; inconsiderato ne par quel Domenico Mantovani, il quale, <lb/>in alcune sue annotazioni sopra la scrittura autografa di Galileo, descrittiva <lb/>della Bilancetta, diceva supporsi ivi dall'Autore, nel risolvere il problema, <lb/>&ldquo; che il composto di due metalli conservi l'istessa proporzione in grandezza <lb/>nel composto, che prima avevano li due metalli semplici che lo compon&shy;<lb/>gono &rdquo; (Alb. </s>

<s>XIV, 206). </s></p><p type="main">

<s>La storia, che da Lucio Pollione raccolse il Fazello, basta a confermare <lb/>l'inconsideratezza del Nardi. </s>

<s>Quanto poi al Mantovani si pu&ograve; dire essere stato <lb/>egli il primo, e non Galileo, a supporre che i due metalli nella loro fusione <lb/>mantengono la medesima mole che separati; giacch&egrave; esso Galileo chiama <lb/><emph type="italics"/>misto<emph.end type="italics"/> la composizione dell'oro e dell'argento nella corona del re Gerone, e <lb/>come si debba per questo misto intendere la semplice soprapposizion delle <lb/>parti dal trascritto Dialogo &egrave; manifesto. </s>

<s>Giova anzi avvertire in tal proposito <lb/>che il Viviani, a quelle parole inserite nelle sue <emph type="italics"/>Osservazioni<emph.end type="italics"/> dall'editore <lb/>Alb&egrave;ri, e che dicono: &ldquo; tanto si &egrave; che il peso sia composto dell'oro e del&shy;<lb/>l'argento separatamente, quanto che sia l'oro mescolato per infusione, poich&egrave; <lb/>non si altera n&egrave; il peso assoluto n&egrave; la mole, e per conseguenza nemmen <lb/>la gravit&agrave; in specie &rdquo; (ivi, pag. </s>

<s>214), scrisse in margine <emph type="italics"/>fanne esperienza<emph.end type="italics"/><lb/>(MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>65). Era poi in grado di apprezzar l'impor&shy;<lb/>tanza di questa postilla quel Viviani, che aveva trascritto il Dialogo di Ga&shy;<lb/>lileo, e che, pur essendo persuaso non andar nemmeno i metalli esenti dai <lb/>pori, poteva dubitare se questi si riempissero sempre nella fusione, cosicch&egrave; <lb/>talvolta la lega serbasse inalterato il volume dei metalli componenti. </s></p><p type="main">

<s>In ogni modo, fra le cose notabili in questo Dialogo, sembra a noi prin&shy;<lb/>cipalissima la dimostrazione sperimentale dei cos&igrave; detti <emph type="italics"/>pori fisici<emph.end type="italics"/> dei corpi, <lb/>alla quale dette forse occasione una lettera, che il 14 Maggio 1611 scriveva <lb/>in questa sentenza allo stesso Galileo, da Bruxelles, Daniele Antonini: &ldquo; Sono <lb/>stato questi giorni in Anversa, dove ho veduto una cosa degna di scrivere <lb/>a V. S. </s>

<s>Un certo, il quale &egrave; sopra la zecca di questo serenissimo Signore, <lb/>fa a chi vuol vederla questa prova. </s>

<s>Lui piglia una pallina di oro, e la fa <lb/>pesare a chi vuole sopra una bilancia giustissima ed esatta. </s>

<s>Poi batte detta <lb/>pallina, e ne fa una focaccetta. </s>

<s>Si ritorna a pesare, e pesa sempre tre, e <lb/>anche quattro grani pi&ugrave; che prima. </s>

<s>La comune opinione di costoro &egrave; che la <lb/>forma pesi. </s>

<s>Non mancano di quelli, che dicono che vi resta del ferro del <lb/>martello nell'oro, ma sono opinioni ridicolose, pare a me. </s>

<s>Questa cosa mi <lb/>conferma l'opinione di V. S. che ci siano de'vacuetti ne'corpi, li quali, per <lb/>il battere del martello, si riempino, onde il corpo non occupi poi tanto loco <lb/>nell'aria, e per conseguenza non sia tanto sostenuto dal medio e pesi pi&ugrave;. <pb xlink:href="020/01/3161.jpg" pagenum="122"/>Non so quello che circa questo giudicaria V. S., n&egrave; ho altro di nuovo &rdquo; <lb/>(MSS. Gal., P. VI, T. VIII, fol. </s>

<s>14). </s></p><p type="main">

<s>Alcuni, tra le prime prove sperimentali dell'esistenza de'pori fisici nei <lb/>corpi, citano il terzo degli sperimenti descritti nel libro de'<emph type="italics"/>Saggi di natu&shy;<lb/>rali esperienze<emph.end type="italics"/> intorno alla compressione dell'acqua. </s>

<s>E veramente non &egrave; que&shy;<lb/>sto altro che un saggio, sopra il solo argento, di parecchie esperienze fatte <lb/>sopra varie specie di metalli, le quali, essendo attribuite al granduca Ferdi&shy;<lb/>nando, si pu&ograve; credere che appartenessero a quel primo periodo dell'Acca&shy;<lb/>demia medicea, che pigliava essere e forma dal Torricelli. </s>

<s>&ldquo; Che l'acqua, <lb/>come acqua, scriveva il Viviani, non si possa, nemmeno con qualsivoglia <lb/>violenza, condensare per minima parte; l'ha sperimentato il Serenissimo <lb/>Granduca. </s>

<s>Ha fatto gettare d'ogni metallo, come argento, rame, ottone ecc. </s>

<s><lb/>pi&ugrave; palle vote per di dentro, e di grossezza di orbe intorno a quella di una <lb/>piastra d'argento, quali poi, per un foro fattovi a vite, ha fatte empir d'acqua, <lb/>e, serrato con vite di simili metalli strettissimamente il foro di dette palle, <lb/>le ha poi fatte posare sopra un'incudine, e fattogli dare colpi gagliardi con <lb/>un martello di acciaio, e ha osservato S. A. che l'acqua inclusa, per non <lb/>poter patire condensazione alla violenza de'colpi, trasudava fuori delle palle <lb/>per i pori del metallo &rdquo; (MSS. Gal. </s>

<s>Disc., T. 134, fol. </s>

<s>5 a t.). Il Borelli, par&shy;<lb/>lando con pi&ugrave; propriet&agrave;, non disse che il Granduca fece l'esperienza, ma <lb/><emph type="italics"/>iussit<emph.end type="italics"/> che fosse fatta (<emph type="italics"/>De motion, natur.,<emph.end type="italics"/> Regio Julio 1670, pag. </s>

<s>333) e il <lb/>comandamento non poteva averlo ricevuto che il Torricelli. </s></p><p type="main">

<s>In ogni modo per&ograve;, non essendo queste che dimostrazioni indirette, la <lb/>esperienza direttamente dimostrativa dell'esistenza dei pori fisici si pu&ograve; dire <lb/>che fosse primo a farla Galileo, come s'argomenta dalla lettera a lui dell'An&shy;<lb/>tonini, e con certezza si conferma dal Dialogo trascritto, sopra cui riman&shy;<lb/>gono solamente a fare alcune osservazioni circa alla disposizione microme&shy;<lb/>trica dei fili spirali. </s>

<s>Il Mantovani, dietro alcuni trascorsi, ch'egli attribuisce <lb/>ai copiatori dell'originale galileiano; immagin&ograve; un sistema di comporre, e <lb/>di numerare essi fili arbitrario, e tutt'affatto fuor del proposito. </s>

<s>Ma nemmeno <lb/>dalla lezione emendata, come ce la dette l'Alb&egrave;ri, si vengono a togliere i <lb/>dubbi, perch'essendo parata la Bilancia per determinati pesi di oro e di ar&shy;<lb/>gento, i punti D e G, nella figura 61, sono prestabiliti, e non occorrendo, <lb/>per aver la proporzione del misto, che di misurare il loro intervallo, basta <lb/>che questo solo sia ricoperto dal filo, e perci&ograve; tanto fa ch'egli sia o di ot&shy;<lb/>tone o di acciaio. </s>

<s>Che se si volesse parar la Bilancia, per pesi differenti da <lb/>A, i punti D e G torneranno sull'ago di lei o pi&ugrave; innanzi o pi&ugrave; indietro, <lb/>cosicch&egrave; si dovrebbe riempir del filo uno spazio diverso da DG. Onde, a evi&shy;<lb/>tar l'incomodo, tornava meglio avvolgere un filo solo andante sopra tutta la <lb/>lunghezza della libbra, ci&ograve; che si suppone esser fatto nello strumento pro&shy;<lb/>posto dal Salviati, il dialogo del quale soccorre dunque opportuno a illustrare <lb/>e a correggere la stessa frettolosa scrittura autografa di Galileo, tutto allora <lb/>in distenderla studioso, come udimmo, di produrre dimostrazioni de'teoremi <lb/>idrostatici, pi&ugrave; fisiche e meno matematiche di quelle di Archimede. </s></p><pb xlink:href="020/01/3162.jpg" pagenum="123"/><p type="main">

<s>&ldquo; Dico primum solidas magnitudines, aeque graves ac aqua, in aquam <lb/>demissas, totas demergi, non autem adhuc deorsum ferri magis quam sur&shy;<lb/>sum &rdquo; (Alb. </s>

<s>XI, 22). Il ragionamento di Galileo per la dimostrazione si ri&shy;<lb/>duce al seguente: Sia il primo stato dell'acqua CD (figura 62), e infusa nel <lb/>vaso la mole B non si sommerga, se &egrave; possibile, tutta, <lb/><figure id="id.020.01.3162.1.jpg" xlink:href="020/01/3162/1.jpg"/></s></p><p type="caption">

<s>Figura 62.<lb/>ma ne resti la parte A sollevata, ascendendo per l'im&shy;<lb/>mersione la superficie del liquido da CD in FG. </s>

<s>Allora <lb/>avremo che il peso di FD fa nella bilancia equilibrio al <lb/>peso AB, ma quello &egrave; minore di questo, perch&egrave; ugua&shy;<lb/>glia una sola parte di lui qual'&egrave; B; dunque ecc. </s></p><p type="main">

<s>&ldquo; Hoc itaque demonstrato, sequitur ut ostendamus <lb/>solidas magnitudines aqua leviores, in aquam demissas, <lb/>non demergi totas, sed earum aliquam partem extare ex aqua &rdquo; (ibid., pag. </s>

<s>23). <lb/>Perch&egrave;, se si demergesse tutta, avremmo, dice Galileo, nella bilancia, equili&shy;<lb/>brio fra un peso pi&ugrave; grave, qual'&egrave; l'acqua, e un pi&ugrave; leggero, qual'&egrave; la gran&shy;<lb/>dezza demersa. </s></p><p type="main">

<s>&ldquo; Demonstrato igitur solidas magnitudines aqua leviores non demergi <lb/>totas, expedit nunc ostendere quaenam illarum partes demergantur. </s>

<s>Dico igi&shy;<lb/>tur quod solidae magnitudines, aqua leviores, in aquam demissae, usque eo <lb/>demerguntur, ut tanta moles aquae, quanta est moles partis demersae ma&shy;<lb/>gnitudinis, eamdem quam tota magnitudo habeat gravitatem &rdquo; (ibid., pag. </s>

<s>24). <lb/>Sia il primo stato della superficie CD, come nella passata figura, e della <lb/>grandeza s'immerga la sola parte B, restandone l'altra A fuori, cosicch&egrave; il <lb/>livello salga da CD in FG, e ivi giunto si faccia l'equilibrio. </s>

<s>Dunque i pesi <lb/>di FD e di AB sono uguali, ma anche i volumi FD e di B sono uguali, <lb/>dunque ecc. </s></p><p type="main">

<s>&ldquo; Nunc autem, prosegue Galileo, antequam ad demonstrationem solido&shy;<lb/>rum aqua graviorum accedamus, demonstrandum est quanta vi solida ma&shy;<lb/>gnitudo aqua levior sursum feratur, si tota vi sub aquam demergatur. </s>

<s>Dico <lb/>igitur solidas magnitudines aqua leviores, in aquam impulsas, ferri sursum <lb/>tanta vi, quanto aqua, cuius moles aequetur moli demersae magnitudinis, <lb/>ipsa magnitudine gravior erit &rdquo; (ibid., pag. </s>

<s>25). Se il solido, nella medesima <lb/>figura 62, faccia la prima superficie del liquido risalire per l'immersione da <lb/>CD in FG, il qual livello egli affiori con la parte sua superiore GA, abbiamo <lb/>da una parte, nella bilancia, FD uguale in mole a B, ma, essendo maggiore <lb/>di peso per supposizione, far&agrave; perci&ograve; traboccare dalla sua parte essa bilan&shy;<lb/>cia, con la forza della sua propria prevalenza, <emph type="italics"/>quod,<emph.end type="italics"/> dice Galileo, <emph type="italics"/>fuit de&shy;<lb/>monstrandum.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Ex his autem quae demonstrata sunt, poi soggiunge, satis perspicuum <lb/>est solidas magnitudines aqua graviores deorsum ferri, si in aqua demittan&shy;<lb/>tur. </s>

<s>Nisi enim ferantur deorsum, aut earum aliqua pars extabit, aut sub <lb/>aqua manebunt, nec sursum aut deorsum ferentur. </s>

<s>At earum nulla pars <lb/>extabit, essent enim, ut demonstratum est, aqua leviores, nec in aqua ma&shy;<lb/>nebunt, quia essent aeque graves ac aqua. </s>

<s>Restat ergo quod deorsum feran-<pb xlink:href="020/01/3163.jpg" pagenum="124"/>tur. </s>

<s>Nunc autem quanta vi deorsum ferantur ostendamus: dico igitur soli&shy;<lb/>das magnitudines aqua graviores, in aquam demissas, ferri deorsum tanta <lb/>vi, quanto aqua, molem habens moli ipsius magnitudinis aequalem, levior <lb/>est ipsa magnitudine &rdquo; (ibid., pag. </s>

<s>26). Sia AE (fig. </s>

<s>63) uguale in mole alla <lb/>grendezza solida BL: e perch&egrave; il peso di quella si &egrave; supposto minore del <lb/><figure id="id.020.01.3163.1.jpg" xlink:href="020/01/3163/1.jpg"/></s></p><p type="caption">

<s>Figura 63.<lb/>peso di questa, sia AO la quantit&agrave; del liquido, che ci bi&shy;<lb/>sogna per l'equilibrio. </s>

<s>Alla BL poi s'immagini essere con&shy;<lb/>giunta una grandezza LM, pi&ugrave; leggera dell'acqua, e la mole <lb/>della quale, uguagliandosi alla mole AO, pesi quanto la <lb/>parte AE. </s>

<s>Dunque AE con AO, e BL con LM, si faranno <lb/>sulla bilancia equilibrio, ci&ograve; che non potrebbe essere, se la <lb/>forza, con cui BL tende a scendere, non fosse pari a quella, <lb/>con cui LM tende a salire. </s>

<s>Ma, per la precedente, questa <lb/>forza &egrave; uguale all'eccesso del peso dell'acqua AO sopra il peso dell'acqua DO, <lb/>ossia al peso dell'acqua AE; dunque ecc. </s></p><p type="main">

<s>Tali sono quelle dimostrazioni fisiche, che Galileo si studiava di sosti&shy;<lb/>tuire alle altre di Archimede, stimate da lui pi&ugrave; matematiche, bench&egrave; pro&shy;<lb/>priamente non sian tali che in apparenza, o nella forma, facilmeute riducibile <lb/>a quella data a loro dallo stesso Galileo, come si riferi da noi sui principii <lb/>del precedente capitolo. </s>

<s>Cos&igrave; fatte dimostrazioni nuove furon poi il frutto <lb/>degli studii giovanili, quando il novello professore di Pisa attendeva al a fab&shy;<lb/>brica e all'uso della sua Bilancetta. </s></p><p type="main">

<s>Ma in ogni modo l'Idrostatica, con queste invenzioni, non veniva so&shy;<lb/>stanzialmente promossa. </s>

<s>Dai teoremi idrostatici, bench&egrave; riformati, non si ve&shy;<lb/>deva direttamente conseguir la ragione di quel paradosso, che il Benedetti, <lb/>piuttosto che spiegare, pareva voler proporre alla spiegazione de'suoi succes&shy;<lb/>sori. </s>

<s>Questa riforma infatti si riduceva a considerare il peso delle grandezze <lb/>da una parte, e il peso dell'acqua da un'altra, come posati sui bacini di <lb/>una bilancia di braccia uguali, ci&ograve; che, se poteva bastare a spiegar l'equili&shy;<lb/>brio ne'due rami del sifone d'ugual calibrio, faceva arretrar la ragione in&shy;<lb/>nanzi al fatto della poca acqua nella gracile <expan abbr="c&atilde;nna">cannna</expan>, che pur vale a sostener <lb/>la grandissima nel mortaio. </s>

<s>Allora Galileo pens&ograve; a quel che similmente ac&shy;<lb/>cade nella bilancia di braccia disuguali, ossia nel vette, in virt&ugrave; di cui qua&shy;<lb/>lunque piccolissimo peso pu&ograve; fare equilibrio a un grandissimo, purch&egrave; i loro <lb/>momenti siano uguali: ond'ei non &egrave; maraviglia, disse fra s&egrave;, che la velo&shy;<lb/>cissima salita della poca acqua resista alla tardissima scesa della molta. </s>

<s>&ldquo; Ac&shy;<lb/>cade dunque in questa operazione, poi soggiungeva esplicandosi nella mente <lb/>quel primo concetto, lo stesso a capello che nella stadera, nella quale un peso <lb/>di due libbre ne contrappeser&agrave; un altro di 200, tuttavolta che, nel tempo <lb/>medesimo, quello si dovesse movere per ispazio cento volte maggiore che <lb/>questo, il che accade, quando l'un braccio della libbra sia cento volte pi&ugrave; <lb/>lungo dell'altro &rdquo; (Alb. </s>

<s>XII, 26). </s></p><p type="main">

<s>Esultando Galileo d'aver conclusa cos&igrave; la ragione del paradosso famoso, <lb/>dalla generalit&agrave; dei principii meccanici da s&egrave; professati, pens&ograve; che, potendosi <pb xlink:href="020/01/3164.jpg" pagenum="125"/>questi anche applicare alla bilancia di braccia uguali; de'comuni teoremi ar&shy;<lb/>chimedei si potevano dare altresi nuove dimostrazioni. </s>

<s>Perch&egrave; infatti, immer&shy;<lb/>gendosi pi&ugrave; e pi&ugrave; il solido, via via gli si solleva maggiore quantit&agrave; d'acqua <lb/>all'intorno, basta conferire i momenti della resistenza del liquido all'essere <lb/>alzato, co'momenti della grandezza che lo preme, &ldquo; e se i momenti della <lb/>resistenza dell'acqua, soggiunge Galileo stesso, pareggiano i momenti del <lb/>solido, avanti la sua totale immersione; allora senza dubbio si far&agrave; l'equi&shy;<lb/>librio, n&egrave; pi&ugrave; oltre si tuffer&agrave; il solido. </s>

<s>Ma se il momento del solido supe&shy;<lb/>rer&agrave; sempre i momenti, co'quali l'acqua scacciata va successivamente fa&shy;<lb/>cendo resistenza; quello, non solamente si sommerger&agrave; tutto sott'acqua, ma <lb/>discender&agrave; sino al fondo. </s>

<s>Ma se finalmente, nel punto della total sommer&shy;<lb/>sione, si far&agrave; l'aggiustamento tra i momenti del solido premente e dell'acqua <lb/>resistente, allora si far&agrave; la quiete, e esso solido, in qualunque luogo del&shy;<lb/>l'acqua, potr&agrave; indifferentemente fermarsi &rdquo; (ivi, pag. </s>

<s>17). </s></p><p type="main">

<s>Per conferire i detti momenti invoca Galileo dalla Statica due principii, <lb/>i quali per&ograve; dipendono da uno solo pi&ugrave; universale, conosciuto e praticato <lb/>dai precedenti Autori, ma che esso Galileo non seppe ridurre alla sua pro&shy;<lb/>pria forma, n&egrave; perci&ograve; valersi di lui a dare quella efficace brevit&agrave;, che manca <lb/>a tante sue conclusioni. </s>

<s>Agli esempi, che ricorrono di ci&ograve; nelle Storie pas&shy;<lb/>sate, s'aggiunge ora questo de'principii fondamentali, posti dall'Autore al <lb/>suo trattato Delle galleggianti, i quali principii, bench&egrave; si distinguano in due, <lb/>sono inclusi nulladimeno, come si diceva, in un altro pi&ugrave; generale, e secondo <lb/>cui i momenti, o quelle che poi si chiameranno forze morte, si misurano dal <lb/>prodotto delle velocit&agrave; e de'pesi assoluti. </s>

<s>&Egrave; facile infatti veder che di qui si <lb/>ha, per conclusione immediata, come, essendo i pesi e le velocit&agrave; uguali, <lb/>anche i momenti sono uguali; e dall'altra parte, essendo i momenti uguali, <lb/>le velocit&agrave; rispondono contrariamente ai pesi, che sono i due principii, di&shy;<lb/>stintamente assunti da Galileo per fondamento alle sue idrostatiche dimo&shy;<lb/>strazioni, in servigio delle quali si premette pure il seguente lemma: &ldquo; I pesi <lb/>assoluti de'solidi hanno la proporzione composta delle proporzioni delle lor <lb/>gravit&agrave; in specie, e delle lor moli &rdquo; (ivi, pag. </s>

<s>21). </s></p><p type="main">

<s>La verit&agrave; della proposta, pi&ugrave; brevemente che nel discorso di Galileo, si <lb/>conclude dalla definizione stessa delle gravit&agrave; specifiche, le quali si dicono <lb/>tanto essere maggiori le une delle altre, quanto pi&ugrave; gran peso &egrave; raccolto <lb/>sotto minor volume, cosicch&egrave;, intendendosi per G, P, M, e per G&prime;, P&prime;, M&prime;, le <lb/>dette gravit&agrave;, i pesi e le moli, o i volumi di due corpi diversi; dalle equa&shy;<lb/>zioni G=P:M, G&prime;=P&prime;:M&prime;, ossia, dalle altre P=M.G, P&prime;=M&prime;.G&prime;, <lb/>se ne conclude il proposito immediatamente. </s>

<s>Che se G>G&prime;, e allora sar&agrave; <lb/>P:M>P&prime;:M&prime;, ossia P:P&prime;>M:M&prime;, ci&ograve; che vuol dire aver maggiore pro&shy;<lb/>porzione il peso assoluto al peso assoluto, che no il volume al volume: co&shy;<lb/>rollario pure invocato a varie occasioni da Galileo, come vedremo. </s></p><p type="main">

<s>Ci&ograve; premesso, s'immagini di avere un vaso prismatico, dentro l'acqua <lb/>del quale sia immerso un solido, pure prismatico: nella disposizione, che ha <lb/>quello di scendere, e questo di salire, riconosce Galileo una specie di libra-<pb xlink:href="020/01/3165.jpg" pagenum="126"/>mento, soggetto alle medesime leggi statiche de'libramenti ordinari, e come <lb/>questi perci&ograve; dimostrabile col principio delle velocit&agrave; virtuali. </s>

<s>Da un tal princi&shy;<lb/>pio infatti &egrave; informato il <emph type="italics"/>Discorso intorno alle cose che stanno in sull'acqua, <lb/>o che in quella si muovono,<emph.end type="italics"/> di cui tale &egrave; l'ordine delle proposizioni: </s></p><p type="main">

<s>PROPOSIZIONE I. &mdash; <emph type="italics"/>&ldquo; La mole dell'acqua, che si alza nell'immergere <lb/>un prisma o cilindro solido, o che s'abbassa nell'estrarlo; &egrave; minore della <lb/>mole di esso solido demersa o estratta, e ad essa ha la medesima pro&shy;<lb/>porzione, che la superficie dell'acqua circonfusa al solido, alla medesima <lb/>superficie circonfusa, insieme con la base del solido &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>18). </s></p><p type="main">

<s>Sia EH (fig. </s>

<s>64) il primitivo naturale livello dell'acqua, la quale siasi <lb/>sollevata in NM, mentre che il solido si &egrave; abbassato in IK. </s>

<s>Essendo LG, NG <lb/><figure id="id.020.01.3165.1.jpg" xlink:href="020/01/3165/1.jpg"/></s></p><p type="caption">

<s>Figura 64.<lb/>due parallelepipedi, con altezze uguali, sta&shy;<lb/>ranno dunque come LM, NM, loro respettive <lb/>basi. </s>

<s>Considerando poi che NG, mole del&shy;<lb/>l'acqua sollevata, &egrave; uguale ad EK, parte del <lb/>solido sotto il primo livello sommersa, per <lb/>cui LG, LK tornano uguali; s'avr&agrave; senz'altro <lb/>concluso essere la mole LK del solido som&shy;<lb/>mersa, alla mole NG dell'acqua, come la su&shy;<lb/>perficie LM, alla superficie NM. </s></p><p type="main">

<s>Si dimostrerebbe, con simile compendioso <lb/>discorso, esser medesima la proporzione tra le <lb/>moli e le superficie, quando il solido, diversamente da quel che si &egrave; fin qui <lb/>supposto, sale, e il liquido scende: ci&ograve; che dall'altra parte si sarebbe potuto <lb/>facilmente prevedere da solo ripensar che il solido riman sommerso, per ca&shy;<lb/>lare egli stesso, e tutt'insieme per sollevarglisi l'acqua all'intorno, d'onde <lb/>viene a rendersi altres&igrave; la ragione della prima parte della proposta. </s></p><p type="main">

<s>PROPOSIZIONE II. &mdash; <emph type="italics"/>&ldquo; Quando in uno dei vasi sopraddetti, di qua&shy;<lb/>lunque larghezza, bench&egrave; immensa o angusta, sia collocato un tal prisma <lb/>o cilindro circondato da acqua, se alzeremo tal solido a perpendicolo, <lb/>l'acqua circumfusa s'abbasser&agrave;, e l'abbassamento dell'acqua, all'alza&shy;<lb/>mento del prisma, avr&agrave; la medesima proporzione, che l'una delle basi <lb/>del prisma, alla superficie dell'acqua circumfusa &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>19). </s></p><p type="main">

<s>Sia la base superiore del prisma, prima a <lb/>un medesimo livello AE (fig. </s>

<s>65) con l'acqua <lb/><figure id="id.020.01.3165.2.jpg" xlink:href="020/01/3165/2.jpg"/></s></p><p type="caption">

<s>Figura 65.<lb/>infusa nel vaso, e poi il detto prisma si sollevi <lb/>per l'altezza GA, abbassandosegli l'acqua infino <lb/>ad AO. </s>

<s>Essendo le moli HA, AN uguali, ossia <lb/>HG.AG=AE.AO, &egrave; manifesto che HG:AE= <lb/>AO:AG, com'era proposto di dimostrare. </s>

<s>E per&shy;<lb/>ch&egrave; gli AO, AG, passati nel medesimo tempo, <lb/>son la misura delle velocit&agrave;, scende altres&igrave; dalle <lb/>cose dimostrate per corollario che le velocit&agrave; <lb/>hanno reciproca ragion delle moli. </s></p><pb xlink:href="020/01/3166.jpg" pagenum="127"/><p type="main">

<s>PROPOSIZIONE III. &mdash; <emph type="italics"/>&ldquo; Un prisma o cilindro retto, di materia in spe&shy;<lb/>cie men grave dell'acqua, se sar&agrave; circondato dall'acqua secondo tutta la <lb/>sua altezza, non rester&agrave; sotto, ma si sollever&agrave;, bench&egrave; l'acqua circonfusa <lb/>fosse pochissima, e di gravit&agrave; assoluta quanto si voglia inferiore alla gra&shy;<lb/>vit&agrave; di esso prisma &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>20). </s></p><p type="main">

<s>Sia il prisma AF (fig. </s>

<s>66) tutto immerso nell'acqua CE del vaso prisma&shy;<lb/>tico BD. </s>

<s>Chiamate G, G&prime; le gravit&agrave; in specie di esso <lb/><figure id="id.020.01.3166.1.jpg" xlink:href="020/01/3166/1.jpg"/></s></p><p type="caption">

<s>Figura 66.<lb/>prisma e dell'acqua, e ritenute le medesime deno&shy;<lb/>minazioni, usate in precedenza, abbiamo per sup&shy;<lb/>posizione G&prime;>G, e per&ograve;, per il corollario del pre&shy;<lb/>messo lemma, P&prime;:P>M&prime;:M. Ma, per il corol&shy;<lb/>lario della precedente, chiamate V&prime;, V le volocit&agrave;; <lb/>&egrave; M&prime;:M=V:V&prime;, dunque P&prime;:P>V:V&prime;, ossia <lb/>P&prime;.V&prime;>P.V, che significa prevalere il momento <lb/>dell'acqua a quello del prisma, il quale perci&ograve; non <lb/>star&agrave; sotto, ma si sollever&agrave;. </s>

<s>Ond'essendo mede&shy;<lb/>sime le conclusioni, qnalunque siasi la maggioranza della gravit&agrave; specifica <lb/>sopra la gravit&agrave; specifica, e qualunque sia pure la grandezza della mole del&shy;<lb/>l'acqua; riman cos&igrave; la proposizione dimostrata per ogni sua parte. </s></p><p type="main">

<s>PROPOSIZIONE IV. &mdash; <emph type="italics"/>&ldquo; Se un cilindro o prisma solido sar&agrave; men grave <lb/>in specie dell'acqua, posto in un vaso come di sopra, di qualsivoglia gran&shy;<lb/>dezza, e infusa poi l'acqua, rester&agrave; il solido senz'esser sollevato, sin che <lb/>l'acqua arrivi a tal parte dell'altezza di quella, alla quale tutta l'al&shy;<lb/>tezza del prisma abbia la medesima proporzione, che la gravit&agrave; in specie <lb/>dell'acqua, alla gravit&agrave; in specie di esso solido. </s>

<s>Ma infondendo pi&ugrave; acqua, <lb/>il solido si sollever&agrave; &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>22). </s></p><p type="main">

<s>Sia il vaso NL (fig. </s>

<s>67), e in esso sia collocato il prisma MD, e qual <lb/>proporzione ha la gravit&agrave; in specie dell'acqua, a quella del prisma, tale <lb/><figure id="id.020.01.3166.2.jpg" xlink:href="020/01/3166/2.jpg"/></s></p><p type="caption">

<s>Figura 67.<lb/>abbia l'altezza DF all'altezza FB: dice Galileo <lb/>che, infondendosi liquido sino all'altezza FB, <lb/>il solido non si sollever&agrave;, ma ben sar&agrave; ridotto <lb/>all'equilibrio, cosicch&egrave; ogni poco pi&ugrave; d'acqua <lb/>che gli si aggiunga far&agrave; sollevarlo. </s>

<s>Abbiamo <lb/>infatti, per supposizione e per ragioni ste&shy;<lb/>reometriche, ritenute le solite denominazioni, <lb/>G:G&prime;=BF:FD=BG:DG. </s>

<s>Moltiplicate la <lb/>prima e l'ultima ragione di questa per l'identica <lb/>GD:AF=GD:AF, e fatte le riduzioni, avre&shy;<lb/>mo G.GD:G&prime;.AF=BG:AF. </s>

<s>Ma G.GD= <lb/>P, G&prime;.AF=P&prime;, per il premesso Lemma in <lb/>principio, e BG ad AF sta come la superficie EM alla superficie BA, le quali <lb/>stanno, per la seconda, come la scesa dell'acqua o la sua velocit&agrave; V&prime;, alla <lb/>salita del solido o alla sua velocit&agrave; V; dunque P:P&prime;=V&prime;:V. Ond'&egrave;, che <lb/>stando i pesi contrariamente alle velocit&agrave;, i momenti si fanno uguali, e perci&ograve; <pb xlink:href="020/01/3167.jpg" pagenum="128"/>il solido, com'era proposto, rimane in quiete, e solo allora si solleva, accre&shy;<lb/>sciuto che gli sia, con qualunque piccola mole di acqua, un tantino del suo <lb/>momento. </s></p><p type="main">

<s>Chiamato P&prime; il peso assoluto di una mole di acqua, uguale a BG, e P <lb/>il peso assoluto del prisma DG, abbiamo, per il premesso lemma, P&prime;:P= <lb/>BG.G&prime;:DG.G. Ma, per le cose ora dimostrate, G&prime;:G=DG:BG; dun&shy;<lb/>que P&prime;:P=BG.DG:DG.BG, e perci&ograve; P&prime;=P: vale a dire tant'acqua <lb/>in mole, quant'&egrave; il solido BG, pesa assolutamente quanto tutto il solido DG, <lb/>d'onde si fa manifesto &ldquo; come i solidi men gravi in specie dell'acqua si <lb/>sommergono solamente, sin tanto che tanta acqua in mole, quanta e la <lb/>parte del solido sommersa, pesi assolutamente quanto tutto il solido &rdquo; (ivi, <lb/>pag. </s>

<s>23). </s></p><p type="main">

<s>PROPOSIZIONE V. &mdash; <emph type="italics"/>&ldquo; Riguardando il solido M<emph.end type="italics"/> (fig. </s>

<s>68) <emph type="italics"/>ora immerso <lb/>nel piccolissimo vaso ES, ora nel grandissimo AC, dico che, nell'alzarsi <lb/><figure id="id.020.01.3167.1.jpg" xlink:href="020/01/3167/1.jpg"/></s></p><p type="caption">

<s>Figura 67.<lb/>esso solido, l'abbassamento della pochissima <lb/>acqua ES si muove tanto pi&ugrave; velocemente della <lb/>grandissima mole dell'acqua AC, quanto ap&shy;<lb/>punto questa &egrave; pi&ugrave; di quella &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>Si ehiami <emph type="italics"/>u<emph.end type="italics"/> la velocit&agrave; dell'abbassamento <lb/>della pochissima mole <emph type="italics"/>m<emph.end type="italics"/> dell'acqua, V&prime; la velo&shy;<lb/>cit&agrave; dell'abbassamento della grandissima mole d'acqua M&prime;, e V la velocit&agrave; <lb/>del sollevamento della mole M: abbiamo, per la seconda di questo, <emph type="italics"/>u<emph.end type="italics"/>:V= <lb/>M:<emph type="italics"/>m,<emph.end type="italics"/> V&prime;:V=M:M&prime;, d'onde <emph type="italics"/>mu<emph.end type="italics"/>=V&prime;.M&prime;, ossia <emph type="italics"/>u<emph.end type="italics"/>:V&prime;=M&prime;:<emph type="italics"/>m,<emph.end type="italics"/> come <lb/>voleva Galileo dimostrare, e come di fatti dimostr&ograve; col suo lungo discorso, <lb/>proponendo cos&igrave; di questa, come delle altre propriet&agrave; de'corpi galleggianti, <lb/>nuove ragioni. </s>

<s>Che se nella prima maniera non faceva altro che renderle, <lb/>come udimmo pi&ugrave; fisiche, in questa seconda diceva di <emph type="italics"/>averle ridotte a prin&shy;<lb/>cipii pi&ugrave; intrinseci e immediati<emph.end type="italics"/> (ivi, pag. </s>

<s>14), quali son quelli della Statica, <lb/>ch'egli si lusingava di veder corrispondere <emph type="italics"/>a capello<emph.end type="italics"/> con le leggi dell'Idro&shy;<lb/>statica. </s>

<s>Se avesse ripensato per&ograve; che i solidi e i liquidi, bench&egrave; convengano <lb/>nell'esser gravi, diversificano sostanzialmente nelle loro propriet&agrave; naturali; <lb/>avrebbe con facilit&agrave; riconosciuto che que'suoi professati principii, tutt'altro <lb/>che essere intrinseci e immediati, venivano, in certi casi specialmente, a in&shy;<lb/>vocarsi cos&igrave; fuor di proposito, da condurre a manifesti e dannosissimi errori, <lb/>di che basti a noi citare i due esempi seguenti. </s></p><p type="main">

<s>Se un solido pi&ugrave; grave dell'acqua dimori in quiete sopra il fondo di <lb/>un vaso, &ldquo; bench&egrave;, dice Galileo, si aggiungesse poi grandissima quantit&agrave; <lb/>d'acqua sopra il livello di quella, che pareggia l'altezza del solido, non per&ograve; <lb/>si accresce la pressione o aggravamento delle parti circonfuse al detto solido, <lb/>per la quale maggior pressione egli avesse ad esser cacciato &rdquo; (ivi, pag. </s>

<s>27). <lb/>E nel seguito del medesimo Discorso anche si legge quest'altra espression <lb/>sentenziosa: &ldquo; Il dir poi che l'acqua possa accrescer peso alle cose che in <lb/>essa sieno collocate &egrave; falsissimo, perch&egrave; l'acqua nell'acqua non ha gravit&agrave; <lb/>veruna, poich&egrave; ella non vi discende &rdquo; (ivi, pag. </s>

<s>50). </s></p><pb xlink:href="020/01/3168.jpg" pagenum="129"/><p type="main">

<s>A chiunque verrebbe voglia qui di rispondere che, se tutti i corpi, i <lb/>quali non scendono, non son gravi; dunque gli oggetti posati sopra una ta&shy;<lb/>vola non son gravi? </s>

<s>Dal veder che l'acqua nell'acqua non scende non pu&ograve; <lb/>perci&ograve; inferirsi che ella non &egrave; grave, ma si dir&agrave; piuttosto aver sotto chi la <lb/>sostiene, come dal veder che un corpo non scende, posato sul bacino di una <lb/>bilancia, nessuno crederebbe ch'egli non pesi, ma direbbe che del peso non <lb/>apparisce l'effetto, per essere dall'altra parte esattamente contrappesato. </s>

<s>Ci&ograve; <lb/>che vale altres&igrave; a scoprire la fallacia di Galileo nell'altro esempio: fallacia <lb/>simile a quella di colui, il quale, a una bilancia equilibrata con un'oncia di <lb/>qua e di l&agrave;, sopraggiungendo altr'once via via sempre uguali di numero da <lb/>una parte e dall'altra, e non vedendo allo strumento perci&ograve; fare alcun moto; <lb/>dicesse che da quell'aggiunta di peso non si cresce la pressione e l'aggra&shy;<lb/>vamento del giogo. </s>

<s>Ritorniamo indietro sopra la figura 42, ch'essendo ser&shy;<lb/>vita per lo Stevino citiamo apposta, perch&egrave; si faccia il confronto delle verit&agrave; <lb/>di lui con le fallacie nel Nostro, e supponendo che GI sia il solido, posato <lb/>in fondo al vaso, non per&ograve; cos&igrave; che alquanto di acqua non gli penetri sotto, <lb/>s'aggiunga sopra il livello EG, che pareggia l'altezza del detto solido, nuova <lb/>acqua via via, n&egrave; importa pure che sia grandissima, per veder se &egrave; vero <lb/><emph type="italics"/>che non si accresce la pressione o l'aggravamento delle parti circonfuse <lb/>al solido,<emph.end type="italics"/> come diceva Galileo. </s></p><p type="main">

<s>Delle dannose conseguenze, che venivano dal professar principii estrin&shy;<lb/>seci e insufficienti, ebbe Galileo stesso a fare esperienza nel risolvere un pro&shy;<lb/>blema, che insomma &egrave; l'argomento principale del suo Discorso. </s>

<s>Perch&egrave; una <lb/>pentola di rame o di terra, ma vuota, galleggia, ne concludevano alcuni Pe&shy;<lb/>ripatetici contro Archimede non esser vero che galleggino i soli corpi pi&ugrave; <lb/>gravi in specie dell'acqua: e dal veder che una palla d'ebano s'affonda, ma <lb/>ridotta in una larga e sottil tavoletta galleggia, vollero dire esser causa del <lb/>galleggiamento di alcuni corpi la loro stessa figura. </s>

<s>A costoro Galileo con&shy;<lb/>trapponeva che l'aria contenuta nel vaso &egrave; quella, che lo sostiene a galla <lb/>&ldquo; avvegnach&egrave; di lei e del rame si faccia un composto men grave di altret&shy;<lb/>tanta acqua, e il luogo che occupa il vaso sott'acqua, mentre galleggia, non <lb/>&egrave; uguale al rame solo, ma al rame e all'aria insieme, che riempie quella <lb/>parte del vaso, che sta sotto il livello dell'acqua &rdquo; (ivi, pag. </s>

<s>51). Quanto <lb/>poi alle tavolette di ebano, che messe sotto l'acqua seguitano a scendere fino <lb/>in fondo, e posatevi su leggermente rimangono a galla; soggiungeva non <lb/>avvenir ci&ograve;, per ragione della loro figura, ma &ldquo; perch&egrave; quello che si mette <lb/>nell'acqua &egrave; la pura falda d'ebano, che, per esser pi&ugrave; grave dell'acqua va <lb/>al fondo, e quello, che si posa sull'acqua, &egrave; un composto d'ebano e di tanta <lb/>aria, che fra ambedue sono in specie men gravi dell'acqua, e per&ograve; non di&shy;<lb/>scendono &rdquo; (ivi, pag. </s>

<s>60). </s></p><p type="main">

<s>Chi, leggendo tali passi nel Discorso intorno alle galleggianti, non si <lb/>persuaderebbe essere per questi espressa la verit&agrave;, secondo la quale il peso <lb/>dell'aria, aggiungendosi al peso della materia del vaso o dell'assicella, sono <lb/>ambedue insieme equilibrati dal contra stante peso dell'acqua? </s>

<s>Eppure, se-<pb xlink:href="020/01/3169.jpg" pagenum="130"/>guitando una sola pagina dopo, sorprende il lettore a trovarci scritto che <lb/>l'aria, nella cavit&agrave; del vaso, o nella fossetta scavatasi dentro l'acqua dal&shy;<lb/>l'assicella, n&egrave; alleggerisce il solido n&egrave; l'aggrava, cosicch&egrave; par che per <emph type="italics"/>aria<emph.end type="italics"/><lb/>non si debba intendere il noto elemento, ma riceversi la parola nel signi&shy;<lb/>ficato di <emph type="italics"/>area<emph.end type="italics"/> o di spazio non occupato da nessun corpo. </s>

<s>Che anzi l'Autore <lb/>la intenda propriamente cos&igrave; ne possiamo esser certi dal proporsi ch'egli fa <lb/>l'assicella IS (fig. </s>

<s>69), la quale, se sia il doppio pi&ugrave; <lb/>grave dell'acqua, e di tal grossezza IO, da uguagliarsi <lb/>alla massima altezza degli arginetti, che le fanno <lb/>sponda all'intorno; dimostra come, posta che sia nel&shy;<lb/>l'acqua, non si sommerger&agrave; per queste ragioni: &ldquo; Im&shy;<lb/>perocch&egrave;, essendo l'altezza AI eguale all'altezza IO, <lb/>sar&agrave; la mole dell'aria ABCI eguale alla mole del so&shy;<lb/>lido CIOS, e tutta la mole AOSB doppia della mole IS. <lb/><figure id="id.020.01.3169.1.jpg" xlink:href="020/01/3169/1.jpg"/></s></p><p type="caption">

<s>Figura 69.<lb/>E avvegnach&egrave; la mole dell'aria AC <emph type="italics"/>non cresca o diminuisca la gravit&agrave; <lb/>della mote IS,<emph.end type="italics"/> e il solido IS si pone doppio in gravit&agrave; all'acqua: adunque <lb/>tant'acqua, quanta &egrave; la mole sommersa AOSB, composta dell'aria AICB e <lb/>del solido IOSC, pesa appunto quanto essa mole sommersa AOSB &rdquo; (ivi, <lb/>pag. </s>

<s>61, 62). E nella seguente proposizione, affermandosi che la gravit&agrave; del <lb/>solido IS &egrave; la medesima che la gravit&agrave; del solido AS, ne fa manifestamente <lb/>intendere Galileo che la gravit&agrave; dell'aria, compresa dentro lo spazio AC, si <lb/>debba ritenere, non gi&agrave; come insensibile, ma come nulla affatto. </s></p><p type="main">

<s>La maraviglia cresce poi anche di pi&ugrave;, leggendosi in questo stesso Di&shy;<lb/>scorso che, non solamente l'aria non aggrava col suo proprio peso l'assi&shy;<lb/>cella sottoposta, ma che anzi, aderendo al solido, ella &egrave; che lo tiene a galla. </s>

<s><lb/>Cosicch&egrave; quest'aderenza dell'aria farebbe l'ufficio della leggerezza positiva <lb/>attribuitale da Leonardo da Vinci, e sostituita alle pressioni idrostatiche, non <lb/>avvertite n&egrave; dall'uno n&egrave; dall'altro Autore. </s>

<s>A chi avesse domandato perch&egrave;, <lb/>penetrata l'acqua, l'assicella non seguita a profondarsi, Galileo rispondeva: <lb/>&ldquo; Perch&egrave; nel sommergersi, finch&egrave; la sua superficie arriva al livello di quella <lb/>dell'acqua, ella perde una parte della sua gravit&agrave;, e il resto poi lo va per&shy;<lb/>dendo nel profondarsi e abbassarsi oltre alla superficie dell'acqua, la quale <lb/>intorno intorno li fa argine e sponda, e tale perdita fa ella mediante il ti&shy;<lb/>rarsi dietro, e far seco discendere l'aria superiore, e a s&egrave; stessa per lo con&shy;<lb/>tatto aderente &rdquo; (ivi, pag. </s>

<s>49). </s></p><p type="main">

<s>La nuova causa assegnata al galleggiamento de'corpi &egrave; tanto strana, <lb/>che potrebbero i gelosi della fama dell'Autore ricorrere a qualche pi&ugrave; be&shy;<lb/>nigna interpetrazione. </s>

<s>Ma, per togliere ad essi ogni refugio, Galileo stesso <lb/>esplica il suo proprio senso e lo conferma col suggello di tali parole, che <lb/>giova a noi trascrivere nella loro integrit&agrave;, bench&egrave; non brevi: &ldquo; Forse, egli <lb/>dice, alcuno di quei signori, che dissentono da me, si maraviglier&agrave; che io <lb/>affermi che l'aria contigua superiore sia potente a sostener quella laminetta <lb/>di rame o d'argento, che su l'acqua si trattiene, come che io voglia in un <lb/>certo modo dare una quasi virt&ugrave; di calamita all'aria di sostenere i corpi <pb xlink:href="020/01/3170.jpg" pagenum="131"/>gravi, co'quali ella &egrave; contigua. </s>

<s>Io per sodisfare, per quanto m'&egrave; permesso, <lb/>a tutte le difficolt&agrave;, sono andato pensando di dimostrare, con qualche altra <lb/>sensata esperienza, come veramente quella poca d'aria contigua e superiore <lb/>sostien que'solidi, che, essendo per natura atti a discendere al fondo, posti <lb/>leggermente su l'acqua non si sommergono, se prima non si bagnano in&shy;<lb/>teramente, e ho trovato che, sceso che sia uno di tali corpi al fondo, col <lb/>mandargli senza altrimenti toccarlo un poco d'aria, la quale colla sommit&agrave; <lb/>di quello si congiunga, ella &egrave; bastante non solo, come prima si faceva, a <lb/>sostenerlo, ma a sollevarlo e ricondurlo ad alto, dove nella stessa maniera <lb/>si ferma e resta, sin che l'aiuto dell'aria congiuntagli non gli vien manco. </s>

<s><lb/>E a questo effetto ho fatta una palla di cera, e fattala con un poco di piombo <lb/>tanto grave, che lentamente discende al fondo, facendo di pi&ugrave; la sua super&shy;<lb/>ficie ben tersa e pulita, e questa posata pian piano sull'acqua si sommerge <lb/>quasi tutta, restando solamente un poco di sommit&agrave; scoperta, la quale, sin <lb/>che star&agrave; congiunta con l'aria, tratterr&agrave; la palla in alto, ma tolta la con&shy;<lb/>tiguit&agrave; dell'aria col bagnarla discender&agrave; al fondo, e quivi rester&agrave;. </s>

<s>Ora, per <lb/>farla, in virt&ugrave; dell'aria medesima, che dianzi la sosteneva, ritornare ad alto, <lb/>e fermarvisi appresso; spingasi nell'acqua un bicchiere rivolto, cio&egrave; colla <lb/>bocca in gi&ugrave;, il quale porter&agrave; seco l'aria da lui contenuta, e questo si muova <lb/>verso la palla, abbassandolo tanto che si vegga, per la trasparenza del vetro, <lb/>che l'aria contenuta dentro arrivi alla sommit&agrave; della palla. </s>

<s>Dipoi ritirisi in <lb/>su lentamente il bicchiere, e vedrassi la palla risorgere e restare anche di <lb/>poi ad alto, se con diligenza si separer&agrave; il bicchiere dall'acqua, sicch&egrave; ella <lb/>non si commova e agiti di soverchio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; &Egrave; dunque tra l'aria e gli altri corpi una certa affinit&agrave;, la quale gli <lb/>tiene uniti, sicch&egrave;, non senza qualche poco di violenza, si separano. </s>

<s>Lo stesso <lb/>parimente si vede nell'acqua, perch&egrave;, se tufferemo in essa qualche corpo, s&igrave; <lb/>che si bagni interamente; nel tirarlo poi fuor piano piano vedremo l'acqua <lb/>seguitarlo, e sollevarsi notabilmente sopra la sua superficie, avanti che da <lb/>quello si separi. </s>

<s>I corpi solidi ancora, se saranno di superficie in tutto si&shy;<lb/>mili, sicch&egrave; esquisitamente si combagino insieme, n&egrave; tra di loro resti aria, <lb/>che si distragga nella separazione, e ceda sin che l'ambiente succeda a riem&shy;<lb/>pier lo spazio; saldissimamente stanno congiunti, n&egrave; senza gran forza si se&shy;<lb/>parano. </s>

<s>Ma perch&egrave; l'aria, l'acqua e gli altri liquidi molto speditamente si <lb/>figurano al contatto de'corpi solidi, si che la superficie loro esquisitamente <lb/>s'adatta a quella de'solidi, senza che altro resti tra loro; per&ograve; pi&ugrave; manife&shy;<lb/>stamente e frequentemente si riconosce in loro l'effetto di questa copula e ade&shy;<lb/>renza, che ne'corpi duri, le cui superficie di rado congruentemente si con&shy;<lb/>giungono. </s>

<s>Questa &egrave; dunque quella virt&ugrave; calamitica, la quale con salda copula <lb/>congiunge tutti i corpi, che senza interposizione di fluidi cedenti si toccano. </s>

<s>E <lb/>chi sa che un tal contatto, quando sia esquisitissimo, non sia bastante cagione <lb/>dell'unione e continuit&agrave; delle parti del corpo naturale? </s>

<s>&rdquo; (ivi, pag. </s>

<s>42-54). </s></p><p type="main">

<s>Qualche anno dopo, l'assegnare, per causa del galleggiare le tavolette <lb/>di ebano o di metallo sull'acqua, le virt&ugrave; calamitiche dell'aria, parve anche <pb xlink:href="020/01/3171.jpg" pagenum="132"/>a Galileo ipotesi tanto strana, che avrebbe voluto ritirarla. </s>

<s>Ma perch&egrave; era <lb/>messa oramai fuori, e non volendo dall'altra parte, non solamente confes&shy;<lb/>sare, ma nemmeno parere di avere sbagliato; bisognava ricorrere a qual&shy;<lb/>cuna di quelle arti, che da'pi&ugrave; destri si sogliono usare in simili casi. </s>

<s>Non <lb/>dir&agrave; come poi, per salvarsi dall'accusa di avere errato intorno alla linea dei <lb/>proietti, che ne'dialoghi dei due Massimi Sistemi se n'era scritto per celia, <lb/>ma, riducendo le cose alle parole, afferma che il termine di <emph type="italics"/>virt&ugrave; calamitica<emph.end type="italics"/><lb/>attribuita all'aria in sostener le assicelle galleggianti, non era suo, ma di un <lb/>cavalier principale discorde dalla sua opinione (Alb. </s>

<s>XII, 104). E nell'armeg&shy;<lb/>g&igrave;o di questa ritirata si perd&egrave; il bel pensiero dell'attrazione molecolare, da <lb/>cui dipende la coesione dei corpi, e che sarebbe nel primo dialogo delle due <lb/>Nuove scienze per cedere il luogo alle chimere della repugnanza del vacuo. </s></p><p type="main">

<s>La ritirata, che si diceva, fu fatta qualche anno dopo nella lettera a <lb/>Tolomeo Nozzolini, dove s'incomincia da Galileo a riconoscere il peso del&shy;<lb/>l'aria, e gli effetti di lei nel galleggiamanto delle assicelle e de'vasi vuoti <lb/>specificamente pi&ugrave; gravi dell'acqua. </s>

<s>&Egrave; dunque in sostanza la detta Lettera <lb/>una corr&egrave;zione fatta al Discorso intorno alle galleggianti, bench&egrave; si voglia <lb/>studiosamente non farla apparir tale nella forma. </s>

<s>Ma perch&egrave; cos&igrave; fatte cor&shy;<lb/>rezioni non riguardano altro che dottrine secondarie, e la scrittura dove si <lb/>fecero non venne alla luce che in sui primi anni del secolo XVIII; i nuovi <lb/>insegnamenti idrostatici di Galileo si tramandarono ai discepoli tali, quali si <lb/>hanno ancora nel citato Discorso al granduca Cosimo secondo, e furono le <lb/>seconde instituzioni, che si videro a que'tempi, dopo quelle dello Stevino. </s>

<s><lb/>Galileo dunque e lo Stevino sono i principali promotori di Archimede, ben&shy;<lb/>ch&egrave; altri precedessero, altri succedessero a loro nell'ufficio, i quali tutti, <lb/>avendo pure e non lievemente concorso a far progredire la Scienza, non vo&shy;<lb/>gliono essere perci&ograve; dimenticati in questa Storia. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Nel 1603 vedeva in Roma la luce un libretto, col titolo di <emph type="italics"/>Promotus <lb/>Archimedes.<emph.end type="italics"/> Marino Ghetaldo, che n'era l'Autore, diceva, in una delle prime <lb/>pagine, a'suoi lettori che il comparare il peso assoluto de'corpi co'loro vo&shy;<lb/>lumi gli era sembrato argomento cos&igrave; giocondo, e cos&igrave; utile notizia, da in&shy;<lb/>vogliarlo a scriverne un trattato, tanto pi&ugrave; che da nessun, diceva, prima di <lb/>lui, almeno diffusamente, ancora non s'era fatto. </s>

<s>Quel dir per&ograve; la proposta <lb/>scienza <emph type="italics"/>nec fuse a quopiam explicata,<emph.end type="italics"/> forse era vero, perch&egrave; il Tartaglia <lb/>s'intrattiene piuttosto in dar fondamento alle dottrine, che in applicarle ai <lb/>fatti particolari, intorno a che si diffonde il Ghetaldo. </s>

<s>Ma perch&egrave; la Scienza <lb/>non consiste propriamente nel descrivere cotali particolari esperienze, o in <lb/>ordinar le numerose Tavole delle varie gravit&agrave; specifiche; non doveva il <lb/>novello Promotor di Archimede dimenticare chi l'aveva preceduto di ben <pb xlink:href="020/01/3172.jpg" pagenum="133"/>52 anni, n&egrave; tacere che la <emph type="italics"/>Bilancetta idrostatica,<emph.end type="italics"/> ch'ei diceva essere <emph type="italics"/>operae <lb/>praetium,<emph.end type="italics"/> e quale si descrive da lui nell'esempio dopo l'ottava proposizione; <lb/>non era cosa punto nuova, se forse la novit&agrave; non si fosse fatta consistere <lb/>nell'aver sostituito allo <emph type="italics"/>spaghetto lunghetto<emph.end type="italics"/> del primo inventore un crino di <lb/>cavallo, per essere in specie quasi ugualmente grave all'acqua. </s>

<s>&ldquo; Corpus, <lb/>quod ponderandum proponitur, seta equina ex altera librae lance appenda&shy;<lb/>tur. </s>

<s>In altera lance ponantur pondera, et corpus appensum demittatur in <lb/>aqua, et ita ponderetur, ac si in aere penderet &rdquo; (<emph type="italics"/>Promotus Archim.,<emph.end type="italics"/> pag. </s>

<s>10). </s></p><p type="main">

<s>A imitazion del Tartaglia anche il Ghetaldo si serve dello strumento, <lb/>per risolvere il problema della corona di Gerone, dop'avere anch'egli notato <lb/>le inesattezze, a cui inevitabilmente conducevano i modi, che Vitruvio rife&shy;<lb/>risce aver tenuti Archimede. </s>

<s>Quanto al calcolo poi, da instituirsi sopra le <lb/>fatte operazioni, molti, dice il Ghetaldo, ne hanno scritto, &ldquo; longa tamen <lb/>methodo atque difficili usi sunt, et quod maximam confusionem et obscuri&shy;<lb/>tatem parit, nullum operationis tradunt praeceptum firmum ac stabile &rdquo; (ivi, <lb/>pag. </s>

<s>54). Ci&ograve; che forse non avrebbe potuto dire in coscienza, se si fosse ri&shy;<lb/>cordato della quarta proposizione dimostrata dal Tartaglia nel suo secondo <lb/>Ragionamento, bench&egrave; forse con la regola del tre, che il Ghetaldo stesso <lb/>passa a proporre, si vada per via pi&ugrave; semplice e piana. </s>

<s>&ldquo; Ego autem unica <lb/>tantum proportionis ratiocinatione, seu regula trium, ut vulgo dicitur, bre&shy;<lb/>viter et expedite idem consequor, eamque geometrica ratione demonstro &rdquo; <lb/>(ibid.). La qual geometrica dimostrazione si d&agrave; infatti nel X teorema cos&igrave; <lb/>proposto: </s></p><p type="main">

<s>&ldquo; Si trium corporum, aeque gravium, primum et tertium fuerint gene&shy;<lb/>ris diversi, secundi autem portio fuerit eiusdem generis cum corpore primo, <lb/>reliqua vero eiusdem generis cum corpore tertio: fuerint etiam tres quan&shy;<lb/>titates aquae praedictis corporibus aequales, prima videlicet corpori primo, <lb/>secunda secundo, et tertia tertio; erit ut differentia gravitatum primae et <lb/>tertiae quantitatis aquae, ad gravitatem corporis secundi, ita differentia gra&shy;<lb/>vitatum primae et secundae quantitatis aquae, ad gravitatem portionis cor&shy;<lb/>poris secundi, quae est eiusdem generis cum corpore tertio. </s>

<s>Et ita differen&shy;<lb/>tia gravitatum secundae et tertiae quantitatis aquae, ad gravitatem portionis <lb/>eiusdem generis cum corpore primo &rdquo; (ibid., pag. </s>

<s>56). </s></p><p type="main">

<s>Abbiansi tre corpi A, B+C, D, di peso assoluto tutti uguali a P, e <lb/>il primo e il terzo di questi corpi siano di natura diversa, ma le parte B <lb/>(la gravit&agrave; assoluta della quale chiameremo <emph type="italics"/>p<emph.end type="italics"/>) sia del genere di A, e l'altra <lb/>parte C, la gravit&agrave; della quale chiameremo <emph type="italics"/>p&prime;,<emph.end type="italics"/> sia del genere di D. </s>

<s>Si pren&shy;<lb/>dano, uguali alle tre dette moli, altre tre moli di acqua, la prima delle quali <lb/>R pesi come G, la terza Q pesi come H, e le parti Q+L corrispondenti <lb/>alle parti B+C abbiano un peso respettivamente rappresentato da F, V. </s>

<s>Si <lb/>propone il Ghetaldo di dimostrare che si verificano le due seguenti equa&shy;<lb/>zioni: H&mdash;G:P=(V+F)&mdash;G:<emph type="italics"/>p&prime;,<emph.end type="italics"/> e H&mdash;G:P=H&mdash;(V+F):<emph type="italics"/>p.<emph.end type="italics"/></s></p><p type="main">

<s>La seconda dimostrazion dell'Autore, assai pi&ugrave; breve e pi&ugrave; matematica <lb/>della prima, procede in questa maniera: Osservando che due equazioni danno <pb xlink:href="020/01/3173.jpg" pagenum="134"/>sempre una proporzione, e che, trattandosi di corpi omogenei, i volumi ri&shy;<lb/>spondono proporzionalmente ai pesi assoluti; sar&agrave; D:C=Q:L, e P:<emph type="italics"/>p&prime;<emph.end type="italics"/>= <lb/>H:V. </s>

<s>Similmente A:B=R:O, e P:<emph type="italics"/>p<emph.end type="italics"/>=G:F. </s>

<s>Dividendo quest'ultima, <lb/>e osservando che P&mdash;<emph type="italics"/>p<emph.end type="italics"/>=<emph type="italics"/>p&prime;,<emph.end type="italics"/> verr&agrave; P:<emph type="italics"/>p&prime;<emph.end type="italics"/>=G:C&mdash;F, e perci&ograve; H:V= <lb/>G:G&mdash;F, ossia H:G=V:G&mdash;F, la quale per divisione dar&agrave; la (*) <lb/>H&mdash;G:G=V+F&mdash;G:G&mdash;F, d'onde si riesce, per composizione <lb/>e per riduzione, alla H:G=V:G&mdash;F. </s>

<s>Questa pure, divisa e permutata, <lb/>si riduce alla H&mdash;G:V+F&mdash;G=G:G&mdash;F, e, per la segnata con <lb/>asterisco, all'altra H&mdash;G:V+F&mdash;G=P:P&mdash;<emph type="italics"/>p,<emph.end type="italics"/> che, per nuova per&shy;<lb/>mutazione e sostituzione di <emph type="italics"/>p&prime;<emph.end type="italics"/> a P&mdash;<emph type="italics"/>p,<emph.end type="italics"/> rende finalmente H&mdash;G:P= <lb/>(V+F)&mdash;G:<emph type="italics"/>p&prime;,<emph.end type="italics"/> che &egrave; la prima equazione promessa. </s></p><p type="main">

<s>Quanto alla seconda, essendo P:<emph type="italics"/>p&prime;<emph.end type="italics"/>=H:V, s'ha da questa per divi&shy;<lb/>sione P:P&mdash;<emph type="italics"/>p&prime;<emph.end type="italics"/>=H:H&mdash;V, ossia P:<emph type="italics"/>p<emph.end type="italics"/>=H:H&mdash;V=G:F (per una <lb/>delle prime equazioni prestabilite al calcolo precedente) e anche insieme <lb/>H:G=H&mdash;V:F, la quale vien, dividendo, H&mdash;G:G=H&mdash;V&mdash;F:F, <lb/>e permutando, H&mdash;G:H&mdash;V&mdash;F=G:F. </s>

<s>In ultimo, perciocch&egrave; G:F= <lb/>P:<emph type="italics"/>p,<emph.end type="italics"/> ancora permutando, ne resulter&agrave; H&mdash;G:P=H&mdash;(V+F):<emph type="italics"/>p,<emph.end type="italics"/> con&shy;<lb/>forme a ci&ograve; che il Ghetaldo erasi proposto di dimostrare in secondo luogo, <lb/>bench&egrave; la prima equazione, anche sola, bastasse a sciogliere il problema. </s>

<s><lb/>Essendo infatti noti, con l'uso della Stadera e della Bilancetta idrostatica, i <lb/>valori di H, di G, di P, e di V+F; s'ha, per essa equazione, il valore di <lb/><emph type="italics"/>p&prime;,<emph.end type="italics"/> ossia del peso dell'argento, e il valore di <emph type="italics"/>p,<emph.end type="italics"/> peso dell'oro, si deduce im&shy;<lb/>mediatamente dall'equazione <emph type="italics"/>p<emph.end type="italics"/>=P&mdash;<emph type="italics"/>p&prime;.<emph.end type="italics"/> Supposto essere P=95, e la <lb/>Bilancetta dare G=5, V+F=6, H=9+6/31, come, nel primo esem&shy;<lb/>pio dopo la proposizione XVIII, ponesi dal Ghetaldo (ivi, pag. </s>

<s>56), si tro&shy;<lb/>ver&agrave; <emph type="italics"/>p&prime;<emph.end type="italics"/>=22+17/26, ond'&egrave; che, per sola differenza e senz'altro computo, <lb/>si conclude <emph type="italics"/>p<emph.end type="italics"/>=72+9/26. </s></p><p type="main">

<s>Nonostante, dalle due equazioni insieme, scende per corollario </s></p><p type="main">

<s><emph type="center"/>H&mdash;(V+F):(V+F)&mdash;G=<emph type="italics"/>p:p&prime;,<emph.end type="italics"/><emph.end type="center"/><lb/>nuova formula, che tir&ograve; a s&egrave; l'attenzione di Galileo, e che gli suggeri il modo <lb/>di risolvere meccanicamente il problema della corona. </s>

<s>Ritornando sopra la <lb/>figura 61, qui addietro, &egrave; facile vedere che il valore di H, nella formula del <lb/>Ghetaldo, &egrave; rappresentato dalla lunghezza della linea CG, sull'ago della Bi&shy;<lb/>lancetta di Galileo; il valore di V+F, dalla lunghezza di CH, e quello di <lb/>GD, dalla linea CD. </s>

<s>Sar&agrave; dunque, scambiando i simboli di <emph type="italics"/>p, p&prime;,<emph.end type="italics"/> in quelli <lb/>di M, N; CG&mdash;CH:CH&mdash;CD=M:N, ossia HG:DH=M:N, che &egrave; <lb/>la regola di ritrovare le proporzioni del peso de'metalli nel misto, secondo <lb/>l'invenzione dello stesso Galileo. </s></p><p type="main">

<s>Vien di qui dunque un nuovo documento a illustrare la storia di que&shy;<lb/>sta invenzione. </s>

<s>Il Viviani poneva di sua propria mano, in fronte alla nota <lb/>scrittura galileiana, il titolo seguente: <emph type="italics"/>Fabbrica ed uso di una esatta Bi&shy;<lb/>lancia da saggiatore, per ritrovare la proporzione di due metalli, con altre <lb/>curiosit&agrave;, inventata nel 1586 dal signor Galileo Galilei, ne'suoi primi<emph.end type="italics"/><pb xlink:href="020/01/3174.jpg" pagenum="135"/><emph type="italics"/>studi intorno alle opere di Archimede<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>60), <lb/>e tutti sono andati e vanno tuttavia, senza discrizione, ripetendo in tal modo. </s>

<s><lb/>Ma le cose fin qui narrate ne fanno accorti essere da distinguer nell'inven&shy;<lb/>zione due progressi: uno, che riguarda lo Strumento come semplicemente <lb/>parato alla ricerca delle gravit&agrave; specifiche de'vari corpi, ci&ograve; che pot&egrave; esser be&shy;<lb/>nissimo occorso a Galileo nel 1586, in assai facile modo, non trattandosi d'al&shy;<lb/>tro, che di perfezionare, con l'aggiunta di organi noti, quali eran le spire dei <lb/>sottilissimi fili micrometrici, la Bilancetta descritta e usata gi&agrave; dal Tartaglia. </s></p><p type="main">

<s>Il secondo progresso riguarda lo Strumento come parato a ritrovare le <lb/>proporzioni di due metalli nel misto, al quale effetto si presupponeva di ne&shy;<lb/>cessit&agrave; il fondamento di quella scienza, che si veniva a rendere per dir cos&igrave; <lb/>manuale, come il Compasso di proporzione presupponeva la Geometria di <lb/>Euclide, e la Catenella per i bombardieri il quarto dialogo delle due nuove <lb/>Scienze. </s>

<s>Or perch&egrave; il fondamento all'arte di ritrovare i pesi nel misto si ve&shy;<lb/>niva a porre nel problema IX, e nella proposizione XIX del Ghetaldo, com&shy;<lb/>parse in pubblico nel 1603; sembra ragionevole concluder che, dopo quel&shy;<lb/>l'anno, venisse in pensiero a Galileo di applicare la Bilancetta stessa, ser&shy;<lb/>vita gi&agrave; per le semplici gravit&agrave; in specie, a risolvere anche il problema, pi&ugrave; <lb/>complicato, della Corona. </s></p><p type="main">

<s>Vorranno dire alcuni che Galileo sciolse geometricamente quello stesso <lb/>problema, o primo, o facendosi a s&egrave; stesso maestro, senza il Ghetaldo, alla <lb/>quale opinione consentiremmo anche noi volentieri, quando se ne producesse <lb/>qualche prova di fatto. </s>

<s>Dall'altra parte non s'ha questo esempio solo degli <lb/>studiosi commenti, che il giovane professore di Pisa e di Padova faceva sopra <lb/>le proposizioni del provetto Matematico di Ragusa: lo stesso Discorso intorno <lb/>alle galleggianti si pu&ograve; dire non essere altro che un commentario prolisso <lb/>di ci&ograve;, che si legge nell'<emph type="italics"/>Archimede promosso.<emph.end type="italics"/> Mentre questo opuscolo era <lb/>sotto i torchi (avverte quivi l'Autore, dopo l'esempio soggiunto alla propo&shy;<lb/>sizione XV) venne un dottissimo uomo a dirmi che, dall'immergere i corpi <lb/>nell'acqua, non si pu&ograve; desumere la ragion vera dei loro pesi, se non forse, <lb/>quando avessero i detti corpi uguale o simile figura, perch&egrave;, se uno sia per <lb/>esempio disteso in forma di tavoletta, e l'altro appuntato a guisa di cono, <lb/>bench&egrave; nell'aria pesassero il medesimo, posti nonostante in acqua si trove&shy;<lb/>rebbe questo, per la pi&ugrave; facile penetrazione, essere pi&ugrave; leggero di quella. <lb/></s>

<s>&ldquo; Hoc argumentum, licet primo aspectu probabile videatur, tamen falso con&shy;<lb/>cludit. </s>

<s>Verum est quod aqua sustentat magis corpns planum quam conum; <lb/>ipsum tamen sustentat ne tanta velocitate feratur deorsum, non ideo ipsius <lb/>gravitati aliquid detrahit. </s>

<s>Neque enim ex velociori motu simpliciter inferri <lb/>potest maior gravitas, illud enim valeret etiam in aere, quod est falsum. </s>

<s>Sed <lb/>ne huiusmodi dubitatio veritatis specie aliquem decipiat, sequenti theoremate <lb/>eam destruere aggrediar: <emph type="italics"/>Corpora eiusdem generis et gravitatis graviora <lb/>quam aqua, etsi dissimilia, uequalem in aqua gravitatem habent &rdquo;<emph.end type="italics"/> (ibid., <lb/>pag. </s>

<s>28). Ed &egrave; questo il teorema che in vario modo dimostra, e, secondo <lb/>altri pi&ugrave; minuti particolari, esplica Galileo nel suo celebre Discorso. </s></p><pb xlink:href="020/01/3175.jpg" pagenum="136"/><p type="main">

<s>Quarant'anni dopo, quasi fossero in questo tempo rimaste morte le pa&shy;<lb/>role di Marino Ghetaldo, e l'ufficio di mantenere in vita la Scienza fosse <lb/>passato nel solo Galileo, avvenne che Giovan Batista Hodierna, a cui, per <lb/>mezzo di Benedetto Castelli suo maestro, era pervenuta la scrittura, dove <lb/>suscitavasi <emph type="italics"/>l'inventione di quel famoso Siragosano in trovare il furto del&shy;<lb/>l'oro nella corona di Hierone;<emph.end type="italics"/> pensasse di pubblicarla co'commenti da s&egrave; <lb/>aggiuntivi, e cos&igrave; far rivivere l'Archimede antico, in quello, che s'andava <lb/>predicando da tutti <emph type="italics"/>Archimede nuovo di Fiorenza.<emph.end type="italics"/> Nel 1644 infatti si vide <lb/>uscire in Palermo alla luce un opuscolo, col titolo in fronte di <emph type="italics"/>Archimede <lb/>redivivo.<emph.end type="italics"/> Premesso per testo il discorso galileiano, soprascrittovi: <emph type="italics"/>Fabbrica <lb/>di un nuovo strumento detto dall'Autore Bilancetta;<emph.end type="italics"/> segue un <emph type="italics"/>Annota&shy;<lb/>mento di varie considerazioni intorno alla proposta dottrina del signor <lb/>Galileo:<emph.end type="italics"/> considerazioni per verit&agrave; di assai lieve momento, quali possono essere <lb/>quelle intorno al modo di contare il numero delle spire, nel sottilissimo filo <lb/>avvolto intorno all'ago della Stadera, preferendo all'uso dell'orecchio, in <lb/>ascoltare gli scatti strisciandovi sopra l'aguto, quello direttamente dell'occhio, <lb/>aiutato da uno squisitissimo microscopio. </s></p><p type="main">

<s>In altre considerazioni, piuttosto che rimettersene a quel che aveva detto <lb/>il Ghetaldo, per voler troppo sminuzzare le cose, e darle a intendere al volgo; <lb/>trascorre incredibilmente l'Hodierna in errori, da non si perdonare a uno <lb/>scolaretto, che avesse veduti appena gli Elementi di Euclide. </s>

<s>Vuol far notare <lb/>la fallacia dell'esperienze, attribuite ad Archimede, per via di quel colmo, <lb/>in che risorge l'acqua intorno intorno agli orli del vaso, prima di strapparsi <lb/>e di traboccare. </s></p><p type="main">

<s>&ldquo; Ma vedasi, egli dice, con un esempio quanto importi questa fallacia, <lb/>per non potersi mai determinare, per questa via incerta, quel che si va cer&shy;<lb/>cando. </s>

<s>Avendo io preso un vaso d'argento, il cui orificio circonferenziale si <lb/>stendeva per diametro precisamente un palmo, e accomodandolo al livello <lb/>dell'orizonte, dop'averlo gi&agrave; pieno d'acqua con esattezza fino all'orlo, se&shy;<lb/>guendo poi con una ampolla di vetro d'aggiungervi acqua, prima che l'ec&shy;<lb/>cesso aggiuntovi cominciasse a traboccare dall'orlo; si ritrov&ograve; quattr'once <lb/>d'acqua, che altrettanto di oro in mole peserebbe libbre sei e due terzi, che <lb/>sono once otto, come appresso anderemo dimostrando. </s>

<s>Ora, secondo questa <lb/>esperienza, quando si desse un vaso con l'orificio assai pi&ugrave; largo, come do&shy;<lb/>veva esser quello, nel quale Archimede doveva immergere la corona di Je&shy;<lb/>rone, che si crede essere stata assai grande; quant'acqua credete voi se le <lb/>possa aggiungere? </s>

<s>Suppongasi per&ograve; che l'orificio del vaso sia stato in diame&shy;<lb/>tro non pi&ugrave; largo di due palmi: allora, perch&egrave; l'area di quella ampiezza sa&shy;<lb/>rebbe stata quasi quadrupla a quella d'un palmo, conseguentemente avrebbe <lb/>potuto sostentare l'eccesso di <emph type="italics"/>sedici<emph.end type="italics"/> once d'acqua, montata sopra il livello <lb/>dell'orlo. </s>

<s>Ma altrettanta massa di oro importerebbe di peso libbre 26, e once <lb/>otto, avendo il peso dell'oro al peso dell'acqua la stessa proporzione di 20 a <lb/>uno, come appresso si far&agrave; manifesto &rdquo; (pag. </s>

<s>12, 13). </s></p><p type="main">

<s>La copia del libro, da cui s'&egrave; cos&igrave; trascritto, ha un pregio singolare, <pb xlink:href="020/01/3176.jpg" pagenum="137"/>per aver fatto parte della biblioteca di Vincenzio Viviani, il quale, avendo <lb/>contrassegnata la parola <emph type="italics"/>sedici,<emph.end type="italics"/> messa nel testo, per dire quanto sia in once <lb/>l'eccesso d'acqua sostentata; vi sottoscriveva di sua propria mano questa <lb/>nota: &ldquo; Anzi di 32 once, perch&egrave;, se tutti i massimi colmi dell'acqua sopra <lb/>vasi circolari di bocca, oppur di altre figure simili, pigliano figura di lenti, <lb/>o di altro corpo, simili fra di loro; essendo i solidi simili in tripla propor&shy;<lb/>zion de'lati omologhi, ed essendo posto il diametro del primo vaso un palmo, <lb/>e il diametro del secondo due palmi, la base dell'uno alla base dell'altro <lb/>sar&agrave; come il cubo di uno, al cubo di due: cio&egrave; come uno a otto. </s>

<s>Ma quello <lb/>di un palmo pesava 4 once, adunque quello di due palmi peser&agrave; once 32. &rdquo; </s></p><p type="main">

<s>Il malcontento del Viviani, per gli annotamenti che l'Hodierna s'era <lb/>messo a fare intorno alle dottrine del suo Maestro, si rivela da un'altra po&shy;<lb/>stilla, scritta in margine della pagina appresso. </s>

<s>Ivi dice cos&igrave; l'Autore del&shy;<lb/>l'Archimede redivivo: &ldquo; Chi volesse intendere qual sia veramente l'intrin&shy;<lb/>seca passione, che induce le materie pi&ugrave; gravi dell'acqua all'andare al fondo, <lb/>e le men gravi al galleggiar sopra l'acqua, siccome anco, d'onde sia che <lb/>l'acqua nell'acqua non &egrave; grave n&egrave; lieve; io li direi ci&ograve; avvenire dalla mag&shy;<lb/>giore o minore, ovvero eguale inclinazione ed appetito delle materie gravi <lb/>tra di loro al discendere &rdquo; (pag. </s>

<s>15). E il Viviani: &ldquo; Per me tanto me ne <lb/>intendo a chiamarla intrinseca passione, che appetito o inclinazione o appe&shy;<lb/>tenza: e credete pure, signor Hodierna, che cos&igrave; saremo sempre da capo. </s>

<s>&rdquo; </s></p><p type="main">

<s>Segue in questo opuscolo, ai detti annotamenti, con assai lungo ordine <lb/>di definizioni, di petizioni e di supposizioni, premesse per dimostrare sei pro&shy;<lb/>posizioncelle; un discorso intitolato: <emph type="italics"/>Archimede siracusano; delle cose che <lb/>pesano nell'acqua, interpetrato nella lingua italiana da Giovan Batista <lb/>Hodierna<emph.end type="italics"/> (pag. </s>

<s>32). &Egrave; una composizione indigesta, una confusion discordante <lb/>de'teoremi del Ghetaldo, e delle proposizioni del Tartaglia, alcune delle quali <lb/>son fedelmente ricopiate, riducendovisi qualche parola dal dialetto bresciano <lb/>al palermitano, senza farne un motto, quasi credesse che, de'Ragionamenti <lb/>intorno alla Travagliata invenzione, fosse spenta in ogni altro la memoria, <lb/>e non ne rimanesse al mondo altra copia da leggervi su, che la sua: tanto <lb/>l'aver Galileo reciso il filo delle tradizioni, con taglio cos&igrave; prepotente, aveva <lb/>infuso baldanza ne'suoi seguaci! </s></p><p type="main">

<s>La proposizione IV &egrave; annunziata come il problema IX del Ghetaldo, <lb/>tradotto dal latino, e si conclude cos&igrave; nella forma stessa del corollario, che <lb/>ne deriva, dal paragonare le due equazioni dimostrate nel X teorema da esso <lb/>Ghetaldo: &ldquo; Dico che la parte del misto, che in esso sar&agrave; del genere pi&ugrave; <lb/>grave, la proporzione all'altra sua parte, la quale &egrave; del genere pi&ugrave; lieve, <lb/>sar&agrave; come la proporzione della differenza del misto al peso del pi&ugrave; lieve, alla <lb/>differenza del peso dello stesso misto al peso del pi&ugrave; grave &rdquo; (ivi, pag. </s>

<s>41). <lb/>Notabile che, per dimostrar ci&ograve;, non segue i modi del Ghetaldo, ma del Tar&shy;<lb/>taglia, senz'avvedersi che la conclusione dell'uno era in forma diversa da <lb/>quella dell'altro, o curarsi di dimostrare che, essendo pure nella forma di&shy;<lb/>verse, concordavano le soluzioni de'due Autori nella sostanza. </s>

<s>Chi vuole, per <pb xlink:href="020/01/3177.jpg" pagenum="138"/>curiosit&agrave;, vedere il gioco, che del povero Tartaglia fece l'Hodierna, legga di <lb/>questo le proposizioni V e VI, dove &egrave; ricopiato non l'ordine solo, non le <lb/>sole parole, n&egrave; i corpi da pesarsi scelti ad esempio: ma perfino le stesse <lb/>lettere dell'alfabeto, da significarne i nomi e le propriet&agrave;. </s>

<s>Vorremmo anche <lb/>nello stesso tempo pregar que'curiosi di attendere a queste parole, che si <lb/>leggono nell'appendice alla proposizione IV: &ldquo; Da questa par che il signor <lb/>Galilei abbia cavato il modo, e trovato l'artificio, che tenne Archimede nello <lb/>scoprire il furto dell'orefice dell'oro della corona di Hierone, con avervi ag&shy;<lb/>giunto l'artificioso strumento, come insegna nel suo Discorso &rdquo; (pag. </s>

<s>41, 42): <lb/>vorremmo, dicevasi, pregare di ci&ograve; i curiosi, perch&egrave; quindi si conferma essere <lb/>l'uso della Bilancetta, per la ricerca delle porzioni di due metalli nel misto, <lb/>suggerita da'teoremi del Ghetaldo: documento di non poca importanza, per <lb/>chi specialmente ripensa che l'Hodierna eruttava, intorno a Galileo, le no&shy;<lb/>tizie imbevute da Benedetto Castelli. </s></p><p type="main">

<s>D'altri promotori di Archimede, fioriti prima che il secolo XVII giun&shy;<lb/>gesse al suo mezzo, non tratterremo pi&ugrave; in lungo il discorso, perch&egrave; le loro <lb/>promozioni non sono altro che intorno al primo libro <emph type="italics"/>De insidentibus in <lb/>aqua,<emph.end type="italics"/> e alle applicazioni de'teoremi di lui all'invenzione delle gravit&agrave; in <lb/>specie. </s>

<s>Il Ghetaldo e l'Hodierna, il Villanpando e il Ventimiglia s'affaccen&shy;<lb/>darono in costruirne Tavole, che ai metalli, ai liquidi, alle pietre preziose e <lb/>alle materie terree estendevano i pochi saggi datine dal Tartaglia, ma &egrave; inu&shy;<lb/>tile sperare di ritrovarvi quell'esattezza, che s'attendeva pure a conseguire <lb/>con tanto ostinata fatica, non sperimentandosi nel vuoto, n&egrave; con l'acqua <lb/>distillata. </s>

<s>Il Barometro, il Termometro e l'Areometro parlavano un linguag&shy;<lb/>gio allora non compreso, ma che in ogni modo annunziava l'impossibilit&agrave; del <lb/>concordare due esperienze, fatte in varie costituzioni di aria, di acqua e di <lb/>temperatura, indipendentemente dalla perizia o dalla diligenza degli speri&shy;<lb/>mentatori, e dalla perfezione dei loro strumenti. </s></p><p type="main">

<s>Nelle inchieste, delle quali &egrave; il presente discorso, gli strumenti, oltre alla <lb/>Bilancetta, sono quegli Idrostammi, de'quali, sulla fine del primo tomo, si <lb/>fece la descrizione storica. </s>

<s>Per quel che poi riguarda la loro teoria, ella fu <lb/>da'Matematici conclusa tutta nella proposizione cos&igrave; formulata dall'Herman: <lb/>&ldquo; Diversae partes unius eiusdemque corporis, diversis liquoribus homogeneis <lb/>immersae, in casu aequilibrii, sunt in reciproca ratione densitatum, seu gra&shy;<lb/>vitatum specificarum liquorum, quibus idem corpus successive immersum <lb/>esse ponitur &rdquo; (<emph type="italics"/>Foron. </s>

<s>Amstelod.,<emph.end type="italics"/> 1716, pag. </s>

<s>155). Chiamandosi infatti P il <lb/>peso assoluto del solido, e G, G&prime; le gravit&agrave; specifiche, ch'egli ha rispetto a <lb/>due liquidi, nell'un de'quali s'immerga per la parte V, e nell'altro per la <lb/>parte V&prime; del suo proprio volume; avremo G=P:V, G&prime;=P&prime;:V&prime;, d'onde <lb/>G.V=G&prime;.V&prime;, ossia V&prime;:V=G:G&prime;, secondo il proposito. </s></p><p type="main">

<s>I cenni storici, dati sin qui, possono bastare a farsi un'idea di cio, che <lb/>fu operato nei primi decenni del secolo XVII per promovere l'Idrostatica di <lb/>Archimede. </s>

<s>Quelle promozioni per&ograve; non riguardavano che la parte, per dir <lb/>cos&igrave;, fisica della scienza, trattata nel primo libro <emph type="italics"/>De insidentibus humido,<emph.end type="italics"/><pb xlink:href="020/01/3178.jpg" pagenum="139"/>come preparazione all'altra parte matematica, trattata nel secondo, e in cui <lb/>coronavasi l'opera dell'Autore. </s>

<s>Le applicazioni perci&ograve; de'teoremi, a trovar <lb/>le proporzioni fra i pesi e i volumi dei corpi, e a scoprire l'impurit&agrave; di al&shy;<lb/>cuni metalli, bench&egrave; gioconde, come parvero al Ghetaldo, e utili alla vita <lb/>c&igrave;vile, come le disse l'Hodierna; sembrano nulladimeno non avere che la <lb/>ragione di semplici corollarii, verso la proposizion principale, che attendeva <lb/>a dimostrare secondo qual legge galleggerebbero, o si salverebbero dal pe&shy;<lb/>ricolo di sommergersi le navi sugl'instabili flutti ondeggianti. </s></p><p type="main">

<s>Unico, fra i promotori, che avesse qualche sentore essere principalissima <lb/>intenzion di Archimede quella di volere applicati alla Nautica i suoi astratti <lb/>teoremi, fu lo Stevino, il quale perci&ograve; coron&ograve; i suoi Elementi idrostatici con <lb/>quella parte, ch'egli intitolava <emph type="italics"/>Des acrobatiques ou des pesanteurs au som&shy;<lb/>met du flottant,<emph.end type="italics"/> e che si conclude tutta in questo unico teorema: &ldquo; Un corps <lb/>flottant sur l'eau prend telle position, que son centre de gravit&egrave; est en la <lb/>perpendicle de gravit&eacute; du creux d'eau qu'il occupa &rdquo; (Oeuvres cit., pag. </s>

<s>512). </s></p><p type="main">

<s>Immagina che il corpo galleggiante sia una nave, rappresentata da BCD <lb/>(fig. </s>

<s>70) e il centro di gravit&agrave; della quale sia O, per il qual pnnto, fatta pas&shy;<lb/><figure id="id.020.01.3178.1.jpg" xlink:href="020/01/3178/1.jpg"/></s></p><p type="caption">

<s>Figura 70.<lb/>sare la perpendicolare MN, dice <lb/>che dentro questa linea si deve <lb/>trovare il punto L, centro di gra&shy;<lb/>vit&agrave; della fossa, che il solido na&shy;<lb/>viculare si scava nell'acqua: per&shy;<lb/>ch&egrave;, se si trovasse fuori, come <lb/>per esempio in P, non potrebbe <lb/>ci&ograve; avvenire, se non che trasfor&shy;<lb/>mandosi la detta fossa, e perci&ograve; <lb/>abbassandosi la sponda, e alzan&shy;<lb/>dosi l'opposta, contro la supposizione. </s></p><p type="main">

<s>Di qui fa derivar lo Stevino alcuni corollarii importanti: &ldquo; I. </s>

<s>Il appert <lb/>que; quand le centre de gravit&eacute; du corps est dessus celuy du creux de l'eau, <lb/>que le sommet flottant est charg&eacute;, et que tout renverse (c'est assavoir s'il <lb/>n'est soustenu) jusqu'&agrave; ce que son centre soit dans la perpendicle de gravit&eacute; <lb/>du creux de l'eau. </s>

<s>II. </s>

<s>Il est evident que, mettant quelque poids dans un bat&shy;<lb/>teau, ou quelque vaisseau, ayant chang&eacute; de place dans iceluy, que le creux <lb/>change aussi de figure, et le centre de gravit&eacute; d'iceluy creux change de lieu. </s>

<s><lb/>III. </s>

<s>Il est aussi manifeste que, mettant une pesanteur sous le plan de gra&shy;<lb/>vit&eacute; (parallele a l'horizon) du creux de l'eau, qu'icelle pesanteur cause plus <lb/>de fermet&eacute; au cours du navire, et au sommet d'iceluy; et au contraire, le <lb/>pesanteur estant mise au dessus du dit plan de gravit&eacute; (a niveau), telle pe&shy;<lb/>santeur surcharge le sommet du navire tellement, qu'il en est moins ferme &rdquo; <lb/>(ivi, pag. </s>

<s>513). </s></p><p type="main">

<s>Termina poi l'Autore il suo trattatello con questa osservazione: Se i <lb/>due centri di gravit&agrave;, egli dice, della nave e della fossa scavata nell'acqua, <lb/>fossero di facile invenzione, egli &egrave; certo che si potrebbe per teoria, prima <pb xlink:href="020/01/3179.jpg" pagenum="140"/>della pratica, sapere <emph type="italics"/>quelle disposition un batteau, navire, ou autre vais&shy;<lb/>seau, tiendroit sur l'eau, et s'il se tiendroit droit ou oblique, et si l'eau, <lb/>entreroit par les bords ou non<emph.end type="italics"/> (ivi). E perci&ograve; Archimede scelse i segmenti <lb/>sferici, e i conoidei parabolici, de'quali sapeva geometricamente indicare il <lb/>centro di gravit&agrave;. </s>

<s>Questa osservazione per&ograve; la lascia lo Stevino a'suoi let&shy;<lb/>tori, l'ingegno de'quali par che volesse mettere ad esercizio, col tenere, di&shy;<lb/>mostrando il suo teorema, le vie oblique all'assurdo, invece delle dirette, che <lb/>tutti avrebbero potuto ritrovar da lui stesso disegnate nel libro degli <emph type="italics"/>Ele&shy;<lb/>menti.<emph.end type="italics"/> Dal terzo corollario infatti della IX proposizione di questi resultava <lb/>&ldquo; que centre C (fondo della nave nell'ultima figura) y a un effort, qui le <lb/>pousse enhaut, de mesme que la colonne d'eau (o il solido BCD a lei equi&shy;<lb/>valente) pousse le mesme fonde C embas &rdquo; (ivi, pag. </s>

<s>488). E perch&egrave; que&shy;<lb/>sto secondo sforzo &egrave; concentrato in O, e l'altro in L, che &egrave; quel centro della <lb/>pressione, le ragioni di ritrovar geometricamente il quale son simili alle di&shy;<lb/>mostrate quivi nelle proposizioni XVIII e XIX; dunque, se ai punti O, L <lb/>s'immagini essere attaccati due pesi, o applicate due forze uguali e contra&shy;<lb/>rie, si ridurranno agli effetti di queste le ragioni dell'equilibrio della mole gal&shy;<lb/>leggiante. </s>

<s>Cos&igrave; ragionando, come tacitamente lo Stevino insinuava, venivasi <lb/>ad avere la dimostrazione diretta del teorema acrobatico, e de'suoi corollarii, <lb/>a solo considerare il gioco delle forze, le quali non si possono equilibrare, <lb/>se non che nella direzion connaturata a loro, ossia nella medesima verticale. </s>

<s><lb/>Cosicch&egrave;, inclinando violentemente la nave, secondo che si rappresenta a de&shy;<lb/>stra della figura; &egrave; manifesto come, lasciata in libert&agrave;, si debba necessaria&shy;<lb/>mente dirizzare, e restituirsi nella prima posizione, rappresentata nella figura <lb/>a sinistra, per effetto degli sforzi, che la sollecitano ugualmente nella natu&shy;<lb/>rale direzione a opposte parti. </s></p><p type="main">

<s>Che se, invece di considerar tutto il peso della nave concentrato in O, <lb/>si assegnassero, in P e in Q, i centri delle parti in acqua e in aria; o al&shy;<lb/>trimenti, se l'unica forza OT si decomponesse nelle due parallele PS, QU; <lb/>verrebbe il teorema dello Stevino ridotto alla precisa forma di quello di Ar&shy;<lb/>chimede, e tal sarebbe per l'uno, quale &egrave; indicata per l'altro, la vera e di&shy;<lb/>retta via della dimostrazione. </s>

<s>Or essendo cos&igrave;, chi non direbbe che i cul&shy;<lb/>tori della Idrostatica, ne'primi anni del secolo XVII, dovevano avere negli <lb/>Elementi steviniani ritrovata la chiave, da aprir finalmente il mistero del <lb/>secondo libro <emph type="italics"/>De insidentibus humido,<emph.end type="italics"/> e avvedersi insieme quanto male il <lb/>Tartaglia e il Commandino, ne'loro commenti, l'avessero interpetrato? </s>

<s>Ma <lb/>vediamo qual corrispondenza le congetture abbian coi fatti. </s></p><p type="main">

<s>Il primo, fra i commentatori di Archimede, che nel secolo XVII ci si <lb/>presenti, &egrave; quel David Rivault, il quale, raccogliendo e ordinando le opere <lb/>del Siracusano, prometteva di darle <emph type="italics"/>novis demonstrationibus, commenta&shy;<lb/>riisque illustrata.<emph.end type="italics"/> Avrebbe forse fatto meglio a tenersi fedelmente alle di&shy;<lb/>mostrazioni antiche, e salvare cos&igrave; la sua propria reputazione dalle censure <lb/>di molti, i quali avrebbero amato meglio di veder procedere la venerata <lb/>figura dell'Autore, colla spedita franchezza del suo passo, che vederglielo <pb xlink:href="020/01/3180.jpg" pagenum="141"/>misurato nella dialettica pedanteria delle <emph type="italics"/>ipotesi<emph.end type="italics"/> e degli <emph type="italics"/>emporasmi,<emph.end type="italics"/> delle <lb/><emph type="italics"/>catatasi<emph.end type="italics"/> e delle <emph type="italics"/>apodisi.<emph.end type="italics"/> Ma, lasciando stare la forma, il peggio sta nella <lb/>sostanza, che ha spesso spesso all'oro antico sostituito l'orpello, per cui non <lb/>a torto dissero alcuni il Rivault commentatore infelicissimo. </s>

<s>La quale infe&shy;<lb/>licit&agrave;, pi&ugrave; che in altra parte, apparisce intorno alla VIII proposizione del <lb/>primo libro <emph type="italics"/>De insidentibus humido,<emph.end type="italics"/> dopo l'enunciazion della quale il Com&shy;<lb/>mentatore scrive questo scolio: &ldquo; Quoniam huius propositionis antiqua de&shy;<lb/>monstratio, quae fuerat Archimedis, ne quidem veteribus translationibus ad <lb/>nos pervenit, et quoniam a Federico Commandino suppleta fuerit, ut aliae <lb/>quae similiter perierant; visum est eius vestigiis inhaerere primum, deinde <lb/>aliam subiungere, erutam ex antea demonstratis ab Archimede, ut magis ac <lb/>magis a seipso lumen accipiat &rdquo; (Parisiis 1615, pag. </s>

<s>500). </s></p><p type="main">

<s>Le vestigia per&ograve; del Commandino, che i nostri Lettori hanno oramai <lb/>vedute impresse in questa Storia, non &egrave; vero sian calcate dal Rivault; che <lb/>anzi par che le sciupi, sbadatamente passandovi sopra col suo piede. </s>

<s>Sola&shy;<lb/>mente l'ipotesi e il simporasma concordano con la dimostrazione del Mate&shy;<lb/>matico di Urbino, il quale del resto si sdegnerebbe che gli fossero fatte dir <lb/>cose, tanto pi&ugrave; aliene dal vero delle sue, e contro la propria intenzione. </s></p><p type="main">

<s>Sia la sfera dell'umido ABC (fig. </s>

<s>71), e la porzione sferica galleggiante <lb/>e inclinata EFH, con la sua inferior parte BZCF immersa, la quale sia dalla <lb/><figure id="id.020.01.3180.1.jpg" xlink:href="020/01/3180/1.jpg"/></s></p><p type="caption">

<s>Figura 71.<lb/>corda BC divisa cos&igrave; in due parti, che l'una <lb/>abbia il centro di gravit&agrave; in Y, e l'altra in Z, <lb/>mentre tutto il peso di detta parte immersa <lb/>suppongasi concentrato in R, e concentrato <lb/>in X il peso di tutto il solido galleggiante. <lb/></s>

<s>&ldquo; Educta linea a centro Y, dice il Rivault, <lb/>ad centrum reliquae partis portionis, quae <lb/>manet in aere, quod sit S; transibit neces&shy;<lb/>sario per centrum X totius portionis &rdquo; (ibid). <lb/>La conseguenza &egrave; manifestamente falsa, non <lb/>essendo possibile che passi per X la linea <lb/>congiungente S con Y, ma con R, secondo <lb/>la catasasi vera del Commandino, il quale si sarebbe maravigliato che il Ri&shy;<lb/>vault gli attribuisse un discorso simile a questo: &ldquo; Cum ergo ponderet pars <lb/>in humido secundum linam YL, pars vero quae in aerem secundum lineam <lb/>SL, et demum tota portio secundum perpendicularem, quae ab X ad L edu&shy;<lb/>ceretur; non manebit portio quousque haec tria centra et punctum L, quod <lb/>est ceutrum Terrae, recta linea iungantur, quod non fiet quin ambae lineae <lb/>LK et FK in unam incidant: scilicet, deorsum ruentibus partibus quae sunt <lb/>ad E, et ascendentibus sursum iis quae sunt ad H, secundum diversas li&shy;<lb/>neas, quarum situs paulatim movetur quousque radii XS, XY fiant aequales <lb/>et aequilibrium accidat. </s>

<s>Vis autem movens in hac titubatione est tam gra&shy;<lb/>vitas ponderis, quae aequamentum quaerit, cum premat in diversis centris, <lb/>quam humidi ponderositas maior quam sit portionis &rdquo; (ibid.). </s></p><pb xlink:href="020/01/3181.jpg" pagenum="142"/><p type="main">

<s>Ma, se la ponderosit&agrave; dell'umido fosse maggiore di quella della por&shy;<lb/>zione, dovrebbe questa nell'inclinarsi sollevarsi anche di pi&ugrave;, ci&ograve; che non &egrave; <lb/>consentito n&egrave; dalla ragione e n&egrave; dalla esperienza, per cui falsamente si sup&shy;<lb/>pone, che le lunghezze de'raggi XS, XY vadano ad uguagliarsi, perch&egrave; av&shy;<lb/>venga l'equilibrio. </s>

<s>Questo equilibrio poi si studia il Rivault di ridurlo al&shy;<lb/>l'esperienza della Bilancia, rimandando i Lettori a quel che aveva scritto <lb/>addietro, in un lungo Scolio, dopo la proposizione VI <emph type="italics"/>De quadratura pa&shy;<lb/>raboles,<emph.end type="italics"/> per dimostrare come ragionevolmente supponesse Archimede tirare <lb/>i pesi, per cos&igrave; brevi distanze, in direzioni parallele, benche in effetto con&shy;<lb/>vergano al centro terrestre. </s>

<s>In quello Scolio dunque cos&igrave; dicevasi dell'equi&shy;<lb/>librio della Bilancia, per applicarlo all'equilibrio della porzion galleggiante <lb/>di sfera: &ldquo; Caeterum duobus modis centra gravitatum et suspensionum, in <lb/>eadem perpendiculari constituta, pariunt et aequipondium et ponderum sta&shy;<lb/>tum ac quietem: primo, nempe cum in statera radii sunt ponderum reci&shy;<lb/>proce proportionales; secundo, cum pondera, sive aequalia sive inaequalia, <lb/>et sive in reciprocis radiis, sive in non reciprocis, ita sursum deorsumque <lb/>feruntur, ut earum perpendiculares suspensionum, vel quibus gravitant, in <lb/>unam conveniant &rdquo; (ibid.). </s></p><p type="main">

<s>Come per&ograve; si possano questi principii statici applicare al teorema idro&shy;<lb/>statico di Archimede &egrave; dubbio, ripensando che, per avere i pesi in S e in Y <lb/>momenti uguali, la bilancia &egrave; in condizione di equilibrio indifferente, e perci&ograve; <lb/>la porzione dovrebbe galleggiando stare cos&igrave; bene o diritta o inclinata, ci&ograve; <lb/>che pure consegue dalla dimostrazione del Commandino. </s>

<s>Un'aperta discor&shy;<lb/>danza poi fra i due commentatori, e pi&ugrave; notabile delle altre, apparisce dal <lb/>fatto che il Rivault mette i pesi ambedue tendere in gi&ugrave;, mentre il Com&shy;<lb/>mandino, stando ad Archimede, faceva solo tendere in gi&ugrave; la parte del gal&shy;<lb/>leggiante in aria, e in su l'altra parte sommersa. </s>

<s>Ma, per vedere come il <lb/>Francese, dilungandosi dal Nostro, si dilunghi anche di pi&ugrave; dalla verit&agrave; delle <lb/>cose; seguitiamolo nel secondo modo di dimostrare, ch'egli crede pi&ugrave; con&shy;<lb/>facevole colla mente di Archimede. </s></p><p type="main">

<s>La dimostrazione &egrave; ridotta a una tale semplicit&agrave;, che conferisce a ren&shy;<lb/>dere l'errore pi&ugrave; manifesto. </s>

<s>Siano, come dianzi, la sfera dell'umido e l'emi&shy;<lb/>sfero galleggiante HFJ, il cui centro di gravit&agrave; R, e della parte sommersa <lb/>sia centro gravitativo L, della emersa sia M, cosicch&egrave; la linea, che congiunge <lb/>questi due stessi centri, sia divisa nel punto K (per cui necessariamente <lb/>passa) con tal ragione, che il raggio LK, al raggio KM, reciprocamente stia <lb/>come la porzione dell'emisferio in aria, alla porzione di lui in acqua: &ldquo; quo&shy;<lb/>niam L (cos&igrave;, fatta l'ipotesi, passa il Rivault all'apodisi della sua dimostra&shy;<lb/>zione) est centrum partis demersae, ponderat secundum perpendicularem EL, <lb/>uti non demersa secundum perpendicularem EM; totum vero haemisphae&shy;<lb/>rium secundum lineam EK, et puncto K videtur fieri suspensio, et esse li&shy;<lb/>bride ML: punctum vero suspensionis G, centrum nempe magnitudinis. </s>

<s><lb/>Ergo M, quae sursum est in suspendio, mittetur deorsum, punctum vero <lb/>L ascendet sursum, ita ut tandem tria puncta E, K, G abeant in rectam <pb xlink:href="020/01/3182.jpg" pagenum="143"/>lineam, et sit axis FG in perpendiculari EK, ut vult propositio &rdquo; (ibid., <lb/>pag. </s>

<s>501). </s></p><p type="main">

<s>La necessit&agrave; del costituirsi i punti L, M nella medesima verticale col <lb/>punto K di sospensione, la fa conseguire il Rivault dal secondo principio <lb/>statico, formulato nello Scolio dopo la VI proposizione del Tetragonismo della <lb/>parabola: principio, che non &egrave; per&ograve; applicabile, se non al caso che i mo&shy;<lb/>menti intorno al punto di sospensione siano diversi, perch&egrave; allora prevalendo <lb/>il maggiore, e facendo abbassare la bilancia dalla sua parte, la fa necessa&shy;<lb/>riamente sollevare dall'altra. </s>

<s>Ma come pu&ograve; esser questo il motivo della re&shy;<lb/>stituzione nell'emisfero inclinato, se i momenti, stando le gravit&agrave; per ipo&shy;<lb/>tesi reciprocamente come le distanze, sono uguali, in piena conformit&agrave; col <lb/>primo principio statico, formulato nel detto scolio? </s>

<s>In questo caso, comun&shy;<lb/>que l'emisfero s'inclini, ivi si rimarrebbe allo stesso modo che dianzi eretto, <lb/>come la bilancia di momenti uguali, e col centro di gravit&agrave; nel punto della <lb/>sospensione, si rimane indifferentemente, comunque sia volta. </s></p><p type="main">

<s>Anche apparisce di qui pi&ugrave; espressamente tendere in basso ambedue le <lb/>forze applicate in M e in L, secondo il Rivault, il quale non sa compren&shy;<lb/>dere come Archimede, e il Commandino che lo segue, possano aver detto <lb/>che il punto L &egrave; spinto in su. </s>

<s>&ldquo; Possemus, sicut Archimedes, dicere M ferri <lb/>deorsum, et L ferri sursum, et tandem axem GF uniri perpendiculari EK, <lb/>verum unde fiat elatio puncti L sursum non videtur constare &rdquo; (ibid., pag. </s>

<s>501). <lb/>Sarebbe potuto ci&ograve; constare dalla seconda supposizione, se avesse inteso il Ri&shy;<lb/>vault a qual fine Archimede, invece di aggiungerla alla prima in principio <lb/>del primo libro, la mettesse a mezzo, innanzi alla proposizione VIII. </s>

<s>Il no&shy;<lb/>vello sapiente volle insegnare all'antico Maestro com'avrebbe dovuto ordinar <lb/>meglio il suo libro: &ldquo; Hanc positionem, egli dice, Archimedes subiungit post <lb/>VIII propositionem huius. </s>

<s>Ego vero malui hic adponere, tum quod positio&shy;<lb/>num ut datarum hic locus sit, tum quia etiam primis propositionibus deser&shy;<lb/>vit. </s>

<s>Caeterum Archimedes posuerat tantum de iis quae sursum feruntur; <lb/>ego vero addidi, et de iis quae deorsum tendunt &rdquo; (ibid., pag. </s>

<s>492). E in&shy;<lb/>fatti cos&igrave;, con incredibile temerit&agrave;, sciaguattava in queste parole la limpi&shy;<lb/>dezza del pensiero archimedeo: &ldquo; Ponatur eorum, quae in humido sursum <lb/>vel deorsum feruntur, unumquodque sursum vel deorsum ferri, secundum <lb/>perpendicularem, quae per centrum gravitatis ipsorum ducitur &rdquo; (ibid.). </s></p><p type="main">

<s>Questo era, per servirsi di un'altra immagine, un ridurre l'ingegno ela&shy;<lb/>boratissimo della chiave alla uniforme crassizie del martello, ond'ei non &egrave; <lb/>maraviglia se il Rivault, invece di aprir la porta, l'and&ograve; tormentando con <lb/>inutili colpi, e, come altre volte si disse, volse in peggio le illustrazioni o le <lb/>divinazioni del Commandino. </s>

<s>Da questa parte perci&ograve; ne, sembra assai com&shy;<lb/>mendevole Isacco Barrow che, nel suo libro <emph type="italics"/>Archimedis opera methodo nova <lb/>illustrata, et succincte demonstrata,<emph.end type="italics"/> venendo al <emph type="italics"/>De insidentibus humido,<emph.end type="italics"/><lb/>restitu&igrave; la supposizione seconda al suo luogo, come in questo, cos&igrave; nel rima&shy;<lb/>nente protestandosi di seguir l'orme di quel Federigo Commandino, <emph type="italics"/>de li&shy;<lb/>teris hisce optime meritum<emph.end type="italics"/> (Londini 1675, pag. </s>

<s>245), da cui compendi&ograve; il <pb xlink:href="020/01/3183.jpg" pagenum="144"/>modo di dimostrare l'VIII proposizione, e cos&igrave; dietro lui la concluse: &ldquo; Cum <lb/>igitur pars immersa sursum feratur secundum rectam EL (nella medesima <lb/>figura 72) pars vero extans deorsum, secundum ME, neque hae lationes sibi <lb/>invicem ullatenus obsistant, utpote per alias, aliasque lineas peractae; non <lb/><figure id="id.020.01.3183.1.jpg" xlink:href="020/01/3183/1.jpg"/></s></p><p type="caption">

<s>Figura 72.<lb/>quiescet portio donec haec centra, cum cen&shy;<lb/>tro terrae, in unam rectam incidant: hoc <lb/>est, donec axis GF sit secundum perpendi&shy;<lb/>cularem. </s>

<s>Tum vero quiescent, quia quanto <lb/>impetu quae in humido est pars sursum, <lb/>tanto quae extra deorsum per eamdem li&shy;<lb/>neam contendit &rdquo; (ibid., pag. </s>

<s>249). </s></p><p type="main">

<s>Pare impossibile che un s&igrave; gran ma&shy;<lb/>tematico, qual'era il maestro del Newton, <lb/>si fosse cos&igrave; lasciato irretire ne'paralogismi <lb/>del Commandino, a sciogliersi da'quali sa&shy;<lb/>rebbegli bastato osservare che l'impeto, fatto <lb/>in su dall'umido, non eguaglia quello fatto <lb/>in gi&ugrave; dalla sola parte emersa, ma da tutta intera la porzione sferica, se&shy;<lb/>condo che Archimede stesso aveva poco innanzi insegnato, nella sesta pro&shy;<lb/>posizione. </s>

<s>Ma pure &egrave; un fatto che, sebbene il Barrow ammetta col Comman&shy;<lb/>dino essere il punto L respinto in su, nonostante anch'egli fra s&egrave; diceva: <lb/><emph type="italics"/>Verum unde fiat elatio ista sursum non videtur constare,<emph.end type="italics"/> ci&ograve; che si con&shy;<lb/>ferma dalla seguente nota, nella quale, come dimostra di partecipare ai dubbi <lb/>del Rivault, cos&igrave; si studia di acquetarsi la mente nelle medesime o in simili <lb/>soluzioni. </s>

<s>&ldquo; Recta LM l&igrave;bram repraesentat, in qua duo gravia BFC, HBCI <lb/>diversimode ponderant (levior est enim pars immersa illa quae extat). Su&shy;<lb/>spensio fit ex puncto K, radii sunt KL, KM. </s>

<s>Descendit M, attolletur L, donec, <lb/>puncto K in EG constituto, contingat aequilibrium &rdquo; (ibid.). </s></p><p type="main">

<s>L'espressione <emph type="italics"/>diversimode ponderant,<emph.end type="italics"/> e il far consistere la diversit&agrave; del <lb/>modo nella maggior leggerezza, ne fa ragionevolmente argomentare che il <lb/>Barrow in questo tenesse pi&ugrave; col Rivault, che col Commandino, per cui non <lb/>fa maraviglia se in seguito, abbandonato affatto il commentatore di Urbino, <lb/>si tenesse dietro dai pi&ugrave; a quell'altro di Fluranzia. </s>

<s>Anche in Italia se n eb&shy;<lb/>bero vari esempi, fra'quali basti a noi citare il seguente. </s>

<s>Quando si fece la <lb/>Raccolta fiorentina degli <emph type="italics"/>Autori, che trattano del moto delle acque,<emph.end type="italics"/> il primo <lb/>posto naturalmente fu riserbato a Archimede. </s>

<s>E perch&egrave; tutti i trattati, in <lb/>qualunque lingua fossero originalmente scritti, dovevan esser tradotti nella <lb/>italiana, fu la traduzione del <emph type="italics"/>De insidentibus humido<emph.end type="italics"/> affidata all'elegante <lb/>penna di Giovanni Bottari, il quale, non sentendosi cos&igrave; forte in matematica, <lb/>come in letteratura, condusse l'opera con l'assistenza di Guido Grandi. </s>

<s>Il <lb/>qual Grandi poi non si fece nessuno scrupolo di seguire il Rivault nella te&shy;<lb/>merit&agrave; e ne'falli. </s>

<s>Tolse perci&ograve; anch'egli la seconda petizione dal suo proprio <lb/>luogo, e la fece succedere alla prima, in principio del libro, rimpastandovi <lb/>i moti <emph type="italics"/>sursum<emph.end type="italics"/> coi <emph type="italics"/>deorsum,<emph.end type="italics"/> come aveva fatto colui, che aveva preso ad esem-<pb xlink:href="020/01/3184.jpg" pagenum="145"/>pio, e da cui lasci&ograve; che il Bottari traducesse cos&igrave; fedelmente la restaurata <lb/>VIII proposizione: </s></p><p type="main">

<s>&ldquo; Sia la parte BFC (nella medesima figura 72) della porzione sferica <lb/>HFI, immersa nel liquido ABC. </s>

<s>E perch&egrave; il centro di gravit&agrave; della detta por&shy;<lb/>zione &egrave; nell'asse FG, sia il punto K, e si congiunga L, centro della parte <lb/>immersa, con M, centro della parte che resta fuori, con una retta linea, che <lb/>passi pel centro K di tutta la porzione sferica, e sar&agrave; obliqua alla linea FG, <lb/>supponendosi la figura inclinata. </s>

<s>E perch&egrave; L &egrave; centro della parte sommersa, <lb/>questa far&agrave; forza in gi&ugrave; per la EL, perpendicolare al liquido, e la parte emer&shy;<lb/>gente per la perpendicolare ME, posto E centro della terra, e tutta la por&shy;<lb/>zione sferica graviter&agrave; per la linea EK. </s>

<s>Adunque nel punto K si fa la so&shy;<lb/>spensione della libbra ML, ed M, che nella libbra &egrave; in su, scender&agrave;, e per <lb/>conseguenza salir&agrave; L, sicch&egrave; i tre punti E, K, G rimangano in una linea <lb/>retta, e venga l'asse FG soprapposta alla perpendicolare EK. </s>

<s>Adunque ecc. </s>

<s>&rdquo; <lb/>(<emph type="italics"/>Raccolta cit.,<emph.end type="italics"/> Ediz. 2a, T. I, Firenze 1755, pag. 5). </s></p><p type="main">

<s>Ecco come, in un secolo e mezzo, vennero a imbozzacchire i dolci pomi <lb/>dello Stevino. </s>

<s>Se ne attribuir&agrave; forse la causa all'essersi condotta per vie <lb/>oblique, come si disse, l'Acrobatica di lui: e senza dubbio, se avesse a di&shy;<lb/>rittura chiamato centro della pressione quello, ch'egli volle chiamar piutto&shy;<lb/>sto <emph type="italics"/>centro di gravit&agrave; della fossa,<emph.end type="italics"/> sarebbesi fatto intendere assai meglio, e <lb/>avrebbe ovviato all'errore del credersi che ambedue le forze tendessero in <lb/>gi&ugrave; al centro della Terra, come vi tendono tutte le gravit&agrave; naturali. </s>

<s>Ma, a <lb/>rendere il magistero dello Stevino inefficace, confer&igrave; un altro magistero, che <lb/>gli successe, e che rimase trionfatore per un complesso di cause, che lungo <lb/>sarebbe e difficile a dire, ma principalmente per la seduzion dell'eloquio, e per <lb/>essersi l'Autore, con l'uso del canocchiale, e presa occasione dal discorrer <lb/>delle galleggianti, fatto messaggero alla terra di nuovi mondi celesti. </s>

<s>Del resto <lb/>Galileo aveva alla scienza spennate le ali, che lo Stevino avevale felicemente <lb/>restituite, per farla risalire alle alture archimedee. </s>

<s>Questi argomenti per l'ar&shy;<lb/>duo volo consistevano nel principio della composizione delle forze parallele, <lb/>nel metodo degl'indivisibili, e principalmente nel fatto dell'uguaglianza delle <lb/>pressioni: argomenti, de'quali, come Archimede aveva fatto uso, cos&igrave; furono <lb/>restaurati tutti dallo Stevino. </s></p><p type="main">

<s>Non giova qui ripetere quali, e quanto gravi danni ricevessero le dot&shy;<lb/>trine dei moti composti e degli indivisibili negli insegnamenti di Galileo, per <lb/>trattenerci intorno a ci&ograve;, che pi&ugrave; nocque ai progressi dell'Idrostatica, volu&shy;<lb/>tasi incautamente ridurre tutta alle leggi della Statica pura. </s>

<s>Cos&igrave; avvenne che <lb/>de'liquidi, come de'solidi, non si consider&ograve; altro che il peso, e trascuratasi <lb/>la mobilit&agrave; delle particelle, di che sono essi liquidi composti, e in cui con&shy;<lb/>siste il dirsi e l'essere propriamente tali; si confusero con i centri di gra&shy;<lb/>vit&agrave; i centri delle pressioni. </s>

<s>Esaminando infatti a qual principio s'informano <lb/>le dimostrazioni di Galileo si trover&agrave; che il liquido, secondo lui, non reagi&shy;<lb/>sce attivamente, ma solo resiste al solido immerso, e non gli resiste per al&shy;<lb/>tro, che per contrapporgli il suo proprio peso. </s>

<s>Fu tale poi il principio stesso, <pb xlink:href="020/01/3185.jpg" pagenum="146"/>che prevalse nelle scuole, e che fece sventuratamente smarrir la via, per la <lb/>quale l'Idrostatica era stata rimessa dallo Stevino. </s>

<s>L'esempio di ci&ograve; pi&ugrave; no&shy;<lb/>tabile lo abbiamo nel Rivault, il quale essere imbevuto degli insegnamenti <lb/>galileiani si mostra nello scolio, ch'egli scrisse dopo la proposizione I del <lb/>secondo libro <emph type="italics"/>De insidentibus humido.<emph.end type="italics"/> Conforme a questi insegnamenti &egrave; la <lb/>ragione, ch'egli ivi adduce del non saper comprendere come Archimede dica <lb/>che il centro della parte sommersa della porzione sferica &egrave; spinto in alto. <lb/></s>

<s>&ldquo; Nam, licet magnitudo humido levior assurgat tanta vi, quanto humidum, <lb/>molem habens magnitudini aequalem, gravius est ipsa magnitudine; tamen <lb/>elatio fit potius ex gravitate magnitudinis immersae, quae centrum quaerit, <lb/>quam ex impulsione humidi &rdquo; (Archim., Op. </s>

<s>cit., pag. </s>

<s>501). </s></p><p type="main">

<s>La negazione dell'impulsione dell'umido, e la sua resistenza passiva, <lb/>erano conseguenze necessarie della statica del vette, invocata da Galileo, e <lb/>alla resistenza della quale da una parte si contrappone la potenza dall'altra. </s>

<s><lb/>Consiste in ci&ograve; principalmente, come s'&egrave; detto pi&ugrave; volte, il vizio radicale <lb/>delle istituzioni idrostatiche di lui, ma &egrave; quasi per una infezione di questo <lb/>stesso vizio, che si dice l'umido non premere che in gi&ugrave;, e non gravitare <lb/>in s&egrave; stesso, come n&egrave; l'aria o altro fluido si insegnava non esser gravi nel <lb/>loro proprio elemento. </s>

<s>Ripensando ai quali dannosissimi errori, s'intender&agrave; <lb/>qual grave e geloso ufficio lasciasse Galileo a'suoi discepoli, i quali l'adem&shy;<lb/>pirono con filosofica libert&agrave;, per amor del vero, rinunziando a ogni ossequio, <lb/>come passeremo a narrare nel seguente capitolo di storia, in cui sembrer&agrave; <lb/>di veder descritta l'opera lunga e affannosa di quei, che si affaccendassero <lb/>intorno a una nave, per riaverla dal fondo e rimetterla in corso, squarciate <lb/>le vele, scavigliati i remi, e rotto o irrigidito sui cardini il timone. </s></p><pb xlink:href="020/01/3186.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO III.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Dei ravviamenti e dei progressi fatti dall'Idrostatica <lb/>dopo le istituzioni di Galileo<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>De'teoremi di Archimede, non assolutamente veri, se non quando, sopra l'umida superficie, sia <lb/>il vuoto. </s>

<s>&mdash; II. </s>

<s>Di ci&ograve; che specularono i Matematici, e sperimentarono i Fisici, per dimostrare, <lb/>contro i Peripatetici e contro Galileo, che l'acqua, l'aria e ogni altro fluido pesa anche nel suo <lb/>proprio elemento. </s>

<s>&mdash; III. Dell'equilibrio de'liquidi fra loro: de'promotori. </s>

<s>e degli oppositori al <lb/>metodo usato da Galileo per dimostrarlo. </s>

<s>&mdash; IV. Dell'equilibrio de'liquidi co'solidi immersi, e <lb/>come, riconosciuto fallace il nuovo metodo usato da Galileo per dimostrarlo, si tornasse all'an&shy;<lb/>tico di Archimede. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Quel che rimaneva a fare ai discepoli di Galileo, per ravviare la scienza <lb/>sulla rettitudine dei sentieri, da cui l'aveva fatta traviare il Maestro, ridu&shy;<lb/>cevasi dunque a riconoscere principalmente l'insufficienza della statica della <lb/>leva, applicata a dimostrare le leggi dell'equilibrio de'liquidi, con s&egrave; stessi <lb/>comunicanti e co'solidi immersi. </s>

<s>S'incominci&ograve; dal dubitare se fosse vero il <lb/>principio delle velocit&agrave; virtuali, introdotto da Galileo nella scienza degli equi&shy;<lb/>librii, e alcuni lo ripudiarono come non a proposito delle dimostrazioni, per <lb/>le quali, o tornarono agli antichi modi di Archimede, o gli promossero col <lb/>principio della composizion delle forze, o paragonando i liquidi ai solidi, ri&shy;<lb/>dotti in una polvere di minutissime ed esattissime sfere. </s>

<s>Altri per&ograve; accetta&shy;<lb/>rono quel principio, purch&egrave; per&ograve; si trattassero le velocit&agrave; virtuali, non co'me&shy;<lb/>todi antichi, ma con quello degl'indivisibili, da cui mostrarono di ricavarne <lb/>ottimi servigi, fra'quali anche quello di riuscire a dar matematica dimostra&shy;<lb/>zione del principio dell'uguaglianza delle pressioni. </s>

<s>Concorsero a esercitarsi <lb/>intorno a una tale variet&agrave; di argomenti i cultori dell'Idrostatica, dopo le isti&shy;<lb/>tuzioni di Galileo, per tutto il rimanente secolo XVII: e avendo avuto quei <pb xlink:href="020/01/3187.jpg" pagenum="148"/>loro esercizi la prima occasione e l'impulso dalla proposta di un quesito, la <lb/>soluzion del quale fu di grande importanza; vuol di qui perci&ograve; cominciare <lb/>il presente capitolo di storia. </s></p><p type="main">

<s>Nel pi&ugrave; volgar modo di dimostrare i teoremi di Archimede, e special&shy;<lb/>mente il VII, s'immagina che lo spazio occupato dal solido rimanga vuoto, <lb/>e che poi sia riempito di altrettanto liquido. </s>

<s>Similmente nell'esperienza, per <lb/>trovare le gravit&agrave; specifiche, o secondo il modo narrato da Vitruvio, per ri&shy;<lb/>solvere il problema della corona, o con l'uso della Bilancetta, si suppone che <lb/>il peso dell'acqua versata, e di cui s'alleggerisce il contrappeso dello stru&shy;<lb/>mento, corrisponda esattamente al peso della mole liquida, in luogo della <lb/>quale &egrave; sottentrato il solido immerso. </s>

<s>Ma &egrave; da fare intorno a ci&ograve; un'osser&shy;<lb/>vazione importante, ed &egrave; che lo spazio scavato in seno al liquido, nel primo <lb/>caso, &egrave; rimasto assolutamente vuoto, come, nel secondo, il solido sottentra <lb/>in uno spazio, che deve esser pure, in forza della supposizione, assoluta&shy;<lb/>mente vuoto. </s>

<s>Ond'ei non par vero che la mole d'acqua, la quale stava den&shy;<lb/>tro al vaso in perfetto vuoto, pesi precisamente tanto, quanto versata fuori, <lb/>e gravitante nel mezzo dell'aria. </s></p><p type="main">

<s>Si pu&ograve; il presente discorso dichiarar meglio con l'esempio della Bilan&shy;<lb/>cia idrostatica, parata a quel modo che tutti sanno, per dimostrar la seconda <lb/>parte della VII proposizione archimedea. </s>

<s>Si chiami P il contrappeso del ci&shy;<lb/><figure id="id.020.01.3187.1.jpg" xlink:href="020/01/3187/1.jpg"/></s></p><p type="caption">

<s>Figura 73.<lb/>lindro A (fig. </s>

<s>73) e del secchio B in aria. </s>

<s><lb/>Immerso il detto cilindro, che si suppone <lb/>essere in tale stato ridotto al peso <emph type="italics"/>p,<emph.end type="italics"/> e re&shy;<lb/>stituito l'equilibrio, col riempire il secchio <lb/>del medesimo liquido di quello, in cui si fa <lb/>l'immersione, e che sia di peso <emph type="italics"/>p&prime;<emph.end type="italics"/>; si os&shy;<lb/>servi che, nell'infondere in esso secchio il <lb/>liquido, &egrave; stata scacciata l'aria, che dentro <lb/>ci gravava, con un tal peso, quale poniamo <lb/>sia <emph type="italics"/>p&Prime;,<emph.end type="italics"/> ond'&egrave; che avremo <emph type="italics"/>p+p&prime;&mdash;p&Prime;<emph.end type="italics"/>=P, <lb/>ossia <emph type="italics"/>p<emph.end type="italics"/>=P&mdash;(<emph type="italics"/>p&prime;&mdash;p&Prime;<emph.end type="italics"/>). Dunque il so&shy;<lb/>lido cilindro non &egrave; alleggerito solamente del <lb/>peso <emph type="italics"/>p<emph.end type="italics"/> di una mole liquida, uguale a quella <lb/>che ha egli stesso, ma di <emph type="italics"/>p&prime;&mdash;p&Prime;,<emph.end type="italics"/> ossia della differenza tra la detta mole <lb/>liquida, e una corrispondente mole di aria. </s>

<s>La qual mole di aria si pu&ograve; forse <lb/>da'Fisici reputare di peso insensibile, ma &egrave; l'esperienza stessa trasformabile <lb/>in modo, da provar anche fisicamente che la perdita del peso, subita dal corpo <lb/>immerso, non &egrave; quale propriamente dice Archimede, ma quale nella sopra <lb/>scritta formula fu conclusa. </s>

<s>S'immagini infatti d'operare con la Bilancia in <lb/>un'ammosfera di olio, galleggiante sopra l'acqua del vaso C o in un'am&shy;<lb/>mosfera di acqua, galleggiante sopra il mercurio, di cui si fosse ripieno il <lb/>medesimo vaso. </s>

<s>Allora il secchio, votandosi d'olio e riempiendosi d'acqua <lb/>nel primo caso, o votandosi d'acqua e riempiendosi di mercurio nel secondo, <lb/>&egrave; manifesto che il valore di <emph type="italics"/>p&Prime;,<emph.end type="italics"/> ossia di tant'olio o di tant'acqua, quanta ne <pb xlink:href="020/01/3188.jpg" pagenum="149"/>pu&ograve; capire nel secchio, non dovrebb'essere insensibile a nessuna Bilancia, e <lb/>riuscirebbe perci&ograve; necessariamente fallace l'esperienza di chiunque lo tra&shy;<lb/>scurasse. </s>

<s>Or, dovendo essere i teoremi idrostatici universalmente veri, vien <lb/>di qui a proporsi il quesito che si diceva: Son da accusar forse di false le <lb/>cose dimostrate nel primo libro <emph type="italics"/>De insidentibus humido,<emph.end type="italics"/> o si verificano so&shy;<lb/>lamente negli umidi non costituiti in aria, ma nel vuoto assoluto? </s></p><p type="main">

<s>La risposta era stata data da quel sottilissimo ingegno dello Stevino. </s>

<s><lb/>Chi, al primo aprire il libro degli <emph type="italics"/>Elementi<emph.end type="italics"/> di lui, legge, fra le numerose <lb/>definizioni scritte, le ultime due, cio&egrave; la XI e la XII: <emph type="italics"/>Vuide est un lieu <lb/>ou il n'y a nul corps &mdash; Vuide est un vase ou il n'y a que de l'air de&shy;<lb/>dans;<emph.end type="italics"/> e dopo queste passa alla petizione prima che dice: <emph type="italics"/>La pesanteur pro&shy;<lb/>pre d'un corps soit celle, de la quelle il est trouv&eacute; estre pesant en l'air, <lb/>mais dans l'eau qu'elle soit dite sa constitution en icelle;<emph.end type="italics"/> chi legge que&shy;<lb/>ste cose, voleva dirsi, pu&ograve; crederle prenozioni superflue, o avvertenze scru&shy;<lb/>polose, e perci&ograve; disprezzate dagli autori moderni. </s>

<s>Ma poi quando uno giunge <lb/>a intendere il fine, per cui tali definizioni e petizioni s'eran premesse, &egrave; co&shy;<lb/>stretto a confessare che gli stessi moderni autori son trascurati, e che la loro <lb/>scienza non giunge a quella precisione mirabile, e a quella finezza, con cui, <lb/>tre secoli prima, l'aveva trattata il Matematico di Bruges. </s>

<s>Egli propone cos&igrave;, <lb/>nel suo libro <emph type="italics"/>Des elemens hydrostatiques,<emph.end type="italics"/> il VII teorema: &ldquo; Tout corps so&shy;<lb/>lide est plus leger dans l'eau, qu'en l'air, de la pesanteur de l'eau egale en <lb/>grandeur a iceluy &rdquo; (pag. </s>

<s>487), e lo dimostra supponendo che sia dentro <lb/>l'acqua scavata una fossa, esattamente capace del solido, il quale deve dun&shy;<lb/>que trovarvisi in mezzo tanto men grave, quanto era il peso dell'acqua vo&shy;<lb/>tata. </s>

<s>Intorno al qual vuoto rimasto occorrono a fare le osservazioni accen&shy;<lb/>nate di sopra, e che lo Stevino stesso fa nel capitolo V dell'<emph type="italics"/>Appendice de <lb/>la Statique.<emph.end type="italics"/> A vederlo procedere snello e sicuro per il lubrico, sopra cui Ga&shy;<lb/>lileo tante volte scivol&ograve; e cadde, ne vien voglia di far risonare alle orecchie <lb/>dei nostri lettori, nella loro integrit&agrave;, le parole di lui, bench&egrave; non brevi, ac&shy;<lb/>ciocch&egrave; riconoscano quanto immeritamente fossero dimenticate. </s></p><p type="main">

<s>&ldquo; Il a est&eacute; dit, en la susdite VIII proposition, <emph type="italics"/>que tout corps solide est <lb/>d'autant plus leger dans l'eau qu'en l'air qu'emporte la pesanteur de l'eau <lb/>&eacute;gale a iceluy.<emph.end type="italics"/> D'ou quelqu'un voudroit tirer en consequence que <emph type="italics"/>tout corps <lb/>solide est d'autant plus leger dans l'argent-vif qu'en l'eau qu'emporte la <lb/>pesanteur de l'argent-vif egal a iceluy.<emph.end type="italics"/> Ou bien ainsi: <emph type="italics"/>que tout corps so&shy;<lb/>lide est d'autant plus leger dans l'eau qu'en l'huile qu'emporte la pesan&shy;<lb/>teur de l'eau egale a iceluy.<emph.end type="italics"/> Et ainsi des autres, les quelles consequences <lb/>necessaires sembleroyent du commencement estre contre l'experience. </s>

<s>Car <lb/>une livre de plomb ne sera (selon la maniere ordinaire) pas plus legere dans <lb/>l'eau qu'en l'huile qu'emporte le pesanteur de l'eau egale a iceluy, mais seu&shy;<lb/>lement plus legere que la difference des deux corps d'eau et d'huyle egaux <lb/>&agrave; iceluy. </s>

<s>Toutefois regardant de plus pr&egrave;s, et posant les choses, comme on <lb/>dit <emph type="italics"/>ceteris paribus,<emph.end type="italics"/> le tout se trouvera estre en son extreme perfection. </s>

<s>Car <lb/>il faut remarquer qu'en la premiere petition des <emph type="italics"/>Elemens hydrostatique<emph.end type="italics"/> on <pb xlink:href="020/01/3189.jpg" pagenum="150"/>requiert que <emph type="italics"/>la pesanteur des corps en l'air soit dite estre leur propre.<emph.end type="italics"/> Et <lb/>en la cinquiesme <emph type="italics"/>que le vasiforme plein d'eau estant icelle ost&eacute;e demeure <lb/>vuide,<emph.end type="italics"/> c'est a dire plein d'air selon la XI definition. </s>

<s>Partant prenant que les <lb/>deux moyens, argent-vif et eau, soyent en la place des autres, qui sont l'eau <lb/>et l'air, assavoir l'argent-vif au lleu de l'eau, et l'eau au lieu de l'air; on <lb/>poutra faire de telles petitions: <emph type="italics"/>Que la propre pesanteur des corps soit celle <lb/>qu'ils ont en l'eau. </s>

<s>Aussi le vasiforme plein d'argent-vif estant vuide de&shy;<lb/>meure plein d'eau.<emph.end type="italics"/> Alors les propositions susdites au commencement seront <lb/>veritables. </s>

<s>Et prenant le cas qu'un homme soit bien profondement sous l'eau <lb/>ayant une Balance, de l'or aussi et de l'argent-vif, que l'eau luy soit comme <lb/>a nous l'air, alors il est certain que l'or sera d'autant plus leger dans l'ar&shy;<lb/>gent-vif qu'en l'eau, qu'emporte la pesanteur de l'argent-vif egal a iceluy. </s>

<s>Il <lb/>est bien vray que si l'on prenoit que <emph type="italics"/>la vraye pesanteur des corps dans le <lb/>vuide soit leur propre,<emph.end type="italics"/> comme il est en simple apparence, on pourroit dite <lb/>que <emph type="italics"/>tout corps est d'autant plus leger en l'eau, qu'au vuide, qu'emporte <lb/>la pesanteur d'eau egale a iceluy.<emph.end type="italics"/> Mais remarquant les circostances de no&shy;<lb/>stre maniere vulgaire &agrave; peser (a la quelle la theorie doit tousiours aspirer) <lb/>ne se fait pas au vuide, mais en l'air; il sera donc plus a propos de dire, <lb/>selon la premiere maniere, que la propre pesanteur des corps est faite en <lb/>l'air. </s>

<s>Et au regard d'icelle la VIII proposition susdite, et celles qui s'en en&shy;<lb/>suivent, sont en leur extreme perfection, comme nous avions entrepis de <lb/>declairer &rdquo; (Ouvrages cit., pag. </s>

<s>503). </s></p><p type="main">

<s>Dalla qual dichiarazione si rileva la risposta al proposto quesito: rispo&shy;<lb/>sta che, per detto dello Stevino, &egrave; tale: I teoremi dimostrati da Archimede <lb/>son veri fisicamente, ossia secondo il comun modo di pesare, che da noi si <lb/>fa sempre nell'aria. </s>

<s>Matematicamente per&ograve; non si verificano, se non che <lb/>quando l'umido, o le solide grandezze che vi galleggiano, o che vi s'immer&shy;<lb/>gono, siano costituite nel vuoto. </s></p><p type="main">

<s>La medesima questione, risoluta cos&igrave; dal Fisico olandese, torn&ograve;, sessanta <lb/>anni dopo, ad agitarsi in Italia, a proposito di un dubbio nato parecchio tempo <lb/>prima (ne'primi cinque mesi dell'anno 1627) in alcuni studiosi di Archi&shy;<lb/>mede, nuovamente illustrato da Galileo: se cio&egrave; l'acqua, aggiunta all'ar&shy;<lb/>gento vivo, faccia che il ferro o si rimanga o s'attuffi o galleggi maggior&shy;<lb/>mente. </s>

<s>Alcuni, ripensando che i Teoremi archimedei erano assoluti, ne con&shy;<lb/>cludevano che il ferro si rimarrebbe: altri dicevano che, gravato dal peso <lb/>dell'acqua, s'affonderebbe di pi&ugrave;: altri poi invece che, per la circumpulsione <lb/>dell'acqua stessa sopra infusavi, si solleverebbe di alquanto. </s>

<s>Fu proposta dai <lb/>disputanti a dimostrare la verit&agrave; al venerato comun loro maestro Benedetto <lb/>Castelli, il quale decise che il ferro si solleverebbe, e anche determin&ograve; se&shy;<lb/>condo qual proporzione. </s></p><p type="main">

<s>Del sollevamento era facile ritrovar la ragione, a quel modo che poi fece <lb/>il Viviani, in una bozza di teorema, dove dice &ldquo; che, se sia il ferro infuso <lb/>nell'argento vivo sino a un certo livello, sopranfusagli acqua, sicch&egrave; lo rico&shy;<lb/>pra abbondantemente, tal solido di ferro si sollever&agrave; ancora pi&ugrave; di prima &rdquo; <pb xlink:href="020/01/3190.jpg" pagenum="151"/>(MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>44) e la ragione di ci&ograve; la ritrov&ograve; semplicis&shy;<lb/>sima, osservando che la parte del ferro emersa, per trovarsi pi&ugrave; leggera nel&shy;<lb/>l'acqua che nell'aria, come pi&ugrave; leggera dunque sarebbesi sollevata alquanto <lb/>pi&ugrave; nell'argento vivo, e perci&ograve; insieme con lei si solleverebbe anche tutto <lb/>il ferro. </s>

<s>Ma secondo qual proporzione farebbesi un tale sollevamento era pi&ugrave; <lb/>difficile inchiesta. </s>

<s>Il Baliani la discorreva cos&igrave; col Castelli, ringraziandolo del&shy;<lb/>l'offerta fattagli della risoluzion del quesito: &ldquo; Se il ferro non fosse pi&ugrave; grave <lb/>dell'acqua non &egrave; dubbio che in tal caso sarebbe tutto fuori dell'argento vivo. </s>

<s><lb/>Ma perch&egrave; &egrave; pi&ugrave; grave uscir&agrave; fuori dell'argento vivo alla rata, cio&egrave; per l'ot&shy;<lb/>tava parte della sua propria quantit&agrave;, attesoch&egrave; il ferro pesa pi&ugrave; dell'acqua <lb/>otto volte tanto, come sa meglio di me &rdquo; (Alb. </s>

<s>IX, 144). </s></p><p type="main">

<s>Questa soluzion del Baliani per&ograve; si prevede facilmente che doveva essere <lb/>sbagliata, perch'egli non attese se non a ci&ograve; che il ferro, circumpulso pi&ugrave; <lb/>in su dall'acqua che non dall'aria, anche di pi&ugrave; s'alleggerisce, senza punto <lb/>pensare che l'alleggerimento si fa sentire in una bilancia, sopra cui gravano <lb/>insieme il mercurio e l'acqua. </s>

<s>Di qui &egrave; che esso ferro non uscir&agrave; fuori alla <lb/>rata della sola gravit&agrave; specifica dell'acqua, ma di quella di lei e del mer&shy;<lb/>curio: o, per usare il linguaggio de'moderni, la proporzione del solleva&shy;<lb/>mento non sar&agrave; data in funzione della gravit&agrave; specifica del solo liquido <lb/>sopra infuso, ma e del liquido soggiacente altres&igrave;, fra'quali due il solido gal&shy;<lb/>leggia. </s></p><p type="main">

<s>Il fallo del Baliani, e in cui tanti altri erano caduti insieme con lui, <lb/>fece, ne'discepoli e negli amici del Castelli, nascere il desiderio <emph type="italics"/>di veder la <lb/>dimostrazione pi&ugrave; distinta<emph.end type="italics"/> (ivi) datane da lui, il quale perci&ograve; la distese or&shy;<lb/>dinatamente, aggiuntovi un corollario importante, in una scrittura, dedicata <lb/>a Giovanni Ciampoli, e che noi vogliamo produrre qui alla notizia dei nostri <lb/>Lettori. </s></p><p type="main">

<s>&ldquo; Il quesito, che mi fu fatto intorno alla materia delle cose, che stanno <lb/>nell'umido, trattata da Archimede, e dal signor Galileo, nel suo particolare <lb/>Discorso; fu di questo tenore: Il ferro, per essere meno grave in spezie del&shy;<lb/>l'argento vivo, non si sommerge tutto, ma parte di esso resta fuori dell'ar&shy;<lb/>gento vivo, e parte ne resta tuffato. </s>

<s>Ora si ricerca se, infondendosi acqua nel <lb/>vaso, dove stiano come si &egrave; detto i medesimi corpi, sicch&egrave; l'acqua li copra <lb/>del tutto; si ricerca dico se il ferro rester&agrave; nell'istessa positura di prima, <lb/>cio&egrave; colla medesima porzione nell'argento vivo, oppure se in parte si solle&shy;<lb/>ver&agrave; fuori di detto argento vivo, o finalmente se si sommerger&agrave; nell'argento <lb/>vivo con maggior porzione di quella, che era avanti all'infusione dell'acqua, <lb/>stante che l'acqua sopra infusa col suo peso lo veniva a comprimere, per <lb/>cos&igrave; dire, pi&ugrave; a basso. </s>

<s>Al qual quesito io rispondo cos&igrave;: Se un solido pi&ugrave; <lb/>grave in spezie dell'acqua, e men grave dell'argento vivo, sar&agrave; posto nell'ar&shy;<lb/>gento vivo, e dopo, sopra infusa l'acqua, sicch&egrave; sopravanzi la parte superiore <lb/>di tal solido; tal solido non istar&agrave;, come nella prima positura, collocato nel&shy;<lb/>l'argento vivo, ma si sollever&agrave; per qualche spazio. </s>

<s>La qual proposizione fu <lb/>da me dimostrata con aver prima notati i tre seguenti lemmi. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/3191.jpg" pagenum="152"/><p type="main">

<s><emph type="italics"/>&ldquo; Lemma I.<emph.end type="italics"/> &mdash; Se saranno quattro grandezze proporzionali, gli antece&shy;<lb/>denti delle quali siano maggiori de'conseguenti, e dalle prime due ne siano <lb/>levate parti uguali; il rimanente della prima, al rimanente della seconda, <lb/>aver&agrave; maggior proporzione, che la terza alla quarta. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia l'AB (fig. </s>

<s>74) alla CD come EF a GH, e AB maggiore di CD, e <lb/>perci&ograve; ancora la EF maggiore di GH, e siano dall'AB e dalla CD levate <lb/><figure id="id.020.01.3191.1.jpg" xlink:href="020/01/3191/1.jpg"/></s></p><p type="caption">

<s>Figura 74.<lb/>parti uguali BI, DK. </s>

<s>Dico che la rimanente AI, alla <lb/>rimanente CK, aver&agrave; maggior proporzione che EF <lb/>a GH. </s>

<s>Facciasi come AB a CD cos&igrave; IB a LD: adun&shy;<lb/>que, per essere AB maggiore di CD, sar&agrave; ancora IB <lb/>maggiore della LD. </s>

<s>F perch&egrave;, come tutta AB a tutta <lb/>la CD, cos&igrave; la levata via IB alla levata via ID; adun&shy;<lb/>que la rimanente AI, alla rimanente CL, sar&agrave; come <lb/>tutta AB a tutta la CD, cio&egrave; come EF alla GH. </s>

<s>Ma perch&egrave; IB &egrave; maggiore <lb/>di LD, come si &egrave; dimostrato, ed uguale alla KD; perci&ograve; sar&agrave; CL maggiore <lb/>di CK. </s>

<s>Adunque la AI a CK aver&agrave; maggior proporzione che la stessa AI <lb/>alla CL, cioe che la EF alla GH, che si dovea dimostrare. </s>

<s>&rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. I, fol. </s>

<s>144, 45). </s></p><p type="main">

<s>Questo lemma &egrave; un caso particolare del seguente pi&ugrave; generale, ma ele&shy;<lb/>mentarissimo teorema: <emph type="italics"/>Ai due termini di una frazione aggiungendo quan&shy;<lb/>tit&agrave; uguali, il quoziente cresce o scema, secondo che la frazione &egrave; appa&shy;<lb/>rente o propria: e avviene tutto il contrario, se la medesima quantit&agrave; dai <lb/>due detti termini invece si tolga.<emph.end type="italics"/> Abbiasi, per esempio, A/B=Q, e (A&plusmn;<emph type="italics"/>a<emph.end type="italics"/>)/(B&plusmn;<emph type="italics"/>a<emph.end type="italics"/>)= <lb/>Q&prime;. </s>

<s>Per vedere in quali casi Q sia maggiore o minore di Q&prime;, si riducano le <lb/>frazioni al medesimo denominatore, per cui si trasformeranno in </s></p><p type="main">

<s><emph type="center"/>(A.B&plusmn;A.<emph type="italics"/>a<emph.end type="italics"/>)/(B(B&plusmn;<emph type="italics"/>a<emph.end type="italics"/>))=Q, (A.B&plusmn;B.<emph type="italics"/>a<emph.end type="italics"/>)/(B(B&plusmn;<emph type="italics"/>a<emph.end type="italics"/>))=Q&prime;.<emph.end type="center"/><lb/>&Egrave; di qui manifesto che, valendo il segno di sopra, se A>B, ossia se la <lb/>frazione &egrave; apparente, Q>Q&prime;. </s>

<s>E se A&lt;B, anche Q&lt;Q&prime;. </s>

<s>Valendo poi il <lb/>segno di sotto ed essendo la frazione propria, manifestamente &egrave; Q>Q&prime;. </s>

<s>Al <lb/>contrario poi Q&lt;Q&prime;, se la frazione &egrave; apparente, che &egrave; il caso particolar&shy;<lb/>mente contemplato dal Castelli in questo suo lemma, la dimostrazion del <lb/>quale, supponendosi A/B=C/D, vien dalla disuguaglianza (A&mdash;<emph type="italics"/>a<emph.end type="italics"/>)/(B&mdash;<emph type="italics"/>a<emph.end type="italics"/>)&lt;C/D. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma II.<emph.end type="italics"/> &mdash; Quando nell'umido sono sommersi due corpi, pi&ugrave; gravi <lb/>in specie dell'umido, nel quale sono immersi, perdono ugual momento di <lb/>gravit&agrave; in specie. </s>

<s>Il che &egrave; manifesto, perch&egrave; quel che si perde dall'uno e <lb/>dall'altro ciascheduno &egrave; uguale alla gravit&agrave; in specie dell'acqua, come si <lb/>deduce dalle cose dimostrate da Archimede, nel primo libro <emph type="italics"/>De insidentibus <lb/>humido. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s><emph type="italics"/>&ldquo; Lemma III.<emph.end type="italics"/> &mdash; Se saranno due prismi o cilindri, simili ed uguali in <lb/>mole, e dell'istessa gravit&agrave; in specie, immersi similmente nello stesso umido <pb xlink:href="020/01/3192.jpg" pagenum="153"/>pi&ugrave; grave in specie di essi prismi e cilindri; l'altezza della parte sommersa <lb/>dell'uno sar&agrave; uguale all'altezza della parte sommersa dell'altro. </s>

<s>Il che, seb&shy;<lb/>bene pare in certo modo noto per s&egrave; stesso, tuttavia si pu&ograve; dimostrare in <lb/>questa maniera: Siano due prismi o cilindri AB, CD (fig. </s>

<s>75) simili, eguali <lb/>di mole, e della stessa gravit&agrave; in specie, e siano posti similmente nello stesso <lb/><figure id="id.020.01.3192.1.jpg" xlink:href="020/01/3192/1.jpg"/></s></p><p type="caption">

<s>Figura 75.<lb/>umido, pi&ugrave; grave in specie di essi solidi, e siano <lb/>sommersi fino alle altezze BE, DF. </s>

<s>Dico che BE <lb/>&egrave; uguale alla DF. </s>

<s>Imperocch&egrave; la GB alla BE ha <lb/>la medesima proporzione, che la gravit&agrave; in specie <lb/>del solido AB (come dimostra il signor Galileo nel <lb/>Discorso delle cose che galleggiano nell'umido) <lb/>cio&egrave;, come la stessa gravit&agrave; in specie dell'umido, <lb/>alla gravit&agrave; in specie del solido CD, giacch&egrave; i solidi sono di gravit&agrave; in specie <lb/>uguali. </s>

<s>Ma come la gravit&agrave; in specie dell'umido, alla gravit&agrave; in specie del <lb/>solido CD, cos&igrave; l'altezza HD all'altezza DF; e per&ograve;, come GB alla BE, cos&igrave; <lb/>&egrave; HD alla DF. E, per essere la prima GB uguale alla terza HD sar&agrave; ancora <lb/>EB uguale alla FD, che era il proposito. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE. &mdash; <emph type="italics"/>Stanti le suddette cose, dico che, se un solido pi&ugrave; <lb/>grave in specie dell'acqua, e men grave dell'argento vivo, sar&agrave; posto nel&shy;<lb/>l'argento vivo, e dopo sopra infusa l'acqua, sicch&egrave; sopravanzi la parte <lb/>superiore del solido; tal solido non star&agrave;, come nella prima posizione, <lb/>posto nell'argento vivo, ma si sollever&agrave; per qualche spazio. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia il cilindro ovvero prisma ABCD (fig. </s>

<s>76) di ferro, ovvero di al&shy;<lb/>cuna materia pi&ugrave; grave in specie dell'acqua, e meno dell'argento vivo, im&shy;<lb/><figure id="id.020.01.3192.2.jpg" xlink:href="020/01/3192/2.jpg"/></s></p><p type="caption">

<s>Figura 76.<lb/>merso nell'argento vivo sino al livello HG, nel vaso EF, <lb/>e il rimanente AGHD resti nell'aria. </s>

<s>Intendasi di pi&ugrave;, <lb/>per maggior chiarezza, un altro prisma, ovvero cilin&shy;<lb/>dro della medesima gravit&agrave; in specie, e uguale e si&shy;<lb/>mile al solido AC, e sia IKLM (fig. </s>

<s>77) immerso si&shy;<lb/>milmente (cio&egrave; col lato LK omologo al lato CB posto <lb/>nella parte inferiore) nell'argento vivo, sino al livello <lb/>NO, nel vaso PR, ed il rimanente IONM intendasi come prima in aria. </s>

<s>Chiara <lb/>cosa &egrave; che l'altezza GB &egrave; uguale all'altezza OK, per il terzo lemma. </s>

<s>Ora <lb/><figure id="id.020.01.3192.3.jpg" xlink:href="020/01/3192/3.jpg"/></s></p><p type="caption">

<s>Figura 77.<lb/>dico che, infondendosi acqua nel vaso PR fino al li&shy;<lb/>vello PQ, sicch&egrave; sopravanzi la parte superiore del so&shy;<lb/>lido MK, il solido MK si sollever&agrave; per qualche spazio. </s>

<s><lb/>Imperocch&egrave; l'altezza IK, all'altezza KO, &egrave; come la <lb/>gravit&agrave; in specie dell'argento vivo alla gravit&agrave; in <lb/>specie del cilindro, posti l'uno e l'altro sotto l'acqua <lb/>del vaso PR, come dimostra il signor Galileo. </s>

<s>E per&shy;<lb/>ch&egrave;, avanti all'infusione dell'acqua, la gravit&agrave; in spe&shy;<lb/>cie dell'argento vivo nel vaso PR, alla gravit&agrave; in specie della MK, era come <lb/>la gravit&agrave; in specie dell'argento vivo nel vaso EF, alla gravit&agrave; in specie del <lb/>solido DB, a tal che erano quattro grandezze proporzionali, e gli antecedenti <pb xlink:href="020/01/3193.jpg" pagenum="154"/>erano maggiori dei conseguenti, e di poi, per l'infusione dell'acqua nel vaso <lb/>PR, si sono levate parti uguali di gravit&agrave; in specie, pel secondo lemma; <lb/>adunque, per il primo lemma, il residuo dell'antecedente, cio&egrave; la gravit&agrave; in <lb/>specie dell'argento vivo nel vaso PR, alla gravit&agrave; in specie del solido MK, <lb/>aver&agrave; maggior proporzione che la gravit&agrave; in specie dell'argento vivo nel <lb/>vaso EF, alla gravit&agrave; in specie del solido DB. </s>

<s>Adunque ancora la linea IK, <lb/>cio&egrave; AB, alla KO, ha maggior proporzione che la gravit&agrave; in specie dell'ar&shy;<lb/>gento vivo, nel vaso EF, alla gravit&agrave; in specie del solido DB, cio&egrave; che AB <lb/>alla BG, e per&ograve; KO &egrave; minore della GB. </s>

<s>Adunque il solido MK &egrave; stato solle&shy;<lb/>vato per l'infusione dell'acqua, come si doveva provare &rdquo; (ivi, fol. </s>

<s>145, 46). </s></p><p type="main">

<s>Questo apparato geometrico fu prescelto forse dal Castelli, per dare quasi <lb/>autentico suggello di verit&agrave; alla conclusione, alla quale vedeva nonostante con&shy;<lb/>dursi assai facilmente, non dilungandosi dalla fisica semplicit&agrave; dei metodi ar&shy;<lb/>chimedei, come fa, soggiungendo immediatamente cos&igrave; al suo primo discorso: </s></p><p type="main">

<s>&ldquo; Sia un vaso con argento vivo fino al segno AB (fig. </s>

<s>78) e sia un ferro <lb/>galleggiante in esso CD, la cui parte C sia immersa, e la D scoperta. </s>

<s>Si cerca <lb/><figure id="id.020.01.3193.1.jpg" xlink:href="020/01/3193/1.jpg"/></s></p><p type="caption">

<s>Figura 78.<lb/>che cosa far&agrave; questo ferro, dop'esser ricoperto <lb/>d'acqua. </s>

<s>Sia infusa l'acqua sino al segno EF, <lb/>ed il ferro CD, se &egrave; possibile, resti fermo nel <lb/>sito, nel quale stava prima, avanti l'infusione <lb/>dell'acqua. </s>

<s>Immaginiamoci la mole acquea G <lb/>simile ed uguale alla mole D, e la mole d'ar&shy;<lb/>gento vivo H simile ed uguale alla C. &Egrave; chiaro <lb/>per Archimede che il solo argento vivo H pesa <lb/>tanto, quanto pesa tutto il ferro CD. </s>

<s>Adunque <lb/>tutta la figura HG, essendovi aggiunta l'acqua <lb/>G, peser&agrave; pi&ugrave; che il ferro CD. </s>

<s>Seghiamo ora <lb/>il vaso col piano IL: e perch&egrave; l'umido LBO <emph type="italics"/>magis pressum est quam humi&shy;<lb/>dum LAO, non quiescet sed impelletur sursum tanta vi, quanta est gra&shy;<lb/>vitas aquae molem habentis figurae G aequalem;<emph.end type="italics"/> non rester&agrave; dunque fermo <lb/>il ferro, dopo l'infusione dell'acqua, ma spinger&agrave; all'in su, con tanta forza o <lb/>momento, quant'&egrave; il peso d'una mole d'acqua eguale alla G, ovvero alla D. &rdquo; </s></p><p type="main">

<s>&ldquo; Ma pi&ugrave; brevemente: sia il ferro AB (fig. </s>

<s>79), ed il livello dell'ar&shy;<lb/>gento vivo CD, ed avanti l'infusione dell'acqua stia il ferro colla parte B <lb/><figure id="id.020.01.3193.2.jpg" xlink:href="020/01/3193/2.jpg"/></s></p><p type="caption">

<s>Figura 79.<lb/>tuffata, e la A scoperta. </s>

<s>Infondasi poi l'acqua, e resti il <lb/>ferro come prima senza moversi. </s>

<s>&Egrave; chiaro che se la figura A <lb/>acquea, e la figura B fosse argento vivo, tutta la composta <lb/>figura AB starebbe senza moversi. </s>

<s>Ma essendo la detta fi&shy;<lb/>gura AB, non d'acqua o d'argento vivo, ma di ferro, sar&agrave; <lb/>meno grave che non &egrave; quella composta d'acqua e d'ar&shy;<lb/>gento vivo, perch&egrave; tutta la figura di ferro pesa solamente <lb/>quanto la figura B d'argento vivo. </s>

<s>Adunque al ferro AB manca, per potere <lb/>star fermo, il peso dell'acqua A, onde <emph type="italics"/>feretur sursum tanto impetu, quanto <lb/>est gravitas aquae molem habentem aequalem figurae<emph.end type="italics"/> A &rdquo; (ivi, fol. </s>

<s>146). </s></p><pb xlink:href="020/01/3194.jpg" pagenum="155"/><p type="main">

<s>Era, con tali ragioni fisiche e matematiche, risposto a quella prima <lb/>parte del quesito, intorno alla quale n&egrave; il Baliani n&egrave; altri, avveduti come <lb/>lui, non ammettevano dubbi. </s>

<s>Rimaneva come pi&ugrave; difficile di rispondere al&shy;<lb/>l'altra, quanta sia, cio&egrave;, la parte del ferro che, per l'infusione dell'acqua, <lb/>s'inalza sopra il livello dell'argento vivo, e il Castelli ci si metteva cos&igrave; ra&shy;<lb/>gionando: </s></p><p type="main">

<s>&ldquo; Sia il ferro AB (fig. </s>

<s>80), di figura prismatica o cilindrica, <lb/><figure id="id.020.01.3194.1.jpg" xlink:href="020/01/3194/1.jpg"/></s></p><p type="caption">

<s>Figura 80.<lb/>immerso nell'argento vivo sino al segno CD, e dopo l'infusione <lb/>dell'acqua s'alzi sino a qualche segno EF: si cerca la quantit&agrave; <lb/>dell'alzamento DF. &rdquo; </s></p><p type="main">

<s>&ldquo; Perch&egrave; il ferro AB, sommerso nell'argento vivo sino al <lb/>segno CD, galleggiava, sar&agrave; il peso dell'argento vivo AD eguale <lb/>al peso di tutto il ferro, per Archimede. </s>

<s>Perch&egrave; poi, dopo l'in&shy;<lb/>fusione dell'acqua, il ferro sollevato sta fermo colla parte AF nell'argento <lb/>vivo, e colla rimanente FH in acqua, peseranno le due figure, AF d'argento <lb/>vivo ed FH d'acqua insieme, quanto tutto il ferro. </s>

<s>Adunque egualmente pe&shy;<lb/>sano la mole d'argento vivo AD, e le due moli AF d'argento vivo, ed FH <lb/>d'acqua insieme. </s>

<s>Levata poi la comune AF, peser&agrave; tanto l'argento vivo ED, <lb/>quanto l'acqua EB. </s>

<s>Ma quando i pesi assoluti sono uguali, le gravit&agrave; in spe&shy;<lb/>cie sono come le moli contrariamente prese, secondo il Galileo; adunque la <lb/>mole EB, alla ED, cio&egrave; la linea BF, alla FD, sar&agrave; come la gravit&agrave; in specie <lb/>dell'argento vivo, alla gravit&agrave; in specie dell'acqua. </s>

<s>Ma perch&egrave; la BD &egrave; nota, <lb/><figure id="id.020.01.3194.2.jpg" xlink:href="020/01/3194/2.jpg"/></s></p><p type="caption">

<s>Figura 81.<lb/>cio&egrave; la parte scoperta del ferro, avanti si coprisse di acqua; <lb/>saranno note ancora le BF, DF, poich&egrave;, <emph type="italics"/>data proportione et <lb/>differentia duorum magnitudinum, ipsae etiam magnitu&shy;<lb/>dines dantur. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Quando il ferro non fosse prisma o cilindro ma solido <lb/>irregolare, come ADBC (fig. </s>

<s>81), tuffato nell'argento vivo colla <lb/>parte ACB, facciasi come la gravit&agrave; in specie dell'argento <lb/>vivo, alla gravit&agrave; in specie dell'acqua, cos&igrave; la mole DEF alla <lb/>mole EABF, e la porzione EABF sar&agrave; quella che, dopo l'infusione dell'acqua, <lb/>si sollever&agrave; sopra il livello dell'argento vivo &rdquo; (ivi, fol. </s>

<s>146, 47). </s></p><p type="main">

<s>Che cos&igrave; veramente, come diceva il Castelli, sia risoluto il problema, <lb/>pu&ograve; dichiararsi meglio col seguente discorso, dop'aver concluso che l'argento <lb/>vivo, di pari mole alla porzione ED della mole del cilindro di ferro, ugua&shy;<lb/>glia al peso della mole EB d'acqua, il luogo della quale &egrave; occupato dalla <lb/>porzione EB dello stesso cilindro. </s>

<s>Imperocch&egrave;, dove i pesi sono uguali, le <lb/>gravit&agrave; specifiche stanno contrariamente ai volumi, o alle loro altezze, es&shy;<lb/>sendo prismi o cilindri di basi uguali. </s>

<s>Chiamate dunque G, G&prime; le gravit&agrave; <lb/>specifiche del mercurio e dell'acqua, sar&agrave; BF:DE=G:G&prime;. </s>

<s>Dividendo, <lb/>BF&mdash;DF:DF=G&mdash;G&prime;:G&prime;, d'onde, sostituito BD a BF&mdash;DF, viene <lb/>(G&prime;.BD)/(G&mdash;G&prime;). Ma G e G&prime; son note, per mezzo della Bilancetta idrostatica, e BD, <lb/>che &egrave; uguale a CH, pu&ograve; aversi dalla proporzione C:G&Prime;=AH:CH, intesa <pb xlink:href="020/01/3195.jpg" pagenum="156"/>per G&Prime; la gravit&agrave; specifica del ferro, o per misura diretta; dunque DF, quan&shy;<lb/>tit&agrave; dell'alzamento, prodotto nel cilindro di ferro, per l'infusione dell'acqua <lb/>sul mercurio, &egrave; nota, ed &egrave; perci&ograve;, come si diceva, risoluto il problema. </s></p><p type="main">

<s>&ldquo; Per corollario (soggiunge il Castelli in fine del suo Discorso) si scio&shy;<lb/>glie un problema, in cui alcuno proponesse di trovare due moli, una d'acqua <lb/>e l'altra d'argento vivo, le quali insieme prese fossero uguali e di mole e <lb/>di peso ad un dato ferro: ovvero si proponesse il vaso AB, nella figura 80, <lb/>da empirsi d'acqua e d'argento vivo in tal modo, che il vaso pieno pesi <lb/>tanto, quanto peserebbe se fosse tutto ferro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Facciasi come la gravit&agrave; in specie dell'argento vivo, alla gravit&agrave; in <lb/>specie del ferro, cos&igrave; HA ad AC. </s>

<s>Di pi&ugrave;, come la medesima gravit&agrave; in spe&shy;<lb/>cie dell'argento vivo, alla gravit&agrave; in specie dell'acqua, cos&igrave; la EH alla EC, <lb/>ed il vaso AB, pieno fino al segno HB d'acqua, peser&agrave; quanto se fosse tutto <lb/>ferro. </s>

<s>N&egrave; vi &egrave; altro segno che il trovato EF, il quale seghi il vaso in modo <lb/>che, riempiutane una parte d'argento vivo, e l'altra d'acqua; faccia che <lb/>tutto il composto pesi tanto, quanto peserebbe, se fosse ferro assoluto &rdquo; (ivi, <lb/>fol. </s>

<s>147). </s></p><p type="main">

<s>Se il cilindro di ferro AB, immerso nel vaso, in cui il livello del mer&shy;<lb/>curio lo sega nel determinato segno EF, e l'acqua ne pareggia la sommit&agrave; <lb/>BH, sta in equilibrio; &egrave; manifesto che, se la parte EB si trasformasse in <lb/>acqua, e la AF in mercurio, l'equilibrio stesso perci&ograve; non sarebbe turbato. </s>

<s><lb/>Ond'essendo il peso del ferro uguale al peso di quest'acqua e di questo <lb/>mercurio, il problema proposto dal Castelli &egrave; risoluto, quando sia nota l'al&shy;<lb/>tezza AE. Ora, supponendo che l'altezza del livello del mercurio senz'acqua <lb/>fosse AC, abbiamo AE=AC&mdash;CE. Cosicch&egrave;, chiamandosi G, G&prime; le gra&shy;<lb/>vit&agrave; in specie del mercurio e dell'acqua, AC &egrave; nota, perch&egrave; G:G&prime;=HA:AC. <lb/>&Egrave; anche poi EC nota, per la formula ritrovata di sopra, dunque &egrave; risoluto il <lb/>problema. </s></p><p type="main">

<s>Del teorema, dimostrato dal Castelli in questo Discorso, fu diffusa la no&shy;<lb/>tizia per le varie copie, che del manoscritto lasci&ograve; il Ciampoli prendere agli <lb/>amici, ma principalmente per gl'insegnamenti del Borelli, il quale, leggendo <lb/>in pubblica scuola gli elementi dell'Idrostatica, faceva notare che le propo&shy;<lb/>sizioni di Archimede, e specialmente la V, son vere solamente, quando la so&shy;<lb/>lida grandezza, come suppone l'Autore, galleggi sopra un fluido solo pi&ugrave; <lb/>denso, senza che la parte emersa si trovi in mezzo a un pi&ugrave; raro. </s>

<s>E cos&igrave;, <lb/>come oralmente il Borelli insegnava, diffuse poi per le stampe i medesimi <lb/>insegnamenti nel libro <emph type="italics"/>De motionibus naturalibus,<emph.end type="italics"/> dove, avendo fatto osser&shy;<lb/>vare come, per la forza che respinge in su il solido piu leggero dell'umido, <lb/>e di cui si tratta nella VI del primo libro <emph type="italics"/>De insidentibus,<emph.end type="italics"/> non si deve in&shy;<lb/>tendere il moto attuale, ma l'energia o il conato al moto; soggiunge: &ldquo; Prae&shy;<lb/>terea altera Archimedis propositio, quod nimirum moles fluidi, aequalis so&shy;<lb/>lidi natantis parti demersae, aeque ponderet ac solidum ipsum; vera est, <lb/>nisi hypothesis varietur. </s>

<s>Oportet en&igrave;m, ex vi hypothesis, ut solidum innatet <lb/>supra unum fluidum, nam, si omnino sit demersum intra rarius, et innatet <pb xlink:href="020/01/3196.jpg" pagenum="157"/>supra aliud densius fluidum, propositio alteratur, ut docuit praeceptor meus <lb/>Benedictus Castellus, qui demonstravit quod ferrum supra mercurium natans, <lb/>si aqua quoque cooperiatur, tunc quidem altius elevabitur quam prius, pro&shy;<lb/>pterea quod pondus aquae collateralis auget magis hydrargyri compressionem, <lb/>quam ferri pondus augeat, proindeque ferrum aliquantisper altius elevat &rdquo; <lb/>(<emph type="italics"/>Regio Julio<emph.end type="italics"/> 1670, pag. </s>

<s>477, 78). </s></p><p type="main">

<s>Fra gli uditori della Lezione, in cui il Borelli cos&igrave; diceva, era quel vi&shy;<lb/>vacissimo ingegno di Donato Rossetti, il quale condusse alle ultime sue con&shy;<lb/>seguenze il discorso udito fare al Maestro. </s>

<s>E l'aria stessa, pensava fra s&egrave;, <lb/>non &egrave; ella un fluido pi&ugrave; raro dell'acqua, o di altr'umido, in cui il solido <lb/>s'immerga? </s>

<s>Dunque le proposizioni <emph type="italics"/>De insidentibus<emph.end type="italics"/> son false nelle espe&shy;<lb/>rienze di tutti coloro, che fisicamente se ne servono per loro assiomi, e si <lb/>verificano, come par che supponga Archimede stesso, solamente nel vuoto, <lb/>perch&egrave; ivi solamente le solide grandezze soprannotano a un unico fluido. </s>

<s>Cos&igrave; <lb/>appunto, come il Rossetti pens&ograve;, disse in questa forma pubblicamente: <emph type="italics"/>Il <lb/>concetto di Archimede che il galleggiante si sommerga sotto il livello del&shy;<lb/>l'acqua, fin tanto che una mole d'acqua, uguale alla parte sommersa, <lb/>pesi assolutamente quanto tutto il galleggiante; &egrave; falsissimo.<emph.end type="italics"/> (<emph type="italics"/>Dimostra&shy;<lb/>zione fisica-matem.,<emph.end type="italics"/> Firenze 1668, pag. </s>

<s>3). Pronunziata la qual sentenza, <lb/>passa l'Autore a dimostrare che il galleggiante non uguaglia in peso asso&shy;<lb/>luto il peso della detta mole dell'acqua, ma di questa, insieme con una mole <lb/>d'aria, pari a quella della parte, che in esso galleggiante soprannota. </s>

<s>La di&shy;<lb/>mostrazione &egrave; simile, anzi &egrave; sostanzialmente la medesima di quella fatta dal <lb/>Castelli, nella seconda sua fisica maniera, sostituito un umido qualunque al <lb/>mercurio, e all'acqua sopra infusagli l'aria. </s></p><p type="main">

<s>Si fecond&ograve; nel Rossetti questo primo concetto, estendendolo, dall'equi&shy;<lb/>librio de'liquidi, a tutti gli altri equilibrii in generale, di che pure, ne'suoi <lb/>libri <emph type="italics"/>De aequiponderantibus,<emph.end type="italics"/> aveva trattato Archimede. </s>

<s>E perch&egrave; il fonda&shy;<lb/>mento a questa causa degli equilibri si poneva da lui nel centro di gravit&agrave; <lb/>de'corpi, osserv&ograve; il nuovo arguto commentatore che, nell'invenzione di que&shy;<lb/>sto centro, si supponeva essere il grave costituito no in aria, ma nel vuoto <lb/>assoluto. </s>

<s>Ne toglieva l'esempio dal triangolo, dalla piramide, dal cono, e da <lb/>somiglianti figure <emph type="italics"/>in alteram partem deficientes,<emph.end type="italics"/> nelle quali il centro di <lb/>gravit&agrave;, variando col variare la densit&agrave; del mezzo, l'indicazione, datane da <lb/><figure id="id.020.01.3196.1.jpg" xlink:href="020/01/3196/1.jpg"/></s></p><p type="caption">

<s>Figura 82.<lb/>Archimede e da'promotori di lui, non potrebb'essere <lb/>cos&igrave;, come si ritiene, di assoluta verit&agrave; matematica. </s>

<s>Nel <lb/>triangolo ABC, per esempio (fig. </s>

<s>82), si determina geo&shy;<lb/>metricamente il centro di gravit&agrave; in tal punto della bis&shy;<lb/>settrice AF, che la parte AO sia due terzi della rima&shy;<lb/>nente. </s>

<s>Cosicch&egrave;, sospesa la figura dal punto O, e fatta <lb/>per lui passare una linea parallela alla base, si dice che il tutto sta in equi&shy;<lb/>librio, perch&egrave; tanto pesa il triangolo ADE da una parte, quanto il trapezio EB <lb/>dall'altra. </s>

<s>Ma che ci&ograve; si verifichi solamente nel vuoto, e no nell'aria o in <lb/>altro mezzo pi&ugrave; denso, come sarebbe l'acqua, &egrave; manifesto dall'esperienza <pb xlink:href="020/01/3197.jpg" pagenum="158"/>Perch&egrave;, lasciando liberamente cadere in alcuno dei detti mezzi, ma special&shy;<lb/>mente nel secondo, il detto triangolo solido, ossia il prisma triangolare so&shy;<lb/>pr'esso costruito; si osserva che l'equilibrio non si mantiene, ma che co&shy;<lb/>stantemente il vertice volge in basso, e si dirizza in alto la base, evidente <lb/>segno che il triangolo non &egrave; ugualmente peso, ma pi&ugrave; grave del trapezio <lb/>a lui contrapposto. </s>

<s>Che poi causa di ci&ograve; sia il mezzo si comprender&agrave; facil&shy;<lb/>mente, osservando che per essere il triangolo in superficie un quinto men del <lb/>trapezio (giacch&egrave; si sa che l'uno sta all'altro come 4 sta a 5) riceve anche <lb/>un quinto meno d'impedimento, e perci&ograve; prepondera sopra l'altro per un <lb/>quinto, rimasto libero della sua gravit&agrave; naturale. </s></p><p type="main">

<s>Dietro le quali osservazioni &egrave; necessario concludere col Rossetti <emph type="italics"/>che <lb/>Archimede non concep&igrave; le sue proposizioni per la Fisica, ma per la Mate&shy;<lb/>matica.<emph.end type="italics"/> &ldquo; Dal che &egrave; pi&ugrave; che necessario il dedurne, soggiunge lo stesso Ros&shy;<lb/>setti, che in errore siano vissuti sinora tutti quelli, che fisicamente se ne <lb/>servirono per loro assiomi. </s>

<s>Dal che si deduce anche la cagione perch&egrave; molte <lb/>cose non abbiano in fatti corrisposto a quanto da questa proposizione si aspet&shy;<lb/>tava, non solo intorno alle materie che dovevano galleggiare, ma ancora in <lb/>quelle che, in aria sospese, dovevano bilanciarsi intorno al loro centro di <lb/>gravit&agrave; &rdquo; (ivi). </s></p><p type="main">

<s>Benche fossero tutte queste conclusioni verissime, &egrave; un fatto per&ograve; che <lb/>i pi&ugrave; non le ascoltarono, e alcuni le contraddissero. </s>

<s>I Fisici, che sperava di <lb/>far ravvedere il Rossetti, si rimasero nell'antico errore intorno alle galleg&shy;<lb/>gianti, come si par dall'uso, che tuttavia seguitano a fare della Bilancia idro&shy;<lb/>statica, la quale non &egrave; esattamente dimostrativa della settima proposizione <lb/>archimedea (in cui supponesi che sopra l'umido non sia fluido alcuno e nem&shy;<lb/>men l'aria) se non che quando il secchio B, della figura 73, sia esso pure <lb/>affatto senz'aria. </s>

<s>Pu&ograve; concedersi che il peso di questa sia insensibile nella <lb/>bilancia ordinaria, ma sperimentando con quella mobilissima e squisitissima, <lb/>descritta dallo's Gravesande nel primo Tomo de'suoi Elementi matematici <lb/>di Fisica (Leida 1748, pag. </s>

<s>423, 24), non sarebbe male tener qualche conto <lb/>di questi avvertimenti del Rossetti, che son poi quelli stessi dati tanti anni <lb/>prima dallo Stevino. </s></p><p type="main">

<s>Fra i contradittori, a cui s'accennava di sopra, abbiamo a notar Gemi&shy;<lb/>niano Montanari, che educatosi in altra scuola, pare ignorasse, o non fosse <lb/>persuaso della soluzion del problema, data dal Castelli nel discorso al Ciam&shy;<lb/>poli. </s>

<s>Cosicch&egrave;, proposto il caso della cera galleggiante nell'acqua, sopra in&shy;<lb/>fusovi olio, non sapeva comprendere il Montanari come questo non oppri&shy;<lb/>messe col suo proprio peso il galleggiante soggetto, il quale vedevasi anzi <lb/>sollevarsi alquanto sopra il primo livello: n&egrave; poteva comprendere la verit&agrave; <lb/>della tesi sostenuta dal Rossetti, il quale andava ripetendo cos&igrave; al suo con&shy;<lb/>tradittore la dimostrazion del Castelli. </s>

<s>Inteso che i settori ELI, ILF, della <lb/>figura 78, siano pieni d'acqua infino al livello AOB, e il resto, infino al li&shy;<lb/>vello EIF, dove prima era aria, in mezzo alla quale emergeva la parte G del <lb/>galleggiante di cera, sia messo olio; nell'infondere questo, dice il Rosseti <pb xlink:href="020/01/3198.jpg" pagenum="159"/>&ldquo; pi&ugrave; peso si pone sopra la superficie AO, che sopra la OB, perch&egrave; l'olio <lb/>EO eccede l'olio OF dell'olio G, che &egrave; in mole uguale alla parte sopranna&shy;<lb/>tante della cera GH. </s>

<s>E per questo, essendo pi&ugrave; premuta la superficie AO <lb/>che la OB, quella discender&agrave;, col far salir questa, in quel modo appunto che <lb/>nella bilancia sale quel braccio, ove &egrave; meno di peso, quando l'altro braccio <lb/>pi&ugrave; aggravato scende &rdquo; (<emph type="italics"/>Insegnamenti fisico-matem.,<emph.end type="italics"/> Livorno 1669, pag. </s>

<s>135). </s></p><p type="main">

<s>Il Montanari dunque non poteva esser disposto a penetrare le argute <lb/>osservazioni del Rossetti, per mancargli i principii necessari. </s>

<s>Ma principal&shy;<lb/>mente giocava nella fantasia di lui quel pregiudizio comune a tanti, che cio&egrave; <lb/>sia infallibile criterio della verit&agrave; di una cosa l'essere approvata da tutti, e <lb/>specialmente dai grandi uomini, fra'quali bastava citare il solo Galileo. </s>

<s>E da <lb/>un'altra parte si faceva Galileo entrare bene a proposito nella questione, per <lb/>quel ch'egli aveva insegnato rispetto all'efficacia dell'aria, in concorrere a <lb/>sostener le assicelle d'ebano galleggianti. </s>

<s>Si not&ograve; pi&ugrave; addietro la stravaganza <lb/>di queste dottrine, perch&egrave;, essendo un fatto che anche l'aria pesa, non vi <lb/>si teneva poi nessun conto del peso di lei: stranezza che il Rossetti si stu&shy;<lb/>diava di togliere col dire che, non essendo l'aria nell'altr'aria n&egrave; grave n&egrave; <lb/>leggera, Galileo dunque intendeva di pesarla nel vuoto. </s>

<s>&ldquo; Vi ricorderete, <lb/>scriveva, che Galileo non fece altre esperienze, in quel suo Trattato delle <lb/>galleggianti, se non di cose, che di sua natura scendono nell'acqua come <lb/>d'ebano e di metalli: e vi ricorderete che queste materie, ridotte in lar&shy;<lb/>ghissime falde, venivano posate leggermente e con gran diligenza sopra <lb/>l'acqua in modo, che si mantenevano a galla, del quale effetto gli avversari <lb/>del Galileo avevano preteso che ne fosse la causa quella figura cos&igrave; ampia, <lb/>ed il Galileo, fondato sopra la dottrina de'galleggianti, provava e dimostrava <lb/>ci&ograve; avvenire, perch&egrave; tanto pesava quella falda di ebano o di metallo, atten&shy;<lb/>dete bene, <emph type="italics"/>con quell'aria, che veniva rinchiusa tra quegli argini, che fa <lb/>l'acqua intorno alla detta falda sino al superior livello dell'acqua; quanto <lb/>pesava una mole di acqua uguale alla detta falda ed aria.<emph.end type="italics"/> Sicch&egrave; se il <lb/>Galileo, in queste sue esperienze, pes&ograve; o intese di pesare, lo fece col met&shy;<lb/>tere da una parte della Bilancia una mole d'acqua, e nell'altra una falda <lb/>di qualche materia pi&ugrave; grave dell'acqua, con qualche massa di aria. </s>

<s>Ma <lb/>l'aria nell'aria non si pu&ograve; pesare; adunque dov&egrave; pesarla ove si potesse pe&shy;<lb/>sare, sicch&egrave; bisogna concludere che la pesasse o intendesse pesarla nel <lb/>vuoto &rdquo; (ivi, pag. </s>

<s>112, 13). </s></p><p type="main">

<s>Il Montanari negava esser questa la vera intenzione di Galileo, e te&shy;<lb/>stualmente citando, dal Discorso intorno alle galleggianti, i passi illustrati <lb/>dalla figura 69, qui addietro: <emph type="italics"/>Et avvegnach&egrave; la mole dell'aria AC non <lb/>cresca, n&egrave; diminuisca la gravit&agrave; della mole IS,<emph.end type="italics"/> e poco pi&ugrave; basso, <emph type="italics"/>E per&shy;<lb/>ch&egrave; l'aria AC non cresce o scema il peso del solido IS;<emph.end type="italics"/> ne concludeva, <lb/>contro il Rossetti, apparire di qui ben chiaro che Gahleo &ldquo; non pone in conto <lb/>il peso dell'aria, se dice che ella non opera cosa alcuna, perch&egrave; infatti l'aria <lb/>nell'aria non ha momento veruno, il che non potrebbe egli dire, se inten&shy;<lb/>desse quell'acqua pesata nel vuoto, perch&egrave; quivi sarebbe necessario mettere <pb xlink:href="020/01/3199.jpg" pagenum="160"/>in conto il peso d'altrettant'aria. </s>

<s>Altrimenti la proposizione non si verifi&shy;<lb/>cherebbe, e sarebbe un paralogismo: laddove dimostrata e vera rimane, se <lb/>si considera il peso assoluto nell'aria. </s>

<s>Resta dunque provato che il Galileo <lb/>intese per peso assoluto il peso de'corpi in aria, e no nel vuoto &ldquo; (<emph type="italics"/>Lezione <lb/>accademica,<emph.end type="italics"/> Torino 1678, pag. </s>

<s>8). </s></p><p type="main">

<s>Se queste dispute non hanno grande importanza per s&egrave; stesse, l'hanno <lb/>per&ograve;, e non piccola, per noi, i quali siamo intanto fatti certi di due cose: <lb/>la prima &egrave; che i paralogismi di Galileo, intorno al galleggiare i corpi pi&ugrave; <lb/>gravi in specie dell'acqua, dipendevano dall'aver egli incautamente profes&shy;<lb/>sato il principio peripatetico che ogni elemento, nel suo proprio elemento, <lb/>non &egrave; n&egrave; grave n&egrave; leggero: la seconda, che oltrepassata di non pochi anni <lb/>la prima met&agrave; del secolo XVII, de'paralogismi del novello Archimede non <lb/>s'erano ancora accorti due non ignobili seguaci di lui. </s>

<s>Che se ritornisi col <lb/>pensiero al Borelli e al Viviani, difensori ingenui delle fallacie del Michelini, <lb/>se ne dovr&agrave; concludere che Galileo aveva, co'suoi nuovi insegnamenti idro&shy;<lb/>statici, tenute lungamente soggiogate alla tirannia peripatetica le pi&ugrave; nobili <lb/>intelligenze della sua scuola. </s>

<s>Il fatto apparisce tanto pi&ugrave; deplorabile, in <lb/>quanto che una mano di valorosi stranieri era venuta a infrangere coteste <lb/>catene. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Il Pascal v'aveva menato sopra tanti colpi potenti, quante sono le varie <lb/>esperienze, immaginate e descritte da lui, per dimostrare che l'acqua nel&shy;<lb/>l'acqua preme per tutti i versi i solidi immersi, e tanto pi&ugrave; gagliardamente <lb/>gli preme, quanto vi scendono pi&ugrave; profondi. </s>

<s>Se il tubo AB (fig. </s>

<s>83), tenu&shy;<lb/>tagli chiusa la bocca B con un dito, s'immerga in un vivaio fino al livello <lb/>CD, e cos&igrave; stando s'empia di mercurio, e poi tolgasi il dito; il mercurio <lb/><figure id="id.020.01.3199.1.jpg" xlink:href="020/01/3199/1.jpg"/></s></p><p type="caption">

<s>Figura 83.<lb/>verser&agrave; dalla bocca B, scendendo sotto l'altra A, fino a un <lb/>certo punto. </s>

<s>&ldquo; Si on enforce le tuyau plus avant, le vif ar&shy;<lb/>gent remonte, car le poids de l'eau est plus grand, et si on <lb/>le hausse au contraire le vif argent baisse, car son poids <lb/>surpasse l'autre &rdquo; (<emph type="italics"/>De l'equilibre des liqueurs,<emph.end type="italics"/> a Paris, 1663, <lb/>pag. </s>

<s>19). Un manticino da focolare, sommerso tutto cos&igrave;, che <lb/>la bocca del cannello assai lungo sopravanzi il livello del&shy;<lb/>l'acqua, s'apre pi&ugrave; difficilmente, essendogli stata chiusa l'ani&shy;<lb/>mella, che in mezzo all'aria &ldquo; a cause du poids de la masse <lb/>de l'eau, qui le presse. </s>

<s>Aussi plus il est avant dans l'eau, plus <lb/>il est difficile &agrave; ouvrir, parce qu'il y a une plus grande hauteur d'eau a sup&shy;<lb/>porter &rdquo; (ivi, pag. </s>

<s>31). Similmente, strinta la bocca di una borsa di pelle <lb/>intorno a un cannello di vetro, aperto da ambedue le parti, poi tutto ripieno <lb/>di mercurio, e tuffato nell'acqua; si vede il mercurio stesso risalir su per il <pb xlink:href="020/01/3200.jpg" pagenum="161"/>detto cannello, e tanto pi&ugrave; altamente, quanto si fa calare pi&ugrave; al fondo, &ldquo; a <lb/>cause que le poids de l'eau, pressant le balon de tous costez le vif argent <lb/>qu'il contient, est presse egalement en tous ses points &rdquo; come a strizzarlo <lb/>con una mano pi&ugrave; o meno forte (ivi, pag. </s>

<s>31, 32). </s></p><p type="main">

<s>Il Boyle nel suo VII Paradosso proponevasi di dimostrare &ldquo; Corpus <lb/>fluido immersum sustinere pressionem lateralem a fluido, eamque auctam <lb/>prout corporis immersi infra superficiem fluidi profunditas augetur &rdquo; (<emph type="italics"/>Pa&shy;<lb/>radoxa hydrost. </s>

<s>Roterodami,<emph.end type="italics"/> 1670, pag. </s>

<s>197). La dimostrazione &egrave; simile alla <lb/>prima, fra quelle dianzi descritte dal Pascal, sostituito l'olio al mercurio, e <lb/>la bocca B, invece di rivoltarsi in su, aperta da lato. </s>

<s>Ma la cosa essendo di <lb/>tanta importanza pose ai Paradossi una prima appendice, per rispondere a <lb/>sette obiezioni, sovvenute a un recente scrittore, onde confermar la dottrina <lb/>del Cartesio, che cio&egrave; le parti superiori dell'acqua non premono le inferiori. </s>

<s><lb/>Data la risposta alle quali obiezioni, soggiunge il Boyle un'esperienza nuova, <lb/>per dimostrare che non solo l'acqua pesa nell'acqua, ma che ella vi pesa, <lb/>quasi con la medesima forza come se fosse in aria. </s>

<s>Si soffi, egli dice, una <lb/>bolla di vetro alla fiamma, lasciandole fuori un picciolo, mentre dentro ri&shy;<lb/>mane vuota di aria, e, aggiungendole un piombino, si tuffi nell'acqua, te&shy;<lb/>nendola sospesa per un filo a un braccio di una esattissima bilancia equili&shy;<lb/>brata. </s>

<s>Poi si rompa colla tanaglia il picciolo alla detta bolla, che s'empir&agrave; <lb/>d'acqua, attratta di mezzo all'altr'acqua, la quale che veramente pesi, e <lb/>quanto, si parr&agrave; dalla bilancia stessa, e da ci&ograve; che le si deve aggiungere per <lb/>restituir&igrave;a al primo equilibrio. </s>

<s>Alla quale aggiunta poi si troverebbe, con po&shy;<lb/>chissima differenza, corrispondere il peso dell'acqua contenuta nella bolla <lb/>stessa, quando questa, detratto il vetro, si pesasse nell'aria. </s>

<s>&ldquo; Unde liquet <lb/>(cos&igrave; il Boyle stesso ne conclude) non modo aquam gravitare sub aqua, sed <lb/>eam vel fere, vel plane tantum inibi ponderare, ac ipsa illa portio liquoris <lb/>ponderaret in aere &rdquo; (ibid., pag. </s>

<s>213). </s></p><p type="main">

<s>Pochi anni dopo la pubblicazione originale, fatta in Oxford, di questi <lb/>Paradossi boileiani, correva per le mani de'curiosi un libro, col titolo <emph type="italics"/>Ars <lb/>nova et magna gravitatis et levitatis,<emph.end type="italics"/> scritto in dialoghi, nel quinto de'quali <lb/>l'Autore, ch'era Giorgio Sinclaro, si proponeva di trattare un tale argomento: <lb/>&ldquo; Ex novo illo Urinatorum machinamento, recens excogitato, cui nomen <emph type="italics"/>Cam&shy;<lb/>panae,<emph.end type="italics"/> eiusque usu, invictissimae eruuntur rationes, quibus elementum aquae <lb/>in suo loco gravitare ostenditur &rdquo; (<emph type="italics"/>Roterodami,<emph.end type="italics"/> 1669, pag. </s>

<s>230). Vi si in&shy;<lb/>comincia a narrare com'essendo nel 1558 affondata, presso una delle isole <lb/>boreali della Scozia, una gran nave, spedita dal re di Spagna in Inghilterra, <lb/>ivi si rimanesse per 77 anni arrenata, infin tanto che un ardito palombaro <lb/>non venne a profferirsi di saperne recuperare dal fondo marino il ricchis&shy;<lb/>simo carico, per via di un macchinamento da s&egrave; allora inventato: macchi&shy;<lb/>namento, che consisteva in quella Campana, pi&ugrave; di un secolo prima propo&shy;<lb/>sta gi&agrave; al medesimo uso dal Tartaglia, ma che si rendeva praticabile, per <lb/>essere costruita di tale capacit&agrave;, da bastar l'aria dentro rinchiusa a respi&shy;<lb/>rarvi in mezzo un uomo, almen per un'ora. </s>

<s>Non era, come quella del No-<pb xlink:href="020/01/3201.jpg" pagenum="162"/>stro, chiusa tutta all'intorno, ma aperta in fondo, e potrebbe aver l'esempio <lb/>nel bicchiere, dentro cui, rovesciato e spinto con la mano in fondo a una <lb/>vasca, si vede tanto solo entrar d'acqua, quanto glie lo permetta la conden&shy;<lb/>sazione dell'aria. </s>

<s>&ldquo; Ope, et auxilio huiuscemodi machinamentorum, sed in <lb/>primis Campanae (prosegue a dire il Sinclaro) multa experiri possumus, quae <lb/>adeo extra omnem controversiae aleam aquae marinae pondus et gravitatem, <lb/>quam in suo exercet loco, demonstrant, ut postea vix supersit alicui dubi&shy;<lb/>tandi locus &rdquo; (ibid., pag. </s>

<s>230). </s></p><p type="main">

<s>I descritti esperimenti, per il Sinclaro, si riducono a cinque. </s>

<s>Vuole in <lb/>primo luogo che il marangone porti seco un Barometro, o Baroscopio come <lb/>ei lo chiama, e gli promette che vedr&agrave;, via via discendendo con la Cam&shy;<lb/>pana, sollevarsi invece dentro il tubo il mercurio. </s>

<s>Poi, gonfiata prima di scen&shy;<lb/>dere una vescica, e fortemente turata una bottiglia vuota, gli giura non dover <lb/>giungere a posarsi sul fondo del mare, senza che quella non sia ridotta flac&shy;<lb/>cida, e questa in frantumi. </s>

<s>Quivi stando, suggerisce al Palombaro, in quarto <lb/>luogo, che prenda un'altra simile bottiglia, ben bene anch'essa turata, e gli <lb/><figure id="id.020.01.3201.1.jpg" xlink:href="020/01/3201/1.jpg"/></s></p><p type="caption">

<s>Figura 84.<lb/>predice che se la vedr&agrave; scoppiare sotto gli occhi, prima <lb/>che sia tornato su a galla. </s>

<s>Dice in ultimo a quel suo <lb/>uomo sottomarino che si prepari uno strumento, simile a <lb/>quello che si rappresenta qui da noi nella 84 figura, e, <lb/>rinchiudendolo nella sua stanza, indovina che, appena <lb/>incominciato a scendere nel mare, vedr&agrave; l'acqua della <lb/>tinozza A risalire su per il sifone BC, infin tanto che <lb/>tutta venga a travasarsi in E. </s>

<s>Dai quali esperimenti, dice <lb/>il Sinclaro, si raccoglie per certo &ldquo; quod Campanae aeris <lb/>elaterium descendendo multum intendatur, multumque ascendendo remitta&shy;<lb/>tur, quod in omne aevum inexplicabile manebit, nisi id ex aquae pressura <lb/>oriri dicas &rdquo; (ibid., pag. </s>

<s>239). </s></p><p type="main">

<s>Cotali esperienze non son facili &egrave; vero a farsi da un Filosofo, non av&shy;<lb/>vezzo ai disagi, e non esperto dell'arte dei marangoni. </s>

<s>Suggerisce perci&ograve; il <lb/>Sinclaro che si costruisca una Campana in piccolo, tanto ch'ella possa ca&shy;<lb/>pire in se un Barometro, e, senza dover profondarsi insieme con lo stru&shy;<lb/>mento n&egrave; sotto l'acqua de'laghi, n&egrave; sotto quella de'mari; seduti comoda&shy;<lb/>mente sulla sponda di un vivaio, osservarne gli effetti. </s>

<s>In ogni modo qua&shy;<lb/>lunque Filosofo pi&ugrave; delicato potrebbe rendere visibile a s&egrave;, e a'suoi scolari, <lb/>l'inflaccidirsi della vescica, fatta entrare, mentre era gonfia, in un bicchiere, <lb/>il quale arrovesciato si spinga colla mano, pi&ugrave; profondamente che sia pos&shy;<lb/>sibile, sotto l'acqua ricevuta in un vaso di vetro. </s></p><p type="main">

<s>Il Pascal, il Boyle e il Sinclaro, con gli sperimenti fin qui descritti, ba&shy;<lb/>stano a persuaderci che i Fisici di Europa avevano cacciati gi&agrave; dalla scienza <lb/>i pregiudizi peripatetici, quando ancora i nostri, imbevuti degl'insegnamenti <lb/>di Galileo, ripetevano con sicurt&agrave; che nessun fluido pesa nel suo proprio ele&shy;<lb/>mento. </s>

<s>&Egrave; da notare per&ograve; che i tre Autori commemorati non pretendevano <lb/>di esser venuti a insegnare nulla di nuovo, contenti a confermare una ve-<pb xlink:href="020/01/3202.jpg" pagenum="163"/>rit&agrave; combattuta, con la pi&ugrave; evidente prova dei fatti. </s>

<s>Cos&igrave;, il Boile non fa altro <lb/>che moltiplicare le sperienze dello Stevino, e renderle pi&ugrave; concludenti, ma <lb/>il Pascal e il Sinclaro, oltre a quelle dello Stevino, seguono altre pi&ugrave; pros&shy;<lb/>sime tradizioni, ravvivate da quel concorrere che facevasi d'ogni parte a il&shy;<lb/>lustrare l'esperienza famosa del Torricelli. </s>

<s>La cosa insomma si riduce a que&shy;<lb/>sto: che fu propriamente in Italia fabbricata l'arme, per abbattere l'orgo&shy;<lb/>glio peripatetico di un colpo, e furono d'Italiani le braccia, che lo menarono, <lb/>non lasciando ai successori altro che il merito di finir di uccidere il nemico <lb/>caduto, o la baldanza di fare intorno al suo cadavere festa e tripudio. </s>

<s>Che <lb/>se la vittoria s'attribuisce agli stranieri &egrave; perch&egrave; il Torricelli non appari&shy;<lb/>sce che quale inventore dell'esperienza, lo splendor della quale invenzione <lb/>eccliss&ograve; in lui un merito molto maggiore, di aver cio&egrave; speculate altres&igrave; le <lb/>ragioni dell'esperienza: ragioni che, riferendosi alle propriet&agrave; de'fluidi, seco <lb/>stesso comunicanti o con altri, illustravano mirabilmente, quasi sopraesal&shy;<lb/>tandole, le comuni leggi dell'Idrostatica. </s></p><p type="main">

<s>Un tale tesoro di speculazioni fu riversato nel privato erario di Miche&shy;<lb/>langiolo Ricci, amico e maestro a quel Tommaso Cornelio, che, ancora gio&shy;<lb/>vane e sconosciuto, pubblicava nel 1648, col titolo <emph type="italics"/>De platonica circumpul&shy;<lb/>sione,<emph.end type="italics"/> una sua epistola pregevolissima, perche vi si raccoglieva, ordinava e <lb/>illustrava tutto ci&ograve; che, intorno all'Idrodinamica, e, a proposito della teoria <lb/>del Barometro, intorno all'Idrostatica, aveva il Torricelli insegnato a voce e <lb/>per lettere al Ricci. </s>

<s>I quali insegnamenti rimeditando io, dice il Cornelio, <lb/>&ldquo; sequens experimentum tentavi: Vitreum orbem, exiguo pertusum foramine, <lb/>in profundiorem aquam mergebam, ostiolumque deorsum vergens digito obtu&shy;<lb/>rabam, ut mox orbis in auras evectus indicaret semper maiorem atque ma&shy;<lb/>iorem aquae copiam in eumdem ingestam, qno profundius ille penetrasset. </s>

<s><lb/>Et res quidem ex sententia successit. </s>

<s>Nam aqua eo maiori nisu, per orbis <lb/>foramen, intruditur, quo illa fuerit altior, atque interea aer in orbe conten&shy;<lb/>tus in minus atque minus spatium cogitur, donec impulsus, a superstantis <lb/>aquae pondere proveniens, sit aequalis conatui, quo aer resistit ne violenter <lb/>comprimatur, unde, aperto deinde foramine, ac deorsum spectante, aqua fo&shy;<lb/>ras extruditur a vi aeris, iuxta debitam mensuram, se se iterum expanden&shy;<lb/>tis &rdquo; (<emph type="italics"/>Appendix ad Progymn.,<emph.end type="italics"/> Neapoli 1688, pag. </s>

<s>343). </s></p><p type="main">

<s>Dice il Cornelio tanto esser piaciute le speculazioni, e l'esperienze messe <lb/>nel suo libretto, che alcuni se le appropriarono. </s>

<s>Non potremmo asserir con <lb/>certezza se, fra'complici di queste usurpazioni, fosse anche il Borelli, il quale, <lb/>a dimostrar che l'acqua gravita in s&egrave; stessa, e con tanto maggior forza, <lb/>quanto &egrave; pi&ugrave; profonda; adduceva, fra le altre, come di sua propria inven&shy;<lb/>zione, l'esperienza descritta trent'anni prima dal suo concittadino. </s>

<s>Comun&shy;<lb/>que sia, a ravvedersi di ci&ograve;, che credeva esser vero sull'autorit&agrave; di Galileo, <lb/>concorsero nel Borelli altre cause, fra le quali, come nel Pascal e nel Sin&shy;<lb/>claro, lo studio de'fenomeni barometrici. </s>

<s>Nel fare il vuoto, specialmente con <lb/>l'acqua, s'ebbe a osservare un brulichio nel tubo, simile a quel che fa l'acqua <lb/>stessa bollendo al fuoco: brulichio che, quanto pi&ugrave; saliva, tanto pi&ugrave; mostra-<pb xlink:href="020/01/3203.jpg" pagenum="164"/>vasi fervoroso. </s>

<s>Il Borelli spiegava il fatto col dire che l'aria, chiusa dentro <lb/>alle bollicelle, essendo, via via che si sale, meno compressa dal peso del&shy;<lb/>l'acqua ambiente, si dilata, e perci&ograve; si rendono esse bollicelle pi&ugrave; cospicue, <lb/>e appariscono pi&ugrave; frequenti. </s>

<s>&ldquo; In pulcherrimo instrumento torricelliano, in <lb/>quo vacuum mediante aqua efficitur, videmus ab aqua tantam copiam am&shy;<lb/>pullarum aerearum egredi, ut repraesentet ebullitionem, quam efficere solet <lb/>fervor ignis in eadem aqua. </s>

<s>Et hoc pendet ex eo quod particulae minimae <lb/>aeris, ibidem, non ut prius comprimuntur ab ingenti pondere aereae regio&shy;<lb/>nis, sed solummodo ab exigua gravitate aquae incumbentis, quod persuade&shy;<lb/>tur ex eo, quod profundiora granula aeris, quae ob parvitatem fere incon&shy;<lb/>spicua erant, quo magis ad summitatem aquae accedunt, eo magis amplian&shy;<lb/>tur, inflantur, grandioresque ampullas constituunt, prout magis vis elastica <lb/>aeris, libertatem nacta, ampliare dilatareque easdem ampullas potest &rdquo; (<emph type="italics"/>De <lb/>motion natur.<emph.end type="italics"/> cit., pag. </s>

<s>552). </s></p><p type="main">

<s>Ai Peripatetici, fra'quali possiam citare il gesuita Daniello Bartoli, osti&shy;<lb/>nati in professare il principio che l'acqua in mezzo all'acqua non pesa, non <lb/>piacque punto la ragion del Borelli, e confessando pure essere stato ci&ograve; detto <lb/>da lui ingegnosamente, non per&ograve; toglie, soggiungevano, il potersi recare il <lb/>fatto ad un'altra ragione, &ldquo; cio&egrave; al venirsi scontrando, in quei diciassette <lb/>cubiti di salita, in altre bolle d'aria, e con esse unendosi formarne di mol&shy;<lb/>tissime piccole una grande &rdquo; (<emph type="italics"/>Del ghiaccio,<emph.end type="italics"/> Roma 1681, pag. </s>

<s>147). </s></p><p type="main">

<s>Ma la principale occasione di riconoscere, e detestare la falsit&agrave; dell'as&shy;<lb/>sunto peripatetico, venne al Borelli ne'frequentati congressi dell'Accademia <lb/>del Cimento, quando si volle discutere la questione della leggerezza positiva. </s>

<s><lb/>Potrebb'essere che il Cornelio, toltasi dal volto la maschera di Timeo Lo&shy;<lb/>crese, e fattosi riconoscere per colui, che tanti meriti s'era venuto acqui&shy;<lb/>stando in tutti gli ordini della Fisica sperimentale; avesse, con l'epistola <emph type="italics"/>De <lb/>circumpulsione<emph.end type="italics"/> raccolta in un volume co'Proginnasmi, eccitato l'ingegno dei <lb/>suoi connazionali. </s>

<s>In ogni modo le parole, dal segretario dell'Accademia pre&shy;<lb/>messe all'argomento, commemorano Platone, autor del Dialogo del Timeo, <lb/>come precursore antico della verit&agrave;, che si voleva confermare con le nuove <lb/>esperienze. </s>

<s>Ma di queste, come di tutte le altre naturali esperienze, si d&agrave; <lb/>dagli Accademici solamente un <emph type="italics"/>saggio<emph.end type="italics"/> di quel tanto pi&ugrave;, e forse meglio, che <lb/>da loro s'era operato. </s>

<s>Gli operatori poi pi&ugrave; efficaci, a cotesto tempo, si sa <lb/>che erano il Borelli e il Viviani, i quali tanto ebbero a persuadersi del bi&shy;<lb/>sogno di assicurare la scienza del moto dalle pericolose incursioni peripate&shy;<lb/>tiche, che s'affaccendarono a speculare ragioni, e ad ammannire esperienze, <lb/>per provare che non vi &egrave; leggerezza positiva, e che l'acqua, l'aria e ogni <lb/>altro fluido insomma fa dentro il proprio fluido la medesima forza all'in gi&ugrave;, <lb/>che fuori di esso. </s>

<s>E perch&egrave; tali argomenti, nel libro scritto a nome di tutta <lb/>l'Accademia, non potevano aver luogo, gli fece il Borelli, per suo proprio <lb/>conto, pubblicamente noti nell'opera <emph type="italics"/>De motionibus naturalibus a gravitate <lb/>pendentibus,<emph.end type="italics"/> bench&egrave; gli altri del Viviani si rimangano tuttavia sconosciuti. </s>

<s><lb/>E perci&ograve; noi gli daremo ora alla luce, nella loro propria scrittura, essendoci <pb xlink:href="020/01/3204.jpg" pagenum="165"/>bastata la pazienza di ricavarla dal manoscritto pi&ugrave; informe, e pi&ugrave; penosa&shy;<lb/>mente leggibile, di quanti altri mai ci siano fin qui capitati. </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE I. &mdash; <emph type="italics"/>Il peso di qualsisia porzione di fluido grave sta&shy;<lb/>gnante fa attualmente, dentro il proprio fluido, la medesima forza allo <lb/>in gi&ugrave;, che fuori di esso.<emph.end type="italics"/> Imperocch&egrave; il peso non &egrave; proprio, libero e indi&shy;<lb/>pendente, ma necessario. </s>

<s>Onde non per elezione o per accidente fa forza <lb/>allo in gi&ugrave;, ma per necessit&agrave;. </s>

<s>Per lo che, dovunque egli si sia o dentro <lb/>o fuori del proprio fluido, &egrave; necessario che faccia la medesima forza allo <lb/>in gi&ugrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il medesimo si dimostra con l'esperienza. </s>

<s>Imperocch&egrave; se, dentro qual&shy;<lb/>sisia fluido stagnante sul fondo di uua bilancia, s'infonder&agrave; una mole del <lb/>medesimo fluido, che sia di doppio peso; &egrave; manifesto che sforzer&agrave; attual&shy;<lb/>mente la bilancia detta con doppia forza allo in gi&ugrave;. </s>

<s>Dunque &egrave; manifesto che <lb/>il peso della mole aggiunta fa attualmente nel proprio fluido la medesima <lb/>forza allo in gi&ugrave;, che fuori di esso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE II. &mdash; <emph type="italics"/>Tutto il peso di un fluido grave stagnante ag&shy;<lb/>grava perpendicolarmente il fondo, perpendicolarmente sottoposto.<emph.end type="italics"/> &Egrave; evi&shy;<lb/>dente per l'esperienza. </s>

<s>Imperocch&egrave; se, alla forza del di lui peso non aver&agrave; <lb/>il fondo dato momento di resistenza bastante, verr&agrave; da questo sforzato ma&shy;<lb/>nifestamente a cedere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE III. &mdash; <emph type="italics"/>Il peso di qualunque porzione superiore di un <lb/>fluido grave stagnante aggrava perpendicolarmente la porzione inferiore, <lb/>perpendicolarmente sottopostale. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sul fondo AB (fig. </s>

<s>85) intendasi stagnante qualsiasi <lb/><figure id="id.020.01.3204.1.jpg" xlink:href="020/01/3204/1.jpg"/></s></p><p type="caption">

<s>Figura 85.<lb/>porzione di fluido EB e sopra EB qualsiasi altra porzione <lb/>perpendicolarmente sovrappostale. </s>

<s>Dico che il peso di CD ag&shy;<lb/>grava perpendicolarmente la porzione EB, perpendicolarmente <lb/>sottopostale. </s>

<s>Imperocch&egrave;, se &egrave; possibile, non sia dal peso della <lb/>porzione CD aggravata perpendicolarmente la porzione EB. </s>

<s><lb/>Dunque non potr&agrave; EB che col proprio peso aggravare perpen&shy;<lb/>dicolamente il fondo. </s>

<s>Dunque non sar&agrave; il fondo detto, dal peso di tutto il <lb/>fluido CB, perpendicolarmente aggravato. </s>

<s>Il che &egrave; impossibile per quel che <lb/>si &egrave; dimostrato. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>&ldquo; Il medesimo direttamente. </s>

<s>&rdquo;<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>&ldquo; Tutto il peso del fluido BC aggrava perpendicolarmente il fondo AB, <lb/>perpendicolarmente sottopostoli. </s>

<s>Dunque tutto il peso di CB fa forza perpen&shy;<lb/>dicolarmente verso AB. </s>

<s>Dunque per necessit&agrave; il peso ancora della porzione <lb/>CD fa perpendicolarmente forza verso AB. </s>

<s>Ma &egrave; impossibile far forza per&shy;<lb/>pendicolarmente verso AB, perpendicolarmente sottoposto, senza far forza <lb/>perpendicolarmente verso la porzione EB, posta perpendicolarmente fra essa <lb/>ed AB; dunque &egrave; necessario che il peso della porzione CD, facendo forza <lb/>perpendicolarmente verso AB, la faccia ancora verso ED, e perci&ograve; perpendi&shy;<lb/>colarmente l'aggravi. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/3205.jpg" pagenum="166"/><p type="main">

<s><emph type="center"/><emph type="italics"/>&ldquo; Il medesimo altrimenti. </s>

<s>&rdquo;<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>&ldquo; Imperocch&egrave;, per qualunque cagione altri dica la superficie ED, dal <lb/>peso della mole sovrastante CD, non essere attualmente aggravata; cagione <lb/>certo non dir&agrave; esserne la di lui fluidezza. </s>

<s>Ma, presupposta la superficie ED <lb/>consistente, &egrave; manifesto, per le cose dette, che, di qualunque natura o gra&shy;<lb/>vezza in specie si dia la mole ED, sar&agrave; dal peso di CD attualmente aggra&shy;<lb/>vata; dunque, data ancora invece della consistenza la fluidezza, di qualun&shy;<lb/>que natura o gravit&agrave; in specie la ED si supponga; non meno del peso della <lb/>mole sovrastante attualmente &egrave; aggravata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Le quali cose s&igrave; per minuto ci siamo sforzati di mostrare, perch&egrave; si <lb/>possa vedere se contro la ragione sia o no l'affermare il contrario, cio&egrave; che <lb/>il fluido nel fluido proprio attualmente non gravi, n&egrave; perci&ograve; le parti inferiori <lb/>di esso siano, dal peso delle superiori, attualmente aggravate. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Il principal motivo di dubitare della verit&agrave; sopraddetta furono alcune <lb/>esperienze, s&igrave; manifestamente a prima vista contrarie, che non &egrave; maraviglia <lb/>se, contro la ragione assai per altro evidente, avesse luogo nell'animo di <lb/>molti la contraria opinione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Perch&egrave; dunque, se possibile fia, ogni scrupolo tor si possa intorno alla <lb/>verit&agrave; di punto cos&igrave; importante, dal quale, come vedremo appresso, gran parte <lb/>della naturale Filosofia dipende, egli &egrave; sopratutto necessario che, deposta ogni <lb/>propria passione, sopra di essa diligente riflessione facciamo. </s>

<s>Imperocch&egrave; mi <lb/>do a credere che se a sufficienza mostreremo gli effetti, in esse esperienze <lb/>contenuti, non essere alla detta verit&agrave;, se non in apparenza, contrari, e tanto <lb/>esser lontano che all'attuale aggravamento delle parti fluide nel proprio fluido <lb/>repugni che, da esso presupposto, questo e altri fatti necessariamente pro&shy;<lb/>vengano; mi do a credere, dico, che baster&agrave;, per fare, in chi altrimenti fin <lb/>ora ha creduto, cessare ogni dubbio. </s>

<s>L'esperienze dunque son queste: &rdquo; </s></p><p type="main">

<s>&ldquo; I.a I marangoni, stando sott'acqua, non sentono peso dall'acqua, che <lb/>all'altezza talvolta di venti o di pi&ugrave; braccia gli sovrasta. </s>

<s>Dal che pare a ta&shy;<lb/>luno evidente che il peso dell'acqua non aggravi i corpi, che in essa sono <lb/>e per conseguenza che ella nel proprio luogo attualmente non pesi. </s>

<s>Ma, per <lb/>la Ia, la conseguenza &egrave; falsa. </s>

<s>Che il peso dell'acqua aggravi e prema attual&shy;<lb/>mente i corpi, che in essa sono, &egrave; per altro dalla esperienza manifesto. </s>

<s>Im&shy;<lb/>perocch&egrave; pongasi sotto l'acqua un mantice dilatato, e per tutto ben chiuso, <lb/>e si vedr&agrave; chiaramente che, quanto maggior copia di acqua vi s'andr&agrave; di <lb/>sopra aggiungendo, tanto maggiormente verr&agrave; dal di lei peso abbassato e <lb/>ristretto. </s>

<s>Inoltre pongasi ferma sott'acqua una palla di sottilissimo vetro ben <lb/>chiusa, e si vedr&agrave; che, aggiungendo nova acqua, verr&agrave; finalmente, per il di <lb/>lei peso, a schiacciarsi e a rompersi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; II.a Una secchia piena d'acqua, essendo nell'acqua, si tira su con la <lb/>medesima, anzi minor forza, che fuori vuota: eppure, oltre il proprio peso, <lb/>vi &egrave; ancora quello di tutta la mole che le sovrasta. </s>

<s>Ci&ograve; stante, come dun&shy;<lb/>que dicono eglino che l'acqua nell'acqua attualmente pesa? </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/3206.jpg" pagenum="167"/><p type="main">

<s>&ldquo; Ma perch&egrave; con un simile effetto resti chiara la verit&agrave; rispondano ora <lb/>a me. </s>

<s>Una secchia piena d'acqua, essendo nella bilancia, se dalla banda op&shy;<lb/>posta ve ne sar&agrave; similmente un'altra, si tira su colla medesima forza, anzi <lb/>minore, che fuori vuota. </s>

<s>Come dunque ci&ograve; stante l'acqua nella bilancia at&shy;<lb/>tualmente pesa? </s>

<s>E che attualmente dentro di essa pesi lo dichiarano il fondo e <lb/><figure id="id.020.01.3206.1.jpg" xlink:href="020/01/3206/1.jpg"/></s></p><p type="caption">

<s>Figura 86.<lb/>i fili che la sostengono, quando, non facendo al <lb/>di lei peso resistenza bastante, sforzati finalmente <lb/>si strappano. </s>

<s>Che diremo di ci&ograve;? </s>

<s>Non altro certo, <lb/>se non che la secchia piena d'acqua pesi attual&shy;<lb/>mente nella bilancia. </s>

<s>Ma perch&egrave; l'altra opposta <lb/>pesa attualmente ancor ella, e con quella contrap&shy;<lb/>pesando la sostenta, fa conseguentemente che, a <lb/>tirarla su, alcuna resistenza non si senta. </s>

<s>Ora, <lb/>il medesimo a capello nel caso nostro succede. </s>

<s><lb/>Imperocch&egrave;, posta la secchia piena dentro l'acqua, viene il di lei peso, insieme <lb/>col peso della mole che le sovrasta, a contrappesarsi col peso di una mole <lb/>opposta, che per di sotto la sostenta. </s>

<s>Il che per chiarezza accenneremo con <lb/>la seguente figura (86). &rdquo; </s></p><p type="main">

<s>&ldquo; Sia AB superficie dell'acqua stagnante AC, dentro la quale intendasi <lb/>il vaso S, la cui superficie inferiore DGE, con l'acqua sovrastante, costitui&shy;<lb/>sca la mole FGL. </s>

<s>Pesando dunque FGL, e facendo forza allo in gi&ugrave;, sfor&shy;<lb/>zer&agrave; la mole perpendicolarmente sottoposta HGN, e questa non pu&ograve; cedere <lb/>se non si riflette e spigne allo in su una mole, quale sia per es. </s>

<s>NB. </s>

<s>Ma il <lb/>peso di questa fa resistenza ad esser mosso allo in su, alla forza dunque allo <lb/>in gi&ugrave; del peso FGL s'oppone di sotto la forza del peso GHN, e perci&ograve; la <lb/>mole HB, con la mole FN contrappesandosi, come appresso dimostreremo, <lb/>la viene di sotto a sostentare. </s>

<s>Onde non si pu&ograve;, a tirare su il vaso S, alcuna <lb/>resistenza sentire, non altrimenti che nella bilancia succede. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E perch&egrave; chiaramente si vegga come, dal sostentamento dell'acqua <lb/>contrappesantesi per di sotto, tal mancamento di resistenza provenga, pon&shy;<lb/>gasi di maniera il vaso S nell'acqua, che l'acqua GHN o altra non lo possa <lb/><figure id="id.020.01.3206.2.jpg" xlink:href="020/01/3206/2.jpg"/></s></p><p type="caption">

<s>Figura 87.<lb/>di sotto sostentare, perch&egrave; nel tirarlo in su si sentir&agrave; su&shy;<lb/>bito tutto il peso e dell'acqua che &egrave; nel vaso, e di quella <lb/>ancora che perpendicolarmente gli sovrasta. </s>

<s>L'esperienza <lb/>pu&ograve; farsi facilmente cos&igrave;: Sia il fondo OC (fig. </s>

<s>87) del <lb/>continente prolungato, verso la parte M, in un tubo ci&shy;<lb/>lindrico, e la superficie inferiore del vaso S rotondo sia <lb/>tutta profondata dentro di esso, sicch&egrave; l'acqua stagnante <lb/>AC non iscorra sotto S. </s>

<s>E per levare ogni sospetto di <lb/>paura di vuoto, come anco per altro, vi siano, di lato alla detta superficie <lb/>inferiore, gli spiragli K, L, con le loro animelle, per potervi entrare libera&shy;<lb/>mente l'aria esteriore. </s>

<s>Dico che, tirando in su il vaso S, si sentir&agrave; il peso <lb/>dell'acqua che &egrave; nel vaso, e di tutta la mole sovrastante. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Intese bene le ragioni degli effetti predetti, si potranno facilmente in-<pb xlink:href="020/01/3207.jpg" pagenum="168"/>tendere quelle ancora di qual si voglia altri effetti simili che, contro l'at&shy;<lb/>tuale aggravamento delle parti fluide si sogliono o si potrebbero addurre, <lb/>quali, non parendo necessario l'esaminarli qui ad uno ad uno, ci siam con&shy;<lb/>tentati di mostrarne la cagione universale, onde possa ciascuno ai dubbi par&shy;<lb/>ticolari per s&egrave; medesimo sodisfare &rdquo; (MSS. Cim., T. XXXIV, fol. </s>

<s>119-20). </s></p><p type="main">

<s>Le repressioni per cui s'alleggerisce il peso della secchia, nell'espe&shy;<lb/>rienza illustrata dalla figura 86, promette il Viviani, com'abbiamo udito, di <lb/>dimostrarle appresso, d'onde apparisce l'intenzion dell'Autore di proseguire, <lb/>intorno all'argomento, il discorso. </s>

<s>E cos&igrave; fece davvero, come si trova poco <lb/>pi&ugrave; avanti, svolgendo le pagine del manoscritto. </s>

<s>Ma cos&igrave; fecondo, e di cos&igrave; <lb/>grande importanza si present&ograve; alla mente dello stesso Viviani il soggetto, che <lb/>dell'equilibrio de'liquidi in s&egrave; medesimi, e con altri liquidi comunicanti, volle <lb/>di proposito trattarne in vari scritti, ora lasciati per qualche tempo interrotti, <lb/>ora ripresi, i quali, essendo stati da noi qua e l&agrave; per le disperse carte rac&shy;<lb/>colti, si pubblicheranno in altre occasioni. </s>

<s>Intanto &egrave; da veder come concor&shy;<lb/>resse il Borelli a ravviar l'Idrostatica sulla medesima rettitudine de'sentieri. </s></p><p type="main">

<s>Il capitolo terzo <emph type="italics"/>De motionibus naturalibus,<emph.end type="italics"/> come general soggetto, da <lb/>trattarsi in quelle XXIV proposizioni ch'ei comprende, porta scritto questo <lb/>titolo in fronte: <emph type="italics"/>Quodlibet corpus fluidum eorum quae innituntur super&shy;<lb/>ficiei Telluris grave est, exercetque vim suae gravitatis etiam dum in pro&shy;<lb/>prio loco, et in ipsomet fluido universali sui generis consistit ac quiescit<emph.end type="italics"/><lb/>(pag. </s>

<s>33). Incomincia l'Autore a far osservare che l'annunziata verit&agrave; si con&shy;<lb/>clude dall'ipotesi, e s'argomenta certissimamente dai processi, tenuti da Ar&shy;<lb/>chimede in dimostrare le sue proposizioni. </s>

<s>E nonostante, soggiunge, vollero <lb/>ci&ograve; negare, e tutt'altrimenti sentirono i Peripatetici, &ldquo; qui censent non sem&shy;<lb/>per verum esse quod partes superiores corporis gravis comprimant, et vim <lb/>inferant inferioribus et contiguis, nisi infimae partes leves sint absolute vel <lb/>respective. </s>

<s>Unde concedunt terram ex. </s>

<s>gr. </s>

<s>super aquam aut super aerem po&shy;<lb/>sitam vim et operationem gravitatis et compressionis exercere, non itidem <lb/>aquam super ipsam terram collocatam, nec aerem aquae incumbentem. </s>

<s>Immo <lb/>nec aerem supra aerem constitutum nec aquam supra aquam positam &rdquo; (ibid., <lb/>pag. </s>

<s>33, 34). </s></p><p type="main">

<s>I primi e principali argomenti, usati dal Borelli per confutare i Peripa&shy;<lb/>tetici, eccettuata l'esperienza della bolla di vetro, descritta gi&agrave; nell'epistola <lb/>del Cornelio, e ripetuta qui nella XV proposizione; consistono nel dimostrar <lb/>la verit&agrave; dell'ipotesi d'Archimede, e di tutte le conseguenze di lei. </s>

<s>Rivol&shy;<lb/>giamo indietro lo sguardo sopra la nostra figura 78, che pu&ograve; servire a illu&shy;<lb/>strar la V proposizione <emph type="italics"/>De insidentibus humido.<emph.end type="italics"/> Se l'umido ALO, dice l'Au&shy;<lb/>tore, &egrave; in equilibrio con l'umido OLB, sopraggiuntovi l'umido EO da una <lb/>parte, e l'umido OF dall'altra; le due superficie AO, OB saranno ugual&shy;<lb/>mente premute. </s>

<s>Ond'&egrave; manifesto che Archimede, al contrario dei Peripate&shy;<lb/>tici, suppone che l'umido nell'umido pesi. </s>

<s>Per confermare la verit&agrave; della quale <lb/>supposizione, giacch&egrave; le due predette superficie AO, OB si riguardano come il <lb/>fondo solido di un vaso, il Borelli dimostra, nelle proposizioni XIII e XIV, che <pb xlink:href="020/01/3208.jpg" pagenum="169"/>un tal fondo &egrave; veramente premuto, come, lasciati tutti gli altri discorsi, lo atte&shy;<lb/>stano i fatti, vedendosi l'acqua &ldquo; ad ingentem altitudinem elevata, nedum so&shy;<lb/>lum ac fundum vasis inflectit, sed ipsum multoties diffringit &rdquo; (ibid., pag. </s>

<s>41). </s></p><p type="main">

<s>Cos&igrave; disposte le cose, passa Archimede a dimostrare che il solido pi&ugrave; <lb/>leggero, immerso per la sua parte C, &egrave; in equilibrio, perch&egrave; la mole H del&shy;<lb/>l'umido, uguale alla mole solida immersa, pesa quanto il solido intero. </s>

<s>Se <lb/>dunque tutti i Fisici e i Matematici del mondo hanno ripetuto e ripetono <lb/>queste dimostrazioni, essendo H nell'umido, tutti i Fisici e i Matematici del <lb/>mondo con Archimede convengono che l'umido dentro l'umido pesi, perch&egrave; <lb/>altrimenti, dice il Borelli, s'incorrerebbe nell'assurdo che il nulla facesse <lb/>equilibrio a una gravezza assoluta. </s>

<s>Di pi&ugrave; si riducevano i Peripatetici, col <lb/>loro assunto, nell'impossibilit&agrave; di spiegare come un solido pesi meno nel&shy;<lb/>l'acqua che nell'aria. </s>

<s>Con la dottrina di Archimede si spiega il fatto, dicendo <lb/>che l'acqua collaterale spinge in su l'acqua a esso solido sottoposta: ra&shy;<lb/>gione che non varrebbe, quando fosse vero che l'acqua nell'acqua non eser&shy;<lb/>cita il momento della sua gravit&agrave; naturale. (ivi, pag. </s>

<s>44, conferito con quel <lb/>che leggesi a pag. </s>

<s>168). </s></p><p type="main">

<s>Bastino questi accenni, a potere estimar giustamente l'efficacia degli ar&shy;<lb/>gomenti del Borelli: efficacia, che principalmente consiste nel dimostrar come <lb/>l'ipotesi peripatetica rovescia tutta l'Idrostatica da'suoi fondamenti. </s>

<s>E per&shy;<lb/>ch&egrave; quella ipotesi fu ricevuta pure da Galileo, si direbbe che il capitolo III <lb/><emph type="italics"/>De motionibus naturalibus<emph.end type="italics"/> fu scritto dal Discepolo apposta, per confutare <lb/>una delle pi&ugrave; perniciose dottrine del suo maestro. </s>

<s>Cos&igrave; &egrave; di fatto. </s>

<s>Risovven&shy;<lb/>gaci di aver letto, nel Discorso famoso intorno alle galleggianti, esser falsis&shy;<lb/>simo che l'acqua possa accrescere peso alle cose in essa collocate, <emph type="italics"/>perch&egrave; <lb/>l'acqua nell'acqua non ha gravit&agrave; veruna, poich&egrave; ella non vi discende.<emph.end type="italics"/><lb/>Contro questa ragione di Galileo &egrave; manifestamente scritta dal Borelli la pro&shy;<lb/>posizione XXII: <emph type="italics"/>Corpora, in bilance aequilibrata, ideo quiescunt et torpent, <lb/>quia gravitatem exercent, comprimunturque aequalibus viribus ab ambien&shy;<lb/>tibus corporibus pariter aequilibratis<emph.end type="italics"/> (ibid. </s>

<s>pag. </s>

<s>55). Dimostrata la quale, <lb/>immediatamente si soggiunge: &rdquo; Eodem fere modo in aqua idem aequili&shy;<lb/>brium effici manifestum est, proindeque partes ipsius aquae partim superne <lb/>comprimi a superstantibus aquae partibus, partim vero inferne sursum expelli, <lb/>non propria vi, sed pondere collateralis aquae, quae cum illa libram imagi&shy;<lb/>nariam, vel siphonem constituit &rdquo; (ibid., pag. </s>

<s>57). </s></p><p type="main">

<s>Bench&egrave; dunque la vera intenzion del Borelli sia facile penetrarla, non <lb/>&egrave; per&ograve; ch'ei ne faccia il minimo segno. </s>

<s>Anzi col&agrave;, dove nella proposizione CC <lb/>gli sarebbe occorso di correggere l'errore di Galileo, il quale co'Peripatetici <lb/>teneva non pesar l'aria costituita sopra l'acqua; par che lo voglia scusare, <lb/>dicendo che il peso dell'aria stessa, scesa nella fossetta scavatasi dall'assi&shy;<lb/>cella d'ebano galleggiante, &egrave; di cos&igrave; lieve momento, da potersi anche trascu&shy;<lb/>rare. </s>

<s>&ldquo; Ex hydrostaticis, moles aquae aequalis spatio AOSB (fig. </s>

<s>69 del ca&shy;<lb/>pitolo prec.) aeque ponderat ac lamina IS, una cum aere BI, qui, ob insen&shy;<lb/>sibilem eius gravitatem, negligi potest &rdquo; (ibid., pag. </s>

<s>414). </s></p><pb xlink:href="020/01/3209.jpg" pagenum="170"/><p type="main">

<s>Si diceva che pare voglia il Borelli scusare il suo Maestro, bench&egrave; in <lb/>effetto non sia cos&igrave;, perch&egrave; Galileo non trascur&ograve; il peso dell'aria nella fos&shy;<lb/>setta come insensibile, ma come nullo affatto. </s>

<s>Sopra le denudate spalle del&shy;<lb/>l'esoso Cartesio sfoga piuttosto il Borelli l'ira della sua sferza (propos. </s>

<s>XXXVI, <lb/>pag. </s>

<s>73), giacch&egrave; &egrave; un destino che i due orgogliosi competitori del nuovo <lb/>principato della scienza, mentre facevano aspro duello insieme, per l'acqui&shy;<lb/>sto di una verit&agrave;, o per il merito di una scoperta, cadessero poi bene spesso, <lb/>pacificamente umiliati, nella medesima fossa. </s>

<s>Il Cartesio, inspiratosi forse a <lb/>quel che il microscopio gli rivelava nel formaggio e nell'aceto, immagin&ograve; che <lb/>le molecole componenti l'acqua rappresentassero la figura e la lubricit&agrave; delle <lb/>anguille, per cui non fossero n&egrave; gravi n&egrave; leggere in s&egrave; stesse, come quelle <lb/>che continuamente si movono per tutti i versi: conclusione, alla quale Ga&shy;<lb/>lileo era invece venuto dal considerare quelle stesse molecole costituite in una <lb/>assoluta impossibilit&agrave; di scendere e di salire. </s></p><p type="main">

<s>Che se tali riguardi di non offendere la reputazione del proprio mae&shy;<lb/>stro ebbe il Borelli, si pu&ograve; credere che non gli dovesse rimanere inferiore <lb/>il Viviani, il quale tanto riconoscendo importante dimostrare che il fluido nel <lb/>proprio fluido attualmente gravita, perch&egrave; da una tale verit&agrave; dipende gran <lb/>parte della Filosofia naturale; veniva a confessare che Galileo aveva sopra <lb/>falsi fondamenti, in gran parte, fondate le sue istituzioni. </s>

<s>Eppure non tra&shy;<lb/>sparisce un motto, nelle sue varie scritture d'Idrostatica, ch'ei l'abbia di&shy;<lb/>stese con l'intenzione di raddirizzare alla scienza i sentieri, e di liberarla da <lb/>quelle angustie, nelle quali l'aveva costretta il suo venerato Autore del Di&shy;<lb/>scorso intorno alle cose che si muovono, o che stanno nell'acqua. </s></p><p type="main">

<s>Alcuni loderanno forse questi atti del Viviani e del Borelli, molto simili <lb/>a quelli di un figlio, che ricopre di un velo pietosamente le vergogne del <lb/>padre. </s>

<s>Ma altri, ripensando che sotto quel velo si nascondeva un agguato, a <lb/>cui potevano rimaner facilmente presi i giovani studiosi; giudicarono meglio <lb/>di avvertirne, con pi&ugrave; ragionevole piet&agrave;, gl'incauti, di che il primo libero <lb/>esempio venne dato dalla cattedra stessa, dalla quale, pi&agrave; di un mezzo se&shy;<lb/>colo avanti, erasi lavorato l'insidioso artificio di quegli agguati. </s>

<s>Stefano Degli <lb/>Angeli, leggendo nello studio di Padova il celebre discorso idrostatico di Ga&shy;<lb/>lileo, aveva fatto notare ai suoi uditori che certi principii ivi professati non <lb/>erano veri, e giunto a quella general proposizione, nella quale l'Autore con&shy;<lb/>clude: <emph type="italics"/>Adunque la gravit&agrave; del solido IS<emph.end type="italics"/> (nella nostra figura 69, interca&shy;<lb/>lata nel capitolo avanti, e che corrisponde allo schema di Galileo) <emph type="italics"/>&egrave; uguale <lb/>alla gravit&agrave; di una mole d'acqua, eguale alla mole AS; ma la gravit&agrave; <lb/>del solido IS &egrave; la medesima che la gravit&agrave; del solido AS, composto del <lb/>solido IS e dell'aria ABCI; adunque tanto pesa tutto il solido composto <lb/>AOSB, quanto pesa l'acqua, che si conterrebbe nel luogo di esso compo&shy;<lb/>sto AOSB<emph.end type="italics"/> (Alb. </s>

<s>XII, 63); diceva liberamente l'Angeli che in questo ragio&shy;<lb/>namento si contiene una aperta fallacia, perch&egrave; anche l'aria ABCI &egrave; pesa, <lb/>n&egrave; il peso di lei pu&ograve; trascurarsi in un teorema, che si dimostra dall'Autore <lb/>con metodo matematico, e che si vuol da lui esaltare alla dignit&agrave; della Geo-<pb xlink:href="020/01/3210.jpg" pagenum="171"/>metria. </s>

<s>Essendo poi questa, come s'&egrave; detto, proposizion generale, tutte le <lb/>altre che ne dipendono son dal medesimo vizio contaminate. </s></p><p type="main">

<s>L'insegnamento orale, riconosciuta l'importanza dell'argomento, volle <lb/>poi l'Angeli ridurre in scritto, in que'dialoghi, che pubblic&ograve; <emph type="italics"/>Della gravit&agrave; <lb/>dell'aria e fluidi esercitata principalmente nelli loro omogenei,<emph.end type="italics"/> dove si sot&shy;<lb/>topongono al giudizio imparziale dei dotti le fallacie peripatetiche del Di&shy;<lb/>scorso intorno alle galleggianti. </s>

<s>Ond'essendo questo un coraggioso esempio <lb/>di filosofica libert&agrave;, per non essere men pericoloso allora, come ora, scrivere <lb/>contro Galileo, di quel che fosse pericoloso a Galileo stesso scrivere contro <lb/>Aristotile; recheremo nella sua integrit&agrave; dal Dialogo I l'interlocuzione che <lb/>esso Angeli, sotto il nome di Matematico di Padova, finge di aver avuto, in <lb/>tal proposito, con un certo Ofredi. </s></p><p type="main">

<s>&ldquo; OFREDI. &mdash; Il Galileo &egrave; d'opinione, in quel suo ammirabile trattato <lb/>delli galleggianti, che l'aria nell'acqua non graviti in conto alcuno. </s>

<s>Onde, <lb/>se V. S. dice di s&igrave;, contraria certo alla sua dottrina. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; MATEMATICO. &mdash; Io stimo che l'aria pesi nell'acqua, perch&egrave; io la tengo <lb/>per corpo grave, come pure &egrave; reputata dal Galileo medesimo; ond'essendo <lb/>tale, deve gravitar da per tutto. </s>

<s>Ma il Galileo porta ragione o esperienza al&shy;<lb/>cuna che l'aria nell'acqua non graviti? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; OFREDI. &mdash; No signore. </s>

<s>Solo lo suppone, come cosa nota e trivialis&shy;<lb/>sima, a carte 42, ove ricerca che grossezza pu&ograve; avere una laminetta, di qual <lb/>si sia materia, pi&ugrave; grave in specie dell'acqua, acciocch&egrave;, collocata legger&shy;<lb/>mente sopr'essa, non s'immerga. </s>

<s>Dice che la laminetta IS, nel suo schema, <lb/>entra nell'acqua, che se gli alza sopra, facendo li arginetti BC, AI, li quali <lb/>contengono una fossarella piena di aria, della quale e della laminetta si fa <lb/>un prisma AS. </s>

<s>Ora dice che quest'aggregato, il quale ha tanto momento, <lb/>quant'&egrave; quello d'una mole d'acqua ad esso uguale; ha tanta gravit&agrave;, quanta <lb/>&egrave; quella della sola laminetta IS, <emph type="italics"/>avvenga che,<emph.end type="italics"/> dice egli, <emph type="italics"/>la mole dell'aria <lb/>AC non cresca o diminuisca la gravit&agrave; della mole IS.<emph.end type="italics"/> Il medesimo da esso <lb/>viene assunto come cosa nota, nella proposizione generale, che segue a <lb/>carte 43. Onde, se questi supposti non sono veri, anco le dette proposizioni <lb/>saranno manchevoli. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; MATEMATICO. &mdash; Certo che essendo cos&igrave;, come realmente &egrave;, e questa <lb/>ed altre sue proposizioni, nelle quali suppone questa cosa, saranno difettose <lb/>in rigor geometrico, poich&egrave; in realt&agrave; AS &egrave; un aggregato di due corpi gravi, <lb/>e cos&igrave; l'acqua, eguale al prisma AS, deve pesare quanto pesano tutte due <lb/>assieme. </s>

<s>N&egrave; il modo di ritrovare l'altezza delli arginetti BC, AI, sar&agrave; total&shy;<lb/>mente quello, che insegna il Galileo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; OFREDI. &mdash; <emph type="italics"/>Quod parum distat nihil distare videtur, e, parum pro <lb/>nihilo reputatur.<emph.end type="italics"/> Onde, anco quando vi sia qualche variet&agrave;, questa sar&agrave; <lb/>tanto poca, che nulla pi&ugrave;. </s>

<s>Poich&egrave;, quanto pu&ograve; pesare un pochino d'aria, <lb/>quant'&egrave; il prisma AC? &rdquo; </s></p><p type="main">

<s>&ldquo; MATEMATICO. &mdash; Pochissimo certo. </s>

<s>Nulladimeno, signor Ofredi, potr&agrave; <lb/>essere che in pratica s'esperimentasse che la Natura non sprezzasse questo <pb xlink:href="020/01/3211.jpg" pagenum="172"/>poco peso, e che l'aria AC in fatti gravitasse, e il modo &egrave; questo. </s>

<s>Si prenda <lb/>la laminetta SI di materia, la quale nou si possa inzuppare, come sarebbe <lb/>argento, oro, ecc., e sia la massima, sicch&egrave;, niente pi&ugrave; grossa, si profondasse, <lb/>e si collochi nell'acqua. </s>

<s>&Egrave; manifesto che, se l'aria non aggiunge peso, come <lb/>dice il Galileo, anco quando s'alterasse, facendosi pi&ugrave; densa o pi&ugrave; rara, non <lb/>per questo la laminetta farebbe mutazione alcuna, quanto al discendere. </s>

<s>Ma <lb/>se l'aria AC in fatti gravita, ogni volta che, con qualche artificio, si far&agrave; pi&ugrave; <lb/>densa, ed in conseguenza pi&ugrave; grave; la laminetta SI subito discender&agrave;, per&shy;<lb/>ch&egrave; allora AS sar&agrave; pi&ugrave; grave in specie di altrettant'acqua. </s>

<s>Ma checch&egrave; suc&shy;<lb/>ceda di questa esperienza, io giudico che assolutamente non solo l'acqua, <lb/>ma anco l'aria graviti nella medesima acqua. </s>

<s>&rdquo; (Padova, 1671, pag. </s>

<s>20, 21). </s></p><p type="main">

<s>Avrebbe fatto meglio l'Angeli a descrivere con accuratezza l'esperienza, <lb/>e dimostrare che cos&igrave; il fatto succede, com'egli affermava, tanto pi&ugrave; che fa&shy;<lb/>cile glie ne porgevano allora il modo il Tubo torricelliano, e la Macchina <lb/>pneumatica. </s>

<s>Ma che avrebbe detto egli, che ne avrebbero detto i Lettori, se <lb/>il Bonaventuri fosse venuto 47 anni prima a mettere a loro sott'occhio la <lb/>lettera a Tolomeo Nozzolini, nella quale Galileo descrive e mostra di aver <lb/>fatto, rarefacendo l'aria al calore, la delicatissima esperienza, per dimostrar <lb/>con visibile effetto come l'aria stessa contenuta nella fossetta ha tal sensi&shy;<lb/>bile gravit&agrave;, che, col crescerne o col diminuirne il momento, conferisce effi&shy;<lb/>cacemente al sommergersi di pi&ugrave; o al respirare dell'assicella? </s>

<s>Avrebbero <lb/>detto tutti costoro che Galileo aveva riconosciuto il suo errore, e che voleva <lb/>emendarlo, indotti in questa opinione dal vedere essersi egli gi&agrave; ritrattato <lb/>rispetto a quel che aveva pronunziato della virt&ugrave; calamitica dell'aria in ri&shy;<lb/>tirare in su, dentro il bicchiere inverso, la pallina galleggiante di cera. </s>

<s>Or <lb/>chi potrebbe avere il minimo dubbio intorno alla verit&agrave; di un tal giudizio, <lb/>essendo le cose descritte nella lettera al Nozzolini di tanto chiara espres&shy;<lb/>sione? </s></p><p type="main">

<s>Cos&igrave;, come tutti giudicherebbero, fu giudicato a principio anche da noi, <lb/>che credemmo fosse avvenuta la conversione dall'essersi, mentr'era sotto i <lb/>torchi la prima edizione del Discorso intorno alle galleggianti, diffusa la no&shy;<lb/>tizia dell'Idrostatica steviniana, l'esperienza descritta nella quale, che cio&egrave; <lb/>tanto pesa un vaso pien d'acqua, quanto essendo quasi vuoto, per averne <lb/>occupato il luogo un solido fisso a un muro; aveva fatto a Galileo, in ri&shy;<lb/>spondere a'suoi contradittori, un si bel gioco. </s></p><p type="main">

<s>Rimaneva nonostante il fatto di tanta curiosit&agrave;, che per sodisfarla si sa&shy;<lb/>rebbe desiderata una dichiarazione espressa di questa repentina mutazione <lb/>d'idee. </s>

<s>Ma perch&egrave; dalla lettera al Nozzolini non s'aveva speranza di rica&shy;<lb/>varla, si pens&ograve; di ricorrere ad altri documenti, e fra questi a quelli parti&shy;<lb/>colarmente riguardanti l'Accademico incognito, di rispondere al quale, piut&shy;<lb/>tosto che allo stesso Nozzolini, tanto si vede premere a Galileo. </s>

<s>Di qui si <lb/>venne naturalmente per noi a ricercar quel libretto, stampato in Pisa nel 1612, <lb/>col titolo di <emph type="italics"/>Considerazioni sopra il discorso del signor Galileo Galilei in&shy;<lb/>torno alle cose che stanno in su l'acqua, o che in quella si muovono,<emph.end type="italics"/><pb xlink:href="020/01/3212.jpg" pagenum="173"/><emph type="italics"/>fatte, a difesa e dichiarazione dell'opinione d'Aristotile, da Accademico <lb/>incognito,<emph.end type="italics"/> e ci fu gran ventura il ritrovarlo in quell'esemplare, che Galileo <lb/>stesso postill&ograve; di sua propria mano. </s>

<s>Dall'esame delle quali postille, e del <lb/>testo, ce ne result&ograve; la piena intelligenza della lettera al Nozzolini, e una <lb/>conclusione inaspettata, ma la pi&ugrave; certa che si potesse desiderare, ed &egrave; che, <lb/>nonostante l'esperienza dimostrativa di tutto il contrario, Galileo persist&egrave; nel <lb/>credere co'Peripatetici che l'aria sopra l'acqua non pesi. </s>

<s>La cosa ha tanto <lb/>dello strano, che non sarebbe facile il crederla, se non ne adducessimo i do&shy;<lb/>cumenti. </s></p><p type="main">

<s>A pag. </s>

<s>14 l'Accademico incognito dice: &ldquo; ..... pongo leggermente con <lb/>l'altra mano la piastra di piombo dentro gli arginetti dell'acqua sopra la <lb/>tavoletta d'ebano, senza per&ograve; toccare n&egrave; questa n&egrave; quelli, e tosto sospinta <lb/>l'aria quivi rinchiusa, questa fuggendo se ne ritira nel suo elemento, et ab&shy;<lb/>bandona la tavoletta, la quale nondimeno, restando salva sopra l'acqua, gi&agrave; <lb/>la figura tutta galleggiando, grida vittoria vittoria. </s>

<s>&rdquo; E Galileo in margine <lb/>scrive tale postilla: &ldquo; Opera l'istesso quella pochissima aria, che se fosse <lb/>tutto pieno e non vi fusse la falda. </s>

<s>E mirabile esempio et esperienza sar&agrave; <lb/>il pigliare una bigoncia, ed accomodarvi dentro un maschio affisso poi fora <lb/>in qualche luogo stabile, sicch&egrave; tal maschio resti 4 dita lontano dal fondo, <lb/>e mezzo dito dalla sponda della bigoncia. </s>

<s>Perch&egrave;, infusovi poi quattro o sei <lb/>fiaschi d'acqua, non si potr&agrave; alzare quelle quattro dita, e peser&agrave; come se <lb/>tutto fosse pieno d'acqua. </s>

<s>Vedi pi&ugrave; distintamente nel principio al segno.... &rdquo; </s></p><p type="main">

<s>Il segno richiama a un discorso, esplicativo di ci&ograve; che qui semplice&shy;<lb/>mente s'accenna, scritto nelle prime due carte bianche, che sono al libro di <lb/>guardia, perch&egrave; l'angusto margine a tanto non bastava. </s>

<s>E perch&egrave; altrimenti <lb/>non sarebbe facile comprendere la virt&ugrave; del nostro argomento, crediamo di <lb/><figure id="id.020.01.3212.1.jpg" xlink:href="020/01/3212/1.jpg"/></s></p><p type="caption">

<s>Figura 88.<lb/>dover dall'autografo trascrivere fedelmente, cos&igrave; com'ora fa&shy;<lb/>remo, il detto discorso di Galileo: &ldquo; Sia un solido di piombo, <lb/>o altra materia gravissima AB (fig. </s>

<s>88), fermato in A, in guisa <lb/>che non discenda, ed intendasi un vaso CDE, capace della <lb/>mole di esso solido, e di un poco pi&ugrave;, il qual vaso, collocato <lb/>prima pi&ugrave; basso della base B del solido, empiasi d'acqua, e <lb/>poi lentamente si elevi contro al solido, sicch&egrave; quello entran&shy;<lb/>dovi faccia traboccar l'acqua, ed uscire dal vaso. </s>

<s>Dico che <lb/>chi sosterr&agrave; il vaso, bench&egrave; per l'ingresso del solido sia par&shy;<lb/>tita quasi tutta l'acqua, e bench&egrave; il solido sia fisso e sostenuto in A, sentir&agrave; <lb/>gravarsi dall'istesso peso appunto, che quando sosteneva il vaso pieno d'acqua. </s>

<s><lb/>Il che si far&agrave; manifesto se considereremo come la virt&ugrave; sostenente il solido <lb/>posta in A, mentre tal solido era fuori di acqua, sentiva maggior peso, che <lb/>dopo che il solido &egrave; venuto immerso nell'acqua. </s>

<s>Il qual peso, non potendo <lb/>essere andato in niente, &egrave; forza che si appoggi sopra quella virt&ugrave;, che ha <lb/>sollevato il vaso. </s>

<s>Considerando poi quanto si sia scemata di fatica alla virt&ugrave;, <lb/>che prima sosteneva il solido in aria, avanti che fosse locato in acqua, facil&shy;<lb/>mente intenderemo tanto essere scemata la fatica della virt&ugrave; in A, quanto <pb xlink:href="020/01/3213.jpg" pagenum="174"/>l'acqua ha scemato la gravit&agrave; del solido AB. </s>

<s>Ma gi&agrave; sappiamo che un solido <lb/>pi&ugrave; grave dell'acqua pesa in quella tanto meno, che nell'aria, quant'e il <lb/>peso in aria d'una mole d'acqua, uguale alla mole del solido sommersa; <lb/>adunque il solido AB grava sopra la virt&ugrave; sostenente il vaso CDE tanto, <lb/>quant'&egrave; il peso di tant'acqua, quant'&egrave; la mole del solido demersa. </s>

<s>Ma alla <lb/>mole del solido demersa &egrave; di mano in mano uguale l'acqua, che si spande <lb/>fuor del vaso; adunque, per tale effusione di acqua, non si scema punto il <lb/>peso, che grava sopra la virt&ugrave;, che sostiene il vaso. </s>

<s>Et &egrave; manifesto che il <lb/>solido AB, sebbene scaccia l'acqua del vaso, nientedimeno, con l'occuparvi <lb/>il luogo dell'acqua scacciata, vi conserva tanto di gravit&agrave;, quanta appunto &egrave; <lb/>quella dell'acqua scacciata. </s>

<s>Per&ograve;, signor Accademico, il solido di piombo, che <lb/>voi collocate nella cavit&agrave; degli arginetti, scaccia ben l'aria che vi trova, ma <lb/>egli stesso conferisce a quel vaso tanto appunto dei proprii momenti, quant'era <lb/>il momento dell'aria discacciata. </s>

<s>Bisogna, se voi volete vedere ci&ograve; che operi <lb/>e non operi l'aria accoppiata con un solido, porvela prima, e poi rimoverla, <lb/>ma senza suggerire in suo luogo altro corpo, che possa fare l'effetto stesso, <lb/>che ella faceva prima, ed un modo assai spedito e sensato sar&agrave; questo: </s></p><p type="main">

<s>&ldquo; Facciasi un vaso di vetro, simile all'ABE (fig. </s>

<s>89), di qualsivoglia <lb/>grandezza, il quale abbia in A un foro assai angusto, nel fondo del quale, <lb/>o dentro o fuori, pongasi piombo, tanto che, messo tal vaso nell'acqua, sendo <lb/><figure id="id.020.01.3213.1.jpg" xlink:href="020/01/3213/1.jpg"/></s></p><p type="caption">

<s>Figura 89.<lb/>il resto pieno di aria, si riduca all'equilibrio, ovvero che <lb/>appena discenda al fondo. </s>

<s>Pongasi poi sopra il foco, sicch&egrave; <lb/>l'aria contenuta in esso sia scacciata o in tutto o in gran <lb/>parte dalle sottilissime parti ignee che, passando per la <lb/>sostanza del vetro, vi entreranno dentro. </s>

<s>Et avanti che il <lb/>vaso si remova dal foco, serrisi esquisitamente il foro A, <lb/>sicch&egrave; l'aria non vi possi rientrare. </s>

<s>Levisi poi dal foco e <lb/>lascisi stare, sinch&egrave; si freddi, e tornisi poi a metter nell'acqua, e vedrassi <lb/>galleggiare, per essergli stata remossa o tutta o gran parte dell'aria, che <lb/>prima lo riempiva, senza che in luogo di quella sia succeduto altro corpo, <lb/>siccome per esperienza si vedr&agrave; aprendo il foro A, per il quale con grand'im&shy;<lb/>peto si sentir&agrave; entrar l'aria a riempire il vaso, che di nuovo posto nell'acqua <lb/>come prima andr&agrave; al fondo. </s>

<s>Ma se il vaso ABE fosse tutto aperto di sopra, et <lb/>aggiustato col piombo, sicch&egrave; galleggiasse bene, ma fosse ridotto vicinissimo <lb/>al sommergersi; se alcuno scaccer&agrave; l'aria, col porvi dentro un solido poco <lb/>minor del suo vano, sostenendo per&ograve; tal solido con la mano, non aspetti di <lb/>veder respirare il vaso, n&egrave; punto sollevarsi sopra il livello dell'acqua, come <lb/>nell'altra esperienza accadeva, perch&egrave; il solido postovi scaccia ben, ma vi <lb/>rimette altrettanto del suo momento &rdquo; (MSS. Gal., P. II, T. XV, a tergo del <lb/>fol. </s>

<s>3 e fol. </s>

<s>4). </s></p><p type="main">

<s>Queste considerazioni poi s'inserirono nella lettera al Nozzolini, ripulite <lb/>nella forma, e quasi ringentilitavi l'esperienza, col trasformare il vaso ABE <lb/>in una caraffella di assai lungo collo, a somiglianza di quelle, che s'usavano <lb/>per il Termometro, e cos&igrave;, dando luogo all'invenzione di un nuovo strumento, <pb xlink:href="020/01/3214.jpg" pagenum="175"/>da misurare il peso dell'aria in mezzo all'acqua. </s>

<s>Che siano poi le cose de&shy;<lb/>scritte non un esercizio rettorico, ma la relazione esatta di un fatto speri&shy;<lb/>mentato, s'argomenta da alcuni particolari, come dal voler che si tenga conto <lb/>del peso della cera, servita per turare la bocca alla caraffa, affinch&egrave;, scac&shy;<lb/>ciata una volta dal foco, non abbia di fuori a sottentrarvi altr'aria. </s></p><p type="main">

<s>Inoltre, che sia la fatta esperienza, come si diceva, delicatissima, potr&agrave; <lb/>giudicarsi da chiunque vada ripensando agli applausi, con i quali fu accolta <lb/>una simile esperienza, descritta nel suo libro <emph type="italics"/>De compositione et resolutione <lb/>mathematica<emph.end type="italics"/> dal Rinaldini (Bononiae 1655, pag. </s>

<s>179), il quale, trasformando <lb/>la caraffella galileiana nel tubo torricelliano, veniva con pi&ugrave; facile modo e <lb/>squisito a espellere quell'aria che, non gravando pi&ugrave; come dianzi nello stru&shy;<lb/>mento, era causa dell'alleggerirsi di lui, e del sollevare il collo pi&ugrave; sopra <lb/>l'acqua. </s>

<s>Ond'ei parrebbe che, come del Rinaldini, cos&igrave; di Galileo fosse l'in&shy;<lb/>tenzione quella di dimostrar che l'aria, anche nell'acqua, &egrave; pesa, e perci&ograve; <lb/>concluderne qui, diversamente da quel che aveva fatto nel Discorso intorno <lb/>alle galleggianti, dover l'acqua, che riempirebbe lo spazio ABSO nel solito <lb/>schema, pesar quanto l'assicella, non per&ograve; sola, ma con tutta l'aria conte&shy;<lb/>nuta nella fossetta. </s></p><p type="main">

<s>Il vaso poi, disegnato nella figura 89, inteso tutto aperto di sopra, e <lb/>avente per fondo l'assicella di piombo FG, a cui aderisse con l'orlo infe&shy;<lb/>riore; pareva fosse immaginato apposta per rendere pi&ugrave; comoda, e d'uso <lb/>pi&ugrave; generale, l'esperienza, sostituendo la stabilit&agrave; delle solide pareti BC, DE <lb/>ai fragili arginetti, non sostenuti che dal visco dell'acqua. </s>

<s>E dall'altra parte, <lb/>dicendosi cos&igrave; chiaramente che il solido di piombo, collocato nella cavit&agrave; degli <lb/>arginetti, come il maschio nella bigoncia, <emph type="italics"/>scaccia ben l'aria che vi trova, <lb/>ma egli stesso conferisce a quel vaso tanto appunto dei propri momenti, <lb/>quant'era il momento dell'aria discacciata;<emph.end type="italics"/> non parrebbe da mettere in <lb/>dubbio se l'aria, in mezzo agli arginetti, abbia momento di gravit&agrave;, e perci&ograve; <lb/>se ella aggravi col suo peso la sottoposta assicella. </s>

<s>Eppure Galileo, colla <lb/>stessa ferma mano, con la quale aveva scritte queste parole, passava imme&shy;<lb/>diatamente a scriver quest'altre in una postilla, dove l'Accademico, a pag. </s>

<s>11, <lb/>dice che, se l'assicella diventa uno stesso corpo coll'aria, si potr&agrave; rendere <lb/>cos&igrave; leggera, da formarsi all'intorno non argini, ma montagne di acqua: <lb/>&ldquo; Diventa un istesso corpo con la tavoletta tutta l'aria; e quando di tal corpo <lb/>se n'&egrave; sommerso tanto, che tant'acqua pesi quanto tutto, non va pi&ugrave; gi&ugrave;. </s>

<s><lb/>e cos&igrave; accade, ma nota che tutta l'aria in s&egrave; stessa, e sopra l'acqua, non <lb/>pesa nulla. </s>

<s>Ma ben quella poca che &egrave; sommersa viene estrusa in su, et in <lb/>certo modo leggera nell'acqua. </s>

<s>N&egrave; si maravigli alcuno che tutta l'aria non <lb/>pesi niente, perch&egrave; il simile &egrave; dell'acqua. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/3215.jpg" pagenum="176"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Peripatetico dunque rimastosi nell'Idrostatica Galileo, e de'vizii peripa&shy;<lb/>tetici contaminatone l'autorevole suo insegnamento, si narr&ograve; come i Disce&shy;<lb/>poli aprissero finalmente gli occhi a riconoscere il vero. </s>

<s>Par dalla Storia che <lb/>si svegliassero troppo tardi, se si bada solamente agli atti esteriori, ma pe&shy;<lb/>netrando nel segreto di quella Scuola, vi troviamo seder nuovo maestro il <lb/>Torricelli a restaurare la scienza, non dalla cattedra, o spiegatamente co'li&shy;<lb/>bri, ma ne'privati colloqui con gli amici. </s>

<s>L'eletta schiera solitaria si com&shy;<lb/>pone del Magiotti, del Ricci, del Cornelio e del Nardi, il quale ultimo sa&shy;<lb/>rebbe forse il pi&ugrave; benemerito di tutti, se ne fossero diffusi quegli scritti, nei <lb/>quali ei censurava le dottrine di Galileo con libert&agrave; di giudizio, ne correg&shy;<lb/>geva le fallacie con senno, e diceva imparzialmente il pro e il contro nella <lb/>gran questione, che, intorno al galleggiare le falde dei corpi pi&ugrave; gravi in <lb/>specie dell'acqua, ebbe con gli Aristotelici il suo proprio Maestro. </s>

<s>Crediamo <lb/>perci&ograve; non sia per dispiacere ai Lettori il vedersi messe sott'occhio queste <lb/>poche pagine, che trascriviamo dalle <emph type="italics"/>Scene Accademiche.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Pare che l'acqua e l'aria appena forza abbiano di tenere insieme av&shy;<lb/>vinte le loro particelle, onde, non che premere gli altri corpi, non possano <lb/>nemmeno resistere a qualsivoglia grave, che divider le voglia. </s>

<s>Cos&igrave; crede il <lb/>Galilei, ma il contrario credesi nel Liceo, dove, d'una lamina di piombo che <lb/>nell'acqua galleggi, altra ragione non rendesi, che la difficolt&agrave; quale essa <lb/>lamina, merc&egrave; della figura, trova nel divider l'acqua. </s>

<s>Primieramente, quando <lb/>che tale sia dell'acqua la natura, quale dell'umido separato da ogni natural <lb/>liquore essere determina Archimede, &egrave; necessario che, se poniamo occuparsi <lb/>dall'aere, fra gli argini rinchiuso dell'acqua, lo spazio, che la distesa lamina <lb/>e quasi sepolta nell'acqua cagiona; &egrave; necessario dico che, quando altrettanto <lb/>spazio insieme con l'occupato dalla lamina occupato venga dall'acqua, tanto <lb/>ancor pesi questa, quanto la lamina e l'aria insieme. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ci&ograve; nondimeno, diranno i Peripatetici, non &egrave; render la ragione, onde <lb/>avvenga che la lamina non si sommerga affatto, essendo per natura il piombo <lb/>pi&ugrave; grave dell'acqua. </s>

<s>Di nuovo, pertanto, cercheranno perch&egrave;, in tale stato <lb/>s&egrave; medesima rattenendo, formi quell'argine, e lo formi ancora, mentre che, <lb/>posta nell'acqua la lamina, muovesi allo in gi&ugrave;. </s>

<s>Ancora cercheranno perch&egrave;, <lb/>se umida sia della lama la superficie, vi scorra sopra l'acqua cos&igrave;, che nullo <lb/>argine fabbricar si possa. </s>

<s>Lo stesso scorgesi quasi, se pulita squisitamente <lb/>sia la superficie del metallo. </s>

<s>Pare ancora che, se l'acqua, mediante il freddo, <lb/>rarefatta rigonfi, molto maggiormente e pi&ugrave; facilmente faccia la stessa fossa. </s>

<s><lb/>E finalmente, se l'acqua nel pavimento versiamo, osservasi la stessa fossetta <lb/>ivi fare, poich&egrave; l'umore nella polvere sdrucciolare non pote. </s>

<s>Quindi conchiu-<pb xlink:href="020/01/3216.jpg" pagenum="177"/>deranno gli avversari che, non al solo peso, n&egrave; alla sola astrazione ricorrer <lb/>basti, mentre che molte altre cose possono avere in natura luogo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Veramente dubbio alcuno non pare che l'acqua alla materia del piombo <lb/>si attacchi, e quindi, quasi in base fermandosi, acquisti vigore di s&egrave; stessa <lb/>rattenere e di contrastare all'altra che, premuta dalla lamina viene incal&shy;<lb/>zandola, sicch&egrave;, aggiungendosi la natural delle sue parti tenacit&agrave;, non tra&shy;<lb/>scorre verso il centro, a cui, senza tal patrocinio, obbedir convenivale. </s>

<s>Resta <lb/>dunque sospesa la lamina, perch&egrave; la forza che preme l'acqua riflettesi in s&egrave; <lb/>medesima. </s>

<s>Ma perch&egrave;, in s&igrave; piccole cose, facilmente celansi le misure a ca&shy;<lb/>pello, n&egrave; puote il senso nostro arrivarle precisamente, quindi &egrave; che, della la&shy;<lb/>mina e dell'umore parer&agrave;, per detto degli avversari, che tanta mole si formi, <lb/>quanto, per adattarla alle conseguenze da Archimede cavate, basti, il quale, <lb/>di pi&ugrave;, parlare delle cose sommerse affatto nell'umido, e non delle poste <lb/>sopra di esso diranno, e cos&igrave; tal caso essersi tralasciato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Pongasi frattanto che, se un solido preme l'acqua, la prema secondo <lb/>la linea della profondit&agrave;. </s>

<s>Onde, se lo stesso solido in figura distesa riducasi, <lb/>molto meno premer potrebbe, quando prima tocchi l'acqua giacente che driz&shy;<lb/>zato, poich&egrave; nel primo caso maggior quantit&agrave; resistente d'acqua circonda la <lb/>base e superficie del solido postavi, che nel secondo. </s>

<s>&Egrave;d essendo noto che la <lb/>superficie del solido giacente abbia all'umida che lo bagna la stessa ragione, <lb/>che a quella ha la superficie uguale di un solido drizzatovi; ne segue che, <lb/>se il drizzatovi si sommerga affatto nell'acqua (che si sommerga finalmente <lb/>&egrave; necessario, quando pi&ugrave; grave sia dell'umido, e s'allunghi sempre assot&shy;<lb/>tigliandosi) confessar fia bisogno che in tal posizione, pi&ugrave; che nell'altra, abbia <lb/>l'acqua forzato. </s>

<s>Poich&egrave; dunque per lo lungo la lamina pi&ugrave; premeva l'acqua, <lb/>che non comportava dell'umide particelle il visco, quindi si sommerse. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Veramente dell'acqua la resistenza alla divisione svanisce nei momenti <lb/>grandi, bench&egrave; per pi&ugrave; vie rintracciarsi diranno i Peripatetici. </s>

<s>E cos&igrave; per <lb/>esempio i tondi e minimi sassolini a fatica e tortamente per l'acqua scen&shy;<lb/>dono, bench&egrave; i grandi e d&igrave; molt'ampia figura presto e a dirittura scendanvi. </s>

<s><lb/>E sebbene con maggior ragione scemano i solidi, che le superficie loro, cre&shy;<lb/>derassi nondimeno poter chiuder la strada a chiunque in tal proposito rico&shy;<lb/>vrar si volesse, col prender qualche lamina di materia men grave assai dei <lb/>sassi: eppure scender&agrave;, quando dell'acqua pi&ugrave; grave sia, veloce, in compa&shy;<lb/>razione dei rotondi atomi, ancorch&egrave; di metallo questi siano. </s>

<s>La stess'acqua <lb/>versata in un bicchier di vino, bench&egrave; pi&ugrave; grave ella sia, non pu&ograve; colle sue <lb/>particelle il pi&ugrave; basso luogo occupare, se non fosse con lunghissimo tempo. </s>

<s><lb/>Dunque non la sola figura delle cose similmente gravi cagione sar&agrave; del pi&ugrave; <lb/>o men presto scendere nello stesso mezzo, ma ancora la grandezza concorrer <lb/>deveci, perch&egrave; con la mole cresce sovente o scema il momento in maggior <lb/>ragione, che nell'acqua la resistenza al dividersi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di nuovo la stessa facolt&agrave;, diranno i Peripatetici, &egrave; quella, che vieta <lb/>la semplice divisione, e che pi&ugrave; facile o difficile la rende. </s>

<s>Ma noi, riguar&shy;<lb/>dando agli effetti, stimiamo falsamente che allora nell'acqua stata non sia <pb xlink:href="020/01/3217.jpg" pagenum="178"/>resistenza, quando divisa miriamola. </s>

<s>E se poi il ferro pi&ugrave; che il piombo si <lb/>attacchi all'acqua, non andranno col medesimo passo le ragioni del peso e <lb/>della sommersione di questi due metalli. </s>

<s>Lo stesso proporzionalmente nelle <lb/>figure occorre, nella pulitezza o asprezza, nella qualit&agrave; dell'acqua, e nella <lb/>disposizione secondo diversi tempi e luoghi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Archimede separa dagli umidi naturali ogni tenacit&agrave; in quella ma&shy;<lb/>niera che dalle lance tolse le braccia naturali, e le linee sostitu&igrave;. </s>

<s>Seppe an&shy;<lb/>cora da un corpo una superficie distinguere, di cui trovar volle il luogo dove <lb/>i suoi momenti concorrono. </s>

<s>Ma non &egrave; tanto al Filosofo naturale concesso, il <lb/>quale, comecch&egrave; verissime essere ad Archimede conceda le sue conclusioni <lb/>(poich&egrave; chi solamente astrae non suppone il falso) va ancora in conseguenza <lb/>che egli dalla materia cavolle, che altre nondimeno rimescolatamente lasci&ograve; <lb/>nella stessa materia, da considerare e distinguersi dal Fisico. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si maravigliano parimente i Peripatetici del Galile&igrave; che, avendo ogni <lb/>viscosit&agrave; tolta all'acqua, conceda poi all'aere forza di reggere e sollevare per <lb/>l'acqua di grandissimi corpi, il che fare senza molta tenacit&agrave; di parti egli <lb/>non potrebbe. </s>

<s>Ma chi non sa che molto meno tenace &egrave; l'aere che l'acqua <lb/>o altri umori? </s>

<s>Chi non sa ancora che negli umori non vanno del pari la <lb/>gravit&agrave; e la tenacit&agrave; loro? </s>

<s>Domanderanno di pi&ugrave; che cosa ritenga l'acqua <lb/>dallo scorrere sopra la lamina. </s>

<s>Che ella stessa regga non &egrave; possibile, secondo <lb/>i principii del Galilei, perch&egrave; tenacit&agrave; averebbe. </s>

<s>E se tenacit&agrave;, ne segue che <lb/>sorreggerassi, sia pur qualsivoglia, ancorch&egrave; gravissima materia, posta sul&shy;<lb/>l'acqua, poich&egrave;, se la sua mole e figura in inflnito s'estenda e s'assottigli, <lb/>bisogner&agrave; alla fine che all'uguagliarsi riducasi il momento suo e la tenacit&agrave; <lb/>dell'acqua, e ci&ograve; l'esperienza approvar dirassi. </s>

<s>Che se poi dica il Galilei <lb/>l'aria impedir l'acqua, che non riempia la fossetta, altri anco dir&agrave; che le <lb/>stille dell'acqua, quali nelle fronde sospese vedonsi, non da s&egrave; stesse so&shy;<lb/>spese, ma dall'aria si tengono, il che poi non so come approvare si possa, <lb/>n&egrave; lo stesso Galilei approvalo, anzi che negli ultimi Dialoghi resta perci&ograve; <lb/>anch'ei sospeso. </s>

<s>Parimente, se le posizioni, che dell'umido prende Archi&shy;<lb/>mede, si debbano nella comunal acqua universalmente ricevere, per qual ca&shy;<lb/>gione avviene poi che in un bicchiere ella si rigonfi intorno agli orli? </s>

<s>Ci&ograve; <lb/>far non doverebbe, anzi, non essendo egualmente le sue particelle premute, <lb/>trascorrer dovrebbe. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Per ultimo, diranno contro il Galilei i seguaci d'altro parere, essere <lb/>una mal fondata o almeno difficile a capirsi distinzione quella di che egli <lb/>servesi fra il resistere alla semplice, e il resistere alla facile o difficile divi&shy;<lb/>sione. </s>

<s>Perch&egrave; l'acqua, cos&igrave;, le condizioni del vano otterrebbe, mentre al sem&shy;<lb/>plice dividersi null&aelig; resistenza avesse, ed inoltre premuta e penetrata sa&shy;<lb/>rebbe dall'aere, che grave stimasi dal Galilei, e grave anch'io credolo. </s>

<s>Ma <lb/>forse che insensibilmente da quello penetrata viene, onde di continuo in mi&shy;<lb/>nime parti risolvesi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Brevemente e benignamente dicasi per il Galilei, e per i capi prin&shy;<lb/>cipali della dottrina, ch'ei professa, come falsa &egrave; la cagione addotta del non <pb xlink:href="020/01/3218.jpg" pagenum="179"/>discender per l'acqua corpi di essa pi&ugrave; gravi a cagione della sola figura, <lb/>poich&egrave; l'istessa figura nulla impedisce ai corpi pi&ugrave; lievi dell'acqua il salire <lb/>per essa, ed a tale esperienza cosa contraria addursi non pu&ograve; di rilievo. </s>

<s>&Egrave; <lb/>ben vero che per ragion remota e parziale, il che s'insinua nel sesto, rice&shy;<lb/>ver si pu&ograve; l'apportata da Aristotile. </s>

<s>N&egrave; il Galilei toglie all'acqua ogni te&shy;<lb/>nacit&agrave; delle parti sue, ma bene avverr&agrave; che tal tenacit&agrave; sia superata da ogni <lb/>solido almeno sensibile, il quale, posto nell'acqua, sia di essa pi&ugrave; grave. </s>

<s><lb/>L'acqua poi si propone come pura o non alterata. </s>

<s>E di pi&ugrave; si considera se&shy;<lb/>parata dalle sue particolari convenienze o disconvenienze con altri partico&shy;<lb/>lari corpi, il che &egrave; un considerarla come umida solamente, e non come na&shy;<lb/>turale e concreta. </s>

<s>Nello stesso modo una natural bilancia devesi solamente <lb/>come bilancia considerare dal Meccanico razionale. </s>

<s>Altrimenti avverr&agrave; che se <lb/>di ferro ella fosse, ma il sostegno e le circostanze fossero magnetiche, si re&shy;<lb/>puter&agrave; falso quello, che gli Scientifici di quella dimostrano. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Concludendo dunque diciamo che possono i naturali avvenimenti sco&shy;<lb/>starsi alquanto dall'indivisibile delle astratte verit&agrave;, per ragione delle circo&shy;<lb/>stanze. </s>

<s>Ma tolte queste, rimangono quell&igrave; nell'assoluta necessit&agrave; loro. </s>

<s>&rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>873-80). </s></p><p type="main">

<s>Cos&igrave;, tutte le questioni riguardanti il trattato idrostatico di Galileo ve&shy;<lb/>nivano risolute in quel suo stile laconico dal Nardi, ora benigno paciere, ora <lb/>arguto censore. </s>

<s>E, prendendo pi&ugrave; volentieri a fare quell'ufficio che questo, <lb/>procede nelle censure indirettamente per via dei contrapposti: facendole cio&egrave; <lb/>risultare da una sentenza che, riscontrandola, si troverebbe tutt'affatto con&shy;<lb/>traria alla pronunziata da Galileo, com'&egrave; questa: <emph type="italics"/>dico che, quando altret&shy;<lb/>tanto spazio, insieme con l'occupato dalla lamina, occupato venga dal&shy;<lb/>l'acqua; tanto ancora pesa questa, quanto la lamina e l'aria insieme.<emph.end type="italics"/><lb/>Galileo attribuiva la causa del galleggiare la lamina e la pallina di cera nel <lb/>bicchiere inverso all'attrazione dell'aria, e il Nardi corregge destramente <lb/>una tale fallacia, insinuando il vero in quell'altra sentenza: <emph type="italics"/>Resta dunque <lb/>sospesa la lamina, perch&egrave; la forza che preme l'acqua riflettesi in s&egrave; me&shy;<lb/><figure id="id.020.01.3218.1.jpg" xlink:href="020/01/3218/1.jpg"/></s></p><p type="caption">

<s>Figura 90.<lb/>desima.<emph.end type="italics"/> Ma contro il principio delle velocit&agrave; virtuali, a <lb/>che tutta s'informa l'Idrostatica galileiana, insorgeva il <lb/>Nardi stesso pi&ugrave; a viso aperto. </s></p><p type="main">

<s>&ldquo; Male, egli dice, si persuadono i Meccanici comu&shy;<lb/>nemente compensarsi in una bilancia di disuguali braccia <lb/>la velocit&agrave; del moto con la grandezza del momento, onde <lb/>cercano di render ragione perch&egrave; questi pesi disuguali, da <lb/>distanze reciprocamente disuguali, pesino ugualmente. </s>

<s>Ma <lb/>ci&ograve; non &egrave; in vero cagione dell'equilibrio, perch&egrave;, cos&igrave; di&shy;<lb/>scorrendo, s'adduce di un effetto in atto una cagione in <lb/>potenza. </s>

<s>Il Galilei, nel libro delle Galleggianti, dice cos&igrave;: <lb/><emph type="italics"/>Sia continuata al vaso larghissimo EDF<emph.end type="italics"/> (fig. </s>

<s>90) <emph type="italics"/>l'angu&shy;<lb/>stissima canna CAB, ed intendasi in essi infusa l'acqua sino al livello LGH, <lb/>la quale in questo stato si quieter&agrave;, non senza maraviglia di alcuno, che<emph.end type="italics"/><pb xlink:href="020/01/3219.jpg" pagenum="180"/><emph type="italics"/>non capir&agrave; cos&igrave; subito come esser possa che il grave carico della gran mole <lb/>dell'acqua GD, premendo abbasso, non sollevi e scacci la piccola quan&shy;<lb/>tit&agrave; dell'altra contenuta dentro alla canna CL, dalla quale gli vien con&shy;<lb/>tesa e impedita la scesa. </s>

<s>Ma tal maraviglia cesser&agrave; se noi cominceremo <lb/>a fingere l'acqua GD essersi abbassata solamente sino a Q, e considere&shy;<lb/>remo poi ci&ograve; che aver&agrave; fatto l'acqua CL, la quale, per dare luogo all'al&shy;<lb/>tra, che si &egrave; scemata dal livello GH sino al livello Q, dover&agrave; per neces&shy;<lb/>sit&agrave; essersi nell'istesso tempo alzata dal livello L, sino in AB, e esser la <lb/>salita LB tanto maggiore della scesa GD, quant'&egrave; l'ampiezza del vaso <lb/>GD maggiore della larghezza della canna LC, che insomma &egrave; quanto <lb/>l'acqua GD &egrave; pi&ugrave; della LC. </s>

<s>Ma essendo che il momento della velocit&agrave; del <lb/>moto in un mobile compensa quello della gravit&agrave; in un altro, qual ma&shy;<lb/>raviglia sar&agrave; se la velocissima salita della poca acqua CL resister&agrave; alla <lb/>tardissima scesa della molta GD?<emph.end type="italics"/> Sino a qui il mio Maestro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma la vera cagione onde l'acqua, contenuta nel maggior vaso, non <lb/>preme la contenuta nella canna LC, dir&agrave; alcuno essere perch&egrave; non tutta la <lb/>quantit&agrave; d'acqua GD preme la detta LC, ma solo tanta parte, quanta v'en&shy;<lb/>tra per la cannella per cui insieme comunicano, restando tutta l'altra late&shy;<lb/>rale oziosa. </s>

<s>E cos&igrave; con tal principio immaginar ci dobbiamo nel maggior vaso <lb/>una simile ed uguale cannella IC, quale corrispondendogli preme l'altra. </s>

<s>E <lb/>perch&egrave; uguali sono niuna supera l'altra. </s>

<s>Quindi, se noi fingeremo la canna <lb/>continuata col vaso non pi&ugrave; in L salire, ma in V, allora dal livello GH scen&shy;<lb/>dere vedremo la quantit&agrave; d'acqua, fino che pareggi la bassezza di V, seb&shy;<lb/>bene occorrer&agrave; che, secondo la stessa proporzione, l'una scenda e l'altra <lb/>salga: qual proporzione, nell'altro caso, impedendo appresso il Galileo il <lb/>moto, dovrebbe anche in queste impedirlo. </s>

<s>E vedesi, in conferma, che, men&shy;<lb/>tre l'acqua GD s'abbassa, apparir&agrave; nella superficie sua certa fossetta, cor&shy;<lb/>rispondente in tutto al sito e larghezza della canna, nella qual fossa conti&shy;<lb/>nuamente d'ogni intorno l'umor circostante sdrucciola. </s>

<s>Onde non tutta <lb/>l'acqua, ma una parte sola premere, almeno principalmente, argomenterassi, <lb/>contenuta dentro alla canna, e in conseguenza non l'ampiezza del vaso, ma <lb/>ben l'altezza esser cagione che fosse o non fosse cacciata l'una dall'altra <lb/>acqua, e con pi&ugrave; o meno impeto. </s>

<s>E se ancora, restando l'acqua nel livello <lb/>di prima LGH, infondiamo per il foro A nuovo umore nella canna, vedremo <lb/>l'infusa premer l'acqua del maggior vaso, o per meglio dire, una parte di <lb/>esso, sino a che facciasi l'equilibrio &rdquo; (ivi, pag. </s>

<s>862-64). </s></p><p type="main">

<s>L'obiezione del Nardi, contro il processo dimostrativo di Galileo, fu ri&shy;<lb/>petuta pubblicamente da alcuni, ai quali anche piacque meglio di dar del <lb/>paradosso idrostatico la spiegazione, che abbiamo ora tratta dal manoscritto. </s>

<s><lb/>Altri per&ograve; non ebbero scrupolo di tenere i medesimi modi, usati nel trat&shy;<lb/>tato delle Galleggianti, riducendo la dimostrazione all'assurdo. </s>

<s>Di costoro <lb/>possiamo citare fra'nostri il De Angeli, il quale, nel secondo Dialogo sopra <lb/>commemorato, all'obiezione che soleva comunemente farsi contro il principio <lb/>delle velocit&agrave; virtuali, che cio&egrave; di un effetto positivo, qual'&egrave; la quiete, s'ad-<pb xlink:href="020/01/3220.jpg" pagenum="181"/>duce per causa il moto, rispondeva &ldquo; non parer nuovo nelle cose che si di&shy;<lb/>mostrano il procedere <emph type="italics"/>per deductionem ad impossibile,<emph.end type="italics"/> dimostrando che, <lb/>quando fosse vero il contrario, ne seguirebbe un assurdo in natura, o cosa <lb/>irragionevole &rdquo; <emph type="italics"/>(Della gravit&agrave; dell'aria ecc.<emph.end type="italics"/> cit., pag. </s>

<s>58). Fra gli stranieri <lb/>poi basti citare il Mariotte, il quale, avendo proposto per principio univer&shy;<lb/>sale della Meccanica quello delle velocit&agrave; virtuali, che, andando reciproca&shy;<lb/>mente ai pesi, mantengono in quiete la leva; rendeva la ragione dell'equi&shy;<lb/>librio fra due superficie, prese per base di due cilindri acquei di pari altezza, <lb/>nel vaso grande GD, e nella piccola canna CL; dicendo che se si moves&shy;<lb/>sero, &ldquo; donc leurs vitesses avroient &eacute;t&eacute; reciproques a leurs poids, et ils <lb/>avroient eu une egale quantit&eacute; de mouvement, ce qui est impossible. </s>

<s>Car, <lb/>par le Principe universel, ces cylindres d'eau doivent faire equilibre, et l'un <lb/>ne peut pas faire mouvoir l'autre, puisqu'ils sont disposes a prendre une <lb/>egale quantit&eacute; de meuvement selon la meme direction &rdquo; <emph type="italics"/>(Oeuvres,<emph.end type="italics"/> T. II, a <lb/>l'Haye 1740, pag. </s>

<s>367). </s></p><p type="main">

<s>Nonostante l'obiezione del Nardi era, specialmente a que'tempi, ripu&shy;<lb/>tata di cos&igrave; grave momento, da indurre, come si sa, il Torricelli a ricono&shy;<lb/>scere la causa dell'equilibrio fra due corpi congiunti in un principio alquanto <lb/>diverso, qual'&egrave; quello del non potere scendere il loro comun centro di gra&shy;<lb/>vit&agrave;. </s>

<s>Anche questo nuovo principio, come l'altro delle velocit&agrave; virtuali, era <lb/>indiretto, riducendosi nel medesimo modo all'assurdo. </s>

<s>Il Terricelli infatti <lb/><figure id="id.020.01.3220.1.jpg" xlink:href="020/01/3220/1.jpg"/></s></p><p type="caption">

<s>Figura 91.<lb/>concludeva doversi, nella data ipotesi dell'im&shy;<lb/>mobilit&agrave; del comun centro gravitativo, rimanere <lb/>i due corpi congiunti in quiete, <emph type="italics"/>alias enim fru&shy;<lb/>stra moverentur.<emph.end type="italics"/> Siano i due corpi A, B (fig. </s>

<s>91) <lb/>disposti in distanze reciprocamente proporzio&shy;<lb/>nali ai loro proprii pesi dal comun centro C. </s>

<s><lb/>Rimarranno quivi in quiete, perch&egrave;, se si mo&shy;<lb/>vessero, come per esempio in A&prime;, B&prime;, le relazioni fra le loro distanze CD, CE <lb/>non sarebbero punto cambiate, per cui, sempre rimanendo C il loro centro <lb/>comune, quel moto sarebbe stato inutile, e perci&ograve; contrario alla Natura, che <lb/>nulla opera mai inutilmente. </s></p><p type="main">

<s>Il Torricelli per&ograve; conduce la sua dimostrazione con tale artificio, da fare <lb/>sparire queste trite riduzioni all'assurdo, e da chiudere nello stesso tempo <lb/>la bocca agli oppositori, non sostituendone propriamente un altro diverso, <lb/><figure id="id.020.01.3220.2.jpg" xlink:href="020/01/3220/2.jpg"/></s></p><p type="caption">

<s>Figura 92.<lb/>ma travestendo cos&igrave; il principio delle velocit&agrave; <lb/>virtuali, da non riconoscerlo per quel desso. </s>

<s>In&shy;<lb/>vece di considerare i gravi pendenti dall'estre&shy;<lb/>mit&agrave; di una leva gl'immagina congiunti con un <lb/>filo, e posati sopra due piani inclinati cos&igrave;, che <lb/>le loro lunghezze siano direttamente propor&shy;<lb/>zionali ai pesi soprapposti. </s>

<s>L'equilibrio, che anco in questo caso si osserva, <lb/>dipende dall'avere i due corpi, bench&egrave; di diversa grandezza, egual disposi&shy;<lb/>zione al moto o momento virtuale. </s>

<s>Imperocch&egrave; posto che A (fig. </s>

<s>92) stia a B, <pb xlink:href="020/01/3221.jpg" pagenum="182"/>come la lunghezza CD alla CE, e moversi i due corpi per tratti uguali DA, <lb/>BE lungo i due piani; gli spazi perpendicolarmente passati sarebbero AG, BH, <lb/>in reciproca ragione delle lunghezze de'piani DC, CE, ossia de'pesi B, A, <lb/>come nella leva. </s>

<s>Il Torricelli per&ograve; suppone che, non virtualmente ma attual&shy;<lb/>mente si movano i due corpi, l'uno ascendendo, e discendendo l'altro, come <lb/>porta l'essere insieme congiunti, e dimostra, com'&egrave; noto, che la via del cen&shy;<lb/>tro di gravit&agrave; del sistema percorre la medesima linea orizzontale, e perci&ograve; l&igrave;, <lb/>dove sono stati quegli stessi corpi rimossi, anche si rimangono nella mede&shy;<lb/>sima quiete. </s></p><p type="main">

<s>Qual uso si facesse, specialmente nella Scuola galileiana, di questo prin&shy;<lb/>cipio torricelliano, per trattare alcuni de'pi&ugrave; difficili problemi statici, oramai <lb/>si sa dalla storia della Meccanica. </s>

<s>Ma primo ad applicarlo all'Idrostatica fu <lb/>il Pascal, non forse per sostituirlo a quell'altro di Galileo, quasi lo repu&shy;<lb/>tasse anch'egli difettoso, ma per dare altro modo alla dimostrazione. </s>

<s>Se A <lb/>e B (fig. </s>

<s>93) son due cilindri di materia omogenea, con pari altezze, ma con <lb/>basi cos&igrave; diverse, da far s&igrave; che questo pesi, poniamo, cento volte pi&ugrave; di <lb/><figure id="id.020.01.3221.1.jpg" xlink:href="020/01/3221/1.jpg"/></s></p><p type="caption">

<s>Figura 93.<lb/>quello; sospesi da una bilancia di braccia uguali <lb/>&egrave; certo che il maggiore preponderer&agrave; con cen&shy;<lb/>tuplo momento. </s>

<s>E nonostante immersi ne'due <lb/>tubi CD, EF, comunicantisi e pieni d'acqua, <lb/>come due stantuffi in due corpi di tromba, si <lb/>vede la Bilancia ridursi in perfetto equilibrio. </s>

<s><lb/>Qual'&egrave;, domanda a s&egrave; il Pascal, la ragione di <lb/>questo apparente paradosso? </s>

<s>E risponde osser&shy;<lb/>vando che la forza, con la quale &egrave; premuto il <lb/>velo acqueo sottoposto allo stantuffo A, si comu&shy;<lb/>nica al velo d'acqua sottoposto allo stantuffo B, <lb/>il qual velo essendo centuplo ricever&agrave; il centu&shy;<lb/>plo della forza, ugualmente distribuita per ogni sua parte, ond'ei si verifica <lb/>qui quel che in ogni caso della comunicazione dei moti, che cio&egrave; le velocit&agrave; <lb/>son reciprocamente proporzionali alle grandezze dei copi mossi. </s>

<s>&ldquo; D'ou il <lb/>paroist qu'un vaisseau plein d'eau est un nouveau principe de Mechanique, <lb/>et une machine nouvelle pour multiplier les forces a tel degre qu'on vou&shy;<lb/>dra.... Et l'on doit admirer qu'il se rencontre en cette machine nouvelle <lb/>cet ordre constant, qui se trouve en toutes les anciennes, s&ccedil;avoir le levier, <lb/>le tour, la vis sans fin etc. </s>

<s>qui est que le chemin est augment&eacute; en mesme <lb/>proportion que la force.... de sorte que le chemin est au chemin comme la <lb/>force a la force. </s>

<s>Ce que l'on peut prendre mesme pour la vraye cause de <lb/>cet effet, estant clair que c'est la mesme chose de faire faire un poulce de <lb/>chemin a cent livres d'eau, que de faire faire cent poulces de chemin a une <lb/>livre d'eau. </s>

<s>Et qu'ainsi lors qu'une livre d'eau est tellement ajust&eacute;e avec cent <lb/>livres d'eau, que les cent livres ne puissent se remuer un poulce, qu'elles <lb/>ne faissent remuer la livre de cent poulces; il faut qu'elles demuerent en <lb/>equilibre, une livre ayant autant de force pour faire faire un poulce de che-<pb xlink:href="020/01/3222.jpg" pagenum="183"/>min a cent livres, que cent livres pour faire faire cent poulces a une livre &rdquo; <lb/><emph type="italics"/>(De l'equilibre des <expan abbr="liq.">lique</expan><emph.end type="italics"/> cit., pag. </s>

<s>6-8). </s></p><p type="main">

<s>Concludesi da questo discorso del Pascal, come da quello simile di Ga&shy;<lb/>lileo, che l'acqua tanto pi&ugrave; velocemente si muove ne'due corpi di tromba, <lb/>quanto son pi&ugrave; piccole le loro sezioni, o i veli d'acqua in esse compresi, i <lb/>quali veli, supposti conglobati in A, B, e pendenti all'estremit&agrave; di una leva <lb/>immaginaria, come nella 91a figura; staranno ivi dunque in quiete per le <lb/>medesime ragioni. </s>

<s>Di qui &egrave; che al Pascal sovviene di dimostrare altrimenti <lb/>questo idrostatico equilibrio, applicandovi il principio del Torricelli. </s>

<s>&ldquo; Voicy <lb/>encore une preuve qui ne pourra estre entendu&eacute;, que par les seuls Geome&shy;<lb/>tres, et peut estre pass&eacute;e par les autres. </s>

<s>Je prends pour principe que ja&shy;<lb/>mais un corps ne se meut par son poids, sans que son centre de gravit&eacute; <lb/>descende. </s>

<s>D'ou je prouve que les deux pistons figurez en la figure 93 sont <lb/>en equilibre en cette sorte: Car leur centre de gravit&eacute; commun est au point <lb/>qui divise la ligne qui joint leurs centres de gravit&eacute; particuliers en la pro&shy;<lb/>portion de leurs poids, qu'ils se meuvent maintenant s'il est possible. </s>

<s>Donc <lb/>leurs chemins seront entre eux comme leurs poids reciproqnement, comme <lb/>nous avons fait voir. </s>

<s>Or si on prend leur centre de gravit&eacute; commun en cette <lb/>seconde situation, on le trouvera precisement au mesme endroit que la pre&shy;<lb/>miere fois, car il se trouvera toujours au point qui divise la ligne, qui joint <lb/>leurs centres de gravit&eacute; particuliers, en la proportion de leurs poids. </s>

<s>Donc, <lb/>&agrave; cause du parallelisme des lignes de leurs chemins, il se trouvera en l'in&shy;<lb/>tersection des deux lignes, qui joignent les centres de gravit&eacute; dans les deux <lb/>situations. </s>

<s>Donc le centre de gravit&eacute; commun sera au mesme point qu'au&shy;<lb/>paravant. </s>

<s>Donc le deux pistons considerez comme un seul corps, se sont <lb/>meus sans que le centre de gravit&eacute; commun soit descendu, ce qui est con&shy;<lb/>tre le principe. </s>

<s>Donc ils ne peuvent se mouvoir. </s>

<s>Donc ils seront en repos, <lb/>c'est &agrave; dire en equilibre, ce qu'il falloit demontrer &rdquo; (ivi, pag. </s>

<s>10-11). </s></p><p type="main">

<s>Valendo la medesima dimostrazione, siano i veli d'acqua L, GH, nella <lb/>figura 90, allo stesso livello, o l'uno rimanga sotto e l'altro sopra, come a <lb/>torcere la canna ABC, e ridurla in dirittura con la CI; l'un velo stia di <lb/>faccia all'altro o in posizione diversa; l'un dall'altro vicino o lontano, <emph type="italics"/>car <lb/>la continuit&eacute; et la fluidit&eacute; de l'eau rend toutes ces choses l&agrave; &eacute;gale et in&shy;<lb/>differentes<emph.end type="italics"/> (pag. </s>

<s>9); resta cos&igrave; da esso Pascal dimostrato il paradosso idro&shy;<lb/>statico sotto tutte le variet&agrave; de'suoi aspetti, facilmente riducibili ai vasi della <lb/>forma rappresentata nelle figure 94 e 95, i fondi dei quali vasi, o i veli <lb/>acquei, o gli stantuffi CD, PQ, son premuti nel primo caso da una colonna <lb/>d'acqua, avente per base CD e per altezza CM, perch&egrave;, supposto esso fondo <lb/>CD scendere, vinto dal peso soprastante, lo farebbe con velocit&agrave; uguale a <lb/>quella, con cui scenderebbe il velo MN, tanto men velocemente del velo FG, <lb/>quanto la sezione FG &egrave; minore della CD. Nell'altro caso essere il fondo PQ <lb/>della figura 95 premuto da una colonna liquida, avente per base PQ e per <lb/>altezza PS, si concluder&agrave; facilmente dai principii del Pascal con simile di&shy;<lb/>scorso. </s></p><pb xlink:href="020/01/3223.jpg" pagenum="184"/><p type="main">

<s>Ma il Wolf, misurando le pressioni sulla regola delle forze morte, e pre&shy;<lb/>supposto il principio delle velocit&agrave; in ragion reciproca delle sez&igrave;oni, dimo&shy;<lb/>strava pi&ugrave; chiaramente la cosa con questa sua proposizione: &ldquo; Si bases va&shy;<lb/><figure id="id.020.01.3223.1.jpg" xlink:href="020/01/3223/1.jpg"/></s></p><p type="caption">

<s>Figura 94.<lb/>sis FD (nella figura 94) inaequales fuerint, fundus eodem <lb/>modo premitur, ac si superior inferiori aequalis existeret &rdquo; <lb/><emph type="italics"/>(Elem. </s>

<s>Mathes. </s>

<s>universae,<emph.end type="italics"/> T. II, Genevae 1746, pag. </s>

<s>260). </s></p><p type="main">

<s>La dimostrazione si pu&ograve; condurre cos&igrave; speditamente: <lb/>La pressione totale P, fatta sopra il fondo CD, resulta <lb/>dalle pressioni parziali dell'acqua AD e dell'acqua EG. </s>

<s><lb/>E perch&egrave; le forze di queste pressioni, essendo morte, si <lb/>misurano dai prodotti delle masse per le velocit&agrave;, che si <lb/>chiameranno V, V&prime;; avremo P=CD.AC.V+FG.EF.V&prime;. </s>

<s><lb/>Ma, stando le velocit&agrave; in ragion reciproca delle sezioni, &egrave; CD.V=FG.V&prime;; <lb/>dunque P=CD.V(AC+EF)=CD.CM.V: che vuol dire essere premuto <lb/>il fondo CD del vaso FD come se non si restringesse, ma fosse in fino a MN <lb/><figure id="id.020.01.3223.2.jpg" xlink:href="020/01/3223/2.jpg"/></s></p><p type="caption">

<s>Figura 95.<lb/>tutto andante. </s>

<s>Con simile ragionamento si concluder&agrave; che le <lb/>pressioni fatte sul fondo, o, come il Pascal lo chiama, sulla <emph type="italics"/>ou&shy;<lb/>verture<emph.end type="italics"/> PQ del vaso, rappresentato nella fig. </s>

<s>95, &egrave; Pq.PS.V&prime;: <lb/>e in generale &ldquo; que la mesure de cette force est toujours le <lb/>poids de toute l'eau, qui seroit contenue dans une colonne de <lb/>la hauteur de l'eau, et de la grosseur de l'ouverture &rdquo; <emph type="italics"/>(De <lb/>l'equilibre etc.,<emph.end type="italics"/> pag. </s>

<s>5). </s></p><p type="main">

<s>La dimostrazione data dal Wolf era implicita nel di&shy;<lb/>scorso del Pascal. </s>

<s>Ma, o che il Varignon non ve la ricono&shy;<lb/>scesse, o che, invaghito del suo principio generale di Meccanica, credesse <lb/>non si poter dare altra legittima dimostrazione de'teoremi di lei, che per <lb/>via della composizion delle forze; &egrave; un fatto che, dop'avere attribuito al <lb/>Pascal l'esperienza del paradosso idrostatico, <emph type="italics"/>mais,<emph.end type="italics"/> soggiunge, <emph type="italics"/>sans que lui <lb/>ni aucun autre, que je s&ccedil;hache, en ait donn&eacute; la raison.<emph.end type="italics"/> Si vede che il <lb/>Varignon non sapeva n&egrave; del Benedetti, n&egrave; dello Stevino, n&egrave; di Galileo, n&egrave; <lb/>dello stesso Pascal, il quale, bench&egrave; in fretta e per <emph type="italics"/>les seuls Geometres,<emph.end type="italics"/> aveva <lb/>pure esteso il principio delle velocit&agrave; virtuali a dimostrar l'equilibrio de'li&shy;<lb/>quidi comunicanti, e le loro pressioni sopra <emph type="italics"/>les ouvertures<emph.end type="italics"/> dei vasi. </s></p><p type="main">

<s>Persuaso dunque il celebre Accademico parigino che a nessuno prima <lb/>di lui fosse ancora riuscito di trovar la desiderata ragione, ei soccorre sol&shy;<lb/>lecito di sodisfare a questi desiderii della Scienza, nella sua <emph type="italics"/>Nouvelle mec&shy;<lb/>canique,<emph.end type="italics"/> trattandovi, nella X sezione, <emph type="italics"/>De l'equilibre des liqueurs.<emph.end type="italics"/> I teoremi <lb/>in proposito sono il XLII, il XLIII e XLIV. </s>

<s>Ma perch&egrave; i due secondi dipen&shy;<lb/>dono dal primo, in cui si piglia a esempio un vaso cilindrico obliquo; di questo <lb/>solo teorema perci&ograve; baster&agrave; riferire il modo della dimostrazione, da che sar&agrave; <lb/>facile intendere il modo tenuto in dimostrar gli altri due, ne'quali i vasi <lb/>hanno figura di un cono tronco, ora con la maggior base in alto, ora in basso. </s></p><p type="main">

<s>Premette un lemma l'Autore, che a noi piace formulare cosi, come poi <lb/>fece l'Herman: &ldquo; Pressiones, quas corpora quaecumque solida vel fluida in <pb xlink:href="020/01/3224.jpg" pagenum="185"/>se invicem exercent, fiunt iusta directiones communi plano contingenti cor&shy;<lb/>pora perpendiculares, atque transeunt per contingentiae punctum eorumdem <lb/>corporum &rdquo; <emph type="italics"/>(Phoron.<emph.end type="italics"/> cit., pag. </s>

<s>128). Se il globo A (fig. </s>

<s>96), spinto nella di&shy;<lb/>rezione AF, preme il globo B, nel punto del contatto C, con una certa forza <lb/><figure id="id.020.01.3224.1.jpg" xlink:href="020/01/3224/1.jpg"/></s></p><p type="caption">

<s>Figura 96.<lb/>AF, decomposta questa in due, la prima AC perpen&shy;<lb/>dicolare al piano DE del contatto, e la seconda AH a <lb/>esso piano parallela; &egrave; manifesto che dalla AC sola &egrave; <lb/>rappresentata la forza della pressione, essendo l'altra AH <lb/>in premere inattiva. </s>

<s>E tale &egrave; la dimostrazione, che d&agrave; <lb/>l'Herman del lemma premesso dal Varignon, il quale, <lb/>propostosi il vaso AKDX (fig. </s>

<s>97), infusovi il liquido <lb/>insino al livello GH, inalzata dal punto K la perpendi&shy;<lb/>colare KY, e dal punto H abbassata la perpendico&shy;<lb/>lare HL, dimostra che il liquido GKY riposa tutto sulla parete GK, e il li&shy;<lb/>quido LHD preme sopra LD col peso della colonna LZ, d'ond'ei ne conclude <lb/>che tutto il fondo KD resiste alla pressione della colonna KZ. </s></p><p type="main">

<s>&ldquo; Il est manifeste, dice il Varignon, que les resistances, que les c&ograve;tez <lb/>opposez AK, XD du tuyau inclin&eacute; AKDX font en M, T, a la descente ver&shy;<lb/>ticale de OM filet de liqueur, et a l'ascension verticale de l'autre filet RT, <lb/><figure id="id.020.01.3224.2.jpg" xlink:href="020/01/3224/2.jpg"/></s></p><p type="caption">

<s>Figura 97.<lb/>que les plus longs que lui tendant a <lb/>faire montere en S jusqu'aleur niveau <lb/>GH prolong&eacute; vers Z; que ces resistan&shy;<lb/>ces, que ces c&ograve;tez opposez AK, XD font <lb/>aux filets OM, RT, sont suivant MN, <lb/>TV egales &agrave; des forces, qui les supplee&shy;<lb/>roient en repoussant seulement comme <lb/>eux suivant ces directions les points M, <lb/>T de ces filets OM, RT de liqueur: <lb/>et qu'ainsi chacune de ces resistances <lb/>se decompose comme en deux forces purement passives suivant MF, ME, et <lb/>TP, TQ, dont chacune des horizontales suivant MF, TP soutient, par son <lb/>invincibilit&eacute;, ce que le liqueur peut avoir d'action directement contraire a <lb/>cette resistance horizontale &rdquo; (A Paris 1725, pag. </s>

<s>253). </s></p><p type="main">

<s>Quanto alle altre forze, dirette secondo le verticali ME, TQ, egli &egrave; ma&shy;<lb/>nifesto, prosegue il Varignon a dire, &ldquo; que la premiere suivant ME directe&shy;<lb/>ment oppos&eacute;e au poids du filet OM, le soutient en M dans le repos, que lui <lb/>exige le suppos&eacute; de ce qu'il y a de liqueur dans le tuyau inclin&eacute; AKDX, <lb/>sans lui laisser aucune action sur le fond KD de ce tuyau, le quel conse&shy;<lb/>quemment n'en est aucunement charge &rdquo; (ivi). Il medesimo si dimostra degli <lb/>altri infiniti filetti, per cu&igrave; si conclude che la mole fluida, compresa nello <lb/>spazio GKY, preme tutta sulla parete inclinata GK, e non punto sul fondo <lb/>del vaso. </s></p><p type="main">

<s>&ldquo; Mais en recompense, soggiunge tosto l'Autore, ce qu'il y a de cette <lb/>liqueur dans l'espace HLD compr&eacute;s entre le plan HL perpendiculaire a la <pb xlink:href="020/01/3225.jpg" pagenum="186"/>droite KD, et ce que ce plan retranche du cot&eacute; de HD de la surface su&shy;<lb/>perieure de ce tuyau inclin&eacute; AKDX, presse ce fond horizontal KD d'une <lb/>force egale a celle, dont il seroit press&eacute; par la portion cylindrique HLDZ, <lb/>que ce meme plan HL retranche du cylindre droit KYZD de la meme li&shy;<lb/>queur. </s>

<s>Car la force suivant TQ, resultante de la resistance, que le cot&eacute; su&shy;<lb/>pericur XD du tuyau inclin&eacute; AKDX fait, suivant la perpendiculaire TV, a <lb/>l'ascension du filet vertical RT de liqueur; se trouvant directement oppos&eacute;e <lb/>a l'effort, dont le poids du surplus de longueur des plus longs tond a le <lb/>faire monter jusqu'au point S de leur niveau GH, et empechant cet effet, <lb/>est egale a cet effort suivant RT, au quel, par la meme raison, le poids <lb/>d'une portion ST de la meme liqueur seroit aussi egal. </s>

<s>Donc le force de <lb/>resistance, avec la quelle le cote oblique XD du tuyau inclin&eacute; AKDX repouse <lb/>le filet vertical TR, suivant sa direction; est egale au poids d'une portion <lb/>ST de cette liqueur. </s>

<s>Par consequent le poids de ce filet TR ainsi, repouss&eacute; <lb/>suivant TQ, fait le meme effort en ce sens, sur le fond vertical KD, du tuyau <lb/>inclin&eacute; AKDX, qu'y feroit ce meme poids du filet TR augment&eacute; du poids <lb/>de ST, c'est-a-dire, le meme effort, qu'y feroit le poids d'un filet vertical <lb/>entier SR de la meme liqueur &rdquo; (ivi, pag. </s>

<s>254). Le medesime cose dimo&shy;<lb/>strandosi degli altri filetti, se ne conclude che il liquido HLD preme il fondo <lb/>LD con la forza del cilindro HD, e tutto il fondo del vaso obliquo vien per&shy;<lb/>ci&ograve; gravato dal peso della colonna retta YD. </s></p><p type="main">

<s>Il discorso insomma del Varignon si riduce a dimostrare che l'acqua <lb/>GKY non preme menomamente il fondo, e che in ricompensa l'acqua KLD <lb/>lo preme col doppio del suo proprio peso. </s>

<s>&Egrave; fresca nei nostri Lettori la me&shy;<lb/>moria di questa dimostrazione, data gi&agrave; dallo Stevino: che se il novello Acca&shy;<lb/>demico di Parigi si fosse contentato di vantare il suo modo come pi&ugrave; facile, <lb/>e pi&ugrave; breve di quel del Matematico del principe di Nassau, gli si potrebbe <lb/>anche concedere, facendogli per&ograve; osservare che deriva un tal vantaggio, piut&shy;<lb/>tosto che dal principio dei moti composti, da quello degl'indivisibili, appli&shy;<lb/>catovi il quale la dimostrazione, che si ricava dagli <emph type="italics"/>Elemens hydrostatiques,<emph.end type="italics"/><lb/>&egrave; assai pi&ugrave; diretta e spedita, di quella che ne sugger&igrave; l'Autore della <emph type="italics"/>Mecha&shy;<lb/>nique nouvelle.<emph.end type="italics"/> Ridotta la parete a un punto, sopra cui perpendicolarmente <lb/>insista un filetto liquido, la prima parte del Teorema varignoniano &egrave; dagli <lb/>insegnamenti dello Stevino per s&egrave; manifesta. </s>

<s>Quanto all'altra parte poi il <lb/>Varignon suppone quel che lo Stevino aveva ben dimostrato, che cio&egrave; nel <lb/>punto T la parete &egrave; premuta dal peso di un filetto liquido, alto quanto ST. </s>

<s><lb/>E perch&egrave; lo sforzo, riflesso da essa parete sul filetto TR, uguaglia lo sforzo <lb/>diretto ST, resta cos&igrave;, senz'altro, concluso che il punto R del fondo &egrave; pre&shy;<lb/>muto da tutto il peso del filetto RS. </s>

<s>Onde il paradosso idrostatico pu&ograve; spie&shy;<lb/>garsi a quel modo che fa il Varignon, per rendere uniforme il metodo d <lb/>trattar, col principio della composizion delle forze, cos&igrave; fatte questioni: non <lb/>gi&agrave; che, senza un tal principio, non sia possibile, com'ei pretende, riuscir <lb/>nell'intento, o che sia vero non esservi prima di lui, e senza quel suo nuovo <lb/>aiuto, nessuno ancora riuscito. </s></p><pb xlink:href="020/01/3226.jpg" pagenum="187"/><p type="main">

<s>Il vantaggio, che viene alla dimostrazione, dal condurla sulla regola idro&shy;<lb/>statica dello Stevino, piuttosto che su quella meccanica del Varignon, si com&shy;<lb/>prender&agrave; anche meglio, proponendosi il caso che i recipienti non siano ci&shy;<lb/>lindrici o prismatici, ma irregolari. </s>

<s>Intorno a che un'altra difficolt&agrave; fu <lb/>promossa contro il metodo usato da Galileo. </s>

<s>Siano i vasi comunicanti AC, <lb/>GD della figura 90, di qual si voglia forma pi&ugrave; capricciosa: riman pure un <lb/>fatto che il liquido si dispone qua e l&agrave; nel medesimo livello, ma come si <lb/>potrebbe applicare a spiegarlo il discorso dell'Autore delle Galleggianti? </s>

<s><lb/>L'obiezione risuon&ograve; alle orecchie di Tommaso Bonaventuri, editore nel 1718 <lb/>in Firenze delle opere galileiane, il quale rifer&igrave; in una nota, d'altre simili <lb/>cose erudita, la risposta avutane in proposito dal p. </s>

<s>ab. </s>

<s>Guido Grandi. </s>

<s>Sup&shy;<lb/>posto che i vasi comunicanti siano ED, AZ (fig. </s>

<s>98), e che, abbassandosi nel&shy;<lb/><figure id="id.020.01.3226.1.jpg" xlink:href="020/01/3226/1.jpg"/></s></p><p type="caption">

<s>Figura 98.<lb/>l'uno il liquido da GR in QO, risalga <lb/>nell'altro da LX in AB, conduce il <lb/>Grandi la sezione MN, media aritme&shy;<lb/>tica fra GR e QO, e la sezione KT me&shy;<lb/>dia aritmetica fra LX e AB, sopra le <lb/>quali due medie sezioni costruisce due <lb/>cilindri con le altezze GQ, AL, osser&shy;<lb/>vando che, per essere nel moto iniziale <lb/>queste altezze piccolissime, le irregola&shy;<lb/>rit&agrave; de'tubi tornano all'esattezza de'cilindri circoscritti, per cui la questione <lb/>si riduce al caso contemplato da Galileo, verificandosi anche qui &ldquo; che le su&shy;<lb/>perficie GH, LX sono reciproche alle altezze o velocit&agrave; AL, GQ, con le quali <lb/>dette superficie sono disposte a muoversi, nel bel principio del moto, e per&ograve; <lb/>ne segue ottimamente che facciano equilibrio &rdquo; (Alb. </s>

<s>XII, 603). </s></p><p type="main">

<s>Cos&igrave; essendo, poteva il Bonaventuri citar piuttosto il Pascal, che tanti <lb/>anni prima, e pi&ugrave; autorevolmente del Grandi, aveva risoluta ogni difficolt&agrave; <lb/>cos&igrave;, nel medesimo modo, geometricamente ragionando: &ldquo; Ces liqueurs se&shy;<lb/>roient aussi bien en equilibre dans ces tuyaux irreguliers, que dans les uni&shy;<lb/>formes, parce que les liqueurs ne pesent que suivant leur hauteur, et non <lb/>pas suivant leur largeur. </s>

<s>Et la demonstration en seroit facile en inscrivant <lb/>en l'un et en l'autre plusieurs petits tuyaux reguliers. </s>

<s>Car on seroit voir, <lb/>par ce que nous avons demontr&eacute;, que deux de ces tuyaux inscripts, qui se <lb/>correspondent dans les deux vaisseaux, sont en equilibre. </s>

<s>Donc tous ceux <lb/>d'un vaisseau seroient en equilibre avec tous ceux de l'autre. </s>

<s>Ceux qui sont <lb/>accoutumez aux inscriptions, et aux circonscriptions de la Geometrie, n'au&shy;<lb/>ront nulle peine a entendre cela, et il seroit bien difficile de le demontrer <lb/>aux autres au moins geometriquement &rdquo; <emph type="italics"/>(De l'equilibre des liqueurs<emph.end type="italics"/> cit., <lb/>pag. </s>

<s>17, 18). </s></p><p type="main">

<s>Alla Geometria degl'inscritti successe pi&ugrave; felicemente l'altra degl'indi&shy;<lb/>visibili, per la quale vennero finalmente a sparire tutte le difficolt&agrave; contro <lb/>il principio delle velocit&agrave; virtuali, professato, come accennammo, dal D'Alem&shy;<lb/>bert oramai senza scrupoli e senza timori. </s>

<s>Nonostante anche il vecchio me-<pb xlink:href="020/01/3227.jpg" pagenum="188"/>todo, usato dal Pascal e dal Grandi, si porgeva atto a dimostrare il para&shy;<lb/>dosso idrostatico, nel caso altresi che uno o ambedue i tubi fossero inclinati. </s>

<s><lb/>Il Sinclaro, fatta la distinzione di gravit&agrave; <emph type="italics"/>sensibile<emph.end type="italics"/> e <emph type="italics"/>insensibile,<emph.end type="italics"/> dimostr&ograve; <lb/>facilmente che il mercurio, &ldquo; aut quodvis aliud fluidum, in siphonis crure <lb/>contentum, gravitatem insensibilem deperdere, et lucrari iuxta eandem pro&shy;<lb/>portionem, iuxta quam describuntur sinus, sive inaequales divisiones semi&shy;<lb/>diametri &rdquo; <emph type="italics"/>(Ars magna<emph.end type="italics"/> cit., pag. </s>

<s>491): teorema che, ritenute le pi&ugrave; comuni <lb/>denominazioni di gravit&agrave; <emph type="italics"/>assoluta<emph.end type="italics"/> e di <emph type="italics"/>respettiva,<emph.end type="italics"/> i moderni, come Leonardo <lb/>Ximenes, in proposito di ridurre alle ragioni del moto il suo <emph type="italics"/>Timpano idrau&shy;<lb/>lico,<emph.end type="italics"/> formulava dicendo che &ldquo; in qualunque fluido, racchiuso in un tubo ret&shy;<lb/>tilineo inclinato all'orizonte, sta la gravit&agrave; assoluta alla respettiva, come il <lb/>seno totale al seno dell'angolo di elevazione sopra l'orizonte &rdquo; <emph type="italics"/>(Raccolta di <lb/>Autori che trattano del moto delle acqae,<emph.end type="italics"/> 2a ediz. </s>

<s>cit., T. IX, pag. </s>

<s>313). </s></p><p type="main">

<s>Per la dimostrazione si pu&ograve; ricorrere alla Meccanica, considerando il <lb/>fluido quale un corpo grave, che ora scenda nel perpendicolo, ora lungo <lb/><figure id="id.020.01.3227.1.jpg" xlink:href="020/01/3227/1.jpg"/></s></p><p type="caption">

<s>Figura 99.<lb/>l'obliquit&agrave; di qualche piano. </s>

<s>E come allora che, di un grave, <lb/>il peso assoluto sta al respettivo, come il seno totale sta al <lb/>seno dell'angolo dell'inclinazione, ossia come la lunghezza <lb/>del piano inclinato sta alla sua altezza perpendicolare, la <lb/>Meccanica dimostra che, congiunti insieme i due pesi, stanno <lb/>in equilibrio; cos&igrave;, con le medesime ragioni, pu&ograve; aversi <lb/>dall'Idrostatica per dimostrato l'equilibrio ne'due tubi AB, <lb/>BC (fig. </s>

<s>99), dentro i quali sono i liquidi cos&igrave; congiunti, <lb/>che non pu&ograve; l'uno scendere, se l'altro non sale. </s></p><p type="main">

<s>Passa inoltre il Ximenes, in una terza proposizione, a dimostrare che <lb/>il fluido si dispone alla medesima altezza ne'due rami del sifone, anco quando <lb/>fossero incurvati in qualunque maniera. </s>

<s>La dimostrazione pu&ograve; pure ricavarsi <lb/>utilmente dalla Meccanica, applicandovi il teorema VIII, dimostrato dall'Huy&shy;<lb/>ghens nella II parte del suo Orologio oscillatorio. </s></p><p type="main">

<s>Nel primo corollario della sopra annunziata terza proposizione dell'ar&shy;<lb/>ticolo V il Ximenes cos&igrave; dice: &ldquo; Se i due rami del sifone composto fossero <lb/>di differente diametro, non perci&ograve; muta punto il Teorema, purch&egrave; il tubo <lb/>non sia capillare. </s>

<s>Poich&egrave; quella parte di fluido, che nel tubo di maggiore <lb/>diametro eccede il diametro del tubo pi&ugrave; angusto, non gravita sopra il fluido <lb/>del medesimo, ma esercita la sua pressione soltanto contro il risalto, che na&shy;<lb/>sce interiormente, quando si fa passaggio dal diametro maggiore al minore &rdquo; <lb/><emph type="italics"/>(Raccolta<emph.end type="italics"/> e T. cit., pag. </s>

<s>316). </s></p><p type="main">

<s>La ragione &egrave; puramente fisica, e si direbbe perci&ograve; impropria, in mezzo <lb/>al rigore geometrico, con cui si conduce il rimanente di questa scrittura. </s>

<s>Pi&ugrave; <lb/>appropriate erano senza dubbio le circoscrizioni, a cui ricorsero il Pascal e <lb/>il Grandi, ma, oltre che risentivano troppo dell'imperfezione de'metodi an&shy;<lb/>tichi, parevano piuttosto cose quasi posticce, che connaturate con l'Idrosta&shy;<lb/>tica. </s>

<s>Ora chi crederebbe mai che la vera, propria e diretta ragione del li&shy;<lb/>vellarsi i fluidi ne'sifoni, siano questi perpendicolari o obliqui, retti o curvi, <pb xlink:href="020/01/3228.jpg" pagenum="189"/>andanti o spezzati, uniformi o irregolari fosse ritrovata da un Discopolo di <lb/>Galileo, pochi anni dopo essersi dato a rimeditare il libro delle Galleggianti <lb/>del suo Maestro? </s>

<s>&Egrave; costui quel Niccol&ograve; Aggiunti, noto oramai in questa Sto&shy;<lb/>ria quale insigne promotore dell'Acustica e della Meccanica galileiana, che <lb/>non vuol mancare a s&egrave; medesimo in confermare nell'assoluta verit&agrave; delle sue <lb/>ragioni uno de'principali teoremi dell'Idrostatica. </s></p><p type="main">

<s>&ldquo; Quel che dimostra Herone del sifone torto, egli dice, non mi sodisfa in&shy;<lb/>teramente. </s>

<s>Per&ograve; mi messi per veder s'io potevo investigarne miglior dimostra&shy;<lb/>zione, quale penserei che fosse questa: Sia il vaso MN (fig. </s>

<s>100), ed in esso il <lb/>sifone torto PDCBA, la cui bocca A sia al pari del livello RS dell'acqua infusa. </s>

<s><lb/>Dico che, intendendosi pieno d'acqua il sifone, bench&egrave; la parte di esso D, C, B, A <lb/><figure id="id.020.01.3228.1.jpg" xlink:href="020/01/3228/1.jpg"/></s></p><p type="caption">

<s>Figura 100.<lb/>fosse difforme, e dove di grandissima, dove di po&shy;<lb/>chissima tenuta; non potr&agrave;, cadendo l'acqua dalla <lb/>bocca A, alzar l'acqua del vaso dall'altra parte P. &rdquo; </s></p><p type="main">

<s>&ldquo; Imperocch&egrave;, dovendosi far questo alzamento, <lb/>&egrave; necessario che l'acqua nelle parti D, C, B, A di&shy;<lb/>scenda, e cos&igrave;, con l'impeto che avr&agrave; discendendo, <lb/>faccia montar l'acqua del vaso. </s>

<s>Notisi dunque che <lb/>l'acqua discendendo ha il suo momento composto <lb/>e della gravit&agrave; di essa e della velocit&agrave;, con la <lb/>quale ella si move. </s>

<s>Inoltre avvertasi che, passando <lb/>l'istessa quantit&agrave; d'acqua per le parti A in tanto <lb/>tempo, in quanto era passata per le parti B, ovvero <lb/>C, ovvero D; &egrave; necessario che, nelle parti pi&ugrave; anguste del sifone, ella corra <lb/>tanto pi&ugrave; velocemente, e nelle pi&ugrave; larghe tanto pi&ugrave; tardamente, quanto ap&shy;<lb/>punto esse parti son pi&ugrave; o meno capaci. </s>

<s>Sicch&egrave; le velocit&agrave; di qualsivoglia <lb/>parti saranno reciprocamente proporzionali alle capacit&agrave; delle altre, con le <lb/>quali si conferiranno. </s>

<s>Ma come stanno le capacit&agrave; delle parti del sifone, cos&igrave; <lb/>sono le moli d'acqua in esse contenute, e come le moli dell'acqua, cos&igrave; sono <lb/>fra loro le gravit&agrave; di esse moli di acqua; adunque per tutto le velocit&agrave; ri&shy;<lb/>spondono contrariamente alle grandezze, e per&ograve; l'impeto delle acque cadenti <lb/>nelle parti A, B, C, D del sifone &egrave; per tutto lo stesso, e il suo momento per <lb/>tutte quelle parti eguale, e come se appunto fosse per tutto ugualmente <lb/>grosso come in A, come in C, ovvero in qualunque altra parte. </s>

<s>Ma quando <lb/>il sifone fosse per tutte le sue parti D, C, B, A uniformemente grosso, e la <lb/><figure id="id.020.01.3228.2.jpg" xlink:href="020/01/3228/2.jpg"/></s></p><p type="caption">

<s>Figura 101.<lb/>sua esteriore bocca pareggiasse solamente il livello <lb/>dell'acqua, noi mostreremo che sempre &egrave; necessario <lb/>che l'acqua RS non s'alzi, bench&egrave; fosse pieno il si&shy;<lb/>fone come sopra; adunque &egrave; impotente l'acqua, in <lb/>D, C, B, A scorrendo, a sollevar l'acqua del vaso <lb/>sopra il livello RS. &rdquo; </s></p><p type="main">

<s>&ldquo; Sia prima, per pi&ugrave; chiara intelligenza, il si&shy;<lb/>fone ABTR (fig. </s>

<s>101), dal quale se intenderemo uscir <lb/>l'acqua SR &egrave; necessario, acci&ograve; non resti spazio va-<pb xlink:href="020/01/3229.jpg" pagenum="190"/>cuo, che dall'altra bocca del sifone sormonti l'acqua NM eguale alla SR. </s>

<s><lb/>Perch&egrave; dunque sono due prismi uguali, le basi corrisponderanno contraria&shy;<lb/>mente alle altezze, cio&egrave; cos&igrave; star&agrave; NL ad SQ, come QR ad LM. </s>

<s>Ma come <lb/>sta NL ad SQ, cos&igrave; la velocit&agrave;. </s>

<s>con la quale s'alza l'acqua NM, alla velo&shy;<lb/>cit&agrave;, con la quale s'abbassa SR, e come sta QR ad LM, cos&igrave; sta il prisma <lb/>VR al prisma BM, cio&egrave; la gravezza dell'acqua contenuta nell'uno, alla gra&shy;<lb/>vezza dell'acqua contenuta nell'altro; adunque le velocit&agrave; rispondono con&shy;<lb/>trariamente alle gravezze, e perci&ograve;, essendo in questo caso i momenti uguali, <lb/>si far&agrave; l'equilibrio. </s>

<s>Ma se la bocca fosse in ST, pi&ugrave; alta del livello dell'acqua <lb/>OP, allora la proporzione delle velocit&agrave;, con le quali si moverebbe l'acqua, <lb/>sarebbe la stessa, ma quella della gravezza sarebbe alterata, ed averebbe la <lb/>gravezza dell'acqua in VT, alla gravezza dell'acqua in BM, minor propor&shy;<lb/>zione che prima. </s>

<s>E per&ograve;, essendo minor di quella che bisogneria, per ri&shy;<lb/>spondere permutatamente a quella delle velocit&agrave;, non saranno pi&ugrave; i loro mo&shy;<lb/>menti uguali, ma la BM preponderer&agrave; alla VT. </s>

<s>E per l'opposito, se la bocca <lb/>fosse in CD, pi&ugrave; bassa della superficie dell'acqua OP, l'acqua VD prepon&shy;<lb/>dererebbe &rdquo; (MSS. Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>102). </s></p><p type="main">

<s>E per dar la questione, cos&igrave; sottile e perci&ograve; cos&igrave; controversa, per ogni <lb/>sua parte risoluta, passa l'Aggiunti a considerare il caso che, essendo pure <lb/>il tubo di uniforme diametro, non sia andante, ma spezzato e flessuoso. </s>

<s>Pre&shy;<lb/>mette un lemma, formulato per&ograve; nella sola sua conclusione, tacendone o ac&shy;<lb/><figure id="id.020.01.3229.1.jpg" xlink:href="020/01/3229/1.jpg"/></s></p><p type="caption">

<s>Figura 102.<lb/>cennandone oscuramente i principii, meritevoli in <lb/>qualunque modo d'esser notati, o si derivino dalla <lb/>statica dello Stevino, o dalla dinamica di Galileo. </s>

<s><lb/>Quel lemma &egrave; tale: se sopra l'orizonte LC (fig. </s>

<s>102) <lb/>si sollevino due linee congiunte in B, e lungo le <lb/>quali s'intendano accomodati due solidi per tutto <lb/>ugualmente grossi, e nen tenacemente seco stessi <lb/>coerenti; la parte L non sollever&agrave; l'altra C, ma staranno insieme in equi&shy;<lb/>librio, e premeranno in L e in C quanto farebbe in M perpendicolarmente <lb/>il solido BM. </s></p><p type="main">

<s>&Egrave; manifesto che la prima parte della proposizione piglia verit&agrave; dal teo&shy;<lb/>rema dello Stevino, supponendo essere i solidi BL, BC ridotti in sezioni tutte <lb/>uguali, rappresentanti gli anelli della catena: e, come questi, cos&igrave; stanno <lb/>quelle in equilibrio, essendo in numero proporzionali alle lunghezze de'piani <lb/>LB, BC, su cui suppone l'Aggiunti che siano accomodate. </s>

<s>La seconda parte <lb/>dipende dal principio dinamico di Galileo, che dice essere uguali gl'impeti <lb/>o le velocit&agrave;, dopo scese perpendicolari uguali. </s>

<s>Che siano poi queste appli&shy;<lb/>cazioni della meccanica de'solidi ai liquidi notabili, massime in un uomo, <lb/>morto due anni prima la pubblicazione de'Dialoghi delle nuove Scienze; ne <lb/>converr&agrave; chiunque ripensi come la ragione del livellarsi il liquido, nei tubi <lb/>rappresentati dalla figura 99, si veniva a far per lui conseguire immediata&shy;<lb/>mente dal dover esso liquido, sceso in B, avere acquistato tale impeto, da <lb/>risalire in A alla medesima altezza da cui fu sceso: e non dipendendo gli <pb xlink:href="020/01/3230.jpg" pagenum="191"/>impeti o le velocit&agrave; dalla quantit&agrave; di materia, ma da sola la quantit&agrave; della <lb/>caduta; s'intender&agrave; senz'altro come si dovesse verificare il teorema, qualun&shy;<lb/>que fosse de'tubi l'inclinazione, la capacit&agrave; e la forma. </s>

<s>Ma dovendo altrove <lb/>ritornare sull'importante argomento, seguitiamo a leggere l'interrotto ma&shy;<lb/>noscritto. </s></p><p type="main">

<s>&ldquo; Se poi fosse un sifone con varie rivolte e flessuosit&agrave;, come ABCDE, <lb/>nella medesima figura 102, purch&egrave; la bocca esteriore E sia nel medesimo <lb/>piano che il livello dell'acqua FG, l'acqua non si mover&agrave;, e si far&agrave; pari&shy;<lb/>mente l'equilibrio. </s>

<s>Il che, acci&ograve; sia manifesto, intendasi la linea AE orizon&shy;<lb/>tale, sopra la quale sia la linea ABCDE in qualsivoglia modo variamente <lb/>inflessa. </s>

<s>Se noi lungo questa linea intenderemo accomodato un solido grave, <lb/>per tutto ugualmente grosso, e con le sue parti non tenacemente coerenti, <lb/>ma ad ogni minima forza flessibili; dico che, rimosso ogni altro impedimento <lb/>dalle estremit&agrave; A, E, detto solido nondimeno non si mover&agrave; da niuna parte, <lb/>n&egrave; una estremit&agrave; potr&agrave; sollevare l'altra. </s>

<s>Perch&egrave;, tirisi dal punto C la linea <lb/>parallela all'orizonte AE, qual sia LMCFH. Dipoi, dai punti L, B, D, H, ti&shy;<lb/>rinsi le perpendicolari all'orizonte LK, BM, DF, HG; la parte del grave, po&shy;<lb/>sata in BC, equipondera a quella che posa in BL, perch&egrave; s&igrave; l'uno che l'altro <lb/>sosterrebbe in equilibrio un solido grave della medesima grossezza e mate&shy;<lb/>ria che son loro, il quale pendesse secondo la linea BM, e fosse alto quanto <lb/>la linea BM. </s>

<s>E per la stessa cagione quella parte che posa in DH equipon&shy;<lb/>dera a quella, che &egrave; nel declive DC, e quella parte, che &egrave; posta rasente HE, <lb/>equilibrerebbe un solido della medesima materia e grossezza, lungo solo <lb/>quanto HG, ovvero LK, se per&ograve; egli fosse sospeso perpendicolarmente, e tanto <lb/>farebbe il grave locato in LA. </s>

<s>Adunque il grave in DHE equipondera il grave <lb/>posto in BLA. </s>

<s>Perch&egrave; dunque tutte le parti del grave, che lo tirano verso <lb/>l'estremit&agrave; E, sono d'ugual momento con quelle, che lo tirano verso l'altra <lb/>estremit&agrave; A; perci&ograve; non si far&agrave; movimento alcuno, ma s&igrave; bene subito che <lb/>l'una delle estremit&agrave; si allungher&agrave; o scorcer&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Lo stesso possiamo tener per certo che avvenga ne'sifoni ritorti, anco <lb/>con superficie curve, imperocch&egrave; la curvit&agrave; della superficie non &egrave; altro che <lb/>infinita inclinazione di piani. </s>

<s>E non importa poi che in questa sorta di sifoni, <lb/>per i quali s'ha da mover l'acqua, la canna sia inegualmente grossa per tutto, <lb/>avendo noi gi&agrave; dimostrato esser lo stesso, atteso che nelle parti pi&ugrave; larghe <lb/>l'acqua si move men velocemente, e nelle strette pi&ugrave; velocemente, sicch&egrave; i <lb/>suoi momenti vengono per tutto in questo modo ragguagliati &rdquo; (ivi, fol. </s>

<s>103). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Come la teoria del sifone ritorto, data cos&igrave; dall'Aggiunti, sia applicabile <lb/>all'equilibrio de'liquidi nei vasi comunicanti, &egrave; cosa per s&egrave; manifesta, non <lb/>occorrendo a far altro, per ridurre alla medesima argione i due casi, che <pb xlink:href="020/01/3231.jpg" pagenum="192"/>riguardare il sifone stesso con le sue braccia rivolte in alto. </s>

<s>N&egrave; meno evi&shy;<lb/>dente &egrave; che si venivano, ragionando a quel modo, a togliere tutte le diffi&shy;<lb/>colt&agrave;, che s'incontravano nella dimostrazione di Galileo, sia rispetto al prin&shy;<lb/>cipio da cui moveva, sia rispetto alle variet&agrave;, alle quali poteva andare sog&shy;<lb/>getta la pi&ugrave; semplice ipotesi ammessa da lui, delle forme cio&egrave; sempre <lb/>regolari dei vas&igrave;. </s>

<s>I successori usarono la medesima arte dell'Aggiunti, per <lb/>salvar dalle contradizioni il metodo galileiano, che perci&ograve; rimane tuttavia in <lb/>onore, e anzi &egrave; bene spesso preferito agli altri dalla Scienza, quando, in qual&shy;<lb/>che pi&ugrave; difficile incontro, vuol pi&ugrave; agile movere i passi. </s></p><p type="main">

<s>Sorte molto diversa ebbe per&ograve; a subire quel metodo, quando Galileo <lb/>pens&ograve; di applicarlo a dimostrare i teoremi fondamentali dell'Idrostatica. </s>

<s>Ri&shy;<lb/>ducendosi in generale a conferire i momenti della resistenza dell'acqua a <lb/>essere alzata, co'momenti della gravit&agrave; premente il solido, si fondava in una <lb/>tal supposizione, la quale, non verificandosi il discorso non riesce concludente, <lb/>essendo che il momento della resistenza dell'acqua &egrave; manifestamente nullo, <lb/>quando il vaso &egrave; pieno, e l'acqua stessa perci&ograve;, immergendovi il solido, non <lb/>s'alza intorno a lui, ma si versa. </s>

<s>Inoltre, perch&egrave; la mole dell'acqua alzata <lb/>&egrave; sempre minore del solido, potendosi dare il caso che l'alzamento di quella <lb/>e l'abbassamento di questo siano uguali, s'avrebbero uguali velocit&agrave; in due <lb/>grandezze diverse, per cui non sarebbe lecito, in tal contingenza, inferirne la <lb/>ragione dell'equilibrio. </s></p><p type="main">

<s>Il difetto poi del metodo generale si fa risentire anche di pi&ugrave; nei casi <lb/>particolari, come quando Galileo, per esempio, vuol dimostrare che un solido <lb/>&egrave; giustamente sostenuto dal momento dell'acqua, che fa alzarglisi intorno, <lb/>sia il recipiente angustissimo o immenso, sembrando per lo meno cosa assai <lb/>strana l'andar ricercando, nell'alzamento che fa lungo i suoi lidi l'acqua <lb/>dell'oceano, il momento della forza, che vi sostien galleggiante una festuca. </s></p><p type="main">

<s>A strette di dubbi ben assai pi&ugrave; forti metteva la proposizione prece&shy;<lb/>dente a questa, che &egrave; la terza ordinata da noi dal trattato delle Galleggianti, <lb/>e nella quale Galileo, propostosi il prisma AF rappresentato dentro il vaso <lb/>DB della figura 66, e supposto men grave in specie dell'acqua, vuol dimo&shy;<lb/>strare che sar&agrave; sollevato dall'acqua CE circonfusa, con queste precise parole <lb/>concludendo la sua dimostrazione: &ldquo; Adunque il peso assoluto dell'acqua CE, <lb/>al peso assoluto del prisma AF, ha maggior proporzione che l'alzamento del <lb/>prisma AF, all'abbassamento di essa acqua CE. </s>

<s>Il momento dunque compo&shy;<lb/>sto della gravit&agrave; assoluta dell'acqua CE, e della velocit&agrave; del suo abbassa&shy;<lb/>mento, mentre ella fa forza premendo di scacciare e di sollevare il solido AF, <lb/>&egrave; maggior del momento composto del peso assoluto del prisma AF, e della <lb/>tardit&agrave; del suo alzamento, col qual momento egli contrasta allo scacciamento <lb/>e forza fattagli dal momento dell'acqua: sar&agrave; dunque sollevato il prisma &rdquo; <lb/>(Alb. </s>

<s>XII, 21). </s></p><p type="main">

<s>A questo punto non potevano gli studiosi non lasciare in sospeso la let&shy;<lb/>tura, per domandare a s&egrave; medesimi in che modo pu&ograve; l'acqua CE esercitare <lb/>contro il solido la sua forza. </s>

<s>Si dice che essa acqua &egrave; circonfusa al prisma, <pb xlink:href="020/01/3232.jpg" pagenum="193"/>ma veramente ella non ne bagna che una faccia sola, rimanendo, per sup&shy;<lb/>posizione, le altre tre laterali, e il fondo, aderenti alle pareti del vaso. </s>

<s>I li&shy;<lb/>beri ingegni e imbevuti alle pi&ugrave; sane dottrine dello Stevino, non avrebbero <lb/>penato a dire che il solido, nella fatta ipotesi, rimarrebbesi eternamente in <lb/>fondo al vaso, dove fu posto, e fosse men grave in specie dell'acqua quanto <lb/>si voglia, e gli fosse questa circonfusa, e sollevatagli a qualunque pi&ugrave; smi&shy;<lb/>surata altezza. </s>

<s>Ma l'esclusivo magistero di Galileo non permettendo una tale <lb/>libert&agrave; di giudizio, si tormentavano stranamente gl'ingegni, per intendere in <lb/>che modo potesse l'acqua scacciar dal fondo il solido, e levarselo in capo. </s>

<s><lb/>Diceva il Maestro che ella <emph type="italics"/>fa forza premendo,<emph.end type="italics"/> e premere non pu&ograve;, se non <lb/>la parete sola che ella bagna. </s>

<s>Come per&ograve; da quest'unica pressione potesse <lb/>resultarne il sollevamento era duro a intendere. </s>

<s>Fosse almeno bagnato il <lb/>prisma da due facce opposte si potrebbe rassomigliar l'effetto a quel che si <lb/>osserva, quando due spingono l'un contro l'altro un peso, che nello stesso <lb/>tempo lo sollevano, ma uno solo, quanto si voglia gagliardo, facendo forza <lb/>nel medesimo modo, non riuscirebbe a sollevarlo mai di un capello. </s>

<s>Poi chi <lb/>cos&igrave; ragionava avrebbe voluto riaversi dalle pene del dubbio, ripensando che <lb/>forse la parete opposta a quella bagnata potrebbe contrastare con la sua <lb/>immobilit&agrave;, facendo sforzo uguale a quello, che si sarebbe fatto dall'acqua. </s></p><p type="main">

<s>Fra i seguaci di Galileo, che s'aggiravano in tal guisa fra le angustie <lb/>del loro pensiero, troviamo l'Aggiunti, mentre era intorno a risolvere un <lb/>problema idrostatico, applicandovi i nuovi principii insegnati dal suo Mae&shy;<lb/>stro. </s>

<s>&ldquo; Sia, egli dice, GH (fig. </s>

<s>103) un vaso parallelepipedo, con la base ori&shy;<lb/>zontale, ed in esso sia il solido CB, men grave in specie dell'acqua, il quale, <lb/><figure id="id.020.01.3232.1.jpg" xlink:href="020/01/3232/1.jpg"/></s></p><p type="caption">

<s>Figura 103.<lb/>con la sua superficie AB e con l'opposta, <lb/>combaci esquisitamente le superficie late&shy;<lb/>rali del vaso, a quel modo che suppone <lb/>il Galileo nel suo <emph type="italics"/>Delle galleggianti.<emph.end type="italics"/> Dipoi <lb/>infondasi acqua dall'una parte del vaso, <lb/>sicch&egrave; ella sia al livello ZU, nel quale stato <lb/>si faccia, tra il solido e l'acqua, l'equi&shy;<lb/>librio. </s>

<s>Sia poi qualunque minima forza Y, <lb/>che tiri orizontalmente detto solido CB. </s>

<s>Di&shy;<lb/>mostreremo tal solido, da qualunque mi&shy;<lb/>nima forza, potere esser mosso e quanto, <lb/>purch&egrave; dall'altra parte GK del vaso s'in&shy;<lb/>tenda di mano in mano tant'acqua, che <lb/>pareggi il livello QZ. </s>

<s>E prima, considerisi <lb/>ch&egrave;, se detto solido si avesse a movere nell'orizonte GD, essendo il vaso <lb/>vuoto, allora sarebbe mosso da qualunque minima forza. </s>

<s>Ma perch&egrave; adesso, <lb/>movendosi verso la parte D, &egrave; necessario che la medesima acqua circonfusa DM, <lb/>da tal movimento spinta in vaso di minor base s'inalzi, e a tale alzamento <lb/>ella contrasta anche lateralmente; adunque bisogna che noi dimostriamo, dalla <lb/>forza Y, all'impulso laterale di quant'acqua si possa far resistenza. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/3233.jpg" pagenum="194"/><p type="main">

<s>&ldquo; Il peso di tutto il solido CB &egrave; uguale al peso di una mole di acqua, <lb/>eguale al solido RB. </s>

<s>Intendasi dunque il solido RB essere ugualmente grave <lb/>in specie all'acqua, e la parte rimanente KC non aver peso alcuno, sicch&egrave; <lb/>il solido tutto CB rimarr&agrave; del medesimo momento che prima. </s>

<s>Sia inoltre la <lb/>forza Y uguale al peso della mole d'acqua I, e sopra la base RS trovisi il <lb/>solido SP, uguale in mole ed in peso al solido I, e l'altezza di detto solido <lb/>SP sia la linea VU. </s>

<s>Dalla linea poi VA piglisi la linea VN, eguale alla VU: <lb/>dico che il solido CB, dalla forza Y, sar&agrave; mosso tanto per l'orizonte GD, <lb/>verso la parte D, sicche l'acqua arrivi colla superficie di sopra al punto N. &rdquo; </s></p><p type="main">

<s>&ldquo; Perch&egrave;, intendasi mosso il solido CB talmente, che l'acqua si sia al&shy;<lb/>zata al detto punto N, e dopo tal movimento il solido CB sia venuto nel <lb/>sito XO, dimodoch&egrave; il solido Q&prime;M sia l'istesso che il solido SP, e la linea <lb/>TL sia l'istessa che VU, e TN sia la UN. </s>

<s>Perch&egrave; l'acqua FZ &egrave; quella, che <lb/>era nel luogo, dove &egrave; subentrato il solido RQ&prime;, adunque il solido RQ&prime; &egrave; uguale <lb/>al solido FZ, e per&ograve;, come sta il solido MQ&prime; al solido RQ&prime;, cos&igrave; star&agrave; al so&shy;<lb/>lido FZ. </s>

<s>Ma al solido RQ&prime; egli sta come la linea LT, alla linea VT; dunque <lb/>l'istesso solido MQ&prime;, anco al solido FZ, sta come la linea LT, o vogliam dire <lb/>VU, cio&egrave; la VN, cio&egrave; la TN, poich&egrave; tutte queste sono uguali, alla TV. </s>

<s>Di&shy;<lb/>remo dunque il solido Q&prime;M, cio&egrave; il solido SP, cio&egrave; il solido I, cio&egrave; la forza, <lb/>ovver peso Y, sta all'acqua FZ, come TN alla TV. </s>

<s>Ma perch&egrave;, nel mede&shy;<lb/>simo tempo che il solido CB, cio&egrave; la forza Y (poich&egrave; il solido e la forza che <lb/>lo tira si muovono con ugual velocit&agrave;) si &egrave; mosso per la distanza VT, l'acqua <lb/>si &egrave; alzata per la distanza TN; adunque la velocit&agrave;, con la quale si muove <lb/>il solido CB, cio&egrave; la forza ovvero peso Y, alla velocit&agrave;, con la quale si move <lb/>l'acqua, ovvero peso FZ: sta come la linea VT alla TN. </s>

<s>Ma il peso Y al <lb/>peso FZ stava come la TN alla TV; adunque la proporzione delle velocit&agrave;, <lb/>con le quali detti pesi si movono, &egrave; contraria alla proporzione dei pesi. </s>

<s>Ma <lb/>quando sono due gravi, che faccian forza di movere l'un l'altro, ogni volta <lb/>che la gravit&agrave; dell'uno, alla gravit&agrave; dell'altro, sta come la velocit&agrave;, con che <lb/>si moverebbe l'altro, a quella con cui si moverebbe l'uno, allora fra que'due <lb/>gravi si fa l'equilibrio, n&egrave; l'uno vince l'altro; adunque, essendo in tal modo <lb/>costituiti la forza Y e l'acqua FZ, l'acqua FZ non mover&agrave; la forza Y, n&egrave; in <lb/>conseguenza il solibo CB. &rdquo; </s></p><p type="main">

<s>&ldquo; Tutto questo passa bene, secondo la dottrina del signor Galileo, se <lb/>noi porremo che l'acqua sia solamente dalla banda D. </s>

<s>Ma qui mi nascono <lb/>molte difficolt&agrave;, che fanno contro al Galileo ancora, perch&egrave; non pare che <lb/>basti, acci&ograve; un solido men grave in specie dell'acqua sia alzato, che l'acqua <lb/>lo bagni da una parte sola, e secondo quell'altezza che vuole il Galileo, ma <lb/>tal sollevamento bisogna che sia a mio giudizio d'ogni intorno, o almeno <lb/>almeno da ambe le superficie opposte. </s>

<s>Altrimenti, siccome due, spingendo <lb/>l'un contro l'altro un solido, e nel medesimo tempo alzando lo sollevano, <lb/>ma se fosse uno solo, quanto si voglia gagliardo, facendo forza nello stesso <lb/>modo, mai l'alzerebbe; cos&igrave; l'acqua da una parte sola, sia quanto si voglia <lb/>alta, non par che possa alzare un solido che tocchi il fondo. <emph type="italics"/>Sed haec pen-<emph.end type="italics"/><pb xlink:href="020/01/3234.jpg" pagenum="195"/><emph type="italics"/>siculatius<emph.end type="italics"/> (?).... Ma se il solido, dalla parte opposta alla bagnata, sar&agrave; ade&shy;<lb/>rente alla sponda immobile del vaso, pare che si possa far l'alzamento.... <lb/>Ma pure considera bene. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>106, 7). </s></p><p type="main">

<s>La tenzone dei dubbi cos&igrave; viva e vera, come la descrive l'Aggiunti, era <lb/>poi quella, che si faceva nel pensiero di tutti gli altri, e che dur&ograve; per pi&ugrave; <lb/>di un mezzo secolo in quelli stessi, i quali pi&ugrave; facevano onore alla Scuola <lb/>galileiana. </s>

<s>Gli stranieri pi&ugrave; liberi, e con la mente aperta a ricevere il ristoro <lb/>di altre tradizioni, se imitarono l'esempio di Galileo in applicare il principio <lb/>delle velocit&agrave; virtuali a dimostrar l'equilibrio ne'vasi comunicanti, rifuggi&shy;<lb/>rono saviamente dall'usare il metodo di lui, riconosciuto vizioso e insuffi&shy;<lb/>ciente, e dar la ragione de'principali fatti idrostatici, per cui ritornarono <lb/>agli antichi modi archimedei, senza altra cura che di renderli pi&ugrave; brevi, pi&ugrave; <lb/>facili ed eleganti. </s></p><p type="main">

<s>Il Pascal, inoculando nel suo trattato il principio delle pressioni, riusc&igrave; <lb/>mirabilmente a condensare in una mezza paginetta il primo libro <emph type="italics"/>De insi&shy;<lb/>dentibus humido.<emph.end type="italics"/> Supposto un solido immerso nell'acqua in forma di cubo, <lb/>&egrave; premuto, egli dice, contro le facce laterali opposte ugualmente, ma pi&ugrave; di <lb/>sotto che di sopra, con forza uguale al peso di una mole di acqua, pari alla <lb/>mole del solido stesso. </s>

<s>&ldquo; De sorte qu'un corps, qui est dans l'eau, y est port&eacute; <lb/>de la mesme sorte, que s'il estoit dans un bassin de balance, dont l'autre <lb/>f&ugrave;t charg&eacute; d'un volume d'eau &eacute;gal au sieu. </s>

<s>D'o&ugrave; il paroist que, s'il est de <lb/>cuivre ou d'une autre matiere qui pese plus que l'eau en pareil volume, il <lb/>tombe, car son poids l'emporte sur celuy qui le contrebalance. </s>

<s>S'il est de <lb/>bois, ou d'une autre matiere plus legere que l'eau en pareil volume, il monte <lb/>avec toute la force, dont le poids de l'eau le surpasse. </s>

<s>Et s'il pese egale&shy;<lb/>ment, il ne descend ny ne monte comme la cire, qui se tient a peu pres <lb/>dans l'eau au lieu ou on l'a met &rdquo; <emph type="italics"/>(De l'equil. </s>

<s>des liquers<emph.end type="italics"/> cit., pag. </s>

<s>26). </s></p><p type="main">

<s>Il Mariotte, in fine al discorso primo della parte seconda del suo trat&shy;<lb/>tato <emph type="italics"/>Du mouvement des eaux,<emph.end type="italics"/> stabilisce quattro regole, la prima delle quali <lb/>corrisponde alla IV proposizione archimedea, la seconda alla V, e la terza e <lb/>la quarta alla VII. </s>

<s>Egli pure, lasciata addietro la teoria statica del vette, e <lb/>il metodo di conferire i momenti del liquido che s'alza, e del solido che <lb/>si abbassa, posato sopra l'umida superficie, fa ricorso alla solita bilancia im&shy;<lb/>maginaria, concludendone con evidente facilit&agrave; le ragioni dello stare, dello <lb/>scendere e del salire, nei vari casi, le varie grandezze immerse. <emph type="italics"/>(Oeuvres,<emph.end type="italics"/><lb/>T. II cit., pag. </s>

<s>372-80). </s></p><p type="main">

<s>L'Huyghens proponeva, col principio della conservazion delle forze, in&shy;<lb/>cluso nella prima ipotesi premessa alla parte IV dell'Orologio oscillatorio, <lb/>che dice <emph type="italics"/>si pondera quodlibet vi gravitatis suae moveri incipiant, non posse <lb/>centrum gravitatis ex ipsis compositae altius quam, ubi incipiente motu <lb/>reperiebatur, ascendere;<emph.end type="italics"/> proponeva dicevasi di dimostrar tutto ci&ograve;, che aveva <lb/>dimostrato Archimede intorno alle propriet&agrave; dei corpi notanti. </s>

<s>&ldquo; Haec autem <lb/>hypothesis nostra ad liquida etiam corpora valet, ac per eam, non solum <lb/>omnia illa, quae de innatantibus habet Archimedes, demonstrari possunt, sed <pb xlink:href="020/01/3235.jpg" pagenum="196"/>et alia pleraque mechanica theoremata &rdquo; <emph type="italics"/>(Opera varia,<emph.end type="italics"/> Vol. </s>

<s>I, Lugduni <lb/>Batav. </s>

<s>1724, pag. </s>

<s>121 e 123). </s></p><p type="main">

<s>Unico forse tra'matematici stranieri il Dechales intese di ritornare ai <lb/>metodi di Galileo. </s>

<s>Il principio, ch'egli pone per fondamento alla sua Idro&shy;<lb/>statica, &egrave; quello delle velocit&agrave;, che stando contrariamente ai pesi danno la <lb/>ragione dell'equilibrio nella stadera. </s>

<s>&ldquo; Ad hoc igitur principium revocabi&shy;<lb/>mus quaecumque de natantibus in humido demonstrabuntur: ita enim exacte <lb/>hoc principium observatur in hac materia, ut nulla sit statera exactior &rdquo; <lb/><emph type="italics"/>(Cursus mathematicus editio secunda,<emph.end type="italics"/> T. III, Lugduni 1690, pag. </s>

<s>93). Se <lb/>dunque da una parte di questa esattissima stadera s'intenda posto il corpo <lb/>immerso, e dall'altra una mole di acqua, tutto il negozio si riduce a con&shy;<lb/>ferire insieme i loro momenti. </s>

<s>&ldquo; Quare restat examinandum utriusque, tam <lb/>corporis demersi quam aquae ascendentis, momentum, ut de toto negotio <lb/>ferri possit iudicium &rdquo; (ibid., pag. </s>

<s>94). </s></p><p type="main">

<s>Incomincia l'esame dal dimostrare che, se la superficie CB (fig. </s>

<s>104) <lb/>dell'acqua circonfusa &egrave; uguale alla base AC del prisma, che vi s'immerge, <lb/>ascender&agrave; del liquido una mole, pari alla met&agrave; della parte del solido demersa. </s>

<s><lb/>La verit&agrave; si rende facilmente manifesta, ripensando che, abbassatosi il pri&shy;<lb/><figure id="id.020.01.3235.1.jpg" xlink:href="020/01/3235/1.jpg"/></s></p><p type="caption">

<s>Figura 104.<lb/>sma DC per esempio in D&prime;C&prime;, l'acqua HB salita &egrave; <lb/>quella, che era dianzi in luogo di AC&prime;, e HB, NC sono <lb/>uguali per supposizione, onde NC&prime;, parte del solido <lb/>immersa, &egrave; doppia dell'acqua HB, che il solido stesso <lb/>ha scacciata. </s></p><p type="main">

<s>Suppongasi ora, soggiunge il Dechales, che la <lb/>mole NC&prime; dell'acqua, o la sua uguale HL, pesi quanto <lb/>il prisma D&prime;C&prime;: dico che i due pesi rimarranno in <lb/>equilibrio. </s>

<s>Chi per&ograve; comincia a leggere la dimostra&shy;<lb/>zione resta maravigliato a trovarci abbandonata la <lb/>statica dei momenti, in che si diceva consistere tutto questo negozio, per <lb/>tornare indietro ai modi fisici di Archimede. </s>

<s>Dice infatti l'Autore che, se <lb/>suppongasi venire il prisma trasformato nell'acqua NC&prime;, pesando questa quanto <lb/>l'acqua HL, le braccia uguali A&prime;C&prime;, C&prime;L della bilancia immaginaria A&prime;L non <lb/>possono non andare equilibrate. </s></p><p type="main">

<s>Chi prosegue anche a leggere scopre la ragione, per cui il Dechales, <lb/>che mostravasi sulle mosse cos&igrave; fedele, diserti a un tratto dalla scuola di <lb/>Galileo. </s>

<s>Quella ragione insomma &egrave; che, applicando i metodi di lui, si veniva <lb/>a concludere il contrario della verit&agrave; dimostrata, non essendo, nella fatta sup&shy;<lb/>posizione, il momento del prisma uguale, ma duplo al momento dell'acqua. </s>

<s><lb/>Il momento infatti della discesa del prisma &egrave; misurato dal prodotto della ve&shy;<lb/>locit&agrave; CC&prime; per il peso D&prime;C&prime;, e il momento dell'acqua dal prodotto della ve&shy;<lb/>locit&agrave; HC per il peso della mole fluida HB. Ma, perch&egrave; le due velocit&agrave; sono <lb/>uguali, i momenti stanno dunque come i semplici pesi, ossia l'uno &egrave; vera&shy;<lb/>mente doppio dell'altro, e perci&ograve; &egrave; impossibile che, tra il prisma immerso <lb/>e l'acqua sollevata, si faccia l'equilibrio. </s>

<s>&ldquo; Nascitur tamen difficultas ex su-<pb xlink:href="020/01/3236.jpg" pagenum="197"/>perioribus propositionibus. </s>

<s>Pars prismatis demersa est dupla aquae ascenden&shy;<lb/>tis, et ascensus unius aequalis est descensus alterius: igitur non potest esse <lb/>aequilibrium &rdquo; (ibid., pag. </s>

<s>95). </s></p><p type="main">

<s>Rispondesi qui alle difficolt&agrave;, non direttamente difendendo il principio <lb/>assunto, ma indirettamente ricorrendo a uno nuovo, col dire che, seb bene il <lb/>prisma scaccia la sola acqua BH, contrasta nulladimeno e con l'acqua BH, <lb/>e con l'altra CL, <emph type="italics"/>prorsus modo ut si essent duo pondera in lance utra&shy;<lb/>que staterae,<emph.end type="italics"/> la qual bilancia &egrave; necessariamente in equilibrio, perch&egrave; tanto <lb/>pesa il prisma sull'un braccio immaginario A&prime;C&prime;, quanto l'acqua HL sul&shy;<lb/>l'altro. </s>

<s>Ma questo era un confessare l'impotenza del nuovo metodo galileiano <lb/>a dimostrare la verit&agrave; del Teorema idrostatico, per cui fu costretto il Dechales, <lb/>suo malgrado, a abbandonarlo, e a ricorrere all'antico: confessione ch'egli <lb/>stesso esprime con queste parole: &ldquo; Ostendo item alio modo esse aequilibrium. </s>

<s><lb/>Cum ex suppositione aqua aequalis in mole parti prismatis NC&prime; sit duarum li&shy;<lb/>brarum, in proposito exemplo, aqua HL erit etiam duarum librarum. </s>

<s>Aquae <lb/>igitur A&prime;M, ML sunt in aequilibrio. </s>

<s>Sed aqua HL duarum librarum est in <lb/>aequilibrio cum prismate, quod supponitur etiam esse duarum librarum; ergo <lb/>aggregatum ex prismate et aqua A&prime;M est in aequilibrio cum aggregato ex <lb/>aqua ML et LH. </s>

<s>Ergo omnia permanent in aequilibrio &rdquo; (ibid., pag. </s>

<s>96). </s></p><p type="main">

<s>Cos&igrave; dunque essendosi dimostrato che, se la parte del corpo immersa <lb/>sia uguale in mole all'acqua che equipondera tutto il corpo, si far&agrave; l'equi&shy;<lb/>librio; passa l'Autore a dimostrare, nelle seguenti proposizioni VII, VIII e IX, <lb/>la ragion del notare, dell'immergersi tutto e dell'affondare un solido, ritor&shy;<lb/>nando alla bilancia archimedea, quasi non avesse nelle presenti novit&agrave; sa&shy;<lb/>puto ritrovar nulla di meglio al suo bisogno. </s></p><p type="main">

<s>Bastino questi esempi per quel che riguarda gli stranieri. </s>

<s>Ora &egrave; da ve&shy;<lb/>dere come si portassero i Nostri, riappiccando il filo della Storia a quel punto, <lb/>in cui lasciammo l'Aggiunti a combattere co'suoi propri pensieri. </s>

<s>Par che <lb/>le cose volgessero in peggio nei successori, se il Michelini giunse a negare <lb/>anche quelle pressioni laterali, unico rifugio, che esso Aggiunti trovava, per <lb/>darsi a intendere in qualche modo come si potesse sollevare il prisma dal <lb/>fondo, a circonfondergli l'acqua da una parte sola del vaso. </s>

<s>L'errore, suc&shy;<lb/>chiato dagl'insegnamenti di Galileo, si trasfuse, per la concordia autorevole <lb/>dei due maestri nel Borelli e nel Viviani, i quali s'ostinarono con incredi&shy;<lb/>bile temerit&agrave; a ripetere che i liquidi non premono, se non ci&ograve; che soggiace <lb/>a loro in direzione perpendicolare. </s>

<s>I depositari fedeli delle private dottrine <lb/>del Torricelli insorsero, per l'amore e per la dignit&agrave; della scienza, contro <lb/>cos&igrave; fatti deliri, e a costoro il Borelli particolarmente rispondeva com'ebro <lb/>irritato ne'suoi sopori. </s>

<s>Quelle risposte, nella loro integrit&agrave;, si leggeranno <lb/>in altra occasione: basti per ora citarne una, tanto per persuadere chi non <lb/>crederebbe un tant'uomo capace di commettere i paralogismi, che si con&shy;<lb/>tengono in questo discorso: </s></p><p type="main">

<s>&ldquo; Passo ora alla ragione addotta dai medesimi signori oppositori, quando <lb/>dicono esser segno evidente che l'acqua faccia forza da'fianchi, perch&egrave; si <pb xlink:href="020/01/3237.jpg" pagenum="198"/>vede che, fatto un forame in una delle sponde del vivaio, o canale, l'acqua <lb/>esce da esso. </s>

<s>Come per esempio, se nel vivaio ABCL (fig. </s>

<s>105) si aprir&agrave; un <lb/>forame in C, si vede che l'acqua esce per CD; adunque &egrave; segno evidente <lb/>che l'acqua non solamente preme perpendicolarmente verso B, ma ancora <lb/>fa forza al liquido per la linea inclinata AHC. </s>

<s>E qui io dico che, se il ve&shy;<lb/><figure id="id.020.01.3237.1.jpg" xlink:href="020/01/3237/1.jpg"/></s></p><p type="caption">

<s>Figura 105.<lb/>dersi cader l'acqua CD &egrave; effetto che necessariamente <lb/>segue dalle pressioni dell'acqua, fatte obliquamente <lb/>per AHC; dunque se tal acqua, in cambio di scen&shy;<lb/>dere all'in gi&ugrave; per CD, si veder&agrave; salire all'in su, <lb/>dovrebbe esser necessario argomento che l'acqua sta&shy;<lb/>gnante facesse forza premendo anco all'in su. </s>

<s>Ma se <lb/>io far&ograve; nel fianco E un forame e vi salder&ograve; un can&shy;<lb/>nello torto all'in su, qual'&egrave; EI, io vedr&ograve; scappare <lb/>l'acqua da B, e salire all'in su verso I, e tale spinta <lb/>vien fatta dalla forza dell'acqua stagnante; adunque ella, oltre al premere <lb/>perpendicolarmente il fondo ed i fianchi, fa ancora forza all'in su. </s>

<s>Ma que&shy;<lb/>sto repugna alla natura de'gravi; adunque ella non fa forza obliquamente <lb/>verso i lati del vivaio &rdquo; (MSS. Gal. </s>

<s>disc., T. XVII, fol. </s>

<s>5). </s></p><p type="main">

<s>Negate le pressioni fatte dal liquido lateralmente, e di sotto in su, &egrave; fa&shy;<lb/>cile giudicare in quale stato si dovesse ritrovare a quel tempo la scienza <lb/>idrostatica nella mente del Borelli. </s>

<s>E supponendo che, nello studiare il Ga&shy;<lb/>lileo, gli occorressero i medesimi dubbi dell'Aggiunti, convien dire che non <lb/>avesse alcun modo a risolverli, se l'acqua non preme il solido n&egrave; in su, <lb/>n&egrave; da lato, e se, per non repugnare alla natura dei gravi, non pu&ograve; ella far <lb/>altro che conficcare pi&ugrave; fortemente il solido bagnato contro il fondo su cui <lb/>riposava. </s></p><p type="main">

<s>Al Viviani, giovane studente nella casa di Arcetri con l'assistenza viva <lb/>di Galileo, parve tutto aureo e maraviglioso quel che leggeva nel Discorso <lb/>intorno alle cose che stanno, e che si movon nell'acqua. </s>

<s>Anzi quelle descri&shy;<lb/>zioni, che ei trovava, della immersione e della demersione de'prismi retti di <lb/>base rettangolare dentro vasi parallelepipedi, a fin di paragonare le moli <lb/>acquee con le solide; tutt'altro che dargli occasione di dubitare gli sugge&shy;<lb/>rirono un'invenzione, di cui poi vecchio, e per bene altri meriti gloriosis&shy;<lb/>simo, si compiacque, e intorno alla quale vogliamo intrattenere alquanto il <lb/>discorso, per la curiosit&agrave; del soggetto, e anche un poco per l'importanza. </s></p><p type="main">

<s>Il Tartaglia, come si rammenteranno i nostri Lettori, concludeva la pro&shy;<lb/>posizione prima del suo secondo Ragionamento, osservando che si poteva per <lb/>essa <emph type="italics"/>conoscere l'area corporale de ogni strania forma di corpo.<emph.end type="italics"/> La solu&shy;<lb/>zione era data per via di Matematica, ma quel richiamar che il Tartaglia <lb/>stesso faceva l'attenzione dei Matematici sull'esperienza, che si diceva aver <lb/>fatto Archimede, per scoprire il furto dell'oro nella corona, sostituendo a mi&shy;<lb/>gliore effetto l'uso della sua Bilancetta; aveva fatto sovvenire ad alcuni un <lb/>modo assai pi&ugrave; spedito e di facile esecuzione meccanica, per quadrare ogni <lb/>forma di corpo pi&ugrave; irregolare. </s></p><pb xlink:href="020/01/3238.jpg" pagenum="199"/><p type="main">

<s>Il Clavio, nel quinto libro della sua <emph type="italics"/>Geometria pratica,<emph.end type="italics"/> diffuse la no&shy;<lb/>tizia dell'invenzione, che egli dice di aver letta in alcuni scrittori, e che poi <lb/>cos&igrave; descrive: &ldquo; Paretur arca lignea, ex asseribus levigatis, instar parallele&shy;<lb/>pipedi cuiusdam, quae pice ita oblinatur, ut aquam continere possit. </s>

<s>Arca <lb/>haec tantae debet esse longitudinis, latitudinis atque altitudinis, ut corpus <lb/>metiendum, intra ipsam positum, aqua totum possit operiri. </s>

<s>Posita autem <lb/>hac arca horizonti aequidistante, beneficio libellae aut perpendiculi, infunda&shy;<lb/>tur in eam tantum aquae, quantum satis est ut corpus impositum omnino <lb/>tegat, notenturque diligenter suprema latera aquae in asseribus arcae, ut <lb/>habeatur altitudo aquae usque ad arcae fundum. </s>

<s>Extracto deinde corpore, ita <lb/>tamen ut nihil aquae extra arcam cadat, notentur rursum latera aquae post&shy;<lb/>quam quievit. </s>

<s>Quod si metiamur duo parallepipeda, quorum basis commu&shy;<lb/>nis est arcae fundus, sive basis, altitudines vero rectae a lateribus aquae <lb/>notatis usque ad basem, et minus a maiore subtrahamus; relinquetur pa&shy;<lb/>rallelepipedum soliditati corporis propositi omnino aequale &rdquo; (Romae 1604, <lb/>pag. </s>

<s>260, 61). In simile modo, soggiunge, s'avrebbe meccanicamente la mi&shy;<lb/>sura della capacit&agrave; di un vaso di qualunque forma, sommergendolo prima <lb/>pieno di arena, ben chiuso dal suo testo che non ci avesse a entrar dentro <lb/>l'acqua, e poi nuovamente sommergendovelo vuoto. </s></p><p type="main">

<s>Galileo, come apparisce dalla fine del suo Dialogo intorno alla Bilan&shy;<lb/>cetta idrostatica da noi pubblicato, fu forse il primo, che applic&ograve; le im&shy;<lb/>mersioni dentro l'acqua, ricevuta in un vaso parallelepipedo, a quadrare le <lb/>figure piane e i solidi geometrici circoscritti da curve, ed essendo stato quel <lb/>Dialogo dettato allo stesso Viviani, il quale pure confessa di aver veduto an&shy;<lb/>che il Clavio, si dovrebbe dire che poco rimanesse del merito nell'inven&shy;<lb/>zione allo studente nell'ospizio di Arcetri, se non si ripensasse che egli non <lb/>aveva allora pi&ugrave; che ventidue anni. </s>

<s>In ogni modo leggiamo quel ch'egli dava <lb/>per frutto primaticcio de'suoi studi: </s></p><p type="main">

<s>&ldquo; Dimostrazioni trovate da me Vincenzio Viviani, nel mese di aprile 1640. <lb/><emph type="italics"/>Teorema lemmatico.<emph.end type="italics"/> Se un cilindro sar&agrave; uguale, ed egualmente alto che un <lb/>parallelepipedo di base quadrata; dico che il cerchio base del cilindro sar&agrave; <lb/>uguale al quadrato base del parallipipedo &rdquo; (MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>30). <lb/>La dimostrazione &egrave; lunga e tediosa: un esercizio giovanile addiritura. </s>

<s>Dal&shy;<lb/>l'altra parte che due solidi prismatici uguali, aventi altezze uguali, debbano <lb/>avere uguali anche le basi, consegue immediatamente dalla loro stereometria. </s>

<s><lb/>Chiamati infatti P, P&prime; i detti prismi, A e A&prime;, B e B&prime; le loro altezze e le loro <lb/>basi, se, nelle due equazioni P=A.B, P&prime;=A&prime;.B&prime;, P &egrave; uguale a P&prime;, e <lb/>A uguale ad A&prime;, necessariamente anche B &egrave; uguale a B&prime;. </s>

<s>Lasciamo perci&ograve; di <lb/>trascrivere la dimostrazione, che ne d&agrave; il Viviani di questo Lemma, e pas&shy;<lb/>siamo al <emph type="italics"/>&ldquo; Problema meccanicamente risoluto:<emph.end type="italics"/> Dato un cerchio trovare un <lb/>quadrato eguale ad esso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia il dato circolo, il cui diametro A: si deve assegnare un rettan&shy;<lb/>golo a esso uguale. </s>

<s>Preparisi un vaso di vetro, di figura di un prisma retto, <lb/>la cui base sia un rettangolo, la larghezza del quale non sia minore del dia <pb xlink:href="020/01/3239.jpg" pagenum="200"/>metro del dato cerchio, e questo vaso sia CD (fig. </s>

<s>106), la base il rettan&shy;<lb/>golo MD, contenuto dai lati MN, ND, il minor de'quali, se saranno dise&shy;<lb/>guali, DN, quale si chiami <emph type="italics"/>larghezza del vaso,<emph.end type="italics"/> non sia minore del diametro <lb/>del cerchio dato A. </s>

<s>Infondasi nel detto vaso l'acqua o altro liquido all'al&shy;<lb/>tezza dell'altro lato MN del medesimo rettangolo MD, e sia questa DV, sic&shy;<lb/><figure id="id.020.01.3239.1.jpg" xlink:href="020/01/3239/1.jpg"/></s></p><p type="caption">

<s>Figura 106.<lb/>ch&egrave; FV sia il livello dell'acqua infusa. </s>

<s>Sia poi <lb/>il cilindro retto AB, la cui base il cerchio dato A, <lb/>e l'altezza BA la medesima DV del prisma <lb/>d'acqua, sicch&egrave;, immergendo questo cilindro <lb/>nel prisma d'acqua, la sua base A superiore <lb/>sar&agrave; nel medesimo piano del livello FV, e l'in&shy;<lb/>feriore nel piano del rettangolo MD, cio&egrave;, quando <lb/>il cilindro toccher&agrave; il fondo del vaso, si sar&agrave; <lb/>appunto finito di immergere tutto sotto il primo <lb/>livello dell'acqua, ed aver&agrave; scacciato sopra di <lb/>s&egrave; una mole d'acqua uguale a s&egrave; stesso, la <lb/>quale terr&agrave; la figura del vaso, cio&egrave; di un pri&shy;<lb/>sma, e sia questo CV. &rdquo; </s></p><p type="main">

<s>&ldquo; Averemo dunque il prisma d'acqua CV, <lb/>uguale al cilindro AB, ed egualmente alto quanto <lb/>detto cilindro, pigliando per altezza di questo <lb/>prisma, non l'alzamento dell'acqua VE, ma la linea CT, la quale, essendo <lb/>uguale alla MN, sar&agrave; ancora eguale all'altezza del cilindro, la quale si fece <lb/>eguale alla MN. Adunque, per il precedente teorema lemmatico, la base del <lb/>medesimo prisma CV, uguale ed ugualmente alto che il cilindro, sar&agrave; uguale <lb/>alla base del medesimo. </s>

<s>Ma la base del prisma &egrave; il rettangolo EG e del ci&shy;<lb/>lindro &egrave; il cerchio dato A; adunque questo &egrave; uguale al detto rettangolo, <lb/>fatto dalla GV, larghezza del vaso, e dalla VE, alzamento dell'acqua, il quale <lb/>si sar&agrave; potuto notare e segnare nell'esterna superficie del vaso, siccome an&shy;<lb/>cora il primo livello FV, per essersi fatto il vaso trasparente. </s>

<s>In questo modo <lb/>dunque potremo quadrare qualunque circolo, poich&egrave;, pigliando la media pro&shy;<lb/>porzionale tra la larghezza VG e l'alzamento VE, il suo quadrato sar&agrave; uguale <lb/>al circolo proposto, essendo il rettangolo delle estreme eguale al quadrato di <lb/>quelle di mezzo, quando tre linee sono continuamente proporzionali. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E se la larghezza VG del vaso si far&agrave; uguale al diametro del cer&shy;<lb/>chio proposto A, sicch&egrave; il cilindro AB entri per l'appunto nel vaso, cio&egrave; <lb/>tocchi le sponde erette CN, SD, radendole nell'immergersi; ne seguir&agrave; che <lb/>la medesima proporzione aver&agrave; la larghezza VG, all'alzamento dell'acqua <lb/>VE, che il quadrato, circoscritto al cerchio A, al medesimo cerchio, il che <lb/>cos&igrave; fo manifesto &rdquo; (ivi, fol. </s>

<s>31). E seguita il Viviani a scrivere la dimostra&shy;<lb/>zione, ci&ograve; che fatto, cos&igrave; osserva: &ldquo; Potevo pi&ugrave; facilmente e pi&ugrave; brevemente <lb/>dimostrar questo di sopra: poich&egrave;, pigliando la medesima proporzione tra la <lb/>larghezza e l'alzamento, il quadrato di essa &egrave; uguale al dato cerchio, come <lb/>di sopra si &egrave; fatto manifesto. </s>

<s>Adunque qual proporzione aver&agrave; la larghezza <pb xlink:href="020/01/3240.jpg" pagenum="201"/>all'alzamento, tale l'avr&agrave; il quadrato della medesima larghezza al quadrato <lb/>della media, cio&egrave; al cerchio dato. </s>

<s>Ma il quadrato della larghezza &egrave; il mede&shy;<lb/>simo che il circoscritto al cerchio, essendo la larghezza uguale al diametro <lb/>del dato cerchio; adunque la medesima proporzione ha la larghezza del vaso <lb/>all'alzamento del livello, che ha il quadrato, circoscritto al cerchio, al me&shy;<lb/>desimo cerchio, quando il cilindro sar&agrave; grosso quanto la larghezza del vaso &rdquo; <lb/>(ivi, fol. </s>

<s>31 a tergo). </s></p><p type="main">

<s>Il discorso pu&ograve; compendiarsi in due parole. </s>

<s>Dall'identica VG:VE= <lb/>VG:VE si ha VG:VE=VG2:VE.VG, che senz'altro
conclude l'intento, <lb/>essendo VG la larghezza del vaso, e VE l'alzamento dell'acqua. VG 2 poi &egrave;, <lb/>nella fatta supposizione, il quadrato circoscritto al cerchio, e VE. VG il ret&shy;<lb/>tangolo che, per le cose dimostrate, s'uguaglia a esso cerchio. </s></p><p type="main">

<s>Si comprende bene che il metodo pu&ograve; estendersi a qualunque figura si <lb/>voglia dare alla base A, come per esempio di ellisse, d'iperbola, di para&shy;<lb/>bola, di cicloide, delle quali sempre si ricaverebbe dal rettangolo EG la <lb/>quadratura. </s>

<s>Se avesse pensato a valersi di questa invenzione Galileo, si sa&shy;<lb/>rebbe forse assicurato, pi&ugrave; facilmente che col pesar le incise figure, dover <lb/>esser lo spazio cicloidale esattamente triplo di quello del circolo genitore: e <lb/>chi sa che il Nardi, fra le altre meccaniche esperienze, che gli rivelarono il <lb/>vero, non ricorresse anche a questa. </s></p><p type="main">

<s>Ma comunque sia di ci&ograve;, il Viviani ha un secondo <emph type="italics"/>&ldquo; Problema, non men <lb/>curioso dello antecedente, pur meccanicamente risoluto, e con facilit&agrave;:<emph.end type="italics"/> Data <lb/>qualsivoglia figura solida, o regolare o irregolare, bench&egrave; rozzamente e strava&shy;<lb/>gantissimamente configurata, questa si deve ridurre in un prisma o cilindro, <lb/>ovvero in frusto di cono o di piramide, o di altra figura, che da una parte <lb/>venga mancando, il che cos&igrave; conseguiremo, mettendo il problema in un parti&shy;<lb/>colar caso, cio&egrave;: data una sfera, ridurla in un parallelepipedo &rdquo; (ivi, fol. </s>

<s>32). </s></p><p type="main">

<s>Reputiamo superfluo il trascrivere la soluzione, che deriva per facile co&shy;<lb/>rollario dalla precedente, supposto che il cilindro AB sia una sfera, o altro <lb/>solido o frusto di solido, che faccia sopra il primo livello del vaso sollevare <lb/>un parallelepipedo d'acqua, ugualissimo alla sua propria mole. </s>

<s>Dall'altra <lb/>parte i lettori del Clavio, che avessero scelte figure geometriche rotonde, per <lb/>immergerle nella cassetta di legno spalmata di bitume, conseguivano il me&shy;<lb/>desimo effetto che a immergerle in questa pi&ugrave; elegante e tersa vasca di cri&shy;<lb/>stallo. </s>

<s>Nonostante il Viviani si compiacque, come dicemmo, di questa sua <lb/>giovanile invenzione, bench&egrave; la riconoscesse per un giochetto, di cui scri&shy;<lb/>veva cos&igrave;, nell'atto di rivendicarsene la propriet&agrave; da un tale, che se l'era <lb/>usurpato: <emph type="italics"/>E per dirla giusta questo giochetto mi sovvenne nello studiare <lb/>quell'opuscolo d'oro delle Galleggianti del mio sovrano Maestro, l&agrave; dove <lb/>egli fa l'immersione e la demersione de'prismi retti di base rettangola o <lb/>de'cilindri in que'vasi parallelepipedi, con paragonar le moli acquee con <lb/>le solide a varii altri fini.<emph.end type="italics"/></s></p><p type="main">

<s>Un poco pi&ugrave; tardi per&ograve;, tornando il Viviani a studiar sopra l'opuscolo <lb/>ammirato, ebbe a notar qualche macchia su quel che gli era prima apparito <pb xlink:href="020/01/3241.jpg" pagenum="202"/>oro schietto, e il quarto e il quinto teorema, per esempio, gli parve che si <lb/>sarebbero potuti dimostrare pi&ugrave; facilmente di quel che non aveva fatto il suo <lb/>sovrano Maestro, e senza alcun bisogno di lemma antecedente. (MSS. Gal. </s>

<s><lb/>Disc., T. CX, a tergo del fol. </s>

<s>32). Ma dalla forma passando a cosa ben assai <lb/>pi&ugrave; importante, alla sostanza, fu il Viviani stesso uno de'primi ad avvertir <lb/>che il principio, a cui s'informava il discorso di Galileo, rispetto al confe&shy;<lb/>rire il momento della gravit&agrave; dell'acqua che sale, col momento della gravit&agrave; <lb/>del solido che scende, per concluderne indi i vari stati di questo dopo l'im&shy;<lb/>mersione; non era applicabile universalmente. </s>

<s>&ldquo; Quando il vaso, nel quale <lb/>si fa l'immersione del solido (scrive in una nota, da mettersi per postilla <lb/>alle Galleggianti della seconda edizione) sar&agrave; pieno d'acqua, non pare che <lb/>cammini questo discorso, che fa qui il signor Galileo, perch&egrave; il momento <lb/>della gravit&agrave; dell'acqua all'essere alzata o &egrave; nullo perch&egrave; immediatamente <lb/>segue il trabocco, o se &egrave; qualche cosa, &egrave; sempre l'istessa. </s>

<s>Sicch&egrave; questo <lb/>pareggiamento di momenti tra l'acqua e il solido o non ci dovr&agrave; esser mai, <lb/>o sempre, in qual si sia stato d'immersione del detto solido &rdquo; (ivi, fol. </s>

<s>54). </s></p><p type="main">

<s>Del difetto capitale per&ograve; di queste idrostatiche istituzioni galileiane non <lb/>s'era, come il Borelli, accorto ancora nemmeno il Viviani, che, col mede&shy;<lb/>simo zelo del suo collega, troviamo a quel tempo concorrere alla difesa del <lb/>Michelini. </s>

<s>Vedremo in quest'altro Tomo le ragioni che egli speculava, e <lb/>l'esperienza che immaginava, per provare che l'acqua non preme obliqua&shy;<lb/>mente, ma secondo la sola direzion perpendicolare, le sponde dei vivai. </s>

<s>Ora <lb/>convien dire come si venissero egli stesso e il Borelli a ravvedere di un tanto <lb/>errore, pigliandone occasione da quella leggerezza positiva, la confutazion <lb/>della quale gli aveva pure condotti a ritrattarsi intorno al credere che l'acqua <lb/>in mezzo all'acqua non pesa. </s></p><p type="main">

<s>Un solenne Peripatetico stringeva i suoi contradittori con un argomento, <lb/>ricavato dalle dottrine del loro proprio Maestro. </s>

<s>Il prisma, diceva, aderente <lb/>con la base al fondo, e con tre delle facce sue laterali a contatto intimo con <lb/>le pareti del vaso, bench&egrave; da una parte sola lo bagni l'acqua, di cui si sup&shy;<lb/>pone men grave in specie, nonostante vien da lei sollevato, come dimostra <lb/>in una delle sue proposizioni il vostro Galileo. </s>

<s>Irragionevolmente per&ograve; egli <lb/>attribuisce quel sollevamento all'acqua circonfusa, la quale, non facendo <lb/>forza n&egrave; di sotto in su, n&egrave; da lato, non opera dunque nulla'in produr quel&shy;<lb/>l'effetto, che non si potrebbe perci&ograve; attribuire ad altro, che a una leggerezza <lb/>propria del solido, connaturata con lui e positiva. </s></p><p type="main">

<s>Il Borelli e il Viviani, che riconobbero conseguir l'argomento, per lo&shy;<lb/>gica necessit&agrave;, dai loro propri principii, non avendo ragioni da rispondere, <lb/>ricorsero alle esperienze, che istituirono insieme nella loro Accademia, e dalle <lb/>quali risult&ograve; di fatto che il prisma adattato come sopra nel vaso, anche a <lb/>circonfondergli un liquido quanto pi&ugrave; si voglia grave in specie, si rimane, <lb/>contro il supposto di Galileo e del Peripatetico, immobile sul fondo, anzi <lb/>affissovi pi&ugrave; che mai. </s>

<s>L'esperienze furono varie, ma la pi&ugrave; bellamente di&shy;<lb/>mostrativa fu quella, in secondo luogo descritta nel libro dei <emph type="italics"/>Saggi<emph.end type="italics"/> (Fi-<pb xlink:href="020/01/3242.jpg" pagenum="203"/>renze 1841, pag. </s>

<s>133, 34), consistente in un vaso di legno, incavatovi sul <lb/>fondo un emisfero perfettamente uguale a quello di una palla d'avorio, la <lb/>quale non fu veduta crollarsi dal suo incastro, bench&egrave; si riempisse il vaso <lb/>del pesantissimo argento vivo. </s>

<s>&ldquo; Porro hoc experti sumus in Academia expe&shy;<lb/>rimentali medicea &rdquo; disse poi il Borelli nella proposizione LXXXII <emph type="italics"/>De motion. </s>

<s><lb/>natur.<emph.end type="italics"/> (pag. </s>

<s>170). Ma quanto alle ragioni dell'esperienza non sapeva egli <lb/>allora, n&egrave; i suoi Colleghi, far altro che ridurle a un nome vago, divenuto <lb/>per le platoniche tradizioni solenne, a quello di <emph type="italics"/>circumpulsione.<emph.end type="italics"/> Lo Stevino, <lb/>tanto tempo prima, aveva descritte simili esperienze, per confermarne la teo&shy;<lb/>ria: i Nostri invece s'erano incontrati nell'esperienza, per non saperne la <lb/>teoria, la quale era inutile chiedere agl'insegnamenti galileiani, dissipatori <lb/>di ogni idea, che si fosse avvicinata alle pressioni idrostatiche, e specialmente <lb/>a quelle che si producono in mezzo ai liquidi di basso in alto. </s></p><p type="main">

<s>Cercando dunque di ridursi sul diritto filo dai primi deliri, il Borelli <lb/>ebbe a riconoscere quanto irragionevolmente avesse creduto e scritto che non <lb/>pu&ograve; l'acqua ripremere in su, perch&egrave; ci&ograve; repugna alla natura dei gravi. </s>

<s>An&shy;<lb/>che nella stadera, pensava, se non &egrave; in equilibrio, va in su il peso che ha <lb/><figure id="id.020.01.3242.1.jpg" xlink:href="020/01/3242/1.jpg"/></s></p><p type="caption">

<s>Figura 107.<lb/>minore il momento, eppure, tutt'altro che repugnare <lb/>alla gravit&agrave;, &egrave; anzi questo un effetto naturale di lei. </s>

<s>Ora, <lb/>anche le parti componenti una mole fluida son congiunte <lb/>insieme, e mobili intorno a un centro immaginario, come <lb/>nella stadera, ond'ei non &egrave; maraviglia se, prevalendo il <lb/>momento d'una parte a quello dell'altra, mentre l'una <lb/>scende naturalmente, l'altra, pure naturalmente, sia costretta a salire. </s>

<s>Scorto <lb/>da questi pensieri il Borelli conferm&ograve; che essendo EG (fig. </s>

<s>107) il prisma, <lb/>come lo suppone Galileo, l'acqua circonfusagli dalla parte FC non vale a <lb/>sollevarlo, perch&egrave; BC &egrave; s&igrave; veramente una libbra, &ldquo; non quidem convertibilem <lb/><figure id="id.020.01.3242.2.jpg" xlink:href="020/01/3242/2.jpg"/></s></p><p type="caption">

<s>Figura 108.<lb/>circa centrum G, sed stabilem et firmam cum in ea mi&shy;<lb/>nime contrarii motus descensus partis GC, et ascensus <lb/>alterius radii GB fieri possint simul et semel. </s>

<s>Unde <lb/>mirum non est lignum GE e fundo vasis non ascen&shy;<lb/>dere &rdquo; (ibid., pag. </s>

<s>167). Affinch&egrave; ci&ograve; avvenga, sog&shy;<lb/>giunge il Borelli, si richiede una condizione, ed &egrave; che <lb/>l'acqua FC (fig. </s>

<s>108) possa scendere, e scendendo sol&shy;<lb/>levare l'acqua con lei congiunta BL, quasi altro ba&shy;<lb/>cino della bilancia. </s>

<s>&ldquo; Et haec est legitima et adae&shy;<lb/>quata causa quare lignum a maiori impulsu aquae <lb/>collateralis prementis sursum impellitur ab aqua, quae infra eius basim in&shy;<lb/>sinuatur &rdquo; (ibid., pag. </s>

<s>168). </s></p><p type="main">

<s>Di qui si vede che il Borelli giunse felicemente a sciogliere il problema, <lb/>innanzi a cui s'era l'Aggiunti mostrato cos&igrave; irresoluto, per vie tutte sue pro&shy;<lb/>prie, men convenienti con quelle nuove segnate da Galileo, che con le an&shy;<lb/>tiche di Archimede, alle quali (fatta esperienza dei difetti delle dottrine del <lb/>suo maestro) fece ritorno in dimostrare i principali teoremi dell'Idrostatica. <pb xlink:href="020/01/3243.jpg" pagenum="204"/>Basti citar la proposizione LI, iu cui si dimostra cos&igrave; la VII del primo <emph type="italics"/>De <lb/>insidentibus humido:<emph.end type="italics"/> &ldquo; Intelligatur vas ELC (rappresentato dalla medesima <lb/>figura 108) aqua plenum, in eoque immergatur corpus aliquod grave durum <lb/>ac consistens DE, quod gravius sit aqua collaterali FC. </s>

<s>Patet ex Archimede <lb/>duo pondera DE et FC collocari in libra quadam imaginaria ac perpetua BC, <lb/>in qua excessus ponderis solidi DE supra gravitatem aquae FC, quae sit ae&shy;<lb/>qualis mole ipsi DE, semper idem est, in quacumque aquae profunditate <lb/>solidum collocetur. </s>

<s>Sitque pondus E excessus, quo pondus DE superat gra&shy;<lb/>vitatem aquae FC; igitur conatus, vis et impetus, quo solidum DE descen&shy;<lb/>dit infra aquam, mensuratur a vi ponderis E &rdquo; (ibid., pag. </s>

<s>110, 11). </s></p><p type="main">

<s>Ma se il Borelli trovava in Archimede il filo, da ridursi in sulla diretta <lb/>via di dimostrare gli equilibri idrostatici, e di risolvere un problema, a cui <lb/>le dottrine di Galileo non somministravano i necessari argomenti, il Viviani <lb/>invece accusava il Siracusano di questo stesso difetto, dipendente dal non <lb/>aver egli trattata la scienza in modo universale. </s>

<s>Diceva che le dimostrazioni <lb/>di lui non valgono se no nel caso, clie le parti infime siano premute dalla <lb/>mole, che le sovrasta perpendicolarmente, ci&ograve; che poteva esser bene creduto <lb/>dall'ossequioso Discepolo, avendoglielo insinuato il suo sovrano Maestro, ma <lb/>quanto fosse falsa una tale opinione &egrave; manifesto dalla Storia, dalla quale re&shy;<lb/>sulta che Archimede, oltre al primo postulato, che l'umido prema perpen&shy;<lb/>dicolarmente, n'aggiunge l'altro che prema di sotto in su: condizione, alla <lb/>quale se avessero atteso gli studiosi, e fosse stata avvertita dal nostro Vi&shy;<lb/>viani, non gli bisognava ricercar nulla di pi&ugrave; a conseguire l'intento suo prin&shy;<lb/>cipale, qual'era di dimostrare che, <emph type="italics"/>se alla superficie inferiore del grave non <lb/>sar&agrave; sottoposta mole alcuna di fluido, in cui &egrave; sommerso; quantunque pi&ugrave; <lb/>grave in specie sia il fluido detto, ed ancorch&egrave; grande sia l'altezza di <lb/>esso, il grave non verr&agrave; su.<emph.end type="italics"/> Avrebbe dovuto dunque pi&ugrave; ragionevolmente <lb/>esso Viviani, invece che Archimede, accusare il suo proprio Maestro, e tutti <lb/>coloro che non avevano saputo comprendere in unit&agrave; di scienza i due libri <lb/><emph type="italics"/>De insidentibus humido.<emph.end type="italics"/> Ma fisso in questa opinione, si volle applicare egli <lb/>stesso a dare all'Idrostatica quella universalit&agrave;, che diceva mancarle. </s></p><p type="main">

<s>Gli giov&ograve; molto in tale studio la nuova Idrodinamica del Torricelli, e <lb/>tutto gli parve si riducesse a dimostrare come mai una particella, premuta <lb/>da tutte le particelle liquide soprastanti infino alla pi&ugrave; superficiale, acquisti <lb/>tale impeto, da risalire alla medesima altezza. </s>

<s>Cosicch&egrave; considerando tutta <lb/><figure id="id.020.01.3243.1.jpg" xlink:href="020/01/3243/1.jpg"/></s></p><p type="caption">

<s>Figura 109.<lb/>intera la mole come composta d'infinito numero di <lb/>zampilli, o di filetti, o di <emph type="italics"/>raggi fluidi,<emph.end type="italics"/> come ei pro&shy;<lb/>priamente gli chiama, riduceva tutto il negozio a con&shy;<lb/>ferire i momenti nella perpendicolare con quelli fatti <lb/>secondo qualsiasi inclinazione. </s>

<s>Cos&igrave; concludeva che, es&shy;<lb/>sendo il punto A per esempio (fig. </s>

<s>109) compreso fra <lb/>le due superficie orizontali CD, EF tanto &egrave; premuto perpendicolarmente dal <lb/>raggio BA quanto obliquamente dal raggio AG, e da tutti gli altri infiniti, <lb/>che indi si conducessero a CD, superficie del liquido stagnante. </s>

<s>AB poi e AG, <pb xlink:href="020/01/3244.jpg" pagenum="205"/>in mezzo alla mole liquida, di cui sono una parte componente infinitesima, <lb/>si possono cos&igrave; bene riguardar quai liberi zampilli o sifoni comunicanti, per <lb/>cui, dal farsi ins&igrave;eme equilibrio i momenti di AB e di AG o dal prevaler l'un <lb/>sopra l'altro, dipenda del punto A soggiacente o la quiete o il moto. </s></p><p type="main">

<s>&Egrave; dunque presentata dal Viviani sotto altra forma, ma in sostanza &egrave; la <lb/>medesima bilancia di Archimede, e vedremo che, trattata con simili ragioni, <lb/>anche serve ai medesimi usi. </s>

<s>Il vantaggio si consegue principalmente dal&shy;<lb/>l'applicatovi metodo degl'indivisibili e il ridur la massa liquida a filetti, di <lb/>cui si possano, per i teoremi della Meccanica, calco ar le proporzioni dei mo&shy;<lb/>menti gravitativi, porge al Viviani il mezzo, per giungere alla prima mate&shy;<lb/>matica dimostrazione dell'uguaglianza delle pressioni per tutti i versi. </s>

<s>Vera&shy;<lb/>mente questo general trattato de'raggi fluidi dovrebbe precedere il trattatello <lb/><emph type="italics"/>Degli abbassamenti, e sollevamenti de'corpi ne'fluidi diversamente gravi, <lb/>attesa la loro gravezza,<emph.end type="italics"/> che ora siam per produrre alla notizia de'nostri <lb/>Lettori, non essendo questo stesso che una derivazione di quello. </s>

<s>Ma si &egrave; <lb/>creduto pi&ugrave; opportuno tenere un ordine diverso, bastando aver accennato ai <lb/>principii, da'quali presupposti noti, fa refluire il Viviani la universalit&agrave; nella <lb/>scienza dei galleggianti. </s></p><p type="main">

<s>&ldquo; Archimede, nel libro intitolato <emph type="italics"/>Delle cose che stanno sull'umido,<emph.end type="italics"/> prese <lb/>a dimostrativamente trattare la materia sopraddetta, il che fece egli ingegno&shy;<lb/>samente come suole, ma con principii poco universali, ed insufficienti a di&shy;<lb/>mostrare molti effetti, che in diversi casi sogliono intorno a tal materia occor&shy;<lb/>rere, e da essa dipendere. </s>

<s>Poich&egrave; tutto il progresso delle sue dimostrazioni <lb/>non vale primieramente, se non in caso che le parti infime del fluido si tro&shy;<lb/>vino ugualmente poste, e continuate fra loro, al che &egrave; necessario che si tro&shy;<lb/>vino o sopra una medesima superficie orizontale collocate, o, com'egli uni&shy;<lb/>camente assume, nel comune centro concorrenti. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Secondariamente, non vale se non in caso che le medesime parti <lb/>infime siano premute dalla mole, che le sovrasta perpendicolarmente. </s>

<s>Ma bi&shy;<lb/>sogna che le dimostrazioni in tal materia valgano universalmente, in qua&shy;<lb/>lunque irregolarit&agrave; di superficie sottoposte, ed in qualunque caso che dalla <lb/>mole superiore, o perpendicolarmente o secondo qualunque inclinazione, obli&shy;<lb/><figure id="id.020.01.3244.1.jpg" xlink:href="020/01/3244/1.jpg"/></s></p><p type="caption">

<s>Figura 110.<lb/>quamente vengano premute. </s>

<s>Il che fare sar&agrave; <lb/>a noi, per le cose dimostrate intorno ai mo&shy;<lb/>menti de'raggi fluidi, facilissimo, come dalle <lb/>proposizioni seguenti potr&agrave; ciascuno vedere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE I. &mdash; <emph type="italics"/>Di qualunque gra&shy;<lb/>vezza o l'uno o l'altro si sia, ogni corpo so&shy;<lb/>pra ogni fluido comincia necessariamente a <lb/>scendere.<emph.end type="italics"/> &rdquo; </s></p><p type="main">

<s>&ldquo; Sopra qual si sia fluido AB (fig. </s>

<s>110), la cui superficie superiore AC, <lb/>intendasi posato qual si voglia corpo grave E, che, con tutta o parte della su&shy;<lb/>perficie inferiore DF, tocchi qual si voglia porzione DF di esso. </s>

<s>Dico che E <lb/>scender&agrave; necessariamente sotto AC. </s>

<s>Imperocch&egrave; premer&agrave; DF una mole sot-<pb xlink:href="020/01/3245.jpg" pagenum="206"/>toposta DK, il cui estremo inferiore LK, al di cui abbassamento resister&agrave; una <lb/>mole simile, dalla sommit&agrave; AC del fluido circostante seco inferiormente con&shy;<lb/>corrente in LK, per esempio KM. </s>

<s>Poich&egrave; dunque a DK, oltre il proprio mo&shy;<lb/>mento, &egrave; aggiunto il momento di E, sar&agrave; in LK il momento DK maggiore <lb/>del momento MK, e perci&ograve; preponderando si rifletter&agrave; verso KM, e si abbas&shy;<lb/>ser&agrave; dalla sommit&agrave; AC, onde il corpo E verr&agrave; necessariamente a scendere. </s>

<s><lb/>Il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE II. &mdash; <emph type="italics"/>Tanto qualsivoglia grave seguiter&agrave; a scendere <lb/>sotto il fluido, finch&egrave; il momento di tutto sia uguale al momento del fluido, <lb/>il cui luogo occupa la parte sommersa. </s>

<s>&rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.3245.1.jpg" xlink:href="020/01/3245/1.jpg"/></s></p><p type="caption">

<s>Figura 111.</s></p><p type="main">

<s>&ldquo; Intendasi nella figura 111 sommersa del grave, <lb/>sotto l'AC, la porzione DFSR, che occupi nel fluido <lb/>AB il luogo DFSR. </s>

<s>Dico che se il momento del <lb/>fluido, in DFSR, sar&agrave; uguale al momento di tutto E, <lb/>rester&agrave; questo di scendere. </s>

<s>Imperocch&egrave;, essendo il <lb/>momento di DK, insieme col momento del fluido <lb/>DFSR, uguale in LK al momento MK; sar&agrave; ancora <lb/>il momento di DK, insieme col momento di E, uguale al momento di MK in <lb/>LK; onde non potr&agrave; DK pi&ugrave; abbassarsi, ed il grave E scendere. </s>

<s>Il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario I.<emph.end type="italics"/> &mdash; Se il fluido sar&agrave; ugualmente grave in specie, il corpo <lb/>sommerso tanto seguiter&agrave; a scendere, fino che sia precisamente immerso tutto. </s>

<s><lb/>Imperocch&egrave; allora il momento della mole tutta sar&agrave; uguale al momento del <lb/>fluido, il cui luogo occupa la sommersa. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario II.<emph.end type="italics"/> &mdash; Se il fluido sar&agrave; pi&ugrave; grave in specie, il corpo so&shy;<lb/>prapposto rester&agrave; di scendere prima d'esser sommerso tutto. </s>

<s>Imperocch&egrave;, es&shy;<lb/>sendo il fluido pi&ugrave; grave, tanto seguiter&agrave; a scendere, fin che occuper&agrave; il <lb/>luogo d'una tal mole fluida, minor di tutto, che aver&agrave; con esso momento <lb/>uguale. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario III.<emph.end type="italics"/> &mdash; Se il fluido sar&agrave; men grave in specie, il corpo <lb/>sommerso non rester&agrave; mai di scendere. </s>

<s>Imperocch&egrave;, ancora tutto sommerso, <lb/>ha momento necessariamente maggiore, che la mole del fluido, il cui luogo <lb/>occupa in esso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE III. &mdash; <emph type="italics"/>Il momento del grave, allo scendere per un <lb/>fluido men grave in specie, &egrave; uguale all'eccesso sopra il momento della <lb/>mole, il cui luogo egli occupa in esso. </s>

<s>&rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.3245.2.jpg" xlink:href="020/01/3245/2.jpg"/></s></p><p type="caption">

<s>Figura 112.</s></p><p type="main">

<s>&ldquo; Intendasi, nella figura 112, il grave E som&shy;<lb/>merso tutto sotto AC, sicch&egrave; gli sovrasti una mole <lb/>fluida PR, e sia E pi&ugrave; grave in specie che AB. </s>

<s><lb/>Dico il momento di E, allo scendere per AB, es&shy;<lb/>sere quanto l'eccesso del momento di E sopra <lb/>il momento della mole, il cui luogo DFRS oc&shy;<lb/>cupa in AB. &rdquo; </s></p><p type="main">

<s>&ldquo; Il grave, col momento del proprio peso e del peso della mole sovra&shy;<lb/>tante PR, cio&egrave; col momento di tutta la mole PF, preme la mole sottoposta, <pb xlink:href="020/01/3246.jpg" pagenum="207"/>al cui abbassamento resiste il momento della mole simile KM. </s>

<s>Allo scendere <lb/>dunque di E s'oppone la mole KM, che da esso potr&agrave; essere respinta, e per&shy;<lb/>ci&ograve; con tanto momento verr&agrave; a scendere verso LK, con quanto il momento <lb/>della di lui pressione in LK, cio&egrave; della mole PK, preponderer&agrave; sopra il mo&shy;<lb/>mento della resistenza di MK in LK, che &egrave; tanto, quanto l'eccesso di E sopra <lb/>il fluido, che era in DFRS. Poich&egrave;, quello essendo in DFRS, il momento della <lb/>mole PK in LK, al momento della mole MK, sarebbe uguale. </s>

<s>Il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE IV. &mdash; <emph type="italics"/>Qualsivoglia grave, posto liberamente dentro <lb/>un fluido di lui pi&ugrave; grave in specie, sar&agrave; dal fluido circostante respinto <lb/>per di sotto allo in su. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Intendasi, nella figura precedente, il fluido AB pi&ugrave; grave in specie <lb/>del grave E posto dentro di esso. </s>

<s>Dico che il grave E sar&agrave; dalla mole MK <lb/>verso lo spazio PR respinto. </s>

<s>Imperocch&egrave; alla riflessione della mole MK verso <lb/>PR non resiste che il momento del grave E, insieme col momento della mole <lb/>sovrastante PR, cio&egrave; il momento di tutta la mole composta PF. </s>

<s>Perch&egrave; dun&shy;<lb/>que il fluido, che era in DFRS, &egrave; pi&ugrave; grave in specie del grave E, sar&agrave; il <lb/>momento di E minore del momento del fluido in DFRS, e perci&ograve; il momento <lb/>della mole PF in LK sar&agrave; tanto minore del momento della mole MK in LK, <lb/>quanto il momento di E &egrave; minore del momento del fluido, che era in DFRS, <lb/>onde preponderando MK in LK, si mover&agrave; col momento dell'eccesso detto <lb/>verso lo spazio PR, e respinger&agrave; verso esso il grave E. </s>

<s>Il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario I.<emph.end type="italics"/> &mdash; Sicch&egrave; il momento, con che il fluido circostante pi&ugrave; <lb/>grave in specie scaccia di sotto in su il grave che sta dentro, &egrave; uguale al&shy;<lb/>l'eccesso del momento del fluido, il cui luogo occupa il grave, sopra il mo&shy;<lb/>mento di esso. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario II.<emph.end type="italics"/> &mdash; Onde universalmente il momento, con che un grave <lb/>dentro il fluido o va in gi&ugrave; o &egrave; scacciato in su, &egrave; uguale alla differenza del <lb/>momento del grave detto dal momento del fluido, il cui luogo egli occupa. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario III.<emph.end type="italics"/> &mdash; Dal che &egrave; manifesto, nel fluido egualmente grave <lb/>in specie, non potere il grave andare n&egrave; in su n&egrave; in gi&ugrave; con momento al&shy;<lb/>cuno, non v'essendo differenza alcuna di momento tra esso, e il fluido, il <lb/>cui luogo egli occupa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE V. &mdash; <emph type="italics"/>Se alla superficie inferiore del grave non sar&agrave; <lb/>sottoposta mole alcuna di fluido, in cui &egrave; sommerso, quantunque pi&ugrave; grave <lb/><figure id="id.020.01.3246.1.jpg" xlink:href="020/01/3246/1.jpg"/></s></p><p type="caption">

<s>Figura 113.<lb/>in specie sia il fluido detto, ed ancor che grande sia <lb/>l'altezza di esso; il grave non verr&agrave; su. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Intendasi nel fluido AB (fig. </s>

<s>113) il grave E, alla <lb/>cui superficie inferiore LK non sia sottoposta parte alcuna <lb/>di AB, ma le sia immediatamente contigua la parte del <lb/>fondo LK. </s>

<s>Dico che, quantunque pi&ugrave; grave in specie sia <lb/>AB, e quantunque grande la di lui altezza si sia, il grave E <lb/>non verr&agrave; su. </s>

<s>Imperocch&egrave; non potr&agrave; dal fluido circostante essere per di sotto <lb/>in su respinto. </s>

<s>Il medesimo seguir&agrave; se alla superficie LK sar&agrave; contigua per LK <lb/>l'aria, onde cessa ogni sospetto che si potrebbe in ci&ograve; avere del vacuo. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/3247.jpg" pagenum="208"/><p type="main">

<s>&ldquo; PROPOSIZIONE VI. &mdash; <emph type="italics"/>Se il fluido, sottoposto alla superficie inferiore <lb/>del grave sommerso, non aver&agrave; comunicazione con alcun fluido superiore, <lb/>quantunque pi&ugrave; grave in specie sia il fluido detto, e quantunque grande <lb/>la di lui altezza si sia; il grave non verr&ugrave; su. </s>

<s>&rdquo;<emph.end type="italics"/><lb/><figure id="id.020.01.3247.1.jpg" xlink:href="020/01/3247/1.jpg"/></s></p><p type="caption">

<s>Figura 114.</s></p><p type="main">

<s>&ldquo; Intendasi nel fluido AB (fig. </s>

<s>114) il grave E, alla <lb/>cui superficie inferiore DF sia sottoposta qualsivoglia mole <lb/>di esso DB, la quale, per essere DF alla superficie circo&shy;<lb/>stante del vaso immediatamente contigua, non possa avere <lb/>comunicazione alcuna col fluido soprastante AF. </s>

<s>Dico che, <lb/>quantunque pi&ugrave; grave in specie sia il fluido AB, e quan&shy;<lb/>tunque grande sia la di lui altezza, il grave E non verr&agrave; <lb/>su. </s>

<s>Imperocch&egrave;, non avendo il fluido superiore AF comunicazione alcuna <lb/>coll'inferiore DB, non potr&agrave; similmente il grave E essere da quello per di <lb/>sotto in su respinto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSIZIONE VII. &mdash; <emph type="italics"/>Se il fluido, sottoposto al grave sommerso, non <lb/>avendo comunicazione col fluido soprastante, l'aver&agrave; con un altro supe&shy;<lb/>riore, quantunque pi&ugrave; grave in specie egli sia; pu&ograve; il grave, secondo va&shy;<lb/>rie altezze di esso, venire o non venire in su. </s>

<s>&rdquo;<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., T. XXXIV, <lb/>fol. </s>

<s>195-98). <lb/><figure id="id.020.01.3247.2.jpg" xlink:href="020/01/3247/2.jpg"/></s></p><p type="caption">

<s>Figura 115.</s></p><p type="main">

<s>La dimostrazione sembra a noi intorbidata <lb/>dalle troppe parole. </s>

<s>Se il grave E (fig. </s>

<s>115) dentro <lb/>il vaso AF ha di sopra il liquido AR, il quale per&ograve; <lb/>di sotto non comunichi col fluido DKM, &egrave; mani&shy;<lb/>festo che il momento esercitato dalla mole com&shy;<lb/>posta AK sopra LK, qualunque egli sia, pu&ograve; sem&shy;<lb/>pre essere vinto dal momento, con cui la mole <lb/>liquida MK preme la medesima LK, purch&egrave; il <lb/>livello MH giunga all'altezza necessaria. </s>

<s>Ond'ei <lb/>s'intende come, secondo queste varie altezze, possa <lb/>il solido E rimanere o esser mosso, e anche s'ha da questa proposizione che, <lb/>per via della sola altezza, vien l'acqua ad acquistare tal forza, da vincero <lb/>qualunque resistenza a lei si opponga. </s></p><p type="main">

<s>Quest'ultima principalmente &egrave; una di quelle verit&agrave;, che il Viviani cre&shy;<lb/>deva non si poter concludere dai teoremi di Archimede, di cui perci&ograve; la <lb/>scienza idrostatica s'intendeva, per queste VII proposizioni con altro metodo <lb/>condotte, di rendere universale. </s>

<s>Non molti anni dopo, rimastisi questi gene&shy;<lb/>rosi propositi del Nostro nelle sue private carte abbandonati, si ripresero con <lb/>ardore dall'Herman, il quale, non solo si mostr&ograve; mal contento di Archimede, <lb/>ma del Pascal stesso, e di quanti altri lo avevano preceduto, dicendo che, <lb/>sebbene avessero tutti costoro dimostrato con facilit&agrave; le ragioni degli equi&shy;<lb/>libri fra i liquidi, e i solidi in essi notanti; non erano nulladimeno i loro <lb/>metodi universali. </s>

<s>&ldquo; Etsi me non lateat (dice nel cap. </s>

<s>III della seconda parte <lb/>della Foronomia) aequilibria fluidorum, cum inter se, tum etiam solidorum <lb/>corporum cum fluidis homogeneis ex aliis principiis nonnihil brevius posse <pb xlink:href="020/01/3248.jpg" pagenum="209"/>deduci, scilicet ex fundamento maximi descensus centri gravitatis, quem omnia <lb/>corpora inter se commissa affectant, seu, quod ferme eodem redit, ab aequa&shy;<lb/>litate momentorum corporum inter se agitandorum, cuiusmodi principiis Pa&shy;<lb/>scalius aliique usi sunt; verum, praeter quam quod talia principia indirecta <lb/>sunt, ea vix ac ne vix quidem absque longis ambagibus fluidis heterogeneis <lb/>applicari posse videntur, in ea universalitate, in qua praecedentes proposi&shy;<lb/>tiones ex principiis suis proximis directe deduximus &rdquo; (Amsteledami 1716, <lb/>pag. </s>

<s>157). </s></p><p type="main">

<s>Ma noi osservammo che questi principii prossimi, da cui dice l'Herman <lb/>id aver direttamente dedotte le sue proposizioni, erano quelli stessi supposti <lb/>gi&agrave; da Archimede, e da'quali aveva egli stesso dedotte le sue ammirabili <lb/>proposizioni, scritte nel secondo libro <emph type="italics"/>De insidentibus humido.<emph.end type="italics"/> Non importa <lb/>ripeter qui quel che dicemmo nella seconda parte del capitolo primo di que&shy;<lb/>sto Tomo, persuasi come siamo che i nostri Lettori non abbiano oramai pi&ugrave; <lb/>nessun dubbio intorno alle pressioni idrostatiche di basso in alto, le quali, <lb/>ora essendo pari, ora inferiori, ora superiori alle pressioni d'alto in basso, <lb/>prodotte dalle gravit&agrave; naturali; fanno s&igrave; che i settori sferici, e i conoidei <lb/>parabolici propostisi dal Siracusano, ora galleggino stabilmente sull'umido, <lb/>ora tornino in su violentemente sommersi, ora scendano senza poter aiutarsi, <lb/>e si rimangano al fondo. </s>

<s>&Egrave; un fatto dunque che l'universalit&agrave;, che si vo&shy;<lb/>leva dare alla Scienza, l'aveva ella avuta gi&agrave; dallo stesso Archimede, di cui <lb/>sventuratamente nessuno seppe indagare il segreto. </s>

<s>Che sia cos&igrave;, dalla Sto&shy;<lb/>ria vien dimostrato abbastanza, ma noi vogliamo che sia suggellato il di&shy;<lb/>scorso per un esempio, offertoci dall'interpetre pi&ugrave; acuto e pi&ugrave; dotto, che <lb/>abbia avuto Archimede fra'nostri. </s></p><p type="main">

<s>Antonio Nardi, in quella parte del suo manoscritto, in cui <emph type="italics"/>ricerca<emph.end type="italics"/> le <lb/>opere del suo antico Maestro, giudicava cos&igrave; i due libri <emph type="italics"/>Delle cose che stanno <lb/>nell'umido:<emph.end type="italics"/> &ldquo; Quest'opera, che non si trova in greco, &egrave; parte fisica, e parte <lb/>meccanica. </s>

<s>&Egrave; divisa in due libri, de'quali il primo al secondo ha quasi la <lb/>stessa ragione, che ha il primo al secondo <emph type="italics"/>De'superficiali equilibri.<emph.end type="italics"/> Investi&shy;<lb/>gansi in essa gli equilibri dell'umido, in quella maniera quasi, che nell'aria <lb/>s'investigano gli equilibri, in altra opera poco sopra rammentata. </s>

<s>Il soggetto <lb/>dunque &egrave; di delicata e sottil materia, sopra la quale moltissime considera&shy;<lb/>zioni far si potrebbero. </s>

<s>&rdquo; </s></p><p type="main">

<s>Come, a dire dunque del Nardi, nel primo libro <emph type="italics"/>De aequiponderanti&shy;<lb/>bus<emph.end type="italics"/> si tratta dell'invenzione del centro di gravit&agrave; nelle figure piane circo&shy;<lb/>scritte da linee rette, e nel secondo, del centro di gravit&agrave; nelle superficie <lb/>paraboliche; cos&igrave; nel primo <emph type="italics"/>De insidentibus humido<emph.end type="italics"/> si tratta del notar dei <lb/>prismi, e nel secondo de'conoidei parabolici. </s>

<s>Il confronto &egrave; per verit&agrave; troppo <lb/>superficiale, e indegno di un tanto uomo, il quale pare impossibile non si <lb/>fosse accorto che il primo libro idrostatico d'Archimede differisce dal secondo, <lb/>non gi&agrave; per la variet&agrave; delle figure galleggianti scelte ad esempio, ma per i <lb/>principii inclusi nelle due supposizioni, la prima delle quali presiede, per cos&igrave; <lb/>dire, al governo delle pressioni perpendicolari, per cui stanno e si muovono <pb xlink:href="020/01/3249.jpg" pagenum="210"/>o in su o in gi&ugrave; le solide grandezze, e la seconda presiede al governo delle <lb/>forze contrarie, restitutrici nella primiera stabilit&agrave; di equilibrio i conoidali <lb/>inclinati. </s>

<s>Se si volesse instituire un paragone pi&ugrave; giusto, si direbbe piutto&shy;<lb/>sto che il primo libro <emph type="italics"/>De insidentibus humido<emph.end type="italics"/> sta al secondo, come gli Ele&shy;<lb/>menti idrostatici stanno all'Acrobatica dello Stevino: giudizio, a cui molto <lb/>s'avvicin&ograve; il Lagrange, quando, del sopra memorato secondo libro archime&shy;<lb/>deo, cos&igrave; scrisse: &ldquo; Ce livre est un des plus beaux monumens du genie <lb/>d'Archimede, et renforme une theorie de la stabilit&eacute; des corps flottans, a la <lb/>quelle les modernes ont peu aj&ograve;ute &rdquo; <emph type="italics"/>(Mechan. </s>

<s>analyt.<emph.end type="italics"/> cit., pag. </s>

<s>124). Nes&shy;<lb/>sun altro forse aveva dato un giudizio cosi vero come questo, da cui perci&ograve; <lb/>vogliam cogliere l'occasione di concludere il proposito fatto sui principii del <lb/>nostro discorso, qual'era di mostrar come l'Idrostatica, profuga per tanti se&shy;<lb/>coli, finalmente tornasse ad Archimede, quasi a rivivere con lui delle so&shy;<lb/>stanze paterne. </s></p><pb xlink:href="020/01/3250.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle pressioni idrostatiche<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Del principio dell'uguaglianza delle pressioni, proposto dal Torricelli, confermato dal Nardi e dal <lb/>Ri<gap/>ci, e sperimentalmente dimostrato dal Magiotti. </s>

<s>&mdash; II. </s>

<s>Del trattato dell'equilibrio de'liquidi <lb/>del Pascal, e de'Paradossi idrostatici del Boyle. </s>

<s>&mdash; III. </s>

<s>Della riforma idrostatica avvenuta, per <lb/>l'impulso delle tradizioni torricelliane, in Italia. </s>

<s>&mdash; IV. De'raggi fluidi e delle ragioni dei loro <lb/>momenti: trattato di Vincenzo Viviani. </s>

<s>&mdash; V. </s>

<s>Della soluzion del problema: perch&egrave; gli animali <lb/>sott'acqua non ne sentano il peso. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Quel rifuggir che fece la Scienza italiana dai savi metodi antichi, cos&igrave; <lb/>felicemente dallo Stevino proseguiti ne'tempi nuovi, ci hanno le cose fin qui <lb/>narrate dimostrato di fatto che deve imputarsi a Galileo, il quale, tutto ridu&shy;<lb/>cendo a conferire insieme le ragioni dei momenti virtuali, band&igrave; dall'Idro&shy;<lb/>statica ogni idea di quelle pressioni, ch'esercitano i liquidi fra loro, e sui <lb/>solidi immersi. </s>

<s>Or perch&egrave; gli Elementi idrostatici del Matematico di Bruges <lb/>furono per lo Snellio pubblicati quattro anni prima del Discorso intorno alle <lb/>galleggianti, importa molto sapere se fossero al Nostro, mentre scriveva, note <lb/>le proposizioni dimostrate dallo straniero. </s></p><p type="main">

<s>Ripensando alla distanza de'paesi, e alla difficolt&agrave; de'commerci letterari <lb/>a que'tempi, &egrave; facile congetturare che non fossero bastanti quattr'anni a fare <lb/>approdare in Italia un libro scientifico, scritto e stampato in Olanda. </s>

<s>Dal&shy;<lb/>l'altra parte Galileo, cos&igrave; geloso d'ottenere il primato in tutto, e cos&igrave; tre&shy;<lb/>pidante che non gli fosse tolto, non poteva pensare, n&egrave; si curava perci&ograve; nem&shy;<lb/>men di cercare se altri l'aveva prevenuto. </s></p><p type="main">

<s>Ma avvenne che si trovasse allora col&agrave; un suo carissimo amico, Daniele <lb/>Antonini, il quale, conversando con que'dotti olandesi, ud&igrave; da loro le nuove <lb/>maraviglie scoperte nelle propriet&agrave; dell'acqua, e come avessero veduto una <pb xlink:href="020/01/3251.jpg" pagenum="212"/>bilancia di braccia uguali, sopra la quale un'oncia d'acqua da una parte <lb/>contrappesava cento libbre dall'altra. </s>

<s>Comunic&ograve; l'Antonini questa curiosit&agrave; <lb/>a Galileo, che rispose non essergli la cosa riuscita punto nuova, perch&egrave;, avendo <lb/>egli gi&agrave; dimostrato come sia possibile <emph type="italics"/>che una nave cos&igrave; bene galleggi in <lb/>dieci botti d'acqua come nell'oceano<emph.end type="italics"/> (Alb. </s>

<s>XII, 26), aveva come lo Stevino, <lb/>e prima di lui, dietro questo principio, immaginato una bilancia, nella quale <lb/>un galeone poteva esser sostenuto da un'inguistara d'acqua. </s>

<s>Nonostante pre&shy;<lb/>gava l'amico gli descrivesse particolarmente l'esperienza olandese, per vedere <lb/>se s'accordava colla sua. </s></p><p type="main">

<s>Avuta la desiderata descrizione, Galileo riconobbe che si trattava d'altro <lb/>da quel che s'aspettava, e sent&igrave; che la cosa davvero era nuova: tanto anzi <lb/>nuova, che non ritrovava nella sua propria scienza ragioni da spiegarla. </s>

<s>Sem&shy;<lb/>bra che gli si rintuzzasse da ci&ograve; la prima concepita baldanza cos&igrave;, da non <lb/>saper che si dire all'Antonini, il quale, maravigliato del veder corrispondere <lb/>le sue premure con quella trascuratezza, veniva a tentar l'amico lontano con <lb/>s&igrave; fatte parole scritte in una lettera il di 11 Gennaio 1611 da Linghen: <lb/>&ldquo; Nell'altra mia V. S. avr&agrave; avuta quella Bilancia idrostatica di braccia uguali, <lb/>nella quale un'oncia d'acqua da una parte pu&ograve; sollevare facilmente cento <lb/>libbre di peso, dall'altra parte posto, con il mezzo di quella forza, per la <lb/>quale potrebbe il galeone notare in una inguistara d'acqua. </s>

<s>Non so se si <lb/>accorder&agrave; colla sua &rdquo; (MSS. Gal., P. VI, T. VIII, fol. </s>

<s>8). </s></p><p type="main">

<s>Di quest'ultime parole dovette Galileo sentir la puntura acuta, costretto <lb/>a confessare che l'invenzione dello Stevino non si poteva far nemmeno di&shy;<lb/>pendere dai principii da s&egrave; professati, non che affermare che s'accordava <lb/>colla sua. </s>

<s>Il Discorso delle galleggianti gi&agrave; scritto si dovette perci&ograve; man&shy;<lb/>dare in pubblico senza l'ornamento di quella magica Bilancia, la quale <lb/>ebbe a contentarsi di far poi nella privata lettera al Nozzolini pi&ugrave; modesta <lb/>comparsa. </s></p><p type="main">

<s>Intanto Giovanni Bardi, in Roma, declamava ai Lincei quella disserta&shy;<lb/>zione idrostatica, nella quale Galileo suo Maestro veniva assunto alla mede&shy;<lb/>sima gloria con Archimede, e finiva per descrivere l'esperienza steviniana <lb/>ai colleghi maravigliati. </s>

<s>Non &egrave; per&ograve; il Bardi semplice relatore di una curio&shy;<lb/>sit&agrave;, come sembra che fosse l'Antonini, ma parla in nome della scienza, sog&shy;<lb/>giungendo le ragioni evidenti a dimostrar ci&ograve; che poteva apparire un para&shy;<lb/>dosso anche agl'ingegni meno volgari. </s>

<s>&ldquo; Nihil enim referre videtur gravis <lb/>sit vel levis cylinder, dummodo ab alio sustentetur, et aquae ut res postulat <lb/>immergatur, atque adeo munus obeat, vel aquae novem librarum quarum <lb/>locum occupat, vel cuiuscumque alterius corporis cum aqua gravitatis, hoc <lb/>enim si eumdem locum occupare cogitatur, non aliter quam ipsa aqua gra&shy;<lb/>varet lancem, et una cum reliqua libra aquae decem plumbi vel marmoris <lb/>libris aeque ponderaret. </s>

<s>Ergo et cylinder, qui potentia gravitati illius corpo&shy;<lb/>ris aequali intra aquam detinetur, eumdem quem idem corpus vel aqua <lb/>effectum praestabit &rdquo; (Targioni, <emph type="italics"/>Notizie degli aggrandim. </s>

<s>ecc.,<emph.end type="italics"/> Firenze 1786, <lb/>T. II, pag. </s>

<s>10). </s></p><pb xlink:href="020/01/3252.jpg" pagenum="213"/><p type="main">

<s>La spiegazione del paradosso steviniano, data qui, &egrave; quella medesima <lb/>che si legge nella lettera al Nozzolini: anzi la conclusione del Bardi, al ri&shy;<lb/>scontro, &egrave; la fedel traduzione latina delle parole originali di Galileo: &ldquo; E cos&igrave; <lb/>verrebbe in certezza che il <emph type="italics"/>cilindro,<emph.end type="italics"/> sebbene scaccia l'acqua del vaso, nien&shy;<lb/>tedimeno, col solo occuparvi il luogo dell'acqua scacciata, vi conserva tanto <lb/>di gravit&agrave;, quanto appunto &egrave; quella dell'acqua scacciata &rdquo; (Alb. </s>

<s>XII, 114). <lb/>Da ci&ograve; siamo certificati che la dissertazione accademica del Discepolo fu scritta <lb/>sotto la direzion del Maestro, che dovette lasciar correre la solenne comme&shy;<lb/>morazione fattavi di Simone Stevino, dal <emph type="italics"/>vastissimo experimentorum oceano<emph.end type="italics"/><lb/>del quale diceva il Bardi d'avere attinta la descrizione del maraviglioso stru&shy;<lb/>mento. </s>

<s>Galileo invece ne parla come di cosa di sua propria invenzione, sug&shy;<lb/>geritagli dalle critiche dell'Accademico incognito, a cui solo perci&ograve; e non allo <lb/>Stevino professa di restare obbligato. </s>

<s>Ma se la prepotente autorit&agrave; del Mae&shy;<lb/>stro non valse a indurre il dissertante linceo ad attribuirgli la Bilancia idro&shy;<lb/>statica, us&ograve; nulladimeno in quel suo dissertare ogni arte, per fare apparire <lb/>che alcune non men belle esperienze, proposte negli Elementi idrostatici, non <lb/>mancavano pure nel Discorso delle Galleggianti. </s></p><p type="main">

<s>La lamina di piombo che, sebben libera, non si stacca dall'orlo infe&shy;<lb/>riore del tubo di vetro, convenientemente profondatasi insieme con lui nel&shy;<lb/>l'acqua, e che lo Stevino descriveva nel suo libro, per dimostrare la pres&shy;<lb/>sione fatta di sotto in su dal liquido; il Bardi la rassomiglia alla tavoletta <lb/>di ebano galleggiante secondo le posizioni di Galileo. </s>

<s>&ldquo; Videtis ut tabella haec <lb/>plumbea, haud parvi ponderis, cylindro vitreo adhaerescere mediis in undis <lb/>malit, quam in fundo loco suo proprio suaviter conquiescere? </s>

<s>Jucundissimum <lb/>profecto spectaculum, et philosopho mathematico dignissimum, in quo, nisi <lb/>plane caecutio, videre mihi videor miraculum Naturae iterum, quod paulo <lb/>ante in tabella natante una conspeximus. </s>

<s>Utrobique puteus aereus est, utro&shy;<lb/>bique fundus e materia aqua graviore: parietes dumtaxat, qui illic sunt aquei <lb/>et fluidi, hic existunt vitrei ac solidi, eum in finem ut putei aerei altitudo <lb/>quae alioquin ad laminarum crassitiem definitam habet a natura proportio&shy;<lb/>nem, augeri ad arbitrium queat. </s>

<s>Qua aucta, necesse est ut aquae moles quae <lb/>antea, cum libere natabat tabella, parti demersae aequalis erat et aeque gra&shy;<lb/>vis, iam secundum molem aucta gravior evadat atque idcirco tabella plumbea <lb/>una cum vitro teneri quidem praeter Naturae leges intra aquam profundius <lb/>possit, mergi vero, quamvis libera sit, non possit &rdquo; (Targioni, <emph type="italics"/>Notizie<emph.end type="italics"/> e <lb/>Tomo cit., pag. </s>

<s>9, 10). </s></p><p type="main">

<s>Questa eloquenza accademica del Bardi mandava soavi profumi d'in&shy;<lb/>censo alle segrete ambizioni del suo Maestro. </s>

<s>Il merito vero per&ograve; non con&shy;<lb/>sisteva nell'inventare e nel descrivere spettacoli giocondissimi, ma nell'illu&shy;<lb/>strarli co'principii della Scienza, ci&ograve; che, per reputarli veramente degni di <lb/>loro, avrebbero piuttosto desiderato i Filosofi matematici. </s>

<s>Ora &egrave; un fatto che <lb/>dal Bardi si declamano ossequiosamente gli errori imbevuti nell'insegnamento <lb/>di Galileo, in cui non par che la Scienza steviniana abbia nulla giovato a <lb/>riformare i giudizi. </s>

<s>Non importa ripetere che, nelle postille all'Incognito e <pb xlink:href="020/01/3253.jpg" pagenum="214"/>nella lettera al Nozzolini, si conferma essere il peso dell'acqua, che riem&shy;<lb/>pirebbe la fossetta scavatasi dall'assicella di ebano, uguale al solo peso di <lb/>essa assicella; come pure il Bardi, sulla parola del suo maestro, confidente&shy;<lb/>mente asserisce essere al solido, senza l'aria che gli sovrasta, la detta mole <lb/>acquea <emph type="italics"/>aeque gravis:<emph.end type="italics"/> a provare che Galileo non ricev&egrave; alcun benefizio dalle <lb/>tradizioni precedenti, basta ripensare a quella attrazione calamitica dell'aria, <lb/>alla quale principalmente egli attribuiva nel suo Discorso il galleggiare sul&shy;<lb/>l'acqua le palline di cera. </s>

<s>Lo Stevino aveva insegnata la vera e adeguata <lb/>causa di un tal galleggiamento nelle pressioni, che d&igrave; sotto in su si susci&shy;<lb/>tano dentro la massa del liquido, onde, essendo per Galileo venuti l'occa&shy;<lb/>sione e il tempo di saper la verit&agrave; a tutti oramai pubblicamente nota, si <lb/>crederebbe che da vero Filosofo si movesse egli il primo ad abbracciarla, per <lb/>valersene opportunamente nel rispondere al Nozzolini. </s></p><p type="main">

<s>A questi, allora professore nello studio di Pisa, pareva cosa dura affer&shy;<lb/>mare che gli arginetti si reggano intorno alla cera e all'ebano dalla virt&ugrave; <lb/>attrattiva dell'aria, ond'egli avrebbe voluto dire piuttosto, a proposito del <lb/>bicchiere vuoto rivolto colla bocca in gi&ugrave;, e tuffato a forza nell'acqua, in <lb/>fondo alla quale stia una pallina di cera; che, nel tirarlo in su, &ldquo; quella <lb/>cera seguita l'aria di quel bicchiere <emph type="italics"/>ratione vacui,<emph.end type="italics"/> perch&egrave; tirandolo in su <lb/>con qualche velocit&agrave;, bisogna che quel che v'&egrave; dentro lo seguiti, siccome, <lb/>alzata con velocit&agrave; la coperta di un libro, si tira dietro due o tre carte &rdquo; <lb/>(Alb. </s>

<s>XII, 99). </s></p><p type="main">

<s>Galileo pens&ograve; che sarebbe, per far pi&ugrave; breve la risposta e renderla pi&ugrave; <lb/>efficace, bastato il dichiararsi meglio intorno al modo, con cui la palla di <lb/>cera si solleva dal fondo, in virt&ugrave; dell'aria che se le manda col bicchiere <lb/>rovesciato, &ldquo; il qual modo, egli dice, non &egrave; altrimenti per attrazione di vacuo, <lb/>mentre che il bicchiere con velocit&agrave; s'alzasse, anzi &egrave; necessario sollevare il <lb/>bicchiere lentissimamente, dando tempo che l'acqua possa subentrare a suo <lb/>bell'agio a proibire il vacuo: ma la causa del sormontar la palla &egrave; l'aria, <lb/>che le resta contigua &rdquo; (ivi, pag. </s>

<s>116). In questa sola contiguit&agrave; poi fa Ga&shy;<lb/>lileo consistere tutto l'effetto, cosicch&egrave; rifioriscono qui le macchie sparse nel <lb/>Discorso idrostatico, e se qualche differenza ci &egrave;, si riduce al modo di spie&shy;<lb/>gar come l'aria cos&igrave; tenacemente si rimanga col galleggiante contigua, da <lb/>acompagnarlo per tutto il suo affondarsi nell'acqua. </s>

<s>Aveva prima attribuito <lb/>il fatto a un'attrazione calamitica, con scandalo universale, di cui per&ograve; d&agrave; <lb/>la colpa al non essersi spiegato cos&igrave; bene allora, come ora che dice di voler <lb/>riferire, e di avere inteso sempre di riferire l'aderenza dell'aria con la falda <lb/>a quel <emph type="italics"/>solo contatto esquisito<emph.end type="italics"/> (ivi, pag. </s>

<s>105), che poi, nelle due Nuove Scienze, <lb/>attribuir&agrave; alla forza del vacuo. </s>

<s>Si ritorna dunque alle ripudiate ragioni del <lb/>Nozzolini, n&egrave; ci&ograve; nulla importa, purch&egrave; si stia lontani dal professare le pres&shy;<lb/>sioni idrostatiche dello Stevino. </s></p><p type="main">

<s>Ma, per confermare anche meglio le prove dell'argomento geloso, tor&shy;<lb/>niamo alla Bilancia idrostatica di braccia uguali. </s>

<s>Si disse che tutt'altro che <lb/>riconoscere, fra quella dello Stevino, e l'altra, che gli era allora balenata <pb xlink:href="020/01/3254.jpg" pagenum="215"/>nella fantasia, un accordo; Galileo non ritrovava ne'suoi principii nessuna <lb/>ragione valevole a spiegare il paradosso, cosicch&egrave; i momenti del solido e del <lb/>liquido, e le loro collazioni, a cui fu costretto ridursi, in conformit&agrave; di que&shy;<lb/>gli stessi principii; non riescono che a parole risonanti senza significato. </s>

<s>Che <lb/>cosa infatti significa conferire il maschio, all'acqua rimasta nella bigoncia, <lb/>o all'aria rimasta nel vaso, <emph type="italics"/>tanto de'propri momenti, quant'era il mo&shy;<lb/>mento dell'acqua o dell'aria scacciata?<emph.end type="italics"/> (ivi, pag. </s>

<s>114). O intendendosi che <lb/>il solido supplisca al peso del liquido, di cui tiene il luogo, non era egli <lb/>questo il soggetto della dimostrazione, quale se l'era proposto lo Stevino, <lb/>l'intenzione del quale fu poi di confermar con l'esperienza le verit&agrave; concluse <lb/>dalla sola teoria? </s></p><p type="main">

<s>Ma che quelle professate da Galileo fossero propriamente parole, e non <lb/>teorie, s'argomenta dalle strane conseguenze ch'egli ne trasse, come s'ar&shy;<lb/>gomenta aver camminato al buio chi si trova caduto nella fossa. </s>

<s>&mdash; Se il <lb/>maschio &egrave; che conferisce il peso all'acqua rimasta nella bigoncia, quest'acqua <lb/>dunque non ha momento proprio, ma partecipato. </s>

<s>E potendosi fare il detto <lb/>maschio di gravit&agrave; in specie pari a quella dell'acqua, dunque, anche quando <lb/>il vaso sar&agrave; tutto pieno di questa, ella avr&agrave; sempre il momento partecipato, <lb/>e non premer&agrave; perci&ograve;, quanto a s&egrave;, altro che pochissimo sopra il fondo e <lb/>contro le pareti del vaso. </s>

<s>Potendosi anzi ridurre il liquido, rimasto preso fra <lb/>il maschio e la bigoncia, a un cos&igrave; sottilissimo velo, da considerarsi come <lb/>di nessun peso, nulla dunque pu&ograve; dirsi che sia la sua pressione. </s>

<s>&mdash; Cos&igrave; ap&shy;<lb/>punto ragionava Galileo col Viviani, il quale, insieme con altri simili docu&shy;<lb/>menti raccolti dalla viva voce del suo maestro in Arcetri, ci volle conservar <lb/>la memoria anche di questo, nelle due note seguenti: </s></p><p type="main">

<s>&ldquo; I. </s>

<s>Sit libra AB (fig. </s>

<s>115), cuius fulchrum E, in extremo A pondus X <lb/>decem librarum, in altero vero B tenuissimum vitreum vas CBD, in quo sit <lb/><figure id="id.020.01.3254.1.jpg" xlink:href="020/01/3254/1.jpg"/></s></p><p type="caption">

<s>Figura 115.<lb/>ligneum solidum F ita coaptatum, <lb/>ut ipsum vas nulla ex parte tangat, <lb/>sed suspensum maneat super sub&shy;<lb/>stentaculum GH parieti infixum. </s>

<s><lb/>Dico iam si in spacio, quod inter <lb/>vas et masculum interest, superin&shy;<lb/>fundatur aqua, ipsam, quamvis parvissimae molis, ope tamen solidi F aequi&shy;<lb/>ponderare sum solido X, licet solidum F non a vase sed a brachio GH sustinea&shy;<lb/>tur. </s>

<s>Parva igitur aquae moles, in interstitio CBD infusa, valet ad sustinendum <lb/>quodcumque vel gravissimum pondus X, dummodo id gravitatem vasis CBD, <lb/>una cum aqua eum replente, non excedat. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Videtur hinc super aquas CBD tantum gravitare pauca illa aquae mo&shy;<lb/>les inter vas et masculum intercepta, ac si idem vas aqua in totum reple&shy;<lb/>tum fuerit, et interstitium CBD sit quantumlibet angustissimum. </s>

<s>At si vero <lb/>hoc, cur dici non poterit vas CBD, cum est aqua plenum, nihil ab ipsa <lb/>gravari? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; II. </s>

<s>Esto vas ex subtilissimo vitro confectum ABCD (fig. </s>

<s>116), cui adhae-<pb xlink:href="020/01/3255.jpg" pagenum="216"/>reat solidum X in parte tantum R. </s>

<s>In reliquis vero partibus sit undique di&shy;<lb/>siunctum a continente ABCD. </s>

<s>Distet autem a vitri interiore superficie per <lb/><figure id="id.020.01.3255.1.jpg" xlink:href="020/01/3255/1.jpg"/></s></p><p type="caption">

<s>Figura 116.<lb/>angustissimum interstitium, eiusque gravitas in specie sit <lb/>eadem cum aqua. </s>

<s>Clarum est, cum solidum X non tangat <lb/>vas ABCD nisi in parte R, nullam aliam vitri partem premi <lb/>a solido X, cum a solido non tangatur. </s>

<s>Superinfundatur <lb/>ergo aqua inter vitrum et solidum, quae, cum sit paucis&shy;<lb/>simae molis, parum etiam premet super vitrum, minusque <lb/>adhuc premeret, si spacium vacuum fuisset angustius. </s>

<s>Attamen aqua gravi&shy;<lb/>tatem ponderis X substinebit, neque magis premet in puncto R, neque basem <lb/>vasis ABCD pressionem ullam patietur. </s>

<s>Si vero, pro solido X, intelligatur <lb/>aqua, idem veniet, ideoque vas aqua plenum in nulla sua parte premi ne&shy;<lb/>cesse est. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXV, a tergo del fol. </s>

<s>13). </s></p><p type="main">

<s>Educato nella palestra di cos&igrave; fatti paralogismi, non &egrave; punto maraviglia <lb/>che poi si facesse il Viviani difensore cos&igrave; liberale del Michelini. </s>

<s>Ma ripen&shy;<lb/>sando alle cure diligentissime, poste dallo Stevino per dimostrar la quantit&agrave; <lb/>delle pressioni idrostatiche, non solo contro il fondo, ma e contro le pareti <lb/>dei vasi, secondo le loro ampiezze, figure e inclinazioni; si direbbe che s'at&shy;<lb/>tendeva in Italia, piuttosto che a promovere con amore la scienza, a farne <lb/>indegnamente la parodia. </s>

<s>S'accennava per&ograve; che alla Scuola galileiana ne <lb/>succedeva un'altra, la quale avrebbe ridonati cos&igrave; alla primiera dignit&agrave; gli <lb/>ingegni speculativi, da rimetterli nella via di progredire, e di avvantaggiar <lb/>gli stranieri. </s>

<s>Quella benefica scuola s'istituiva dal Torricelli, e gli uffici, che <lb/>fu ordinata a fare nella vita dell'Idrostatica, son quelli stessi della radice e <lb/>del cuore nella vita della pianta, e dell'animale. </s></p><p type="main">

<s>Il mondo ha esaltato alla massima gloria un tal uomo, per essere stato <lb/>autore dell'esperienza del vuoto, e inventor del Barometro. </s>

<s>Eppure noi l'ab&shy;<lb/>biamo udito confessar da s&egrave; stesso che l'invenzione <emph type="italics"/>non gli fu potuta riu&shy;<lb/>scire,<emph.end type="italics"/> e sappiamo d'altronde che, essendo stata l'esperienza del vacuo gi&agrave; <lb/>fatta, tutto il merito si riduceva a sostituire il mercurio all'acqua, cosicch&egrave; <lb/>in un maneggevole tubo di vetro si potesse comodamente vedere quel che <lb/>in una canna si lunga, da giunger di terra a toccare il tetto di un palazzo <lb/>di Roma. </s>

<s>S'osservi poi che l'esperienza stessa, cos&igrave; accomodata, s'appella <lb/>dall'Autore col nome di <emph type="italics"/>filosofica,<emph.end type="italics"/> e, discorrendo con M. A. </s>

<s>Ricci di altri <lb/>simili fatti, gli dice che pu&ograve; averli per certi, <emph type="italics"/>come se ne avesse fatta espe&shy;<lb/>rienza.<emph.end type="italics"/></s></p><p type="main">

<s>&Egrave; manifesto dunque che l'opera del Torricelli &egrave; intorno a una specu&shy;<lb/>lazione, e non intorno a una osservazione sensata, e consiste in quella spe&shy;<lb/>culazione tutto il merito di lui, che la traviata Idrostatica di Galileo, con <lb/>generosa libert&agrave;, riduceva sopra i retti sentieri. </s>

<s>Com'era possibile che co&shy;<lb/>loro, a'quali s'insegnava che l'acqua non preme in su, perch&egrave; ci&ograve; sarebbe <lb/>contrario alla sua gravit&agrave; naturale; che un solido immerso non contrasta con <lb/>tutta l'acqua, ma con quella parte sola di lei che si moverebbe, movendosi <lb/>esso solido; com'era possibile cadesse in mente a costoro che sia la pres-<pb xlink:href="020/01/3256.jpg" pagenum="217"/>sione di tutta l'altissima sfera dell'aria la vera adeguata causa del sosten&shy;<lb/>tarsi l'argento vivo nel tubo? </s>

<s>Anzi avrebbero reluttato all'idea, se fosse ve&shy;<lb/>nuto qualcuno innanzi a loro a proporla, come il Torricelli gi&agrave; s'aspettava, <lb/>e come di fatto gli avvenne col Ricci, il quale, appena avuta la descrizion <lb/>dall'Autore, cos&igrave; il d&igrave; 2 Luglio 1644 gli rispondeva da Roma: </s></p><p type="main">

<s>&ldquo; Il modo, con che V. S. salva l'esperienza fatta in riprova del vacuo, <lb/>cio&egrave; del salire le cose gravi contro la sua naturale inclinazione, io lo giudico <lb/>tanto pi&ugrave; buono dell'altro, quanto che con questo ci conformiamo alla sem&shy;<lb/>plicit&agrave; della Natura nelle opere sue, la quale, potendo salvare l'unione dei <lb/>corpi col solo moto all'in gi&ugrave;, invano averebbe inserito loro una nuova na&shy;<lb/>turale inclinazione d'obbedire alla Causa universale, moderatrice del mondo, <lb/>com'essi dicono. </s>

<s>Ed ammiro il nobile ardimento di V. S. nell'avere in con&shy;<lb/>siderazione cosa non tocca da nessuno finora, la quale ha parimente tanto <lb/>di probabilit&agrave; che, toltone due o tre obiezioni che sono per dire, e le quali <lb/>prego V. S. a volermele risolvere, siccome so che ella potr&agrave; fare agevol&shy;<lb/>mente; stimo essere il pi&ugrave; vero, ed il pi&ugrave; ragionevole che possa dirsi in si&shy;<lb/>mile questione &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>23, 24). </s></p><p type="main">

<s>Della prima obiezione ci passeremo, perch&egrave; non importante al presente <lb/>nostro proposito, e perch&egrave; se ne disse quanto basta a pag. </s>

<s>460 e 461 del <lb/>primo Tomo, trattenendoci piuttosto a esaminare la seconda e la terza, dal <lb/>Ricci stesso proposte in questa forma: &ldquo; Secondariamente, preso uno schiz&shy;<lb/>zatoio, che suole essere usato assai in questo soggetto, e che abbia la sua <lb/>animella <emph type="italics"/>(stantuffo)<emph.end type="italics"/> dentro onninamente, acci&ograve; escluda con la sua corpulenza <lb/>ogni altro corpo; turando in cima il foro, e ritirando per forza l'animella <lb/>indietro, sentiamo grandissima resistenza, e ci&ograve; non segue solamente, tenendo <lb/>in gi&ugrave; lo schizzatoio e voltando in su l'animella, sopra il cui manico grava <lb/>l'aria, ma segue per ogni verso che si faccia. </s>

<s>Eppure, non pare che si possa <lb/>in questi casi facilmente intendere come il peso dell'aria v'abbia che fare. </s>

<s><lb/>Finalmente un corpo immerso nell'acqua non contrasta con tutta l'acqua <lb/>che vi sta sopra, ma con quella sola, che al moto del corpo immerso si <lb/>muove, la quale non &egrave; maggiore di esso corpo. </s>

<s>E perch&egrave; stimerei che la <lb/>stessa dottrina fosse da applicarsi alla librazione dell'argento vivo, dovrebbe <lb/>esso contrastare con tanto d'aria, quanto &egrave; la sua mole. </s>

<s>Or come potrebbe <lb/>l'aria preponderar mai? </s>

<s>&rdquo; (ivi, fol. </s>

<s>24). </s></p><p type="main">

<s>A quel che il Ricci obiettava in secondo luogo rispondeva il Torricelli <lb/>a quel modo, che &egrave; pi&ugrave; proprio a persuadere i semplici, per via dell'apo&shy;<lb/>logo socratico, con gentile arguzia avvertendo gli studiosi delle Galleggianti <lb/>galileiane (tutti insieme da lui compresi nella persona del suo giovane amico) <lb/>che per troppa semplicit&agrave; erano rimasti ingannati. </s>

<s>&ldquo; Fu una volta un Filo&shy;<lb/>sofo che, vedendo la cannella messa alla botte da un servitore, lo brav&ograve; con <lb/>dire che il vino non sarebbe mai venuto, perche natura de'gravi &egrave; di pre&shy;<lb/>mere in gi&ugrave; e non orizontalmente e dalle bande. </s>

<s>Ma il servitore fece toc&shy;<lb/>cargli con mano che, sebbene i liquidi gravano per natura in gi&ugrave;, in ogni <lb/>modo spingono e schizzano per tutti i versi, anco allo in su, purch&egrave; trovino <pb xlink:href="020/01/3257.jpg" pagenum="218"/>luoghi dove andare, cio&egrave; luoghi tali, che resistano con forza minore della <lb/>forza di essi liquidi. </s>

<s>Infonda V. S. un boccale tutto nell'acqua, colla bocca <lb/>all'in gi&ugrave;, poi gli buchi il fondo, sicch&egrave; l'aria possa uscire: vedr&agrave; con che <lb/>impeto l'acqua si muove di sotto all'in su per riempirlo &rdquo; <emph type="italics"/>(Dati, nella Let&shy;<lb/>tera a'Filaleti,<emph.end type="italics"/> Firenze 1663, pag. </s>

<s>23). </s></p><p type="main">

<s>L'ultima obiezione si concludeva dal Ricci per un'applicazion pi&ugrave; di&shy;<lb/>retta degli insegnamenti idrostatici di Galileo, il quale, dopo aver detto che <lb/>un solido pi&ugrave; grave in specie dell'acqua resiste all'esser sollevato da lei su <lb/>dal fondo del vaso, con l'eccesso del suo peso assoluto, sopra il peso asso&shy;<lb/>luto di una mole acquea a s&egrave; uguale; soggiunge: &ldquo; E bench&egrave; si aggiungesse <lb/>poi grandissima quantit&agrave; d'acqua sopra il livello di quella, che pareggia l'al&shy;<lb/>tezza del solido, non per&ograve; s'accresce la pressione o aggravamento delle parti <lb/>circonfuse al detto solido, per la quale maggior pressione egli avesse ad esser <lb/>cacciato. </s>

<s>Perch&egrave; il contrasto non gli vien fatto se non da quelle parti del&shy;<lb/>l'acqua, le quali, al moto di esso solido, esse ancora si muovono, e queste <lb/>son quelle solamente, che son comprese tra le due superficie equidistanti <lb/>all'orizonte, e fra di loro parallele, le quali comprendon l'altezza del solido <lb/>immerso nell'acqua &rdquo; (Alb. </s>

<s>XII, 26, 27). </s></p><p type="main">

<s>La proposizione, cos&igrave; assolutamente annunziata, &egrave; falsa non essendo vero, <lb/>come altrove osservammo, che per nuova aggiunta di liquido non s'accre&shy;<lb/>sca, intorno e sopra il solido, l'aggravamento. </s>

<s>La ragion poi addotta da Ga&shy;<lb/>lileo, e ripetuta dal Ricci, che cio&egrave; non si faccia il contrasto se non con sole <lb/>quelle parti dell'aequa, le quali si moverebbero movendosi il solido, a cui <lb/>possono dette parti essere tutto al pi&ugrave; uguali in mole, ma non mai mag&shy;<lb/>giori; non vale se non nel caso che il corpo immerso abbia l'acqua da'lati <lb/>e di sopra. </s>

<s>Cos&igrave;, per esempio, nella figura 108 illustrativa delle dottrine del <lb/>Borelli, che si riferiscono alla presente questione, &egrave; vero che il solido EG <lb/>contrasta solamente con l'acqua FC, se tutto il vaso AC sar&agrave; pieno. </s>

<s>Ma se, <lb/>facendo HF argine all'acqua HI, lo spazio AF rimanga assolutamente vuoto, <lb/>o pieno di aria; e allora il grave solido EG contrasta con tutta l'acqua HC, <lb/>e si farebbe sempre maggiore il contrasto, col crescer l'altezza perpendico&shy;<lb/>lare del liquido sopra il primo livello. <lb/><figure id="id.020.01.3257.1.jpg" xlink:href="020/01/3257/1.jpg"/></s></p><p type="caption">

<s>Figura 117.</s></p><p type="main">

<s>Ora il Torricelli, mentre illustrava e correggeva <lb/>la proposizione idrostatica di Galileo, mostrava al Ricci <lb/>che, avendo il mercurio dentro il tubo di sopra il vuoto, <lb/>falsamente ei ne concludeva dover esso mercurio con&shy;<lb/>trastare con una parte minore, o tutt'al pi&ugrave; eguale a <lb/>s&egrave; in mole: ma confermava che un tal contrasto era <lb/>veramente con tutta l'altezza dell'ammosfera. </s>

<s>E, per <lb/>dargli a intender la cosa con pi&ugrave; sensata dimostrazione, <lb/>ricorreva a un esempio, in cui l'aria era invece del <lb/>vuoto, e invece dell aria l'acqua. </s>

<s>Se nel sifone ABCD <lb/>(fig. </s>

<s>117), aperto in D, s'infonda argento vivo, &egrave; certo <lb/>che si liveller&agrave; ugualmente in A, E nell'un braccio e <pb xlink:href="020/01/3258.jpg" pagenum="219"/>nell'altro. </s>

<s>Ma si cali lo strumento in fondo a un vaso, dentro cui si versi <lb/>acqua in sino a un certo livello. </s>

<s>Sopraggiungendone altra via via, si vedr&agrave; <lb/>che anche il mercurio s'alza via via dentro la canna, con tal regola per&ograve; <lb/>che sempre l'altezza, a cui giunge dopo ogni infusione, sia la quattordicesima <lb/>parte di quella dell'acqua. </s>

<s>Falso &egrave; dunque che, coll'aggiungere nuova <lb/>quantit&agrave; d'acqua sopra il primo livello, non si venga a crescere la pressione, <lb/>e falso anco &egrave; perci&ograve; che il contrasto si faccia con una parte sola, e non <lb/>con tutta l'acqua soprastante secondo la sua altezza perpendicolare. </s>

<s>Cos&igrave; <lb/>rispondeva in sostanza il Torricelli, e tali erano propriamente le sue parole: </s></p><p type="main">

<s>&ldquo; La terza obiezione non mi par troppo a proposito: certo &egrave; che &egrave; meno <lb/>valida dell'altre, ancorch&egrave;, essendo presa dalla Geometria, paia pi&ugrave; gagliarda <lb/>di tutte. </s>

<s>Che un corpo posto nell'acqua contrasti solo con tanta mole d'acqua, <lb/>quanta &egrave; la mole sua, &egrave; vero, ma il metallo sostenuto in quel collo di vaso <lb/>non mi pare che si possa dire n&egrave; immerso in acqua, n&egrave; in aria, n&egrave; in vetro, <lb/>n&egrave; in vacuo. </s>

<s>Solamente si pu&ograve; dire ch'egli &egrave; un corpo fluido e libratile, <lb/>una superficie del quale confina col vacuo, o quasi vacuo, che non gravita <lb/>punto. </s>

<s>L'altra superficie confina con aria premuta da tante miglia d'aria <lb/>ammassata, e perci&ograve; quella superficie non premuta punto ascende scacciata <lb/>da quell'altra, e ascende tanto, sin che il peso del metallo sollevato arrivi ad <lb/>agguagliare il peso dell'aria premente dall'altra parte. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; V. S. s'immagini il vaso A col tubo BCD congiunto e aperto in D, <lb/>come sta dipinto, e sia il vaso A pieno d'argento vivo: certo &egrave; che il me&shy;<lb/>tallo salir&agrave; nel tubo fino al suo livello E. </s>

<s>Ma se immerger&ograve; detto strumento <lb/>nell'acqua, sino al segno F, l'argento vivo non salir&agrave; fino ad F, ma solo <lb/>tanto, fino che l'altezza del livello nel tubo avanzi il livello del vaso A della <lb/>quattordicesima parte in circa dell'altezza, che aver&agrave; l'acqua F sopra il li&shy;<lb/>vello del vaso A, e questo V. S. l'abbia per certo, come se avesse fatto <lb/>l'esperienza. </s>

<s>Ora qui si vede che si pu&ograve; dar caso che l'acqua F sia alta <lb/>quattordici braccia, ed il metallo nel tubo ED sia alto un braccio solo. </s>

<s>Dun&shy;<lb/>que quel braccio solo di metallo non contrasta con altrettanta acqua, ma con <lb/>tutta l'altezza d'acqua, che &egrave; tra A ed F, ed in questi casi ella sa che non <lb/>si guarda alle larghezze e grossezze de'solidi, ma solo alle perpendicolari, <lb/>ed alle gravit&agrave; in specie, e non ai pesi assoluti. </s>

<s>&rdquo; <emph type="italics"/>(Lettera ai Filateti<emph.end type="italics"/> cit., <lb/>pag. </s>

<s>23). </s></p><p type="main">

<s>Quattordici anni prima, l'idea, che fosse la pressione ammosferica la <lb/>vera causa adequata del sostenersi l'acqua a una determinata altezza, den&shy;<lb/>tro un sifone costruito, e accomodato con la speranza di poter travasare un <lb/>lago da una valle in un'altra, attraverso al monte di separazione; era bale&shy;<lb/>nata alla mente del Baliani, che pure non avrebbe nemmen egli, come si <lb/>disse del Torricelli, ricevuto il benefico raggio di quella luce, se gli errori <lb/>idrostatici, predominanti allora nella scuola a cui s'era educato il Ricci, glie <lb/>ne avessero adombrate le pupille. </s>

<s>Dal passo, da noi trascritto a pag. </s>

<s>439 del <lb/>primo Tomo, apparisce chiaro che il Baliani professa premer l'acqua, l'aria <lb/>e ogni altro fluido, non solo secondo la natural direzione dei gravi, ma an-<pb xlink:href="020/01/3259.jpg" pagenum="220"/>che di sotto in su e per tutti i versi: ogni fluido inoltre pesare nel suo pro&shy;<lb/>prio elemento a proporzion dell'altezza: e cos&igrave; sicuramente affermando che, <lb/>se fosse il nostro corpo costituito nel vuoto, si sentirebbe oppresso da tutto <lb/>il soprastante peso dell'ammosfera, mostrava di aver saputo bene scansare <lb/>la terza difficolt&agrave; del Ricci, e di esser cos&igrave; per s&egrave; medesimo persuaso della <lb/>verit&agrave;, da non aver bisogno che venisse a insegnargliela il Torricelli. </s></p><p type="main">

<s>Le splendide rivelazioni del Filosofo genovese, in attribuire alla pres&shy;<lb/>sione dell'aria esterna il non potersi l'acqua aspirata dalle trombe solle&shy;<lb/>varsi pi&ugrave; su che a un'altezza determinata; rimasero oscurate da'pregiudizi <lb/>di Galileo, per cui l'opera stessa restauratrice del fondamento idrostatico ri&shy;<lb/>mase pel Baliani di nessuna efficacia. </s>

<s>Piu fortunato il Torricelli, che seppe <lb/>resistere alla tentatrice autorit&agrave; del Maestro, e sugli amici che gli stavano <lb/>intorno pigliare egli stesso pi&ugrave; legittima autorit&agrave;, da instituire in mezzo a <lb/>quei valorosi una scuola nuova, la quale, bench&egrave; fosse ristretta in cos&igrave; piccol <lb/>numero di persone, e s'esercitasse in private scritture, e in familiari collo&shy;<lb/>qui, non manc&ograve; di produrre i suoi benefici effetti. </s></p><p type="main">

<s>Il Magiotti, com'aveva dato mano a confermare con l'esperienza il fon&shy;<lb/>damento idrodinamico proposto dal Torricelli; cos&igrave; concorse poi con altre <lb/>esperienze maravigliose a dimostrare la verit&agrave; de'principii idrostatici rifor&shy;<lb/>mati. </s>

<s>Vedremo pi&ugrave; qua l'efficacia, che in affrettare i progressi della scienza <lb/>ebbero le geniali invenzioni di lui, ma, del Nardi, i documenti gi&agrave; riferiti <lb/>bastano a farlo riconoscere e annoverare tra'primi e pi&ugrave; benemeriti rifor&shy;<lb/>matori dell'Idrostatica galileiana. </s>

<s>Nella questione delle lamine galleggianti, <lb/>v'aveva egli gi&agrave; sgombrati gli errori, e ridotta la cosa alla verit&agrave; delle sue <lb/>ragioni, dicendo che l'acqua, sostentatrice del solido, pesa quant'esso solido <lb/>e l'aria insieme, n&egrave; tal forza di sostentamento riconosce in altro, che in <lb/>quelle pressioni di sotto in su, fatte prima avvertire, e sperimentalmente di&shy;<lb/>mostrate dal Torricelli. </s>

<s>La verit&agrave; della qual dimostrazione parve poi inten&shy;<lb/>desse il Nardi di salvare dalle obiezioni, osservando che quel premer del <lb/>liquido in direzion contraria a quella, che hanno tutti i corpi gravi, era per <lb/>una riflessione del moto, direttamente causato dalla stessa gravit&agrave; naturale. <lb/><emph type="italics"/>Resta dunque sospesa la lamina perch&egrave; la forza, che preme l'acqua, ri&shy;<lb/>flettesi in s&egrave; medesima.<emph.end type="italics"/></s></p><p type="main">

<s>In mezzo a questo fervoroso rinnovamento d'idee non &egrave; da credere si <lb/>rimanesse inoperoso quel Ricci, a cui erano venuti i primi consigli. </s>

<s>Il Tor&shy;<lb/>ricelli sapeva bene qual'ingegno avesse, bench&egrave; giovane, colui col quale ei <lb/>trattava, intanto che lo spendervi molte parole, per rispondere alle proposte <lb/>difficolt&agrave;, lo reputava tedio comune, persuaso com'era che una semplice rifles&shy;<lb/>sione sarebbe all'amico bastata, perch&egrave; potesse per s&egrave; medesimo deliberarsi <lb/>la mente da tutti i dubbi. </s>

<s>Cos&igrave; infatti avvenne, e si fece agli altri maestro <lb/>di quelle verit&agrave;, alle quali gli aveva fatto ripensare il Torricelli. </s></p><p type="main">

<s>Il Cornelio, nel dedicare allo stesso Ricci il suo VII proginnasma <emph type="italics"/>De <lb/>vita,<emph.end type="italics"/> gli diceva: &ldquo; Nam, quum ego Romam venissem vulgari quadam im&shy;<lb/><gap/>utus literatura, tu me ad Geometriae ac Physiologiae studia acrius incita-<pb xlink:href="020/01/3260.jpg" pagenum="221"/>sti, facemque mihi ad optimarum artium notitiam praetulisti &rdquo; (Neapoli 1688, <lb/>pag. </s>

<s>263, 64). Fra queste ottime arti una delle principali fu l'Idrostatica, la <lb/>quale, com'ebbe il Cornelio imbevuta in Roma dal Ricci, cos&igrave; ei la rivers&ograve; <lb/>nell'epistola <emph type="italics"/>De circumpulsione<emph.end type="italics"/> stampata infin dal 1648 sotto il finto nome <lb/>di Timeo Locrese, e d'onde veniva a rendersi di pubblica utilit&agrave; un gran <lb/>tesoro nascosto. </s>

<s>I seguaci di Galileo avrebbero potuto di l&igrave;, per la prima volta, <lb/>imparare che tutte le particelle stanno dentro la massa liquida in equilibrio, <lb/>perch&egrave; &ldquo; vis illa, qua singulae feruntur deorsum, aequalis est virtuti, qua <lb/>aeedem resistunt ac sursum impelluntur &rdquo; <emph type="italics"/>(Progymnasmata cit. </s>

<s>Appendix,<emph.end type="italics"/><lb/>pag. </s>

<s>341). Contro gl'incredibili paralogismi, co'quali si studiava il loro Mae&shy;<lb/>stro di dimostrar che il liquido, non solamente non preme le pareti, ma nem&shy;<lb/>meno il fondo dei vasi; udivano que'Discepoli annunziarsi la salutare verit&agrave; <lb/>di quest'altri insegnamenti: &ldquo; Quemadmodum vero pila plumbea per pla&shy;<lb/>num inclinatum, vel per tubum in helicis formam revolutum, a summo ad <lb/>imum repens tantam denique acquirit velocitatem, quantam propemodum in&shy;<lb/>depta fuisset, si per rectam perpendicularem expositae altitudini aequalem <lb/>descendisset; ita ferme aqua in vase contenta, non modo subiectum fundum <lb/>sed et latera quoque urgens, aperto foramine erumpit tanto impetu, quan&shy;<lb/>tum postulare videtur eiusdem altitudo &rdquo; (ibid., pag. </s>

<s>342). D'onde prende <lb/>il Cornelio occasione di divulgare il principio delle pressioni, che ugualmente <lb/>si trasmettono per tutti i versi, come conseguenza del fatto semplicissimo <lb/>dell'acqua, che per ogni verso zampilla, secondo che nella sua lettera al <lb/>Ricci aveva fatto osservare il Torricelli: &ldquo; Ubi similiter observandum aquam <lb/>e foramine rumpentem, non iuxta unam tantum situs determinationem ferri, <lb/>sed susque deque, dextrorsum ac sinistrorsum, et quocumque tandem fora&shy;<lb/>men vergat proruere &rdquo; (ibid., pag. </s>

<s>343). </s></p><p type="main">

<s>Uno de'pi&ugrave; dannosi insegnamenti di Galileo consisteva nel dire che, per <lb/>aggiungere acqua sopr'acqua, non s'accresce perci&ograve; l'aggravamento sugli <lb/>strati inferiori, perch&egrave; nessun fluido &egrave; grave nel suo proprio elemento. </s>

<s>L'espe&shy;<lb/>rienza torricelliana descritta al Ricci, e illustrata dalla figura 117, era oppor&shy;<lb/>tunissima a dimostrare quanto fosse falso l'assunto peripatetico, vedendosi <lb/>di fatto che l'acqua nel vaso tanto ha pi&ugrave; forza di sostener col suo peso il <lb/>mercurio dentro il cannello EF, quanto &egrave; maggiore il numero degli strati, <lb/>che si sopraggiungono al primo. </s>

<s>Alla quale esperienza sostituiva il Corne&shy;<lb/>lio, nella sua epistola, l'altra della caraffella di vetro, colla bocca all'in gi&ugrave;, <lb/>piena d'aria, la quale esperienza nuova, mentre da una parte si porgeva pi&ugrave; <lb/>facile di quella del Torricelli, e si mostrava pi&ugrave; spettacolosa; essendo dal&shy;<lb/>l'altra ugualmente dimostrativa del premere sempre maggiormente l'acqua <lb/>dentro l'acqua <emph type="italics"/>quo illa fuerit altior,<emph.end type="italics"/> avrebbe potuto conferire, non meno effi&shy;<lb/>cacemente della torricelliana, a dissipare gli errori dall'Idrostatica, alquanti <lb/>anni prima degli Accademici del Cimento. </s></p><p type="main">

<s>Da ci&ograve; che s'&egrave; detto si potr&agrave; facilmente argomentare all'importanza del&shy;<lb/>l'epistola del Cornelio, per la quale si divulgava in Italia, intorno alle pres&shy;<lb/>sioni idrostatiche, una scienza affatto nuova. </s>

<s>N&egrave; senza ragione s'appella que-<pb xlink:href="020/01/3261.jpg" pagenum="222"/>sta da noi col nome di scienza, essendo che dallo Stevino si supponesse, <lb/>piuttosto che dimostrare, come il liquido preme per tutti i versi: e se qual&shy;<lb/>che dimostrazione ei ne d&agrave;, non &egrave; che indiretta o sperimentale. </s>

<s>Il Nostro <lb/>invece la concludeva dai principii della Meccanica, e, riguardata la massa <lb/>fluida come compilata di filetti infiniti, comunque andanti o a diritto o fles&shy;<lb/>suosi o perpendicolari o obliqui, riduceva la ragion del premere contro s&egrave; <lb/>stessi, e contro le pareti e il fondo de'vasi, a quella de'momenti de'gravi <lb/>cadenti sopra varie inclinazioni di piani. </s>

<s>Vedremo come si svolgessero que&shy;<lb/>sti concetti ordinati in un trattatello che, se fosse stato pubblicamente noto, <lb/>dava alla Scienza italiana la prima matematica dimostrazione delle pressioni <lb/>idrostatiche. </s>

<s>Ma mentre si rimaneva tuttavia nel campo della Fisica, veniva <lb/>a frugare gl'ingegni una gran curiosit&agrave; di sapere per quale intima causa, <lb/>in diffondersi per tutta intera la massa i moti, incominciati in qualunque <lb/>punto di lei, si differenzino cos&igrave; notabilmente i liquidi dai solidi. </s>

<s>La questione <lb/>si proponeva fra gli amici del Torricelli, e ora si vogliono da noi narrar le <lb/>occasioni, e dire i modi come fu risoluta. </s></p><p type="main">

<s>Ne'primi tempi dell'Accademia medicea il Torricelli stesso, dietro il <lb/>principio della rarefazione e della condensazione de'corpi, secondo il crescere <lb/>e il diminuire della temperatura; aveva, per dar gusto al Granduca, inven&shy;<lb/>tato il giochetto di una bolla di vetro, con un piccolo foro cos&igrave;, che immersa <lb/>standosi appena in fondo al vaso, bastasse aggiungervi un po'd'acqua tie&shy;<lb/>pida, per veder quella stessa bolla salire a galla, e poi di nuovo scendere, <lb/>essendosi il liquido raffreddato. </s>

<s>Per render poi lo spettacolo anche pi&ugrave; gio&shy;<lb/>condo, aveva insieme con quella detta immersa un'altra simile bolla, tutta <lb/>chiusa per&ograve; e aggiustata in modo che galleggiasse, ma che riscaldandosi <lb/>l'acqua scendesse, mentre risaliva l'altra, che riposava in fondo, e raffred&shy;<lb/>dandosi facessero i due mobili effetto contrario. </s>

<s>L'invenzione deve esser occorsa <lb/>ne'primi mesi del 1646, giacch&egrave; il di 7 novembre di quell'anno, trovandosi <lb/>il Moncony in Firenze, ed essendo andato a far visita al Torricelli, narra <lb/>avergli sentito dire &ldquo; que le Gran Duc avoit divers Thermometres pour con&shy;<lb/>no&igrave;tre le chaud et le froid, tout avec l'eau de vie, et des boules de verre <lb/>pleines d'air, mais une ou sont deux boules, l'une en haut, l'autre en bas. </s>

<s><lb/>Quand'il fait chaud celle d'en bas monte, et quand il fait froid celle d'en <lb/>haut decend &rdquo; <emph type="italics"/>(Voyages,<emph.end type="italics"/> P. I, a Paris 1695, pag. </s>

<s>261). </s></p><p type="main">

<s>Gli strumenti, fatti costruire con eleganza, gli riteneva appresso di s&egrave; <lb/>il Granduca, e se ne serviva per divertire i curiosi che capitavano in palazzo, <lb/>e per tentare i dotti, ai quali proponeva di scoprire l'occulta causa di que&shy;<lb/>gli effetti. </s>

<s>N&egrave; fra que'dotti erano solamente i cortigiani fiorentini, ma quanti <lb/>si trovassero allora da per tutto cultori di questi studi pi&ugrave; noti. </s>

<s>Narra il <lb/>gesuita Gaspero Scott che il problema fu mandato dal Granduca a Roma <lb/>&ldquo; ad celeberrimum sibique notissimum virum p. </s>

<s>Athanasium Kircherium, si&shy;<lb/>mulque ad excellentissimum mathematicum Raphaelem Magiottum, ut utrius&shy;<lb/>que de eo iudicium exquireret. </s>

<s>Nodum solvit uterque felicissime &rdquo; <emph type="italics"/>(Mecha&shy;<lb/>nica hydraulica-pneumatica,<emph.end type="italics"/> Herbipoli 1657, pag. </s>

<s>292). </s></p><pb xlink:href="020/01/3262.jpg" pagenum="223"/><p type="main">

<s>Ma l'aveva risoluto un anno prima, e non meno felicemente, il Cornelio, <lb/>il quale, nella citata epistola <emph type="italics"/>De circumpulsione,<emph.end type="italics"/> che ha la data del primo <lb/>di Giugno 1648, cos&igrave; scriveva: &ldquo; Jam volvitur alter annus ex quo Ludovi&shy;<lb/>cus Casalius vir, ut nosti, non minus genere clarus, quam disciplinarum or&shy;<lb/>namentis conspicuus, nunciavit mihi inventum fuisse Florentiae experimen&shy;<lb/>tum huiusmodi. </s>

<s>Duo globuli vitrei, in cyatum aquae plenum immissi, sic <lb/>alternatim movebantur, ut, quum aqua frigidior esset, alter fundum peteret, <lb/>reliquo supernatante, et mox, adiecta aqua calida, ille e fundo adsurgeret, <lb/>atque hic e summa aquae superficie pessum iret &rdquo; <emph type="italics"/>(Progymnasm. </s>

<s>Appen&shy;<lb/>dix<emph.end type="italics"/> cit., pag. </s>

<s>359). E soggiunge che, sebben rimanesse a sentir questa nuova <lb/>perplesso, e l'inventore ne tacesse la struttura dell'artificio, nonostante, ri&shy;<lb/>ducendosi alla ragion fisica de'condensamenti e delle rarefazioni, prodotte <lb/>dalle varie temperature ne'corpi, gli venne fatto finalmente di scoprire <lb/>l'arcano. </s></p><p type="main">

<s>&ldquo; Sed quum (cos&igrave; il Cornelio stesso prosegue il suo racconto) in eius&shy;<lb/>modi ludicris inventis occuparemur, rumor ad aures nostras perfertur ver&shy;<lb/>sari in manibus viri cuiusdam ingeniosi admirabile artificium, nempe vitreum <lb/>tubum aquae plenum, in quo plures orbiculi vitrei sursum deorsumque fere&shy;<lb/>bantur ad nutum eius, qui tubi ostium digito obturabat &rdquo; (ibid., pag. </s>

<s>360, 61). <lb/>Quell'uomo ingegnoso era Raffaello Magiotti, e noi dobbiamo ora dire in che <lb/>consistesse il maraviglioso artifizio, ch'egli aveva per le mani. </s></p><p type="main">

<s>Era stato da lui felicemente, come diceva lo Scott, risoluto il problema <lb/>inviatogli da Firenze, ma, nel capovolgere il bocciolo, per osservare il con&shy;<lb/>trario moto delle palline di vetro, o delle lumachelle, com'ei le chiama, tu&shy;<lb/>rando con la polpa del pollice, perch&egrave; non si versasse l'acqua, la bocca al <lb/>vaso; ebbe con sua grande maraviglia a notare che i due corpiccioli im&shy;<lb/>mersi, indipendentemente da ogni variazione di temperatura, si movevano <lb/>pi&ugrave; o meno veloci secondo la maggiore o minor forza, con cui si veniva a <lb/>stringere il dito otturatore. </s>

<s>Certo com'egli era che il liquido premuto ripreme <lb/>per tutti i versi, non ebbe difficolit&agrave; a intender che l'aria dentro la luma&shy;<lb/>chella poteva esservi pi&ugrave; o men costipata dalla maggiore o minor pressione <lb/>partecipatagli dal dito, e cos&igrave; produrre i medesimi effetti del calore e del <lb/>freddo. </s>

<s>Ma ci&ograve; che lo sorprese fu la trasmissione istantanea di que'moti. </s>

<s><lb/>Ne'fluidi aerosi, pensava, e anche ne'corpi duri, non &egrave; cos&igrave;, perch&egrave; la per&shy;<lb/>cossa per esempio del martello si comunica a tutto il cuneo con tempo, ci&ograve; <lb/>che dipendendo dal subire il legno o il ferro nel colpo qualche compressione <lb/>o rientramento in s&egrave; stesso, ne concludeva che dunque l'acqua si mostrava <lb/>renitente a essere in qualunque modo compressa. </s>

<s>E in questa dimostrata <lb/>incompressibilit&agrave;, per cui s'intendeva come, premuto il liquido in una sua <lb/>parte qualunque, si trasmettesse ugualmente la forza per ogni verso, faceva <lb/>il Magiotti consistere il merito della sua invenzione. </s></p><p type="main">

<s>Si risolveva dunque un'altissima questione della Scienza, mentre pa&shy;<lb/>reva non s'attendesse ad altro, che a scoprire l'artifizio di un gioco, il quale, <lb/>essendo gustato dai pi&ugrave;, fu portato attorno sull'ali della fama, mentre il <pb xlink:href="020/01/3263.jpg" pagenum="224"/>Magiotti stesso pensava di scriverne ordinatamente, e di pubblicarne la no&shy;<lb/>tizia. </s>

<s>Fu in questo tempo che pervenne la cosa all'orecchio del Cornelio, il <lb/>quale ebbe a ritrovare facilmente da s&egrave; la fisica ragione del fatto. </s>

<s>Gli venne <lb/>anzi allora in mente che, essendo l'acqua pi&ugrave; o men premuta, secondo la <lb/>maggiore o minore altezza dell'altr'acqua che a lei sta sopra, si potevano <lb/>produrre i medesimi giocosi moti, a solo inclinare pi&ugrave; o meno il bocciolo, <lb/>ridotto alla strettezza di un lungo tubo ritorto, &ldquo; nam ex inclinatione ipsius <lb/>tubi aquae altitudo decrescit, ac proinde eiusdem conatus fit minor &rdquo; (ibid., <lb/>pag. </s>

<s>363). </s></p><p type="main">

<s>Bench&egrave; il Cornelio non nomini espressamente l'Autore, pure ei ricono&shy;<lb/>sce il fatto come invenzione altrui. </s>

<s>Ma non mancarono alcuni, che se l'at&shy;<lb/>tribuirono, e ci&ograve; fece risolvere il Magiotti a stampare in fretta quel suo <lb/>primo discorso, rozzo, com'ei lo chiama, e imperfetto, col quale aveva poche <lb/>settimane prima accompagnato al Granduca lo strumento. </s>

<s>Quel discorso por&shy;<lb/>tava il titolo di <emph type="italics"/>Renitenza certissima dell'acqua alla compressione,<emph.end type="italics"/> sotto&shy;<lb/>scritto, con la data da Roma, il di 26 Luglio 1648, e dedicato al principe <lb/>don Lorenzo de'Medici. </s>

<s>Essendo poi divenuto l'opuscolo rarissimo, il Tar&shy;<lb/>gioni lo inser&igrave; da pag. </s>

<s>182-91 nel secondo tomo delle sue <emph type="italics"/>Notizie.<emph.end type="italics"/> Si pu&ograve; <lb/>di qui raccogliere ci&ograve; che pi&ugrave; importa al nostro argomento. </s>

<s>Incomincia a <lb/>dire il Magiotti che gli fu il problema inviato da Firenze nel 1648, verso la <lb/>fine di Giugno, e seguita a narrare in che modo gli venisse risoluto. </s>

<s>Poi sog&shy;<lb/>giunge: &ldquo; L'invenzione mia non consiste nel caldo e nel freddo, ma nella <lb/>renitenza alla compressione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia un cannello o cilindro AB (fig. </s>

<s>118), aperto da una delle basi, <lb/>come in A, e pieno o quasi pieno d'acqua comune, o d'ogni altro liquore, <lb/><figure id="id.020.01.3263.1.jpg" xlink:href="020/01/3263/1.jpg"/></s></p><p type="caption">

<s>Figura 118.<lb/>dove una caraffina C aperta in D, con difficolt&agrave; (ben s'aggiusta con <lb/>filo di ottone o piombo) vi galleggi. </s>

<s>Questa, chiudendosi il cilindro <lb/>AB con il dito grosso o polpa della mano, scender&agrave; pi&ugrave; o meno <lb/>veloce, secondo la maggiore o minor compressione, che fa la mano <lb/>in chiudere il cilindro, e quanto pi&ugrave; s'allenter&agrave; la compressione, <lb/>o s'aprir&agrave; il cilindro, tanto pi&ugrave; presto torner&agrave; a galleggiare. </s>

<s>Ci&ograve; <lb/>avviene, dato che il cilindro sia pieno, perch&egrave; l'acqua, che non <lb/>ammette compressione, far&agrave; forza all'aria della caraffina, salendo <lb/>per il collo di lei, come ben si vede, quando le caraffine son tra&shy;<lb/>sparenti. </s>

<s>Dunque la caraffina sar&agrave; pi&ugrave; grave in specie, per l'acqua <lb/>che v'&egrave; salita, e per l'aria che s'&egrave; condensata, e cos&igrave; discender&agrave;. </s>

<s>Ma, nel <lb/>caso che sopra l'acqua sia l'aria, questa compressa dalla mano far&agrave; qualche <lb/>forza all'acqua, e l'acqua all'aria della caraffina. </s>

<s>E finalmente, allentandosi <lb/>sempre pi&ugrave; la compressione, sempre pi&ugrave; scema quella forza, che si faceva <lb/>all'aria della caraffina, ed ella sempre pi&ugrave; respirando, e sputando l'acqua, <lb/>si riduce in una costituzione da poter galleggiare &rdquo; (pag. </s>

<s>187). </s></p><p type="main">

<s>Il trasmettersi le pressioni per tutti i versi ugualmente, e in ogni punto <lb/>della massa liquida, come si mostra dal fatto delle caraffine, che scendono <lb/>e salgono in qualunque luogo sian poste; era dunque per il Magiotti un <pb xlink:href="020/01/3264.jpg" pagenum="225"/>effetto dimostrativo della renitenza alla compressione, nella quale riconoscendo <lb/>una delle pi&ugrave; essenziali propriet&agrave; che differenziano i liquidi dai solidi, si di&shy;<lb/>chiarava cos&igrave; intorno a ci&ograve;, che era la parte seria della sua invenzione: &ldquo; Noto <lb/>che, siccome un ferro o legno mosso da noi, si muove tutto, bench&egrave; lun&shy;<lb/>ghissimo, nel medesimo istante; cos&igrave; dal dito o polpa della mano s'imprime <lb/>nel medesimo istante la virt&ugrave; in tutta l'acqua del cilindro, sia pur lungo e <lb/>largo quanto un pozzo, e siano pur alte o basse le figurine come si vuole. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La similitudine del ferro e dell'acqua, circa l'operazione istantanea, <lb/>corre benissimo, sebbene per movere il ferro ci vuol tanta forza, che superi <lb/>il peso di lui, ma nell'acqua, fuor che quella particolar diligenza e forza nel <lb/>serrare il cilindro, non ci vuol altro che un minimo tratto e momento ba&shy;<lb/>stante a sollevar quella pochissima acqua, che sale per le caraffine. </s>

<s>Adun&shy;<lb/>que una forza minima imprime la virt&ugrave; in tutta l'acqua del cilindro, o d'un <lb/>pozzo, sebben fosse lungo fino al centro della Terra. </s>

<s>E questa &egrave; una diffe&shy;<lb/>renza tra i liquidi e i solidi molto notabile. </s>

<s>Or ecco un'altra differenza si&shy;<lb/>mile. </s>

<s>Se con un martello io percotessi quel ferro, o altro solido, la virt&ugrave; <lb/>della percossa, sebbene infinita, con tempo si comunicherebbe a tutto il ferro, <lb/>mentre la vibrazione e frequenza ricerca e muove tutte le parti di lui: dove <lb/>quella minima forza del dito imprime nel medesimo istante la virt&ugrave; a tutta <lb/>l'acqua del cilindro, sebben fosse grande quanto sopra &rdquo; (pag. </s>

<s>189). </s></p><p type="main">

<s>A tal punto era, per i validi impulsi del Torricelli, stata promossa in <lb/>Italia, infin dal 1648, la Scienza idrostatica delle pressioni, ond'ei non par&shy;<lb/>rebbe credibile che nel 1663, quando il Michelini era in sul rivedere il ma&shy;<lb/>noscritto del suo trattato Della direzione de'fiumi, lasciasse correre la pro&shy;<lb/>posizione, in cui pretendeva di dimostrare che l'acqua o non preme affatto <lb/>o assai poco le sponde dei vasi, e che potesse aver del suo errore difensori <lb/>il Borelli e il Viviani. </s>

<s>Ma si spiega il fatto, osservando che rimase il filo <lb/>delle tradizioni torricelliane sventuratamente reciso nelle mani de'cultori di <lb/>questa scienza, eccettuati que'pochissimi che di Roma si fecero del Miche&shy;<lb/>lini stesso liberi censori. </s>

<s>Le parole del Cornelio, nella sua epistola <emph type="italics"/>De cir&shy;<lb/>cumpulsione,<emph.end type="italics"/> parvero scritte sopra foglie trasportate dal vento, per le ragioni <lb/>altrove narrate, ma principalmente perch&egrave; i documenti originali, che pote&shy;<lb/>vano dare autorit&agrave; a quelle nuove dottrine, cio&egrave; le lettere del Torricelli, ri&shy;<lb/>masero nelle mani del Ricci infino al 1658, e non si fecero pubblicamente <lb/>note che nel 1663, nella Lettera ai Filaleti. </s></p><p type="main">

<s>Il Discorso poi del Magiotti si pu&ograve; dir che morisse appena nato. </s>

<s>La me&shy;<lb/>moria di lui non era solamente spenta ai tempi del Targioni, ma molti anni <lb/>prima. </s>

<s>Nella stessa Accademia del Cimento, in un congresso, tenutovi cer&shy;<lb/>tamente dopo il 1660, i problemi inviati dal Granduca Ferdinando II al Ma&shy;<lb/>giotti, e al Kircher, dodici anni prima, si proponevano a risolvere come cosa <lb/>nuova. </s>

<s>&ldquo; Dopo scritto, cos&igrave; leggesi in un foglio del Viviani, mi &egrave; sovvenuto <lb/>un modo di risolvere un altro problema, che nel medesimo congresso d'ieri <lb/>fu messo in campo, ed &egrave; come si possa far due corpi, come due pescetti di <lb/>vetro, che stando nell'istesso tempo uno di loro a galla in un'acqua, e l'al-<pb xlink:href="020/01/3265.jpg" pagenum="226"/>tro in fondo nella medesima, ad un'istessa mutazione che faccia nell'acqua <lb/>di pi&ugrave; calore, quello che &egrave; galleggiante se ne vada in fondo, e nello stesso <lb/>momento quello che &egrave; in fondo ne venga a galla. </s>

<s>E tornando a raffreddar <lb/>l'acqua, quello di fondo torni a galla e l'altro ne vada in fondo, onde la <lb/>medesima causa, nel medesimo tempo, partorisca contrari modi &rdquo; (MSS. <lb/>Cim., T. X, fol. </s>

<s>102). </s></p><p type="main">

<s>Cos&igrave; dunque certi essendo che del principio dell'uguaglianza delle pres&shy;<lb/>sioni, professato dal Torricelli e sperimentalmente dimostrato dal Magiotti, <lb/>ne fu perduta fra noi per qualche tempo ogni scienza, convien narrare in <lb/>che modo si venisse a recuperarla. </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Nell'anno 1663, in cui si pubblicarono in Firenze le Lettere torricel&shy;<lb/>liane al Ricci, usciva alla luce in Parigi il trattato del Pascal <emph type="italics"/>De l'equilibre <lb/>des liqueurs,<emph.end type="italics"/> che dalle carte postume dell'Autore diligentemente raccolsero <lb/>gli amici e gli ammiratori. </s>

<s>A ripensar che, sebben fosse pari de'due uomini <lb/>la celebrit&agrave; del nome, l'uno nulladimeno gettava incidentalmente il seme <lb/>de'suoi pensieri, che l'altro svolgeva di proposito ordinatemente in un libro; <lb/>non fa maraviglia che una fama oramai universale abbia attribuito la scienza <lb/>del principio fondamentale idrostatico al Francese, piuttosto che al Nostro. </s>

<s><lb/>Fa per&ograve; maraviglia che quella fama non sia stata, in pi&ugrave; di due secoli e <lb/>mezzo, contradetta da chi, pi&ugrave; attentamente leggendo, si sarebbe dovuto ac&shy;<lb/>corgere che il Pascal non istituiva propriamente quella scienza idrostatica, <lb/>ma la supponeva, senza presumer forse di averci dato altr'opera, o attri&shy;<lb/>buirsi altro merito, che di averla esplicata, e confermata con qualche espe&shy;<lb/>rienza. </s>

<s>La proposta deve ai nostri lettori apparir nuova, e perci&ograve; passeremo <lb/>senza indugio all'esame di que'fatti, che ce la mostrino vera. </s></p><p type="main">

<s>Descritti nel capitolo primo vari esempi di paradossi idrostatici, viene <lb/>il Pascal nel secondo a dire in qual modo potrebbero spiegarsi, assumendo <lb/>per principio della dimostrazione quel singolare fatto meccanico, che poi dette <lb/>cos&igrave; facilmente in mano al Bramah quel suo torchio nuovo. </s>

<s>&Egrave; passato per <lb/>la mente a qualcuno che l'idea di far equilibrare due stantuffi, in due corpi <lb/>di tromba comunicanti, bench&egrave; di diametro molto diverso, potesse esser sug&shy;<lb/>gerita al Pascal da quella epistola al Capra, nella quale il Benedetti faceva <lb/>i primi generosi sforzi, per dimostrar come la molta acqua del mortaio possa <lb/>essere cos&igrave; facilmente sostenuta dalla poca della fistola annessa. </s>

<s>Le precise <lb/>parole che usa l'Autore, dop'aver divertito il discorso in provare, a quel <lb/>modo insufficiente che si rifer&igrave;, come sia premuto il fondo del vaso, non in <lb/>ragione della quantit&agrave; del liquido, ma dell'altezza di lui perpendicolare; le <lb/>precise parole, scritte nella citata epistola, son queste: </s></p><pb xlink:href="020/01/3266.jpg" pagenum="227"/><p type="main">

<s>&ldquo; Sed redeundo ad vasa AU et F (fig. </s>

<s>119) dico quod, sicut aqua F <lb/>sufficit ad resistendum aquae AU; ita quodlibet aliud pondus aequale F, <lb/><figure id="id.020.01.3266.1.jpg" xlink:href="020/01/3266/1.jpg"/></s></p><p type="caption">

<s>Figura 119.<lb/>cuiusvis materiae, in fistula F positum, sufficiens erit, dum&shy;<lb/>modo illud corpus ita sit adaequatum concavitati fistulae F, <lb/>quod non permittat transitum aliquem aquae vel aeris inter <lb/>convexum ipsius corporis et, devexum fistulae F, et hoc ex <lb/>se satis patet. </s>

<s>Sed in vasa AU, cum ex hypothesi latius sit <lb/>ipso F, nullum aliud corpus sufficiens erit ad resistendum <lb/>aquae ipsius F, quin tam grave sit quam tota aqua AU, exi&shy;<lb/>stente AU tam alto quam F. Unde, si aqua ipsius F nil plus esset quam una <lb/>tantummodo libra, et vas AU existeret latius ipso F in decupla proportione; <lb/>tunc in ipso AU oporteret corpus adaequatum ipsi concavitati ponere, cuius <lb/>pondus esset decem librarum, ut sufficeret ad sustinendum aquam ipsius F: <lb/>et ad impellendum ipsam aquam F deberet esse plus quam decem librarum. </s>

<s><lb/>Ponamus nunc illud corpus ita densius esse aqua, ut maius intervallum non <lb/>occupet quam OE: corpus igitur OE sufficiens erit ad impellendum aquam <lb/>F, et non eo minus &rdquo; <emph type="italics"/>(Speculationum liber,<emph.end type="italics"/> Venetiis 1599, pag. </s>

<s>288). </s></p><p type="main">

<s>Secondo questa descrizione si potrebbe vedere in qualche modo rappre&shy;<lb/>sentato, nello zaffo OE, uno degli stantuffi della macchina del Pascal, ma <lb/>non v'&egrave; ben definito il peso dell'altro stantuffo nella fistola F, e, quel che <lb/>pi&ugrave; importa, non vi si tien conto dell'acqua di comunicazion fra'due solidi, <lb/>per cui, se questo scende, quello necessariamente &egrave; costretto a salire. </s>

<s>Il Be&shy;<lb/>nedetti propone piuttosto un solido che, posto dentro il mortaio, sostiene <lb/>colla sua gravit&agrave; propria la gravit&agrave; dell'acqua nella fistola aggiunta, purch&egrave; <lb/>sia esso solido tale, da adeguare la concavit&agrave; che lo riceve, e da ci&ograve; ne con&shy;<lb/>clude che dieci libbre da una parte possono pareggiare una libbra sola dal&shy;<lb/>l'altra. </s>

<s>Ma se la conclusione scenda dai legittimi principii professati dal Pascal, <lb/>e se possa essere sostanzialmente qualche somiglianza, o qualche punto di <lb/>riscontro, fra le due speculazioni; sel vedranno da s&egrave; i nostri giudiziosi <lb/>Lettori. </s></p><p type="main">

<s>Comunque sia, la scintilla, che doveva accender la face, la trasse il <lb/>Pascal da selce, per dir cos&igrave;, pi&ugrave; domestica, e a quel nobile uso assai me&shy;<lb/>glio disposta. </s>

<s>Il Magiotti, dop'aver detto, ne'principii del suo Discorso, che <lb/>aveva mostrata l'operazione del suo strumento a molti virtuosi di Roma, e <lb/><figure id="id.020.01.3266.2.jpg" xlink:href="020/01/3266/2.jpg"/></s></p><p type="caption">

<s>Figura 120.<lb/>fra questi principalmente a que'due pellegrini ingegni <lb/>di Michelangiolo Ricci e di Antonio Nardi; &ldquo; di pi&ugrave;, <lb/>soggiunge, lo inviai in Francia, ed altre parti, a diversi <lb/>amici virtuosi come s'usa. </s>

<s>Oggi mi viene accennato <lb/>che altri, con aggiungere o variare qualche cosa, vor&shy;<lb/>rebbe farsene bello &rdquo; (Appresso il Targioni cit., pag. </s>

<s>183) <lb/>Quell'aggiunta consisteva in uno stantuffo, fatto pas&shy;<lb/>sare per la bocca A del vaso (fig. </s>

<s>120), ed essendo <lb/>esso stantuffo munito di un'asticciola, con un botton&shy;<lb/>cino in capo, si premeva pi&ugrave; comodamente con questo il liquido sottoposto, <pb xlink:href="020/01/3267.jpg" pagenum="228"/>che con la polpa del dito, o con la palma della mano. </s>

<s>La variazione poi, che <lb/>si fece in Francia all'invenzione del Magiotti, si riduceva a trasformare il <lb/>corpo della caraffina nella figura di un diavoletto, e il sottil collo di lei nella <lb/>lunga coda, con che il piccolo Minosse s'avvinghia. </s>

<s>Non giovarono nulladi&shy;<lb/>meno le parole del Nostro, per rivendicarsi e assicurarsi la propriet&agrave; dell'in&shy;<lb/>venzione, della quale oramai si era fatto bello il Cartesio. </s></p><p type="main">

<s>Cos&igrave; diffusasi tra i Francesi la notizia dello strumento, il Mersenno, nel <lb/>ritornare fra'suoi, dop'esser venuto a fiutar per tutto in Firenze e in Roma, <lb/>e a perquisire il Ricci, depositario della scienza del Torricelli e del Magiotti; <lb/>ne riferiva forse pi&ugrave; particolarmente le ragioni idrostatiche, che in Italia si <lb/>davano di que'giochi. </s>

<s>Fatto sta che, quando il Pascal rivolse il suo studio <lb/>all'equilibrio de'liquidi, era in Francia notissimo a tutti che la pressione, <lb/>fatta dallo stantuffo A (nella medesima figura 120) sopra l'acqua che tocca, <lb/>si trasmette istantaneamente in tutta la massa, e si diffonde per ogni verso, <lb/>qualunque siasi l'ampiezza e la figura del vaso. </s>

<s>Cosicch&egrave;, proseguiva il Pascal <lb/>a ragionare, se al cilindro AB ne fosse congiunto un altro CD, quanto si <lb/>voglia pi&ugrave; ampio, si dovrebbe la pressione, esercitata dallo stantuffo A sopra <lb/>la superficie liquida EF, far risentire alla superficie GH, con tal impeto di <lb/>leva all'in su, la misura del quale, forse dal Benedetti, ma pi&ugrave; ragionevol&shy;<lb/>mente dall'esperienza, gli fu mostrata nel peso di un altro stantuffo C, della <lb/>medesima materia, di pari altezza, e <emph type="italics"/>adeguato alla concavit&agrave; della fistola.<emph.end type="italics"/><lb/>Cos&igrave;, mentre sperava d'aver trovata la via di spiegare un paradosso, si vide <lb/>il Pascal comparire innanzi la faccia mostruosa di un altro paradosso, qual'era <lb/>che lo stantuffo C, del peso di cento libbre, non faceva all'in gi&ugrave; maggiore <lb/>sforzo dello stantuffo A, di una libbra sola. </s>

<s>Ma poi, ripensando esser que&shy;<lb/>sto il paradosso volgare offertoci dalla stadera, sospett&ograve; che avvenisse qui <lb/>quello, che in tutte le altre macchine, di che non pen&ograve; molto a confermarsi <lb/>nel vero, osservando che, se lo stantuffo C &egrave; cento volte pi&ugrave; peso, anche si <lb/>moverebbe cento volte pi&ugrave; tardo. </s>

<s>Della semplice dimostrazion di ci&ograve;, con&shy;<lb/>dotta dal principio delle velocit&agrave; virtuali, se ne sarebbe potuto passare, aven&shy;<lb/>dola gi&agrave; data magistralmente il nostro Galileo, ma s'introduceva nella que&shy;<lb/>stione un elemento nuovo, quello cio&egrave; della trasfusion delle forze, regolate <lb/>dalla legge che le velocit&agrave; sempre son reciproche delle grandezze mosse. </s>

<s><lb/>Ond'&egrave; che il moto impresso dallo stantuffo nella superficie E, trasfondendosi <lb/>nella superficie GH cento volte pi&ugrave; grande, vi si riduce a velocit&agrave; cento volte <lb/>minore. </s></p><p type="main">

<s>Da ci&ograve; ne concludeva il Pascal la ragione dell'equilibrio idrostatico nei <lb/>due vasi, perch&egrave; l'acqua &egrave; premuta ugualmente sotto i due stantuffi. </s>

<s>&ldquo; On <lb/>peut encore ajouter, pour plus grand eclaireissement, que l'eau est egalement <lb/>press&eacute;e sous ces deux pistons. </s>

<s>Car, si l'un a cent fois plus de poids que <lb/>l'autre, aussi en revanche il touche cent fois plus de parties: et ainsi cha&shy;<lb/>cune l'est egalement. </s>

<s>Donc toutes doivent estre en repos, parce qu'il n'y &agrave; <lb/>pas plus de raison pourquoy l'une cede que l'autre &rdquo; <emph type="italics"/>(Trait&eacute;<emph.end type="italics"/> cit., pag. </s>

<s>8). </s></p><p type="main">

<s>Qui pare che s'ammetta l'uguaglianza della pressione sotto le due varie <pb xlink:href="020/01/3268.jpg" pagenum="229"/>ampiezze di superficie, ma seguitando a leggere si trova stabilito per regola <lb/>certa che la parete di un vaso pieno di liquido soffre pi&ugrave; o meno, a pro&shy;<lb/>porzione della sua grandezza. </s>

<s>&ldquo; Si un vaisseau plein d'eau n'a qu'une seule <lb/>ouverture large d'un poulce, par exemple, ou l'on mette un piston charg&eacute; <lb/>d'un poids d'une livre, ce poids fait effort contre toutes les parties du vais&shy;<lb/>seau generalement, a cause de la continuit&eacute; et de la fluidit&eacute; de l'eau. </s>

<s>Mais <lb/>pour determiner combien chaque partie souffre, en voicy la regle: Chaque <lb/>partie large d'un poulce, comme l'ouverture, souffre autant que si elle estoit <lb/>pouss&eacute;e par le poids d'une livre (sans compter le poids de l'eau, dont je ne <lb/>parle pas icy, car je ne parle que du poids du piston) parce que le poids <lb/>d'une livre presse le piston qui est a l'ouverture, et chaque portion du vais&shy;<lb/>seau, plus ou moins grande, souffre precisement plus ou moins a proportion <lb/>de la grandeur &rdquo; (ivi, pag. </s>

<s>8, 9). </s></p><p type="main">

<s>La contradizione forse dipende dal confondersi, nel medesimo nome di <lb/>pressione, la <emph type="italics"/>potenza<emph.end type="italics"/> e la <emph type="italics"/>resistenza<emph.end type="italics"/> della macchina. </s>

<s>Se il peso A &egrave; la po&shy;<lb/>tenza, il contrapposto a lei peso C sar&agrave; la resistenza, la quale &egrave; propria&shy;<lb/>mente proporzionale alla superficie, ma i due momenti di qua e di l&agrave;, in <lb/>ogni modo, rimangono uguali, per cui riesce una lusinghiera promessa quella <lb/>del Pascal, che cio&egrave; un vaso pien d'acqua sia <emph type="italics"/>une machine nouvelle, pour <lb/>multiplier les forces a tel degr&eacute; qu'on vaudra<emph.end type="italics"/> (pag. </s>

<s>6, 7). Galileo aveva <lb/>saviamente avvertiti di questa vana presunzione i meccanici de'suoi tempi, <lb/>e forse l'acuto Francese si lasciava andar a un'espression popolare, ma non <lb/>par che con la poca precision del linguaggio si possa scusar d'errore il dire <lb/>che in tutte le macchine <emph type="italics"/>le chemin est augment&eacute; en mesme proportion que <lb/>la force<emph.end type="italics"/> (pag. </s>

<s>7) e il formular poco appresso la legge <emph type="italics"/>que le chemin est <lb/>au chemin comme la force a la force.<emph.end type="italics"/> Che se poi dice esser la medesima <lb/>cosa tanto a far fare un pollice di cammino a cento libbre d'acqua, quanto <lb/>a far fare cento pollici a una libbra, e ci&ograve; che fa fare &egrave; la forza; dunque <lb/>la forza non sta alla forza nella ragion semplice degli spazi, ma nella com&shy;<lb/>posta di loro, e de'pesi. </s></p><p type="main">

<s>Comunque sia, la novella macchina non era destinata dal Pascal ad <lb/>alzar pesi, ma a spiegare i paradossi idrostatici, i vari esempi offerti dai <lb/><figure id="id.020.01.3268.1.jpg" xlink:href="020/01/3268/1.jpg"/></s></p><p type="caption">

<s>Figura 121.<lb/>quali vi riducono alle pressioni, fatte nei vasi delle <lb/>figure 121 e 122. Supponiamo che il velo d'acqua <lb/>AB (l'<emph type="italics"/>ouverture<emph.end type="italics"/> insomma del <lb/>Pascal) riceva tale impeto da <lb/>moversi per lo spazio AC, in <lb/>un dato tempo: questo stesso <lb/>impeto, comunicato al velo in&shy;<lb/>fimo EF, lo farebbe movere, <lb/>in quel medesimo tempo, per <lb/><figure id="id.020.01.3268.2.jpg" xlink:href="020/01/3268/2.jpg"/></s></p><p type="caption">

<s>Figura 122.<lb/>tale spazio EG, che ad AC avesse la ragion reciproca <lb/>della grandezza AB alla EF, in modo cio&egrave; che, prese <lb/>LM, LN uguali alle EF, EG, dovessero aversi l'equa-<pb xlink:href="020/01/3269.jpg" pagenum="230"/>zioni AB.AC=EF.EG=LM.LN. </s>

<s>Dunque se il velo AB e il velo LM, <lb/>movendosi questo per lo spazio LN, mentre quello si muove per lo spazio AC, <lb/>fanno la medesima forza; il fondo EF del vaso tanto soffre dall'acqua sopra&shy;<lb/>stante AF, quanto da tutta l'acqua FL. </s></p><p type="main">

<s>Con simile ragionamento si prova che il fondo CD, della figura 122, <lb/>sopporta la sola acqua ED, perch&egrave; il velo AB, mosso per lo spazio AG, co&shy;<lb/>municando la sua forza al velo CD, lo farebbe movere per lo spazio misu&shy;<lb/>rato dalla CH, quarta proporzionale dopo CD, AB, AG. Ond'&egrave; manifesto che <lb/>presa EK=CH, tanta &egrave; la forza comprimente, fatta dal velo AB nel pas&shy;<lb/>sare lo spazio AG, quant'&egrave; la forza comprimente del velo EF, nel passare <lb/>lo spazio EK, e perci&ograve; il fondo CD soffre da tutta l'acqua AD quel che dalla <lb/>sola ED. </s></p><p type="main">

<s>Cos&igrave; in sostanza si dimostra dal Pascal, nel suo capitolo secondo, <emph type="italics"/>pour&shy;<lb/>quoy les liqueurs pesent suivant leur hauteur.<emph.end type="italics"/> Che poi la dimostrazione di <lb/>questi paradossi veramente dipenda dal principio, che governa la prima mac&shy;<lb/>china descritta, e illustrata per la figura 120; &egrave; facile vederlo, perch&egrave;, anche <lb/>ne'due contemplati esempi, la potenza, che facciasi risiedere nel moto del <lb/>velo acqueo AB (nella figura 121), alta resistenza del fondo EF, ha la pro&shy;<lb/>porzion reciproca della velocit&agrave; EG alla velocit&agrave; AC, come in tutte le altre <lb/>macchine ordinarie, rappresentate nella leva, ad imitazion di ci&ograve;, che pu&ograve; <lb/>dirsi intorno alla quale, s'&egrave; ridotto alla ragion dell'uguaglianza de'pesi LM, <lb/>EF, e delle velocit&agrave; LN, EG, la ragion dell'eguaglianza de'momenti. </s>

<s>La virt&ugrave; <lb/>dunque di concludere efficacemente si deriva tutta, nel discorso del Pascal, <lb/>dal fatto che le pressioni si trasmettono dalla porzione EF alla SH, cos&igrave; nei <lb/>vasi comunicanti rappresentati dalla figura 120, come dalla porzione AB si <lb/>trasmette alla EF nel vaso rappresentato dalla figura 121, e in tutti gli <lb/>altri, di qualunque forma siano, pi&ugrave; capaci in basso che in alto: secondo <lb/>l'espression propria dell'Autore il fatto insomma &egrave; il medesimo &ldquo; soit que <lb/>cette portion soit vis a vis de l'ouverture ou a cost&eacute;, loin ou prest; car la <lb/>continuit&eacute; et la fluidit&eacute; de l'eau rend toutes ces choses la egales et indiffe&shy;<lb/>rentes &rdquo; <emph type="italics"/>(De l'equil. </s>

<s>des liqueurs<emph.end type="italics"/> cit., pag. </s>

<s>9). </s></p><p type="main">

<s>Riducendosi ora qui tutta l'importanza, pu&ograve; sembrare inconveniente che <lb/>il Pascal asserisca senza prove. </s>

<s>Ma a che provar ci&ograve; che a tutti era noto? </s>

<s><lb/>Bastava l'esperienza del diavolino del Cartesio a persuadere chiunque che la <lb/>pressione fatta dallo stantuffo si comunica indifferentemente a ogni porzion <lb/>dell'acqua, comunque ella sia disposta, perch&egrave;, dentro il foro del cannellino, <lb/>si vedeva essere spinto il liquido, o sia la figura in alto, in basso e nel <lb/>mezzo, o rimanga esso foro di sotto o di sopra, dal sinistro lato o dal de&shy;<lb/>stro. </s>

<s>Tutt'altro dunque ch'essere stato primo, come si dice, il Pascal a di&shy;<lb/>mostrare che la pressione, fatta sopra un punto qualunque del liquido, si <lb/>trasmette per tutto e per ogni verso in mezzo alla mole intera, ei la sup&shy;<lb/>pone come cosa nota, non ai soli spettatori curiosi de'giocattoli del Carte&shy;<lb/>sia, ma a que'dotti principalmente, i quali avevano applaudito all'esperienza <lb/>dell'argento vivo, come dimostrativa del peso dell'ammostera, per cui si pu&ograve; <pb xlink:href="020/01/3270.jpg" pagenum="231"/>credere facilmente che, del principio dell'uguaglianza delle pressioni, con&shy;<lb/>fermato dalle spettacolose esperienze del Magiotti, riconoscesse il Pascal stesso <lb/>autore il Torricelli. </s></p><p type="main">

<s>In una cosa per&ograve; differiva la dottrina del Francese: in attribuire cio&egrave; <lb/>alla continuit&agrave;, e alla fluidit&agrave; dell'acqua, quel che i Nostri attribuivano alla <lb/>renitenza certissima di lei all'esser compressa. </s>

<s>Nel vaso rappresentato dalla <lb/>figura 121, capace per esempio di una sola oncia d'acqua, il fondo EF &egrave; <lb/>premuto dal peso di tutta l'acqua LF, che pu&ograve; esser di cento libbre. </s>

<s>Di una <lb/>tale strana moltiplicazione di forza &egrave; causa la pressione che, esercitata sul <lb/>velo AB o dal proprio peso del velo AB, si trasmette istantaneamente al <lb/>velo EF, per la renitenza dell'acqua alla compressione, diceva il Magiotti, <lb/>ma per la continuit&agrave; e fluidit&agrave; di lei diceva invece il Pascal, che dimostrava <lb/>il suo asserto con questa bella esperienza: S'immagini essere il fondo EF <lb/>mobile come uno stantuffo dentro un corpo di tromba, e sia sostenuto per <lb/>mezzo di un filo, raccomandato a un braccio della bilancia: per mantener <lb/>l'equilibrio converr&agrave;, nella fatta supposizione, appendere dall'altro braccio <lb/>un peso di cento libbre, bench&egrave; propriamente l'acqua contenuta nel vaso non <lb/>pesi che un oncia sola. </s>

<s>Nonostante che sia cos&igrave; come si dice, e come av&shy;<lb/>viene di fatto, &ldquo; si cette eau vient &agrave; se glacer, et que la glace ne prenne <lb/>pas au vaisseau, comme en effet elle ne s'y attache pas d'ordinaire; il ne <lb/>faudra a l'autre bras de la balances qu'une once pour tenir le poids de la <lb/>glace en equilibre. </s>

<s>Mais si on approche du feu contre le vaisseau, qui faisse <lb/>fondre la glace, il faudra un poids de cent livres pour contrebalancer la pe&shy;<lb/>santeur de cette glace fondu&edot; en eau, quoy que nous ne la supposions que <lb/>d'une once &rdquo; (ivi, pag. </s>

<s>3). </s></p><p type="main">

<s>Questi altri fatti, soggiunge altrove il Pascal, per conferma della sua <lb/>opinione: &ldquo; Si l'eau qui est dans le petit tuyau se glacoit, et que celle qui <lb/>est dans le vaisseau large du fond demeurast liquide, il faudroit cent livres <lb/>pour soutenir le poids de cette glace. </s>

<s>Mais si l'eau qui est dans le fond se <lb/>glace, soit que l'autre se gele ou demeure liquide, il ne faut qu'une once <lb/>pour la contrepeser &rdquo; (ivi, pagina 14). Dalle quali osservazioni l'Autore <lb/>conclude &ldquo; que c'est la liquidit&eacute; du corps, qui communique d'une des <lb/>ouvertures &agrave; l'autre, qui cause cette multiplication de forces &rdquo; (ivi, <lb/>pagina 15). </s></p><p type="main">

<s>Comunque sia i Fisici composero insieme le ipotesi del Magiotti e del <lb/>Pascal, dicendo che, per la trasmissione istantanea delle pressioni per tutti <lb/>i versi, richiedevasi una perfetta liquidit&agrave;, e una incompressibilit&agrave; perfetta. </s>

<s><lb/>Poi dopo, quando si volle aver ricorso alle attrazioni e alle repulsioni mo&shy;<lb/>lecolari, per spiegare il trasmettersi delle pressioni, secondo qualche loro so&shy;<lb/>miglianza colla vibrazione e frequenza dell'onde, si richiese non pi&ugrave; la re&shy;<lb/>nitenza, ma un certo assecondamento delle particelle dell'acqua all'esser <lb/>compresse e al dilatarsi, riducendo cos&igrave;, in qualche modo, anche i liquidi a <lb/>partecipare della costituzione e della natura dei corpi elastici. </s>

<s>Ma essendo <lb/>cos&igrave; fatte speculazioni il frutto di studi pi&ugrave; maturi, le lasceremo, per non <pb xlink:href="020/01/3271.jpg" pagenum="232"/>dilungarci di troppo dai tempi, in cui la scienza delle pressioni idrostatiche <lb/>era ne'suoi principii. </s></p><p type="main">

<s>Vedemmo quale di cos&igrave; fatti principii fosse l'avvenimento in Italia, e <lb/>s'accennava che di ci&ograve; erano ben persuasi col Pascal tutti que'dotti, i quali <lb/>riconobbero nell'esperienza famosa del Torricelli una dimostrazione non dub&shy;<lb/>bia del peso dell'ammosfera. </s>

<s>In Francia, sotto il dominio della Scuola car&shy;<lb/>tesiana, si trovavano gli studiosi nelle medesime condizioni che fra noi. </s>

<s>Il <lb/>Cartesio e Galileo professavano in idrostatica i medesimi falsi principii, e non <lb/>fa perci&ograve; maraviglia che giungessero alla medesima falsit&agrave; delle conclusioni. </s>

<s><lb/>Come poteva il Baliani, quando proponeva che la misura del vacuo fosse la <lb/>pressione ammosferica, alla quale si dovesse il non si poter sostener l'acqua <lb/>nelle trombe, se non che sino a una determinata altezza; come poteva tro&shy;<lb/>var favore in coloro, i quali credevano e insegnavano che i fluidi non pesano <lb/>nel loro proprio elemento, e n&egrave; perci&ograve; pesa l'aria dentro il pozzo, per so&shy;<lb/>stener l'acqua nel tubo della tromba, come non pesa l'aria nella fossetta <lb/>scavatasi dall'assicella d'ebano che galleggia? </s>

<s>Galileo perci&ograve; si ridusse a dire <lb/>che il limite di questa altezza nel tubo non era posto dal peso estraneo del&shy;<lb/>l'aria, ma dal peso proprio del cilindro liquido, rassomigliato a una corda, <lb/>che resiste in sino a un certo punto, oltrepassato il quale, necessariamente <lb/>si strappa. </s>

<s>Lo stesso diceva il Cartesio, nel rendere al Mersenno la ragione <lb/>del perch&egrave; sia meglio, per sollevar l'acqua a qualche grande altezza, ser&shy;<lb/>virsi del moto interrotto di pi&ugrave; trombe, piuttosto che del continuato di una <lb/>tromba sola. </s>

<s>&ldquo; Ratio autem quamobrem praestaret interruptus motus, est <lb/>quod corium subtensum substinere debet totam aquae columnam viginti <lb/>sexpedas altam, quod quidem pondus est tantum, ut illud diu ferre nequeat <lb/>quin frangatur &rdquo; <emph type="italics"/>(Epistol.,<emph.end type="italics"/> P. II, Amstelodami 1682, pag. </s>

<s>128). </s></p><p type="main">

<s>Le ragioni, da cui fu mosso Galileo a ripudiare la proposta del Baliani, <lb/>erano quelle medesime, che davano ai galileiani occasione di dubitare della <lb/>proposta del Torricelli, il quale ebbe perci&ograve; a riformar l'Idrostatica, dimo&shy;<lb/>strando che anche l'aria pesa nell'aria, e che come fluido esercita le sue <lb/>pressioni per tutti i versi. </s>

<s>Quel che fece il Nostro nelle lettere private al <lb/>Ricci, e ne'familiari colloqui con gli amici, volle poi fare il Pascal ordina&shy;<lb/>tamente ne'suoi due celebri trattati, per rispondere ai dubbi dei cartesiani. <lb/></s>

<s>&ldquo; C'est pourquoy j'ay monstr&eacute; dans <emph type="italics"/>L'equilibre des liqueurs,<emph.end type="italics"/> que l'eau pese <lb/>dans elle mesme autant qu'au dehors, et j'y ay expliqu&eacute; pourquoy nonobstant <lb/>ce poids un seau n'y est pas difficile a hausser et pourquoy on n'en sent <lb/>pas le poids. </s>

<s>Et dans le trait&eacute; <emph type="italics"/>De la pesanteur de la masse de l'air<emph.end type="italics"/> j'ay <lb/>monstr&eacute; la mesme chose de l'air, afin d'&eacute;claireir tous les doutes &rdquo; <emph type="italics"/>(Conclu&shy;<lb/>sion des deux traitez<emph.end type="italics"/> cit., pag. </s>

<s>132). </s></p><p type="main">

<s>Ma nella lettera del di 15 Novembre 1647 dichiarava il Pascal al Perier <lb/>anche pi&ugrave; espressamente le ragioni, ch'egli ebbe di congiungere insieme i <lb/>due trattati, e di premettere, a quello <emph type="italics"/>De la pesanteur de la masse de l'air,<emph.end type="italics"/><lb/>l'altro <emph type="italics"/>De l'equilibre des liqueurs.<emph.end type="italics"/> &ldquo; J'ay peine a croire que la Nature, qui <lb/>n'est point anim&eacute;e ny sensible, soit susceptible d'horreur, puisque les pas-<pb xlink:href="020/01/3272.jpg" pagenum="233"/>sions presupposent une ame capable de les ressentir, et j'incline bien plus <lb/>a imputer tous ces effets a la pesanteur et pression de l'air, parce que je <lb/>ne les considere que comme des cas particuliers d'une proposition univer&shy;<lb/>selle de l'equilibre des liqueurs, qui doit faire la plus grande partie du Trait&eacute; <lb/>que j'ay promis. </s>

<s>&rdquo; <emph type="italics"/>(Recit de la grande experience etc.<emph.end type="italics"/> in appendice ai due <lb/>trattati cit., pag. </s>

<s>168, 69). Ed essendo la promessa fatta nel detto anno 1647 <lb/>non fu mantenuta, se non che dopo il 1651, quando l'esperienze eseguite <lb/>sul Puy de Domme, a Clermont, a Parigi e a Stokol<gap/>, confermarono essere <lb/>la maggiore o minore altezza, e perci&ograve; il maggiore o minor peso dell'aria <lb/>verissima causa dell'alzarsi e dell'abbassarsi l'argento vivo nel tubo torri&shy;<lb/>celliano. </s></p><p type="main">

<s>Tale &egrave; la breve storia del libro, e dell'argomento da lui trattato, a pro&shy;<lb/>posito del quale nessuno dubiter&agrave; essere stato il Pascal, nel restaurar l'Idro&shy;<lb/>statica, preceduto dal Torricelli. </s>

<s>Ma forse alcuni potrebbero mettere in dub&shy;<lb/>bio quel che s'e dato da noi per certo, che cio&egrave; il Francese riconoscesse da <lb/>s&egrave; stesso cos&igrave; la preminenza del Nostro, da far quasi come il discepolo, che <lb/>commenta la lezione del suo maestro. </s>

<s>Ai dubitanti risponderemo, e confer&shy;<lb/>meremo noi stessi e gli altri nella propria opinione, adducendo un esempio, <lb/>che dimostri come in un soggetto, da questo non molto diverso, il Pascal <lb/>adempia di fatto verso il Torricelli l'ufficio che abbiamo detto. </s></p><p type="main">

<s>Come l'equilibrio di un liquido in due vasi comunicanti, prima dimo&shy;<lb/>strato col principio delle velocit&agrave; virtuali, pensasse poi esso Pascal d'assicu&shy;<lb/>rarlo dalle contradizioni, invocando l'assioma torricelliano de'due corpi con&shy;<lb/>giunti, che si rimangono in quiete, quando il loro comun centro di gravit&agrave; <lb/>non pu&ograve; scendere; fu precedentemente da noi fatto notare. </s>

<s>Ora per&ograve; sog&shy;<lb/>giungiamo che il Torricelli, nel premettere al suo trattato quell'assioma, <lb/>diceva che i due corpi congiunti, avverandosi la fatta supposizione dell'im&shy;<lb/>possibile scesa del loro comun centro gravitativo, si rimarrebbero in quiete <lb/>&ldquo; sive id libra fiat, sive troclea, sive qualibet alia mechanica ratione, grave <lb/>autem huiusmodi non movebitur unquam, nisi centrum gravitatis ipsius de&shy;<lb/>scendat &rdquo; <emph type="italics"/>(Opera geom.,<emph.end type="italics"/> P. I, Florentiae 1644, pag. </s>

<s>99). </s></p><p type="main">

<s>La dimostrazione taciuta dal Torricelli fu distesa dal Pascal in un trat&shy;<lb/>tatello delle Macchine, ch'egli commemora con queste parole, quasi compia&shy;<lb/>cente d'aver salvata, col nuovo metodo torricelliano, la Meccanica, rimasta <lb/>da Aristotile a Galileo senza difesa, da'contradittori delle velocit&agrave; virtuali: <lb/>&ldquo; J'ay d&eacute;montr&eacute;, par cette methode, dans un petit trait&eacute; de Mechanique, la <lb/>raison de toutes les multiplications de forces, qui se trouvent en tous les <lb/>autres instrumens de Mechanique, qu'on a jusques a present inventez. </s>

<s>Car <lb/>je fais voir en tous que les poids inegaux, qui se trouvent en equilibre, par <lb/>l'avantage des machines sont tellement disposez, par la construction des ma&shy;<lb/>chines, que leur centre de gravit&eacute; commun ne s&ccedil;avroit jamais descendre, <lb/>quelque situation qu'ils prissent. </s>

<s>D'ou il s'ensuit qu'ils doivent demeurer en <lb/>repos, c'est a dire en equilibre &rdquo; <emph type="italics"/>(Traitez<emph.end type="italics"/> cit., pag. </s>

<s>11). </s></p><p type="main">

<s>Giovi aver resuscitata questa memoria, perch&egrave; si riconosca l'importanza <pb xlink:href="020/01/3273.jpg" pagenum="234"/>di un tale trattato nella storia della Statica. </s>

<s>Ma quel che per ora a noi preme <lb/>&egrave; di concludere che il principio dell'uguaglianza delle pressioni il Pascal non <lb/>lo d&agrave; come nuovo, ma, supponendolo gi&agrave; noto, lo conferma con esperienze <lb/>nuove, lo spiega con nuove ragioni, e l'applica a dimostrar l'equilibrio dei <lb/>liquidi con s&egrave; stessi, ch'&egrave; l'argomento della prima parte del suo libro. </s>

<s>Nella <lb/>seconda si propone di trattare <emph type="italics"/>De l'equilibre d'une liqueur avec un corps <lb/>solide,<emph.end type="italics"/> e supponendo questo solido aver forma di cubo, ed essere sotto l'acqua <lb/>tutto sommerso, cos&igrave; comincia il suo ragionamento: &ldquo; Nous voyons par l&agrave; <lb/>que l'eau pousse en haut les corps qu'elle touche par dessous; qu'elle pousse <lb/>en bas ceux qu'elle touche par dessus, et qu'elle pousse de cost&eacute; ceux qu'elle <lb/>touche par le cost&eacute; oppos&eacute;. </s>

<s>D'o&ugrave; il est ais&eacute; de conclure que quand un corps <lb/>est tout dans l'eau, comme l'eau le touche par dessus, par dessous, et par <lb/>tous les costez, elle fait effort pour le pousser en haut, en bas, et vers tous <lb/>les cost&eacute;s. </s>

<s>Mais comme sa hauteur est la mesure de la force, qu'elle a dans <lb/>toutes ces impressions, on verra bien ais&eacute;ment le quel de tous ces efforts <lb/>doit prevaloir &rdquo; (ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>Quel che, nel principio di questo discorso, dice di aver fatto vedere il <lb/>Pascal, consiste nelle esperienze descritte nel capitolo precedente, una delle <lb/><figure id="id.020.01.3273.1.jpg" xlink:href="020/01/3273/1.jpg"/></s></p><p type="caption">

<s>Fig. </s>

<s>123.<lb/>quali &egrave; quella della canna AB (fig. </s>

<s>123), turata in fondo con lo <lb/>stoppaccio B a sfregamento dolce, che messa in acqua, in modo <lb/>per&ograve; che la sua bocca A rimanga sempre aperta nell'aria, mostra <lb/>come lo stoppaccio stesso &egrave; sempre spinto pi&ugrave; in su, quanto pi&ugrave; la <lb/>canna s'abbassa. </s>

<s>L'altra esperienza &egrave; della canna ritorta (fig. </s>

<s>124), <lb/>in cui lo stoppaccio al contrario &egrave; cacciato sempre pi&ugrave; gi&ugrave;, e in <lb/>ultimo vien descritta la canna a gruccia (fig. </s>

<s>125), in cui si vede <lb/>esso stoppaccio premuto sempre pi&ugrave; indentro e di traverso, secondo <lb/>che l'immersione via via si fa pi&ugrave; profonda. <lb/><figure id="id.020.01.3273.2.jpg" xlink:href="020/01/3273/2.jpg"/></s></p><p type="caption">

<s>Fig. </s>

<s>124.</s></p><p type="main">

<s>Da questi fatti il Pascal. </s>

<s>conclude che, essendo il solido cubo <lb/>premuto ugualmente sulla faccia davanti e su quella di dietro, <lb/>sulla faccia destra e sulla sinistra; se sar&agrave; altres&igrave; con pari forza <lb/>premuto anche sulla faccia di sotto e su quella di sopra, si rimarr&agrave; <lb/>in equilibrio. </s>

<s>Ma prevalendo le due spinte in gi&ugrave; e in su l'una <lb/>all'altra, il solido stesso o caler&agrave; in fondo o risalir&agrave; su a galla. <lb/></s>

<s>&ldquo; Car il paroist d'abord que comme elle (l'eau) a una pareille hau&shy;<lb/>teur sur toutes les faces des cost&eacute;s, elle les poussera &eacute;galement, et <lb/><figure id="id.020.01.3273.3.jpg" xlink:href="020/01/3273/3.jpg"/></s></p><p type="caption">

<s>Figura 125.<lb/>partant ce corps ne recevra aucune impression vers aucun <lb/>cost&eacute;, non plus qu'une girovette entre deux vents &eacute;gaux &rdquo; <lb/>(ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>Ora &egrave; notabile questo sentenziar cos&igrave; assoluto in cosa <lb/>di tanta importanza. </s>

<s>Non sembrava che dovesse essere prin&shy;<lb/>cipale ufficio dello scrittore quello di provare che, essendo <lb/>l'acqua di pari altezza, le facce laterali del cubo son pre&shy;<lb/>mute tutte ugualmente? </s>

<s>Ma ei reputava inutile spendere in&shy;<lb/>torno a ci&ograve; tante parole, avendosene dallo Stevino cos&igrave; chiara, <pb xlink:href="020/01/3274.jpg" pagenum="235"/>matematica dimostrazione. </s>

<s>Se la forza, che preme le opposte facce laterali <lb/>del cubo, uguaglia il peso della mezza colonna d'acqua, avente per base <lb/>esse facce, e per altezza la perpendicolare, condotta in fin su al supremo <lb/>livello del liquido dal centro della figura; non era egli evidente che, essendo <lb/>le basi e le altezze uguali, debbono anche i pesi delle colonne prementi es&shy;<lb/>sere uguali? </s></p><p type="main">

<s>Dunque il Pascal presupponeva la notizia degli Elementi idrostatici dello <lb/>Stevino, di cui intendeva render pi&ugrave; facili e pi&ugrave; naturali l'esperienze di&shy;<lb/>mostrative della spinta in su del liquido, e per tutti i versi. </s>

<s>Anzi &egrave; da os&shy;<lb/>servare com'anco, rispetto all'equilibrio de'liquidi con s&egrave; stessi, esso Pascal <lb/>presuppone i teoremi steviniani, la ragion de'quali niente altro fa che con&shy;<lb/>fermare col principio delle velocit&agrave; virtuali, e della stabilit&agrave; orizontale del <lb/>centro gratitativo, secondo il metodo di Galileo e l'assioma meccanico del <lb/>Torricelli. </s>

<s>Non tutti i torti aveva dunque il Boyle, quando, dell'aver ridotto <lb/>alle genuine leggi idrostatiche il premersi i liquidi in s&egrave; stessi, non dava <lb/>nessun merito al Pascal, ma l'attribuiva tutto a s&egrave; stesso e allo Stevino. <lb/></s>

<s>&ldquo; Stevinus et ego, diversimode licet, particulatim probavimus, iuxta genui&shy;<lb/>nae hydrostaticae leges, duorum liquorum prementium se invicem praeva&shy;<lb/>lentiam determinandam non esse ex eorumdem quantitatem, sed tribuendam <lb/>ei qui excedit alterum in perpendiculari altitudine &rdquo; <emph type="italics"/>(De salsedine maris. </s>

<s><lb/>Op. </s>

<s>omnia,<emph.end type="italics"/> T. II, Venetiis 1697, pag. </s>

<s>342). </s></p><p type="main">

<s>Dalle cose dette fin qui l'opera, data dal Pascal intorno all'Idrostatica, <lb/>viene a mettersi nel suo proprio aspetto, cos&igrave; che non &egrave; difficile formarsene <lb/>il pi&ugrave; giusto giudizio. </s>

<s>Il non avere insegnato in sostanza nulla di nuovo non <lb/>diminuisce perci&ograve; punto il suo merito, mancando agl'insegnamenti dello Ste&shy;<lb/>vino e del Torricelli le qualit&agrave; necessarie al loro diffondersi con facilit&agrave;, e <lb/>persuadere con efficacia. </s>

<s>Gli Elementi idrostatici dell'Olandese avevano troppo <lb/>del matematico, non solo nell'esposizion de'principii generali, ma nelle loro <lb/>stesse applicazioni, e le teorie del Nostro, non essendo ancora pubblicamente <lb/>note le lettere al Ricci, si dovevano far conseguire dall'esperienza dell'ar&shy;<lb/>gento vivo. </s>

<s>Il Pascal, premettendo il trattato <emph type="italics"/>Dell'equilibrio de'liquidi<emph.end type="italics"/> a <lb/>quello <emph type="italics"/>Del peso della massa dell'aria,<emph.end type="italics"/> dimostr&ograve; l'ordine logico di quelle <lb/>conseguenze, e ridusse a fatti fisici le matematiche astrazioni. </s>

<s>L'ordine, la <lb/>precisione e la chiarezza, che dispensavano l'Autore dalle molte parole, co&shy;<lb/>sicch&egrave; il libro di lui si conclude in 44 pagine di un volumetto in 12&deg;; ba&shy;<lb/>stano a spiegar l'efficacia, ch'egli ebbe in diffondere e in persuadere la <lb/>scienza, la quale, apparendo nuova, non fa maraviglia se, contro l'intenzion <lb/>dell'Autore, tale anche fosse creduta. </s></p><p type="main">

<s>Istituitasi in ogni modo nel libro del Pascal l'Idrostatica, non potevano <lb/>lungamente mancarne i promotori. </s>

<s>Roberto Boyle, esaminando il trattato <emph type="italics"/>De <lb/>l'equilibre des liqueurs,<emph.end type="italics"/> lo trov&ograve; constare di conclusioni e di sperimenti: e <lb/>bench&egrave; di quelle, almeno in generale, non dubitasse, aveva questi per&ograve; per <lb/>non bene dimostrativi, per diverse ragioni, la prima delle quali &egrave; &ldquo; quia <lb/>licet experimenta ab ipso commemorata eo modo tradantur, qui in consi-<pb xlink:href="020/01/3275.jpg" pagenum="236"/>gnandis rebus facti est solemnis, non tamen memini diserte eum affirmare <lb/>semet actu illa sumpsisse, atque ideo forte ea tradidit ceu talia, quae, ex eo <lb/>quod confidat se in ratiociniis suis non errasse, oporteat evenire &rdquo; <emph type="italics"/>(Para&shy;<lb/>doxa hydros.,<emph.end type="italics"/> Roterodami 1670, pag. </s>

<s>4). E promette il Boyle di confermare <lb/>questo suo giudizio con qualche esempio, un de'quali gli fu porto dall'espe&shy;<lb/>rienza, che il Pascal descrive cos&igrave;: &ldquo; Un tuyau ouvert par en haut et par <lb/>en bas, estant plein de vif argent, et enfonc&eacute; dans une riviere, pourveu que <lb/>le bout d'en haut sorte hors de l'eau, si le bont d'en bas est a quatorze <lb/>pieds avant dans l'eau, le vif argent tombera jusques &agrave; ce qu'il n'en reste <lb/>plus que la hauteur d'un pied, et l&agrave; il demereura suspendu par le poids de <lb/>l'eau &rdquo; <emph type="italics"/>(De l'equilibre etc.,<emph.end type="italics"/> pag. </s>

<s>20). </s></p><p type="main">

<s>A quanti per&ograve;, bench&egrave; abilissimi sperimentatori, ci s'erano provati, non <lb/>era riuscito mai di vedere questa curiosit&agrave; del mercurio sospeso in mezzo <lb/>all'acqua, e il Boyle confermava che, specialmente con quelle grossezze di <lb/>tubi soliti a usarsi, non era in nessun modo possibile che riuscisse, perch&egrave; <lb/>il liquido metallo, caduto da una tale altezza, acquista tant'impeto, da scap&shy;<lb/>par tutto fuori, vincendo ogni resistenza dell'acqua. </s>

<s>Ond'essendo anche al <lb/>Pascal la cosa d'impossibile riuscita, s'argomenta ragionevolmente non dover <lb/>aver egli messa in atto l'esperienza, che solamente propone come consona <lb/>con le verit&agrave; da lui professate. </s>

<s>&ldquo; Et sane, ni esset impetus, quem acquirit <lb/>mercurius ex tanta labens altitudine, haud indigna ipso foret ratiocinatio. </s>

<s><lb/>Sed experimenta nonnisi theorice vera proponi debebant ut talia, possuntque <lb/>ea saepius in praxi fallere &rdquo; <emph type="italics"/>(Paradoxa<emph.end type="italics"/> cit., pag. </s>

<s>63). </s></p><p type="main">

<s>Non diverso giudizio da questo fa il Boyle dello Stevino, a proposito <lb/>della terza esperienza, descritta nel V libro della Statica, <emph type="italics"/>commen&ccedil;ant la <lb/>practique de l'Hydrostatique:<emph.end type="italics"/> esperienza che, non essendo riuscita al Wal&shy;<lb/>lis, doveva presentar tali difficolt&agrave;, da credere facilmente che nemmen lo <lb/>Stevino l'avesse ridotta a rigoroso esame. </s>

<s>&ldquo; Et sane, propter difficultatem <lb/>ad examen ea reducendi, addubitavi ego nunquam hic Author experimenta <lb/>ista ipse sumpserit, an potius consignaverit eventa, quae ea omnino sortitura <lb/>supposuit, coniecturas suas ex veritate demonstrativa rite deductas persua&shy;<lb/>sus &rdquo; (ibid., pag. </s>

<s>133). </s></p><p type="main">

<s>Son dietro a ci&ograve; facili a prevedersi le intenzioni del Boyle, le quali non <lb/>erano d'istituire dell'Idrostatica elementi o sistemi, ma di confermarla con <lb/>l'esperienze, perfezionando le antiche, e proponendone delle nuove. </s>

<s>Cos&igrave; venne <lb/>a mettere in ordine quegli XI paradossi, pubblicati nel 1664 in Oxford in <lb/>lingua inglese, e de'quali poi si vide in Rotterdam, nel 1670, la traduzione <lb/>latina, che si cita da noi. </s></p><p type="main">

<s>Cos&igrave; fatti Paradossi dunque, che lo Stevino e il Pascal proposero, e in&shy;<lb/>gegnosamente ridussero alle vere loro ragioni, il Boyle vuol dimostrare con <lb/>l'esperienze in un altro modo, giacch&egrave; quello tenuto da'due suoi illustri pre&shy;<lb/>decessori non lo sodisfa pienamente. </s>

<s>&Egrave; perci&ograve; che, nel Paradosso VI, dopo <lb/>aver trascritta la X proposizione del libro dello Stevino, passa a esaminare <lb/>il terzo sperimento, quivi immaginato per confermarla, il quale sperimento, <pb xlink:href="020/01/3276.jpg" pagenum="237"/>sebbene sia di difficile esecuzione a quel modo, che l'insegna a far l'inven&shy;<lb/>tore, mostra nulladimeno il Boyle con quale e con quanta diligenza debba <lb/>condursi, perch&egrave; si possa veder la pratica esattamente corrispondere con la <lb/>teoria. </s></p><p type="main">

<s>Similmente, ai curiosi di veder lo spettacolo del mercurio, sospeso non <lb/>solamente in mezzo all'acqua, ma in mezzo a un liquido molto men grave <lb/>in specie di lei, qual'&egrave; l'olio di terebinto; sodisfaceva l'Autore dei Para&shy;<lb/>dossi, insegnando a prendere una canna di vetro, un po'pi&ugrave; stretta e pi&ugrave; <lb/>corta di quella usata dal Pascal, e, immersa nel mercurio tanto che la bocca <lb/>inferiore n'attinga un poco, turar la superiore col dito, come si fa del sag&shy;<lb/>giatore del vino. </s>

<s>Estratta poi la canna, col liquido metallo rimastovi in fondo, <lb/>voleva s'immergesse nell'olio, dove, ora abbassandola ora alzandola, dopo <lb/>averle levato di sopra il dito, si vedr&agrave;, diceva, &ldquo; non iniucundo spectaculo <lb/>ponderosum mercurii corpus ut nunc surgat nunc cadat, ita tamen ut sem&shy;<lb/>per super liquoris, ipso communi spiritus vini levioris, superficie fluitet &rdquo; <lb/>(pag. </s>

<s>100). </s></p><p type="main">

<s>Se tutto, nel Pascal e nello Stevino, fosse di questo genere, l'assunto <lb/>del Boyle riusciva utilissimo all'arte sperimentale. </s>

<s>Generalmente per&ograve; l'espe&shy;<lb/>rienze idrostatiche prime non differiscono da queste nuove, che nella sem&shy;<lb/>plicit&agrave; degli strumenti, e nel modo pi&ugrave; facile di usarli. </s>

<s>Per esempio: pre&shy;<lb/>parare uno stoppaccio, uno zaffo, per turare in B la bocca della canna a <lb/>gruccia, disegnata nella figura 125; era molto pi&ugrave; facile che procurarsi olio <lb/>della qualit&agrave; richiesta, e canna adatta a ritenerlo dentro; e in sostanza la <lb/>pression laterale dell'acqua veniva allo stesso modo ben dimostrata. </s>

<s>Simile <lb/>dicasi delle pressioni esercitate dal liquido di sotto in su, la maniera sem&shy;<lb/>plicissima d&igrave; sperimentar le quali, come la sugger&igrave; il Torricelli al Ricci e il <lb/>Pascal ai suoi lettori, differisce in ci&ograve; solamente dalla maniera del Boyle, che <lb/>quella pu&ograve; facilmente praticare ognuno con gli oggetti comuni, e questa non <lb/>pu&ograve; che il Filosofo, e chiunque abbia un artefice costruttore degl'immagi&shy;<lb/>nati strumenti. </s>

<s>Il nobilissimo Barone inglese ridusse anche gli oggetti del <lb/>gabinetto fisico alla magnificenza e al lusso degli altri mobili di casa, i pi&ugrave; <lb/>poveri de'quali credeva non poter servire al medesimo uso, quasi che una <lb/>scranna di rozzo faggio non fosse buona a sedervi sopra, come una sedia <lb/>d'ebano dorato. </s></p><p type="main">

<s>Si legga per esempio il Paradosso XI. </s>

<s>A questo, appena annunziato ai <lb/>colleghi della R. </s>

<s>Societ&agrave; di Londra, premette l'Autore una tale osservazione: <lb/>&ldquo; Paradoxum hoc, cum nunquam fuerit, me quidem conscio, a quoquam <lb/>hactenus propositum, adeo parum verisimile iis fuit visum, quibus id obtuli, <lb/>mathematicis ipsis non exceptis, ut sperare vix possim illustrissimam hanc <lb/>Societatem ei prompte et universim assensuram, nisi inductam experientia &rdquo; <lb/>(pag. </s>

<s>175). Eppure la maraviglia, che si dava agli accademici di Londra per <lb/>nuova, era quella medesima annunziata cinquant'anni prima da Giovanni <lb/>Bardi agli accademici di Roma, come cosa notissima a tutti, e descritta dallo <lb/>Stevino, la ragion del quale, rispetto al sostenersi in mezzo all'acqua una <pb xlink:href="020/01/3277.jpg" pagenum="238"/>tavoletta di piombo, valeva altres&igrave; per un corpo molto pi&ugrave; ponderoso, come <lb/>il cubo di bronzo, che ivi il Boyle propone. </s>

<s>La differenza poi tra il vecchio <lb/>paradosso e il nuovo non consiste se non in ci&ograve;, che a quello serve un sem&shy;<lb/>plice tubo, applicato con esquisito contatto a una faccia del solido, il quale, <lb/>se in aria vuol essere sostenuto colla mano, tuffato in acqua a una profon&shy;<lb/>dit&agrave; conveniente non ha bisogno d'altro sostegno, bastando a lui la spinta <lb/>idrostatica. </s>

<s>In questo poi, nel paradosso del Boyle, quanto sia pi&ugrave; compli&shy;<lb/>cato, e, diciamo cos&igrave;, lussureggiante l'apparato dell'esperienza, pu&ograve; facil&shy;<lb/>mente riconoscersi da chiunque rivolga gli occhi alla figura XX, impressa <lb/>in fine al libro sulla tavola terza. </s></p><p type="main">

<s>Non poco si compiace il Boyle stesso di quella esperienza, ch'egli crede <lb/>essere un'invenzione sua nuova, per confermare il peso dell'aria contro chi <lb/>lo metteva in dubbio perch&egrave;, usandovi il metodo aristotelico di gonfiarla e <lb/>di condensarla in una vescica, dicevano non doversi quell'accrescimento di <lb/>gravit&agrave;, mostrato dalla stadera, attribuire all'aria stessa moltiplicata, ma agli <lb/>effluvii crassi espirati dal petto, e passati per la bocca dell'uomo. </s>

<s>La van&shy;<lb/>tata esperienza boileiana consisteva nell'avere una bolla di vetro, in forma <lb/>di una pera col suo picciolo, dentro alla quale si rarefaceva l'aria al calore, <lb/>e, sigillatone il picciolo alla fiamma, si lasciava freddare e s'imponeva sul <lb/>bacino di una esattissima bilancia accuratamente equilibrata. </s>

<s>Rotto poi il <lb/>picciolo, e irrompendo violentemente dentro la bolla vuota l'aria esterna, si <lb/>not&ograve; che subito lo strumento s'inclinava da questa parte con insigne prepon&shy;<lb/>deranza. </s>

<s>In questo modo avrebbe certamente dovuto istituir Galileo la sua <lb/>esperienza, per decider se vero o falso era quel che diceva un Peripatetico <lb/>suo avversario, aver cio&egrave; sensibile peso anche l'aria in mezzo all'altr'aria. </s>

<s><lb/>E invece suggeriva di pesare &ldquo; una gran boccia di vetro, serrandovi dentro <lb/>l'aria naturale, senza comprimerne altra, perch&egrave;, se poi si romper&agrave; la boc&shy;<lb/>cia, e si peseranno i pezzi del vetro, si trover&agrave; l'istesso peso a capello &rdquo; <lb/><emph type="italics"/>(Risposta a V. di Grazia,<emph.end type="italics"/> Alb. </s>

<s>XIII, 530). Ma in ogni modo la vera espe&shy;<lb/>rienza decisiva sarebbe stata quella, descritta nella Lettera al Nozzolini, la <lb/>quale esperienza, mentre pareggiava la sopra riferita del Boyle nella preci&shy;<lb/>sione, la superava forse per la semplicit&agrave; e per la eleganza. </s></p><p type="main">

<s>&Egrave; molto probabile che il Fisico inglese ignorasse quella scrittura gali&shy;<lb/>leiana, non nota se non a pochi fra gli stessi Italiani, ma non si pu&ograve; in ogni <lb/>modo passar senza considerazione quel che dice nel Paradosso terzo, a pro&shy;<lb/>posito del celebre teorema idrostatico, in cui dimostra Archimede che il so&shy;<lb/>lido immerso tanto perde del suo proprio peso, quant'&egrave; il peso di un'egual <lb/>mole di liquido. </s>

<s>Il qual teorema, dice il Boyle, &ldquo; non memini me in ullo <lb/>vidisse libro excuso, et solide et clare demonstratum, doctissimo Stevino ipso, <lb/>ad quem recentiores nos remittere authores solent, nonnisi obscuram eius, <lb/>nec physicam demonstrationem tradente &rdquo; (pag. </s>

<s>71). Crede perci&ograve; che nes&shy;<lb/>suno abbia ancora solidamente e chiaramente dimostrato il teorema prima <lb/>di lui, col proporre che fa e descrivere il seguente esperimento; &ldquo; Si enim <lb/>capias v. </s>

<s>g. </s>

<s>frustum plumbi, idque ex crine equino, qui supponitur aquae <pb xlink:href="020/01/3278.jpg" pagenum="239"/>proxime aequiponderare, ad unam lancium exactae trutinae appendas, sique <lb/>iusto sacomate alteri lanci imposito patiaris plumbum vasi aquam continen&shy;<lb/>tem immergi, donec ea plane contegatur, sed libere in ipsa pendeat; sacoma <lb/>permultum praeponderabit. </s>

<s>Atque parte sacomatis exempta, donec rursus ad <lb/>aequilibrium reducatur bilanx, facile poteris, subducendo quod exemisti, idque <lb/>comparando cum toto pondere plumhi in aere, invenire quantam sui ponde&shy;<lb/>ris partem amittat in aqua &rdquo; (ibid., pag. </s>

<s>72). </s></p><p type="main">

<s>Pu&ograve; ragionevolmente supporsi che il Boyle non sapesse quel che s'era <lb/>speculato in Italia, intorno alla Bilancetta idrostatica, da Galileo, dal Castelli, <lb/>dal Viviani e da altri, che non pensarono a divulgare le loro invenzioni. </s>

<s>Ma <lb/>bastava aver letto il Ghetaldo, ch'esso Boyle annovera, insieme col mede&shy;<lb/>simo Galileo e con lo Stevino, fra i principali promotori dell'Idrostatica: ba&shy;<lb/>stava aver veduto il Tartaglia, per persuadersi che lo sperimento descritto <lb/>ne'Paradossi inglesi era tutt'altro che nuovo. </s>

<s>N&egrave; l'Autor di questi paradossi <lb/>inglesi credeva fosse rimasto indimostrato solo il teorema principale, ma e <lb/>i corollari di lui, concernenti le ragioni dell'affondarsi i corpi pi&ugrave; gravi del&shy;<lb/>l'acqua, e dell'emergere i pi&ugrave; leggeri. </s>

<s>Le nuove desiderate ragioni, solide <lb/>e chiare, poteva dirsi che mancavano in Galileo, ma no nello Stevino, in cui <lb/>anzi il Pascal le riconobbe di cos&igrave; facile deduzione, da stimare inutile il sug&shy;<lb/>gerirle ai lettori. </s></p><p type="main">

<s>Ritorniamo sul capitolo V <emph type="italics"/>De l'equilibre des liqueurs,<emph.end type="italics"/> in principio del <lb/>quale, supponendo l'Autore i teoremi steviniani da s&egrave; stesso precedentemente <lb/>confermati con l'esperienza, si propone un solido tutto sott'acqua. </s>

<s>E dopo <lb/>aver quivi detto ch'egli &egrave; premuto per ogni sua parte, e anche di basso in <lb/><figure id="id.020.01.3278.1.jpg" xlink:href="020/01/3278/1.jpg"/></s></p><p type="caption">

<s>Figura 126.<lb/>alto e d'alto in basso, conclude: <emph type="italics"/>on verra bien le quel <lb/>de tous ces efforts doit prevaloir.<emph.end type="italics"/> Essendo infatti le <lb/>contrarie pressioni d'avanti e indietro, da destra e si&shy;<lb/>nistra, sempre necessariamente uguali, non pu&ograve; la que&shy;<lb/>stion cadere se non che circa le pressioni di sopra in <lb/>gi&ugrave;, e di sotto in su, l'uguaglianza o la prevalenza delle <lb/>quali si vedr&agrave; bene, vuol dire insomma il Pascal, per <lb/>gl'insegnamenti dello Stevino, secondo cui la base AB <lb/>del solido CB (fig. </s>

<s>126) &egrave; spinta in su da una forza <lb/>uguale al peso della colonna d'acqua, avente quella me&shy;<lb/>desima base, e AE per altezza; in gi&ugrave; poi &egrave; calcata dal peso proprio del <lb/>solido, e da quello che gli soprasta: dalla colonna cio&egrave;, che ha per base la <lb/>base superiore del solido stesso, e per altezza CE, supposto che sia FG il <lb/>livello del liquido nel vaso. </s>

<s>Di qui si vedr&agrave; anche meglio <emph type="italics"/>le quel de ces <lb/>efforts doit prevaloir,<emph.end type="italics"/> perch&egrave;, se il solido &egrave; pi&ugrave; grave in specie dell'acqua, <lb/>il luogo della quale egli occupa nella colonna EB, prevarr&agrave; la spinta di <lb/>sopra, che lo tirer&agrave; in fondo; se &egrave; pi&ugrave; leggero, prevarr&agrave; la spinta di sotto, <lb/>che lo mener&agrave; a galla. </s></p><p type="main">

<s>Ora questa pronta facilit&agrave;, e sicurezza di ragioni, fa un singolare con&shy;<lb/>trasto con l'incerto procedere del Boyle, simile a quel di colui, che fosse <pb xlink:href="020/01/3279.jpg" pagenum="240"/>entrato per una via, da nessun orma segnata. </s>

<s>&ldquo; Ratio igitur emersionis le&shy;<lb/>viorum corporum in gravioribus fluidis esse haec videtur: quod aquae, cor&shy;<lb/>poris parti inferiori contiguae, conatus sursum fortius est eiusdem corporis <lb/>et aquae ei incumbenti, conatu deorsum &rdquo; <emph type="italics"/>(Parad.<emph.end type="italics"/> cit., pag. </s>

<s>75). Ma questa <lb/>&egrave; ragion fisica. </s>

<s>Avrebbe dovuto sapere il Boyle altres&igrave; che lo Stevino sog&shy;<lb/>giungeva un'altra ragion matematica, per cui, non solamente veniva a pre&shy;<lb/>cedere l'idrostatica dei Paradossi, ma quella stessa, che si sarebbe insegnata <lb/>un secolo di poi. </s>

<s>Se O sia il centro di gravit&agrave; del corpo CB, sar&agrave;, secondo <lb/>l'autore dell'Acrobatica, in quello stesso punto il centro della pressione, co&shy;<lb/>sicch&egrave; concorreranno in O tre forze, una di basso in alto, uguale al peso C <lb/>della colonna d'acqua gi&agrave; detta, e due d'alto in basso: quella uguale al <lb/>peso P del solido, e questa uguale al peso C&prime; della colonna liquida, a lui <lb/>soprastante. </s>

<s>Onde, essendo C=P+C&prime;, si far&agrave; l'equilibrio: e se, rima&shy;<lb/>nendo C&prime; invariabile, P cresce o scema, &egrave; manifesto quale sia, nelle due con&shy;<lb/>trapposte direzioni, la forza che prevale. </s></p><p type="main">

<s>Si &egrave; supposto C&prime; invariabile, ed essendo CB men grave in specie del&shy;<lb/>l'acqua, s'&egrave;, per queste chiarissime dottrine steviniane, concluso che verr&agrave; <lb/>spinto in alto. </s>

<s>Or s'immagini il solido rimaner sulla medesima base AB, <lb/>ma raddoppiare in AD la sua altezza. </s>

<s>&Egrave; manifesto che la spinta in su sar&agrave; <lb/>la medesima, ma diminuir&agrave; la spinta in gi&ugrave;, perch&egrave; l'accrescimento del so&shy;<lb/>lido &egrave; entrato in luogo dell'acqua, la quale &egrave; per ipotesi pi&ugrave; grave. </s>

<s>Ond'&egrave; <lb/>che se CB, DB son due cubi, o due cilindri di legno, il pi&ugrave; lungo verr&agrave; so&shy;<lb/>spinto in su, con pi&ugrave; veloce moto dell'altro. </s></p><p type="main">

<s>Non &egrave; dunque vero che agli scrittori idrostatici mancassero le ragioni <lb/>da risolvere il problema, come si lusingava il Boyle, il quale, dop'aver posto <lb/>il fondamento alle cose che stanno in sull'acqua, o che in quella si muo&shy;<lb/>vono, soggiungeva queste parole: &ldquo; Atque ex iisdem fundamentis afferre pos&shy;<lb/>sumus (quam apud alios nondum invenimus) veram problematis istius a <lb/>scriptoribus hydraulicis propositi, solutionem, quare, scilicet, si baculus ali&shy;<lb/>quis cylindricus secetur in duas partes, quarum una duplam habeat longi&shy;<lb/>tudinem alterius, et ambae sub aqua aequali profunditate detentae dimittan&shy;<lb/>tur, eodem tempore et emergere sinantur, maior celerius adscendet minori &rdquo; <lb/>(ibid., pag. </s>

<s>77). </s></p><p type="main">

<s>Constando dunque l'Idrostatica, ne'trattati dei precedenti Autori, vera&shy;<lb/>mente di conclusioni e di sperimenti, si pu&ograve; dire che il Boyle non dette a <lb/>quelle nessuna promozione, cosicch&egrave; l'opera sua si ridusse tutta a confer&shy;<lb/>mare verit&agrave; gi&agrave; dimostrate. </s>

<s>Quanto agli sperimenti non &egrave; che la Scienza, <lb/>prima di lui, ne patisse difetto, ma non erano tutti praticabili a quel modo, <lb/>che si proponevano dagli speculativi, e il Boyle mostr&ograve; come si dovevano <lb/>disporre ed esercitare gli strumenti, perch&egrave; rispondessero esattamente alle <lb/>intenzioni. </s>

<s>Spesso la prescrizione di certi organi &egrave; superflua: alcune osser&shy;<lb/>vanze son cos&igrave; minuziose, da somigliare molto a pedanterie, ma &egrave; nono&shy;<lb/>stante il Boyle, come sempre, anche qui grande maestro dell'arte speri&shy;<lb/>mentale. </s></p><pb xlink:href="020/01/3280.jpg" pagenum="241"/><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Tali furono i progressi, fatti dall'Idrostatica appresso gli stranieri, mentre <lb/>in Italia si rimaneva tuttavia rattratta nel Discorso galileiano delle galleg&shy;<lb/>gianti. </s>

<s>Eppure gl'impulsi al progredire erano agli altri venuti da noi, comu&shy;<lb/>nicandosi al Boyle dal Pascal, e al Pascal dal Torricelli e dal Magiotti. </s>

<s>Ma <lb/>come sia avvenuto che la scintilla delle tradizioni corresse prima ad accen&shy;<lb/>dere il fuoco in Francia, si comprender&agrave; dai fatti narrati, rammemorandoci <lb/>che le lettere torricelliane al Ricci non si resero pubblicamente note, che <lb/>nel 1663, insieme col trattato del Pascal, e un anno prima de'Paradossi del <lb/>Boyle. </s>

<s>Quell'anno 1663 segna l'epoca del risorgimento dell'Idrostatica in <lb/>Italia: risorgimento, che gli Accademici fiorentini par che volessero far pro&shy;<lb/>clamare al Magliabechi solennemente, in questo, fra i suoi celebri <emph type="italics"/>Avvisi <lb/>letterari,<emph.end type="italics"/> che trascriviamo dall'autografo: &ldquo; Il Boyle ha stampato in Oxford <lb/><emph type="italics"/>Paradoxa hydrostatica,<emph.end type="italics"/> dove con varie esperienze cerca di stabilire l'equi&shy;<lb/>librio de'liquori secondo il libretto di mons&ugrave; Pascal, o piuttosto secondo <lb/>l'invenzione del Torricelli, che veramente fu il primo &rdquo; (MSS. Cim., T. XXI, <lb/>fol. </s>

<s>42). </s></p><p type="main">

<s>Si disse come l'invenzione fosse spiegata, e pubblicamente da Tommaso <lb/>Cornelio diffusane la notizia. </s>

<s>E bench&egrave; l'Epistola di lui si rimanesse per <lb/>quindici anni non curata, per le ragioni accennate, e per altre che non im&shy;<lb/>porta mettersi a investigare; ora era naturale si rivolgessero gli studiosi con <lb/>vivo desiderio a lei, ch'ebbe perci&ograve; la massima efficacia nel detto risorgi&shy;<lb/>mento della Scienza. </s>

<s>Giovanni Finchio, mandato dal principe Leopoldo de'Me&shy;<lb/>dici per l'Italia, a raccogliere oggetti di Storia naturale, notizie d'autori e <lb/>di libri; non manc&ograve; d'informarsi del Cornelio, che il Borelli, negli accade&shy;<lb/>mici consessi intorno al confutar la leggerezza positiva, riconosceva beneme&shy;<lb/>rito banditore dell'Idrostatica torricelliana, attinta dalla bocca del Ricci. </s>

<s>&ldquo; A <lb/>Napoli (cos&igrave; il Finchio riferiva al Principe, in una lettera del 24 Novem&shy;<lb/>bre 1663) abbiamo avuto particolarissima notizia del signor Tommaso Cor&shy;<lb/>nelio, matematico e medico di grande grido, e amico del signor Michelan&shy;<lb/>giolo Ricci. </s>

<s>Lui ha scritto un libro intitolato <emph type="italics"/>Progymnasmata:<emph.end type="italics"/> pretende che <lb/>lui sia stato inventore della ipotesi della compressione dell'aria, e forza ela&shy;<lb/>stica di lei, innanzi Pecqueto &rdquo; (ivi, T. XVII, fol. </s>

<s>224). </s></p><p type="main">

<s>Ma il Viviani, non contento a leggere l'Epistola corneliana nell'origi&shy;<lb/>nale latino, si dette diligentemente a tradurla, o intendesse cos&igrave; d'imprimer <lb/>meglio nella sua propria mente quelle dottrine, o di divulgarle negli altri, <lb/>cos&igrave;, pi&ugrave; facilmente. </s>

<s>&Egrave; notabile in ogni modo che rimanesse questa fatica <lb/>interrotta proprio col&agrave;, dove s'entrava nell'argomento dell'Idrostatica, di&shy;<lb/>stratto senza dubbio il Viviani dal concepire, e poi dal distendere il trattato <lb/>che diremo, e che gli fu suggerito dal rimeditar le cose, che stava per tra-<pb xlink:href="020/01/3281.jpg" pagenum="242"/>durre in su quel punto. </s>

<s>Ci&ograve; che n'&egrave; rimasto &egrave; dal fol. </s>

<s>48-66 del T. CXXXVI <lb/>de'Discepoli di Galileo, dove in principio, dopo l'avvertenza <emph type="italics"/>Mia traduzione,<emph.end type="italics"/><lb/>si legge: &ldquo; Lettera all'illustrissimo signor marchese Marcello Crescenti, di <lb/>Tommaso Cornelio da Cosenza, nella quale si esplicano, per mezzo della cir&shy;<lb/>cumpulsione, secondo l'opinione platonica, le vere cagioni di que'moti, che <lb/>volgarmente dicono farsi per ragione di fuggire il vacuo. </s>

<s>Si sciolgono ancora <lb/>alcune questioni naturali, che cadono in proposito del discorso, e si appor&shy;<lb/>tano in campo alcuni nuovi problemi. </s>

<s>Stampata in Roma nel 1648. &rdquo; </s></p><p type="main">

<s>Il passo originale in questa lettera, a cui rimase nel tradurre il Viviani, <lb/>per mettersi a svolgere ordinatamente i pensieri di l&igrave; concepiti, &egrave; il seguente, <lb/>che si trascrive dalla citata appendice ai <emph type="italics"/>Proginnasmi.<emph.end type="italics"/> &ldquo; Aqua premit in&shy;<lb/>teriorem vasis superficiem, non modo iuxta perpendiculares, sed iuxta incli&shy;<lb/>natas quoque lineas: immo, non solum iuxta rectas, sed etiam iuxta flexuo&shy;<lb/>sas, quae rectis aequiparantur. </s>

<s>In omni tamen casu tantus fit impulsus, <lb/>quantus omnino fieret a perpendiculo aquae altitudinem definiente. </s>

<s>Eadem <lb/>enim pressioni aquarum contingunt, quae in motu gravium naturaliter de&shy;<lb/>scendentium observantur, quum pressus hic oriatur ex propensione, quam <lb/>habet aqua ad motum deorsum. </s>

<s>Quemadmodum vero pila plumbea per pla&shy;<lb/>num inclinatum, vel per tubum in helicis formam revolutum, a summo ad <lb/>imum repens, tantam denique acquirit velocitatem, quantam propemodum <lb/>indepta fuisset, si per rectam perpendicularem expositae altitudini aequalem <lb/>descendisset; ita ferme aqua in vase contenta non modo subiectum fundum, <lb/>sed et latera quoque urgens aperto foramine erumpit tanto impetu, quantum <lb/>postulare videtur eius altitudo &rdquo; (pag. </s>

<s>342). </s></p><p type="main">

<s>Come venisse di qui suggerito al Viviani quel suo metodo di risolvere <lb/>il liquido in una matassa di filetti infiniti, lungo i quali gravitassero le loro <lb/>moli, supposte concentrate in un punto, co'momenti convenevoli alle scese <lb/>lungo piani inclinati, che di essi filetti avessero le medesime lunghezze e <lb/>direzioni; &egrave; assai facile a comprendere: n&egrave; men facile &egrave; a indovinare che <lb/>venisse di qui al Viviani stesso inspirata quella riforma, intesa a rendere i <lb/>processi idrostatici di Archimede universali. </s>

<s>Essendo gi&agrave; da noi pubblicato <lb/>addietro il trattatello, in cui restituiva l'Autore alla desiderata universalit&agrave; i <lb/>teoremi <emph type="italics"/>De insidentibus humido,<emph.end type="italics"/> sembrerebbe esser ora venuta l'occasione <lb/>di mantenere le accennate promesse, riducendo dai manoscritti le generali <lb/>proposizioni, dimostrative delle ragioni, secondo le quali i raggi fluidi eser&shy;<lb/>citano i loro momenti: ragioni, da cui i teoremi, scritti nel trattatello gi&agrave; <lb/>noto, dipendono come legittimi corollari immediati. </s>

<s>Indugeremo nonostante <lb/>ancora un poco a sodisfare alla dotta curiosit&agrave; dei nostri Lettori, per tratte&shy;<lb/>nerci a considerar brevemente quali altri benefici influssi piovessero dall'epi&shy;<lb/>stola del Cornelio a rinfrescare l'aridit&agrave; degli studii idrostatici del Borelli. </s></p><p type="main">

<s>Il fautore del Michelini, il corto interpetre di Archimede, che credeva <lb/>repugnare alla natura dell'acqua, corpo anch'essa grave, lo spingere in su, <lb/>e non potere perci&ograve; premere su s&egrave; stessa e contro i solidi sottoposti, se non <lb/>che in direzion perpendicolare; ecco, dopo aver meditata l'Epistola del Cor-<pb xlink:href="020/01/3282.jpg" pagenum="243"/>nelio, come la pensi molto diversamente. </s>

<s>Nella proposizione CXC <emph type="italics"/>De motio&shy;<lb/>nibus naturalibus,<emph.end type="italics"/> appena detto che Archimede suppone premere solamente <lb/>il fluido per linea perpendicolare all'orizonte, cos&igrave; soggiunge: &ldquo; Hoc pro&shy;<lb/><figure id="id.020.01.3282.1.jpg" xlink:href="020/01/3282/1.jpg"/></s></p><p type="caption">

<s>Figura 127.<lb/>fecto verissimum est, quotiescumque innatet intra aquam <lb/>prisma aliquod consistens et durum. </s>

<s>At si in vase BCEI <lb/>(fig. </s>

<s>127), aqua pleno, intra spatium AIFG collocetur <lb/>non prisma ligneum, sed aliud corpus molle vel fluidum <lb/>cedens, minus grave specie quam sit aqua collateralis; <lb/>tunc nedum fluidi IG sursum perpendiculariter superfi&shy;<lb/>cies FG versus IA, sed praeterea latus eius AG propel&shy;<lb/>letur constringeturque versus IF, ita ut eodem tempore <lb/>fluidum minus grave IG simul ascendat perpendiculariter <lb/>versus IA, et lateraliter quoque ab AG versus IF transportetur. </s>

<s>Hinc colligitur <lb/>quod aqua, seu quodlibet fluidum BG, gravius specie quam corpus IG, nedum <lb/>vim facit premendo perpendiculariter, sed etiam vim exercet lateraliter, non <lb/>quidem per horizontales lineas BA et HG, sed per lineas inclinatas BK et <lb/>LG. </s>

<s>Et hoc suppleri archimedeo assumpto debere censeo, cum instinctu na&shy;<lb/>turae corpora omnia gravia descendere conentur versus terrae centrum, qui&shy;<lb/>buscumque modis hoc ab eis consequi possit, nedum itinere perpendiculari <lb/>ad horizontem sed etiam inclinato &rdquo; )pag. </s>

<s>393). </s></p><p type="main">

<s>Questa teoria, che abbiamo con parole simili dianzi letta nel Cornelio, <lb/>il Borelli passa a confermare con l'esperienza della borsa di pelle, tesa in <lb/>forma di parallelepipedo da verghe rigide, interiormente appuntate e rego&shy;<lb/>larmente disposte, la qual borsa, dice il Borelli, se tu immergerai nell'acqua, <lb/>in modo che la bocca di lei, come quella di un pozzo, rimanga fuori sco&shy;<lb/>perta: &ldquo; videbis quod, nedum basis et fundum, sed etiam quatuor faces col&shy;<lb/>laterales bursae incurventur convexe versus intermedium axim eiusdem pu&shy;<lb/>tei. </s>

<s>Et si simul digiti aut virgulae educantur, nec amplius vim exerceant, <lb/>nedum basis et fundum putei ascendet sursum, sed etiam eius parietes <lb/>collaterales se se constringent, et ad se se invicem accedent, quod est evi&shy;<lb/>dentissimum signum aquam, nedum vim facere sursum perpendiculariter <lb/>aerem expellendo, sed etiam lateraliter conari excurrere per lineas obliquas, <lb/>constringendo laterales parietes praedicti putei coriacei &rdquo; (ibid., pag. </s>

<s>394, 95). </s></p><p type="main">

<s>Il Borelli dunque, come il Pascal e il Boyle, non esce fuori de'termini <lb/>delle esperienze, e la proposizione di lui &egrave; puramente fisica, come son tutte <lb/>quelle de'suoi due illustri predecessori. </s>

<s>L'Idrostatica matematica, perci&ograve;, in <lb/>questa che fu pure epoca gloriosa di risorgimento, parve rimanersi ne'teo&shy;<lb/>remi dello Stevino come assiderata. </s>

<s>Il Torricelli era opportunamente soccorso <lb/>a stiepidirne le membra, facendovi sopra riflettere i calori della idrodinamica <lb/>nuova, e il Cornelio, nella sua Epistola, aveva raccolti e indirizzati allo scopo <lb/>quei benefici raggi, come in uno specchio ustorio, nel foco del quale collo&shy;<lb/>cando il Viviani la conveniente materia, venne ad accendere la nuova lam&shy;<lb/>pada nel tempio della Scienza. </s></p><p type="main">

<s>Che il liquido si dovesse disporre in una superficie orizontale, concen-<pb xlink:href="020/01/3283.jpg" pagenum="244"/>trica con la terra, fu per Archimede e per lo Stevino piuttosto un'ipotesi <lb/>che una dimostrazione. </s>

<s>E se pure qualche dimostrazione si provarono a darne <lb/>gl'Idrostatici di poi, la desunsero dalle particolarit&agrave; de'fatti, e non dalla uni&shy;<lb/>versait&agrave; dei principii. </s>

<s>Vedremo come, dall'aver matematicamente dimostrato <lb/>dover nell'umido stagnante ogni assegnato raggio finalmente posarsi in equi&shy;<lb/>librio, fosse il primo il Viviani a concluderne, per matematica dimostrazione, <lb/>che di ogni umido stagnante la superficie &egrave; necessariamente sferica, e con&shy;<lb/>centrica con la Terra. </s></p><p type="main">

<s>Le spinte idrostatiche di sotto in su il Torricelli s'era contentato di <lb/>persuaderle frettolosamente al Ricci, per via di ovvie esperienze. </s>

<s>Il Nardi poi <lb/>accennava a una riflessione del moto, e se di questo moto riflesso aveva lo <lb/>Stevino detto le misure, non concludeva per&ograve; da principii universali il suo <lb/>discorso. </s>

<s>Il Viviani fu il primo, dietro matematiche prenozioni, a dimostrar <lb/>che, se un raggio qualunque assegnato nell'umido non trova sufficiente mo&shy;<lb/>mento di resistenza in un altro adiacente raggio, a s&egrave; simile e dal comun <lb/>termine sporgente infino alla suprema superficie; verr&agrave; in su respinto neces&shy;<lb/>sariamente. </s>

<s>Il teorema poi confermava con una esperienza, che, non paren&shy;<lb/>doci bene il tacerla, mettiamo qui, per non riferirsi al trattato dei Raggi <lb/>fluidi, se non che come una nota, a pi&egrave; di pagina, scritta, per avvertire i <lb/>lettori che le ragioni idrostatiche dei momenti si confermano dai pesi stessi <lb/>posti sulla stadera. </s>

<s>&ldquo; Nell'abbassare con la mano un solido galleggiante nel <lb/>fluido di un vaso, posto sulla stadera, e sommergerlo pi&ugrave; del suo stato na&shy;<lb/>turale, purch&egrave; non si faccia toccare il fondo; non si alterer&agrave; l'equilibrio, <lb/>perch&egrave; tanta &egrave; la forza premente all'in gi&ugrave; della mano, che quella del so&shy;<lb/>lido nel volere ascendere e tornare al suo stato. </s>

<s>Lo stesso segue se, invece <lb/>di mano, si metter&agrave; sopra una molla, che sia ferma fuori del vaso, e posi <lb/>con tensione sopra il solido, perch&egrave; la molla servir&agrave; in luogo di mano &rdquo; <lb/>(MSS. Cim., T. X, fol. </s>

<s>46). </s></p><p type="main">

<s>Delle pressioni di sotto in su quelle fatte dal liquido lateralmente erano <lb/>una conseguenza necessaria, e abbiamo poco fa veduto come il Borelli le <lb/>dimostrasse sperimentalmente, e come, con operazioni alquanto diverse nei <lb/>modi, ma pur della medesima natura, le avessero dimostrate il Pascal e il <lb/>Boyle. </s>

<s>Il Magiotti, prima di tutti loro, aveva delle pressioni idrostatiche per <lb/>tutti i versi data la dimostrazione pi&ugrave; bella e pi&ugrave; efficace, ma nemmeno que&shy;<lb/>sta usciva fuori de'termini dell'esperienza. </s></p><p type="main">

<s>La prima dimostrazion matematica, che in pubblico si sapesse, fu quella <lb/>tentata dal Guglielmini, per via del principio della composizion delle forze, <lb/>supponendo che le infinite molecole componenti il fluido siano per s&egrave; stesse <lb/>tutte uguali di peso, e in figura di tante esatte piccolissime sfere. </s>

<s>Glie ne <lb/>aveva dato l'esempio il maestro suo Geminiano Montanari, il quale, per ri&shy;<lb/>solvere alcuni problemi idrostatici, propostigli nella bolognese Accademia del&shy;<lb/>l'abate Sampieri, non volendo semplicemente supporre i principii, da cui si <lb/>deriverebbero le sue conclusioni, pens&ograve; di dimostrarli in altri modi, da quelli <lb/>dello Stevino e di Galileo. </s>

<s>&ldquo; Ma perch&egrave;, egli dice, di tai corpiccioli liquidi <pb xlink:href="020/01/3284.jpg" pagenum="245"/>ed insensibili, di che il liquido si compone, non pu&ograve; cos&igrave; bene l'intelletto <lb/>discorrere, se prima non se gli propone come sensibili, e di una determinata <lb/>figura; non sar&agrave; perci&ograve; fuori di proposito, ad effetto d'investigare la natura <lb/>de'corpi liquidi, figurarci prima diversi vasi ripieni di palline di sensibile <lb/>grandezza, sferiche e perfettamente terse, e, conosciuta la natura ed opera&shy;<lb/>zione loro, dedurne quelle conclusioni, che similmente a'liquidi vederemo <lb/>potersi adattare. </s>

<s>Il che supponendo, vengo prima a provare come, dato un <lb/>vaso, il di cui fondo, per chiarezza di discorso, supporremo prima sia per&shy;<lb/>fettamente posto orizontale, e le sponde erette al medesimo, e sia ripieno di <lb/>palline perfettamente terse, di egual peso e grandezza; intesa qualsivoglia <lb/>di dette palline sentir&agrave; essa porzione del peso di tutte quelle, che a lei in <lb/>livello sono superiori non solo a perpendicolo, ma lateralmente in qualsivo&shy;<lb/>glia posto del vaso &rdquo; (Discorso idrostatico pubblicato dal Targioni, Aggran&shy;<lb/>dimenti ecc. </s>

<s>cit., T. II, pag. </s>

<s>725). </s></p><p type="main">

<s>E dietro questa si fa via il Montanari a dimostrare altre tre proposi&shy;<lb/>zioni idrostatiche, concludendo che la pressione patita da una delle palline <lb/>&egrave; quella stessa, che patiscono tutte le altre simili, disposte nel medesimo <lb/>strato orizontale, e che la forza di essa pressione da null'altro dipende, se <lb/>non che dal numero degli strati soprapposti: cosicch&egrave; insomma la pressione <lb/>esercitata dal liquido contro il fondo &egrave; quella di una colonna, avente per <lb/>base esso fondo, e per altezza la perpendicolare, compresa fra lui e il su&shy;<lb/>premo livello, qualunque sia la forma e la disposizione del vaso. </s></p><p type="main">

<s>Il Guglielmini introdusse la matematica nel discorso fisico del suo pro&shy;<lb/>prio Maestro, e, nel capitolo primo del trattato <emph type="italics"/>Della natura dei fiumi,<emph.end type="italics"/> si <lb/>propose in primo luogo di dimostrare che &ldquo; se sar&agrave; uno strato retto di sfere, <lb/><figure id="id.020.01.3284.1.jpg" xlink:href="020/01/3284/1.jpg"/></s></p><p type="caption">

<s>Figura 1<gap/>8.<lb/>e sopra uno de'di lui interstizi sar&agrave; situata un'altra sfera; <lb/>premer&agrave; questa le quattro sottoposte egualmente, s&igrave; per la linea <lb/>perpendicolare, che per l'orizzontale &rdquo; (Milano 1821, Vol. </s>

<s>I, <lb/>pag. </s>

<s>46). Supponendo esser Y (fig. </s>

<s>128) la sfera soprapposta, <lb/>e N una delle quattro soggiacenti, se per YN si rappresenta <lb/>la forza, con la quale l'una delle dette sfere preme l'altra, e <lb/>se una tal forza si decompone nella verticale YR, ossia PN, e <lb/>nella orizontale YP, ossia RN, &egrave; manifesto il proposito, perch'essendo PR un <lb/>quadrato le linee PN, RN sono uguali, e perci&ograve; son altres&igrave; uguali le forze con <lb/>esse linee rappresentate, come in simil modo si dimostrerebbe di tutt'e tre <lb/>le altre sfere premute dalla medesima Y. </s></p><p type="main">

<s>Di qui procede il Guglielmini alla dimostrazione delle proposizioni se&shy;<lb/>guenti, fra le quali notabile &egrave; la IV, d'onde si trae dall'Autore questo prin&shy;<lb/>cipale importantissimo corollario, che cio&egrave; &ldquo; un mucchio di sfere affetter&agrave; <lb/>sempre di avere la superficie disposta in uno strato, ossia piano orizontale: <lb/>o pi&ugrave; propriamente in una superficie sferica, il cui centro sia quello dei <lb/>gravi &rdquo; (ivi, pag. </s>

<s>57). Nel qual discorso del Guglielmini il pubblico ebbe la <lb/>prima dimostrazion matematica del teorema secondo di Archimede. </s></p><p type="main">

<s>La novit&agrave; conferi molto a dar sodisfazione agli speculativi, i quali per&ograve;, <pb xlink:href="020/01/3285.jpg" pagenum="246"/>ripensando che la citata IV, insieme con le proposizioni precedentemente <lb/>scritte in principio del trattato della Natura dei fiumi, dipendevano dalla <lb/>prima, trovarono che questa per pi&ugrave; ragioni era difettosa. </s>

<s>Iacopo Riccati, <lb/>come nelle sue <emph type="italics"/>Annotazioni<emph.end type="italics"/> riferisce il Manfredi (ivi, pag. </s>

<s>74), osserv&ograve; che, <lb/>supponendo l'acqua essere un aggregato di piccole sfere, non sarebbe pos&shy;<lb/>sibile spiegare come si trovi in natura un corpo, che ecceda del doppio la <lb/>gravit&agrave; specifica di lei. </s>

<s>Il D'Alembert poi nel Dizionario enciclopedico delle <lb/>Matematiche, all'articolo <emph type="italics"/>fluido,<emph.end type="italics"/> ridusse a tre le ragioni di quei difetti: pri&shy;<lb/>mieramente, perch&egrave; l'ipotesi che le particelle minime componenti il liquido <lb/>sian perfettamente sferiche &egrave; affatto arbitraria: in secondo luogo, perch&egrave; la <lb/>proposizione del Guglielmini &egrave; troppo limitata, supponendovisi i centri di <lb/>gravit&agrave; delle sfere disposti in un piano orizontale, e finalmente perch&egrave; la <lb/>dimostrazione di lui non vale se non nel caso che la NY, secondo la quale <lb/>&egrave; diretta la forza della pressione, faccia con la verticale un angolo di 45 gradi. </s></p><p type="main">

<s>Il D'Alembert giudicava cos&igrave; severamente, quando l'uso oramai intro&shy;<lb/>dotto del calcolo infinitesimale agevolava il modo di risolvere cos&igrave; fatti pro&shy;<lb/>blemi, col ridurre il liquido a particelle infinitesime, delle quali perci&ograve; non <lb/>&egrave; propria nessuna figura, o determinata posizione di parte. </s>

<s>I vantaggi di que&shy;<lb/>sto calcolo erano stati saggiati gi&agrave; da chi aveva imparato a far uso degli <lb/>indivisibili, come dal Castelli, per esempio, che considerava le correnti per <lb/>gli alvei e dentro i tubi esser divise in tante minime sezioni, e dall'Aggiunti <lb/>e dal Cornelio, che riguardavano la massa fluida come composta di tanti <lb/>infiniti filetti, de'quali si comparavano insieme i momenti, con la regola dei <lb/>gravi ora cadenti nel perpendicolo, ora lungo piani variamente inclinati. </s>

<s>Ma <lb/>chi dette esplicazione e ordine a questo primo pensiero fu il Viviani, la di&shy;<lb/>mostrazion meccanica dell'uguaglianza delle pressioni, e d'altre idrostatiche <lb/>conseguenze, data dal quale, se va per vie pi&ugrave; oblique di quelle del D'Alem&shy;<lb/>bert e del Bernoulli, non &egrave; perci&ograve; da dire n&egrave; men ferma, n&egrave; meno esatta. </s>

<s><lb/>Il Guglielmini perci&ograve; era stato, in queste matematiche applicazioni, prece&shy;<lb/>duto dal Viviani, ci&ograve; che fu scritto dal quale, non saputo fin qui, &egrave; tempo <lb/>finalmente di dare alla luce. </s></p><p type="main">

<s>S'intitola quella scrittura <emph type="italics"/>De radiis fluidis,<emph.end type="italics"/> per i quali che cosa debba <lb/>intendersi precisamente definisce in principio l'Autore, dopo le prenozioni di <lb/>Statica, alle quali s'informa, e dalle quali si svolge tutto intero il trattato. </s>

<s><lb/>Si vedr&agrave; questo resultar di XXV proposizioni, le quali, essendosi trovate di&shy;<lb/>sperse per il volume manoscritto, si sono da noi ordinate, e ridotte a po&shy;<lb/>tersi leggere dalle postille, e dalle confusissime cassature, ci&ograve; che s'&egrave; creduto <lb/>sufficiente alla loro pi&ugrave; chiara intelligenza, senza bisogno d'altro commento. </s>

<s><lb/>I lettori troveranno forse le dimostrazioni prolisse, e giudicheranno che la <lb/>sostanza poteva raccogliersi in assai meno parole. </s>

<s>Ma se penseranno a quei <lb/>tempi, ne'quali l'Idrostatica aveva bisogno, specialmente fra noi, di una ri&shy;<lb/>forma cos&igrave; radicale, da apparire quasi una Scienza nuova; vedranno quanto <lb/>saviamente il Viviani si consigliasse di condiscendere alle minuziose facilit&agrave; <lb/>di un libro elementare. </s></p><pb xlink:href="020/01/3286.jpg" pagenum="247"/><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>DE RADIIS FLUIDIS<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>PRAENOTIONES<emph.end type="center"/></s></p><p type="main">

<s>Acturi itaque de humidorum gravitatibus, atque momentis, aliqua nobis <lb/>praemittenda necessario sunt de momentis gravium in genere. </s>

<s>Ex demonstra&shy;<lb/>tis autem a'Galileo, eiusque doctrinae promotore Torricellio, in libris <emph type="italics"/>De motu <lb/>gravium naturaliter descendentium,<emph.end type="italics"/> habemus: </s></p><p type="main">

<s>I. </s>

<s>Quod si in planis inaequaliter inclinatis, eamdem tamen elevatio&shy;<lb/>nem habentibus, duo gravia constituantur, quae inter se eamdem homologe <lb/>rationem habeant quam habent longitudines planorum; gravia aequale mo&shy;<lb/>mentum habebunt. </s></p><p type="main">

<s>II. </s>

<s>Quod momenta gravium aequalium, super planis inaequaliter in&shy;<lb/>clinatis, eamdem tamen elevationem habentibus, sunt in reciproca ratione <lb/>cum longitudinibus planorum. </s></p><p type="main">

<s>III. </s>

<s>Quod momentum totale gravis, ad momentum quod habet in plano <lb/>inclinato, est ut longitudo ipsius plani inclinati ad perpendiculum. </s></p><p type="main">

<s>IV. </s>

<s>Quod momenta gravium aequalium, super planis inaequaliter in&shy;<lb/>clinatis, sunt in homologa ratione cum perpendiculis partium aequalium. </s></p><p type="main">

<s><emph type="center"/>DEFINITIONES<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Radium<emph.end type="italics"/> seu lineam physicam dicemus uniformem cuiuscumque datae <lb/>molis tractum, seu longitudinem, nulla fere, quatenus imaginari nobis licet, <lb/>crassitudine praeditam. </s></p><p type="main">

<s><emph type="italics"/>Punctum<emph.end type="italics"/> vero <emph type="italics"/>physicum<emph.end type="italics"/> dicemus radii dicti principium sive extremum, <lb/>particulam scilicet nulla fere, quatenus nobis imaginari licet, aut crassitu&shy;<lb/>dine aut longitudine praeditam. </s></p><p type="main">

<s><emph type="italics"/>Radios similes<emph.end type="italics"/> dicimus eos, qui eadem uniformi crassitudine sunt praediti. </s></p><p type="main">

<s><emph type="center"/>POSTULATUM<emph.end type="center"/></s></p><p type="main">

<s>Radiorum similium moles sunt invicem ut eorum inter se longitudines </s></p><p type="main">

<s>PROPOSITIO I. &mdash; <emph type="italics"/>Radii fluidi similes, ac specie aeque graves, ab eadem <lb/>horizontali ad eamdem aliam inferiorem, secundum perpendicularem li&shy;<lb/>neam protensi, et secundum easdem gravitantes; momentum habent ae&shy;<lb/>quale.<emph.end type="italics"/></s></p><pb xlink:href="020/01/3287.jpg" pagenum="248"/><p type="main">

<s>Sit ABC (fig. </s>

<s>129) superficies horizontalis superior, DEF inferior, BE <lb/>et CF radii similes, ac specie aeque graves, ab ABC ad EDF, secundum per&shy;<lb/><figure id="id.020.01.3287.1.jpg" xlink:href="020/01/3287/1.jpg"/></s></p><p type="caption">

<s>Figura 129.<lb/>pendiculares lineas BE, et CF protensi, et secundum <lb/>easdem gravitantes: dico eorum momenta aequalia <lb/>esse. </s>

<s>Nam, ob concentritatem orizontalium ABC, DEF, <lb/>aequ&agrave;les ostendent inter se perpendiculares longitu&shy;<lb/>dines interceptae BE et CF. </s>

<s>Ut autem longitudines <lb/>invicem radiorum BE et CF, ita et totalia eorumdem <lb/>momenta. </s>

<s>Momenta autem radiorum BE et CF, secundum lineas BE, CF, <lb/>totalia sunt, cum eaee ponantur perpendiculares; erunt ergo ut longitudines, <lb/>adeoque aequalia. </s></p><p type="main">

<s>PROPOSITIO II. &mdash; <emph type="italics"/>Radii fluidi, ab una horizontali ad aliam inferio&shy;<lb/>rem, secundum quamcumque lineam inclinatam, recta protensi, et secun&shy;<lb/>dum eamdem gravitantes; momentum aequale est momento radii perpen&shy;<lb/>dicularis inter easdem horizontales perpendiculariter gravitantis.<emph.end type="italics"/></s></p><p type="main">

<s>Sit HG (fig. </s>

<s>130) radius fluidus, secundum li&shy;<lb/><figure id="id.020.01.3287.2.jpg" xlink:href="020/01/3287/2.jpg"/></s></p><p type="caption">

<s>Figura 130.<lb/>neam utcumque inclinatam GH, ab horizontali su&shy;<lb/>periori ABC ad inferiorem DEF recta pertingens, et <lb/>secundum eamdem gravitans. </s>

<s>BE vero radius fluidus <lb/>similis, ac specie aeque gravis, perpendiculariter ab <lb/>eadem ABC ad eamdem DEF pertingens, ac perpen&shy;<lb/>diculariter gravitans: dico momentum radii HG momento radii BE aequale esse. </s></p><p type="main">

<s>Sit enim radii inclinati HG perpendiculum HI. </s>

<s>Erit igitur momentum <lb/>actuale radii HG, secundum lineam HG gravitantis, ad momentum totale <lb/>eiusdem, ut longitudo perpendicularis HI, idest BE, ad longitudinem lineae <lb/>inclinatae HG. </s>

<s>Ut autem longitudo BE, ad longitudinem HG, ita etiam est <lb/>momentum totale radii BE, idest momentum actuale ipsius secundum per&shy;<lb/>pendicularem BE, ad momentum totale radii HG. </s>

<s>Momentum igitur radii BE <lb/>secundum BE, ad momentum radii HG secundum HG, eamdem proportio&shy;<lb/>nem habent ad momentum totale radii HG, eam videlicet quam longitudo <lb/>BE ad longitudinem HG. </s>

<s>Erunt igitur inter se necessario aequalia, quod etc. </s></p><p type="main">

<s><emph type="italics"/>Corollarium.<emph.end type="italics"/> &mdash; Hinc radiorum omnium similium, ac specie aeque gra&shy;<lb/>vium, ab eadem horizontali ad eamdem aliam inferiorem, secundum lineas <lb/>utcumque inclinatas, recta pertingentium, et secundum easdem gravitantium; <lb/>momenta erunt invicem aequalia. </s>

<s>Ostenditur enim singula eidem tertio ae&shy;<lb/>qualia: momento scilicet radii similis, ac specie aeque gravis, ab eadem <lb/>horizontali ad eamdem perpendicularem protensi, ac perpendiculariter gra&shy;<lb/>vitantis, ut patet ex praecedenti. <lb/><figure id="id.020.01.3287.3.jpg" xlink:href="020/01/3287/3.jpg"/></s></p><p type="caption">

<s>Figura 131.</s></p><p type="main">

<s>PROPOSITO III. &mdash; <emph type="italics"/>Sit OL<emph.end type="italics"/> (fig. </s>

<s>131) <emph type="italics"/>radius flui&shy;<lb/>dus, ab horizontali ABC ad inferiorem DEF, se&shy;<lb/>cundum lineam utcumque tortuosam OMNL per&shy;<lb/>tingens, et secundum eamdem gravitans, BE vero <lb/>radius similis ac specie aeque gravis, ab eadem <lb/>ABC, ad eamdem DEF perpendiculariter proten-<emph.end type="italics"/><pb xlink:href="020/01/3288.jpg" pagenum="249"/><emph type="italics"/>sus: dico momentum radii OL, secundum lineam OMNL, aequale esse <lb/>momento radii BE, secundum perpendicularem BE.<emph.end type="italics"/></s></p><p type="main">

<s>Cum enim radii OL partes in directum, ob tortuositatem, non sint, erit <lb/>ab extremo O aliqua eius portio, quae primum cum alia sibi continuo suc&shy;<lb/>cedenti in directum non est posita. </s>

<s>Sit huiusmodi portio OM. </s>

<s>Quidquid igi&shy;<lb/>tur interiacet extremis OM tortuositate utique caret. </s>

<s>Per extremum itaque <lb/>ipsius M intelligatur transire horizontalis MS, quae concentrica cum sit ABC, <lb/>et punctum ipsius M cadat infra AB, tota necessario infra ABC cadet, se&shy;<lb/>cabitque necessario radium BE, puta in S. </s>

<s>Erit igitur momentum portionis <lb/>OM aequale momento portionis BS. </s>

<s>Rursus ab extremo M erit alia portio <lb/>subsequens, puta MN, quae primum similiter cum reliqua sibi continuo suc&shy;<lb/>cedenti in directum non est posita. </s>

<s>Si igitur extremum N infra horizontalem <lb/>MS cadit, transiens horizontaliter per N, secabit rursus BE, puta in Q, erit&shy;<lb/>que similiter momentum portionis MN aequale momento portionis <expan abbr="Sq.">Sque</expan> Ea&shy;<lb/>demque ratione reliqua, puta ultima radii OL portio, continuo succedens NL, <lb/>cum reliqua et ultima radii BE, continuo succedens, aequale momentum habe&shy;<lb/>bit, ut ostendi potest, Adeoque totius radii OL momentum totius radii BE <lb/>momento aequale esse manifestum erit. </s></p><p type="main">

<s>Si vero portionis subsequentis MN extremum N supra horizontalem MS <lb/>cadat, ut in 132 schemate ostenditur, transiens scilicet per N horizontalis <lb/><figure id="id.020.01.3288.1.jpg" xlink:href="020/01/3288/1.jpg"/></s></p><p type="caption">

<s>Figura 132.<lb/>PNQ, secabit OM, puta in P, et BE, puta in <expan abbr="q.">que</expan> <lb/>Momentum autem radii OMN, ad N, aequale est mo&shy;<lb/>mento portionis OP, supra horizontalem PNQ extan&shy;<lb/>tis, adeoque momento portionis BQ, iisdem horizon&shy;<lb/>talibus ABC et PNQ interceptae. </s>

<s>Eademque ratione <lb/>erit momentum reliquae et ultimae portionis continuo <lb/>subsequentis NL aequale momento reliquae, et ul&shy;<lb/>timae continuo subsequentis QE. </s>

<s>Unde totius simul radii OL momentum <lb/>momento totius radii BE aequale erit. </s></p><p type="main">

<s>Si denique eiusdem portionis subsequentis MN extremum N in ipsa <lb/><figure id="id.020.01.3288.2.jpg" xlink:href="020/01/3288/2.jpg"/></s></p><p type="caption">

<s>Figura 133.<lb/>horizontali MS reperiatur, ut in 133 schemate, erit <lb/>momentum OMN, ad N, aequale momento BS, et <lb/>momentum reliquae atque ultimae NL momento re&shy;<lb/>liquae et ultimae SE. </s>

<s>Unde momentum totius OL <lb/>momento totius BE semper aequale ostendetur. </s></p><p type="main">

<s>PROPOSITIO IV. &mdash; <emph type="italics"/>Si super punctis eiusdem <lb/>sphaericae superficiei, Orbi concentricae, intelligan&shy;<lb/>tur gravitare duo radii similes, ac specie aeque graves, qui ad idem <lb/><figure id="id.020.01.3288.3.jpg" xlink:href="020/01/3288/3.jpg"/></s></p><p type="caption">

<s>Figura 134.<lb/>punctum alterius superficiei superioris sphae&shy;<lb/>ricae pariter atque Orbi concentricae oblique <lb/>utcumque sint erecti; erunt momenta ipsorum <lb/>necessario aequalia.<emph.end type="italics"/></s></p><p type="main">

<s>Super punctis B, H (fig. </s>

<s>134) superficiei <lb/>ABHC, cuius centrum idem est ac centrum Or-<pb xlink:href="020/01/3289.jpg" pagenum="250"/>bis, intelligantur gravitare duo radii similes, ac specie aeque graves EH, <lb/>et EB, qui ad idem punctum E alterius sphaericae superficiei superioris DEG, <lb/>cuius idem est centrum, oblique utcumque sint erecti; dico radiorum EH et <lb/>EB momenta fore necessario inter se aequalia. </s></p><p type="main">

<s>Ducto enim, per pucta B et H, plano horizontali BH, intelligatur radio <lb/>EB subiectum planum immediate adiacens EB, radio vero EH planum im&shy;<lb/>mediate adiacens EH. </s>

<s>Erunt utique plana EH et EB super eodem horizon&shy;<lb/>tali plano BH inaequaliter inclinata, eamdem tamen supra ipsum perpendi&shy;<lb/>cularem elevationem habentia, eruntque longitudines planorum dictorum aee&shy;<lb/>dem ac longitudines radiorum sibi immediate adiacentium. </s>

<s>Ut autem radiorum <lb/>EH et EB longitudines inter se, ita, ob suppositam similitudinem, sunt <lb/>ipsorum inter se magnitudines seu moles. </s>

<s>Ut autem moles inter se, ita, ob <lb/>eamdem suppositam in specie gravitatem, sunt necessario inter se eorumdem <lb/>pondera. </s>

<s>Erunt igitur radiorum EH et EB inter se pondera ut eorumdem <lb/>inter se longitudines, scilicet pondus radii EH, ad pondus radii EB, ut lon&shy;<lb/>gitudo radii EH ad longitudinem radii EB, adeoque ut longitudo plani EH, <lb/>ad longitudinem plani EB. </s>

<s>Igitur erunt graviorum datorum EH et EB pon&shy;<lb/>dera in homologa ratione cum longitudinibus planorum, super quibus consti&shy;<lb/>tuta intelliguntur. </s>

<s>Igitur aequalia necessario erunt ipsorum momenta. </s></p><p type="main">

<s>Si autem, demptis planis adiacentibus in eadem constructione erecti, <lb/>maneant iidem radii EH et EB, manifestum est quod eadem manebit ratio <lb/>momenti. </s>

<s>Unde universaliter huiusmodi radii sic dispositi aequalia erunt ne&shy;<lb/>cessario momenta, quod erat propositum. </s></p><p type="main">

<s>PROPOSITIO V. &mdash; <emph type="italics"/>Si vero radiorum dictorum alter quidem oblique, <lb/>alter vero ad perpendiculum erectum ponatur, erunt ipsorum momenta <lb/>etiam aequalia.<emph.end type="italics"/></s></p><p type="main">

<s>Sit radiorum EH et EB, in secunda constructione eiusdem schematis, <lb/>alter quidem nempe EH ad perpendiculum, alter vero, nempe EB, oblique <lb/>erectus: dico ipsorum momenta esse necessario inter se aequalia. </s>

<s>Erit enim <lb/>momentum totale radii EB, ad momentum quod modo habet super plano <lb/>inclinato EB, ut longitudo EB ad ipsius perpendiculum, nempe ad EH. </s>

<s>Et <lb/>convertendo erit momentum, quod modo habet EB radius super plano in&shy;<lb/>clinato EB, ad momentum totale ipsius, ut longitudo perpendiculi EH, nempe <lb/>radii EH, ad longitudinem plani inclinati EB. </s>

<s>Ut autem longitudo radii EH, <lb/>ad longitudinem radii EB, ita etiam est, ob similitudinem, moles ad molem, <lb/>et, ob eamdem gravitatis speciem, pondus ad pondus. </s>

<s>Adeoque ut longitudo <lb/>ad longitudinem, ita momentum totale radii EH, ad momentum totale radii <lb/>EB. </s>

<s>Momentum autem, quod actu habet radius EH, totale est, cum ponatur <lb/>ad perpendiculum erectum; unde momentum, quod actu habet radius per&shy;<lb/>pendicularis EH, ad momentum totale radii oblique erecti EB, est ut longi&shy;<lb/>tudo ipsius radii perpendicularis EH, ad longitudinem radii oblique erecti <lb/>EB. </s>

<s>Dictum est autem quod momentum, quod actu habet EB, ad momen&shy;<lb/>tum totale ipsius EB, est etiam ut longitudo perpendicularis EH, ad longi&shy;<lb/>tudinem EB; momentum igitur actuale radii EB, et momentum actuale radii <pb xlink:href="020/01/3290.jpg" pagenum="251"/>EH, eamdem rationem habent ad idem tertium, nempe ad momentum to&shy;<lb/>tale radii EB. </s>

<s>Erunt igitur momenta actualia radiorum EH et EB necessario <lb/>aequalia, quod erat propositum. </s></p><p type="main">

<s>PROPOSITIO VI. &mdash; <emph type="italics"/>Si super punctis eiusdem sphaericae superficiei, <lb/>Orbi concentricae, intelligantur gravitare duo radii similes, ac specie aeque <lb/>graves, qui extra superficiem cadentes alterius superficiei superioris, Orbi <lb/>pariter concentricae, oblique utcumque sint erecti; erunt ipsorum momenta <lb/>necessario aequalia.<emph.end type="italics"/></s></p><p type="main">

<s>Super punctis B et C (fig. </s>

<s>135) sphaericae superficiei HBC, cuius cen&shy;<lb/>trum sit centrum Orbis, intelligantur gravitare duo radii similes, ac specie <lb/><figure id="id.020.01.3290.1.jpg" xlink:href="020/01/3290/1.jpg"/></s></p><p type="caption">

<s>Figura 135.<lb/>aeque graves AB et FC, qui extra superficiem HBC <lb/>cadentes ad puncta A et F alterius sphaericae superfi&shy;<lb/>ciei superiori, atque Orbi pariter concentricae, oblique <lb/>utcumque sint erecti: dico radiorum AB et FC mo&shy;<lb/>menta fore invicem necessario aequalia. </s>

<s>Intelligantur <lb/>enim ad eadem puncta A et F erecti, super eadem subiecta superficie HBC, <lb/>perpendiculares radii AH et FG, similes ac specie aeque graves cum radiis <lb/>AB et FC, eritque longitudo radii AH aequalis longitudini radii FG. </s>

<s>Igitur <lb/>moles moli, ob similitudinem, et pondus ponderi, ob eamdem gravitatis spe&shy;<lb/>ciem, erit aequale. </s>

<s>Unde momentum totale unius momento totali alterius <lb/>erit aequale. </s>

<s>Momentum autem actuale radii AH, cum ponatur ad perpen&shy;<lb/>diculum erectus, idem est ac momentum ipsius totale, eademque ratione <lb/>idem erit momentum actuale radii FG, ac momentum totale eiusdem. </s>

<s>Mo&shy;<lb/>mentum igitur actuale radii AH aequale est momento actuale radii FG. </s>

<s><lb/>Atqui ex praecedenti momentum radii AH aequale est momento radii AB, <lb/>momentum vero radii FG aequale momento radii FC; momentum igitur <lb/>radii AB momento radii FC aequale erit, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><p type="main">

<s>PROPOSITIO VII. &mdash; <emph type="italics"/>Si super eodem puncto sphaericae superficiei, Orbi <lb/>concentricae, intelligantur gravitare duo radii similes, ac specie aeque gra&shy;<lb/>ves. </s>

<s>qui extra superficiem datam cadentes ad puncta alterius superficiei su&shy;<lb/>perioris, atque Orbi pariter concentricae, utcumque sint erecti; momenta ip&shy;<lb/>sorum super dato puncto necessario erunt aequalia.<emph.end type="italics"/></s></p><p type="main">

<s>Super eodem puncto B (fig. </s>

<s>136) sphaericae super&shy;<lb/><figure id="id.020.01.3290.2.jpg" xlink:href="020/01/3290/2.jpg"/></s></p><p type="caption">

<s>Figura 136.<lb/>ficiei HBF, cuius centrum idem est ac centrum Orbis, <lb/>intelligantur gravitare duo radii similes, ac specie aeque <lb/>graves BD, BE, qui extra superficiem dictam HBF <lb/>cadentes ad puncta D et E alterius sphaericae super&shy;<lb/>ficiei superioris GDE, cuius pariter est centrum Orbis, utcumque sint erecti; <lb/>dico radiorum DB, EB momenta fore necessario inter se aequalia. </s>

<s>Erectis <lb/>enim super eadem superficie HBF, ad puncta D et E, perpendicularibus radiis <lb/>similibus, ac specie aeque gravibus DH, EF, erit ex demonstratis momentum <lb/>radii DH aequale momento radii DB, et momentum radii EF aequale momento <lb/>radii EB. Unde, cum momenta DH et EF ostensa sint in praecedentibus invicem <lb/>aequalia, erunt etiam momenta radiorum DB et EB invicem aequalia, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><pb xlink:href="020/01/3291.jpg" pagenum="252"/><p type="main">

<s>PROPOSITIO VIII. &mdash; <emph type="italics"/>Si radii similes, ac specie aeque graves, super <lb/>eadem sphaerica superficie Orbi concentrica erecti, aequale momentum <lb/>habuerint; eorum altitudinum termini in eadem sphaerica superficie, Orbi <lb/>pariter concentrica, necessario erunt.<emph.end type="italics"/></s></p><p type="main">

<s>Sint super eadem sphaerica superficie ABC (fig. </s>

<s>137), cuius centrum est <lb/>centrum Orbis, erecti radii similes ac specie aeque graves EB, DB, quorum <lb/><figure id="id.020.01.3291.1.jpg" xlink:href="020/01/3291/1.jpg"/></s></p><p type="caption">

<s>Figura 137.<lb/>momenta sint aequalia: dico eorum altitudinum ter&shy;<lb/>minos E et D in eadem sphaerica superficie, Orbi pa&shy;<lb/>riter concentrica, reperiri. </s></p><p type="main">

<s>Non sint, si possibile est, termini E, D in eadem <lb/>superficie sphaerica Orbi concentrica. </s>

<s>Igitur non aequi&shy;<lb/>distabunt a centro, sed alter eorum, ex gr. </s>

<s>E, erit centro <lb/>proprinquior quam D. </s>

<s>Itaque sphaerica ducatur superficie <lb/>EGH: cadet igitur terminus D extra superficiem dictam, cum sit a centro <lb/>remotior, et radius BD secabitur a superficie EGH in H. </s>

<s>Sunt igitur duo <lb/>radii similes, ac specie aeque graves, EB et BH, qui, super eadem sphae&shy;<lb/>rica superficie Orbi concentrica ABC, erecti, ad eamdem superficiem sphae&shy;<lb/>ricam superiorem, Orbi pariter concentricam, EGH pertingunt. </s>

<s>Igitur erunt <lb/>eorum momenta aequalia. </s>

<s>Maius autem est momentum radii DB, quam radii <lb/>BH, cum DB addat super BH momentum portionis HD; igitur maius erit <lb/>momentum radii BD, quam radii EB, quod est contra suppositionem. </s>

<s>Non <lb/>igitur cadit terminus D extra superficiem FGH, sed in eadem est necessario <lb/>cum termino E, quod erat propositum. </s></p><p type="main">

<s>PROPOSITIO IX. &mdash; <emph type="italics"/>Si cuiusvis molis gravis radius, a dato termino <lb/>sphaericae superficiei Orbi concentricae productus, non transiens per cen&shy;<lb/>trum, superficiem dictam secet; tantum erit versus datum terminum dati <lb/>radii momentum gravitatis, quantum solius portionis ultra intersectionis <lb/>terminum utcumque productae.<emph.end type="italics"/></s></p><p type="main">

<s>A dato termino B superficiei sphaericae, atque Orbi concentricae BAC <lb/>(fig. </s>

<s>138), intelligatur productus radius cuiuscumque molis gravis BCF, qui, <lb/><figure id="id.020.01.3291.2.jpg" xlink:href="020/01/3291/2.jpg"/></s></p><p type="caption">

<s>Figura 138.<lb/>per centrum Orbis K non transiens, superficiem di&shy;<lb/>ctam secet ut in C: dico radii BCF momentum versus <lb/>terminum B tantum esse, quantum solius portionis <lb/>CF ultra terminum intersectionis C utcumque pro&shy;<lb/>ductae. </s></p><p type="main">

<s>Ducatur a centro K recta KE secans BC bifa&shy;<lb/>riam, puta in E, secabitque eam ad angulos rectos. </s>

<s><lb/>Si igitur semidiametro KE intelligatur ducta per <lb/>punctum E sphaerica superficies DEG, erit BC tangens DEG in E. </s>

<s>Sunt ita&shy;<lb/>que super eodem termino E, superficiei Orbi concentricae DEG, erecti duo <lb/>radii similes, ac specie aeque graves BE et FE, unus a termino elevationis F <lb/>versus lineam FE, alter vero, scilicet BE, a termino elevationis B versus li&shy;<lb/>neam BE, et proinde erit momentum radii BE momento radii FE directe <lb/>oppositum. </s>

<s>Momentum autem radii BE aequale est momento portionis oppo-<pb xlink:href="020/01/3292.jpg" pagenum="253"/>sitae CE, cum sint radii similes, specie aeque graves, et ab eodem termino <lb/>superficiei Orbi concentricae DEG, ad superficiem aliam Orbi pariter con&shy;<lb/>centricam BAC exporrecti. </s>

<s>Non gravitat igitur radius FE versus terminum B, <lb/>nempe contra momentum oppositum radii BE, nisi secundum momentorum <lb/>excessus CF. </s>

<s>Tantum igitur est momentum totale radii BF versus termi&shy;<lb/>num B, quantum solius portionis CF, <expan abbr="q.">que</expan> e. </s>

<s>propositum. </s></p><p type="main">

<s>PROPOSITIO X. &mdash; <emph type="italics"/>Si ab eodem termino sphaericae superficiei Orbi <lb/>concentricae duo radii similes, ac specie aeque graves protensi intelligan&shy;<lb/>tur, quorum alter superficiem datam, sed non per centrum secet, alter vero <lb/>extra eamdem cadat, ambo tamen ad eamdem sphaericam superficiem <lb/>superiorem Orbi pariter concentricam pertingant; erunt momenta ipso&shy;<lb/>rum versus communem terminum dictum necessario aequalia.<emph.end type="italics"/></s></p><p type="main">

<s>Ab eodem termino B (fig. </s>

<s>139), sphaericae superficiei Orbi concentri&shy;<lb/>cae ABC, intelligantur porrecti duo radii similes, ac specie aeque graves BF <lb/><figure id="id.020.01.3292.1.jpg" xlink:href="020/01/3292/1.jpg"/></s></p><p type="caption">

<s>Figura 139.<lb/>et BH, quorum alter, nempe BF, superficiem <lb/>ABC, sed non per centrum secet, puta in C, <lb/>alter vero, scilicet BH, extra eamdem cadat, <lb/>ita tamen ut ambo ad eamdem sphaericam <lb/>superficiem superiorem, Orbi pariter concen&shy;<lb/>tricam, DHF pertingant: dico radiorum HB, et FB momenta, versus eum&shy;<lb/>dem communem terminum B, esse necessario inter se aequalia. </s>

<s>Momentum <lb/>enim radii FB versus terminum B, ex antecedenti, tantum est, quantum to&shy;<lb/>tius portionis CE. </s>

<s>Momentum autem radii CF aequale est momento radii sibi <lb/>similis, ac specie aeque gravis BH, super eadem superficie sphaerica Orbi <lb/>concentrica ABC, ad eamdem sphaericam superficiem, Orbi pariter concen&shy;<lb/>tricam DHF, utcumque porrecti. </s>

<s>Radiorum igitur FB et HB, versus eumdem <lb/>terminum B, aequalia sunt momenta, quod erat propositum. </s></p><p type="main">

<s><emph type="italics"/>Corollarium.<emph.end type="italics"/> &mdash; Unde universaliter si, ab eodem quolibet puncto com&shy;<lb/>muni, duo radii similes ac specie aeque graves ad eamdem sphaericam su&shy;<lb/>perficiem Orbi concentricam, utcumque erecti, pertingant; erunt ipsorum <lb/>momenta super communi puncto necessario aequalia. </s>

<s>Quodvis enim punctum <lb/>est in aliqua superficie sphaerica Orbi concentrica. </s>

<s>Ostensum est autem quod <lb/>radii similes ac specie aeque graves, sive extra ipsam cadant, sive ipsam <lb/>secent, dummodo ad eamdem aliam Orbi concentricam pertingant, aequalia <lb/>habebunt momenta. </s>

<s>Unde etc. </s></p><p type="main">

<s>PROPOSITIO XI. &mdash; <emph type="italics"/>Si dati cuiuscumque radii extremum versus quem&shy;<lb/><figure id="id.020.01.3292.2.jpg" xlink:href="020/01/3292/2.jpg"/></s></p><p type="caption">

<s>Figura 140.<lb/>cumque terminum infra humidum stagnans moveri in&shy;<lb/>telligatur, necesse est radium similem ei, cuius est extre&shy;<lb/>mum, versus eam partem sibi directe oppositam im&shy;<lb/>pellat.<emph.end type="italics"/></s></p><p type="main">

<s>Intelligatur radii cuiuscumque AB (fig. </s>

<s>140) extremum <lb/>punctum B, intra humidum KL existens, versus quemcum&shy;<lb/>que terminum D moveri: dico quod a puncto B impelletur <lb/>necessario radius BD, similis radio AB. </s>

<s>Moveatur enim <pb xlink:href="020/01/3293.jpg" pagenum="254"/>punctum B versus D: impellet igitur versus D punctum sibi aequale, ac simile <lb/>sibi immediate succedens, cum in ipsius locum necesse est ipsum transire. </s>

<s><lb/>Eademque ratione, simul ac punctum primum versus D impellitur, necesse est <lb/>ut punctum secundum, aequale ac simile primo sibi immediate succedens, ver&shy;<lb/>sus D impellat. </s>

<s>Eademque ratione quotquot fuerint inter B et D puncta aequa&shy;<lb/>lia, ac similia, sibi immediate succedentia, ostendentur omnia ac singula <lb/>simul versus eamdem partem mota. </s>

<s>Series autem punctorum aequalium in&shy;<lb/>vicem ac similium, inter extrema B et D immediate sibi succedentia, lineam <lb/>physicam uniformis subtilitatis, quem radium dicimus, constituit. </s>

<s>Qui, cum <lb/>singula eius puncta aequalia ac similia sint eidem puncto B radii AB, erit <lb/>eiusdem necessario subtilitatis ac radium AB. </s>

<s>Impellet igitur punctum B <lb/>radium BD similem radio AB, cuius est extremum, quod erat propositum. </s></p><p type="main">

<s>PROPOSITIO XII. &mdash; <emph type="italics"/>Si quaelibet humidae molis, sive perpendiculariter <lb/>sive oblique, super subiecto termino incumbentis, altitudo a directo de&shy;<lb/>scensu, quacumque de causa, arceatur; ex ea parte, qua sufficiens non <lb/>invenerit resistentiae momentum, sursum transversimve reflectetur. </s>

<s>Et <lb/>quidquid in cedenti spatio alterius cuiuscumque molis praestiterit, versus <lb/>eamdem partem expellet.<emph.end type="italics"/></s></p><p type="main">

<s>Manifestum est hoc experientia siphonis ABC (fig. </s>

<s>141). <lb/><figure id="id.020.01.3293.1.jpg" xlink:href="020/01/3293/1.jpg"/></s></p><p type="caption">

<s>Figura 141.</s></p><p type="main">

<s>PROPOSITIO XIII. &mdash; <emph type="italics"/>Radius quilibet in humido, <lb/>super subiecta superficie stagnante, assignatus, nisi <lb/>sufficiens habuerit resistentiae momentum ab uno et <lb/>solo adiacientium radiorum sibi simili, et a communi <lb/>termino ad supremam humidi superficiem utcumque <lb/>porrecto; sursum impelletur.<emph.end type="italics"/></s></p><p type="main">

<s>Sit in humido stagnante KL (fig. </s>

<s>142), cuius subiecta superficies sit OL, <lb/><figure id="id.020.01.3293.2.jpg" xlink:href="020/01/3293/2.jpg"/></s></p><p type="caption">

<s>Figura 142.<lb/>assignatus radius quilibet BC, et a puncto quolibet A su&shy;<lb/>premae superficiei KAC intelligatur, ad communem ter&shy;<lb/>minum B, porrectus radius AB: dico quod, nisi radius <lb/>BC sufficienter valebit resistere, a momento radii AB sur&shy;<lb/>sum necessario impelletur. </s></p><p type="main">

<s>Non habeat itaque CB sufficiens resistentie momentum. </s>

<s>Data igitur est <lb/>altitudo quaedam humidae molis AB, quae recta deorsum versus B, ex sup&shy;<lb/>positione, procedere non potest. </s>

<s>Ponitur autem radius BC sufficiens resisten&shy;<lb/>tiae momentum non habere. </s>

<s>Igitur spatium BC sufficientis resistentiae mo&shy;<lb/>mento ponitur expers. </s>

<s>Flectetur igitur a termino B moles AB, et in spatium <lb/>cedens BC pro viribus necessario erumpet versus C: nempe sursum impelletur <lb/>versus C radium in dato spatio praeesistente BC, quod erat primo propositum. </s></p><p type="main">

<s>Dico rursus radium BC a momento alterius radii ex adiacentibus, quot&shy;<lb/>cumque tamdem illi sint, praeter AB impelli simul non posse. </s>

<s>In spatium <lb/>enim BC impossibile est flecti nisi unicum radium, similem radio BC, cuius <lb/>est adaequatum spatium. </s>

<s>Non expellet igitur radium BC a spatio BC, nisi <lb/>momentum unius dumtaxat radii sibi similis, quicumque tandem ille ex adia&shy;<lb/>centibus ponatur esse, quod erat secundo loco propositum. </s></p><pb xlink:href="020/01/3294.jpg" pagenum="255"/><p type="main">

<s><emph type="italics"/>Corollarium.<emph.end type="italics"/> &mdash; Ex quo patet radium quemlibet, in humido stagnante <lb/>assignatum, inter duo reperiri momenta opposita: alterum scilicet proprium <lb/>gravitatis quo deorsum premitur, alterum vero radii cuiusdam adiacentis si&shy;<lb/>milis, a communi termino ad superficiem supremam porrecti, quo sursum, nisi <lb/>par habeat momentum, necessario repelletur. </s></p><p type="main">

<s>PROPOSITIO XIV. &mdash; <emph type="italics"/>Motu omni extrinsecus ablato, necesse est in hu&shy;<lb/>mido stagnante radium quemlibet assignatum quiescere tandem ac librari.<emph.end type="italics"/></s></p><p type="main">

<s>In humido stagnante EM (fig. </s>

<s>143) sit radius quilibet assignatus AB. </s>

<s><lb/>Opponetur igitur eius descensui momentum solius radii ex adiacentibus si&shy;<lb/><figure id="id.020.01.3294.1.jpg" xlink:href="020/01/3294/1.jpg"/></s></p><p type="caption">

<s>Figura 143.<lb/>milis, puta BH, qui a communi termino B ad <lb/>supremam humidi superficiem EAH porrectus <lb/>existit. </s>

<s>Dico radium AB, motu omni extrinsecus <lb/>ablato, quiescere tandem, et necessario libratum <lb/>manere cum radio BH. </s></p><p type="main">

<s>Cum enim ab eodem termino B erigantur <lb/>radii AB et BH, erunt utique super eadem <lb/>sphaerica superficie Orbi concentrica, quae in&shy;<lb/>telligitur transire per B. </s>

<s>Si igitur eorum ter&shy;<lb/>mini A et H in eadem fuerint sphaerica superficie Orbi concentrica, cum <lb/>similes positi sint ac specie aeque graves, manifestum est quod aequalia erunt <lb/>radiorum AB et BH super communi termino B momenta. </s>

<s>Premitur autem <lb/>deorsum radius AB momento ipsius AB, reprimitur vero sursum momento <lb/>radii adiacentis BH; aequalia igitur erunt contra radium AB sursum deor&shy;<lb/>sumque momenta. </s>

<s>Neutram igitur in partem movebitur, sed quiescet neces&shy;<lb/>sario ac libratus manebit. </s></p><p type="main">

<s>Si vero altitudinum termini A et C in eadem non fuerint sphaerica su&shy;<lb/>perficie Orbi concentrica, non aequidistabunt a centro Orbis, sed alter eo&shy;<lb/>rum, puta A, depressior erit, eidemque centro proprinquior quam C, sphae&shy;<lb/>rica itaque ducatur superficies EAH: cadet igitur extra eam terminus C, <lb/>secabitque superficies EAH radium BC puta in H. </s>

<s>Momentum igitur radii AB <lb/>aequale erit momento radii BH, unde minus erit momentum radii AB quam <lb/>radii BC. </s>

<s>Cum igitur radius AB non habeat par momentum resistentiae, <lb/>expelletur sursum a momento opposito radii CB, qui in spatium cedens BA <lb/>necessario flectetur a puncto B, et descendet ab altitudine C. </s>

<s>Dividatur ita&shy;<lb/>que excessus HC in partes HF, et FC, ita scilicet ut longitudo HF sit ad <lb/>longitudinem FC ut longitudo totius radii HB ad longitudinem totius radii BA. </s>

<s><lb/>Dico quod, si radio praeponderantis BC descenderit pars aequalis FC, aequale <lb/>fiet utriusque radii oppositi momentum super termino B. </s>

<s>Reflectetur itaque <lb/>CB in spatium cedens BA, et descendet infra terminum C pars ipsius aequa&shy;<lb/>lis CF. </s>

<s>Manifestum est etiam quod radii BA elevabitur sursum, supra ter&shy;<lb/>minum A, pars aequalis eidem CF, nempe NA. </s>

<s>Dempta igitur a radio BC <lb/>longitudine FC, remanet radio BH superaddita longitudo radii similis HF, <lb/>radio vero BA addita est longitudo radii similis NA. </s>

<s>Est autem longitudo <lb/>portionis additae NA, ad longitudinem portionis additae FH, ut longitudo <pb xlink:href="020/01/3295.jpg" pagenum="256"/>totius radii AB, ad longitudinem totius radii BH ex constructione; eamdem <lb/>itaque homologe rationem habebunt longitudines additae, ac ipsae radiorum, <lb/>quibus adduntur longitudines. </s>

<s>Unde, cum radiorum AB et BH momenta po&shy;<lb/>sita sint aequalia, erunt etiam radiorum BN et BF momenta necessario ae&shy;<lb/>qualia. </s>

<s>Librabitur itaque necessario radius BA, quod erat demonstrandum. </s></p><p type="main">

<s><emph type="italics"/>Corollarium I.<emph.end type="italics"/> &mdash; Unde patet radiorum BN et BF terminos N et F in <lb/>eadem esse superficie Orbi concentrica. </s></p><p type="main">

<s><emph type="italics"/>Corollarium II.<emph.end type="italics"/> &mdash; Cum igitur omnes et singuli radii cuiuscumque da&shy;<lb/>tae molis humidae, motu omni extrinsecus ablato, necessario tandem libren&shy;<lb/>tur, ac immoti quiescant; manifestum est quod universa ipsa moles cuius&shy;<lb/>cuiusque dati humidi stagnantis necessario tandem, motu omni extrinsecus <lb/>cessante, manebit, ac immota quiescet. </s></p><p type="main">

<s>PROPOSITIO XV. &mdash; <emph type="italics"/>Omnis humidi manentis superficies sphaerica ne&shy;<lb/>cessario est, atque Orbi concentrica.<emph.end type="italics"/></s></p><p type="main">

<s>Sit humidum quodlibet manens EM (fig. </s>

<s>144). Dico superficiem eius <lb/>supremam ED sphaericam necessario esse, cuius centrum idem est ac cen&shy;<lb/><figure id="id.020.01.3295.1.jpg" xlink:href="020/01/3295/1.jpg"/></s></p><p type="caption">

<s>Figura 144.<lb/>trum Orbis. </s>

<s>Si enim superficies ED sphaerica non sit, <lb/>atque Orbi concentrica, non aeque distabit quodlibet <lb/>ipsius punctum a centro Orbis, sed alterum altero re&shy;<lb/>motius necessario erit. </s>

<s>Sit igitur punctum C remotius <lb/>puncto A, et a puncto A assignetur radius quilibet AB, <lb/>et a communi deinde termino B assignetur radius si&shy;<lb/>milis, ad punctum C exporrectus. </s>

<s>Ducta igitur a puncto A sphaerica superficies <lb/>AGH, infra punctum C cadet, secabitque necessario radium BC, puta in H, <lb/>eritque momentum radii AB aequale momento radii BH. </s>

<s>Momentum igitur <lb/>radii BC maius erit momento radii BA, unde flectetur necessario a termino <lb/>B, et in spatium cedens BA expellet sursum radium BA. </s>

<s>Non manebit igitur <lb/>humidum FM, sed movebitur necessario, contra suppositionem. </s>

<s>Nullum igitur <lb/>superficiei ED manentis punctum remotius est altero a centro Orbis, sed <lb/>omnia et singula a centro dicto necessario aequidistant. </s>

<s>Adeoque in eadem <lb/>necessario sunt sphaerica superficie Orbi concentrica, quod erat propositum. </s></p><p type="main">

<s>PROPOSITIO XVI. &mdash; <emph type="italics"/>In humido manente quilibet ipsius radius inter <lb/>momenta opposita sursum deorsumque aequalia reperitur.<emph.end type="italics"/></s></p><p type="main">

<s>Sit supra datam superficiem subiectam, puta ipsius Terrae DEF (fig. </s>

<s>145), <lb/>humidum quodlibet manens, cuius superficies ABCH, et sit quilibet eius ra&shy;<lb/><figure id="id.020.01.3295.2.jpg" xlink:href="020/01/3295/2.jpg"/></s></p><p type="caption">

<s>Figura 145.<lb/>dius assignatus BE: dico radium BE inter momenta <lb/>opposita sursum deorsumque reperiri. </s>

<s>Cum enim hu&shy;<lb/>midum manens ponatur, erit eius superficies ABCH <lb/>sphaerica necessario, atque Orbi concentrica. </s>

<s>Unde <lb/>momentum uniuscumque radii similis, ac specie <lb/>aeque gravis, a communi termino E ad eamdem su&shy;<lb/>perficiem ABCH porrecti, aequale est momento radii <lb/>BE. </s>

<s>Radius autem BE non pellitur sursum, nisi momento solius radii similis <lb/>a communi termino E ad supremam superficiem ABH porrecti, puta EC. <pb xlink:href="020/01/3296.jpg" pagenum="257"/>Unde momentum EC, quo sursum pellitur BE, aequale necessario est mo&shy;<lb/>mento ipsius BE. </s>

<s>Inter aequalia igitur momenta sursum deorsum reperire <lb/>necesse est, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><p type="main">

<s>PROPOSITIO XVII. &mdash; <emph type="italics"/>In quolibet humidi quiescentis puncto concur&shy;<lb/>runt, secundum quamlibet lineam per ipsum ductam, duo momenta ae&shy;<lb/>qualia ad oppositos terminos ipsum iungentia.<emph.end type="italics"/></s></p><p type="main">

<s>Sit super qualibet continente superficie GBM (fig. </s>

<s>146) quiescens humi&shy;<lb/>dum GAM, cuius superficies FAD, centrum habens centrum Terrae, et sit <lb/><figure id="id.020.01.3296.1.jpg" xlink:href="020/01/3296/1.jpg"/></s></p><p type="caption">

<s>Figura 146.<lb/>punctum quodlibet humidi C. </s>

<s>Manifestum est cuius&shy;<lb/>libet lineae pereductae vel alterum extremum in&shy;<lb/>cidet in superficie FAD, alterum in superficiem con&shy;<lb/>tinentem GBM, vel utrumque incidet in superficiem <lb/>FAD, vel utrumque in superficiem continentem GBM. </s></p><p type="main">

<s>Transeat primo per punctum C quaelibet linea, <lb/>cuius utrumque extremum sit in superficie FAD, <lb/>puta ECH: dico quod in puncto C concurrunt <lb/>duo momenta aequalia, quorum unum ipsum impellit versus terminum E, <lb/>alterum vero versus terminum oppositum H. </s>

<s>Sit enim positus secundum li&shy;<lb/>neam ECH quilibet radius ECH. </s>

<s>Versus lineam igitur HC, idest HE, gravi&shy;<lb/>tat super C radius HC. </s>

<s>Versus lineam vero EC, idest EH, gravitat super C <lb/>radius similis EC. </s>

<s>Alter igitur versus terminum E, alter vero versus termi&shy;<lb/>num H oppositum impellit idem punctum C. </s>

<s>Momenta autem radiorum si&shy;<lb/>milium, ac specie aeque gravium EC et HC, super C aequalia sunt, cum sint <lb/>ab eodem puncto ad eamdem sphaericam superficiem Orbi concentricam por&shy;<lb/>recti; unde etc. </s></p><p type="main">

<s>Transeat, secundo, per C (fig. </s>

<s>147) quaelibet linea, cuius alterum extre&shy;<lb/>mum incidat in superficiem FAD, alterum vero in superficiem GBM, puta <lb/><figure id="id.020.01.3296.2.jpg" xlink:href="020/01/3296/2.jpg"/></s></p><p type="caption">

<s>Figura 147.<lb/>ACB. </s>

<s>Dico quod in puncto C concurrunt pariter <lb/>duo momenta aequalia, ad oppositos terminos A <lb/>et B, ipsum impellentia. </s>

<s>Sit enim secundum li&shy;<lb/>neam AB quilibet radius AB, a cuius termino B <lb/>ad superficiem FAD porrigatur utcumque radius <lb/>alius similis BD, et semidiametro KC sit sphae&shy;<lb/>rica superficies Orbi concentrica CL, secans BD <lb/>in L. </s>

<s>A radio igitur BD impelletur, nisi resisteret, versus linem C A, radium <lb/>ipsi conterminum BC, adeoque ipsum punctum C. </s>

<s>Momentum autem CB op&shy;<lb/>ponitur momento aequali BL. </s>

<s>Radius igitur BC, ipsumque proinde punctum <lb/><figure id="id.020.01.3296.3.jpg" xlink:href="020/01/3296/3.jpg"/></s></p><p type="caption">

<s>Figura 148.<lb/>C, impelletur versus A momento solius radii LD. </s>

<s><lb/>Idem autem punctum C impellitur versus lineam <lb/>CB, idest terminum oppositum B, momento radii <lb/>AC, momenta enim AC et BL aequalia sunt; <lb/>concurrunt igitur in C momenta aequalia versus <lb/>terminos oppositos A et B, ipsum impellentia, <expan abbr="q.">que</expan> e. </s>

<s>d. </s></p><p type="main">

<s>Transeat, tertio, per punctum C (fig. </s>

<s>148) <pb xlink:href="020/01/3297.jpg" pagenum="258"/>quaelibet linea cuius utrumque extremum incidat in superficiem continentem <lb/>SBM, puta linea GCN. </s>

<s>Dico quod in C conveniunt etc. </s>

<s>ut supra. </s>

<s>Sit enim <lb/>radius GCN, cuius extremi G et N, secundum quamcumque lineam, pertin&shy;<lb/>gant ad superficiem FPO, per radios similes PG et NO. </s>

<s>Nisi igitur resisten&shy;<lb/>tiam invenerit, flectetur ON versus lineam NC, idest NG, impelletque pun&shy;<lb/>ctum C. </s>

<s>Eademque ratione radius PGC impellet idem punctum C versus <lb/>oppositum terminum N. </s>

<s>Momenta autem radiorum tortuosorum PGC, et <lb/>ONC aequalia sunt, utpote qui ab eodem puncto C ad eamdem superficiem <lb/>Orbi concentricam FPO sint producti; unde etc. </s></p><p type="main">

<s>PROPOSITIO XVIII. &mdash; <emph type="italics"/>Puncto cuilibet intra manens humidum dato <lb/>momenta, secundum quamcumque lineam, aequalia opponuntur.<emph.end type="italics"/></s></p><p type="main">

<s>Sit supra datam quamcumque superficiem continentem FGL (fig. </s>

<s>149) <lb/>humidum quiescens, cuius superficies ABD, et sit intra ipsum datum pun&shy;<lb/><figure id="id.020.01.3297.1.jpg" xlink:href="020/01/3297/1.jpg"/></s></p><p type="caption">

<s>Figura 149.<lb/>ctum quodlibet C. </s>

<s>Dico quod secundum quam&shy;<lb/>cumque lineam punctum C moveri intelli&shy;<lb/>gatur, sive sursum, sive deorsum, sive tran&shy;<lb/>sversim, momenta undique ei opponuntur <lb/>aequalia. </s></p><p type="main">

<s>Intelligatur primo moveri sursum secun&shy;<lb/>dum lineam perpendicularem CB: repellet <lb/>igitur radium BC a termino C. </s>

<s>Gravitat autem <lb/>BC versus terminum C, unde momento quod <lb/>habet versus C, resistet motui puncti C. </s></p><p type="main">

<s>Deinde intelligatur moveri secundum lineam quamcumque obliquam CE, <lb/>aut CD, quae incidat directe in superficiem ABD. </s>

<s>Repellet igitur a termino C <lb/>radium CE aut CD similem radio BC. </s>

<s>Ponitur autem humidum datum quie&shy;<lb/>scere. </s>

<s>Igitur eius superficies ABD sphaerica necessario est, cuius centrum <lb/>idem est ac centrum orbis K. </s>

<s>Radii igitur CB, CE, et CD, a communi ter&shy;<lb/>mino C, ad eamdem sphaericam superficiem Orbi concentricam ABD sunt <lb/>porrecti. </s>

<s>Unde, cum similes ac specie acque graves sint, erunt momenta ipso&shy;<lb/>rum versus terminum C invicem aequalia. </s>

<s>Sive igitur punctum C repellat a <lb/>termino C radium CB, sive radium CE, sive radium CD, semper opponetur <lb/>ci momentum aequale versus terminum C. </s>

<s>Idemque eadem ratione valebit <lb/>de quocumque alio radio a termino C ad superficiem ABD directe producto. </s>

<s><lb/>Unde secundum quamcumque lineam, ad superficiem ABD directe pertin&shy;<lb/>gentem, moveri intelligatur punctum C, semper ei momentum opponetur <lb/>aequale. </s></p><p type="main">

<s>Denique intelligatur moveri idem punctum C secundum lineam quam&shy;<lb/>libet, quae in superficiem continentem FGL impingat, sive perpendiculariter <lb/>ut CG, sive oblique ut CF. </s>

<s>Si itaque versus CG moveri intelligatur, impel&shy;<lb/>let radium CG similem radio CB. </s>

<s>Radius autem CG, cum recta procedere <lb/>non possit versus G, flecti necesse est versus quamcumque lineam GH, im&shy;<lb/>pelletque radium GH. </s>

<s>Motui igitur puncti C resistit momentum radii GH. </s>

<s><lb/>Semidiametro itaque KC sphaerica intelligatur ducta superficies NCM, quae <pb xlink:href="020/01/3298.jpg" pagenum="259"/>secabit radium GH, puta in O. </s>

<s>Erit igitur momento portionis OG oppositum <lb/>aequale momentum radii similis CG. </s>

<s>Remanet igitur, contra momentum <lb/>puncti C, momentum radii OH. </s>

<s>Momentum autem radii OH aequale est mo&shy;<lb/>mento radii CB, aut CE, super eadem superficie sphaerica concentrica NCM <lb/>ad eamdem pariter ABD erecti. </s></p><p type="main">

<s>Si vero secundum lineam obliquam CI noveri intelligatur, eadem ra&shy;<lb/>tione ac modo ostendetur motui puncti C resistere momentum solius por&shy;<lb/>tionis AS, cuius momentum momento tum radii OH, tum radii CB ostende&shy;<lb/>tur, ex dictis, aequale, et sic de quacumque alia linea reflexa. </s>

<s>Unde secundum <lb/>quamcumque lineam, sive directam, sive a continente superficie reflexam, <lb/>idem punctum C moveri intelligatur, semper ipsius motui invenietur oppo&shy;<lb/>situm momentum aequale, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><p type="main">

<s><emph type="italics"/>Corollarium I.<emph.end type="italics"/> &mdash; Humido igitur manente, quodlibet ipsius punctum, <lb/>ubicumque extiterit, ibi necessario manebit. </s>

<s>Cum enim aequalibus momentis <lb/>undique interceptum et circumpulsum existat, nulla ex parte cedere potest, <lb/>sed libratum necessario consistet. </s></p><p type="main">

<s><emph type="italics"/>Corollarium II.<emph.end type="italics"/> &mdash; Idemque patet de qualibet sensibili eiusdem humidi <lb/>mole. </s>

<s>Ostendetur enim de quolibet eius puncto quod libratum undique ne&shy;<lb/>cessario maneat, nec moveri ratione gravitatis versus nullam lineam possit. </s></p><p type="main">

<s><emph type="italics"/>Corollarium III.<emph.end type="italics"/> &mdash; Idem denique patet de qualibet alia mole homoge&shy;<lb/>nea, dummodo sit eiusdem gravitatis in specie cum humido, in quo existit. </s>

<s><lb/>Idem enim habebit momentum ac portio illa humidi, cuius loco substituitur, <lb/>unde idem perseverabit in humido aequilibrium. </s></p><p type="main">

<s>PROPOSITIO XIX. &mdash; <emph type="italics"/>Si radiorum similium, super eadem sphaerica su&shy;<lb/>perficie Orbi concentrica utcumque erectorum, momenta fuerint aequalia, <lb/>perpendiculares eorum altitudines gravitatibus eorumdem in specie con&shy;<lb/>trarie respondebunt.<emph.end type="italics"/></s></p><p type="main">

<s>Sint super eadem superficie sphaerica, Orbi concentrica, DBF (fig. </s>

<s>150) <lb/>duo radii similes, cuiuscumque gravitatis in specie, AB et EF, qui aequale <lb/><figure id="id.020.01.3298.1.jpg" xlink:href="020/01/3298/1.jpg"/></s></p><p type="caption">

<s>Figura 150.<lb/>momentum habeant. </s>

<s>Dico quod altitudines perpendi&shy;<lb/>culares radiorum AB, et EF gravitatibus eorumdem <lb/>in specie contrarie respondebunt. </s></p><p type="main">

<s>Sit autem radii EF altitudo perpendicularis EC, <lb/>et radii AB altitudo perpendicularis sit AD, sintque <lb/>perpendiculares radii AD, et EC, quorum AD similis <lb/>ac specie aeque gravis sit cum AB, EC autem similis, ac specie aeque <lb/>gravis cum EF. </s>

<s>Erit igitur momentum radii AD aequale momento radii <lb/>AB, momentum vero radii EC aequale momento radii EF. </s>

<s>Unde momentum <lb/>radii perpendicularis AD aequale erit momento radii perpendicularis EC. </s>

<s>Sunt <lb/>autem ambo perpendiculares, unde gravitas absoluta radii AD aequalis erit <lb/>gravitati absolutae radii EC. </s>

<s>Atqui demonstratum habemus a Galileo, in suo <lb/><emph type="italics"/>Discursu hydrostatico,<emph.end type="italics"/> quod, si gravitates absolutae aequales fuerint, moles <lb/>gravitatibus in specie contrarie respondebunt; ut igitur moles radii AD, ad <lb/>molem radii EC, ita reciproce erit gravitas in specie radii EC, ad gravita-<pb xlink:href="020/01/3299.jpg" pagenum="260"/>tem in specie radii AD. </s>

<s>Sunt autem radii similes, erunt igitur moles ut eo&shy;<lb/>rumdem altitudines. </s>

<s>Ut igitur altitudo radii AD, ad altitudinem radii EC, ita <lb/>gravitas in specie radii EC, ad gravitatem in specie radii AD, idest gravitas <lb/>in specie radii EF ad gravitatem in specie radii AB. </s>

<s>Est autem EC altitudo <lb/>perpendicolaris radii EF, AD altitudo perpendicolaris radii AB; ut igitur al&shy;<lb/>titudo perpendicularis radii AB, ad altitudinem perpendicolarem radii EF, ita <lb/>gravitas in specie radii EF ad gravitatem in specie radii AB, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><p type="main">

<s>PROPOSITIO XX. &mdash; <emph type="italics"/>Si supra quiescentis humidi superficiem humidum <lb/>aliud specie minus grave quieverit, nullus subiectae humidae superflciei <lb/>radius a superficie deprimetur aut assurget, sed sphaerica ac Orbi con&shy;<lb/>centrica manebit eius superficies ut antea.<emph.end type="italics"/></s></p><p type="main">

<s>Sit humidum quiescens FN (fig. </s>

<s>151), cuius superficies FG. </s>

<s>Supra ipsum <lb/>quiescens humidum sit aliud specie minus grave EG, cuius superficies ED: <lb/><figure id="id.020.01.3299.1.jpg" xlink:href="020/01/3299/1.jpg"/></s></p><p type="caption">

<s>Figura 151.<lb/>dico nullum humidi subiecti quiescentis FN radium a <lb/>superficie FG deprimi aut elevari. </s></p><p type="main">

<s>Si enim possibile est, sit quilibet radius BO, as&shy;<lb/>surgens supra superficiem FG ad quamcumque altitu&shy;<lb/>dinem HO, et producatur radius BHO usque ad super&shy;<lb/>ficiem humidi quiescentis specie minus grave EG, ut <lb/>sit radius BA, et a termino B pertingat ad ED quilibet alius radius BMC, <lb/>secans FG in M. </s>

<s>Quia igitur HO pars est humidi subiecti specie magis <lb/>gravis, maius erit momentum radii AH, quam radii CM. </s>

<s>Posito igitur aequali <lb/>utrobique momento BH et BM, erit momentum radii AB maius momento <lb/>radii BC. </s>

<s>Flectetur igitur necessario versus lineam BC ac descendet radius <lb/>AB, quod est contra suppositum, ponitur enim humidum utrumque quie&shy;<lb/>scere. </s>

<s>Unde etc. </s></p><p type="main">

<s><emph type="italics"/>Corollarium I.<emph.end type="italics"/> &mdash; Unde patet radium quemlibet, ab eodem puncto su&shy;<lb/>biecti humidi, specie gravioris, ad supremam superficiem humidorum, specie <lb/>minus gravium ipsi incumbentium, utcumque pertingentem; aequale momen&shy;<lb/>tum habere. </s></p><p type="main">

<s><emph type="italics"/>Corollarium II.<emph.end type="italics"/> &mdash; Unde facili negotio demonstrabitur in humido, ex <lb/>pluribus gravitate in specie differentibus, atque invicem incumbentibus com&shy;<lb/>posito; punctum quodlibet a momentis aequalibus ad oppositos terminos se&shy;<lb/>cundum quamcumque lineam per ipsum ductam urgeri, nec non aequalia <lb/>ipsi gravitatum momenta secundum quamcumque lineam opponi. </s></p><p type="main">

<s>PROPOSITIO XXI. &mdash; <emph type="italics"/>Humido quiescenti FG<emph.end type="italics"/> (fig. </s>

<s>152), <lb/><figure id="id.020.01.3299.2.jpg" xlink:href="020/01/3299/2.jpg"/></s></p><p type="caption">

<s>Figura 152.<lb/><emph type="italics"/>cuius superficies FI, tubi utcumque erecti LM inferius <lb/>orificium M demergatur, superius vero L ad quamcumque <lb/>altitudinem supra libellam NO promineat, et supra su&shy;<lb/>biectam superficiem FI quiescat humidum aliud HI, <lb/>specie minus grave, cuius superficies HV, ita scilicet ut <lb/>summa ipsius altitudo ad orificium L non pertingat: <lb/>dico quod subiectum humidum, pondere superincum&shy;<lb/>bentis humidi pressum, supra libellam NO assurget.<emph.end type="italics"/></s></p><pb xlink:href="020/01/3300.jpg" pagenum="261"/><p type="main">

<s>Subiaceat enim libellae NO e directo sectio quaelibet NQ: ostendetur <lb/>quemlibet radium assignabilem in sectione NQ, vi prementis humidi HV, <lb/>supra libellam NO necessario extrudi. </s>

<s>Sit enim radius quilibet AB, et a ter&shy;<lb/>mino B pertingat, secundum quamcumque lineam, ad superficiem HV radius <lb/>similis BDE, secans FI in D. </s>

<s>Gravitat igitur super puncto D, versus lineam <lb/>DB, totus et solus radius superincumbentis humidi ED, unde universus ra&shy;<lb/>dius EDB gravitat super B. </s>

<s>Secundum lineam autem AB gravitat, super eo&shy;<lb/>dem puncto B, solus radius AB, cui nullus superincumbit, ex suppositione, <lb/>radius humidi HI. </s>

<s>Posito igitur aequali utrobique momento AB et DB, maius <lb/>erit momentum radii EDB quam AB. </s>

<s>Flectetur igitur EDB secundum lineam <lb/>BA, impelletque ultra libellam NO radium BA, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><p type="main">

<s><emph type="italics"/>Corollarium I.<emph.end type="italics"/> &mdash; Unde patet quilibet radio humidi, secundum quam&shy;<lb/>cumque lineam assurgentis, non opponi nisi radium similem humidi sibi in&shy;<lb/>cumbentis. </s>

<s>Patet enim radio AB non opponi nisi radium DB. </s></p><p type="main">

<s><emph type="italics"/>Corollarium II.<emph.end type="italics"/> &mdash; Quilibet subiecti humidi radius, vi superincumben&shy;<lb/>tis humidi, supra libellam, pressura expertem, eatenus assurget, quatenus <lb/>portio assurgentis radii, supra libellam existens, momentum habet aequale <lb/>momento cuiuslibet radii humidi superincumbentis, ab eadem libella ad su&shy;<lb/>premam eius superficiem producti. </s></p><p type="main">

<s>PROPOSITIO XXII. &mdash; <emph type="italics"/>Si, ut in figura praecedenti, extrudatur radius <lb/>BA supra libellam NO usque ad Y, ita scilicet ut portio AY, supra libel&shy;<lb/>lam NO existens, momentum habeat aequale momento cuiuslibet radii <lb/>similis, ab eadem libella FI ad supremam humidi super incumbentis su&shy;<lb/>perficiem HV producti, puta OS; radius BA ultra Y non impelletur.<emph.end type="italics"/></s></p><p type="main">

<s>Est enim momentum radii OS aequale momento radii DE, unde mo&shy;<lb/>mentum AY aequale etiam erit momento radii DE. </s>

<s>Posito igitur aequali utro&shy;<lb/>bique momento AY, et DE, erit momentum totius EDB aequale momento <lb/>totius YAB. </s>

<s>Non flectetur igitur EDB versus lineam BAY amplius, nec pro&shy;<lb/>inde radius BAY ulterius, secundum lineam dictam impelletur. </s>

<s>Sed nec a <lb/>nullo alio radio sibi contermino impelletur, unde etc. </s></p><p type="main">

<s><emph type="italics"/>Corollarium.<emph.end type="italics"/> &mdash; Ex hac igitur, et ex propositione XIX, colligetur: qui&shy;<lb/>libet subiecti humidi radius, vi superincumbentis humidi extrusus, eatenus <lb/>supra libellam assurget, quatenus pressionis supra libellam existentis perpen&shy;<lb/>dicularis altitudo, perpendiculari altitudini unius cuiuslibet radii ab eadem <lb/><figure id="id.020.01.3300.1.jpg" xlink:href="020/01/3300/1.jpg"/></s></p><p type="caption">

<s>Figura 153.<lb/>superficie ad supremam humidi incumbentis su&shy;<lb/>perficiem producti, contrariam proportionem ha&shy;<lb/>beat quam gravitas in specie, ad gravitatem. </s></p><p type="main">

<s>PROPOSITIO XXIII. &mdash; <emph type="italics"/>Humidi, intra humi&shy;<lb/>dum homogeneum existentis, pondus quantum&shy;<lb/>cumque sit, ab extrinsecus trahente aut retinente <lb/>impossibile est sentiri.<emph.end type="italics"/></s></p><p type="main">

<s>Sit, supra continentem superficiem EB (fig. </s>

<s><lb/>153), quiescens humidum, cuius superficies GAD, <lb/>et intra humidum dictum sit data quaelibet eius <pb xlink:href="020/01/3301.jpg" pagenum="262"/>portio P, intra ipsum ubicumque existens, per cuius extrema cadant a suprema <lb/>humidi superficie perpendiculares, eam undique intercipientes AE, CB, erit&shy;<lb/>que comprehensa sectio humida AEBC. </s>

<s>Manifestum autem est quod quilibet <lb/>sectionis AB radius aequilibratur cum momento radii sibi similis, a communi <lb/>termino ad eamdem superficiem producti. </s>

<s>Omnes igitur simul radii sectio&shy;<lb/>nis AB, sive aequalis, a communibus terminis ad supremam superflciem por&shy;<lb/>rectis, aequilibrantur radiis comprehensis inter EH et BF. </s>

<s>Transeat itaque <lb/>immediate sub portione P superficies sphaerica Orbi concentrica NOM, se&shy;<lb/>cabitque AB in RS, EH vero et BF, puta, in LN, et OM. </s>

<s>Sicut igitur sin&shy;<lb/>gulis radiis contentis in AB respondebant singuli radii similes contenti in <lb/>EH, et BF; ita singulis portionis eorumdem radiorum, contentis in BR, re&shy;<lb/>spondent singulae portiones similes contentae in ELN, et BOM, a communi&shy;<lb/>bus terminis ad eamdem superficiem sphaericam, Orbi concentricam, NLOM <lb/>pertingentes. </s>

<s>Singularum igitur portionum contentarum in BR momentum, <lb/>momento singularum sibi respondentium, ac oppositarum in EL et BO ae&shy;<lb/>quale est. </s>

<s>Ac proinde momentum totius molis BR momento totius molis EL, <lb/>et BO est aequale. </s>

<s>Unde reliquae molis AS momentum momento reliquae <lb/>GL et FM remanet aequale. </s></p><p type="main">

<s>His ita dispositis, dico pondus portionis P non posse ab ullo extrinse&shy;<lb/>cus trahente aut retinente experiri, sed proinde se habere ac si non esset. </s>

<s><lb/>Extra humidi superficiem GAD sit enim libra, cuius centrum I, et aequales <lb/>a centro distantiae IK, IQ, et, manente centro I, intelligatur funiculus KP <lb/>retinens pondus molis P. </s>

<s>Dico quod, quantumcumque sit pondus molis P <lb/>pendentis ab extremo K, excepto pondere funiculi KP, non movebit deorsum <lb/>dictum extremum librae K, sed perinde manebit libra in aequipondio, ac si <lb/>nullum eius extremo pondus appensum fuisset. </s>

<s>Nam pondere molis BF et <lb/>EH impellitur sursum moles BR. </s>

<s>Resistit autem BR aequali momento, ex <lb/>dictis, momento molis EL et BO. </s>

<s>Momento igitur molis OD et NH impelli&shy;<lb/>tur sursum moles BERS. </s>

<s>Impelli autem non potest sursum moles BERS, <lb/>nisi impellat sursum molem sibi immediate sursum obiectam P; eodem igi&shy;<lb/>tur momento molis NH et OD impelletur sursum moles P. Unde, nisi mo&shy;<lb/>les P maiori momento deorsum prematur, quam sit molis NH et OD, ipsam <lb/>sursum impellentis; non poterit moles P deorsum moveri. </s>

<s>Premitur autem P <lb/>deorsum tum proprio pondere, tum pondere molis APC, sibi ad perpendicu&shy;<lb/>lum incumbentis; unde premitur P deorsum momento totius molis AS. </s>

<s>Mo&shy;<lb/>mentum autem AS aequale ostensum est momento molis NH et OD, ideo&shy;<lb/>que maius illo non est. </s>

<s>Igitur moles P moveri sursum nullatenus poterit, <lb/>nec igitur extremum K, cui appensam ponitur, deorsum trahet. </s>

<s>Quantum&shy;<lb/>cumque igitur prematur pondus molis P, intra humidum homogeneum exi&shy;<lb/>stentis, manebit necessario extremum K perinde ac si nullum ei pondus <lb/>appensum fuisset, quod erat ostendendum. </s></p><p type="main">

<s><emph type="italics"/>Corollarium.<emph.end type="italics"/> &mdash; Unde patet qualiter, dato pondere in mole humida intra <lb/>humidum homogeneum posita, percipi id extrinsecus a retinente ex eo im&shy;<lb/>possibile sit, quod pondus datum aequali semper momento a subiecta mole <pb xlink:href="020/01/3302.jpg" pagenum="263"/>repulsum sustentetur, atque a descensu prohibeatur. </s>

<s>Quod idem in omni <lb/>pondere continget, si ipsum, librae extremo appensum, subiecta manu, aut <lb/>quovis alio retinaculo, sustentetur, atque arceatur a descensu. </s></p><p type="main">

<s>PROPOSITIO XXIV. &mdash; <emph type="italics"/>Moles intra humidum specie minus grave exi&shy;<lb/>stens, ubicumque fuerit, descendet, et momentum descensus eiusdem tan&shy;<lb/>tum erit, quantus est excessus supra momentum molis humidae aequalis, <lb/>cuius locum occupat.<emph.end type="italics"/></s></p><p type="main">

<s>Iisdem positis, in locum molis homogeneae P, substituatur quaelibet alia <lb/>aequalis moles Z, sed eadem utcumque gravior in specie. </s>

<s>Dico quod moles Z <lb/>non manebit, sed descendet necessario, eritque momentum ipsius in descen&shy;<lb/>dendo idem ac excessus supra momentum aequalis molis P, in cuius locum <lb/>substituitur. </s></p><p type="main">

<s>Cum enim moles Z mole P gravior in specie, eidemque aequalis pona&shy;<lb/>tur; erit pondus molis Z maius pondere molis P. </s>

<s>Pondus autem molis P, <lb/>cum pondere reliquae molis APC, aequale momentum habere ostensum est <lb/>cum NH et OD. </s>

<s>Pondus igitur molis Z, cum pondere eiusdem molis APC, <lb/>maius momentum habebit quam NH et OD, tanto scilicet maius, quanto mo&shy;<lb/>mentum gravioris molis Z maius est momento molis P sibi aequalis. </s>

<s>Premi&shy;<lb/>tur itaque deorsum subiecta moles ES tum proprio pondere, tum pondere <lb/>molis APC et Z, ad perpendiculum sibi incumbentium, eius autem de&shy;<lb/>scensui opponitur momentum molis EH et BF. </s>

<s>Cum igitur momentum ES <lb/>aequale sit, ex dictis, momento FL et BO; erit momentum totius AB maius <lb/>momento totius EH, et BF. </s>

<s>Cedet igitur EH et BF momento deorsum molis <lb/>ES, et descendet, ac proinde moles Z, cum mole APC ipsam premente, quod <lb/>erat primo ostendendum. </s></p><p type="main">

<s>Ostendam id, quod secundo venit, breviter sic: Si moles Z aequale mo&shy;<lb/>mentum haberet cum mole sibi aequali P, momentum ei in descendendum <lb/>nullum esset. </s>

<s>Maneret enim necessario in aequilibrio, ut patet ex dictis. </s>

<s>Tan&shy;<lb/>tum igitur momentum habebit in descendendo moles Z, quantum ei superest <lb/>praeter momentum aequale momento molis sibi aequalis P, cuius locum occu&shy;<lb/>pat. </s>

<s>Unde manifestum est quod humidum quodlibet, ex momento deorsum <lb/>cuiuscumque molis intra ipsum existentis, momentum auferat aequale mo&shy;<lb/>mento eius molis humidae, cuius locum occupat, idest molis humidae sibi <lb/>aequalis. </s></p><p type="main">

<s>PROPOSITIO XXV. &mdash; <emph type="italics"/>Si intra humidum, specie magis grave, moles <lb/>quaelibet extiterit, inter cuius inferiorem superficiem, superficiemque per&shy;<lb/>pendicularem subiectam continentem, humidum intercesserit; data moles <lb/>non manebit, sed a subiecto sibi humido sursum necessario impelletur.<emph.end type="italics"/></s></p><p type="main">

<s>Iisdem positis, substituatur in locum molis P moles sibi aequalis X, sed <lb/>specie minus gravis, inter quam et continentem superficiem EB intercedat <lb/>humidum ES. </s>

<s>Dico quod moles X, a subiecto sibi humido ES, sursum ne&shy;<lb/>cessario impelletur. </s>

<s>Erit enim moles X minus pondere molis sibi aequalis P. </s>

<s><lb/>Momentum autem molis ASP aequale ostensum est momento NH et DO. </s>

<s>Mo&shy;<lb/>mentum igitur molis OD et NH maius erit momento ASX, tantoque maius, <pb xlink:href="020/01/3303.jpg" pagenum="264"/>quanto maius est momentum molis P momento sibi aequalis X. </s>

<s>Ostensum <lb/>autem est quod subiecta moles ES impellitur sursum momento molis NH <lb/>et OD. </s>

<s>Eius autem ascensui resistit momentum molis ASX, quod minus po&shy;<lb/>situm est momento NH et OD, quo ES sursum impellitur; impellet igitur <lb/>sursum moles ES molem sibi immediate incumbentem X, quod erat osten&shy;<lb/>dendum. </s></p><p type="main">

<s>Impellet autem ES molem X sursum ea momenti quantitate, qua mo&shy;<lb/>mentum NH, OD, quo sursum impellitur, superat aequilibrium momenti, <lb/>quo X premitur deorsum, momenti scilicet ASX. </s>

<s>Ea autem quantitate osten&shy;<lb/>sum est momentum NH et OD excedere momentum ASX, qua momentum <lb/>molis P excedit momentum molis sibi aequalis X. </s>

<s>Momentum igitur, quo X <lb/>sursum impellitur, aequale est ei axcessui, quo momentum ipsius X supe&shy;<lb/>ratur a momento molis humidae sibi aequalis P, cuius locum occupat. </s>

<s>Unde <lb/>cuiuscumque molis, intra humidum specie magis grave existentis, momen&shy;<lb/>tum sursum tantum erit, quantus est excessus momenti alterius molis, sibi <lb/>aequalis et dato humido, supra momentum ipsius. </s></p><p type="main">

<s><emph type="italics"/>Corollarium.<emph.end type="italics"/> &mdash; Hinc manifestum est quod, si intra humidum specie <lb/>magis grave moles quaelibet ita posita fuerit, ut, inter ipsam superficiemque <lb/>continentem perpendiculariter ei subiectam, humidum non intercesserit; nul&shy;<lb/>lum habebit sursum momentum, sed a momento universae molis humidae, <lb/>ad perpendiculum sibi iucumbentis, deorsum pressa, necessario manebit, nec, <lb/>quantumcumque humidum gravius fuerit, per ipsum ascendet. </s></p><p type="main">

<s><emph type="italics"/>Experimentum.<emph.end type="italics"/> &mdash; Prisma, seu vas quodcumque aliud AB (fig. </s>

<s>154), <lb/>cuius fundum, puta ligneum, CD crassius existat, et ab ipsius superficie su&shy;<lb/><figure id="id.020.01.3303.1.jpg" xlink:href="020/01/3303/1.jpg"/></s></p><p type="caption">

<s>Figura 154.<lb/>periori CB cavitas excidatur deorsum hemi&shy;<lb/>sphaerica ELH, eique applicetur lignea sphaera, <lb/>cuius hemisphaerium alterum concavitati dic&shy;<lb/>tae ELH congruat, alterum vero, puta EMH, <lb/>extra ipsam promineat. </s>

<s>Ea tamen industria <lb/>cavitati dictae sphaera inseratur, ut orificium <lb/>quidem EH perfecte obstruat, nec permittat <lb/>humidum per commissuras dilabi: interim <lb/>autem eidem orificio pertinaciter non adhereat, <lb/>sed levi motu trahente sequatur. </s>

<s>Hisce con&shy;<lb/>stitutis, impleatur vas AB humido in specie <lb/>gravissimo, puta hydrargirio, et experimento <lb/>manifestum fiet quoniam lignea sphaera ELHM <lb/>per gravissimum hydrargirium non ascendet, sed manebit, ut supra a nobis <lb/>conclusum est. </s>

<s>Si quis autem vacui metum suspicetur, foramen aperiat ca&shy;<lb/>vitati EGH, puta in G, ut aer ad subeundum in promptu sit, quoties sphae&shy;<lb/>ram sursum elevari contigerit, nec propterea sphaera sursum movebitur, <lb/>sed manebit ut antea. (MSS. Cim., T. XXXIV, fol. </s>

<s>204-77). </s></p><pb xlink:href="020/01/3304.jpg" pagenum="265"/><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>In questo trattato del Viviani si pu&ograve; dire che sia compendiata la storia <lb/>delle pressioni idrostatiche, una delle principali questioni agitate intorno alle <lb/>quali, nell'Accademia fiorentina, e anzi in tutta la Scuola galileiana, abbiamo <lb/>veduto esser quella de'corpi pi&ugrave; leggeri, che rimangono sul fondo del vaso, <lb/>quando l'acqua non possa esercitarvi la sua circumpulsione. </s>

<s>Dunque, occor&shy;<lb/>reva a domandar qui, in proposito della palla di legno esattamente incastrata <lb/>sul fondo del vaso pieno; l'acqua di sopra, invece di conferire a sollevarla, <lb/>la conficca pi&ugrave; fortemente che mai dentro il suo incavo? </s>

<s>Ed essendo cos&igrave;, <lb/>perch&egrave; i palombari non rimangono oppressi, e nel cupo de'vivai si veggono <lb/>i pesci notare con s&igrave; agili moti? </s>

<s>Il problema sembrava non trovare, ne'prin&shy;<lb/>cipii idrostatici generali, la sua soluzione, e perci&ograve; il dire come vi si ridu&shy;<lb/>cesse &egrave; di tale curiosit&agrave;, e di tanta importanza, che senza ci&ograve; la storia delle <lb/>pressioni idrostatiche si rimarrebbe incompiuta. </s></p><p type="main">

<s>Gi&agrave; sappiamo quel che ne pensasse Herone Alessandrino, le ragioni del <lb/>quale si ripeterono da Galileo, e da tutti gl'Idrostatici pi&ugrave; savi, che, per una <lb/>parte, rifuggivano dalle sciocchezze di chi rassomigliava i pesci nell'acqua <lb/>ai topi ne'buchi del muro, e non volevano, per l'altra, mettersi a tenzonare <lb/>co'dubbi di Leonardo da Vinci. </s>

<s>A Leonardo, come a tutti gli altri, compresi <lb/>nel lungo spazio di tempo, che intercede fra Herone e Galileo; troppo an&shy;<lb/>cora faceva difetto la Scienza che, instituitasi nuovamente dallo Stevino, a <lb/>lui solo dava in mano gli argomenti, da risolvere il problema curioso. </s>

<s>In <lb/>che modo ei veramente lo risolvesse lo vedemmo col&agrave;, dove si faceva la sto&shy;<lb/>ria delle sue dottrine, le quali, come si neglessero per le altre parti, cos&igrave; <lb/>non si curarono nemmen per questa dalle due grandi scuole, allora domi&shy;<lb/>natrici in Francia e in Italia. </s></p><p type="main">

<s>Viene un giorno il Mersenno a rammemorare al Cartesio le ragioni dette <lb/>dallo Stevino, perch&egrave; quelli che ci son sotto non sentano il peso dell'acqua, <lb/>e il Cartesio orgogliosamente risponde: Quel che il vostro Stevino abbia <lb/>detto non mi ricordo, e non so, ma la ragion vera del fatto non pu&ograve; esser <lb/>che questa, &ldquo; quod non plus aquae gravitat in corpus, quod in aqua est vel <lb/>sub aqua, quam quantum aquae descenderet, si corpus illud loco suo cede&shy;<lb/><figure id="id.020.01.3304.1.jpg" xlink:href="020/01/3304/1.jpg"/></s></p><p type="caption">

<s>Figura 155.<lb/>ret. </s>

<s>Sic ex. </s>

<s>gr. </s>

<s>si supponamus homo in vase B (fig. </s>

<s>155), qui <lb/>corpore suo ita incumbat foramini A, ut exitum aquae impediat, <lb/>sentiet sibi impendere totum pondus cylindri aquae ABC, cuius <lb/>basim suppono esse eiusdem magnitudinis cum foramine A, quia, <lb/>si ipse per illud foramen descenderet, totus etiam iste cylindrus <lb/>aquae descenderet. </s>

<s>Sed si paulo altius supponatur, ut ad B, ita <lb/>ut non prohibeat amplius egressum aquae per foramen A; tum <lb/>nullam gravitatem sentiet ex aqua, quae inter B et C ipsi super incumbit, <pb xlink:href="020/01/3305.jpg" pagenum="266"/>quia, si ipsa descenderet versus A, nequaquam descenderet aqua ista cum <lb/>illo, sed contra pars aquae, quae illi versus A subiacet, paris cum eius cor&shy;<lb/>pore magnitudinis, in eius locum ascenderet. </s>

<s>Unde fit ut aqua illum sursum <lb/>evehat, potius quam deprimat, prout experientia comprobatur &rdquo; <emph type="italics"/>(Epistol.,<emph.end type="italics"/><lb/>P. II, Amstelodami 1682, pag. </s>

<s>123). </s></p><p type="main">

<s>Sembra che al Mersenno sodisfacesse meglio la ragione dello Stevino <lb/>che questa, e perci&ograve;, giacch&egrave; il Cartesio diceva di non saperla, o d'averla <lb/>dimenticata, glie ne veniva ripetendo ne'precisi termini il sillogismo, a cui <lb/>esso Cartesio per&ograve; negava la virt&ugrave; di concludere, scoprendosi falsa la minore. <lb/></s>

<s>&ldquo; Ad probandum quod homo in aqua demersus aquae gravitatem non sen&shy;<lb/>tiat, pessimum est hoc argumentum: <emph type="italics"/>Omnis pressio, quae laedit corpus, <lb/>partem istius corporis aliquam loco suo naturali depellit. </s>

<s>Sed aqua, ae&shy;<lb/>qualiter premens undique corpus in aqua demersum, nullam eius partem <lb/>loco suo naturali depellit; ergo etc.<emph.end type="italics"/> Nam neganda est minor, et falsissimum <lb/>est quod, si omnes hominis in aqua demersi partes satis valide ab illa com&shy;<lb/>primantur, non possent loco suo naturali depelli, quamquam partes cutis <lb/>omnes aequaliter premerentur, satis enim depellerentur loco suo naturali, si <lb/>omnes tam aequaliter compellerentur introrsum, ut iste homo minus solito <lb/>spatii occuparet &rdquo; (ibid., pag. </s>

<s>132). E rimanendosi ostinato nella sua pro&shy;<lb/>pria opinione, o per dirla addirittura nel suo errore intorno alla ragion vera <lb/>delle pressioni idrostatiche, soggiungeva: &ldquo; Sed praeterea falsum est quod <lb/>tota aqua, quae hominis corpori superincumbit, illum premat, immo po&shy;<lb/>tius illum sublevat, cuius rei veram, ut opinor, rationem ad te antehac <lb/>scripsi &rdquo; (ibid.). </s></p><p type="main">

<s>Il Baliani in Italia, o fosse inspirato alle altrui dottrine, o concludesse <lb/>il discorso da ci&ograve;, che senza alcun progiudizio di scuola gli venivano sugge&shy;<lb/>rendo la sua propria ragione e le naturali esperienze; fu il primo a far ri&shy;<lb/>flettere, sull'abbacinato pensiero dello Stevino, nuovi raggi vivi di luce. </s>

<s>&ldquo; Io <lb/>mi figuro, diceva, di esser nel fondo del mare, ove sta l'acqua profonda die&shy;<lb/>cimila piedi, e, se non fosse il bisogno di rifiatare, io credo che vi starei, <lb/>sebbene mi sentirei pi&ugrave; compresso e premuto da ogni parte, di quel che io <lb/>mi sia di presente. </s>

<s>Ma dalla detta compressione in fuori io non sentirei altro <lb/>travaglio, n&egrave; sentirei maggiormente il peso dell'acqua di quel ch'io mi fac&shy;<lb/>cia, quando, entrando sott'acqua la state bagnandomi nel mare, io ho dieci <lb/>piedi d'acqua sul capo, senza che io ne senta il peso. </s>

<s>Ma se io non fussi <lb/>entro l'acqua, che mi preme da ogni parte, e fussi, non dico in vacuo, ma <lb/>nell'aria, e che dalla mia testa in su vi fosse l'acqua; allora io sentirei un <lb/>peso, che io non potrei sostenere, che quando avessi forza a lui proporzio&shy;<lb/>nata.... Lo stesso mi &egrave; avviso che ci avvenga nell'aria, che siamo nel fondo <lb/>della sua immensit&agrave;, n&egrave; sentiamo n&egrave; il suo peso n&egrave; la compressione, che ci <lb/>fa d'ogni parte, perch&egrave; il nostro corpo &egrave; stato fatto da Dio di tal qualit&agrave;, <lb/>che possa resistere benissimo a questa compressione, senza sentirne offesa. </s>

<s><lb/>Anzi ci &egrave; per avv&eacute;ntura necessaria, n&egrave; senza di lei si potrebbe stare, ond'io <lb/>credo che, ancorch&egrave; non avessimo a respirare, non potremmo stare nel vacuo, <pb xlink:href="020/01/3306.jpg" pagenum="267"/>ma, se fossimo nel vacuo, allora si sentirebbe il peso dell'aria, che avessimo <lb/>sopra il capo, il quale io credo grandissimo &rdquo; (Alb. </s>

<s>IX, 212, 13). </s></p><p type="main">

<s>Questi pensieri gli esponeva nel 1630 il Baliani in una lettera a Gali&shy;<lb/>leo, il quale non gli poteva approvare in nesssun modo, perch&egrave;, sebbene a <lb/>quel tempo fossero in Italia oramai noti gli Elementi idrostatici steviniani, <lb/>ei non s'era potuto ancora persuadere dell'uguaglianza delle pressioni, che <lb/>si diceva fare i fluidi per tutti i versi: e persistendo nel credere che n&egrave; <lb/>l'acqua n&egrave; l'aria pesino su s&egrave; stesse, o sui corpi solidi a loro sottoposti, si <lb/>intende come, del non essere oppressi i palombari e i pesci, rifiutasse le ra&shy;<lb/>gioni date nuovamente dal Baliani, per non rimoversi da quelle antiche di <lb/>Herone, fatte gi&agrave; sue da quarant'anni. </s>

<s>N&egrave; si ricred&egrave; Galileo nemmeno negli <lb/>ultimi tempi della sua vita, ne'quali dettava al Viviani, come vedemmo, di&shy;<lb/>mostrazioni del non premere i liquidi i fondi dei vasi, e n&egrave; perci&ograve; i corpi <lb/>sopr'essi posati, o gli animali lungh'essi repenti. </s>

<s>Cosicch&egrave;, volendo il gio&shy;<lb/>vane alunno rendersi particolarmente le ragioni di questo problema curioso, <lb/>le riduceva cos&igrave; dai manoscritti <emph type="italics"/>Sermones de motu gravium,<emph.end type="italics"/> mutando qual&shy;<lb/>che parola nella scrittura del suo Maestro: </s></p><p type="main">

<s>&ldquo; Dubitatur quomodo pisces in aqua et homines, tam in aqua, quam <lb/>in aere existentes, vastissimam aquae et aeris gravitatem sustinere possint. </s>

<s><lb/>Forsan quia tunc dicimur gravari, quando super nos incumbit aliquod pon&shy;<lb/>dus, quod sua gravitate deorsum tendit, nobis autem opus est nostra vi re&shy;<lb/>sistere ne amplius descendat; illud autem resistere est quod gravari appel&shy;<lb/>lamus. </s>

<s>At quia Archimedes demonstravit corpora quae sunt aqua graviora <lb/>in aquam demissa descendere, et esse in humido gravia quidem, attamen <lb/>minus gravia quam in aere, quanta est gravitas molis aquae aequalis molis <lb/>illius corporis; leviora autem aqua, vi sub aqua impulsa, sursum attolli tanta <lb/>vi, quanta moles aquae aequalis moli illius corporis gravior est illo corpore; <lb/>quae autem sunt aeque gravia ac aqua, in aqua submersa, neque sursum <lb/>neque deorsum ferri, sed ibi manere ubi collocantur, si tamen tota fuerint <lb/>sub aqua; ex hoc patet quod, si fuerimus sub aqua, et super nos incumbat <lb/>aliquod corpus aqua gravius ut lapis, gravabimur quidem, sed minus quam <lb/>si essemus in aere, quia lapis in aqua est minus gravis quam in aere. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si autem, in aqua existentibus nobis, aliquod corpus aqua levius alli&shy;<lb/>gatum fuerit, nedum gravabimur, verum etiam attolleremur ab illo, ut patet <lb/>in natantibus cum cucurbita, cum alioquin, in aere existentes, a cucurbita <lb/>gravaremur. </s>

<s>Et ratio est quia cucurbita, sub aqua impulsa, fertur sursum <lb/>et allevat, in aere autem fertur deorsum et gravat. </s>

<s>Si autem in aqua exi&shy;<lb/>stentes aliquod corpus aeque grave ac aqua nobis immineat, neque ab illo <lb/>gravabimur neque attollemur, quia neque sursum neque deorsum ferretur. </s>

<s><lb/>At non invenitur corpus quod magis aequet gravitatem vel levitatem aquae, <lb/>quam ipsa aqua; non ergo est mirum, si aqua in aqua non descendat et <lb/>gravet, neque ascendat et attollat: diximus autem gravari esse resistere, no&shy;<lb/>stra vi, corpori deorsum petenti. </s>

<s>Et eadem ratio de aere habeatur &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>23, e Alb. </s>

<s>XI, 31, 32). </s></p><pb xlink:href="020/01/3307.jpg" pagenum="268"/><p type="main">

<s>Galileo e il Cartesio, avendo nell'Idrostatica comune la falsit&agrave; dei prin&shy;<lb/>cipii, non discordavano dunque nemmen nelle conclusioni, che per&ograve; non po&shy;<lb/>tevano non essere sospette ad alcuni de'loro discepoli pi&ugrave; sagaci. </s>

<s>Anche il <lb/>Viviani mette in dubbio la spiegazione, che il suo Maestro faceva pronun&shy;<lb/>ziare al protagonista del Dialogo, in forma cos&igrave; assoluta. <emph type="italics"/>Forsan quia....<emph.end type="italics"/><lb/>N&egrave; cessarono i dubbi che per opera del Pascal, l'arte usata dal quale appa&shy;<lb/>risce da questo lato pi&ugrave; che mai maravigliosa. </s>

<s>S'avvide il prudente uomo <lb/>che i Fisici de'suoi tempi, sedotti dall'autorit&agrave; de'due loro grandi maestri, <lb/>rifuggivano inconsideratamente dalle verit&agrave; steviniane, e fece come certe nu&shy;<lb/>trici che, rifiutato un siroppo ristorativo dal bambino per disgustoso, glie <lb/>l'hanno fatto poi parer dolce, e avidamente sorbire, a solo mutar figura e <lb/>materia all'ampolla. </s>

<s>Quell'arte, che in tutto intero il trattato <emph type="italics"/>De l'equilibre <lb/>des ligueurs<emph.end type="italics"/> &egrave; davvero, come si diceva, maravigliosa, spicca anche di pi&ugrave; nel <lb/>capitolo ultimo, in cui l'Autore non fa che rompere le giunture al sillogi&shy;<lb/>smo dello Stevino, la maggior del quale, tolta di sotto alla pressa dialettica, <lb/>si sciorina cos&igrave; pi&ugrave; amabilmente alla vista: </s></p><p type="main">

<s>&ldquo; La douleur que nous sentons, quand quelque chose nous presse, est <lb/>grande, si la compression est grande, parce que la partie press&eacute;e est &eacute;puis&shy;<lb/>s&eacute;e de sang, et que les chairs, les nerfs, et les autre partie qui la compo&shy;<lb/>sent, sont pouss&eacute;es hors de leur place naturelle, et cette violence ne peut <lb/>arriver sans douleur. </s>

<s>Mais si la compression est petite, comme quand on <lb/>effleure si doucement la peau avec le doigt, qu'on ne prive pas la partie <lb/>qu'on touche de sang, qu'on n'en detourne ny la chair ny les nerfs, et qu'on <lb/>n'y apporte aucun changement; il n'y doit aussi avoir aucune douleur sen&shy;<lb/>sible &rdquo; (pag. </s>

<s>38). E insomma non pu&ograve; la sensibilit&agrave; eccitarsi sull'animale, <lb/>se non a queste due condizioni: o che il corpo estraneo tocchi le parti sen&shy;<lb/>sibili in un punto solo, o che le tocchi tutte ugualmente, fuor che in un <lb/>punto. </s>

<s>Per conferma di che proponeva il Pascal l'esperienza di un uomo, <lb/>seduto sul cupo fondo di un vivaio. </s>

<s>Ei veramente non soffre alcuna passione <lb/>dal peso dell'acqua, quand'ella lo circonda tutto, ma se s'applica la bocca <lb/>di un lungo tubo a una coscia, in modo che l'altra bocca di sopra resti <lb/>aperta nell'aria, &ldquo; sa chair s'enflera, a la partie qu'est a l'ouverture du <lb/>tuyau, et il s'y formera une grosse tumeur avec douleur, comme si sa chair <lb/>y estoit succ&eacute;e et attir&eacute;e par une vantouze &rdquo; (pag. </s>

<s>32). </s></p><p type="main">

<s>La minore del sillogismo dello Stevino udimmo come il Cartesio la con&shy;<lb/>dannasse per falsa, e il Pascal risolutamente invece l'assolveva, condensando <lb/>le virt&ugrave; delle verit&agrave; precedentemente dimostrate in questa sentenza: &ldquo; La <lb/>vraye cause, qui fait que les animaux dans l'eau n'en sentent pas le poids, <lb/>est qu'ils sont pressez egalement de toutes partes &rdquo; (pag. </s>

<s>40). E perch&egrave; il <lb/>Cartesio audacemente negava anche queste pressioni per tutto le parti, di&shy;<lb/>cendo che l'animale, non ch'essere oppresso dal peso dell'acqua, n'&egrave; sol&shy;<lb/>levato; il Pascal, a confermare la verit&agrave; del fatto, proponeva una tale espe&shy;<lb/>rienza: Prendasi un bocciolo di vetro, e ripieno d'acqua vi s'infondano tre <lb/>cose: una vescica ben gonfiata e distesa, un'altra flaccida, e una mosca (car <pb xlink:href="020/01/3308.jpg" pagenum="269"/>elle vit dans l'eau tiede aussi bien que dans l'air) e comprimendo l'acqua <lb/>fortemente con uno stantuffo si vedr&agrave; la seconda vescica costringersi di pi&ugrave; <lb/>alla pressione, ma la prima rimanersi immutata, e la mosca &ldquo; se promener <lb/>avec libert&eacute; et vivacit&eacute; le long du verre, et mesme s'envoler des qu'elle sera <lb/>hors de cette prison &rdquo; (pag. </s>

<s>41), eppure ella non doveva esser premuta meno <lb/>della seconda vescica, che, cos&igrave; visibilmente cedendo allo sforzo, rientrava in <lb/>s&egrave; stessa. </s></p><p type="main">

<s>Che il Pascal, rendendo cos&igrave; alla libert&agrave; della vita lo Stevino, intendesse <lb/>di rivendicarne l'onta fattagli da'seguaci di Galileo e del Cartesio, si par <lb/>dal tuono insolito che piglia, verso la fine il suo discorso, simile a quello, <lb/>con cui concluderebbe una lunga riprensione qualche padre adirato o qual&shy;<lb/>che maestro. </s>

<s>&ldquo; Qu'on ne dise donc plus que c'est parce que l'eau ne pese <lb/>pas sur elle mesme; car elle pese par tout &eacute;galement: ou qu'elle pese d'une <lb/>autre maniere que les corps solides, car tous les poids sont de mesme na&shy;<lb/>ture, et voicy un poids solide qu'une mouche supporte sans le sentir &rdquo; (pag. </s>

<s>43). <lb/>Provate infatti ad aggiungere nel bocciolo alla prima altr'acqua, che equi&shy;<lb/>valga in peso alla forza fatta dallo stantuffo, e osserverete le medesime cose. </s>

<s><lb/>Che se al pesce non rimanga in fondo alla vasca se non l'acqua che lo cir&shy;<lb/>conda, essendosi il resto indurato nel ghiaccio, serber&agrave; l'agilit&agrave; che aveva <lb/>prima, e che serberebbe anche dopo essersi tutta l'acqua liquefatta. </s>

<s>Dun&shy;<lb/>que, cos&igrave; finalmente concludeva il Pascal, a favore dello Stevino, e contro i <lb/>paralogismi del Cartesio; &ldquo; les animaux dans l'eau n'en sentent pas le poids, <lb/>non pas parce que ce n'est que de l'eau qui pese dessus, mais parce que <lb/>c'est de l'eau qui les environne &rdquo; (pag. </s>

<s>44). </s></p><p type="main">

<s>La questione parve al Boyle di tanta curiosit&agrave; e di tanta importanza, <lb/>che volle riserbare l'appendice II de'suoi Paradossi a esaminarla. </s>

<s>Gli cade <lb/>per prima cosa sotto la considerazione il detto di uno scrittore d'Idrostatica, <lb/>ch'egli chiama celebre, non sappiamo per qual titolo, ma che certamente era <lb/>gonfio di filosofico orgoglio cartesiano, affermando che, del non sentire il peso <lb/>dell'acqua gli animali che ci son sotto, non poteva esser altra la causa, da <lb/>quella in fuori, ch'egli stesso assegnava con questo discorso: Le parti supe&shy;<lb/>riori dell'acqua non premono le inferiori, se non sia in mezzo a queste col&shy;<lb/>locato un corpo pi&ugrave; leggero dell'acqua stessa. </s>

<s>Ma il corpo dell'uomo &egrave; anzi <lb/>pi&ugrave; grave, dunque ecc. </s>

<s>concludendo che chiunque dice altrimenti s'inganna. </s>

<s><lb/>A cui il Boyle rispondeva che, nonostante una si gran fiducia, era certo do&shy;<lb/>verci essere, e che fosse perci&ograve; da ricercarsi del fatto una causa diversa. <lb/></s>

<s>&ldquo; Abunde enim probavi quod (contra assertionem cui innititur eius explica&shy;<lb/>tio) partes aquae superiores premunt inferiores, sive corpus aqua in specie <lb/>gravius, sive levius sit infra inferiores &rdquo; <emph type="italics"/>(Paradoxa<emph.end type="italics"/> cit., pag. </s>

<s>216) </s></p><p type="main">

<s>L'altra soluzion del problema, che l'autore di questi Paradossi passa <lb/>a esaminare nella detta Appendice, &egrave; quella che il Cartesio dava al Mer&shy;<lb/>senno, nella forma per noi dianzi ritratta dall'epistola XXXII della parte <lb/>seconda. </s>

<s>Ci&ograve; che avendo fatto anche il Boyle, appena finito di trascrivere, <lb/>cos&igrave; dice: Hactenus subtilis hic Philosophus, cuius ratiocinationes, licet magni <pb xlink:href="020/01/3309.jpg" pagenum="270"/>facere sim solitus, libere tamen fatendum hance mihi non satisfacere. </s>

<s>Ete&shy;<lb/>nim, cum iam satis superque probaverim superiores partes aquae premere <lb/>inferiores, corporaque iis subiacentia, sive corpora illa sint aqua in specie <lb/>leviora, sive graviora; fundamentum evertimus, cui domini Cartesii ingeniosa <lb/>at minus solida superstruitur explicatio &rdquo; (ibid., pag. </s>

<s>223, 24). </s></p><p type="main">

<s>Soggiunger&ograve; anche di pi&ugrave;, dice il Boyle, che il Cartesio s'inganna, at&shy;<lb/>tribuendo la causa del sentirne o no l'uomo il peso allo scendere o no che <lb/>fa l'acqua insieme con lui. </s>

<s>Perch&egrave; poniamo che quell'uomo, il quale gia&shy;<lb/>cendosi sul foro A (nella figura 155) lo turava, sia collocato in B, d'onde <lb/>egli poi scenda, insieme con l'acqua C, verso il foro A rimasto aperto: se <lb/>vero fosse quel che dice il Cartesio, dovrebbe il marangone sentire il peso <lb/>dell'acqua C. Eppure, verificandosi la chiesta posizione, &egrave; certo che non sen&shy;<lb/>tirebbe niente. </s>

<s>Dunque il conferire i momenti delle scese de'liquidi con quelle <lb/>dei solidi, come fa il Cartesio, calcando, senza voler parere, le orme di Ga&shy;<lb/>lileo; &egrave; mezzo ingannevole e insufficiente a risolvere una questione idrosta&shy;<lb/>tica cos&igrave; sottile, la quale da null'altra vera causa dipende se non dall'avere <lb/>in B il marangone acqua di sotto e di sopra, e in A acqua solamente di <lb/>sopra, e di sotto aria. </s>

<s>&ldquo; Dico itaque causam cur solidum quod, dum est ad A, <lb/>magnam sustinebat pressionem ab aqua incumbente non sentiat pondus eius, <lb/>quando locatur ad B, non esse quam assignat dom. </s>

<s>Des-Cartes, sed hanc <lb/>quod solido aqua circumdato aqua subiacens, ut frequens nobis fuit occasio <lb/>ostendendi, illud sursum premit aeque omnino vehementer, et aliquando am&shy;<lb/>plius, ac pondus aquae incumbentis id premit deorsum. </s>

<s>Cum e contra, quando <lb/>solidum erat id solum quod tegebat obturabatque foramen, causa esset ma&shy;<lb/>nifesta cur id cum violentia deorsum truderetur a pondere incumbentis aquae <lb/>ABC. </s>

<s>In isto quippe casu nulla ei subiacebat aqua ad A, quae solidum su&shy;<lb/>stentaret ac sua sursum pressione ipsum vi instrueret tanto ponderi resi&shy;<lb/>stendi &rdquo; (ibid., pag. </s>

<s>225, 26). </s></p><p type="main">

<s>Rimane, prosegue il Boyle, a esaminar la soluzione, che di questo pro&shy;<lb/>blema avea dato lo Stevino, assai prima del Cartesio, e, riferita l'argomen&shy;<lb/>tazione tradotta in latino dal libro degli Elementi idrostatici, soggiunge: &ldquo; Hanc <lb/>solutionem Stevini longe existimem esse praeferendam iis, quae de difficili <lb/>hoc problemate afferri solent &rdquo; (ibid., pag. </s>

<s>230). </s></p><p type="main">

<s>Nonostante esso Boyle, che aveva accusato l'autore degli Elementi idro&shy;<lb/>statici d'aver proposte esperienze, piuttosto razionali che di fatto, a confer&shy;<lb/>mare la verit&agrave; degli altri suoi teoremi; non pu&ograve; passare ora in questo l'esem&shy;<lb/>pio dell'uomo in fondo al tino ripieno d'acqua, che, dovendovi necessariamente <lb/>rimanere affogato, non potrebbe far testimonianza n&egrave; della insensibilit&agrave; pro&shy;<lb/>vata, n&egrave; della passione. </s>

<s>Vero &egrave; bene che, dalla somiglianza di quel che segue <lb/>alle cose insensibili, come alle tavolette di legno o di metallo poste nelle <lb/>medesime condizioni; si pu&ograve; ragionevolmente argomentare a ci&ograve;, che pati&shy;<lb/>rebbe un uomo, supposto ch'egli durasse a vivere anche nell'acqua. </s>

<s>Nulla&shy;<lb/>dimeno, dice il Boyle, si pu&ograve; l'esperienza praticar facilmente e con esattis&shy;<lb/>sima somiglianza dei fatti, per via della mia Macchina pneumatica. </s>

<s>&ldquo; Etenim, <pb xlink:href="020/01/3310.jpg" pagenum="271"/>licet aer sit fluidum grave, licetque, dum uniformiter premit totam corporis <lb/>superficiem, pressionem eius non sentiamus; et quamvis hanc ob causam <lb/>palmam manus imponere possis, aperto orificio parvi cylindri aenei, appli&shy;<lb/>cati machinae loco <emph type="italics"/>Recipientis,<emph.end type="italics"/> citra ullam noxam; quando tamen, antliam <lb/>exercendo, aer qui prius suberat palmae manus est subductus, proindeque <lb/>conferre nil amplius potest ad manum, adversus aeris externi et incumben&shy;<lb/>tis, pressionem sustentandam; utique aer externus tam graviter incumbet <lb/>manus metacarpio, ac si pondus quoddam grave ipsi esset impositum. </s>

<s>Ac <lb/>memini, tali facto experimento, non tantum manum meam gravi dolore fuisse <lb/>affectam, sed et convexitatem eius ultro deorsum pressam, ac si fracturae <lb/>esset periculum &rdquo; (ibid., pag. </s>

<s>233). </s></p><p type="main">

<s>Bench&egrave; questa esperienza, fatta con la Macchina pneumetica, possa qual&shy;<lb/>che poco diminuir la difficolt&agrave;, riman nonostante, dice il Boyle, sempre a <lb/>stupire come, sotto il peso, che, secondo i calcoli dello stesso Stevino, &egrave; in&shy;<lb/>gente, costringendosi le costole verso la cavit&agrave; del petto, e i muscoli contro <lb/>l'ossa; il marangone non senta alcun dolore. </s>

<s>L'esperienza della mosca de&shy;<lb/>scritta dal Pascal era lusinghiera, ma in sul primo leggerla sospett&ograve; il Boyle <lb/>che, insieme co'naturalisti di que'tempi, anche l'Autore credesse non avere <lb/>gli insetti bisogno alcuno di respirare, e che perci&ograve; quella, come e altre che <lb/>si trovano in mezzo al libro di lui, non foss'altro che una semplice specu&shy;<lb/>lazione. </s>

<s>Provato infatti pi&ugrave; volte a sommergere nell'acqua anche tiepida mo&shy;<lb/>sche assai gagliarde, ebbe a trovar che sempre vi rimanevano immobili, come <lb/>cose morte. </s>

<s>Allora pens&ograve; di far l'esperienza con qualche animale acquatico, <lb/>fra cui scelse i <emph type="italics"/>girini,<emph.end type="italics"/> per la loro piccolezza e mollezza di membra, pi&ugrave; facil&shy;<lb/>mente sensibili alla pressione. </s>

<s>Messo dunque l'animaletto nello strumento del <lb/>Pascal, e premuto lo stantuffo cos&igrave;, che il Boyle stesso calcol&ograve; uguagliar la <lb/>pressione al peso di un cilindro d'acqua, di quasi trecento piedi di altezza; <lb/>&ldquo; nihilominus, licet gyrinus in paulo minorem quam prius molem videre&shy;<lb/>tur compressus, libere tamen ipse hac illac in aqua natabat, subinde etiam <lb/>in summitatem ipsam pervadens. </s>

<s>Nec manifestum erat nobis laesum fuisse <lb/>ab hac compressione animalculum: manifestissimum vero erat id contusum <lb/>non fuisse ad necem, sensibilemve ei noxam illatam &rdquo; (ibid., pag. </s>

<s>238). </s></p><p type="main">

<s>Il curioso e difficile problema, qual'era stato risoluto dallo Stevino, ve&shy;<lb/>niva dunque a confermarsi cos&igrave; per ogni sua parte, che agli scrittori d'Idro&shy;<lb/>statica non rimase poi a fare altro ufficio, che diffondere la notizia. </s>

<s>A tale <lb/>infatti si riduce insomma il merito del Sinclaro, che, nel terzo libro della <lb/>sua <emph type="italics"/>Ars magna,<emph.end type="italics"/> riserb&ograve; il secondo dialogo, per applicare all'argomento le <lb/>verit&agrave; idrostatiche, rimaste vincitrici. </s>

<s>Il principio alla battaglia vedemmo come <lb/>fosse dato in Italia, la quale parve nonostante esser venuta una delle ultime <lb/>a raccogliere i frutti della vittoria. </s></p><p type="main">

<s>Non prima del 1670 apparve in Reggio dell'Emilia il libro <emph type="italics"/>De motio&shy;<lb/>nibus naturalibus,<emph.end type="italics"/> in cui il Borelli, ravvedutosi gi&agrave; degli errori imbevuti <lb/>alle fonti galileiane, risolveva il problema <emph type="italics"/>quare animal nullam noxam ex <lb/>compressione aquae incumbentis pati debeat,<emph.end type="italics"/> applicandovi il principio del-<pb xlink:href="020/01/3311.jpg" pagenum="272"/>l'uguaglianza delle pressioni per tutti i versi. </s>

<s>Abbiasi, diceva, una vessica <lb/>tutta piena d'acqua, o di mercurio, o d'arena, o d'altri minutissimi corpi <lb/>cristallini, che perci&ograve; saranno incompressibili, e s'immerga nel liquido di un <lb/>vaso. </s>

<s>Essendo quivi ugualmente premuta tutta intorno, come da tanti cunei <lb/>confitti in ogni punto di una v&ograve;lta sferica, &egrave; facile dimostrare come nessun <lb/>granello di arena, e nessuna particella d'acqua o di mercurio potr&agrave; cedere <lb/>a un'altra il suo proprio posto. </s>

<s>Or suppongasi che la detta vessica sia la <lb/>pelle involgente l'ossa, i muscoli e gli umori dell'animale: non potendosi <lb/>sentir passione per altra causa, che per la division del continuo, la quale, <lb/>per le cose dette, &egrave; impossibile ad avvenir nelle parti involte e ugualmente <lb/>premute; ne segue che l'acqua non fa sul corpo animale sentir lo sforzo, <lb/>bench&egrave; grandissimo, del suo peso. </s>

<s>&ldquo; Quapropter, cum urinatores in profundo <lb/>mari demersi ab aqua aequali vi undique comprimantur, superne scilicet, <lb/>inferne et lateraliter, circumcirca a pondere ipsius aquae; sequitur ex de&shy;<lb/>monstratis nullam scissionem, luxationem aut contusionem in eis creari: sci&shy;<lb/>licet nullam continui divisionem a pondere aquae incumbentis produci. </s>

<s>Igi&shy;<lb/>tur nullam noxam, nec sensum dolorificum patientur &rdquo; (pag. </s>

<s>69, 70). </s></p><p type="main">

<s>Non si pu&ograve; nonostante negare, soggiunge il Borelli, che non siano nel&shy;<lb/>l'animale alcune parti aerose, le qualr, compresse, venendo a cedere, parrebbe <lb/>che inevitabilmente dovessero produr qualche senso di dolore, se non si ri&shy;<lb/>pensasse che anco questa compressione non si fa in un luogo solo, ma &egrave; <lb/>universale. </s>

<s>Quanto differentemente non siam noi, che viviamo in fondo al&shy;<lb/>l'oceano dell'aria, gravati dal peso di lei, o quando stiamo in riva al mare, <lb/>o quando sulla vetta di un altissimo monte? </s>

<s>Eppure, per la differenza di <lb/>questi due stati, non sentiamo dolerci in nessuna parte (Proposiz. </s>

<s>XXV, <lb/>pag. </s>

<s>71, 72). </s></p><p type="main">

<s>Vedemmo il Viviani, a cui mancavano ancora i principii necessari, come, <lb/>nel presente proposito, s'accostasse, bench&egrave; dubitoso, col suo Galileo. </s>

<s>Ma <lb/>sovvenutigli quei principii, ritrov&ograve; e scrisse la vera spiegazione del fatto, la <lb/>quale non dee far maraviglia che in molte parti riscontri con quella del suo <lb/>Collega, e degli stranieri suoi precursori, perch'essendo il termine fisso, e <lb/>fisso il punto della partenza, la via di ricongiunzione non poteva variare che <lb/>nell'essere pi&ugrave; o meno piana, pi&ugrave; o men tortuosa. </s></p><p type="main">

<s>&ldquo; I marangoni stando sott'acqua (scrive ora il Viviani nella sua propria <lb/>casa molto diversamente, da quel che aveva fatto nell'ospizio di Arcetri) <lb/>non sentono il peso dell'acqua, che all'altezza talvolta di venti o pi&ugrave; brac&shy;<lb/>cia gli sovrasta, dal che pare a taluno evidente che il peso dell'acqua non <lb/>aggravi i corpi, che in essa sono, e per conseguenza che ella nel proprio <lb/>luogo attualmente non pesi. </s>

<s>Ma, per la prima, la conseguenza &egrave; falsa, ne &egrave; <lb/>necessario che, gravitando attualmente un peso sopra un corpo sensitivo, an&shy;<lb/>corch&egrave; tenero e cedente, ei lo senta. </s>

<s>Imperocch&egrave; si pu&ograve; dare il caso che, da <lb/>forza grandissima di peso o d'altro, premuto, ad ogni modo gli sia impos&shy;<lb/>sibile il poterlo sentire, il che avverr&agrave; necessariamente, quando, essendo egli <lb/>incapace di restringimento, sar&agrave; la di lui superficie ugualmente, secondo qual <pb xlink:href="020/01/3312.jpg" pagenum="273"/>si voglia linea assegnabile, nel medesimo tempo premuta o respinta, come <lb/>per chiarezza nella seguente figura 156 dimostreremo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia ABC superficie di qualsivoglia dato corpo sensitivo D, quantunque <lb/>tenero e cedente, purch&egrave; incapace di ristringimento, la quale s'intenda se&shy;<lb/><figure id="id.020.01.3312.1.jpg" xlink:href="020/01/3312/1.jpg"/></s></p><p type="caption">

<s>Figura 156.<lb/>condo qualsivoglia linea assegnabile con egual forza pre&shy;<lb/>muta o respinta. </s>

<s>Dico essere impossibile che tal forza sia <lb/>in modo alcuno dal detto corpo sentita. </s>

<s>Imperocch&egrave; in&shy;<lb/>tanto il corpo sensitivo D pu&ograve; sentire la forza premente, <lb/>in quanto fa nella di lui superficie qualche impressione. </s>

<s><lb/>Se dunque, per qualsisia cagione ci&ograve; avvenga, si dar&agrave; il <lb/>caso che dalla forza detta non venga la superficie a patire <lb/>impressione alcuna o alterazion di figura; rester&agrave; ancora <lb/>dimostrato che non puossi la detta forza, quantunque grandissima, dal corpo D <lb/>sentire, il che cos&igrave; mostreremo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Si pigli in ABC qualsivoglia punto B, il quale, secondo qualsivoglia <lb/>linea EB premuto, ceda se &egrave; possibile, e si rimova dal suo luogo verso qua&shy;<lb/>lunque linea, o per di fuori del corpo D, come per BF, o per di dentro, come <lb/>per BH. Ma, per la supposizione, tanto secondo la BF, quanto secondo la BH, <lb/>vi s'oppone forza di pressione e di resistenza uguale alla forza premente <lb/>secondo EB; dunque il punto B, secondo EB premuto, non potr&agrave; verso parte <lb/>alcuna cedere o mutarsi di luogo. </s>

<s>E cos&igrave; di qualsivoglia altro punto assegna&shy;<lb/>bile in ABC. Ond'&egrave; manifesto che, non potendo ABC, secondo alcuno suo <lb/>punto assegnabile, alla forza della pressione, quantunque grandissima, ce&shy;<lb/>dere; non potr&agrave; patire da essa impressione alcuna o alterazione della propria <lb/>figura. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, per venire al particolare dei marangoni, come mai il peso del&shy;<lb/>l'acqua, che aggrava e preme manifestamente i mantici e le palle di vetro, <lb/>pu&ograve; non aggravare e premere similmente gli uomini? </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Che dal non sentire il gran peso della mole che gli sovrasta sia falso <lb/>l'argomento che attualmente non gli aggravi e prema, si dimostrer&agrave; chia&shy;<lb/>ramente con un caso nel quale, bench&egrave; per ognuno sia certo che l'uomo sia <lb/>dal di lei peso attualmente aggravato e premuto, nonostante egli similmente <lb/>non lo senta. </s>

<s>Intendasi sopra il fondo di un vaso posta dell'arena o altra <lb/>materia incapace di restringersi, che serva per letto, sul quale si distenda <lb/>un uomo, sicch&egrave;, sovrappostoli qualche mole di acqua, egli verr&agrave; ad essere <lb/>il fondo, sul quale immediatamente l'acqua sovrastante si posa, e non si pu&ograve; <lb/>revocare in dubbio che tutto il peso dell'acqua sovrastante far&agrave; forza per&shy;<lb/>pendicolare ad aggravare la superficie dell'uomo sottoposto per fondo. </s>

<s>Ep&shy;<lb/>pure &egrave; vero che egli il di lei peso nella medesima maniera non sentir&agrave; che <lb/>se fosse in qualunque altro luogo di essa collocato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ma che un poco ad ogni modo lo senta, pu&ograve; ancora, a chi diligen&shy;<lb/>temente vorr&agrave; abbadarvi, per esperienza essere manifesto. </s>

<s>Imperocch&egrave;, men&shy;<lb/>tre pian piano ander&agrave; sott'acqua tuffandosi, sentir&agrave; principalmente intorno <lb/>al petto e alla gola una tale oppressione o soffocazione, che gli arrecher&agrave; il <pb xlink:href="020/01/3313.jpg" pagenum="274"/>peso circostante, e questa ne'marangoni, che sotto altezze d'acqua assai con&shy;<lb/>siderabili restano sepolti, viene ad essere ancora pi&ugrave; notabile. </s>

<s>Ma eglino per&ograve; <lb/>che molto maggiore dal peso dell'acqua soprastante se l'aspettano, all im&shy;<lb/>pedimento della respirazione piuttosto cotale oppressione o soffocamento at&shy;<lb/>tribuiscono. </s>

<s>Ma, se faranno l'esperienza, accorgerannosi che, ritenendo il <lb/>fiato fuor dell'acqua per lo spazio medesimo di tempo, non sentiranno il <lb/>medesimo, ma molto minore affanno. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Resta ora che dichiamo la cagione, per la quale non tutto ma parte <lb/>solamente del detto peso sentir ne debbano. </s>

<s>Bisogna dunque sapere qual&shy;<lb/>mente alla superficie d'un corpo, di consistenza simile all'umano, posta <lb/>dentro l'acqua, o a qualsivoglia altro fluido, stanno d'intorno, secondo ogni <lb/>linea assegnabile, momenti di pressione e di resistenza uguali, e da questo <lb/>canto, se fosse incapace di restringimento, non averebbe egli, per quel che <lb/>s'&egrave; di sopra dimostrato, a sentirne punto del di lui peso. </s>

<s>Ma perch&egrave; nel <lb/>corpo umano vi sono molte cavit&agrave;, che danno all'aria ricetto, e per conto di <lb/>esse di qualche compressione e restringimento capace lo rendono; quindi &egrave; <lb/>che al peso del sovrastante fluido in qualche parte gli &egrave; forza cedere, cio&egrave; <lb/>infino a tanto che l'aria contenuta puo dal detto peso essere ristretta. </s>

<s>Al <lb/>qual segno pervenuta, il cedere della di lui superficie, e conseguentemente <lb/>il senso dell'aggravamento, naturalmente cessa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E perch&egrave; chiaramente apparisce come il peso dell'acqua, sovrastante <lb/>il corpo in essa collocato, attualmente aggravi e prema, ma, stando intorno <lb/>la di lui superficie momenti di pressione e di resistenza uguali, e non po&shy;<lb/>tendo perci&ograve; quella secondo alcun suo punto cedere, non possa egli la forza <lb/>di cotal peso sentire; tolgasi per qualche via o la pressione o la resistenza <lb/>secondo qualche linea, sicch&egrave; possa verso quella alla circostante pressione <lb/>cedere, e la forza del peso si verr&agrave; subitamente in tal parte a sentire. </s>

<s>Del <lb/>quale effetto in cotal guisa potr&agrave; farsene l'esperienza. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; S'applichi un marangone, a qualche parte polposa del corpo, la bocca <lb/>d'una lunga canna di vetro, in maniera che non possa l'acqua tra il vetro <lb/>e la carne trovar adito, e tuffandosi notabilmente sott'acqua, purch&egrave; intanto <lb/>l'altra bocca della canna resti sempre di fuora; ei sentir&agrave; in quella parte <lb/>la forza della oppressione. </s>

<s>Imperocch&egrave; il peso dell'acqua intorno premente, <lb/>non trovando resistenza verso lo spiracolo cedente della canna, scaccer&agrave; verso <lb/>quello la carne, non senza qualche senso di dolore. </s>

<s>&rdquo; (MSS. Cim., T. XXXIV, <lb/>fol. </s>

<s>122-27). </s></p><p type="main">

<s>Questa esperienza fa tornare a mente il Pascal, bench&egrave; il Francese ci <lb/>rappresenti l'uomo in fondo al pelago come una naiade favolosa, e il Nostro <lb/>riduca il caso alla realt&agrave; dei marangoni, che respirano di fatto, e vivono <lb/>e sentono dentro alla loro campana. </s>

<s>In ogni modo deve la detta esperienza <lb/>essere stata suggerita al Viviani dalla lettura del capitolo VI <emph type="italics"/>De l'equilibre <lb/>des liqueurs,<emph.end type="italics"/> trattato, che non poteva in Italia non trovare lieta accoglienza. </s>

<s><lb/>L'intenzione infatti, ch'ebbe principalmente l'Autore, fu quella di esplicare <lb/>e di confermare la grande Esperienza torricelliana, la quale sanno bene i <pb xlink:href="020/01/3314.jpg" pagenum="275"/>nostri Lettori che non riusc&igrave; all'invenzione dello strumento desiderato, ma <lb/>alla fisica dimostrazione del premere, che fanno i fluidi in s&egrave; stessi e sui <lb/>corpi sottoposti, no nella sola direzion verticale, ma per tutti i versi, cosic&shy;<lb/>ch&egrave;, dalle vette del Puy de Domme, si pu&ograve; dire che movessero l'aure a in&shy;<lb/>sufflar l'anima nella scienza plasmata dallo Stevino. </s></p><p type="main">

<s>Nonostante &egrave; notabile che al Pascal si facesse forse maggiore accoglienza <lb/>in Italia, che in Francia, dove l'Idrostatica cartesiana aveva messe pi&ugrave; lar&shy;<lb/>ghe e pi&ugrave; profonde le radici, che la galileiana fra noi, e l&agrave; come qua non <lb/>erano stati con pari soavit&agrave; di potenza scommossi gli errori dal grande av&shy;<lb/>venimento patrio del Torricelli. </s>

<s>Cos&igrave;, se a riavviarsi nella rettitudine de'sen&shy;<lb/>tieri bastarono agli Accade&mgrave;ici fiorentini quasi sole le lettere a M. A. Ricci, <lb/>bisogn&ograve; a'Francesi aspettare quella universale potenza, che doveva tutta la <lb/>natural Filosofia cartesiana rovesciare dai fondamenti. </s>

<s>Del turbinare tempe&shy;<lb/>stoso e polveroso de'vortici fu sgombrato il cielo della Scienza dal benefico <lb/>apparire dell'astro di una Filosofia nuova, che si stabiliva, non sopra le chi&shy;<lb/>mere, ma sui principii della Matematica. </s></p><p type="main">

<s>Il Newton insomma, com'era venuto a restaurare matematicamente ogni <lb/>altra parte della Fisica, cosi, nella sezione V del suo tomo secondo, non la&shy;<lb/>sciava di provvedere all'Idrostatica. </s>

<s>Incomincia dal dimostrare l'uguaglianza <lb/>delle pressioni, proponendosi un vaso sferico tutto pieno di un fluido omo&shy;<lb/>geneo, e d'ogni parte ugualmente compresso, come la vessica del Borelli, a <lb/>cui molto somiglia il Newton anche nel modo di ragionare. </s>

<s>Ma non era spe&shy;<lb/>ranza di persuadere che il liquido preme ugualmente i corpi ch'egli cir&shy;<lb/>conda, in modo da mantenere inalterata la loro figura, se non sradicavasi <lb/>prima dalle menti quel dannosissimo pregiudizio, che nessuna porzion di <lb/>liquido pesa in mezzo a tutta l'altra mole. </s>

<s>&Egrave; cosa veramente da stupire come <lb/>Galileo non ripensasse che, se nessuno strato fluido pesa in s&egrave; non potrebbe <lb/>nemmeno pesar nel tutto, sulla mano che sostiene, e sulla bilancia che equi&shy;<lb/>libra il vaso pieno, le pareti del quale, se sian troppo deboli, si vedon ce&shy;<lb/>dere allo sforzo. </s>

<s>E anco &egrave; pi&ugrave; da stupire che, contro una tale evidenza di <lb/>fatto, Galileo stesso dettasse al Viviani quelle due proposizioni, da noi rife&shy;<lb/>rite di sopra, nelle quali contenevasi un paralogismo molto simile all'altro <lb/>di quell'antico Filosofo, che voleva, passeggiando, provare non darsi in na&shy;<lb/>tura il moto. </s></p><p type="main">

<s>L'Idrostatica del Cartesio s'avvolgeva ne'medesimi paralogismi, a cor&shy;<lb/>reggere i quali i discorsi lunghi del Boyle, confortati d'esperienze cos&igrave; la&shy;<lb/>boriose, non valsero quanto le matematiche proposizioni del Newton, pene&shy;<lb/>tranti come punte di freccie, che si sentono ferire, prima di saper come, e <lb/>d'onde siano venute. </s>

<s>Egli pone il fondamento al discorso in quella stessa <lb/>evidenza che, sebbene rimanesse annuvolata alle menti dei due grandi <lb/>Maestri, suoi precursori, rifulgeva pure cos&igrave; limpida al senso comune, <lb/>dimostrando che, diviso il liquido in tante sezioni, porzion ciascuna di <lb/>un orbe concentrico con la terra, la seconda, la terza, la quarta, ecc., <lb/>oltre al proprio peso, hanno quello delle sezioni, che a loro stanno di sopra, <pb xlink:href="020/01/3315.jpg" pagenum="276"/>cosicch&egrave; l'infima grava il fondo del vaso con la forza dovuta alla gravit&agrave; sua <lb/>propria, moltiplicata per il numero delle sezioni, o degli orbi concentrici infino <lb/>alla superficie. </s>

<s>&ldquo; Pressio igitur, qua superficies unaquaeque urgetur, non est <lb/>ut quantitas solida fluidi incumbentis, sed ut numerus orbium ad usque sum&shy;<lb/>mitatem fluidi, et aequatur gravitati orbis infimi multiplicati per numerum <lb/>orbium &rdquo; (Genevae 1711, pag. </s>

<s>169). Derivava di qui, per corollario imme&shy;<lb/>diato, che la pressione sul fondo del vaso &egrave; la medesima, &ldquo; sive fluidum a <lb/>superficie pressa sursum continuatum surgat perpendiculariter, secundum <lb/>lineam rectam, sive serpit oblique per tortas cavitates et canales, easque re&shy;<lb/>regulares, vel maxime irregulares, amplas vel angustissimas &rdquo; (ibid., pag. </s>

<s>171). </s></p><p type="main">

<s>Per quinto corollario della medesima proposizione si derivano i teoremi <lb/>idrostatici di Archimede, osservando, a quel modo che avevano fatto il Pa&shy;<lb/>scal e il Borelli, costituirsi in mezzo al fluido una specie di bilancia, sulla <lb/>quale i corpi da una parte discendono o ascendono, in ragion degli eccessi <lb/>e de'difetti de'pesi relativi a un egual volume di acqua, che s'immagini <lb/>contrappesare dall'altra. </s>

<s>Ma il sesto corollario &egrave; quello, in cui si propone il <lb/>Newton di scoprire per quale volgarit&agrave; di fallacie si lasciassero aggirare co&shy;<lb/>loro, i quali ripetevano col Galileo e col Cartesio che il fluido in mezzo al <lb/>fluido non &egrave; n&egrave; grave n&egrave; leggero, perch&egrave; non tende a moversi n&egrave; in basso <lb/>n&egrave; in alto. </s>

<s>&ldquo; Corporum igitur in fluidis constitutorum duplex est gravitas: <lb/>altera vera et absoluta, altera apparens, vulgaris et comparativa. </s>

<s>Gravitas <lb/>absoluta est vis tota, qua corpus deorsum tendit; relativa et vulgaris est <lb/>excessus gravitatis, quo corpus magis tendit deorsum quam fluidum am&shy;<lb/>biens. </s>

<s>Prioris generis gravitate partes fluidorum et corporum omnium gra&shy;<lb/>vitant in locis suis, ideoque coniunctis ponderibus componunt pondus totius. </s>

<s><lb/>Nam totum omne grave est, ut in vasis liquorum plenis experiri licet, et <lb/>pondus totius aequale est ponderibus omnium partium, ideoque ex iisdem <lb/>componitur. </s>

<s>Alterius generis gravitate corpora non gravitant in locis suis, <lb/>idest inter se collata non praegravant, sed mutuos ad descendendum cona&shy;<lb/>tus impedientia permanent in locis suis, perinde ac si gravia non essent.... <lb/>Quae vero, nec praegravando descendunt, nec praegravanti cedendo ascen&shy;<lb/>dunt, etiamsi veris suis ponderibus adaugeant pondus totius, comparative ta&shy;<lb/>men et in sensu vulgi non gravitant in aqua &rdquo; (ibid., pag. </s>

<s>172, 73). Or chi, <lb/>non dietro l'autorit&agrave; dell'Uomo, ma, per la forza del suo argomento, non <lb/>si sarebbe finalmente persuaso che la ragione addotta del non gravare il <lb/>liquido nel liquido, perch&egrave; non vi ascende n&egrave; vi discende, era veramente non <lb/>filosofica ma volgare? </s></p><p type="main">

<s>E perch&egrave; fra i problemi idrostatici quello, risoluto in ultimo luogo nel <lb/>libro dello Stevino, era, specialmente per l'opera datavi dal Pascal. </s>

<s>dal Boyle <lb/>e dal Borelli, uno de'pi&ugrave; famosi; il Newton cos&igrave;, nell'ultimo corollario, com&shy;<lb/>pendiosamente ne confermava, contro Galileo e il Cartesio, la verit&agrave; delle <lb/>ragioni: &ldquo; Cum autem fluida, premendo corpora inclusa, non mutent eorum <lb/>figuras externas, patet insuper, per corollarium propos XIX, quod non mu&shy;<lb/>tabunt situm partium internarum inter se; proindeque, si animalia immergan-<pb xlink:href="020/01/3316.jpg" pagenum="277"/>tur et sensatio omnis a motu partium oriatur, nec laedent corpora immersa, <lb/>nec sensationem ullam excitabunt nisi quatenus haec corpora a compres&shy;<lb/>sione condensari possunt &rdquo; (ibid., pag. </s>

<s>173). </s></p><p type="main">

<s>Cos&igrave; il Newton potentemente riassumeva gli svolgimenti, ch'ebbe il <lb/>primo libro idrostatico di Archimede dallo Stevino e dal Torricelli, dal Pa&shy;<lb/>scal e dal Boyle, dal Borelli e dal Viviani. </s>

<s>Poi l'Herman additava la scienza, <lb/>che ascondevasi sotto il velo de'conoidi galleggianti, descritti dal Siracusano <lb/>nel suo libro secondo, per cui, tra il finir del secolo XVII, e il cominciar <lb/>del seguente, prese l'Idrostatica il suo libero e sicuro cammino, per andar <lb/>presto a scendere in quel mare dell'infinito, apertole dal Bernoulli, dal <lb/>D'Alembert e dal Lagrange, per le placide e profonde acque del quale si <lb/>pu&ograve; ora navigare da noi. </s></p><pb xlink:href="020/01/3317.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO V.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Della viscosit&agrave; dei liquidi e delle azioni capillari<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle questioni, insorte fra i Peripatetici e Galileo, intorno alla viscosit&agrave; dell'acqua, e all'efficacia <lb/>di lei in sostenere le tavolette d'ebano gallegginnti: e come le osservazioni, l'esperienze, le ipo&shy;<lb/>tesi, e finalmente le teorie neutoniane aggiudicassero il torto a Galileo. </s>

<s>&mdash; II. </s>

<s>Delle osservazioni <lb/>e delle esperienze, fatte in Italia e in Francia, e poi in Inghilterra intorno alle azioni capillari. <lb/></s>

<s>&mdash; III. </s>

<s>Delle varie ipotesi immaginate a spiegar gli effetti delle azioni capillari. </s>

<s>&mdash; IV. </s>

<s>Delle <lb/>forze attrattive, che l'esperienze rivelarono esser causa degli effetti capillari. </s>

<s>&mdash; V. </s>

<s>Delle me&shy;<lb/>desime forze attrattive assoggettate all'anahsi matematica. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>I deliri dell'Idrostatica, fin qui particolarmente narrati, &egrave; dunque ma&shy;<lb/>nifesto non avere avuto d'altronde l'origine che dal non essersi riconosciuti, <lb/>della rettitudine, i vestigi rimasti ne'libri di Archimede leggermente segnati. </s>

<s><lb/>Cotesta leggerezza si rassomiglia molto a quella di chi corre velocissima&shy;<lb/>mente, nel quale atto il corpo, vinta la natural tendenza dei gravi, non la&shy;<lb/>scia sul suolo visibile orma del piede. </s>

<s>Cos&igrave; par che avvenga delle cose fisiche <lb/>trattate da Archimede, il quale, come tolse, per citar uno solo de'tanti esempi, <lb/>le braccia materiali alle bilance, per sostituirvi le linee geometriche; cos&igrave; <lb/>tolse ogni tenacit&agrave; fra le liquide particelle. </s>

<s>A che non ripensando il Tarta&shy;<lb/>glia e il Commandino male tradussero nella parola <emph type="italics"/>acqua<emph.end type="italics"/> quella di umido, <lb/>per cui si voleva intendere un corpo, che avesse l'essenza pura, senza le <lb/>passioni e le propriet&agrave; dei liquidi naturali. </s>

<s>E di qui avvenne che negassero <lb/>alcuni all'acqua quella tenacit&agrave;, dalla quale s'astraeva nell'umido contem&shy;<lb/>plato dal Siracusano. </s></p><p type="main">

<s>Notabili fra costoro, che non entrarono addentro ai sensi archimedei, <lb/>sono il Cartesio e Galileo. </s>

<s>Ma se il primo salv&ograve; i fatti, attribuendo al moto <lb/>intestino, e all'implicarsi le molecole anguilliformi dell'acqua quella, che vol-<pb xlink:href="020/01/3318.jpg" pagenum="279"/>garmente si chiama viscosit&agrave; di lei; il secondo la neg&ograve; assolutamente, osser&shy;<lb/>vando che l'acqua stessa, cos&igrave; nella superficie come nel mezzo, non fa mi&shy;<lb/>nima resistenza alla divisione. </s>

<s>Il pensiero ebbe occasion d'esplicarsi ne'suoi <lb/>pi&ugrave; minuti particolari, a proposito d'una disputa, che Galileo ebbe co'Peri&shy;<lb/>patetici, intorno alla ragione del galleggiar sull'acqua lamine sottilissime di <lb/>metallo o d'altra materia pi&ugrave; grave in specie di lei. </s></p><p type="main">

<s>La questione era stata proposta da Aristotile, nell'ultimo capitolo del <lb/>quarto libro <emph type="italics"/>De coelo,<emph.end type="italics"/> sotto questa forma: &ldquo; Dubitatur nunc cur lata ferra&shy;<lb/>menta et plumbum innatant super aquam, alia autem minora et minus gra&shy;<lb/>via, si rotunda sint aut longa ut acus, deorsum feruntur &rdquo; <emph type="italics"/>(Operum,<emph.end type="italics"/> T. V, <lb/>Venetiis 1560, a t. </s>

<s>del fol. </s>

<s>272). E si risolve dal Filosofo, attribuendo il fatto <lb/>alla maggiore ampiezza delle figure, che perci&ograve; trovano resistenza tanto mag&shy;<lb/>giore, quanto son pi&ugrave; le particelle dell'acqua, che si debbon distrarre. </s>

<s>&ldquo; Quae <lb/>igitur habent latitudinem, quia multum comprehendunt, supra manent, pro&shy;<lb/>pterea quod non facile distrahitur quod maius est. </s>

<s>Quae vero contrario modo <lb/>se se habent figuris, quia pauca comprehendunt, feruntur deorsum &rdquo; (ibid., <lb/>fol. </s>

<s>274). </s></p><p type="main">

<s>La spiegazione di Aristotile era quella medesima, che si dava dai Peri&shy;<lb/>patetici contemporanei di Galileo, il quale invece, affermando non aver la <lb/>resistenza dell'acqua nessuna parte nel fatto, riduceva tutto esattamente alle <lb/>ragioni dell'equilibrio idrostatico. </s>

<s>La propria opinione, cos&igrave; contraria alla pe&shy;<lb/>ripatetica, la confortava l'autore del Discorso intorno i galleggianti non so&shy;<lb/>lamente per via dell'esperienza, ma anche a priori, ritirandosi a pi&ugrave; interna <lb/>contemplazione della natura dei fluidi. </s>

<s>Cos&igrave; facendo, egli dice, &ldquo; forse scor&shy;<lb/>geremmo la costituzione delle parti loro esser tale che, non solamente non <lb/>contrasti alla divisione, ma che niente vi sia che a divider s'abbia, sicch&egrave; <lb/>la resistenza che si sente nel moversi per l'acqua sia simile a quella, che <lb/>proviamo nel camminare avanti per una gran calca di persone, dove sen&shy;<lb/>tiamo impedimento, e non per difficolt&agrave; che si abbia nel dividere, non si di&shy;<lb/>videndo alcuni di quelli, onde la calca &egrave; composta; ma solamente nel mover <lb/>lateralmente le persone gi&agrave; divise, e non congiunte. </s>

<s>E cos&igrave; proviamo resi&shy;<lb/>stenza nel cacciare un legno in un monte di rena, non perch&egrave; parte alcuna <lb/>della rena si abbia a segare, ma solamente a muovere e sollevare. </s>

<s>Due ma&shy;<lb/>niere pertanto di penetrare ci si rappresentano, una nel corpo, le cui parti <lb/>fossero continue, e qui par necessaria la divisione: l'altra, negli aggregati <lb/>di parti, non continue ma contigue solamente, e qui non fa bisogno di divi&shy;<lb/>dere, ma di movere solamente. </s>

<s>Ora io non son ben risoluto se l'acqua e <lb/>gli altri fluidi si debbano stimar di parti continue o contigue solamente: <lb/>sento ben inclinarmi al crederle pi&ugrave; presto contigue &rdquo; (Alb. </s>

<s>XII, 57). </s></p><p type="main">

<s>Comunque sia, non aver le particelle dell'acqua coerenza tale, da im&shy;<lb/>pedire a un solido pi&ugrave; grave in specie, bench&egrave; di minimo peso assoluto, il <lb/>dividerle, per fare in mezzo ad esse la sua naturale discesa; ci vien dimo&shy;<lb/>strato da varie esperienze. </s>

<s>&ldquo; E qual maggiore esperienza di ci&ograve;, dice Galileo, <lb/>ricercheremo noi di quella, che tutto il giorno veggiamo nell'acque torbide, <pb xlink:href="020/01/3319.jpg" pagenum="280"/>le quali, riposte in vasi ad uso di bere, ed essendo dopo la deposizione di <lb/>alcune ore ancora, come diciamo noi, albicce, finalmente, dopo il quarto o <lb/>il sesto giorno, depongono il tutto restando pure e limpide? </s>

<s>N&egrave; pu&ograve; la loro <lb/>resistenza alla penetrazione fermare quegli impalpabili e insensibili atomi di <lb/>rena, che per la loro minimissima forza consumano sei giorni a discendere <lb/>lo spazio di un mezzo braccio &rdquo; (ivi, pag. </s>

<s>54). E dopo questa esperienza Ga&shy;<lb/>lileo ne soggiunge altre due, dimostrative del medesimo assunto: quella cio&egrave; <lb/>di una larga falda di cera che, costretta a rimanersi in fondo al vaso per <lb/>l'aggiunta di tanto piombo, quant'&egrave; la quarta parte di un grano di miglio; <lb/>tolto questo, risale, bench&egrave; lentamente su a galla: e l'altra di qualunque <lb/>grandissima mole collocata in acqua ferma e stagnante, che si pu&ograve;, senza <lb/>contrasto alcuno, condurre di luogo in luogo, tirandola con un solo capello <lb/>di donna (ivi, pag. </s>

<s>55, 56). </s></p><p type="main">

<s>A difendere le dottrine peripatetiche contro Galileo sorsero alcuni, fra <lb/>i quali Lodovico delle Colombe, che in un suo Discorso adduceva molte sen&shy;<lb/>sate ragioni, da persuader che nell'acqua doveva essere una certa viscosit&agrave;, <lb/>come conseguenza dell'esser ella costituita di particelle continue, tutte in&shy;<lb/>sieme comprese sotto un'unica superficie. </s>

<s>&ldquo; Quelle gocciole d'acqua, diceva, <lb/>che pendono dalle gronde dei tetti, se non fossero viscose, non caderebbono <lb/>a poco a poco allungando, e non si staccano fin che il soverchio peso non <lb/>vinca la tenacit&agrave; loro, che per&ograve; il verno si veggono alle gronde alcuni ghiac&shy;<lb/>cioli cos&igrave; lunghi, che paiono di cera. </s>

<s>Aggiungo un esempio vostro, per pro&shy;<lb/>var pi&ugrave; chiaramente al senso la crassizie dell'acqua, e insieme la continuit&agrave;. </s>

<s><lb/>Ricordatevi a c. </s>

<s>75, che voi fate abbassar la testa all'amico, e gli mostrate <lb/>che, nel cavar l'assicella fuor dell'acqua, seguita sopra il suo livello, per la <lb/>grossezza d'una piastra, di stare attaccata alla superficie di sotto di detta <lb/>assicella, e l'abbandona mal volentieri, come anche dite a c. </s>

<s>53, concedendo <lb/>la violenza alla divisione per la resistenza del divisibile: segno che, non solo <lb/>&egrave; continua, ma viscosa ancora, il che non pu&ograve; fare n&egrave; la rena n&egrave; la farina &rdquo; <lb/><emph type="italics"/>(Discorso apologetico di L. delle Colombe,<emph.end type="italics"/> Alb. </s>

<s>XII, 145). E pi&ugrave; sotto ar&shy;<lb/>gomenta il Colombo alla viscosit&agrave; dell'acqua dal vederla, distendendosi, ora <lb/>pannicolarsi, come fra le maglie di una rete, e ora avvolgersi, come nella <lb/>pelle di una vescica, quando agitata forma bolle e sonagli. </s>

<s>&ldquo; Quelle bolle, <lb/>che i fanciulli chiamano sonagli, che vedete fare alle volte nei rigagnoli, per <lb/>qualche grossa pioggia, come si farebbero, se l'acqua non fosse continova <lb/>e tenace? </s>

<s>&rdquo; (ivi, pag. </s>

<s>136). </s></p><p type="main">

<s>Queste prove erano cos&igrave; semplici e concludenti, che, non osando Gali&shy;<lb/>leo contradirle ne'fatti, s'argoment&ograve; d'infirmarle nelle ragioni, fatte consi&shy;<lb/>stere in quella tenacit&agrave;, che tutti i Peripatetici ammettevan nell'acqua. </s>

<s>E <lb/>perch&egrave;, per una delle principali tra cos&igrave; fatte ragioni, s'adduceva dal Co&shy;<lb/>lombo quella del vedersi due liquidi con tanta facilit&agrave; rimescolarsi insieme; <lb/>Galileo insisteva nel contradirgli, cos&igrave; ragionando: &ldquo; E pi&ugrave; vi dir&ograve; che chi <lb/>ben considera questo mescolamento che da esso trarr&agrave; pi&ugrave; presto conghiet&shy;<lb/>tura di discontinuazione delle parti de'corpi, che si mescolano, che per l'op-<pb xlink:href="020/01/3320.jpg" pagenum="281"/>posito. </s>

<s>Perch&egrave;, se io metter&ograve; due corpi solidi insieme, ancorch&egrave; alcuno molto <lb/>gli commovesse e agitasse, mai non si mescolerebbono, ma, se i medesimi <lb/>si dividessero in molte parti, queste pi&ugrave; agevolmente si confonderebbono, e <lb/>ci apparirebbono mescolarsi, e finalmente molto pi&ugrave; farebbono ci&ograve;, se in sot&shy;<lb/>tilissima polvere si risolvessero, che &egrave; quanto a dire che sommamente si di&shy;<lb/>scontinuassero. </s>

<s>Ora, perch&egrave; le parti de'fluidi agitate e commosse assai pronta&shy;<lb/>mente si confondono e mescolano, quindi &egrave; che molto ragionevolmente discon&shy;<lb/>tinuatissime si devono stimare &rdquo; <emph type="italics"/>(Risposta a L. delle Colombe,<emph.end type="italics"/> ivi, pag. </s>

<s>333). </s></p><p type="main">

<s>In ogni modo, soggiunge Galileo, anche quando si dovesse ammettere <lb/>una continuit&agrave; di parti nella costituzione dell'acqua, non perci&ograve; ne segui&shy;<lb/>rebbe la pretesa viscosit&agrave; di lei: anzi bisognerebbe argomentare tutto al ro&shy;<lb/>vescio di quel che fa il signor Colombo, &ldquo; perch&egrave; il corpo, che fusse vera&shy;<lb/>mente continuo, non ha bisogno di visco o colla, che tenga unite le sue <lb/>parti, ma bene con ragione si pu&ograve; domandare qual sia il visco, che tiene <lb/>attaccate le parti di un aggregato discreto. </s>

<s>E cos&igrave; ragionevolmente doman&shy;<lb/>der&agrave; alcuno qual sia il glutine, che tiene attaccate le parti di una tavola <lb/>commessa di mille pezzetti di marmi, ma il ricercare tal viscosit&agrave; in un sol <lb/>pezzo di marmo, che forse, secondo il sig. </s>

<s>Colombo, &egrave; un corpo solo conti&shy;<lb/>nuato; sarebbe bene gran semplicit&agrave;. </s>

<s>E per&ograve;, se l'acqua &egrave; un continuo, non <lb/>si ricerca in lei viscosit&agrave; alcuna &rdquo; (ivi, pag. </s>

<s>335, 36). </s></p><p type="main">

<s>Contro poi Vincenzio di Grazia, altro peripatetico insorto alla difesa di <lb/>Aristotile, Galileo argomentava che, se l'acqua fosse un corpo continuo, e <lb/>che le particelle di lei resistessero alla divisione; non solamente le tavolette <lb/>di ebano, ma nemmeno qualsivoglia altro corpo gravissimo sarebbe potente <lb/>a dividerle, &ldquo; perch&egrave;, essendo le parti del continuo innumerabili, per pic&shy;<lb/>cola che fosse la resistenza di ciascheduna nel separarsi dall'altra, ad im&shy;<lb/>mensa forza potrebbono resistere, al che contraria l'esperienza. </s>

<s>Onde mi <lb/>pare di mettervi in necessit&agrave; di confessare la resistenza delle parti dell'acqua <lb/>alla divisione esser nulla &rdquo; <emph type="italics"/>(Risposta al V. di Grazia,<emph.end type="italics"/> ivi, pag. </s>

<s>539). </s></p><p type="main">

<s>In mezzo a queste dispute, che n&egrave; per l'una parte n&egrave; per l'altra an&shy;<lb/>darono esenti, com'&egrave; naturale, da motti mordaci, sorprendono queste parole <lb/>di Lodovico delle Colombe, che con la vittoria sopra le labbra, e col pre&shy;<lb/>sentimento della sconfitta nel cuore, par che voglia consolarsene e vendicar&shy;<lb/>sene con la speranza che il vincitore superbo si sarebbe inchinato a terra, <lb/>a raccogliere l'armi stesse del vinto: &ldquo; Signori lettori, l'avversario mio co&shy;<lb/>mincia dolcemente a calar le vele, e rendersi vinto, perch&egrave;, nella aggiunta <lb/>che seguita la soprannominata, non ist&agrave; pi&ugrave; tanto risoluto nel parer suo, che <lb/>nell'acqua non sia resistenza alla divisione, dicendo egli: <emph type="italics"/>Ora io non son ben <lb/>risoluto, se l'acqua e gli altri fluidi si devon chiamare di parti continue o <lb/>contigue solamente.<emph.end type="italics"/> Non vi paia gran fatto che egli dica di inclinare a cre&shy;<lb/>dere che siano contigue, perch&egrave; la cagione che lo muove, sebbene &egrave; senza <lb/>fondamento, non &egrave; stata conosciuta da lui come tale, come conoscer&agrave; per <lb/>questi miei scritti, dove s'&egrave; provato efficacissimamente l'acqua esser conti&shy;<lb/>nua &rdquo; <emph type="italics"/>(Discorso apolog. </s>

<s>citato,<emph.end type="italics"/> pag. </s>

<s>140). </s></p><pb xlink:href="020/01/3321.jpg" pagenum="282"/><p type="main">

<s>Avrebbe Galileo rinnegata la sua propria coscienza, se si fosse ardita <lb/>di testimoniar l'efficacia degli scritti altrui, in riformare i suoi propri pen&shy;<lb/>sieri, a quel modo che si chiuse gli orecchi, per non ascoltare la esecrata <lb/>sentenza profferitagli da Lodovico poche righe pi&ugrave; sotto, <emph type="italics"/>mille volte al di <lb/>vuole e disvuole.<emph.end type="italics"/> Ma come &egrave; un fatto che Galileo si ridisse pi&ugrave; volte, anche <lb/>nel medesimo Discorso intorno i galleggianti; cos&igrave; &egrave; un fatto che, rimasto <lb/>a principio ambiguo, e poi inchinando ad ammettere la contiguit&agrave; nelle parti <lb/>dell'acqua, fin&igrave; davvero per convertirsi alle ragioni dell'avversario, profes&shy;<lb/>sando con lui la continuit&agrave; peripatetica. </s></p><p type="main">

<s>La conversione dev'essere incominciata pochi mesi dopo, e precisamente <lb/>in quel tempo, che Galileo attendeva a postillar sottilmente le Considerazioni <lb/>d'Accademico incognito, perch&egrave;, in fronte a una delle carte, che fan da guar&shy;<lb/>dia al volume postillato, fuor di proposito dalla rimanente scrittura, e perci&ograve; <lb/>separata da lei per una linea, si legge scritta questa nota: &ldquo; Un metallo <lb/>resta nell'acqua forte senza discendere, perch&egrave; la mistione &egrave; fatta per gli <lb/>ultimi indivisibili &rdquo; (MSS. Gal., P. II, T. XV, fol. </s>

<s>4). </s></p><p type="main">

<s>Il motivo di riformare i primi giudizi intorno alla costituzione de'liquidi, <lb/>deve a Galileo esser venuto dal sentirsi opporre che, sebbene sia vero andar <lb/>finalmente al fondo le minime particelle terrose, che intorbidan l'acqua dei <lb/>fiumi; rimangono nonostante immobili, sciolti nell'acqua forte, i metalli. </s>

<s>N&egrave; <lb/>si vedeva come poter meglio rispondere che col dire essere i metalli stessi <lb/>ridotti a tal divisione di parti, da somigliare a quelle dei liquidi, per cui me&shy;<lb/>scolate insieme non si discernono, come non si discerne l'acqua mescolata <lb/>col vino. </s>

<s>E di qui venne Galileo a concludere che i liquidi son corpi, ridotti <lb/>ultimamente cos&igrave; ne'loro atomi, da tornar veramente in quel continuo, che <lb/>contro il Colombo e il Grazia aveva prima negato. </s>

<s>I riformati pensieri fu&shy;<lb/>rono poi solennemente espressi nella prima Giornata delle due Nuove Scienze, <lb/>dove, che i fluidi sian tali, perch&egrave; son risoluti ne'loro primi indivisibili com&shy;<lb/>ponenti, lo prova cos&igrave; ragionando il Salviati: </s></p><p type="main">

<s>&ldquo; Mentre io piglio un corpo duro, o sia pietra o metallo, e che con un <lb/>martello o sottilissima lima lo vo al possibile dividendo in minutissima e <lb/>impalpabile polvere, chiara cosa &egrave; che i suoi minimi, ancorch&egrave; per la lor <lb/>piccolezza siano impercettibili a uno a uno dalla nostra vista e dal tatto; <lb/>tuttavia sono eglino ancor quanti, figurati e numerabili, e di essi accade che <lb/>accumulati insieme si sostengono ammucchiati, e scavati sino a certo segno <lb/>resta la cavit&agrave;, senza che le parti d'intorno scorrano a riempirla: agitati e <lb/>commossi, subito si fermano, tantosto che il motore esterno li abbandona. </s>

<s><lb/>E questi medesimi effetti fanno ancora tutti gli aggregati di corpuscoli mag&shy;<lb/>giori e maggiori, e di ogni figura, ancor che sferica, come vediamo nei monti <lb/>di miglio, di grano, di migliarole di piombo e di ogni altra materia. </s>

<s>Ma se <lb/>noi tenteremo di vedere tali accidenti nell'acqua, nessuno ve ne troveremo, <lb/>ma sollevata immediatamente si spiana. </s>

<s>Se da vaso o altro esterno ritegno <lb/>non sia sostenuta, incavata, subito scorre a riempire la cavit&agrave;, ed agitata per <lb/>lunghissimo tempo va fluttuando, e per ispazi grandissimi distendendo le sue <pb xlink:href="020/01/3322.jpg" pagenum="283"/>onde. </s>

<s>Da questo mi par di potere molto ragionevolmente arguire i minimi <lb/>dell'acqua, nei quali ella pur sembra esser risoluta,.... esser differentissimi <lb/>dai minimi quanti e divisibili, n&egrave; saprei ritrovarvi altra differenza, che l'es&shy;<lb/>sere indivisibili &rdquo; (Alb. </s>

<s>XIII, 43, 44). </s></p><p type="main">

<s>Quanto per&ograve; al concluderne, da cos&igrave; fatta costituzione de'fluidi, la tena&shy;<lb/>cit&agrave;, Galileo si mantenne contrario ai Peripatetici. </s>

<s>Pi&ugrave; avanti infatti, in que&shy;<lb/>sto stesso Dialogo primo, dop'aver descritta l'esperienza della palla di cera, <lb/>ch'essendo scesa in un'acqua bastava aggiungervi pochi grani di sale per <lb/>farvela risalire, il Salviati soggiunge: &ldquo; Or vedete quanto s'ingannino quei <lb/>Filosofi, che voglion metter nell'acqua viscosit&agrave; o altra coagulazione di parti, <lb/>che la facciano resistente alla divisione o penetrazione &rdquo; (ivi, pag. </s>

<s>73). </s></p><p type="main">

<s>Apparisce manifesto di qui non aver Galileo riformate le proprie opi&shy;<lb/>nioni, espresse nel Discorso intorno ai Galleggianti, se non che rispetto alla <lb/>costituzione dei liquidi, ma che del resto persever&ograve; infino all'ultimo nell'as&shy;<lb/>serire che il galleggiar dell'assicelle di ebano dipendeva solamente dall'equi&shy;<lb/>librio idrostatico. </s>

<s>L'Accademico incognito terminava le sue <emph type="italics"/>Considerazioni<emph.end type="italics"/><lb/>con una proposta di pace, che consisteva nel dover Galileo ammettere la re&shy;<lb/>sistenza del liquido, e i Peripatetici l'effetto della leggerezza dell'aria, nel <lb/>qual mezzo avrebbe voluto volentieri far convenire le parti, se avesse avuto <lb/>speranza che si fosse contentata ciascuna della met&agrave; della vittoria. </s>

<s>Galileo <lb/>di fatti non se ne content&ograve;, e volle avere la vittoria intera, come resulta dal <lb/>sopra riferito documento, ma se ne sarebbero contentati i Peripatetici pi&ugrave; <lb/>modesti, e specialmente Lodovico delle Colombe, il quale anzi era andato <lb/>spontaneo a costituirsi in quel mezzo, in cui si voleva far riposare la pace <lb/>fra i dissidenti, non negando che, fra le cause del galleggiar le assicelle, si <lb/>dovessero mettere quelle volute da Galileo, ma nel medesimo tempo affer&shy;<lb/>mando non si potere escludere dagli efficienti la larghezza della figura, che <lb/>perci&ograve; trova nell'acqua una resistenza maggiore all'esser divisa. </s>

<s>&ldquo; Perch&egrave; la <lb/>gravit&agrave; dell'acqua, egli dice, non &egrave; sufficiente a resistere a un corpo pi&ugrave; <lb/>grave di lei, che non la penetri e divida; di qui &egrave; che altre cagioni bisogna <lb/>che concorrano a far la totale resistenza, tra le quali &egrave; principale la figura, <lb/>delle cagioni estrinseche parlando, come intese Aristotile, che perci&ograve; attribui <lb/>a lei cotali accidenti, non escludendo l'altre cagioni &rdquo; <emph type="italics"/>(Discorso apolog. </s>

<s>cit.,<emph.end type="italics"/><lb/>pag. </s>

<s>133). In ogni modo ebbe il Colombo a cedere alla prepotenza dell'av&shy;<lb/>versario, ma ora verr&agrave; la Storia a rivendicare i diritti dell'oppresso. </s></p><p type="main">

<s>Incominceremo dalla viscosit&agrave; dell'acqua, a rivendicar la verit&agrave; della <lb/>quale concorsero tutti i Fisici, e particolarmente i Discepoli stessi di Gali&shy;<lb/>leo. </s>

<s>Non importa ripeter le censure alle dottrine galileiane fatte in questo <lb/>proposito dal Nardi, e nemmeno osservar che l'Aggiunti non intese propria&shy;<lb/>mente negare l'esistenza di un glutine nell'acqua, ma volle solamente dire <lb/>che da questo glutine non poteva dipendere il formarsi, e lo stare attaccate <lb/>ai fili dell'erba le gocciole della rugiada. </s>

<s>Del Viviani idraulico, e che tanto <lb/>ben conobbe le resistenze incontrate nelle acque correnti, per la loro ade&shy;<lb/>sione alle asperit&agrave; degli alvei, e delle ripe dei fiumi; non parrebbe da du-<pb xlink:href="020/01/3323.jpg" pagenum="284"/>bitare, nonostante qualche nota, scritta da lui, ma dettatagli da Galileo, come <lb/>postilla al Discorso dei galleggianti, o al primo dialogo delle due nuove <lb/>Scienze, per dichiarar meglio e confermare le sue proprie opinioni. </s>

<s>Tale, fra <lb/>le dette note, sarebbe questa, l'esperienza descritta nella quale fu poi pro&shy;<lb/>posta agli Accademici del Cimento: &ldquo; Fare una piastra tonda di cera, che <lb/>salga lentamente per taglio: posta poi per piano, si vede che la figura non <lb/>&egrave; impotente a fender l'acqua, e che in essa non ci &egrave; minima coesione o vi&shy;<lb/>scosit&agrave; &rdquo; (MSS. Cim., T. X, fol. </s>

<s>27). E per meglio dichiarar le ragioni della <lb/>continuit&agrave; dei liquidi, col paragonare gli effetti, che si osservano in loro e <lb/>ne'corpi cos&igrave; detti discreti, secondo quel che aveva fatto dire al Salviati, nel <lb/>primo dialogo delle due nuove Scienze, a pag. </s>

<s>44 della citata edizione del&shy;<lb/>l'Alb&egrave;ri; Galileo dettava una tale postilla allo stesso Viviani. </s>

<s>&ldquo; Che i mi&shy;<lb/>nimi dell'acqua non siano quanti ce ne d&agrave; assai gagliardo argomento il <lb/>vedere che i minimi di qualsivoglia minutissima polvere, di materie anco gra&shy;<lb/>vissime, e le migliarole di piombo, bench&egrave; minutissime, agitate non riten&shy;<lb/>gono il moto, ma subito si fermano. </s>

<s>Ma l'acqua agitata conserva per lungo <lb/>tempo la fluttuazione; par dunque l'acqua esser costituita d'infiniti indivi&shy;<lb/>sibili, e perci&ograve; essere come un continuo &rdquo; (MSS, Gal. </s>

<s>Disc., T. CXXXV, <lb/>fol. </s>

<s>22). </s></p><p type="main">

<s>Che il Viviani fosse persuaso allora di ci&ograve;, che con tanta autorit&agrave; gli <lb/>s'insinuava, non fa maraviglia, n&egrave; fa pur maraviglia che rimanessero salde <lb/>in lui le medesime opinioni, anche qualche tempo dopo la morte del suo <lb/>Maestro, com'apparisce da ci&ograve;, che soggiunge in quest'altra nota, dop'aver <lb/>argomentato alla resistenza, che oppone al moto di un proiettile il mezzo, <lb/>da quel che si osserva in esso proiettile, quando trapassa dall'aria imme&shy;<lb/>diatamente nell'acqua. </s>

<s>&ldquo; Eppure l'acqua, egli dice, come priva in tutto di <lb/>tenacit&agrave;, non resiste con altro, che col doversi movere lateralmente, come a <lb/>lungo dimostr&ograve; il Galileo nel suo trattato delle Galleggianti &rdquo; (ivi, fol. </s>

<s>15). </s></p><p type="main">

<s>La saldezza di queste opinioni, intorno al non aver l'acqua nessuna te&shy;<lb/>nacit&agrave; di parti, incominci&ograve; a crollar nel Viviani alle osservazioni e all'espe&shy;<lb/>rienze, che gli contrapponeva il Borelli nell'Accademia: poi gli studiati moti <lb/>delle acque per gli alvei dei fiumi, e per gli stessi canali artificiali, finirono <lb/>di persuadergli che a cos&igrave; fatta tenacit&agrave; si dovevano principalmente attribuire <lb/>le cause ritardatrici di que'moti. </s>

<s>Ma nella Scuola galileiana il primo, che <lb/>sorgesse a contradire apertamente e in pubblico le dottrine del Maestro, fu <lb/>Geminiano Montanari, che ne prese motivo da certe esperienze instituitesi <lb/>nella bolognese Accademia dell'abate Sampieri, e dalla quale resultava che <lb/>i corpi gravi discendono pi&ugrave; velocemente che per l'acquavite e per l'olio, <lb/>per l'acqua comune. </s></p><p type="main">

<s>Ripensando il Montanari a ci&ograve;, che potesse esser causa di questa variet&agrave; <lb/>di moti, si sent&igrave; fortemente tentato d'attribuirla alla varia viscosit&agrave; de'li&shy;<lb/>quidi, come, con queste parole, significava in una lettera al principe Leo&shy;<lb/>poldo de'Medici: &ldquo; Essendosi nelle nostre radunanze appresso il sig. </s>

<s>ab. </s>

<s>Sam&shy;<lb/>pieri, osservato per esperienza che li corpi discendono pi&ugrave; velocemente per <pb xlink:href="020/01/3324.jpg" pagenum="285"/>l'acqua comune, che per l'acquavite e per l'olio comune ed altri; si &egrave; con&shy;<lb/>derato cio poter provenire dalla viscosit&agrave; maggiore, nelle parti dell'acquavite <lb/>e dell'olio, che di quelle dell'acqua. </s>

<s>E perci&ograve; si &egrave; supposto che, oltre la di&shy;<lb/>versit&agrave; della levigatezza de'mobili, della mole de'medesimi, della gravit&agrave; in <lb/>spezie di essi, e de'liquidi per li quali si muovono; essere in primo luogo <lb/>causa potentissima a ritardare la velocit&agrave; loro questa diversit&agrave; della visco&shy;<lb/>sit&agrave;, o se pure altra cosa ne fosse cagione dell'effetto suddetto.... Si ricerca <lb/>dunque il modo di potere, osservando le velocit&agrave; delle scese de'solidi in di&shy;<lb/>versi liquidi, separarne cos&igrave; le prime tre cause accennate, che ci rimanga <lb/>nuda la proporzione, che ha la viscosit&agrave;, o se con altro nome si dee chia&shy;<lb/>mar la supposta causa suddetta, in un liquido e in un'altro &rdquo; (MSS. Cim., <lb/>T. XIX, fol. </s>

<s>69). </s></p><p type="main">

<s>La titubanza, che apparisce da queste parole, nasceva dal dover mani&shy;<lb/>festamente contradire all'opinione di Galileo. </s>

<s>Ma pure i nuovi fatti osser&shy;<lb/>vati decidevano contro di lui, perch&egrave;, se veramente i liquidi non resistessero <lb/>che col doversi movere lateralmente, &egrave; chiaro che l'acqua e l'olio avrebbero <lb/>meno impedito il solido, il quale vi si sarebbe perci&ograve; dovuto scendere pi&ugrave; <lb/>veloce, che in mezzo all'acqua, contro l'esperienza. </s>

<s>In ogni modo non avrebbe <lb/>forse osato il Montanari di mettere in campo la viscosit&agrave;, se non gli veniva <lb/>l'animo di farlo da due potentissimi esempi. </s>

<s>Il primo fu quello del Grimaldi, <lb/>il quale, tutto in pensiero di cercar la causa dell'ascendere i liquidi ne'tu&shy;<lb/>betti capillari, non vide come ritrovarla migliore, che in quella viscosit&agrave;, la <lb/>quale, sebben sapesse esser negata da alcuni, resultava in ogni modo dalle <lb/>quotidiane osservazioni volgari. </s>

<s>&ldquo; Consideravi aquam esse corpus aliqua tan&shy;<lb/>dem viscositate praeditum &rdquo; <emph type="italics"/>(De lumine,<emph.end type="italics"/> Bononiae 1665, pag. </s>

<s>106). </s></p><p type="main">

<s>Ma l'impulso pi&ugrave; efficace venne al Montanari da ci&ograve; che i fratelli Del <lb/>Buono, amici suoi e Accademici del Cimento, gli avevano riferito del Bo&shy;<lb/>relli, dicendogli come questi, non perdonando al suo proprio Maestro, dimo&shy;<lb/>strasse nella stessa Accademia, con ragioni comuni e con filosofiche espe&shy;<lb/>rienze, dover essere tutti i fluidi nelle loro parti viscosi. </s>

<s>E, rimanendosi la <lb/>questione tuttavia ne'privati atti accademici, prese animo il Montanari di <lb/>darla pubblicamente risoluta nei suoi <emph type="italics"/>Pensieri fisico-matematici.<emph.end type="italics"/> &ldquo; E pri&shy;<lb/>mieramente non &egrave; dubbio alcuno, egli dice, darsi nell'acqua ed altri liquidi <lb/>quella coerenza o adesione di parti, che viscosit&agrave; sogliamo chiamare, osser&shy;<lb/>vata dal p. </s>

<s>Grimaldi, e conosciuta da tutti, per quotidiane esperienze che se <lb/>ne vedono, e della quale abbiamo fatti, come sapete, in altre nostre espe&shy;<lb/>rienze lunghi esami, per conoscere in qual proporzione rispondessero fra di <lb/>loro le viscosit&agrave; di diversi liquidi, ed altre particolarit&agrave;. </s>

<s>E da questa ade&shy;<lb/>sione delle parti fra loro nasce che non pu&ograve; facilmente moversi l'una di <lb/>esse, che seco non ne tragga molt'altre, che per tal cagione a lei s'attac&shy;<lb/>cano &rdquo; (Bologna 1667, pag. </s>

<s>30). </s></p><p type="main">

<s>Tre anni dipoi, pubblicando il Borelli il suo libro <emph type="italics"/>De motionibus natu&shy;<lb/>ralibus,<emph.end type="italics"/> v'inseriva quelle ragioni e quelle esperienze, con le quali aveva dianzi <lb/>persuasi gli Accademici fiorentini esser necessariamente ne'fluidi un glutine, <pb xlink:href="020/01/3325.jpg" pagenum="286"/>che ne tenga insieme le minime parti. </s>

<s>Notabile &egrave; che cos&igrave; fatte ragioni, quali <lb/>si leggono esposte nella proposizione CLVI, sian quelle medesime di Lodo&shy;<lb/>vico delle Colombe, di cui si ripetono gli argomenti, ricavati dal vedersi cre&shy;<lb/>scere all'acqua la viscosit&agrave;, mescendovi albume d'uovo o farina: n&egrave; si tace <lb/>pure l'esempio delle bolle di sapone che, soffiando con le guancie, sogliono <lb/>formar per gioco i fanciulli (ediz. </s>

<s>cit., pag. </s>

<s>327). </s></p><p type="main">

<s>Sopra il Peripatetico per&ograve; si solleva il Borelli, quando ripensa alla grande <lb/>importanza di questa fisica propriet&agrave; nel modificare le leggi delle acque cor&shy;<lb/>renti, per esempio dentro fistole strette, e tenute verticalmente erette, in cui <lb/>il liquido v&agrave; pi&ugrave; veloce nel mezzo, intorno all'asse, che non da'lati a con&shy;<lb/>tatto con le pareti, come s'argomenta dal veder la liquida superficie incur&shy;<lb/>varsi di sopra in forma di scodella, e protuberare di sotto in una gocciola <lb/>conoidea. </s>

<s>Ora, come si potrebbe spiegar ci&ograve;, se non fosse un glutine nel&shy;<lb/>l'acqua, &ldquo; quae superficiei asperae internae fistulae adhaerendo, magis re&shy;<lb/>tardat descensum et fluxum aquae, quam in intermedia parte cavitatis fistu&shy;<lb/>lae, ubi insensibili tenacitate aquae particulae vicissim impediuntur? </s>

<s>&rdquo; (ibid., <lb/>pag. </s>

<s>454). E nella proposizione appresso, che &egrave; la CCXVI, osserva il Borelli <lb/>che, cadendo liberamente l'acqua uscita da un tubo, non potrebbe nemmen <lb/>presso alla bocca mantenersi unita, per la progressiva e rapida accelerazione <lb/>delle parti anteriori. </s>

<s>E perci&ograve;, considerate due sezioni o lamine nel primo <lb/>tempo contigue, &ldquo; igitur in secundo tempore divelli ac separari ab invicem <lb/>deberent, quod, cum non contingat, procul dubio aderit aliqua causa, a qua <lb/>colligatae retinerentur, et haec profecto erit gluten et viscositas illa exigua <lb/>superius declarata &rdquo; (ibid., pag. </s>

<s>456). </s></p><p type="main">

<s>Cos&igrave; veniva il Borelli a salvare le ragioni di Lodovico delle Colombe <lb/>contro gli assalti di Galileo, il quale insomma riduceva ogni ragione speri&shy;<lb/>mentale del non resister l'acqua alla menoma forza di divisione, e del non <lb/>essere perci&ograve; viscosa, al fatto delle torbide ne'fiumi, che col tempo si chia&shy;<lb/>rificano pur finalmente, di modo che a tali minime particelle terrose &egrave; in&shy;<lb/>dugiato s&igrave; il moto della discesa, ma &egrave; impossibile che vi sian ridotte alla <lb/>quiete assoluta, &ldquo; ut fatentur Ghetaldus, Stevinus et alii &ldquo; (pag. </s>

<s>332). Fra <lb/>cotesti <emph type="italics"/>alii<emph.end type="italics"/> intendeva certamente il Borelli comprendere Galileo, che non no&shy;<lb/>mina apertamente, perch&egrave; la proposizione, insieme con tutte l'altre in que&shy;<lb/>sto subietto, &egrave; scritta per convincerne di falsit&agrave; le dottrine, della qual falsit&agrave; <lb/>l'esser fatto complice col Ghetaldo dovrebbe dar gran materia di pensare <lb/>agli ammiratori della originalit&agrave; de'principii professati nel Discorso intorno <lb/>alle galleggianti. </s></p><p type="main">

<s>Stavasene dunque Galileo col suo Ghetaldo sicuro, quando inaspettata&shy;<lb/>mente venne un gran colpo a turbargli quel riposo: i sali, che si rimangono <lb/>in assoluta quiete sciolti nell'acqua dei mari; i metalli attaccati dall'acqua&shy;<lb/>forte. </s>

<s>S'accenn&ograve; come fosse questa obiezione, che lo fece andare ad ammet&shy;<lb/>tere la continuit&agrave; de'fluidi, e la riduzione delle loro particelle agli ultimi <lb/>indivisibili. </s>

<s>Ma questi indivisibili, intesi al modo cavalieriano, non essendo <lb/>altro insomma che gl'infinitamente piccoli dei matematici, non potevano es-<pb xlink:href="020/01/3326.jpg" pagenum="287"/>sere accetti a coloro, i quali erano persuasi non darsi l'infinito fisico, o in <lb/>atto. </s>

<s>Le dottrine perci&ograve;, esposte nel primo dialogo delle due Scienze nuove, <lb/>venivano prima ripudiate dalla Filosofia speculativa, e poi dalla Naturale, la <lb/>quale ebbe a rivolgersi a cercare altre ragioni, onde spiegare come potes&shy;<lb/>sero rimanersi imperturbatamente sospese, in mezzo a liquidi tanto men gravi <lb/>in specie, le solide particelle dei sali e dei metalli. </s></p><p type="main">

<s>Luc'Antonio Porzio, sotto gl'influssi della Filosofia cartesiana, era ri&shy;<lb/>corso a un agitamento intestino, di che credeva esser naturalmente compresi <lb/>i fluidi, i quali non si compongono perci&ograve; in quiete assoluta, ma solo appa&shy;<lb/>rente ai deboli occhi nostri. </s>

<s>&ldquo; Ed io stimo, diceva, che conforme senza ar&shy;<lb/>tificio non possiamo noi osservare il velocissimo corso d'alcuni fiumi, n&egrave; il <lb/>moto rapido di molte altre sostanze; cos&igrave; nemmeno possa il nostro senso, <lb/>ne'licori che ci appariscono stagnanti, conoscere il moto e l'agitazione con&shy;<lb/>tinua delle loro parti. </s>

<s>Avvegnach&egrave; le parti de'liquidi, o siano similissime <lb/>tra loro, o se pure abbiano qualche dissomiglianza sia ella impercettibile <lb/>dagli occhi nostri, i quali non han virt&ugrave; di conoscere ci&ograve; che v'&egrave; nelle cose, <lb/>n&egrave; di osservare tutte le similitudini e dissimilitudini delle loro parti. </s>

<s>Laonde, <lb/>movendosi i licori, e agitandosi le loro parti, perch&egrave; sempre ad una che muti <lb/>luogo succede un'altra simile; pare all'occhio nostro di veder l'istessa che <lb/>prima vedeva, e crede che ella non abbia mutato luogo. </s>

<s>E che ci&ograve; sia vero <lb/>chiaramente a mio parere lo dimostrano tutte l'estrazioni chimiche, e i di&shy;<lb/>scioglimenti delle varie sostanze ne'licori, e l'amalgamazione de'metalli col <lb/>mercurio, ed il mescolamento insieme di varii corpi liquidi &rdquo; <emph type="italics"/>(Del sorgi&shy;<lb/>mento de'licori nelle fistole,<emph.end type="italics"/> Venezia 1667, pag. </s>

<s>48). </s></p><p type="main">

<s>Il Guglielmini, qualche tempo dopo, ripeteva col Porzio che le particelle <lb/>de'sali, dissoluti dall'acqua, son ridotte a tal minima piccolezza, da non re&shy;<lb/>sistere al moto intestino, che si progaga per tutta intera la liquida sostanza, <lb/>ma soggiungeva di pi&ugrave; le ragioni di quel moto intestino, e ne assegnava le <lb/>varie forze motrici, notabili, perch&egrave; parvero poi confermate dall'esperienza <lb/>del <emph type="italics"/>Radiometro.<emph.end type="italics"/> &ldquo; Cumque tales potentiae motrices plures adsint, aether <lb/>praeterfluens, lucis pressio, et praecipue calor, cuius, in media licet hyeme, <lb/>semper aliquis gradus in aere existit; vix possumus nos cohibere quin cre&shy;<lb/>damus, non modo promptissima mobilitate pollere globulos aquae, sed con&shy;<lb/>tinuo motu agitari &rdquo; <emph type="italics"/>(De salibus,<emph.end type="italics"/> Venetiis 1705, pag. </s>

<s>99). </s></p><p type="main">

<s>Se questi pensieri del Guglielmini non erano ancora noti al Borelli, sa&shy;<lb/>peva egli per&ograve; molto bene quegli del Porzio, amico suo e connazionale, con&shy;<lb/>tro cui par che sia scritta la proposizione CLV, dove l'Autore <emph type="italics"/>De motionibus <lb/>naturalibus,<emph.end type="italics"/> parlando de'metalli sciolti nell'acqua forte, attribuiva alla so&shy;<lb/>stanza ignea, spremuta dal metallo nell'atto della sua dissoluzione, l'esser <lb/>le minime particelle gittate e sparse per tutta la massa liquida. </s>

<s>Che se quivi <lb/>si vedono rimanere in perpetua quiete, da null'altro dipende che dalla vi&shy;<lb/>scosit&agrave; del menstruo, sopraggiunta a impedirne la scesa, appena cessato quel <lb/>primo fervor del fuoco, da cui, come pi&ugrave; manifestamente osservasi nella <lb/>calce, nasceva quell'intestino moto fermentativo. </s>

<s>&ldquo; Unde elicere possumus <pb xlink:href="020/01/3327.jpg" pagenum="288"/>quod, ex praedicto motu fermentationis, deduci non potest quod in fluido <lb/>partes eius perpetuo intestino motu agitentur, a qua commotione fluiditas <lb/>efficiatur, et ab hac causa dissolutiones salium, metallorum etc. </s>

<s>non depen&shy;<lb/>deant &rdquo; (pag. </s>

<s>324). </s></p><p type="main">

<s>Ci&ograve; che il Porzio attribuiva al moto intestino, da cui naturalmente &egrave; <lb/>invasa la massa fluida, doversi invece attribuire alla viscosit&agrave;, l'aveva dimo&shy;<lb/>strato il Borelli nella proposizione CLII, la quale vogliamo riferir con le pa&shy;<lb/>role del Montanari, perch&egrave; si confermi com'egli veramente derivasse i suoi <lb/>pensieri da chi gli era stato maestro con la voce viva, prima che co'libri <lb/>stampati. </s>

<s>&ldquo; Io considero dunque, egli dice, che dovendo i corpi, che per un <lb/>fluido si muovono, superare con l'impeto o momento loro la resistenza, che <lb/>dal fluido gli vien fatta, mediante non solo la necessit&agrave; che ha questo di <lb/>muoversi cedendole il luogo (il che non pu&ograve; farsi che in tempo, come ben <lb/>considera il Galileo) ma anche mediante la viscosit&agrave; delle sue parti; che non <lb/>senza alcuna difficolt&agrave; si separano. </s>

<s>Ed essendo perci&ograve; questa resistenza dei <lb/>fluidi proporzionata alle basi...., ed essendo vero eziandio che de'corpi si&shy;<lb/>mili di figura, ma differenti in grandezza, la proporzione della superficie del <lb/>grande a quella del piccolo &egrave; sempre suddupla della proporzion della mole <lb/>del grande a quella del piccolo ....; seguitando tali suddivisioni, finalmente <lb/>si giungerebbe ad avere cos&igrave; diminuita la forza di quel mobile, che in pro&shy;<lb/>porzione della resistenza ella resterebbe minore, e perci&ograve; impotente a fen&shy;<lb/>dere quel fluido, nel quale ella fosse immersa, essendoch&egrave; tale resistenza, <lb/>come ho detto, non solo dalla necessit&agrave; di moversi, come asseriva il famoso <lb/>Galileo, e nel qual caso, almeno in lungo tempo sarebbe superata; ma da <lb/>questa e dalla viscosit&agrave;, che tiene unite quelle parti, procede. </s>

<s>Nel qual caso, <lb/>avendo la viscosit&agrave; predetta una forza determinata, che dal solo tempo non <lb/>pu&ograve; essere superata, fa di mestieri che il momento del corpo, che deve su&shy;<lb/>perarla, sia di lei maggiore, altrimenti per alcuna lunghezza di tempo non <lb/>potrebbe disciorla. </s>

<s>E infatti noi vediamo, fra le altre esperienze, che il sale, <lb/>quantunque pi&ugrave; grave dell'acqua, quando in essa &egrave; liquefatto, non scende <lb/>pi&ugrave; abbasso, ma egualmente per esso disperso si mantiene, anzi ascende dal <lb/>fondo &rdquo; <emph type="italics"/>(Pensieri fisico-matem. </s>

<s>cit.,<emph.end type="italics"/> pag. </s>

<s>71). </s></p><p type="main">

<s>L'Hauksbee per&ograve; ebbe a considerare che se fosse questa creduta dal <lb/>Montanari, e confermata poi pi&ugrave; autorevolmente dal Borelli, la vera causa <lb/>del rimaner galleggianti le particelle saline, e le altre minuzie de'corpi spe&shy;<lb/>cificamente pi&ugrave; gravi de'loro menstrui; dovrebbe riscontrarsi qualche nota&shy;<lb/>bile differenza a pesar nell'acqua un corpo intero o minutamente diviso. </s>

<s>Die&shy;<lb/>tro ci&ograve;, prese una lamina di ottone, un dito quadra, del giusto peso di <lb/>482 grani, e il medesimo peso avendo fatto con 255 simili quadrati di or&shy;<lb/>pello, s'aspettava che, avendosi cos&igrave; gran differenza tra le superficie, non <lb/>piccola dovess'esser ne'pesi. </s>

<s>Ma con sua gran maraviglia trov&ograve; che quella <lb/>differenza non andava punto pi&ugrave; l&agrave; di due grani. </s>

<s>Da che fu indotto a con&shy;<lb/>cludere che, non potendo esser quella generalmente ammessa la causa vera <lb/>del fatto, ce ne doveva essere un'altra. </s>

<s>&ldquo; Insomma, egli dice, la sospensione <pb xlink:href="020/01/3328.jpg" pagenum="289"/>delle pi&ugrave; gravi particelle delle materie ne'liquidi io l'attribuisco alla mede&shy;<lb/>sima cagione, che tiene i liquori sospesi ne'piccoli tubi, voglio dire all'attra&shy;<lb/>zione. </s>

<s>Le minute parti dei corpi, che costano di superficie piane, essendo <lb/>gagliardamente attratte dalle parti di un fluido, in cui elle siano poste, e <lb/>perci&ograve; reciprocamente attraendo di nuovo le parti di quel fluido; possono <lb/>dall'azione di queste forze essere col&agrave; dentro tenute sospese. </s>

<s>E quei piccoli <lb/>corpi, che non sono o che non vogliono essere sospesi in un liquido ...., <lb/>credo che sieno di tal natura, per una di queste due cause: o che le parti <lb/>del liquido pi&ugrave; gagliardamente attraggansi l'una l'altra, che elle si attrag&shy;<lb/>gano quei piccoli corpi sparsi, ovvero che, per mezzo della propria loro at&shy;<lb/>trazione, si compongano in piccoli mucchietti, la cui mole e superior mo&shy;<lb/>mento gli aiuta a precipitare all'ingi&ugrave; &rdquo; <emph type="italics"/>(Esperienze fisico-meccaniche,<emph.end type="italics"/> trad. </s>

<s><lb/>dall'inglese, Firenze 1716, pag. </s>

<s>150). </s></p><p type="main">

<s>Nonostante, ne'primi anni di questo secolo, il Rumfort torn&ograve; a profes&shy;<lb/>sare l'ipotesi del Borelli, e com'esso persuaso che la tenacit&agrave; del liquido <lb/>resiste alla gravit&agrave; naturale de'minutissimi gravi dentrovi sospesi; pens&ograve; che <lb/>si potesse ritrovar la misura della detta tenacit&agrave; dai gradi di quella stessa <lb/>resistenza. </s>

<s>Per far ci&ograve; pesava prima nell'acqua una matassa attorta di seta, <lb/>e poi nuovamente sparsa nelle sue fila, e trov&ograve; che i due pesi differivano <lb/>tra loro, secondo quella giusta ragione, che la cos&igrave; tanto moltiplicata super&shy;<lb/>ficie gli prometteva. <emph type="italics"/>(Bibloteque britanniques,<emph.end type="italics"/> T. XXXIV). </s></p><p type="main">

<s>I commemorati autori di queste esperienze non ebbero nessuno l'inten&shy;<lb/>zione, almeno diretta ed espressa, di servirsene a risolvere la questione an&shy;<lb/>tica insorta fra Galileo e i Peripatetici de'suoi tempi, ma dopo che il Bo&shy;<lb/>naventuri e i suoi colleghi vennero a dare alla critica delle Opere galileiane <lb/>gl'inizi, Giovan Batista Venturi si propose a risolvere questo primo quesito: <lb/>&ldquo; &Egrave; egli vero, come sostenne il Galileo, che l'acqua nel suo interno possa <lb/>bene colla sua inerzia ritardare il movimento de'corpi nella medesima im&shy;<lb/>mersi, ma non possa mai impedirlo affatto, ove siavi un qualunque menomo <lb/>disquilibrio di gravit&agrave; tra il corpo immerso e l'acqua stessa? </s>

<s>&rdquo; <emph type="italics"/>(Memorie <lb/>e Lettere inedite di Galileo,<emph.end type="italics"/> Modena 1818, P. I, pag. </s>

<s>197). </s></p><p type="main">

<s>La risposta si fa dipendere dalla descrizione di due esperimenti, nel <lb/>primo dei quali s'abbiano due vasi cilindrici, co'fondi comunicantisi per <lb/>uno assai lungo e strettissimo tubo, e pieni d'acqua in fino a mezzo. </s>

<s>So&shy;<lb/>prainfusavene poi un'altra piccola quantit&agrave;, con un cucchiaino, trov&ograve; il Ven&shy;<lb/>turi che un centoventesimo di linea d'altezza produceva una pressione suf&shy;<lb/>ficiente a far movere il liquido nel suo interno, per ridursi dalle due parti <lb/>in perfetto equilibrio. </s>

<s>L'altro esperimento consisteva nell'osservare che il <lb/>moto dell'acqua, dentro un tubo di vetro da livella, avveniva anche quando <lb/>il seno dell'inclinazione non era che la settantamillesima parte del seno to&shy;<lb/>tale, o della lunghezza dello stesso tubo, d'onde ne concludeva il Venturi <lb/>che, a far movere l'acqua nel suo interno basta una forza uguale alla set&shy;<lb/>tantamillesima parte della sua gravit&agrave; assoluta (ivi, pag. </s>

<s>197, 98). </s></p><p type="main">

<s>Veramente non sarebbe stato necessario, per giungere a queste conclu-<pb xlink:href="020/01/3329.jpg" pagenum="290"/>sioni, valersi di strumenti cos&igrave; raffinati, come con tanta diligenza se li volle <lb/>procacciare il Venturi. </s>

<s>Dal diavolino del Cartesio gi&agrave; sapevano tutti che la <lb/>pi&ugrave; leggera pressione alla superficie del liquido bastava per mettere in su&shy;<lb/>bitaneo moto le parti nell'interno, e sapevasi pure che non solo con una <lb/>inclinazione minima, ma nulla affatto, si sarebbe mosso il liquido dentro il <lb/>tubo di vetro, quando gli si fosse aperto un piccolo foro a uno estremo, a <lb/>quel modo che i Meccanici insegnano non volerci nessuna forza a movere <lb/>un perfetto globo sopra un perfettissimo piano orizontale. </s>

<s>Da che si pu&ograve; con&shy;<lb/>cludere che gli sperimenti del Venturi, oltre ad avere una squisitezza super&shy;<lb/>flua, non valevano a risolvere la questione, perch&egrave; non si disputava delle <lb/>difficolt&agrave; del moversi l'una particella d'acqua intorno a un'altra, con sola&shy;<lb/>mente variare il punto del contatto, ma della difficolt&agrave; della separazione di <lb/>due o pi&ugrave; particelle per una qualche sensibile distanza, qual sarebbe il diame&shy;<lb/>tro per esempio di quei granellini terrosi che intorbidano i fiumi. </s></p><p type="main">

<s>Non risolvendosi dunque il quesito da'suoi veri principii, non par si <lb/>possa logicamente concludere che, supposto non intercedere alcuna affinit&agrave; <lb/>tra il liquido e il solido, avesse Galileo ragione di dire che le minuzie gal&shy;<lb/>leggianti dei corpi son dal mezzo ritardate nello scendere, ma non affatto <lb/>impedite, perch&egrave; riman sempre fra le particelle liquide un'aderenza mutua <lb/>o tenacit&agrave;, che resiste alla loro divisione. </s>

<s>A che ripensando non s'intende <lb/>come, secondo l'Hauksbee, vi possano essere certi piccoli corpi naturalmente <lb/>scendenti in mezzo a un liquido, quando le molecole di lui s'attraggono pi&ugrave; <lb/>gagliardamente, ossia, quando pi&ugrave; fortemente resistono ad aprire in mezzo <lb/>a loro il passaggio a corpi stranieri. </s>

<s>Che del resto i resultati sperimentali <lb/>del Fisico inglese, rispetto al pesar nell'acqua ora un solido intero, ora mi&shy;<lb/>nutamente diviso; si vedr&agrave; che non contradicono ai resultati sperimentali del <lb/>Rumfort, considerando che altrimenti si comportano verso l'acqua l'ottone <lb/>e la seta. </s></p><p type="main">

<s>Il Borelli non faceva a'suoi tempi questa distinzione, ma, supponendo <lb/>che i sali e i metalli dissoluti non rimanessero ad altra forza soggetti, che <lb/>a quella della loro gravit&agrave; naturale, rettamente concludeva che, ridotti a una <lb/>certa piccolezza, era la solita tenacit&agrave; del menstruo che ve li tratteneva. </s>

<s>&Egrave; <lb/>senza dubbio una finzione alla cartesiana quella lanugine, di che egli volle <lb/>tutto intorno rivestir le molecole dell'acqua, per darsi a intendere com'elle <lb/>si tengano insieme: ci&ograve; che ora s'attribuisce all'attrazione molecolare, e quel <lb/>glutine immaginario prende il nome di coesione. </s>

<s>Ma la Fisica moderna ha <lb/>confermato esser di fatto nell'acqua, a volerne staccare una parte dall'altra, <lb/>resistenza molto maggiore di quella, che non avessero pensato il Borelli, e <lb/>Lodovico delle Colombe. </s></p><p type="main">

<s>Quel Gay-Lussac, che il Laplace diceva aver introdotto in questo genere <lb/>d'esperienze <emph type="italics"/>l'exactitudo des observations astronomiques<emph.end type="italics"/> (Mecanique cele&shy;<lb/>ste, T. IV, Supplement II, pag. </s>

<s>76) misurava la detta resistenza alla separa&shy;<lb/>zion delle parti dal peso, che si doveva aggiungere a uno de'bracci della <lb/>bilancia, per far sollevar l'altro, da cui pendeva una lamina di vetro, appli-<pb xlink:href="020/01/3330.jpg" pagenum="291"/>cata alla superficie dell'acqua. </s>

<s>Altri fisici osservarono che questo modo di <lb/>sperimentare non era esatto, e insomma Tommaso Young ridusse quelle mi&shy;<lb/>sure tali, che parvero esagerate, ma che pure confermavano la legittimit&agrave; <lb/>della difesa del Borelli a favore di Lodovico delle Colombe, e contro Gali&shy;<lb/>leo. </s>

<s>N&egrave; si volle questa difesa limitare alla detta propriet&agrave; dell'acqua, ma si <lb/>estese all'efficacia, che ha la viscosit&agrave; stessa nel sostener le tavolette d'ebano, <lb/>o d'altre pi&ugrave; gravi materie, incominciandosi a dimostrar cos&igrave;, nel citato libro <lb/><emph type="italics"/>De motion. </s>

<s>natural.,<emph.end type="italics"/> la CLVIII proposizione: &ldquo; Dici potest quod revera adsit <lb/>pusilla aliqua resistentia, cum dura lamina fluidum penetrat, et confricat la&shy;<lb/>terales partes eius &rdquo; (pagi 331), ch'era ci&ograve; insomma, che contro Galileo si <lb/>voleva sostener dal Colombo, la completa rivendicazion del quale, dalle pa&shy;<lb/>tite oppressioni, non si fece per&ograve;, com'ora siam per narrare, che un secolo <lb/>e mezzo pi&ugrave; tardi. </s></p><p type="main">

<s>La filosofica libert&agrave; del Borelli, la quale aveva dato animo al Montanari, <lb/>infin da quando si manifest&ograve; dai privati consessi accademici, parve aver rotto <lb/>ogni vincolo, dopo la pubblicazione del libro <emph type="italics"/>De motionibus naturalibus.<emph.end type="italics"/><lb/>S'era aggiunto allora un altro validissimo motivo di disertare dalle opinioni <lb/>di Galileo, il quale, a spiegar certi fatti, che s'attribuivano comunemente alla <lb/>viscosit&agrave;, come per esempio il rotondarsi le gocciole della pioggia e della ru&shy;<lb/>giada; invocava <emph type="italics"/>una dissensione tra l'aria e l'acqua<emph.end type="italics"/> (Alb. </s>

<s>XIII, 73) essen&shy;<lb/>dosi fatto oramai pubblicamente noto, per l'esperienze dell'Accademia del <lb/>Cimento, che le dette gocciole serbano la medesima forma rotonda, anche <lb/>nel vuoto torricelliano. </s>

<s>Di qui &egrave; che, del sostenersi i globi d'acqua assai <lb/>rilevati e grandi, nessuno pens&ograve; pi&ugrave; che la causa risedesse di fuori, come <lb/>nel primo dialogo delle due nuove Scienze insinuava il Salviati, ma, tutti <lb/>essendo ben persuasi che dovesse essere interna, si volsero con gran pre&shy;<lb/>mura a cercarla. </s></p><p type="main">

<s>&Egrave; fra costoro da annoverare principalmente Giuseppe Del Papa, il quale, <lb/>ripensando come si potesse conciliare la fluidit&agrave; con certi fatti, che mostra&shy;<lb/>vano essere le liquide particelle fra loro insieme tenaci; immagin&ograve; di esse <lb/>particelle una costituzione molto diversa da quella, ch'era stata descritta dal <lb/>Borelli, dicendole composte di un nucleo duro, involto da una membrana <lb/>tessuta di fila resistenti, contrattili e appiccaticce. </s>

<s>&ldquo; Anzi, egli aggiunge, le <lb/>medesime membrane, nei sopradetti corpulenti ed opachi liquori, appariscono <lb/>con assai di chiarezza, essendo che alcune di esse possano ancora distaccarsi <lb/>dalle fluide particelle, merc&egrave; della quale separazione quegli stessi liquori vie <lb/>pi&ugrave; liquidi e pi&ugrave; purgati divengono. </s>

<s>Ed &egrave; ci&ograve; manifesto ad ognuno, il quale <lb/>abbia alcuna volta, per mera curiosit&agrave;, maneggiato l'argentovivo o i metalli <lb/>liquefatti, perocch&egrave;, comprimendo, con un ferro o con altro solido corpo, una <lb/>qualche loro porzione, si vedono da essa immantinente fuggire alcune parti <lb/>fluide, restando al predetto ferro attaccate ed immobili alcune altre parti, <lb/>inabili per loro medesime a fluire ed a scorrere, la di cui materia vedesi <lb/>essere a guisa di una pelle molto flessibile, e idonea ad attaccarsi seco me&shy;<lb/>desima e con molti altri corpi, da cui sia toccata, la qual materia molto pro-<pb xlink:href="020/01/3331.jpg" pagenum="292"/>babile cosa &egrave; che ella, quand'era nella composizion del metallo, facesse l'of&shy;<lb/>ficio d'involucro o di vesta ai volubili corpicelli di esso &rdquo; <emph type="italics"/>(Della natura <lb/>dell'umido e del secco,<emph.end type="italics"/> Firenze 1681, pag. </s>

<s>117). </s></p><p type="main">

<s>&Egrave; manifesto di qui esser sovvenuta l'immagine di cos&igrave; fatte pellicole <lb/>superficiali da ci&ograve;, che &egrave; un effetto estraneo alla natura del liquido metallo, <lb/>com'&egrave; estraneo anche all'acqua, la pellicola involgente la quale, visibile con <lb/>assai chiarezza, &egrave; dovuta talvolta al carbonato di calce, che si forma al con&shy;<lb/>tatto con l'aria. </s>

<s>Ma, indipendentemente da ogni azione chimica, non pote&shy;<lb/>vano essere sfuggite all'osservazione le colmature de'bicchieri, ne'quali par <lb/>che naturalmente vi sia ritenuta l'acqua dalla resistenza di un panno, cuci&shy;<lb/>tovi intorno agli orli, e che a squarciarlo fa per la rottura versare il liquido <lb/>contenuto. </s>

<s>N&egrave; poteva non esser palese al senso quella borsa di pelle, che <lb/>circonda le gocciole della pioggia: borsa che, nel cader su un piano duro e <lb/>asciutto, per la diminuita capacit&agrave; nello schiacciarsi, si squarcia e getta il <lb/>liquido che aveva dentro in que'filamenti, de'quali ella stessa tutto intorno <lb/>s'irraggia. </s>

<s>A che s'aggiunga, come pi&ugrave; evidente di tutte le altre, la quoti&shy;<lb/>diana osservazione dell'acqua pannicolata intorno agli orli degli anelli, o alle <lb/>maglie delle reti da pescare, nell'estrarle dai fiumi. </s></p><p type="main">

<s>Che non fossero poi questi pannicoli illusioni l'avr&agrave; persuaso al volgo <lb/>le mille volte il vederli sostenere, senza sfondarsi, i granelli dell'arena, a caso <lb/>rimastivi sopra. </s>

<s>Conferiva ci&ograve; molto a confermare che non fossero illusioni <lb/>nemmeno le pellicole involgenti i colmi dei piccoli vasi, d'onde prendevasi <lb/>ragionevole occasione di credere che simile avvenisse anche ne'vasi pi&ugrave; lar&shy;<lb/>ghi, l'acqua de'quali avesse la superficie coperta come da un sottilisssimo <lb/>lenzuolo, distesovi sopra. </s>

<s>Da questo sostenuti gl'insetti, conosciuti sotto il <lb/>nome di <emph type="italics"/>idrometri,<emph.end type="italics"/> passeggiano sopra gli stagni a piedi asciutti, e le mo&shy;<lb/>sche pure son sostenute da quel medesimo velo, che cede alquanto senza <lb/>rompersi sotto i loro piedi, com'ebbe a osservare il Newton, bench'egli at&shy;<lb/>tribuisca il fatto a una causa pi&ugrave; sottile, cio&egrave; alla repulsione molecolare. <lb/></s>

<s>&ldquo; Porro eidem vi repellenti tribuendum videtur quod muscae in aqua inam&shy;<lb/>bulent, nec tamen pedes suos madefaciant &rdquo; <emph type="italics"/>(Op. </s>

<s>optica omnia,<emph.end type="italics"/> Patavii 1773, <lb/>pag. </s>

<s>162). E alla medesima resistenza della pellicola superficiale si deve at&shy;<lb/>tribuire il sostenersi a galla quelle minute polveri terrose, che sulla super&shy;<lb/>ficie di un'acqua ferma vi lasciano talvolta cadere i venti. </s></p><p type="main">

<s>Tutte queste osservazioni, applicate al galleggiare delle assicelle d'ebano, <lb/>sarebbero state altrettanti validissimi argomenti, da decidere la questione agi&shy;<lb/>tatasi nel famoso Discorso intorno a quelle cose che stanno o che si muo&shy;<lb/>vono per l'acqua, ma la sentenza non avrebbe forse avuto ancora l'autorit&agrave; <lb/>necessaria, per far cancellare dal libro dell'Idrostatica un insegnamento di <lb/>Galileo. </s>

<s>Quell'autorit&agrave; dunque, che le mancava, venne presto ad acquistarla, <lb/>quando salirono in potenza gl'insegnamenti neutoniani, per i quali si ven&shy;<lb/>nero a ridurre alla loro vera e propria natura que'vischi e quelle mem&shy;<lb/>brane, intorno a che il Borelli e il Del Papa avevano lavorato pi&ugrave; di fanta&shy;<lb/>sia, che di scienza. </s></p><pb xlink:href="020/01/3332.jpg" pagenum="293"/><p type="main">

<s>Essere la viscosit&agrave; de'liquidi un effetto dell'attrazion molecolare, che si <lb/>distinse col nome di <emph type="italics"/>coesione,<emph.end type="italics"/> conseguiva immediatamente dalle nuove dot&shy;<lb/>trine, ma intorno a quelle pellicole superficiali i neutoniani stessi rimasero <lb/>incerti. </s>

<s>Il Monge, il Rumfort, l'Young, che ci dispensano dal nominarne <lb/>altri, seguitarono ad usare il medesimo linguaggio metaforico del nostro Del <lb/>Papa, infino al Laplace, da cui i Fisici derivarono il vero, riducendone a pi&ugrave; <lb/>legittima conclusione il ragionamento di lui, ch'&egrave; tale: Se in mezzo a una <lb/>massa indefinita d'acqua stagnante s'immagina un canale infinitamente <lb/>stretto, e di pareti infinitamente sottili, con le sue due estremit&agrave; a fior <lb/>d'acqua, tutti gli strati liquidi, situati in esso canale a sensibili distanze dal <lb/>supremo livello, saranno ugualmente premuti da una parte e dall'altra. <lb/></s>

<s>&ldquo; Chaque couche du liquide interieur est donc comprim&eacute;e par ces deux for&shy;<lb/>ces oppos&eacute;es. </s>

<s>A la surface du liquide, cette compression est evidemment <lb/>nulle &rdquo; <emph type="italics"/>(Supplement II cit.,<emph.end type="italics"/> pag. </s>

<s>74). </s></p><p type="main">

<s>I Fisici per&ograve; non convennero in questa sentenza, la quale parve a loro <lb/>essere stata pronunziata dal riguardare la massa liquida come continua, e <lb/>non come discreta ne'suoi atomi componenti, sollecitati ciascuno da una forza <lb/>attrattiva verso tutti gli altri, che lo circondano, e che riattraggono scambie&shy;<lb/>volmente con forze uguali da tutte le parti, cosicch&egrave; ognuno si rimane al <lb/>suo posto in equilibrio. </s>

<s>Ma se cos&igrave; &egrave; dentro il liquido, diversamente avviene <lb/>alla superficie, gli atomi componenti la quale non son cos&igrave; attratti dai so&shy;<lb/>prastanti, che non esistono, come dai sottostanti, verso i quali debbon dun&shy;<lb/>que, al contrario di quel che aveva sentenziato il Laplace, patire una pres&shy;<lb/>sione, da cui solamente, e non da altro, dipende quella maggior coerenza, <lb/>che la stessa superficie liquida fece rassomigliare a una membrana. </s></p><p type="main">

<s>A questo punto si cred&egrave; la Scienza di esser giunta a tale autorit&agrave;, da <lb/>dar sentenza definitiva nella disputa, che Galileo ebbe co'peripatetici intorno <lb/>al galleggiare dei corpi, e per pronunziarla si serv&igrave; del ministero di Giovan <lb/>Batista Venturi. </s>

<s>Egli, descrivendo gli sperimenti fatti in questo proposito, dice <lb/>di aver preso dischi di latta unti con burro, e posatili lievemente sull'acqua <lb/>aver trovato che si scavavano una fossetta, non per&ograve; tanto fonda, quanto si <lb/>sarebbe richiesta, perch&egrave; si potesse attribuire il galleggiamento al solo equili&shy;<lb/>brio idrostatico, e cos&igrave; ne concluse: &ldquo; A sostenere i dischi, oltre l'equilibrio <lb/>della gravit&agrave;, concorre l'altra cagione della consistenza della pellicola dell'acqua, <lb/>la quale non pu&ograve; cedere all'interno senza spinger fuori, sia all'alto, sia ai lati <lb/>del colmo, le parti vicine, sicch&egrave; queste resistono per la loro coesione super&shy;<lb/>ficiale. </s>

<s>Quindi i piccoli dischi profondan la pozza notabilmente meno di ci&ograve;, <lb/>che importerebbe l'equilibrio della gravit&agrave; &rdquo; <emph type="italics"/>(Memorie cit.,<emph.end type="italics"/> pag. </s>

<s>201). </s></p><p type="main">

<s>Aveva dunque ragione Lodovico delle Colombe a dire che, non dubi&shy;<lb/>tando pure della verit&agrave; de'teoremi archimedei, non piccola parte, in soste&shy;<lb/>ner le tavolette d'ebano a galla, aveva l'ampiezza della figura, la quale trova <lb/>maggior difficolt&agrave; a rompere il velo superficiale dell'acqua, e a vincere quella <lb/>coesione delle particelle di lei, che, rappresentatasi sotto il nome di viscosit&agrave;, <lb/>Galileo cos&igrave; a torto negava. </s></p><pb xlink:href="020/01/3333.jpg" pagenum="294"/><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>La coesione tra le molecole superficiali di una massa liquida, e il for&shy;<lb/>marsi che indi nasce que'rotondi arginetti, intorno alle solide lamine gal&shy;<lb/>leggianti, si riferiscono a quel genere di fatti fisici, che si designarono col <lb/>nome di capillari, perch&egrave; si rivelano principalmente, per la somiglianza delle <lb/>cause, nell'ascese de'liquidi dentro cannellini di cos&igrave; piccolo diametro, da <lb/>passarvi appena un capello. </s>

<s>L'incertezza e l'insufficienza a penetrar le ra&shy;<lb/>gioni di questi fatti, ingenuamente confessate da Galileo, son documento certo <lb/>dello stato, in cui si trovava questa nobilissima parte della Scienza idrosta&shy;<lb/>tica a que'tempi, quando anzi i fatti stessi, pi&ugrave; notabili in tale soggetto, si <lb/>passavano inosservati. </s>

<s>Nella prefazione ai due trattati postumi del Pascal si <lb/>avverte che l'Autore, nel dimostrar l'uguaglianza di livello d'un medesimo <lb/>liquido in due vasi comunicanti, non ha eccettuato il caso, che uno dei detti <lb/>vasi sia un cannello strettissimo, perch&egrave;, quand'egli scriveva, &ldquo; on n'avoit <lb/>pas encore trouv&eacute; ces nouvelles experiences des petits tuyaux, dont l'invention <lb/>est deu&eacute; a monsieur Rho, qui a une adresse meveilleuse peur trouver de <lb/>experiences, et pour les expliquez &rdquo; <emph type="italics"/>(Traitez cit.,<emph.end type="italics"/> pag. </s>

<s>XXII). Dunque in <lb/>Francia nel 1651 non era stato ancora osservato lo spontaneo ascendere dei <lb/>liquidi ne'sottilissimi tubi, per conferma di che, nel 1645, com'osservammo <lb/>a suo luogo, il Pecquet non seppe assegnare altra causa all'impulsion del <lb/>chilo nel mesenterio degli animali, che la contrazion vermicolare dei vasi, <lb/>e la compressione toracica prodotta dai moti respiratorii. </s></p><p type="main">

<s>In Inghilterra il Boyle, che nel 1659 pubblicava i suoi Nuovi esperi&shy;<lb/>menti fisico-meccanici, confessava, nel descriver l'esperimento XXXV, d'aver <lb/>avuto poco fa da un insigne matematico amico suo la notizia delle nuove <lb/>osservazioni, fatte da alcuni francesi, de'quali dice di non sapere il nome, <lb/>ma che dovevano senza dubbio essere il Rho e il Therenot, e soggiunge <lb/>che gli torn&ograve; allora a mente d'avere osservato questa spontanea ascesa dei <lb/>liquidi in que'sottili cannellini di vetro, fatti da s&egrave; fabbricare apposta per <lb/>uso di termometri &ldquo; quamvis, casu illud evenisse suspicatus, pene animad&shy;<lb/>versum praeterierim &rdquo; <emph type="italics"/>(Opera omnia,<emph.end type="italics"/> T. I, Venetiis 1697, pag. </s>

<s>79). </s></p><p type="main">

<s>In Italia per&ograve;, anche noi ripeteremo col Borelli, <emph type="italics"/>erano queste materie <lb/>un pezzo fa considerate,<emph.end type="italics"/> e per non ritornare su quel che altrove dicemmo <lb/>del Cesalpino, che all'azion capillare dei vasi attribuiva l'ascender cos&igrave; fa&shy;<lb/>cilmente la linfa su dalle radici degli alberi ai rami; citeremo, l'Aggiunti, <lb/>le note del quale, scritte poco dopo il 1630, e in parte pubblicate dal Nelli, <lb/>riduciamo qui con fedele integrit&agrave; dai manoscritti: </s></p><p type="main">

<s>&ldquo; Lo scoprimento del moto occulto dell'acqua risolver&agrave; moltisssimi pro&shy;<lb/>blemi: I. </s>

<s>Perch&egrave; una quisquilia, festuca o paglia s'inclini all'acqua, e con <lb/>questo insegneremo il modo di fare un uccello, che di per s&egrave;, accostato al-<pb xlink:href="020/01/3334.jpg" pagenum="295"/>l'acqua, abbassi il capo e beva. </s>

<s>&mdash; II. </s>

<s>Come possino (bevere) le zanzare, <lb/>mosche, ecc., alle quali abbiamo osservato la Natura aver fatto la proboscide <lb/>piena d'umido, per cui per essa pi&ugrave; facilmente ascende l'alimento umido, <lb/>e l'estate mi sono abbattuto pi&ugrave; di una volta a vedergli in cima di essa una <lb/>sperettina di umido limpido, che da loro veniva risorbito e rigettato scam&shy;<lb/>bievolmente. (Cos&igrave; fanno) forse le api e farfalline bianche con occhi neri, <lb/>nate di que'bruchi, de'quali a questi anni ne fu tanti. </s>

<s>Queste farfalline, <lb/>come anco tutte quelle, che hanno sotto il muso un sottil filo o viticchio <lb/>avvolto in spira, si nutriscono, ne attraggono il nutrimento dai fiori o altro, <lb/>con quel filo o cannellino avvolto, che allora svolgono e distendono. </s>

<s>Le mo&shy;<lb/>sche hanno comodit&agrave; di mangiare il zucchero, perch&egrave; l'inumidiscono con <lb/>l'umido della loro proboscide, e cos&igrave; facilmente lo fanno ascendere in alto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; III. (S'intender&agrave; inoltre) come possino i moscioni succhiar dalle botti <lb/>il vino, le pulci, cimici, che hanno manifestamente un cannellino diritto in <lb/>cima al capo, ed infiniti altri animalucci: come possino, dico, nutrirsi e ci&shy;<lb/>barsi. </s>

<s>Che se non fusse questo natural movimento dell'umido nell'angustie, <lb/>gli sarebbe stato difficile l'attrarlo nel succhiare, attesoch&egrave;, a far salire e <lb/>movere l'umido in cannelli stretti, col tirare a s&egrave; il fiato, ci &egrave; fatica gran&shy;<lb/>dissima, per il molto contatto, siccome si prova in fatto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; IV. (Da ci&ograve; nasce) il velo d'acqua, che si fa alle fonti, col far che <lb/>l'acqua esca per sottilissima angustia; &mdash; V. per che causa, con un can&shy;<lb/>nello, si cavi l'acqua d'un vaso: il cannello diventa un sifone, del quale <lb/>l'estremo pi&ugrave; alto viene ad esser l'acqua intorno ad esso; &mdash; VI. perch&egrave; <lb/>si sostenghino le gocce d'acqua a un dito o altro; &mdash; VII. come si possino <lb/>nutrire le piante ed i vegetabili: il basilico minuto nell'acqua perch&egrave; cre&shy;<lb/>sca e si nutrisca: perch&egrave; si conservino i fiori in molle: perch&egrave; le spugne, <lb/>pannilini e altro attragghino l'umido: riprovar la sciocchezza de'Peripate&shy;<lb/>tici in questo proposito. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; (Da ci&ograve; pure s'intende), VIII, perch&egrave; l'acqua non si livelli in un vaso <lb/>cos&igrave; fatto (come si rappresenta dalla figura 157) ma sia pi&ugrave; alta nella can&shy;<lb/><figure id="id.020.01.3334.1.jpg" xlink:href="020/01/3334/1.jpg"/></s></p><p type="caption">

<s>Figura 157.<lb/>nella angusta; IX. perch&egrave; si dilatino le macchie di olio, <lb/>su qualunque cosa, in una piccola parte tocca dall'umido: <lb/>perch&egrave; si vegga in pi&ugrave; largo spazio bagnato un panno; <lb/>X. perch&egrave; un grano di frumento si corrompa per germo&shy;<lb/>gliare, e divenga umido, e perch&egrave; il nostro nutrimento, e <lb/>di qualsivoglia animale, divenga chilo tenuissimo, acci&ograve; pi&ugrave; <lb/>facilmente sormonti alla nutrizion delle parti. </s>

<s>Errore dei <lb/>medici nel dire che la parte da nutrirsi attragga a s&egrave; il nutrimento, essendo <lb/>l'opposto che il nutrimento sale lui a nutrire, o almeno cospira e inclina a <lb/>salire e infondersi, perch&egrave; tanto ascende in un angusto meato di carne, quanto <lb/>di vetro. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; XI. (&Egrave; di qui anco facile intendere) perch&egrave; bisogni applicare nei ne&shy;<lb/>sti e surcoli e gemme, che corrispondano co'lor meati a quelli del ramo <lb/>innestato, e l'umore subentri in essi, e non &egrave; maraviglia se, colla medesima <pb xlink:href="020/01/3335.jpg" pagenum="296"/>diligenza fatti alcuni nesti, si attaccano ed altri no, perch&egrave;, secondo che po&shy;<lb/>chi o molti meati, per i quali ha da passare il nutrimento, corrisponderanno <lb/>con quelli della parte innestata, dalla quale vien somministrato il succo nu&shy;<lb/>tritivo; succeder&agrave; il fatto: e perch&egrave;, a far questa corrispondenza, ci ha parte <lb/>pi&ugrave; la fortuna che l'arte, non arrivando il nostro senso a conoscere questa <lb/>differenza. </s>

<s>XII. (S'intender&agrave; finalmente per questo moto occulto dell'acqua) <lb/>perch&egrave;, sendo l'istessa materia il foglio e la corda, l'uno bagnato allunghi, <lb/>e l'altra si serri e indurisca: provar quel che fa un panno lino tirato su <lb/>un telaio, quale non credo che bagnato venga tirato pi&ugrave; che asciutto &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>59, 60). </s></p><p type="main">

<s>Possono di qui giudicare i Lettori quale finezza di osservazioni avesse <lb/>portato, nell'esame de'fatti capillari, l'Aggiunti, e come avesse felicemente <lb/>applicato quegli stessi fatti osservati alla soluzione de'pi&ugrave; varii e pi&ugrave; incerti <lb/>problemi della Fisica, e della Storia naturale. </s>

<s>Nonostante, a giudicare anche <lb/>meglio i meriti di lui, giova osservare com'ei riducesse sotto un'unica causa <lb/>effetti cos&igrave; molteplici, e in apparenza cos&igrave; dissomiglianti, com'&egrave; l'ascendere <lb/>il liquido per i sottilissimi tubi, sia continuati che interrotti, e il rotondarsi <lb/>le gocciole pendenti dall'estremit&agrave; di un fuscello, o il circondarsi di que'cer&shy;<lb/>chi lucidi e rilevati le superficie dell'acqua, rasente le pareti di un bicchiere <lb/>o di un pozzo. </s>

<s>Eppure anche questi fatti, o trascurati fin allora o male in&shy;<lb/>tesi, non dubit&ograve; l'Aggiunti di attribuire al moto occulto dell'acqua, riducen&shy;<lb/>doli insomma, come poi fecero i Fisici, al medesimo genere de'fenomeni <lb/>capillari. </s></p><p type="main">

<s>&ldquo; In puteorum aquis quid sit lucidus ille circulus, qui in summae aquae <lb/>extremo habitu circumquaque visitur, aquae clandestina motio docebit. </s>

<s>Aquae <lb/>gutta digito, aut bacillo, pendula, adhaerescit nec decidit, non quia glutine <lb/>aliquo eius partes iungantur, nam, si hoc esset cum guttulam illam penden&shy;<lb/>tem alteri corpori paullatim admovimus, et vix minima eius particula corpus <lb/>aliquod tangimus, cur statim distrahitur et alteri corpori, cui admovetur, se <lb/>iungit, nec eo glutine impeditur? </s>

<s>Profecto tunc multo magis digito tota hae&shy;<lb/>rere deberet, cum non adeo suo pondere degravetur, sed subiecto plano su&shy;<lb/>stineatur. </s>

<s>Non tamen sustinet; ergo neque hoc argumento aquae gluten ali&shy;<lb/>quod esse probatur, neque aquae suspensionis causa redditur, quae non <lb/>aliunde petenda est, nisi ab illo quem diximus motum occultum aquae ad <lb/>omnes partes &rdquo; (ibid., fol. </s>

<s>61). </s></p><p type="main">

<s>Quale efficacia avessero queste tradizioni, a far progredire in Italia la <lb/>fisica dei capillari, non &egrave; difficile indovinarlo, ripensando che l'Aggiunti do&shy;<lb/>vette aver diffusa dalla Cattedra pisana la notizia de'fatti osservati, e la sco&shy;<lb/>perta dell'occulta causa, dalla quale, secondo lui, eran prodotti. </s>

<s>I cenni, <lb/>che ne fa ne'suoi <emph type="italics"/>Circoli<emph.end type="italics"/> il Beriguardi, starebbero a confermare una tale <lb/>opinione. </s></p><p type="main">

<s>Comunque sia, i rivoli sotterranei delle dette tradizioni, bench&egrave; trape&shy;<lb/>lino pi&ugrave; su da molte parti, non si vedono scaturire all'aperto, che nelle <lb/>prime sessioni dell'Accademia del Cimento. </s>

<s>Fedel guida di questi, non altro <pb xlink:href="020/01/3336.jpg" pagenum="297"/>per verit&agrave; che sprazzi o zampilli, ci sono i Diarii, in uno de'quali si legge: <lb/>&ldquo; A'di 22 Giugno 1657, si prov&ograve; quanto salisse l'acqua in proporzione del <lb/>suo scendere, e si trov&ograve; che in un sifone, che abbia l'istesso diametro, tanto <lb/>nella scesa quanto nella ritorta, sale a capello quanto scende. </s>

<s>Ma se il sifone <lb/>sar&agrave;, dalla parte dove sale, stretto assaissimo, come nella figura 157; allora, <lb/>essendo pi&ugrave; grosso di dove scende, sale notabilmente pi&ugrave; su che non cala &rdquo; <lb/>(Targioni, <emph type="italics"/>Notizie degli aggrandimenti ecc.,<emph.end type="italics"/> T. II, Firenze 1780, pag. </s>

<s>652). </s></p><p type="main">

<s>Par che si volesse dare a questi studii principio col confermar l'espe&shy;<lb/>rienza dell'Aggiunti, ma si fecero presto notabili progressi, e il di 29 Lu&shy;<lb/>glio appresso si osservarono, di differenti fluidi, <emph type="italics"/>le differenze dell'ascenso <lb/>per un sifoncino di cristallo, assai ben lavorato, e d'apertura quanto vi <lb/>potesse entrare uno spillo di mediocre grandezza<emph.end type="italics"/> (ivi, pag. </s>

<s>657). Nel d&igrave; 11 <lb/>poi del seguente Agosto, fu riconosciuto un fatto importantissimo e nuovo, <lb/>che cioe, &ldquo; dove gli altri liquidi s'alzano in velo sottilissimo, come argini <lb/>intorno ad un solido, o sia stilo o cilindro immerso in essi; l'argento vivo <lb/>per contrario attorno attorno si profonda, arginandosegli incontro all'ingi&ugrave; &rdquo; <lb/>(ivi, pag. </s>

<s>637, 38). </s></p><p type="main">

<s>Pochi giorni prima per&ograve; aveva il Segretario dell'Accademia registrato <lb/>nel Diario l'osservazione di certi fatti, intorno a cui ci dobbiamo intratte&shy;<lb/>nere alquanto, non perdonando a interrompere e accavallare il filo della sto&shy;<lb/>ria. </s>

<s>Quel che ivi s'ha in proposito &egrave; questo: &ldquo; A'd&igrave; 7 Agosto 1657. Di vari <lb/>galleggianti alcuni si profondano sotto il livello dell'acqua, facendosi attorno <lb/>arginetti, altri s'inalzano, come un velo sottilissimo, a foggia di padiglione. </s>

<s><lb/>Ora questi accostandosi a quei primi, come attratti da virt&ugrave; magnetica, sol&shy;<lb/>levandoli dal loro abbassamento gli attraggono, facendoli salire sul velo al&shy;<lb/>zato attorno di loro medesimi &rdquo; (ivi, pag. </s>

<s>654). </s></p><p type="main">

<s>Chi prima s'&egrave; imbattuto a legger ci&ograve;, sentesi curioso di domandare: &egrave; <lb/>ella questa un'osservazione a que'tempi nuova, o gli Accademici almeno <lb/>la credevano tale? </s>

<s>Per rispondere convien travalicare dieci anni, a leggere, <lb/>nei <emph type="italics"/>Pensieri fisici matematici<emph.end type="italics"/> del Montanari, l'elenco di quelle XXXVI espe&shy;<lb/>rienze intorno a vari fenomeni capillari, che l'Autore dice essersi istituite <lb/>nella bolognese Accademia dell'abate Sampieri. </s>

<s>Le XXXIII, XXXIV e XXXV <lb/>delle dette esperienze vi sono cos&igrave; descritte: &ldquo; Posti in acqua piana pi&ugrave; cor&shy;<lb/>piccioli galleggianti, in certa distanza fra loro, corrono un contro l'altro ad <lb/>accostarsi, com'avessero virt&ugrave; magnetica. </s>

<s>&mdash; Accostando un fuscello alle sud&shy;<lb/>dette cose, atto a bagnarsi, esse vi corrono, e lo seguono ovunque si muove. <lb/></s>

<s>&mdash; Se detti corpiccioli non saranno facili a inumidirsi esteriormente, invece <lb/>di accostarsi, si scostano d'insieme, e fuggono il contatto d'un fuscello che <lb/>gli s'accosti &rdquo; (Bologna 1667, pag. </s>

<s>13). </s></p><p type="main">

<s>Il libretto dov'erano, fra le altre, narrate queste esperienze, e che si <lb/>componeva di varie epistole raccolte insieme col titolo sopra detto di <emph type="italics"/>Pen&shy;<lb/>sieri fisici matematici,<emph.end type="italics"/> capit&ograve; alle mani del Borelli che, ritiratosi dalla To&shy;<lb/>scana, se ne stava allora tutto incocciato a Messina, di dove il d&igrave; primo Di&shy;<lb/>cembre 1667, dopo varie altre cose, scriveva cos&igrave; a Firenze al principe <pb xlink:href="020/01/3337.jpg" pagenum="298"/>Leopoldo: &ldquo; Ho anche avute certe epistole, ultimamente stampate dal Mon&shy;<lb/>tanari, nelle quali scrive come cosa propria quello, che egli sa essere stato <lb/>molti e molti anni prima esperimentato pubblicamente nell'Accademia di <lb/>V. A., e particolarmente pone quell'accostarsi e scostarsi fra di loro i fu&shy;<lb/>scellini galleggianti, la qual cosa ricordo a V. A. che io la prima volta la <lb/>mostrai, dodici anni sono, al serenissimo Granduca, e a V. A., e al serenis&shy;<lb/>simo signor Principe, e vi erano anco presenti, credo, il signor marchese <lb/>Corsini, ed altri signori di corte, una sera, in camera di S. A. </s>

<s>E di pi&ugrave; mi <lb/>ricordo che il signor Volunnio Bandinelli, poi cardinale, domandato dal Gran&shy;<lb/>duca della cagione, rispose esser la simpatia. </s>

<s>E poi, negli anni seguenti, <lb/>V. A. sa benissimo che, nella sua Accademia, feci pi&ugrave; volte tale esperienza, <lb/>ed al p. </s>

<s>Kircher la diedimo a bere per cosa simpatica. </s>

<s>E perch&egrave; nel mede&shy;<lb/>simo tempo dimorava a Firenze il detto Montanari, e praticando con i si&shy;<lb/>gnori Buoni <emph type="italics"/>(Del Buono)<emph.end type="italics"/> da loro s'informava di tutte le cose; non pu&ograve; alle&shy;<lb/>gare ignoranza di queste cose: parlo delle esperienze, non delle ragioni quali <lb/>adduce, che tutte gli si possono donare, per non essere il filosofare mestiero <lb/>da procuratore. </s>

<s>Ho ricordato questo a V. A., vedendo la troppa avidit&agrave; di <lb/>gloria, che ha questo giovane, e la poca gratitudine che ha con i suoi mae&shy;<lb/>stri &rdquo; (MSS. Cim., T. XIX, fol. </s>

<s>96). </s></p><p type="main">

<s>Ma chi aveva detto al Borelli che il Montanari si voleva appropriar <lb/>quelle cose? </s>

<s>Da nessuna parte degli scritti di lui apparisce per verit&agrave; che <lb/>tale fosse la sua intenzione, la quale anzi &egrave; solamente quella di raccogliere <lb/>il pi&ugrave; gran numero di fatti, alcuni, s&igrave;, nuovamente osservati, ma la mag&shy;<lb/>gior parte richiamati al cimento, per confermare la verit&agrave; di ci&ograve;, che ave&shy;<lb/>vano detto i loro primi osservatori. </s>

<s>Cos&igrave;, il Borelli, se avesse avuto l'animo <lb/>sereno, poteva aver riscontrato che, nell'elenco del Montanari, venivano quasi <lb/>tutte comprese l'esperienze varie, che il Thevenot aveva mandato per sag&shy;<lb/>gio al principe Leopoldo dei Medici, n&egrave; perci&ograve; avrebbe potuto dire che gli <lb/>Accademici di Bologna s'erano appropriate le scoperte degli Accademici pa&shy;<lb/>rigini. </s></p><p type="main">

<s>Ma &egrave; bene rammemorare alcuni esempi, ne'quali altri avrebbero potuto <lb/>reclamare con uguali, anzi con maggiori diritti, e nonostante tacquero, per <lb/>non parere ingiusti, o ridicolmente gelosi. </s>

<s>L'esperienze, che il Borelli stesso <lb/>aveva mostrate a spettacolo de'curiosi nella corte del Granduca, e poi ai <lb/>colleghi nell'Accademia, destarono, cos&igrave; com'era avvenuto d'altri soggetti, <lb/>l'emulazion del Viviani, il quale, avendo prese per galleggianti palline di <lb/>cera, e quelle monete, coniate in sottilissima foglia di argento, del valore di <lb/>sette centesimi della lira presente, allora e molto tempo di poi in corso per <lb/>la Toscana, sotto il nome di <emph type="italics"/>crazie;<emph.end type="italics"/> osserv&ograve; certi fatti, non meno spetta&shy;<lb/>colosi di quelli, de'quali s'andava tanto compiacendo il suo geloso rivale. </s>

<s><lb/>Di queste osservazioni n'&egrave; rimasto memoria in una nota, che il Viviani <lb/>stesso ci lasciava cos&igrave; manoscritta: </s></p><p type="main">

<s>&ldquo; Ne'corpi galleggianti (due palle di cera) argine con argine si unisce, <lb/>cio&egrave; alto con alto. </s>

<s>Due crazie, fossa con fossa, s'uniscono, cio&egrave; basso con <pb xlink:href="020/01/3338.jpg" pagenum="299"/>basso. </s>

<s>Una palla e una crazia, argine con fossa, si sfuggono, cio&egrave; alto con <lb/>basso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Su l'acqua di un bicchier colmo posata una crazia, che si fa argine <lb/>intorno, ed un fiocchetto di bambagia asciutta, posto leggermente in mezzo, <lb/>corre alle sponde, perch&egrave; scende per un piano inclinato, e perch&egrave; basso con <lb/>basso s'uniscono. </s>

<s>Legnuzzi galleggianti su dett&agrave; acqua colma, che s'inzup&shy;<lb/>pino e s'immergano sotto il livello, alzandosi argini attorno, posti alle sponde <lb/>tornano verso il mezzo, perch&egrave;.... o perch&egrave; alto con basso si fuggono &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>11). </s></p><p type="main">

<s>Ora, la seconda parte di questa descrizione corrisponde perfettamente <lb/>con l'esperienze scritte sotto i numeri XXX e XXXI del Montanari: &ldquo; Se <lb/>si pongono corpiccioli galleggianti sulla superficie dell'acqua d'un vaso colmo, <lb/>ancorch&egrave; s'applicassero alle parti basse del liquido vicino all'orlo, montano <lb/>in alto, n&egrave; di li scendono. </s>

<s>&mdash; Se si pone in detti vasi bambagia, lana o altro <lb/>corpo, che non cos&igrave; facilmente s'inumidisca, fanno contrario effetto, scen&shy;<lb/>dendo in mezzo ne'vasi non pieni, e cadendo dal colmo verso l'orlo, ne'vasi <lb/>colmeggianti e untuosi &rdquo; <emph type="italics"/>(Pensieri fisici matem. </s>

<s>cit.,<emph.end type="italics"/> pag. </s>

<s>12, 13). </s></p><p type="main">

<s>Si dir&agrave; che il Montanari seppe anche ci&ograve; dai signori Buoni? </s>

<s>Ma questa <lb/>volta si sarebbe potuto risparmiar l'industria di spiare il segreto, essendo <lb/>in pubblico rivelato da Isacco Vossio, nel suo libro pubblicato nel 1663 al&shy;<lb/>l'Aia col titolo <emph type="italics"/>De motu marium et ventorum.<emph.end type="italics"/> Quivi, contratto il mare in <lb/>un bicchier d'acqua, e un gran naviglio in un guscio di castagna, vede <lb/>fra'due galleggianti l'Autore una stupenda analogia, perch&egrave;, come il navi&shy;<lb/>glio in superar l'equatore ascende facilmente il clivo dell'acqua, ma ascesovi <lb/>difficilmente ne discende; cos&igrave; fa il guscio che, messo nel bicchiere scemo, <lb/>si vede &ldquo; ad marginem confluere et altiora petere, idque tanto velocius, <lb/>quanto propius a margine abfuerit. </s>

<s>Affundatur dein leniter alia aqua, et im&shy;<lb/>pleatur vitrum, ita ut aqua protuberet et excedat crepidinem, illicoque vi&shy;<lb/>debis corpuscula istaec, relicta ora, ascendere versus medium et ibi consi&shy;<lb/>stere &rdquo; (pag. </s>

<s>43). </s></p><p type="main">

<s>Il Vossio stava troppo lontano, per sapere quel che si stampava a Bo&shy;<lb/>logna, ma &egrave; certo che il libro dei <emph type="italics"/>Pensieri fisici matematici<emph.end type="italics"/> recapit&ograve; al <lb/>Viviani, che vi lesse le sue proprie osservazioni, e non se ne offese, n&egrave; re&shy;<lb/>clam&ograve;. </s>

<s>Giova anzi credere sentisse gratitudine verso il Montanari, che pub&shy;<lb/>blicamente confermava l'esattezza delle osservazioni, e dall'altra parte pen&shy;<lb/>sava che di nessuna disse il nome proprio degli osservatori, perch&egrave;, ad asserir <lb/>con coscienza una tal propriet&agrave; di tutte, gli mancavano i documenti. </s></p><p type="main">

<s>Mancavano questi documenti particolarmente rispetto al Borelli, l'espe&shy;<lb/>rienze del quale non appartenevano per diritto a lui solo, ma a tutta l'Ac&shy;<lb/>cademia. </s>

<s>Tanto &egrave; vero che Donato Rossetti, alle orecchie del quale non erano <lb/>ancora giunti da Messina i rumori, accennando, in principio al Dialogo se&shy;<lb/>condo della sua <emph type="italics"/>Antignome,<emph.end type="italics"/> all'esperienze fatte in Bologna, ingenuamente <lb/>soggiungeva: &ldquo; oppure, come confessa il signor Montanari, osservate nella <lb/>corte di Toscana, prima che in niuno altro luogo &rdquo; (Livorno 1667, pag. </s>

<s>51). <pb xlink:href="020/01/3339.jpg" pagenum="300"/>Ma il Borelli, che attendeva allora a scrivere il suo libro <emph type="italics"/>De motionibus <lb/>naturalibus,<emph.end type="italics"/> in cui le attrazioni e le repulsioni dei piccoli galleggianti do&shy;<lb/>vevano fare la loro prima e solenne comparsa; si sdegnava pi&ugrave; fieramente <lb/>che mai che un giovane suo discepolo, vinta la gratitudine dall'ambizione, <lb/>l'avesse cos&igrave; prevenuto. </s>

<s>Nel turbine della quale ira temendo di trovarsi an&shy;<lb/>che involto il Rossetti, penso di ripararsene alla prima occasione, che gli si <lb/>porse nel 1668, quando pubblic&ograve; l'opuscolo delle <emph type="italics"/>Sette proposizioni,<emph.end type="italics"/> nella <lb/>sesta pagina innumerata del quale, tra le altre cose, che prega voler tener <lb/>bene a mente i lettori, mette anche questa: &ldquo; Che fu pi&ugrave; che inavvertenza, <lb/>quando al suo luogo non confessai che l'eccellentissimo signor dottor Bo&shy;<lb/>relli fosse il primo osservatore, ed il primo che agli altri lo mostrasse, di <lb/>quell'incontrarsi e fuggirsi che fanno i fuscelli o altro che galleggi. </s>

<s>&rdquo; </s></p><p type="main">

<s>Ma con qual pudore si potesse pretendere un tal primato, e con qual <lb/>coscienza si potesse essere di una tal pretensione cos&igrave; facili fautori, non si <lb/>comprende. </s>

<s>L'incontrarsi e il fuggirsi, che fanno i fuscelli bagnati, era stato <lb/>osservato e descritto in un libro de'pi&ugrave; celebri, e da cui come dalla pi&ugrave; <lb/><figure id="id.020.01.3339.1.jpg" xlink:href="020/01/3339/1.jpg"/></s></p><p type="caption">

<s>Figura 158.<lb/>larga fonte, infin dal primo anno del secolo XVII, era <lb/>scaturita, e seguitava a diffondersi per tutto una delle <lb/>pi&ugrave; nobili parti della Filosofia sperimentale. </s>

<s>Guglielmo <lb/>Gilbert, nel capitolo secondo del secondo libro <emph type="italics"/>De ma&shy;<lb/>gnete,<emph.end type="italics"/> scriveva queste parole: &ldquo; Perinde uniri corpora <lb/>contendunt, et moventur in superficie aquarum veluti <lb/>bacillum quod immittitur paululum in aquas. </s>

<s>Manife&shy;<lb/>stum est quod EF (fig. </s>

<s>158) bacillum, quod propter <lb/>corticem H natat in aqua, et finem habet tantum F <lb/>udum supra superficiem aquarum, attrahitur a ba&shy;<lb/>cillo C, si bacillum C udum fuerit paululum sopra aquae superficiem..... <lb/>Sin vero bacillum totum supra aquam siccum fuerit, non amplius attrahit sed <lb/>fugat virgulam EF. </s>

<s>In bullis etiam illis idem conspicitur, quae in aqua fue&shy;<lb/>rint: videmus enim unam ad aliam appellere, et eo velocius quo proximiora <lb/>fuerint &rdquo; (Londini 1600, pag. </s>

<s>57, 58). </s></p><p type="main">

<s>Pi&ugrave; gran maraviglia fa la temerit&agrave; del Borelli, in quanto che egli stesso <lb/>narra di essersi incontrato a osservar l'amplesso e la fuga de'piccoli na&shy;<lb/>tanti, all'occasione di voler verificare se i filamenti di ferro, posti su un su&shy;<lb/>ghero nell'acqua, prendano spontaneamente la direzione medesima, che ave&shy;<lb/>vano nel batterli sull'incudine, <emph type="italics"/>ut Gulielmus Gilbertus ait.<emph.end type="italics"/> Potrebb'essere <lb/>che la mente del Borelli si concentrasse cos&igrave; nel concetto, da creder sua <lb/>l'esplicazion del Gilberto, ma non si pu&ograve; tanto concedere alle illusioni pa&shy;<lb/>terne, che, nello stesso atto di carezzare il parto, non si dovesse accorgere <lb/>che non era legittimo. </s>

<s>In pi&ugrave; di trent'anni, che dur&ograve; questa illusione, biso&shy;<lb/>gna dir che il Borelli non tornasse mai pi&ugrave; a svolgere il libro <emph type="italics"/>De magnete,<emph.end type="italics"/><lb/>o che tornandovi non posasse mai gli occhi sopra quelle figure de'fuscelli <lb/>bagnati, con largo margine intercalate a illustrare la descrizione del testo. </s></p><p type="main">

<s>In qualunque modo, non essendo a noi possibile penetrare cos&igrave; fatti se-<pb xlink:href="020/01/3340.jpg" pagenum="301"/>greti, seguitiamo il Borelli nelle sue proprie illusioni. </s>

<s>Incomincia il capi&shy;<lb/>tolo IX <emph type="italics"/>De motionibus naturalibus<emph.end type="italics"/> col dire che erano passati <emph type="italics"/>fere triginta <lb/>duo anni,<emph.end type="italics"/> da che all'occasione di verificare il detto del Gilberto, &ldquo; mirabile <lb/>spectaculum se se obtulit, hactenus non animadversum, quod nimirum ali&shy;<lb/>quae extremitates natantium corporum avido cursu se uniebant amplecte&shy;<lb/>banturque, aliae vero segregabantur, non secus ac in magnete et ferro con&shy;<lb/>tingit &rdquo; (pag. </s>

<s>386). </s></p><p type="main">

<s>Essendo queste parole pronunziate nel 1670, dunque il maraviglioso <lb/>spettacolo dell'amore e dell'odio de'piccoli galleggianti s'offerse, infin dal <lb/>1638, agli occhi del Borelli, il quale, scrivendo poi nel 1667 esser dodici <lb/>anni, che per la prima volta l'aveva mostrato al Granduca, e a'suoi corti&shy;<lb/>giani; ne fa argomentare che, non prima del 1655, si diffondesse la notizia <lb/>dell'esperienza nella corte di Toscana. </s>

<s>E di qui, dopo tanto divagare, viene <lb/>la risposta alla domanda, che speriamo i nostri Lettori non abbiano dimen&shy;<lb/>ticata: l'osservazione fatta il d&igrave; 7 Agosto 1657 non riusciva agli Accademici <lb/>cosa nuova, ma il Borelli, che l'aveva prima proposta ai cortigiani curiosi, <lb/>tornava ora a ripeterla, in quel medesimo palazzo granducale, ai suoi dotti <lb/>Colleghi, de'quali, ripigliando il filo della storia, vorremmo seguitare a nar&shy;<lb/>rar gli esercizi intorno ai capillari, se una notizia non fosse in questo tempo <lb/>venuta a infiacchire la giovanile alacrit&agrave; di quei primi passi. </s></p><p type="main">

<s>La notizia si partecipava cos&igrave; dallo stesso Borelli, in una lettera, scritta <lb/>il d&igrave; 11 Novembre 1658 di Pisa al principe Leopoldo de'Medici: &ldquo; Il signor <lb/>Thevenot i giorni addietro mi scrisse dell'Accademia nuova di Parigi, la <lb/>quale concorse ne'medesimi pensieri di cotesta, che si fa sotto gli auspici <lb/>dei serenissimi Principi di Toscana. </s>

<s>Dice che hanno esaminato quel solle&shy;<lb/>varsi dell'acqua sopra il suo ordinario livello, quando s'immerge un sotti&shy;<lb/>lissimo cannello di vetro, e quando l'acqua &egrave; in una caraffa di collo sottile, <lb/>e si alza tanto pi&ugrave;, quanto pi&ugrave; &egrave; sottile il cannello e il collo.... Queste in <lb/>Italia, come sa V. A., sono materie un pezzo fa considerate. </s>

<s>Se poi quei <lb/>signori Francesi hanno trovato la vera ragione di tutto questo, allora dir&ograve; <lb/>che abbiano preoccupato in ci&ograve; il posto e la gloria agl'ingegni italiani &rdquo; <lb/>(Fabbroni, <emph type="italics"/>Lettere inedite,<emph.end type="italics"/> T. I, Firenze 1773, pag. </s>

<s>115, 16). </s></p><p type="main">

<s>Nonostante la baldanza di queste espressioni, &egrave; un fatto che il saper <lb/>d'aver emuli e concorrenti confer&igrave; molto a raffreddare il primo fervore negli <lb/>Accademici fiorentini, i quali, ne'd&igrave; 1, 5 e 8 Giugno 1660, si perderono inu&shy;<lb/>tilmente intorno al misurar le altezze di varie qualit&agrave; di liquidi, in un me&shy;<lb/>desimo cannello, per veder se corrispondessero con le loro gravit&agrave; in specie &rdquo; <lb/>(Targioni, T. cit., pag. </s>

<s>659, 60). </s></p><p type="main">

<s>Intanto, entrato il Thevenot in diretta corrispondenza col principe Leo&shy;<lb/>poldo, a lui presentava di Parigi, il d&igrave; 7 Aprile 1661, la nota di XXXVII os&shy;<lb/>servazioni, fatte nella nuova Accademia intorno ai fenomeni capillari, aggiun&shy;<lb/>tevi altre sei osservazioni relative al medesimo soggetto. </s>

<s>Bene esaminati in <lb/>Firenze gli articoli di questa Nota, si dov&egrave; confessare che s'erano osservate <lb/>molte cose di pi&ugrave; del semplice sollevarsi l'acqua, sull'ordinario livello, nei <pb xlink:href="020/01/3341.jpg" pagenum="302"/>sottilissimi cannelli, e ci&ograve; tanto pi&ugrave;, quanto sono pi&ugrave; stretti. </s>

<s>Potevano com&shy;<lb/>piacersi i Nostri d'essere stati primi a osservar che l'argento vivo non fa, <lb/>intorno ai solidi che tocca, un'argine ma una fossa. </s>

<s>Leggendo per&ograve; il foglio <lb/>del Thevenot ebbero a riconoscere che la loro osservazione non era com&shy;<lb/>piuta, perch&egrave; il liquido metallo non si comporta cos&igrave; con tutti i solidi, come <lb/>avevano creduto, ma solo con la maggior parte di essi, eccettuati l'oro, <lb/>l'argento, lo stagno e il piombo, ne'vasi formati da'quali, purch&egrave; siano ben <lb/>puliti, il mercurio si solleva arginandosi intorno alle pareti. </s>

<s>Il fatto &egrave; pi&ugrave; <lb/>compiutamente descritto dal Thevenot, nelle due forme seguenti: &ldquo; Se s'im&shy;<lb/>merger&agrave; in qualche parte nell'argento vivo un pezzuol di vetro, di legno, <lb/>di ferro, d'ottone, ecc., l'argento si profonder&agrave;, facendogli arginetti all'in&shy;<lb/>torno. </s>

<s>&mdash; Al contrario, tuffandoci una verghetta ben pulita d'oro, d'argento, <lb/>di stagno o di piombo, si vedr&agrave; il medesimo argento sollevarsegli intorno &rdquo; <lb/>(ivi, pag. </s>

<s>718). </s></p><p type="main">

<s>&Egrave; molto probabile che, nell'Accademia di Firenze, si verificassero que&shy;<lb/>sti con tutti gli altri fatti sperimentali, dal Thevenot particolarmente descritti, <lb/>bench&egrave; gli Accademici non si curassero di tenerne conto nei loro Diari. </s>

<s>Ma <lb/>si not&ograve; bene qualche punto, in cui le osservazioni erano discordi, come in <lb/>questa per esempio, che riguarda le differenti altezze de'liquidi nei cannel&shy;<lb/>lini, secondo le varie temperature. </s>

<s>Parve ai Francesi di poter asserir da <lb/>molte osservazioni <emph type="italics"/>che l'acqua fredda si sollevi assai pi&ugrave; della calda<emph.end type="italics"/> (Tar&shy;<lb/>gioni, T. cit., pag. </s>

<s>719) mentre i Nostri fecero per contrapposto scrivere nel <lb/>loro diario, sotto il d&igrave; 28 Novembre 1661, la conclusione seguente: &ldquo; Messo <lb/>un cannellino nell'acqua fredda, e notato l'altezza, alla quale per esso si <lb/>inalza l'acqua, votata per attrazione l'acqua fredda del vaso, e messavene <lb/>ugual mole della calda; l'altezza di quella che si solleva si mantiene l'istessa &rdquo; <lb/>(ivi, pag. </s>

<s>660). </s></p><p type="main">

<s>Molte, nella Nota dataci dai Fisici francesi, son minuzie da non doverne <lb/>menar tanta gloria, ma ci sono osservazioni nuove, l'importanza delle quali <lb/>si pu&ograve; ora stimar da noi, dopo le teorie del Clairaut e del Laplace, molto <lb/>pi&ugrave; giustamente degli Accademici di Firenze, e di quelli stessi di Parigi. </s>

<s><lb/>Tali sarebbero le seguenti: &ldquo; La superficie dell'acqua, sollevata nel cannello <lb/>inclinato e contiguo all'aria, apparisce concava. </s>

<s>&mdash; Se la figura del cannello <lb/>andasse restringendosi dall'una all'altra estremit&agrave;, quale sarebbe la figura <lb/>di un cono, l'acqua sollevata dal vertice potr&agrave; ben discendere verso la base, <lb/>purch&egrave;, voltato sossopra il cannello, si tenesse perpendicolare all'orizzonte. </s>

<s><lb/>Ma ancorch&egrave; l'acqua si fosse presso che condotta all'inferiore estremit&agrave; del <lb/>cannello, dandosi a questo una bench&egrave; minima inclinazione, quella torner&agrave; <lb/>a sollevarsi colass&ugrave;, d'onde era discesa &rdquo; (ivi, pag. </s>

<s>718, 19). </s></p><p type="main">

<s>Riconosciutasi da'Nostri la superiorit&agrave; dei Francesi, rispetto all'abbon&shy;<lb/>dante variet&agrave; e alla squisitezza delle osservazioni, non rimaneva, secondo il <lb/>proposito del Borelli, a far altro, per non lasciarsi preoccupar nella gloria, <lb/>che a ritrovare la causa vera di quegli effetti. </s>

<s>E il Borelli si lusingava di <lb/>averla ritrovata davvero, in que'fantastici macchinamenti, che poi descrisse <pb xlink:href="020/01/3342.jpg" pagenum="303"/>nel suo libro dei Moti naturali. </s>

<s>A quelle fantasie s'era, per dirla giusta, <lb/>studiato di dar qualche fondamento in certi fatti esaminati da lui stesso nel&shy;<lb/>l'Accademia, e che, essendo passati di vista ai Francesi, costituivano forse <lb/>l'unico punto della superiorit&agrave;, che, dopo il 1661, ebbero verso que'loro <lb/><figure id="id.020.01.3342.1.jpg" xlink:href="020/01/3342/1.jpg"/></s></p><p type="caption">

<s>Figura 159.<lb/>emuli gli Accademici nostri. </s>

<s>&ldquo; Sit fistula stricta vitrea (cos&igrave; pub&shy;<lb/>blicava il Borelli le sue proprie accademiche osservazioni) haec <lb/>quidem arida, perpendiculariter aquam contingens, eam elevet <lb/>per spatium BF (fig. </s>

<s>159). Si vero interne fistula prius humectata <lb/>fuerit, et deinde exinanita, in contactu aquae subiectae altius ele&shy;<lb/>vatur per spatium BE. </s>

<s>Si postea eadem fistula profundius demer&shy;<lb/>gatur infra aquam, vel inclinetur, aqua exucta maius spatium BC <lb/>occupabit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; His positis, transportetur integra fistula, una cum aqua <lb/>contenta, ab aqua ad aerem, perpendiculariter tamen erecta ad <lb/>planum horizontis: tunc effluere cunctanter conspicitur ab infimo <lb/>orificio B guttula quaedam, quae sensim colligitur tumescitque, <lb/>et hoc contingit quando valde excedens est altitudo aquae BC. </s>

<s><lb/>At si non nimia fuerit quiescet in situ perpendiculari, absque <lb/>eo quod ex orificio B defluat nova aquae gutta. </s>

<s>Modo, dum aqua <lb/>supra terminum E, versus C, perseverat, orificium fistulae B contingat <lb/>aquam vasis, vel guttulam D suspensam a palma manus, vel adhaerentem <lb/>externae et extremae parti ipsius fistulae B: videbis aquam BC deprimi deor&shy;<lb/>sum usque ad E, ubi nimirum consistebat aqua exucta e vase, quando in&shy;<lb/>terna cavitas humectata fuerat. </s>

<s>E contra, si altitudo aquae internae valde <lb/>diminuta fuerit, ut BG, tunc quidem, in contactu guttulae inferioris, augetur <lb/>eius altitudo, exugendo nimirum aquam ipsius guttulae D &rdquo; <emph type="italics"/>(De motion. </s>

<s><lb/>natur. </s>

<s>cit.,<emph.end type="italics"/> pag. </s>

<s>378, 79). </s></p><p type="main">

<s>I colleghi del Borelli avranno con applauso accolte queste dimostrazioni, <lb/>e specialmente l'osservazione, che dev'essere a loro apparita nuova, del ri&shy;<lb/>salire pi&ugrave; su il liquido ne'cannellini bagnati che negli asciutti. </s>

<s>S'&egrave; detto che <lb/>dev'essere apparita nuova, perch&egrave;, sebbene anche il Boyle avesse gi&agrave; osser&shy;<lb/>vato &ldquo; quod, quoties interna tubi superficies prius erat humore aliquo made&shy;<lb/>facta, toties quam et arida, multo melius aqua insurgeret &rdquo; <emph type="italics"/>(Opera omnia cit.,<emph.end type="italics"/><lb/>T. I, pag. </s>

<s>81); non era facile che ne foss&egrave; giunta a Firenze la notizia. </s>

<s>Ma <lb/>le ragioni che s'adducevano dal Borelli stesso a spiegare i fatti osservati <lb/>ebbero sorte molto diversa. </s>

<s>Quelle addentellature delle pareti, nelle quali si <lb/>facevano incastrar le sporgenze delle molecole liquide per salire; anzi che <lb/>ingegnose, come le teneva l'inventore, parvero cose di una meccanica troppo <lb/>volgare. </s>

<s>Pi&ugrave; ragionevole, o a dir meglio pi&ugrave; lusinghiera ai memori, e com&shy;<lb/>partecipi de'trionfi del Tubo torricelliano, riusciva la ragion di coloro, i quali <lb/>dicevano che, per le angustie de'cannellini rallentandosi all'aria la molla, <lb/>non &egrave; maraviglia se, premendovi meno, fa risalire il liquido sopra l'altezza <lb/>sua ordinaria. </s></p><p type="main">

<s>Ma svani presto anche questa lusinga. </s>

<s>In tutte l'esperienze, che dal <pb xlink:href="020/01/3343.jpg" pagenum="304"/>22 Novembre 1661, al 9 Settembre 1662, s'instituirono nell'Accademia del <lb/>Cimento, intorno ai fenomeni capillari (Targioni, T. cit., pag. </s>

<s>217, 434, <lb/>660, 661) non s'attese ad altro, se non a vedere &ldquo; se i cannellini, che at&shy;<lb/>traggono l'acqua per la immersione, l'attraessero in un vaso pien d'aria <lb/>rarissima a quell'altezza medesima, che sogliono nell'aria libera &rdquo; (MSS. <lb/>Cim., T, II, P. I, fol. </s>

<s>217). E furono i resultati pubblicamente esposti nel <lb/>libro de'<emph type="italics"/>Saggi,<emph.end type="italics"/> dove, descrivendosi le varie delicatissime esperienze intorno <lb/>al sollevamento de'fluidi, nel vano de'cannellini sottilissimi, dentro al voto; <lb/>il Segretario termina con queste parole: &ldquo; Onde, da tutte queste esperienze, <lb/>e da qualche altra di simil sorta, che ora non &egrave; tempo di raccontare, parve <lb/>ad alcuno di poter fermare che quest'opinione del premer pi&ugrave; languido, che <lb/>fa l'aria per gli angustissimi seni, presa cos&igrave; assolutamente, non sia per s&egrave; <lb/>sola bastante a spiegar questi ed altri simili effetti, ma credono che per lo <lb/>meno alcun altra cagione debba unitamente concorrervi &rdquo; (Firenze 1691, <lb/>pag. </s>

<s>CVIII). </s></p><p type="main">

<s>Si sente da queste espressioni quanto mal volentieri, quegli esecutori <lb/>fedeli e promotori indefessi dell'esperienza dell'argento vivo, abbandonassero <lb/>la speranza d'ingerire le pressioni dell'aria nella spiegazione di quegli ef&shy;<lb/>fetti. </s>

<s>Tanto era poi seducente per tutti i Fisici, specialmente italiani, quella <lb/>facile via di aprire il mistero, che molti, o ignari delle esperienze degli Ac&shy;<lb/>cademici del Cimento non ancora pubblicate, o colla speranza di deluderne <lb/>o d'attenuarne almeno il rigore della sentenza, seguitarono ad affidare il ge&shy;<lb/>loso ufficio di sostenere i liquidi nei cannellini alle differenti pressioni del&shy;<lb/>l'aria. </s>

<s>Fra costoro &egrave; da annoverare principalmente il Montanari, con tutta <lb/>l'Accademia di Bologna, alla quale nonostante &egrave; dovuto il merito d'aver ge&shy;<lb/>nerosamente proseguita l'opera, lasciata a mezzo dall'Accademia di Firenze, <lb/>per le gelosie, che si prese il Borelli del Thevenot e de'suoi partigiani. </s>

<s>I <lb/>Bolognesi invece, con animo pi&ugrave; tranquillo, riconobbero che alcune tra le <lb/>osservazioni di costoro, e delle pi&ugrave; importanti, non eran perfette, e che non <lb/>avevano posti cos&igrave; i segni agli osservatori futuri, da non rimanere a loro <lb/>nulla da scoprirvi di nuovo. </s></p><p type="main">

<s>In Parigi, per esempio, s'era solamente osservato che la superficie del&shy;<lb/>l'acqua nei cannellini <emph type="italics"/>apparisce concava,<emph.end type="italics"/> ma in Bologna si defini che cos&igrave; <lb/>era veramente, quando essi cannellini sono scemi, com'&egrave; di fatto convessa <lb/>quella medesima superficie, quando invece son colmi. </s>

<s>Vero &egrave; bene che il <lb/>Boyle, non solo aveva detto <emph type="italics"/>guod aquac superficies soleat essc concava,<emph.end type="italics"/> e <lb/>che aveva soggiunto di pi&ugrave; <emph type="italics"/>quod in hydrargirio sit convexa et depressior<emph.end type="italics"/><lb/><emph type="italics"/>(Op. </s>

<s>omnia,<emph.end type="italics"/> T. </s>

<s>I cit., pag. </s>

<s>81); ma i Nostri vi fecero intorno esame pi&ugrave; di&shy;<lb/>ligente. </s>

<s>N&egrave; s'affidarono in ci&ograve; all'occhio solo, ma all'acume di lui scorto <lb/>dalla ragione, considerando quel che dovrebbe avvenire in un vaso rotondo, <lb/>qual sarebbe un bicchiere, supposto che il diametro di lui si venisse a re&shy;<lb/>stringere via via, infino a ridursi a quello di un tubo capillare. </s>

<s>L'alzamento <lb/>dell'acqua alle sponde si mantiene, anche in questa supposizione, costante, <lb/>e fu trovato <emph type="italics"/>esser circa un quarto d'un dito sopra il livello di mezzo<emph.end type="italics"/> (Pen-<pb xlink:href="020/01/3344.jpg" pagenum="305"/>sieri fisici matem. </s>

<s>cit., pag. </s>

<s>12). Di qui &egrave; che, diminuendosi sempre pi&ugrave; il <lb/>raggio del detto vaso rotondo, si deve giungere a un punto, in cui il livello <lb/>di mezzo sparisce, e non rimangon che gli argini, i quali raggiungendosi <lb/>co'loro lembi inferiori, chiudono la superficie intera nella concavit&agrave; di un <lb/>menisco. </s>

<s>Gli Accademici di Bologna assegnarono per limiti alla diminuzion <lb/>del raggio, affinch&egrave; la liquida superficie si disponga in quella figura, una <lb/>mezz'oncia circa del loro piede. </s>

<s>&ldquo; Il tondeggiamento colmo o concavo del&shy;<lb/>l'acqua presso alle sponde, ne'vasi che non passino un'oncia circa di piede <lb/>bolognese di diametro, giunge fino al mezzo della superficie, non lasciandone <lb/>parte alcuna piana. </s>

<s>Ma in vasi di maggior larghezza ne lascia porzione <lb/>piana &rdquo; (ivi). </s></p><p type="main">

<s>Nel foglio del Thevenot niente altro pi&ugrave; si leggeva, se non che l'acqua, <lb/>ne'sifoncini ritorti e ne'cannellini diritti, <emph type="italics"/>s'alza tanto maggiormente, quanto <lb/>l'orifizio &egrave; pi&ugrave; angusto,<emph.end type="italics"/> ma i Bolognesi determinarono l'esatta proporzione, <lb/>formulando essi i primi la legge sperimentale delle altezze reciprocamente <lb/>proporzionali ai raggi dei tubi capillari. </s>

<s>&ldquo; Si &egrave; preso un cannellino sottile, <lb/>e trovato un filo d'ottone di trafila, che precisamente empiva l'interno cavo <lb/>di esso, poi s'&egrave; trovato un cannellino pi&ugrave; grosso, nel foro del quale entra&shy;<lb/>vano precisamente due dei suddetti fili del pari, onde il diametro di questi <lb/>si giudic&ograve; doppio del primo. </s>

<s>E provati ambedue con diligenza, l'acqua sa&shy;<lb/>liva nel pi&ugrave; sottile precisamente il doppio in altezza, di quello che facesse <lb/>nell'altro pi&ugrave; grosso &rdquo; (ivi, pag. </s>

<s>9, 10). </s></p><p type="main">

<s>Che poi, oltre a render compiute le osservazioni de'Francesi, i Nostri <lb/>ne trovassero da far delle nuove, se ne potrebbe persuader facilmente chiun&shy;<lb/>que percorresse quelle loro XXXVI descrizioni, fra le quali basti a noi citar <lb/>questa, che ci comparisce nella storia sotto un suo particolare aspetto di no&shy;<lb/>vit&agrave; e d'importanza. </s>

<s>&ldquo; Prese due lastre di vetro piane, legate insieme con <lb/>un foglio di carta framezzo, ed adattato in modo che, levandone il foglio <lb/>destramente, restino senza accostarsi di pi&ugrave;; applicato poi il fesso perpendi&shy;<lb/>colarmente all'acqua, essa vi s'inalza come ne'cannellini, ed il simile fa <lb/>qualsivoglia fessura di corpi solidi, purch&egrave; piccola ella sia &rdquo; (ivi, pag. </s>

<s>10). </s></p><p type="main">

<s>Dietro questi cenni, i Lettori si faranno del Montanari, e dell'Accade&shy;<lb/>mia, ch'egli col suo proprio senno presiedeva, un giudizio molto diverso da <lb/>quello, che gli avrebbero voluto insinuare le malevole parole del Borelli e <lb/>del Rossetti. </s>

<s>Meno usurpatori dell'altrui, che prodighi del proprio, que'be&shy;<lb/>nemeriti Bolognesi raccolsero tutto insieme ci&ograve; che s'era esaminato dalla Re&shy;<lb/>pubblica degli scienziati, intorno ai fenomeni capillari, e lo tramandarono <lb/>qual prezioso documento alla Storia. </s>

<s>Delle notizie poi di tali esami la rac&shy;<lb/>colta si fece pi&ugrave; dai portati della fama, che dalla lettura dei libri, i quali <lb/>non si riducevano insomma che ai soli due del Gilberto e del Grimaldi. </s>

<s>Il <lb/>celebre istitutore della Scienza del Magnete, e il non men celebre promo&shy;<lb/>tore dell'Ottica, non potevano non avere una grande efficacia in diffondere <lb/>lo studio dei fenomeni capillari sotto le loro due pi&ugrave; svariate forme dell'at&shy;<lb/>trazion de'corpuscoli galleggianti, e della salita per i sottilissimi cannelli. </s>

<s>Or <pb xlink:href="020/01/3345.jpg" pagenum="306"/>chi sa quanti altri avranno avuto l'inspirazione dal Gilbert a invenzioni an&shy;<lb/>teriori di tempo, e pi&ugrave; spettacolose nell'apparenza, di quelle stesse descritteci <lb/>dall'autor del libro dei Moti naturali? </s>

<s>Rammentiamoci dell'uccellino auto&shy;<lb/>matico dell'Aggiunti. </s>

<s>Tutti coloro dunque volevano essere saputi e comme&shy;<lb/>morati dal Montanari? </s>

<s>Ma sarebbe bastato a lui, per far giustizia di tutti, <lb/>citare il solo Gilberto, di cui anzi poteva dire che s'era appropriata l'inven&shy;<lb/>zione il Borelli. </s></p><p type="main">

<s>Il Grimaldi coglieva l'occasione, a trattar degli effetti capillari, dalla so&shy;<lb/>luzione di questo assai volgare problema: perch&egrave;, nel far la zuppa, la mi&shy;<lb/>dolla del pane attragga cos&igrave; avidamente il vino da ogni sua parte? </s>

<s>E rispon&shy;<lb/>deva che le sostanze porose, o intessute di filamenti, formano, in continuit&agrave; <lb/>fra loro, tanti sottilissimi tubi. </s>

<s>Sembra ora a noi ovvia la risposta, ma venne <lb/>di qui non lieve impulso alla Fisica capillare, e furono suggerite di qui al&shy;<lb/>cune osservazioni agli Accademici bolognesi, come quella per esempio che il <lb/>liquido sale sul convesso di pi&ugrave; cannellini legati insieme, o in que'pennelli <lb/>di vetro, che si fabbricavano in Venezia per ornamento delle donne: ma anche <lb/>meglio sentesi l'ispirazione in quest'altra esperienza, cos&igrave; descritta: &ldquo; Si <lb/>sono provati molti legni, de'quali ponendone un pezzo tagliato, come si dice, <lb/>per testa, su un piano bagnato d'acqua, si veggono comparire d'improvviso <lb/>nella parte superiore gocciole d'acqua in diversi luoghi, salite per li pori del <lb/>legno, come fa ne'cannellini, ed in breve si inumidisce tutto il legno den&shy;<lb/>tro e fuori &rdquo; (Montanari, <emph type="italics"/>Pensieri cit.,<emph.end type="italics"/> pag. </s>

<s>11). </s></p><p type="main">

<s>Ma il Montanari, cos&igrave; riferendo le cose a nome dell'Accademia, con&shy;<lb/>fessa l'efficacia ch'ebbe il Grimaldi in promovere questi loro studi, ci&ograve; che <lb/>non si poteva dir del Borelli, il libro del quale avrebbe indugiato ancora a <lb/>venire alla luce cinque anni. </s>

<s>Il sospetto delle relazioni, ch'esso Montanari <lb/>ebbe co'fratelli Del Buono, non ha nessun fondamento, e quand'anche avesse <lb/>per questo mezzo risaputo quel che s'era sperimentato nell'Accademia del <lb/>Cimento, non sarebbe stato prudenza preoccupare gli uffici del Segretario. </s>

<s><lb/>Prudenza fu invece il tacere, e nel silenzio lasciare a ciascuno osservatore <lb/>la parte del merito non distribuita, incerto cos&igrave; com'era, per mancanza di <lb/>documenti, di fare la distribuzion con giustizia. </s>

<s>Queste considerazioni poi <lb/>vogliamo applicare a noi stessi, che francamente assegniamo il primato a <lb/>quello e a quell'altro, dietro i soli documenti scarsi, che si son potuti esa&shy;<lb/>minare. </s>

<s>Ma chi sa quanti ce ne sono, non saputi da noi, i quali essendo <lb/>prodotti scoprirebbero le imperfezioni della nostra Storia, e ci meriterebbero <lb/>un'accusa, dal timor della quale fece bene a liberarsene il Montanari. </s></p><p type="main">

<s>Fin qui non abbiamo trovato concorrere nello studio di questi fatti, che <lb/>l'Italia e la Francia. </s>

<s>L'Inghilterra, non essendo troppo facile riconoscere le <lb/>relazioni, che passano fra le attrazioni elettriche de'fuscelli galleggianti de&shy;<lb/>scritti dal Gilberto, e le salite de'liquidi nei tubi capillari; dicemmo come <lb/>tardi si risvegliasse nel Boyle. </s>

<s>E anche, mentre altrove era un gran fervore, <lb/>ella parve dormirsene nell'inerzia, ma era invece quel benefico sonno, ristora&shy;<lb/>tor delle forze, che poi si risvegliarono nell'Hauksbee, e nel Newton. </s>

<s>Le loro <pb xlink:href="020/01/3346.jpg" pagenum="307"/>esperienze istituite, con non lungo intervallo di tempo, innanzi alla R. </s>

<s>Societ&agrave; <lb/>di Londra, si consociano veramente, e quasi si direbbe si contessono, come <lb/>i rami e le fronde di due alberi vicini, de'quali ora vien che descriviamo <lb/>la fraganza de'fiori, e la squisitezza dei frutti. </s></p><p type="main">

<s>Il libro delle <emph type="italics"/>Esperienze fisico-meccaniche sopra vari soggetti<emph.end type="italics"/> comparve <lb/>provvidamente in mezzo a noi, in veste italiana, e possiamo perci&ograve; conver&shy;<lb/>sare alla dimestica con l'Autore, per sapere da lui quello che pi&ugrave; c'importa. </s></p><p type="main">

<s>Le narrazioni, con le quali incomincia l'Hauksbee la V sezione, non son <lb/>altro che un autorevole conferma di cose gi&agrave; note, premendosi principal&shy;<lb/>mente nel dimostrare che non pu&ograve; esser l'aria la causa del risalire i liquidi <lb/>nei piccoli tubi (Firenze 1716, pag. </s>

<s>63-66). Divagatosi lungamente l'Autore <lb/>ne'racconti d'esperienze di vario genere, ritorna finalmente ai fenomeni ca&shy;<lb/>pillari, ora osservati in varie accidentalit&agrave; di tubi, ora nelle superficie quasi <lb/>contigue dei corpi. </s>

<s>All'ordine di queste prime osservazioni appartien la se&shy;<lb/>guente: &ldquo; Avendo procurato due tubi, i diametri delle cui cavit&agrave; erano vi&shy;<lb/>cini ad essere uguali, quanto era stato possibile il fargli, ma uno di vetro <lb/>grosso, almeno dieci volte pi&ugrave; dell'altro; gli messi nel preaccennato liquore <lb/>tinto. </s>

<s>L'effetto si fu che non si pot&egrave; distinguere differenza alcuna tra l'al&shy;<lb/>tezze, che il liquore in ambi i tubi aveva salite &rdquo; (ivi, pag. </s>

<s>123). </s></p><p type="main">

<s>Quest'osservazione dell'Accademico di Londra non vuol esser disgiunta <lb/>da quell'altre, ch'erano state fatte dagli Accademici di Bologna, quasi parti <lb/>di una medesima armatura, della quale vedremo come, a combattere gli er&shy;<lb/>rori, si servisse la teoria; perch&egrave; se, per l'Inglese, veniva a escludersi dalle <lb/>cause dell'ascesa del liquido la grossezza del tubo, per i Nostri era venuta <lb/>a escludersene altres&igrave; la lunghezza. </s>

<s>&ldquo; Dop'avere adoperato un cannellino <lb/>assai lungo (si legge ne'<emph type="italics"/>Pensieri<emph.end type="italics"/> del Montanari) e notate l'altezze, ove si ri&shy;<lb/>duce l'acqua per la nona esperienza, rompendo parte del cannellino mede&shy;<lb/>simo, sino al ridurlo poco pi&ugrave; lungo di quanto s'alzava l'acqua la prima <lb/>volta; ella sempre vi saglie alla medesima altezza. </s>

<s>&mdash; Se la canna maggiore <lb/>sar&agrave; lunga due, o tre braccia o quanto si vuole, ponendoci in fondo un poco <lb/>d'acqua, v. </s>

<s>g. </s>

<s>all'altezza di un dito o due, sicch&egrave; il rimanente resti vuoto; <lb/>si solleva nel cannellino sottile con altrettanta differenza, quanta ne fa poi <lb/>togliendo via tutta la canna lunga &rdquo; (pag. </s>

<s>8, 9). </s></p><p type="main">

<s>A questo medesimo genere di osservazioni appartien quell'altra, descritta <lb/>dall'Hauksbee, intorno alla salita dell'acqua dentro un tubo pieno di cenere, <lb/>calcatavi ben bene con una bacchetta, e che pu&ograve; avere l'esempio naturale <lb/>nella straordinaria altezza, a cui giunge talvolta l'umidit&agrave; del suolo, su per <lb/>l'intonaco di una vecchia muraglia. </s>

<s>Il moto dell'ascesa, qua e l&agrave; si fa lento e <lb/>sempre pi&ugrave; ritardato, ci&ograve; che l'Hauksbee stesso attribuisce alla sempre pi&ugrave; cre&shy;<lb/>scente resistenza dell'aria, in luogo della quale vuole a forza sottentrar l'acqua. </s></p><p type="main">

<s>Quanto poi all'ascendimento de'liquidi, tra le superficie quasi contigue, <lb/>l'Hauksbee, dalle lastre di vetro, sole usate dagli Accademici di Bologna, <lb/>estese le osservazioni ai piani di marmo e di ottone, variandone la figura, <lb/>da rettangolare o quadrata, in circolare, dalla quale, fatta toccare in qualche <pb xlink:href="020/01/3347.jpg" pagenum="308"/>punto allo spirito di vino o all'olio di trementina, vedeva il liquido risalire, <lb/>in sottili filamenti divisi, con gran velocit&agrave; su agli orli, come corde, dal me&shy;<lb/>desimo punto inferiore di un diametro perpendicolare, tirate alla circonfe&shy;<lb/>renza. </s>

<s>E supponendo che giungessero que'raggi fluidi lutti a essa circonfe&shy;<lb/>renza in un tempo, come vide fare l'Hauksbee, senz'alcuna differenza no&shy;<lb/>tabile al senso, &ldquo; abbiamo qui dunque, egli dice, in un certo modo, per la <lb/>contraria, la riprova della famosa proposizione del Galileo, sopra l'equitem&shy;<lb/>poranee discese de'corpi pesanti nelle corde d'un cerchio. </s>

<s>Poich&egrave; in questo <lb/>caso l'ascendente liquido le descrive tutte in tempi eguali, come in quel caso <lb/>fa il discendente solido. </s>

<s>E se l'uno sale e l'altro scende, per virt&ugrave; d'una <lb/>medesima causa, come io non posso far di meno di non credere che segua; <lb/>egli non &egrave; maraviglia dunque che vi sia una concordia tale fra loro, e che <lb/>la medesima causa produca un somigliante effetto, cos&igrave; ne'solidi come ne'li&shy;<lb/>quidi, quando vengono supposte somiglianti circostanze per ambe le parti. </s>

<s><lb/>E il tutto per null'altro ascende, se non per l'attrazione all'in su in un <lb/>caso, e all'ingi&ugrave; nell'altro, e ci&ograve; nella medesima sorta di figura, nominata&shy;<lb/>mente in un cerchio &rdquo; <emph type="italics"/>(Esperienze fisico-meccaniche cit.,<emph.end type="italics"/> pag. </s>

<s>125, 26). </s></p><p type="main">

<s>Vedremo pi&ugrave; qua l'importanza di queste analogie tra la meccanica dei <lb/>liquidi e de'solidi, ma, per non interrompere il filo della storia, si noti qui <lb/>un'altra analogia, che intravide l'Hauksbee tra i cannelli cilindrici, e le su&shy;<lb/>perficie quasi contigue dei corpi, dicendo che queste <emph type="italics"/>compongono un tubo <lb/>della forma di un parallelepipedo, la cui grossezza &egrave; eccedentemente pic&shy;<lb/>cola<emph.end type="italics"/> (ivi, pag. </s>

<s>127). Soggiungendo poi l'Autore esser medesima la causa, che <lb/>fa ascendere il liquido per i due sottilissimi spazi, ne fa ragionevolmente <lb/>argomentare che procedessero altres&igrave; con analoghi effetti, cosicch&egrave; se per <lb/>esempio il diametro di un cannellino &egrave; un millimetro, e un millimetro pure <lb/>&egrave; la distanza fra le due lastre, il liquido giunga a pari altezza, nel cilin&shy;<lb/>dretto, e nel prisma di un millimetro di base quadrata. </s>

<s>L'argomentazione <lb/>dall'altra parte era cos&igrave; seducente, che vi rimasero presi in fallacia tutti i <lb/>Fisici, infino al Newton, a cui result&ograve;, per esperienze fatte innanzi alla R. </s>

<s>So&shy;<lb/>ciet&agrave; di Londra, che l'altezza del liquido &egrave; la medesima, non gi&agrave; quando la <lb/>distanza fra le due lastre vicine uguaglia il diametro, ma si bene il rag&shy;<lb/>gio del tubo capillare. </s>

<s>&ldquo; Quod si tubuli vitrei tenues in aquam stagnantem <lb/>ab inferiore sui parte intingantur, aqua intra tubulum ascendet, idque ea <lb/>ratione, ut eius altitudo reciproce proportionalis sit tubi cavitatis diametro, <lb/>et par altitudini aquae inter binas laminas vitreas ascendentis, siquidem tubi <lb/>cavitas semidiametro par sit, aut fere par laminarum istarum intervallo. </s>

<s>At&shy;<lb/>que horum quidem omnium experimentorum, coram Societate regia capto&shy;<lb/>rum, sive in vacuo, sive in aperto aere, unus fuit exitus &rdquo; <emph type="italics"/>(Optices,<emph.end type="italics"/> Lib. </s>

<s>III, <lb/>quaestio XXXI, Patavii 1773, pag. </s>

<s>160). </s></p><p type="main">

<s>Ma comunque fossero le ragioni, da istituirsi fra i diametri o i raggi, <lb/>rimaneva sempre vero che, anche tra le due lastre, le altezze son reciproche <lb/>alle distanze, ci&ograve; che volle sperimentare l'Hauksbee in due modi, ora sco&shy;<lb/>stando parallelamente, ora facendo inclinar l'una lastra sull'altra. </s>

<s>E perci&ograve; <pb xlink:href="020/01/3348.jpg" pagenum="309"/>sembra si debba a lui il primo la bella esperienza, che rappresenta la su&shy;<lb/>perficie del liquido fra le due lastre scendere dallo spigolo verticale, via via <lb/>disponendosi in quella curva elegante, che poi non difficilmente si dimostr&ograve; <lb/>essere una <emph type="italics"/>iperbola equilatera.<emph.end type="italics"/> &ldquo; L'altezza della salita del liquido tinto <lb/>(affinch&egrave; si sappia ci&ograve; che propriamente osserv&ograve; l'Hauksbee in questo pro&shy;<lb/>posito) variava secondo la distanza de'piani. </s>

<s>Poich&egrave;, se invece d'un pezzo <lb/>di foglio per la sua grossezza, ve n'erano posti due, il liquore non giungeva <lb/>a salire tant'alto in questo caso, come nell'altro, quando i piani erano so&shy;<lb/>lamente separati da un semplice pezzo di foglio. </s>

<s>E allora, se i piani pende&shy;<lb/>vano da qualche parte, il liquore sempre si spandeva pi&ugrave; e pi&ugrave; oltre, pro&shy;<lb/>porzionatamente al grado della declinazione. </s>

<s>E a diverse prove tutto questo <lb/>successe nel medesimo modo &rdquo; <emph type="italics"/>(Esperienze fisico-meccan. </s>

<s>cit.,<emph.end type="italics"/> pag. </s>

<s>115). </s></p><p type="main">

<s>Lo spigolo, formato dalla detta pendenza, s'intende bene come rima&shy;<lb/>nesse eretto perpendicolarmente, ma l'Hauksbee vari&ograve; il caso, tenendo la <lb/>soggetta lamina orizontale, cosicch&egrave; pure orizontale rimanesse lo spigolo, for&shy;<lb/>mato dalla congiunzione di questa con la lamina superiore. </s>

<s>Se possa aver <lb/>avuto qualche efficacia, a cos&igrave; fatte promozioni, quel che ne'tubi conici era <lb/>stato osservato dagli Accademici parigini, non &egrave; facile a decidersi. </s>

<s>Ma &egrave; un <lb/>fatto che, da'piani con i quali sperimentava il Fisico inglese, vedremo poi <lb/>ritornare ai tubi conici un Francese insigne, per quel perpetuo circolo della <lb/>vita, che si scopre fra le idee de'vari Autori, quasi corrente elettrica, che <lb/>per tacita influenza trapassa da un globo metallico a un altro, bench&egrave; vario <lb/>di materia e succedentegli a distanza. </s>

<s>Prima per&ograve; di passare a riferir ci&ograve;, <lb/>che osservasse l'Hauksbee, nel liquido interposto fra la lastra inferiore ori&shy;<lb/>zontale, e la superiore inclinata, osserviamo che la descrizione non si trova <lb/>raccolta fra le altre Esperienze fisico-meccaniche, ma in una loro Appendice, <lb/>dalla quale il Laplace la tradusse in francese <emph type="italics"/>(Supplement au X livre du <lb/>Mechan. </s>

<s>celeste)<emph.end type="italics"/> e molto prima il Newton l'aveva cos&igrave; ridotta nel libro delle <lb/>Questioni: &ldquo; Si duo planae et politae vitri laminae, uncias ternas aut qua&shy;<lb/>ternas latae, et vicenas aut vicenas quinas longae, ita disponantur, ut earum <lb/>altera horizonti parallela iaceat altera autem ei ita interponatur, ut earum <lb/>extremitates alterae se inter se contingant, angulumque circiter 10 aut 15 mi&shy;<lb/>nutorum contineant; harum autem laminarum facies interiores linteo mundo, <lb/>in mali aurei oleum vel sqiritum terebinthinum intincto prius madefiant, et <lb/>deinde olei istius, sive spiritus, gutta una vel altera in vitri inferioris extre&shy;<lb/>mum, id quod a dicto angulo maxime distat, demittatur, utique simul pri&shy;<lb/>mum ac vitri lamina superior inferiori ita superposita sit, ut eam, quomodo <lb/>supra dictum est, altera sui extremitate contingat, altera autem guttam, con&shy;<lb/>tinens nimirum cum inferiori vitro angulum circiter 10 aut 15 minutorum; <lb/>gutta continuo eam se in partem, qua parte binae laminae se contingunt <lb/>inter se, movere incipiet, motuque ferri perget perpetim accelerato, usque <lb/>dum ad ipsum vitrorum concursum perveniat. </s>

<s>Etenim bina vitra guttam at&shy;<lb/>trahunt, efficiuntque ut illa illo moveatur, quo attractiones vergunt &rdquo; <emph type="italics"/>(Opti&shy;<lb/>ces,<emph.end type="italics"/> lib. </s>

<s>cit., pag. </s>

<s>160). </s></p><pb xlink:href="020/01/3349.jpg" pagenum="310"/><p type="main">

<s>Questa esperienza fu ridotta alla sua massima semplicit&agrave;, e alla sua pi&ugrave; <lb/>conveniente significazione, per la teoria del Laplace, il quale, tornando a ri&shy;<lb/>prendere in mano uno strumento de'suoi antenati, forse da lui stesso dimen&shy;<lb/>ticato, osserv&ograve; che &ldquo; une petite colonne d'eau, dans un tube conique ouvert <lb/>par ses deux extremit&eacute;s, et maintenu horizontalement, se porte vers le som&shy;<lb/>met du tube, et la surface de la colonne fluide est concave a ses deux extre&shy;<lb/>mit&eacute;s.... Si la colonne fluide est de mercure, alors sa surface est convexe <lb/>et la colonne doit se porter vers la base du tube &rdquo; (<emph type="italics"/>Supplement I cit.,<emph.end type="italics"/><lb/>pag. </s>

<s>6, 7). Ma perch&egrave; cos&igrave; fatte esperienze si riferiscono troppo strettamente <lb/>alle teorie, delle quali non &egrave; ancora il tempo a parlare, giova porre il ter&shy;<lb/>mine alla presente storia col rammemorare un fatto singolarissimo, che, ap&shy;<lb/>parito ai Fisici senza legge, il Newton ridusse al genere de'fenomeni ca&shy;<lb/>pillari. </s></p><p type="main">

<s>Negli Esperimenti fisico-meccanici del Boyle, pubblicati nel 1661 in in&shy;<lb/>glese, e nell'anno appresso tradotti in latino, si leggeva la descrizione di <lb/>quel tubo di vetro da termometri, che pieno d'acqua, e secondo il modo tor&shy;<lb/>ricelliano capovolto in una vaschetta, restava pieno, cos&igrave; stando all'aperto, <lb/>ma sotto la campana della macchina pneumatica si votava, tanto rimanen&shy;<lb/>dovene solo, quanto a dire del Boyle si potesse credere esservi sostenuto dal <lb/>debole sforzo dell'aria rarefatta. </s>

<s>L'Huyghens fu curioso di veder co'suoi <lb/>propri occhi la cosa, e trov&ograve; che veramente avveniva com'aveva detto il <lb/>Boyle, se per&ograve; l'acqua era mescolata con l'aria. </s>

<s>Ma se di questa si fosse <lb/>quella in qualche modo espurgata, il tubo rimaneva pieno, anche nel vuoto <lb/>della campana. </s>

<s>Parve a principio l'annunzio tanto strano, che non si volle <lb/>credere, ma venutisi alle prove, che si fecero nel 1663 innanzi alla R. </s>

<s>So&shy;<lb/>ciet&agrave; di Londra, e ripetutesi per maggior conferma col mercurio nello stru&shy;<lb/>mento torricelliano dallo stesso Boyle, ebbe questi a convincersi con sua gran <lb/>maraviglia che, dai 27 o 28 pollici consueti, il liquido si poteva ridurre infino <lb/>a 75 alto dentro la canna. </s></p><p type="main">

<s>Riposati gli animi dallo stupore, s'incominci&ograve; a ripensare qual potesse <lb/>esser la causa di un fatto cos&igrave; nuovo. </s>

<s>L'Huyghens, che stava allora fanta&shy;<lb/>sticando intorno a quel suo etere cosmico, da sostituirsi alla materia sottile <lb/>del Cartesio, onde spiegare la gravit&agrave; naturale de'corpi, e le propriet&agrave; della <lb/>luce; non dubit&ograve; d'ingerire il vagheggiato idolo suo taumaturgo a spiegare <lb/>i misteri dello sperimento boileiano. </s>

<s>Disse che, estratta l'aria, vi sottentra <lb/>l'etere, penetrativo come di tutti i corpi cos&igrave; e del vetro della campana, a <lb/>sostener l'acqua e il mercurio a una tale incredibile altezza. </s>

<s>Ma ascoltiamo <lb/>com'egli stesso pi&ugrave; efficacemente si esprima, in uno di que'suoi, che i di&shy;<lb/>ligenti raccoglitori intitolarono <emph type="italics"/>Experimenta phisica.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Praeter pressionem aeris, quae sustinet mercurium ad altitudinem <lb/>27 pollicum in experimento torricelliano, et quam dari ex infinitis aliis effe&shy;<lb/>ctibus quos videmus constat; concipio et aliam pressionem illa fortiorem, <lb/>materiae aere subtilioris, quae haud difficulter penetrat vitrum, aquam, mer&shy;<lb/>curium, et omnia alia corpora, quae aeri impenetrabilia observamus. </s>

<s>Haec <pb xlink:href="020/01/3350.jpg" pagenum="311"/>pressio, addita ad aeris pressionem, potest sustinere 75 pollices mercurii, et <lb/>forte adhuc plures, quam diu tantum agit in superficiem inferiorem, vel in <lb/>superficiem mercurii, in quem aperta tubi extremitas immergitur. </s>

<s>Sed quam <lb/>primum materia haec potest agere etiam ad alteram partem, quod evenit si <lb/>tubum concutiendo, vel immittendo parvam aeris bullam occasio detur huic <lb/>materiae effectum suum inchoandi; pressio illius aequalis erit ab utraque <lb/>parte, ita ut sola supersit aeris pressio, quae sustinet mercurium ad ordina&shy;<lb/>riam altitudinem 27 pollicum. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Eadem de causa, in experimento aquae aere purgatae, post remotam <lb/>pressionem aeris, evacuando recipiens B (fig. </s>

<s>160), altera illa pressio eius&shy;<lb/>dem materiae agit etiam ut antea in superficiem aquae in vitro D, et cohi&shy;<lb/>bet ne aqua in phiala C descendat. </s>

<s>Sed ubi minima bulla aeris intrat phia&shy;<lb/><figure id="id.020.01.3350.1.jpg" xlink:href="020/01/3350/1.jpg"/></s></p><p type="caption">

<s>Figura 160.<lb/>lam, materia, quam dixi transire per vitrum et aquam, <lb/>subito inflat bullam, editque pressionem aequalem illi, <lb/>quae agit in superficie aquae in vitro D. </s>

<s>Quare omnis <lb/>aqua phialae defluit, et ad libellam cum illa, quae est <lb/>in vitro, se constituit &rdquo; (<emph type="italics"/>Opera varia,<emph.end type="italics"/> T. II, Lugd. </s>

<s><lb/>Batav. </s>

<s>1724, pag. </s>

<s>773, 74). </s></p><p type="main">

<s>Nel quinto esperimento poi conferma l'Huyghens <lb/>l'esperienza dell'etere, attribuendo alla pressione di lui <lb/>il rimanere aderenti due lastre contigue da specchi, <lb/>anche nel vuoto. </s>

<s>Ma venuto poi il Newton disse che, <lb/>cos&igrave; questo fatto, come l'altro del sostenersi l'acqua <lb/>e il mercurio, purificati dall'aria, nel tubo torricelliano, <lb/>a maggiore altezza di quella dovuta alla pressione ammosferica; non era da <lb/>attribuirsi ad altro, che all'attrazione molecolare del liquido in s&egrave;, e alla ma&shy;<lb/>teria del vetro: attrazion ch'&egrave; rotta, sia per l'interposizione dell'aria, sia per <lb/>la violenta succussione del tubo. </s>

<s>&ldquo; Porro rem eamdem inde quoque infero <lb/>quod bina marmora perpolita cohaereant, etiam in vacuo, et quod argentum <lb/>vivum in Barometro subsistat ad altitudinem 50, 60 vel 70 unciarum, vel <lb/>etiam amplius eo: ita scilicet si prius ab aere omni probe depurgatum fue&shy;<lb/>rit, et in tubum cauta manu infusum, ut adeo partes eius sint usquequaque <lb/>contiguae, et sibi invicem et vitro. </s>

<s>Atmosphaera pondere suo argentum vi&shy;<lb/>vum sursum in tubum premit ad usque altitudinem 29 aut 30 unciarum. </s>

<s><lb/>Alia autem aliqua causa efficiens id deinceps amplius sustollit, non id in tu&shy;<lb/>bum sursum premendo, sed efficiendo ut partes eius et vitro et sibi invicem <lb/>adhaerescant. </s>

<s>Etenim, si qu&ograve; pacto partes eius, vel interiectis bullulis, vel <lb/>succutiendo vitrum, disiungantur, corruit continuo argentum vivum omne, <lb/>usque eo donec haud amplius 29 aut 30 uncias in altitudinem habeat &rdquo; <lb/>(<emph type="italics"/>Opticae,<emph.end type="italics"/> lib. </s>

<s>III cit., pag. </s>

<s>158). </s></p><p type="main">

<s>Cos&igrave; dunque il Newton veniva ad arricchire la Fisica capillare di un <lb/>fatto nuovo, in cui gloriosamente si compie la storia di queste osservazioni, <lb/>le quali anche noi col Laplace, chiameremo antiche. </s>

<s>Delle nuove, che servi&shy;<lb/>rono o per pi&ugrave; sicura scorta o per pi&ugrave; piena conferma delle teorie, diremo <pb xlink:href="020/01/3351.jpg" pagenum="312"/>pi&ugrave; qua, quando, passata dalle ipotesi vaghe, vedremo la Scienza studiosa di <lb/>fermare il pi&egrave; ne'teoremi. </s></p><p type="main">

<s>Per queste ipotesi non s'intende per&ograve;, secondo la comune accettazione <lb/>della parola, un principio che sembra ragionevolmente vero, e che aspetti <lb/>d'essere dimostrato, ma una cogitazione qualunque che, venuta a mancare <lb/>la notizia del vero, siasi presa a rappresentarlo e a supplirlo. </s>

<s>Le scambie&shy;<lb/>voli attrazioni delle particelle della materia, da che dipendono i fenomeni ca&shy;<lb/>pillari, costituiscon quel vero, che poi venne per qualche tempo a mancare, <lb/>e che intanto, prima di riaversi negli spiriti e nella libert&agrave; della vita, fu sup&shy;<lb/>plito dalle ipotes&igrave; che si diceva, a quel modo che si supplisce talvolta all'in&shy;<lb/>terruzione di una linea curva, tirata con lo strumento in perfetta regola, <lb/>ricongiungendone i tratti con la mano incerta. </s>

<s>La somiglianza tra l'imma&shy;<lb/>gine e la realt&agrave; viene ora a dimostrarsi per la seguente storia. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Una delle forme pi&ugrave; ovvie, sotto cui si rappresentano le azioni della ca&shy;<lb/>pillarit&agrave;, s'offerse nelle gocciole dell'acqua, che attirarono a s&egrave; da lungo <lb/>tempo l'attenzione e lo studio dei Fisici, com'&egrave; manifesto dagli scritti di Leo&shy;<lb/>nardo da Vinci. </s>

<s>Il fatto che due delle dette gocciole, poste a breve distanza <lb/>fra loro, s'attraggono a vicenda come la calamita e il ferro, era allora co&shy;<lb/>munemente noto, e perci&ograve; Leonardo avvertiva, in principio al suo libro <emph type="italics"/>Del <lb/>moto e della misura dell'acque,<emph.end type="italics"/> non essere sua intenzione di trattarvi di <lb/>una tale occulta propriet&agrave; de'liquidi minutamente divisi, ma di quelle, che <lb/>pi&ugrave; manifestamente si osservano in essi, essendo raccolti insieme in pi&ugrave; grandi <lb/>moli. </s>

<s>&ldquo; Non parlo, egli dice nel capitolo IV del libro citato, delle gocciole o <lb/>altre piccole quantit&agrave;, che si tirano l'una all'altra, come l'acciaio la sua li&shy;<lb/>matura, ma delle gran quantit&agrave; &rdquo; (Bologna 1828, pag. </s>

<s>275). </s></p><p type="main">

<s>Non contenti que'Fisici d'osservare il fatto, si dettero a specularne an&shy;<lb/>che le ragioni, e Leonardo dice le sue, risolvendo con esse alcuni problemi, <lb/>relativi a questo soggetto, dei pi&ugrave; curiosi, come sarebbe questo, in cui si <lb/>domanda: <emph type="italics"/>perch&egrave; quella gocciola fia di pi&ugrave; perfetta sfericit&agrave;, la quale sia <lb/>di minor quantit&agrave;;<emph.end type="italics"/> o quell'altro assai simile: <emph type="italics"/>perch&egrave;, se due liquidi sfe&shy;<lb/>rici di quantit&agrave; ineguali verranno al principio del contatto infra loro, il <lb/>maggiore tira a s&egrave; il minore, e immediatamente se lo incorpora, senza <lb/>distruggere la perfezione della sua sfericit&agrave;.<emph.end type="italics"/> E bench&egrave; confessi di sentire <lb/>tutta la difficolt&agrave; della proposizione, &ldquo; non per questo, soggiunge Leonardo, <lb/>rester&ograve; di dire il mio parere. </s>

<s>L'acqua, vestita dell'aria, naturalmente desi&shy;<lb/>dera stare unita nella sua sfera, perch&egrave; in tal sito essa si priva di sua gra&shy;<lb/>vit&agrave;, la qual gravit&agrave; &egrave; dupla: cio&egrave; che il suo tutto ha gravit&agrave;, atteso al cen&shy;<lb/>tro degli elementi; la seconda gravit&agrave;, atteso al centro della sfericit&agrave; del&shy;<lb/>l'acqua. </s>

<s>Il che, se cos&igrave; non fosse, essa farebbe di s&egrave; solamente una mezza <pb xlink:href="020/01/3352.jpg" pagenum="313"/>sfera, la quale &egrave; quella, che sta dal centro in su. </s>

<s>Ma di questo non vedo <lb/>nell'umano ingegno modo di darne scienzia, ma direi come si dice della ca&shy;<lb/>lamita, che tira il ferro, cio&egrave; che tale virt&ugrave; &egrave; occulta propriet&agrave;, delle quali <lb/>ve ne sono infinite in natura &rdquo; (ivi, pag. </s>

<s>291). </s></p><p type="main">

<s>&Egrave; manifesto dunque che, nel concetto di Leonardo, si trova involuto <lb/>quello di una attrazione della massa fluida al centro della Terra: attrazione <lb/>distinta da quell'altra simile, che le particelle componenti esercitano fra s&egrave; <lb/>medesime, come tra il ferro e la calamita. </s>

<s>La relazione che passa fra que&shy;<lb/>ste, e le idee del Newton, &egrave; manifesta, ma che fossero veramente in Leo&shy;<lb/>nardo involute, e impedite di schiudersi liberamente, serrate e strette, diciam <lb/>cos&igrave;, da una certa dura corteccia peripatetica; si par dal modo com'ei ri&shy;<lb/>sponde al nuovo propostosi quesito: <emph type="italics"/>perch&egrave; &egrave; pi&ugrave; perfezione nella minore <lb/>sfera del liquido, che nella grande.<emph.end type="italics"/> Sembrava che si dovesse direttamente <lb/>concludere, dai professati principii, cos&igrave; la risposta: perch&egrave;, nella grande, <lb/>maggiormente prevale l'attrazione al centro degli elementi, sopra quella al <lb/>centro della sfericit&agrave; dell'acqua, ma sfugg&igrave; a Leonardo la considerazione di <lb/>queste forze interne, per ridursi a non attribuir l'effetto che all'azione esterna <lb/>dell'ambiente. </s>

<s>&ldquo; Qui si risponde che la minima goccia ha levit&agrave; pi&ugrave; simile <lb/>all'aria, che la circonda, che la gocciola grande, e per la poca differenza &egrave; <lb/>sostenuta pi&ugrave; dal mezzo in gi&ugrave; da essa aria, che la grande. </s>

<s>E per prova di <lb/>questo si allegher&agrave; le minime gocciole, che sono di tanto minima figura, che <lb/>elle sono quasi invisibili per s&egrave;. </s>

<s>Ma molte ed in quantit&agrave; sono visibili, e que&shy;<lb/>ste sono le particole componenti le nuvole, la nebbia, la pioggia etc. </s>

<s>&rdquo; (ivi). </s></p><p type="main">

<s>Le attrazioni calamitiche fra le minime particelle dell'acqua, che il Gil&shy;<lb/>berto trov&ograve; cos&igrave; bene studiate dai Fisici anteriori, gli resero un bel servigio, <lb/>per confermare il principio, da s&egrave; posto per uno de'principali fondamenti <lb/>alla sua Filosofia magneto-elettrica, dell'umido cio&egrave; <emph type="italics"/>rerum omnium unito&shy;<lb/>ris.<emph.end type="italics"/> La descrizione de'fuscelli galleggianti ricorre a questo proposito, e dice <lb/>che s'attraggono &ldquo; veluti gutta adiuncta guttae attrahitur, et subito uniun&shy;<lb/>tur. </s>

<s>Sic humidum in aquae superficie unitatem petit humidi, cum aquae su&shy;<lb/>perficies in utrisque attollitur, quae illico, sicut guttae aut bullae, conflu&shy;<lb/>unt, sunt in maiore multo proprinquitate, quam electrica et vapidis naturis <lb/>uniuntur &rdquo; (<emph type="italics"/>De magnete cit.,<emph.end type="italics"/> pag. </s>

<s>57). </s></p><p type="main">

<s>Pochi convennero per verit&agrave; che i moti descritti dal Gilberto dipendes&shy;<lb/>sero dall'attrazione elettrica delle cose umide, e il Cabeo, fra gli altri uno <lb/>de'pi&ugrave; animosi, insorgeva a contradirlo cos&igrave; ragionando: &ldquo; Nunc ostendo illos <lb/>motus a Gilberto enumeratos esse motus elementares gravium, quae tendunt <lb/>ad centrum, non electricas humidorum attractiones. </s>

<s>Imo ad hominem contra <lb/>Gilbertum prius dico: sicut bacillum siccum non attrahit humidum, vel con&shy;<lb/>tra nec fluit ad siccam ripam humidum: igitur solum humida in se mutuo <lb/>trahunt. </s>

<s>Ergo etiam electrica, quae trahuntur ex humiditate, non trahent <lb/>nisi humida, sicca fugabunt. </s>

<s>Sed trahunt omnia sicca, immo fortasse luben&shy;<lb/>tius; ergo non trahunt ex humiditate &rdquo; (<emph type="italics"/>Philosophia magnetica,<emph.end type="italics"/> Colo&shy;<lb/>niae 1629, pag. </s>

<s>187). </s></p><pb xlink:href="020/01/3353.jpg" pagenum="314"/><p type="main">

<s>Nonostante che pochi, per queste dette dal Cabeo, e per simili altre ra&shy;<lb/>gioni, accettassero le nuove teorie elettriche, giovarono le osservazioni e le spet&shy;<lb/>tacolose esperienze del Gilberto a confermare l'essere e la natura di una occulta <lb/>virt&ugrave; calamitica, fra le particelle componenti l'acqua. </s>

<s>Galileo, nel suo Discorso <lb/>idrostatico, la professava apertamente, e vedeva in essa quella copula che tiene <lb/>unite le particelle non dell'acqua sola, ma e di tutti i corpi. </s>

<s>Questa calami&shy;<lb/>tica virt&ugrave; poi non differisce che nel nome dall'attrazione molecolare del New&shy;<lb/>ton, e da quel moto occulto dell'acqua <emph type="italics"/>ad omnes partes,<emph.end type="italics"/> da cui sapientemente <lb/>l'Aggiunti derivava la causa universale dei multiformi fenomeni capillari. </s></p><p type="main">

<s>Ora &egrave; notabile che, non giunto ancora il secolo XVII a compiere i suoi <lb/>primi quarant'anni, erano gi&agrave; state spente queste luminose apparizioni della <lb/>Fisica molecolare. </s>

<s>Ne fu causa il vento sollevatosi, dalle due parti opposte <lb/>dell'orizonte scientifico, a dissipare quelle occulte propriet&agrave; della materia, <lb/>nelle quali troppo spesso andavasi a rifugiare la Fisica peripatetica. </s>

<s>Galileo <lb/>ha in tal proposito certe espressioni, significantissime di questo incorrere le <lb/>idee nuove contro le vecchie, l&agrave; dove, al nome di <emph type="italics"/>simpatia,<emph.end type="italics"/> sotto il quale <lb/>si velavano ai peripatetici le repulsioni o le indebolite forze attrattive del&shy;<lb/>l'aria verso l'acqua, si studia di sostituire i nomi di <emph type="italics"/>dissensione<emph.end type="italics"/> o di <emph type="italics"/>discon&shy;<lb/>venienza.<emph.end type="italics"/> Di che accortosi Simplicio, cos&igrave; argutamente dice al suo interlo&shy;<lb/>cutore: &ldquo; Mi vien quasi da ridere nel veder la grande antipatia, che ha il <lb/>signor Salviati con l'antipatia, che neppur vuol nominarla, eppure &egrave; tanto <lb/>accomodata a scior la difficolt&agrave; &rdquo; (Alb. </s>

<s>XIII, 74). </s></p><p type="main">

<s>Ma l'usare un nome piuttosto che un altro non era certo un far pro&shy;<lb/>gredire la Scienza, la quale anzi ebbe a indietreggiare per Galileo, quando <lb/>all'attrazion calamitica, copulatrice delle particelle discrete dei corpi, secondo <lb/>le idee, che prevalevano nel tempo, in cui fu scritto il Discorso delle gal&shy;<lb/>leggianti; sostitu&igrave;, ne'Dialoghi delle due nuove Scienze, per antipatia alle <lb/>qualit&agrave; occulte, le pressioni prodotte dal peso dell'aria. </s>

<s>E cos&igrave; egli si lusing&ograve; <lb/>d'aver progredito, mostrando palese al di fuori quel che invisibile si credeva <lb/>esser dentro. </s>

<s>Ebbe da ci&ograve; motivo la riforma delle dottrine, che Galileo stesso <lb/>applicava a rendere la ragione del sostenersi i globuli d'acqua sollevati e <lb/>grandi. </s>

<s>E bench&egrave; confessi di non saper come propriamente vada il negozio, <lb/>egli &egrave; per&ograve; certo che di un tale effetto non sia la causa interna, ma che ne&shy;<lb/>cessariamente risegga fuori. </s>

<s>&ldquo; Che ella non sia interna, oltre all'esperienze <lb/>mostrate, ve lo posso confermare con un'altra efficacissima. </s>

<s>Se le parti di <lb/>quell'acqua, che rilevata si sostiene, mentre &egrave; circondata dall'aria, avessero <lb/>cagione interna per ci&ograve; fare, molto pi&ugrave; si sosterrebbono circondate che fos&shy;<lb/>sero da un mezzo, nel quale avessero minor propensione di discendere, che <lb/>nell'aria ambiente non hanno. </s>

<s>Ma un mezzo tale sarebbe ogni fluido pi&ugrave; <lb/>grave dell'aria, v. </s>

<s>g. </s>

<s>il vino, e per&ograve;, infondendo intorno a quel globo d'acqua <lb/>del vino, se gli potrebbe alzare intorno intorno, senza che le parti dell'acqua, <lb/>conglutinate dall'interna viscosit&agrave;, si dividessero. </s>

<s>Ma ci&ograve; non accade egli, <lb/>anzi non prima se gli accoster&agrave; il liquido sparsogli intorno, che, senza aspet&shy;<lb/>tar che molto se gli elevi intorno, si dissolver&agrave; e spianer&agrave;, restandogli di <pb xlink:href="020/01/3354.jpg" pagenum="315"/>sotto, se sar&agrave; vino rosso. </s>

<s>&Egrave; dunque esterna, e forse dell'aria ambiente, la <lb/>cagione di tale effetto &rdquo; (ivi, pag. </s>

<s>73). </s></p><p type="main">

<s>Le cose, che Galileo soggiunge intorno alla gran dissensione tra l'aria <lb/>e l'acqua, dimostrata per l'esperienza della palla di cristallo, dall'angustis&shy;<lb/>simo foro della quale l'acqua stessa contenutavi &egrave; proibita d'uscir fuori dal&shy;<lb/>l'aria ambiente, e no dal vino; par che non si riferiscano direttamente ai <lb/>fenomeni capillari. </s>

<s>Ma vedremo come s'invocassero opportunamente nella <lb/>Scuola galieiana, a spiegar il salir l'acqua, e l'abbassarsi il mercurio in&shy;<lb/>torno ai corpi solidi, e nell'interno dei sottilissimi tubi. </s></p><p type="main">

<s>L'altro vento, che si diceva essersi sollevato a spazzare il chicco del <lb/>grano, rimasto fra le pule della Fisica peripatetica, veniva non meno ga&shy;<lb/>gliardamente soffiato dalle guance del Cartesio, il quale, a legger che Gali&shy;<lb/>leo confessava di non sapere il negozio delle gocciole d'acqua, che cos&igrave; ro&shy;<lb/>tonde stanno sulle foglie de'cavoli; se ne fece gran maraviglia, tanto pi&ugrave; <lb/>ch'egli presumeva di aver nelle sue <emph type="italics"/>Meteore<emph.end type="italics"/> gi&agrave; spiegato il fatto abbastanza. <lb/></s>

<s>&ldquo; Dicit Galileus se ignorare causam, quae guttas aquae super brassicis su&shy;<lb/>stentet, quam quidem in Meteoris meis satis explicui &rdquo; (<emph type="italics"/>Epistolar.,<emph.end type="italics"/> P. II, <lb/>Amstelodami 1682, pag. </s>

<s>279). </s></p><p type="main">

<s>Andiamo a cercare i discorsi <emph type="italics"/>Delle meteore,<emph.end type="italics"/> e leggiamo per curiosit&agrave; <lb/>quel che dice il Cartesio essere ragion certissima del formarsi le gocciole <lb/>dell'acqua esattamente rotonde. </s>

<s>&ldquo; La matiere subtile coulant par les pores <lb/>des autres cors, en mesme fa&ccedil;on qu'une riv&igrave;ere par les intervalles des her&shy;<lb/>bas, qui croissent en son lit, et passant plus librement d'un endroit de l'air <lb/>en l'autre, et d'un endroit de l'eau aussy en l'autre, que de l'air en l'eau <lb/>au reciproquement de l'eau en l'air, comme il a est&eacute; ailleurs remarqu&eacute;; elle <lb/>doit tournoyer au dedans de ce goutte, et aussi au dehors en l'air qui l'en&shy;<lb/>vironne, mais d'autre mesure qu'au dedans, et par ce moyen disposer en <lb/>rond toutes les parties de sa superficie. </s>

<s>Car elles ne peuvent manquer d'obeir <lb/>a ses mouvemens, d'autant que l'eau est un cors liquide. </s>

<s>Et sans doute cecy <lb/>est suffisant pour faire entendre que les gouttes d'eau doivent estre exacte&shy;<lb/>ment rondes &rdquo; (<emph type="italics"/>Discours de la methode,<emph.end type="italics"/> a Leyde 1637, pag. </s>

<s>205). </s></p><p type="main">

<s>Non resulta dai documenti osservati da noi se il Cartesio estendesse lo <lb/>studio dell'azion capillare anche alle altre forme, sotto cui suole manifestarsi, <lb/>e principalmente alla salita de'liquidi nei sottilissimi cannellini, ma i seguaci <lb/>di lui trovaron facile modo a spiegare il fatto, ricorrendo a quelle flessuosit&agrave; <lb/>anguilliformi, che a tutte le particelle componenti i liquidi aveva per loro <lb/>propriet&agrave; naturale assegnate il Maestro. </s>

<s>Cos&igrave;, per via di questi moti intestini, <lb/>e della pressione dell'aria, ora accomunandosi dalle due scuole del Cartesio <lb/>e di Galileo gli argomenti, ora adoprandoli ciascuna per s&egrave; divisi, s'inco&shy;<lb/>minci&ograve;, e si prosegul per varie vicende a dare scienza de'fenomeni capillari, <lb/>ripudiata ogni idea di attrazion calamitica fra le particelle della materia. </s></p><p type="main">

<s>Ai nostri Accademici fiorentini, cos&igrave; aborrenti dalle girandole cartesiane, <lb/>fu sufficiente invocare l'azion dell'aria, suggerita gi&agrave; dal loro Galileo, e con&shy;<lb/>fermata dall'esperienza del Torricelli. </s>

<s>Com'era possibile infatti, colla mente <pb xlink:href="020/01/3355.jpg" pagenum="316"/>com'avevano piena del grande avvenimento, che vedendo una cos&igrave; grande <lb/>analogia tra il sostenersi l'acqua nel cannellino, e il mercurio nel tubo, non <lb/>pensassero che si dovessero attribuire i due effetti a somiglianti cagioni? </s>

<s>N&egrave; <lb/>la somiglianza era difficile a ravvisarsi, perch&egrave;, se sopra il tubo chiuso ri&shy;<lb/>mane il vuoto, sopra il cannellino aperto riman l'aria, debilitata, per le an&shy;<lb/>gustie in cui si trova, d'esercitare il libero momento della sua spira, e perci&ograve; <lb/>qua e l&agrave;, prevalendo similmente il peso dell'aria esterna, la diversit&agrave; delle <lb/>pressioni sembrava dover esser giusta causa proporzionata delle differenti al&shy;<lb/>tezze, a cui giungono il mercurio e l'acqua ne'due diversi strumenti. </s>

<s>Vero <lb/>&egrave; bene che quella prima compiacenza venne presto amareggiata dai dubbi, <lb/>non potendosi star sicuri nella verit&agrave; della supposta ragione, senza prima <lb/>esaminar diligentemente come la cosa procedesse nel vuoto. </s>

<s>Ma il vuoto, come <lb/>sempre s'us&ograve; di fare a Firenze, per via cio&egrave; del tubo torricelliano, senza <lb/>l'uso diretto della Macchina pneumatica, prolung&ograve; a que'dubbi l'agonia, non <lb/>finita se non in quella sentenza, che i Nostri accademici furono costretti di <lb/>sottoscrivere, della loro propria condanna. </s></p><p type="main">

<s>Ma mentre fiorivano ancora le prime speranze, corse voce di questa in&shy;<lb/>gerenza dell'aria in sostenere i liquidi ne'sottilissimi tubi, e giuntane la no&shy;<lb/>tizia alle orecchie del Boyle, fu giudicata da lui una congettura ingegnosa. </s>

<s><lb/>L'uso che egli, come inventore, faceva assiduo della Macchina pneumatica, <lb/>sembrava che dovesse affrettare la decisione della sentenza, ma qui occorre <lb/>un fatto singolare. </s>

<s>Il Boyle &egrave; cos&igrave; lusingato anch'egli da quella congettura, <lb/>e n'&egrave; si geloso, che quasi non vorrebbe venissero gli occhi a disingannarlo, <lb/>infirmandone il valore della testimonianza col dire che, sebbene avesse usato, <lb/>invece dell'acqua vin rosso, quel sottilissimo filettino nulladimeno <emph type="italics"/>aegre per&shy;<lb/>ceptibilis erat<emph.end type="italics"/> attraverso alla crassizie del vetro. </s>

<s>Come poi questo detto si <lb/>concilii con ci&ograve; che immediatamente soggiunge &ldquo; quantum autem nos digno&shy;<lb/>scere potuimus nulla magna inde (cio&egrave; dall'essere il tubo sotto la campana <lb/>della Macchina pneumatica) liquori contigit alteratio &rdquo; da quando cio&egrave; era al&shy;<lb/>l'aperto; non si comprende, senz'ammetter che il Boyle fosse allora preoc&shy;<lb/>cupato dal timore che la realt&agrave; de'fatti si mostrasse ritrosa d'accomodarsi <lb/>a secondare le lusinghe della ragione. </s></p><p type="main">

<s>In qualunque modo, par ch'egli dica, se non si vogliono far gli occhi <lb/>complici di queste lusinghe, confessiamo liberamente che l'altezza del liquido <lb/>non si muti, per passar che si faccia il cannello dall'aria aperta sotto la <lb/>campana della Macchina pneumatica: non &egrave; per questo che si debba renun&shy;<lb/>ziare alla congettura, perch&egrave; l'aria non &egrave; tolta affatto dal recipiente, ma vi <lb/>riman rarefatta, onde essendo cos&igrave; debilitata la forza della sua spira propor&shy;<lb/>zionatamente sopra la superficie del liquido nel vaso dell'immersione, e nel <lb/>cannellino; non &egrave; maraviglia se il fatto ne'due casi si mostra inalterato. <lb/></s>

<s>&ldquo; Quod ideo minus admirandum videbatur quod illius aeris spira, quae aquam <lb/>in tubo deprimere posset, aeque fuit debilitata cum ea, quae superficiei aquae, <lb/>in parvo vitro contentae, innixa permansit &rdquo; (<emph type="italics"/>Nova experimenta physico&shy;<lb/>mechanica, Op. </s>

<s>omnia,<emph.end type="italics"/> T. </s>

<s>I cit., pag. </s>

<s>82). </s></p><pb xlink:href="020/01/3356.jpg" pagenum="317"/><p type="main">

<s>Per conferma di che il Boyle aggiunge l'esperienza del riseder l'acqua <lb/>a un tratto, aspirando l'aria con la bocca applicata alla sommit&agrave; del can&shy;<lb/>nello, e conclude il suo discorso cos&igrave;, inserendo fra parentesi, a questi argo&shy;<lb/>menti derivati dalla scuola di Galileo, quegli altri, che venivano suggeriti <lb/>dalla scuola del Cartesio: &ldquo; Quocirca in ingeniosae illius coniecturae patro&shy;<lb/>cinium, qui isthoc de quo hic agitur phaenomenon vertendum duxerit po&shy;<lb/>tentiori in aquam pressioni aeris, qui extra tubum erat, quam qui intra eum&shy;<lb/>dem, ubi tantum aquae (quae ex corpusculis forsitan flexilioribus, et facilius <lb/>internis vitri superficiebus cedentibus corpusculis constare possit) lateribus <lb/>erat contiguum; ostensum est quod, si parvulum illud vas vitreum, quod <lb/>aquam cuius pars in exilem illud siphonem ascenderat continebat, ita occlu&shy;<lb/>deretur, ut quis ore suo inde posset aerem exugere, aqua in exilem tubum <lb/>elata derepente subsideret. </s>

<s>Quod quidem arguere videretur priorem illius <lb/>ascensum a pressione sola aeris incumbentis fuisse ortum, nisi (quam iuste <lb/>non statuo) obiici posset hoc fortasse non eventurum, si superius tubi extre&shy;<lb/>mum in vacuo sisteretur &rdquo; (ibid.). </s></p><p type="main">

<s>Si sente bene che il Boyle, bench&egrave; se ne sia con ogni arte schermito, <lb/>si trova tuttavia assalito dal dubbio, n&egrave; trovando modo a liberarsene, abban&shy;<lb/>dona l'argomento, rimettendo il discuterne ulteriormente a cui <emph type="italics"/>non desit <lb/>otium.<emph.end type="italics"/> &ldquo; Utcumque, hoc unum te velim commonifacere quod, si speculatio&shy;<lb/>nem hane tibi adlubescat ulterius prosequi, ad rem etiam erit excrutari quo <lb/>pacto fiat quod aquae superficies, ut in tubis est manifestum, soleat esse con&shy;<lb/>cava, in medio scilicet depressior, in lateribus altior. </s>

<s>Et e contra qui fiat <lb/>quod in hydrargyrio, non solum convexa sit in medio atque illic intumescat <lb/>superficies, verum, si exilioris tubi extremum ei immergas, superficies liquo&shy;<lb/>ris intra tubum, quam axtra eumdem, erit depressior &rdquo; (ibid.). Cos&igrave; venivano <lb/>a proporsi due capitalissimi problemi, de'quali &egrave; notabile che il proponente <lb/>solo riconoscesse l'importanza, sfuggita forse all'attenzione di tutti, per la <lb/>difficolt&agrave; che appariva in voler risolverli nelle loro ragioni, le quali non si <lb/>sarebbero potute dedurre, come il Boyle sperava, n&egrave; dalla figura de'corpu&shy;<lb/>scoli mercuriali, n&egrave; dalla fabbrica delle particelle elastiche dell'aria. </s>

<s>Questi <lb/>argomenti, temperati alla fucina del Cartesio, troppo erano deboli e spropor&shy;<lb/>zionati all'effetto, ond'esso Boyle avrebbe dovuto ancora aspettare un mezzo <lb/>secolo, prima di vedere adempito il suo voto. </s></p><p type="main">

<s>Il modo, come dal celebre uomo trattavasi l'argomento, pareva studiato <lb/>apposta, per disanimare chiunque avesse osato d'entrar con lui nell'arringo, <lb/>come di fatto avvenne per qualche tempo, infin tanto che Roberto Hook, <lb/>amico al Boyle, connazionale e collega, presa occasione dal XXXV esperi&shy;<lb/>mento fisico-meccanico, non tolse via gli scrupoli, confortandolo di nuove ra&shy;<lb/>gioni, e studiandosi di persuadere che precipua causa del salire i liquidi su <lb/>per i sottilissimi tubi non era altra veramente, che la pressione dell'aria. </s></p><p type="main">

<s>Intanto che si sgombravano cos&igrave; i sentieri ai progressi boileiani, il Gri&shy;<lb/>maldi, che non addetto a nessuna delle due Scuole dominanti faceva parte <lb/>da s&egrave;, e con pi&ugrave; libert&agrave; forse, ma certo con pi&ugrave; acume degli altri contem-<pb xlink:href="020/01/3357.jpg" pagenum="318"/>plava gli spettacoli della Natura; dava del fenomeno capillare una spiega&shy;<lb/>zione molto semplice, bench&egrave; non fosse la vera. </s>

<s>Persuaso, in mezzo alle con&shy;<lb/>troversie che s'agitavano allora, tenersi insieme le particelle dell'acqua per <lb/>una certa loro viscosit&agrave; naturale, considerava che il sottilissimo filetto liquido, <lb/>per questa stessa viscosit&agrave; e per la piccolezza delle sue parti, non poteva <lb/>conglobarsi a premere con tutta la libert&agrave; del suo peso, sostenuto com'&egrave; fra <lb/>le angustie della concava parete: ond'&egrave; che l'acqua, nel vaso ampio e nella <lb/>fistola, non possa consistere in equilibrio, se non a patto che la maggiore <lb/>altezza compensi la subita diminuzione del momento gravitativo. </s>

<s>&ldquo; Cogitan&shy;<lb/>dum est non aeque ponderare aquam utramque, illam scilicet quae in fistula <lb/>includitur, et illam quae in vase extra fistulam. </s>

<s>Quamvis enim per se et na&shy;<lb/>tura sua utraque aequaliter gravitet, per accidens tamen quae in fistula con&shy;<lb/>tinetur minus gravitat, co quod sustinetur ab interna cavitate fistulae, et a <lb/>difficultate defluxus iam explicata. </s>

<s>Igitur non debet utraque aqua consistere <lb/>in aequilibrio, sed potius, compensatis momentis gravitationis, ea quae in vase <lb/>continetur utpote gravior, debet se totam ita dimittere, ut subingrediendo <lb/>per imum fistulae immersae pellat sursum eam, quae in fistula continetur, <lb/>et haec suapte, ut tamquam levior, debet altius evehi &rdquo; (<emph type="italics"/>De lumine<emph.end type="italics"/> cit., <lb/>pag. </s>

<s>106, 7). </s></p><p type="main">

<s>Ricordiamoci per&ograve; che il Grimaldi non intendeva di trattar di proposito <lb/>de'fenomeni capillari, contento a risolvere il problema dell'attrarsi nella zuppa <lb/>il vino alla midolla del pane, in mezzo a cui diceva formarsi, dalla conti&shy;<lb/>nuit&agrave; de'pori, l'intricato laberinto di tanti sottilissimi tubi. </s>

<s>Lasciava perci&ograve; <lb/>l'Autore a desiderar la ragione del vedersi fare al mercurio contrari effetti <lb/>a quelli dell'acqua e del vino, come pure lasciava in desiderio di sapere il <lb/>perch&egrave; di tanti altri fatti curiosi, che in questo stesso genere s'erano speri&shy;<lb/>mentati. </s>

<s>D'onde avvenne che pensasse di soddisfare a un tal desiderio Isacco&shy;<lb/>Vossio, il quale attribui alla viscosit&agrave; dell'acqua e all'aderenza di lei al vetro <lb/>(per cui ella viene a privarsi del proprio peso) il risalir ch'ella fa sul li&shy;<lb/>vello ordinario. </s>

<s>&ldquo; Quia vero caret pondere attollitur et expellitur supra libra&shy;<lb/>mentum ambientis aquae &rdquo; (<emph type="italics"/>De Nili origine,<emph.end type="italics"/> Hagae Comitis 1666, pag. </s>

<s>6). <lb/>Al mercurio poi, mancando questa viscosit&agrave; e aderenza, non fa maraviglia <lb/>se invece di alzarsi, per le angustie del tubo che ne retundono il moto, si <lb/>abbassa. </s>

<s>&ldquo; Cum vero hydrargyrius careat illa viscositate, minimeque adhae&shy;<lb/>reat, et insuper conatus ille qui aequilibrium adfectat retardetur, et retun&shy;<lb/>datur ab angustia fistulae exilioris; nequaquam mirum videri debet si mi&shy;<lb/>nus alte in fistulis quam in spatiis latis et minus in minutis quam in laxis <lb/>ascendat canalibus &rdquo; (ibid.). </s></p><p type="main">

<s>Il Vossio aveva avvertita questa legge, che cio&egrave; le depressioni del mer&shy;<lb/>curio e le altezze dell'acqua nei cannelli stanno in ragion reciproca delle se&shy;<lb/>zioni, e come i nostri Accademici di Bologna la dimostrarono sperimental&shy;<lb/>mente, cos&igrave; egli, il Vossio, fu il primo a riconoscerne la causa, geometrica&shy;<lb/>mente concludendola dal principio che i corpi piccoli hanno, a proporzione <lb/>delle moli, superficie maggiore dei grandi. </s>

<s>&ldquo; Quod autem quanto fiant mi-<pb xlink:href="020/01/3358.jpg" pagenum="319"/>nutiores fistulae, tanto altius ascendat aqua, huius rei ratio est manifesta. </s>

<s><lb/>Quemadmodum enim minora corpora maiorem habent superficiem respectu <lb/>suae molis, quam magna; similiter etiam minores canales plura habent puncta <lb/>contactus, ratione sui spatii, quam maiores. </s>

<s>Quanto autem plus superficiei, <lb/>pluraque contactus sunt puncta, tanto facilius aqua adhaeret &rdquo; (ibid.). </s></p><p type="main">

<s>A ripensare che questa &egrave; la ragion medesima del Borelli e del Newton, <lb/>e che nessun altro a que'tempi aveva n&egrave; pi&ugrave; facilmente, n&egrave; pi&ugrave; compiuta&shy;<lb/>mente del Vossio spiegati i fenomeni capillari; ognuno s'aspetterebbe di sen&shy;<lb/>tir dire che con applauso fossero accolti gl'insegnamenti di lui. </s>

<s>Noi invece <lb/>siam qui per annunziare che quella accoglienza se l'ebbe tutta il Boyle. </s>

<s>La <lb/>preferenza, che non si saprebbe a primo aspetto spiegare, si comprende poi <lb/>facilmente, ripensando all'efficacia, che dovette avere sul giudizio di tutti i <lb/>fisici la somiglianza tra il barometro, e questi tubi capillari: efficacia, che <lb/>l'Hook contribu&igrave; a rendere pi&ugrave; potente, sia riducendo il fatto a rappresen&shy;<lb/>tarsi inalterato o in mezzo all'aria naturale o in mezzo alla rarefatta dentro <lb/>la campana della Macchina pneumatica, sia dicendo il perch&egrave; l'aria stessa <lb/>o naturale o rarefatta preme assai meno sulla superficie della fistola stretta, <lb/>che dell'ampia del vaso. </s>

<s>Il Boyle aveva appena accennato che questa minor <lb/>pressione dipendeva dall'essere l'elaterio dell'aria impedito dalla troppa an&shy;<lb/>gustia dello spazio, ma l'Hook sostitu&igrave; a questa meccanica l'altra causa fisica <lb/>dell'affinit&agrave; al vetro, che l'aria mostra di aver sempre minore dell'acqua. </s>

<s>I <lb/>principii insomma dell'Hook si riducevano a questi due: &ldquo; I.o Quod inae&shy;<lb/>qualis aeris incumbentis pressura efficiat inaequalem altitudinem in superfi&shy;<lb/>ciebus aquarum, id quod experimento probatur, ope inversi siphonis vitrei, <lb/>cui, si indatur aliqua quantitas aquae, et applicato ore ad alteram eius extre&shy;<lb/>mitatem leniter infletur; statim elevatur in opposito erure aquae superficies, <lb/>et si leniter sugatur statim deprimitur. </s>

<s>II.o Quod in his phaenomenis occur&shy;<lb/>rat eiusmodi inaequalis aeris pressura, et illa quidem oriunda ex maiore non <lb/>conformitate, seu incongruitate aeris ad vitrum, quam aquae ad idem vitrum. </s>

<s>&rdquo; </s></p><p type="main">

<s>Questi due principii dell'Hook, cos&igrave; come gli abbiamo trascritti, si leg&shy;<lb/>gono formulati a pag. </s>

<s>82 del <emph type="italics"/>Collegium experimentale<emph.end type="italics"/> di Cristoforo Sturm, <lb/>a cui siam debitori delle seguenti notizie storiche: &ldquo; Post Boylium quidam <lb/>eius cultor R. H. (non sappiamo perch&egrave; siasi attorzato in questo monogramma <lb/>il fulgor del nome di Roberto Hook) occasione arrepta ex ipso illo experi&shy;<lb/>mento XXXV, quod sub initium citavimus anglico scrmone, observationis no&shy;<lb/>vellae causam hypothesi peculiari declarare conatus est, quam in latinum <lb/>sermonem conversam anno 1662 edidit quidam M. Bohem, sub inscriptione <lb/><emph type="italics"/>Conatus ad explicanda phaenomena notabilia, in Experimento publicato <lb/>ab honorabili viro Roberto Boyle &rdquo;<emph.end type="italics"/> (<emph type="italics"/>Colleg. </s>

<s>experim.,<emph.end type="italics"/> Norimbergae 1676, <lb/>pag. </s>

<s>78). </s></p><p type="main">

<s>La spiegazion del fenomeno, qual si leggeva nell'opuscolo del Bohem, <lb/>lo Sturm la dice <emph type="italics"/>nostrae quidem cognatam,<emph.end type="italics"/> ma prima che in Germania <lb/>s'era diffusa in Francia, e in Italia, quando ancora i progressi, diretti dal&shy;<lb/>l'Hook, non erano venuti ad arrestarsi innanzi all'esperienze degli Accade-<pb xlink:href="020/01/3359.jpg" pagenum="320"/>mici fiorentini. </s>

<s>Per quel che riguarda i Francesi il Monconys ci lasci&ograve; larga <lb/>copia di documenti. </s>

<s>Descrivendo il suo viaggio erudito in Inghilterra, narra <lb/>come una mattina del Giugno 1663 part&igrave; di Londra, in carrozza, insieme col <lb/>suo proprio figlio e coll'Oldemburg, per andare a far visita al Boyle, che vil&shy;<lb/>leggiava a tre miglia di distanza. </s>

<s>Entrato in discorso de'mirabili effetti, che <lb/>s'osservano nei tubi capillari, il Boyle, riferita l'opinion di coloro che gli at&shy;<lb/>tribuivano all'aria, concludeva <emph type="italics"/>que estoit la veritable.<emph.end type="italics"/> (<emph type="italics"/>Journal des voyages,<emph.end type="italics"/><lb/>seconde partie, a Lion 1666, Voyage d'Angleterre, pag. </s>

<s>44). Poi rifer&igrave; agli <lb/>ospiti quel che un amico suo ne pensava della convenienza che l'acqua ha <lb/>col vetro, maggiore dell'aria, affermando <emph type="italics"/>que la pensee luy plaisoit fort<emph.end type="italics"/> (ivi). </s></p><p type="main">

<s>Inspirato da queste dottrine, attinte in Inghilterra, il Monconys scrisse <lb/>un suo trattatello <emph type="italics"/>De humidorum aequilibrio in syphonibus,<emph.end type="italics"/> dove, propo&shy;<lb/>nendosi un sifone, sull'andare di quello rappresentato da noi nella figura 157, <lb/>dimostrava che, dato premer l'aria alquanto meno nel cannello stretto che <lb/>nel pi&ugrave; largo, il liquido deve in quello risalire a maggiore altezza che in <lb/>questo. </s>

<s>&ldquo; Aer autem potest minus gravitare in angustioribus, quam in latio&shy;<lb/>ribus tubis, ex multiplici capite. </s>

<s>Primum, si moleculae, quibus texitur aer, <lb/>et quae perpetuo motu cientur, ut in sole videre est, non possint in exilio&shy;<lb/>ribus tubis perinde agitari et moveri, propter angustias loci, uti moventur <lb/>in latioribus, sicuti librae vel staterae pondera, dum quiescunt, minus gra&shy;<lb/>vitare: ubi autem moventur, magis ponderare quotidie cernimus. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Deinde cum superficies tuborum, sicut omnium corporum, sint aspe&shy;<lb/>rae et salebrosae, ita ut quaedam partes caeteris promineant, fieri potest ut <lb/>illae partes prominentes sistant, et morentur gravitatem superioris aeris, ideo&shy;<lb/>que procul dubio iuxta eas superficies aer suam gravitatem minus exercere <lb/>videbitur. </s>

<s>Unde, quo tubi plus superficiei habebunt, plus etiam in iis de&shy;<lb/>trahitur ex gravitate aeris, quem continent. </s>

<s>Et quia, quo tubi eiusdem alti&shy;<lb/>tudinis angustiores evadunt, plus habent superficiei, respectu aliorum (nam <lb/>capacitates eorum decrescunt in ratione duplicata diametrorum, superficies <lb/>autem solum ut diametri, et sic duplo magis decrescunt soliditates quam su&shy;<lb/>perficies corum) ergo in tubis exilioribus, hoc est minoris diametri, plus de&shy;<lb/>trahetur ex gravitate aeris, propter obicem factum a superficiei salebris, quam <lb/>in tubis latioribus. </s>

<s>Ideoque minus gravitabit aer in exiliori tubo quam in <lb/>patentiori &rdquo; (<emph type="italics"/>Journal des voyages,<emph.end type="italics"/> III partie, a Lion 1666, pag. </s>

<s>31, 32). </s></p><p type="main">

<s>A questo trattatello latino succede un discorso accademico <emph type="italics"/>Sur l'ascen&shy;<lb/>sion de l'eau sur un niveau en un tuyau estroit,<emph.end type="italics"/> dove, confermata la sua <lb/>propria opinione, il Monconys riferisce quella di parecchi altri suoi colleghi, <lb/>fra'quali il Tornier <emph type="italics"/>docte personnage et s&ccedil;avant philosophe<emph.end type="italics"/> &egrave; notabile per <lb/>la novit&agrave; del pensiero. </s>

<s>&ldquo; Il disoit que l'air, de sa nature estant plus chaud <lb/>que l'eau, si tost qu'on appliquoit le tuyau sur l'eau elle communiquoit la <lb/>froideur et au verre du tuyau, et a l'air qui y estoit contenu, le quel par <lb/>cette froideur se condensoit: que la condensation, se faisant de la circum&shy;<lb/>ference au centre, tout l'air se reduisoit en un petit cylindre, au milieu de <lb/>canal du tuyau, et laissoit tout autour de luy un vuide, ou l'eau se pouvoit <pb xlink:href="020/01/3360.jpg" pagenum="321"/>introduire iusques au haut du tuyau. </s>

<s>Mas parce qu'en montant ainsi entre <lb/>le cylindre d'eau, et le canal du tuyau, l'air qu'elle eust envelopp&eacute; estoit <lb/>d'une nature plus legere qu'elle, il estoit oblig&eacute; de remonter iusques en haut, <lb/>et l'eau occupoit apres ou en mesme temps toute la place qu'il quittoit, et <lb/>montoit ainsi tres-promptement apres luy en le chassant, a mesure qu'il le <lb/>condensoit &rdquo; (ivi, pag. </s>

<s>15, 16). </s></p><p type="main">

<s>Questa sottile ragione, soggiunge il Monconys, <emph type="italics"/>n'est plus considerable, <lb/>apres avoir l'experience de l'ascension de l'eau chaude,<emph.end type="italics"/> e termina con un <lb/>elenco delle varie ragioni pensate in cos&igrave; difficile soggetto dal Roberval, dal <lb/>R&ograve;, dall'Ausoul, dal Pecquet, dal De Mommor. </s>

<s>Il Roberval la pensava presso <lb/>a poco come il nostro Grimaldi, attribuendo il fatto alla viscosit&agrave; del liquido, <lb/>che lo fa aderire alle pareti del tubo, ma il R&ograve; cartesiano rifletteva che, non <lb/>potendosi il liquido intestinamente agitato spandersi orizontalmente per lo <lb/>largo, essendo impedito, si sfoga dirigendosi tutto su in alto. </s>

<s>L'Ausoul si ri&shy;<lb/>scontr&ograve; co'pensieri del nostro Rossetti, ammettendo ora una convenienza, ora <lb/>una disconvenienza del liquido con la materia del tubo, mentre il Pecquet, <lb/>non sapendo rinunziare all'azione dell'aria, diceva che nel tubo stretto ri&shy;<lb/>man sospesa, come lo stoppaccio dentro la canna di uno schizzatoio, e perci&ograve; <lb/>fa sopra il liquido sottoposto minore la sua presssione. </s>

<s>Il De Mommor final&shy;<lb/>mente &ldquo; dit presque la mesme chose de la diversit&eacute; de la nature de l'air, <lb/>dont les parties grossieres ne peuvent entrer dans un petit canal, les quel&shy;<lb/>les entrent bien dans un gros et de plus que les parties du premier element <lb/>cartesien, poussant esgalement de tous les costes toutes les parties du troi&shy;<lb/>sieme element; les plus grosses de ce troisieme sont plus agitees, et les pe&shy;<lb/>tites moins. </s>

<s>Ainsi l'air du petit tuyau, resistant moins au mouvement, qui <lb/>luy vient d'en bas, est contraint de ceder, et de faire place a l'eau, qui est <lb/>pouss&eacute;e par le grand air ambient &rdquo; (ivi, pag. </s>

<s>37, 38). </s></p><p type="main">

<s>Manca nell'elenco del Monconys Onorato Fabry, il quale, come a tutte <lb/>le altre idee, cos&igrave; dava anche a questa la stampa mostruosa del suo cer&shy;<lb/>vello. </s>

<s>I raggi aerei prementi, immaginati da lui a spiegare il flusso marino, <lb/>son quelli stessi che invoca per i fenomeni capillari, prendendo per princi&shy;<lb/>pio che, tanto pi&ugrave; premono i detti raggi, quanto concorrono con angolo meno <lb/>acuto. </s>

<s>Di qui conclude &ldquo; aquam attolli altius in longiore canaliculo: nempe <lb/>in longiore angulus pressionis acutior et minor est, quam in breviore &rdquo; (<emph type="italics"/>De <lb/>motu Terrae,<emph.end type="italics"/> Lugduni 1665, pag. </s>

<s>162). <lb/><figure id="id.020.01.3360.1.jpg" xlink:href="020/01/3360/1.jpg"/></s></p><p type="caption">

<s>Figura 161.</s></p><p type="main">

<s>Con questi medesimi principii non dubita di risolvere il <lb/>problema proposto dal Boyle perch&egrave; la superficie dell'acqua <lb/>nel cannellino sia concava. </s>

<s>Risponde che, supposto essere il <lb/>cannellino AC (fig. </s>

<s>161) l'acqua in D, essendo pi&ugrave; premuta <lb/>che in H e in K, perch&egrave; l'angolo ADB &egrave; maggiore di AHB, <lb/>e anche di AKB, <emph type="italics"/>ut patet ex geometria<emph.end type="italics"/> (ibid., pag. </s>

<s>163); non <lb/>fa maraviglia che in D la superficie dell'acqua sia pi&ugrave; de&shy;<lb/>pressa. </s>

<s>Eppure ei si compiace di aver prescrutata cos&igrave; la causa <lb/>di un effetto s&igrave; pellegrino, <emph type="italics"/>nec erediderim ab ullo uspiam proditum fuisse.<emph.end type="italics"/><pb xlink:href="020/01/3361.jpg" pagenum="322"/>Anzi ne poteva esser certo, come era certo d'esser superiore agli altri nella <lb/>ricchezza delle invenzioni, di cos&igrave; facile acquisto per lui, che ai fogli raccat&shy;<lb/>tati nella spazzatura dava il valore dei biglietti di banca. </s></p><p type="main">

<s>Si potrebbero aggiungere a queste le ragioni, che dava il Fabry, del <lb/>deprimersi il mercurio intorno alle pareti del tubo, per non avere, diceva, <lb/>ad esso aderenza, la quale, dipendendo secondo lui dall'entrar che fa il li&shy;<lb/>quido nella cavit&agrave; delle strie, e per le boccuzze de'pori del vetro &ldquo; certe <lb/>mercurius, prae crassitudine, in eas angustias sese minime ingerit &rdquo; (ibid., <lb/>pag. </s>

<s>169). Ma basti questo a dimostrar lo stato della cultura, che ebbe a <lb/>que'tempi la Fisica de'capillari appresso i Francesi. </s></p><p type="main">

<s>Fra'nostri abbiamo in primo luogo a citare il Montanari. </s>

<s>Qualunque <lb/>siano le pretese relazioni, ch'egli ebbe co'fratelli Del Buono, &egrave; certo che <lb/>l'indirizzo a questi studii l'ebbe, come tutti gli altri, dagli Sperimenti boi&shy;<lb/>leiani, i quali egli non ha appena citati, nel principio del suo discorso, che <lb/>immediatamente soggiunge. </s>

<s>&ldquo; E veramente il Boyle, come ingegno che non <lb/>cos&igrave; di tutto s'appaga sinceramente, ha confessato la difficolt&agrave; della questione, <lb/>ed accennando solo alcuna cosa circa la pressione maggiore dell'aria esterna, <lb/>che dell'interna al cannellino sopra l'acqua sottoposta, vi frammette in pa&shy;<lb/>rentesi non so che della flessibilit&agrave; delle particole acquee, che meglio s'adat&shy;<lb/>tano al vetro, e senza dilatarsi a spiegare pi&ugrave; oltre i suoi pensieri, lascia inde&shy;<lb/>ciso il problema. </s>

<s>Onde piuttosto gli si deve la lode d'aver tentando ricono&shy;<lb/>sciuta, sebbene in dubbio, la via di scioglierlo, che di averlo perfettamente <lb/>disciolto &rdquo; (<emph type="italics"/>Pensieri fisico-matem.<emph.end type="italics"/> cit., pag. </s>

<s>15). </s></p><p type="main">

<s>Il Montanari non crede dunque gli sia rimasto altro ufficio, che di dar <lb/>perfezione all'opera altrui. </s>

<s>I due suoi nemici pi&ugrave; fieri, Borelli e Rossetti, lo <lb/>censurarono aspramente, o per dir pi&ugrave; giusto lo calunniarono, ma pure, in <lb/>mezzo agli errori, gli rimane un merito singolare, quello di essere stato il <lb/>primo e l'unico, infino al Clairaut e al Laplace, a dare importanza al me&shy;<lb/>nisco concavo, facendo principalmente da lui dipendere la salita dell'acqua <lb/>ne'sottilissimi tubi di vetro. </s>

<s>&ldquo; Perch&egrave; dunque vediamo l'acqua, e altri li&shy;<lb/>quidi che per i cannellini ascendono, tali essere che, o per la figura parti&shy;<lb/>colare de'loro minimi, o per la flessibilit&agrave; dei medesimi, meglio s'adattano <lb/>alla superficie di esso vetro, che non fa l'aria; non sar&agrave; difficile da capire, <lb/>come, intorno alle sponde d'un vaso, per necessit&agrave; debbano sollevarsi pi&ugrave; <lb/>dal livello che in mezzo, essendo che, per esser premuti nel mezzo dall'aria <lb/>soprastante, sono forzati subentrare in tutti que'luoghi, ove comodo loro rie&shy;<lb/>sce d'entrare, e dove meno resistenza essi trovano, di quello sia la pressione <lb/>che gli sospinge &rdquo; (ivi, pag. </s>

<s>34). </s></p><p type="main">

<s>E perch&egrave; si poteva dubitare che, sollevandosi le sole particelle contigue <lb/>al tubo, lascerebbero una cavit&agrave; cilindrica, piuttosto che un menisco; il Mon&shy;<lb/>tanari soggiunge che le dette particelle, a cagione della loro viscosit&agrave;, non <lb/>solo conducono in alto le particelle sottoposte a perpendicolo &ldquo; ma molte <lb/>laterali ancora verso il mezzo del vaso, le quali nel sollevarsi incontrano la <lb/>gravit&agrave; dell'aria che li sovrasta, onde, tanto solamente si sollevano contro il <pb xlink:href="020/01/3362.jpg" pagenum="323"/>peso dell'aria, quanto la forza di quell'ultime, che sono immediate alla <lb/>sponda del vaso, pu&ograve; sollevarle &rdquo; (ivi, pag. </s>

<s>35, 36). </s></p><p type="main">

<s>Quanto ai contrari effetti, che si osservano nel mercurio, bench&egrave; il Mon&shy;<lb/>tanari censuri l'opinione del Fabry, dicendo che, se il liquido crasso trova <lb/>difficolt&agrave; a entrar ne'pori e nelle strie del vetro, dovrebbe anche trovarla <lb/>simile nell'uscire; non sa sostituirvi molto di meglio. </s>

<s>&ldquo; Non &egrave; punto inve&shy;<lb/>risimle, egli dice, che siccome sono alcuni fluidi, che meglio s'accomodano <lb/>alla superficie d'alcuni corpi, che non fa l'aria; cos&igrave; alcun altro si trovi che <lb/>peggio di lui vi s'adatti, come sarebbe il mercurio. </s>

<s>Onde, siccome l'acqua <lb/>s'inalza alle sponde de'vasi, per riempire li spazietti fra l'aria e le sponde; <lb/>cos&igrave;, per le medesime ragioni, dovr&agrave; l'aria appresso le medesime sponde <lb/>profondarsi, a riempir quelli che fra il mercurio e le sponde rimangono &rdquo; <lb/>(ivi, pag. </s>

<s>40, 41). </s></p><p type="main">

<s>La corrente delle idee, pel giro della quale abbiamo fin qui menati i <lb/>Lettori, ebbe, come si disse, gl'impulsi dall'Accademia del Cimento, rima&shy;<lb/>sta tuttavia chiusa dalle porte del palazzo mediceo, che noi dobbiam pene&shy;<lb/>trare. </s>

<s>Che la salita de'liquidi nei cannellini fosse da attribuire alle pressioni <lb/>dell'aria, fu opinione degli Accademici, infino dal 1658, quando, almeno per <lb/>avere investigate le ragioni del fatto, si compiacquero di restar superiori ai <lb/>Francesi. </s>

<s>Non poteva per&ograve; la compiacenza essere assoluta, se quella loro opi&shy;<lb/>nione non si vedeva confermata dalla esperienza, osservando quel che av&shy;<lb/>viene, costituito lo strumento capillare nel vuoto. </s>

<s>E perch&egrave; i Nostri usarono <lb/>sempre di farlo col tubo torricelliano, dovettero incontrare quelle difficolt&agrave;, <lb/>delle quali fanno testimonianza gli stessi loro diari, relativi ai giorni 14, 15 <lb/>e 16 Giugno 1660, ne'quali il frutto, che se ne raccolse, &egrave; confessato da <lb/>queste parole: &ldquo; Nulla per&ograve; si pot&egrave; ritrarre da tal maniera di praticare que&shy;<lb/>ste esperienze &rdquo; (Targioni, <emph type="italics"/>Notizie<emph.end type="italics"/> cit., T. II, pag. </s>

<s>435). </s></p><p type="main">

<s>Letta la nota del Thevenot, e per essa facilmente persuasi che, rimasti <lb/>indietro ai Francesi per la copia delle osservazioni dei fatti, non s'aveva <lb/>altra speranza di superiorit&agrave;, che nella scoperta delle loro vere cagioni; gli <lb/>Accademici fiorentini, negli ultimi giorni del mese d'Agosto 1662, ripresero <lb/>in mano l'esperienze, che poi ridussero a tal perfezione, quale apparisce dalle <lb/>descrizioni del loro libro dei <emph type="italics"/>Saggi.<emph.end type="italics"/> I resultati, che cos&igrave; ottennero, erano de&shy;<lb/>cisivi, non lasciando oramai pi&ugrave; appiglio a introdur nella questione l'aria <lb/>rarefatta, che, se pu&ograve; rimaner sotto la campana del Boyle, viene affatto <lb/>esclusa dal tubo del Torricelli. </s>

<s>E fu la decisione, come sappiamo, che il pre&shy;<lb/>mer pi&ugrave; languido, che fa l'aria per gli angustissimi seni dei cannellini, non <lb/>sia per s&egrave; sola causa bastante a spiegare i loro effetti. </s></p><p type="main">

<s>Reciso cos&igrave; dalle radici il rigoglio dell'ipotesi boileiana, la scienza dei <lb/>fenomeni capillari cadde d'un colpo, e a rilevarla concorsero primi coloro <lb/>che, costretti da una certa fatale necessit&agrave;, avevano menato la scure. </s>

<s>Il Ri&shy;<lb/>naldini, uscito fuori dall'Accademia, dette il primo pubblico documento della <lb/>restaurazione, la quale si faceva consistere nell'ammetter che il liquido sale <lb/>su per il cannellino, perch&egrave; fra le angustie di lui molto perde del suo pro-<pb xlink:href="020/01/3363.jpg" pagenum="324"/>prio momento. </s>

<s>S'era, egli dice, creduto da principio che la cosa dipendesse <lb/>dalla pressione dell'aria, &ldquo; non autem sic se habet, nam idem contingit in <lb/>loco, ubi nullus aer, vel saltem adeo exiguae quantitatis, ne vix credas ei <lb/>quidquam deferendum, quod nos Florentiae sumus experti. </s>

<s>Sed potius aliunde <lb/>id provenit, quia scilicet dum exilis ille tubulus immergitur nonnihil in flui&shy;<lb/>dum, huius pars inclusa in angustia ipsius tubuli multum amittit momenti, <lb/>unde nequit aeque ponderare partibus circumiacentibus, sed his urgentibus <lb/>prementibusque cylindrus ex humido intra tubuli angustiam cedit, eousque <lb/>ascendens, ut eius altitudo possit in aequilibrio esse cum cylindris ex humido <lb/>circumiacente. </s>

<s>Nihil enim refert, sive desuper premat, vel non premat aer &rdquo; <lb/>(<emph type="italics"/>De resolutione et compositione<emph.end type="italics"/> cit., pag. </s>

<s>160). </s></p><p type="main">

<s>D'onde avvenga per&ograve; che il liquido perde fra le angustie del cannellino <lb/>parte del suo momento, il Rinaldini non dice, ma supplisce al difetto il Bo&shy;<lb/>relli, il quale narra che l'opinioni proposte, esclusa quella di coloro che in&shy;<lb/>vocavano la pressione dell'aria, si riducevano a due: l'una delle quali era <lb/>che l'acqua non scendesse, rimanendo sospessa ne'cannellini, per l'asprezza <lb/>delle loro superficie; l'altra che l'acqua stessa salisse per impulso suo pro&shy;<lb/>prio e naturale. </s>

<s>Questa opinione era merce straniera, insinuatasi nell'Acca&shy;<lb/>demia da'cartesiani, al numero de'quali apparteneva Luc'Antonio Porzio, <lb/>che cos&igrave; scrisse: &ldquo; Sorge l'acqua, nelle fistole molto anguste aperte da am&shy;<lb/>bedue gli estremi, essendo elle umide alquanto, cio&egrave; contenendo ne'loro pori, <lb/>appunto come se fossero piccole conchette, o acqua o altro licore analogo <lb/>all'acqua, e vi sorge ella da s&egrave; stessa, in virt&ugrave; del suo proprio momento, col <lb/>quale si unisce e mischia coll'acqua contenuta ne'pori delle fistole. </s>

<s>Laonde, <lb/>essendo elle molto anguste, di modo che l'acqua da un lato di avvantaggio <lb/>possa toccar l'acqua del lato opposto; se ne vedranno ripiene fin a cinque <lb/>o sei dita della loro longitudine e talora assai pi&ugrave; &rdquo; (<emph type="italics"/>Del sorgimento de'li&shy;<lb/>cori<emph.end type="italics"/> cit., pag. </s>

<s>84). </s></p><p type="main">

<s>Il Borelli facilmente confut&ograve; queste due opinioni, proponendone una sua <lb/>propria, dietro il supposto che le molecole liquide siano rivestite di una certa <lb/>lanugine, i peli della quale entrando nella porosit&agrave; delle pareti, e nelle emi&shy;<lb/>nenze di esse ritrovando il convenevole appoggio, facessero le funzioni di <lb/>vette, e cos&igrave; venissero a sollevarsi via via le particelle stesse aderenti alle <lb/>dette pareti, in virt&ugrave; di un tale macchinamento. </s>

<s>&ldquo; Quia aquae particulae, <lb/>adhaerentes parieti vasis, insinuant ramos suarum machinularum intra po&shy;<lb/>rositates et foveolas parietis, a cuius eminentiis et asperitatibus fulciuntur <lb/>extremitates particularum aquae, quarum oppositi termini sustinentur, a su&shy;<lb/>biecta collaterali aqua; propterea efficiuntur veluti totidem vectes, converti&shy;<lb/>biles circa eorum fulcimenta, parieti annexa. </s>

<s>Hinc fit ut praedictae aquae <lb/>particulae exiguam vim compressivam exerceant, et minori momento su&shy;<lb/>biectam aquam comprimant, cum partes aquae collaterales, libere premendo <lb/>supra aquam subiectam, integram suam vim et momentum exerceant. </s>

<s>Igi&shy;<lb/>tur partes minus pressae sursum impelli debent a partibus magis compres&shy;<lb/>sis &rdquo; (<emph type="italics"/>De motion. </s>

<s>natur.<emph.end type="italics"/> cit., pag. </s>

<s>371). </s></p><pb xlink:href="020/01/3364.jpg" pagenum="325"/><p type="main">

<s>Prosegue il Borelli ad applicare la meccanica di questi moti alla spie&shy;<lb/>gazione dei vari fenomeni, osservati nelle fistole capillari, e finalmente riserba <lb/>il capitolo IX dell'opera a trattar dell'amplesso e della fuga de'corpuscoli <lb/>galleggianti. </s>

<s>Descritte particolarmente l'esperienze, che si riducon per lui a <lb/>far galleggiare sull'acqua ora due laminette di rame insieme, ora due assi&shy;<lb/>celle di legno, e ora una laminetta e un'assicella; fa consistere il merito <lb/>della sua scoperta nell'avere osservato che tutto il negozio da null'altro di&shy;<lb/>pende, che dal formarsi o una fossa o un'argine intorno ai detti corpuscoli, <lb/>e conclude all'ultimo cos&igrave; il suo discorso: &ldquo; Et haec est vera et accurata <lb/>historia huius admirandi effectus. </s>

<s>Non igitur miror veram causam huius <lb/>effectus adductam non fuisse, cum non constabat, neque perfecte inno&shy;<lb/>tuerat, historia huius operationis, quae tantummodo clare et evidenter ob&shy;<lb/>servari potest, mediantibus supradictis laminulis a me excogitatis &rdquo; (ibid., <lb/>pag. </s>

<s>389). </s></p><p type="main">

<s>Il Viviani, come i nostri Lettori gi&agrave; sanno, aveva creduto di poter ren&shy;<lb/>dere l'ammirabile effetto ugualmente chiaro e manifesto, anche senza queste <lb/>lamine cos&igrave; elaborate, servendosi con molta semplicit&agrave; delle pallottole di cera, <lb/>e delle crazie, e nello stesso tempo formulava queste leggi col dire che ar&shy;<lb/>gine con argine, e fossa con fossa si uniscono, e argine con fossa si sfug&shy;<lb/>gono. </s>

<s>Ma soggiungeva oltre a ci&ograve;, in questo genere, uno spettacolo nuovo, <lb/>di cui non fa menzione il Borelli, quello cio&egrave; del vedere alcuni corpuscoli dal <lb/>mezzo di un bicchiere colmo scendere ai labbri, mentre altri dai labbri ri&shy;<lb/>salivano a posarsi nel mezzo. </s>

<s>Il Vossio, che come si disse fu primo a descri&shy;<lb/>vere e a divulgar questo gioco, pens&ograve; che l'osservata contrariet&agrave; degli effetti <lb/>dipendesse dal peso assoluto dei galleggianti, ingannato senza dubbio dalla <lb/>qualit&agrave; delle materie scelte a quest'uso, ch'erano limature di vari metalli, <lb/>e gusci di noci. </s>

<s>&ldquo; Immittatur in aquam putamen nucis, aut sphaera vitrea <lb/>intus cava, aut quaecumque alia res aqua levior: illico videbis corpuscula <lb/>istaec, relicta ora, adscendere versus medium, et ibi consistere.... Quod si <lb/>etiam alia immiseris corpuscula innatantia, quae sint aqua graviora, scobem <lb/>nempe ferri, aeris, aut alius metalli, contrarium videbis: illa quippe ad de&shy;<lb/>pressiorem oram descendent &rdquo; (<emph type="italics"/>De motu marium et ventor<emph.end type="italics"/> cit., pag. </s>

<s>43). </s></p><p type="main">

<s>Il Mariotte poi (<emph type="italics"/>Du mouvement des eaux,<emph.end type="italics"/> Oeuvres, a Leyde 1727, <lb/>pag. </s>

<s>374) corresse l'errore, osservando che non dalla leggerezza o dalla gra&shy;<lb/>vit&agrave; de'corpuscoli, ma dall'essere o no bagnati dall'acqua dipendono le con&shy;<lb/>trariet&agrave; de'loro moti, a quel modo che, nella nota autografa pubblicata da <lb/>noi di sopra, aveva prima scritto il Viviani. </s></p><p type="main">

<s>Il Viviani nulladimeno non sembra che fosse, come il Borelli, geloso <lb/>della scoperta, ripensando che ella principalmente consisteva, no nella chiara <lb/>ed evidente dimostrazione degli argini e delle fosse, ma nella vera ragione <lb/>del loro formarsi cos&igrave; intorno alle pareti dei galleggianti. </s>

<s>Quel che del resto <lb/>aveva, a questo effetto, immaginato esso Borelli si disse che non trov&ograve; quella <lb/>piena e perfetta approvazione, che egli sperava ne'suoi colleghi. </s>

<s>Venuta a <lb/>mancar la pressione dell'aria, questi vollero confessar piuttosto, con filosofica <pb xlink:href="020/01/3365.jpg" pagenum="326"/>ingenuit&agrave;, di non sapere a che altro dare ingerenza di sostenere i liquidi nei <lb/>sottilissimi tubi. </s></p><p type="main">

<s>In mezzo a questi accorati silenzi, usc&igrave; fuori la voce di Donato Rossetti <lb/>che, vedute le male prove delle ipotesi nuove, prese animo di restaurare le <lb/>antiche. </s>

<s>Se dell'effetto in questione, cominci&ograve; a dire, la causa non &egrave; esterna <lb/>nel peso dell'aria, &egrave; forza ricorrere a un'interna virt&ugrave; calamitica, che faccia <lb/>l'acqua correre al vetro per esservi attratta. </s>

<s>&ldquo; E perch&egrave;, soggiunge, la na&shy;<lb/>tura elegge la via pi&ugrave; facile, &egrave; cosa sicura che l'acqua sempre orizontal&shy;<lb/>mente corre al vetro. </s>

<s>Ma, per essere in maggior numero i minimi, che vi <lb/>accorrono, di quelli che possono fare una circonferenza fisica, e coronare la <lb/>sponda interiore del vaso; di qui &egrave; che i contendenti e sottendenti elevino <lb/>gi&agrave; li aderenti, col sottentrare e subsottentrare, dal che ne segue la massa <lb/>elevata &rdquo; (<emph type="italics"/>Antignome fisico-matem.,<emph.end type="italics"/> Livorno 1667, pag. </s>

<s>72). </s></p><p type="main">

<s>Che se, essendo unto il vetro, o in luogo dell'acqua il mercurio, s'os&shy;<lb/>serva la massa non s'elevar, ma abbassarsi, &egrave; da dire che tra il liquido e il <lb/>solido &egrave; un respingimento, piuttosto che un'attrazione; un aborrimento in&shy;<lb/>vece di un'appetenza. </s>

<s>&ldquo; E cos&igrave; l'aria nell'acqua si restringe in palla, per <lb/>esser contigua a minor superficie d'acqua, che sia possibile, e cos&igrave; fa l'acqua <lb/>nell'aria, che nel piano sottoposto vi si stende pi&ugrave; o meno o punto, secondo <lb/>l'appetenza che vi ha, ma dalla parte dell'aria si stringe al possibile, e si <lb/>ammassa o in sfera o in porzion di quella, per esser circondata da meno <lb/>aria, che gli sia riuscibile. </s>

<s>E questa &egrave; la cagione perch&egrave; l'acqua si faccia <lb/>colma in vasi untuosi, ed il mercurio nei vasi di vetro. </s>

<s>E per questa ragione, <lb/>e per il resistere alla cessione repugnante e violenta, se ne causa il colmeg&shy;<lb/>giare de'liquidi ne'vasi pieni. </s>

<s>Adunque, perch&egrave; il mercurio quasi sopra tutti <lb/>i piani s'agglobi, n'&egrave; cagion l'appetenza, che le sue particelle hanno tra <lb/>s&egrave;, e l'aborrimento, che ha all'aria ed al piano, sopra il quale scorre, per <lb/>non vi avere confacenza ed appetenza alcuna &rdquo; (ivi, pag. </s>

<s>83). </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Essendo l'<emph type="italics"/>Antignome<emph.end type="italics"/> distesa in dialogo, fa dire il Rossetti a uno dei <lb/>suoi interlocutori che questi pensieri gli giungevano nuovi. </s>

<s>N&egrave; desta punto <lb/>la maraviglia l'apparizione di una tal novit&agrave;, specialmente agli amici del&shy;<lb/>l'Autore, perch&egrave; quei pensieri, che spuntavano dal Discorso galileiano in&shy;<lb/>torno alle galleggianti, erano rimasti soffocati dai discorsi nuovi del Salviati, <lb/>quasi costrutto gi&agrave; scritto, sopra il quale, invece che a cancellarlo, sia pas&shy;<lb/>sata la punta della penna a sostituirvene un altro, con carattere pi&ugrave; scolpito. </s></p><p type="main">

<s>Avvenne perci&ograve; ai pensieri del Rossetti quel ch'&egrave; solito avvenire a tutte <lb/>le cose nuove, ma veramente mancavano a loro, per trovar nel pubblico la <lb/>meritata accoglienza, certe qualit&agrave;, che s'intenderanno meglio per questa di&shy;<lb/>versione del nostro discorso. </s></p><pb xlink:href="020/01/3366.jpg" pagenum="327"/><p type="main">

<s>Sulla superficie AB (fig. </s>

<s>162) di un'acqua galleggi l'assicella CD, che <lb/>sostiene la gocciola concentrata in K. Un'altra simile gocciola pendente, col <lb/>centro in I, dalla lamina EF, si accosti alla prima, per via del filo HG, te&shy;<lb/><figure id="id.020.01.3366.1.jpg" xlink:href="020/01/3366/1.jpg"/></s></p><p type="caption">

<s>Figura 162.<lb/>nuto, per il suo capo G, in mano. </s>

<s>Si osserva che le due <lb/>dette gocciole non s'acquietano nel contatto, ma segui&shy;<lb/>tano a moversi, stringendosi l'una sempre pi&ugrave; contro <lb/>l'altra, infin tanto che i loro vertici non cadano sopra <lb/>la medesima linea perpendicolare all'orizonte. </s>

<s>Il Borelli, <lb/>che osserv&ograve; e descrisse il fatto curioso, disse, volendolo <lb/>spiegare, che avvien delle due gocciole quel che di due <lb/>lastre di vetro ben piane a contatto, le quali, bench&egrave; siano cos&igrave; renitenti a <lb/>separarsi, mettendosi a tirarle, in direzione perpendicolare alla loro superfi&shy;<lb/>cie, scivolano poi facilmente, ponendole inclinate, &ldquo; impulsa ab istinctu na&shy;<lb/>turali, quo gravia conantur semper magis ad centrum gravium accedere, <lb/>eo modo quo possunt; scilicet via inclinata, cum directa et perpendicularis <lb/>fuerit impedita &rdquo; (<emph type="italics"/>De motion. </s>

<s>natur.<emph.end type="italics"/> cit., pag. </s>

<s>390). </s></p><p type="main">

<s>Avendo il Montanari osservato che l'aderenza fra le due lastre di vetro <lb/>si ottiene anche pi&ugrave; facilmente, quando interceda fra loro un sottilissimo velo <lb/>di acqua; volle a modo suo anche spiegare perch&egrave;, strisciando l'una sopra <lb/>l'altra, bench&egrave; tenute orizontalmente, cedano alla pi&ugrave; piccola forza. </s>

<s>La spie&shy;<lb/>gazione per&ograve; fu giudicata dal Rossetti insufficiente, anzi falsa, sostituendovi, <lb/>dietro il principio dell'attrazione molecolare, quest'altra, che secondo lui era <lb/>la vera: &ldquo; Ma volete vedere colla mia dottrina quanto mirabilmente si spie&shy;<lb/>ghino questi effetti? </s>

<s>Da voi medesimo consideratelo, che concluderete che, <lb/>avendo l'acqua <emph type="italics"/>appetenza<emph.end type="italics"/> al vetro, con quello sta <emph type="italics"/>aderente<emph.end type="italics"/> a segno, che non <lb/>si distaccher&agrave;, senza qualche violenza. </s>

<s>Ma perch&egrave;, a volerle staccare per le <lb/>perpendicolari, devesi far violenza nel medesimo tempo a tutti i minimi <lb/>d'acqua, che sono fra le due lastre, e che ad ambedue stanno aderenti, ov&shy;<lb/>vero fra loro e con la lastra, e per staccarli lateralmente non si fa violenza, <lb/>se non che a tanti minimi, quanti bastano a fare una linea fisica lunga, <lb/>quant'&egrave; larga la lastra per quel verso, dal quale si tira, perch&egrave; questi soli <lb/>devono lasciare in tanto tempo una lastra; quindi ne &egrave; che, con pochissima <lb/>forza e facilissimamente, si staccano tali lastre, a guidarle orizontalmente. </s>

<s><lb/>Ma a perpendicolo fa di mestieri ci&ograve; segua per una gran forza, e per una <lb/>forza tale, che abbia a quella prima forza la proporzione, che hanno tutti i <lb/>minimi, che <emph type="italics"/>aderiscono<emph.end type="italics"/> alle lastre, a quelli che compongono l'accennata linea <lb/>fisica &rdquo; (<emph type="italics"/>Insegnamenti fisico-matem.,<emph.end type="italics"/> Livorno 1669, pag. </s>

<s>169). </s></p><p type="main">

<s>Applicando queste dottrine del Rossetti al fatto delle gocciole, descritto <lb/>dal Borelli, si direbbe che l'aderenza &egrave; un effetto della loro scambievole <lb/>attrazione, la forza della quale essendo rappresentata per IK (nella medesima <lb/>ultima figura) se questa si decomponga nella orizontale IL, e nella verticale <lb/>IM, avremo la ragion manifesta dello spettacoloso moto descritto e della <lb/>quiete. </s>

<s>Imperocch&egrave;, essendo la IM equilibrata dal filo HG, riman la sola IL <lb/>attiva in far avvicinar sempre pi&ugrave; le gocciole insieme. </s>

<s>E perch&egrave; questa atti-<pb xlink:href="020/01/3367.jpg" pagenum="328"/>vit&agrave; diminuisce via via, col diminuir dell'angolo KIM, e con esso finalmente <lb/>svanisce; &ldquo; hae duae guttulae non quiescent, sed lateraliter excurrent, quo&shy;<lb/>usque vertices earum in eadem recta perpendiculari ad horizontem excide&shy;<lb/>rint &rdquo; come dice, nell'annunziare la sua CLXXXIX proposizione, il Borelli <lb/>(Op. </s>

<s>cit., 390). </s></p><p type="main">

<s>Ora, il libero e sincero uso del parallelogrammo delle, forze era una di <lb/>quelle qualit&agrave; che, siccome a quelle del Borelli, venivano a mancare alle <lb/>nuove dottrine del Rossetti. </s>

<s>Ma &egrave; da soggiungere che qualit&agrave; pi&ugrave; intrinseche <lb/>mancavano a quelle stesse dottrine, affinch&egrave; tutti le potessero accoglier con <lb/>fede. </s>

<s>Il principio dell'attrazione molecolare fra i corpi si pu&ograve; dire una gemma <lb/>sepolta, che l'aratro abbia messa a fior di terra. </s>

<s>Il luccicare per&ograve; al sole, <lb/>in mezzo alle zolle, non bastava ai riguardanti, per riconoscerne il pregio, <lb/>che nessuno poi metterebbe pi&ugrave; in dubbio, quando se ne vedesse il cristallo <lb/>legato in un anello d'oro, e che di pi&ugrave; quell'anello splendesse a un gran <lb/>signore nel dito. </s>

<s>L'orefice fu la Matematica di Filosofia naturale, che leg&ograve; <lb/>la sciolta dottrina del Rossetti nell'universal sistema dell'attrazione, e quel <lb/>gran signore che si diceva &egrave; Isacco Newton. </s>

<s>Il primo Tomo della grande <lb/>Opera di lui si conclude in alcuni teoremi, dimostrativi dell'intensit&agrave;, e della <lb/>direzione delle forze sollecitanti un corpuscolo, che sia attratto, e che passi <lb/>attraverso a un mezzo similare. </s>

<s>Applicando poi questi teoremi alla luce, che <lb/>il Newton non dubita di riguardar come composta di minutissimi corpuscoli <lb/>duri, attratti al cristallo, per mezzo al quale trapassano, osservando le leggi <lb/>precedentemente dimostrate; ne desume le principali propriet&agrave; delle ottiche <lb/>rifrazioni. </s></p><p type="main">

<s>Come, seguitandosi ad agitar tuttavia la questione dei capillari, fosse <lb/>di qui suggerita all'Hauksbee l'idea dell'attrazione dei corpuscoli, compo&shy;<lb/>nenti l'acqua, al vetro del tubo, con cui sono a contatto; si comprender&agrave; <lb/>assai facilmente. </s>

<s>Quell'insigne uomo del cav. </s>

<s>Isacco Newton, che esso Hauk&shy;<lb/>sbee commemora qual gloria della sua Nazione, e della Societ&agrave; regia, gli <lb/>avrebbe altresi suggerito il modo di decomporre nel parallelogrammo quelle <lb/>forze attrattive. </s>

<s>E bench'egli mostri di non sapersene prevalere con tutta la <lb/><figure id="id.020.01.3367.1.jpg" xlink:href="020/01/3367/1.jpg"/></s></p><p type="caption">

<s>Figura 163.<lb/>perfezione, non lascia per&ograve; la speranza che, della ra&shy;<lb/>gion del salire i liquidi nei piccoli tubi, non sia la se&shy;<lb/>guente sua una <emph type="italics"/>narrativa appagante.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia ABCD (fig. </s>

<s>163) un piccolo tubo, perpendico&shy;<lb/>larmente immerso in un liquido, la superficie orizontale <lb/>di cui sia EF. </s>

<s>Le parti del fluido X, Y, congiungendosi <lb/>alla concava superficie del tubo, ne sono gagliardamente <lb/>attratte, e ci&ograve; in una direzione perpendicolare ai lati del <lb/>vetro cilindrico. </s>

<s>Ora le particelle X, Y; gravitando in <lb/>direzioni perpendicolari ad EF, hanno tutte un molto <lb/>minor momento o forza gravante di quello, che elle per altro avrebbero, <lb/>se fosse tolta via l'attrazione. </s>

<s>Perci&ograve; le parti del fluido, che sono a loro <lb/>immediatamente sotto, ricevono minor pressione di quella, che altrimenti <pb xlink:href="020/01/3368.jpg" pagenum="329"/>avrebbero. . . . Ma le parti del fluido, che stanno nel mezzo tra la superficie <lb/>EF e il fondo del tubo, in pi&ugrave; rimota distanza dai lati del tubo, di quella <lb/>del proprio loro semidiametro; queste particelle, dico, essendo fuori del tiro <lb/>di tali attrazioni, gravitano con tutta quanta la loro forza o momento sopra <lb/>le parti, che stanno loro sotto. </s>

<s>Onde appare che, per l'immersione del pic&shy;<lb/>colo tubo dentro il liquido, si distrugga l'equilibrio tra quelle parti del li&shy;<lb/>quido giacenti dentro la circonferenza della base inferiore, e quelle che sono <lb/>al di fuori. </s>

<s>Laonde, secondo le leggi idrostatiche, bisogna che il liquido salga <lb/>dentro la superficie del tubo &rdquo; (<emph type="italics"/>Esperienze fisico-meccan.<emph.end type="italics"/> cit., pag. </s>

<s>130, 31). </s></p><p type="main">

<s>Essendosi dimostrate le ragioni, prosegue a dire l'Hauksbee, del risa&shy;<lb/>lire i liquidi ne'piccoli tubi, resta a dire perch&egrave; maggiori siano queste ri&shy;<lb/>salite nei pi&ugrave; stretti. </s>

<s>E per venire alla conclusione, osserva che, essendo le <lb/>forze attrattive proporzionali alle superficie concave dei tubi, e i pesi alle <lb/>colonne liquide, che gli riempiono; quelle stanno a questi come le circon&shy;<lb/>ferenze alle superficie dei circoli. </s>

<s>Ora, perch&egrave; sempre &egrave; maggior proporzione <lb/>tra la circonferenza e la superficie nei cerchi piccoli, che ne'grandi; perci&ograve; <lb/>il piccolo tubo &egrave; maggiormente proporzionato del grande a sollevare il peso, <lb/>&ldquo; e per questa ragione il liquido dovr&agrave; salire pi&ugrave; alto nel primo, che nel <lb/>secondo &rdquo; (ivi, pag. </s>

<s>134). </s></p><p type="main">

<s>A questo proposito non si vuol lasciare inosservato che il Borelli aveva, <lb/>dopo il Vossio, assegnato del fatto le medesime ragioni. </s>

<s>Se non che il Nostro, <lb/>misurando l'effetto non solo estensivamente, ma anche intensivamente, ne ren&shy;<lb/>deva pi&ugrave; compiuta la dimostrazione, e tale che, se l'aderenza dell'acqua al <lb/>vetro di cui parla, si volesse attribuire all'attrazione molecolare, s'accenne&shy;<lb/>rebbe dal Borelli a un'altra causa del sostenersi maggiormente i liquidi nei <lb/>tubi pi&ugrave; stretti, sfuggita forse alla sottilissima analisi dei moderni: &ldquo; Et <lb/>quoad extensionem pertinet, quia vis adhaesionis mensuratur a contactibus, <lb/>et ideo a superficie interna canaliculorum, e contra resistentia mensuratur <lb/>a pondere cylindri aquei, contenti in iisdem canaliculis, estque proportio cy&shy;<lb/>lindrorum aqueorum eiusdem altitudinis duplicata eius rationis, quam habent <lb/>eorum perimetri interni; igitur quanto magis crescit interna canalis ampli&shy;<lb/>tudo, tanto magis minuitur adhaesio, et augetur resistentia ponderis ipsius <lb/>aquae contentae. </s>

<s>Imminuitur postea gradus intensivus internae adhaesionis, <lb/>propterea quod, ut dictum est supra, non est aeque valida facultas et ener&shy;<lb/>gia adhaesionis aquae, et connexionis cum parietibus internis in universo illo <lb/>argine montuoso, sed est minus efficax, quanto magis ab internis parietibus <lb/>removetur. </s>

<s>Modo in fistulis amplioribus aqua contenta versus axim cavitatis <lb/>eius magis recedit a superficie interna fistulae dilatatae, quam in fistula stri&shy;<lb/>ctiori, et ideo in illa debilius aqua sustinebitur suspendeturque. </s>

<s>Et quanto mi&shy;<lb/>nor est vis sustinens et elevans, respectu ponderis fluidi contenti, tanto debet <lb/>imminui sublimitas eius elevationis &rdquo; (<emph type="italics"/>De motion. </s>

<s>natur.<emph.end type="italics"/> cit., pag. </s>

<s>384, 85). </s></p><p type="main">

<s>Ora, per tornare all'Hauksbee, avendo egli gi&agrave; detto perch&egrave; il liquido <lb/>salga a maggiore altezza ne'cannellini pi&ugrave; stretti, vorrebbe assegnarne inol&shy;<lb/>tre le proporzioni; vorrebbe dimostrare cio&egrave; che le altezze stanno reciproca-<pb xlink:href="020/01/3369.jpg" pagenum="330"/>mente come i raggi delle sezioni. </s>

<s>Non sembra per&ograve; a noi che ci riesca, al&shy;<lb/>meno con quella precisione, che si richiederebbe a un teorema di Geometria, <lb/>e chi cos&igrave; legge potrebbe per s&egrave; medesimo darne pi&ugrave; giusto giudizio: &ldquo; Come <lb/>la diminuita gravit&agrave; del liquido nei tubi sta all'assoluta gravit&agrave; del cilindro <lb/>collaterale del liquido esterno; cos&igrave; star&agrave; la profondit&agrave; dell'immersione al&shy;<lb/>l'altezza del liquido nel piccolo tubo. </s>

<s>Poich&egrave; suppongo che il cilindro di <lb/>fluido nel tubo sia equilibrato da un altro al di fuori, che abbia la medesima <lb/>base, e la cui altezza sia uguale all'immersione. </s>

<s>Conciossiach&egrave;, le basi es&shy;<lb/>sendo le medesime, l'altezze stanno come i contenuti, ovvero le quantit&agrave; <lb/>della materia. </s>

<s>E per fare un equilibrio o eguaglianza di momenti, le forze <lb/>debbon essere reciprocamente conforme le moli o quantit&agrave;, cio&egrave;, in questo <lb/>caso, reciprocamente quanto le altezze &rdquo; (<emph type="italics"/>Esperienze fisico-meccaniche<emph.end type="italics"/> cit., <lb/>pag. </s>

<s>134). </s></p><p type="main">

<s>&Egrave; nonostante l'Hauksbee benemerito di questi studii, per aver dimo&shy;<lb/>strato quanto ragionevolmente si spieghino i fatti in questione, per via del&shy;<lb/>l'attrazion molecolare. </s>

<s>In questo tempo il Newton veniva, nel terzo libro <lb/>dell'Ottica, a dare autorit&agrave; a cos&igrave; fatti principii, estendendogli a ogni qua&shy;<lb/>lit&agrave; di materia, ch'egli riguardava come composta d'innumerevoli particelle <lb/>dure, le quali diceva non s'intenderebbe come potessero nella composizione <lb/>dei corpi cos&igrave; tenacemente aderire insieme, &ldquo; nisi causa sit aliqua, quae ef&shy;<lb/>ciat ut aee ad se invicem attrahantur &rdquo; (<emph type="italics"/>Opera aptica omnia<emph.end type="italics"/> cit., pag. </s>

<s>159). <lb/>Soggiunge poi le leggi, che governano questa attrazione, l'intensit&agrave; della <lb/>quale diminuisce cos&igrave; rapidamente, che a una distanza sensibile non sola&shy;<lb/>mente riesce nulla, ma si converte in una repulsione. </s>

<s>&ldquo; Jam quidem fieri <lb/>potest ut materiae particulae exiguissimae attractionibus fortissimis inter se <lb/>cohaereant, constituantque particulas maiusculas, quarum vis illa attrahens <lb/>debilior sit, harumque particularum maiuscularum permultae, inter se iti&shy;<lb/>dem cohaerentes, particulas maiores constituant, quarum vis attrahens adhuc <lb/>sit debilior. </s>

<s>Et sic deinceps continuata serie, donec ad maximas tandem de&shy;<lb/>ventum sit particularum illarum, a quibus operationes chymicae et colores <lb/>corporum naturalium pendent, quaeque, inter se cohaerentes, corpora demum <lb/>constituant, magnitudine sub sensum cadente. . . . Et sicuti in algebra, ubi <lb/>quantitates affirmativae evanescunt et desinunt, ibi negativae incipiunt; ita <lb/>in mechanicis, ubi attractio desinit, ibi vis repellens succedere debet &rdquo; (ibid., <lb/>pag. </s>

<s>161). </s></p><p type="main">

<s>Per rendere poi accettevole l'applicazione di queste dottrine ai fenomeni <lb/>capillari, il Newton, come non manc&ograve; di verificare i fatti osservati dall'Hauk&shy;<lb/>sbee, cos&igrave; non lasci&ograve; di confutare la falsit&agrave; delle correnti opinioni. </s>

<s>L'Hook, <lb/>nell'osservazione VI della Micrografia, e pi&ugrave; diffusamente nell'opuscolo del <lb/>Bohem; il Sinclaro, lo Sturm, il Fabry nelle opere da noi citate; e pi&ugrave; pros&shy;<lb/>simamente il Leeuwenhock nell'epistola CXXXI, in continuazione degli <emph type="italics"/>Ar&shy;<lb/>cani della Natura;<emph.end type="italics"/> il Rohault, nel suo trattato di Fisica, il Mairan, nella <lb/>sua Storia dell'Accademia di Parigi; avevano dato, e seguitavano tuttavia a <lb/>dare autorit&agrave; all'opinione che, del salire i liquidi nei tubi capillari, fossero <pb xlink:href="020/01/3370.jpg" pagenum="331"/>unica causa il peso e l'elasticit&agrave; dell'aria. </s>

<s>S'aggiungeva a questi autori <lb/>Giacomo Bernoulli, che, pubblicando nel 1683 quella sua cos&igrave; celebrata dis&shy;<lb/>sertazione <emph type="italics"/>De gravitate aetheris,<emph.end type="italics"/> citava, a proposito dell'argomento che ora <lb/>trattiamo, l'ipotesi di alcuni Fisici, per confermarla con le ragioni e coi <lb/>fatti. </s>

<s>&ldquo; Secundum itaque Physiologos modernos in aere, praeter gravitatem, <lb/>considerare debemus vim quamdam, quam vocant elasticam, ita comparatam, <lb/>ut minima portio aeris alicubi incarcerati vel inclusi, in sustentandis aut <lb/>pellendis liquoribus, tantum possit, quantum totius atmosphaerae pondus &rdquo; <lb/>(<emph type="italics"/>Opera,<emph.end type="italics"/> Genevae 1744, pag. </s>

<s>82). </s></p><p type="main">

<s>Il Newton aveva, insieme con l'Hauksbee, concluso il suo discorso dei <lb/>fenomeni capillari, come udimmo, in una sentenza tutt'affatto contraria: <lb/><emph type="italics"/>Quare ex atmosphaerae pondere aut pressu nullo modo pendent.<emph.end type="italics"/> Il Ber&shy;<lb/>noulli nonostante e l'Huyghens avevano aperto un refugio, over ripararsi dai <lb/>colpi della detta sentenza (pronunziata gi&agrave; dagli Accademici del Cimento, e <lb/>confermata dal Rossetti assai prima) dicendo che, a sostentare i liquidi nei <lb/>sottilissimi tubi, sottentra la gravit&agrave; dell'etere a quella dell'aria evacuata. </s>

<s><lb/>E perci&ograve; il Newton volle cacciar l'errore anco da questo suo nascondiglio, <lb/>dimostrando, come si disse, che l'adesione delle due lamine levigate, e la <lb/>sospension dell'acqua o del mercurio dentro il tubo torricelliano, anche nel <lb/>vuoto; eran fatti, da non si dovere attribuire alla gravit&agrave; dell'etere, ma al&shy;<lb/>l'attrazione molecolare. </s></p><p type="main">

<s>Comunque sia per&ograve; bisogna confessare che, sebbene l'Hauksbee dichia&shy;<lb/>rasse pi&ugrave; particolarmente, e il Newton confermasse con la sua autorit&agrave; il <lb/>principio dell'attrazione fra i solidi e i liquidi, applicandolo alla spiegazion <lb/>dei fenomeni capillari; i due insigni uomini non promossero da pari loro la <lb/>scienza, lasciandola al punto, dove l'aveva condotta il Rossetti. </s>

<s>Egli us&ograve; la <lb/>parola <emph type="italics"/>appetenza,<emph.end type="italics"/> alla quale i due Inglesi ne sostituirono un'altra meno me&shy;<lb/>taforica, e quel bisticcio del <emph type="italics"/>sottoentrare e subsottoentrare delle molecole <lb/>contendenti e sottendenti<emph.end type="italics"/> usato dal Nostro, dettero, con pi&ugrave; proprio e con&shy;<lb/>veniente linguaggio, risoluto nella ragion meccanica dei momenti fra le forze <lb/>attrattive. </s></p><p type="main">

<s>La promozione, che manc&ograve; di dare il Newton ai fatti particolari della <lb/>Fisica, per essere il suo scopo quello di prestabilirle i principii matematici <lb/>universali; venne presto ad aversi per Guglielmo Giacomo's Gravesande, <lb/>che i suoi Elementi dichiarava col titolo <emph type="italics"/>Introductio ad Philosophiam newto&shy;<lb/>nianam.<emph.end type="italics"/> Nel capitolo V del I libro, trattando <emph type="italics"/>De cohaesione partium,<emph.end type="italics"/> mo&shy;<lb/>stra come un effetto insigne di questa coesione si riveli ne'fenomeni capil&shy;<lb/>lari, secondo le esperienze hausbeiane, ch'egli cita dalle Filosofiche transa&shy;<lb/>zioni, perch&egrave; forse, quando scriveva, non era stata fatta quella raccolta, nella <lb/>quale lo stesso Hauksbee, non contento di descrivere i fatti, ne concludeva <lb/>dai principii del Newton altres&igrave; le ragioni. </s>

<s>Di qui &egrave; che's Gravesande parla <lb/>come se fosse venuto il primo a bandire il vero, raccomandando di non dar <lb/>retta a quel che tutti gli altri ne avessero predicato. </s>

<s>&ldquo; Plures de causis ho&shy;<lb/>rum phaenomenorum scripserunt, sed nos ex aliis principiis haec in scholiis <pb xlink:href="020/01/3371.jpg" pagenum="332"/>illustrare conamur. </s>

<s>Quare iis, quae alii dederunt, inhaerendum non est &rdquo; <lb/>(<emph type="italics"/>Physicae elementa mathem. </s>

<s>editio IV,<emph.end type="italics"/> Leidae 1748, Praefatio pag. </s>

<s>XIX). </s></p><p type="main">

<s>Definita la forza dell'attrazione molecolare, secondo i principii della Fi&shy;<lb/>losofia newtoniana, e soggiunto ch'ella non agisce a sensibile distanza, dove <lb/>anzi convertesi in repulsione; descrive esso's Gravesande alcune esperienze <lb/>scelte da vari Autori, sopra le quali poi passa a ragionar matematicamente <lb/>in quattro Scolii. </s>

<s>De'primi due son queste che trascriviamo le conclusioni: <lb/>&ldquo; Vis ergo, quae sustinet aquam, proportionem sequitur latitudinis superfi&shy;<lb/>ciei, iuxta quam aqua ascendit, mensuratae ad altitudinem, ad quam aqua <lb/>pertingit in linea, ad superficiem ipsius aquae parallela. </s>

<s>Quam eamdem ra&shy;<lb/>tionem sequitur pondus aquae elevatae. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Aquam in tubos vitreos minores sponte adscendere vidimus, quod <lb/>quomodo fiat nunc evidenter patet. </s>

<s>Quantitas autem aquae quae sustinetur <lb/>sequitur rationem circumferentiae superficiei aquae elevatae, et circumfe&shy;<lb/>rentia haec, si agatur de tubis cylindricis perpendiculariter immersis, ad <lb/>instar diametri ipsius tubi crescit aut minuitur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sint duo tubi, quorum diametri dicantur D, <emph type="italics"/>d;<emph.end type="italics"/> altitudines aquae in <lb/>tubis A, <emph type="italics"/>a<emph.end type="italics"/>: quantitates aquae elevatae erunt inter se ut D2.A ad <emph type="italics"/>d<emph.end type="italics"/>2.<emph type="italics"/>a.<emph.end type="italics"/><lb/>Ideo D2.A:<emph type="italics"/>d2.a<emph.end type="italics"/>=D:<emph type="italics"/>d.<emph.end type="italics"/> Dividendo antecedentia per D2, et consequentia <lb/>per <emph type="italics"/>d2,<emph.end type="italics"/> habebimus A:<emph type="italics"/>a=d<emph.end type="italics"/>:D, idest altitudines sunt inverse ut diame&shy;<lb/>tri &rdquo; (ibid., T. I, pag. </s>

<s>26): ci&ograve; che per&ograve; non &egrave; conseguenza del calcolo, ma del&shy;<lb/>l'esperienza, sopra la quale &egrave; fondata la conclusione scritta nel primo Scolio. </s></p><p type="main">

<s>Il Musschenbroek fu pi&ugrave; preciso e ordinato. </s>

<s>Nel secondo capitolo della <lb/>sua dissertazione <emph type="italics"/>De tubis capillaribus vitreis,<emph.end type="italics"/> dop'aver concluso, dietro le <lb/>pi&ugrave; diligenti esperienze, che &ldquo; sunt altitudines aquae in his tubis accurate <lb/>in ratione inversa diametrorum tuborum &rdquo; (Lugduni Batav. </s>

<s>1729, pag. </s>

<s>296); <lb/>ne trae, dall'osservazione del fatto, i seguenti corollari: </s></p><p type="main">

<s>Chiamate A, A&prime; le altezze, a cui sale il liquido in due tubi capillari, i <lb/>raggi interni de'quali siano R, R&prime;, ricorrono le proporzioni A:A&prime;=R&prime;:R= <lb/>2<foreign lang="greek">p</foreign>R&prime;:2<foreign lang="greek">p</foreign>R; dunque &ldquo; erunt adscensus aquae in hos tubos in ratione in&shy;<lb/>versa peripheriarum basium &rdquo; (ibid.). Se L &egrave; la lunghezza uguale di due <lb/>tubi, A:A&prime;=2<foreign lang="greek">p</foreign>R&prime;.L:2<foreign lang="greek">p</foreign>R.L, ossia, &ldquo; sunt adscensus aquae, in tubos <lb/>aeque altos, in ratione inversa superficierum, quas tubi habent interne &rdquo; (ibid) <lb/>e si pu&ograve; soggiungere che, dalla proporzione A:A&prime;=2<foreign lang="greek">p</foreign>R&prime;:2<foreign lang="greek">p</foreign>R resultando <lb/>2<foreign lang="greek">p</foreign>R.A=2<foreign lang="greek">p</foreign>R&prime;.A&prime;, le interne superficie bagnate, ne'due tubi, sono uguali. </s>

<s><lb/>Se poi si moltiplichino ambedue i membri di questa equazione per R.R&prime;, <lb/>avremo 2<foreign lang="greek">p</foreign>R2.R&prime;.A=2<foreign lang="greek">p</foreign>R&prime;2.R.A&prime;, ossia <foreign lang="greek">p</foreign>R2.A:<foreign lang="greek">p</foreign>R&prime;2.A&prime;=R:R&prime;. <lb/>&ldquo; Erunt itaque quantitates aquae elevatae, in omnibus his tubis tam amplis <lb/>quam angustis, uti sunt semidiametri basium inter se. . . . Quamobrem tubi <lb/>ampliores maiorem quantitatem aquae elevant quam angustiores, licet ad <lb/>maiorem altitudinem elevent suam aquam, nam semper sunt quantitates ele&shy;<lb/>vatae uti semidiametri basium &rdquo; (ibid., pag. </s>

<s>297). </s></p><p type="main">

<s>Nel III Scolio's Gravesande dimostra che la curva, in cui si dispone <lb/>il lembo superiore del velo d'acqua sollevatasi fra due lamine di vetro, la <pb xlink:href="020/01/3372.jpg" pagenum="333"/>piccolissima inclinazion delle quali le faccia concorrere in una linea perpen&shy;<lb/>dicolare all'orizonte; &egrave; un'iperbola. </s>

<s>I Matematici di que'tempi, fra'quali il <lb/>Musschenbroek, nella dissertazione <emph type="italics"/>De attractione speculorum planorum vi&shy;<lb/>treorum,<emph.end type="italics"/> soggiunta all'altra dei tubi capillari; fecero alla detta dimostrazione <lb/>accoglienza, per la facilit&agrave; dei principii geometrici, sopra i quali, a questo <lb/>modo che riferiamo, presso a poco &egrave; condotta. </s>

<s>Sia ACB (fig. </s>

<s>164) il semian&shy;<lb/>golo formato dalle due lamine o specchi di vetro, e presa AT, che rappre&shy;<lb/><figure id="id.020.01.3372.1.jpg" xlink:href="020/01/3372/1.jpg"/></s></p><p type="caption">

<s>Figura 164.<lb/>senti la superficie dell'acqua nel vaso dell'immer&shy;<lb/>sione, uguale a BC, e sopra alzatavi perpendicolar&shy;<lb/>mente la TS, che rappresenti lo spigolo fatto dalle <lb/>due lamine: suppongasi che il velo d'acqua, sol&shy;<lb/>levatosi in mezzo ad esse, incurvi il suo lembo su&shy;<lb/>periore, disponendosi secondo la NPV, della qual <lb/>curva si vuol cercar l'equazione riferita agli assi <lb/>AT, TS. </s>

<s>Siano le due ordinate NM, PO le altezze <lb/>corrispondenti alle colonne liquide, aventi per basi <lb/>DG, HL. </s>

<s>Se i due specchi fossero paralleli, queste <lb/>colonne sarebbero uguali, e tali pure potendosi ri&shy;<lb/>tenere nel nostro caso, in cui la convergenza verso <lb/>l'angolo C si suppon piccolissima, avremo DG.MN=HL.OP, ossia DG:HL= <lb/>OP:MN. </s>

<s>E perch&egrave;, per le medesime ragioni, DG, HL si possono considerar <lb/>come rettangoli, i quali, avendo le basi EG, IL per costruzione uguali, stanno <lb/>come le altezze DE, HI, ossia come le EC, CI, o come le TM, TO; sar&agrave; <lb/>dunque TM:TO=OP:MN, e perci&ograve; la curva un'iperbola, descritta fra <lb/>gli asintoti AT, TS. </s></p><p type="main">

<s>Gli Elementi di's Gravesande, che introdussero le esperienze dell'Hauk&shy;<lb/>sbee nelle scuole, ebbero grandissima efficacia in diffondere i principii neu&shy;<lb/>toniani dell'attrazione molecolare, specialmente applicata ai fenomeni capil&shy;<lb/>lari. </s>

<s>Ma non mancarono le contradizioni di chi sempre si mostra ritroso alle <lb/>novit&agrave;, intorno a qualunque soggetto esse versino, e da qualunque autorit&agrave; <lb/>sian promosse. </s>

<s>Il Jurin non rimaneva sodisfatto della teoria hausbeiana, se&shy;<lb/>condo la quale sarebbero le forze attrattive diffuse per tutta l'interiore su&shy;<lb/>perficie del tubo. </s>

<s>Dal fatto che sempre le altezze de'liquidi sollevati sono in <lb/>ragion reciproca de'diametri dei cannellini, se ne conclude, ei ragionava, che <lb/>le superficie bagnate, e perci&ograve; le forze attrattive ad esse superficie propor&shy;<lb/>zionali, sono in ogni caso sempre le medesime, mentre il tubo pi&ugrave; largo <lb/>solleva maggior copia di liquido del pi&ugrave; stretto. </s>

<s>Ma non possono forze uguali <lb/>sostener pesi differenti; dunque, ne concludeva il Jurin, dev'essere una fal&shy;<lb/>lacia nell'assunto dell'Hauksbee, e per ritrovare il vero si rivolse alle espe&shy;<lb/>rienze. </s>

<s>Fra qu&egrave;ste, ad aprirgli la mente, glie ne sovvenne una, che fra le <lb/>narrate da noi comparisce nuova, ed &egrave; che, variando il tubo di raggio, come <lb/>se fossero due tronchi saldati insieme, e l'uno perpendicolarmente soprap&shy;<lb/>posto all'altro; la regola della salita &egrave; data sempre da quello di sopra. </s></p><p type="main">

<s>Cos&igrave;, per esempio, se il tubo avesse da A infino in B diametro pi&ugrave; pic-<pb xlink:href="020/01/3373.jpg" pagenum="334"/>colo, che da B fino in C, come nella fig. </s>

<s>165; o se da D fino in E l'avesse <lb/>pi&ugrave; grande, che da E fino in F come nella figura 166; immerse le bocche <lb/>inferiori CH, FN nel liquido, questo non salir&agrave; verso le bocche superiori AG, <lb/><figure id="id.020.01.3373.1.jpg" xlink:href="020/01/3373/1.jpg"/></s></p><p type="caption">

<s>Figura 165.<lb/><figure id="id.020.01.3373.2.jpg" xlink:href="020/01/3373/2.jpg"/></s></p><p type="caption">

<s>Figura 166.<lb/>DO, secondo la regola de'diametri CH, FN, ma <lb/>degli altri AG, DO, d'onde il Jurin argomentava es&shy;<lb/>sere le forze attrattive solamente limitate agli anelli <lb/>del vetro, che han per diametri AG, DO, e non <lb/>estese a tutta la superficie. </s>

<s>E cos&igrave;, soggiungeva, &egrave; <lb/>ragionevole che sia, avendosi allora propriamente le <lb/>cause proporzionali agli effetti. </s>

<s>Se infatti il liquido nel <lb/>cannello maggiore AF, rappresentato dalla fig. </s>

<s>167, <lb/>risale infino a BC, e nel minore infino a LM (fig. </s>

<s>168); <lb/>la forza in BC, alla forza in LM, sta come BC a LM. </s>

<s>Ma come GF ad HE, <lb/>ossia, come BC ad LM, stanno anche le colonne liquide; dunque le forze <lb/>sollevatrici son proporzionali ai pesi sollevati. <lb/><figure id="id.020.01.3373.3.jpg" xlink:href="020/01/3373/3.jpg"/></s></p><p type="caption">

<s>Figura 167.</s></p><p type="main">

<s>Altri Fisici non attaccarono la teoria hausbeiana nella forma, <lb/>ma la negarono nella sostanza. </s>

<s>Contro costoro il Musschenbroek, <lb/>annunziando ai Lettori i soggetti delle sue varie Dissertazioni, e <lb/>particolarmente di quella, in cui si proponeva di dimostrare che la <lb/>causa della ascesa dei liquidi nei tubi capillari &egrave; dovuta all'attra&shy;<lb/>zione; si rivolgeva con queste parole: &ldquo; Non dubito fore plerosque, <lb/>qui <emph type="italics"/>attractionis<emph.end type="italics"/> voce offendantur, eamque contemnant, derideant, <lb/>explodant. </s>

<s>His autem, si tanta sit animi aequitas, ut suspenso <lb/>praeiudicio Experimenta prius legant, et inter se comparent; tum, <lb/><figure id="id.020.01.3373.4.jpg" xlink:href="020/01/3373/4.jpg"/></s></p><p type="caption">

<s>Figura 168.<lb/>causam eorum eruere conantibus, facile apparebit propter quasnam <lb/>rationes hac voce usi fuimus &rdquo; (<emph type="italics"/>Dissertationes physicae experi&shy;<lb/>mentales,<emph.end type="italics"/> Lugduni Batav. </s>

<s>1729, pag. </s>

<s>IV). </s></p><p type="main">

<s>Anche il Musschenbroek per&ograve; ebbe a partecipare degli errori <lb/>del Jurin, studiandosi di ricavare dall'esperienza le leggi dell'at&shy;<lb/>trazione. </s>

<s>&ldquo; Haec vis (egli dice dop'avere sfrattate con lungo di&shy;<lb/>scorso le virt&ugrave; del suo argomento) terminatur in crustam aeream <lb/>tuborum antiquorum, in qua attrahendo se totam consumit, vel <lb/>impendit maximam saltem sui partem, hinc inepta est elevando <lb/>liquori aut debilitata admodum. </s>

<s>Et quia haec vis eo est fortior quo cor&shy;<lb/>poreo sui puncto, e quo egreditur, est propior; erit fortissima, cum super&shy;<lb/>ficies cava proxima sibi puncta habebit, sive cum crit arctissima. </s>

<s>Idcirco <lb/>altissime elevabitur liquor a tubis gracillimis, humilius ab amplioribus: imo <lb/>in graciles maiori velocitate adscendet, utpote actus maioribus viribus quam <lb/>in amplos. </s>

<s>Haec vis, ex quolibet puncto sui corporis emissa ad distantiam <lb/>aliquam, non modo elevat particulas liquoris superficiei tubi proximas, sed <lb/>quoque alias contiguas prioribus, aliasque hisce iterum contiguas, licet mi&shy;<lb/>nori robore, quae tamen, cum eamdem gravitatem inter se habent, minus ele&shy;<lb/>vari possunt: idcirco superficiem concavam componentes &rdquo; (ibid., pag. </s>

<s>331). </s></p><p type="main">

<s>Quella <emph type="italics"/>crusta aerea,<emph.end type="italics"/> della quale si tratta nel principio della citazione, <pb xlink:href="020/01/3374.jpg" pagenum="335"/>dette al Musschenbroek motivo a scoprir l'origine delle fallacie del Boyle, <lb/>e di altri esperimentatori insieme con lui, i quali, se trovarono che il li&shy;<lb/>quido sale pi&ugrave; su nei tubi prima bagnati, che negli asciutti, fu perch&egrave; si <lb/>servirono di vetri usati, piuttosto che nuovi (ivi, pag. </s>

<s>281). Ma pi&ugrave; devono <lb/>gli orecchi dei Lettori essere rimasti offesi da quel che soggiunge l'Autore <lb/>delle forze attrattive del solido, che si fanno sentire al liquido a distanza, <lb/>anzi a grande distanza: &ldquo; Agit igitur vis elevans tubi in distantiam, et qui&shy;<lb/>dem in magnam &rdquo; (ibid. </s>

<s>pag. </s>

<s>287), ci&ograve; che egli conclude dietro l'esperienza <lb/>descritta nel capitolo I della sua Dissertazione. </s></p><p type="main">

<s>Si narr&ograve; come nell'Accademia di Bologna si sperimentasse essere le al&shy;<lb/>tezze dei liquidi indipendenti dalle lunghezze dei tubi, e come il Montanari <lb/>avesse disingannato il Fabry, a cui parvero quelle altezze maggiori nei can&shy;<lb/>nellini pi&ugrave; lunghi. </s>

<s>Ora il Musschenbroek, rimproverando il Carr&eacute;, caduto poi <lb/>nel medesimo errore del Montanari &ldquo; miror, egli dice, cl. </s>

<s>Carreum non con&shy;<lb/>suluisse observationes Honorati Fabry, in <emph type="italics"/>Phys.,<emph.end type="italics"/> lib. </s>

<s>II, atque Sturmium, in <lb/><emph type="italics"/>Colleg. </s>

<s>curios.,<emph.end type="italics"/> qui observaverunt quo altius emineret tubulus, super aquae <lb/>superficiem, eo altius in ipsum adscendere aquam &rdquo; (ibid., pag. </s>

<s>285). </s></p><p type="main">

<s>Che la lunghezza immobile del cannello faccia qualche differenza dalla <lb/>lunghezza, che se gli aggiunge via via, sollevandolo sempre pi&ugrave; sul livello <lb/>dell'acqua, dove aveva la bocca immersa; non fa maraviglia, e con ci&ograve; ven&shy;<lb/>gono a conciliarsi le apparenti contrariet&agrave; delle esperienze. </s>

<s>Ma ben fa pi&ugrave; <lb/>maraviglia che, sopra una tal differenza accidentale, fondasse il Musschen&shy;<lb/>broek una conclusione tanto importante, qual'&egrave; che le forze attrattive si <lb/>estendano per tutta la lunghezza del tubo, anche molto di sopra al punto, <lb/>dove &egrave; salito il liquido che lo bagna. </s>

<s>&ldquo; Concludimus ex his experimentis vim <lb/>aut causam elevantem aquam per totam tubi longitudinem esse diffusam. </s>

<s><lb/>Quo igitur longior tubus existit, eo maior quantitas virium elevantium aquam <lb/>datur &rdquo; (ibid., pag. </s>

<s>287), ci&ograve; che ben si comprende essere l'errore stesso <lb/>del Jurin, molto pi&ugrave; esagerato. </s>

<s>L'Hauksbee invece aveva concluso che son <lb/>solamente attratte le particelle dell'acqua contigue al vetro, e che gli strati <lb/>cilindrici esterni, e concentrici alla superficie di contatto, per essere a sen&shy;<lb/>sibile distanza, non hanno efficacia in attrarre, e in far sollevare il liquido <lb/>nell'interno. </s>

<s>Lo's Gravesande pure, in piena conformit&agrave; con le dottrine del <lb/>Newton, aveva scritto: &ldquo; Haec autem attractio minimarum particularum hisce <lb/>legibus subiicitur, ut in ipso particularum contactu sit per quam magna, et <lb/>subito decrescat, ita ut, ad distantiam quam minimam, quae sub sensus ca&shy;<lb/>dit, non agat &rdquo; (<emph type="italics"/>Physicae elem.<emph.end type="italics"/> cit., pag. </s>

<s>18). </s></p><p type="main">

<s>Questi Elementi di fisica matematica, de'quali, dal 1719 al 1748, si fe&shy;<lb/>cero quattro edizioni, e le <emph type="italics"/>Esperienze fisico-meccaniche<emph.end type="italics"/> dell'Hauksbee, dal&shy;<lb/>l'originale inglese tradotte in varie lingue; cooperarono cos&igrave; in stabilir la <lb/>Fisica molecolare, che, verso la met&agrave; del secolo XVIII, nessuno oramai pi&ugrave; <lb/>dubitava che la salita de'liquidi nei cannellini non fosse per effetto del ve&shy;<lb/>tro, che potentemente gli attrae a non sensibile distanza. </s>

<s>In tali condizioni <lb/>trovava appunto la scienza M. Clairaut, il quale, de'tanti che l'avevano trat-<pb xlink:href="020/01/3375.jpg" pagenum="336"/>tata, giudic&ograve; il Jurin il pi&ugrave; eccellente, e perci&ograve; raccomandava la dissertazione <lb/>di lui, inserita nelle <emph type="italics"/>Filosofiche transazioni,<emph.end type="italics"/> a chiunque si volesse erudire <lb/>intorno alla Storia sperimentale dei fenomeni capillari. </s>

<s>&ldquo; Mais, seggiunge, <lb/>quoiqu'il y ait beaucoup &agrave; profiter dans la lecture de cette piece, j'avoue que <lb/>je n'ai pas p&ugrave; &egrave;tre satisfait de la theorie, que M. </s>

<s>Jurin y donn&eacute;, et que j'ai <lb/>cr&ucirc; que l'examen de cette question demandoit plus de principes, que cet <lb/>Auteur n'en a employ&eacute;s &rdquo; (<emph type="italics"/>Theorie de la figure de la Terre,<emph.end type="italics"/> a Paris 1743, <lb/>pag. </s>

<s>106). </s></p><p type="main">

<s>Il principio impiegato dal Jurin si riduce a quello dell'attrazione, non <lb/>determinata per&ograve; nei particolari modi di agire, se non per un argomento <lb/>logico, e per varii altri tutti sperimentali. </s>

<s>Quanto a quello osservava il Clai&shy;<lb/>raut che gli effetti son proporzionali alle cause solamente, quando si risale <lb/>a una causa prima e unica, ma non quando s'esamina un effetto, risultante <lb/>dal concorso di pi&ugrave; cause particolari (ivi, pag. </s>

<s>108). Quanto agli argomenti <lb/>sperimentali, e a quello principalmente che suggeri al Jurin l'idea di limi&shy;<lb/>tare le forze attrattive del vetro a quel solo anello di lui, che sovrasta im&shy;<lb/>mediatamente alla superficie dell'acqua; il Clairaut, considerando i filetti <lb/>liquidi IK, LM, lungo l'asse dei tubi rappresentati dalle figure 165 e 166, <lb/>concludeva dalla sua analisi matematica che i due tronchi inferiori, attraendo <lb/>in alto e in basso con forze eguali le porzioni de'filetti da essi circoscritti, <lb/>&egrave; come se non esistessero, o come se i due tubi procedessero in basso, per <lb/>tutte le loro altezze IK, LM, colle medesime aperture dei raggi AI, DL, che <lb/>hanno alle cime (ivi, pag. </s>

<s>125-27). </s></p><p type="main">

<s>I modi poi dell'attrazione, proseguiva a ragionare il Clairaut, non si <lb/>possono determinare, se non col sottoporre a un calcolo esatto tutte le forze <lb/>attrattive, ci&ograve; che se avesse fatto il Jurin si sarebbe facilmente accorto che, <lb/>pur supponendo esser le forze dell'anello di vetro in ragion costante col suo <lb/>diametro, &ldquo; on n'en pourrait pas conclure qu'une colonne de fluide d'un <lb/>poids proportionnel a cette force seroit suspendue par son moyen &rdquo; (ivi, <lb/>pag. </s>

<s>109). N&egrave; alcun altro ancora s'era applicato a questo calcolo esatto. </s>

<s>Che <lb/>se's Gravesande aveva ritrovata l'equazione alla curva, in cui termina il <lb/>velo d'acqua, risalito fra i due specchi inclinati; non poteva non sentire che, <lb/>a condur la sottile dimostrazione, troppo ottuso strumento erano gli Ele&shy;<lb/>menti di Euclide e i Conici di Apollonio. </s>

<s>Ma in ogni modo gli fu forza ar&shy;<lb/>retrarsi, quando nel IV dei citati Scolii si popose di trattare <emph type="italics"/>De motu gut&shy;<lb/><figure id="id.020.01.3375.1.jpg" xlink:href="020/01/3375/1.jpg"/></s></p><p type="caption">

<s>Figura 169.<lb/>tae,<emph.end type="italics"/> della gocciola cio&egrave; dell'olio, che, compresa fra <lb/>due specchi inclinati, spontaneamente si muove, <lb/>spandendosi verso l'angolo dell'inclinazione. </s></p><p type="main">

<s>Il Musschenbroek, in tanta necessit&agrave;, pens&ograve; <lb/>d'invocare il valido aiuto del parallelogrammo <lb/>delle forze. </s>

<s>Siano i due specchi AC, AE (fig. </s>

<s>169), <lb/>e il centro O della gocciola d'olio sia attratto <lb/>dalle forze OP, OS. </s>

<s>La resultante OB dimostra <lb/>senza dubbio che il moto della gocciola &egrave; diretto <pb xlink:href="020/01/3376.jpg" pagenum="337"/>verso l'angolo A, come, trasformandosi le supposte forze attrattive nelle re&shy;<lb/>pulsive OD, OH, la resultante OF mostrerebbe che il moto &egrave; rivolto in verso <lb/>contrario, ci&ograve; che di fatto s'osserverebbe accadere, se la gocciola O fosse mer&shy;<lb/>curio. </s>

<s>Ma tutto questo non &egrave; preparazion sufficiente alle conclusioni, che il <lb/>Musschenbroek stesso soggiunge: &ldquo; Insuper, quo centrum gravitatis O pro&shy;<lb/>pius accesserit ad speculorum superficies, eo fortius attrahetur, sed propius <lb/>accedit, quo gutta magis applanatur, hoc est magis ad A approprinquarit. </s>

<s><lb/>Adeoque fortius attracta gutta a superficiebus, et obliqua directione, neces&shy;<lb/>sario velocius feretur, quae est altera causa accelerati motus in gutta obser&shy;<lb/>vati. </s>

<s>Fortissima quoque speculorum attractio, cum sit in contactu A, necesse <lb/>est ut gutta secundum hunc contactum expandatur per omnem speculorum <lb/>latitudinem &rdquo; (<emph type="italics"/>Dissertationes<emph.end type="italics"/> cit., pag. </s>

<s>347, 48). </s></p><p type="main">

<s>Che la conclusione non sia veramente, come si diceva, compresa nei <lb/>principii, &egrave; facile riconoscerlo, a pensar solamente che, se le forze OP, OS <lb/>crescono, con l'avvicinarsi che fa la gocciola ad A, la resultante OB invece <lb/>diminuisce. </s>

<s>Ond'&egrave; che, anco a spiegar l'accelerazione del moto, le sopra <lb/>dette dall'Autore non son ragioni assolute, e n&egrave; perci&ograve; sufficienti. </s>

<s>L'insuf&shy;<lb/>ficienza poi si rende anche pi&ugrave; manifesta, osservando che, nella spiegazione <lb/>di questi fatti, si tien solamente conto dell'attrazione del solido, trascurata <lb/>quella del liquido in s&egrave; medesimo. </s>

<s>Di che accortosi il sagace Clairaut, con&shy;<lb/>cluse che non si sarebbe potuta esaminar bene la questione dei tubi capil&shy;<lb/>lari, se non applicandovi la legge generale dell'equilibrio dei fluidi. </s>

<s>&ldquo; Je <lb/>vais donc examiner la question des tuyaux capillaires, par les loix generales <lb/>de l'equilibre des fluides &rdquo; (<emph type="italics"/>Theorie<emph.end type="italics"/> cit., pag. </s>

<s>109, 10). </s></p><p type="main">

<s>In che questo esame consista, e come cominciassero di qui le gocciole <lb/>della rugiada, sopra le foglie dei cavoli, a riconoscer loro cognate le stelle <lb/>erranti per gli eterei spazii celesti, &egrave; ci&ograve; che ne rimane a dire in quest'ul&shy;<lb/>tima parte del nostro discorso. </s></p><p type="main">

<s><emph type="center"/>V.<emph.end type="center"/></s></p><p type="main">

<s>Il Clairaut era giunto a questa conclusione: che se le parti di una gran <lb/>mole fluida, rivolgentesi intorno a un asse, come sarebbe il nostro globo ter&shy;<lb/>racqueo, o un pianeta, sarauno attratte al centro nella semplice ragion di&shy;<lb/>retta delle distanze; il pianeta stesso deve configurarsi in una sferoide ellit&shy;<lb/>tica (ivi, pag. </s>

<s>61): cosicch&egrave; tutte le sezioni, condotte perpendicolarmente sul&shy;<lb/>l'asse di rotazione, son circoli, e la superficie del corpo, che in s&egrave; stessa &egrave; <lb/>rotonda, per un breve spazio apparisce piana. </s>

<s>Nonostante, intorno agli orli <lb/>dei piccoli vasi, o a contatto di certi corpi, quella stessa superficie si vede <lb/>incurvarsi, n&egrave; ci&ograve; pu&ograve; avvenire, se non perch&egrave; alla gravit&agrave; naturale s'aggiun&shy;<lb/>gono altre forze, dal concorso delle quali viene a resultarne una direzione <lb/>diversa. </s></p><pb xlink:href="020/01/3377.jpg" pagenum="338"/><p type="main">

<s>In questo ragionamento del Clairaut, molto pi&ugrave; espressamente che in <lb/>quello degli sperimentatori precedenti, viene la Filosofia neutoniana a com&shy;<lb/>prendere nel suo magistero le gocciole dell'acqua, e le moli de'pianeti. </s>

<s>Per&shy;<lb/>ch&egrave;, se l'attrazione al centro dello sferoide &egrave; quella, che ne rende regolare <lb/>la superficie, l'attrazione, agli orli del vaso o al solido immerso deve essere <lb/>che la perturba. </s>

<s>Sottoporre a un calcolo rigoroso queste forze perturbatrici, ci&ograve; <lb/>che nessuno aveva ancora tentato, &egrave; l'intenzione dell'Accademico di Parigi. </s></p><p type="main">

<s>L'Hauksbee non aveva saputo dir altro, se non che la gravit&agrave; naturale <lb/>di una particella d'acqua, sopravvenendo l'attrazione al vetro, perde alquanto <lb/>del suo proprio momento. </s>

<s>Con qual ragione si faccia questa perdita, che pure <lb/>per un altro liquido, come per esempio il mercurio, o in altre condizioni del <lb/><figure id="id.020.01.3377.1.jpg" xlink:href="020/01/3377/1.jpg"/></s></p><p type="caption">

<s>Figura 170.<lb/>vetro potrebb'essere invece un acquisto; il Clairaut <lb/>lo dimostrava in questo modo: Sia AD (fig. </s>

<s>170) <lb/>la sezione di un tubo, o di un solido immerso in&shy;<lb/>fino al livello MN in qual si voglia liquido, di cui N <lb/>&egrave; una particella a contatto. </s>

<s>Questa verr&agrave; sollecitata <lb/>da tre forze: dalla gravit&agrave; naturale, rappresentata <lb/>per NO; dall'attrazione al solido, rappresentata per <lb/>NL, e dall'attrazione verso l'interno della massa <lb/>liquida, per trovar la misura e la direzion della <lb/>quale si oostruisca il quadrato MO. Nell'incontro K <lb/>delle due diagonali una molecola ivi costituita, es&shy;<lb/>sendo in equilibrio, perch&egrave; &egrave; ugualmente attratta, <lb/>e attrae le molecole D, N; pu&ograve; dunque KN pren&shy;<lb/>dersi per la direzione, e per la misura della forza, con cui la stessa mole&shy;<lb/>cola N &egrave; attratta verso l'interno di tutta la mole. </s>

<s>Di qui &egrave; manifesto come <lb/>la disposizion naturale, che prenderebbe N nella liquida superficie, quando <lb/>non avesse altra sollecitazione che dalla NO; vien perturbata dal concorso <lb/>delle forze KN, NL, la resultante delle quali &egrave; NR. </s>

<s>E perch&egrave; la detta dispo&shy;<lb/>sizion naturale era perpendicolare a NO, e la perturbazione subita la co&shy;<lb/>stringe invece a disporsi perpendicolarmente a NR; &egrave; altres&igrave; manifesto come <lb/>il liquido stagnante, di piano che sarebbe stato per sua natura, debba incur&shy;<lb/>varsi verso il solido AD che l'attrae, in una concava superficie. </s></p><p type="main">

<s>Qui il Clairaut ci richiama a considerar meglio la resultante delle forze <lb/>perturbatrici, dalla sola direzion della quale nascono i varii effetti. </s>

<s>Perch&egrave; <lb/>se, essendo tal direzione secondo NR, la superficie liquida &egrave; concava, e se <lb/>secondo NO &egrave; piana; quando invece fosse secondo NH riuscirebbe convessa. </s>

<s><lb/>Ora la variet&agrave; di queste direzioni si vede bene che dipende dal variar del <lb/>lato NL, o del suo uguale KR, che &egrave; uno dei lati, sopra il quale si costrui&shy;<lb/>sce il parallelogrammo delle forze; e la variazione si fa intorno al punto C, <lb/>per accesso o per recesso dal punto K. </s>

<s>In C poi &egrave; il giusto mezzo della NO, <lb/>e KC, NC, OC son linee tutte uguali, come raggi del semicircolo circoscritto <lb/>a KNO, angolo retto. </s>

<s>Dunque, quando NF=KC=NC=NO/2, ossia, quando <pb xlink:href="020/01/3378.jpg" pagenum="339"/>l'attrazione del solido sopra la molecola liquida uguaglia la met&agrave; dell'attra&shy;<lb/>zione della molecola stessa al centro dello sferoide terrestre; la superficie &egrave; <lb/>piana. </s>

<s>E perch&egrave; le resultanti divengono ora NR, ora NH, cio&egrave; quella positiva <lb/>e questa negativa rispetto alla direzion normale NO, secondo che NL>NO/2, <lb/>o NE&lt;NO/2; dunque la superficie &egrave; concava o convessa, secondo che l'at&shy;<lb/>trazion del solido &egrave; maggiore o minore della met&agrave; dell'attrazione della mo&shy;<lb/>lecola liquida al centro dello sferoide terrestre; ossia, secondo che la resul&shy;<lb/>tante delle forze perturbatrici &egrave; positiva o negativa, rispetto alla verticale. <lb/><figure id="id.020.01.3378.1.jpg" xlink:href="020/01/3378/1.jpg"/></s></p><p type="caption">

<s>Figura 171.</s></p><p type="main">

<s>Da ci&ograve; venne il Clairaut ad aprirsi la <lb/>via di risolvere analiticamente il problema <lb/>de'fenomeni capillari, assoggettando al cal&shy;<lb/>colo tutte le forze che, sollecitando in basso <lb/>il filetto liquido IK (fig. </s>

<s>171) lungo l'asse <lb/>del tubo di vetro, di cui la sezion verticale <lb/>sia AH, e il raggio interno sia <emph type="italics"/>b;<emph.end type="italics"/> lo man&shy;<lb/>tengono in equilibrio col filetto ML, preso <lb/>in mezzo al liquido, nel quale il detto tubo, <lb/>infino al livello MP, si supponga essere <lb/>immerso. </s>

<s>Chiamata <emph type="italics"/>h<emph.end type="italics"/> l'intensit&agrave; dell'at&shy;<lb/>trazione del vetro, <emph type="italics"/>k<emph.end type="italics"/> quella dell'acqua, una <lb/>delle principali forze, che sollecitano le mo&shy;<lb/>lecole componenti il filetto ML, &egrave; quella <lb/>del loro peso <emph type="italics"/>p:<emph.end type="italics"/> forza, che perci&ograve; sar&agrave; <lb/>espressa da <emph type="italics"/>p<emph.end type="italics"/>.ML. S'aggiunga a questa <lb/>l'attrazion delle molecole sopra s&egrave; mede&shy;<lb/>sime, la quale essendo in funzione della distanza <emph type="italics"/>x<emph.end type="italics"/> dal centro attrattivo, e <lb/>dovendo avere per coefficiente <emph type="italics"/>k,<emph.end type="italics"/> sar&agrave;, per una sola particella, misurata da <lb/><emph type="italics"/>kdx<foreign lang="greek">f</foreign>(x),<emph.end type="italics"/> e per tutte sommate insieme da <emph type="italics"/>&int;kdx<foreign lang="greek">f</foreign>(x).<emph.end type="italics"/> Ond'&egrave; che, signifi&shy;<lb/>candosi con P la pression totale, che il soprastante filetto liquido fa in L; <lb/>avremo <emph type="italics"/>P=p.ML+&int;kdx<foreign lang="greek">f</foreign>(x).<emph.end type="italics"/></s></p><p type="main">

<s>Fra le forze sollecitanti il filetto IK si distingueranno quelle, applicate <lb/>alla parte superiore I, dall'altre applicate verso O, alla parte inferiore. </s>

<s>Si <lb/>consideri la molecola <emph type="italics"/>m,<emph.end type="italics"/> alla quale si vedr&agrave; essere applicate tre forze: la <lb/>prima dovuta all'attrazione dell'acqua soggiacente al piano ST, e che, per <lb/>le cose dette, e ritenute le medesime denominazioni, la tira in basso con una <lb/>intensit&agrave; uguale a <emph type="italics"/>k&int;dx<foreign lang="greek">f</foreign>(x);<emph.end type="italics"/> le altre due, che la detta molecola tirano in <lb/>verso contrario; son dovute all'attrazione delle pareti solide AV, ET, e del <lb/>menisco liquido YX. </s>

<s>Ed essendo quella in funzione del raggio del tubo, e <lb/>della distanza dal centro di attrazione, e perci&ograve; espressa da <emph type="italics"/><foreign lang="greek">f</foreign>(b, x),<emph.end type="italics"/> che fa&shy;<lb/>remo uguale a <foreign lang="greek">*f</foreign>, e questa in funzione del raggio, della detta distanza cen&shy;<lb/>trale, e inoltre delle attrazioni del vetro e dell'acqua, e perci&ograve; espressa da <lb/><emph type="italics"/><foreign lang="greek">f</foreign> (b, x, h, k)<emph.end type="italics"/> che faremo uguale a <foreign lang="greek">*f</foreign>&prime;; saranno nella somma di tutti i loro <pb xlink:href="020/01/3379.jpg" pagenum="340"/>elementi quelle stesse forze rappresentate da <emph type="italics"/>k&int;dx<foreign lang="greek">*f</foreign>,&int;dx<foreign lang="greek">*f</foreign>&prime;.<emph.end type="italics"/> &ldquo; Donc le <lb/>poids total de toutes les parties voisines de I sera <emph type="italics"/>k&int;dx<foreign lang="greek">f</foreign>(x)&mdash;k&int;dx<foreign lang="greek">*f</foreign>&mdash; <lb/>&int;dx<foreign lang="greek">*f</foreign>&prime; &rdquo;<emph.end type="italics"/> (ivi, pag. </s>

<s>117). </s></p><p type="main">

<s>Resta a calcolar le forze, che sollecitano le particelle del filetto liquido <lb/>verso la bocca inferiore del tubo, terminata dal piano DG, a ugual distanza <emph type="italics"/>x<emph.end type="italics"/><lb/>dal quale considerati due elementi Q, R, si vedr&agrave; che son con pari forze <lb/>attratti in gi&ugrave; dall'acqua soggiacente al piano DG, e in su dal vetro: di modo <lb/>che, il coefficiente della loro funzione essendo <emph type="italics"/>h&mdash;k,<emph.end type="italics"/> s'avranno le dette <lb/>forze espresse da <emph type="italics"/>(k&mdash;h)dx<foreign lang="greek">*f</foreign>,<emph.end type="italics"/> e perci&ograve; le forze di tutti gli elementi in&shy;<lb/>sieme s'otterranno dal prendere due volte la somma di <emph type="italics"/>(k&mdash;h)dx<foreign lang="greek">*f</foreign>,<emph.end type="italics"/> ossia <lb/>da &mdash; <emph type="italics"/>2(h&mdash;k)dx<foreign lang="greek">*f</foreign>.<emph.end type="italics"/> Dunque, raccogliendo insieme le forze, all'impulso <lb/>delle quali va soggetto il filetto liquido IK, e aggiuntavi quella della sua gra&shy;<lb/>vit&agrave; naturale <emph type="italics"/>p<emph.end type="italics"/>.IK; avremo la pressione Q, ch'egli esercita in K, espressa da <lb/><emph type="italics"/>Q=p.IK+k&int;dx<foreign lang="greek">f</foreign>(x)&mdash;k&int;dx<foreign lang="greek">*f</foreign>&mdash;&int;dx<foreign lang="greek">*f</foreign>&prime;&mdash;2(h&mdash;k)dx<foreign lang="greek">*f</foreign>.<emph.end type="italics"/><lb/>Uguagliando insieme i valori di P e di Q, sottraendo l'uno dall'altro, e fa&shy;<lb/>cendo le assai facili riduzioni, s'ottiene finalmente la formula <lb/>IK&mdash;ML=IU=<emph type="italics"/>((2h&mdash;k)dx<foreign lang="greek">*f</foreign>+&int;dx<foreign lang="greek">*f</foreign>&prime;)/p.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; On tire de l'expression precedente de IU, dice il Clairaut, une propo&shy;<lb/>sition assez singuliere &rdquo; (ivi, pag. </s>

<s>121): singolarit&agrave; che si rende anche pi&ugrave; <lb/>manifesta esplicando il concetto dell'Autore, col mettere da ogni parte a ri&shy;<lb/>scontro questa soluzione analitica con la geometrica, illustrata dalla nostra <lb/>CLXX figura. </s>

<s>Da <emph type="italics"/>k<emph.end type="italics"/> &egrave; sempre rappresentata NO, ma da <emph type="italics"/>h<emph.end type="italics"/> le lunghezze va&shy;<lb/>riabili NL, NF, NE, di una delle componenti: come da <foreign lang="greek">*f</foreign>&prime; si rappresentano <lb/>le variabili direzioni NR, NC, NH delle resultanti. </s>

<s>Se <emph type="italics"/>k=2h,<emph.end type="italics"/> il primo ter&shy;<lb/>mine dell'espressione di IU &egrave; zero. </s>

<s>Ma &egrave; assai facile vedere che zero &egrave; anche <lb/>il secondo, a cagion di <foreign lang="greek">*f</foreign>&prime;, da cui viene allora a rappresentarsi la direzione <lb/>verticale NC della resultante. </s>

<s>Dunque IU &egrave; zero, ossia il liquido, ne'due rami <lb/>del sifone MLKU, &egrave; a perfetto livello, ci&ograve; che sempre avviene, quando la su&shy;<lb/>perficie del liquido non &egrave; perturbata dalla sua natural direzione al centro <lb/>dello sferoide terrestre, e perci&ograve; la formola del Clairaut esprime analitica&shy;<lb/>mente in questo caso l'uguaglianza di livello e d'equilibrio de'liquidi nei <lb/>vasi comunicanti. </s></p><p type="main">

<s>Se <emph type="italics"/>k<emph.end type="italics"/> &egrave; minore di 2<emph type="italics"/>h,<emph.end type="italics"/> e perci&ograve; <foreign lang="greek">*f</foreign>&prime; rappresenta la direzion della resul&shy;<lb/>tante NR, alla destra di NC; ambedue i termini di IU, e perci&ograve; IU stessa <lb/>&egrave; positiva, ossia il liquido risalir&agrave; sopra il livello MP, che &egrave; il caso dell'acqua <lb/>in un tubo capillare di vetro. </s>

<s>Se finalmente <emph type="italics"/>k<emph.end type="italics"/> &egrave; maggiore di 2<emph type="italics"/>h,<emph.end type="italics"/> e <foreign lang="greek">*f</foreign>&prime; rap&shy;<lb/>presenta la direzione della resultante a sinistra, IU sar&agrave; negativa, ossia il <lb/>liquido s'abbasser&agrave; al di sotto del livello MP, che &egrave; il caso del mercurio. </s></p><p type="main">

<s>Il Clairaut dice di non volere spingere oltre il suo calcolo &ldquo; pour s&ccedil;a&shy;<lb/>voir ce que seroient les quantit&eacute;s <foreign lang="greek">*f</foreign> et <foreign lang="greek">*f</foreign>&prime;, suivant les differentes fonctions <lb/>de la distance qu'on pourroit prendre pour exprimer la loi de l'attraction &rdquo; <pb xlink:href="020/01/3380.jpg" pagenum="341"/>(ivi, pag. </s>

<s>121). Ci&ograve; ei lasciava allo studio dei Matematici suoi successori, i <lb/>quali, riconoscendo la difficolt&agrave; dell'impresa, pensarono di volgersi ad altro <lb/>partito. </s>

<s>L'equazione della catenaria, o della lamina elastica, o della velaria, <lb/>felicemente ritrovata per via del nuovo calcolo infinitesimale, inger&igrave; nel Se&shy;<lb/>gner e in Tommaso Young la speranza di risolvere il problema dei capil&shy;<lb/>lari, assomigliando a quelle curve i menischi che, per la tensione e per la <lb/>elasticit&agrave; superficiale dei liquidi, si formano dentro i tubi capillari. </s>

<s>Il La&shy;<lb/>place invece cred&egrave; non c'essere altra via diretta, da condursi alla desiderata <lb/>soluzione, che quella di determinare le funzioni della formula del Clairaut, <lb/>nella legge di un'attrazione insensibile a sensibili distanze, come nella luce. </s>

<s><lb/>Di che avendo gi&agrave; trattato nel X libro della Meccanica celeste, a proposito <lb/>delle rifrazioni astronomiche, pens&ograve; di aggiungere al detto libro un Supple&shy;<lb/>mento, in cui le medesime leggi ottiche si applicherebbero ai fenomeni ca&shy;<lb/>pillari. </s></p><p type="main">

<s>Le benefiche inspirazioni, ricevute dal Clairaut, come il Laplace le sent&igrave; <lb/>nell'animo, cos&igrave; l'espresse con le parole: &ldquo; Clairaut est le premier et jusqu'&agrave; <lb/>pr&eacute;sent le seul, qui ait soumis a un calcul rigoureux les ph&eacute;nom&eacute;nes des <lb/>tubes capillaires, dans son trait&eacute; sur la Figure de la Terre &rdquo; (<emph type="italics"/>Supplement <lb/>au X livre du trait&eacute; De mecanique celeste,<emph.end type="italics"/> T. IV, a Paris 1805, pag. </s>

<s>2). <lb/>Nonostante fa alcune censure, che a noi per verit&agrave; non sembrano giuste, <lb/>come per avere il Clairaut supposto che l'attrazion del vetro si faccia sen&shy;<lb/>tire a distanza sul filetto liquido, che riempie l'asse del tubo, contro le no&shy;<lb/>tissime esperienze dell'Hauksbee. </s>

<s>Vero &egrave; che questi, sperimentando con due <lb/>tubi ugualmente cavi, ma differentemente massicci, &ldquo; non pot&egrave; distinguere <lb/>differenza alcuna tra le altezze, che il liquore in ambi i tubi aveva salite &rdquo; <lb/>(<emph type="italics"/>Esperienze fisico-meccan.<emph.end type="italics"/> cit., pag. </s>

<s>123), e poche pagine appresso, da quelle <lb/>stesse esperienze e dalle analogie con la calamita, conclude &ldquo; che l'attrat&shy;<lb/>tiva potenza delle piccole particelle della materia opera solamente sopra quei <lb/>tali corpiccioli, che le toccano, ovvero che siano da loro a una infinitamente <lb/>piccola distanza rimosse &rdquo; (ivi, pag. </s>

<s>130). Ma prima di sentenziare che il <lb/>Clairaut non seppe, o non volle tener conto di queste verit&agrave; dimostrate, con&shy;<lb/>veniva pensar che la formula scritta da lui sussiste anche nel caso che <emph type="italics"/>b,<emph.end type="italics"/><lb/>raggio del tubo, sia d'insensibile lunghezza. </s>

<s>Il Laplace, e tutti coloro che <lb/>ripeterono le censure di lui, forse rimasero ingannati dalle dimensioni esa&shy;<lb/>gerate, che l'Autore fu costretto di dare alla sua figura. </s>

<s>N&egrave; meno ingiusta <lb/>sembra a noi l'altra accusa, dallo stesso Laplace data al Clairaut, che cio&egrave; <lb/>il gran Geometra &ldquo; n'&agrave; pas expliqu&eacute; le principal phenom&egrave;ne capillaire, celui <lb/>de l'ascension et de la depression des liquides dans des tubes tres-&eacute;troits, <lb/>en raison inverse du diametre de ces tubes &rdquo; (<emph type="italics"/>Supplement au supplement<emph.end type="italics"/><lb/>cit., pag. </s>

<s>76), considerando che il valore di IU &egrave; dato in ragione inversa di <lb/><emph type="italics"/>p,<emph.end type="italics"/> ossia de'pesi delle colonne liquide, le quali si sa essere proporzionali ai <lb/>raggi delle basi. </s></p><p type="main">

<s>L'ispirazione pi&ugrave; principalmente benefica, che dal Clairaut ricevesse il <lb/>Laplace, fu quella di attendere e di dare importanza ai menischi. </s>

<s>&ldquo; Les phy-<pb xlink:href="020/01/3381.jpg" pagenum="342"/>siciens n'ayant considere jusqu'ici la concavit&eacute; et la convexit&eacute; des surfaces <lb/>des fluides, dans les espaces capillaires, que comme un effet secondaire de <lb/>la capillarit&eacute; &rdquo; (<emph type="italics"/>Supplement<emph.end type="italics"/> cit., pag. </s>

<s>8). L'Hauksbee anzi e il Jurin riguar&shy;<lb/>darono quelle superficie come piane, e le loro curvit&agrave;, per le loro dimostra&shy;<lb/>zioni, come indifferenti. </s>

<s>Il Laplace invece sent&igrave; che risiedeva quivi <emph type="italics"/>la prin&shy;<lb/>cipale cause de ce genre de phenom&egrave;nes,<emph.end type="italics"/> cosicch&egrave; la stessa attrazione dei <lb/>tubi capillari, in che facevano i detti fisici consistere quella causa principale, <lb/>&ldquo; n'a d'influence sur l'elevation, ou sur l'abaissement des fluides, qu'ils ren&shy;<lb/>ferment, qu'en determinant l'inclinaison des premiers plans de la surface du <lb/>fluide interieur, extremement voisins des parois du tube: inclinaison, dont <lb/>d&eacute;pend la concavit&eacute; ou la convexit&eacute; de cette surface, et la grandeur de son <lb/>rayon &rdquo; (ivi, pag. </s>

<s>5). </s></p><p type="main">

<s>Fu per questa riconosciuta influenza che il Laplace attese a istituir di <lb/>proposito, e con la massima diligenza, l'esperienze che gli dovevano prima <lb/>servir di regola, e poi di conferma alla teoria. </s>

<s>Sia ABC (fig. </s>

<s>172) un sifone <lb/><figure id="id.020.01.3381.1.jpg" xlink:href="020/01/3381/1.jpg"/></s></p><p type="caption">

<s>Figura 172.<lb/>capillare di vetro, e si tuffi nell'acqua in modo, che il suo <lb/>ramo pi&ugrave; corto AB rimanga tutto sommerso. </s>

<s>Siasi elevato <lb/>il liquido infino in G, nel ramo pi&ugrave; lungo: estratto lo stru&shy;<lb/>mento si former&agrave; in A una gocciola, e il liquido si vedr&agrave; <lb/>risalire pi&ugrave; su di G. </s>

<s>Levisi col dito la gocciola, e il liquido <lb/>si abbasser&agrave; sotto G. </s>

<s>Si ritorni con una pipetta legger&shy;<lb/>mente a rimetter la gocciola, e il liquido raggiunger&agrave; di <lb/>nuovo il primiero livello. </s></p><p type="main">

<s>Per dimostrare anche pi&ugrave; efficacemente gli effetti dei <lb/>menischi sia, soggiunge il Laplace, ABC (fig. </s>

<s>173) un si&shy;<lb/>fone capillare, dentro cui, tenuto colle braccia verticali, <lb/>s'equilibri il mercurio. </s>

<s>Inclinando lo strumento dalla parte <lb/><figure id="id.020.01.3381.2.jpg" xlink:href="020/01/3381/2.jpg"/></s></p><p type="caption">

<s>Figura 173.<lb/>di A, il liquido risale in A&prime;, e scende in C&prime;, dalla parte op&shy;<lb/>posta. </s>

<s>Riducendolo alla primiera stazione, si osserva che non <lb/>perci&ograve; il liquido torna al primiero livello orizontale, ma ri&shy;<lb/>mane alquanto pi&ugrave; elevato dalla parte di A, dove il meni&shy;<lb/>sco s'&egrave; fatto anche meno convesso che dall'altra. </s>

<s>&ldquo; Cette <lb/>differance, dans la convexit&eacute; des deux surfaces, tient au frot&shy;<lb/>tement du mercure contre les parois du tube: les parties <lb/>de la surface, dans la branche AB, qui se retirent vers A, <lb/>et qui touchent le tube, sont un peu arretr&eacute;es par ce frot&shy;<lb/>tement, tandis que les parties du milieu de cette surface n'&eacute;prouvent point <lb/>le m&egrave;me obstacle; et de l&agrave; doit resulter une surface moins convexe; au <lb/>lieu que le m&ecirc;me frottement doit produire un effet contraire sur la sur&shy;<lb/>face du mercure de la branche BC. </s>

<s>Or de ce que la premiere de ces surfa&shy;<lb/>ces est moins convexe que la seconde, il en resulte que le mercure &eacute;prouve, <lb/>par son action sur lui-meme, une moindre pression dans la branche BA, que <lb/>dans la branche BC, et qui ainsi sa hauteur, dans la premiere de ces deux <lb/>branches, doit surpasser un peu sa hauteur dans la seconde &rdquo; (ivi, pag. </s>

<s>61, 62). </s></p><pb xlink:href="020/01/3382.jpg" pagenum="343"/><p type="main">

<s>Tale essendo l'efficacia del menisco concavo YIZ, nella figura CLXXI, <lb/>si ricerca il modo dell'operare di lui, il quale non pu&ograve; consistere in altro, <lb/>che in attrarre il filetto liquido IK, cosicch&egrave; questo, divenuto quasi pi&ugrave; leg&shy;<lb/>gero, debba sollevarsi, per equilibrar la pressione del filetto LM. &ldquo; La loi de <lb/>cette ascension, dans les tubes de differens diametres, depend de l'attraction <lb/>du m&eacute;nisque, et ici, comme dans la theorie de la figure des plan&eacute;tes, il y <lb/>a una dependance reciproque de la figure, et de l'attraction du corps, qui <lb/>rend leur determination difficile. </s>

<s>Pour y parvenir nous allons considerer <lb/>l'action d'un corps, de figure quelconque, sur une colonne fluide renform&eacute;e <lb/>dans un canal infiniment etroit perpendiculaire &agrave; se surface, et dont nous <lb/>prendrons la base pour unit&eacute; &rdquo; (ivi, pag. </s>

<s>10). </s></p><p type="main">

<s>Si prepara il Laplace la via alla general considerazione di un corpo qua&shy;<lb/>lunque, supponendo primieramente che quel corpo sia una sfera di raggio <emph type="italics"/>b,<emph.end type="italics"/><lb/>compaginata di strati indivisibili concentrici, l'azione d'un de'quali, avente <lb/>per raggio <emph type="italics"/>u,<emph.end type="italics"/> sul filetto, trova essere espressa da <emph type="italics"/>2<foreign lang="greek">p</foreign>udu/b.<foreign lang="greek">*y</foreign>(b&mdash;u)<emph.end type="italics"/> dove <lb/><foreign lang="greek">*y</foreign> &egrave; il resultato di quantit&agrave; dipendenti da <emph type="italics"/>&int;df<foreign lang="greek">f</foreign>(f),<emph.end type="italics"/> intendendosi per <emph type="italics"/><foreign lang="greek">f</foreign>(f)<emph.end type="italics"/><lb/>la legge dell'attrazione molecolare, alla distanza <emph type="italics"/>f.<emph.end type="italics"/> Se invece dell'attrazione <lb/>dello strato sferico si considera la pressione, esercitata sul filetto liquido in <lb/>virt&ugrave; della detta attrazione, &egrave; manifesto che <emph type="italics"/>2<foreign lang="greek">p</foreign>udu/b.<foreign lang="greek">*y</foreign>(b&mdash;u)<emph.end type="italics"/> deve con&shy;<lb/>vertirsi in &mdash; <emph type="italics"/>2<foreign lang="greek">p</foreign>udu/b.<foreign lang="greek">*y</foreign> (b&mdash;u)<emph.end type="italics"/> e perci&ograve;, fatto <emph type="italics"/>b&mdash;u=z,<emph.end type="italics"/> s'avr&agrave; l'azione S <lb/>della sfera intera espressa da <emph type="italics"/>2<foreign lang="greek">p</foreign>&int;(b&mdash;z)/b.dz<foreign lang="greek">*y</foreign>z,<emph.end type="italics"/> ossia da <emph type="italics"/>S&prime;=2<foreign lang="greek">p</foreign>&int;dz<foreign lang="greek">*y</foreign>z= <lb/>2<foreign lang="greek">p</foreign>&int;zdz/b.<foreign lang="greek">*y</foreign>z,<emph.end type="italics"/> esteso l'integrale da <emph type="italics"/>z=o,<emph.end type="italics"/> infino a <emph type="italics"/>z=b.<emph.end type="italics"/> Facendosi poi <lb/><emph type="italics"/>2<foreign lang="greek">p</foreign>&int;dz<foreign lang="greek">*y</foreign>z=H,<emph.end type="italics"/> e <emph type="italics"/>2<foreign lang="greek">p</foreign>&int;zdz<foreign lang="greek">*y</foreign>z=K,<emph.end type="italics"/> si ridurr&agrave; la formula alla semplicis&shy;<lb/>sima significazione di S=H&mdash;K/<emph type="italics"/>b.<emph.end type="italics"/> Se <emph type="italics"/>b<emph.end type="italics"/> &egrave; negativo, ossia se la sfera com&shy;<lb/>prende il filetto liquido, e la superficie YIZ concava si trasforma nella con&shy;<lb/>vessa Y&prime;IZ&prime;, sar&agrave; invece S=K+H/<emph type="italics"/>b.<emph.end type="italics"/> Dunque, &ldquo; l'action d'un corps, termin&eacute; <lb/>per una portion sensible de surface spherique, sera K&plusmn;H/<emph type="italics"/>b,<emph.end type="italics"/> le signe+ayant <lb/>lieu, si la surface est convexe, et le signe &mdash; si elle est concave &rdquo; (ivi, pag. </s>

<s>15). </s></p><p type="main">

<s>L'espressione dell'azion della sfera intera s'&egrave; applicato ai menischi YIZ, <lb/>Y&prime;IZ&prime;, ossia ai segmenti sferici sensibili, fatti per un piano, a cui il filetto o <lb/>la colonna liquida IK sia perpendicolare: applicazione, che pu&ograve; nel presente <lb/>caso farsi a buon diritto, &ldquo; car la partie de la sfh&egrave;re, situ&eacute;e au-del&agrave; de ce <lb/>plan, etant &agrave; une distance sensible de la colonne, sen action sur cette co&shy;<lb/>lonne est insensible &rdquo; (ivi, pag. </s>

<s>14). </s></p><p type="main">

<s>La ritrovata formula K&plusmn;H/<emph type="italics"/>b<emph.end type="italics"/> &egrave; perci&ograve; applicabile ai menischi, che si <pb xlink:href="020/01/3383.jpg" pagenum="344"/>formano dai vari liquidi, dentro i tubi capillari, ma prima di venire a farne <lb/>l'applicazione giova, col Laplace, premettere alcune osservazioni. </s>

<s>Resultando <lb/>K=H.<emph type="italics"/>z/b,<emph.end type="italics"/> e <emph type="italics"/>z/b<emph.end type="italics"/> essendo un rotto proprio, &egrave; manifesto che il valore di S <lb/>&egrave; sempre notabilmente pi&ugrave; piccolo del primo. </s>

<s>Si noti inoltre il diverso uffi&shy;<lb/>cio rappresentativo, che hanno i due termini componenti il detto valore di S. <lb/>&ldquo; K represente l'action d'un corps, termin&eacute; par une surface plane, car alors <emph type="italics"/>b<emph.end type="italics"/><lb/>etant infini, le terme H/<emph type="italics"/>b<emph.end type="italics"/> disparait &rdquo; (ivi), ond'&egrave; che resta particolarmente al <lb/>termine H/<emph type="italics"/>b,<emph.end type="italics"/> essendo <emph type="italics"/>b<emph.end type="italics"/> finito, l'ufficio di rappresentare l'azion del menisco. </s>

<s><lb/>Ed essendo una tale azione in ragion reciproca del raggio della curvatura, <lb/>ne consegue manifestamente che, nel caso di K&mdash;H/<emph type="italics"/>b,<emph.end type="italics"/> ossia quando il me&shy;<lb/>nisco &egrave; concavo, che la pressione cresce insieme col crescer del raggio, men&shy;<lb/>tre, nel caso di K+H/<emph type="italics"/>b<emph.end type="italics"/> ossia, quando il menisco &egrave; convesso, crescendo il <lb/>raggio, la pressione invece diminuisce. </s></p><p type="main">

<s>Si pu&ograve; graficamente cos&igrave; rappresentare l'espressione propria a ciascuno <lb/>dei due detti termini. </s>

<s>Sia il tubo ABCD (fig. </s>

<s>174) e nel filetto EF, lungo <lb/><figure id="id.020.01.3383.1.jpg" xlink:href="020/01/3383/1.jpg"/></s></p><p type="caption">

<s>Figura 174.<lb/>l'asse, si consideri la molecola S fra gli archi simmetrici <lb/>GEH, IRK, che ne limitano la sfera dell'attrazione. </s>

<s>Si <lb/>conduca al piano LM parallelo il piano NO, e all'arco AEB <lb/>simmetrico l'arco <expan abbr="PRq.">PRque</expan> &Egrave; manifesto che, sopra la mole&shy;<lb/>cola S, non agisce per attrazione se non che il liquido <lb/>sottoposto, venga egli limitato dal piano NO, o dal meni&shy;<lb/>sco PRQ, simmetrico al concavo AEB, o dal menisco IRK, <lb/>simmetrico al convesso GEH. </s>

<s>Nel primo caso, essendo NO <lb/>piano e perci&ograve; il raggio <emph type="italics"/>b<emph.end type="italics"/> della formula infinito; non ri&shy;<lb/>mane che il termine K, da cui vien perci&ograve; rappresentata <lb/>l'azione del liquido NODC. </s>

<s>Nel secondo caso, tutta la forza <lb/>attrattiva risiede nel liquido PRQDC, uguale a ND, dimi&shy;<lb/>nuito di PRQON, a cui perci&ograve; nella formula corrisponde <lb/>il termine &mdash;K/<emph type="italics"/>b.<emph.end type="italics"/> Nel terzo caso finalmente l'azione s'estende al liquido <lb/>IRKDC, ossia al liquido ND, insieme col liquido INROK, a cui nella formula <lb/>corrisponde il termine +K/<emph type="italics"/>b.<emph.end type="italics"/> Come poi, trasformandosi col diminuire del <lb/>raggio l'arco PRQ in P&prime;RQ&prime;, e l'arco IRK in I&prime;RK&prime;, l'azione diminuisca <lb/>nel primo caso e cresca nel secondo; e come il liquido NOQRP sia picco&shy;<lb/>lissimo, rispetto al liquido ND, a quel modo si dimostr&ograve; H/<emph type="italics"/>b<emph.end type="italics"/> esser piccolissimo <lb/>rispetto a K; son cose tanto parventi alla vista, da non aver bisogno di prove. </s></p><p type="main">

<s>Ma si ascolti il Laplace stesso, che nella prefazione al citato <emph type="italics"/>Supple-<emph.end type="italics"/><pb xlink:href="020/01/3384.jpg" pagenum="345"/><emph type="italics"/>mento<emph.end type="italics"/> cos&igrave; discorre intorno al carattere proprio a ciascuno dei due termini, <lb/>di che si comporrebbe la sua formula: &ldquo; Son expression analityque est com&shy;<lb/>pos&eacute;e de deux termes: le premier, beaucoup plus grand que le second, <lb/>exprime l'action de la masse, termin&eacute;e par une surface plane; et je pense <lb/>que de ce terme d&eacute;pendent la suspension du mercure, dans un tube de ba&shy;<lb/>rometre, a une hauteur deux ou trois fois plus grande que celle, qui est <lb/>due &agrave; la pression de l'atmosph&egrave;re, le pouvoir refringent de corps diaphanes <lb/>la cohesion, et generalement les affinit&eacute;s chimiques. </s>

<s>Le second terme exprime <lb/>la partie de l'action due &agrave; la sphericit&eacute; de la surface, c'est-a-dire l'action du <lb/>menisque, compris entre cette surface, et le plan qui la touche. </s>

<s>Cette action <lb/>s'ajoute a la precedente, ou s'en tranche, suivant que la surface est convexe <lb/>ou concave. </s>

<s>Elle est reciproque au rayon de la surface spherique: il est vi&shy;<lb/>sible en effet que, plus ce rayon est petit, plus le menisque est considera&shy;<lb/>ble, pres du point de contingence. </s>

<s>C'est a ce second terme, <lb/>qu'est due l'action capillaire, qui diff&egrave;re ainsi des affinit&eacute; <lb/>chimiques represent&eacute;es par le premier terme &rdquo; (pag. </s>

<s>3, 4). </s></p><p type="main">

<s>Le varie forme, sotto cui si presentano queste azioni <lb/><figure id="id.020.01.3384.1.jpg" xlink:href="020/01/3384/1.jpg"/></s></p><p type="caption">

<s>Figura 175.<lb/>capillari, si possono ridurre a quelle, che si osservano ne'due <lb/>vasi di vetro comunicanti ABC (fig. </s>

<s>175) e DEF (fig. </s>

<s>176) <lb/>nel primo de'quali sia l'acqua, e nel secondo il mercurio. </s>

<s><lb/>Resulta costantemente da cos&igrave; fatte osservazioni che, nel <lb/>ramo del tubo pi&ugrave; largo, della figura 175, il livello del li&shy;<lb/>quido &egrave; pi&ugrave; basso che nel cannello pi&ugrave; stretto, mentre, nel <lb/><figure id="id.020.01.3384.2.jpg" xlink:href="020/01/3384/2.jpg"/></s></p><p type="caption">

<s>Figura 176.<lb/>sifone rappresentato dalla figura 176, le dette altezze di li&shy;<lb/>vello si rispondono al contrario. </s>

<s>La ragion del fatto sarebbe <lb/>manifesta, quando il concavo GH premesse in gi&ugrave; il liquido <lb/>sottoposto, con pi&ugrave; forza del concavo IK, e il convesso <lb/>LM premesse invece, nella medesima direzione, con minor <lb/>forza del convesso NO. </s>

<s>Ma tale &egrave; giusto il responso che <lb/>ne d&agrave; la formula del Laplace interpetrata. </s>

<s>Le colonne li&shy;<lb/>quide infatti, e infinitamente strette, PQ, RS, possono, con <lb/>le loro estremit&agrave; superiori, terminare o in una superficie <lb/>piana, o nel respettivo menisco, secondo che maggiore o <lb/>minore &egrave; il diametro del tubo. </s>

<s>Se la superficie &egrave; piana, la <lb/>pressione S in P &egrave; S=K, e nel mezzo di IK &egrave; S&prime;=K&mdash;H/<emph type="italics"/>b&prime;.<emph.end type="italics"/> Se la su&shy;<lb/>perficie &egrave; concava, la pressione in P &egrave; S=K&mdash;H/<emph type="italics"/>b,<emph.end type="italics"/> e nel mezzo di IK &egrave; <lb/>S&prime;=K&mdash;H/<emph type="italics"/>b&prime;.<emph.end type="italics"/> Ma perch&egrave; <emph type="italics"/>b,<emph.end type="italics"/> raggio dell'arco GH, &egrave; maggiore di <emph type="italics"/>b&prime;,<emph.end type="italics"/> raggio <lb/>dell'arco IK; &egrave; dunque il portato della formula che sempre GH preme in gi&ugrave; <lb/>maggiormente che IK, d'onde avviene quella differente altezza di livello, che <lb/>s'&egrave; detto osservarsi per esperienza. </s></p><p type="main">

<s>Se la colonnetta liquida RS, nella figura 176, termina in R, a una su-<pb xlink:href="020/01/3385.jpg" pagenum="346"/>perficie piana, abbiamo S=K, S&prime;=K+H/<emph type="italics"/>b&prime;:<emph.end type="italics"/> se poi termina alla conves&shy;<lb/>sit&agrave; del menisco, sono invece l'equazioni S=K+H/<emph type="italics"/>b,<emph.end type="italics"/> S&prime;=K+H/<emph type="italics"/>b&prime;.<emph.end type="italics"/><lb/>E perche <emph type="italics"/>b,<emph.end type="italics"/> raggio della curvatura LRM, &egrave; maggiore d&igrave; <emph type="italics"/>b&prime;,<emph.end type="italics"/> raggio della cur&shy;<lb/>vatura NO, &egrave; dunque manifesto che in R &egrave; sempre minor la pressione, che <lb/>nel mezzo del medesimo arco NO, e per conseguenza quella delle due co&shy;<lb/>lonne liquide sottoposte deve rimanere, come di fatto s'osserva che rimane, <lb/>pi&ugrave; sollevata di questa. </s></p><p type="main">

<s>La resultante della forza maggiore sulla minore, ne'due descritti sifoni, <lb/>non &egrave; visibile in atto perch&egrave;, per l'uguaglianza de'momenti idrostatici, nei <lb/>due rami si fa l'equilibrio, a quel modo che da un peso di due libbre non <lb/>si vede sollevare il peso di una libbra sola, posto a una distanza doppia dal <lb/>centro della bilancia. </s>

<s>Ma se, come nella bilancia d&igrave; braccia uguali, si potes&shy;<lb/>sero disporre i liquidi nei recipienti, si vedrebbero attualmente i menischi <lb/>GH, NO di maggiori potenze spingere le colonne alla parte opposta, dove le <lb/>resistenze si sono dimostrate minori. </s>

<s>La desiderata disposizione la trov&ograve; bene <lb/>il Laplace in una esperienza antica, e della quale il Musschenbroek, bench&egrave; <lb/>s'aiutasse col parallelogrammo delle forze, non riusc&igrave;, come vedemmo, a <lb/>dare una dimostrazione assoluta. </s></p><p type="main">

<s>&ldquo; Considerons maintenant une petite colonne de fluide, renform&eacute;e dans <lb/>un tube conique capillaire, ouvert par ses deux extremit&eacute;. </s>

<s>Soit ABCD (fig. </s>

<s>177) <lb/>ce tube, et M M&prime;N&prime;N le colonne fluide. </s>

<s>Supposons d'abord l'axe OE du tube <lb/><figure id="id.020.01.3385.1.jpg" xlink:href="020/01/3385/1.jpg"/></s></p><p type="caption">

<s>Figura 177.<lb/>horizontal, O &eacute;tant le sommet du c&ograve;ne pro&shy;<lb/>long&eacute; par la pens&eacute;e. </s>

<s>Supposons de plus <lb/>la surface du fluide concave. </s>

<s>Il viessible <lb/>que le tube, etant plus etroit en <emph type="italics"/>p<emph.end type="italics"/> qu'en <emph type="italics"/>p&prime;,<emph.end type="italics"/><lb/>le rayon de courbure de sa surface est plus <lb/>petit, dans le premier point, que dans le <lb/>second. </s>

<s>En nominant donc <emph type="italics"/>b<emph.end type="italics"/> et <emph type="italics"/>b&prime;<emph.end type="italics"/> ces ra&shy;<lb/>yons l'action du fluide en <emph type="italics"/>p,<emph.end type="italics"/> sur un canal infiniment etroit <emph type="italics"/>pp&prime;,<emph.end type="italics"/> sera K&mdash;H/<emph type="italics"/>b,<emph.end type="italics"/> et <lb/>en <emph type="italics"/>p&prime;<emph.end type="italics"/> cette action sera K&mdash;H/<emph type="italics"/>b:<emph.end type="italics"/> ainsi <emph type="italics"/>b&prime;<emph.end type="italics"/> &eacute;tant plus grand que <emph type="italics"/>b,<emph.end type="italics"/> cette action <lb/>sera plus grande en <emph type="italics"/>p&prime;<emph.end type="italics"/> qu'en <emph type="italics"/>p,<emph.end type="italics"/> et par cons&eacute;quent le fluide renform&eacute; dans <lb/>le canal tendra a se mouvroir vers le sommet O du c&ograve;ne. </s>

<s>Ce serait le con&shy;<lb/>traire, si la surface du fluide &eacute;tait convexe, car alors ces actions seraient <lb/>respectivement K+H<emph type="italics"/>b,<emph.end type="italics"/> et K&mdash;H/<emph type="italics"/>b&prime;.<emph.end type="italics"/> L'action du fluide sur le canal est donc <lb/>alors plus grande en <emph type="italics"/>p<emph.end type="italics"/> qu'en <emph type="italics"/>p&prime;,<emph.end type="italics"/> et par consequent le fluide tend a se mou&shy;<lb/>voir de <emph type="italics"/>p<emph.end type="italics"/> vers <emph type="italics"/>p&prime;<emph.end type="italics"/> (ivi, pag. </s>

<s>32, 33), ce que (ripeteremo il detto dal Laplace <lb/>in altri simili propositi) l'experience indique encore &rdquo; (ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>A cos&igrave; fatte matematiche ragioni l'autore del Supplemento al X libro <lb/>della Meccanica celeste riduceva il moto dell'ascesa e della discesa de'li-<pb xlink:href="020/01/3386.jpg" pagenum="347"/>quidi nei tubi capillari, non rimanendogli a far altro che dimostrare come <lb/>conseguissero dalla teoria i particolari accidenti, che si osservano in simili <lb/>esperienze, e particolarmente quello del vedere le dette ascese e discese farsi <lb/>con lunghezze, che sempre stanno in reciproca ragione dei raggi. </s>

<s>Attribuito <lb/>ad H il solito valore, e intendendosi per <foreign lang="greek">q</foreign>, nella figura 171, l'angolo IYV, <lb/>che il liquido, la gravit&agrave; del quale sia <emph type="italics"/>g,<emph.end type="italics"/> fa con la parete del tubo di rag&shy;<lb/>gio <emph type="italics"/>l;<emph.end type="italics"/> il Laplace, nel caso che esso liquido salga, ne ritrova l'altezza <emph type="italics"/>q<emph.end type="italics"/><lb/>espressa dall'equazione <emph type="italics"/>q=H/g.cos<foreign lang="greek">q</foreign>/l.<emph.end type="italics"/> Tale espressione analitica completa&shy;<lb/>mente risponde ai fatti, la verit&agrave; dei quali sappiamo oramai che dipende <lb/>dalla figura della superficie di livello, ossia dall'angolo <foreign lang="greek">q</foreign>, che, potend'essere <lb/>o minore o uguale o maggiore di novanta gradi, fa s&igrave; che la detta superfi&shy;<lb/>cie ora sia concava, ora piana, ora convessa. </s>

<s>Nel primo caso <emph type="italics"/>cos<foreign lang="greek">q</foreign><emph.end type="italics"/> &egrave; positivo, <lb/>e positivo con esso anche <emph type="italics"/>q,<emph.end type="italics"/> e ci&ograve; vuol dire che il liquido s'alza al di sopra <lb/>dell'ordinario livello idrostatico. </s>

<s>Nel secondo caso <emph type="italics"/>cos<foreign lang="greek">q</foreign><emph.end type="italics"/> e <emph type="italics"/>q<emph.end type="italics"/> sono zero, o sia <lb/>il liquido non s'alza n&egrave; s'abbassa: nel terzo caso finalmente <emph type="italics"/>cos<foreign lang="greek">q</foreign>,<emph.end type="italics"/> e perci&ograve; <emph type="italics"/>q,<emph.end type="italics"/><lb/>son negativi, e ci&ograve; significa che .il liquido si abbassa. </s></p><p type="main">

<s>Per concluderne poi di qui che, o avvenga un'elevazione o un abbas&shy;<lb/>samento, sempre le distanze dal livello ordinario son reciprocamente propor&shy;<lb/>zionali alle grandezze dei raggi, preso un tubo di raggio <emph type="italics"/>l&prime;<emph.end type="italics"/> diverso da <emph type="italics"/>l,<emph.end type="italics"/> e <lb/>in cui l'altezza della salita sia <emph type="italics"/>q&prime;,<emph.end type="italics"/> avremo <emph type="italics"/>q:q&prime;=H/g.cos<foreign lang="greek">q</foreign>/l:H/g.cos<foreign lang="greek">q</foreign>&prime;/l&prime;,<emph.end type="italics"/><lb/>ossia, nel caso che medesimo sia il liquido, e medesima la materia del tubo, <lb/><emph type="italics"/>q:q&prime;=l&prime;cos<foreign lang="greek">q</foreign>:lcos<foreign lang="greek">q</foreign>&prime;.<emph.end type="italics"/></s></p><p type="main">

<s>Si osservi ora che <foreign lang="greek">q</foreign> e <foreign lang="greek">q</foreign>&prime; son, nella figura 170, l'angolo formato dalla NR <lb/>(condotta perpendicolare alla tangente la curvit&agrave; dell'arginetto nel punto N) <lb/>con essa tangente: la quale NR essendo la resultante delle NL, NK, non <lb/>varia direzione, mentre che invariabili rimangano le materie del solido e del <lb/>liquido, n&egrave; dipende affatto dallo spazio, in cui s'&egrave; descritto il quadrato MO, <lb/>o dalla distanza della parete AO all'altra opposta del vaso: e insomma, trat&shy;<lb/>tandosi di vasi cilindrici, quali sono i tubi che contempliamo, &egrave; affatto indi&shy;<lb/>pendente dalla grandezza dei loro diametri. </s>

<s>Il Laplace faceva le medesime <lb/>osservazioni con quest'altro, forse men facile, e meno chiaro discorso: &ldquo; La <lb/>surface du tube peut donc <gap/>tre consider&eacute;e comme etant plane a tres-peu&shy;<lb/>pres, dans un rayon egal a celui de sa sph&egrave;re d'activit&eacute; sensible. </s>

<s>Le fluide <lb/>dans cette intervalle s'abaissera donc ou s'elevera depuis cette surface, a <lb/>tres-peu-pres comme si elle etait plane. </s>

<s>Au-de-la ce fluide, n'etant plus sou&shy;<lb/>mis sensiblement qu'&agrave; la pesanteur et a son action sur lui-meme, sa surface <lb/>sera &agrave;-peu-pres celle d'un segment sph&egrave;rique, dont les plans extr&egrave;mes etant <lb/>ceux de la surface fluide, aux limites de la sph&egrave;re d'activit&eacute; sensible du tube, <lb/>seront &agrave; tres-peu-pres dans le divers tubes egalement inclin&eacute;s &agrave; leurs pa&shy;<lb/>rois, d'ou il suit que tous ces segmens seroint semblables &rdquo; (pag. </s>

<s>4, 5). </s></p><p type="main">

<s>Se dunque <foreign lang="greek">q</foreign> e <foreign lang="greek">q</foreign>&prime; sono uguali, <emph type="italics"/>q:q&prime;=l&prime;:l,<emph.end type="italics"/> secondo che, per corri&shy;<lb/>spondere con l'esperienza, doveva resultarne dalla teoria. </s>

<s>Come poi ci&ograve; re-<pb xlink:href="020/01/3387.jpg" pagenum="348"/>sultasse anche dalla formula del Clairaut, fu da noi gi&agrave; fatto notare, contro <lb/>il giudizio che ne dette lo stesso Laplace, il quale ebbe nonostante ragione, <lb/>quando disse che quel grande Geometra non aveva nella sua formula inse&shy;<lb/>riti i principii, dai quali far conseguire un'altra legge, che s'osserva costan&shy;<lb/>temente nella quantit&agrave; dell'ascesa de'liquidi su per spazii strettissimi, in co&shy;<lb/>lonne parallelepipede, come fra due lamine parallele di vetro, pochissimo fra <lb/>s&egrave; distanti. </s>

<s>L'impotenza di dimostrar la qual legge fece il Laplace derivare <lb/>dal non aver saputo il Clairaut spiegare co'suoi principii le proporzioni delle <lb/>salite de'liquidi, nei tubi cilindrici, in virt&ugrave; di alcune proprie e ben definite <lb/>leggi dell'attrazione. </s>

<s>&ldquo; La connaissance de ces lois est cependant le point <lb/>le plus delicat, et le plus important de cette theorie: elle est indispensable <lb/>pour lier entre eux les divers ph&eacute;nom&egrave;nes capillaires, et Clairaut en e&ugrave;t <lb/>lui-meme reconnu la necessit&eacute;, s'il e&ucirc;t voulu, par exemple, passer des tubes <lb/>aux espaces capillaires renform&eacute;s entre des plans paralleles, et deduire de <lb/>l'analyse le rapport d'egalit&eacute;, que l'experience indique entre l'ascension du <lb/>fluide dans un tube cylindrique, et son ascension entre deux plans paralle&shy;<lb/>les, dont la distance mutuelle est &eacute;gale au dem&igrave;-diametre du tube, ce que <lb/>personne encore n'a tent&eacute; d'expliquer &rdquo; (ivi, pag. </s>

<s>2). </s></p><p type="main">

<s>Di giungere alla quale spiegazione il Laplace si preparava le vie, appli&shy;<lb/>cando l'analisi precedente a determinar l'altezza, a cui pu&ograve; giungere un li&shy;<lb/>quido, dentro l'angusto spazio interposto fra la superficie convessa di un ci&shy;<lb/>lindro solido, e la concava di un tubo a lui concentrico, e ambedue composte <lb/>della stessa materia. </s>

<s>Se <emph type="italics"/>l<emph.end type="italics"/> sia il raggio della sezione del tubo, e <emph type="italics"/>l&prime;<emph.end type="italics"/> quello <lb/>della sezion del cilindro, rappresentando H, <emph type="italics"/>g,<emph.end type="italics"/> <foreign lang="greek">q</foreign> i medesimi valori della for&shy;<lb/>mula precedente, il Laplace giunge &agrave; determinare la quantit&agrave; <emph type="italics"/>q&prime;<emph.end type="italics"/> della richie&shy;<lb/>sta altezza, per via dell'equazione <emph type="italics"/>q&prime;=H/g.cos<foreign lang="greek">q</foreign>/(l&mdash;l&prime;),<emph.end type="italics"/> la quale, paragonata con <lb/>quell'altra di <emph type="italics"/>q,<emph.end type="italics"/> che dianzi l'Autore stesso ritrovava; gli fa legittimamente <lb/>argomentare essere l'altezza del liquido dentro l'anello la medesima, che <lb/>dentro un tubo cilindrico, avente raggio uguale a <emph type="italics"/>l&mdash;l'.<emph.end type="italics"/> Giunto alla qual <lb/>conclusione, &egrave; notabile che il Laplace confidi al corollario seguente il me&shy;<lb/>rito e i vanti della sua scoperta: &ldquo; En supposant infinis les rayon du tube <lb/>et du cylindre, on avra le cas de deux plans verticaus et paralleles tres&shy;<lb/>precues l'un de l'autre: le theorema precedent a donc encore lieu dans ce cas, <lb/>que nous allons traiter par une analyse particuliere &rdquo; (ivi, pag. </s>

<s>28). </s></p><p type="main">

<s>Da questa storia argomenteranno forse i Lettori che le speculazioni ana&shy;<lb/>litiche del Laplace, quanto sono ingegnose, altrettanto sian semplici. </s>

<s>Vero &egrave; <lb/>bene che, de'calcoli di lui, abbiamo riferite le sole conclusioni, ma chi vo&shy;<lb/>lesse ritesserne i processi non ci troverebbe difficolt&agrave;, pur che egli avesse <lb/>notizia delle regole elementari del calcolo infinitesimale. </s>

<s>Nonostante, chiun&shy;<lb/>que si metta a svolgere le pagine del citato <emph type="italics"/>Supplemento,<emph.end type="italics"/> in ritrovarle cos&igrave; <lb/>per tutto cincischiate di simboli algebriei e d'equazioni, involte in grappe <lb/>corpulente, e in parentesi, riformerebbe il giudizio intorno alla semplicit&agrave; delle <lb/>supposte regole elementari. </s></p><pb xlink:href="020/01/3388.jpg" pagenum="349"/><p type="main">

<s>Di qui coglieranno i curiosi occasione di domandare: se quel suntuoso <lb/>macchinamento di calcoli fu scelto dall'Autore, per fare sfoggio della sua <lb/>arte analitica, o perch&egrave; veramente fosse di necessit&agrave; richiesto dall'indole del <lb/>soggetto. </s>

<s>Per rispondere a ci&ograve;, giova rammemorare quel che altrove osser&shy;<lb/>vammo dell'onnipotenza, che s'incominci&ograve; ad attribuire all'analisi matema&shy;<lb/>tica, dopo l'Eulero. </s>

<s>Per quel che poi particolarmente riguarda il Laplace, <lb/>non si vuol dimenticare l'esempio, che ne dette nella dimostrazione del pa&shy;<lb/>rallelogrammo delle forze: e come questa, condotta per via del calcolo dif&shy;<lb/>ferenziale, riusc&igrave; inutile, anzi dannosa; cos&igrave; potrebb'essere che inutili e dan&shy;<lb/>nosi riuscissero certi processi, nel trattato delle azioni capillari. </s>

<s>Si vorr&agrave; <lb/>dunque dire che fu questa un'arte dell'Autore, per soggiogare gl'ingegni? </s>

<s><lb/>Veramente una tal'arte &egrave; molto in voga presso certi filosofi, e certi poeti, <lb/>che si fanno ammirare, per non essere intesi, e per saper, con un gioco di <lb/>prospettiva, far apparire gli oggetti cos&igrave; lontani, da non si credere accessi&shy;<lb/>bili alle braccia di tutti, i quali perci&ograve; si rassegnano a riconoscersi pigmei, <lb/>umiliandosi a quelli, che, rispetto a loro, debbon dunque esser giganti. </s></p><p type="main">

<s>Comunque sia, il Laplace trov&ograve; molti che rimasero cos&igrave; soggiogati, fra <lb/>i quali il Rumfort basti per tutti. </s>

<s>Gettandosi in faccia al valoroso Fisico che <lb/>la pellicola superficiale de'liquidi veniva a dissiparsi, come un fantasma, in&shy;<lb/>nanzi alle verit&agrave; dimostrate dal Laplace; rispondeva che la <emph type="italics"/>coesione<emph.end type="italics"/> fra le <lb/>minime particelle, necessaria al formarsi le dette pellicole, non differiva in <lb/>sostanza dall'attrazione molecolare. </s>

<s>Che se non ne aveva dimostrate le leggi, <lb/>ingenuamente confessava esserne causa la cos&igrave; poco profonda conoscenza, che <lb/>trovava in s&egrave; dell'alta analisi matematica. </s>

<s>&ldquo; Je dois pourtant avouer que je <lb/>ne suis pas assez vers&eacute; dans la haute Geometrie, pour pouvoir bien com&shy;<lb/>prendre les calculs de M. </s>

<s>De la Place sur ce sujet, et je me garderai bien <lb/>de les juger. </s>

<s>Il faudroit sans doute avoir une connoissance tres-profonde des <lb/>methodes analityques, pour sentir la force de ses demonstrations &rdquo; (<emph type="italics"/>Bibl. </s>

<s><lb/>Brit., mois de Mai 1807, Sciences et Arts,<emph.end type="italics"/> pag. </s>

<s>3). </s></p><p type="main">

<s>Quel che per&ograve; a noi pi&ugrave; importa &egrave; di narrare le sorti, che le teorie del <lb/>Laplace incontrarono in Italia: sorti ch'essendo state varie ci contenteremo <lb/>di veder rappresentate negli scritti de'due valenti fisici e matematici, Gio&shy;<lb/>vacchino Pessuti, e Fabrizio Mossotti. </s></p><p type="main">

<s>Il d&igrave; 22 Maggio 1808 la Societ&agrave; italiana delle Scienze riceveva la Me&shy;<lb/>moria del Pessuti intorno alla <emph type="italics"/>Teoria dell'azion capillare del signor De-la&shy;<lb/>Place, ridotta alla pi&ugrave; semplice ed elementare Geometria.<emph.end type="italics"/> Diceva nel proe&shy;<lb/>mio l'Autore di essersi messo all'opera, in grazia di coloro che, non avendo <lb/>le sottigliezze dell'analisi sublime cos&igrave; familiari, erano perci&ograve; impediti di gu&shy;<lb/>star le bellezze delle verit&agrave; dimostrate dall'Autore della Meccanica celeste. </s>

<s><lb/>Ma accadde per verit&agrave; al Pessuti come a chi troppo largamente promette. </s>

<s><lb/>La semplice Geometria elementare, essendo strumento troppo ottuso a pene&shy;<lb/>trar la durezza del soggetto; non pot&egrave; nemmeno il Nostro fare a meno di <lb/>introdurre qualche equazione differenziale, con i suoi integrali, chi sa la re&shy;<lb/>gola delle quali operazioni non trova difficolt&agrave; nel tener dietro ai passi del <pb xlink:href="020/01/3389.jpg" pagenum="350"/>Matematico francese, bench&egrave; siano pi&ugrave; lunghi, e pi&ugrave; intricati. </s>

<s>N&egrave; dall'altra <lb/>parte ci deliberano da questa pena parecchie analisi geometriche della detta <lb/>Memoria, il merito della quale consiste nell'aver dato miglior ordine al me&shy;<lb/>todo, d'onde vengono a scoprirsi certe fallacie, e a scansarsi alcuni errori, <lb/>ne'quali nessuno forse, prima del Pessuti, avrebbe sospettato mai fosse ca&shy;<lb/>duto un matematico come il Laplace. </s></p><p type="main">

<s>Nel citato <emph type="italics"/>Supplemento<emph.end type="italics"/> fa l'Autore conseguir dalla sua analisi generale <lb/>la soluzion del problema, fisicamente risoluto gi&agrave; dal Borelli, il quale per&ograve; <lb/>non aveva ancora osservato che quell'attrarsi scambievole de'leggieri corpu&shy;<lb/><figure id="id.020.01.3389.1.jpg" xlink:href="020/01/3389/1.jpg"/></s></p><p type="caption">

<s>Figura 178.<lb/>scoli sull'acqua, era proprio anche a due la&shy;<lb/>stre di vetro, poste nelle medesime condizioni. </s></p><p type="main">

<s>Siano NR, MB (fig. </s>

<s>178) i profili delle <lb/>due dette lastre, fra le quali, standosi elle <lb/>prossime, salga sopra il naturale livello VPV&prime; <lb/>il liquido infino in NOM, formando all'esterno <lb/>gli arginetti VZ, V&prime;Z&prime;. </s>

<s>Il Laplace dimostra <lb/>che la pressione del liquido sopra la NR, per <lb/>farla aderire alla MB, uguaglia il peso di <lb/>una mezza colonna parallelepipeda di liquido, <lb/>avente per base il rettangolo di NZ nella lar&shy;<lb/>ghezza della lastra, e per altezza NG+GZ. </s>

<s><lb/>Dopo che immediatamente cos&igrave; soggiunge: <lb/>&ldquo; Un resultat semblable a lieu pour le plan MB, on a donc ainsi la force, <lb/>avec la quelle les deux plans tendent a se rapprocher, et l'on voit que cette <lb/>force eroit en raison inverse de leur distance mutuelle &rdquo; (pag. </s>

<s>44). </s></p><p type="main">

<s>Ma si contiene in queste parole un'errore manifesto. </s>

<s>Chiamata infatti L <lb/>la larghezza della lamina, la forza F della pressione &egrave; dunque, secondo il <lb/>Laplace, uguale a (L.NZ(NG+GZ))/2=(L.NZ(NZ+2GZ))./2 Accostandosi di <lb/>pi&ugrave; o scostandosi NR da MB, e perci&ograve; il livello da N alzandosi o abbassan&shy;<lb/>dosi in N&prime;, la nuova forza che ne resulta sar&agrave; uguale a L.N&prime;Z(N&prime;Z+2GZ)/2, <lb/>e perci&ograve; avremo F:F&prime;=NZ(NZ+2GZ):N&prime;Z(N&prime;Z+2GZ). E perch&egrave; <lb/>GZ, che &egrave; quantit&agrave; piccolissima rispetto a NZ e a N&prime;Z, pu&ograve; trascurarsi; <lb/>F:F&prime;=NZ2:N&prime;Z2. </s>

<s>Considerando poi che, essendo uguali gli arginetti dalla <lb/>parte di dentro e da quella di fuori, NL=ZG, e perci&ograve; NZ=OP, N&prime;Z= <lb/>O&prime;P: e che inoltre OP, OP&prime;, altezze delle colonne liquide fra le due lastre, <lb/>stanno reciprocamente come le D&prime;, D, loro mutue distanze; s'otterr&agrave; final&shy;<lb/>mente F:F&prime;=D&prime;2:D2. </s>

<s>E di qui appar manifesto che le forze impellenti <lb/>le lastre al contatto sono in ragion dei quadrati, e non in semplice <emph type="italics"/>raison <lb/>inverse de leur distance mutuelle.<emph.end type="italics"/></s></p><p type="main">

<s>Il Pessuti si conferma nella verit&agrave; di questa legge, per analogia di ci&ograve; <lb/>che si osserva in tutte le attrazioni a sensibile distanza, e attribuisce l'as&shy;<lb/>serzione del signor De la Place, che lo fa stupire, <emph type="italics"/>o a una svista o a un<emph.end type="italics"/><pb xlink:href="020/01/3390.jpg" pagenum="351"/><emph type="italics"/>crrore di stampa. (Memorie<emph.end type="italics"/> cit., T. XIV, P. I, Verona 1809, pag. </s>

<s>142 in <lb/>nota). Comunque sia, non sembra a noi che valgano queste scuse l&agrave;, dove <lb/>il Laplace stesso deduce, dal valore di <emph type="italics"/>q&prime;=H/g.cos<foreign lang="greek">q</foreign>&prime;/(l&mdash;l&prime;),<emph.end type="italics"/> la quantit&agrave; del&shy;<lb/>l'altezza, a cui giunge il liquido fra due lastre parallele, supponendo che <lb/><emph type="italics"/>l<emph.end type="italics"/> e <emph type="italics"/>l&prime;,<emph.end type="italics"/> raggi, siano di lunghezza infinita. </s>

<s>Perch'essendo gl'infiniti uguali, la <lb/>loro differenza <emph type="italics"/>l&mdash;l&prime;<emph.end type="italics"/> &egrave; zero, e il non si concluder nulla dall'equazione d&agrave; <lb/>segno manifesto che il metodo &egrave; sbagliato. </s></p><p type="main">

<s>L'origine dello sbaglio &egrave; dall'avere il Laplace giudicata la formula del <lb/>Clairaut difettosa, in dimostrare le proporzioni dell'ascesa de'liquidi in due <lb/>tubi di vario diametro, e in mezzo a due lastre, poste a pi&ugrave; o men prossima <lb/>distanza fra loro. </s>

<s>Ma principalmente &egrave; a riconoscersi quella origine dall'aver <lb/>voluto far dipendere la dimostrazione dei due fatti distinti da una medesima <lb/>analisi generale. </s>

<s>Il bisogno di questa analisi non si faceva per&ograve; giustamente <lb/>sentire, se non col&agrave;, dove, dai semmenti di sfera o dai menischi, si faceva <lb/>trapasso ad altra qualit&agrave; di figure, come sarebbe quella, che prende la li&shy;<lb/>quida superficie fra due lastre di vetro, molto prossime e parallele. </s></p><p type="main">

<s>Che del resto la particolar formula del Clairaut, non solo era sufficiente, <lb/>ma porgeva il mezzo pi&ugrave; semplice e pi&ugrave; diretto di dimostrare che, nei tubi <lb/>assai stretti, le altezze son reciprocamento proporzionali ai raggi delle se&shy;<lb/>zioni, come conseguenza immediata delle forze attrattive dei menischi. </s>

<s>Il La&shy;<lb/>place invece volle ci&ograve; dedurre dalla formula generale, che concludeva il va&shy;<lb/>lore di quelle stesse forze attrattive per qualunque genere di superficie, e <lb/>giunse, come si sa, a dar l'altezza della colonna liquida nell'interno del <lb/>tubo, espressa dal prodotto della costante H, nel coseno di <foreign lang="greek">q</foreign>, diviso per il <lb/>raggio. </s>

<s>Per fare apparir poi la relazione, che questa legge della salita nei <lb/>tubi cilindrici ha con la legge della salita nell'interstizio di due lastre pa&shy;<lb/>rallele, collega i due fatti con quello della salita su per lo spazio annulare, <lb/>lasciato fra un cilindro e il tubo che lo circonda, perche questi, mentre <lb/>partecipano delle propriet&agrave; de'cannelli, essendo piccoli i raggi, si rendono <lb/>poi facilmente alle condizioni delle lastre parallele, supponendo quegli stessi <lb/>raggi grandissimi o infiniti. </s>

<s>Ma come in questo caso divenga muta di ogni <lb/>espressione la formula del Laplace, gi&agrave; fu detto, e di ci&ograve; accortosi il Pes&shy;<lb/>suti, pur serbandosi fedele alle dottrine del grande Matematico francese, <lb/>dette altr'ordine al metodo di lui, e, se non sempre pi&ugrave; semplice, lo ridusse <lb/>certamente a pi&ugrave; logica ragione. </s></p><p type="main">

<s>Come, dal caso particolare che la superficie attraente sia in figura di <lb/>semmento sferico, si deduca la quantit&agrave; dell'altezza del liquido, in un can&shy;<lb/>nello cilindrico, molto pi&ugrave; facilmente che deducendola dalla general formula <lb/>del Laplace; il Pessuti lo dimostra con un esempio, che si pu&ograve;, col seguente <lb/>discorso, rendere anche pi&ugrave; semplice e pi&ugrave; spedito. </s>

<s>Sia nel tubo AF (fig. </s>

<s>179) <lb/>il solito filetto DQ, comunicante, per mezzo del canaliculo QR, con RI, ter&shy;<lb/>minato in I a un punto della GH, superficie del liquido, in cui si suppone <lb/>il detto tubo essere immerso. </s>

<s>Tenendosi per ragione idrostatica IR con LQ <pb xlink:href="020/01/3391.jpg" pagenum="352"/>in equilibrio, dunque DL non preme niente sopra la sua base L, ci&ograve; che <lb/>dev'essere, perch&egrave; alla forza del peso di lui &egrave; uguale e contraria l'azion del <lb/>menisco. </s>

<s>Ma questa &egrave; K/<emph type="italics"/>b,<emph.end type="italics"/> e quello, cioe il peso della porzione DL, chia&shy;<lb/>mata <emph type="italics"/>g<emph.end type="italics"/> la gravit&agrave; specifica del liquido, &egrave; manifestamente <emph type="italics"/>g<emph.end type="italics"/>.DL; dunque <lb/><emph type="italics"/>K/b=g.DL,<emph.end type="italics"/> ossia DL=K/<emph type="italics"/>g.b.<emph.end type="italics"/></s></p><p type="main">

<s>Come poi questa espressione semplicissima risponda alle varie condi&shy;<lb/><figure id="id.020.01.3391.1.jpg" xlink:href="020/01/3391/1.jpg"/></s></p><p type="caption">

<s>Figura 179.<lb/>zioni del problema, non meno di <lb/>quell'altra, che il Laplace ricav&ograve; <lb/>con calcolo s&igrave; laborioso dalla sua <lb/>formula generale; si vedr&agrave; facil&shy;<lb/>mente per ognuno, che voglia met&shy;<lb/>tersi a farne la prova. </s>

<s>Se <emph type="italics"/>b<emph.end type="italics"/> infatti <lb/>che risponde al raggio DC, dise&shy;<lb/>gnato nella figura, &egrave; infinito (ci&ograve; <lb/>che significa essere la superficie <lb/>piana) DL &egrave; zero. </s>

<s>E se <emph type="italics"/>b<emph.end type="italics"/> &egrave; nega&shy;<lb/>tivo, che vuol dire trasformarsi la <lb/>superficie di concava in convessa, <lb/>anche DL ha valor negativo, ossia, <lb/>come nel mercurio si osserverebbe, <lb/>avremmo una depressione della co&shy;<lb/>lonnetta liquida sotto il livello di <lb/>GH, in luogo di un alzamento. </s></p><p type="main">

<s>Con la medesima semplicit&agrave; vien portato, da questo indirizzo, il Pessuti <lb/>a concludere le ragioni delle altezze, in due tubi, reciproche alle lunghezze <lb/>dei raggi. </s>

<s>Perch&egrave;, preso insieme con l&prime;AF, un altro tubo NM, in cui l'al&shy;<lb/>tezza del liquido viene espressa per XM=K/<emph type="italics"/>g.b&prime;,<emph.end type="italics"/> essendo <emph type="italics"/>b&prime;<emph.end type="italics"/>=PX, raggio <lb/>della curvatura del menisco NXO; si giunge alla proporzione DL:XM= <lb/>PX:CD. </s>

<s>E perch&egrave; i raggi PX, CD, per la similitudine degli archi NXO, <lb/>ADB, stanno come le respettive corde, che sono i diametri dei tubi; dun&shy;<lb/>que DL:XM=NO:AB. </s></p><p type="main">

<s>Il teorema della salita del liquido, fra due lamine parallele, &egrave; di un or&shy;<lb/>dine superiore a questo, e perci&ograve; saggiamente il Pessuti ne distinse la dimo&shy;<lb/>strazione, facendola dipendere da principii pi&ugrave; complicati, secondo il com&shy;<lb/>plicarsi della figura, che l&agrave; era un semmento di sfera o un menisco, e qua <lb/>un semmento di cilindro o una doccia. </s>

<s>Nella sfera basta la sezione di un <lb/>piano, essendo la curvatura simmetrica intorno a un asse solo. </s>

<s>Ma, dove <lb/>manca una tale semplicit&agrave; di simmetria, ci vogliono due sezioni perpendi&shy;<lb/>colari, e perci&ograve; due saranno i raggi delle curvature, o delle osculazioni, che <lb/>debbono considerarsi. </s>

<s>Di qui &egrave; che il Laplace formulava cos&igrave; quel suo prin&shy;<lb/>cipio generale, per altre pi&ugrave; semplici vie dimostrato poi dal nostro Pessuti: <pb xlink:href="020/01/3392.jpg" pagenum="353"/>&ldquo; Dans toutes les lois, qui rendent l'attraction insensible &agrave; des distances sen&shy;<lb/>sibles, l'action d'un corps termin&eacute; par une surface courbe, sur un canal in&shy;<lb/>terieur infiniment etroit, perpendiculaire a cette surface, dans un point quel&shy;<lb/>conque; est egale &agrave; la demi-somme des actions sur le meme canal de deux <lb/>sph&egrave;res, qui auraient pour rayons le plus grand, et le plus petit des rayons <lb/>osculateurs de la surface a ce point &rdquo; (<emph type="italics"/>Supplement<emph.end type="italics"/> cit., pag. </s>

<s>4). E perci&ograve; <lb/>sar&agrave; per simboli questo principio espresso da <emph type="italics"/>H/z(1/b+1/b&prime;)<emph.end type="italics"/> dove H &egrave; la <lb/>solita costante, e <emph type="italics"/>b, b&prime;<emph.end type="italics"/> i due detti raggi osculatori. </s></p><p type="main">

<s>Rappresenti ora ABCD (fig. </s>

<s>180) un piccolo tratto della doccia, secondo <lb/>la quale si dispone il livello del liquido, fra le due lastre, e si consideri <lb/>l'azione attrattiva di lei nel punto I, uno de'raggi osculatori al quale, cio&egrave; <lb/><emph type="italics"/>b<emph.end type="italics"/> sar&agrave; quello del circolo, a cui appartiene l'arco BIC. </s>

<s>Ma l'altro raggio, rap&shy;<lb/>presentato da <emph type="italics"/>b&prime;<emph.end type="italics"/> e diretto secondo la IK, torner&agrave; infinito, essendo EF una <lb/>linea retta. </s>

<s>Dunque in questo caso 1/<emph type="italics"/>b&prime;<emph.end type="italics"/> sparisce dalla formula, la quale perci&ograve; <lb/>si riduce ad H/2<emph type="italics"/>b.<emph.end type="italics"/></s></p><p type="main">

<s>Ci&ograve; stante, si applichi l'azione della superficie ABCD in attrarre il filetto <lb/>IG in mezzo alla colonna parallelepipeda AM, e si consideri insieme il me&shy;<lb/><figure id="id.020.01.3392.1.jpg" xlink:href="020/01/3392/1.jpg"/></s></p><p type="caption">

<s>Figura 180.<lb/>nisco NOP, il raggio di curva&shy;<lb/>tura del quale uguagli quello di <lb/>BC, applicato ad attrarre nel <lb/>punto O il filetto OQ, dentro <lb/>il cilindro NR. </s>

<s>Essendo la su&shy;<lb/>perficie, nel vaso dell'immer&shy;<lb/>sione, TV, e SG in equilibrio <lb/>idrostatico con LH, il peso della <lb/>porzione IS, che, ritenute le de&shy;<lb/>nominazioni di sopra, &egrave; <emph type="italics"/>g<emph.end type="italics"/>.IK, <lb/>vien sostenuto dall'azion contra&shy;<lb/>ria della superficie a doccia, nel <lb/>punto I. </s>

<s>E perch&egrave; l'intensit&agrave; di quest'azione ha, come s'&egrave; detto, per misura H/2<emph type="italics"/>b;<emph.end type="italics"/><lb/>dunque <emph type="italics"/>g.IS=H/2b.<emph.end type="italics"/></s></p><p type="main">

<s>Similmente, essendo XQ equilibrato da YQ, e il peso della porzione OX, <lb/>che &egrave; uguale a <emph type="italics"/>g<emph.end type="italics"/>.OX, sostenuto dall'azione attrattiva del menisco nel punto O, <lb/>con intensit&agrave; espressa da H/<emph type="italics"/>b;<emph.end type="italics"/> s'avr&agrave; <emph type="italics"/>g.OX=H/b,<emph.end type="italics"/> e perci&ograve; IS:OX=1:2. <lb/>Abbiasi poi un altro tubo cilindrico, di diametro uguale alla met&agrave; di NP, e <lb/>in cui salga il medesimo liquido all'altezza A: sar&agrave; per la nota legge spe&shy;<lb/>rimentale OX:A=2:1, la qual proporzione, moltiplicata per la prece&shy;<lb/>dente, d&agrave; IS.OX=A.OX, ossia IS=A. </s>

<s>Ci&ograve; vuol dire tale essere l'al-<pb xlink:href="020/01/3393.jpg" pagenum="354"/>tezza della colonna parallelepipeda AM, e di tutte le altre simili, in che pu&ograve; <lb/>distinguersi il liquido, salito fra due lamine parallele, quale in un tubo cilin&shy;<lb/>drico, avente un raggio pari alla distanza fra le lamine stesse, conforme a ci&ograve; <lb/>che fu primo a dimostrare il Laplace, e che fu l'oggetto delle sue compiacenze. </s></p><p type="main">

<s>L'altro simile teorema delle salite de'liquidi su per gl'interstizi annu&shy;<lb/>lari; dallo stesso Laplace introdotto, per collegare insieme gli effetti, che si <lb/>osservano nei tubi cilindrici, con quelli, che si osservano nelle lamine paral&shy;<lb/>lele, diviene per il Pessuti indipendente, e pu&ograve; riguardarsi come nn corol&shy;<lb/>lario delle azioni attrattive della liquida superficie fra le lamine stesse. </s>

<s>&Egrave; ma&shy;<lb/>nifesto infatti valere la medesima dimostrazione, sia quando la base della <lb/>superficie a doccia &egrave; un rettangolo, sia quando ella invece &egrave; un trapezio, per <lb/>essere il lato del poligono inscritto al tubo sempre maggiore del corrispon&shy;<lb/>dente lato del poligono circoscritto al cilindro concentrico, fra cui e lo stesso <lb/>tubo si forma l'anello. </s></p><p type="main">

<s>Non &egrave; che, sebben rese cos&igrave; pi&ugrave; dimestiche, le teorie del Laplace sodi&shy;<lb/>sfacessero in tutto ai nostri Fisici e Matematici. </s>

<s>Ma la fama dell'Autore, il <lb/>periglioso gorgo, toccato in ogni pi&ugrave; riposto seno del suo fondo, e lo stesso <lb/>magnifico apparato dell'analisi infinitesimale, concorsero tutt'insieme a dif&shy;<lb/>fondere anche fra noi le dottrine del Matematico francese, pi&ugrave; efficacemente <lb/>dei commentarii fattivi dal Pessuti. </s>

<s>Esaminatasi poi, con mente pi&ugrave; riposata, <lb/>la sottile questione, la facile onda dei plausi s'arretr&ograve; al soffiare avverso <lb/>delle censure, intanto che il Mossotti (<emph type="italics"/>Lezioni di Fisica matemat.,<emph.end type="italics"/> T. I, Fi&shy;<lb/>renze 1843, pag. </s>

<s>130) giudic&ograve; non aver fatto altro il Laplace che <emph type="italics"/>adombrare, <lb/>con poca esattezza,<emph.end type="italics"/> la teoria del Joung, ripresa dal Poisson, e condotta alla <lb/>sua perfezione. </s></p><p type="main">

<s>Il quinto libro del <emph type="italics"/>Trait&eacute; de Macanique<emph.end type="italics"/> &egrave; dal Poisson riserbato all'Idro&shy;<lb/>statica, e nel secondo capitolo si propone di trovar l'equazion generale del&shy;<lb/>l'equilibrio dei fluidi, le particelle de'quali, prese d'insensibile grandezza, <lb/><figure id="id.020.01.3393.1.jpg" xlink:href="020/01/3393/1.jpg"/></s></p><p type="caption">

<s>Figura 181.<lb/>si possono riguardare, egli dice, <emph type="italics"/>comme <lb/>une masse continue, dont la densit&eacute; est <lb/>constante,<emph.end type="italics"/> bench&egrave; anch'essi fluidi, come <lb/>tutte le altre sostanze, e i corpi solidi, <lb/>nel complesso della loro mole, siano com&shy;<lb/>posti <emph type="italics"/>des molecoles disjointes et separ&eacute;es <lb/>par des espaces vides<emph.end type="italics"/> (Bruxelles 1838, <lb/>pag. </s>

<s>366). Dentro la massa fluida ABCD <lb/>(fig. </s>

<s>181) si consideri un punto M, rife&shy;<lb/>rito ai tre assi ortogonali O<emph type="italics"/>x,<emph.end type="italics"/> O<emph type="italics"/>y,<emph.end type="italics"/> O<emph type="italics"/>z<emph.end type="italics"/> dalle <lb/>ordinate <emph type="italics"/>x, y, z,<emph.end type="italics"/> e siano X, Y, Z le forze <lb/>date, che lo sollecitano secondo quelle tre <lb/>direzioni: chiamata <foreign lang="greek">r</foreign> la densit&agrave; del fluido, la pressione <emph type="italics"/>p<emph.end type="italics"/> sofferta dal detto <lb/>punto M &egrave; per il Poisson espressa dall'equazione <emph type="italics"/>dp=<foreign lang="greek">r</foreign>(Xdx+Ydy+Zdz).<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Lorsque le point M (osserva poi l'Autore) est situe a la surface du <lb/>fluide, ou qu'il n'en est eloign&eacute; que d'une distance moindre que le rayon <pb xlink:href="020/01/3394.jpg" pagenum="355"/>d'activit&eacute; des forces moleculaires, on doit avoir &eacute;gard a ces forces, et &agrave; la <lb/>variation rapide de la densit&eacute; superficielle, dans le calcul des composantes <lb/>X, Y, Z, et par suite de la valeur de <emph type="italics"/>p,<emph.end type="italics"/> d&eacute;duite de la formule. </s>

<s>Il en resulte <lb/>une influence des forces moleculaires sur la figure du liquide en equilibre, <lb/>qui n'est pas sensible en general, et qui ne le devient que dans les espaces <lb/>capillaires. </s>

<s>On ny aura point &eacute;gard dans ce Trait&eacute;, et, pour tout ce qui con&shy;<lb/>cerne les phenom&egrave;nes de la capillarit&eacute;, je renverrai &agrave; la <emph type="italics"/>Nouvelle theorie <lb/>de l'action capillaire,<emph.end type="italics"/> que j'ai publi&eacute;e il y a deux ans &rdquo; (ivi, pag. </s>

<s>375). </s></p><p type="main">

<s>Abbiamo voluto trascrivere nella sua integrit&agrave; questo passo, perch&egrave; con&shy;<lb/>tiene in germe la teoria, che il Poisson dava delle azioni capillari, per ve&shy;<lb/>dere lo svolgimento della quale converrebbe consultare il trattato, che vi s&igrave; <lb/>cita, e donde apparirebbero i criteri, a cui s'inform&ograve; il giudizio del Mos&shy;<lb/>sotti. </s>

<s>Ma di questa consultazione dobbiam lasciare agli studiosi ogni cura, <lb/>per non dilungarci di troppo dai termini, che sono stati imposti alla nostra <lb/>Storia. </s></p><pb xlink:href="020/01/3395.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VI.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Delle prime speculazioni ed esperienze <lb/>d'Idrodinamica<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Delle leggi idrodinamiche incluse nei teoremi idrostatici di Galileo, e spiegate dal Castelli nel primo <lb/>libro Della misura delle acque correnti. </s>

<s>&mdash; II. </s>

<s>Delle relazioni tra il Discorso galileiano intorno <lb/>i galleggianti, e il primo libro Della misura delle acque correnti: della pubblicazione di questo <lb/>libro, di cui si volle dire che la scienza non era nuova. </s>

<s>&mdash; III. </s>

<s>Della legge delle velocit&aacute; pro&shy;<lb/>porzionali alle altezze, assegnata dal Castelli nel secondo libro Della misura delle acque cor&shy;<lb/>renti, di cui si difende la propriet&agrave; contro le accuse di plagio. </s>

<s>&mdash; IV. </s>

<s>Delle prime rivelazioni, <lb/>e delle prime proposte relative alla legge delle velocit&agrave; proporzionali alle radici delle altezze, </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>L'ascesa dei liquidi nei tubi capillari, e la loro discesa rispetto al li&shy;<lb/>vello del pi&ugrave; largo vaso, dentro cui si siano immersi, o la differente altezza, <lb/>a cui essi liquidi giungono, essendo il cannello e il vaso continuati, si no&shy;<lb/>tarono da lungo tempo come fatti eccezionali alla legge idrostatica, che co&shy;<lb/>stantemente s'osserva in tutti i fluidi comunicanti. </s>

<s>Altri fatti per&ograve; occorsero <lb/>ad osservarsi, che fanno alla detta legge un'eccezione anche pi&ugrave; singolare, <lb/>per cui richiamarono a s&egrave; l'attenzione dei Fisici moderni. </s></p><p type="main">

<s>Vincenzo Brunacci incomincia cos&igrave; un suo opuscolo che, insieme con <lb/>altri scritti in diverse occasioni, fu pubblicato dal Silvestri di Milano, dopo <lb/>la <emph type="italics"/>Memoria sulla dispensa delle acque<emph.end type="italics"/> del medesimo Autore: &ldquo; Dal sapersi <lb/>dimostrato nella Idraulica che in due vasi comunicanti il fluido si pone al <lb/>livello; dal vedersi sempre verificata questa legge negli sperimenti instituiti <lb/>a bella posta, e riferiti in tutte le Scuole; &egrave; dessa passata, per cos&igrave; dire, in <lb/>proverbio, in guisa che, anche gl'ignari delle pi&ugrave; semplici dottrine delle acque <lb/>correnti, ogni momento te la ripetono. </s>

<s>Ma &egrave; ella poi vera, anco quando la <pb xlink:href="020/01/3396.jpg" pagenum="357"/>comunicazione da un vaso all'altro &egrave; oltremodo difficile ed impedita? </s>

<s>&rdquo; (<emph type="italics"/>Bi&shy;<lb/>blioteca scelta,<emph.end type="italics"/> T. CCVIII, Milano 1827, pag. </s>

<s>151). </s></p><p type="main">

<s>Che il fatto comunemente asserito non si verifichi, nel caso che alla <lb/>libera comunicazione si frapponga qualche impedimento, il Brunacci lo dimo&shy;<lb/>stra con tre varie esperienze, nelle quali l'acqua non pu&ograve; comunicare da un <lb/>vaso all'altro, se non che attraversando strati ora di terra, ora di sabbia, <lb/>ora di ghiaia. </s>

<s>N&egrave; a diverse cause da questa, cio&egrave; dalla comunicazione impe&shy;<lb/>dita, attribuisce il fatto delle pozzanghere, che si osservano a pi&egrave; degli ar&shy;<lb/>gini, e sul fondo delle navi, dove l'acqua, che dee filtrare attraverso ai <lb/>pori della terra e alle commessure del legno, rimane di tanto inferiore al <lb/>livello del fiume. </s></p><p type="main">

<s>Altre simili esperienze, descritte dall'Hauksbee e confermate dal Newton, <lb/>avevano condotto a resultati tutt'affatto contrari, ma &egrave; da osservare che, <lb/>sebbene l'acqua, su per il tubo pieno di cenere, incontra non lieve la resi&shy;<lb/>stenza, com'apparisce dal vedere la velocit&agrave; della sua ascesa sempre pi&ugrave; ri&shy;<lb/>tardata; viene a superarsi nulladimeno una tal resistenza dall'attrazione mo&shy;<lb/>lecolare, che tanto si fa maggiore, quanto la cenere stessa dentro il tubo &egrave; <lb/>pi&ugrave; fortemente compressa. </s></p><p type="main">

<s>In qualunque modo, anche il dislivello, che si osserva ne'tubi capillari, <lb/>si pu&ograve; ridurre al principio della comunicazione impedita. </s>

<s>Ne'vasi infatti, rap&shy;<lb/>presentati dalle figure 175 e 176 intercalate qui addietro, il livello GH del&shy;<lb/>l'acqua non risale infino al livello IK, perch&egrave; il menisco maggiore, anche <lb/>maggiormente ne impedisce il moto. </s>

<s>In simil guisa il mercurio NO non rag&shy;<lb/>giunge il livello del mercurio LM, perch&egrave; nella canna pi&ugrave; stretta trova mag&shy;<lb/>giore la resistenza. </s>

<s>Sempre dunque il dislivello idrostatico &egrave; un effetto delle <lb/>resistenze, siano queste dovute alle azioni capillari o ad altre cause mecca&shy;<lb/>niche. </s>

<s>Quindi &egrave; che, negli esperimenti instituiti a bella posta e riferiti in <lb/>tutte le Scuole, i liquidi si costituiscono ad ugual livello, perch'essendo i vasi <lb/>piccoli, e perci&ograve; i moti brevi, gl'impedimenti sono insensibili. </s>

<s>Ma nei grandi <lb/>condotti, come sarebbero per esempio quelli costruiti per menar l'acqua da <lb/>un colle vicino sulla piazza di una citt&agrave;, non &egrave; possibile far s&igrave; che l'acqua <lb/>stessa, nei getti e nelle conserve, giunga alla precisa altezza da cui fu scesa. </s></p><p type="main">

<s>A mezzo il secolo XVI sembra che gl'ingneri d'acque, anch'essi illusi <lb/><figure id="id.020.01.3396.1.jpg" xlink:href="020/01/3396/1.jpg"/></s></p><p type="caption">

<s>Figura 182.<lb/>dall'esperienze delle Scuole, non avessero fatto una <lb/>tale avvertenza, per cui spesso rimasero senza effetto <lb/>le loro imprese, con grave danno del pubblico e dei <lb/>privati. </s>

<s>Sorse allora il Cardano, con grande zelo, a <lb/>fargli ravvedere dei loro errori, osservando che altri&shy;<lb/>menti avviene nei lunghi condotti, ne'quali l'acqua <lb/>prima scende e poi sale, da quel che avvien nei sifoni <lb/>da travasare, ne'quali il liquido prima sale e poi scende. <lb/></s>

<s>&ldquo; Si autem aqua descendat primo, deinde ascendat ut <lb/>in figura sequenti 182 ex A in B, inde in E, et postmo&shy;<lb/>dum in C et in D: tune pervenire poterit si D minus <pb xlink:href="020/01/3397.jpg" pagenum="358"/>distet a linea BC, quam A locus ex quo descendit. </s>

<s>Sed oportet in singulis <lb/>spatiis certam esse differentiam altitudinis A et D. </s>

<s>Quanto enim longior via <lb/>fuerit eo maior differentia A et D, iuxta altitudinis mensuram, esse debet. </s>

<s><lb/>Hinc errores quorumdam, qui, ad libramentum eum conati essent aquas de&shy;<lb/>ducere, maximas iacturas impensarum susceperunt. </s>

<s>In singulis igitur milli&shy;<lb/>bus passuum A altius palmo esse debet quam D, ut in decem millibus pas&shy;<lb/>suum decem palmis &rdquo; (<emph type="italics"/>De subtilitate,<emph.end type="italics"/> Lugduni 1580, pag. </s>

<s>25). </s></p><p type="main">

<s>Notabile &egrave; per&ograve; la causa, che il Cardano assegna a questo rimaner l'acqua <lb/>che sale, al di sotto di quella che scende, un palmo per miglio. </s>

<s>E bench&egrave;, <lb/>accennando al bisogno di ristorar l'impeto perduto, sembri voler dar qual&shy;<lb/>che parte alle resistenze, la ragion principale nulladimeno ei la riconosce <lb/>dall'evidente rotondit&agrave; dell'acqua, la quale dalla superficie degli orci pieni <lb/>&egrave; manifesta. </s>

<s>&ldquo; Causa huius est aquae rotunditas evidens, quae etiam in ur&shy;<lb/>ceorum superficie apparet. </s>

<s>Unde ad libramentum, licet A sit altius quam D <lb/>(non tamen erit altius, quandoque loco medio inter A et D) indiget etiam <lb/>impetu quodam. </s>

<s>Sed haec nunc praeter intentum quasi sunt: volui tamen, <lb/>ob magnitudinem periculi et erroris frequentiam, haec subiecisse &rdquo; (ibid.). </s></p><p type="main">

<s>Se O, nella medesima figura 182, &egrave; il centro della sfera dell'acqua, e <lb/>AO, DO sono i raggi, che ne misurano le distanze, apparisce chiaro perch&egrave;, <lb/>secondo il Cardano, il punto D sia costituito in pi&ugrave; umile luogo di A. L'er&shy;<lb/>rore dunque dipende dalle illusioni, che la rotondit&agrave; del mare suol fare agli <lb/>occhi dei naviganti, ond'&egrave; che il Porta non ebbe tutti i torti a riconoscere <lb/>per una pazzia questa vantata sottilit&agrave; di pensieri. </s>

<s>&ldquo; Cardano dice che la <lb/>superficie del mare sia rotonda, e si riconosce per gli orcioli pieni. </s>

<s>Ma io <lb/>non so com'egli possa lasciarsi uscir di bocca tante pazzie &rdquo; (Spiritali, Na&shy;<lb/>poli 1606, pag. </s>

<s>23). </s></p><p type="main">

<s>In ogni modo, non curandoci per ora delle teorie, dietro i fatti, da cos&igrave; <lb/>lungo tempo osservati negli equilibri idrostatici, si pu&ograve; dunque concludere <lb/>che i liquidi soggiacciono alle medesime leggi dei solidi, i quali risalirebbero <lb/>alla medesima altezza da cui scesero, sempre che se ne rimovessero tutti <lb/>gl'impedimenti. </s>

<s>E perch&egrave; questo &egrave; uno dei principii fondamentali della Di&shy;<lb/>namica nuova sembrerebbe che a Galileo si dovesse presentare spontenea <lb/>l'applicazione di quello stesso principio, a rinnovellare l'Idrodinamica. </s>

<s>Tanto <lb/>pi&ugrave; che, a ingerire una tale opinione, predisponeva le menti qualche passo, <lb/>da noi citato a suo luogo dai dialoghi dei due Massimi Sistemi, in cui l'Au&shy;<lb/>tore, per confermare il supposto che, nella scesa, il solido acquista tant'im&shy;<lb/>peto, da risalire alla medesima altezza perpendicolare; adduceva per argo&shy;<lb/>mento il ridursi l'acqua, ne'due rami del sifone, allo stesso livello. </s>

<s>E vera&shy;<lb/>mente da questa esperienza fatta in vasi piccoli, e conferita con ci&ograve; che <lb/>altrimenti s'osserva nei lunghi condotti, s'ebbero, come vedremo, le prime <lb/>rivelazioni d'Idrodinamica nuova. </s>

<s>Apparirono per&ograve; pi&ugrave; tardi di quel che non <lb/>pareva prometterci Galileo, il quale ebbe a trovare non poche difficolt&agrave;, a <lb/>riconoscer che il liquido, nella sua mole continuata, giunto in fondo al si&shy;<lb/>fone, acquista quell'impeto, che si concepirebbe da una sfera solida in s&egrave; <pb xlink:href="020/01/3398.jpg" pagenum="359"/>raccolta e distinta. </s>

<s>Di qui &egrave; che, rimanendogli circoscritti i pensieri dentro <lb/>gl'insegnamenti della Statica antica, secondo cui le pressioni fatte sul fondo <lb/>del vaso son misurate dal numero degli strati sopraincumbenti, o dalle sem&shy;<lb/>plici altezze; l'Idrodinamica non venne perci&ograve; promossa da lui, n&egrave; dallo stesso <lb/>Castelli se non che assai debolmente. </s>

<s>La conclusione che si pronunzia ora <lb/>da noi cos&igrave; sentenziosa, ci verr&agrave; dimostrata dalla Storia, al pi&ugrave; ordinato svol&shy;<lb/>gimento della quale convien premettere alcune considerazioni intorno allo <lb/>stato della Scienza antica, per vedere com'ella preparasse i progressi alla <lb/>nuova. </s></p><p type="main">

<s>La Dinamica riconosce le sue prime e pi&ugrave; antiche origini dal modo usato <lb/>di misurare i momenti, e quelle che poi si dissero quantit&agrave; di moto, dal <lb/>prodotto della massa per la velocit&agrave; impressa. </s>

<s>In Aristotile si trova questo <lb/>principio sotto la forma di quell'altro, pi&ugrave; noto oggid&igrave; col nome di principio <lb/>delle velocit&agrave; virtuali, applicato a dimostrar l'equilibrio nelle Macchine, ma <lb/>il Nemorario fu che l'estese ai gravi naturalmente cadenti. </s>

<s>E perch&egrave; dal nu&shy;<lb/>mero dei corpi gravi non si escludono i liquidi, s'intende come la Dinamica <lb/>e l'Idrodinamica, infin da quei tempi, nascessero gemelle. </s>

<s>Dalla detta mi&shy;<lb/>sura universale dei momenti, applicata al moto dell'acque, conseguiva legit&shy;<lb/>timamente, e quale verit&agrave; immediata, doversi la quantit&agrave; de'flussi e delle <lb/>correnti misurare dal prodotto delle velocit&agrave; per le sezioni, d'onde, suppo&shy;<lb/>ste le quantit&agrave; uguali, resultava dimostrata la legge fondamentale idrodina&shy;<lb/>mica del rispondersi le velocit&agrave; e le sezioni in ragione contraria. </s>

<s>Similmente, <lb/>dall'essere, in eguale quantit&agrave; di discesa perpendicolare, uguali i momenti <lb/>di due moli uguali, si concludeva legittimamente che da due bocche uguali <lb/>uscivano nel medesimo tempo quantit&agrave; uguali d'acqua, comunque fossero i <lb/>canali inclinati. </s>

<s>Quale esplicazione avessero questi principii, e quali appli&shy;<lb/>cazioni ne facessero gl'Idraulici del secolo XVI, alla dispensa delle acque e <lb/>al regolamento dei fiumi, di disse nel capitolo primo di questo Tomo e basta <lb/>il gi&agrave; detto quivi a rappresentare lo stato, in cui si trovava la Scienza poco <lb/>tempo prima di quella sua, ch'ebbe il nome di restaurazione. </s>

<s>Ci esprimiamo <lb/>cos&igrave;, perch&egrave; in verit&agrave; fu piuttosto una demolizione, come or ora vedremo, <lb/>dop'avere accennato ai progressi, che naturalmente s'aspettava da un tale <lb/>stato di cose. </s></p><p type="main">

<s>&Egrave; assai facile intendere che quei progressi consisterebbero nel sostituire <lb/>la vera legge delle velocit&agrave;, acceleratrici il moto delle acque, a quella, che <lb/>i Matematici del secolo XVI assegnavano alle cadute di tutti i corpi gravi. </s>

<s><lb/>Si sa dalla Storia della Meccanica che costoro ammettevano le dette velocit&agrave; <lb/>proporzionali agli spazi, e non eccettuando, com'era giusto, da questa gene&shy;<lb/>ralit&agrave; i liquidi, ne conclusero legittimamente essere proporzionali alle sem&shy;<lb/>plici altezze le velocit&agrave; delle acque correnti. </s>

<s>Galileo, dimostrando che gli <lb/>spazi passati non serbano altrimenti la proporzione delle velocit&agrave; semplici, <lb/>ma dei loro quadrati, aveva rinnovellata la Dinamica, e, se procedeva con <lb/>la logica degli antichi, avrebbe nello stesso tempo rinnovellata altres&igrave; l'Idro&shy;<lb/>dinamica, argomentando che, per essere i liquidi corpi come tutti gli altri <pb xlink:href="020/01/3399.jpg" pagenum="360"/>gravi, le velocit&agrave; delle loro cadute perpendicolari, non avrebbero dovuto cor&shy;<lb/>rispondere con le semplici altezze, ma con le loro radici. </s>

<s>Questi erano i pro&shy;<lb/>gressi che la Scienza del moto delle acque s'aspettava da Galileo, e ora &egrave; <lb/>da narrare come ne rimanesse defraudata. </s></p><p type="main">

<s>S'accennava di sopra a una demolizione, alla quale soggiacque la Di&shy;<lb/>namica, miseramente avvolta fra le rovine dell'edifizio peripatetico. </s>

<s>Dal Be&shy;<lb/>nedetti Galileo, e da Galileo il Cartesio prese l'esempio, ma ambedue gli <lb/>arditi rinnovatori trapassarono le intenzioni del Matematico veneziano, che <lb/>da quella distruzione avrebbe prudentemente voluto salvare il buono, e non <lb/>disperdere i materiali utili, ma servirsene alla costruzione del nuovo edifi&shy;<lb/>zio. </s>

<s>Che del buono e dell'utile, particolarmente rispetto all'Idrodinamica, <lb/>veramente ci fosse, lo sanno oramai bene i nostri Lettori, ai quali additammo <lb/>gli esempi, datine dai discepoli del Nemorario, rimasti segnatamente impressi <lb/>nelle opere del Cardano. </s>

<s>Ma Galileo non vuol nulla saper di costoro, i quali <lb/>non scrissero, intorno alla Scienza, a parer suo, fuor che favole e romanzi, <lb/>cosicch&egrave; sopra un'area pi&ugrave; libera vuol esserne ricostruito l'edifizio da'suoi <lb/>fondamenti, in disparte, e lontano dall'edifizio peripatetico, che non avesse a <lb/>nuocere colle rovine e coll'ombra. </s></p><p type="main">

<s>La prima mano alla costruzione fu data col Discorso intorno alle cose <lb/>che stanno in su l'acqua, o che in quella si muovono. </s>

<s>Ci avverte in prin&shy;<lb/>cipio l'Autore che di ci&ograve; fu trattato gi&agrave; da Archimede, ma ch'egli viene a <lb/>confermarne la verit&agrave; delle dimostrazioni <emph type="italics"/>con metodo differente, e con altri <lb/>mezzi<emph.end type="italics"/> (Alb. </s>

<s>XII, 13). Quel metodo per&ograve;, che consiste nel fare i ragguaglia&shy;<lb/>menti tra la gravit&agrave; e la velocit&agrave;, confessa che non &egrave; nuovo, ma che <emph type="italics"/>fu con&shy;<lb/>siderato da Aristotile come principio, nelle sue Questioni meccaniche<emph.end type="italics"/> (ivi, <lb/>pag. </s>

<s>16) ed &egrave; precisamente il principio delle velocit&agrave; virtuali, che Galileo <lb/>vuole applicare all'equilibrio tra i liquidi e i solidi immersi, e perci&ograve; tutta <lb/>la novit&agrave; si farebbe consistere in cos&igrave; fatte applicazioni. </s></p><p type="main">

<s>Ma era ella questa propriamente una novit&agrave;? </s>

<s>Potrebbe forse ritenersi <lb/>per tale, rispetto al particolar modo di dimostrare i teoremi di Archimede, <lb/>ma nella sua universalit&agrave; quel metodo l'avevano usato i Matematici del se&shy;<lb/>colo precedente, con applicar la misura dei momenti a ogni genere di que&shy;<lb/>stioni idrostatiche. </s>

<s>I teoremi di Galileo si pu&ograve; dire insomma che fossero un <lb/>corollario di proposizioni precedentemente gi&agrave; dimostrate, e dal non aver ri&shy;<lb/>conosciuto l'ordine assiomatico di questo processo logico si pu&ograve; dir che di&shy;<lb/>penda tutta l'imperfezione dell'opera data all'Idrodinamica da lui stesso. </s>

<s>Ma <lb/>a voler che avesse riconosciuto ci&ograve; bisognava non avesse disprezzate, cos&igrave; <lb/>come fece, le tradizioni precedenti, o che non le avesse accolte solo in parte <lb/>ma intere: non si doveva trattener nelle Questioni di Aristotile, ma consi&shy;<lb/>derare gli svolgimenti, che avevano avuto dai Discepoli del Nemorario, quali <lb/>furono per esempio il Tartaglia, il Cardano e il Buteone. </s>

<s>Le voci di costoro <lb/>risonavano allora alte per tutto il mondo scientifico, e per quanto Galileo si <lb/>turasse le orecchie, o ne rifuggisse lontano, non era possibile che non gli <lb/>rimanessero impresse l'arie, se non le parole, del canto. </s>

<s>Come poteva, nel <pb xlink:href="020/01/3400.jpg" pagenum="361"/>trattar de'proietti, usare il linguaggio stesso introdotto nell'arte dal Tarta&shy;<lb/>glia, senza risentirne l'eco delle dottrine? </s>

<s>E nella legge delle cadute dei <lb/>gravi lungo i piani inclinati, o nell'uso della Bilancetta idrostatica, com'&egrave; <lb/>credibile che, inconsapevole affatto, si riscontrasse nei teoremi e nelle inven&shy;<lb/>zioni del rude Matematico di Brescia? </s></p><p type="main">

<s>Ma non si pu&ograve; tacere in questo proposito un esempio offertoci dal Bu&shy;<lb/>teone. </s>

<s>Fra le Opere geometriche di lui, applicate a questioni giuridiche, si <lb/>legge un capitoletto intitolato <emph type="italics"/>Geometriae cognitionem Jureconsulto neces&shy;<lb/>sariam,<emph.end type="italics"/> a dimostrare la qual necessit&agrave; propone questo caso curioso: Tizio, <lb/>essendo in viaggio, lascia a Lucio un sacco, formato d'un'assicella rotonda <lb/>per fondo, intorno alla quale essendo cucita una tela, tenuto ritto, figurava <lb/>un cilindro; perch&egrave; glie lo empisse di grano, dandogli libert&agrave;, se gli fosse <lb/>tornato comodo, di metter la medesima misura in altri sacchi. </s>

<s>Ora, Lucio, <lb/>misurato il fondo di quello portatogli da Tizio, e trovatolo sedici piedi di <lb/>circonferenza, e sei di altezza della tela, emp&igrave; quattro sacchi della medesima <lb/>forma, ma di quattro piedi di circonferenza ciascuno e ugualmente alti, e <lb/>tornato il compratore gli disse, nell'atto di volerglieli consegnare, che i quat&shy;<lb/>tro piccoli facevano insieme la misura stessa del grande, secondo la richie&shy;<lb/>sta. </s>

<s>Tizio, per qualche esperienza che ne aveva, sospett&ograve; che vi fosse in&shy;<lb/>ganno, ma quell'altro badava a dire che la cosa era certa, come si pu&ograve; essere <lb/>certi d'aver sedici da quattro via quattro. </s>

<s>&ldquo; Sed quid faciat, soggiunge il <lb/>Buteone, aut quo se vertat Titius, volens contra Lucium agere depositi? </s>

<s>Nus&shy;<lb/>quam enim patronum sibi, nisi sit idem Geometriae peritus inveniet, qui <lb/>causam tam apparenter malam defendere velit, aut certe possit. </s>

<s>Sed pona&shy;<lb/>mus invenisse: is igitur apud Praetorem causam sui clientis sustinebit in <lb/>hunc modum. </s>

<s>Dolo malo fecit Lucius, illustrissime Praeses, qui solum qua&shy;<lb/>drantem depositi pro toto reddere falsis argumentis praetendit: hoc est qua&shy;<lb/>tuor saccos frumenti pro sexdecim quot habuit depositum. </s>

<s>Hoc autem ita de&shy;<lb/>monstro &rdquo; (<emph type="italics"/>Opera geometrica,<emph.end type="italics"/> Lugduni 1554, pag. </s>

<s>136). </s></p><p type="main">

<s>La dimostrazione, che fa l'avvocato di Tizio innanzi al Pretore, &egrave; con&shy;<lb/>dotta facilmente cos&igrave;, dietro le regole pi&ugrave; elementari della Stereometria. </s>

<s>Si <lb/>chiami S il sacco grande, col fondo circolare di raggio R, <emph type="italics"/>ss<emph.end type="italics"/> si chiamino i <lb/>quattro sacchi pi&ugrave; piccoli, col fondo di raggio <emph type="italics"/>r<emph.end type="italics"/> ciascuno, e sia A l'altezza <lb/>uguale per tutti. </s>

<s>Dalle due equazioni S=8.R.A, <emph type="italics"/>ss=4.2r.A,<emph.end type="italics"/> verr&agrave; <lb/>istituita la proporzione <emph type="italics"/>S:ss=R:r.<emph.end type="italics"/> E perch&egrave; i raggi stanno come le cir&shy;<lb/>conferenze, ossia nel caso proposto come 16 a 4; dunque S:<emph type="italics"/>ss<emph.end type="italics"/>=16:4= <lb/>4:1, d'onde viene a decidersi aver avuto Tizio ragione di reclamar contro <lb/>Lucio, non contenendo i quattro sacchi piccoli, se non che la quarta parte <lb/>del grano, che si sarebbe contenuta nel grande. </s></p><p type="main">

<s>Ora si sovverranno i Lettori che, nella prima giornata delle due Scienze <lb/>nuove, Galileo risolveva un problema assai simile a questo, d'onde viene a <lb/>rendere &ldquo; la ragione di un accidente, che non senza maraviglia vien sentito <lb/>dal popolo, ed &egrave; come possa essere che il medesimo pezzo di tela, pi&ugrave; lungo <lb/>per un verso che per l'altro, se se ne facesse un sacco da tenervi dentro <pb xlink:href="020/01/3401.jpg" pagenum="362"/>del grano, come costumano di fare con un fondo di tavola, terr&agrave; pi&ugrave;, ser&shy;<lb/>vendoci per l'altezza del sacco della minor misura della tela, e con l'altra <lb/>circondando la tavola del fondo, che facendo per l'opposito &rdquo; (Alb. </s>

<s>XIII, 59). </s></p><p type="main">

<s>Non diremo che Galileo perdesse i suoi sonni a meditar sulle opere geo&shy;<lb/>metriche del Buteone, ma s&igrave; che egli, riprendendo la solita immagine, sent&igrave; <lb/>nelle orecchie spirarsi l'aria o le intonazioni, se non le precise parole del <lb/>canto, che penetravano allora per tutto, anche attraverso alle pi&ugrave; salde pa&shy;<lb/>reti. </s>

<s>Dall'altra parte era in quell'aria certa armonia, la quale si sarebbe <lb/>tanto meglio notata, in mezzo alle stonature: e il carattere scientifico del Di&shy;<lb/>scorso intorno i galleggianti non si potrebbe forse ritrar meglio, che col dire <lb/>aver Galileo a quell'aria languida e incerta adattate le proprie parole, che, <lb/>non rendendo intero il costrutto, non fa maraviglia s'egli stesso talvolta non <lb/>ne riconosce l'ampiezza del significato. </s></p><p type="main">

<s>Nella V proposizione idrostatica del citato Discorso galileiano, secondo <lb/>l'esposizione, che analiticamente se ne fece da noi nella seconda parte del <lb/>capitolo secondo di questo Tomo, chiamando <emph type="italics"/>v<emph.end type="italics"/> la velocit&agrave; dell'abbassamento <lb/>della piccolissima mole o della sezione <emph type="italics"/>s<emph.end type="italics"/> dell'acqua contenuta nel vaso, in <lb/>cui si suppone essere immerso il solido, V la velocit&agrave; dell'abbassamento della <lb/>grandissima mole, o della sua sezione S; vedemmo che il ragionamento del&shy;<lb/>l'Autore portava a concludere <emph type="italics"/>v:V=S:s,<emph.end type="italics"/> ossia che, avendosi quantit&agrave; <lb/>d'acqua uguali, le velocit&agrave; stanno reciprocamente alle sezioni. </s></p><p type="main">

<s>Questa medesima legge anche pi&ugrave; immediatamente si concludeva dalla <lb/>dimostrazione, che in questo stesso Discorso si d&agrave; dell'equilibrio nel sifone <lb/>tra l'acqua contenuta nel vaso pi&ugrave; largo, e nella canna con lui continuata, <lb/>perch&egrave; quel che quivi si dice &ldquo; essere la salita IH (fig. </s>

<s>183) tanto maggiore <lb/>della scesa LD, quant'&egrave; l'ampiezza ML del vaso maggiore della larghezza IG <lb/><figure id="id.020.01.3401.1.jpg" xlink:href="020/01/3401/1.jpg"/></s></p><p type="caption">

<s>Figura 183.<lb/>della canna &rdquo; (Alb. </s>

<s>XII, 25, 26); si traduce, per <lb/>essere gli spazi proporzionali alle velocit&agrave;, nella for&shy;<lb/>mula che esse velocit&agrave; son reciproche delle sezioni. </s>

<s><lb/>Ora, che Galileo, tutto intento a dimostrare le pro&shy;<lb/>posizioni idrostatiche di Archimede, con metodo di&shy;<lb/>verso, non si accorgesse che da questo stesso me&shy;<lb/>todo veniva condotto a dimostrare altres&igrave; una legge <lb/>idrodinamica fondamentale; &egrave; quel che da noi s'as&shy;<lb/>seriva, e che si rappresenter&agrave; come cosa di fatto, <lb/>dop avere investigate le cause di una tale inco&shy;<lb/>scienza. </s></p><p type="main">

<s>Queste cause si riducono da noi, come s'ac&shy;<lb/>cennava di sopra, e come fu notato in altro pro&shy;<lb/>posito, al non aver saputo Galileo formulare nella sua universalit&agrave; quella <lb/>massima legge dinamica, dalla quale conseguivano e la teoria statica dei <lb/>momenti, e le ragioni della comunicazione dei moti. </s>

<s>Di qui avvenne che il <lb/>Nostro rimanesse tanto inferiore a Giovan Marco, nel confutare l'errore ari&shy;<lb/>stotelico delle velocit&agrave; proporzionali alle masse, e che tanto imperfettamente <pb xlink:href="020/01/3402.jpg" pagenum="363"/>discorresse della forza della percossa. </s>

<s>La statica stessa dei momenti, che Ga&shy;<lb/>lileo non sdegn&ograve; di ricevere da Aristotile, e della quale unica fece l'appli&shy;<lb/>cazione alle sue questioni idrostatiche, era nella rinnovellata scienza cos&igrave; <lb/>dubbiosa, che il Nardi e poi tutti i suoi condiscepoli finirono per rifiutarla. </s>

<s><lb/>Dicevano come si sa che, nel trattare di cos&igrave; fatte questioni idrostatiche, di <lb/>un effetto in atto s'adduceva una cagione in potenza, e che non era logico <lb/>dal moto argomentare alla quiete. </s>

<s>Il Maestro non aveva che rispondere a <lb/>queste difficolt&agrave;, e perci&ograve; non a torto il Viviani, ne'Dialoghi delle due <lb/>Scienze nuove, e il Nardi, nel Discorso intorno i galleggianti, volevano far&shy;<lb/>gli sostituire a quello delle velocit&agrave; virtuali altro pi&ugrave; ragionevole principio, <lb/>e non aveva Galileo che si rispondere perch'era persuaso che il moto e la <lb/>quiete fossero due posizioni contrarie. </s>

<s>I precedenti Maestri per&ograve;, ch'ei di&shy;<lb/>sprezzava, avevano invece insegnato non esser altro la quiete che il termine <lb/>del moto, per cui successive e non contrarie son le due posizioni, e l'argo&shy;<lb/>mentar l'una dall'altra &egrave; anzi logica necessit&agrave;, dalla quale il volgo stesso &egrave; <lb/>menato, nel pesare specialmente gli oggetti preziosi. </s>

<s>I venditori infatti non <lb/>s'assicurano dell'equilibrio, se non col fare ondeggiare le braccia della bi&shy;<lb/>lancia o far sollevare l'ago della stadera, onde anch'essi non argomentano <lb/>alla quiete, se non che dagli inizi o dai termini del moto. </s>

<s>Di qui si pu&ograve; <lb/>comprendere quanto sani e saldi fondamenti avesse ne'matematici antichi <lb/>il principio delle velocit&agrave; virtuali, e come di una simile certezza fisica e ma&shy;<lb/>tematica partecipasse per loro la legge della comunicazione dei moti: fon&shy;<lb/>damentale certezza che, come manc&ograve; a Galileo, cos&igrave; venne a mancare nella <lb/>massima parte de'suoi seguaci. </s></p><p type="main">

<s>Il pi&ugrave; insigne esempio di ci&ograve; l'abbiamo nel Castelli. </s>

<s>Egli dava nel 1628 <lb/>alla luce in Roma il suo primo libro <emph type="italics"/>Della misura delle acque correnti,<emph.end type="italics"/><lb/>annunziando che il mondo era stato fin allora in errore, intorno al deter&shy;<lb/>minar giustamente la quantit&agrave; del moto nei fluidi. </s>

<s>Per ridurre per&ograve; alla ve&shy;<lb/>rit&agrave; gli erranti, non risale alla Scienza meccanica, che avrebbe potuto dare <lb/>alle sue invenzioni una certezza matematica, ma si contenta di quella sola <lb/>certezza fisica, che gli poteva derivare dall'esperienza. </s>

<s>Dop'avere infatti ac&shy;<lb/>cennato, in sul principio del libro, ai dubbi che gli nacquero dal ripensare <lb/>al modo comunemente usato dai periti e dagli ingegneri per misurar la me&shy;<lb/>desima acqua corrente ora nei foss&igrave;, ora nelle cascate; ringrazia il Ciampoli <lb/>d'avergli dato generosamente &ldquo; occasione, alli anni passati, di tentare, con <lb/>esatta esperienza, quanto passava intorno a questo particolare &rdquo; (Edizione del <lb/>Manolessi, Bologna 1660, pag. </s>

<s>4). E dietro questa esperienza, senza proporre <lb/>altro principio fondamentale, ne concludeva doversi misurare l'acqua, che <lb/>esce dalla bocca di un canale o che passa per la sezione di un fiume, non <lb/>gi&agrave; dalla sezione sola, com'allora si faceva da tutti, ma dal prodotto di lei <lb/>per la velocit&agrave; impressa, onde &ldquo; essendo verissimo che in diverse parti del <lb/>medesimo fiume o alveo di acqua corrente sempre passano eguali quantit&agrave; <lb/>d'acqua in tempi uguali, ed essendo ancora vero che in diverse parti il me&shy;<lb/>desimo fiume pu&ograve; avere varie o diverse velocit&agrave;; ne seguir&agrave; per necessaria <pb xlink:href="020/01/3403.jpg" pagenum="364"/>conseguenza che, dove aver&agrave; il fiume minore velocit&agrave;, sar&agrave; di maggior misura, <lb/>ed in quelle parti, nelle quali aver&agrave; maggior velocit&agrave;, sar&agrave; di minor misura, <lb/>ed insomma le velocit&agrave; di diverse parti dell'istesso fiume averanno eterna&shy;<lb/>mente reciproca e scambievole proporzione con le loro misure &rdquo; (ivi, pag. </s>

<s>7). </s></p><p type="main">

<s>Nello stesso Trattato geometrico, aggiunto nella fine del libro, la pro&shy;<lb/>posizione II, dalla quale facilmente si svolgono tutte le altre, ha il suo fon&shy;<lb/>damento nei cinque pronunziati premessi, i quali sono altrettanti fatti par&shy;<lb/>ticolarmente osservati, e insigniti perci&ograve; di quella sola certezza fisica, che pu&ograve; <lb/>essere a loro partecipata dall'esperienza. </s>

<s>Sperimentale dunque, bench&egrave; sotto <lb/>le apparenze geometriche, &egrave; quella stessa seconda proposizione, che dal Ca&shy;<lb/>stelli si mette in questa forma: &ldquo; Se saranno due sezioni di fiumi, la quan&shy;<lb/>tit&agrave; dell'acqua che passa per la prima, a quella che passa per la seconda, <lb/>ha la proporzione composta delle proporzioni della prima sezione alla seconda, <lb/>e della velocit&agrave; per la prima, alla velocit&agrave; per la seconda &rdquo; (ivi, pag. </s>

<s>65). </s></p><p type="main">

<s>Del medesimo carattere sperimentale rimangono perci&ograve; impresse tutte <lb/>le proposizioni, che conseguon da questa, la dimostrazion delle quali, che <lb/>secondo il metodo usato dall'Autore riesce prolissa, intralciata cos&igrave; com'&egrave; di <lb/>mezzi termini geometrici, si pu&ograve; rendere, con l'analisi, facilissima e spedita. </s>

<s><lb/>Chiamate infatti Q, S, V; <emph type="italics"/>q, s, v<emph.end type="italics"/> le due diverse quantit&agrave;, sezioni, e velocit&agrave; <lb/>respettive, l'annunziata proposizione seconda &egrave; conclusa nella formula (1) <lb/><emph type="italics"/>Q:q=S.V:s.v.<emph.end type="italics"/> Che se Q=<emph type="italics"/>q,<emph.end type="italics"/> dalla proporzionalit&agrave;, che ne consegue, <lb/><emph type="italics"/>S:s=v:V,<emph.end type="italics"/> viene immediatamente a dimostrarsi la terza proposizion del <lb/>Castelli, ch'&egrave; tale: &ldquo; Se saranno due sezioni ineguali, per le quali passino <lb/>quantit&agrave; d'acqua eguali, in tempi eguali; le sezioni hanno fra di loro reci&shy;<lb/>proca proporzione delle loro velocit&agrave; &rdquo; (ivi, pag. </s>

<s>67). </s></p><p type="main">

<s>Seguitando pure a supporre Q=<emph type="italics"/>q,<emph.end type="italics"/> se, intendendosi per A, <emph type="italics"/>a<emph.end type="italics"/> le altezze, <lb/>e per L, <emph type="italics"/>l<emph.end type="italics"/> le larghezze respettive delle due sezioni, si faccia S=A,L, <lb/><emph type="italics"/>s=a.l;<emph.end type="italics"/> dalla citata proporzione (1) si deriva l'equazione A.L.V= <lb/><emph type="italics"/>a.l.v,<emph.end type="italics"/> e da questa la nuova proporzione <emph type="italics"/>a:A=L.V:l.v,<emph.end type="italics"/> la quale &egrave; <lb/>dimostrativa della quarta proposizione, dal Castelli formulata in tal guisa: <lb/>&ldquo; Se un fiume entrer&agrave; in un altro fiume, l'altezza del primo nel proprio <lb/>alveo, all'altezza che far&agrave; nel secondo alveo, ha la proporzione composta delle <lb/>proporzioni della larghezza dell'alveo del secondo, alla larghezza, dell'alveo <lb/>del primo, e della velocit&agrave;, acquistata nell'alveo del secondo, e quella, che <lb/>aveva nel proprio e primo alveo &rdquo; (ivi, pag. </s>

<s>79). </s></p><p type="main">

<s>La proporzione (2) <emph type="italics"/>Q:q=A.L.V:a.l.v,<emph.end type="italics"/> che si ottiene sostituendo <lb/>i valori di S, <emph type="italics"/>s<emph.end type="italics"/> nella (1), trattandosi del medesimo fiume, ed essendo perci&ograve; <lb/>L=<emph type="italics"/>l;<emph.end type="italics"/> si riduce nell'altra <emph type="italics"/>Q:q=A.V:a.v,<emph.end type="italics"/> dalla quale &egrave; significata <lb/>la Va proposizione, che dal Castelli &egrave; cos&igrave; espressa: &ldquo; Se un fiume seari&shy;<lb/>cher&agrave; una quantit&agrave; d'acqua in un tempo, e poi gli sopravverr&agrave; una piena, <lb/>la quantit&agrave; dell'acqua, che si scarica in altrettanto tempo nella piena, a quella <lb/>che si scaricava prima, mentre il fiume era basso; ha la proporzione com&shy;<lb/>posta delle proporzioni della velocit&agrave; della piena alla velocit&agrave; della prima <lb/>acqua, e dell'altezza della piena all'altezza della prima acqua &rdquo; (ivi, pag. </s>

<s>72). </s></p><pb xlink:href="020/01/3404.jpg" pagenum="365"/><p type="main">

<s>Nella sopra scritta proporzione (2) suppongasi Q=<emph type="italics"/>q,<emph.end type="italics"/> ed L=<emph type="italics"/>l,<emph.end type="italics"/> trat&shy;<lb/>tandosi al solito del medesimo torrente: essa verr&agrave; a ridursi all'equazione <lb/>A.V=<emph type="italics"/>a.v,<emph.end type="italics"/> la quale, sotto la forma proporzionale A:<emph type="italics"/>a<emph.end type="italics"/>=<emph type="italics"/>v:<emph.end type="italics"/>V, dimo&shy;<lb/>strer&agrave; la VI proposizione del Castelli, che dice: &ldquo; Se due piene uguali del <lb/>medesimo torrente entreranno in un fiume, in diversi tempi, l'altezze fatte <lb/>dal torrente nel fiume averanno fra di loro la proporzione reciproca delle <lb/>velocit&agrave; acquistate nel fiume &rdquo; (ivi, pag. </s>

<s>74). </s></p><p type="main">

<s>Questo trattatello geometrico della Misura delle acque correnti, che fu <lb/>come si disse pubblicato nel 1628, era stato gi&agrave; composto nel Novembre del <lb/>1625, ne'primi giorni del qual mese il Castelli conferiva i frutti delle sue <lb/>proprie esperienze con Galileo, a cui diceva che, dovendosi misurar l'acqua <lb/>che passa per un canale compostamente dalla velocit&agrave; e dalla sezione, essendo <lb/>le quantit&agrave; uguali, velocit&agrave; e sezioni si debbono necessariamente corrispon&shy;<lb/>dere in ragione contraria. </s>

<s>Il d&igrave; 12 di quel medesimo mese, tornato il Ca&shy;<lb/>stelli a Pisa, col pensiero tutto rivolto alla Geometria delle acque, della quale, <lb/>nei passati familiari colloqui in Firenze, aveva manifestato il principio; sog&shy;<lb/>giungeva, per lettera al suo proprio Maestro, un tale avviso: &ldquo; In questi <lb/>giorni ho dimostrato geometricamente la seguente proposizione, con assai <lb/>facilit&agrave;: <emph type="italics"/>Che la quantit&agrave; di acqua, che scorre per un fiume, mentre &egrave; con <lb/>una altezza d'acqua, alla quantit&agrave; dell'acqua che scorre nel medesimo <lb/>fiume, mentre si ritrover&agrave; in un'altra altezza d'acqua; ha la propor&shy;<lb/>zione composta della velocit&agrave; alla velocit&agrave;, e dell'altezza all'altezza &rdquo;<emph.end type="italics"/><lb/>(MSS. Gal., P. VI, T. X, fol. </s>

<s>216). </s></p><p type="main">

<s>La proposizione cos&igrave; annunziata si riconosce bene per quella che, nel <lb/>trattatello a stampa, ricorre in ordine la Va, e preso cos&igrave; l'indirizzo era fa&shy;<lb/>cile progredire alla dimostrazione delle altre proposizioni, delle quali, pochi <lb/>giorni dopo, il Castelli mandava a Galileo il solo pronunziato. </s>

<s>Queste propo&shy;<lb/>sizioni, in cui consisteva quel progresso idraulico, di che il Castelli stesso <lb/>si compiaceva nel darne avviso al Maestro, erano tre: cio&egrave; la IV e la VI del <lb/>trattatello geometrico, alle quali se n'aggiungeva un'altra, che poi, nella <lb/>ristampa del libro, fu dall'Autore inserita nella XII appendice, sotto la forma: <lb/>&ldquo; Se sar&agrave; un vaso d'acqua di qualsivoglia grandezza, e che abbia un emis&shy;<lb/><figure id="id.020.01.3404.1.jpg" xlink:href="020/01/3404/1.jpg"/></s></p><p type="caption">

<s>Figura 184.<lb/>sario, per il quale si scarichi la sua acqua; qual propor&shy;<lb/>zione ha la superficie del vaso alla misura della sezione <lb/>dell'emissario, tale aver&agrave; la velocit&agrave; delle acque per <lb/>l'emissario all'abbassamento del lago &rdquo; (<emph type="italics"/>Della misura <lb/>delle acque correnti<emph.end type="italics"/> cit., pag. </s>

<s>44.) </s></p><p type="main">

<s>La dimostrazione, usandovi il metodo analitico, non <lb/>presentava difficolt&agrave; punto maggiori delle altre. </s>

<s>Sia in&shy;<lb/>fatti un vaso AG (fig. </s>

<s>184) dal quale si scarichi l'acqua <lb/>per il tubo addizionale IH. </s>

<s>Chiamisi S la sezione CD <lb/>del vaso, <emph type="italics"/>s<emph.end type="italics"/> la sezione IG del tubo. </s>

<s>Se in un dato tempo, <lb/>per l'esito da questo, l'acqua si sia abbassata da D in F dentro il vaso, la <lb/>quantit&agrave; Q=S.DF &egrave; quella medesima dell'acqua uscita nel medesimo <pb xlink:href="020/01/3405.jpg" pagenum="366"/>tempo dal tubo, la quale &egrave; misurata da Q=<emph type="italics"/>s<emph.end type="italics"/>.V. chiamandosi con V la ve&shy;<lb/>locit&agrave; propria dell'efflusso. </s>

<s>E perch&egrave; queste due quantit&agrave; debbono essere evi&shy;<lb/>dentemente uguali, sar&agrave; dunque S.DF=<emph type="italics"/>s.<emph.end type="italics"/> V, ossia S:<emph type="italics"/>s<emph.end type="italics"/>=V:DF, secondo <lb/>che si proponeva di dimostrare il Castelli. </s></p><p type="main">

<s>Nonostante parve a Galileo la dimostrazione di questa, e delle due pre&shy;<lb/>cedenti, men facile a ritrovarsi di quella prima annunziatagli da Pisa, nella <lb/>lettera del d&igrave; 12 Novembre, e il d&igrave; 21 appresso se ne esprimeva cos&igrave; con lo <lb/>stesso Castelli: &ldquo; Mi rallegro assai del progresso idraulico, e aspetter&ograve; con <lb/>desiderio le tre ultime proposizioni con le loro dimostrazioni: dico di queste <lb/>tre, perch&egrave; la prima &egrave; assai chiara, atteso che, stante la medesima altezza, <lb/>l'acqua che passa &egrave; come la velocit&agrave;, e, stante la medesima velocit&agrave;, l'acque <lb/>che passano son come l'altezze, e per&ograve;, mutate altezze e velocit&agrave;, l'acque che <lb/>passano hanno la proporzione composta delle due dette &rdquo; (Alb. </s>

<s>VI, 305, 6). </s></p><p type="main">

<s>Il desiderio, manifestatosi nel principio di queste parole, non tard&ograve; molto <lb/>a essere sodisfatto. </s>

<s>A mezzo Dicembre il Discorso della misura delle acque <lb/>correnti, con alcuni corollari, aggiuntevi le dimostrazioni geometriche, era <lb/>fatto recapitar manoscritto a Firenze nelle mani di Mario Guiducci, affinch&egrave; <lb/>lo presentasse a Galileo, il quale in una lettera del d&igrave; 27 da Bellosguardo <lb/>cos&igrave; scriveva all'Autore: &ldquo; Non ho ancor veduto l'ultime sue scritture: ma <lb/>intendo che sono in mano del signor Mario, e le vedr&ograve; presto. </s>

<s>Io ancora <lb/>v&ograve; ghiribizzando, e tra gli altri problemi sono attorno all'investigare come <lb/>cammini il negozio dell'accelerarsi l'acqua, nel dover passare per un canale <lb/>pi&ugrave; stretto, ancorch&egrave; il letto abbia l'istessa declivit&agrave; nel largo e nell'angu&shy;<lb/>sto &rdquo; (ivi, pag. </s>

<s>308). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>Si rileva dai riferiti documenti che a Galileo giunsero nuove queste spe&shy;<lb/>culazioni idrauliche, e che il Castelli gli dette occasione di rivolgervi allora <lb/>intorno la mente. </s>

<s>Quelle applicazioni della Geometria al moto delle acque <lb/>gli fecero nascere il pensiero di altre simili applicazioni, che si potrebbero <lb/>fare delle leggi geometriche, gi&agrave; da s&egrave; dimostrate intorno ai moti locali, e <lb/>in cui vedeva, secondo che egli stesso si esprime, la chiave per aprire in&shy;<lb/>gressi ad accidenti maggiori. </s>

<s>Gli sovvenne di qui quella prima idea di ri&shy;<lb/>guardar le acque dei fiumi, correnti per il pendio de'loro alvei, come corpi <lb/>gravi, che scendono lungo piani inclinati: idea, che pi&ugrave; tardi gli si svolse <lb/>nella lettera allo Staccoli, ma che intanto, manifestata al Castelli, questi cos&igrave; <lb/>rispondeva agl'impulsi, che di proseguire per l'intrapresa via gli venivano dal <lb/>Maestro: &ldquo; Rendo molte grazie a V.S., che si sia degnata di mandarmi le sue <lb/>considerazioni intorno al moto de'fiumi, e maggiore sar&agrave; il mio obbligo, se <lb/>lei applicher&agrave; la mente a quelle chiavi per aprire ingressi ad accidenti mag&shy;<lb/>giori, come mi accenna nella sua &rdquo; (Campori, Carteggio cit., pag. </s>

<s>231). </s></p><pb xlink:href="020/01/3406.jpg" pagenum="367"/><p type="main">

<s>Il problema, intorno al quale diceva dianzi Galilco di andare ghiribiz&shy;<lb/>zando, si collegava con la memoria di speculazioni anteriori, e che gli avevan <lb/>preoccupata la mente, in fin da quando volle rendersi, del flusso e riflusso <lb/>del mare, una ragione, alla quale si riferisce, fra le altre considerazioni che <lb/>si leggono nell'ultimo dialogo dei due Massimi sistemi, anche la seguente: <lb/>&ldquo; Inoltre, considerando come la medesima quantit&agrave; d'acqua mossa, bench&egrave; <lb/>lentamente, per un alveo spazioso, nel dover poi passare per luogo ristretto, <lb/>per necessit&agrave; scorre con impeto grande; non avremo difficolt&agrave; d'intendere <lb/>la causa delle gran correnti, che si fanno nello stretto canale, che separa la <lb/>Calabria dalla Sicilia, poich&egrave; tutta l'acqua, che dall'ampiezza dell'isola e dal <lb/>Golfo ionico vien sostenuta nella parte del mare orientale, bench&egrave; in quello, <lb/>per la sua ampiezza, lentamente discenda verso occidente, tuttavia nel re&shy;<lb/>stringersi nel Bosforo, fra Scilla e Cariddi, rapidamente cala, e fa grandis&shy;<lb/>sima agitazione. </s>

<s>Simile alla quale, e molto maggiore, s'intende esser tra <lb/>l'Affrica e la grande isola di S. </s>

<s>Lorenzo &rdquo; (Alb. </s>

<s>I, 470). </s></p><p type="main">

<s>Ai fatti cos&igrave; semplicemente descritti si riferiva la proposizione III del <lb/>trattatello geometrico del Castelli, e in sentirsela cos&igrave; formulare Galileo torn&ograve; <lb/>a ghiribizzare intorno alle ragioni di quegli stessi fatti, osservati negli stretti <lb/>di mare, e negli alvei dei fiumi, con quali effetti vedremo tra poco. </s>

<s>Ma prin&shy;<lb/>cipalmente efficaci sulla mente del Maestro furono que'privati colloqui che, <lb/>nei primi giorni del Novembre 1625, ebbe con esso lui lo stesso Castelli, <lb/>quando gli scopriva le ragioni dell'essersi fin allora trascurate le velocit&agrave; <lb/>nella misura delle acque correnti: ragioni, che poi gli venne a ripetere in <lb/>pubblico confermandole con queste parole: &ldquo; Forse tale mancamento &egrave; stato <lb/>commesso per essere riputata la lunghezza dell'acqua corrente in un certo <lb/>modo infinita, mentre non finisce mai di passare, e come infinita &egrave; stata <lb/>giudicata incomprensibile, e tale che non se ne possa avere determinata no&shy;<lb/>tizia, e per tanto non &egrave; stato di essa tenuto conto alcuno &rdquo; (<emph type="italics"/>Copia di let&shy;<lb/>tera al sig. </s>

<s>G. </s>

<s>Galilei aggiunta al libro della Misura delle acque cor&shy;<lb/>renti,<emph.end type="italics"/> Bologna 1660, pag. </s>

<s>58). </s></p><p type="main">

<s>Fra il numero degli illus&igrave;, rispetto al reputare impossibile di misurar <lb/>l'acqua fluente, per essere d'indefinita lunghezza, ebbe Galileo a riconoscere <lb/>anche s&egrave; stesso, ripensando che aveva disperato d'ottener la quantit&agrave; del&shy;<lb/>l'acqua cadente fra l'una e l'altra delle due secchie, descritte, in sul comin&shy;<lb/>ciar del suo Dialogo, per la misura della forza della percossa. </s>

<s>I teoremi del <lb/>Castelli invece mostravano che il misurare la data quantit&agrave; dell'acqua nella <lb/>troscia si riduceva a una assai semplice questione di Geometria. </s>

<s>Ma in ri&shy;<lb/>pensare a ci&ograve; Galileo s'accorse che i medesimi teoremi erano inclusi in quegli <lb/>altri, da tanto tempo scritti nel Discorso intorno i galleggianti, d'ond'egli <lb/>prese animo di risolvere il problema, innanzi al quale erasi arretrato il Sal&shy;<lb/>viati, derivandolo non dalle altrui, ma dalle sue proprie dottrine. </s>

<s>Documento <lb/>importantissimo di ci&ograve; son le cose seguenti, che Galileo stesso, aspettando il <lb/>tempo di distenderle in dialogo, scriveva cosi, come si direbbe, in punta <lb/>di penna: </s></p><pb xlink:href="020/01/3407.jpg" pagenum="368"/><p type="main">

<s><emph type="italics"/>&ldquo; Per poter misurare e pesare la quantit&agrave; dell'acqua, compresa in <lb/>aria tra le due secchie. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Quando tu sollevi il solido M (fig. </s>

<s>185) dal vaso, l'acqua gli entra di <lb/>sotto a riempire il vacuo lasciato, e cos&igrave; avviene a lei come se, da un can&shy;<lb/>none largo quanto il vaso, entrasse per uno stretto quanto il solido. </s>

<s>Ma io <lb/><figure id="id.020.01.3407.1.jpg" xlink:href="020/01/3407/1.jpg"/></s></p><p type="caption">

<s>Figura 185.<lb/>t'ho dimostrato, nel mio Discorso delle cose che <lb/>galleggiano, che l'abbassamento della superficie <lb/>AC &egrave; superato dall'alzamento della superficie EF, <lb/>quanto questa in larghezza &egrave; superata da quella; <lb/>dunque potrai tenere per cosa certa e dimostrata <lb/>che, quando l'acqua da un cannone largo entra <lb/>in un pi&ugrave; stretto, vi si muove dentro tanto pi&ugrave; veloce a quella proporzione, <lb/>che lo stretto entra nel largo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Vedrai farsi la cosa pi&ugrave; manifesta nel moto dell'acqua dentro il vaso <lb/>MLB (fig. </s>

<s>183 qui addietro), che tu puoi immaginare larghissimo, e nella <lb/>angustissima canna AHC, che gli &egrave; congiunta. </s>

<s>Metti uno zaffo e pigialo in <lb/>gi&ugrave;, come tu faresti in uno schizzatoio, sicch&egrave; l'acqua nel vaso cos&igrave; sforzata <lb/>s'abbassi da L in D, risalendo da I in H alla parte opposta. </s>

<s>Non si pu&ograve; du&shy;<lb/>bitare che i due cilindri MD, HG non siano uguali. </s>

<s>M&agrave; in cilindri uguali le <lb/>basi corrispondono contrariamente alle altezze, le quali son la misura delle <lb/>velocit&agrave;, come le basi son la misura delle larghezze o delle sezioni; dunque <lb/>le velocit&agrave;, con cui si muovono l'acque, nel largo e nello stretto, son reci&shy;<lb/>proche delle sezioni. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Di qui caverai la risposta a un bel quesito: Immagina che, dopo di <lb/>aver pigiato lo zaffo, tu non avessi avvertito o non ti ricordassi pi&ugrave; a qual <lb/>punto giungeva l'acqua, quietandosi nei due vasi, e che tu volessi ora ritro&shy;<lb/>varlo per regola geometrica ......... &rdquo; </s></p><p type="main">

<s>&ldquo; Questo che io t'ho concluso dal mio nuovo modo di dimostrare le <lb/><figure id="id.020.01.3407.2.jpg" xlink:href="020/01/3407/2.jpg"/></s></p><p type="caption">

<s>Figura 186.<lb/>proposizioni di Archimede, con conferire insieme i mo&shy;<lb/>menti dell'acqua che sale, con quella che scende, ho io <lb/>tante volte osservato in natura nell'acqua dei ruscelli o <lb/>delle fosse aperte per i campi, le quali acque essendo <lb/>sparse vanno pigramente, ma, come elle sono entrate nello <lb/>stretto della fossa si mettono a correre con furia improv&shy;<lb/>visa, e, se alla fossa s'attraversasse un sasso o altro osta&shy;<lb/>colo, sfogano mormorando l'ira e, raddoppiando la fretta, <lb/>fuggono via. </s>

<s>Simile assottigliamento di parti s'osserva <lb/>nelle trosce cadenti per l'aria libera. </s>

<s>E a quel modo che <lb/>restringendosi lo spazio ne consegue augumento di velo&shy;<lb/>cit&agrave;, cosi dal farsi augumento di velocit&agrave; s'argomenta do&shy;<lb/>versi restringere lo spazio. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sia ora la secchia CBD (fig. </s>

<s>186) col foro aperto <lb/>in B, da cui cada la troscia BH. </s>

<s>Sia l'altezza del cilindro, <lb/>nel primo tempo dell'effusione, BE: nel secondo tempo <pb xlink:href="020/01/3408.jpg" pagenum="369"/>sar&agrave; EF, tripla di BE, nel terzo sar&agrave; FG, quintupla della stessa BE, e cos&igrave; <lb/>seguitando col progresso de'numeri impari ab unitate, come io ho dimostrato <lb/>essere l'affrettamento di tutti i gravi cadenti. </s>

<s>Intorno a FE, a FG ecc. </s>

<s>do&shy;<lb/>vendo essere la medesima acqua, che intorno a BE, si vedr&agrave; che i cilindri <lb/>tanto debbono diminuire le basi, quanto sono cresciute le altezze, e cos&igrave; la <lb/>base del cilindro EF dovr&agrave; essere tre volte pi&ugrave; piccola della B, e la base del <lb/>cilindro FG cinque volte pi&ugrave; piccola, e cos&igrave; sempre con simile progresso. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; La quantit&agrave; dunque dell'acqua che &egrave; nella troscia BG s'aver&agrave; dalla <lb/>somma dei detti cilindri, e universalmente la mole d'acqua, contenuta in <lb/>qualsivoglia effusione come in BH, se tu la vorrai conferire col cilindro sopra <lb/>il foro B, e avente la medesima altezza BH; potrai facilmente conseguire la <lb/>desiderata proporzione facendo la detta mole al cilindro come l'AB a quella, <lb/>che &egrave; media proporzionale tra la stessa AB, o tra la BE che suppongo es&shy;<lb/>sere ad AB uguale, e la BH. &rdquo; </s></p><p type="main">

<s>Queste note, prese cos&igrave; in fretta, le abbiamo trascritte dal volume, altre <lb/>volte citato, <emph type="italics"/>Roba del gran Galileo, in parte copiata dagli originali, e in <lb/>parte dettata da lui cieco a me Vincenzio Viviani, mentre dimoravo nella <lb/>sua casa di Arcetri.<emph.end type="italics"/> Poche pagine appresso si trova messa in dialogo la <lb/>sostanza di queste note, e in principio vi si legge <emph type="italics"/>ad mentem Galilei,<emph.end type="italics"/> come <lb/>in capo a esse note leggevasi <emph type="italics"/>di questo ho l'originale.<emph.end type="italics"/> Ma fra la prima copia <lb/>di tale scrittura originale, e la stesura del Dialogo dovette intercedere un <lb/>certo spazio di tempo, della succession del quale ci rimangono le vestigia <lb/>nei fatti seguenti. </s></p><p type="main">

<s>Essendo il dialogo della forza della percossa, che Galileo aveva comin&shy;<lb/>ciato a scrivere, rimasto ignoto a tutti, come s&igrave; sa dalla Storia, nel cap. </s>

<s>III <lb/>del Tomo precedente da noi narrata; il Viviani non era ancora entrato adden&shy;<lb/>tro nel significato di quelle parole: <emph type="italics"/>Per poter misurare e pesare la quan&shy;<lb/>tit&agrave; dell'acqua, compresa in aria fra le due secchie.<emph.end type="italics"/> Ond'&egrave; che, creden&shy;<lb/>dolo un problema astratto proposto a s&egrave; medesimo da Galileo, per sodisfare <lb/>a una delle sue solite filosofiche curiosit&agrave;, non si dette a principio altra cura <lb/>che di compiere, e d'illustrare la scrittura del suo proprio Maestro. </s>

<s>Il que&shy;<lb/>sito di ritrovare il punto, infino a cui nella cannella scenderebbe l'acqua, <lb/>tenutavi sollevata violentemente dalla pression dello zaffo, sopra l'acqua del <lb/>vaso pi&ugrave; grande; mancava della sua risposta, e il Viviani vi suppl&igrave; in que&shy;<lb/>sta maniera: &ldquo; Se nel sifone ABC (fig. </s>

<s>183 qui poco addietro) fosse un tal <lb/>fluido, il quale in una parte di esso sifone stesse all'altezza AD, e nell'al&shy;<lb/>tra si reggesse, con usar qualche artifizio che molti ce ne sono, all'altezza C <lb/>superiore al livello AD; cercasi, posto tal fluido in libert&agrave;, nel librarsi nel&shy;<lb/>l'uno e nell'altro cannello, a qual segno sia per arrivare. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Prolunghisi il livello AD in EF, e facciasi come la grossezza del can&shy;<lb/>nello AD, alla grossezza del cannello HC, cio&egrave; come il cerchio AD al cer&shy;<lb/>chio HC, ovvero EF (supposti i cannelli cilindrici e di note grossezze) cos&igrave; <lb/>l'altezza CG alla GF; ovvero dividasi l'altezza CF in G nella proporzione <lb/>dei detti cerchi: che il punto G sar&agrave; il punto cercato. </s>

<s>Poich&egrave; prodotto il li-<pb xlink:href="020/01/3409.jpg" pagenum="370"/>vello GILM, sta il cilindro AL al cilindro EG come la base AD alla EF, ov&shy;<lb/>vero, per costruzione, come la GC alla GF, ovvero, come il cilindro CI al <lb/>cilindro EG. </s>

<s>Dunque i cilindri AL, CI, cio&egrave; le moli del fluido, sono uguali, <lb/>e per&ograve; ecc. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>53). </s></p><p type="main">

<s>Quanto al misurar l'acqua, compresa nella troscia, Galileo non aveva <lb/>messo altro che la conclusione, e il Viviani si studi&ograve; di ritrovarne, cos&igrave; ra&shy;<lb/>gionando, i principii: &ldquo; Esto infundibulum CBD (nell'ultima figura 186) <lb/>aqua indeficienter plenum, ex cuius fundo B perforato effluat aqua, sitque <lb/>fluxus altitudo vel BE, vel BF, vel BG, vel BH: quaeritur aquae quantitas, <lb/>quae semper extra vas reperitur. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Sit altitudo aquae in infundibulo secundum imaginarium cylindrum <lb/>BA, aequalis BE, eiusdem vero sit tripla EF, quintupla FG, septupla BH etc., <lb/>secundum proportionem accelerationis motus naturalis, a Galileo assignatum. </s>

<s><lb/>Quo tempore aliqua pars aquae permeat intervallum BE, eodem vel aequali <lb/>permeat alia spacia EE, FG, GH. </s>

<s>Ergo moles aquae, in singulis partibus effu&shy;<lb/>sionis BE, EF, FG, GH sunt aequales. </s>

<s>Ipsae autem ad cylindrum aqueum, <lb/>cuius hasis sit foramen B, altitudo vero BH, eam habent rationem, quam <lb/>numerus BE, EF, FG, GH etc. </s>

<s>ad quadratum eiusdem numeri. </s>

<s>Ita ut tan&shy;<lb/>dem universaliter quaecumque moles aquae, in qualibet effusione BH con&shy;<lb/>tenta, ad cylindrum aqueum eiusdem altitudinis BH, super basi foraminis <lb/>erecti, eam habeat rationem quam altitudo AB, ad eam quae inter AB et BH <lb/>sit media proportionalis &rdquo; (ibid., T. CXXXV, fol. </s>

<s>15). </s></p><p type="main">

<s>Tale &egrave; la conclusione di Galileo, alla quale sta bene che si siano ritro&shy;<lb/>vati i principii. </s>

<s>Ma quei principii non erano legittimi, ne la soluzion del pro&shy;<lb/>blema idrodinamico, data dallo stesso Galileo, era la vera, com'appariva ma&shy;<lb/>nifesto a chiunque avesse conferito queste dottrine con quelle <emph type="italics"/>De motu aqua&shy;<lb/>rum,<emph.end type="italics"/> allora gi&agrave; insegnate dal Torricelli, dalla VI proposizion del quale <lb/>resultava che la troscia non piglia forma di un cono, ma di un conoide, quale <lb/>si descriverebbe dal rivolgersi intorno all'asse BH, come a suo asintoto prin&shy;<lb/>cipale, un'iperbola biquadratica. </s>

<s>Al qual difetto della soluzione galileiana <lb/>accennava il Viviani con queste parole, con le quali egli terminava la rife&shy;<lb/>rita illustrazione: &ldquo; Num autem hoc verum sit, diligenter expende, et ideo <lb/>ad doctrinam Torricellii <emph type="italics"/>De motu aquarum<emph.end type="italics"/> te conferas &rdquo; (ibid.). </s></p><p type="main">

<s>Qualunque si fosse l'intenzione, ch'ebbe il Viviani di spiegare cos&igrave; i <lb/>pensieri del suo proprio Maestro, era tuttavia lontano dall'indovinare che se <lb/>ne sarebbe un giorno servito per quel Dialogo della forza della percossa, di <lb/>cui anch'egli a que'tempi deplorava, col Torricelli e col principe Leopoldo <lb/>dei Medici, la irreparabile iattura. </s>

<s>Ma pervenutogli, per quelle avventure che <lb/>si narrarono a suo tempo, il detto Dialogo alle mani, ebbe a leggervi la <lb/>proposta, messa in bocca all'Aproino, che quando fosse possibile misurare <lb/>e pesare la quantit&agrave; dell'acqua, compresa in aria fra'due secchi appesi alla <lb/>bilancia, si potrebbe anche sicuramente affermare &ldquo; la tal percossa esser po&shy;<lb/>tente ad operar gravitando quello che opera un peso uguale a dieci o dodici <lb/>libbre d'acqua cadente &rdquo; (Alb. </s>

<s>XIII, 331). Ma perch&egrave; il Salviati reputava la <pb xlink:href="020/01/3410.jpg" pagenum="371"/>misura di quell'acqua in aria impossibile, si volge a immaginar altre espe&shy;<lb/>rienze, per agevolarsi la strada all'intera cognizione desiderata. </s></p><p type="main">

<s>Or il Viviani, risovvenendosi, in legger ci&ograve;, di quel che aveva, parecchi <lb/>anni prima, letto nell'originale, fatto poi copiare fra l'altra <emph type="italics"/>Roba<emph.end type="italics"/> nel citato <lb/>volume; intese che Galileo aveva finalmente ritrovata ne'suoi propri teoremi <lb/>idrostatici la chiave a quell'entrata, ch'egli aveva creduto prima impossi&shy;<lb/>bile, e che perci&ograve; avrebbe riformato in quella parte il suo Dialogo, sosti&shy;<lb/>tuendo alle confessate difficolt&agrave; la diretta risoluzion del problema. </s>

<s>Il propo&shy;<lb/>sito per&ograve; non fu mandato ad effetto (forse perch&egrave; Galileo pens&ograve; alla forza <lb/>della percossa molto meno di quel che volle fare apparire) e perci&ograve; attese <lb/>a supplirvi il Viviani, dialogizzando le note del suo Maestro, ed esplicandole <lb/>cos&igrave;, come le abbiamo lette, e con fedelt&agrave; ricopiate dal manoscritto. </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; <emph type="italics"/>Il discorso di V. S. &egrave; puntualmente conforme a quello <lb/>che facemmo noi di subito sopra la veduta esperienza; ed a noi ancora <lb/>parve di poter concludere che l'operazione della sola velocit&agrave;, acquistata <lb/>per la caduta di quella quantit&agrave; di acqua, dall'altezza delle due braccia, <lb/>operasse nell'aggravare senza il peso dell'acqua quel medesimo appunto, <lb/>che il peso dell'acqua senza l'impeto della percossa. </s>

<s>Sicch&egrave;, quando si <lb/>potesse misurare e pesare la quantit&agrave; dell'acqua compresa in aria tra i <lb/>vasi, si potesse sicuramente affermare la tal percossa esser potente ad ope&shy;<lb/>rare gravitando quello, che opera un peso uguale a dieci o dodici libbre <lb/>dell'acqua cadente &rdquo;<emph.end type="italics"/> (Alb. </s>

<s>XIII, 311). </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Piacemi molto l'arguta invenzione, e bench&egrave; da voi si&shy;<lb/>gnor Aproino, si creda di dovervi incontrare grande difficolt&agrave; quanto al poter <lb/>misurare la mole dell'acqua, compresa in aria tra i vasi, io ho nonostante <lb/>pensato al modo di ritrovare dimostrativamente, e con una certa precisione, <lb/>quella desiderata misura. </s>

<s>E per primo e principal fondamento di quella spe&shy;<lb/>culazione io vi porr&ograve; innanzi a considerare il fatto, che la troscia si va sem&shy;<lb/>pre pi&ugrave; assottigliando, com'ella si dilunga sempre pi&ugrave; dal suo principio, co&shy;<lb/>sicch&egrave; non mantiene la sua prima figura di cilindro, ma s'assottiglia via via, <lb/>affusolandosi, per cos&igrave; dire, e riducendosi nell'aspetto di un cono. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Questo io penserei che avvenga per lo continuo accre&shy;<lb/>scersi la velocit&agrave;, nelle particelle dell'acqua, secondo che pi&ugrave; e pi&ugrave; si dipar&shy;<lb/>tono dal principio del moto, ma come da ci&ograve; direttamente consegua quel&shy;<lb/>l'assottigliamento, che sempre si osserva, cadendo l'acqua da una doccia <lb/>per aria, io non so per me trovare cos&igrave; ragionevole discorso, che me lo <lb/>persuada. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Non mancherebbe questo ragionevole fondamento al vo&shy;<lb/>stro discorso, quando voi ritornaste col pensiero sopra ci&ograve;, che il nostro <lb/>Accademico ha dimostrato nel suo libro delle cose che stanno, o che si muo&shy;<lb/>von per l'acqua, dov'ei riduce, come nella libbra, quel loro stare o quel loro <lb/>muoversi alle ragioni dei momenti, composti come sepete, delle velocit&agrave; e <lb/>delle moli. </s>

<s>Il metodo, affatto nuovo a chi non aveva saputo scostarsi dai <lb/>processi antichi di Archimede, portava a conseguenze ammirande e nuove, <pb xlink:href="020/01/3411.jpg" pagenum="372"/>intorno al misurare, per via dei momenti, le quantit&agrave; di un'acqua che corre. </s>

<s><lb/>Perch&egrave; se i detti momenti stanno compostamente come le velocit&agrave; e le moli, <lb/>essendo essi momenti uguali, necessariamente le velocit&agrave; debbono in ragione <lb/>contraria, corrispondere colle moli. </s>

<s>Ora io vi dico che questa applicazione della <lb/>Scienza meccanica all'acque fu fatta dal nostro Accademico, nel suo Discorso <lb/>intorno ai galleggianti, dove con vari esempi conclude che, passando una me&shy;<lb/>desima quantit&agrave; d'acqua da un cannone pi&ugrave; largo in un pi&ugrave; stretto, tanto ella <lb/>acquista velocit&agrave; nel correre, quanto ella viene a diminuir nella mole. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Voi mi fate stupir veramente, perch&egrave;, sebbene io abbia <lb/>letto e riletto il Discorso del nostro Amico, non ci ho trovato mai, n&egrave; perci&ograve; <lb/>m'&egrave; rimasto memoria di queste cose. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; E a me pure succede lo stesso, n&egrave; so risovvenirmi d'al&shy;<lb/>tro, ora che ci ripenso, se non che l&igrave; si tratta di vasi e di solidi immersi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; &Egrave; vero che per lo pi&ugrave; si rappresentano que'vasi e que'so&shy;<lb/>lidi in figura di prismi, ma la dimostrazione correrebbe ugualmente bene, <lb/>quando fossero cilindri. </s>

<s>Supponete perci&ograve; che sia cilindrico il solido M (nella <lb/>figura 185) e cilindrico il vaso AD, nell'acqua del quale s'intenda essere <lb/>immerso. </s>

<s>Sollevandosi il detto solido, l'acqua che sottentra in suo luogo &egrave; <lb/>come se, da un tubo largo quanto AC, entrasse in uno stretto quanto EF. </s>

<s><lb/>Ora il nostro Accademico dimostra che l'alzamento della superficie EF, che <lb/>seguita l'alzamento del solido, all'abbassamento della superficie AC, ha la <lb/>medesima proporzione, che la superficie AC alla superficie EF. </s>

<s>Ma da que&shy;<lb/>ste superficie son misurate le larghezze delle sezioni dei tubi, e da quegli <lb/>alzamenti e abbassamenti le velocit&agrave; dell'acque per essi tubi correnti; dun&shy;<lb/>que le velocit&agrave; stanno in reciproca ragione delle sezioni. </s>

<s>Voi avreste per&ograve; <lb/>potuta ritrovare la dimostrazione anche pi&ugrave; esplicita di questa legge in que'due <lb/>vasi, uno dei quali larghissimo come MLB (nella passata figura 183) e l'altro <lb/>con lui continuato e angusto come la cannella BHC, secondo che lo stesso <lb/>nostro Accademico descrive nel citato Discorso, concludendo esser la salita IH <lb/>tanto maggiore della discesa MA, quant'&egrave; l'ampiezza ML del vaso maggiore <lb/>della larghezza HC della canna, la qual concl&ugrave;sione si riduce dunque a dire <lb/>quel che si diceva di sopra, che cio&egrave; le velocit&agrave; stanno in ragion reciproca <lb/>delle sezioni. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Il signor Salviati ha fatto il miracolo di restituire la vista <lb/>ai ciechi, intanto che ora vedo, per vostro benefizio, come, essendo livellato <lb/>in ML e in IG il liquido nei due vasi, se io introducessi nella bocca di que&shy;<lb/>sto o di quello uno zaffo, e se con esso premendo facessi violentemente abbas&shy;<lb/>sare il liquido sottoposto nell'uno; potrei con certa regola geometrica sapere <lb/><gap/>uanto fosse per sollevarsi nell'altro. </s>

<s>Come per esempio, se nel vaso grande <lb/><gap/> facessi l'abbassamento da M in A, potrei sapere l'alzamento giusto IH, <lb/><gap/>e gli corrisponde nel vaso piccolo, perch&egrave; stando, per le cose dimostrate <lb/><gap/>nostro Accademico, IG a LM, come AM a IH, ed essendomi le prime tre <lb/><gap/>tit&agrave;, com'io presuppongo, note, mi sar&agrave; nota anche insieme la IH loro <lb/><gap/> proporzionale. </s>

<s>&rdquo; </s></p><pb xlink:href="020/01/3412.jpg" pagenum="373"/><p type="main">

<s>&ldquo; SALVIATI. &mdash; Si potrebbe anzi, signor Sagredo, sciogliere, con questa <lb/>medesima scienza suggeritaci dal nostro Amico, il problema inverso, non <lb/>men bello &oacute; meno curioso. </s>

<s>Supponete che, in forza dello zaffo da voi cac&shy;<lb/>ciato nel maggior vaso infino ad AD, il liquido nel minore si sia violente&shy;<lb/>mente sollevato in HC, e che, lasciato poi a un tratto in libert&agrave;, col rimo&shy;<lb/>vere il detto zaffo, voi voleste, non avendoci fatto prima avvertenza, ritrovare <lb/>il segno, in cui scendendo esso liquido si fermer&agrave;, dop'aver fatti i soliti on&shy;<lb/>deggiamenti. </s>

<s>Prolungate il livello AD in EF, e l'altezza FC dividete in G <lb/>per modo, che stia CG a GF come la sezione o il circolo AD alla sezione <lb/>o al circolo EF. Poi, dal punto G conducete la orizontale GILM, che ne'punti <lb/>segnati da lei si costituiranno le cercate superficie nei due vasi. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Mi par che tutto si riduca a dimostrare che il cilindro <lb/>d'acqua CI, di che si scema la canna, &egrave; uguale al cilindro d'acqua DM, di <lb/>che s'accresce il vaso, n&egrave; la dimostrazione mi si presenta molto difficile. </s>

<s>Per&shy;<lb/>ch&egrave; il cilindro AL, al cilindro EG di pari altezza, sta come la base AD alla <lb/>base EF, ossia, per la costruzione del signor Salviati, come la CG alla GF, <lb/>e anche come CG moltiplicata per la base IG, alla GF moltiplicata per la <lb/>medesima IC, o per la sua uguale EF. </s>

<s>Ma l'altezza CG, moltiplicata per la <lb/>base IG, d&agrave; la misura del cilindro IC, e l'altezza GF, moltiplicata per la base <lb/>EF, d&agrave; la misura del cilindro EG; dunque il cilindro AL sta al cilindro EG <lb/>come il cilindro CI sta al medesimo cilindro EG, e perci&ograve;, essendo i conse&shy;<lb/>guenti uguali, saranno anche insieme uguali gli antecedenti, cio&egrave; il cilindro <lb/>AM uguale al cilindro CI, come si richiedeva per confermare la verit&agrave; della <lb/>soluzione di questo problema, data dal nostro signor Salviati. </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Bellissime verit&agrave; mi avete scoperte intorno ai mirabili <lb/>effetti, che produce nell'acqua il moto pi&ugrave; o meno veloce, ma di questi ef&shy;<lb/>fetti non mi avete ancora, signor Salviati, dichiarato quello, che da me mag&shy;<lb/>giormente si desiderava, come cio&egrave; si possa misurare e pesare la quantit&agrave; <lb/>dell'acqua cadente fra le due secchie. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Il problema proposto dal signor Sagredo, e quell'altro <lb/>simile, che mi ha fatto sovvenire a quel proposito, hanno interrotto il filo <lb/>del nostro discorso, che mi avrebbe direttamente guidato a sodisfare il vo&shy;<lb/>stro principal desiderio. </s>

<s>Vi ricorderete, signor Aproino, che voi diceste poter <lb/>essere la maggiore velocit&agrave;, acquistata dalle particelle dell'acqua nel cadere, <lb/>causa efficiente dell'assottigliarsi la troscia: e come dalla scienza del nostro <lb/>Accademico s'&egrave; ricavato che, restringendosi le sezioni crescono a quella pro&shy;<lb/>porzione le velocit&agrave;; cos&igrave;, per la conversa, argomenteremo che, crescendo le <lb/>velocit&agrave;, a quella medesima ragione, diminuiscono le sezioni. </s>

<s>Per dichiararvi <lb/>anche meglio il m&igrave;o pensiero, sia CBD (nella figura 186 ultimamente im&shy;<lb/>pressa) la secchia di sopra, col foro aperto in B, da cui cada l'acqua intorno <lb/>all'asse verticale BH. </s>

<s>Essendo BA l'altezza del liquido nel vaso, consideriamo <lb/>il cilindro AB, che nel primo tempo dell'effusione giunga in E, da un'al&shy;<lb/>tezza BE, uguale ad AB. </s>

<s>Nel secondo tempo passer&agrave; lo spazio EF triplo di <lb/>BE, nel terzo lo spaz&igrave;o FG quintuplo di BE, e cos&igrave; seguitando, secondo la <pb xlink:href="020/01/3413.jpg" pagenum="374"/>legge dal nostro Accademico scoperta, e dimostrata in tutti i gravi cadenti. </s>

<s><lb/>Essendo ora intorno EF, intorno FG, e intorno a tutte le altre parti rima&shy;<lb/>nenti la medesima quantit&agrave; d'acqua, che intorno a BE, dovr&agrave; in E la se&shy;<lb/>zione o la base del cilindro successivo tanto restringersi, quanto l'altezza EF <lb/>&egrave; cresciuta sopra la BE, e in F restringersi ancora pi&ugrave; che in E, quanto <lb/>la FG sopra la EF &egrave; cresciuta di grandezza. </s>

<s>Cos&igrave; proseguendo il discorso, <lb/>averemo le ragioni dell'assottigliarsi sempre pi&ugrave; l'acqua, com'ella si va sem&shy;<lb/>pre pi&ugrave; dilungando dal fondo B della secchia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Di modo che, supponendo che il termine sia G, l'acqua <lb/>compresa in aria fra G e B &egrave; tanta, quant'&egrave; quella dei tre cilindri, intorno <lb/>gli assi BE, EF, FG; ossia quant'&egrave; nel cilindro BE, preso tre volte, essendo <lb/>a lui, per supposizione, i cilindri intorno EF, FG ciascuno uguali di mole. </s>

<s><lb/>Se s'avesse poi da conferire questa quantit&agrave; d'acqua, contenuta nella tro&shy;<lb/>scia, con la quantit&agrave; contenuta nel cilindro sopra la medesima base B, e con <lb/>l'altezza BG; imperocch&egrave; tale altezza &egrave; nove volte pi&ugrave; grande della BE, di&shy;<lb/>remo dunque che quella, cio&egrave; la troscia, sta al cilindro a lei circoscritto, come <lb/>tre sta a nove. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Cos&igrave; &egrave; la verit&agrave;, come voi, signor Sagredo, da buon ma&shy;<lb/>tematico ragionando, l'avete conclusa. </s>

<s>Se supponete inoltre che i cilindri o <lb/>le parti dello spazio, passato nella caduta in tempi uguali, sian quattro, il <lb/>vostro ragionamento v'avrebbe portato a concludere che la troscia sta al ci&shy;<lb/>lindro, come quattro sta a sedici, e universalmente, come il numero delle <lb/>parti sta al quadrato di questo stesso numero. </s>

<s>Che se voi voleste ridurvi <lb/>alla ragione geometrica, direte che, per qualunque effusione BH, la mole <lb/>d'acqua al cilindro circoscritto sta come l'altezza AB del livello nel vaso, a <lb/>quella che &egrave; media proporzionale tra la stessa AB e la BH. &rdquo; </s></p><p type="main">

<s>&ldquo; SAGREDO. &mdash; Questa vostra data ragione geometrica io la credo veris&shy;<lb/>sima, ma perch&egrave; la non mi appare cos&igrave; manifesta, non vi dispiaccia, signor <lb/>Salviati, di condurmela dai suoi principii. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Vi far&ograve; a questo effetto dunque prima considerare che <lb/>il numero delle parti cilindriche, nelle quali s'&egrave; divisa mentalmente la tro&shy;<lb/>scia, &egrave; dato dalla radice del numero delle parti, tutte uguali ad AB, che en&shy;<lb/>trano nella lunghezza di essa troscia. </s>

<s>Cos&igrave; voi vedete come nella lunghezza <lb/>BF, che &egrave; quattro volte AB, e nella lunghezza BG, che &egrave; nove volte la <lb/>stessa AB, entrano due e tre parti, che sono i numeri corrispondenti alle <lb/>radici di quattro e di nove. </s>

<s>E perci&ograve;, in universale argomentando, diremo <lb/>che, se la lunghezza sia qualunque BH, il numero delle parti sar&agrave; dato dalla <lb/>radice di BH, divisa per la radice di AB. Ora, poich&egrave; fu convenuto che la <lb/>troscia sta al cilindro come il numero delle parti sta al suo quadrato, o come <lb/>l'unit&agrave; sta al medesimo numero; anche diremo stare le due dette quantit&agrave; <lb/>d'acqua cadente come l'unit&agrave; alla radice di BH, divisa per la radice di AB, <lb/>o come la radice di AB alla radice di BH, o finalmente come l'AB sta alla <lb/>radice di BH, moltiplicata per la radice di AB. </s>

<s>Ma alla radice di BH mol&shy;<lb/>tiplicata per la radice di AB s'uguaglia la linea, che media fra BH e AB; <pb xlink:href="020/01/3414.jpg" pagenum="375"/>dunque la troscia sta al cilindro a lei circoscritto come l'AB sta a quella, <lb/>che &egrave; media proporzionale tra la stessa AB e la BH. &rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Il signor Sagredo mostra di aver avuto sodisfazione con <lb/>gli atti, e io la confermo con le parole, quanto all'approvare la verit&agrave; della <lb/>vostra ultima conclusione geometrica, ma non per ci&ograve; mi si viene a rimo&shy;<lb/>vere un dubbio, che mi nasce da un'altra parte. </s>

<s>Voi, signor Salviati, sup&shy;<lb/>ponete che l'altezza AB del livello, per qualunque tempo dell'effusione, si <lb/>mantenga costante, ossia ammettete che il vaso non iscemi, come farebbe <lb/>se ricevesse dentro s&egrave; tant'acqua nuova, quant'&egrave; quella che ha versato di <lb/>fuori. </s>

<s>Tal supposizione per&ograve; non si verifica delle due secchie, quali io vi <lb/>dissi che il nostro Accademico aveva immaginate, per conseguire qualche <lb/>notizia della recondita forza della percossa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Si potrebbe nonostante far la secchia tanto larga, ri&shy;<lb/>spetto al foro, che per quell'istante dell'effusione, richiesto per l'effetto <lb/>principale dell'esperienza, il livello s'abbassasse cos&igrave; poco, da riguardarlo <lb/>come invariato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; APROINO. &mdash; Vi si potrebbe senza difficolt&agrave; concedere questo che voi <lb/>volete, ma altro anco di pi&ugrave; richiede il vostro discorso, a danno del buon <lb/>esito della esperienza, ed &egrave; che l'acqua nella secchia sia pochissimo fonda. </s>

<s><lb/>Perch&egrave;, a voler ridurre la continuit&agrave; della troscia a que'vostri cilindri, e <lb/>affinch&egrave; spariscano quegli addentellati nell'uniformit&agrave; della superficie conter&shy;<lb/>mina all'acqua cadente, convien che dei detti cilindri la lunghezza sia pic&shy;<lb/>colissima, intanto che quella, che serve a loro per unit&agrave; di misura, e che &egrave; <lb/>uguale all'altezza del livello, fosse quasi insensibile, e insomma, per aggiu&shy;<lb/>star le cose alla vostra dimostrazione, il liquido dovrebb'essere cos&igrave; poco nel <lb/>vaso, da ricoprirne appena appena la superficie del fondo. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; SALVIATI. &mdash; Comunque sia, poich&egrave; sento che vi arreca ancora qual&shy;<lb/>che ambiguit&agrave; la difficult&agrave; del misurare la quantit&agrave; dell'acqua cadente; po&shy;<lb/>tremo &rdquo; ecc., come nella edizion dell'Alb&egrave;ri, alla pagina sopra citata. </s></p><p type="main">

<s>Se avesse avuto il Viviani occasione di pubblicare egli stesso il Dialogo <lb/>della forza della percossa, non &egrave; dubbio che vi avrebbe, insieme con altre <lb/>parti, forse meno importanti, ridotto anche questa. </s>

<s>Ma perch&egrave; l'ufficio era <lb/>riserbato al Bonaventuri, se questi non integr&ograve; cos&igrave; come sarebbesi deside&shy;<lb/>rato la sua edizione, &egrave; da credere non fosse per altro, se non perch&egrave; il Grandi, <lb/>che doveva aver letto questo dialogismo fra le carte ricevute dal Panzanini, <lb/>non lo esib&igrave; all'amico editore, qualunque poi se ne fosse il motivo. </s></p><p type="main">

<s>Ma &egrave; da tornare al Castelli, che attendendo in questo tempo con grande <lb/>alacrit&agrave; a dar perfezione al suo manoscritto Della misura delle acque cor&shy;<lb/>renti, incominciava cos&igrave;, il d&igrave; primo del 1626, una sua lettera indirizzata da <lb/>Pisa a Galileo: &ldquo; Non scrissi a V. S., per l'ordinario passato, perch&egrave; non <lb/>avevo ricevuta la sua de'27, e non avendo cosa di nuovo, se non due Ap&shy;<lb/>pendice al mio trattatello del moto de'fiumi, che mandai al sig. </s>

<s>Mario, pre&shy;<lb/>gandolo le comunicasse a V. S. </s>

<s>In una toccavo un particolare scritto da Giu&shy;<lb/>lio Frontino, antico scrittore illustre <emph type="italics"/>De Aquaeductibus Romae,<emph.end type="italics"/> nel quale <pb xlink:href="020/01/3415.jpg" pagenum="376"/>mi pare che Frontino possa avere errato nella misura dell'acqua, per non <lb/>aver considerata la velocit&agrave;, e tocco volentieri questo punto, perch&egrave; insieme <lb/>vengo a significare che il mio pensiero non &egrave; stato messo in campo da nes&shy;<lb/>suno ancora. </s>

<s>Nell'altra Appendice noto il mancamento specificatamente degli <lb/>ingegneri del nostro tempo, e pi&ugrave; di quei di Ferrara, i quali, nel concludere <lb/>l'alzamento che pu&ograve; fare il Reno in Po, non tengono conto della variazione <lb/>della velocit&agrave; &rdquo; (Campori, Carteggio cit., pag. </s>

<s>253). </s></p><p type="main">

<s>A queste prime Appendici ne aggiunse il Castelli altre, che gli sovven&shy;<lb/>nero via via, intanto che si ridussero al numero di XI, quasi scolii al Di&shy;<lb/>scorso della misura delle acque correnti. </s>

<s>Gli amici di Firenze avevano dimo&shy;<lb/>strato gran desiderio di veder questo Discorso, che avevano letto manoscritto, <lb/>uscir fuori per le stampe, le quali poi ebbero effetto per le premure di quegli <lb/>altri amici di Roma, e specialmente de'due monsignori Ciampoli e Corsini, <lb/>che fecero conoscere l'utilit&agrave; e l'importanza di quelle nuove scritture idrau&shy;<lb/>liche ai cos&igrave; detti Padroni, quali erano allora papa Urbano VIII, e i prin&shy;<lb/>cipi Barberini. </s>

<s>Il d&igrave; 16 Settembre 1628 il Castelli dava da Roma in una let&shy;<lb/>tera a Galileo questo annunzio: &ldquo; Oggi ho avuto ordine dai Padroni di far <lb/>stampare la mia scrittura dell'Acqua, e fa la spesa la Camera &rdquo; (ivi, pag. </s>

<s>272). <lb/>Sul finir di quell'anno infatti usciva in Roma, dalla Stamperia Camerale, alla <lb/>luce il Discorso della misura delle acque correnti, con XVI corollari e XI <lb/>appendici, dedicato a papa Urbano VIII, aggiuntevi le Dimostrazioni geome&shy;<lb/>triche dedicate al principe don Taddeo Barberini. </s></p><p type="main">

<s>Nella lettera del d&igrave; 16 Settembre, ora citata, soggiungeva il Castelli a <lb/>Galileo, dop'avergli annunziato l'ordine di stampare la sua scrittura: &ldquo; Stam&shy;<lb/>pata che sar&agrave;, glie ne mander&ograve; copia, e vedr&agrave; una moltitudine di strava&shy;<lb/>ganti particolari, tutti dipendenti dal medesimo principio. </s>

<s>Son per&ograve; stato ne&shy;<lb/>cessitato ridurla a chiarezza tale, che possa essere intesa ancora da quelli, <lb/>che non hanno mai inteso niente di bello &rdquo; (ivi). Il d&igrave; 17 del seguente No&shy;<lb/>vembre tornava a scrivere: &ldquo; Per l'ordinario che viene, non avendo potuto <lb/>finire, per diversi rispetti, mander&ograve; il mio trattato Della misura delle acque <lb/>correnti, e ne mander&ograve; alcune copie a V. S., da distribuire a cotesti signori <lb/>miei Padroni &rdquo; (MSS. Gal., P. I, T. IX, fol. </s>

<s>133). Nell'ultima settimana del <lb/>detto mese, poche copie ancora essendone tirate, ne mand&ograve; a Galileo tre: <lb/>una, perch&egrave; se la ritenesse per s&egrave;, e delle altre due facesse presente al Gran&shy;<lb/>duca, e al principe don Lorenzo dei Medici. </s>

<s>Verso la fine di Dicembre, es&shy;<lb/>sendo oramai le copie finite di tirar tutte, ne furono da Roma spedite a Ga&shy;<lb/>lileo 50 copie, perch&egrave; a nome dell'Autore, le dispensasse fra gli amici e <lb/>studiosi padroni suoi di Toscana. </s>

<s>&ldquo; Mando a V. S. cinquanta copie della mia <lb/>Scrittura, acci&ograve; le dispensi a quei Signori miei padroni che lei sa che sono <lb/>la mia corona &rdquo; (Alb. </s>

<s>IX, 141). </s></p><p type="main">

<s>Non &egrave; tempo ancora di riferire particolarmente i giudizi, che si fecero <lb/>dell'Opera, cos&igrave; diffusa: basti il dire che fu ricevuta con ammirazione, e sa&shy;<lb/>lutata in generale quale rivelazion benefica di una scienza utilissima e nuova. <lb/></s>

<s>&ldquo; La Scrittura, scriveva Galileo all'Autore nel Gennaio 1629, &egrave; piaciuta a <pb xlink:href="020/01/3416.jpg" pagenum="377"/>tutti che l'hanno letta, e qu&agrave; si trattava di ristamparla, ma intendo che ella <lb/>non se ne contenta &rdquo; (Alb. </s>

<s>VI, 324). Nel 1634 per&ograve;, mutato consiglio, il Ca&shy;<lb/>stelli stesso iniziava le trattative di questa seconda edizione, da farsi in Fi&shy;<lb/>renze, come apparisce da queste parole, che il d&igrave; primo Novembre di quel&shy;<lb/>l'anno scriveva di Roma in una sua lettera a Galileo: &ldquo; Gli ho dato ordine <lb/>(al padre Francesco, cio&egrave; a don Famiano Michelini) che tratti col signor An&shy;<lb/>drea Arrighetti di fargli stampare il mio Discorso della misura delle acque <lb/>correnti, e perch&egrave; forse vi sar&agrave; qualche aggiunta e di postille e di scolii, <lb/>supplico V. S. farmi grazia ed onore di qualche particolare, che avesse os&shy;<lb/>servato in questa materia &rdquo; (Campori, Carteggio cit., pag. </s>

<s>417). </s></p><p type="main">

<s>Queste trattative per&ograve; non ebbero effetto, e la nuova edizione indugi&ograve; <lb/>ancora per qualche anno, infintantoch&egrave; nel 1639 non si fece anch'essa in <lb/>Roma dalla stamperia di Francesco Cavalli. </s>

<s>Le appendici vi son ridotto al <lb/>numero di XIII, e si fa ad esse succedere la &ldquo; Copia di lettera al signor Ga&shy;<lb/>lileo Galilei, primo Filosofo del serenissimo Granduca di Toscana. </s>

<s>&rdquo; Nei primi <lb/>di Agosto ricev&egrave; copia del nuovo libro Galileo stesso, che il d&igrave; 8, da Arce&shy;<lb/>tri, cos&igrave; rispondeva all'Autore: &ldquo; Mentre stavo aspettando lettere dalla P. V. <lb/>Reverendissima, m'&egrave; pervenuto il trattato Delle acque correnti da lei ristam&shy;<lb/>pato, con l'aggiunta della sua curiosissima e ingegnosa Lettera, da lei a me <lb/>scritta in proposito del lago Trasimeno, e del Diluvio universale registrato <lb/>nelle Sacre carte. </s>

<s>Per lo che la ringrazio della memoria che tiene di me, <lb/>e del procurare che il mio nome non s'estingua, ma si vada continuando <lb/>nella memoria delle future genti &rdquo; (Alb. </s>

<s>VII, 232). </s></p><p type="main">

<s>Detto ci&ograve; che riguarda la pubblicazione, &egrave; tempo di soggiungere i giu&shy;<lb/>dizi, che particolarmente si dettero dell'Opera nuova, incominciando da quelli <lb/>stessi richiesti dall'Autore. </s>

<s>Dopo Galileo, uno de'pi&ugrave; stimati in questa Scienza, <lb/>che si ritrovassero allora in Italia, era Giovan Batista Baliani. </s>

<s>Con lui il Ca&shy;<lb/>stelli, mentre attendeva a perfezionare il suo manoscritto, si volle consigliare <lb/>intorno alle leggi delle velocit&agrave;, da applicarsi pi&ugrave; propriamente al moto del&shy;<lb/>l'acqua, mandandogli nello stesso tempo quelle due prime Appendici, man&shy;<lb/>date gi&agrave; a Galileo, intorno all'errore in che era incorso Frontino, e in cui <lb/>incorrevano tuttavia gli ingegneri moderni, rispetto all'alzamento, che fareb&shy;<lb/>bero le piene, mettendosi in Po il Reno. </s>

<s>Il Baliani dunque, dop'aver fatto <lb/>osservare che i liquidi, per aver le parti disgiunte, non vanno nello stesso <lb/>modo come i solidi, soggiungeva: &ldquo; La penna mi ha trasportato forse troppo <lb/>avanti, mentre che io voleva solo accennare il dubbio che io ho avuto in <lb/>quella seconda Appendice, come che del resto non mi paia che al suo di&shy;<lb/>scorso, tanto circa le dimostrazioni, come a'corollari e prime Appendice, vi <lb/>sia che aggiungere &rdquo; (Alb. </s>

<s>IX, 142, 43). </s></p><p type="main">

<s>Ma era naturale che, pi&ugrave; di quegli del Baliani, premessero al Castelli <lb/>i giudizi di Galileo, il quale sebben fosse, per le sue proprie esperienze, per&shy;<lb/>suaso pur troppo che ne'tempi anteriori era a tutti rimasto incomprensibile <lb/>il modo di misurar l'acque, per esssere il loro corso indeficiente; dubitava <lb/>nulladimeno se il riconoscer gli effetti della velocit&agrave;, in quelle misure, fosse <pb xlink:href="020/01/3417.jpg" pagenum="378"/>pensiero del tutto nuovo. </s>

<s>Il dubbio prese forma definita, quando in quella <lb/>copia del libro, che dicemmo avergli mandata il Castelli stesso nell'ultima <lb/>settimana del Novembre 1728, lesse attentamente la quarta Appendice, dalla <lb/>quale resultava che non tutti gl'ingegneri e i periti dovevano aver trascu&shy;<lb/>rato di considerare le velocit&agrave;, se agli effetti di loro, mettendosi il Reno in <lb/>Po, attribuivano il non farsi alzamento nessuno d'acqua. </s>

<s>Al qual dubbio il <lb/>Castelli, che aveva prima assolutamente asserito <emph type="italics"/>non essere il suo pensiero <lb/>stato messo in campo da nessuno ancora,<emph.end type="italics"/> rispondeva cos&igrave;, limitando il suo <lb/>asserto: &ldquo; Quanto allo scrupolo, che V. S. mi scrive, che nella quarta Ap&shy;<lb/>pendice pare che io ammetta che altri abbiano avuto considerazione della ve&shy;<lb/>locit&agrave;, mentre noto che alcuni hanno avuto pensiero che, mettendosi il Reno <lb/>in Po non sarebbe cresciuto il Po; sappia che io non nego che non sia stata <lb/>avvertita la velocit&agrave; nell'acqua, ma dico bene che non &egrave; stata mai bene in&shy;<lb/>tesa, e nel particolare di quell'Appendice tocco di un Bolognese, il quale <lb/>semplicemente dice che il Reno non farebbe crescere il Po, mettendo certe <lb/>considerazioni ridicole, senza considerare la forza della velocit&agrave; &rdquo; (Alb. </s>

<s>IX, 141). </s></p><p type="main">

<s>Questo discorso non manc&ograve; di produrre il suo effetto. </s>

<s>Tanto &egrave; vero che, <lb/>proponendosi una questione simile, quando si trattava degli alzamenti, che <lb/>farebbero nel Bisenzio le acque dell'Ormannoro, Galileo la risolveva espres&shy;<lb/>samente invocando gli avvertimenti, dati in questo proposito agl'ingegneri <lb/>dal padre don Benedetto Castelli. </s>

<s>&ldquo; Quanto all'ovviare (si legge in una nota <lb/>autografa) che sopraggiungendo le piene di Bisenzio proprio non trovino oc&shy;<lb/>cupato parte dell'alveo loro dall'acque dell'Ormannoro, che ci&ograve; possa esser <lb/>di qualche poco di profitto come si propone; concorro a dire che tal giova&shy;<lb/>mento sarebbe poco, anzi pochissimo, e quasi insensibile. </s>

<s>E qui &egrave; da notarsi <lb/>quel gravissimo errore mai stato avvertito da alcuno degli ingegneri antichi <lb/>e moderni, ma scoperto dal M. R. padre don Benedetto Castelli, nel suo trat&shy;<lb/>tato Del corso dei fiumi, il quale errore era che, entrando un fiume in un <lb/>altro, con acqua, che sia verbigrazia la terza parte di quella del principale; <lb/>debba accrescergli la terza parte di pi&ugrave; della prima altezza: cosa che &egrave; fal&shy;<lb/>sissima, imperocch&egrave; l'acqua sopravveniente, con alzar la prima, gli d&agrave; tanto <lb/>maggior pendenza ed impeto, cio&egrave; velocit&agrave;, che amendue si smaltiscono e <lb/>scaricano con poco pi&ugrave; d'alzamento. </s>

<s>Onde al nostro proposito quell'acqua <lb/>dell'Ormannoro, la quale aver&agrave; alzato quella di Bisenzio, avanti l'arrivo della <lb/>sua piena, per esempio, un braccio, non importer&agrave; talvolta, in far ricrescere <lb/>la sopravvegnente piena di Bisenzio, quattro dita, con tanta furia verr&agrave; quella <lb/>di Bisenzio, e porter&agrave; seco quella dell'Ormannoro &rdquo; (MSS. Gal., P. V, T. III, <lb/>fol. </s>

<s>16). </s></p><p type="main">

<s>Dagli scrupoli per&ograve;, cos&igrave; facilmente in Galileo rimossi, e dai dubbi, cos&igrave; <lb/>prestamente risoluti nel Baliani, si pass&ograve; presto per altri a censure pi&ugrave; gravi. </s>

<s><lb/>Iu quella lettera del d&igrave; primo Novembre 1634, dopo le cose riferite pi&ugrave; sopra, <lb/>il Castelli cos&igrave; soggiungeva: &ldquo; Mi viene anco scritto di Firenze che il signor <lb/>Aggiunti ci ha notati alcuni errori gravi, presi da me, e che se ne dichiara <lb/>assai largamente. </s>

<s>Mi pare strano che con me non ne abbia mai trattato: mi <pb xlink:href="020/01/3418.jpg" pagenum="379"/>consolo per&ograve; dall'intendere che i miei pensieri sono conosciuti veri, e le sue <lb/>obiezioni per false, e tanto mi basta &rdquo; (Campori, Carteggio cit., pag. </s>

<s>417). </s></p><p type="main">

<s>Quali erano particolarmente gli errori notati dall'Aggiunti? </s>

<s>Il Castelli <lb/>stesso mostra di averne avuto un'assai vaga notizia, la quale, se non si ri&shy;<lb/>duce ne'termini precisi, non &egrave; possibile decidere se le apposte censure siano <lb/>state dettate da un retto giudizio, o da qualche malevolenza verso l'Autore. </s>

<s><lb/>E perch&egrave; la questione &egrave; di non lieve importanza, giova rapidamente risalire <lb/>a trattarla dai suoi principii. </s></p><p type="main">

<s>La prima e pi&ugrave; efficace occasione di pensare al moto delle acque l'ebbe <lb/>senza dubbio anche l'Aggiunti da quelle proposizioni geometriche, e da quel <lb/>progresso idraulico, che nella sua propria casa si senti leggere, in Firenze, <lb/>da Galileo, il quale giusto di l&igrave; rispondeva al Castelli: &ldquo; Scrivo in fretta in <lb/>casa del signor Niccol&ograve; Aggiunti &rdquo; (Alb. </s>

<s>VI, 306) insieme col quale finiva <lb/>per baciargli le mani. </s>

<s>Intorno all'argomento, che nelle condizioni, in cui tro&shy;<lb/>vavasi allora la rinnovata Scuola sperimentale, si presentava sotto l'aspetto <lb/>di una novit&agrave; curiosa e di s&igrave; grande importanza; era naturalissimo che si <lb/>rivolgessero a speculare Galileo e l'Aggiunti, comunicandosi insieme i loro <lb/>propri pensieri. </s>

<s>De'frutti di questa comunione di studii, bench&egrave; non molti <lb/>se n'abbiano i documenti, si potrebbero pure addurre alcuni prestantissimi <lb/>esempi, fra quali il primo sia quello delle leggi de'momenti de'gravi sopra <lb/>i piani inclinati, applicate dall'uno de'due ora commemorati all'equilibrio <lb/>dei liquidi ne'sifoni ritorti, e dall'altro al corso dell'acqua per l'alveo dei <lb/>fiumi. </s></p><p type="main">

<s>Si sovverrano forse i nostri Lettori che, rappresentandosi con BA, BE <lb/>(fig. </s>

<s>187) i due rami del sifone, dimostrava l'Aggiunti equilibrarvisi dentro <lb/>il liquido, perch&egrave; sui punti A ed E della medesima linea orizontale preme <lb/><figure id="id.020.01.3418.1.jpg" xlink:href="020/01/3418/1.jpg"/></s></p><p type="caption">

<s>Figura 187.<lb/>ugualmente: e per dimostrar ci&ograve; considerava i due <lb/>corpi d'acqua BA, BE come due solidi d'ugual <lb/>materia, e di pari grossezza, attestati in B, i quali <lb/>solidi diceva che, avendo in premere ugual mo&shy;<lb/>mento, necessariamente perci&ograve; rimangono in equi&shy;<lb/>librio. </s>

<s>Ora, dietro le poste condizioni, &egrave; manifesto <lb/>che il principio, da cui fa l'Aggiunti dipendere la sua conclusione, &egrave; il teo&shy;<lb/>rema meccanico dell'uguaglianza dei momenti di due solidi, quando le loro <lb/>gravit&agrave; assolute son proporzionali alle lunghezze dei piani inclinati. </s>

<s>Immagi&shy;<lb/>nando infatti il liquido esser ridotto in tante minime sfere, di raggio tutte <lb/>uguali, &egrave; chiaro che queste tanto son pi&ugrave; di numero, e perci&ograve; di peso, quanto <lb/>maggiori son le lunghezze dei tubi. </s>

<s>Il teorema famoso dello Stevino avrebbe <lb/>ritrovato in queste sferette d'acqua pi&ugrave; propria, e pi&ugrave; elegante conferma <lb/>sperimentale, che negli anelli della catena. </s></p><p type="main">

<s>Simile al discorso dell'Aggiunti era quell'altro, che faceva Galileo, per <lb/>provare che, essendo BA, BE due alvei, come il tortuoso e il diritto, in cui <lb/>si voleva ridurre il Bisenzio, &ldquo; tanto scarica il pi&ugrave; lungo e meno declive, <lb/>quanto il pi&ugrave; corto e il pi&ugrave; pendente: cio&egrave; tanto il tortuoso quanto il diritto &rdquo; <pb xlink:href="020/01/3419.jpg" pagenum="380"/>(Alb. </s>

<s>VI, 357). Avendo le quantit&agrave; la ragion composta degl'impeti e delle <lb/>sezioni, che son manifestamente uguali, dovendo avere il Bisenzio corretto <lb/>il medesimo sbocco, tutto riducevasi a dimostrare che in A e in E, cio&egrave; agli <lb/>sbocchi dell'alveo diritto e del tortuoso, giunge sempre la piena con impeti <lb/>uguali: e per dimostrar ci&ograve;, Galileo ricorre e applica, come l'Aggiunti, al&shy;<lb/>l'acque le leggi de'momenti dei solidi sopra piani ugualmente cadenti, ben&shy;<lb/>ch&egrave; variamente inclinati. </s>

<s>E perch&egrave; pareva agli avversari duro il concedere <lb/>che, essendo tanto pi&ugrave; l'acqua nel canale BE che nel BA, ne dovesse nono&shy;<lb/>stante giungere una medesima quantit&agrave; allo sbocco: o ammettendosi pure <lb/>le dottrine del Castelli, professate anche qui, perch&egrave; non pareva possibile che, <lb/>essendo in A l'acqua tanto pi&ugrave; precipitosa che in E, dovessero nulladimeno <lb/>avere in ambedue i casi l'impeto stesso; Galileo risolveva il liquido in tante <lb/>sfere, e supposto che in BA ne fossero quattro, e in BE otto, diceva non <lb/>dovere far maraviglia se l'ultima sfera in A ha impeto quanto l'ultima sfera <lb/>in E, perch&egrave;, sebben quella abbia la met&agrave; del pendio, questa &egrave; incalzata e <lb/>premuta da un doppio numero di sfere, ond'&egrave; manifesto come, compensan&shy;<lb/>dosi le parti, si vengano qua e l&agrave; nella composizione a ragguagliare i mo&shy;<lb/>menti. </s></p><p type="main">

<s>Un altro esempio del comunicarsi insieme Galileo e l'Aggiunti, intorno <lb/>al moto delle acque, i loro pensieri, l'abbiamo nella proposta, e nella solu&shy;<lb/>zione di un problema, che nell'Idraulica vedremo essere dei principali, &ldquo; come <lb/>cio&egrave; cammini il negozio dell'accelerarsi l'acqua nel dover passare in un ca&shy;<lb/>nale pi&ugrave; stretto &rdquo; (Alb. </s>

<s>VI, 303). Intorno a ci&ograve; sappiamo che ghiribizzava <lb/>Galileo, infin da quando il primo libro del Castelli correva per Firenze ma&shy;<lb/>noscritto, e lo leggeva l'Aggiunti insieme con Galileo stesso, che a quella <lb/>occasione e in quel tempo, essendogli sovvenuto il sopraddetto problema idrau&shy;<lb/>lico, intanto che ci ripensava egli fra s&egrave;, ne proponeva la soluzione al disce&shy;<lb/>polo e all'amico. </s>

<s>L'investigare quali fossero i pensieri d'ambedue &egrave; la pre&shy;<lb/>sente nostra intenzione, e fra'documenti, dietro i quali ella s'indirizza, per <lb/>quel che principalmente riguarda Galileo, uno ci se ne presenta, da cui si <lb/>vede ch'egli, in mezzo a tante incertezze, ricercava ne'fatti qualche scorta <lb/>pi&ugrave; fida. </s>

<s>L'osservazione di questi fatti, non fidandosi forse degli occhi pro&shy;<lb/>pri, la raccomandava alla sperimentata diligenza del Castelli, che in tal pro&shy;<lb/>posito cos&igrave; rispondeva: &ldquo; Del resto, quanto al problema, che V. S. m'ac&shy;<lb/>cenna, potrei dirli quello che ho considerato qui in Pisa nelle piene d'Arno, <lb/>mentre l'acqua passa sotto gli archi dei ponti, minore sezione di quelle che <lb/>sono avanti il ponte, e dopo passato il ponte. </s>

<s>Ma perch&egrave; ci vorrebbe piutto&shy;<lb/>sto comodit&agrave; di voce, che di penna, mi riserbo a dirle questo con alcune <lb/>altre cosette a bocca &rdquo; (Campori, Carteggio cit., pag. </s>

<s>253, 54). Ma perch&egrave; <lb/>quel che disse a bocca il Castelli a Galileo non ci &egrave; noto, il primo docu&shy;<lb/>mento de'pensieri, ch'ebbe esso Galileo intorno all'accelerarsi l'acqua, pas&shy;<lb/>sando per uno stretto, si ricava da una lettera, nella quale s'espone il dubbio, <lb/>natogli in leggere, nel corollario XI della misura delle acque correnti, l'ar&shy;<lb/>ticolo VI. </s>

<s>Quivi s'accusa dall'Autore di debolezza l'ingegnere Giovanni Fon-<pb xlink:href="020/01/3420.jpg" pagenum="381"/>tana, per aver detto che passasse sotto il ponte Quattrocapi cento cinquant'una <lb/>canna d'acqua premuta, quasi fosse bambagia o lana (Ediz. </s>

<s>cit., pag. </s>

<s>19). <lb/>Ora a Galileo, che aveva anch'egli pensato doversi attribuire l'acceleramento <lb/>dell'acqua sotto il ponte a qualche pressione, parve l'accusa del Castelli incon&shy;<lb/>siderata, potendo esser premute anche le materie, che non cedono, come cede <lb/>la bambagia o la lana: anzi il non cedere &egrave; talvolta condizione richiesta al <lb/>moto progressivo, com'avviene del nocciolo di ciriegia premuto dalle dita. </s></p><p type="main">

<s>A questo esempio, che tante volte ricorre in Aristotile e nei seguaci di <lb/>lui, pare si riducesse per Galileo a principio la desiderata soluzione, alla <lb/>quale per&ograve; sentiva di non potere acquietarsi, per aver troppo del peripate&shy;<lb/>tico e del volgare. </s>

<s>Rivolgendosi perci&ograve; a cercare qualche altra cosa di me&shy;<lb/>glio, pens&ograve; a quelle pressioni, che si fanno perpendicolarmente dall'acqua, <lb/>sopra l'acqua che le soggiace, o che si producono dall'embolo dello stan&shy;<lb/>tuffo dentro una canna, secondo qualunque direzione: pensiero, natogli senza <lb/>dubbio dalla languida risonanza di quelle tradizioni, alle quali l'Innovator <lb/>baldanzoso protestava di voler chiuder le orecchie. </s>

<s>Le relazioni che, per lo&shy;<lb/>gica e naturale necessit&agrave;, passano fra il nuovo e l'antico, appariranno in <lb/>seguito pi&ugrave; manifeste, ma intanto &egrave; bene riferire quel documento di lettera. </s>

<s><lb/>che il d&igrave; 8 Gennaio 1629 Galileo scriveva al Castelli: &ldquo; Per diligenza usata, <lb/>cos&igrave; egli comincia, non ho potuto ritrovare le cinquanta copie, che scrive <lb/>mandarmi della sua Scrittura, ed essa non mi dice niente dove io debba far <lb/>capo per ritrovarle: per&ograve; supplisca con altra sua. </s>

<s>Feci presentare le due al <lb/>serenissimo Granduca, e principe don Lorenzo, da Vincenzio mio figlio, es&shy;<lb/>sendo che li tempi contrarissimi alla mia sanit&agrave; m'hanno tenuto finora per <lb/>tre settimane con doglie acerbissime. </s>

<s>La Scrittura &egrave; piaciuta assai a tutti che <lb/>l'hanno letta, e qua si trattava di ristamparla, ma intendo ch'ella non se <lb/>ne contenta. </s>

<s>Io la rilegger&ograve; pi&ugrave; volte, e se mi parr&adot; alcuna cosa da notarsi <lb/>l'avviser&ograve;, in occasione che bisognasse ristamparla, e per ora mi sovviene di <lb/>quell'acqua premuta, che ella interpetra come condensata, dalla quale oppo&shy;<lb/>sizione potrebbe l'Autore difendersi che non &egrave; necessario che l'acqua pre&shy;<lb/>muta si condensi, per scappar con maggior impeto, siccome il nocciolo di <lb/>ciriegia, premuto dalle dita, scappa con velocit&agrave; senza condensarsi, e l'acqua <lb/>stessa premuta nello schizzatoio salta anche in su, e compressa dal proprio <lb/>peso esce dalla botte velocemente &rdquo; (Alb. </s>

<s>VI, 323, 24). </s></p><p type="main">

<s>Dopo due settimane il Castelli rispondeva a questa di Roma cos&igrave;, dimo&shy;<lb/>strando di non esser ben penetrato addentro al pensiero di Galileo: &ldquo; Quanto <lb/>a quella difficolt&agrave;, che fa dell'acqua premuta, non credo che il Fontana possa <lb/>pretendere quella fuga, che V. S. pensa: prima, perch&egrave; non l'ha detto, e <lb/>di pi&ugrave;, se lo voleva dire, e se intendeva questo punto della velocit&agrave;, fu in <lb/>tutto vanissima l'opera sua di quelle misure. </s>

<s>Ma rispondendo pi&ugrave; vivamente <lb/>dico che in tal senso non &egrave; vero che l'acqua occupi minor loco, per essere <lb/>premuta, come dice il Fontana, ma per essere veloce, come dico io &rdquo; (ivi. </s>

<s><lb/>IX, 147). Ripetiamo che il Castelli, cosi rispondendo, non aveva penetrato il <lb/>pensiero di Galileo, qual'era, non d'investigar la ragione perch&egrave; l'acqua <pb xlink:href="020/01/3421.jpg" pagenum="382"/>occupi minor luogo, ci&ograve; che egli non dubitava d'attribuire alla sopravvenuta <lb/>velocit&agrave;, ma di ricercar la causa, che produce una tale velocit&agrave;, e per cui <lb/>di fatto passa tutta la piena sotto l'arco del ponte. </s>

<s>Dichiaratosi perci&ograve; me&shy;<lb/>glio col Castelli, e significatogli espressamente non potere la ricercata causa <lb/>dipender da altro, che da qualche pressione, comunque ella avvenga, e in <lb/>qualunque modo si faccia; avendo esso Castelli allora ben inteso lo stato <lb/>della questione, vi rivolse sopra il pensiero, e per lettera del 24 Febbraio 1629 <lb/>annunziava cos&igrave; di averla risoluta: &ldquo; Io credo di avere incontrate alcune cose <lb/>belle in risposta di quell'acqua premuta, le quali non ho ancora ben disteso <lb/>in netto, ed avrei estremo bisogno d'esserle per quattro o sei giorni appresso, <lb/>ma in ogni modo spero, per l'ordinario che viene, mandarle l'ossatura del <lb/>mio pensiero, che credo che le sar&agrave; di gusto &rdquo; (Campori, Casteggio cit., <lb/>pag. </s>

<s>279). </s></p><p type="main">

<s>Ignoriamo se queste speranze avessero effetto, e non si potendo perci&ograve; dire <lb/>ai Lettori qual si fosse propriamente il pensiero del Castelli, passeremo a ri&shy;<lb/>ferire quello di Galileo, che si &egrave; intanto risoluto di mezzo ai dubbi, e di que&shy;<lb/>sta risoluzione ci &egrave; rimasto spiegatissimo documento. </s>

<s>Ripudiata l'ipotesi che <lb/>l'acqua possa scivolare, premuta dalle pile del ponte, come, fra le dita che lo <lb/>premono, schizza il nocciolo di ciriegia; non rimaneva a Galileo di scegliere, <lb/>in quelle sue prime speculazioni, se non che fra l'ipotesi degli Idraulici con&shy;<lb/>temporanei di Leonardo da Vinci, che cio&egrave; le pressioni nascessero dal peso <lb/>dell'acqua sollevatosi prima d'entrar nello stretto, o fra quell'altra ipotesi <lb/>del Cardano, che cio&egrave; le moli stesse sollevatesi precedentemente, incalzino <lb/>via via e sospingano al moto le susseguenti. </s>

<s>Ma poi ripudi&ograve; anche queste <lb/>ragioni, per attenersi a una sua propria nuovamente pensata, e che &egrave; gran <lb/>parte dell'Idraulica galileiana; quella vogliam dire che gli accrescimenti delle <lb/>velocit&agrave;, piuttosto che alla pendenza dell'alveo, si debbano attribuire alla <lb/>pendenza della superficie. </s>

<s>Nella maggior pendenza dunque, che prende l'acqua <lb/>in passar sotto gli archi dei ponti, Galileo riconosceva la causa di quella mag&shy;<lb/>gior velocit&agrave;, che fa smaltire la piena come se corresse libera fra le aperte <lb/>sponde del fiume. </s>

<s>&ldquo; Forse potrebbe accadere (cos&igrave; leggesi nel trattato allo <lb/>Staccoli intorno al regolare il Bisenzio) che l'acqua rigurgitando, rigonfiasse <lb/>alquanto sulle svolte: ma questo non diminuir&agrave; punto la sua velocit&agrave;, perch&egrave; <lb/>tale alzamento le servir&agrave; per far divenire la sua pendenza maggiore nella <lb/>parte del canale seguente, dove col crescer velocit&agrave; verr&agrave; a compensare il <lb/>ritardamento patito sul principio della svolta, operando un effetto simile a <lb/>quello, che noi giornalmente vediamo accader nei fiumi assai colmi, mentre <lb/>nel passare sotto gli archi dei ponti, urtando nelle pile o imposte di detti <lb/>archi, gli conviene ristringere l'acque, le quali rialzandosi nelle parti di sopra <lb/>si fanno pendenza tale sotto gli archi, che correndovi velocissimamente senza <lb/>scapito alcuno, continovando il corso loro non consumano un sol momento <lb/>di tempo di pi&ugrave; nel loro intero viaggio, che se avessero avuto il canale li&shy;<lb/>bero &rdquo; (Alb. </s>

<s>VI, 366, 67). </s></p><p type="main">

<s>Cos&igrave; veniva finalmente risoluto da Galileo il problema del crescersi le <pb xlink:href="020/01/3422.jpg" pagenum="383"/>velocit&agrave;, diminuendosi le sezioni, intorno al quale era stato per lungo tempo <lb/>in cos&igrave; gran travaglio. </s>

<s>E come l'ebbe risoluto, lo confer&igrave; negli amichevoli <lb/>colloqui con l'Aggiunti, che ebbe presto, ripensandoci meglio, a scoprire in <lb/>quella soluzione qualche difetto, sembrandogli derivata piuttosto da partico&shy;<lb/>lari osservazioni, che da leggi universali. </s>

<s>L'acqua diceva non s'affretta so&shy;<lb/>lamente sotto gli archi dei ponti in tempo di piena, ma e nello stretto di <lb/>piccoli canali, dove l'alzamento della superficie che precede l'entrata, e il <lb/>pendio di quella che succede son di tanto poco momento, da non si potere <lb/>attribuire a loro la causa di cos&igrave; repentina sollecitazione di moto. </s></p><p type="main">

<s>Non potendosi dunque, proseguiva l'Aggiunti a ragionare, fare in tali <lb/>accidentalit&agrave; di superficie consistere un effetto tanto essenziale, convien ri&shy;<lb/>dursi a pi&ugrave; alti principii. </s>

<s>Si sa dalle Storie passate che egli fu il primo e <lb/>l'unico, nella Scuola galileiana, a formulare le leggi della comunicazione dei <lb/>moti, derivandole dal modo di misurar le forze compostamente per la velo&shy;<lb/>cit&agrave;, e per la quantit&agrave; di materia. </s>

<s>Di qui veniva a formularsi la proposizione, <lb/>in particolar modo da lui stesso poi dimostrata: <emph type="italics"/>La medesima velocit&agrave;, nelle <lb/>maggiori e minori quantit&agrave; di materia, opera pi&ugrave; o meno potentemente, <lb/>secondo la proporzione di essa materia.<emph.end type="italics"/> Che se le potenze o le forze sol&shy;<lb/>lecitanti al moto sono uguali, velocit&agrave; dunque e quantit&adot; di materia si rispon&shy;<lb/>deranno costantemente in ragione contraria. </s>

<s>Ecco a quali principii essenziali <lb/>s'informava, e da quale appropriata universalit&agrave; di ragioni faceva l'Aggiunti <lb/>dipendere la soluzion del problema: La potenza che incalza la piena &egrave; la me&shy;<lb/>desima nel largo dell'alveo e sotto l'arco del ponte: ma perch&egrave; qui la quan&shy;<lb/>tit&agrave; di materia &egrave; diminuita, necessariamente consegue che a quella propor&shy;<lb/>zione la velocit&agrave; invece s'accresca. </s></p><p type="main">

<s>La principal proposizione, dalla quale svolgevasi il progresso idraulico <lb/>del Castelli, veniva cos&igrave; dimostrata dai suoi veri principii, e a ci&ograve; intende&shy;<lb/>vano le critiche dell'Aggiunti. </s>

<s>Non &egrave; vero ch'egli avesse, come fu riferito <lb/>da malevoli o da male informati all'Autore della Misura delle acque correnti, <lb/>notati errori nel libro di lui: non si dubitava per niente della verit&agrave; delle <lb/>conclusioni, ma si diceva solo che mancavano di fondamento, perch&egrave; i sem&shy;<lb/>plici fatti osservati e l'esperienze non possono partecipare alle proposizioni <lb/>quella certezza geometrica, della quale presumeva di averle insignite lo stesso <lb/>Castelli. </s>

<s>Noi, mentre da una parte confermiamo che l'Aggiunti, in tal pro&shy;<lb/>posito, aveva ragione, non possiamo non deplorare dall'altra i danni dalla <lb/>morte recati ai progressi della Scienza italiana, la quale sarebbe venuta per <lb/>lui a dare cos&igrave; per tempo le leggi della percossa e del corso dei fiumi, non <lb/>dimostrate dietro alcune fisiche propriet&agrave; dei solidi e dei liquidi, com'ave&shy;<lb/>vano fatto Galileo e il Castelli, ma concluse da quella universalit&agrave; di prin&shy;<lb/>cipii, da cui dipendono le ragioni del moto in ogni sorta di corpi gravi. </s></p><p type="main">

<s>Le censure dell'Aggiunti, come si vede, erano cose di bene altra im&shy;<lb/>portanza, da que'primi dubbi mossi da Galileo intorno a certe storiche im&shy;<lb/>propriet&agrave;, che alcuno avrebbe potuto notar facilmente nel libro del Castelli. </s>

<s><lb/>Bench'esso Galileo sembrasse rimaner sodisfatto delle risposte, forse non si <pb xlink:href="020/01/3423.jpg" pagenum="384"/>rimosse mai dalla mente di lui la persuasione che a nessuno fosse prima <lb/>sovvenuto il pensiero d'applicare le velocit&agrave; alla misura delle acque correnti. </s>

<s><lb/>Dai documenti poco addietro citati apparisce che il Castelli stesso ebbe a <lb/>temperare quella sua prima sentenza, cos&igrave; assolutamente pronunziata, intorno <lb/>alla novit&agrave; della sua Scienza idraulica, e quasi presentisse nell'animo che <lb/>le osservazioni amorevoli del Maestro si sarebbero nel pi&ugrave; libero giudizio <lb/>dei posteri convertite in accuse acerbe di plagio; &egrave; sollecito di dichiararsi <lb/>ch'ei non nega essere le velocit&agrave; state prima avvertite, ma vuol dir sola&shy;<lb/>mente che non furono bene intese e spiegate. </s>

<s>Aveva infatti appena finito di <lb/>rispondere in fretta a Galileo, giustificandosi dell'accusa data all'ingegnere <lb/>Fontana, che cos&igrave; caldamente soggiunge: &ldquo; La voglio solo pregare che os&shy;<lb/>servi la cautela, con la quale io cammino nella mia scrittura, di dire sem&shy;<lb/>pre che non &egrave; stata bene intesa, p&igrave;enamente spiegata, al vivo penetrata, e <lb/>simili cose, la velocit&agrave; dell'acqua e la sua forza in fare scemare la misura &rdquo; <lb/>(Alb. </s>

<s>IX, 146, 47). </s></p><p type="main">

<s>Nonostante queste cautele, rimase la scrittura del Castelli improntata di <lb/>tale presunzione, che, non potendola alcuni patire, non risparmiarono perci&ograve; <lb/>all'Autore quella presentita acerbit&agrave; delle censure. </s>

<s>Raffaello Fabbretti, nel <lb/>suo trattato <emph type="italics"/>De aquis et aquaeductibus veteris Romae,<emph.end type="italics"/> non poteva natural&shy;<lb/><gap/>ente dispensarsi dal commemorare Giulio Sesto Frontino, dai citati passi <lb/>del quale argomentando alla principale importanza, che dall'antico Prefetto <lb/>romano si dava alle velocit&agrave; nel dispensar l'acque, secondo la loro pi&ugrave; giu&shy;<lb/>sta misura; conclude con l'ironia di queste parole: &ldquo; Unde explodendum <lb/>esse dicimus p. </s>

<s>Castelli, quasi Frontinus magnum illud suum theorema, ex <lb/>velocitate aquae modum ipsius variare ignoraverit &rdquo; (<emph type="italics"/>De aquis<emph.end type="italics"/> cit., Ro&shy;<lb/>mae 1680, pag. </s>

<s>128). Segue poi il Fabbretti a citar da Frontino l'articolo, <lb/>in cui, dop'aver narrato com'avesse raccolte varie misure d'acqua, in vari <lb/>stati e condizioni di un medesimo acquedotto; soggiunge: &ldquo; cuius rei ratio <lb/>est quod vis aquae rapacior, ut ex largo et celeri flumine excepta, <emph type="italics"/>veloci&shy;<lb/>tate ipsa ampliat modum &rdquo;<emph.end type="italics"/> (ibid.). E perch&egrave; insomma, a giudizio dello <lb/>stesso Fabbretti, non ha fatto altro il Castelli che stemperare in lunghe e <lb/>noiose parole il laconico linguaggio dello Scrittore antico, per dare di ci&ograve; una <lb/>prova ai Lettori, vuol che confrontino quel che si legge, nel proemio del <lb/>Moderno, dell'acqua che, uscendo da due cannelle soprapposte, la pi&ugrave; alta <lb/>getta men della pi&ugrave; bassa a proporzion dell'altezza; con questo che Fron&shy;<lb/>tino, fatta la medesima supposizione, potentemente condensa in tali parole: <lb/><emph type="italics"/>&ldquo; Inferior plus trahit, superius minus ducit quia cursus aquae ab infe&shy;<lb/>riori rapitur &rdquo;<emph.end type="italics"/> (ibid.). </s></p><p type="main">

<s>Dopo il Fabbretti venne il Poleni, che divulgando, come altrove dicemmo, <lb/>la scrittura geometrica del Buteone, <emph type="italics"/>De fluentis aquae mensura,<emph.end type="italics"/> ebbe inten&shy;<lb/>zione di rammentare a chi l'aveva oramai dimenticato come, infino dal 1554, <lb/>che vuol dire 74 anni prima del Castelli, era in Francia divulgato un libro, <lb/>in cui s'insegnava il pi&ugrave; giusto modo di dispensar l'acqua, misurandone la <lb/>velocit&agrave; del corso con l'orologio alla mano, non importa s'egli era una cles-<pb xlink:href="020/01/3424.jpg" pagenum="385"/>sidra antica, invece di un pendolo nuovo. </s>

<s>All'ultimo il Venturi, mandando <lb/>il fiato dalla sua propria trachea nella muta laringe dell'Arconati, annun&shy;<lb/>ziava al mondo scientifico, stupito, che la Scienza idraulica del Castelli, tutt'al&shy;<lb/>tro ch'essere a quel tempo nuova, si trovava pi&ugrave; ampiamente e pi&ugrave; sottil&shy;<lb/>mente trattata nei manoscritti di Leonardo da Vinci. </s>

<s>La piccola scintilla, <lb/>in Parigi, second&ograve; quella gran fiamma, che trov&ograve; pascolo cos&igrave; gradito nella <lb/>penna di tanti scrittori, alcuni de'quali, per vendetta dell'usurpazione e per <lb/>amor di giustizia, proposero che l'essere le velocit&agrave; in reciproca ragione delle <lb/>sezioni si dovesse dire dall'ora in poi legge di Leonardo da Vinci, e non pi&ugrave; <lb/>del Castelli. </s></p><p type="main">

<s>Vorremmo volentieri sussurrar nelle orecchie di cotesti zelanti che pi&ugrave; <lb/>giusto sarebbe stato appellare la detta legge idraulica dal nome del Cardano, <lb/>il quale non la scrisse in private carte disperse, ma in bei volumoni in folio <lb/>stampati, se non ci premesse maggiore curiosit&agrave; di domandare, perch&egrave; mai, <lb/>volendosi in ogni modo far la rivendicazione a favore di un nome famoso, <lb/>non preferissero costoro a Leonardo lontano, e dal partecipare con gli studii <lb/>del Castelli s&igrave; alieno, il pi&ugrave; prossimo e immediato magistero di Galileo. </s>

<s>Dai <lb/>teoremi idrostatici di lui infatti vedemmo come scendesse per facile corolla&shy;<lb/>rio la legge delle velocit&agrave; reciproche delle sezioni. </s>

<s>Anzi &egrave; notabile che Ga&shy;<lb/>lileo stesso, nelle s&igrave; frequenti conferenze ch'egli ebbe col Castelli intorno al <lb/>moto dell'acqua, non ne facesse mai motto, e lasciasse intera al Discepolo <lb/>la compiacenza di quel ch'egli diceva pensiero suo nuovo. </s>

<s>Nemmeno il Vi&shy;<lb/>viani, anche dopo aver vedute le note, nelle quali Galileo si proponeva di <lb/>risolvere il problema della quantit&agrave; d'acqua compresa nella troscia, accenn&ograve; <lb/>mai, che da noi si sappia, alle relazioni che passano fra le dottrine del Di&shy;<lb/>scorso intorno i galleggianti, e il libro della Misura delle acque correnti. </s></p><p type="main">

<s>Unico forse il Montanari, in mezzo alla numerosa Scuola galileiana, in&shy;<lb/>dic&ograve; le dette relazioni nel suo dialogo intitolato <emph type="italics"/>Le forze di Eolo,<emph.end type="italics"/> l&agrave; dove, <lb/>dai momenti nella stadera passando ai momenti nel sifone idrostatico, af&shy;<lb/>ferma che le loro leggi, dimostrate da Galileo nel suo strumento, son quelle <lb/>stesse applicate poi dal Castelli al corso dei fiumi. </s>

<s>&ldquo; Leggete, dice nel Dia&shy;<lb/>logo citato il Montanari stesso all'interlocutor suo Gozzadini, a carte 15 delle <lb/>Galleggianti, ove il Galileo mostra come la forza, ossia il momento dell'acqua <lb/>stagnante in un vaso grande, che comunica con altro vaso angusto, e seco <lb/>s'equilibra in orizonte, non per altro s'eguaglia al momento di quella del <lb/>vaso pi&ugrave; angusto, se non perch&egrave; l'acqua, nel vaso pi&ugrave; angusto, quando do&shy;<lb/>vesse moversi, e cedere alla pressione del maggiore, si moverebbe ad alto <lb/>con velocit&agrave;, appunto tanto pi&ugrave; grande dell'abbassamento che ella farebbe <lb/>nel vaso maggiore, quanto &egrave; pi&ugrave; grande la superficie del maggiore di quella <lb/>del minore. </s>

<s>Onde, a causa di questa reciproca proporzione della poca ve&shy;<lb/>locit&agrave; nel primo, alla molta nel secondo, e dell'angusta sezione del secondo <lb/>vaso alla pi&ugrave; ampia e capace del primo; si mantengono in equilibrio. </s>

<s>Ed <lb/>a maggior chiarezza notate ancora ci&ograve; che dimostra l'abate Castelli, nelle <lb/>sue <emph type="italics"/>Acque correnti,<emph.end type="italics"/> ove fa vedere che un fiume, correndo per un canale <pb xlink:href="020/01/3425.jpg" pagenum="386"/>or pi&ugrave; largo or pi&ugrave; stretto, ad ogni modo passa in tempi uguali ugual quan&shy;<lb/>tit&agrave; d'acqua per le sezioni medesime, ancorch&egrave; tanto disuguali, mercecch&egrave; <lb/>nella sezione pi&ugrave; angusta egli per appunto altrettanto pi&ugrave; veloce si muove <lb/>che nell'ampla, quanto questa &egrave; pi&ugrave; grande di quella. </s>

<s>Onde potiamo dire <lb/>che tutta la forza e momento di quel fiume, che era diffusa nell'alveo pi&ugrave; <lb/>amplo, al passar per un altro pi&ugrave; angusto si converte in tanta maggior ve&shy;<lb/>locit&agrave;, quanta &egrave; la diminuzione che gli accade nell'ampiezza &rdquo; (Parma 1694, <lb/>pag. </s>

<s>146, 47). </s></p><p type="main">

<s>L'osservazione giustissima del Montanari sfuggi ai magnificatori di Ga&shy;<lb/>lileo, che perci&ograve; a lei sostituirono giudizi senza criterio. </s>

<s>Il Nelli per esem&shy;<lb/>pio asser&igrave; e conferm&ograve; che &ldquo; il Trattato sopra la misura delle acque correnti, <lb/>pubblicato dal Castelli, &egrave; parto dell'ingegno di Galileo, e che questo Filosofo <lb/>permesse a quel Monaco di pubblicarlo col suo nome, come fece della scrit&shy;<lb/>tura contro Lodovico delle Colombe &rdquo; (<emph type="italics"/>Vita di Galileo,<emph.end type="italics"/> Losanna 1793, <lb/>pag. </s>

<s>490). L'Alb&egrave;ri, in nota a pag. </s>

<s>324 del T. VI della sua Edizione com&shy;<lb/>pleta, ridusse a miglior senno l'asserzione inconsiderata, ma ambedue troppo <lb/>alla lettera interpetrarono l'espressione: <emph type="italics"/>se le cose che sono scritte nell'ope&shy;<lb/>retta son vere, come io credo, ella sa che l'opera &egrave; sua<emph.end type="italics"/> (Alb. </s>

<s>IX, 146): <lb/>espressione, che poteva ridursi al suo vero significato, collazionandola con <lb/>quest'altra, dallo stesso Castelli precedentemente usata nello scrivere al me&shy;<lb/>desimo Galileo: <emph type="italics"/>ho cercato di seguitare i vestigi di V. S., alla quale, se <lb/>nella mia Scrittura ci &egrave; cosa di buono, tutto riferisco<emph.end type="italics"/> (ivi, pag. </s>

<s>141). </s></p><p type="main">

<s>Del resto la questione del mio e del tuo, relativamente alla risposta <lb/>contro Lodovico delle Colombe, &egrave; decisa dalle seguenti parole, scritte a Ga&shy;<lb/>lileo il d&igrave; 21 Gennaio 1615 dal Castelli, a proposito della pubblicazione della <lb/>citata Scrittura apologetica: &ldquo; Mi vien fatta istanza grandissima del mio <lb/>libro, se per&ograve; si pu&ograve; chiamar mio, dove V. S. ha posto tanto del suo &rdquo; (MSS. <lb/>Gal., P. III, T. VII, fol. </s>

<s>40): come l'altra questione, relativa al trattato delle <lb/>acque correnti, resta con non minor certezza decisa dai fatti sopra narrati, <lb/>dai quali apparisce che Galileo si mostr&ograve; nuovo alle proposte del Castelli, e <lb/>ricev&egrave; da esse, a speculare intorno al moto delle acque, l'occasione e l'im&shy;<lb/>pulso. </s>

<s>Le quali cose, quando fossero state considerate dal Zendrini, non si <lb/>sarebbe fatto maraviglia, nella sua prefazione al Trattato delle acque cor&shy;<lb/>renti, che la repubblica di Venezia, allora in gran sollecitudine e dispendio <lb/>di dare un nuovo alveo al Po e alla Brenta, non avesse consultato mai in&shy;<lb/>torno a ci&ograve; Galileo, suo celebre matematico nello studio di Padova (<emph type="italics"/>Autori <lb/>che trattano del moto delle acque,<emph.end type="italics"/> T. VIII, Firenze 1770, pag. </s>

<s>XIII). </s></p><p type="main">

<s>La scienza era da'suoi principii matematici dimostrata nelle Scuole, ai <lb/>tempi di Leonardo da Vinci, e le dimostrazioni scientifiche venivano divul&shy;<lb/>gate dai libri del Cardano e del Buteone, ma intanto, non solamente in Ve&shy;<lb/>nezia e nel rimanente d'Italia, ma anche appresso le altre nazioni erano le <lb/>opere idrauliche affidate alla pratica dei cos&igrave; detti Periti ingegneri, e nella <lb/>dispensa delle acque si duravano a commettere i medesimi errori, cos&igrave; nel <lb/>Delfinato, patria del Buteone, come nella Lombardia, patria del nostro Ca-<pb xlink:href="020/01/3426.jpg" pagenum="387"/>stelli. </s>

<s>Qualunque siano perci&ograve; le censure, date al Matematico di Papa Ur&shy;<lb/>bano VIII, nessuno potr&agrave; negare che da lui primo e solo cominci&ograve; la scienza <lb/>a dar regola all'arte: da lui primo e solo s'impar&ograve; a far con giustizia la <lb/>dispensa delle acque. </s></p><p type="main">

<s>Ma, esaminando pi&ugrave; diligentemente, quelle censure si trovano concluse <lb/>nel dire che la scienza del Castelli non era nuova. </s>

<s>Il detto verissimo, e con&shy;<lb/>fermato gi&agrave; dalla Storia, non dissente dal concedere che il Castelli abbia <lb/>fatto rivivere una cosa morta, ci&ograve; che alcuni riducono a qualche clandestino <lb/>connubio con le vecchie tradizioni, repudiate allora da tutti, e perci&ograve; da tutti <lb/>dimenticate. </s>

<s>La falsit&agrave; per&ograve; di questa opinione si scopre, ripensando alle ori&shy;<lb/>gini tanto diverse per la scienza degli Autori antichi, e per quella del mo&shy;<lb/>derno Scrittore, cosicch&egrave; questi pot&egrave; con coscienza pura asserire che il suo <lb/>pensiero, se non cos&igrave; nudo come lo presentava anche Frontino, almeno qual <lb/>si dava ordinato a sistema, era nuovo. </s>

<s>Mentre infatti l'Idraulica di Leonardo <lb/>e del Cardano s'informava ai principii matematici del Nemorario, quella del <lb/>Castelli non ebbe altro fondamento che nella osservazione di alcuni fatti pre&shy;<lb/>senti, e dai quali con rammarico si conosceva doverne non legger danno se&shy;<lb/>guitare al pubblico e ai privati. </s>

<s>Da questa medesima diversa origine di prin&shy;<lb/>cipii s'argomenta altres&igrave; all'indipendenza del Castelli dal magistero di Galileo, <lb/>il quale, non dai fatti, ma dalle leggi dei momenti dimostrando le ragioni <lb/>degli equilibrii idrostatici, dava altro modo a dedur che le velocit&agrave; hanno <lb/>reciproca ragione delle sezioni. </s></p><p type="main">

<s>Tale essendosi dunque la conclusione, alla quale siamo stati condotti dal <lb/>confrontare la scienza antica con la nuova, per quel che semplicemente ri&shy;<lb/>guarda la considerazione delle velocit&agrave; nella misura delle acque correnti; c&igrave; <lb/>rimane, come soggetto anche di maggiore importanza, a proseguire il con&shy;<lb/>fronto, tra le leggi assegnate a quelle medesime velocit&agrave; nell'Idraulica trattata <lb/>da Leonardo e dal Cardano, e in quella nuovamente restaurata dal Castelli. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>Come le leggi delle velocit&agrave; nei solidi ebbero una trattazione diversa, <lb/>ora considerandoli nelle loro libere cadute, ora nelle loro scese lungo i piani <lb/>inclinati; cos&igrave; per analogia dev'essere stato delle acque. </s>

<s>Diremo perci&ograve; di&shy;<lb/>stintamente delle proporzioni delle velocit&agrave; assegnate dai varii autori al moto <lb/>di esse acque, sia quando scendono o salgono nel fluire dai vasi, in trosce <lb/>e in zampilli, sia quando scorrono per le pendenze dei canali o per gli alvei <lb/>dei fiumi. </s></p><p type="main">

<s>Per quel che riguarda le trosce, anche gli antichi, come s'ha da alcune <lb/>note di Leonardo da Vinci, attribuivano il loro assottigliarsi agl'incrementi <lb/>successivi delle velocit&agrave;, le quali non dubitarono di far proporzionali agli <lb/>spazi, a quel modo che facevano per tutti gli altri corpi gravi cadenti. </s>

<s>Sco-<pb xlink:href="020/01/3427.jpg" pagenum="388"/>pertosi poi che esse velocit&agrave; stanno invece come le radici degli spazi, pareva <lb/>certissima l'applicazione della nuova legge anche ai liquidi. </s>

<s>Galileo infatti <lb/>ne porgeva l'esempio nel risolvere il problema, per noi fatto noto, della quan&shy;<lb/>tit&agrave; d'acqua compresa nella troscia cadente dalla secchia, per la misura della <lb/>forza della percossa, e nel segnar la scala degli spazi sempre pi&ugrave; brevi, pas&shy;<lb/>sati dalle gocciole separate, quanto pi&ugrave; zampillando salgono in alto, dove il <lb/>moto &egrave; pi&ugrave; lento (V. nel nostro V Tomo a pag. </s>

<s>217). </s></p><p type="main">

<s>Il Castelli per&ograve; lascia i Lettori in una incertezza penosa. </s>

<s>Nel XV corol&shy;<lb/>lario del suo primo libro, applicando la proposizione, da s&egrave; generalmente di&shy;<lb/>mostrata, a spiegar quell'assottigliarsi, che si osserva nelle acque cadenti; <lb/>dice un tal fatto da null'altro dipendere, che dall'acquisto di maggior ve&shy;<lb/>locit&agrave; dell'acqua nel seguitare a cadere, &ldquo; essendo notissima conclusione ap&shy;<lb/>presso i Filosofi che i corpi gravi cadenti, quanto pi&ugrave; si scostano dal princi&shy;<lb/>pio del loro movimento, tanto pi&ugrave; acquistano di velocit&agrave;, e perci&ograve; l'acqua, <lb/>come corpo grave cadendo, si va velocitando, e per&ograve; scema di misura e si <lb/>rassottiglia (<emph type="italics"/>Della misura delle acque<emph.end type="italics"/> cit., pag. </s>

<s>28). Qui la legge della ve&shy;<lb/>locit&agrave;, rispetto al tempo e allo spazio, non &egrave; determinata, e non si dubite&shy;<lb/>rebbe doversi intendere per que'Filosofi i peripatetici (che pure ammette&shy;<lb/>vano tanto pi&ugrave; velocitarsi i cadenti, quanto pi&ugrave; si dilungano dal principio del <lb/>moto) piuttosto che Galileo, quando a intender cos&igrave; non consigliasse il pensiero <lb/>che doveva esser gi&agrave; partecipata al Castelli, dal suo proprio Maestro, la sco&shy;<lb/>perta legge dei moti accelerati. </s>

<s>N&egrave; da altro che dal pensar cos&igrave; dee essere <lb/>il Barattieri stato indotto a scriver queste parole: &ldquo; Pu&ograve; nascere ancora <lb/>qualche difficolt&agrave; nel considerare quell'effetto, che si concede a'pesi gravi <lb/>cadenti, che si fanno pi&ugrave; veloci quanto pi&ugrave; si discostano dal suo principio, <lb/>pensando forse che si abbi da considerare che segua tal effetto, anche nel <lb/>corso delle acque correnti dei fiumi, come appunto pare che ne sia il pen&shy;<lb/>siero dell'abbate Castelli, al XV de'suoi corollari, e del sig. </s>

<s>Bagliani, quando <lb/>nel proemio de'suoi Liquidi mostra che tale aumento non solo si faccia, ma <lb/>che segua, crescendo la sua velocit&agrave; con la regola delle progressioni aritme&shy;<lb/>tiche. </s>

<s>&rdquo; Cos&igrave; il Barattieri (<emph type="italics"/>Architettura delle acque,<emph.end type="italics"/> P. I, Piacenza 1697, <lb/>pag. </s>

<s>169, 70) senza dichiararsi che il Baliani certamente intendeva, che <lb/>quelle progressioni aritmetiche erano de'numeri impari ab unitate. </s></p><p type="main">

<s>In ogni modo, come nel corollario XV <emph type="italics"/>pare<emph.end type="italics"/> che il Castelli ammetta ve&shy;<lb/>locitarsi l'acqua, che liberamente cade, a proporzione delle radici delle al&shy;<lb/>tezze; cos&igrave; <emph type="italics"/>pare<emph.end type="italics"/> che nel Proemio ammetta essere le velocit&agrave; degli efflussi dai <lb/>vasi proporzionali alle semplici altezze dei livelli. </s>

<s>&ldquo; Esca, egli dice, l'acqua <lb/>per due cannelle uguali d'ampiezza, una posta nella parte inferiore del vaso, <lb/>e l'altra nella parte superiore: &egrave; manifesto che, nel tempo, nel quale dalla <lb/>parte superiore uscir&agrave; una determinata misura d'acqua, dalla parte inferiore <lb/>usciranno quattro, cinque e assai pi&ugrave; delle medesime misure, secondo che <lb/>sar&agrave; maggior la differenza dell'altezza delle cannelle, e la lontananza della <lb/>superiore cannella dalla superficie o livello dell'acqua del vaso &rdquo; (<emph type="italics"/>Della mi&shy;<lb/>sura ecc.,<emph.end type="italics"/> pag. </s>

<s>5). </s></p><pb xlink:href="020/01/3428.jpg" pagenum="389"/><p type="main">

<s>Elia Lombardini argutamente not&ograve; che in questa proposizione si con&shy;<lb/>tiene un errore manifesto, &ldquo; non gi&agrave; di stampa, ma di concetto, dovendo <lb/>essere maggiore l'efflusso della cannella inferiore, al confronto della supe&shy;<lb/>riore, quanto <emph type="italics"/>minore<emph.end type="italics"/> e non <emph type="italics"/>maggiore<emph.end type="italics"/> &egrave; la distanza di questa dalla super&shy;<lb/>ficie della conserva &rdquo; (<emph type="italics"/>Dell'origine e del progresso dell'Idraulica in Italia,<emph.end type="italics"/><lb/>Milano 1872, pag. </s>

<s>48). Noi saremmo inclinati ad attribuir l'errore, se non <lb/>alla stampa, a una certa sbadataggine nell'Autore, occasionata senza dubbio <lb/>dall'esser certo da una parte <emph type="italics"/>che l'acqua per la cannella inferiore corre <lb/>e passa con assai maggiore velocit&agrave;, di quello che fa per la superiore,<emph.end type="italics"/> e <lb/>dal non potere intendere dall'altra <emph type="italics"/>qual si sia la cagione di questo negozio.<emph.end type="italics"/><lb/>Ma che una tale ignoranza, cos&igrave; dallo Scrittore stesso confessata, consista nel <lb/>non aver egli saputo intendere che la botte, quanto &egrave; pi&ugrave; piena, per aver <lb/>maggior carico di sopra, tanto getta con pi&ugrave; &igrave;mpeto dalla cannella; non si <lb/>consentir&agrave; al Lombardini da nessuno, che non voglia fare il Castelli piu stu&shy;<lb/>pido dei villici e dei canovai. </s></p><p type="main">

<s>Il mistero dunque non riguardava propriamente le pressioni, fatte se&shy;<lb/>condo le altezze perpendicolari. </s>

<s>Quel che non sapeva intendere il Castelli <lb/>era come quelle pressioni, che dietro la prima supposizione archimedea aveva <lb/>creduto non poter essere che perpendicolari, si rivolgessero poi orizontal&shy;<lb/>mente, anzi per tutti i versi. </s>

<s>Cos&igrave; viene a scoprirsi la radice del male, che <lb/>non in altro s'asconde, se non in que'difetti, ne'quali si rimaneva la domi&shy;<lb/>nante Idrostatica galileiana, e della quale, come fu imbevuto il Castelli, cos&igrave; <lb/>ritroveremo il Cavalieri, insieme con gli altri della medesima Scuola infino <lb/>al Torricelli, che felicemente applic&ograve; all'Idrodinamica la dottrina steviniana <lb/>dell'uguaglianza delle pressioni. </s></p><p type="main">

<s>Il concetto nonostante di una tale uguaglianza essendo balenato per la <lb/>mente degli Idraulici del secolo precedente, fu potissima causa dell'essere, <lb/>intorno al modo di risolvere cos&igrave; fatte questioni, rimasti superiori al Disce&shy;<lb/>polo di Galileo i seguaci del Nemorario. </s>

<s>Questi trovarono assai facile spie&shy;<lb/>gare, come fra gli altri fece il Cardano, &ldquo; cur aquae, a lateribus etiam stan&shy;<lb/>tium paludum, per rimas tabularum impetum secum afferant, cum aqua, <lb/>quae sursum est, et a lateribus premat, ideoque etiam, absque alio cursu <lb/>impetum faciat et impellat. </s>

<s>Velociter igitur aqua fertur per angusta foramina <lb/>iuxta proportionem prementis aquae, ad eam quae protruditur &rdquo; (<emph type="italics"/>De rerum <lb/>var.<emph.end type="italics"/> cit., pag. </s>

<s>69). La pressione dunque dell'acqua <emph type="italics"/>quae sursum est,<emph.end type="italics"/> si ri&shy;<lb/>flette con egual forza anche <emph type="italics"/>a lateribus,<emph.end type="italics"/> ed ecco come riuscisse facile al Car&shy;<lb/>dano spiegare il fatto, rimasto inesplicabile al Castelli, del correr maggior&shy;<lb/>mente veloce l'acqua nella cannella inferiore che nella superiore; e nel <lb/>medesimo tempo ecco aperta la via di dimostrare come, essendo le due can&shy;<lb/>nelle uguali, le quantit&agrave; dell'acqua, versate da quella di sotto e da quella <lb/>di sopra, sian proporzionali alle loro respettive distanze dal supremo livello. </s></p><p type="main">

<s>Leonardo, nella potente sobriet&agrave; del suo proprio linguaggio, va, anche <lb/>pi&ugrave; direttamente, a coglier nel segno. </s>

<s>Dop'avere stabilito che le pressioni <lb/>perpendicolari crescono come le altezze del liquido soprapposto, rispetto alle <pb xlink:href="020/01/3429.jpg" pagenum="390"/>orizzontali conclude che, in ogni grado d'altezza del liquido, la cannella <lb/><emph type="italics"/>acquista gradi di distantia nel gettar da lontano:<emph.end type="italics"/> che vuol dire essere <lb/>le velocit&agrave; del corso, dentro la cannella orizzontale, proporzionali alle altezze. </s>

<s><lb/>Di qui riusc&igrave; a concludere, con tutta quella precision di linguaggio scientifico <lb/>che tanto si fa desiderar nel Castelli, la proposizione altrove da noi citata: <lb/><emph type="italics"/>Dell'acqua, che non manca di una ordinata altezza nella sua superficie, <lb/>tale sar&agrave; la quantit&agrave; dell'acqua, che versa per un dato spiracolo in un <lb/>dato tempo, quale quella della data altezza di esso spiracolo.<emph.end type="italics"/> Cosicch&egrave;, se <lb/>l'altezza sopra lo spiracolo B &egrave; la met&agrave; di quella sopra lo spiracolo G, <emph type="italics"/>dico,<emph.end type="italics"/><lb/>soggiunge quivi Leonardo, <emph type="italics"/>che G verser&agrave; due tanti pi&ugrave; di B, nel medesimo <lb/>tempo, perch&egrave; ha due tanti pi&ugrave; di peso d'acqua sopra di s&egrave;.<emph.end type="italics"/></s></p><p type="main">

<s>Passiamo ora a narrare le varie opinioni intorno alle leggi del veloci&shy;<lb/>tarsi l'acqua, nei canali inclinati, e dentro l'alveo dei fiumi. </s>

<s>Il Cardano, <lb/>in conformit&agrave; co'principii gi&agrave; professati, pronunzi&ograve; dell'acqua corrente per <lb/>un canale inclinato che <emph type="italics"/>quanto magis a principio ortus distiterit<emph.end type="italics"/> (prese le <lb/>distanze secondo le cadenti perpendicolari) <emph type="italics"/>eo velocius movebit.<emph.end type="italics"/> E cos&igrave; ve&shy;<lb/>demmo anche Leonardo applicare al corso dei fiumi la legge delle velocit&agrave; <lb/>proporzionali alle altezze perpendicolari, secondo gl'insegnamenti dati a lui, <lb/>e a tutti gli altri di que'tempi, dal gran Maestro <emph type="italics"/>De ponderibus.<emph.end type="italics"/></s></p><p type="main">

<s>Venuto l'altro grande Maestro ad assegnare ai cadenti altre leggi, il Ca&shy;<lb/>stelli, anche in questo caso, incominci&ograve; a dubitare se fosse la nuova legge <lb/>scoperta applicabile al moto dell'acque. </s>

<s>Volle perci&ograve;, in tali dubbi, aver con&shy;<lb/>siglio con Giovan Batista Baliani, il quale rispose che, da qualche accenno <lb/>avutone da Galileo, venne a incontrarsi, senza cercarla, nella proposizione <lb/>che i corpi di moto naturale vanno aumentando le loro velocit&agrave;, con la pro&shy;<lb/>gressione dei numeri impari, e soggiungeva non creder questa legge appli&shy;<lb/>cabile all'acque, se non fosse per qualche loro breve corso e assai poco in&shy;<lb/>clinato, come il fosso di un mulino. </s>

<s>Ma trattandosi di un canale lungo o di <lb/>un fiume, che declini circa sei o otto per cento, &ldquo; non mi pare, egli dice, <lb/>che l'acqua si vada aumentando di velocit&agrave; con quella proporzione, che cor&shy;<lb/>rerebbe una palla sferica in un piano perfettamente declinante. </s>

<s>So che il <lb/>fiume terminando al mare non casca, ma ritrova intoppo dell'acqua, che lo <lb/>va trattenendo, onde l'acqua del fiume, per questo trattenimento, fa anche <lb/>resistenza a quella di dietro: per&ograve; non mi pare che questa sia bastante ra&shy;<lb/>gione per un tal effetto &rdquo; (Alb. </s>

<s>IX, 142). </s></p><p type="main">

<s>Parve anche al Castelli ragionevole l'opinione del suo dotto amico, ma <lb/>cos&igrave; incerto come rimaneva in assegnare ai liquidi una legge delle velocit&agrave;, <lb/>che fosse a loro tutta propria, scans&ograve; di entrare nei fatti particolari. </s>

<s>Anche <lb/>Galileo sent&igrave; questa difficolt&agrave;, ripensando alle differenze del moto, che son <lb/>tra i solidi e i liquidi, a'quali ultimi applic&ograve; diversa legge, secondo il diverso <lb/>riguardo che aveva, ora alla sola corpulenza delle loro escrescenze, ora al <lb/>solo impeto delle loro cadute. </s></p><p type="main">

<s>Dop'aver dimostrato all'ingegner Bartolotti che una sfera solida ha uguale <lb/>velocit&agrave; sopra due piani, bench&egrave; variamente inclinati, purch&egrave; sia scesa per <pb xlink:href="020/01/3430.jpg" pagenum="391"/>un uguale spazio perpendicolare; soggiunge che &ldquo; sebbene tali conseguenze <lb/>ben seguano nei mobili solidi, nei fluidi credo che procedano assai differen&shy;<lb/>temente &rdquo; (Alb. </s>

<s>VI, 361). Imperocch&egrave;, posta la detta sfera sopra un piano <lb/>perfettamente orizontale, non si muove n&egrave; dall'una parte n&egrave; dall'altra, ma <lb/>resta in quiete, mentre, immaginando una mole sferica d'acqua, questa si <lb/>dissolver&agrave; spianandosi per tutti i versi. </s>

<s>&ldquo; E se le bocche del canale, sog&shy;<lb/>giunge, saranno aperte, scoler&agrave; fuora tutta, salvo che quella minima parti&shy;<lb/>cella, che rimane solamente bagnando il fondo del canale .... essendo che <lb/>l'acqua nello spianarsi acquista pendio &rdquo; (ivi). </s></p><p type="main">

<s>Questa pendenza della superficie nulladimeno non parve a Galileo in <lb/>tutti i casi sufficiente ragione del moto, vedendosi, per esempio nelle piene <lb/>dell'Arno, non aver proporzione il declivio superficiale dell'acqua, verso la <lb/>gran velocit&agrave;, che le si vede acquistare nel corso. </s>

<s>&ldquo; Bisogna dunque, con&shy;<lb/>clude, ricorrere ad altro, per causa del grande augumento nella velocit&agrave;, che <lb/>all'accrescimento della pendenza, e dire che pur una delle potenti ragioni &egrave; <lb/>che, nell'accrescere in tal modo la pendenza, s'accresce sommamente la mole <lb/>e il cumulo dell'acqua, la quale, gravitando e premendo sopra le parti pre&shy;<lb/>cedenti, col peso delle susseguenti, le spinge impetuosamente &rdquo; (ivi, pag. </s>

<s>364). <lb/>Or perch&egrave; le prementi gravit&agrave; crescono come le altezze, si pu&ograve; concludere <lb/>da queste galileiane dottrine che le crescenti acque del fiume ne fanno cre&shy;<lb/>scere la velocit&agrave;, a proporzion delle semplici altezze. </s></p><p type="main">

<s>Trattandosi per&ograve; delle accelerazioni, che in esse acque sopraggiungono <lb/>per effetto delle sole cadute, &egrave; un fatto che Galileo assegna a loro la ragion <lb/>delle radici delle altezze, applicandovi i teoremi dimostrati in quel, ch'egli <lb/>stesso cita, suo <emph type="italics"/>Libro del moto.<emph.end type="italics"/> Proposto infatti il caso che l'alveo d'incli&shy;<lb/>nato si faccia orizontale, &ldquo; non temerei, egli dice, che l'acqua fosse per allen&shy;<lb/>tare il suo corso, essendo sicuro che nel piano orizontale (quando non vi <lb/>sieno impedimenti esterni ed accidentari) la velocit&agrave;, concepita dal mobile nel <lb/>moto precedente sopra un piano declive, si conserva uniforme e tale, che nel <lb/>piano passer&agrave; spazio doppio del passato nell'inclinato, in tempo uguale al tempo <lb/>del passaggio per l'inclinato, mentre il suo principio fu dallo stato di quiete, <lb/>come io dimostro nel mio soprannominato libro del moto (ivi, pag. </s>

<s>371). Dal <lb/>qual libro aveva poco prima citato il teorema del brachistocronismo per gli <lb/>archi, rispetto alle corde suttese, applicandolo agli alvei e alle svolte dei fiumi. </s></p><p type="main">

<s>In queste applicazioni della dinamica dei solidi, a quella dei fluidi, sta <lb/>come accennammo la chiave, che Galileo diceva d'aver trovata, <emph type="italics"/>per aprire <lb/>ingressi ad accidenti maggiori<emph.end type="italics"/> di quegli stessi scoperti dal Castelli, ma non <lb/>si vedr&agrave; volgersi dentro la chiusura libera e spedita, se non che nelle mani <lb/>del Baliani e del Borelli, dopo che il Torricelli sar&agrave; venuto a inciderne sottil&shy;<lb/>mente gl'ingegni. </s>

<s>Forse Galileo scans&ograve; le incertezze e si dispens&ograve; dalle cure <lb/>di dare espressione pi&ugrave; propria al teorema delle velocit&agrave; delle acque cadenti, <lb/>proporzionali alle radici delle altezze, perch&egrave; ci&ograve; non pareva richiedersi dal&shy;<lb/>l'intenzion sua principale, qual'era di dimostrar che il Bisenzio, cos&igrave; per <lb/>l'alveo tortuoso, come per il raddirizzato, giunge ugualmente veloce al me-<pb xlink:href="020/01/3431.jpg" pagenum="392"/>desimo sbocco. </s>

<s>Vedemmo come la conclusione fosse gi&agrave; scesa dalla Dina&shy;<lb/>mica vecchia, la quale pronunzi&ograve; per bocca di Leonardo che <emph type="italics"/>la obliquit&agrave; <lb/>del corso dell'acqua adopera come fussi perpendicolare,<emph.end type="italics"/> qualunque poi si <lb/>fosse il modo del cos&igrave; adoperare. </s>

<s>Mentre per&ograve; Leonardo non pronunziava che <lb/>una proposizione astratta, Galileo la intendeva in concreto, non rimovendosi <lb/>dall'opinione &ldquo; che l'acqua si serva per canale ugualissimo della stessa sua <lb/>acqua ambiente, sicch&egrave; scorre per un letto o condotto sommamente terso e <lb/>polito &rdquo; (MSS. Gal., P. V, T. III, fol. </s>

<s>14). Da che &egrave; facile argomentare che <lb/>essa acqua corrente per l'alveo di un fiume osserva le leggi dell'accelera&shy;<lb/>zione del moto, pi&ugrave; puntualmente di quella palla di bronzo, che nel III dia&shy;<lb/>logo delle due Nuove Scienze ci vien descritta discendere sopra un piano <lb/>inclinato, ricoperto di carta pecora zannata (Alb. </s>

<s>XIII, 172). Come poi que&shy;<lb/>ste cose si concilino con quell'altre, scritte nella lettera allo Staccoli, &egrave; dif&shy;<lb/>ficile indovinare, e noi non vi ci intratterremo qui, dovendoci tornar sopra <lb/>nel Tomo seguente. </s>

<s>Ma pure non vogliamo lasciar l'occasione di riferire un <lb/>documento, da cui apparisce che il Castelli, dop'aver letto il Discorso in&shy;<lb/>torno al fiume Bisenzio, non rimase persuaso delle ragioni di Galileo, ma <lb/>che anzi pi&ugrave; stabilmente si conferm&ograve; in quel che, essendo vero, aveva come <lb/>verissimo creduto e scritto nella VII appendice: &ldquo; Pare che si possa osser&shy;<lb/>vare che, mentre l'acqua scorre per un alveo, canale o condotto, venga ri&shy;<lb/>tardata, trattenuta e impedita la sua velocit&agrave; dal toccamento, che fa con la <lb/>ripa o sponda del canale o alveo, la quale come immobile, non secondando <lb/>il moto dell'acqua, interrompe la sua velocit&agrave; &rdquo; (<emph type="italics"/>Della misura delle acque <lb/>correnti,<emph.end type="italics"/> lib. </s>

<s>I cit., pag. </s>

<s>32). Quel documento poi che si diceva lo raccolsero <lb/>i discepoli dello stesso Castelli dalla viva voce del Maestro, e nella forma, che <lb/>qui appresso riproduciamo, ne lasciarono diligente memoria: </s></p><p type="main">

<s>&ldquo; Dicono che il padre don Benedetto faciliti assai i mulini, con osser&shy;<lb/>vare che le ruote avessero le pale, che stessero forte, acci&ograve; non si perdesse <lb/>il colpo dell'acqua: l'acqua cascasse in luogo pi&ugrave; lontano che si pu&ograve; dal <lb/>centro di detta ruota. </s>

<s>Per di pi&ugrave;, ai ritrecini, che la doccia che porta l'acqua <lb/>non fosse inclinata come la BI (fig. </s>

<s>188), ma fosse detto ritrecine AIS sfon&shy;<lb/><figure id="id.020.01.3431.1.jpg" xlink:href="020/01/3431/1.jpg"/></s></p><p type="caption">

<s>Figura 188.<lb/>dato o voto fino al fondo AS, e l'acqua uscisse <lb/>per la bocca A, e percotesse nella ruota. </s>

<s>E <lb/>sebbene in teoria &egrave; vero che l'impeto, che <lb/>acquista detta acqua perpendicolare IO, &egrave; <lb/>uguale a quello, che acquista per la inclinata <lb/>IB; la sperienza nonostante mostra di no, <lb/>mediante gl'impedimenti che, nello scorrere <lb/>per la doccia inclinata, continuamente riceve <lb/>l'acqua, ancora che piccoli. </s>

<s>Ma ricevendoli in <lb/>tutti i luoghi di detta acqua, che tocca la <lb/>doccia, e in tutti i tempi, e la perpendicolare non ne ricevendo veruno; ven&shy;<lb/>gono a operare in maniera, che la sperienza ne mostra variazioni assai <lb/>grandi &rdquo; (<emph type="italics"/>Appendice ai MSS. Gal. </s>

<s>della Bibliot. </s>

<s>naz. </s>

<s>di Firenze<emph.end type="italics"/>). </s></p><pb xlink:href="020/01/3432.jpg" pagenum="393"/><p type="main">

<s>Nella VII appendice, sopra citata, lo stesso p. </s>

<s>don Benedetto prosegue <lb/>a dare utili avvertimenti intorno al variarsi le misure dell'acqua, mentre <lb/>vengono rallentate nel loro impeto dagli attriti contro l'ambito delle fistole, <lb/>formulando in tal proposito questo teorema: &ldquo; L'acqua che passa per la <lb/>maggior fistola, a quella che passa per la minore, ha sempre maggior pro&shy;<lb/>porzione che la fistola maggiore alla fistola minore &rdquo; (<emph type="italics"/>Della misura ecc.,<emph.end type="italics"/><lb/>lib. </s>

<s>I cit., pag. </s>

<s>34): ci&ograve; che supposte le fistole cilindriche, e le loro bocche <lb/>circolari, ha la sua facile dimostrazione nelle propriet&agrave; geometriche delle cir&shy;<lb/>conferenze, che crescono come i raggi, e de'circoli, che crescono invece come <lb/>i quadrati dei raggi. </s></p><p type="main">

<s>Come il teorema si trovasse dimostrato cos&igrave;, nei manoscritti di Leonardo <lb/>da Vinci, &egrave; ben noto ai nostri Lettori. </s>

<s>Ma ora &egrave; il tempo di soggiungere che <lb/>il discepolo del Nemorario riman superiore al discepolo di Galileo, non per <lb/>la sola precedenza del tempo, ma, ci&ograve; che importa anche pi&ugrave;, per la mag&shy;<lb/>giore perfezione dell'opera. </s>

<s>Suppongasi che la bocca della fistola sia in figura <lb/>di un triangolo equilatero, ora con l'apice in basso, ora con la base. </s>

<s>Per il <lb/>teorema del Castelli dovrebbe la fistola rendere la medesima quantit&agrave; in am&shy;<lb/>bedue le posizioni, mentre per Leonardo vedemmo esser concluso che, stando <lb/>il vertice del triangolo in alto, la fistola rende pi&ugrave; che stando in alto la base, <lb/>e fu la ragion della conclusione che, essendo gli strati inferiori pi&ugrave; premuti, <lb/>e perci&ograve; pi&ugrave; velocemente sospinti dei superiori, maggior quantit&agrave; d'acqua <lb/>premuta e velocitata si trova dal mezzo in gi&ugrave; nel triangolo risedente, che <lb/>nel supino. </s></p><p type="main">

<s>Se non s'intendono dunque i vari strati ridotti alle loro velocit&agrave; medie, <lb/>il teorema del Castelli, che fisicamente &egrave; imperfetto, geometricamente &egrave; ad&shy;<lb/>dirittura falso. </s>

<s>E perch&egrave; si tratta di cosa di non lieve importanza, si vuol <lb/>pi&ugrave; diligentemente ricercare questo punto di Storia, a far che, il seguente <lb/>passo di lettera, scritta dallo stesso Castelli a Galileo il d&igrave; 10 Dicembre 1625; <lb/>ci viene a preparare la via: &ldquo; Mi occorre signif&igrave;cargli un garbuglio, che mi <lb/>passa per il capo, il quale &egrave; stato in gran parte e forse totale causa che io <lb/>non dimostrassi i due ultimi Pronunziati, e che, nel dimostrare la III pro&shy;<lb/>posizione, io tenessi il metodo, che ho tenuto. </s>

<s>Il garbuglio &egrave; questo, che non <lb/>ho mai potuto saldar la partita, n&egrave; trovo modo di saldarla: se l'acqua corra <lb/>con la medesima velocit&agrave; nelle parti superiori come nelle inferiori, e per&shy;<lb/>tanto, per isfuggire questo punto, o per dir meglio, per non averne bisogno, <lb/>ho tralasciato il concetto di quei prismi d'acqua, che passano per le se&shy;<lb/>zioni ecc. </s>

<s>Perch&egrave; se queste correnti non sono le medesime nelle parti su&shy;<lb/>periori che nelle inferiori, non ritrovo quei prismi, e so che nasce dalla mia <lb/>debolezza. </s>

<s>Per&ograve; V. S. mi scusi, e apra la mente, perch&egrave; dovento matto in&shy;<lb/>torno a questa materia &rdquo; (Campori, Carteggio cit., pag. </s>

<s>231). </s></p><p type="main">

<s>Bench&egrave; non ci sia nota la risposta di Galileo, pur crediamo di assicu&shy;<lb/>rare i Lettori che non furono per lui saldate le partite, n&egrave; aperta per lui <lb/>la mente del Castelli, a levargli di dentro il male di quella mattia. </s>

<s>Non era <lb/>a ci&ograve; infatti altro rimedio, che nel principio dell'uguaglianza delle pressioni, <pb xlink:href="020/01/3433.jpg" pagenum="394"/>rimasto ignoto parimente al Discepolo e al Maestro. </s>

<s>Alla penosa incertezza <lb/>per&ograve; d'ambedue fa notabile riscontro la franchezza di Leonardo da Vinci, il <lb/><figure id="id.020.01.3433.1.jpg" xlink:href="020/01/3433/1.jpg"/></s></p><p type="caption">

<s>Figura 189.<lb/>quale passava, cos&igrave; ragionando, a trovar la legge del corso <lb/>dalla stagnante acqua del vaso. </s>

<s>Segnati i gradi delle al&shy;<lb/>tezze BE, EF, FG, ecc. (fig. </s>

<s>189) nel vaso pieno AD, s'im&shy;<lb/>magini rimossa la parete AB: l'acqua ferma piglier&agrave; corso, <lb/>servando i vari strati di lei le medesime velocit&agrave; orizon&shy;<lb/>tali, eccitate dalle pressioni perpendicolari, cosicch&egrave; il moto <lb/>non &egrave; per tutto uniforme, ma nelle parti inferiori pi&ugrave; ve&shy;<lb/>loce che nelle superiori, a proporzion delle altezze. </s>

<s>Gli at&shy;<lb/>triti contro le ineguaglianze dell'alveo e delle ripe per&shy;<lb/>turbano questa legge, ma non le tolgono il predominio, come Leonardo stesso <lb/>speriment&ograve; con l'Idrometro baculare, descrittoci nelle sue note. </s></p><p type="main">

<s>Col&agrave;, dove noi ne riferimmo la descrizione, si narr&ograve; le contradizioni del <lb/>Cardano, il quale non negava gli effetti delle pressioni perpendicolari, che <lb/>con uguale impulso si volgono per l'orizonte e per altri versi, ma diceva <lb/>che le minori velocit&agrave; degli strati superiori son cos&igrave; compensate dalle mag&shy;<lb/>giori velocit&agrave; degli strati inferiori, che ne risulta nel tutto una velocit&agrave; media. </s>

<s><lb/>Di qui &egrave; che, tenendo per illusorie le osservazioni fatte con l'Idrometro ba&shy;<lb/>culare, cred&egrave; che impunemente si potesse sostituire a lui nel medesimo uffi&shy;<lb/>cio qualunque semplice galleggiante. </s></p><p type="main">

<s>Il Castelli non trov&ograve; riposo alla mente, in pericolo di ammattire, che <lb/>riducendosi a professare queste medesime cardaniche dottrine. </s>

<s>Nell'XI Ap&shy;<lb/>pendice, per esaminare e confrontare la velocit&agrave; dell'acqua, che passa per un <lb/>fosso, a quella che passa per un altro, insegna &ldquo; a tener conto per quanto <lb/>spazio sia trasportata una palla di legno, o di altro corpo che galleggi, in <lb/>un determinato tempo, come sarebbe v. </s>

<s>g. </s>

<s>in cinquanta battute di polso &rdquo; <lb/>(<emph type="italics"/>Della misura<emph.end type="italics"/> ecc., lib. </s>

<s>I cit., pag. </s>

<s>41) evidentemente supponendo che il <lb/>fosso, per tutta la profondit&agrave;, serbi il medesimo corso che nella superficie. </s>

<s><lb/>Sembrerebbe di qui che anch'egli, il Castelli, volesse fare, come il Cardano, <lb/>la riduzione alle velocit&agrave; medie, in che forse veniva a ritrovare que'prismi, <lb/>che aveva creduti vacillanti, e che, nel dubbio non corresse l'acqua per <lb/>tutto con la medesima velocit&agrave;, vedeva andare smarriti. </s>

<s>Per conferma della <lb/>quale opinione soccorrerebbero la seconda definizione, e la proposizione se&shy;<lb/>conda del secondo libro delle Acque correnti, ma pi&ugrave; espressamente la te&shy;<lb/>stimonianza di uno dei pi&ugrave; affezionati discepoli del Castelli, Giovan Batista <lb/>Hodierna. </s>

<s>Nell'opuscolo, che questi intitol&ograve; <emph type="italics"/>Stadera del momento,<emph.end type="italics"/> trattando <lb/>dello scompartir l'acque pi&ugrave; giustamente che sia possibile, accenna al ritar&shy;<lb/>damento, ch'elle subiscono, per attaccarsi le loro parti contigue all'ambito <lb/>del canaletto, per l'aperta del quale escon fuori. </s>

<s>&ldquo; Ma tolto questo impedi&shy;<lb/>mento, soggiunge, e supposto che da ciaschedun canaletto scorra liberamente <lb/>l'acqua, secondo la misura che contiene; ve n'&egrave; un altro, qual'&egrave; che, situati <lb/>diversi canaletti di diverse misure sotto l'istessa altezza dell'acqua, sicch&egrave; <lb/>v. </s>

<s>g. </s>

<s>l'orizzonte dell'acqua s'elevasse mezzo palmo, sopra il centro delli fo-<pb xlink:href="020/01/3434.jpg" pagenum="395"/>rami; dico che in questo caso delli forami maggiori non scorre quella quan&shy;<lb/>tit&agrave; d'acqua per tutte le bande, perch&egrave;, dal centro in gi&ugrave;, l'acque scorrono <lb/>con pi&ugrave; velocit&agrave; che dal centro in su, per essere le parti inferiori dell'acqua <lb/>pi&ugrave; compresse delle superiori. </s>

<s>Ma in questo caso non si perderebbe, perch&egrave; <lb/>gi&agrave; la maggior celerit&agrave; delle parti inferiori ricompensa precisamente la tar&shy;<lb/>dit&agrave; delle superiori &rdquo; (Palermo 1641, pag. </s>

<s>67, 68). </s></p><p type="main">

<s>Noi crediamo che questi dell'Hodierna fossero i pensieri medesimi del <lb/>Castelli, il quale industriosamente seguitava a sfuggire il punto della que&shy;<lb/>stione: <emph type="italics"/>se l'acqua corra con la medesima velocit&agrave; nelle parti superiori, <lb/>come nelle inferiori,<emph.end type="italics"/> scusandosi di aver tralasciato un tal concetto, <emph type="italics"/>per non <lb/>averne bisogno.<emph.end type="italics"/> Ma perch&egrave; giusto in questo concetto consisteva la perfezione <lb/>della Scienza che professava, non pen&ograve; molto il bisogno a farglisi sentire, e <lb/>ora vien per noi che si narri a quale occasione, e com'ei lo sodisfacesse. </s></p><p type="main">

<s>L'occasione venne nell'estate del 1641, a proposito della laguna di Ve&shy;<lb/>nezia, disputandosi allora vivamente intorno agli effetti, che vi produrreb&shy;<lb/>bero le diversioni o le influenze dell'acque della Brenta e degli altri fiumi. </s>

<s><lb/>I periti si regolavano in questo negozio, supponendo che gli alzamenti del <lb/>livello si facessero a proporzione delle quantit&agrave; d'acqua versate, e cos&igrave; tra&shy;<lb/>scorrevano, sccondo il Castelli, in que'medesimi errori degli Ingegneri bolo&shy;<lb/>gnesi e ferraresi, quando giudicarono che, mettendosi il Reno in Po, ne <lb/>avrebbe fatto alzar tanto l'acqua, da temerne straordinarie inondazioni. </s>

<s>&ldquo; Ma <lb/>ora, soggiunge nella III appendice, dalle cose dimostrate &egrave; manifesto che la <lb/>misura del Reno in Reno sarebbe diversa dalla misura del Reno in Po, ogni <lb/>volta che sar&agrave; diversa la velocit&agrave; del Reno in Po, dalla velocit&agrave; del Reno <lb/>in Reno, come pi&ugrave; esattamente si determina nella quarta proposizione &rdquo; <lb/>(<emph type="italics"/>Della misura delle acque ecc.,<emph.end type="italics"/> lib. </s>

<s>I cit., pag. </s>

<s>31). </s></p><p type="main">

<s>Da quella quarta proposizione infatti si conclude che nel medesimo fiume, <lb/>rimanendo la medesima quantit&agrave; d'acqua, le altezze son reciproche delle ve&shy;<lb/>locit&agrave;, cosicch&egrave; se il Reno non facesse altro che velocitare il Po, vi produr&shy;<lb/>rebbe uno sbassamento, tutt'altro che una piena. </s>

<s>Ma perch&egrave; la quantit&agrave; del&shy;<lb/>l'acqua, versata dal minor fiume nel maggiore, non &egrave; trascurabile, e vi pro&shy;<lb/>duce perci&ograve; un certo alzamento necessariamente, si trattava di cercar la <lb/>proporzione di questo a quella; si proponeva cio&egrave; a risolvere un tale pro&shy;<lb/>blema: Se, raddoppiandosi la quantit&agrave; d'acqua, l'alzamento, come s'apprende <lb/>dalla detta quarta proposizione, &egrave; men che doppio, contro l'opinion di co&shy;<lb/>loro, che furono ammoniti nella III appendice, ed &egrave; pi&ugrave; che nulla, contro <lb/>l'opinion di quegli altri ammoniti nell'appendice IV: si domanda qual'&egrave;, <lb/>fra questi due termini estremi, la ragion di mezzo precisa? </s>

<s>N&egrave; ritrovando <lb/>il Castelli, nelle sue proprie teorie, la soluzione desiderata, si volse con gran <lb/>deligenza agli esperimenti. </s>

<s>Pens&ograve; dunque a quella macchina semplicissima, <lb/>detta il <emph type="italics"/>Regolatore,<emph.end type="italics"/> per la pi&ugrave; precisa misura delle sezioni: e per la misura delle <lb/>velocit&agrave; o dei tempi, lasciate quelle battute di polso, proposte gi&agrave; per eseguire <lb/>le operazioni descritte nella XI appendice; si serv&igrave; in vece di strumento assai <lb/>pi&ugrave; esatto, qual era il pendolo a secondi, che mandava lungo tre piedi romani. </s></p><pb xlink:href="020/01/3435.jpg" pagenum="396"/><p type="main">

<s>Cos&igrave; sperimentando, gli parve aver trovato che, se una quantit&agrave; d'acqua <lb/>fa un alzamento, per avere un alzamento doppio, triplo, quadruplo, ecc., ci <lb/>volevano quattro, nove, sedici quantit&agrave; d'acqua, e cos&igrave; sempre, secondo la <lb/>serie progressiva dei numeri quadrati. </s>

<s>Non credendo a s&egrave; medesimo di avere <lb/>scoperto un tal miracolo della Natura, and&ograve; pi&ugrave; volte, e in vario modo, ri&shy;<lb/>petendone l'esperienza, e finalmente concluse per certissima legge, da dimo&shy;<lb/>strare infino a qual punto eran giunti gli errori di coloro, che avevano con&shy;<lb/>sigliato di divertire la Brenta dalla laguna; che le quantit&agrave; influenti son pro&shy;<lb/>porzionali ai quadrati, e non alle semplici altezze che farebbero nel recipiente. </s></p><p type="main">

<s>A persuadere anche meglio la verit&agrave; di questi naturali effetti, e per aver <lb/>comodit&agrave; di darne dimostrazione, ogni volta che lo richiedessero i curiosi o <lb/>i diffidenti, fece costruire quello strumento, che poi ci dette descritto cos&igrave; nel <lb/>suo libro: &ldquo; Io ho preparato cento sifoni, o vogliam dir canne ritorte, tutte <lb/>uguali, e postele al labbro d'un vaso, nel quale si mantiene l'acqua con uno <lb/>stesso livello, o lavorino tutte le canne, o qualsivoglia numero di loro, col&shy;<lb/>locate le bocche, dalle quali esce l'acqua, tutte al medesimo livello parallelo <lb/>all'orizonte, ma pi&ugrave; basse di livello dell'acqua del vaso. </s>

<s>E raccolta tutta <lb/>l'acqua cadente dai sifoni in un altro vaso pi&ugrave; basso, l'ho fatta scorrere per <lb/>un canale, inclinandolo in modo che; mancando l'acque dai sifoni, il canale <lb/>rimane affatto senz'acqua asciutto. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; E fatto questo misurai l'altezza viva del canale diligentemente, e poi <lb/>la divisi in dieci parti uguali precisamente. </s>

<s>E facendo levare via 19 di que&shy;<lb/>sti sifoni, in modo che nel canale non scorreva l'acqua se non di 81 di <lb/>questi sifoni, di nuovo, osservando l'altezza viva dell'acqua nel medesimo <lb/>sito osservato di prima, trovai che l'altezza sua era scemata la decima parte <lb/>precisamente di tutta la sua prima altezza. </s>

<s>E cos&igrave;, seguitando a levare altri <lb/>17 sifoni, l'altezza era pure scemata un decimo di tutta la prima sua al&shy;<lb/>tezza viva. </s>

<s>E provando a levare 15 sifoni, poi 13, poi 11, e poi 9, e poi 7, <lb/>poi 5 e poi 3, sempre in queste diversioni, fatte ordinatamente come s'&egrave; <lb/>detto, ne seguiva ogni sbassamento di un decimo di tutta l'altezza &rdquo; (<emph type="italics"/>Della <lb/>misura delle acque,<emph.end type="italics"/> lib. </s>

<s>II, Bologna 1660, pag. </s>

<s>92, 93). Soggiunge poi come <lb/>aprendosi le cannelle stesse in ordine contrario, trov&ograve; che se una sola fa un <lb/>decimo di altezza, non pi&ugrave; di un decimo se ne fa aggiungendovene 3, 5, 7, <lb/>e cos&igrave; di seguito crescendo il numero dei confluenti. </s></p><p type="main">

<s>Tanto rimase commosso il Castelli, e tanto paterno amore sent&igrave; per que&shy;<lb/>sta sua scoperta, che fatto dello strumento un modello in piccolo, con quat&shy;<lb/>tro o cinque scompartimenti, il primo di una cannella, il secondo di quattro, <lb/>il terzo di nove, il quarto di sedici, lo colloc&ograve; nelle stanze terrene della sua <lb/>abbazia, per ricrearne i forestieri che capitavano e gli amici. </s>

<s>E certo era <lb/>spettacolo non ingiocondo il vedere le sedici cannelle vomitar acqua dalle <lb/>bocche aperte in gareggiante concordia, e n&egrave; perci&ograve; fare ingrossare il fiumi&shy;<lb/>cello un pelo di pi&ugrave; di quel che facessero da s&egrave; sole nove, anzi quattro, anzi <lb/>una cannella sola! </s></p><p type="main">

<s>Di qui ebbe origine il secondo libro Della misura delle acque correnti: <pb xlink:href="020/01/3436.jpg" pagenum="397"/>origine dunque puramente sperimentale, come l'aveva avuta il primo. </s>

<s>Se non <lb/>che tanto pi&ugrave; difficile di questo trov&ograve; quello il Castelli a ridursi alle ragioni <lb/>geometriche, che si rivolse a invocare il valido aiuto del Cavalieri. </s>

<s>Questi <lb/>rispose che dalla V proposizione delle <emph type="italics"/>Dimostrazioni geometriche<emph.end type="italics"/> s'avrebbe <lb/>facilmente concluso l'intento, qual'era di provare che le quantit&agrave; son pro&shy;<lb/>porzionali ai quadrati delle altezze, quando fosse vero che le velocit&agrave; stanno <lb/>come le semplici altezze. </s>

<s>Essendo infatti quella V proposizione espressa dai <lb/>noti simboli Q:<emph type="italics"/>q<emph.end type="italics"/>=A.V:<emph type="italics"/>a.v,<emph.end type="italics"/> se V:<emph type="italics"/>v<emph.end type="italics"/>=A:<emph type="italics"/>a,<emph.end type="italics"/> &egrave; manifestamente Q:<emph type="italics"/>q<emph.end type="italics"/>= <lb/>A2:<emph type="italics"/>a<emph.end type="italics"/>2. </s>

<s>Ma per ammettere che le velocit&agrave; son proporzionali alle altezze, &ldquo; non <lb/>ho, confessava ingenuamente il Cavalieri, avuto fortuna d'incontrarmi in ra&shy;<lb/>gione, che appieno mi sodisfaccia &rdquo; (<emph type="italics"/>Autori che trattano del moto delle <lb/>acque,<emph.end type="italics"/> T. I, Firenze 1765, pag. </s>

<s>175). </s></p><p type="main">

<s>Consistendo un tal fortunato incontro nel principio dell'uguaglianza delle <lb/>pressioni, che cos&igrave; buon servigio aveva prestato a Leonardo da Vinci, ma che <lb/>poi fu travolto nella ruina di tutte l'altre tradizioni; non sarebbe rimasto <lb/>al Cavalieri altro esempio, che quello dato da Galileo, il quale, come accen&shy;<lb/>nammo, dal suppor che le moli d'acqua precedenti, gravitando sopra le sus&shy;<lb/>seguenti, le sospingano al moto, lasciava a concluderne immediatamente che <lb/>i momenti delle velocit&agrave; crescono come 1e moli, o come le altezze vive delle <lb/>sezioni. </s>

<s>Nonostante, il metodo degli indivisibili trasportava il Cavalieri per <lb/>altre vie, e riguardando la corrente divisa in strati paralleli dal fondo alla <lb/>superficie, e considerando che gli strati superiori, oltre al proprio moto di&shy;<lb/>pendente dall'inclinazione dell'alveo, partecipano di quello degl'inferiori, <lb/>sopra cui come da veicolo son trasportati; ne concludeva che dunque le ve&shy;<lb/>locit&agrave; debbon crescere come il numero degli strati superiori, ossia come le <lb/>altezze medesime della corrente. </s>

<s>Ma giova ascoltare il Cavalieri stesso, che, <lb/>in una sua lettera dell'11 Gennaio 1642, diceva al Castelli il proprio e par&shy;<lb/>ticolar modo del suo discorso: </s></p><p type="main">

<s>&ldquo; Io discorro cos&igrave;: Sia, nella fig. </s>

<s>190, ABCD l'alveo, nel quale cam&shy;<lb/>mini l'acqua per la sezione EC, alta come BE, con una tale velocit&agrave;. </s>

<s>Inten&shy;<lb/><figure id="id.020.01.3436.1.jpg" xlink:href="020/01/3436/1.jpg"/></s></p><p type="caption">

<s>Figura 190.<lb/>dasi poi messa tant'acqua nello stesso fiume, che cresca <lb/>sino in GH, correndo nel fiume con l'altezza BG, dop&shy;<lb/>pia di EB. </s>

<s>Dico che l'acqua vi camminer&agrave; con doppia <lb/>velocit&agrave;, e per concludere questo, intendo tutta l'acqua <lb/>che scorre per GC divisa in due pezzi GF, EC, me&shy;<lb/>diante la superficie superiore dell'acqua EC, che passa <lb/>per EF, e considero che l'acqua GF, come portata dal&shy;<lb/>l'acqua EC, dee fare nello stesso tempo lo spazio, che <lb/>far&agrave; la EC, e di pi&ugrave;, intendendosi scorrere l'acqua GF <lb/>sopra la superficie che passa per EF, come sopra suo letto, nella guisa che <lb/>EC scorre sopra il fondo; dee l'acqua GF avere forza di trapassare altret&shy;<lb/>tanto spazio, quanto ne passa la EC. </s>

<s>Adunque l'acqua GF aver&agrave; la forza di <lb/>trapassare doppio spazio di quello, che passa la EC nell'istesso tempo, onde <lb/>sar&agrave; doppiamente veloce &rdquo; (ivi, pag. </s>

<s>175, 76). </s></p><pb xlink:href="020/01/3437.jpg" pagenum="398"/><p type="main">

<s>Aveva il Cavalieri finito appena di scrivere questa dimostrazione, che <lb/>la sent&igrave; forte combattuta da due dubbi: il primo, per il supposto che gli <lb/>strati acquei siano tutti paralleli fra loro, e il secondo, per il corollario che <lb/>la scala delle velocit&agrave; sia in un triangolo col suo vertice in basso. </s>

<s>Cose, che <lb/>non sapeva come s'accordassero con l'esperienza, dalla quale si par che in <lb/>tempo di piena la superficie del fiume non sia parallela al fondo, ma con&shy;<lb/>verga con lui verso lo sbocco, e che le velocit&agrave; debban piuttosto crescere <lb/>dalla superficie al fondo che dal fondo alla superficie. </s></p><p type="main">

<s>Lette e meditate queste cose, il Castelli sent&igrave; allora imperiosamente <lb/>l'invito a dichiararsi finalmente intorno a quel concetto, che aveva potuto <lb/>fin qui scansar destramente, se cio&egrave; gli strati, che corrono per una sezione, <lb/>vadano, come diceva Leonardo, a un medesimo o a differente aspetto. </s>

<s>E pa&shy;<lb/>rendogli veramente non consentito dall'esperienza il corollario del Cavalieri, <lb/>lo accomod&ograve; nella dimostrazione di lui, il processo della quale del resto ac&shy;<lb/>cettava, pensando che, sebbene gli strati superiori sian trasportati dagl'in&shy;<lb/>feriori, ne resulta d'ambedue nonostante un moto misto ossia medio: co&shy;<lb/>sicch&egrave; la scala, che riferisce le velocit&agrave; degli strati AB, CD, EF (fig. </s>

<s>191) <lb/><figure id="id.020.01.3437.1.jpg" xlink:href="020/01/3437/1.jpg"/></s></p><p type="caption">

<s>Figura 191.<lb/>non sia nel triangolo AEG, ma nel rettan&shy;<lb/>golo LE che lo uguaglia, per essere l'AG nel <lb/>punto I divisa nel mezzo. </s>

<s>Quanto al dubbio <lb/>poi se gli strati della corrente siano tutti <lb/>paralleli fra loro, il Castelli non ne fece <lb/>alcun conto, mantenendo ferma la suppo&shy;<lb/>sizione del Cavalieri. </s>

<s>Cos&igrave; gli venne fatta la <lb/>dimostrazione di quella, che fu in secondo luogo scritta fra le proposizioni del <lb/>secondo libro delle Acque correnti, e che noi non possiamo non compian&shy;<lb/>gere, per essere stata cos&igrave; disgraziata infin dal suo primo apparire alla luce <lb/>in Bologna, per le stampe del Dozza. </s></p><p type="main">

<s>Desiderosi di ridurla pietosamente alla sua vera lezione, non s'&egrave; potuto <lb/>in tutto conseguire l'intento, per esserci venuto a mancare l'autografo, o la <lb/>copia autentica di lui, quale, sapendosi essere stata depositata dall'Autore <lb/>stesso nelle mani del principe Leopoldo de'Medici, si sperava di ritrovare <lb/>nella Raccolta palatina fra i Manoscritti galileiani. </s>

<s>Ma nel primo volume della <lb/>sezione <emph type="italics"/>Discepoli,<emph.end type="italics"/> in cui sono alligati i manoscritti del Castelli, e gli altri <lb/>relativi alle Opere di lui, non abbiamo trovato, di quel che si cercava, se non <lb/>una copia di mano del Viviani, che v&agrave; fino alla Considerazione seconda, dopo <lb/>la quinta proposizione. </s>

<s>Quivi dunque consultando, al foglio 85, la detta pro&shy;<lb/>posizione II, la riscontrammo fedelmente copiata dalla stampa bolognese, non <lb/>correttovi nemmeno il cos&igrave; evidentemente sbagliato richiamo alla <emph type="italics"/>terza sup&shy;<lb/>posizione,<emph.end type="italics"/> invece che alla seconda. </s></p><p type="main">

<s>Non sapendo perci&ograve; farci altro di meglio, collazionammo questa del Ma&shy;<lb/>nolessi con l'edizione del Barattieri (<emph type="italics"/>Architettura d'acque,<emph.end type="italics"/> P. II, ediz. 2a, <lb/>Piacenza 1699, pag. </s>

<s>57) e ci parve ricavarne una lezione, se non certamente <lb/>conforme con l'autografo, corretta per&ograve; in modo, da riferire almeno il si-<pb xlink:href="020/01/3438.jpg" pagenum="399"/>gnificato dell'Autore, se non il preciso costrutto grammaticale. </s>

<s>Propostasi la <lb/>figura medesima 190 del Cavalieri, anche il Castelli afferma che, essendo <lb/>l'altezza EB raddoppiata in BG, vien perci&ograve; l'acqua GC ad acquistare una <lb/>velocit&agrave; doppia dell'acqua EC, per queste ragioni, che, secondo ci &egrave; resul&shy;<lb/>tato dalla detta collazione, debbon essere state espresse nella forma seguente: <lb/><emph type="italics"/>Imperocch&egrave;, havendo l'acqua GF per suo letto il fondo EF, ugualmente <lb/>inclinato come il letto BC, ed essendo la sua altezza viva GE uguale &agrave;l&shy;<lb/>l'altezza viva EB, ed havendo la medesima larghezza BC: haver&agrave; per s&egrave; <lb/>stessa una velocit&agrave; uguale alla velocit&agrave; della prima acqua EC. </s>

<s>Ma perch&egrave;, <lb/>oltre al proprio moto, vien portata dal moto dell'acqua EC, haver&agrave; an&shy;<lb/>cora, oltre al proprio moto, il moto dell'EC. </s>

<s>E perch&egrave; le due acque GF <lb/>ed EC sono simili di velocit&agrave;, per la seconda supposizione, per&ograve; tutta <lb/>l'acqua GC sar&agrave; doppia di velocit&agrave; di quella, che haver&agrave; l'acqua EC, <lb/>che era quello che si doveva dimostrare.<emph.end type="italics"/></s></p><p type="main">

<s>Ma, a dover dire un parto disgraziato, basta il non essersi meritate le <lb/>affezioni paterne: il Castelli infatti si dichiar&ograve;, come vedremo, di non esser <lb/>rimasto contento di questa dimostrazione. </s>

<s>I dubbi del Cavalieri non gli par&shy;<lb/>vero affatto risoluti, specialmente per ci&ograve; che riguardava la scala delle ve&shy;<lb/>locit&agrave;: e da quelle loro similitudini, bench&egrave; cos&igrave; studiosamente introdotte, si <lb/>sentiva penosamente aggirato in qualche paralogismo. </s>

<s>E in vero la somi&shy;<lb/>glianza, tra le velocit&agrave; di due fiumi di larghezze uguali, non pu&ograve; riferirsi <lb/>ad altro, che alle altezze, per cui, tanto essendo il supporre essere le velo&shy;<lb/>cit&agrave; simili nelle altezze, quanto il dimostrare che le velocit&agrave; son proporzio&shy;<lb/>nali alle altezze; il paralogismo che si diceva consiste nell'aver dimostrata <lb/>una proposizione, che gi&agrave; supponevasi vera. </s></p><p type="main">

<s>Nonostante, la maggiore di tutte le disgrazie, alle quali and&ograve; soggetta <lb/>questa stessa proposizione, fu quella di avere attirato addosso all'Autore l'ob&shy;<lb/>brobriosa accusa di plagio. </s>

<s>Il Lombardini, nello scritto sopra citato, annun&shy;<lb/>ziava proemiando, dimostrava discorrendo, e finalmente riepilogava la sen&shy;<lb/>tenza essersi il Castelli <emph type="italics"/>valso degli autografi di Leonardo da Vinci, della <lb/>Scienza idraulica del quale s'attribuiva il merito<emph.end type="italics"/> (pag. </s>

<s>72). Il valente critico, <lb/>per provare il suo assunto, confronta la proposizione, da noi trascritta a pag. </s>

<s>69 <lb/>qui addietro, con la seconda del secondo libro delle Acque correnti, e perch&egrave; <lb/>ebbe a mano una di quelle edizioni del Manolessi, nella quale la dimostrazione <lb/>mancava, l'and&ograve; a cercare nel Barattieri, al luogo sopra citato, notandovi prin&shy;<lb/>cipalmente questo argomento: <emph type="italics"/>E perch&egrave; l'acqua EB vien caricata di proprio <lb/>peso, per avere il peso di s&egrave; stessa, e quello di EG, per la quale riceve anche <lb/>doppio impulso, e forma perci&ograve; doppia la sua potenza nella velocit&agrave;.....<emph.end type="italics"/></s></p><p type="main">

<s>Poteva un tal censore avvedersi dello sbaglio <emph type="italics"/>caricata di proprio peso,<emph.end type="italics"/><lb/>e liberamente correggere <emph type="italics"/>caricata di doppio peso,<emph.end type="italics"/> ma quel che non seppe <lb/>&egrave; che un tale argomento, com'apparisce dalla vera lezione, manca nell'ori&shy;<lb/>ginale del Castelli, dentro cui d'altra mano fu intruso, onde al discorso del <lb/>Lombardini viene a mancare ogni virt&ugrave; di concluder l'intento, venendogli a <lb/>mancare uno dei termini del confronto. </s></p><pb xlink:href="020/01/3439.jpg" pagenum="400"/><p type="main">

<s>Ma chi mai, dop'avere ascoltata ne'suoi particolari la storia del prin&shy;<lb/>cipio e de'progressi della scoperta, a cui diceva il Castelli <emph type="italics"/>non poter far di <lb/>meno di non pensarci giorno e notte;<emph.end type="italics"/> vorr&agrave; credere alle asserzioni di que&shy;<lb/>sti critici novelli? </s>

<s>Se i teoremi delle velocit&agrave; proporzionali alle altezze, e <lb/>delle quantit&agrave; proporzionali ai quadrati delle altezze, furono ricopiati dagli <lb/>autografi di Leonardo da Vinci, a che ricorrere il Castelli, per la sua dimo&shy;<lb/>strazione, agli aiuti del Cavalieri? </s>

<s>Il qual Cavalieri dunque dovrebbe esser <lb/>complice del plagio, suo essendo quel modo di dimostrare: modo lubrico e fal&shy;<lb/>lace, per questo solo motivo seguitato da lui, come vedemmo, perch&egrave; non gli era <lb/>approdato l'altro pi&ugrave; legittimo, di che aveva potuto far uso lo stesso Leonardo. </s></p><p type="main">

<s>In ogni modo, l'assunto del Lombardini &egrave; falso nella sua radice, e con&shy;<lb/>trario alla legge storica: falso cio&egrave; che fosse esso Leonardo il creatore del&shy;<lb/>l'Idraulica, e che dagli autografi di lui si divulgassero i teoremi, riappariti <lb/>per tutt'altre vie, pi&ugrave; di un secolo dopo, nelle opere del Castelli. </s>

<s>Cotesti <lb/>teorem&igrave; erano gi&agrave; germogliati nella scuola del Nemorario, e da essa deriva&shy;<lb/>rono negl'Idraulici del secolo XV, e del XVI per tradizione, che ai tempi <lb/>del cos&igrave; detto <emph type="italics"/>Instauramento del metodo sperimentale<emph.end type="italics"/> rimase infelicemente <lb/>interrotta. </s>

<s>Largo campo s'aprirebbe di qui al nostro discorso, a cui ora solo <lb/>ci contentiamo di aggiungere quel tanto, che valga a confermare il gi&agrave; detto. </s></p><p type="main">

<s>Fra gl'idraulici del secolo XVI il pi&ugrave; noto e pi&ugrave; celebre di tutti &egrave; il <lb/>Cardano, ne'libri del quale vedemmo, non solamente proposti, ma dimo&shy;<lb/>strati dai loro principii matematici quei due massimi teoremi, quali sono che <lb/>le quantit&agrave; dell'acqua stanno in ragion composta delle velocit&agrave; e delle se&shy;<lb/>zioni, e che le velocit&agrave; stesse son proporzionali alle altezze. </s>

<s>Di qui veniva a <lb/>concludersi legittimamente la proposizione, principale soggetto del presente <lb/>discorso, che le quantit&agrave; stanno come i quadrati delle altezze. </s>

<s>Le premesse <lb/>poi a una tal conclusione erano tanto ben confermate nella scienza del Car&shy;<lb/>dano, ch'egli non vuol per&ograve; accettarle cos&igrave; assolutamente, com'avevano fatto <lb/>i suoi precedessori, senza eccettuare il caso dei grandi fiumi, ne'quali par <lb/>che l'acqua, per esser pi&ugrave; alta, anche pi&ugrave; lentamente si muova. </s>

<s>&ldquo; Tertium <lb/>scitu dignum, et quod omnibus difficilius, est an altior aqua tardius mo&shy;<lb/>veatur. </s>

<s>Nam sic esse videtur, quod omnia flumina magna lentius fluere vi&shy;<lb/>deamur &rdquo; (<emph type="italics"/>De rerum var.<emph.end type="italics"/> cit., pag. </s>

<s>69). La soluzion del problema la fa il <lb/>Cardano dipendere da&igrave; principio delle velocit&agrave; medie, e dal supposto che, <lb/><figure id="id.020.01.3439.1.jpg" xlink:href="020/01/3439/1.jpg"/></s></p><p type="caption">

<s>Figura 192.<lb/>quanto pi&ugrave; cresce l'acqua d'un gran <lb/>fiume, tanto pi&ugrave; la superficie di lui si <lb/>riduca all'equilibrio, cio&egrave; s'avvicini ad <lb/>essere orizontale. </s></p><p type="main">

<s>Cos&igrave;, per esempio, se la linea CD <lb/>(fig. </s>

<s>192) rappresenta la pendenza del&shy;<lb/>l'alveo, e per un'altezza CE la super&shy;<lb/>ficie declina secondo EF assai meno di <lb/>CD, crescendo il fiume fino in CK, la superficie AK si dispone quasi in un <lb/>piano orizontale, e perci&ograve; la velocit&agrave; media degli strati, compresi fra AK, <pb xlink:href="020/01/3440.jpg" pagenum="401"/>e DC, deve resultare minore della velocit&agrave; media degli strati compresi fra <lb/>FE, e DC. &ldquo; Unde etiam tertii quaesiti explicatio apparet: aqua enim velut <lb/>iuxta inclinationem eamdem lentius movetur sub longiore distantia; ita etiam <lb/>sub pari inclinatione, maioreque altitudine, quoniam enim, ut dictum est, in <lb/>imo inclinationem habet, in summo dum fluit nullam, tota vero aequaliter. </s>

<s><lb/>Igitur iuxta mediae inclinationis impetum tota aqua movebitur, atque ita <lb/>omnia flumina quo altiora eo lenius feruntur &rdquo; (ibid., pag. </s>

<s>71). Ora in que&shy;<lb/>ste discussioni il Cardano rivolge il discorso in generale agli Idraulici, che <lb/>l'avevano preceduto e non personalmente a Leonardo da Vinci, che nessuno <lb/>riconosceva di questa Scienza maestro, ma condiscepolo con tutti gli altri di <lb/>un Maestro pi&ugrave; antico, del qual condiscepolo, se l'Autor <emph type="italics"/>De rerum varie&shy;<lb/>tate<emph.end type="italics"/> aveva notizia per la fama, non aveva certamente studiato i manoscritti <lb/>di lui, e, straniero all'arte del disegno, non avr&agrave; forse desiderato di vederli, <lb/>come tanti, di null'altro propriamente curiosi, che d'ammirare nelle carte <lb/>preziose i prodigi della penna e della matita. </s></p><p type="main">

<s>Che poi le tradizioni della scuola del Nemorario avessero libero corso, <lb/>non arrestato per la reclusione dei manoscritti vinciani nella villa di Vaprio, <lb/>si potrebbe provare con varii esempi, e specialmente con quello offertoci da <lb/>Alessandro Betinzoli di Crema, nelle carte postume del quale il Barattieri atte&shy;<lb/>sta di aver letto il teorema delle quantit&agrave; proporzionali ai quadrati delle altezze, <lb/>proposto e dimostrato in questa maniera: &ldquo; Volendosi sapere quanto cresce <lb/>un'acqua, alzandosi a oncia per oncia, si dee sapere che un'oncia d'altezza <lb/>fa un'oncia: che due oncie alte faranno quattro volte tant'acqua, perch&egrave; <lb/>due volte sar&agrave; per la quantit&agrave; del corpo, e due volte per la quantit&agrave; della <lb/>gravezza, che cresce per l'altezza: e alzandosi a once tre far&agrave; nove volte tanto, <lb/>e quattro d'altezza faranno sedici volte tanto &rdquo; (<emph type="italics"/>Architettura d'acque<emph.end type="italics"/> cit., <lb/>P. I, pag. </s>

<s>182). </s></p><p type="main">

<s>Al qual Betinzoli soggiunge il Barattieri doversi molta lode, per aver <lb/>preceduto di parecchi anni il Castelli: lode, che ora il Lombardini gli vor&shy;<lb/>rebbe detrarre, facendo anche di lui un plagiario o un frugatore delle al&shy;<lb/>trui carte, giudizioso e fortunato. </s>

<s>Dalla quale opinione viene ora a rimoverci <lb/>una critica pi&ugrave; sana, dimostrandoci com'esso Betinzoli e tutti gli altri, dei <lb/>quali a nessuno caddero sotto gli occhi i manoscritti vinciani, attingessero la <lb/>loro scienza, non a un privato bottino chiuso a chiave, ma alla bocca aperta <lb/>di una pubblica fonte. </s></p><p type="main">

<s>Come poi il libero corso di queste tradizioni non andasse a cader tutto <lb/>nel morto e profondo pozzo di Vaprio, ma proseguisse all'aperto, infin presso <lb/>alla soglia del secolo XVII, e di li fosse risospinto indietro, come una pu&shy;<lb/>trida gora, che venisse a intorbidare le nuove scaturigini rigogliose; appa&shy;<lb/>risce da un documento, che vuol essere ora meglio esaminato, e che consi&shy;<lb/>ste in quella scrittura idraulica di Galileo, alla quale i primi editori posero <lb/>il titolo di <emph type="italics"/>Risposta al Bertizzolo.<emph.end type="italics"/> Forse era scritto <emph type="italics"/>Bertazzolo,<emph.end type="italics"/> e dee esser <lb/>costui quel Gabriele, che pubblic&ograve; nel 1609 in Mantova il <emph type="italics"/>Discorso sopra <lb/>il nuovo sostegno alla chiusa di Governolo:<emph.end type="italics"/> ingegnere idraulico allora di <pb xlink:href="020/01/3441.jpg" pagenum="402"/>s&igrave; gran nome in Italia, che fu chiamato a Firenze a prepararvi certi giochi <lb/>argonautici, per una festa nuziale di corte. </s></p><p type="main">

<s>Questo Bertizzolo dunque professava, in un suo Discorso in materia di <lb/>acque, che, secondo crescono esse acque in altezza, debbono ancora crescere <lb/>in velocit&agrave;, e di qui concludeva che le quantit&agrave; versate in un dato tempo <lb/>dovevano aver la proporzione medesima de'quadrati delle altezze: professava <lb/>perci&ograve; e riusciva alle conclusioni medesime di Leonardo, del Cardano e del <lb/>Betinzoli, e cos&igrave;, quella che il Castelli dava per la scoperta nuova di un mira&shy;<lb/>colo della Natura, s'annunziava quarant'anni prima al maestro di lui, a Ga&shy;<lb/>lileo, a cui la novit&agrave; parve, invece di un miracolo, un mostro, e come tale <lb/>studiavasi, ragionando in tal guisa, di cacciarlo da s&egrave; con la forca di una <lb/>scienza nuova: &ldquo; Molto vivamente e con gran sottigliezza risponde il sig. </s>

<s>Ber&shy;<lb/>tizzolo alle mie difficolt&agrave;, per mantenere in piede la sua conclusione, che se&shy;<lb/>condo che cresce l'altezza dell'acqua sopra il medesimo declive, e per con&shy;<lb/>seguenza la gravit&agrave;, debba ancora crescere la celerit&agrave; del suo moto, il che <lb/>era stato da me messo in dubbio, pigliando occasione di dubitare da quello, <lb/>che vedo per esperienza farsi nelli altri movimenti naturali, ne'quali i mo&shy;<lb/>bili omogenei, ancorch&egrave; disugualissimi in moto, e per conseguenza in peso, <lb/>si muovono tuttavia con pari velocit&agrave;, come ciascheduno pu&ograve; ad ogni ora ve&shy;<lb/>dere in due palle di ferro, o d'altra materia grave, delle quali una sia gran&shy;<lb/>dissima e l'altra piccolissima, che cadendo a perpendicolo, ovvero sopra il me&shy;<lb/>desimo piano inclinato, si muovono con la medesima velocit&agrave; &rdquo; (Alb. </s>

<s>VII, 222). <lb/>E dopo aver confermato, co'soliti argomenti sperimentali, che le velocit&agrave; di <lb/>ogni cadente son le medesime, comunque se gli aggiunga gravit&agrave; con accre&shy;<lb/>scergli la mole; francamente Galileo ne conclude &ldquo; che sopra il medesimo <lb/>declive con tanta velocit&agrave; ander&agrave; un'acqua alta cento braccia, con quanta <lb/>una che sia alta un solo &rdquo; (ivi, pag. </s>

<s>224). </s></p><p type="main">

<s>Confutato il teorema delle velocit&agrave; proporzionali alle altezze, per passare <lb/>a confutar l'altro delle quantit&agrave; proporzionali ai quadrati delle altezze, che <lb/>il Bertizzolo ne faceva per logica necessit&agrave; conseguire, Galileo ebbe ricorso <lb/>alle esperienze. </s>

<s>Siano, egli dice, due canali parallelepipedi serrati AB, CD <lb/>(fig. </s>

<s>193) colle lunghezze EF, GH delle bocche rettangolari uguali, ma con <lb/>le altezze AE, CG differenti, ed abbiano essi canali la medesima inclinazione, <lb/><figure id="id.020.01.3441.1.jpg" xlink:href="020/01/3441/1.jpg"/></s></p><p type="caption">

<s>Figura 193.<lb/>e da vene inessiccabili passin l'acque dalle <lb/>parti B, D verso AF, CH. </s>

<s>Avendo le quantit&agrave;, <lb/>secondo il Bertizzolo la ragion composta delle <lb/>velocit&agrave; e delle sezioni, e tanto queste, per es&shy;<lb/>sere ugualmente larghe, quanto quelle, per le <lb/>posizioni dell'avversario, stando come le al&shy;<lb/>tezze; manifestamente dovrebbe l'acqua ver&shy;<lb/>sata dalla bocca CH esser tanto maggiore di <lb/>quella versata dalla bocca AF, quanto il qua&shy;<lb/>drato di CG &egrave; maggiore del quadrato di AE. Cosicch&egrave;, se CG ad AE fosse <lb/>doppio, dovrebbe la bocca CH gittare il quadruplo della AF. &ldquo; La qual cosa, <pb xlink:href="020/01/3442.jpg" pagenum="403"/>conclude Galileo, indubitatamente non si trover&agrave; esser cos&igrave;, n&egrave; si vedr&agrave; but&shy;<lb/>tare il canale DC una goccia pi&ugrave; che il doppio di BA, segno necessarissimo <lb/>che l'acque, nell'uno e nell'altro, vanno con pari corso &rdquo; (ivi, pag. </s>

<s>226). </s></p><p type="main">

<s>L'esperienza non si poteva asserire con tanta sicurt&agrave;, se non fosse stata <lb/>trovata vera. </s>

<s>Ed essendo verissima, c'incontriamo con nostra maraviglia nella <lb/>soluzione di un magno problema, per cui dunque non dovevano allora man&shy;<lb/>care gli argomenti. </s>

<s>Come poteva Galileo essersi certificato che la bocca CH <lb/>non getta una gocciola pi&ugrave; del doppio della bocca AF, se non raccoglien&shy;<lb/>done l'acqua, uscita qua e l&agrave; nel medesimo tempo, in un vaso cilindrico o <lb/>prismatico e, misuratene le altezze, veder l'una tornare al doppio dell'altra? </s>

<s><lb/>E qual era lo strumento usato per la misura del tempo? </s>

<s>Alle quali domande <lb/>non si pu&ograve; aspettar la risposta da Galileo ma dal Bertizzolo, con l'esperienza <lb/>del quale si conformava Galileo stesso, per ridurre <emph type="italics"/>ad hominem<emph.end type="italics"/> la sua con&shy;<lb/>futazione, e perci&ograve; renderla pi&ugrave; efficace. </s></p><p type="main">

<s>Forse il Buteone aveva trovato qualcuno de'pi&ugrave; sagaci, che raccolse il <lb/>seme delle sue parole, e il Bertizzolo, facendo uso della clessidra ad acqua, <lb/>e de'metodi di lui, erasi assicurato che l'esperienza confermava cos&igrave; la teo&shy;<lb/>ria, da non rimoverne il pensiero per le contradizioni del suo potente av&shy;<lb/>versario. </s>

<s>Non ci son note le ragioni di questa filosofica fermezza, ma le deve <lb/>aver ricavate dalle dottrine de'suoi maestri, dietro le quali non gli fu diffi&shy;<lb/>cile il darsi una spiegazione dell'anomalia, che l'esperienza di Galileo faceva <lb/>alla legge universale. </s>

<s>Nel Cardano si leggevano queste cose, da noi riferite <lb/>anche altrove: <emph type="italics"/>Itaque haud dubium est aquas, quae per fistulas et sipho&shy;<lb/>nes deducuntur, et impetu, et continuitute agi: quae vero per canales, <lb/>rivos et locos patentes, solo impetu. </s>

<s>Quamobrem velocius semper fertur <lb/>aqua per siphones quam per rivos, pari ratione, paribusque auxiliis et <lb/>impedimentis constitutis.<emph.end type="italics"/></s></p><p type="main">

<s>Ora essendo i due canali AB, CD di Galileo due sifoni, &egrave; manifesto per&shy;<lb/>ch&egrave; non si osservino in essi le medesime leggi, che ne'canali aperti o ne&igrave; <lb/>rivi patenti: perch&egrave;, cio&egrave;, l'acqua v'&egrave; dedotta in quelli, non per solo im&shy;<lb/>peto come in questi, ma per impeto e continuit&agrave;, non potendo l'una sezione, <lb/>per esser maggiormente velocitata, dilungarsi dall'altra, senza lasciarvi fra <lb/>mezzo uno spazio vuoto, d'onde il moto ne'sifoni &egrave; pi&ugrave; veloce, come quello <lb/>che, secondo il Cardano stesso, <emph type="italics"/>ab aere iuvatur.<emph.end type="italics"/> Consegue, per la detta ra&shy;<lb/>gion della continuit&agrave;, che gl'impeti del gettare sono que'medesimi, con cui <lb/>si muovono le sezioni per tutta la lunghezza dei canali. </s>

<s>E perch&egrave; cotali im&shy;<lb/>peti dipendono dalle sole cadute, che sono uguali, supponendosi uguali le <lb/>inclinazioni; dunque anche essi impeti sono uguali. </s>

<s>Ora stando in questo <lb/>caso le quantit&agrave; come le semplici altezze non fa maraviglia che la bocca GH, <lb/>rispetto alla AF, non si trovi gittar nel medesimo tempo altro che il doppio. </s>

<s><lb/>Nei canali aperti invece e nei fiumi, intorno a che propriamente cadeva la <lb/>controversia, il moto non &egrave; uniforme per tutta la lunghezza dell'alveo, ma <lb/>sempre pi&ugrave; accelerato. </s>

<s>Ond'essendo le velocit&agrave; varie, le quantit&agrave; non stanno <lb/>nella ragion semplice delle altezze, ma nella composta di loro e delle sezioni, <pb xlink:href="020/01/3443.jpg" pagenum="404"/>e perci&ograve; per una sezione di doppia altezza deve necessariamente passare una <lb/>mole d'acqua quadruplicata. </s></p><p type="main">

<s>N&egrave; possiamo qui trattenerci dal ripensare alle dovizie della Scienza, cos&igrave; <lb/>improvvidamente rifiutate da Galileo. </s>

<s>Si potrebbe disputar se le perdite va&shy;<lb/>lessero i nuovi acquisti, ma non si pu&ograve; da nessuno non prevedere la tanto <lb/>maggiore ubert&agrave;, a cui sarebbe potuto giungere l'albero della Scienza, quando <lb/>il surculo nuovo fosse stato inserito nella vecchia radice. </s>

<s>La faticosa eredit&agrave; <lb/>di tanti secoli, non inerti certamente, al giudizio dei savi, l'avrebbero po&shy;<lb/>tuta Galileo e il Cartesio tramandare intera, e invece la dilapidarono per una <lb/>insana ambizione d'esser essi i primi e i soli, costringendo i discepoli a <lb/>riconquistar a frusto a frusto, con la propria fatica, le disperse sostanze degli <lb/>avi. </s>

<s>L'esempio di ci&ograve; vivo e presente l'abbiamo nel Castelli, che dovette da <lb/>s&egrave; ricostruire pietra per pietra il demolito edifizio idraulico, di che a lui <lb/>solo, e non gi&agrave; a Frontino o a Leonardo da Vinci, noi posteri dobbiam tutto <lb/>il merito: merito, che non gli potrebbe esser mai tolto n&egrave; menomato dal&shy;<lb/>l'eloquenza dei Fabbretti e dei Lombardini. </s></p><p type="main">

<s>Consideriamo le condizioni, a cui si ridusse lo stesso Galileo, che, avendo <lb/>rifiutato di sedersi al lauto convito de'suoi precursori, si chin&ograve; poi a raccat&shy;<lb/>tare le miche dalla mensa, che il suo Discepolo aveva scarsamente riappa&shy;<lb/>recchiata. </s>

<s>Le controversie col Bertizzolo risalgono ai principii del secolo XVII, <lb/>e a questo tempo &egrave; da riferire il Discorso galileiano in risposta a lui: scrit&shy;<lb/>tura, che non ha forma epistolare, e tanto meno ha la data del 1638, asse&shy;<lb/>gnatale dall'Alb&egrave;ri (VII, 222 in nota). Nel 1625 le risecchite dottrine del <lb/>Bertizzolo rinverdirono nel <emph type="italics"/>Progresso idraulico<emph.end type="italics"/> del Castelli, e Galileo accet&shy;<lb/>tava dalle amiche mani del Discepolo ci&ograve; che prima aveva cos&igrave; risolutamente <lb/>rifiutato da quelle dell'avversario. </s>

<s>Allora aveva affermato e dimostrato che <lb/>una palla di ferro e una mole di acqua non variano velocit&agrave;, se con accre&shy;<lb/>scimento di gravitante materia si facciano scendere nel perpendicolo o lungo <lb/>un piano inclinato, e ora, nella lettera sul fiume Bisenzio, dice che, sebbene <lb/>ci&ograve; propriamente segua nei mobili solidi, <emph type="italics"/>ne'fluidi per&ograve; credo che la cosa <lb/>proceda assai differentemente.<emph.end type="italics"/> Allora aveva attribuito tutto il velocitarsi dei <lb/>fiumi alla pendenza della superficie, e ora avverte che questa non pu&ograve; es&shy;<lb/>sere causa sufficiente, se non si ricorre al premere, che le sezioni precedenti <lb/>fanno gravitando sopra le susseguenti, d'onde si viene a concludere quel <lb/>teorema delle velocit&agrave; proporzionali alle altezze, che prima aveva confutato <lb/>al Bertizzolo, con tante prove di ragioni e di fatti. </s></p><p type="main">

<s>Nonostante questa lettera galileiana, scritta a Raffaello Staccoli il di <lb/>16 Gennaio 1631, &egrave; documento importante alla storia dell'Idrodinamica, per <lb/>le prime applicazioni, che vi si fanno all'acque, delle leggi nuovamente sco&shy;<lb/>perte intorno al moto dei gravi. </s>

<s>La Scienza v'&egrave; senza dubbio sostanzialmente <lb/>promossa, ma rimane cos&igrave; in difetto, in ordine all'unit&agrave; dei principii, che <lb/>la nuova istituzione rimane da questa parte alquanto inferiore all'antica. </s>

<s><lb/>Abbiamo veduto infatti come Leonardo, il Cardano e tutti gl'Idraulici di <lb/>que'tempi, applicassero universalmente ai fluidi quella legge delle velocit&agrave; <pb xlink:href="020/01/3444.jpg" pagenum="405"/>proporzionali alle altezze, che avevano creduto esser propria a tutti i gravi <lb/>cadenti, mentre Galileo e il Castelli professarono questa stessa legge in certi <lb/>casi, eccettu&aacute;ndone altri, ai quali soli applicarono la nuova legge delle ve&shy;<lb/>locit&agrave; proporzionali alle radici delle altezze. </s></p><p type="main">

<s>Per questa mancanza d'unit&agrave; nel principio informativo, l'Idrodinamica, <lb/>nonostante i felici ardimenti di Galileo, non si poteva dire istituita, e perch&egrave; <lb/>ci&ograve; avvenisse, era necessario che se la legge degli spazii proporzionali ai <lb/>quadrati dei tempi era vera, dovesse anch'essere universale, e perci&ograve; indi&shy;<lb/>pendente da ogni accidental differenza, che potesse passare fra solidi e liquidi, <lb/>e dal diverso modo del fluire di questi dai vasi artificiali, o dal loro correre <lb/>naturalmente nei fiumi. </s>

<s>L'universalit&agrave; poi di questa legge, per la quale venne <lb/>a istituirsi l'Idrodinamica nuova, fu con metodi matematici dimostrata dal <lb/>Torricelli, e rimane ora a noi a narrare della felice istituzione i principii <lb/>avventurosi e i progressi. </s></p><p type="main">

<s><emph type="center"/>IV.<emph.end type="center"/></s></p><p type="main">

<s>Per risalire a cotesti principii convien penetrare in quelle stanze delle <lb/>ville di Bellosguardo e di Arcetri, nelle quali Galileo raccoglieva intorno a s&egrave; <lb/>gli amici, che per il soggetto della conversazione si rendevano altrettanti sco&shy;<lb/>lari. </s>

<s>Erano per lo pi&ugrave; gentiluomini fiorentini, fra'quali Mario Guiducci, Lo&shy;<lb/>dovico Incontri, Tommaso Renuccini, Niccol&ograve; e Andrea Arrighetti, che sta&shy;<lb/>vano volentieri ad ascoltare il Maestro, perch&egrave; aveva sempre qualche cosa di <lb/>nuovo tra curioso e utile a sapersi, e per cui pareva che diventassero a cos&igrave; <lb/>dire umane, le astratte speculazioni della Scienza. </s>

<s>Ora aveva ricette da gua&shy;<lb/>rire alcune fra le infermit&agrave; o incomodi pi&ugrave; comuni, ora suggeriva espedienti <lb/>contro gl'insetti nocivi, ora insegnava certi segreti, da far nelle pi&ugrave; umili <lb/>domestiche faccende apparir l'eccellenza del filosofo sopra la gente volgare. </s>

<s><lb/>Ma pi&ugrave; spesso erano cos&igrave; fatti segreti intorno agli esercizi dell'agricoltura, <lb/>e que'gentiluomini, tutti possessori di ville nelle campagne toscane, erano <lb/>curiosi di ascoltarli sopra gli altri, perch&egrave;, praticandoli, si dilettavano di farne <lb/>stupire i loro villici e i castaldi. </s></p><p type="main">

<s>Di tutto ci&ograve;, come di cose indegne della fama e della sapienza di Ga&shy;<lb/>lileo, non ci sarebbe rimasto memoria, se il Viviani non ce l'avesse conser&shy;<lb/>vata in uno de'suoi tanti volumi manoscritti, in cui l'esperienze e i pen&shy;<lb/>sieri raccoltivi dentro, con mano giovanile, ci siam dovuti persuadere oramai <lb/>che son per la massima parte non suoi, ma del Maestro. </s>

<s>Fra cotesti varii <lb/>pensieri intorno a materie meccaniche, fisiche, astronomiche, filosofiche e <lb/>altro, che il Viviani stesso dice di avere scritti senz'ordine, ci troviamo rac&shy;<lb/>colti anche questi: &ldquo; I calli de'piedi, racconta chi l'ha sperimentato in s&egrave; <lb/>e in altri, che si guariscono per sempre col tenere i piedi nell'acqua del <lb/>bagno detto della Doccia, lontan da Pisa due miglia, per tempo di un'ora e <pb xlink:href="020/01/3445.jpg" pagenum="406"/>mezzo il giorno, per tre o quattro giorni &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXXXV, <lb/>fol. </s>

<s>4). &ldquo; Per far morire i moscerini del grano, nella medesima stanza, farai <lb/>prendere il tabacco in fumo, e ben piena di detto fumo chiudi la stanza, <lb/>che quel fumo gli ammazzer&agrave;. </s>

<s>Non per anco provato. </s>

<s>&mdash; Per levar via la <lb/>febbre, acqua stillata di gusci verdi di noci fresche: prendine quanto un bic&shy;<lb/>chiere nel principio della febbre, che ti liberer&agrave;. </s>

<s>&mdash; Per il dolore dei denti, <lb/>cera gialla, seme di porri, seme iusquiamo o veramente di dente cavallino: <lb/>fattone palla, quale posta sopra un ferro infocato e per mezzo di un imbuto, <lb/>che con la campana di esso riceva il fumo, e col fusto faccia penetrare il <lb/>dente guasto; che lever&agrave; il dolore. </s>

<s>&mdash; Per lavare indiane, pezzuole di seta, <lb/>di filaticcio o di stame, prendi il fiele di bue o di vitello: dimenalo ben bene <lb/>in una catinella, tanto che faccia molta schiuma, e poi lava in detto fiele <lb/>quello che vuoi di seta, bambagia o stame, che sia colorito, e poi risciac&shy;<lb/>qualo in acqua fresca; che lo vederai pulito, senza perder punto di colore. </s>

<s><lb/>Provato e riuscito &rdquo; (ivi, fol. </s>

<s>10 a tergo). </s></p><p type="main">

<s>Ma ad avviarci pi&ugrave; direttamente per i nostri sentieri, fa a proposito la <lb/>nota seguente: &ldquo; Per cavar da un medesimo tino il vino dolce e maturo, <lb/>e far che vi resti l'agro, si faccia empire il tino di uve senza ammostare in <lb/>grappoli interi, e si lasci cos&igrave; stare per qualche poco di tempo, che, stu&shy;<lb/>rando la cannella, uscir&agrave; vino maturo, che sar&agrave; quello dei grani dell'uva pi&ugrave; <lb/>maturi, spremuti dal peso e carico proprio de'grappoli, che sono i primi a <lb/>scoppiare. </s>

<s>E dopo che sar&agrave; uscito tal vino dolce, pigiando e ammostando <lb/>l'uve, ne uscir&agrave; il vino assai meno maturo, anzi assai aspro, secondo per&ograve; <lb/>che l'uve per loro stesse saranno pi&ugrave; o meno mature generalmente. </s>

<s>Inven&shy;<lb/>zione del Galileo provata e riuscita, e insegnata dal sig. </s>

<s>Andrea Arrighetti &rdquo; <lb/>(ivi, fol. </s>

<s>7). </s></p><p type="main">

<s>Un'altra volta, essendo il discorso caduto in un argomento di simil <lb/>genere, fu proposta la soluzioue di un tal problema: &mdash; in che maniera <lb/>il primo vino, che esce da una botte quando si manomette, &egrave; pi&ugrave; debole di <lb/>quello ch'esce di poi, e perch&egrave;, per un po'di tempo, si trova che va mi&shy;<lb/>gliorando? </s>

<s>&mdash; Furono date varie risposte, e la migliore, che sembra avere <lb/>approvata anche Galileo, si riduceva a dire che, insieme col primo vino, <lb/>escono le fecce, deposte e appastate intorno allo zipolo o alla cannella, di <lb/>che, venendosi via via a rilavare il foro, &egrave; perci&ograve; che il vino stesso si sente <lb/>venir via via sempre pi&ugrave; migliorando. </s>

<s>Andrea Arrighetti per&ograve; non rimaneva <lb/>sodisfatto di queste ragioni, e ripensando a ci&ograve;, che aveva tante volte osser&shy;<lb/>vato negli orologi a polvere, stim&ograve; che similmente avvenisse del vino della <lb/>botte, cosicch&egrave;, scendendo al foro per il primo quello, che &egrave; alla superficie, <lb/>per questo solo si mostri pi&ugrave; debole dell'altro, perch&egrave;, rimasto nello scemare <lb/>al contatto con l'aria filtratavi di fuori, non pu&ograve; non aver preso, e non rite&shy;<lb/>nere in s&egrave; alquanto dello scipito. </s></p><p type="main">

<s>Il pensiero, nato nella mente dell'Arrighetti da cos&igrave; umile luogo, trov&ograve; <lb/>presto da nobilitarsi nella risoluzione di alcuni problemi, che a chiunque <lb/>avesse professate le dottrine idrostatiche di Galileo rimanevano irresolubili. <pb xlink:href="020/01/3446.jpg" pagenum="407"/>Insegnandosi infatti, nel Discorso intorno i galleggianti, che l'acqua nel&shy;<lb/>l'acqua non pesa, si veniva a escludere, dai vari mezzi di dimostrare le ve&shy;<lb/>rit&agrave; fondamentali della Scienza, quel principio delle pressioni proporzionali <lb/>al numero degli strati soprapposti, di che avevano fatto uso il Cardano e <lb/>Leonardo da Vinci, e a cui perci&ograve; il Cavalieri e il Castelli sostituirono il <lb/>moto di que'medesimi strati, dipendente dall'inclinazione dei letti. </s>

<s>Ma es&shy;<lb/>sendo l'acqua stagnante, cio&egrave; senza peso e senza moto, rimaneva inesplica&shy;<lb/>bile come mai, attraverso al medesimo foro, partendosi in ogni modo il li&shy;<lb/>quido dalla quiete, si vedesse nulladimeno uscire pi&ugrave; veloce dal vaso pieno, <lb/>che dallo scemo. </s>

<s>Ora l'Arrighetti, in quel suo nuovo pensiero, trovava fa&shy;<lb/>cile la soluzione di questo dubbio, dicendo che le velocit&agrave; non dipendono dai <lb/>pesi ma dalle cadute, le quali, quanto il vaso &egrave; pi&ugrave; pieno, tanto natural&shy;<lb/>mente si fanno da maggiori altezze. </s>

<s>Incominciatosi poi a diffidare del prin&shy;<lb/>cipio delle velocit&agrave; virtuali, anco il paradosso idrostatico rimaneva negli in&shy;<lb/>segnamenti galileiani senza spiegazione, che l'Arrighetti dall'altra parte <lb/>ricavava assai facilmente dal suo proprio supposto, perch&egrave; se l'equilibrio, fra <lb/>l'acqua del vaso grande e della piccola canna con lui congiunta, non dipende <lb/>dalla quantit&agrave; di materia, ma da sola la velocit&agrave;, s'intende come, per con&shy;<lb/>dizion necessaria di esso equilibrio, non si richieda se non che siano uguali <lb/>le velocit&agrave; naturalmente acquistate per la discesa, ossia che siano uguali le <lb/>altezze de'supremi livelli. </s></p><p type="main">

<s>Di queste speculazioni, rimaste per qualche tempo un commento a'suoi <lb/>privati studi d'Idrostatica, trov&ograve; l'Arrighetti da farne l'applicazione, quando <lb/>fu chiamato a consulto dal Granduca intorno al riparare i guasti, e a prov&shy;<lb/>vedere che avesse buon effetto il condotto delle acque dalla collina di Mon&shy;<lb/>tereggi nel giardino di Boboli. </s>

<s>S'incorreva dagl'ingegneri in quell'errore, <lb/>ammonito gi&agrave; dal Cardano, che dovesse l'acqua risalire in ogni modo alla <lb/>medesima altezza da cui fu scesa, come nei piccoli vasi comunicanti, e le re&shy;<lb/>sistenze, che dovevano far le canne del condotto, si calcolavano dal solo peso <lb/>morto dell'acqua. </s>

<s>Ora l'Arrighetti aveva intorno a questo proposito altri pen&shy;<lb/>sieri, e prima di comunicargli volle sentire il parere del Castelli, a cui scrisse <lb/>sopra questo soggetto varie lettere, in una delle quali diceva ch'egli consi&shy;<lb/>glierebbe di fare le dette canne, non di pi&ugrave; resistente materia, ma pi&ugrave; lar&shy;<lb/>ghe, acciocch&egrave; meglio potessero resistere alla forza, &ldquo; che gli far&agrave; il peso, o <lb/>per dir meglio la velocit&agrave;, che andr&agrave; acquistando l'acqua nel venire a basso. </s>

<s><lb/>Dico nel venire a basso, perch&egrave;, come comincier&agrave; a trovare qualche salita <lb/>o altro impedimento, quanto si andr&agrave; ritardando la sua velocit&agrave; in qualsi&shy;<lb/>voglia luogo, tanto andr&agrave; scemando la forza, che ricevono le canne nel me&shy;<lb/>desimo luogo, essendo io di parere che dipenda interamente dalle velocit&agrave;, <lb/>e non dal peso dell'acqua, n&egrave; credo che in questo negozio il peso operi cosa <lb/>alcuna, mentre non sia congiunto con velocit&agrave; &rdquo; (<emph type="italics"/>Autori che trattano del <lb/>moto dell'acque,<emph.end type="italics"/> ediz. </s>

<s>cit., T. IV, pag. </s>

<s>204). </s></p><p type="main">

<s>La proposizione riscontra con quell'altra, che cos&igrave; leggemmo altrove <lb/>dall'Aggiunti formulata: <emph type="italics"/>Anco la sola velocit&agrave;, senza il peso, opera ed ha<emph.end type="italics"/><pb xlink:href="020/01/3447.jpg" pagenum="408"/><emph type="italics"/>momento.<emph.end type="italics"/> E come a provarla esso Aggiunti ricorreva all'esempio dei venti, <lb/><emph type="italics"/>i quali, non essendo altro che aria mossa nell'aria, non hanno forza altro <lb/>che dalla velocit&agrave;, perch&egrave; un grave, in un mezzo ugualmente grave in <lb/>specie, come dimostra Archimede, non ha peso alcuno in detto mezzo;<emph.end type="italics"/><lb/>cos&igrave; l'Arrighetti diceva persuadergli la verit&agrave; della medesima proposizione <lb/>&ldquo; il vedere che l'acqua nell'acqua non pesa, e che in un sifone piramidale <lb/>tanto si livella nel vaso l'una, quanto l'altra estremit&agrave; &rdquo; (ivi). </s></p><p type="main">

<s>Cos&igrave;, avendo fatto apparire il pensiero per spiraglio, non pot&egrave; l'Arri&shy;<lb/>ghetti ritenersi dall'aprir tutto, e dal rendere scoperto alla vista del Castelli <lb/>quello, cli'egli chiamava una girandola, una fantasia, un sogno, una cosa <lb/>insomma, da non si registrar fra le chiare e certe. </s>

<s>&ldquo; Io osservo, egli dice, <lb/>negli orologi a polvere, nelle tramogge e in altri simili vasi, che come sieno <lb/>avvivati fanno di sopra un certo foro, per il quale va calando la polvere o <lb/>altro, riducendosi verso il pertugio, che &egrave; nel fondo di detto vaso, e pare che <lb/>le particelle superiori, nel calare abbasso per quel declive, impediscano in <lb/>un certo modo, con la velocit&agrave; del loro moto quasi perpendicolare, il moto <lb/>transversale, che le particelle inferiori dovrebbero fare, per accostarsi al detto <lb/>foro. </s>

<s>Il medesimo effetto, e molto pi&ugrave;, pare che si osservi in un pilo o altro <lb/>vaso, che nel versare l'acqua o altro fa di sopra ancor lui il medesimo, sic&shy;<lb/>ch&egrave;, avviato che sia, per le medesime ragioni, pare che le particelle dell'acqua <lb/>superiori debbano impedire, con il loro moto perpendicolare, il moto trasver&shy;<lb/>sale delle parti inferiori ed esser le prime a calare a basso, accrescendo la <lb/>velocit&agrave; continuamente, finch&egrave; arrivate al buco, che &egrave; nel fondo del vaso, si <lb/>partano dal detto luogo con quella velocit&agrave;, che hanno acquistata fin l&igrave;. </s>

<s>E <lb/>questa mi viene in fantasia che possa essere la cagione, mediante la quale <lb/>un tino o botte getta, per la medesima canna, pi&ugrave; quando &egrave; pieno, che <lb/>quando &egrave; scemo, poich&egrave; quel lquido arriva alla canna con maggior velocit&agrave; <lb/>una volta che l'altra, secondo che la caduta &egrave; maggiore o minore, non es&shy;<lb/>sendo io capace che se, quando comincia a uscire per la cannella, si parte <lb/>dalla quiete tanto quando &egrave; pieno, che quando &egrave; scemo, non abbia da uscire <lb/>sempre con la medesima velocit&agrave;. </s>

<s>E questa per avventura potria essere la <lb/>soluzione di un problema assai ridicolo di questi canovai, che dicono che il <lb/>primo vino, che esce da una botte, quando si manomette, &egrave; pi&ugrave; debole di <lb/>quello, ch'esce dipoi, e che per un po'di tempo va migliorando, che po&shy;<lb/>trebb'essere, come dicono loro, che uscisse prima quel di sopra, molto pi&ugrave; <lb/>debole per essere stato scemo. </s>

<s>Il che, come mi son dichiarato, sia detto per <lb/>un sogno, e solo per significarle le difficolt&agrave;, che mi s'aggirano per la fan&shy;<lb/>tasia circa quello, che possa operare il peso in questo particolare, che non <lb/>credo ci operi cosa alcuna, ma sibbene la maggiore o minor calata &rdquo; (ivi, <lb/>pag. </s>

<s>204, 5). </s></p><p type="main">

<s>Se dunque le velocit&agrave; son tali, quali si convengono alle calate dal su&shy;<lb/>premo livello del liquido, il discorso dell'Arrighetti portava manifestamente <lb/>a concludere, per le leggi galileiane nuovamente pubblicate, che esse velo&shy;<lb/>cit&agrave; son proporzionali alle radici delle altezze, da cui si suppongon calare: <pb xlink:href="020/01/3448.jpg" pagenum="409"/>conclusione, che se il Castelli non reput&ograve; una girandola, un sogno, una fan&shy;<lb/>tasia, &egrave; un fatto per&ograve; che non seppe riconoscerne allora l'importanza, e per&shy;<lb/>suaso esser differente il modo del correr l'acqua dentro i sifoni e per gli <lb/>alvei, non dubit&ograve; punto, ammaestrato dall'esperienze, della verit&agrave; della pro&shy;<lb/>posizione, che poi dimostrerebbe, dicendo che, se diventa un fiume alto il <lb/>doppio, si deve anche movere doppiamente veloce. </s>

<s>Dalla qual proposizione, <lb/>ricalcando l'orme del Cavalieri, passava immediatamente anche il Castelli a <lb/>dimostrar l'altra, che dice aver le quantit&agrave; dell'acqua la proporzion com&shy;<lb/>posta dell'altezza viva all'altezza viva, e della velocit&agrave; alla velocit&agrave;. </s>

<s>E perch&egrave; <lb/>questa della velocit&agrave; alla velocit&agrave; aveva prima dimostrato esser la propor&shy;<lb/>zion medesima, che ha l'altezza all'altezza; ne faceva finalmente conseguire <lb/>di qui la verit&agrave; desiderata, che cio&egrave; &ldquo; la quantit&agrave; dell'acqua che scorre, <lb/>quando il fiume &egrave; alto, a quella che scorre, mentre &egrave; basso, ha duplicata <lb/>proporzione dell'altezza all'altezza, cio&egrave; la proporzione, che hanno i quadrati <lb/>delle altezze &rdquo; (<emph type="italics"/>Della misura delle acque,<emph.end type="italics"/> lib. </s>

<s>II, Bologna 1660, pag. </s>

<s>83). </s></p><p type="main">

<s>Di queste proposizioni, ordinatamente disposte, illustrate con considera&shy;<lb/>zioni, e svolte in corollari, aggiuntivi alcuni discorsi, ne'quali s'applicavano <lb/>le dimostrate dottrine alle questioni della laguna veneta; il Castelli aveva <lb/>compilata una scrittura, che quasi secondo libro poteva aggiungersi a quello <lb/>gi&agrave; pubblicato della Misura delle acque correnti. </s>

<s>Il manoscritto fu spedito di <lb/>Roma il d&igrave; 20 Settembre 1642 al principe Leopoldo de'Medici, per dedicar <lb/>l'opera <emph type="italics"/>subito nata<emph.end type="italics"/> ai felicissimi natali di colui, che fu poi Cosimo III di <lb/>Toscana, e il Castelli cos&igrave; diceva a esso principe Leopoldo nella lettera, con <lb/>la quale gli accompagnava l'offerta: &ldquo; Quando non sia per servizio del se&shy;<lb/>renissimo Granduca, mi sarebbe caro che non si pubblicasse ad alcuno que&shy;<lb/>sto mio ritrovamento, eccettuati il p. </s>

<s>Francesco delle Scuole pie (Famiano <lb/>Michelini) ed i signori Andrea Arrighetti, Mario Guiducci, Tommaso Rinuc&shy;<lb/>cini ed Evangelista Torricelli, i quali desidero che vedano la scrittura per <lb/>emendare i miei falli &rdquo; (Fabbroni, <emph type="italics"/>Lettere inedite,<emph.end type="italics"/> T. I, Firenze 1773, pag. </s>

<s>78). </s></p><p type="main">

<s>Fra gli esaminatori della scrittura, che il Castelli stesso cos&igrave; a nome <lb/>additava, il principe Leopoldo scelse particolarmente il Torricelli e l'Arri&shy;<lb/>ghetti: il primo per la celebrit&agrave; del nome, acquistatasi in ogni genere di <lb/>scienze fisiche e matematiche, il secondo per i saggi, che aveva dato de'suoi <lb/>studi in materia di acque. </s>

<s>L'Arrighetti ferm&ograve; principalmente la sua atten&shy;<lb/>zione sopra quella, che trov&ograve; messa nel manoscritto per la proposizione se&shy;<lb/>conda, e conferendo i dubbi, che si sentiva nascere di li, col Torricelli, gli <lb/>esplicava il suo proprio pensiero, concludendogli che, se non era una giran&shy;<lb/>dola o un sogno, le velocit&agrave; dell'acqua, corrente attraverso il regolatore di <lb/>un fiume, dovevano crescere come le radici, e non come le semplici altezze. </s></p><p type="main">

<s>Questa volta il fecondo seme dell'Idrodinamica cadde sul terreno meglio <lb/>disposto a riceverlo, e a farlo germogliare. </s>

<s>Il Torricelli infatti supporr&agrave; tra <lb/>poco, per fondamento al suo nuovo edifizio, il pensiero stesso dell'Arrighetti: <lb/>&ldquo; Supponimus aquas violenter erumpentes, in ipso eruptionis puncto, eum&shy;<lb/>dem impetum habere, quem haberet grave aliquod, sive ipsius aquae gutta <pb xlink:href="020/01/3449.jpg" pagenum="410"/>una, si ex suprema eiusdem aquae superficie, usque ad orificium eruptionis, <lb/>naturaliter cecidisset &rdquo; (<emph type="italics"/>Opera geom.,<emph.end type="italics"/> P. I, Florentiae 1644, pag. </s>

<s>191). </s></p><p type="main">

<s>Se non che, mentre l'Arrighetti non aveva a confortare la verit&agrave; del <lb/>suo supposto che l'osservazione della <emph type="italics"/>cateratta,<emph.end type="italics"/> formatasi dentro la polvere <lb/>degli orologi, o dentro l'acqua de'pili; il Torricelli pens&ograve; ad altre osserva&shy;<lb/>zioni o sperienze che, illustrate dalla nuova scienza del moto, sarebbero per <lb/>riuscire anche pi&ugrave; concludenti. </s>

<s>Il primo pensiero fu quello dell'acqua che, <lb/>scesa in fondo a uno de'rami del sifone ritorto, acquista impeto di risalire <lb/>alla medesima altezza nell'altro, a quel modo che Galileo aveva supposto ve&shy;<lb/>rificarsi ne'rimbalzi di una palla perfettamente elastica, e dalla quale s'in&shy;<lb/>tendesse rimossa ogni sorta d'impedimenti. </s>

<s>Che se ci&ograve; avviene nel risalir <lb/>che fa l'acqua, ritenut&agrave; dalle pareti del tubo, par verosimile, proseguiva a <lb/>ragionare il Torricelli, che non altrimenti da ci&ograve; avvenga, quando erompe <lb/>nell'aria aperta, come si ricordava di avere osservato pi&ugrave; volte negli zampilli. </s></p><p type="main">

<s>Considerava inoltre che, per questa eruzione violenta, ogni gocciola <lb/>d'acqua &egrave; un proietto, in cui, dovendosi verificare le propriet&agrave; del moto pa&shy;<lb/>rabolico, soccorrerebbero dunque opportune le esperienze a decidere della <lb/>verit&agrave; del supposto. </s>

<s>Dato infatti un foro aperto nella parete verticale di un <lb/>vaso, la distanza di lui, dal livello del liquido che gli sta sopra, sarebbe la <lb/>sublimit&agrave; della parabola, della quale calcolandosi per i teoremi galileiani <lb/>l'ampiezza, per l'estremit&agrave; di lei, eretta perpendicolarmente alla parete, si <lb/>dovrebbe veder passare la curva del getto. </s>

<s>A queste esperienze meccaniche <lb/>pensava il Torricelli stesso che se ne sarebbe potuta aggiungere un'altra <lb/>idrometrica, prendendo vari vasi cilindrici o prismatici, tutti di fondo uguale, <lb/>ma con altezze, che crescessero via via da uno, a quattro, a nove, a sedici, <lb/>secondo la serie dei numeri quadrati. </s>

<s>Fatti in fondo a ciascun vaso fori <lb/>uguali, e mantenutavi l'acqua indeficiente in tutti, raccogliendo con diligenza <lb/>le quantit&agrave; fluite nel medesimo tempo, si dovrebbe trovar che stanno come <lb/>uno, due, tre, quattro, secondo la serie dei numeri naturali, se fosse vero <lb/>che gl'impeti nell'uscire dai fori son qualmente si convengono alle cadute, <lb/>e perci&ograve; proporzionali alle radici delle linee, che misurano nel perpendicolo <lb/>quelle stesse cadute. </s></p><p type="main">

<s><emph type="italics"/>Haec speculatio convenit exactissime cum experimento, a nobis cum <lb/>summa diligentia facto,<emph.end type="italics"/> scrisse poi il Torricelli (<emph type="italics"/>Op. </s>

<s>geom.<emph.end type="italics"/> cit., pag. </s>

<s>200), <lb/>bench&egrave; poco prima avesse confessato che lo sperimento l'aveva eseguito in <lb/>Roma l'amico suo Raffaello Magiotti, <emph type="italics"/>eruditissimus vir, aeque literis scien&shy;<lb/>tiisque omnibus ornatus<emph.end type="italics"/> (ibid., pag. </s>

<s>196). N&egrave; solamente l'esperienza idro&shy;<lb/>metrica crediamo essere stata fatta dal Magiotti, ma le due meccaniche sopra <lb/>dette altresi, almeno con quella diligenza, con la quale il Torricelli stesso <lb/>poi le descrisse nel suo libro, per rimovere dai lettori ogni occasione di <lb/>dubbio. </s></p><p type="main">

<s>Il Magiotti dunque, dietro le proposte venutegli di Firenze per lettera <lb/>dell'amico, fece costruire una cassetta parallelepipeda di rame, <emph type="italics"/>cuius alti&shy;<lb/>tudo passum geometricum excedebat, cuius basis uno palmo quadrato non<emph.end type="italics"/><pb xlink:href="020/01/3450.jpg" pagenum="411"/><emph type="italics"/>erat minor<emph.end type="italics"/> (ibid., pag. </s>

<s>164). In fondo alla cassetta era applicato un tubo, <lb/>pure parallelepipedo, colla bocca esteriore chiuso, e sul fondo superiore di&shy;<lb/>sposto in perfetto piano orizontale, praticatovi un foro <emph type="italics"/>circulo humanae pu&shy;<lb/>pillae maior, non perperam factum, sed solertissime excavatum in lamella <lb/>cuprea<emph.end type="italics"/> (ibid.). Turato poi il foro, mantenuto indeficientemente pien d'acqua <lb/>il vaso in fino all'orlo, sopra il quale posata sporgeva una riga per segnare <lb/>il livello, dato l'esito, vedeva il Magiotti risalir lo zampillo cos&igrave; fin presso <lb/>al segno, da poter dire che fosse giunto all'altezza medesima, da cui sup&shy;<lb/>ponevasi sceso, avuto riguardo alla resistenza dell'aria e all'impedimento, <lb/>che le prime gocciole, nel dar la volta in gi&ugrave;, fanno sopra le antecedenti, <lb/>che non hanno ancora finito di salire. </s>

<s>Che poi a cos&igrave; fatte cause fosse da <lb/>attribuire il non rispondere sempre puntualmente l'esperienze alle teorie, se <lb/>ne persuadeva il Magiotti con l'osservare che, aprendosi il foro a un tratto, <lb/>le prime gocciole, che non avevano chi le antecedesse, giungevano pi&ugrave; ad <lb/>alto, e col sostituire all'acqua il mercurio, che pure si vide toccar pi&ugrave; presso <lb/>al segno, perch&egrave; la maggior gravit&agrave; naturale &egrave; meglio atta a vincere la re&shy;<lb/>ristenza del mezzo. </s></p><p type="main">

<s>Quanto ai getti fu pure sperimentato dallo stesso Magiotti che, se usci&shy;<lb/>vano con direzione orizontale, descrivevano una mezza parabola, e se con <lb/>direzione inclinata una parabola intera, esattamente corrispondente con ci&ograve;, <lb/>che Galileo aveva dimostrato dei moti proiettizi. </s>

<s>Perch&egrave; poi non dovessero <lb/>opporre alcuni alla teoria, non trovando la predetta corrispondenza coi fatti, <lb/>notava alcune diligenze, che lo sperimentatore non avrebbe dovuto trascu&shy;<lb/>rare, e prima di tutto che il foro &egrave; da farsi in una lamina sottilissima e <lb/>piana, applicata alla bocca del tubo esterno, e talmente disposta, da tornar <lb/>perpendicolare alla tangente la curva, descritta dal getto nel punto in cui <lb/>comincia. </s>

<s>&ldquo; Reliquum vero exterioris tubi, usque ad initium aequaeductus, <lb/>debet esse capacissimum, quo enim laxius erit, eo exactius experimentum <lb/>evadet. </s>

<s>Quotiescumque autem aqua, per tubum latentem decurrens, per an&shy;<lb/>gustias transire debuerit, falsa omnia reperientur. </s>

<s>Quemadmodum accidet <lb/>etiam si, prae nimio impetu, aqua, statim atque emissa est, in tenuissum <lb/>rorem dispergatur &rdquo; (ibid., pag. </s>

<s>198). </s></p><p type="main">

<s>Vedendo il Torricelli cos&igrave; ben confermato, per queste esperienze, che il <lb/>liquido esce dal foro aperto nelle pareti del vaso con tal impeto, quale si con&shy;<lb/>verrebbe, se fosse sceso dal supremo livello; pensava fra s&egrave; medesimo come <lb/><figure id="id.020.01.3450.1.jpg" xlink:href="020/01/3450/1.jpg"/></s></p><p type="caption">

<s>Figura 194.<lb/>si potesse il fatto, sperimentato nei vasi, applicare <lb/>alle acque correnti, persuaso che non si dovevano <lb/>nemmen queste sottrarre alla legge universale <lb/>dei gravi. </s>

<s>E il pensiero lo condusse a riguardare <lb/>nell'acqua stagnante un conato al moto, che <lb/>si attua rompendo la parete, o sollevando a un <lb/>tratto la cateratta dallo sbocco di un canale. </s></p><p type="main">

<s>Sia di questo canale rappresentata in CB (fig. </s>

<s>194) la sezione, e in CD <lb/>la cateratta, sopra gl'infiniti punti della quale, come in D e in A, l'acqua <pb xlink:href="020/01/3451.jpg" pagenum="412"/>esercitando il suo conato, uscirebbe in moto attuale per essi, supposti forati, <lb/>con gl'impeti convenienti alle cadute naturali dalle altezze CD, CA, cosic&shy;<lb/>ch&egrave;, se sopra CL, intesa verticalmente eretta, s'alzino le ordinate perpen&shy;<lb/>dicolari DE, AF, a rappresentare le velocit&agrave; respettive; queste staranno come <lb/>le radici delle altezze corrispondenti CD, CA. </s>

<s>Facendosi poi le medesime c&ograve;&shy;<lb/>struzioni per tutti gli altri infiniti punti compresi fra CA, AD, verr&agrave; cos&igrave; <lb/>descritta la scala delle velocit&agrave;, la quale dunque, concludeva il Torricelli il <lb/>suo ragionamento, non &egrave; in un triangolo supino, dove la poneva il Cava&shy;<lb/>lieri, e tanto meno in un rettangolo, in che s'argomentava di ridurla il Ca&shy;<lb/>stelli, ma in una semiparabola. </s></p><p type="main">

<s>Venendo ora a istituire il confronto, fra ci&ograve; che si concludeva da cos&igrave; <lb/>fatti principii, e ci&ograve; che si annunziava nella seconda proposizione della scrit&shy;<lb/>tura, sopra la quale si doveva dare il giudizio, il Torricelli v'ebbe a notare <lb/>una sostanzial differenza. </s>

<s>Da A, nella medesima figura, risalga l'acqua in C <lb/>a un'altezza doppia: dimostra il Castelli, nella detta proposizione, che la ve&shy;<lb/>locit&agrave; del fiume in questo stato, alla velocit&agrave; che aveva in quello, sta come <lb/>due a uno, o come quattro a due, mentre, per la legge dei cadenti appli&shy;<lb/>cata all'acqua, dovrebbe stare come quattro alla radice di due. </s></p><p type="main">

<s>Si rappresentino infatti, per rendere analiticamente pi&ugrave; spedito il di&shy;<lb/>scorso del Torricelli, le due velocit&agrave; con le due semiparabole CED, CFA, <lb/>rappresentate per la medesima figura 194, e che chiameremo P, <emph type="italics"/>p.<emph.end type="italics"/> Essendo, <lb/>per le cose dimostrate nel libro <emph type="italics"/>De dimensione parabolae,<emph.end type="italics"/> P=2/3 ED.DC, <lb/><emph type="italics"/>p<emph.end type="italics"/>=2/3 AF.AC, avremo P:<emph type="italics"/>p<emph.end type="italics"/>=ED.DC:AF.AC. </s>

<s>E perch&egrave; DC=2AC <lb/>per supposizione, e per la nuova professata teoria, ED:AF=&radic;DC:&radic;AC; <lb/>dunque P:<emph type="italics"/>p<emph.end type="italics"/>=2&radic;DC:&radic;AC. </s>

<s>Che se facciasi AC uguale a due, e DC uguale <lb/>a quattro, se ne concluder&agrave;, estraendo dal quarto termine la radice, P:<emph type="italics"/>p<emph.end type="italics"/>= <lb/>2.2:&radic;2, ossia che le velocit&agrave; della corrente stanno, conforme a ci&ograve; che fu <lb/>pronunziato, come quattro alla radice di due. </s></p><p type="main">

<s>Un tal giudizio, fondato sulla differenza di cos&igrave; fatte conclusioni, fu dal <lb/>Torricelli riferito al principe Leopoldo, il quale temeva che potesse dispia&shy;<lb/>cere al Castelli, e fu forse per questo motivo che consigli&ograve; il Torricelli stesso <lb/>a rivolgersi piuttosto al Cavalieri, tanto pi&ugrave; che oramai sapevasi molto bene <lb/>essere invenzione di lui quel proprio modo di condurre la dimostrazione, in&shy;<lb/>torno a cui cadevano i dubbi. </s>

<s>Infatti, sul finir di Ottobre del 1642, giungeva <lb/>a fra Bonaventura una lettera, scritta il d&igrave; 25 di quello stesso mese da Fi&shy;<lb/>renze, nella quale il Torricelli, dop'avere accennato a que'vetri per i Tele&shy;<lb/>scopi, de'quali allora aveva piena la testa, cos&igrave; soggiungeva: &ldquo; Intesi poi <lb/>anche che ella s'ingegnava di provare una conclusione intorno all'acque, <lb/>nella quale ho qualche scrupolo, tanto nella conclusione, quanto nella dimo&shy;<lb/>strazione. </s>

<s>Che la conclusione sia vera io lo credo, ma la difficolt&agrave;, quanto a <lb/>me, io non la so sciorre. </s>

<s>La proporr&ograve; pertanto a V. P., supplicandola a si&shy;<lb/>gnificarmi brevemente se &egrave; una vanit&agrave;. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Suppongo che, se un tubo o altro vaso, sempre pieno d'acqua AB <lb/>(fig. </s>

<s>195), sar&agrave; forato in diversi luoghi C, D, ecc.; suppongo che l'acqua, <pb xlink:href="020/01/3452.jpg" pagenum="413"/>che esce dal foro C, abbia tant'impeto, quanto avrebbe una goccia d'acqua, <lb/>caduta dal livello A fino in C: cio&egrave; che gl'impeti delle acque scaturienti <lb/><figure id="id.020.01.3452.1.jpg" xlink:href="020/01/3452/1.jpg"/></s></p><p type="caption">

<s>Figura 195.<lb/>da C, D ecc. </s>

<s>siano gli stessi, che di una gocciola caduta per gli <lb/>spazi AC, AD. </s>

<s>Questo si prova con alcune ragioni, e con pi&ugrave; <lb/>di una esperienza. </s>

<s>Ne dir&ograve; una fatta in Roma esattamente, ed &egrave; <lb/>che, posti uguali li fori C, D, l'acqua, che nel medesimo tempo <lb/>esce per C, a quella che esce per D, sta in sudduplicata pro&shy;<lb/>porzione delle altezze AC, AD, e questo basta per la mia sup&shy;<lb/>posizione. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Ora, sia un'acqua AB (nella precedente fig. </s>

<s>194) la quale <lb/>poi venga accresciuta tanto, che la sezione CB sia doppia d'altezza della prima <lb/>AB. </s>

<s>Si crede che anco la velocit&agrave; sar&agrave; cresciuta al doppio. </s>

<s>Ora discorro cos&igrave;: <lb/>Facciasi intorno al diametro CD una semiparabola. </s>

<s>L'impeto adunque del velo <lb/>d'acqua, che passa per A, &egrave; misurato dalla linea AF, <emph type="italics"/>et sic de reliquis.<emph.end type="italics"/> Per&ograve; <lb/>tutti gl'impeti della sezione CB, a tutti gl'impeti della sezione AB, saranno <lb/>come la semiparabola ECD, alla semiparabola FCA, cio&egrave; come quattro alla <lb/>radice di due, e non a due come si crede. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; So che questo mio &egrave; qualche paralogismo, in materia tanto difficile, <lb/>per&ograve; non ne fo capitale alcuno. </s>

<s>So bene certo che sar&agrave; subito scoperto dal <lb/>perspicacissimo ingegno di V. P. </s>

<s>Non mi sono neanco spiegato bene intera&shy;<lb/>mente, perch&egrave; troppa sarebbe stata la prolissit&agrave;. </s>

<s>Riverisco ecc. </s>

<s>&rdquo; (MSS Gal. </s>

<s><lb/>Disc., T. XL, fol. </s>

<s>119, 29). </s></p><p type="main">

<s>Notabile cosa &egrave; che sebbene, nella loro concisione, le parole del Torri&shy;<lb/>celli riescano a tutti noi cos&igrave; chiare, al Cavalieri nulladimeno facessero dav&shy;<lb/>vero l'effetto di chi non s'&egrave; neanco spiegato bene interamente, come appa&shy;<lb/>risce dalla seguente risposta, fatta pochi giorni dopo, per lettera del d&igrave; 29 Ot&shy;<lb/>tobre da Bologna: &ldquo; Circa l'acqua non sono ne anch'io lontano dal suo pen&shy;<lb/>siero di credere che non sia cos&igrave; certa la conclusione, n&egrave; la supposta dimo&shy;<lb/>strazione, da me mandata al padre don Benedetto, siccome egli pot&egrave; vedere <lb/>i dubbi, che io avevo nella medesima lettera, che gli scrissi sopra questo <lb/>fatto. </s>

<s>Vero &egrave; che la sua supposizione non mi leva affatto l'assenso, poich&egrave;, <lb/>stante il suo esempio del vaso pieno d'acqua forato in diverse altezze, parmi <lb/>che ella consideri nell'acqua solo l'impeto, cagionato dal premer dell'acqua <lb/>superiore mediante la di lei gravezza. </s>

<s>Ma nell'acqua de'fiumi parmi che, <lb/>oltre quella, vi sia ancora da considerare l'impeto o velocit&agrave;, che conferisce <lb/>l'acqua inferiore alla superiore, onde un tal velo d'acqua parmi che, non <lb/>solo alteri il detto impeto, cagionato dalla gravezza dell'acqua superiore, ma <lb/>anco quello, che gli conferisce l'acqua inferiore, che si muove per la pen&shy;<lb/>denza del letto, ci&ograve; che non mi pare accada nel vaso. </s>

<s>E perci&ograve; resto ancora <lb/>irresoluto in questo negozio, non avendo avuto tempo d'applicarvi, ma credo <lb/>che lei, con la sua sottigliezza, chiarir&agrave; il tutto &rdquo; (ivi, T. LXI, fol. </s>

<s>132, 33). </s></p><p type="main">

<s>Apparisce di qui manifesto che il Cavalieri non era entrato addentro al <lb/>pensiero del Torricelli, il quale non consisteva nel considerare i conati, pro&shy;<lb/>dotti dalla gravit&agrave; dell'acqua contro le pareti del vaso, o quelle che, con vo-<pb xlink:href="020/01/3453.jpg" pagenum="414"/>cabolo non usato allora, si dicono <emph type="italics"/>forze morte,<emph.end type="italics"/> ma nel considerare il moto <lb/>attuale, o le forze che, per effetto di questa attuazione, diventano <emph type="italics"/>vive.<emph.end type="italics"/> La <lb/>proposta inaspettata, e la fretta dell'esaminarla, dovettero esser le cause, <lb/>per cui il valent'uomo non senti la fecondit&agrave; del pensiero torricelliano, com&shy;<lb/>prendente in s&egrave; il vero modo di misurare le forze vive dai quadrati delle <lb/>velocit&agrave;, e l'applicazione del principio dell'uguaglianza delle pressioni. </s>

<s>Ma <lb/>rimane tuttavia a far le maraviglie come mai non s'avvedesse che la sua <lb/>risposta, non solamente non faceva al proposito, ma che di pi&ugrave; contradiceva <lb/>alle sue proprie intenzioni. </s>

<s>Se il pensiero infatti del Torricelli fosse stato <lb/>quello di considerar solamente l'impeto, cagionato dal premer che fa l'acqua <lb/>superiore contro l'inferiore, mediante la di lei gravezza; essendo questa gra&shy;<lb/>vezza proporzionale al numero degli strati, non avrebbe potuto altro conclu&shy;<lb/>dere da ci&ograve;, se non che le velocit&agrave; stanno come le altezze, e invece ne con&shy;<lb/>cludeva che stanno come le radici delle altezze. </s>

<s>Se poi si dice che questa <lb/>conclusione &egrave; solamente applicabile alle acque stagnanti, e no alle correnti, <lb/>nelle quali all'impeto cagionato dalla gravezza delle acque superiori s'ag&shy;<lb/>giunge quello, che conferisce a loro il moto delle acque inferiori; si viene <lb/>a concedere che in esse acque correnti le velocit&agrave; non siano proporzionali <lb/>alle altezze, come nelle stagnanti, che contradice all'intenzione del rispon&shy;<lb/>dente, qual era di mantener la verit&agrave; della prima proposta contro la nuova. </s></p><p type="main">

<s>Dei dubbi venuti da Firenze dando parte il Cavalieri al Castelli, gli fa&shy;<lb/>ceva insieme premura di pensare a una soluzione migliore della sua, di che <lb/>per&ograve; il Lombardini non ha speranza, perch&egrave;, se noi dicemmo che il Cava&shy;<lb/>lieri non riusc&igrave; a trovarla per la fretta, egli crede che il Castelli non ci <lb/>avrebbe potuto nemmen pensare, per trovarsi, a cagione della vecchiaia, la <lb/>mente <emph type="italics"/>alquanto indebolita. (Dell'origine ecc.,<emph.end type="italics"/> Discorso cit., pag. </s>

<s>40). Per <lb/>conferma di che il Lombardini dice che, sebbene fosse all'Autore del secondo <lb/>libro della Misura delle acque correnti nota la vera legge torricelliana, egli <lb/>attese nonostante, nella seconda proposizione, a dimostrare che le velocit&agrave; <lb/>stanno, non come le radici, ma come le semplici altezze. </s>

<s>Che poi il Castelli <lb/>conoscesse allora la vera legge torricelliana l'argomenta il Lombardini da <lb/>quelle parole, ch'egli, a pag. </s>

<s>4 del citato Discorso storico, trascrive dalla <lb/>Considerazione seconda dopo la V proposizione, dove cos&igrave; soggiunge il Ca&shy;<lb/>stelli, avendo prima notati i disordini, che si commettono nelle operazioni <lb/>idrauliche tutti i giorni, &ldquo; i quali disordini saranno fuggiti dall'ingegnere, <lb/>instruito delle cose sopradette, particolarmente ove a queste notizie aggiun&shy;<lb/>gesse la cognizione della Filosofia e Matematica, conforme a quello, che al&shy;<lb/>tamente ha penetrato il signor Galileo, e dopo lui, passando pi&ugrave; oltre, il <lb/>signor Evangelista Torricelli, matematico del serenissimo Granduca di To&shy;<lb/>scana, <emph type="italics"/>il quale sottilmente e maravigliosamente tutta questa materia del <lb/>moto ha trattata. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Richiama il Lombardini particolarmente l'attenzion dei lettori sopra <lb/>queste ultime parole, quasi volessero significare che il Torricelli, insieme con <lb/>tutte le altre materie del moto, avesse in fin d'allora sottilmente e maravi-<pb xlink:href="020/01/3454.jpg" pagenum="415"/>gliosamente trattato anche dell'acqua. </s>

<s>L'inganno dell'interpetrazione &egrave; sco&shy;<lb/>perto gi&agrave; dalla storia, per illustrar meglio la quale giova rammemorare che, <lb/>essendo stato il Torricelli in Roma discepolo del Castelli, e attendendovi poi <lb/>per suo proprio esercizio a illustrare e a promovere la Scienza meccanica, <lb/>studiata ne'Dialoghi delle due Scienze nuove; gli vennero composti due libri, <lb/>uno <emph type="italics"/>De motu gravium naturaliter descendentium,<emph.end type="italics"/> e l'altro <emph type="italics"/>De motu pro&shy;<lb/>iectorum,<emph.end type="italics"/> che veduti dal Maestro gli stim&ograve; degni d'essere presentati allo <lb/>stesso Galileo, a cui scriveva da Roma il d&igrave; 2 Marzo 1641: &ldquo; Spero (nel <lb/>venire a Firenze a riverire V. S.) di portargli un libro, e forse ancora il se&shy;<lb/>condo, fatto da un mio discepolo, il quale, avendo avuti i primi principii di <lb/>Geometria dieci anni sono alla mia Scuola, ha poi fatto tal progresso, che <lb/>ha dimostrate molte proposizioni di quelle <emph type="italics"/>De motu,<emph.end type="italics"/> dimostrate gi&agrave; da V. S., <lb/>ma diversamente &rdquo; (Alb. </s>

<s>X, 407, 8). Il d&igrave; 15 del detto mese di Marzo par&shy;<lb/>tiva infatti il Castelli da Roma, portandosi nel baule i due libri manoscritti, <lb/>de'quali fece pochi giorni appresso la presentazione, insieme con una lettera <lb/>del Torricelli, nella quale si scusava delle imperfezioni, specialmente rima&shy;<lb/>ste nella seconda parte dell'opera, trattante <emph type="italics"/>De motu proiectorum,<emph.end type="italics"/> non rico&shy;<lb/>piata &ldquo; ma scritta per la prima volta con molta fretta &rdquo; (ivi, pag. </s>

<s>413). </s></p><p type="main">

<s>Ecco quali sono i libri in materia di moto, da applicarsi utilmente al&shy;<lb/>l'acqua, de'quali intendeva parlare il Castelli, nel luogo sopra trascritto dal <lb/>Lombardini. </s>

<s>Ma l'applicazione, bench&egrave; presentita, e della quale, nella lettera <lb/>allo Staccoli sopra il fiume Bisenzio, s'avevano alcuni esempi; non era stata <lb/>fatta ancora nel 1641: non era cio&egrave; stata fatta ancora, alla seconda parte del <lb/>trattato torricelliano <emph type="italics"/>De motum geavium<emph.end type="italics"/> presentato manoscritto a Galileo, <lb/>l'aggiunta <emph type="italics"/>De motu aquarum,<emph.end type="italics"/> alla quale occorsero, tra il Settembre e l'Ot&shy;<lb/>tobre del 1642, come vedemmo, il principio e l'occasione, e non prima del 1644 <lb/>fu data dall'Autore in Firenze alla luce. </s></p><p type="main">

<s>Essendo dunque un fatto che, quando il Castelli present&ograve; il suo mano&shy;<lb/>scritto al principe Leopoldo di Firenze, la legge degli efflussi non era stata <lb/>dimostrata ancora dal Torricelli, il quale anzi dall'esame del detto ma&shy;<lb/>noscritto prese motivo di far la scoperta; riman privo del suo principale ar&shy;<lb/>gomento il giudizio del Lombardini, a cui ne prevale un altro tutt'affatto <lb/>contrario, che cio&egrave; il Castelli serbava allora tutta la vigoria della mente, <lb/>bench&egrave; temperata dal senno e dalla prudenza senile, come apparir&agrave; dalla <lb/>storia, quale sia ora a noi lecito ordire sopra la trama offertaci dai do&shy;<lb/>cumenti. </s></p><p type="main">

<s>Informato dal Cavalieri di tutto ci&ograve;, ch'era passato fra lui e il Torri&shy;<lb/>celli, relativamente alle proporzioni da assegnarsi tra le velocit&agrave; e le altezze <lb/>nel moto delle acque, il Castelli, a cui troppo premeva la questione, si dette <lb/>a esaminarla con tutta la diligenza. </s>

<s>Era naturale che in questo esame occor&shy;<lb/>resse anche a lui a fare la distinzione, fra l'acqua fluente dai vasi, e la cor&shy;<lb/>rente per le sezioni dei fiumi. </s>

<s>In proposito del primo caso deve essersi sov&shy;<lb/>venuto del pensiero, che otto anni fa l'Arrighetti gli aveva confidato come <lb/>una sua fantasia, da non farne conto, ma che ora vedeva esaltata alla di-<pb xlink:href="020/01/3455.jpg" pagenum="416"/>gnit&agrave; di teorema; e dall'altra parte aveva in Roma presente quello stesso <lb/>Magiotti, da cui s'era con le sue esperienze cos&igrave; efficacemente cooperato a <lb/>confermare la verit&agrave; della nuova proposta. </s>

<s>Spettatore di cos&igrave; fatte esperienze, <lb/>non poteva il Castelli dubitare che le copie dell'acqua, raccolta dai fori aperti <lb/>nelle cassette parallelepipede di rame preparate dal Magiotti, non facessero <lb/>necessariamente argomentare esser le velocit&agrave; degli efflussi proporzionali alle <lb/>radici delle altezze dei livelli. </s>

<s>Dall'altro canto il Magiotti spettatore delle <lb/>esperienze, fatte nelle stanze terrene dell'abbazia di S. Callisto, non poteva <lb/>negare che, dal vedersi far la medesima altezza nel fiumicello, sia da una, <lb/>sia da quattro, sia da nove cannelle aperte, o dal veder che se una cannella <lb/>sola faceva un'altezza, aggiungendovene tre, cinque, sette, l'altezza si faceva <lb/>solamente doppia, tripla, quadrupla; non si dovesse necessariamente argo&shy;<lb/>mentarne che le velocit&agrave; della corrente stanno come le semplici altezze delle <lb/>sezioni. </s></p><p type="main">

<s>Strigar questo nodo non era davvero da menti indebolite, e il Castelli <lb/>lo strigava col vigore assennato della sua mente, ripensando che, poich&egrave; da <lb/>due fatti certissimi s'avevano due conclusioni diverse; diverso dovess'essere <lb/>il modo del fluire l'acqua dai vasi o del correre per i canali. </s>

<s>Ma poi, riflet&shy;<lb/>tendo che costante dev'esser il modo dell'operar la Natura in ogni genere <lb/>di gravi, ne ebbe a concludere che universalmente si verifica la legge delle <lb/>velocit&agrave; proporzionali alle radici delle altezze, ma che nelle acque correnti <lb/>questa medesima legge viene alterata, sia per non esser l'acqua un corpo <lb/>unito, come gli aveva detto il Baliani, sia per conferire gli strati inferiori <lb/>al moto de'superiori, come ora gli veniva dicendo il Cavalieri, sia per altre <lb/>ragioni inescogitabili a lui. </s></p><p type="main">

<s>Dietro ci&ograve; si proponeva di rimetter mano al secondo libro delle Acque <lb/>correnti, in cui si darebbe per legge universale delle velocit&agrave; quella, che re&shy;<lb/>sultava dalle nuove speculazioni e dalle esperienze del Torricelli. </s>

<s>Quanto poi <lb/>alla proposizione seconda, avrebbe avvertito che, secondo la teoria, la scala <lb/>delle velocit&agrave; nelle varie parti della corrente dovrebb'essere una parabola, <lb/>ma in effetto, qualunque siasi la ragione, &egrave; un triangolo, non supino, ma <lb/>con la base in basso. </s>

<s>O altrimenti: se un fiume, movendosi con una tal ve&shy;<lb/>locit&agrave; per un suo regolatore, avr&agrave; una data altezza viva, e poi per nuova <lb/>acqua crescer&agrave; il doppio; per la teoria la velocit&agrave; nel primo stato, alla ve&shy;<lb/>locit&agrave; nel secondo, dovrebbe avere la proporzione della radice di due a quat&shy;<lb/>tro, ma in effetto quella proporzione si trover&agrave; essere invece di due e quat&shy;<lb/>tro, ossia del semplice doppio. </s>

<s>Avrebbe voluto trattar di ci&ograve; a voce col Torricelli, <lb/>e non potendo far altro, significava intanto cos&igrave;, per lettera, pubblicata in parte <lb/>dal Bonaventuri, i suoi desiderii: &ldquo; Io avrei bisogno estremo di essere con <lb/>V. S., per dare l'ultima mano al secondo libro Della misura delle acque cor&shy;<lb/>renti, non gi&agrave; per istamparlo adesso, ma per finirlo in termine di poterlo <lb/>stampare, occorrendo come spero ch'io sia chiamato a Venezia. </s>

<s>Basta, se il <lb/>caso succeder&agrave;, passer&ograve; per Firenze e ci vedremo. </s>

<s>Mi pare d'avere scoperto <lb/>una mano di cose totalmente incognite, e di grandissimo momento, e di pi&ugrave; <pb xlink:href="020/01/3456.jpg" pagenum="417"/>vedo il campo aperto per scoprimenti maggiori, ma conosco che la materia <lb/>supera la mia debolezza. </s>

<s>V. S. tenga conto delle cose, che ella va ritrovando <lb/>in questa materia d'acque, perch'io penso d'ornare il mio libro col nome, <lb/>e con l'opere di V. S., come, piacendo a Dio, dir&ograve; a bocca &rdquo; (<emph type="italics"/>Prefaz. </s>

<s>alle <lb/>Lezioni accad. </s>

<s>del Torricelli,<emph.end type="italics"/> Milano 1823, pag. </s>

<s>59). </s></p><p type="main">

<s>Di quel che deve aver detto a bocca il Castelli a colui, ch'essendogli <lb/>stato discepolo ora si faceva collega de'suoi studi, e prometteva di divenirne <lb/>maestro; siamo oramai prevenuti: deve avergli confessato che il modo di <lb/>dimostrare la sua seconda proposizione conteneva un paralogismo, ma che <lb/>non poteva cader dubbio sopra la verit&agrave; di lei, essendo il resultato d'espe&shy;<lb/>rienze ripetute cento volte alla presenza di tanti, fra'quali, a farne testimo&shy;<lb/>nianza, il Magiotti solo sarebbe bastato per tutti. </s>

<s>Il Torricelli, che per sola <lb/>teoria aveva intorno a quella seconda proposizione concluso i suoi dubbi, se <lb/>n'ebbe a persuader facilmente, e tanto &egrave; ci&ograve; vero che, mettendosi poi a <lb/>esplicare nell'appendice <emph type="italics"/>De motu aquarum<emph.end type="italics"/> quel suo concetto, significato <lb/>nella lettera al Cavalieri, applica la nuova legge idrodinamica a'soli efflussi <lb/>dai vasi, o agli zampilli dai piccoli fori, lasciando intatta la questione dei <lb/>fiumi, per la quale si rimetterebbe a ci&ograve; che, pubblicando il suo manoscritto <lb/>corretto, ne deciderebbe il Castelli. </s>

<s>E cos&igrave;, come prudentemente s'era intorno <lb/>a ci&ograve; governato il Maestro, fecero, secondo si narrer&agrave; nel capitolo appresso, <lb/>i discepoli, i quali, mentre da una parte attendevano a esplicare i teoremi di <lb/>lui concernenti le cadute accelerate delle gocciole dal supremo livello verso <lb/>il foro, e il moto parabolico, che da una tale accelerazione consegue; accet&shy;<lb/>tarono dall'altra le verit&agrave; sperimentali, descritte nel secondo libro delle Acque <lb/>correnti: verit&agrave;, che si mantennero salve nella scienza, infino al Guglielmini <lb/>e all'Herman, primi a rimettere in onore la scala parabolica, e perci&ograve; a re&shy;<lb/>stituire alla prima universalit&agrave;, proposta nella detta lettera al Cavalieri, la <lb/>Scienza idrodinamica, rimastasi instituita solo a mezzo in quell'appendice <lb/>del Torricelli, dalla quale si vuole incominciare il seguente nostro discorso. </s></p><pb xlink:href="020/01/3457.jpg"/><p type="main">

<s><emph type="center"/>CAPITOLO VII.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="bold"/>Della nuova istituzione idrodinamica del Torricelli <lb/>e delle prime promozioni di lei<emph.end type="bold"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>SOMMARIO<emph.end type="center"/></s></p><p type="main">

<s>I. </s>

<s>Del trattato torricelliano <emph type="italics"/>De motu aquarum,<emph.end type="italics"/> illustrato e ampliato dal Viviani. </s>

<s>&mdash; II. Dell'Idrodi&shy;<lb/>namica torricelliana, nelle Cogitazioni fisico-matematiche del Mersenno, nelle Epistole del Car&shy;<lb/>tesio, e nel trattato <emph type="italics"/>De motu liquidorum<emph.end type="italics"/> di G. B. Baliani. </s>

<s>&mdash; III. Dell'Idrodinamica torricel&shy;<lb/>liana, esclusa dalle applicazioni al corso del fiumi, come principalmente resulta dalla storia <lb/>delle correzioni, che si pens&ograve; di fare all'Idrometria del Castelli. </s></p><p type="main">

<s><emph type="center"/>I.<emph.end type="center"/></s></p><p type="main">

<s>Bench&egrave; quella, che l'Arrighetti chiamava e forse anche credeva una <lb/>fantasia, sembrasse prendere aspetto di realt&agrave;, per le varie esperienze del <lb/>Magiotti, nonostante il Torricelli andava con passo incerto, in proporre al <lb/>pubblico una cosa tanto nuova. </s>

<s>Il dubbio, che gli tenzonava nella mente, <lb/>l'esprimeva cos&igrave; con queste parole: &ldquo; Caeterum si quis, praedictis rationi&shy;<lb/>bus non acquiescat, videat an inter sequentes propositiones ullam probet: <lb/>quod, si ita erit, facile per resolutionem, ex approbata propositione, primam <lb/>suppositionem demonstrabimus. </s>

<s>Sin minus, totam hanc Appendicem de motu <lb/>aquarum, vel saltu praetermittat, vel funditus e libello evellat, quod equidem <lb/>libentissime concedo &rdquo; (Op. </s>

<s>geom. </s>

<s>cit., P. I, pag. </s>

<s>193). La sincerit&agrave; delle <lb/>quali parole sembra a noi confermata dal fatto che, nel dimostrare le XIV pro&shy;<lb/>posizioni, delle quali si compone la detta Appendice; procede l'Autore con <lb/>quella fretta, che sogliono usare le persone discrete, nel proporre un partito, <lb/>a cui s'aspettano che pochi faranno accoglienza. </s></p><p type="main">

<s>Invece avvenne tutto il contrario: son gi&agrave; passati pi&ugrave; di due secoli e <lb/>mezzo, e in fronte a tutti i trattati d'Idrodinamica, in qualunque lingua <pb xlink:href="020/01/3458.jpg" pagenum="419"/>dettati, e di qualunque nazione siano gli autori, &egrave; scritto solennemente il <lb/>nome del Torricelli. </s>

<s>L'appendice di lui, tutt'altro ch'essere svelta <emph type="italics"/>funditus<emph.end type="italics"/><lb/>dal trattato <emph type="italics"/>De motu proiectorum,<emph.end type="italics"/> fu subito coltivata con tanta industria, che <lb/>l'umile rampollo giunse presto a emulare la stessa pianta madre, a lato alla <lb/>quale ora grandeggia nel campo della scienza. </s></p><p type="main">

<s>Fra que'primi cultori sarebbero da annoverare i Francesi, se dovesse <lb/>la Storia starsene solamente a ci&ograve;, che &egrave; noto per i pubblici documenti. </s>

<s>Ma <lb/>le private e, per dir cos&igrave;, domestiche notizie, che ci sono rimaste, confer&shy;<lb/>mano, com'&egrave; da aspettarsi, quel legittimo primato de'Nostri, che furono <lb/>amici e discepoli del Torricelli, il pi&ugrave; operoso fra i quali, come in ogni altro <lb/>proposito, cos&igrave; e in questo, ci si presenta il Viviani. </s>

<s>Fra i manoscritti di lui <lb/>gli argomenti idrodinamici, e le questioni d'Idrometria, son quelle, che vi si <lb/>trattano pi&ugrave; diffusamente. </s>

<s>Sembra anzi a noi di scoprire, per questi studi <lb/>intorno al moto dell'acque, una certa predilezione, natagli forse dal trovarsi <lb/>aperto innanzi un cos&igrave; largo campo, da poter nel percorrerlo misurarvi den&shy;<lb/>tro la validit&agrave; delle sue proprie forze. </s>

<s>Basti dire che le principali proposi&shy;<lb/>zioni d'Idrodinamica, di che tanto onore si fecero il Guglielmini e il Grandi, <lb/>si trovano tutte premostrate in quei manoscritti. </s>

<s>Chi proseguir&agrave;, senza stan&shy;<lb/>carsi, la lettura di questa storia, trover&agrave; di quel che s'&egrave; annunziato la pi&ugrave; <lb/>piena conferma, ma qualunque sia l'importanza, e qualunque il merito del&shy;<lb/>l'opera data dal Viviani all'Idrometria, egli non riconosce altro maestro che <lb/>il Torricelli, dallo studio di cui confessa essergli venute le inspirazioni, le <lb/>prime delle quali cominciano da quel mettersi, ch'egli fece intorno ad am&shy;<lb/>pliare l'appendice <emph type="italics"/>De motu aquarum.<emph.end type="italics"/></s></p><p type="main">

<s>Interrotto l'esercizio, e tante volte ripreso, scriveva sul primo foglio, che <lb/>gli veniva a mano, ora frettolosamente, ora a stento, le proposizioni da ag&shy;<lb/>giungersi, e i commenti da farsi, e cos&igrave; il materiale, bench&egrave; disperso, non <lb/>solamente fra le varie pagine, ma fra i varii volumi manoscritti, in qualche <lb/>modo s'&egrave; potuto ritrovare, almeno nella sua parte migliore. </s>

<s>Ma &egrave; difficile <lb/>indovinare la forma, che il Viviani stesso aveva intenzion di dare al nuovo <lb/>trattato. </s>

<s>Alcune proposizioni sono scritte in latino, altre in volgare, ma sem&shy;<lb/>bra che dovess'esser tutto dettato in questa lingua, nella quale si trova es&shy;<lb/>sere stata gi&agrave; distesa una specie di prefazione. </s>

<s>Comunque sia, l'ufficio no&shy;<lb/>stro di storici, e non di editori, concedendoci libert&agrave; di riferire i documenti <lb/>con qual ordine meglio ci piace, ne abbiamo scelto uno, che consiste nel&shy;<lb/>l'inserire fra le proposizioni torricelliane le relative soggiunte dal Viviani, <lb/>segnate con numeri progressivi, senza tralasciar la scrittura, che, quale ora <lb/>da noi si produce, doveva servir di proemio all'opera riformata. </s></p><p type="main">

<s>&ldquo; L'acutissimo dei geometri, Evangelista Torricelli necessitato dalla forza <lb/>del vero a seguitar la dottrina del mio Galileo, primo e vero scrutatore della <lb/>Natura, e delle propriet&agrave; dei moti equabile, naturale e violento; suppose che <lb/>l'acqua, forzata dal carico della propria altezza, nell'istante del suo scap&shy;<lb/>pare da qualche foro di un vase, in cui ella si trovi, abbia in s&egrave; quell'im&shy;<lb/>peto stesso o velocit&agrave;, che avrebbe un grave libero o una gocciola di detta <pb xlink:href="020/01/3459.jpg" pagenum="420"/>acqua, se ella, col progresso dell'accelerazione gi&agrave; assegnata dal medesimo <lb/>Galileo, cadesse naturalmente dal suo supremo livello, fino all'orifizio del <lb/>foro d'onde ella scappa. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Questo tal supposto s'ingegn&ograve; il Torricelli di comprovarlo coll'espe&shy;<lb/>rienza, mostrando che, quando nella sponda di un vaso, tenuto sempre pieno <lb/>d'acqua, sta inserita orizontalmente una cannella prossima al fondo, la qual <lb/>serrata all'estremit&agrave; abbia un solo angustissimo foro ben tondo sul colmo <lb/>del suo dorso, e che questo, tenuto chiuso col polpastrello di un dito, a ora <lb/>a ora si va serrando e subito sturando; quella prima minutissima gocciola, <lb/>che ne schizza in aria, s'alza poco men che al piano del sopraddetto livello, <lb/>massime, quando l'ampiezza del vaso sia molta, rispetto a quella del foro, <lb/>e poca sia l'altezza dell'acqua, ponendo egli in considerazione che, del non <lb/>arrivarvi precisamente, nei casi di maggiori altezze, ne sia cagione la mag&shy;<lb/>gior resistenza, che trova l'acqua nel passare per la corpulenza dell'aria. </s>

<s>Con <lb/>che, se invece di acqua si pigliasse, per far questa prova, dell'argento vivo, <lb/>quella sua prima gocciola che sale in su, come in s&egrave; stessa tante volte pi&ugrave; <lb/>grave dell'acqua, e perci&ograve; pi&ugrave; atta a ritenere per pi&ugrave; tempo l'impeto con&shy;<lb/>ceputo, e a superar la resistenza dell'aria; si osserverebbe esattamente ar&shy;<lb/>rivare al livello interno del vaso. </s>

<s>Lo che ha molto del verisimile, imperoc&shy;<lb/>ch&egrave; tale impedimento manca bens&igrave; all'acqua premente dentro il vaso, ma <lb/>non gi&agrave; alla spremuta fuori e fendente la corpulenza dell'aria. </s>

<s>Tanto pi&ugrave; <lb/>che e'si vede che nell'altro caso, quando cio&egrave; quell'orifizio va su su accom&shy;<lb/>pagnato con un cannello fin sopra il piano dell'acqua del vaso congiuntogli, <lb/>questa allora non ha difficolt&agrave; a sormontare appunto fino a quel piano, sia <lb/>pure il vaso e il cannello alto e lungo quanto si voglia. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Se dunque la prima gocciola sola vi arriva, e se, per la Scienza ga&shy;<lb/>lileiana del moto naturale dei gravi, qualunque di questi, rimossi gl'impe&shy;<lb/>dimenti, quando si solleva da basso in alto si parte con un impeto eguale <lb/>a quello, che egli acquisterebbe per altrettanta caduta dalla quiete; ci&ograve; &egrave; <lb/>segno che quella gocciola saliente, nell'atto dell'uscir da quel foro angusto, <lb/>si trov&ograve; imbevuta dell'impeto stesso, che nel cader dalla medesima altezza <lb/>ella vi averebbe naturalmente acquistato. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Con tal supposto dunque, assai chiaro, diedi ancor io principio a questo <lb/>trattato pi&ugrave; ampio, in supplemento del promosso dal Torricelli &rdquo; (MSS. Gal. <lb/><figure id="id.020.01.3459.1.jpg" xlink:href="020/01/3459/1.jpg"/></s></p><p type="caption">

<s>Figura 196.<lb/>Disc., T. CXVIII, fol. </s>

<s>16). E comincia dal dimo&shy;<lb/>strare alcune proposizioni illustrative di quelle, <lb/>che ricorrono in ordine le ultime dello stesso <lb/>trattato, che s'intendeva di ampliare. </s>

<s>Secondo il <lb/>nostro sopra espresso proposito, invece, comince&shy;<lb/>remo dal riferire le prime proposizioni torricel&shy;<lb/>liane, dipendenti, secondo la fatta supposizione, <lb/>dal moto parabolico, cos&igrave; ordinatamente pronun&shy;<lb/>ziate colle parole medesime dell'Autore. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO I. &mdash; <emph type="italics"/>Dato tubo AB<emph.end type="italics"/> (fig. </s>

<s>196), <pb xlink:href="020/01/3460.jpg" pagenum="421"/><emph type="italics"/>semper pleno et apte perforato foraminibus C, D, E, hoc est quae sint <lb/>figurae circularis, sitque illorum ductus horizontalis, hoc est in tenui la-<emph.end type="italics"/><lb/><figure id="id.020.01.3460.1.jpg" xlink:href="020/01/3460/1.jpg"/></s></p><p type="caption">

<s>Figura 197.<lb/><emph type="italics"/>mella plan&aacute; perpendiculari, datoque horizonte quolibet <lb/>BG; invenire amplitudinem uniuscuiusque parabolae &rdquo;<emph.end type="italics"/><lb/>(Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>194). </s></p><p type="main">

<s>&ldquo; PROPOSITIO II. &mdash; <emph type="italics"/>Dato dolio, sive tubo AB<emph.end type="italics"/> (fig. </s>

<s>197), <lb/><emph type="italics"/>quod apte perforatum sit in C, et emissionem faciat CD, <lb/>invenienda sit aqua in tubo latentis libella horizontalis, <lb/>sive superficies suprema &rdquo;<emph.end type="italics"/> (ibid., pag. </s>

<s>195). </s></p><p type="main">

<s>&ldquo; PROPOSITIO III. &mdash; <emph type="italics"/>Si tubus AB<emph.end type="italics"/> (in eadem figura) <lb/><emph type="italics"/>apte perforetur ubicumque in C, emissio fluentis aquae <lb/>coni rectanguli superficiem continget, cuius axis sit ipse tubus, vertex vero <lb/>sit in aquae libella &rdquo;<emph.end type="italics"/> (ibid.). </s></p><p type="main">

<s>&ldquo; PROPOSITIO IV. &mdash; <emph type="italics"/>Aquarum, ex tubo AB<emph.end type="italics"/> (fig. </s>

<s>198), <emph type="italics"/>perforato, erum&shy;<lb/>pentium, velocitates sunt ut lineae in parabola applicatae ad suam unius&shy;<lb/>cuiusque sublimitatem &rdquo;<emph.end type="italics"/> (ibid., pag. </s>

<s>196). <lb/><figure id="id.020.01.3460.2.jpg" xlink:href="020/01/3460/2.jpg"/></s></p><p type="caption">

<s>Figura 198.</s></p><p type="main">

<s>Tutte queste quattro, cos&igrave; proposte, vengono con <lb/>gran facilit&agrave; e speditezza dimostrate e risolute die&shy;<lb/>tro le note propriet&agrave; dei moti parabolici. </s>

<s>Basta infatti <lb/>risovvenirsi che la met&agrave; dell'ampiezza &egrave; media pro&shy;<lb/>porzionale fra l'altezza e la sublimit&agrave;, per veder che <lb/>il seno EI, nella figura 196, medio proporzionale fra <lb/>il segmento AE, sublimit&agrave;, e il segmento EB, al&shy;<lb/>tezza della parabola EG; &egrave; quello, che risolve il <lb/>primo problema. </s>

<s>Il secondo altres&igrave; &egrave; risoluto dal <lb/>medesimo principio, perch&egrave;, chiamate A, M, S l'altezza, la met&agrave; dell'am&shy;<lb/>piezza, e la sublimit&agrave;, dall'equazione A:M=M:S, nella quale A e M <lb/>son note, s'ha direttamente S sublimit&agrave; cercata. </s>

<s>La verit&agrave; della III pro&shy;<lb/>posizione dipende dalle note propriet&agrave; della tangente alla parabola, la qual <lb/>tangente, che sia per esempio AD nella figura 197, rivolgendosi intorno <lb/>all'asse AB, descrive la superficie di un cono. </s>

<s>La IV infine &egrave; una conse&shy;<lb/>guenza immediata del supposto principio sperimentale, perch&egrave;, se le velocit&agrave; <lb/>in C e in D, rappresentate dalla figura 198, son proporzionali alle radici <lb/>delle altezze AC, AD; sono anche proporzionali alle linee CE, DF, ordina&shy;<lb/>tamente applicate a qualunque parabola che, col vertice in A, intorno al&shy;<lb/>l'asse AD sia descritta. </s></p><p type="main">

<s>Di qui &egrave; che, stando le quantit&agrave; in ragion composta delle velocit&agrave; e <lb/>delle sezioni, essendo i fori C, D uguali, staranno in ragion semplice delle <lb/>radici delle altezze, e in reciproca ragione di queste saranno le sezioni, se le <lb/>quantit&agrave; si suppongano uguali: corollari espressamente notati dal Torricelli, <lb/>perch&egrave; continuamente si richiamano come principii, da cui son per dipendere le <lb/>future conclusioni, la prima fra le quali, che in ordine succede, &egrave; la seguente: </s></p><p type="main">

<s>&ldquo; PROPOSITIO V. &mdash; <emph type="italics"/>Si tubus AB<emph.end type="italics"/> (fig. </s>

<s>199) <emph type="italics"/>cylindricus, sive prismati&shy;<lb/>cus, perforatus in fundo B fluat, neque alius humor superinfundatur,<emph.end type="italics"/><pb xlink:href="020/01/3461.jpg" pagenum="422"/><emph type="italics"/>velocitates supremae superficiei humoris latentis decrescent cum eadem <lb/><figure id="id.020.01.3461.1.jpg" xlink:href="020/01/3461/1.jpg"/></s></p><p type="caption">

<s>Figura 199.<lb/>ratione, qua decrescunt etiam lineae ordinatim ap&shy;<lb/>plicatae in parabola BD, quae axem habeat BA, <lb/>verticem vero B &rdquo;<emph.end type="italics"/> (ibid., pag. </s>

<s>197). </s></p><p type="main">

<s>Per la dimostrazione, se ne spedisce il Torri&shy;<lb/>celli dicendo <emph type="italics"/>hoc manifestum est,<emph.end type="italics"/> ci&ograve; che per&ograve; a <lb/>molti non parve, onde il Viviani, quasi postilla al <lb/>testo, cos&igrave; scriveva: &ldquo; Questa dimostrazione, deside&shy;<lb/>randosi da qualcuno di averla un po'pi&ugrave; spiegata, <lb/>me ne ingegnai come appresso: &rdquo; </s></p><p type="main">

<s>&ldquo; Sit tubus cylindricus, vel prismaticus, AB (nella medesima figura 199) <lb/>perforatus in fundo B: fluat, neque alius humor superinfundatur. </s>

<s>Erunt ve&shy;<lb/>locitates aquae, exeuntes per B, positis libellis C et E, ut sunt lineae appli&shy;<lb/>catae ex punctis libellarum CD, EF in parabola CFD, cuius axis sit BC, ver&shy;<lb/>tex foramen B. &rdquo; </s></p><p type="main">

<s>&ldquo; Ponatur CG aequalis BE, et circa eumdem axem CB, vertice C, de&shy;<lb/>scribatur parabola CHI, penitus ipsi BFD aequalis. </s>

<s>Essent BI, GH ordinatim <lb/>applicatae aequales CD, EF. </s>

<s>Cum enim velocitas per foramen B, post CB, <lb/>ad velocitatem per aequale foramen G, post CG, sit, per praecedentem, ut BI <lb/>ad GH, vel ut CD ad EF, et velocitas in G, post CG, eadem sit ac veloci&shy;<lb/>tas in B, post EB, cum CG, EB, per constructionem, sint aequales; ergo ve&shy;<lb/>locitas in B, post CB, ad velocitatem B, post EB, erit ut CD ad EF, quod <lb/>fuit propositum &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>44, 45). </s></p><p type="main">

<s>La proposizione, che immediatamente succede nell'appendice del Tor&shy;<lb/><figure id="id.020.01.3461.2.jpg" xlink:href="020/01/3461/2.jpg"/></s></p><p type="caption">

<s>Figura 200.<lb/>ricelli, dopo questa che il Viviani ha cos&igrave; <lb/>spiegata, &egrave; quella del <emph type="italics"/>Solido dell'acqua,<emph.end type="italics"/><lb/>messa dall'Autore stesso in tal forma: </s></p><p type="main">

<s>&ldquo; PROPOSITIO VI. &mdash; <emph type="italics"/>Sit vas aqua sem&shy;<lb/>per plenum CE<emph.end type="italics"/> (fig. </s>

<s>200) <emph type="italics"/>amplissimum, <lb/>cuius foramen in fundo circulare sit AB, <lb/>solidum autem aquae ex eo fluentis sit <lb/>ASNB, et solidi axis sit IH: Dico lineam <lb/>BN, solidi huius genitricem, talem esse ut <lb/>numerus biquadratus diametri AB, ad bi&shy;<lb/>quadratum diametri SN, sit reciproce ut <lb/>altitudo IH ad altitudinem IG &rdquo;<emph.end type="italics"/> (Op. </s>

<s>geom. </s>

<s><lb/>cit., pag. </s>

<s>197). </s></p><p type="main">

<s>La dimostrazione si conduce con un <lb/>solo e brevissimo passo dalla IVa, e dai co&shy;<lb/>rollari di lei. </s>

<s>Imperocch&egrave;, dovendo, per il <lb/>circolo AB e per l'SN, passare nel medesimo tempo uguale quantit&agrave; d'acqua, <lb/>le sezioni dunque staranno reciprocamente come le radici delle altezze, onde <lb/>non altro occorre a fare che a quadrar l'equazione AB2:SN2=&radic;IH:&radic;IG, <lb/>per conseguire il proposito. </s></p><pb xlink:href="020/01/3462.jpg" pagenum="423"/><p type="main">

<s>Di qui il Guglielmini, nella proposizione IX del V libro <emph type="italics"/>Mensura aqua&shy;<lb/>rum fluentium,<emph.end type="italics"/> e il Grandi, nella proposizione IX del suo trattato <emph type="italics"/>Del mo&shy;<lb/>vimento delle acque,<emph.end type="italics"/> facilmente conclusero che il solido dell'acqua, cos&igrave; <lb/>astrattamente considerato come lo considera il Torricelli, &egrave; un'iperboloide, <lb/>quale si descriverebbe dal rivolgersi, intorno all'asse GH, la linea BN, la <lb/>quale nient'altro &egrave; che un'iperbola del quarto grado. </s>

<s>Il Jurin e gli annotatori <lb/>del Newton poi, riducendo la teoria a pi&ugrave; prossima corrispondenza coi fatti, <lb/>dimostrarono che tale &egrave; pur la figura del vano o della <emph type="italics"/>cateratta,<emph.end type="italics"/> che si forme&shy;<lb/>rebbe intorno all'asse IG, in mezzo all'acqua del pilo. </s>

<s>Ma prima di tutti <lb/>costoro il Viviani aveva risoluto, intorno al solido torricelliano dell'acqua, <lb/>varii problemi, che, fatti ora noti, si giudicheranno uno dei pi&ugrave; belli orna&shy;<lb/>menti all'appendice <emph type="italics"/>De motu aquarum.<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; PROPOSITIO VII. &mdash; <emph type="italics"/>Data la grossezza o'il diametro AB<emph.end type="italics"/> (nella me&shy;<lb/>desima figura 200) <emph type="italics"/>di un foro circolare, fatto nel fondo DE, il quale stia <lb/>sempre pieno d'acqua fino all'altezza GI perpendicolare ad esso fondo <lb/>sul centro G di esso foro, pel quale esce l'acqua cadente; si cerchi, del <lb/>corpo acqueo, che si former&agrave; sotto esso fondo, quale sia per essere il dia&shy;<lb/>metro della grossezza di esso corpo cadente, in tanta distanza dal mede&shy;<lb/>simo fondo DE, quanta &egrave; GH &rdquo;<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>13). </s></p><p type="main">

<s>Per la risoluzione della proposta s'invoca l'aiuto di un Lemma mate&shy;<lb/>matico, che vedremo servire al Viviani per altri simili bisogni, dimostran&shy;<lb/>dolo per&ograve; volta per volta, secondo i vari casi particolari. </s>

<s>A ci&ograve; fare lo co&shy;<lb/>stringeva il metodo, a cui sempre vollesi mantenere fedele, contro le novit&agrave; <lb/>dell'analisi cartesiana, per via della quale nonostante si sarebbe potuto pro&shy;<lb/>porre una volta sola quello stesso Lemma, cos&igrave; generalmente pronunziandolo, <lb/>in questa forma: <emph type="italics"/>Se sia un numero<emph.end type="italics"/> n <emph type="italics"/>qualunque di quantit&agrave; continua&shy;<lb/>mente proporzionali, la prima star&agrave; all'ultima come la potenza<emph.end type="italics"/> n-1 <emph type="italics"/>della <lb/>prima sta alla potenza<emph.end type="italics"/> n-1 <emph type="italics"/>della seconda.<emph.end type="italics"/></s></p><p type="main">

<s>Esser ci&ograve; vero poteva resultare per induzione anche dalle regole tenute <lb/>dal Viviani, le quali in ogni modo si rendono cos&igrave;, con metodo analitico, pi&ugrave; <lb/>spedite. </s></p><p type="main">

<s>Siano tre i termini continuamente proporzionali <emph type="italics"/>a:b=b:c.<emph.end type="italics"/> Sar&agrave; <emph type="italics"/>b2= <lb/>ac,<emph.end type="italics"/> e anche <emph type="italics"/>ab2=a2c,<emph.end type="italics"/> e perci&ograve; <emph type="italics"/>a:c=a2:b2.<emph.end type="italics"/></s></p><p type="main">

<s>Siano i detti termini quattro, <emph type="italics"/>a:b=b:c=c:d.<emph.end type="italics"/> Sostituendo, nel&shy;<lb/>l'equazione <emph type="italics"/>b2=ac,<emph.end type="italics"/> il valore di <emph type="italics"/>c,<emph.end type="italics"/> verr&agrave; <emph type="italics"/>b2=a&radic;bd.<emph.end type="italics"/> Quadrando, <emph type="italics"/>b1=a2bd,<emph.end type="italics"/><lb/>ossia <emph type="italics"/>b3=a2d.<emph.end type="italics"/> Moltiplicando per <emph type="italics"/>a, ab3=a3d,<emph.end type="italics"/> e perci&ograve; <emph type="italics"/>a:d=a3:b3.<emph.end type="italics"/></s></p><p type="main">

<s>Se poi i termini saranno cinque <emph
type="italics"/>a:b=b:c=c:d=d:e,<emph.end type="italics"/> sostituendo
<lb/>nella <emph type="italics"/>b3=a3d,<emph.end type="italics"/> trovata di sopra, il valore di <emph type="italics"/>d=ae/b,<emph.end type="italics"/> avremo <emph type="italics"/>b3=a3e/b,<emph.end type="italics"/><lb/>ossia <emph type="italics"/>b4=a3e.<emph.end type="italics"/> Moltiplicando per <emph type="italics"/>a, ab4=a4e,<emph.end type="italics"/> e perci&ograve; <emph type="italics"/>a:e=a4:b4....<emph.end type="italics"/><lb/>Proseguendo si trover&agrave; questa regola costante, che cio&egrave; il grado della potenza <lb/>&egrave; sempre meno uno de'termini in proporzione continua, e perci&ograve;, se i ter&shy;<lb/>mini sono <emph type="italics"/>n,<emph.end type="italics"/> e l'ultimo si chiami <emph type="italics"/>z<emph.end type="italics"/>, se ne potr&agrave; concludere <emph type="italics"/>a:z= <lb/>a n-1:b n-1,<emph.end type="italics"/> equazione, che riduce gli sparsi lemmi del Viviani in una formula <pb xlink:href="020/01/3463.jpg" pagenum="424"/>generale. </s>

<s>Da questa scendono alcuni corollari importanti, de'quali per&ograve; no&shy;<lb/>teremo due soli, perch&egrave; si vedranno in seguito invocati dal Viviani stesso per <lb/>lemmi alla dimostrazione di altre sue proposizioni d'Idrometria. </s></p><p type="main">

<s><emph type="italics"/>Corollario I.<emph.end type="italics"/> &mdash; Nel caso, che le quantit&agrave; continue siano tre, s'&egrave; dimo&shy;<lb/>strato <emph type="italics"/>a:c=a2:b2,<emph.end type="italics"/> ossia <emph type="italics"/>ab2=ca2.<emph.end type="italics"/> Moltiplichiamo questa per <emph type="italics"/>b2<emph.end type="italics"/>, e avremo <lb/><emph type="italics"/>ab4=ca2b2.<emph.end type="italics"/> Poniamo in questo secondo membro <emph type="italics"/>b2=ac,<emph.end type="italics"/> e avremo <emph type="italics"/>ab4= <lb/>ca2.ac=a3c2,<emph.end type="italics"/> che dimostra il teorema cos&igrave; proposto dal Viviani: <emph type="italics"/>Se tre <lb/>linee sono in continua proporzione geometrica, il fatto dalla prima nel <lb/>quadrato della seconda, &egrave; uguale al fatto dal cubo della prima nel qua&shy;<lb/>drato della terza.<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., T. CXVI, fol. </s>

<s>113). </s></p><p type="main">

<s><emph type="italics"/>Corollario II.<emph.end type="italics"/> &mdash; Nel caso, che le continue sian quattro, da <emph type="italics"/>b2=ac<emph.end type="italics"/><lb/>abbiamo <emph type="italics"/>c3=b6/a3,<emph.end type="italics"/> e da <emph type="italics"/>b4=a2bd<emph.end type="italics"/> abbiamo <emph type="italics"/>a3=ab3,/d<emph.end type="italics"/> e perci&ograve; <emph type="italics"/>a3:c3= <lb/>ab3/d:b6/a3=a4.b3:db6=a4:db3.<emph.end type="italics"/> E perch&egrave; <emph type="italics"/>b3=a2d,<emph.end type="italics"/> dunque <emph type="italics"/>a3:c3= <lb/>a4:d2a2=a2:d2,<emph.end type="italics"/> che dimostra l'altro pronunziato del Viviani: <emph type="italics"/>Se quat&shy;<lb/>tro linee sono in continua proporzione geometrica, il cubo della prima, al <lb/>cubo della terza, sta come il quadrato della prima al quadrato della <lb/>quarta<emph.end type="italics"/> (ivi, fol. </s>

<s>120). </s></p><p type="main">

<s>Premesse le quali cose, in servigio delle proposizioni d'Idrometria, che il <lb/>Viviani dimostrer&agrave; qui, e nel capitolo seguente, ecco intanto l'uso, ch'egli stesso <lb/>fa del detto Lemma generale, nella dimostrazione della VII ora annunziata. </s></p><p type="main">

<s>&ldquo; Si prenda IL (nella stessa figura 200) media proporzionale fra le <lb/>HI, IG, ed anche la IM, media proporzionale fra le HI, IL, e di poi, come <lb/>la nota IH, alla trovata IM, cos&igrave; si faccia il semidiametro BG noto, all'HN, <lb/>quale da H s'applichi parallelo alla GR: dico che l'HN &egrave; il semidiametro <lb/>della grossezza cercata. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Prendasi IO media proporzionale fra le LI, IG. </s>

<s>Or perch&egrave; IH all'IL <lb/>sta come IL all'IG, ed &egrave; l'IM media fra HI, IL, siccome la IO &egrave; media fra <lb/>le LI, IG; saranno le cinque IH, IM, IL, IO, IG in una medesima continua <lb/>proporzione, e perci&ograve;, in virt&ugrave; del premesso Lemma, la prima HI, alla quinta <lb/>IG, sta come il quadrato-quadrato della prima HI, al quadrato-quadrato della <lb/>seconda IM. </s>

<s>Ma come HI all'IM, cos&igrave; sta ancora la GB alla HN; che per&ograve; <lb/>anche il quadrato-quadrato HI, al quadrato-quadrato IM, sta come il quadrato&shy;<lb/>quadrato GB, al quadrato-quadrato HN. </s>

<s>Adunque ancora la HI alla IG sta come <lb/>il quadrato-quadrato GB, al quadrato-quadrato HN &rdquo; (ivi, T. CXVII, fol. </s>

<s>13). </s></p><p type="main">

<s>Per dichiarar meglio le premesse di questa conclusione, si ordinino le <lb/>quattro istituite proporzioni: 1.a HI:IL=IL:IG, 2.a HI:IM=IM:IL, <lb/>3.a HI:IM=GB:HN, 4.a IL:IO=IO:IG. </s>

<s>Preso ora il valore di IL <lb/>dalla seconda, e sostituito nella prima, in luogo del secondo termine della <lb/>prima ragione; preso inoltre il valore di IG dalla quarta, e sostituito in luogo <lb/>del secondo termine nella seconda ragione della detta prima; avremo </s></p><p type="main">

<s><emph type="center"/>HI:IM2/HI=IL=IO2/IL,<emph.end type="center"/><pb xlink:href="020/01/3464.jpg" pagenum="425"/>ossia, riducendo e estraendo la radice, HI:IM=IL:IO, dalla quale, inse&shy;<lb/>rita in continuit&agrave; fra la seconda e la terza, avremo HI:IM=IM:IL= <lb/>IL:IO=IO:IG. </s>

<s>Cos&igrave; essendo cinque quantit&agrave; continuamente proporzionali <lb/>s'avr&agrave;, in virt&ugrave; dello stesso predetto lemma, HI:IG=HI4:IM4, e anche <lb/>insieme, biquadrando la terza, (*) HI:IG=GB4:HN4, secondo era stato <lb/>trovato dal Viviani, il quale cos&igrave; conclude l'interrotto discorso: &ldquo; Se dun&shy;<lb/>que le altezze HI, IG hanno proporzion reciproca del quadrato-quadrato GB, <lb/>al quadrato-quadrato HN, questo, per la proposizione VI del Torricelli, sar&agrave; <lb/>il semidiametro della grossezza che aver&agrave; il corpo fluido nel dato punto H. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Aggiunta I.<emph.end type="italics"/> &mdash; Di qui si ha il modo pratico di segnare per punti <lb/>continuati questa curva BN, la quale non &egrave; altro che l'iperbola quadrato&shy;<lb/>quadratica, cio&egrave; la quarta delle infinite iperbole, il di cui centro &egrave; il punto I, <lb/>e li asintoti sono IF, IH, e ci&ograve; si far&agrave; col prendere IL media proporzionale <lb/>fra le IH, IG, date altezze, e poi la IM, media fra le IH, IL, e tagliare HV <lb/>eguale a GB, congiungere I, V, per M tirare MR parallela ad HV, ed infine <lb/>pigliare HN eguale ad MR, che il punto N col B si trova nella detta iper&shy;<lb/>bola biquadratica, perch&egrave; sta HV, ovvero GB, ad MR, cio&egrave; ad HN, come HI <lb/>ad IM. </s>

<s>E nello stesso modo si troveranno altri punti di tale iperbola &rdquo; (ivi). </s></p><p type="main">

<s>L'equazione infatti GB:HN=HI:IM si riduce alla forma ordinaria <lb/>dell'iperbola del quarto grado, biquadrandola, e sostituendo, alla ragione di <lb/>HI4 a IM4, quella di HI a IG, data dalla contrassegnata di sopra con (*). Per <lb/>la qual semplicissima operazione s'ottiene HI:IG=GB4:HN4. </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Aggiunta II.<emph.end type="italics"/> &mdash; Essendosi fatto, nella costruzione del passato pro&shy;<lb/>blema, che il semidiametro GB all'HM sta come l'altezza HI alla IM, se&shy;<lb/>conda delle cinque continue proporzionali, star&agrave; anche il quadrato GB, al <lb/>quadrato HN, come il quadrato HI al quadrato IM; cio&egrave; come la linea HI <lb/>alla IL, terza proporzionale dopo HI, IM. </s>

<s>Ma la linea HI alla IL, che &egrave; media <lb/>proporzionale tra le HI, IG, ha suddupla proporzione della HI alla IG; adun&shy;<lb/>que anche il quadrato GB, al quadrato HN, cio&egrave; il foro circolare AB, alla <lb/>sezione circolare SN, ha suddupla proporzione di quella, che &egrave; fra le HI, IG, <lb/>altezze reciproche delle sezioni del supremo livello del fluido contenuto nel <lb/>vaso DF &rdquo; (ivi, fol. </s>

<s>14). </s></p><p type="main">

<s>Con pi&ugrave; chiarezza potremo giungere cos&igrave; alla medesima conclusione. </s>

<s><lb/>Quadrando la terza fra le ordinate di sopra, viene HI2:IM2=GB2:HN2, e <lb/>sostituendovi il valore di IM2, preso dalla seconda delle medesime, </s></p><p type="main">

<s><emph type="center"/>HI2:HI.IL=GB2:HN2=HI:IL.<emph.end type="center"/></s></p><p type="main">

<s>Essendo poi, per la prima, IL=&radic;HI.IG, dunque HI:&radic;HI.IG=GB2:HN2, <lb/>ossia &radic;HI:&radic;IG=<foreign lang="greek">p</foreign> GB2:<foreign lang="greek">p</foreign> HN2, secondo che conclude il Viviani, e anche <lb/><foreign lang="greek">p</foreign> GB2:<foreign lang="greek">p</foreign> HN2=HI:IL, secondo che il Viviani stesso soggiunge nel se&shy;<lb/>guente </s></p><p type="main">

<s><emph type="italics"/>Corollario.<emph.end type="italics"/> &mdash; &ldquo; Di qui &egrave; che nel solido fluido, che si forma sotto il <lb/>vaso, la sezione AB maggiore del fondo, a qualunque altra minore SN, sta <lb/>come la maggiore altezza HI, alla IL, presa media fra la maggiore HI, e la <pb xlink:href="020/01/3465.jpg" pagenum="426"/>minore IG, altezza del fluido nel vaso. </s>

<s>Poich&egrave; HI ad IL ha pure suddupla <lb/>proporzione della HI alla IG &rdquo; (ivi). </s></p><p type="main">

<s>&ldquo; PPOPOSITIO VIII. &mdash; <emph type="italics"/>Dato il diametro AB<emph.end type="italics"/> (nella medesima figura 200) <lb/><emph type="italics"/>del foro nel fondo della conserva, ed il diametro SN del fluido cadente <lb/>nella nota distanza GH; assegnar quanta sia l'altezza ignota del fluido, <lb/>dentro la medesima conserva. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Prendansi dopo AB, SN, le tre T, V, X continue proporzionali, ed <lb/>alla prima AB si tolga AY, eguale all'ultima X, e come BY a YA cos&igrave; si <lb/>faccia HG a GI, che questa &egrave; la cercata altezza del fluido dentro la con&shy;<lb/>serva. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Imperocch&egrave;, stando BY a YA come HG a GI, componendo, star&agrave; AB <lb/>ad AY, ossia ad X, come HI ad IG. </s>

<s>Ma AB, prima, ad X, quinta della pro&shy;<lb/>porzione, sta, per il solito Lemma, come il quadrato-quadrato della prima <lb/>AB, al quadrato-quadrato della seconda SN; adunque anche HI ad IG sta <lb/>come il quadrato-quadrato AB, al quadrato-quadrato SN, e per&ograve; IG &egrave; l'al&shy;<lb/>tezza cercata &rdquo; (ivi). </s></p><p type="main">

<s>&ldquo; PROPOSITIO IX. &mdash; <emph type="italics"/>L'altezze vive invariabili, che si fanno dall'acqua <lb/>medesima di un fonte, ch'entri in un vaso, nell'uscirne dal fondo di esso, <lb/>per diversi fori tondi di figure simili orizontali; sono tra loro in ragion <lb/>reciproca de'quadrato-quadrati de'lati omologhi de'medesimi fori. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Siano i fori B, C (fig. </s>

<s>201) orizontali, di forma per es. </s>

<s>circolare, fatti <lb/><figure id="id.020.01.3465.1.jpg" xlink:href="020/01/3465/1.jpg"/></s></p><p type="caption">

<s>Figura 201.<lb/>nel fondo orizontale GH del vaso AH, e sia l'altezza <lb/>viva invariabile del fluido, che esce per B, la FG, e <lb/>quella viva invariabile del medesimo fluido, che esce <lb/>per C, altro foro circolare, sia la AG. </s>

<s>Dico che l'al&shy;<lb/>tezza viva FG sul foro B, alla viva AG sul foro C, sta <lb/>come il quadrato-quadrato del diametro del foro C, al <lb/>quadrato-quadrato del diametro del foro B. &rdquo; </s></p><p type="main">

<s>&ldquo; Imperocch&egrave;, per l'Aggiunta seconda alla precedente, l'altezza AG, <lb/>alla FG, ha doppia ragione del cerchio B al cerchio C, ed il cerchio B al C <lb/>ha doppia ragione del diametro al diametro. </s>

<s>Ma anche il quadrato-quadrato <lb/>del diametro di B, al quadrato-quadrato del diametro di C, ha doppia ra&shy;<lb/>gione di quella de'medesimi cerchi; adunque l'altezza viva AG sul foro C, <lb/>alla viva FG sul foro B, sta come il quadrato-quadrato del diametro del foro <lb/>B, al quadrato-quadrato del diametro del foro C, il che ecc. </s>

<s>&rdquo; (ivi, fol. </s>

<s>5). <lb/><figure id="id.020.01.3465.2.jpg" xlink:href="020/01/3465/2.jpg"/></s></p><p type="caption">

<s>Figura 202.</s></p><p type="main">

<s>Con queste tre proposi&zgrave;ioni venendo ampliata dal <lb/>Viviani la VI del Torricelli, quella, che era la VII nel <lb/>l'Appendice di lui, diventa in ordine la X, cos&igrave; for&shy;<lb/>mulata: </s></p><p type="main">

<s>&ldquo; PROPOSITIO X. &mdash; <emph type="italics"/>Data BD<emph.end type="italics"/> (figura 202) <emph type="italics"/>di&shy;<lb/>rectione fistulae AB, et puncto C, in quod incidat <lb/>aqua fluens, invenire summam latentis aquae libel&shy;<lb/>lam, sive superficiem. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Dal punto C condotta a BD una parallela, che <pb xlink:href="020/01/3466.jpg" pagenum="427"/>incontri in F il perpendicolo BF, &egrave; manifesto che, data l'ampiezza FC, e BF <lb/>altezza della parabola, ci&ograve; che si cerca &egrave; la sublimit&agrave;. </s>

<s>Onde il presente pro&shy;<lb/>blema, non essendo altro in sostanza che il IIo proposto sotto altra forma, <lb/>si pu&ograve; risolvere perci&ograve; allo stesso modo. </s></p><p type="main">

<s>Succede a questo, nell'Appendice torricelliana, un problema, e l'oc&shy;<lb/>casione, ch'ebbe l'Autore di metterlo qui, &egrave; meritevole di storia, per le <lb/>strette relazioni, ch'egli ha con la scienza de'proietti. </s>

<s>Le tavole ballisti&shy;<lb/>che di Galileo, come e quelle medesime costruite dal Torricelli, non da&shy;<lb/>vano altro che l'ampiezze paraboliche sopra un piano orizontale. </s>

<s>Ma spesso <lb/>occorrendo di adoprare le artiglierie, per tirar sopra una spiaggia o sopra <lb/>un colle acclive o declive, e non potendosi dalle Tavole, in questo caso, ri&shy;<lb/>cavare l'ampiezza del tiro, era necessario istituire un calcolo particolare, <lb/>che dette al Torricelli stesso occasione di risolvere in Ballistica un pro&shy;<lb/>blema nuovo. </s></p><p type="main">

<s>Sopra la spiaggia AB (fig. </s>

<s>203), inclinata con l'orizzonte AC di un an&shy;<lb/>golo noto, perch&egrave; si suppone essere stato esattamente misurato con lo stru&shy;<lb/><figure id="id.020.01.3466.1.jpg" xlink:href="020/01/3466/1.jpg"/></s></p><p type="caption">

<s>Figura 203.<lb/>mento, si faccia da A, secondo la direzione AE, il tiro <lb/>ADB, di cui si cerca l'ampiezza AB. </s>

<s>Le Tavole ballistiche, <lb/>com'erano costruite, non davano altro che il tratto orizon&shy;<lb/>tale AD, misurato in passi. </s>

<s>Il rimanente si lasciava alle <lb/>inquisizioni della Geometria, la quale sugger&igrave;, per primo <lb/>espediente, al Torricelli di condurre, per D e per B, le <lb/>due verticali, e perci&ograve; parallele fra loro, FH, EB, d'onde, <lb/>per via dei triangoli ADH, ACB, nati dalla fatta costru&shy;<lb/>zione, veniva ad aversi AB, quarta proporzionale dopo <lb/>AD, AH e AC. Ora, essendo AD nota, e nota pure AH, <lb/>secante dell'angolo dell'inclinazione della spiaggia, rima&shy;<lb/>neva solo a notificarsi DC, che, dovendo perci&ograve; far parte di un triangolo, sug&shy;<lb/>ger&igrave; al Geometra di condurre la linea CH, la quale fece mirabilmente il gioco <lb/>che si voleva. </s>

<s>Perch&egrave;, avendosi dimostrato da Archimede, nel libro degli Sfe&shy;<lb/>roidei e Conoidei, che HB ad AH sta come HD e DF, ossia come BC a CE; <lb/>ne resultava che HC &egrave; parallela ad AE, e che perci&ograve;, tornando simili i trian&shy;<lb/>goli ADF, HDC, la DC richiesta era quarta proporzionale dopo FD, tangente <lb/>dell'angolo dell'elevazione del tiro, DH, tangente dell'angolo dell'inclinazione <lb/>della spiaggia, ambedue note, e AD, pure essa nota. </s></p><p type="main">

<s>Nel tempo che il Torricelli attendeva a cos&igrave; fatti esercizi ballistici, fer&shy;<lb/>veva tuttavia fra i Geometri una gara di proporre modi nuovi, per descri&shy;<lb/>vere le parabole e anche a lui n'era sovvenuto uno, che lo fece compiacere <lb/>d'essere entrato nel numero degli applauditi inventori. </s>

<s>La compiacenza per&ograve; <lb/>s'ebbe a convertire in dispetto, quando la bella invenzione, che credeva tutta <lb/>sua, lesse nello Specchio ustorio del Cavalieri essere, molto prima, stata fatta <lb/>e divulgata da Bartolommeo Sovero. </s>

<s>Ripensando poi meglio al problema bal&shy;<lb/>listico, che aveva dianzi risoluto, come s'&egrave; detto, ricover&ograve; la speranza certa <lb/>di rivendicarsi il merito perduto, venendogli di l&igrave; suggerito un modo facile <pb xlink:href="020/01/3467.jpg" pagenum="428"/>di descrivere la parabola per punti, che questa volta credeva essere esclusivo <lb/>parto del suo cervello, se il diavolo non gli faceva qualche altro scherzo. </s>

<s>Mo&shy;<lb/>vendosi infatti la linea AC intorno al centro A, dentro l'angolo BAE, con <lb/>qualunque inclinazione, se dal punto, dov'ella tocca con la sua estremit&agrave; la <lb/>verticale BE, si conduca la CH parallela alla direzione AE, e da H si alzi <lb/>la HF verticale; il punto dell'intersezione di questa con la linea AC, comun&shy;<lb/>que ella venga da A tirata, sar&agrave;, per quel ch'&egrave; stato detto, sempre nella <lb/>parabola, che dentro il triangolo AEB pu&ograve; esser descritta. </s></p><p type="main">

<s>Significava il Torricelli stesso queste passioni della vita sua matematica, <lb/>per lettera scritta da Fabriano il d&igrave; 8 gennaio 1640, al Magiotti, e n&ograve; al <lb/>Renieri, come parve a qualcuno, che troppo superficialmente svolse il ma&shy;<lb/>noscritto, nel quale autografa &egrave; rimasta la sopraccarta: <emph type="italics"/>Al molto illustre e <lb/>Rev.do sig. </s>

<s>Pron Colmo il sig. </s>

<s>d. </s>

<s>Raffaello Magiotti, in S. </s>

<s>Lucia della Chia&shy;<lb/>vica, a Roma<emph.end type="italics"/> (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>21). Quel che poi, nel presente <lb/>proposito, quivi autografo si legge &egrave; come segue: </s></p><p type="main">

<s>&ldquo; Mi venne voglia di stracciare ogni cosa, quando un giorno, sul li&shy;<lb/>bretto dello Specchio ustorio di fra Bonaventura, lessi quel modo di descri&shy;<lb/>vere la parabola (fra Bonaventura l'attribuisce al Sovero) che era in questo <lb/>libro mio <emph type="italics"/>De motu proiectorum,<emph.end type="italics"/> dop'averlo stimato per mia invenzione, gi&agrave; <lb/>sono pi&ugrave; di due anni. </s>

<s>&Egrave; vero che bisogna che io l'avessi visto gi&agrave; sette o <lb/>ott'anni sono, ma il galantuomo m'era uscito di memoria, e poi ci era ri&shy;<lb/>tornato come mio. </s>

<s>Ora, basta, questo errore di memoria &egrave; stato causa che <lb/>io abbi trattato del descriver la parabola, perch&egrave;, se non stimavo per mia <lb/>questa invenzione, non ne avrei parlato, perch&egrave; questa mi piace pi&ugrave; di tutte <lb/>quelle, che abbi mai visto appresso tanti Autori, che tutti vogliono dar del <lb/>naso a descrivere la parabola. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; In questi altri fogli ne aver&ograve; uno, il quale, se il demonio non fa un <lb/>altro miracolo, lo stimo per mio, ed &egrave; tale, a proposito de'proietti: Dato il <lb/>cannone AB (fig. </s>

<s>204) d'una fontana appresso un muro, ovvero che sia un <lb/><figure id="id.020.01.3467.1.jpg" xlink:href="020/01/3467/1.jpg"/></s></p><p type="caption">

<s>Figura 204.<lb/>pezzo d'artiglieria, e dato un solo punto C, per dove <lb/>passi o l'acqua o la palla; io fo tutta la parabola in <lb/>queste modo: &rdquo; </s></p><p type="main">

<s>&ldquo; Prolungo la AB fino in D, e alzo CD perpen&shy;<lb/>dicolare all'orizzonte, e congiungo BC. </s>

<s>Fatto il trian&shy;<lb/>golo BCD, tiro a caso la BE dal punto B, e faccio EF <lb/>parallela a BD, ed FH parallela a CD, e per H passa <lb/>la parabola. </s>

<s>E nello stesso modo trovo pi&ugrave; e pi&ugrave; punti, <lb/>finch&egrave; bastano per tirar la linea curva &rdquo; (ivi, fol. </s>

<s>17). </s></p><p type="main">

<s>La gentile invenzione, affinch&egrave; non andasse smarrita, volle il Torricelli <lb/>stesso raccoglierla nel suo trattatello <emph type="italics"/>De motu aquarum,<emph.end type="italics"/> proponendola in <lb/>questa forma: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XI. &mdash; <emph type="italics"/>Data directione AD tubi, sive fistulae BA, et <lb/>puncto C, in quod incidat aquae emissio; totam parabolam aquae fluen&shy;<lb/>tis describere<emph.end type="italics"/> &ldquo; (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>198). </s></p><pb xlink:href="020/01/3468.jpg" pagenum="429"/><p type="main">

<s>Parve al Viviani cos&igrave; bello, nella sua facilit&agrave;, questo argomento dei getti <lb/>parabolici, che volle ampliarlo con quest'altra sua proposizione. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XII. &mdash; <emph type="italics"/>Date, nel medesimo perpendicolo AB<emph.end type="italics"/> (fig. </s>

<s>205), <lb/><emph type="italics"/>le distanze CE di due zampilli CLD, ELF, con proiezione orizontale dai <lb/><figure id="id.020.01.3468.1.jpg" xlink:href="020/01/3468/1.jpg"/></s></p><p type="caption">

<s>Figura 205.<lb/>fori C, E, per un medesimo piano verticale, e <lb/>con diversi carichi o sublimit&agrave; note, cio&egrave; il pi&ugrave; <lb/>alto C con la sublimit&agrave; AC, ed il pi&ugrave; basso E <lb/>con la sublimit&agrave; GE; cercasi dove questi s'in&shy;<lb/>contreranno. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Io prendo GH eguale ad AC, e come EH <lb/>ad HG, cos&igrave; si faccia CE ad EI, e per I si tiri <lb/>l'orizontale IL, segante uno degli zampilli, come <lb/>l'ELF, in L: dico che l'altro ancora passa per L &rdquo; <lb/>(MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>7). </s></p><p type="main">

<s>La verit&agrave; dell'asserto rimarrebbe confermata <lb/>dal dimostrare che IL &egrave; l'ampiezza comune alle <lb/>due parabole. </s>

<s>Chiamato P, infatti, il parametro <lb/>della CLP, P'il parametro della ELF, per le note propriet&agrave; <emph type="italics"/>De motu proiecto&shy;<lb/>rum,<emph.end type="italics"/> abbiamo IL2=P.CI, IL2=P&prime;.EI. </s>

<s>E perch&egrave; P=4AC, P&prime;=4GE, <lb/>dunque tutto si riduce a provare che IL2=AC.CI=GE.EI, come fa il <lb/>Viviani, cos&igrave; proseguendo il discorso: &ldquo; Imperocch&egrave; stando, per costruzione, EH <lb/>ad HG come CE ad EI, componendo, EG a GH, ovvero a CA, star&agrave; come CI <lb/>a IE, onde il rettangolo di EG in IE &egrave; uguale al rettangolo di CA in CI &rdquo; (ivi). </s></p><p type="main">

<s>Ritornando al Torricelli, la proposizion che succede a quella, nella quale, <lb/>dato un punto dove cade una gocciola d'acqua e la direzione del tubo, si <lb/>insegna a rintracciar la via parabolica, per la quale dietro a lei pass&ograve; tutto <lb/>lo zampillo; &egrave; come segue: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XIII. &mdash; <emph type="italics"/>Posito vase AB<emph.end type="italics"/> (fig. </s>

<s>206), <emph type="italics"/>sive cylindrico sive <lb/>prismatico, quod in fundo perforatum sit foramine B; velocitas aquae <lb/><figure id="id.020.01.3468.2.jpg" xlink:href="020/01/3468/2.jpg"/></s></p><p type="caption">

<s>Figura 206.<lb/>exeuntis ex B, velocitati libellae, sive supremae su&shy;<lb/>perficiei descendentis in vase, semper eadem ratione <lb/>respondebit &rdquo;<emph.end type="italics"/> (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>199). </s></p><p type="main">

<s>Costruite intorno alla parete AM, come intorno <lb/>a loro proprio asse, le due parabole MLC, MIE, co&shy;<lb/>sicch&egrave; quella sia maggiore di questa, risulta dalle pre&shy;<lb/>cedenti istituzioni che la velocit&agrave; dell'acqua versata <lb/>dal foro B, alla velocit&agrave; della scesa dal livello, in <lb/>qualunque punto si trovi dell'altezza del vaso, sta <lb/>sempre come la linea applicata nella parabola maggiore, all'applicata dal <lb/>medesimo punto nella minore: <emph type="italics"/>hoc est in eadem semper ratione.<emph.end type="italics"/></s></p><p type="main">

<s>Quella che soggiunge il Torricelli in X luogo della sua Appendice, es&shy;<lb/>sendosi avuta gi&agrave; per corollario dalla IVa, si tralascia, tanto pi&ugrave; che la ve&shy;<lb/>dremo scendere pure per corollario da un'altra, e si passa a un problema, <lb/>che il Torricelli stesso nel suo libro propone in tal maniera. </s></p><pb xlink:href="020/01/3469.jpg" pagenum="430"/><p type="main">

<s>&ldquo; PROPOSITIO XIV. &mdash; <emph type="italics"/>Quoddam vas, cuius summitas A<emph.end type="italics"/> (fig. </s>

<s>207), <lb/><emph type="italics"/>perforatum est foramine B ita ut, superinfluente quodam aquae ductu<emph.end type="italics"/><lb/><figure id="id.020.01.3469.1.jpg" xlink:href="020/01/3469/1.jpg"/></s></p><p type="caption">

<s>Figura 207.<lb/><emph type="italics"/>in A, semper plenum permaneat. </s>

<s>Quaeritur quo fora&shy;<lb/>mine perforari debeat in C, ut, eadem superinfluente <lb/>aqua, plenum praecise sicut antea permaneat &rdquo;<emph.end type="italics"/> (ibid., <lb/>pag. </s>

<s>200). </s></p><p type="main">

<s>Dovendo essere le quantit&agrave; versate uguali, l'apertura <lb/>e la sezione data B, alla cercata X, dovr&agrave; reciprocamente <lb/>stare come la velocit&agrave; alla velocit&agrave;. </s>

<s>Ond'&egrave; che, descritta <lb/>la parabola ADE, e condottevi da B e da C le ordinate <lb/>BD, CE, sar&agrave; CE:BD=B:X, l'equazione che risolve il problema. </s></p><p type="main">

<s>Il Viviani promosse questo del Torricelli in un altro problema idrome&shy;<lb/>trico pi&ugrave; complicato, cos&igrave; proponendolo: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XV. &mdash; <emph type="italics"/>Data una botte, o una conserva d'acqua ABCD<emph.end type="italics"/><lb/>(fig. </s>

<s>208), <emph type="italics"/>mantenuta da una indeficiente o soprabbondante fontana sem-<emph.end type="italics"/><lb/><figure id="id.020.01.3469.2.jpg" xlink:href="020/01/3469/2.jpg"/></s></p><p type="caption">

<s>Figura 208.<lb/><emph type="italics"/>pre piena fino al livello AD, cd in uno dei <lb/>lati di essa cisterna, come in AB, sia un foro <lb/>B, per il quale, senza variarsi il livello AD, <lb/>in un dato tempo, esca per B una nota quan&shy;<lb/>tit&agrave; d'acqua, la quale sia rappresentata per <lb/>esempio dalla retta BG, presa perpendicolar&shy;<lb/>mente ad AB; sia proposto di fare, nel mede&shy;<lb/>simo corpo della conserva, un nuovo foro, in <lb/>un altro dato luogo E, pel quale ancora esca <lb/>nel medesimo tempo un'altra data quantit&agrave; d'acqua che, rispetto alla <lb/>prima CB, sia GH. </s>

<s>Cercasi quanto dovr&agrave; esser largo il foro in E. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Intorno all'asse AB, per la cima A e sulla mezza ordinata BG, si <lb/>descriva la mezza parabola AFG, dentro la quale, da E, s'applichi ordina&shy;<lb/>tamente la EF. </s>

<s>Di poi, come EF a GH, cos&igrave; si faccia il foro B ad un altro <lb/>nuovo, che questo sar&agrave; quello, che fatto in E getter&agrave; in detto tempo la quan&shy;<lb/>tit&agrave; GH. &rdquo; </s></p><p type="main">

<s>&ldquo; S'immagini in E un foro, uguale al B: la quantit&agrave; dunque dell'acqua, <lb/>che esce per B, a quella, che esce per l'egual foro E, star&agrave;, per la IVa del <lb/>Torricelli, come BG a EF, e la quantit&agrave; dell'acqua, che esce pel foro E, <lb/>uguale al B, alla quantit&agrave;, che esce pel nuovo foro fatto in E, sta come il <lb/>foro in E, uguale al B, al foro in E fatto di nuovo (stante che l'una e l'al&shy;<lb/>tra esca dal luogo E con la stessa velocit&agrave;, mediante che l'altezza premente <lb/>sia sempre la stessa AE) cio&egrave; come FE a GH. Adunque, per l'egualit&agrave;, la <lb/>quantit&agrave; dell'acqua per B, alla quantit&agrave; pel nuovo foro in E, sta come la <lb/>BG alla GH. </s>

<s>Ma la quantit&agrave;, che esce per B, &egrave; rappresentata dalla BG; dun&shy;<lb/>que la quantit&agrave;, che esce pel detto nuovo foro in E, verr&agrave; rappresentata <lb/>dalla GH, che &egrave; la quantit&agrave; data, che si voleva uscisse dal nuovo foro in E. </s>

<s><lb/>Il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario.<emph.end type="italics"/> &mdash; Dalla costruzione del problema si cava che, se la quan-<pb xlink:href="020/01/3470.jpg" pagenum="431"/>tit&agrave; richiesta GH per il nuovo foro da farsi in E, sar&agrave; uguale a quella che <lb/>esce pel foro B; sar&agrave; la GH uguale alla BG. </s>

<s>Ed essendosi fatto, come EF <lb/><figure id="id.020.01.3470.1.jpg" xlink:href="020/01/3470/1.jpg"/></s></p><p type="caption">

<s>Figura 209.<lb/>GH, cos&igrave; il foro dato B, al nuovo in E; tali fori B, E, per <lb/>i quali escono quantit&agrave; d'acqua uguali, sono in proporzione <lb/>reciproca delle ordinate per essi nella parabola AFG &rdquo; (MSS. <lb/>Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>13). </s></p><p type="main">

<s>La proposizione del Torricelli, che vien dopo questa, dal <lb/>Viviani cos&igrave; promossa, nelle prime bozze del manoscritto era <lb/>stata messa in tal forma: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XVI. &mdash; <emph type="italics"/>Vas aliquod ABC<emph.end type="italics"/> (fig. </s>

<s>209), <emph type="italics"/>cu&shy;<lb/>iuscumque figurae, sit perforatum in fundo foramine B. </s>

<s><lb/>Influat in vas aqua tubi F, faciatque intra eum altitudi&shy;<lb/>nem BE. </s>

<s>Quaeritur quantitas aquae, quae influens fa&shy;<lb/>ciat intra vas altitudinem BL &rdquo;<emph.end type="italics"/> (Fra i MSS. di Gal., P. V, T. V). </s></p><p type="main">

<s>La soluzion del problema &egrave; ridotta all'assurdo, col dimostrare l'impos&shy;<lb/>sibilit&agrave; del rimanersi il livello dell'acqua dentro il vaso, o superiore o infe&shy;<lb/><figure id="id.020.01.3470.2.jpg" xlink:href="020/01/3470/2.jpg"/></s></p><p type="caption">

<s>Figura 210.<lb/>riore a quello, che vien designato da questa imperata costru&shy;<lb/>zione: &ldquo; Sumatur media proportionalis inter BE, BL, quae sit <lb/>BI, fiatque, ut BE ad BI, ita aqua F ad aliam O. </s>

<s>Dico aquam <lb/>O solam facere altitudinem BL &rdquo; (ibid.). </s></p><p type="main">

<s>Poi nel dare il trattato alle stampe prefer&igrave; il Torricelli la <lb/>via diretta, nel dimostrar la medesima proposizione, messa per&ograve; <lb/>cos&igrave; sotto altra forma: &ldquo; Quoddam vas AB (fig. </s>

<s>210), cum per&shy;<lb/>foratum sit in fundo foramine B, superinfluente quodam dato <lb/>aquae ductu D plenum permanet usque ad signum C. </s>

<s>Quaeri&shy;<lb/>tur quantitas aquae in idem vas ingerendae ad hoc, ut repleatur <lb/>usque ad signum A &rdquo; (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>200, 1). </s></p><p type="main">

<s>La via diretta del dimostrare, quivi tenuta, consiste nell'osservare che, <lb/>per essere le sezioni uguali, la quantit&agrave; data D, e la cercata X, stanno come <lb/>le radici delle altezze: cio&egrave; &radic;CB:&radic;AB=CB:&radic;CB.AB=D:X. </s>

<s>E perci&ograve;, <lb/>essendo CB e D note, il problema vien risoluto col ritrovar la media pro&shy;<lb/>porzionale fra le CB, AB, altezze date. <lb/><figure id="id.020.01.3470.3.jpg" xlink:href="020/01/3470/3.jpg"/></s></p><p type="caption">

<s>Figura 211.</s></p><p type="main">

<s>Risoluto in un modo, che presso a poco si riduce a que&shy;<lb/>sto, il problema, si soggiungono dall'Autore alcune parole, <lb/>alle quali il Viviani riferisce la seguente sua avvertenza: <lb/>&ldquo; Il Torricelli, verso il fine, del suo trattatello dell'Acque, <lb/>un dopo l'altro, scioglie tre curiosi problemi, e nell'estremo <lb/>soggiunge: <emph type="italics"/>quod, cum multis aliis huius generis, facile de&shy;<lb/>monstratur ex praecedentibus.<emph.end type="italics"/> Ora tra questi molti altri io <lb/>me ne proposi alcuni, facili veramente, ma perch&egrave; la faci&shy;<lb/>lit&agrave; non toglie loro l'esser veri, per questa ragione dell'esser <lb/>veri, che &egrave; pure assai, e per l'altra ancora dell'esser fa&shy;<lb/>cili, mi piace addurgli e sono i seguenti: &rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO XVII. &mdash; <emph type="italics"/>Dato il vaso ABC<emph.end type="italics"/> (fig. </s>

<s>211), <pb xlink:href="020/01/3471.jpg" pagenum="432"/><emph type="italics"/>forato nel fondo B e mantenuto pieno dalla fonte D fino al livello AC, <lb/>alto sopra il foro quanto CE, si cerca a qual altezza sia per mantenersi <lb/>l'acqua, che esce per B, ricevuta nel sottoposto vaso FGH, forato col foro <lb/>G, di nota proporzione col foro B. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Si faccia, come il foro G al B, cos&igrave; l'altezza nota CE, alla I, dopo <lb/>le quali si prenda terza proporzionale la HL, posta sopra il foro G, che que&shy;<lb/>sta sar&agrave; l'altezza cercata. </s>

<s>Imperocch&egrave;, essendo l'acqua, che esce per B, uguale <lb/>a quella, che entra nel vaso di sotto, e che, alzatavi sino ad un livello per&shy;<lb/>manente, esce pel foro G; sar&agrave; la velocit&agrave; per B, alla velocit&agrave; per G, come <lb/>il foro G al B, per la IVa di questo, cio&egrave; sar&agrave; come CE ad I. </s>

<s>Ma CE ad I <lb/>ha suddupla ragione di CE ad HL, dunque anche il foro G al B ha suddu&shy;<lb/>pla ragione di CE ad HL. </s>

<s>Ma CE &egrave; l'altezza invariabile del vaso ABC, dun&shy;<lb/>que HL &egrave; l'altezza invariabile cercata del vaso FGH &rdquo; (MSS. Gal. </s>

<s>Disc., <lb/>T. CXVII, fol. </s>

<s>3). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XVIII. &mdash; <emph type="italics"/>Date le AB, DE<emph.end type="italics"/> (fig. </s>

<s>212), <emph type="italics"/>altezze invariabili <lb/>dell'acqua, che da due fonti entra in due vasi ABC, DEF, e dati i fori<emph.end type="italics"/><lb/><figure id="id.020.01.3471.1.jpg" xlink:href="020/01/3471/1.jpg"/></s></p><p type="caption">

<s>Figura 212.<lb/><emph type="italics"/>G, H ne'loro fondi, per i quali ella esce; asse&shy;<lb/>gnare la proporzione delle quantit&agrave;, che ne <lb/>scappano dentro un medesimo tempo, o che <lb/>gettano i fonti. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Si prenda la I, media proporzionale fra <lb/>le altezze AB, DE, e come il foro G, al foro H, <lb/>cos&igrave; sia I ad L: dico che la quantit&agrave; per G, alla <lb/>quantit&agrave; per H, sta come AB ad L. </s>

<s>Imperocch&egrave; <lb/>la quantit&agrave; per G, alla quantit&agrave; per H, ha ragion composta della velocit&agrave; <lb/>per G, alla velocit&agrave; per H, e del foro G al foro H. </s>

<s>Ma la velocit&agrave; per G, <lb/>alla velocit&agrave; per H, ha suddupla ragione dell'altezza AB alla DE, cio&egrave; sta <lb/>come AB ad I, ed il foro G, all'H, sta come I ad L, per costruzione, e AB <lb/>ad L ha ragion composta di AB ad I, e di I ad L; adunque la quantit&agrave; per <lb/>G, a quella per H, sta come AB ad L. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Esempio.<emph.end type="italics"/> &mdash; Sia AB parti 26, e DE 5: il foro G once 4, e H once 1. <lb/>Si prenda la media proporzionale fra 20 e 5, che &egrave; 10, e si faccia, come <lb/>4 a 1, cos&igrave; 10 a 2 1/2, ch&egrave; la quantit&agrave; per G, alla quantit&agrave; per H, star&agrave; <lb/><figure id="id.020.01.3471.2.jpg" xlink:href="020/01/3471/2.jpg"/></s></p><p type="caption">

<s>Figura 213.<lb/>come 20 a 2 1/2, cio&egrave; come 40 a 5. Onde, se in un tal <lb/>tempo, per G, usciranno 40 barili di acqua, nel mede&shy;<lb/>simo tempo, per H, ne usciranno barili 5, ed altrettanto <lb/>ne renderanno le fonti, che s'introducono in tali vas&igrave; &rdquo; <lb/>(ivi, fol. </s>

<s>4). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XIX. &mdash; <emph type="italics"/>Data la proporzione di H <lb/>ad I, fra le quantit&agrave; dell'acqua, che escono da due <lb/>fonti invariabili A e B<emph.end type="italics"/> (fig. </s>

<s>213), <emph type="italics"/>e data l'altezza CD, <lb/>che uno di essi A mantiene dentro il vaso CDE, nel&shy;<lb/>l'uscire per il noto foro F del fondo: assegnare l'altezza, che vi manter&shy;<lb/>ranno ambedue, nell'uscire pel medesimo foro F. &rdquo;<emph.end type="italics"/></s></p><pb xlink:href="020/01/3472.jpg" pagenum="433"/><p type="main">

<s>&ldquo; Si faccia come H, ad H con I, cos&igrave; DC a DL, e dopo questa si prenda <lb/>la terza proporzionale, ch&egrave; questa sar&agrave; l'altezza cercata. </s>

<s>Imperocch&egrave;, essendo <lb/>H ad I come la quantit&agrave; dell'acqua, che rende la fonte A, alla quantit&agrave; che, <lb/>nel medesimo tempo, rende la fonte B; star&agrave; H ad H con I, cio&egrave;, per co&shy;<lb/>struzione, DC a DL, come la quantit&agrave; A, alle quantit&agrave; A e B insieme prese. </s>

<s><lb/>Ma DC a DL ha suddupla ragione dell'altezza DC, alla terza proporzionale <lb/>DM, adunque anche la quantit&agrave; di A, alle due insieme A, B, ha suddupla <lb/>ragione dell'altezza DC, all'altezza DM. </s>

<s>Ma la quantit&agrave; di A si pose esser <lb/>quella, che introdotta nel vaso esce per F, e vi fa l'altezza invariabile DC; <lb/>dunque le due quantit&agrave; insieme A, B, nell'uscire pel medesimo foro F, vi <lb/>faranno l'altezza MD, onde questa &egrave; la cercata. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Esempio.<emph.end type="italics"/> &mdash; Renda la fonte A 60 barili l'ora, e la B 37, e l'altezza nota <lb/>CD sia parti 34. Facciasi, come 60 a 97, somma della rendita, cos&igrave; 34 al nu&shy;<lb/>mero, che se ne ottiene; e come 34 al numero ottenuto, cos&igrave; lo stesso numero <lb/>ottenuto a un altro, ch&egrave; tante parti sar&agrave; l'altezza cercata DM &rdquo; (ivi, fol. </s>

<s>8). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XX. &mdash; <emph type="italics"/>La medesima quantit&agrave; d'acqua, che, uscendo <lb/>dal fonte invariabile E<emph.end type="italics"/> (fig. </s>

<s>214), <emph type="italics"/>entra nel vaso ABCD, secondo la diver-<emph.end type="italics"/><lb/><figure id="id.020.01.3472.1.jpg" xlink:href="020/01/3472/1.jpg"/></s></p><p type="caption">

<s>Figura 214.<lb/><emph type="italics"/>sit&agrave; de'fori B, C orizontali, di nota grandezza, vi <lb/>s'alza a diverse altezze ignote invariabili FG, AG: <lb/>cercasi la proporzione di tali altezze. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Si faccia, come il foro B al C, cos&igrave; il C ad un <lb/>altro I. </s>

<s>Dico che l'altezza AG, alla FG, sta come B ad I. </s>

<s><lb/>Giacch&egrave; per B esce la quantit&agrave; dell'acqua, che in qua&shy;<lb/>lunque tempo rende la fonte E, col far nel vaso l'al&shy;<lb/>tezza invariabile FG, e per C, nel medesimo tempo, <lb/>esce la medesima quantit&agrave;, con farvi l'altezza invaria&shy;<lb/>bile AG; il foro B al C star&agrave; reciprocamente come la velocit&agrave; per C. alla <lb/>velocit&agrave; per B. </s>

<s>Ma la velocit&agrave; per C, alla velocit&agrave; per D, ha suddupla ragione <lb/>di quella delle loro proprie altezze AG, FG; adunque anche il foro B, al <lb/>foro C, ha suddupla ragione di quella dell'altezza AG alla FG. </s>

<s>Ma il foro <lb/>B al C ha parimente suddupla ragione del B all'I, adunque l'altezza AG, <lb/>alla FG, sta come il foro B all'I, il che ecc. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Esempio.<emph.end type="italics"/> &mdash; Sia il foro B once 5, ed il C once 4, e si faccia, come <lb/>5 a 4, cos&igrave; 4 a 3 1/5, che l'altezza AG, alla FG, star&agrave; come 5 a 3 1/5, o <lb/>come 25 a 16. Onde, se una di queste sar&agrave; nota in parti 25, si far&agrave; nota <lb/>anche l'altra in parti 16. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollario.<emph.end type="italics"/> &mdash; Conclusi dianzi che l'altezza AG, alla FG, sta come il <lb/>foro B al foro I. </s>

<s>Ma il foro B all'I ha doppia ragione del B al C, adunque <lb/>anche l'altezza AG, alla FG, ha doppia ragione del foro B al C. &rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scolio I.<emph.end type="italics"/> &mdash; Se i fori B, C, orizontali nel fondo del vaso, saranno di <lb/>figure simili come di cerchi, la proporzione cercata delle altezze invariabili <lb/>sopraddette sempre &egrave; la stessa della proporzione de'lati omologhi dei fori, <lb/>cio&egrave;, qui, dei diametri. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scolio II.<emph.end type="italics"/> &mdash; Notisi che ho sempre inteso, ed intendo, che i fori dei <pb xlink:href="020/01/3473.jpg" pagenum="434"/>vasi sien fatti orizontali, e non verticali, come spesso gli considera il Torri&shy;<lb/>celli, perch&egrave; le rendite di quegli son sempre proporzionali ai medesimi fori, <lb/>e non gi&agrave; di questi, mentre per&ograve; le figure loro ne'piani verticali non si <lb/><figure id="id.020.01.3473.1.jpg" xlink:href="020/01/3473/1.jpg"/></s></p><p type="caption">

<s>Figura 215.<lb/>dessero condizionate, lo che non &egrave; mai necessario in quegli <lb/>altri, potendo esser fra loro di qualunque diversa figura &rdquo; <lb/>(ivi, fol. </s>

<s>11). </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXI. &mdash; <emph type="italics"/>Data A la quantit&agrave; dell'acqua, <lb/>che esce per il dato foro B nel fondo del vaso CDE<emph.end type="italics"/> (fig. </s>

<s>215), <lb/><emph type="italics"/>con la data invariabile altezza CD, e dato il foro F e l'al-<emph.end type="italics"/><lb/><figure id="id.020.01.3473.2.jpg" xlink:href="020/01/3473/2.jpg"/></s></p><p type="caption">

<s>Figura 216.<lb/><emph type="italics"/>tezza invariabile GH, nel medesimo o in altro vaso GHI<emph.end type="italics"/> (fig. </s>

<s>216): <lb/><emph type="italics"/>d&iacute;re la quantit&agrave; dell'acqua che, a proporzione della data quan&shy;<lb/>tit&agrave;, ne uscir&agrave; per questo. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Si prenda HL media proporzionale fra le date altezze HG, <lb/>DC, e come DC ad HL, cos&igrave; sia A ad M, e come il foro B al foro <lb/>F, cos&igrave; sia M ad N: dico che la quantit&agrave; nota per B, alla quantit&agrave; <lb/>ignota per F, sta come A ad N. </s>

<s>Imperocch&egrave; la quantit&agrave; per B, con l'altezza <lb/>CD, alla quantit&agrave; per F, con l'altezza GH, ha ragion composta della velocit&agrave; <lb/>per B, alla velocit&agrave; per F, cio&egrave; della CD alla HL, cio&egrave; di A ad M, e del <lb/>foro B al foro F, ossia della M alla N. </s>

<s>Ma anche A ad N ha ragion com&shy;<lb/>posta della medesima di A ad M, e di M ad N; adunque anche la quantit&agrave; <lb/>per B, alla quantit&agrave; per F, sta come A ad N. </s>

<s>Ma A esprime la quantit&agrave; <lb/>per B coll'altezza CD, adunque anche N esprime la quantit&agrave; per F, coll'al&shy;<lb/>tezza GH, il che ecc. </s>

<s>&rdquo; (ivi, fol. </s>

<s>9). </s></p><p type="main">

<s>In queste cinque proposizioni il Viviani mostrava di quanta fecondit&agrave; <lb/>fosse l'applicazione delle nuove dottrine insegnate dal Torricelli, il quale, in <lb/>sul finire del suo trattato, ne aveva egli stesso gi&agrave; dati alcuni esempi. </s>

<s>La <lb/>chiusa per&ograve; di quel medesimo trattato sembra rassomigliarsi a una cateratta, <lb/>calata innanzi a una fiaccola, nell'atto stesso che pi&ugrave; prometteva di sfolgo&shy;<lb/>rare, ond'ei non &egrave; maraviglia che il Viviani si studiasse di sollevarla, per <lb/>diffondere la benefica luce pi&ugrave; largamente sopra i campi della Scienza. </s>

<s>Il <lb/><figure id="id.020.01.3473.3.jpg" xlink:href="020/01/3473/3.jpg"/></s></p><p type="caption">

<s>Figura 217.<lb/>centro di cotesta diffusione &egrave; un teorema, che il <lb/>Torricelli stesso cos&igrave;, in ultimo luogo, proponeva: <lb/>&ldquo; Esto vas irregulare GHDEF (fig. </s>

<s>217) perforatum <lb/>in fundo foramine D, et considerentur duae ipsius <lb/>sectiones GH, HE. </s>

<s>Dico velocitatem summae su&shy;<lb/>perficiei aquae descendentis, quando erit GF, ad <lb/>velocitatem superficiei, quando erit HE, rationem <lb/>habere compositam ex ratione subduplicata altitu&shy;<lb/>dinum GD ad HD, et reciproca sectionum, nempe sectionis HE ad GF &rdquo; <lb/>(Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>203). </s></p><p type="main">

<s>Il primo pensiero del Viviani fu quello di esplanare una difficolt&agrave;, la <lb/>quale nasceva dal non sapersi ridurre a significato fisico la ragion geome&shy;<lb/>trica delle linee, che si fanno entrare in composizione co'veli acquei delle <lb/>sezioni, intorno a che dettava la seguente nota. </s></p><pb xlink:href="020/01/3474.jpg" pagenum="435"/><p type="main">

<s>&ldquo; Quando il Torricelli, nell'ultima sua proposizione, dice che la velocit&agrave; <lb/>del supremo livello GF (nella medesima figura 217) alla velocit&agrave; del supremo <lb/>livello HE, ha proporzione composta della GD alla ID, media proporzionale <lb/>fra le altezze GD, HD, e della proporzione della sezione per HE, alla sezione <lb/>per GF: quella prima proporzione di HD a ID la considera come esprimente <lb/>la proporzione, che &egrave; fra la quantit&agrave; del fluido, che passa in quell'istante <lb/>per la sezione GF, quando il vaso dall'altezza GD si vota pel foro D, e la <lb/>quantit&agrave; del fluido, che in quell'istante, premuto dall'altezza HD, passa per <lb/>la sezione HE, nell'uscire pel medesimo foro D. &rdquo; </s></p><p type="main">

<s>&ldquo; Esser questo verissimo cos&igrave; lo provo: Perch&egrave;, mantenuta l'altezza GD, <lb/>per la Ia proposizion del Castelli, tanta &egrave; l'acqua che esce in un tal tempo <lb/>pel foro D, che quella, che passa nel medesimo tempo per la sezione GF: <lb/>e tanta &egrave; l'acqua, che in un tal tempo, esce pel foro D, mantenuta l'al&shy;<lb/>tezza HD, che quella, che nel medesimo tempo passa per la sezione HE. </s>

<s>Ma <lb/>la quantit&agrave; dell'acqua, che in un tal tempo esce per D dall'altezza GD, alla <lb/>quantit&agrave;, che nel medesimo tempo esce per D dall'altezza HD, sta come la <lb/>GD alla ID, per la Xa del Torricelli; adunque anche la quantit&agrave; dell'acqua, <lb/>che passa per GF, nel votarsi il vaso per D dall'altezza GD, alla quantit&agrave; <lb/>dell'acqua, che passa per HE, nel votarsi per C dall'altezza HD; sta come <lb/>GD a ID, il che ecc. </s>

<s>&rdquo; (MSS. Gal. </s>

<s>Disc., T. CXVI, fol. </s>

<s>118). </s></p><p type="main">

<s>Non bast&ograve; al Viviani d'aver dichiarate queste parti, intorno alla Propo&shy;<lb/>sizione torricelliana, la quale, per costituirsi qual fondamento alle nuove spe&shy;<lb/>culazioni, che gli si paravano nella mente, riconobbe essere di tanta impor&shy;<lb/>tanza, che volle renderla anche pi&ugrave; perfetta. </s>

<s>Pens&ograve;, per questo, di applicare <lb/>all'asse del vaso, per la scala della velocit&agrave;, la parabola, e si dispens&ograve; dal <lb/>ridurre il vaso stesso, dato irregolare, a prismatico, com'aveva fatto il Tor&shy;<lb/>ricelli, il teorema stesso del quale proponeva cos&igrave;, sotto altra forma, e ne <lb/>conduceva cos&igrave; la dimostrazione per un'altra via, se non pi&ugrave; breve, senza <lb/>dubbio pi&ugrave; retta: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXII. &mdash; <emph type="italics"/>Se qualunque vaso GDF<emph.end type="italics"/> (nella medesima figura <lb/>ultima) <emph type="italics"/>sar&agrave; pieno di fluido fino al livello GF, col foro in fondo D, pel <lb/>quale e'vada votandosi, e la sua altezza sia GD, intorno alla quale come <lb/>asse, per la cima D, sia descritta qualunque parabola supina DNM, e no&shy;<lb/>tato nel vaso qualsiasi altro livello HE, segante l'asse in H, e per G, H, <lb/>dentro essa parabola, siano ordinatamente applicate all'asse le GM, HN; <lb/>dico che, nel votarsi il vaso, la velocit&agrave; del superiore livello GF, alla ve&shy;<lb/>locit&agrave; dell'inferiore HE, quando egli &egrave; calato in HE, ha ragion compo&shy;<lb/>sta dell'ordinata GM alla HN, e della sezione del vaso, pel livello HE, <lb/>alla sezione pel livello GF, cos&igrave; reciprocamente prese. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Imperocch&egrave; la ragion della velocit&agrave; del livello fluido, per la sezione GF, <lb/>nell'uscire pel foro D dall'altezza GD, alla velocit&agrave; del livello fluido, per la <lb/>sezione HE, nell'uscire per il medesimo foro D dall'altezza HD, &egrave; compo&shy;<lb/>sta di tre ragioni: cio&egrave; della ragione della velocit&agrave; per GF dall'altezza GD, <lb/>alla velocit&agrave; per D dalla medesima altezza GD, cio&egrave;, per la dottrina di d. </s>

<s>Be-<pb xlink:href="020/01/3475.jpg" pagenum="436"/>nedetto Castelli, della ragione della sezione del foro D, alla sezione per GF, <lb/>cos&igrave; reciprocamente prese (stante che il fluido medesimo esce per l'una e <lb/>per l'altra sezione nel medesimo tempo) e della ragione della velocit&agrave; per D, <lb/>dalla detta altezza GD, alla velocit&agrave; per esso foro D, dall'altezza minore HD, <lb/>cio&egrave; della ragione della ordinata GM alla HN, nella parabola DNM, e della <lb/>ragione della velocit&agrave; pel medesimo foro D, dalla medesima altezza HD, alla <lb/>velocit&agrave; per la sezione HE, dall'istessa altezza HD; cio&egrave;, per la stessa dot&shy;<lb/>trina del Castelli, della ragione della sezione HE alla sezione D, cos&igrave; alter&shy;<lb/>nativamente prese. </s>

<s>Ma di queste tre ragioni, la terza, cio&egrave; quella della se&shy;<lb/>zione HE alla D, e la prima, cio&egrave; quella della sezione D alla GF, compon&shy;<lb/>gono la ragione della sezione HE alla GF; adunque la ragion della velocit&agrave; <lb/>del livello, per la sezione GF, superiore al foro quanto &egrave; la GD, alla velo&shy;<lb/>cit&agrave; del livello per la sezione HE, superiore al foro quanto &egrave; l'HD, &egrave; com&shy;<lb/>posta di due sole ragioni, cio&egrave; di quella dell'ordinata GM alla HN, e di <lb/>quest'ultima ridotta: cio&egrave; della sezione HE alla sezione GF, cos&igrave; reciproca&shy;<lb/>mente prese, osservando qui, come si fece per la dimostrazione del Torri&shy;<lb/>celli, ci&ograve; che importi la ragione fra l'ordinata GM alla HN, fra quelle due <lb/>proporzioni componenti la proporzione delle velocit&agrave; del primo supremo li&shy;<lb/>vello GF, alla velocit&agrave; del secondo inferiore livello HE, essendosi veduto che <lb/>tal ragione altro non esprime, che quella, che &egrave; fra le quantit&agrave; del fluido, <lb/>che passa per la sezione del livello GF, alla quantit&agrave;, che nel medesimo <lb/>tempo passa per l'altra sezione del livello HE &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXVII, <lb/>fol. </s>

<s>18 e 20). </s></p><p type="main">

<s>Tanto poi parve premesse al Viviani questa osservazione, che volle con&shy;<lb/>fermarla col soggiungere la seguente </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXIII. &mdash; <emph type="italics"/>Se qualunque vaso, rotondo o non rotondo<emph.end type="italics"/><lb/>(fig. </s>

<s>218), <emph type="italics"/>forato nel fondo in O, sia mantenuto pieno d'acqua or fino al<emph.end type="italics"/><lb/><figure id="id.020.01.3475.1.jpg" xlink:href="020/01/3475/1.jpg"/></s></p><p type="caption">

<s>Figura 218.<lb/><emph type="italics"/>livello AF, formante la superficie o la sezione G, <lb/>ed or fino al livello BE, formante la superficie <lb/>o sezione H; la quantit&agrave; dell'acqua, che esce per <lb/>O, quando il livello &egrave; G, alla quantit&agrave; dell'acqua, <lb/>che nel medesimo tempo esce per O, quando il <lb/>livello &egrave; H, sta sempre come l'ordinata FM al&shy;<lb/>l'ordinata EL, nella parabola intorno all'asse FK, <lb/>alto quanto &egrave; il superiore livello G sopra il foro O. &rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Imperocch&egrave;, allor che il vaso sta sempre pieno sino al livello G, tanta <lb/>&egrave; la mole dell'acqua, che esce pel foro O, quanta quella, che passa nel me&shy;<lb/>desimo tempo per la sezione G. </s>

<s>E parimente, allor che il vaso sta sempre <lb/>pieno sino al livello H, tanta &egrave; la mole del fluido, che esce pel medesimo <lb/>foro O, quanta &egrave; quella, che nel medesimo tempo passa per la sezione H. </s>

<s><lb/>Ma la mole, che passa per la sezione G, alla mole, che nel medesimo tempo <lb/>passa per la sezione H, ha ragion composta della velocit&agrave; per G, alla velo&shy;<lb/>cit&agrave; per H, e della sezione G, alla sezione H, e la velocit&agrave; per G, alla ve&shy;<lb/>locit&agrave; per H, sta, per la precedente, come il prodotto della ordinata FM nella <pb xlink:href="020/01/3476.jpg" pagenum="437"/>sezione H, al prodotto della ordinata EL nella sezione G; adunque la mole <lb/>per G, alla mole per H, ha ancora ragion composta del prodotto della FM <lb/>nella sezione H, al prodotto della EL nella sezione G, e della sezione G alla <lb/>sezione H: ci&ograve; che tutto viene a ridursi alla semplice ragione della ordinata <lb/>FM, alla EL. </s>

<s>Onde abbiam dimostrato quel che si proponeva, esser la mole <lb/>per G alla mole per H, cio&egrave; la mole per O, quando il vaso &egrave; pieno sino <lb/>al livello G, alla mole, che nel medesimo tempo esce per O, quando egli &egrave; <lb/>pieno sino al livello H, come la FM, alla NL &rdquo; (MSS. Gal. </s>

<s>Disc., T. XCIII, <lb/>fol. </s>

<s>86). </s></p><p type="main">

<s>Confermata cos&igrave; meglio, e dichiarata fra le linee ordinate nella parabola <lb/>e le liquide sezioni, quella ragione, che s'annunziava e si concludeva di sopra <lb/>nella XXII proposizione; il Viviani volle applicar questa medesima a dimo&shy;<lb/>strar generalmente ci&ograve; che il Torricelli aveva solo considerato in un caso <lb/>particolare: la proporzion cio&egrave; degli spazi passati in tempi uguali dai livelli <lb/>dell'acqua, che si versa per foro in fondo a un vaso, non tirato a perfezion <lb/>di cilindro o di prisma, ma proposto della pi&ugrave; irregolare figura, che a uno <lb/>piaccia. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXIV. &mdash; <emph type="italics"/>In qualunque vaso forato in fondo, la velo&shy;<lb/>cit&agrave; che ha il fluido, nell'uscire dal principio del votar del vaso, sino al-<emph.end type="italics"/><lb/><figure id="id.020.01.3476.1.jpg" xlink:href="020/01/3476/1.jpg"/></s></p><p type="caption">

<s>Figura 219.<lb/><emph type="italics"/>l'ultimo, considerata in quegli istanti, nei <lb/>quali si trovano i livelli discesi a diverse al&shy;<lb/>tezze sopra il fondo; son proporzionali alle <lb/>velocit&agrave;, che alle medesime altezze avrebbe un <lb/>proietto, che da qualche impellente fosse cac&shy;<lb/>ciato dal fondo allo in su perpendicolar&shy;<lb/>mente. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sia ABCD (fig. </s>

<s>219) qualunque vaso, <lb/>forato nel fondo in BC, col fluido, che a prin&shy;<lb/>cipio arrivi al livello AD, alto quanto AE, e <lb/>fatta la parabola EFG, per la cima E, intorno <lb/>l'asse EA, si consideri il vaso andarsi votando <lb/>per BC, e il livello AD pervenire in HI. </s>

<s>Dico che la velocit&agrave; per BC, quando <lb/>il livello &egrave; in AD, alla velocit&agrave;, quando &egrave; in HI, sta come l'ordinata AG <lb/>alla OF. &rdquo; </s></p><p type="main">

<s>&ldquo; La velocit&agrave; per la sezione BC dall'altezza AE, alla velocit&agrave; della se&shy;<lb/>zione del livello AD, sta come la sezione del livello AD, alla sezione BC, per <lb/>il Castelli, o come il fatto dalla sezione AD nella OF, al fatto dalla sezione BC <lb/>nell'OF. </s>

<s>E la velocit&agrave; della sezione AD, alla velocit&agrave; della sezione HI, sta, per <lb/>la XXII di questo, come il fatto dalla sezione HI nella AG, al fatto dalla <lb/>sezione AD nella OF. Adunque, per la ugualit&agrave; perturbata, la velocit&agrave; per <lb/>la sezione BC dall'altezza AE, alla velocit&agrave; per la sezione HI, sta come il <lb/>fatto dalla sezione HI nella AG, al fatto dalla sezione BC nella OF. </s>

<s>E la ve&shy;<lb/>locit&agrave; per la sezione HI, alla velocit&agrave; per la BC dall'altezza OE, sta, per il <lb/>Castelli, come la sezione BC alla sezione HI, o come il fatto dalla sezione <pb xlink:href="020/01/3477.jpg" pagenum="438"/>BC nella OF, al fatto dalla sezione HI nella medesima OF; adunque, per <lb/>l'ugualit&agrave; ordinata, la velocit&agrave; per la sezione BC dall'altezza AE, alla velo&shy;<lb/>cit&agrave; per la medesima BC dall'altezza OE, sta come il fatto dalla sezione HI <lb/>nella AG, al fatto dalla medesima sezione HI nella OF: cio&egrave; sta come la AG <lb/>alla OF, nella parabola. </s>

<s>Ma le velocit&agrave;, procedenti secondo le ordinate AG, OF <lb/>in essa parabola, son proporzionali a quelle di un grave ascendente con moto <lb/>di proiezione da E in A; adunque &egrave; manifesto quanto fu proposto di dimo&shy;<lb/>strare &rdquo; (ivi, T. CXVIII, fol. </s>

<s>128). </s></p><p type="main">

<s>Se il vaso non &egrave; irregolare, come qui suppone il Viviani, ma cilindrico <lb/>o prismatico, cosicch&egrave; tutte le sezioni di lui, dal supremo livello infino al <lb/>fondo, si mantengano uguali, le velocit&agrave; delle scese nel votarsi il vaso, <lb/>non solamente avranno ragione di proporzionalit&agrave;, ma d'uguaglianza, verso <lb/>le velocit&agrave;, che raggiungerebbe ne'punti omologhi un proietto, il quale fosse <lb/>da qualche impellente cacciato dal fondo in su alla medesima altezza per&shy;<lb/>pendicolare. </s>

<s>Non &egrave; dunque che un corollario di questa la proposizione stessa <lb/>dal Torricelli cos&igrave; formulata: &ldquo; Vasa cylindrica, sive prismatica in fundo per&shy;<lb/>forata, ea lege exhauriuntur, ut, diviso tempore in partes aequales, emissio <lb/>ultimi temporis sit ut unum, emissio autem penultimi temporis sit ut 3, an&shy;<lb/>tepenultimi temporis ut 5, et sic deinceps ut numeri impares ab unitate &rdquo; <lb/>(Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>202). </s></p><p type="main">

<s>&Egrave; manifesto infatti che, immaginata l'altezza QB (nella medesima <lb/>figura 219) uguale e antipoda alla BP, se ambedue si dividano negli uguali <lb/>spazi VP, BS; VT, SR; TB, RQ, crescenti da uno a tre a cinque ecc., <lb/>l'acqua, votandosi pel foro BC, e perci&ograve; scendendo via via dentro il vaso, <lb/>avr&agrave; in R, in S, in B raggiunta la velocit&agrave; medesima, che si troverebbe <lb/>avere in T, V, P un proietto, il quale fosse, con l'impeto acquistato dal&shy;<lb/>l'acqua stessa nel cadere da Q in B, cacciato in su perpendicolarmente in&shy;<lb/>fino all'altezza P. &Egrave; anche manifesto che, essendo gli spazi BS, SR, RQ pas&shy;<lb/>sati nel medesimo tempo, le quantit&agrave; dell'acqua, o le sue emissioni, suppo&shy;<lb/>sto il vaso prismatico, crescono come essi spazi, cio&egrave; secondo la serie de'nu&shy;<lb/>meri impari, cosicch&egrave;, se una misura sola &egrave; quella versata nell'ultimo tempo, <lb/>nel penultimo ne saranno state versate tre, nell'antipenultimo cinque, e cos&igrave; <lb/>sempre di seguito. </s></p><p type="main">

<s>Notava il Viviani, dop'aver dimostrata a quel modo che abbiamo letto, <lb/>la corrispondenza del moto fra l'acqua che scende, e il proietto che sale, <lb/><emph type="italics"/>esser questo un teorema elementare e importantissimo alla cognizione di <lb/>altre curiose, e assai utili dottrine.<emph.end type="italics"/> Fra queste una delle pi&ugrave; curiose e utili <lb/>che, come ora si vedr&agrave;, e meglio nel capitolo seguente, furono dal Viviani <lb/>stesso pi&ugrave; promosse, &egrave; quella che riguarda il tempo del votarsi l'acqua, ri&shy;<lb/>cevuta dentro varie forme di vasi, fra le quali il Torricelli non accennava <lb/>che a solo il conoide parabolico. </s>

<s>E par che facesse questo, pi&ugrave; per stuzzi&shy;<lb/>care la curiosit&agrave; dei lettori, che per darne scienza, contentandosi di avver&shy;<lb/>tirli che si rimarrebbero ingannati a credere essere esso conoide quello che <lb/>si vuota equabilmente, facendosi anzi gli abbassamenti dell'acqua dentro lui <pb xlink:href="020/01/3478.jpg" pagenum="439"/>con moto sempre pi&ugrave; accelerato, di che volle il Viviani non lasciare i Let&shy;<lb/>tori in desiderio d'averne la dimostrazione espressa, soggiungendo la se&shy;<lb/>guente. </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXV. &mdash; <emph type="italics"/>Si vas conoidale parabolicum, aqua plenum, <lb/>perforetur in fundo, dico velocitatem supremae superficiei, ad velocitatem <lb/>inferioris eiusdem aquae descendentis, esse ut ordinatim applicatae, vel <lb/>diametri earumdem superficierum, vel sectionum, reciproce sumptarum &rdquo;<emph.end type="italics"/><lb/>(MSS. Gal., T. CXVII, fol. </s>

<s>44). </s></p><p type="main">

<s>Rappresentandoci infatti, nella figura 220, la parabola genitrice del vaso, <lb/>e intendendo per <emph type="italics"/>V<emph.end type="italics"/> significata la velocit&agrave;, abbiamo, per la XXII di questo, <lb/><emph type="italics"/>V<emph.end type="italics"/>.AC:<emph type="italics"/>V<emph.end type="italics"/>.GF=<foreign lang="greek">p</foreign>GF2.AC:<foreign lang="greek">p</foreign>AC2.GF=GF:AC.E perch&egrave; AC &egrave; ma&shy;<lb/><figure id="id.020.01.3478.1.jpg" xlink:href="020/01/3478/1.jpg"/></s></p><p type="caption">

<s>Figura 220.<lb/>giore di GF, dunque anche la velocit&agrave; di GF sar&agrave; maggiore <lb/>della velocit&agrave; di AC, e cos&igrave; sar&agrave; sempre di ciascuna sezione <lb/>inferiore, rispetto alla superiore. </s></p><p type="main">

<s>La curiosit&agrave;, che si disse aver avuto intenzione il Tor&shy;<lb/>ricelli di destar nei Lettori, si modulava in questa domanda: <lb/>se non &egrave; il conoide parabolico, che equabilmente si vuota, <lb/>quale dunque altra forma di vaso &egrave; quella, che fa l'effetto? <lb/></s>

<s>&Egrave; naturale che, nel numero di cos&igrave; fatti curiosi, fosse principalmente il Vi&shy;<lb/>viani, il quale dette, come vedremo, al quesito la pi&ugrave; ampia risposta, che <lb/>si potesse desiderare. </s>

<s>Ma intanto egli non vuol divagare la speculazione <lb/>dal propostogli esempio del conoide, a cui mette a riscontro il cono, e fin&shy;<lb/>gendosi vasi di questa forma pieni di acqua, che si versa per foro in <lb/>fondo, gli viene felicemente in pensiero di rappresentarsi la successione e <lb/>la quantit&agrave; degli abbassamenti, per via di una serie ordinata di linee termi&shy;<lb/>nate a una curva, la quale s'incominci&ograve; a chiamare per lui <emph type="italics"/>Scala delle ve&shy;<lb/>locit&agrave;.<emph.end type="italics"/></s></p><p type="main">

<s>PROPOSITIO XXVI. &mdash; <emph type="italics"/>La scala delle velocit&agrave;, per la quale scendono <lb/>i livelli dell'acqua, nel votarsi che ella fa per foro in fondo a un vaso, <lb/>in figura di conoide parabolico, &egrave; nelle ordinatamente applicate a un'iper&shy;<lb/>bola del secondo grado. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>Il Grandi, nel corollario III alla XXII del suo trattato <emph type="italics"/>Del movimento delle <lb/>acque<emph.end type="italics"/> (Raccolta di Autori cit., T. III, pag. </s>

<s>90) fu primo a pubblicare per <lb/>sua la nuova proposta, da lui stesso senza dubbio veduta in questi mano&shy;<lb/>scritti, che, per esaminarli e ricavarne il meglio, furono a lui consegnati dal <lb/>Panzanini. </s>

<s>La dimostrazione, com'era da aspettarsi, comparve in pubblico <lb/>ordinata e pi&ugrave; facile che nell'originale, specialmente in quel primo, prepa&shy;<lb/>rato per servire ad ampliare il Torricelli, e che di lungo tempo precedette <lb/>all'altro, in cui si distendeva la medesima proposizione, per inserirla fra le <lb/>altre nel generale trattato delle Clessidre. </s>

<s>Vedremo quivi l'Autore procedere <lb/>con mano pi&ugrave; sicura, ma la prima rivelazione della nuova verit&agrave; matema&shy;<lb/>tica gli result&ograve; da un calcolo, alquanto laborioso, che a volerlo riferire ana&shy;<lb/>litieamente, sopra la rappresentazione della figura 221, e facendo uso de'so&shy;<lb/>liti simboli, procedeva in questa maniera. </s></p><pb xlink:href="020/01/3479.jpg" pagenum="440"/><p type="main">

<s>Se DA, EB segnano due livelli dell'acqua, dentro il vaso conoideo descritto <lb/>dalla semiparabola DCA, abbiamo, per la XXII di questo, <emph type="italics"/>V<emph.end type="italics"/>.DA:<emph type="italics"/>V<emph.end type="italics"/>.EB= <lb/>EB2.&radic;DC:DA2.&radic;CE, e per la similitudine dei triangoli, e per le propriet&agrave; <lb/><figure id="id.020.01.3479.1.jpg" xlink:href="020/01/3479/1.jpg"/></s></p><p type="caption">

<s>Figura 221.<lb/>della parabola, EH:AD=CE:CD=EB2:AD2, <lb/>onde EH:1=EB2:AD, ossia EH:EB=EB: <lb/>EH. </s>

<s>La parabola stessa poi d&agrave; (*) EB2:DA2= <lb/>CE:CD=EH:EG; dunque <emph type="italics"/>V<emph.end type="italics"/>.DA:<emph type="italics"/>V<emph.end type="italics"/>.EB= <lb/>EH.EB:EG.EH=EB:EG.E perch&egrave;, essendo <lb/>DA uguale ad EG, abbiamo, per la segnata con <lb/>asterisco, EG2=(EB2.EG)/EH, d'onde EB:EG= <lb/>FG:(EB.EG)/HE; presa EO, quarta proporzionale <lb/>dopo EH, EB, EG, s'otterr&agrave; la nuova espressione <emph type="italics"/>V<emph.end type="italics"/>.DA:<emph type="italics"/>V<emph.end type="italics"/>.EB=EG:EO. <lb/>Ora, avendosi, per la medesima sopra segnata, CE:CD=EH:EG= <lb/>EG2:EG3/EH, e osservando che EG3/EH=EO2, ne conseguir&agrave; finalmente CE:CD= <lb/>EG2:EO2=DA2:EO2. </s>

<s>&ldquo; Quare (dal lungo giro di questo calcolo ne con&shy;<lb/>cludeva il Viviani) scala ordinatarum ad DC, repraesentantium velocitates su&shy;<lb/>premarum velocitatum, dum vas conoidale parabolicum exinanitur; est ad <lb/>curvam lineam PAO, fortasse infinitam: infinitam profecto, cum sit hyper&shy;<lb/>bola secunda, nempe in qua quadrata applicatarum DA, EO, sunt reciproce <lb/>ut CE, CD &rdquo; (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>30). </s></p><p type="main">

<s>Si supponga che, rivolgendosi intorno all'asse DC della parabola il ret&shy;<lb/>tangolo IC, generi un vaso cilindrico. </s>

<s>In questo le velocit&agrave; del supremo li&shy;<lb/>vello si sa, per le precedenti dimostrazioni, che scemano come le applicate <lb/>alla parabola da D in C, mentre, nel conoide parabolico, crescono secondo <lb/>le medesime applicate, che per&ograve; debbon prendersi in ordine inverso, cio&egrave; da <lb/>C in D. </s>

<s>La quale osservazione d&agrave; luogo al Viviani di soggiungere il seguente </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollarium I.<emph.end type="italics"/> &mdash; In vase cylindrico, vel prismatico IC, et in conoide <lb/>parabolico ICA, velocitates EF, ID; ID, EH augentur in continua eademque <lb/>ratione, cum inter se rationem habeant EH ad ID. </s>

<s>Hinc schala velocitatum, <lb/>etiam in vase cylindrico, est in lineis ordinatim ductis ad hyperbola quadra&shy;<lb/>tica PAO, cuius asymptoti sint DC, CM &rdquo; (ibid., fol. </s>

<s>44). </s></p><p type="main">

<s>Si supponga inoltre essere il triangolo ICD, nella medesima figura 221, <lb/>il lato di un prisma vuoto, con la base orizontalmente collocata in alto, e <lb/>forato in qualche punto del suo spigolo inferiore, d'onde versando l'acqua <lb/>&egrave; certo che si abbasser&agrave; in modo (dice ancora il Grandi nel Corollario IV <lb/>dopo la citata proposizione del <emph type="italics"/>Movimento delle acque<emph.end type="italics"/>) analogo al conoide <lb/>parabolico. </s>

<s>Avendo infatti tutte le sezioni rettangolari del detto prisma la <lb/>medesima lunghezza, staranno come le basi ID, PR, ossia come le ascisse <lb/>DC, RC, o i quadrati delle ordinate DI, RQ, o finalmente come le sezioni <lb/>circolari del conoide. </s>

<s>Di qui ne concludeva il Viviani l'altro corollario, che <lb/>cio&egrave; medesima &egrave; la scala delle velocit&agrave;, per ambedue le forme dei vasi. </s></p><pb xlink:href="020/01/3480.jpg" pagenum="441"/><p type="main">

<s><emph type="italics"/>&ldquo; Corollarium II.<emph.end type="italics"/> &mdash; In prismate basis triangularis ICD ordinatae DA, <lb/>EO exhibent velocitates superficierum supremarum ID, PR, dum vas esina&shy;<lb/>nitur &rdquo; (ibid., fol. </s>

<s>116). </s></p><p type="main">

<s>Lieto di cos&igrave; fatti progressi il Viviani sent&igrave; nascersi la curiosit&agrave; di ritro&shy;<lb/>vare la scala, per la quale scendono dentro il cono i livelli dell'acqua, che <lb/>si versa per la troncata punta rivolta in basso. </s>

<s>Al Grandi, che aveva tro&shy;<lb/>vato in questi manoscritti essere la detta scala nelle ordinatamente applicate <lb/>a una iperbola cubica del secondo grado, fu facile cosa confermarne la ve&shy;<lb/>rit&agrave;, concludendola immediatamente dai principii idrodinamici gi&agrave; dimostrati. </s>

<s><lb/>Se infatti &egrave; ABC, nella figura 222, il triangolo genitore del vaso, dentro il <lb/>quale siano le velocit&agrave; dei livelli in AC, DE ordinatamente rappresentate <lb/>dalle linee AC, DL; abbiamo, per la XXII di questo, <lb/>AC:DL=DE2.&radic;AB:AC2.&radic;BD. </s>

<s><lb/>E perch&egrave;, per la similitudine de'triangoli, DE2:AC2=BD2:AB2, sar&agrave; <lb/>AC:DL=BD2.&radic;AB:AB2.&radic;BD. </s>

<s>E quadrando, <lb/>AC2:DL2=BD4.AB:AB4.BD=BD3:AB3, <lb/>ond'&egrave; veramente, come il Grandi stesso concludeva, nel corollario V della <lb/>citata proposizione XXII del suo trattato del Movimento delle acque, la scala <lb/><figure id="id.020.01.3480.1.jpg" xlink:href="020/01/3480/1.jpg"/></s></p><p type="caption">

<s>Figura 222.<lb/>delle velocit&agrave; del liquido, fluente <lb/>per l'apice di un vaso conico, una <lb/>iperbola cubica del secondo gra&shy;<lb/>do. (Raccolta d'Autori cit., T. III, <lb/>pag. </s>

<s>91). </s></p><p type="main">

<s>Il Viviani per&ograve;, che non sa&shy;<lb/>peva ancora sotto quale aspetto gli <lb/>si presenterebbe la verit&agrave;, rimasta <lb/>agli occhi dei Matematici tuttavia <lb/>nascosta; non ha la mano cos&igrave; <lb/>franca e spedita, nello svilupparle <lb/>il geloso velo dalla faccia divina. </s>

<s><lb/>Ma riconosciuto appena il mistero, <lb/>quasi a modo di epigrafe solen&shy;<lb/>nemente commemorativa del fatto, <lb/>scrive in linea, che seconda la concavit&agrave; della disegnata curva PCL, <emph type="italics"/>Hyper&shy;<lb/>bola, in qua quadrata ordinatarum sunt ut cubi abscissarum reciproce, <lb/>et punctum B est omnium centrum, asymptoti vero BA, BM<emph.end type="italics"/> (MSS. Gal. </s>

<s><lb/>Disc., T. CXVII, fol. </s>

<s>9). Il calcolo, che si concludeva in questa iscrizione, &egrave; <lb/>al solito avvolto come i passi di chi &egrave; incerto dove sar&agrave; per riuscire. </s>

<s>Tali <lb/>poi, quali noi le riferiamo in modo analitico, sono del detto calcolo le tracce, <lb/>rimasteci nel manoscritto, il quale comincia dal comandare che, dopo le DE, <lb/>DF, DG, sian prese le tre continue proporzionali DH, DI, DL. </s></p><p type="main">

<s>&Egrave; per la XXII di questo, <emph type="italics"/>V<emph.end type="italics"/>,AC:<emph type="italics"/>V<emph.end type="italics"/>.DE=DG.DE2:DF.DG2, e <pb xlink:href="020/01/3481.jpg" pagenum="442"/>per costruzione DE:DF=DF:DG=DG:DH=DH:DI=DI:DL, fra <lb/>la serie delle quali equazioni si noti particolarmente la DE:DG=DG:DI, <lb/>d'onde DG2/DE=DI. Ora, per l'identica DE2:DG2=DE2/DE:DG2/DE, sar&agrave; <lb/>DE2:DG2=DE:DI, e perci&ograve; <emph type="italics"/>V<emph.end type="italics"/> AC:<emph type="italics"/>V<emph.end type="italics"/>.DE=DG.DE:DF.DI.E per&shy;<lb/>ch&egrave;, per la stessa imperata costruzione, DE:DI=DF:DL; dunque in ul&shy;<lb/>timo <emph type="italics"/>V<emph.end type="italics"/>.AC:<emph type="italics"/>V<emph.end type="italics"/>.DE=DG.DF=DF.DL=DG:DL=AC:DL. </s>

<s>Al <lb/>qual punto ridottosi il calcolo, non rimane a far altro che a invocare il <lb/>Lemma matematico, premesso alla VII di questo, per concluder l'intento <lb/>cos&igrave;, come lo conclude propriamente il Viviani con queste parole: &ldquo; Ma per&shy;<lb/>ch&egrave; le quattro DG, DH, DI, DL son continue proporzionali, il quadrato DG, <lb/>ovvero AC, al DL, star&agrave; come il cubo DG al cubo DI, per il mio Lemma, <lb/>o come il cubo DE al cubo DG, o come il cubo BD al BA. </s>

<s>Adunque i punti <lb/><figure id="id.020.01.3481.1.jpg" xlink:href="020/01/3481/1.jpg"/></s></p><p type="caption">

<s>Figura 223.<lb/>C, L sono all'iperbola, nella quale i quadrati delle or&shy;<lb/>dinate son fra loro in ragion reciproca de'cubi delle <lb/>ascisse &rdquo; (ivi). </s></p><p type="main">

<s>Sembrava perci&ograve; che fosse per formularsi la pro&shy;<lb/>posizione: <emph type="italics"/>Scala velocitatis in cono, dum esinanitur, <lb/>est hyperbola, in qua quadrata ordinatarum sunt ut <lb/>cubi abscissarum reciproce,<emph.end type="italics"/> ma pure piacque al Vi&shy;<lb/>viani di metterla piuttosto sotto quest'altra forma: </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXVII. &mdash; <emph type="italics"/>In cono ABC<emph.end type="italics"/> (fig. </s>

<s>223) <lb/><emph type="italics"/>velocitas superioris superficiei AB aquae descendentis, <lb/>et per forum C in fundo exeuntis, ad velocitatem <lb/>ciusdem superficiei in DE, est ut FC, media inter <lb/>altitudines HC, GC, ad tertiam proportionalem CI <lb/>continuam post CG, CH &rdquo;<emph.end type="italics"/> (ivi, fol. </s>

<s>44). </s></p><p type="main">

<s>Soggiungesi immediatamente a queste parole del manoscritto: <emph type="italics"/>Hine <lb/>scula velocitatum in cono.<emph.end type="italics"/> E che veramente resulti dalla nuova forma pro&shy;<lb/>posta la scala delle velocit&agrave;, dimostrata dianzi dallo stesso Autore per altra <lb/>via, &egrave; facile persuadersene cos&igrave; ragionando: Secondo la proposta, AB:DE= <lb/>FC:CI. </s>

<s>Ma FC=VHC.CG, e, dall'esser per costruzione CG:CH= <lb/>HC:CI, ne viene CI=CH2/CG; dunque AB:DE=VHC.CG:CH2/CG= <lb/>&radic;HC.CG3:CH2=&radic;CG3:CH2/&radic;CH=&radic;CG3:&radic;CH3, e perci&ograve; AB2:DE2= <lb/>CG3:CH3, che &egrave; l'equazione alla seconda iperbola cubica, nelle ordinate alla <lb/>quale era stata imposta la scala delle velocit&agrave; del cono, mentre, essendo <lb/>stato ripieno d'acqua, a poco a poco si vuota. </s></p><p type="main">

<s>Il Viviani prefer&igrave; questa seconda forma di proposizione alla prima, per&shy;<lb/>ch<gap/> gli serviva meglio all'intenzion di paragonare insieme le velocit&agrave; de'li&shy;<lb/>velli supremi, nel votarsi il cono e il conoide parabolico della medesima base <lb/>e della medesima altezza, ricavandone un corollario notabile, qual'&egrave; che il <lb/>cono, bench&egrave; vaso minore e contenuto, s'evacua assai pi&ugrave; presto del conoide, <pb xlink:href="020/01/3482.jpg" pagenum="443"/>vaso maggiore e contenente. </s>

<s>Nel conoide ADCEB infatti la velocit&agrave; del li&shy;<lb/>vello DE, a quella del livello AB, sta, per le cose dimostrate, come HC a <lb/>CF, e nel cono la velocit&agrave; del livello medesimo AB, alla velocit&agrave; del livello <lb/>D&prime;E&prime;, sta come CF a CI. Cos&igrave;, dal moltiplicare insieme queste due propor&shy;<lb/>zioni, ne resulta, riducendole, che la velocit&agrave; della sezione DE del conoide, <lb/>alla velocit&agrave; della sezione D&prime;E&prime; del cono, sta come CH a CI, ond'&egrave; minore in <lb/>quello che in questo, come dice, nelle proprie parole dell'Autore, il seguente </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Corollarium.<emph.end type="italics"/> &mdash; Si circa ABC (nella medesima figura 223) describa&shy;<lb/>tur conois parabolicus ADCEB, patet superficiem superiorem aquae, descen&shy;<lb/>dentis in utroque vase, velocius descendere in cono, quam in conoide, cum, <lb/>per praecedentem, in conoide velocitas DE, ad velocitatem AB, sit ut HC <lb/>ad CF, et velocitas AB in cono, per praesentem, ad velocitatem D&prime;E&prime; in cono, <lb/>est ut CF ad CI. </s>

<s>Ergo velocitas DE in conoide, ad velocitatem D&prime;E&prime; in cono, est <lb/>ut CH ad CI. </s>

<s>Ergo maior in cono, quam in conoide. </s>

<s>Si igitur superficies su&shy;<lb/>perior aquae velocius descendit in cono, quam in conoide eiusdem altitudi&shy;<lb/>nis et basis, breviori etiam tempore vacuus remanebit conus, quam conois: <lb/>hoc est vas minus et contentum, quam maius ac continens &rdquo; (ivi, fol. </s>

<s>45). </s></p><p type="main">

<s>Cos&igrave; veniva il Viviani a svolgere, intorno al conoide parabolico che si <lb/>vuota, il concetto del Torricelli. </s>

<s>Ma ai Lettori, che avevano per le mani il <lb/>trattato <emph type="italics"/>De motu aquarum,<emph.end type="italics"/> anche quando fossero state notificate queste <lb/>belle illustrazioni, rimaneva intera la curiosit&agrave; d'aver quella propria forma <lb/>di vaso, in cui i livelli del liquido nel votarsi scendono per uguali parti del&shy;<lb/>l'asse, in tempi uguali. </s>

<s>Fra cotesti curiosi ha la storia principalmente da <lb/>commemorare il Mersenno, che, avendo assistito in Roma, ne'familiari col&shy;<lb/>loqui col Magiotti e col Ricci, al concepimento dell'Idrodinamica torricel&shy;<lb/>liana; n'ebbe poi in Firenze, per le mani dell'Autore stesso, pubblicamente <lb/>esposto il parto in quel libro, dove si trattava delle acque salienti. </s>

<s>Quivi leg&shy;<lb/>gendo il Mersenno per viaggio, nel tornarsene a Roma, avrebbe voluto vo&shy;<lb/>lentieri dare indietro, per sentire che cosa l'Autore stesso gli risponderebbe, <lb/>a leggergli ci&ograve; che aveva scritto a pagine 202 e 203 del suo libro, e a do&shy;<lb/>mandargli di quale altra figura si dovesse dunque costruire il vaso, che, per <lb/>la novit&agrave; dell'invenzione di misurare il tempo, si sarebbe tanto desiderato. </s>

<s><lb/>Ma costretto a proseguire, appena giunto al termine del suo viaggio, se ne <lb/>and&ograve; tutto premuroso in cerca del Ricci, il quale ingenuamente confess&ograve; rima&shy;<lb/>nersi tuttavia il problema un desiderio anche per lui, promettendo nonostante <lb/>che avrebbe pregato il Torricelli a dare sodisfazione di ci&ograve;, almeno agli amici, <lb/>come infatti mantenne, cos&igrave; scrivendo, nella prima parte della lettera, che <lb/>ha la data del 31 Dicembre 1644. &ldquo; Il Mersenno mi ha pregato che volessi <lb/>scrivere a V. S. qual debba esser quel vaso, che, riempito d'acqua e poi <lb/>votato per di sotto, in esso scenda la superficie dell'acqua contenutavi per <lb/>parti uguali dell'asse, in tempi uguali, supposto l'asse perpendicolare al&shy;<lb/>l'orizonte. </s>

<s>E cos&igrave; &egrave; indotto a far la presente richiesta, per aver letto nel <lb/>libro di V. S. che il vaso parabolico mostra a prima vista di prestar questo, <lb/>ma in effetto poi cos&igrave; non succede &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>69). </s></p><pb xlink:href="020/01/3483.jpg" pagenum="444"/><p type="main">

<s>Fu risposto pochi giorni dopo dover essere il vaso desiderato quello, che <lb/>si descriverebbe da una semiparabola biquadratica, rivolgendosi intorno al&shy;<lb/>l'asse. </s>

<s>La dimostrazione di ci&ograve; correva tuttayia per le poste da Firenze a <lb/>Roma, quando il Mersenno, impaziente dell'indugio di soli dieci giorni da <lb/>che aveva fatta la domanda, cos&igrave; direttamente scriveva allo stesso Torricelli, <lb/>sollecitandone la risposta: &ldquo; Credo dominum Ricci ad te scripsisse ut for&shy;<lb/>mam vasis ad nos mittas, quod aquam suam, per idem foramen, in tempo&shy;<lb/>ribus aequalibus redderet, cum conoidale parabolicum, pag. </s>

<s>202 minime tibi <lb/>satisfecerit. </s>

<s>Itaque vas ad id proprium expectamus, quod, ubi vino falerno <lb/>oppletum fuerit, tuae saluti, paribus intervallis et temporibus, evacuemus &rdquo; <lb/>(ivi, T. XLI, fol. </s>

<s>15). </s></p><p type="main">

<s>La lettera, nella quale si mandava scritta la forma del vaso, aveva avuto <lb/>recapito, e il Ricci l'aveva gi&agrave; partecipata, ma rimaneva a sapersi il modo <lb/>di scavar la clessidra, che, prima d'esser forata in fondo e ripiena d'acqua, <lb/>doveva, secondo la promessa, servir da calice pieno di generoso falerno, per <lb/>farne un brindisi con gli amici alla salute del Torricelli. </s>

<s>E il Torricelli, ap&shy;<lb/>pena richiestone, mandava descritto il modo di segnar per punti la parabola <lb/>biquadratica, la quale, usata per sagoma, avrebbe dato in mano all'artefice <lb/>il tornio esatto del calice e della clessidra. </s>

<s>Ma del brindisi non se ne di&shy;<lb/>scorse pi&ugrave;: il fervore di quella prima curiosit&agrave; s'attut&igrave; a un tratto, come a <lb/>una pentola che bolla, sollevandone il testo. </s>

<s>Il Torricelli stesso n'ebbe a re&shy;<lb/>stare con maraviglia, anzi, a parer nostro, mortificato, cosicch&egrave;, vedendo la <lb/>sua invenzione, contro ci&ograve; che si sarebbe aspettato, cos&igrave; indegnamente di&shy;<lb/>menticata, disse un giorno a s&egrave; stesso: &mdash; O vediamo un po'se, dopo tanto <lb/>tempo, mi ricordo di quel che scrissi a quel giovanotto del Ricci &mdash; e parve <lb/>se ne ricordasse molto bene, perch&egrave; seguit&ograve; a scrivere in fretta, sopra un <lb/>prezioso foglio che c'&egrave; rimasto, la dimostrazione della figura del vaso, che <lb/>equabilmente si vuota, insieme col modo di descrivere, per fabbricarla, la <lb/>parabola del quarto grado. </s></p><p type="main">

<s>Rimasto per&ograve; quel foglio, insieme con la mano che l'aveva scritto, lun&shy;<lb/>gamente sepolto, nessuno seppe nulla della nuova proposizione, che, per so&shy;<lb/>disfare la curiosit&agrave; de'Lettori, aveya preparato l'Autore, da aggiungersi al <lb/>libro <emph type="italics"/>De motu aquarum,<emph.end type="italics"/> il qual libro, lasciato nella speculazione del conoide <lb/>parabolico cos&igrave; imperfetto, fece credere a molti che il Torricelli si fosse pro&shy;<lb/>vato bene a investigar la figura della clessidra, ma che non fosse per la diffi&shy;<lb/>colt&agrave; riuscito a sciogliere il problema. </s></p><p type="main">

<s>&Egrave; fra costoro notabile il Mariotte, il quale, dop'avere nel III discorso <lb/>della III parte del suo trattato <emph type="italics"/>Du mouvement des eaux,<emph.end type="italics"/> spiegata la XIII pro&shy;<lb/>posizione, nella quale si dimostra dal Nostro che le emissioni dei vasi cilin&shy;<lb/>drici stanno come la serie dei numeri impari ab unitate; soggiunge: &ldquo; Il est <lb/>bon de resoudre icy un probleme assez curieux, que Torricelly n'a pas en&shy;<lb/>trepris de resoudre, quoy qu'il l'ait propos&eacute; &rdquo; (A Paris 1686, pag. </s>

<s>292): no&shy;<lb/>tabile si disse, perch&egrave;, fra le tante maniere di dimostrare che la figura del <lb/>vaso, dentro cui l'acqua scende con moto eguale, &egrave; la rotonda, generata dal <pb xlink:href="020/01/3484.jpg" pagenum="445"/>rivolgimento di una semiparabola quadrato-quadratica; se ne sceglie per l'ap&shy;<lb/>punto una somigliantissima a quella, che ci &egrave; rimasta nel manoscritto tor&shy;<lb/>ricelliano. </s></p><p type="main">

<s>Cos&igrave; venne a ingerirsi fra i matematici l'opinione che fosse il Mariotte <lb/>primo ritrovatore di questa bella novit&agrave;, la quale, pure ignorandosene ancora <lb/>la storia, ebbe nel mondo il nome di teorema celebre. </s>

<s>Basti per tutti citare <lb/>il Varignon, autore della <emph type="italics"/>Maniere geometrique et generale de faire des <lb/>clapsydres,<emph.end type="italics"/> che, a proposito della clessidra <emph type="italics"/>de descente uniforme,<emph.end type="italics"/> scriveva: <lb/>la quelle semble avoir &eacute;t&eacute; cherch&eacute;e par Torricelli, et que M. </s>

<s>Mariotte a trou&shy;<lb/>v&eacute;e &rdquo; (Fra le Memorie dell'Accademia di Parigi per l'anno 1699, Paris 1627, <lb/>pag. </s>

<s>61). </s></p><p type="main">

<s>N&egrave; si creda che cos&igrave; giudicassero solamente gli stranieri: era tale l'opi&shy;<lb/>nione anche dei Nostri, i quali dissero, per pudore, non che al Torricelli <lb/>non era riuscito, ma che aveva voluto far cos&igrave;, per provocare i lettori col <lb/>silenzio. </s>

<s>In tal modo, fra gli altri, la pensava il Viviani, uno de'pochi i quali <lb/>accettaron la provoca, e che poi si compiacque d'esserne rimasto vincitore, <lb/>proponendo per segno di ci&ograve;, come vedremo, la clessidra parabolica in forma <lb/>di cuna. </s>

<s>Ci&ograve; gli occorse verso il 1650, mentre studiava il libro <emph type="italics"/>De motu <lb/>aquarum,<emph.end type="italics"/> e mentre che, morto l'Autore di questo, i manoscritti di lui si <lb/>conservavano gelosamente dal Serenai. </s>

<s>Quando poi questi stessi manoscritti <lb/>furono consegnati, perch&egrave; gli mettesse in ordine e gli pubblicasse, al Viviani, <lb/>egli ebbe a leggervi, maravigliato che non se ne fosse diffusa, almeno fra i <lb/>discepoli di tanto Autore, la desiderata notizia, anche il teorema della clas&shy;<lb/>sidra, e lo ricopi&ograve; la prima volta per suo proprio memoriale, e torn&ograve; a ri&shy;<lb/>copiarlo anche la seconda, per inserirlo fra le altre proposizioni, delle quali <lb/>intendeva di compilare il trattatello <emph type="italics"/>De motu ac momentis.<emph.end type="italics"/> Ma rimasto senza <lb/>effetto il proposito di pubblicar, cos&igrave; questa come e le altre opere postume <lb/>del Torricelli, il prezioso documento, brevemente resuscitato, ritorn&ograve; a gia&shy;<lb/>cersi dentro l'arche dorate del palazzo Pitti, dov'ebbe pi&ugrave; nobilmente custo&shy;<lb/>dito il sepolcro. </s>

<s>Venne quivi nonostante a visitarlo il Fabbroni, con queste <lb/>parole, scritte in quel suo classico latino, commemorandolo ai vivi: &ldquo; Quod <lb/>ad hydraulica Toricelli scripta pertinet, commemorandum videtur problema, <lb/>quod nemini tum notum, propositumque a Michaele Angelo Riccio, ipse fa&shy;<lb/>cillime solvit. </s>

<s>Quaerebatur enim quaenam esse deberet figura vasis, quod <lb/>aequabili motu exhauriretur &rdquo; (<emph type="italics"/>Vitae Italorum,<emph.end type="italics"/> Vol. </s>

<s>I, Pisis 1778, pag. </s>

<s>369). </s></p><p type="main">

<s>Ma ora &egrave; tempo di coronar l'opera ampliatrice del Viviani con quella <lb/>proposizione, che l'Autore stesso <emph type="italics"/>De motu aquarum<emph.end type="italics"/> ci lasci&ograve; scritta di sua <lb/>propria mano, forse con la speranza che verrebbe un giorno qualcuno a ri&shy;<lb/>vendicargli, dall'invidia della morte e dalla ingratitudine degli uomini, l'an&shy;<lb/>tica propriet&agrave;, e il primato dell'invenzione. </s></p><p type="main">

<s>&ldquo; Ingeniosissimus iuvenis M. A. </s>

<s>Riccius certiorem fecit me de deside&shy;<lb/>derio suo, circa illud vas quod aequabili motu exhauritur. </s>

<s>Dicam igitur, si <lb/>per memoriam licebit. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; PROPOSITIO XXVIII. &mdash; <emph type="italics"/>Esto conoides parabolae quadratoquadra-<emph.end type="italics"/><pb xlink:href="020/01/3485.jpg" pagenum="446"/><emph type="italics"/>ticae ABC<emph.end type="italics"/> (fig. </s>

<s>224) <emph type="italics"/>perforatum in fundo B. </s>

<s>Dico illud ea lege exhauriri, <lb/>ut motus supremae superficiei humoris contenti AC aequabilis sit. </s>

<s>&rdquo;<emph.end type="italics"/></s></p><p type="main">

<s>&ldquo; Sumatur enim quaelibet alia vasis sectio DI, et super basi AC con&shy;<lb/>cipiatur cylindrus AE. </s>

<s>Esto BO media proportionalis inter GB, BH, et quo&shy;<lb/><figure id="id.020.01.3485.1.jpg" xlink:href="020/01/3485/1.jpg"/></s></p><p type="caption">

<s>Figura 224.<lb/>niam est quadratoquadratum AG, ad quadratoquadratum <lb/>DH, ut GB ad BH erit quadratum AG, ad quadratum <lb/>DH, ut GB ad BO. </s>

<s>Jam velocitas superficiei descenden&shy;<lb/>tis, quando est AG, ad velocitatem superficiei, quando <lb/>erit FH in cylindro, est, per demonstrata, ut CB ad BO, <lb/>sive ut quadratum AG, ad quadratum DH. </s>

<s>Velocitas vero <lb/>sectionis FH, ad HD, est ut quadratum HD ad HF, sive <lb/>ut quadratum HD, ad quadratum AG. </s>

<s>Ergo ex aequeo velocitas sectionis AG, <lb/>ad velocitatem sectionis DH, erit ut quadratum AG ad quadratum AG, nempe <lb/>aequalis. </s>

<s>&rdquo; </s></p><p type="main">

<s><emph type="italics"/>&ldquo; Scholium.<emph.end type="italics"/> &mdash; Si quis desideret descriptionem eiusmodi lineae, nempe <lb/>parabolae quadratoquadraticae, talem excogitabamus: Ponatur parabola qua&shy;<lb/><figure id="id.020.01.3485.2.jpg" xlink:href="020/01/3485/2.jpg"/></s></p><p type="caption">

<s>Figura 225.<lb/>dratica vulgaris ABC (fig. </s>

<s>225), cuius axis AD, <lb/>una applicata BD. </s>

<s>Secetur AE aequalis BD, et <lb/>item BF aequalis CE, eritque punctum F in <lb/>parabola quaesita, et sic de reliquis punctis. </s>

<s>&rdquo; </s></p><p type="main">

<s>&ldquo; Quod verum sit hoc, sumatur AH latus <lb/>rectum parabolae quadraticae, et erunt aequa&shy;<lb/>les GH, AH. </s>

<s>Tum quadratum GH ad quadra&shy;<lb/>tum BD, sive quadratum AH ad AE, erit ut <lb/>recta HA ad AD. </s>

<s>Ergo continuae sunt AH, AE, <lb/>AD. Propterea, si quadratum GH ad CE, vel <lb/>FD, est ut recta HA ad AE, erit quadratoqua&shy;<lb/>dratum GH, ad quadratoquadratum FD, ut AH ad AD. </s>

<s>Deinde ex aequo pro&shy;<lb/>batur quadratoquadratum FD ad IM esse ut recta DA ad AM. &rdquo; (MSS. Gal. </s>

<s><lb/>Disc., T. XXVI a tergo del fol. </s>

<s>167). </s></p><p type="main">

<s><emph type="center"/>II.<emph.end type="center"/></s></p><p type="main">

<s>In quel medesimo anno 1644, in cui, dalla tipografia de'Landi, usciva <lb/>in Firenze, insieme con l'altre opere geometriche del Torricelli, il trattato <lb/><emph type="italics"/>De motu gravium,<emph.end type="italics"/> con l'appendice <emph type="italics"/>De motu aquarum<emph.end type="italics"/> di sole XIV propo&shy;<lb/>sizioni, fecondissime per&ograve; di tante altre ad esempio delle aggiuntevi dal Vi&shy;<lb/>viani; il Mersenno pubblicava in Parigi, a spese del Bertier, i suoi <emph type="italics"/>Cogitata <lb/>physico-matematica,<emph.end type="italics"/> fra'quali principalmente si comprendeva l'<emph type="italics"/>Hydraulica.<emph.end type="italics"/><lb/>Come il titolo era nuovo, cos&igrave; nuovo efa in quel paese il soggetto, che si <lb/>svolgeva in sostanza da quello stesso pensiero, scritto dal Torricelli, per let&shy;<lb/>tera del 25 Ottobre 1642, al Cavalieri, e che s'incardinava in quelle mede-<pb xlink:href="020/01/3486.jpg" pagenum="447"/>sime esperienze fatte in Roma, per confermare la supposta verit&agrave;, da Raf&shy;<lb/>faello Magiotti. </s></p><p type="main">

<s>L'opera del Francese, standosene ai numeri, appariva contemporanea <lb/>con quella del Nostro, ma ne facevano argomentare la pretension di un di&shy;<lb/>ritto di precedenza certe espressioni, come sarebbe quella, in cui, dop'aver <lb/>commemorato Galileo insieme co'pi&ugrave; illustri Matematici francesi, taccio, si <lb/>soggiunge, la sottile Geometria nuova del Cavalieri, &ldquo; praeclarosque tracta&shy;<lb/>tus, quos ab acutissimo Tauricello, Galilaei successore, brevi speramus &rdquo; <lb/>(Hydraulica cit., pag. </s>

<s>193). </s></p><p type="main">

<s>Cos&igrave; essendo, non fa maraviglia se alcuni dotti, specialmente stranieri, <lb/>leggendo in questo libro d'Idraulica per la prima volta annunziato che le <lb/>altezze dell'acqua fiuente dai tubi stanno in ragione duplicata dei tempi; <lb/>credettero che del nuovo teorema fosse autore il Mersenno. </s>

<s>Fra i seguaci di <lb/>cos&igrave; fatta opinione &egrave; principalissimo il Boyle, che in una sua operetta in&shy;<lb/>torno all'utilit&agrave; della Filosofia sperimentale, annoverando le pi&ugrave; insigni sco&shy;<lb/>perte fatte dai varii cultori di essa, non lascia, come degnissimo di esser <lb/>notato, quel &ldquo; theorema hydrostaticum, cuius inventionem Mersenno debe&shy;<lb/>mus, a scriptore quodam recentiori ita propositum: Velocitates motus aquae <lb/>descendentis, et effluentis per tubos aequalium foraminum sed inaequalium <lb/>altitudinum, habent subduplicatam rationem &rdquo; (Opera omnia, T. II, Vene&shy;<lb/>tiis 1607, pag. </s>

<s>850). E pi&ugrave; sotto, accennando ai getti parabolici dell'acqua, <lb/>e come dalla proporzione che passa tra l'altezza del liquido e il diametro <lb/>del foro sia possibile computar giustamente la velocit&agrave; e la quantit&agrave; stessa <lb/>del flusso; dice lo stesso Boyle essere a tutti venuta a mancare una si bella <lb/>notizia, &ldquo; donec Galileius et diligentissimus Mersennus (quibus observatio&shy;<lb/>nes quasdam et nos iunximus) materiam hanc definire conati fluerint &rdquo; (ibid., <lb/>pag. </s>

<s>886). </s></p><p type="main">

<s>Essendo le esercitazioni boileiane, dalle quali abbiamo estratti questi do&shy;<lb/>cumenti, scritte dopo il 1680, par che non fossero fino a quel tempo in In&shy;<lb/>ghilterra penetrate le nuove dottrine idrodinamiche direttamente d'Italia, ma <lb/>di Francia, per il magistero del Mersenno, il quale perci&ograve; verrebbe a riven&shy;<lb/>dicarsi un merito e un'importanza che, a giudicare dai fatti fin qui occor&shy;<lb/>sici, gli fu sempre giustamente negata. </s>

<s>Fra cotesti giudizii il pi&ugrave; antico e il <lb/>pi&ugrave; a proposito &egrave; quello del Magiotti, il quale scriveva cos&igrave; a Galileo da <lb/>Roma, il d&igrave; 25 Aprile 1637, quando gli Elzeviri in Olanda erano proprio in <lb/>sul punto di pubblicare i dialoghi delle due Scienze nuove, in appendice ai <lb/>quali era stabilito di mettere le dimostrazioni <emph type="italics"/>De centro gravitatis;<emph.end type="italics"/> &ldquo; Non <lb/>credo che queste dimostrazioni siano arrivate in Francia con le altre opere, <lb/>perch&egrave; il p. </s>

<s>Mersenno minorita, che ha veduto il libro <emph type="italics"/>De motu,<emph.end type="italics"/> con le altre <lb/>osservazioni, di queste non fa menzione alcuna, eppure &egrave; vero che egli vuole <lb/>scompuzzare ogni cosa. </s>

<s>Questo frate stampa grandi e molti libracci, cercando <lb/>con lo sgradire altrui di acquistarsi reputazione, e forse gli riuscir&agrave; appresso <lb/>della marmaglia. </s>

<s>L'opere, che mi sono state prestate di suo, la maggior <lb/>parte sono in francese, e mi sa male non esserne padrone, ch&egrave; le manderei <pb xlink:href="020/01/3487.jpg" pagenum="448"/>acci&ograve; ella le vedesse, e a suo tempo e luogo l'arrivasse con qualche fru&shy;<lb/>stata &rdquo; (Alb. </s>

<s>X, 205). E in quello stesso giorno scriveva esso Magiotti nella <lb/>medesima sentenza al Michehni, soggiungendo che fra gli emuli, i sindaca&shy;<lb/>tori, anzi i nemicissimi, che Galileo aveva in Fiandra e in Francia, poneva <lb/>tra i primi <emph type="italics"/>l'abate Mersenno minorita<emph.end type="italics"/> (ivi, pag. </s>

<s>206). </s></p><p type="main">

<s>Questi erano per&ograve; giudizi passionati. </s>

<s>L'emulazione, veramente non pro&shy;<lb/>pria d'altri che del Cartesio, era facile attribuirla a tutti i Francesi capita&shy;<lb/>nati da lui, e il Magiotti si veniva a confermare in questo sospetto da qualche <lb/>cosa, intraveduta ne'primi libri mersenniani pubblicati in lingua francese, come <lb/>quella per esempio, che riguarda la linea percorsa da un grave cadente dalla <lb/>cima di una torre, rivolgendosi la Terra intorno al suo proprio asse, bench&egrave; <lb/>poi non facesse, rispetto a ci&ograve;, il Mersenno altro che ripetere quel che aveva <lb/>udito dire al Fermat, e il Fermat veramente non censurasse in odio all'Au&shy;<lb/>tore dei dialoghi de'due Massimi sistemi, ma per solo amore del vero. </s></p><p type="main">

<s>Dell'ingiusta accusa dev'essersi poi ravveduto il Magiotti, quando in <lb/>Roma ebbe a conversare familiarmente col Mersenno, e quando, a svolgere <lb/>d'Idraulica di lui, dop'aver letto in fronte alla pag. </s>

<s>193 il titolo <emph type="italics"/>Magni Ga&shy;<lb/>lilei, et nostrorum geometrarum elogium utile,<emph.end type="italics"/> trov&ograve; nelle due proposizioni <lb/>appresso compendiato, con lucido ordine e con studio a<gap/>oroso, il Discorso <lb/>galileiano delle Galleggianti. </s>

<s>Quanto per&ograve; al giudicare il Frate uno scompuz&shy;<lb/>zatore, i fatti, che si potevano cos&igrave; spesso notare leggendo, assicurarono il Ma&shy;<lb/>giotti che non s'era punto ingannato. </s>

<s>Ci par di vederlo sogghignar sopra il <lb/>libro, tenutosi innanzi aperto alla pag. </s>

<s>137, tutto intento a quel <emph type="italics"/>Monitum<emph.end type="italics"/><lb/>soggiunto alla XXVII proposizione, e le seguenti notizie gioveranno ai nostri <lb/>Lettori, perch&egrave; possano penetrare addentro alle ragioni di quei sogghigni. </s></p><p type="main">

<s>Dalla lettera, in altra occasione da noi citata, scritta dal Torricelli nei <lb/>primi giorni del 1640 al Magiotti, resulta che, fin da quel tempo, era stato <lb/>composto il trattato <emph type="italics"/>De motu proicctorum,<emph.end type="italics"/> al quale argomento si riferiva <lb/>l'altro libretto sul principio della detta lettera commemorato, e in cui di&shy;<lb/>ceva il Torricelli stesso non esister che baie, rispetto all'altro che gli pa&shy;<lb/>reva contenere in s&egrave; qualche cosa di suo gusto. </s>

<s>Cos&igrave; fatte espressioni fecero <lb/>nascere nel Magiotti la curiosit&agrave; di vedere un saggio di quelle proposizioni <lb/>intorno ai proietti, nelle quali s'aspettava che non qualche cosa, ma che tutto <lb/>anzi dovess'esservi di squisitissimo gusto. </s>

<s>E il Torricelli volle compiacere <lb/>l'amico, mandandogli da Fabriano a Roma, fra le altre proposizioni, dimo&shy;<lb/>strata anche quella inserita poi a pag. </s>

<s>183 del libro stampato, e che dice <lb/><figure id="id.020.01.3487.1.jpg" xlink:href="020/01/3487/1.jpg"/></s></p><p type="caption">

<s>Figura 226.<lb/>come, essendo descritta intorno all'asse verticale BA <lb/>(fig. </s>

<s>226) una parabola BDC, tutti i tiri, che col mede&shy;<lb/>simo impeto e con qualunque inclinazione sian fatti da <lb/>A, punto focale, toccano in qualche parte la concavit&agrave; <lb/>della parabola stessa. </s></p><p type="main">

<s>Al Magiotti parve la proposizione bellissima, e ap&shy;<lb/>plicandola ai getti dell'acqua, circoscritti intorno al <lb/>punto A, con varie inclinazioni, da riempir sufficien-<pb xlink:href="020/01/3488.jpg" pagenum="449"/>temente lo spazio angolare BAC; si vide apparire nella viva immaginazione <lb/>lo spettacolo graziosissimo di una fontana, le ripioventi fila della quale si <lb/>componevano insieme in una chioma configurata in conoide parabolico. </s>

<s>Pochi <lb/>giorni dopo correva la voce per Roma che, suggerita da un teorema del Tor&shy;<lb/>ricelli, si sarebbe veduta la nuova Naiade, con s&igrave; gentile geometrico artifi&shy;<lb/>zio chiomata, nei giardini del cardinale Sacchetti, alla corte del quale il Ma&shy;<lb/>giotti apparteneva. </s></p><p type="main">

<s>Quella voce giunse alle orecchie del Mersenno, che si trovava allora col&agrave;, <lb/>e tutto affaccendato com'era in rifondere i teoremi di Galileo, intorno al <lb/>moto de'proietti, pens&ograve; di ornare la sua <emph type="italics"/>Ballistica<emph.end type="italics"/> della bella osservazione <lb/>torricelliana, come di fatti fece nella proposizione XXVIII, dop'averne dato <lb/>un cenno in quel <emph type="italics"/>Monitum,<emph.end type="italics"/> sopra il quale abbiamo dianzi lasciato il Ma&shy;<lb/>giotti a sogghignare cos&igrave; leggendo. </s>

<s>&ldquo; Plurima hic adderem de salientibus, si <lb/>figurae incisae non de<gap/>ssent, quibus lectores subleventur: v. </s>

<s>g. </s>

<s>mediam sa&shy;<lb/>lientem longitudine duplam esse verticalis, altitudine vero subduplam. </s>

<s>Cum <lb/>verticalis est pars quarta parametri, omnes alias salientes, inter verticalem <lb/>et horizontalem interceptas, tangere concavam conoidis parabolici superficiem, <lb/>cuius focus est in medio salientium lumine, quod a clarissimo Toricello iam <lb/>observatum didici &rdquo; (Hydraulica cit.). </s></p><p type="main">

<s>Nella Ballistica, essendo state gi&agrave; le figure incise, torn&ograve; il Mersenno a <lb/>mostrare, con l'aiuto di quelle, come nelle medie salienti, ossia ne'getti in&shy;<lb/>clinati ad angolo semiretto, la parabola sia nell'ampiezza doppia, e nell'al&shy;<lb/>tezza la met&agrave; della verticale, ossia della sublimit&agrave;, non lasciando d'osservar <lb/>la tangenza di tutte le parabole interne, quali AEDC, AFC, nella medesima <lb/>figura 226, con la parabola esterna BDC, e concludendo cos&igrave; il suo discorso: <lb/>&ldquo; Reliqua istius figurae explicatio in Hydraulicorum praefatione videatur, <lb/>donec sublimiora egregii Tauricelli liber docuerit &rdquo; (Paris, 1644, pag. </s>

<s>96). </s></p><p type="main">

<s>Il Magiotti avrebbe voluto che di queste cose fosse lasciato libero il ma&shy;<lb/>gistero a chi s'apparteneva, senza quell'altrui preventiva non richiesta in&shy;<lb/>gerenza, che nel materno suo linguaggio toscano efficacemente esprimeva col <lb/>verbo <emph type="italics"/>scompuzzare.<emph.end type="italics"/> Che se, rispetto alla Ballistica, della quale il Torricelli <lb/>non era poi infine che un promotore di Galileo, quella inopportuna inge&shy;<lb/>renza fratesca fini per eccitar sulle labbra del Magiotti un sogghigno; veniva <lb/>per&ograve; a commovergli l'animo negl'insulti dell'ira, quando si trattava di pre&shy;<lb/>venir l'opera del Torricelli e sua, in una istituzione di tanta novit&agrave; e di <lb/>tanta importanza, qual'era l'ldrodinamica. </s>

<s>E perch&egrave; non si dubiti da nes&shy;<lb/>suno della giusta ragione di questi primi risentimenti, ascoltiamo la storia <lb/>che cerca, esamina e giudica i fatti. </s></p><p type="main">

<s>In un libro, che il Mersenno aveva scritto in latino, e poi pi&ugrave; ampia&shy;<lb/>mente in francese, intorno ai suoni armonici, aveva proposto a risolvere ai <lb/>fisici de'suoi tempi il problema: perch&egrave; mai, a voler portare una corda al <lb/>diapason, in cui va doppiamente veloce, non basta raddoppiare il peso che <lb/>la tende, ma bisogna quadruplicarlo? </s>

<s>Nessuno ancora aveva dato in Francia <lb/>sodisfacente risposta, quando il Mersenno stesso fece il suo primo viaggio in <pb xlink:href="020/01/3489.jpg" pagenum="450"/>Italia, e passato per Firenze si trattenne in Roma, dove torn&ograve; a proporre il <lb/>quesito armonico, in quel tempo che il Magiotti attendeva con ogni diligenza <lb/>a fare e a ripetere quelle esperienze idrodinamiche, raccomandategli, per <lb/>confermare la verit&agrave; del suo supposto, pochi giorni prima dal Torricelli. </s>

<s>Si <lb/>discorreva da tutti i dotti della citt&agrave; di queste esperienze, dalle quali resul&shy;<lb/>tava con certezza che, a voler attinger da un vaso doppia quantit&agrave; d'acqua <lb/>nel medesimo tempo, come a fare che il getto sopra la medesima orizontale <lb/>salti a doppia distanza, non basta raddoppiar nel vaso il liquido, ma biso&shy;<lb/>gna quadruplicarlo. </s>

<s>Il Mersenno allora fu sorpreso da grande ammirazione, <lb/>ripensando all'analogia che vedeva passare fra il salto della corda, e quello <lb/>dell'acqua, rallegrandosi che un medesimo argomento sarebbe servito per <lb/>risolvere ambedue i curiosi problemi. </s>

<s>Rimasero per&ograve; per un poco deluse le <lb/>sue speranze, quando seppe che la questione idraulica si riduceva alle leggi <lb/>dei gravi cadenti, le quali non vedeva allora per s&egrave; medesimo come si po&shy;<lb/>tessero accomodare alle corde, che producono i suoni. </s>

<s>Bast&ograve; nulladimeno quel <lb/>che pot&egrave; raccogliere in Roma dal Magiotti e dal Ricci, e in Firenze dallo <lb/>stesso Torricelli, perch&egrave;, tornato a Parigi, si trovasse in mano tanta mate&shy;<lb/>ria, che, stemperata nelle sue proprie speculazioni, bastasse a compilare il <lb/>volume intitolato <emph type="italics"/>Hydraulica,<emph.end type="italics"/> tutta l'importanza del quale si riduce alle <lb/>prime proposizioni, in cui si dimostrano le velocit&agrave; proporzionali alle radici <lb/>delle altezze, e a que'teoremi, che si propongono di mettere in relazione fra <lb/>loro gli elementi parabolici dei getti inclinati. </s></p><p type="main">

<s>Nella seconda proposizione idraulica non si fa altro che annunziare il <lb/>semplice fatto sperimentale, affermandosi che in egual tempo, e per luci <lb/>eguali, &ldquo; erit inter aquae fusae quantitates ratio subduplicata altitudinum, <lb/>quas tubi habuerint &rdquo; (pag. </s>

<s>47), e nella III si rende la ragion del fatto, di <lb/>cui, dice l'Autore, tu che leggi potresti forse restar maravigliato: &ldquo; Verum <lb/>mirari desines, ubi noveris aquam eo solummodo premere, vel ea dumtaxat <lb/>velocitate tubum egredi qua moveretur, si ex eadem tubi altitudine cecidis&shy;<lb/><figure id="id.020.01.3489.1.jpg" xlink:href="020/01/3489/1.jpg"/></s></p><p type="caption">

<s>Figura 227.<lb/>set, adeo ut sit eadem istius phaenomeni ratio, quae descensus <lb/>gravium &rdquo; (ibid., pag. </s>

<s>51). Nella quarta proposizione poi si dimo&shy;<lb/>stra tanto esser maggiore la quantit&agrave; dell'acqua, quanto &egrave; mag&shy;<lb/>giore la luce d'ond'esce, rimanendo per&ograve; sempre il tubo pieno <lb/>alla medesima altezza (pag. </s>

<s>55). </s></p><p type="main">

<s>Si prosegue di qui a dimostrar cose, che sono un semplice <lb/>corollario di queste, infin tanto che si passa a confermare le leggi <lb/>proprie delle velocit&agrave;, desumendole dalle relazioni che passano tra <lb/>le ampiezze, e le sublimit&agrave; paraboliche delle <lb/>salienti. </s>

<s>Se quando l'altezza &egrave; BH (fig. </s>

<s>227) <lb/>l'acqua salta dalla bocca C del tubo in D, <lb/>per lo spazio orizontale GD, a volere che <lb/>salti in F, per doppio spazio, dimostravano <lb/>l'esperienze fatte in Roma, e verificate poi <lb/>dal Mersenno, che non basta raddoppiare <pb xlink:href="020/01/3490.jpg" pagenum="451"/>l'altezza in I, ma che &egrave; necessario in A quadruplicarla. </s>

<s>Ora, i lunghi di&shy;<lb/>scorsi dell'Autore, per confermare dai fatti, in questo modo nuovo osservati, <lb/>la legge delle velocit&agrave; proporzionali alle radici delle altezze, come in tutti i <lb/>gravi cadenti; si compendiano facilmente riducendoci ai teoremi dimostrati <lb/>da Galileo e dal Torricelli intorno ai proietti, per i quali teoremi &egrave; noto <lb/>come, essendo le altezze uguali, le sublimit&agrave; delle parabole BCD, BCF stanno <lb/>come i quadrati delle ampiezze GD, GF. </s>

<s>E perch&egrave; queste, essendo equabil&shy;<lb/>mente passate nell'orizzonte, son le misure delle velocit&agrave;, si vedranno da <lb/>queste semplici osservazioni intorno al moto de'proietti derivare tutte le <lb/>conseguenze, che il Mersenno fa soggetto delle sue proposizioni, relative alle <lb/>propriet&agrave; delle acque salienti. </s></p><p type="main">

<s>Quel che dunque era passato ne'privati scientifici commerci fra s&egrave; e il <lb/>Torricelli, ora se lo vedeva il Magiotti palesato da uno straniero, con tale <lb/>indiscretezza, da giustificare in lui que'primi risentimenti dell'ira. </s>

<s>Forse una <lb/>cosa veniva a temperargliela, ed &egrave; che il Mersenno, bench&egrave; nella seconda <lb/>proposizione lasciasse credere come propria l'esperienza, la ragion nulladi&shy;<lb/>meno dell'esperienza, che passa a dare nella proposizione terza, confessa in&shy;<lb/>genuamente che non &egrave; sua. </s>

<s>Fra le XIV dichiarazioni infatti ch'egli premette, <lb/>chiedendo scusa al lettore di non averlo fatto nel corpo dell'opera, &egrave; scritta <lb/>anche questa: &ldquo; Decimumtertium addo Virum illustrem rogatum cur tubi <lb/>ex quibus salit aqua debeant esse in ratione duplicata, ut duplam aquam <lb/>tribuant, eamdem quam III propos. </s>

<s>Hydraulicorum assero, confestim inve&shy;<lb/>nisse, idque hoc modo &rdquo; (Praefatio ad Lectorem, pag. </s>

<s>XXXIII), e il modo &egrave; <lb/>tale, da non restar dubbio a nessuno, ma specialmente al Magiotti, che quel&shy;<lb/>l'uomo illustre era lo stesso Torricelli. </s>

<s>Certo non il Magiotti solo, ma tutti <lb/>gli uomini onesti, direbbero che avrebbe fatto molto meglio il Mersenno a <lb/>pronunziare espresso quel nome, ma gli perdoneranno volentieri il fatto, in <lb/>grazia di quel suo XIII avvertimento, da cui principalmente ci si rivela che <lb/>esso Mersenno, per aver la ragione dei fatti uditi in Roma, si rivolse allo <lb/>stesso Torricelli, che lo fece stupire di quella sua cos&igrave; pronta risposta. </s>

<s>Que&shy;<lb/>sta, a metterla in termini, si riduceva a una proposizione e ad uno scolio. </s>

<s><lb/>La proposizione rimaneva per s&egrave; medesima dimostrata, riguardando le goc&shy;<lb/>ciole dell'acqua affilate lungo l'asse del tubo rappresentato dalla 227a figura, <lb/>come liberamente cadenti da A e da H in B, dove giunte hanno, per la <lb/>legge galileiana, acquistato tali gradi di velocit&agrave;, che stanno come le radici <lb/>degli spazi passati. </s>

<s>Ma lo scolio, soggiunto dal Torricelli alla proposizione, <lb/>&egrave; tale, quale cos&igrave; il Mersenno lo riferisce: &ldquo; Nec obstat quod aquae prima <lb/>gutta incumbens lumini B (nella medesima figura) non descenderit revera <lb/>ex A, cum enim gutta in A, postquam descendit usque ad lumen B, sa&shy;<lb/>liat eadem velocitate ex B, qua gutta prior, quae non descenderat ex A; se&shy;<lb/>quitur quamcumque aliam guttam eadem velocitate ex B salire, quamdiu <lb/>tubus BA plenus est &rdquo; (ibid., pag. </s>

<s>XXXIV). </s></p><p type="main">

<s>Le altre cose, che ci si rivelano di qui, riguardano le ragioni del sup&shy;<lb/>posto torricelliano. </s>

<s>Come mai, si saranno domandati i Lettori di questa sto-<pb xlink:href="020/01/3491.jpg" pagenum="452"/>ria, il Torricelli non fece nessun conto delle osservazioni della <emph type="italics"/>cateratta,<emph.end type="italics"/> da <lb/>cui mossero le speculazioni dell'Arrighetti: e, potendo mostrare che la su&shy;<lb/>prema superficie dell'acqua scende al foro di fatto, si content&ograve; di supporlo, <lb/>con tutt'altri argomenti confortando la ragionevolezza del suo supposto? </s>

<s>Si <lb/>risponde che l'osservazione fatta dall'Arrighetti, nella polvere degli orioli e <lb/>nella farina delle tramogge, la stim&ograve; lusinghiera, e in ogni modo gli parve <lb/>non si verificare nell'acqua de'pili. </s>

<s>Il documento di ci&ograve; l'abbiamo da un <lb/>Registro d'esperienze, che si dicono essere state <emph type="italics"/>fatte dal serenissimo gran&shy;<lb/>duca Ferdinando <gap/>, e da alcuni suoi cortigiani,<emph.end type="italics"/> ma che sappiamo oramai <lb/>doversi attribuire al Torricelli, per quella parte almeno che fra esse &egrave; di pi&ugrave; <lb/>importante. </s>

<s>Quivi dunque, sotto il numero LXI, trovasi registrato: &ldquo; Messo <lb/>in un vaso acqua e sopra vino, di grossezza due dita, usc&igrave; prima l'acqua che <lb/>stava sotto il vino &rdquo; (Targioni, <emph type="italics"/>Notizie degli aggrandimenti ecc.,<emph.end type="italics"/> T. <gap/> cit., <lb/>pag. </s>

<s>173). Ritrovato poi questo cenno dell'esperienza, gli Accademici del Ci&shy;<lb/>mento la vollero verificare il d&igrave; 16 Luglio 1657, lasciandocela cos&igrave; pi&ugrave; par&shy;<lb/>ticolarmente descritta: &ldquo; Per conoscere quali parti nei liquidi sono le prime <lb/>a scendere nell'uscire da un vaso, si empi d'acqua un cilindro di vetro, e <lb/>sopra di essa diligentemente si messero due dita di vin rosso, in modo che <lb/>galleggiasse. </s>

<s>E poi fatto un buco in fondo al vaso si vidde uscire tutta l'acqua <lb/>ed il vino rimanere sempre l'ultimo a calare, senza mai vedersi punto fili <lb/>di esso discendere per la profondit&agrave; del vaso &rdquo; (ivi, pag. </s>

<s>661). </s></p><p type="main">

<s>Di qui, entrato in sospetto il Torricelli se le polveri e i liquidi calino <lb/>propriamente, come credeva l'Arrighetti, per quella cavit&agrave; o per quell'im&shy;<lb/>buto, che si osserva in essi, riducendosi verso il pertugio del vaso; non stim&ograve; <lb/>prudente fondare la nuova Idrodinamica sopra un'osservazione, che non si <lb/>trovava corrispondere con l'esperienza. </s>

<s>E giacch&egrave;, se il liquido non cala di <lb/>fatto, opera nonostante colla pressione come se vi fosse calato, pens&ograve; di ri&shy;<lb/>durre il principio a un semplice supposto, come fece nel proemio al <emph type="italics"/>De motu <lb/>aquarum,<emph.end type="italics"/> che &egrave; una pi&ugrave; larga esplicazion dello scolio, nella detta risposta <lb/>al Mersenno. </s></p><p type="main">

<s>Che il Boyle non penetrasse addentro a questi segreti facilmente si com&shy;<lb/>prende, ma non si comprende com'egli potesse credere autore del teorema <lb/>idrodinamico il Mersenno, se il Mersenno stesso pubblicamente confessa di <lb/>averlo avuto da un <emph type="italics"/>illustre uomo.<emph.end type="italics"/> Ben per&ograve; era in grado di penetrare le cose <lb/>il Magiotti, nell'animo del quale, se si attut&igrave; alquanto l'ira, rimase oggetto <lb/>di piet&agrave; e di disprezzo uno scrittore, che cercava d'acquistarsi reputazione, <lb/>talora forse con lo sgradire, ma pi&ugrave; spesso col rivestirsi de'panni altrui. </s>

<s>No&shy;<lb/>nostante non fu mai meglio qualificato il Mersenno, che dal Dati: ricono&shy;<lb/>sciutosi povero del suo, s'aiutava, quanto poteva pi&ugrave;, col negoziare la merce, <lb/>e con lo spendere il danaro dei ricchi. </s>

<s>L'avrebbero potuto rimproverare di <lb/>ci&ograve; costoro, se avessero sempre saputo o voluto fare da s&egrave;, ma trattandosi <lb/>del nascosto tesoro di certi avari, o delle robe di certi inetti o ritrosi ai liberi <lb/>scambi, l'operosit&agrave; di quell'ape industriosa riusciva profittevolissima, come <lb/>nell'esempio che abbiamo ora fra mano, dal quale apparisce essere stata, <pb xlink:href="020/01/3492.jpg" pagenum="453"/>sull'ali e sul dorso di quell'istancabile volante, trasportata l'Idraulica d'Italia <lb/>al di l&agrave; delle alpi. </s></p><p type="main">

<s>Che infino al 1644 non fosse ancora penetrata col&agrave; nessuna notizia di <lb/>quella Idrometria, alla quale il nostro Castelli aveva da sedici anni dato or&shy;<lb/>dine di scienza, si rileva da ci&ograve; che, intorno a questo argomento, scrive in <lb/>varie sue epistole il Cartesio. </s>

<s>A lui deve, senza dubbio, il Mersenno aver <lb/>mandato il libro delle sue Cogitazioni fisico-matematiche appena stampato, <lb/>ma perch&egrave; il Filosofo era avvezzo a non spender pi&ugrave; che un quarto d'ora, <lb/>o alla pi&ugrave; lunga un giorno intorno a un libro di scienza nuova, per com&shy;<lb/>prenderlo e per giudicarlo, com'aveva fatto della Geometria del Cavalieri <lb/>e de'Dialoghi di Galileo; non sarebbe nella mente rimasto forse vestigio del&shy;<lb/>l'Idraulica mersenniana, se l'Autore stesso non fosse venuto via via a ri&shy;<lb/>chiamargliene l'attenzione sopra le verit&agrave; pi&ugrave; fondamentali, o a viva voce <lb/>o per lettere familiari, alla prima delle quali cos&igrave; rispondeva: &ldquo; Non me&shy;<lb/>mini te scripsisse antehac ad me quod altitudo aquae sit in ratione dupli&shy;<lb/>cata temporis, quo per foramen effluit &rdquo; (R. Descartes, Epistolae, T. II, <lb/>Amstelodami 1682, pag. </s>

<s>116). E pochi giorni appresso: &ldquo; Experimentum <lb/>tuum verissimum puto, scilicet aquam, quae ex tubo novempedali effluit, de&shy;<lb/>bere triplo fere celerius effluere quam aquam, quae ex tubo pedali effluit, <lb/>per foramen eiusdem magnitudinis &rdquo; (ibid., pag. </s>

<s>119). </s></p><p type="main">

<s>Ma perch&egrave; il Mersenno, annunziando i semplici fatti voleva dar motivo <lb/>a ritrovarne le ragioni, il Cartesio si sent&igrave; mancar nella mente il fondamento <lb/>idrometrico necessario. </s>

<s>Quel fondamento si riduceva al teorema del Castelli, <lb/>che cio&egrave; le quantit&agrave; fluenti stanno in ragion composta delle velocit&agrave; e delle <lb/>luci, n&egrave; occorreva far altro che sostituire alla ragion delle velocit&agrave; quella <lb/>delle radici delle altezze, per confermare la verit&agrave; degli sperimenti mersen&shy;<lb/>niani. </s>

<s>Invece il Cartesio formulava il teorema idrometrico dietro un certo <lb/>giudizio, che si suole di queste cose formar la gente volgare, dicendo che le <lb/>quantit&agrave; dell'acqua dipendono dal tempo dell'efflusso e dall'altezza ch'ella <lb/>ha nel tubo. </s>

<s>&ldquo; Mihi videtur posse probari quod altitudo aquae sit in ratione <lb/>duplicata temporis, eodem modo quo d. </s>

<s>De Beaune probavit tensionem chor&shy;<lb/>darum esse suorum sonorum duplicatam. </s>

<s>Nam, quandoquidem quantitas quae <lb/>per foramen effluentis pendet ex tempore quo effluit, et ex altitudine tubi, <lb/>potest illa repraesentari per areas triangulorum &rdquo; (ibid., pag. </s>

<s>116). </s></p><p type="main">

<s>Si chiamino Q, T, A, <emph type="italics"/>q, t, a<emph.end type="italics"/> due diverse quantit&agrave; d'acqua, due diversi <lb/>tempi dei flussi, e due altezze diverse del liquido, nel medesimo o in due <lb/>tubi distinti. </s>

<s>Sar&agrave; secondo il Cartesio Q:<emph type="italics"/>q<emph.end type="italics"/>=A.T:<emph type="italics"/>a.t.<emph.end type="italics"/> E perch&egrave; da lui <lb/>si propone come da dimostrarsi per vera la proporzione A.<emph type="italics"/>a<emph.end type="italics"/>=T2:<emph type="italics"/>t2<emph.end type="italics"/>, dun&shy;<lb/>que <expan abbr="q.">que</expan><emph type="italics"/>q<emph.end type="italics"/>=T&prime;:<emph type="italics"/>t3<emph.end type="italics"/>, e ci&ograve; manifestamente contradice all'esperienza che si <lb/>voleva confermar per verissima. </s></p><p type="main">

<s>Il medesimo paralogismo veniva altres&igrave; a scoprirsi da quell'altro modo, <lb/>che cos&igrave; sovvenne al Cartesio, per dimostrare la verit&agrave; della stessa espe&shy;<lb/>rienza: &ldquo; Sit tulms AHB (nella figura 227) plenus aqua usque ad A: atten&shy;<lb/>dendum est quod aqua, quae effluit per B, defluat ex alto A, et quod, si <pb xlink:href="020/01/3493.jpg" pagenum="454"/>totus ille tubus esset vacuus, atque una tantum aquae gutta decideret ex A <lb/>versus B, et alia ex H, etiam versus B, esset autem HB 1/8 AB, nec plures <lb/>essent in isto tubo quam duae illae guttae, una ad A, altera ad H, quae se&shy;<lb/>paratim descendentes concurrerent et coniungerentur in puncto B; liquet <lb/>guttam aquae a puncto A demissam, ubi pervenerit ad punctum B, habitu&shy;<lb/>ram noncuplum velocitatis eius quam habet gutta illa, quae ex puncto H de&shy;<lb/>scendit. </s>

<s>Et proinde harum duarum guttarum simul iunctarum in puncto B, <lb/>velocitatem fore mediam proportionalem inter 1 et 9, hoc est triplam &rdquo; (ibid., <lb/>pag. </s>

<s>120). </s></p><p type="main">

<s>Se dunque le velocit&agrave; son proporzionali alle radici delle altezze, si so&shy;<lb/>stituisca nella proporzion sopra scritta alla ragione di T a <emph type="italics"/>t,<emph.end type="italics"/> quella di V a <emph type="italics"/>v,<emph.end type="italics"/><lb/>significanti le velocit&agrave;, e si sostituisca ancora a quella di V a <emph type="italics"/>v<emph.end type="italics"/> la ragion <lb/>della radice di A alla radice di <emph type="italics"/>a<emph.end type="italics"/>:sar&agrave; Q:<emph type="italics"/>q<emph.end type="italics"/>=&radic;A3:&radic;<emph type="italics"/>a3<emph.end type="italics"/>, che sotto altra <lb/>forma contradice alla creduta verit&agrave; dell'esperienza. </s>

<s>Di che accortosi il Car&shy;<lb/>tesio, disse fra s&egrave; &mdash; smettiamo, mi bisogna studiar queste cose un po'me&shy;<lb/>glio &mdash; e poi confermava il poposito fatto, cos&igrave; scrivendo al Mersenno: &ldquo; Sed <lb/>animus est ea omnia, quae ad hanc de motibus aquae materiam pertinent, <lb/>aliquando, curiosius examinare. </s>

<s>Et ne porro cogar quae iam scripsero re&shy;<lb/>tractare, nihil superaddam &rdquo; (ibid., pag. </s>

<s>120). </s></p><p type="main">

<s>Quell'<emph type="italics"/>aliquando<emph.end type="italics"/> per&ograve;, a cui rimetteva il Cartesio lo studio dell'Idrome&shy;<lb/>tria, non venne cos&igrave; presto. </s>

<s>Alcune settimane dopo il Mersenno tornava ad <lb/>annunziargli un altro simile sperimento, dicendogli di aver raccolto quattro <lb/>volte meno acqua da una luce circolare di una mezza linea di diametro, che <lb/>da quella di una linea intera, supposto che rimanga il tubo pieno, in am&shy;<lb/>bedue i casi, alla medesima altezza. </s>

<s>Il fatto conseguiva immediatamente certo <lb/>dal teorema del Castelli, che dava, essendo uguali le altezze, le quantit&agrave; pro&shy;<lb/>porzionali alle aree delle luci, le quali aree, stando come i quadrati de'raggi, <lb/>ossia, nella fatta supposizione, come uno a quattro; doveva necessariamente <lb/>la portata della luce piccola essere un quarto solo della pi&ugrave; grande. </s>

<s>Cos&igrave; pure <lb/>aveva dimostrato il Mersenno, nella sua IV proposizione, e cos&igrave; aveva con&shy;<lb/>cluso, astrazion fatta da tutte le resistenze, secondo l'avvertimento ch'egli <lb/>cita dalla VII appendice del Castelli. </s>

<s>Il Cartesio per&ograve; che non avendo preso <lb/>ancora abito di scienza in queste cose, giudicava a modo del volgo, disse pa&shy;<lb/>rergli incredibile che per solo diminuire della met&agrave; il raggio alla luce, le <lb/>altre cose rimanendo pari, si dovesse ridurre a un quarto l'erogazione. <lb/></s>

<s>&ldquo; Experimentum tuum, quo dimidiae lineae foramen quadruplo pauciorem <lb/>aquam effundit quam integrae, mihi videtur prorsus incredibile, caeteris pa&shy;<lb/>ribus, hoc est curando ut tubus usque ad fastigium semper plenus maneat &rdquo; <lb/>(ibid., pag. </s>

<s>131). </s></p><p type="main">

<s>Nell'epistola seguente par che tenga pi&ugrave; credibile essere le portate pro&shy;<lb/>porzionali ai diametri delle luci (ivi, pag. </s>

<s>136), ma finalmente incominciano <lb/>a rivelarglisi le cose nel loro pi&ugrave; vero aspetto. </s>

<s>Se i due tubi AE, BG (fig. </s>

<s>228) <lb/>sian fra le medesime parallele AC, DG, e sian dal piano orizontale, che passa <lb/>per DG, tagliati in modo, che l'area dell'ellisse FG torni uguale all'area <pb xlink:href="020/01/3494.jpg" pagenum="455"/>del circolo ED; credeva il Cartesio che, anch'essendo BG pi&ugrave; stretto di AE, <lb/>verserebbero ambedue i tubi dalle loro bocche uguali quantit&agrave; d'acqua, nei <lb/><figure id="id.020.01.3494.1.jpg" xlink:href="020/01/3494/1.jpg"/></s></p><p type="caption">

<s>Figura 228.<lb/>medesimi tempi. </s>

<s>&ldquo; Si tubi AE, BG inter parallelas <lb/>AC, DG positi sint, aut inter corum aperturas, seu <lb/>bases aequales et similes, etiamsi si longior sit <lb/>breviori angustior, credo illos parem aquae quan&shy;<lb/>titatem emissuros &rdquo; (ibid., pag. </s>

<s>166). N&egrave; del creder <lb/>cos&igrave; poteva d'altronde essergli venuto il motivo, <lb/>che dall'essersi finalmente persuaso non dipendere <lb/>le quantit&agrave; dalle altezze e dal tempo, ma dalle <lb/>sezioni, e dalle velocit&agrave;, che sono manifestamente uguali, essendo, cos&igrave; nel <lb/>tubo retto come nell'inclinato, scese l'acque per uguali spazi perpendicolari. </s></p><p type="main">

<s>In ogni modo la certezza di queste verit&agrave; idrometriche non apparisce, <lb/>che dopo qualche tempo, in una, che &egrave; delle ultime epistole raccolte in que&shy;<lb/>sta seconda parte. </s>

<s>Quivi, ammettendo il Cartesio che le gocciole scendano <lb/>realmente dalla sommit&agrave; del tubo, rappresentato nella figura 227, e giunte <lb/>in B, con l'accelerazione della discesa, si rivolgano orizontalmente per la <lb/>CL; dimostra che le CD, CF son curve paraboliche, &ldquo; quemadmodum optime <lb/>observavit Galileius &rdquo; (ivi, pag. </s>

<s>392). Ma il pi&ugrave; bello argomento, da provare <lb/>che, dopo tanti penosi errori, la mente del Cartesio erasi finalmente riposata <lb/>nel vero, &egrave; una osservazione, nella quale poi s'incontr&ograve; il Borelli. </s>

<s>Se in <lb/>fondo al vaso AB (fig. </s>

<s>229), mantenuto costantemente pieno fino al livello <lb/><figure id="id.020.01.3494.2.jpg" xlink:href="020/01/3494/2.jpg"/></s></p><p type="caption">

<s>Figura 229.<lb/>AC, siano applicati due tubi DF, FG, d'ugual diametro, <lb/>ma di differente lunghezza, i due cilindri d'acqua escono <lb/>dalle bocche E, G con velocit&agrave; proporzionali alle radici <lb/>delle altezze EH, GI, cosicch&egrave; le quantit&agrave; d'acqua, rac&shy;<lb/>colte qua e l&agrave; nel medesimo tempo, corrispondono ai teo&shy;<lb/>remi, che il Mersenno traduceva nella sua Idraulica dal <lb/>trattato del Castelli, e dalle speculazioni del Torricelli. <lb/></s>

<s>&ldquo; Deinde etiam adverto cylindros ex aqua, aut ex alia&shy;<lb/>que vis materia, primo quo incipiunt descendere mo&shy;<lb/>mento, co celerius moveri, quo longiores sunt, idque in ratione longitudinum <lb/>subduplicata &rdquo; (ibid., pag. </s>

<s>392). </s></p><p type="main">

<s>A questo punto non vogliamo proseguire la storia, senza fare un'osser&shy;<lb/>vazione. </s>

<s>Ci tornano alla memoria coloro, che intesero di togliere o di me&shy;<lb/>nomare i meriti del Castelli, dicendolo un plagiario, un restauratore della <lb/>scienza di Frontino e del Buteone. </s>

<s>Ora &egrave; certo che, mentre la letteratura <lb/>romana era a Italiani e a Francesi comune, i Francesi avevano il Buteone <lb/>per loro connazionale, e nonostante s'&egrave;, per l'esempio del Mersenno e del <lb/>Cartesio, veduto come nel 1644, quando fra noi era da sedici anni divulgato <lb/>il libro della Misura delle acque correnti, l&agrave; s'ignorassero dell'Idrometria i <lb/>primi principii. </s></p><p type="main">

<s>S'osservi inoltre che quasi connazionale ai Francesi era lo Stevino, e <lb/>nonostante aspettarono, a riconoscere le pressioni idostatiche, che il Pascal <pb xlink:href="020/01/3495.jpg" pagenum="456"/>s'inspirasse alle spiegazioni, che il Torricelli dava dell'esperienza dell'ar&shy;<lb/>gento vivo. </s>

<s>Chi vuol conoscere in quali condizioni si trovasse fra loro l'Idro&shy;<lb/>statica, prima di questo tempo, ripensi alle parole, che premetteva alla sua <lb/>XLIII proposizione il Mersenno: &ldquo; Omnes fere eredunt corpus aqua gravius <lb/>ad usque fundum descendere, quod moles aquae illi corpori aequalis nequeat <lb/>ei resistere, vique maiore cogatur loco cedere: corpus vero aqua levius ali&shy;<lb/>quam sui partem mergere, quod vim habeat eiiciendi, et elevandi aquae mo&shy;<lb/>lem parti mersae aequalem &rdquo; (Hydraulica cit., pag. </s>

<s>195). E a ridurre al <lb/>senno le menti, cos&igrave; dannosamente traviate, di quasi tutti, non le richiama <lb/>il Mersenno alla verit&agrave; delle proposizioni steviniane, ma al Discorso di Ga&shy;<lb/>lileo intorno alle galleggianti, ch'ei magnifica, e dentro cui crede pigliar sug&shy;<lb/>gello di verit&agrave; anche le proposizioni, che dalla verit&agrave; son pi&ugrave; aliene, qual'&egrave; <lb/>quella per esempio che non si senta il marangone oppresso, certi essendo <lb/>&ldquo; aquam, in aqua gravitatis aequalis, nihil ponderare &rdquo; (ibid., pag. </s>

<s>205). </s></p><p type="main">

<s>Ma bench&egrave; sia la fiaccola fumosa, &egrave; pure un gran benefizio a chi ri&shy;<lb/>trovasi al buio. </s>

<s>Del qual benefizio debbono i Francesi esser grati al Mer&shy;<lb/>senno, che rec&ograve; a loro, insieme con l'Idrostatica di Galileo, l'Idrometria del <lb/>Castelli, e l'Idrodinamica torricelliana. </s>

<s>Grati pure, placate l'ire al Magiotti, <lb/>glie ne dovrebbero essere gl'Italiani, non solamente per avere diffusa la loro <lb/>scienza oltremonti, ma per essere stato cote ai loro ingegni. </s>

<s>Gli esempi, che <lb/>di ci&ograve; ne porge la storia in vari soggetti, non mancano in questo, che ab&shy;<lb/>biamo per le mani. </s></p><p type="main">

<s>Il trattato <emph type="italics"/>De motu aquarum<emph.end type="italics"/> era gi&agrave; da un anno venuto in Firenze alla <lb/>luce. </s>

<s>Il Mersenno sente che ci manca qualche cosa, e vuol che il Torricelli <lb/>riduca l'opera alla sua perfezione. </s>

<s>Tendono a questo fine le seguenti parole, <lb/>che scriveva, non all'emulo, ma al maestro, da Roma, il di 15 Marzo 1645: <lb/>&ldquo; Hactenus expectavi Vir illustrissime, mei dubii harmonici solutionem, quam <lb/>Vestra Dommatio meditata est: cur nempe nervus ad aliquem sonum acu&shy;<lb/>tiorem adducendo ac tendendo, pondera seu vires tendentes in ratione du&shy;<lb/>plicata intervallorum harmonicorum appendenda sint. </s>

<s>Cum enim, ut iam <lb/>scripseram, diapason v. </s>

<s>g. </s>

<s>habeat suam rationem 1 ad 2, quare vis tendens <lb/>nervum ad sonum acutum ut 2 debet esse, ad vim facientem sonum ut <lb/>unum, ut 4 ad 1. Erat etiam ex re ut doceret V. D. cur aqua fluens ex fo&shy;<lb/>ramine facto in imo tubi censeatur eadem exilire velocitate, ac si descendis&shy;<lb/>set a tubi summitate. </s>

<s>Id enim supponit V. D., et tamen aqua in imo fluens <lb/>re vera non descendit ex summitate tubi &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLI, fol. </s>

<s>16). </s></p><p type="main">

<s>Si vede che di ci&ograve;, che aveva scritto nella prefazione <emph type="italics"/>ad Lectorem,<emph.end type="italics"/> &ldquo; Nec <lb/>obstat quod aquae prima gutta non descenderit revera &rdquo; il Mersenno o se <lb/>n'era dimenticato, o che gli era in questo tempo venuta a mancar la fede <lb/>a quell'Uomo illustre che, domandato del perch&egrave; si richiedesse altezza qua&shy;<lb/>drupla a voler ottenere quantit&agrave; doppia, l'aveva compiaciuto di cos&igrave; pronta <lb/>risposta. </s>

<s>Il Torricelli dall'altra parte che, nel proemio alla sua appendice <lb/><emph type="italics"/>De motu aquarum,<emph.end type="italics"/> credeva d'essersi intorno a ci&ograve; spiegato abbastanza, ri&shy;<lb/>mase in silenzio, ma il Mersenno, anche tornato a Parigi, non gli dava pace. <pb xlink:href="020/01/3496.jpg" pagenum="457"/>Di l&agrave; scrivendogli il d&igrave; 26 Agosto 1646, dop'avergli fatto un monte di do&shy;<lb/>mande, &ldquo; denique, voleva sapere, si rationem repereris meae, quum essem <lb/>Romae, quaestionis de Musica: nempe cur vis requiratur quadrupla ad ner&shy;<lb/>vum elevandum vel acuendum usque ad diapason seu octavam, cum ratio <lb/>diapasonis sit tantum dupla. </s>

<s>Me novis amiciliae vinculis obstringes, si eam <lb/>mihi explicaveris, quemadmodum et cur tubus aqueus debeat esse in ratione <lb/>dupla quoad altitudinem, ut duplam aquam effundat, utriusque enim diffi&shy;<lb/>cultatis vel eamdem vel germanam rationem esse vix dubito &rdquo; (ivi, fol. </s>

<s>64). </s></p><p type="main">

<s>Il pensiero gli era nato, come dicemmo, quattro anni prima in Roma, <lb/>ma non aveva ancora potuto trovar chi gli dicesse quella ragione, che alle <lb/>due difficolt&agrave; sentiva dover esser germana. </s>

<s>Solamente mons&ugrave; De Beaune <lb/>aveva in questo tempo tentato di risolvere il quesito armonico, per via di <lb/>due triangoli, gli spazi de'quali, presi a rappresentare le forze tendenti la <lb/>corda, dimostrava esser proporzionali ai quadrati de'lati omologhi, rappre&shy;<lb/>sentanti le celerit&agrave; delle vibrazioni, da cui dipendono le acutezze dei suoni. </s>

<s><lb/>Il Cartesio vedemmo come, nell'epistola XXIX, si studiasse di applicare il <lb/>metodo del Beaune a risolvere il quesito armonico, ma non par che il Mer&shy;<lb/>senno ne rimanesse appagato. </s>

<s>In una infatti delle ultime proposizioni della <lb/><emph type="italics"/>Ballistica,<emph.end type="italics"/> mentre la difficolt&agrave; &ldquo; de necessaria chordae tensione in ratione <lb/>quadrupla, ut duplo moveatur celerius &rdquo; dice &ldquo; ab acutissimo viro domino De <lb/>Beaune explicata &rdquo; (Paris 1644, pag. </s>

<s>132), dell'altra difficolt&agrave;, riguardante <lb/>l'acqua, d&agrave; una spiegazione diversa, e tale da valer veramente per ambedue i <lb/>quesiti. </s>

<s>&ldquo; Quemadmodum enim, cum tubus aquae libra plenus salit uno gradu <lb/>velocitatis a lumine, debent add&igrave; 3 librae ut duplo, quinque praeterea librae <lb/>ut triplo, et postea 7 aquae librae ut quadruplo velocitatis gradu saliant; <lb/>ita funi seu fidibus addenda sunt pondera 1, 4, 9 et 16, ut praedictis gra&shy;<lb/>dibus vadant et redeant &rdquo; (ibid., pag. </s>

<s>130). </s></p><p type="main">

<s>Risoluto, in questa medesima proposizione XXXVI della <emph type="italics"/>Ballistica,<emph.end type="italics"/> infino <lb/>dal 1644, il quesito delle corde tese, e insieme anche l'altro delle acque sa&shy;<lb/>lienti; nel 1646 il Mersenno stesso tornava a domandar di ci&ograve; la soluzione <lb/>al Torricelli, il quale aveva mostrato di non approvare la sopra riferita ana&shy;<lb/>logia. </s>

<s>Ma ora sarebbe il tempo di dire quello che ne pensava, giacch&egrave; di <lb/>pensarci aveva promesso, e si sperava che avesse mantenuto. <emph type="italics"/>Hactenus <lb/>expectavi solutionem quam V. D. meditata est.<emph.end type="italics"/> A voler sapere con cer&shy;<lb/>tezza il resultato di queste meditazioni bisognerebbe veder le lettere del Tor&shy;<lb/>ricelli al Mersenno, ma perch&egrave; queste ci mancano, non si pu&ograve; che per via <lb/>di congetture, in qualche modo, supplire al difetto. </s></p><p type="main">

<s>S'accenn&ograve; altrove che la nuova regola di misurare le quantit&agrave; dell'acqua <lb/>era quella medesima, che un mezzo secolo dopo si proporrebbe generalmente, <lb/>per misurare qualunque sorta di forze vive. </s>

<s>Come Galileo paragonava la forza <lb/>della percossa ai pesi morti, cos&igrave; il Castelli prendeva le pressioni dell'acqua <lb/>stagnante per la misura delle velocit&agrave; dell'acque correnti. </s>

<s>Quest'errore degli <lb/>antichi, e di cui non s'erano avveduti i due grandi Maestri, fu sagacemente <lb/>scoperto dal Torricelli, il quale pens&ograve; che, per passar dal conato al moto at-<pb xlink:href="020/01/3497.jpg" pagenum="458"/>tuale, era necessario che la virt&ugrave; si moltiplicasse in s&egrave; stessa, cosicch&egrave; di <lb/>doppia diventasse quadrupla, di tripla nonupla e cos&igrave; di seguito, secondo la <lb/>progressione dei numeri quadrati, d'onde la regola di misurare dai quadrati <lb/>delle velocit&agrave; tutte le forze vive. </s></p><p type="main">

<s>Il ragionamento germano a questo, fatto dal Torricelli per risolvere l'al&shy;<lb/>tra difficolt&agrave; relativa alle corde armoniche, secondo che desiderava il Mer&shy;<lb/>senno, &egrave; facile congetturare di qui che fosse tale: Un peso doppio pu&ograve; dop&shy;<lb/>piamente tendere la corda. </s>

<s>Ma perch&egrave; la forza morta della tensione diventi <lb/>viva, nel moto doppio della v<gap/>brazione, bisogna che si moltiplichi in s&egrave; stessa, <lb/>cosicch&egrave;, se quella era due, questa si riduca a quattro, com'&egrave; confermato <lb/>dall'esperienza. </s></p><p type="main">

<s>Il Mersenno non poteva penetrare la profondit&agrave; di questi pensieri, come <lb/>non la penetrarono i Matematici contemporanei e i posteriori, che dettero <lb/>tanta faccenda al Leibniz, quando volle formulare il teorema delle forze vive: <lb/>Di qui &egrave; che i primi promotori dell'Idrodinamica torricelliana trovarono espe&shy;<lb/>diente l'ammettere che la velocit&agrave; dell'acqua, nell'atto dell'uscire dai fori <lb/>dei vasi, sia tale, non perch&egrave; essa acqua operi con la sua pressione come se <lb/>vi fosse scesa dal supremo livello, secondo che supponeva il Torricelli, ma <lb/>perch&egrave; ella vi discenda in realt&agrave;, non in tutta la sua mole, ma nelle goc&shy;<lb/>ciole via via componenti il cilindro liquido, che ha l'apertura del foro per <lb/>base. </s>

<s>&ldquo; Neque enim dubium est, osservava il Cartesio, quin primae quaelibet <lb/>guttae huius aquae eadem cum sequentibus celeritate effluant, modo suppo&shy;<lb/>natur tubus manere interea semper aequaliter plenus, et si attendatur quod, <lb/>cum aqua ex hoc tubo effluit per foramen C (figura 227 qui addietro), non <lb/>opus est ut tota aqua in eo contenta moveatur, sed solum ut guttae omnes <lb/>quae componunt exiguum cylindrum, cuius basis est foramen C, et qui ad <lb/>fastigium usque extenditur, alia post aliam descendant; facile concipietur fore <lb/>ut gutta, quae est in puncto A, postquam pervenerit ad puntum C, acquisi&shy;<lb/>verit, descendendo ab A usque ad C, duplum celeritatis eius, quam acqui&shy;<lb/>sivisset si descendisset tantum ab H, et proinde, cum egreditur per C, duplo <lb/>celerius movetur, quando tubus ad quatuor pedum, quam cum ad unius tan&shy;<lb/>tum altitudinem plenus est, atque idem est de reliquis guttis, quandoquidem <lb/>eadem vi moventur (Epistol., P. </s>

<s>H cit., pag. </s>

<s>391). </s></p><p type="main">

<s>A questa medesima conclusione conduceva il ragionamento del Nardi, <lb/>quando, alla ragion meccanica di Galileo, volle sostituirne una fisica, per <lb/>poter pi&ugrave; facilmente spiegare l'equilibrio de'liquidi in vasi comunicanti di <lb/><gap/> grandezze, come sarebbe un tino e una gracile canna, dicendo che <lb/>l'acqua in questa &egrave; solamente premuta da altrettant'acqua, quanta se ne <lb/>conterrebbe in una simile canna, immaginata continuarsi in mezzo al liquido <lb/>del vaso grande: c<gap/>&ograve; che si conferma, dice egli, <emph type="italics"/>dall'apparire nella super&shy;<lb/>ficie sua certa fossetta, corrispondente in tutto al sito e lunghezza della <lb/>canna, nella qual fossa continuamente d'ogni intorno l'umore circostante <lb/>sdrucciola.<emph.end type="italics"/></s></p><p type="main">

<s>Il Borelli pur<gap/>olse questi pensieri del Nardi, nel suo hbro <emph type="italics"/>De mo-<emph.end type="italics"/><pb xlink:href="020/01/3498.jpg" pagenum="459"/><emph type="italics"/>tionibus naturalibus<emph.end type="italics"/> alla CCXVII proposizione, dove, per dichiarar come le <lb/>velocit&agrave; e le moli attinte dipendono solamente dalla grandezza del foro, e <lb/>dall'altezza del liquido, qualunque sia del resto l'ampiezza del vaso, si serve <lb/>di questo esempio: &ldquo; Si fuerit fistula aliqua vitrea ad horizontem perpen&shy;<lb/>dicularis, et puteus aeque altus, in cuius fundo aperiatur foramen, prorsus <lb/>aequale infimo fistulae foramini; tunc aqua ab orificio putei profluit eadem <lb/>fere velocitate, et aequali mole ac ex illa fistula vitrea aeque plena egredi&shy;<lb/>tur, proterea quod in aqua putei concipi debet fistula perpendiculariter <lb/>horizonti erecta ab infimo foramine usque ad summitatem aquae, et solum&shy;<lb/>modo praedicta aqua in fistula imaginaria contenta fluit, reliqua vero colla&shy;<lb/>teralis innititur sustentaturque a fundo impenetrabili et firmo ipsius putei, <lb/>a quo aquae fluxus perpendicularis impeditur, et ideo perinde aqua excur&shy;<lb/>rit perpendiculariter, ac si in fistula vitrea contineretur &rdquo; (pag. </s>

<s>457). </s></p><p type="main">

<s>Il Nardi e il Borelli toccarono il soggetto per incidenza, ma il Baliani <lb/>ne compose un trattato a parte, intitolato <emph type="italics"/>De motu gravium liquidorum,<emph.end type="italics"/><lb/>che distinse in tre libri. </s>

<s>Per dare un'idea del particolar modo della tratta&shy;<lb/>zione, vogliamo citare dal libro primo il teorema secondo, e i due problemi <lb/>che gli succedono. </s>

<s>Quel teorema &egrave; proposto cos&igrave;: &ldquo; In pluribus canalibus, <lb/>ductis ad idem planum orizontale, aquae quantitates sunt ut canales &rdquo; (Ge&shy;<lb/>nuae 1646, pag. </s>

<s>117). E si dimostra dietro il postulato che le quantit&agrave; d'acqua <lb/>son proporzionali ai tempi degli efflussi, applicandovi il teorema di Mecca&shy;<lb/>nica che dice i tempi stare come le lunghezze dei piani, ossia, nel caso pre&shy;<lb/>sente, come le lunghezze degli stessi canali. </s></p><p type="main">

<s>Il primo poi dei detti problemi &egrave; tale: &ldquo; In canali declinante reperire <lb/>portionem continentem aquam aequalem eius, quae est in perpendiculari &rdquo; <lb/><figure id="id.020.01.3498.1.jpg" xlink:href="020/01/3498/1.jpg"/></s></p><p type="caption">

<s>Figura 230.<lb/>(ibid., pag. </s>

<s>118). E supposto essere sopra l'orizontale CB <lb/>(fig. </s>

<s>230) il canale inclinato AC, e il perpendicolo AD, si <lb/>risolve il quesito conducendo da B, sopra l'AC, la perpen&shy;<lb/>dicolare DB, che precide in D tal porzione AD del canale, <lb/>qual'&egrave; quella richiesta. </s></p><p type="main">

<s>L'altro problema, che si diceva, &egrave; cos&igrave; esposto: &ldquo; In <lb/>quibusdam canalibus, quomodolibet inclinatis, reperire por&shy;<lb/>tiones continentes aquam aequalem cuiusvis dicti canalis &rdquo; (ibid., pag. </s>

<s>119). <lb/><figure id="id.020.01.3498.2.jpg" xlink:href="020/01/3498/2.jpg"/></s></p><p type="caption">

<s>Figura 231.<lb/>Siano AB, AC, AD (fig. </s>

<s>231) i proposti canali: se in&shy;<lb/>torno al perpendicolo AE si descriva un mezzo cer&shy;<lb/>chio, le porzioni AB&prime;, AC&prime;, AD&prime;, tagliate da lui, son <lb/>quelle cercate. </s></p><p type="main">

<s>Si vede bene come, cos&igrave; procedendo, tutte le pro&shy;<lb/>posizioni del terzo dialogo delle due Nuove Scienze si <lb/>possano trasformare in un trattato d'Idrodinamica, senza <lb/>far altro che cambiare i piani inclinati e le cadenti per&shy;<lb/>pendicolari in canali pieni d'acque correnti. </s>

<s>N&egrave; diversa <lb/>indole da questo ha il libro secondo. </s>

<s>Nel terzo poi, pro&shy;<lb/>ponendosi l'Autore di trattare del flusso dai vasi, a <pb xlink:href="020/01/3499.jpg" pagenum="460"/>dimostrar la proposizione fondamentale formulata: &ldquo; Impetus foraminum <lb/>aequalium vasis sunt in subduplicata ratione distantiae a summo vasis &rdquo; <lb/>(pag. </s>

<s>162), gli basta richiamarsi all'esperienza, che mostra l'acqua ca&shy;<lb/>dere al foro con l'impeto suo naturale dal sommo dal vaso. </s>

<s>&ldquo; Aqua tran&shy;<lb/>siens per vasis foramen decurrit a summo vasis ad foramen, tamquam per <lb/>canalem perpendicularem. </s>

<s>Quod experieris, si vas aqua plenum, in cuius imo <lb/>sit foramen, sit perspicuum: videbis etenim in eo formali canale per quod <lb/>aqua superior exeat &rdquo; (ibid., pag. </s>

<s>158). </s></p><p type="main">

<s>Ai magnificatori del Newton, autore della famosa cateratta, questi del <lb/>Cartesio, del Nardi, del Borelli e del Baliani sembreranno promozioni di <lb/>grande importanza. </s>

<s>L'importanza per&ograve; svanisce in tutto o in grandissima <lb/>parte, riflettendo che al Torricelli non era sfuggito il pensiero di tutti i suoi <lb/>promotori, dal Cartesio al Newton, ma ch'egli fu costretto a rinunziarvi dalle <lb/>diligenti osservazioni dei fatti. </s>

<s>La promozione desiderata si sarebbe dovuta <lb/>far consistere piuttosto nell'applicazione delle leggi delle velocit&agrave; al corso <lb/>dei fiumi, ma nessun si rimosse, rispetto a ci&ograve;, dal proposito del Torricelli, <lb/>da noi esposto con le ultime parole del capitolo precedente. </s></p><p type="main">

<s>Il Mersenno, dop'aver notate le differenze del moto dell'acqua, dentro <lb/>i tubi o per i fiumi, mentre per quelli dimostra verificarsi, come vedemmo, <lb/>la legge torricelliana, per questi non crede prudente dilungarsi dai principii <lb/>e dalla proposizion del Castelli, bench&egrave; conosca dover questa venire alterata <lb/>da innumerevoli impedimenti. </s>

<s>&ldquo; Jam vero statuamus fluminis alicuius cur&shy;<lb/>rentis altitudinem, ex alterius fluminis aequalis adventu, duplo maiorem. </s>

<s>Si <lb/>praeterea novi fluminis advenientis impetus seu velocitas prioris fluminis sit <lb/>duplo maior, fiat altitudo nova composita ex ratione altitudinum et ex ra&shy;<lb/>tione velocitatum utriusque fluvii, adeo ut qui prius, ob solam aequalem <lb/>advenientis altitudinem duplo fuerat altior, ob duplam advenientis veloci&shy;<lb/>tatem quadruplo fiat altior. </s>

<s>Sed cum mare refluens non parum videatur in&shy;<lb/>terturbare fluviorum in illud ingredientium velocitates, et alia occurrant im&shy;<lb/>pedimenta innumera, haec libenter omitto studiosoribus: videatur interea <lb/>tractatus Benidicti Castelli, qui nuper ad plures abiit &rdquo; (Hydraulica cit., <lb/>pag. </s>

<s>177, 78). </s></p><p type="main">

<s>Tale udimmo essere stato il motivo per cui, volendo il Baliani passar <lb/>da quello de'solidi a trattar del moto de'liquidi, lasci&ograve; l'opera imperfetta <lb/>(Alb. </s>

<s>IX, 142). E il Cartesio, dop'aver risposto secondo qual proporzione si <lb/>faccia il moto dell'acqua dentro i tubi, soggiungeva: &ldquo; Sed hoc ad flumi&shy;<lb/>num decursum aptari nequit, co quod ad ostium suum occursu maris valde <lb/>tardentur &rdquo; (Epist. </s>

<s>cit., pag. </s>

<s>137). Altrove, mettendo in campo la questione <lb/>se il fiume corra pi&ugrave; lento in fondo o alla superficie, e risolvendola a modo <lb/>del Cardano, terminava il Cartesio stesso cos&igrave;, con questa notabile osserva&shy;<lb/>zione, il suo discorso: &ldquo; Neque etiam credo posse illorum declivitatem ex <lb/>illorum celeritatis inaequalitate colligi, sed solum libella explorando &rdquo; (ibid., <lb/>pag. </s>

<s>167), come, a proposito delle Chiane, diceva il Torricelli, e aveva detto <lb/>gi&agrave; Galileo, a proposito del Bisenzio. </s></p><pb xlink:href="020/01/3500.jpg" pagenum="461"/><p type="main">

<s>Il Borelli, dop'aver, nel capitolo XI <emph type="italics"/>De motionibus natur.,<emph.end type="italics"/> illustrata in <lb/>modi nuovi la legge delle velocit&agrave; proporzionali alle radici delle altezze, men&shy;<lb/>tre si consideri l'acqua scorrere per i tubi; trattandosi poi dei fiumi rit&egrave;&shy;<lb/>neva anch'egli per verissima la proposizione seconda del secondo libro idro&shy;<lb/>metrico del Castelli. </s>

<s>Il documento di ci&ograve; ce lo esibisce la storia delle correzioni <lb/>da farsi alla dimostrazion della detta proposizione. </s>

<s>E perch&egrave; in essa storia <lb/>si comprendono, insieme col Borelli, i pi&ugrave; valenti Idraulici italiani di quei <lb/>tempi, non vogliamo lasciar di narrarla ne'suoi particolari, sembrandoci che <lb/>in tanta variet&agrave; d'ingegni non si possa meglio che di qui far apparire la <lb/>concorde unit&agrave; delle opinioni. </s></p><p type="main">

<s><emph type="center"/>III.<emph.end type="center"/></s></p><p type="main">

<s>La radicale riforma, che veniva a subir l'opera della Misura delle acque <lb/>correnti dopo la nuova istituzione idrodinamica, vedemmo come fosse sen&shy;<lb/>tita e consentita dal Castelli stesso ne'colloqui, e negli epistolari commerci <lb/>col Torricelli. </s>

<s>Si disse, in sull'ultimo del precedente capitolo, altres&igrave; il modo <lb/>come si pensava particolarmente d'introdur nel libro la detta riforma, asse&shy;<lb/>gnando alle acque fluenti dai piccoli fori dei vasi altra legge, che a quelle <lb/>correnti per i canali e per gli alvei dei fiumi, secondo che, dietro esperienze <lb/>diligentemente istituite in ambedue i casi, pareva consigliar la Natura stessa <lb/>alla scienza dell'uomo. </s>

<s>Ma gli stami, cos&igrave; bene orditi dal Castelli, furono <lb/>nell'Aprile del 1643 recisi dalla morte, cosicch&egrave; il manoscritto originale del <lb/>secondo libro Delle acque correnti si rimase in Roma, nella cella del mona&shy;<lb/>stero di S. Callisto, non variato di nulla dalla copia dedicata al neonato prin&shy;<lb/>cipe di Toscana, e consegnata come si disse nelle mani del principe Leopoldo. </s></p><p type="main">

<s>Il Torricelli allora sent&igrave; nel pio animo il dovere di ricambiare il be&shy;<lb/>nefizio. </s>

<s>E come il Castelli avevagli promesso di onorare col nome e con le <lb/>opere di lui il suo libro della Misura delle acque correnti, cos&igrave; ora egli pro&shy;<lb/>poneva di ornare il suo trattato <emph type="italics"/>De motu aquarum<emph.end type="italics"/> col nome e con l'opere <lb/>del Castelli. </s>

<s>L'idrometria di questo, che nell'aspetto presente discordava, si <lb/>doveva conciliar con l'Idrodinamica nuova, e la bellezza e la perfezion del&shy;<lb/>l'opera, che ne sarebbe di qui resultata, si pu&ograve; facilmente immaginar da <lb/>ognuno, che ripensi all'ingegno del Torricelli, e allo zelo di mantenere inte&shy;<lb/>merata dagli attacchi degli emuli la reputazione del suo caro maestro. </s>

<s>Ma <lb/>tutto intento com'era allora alle opere sue geometriche, aspettava, a metter <lb/>mano al nuovo libro del Moto delle acque, di aver dato quelle stesse opere <lb/>alle stampe. </s></p><p type="main">

<s>Intanto a Michelangiolo Ricci era aperta dai monaci la cella, dov'era <lb/>morto colui, che l'aveva amato e onorato tanto, e gli erano presentate le <lb/>opere postume perch&egrave; l'esaminasse, e specialmente il secondo libro della <lb/>Misura delle acque. </s>

<s>Concorse allora col desiderio di quei padri il suo vivis-<pb xlink:href="020/01/3501.jpg" pagenum="462"/>simo di pubblicare il manoscritto, de'pregi del quale era assai bastante ca&shy;<lb/>parra il nome dell'Autore. </s>

<s>E mentre era in trattare di ci&ograve; col tipografo, ne <lb/>dette avviso a Firenze al Torricelli, il quale volle avvertirlo di quel ch'era <lb/>passato fra s&egrave; e il padre don Benedetto, a proposito di alcune correzioni da <lb/>farsi al libro di lui, e come, lasciandolo uscir fuori a quel modo, potrebbe <lb/>dare occasion di censure agli emuli, e di calunnie agli invidiosi, specialmente <lb/>stranieri: per cui, speditosi appena il suo, avrebbe dato mano a pubblicare <lb/>il libro del Castelli. </s>

<s>Inteso ci&ograve;, rispondeva il Ricci cos&igrave; da Roma, in una <lb/>lettera del d&igrave; 12 Settembre 1643: </s></p><p type="main">

<s>&ldquo; Fu mio pensiero il procurar la luce della stampa delle opere di don <lb/>Benedetto, avendomi ci&ograve; persuaso quella gratitudine, che io sempre ho detto <lb/>a V. S. aver nell'animo mio altamente fisse le sue radici. </s>

<s>Sono troppo grandi <lb/>le obbligazioni, che io debbo alla memoria immortale di quel Padre, che con <lb/>affetti di non ordinaria umanit&agrave; sempre mi ha ricevuto ed onorato e amato. </s>

<s><lb/>Ma poich&egrave; le cose passano nel modo che ella mi dice, ed il pubblicar le sue <lb/>scritture potrebbe fomentare in altrui qualche livido affetto di malignit&agrave;, non <lb/>tirer&ograve; pi&ugrave; avanti il negoziato, ma distorner&ograve; quel poco trattato, che ordito <lb/>avevo co'monaci e con il libraio, e attenda pure frattanto V. S. a sollecitare <lb/>il suo libro, perch&egrave; possa poi affaticare a pubblica utilit&agrave;, e ridurre in netto <lb/>quest'opera di don Benedetto &rdquo; (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>9). </s></p><p type="main">

<s>Il libro a cui qui s'accenna, contenente le due parti delle Opere geo&shy;<lb/>metriche, era da qualche mese venuto in Firenze alla luce, e in questo tempo <lb/>un tipografo s'era profferto ai monaci di S. </s>

<s>Callisto di pubblicare le opere <lb/>postume del loro padre abate, a sue spese. </s>

<s>Onde il Ricci avendo, l'ultimo <lb/>giorno dell'anno 1644, occasione di scrivere al Torricelli, lo pregava cos&igrave; a <lb/>voler mantener le fatte promesse, prendendosi egli la cura dell'edizione: <lb/>&ldquo; Un monaco di S. Callisto, che tien cura delle scritture postume del padre <lb/>abate Castelli, prega V. S. a volergli far grazia del proprio parere intorno <lb/>la seconda parte delle Acque correnti, perch&egrave; si trova un libraro che la <lb/>stamperebbe a sue spese, e li padri non vedono volentieri sepolte le gloriose <lb/>fatiche del buon vecchio. </s>

<s>Quando ancora V. S. si trovasse in istato di porvi <lb/>mano, e perfezionarle, credo che i padri se ne reputerebbero favoriti &rdquo; (ivi, <lb/>fol. </s>

<s>71). </s></p><p type="main">

<s>Il perfezionamento per&ograve;, quale s'intendeva dare allo scritto altrui dallo <lb/>squisito gusto del Torricelli, non era faccenda n&egrave; cos&igrave; lieve, n&egrave; cos&igrave; pronta. </s>

<s><lb/>La mano voleva esser rimessa, non sopra il secondo libro solamente, ma e <lb/>sopra il primo, in cui si poneva per legge fondamentale dei flussi laterali <lb/>dai vasi le velocit&agrave; proporzionali alle semplici altezze. </s>

<s>In che modo si po&shy;<lb/>tesse a questa sostituire la legge idrodinamica nuovamente scoperta, e dalle <lb/>esperienze approvata, senza che perci&ograve; venisse a offendersene il magistero <lb/>del Castelli, per varii anni oramai, e con tanta autorit&agrave; pubblicamente eser&shy;<lb/>citato; era quel che metteva in gran pensiero il Torricelli, e mentre pas&shy;<lb/>sava, nel tacito meditar, da un proposito a un altro, lo venne inaspettata&shy;<lb/>mente a coglier la morte. </s>

<s>Distratto il Ricci dagli onori della dignit&agrave; cardi-<pb xlink:href="020/01/3502.jpg" pagenum="463"/>nalizia e dagli uffici, successi altri monaci a quelli, co'quali era convissuto <lb/>il Castelli, nessuno poi pens&ograve; pi&ugrave; agli scritti postumi di lui, de'quali nono&shy;<lb/>stante si lasci&ograve; prendere copia ad alcuni periti d'acque, per servirsene ai <lb/>loro studii. </s></p><p type="main">

<s>Una di coteste copie giunse alle mani del Barattieri quando, pubblicata <lb/>nel 1656 la prima parte della sua <emph type="italics"/>Architettura d'acque,<emph.end type="italics"/> attendeva a scri&shy;<lb/>vere la seconda. </s>

<s>E perch&egrave; l'esperienze, che avevano indotto il Castelli a sta&shy;<lb/>bilire le velocit&agrave; proporzionali alle altezze, trov&ograve; che riscontravano con le sue <lb/>proprie, fatte nell'acquedotto della Codogna; volle che ne fosse nota a tutti <lb/>la dimostrazione, incominciando a inserir nella stampa delle cose sue le pro&shy;<lb/>posizioni inedite dello stesso Castelli. </s>

<s>Variet&agrave; d'accidenti avendo fermata <lb/>l'impressione dell'Opera alla fine del quarto libro, quando il Barattieri torn&ograve; <lb/>a ripigliarla in mano erano gi&agrave; in Bologna dal Manolessi mandati insieme <lb/>alla luce per le stampe del Dozza, i due libri della Misura delle acque cor&shy;<lb/>renti, conforme all'edizione del 1626 rispetto al primo, e conforme al ma&shy;<lb/>noscritto, copiato nell'abbazia di S. </s>

<s>Callisto di Roma, rispetto al secondo. </s>

<s><lb/>Alcuni forse dei nostri Lettori, syolgendo il volume, avranno a pag. </s>

<s>82 tro&shy;<lb/>vata scritta la proposizione seconda con la sua dimostrazione; altri per&ograve;, <lb/>bench&egrave; lusingati d'aver copia identica a questa, come quella che in tutto <lb/>corrisponde all'esterno, e che &egrave; del medesimo anno, e del medesimo edi&shy;<lb/>tore; troveranno alla detta pagina, invece della dimostrazione, un avverti&shy;<lb/>mento scritto in carattere corsivo. </s>

<s>Il fatto, non nuovo forse ai bibliofili, ma <lb/>per&ograve; non comune, deve aver messo una certa curiosit&agrave; in tutti coloro che <lb/>l'hanno osservato, e noi ci proponiamo di sodisfarla, com'assunto princi&shy;<lb/>pale di questa storia. </s></p><p type="main">

<s>Si disse che, andato a monte il negoziato del Ricci, nessuno pensava <lb/>pi&ugrave; alla pubblicazione degli scritti postumi del Castelli, e ne aveva forse de&shy;<lb/>posta ogni speranza lo stesso principe Leopoldo dei Medici, nelle mani del <lb/>quale erano i venerati manoscritti, perch&egrave;, venuta la morte a rapirgli di pa&shy;<lb/>lazzo il Torricelli, non vedeva chi tra i discepoli potesse degnamente sosti&shy;<lb/>tuirlo nel glorioso ufficio di correggere l'opera del Maestro. </s>

<s>Ma la notizia <lb/>ch'egli ebbe della stampa in Bologua, nell'atto stesso del venir pubblicata, <lb/>non lasciava oramai pi&ugrave; a dubitare di quel che fosse da farsi: al marchese <lb/>Cospi, luogotenete del Granduca a Bologna, faceva scrivere in tali termini, <lb/>quali si ricavano dalla seguente minuta, che c'&egrave; rimasta: </s></p><p type="main">

<s>&ldquo; Il Manolessi, stampatore di Bologna, ha gi&agrave; finito di stampare le opere <lb/>di don Benedetto Castelli sopra l'Acque correnti, e di pi&ugrave; v'ha aggiunte <lb/>altre cosette, o rifiutate o falsamente attribuite al detto Padre. </s>

<s>Per&ograve; si de&shy;<lb/>sidera che il Manolessi sospenda la pubblicazione di tale opera, e ne mandi <lb/>qua una copia, per poterla far correggere dai discepoli del detto padre Ca&shy;<lb/>stelli, ed anco s'invieranno due altri libretti bellissimi, e desideratissimi, del <lb/>medesimo Autore, uno <emph type="italics"/>Del modo di farsi la vista,<emph.end type="italics"/> e l'altro <emph type="italics"/>Del bianco e <lb/>del nero,<emph.end type="italics"/> non mai stampati, i quali rendano pi&ugrave; caro e desiderato il libro <lb/>di quel grand'Uomo, di quel che non sar&agrave; pubblicandolo manchevole ed adul-<pb xlink:href="020/01/3503.jpg" pagenum="464"/>terato, com'egli &egrave;, nella forma che l'ha stampato il Manolessi &rdquo; (MSS. Cim., <lb/>T. XXIII, fol. </s>

<s>22). </s></p><p type="main">

<s>Il qual Manolessi, ricevutone cos&igrave; il comando, sospese la pubblicazione, <lb/>e sped&igrave; la copia desiderata, avuta la quale in mano &egrave; naturale che il Prin&shy;<lb/>cipe ricorresse con l'occhio e col pensiero alla proposizione seconda del se&shy;<lb/>condo libro, e al trovarla stampata conforme al manoscritto si deve essere <lb/>risovvenuto del Torricelli, e come gli avesse, 17 anni fa, fatto osservare che <lb/>se<gap/>la nuova acqua nel regolatore del fiume sta in altezza alla prima come <lb/>quattro a due; non per&ograve; come quattro a due staranno le velocit&agrave; respettive, <lb/>ma come quattro alla radice di due. </s>

<s>Dev'essere inoltre esso Principe stato <lb/>informato come, risaputa l'osservazione, il Castelli rispondesse, che sebben <lb/>non si trovasse sodisfatto della dimostrazione, nonostante la proposizione in <lb/>s&egrave; stessa, essendo il legittimo resultato dell'esperienza, non poteva non esser <lb/>vera. </s>

<s>Ond'essendo dovuto convenir di ci&ograve; il Torricelli, non rimaneva dubbio <lb/>intorno alla parte della detta proposizione, che aveva bisogno d'esser cor&shy;<lb/>retta, secondo le convenzioni stesse fatte fra que'due grandi uomini. </s>

<s>La dif&shy;<lb/>ficolt&agrave; per&ograve; consisteva nel saper trovare la ragion di un fatto particolare, che <lb/>si sottrae alle leggi universali de'corpi naturalmente cadenti, per cui, essendo <lb/>in quel punto presente in Firenze il-Borelli, volle il principe Leopoldo con&shy;<lb/>ferir la cosa primieramente con lui, comandandogli di dirne il suo parere. </s>

<s><lb/>Il Borelli allora rispose che questo sarebbe di sopprimere la dimostrazione, <lb/>e in carattere corsivo stamparvi invece un avvertimento, che dicesse come <lb/>quella mancava, perch&egrave; l'Autore fu sorpreso dalla morte, mentr'era in cer&shy;<lb/>carla, e che perci&ograve; aveva pensato di supplirvi uno scolare di lui, mettendola <lb/>in fondo al libro. </s>

<s>Non decidendo il Principe nulla ancora del resto, comand&ograve; <lb/><figure id="id.020.01.3503.1.jpg" xlink:href="020/01/3503/1.jpg"/></s></p><p type="caption">

<s>Figura 232.<lb/>al Borelli facesse egli stesso quella <lb/>dimostrazione, che pochi giorni <lb/>dopo recapitava in palazzo, scritta <lb/>in questa maniera: </s></p><p type="main">

<s>&ldquo; Sia il fiume SBC (fig. </s>

<s>232) <lb/>per il regolatore CEBF, annesso al <lb/>vaso QIDR, che sia prisma con le <lb/>sponde erette all'orizonte. </s>

<s>E prima, <lb/>l'origine del fiume M versi tanta <lb/>acqua, che arrivi al livello OP, e <lb/>scorrendo con la velocit&agrave; S faccia <lb/>nel regolatore la sezione rettangolare EBH. </s>

<s>Poi l'altro sifone o torrente N, <lb/>versi nuova acqua, ed arrivi al livello QR, e scorrendo con la velocit&agrave; T <lb/>per il fiume riempia la sezione rettangolare EF. </s>

<s>Dico che la velocit&agrave; T, alla <lb/>velocit&agrave; S, ha l'istessa proporzione che l'altezza FB, all'altezza HB. &rdquo; </s></p><p type="main">

<s>&ldquo; La quantit&agrave; d'acqua, che passa per la sezione EF, cio&egrave; il prisma <lb/>acqueo QIDR, alla quantit&agrave; dell'acqua, che passa per la sezione EH, cio&egrave; il <lb/>prisma acqueo OIDP, ha l'istessa proporzione che l'altezza QI all'altezza <lb/>OI, per avere i detti prismi la base comune. </s>

<s>Di pi&ugrave;, la velocit&agrave; T, con la </s></p><pb xlink:href="020/01/3504.jpg" pagenum="465"/><p type="main">

<s>Finito di stampare in Bologna presso la <lb/>Libreria Editrice Forni nel
Giugno 1970 </s></p></chap></body><back></back>	</text></archimedes>